LMFDB - Embedded newform 69.8.e.b.58.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,8,Mod(4,69)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("69.4");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	69.e (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$21.5545667584$
Analytic rank:	$0$
Dimension:	$140$
Relative dimension:	$14$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			58.5
Character	$\chi$	$=$	69.58
Dual form			69.8.e.b.25.5

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-8.71638 + 5.60168i) q^{2} +(3.84250 - 26.7252i) q^{3} +(-8.57661 + 18.7802i) q^{4} +(279.359 - 82.0273i) q^{5} +(116.213 + 254.471i) q^{6} +(998.192 + 1151.98i) q^{7} +(-219.186 - 1524.47i) q^{8} +(-699.470 - 205.383i) q^{9} +O(q^{10})$	\(q+(-8.71638 + 5.60168i) q^{2} +(3.84250 - 26.7252i) q^{3} +(-8.57661 + 18.7802i) q^{4} +(279.359 - 82.0273i) q^{5} +(116.213 + 254.471i) q^{6} +(998.192 + 1151.98i) q^{7} +(-219.186 - 1524.47i) q^{8} +(-699.470 - 205.383i) q^{9} +(-1975.51 + 2279.86i) q^{10} +(-1819.05 - 1169.03i) q^{11} +(468.948 + 301.374i) q^{12} +(2125.06 - 2452.45i) q^{13} +(-15153.6 - 4449.50i) q^{14} +(-1118.76 - 7781.12i) q^{15} +(8719.52 + 10062.9i) q^{16} +(-1408.36 - 3083.88i) q^{17} +(7247.34 - 2128.01i) q^{18} +(2404.47 - 5265.06i) q^{19} +(-855.471 + 5949.93i) q^{20} +(34622.3 - 22250.4i) q^{21} +22404.0 q^{22} +(53304.6 - 23737.0i) q^{23} -41584.0 q^{24} +(5590.28 - 3592.65i) q^{25} +(-4784.99 + 33280.4i) q^{26} +(-8176.61 + 17904.3i) q^{27} +(-30195.4 + 8866.17i) q^{28} +(51902.5 + 113651. i) q^{29} +(53338.8 + 61556.3i) q^{30} +(-2146.26 - 14927.5i) q^{31} +(56781.8 + 16672.6i) q^{32} +(-38232.2 + 44122.4i) q^{33} +(29550.7 + 18991.1i) q^{34} +(373348. + 239936. i) q^{35} +(9856.21 - 11374.7i) q^{36} +(512184. + 150391. i) q^{37} +(8534.88 + 59361.4i) q^{38} +(-57376.6 - 66216.1i) q^{39} +(-186280. - 407896. i) q^{40} +(128825. - 37826.5i) q^{41} +(-177142. + 387886. i) q^{42} +(-118770. + 826066. i) q^{43} +(37555.9 - 24135.7i) q^{44} -212251. q^{45} +(-331656. + 505496. i) q^{46} +1.21816e6 q^{47} +(302437. - 194364. i) q^{48} +(-213457. + 1.48463e6i) q^{49} +(-28602.1 + 62629.8i) q^{50} +(-87828.9 + 25788.9i) q^{51} +(27831.6 + 60942.6i) q^{52} +(-291500. - 336409. i) q^{53} +(-29023.6 - 201863. i) q^{54} +(-604061. - 177368. i) q^{55} +(1.53736e6 - 1.77421e6i) q^{56} +(-131471. - 84491.0i) q^{57} +(-1.08904e6 - 699881. i) q^{58} +(1.06529e6 - 1.22941e6i) q^{59} +(155726. + 45725.2i) q^{60} +(-300634. - 2.09096e6i) q^{61} +(102327. + 118091. i) q^{62} +(-461610. - 1.01078e6i) q^{63} +(-2.22362e6 + 652913. i) q^{64} +(392487. - 859427. i) q^{65} +(86087.6 - 598752. i) q^{66} +(2.58122e6 - 1.65885e6i) q^{67} +69994.8 q^{68} +(-429553. - 1.51578e6i) q^{69} -4.59829e6 q^{70} +(-3.07638e6 + 1.97707e6i) q^{71} +(-159786. + 1.11134e6i) q^{72} +(-103687. + 227044. i) q^{73} +(-5.30683e6 + 1.55823e6i) q^{74} +(-74533.6 - 163206. i) q^{75} +(78256.5 + 90312.9i) q^{76} +(-469065. - 3.26242e6i) q^{77} +(871037. + 255760. i) q^{78} +(-1.04348e6 + 1.20425e6i) q^{79} +(3.26131e6 + 2.09592e6i) q^{80} +(447077. + 287319. i) q^{81} +(-910997. + 1.05135e6i) q^{82} +(6.79236e6 + 1.99442e6i) q^{83} +(120924. + 841046. i) q^{84} +(-646402. - 745987. i) q^{85} +(-3.59211e6 - 7.86562e6i) q^{86} +(3.23677e6 - 950401. i) q^{87} +(-1.38344e6 + 3.02932e6i) q^{88} +(-751956. + 5.22997e6i) q^{89} +(1.85006e6 - 1.18896e6i) q^{90} +4.94638e6 q^{91} +(-11387.6 + 1.20465e6i) q^{92} -407188. q^{93} +(-1.06180e7 + 6.82376e6i) q^{94} +(239833. - 1.66808e6i) q^{95} +(663763. - 1.45344e6i) q^{96} +(-1.28047e7 + 3.75980e6i) q^{97} +(-6.45582e6 - 1.41363e7i) q^{98} +(1.03227e6 + 1.19130e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - 12 q^{2} + 378 q^{3} - 740 q^{4} + 2 q^{5} - 1755 q^{6} - 394 q^{7} - 1612 q^{8} - 10206 q^{9}+O(q^{10}) $ 140 * q - 12 * q^2 + 378 * q^3 - 740 * q^4 + 2 * q^5 - 1755 * q^6 - 394 * q^7 - 1612 * q^8 - 10206 * q^9	\( 140 q - 12 q^{2} + 378 q^{3} - 740 q^{4} + 2 q^{5} - 1755 q^{6} - 394 q^{7} - 1612 q^{8} - 10206 q^{9} + 9178 q^{10} - 5996 q^{11} + 19980 q^{12} - 44394 q^{13} - 9524 q^{14} - 351 q^{15} - 165236 q^{16} + 152531 q^{17} - 8748 q^{18} + 4037 q^{19} - 6167 q^{20} + 10638 q^{21} + 98494 q^{22} - 160732 q^{23} + 5508 q^{24} - 14760 q^{25} + 403412 q^{26} + 275562 q^{27} + 84152 q^{28} + 205532 q^{29} - 247806 q^{30} - 1262119 q^{31} - 1781780 q^{32} + 735399 q^{33} + 2963321 q^{34} - 955354 q^{35} - 1269189 q^{36} - 1369770 q^{37} + 3950922 q^{38} + 1198638 q^{39} - 839075 q^{40} + 4017556 q^{41} - 798390 q^{42} - 2474862 q^{43} - 5279389 q^{44} + 2006208 q^{45} - 3642508 q^{46} - 5306766 q^{47} + 1755999 q^{48} + 4554906 q^{49} + 3476227 q^{50} + 3473280 q^{51} + 15615773 q^{52} + 3269752 q^{53} + 452709 q^{54} - 7825001 q^{55} - 23842824 q^{56} - 6117309 q^{57} - 1584991 q^{58} + 1692452 q^{59} + 4240161 q^{60} + 6133200 q^{61} - 11065051 q^{62} - 287226 q^{63} + 5056548 q^{64} + 13947245 q^{65} - 7185321 q^{66} - 6003959 q^{67} + 37775092 q^{68} - 1069794 q^{69} - 27634536 q^{70} + 5868445 q^{71} - 1175148 q^{72} - 23836857 q^{73} + 8638944 q^{74} + 5583546 q^{75} - 13476319 q^{76} - 19300986 q^{77} + 16707492 q^{78} - 16058510 q^{79} - 1951148 q^{80} - 7440174 q^{81} + 47661526 q^{82} + 21531792 q^{83} + 33361956 q^{84} + 51859503 q^{85} - 20977372 q^{86} + 1565568 q^{87} - 35256744 q^{88} - 26730592 q^{89} + 6690762 q^{90} - 42532184 q^{91} - 71328833 q^{92} - 19877886 q^{93} - 70960921 q^{94} - 43191119 q^{95} + 17543196 q^{96} + 52039436 q^{97} + 98000731 q^{98} - 19855773 q^{99}+O(q^{100}) \) 140 * q - 12 * q^2 + 378 * q^3 - 740 * q^4 + 2 * q^5 - 1755 * q^6 - 394 * q^7 - 1612 * q^8 - 10206 * q^9 + 9178 * q^10 - 5996 * q^11 + 19980 * q^12 - 44394 * q^13 - 9524 * q^14 - 351 * q^15 - 165236 * q^16 + 152531 * q^17 - 8748 * q^18 + 4037 * q^19 - 6167 * q^20 + 10638 * q^21 + 98494 * q^22 - 160732 * q^23 + 5508 * q^24 - 14760 * q^25 + 403412 * q^26 + 275562 * q^27 + 84152 * q^28 + 205532 * q^29 - 247806 * q^30 - 1262119 * q^31 - 1781780 * q^32 + 735399 * q^33 + 2963321 * q^34 - 955354 * q^35 - 1269189 * q^36 - 1369770 * q^37 + 3950922 * q^38 + 1198638 * q^39 - 839075 * q^40 + 4017556 * q^41 - 798390 * q^42 - 2474862 * q^43 - 5279389 * q^44 + 2006208 * q^45 - 3642508 * q^46 - 5306766 * q^47 + 1755999 * q^48 + 4554906 * q^49 + 3476227 * q^50 + 3473280 * q^51 + 15615773 * q^52 + 3269752 * q^53 + 452709 * q^54 - 7825001 * q^55 - 23842824 * q^56 - 6117309 * q^57 - 1584991 * q^58 + 1692452 * q^59 + 4240161 * q^60 + 6133200 * q^61 - 11065051 * q^62 - 287226 * q^63 + 5056548 * q^64 + 13947245 * q^65 - 7185321 * q^66 - 6003959 * q^67 + 37775092 * q^68 - 1069794 * q^69 - 27634536 * q^70 + 5868445 * q^71 - 1175148 * q^72 - 23836857 * q^73 + 8638944 * q^74 + 5583546 * q^75 - 13476319 * q^76 - 19300986 * q^77 + 16707492 * q^78 - 16058510 * q^79 - 1951148 * q^80 - 7440174 * q^81 + 47661526 * q^82 + 21531792 * q^83 + 33361956 * q^84 + 51859503 * q^85 - 20977372 * q^86 + 1565568 * q^87 - 35256744 * q^88 - 26730592 * q^89 + 6690762 * q^90 - 42532184 * q^91 - 71328833 * q^92 - 19877886 * q^93 - 70960921 * q^94 - 43191119 * q^95 + 17543196 * q^96 + 52039436 * q^97 + 98000731 * q^98 - 19855773 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{10}{11}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−8.71638	+	5.60168i	−0.770427	+	0.495123i	−0.865844	−	0.500314i	$-0.833218\pi$
$2$	−8.71638	+	5.60168i	−0.770427	+	0.495123i	0.0954173	+	0.995437i	$0.469581\pi$
$3$	3.84250	−	26.7252i	0.0821655	−	0.571474i
$3$	3.84250	−	26.7252i	0.0821655	−	0.571474i
$4$	−8.57661	+	18.7802i	−0.0670048	+	0.146720i
$5$	279.359	−	82.0273i	0.999467	−	0.293470i	0.259230	−	0.965816i	$-0.416531\pi$
$5$	279.359	−	82.0273i	0.999467	−	0.293470i	0.740237	+	0.672346i	$0.234713\pi$
$6$	116.213	+	254.471i	0.219647	+	0.480961i
$7$	998.192	+	1151.98i	1.09995	+	1.26940i	0.960229	+	0.279213i	$0.0900735\pi$
$7$	998.192	+	1151.98i	1.09995	+	1.26940i	0.139716	+	0.990192i	$0.455381\pi$
$8$	−219.186	−	1524.47i	−0.151355	−	1.05270i
$9$	−699.470	−	205.383i	−0.319831	−	0.0939109i
$10$	−1975.51	+	2279.86i	−0.624712	+	0.720956i
$11$	−1819.05	−	1169.03i	−0.412069	−	0.264820i	0.318141	−	0.948043i	$-0.396941\pi$
$11$	−1819.05	−	1169.03i	−0.412069	−	0.264820i	−0.730210	+	0.683223i	$0.760578\pi$
$12$	468.948	+	301.374i	0.0783412	+	0.0503468i
$13$	2125.06	−	2452.45i	0.268268	−	0.309598i	−0.605592	−	0.795775i	$-0.707064\pi$
$13$	2125.06	−	2452.45i	0.268268	−	0.309598i	0.873860	+	0.486177i	$0.161609\pi$
$14$	−15153.6	−	4449.50i	−1.47594	−	0.433375i
$15$	−1118.76	−	7781.12i	−0.0855886	−	0.595282i
$16$	8719.52	+	10062.9i	0.532197	+	0.614188i
$17$	−1408.36	−	3083.88i	−0.0695253	−	0.152239i	0.871679	−	0.490078i	$-0.163032\pi$
$17$	−1408.36	−	3083.88i	−0.0695253	−	0.152239i	−0.941204	+	0.337838i	$0.890304\pi$
$18$	7247.34	−	2128.01i	0.292904	−	0.0860043i
$19$	2404.47	−	5265.06i	0.0804234	−	0.176103i	−0.865149	−	0.501516i	$-0.832776\pi$
$19$	2404.47	−	5265.06i	0.0804234	−	0.176103i	0.945572	+	0.325413i	$0.105503\pi$
$20$	−855.471	+	5949.93i	−0.0239111	+	0.166306i
$21$	34622.3	−	22250.4i	0.815809	−	0.524288i
$22$	22404.0			0.448587
$23$	53304.6	−	23737.0i	0.913518	−	0.406798i
$23$	53304.6	−	23737.0i	0.913518	−	0.406798i
$24$	−41584.0			−0.614026
$25$	5590.28	−	3592.65i	0.0715555	−	0.0459859i
$26$	−4784.99	+	33280.4i	−0.0533918	+	0.371348i
$27$	−8176.61	+	17904.3i	−0.0799467	+	0.175059i
$28$	−30195.4	+	8866.17i	−0.259949	+	0.0763278i
$29$	51902.5	+	113651.i	0.395180	+	0.865324i	0.997736	+	0.0672475i	$0.0214217\pi$
$29$	51902.5	+	113651.i	0.395180	+	0.865324i	−0.602556	+	0.798077i	$0.705851\pi$
$30$	53338.8	+	61556.3i	0.360678	+	0.416244i
$31$	−2146.26	−	14927.5i	−0.0129394	−	0.0899958i	0.982328	−	0.187166i	$-0.0599301\pi$
$31$	−2146.26	−	14927.5i	−0.0129394	−	0.0899958i	−0.995268	+	0.0971698i	$0.969021\pi$
$32$	56781.8	+	16672.6i	0.306326	+	0.0899455i
$33$	−38232.2	+	44122.4i	−0.185196	+	0.213727i
$34$	29550.7	+	18991.1i	0.128941	+	0.0828656i
$35$	373348.	+	239936.i	1.47189	+	0.945927i
$36$	9856.21	−	11374.7i	0.0352088	−	0.0406331i
$37$	512184.	+	150391.i	1.66234	+	0.488107i	0.971922	−	0.235304i	$-0.0756087\pi$
$37$	512184.	+	150391.i	1.66234	+	0.488107i	0.690418	+	0.723411i	$0.257427\pi$
$38$	8534.88	+	59361.4i	0.0252322	+	0.175494i
$39$	−57376.6	−	66216.1i	−0.154885	−	0.178746i
$40$	−186280.	−	407896.i	−0.460210	−	1.00772i
$41$	128825.	−	37826.5i	0.291915	−	0.0857141i	−0.132496	−	0.991184i	$-0.542299\pi$
$41$	128825.	−	37826.5i	0.291915	−	0.0857141i	0.424411	+	0.905469i	$0.360481\pi$
$42$	−177142.	+	387886.i	−0.368933	+	0.807852i
$43$	−118770.	+	826066.i	−0.227808	+	1.58444i	0.479507	+	0.877538i	$0.340816\pi$
$43$	−118770.	+	826066.i	−0.227808	+	1.58444i	−0.707315	+	0.706899i	$0.750094\pi$
$44$	37555.9	−	24135.7i	0.0664651	−	0.0427145i
$45$	−212251.			−0.347220
$46$	−331656.	+	505496.i	−0.502384	+	0.765712i
$47$	1.21816e6			1.71145			0.855723	−	0.517435i	$-0.173113\pi$
$47$	1.21816e6			1.71145			0.855723	+	0.517435i	$0.173113\pi$
$48$	302437.	−	194364.i	0.394721	−	0.253672i
$49$	−213457.	+	1.48463e6i	−0.259193	+	1.80273i
$50$	−28602.1	+	62629.8i	−0.0323596	+	0.0708576i
$51$	−87828.9	+	25788.9i	−0.0927133	+	0.0272231i
$52$	27831.6	+	60942.6i	0.0274490	+	0.0601049i
$53$	−291500.	−	336409.i	−0.268951	−	0.310386i	0.605168	−	0.796098i	$-0.293106\pi$
$53$	−291500.	−	336409.i	−0.268951	−	0.310386i	−0.874119	+	0.485712i	$0.838560\pi$
$54$	−29023.6	−	201863.i	−0.0250826	−	0.174453i
$55$	−604061.	−	177368.i	−0.489566	−	0.143749i
$56$	1.53736e6	−	1.77421e6i	1.16982	−	1.35004i
$57$	−131471.	−	84491.0i	−0.0940301	−	0.0604294i
$58$	−1.08904e6	−	699881.i	−0.732899	−	0.471006i
$59$	1.06529e6	−	1.22941e6i	0.675282	−	0.779317i	−0.309911	−	0.950766i	$-0.600299\pi$
$59$	1.06529e6	−	1.22941e6i	0.675282	−	0.779317i	0.985193	+	0.171449i	$0.0548447\pi$
$60$	155726.	+	45725.2i	0.0930746	+	0.0273292i
$61$	−300634.	−	2.09096e6i	−0.169584	−	1.17948i	−0.879747	−	0.475443i	$-0.842288\pi$
$61$	−300634.	−	2.09096e6i	−0.169584	−	1.17948i	0.710163	−	0.704037i	$-0.248621\pi$
$62$	102327.	+	118091.i	0.0545279	+	0.0629285i
$63$	−461610.	−	1.01078e6i	−0.232586	−	0.509292i
$64$	−2.22362e6	+	652913.i	−1.06030	+	0.311333i
$65$	392487.	−	859427.i	0.177267	−	0.388161i
$66$	86087.6	−	598752.i	0.0368584	−	0.256356i
$67$	2.58122e6	−	1.65885e6i	1.04849	−	0.673823i	0.101417	−	0.994844i	$-0.467662\pi$
$67$	2.58122e6	−	1.65885e6i	1.04849	−	0.673823i	0.947072	+	0.321021i	$0.104026\pi$
$68$	69994.8			0.0269951
$69$	−429553.	−	1.51578e6i	−0.157415	−	0.555476i
$70$	−4.59829e6			−1.60233
$71$	−3.07638e6	+	1.97707e6i	−1.02008	+	0.655568i	−0.939984	−	0.341219i	$-0.889160\pi$
$71$	−3.07638e6	+	1.97707e6i	−1.02008	+	0.655568i	−0.0801001	+	0.996787i	$0.525524\pi$
$72$	−159786.	+	1.11134e6i	−0.0504517	+	0.350900i
$73$	−103687.	+	227044.i	−0.0311958	+	0.0683092i	−0.924588	−	0.380967i	$-0.875591\pi$
$73$	−103687.	+	227044.i	−0.0311958	+	0.0683092i	0.893393	+	0.449277i	$0.148318\pi$
$74$	−5.30683e6	+	1.55823e6i	−1.52238	+	0.447012i
$75$	−74533.6	−	163206.i	−0.0204004	−	0.0446706i
$76$	78256.5	+	90312.9i	0.0204490	+	0.0235995i
$77$	−469065.	−	3.26242e6i	−0.117089	−	0.814370i
$78$	871037.	+	255760.i	0.207829	+	0.0610240i
$79$	−1.04348e6	+	1.20425e6i	−0.238118	+	0.274802i	−0.862213	−	0.506546i	$-0.830922\pi$
$79$	−1.04348e6	+	1.20425e6i	−0.238118	+	0.274802i	0.624096	+	0.781348i	$0.285468\pi$
$80$	3.26131e6	+	2.09592e6i	0.712159	+	0.457677i
$81$	447077.	+	287319.i	0.0934726	+	0.0600712i
$82$	−910997.	+	1.05135e6i	−0.182460	+	0.210570i
$83$	6.79236e6	+	1.99442e6i	1.30391	+	0.382862i	0.858660	−	0.512545i	$-0.171297\pi$
$83$	6.79236e6	+	1.99442e6i	1.30391	+	0.382862i	0.445248	+	0.895407i	$0.353115\pi$
$84$	120924.	+	841046.i	0.0222605	+	0.154825i
$85$	−646402.	−	745987.i	−0.114166	−	0.131754i
$86$	−3.59211e6	−	7.86562e6i	−0.608982	−	1.33349i
$87$	3.23677e6	−	950401.i	0.526980	−	0.154735i
$88$	−1.38344e6	+	3.02932e6i	−0.216407	+	0.473866i
$89$	−751956.	+	5.22997e6i	−0.113065	+	0.786383i	0.851844	+	0.523796i	$0.175485\pi$
$89$	−751956.	+	5.22997e6i	−0.113065	+	0.786383i	−0.964908	+	0.262587i	$0.915424\pi$
$90$	1.85006e6	−	1.18896e6i	0.267508	−	0.171917i
$91$	4.94638e6			0.688085
$92$	−11387.6	+	1.20465e6i	−0.00152467	+	0.161289i
$93$	−407188.			−0.0524934
$94$	−1.06180e7	+	6.82376e6i	−1.31854	+	0.847376i
$95$	239833.	−	1.66808e6i	0.0286997	−	0.199611i
$96$	663763.	−	1.45344e6i	0.0765709	−	0.167667i
$97$	−1.28047e7	+	3.75980e6i	−1.42452	+	0.418277i	−0.901031	−	0.433756i	$-0.857188\pi$
$97$	−1.28047e7	+	3.75980e6i	−1.42452	+	0.418277i	−0.523489	+	0.852032i	$0.675370\pi$
$98$	−6.45582e6	−	1.41363e7i	−0.692884	−	1.51720i
$99$	1.03227e6	+	1.19130e6i	0.106923	+	0.123396i
$100$	19525.0	+	135799.i	0.00195250	+	0.0135799i
$101$	3.64801e6	+	1.07115e6i	0.352316	+	0.103449i	0.453101	−	0.891459i	$-0.350318\pi$
$101$	3.64801e6	+	1.07115e6i	0.352316	+	0.103449i	−0.100786	+	0.994908i	$0.532136\pi$
$102$	621089.	−	716775.i	0.0579500	−	0.0668779i
$103$	4.99147e6	+	3.20782e6i	0.450089	+	0.289255i	0.745982	−	0.665967i	$-0.231981\pi$
$103$	4.99147e6	+	3.20782e6i	0.450089	+	0.289255i	−0.295893	+	0.955221i	$0.595617\pi$
$104$	−4.20447e6	−	2.70205e6i	−0.366517	−	0.235546i
$105$	7.84693e6	−	9.05583e6i	0.661511	−	0.763424i
$106$	4.42528e6	+	1.29938e6i	0.360886	+	0.105966i
$107$	966817.	+	6.72436e6i	0.0762959	+	0.530649i	0.991746	+	0.128218i	$0.0409257\pi$
$107$	966817.	+	6.72436e6i	0.0762959	+	0.530649i	−0.915450	+	0.402431i	$0.868165\pi$
$108$	−266118.	−	307116.i	−0.0203278	−	0.0234596i
$109$	4.96259e6	+	1.08666e7i	0.367042	+	0.803709i	0.999574	+	0.0291756i	$0.00928819\pi$
$109$	4.96259e6	+	1.08666e7i	0.367042	+	0.803709i	−0.632533	+	0.774534i	$0.717985\pi$
$110$	6.25878e6	−	1.83774e6i	0.448348	−	0.131647i
$111$	5.98728e6	−	1.31103e7i	0.415527	−	0.909878i
$112$	−2.88841e6	+	2.00893e7i	−0.194266	+	1.35115i
$113$	1.81771e7	−	1.16817e7i	1.18509	−	0.761609i	0.208772	−	0.977964i	$-0.433053\pi$
$113$	1.81771e7	−	1.16817e7i	1.18509	−	0.761609i	0.976315	+	0.216356i	$0.0694171\pi$
$114$	1.61924e6			0.102363
$115$	1.29441e7	−	1.10036e7i	0.793648	−	0.674671i
$116$	−2.57952e6			−0.153439
$117$	−1.99011e6	+	1.27896e6i	−0.114875	+	0.0738257i
$118$	−2.39871e6	+	1.66834e7i	−0.134397	+	0.934754i
$119$	2.14674e6	−	4.70071e6i	0.116779	−	0.255711i
$120$	−1.16169e7	+	3.41102e6i	−0.613698	+	0.180198i
$121$	−6.15296e6	−	1.34731e7i	−0.315744	−	0.691384i
$122$	1.43333e7	+	1.65415e7i	0.714639	+	0.824738i
$123$	−515908.	−	3.58822e6i	−0.0249980	−	0.173865i
$124$	298749.	+	87720.7i	0.0140712	+	0.00413167i
$125$	−1.36287e7	+	1.57283e7i	−0.624121	+	0.720274i
$126$	9.68566e6	+	6.22459e6i	0.431352	+	0.277213i
$127$	−1.11967e7	−	7.19571e6i	−0.485041	−	0.311717i	0.275167	−	0.961396i	$-0.411267\pi$
$127$	−1.11967e7	−	7.19571e6i	−0.485041	−	0.311717i	−0.760208	+	0.649679i	$0.774903\pi$
$128$	1.07640e7	−	1.24223e7i	0.453668	−	0.523561i
$129$	2.16204e7	+	6.34832e6i	0.886746	+	0.260372i
$130$	1.39317e6	+	9.68968e6i	0.0556162	+	0.386819i
$131$	−8.33727e6	−	9.62172e6i	−0.324022	−	0.373941i	0.570245	−	0.821474i	$-0.306848\pi$
$131$	−8.33727e6	−	9.62172e6i	−0.324022	−	0.373941i	−0.894267	+	0.447533i	$0.852303\pi$
$132$	−500722.	−	1.09643e6i	−0.0189491	−	0.0414927i
$133$	8.46535e6	−	2.48565e6i	0.312007	−	0.0916135i
$134$	−1.32066e7	+	2.89184e7i	−0.474159	+	1.03826i
$135$	−815573.	+	5.67244e6i	−0.0285295	+	0.198427i
$136$	−4.39260e6	+	2.82295e6i	−0.149739	+	0.0962314i
$137$	−2.15815e6			−0.0717067			−0.0358534	−	0.999357i	$-0.511415\pi$
$137$	−2.15815e6			−0.0717067			−0.0358534	+	0.999357i	$0.511415\pi$
$138$	1.22351e7	+	1.08059e7i	0.396306	+	0.350014i
$139$	−5.18017e7			−1.63603			−0.818017	−	0.575194i	$-0.804926\pi$
$139$	−5.18017e7			−1.63603			−0.818017	+	0.575194i	$0.804926\pi$
$140$	−7.70810e6	+	4.95370e6i	−0.237410	+	0.152574i
$141$	4.68079e6	−	3.25556e7i	0.140622	−	0.978046i
$142$	1.57400e7	−	3.44658e7i	0.461313	−	1.01013i
$143$	−6.73257e6	+	1.97686e6i	−0.192533	+	0.0565327i
$144$	−4.03230e6	−	8.82951e6i	−0.112534	−	0.246416i
$145$	2.38219e7	+	2.74919e7i	0.648916	+	0.748889i
$146$	−368047.	−	2.55982e6i	−0.00978742	−	0.0680730i
$147$	3.88567e7	+	1.14093e7i	1.00892	+	0.296244i
$148$	−7.21716e6	+	8.32905e6i	−0.183000	+	0.211193i
$149$	4.64469e6	+	2.98496e6i	0.115028	+	0.0739241i	0.596890	−	0.802323i	$-0.296403\pi$
$149$	4.64469e6	+	2.98496e6i	0.115028	+	0.0739241i	−0.481862	+	0.876247i	$0.660039\pi$
$150$	1.56389e6	+	1.00505e6i	0.0378344	+	0.0243147i
$151$	3.17119e7	−	3.65975e7i	0.749555	−	0.865033i	−0.244970	−	0.969531i	$-0.578778\pi$
$151$	3.17119e7	−	3.65975e7i	0.749555	−	0.865033i	0.994525	+	0.104498i	$0.0333236\pi$
$152$	−8.55346e6	−	2.51152e6i	−0.197556	−	0.0580076i
$153$	351730.	+	2.44634e6i	0.00793944	+	0.0552200i
$154$	2.23635e7	+	2.58089e7i	0.493422	+	0.569439i
$155$	−1.82404e6	−	3.99410e6i	−0.0393436	−	0.0861505i
$156$	1.73565e6	−	509632.i	0.0366037	−	0.0107478i
$157$	−2.81209e7	+	6.15762e7i	−0.579937	+	1.26988i	0.361398	+	0.932411i	$0.382299\pi$
$157$	−2.81209e7	+	6.15762e7i	−0.579937	+	1.26988i	−0.941335	+	0.337473i	$0.890428\pi$
$158$	2.34962e6	−	1.63419e7i	0.0473911	−	0.329612i
$159$	−1.01107e7	+	6.49774e6i	−0.199476	+	0.128195i
$160$	1.72301e7			0.332559
$161$	8.05527e7	+	3.77115e7i	1.52121	+	0.712168i
$162$	−5.50636e6			−0.101756
$163$	−284711.	+	182973.i	−0.00514929	+	0.00330925i	−0.543213	−	0.839595i	$-0.682792\pi$
$163$	−284711.	+	182973.i	−0.00514929	+	0.00330925i	0.538064	+	0.842904i	$0.319156\pi$
$164$	−394496.	+	2.74378e6i	−0.00698376	+	0.0485731i
$165$	−7.06130e6	+	1.54621e7i	−0.122374	+	0.267963i
$166$	−7.03769e7	+	2.06645e7i	−1.19413	+	0.350628i
$167$	−4.07869e7	−	8.93109e7i	−0.677662	−	1.48387i	−0.865101	−	0.501597i	$-0.832746\pi$
$167$	−4.07869e7	−	8.93109e7i	−0.677662	−	1.48387i	0.187439	−	0.982276i	$-0.439981\pi$
$168$	−4.15088e7	−	4.79037e7i	−0.675395	−	0.779447i
$169$	7.43142e6	+	5.16866e7i	0.118432	+	0.823711i
$170$	9.81307e6	+	2.88138e6i	0.153191	+	0.0449810i
$171$	−2.76321e6	+	3.18892e6i	−0.0422599	+	0.0487705i
$172$	−1.44950e7	−	9.31537e6i	−0.217204	−	0.139589i
$173$	−2.48341e7	−	1.59599e7i	−0.364659	−	0.234352i	0.345460	−	0.938433i	$-0.387723\pi$
$173$	−2.48341e7	−	1.59599e7i	−0.364659	−	0.234352i	−0.710120	+	0.704081i	$0.751359\pi$
$174$	−2.28891e7	+	2.64154e7i	−0.329386	+	0.380132i
$175$	9.71882e6	+	2.85370e6i	0.137082	+	0.0402509i
$176$	−4.09742e6	−	2.84982e7i	−0.0566522	−	0.394024i
$177$	−2.87628e7	−	3.31940e7i	−0.389874	−	0.449939i
$178$	−2.27423e7	−	4.97986e7i	−0.302248	−	0.661832i
$179$	−3.72977e7	+	1.09516e7i	−0.486067	+	0.142722i	−0.515579	−	0.856842i	$-0.672423\pi$
$179$	−3.72977e7	+	1.09516e7i	−0.486067	+	0.142722i	0.0295114	+	0.999564i	$0.490605\pi$
$180$	1.82039e6	−	3.98610e6i	0.0232654	−	0.0509442i
$181$	8.58530e6	−	5.97121e7i	0.107617	−	0.748492i	−0.862536	−	0.505996i	$-0.831125\pi$
$181$	8.58530e6	−	5.97121e7i	0.107617	−	0.748492i	0.970153	−	0.242495i	$-0.0779660\pi$
$182$	−4.31145e7	+	2.77080e7i	−0.530119	+	0.340687i
$183$	−5.70364e7			−0.687975
$184$	−4.78700e7	−	7.60585e7i	−0.566502	−	0.900088i
$185$	1.55419e8			1.80470
$186$	3.54921e6	−	2.28094e6i	0.0404423	−	0.0259907i
$187$	−1.04328e6	+	7.25615e6i	−0.0116669	+	0.0811448i
$188$	−1.04477e7	+	2.28773e7i	−0.114675	+	0.251103i
$189$	−2.87871e7	+	8.45266e6i	−0.310157	+	0.0910704i
$190$	7.25356e6	+	1.58831e7i	0.0767209	+	0.167995i
$191$	−4.22847e7	−	4.87991e7i	−0.439103	−	0.506752i	0.492459	−	0.870336i	$-0.336098\pi$
$191$	−4.22847e7	−	4.87991e7i	−0.439103	−	0.506752i	−0.931561	+	0.363584i	$0.881553\pi$
$192$	8.90497e6	+	6.19354e7i	0.0907984	+	0.631517i
$193$	−5.09771e7	−	1.49682e7i	−0.510416	−	0.149872i	0.0163761	−	0.999866i	$-0.494787\pi$
$193$	−5.09771e7	−	1.49682e7i	−0.510416	−	0.149872i	−0.526792	+	0.849994i	$0.676605\pi$
$194$	9.05495e7	−	1.04500e8i	0.890389	−	1.02756i
$195$	−2.14602e7	−	1.37916e7i	−0.207259	−	0.133197i
$196$	−2.60508e7	−	1.67418e7i	−0.247129	−	0.158820i
$197$	5.38190e7	−	6.21105e7i	0.501538	−	0.578806i	−0.447374	−	0.894347i	$-0.647641\pi$
$197$	5.38190e7	−	6.21105e7i	0.501538	−	0.578806i	0.948912	+	0.315541i	$0.102186\pi$
$198$	−1.56710e7	−	4.60141e6i	−0.143472	−	0.0421272i
$199$	−1.53482e7	−	1.06749e8i	−0.138062	−	0.960239i	−0.934612	−	0.355668i	$-0.884253\pi$
$199$	−1.53482e7	−	1.06749e8i	−0.138062	−	0.960239i	0.796551	−	0.604571i	$-0.206656\pi$
$200$	−6.70220e6	−	7.73475e6i	−0.0592397	−	0.0683662i
$201$	−3.44148e7	−	7.53578e7i	−0.298923	−	0.654549i
$202$	−3.77977e7	+	1.10984e7i	−0.322653	+	0.0947396i
$203$	−7.91140e7	+	1.73236e8i	−0.663770	+	1.45345i
$204$	268955.	−	1.87062e6i	0.00221806	−	0.0154270i
$205$	3.28857e7	−	2.11344e7i	0.266605	−	0.171337i
$206$	−6.14768e7			−0.489977
$207$	−4.21602e7	+	5.65549e6i	−0.330374	+	0.0443174i
$208$	4.32081e7			0.332923
$209$	−1.05289e7	+	6.76650e6i	−0.0797756	+	0.0512687i
$210$	−1.76689e7	+	1.22890e8i	−0.131657	+	0.915692i
$211$	9.07956e7	−	1.98815e8i	0.665390	−	1.45700i	−0.212022	−	0.977265i	$-0.568005\pi$
$211$	9.07956e7	−	1.98815e8i	0.665390	−	1.45700i	0.877413	−	0.479737i	$-0.159268\pi$
$212$	8.81789e6	−	2.58917e6i	0.0635608	−	0.0186631i
$213$	4.10166e7	+	8.98137e7i	0.290824	+	0.636816i
$214$	−4.60948e7	−	5.31963e7i	−0.321517	−	0.371050i
$215$	3.45804e7	+	2.40512e8i	0.237298	+	1.65045i
$216$	2.90868e7	+	8.54064e6i	0.196385	+	0.0576637i
$217$	1.50538e7	−	1.73730e7i	0.100008	−	0.115416i
$218$	−1.04127e8	−	6.69182e7i	−0.680714	−	0.437468i
$219$	5.66936e6	+	3.64348e6i	0.0364737	+	0.0234402i
$220$	8.51180e6	−	9.82314e6i	0.0538942	−	0.0621972i
$221$	−1.05559e7	−	3.09950e6i	−0.0657844	−	0.0193160i
$222$	2.12524e7	+	1.47813e8i	0.130368	+	0.906731i
$223$	6.93353e7	+	8.00172e7i	0.418685	+	0.483188i	0.925436	−	0.378904i	$-0.123699\pi$
$223$	6.93353e7	+	8.00172e7i	0.418685	+	0.483188i	−0.506751	+	0.862092i	$0.669154\pi$
$224$	3.74727e7	+	8.20537e7i	0.222765	+	0.487787i
$225$	−4.64810e6	+	1.36481e6i	−0.0272043	+	0.00798789i
$226$	−9.30013e7	+	2.03645e8i	−0.535932	+	1.17353i
$227$	3.21433e7	−	2.23561e8i	0.182389	−	1.26855i	−0.668703	−	0.743529i	$-0.733150\pi$
$227$	3.21433e7	−	2.23561e8i	0.182389	−	1.26855i	0.851092	−	0.525016i	$-0.175941\pi$
$228$	2.71433e6	−	1.74439e6i	0.0151667	−	0.00974703i
$229$	1.81199e8			0.997082			0.498541	−	0.866866i	$-0.333869\pi$
$229$	1.81199e8			0.997082			0.498541	+	0.866866i	$0.333869\pi$
$230$	−5.11867e7	+	1.68420e8i	−0.277402	+	0.912738i
$231$	−8.89910e7			−0.475012
$232$	1.61881e8	−	1.04034e8i	0.851113	−	0.546977i
$233$	4.51147e7	−	3.13780e8i	0.233653	−	1.62510i	−0.448428	−	0.893819i	$-0.648016\pi$
$233$	4.51147e7	−	3.13780e8i	0.233653	−	1.62510i	0.682081	−	0.731277i	$-0.261075\pi$
$234$	1.01822e7	−	2.22959e7i	0.0519500	−	0.113755i
$235$	3.40305e8	−	9.99227e7i	1.71053	−	0.502258i
$236$	1.39519e7	+	3.05505e7i	0.0690943	+	0.151295i
$237$	2.81741e7	+	3.25146e7i	0.137477	+	0.158657i
$238$	7.62003e6	+	5.29985e7i	0.0366385	+	0.254826i
$239$	−6.72762e7	−	1.97541e7i	−0.318763	−	0.0935974i	0.118437	−	0.992962i	$-0.462212\pi$
$239$	−6.72762e7	−	1.97541e7i	−0.318763	−	0.0935974i	−0.437200	+	0.899364i	$0.644030\pi$
$240$	6.85453e7	−	7.91055e7i	0.320065	−	0.369375i
$241$	1.81334e8	+	1.16536e8i	0.834488	+	0.536293i	0.886701	−	0.462343i	$-0.152991\pi$
$241$	1.81334e8	+	1.16536e8i	0.834488	+	0.536293i	−0.0522134	+	0.998636i	$0.516628\pi$
$242$	1.29104e8	+	8.29698e7i	0.585578	+	0.376328i
$243$	9.39654e6	−	1.08442e7i	0.0420093	−	0.0484814i
$244$	4.18469e7	+	1.22874e7i	0.184416	+	0.0541495i
$245$	6.21486e7	+	4.32253e8i	0.269992	+	1.87783i
$246$	2.45969e7	+	2.83864e7i	0.105344	+	0.121573i
$247$	−7.80265e6	−	1.70854e7i	−0.0329460	−	0.0721417i
$248$	−2.22862e7	+	6.54381e6i	−0.0927800	+	0.0272427i
$249$	7.94008e7	−	1.73863e8i	0.325932	−	0.713692i
$250$	3.06877e7	−	2.13438e8i	0.124215	−	0.863935i
$251$	−3.80314e8	+	2.44413e8i	−1.51804	+	0.975587i	−0.525891	+	0.850552i	$0.676268\pi$
$251$	−3.80314e8	+	2.44413e8i	−1.51804	+	0.975587i	−0.992152	+	0.125035i	$0.960096\pi$
$252$	2.29417e7			0.0903077
$253$	−1.24713e8	−	1.91359e7i	−0.484161	−	0.0742896i
$254$	1.37903e8			0.528027
$255$	−2.24204e7	+	1.44087e7i	−0.0846747	+	0.0544171i
$256$	1.79789e7	−	1.25046e8i	0.0669765	−	0.465832i
$257$	−9.00472e7	+	1.97176e8i	−0.330906	+	0.724582i	−0.999824	−	0.0187534i	$-0.994030\pi$
$257$	−9.00472e7	+	1.97176e8i	−0.330906	+	0.724582i	0.668918	+	0.743336i	$0.266758\pi$
$258$	−2.24013e8	+	6.57761e7i	−0.812089	+	0.238451i
$259$	3.38011e8	+	7.40142e8i	1.20888	+	2.64707i
$260$	1.27740e7	+	1.47420e7i	0.0450733	+	0.0520174i
$261$	−1.29624e7	−	9.01551e7i	−0.0451276	−	0.313869i
$262$	1.26569e8	+	3.71639e7i	0.434782	+	0.127664i
$263$	−3.29860e8	+	3.80679e8i	−1.11811	+	1.29037i	−0.165489	+	0.986212i	$0.552920\pi$
$263$	−3.29860e8	+	3.80679e8i	−1.11811	+	1.29037i	−0.952622	+	0.304158i	$0.901625\pi$
$264$	7.56432e7	+	4.86130e7i	0.253021	+	0.162607i
$265$	−1.09028e8	−	7.00680e7i	−0.359896	−	0.231291i
$266$	−5.98634e7	+	6.90861e7i	−0.195018	+	0.225063i
$267$	1.36883e8	+	4.01923e7i	0.440107	+	0.129227i
$268$	9.01535e6	+	6.27032e7i	0.0286096	+	0.198984i
$269$	−1.80392e8	−	2.08184e8i	−0.565047	−	0.652099i	0.399275	−	0.916831i	$-0.369262\pi$
$269$	−1.80392e8	−	2.08184e8i	−0.565047	−	0.652099i	−0.964322	+	0.264732i	$0.914716\pi$
$270$	−2.46663e7	−	5.40117e7i	−0.0762660	−	0.166999i
$271$	7.24839e6	−	2.12832e6i	0.0221232	−	0.00649597i	−0.270652	−	0.962677i	$-0.587239\pi$
$271$	7.24839e6	−	2.12832e6i	0.0221232	−	0.00649597i	0.292775	+	0.956181i	$0.405421\pi$
$272$	1.87524e7	−	4.10621e7i	0.0565024	−	0.123723i
$273$	1.90065e7	−	1.32193e8i	0.0565369	−	0.393223i
$274$	1.88113e7	−	1.20893e7i	0.0552448	−	0.0355037i
$275$	−1.43689e7			−0.0416638
$276$	3.21508e7	+	4.93321e6i	0.0920470	+	0.0141237i
$277$	−4.03509e8			−1.14071			−0.570354	−	0.821399i	$-0.693194\pi$
$277$	−4.03509e8			−1.14071			−0.570354	+	0.821399i	$0.693194\pi$
$278$	4.51523e8	−	2.90176e8i	1.26044	−	0.810038i
$279$	−1.56462e6	+	1.08822e7i	−0.00431315	+	0.0299986i
$280$	2.83943e8	−	6.21749e8i	0.772998	−	1.69263i
$281$	1.08255e8	−	3.17866e7i	0.291056	−	0.0854618i	−0.132945	−	0.991123i	$-0.542443\pi$
$281$	1.08255e8	−	3.17866e7i	0.291056	−	0.0854618i	0.424001	+	0.905662i	$0.360625\pi$
$282$	1.41567e8	+	3.09988e8i	0.375914	+	0.823138i
$283$	−1.69171e8	−	1.95234e8i	−0.443684	−	0.512039i	0.489222	−	0.872160i	$-0.337281\pi$
$283$	−1.69171e8	−	1.95234e8i	−0.443684	−	0.512039i	−0.932906	+	0.360121i	$0.882735\pi$
$284$	−1.07448e7	−	7.47315e7i	−0.0278345	−	0.193593i
$285$	−4.36581e7	−	1.28192e7i	−0.111714	−	0.0328022i
$286$	4.76099e7	−	5.49448e7i	0.120342	−	0.138882i
$287$	1.72167e8	+	1.10645e8i	0.429897	+	0.276278i
$288$	−3.62929e7	−	2.33240e7i	−0.0895257	−	0.0575347i
$289$	2.61188e8	−	3.01427e8i	0.636518	−	0.734581i
$290$	−3.61642e8	−	1.06188e8i	−0.870734	−	0.255671i
$291$	5.12792e7	+	3.56655e8i	0.121988	+	0.848443i
$292$	−3.37463e6	−	3.89453e6i	−0.00793206	−	0.00915409i
$293$	−1.22239e6	−	2.67667e6i	−0.00283906	−	0.00621667i	0.908207	−	0.418521i	$-0.137451\pi$
$293$	−1.22239e6	−	2.67667e6i	−0.00283906	−	0.00621667i	−0.911046	+	0.412304i	$0.864724\pi$
$294$	−4.02601e8	+	1.18214e8i	−0.923973	+	0.271303i
$295$	1.96753e8	−	4.30830e8i	0.446216	−	0.977076i
$296$	1.17003e8	−	8.13772e8i	0.262226	−	1.82382i
$297$	3.58043e7	−	2.30100e7i	0.0793027	−	0.0509647i
$298$	−5.72056e7			−0.125222
$299$	5.50615e7	−	1.81169e8i	0.119124	−	0.391954i
$300$	3.70428e6			0.00792099
$301$	−1.07016e9	+	6.87752e8i	−2.26187	+	1.45361i
$302$	−7.14058e7	+	4.96638e8i	−0.149179	+	1.03757i
$303$	4.26443e7	−	9.33779e7i	0.0880667	−	0.192839i
$304$	7.39475e7	−	2.17129e7i	0.150961	−	0.0443263i
$305$	−2.55500e8	−	5.59468e8i	−0.515635	−	1.12908i
$306$	−1.67694e7	−	1.93529e7i	−0.0334575	−	0.0386120i
$307$	−5.63458e7	−	3.91893e8i	−0.111142	−	0.773007i	−0.966813	−	0.255487i	$-0.917764\pi$
$307$	−5.63458e7	−	3.91893e8i	−0.111142	−	0.773007i	0.855671	−	0.517520i	$-0.173145\pi$
$308$	6.52917e7	+	1.91714e7i	0.127330	+	0.0373874i
$309$	1.04909e8	−	1.21072e8i	0.202283	−	0.233447i
$310$	3.82727e7	+	2.45964e7i	0.0729664	+	0.0468927i
$311$	−4.18863e8	−	2.69187e8i	−0.789607	−	0.507450i	0.0826022	−	0.996583i	$-0.473677\pi$
$311$	−4.18863e8	−	2.69187e8i	−0.789607	−	0.507450i	−0.872209	+	0.489133i	$0.837313\pi$
$312$	−8.83684e7	+	1.01983e8i	−0.164724	+	0.190101i
$313$	7.00977e7	+	2.05825e7i	0.129211	+	0.0379397i	0.345699	−	0.938346i	$-0.387642\pi$
$313$	7.00977e7	+	2.05825e7i	0.129211	+	0.0379397i	−0.216488	+	0.976285i	$0.569460\pi$
$314$	−9.98175e7	−	6.94246e8i	−0.181950	−	1.26549i
$315$	−2.11867e8	−	2.44508e8i	−0.381923	−	0.440763i
$316$	−1.36664e7	−	2.99252e7i	−0.0243640	−	0.0533497i
$317$	−7.62916e8	+	2.24012e8i	−1.34515	+	0.394970i	−0.873503	−	0.486819i	$-0.838157\pi$
$317$	−7.62916e8	+	2.24012e8i	−1.34515	+	0.394970i	−0.471643	+	0.881790i	$0.656339\pi$
$318$	5.17303e7	−	1.13273e8i	0.0902090	−	0.197530i
$319$	3.84480e7	−	2.67411e8i	0.0663141	−	0.461225i
$320$	−5.67632e8	+	3.64795e8i	−0.968371	+	0.622335i
$321$	1.83425e8			0.309521
$322$	−9.13375e8	+	1.22523e8i	−1.52459	+	0.204513i
$323$	−1.96232e7			−0.0324012
$324$	−9.23030e6	+	5.93195e6i	−0.0150768	+	0.00968925i
$325$	3.06887e6	−	2.13445e7i	0.00495891	−	0.0344900i
$326$	1.45670e6	−	3.18972e6i	0.00232867	−	0.00509907i
$327$	3.09479e8	−	9.08713e7i	0.489457	−	0.143718i
$328$	−8.59020e7	−	1.88099e8i	−0.134414	−	0.294326i
$329$	1.21596e9	+	1.40329e9i	1.88250	+	2.17252i
$330$	−2.50647e7	−	1.74329e8i	−0.0383940	−	0.267036i
$331$	1.92381e8	+	5.64883e7i	0.291585	+	0.0856170i	0.424254	−	0.905543i	$-0.360536\pi$
$331$	1.92381e8	+	5.64883e7i	0.291585	+	0.0856170i	−0.132669	+	0.991160i	$0.542355\pi$
$332$	−9.57109e7	+	1.10456e8i	−0.143542	+	0.165656i
$333$	−3.27370e8	−	2.10388e8i	−0.485829	−	0.312223i
$334$	8.55805e8	+	5.49993e8i	1.25679	+	0.807689i
$335$	5.85018e8	−	6.75147e8i	0.850183	−	0.981164i
$336$	5.25792e8	+	1.54387e8i	0.756183	+	0.222035i
$337$	3.40921e7	+	2.37116e8i	0.0485232	+	0.337486i	0.999593	+	0.0285117i	$0.00907677\pi$
$337$	3.40921e7	+	2.37116e8i	0.0485232	+	0.337486i	−0.951070	+	0.308975i	$0.900014\pi$
$338$	−3.54307e8	−	4.08892e8i	−0.499081	−	0.575970i
$339$	−2.42350e8	−	5.30673e8i	−0.337866	−	0.739824i
$340$	1.95537e7	−	5.74149e6i	0.0269807	−	0.00792224i
$341$	−1.35466e7	+	2.96629e7i	−0.0185008	+	0.0405111i
$342$	6.22193e6	−	4.32745e7i	0.00841073	−	0.0584979i
$343$	−8.67287e8	+	5.57372e8i	−1.16047	+	0.745788i
$344$	1.28535e9			1.70241
$345$	−2.44335e8	−	3.88213e8i	−0.320346	−	0.508984i
$346$	3.05866e8			0.396976
$347$	3.67655e8	−	2.36278e8i	0.472375	−	0.303577i	−0.282708	−	0.959206i	$-0.591233\pi$
$347$	3.67655e8	−	2.36278e8i	0.472375	−	0.303577i	0.755083	+	0.655629i	$0.227596\pi$
$348$	−9.91183e6	+	6.89383e7i	−0.0126074	+	0.0876866i
$349$	−4.46321e8	+	9.77308e8i	−0.562029	+	1.23067i	0.388905	+	0.921278i	$0.372853\pi$
$349$	−4.46321e8	+	9.77308e8i	−0.562029	+	1.23067i	−0.950934	+	0.309394i	$0.899874\pi$
$350$	−1.00698e8	+	2.95677e7i	−0.125541	+	0.0368621i
$351$	2.65335e7	+	5.81004e7i	0.0327507	+	0.0717140i
$352$	−8.37979e7	−	9.67080e7i	−0.102408	−	0.118185i
$353$	4.90235e7	+	3.40966e8i	0.0593188	+	0.412572i	0.997747	+	0.0670959i	$0.0213733\pi$
$353$	4.90235e7	+	3.40966e8i	0.0593188	+	0.412572i	−0.938428	+	0.345476i	$0.887718\pi$
$354$	4.36650e8	+	1.28212e8i	0.523145	+	0.153609i
$355$	−6.97242e8	+	8.04661e8i	−0.827150	+	0.954583i
$356$	−9.17705e7	−	5.89773e7i	−0.107802	−	0.0692803i
$357$	−1.17378e8	−	7.54345e7i	−0.136537	−	0.0877468i
$358$	2.63754e8	−	3.04388e8i	0.303814	−	0.350620i
$359$	−3.36647e8	−	9.88485e7i	−0.384012	−	0.112756i	0.0840282	−	0.996463i	$-0.473221\pi$
$359$	−3.36647e8	−	9.88485e7i	−0.384012	−	0.112756i	−0.468040	+	0.883707i	$0.655040\pi$
$360$	4.65223e7	+	3.23570e8i	0.0525536	+	0.365519i
$361$	5.63422e8	+	6.50224e8i	0.630316	+	0.727424i
$362$	2.59655e8	+	5.68565e8i	0.287685	+	0.629942i
$363$	−3.83714e8	+	1.12669e8i	−0.421051	+	0.123632i
$364$	−4.24232e7	+	9.28938e7i	−0.0461050	+	0.100956i
$365$	−1.03423e7	+	7.19320e7i	−0.0111324	+	0.0774278i
$366$	4.97151e8	−	3.19499e8i	0.530035	−	0.340633i
$367$	−1.16333e9			−1.22849			−0.614245	−	0.789115i	$-0.710540\pi$
$367$	−1.16333e9			−1.22849			−0.614245	+	0.789115i	$0.710540\pi$
$368$	7.03653e8	+	3.29421e8i	0.736022	+	0.344575i
$369$	−9.78783e7			−0.101413
$370$	−1.35470e9	+	8.70610e8i	−1.39039	+	0.893547i
$371$	9.65617e7	−	6.71601e8i	0.0981739	−	0.682815i
$372$	3.49230e6	−	7.64706e6i	0.00351731	−	0.00770183i
$373$	−1.38481e9	+	4.06617e8i	−1.38169	+	0.405700i	−0.886356	−	0.463005i	$-0.846771\pi$
$373$	−1.38481e9	+	4.06617e8i	−1.38169	+	0.405700i	−0.495331	+	0.868704i	$0.664953\pi$
$374$	−3.15530e7	−	6.90914e7i	−0.0311882	−	0.0682926i
$375$	3.67975e8	+	4.24665e8i	0.360337	+	0.415851i
$376$	−2.67004e8	−	1.85705e9i	−0.259036	−	1.80164i
$377$	3.89018e8	+	1.14226e8i	0.373917	+	0.109792i
$378$	2.03570e8	−	2.34933e8i	0.193862	−	0.223729i
$379$	1.76672e9	+	1.13540e9i	1.66698	+	1.07131i	0.906762	+	0.421642i	$0.138546\pi$
$379$	1.76672e9	+	1.13540e9i	1.66698	+	1.07131i	0.760222	+	0.649664i	$0.225090\pi$
$380$	2.92698e7	+	1.88106e7i	0.0273639	+	0.0175857i
$381$	−2.35330e8	+	2.71585e8i	−0.217992	+	0.251576i
$382$	6.41926e8	+	1.88487e8i	0.589201	+	0.173005i
$383$	−2.70252e8	−	1.87964e9i	−0.245795	−	1.70954i	−0.622012	−	0.783008i	$-0.713684\pi$
$383$	−2.70252e8	−	1.87964e9i	−0.245795	−	1.70954i	0.376217	−	0.926532i	$-0.377225\pi$
$384$	−2.90628e8	−	3.35402e8i	−0.261925	−	0.302278i
$385$	−3.98645e8	−	8.72910e8i	−0.356019	−	0.779574i
$386$	5.28183e8	−	1.55088e8i	0.467443	−	0.137254i
$387$	2.52736e8	−	5.53415e8i	0.221656	−	0.485358i
$388$	3.92113e7	−	2.72721e8i	0.0340801	−	0.237032i
$389$	−1.16251e9	+	7.47100e8i	−1.00132	+	0.643509i	−0.935133	−	0.354298i	$-0.884720\pi$
$389$	−1.16251e9	+	7.47100e8i	−1.00132	+	0.643509i	−0.0661876	+	0.997807i	$0.521084\pi$
$390$	2.64312e8			0.225627
$391$	−1.48274e8	−	1.30955e8i	−0.125443	−	0.110791i
$392$	2.31005e9			1.93696
$393$	−2.89178e8	+	1.85844e8i	−0.240321	+	0.154445i
$394$	−1.21184e8	+	8.42856e8i	−0.0998182	+	0.694251i
$395$	−1.92726e8	+	4.22012e8i	−0.157344	+	0.344536i
$396$	−3.12263e7	+	9.16886e6i	−0.0252689	+	0.00741963i
$397$	3.16435e8	+	6.92895e8i	0.253815	+	0.555777i	0.993053	−	0.117667i	$-0.0375415\pi$
$397$	3.16435e8	+	6.92895e8i	0.253815	+	0.555777i	−0.739238	+	0.673444i	$0.764814\pi$
$398$	7.31757e8	+	8.44492e8i	0.581803	+	0.671436i
$399$	−3.39014e7	−	2.35789e8i	−0.0267185	−	0.185831i
$400$	8.48969e7	+	2.49280e7i	0.0663257	+	0.0194750i
$401$	9.81794e8	−	1.13305e9i	0.760352	−	0.877493i	−0.235176	−	0.971953i	$-0.575567\pi$
$401$	9.81794e8	−	1.13305e9i	0.760352	−	0.877493i	0.995529	+	0.0944593i	$0.0301122\pi$
$402$	7.22103e8	+	4.64067e8i	0.554380	+	0.356279i
$403$	−4.11699e7	−	2.64583e7i	−0.0313338	−	0.0201370i
$404$	−5.14041e7	+	5.93234e7i	−0.0387849	+	0.0447602i
$405$	1.48463e8	+	4.35927e7i	0.111052	+	0.0326078i
$406$	−2.80822e8	−	1.95316e9i	−0.208252	−	1.44843i
$407$	−7.55875e8	−	8.72326e8i	−0.555737	−	0.641355i
$408$	5.85653e7	+	1.28240e8i	0.0426904	+	0.0934788i
$409$	−4.43150e8	+	1.30121e8i	−0.320272	+	0.0940404i	−0.437917	−	0.899015i	$-0.644284\pi$
$409$	−4.43150e8	+	1.30121e8i	−0.320272	+	0.0940404i	0.117645	+	0.993056i	$0.462465\pi$
$410$	−1.68256e8	+	3.68430e8i	−0.120567	+	0.264005i
$411$	−8.29270e6	+	5.76770e7i	−0.00589182	+	0.0409785i
$412$	−1.03053e8	+	6.62284e7i	−0.0725976	+	0.0466556i
$413$	2.47961e9			1.73204
$414$	3.35804e8	−	2.85463e8i	0.232586	−	0.197719i
$415$	2.06111e9			1.41557
$416$	1.61553e8	−	1.03824e8i	0.110024	−	0.0707084i
$417$	−1.99048e8	+	1.38441e9i	−0.134426	+	0.934950i
$418$	5.38700e7	−	1.17959e8i	0.0360769	−	0.0789975i
$419$	−6.19548e8	+	1.81916e8i	−0.411458	+	0.120815i	−0.480909	−	0.876770i	$-0.659693\pi$
$419$	−6.19548e8	+	1.81916e8i	−0.411458	+	0.120815i	0.0694510	+	0.997585i	$0.477875\pi$
$420$	1.02770e8	+	2.25035e8i	0.0676852	+	0.148210i
$421$	1.94679e9	+	2.24672e9i	1.27155	+	1.46744i	0.816912	+	0.576762i	$0.195684\pi$
$421$	1.94679e9	+	2.24672e9i	1.27155	+	1.46744i	0.454633	+	0.890679i	$0.349770\pi$
$422$	3.22287e8	+	2.24155e9i	0.208761	+	1.45196i
$423$	−8.52069e8	−	2.50190e8i	−0.547373	−	0.160723i
$424$	−4.48953e8	+	5.18119e8i	−0.286036	+	0.330103i
$425$	−1.89524e7	−	1.21800e7i	−0.0119758	−	0.00769637i
$426$	−8.60624e8	−	5.53089e8i	−0.539361	−	0.346626i
$427$	2.10864e9	−	2.43350e9i	1.31070	−	1.51263i
$428$	−1.34577e8	−	3.95152e7i	−0.0829691	−	0.0243619i
$429$	2.69621e7	+	1.87525e8i	0.0164874	+	0.114672i
$430$	−1.64868e9	−	1.90268e9i	−0.999995	−	1.15406i
$431$	−1.24730e9	−	2.73120e9i	−0.750411	−	1.64317i	−0.765626	−	0.643286i	$-0.777571\pi$
$431$	−1.24730e9	−	2.73120e9i	−0.750411	−	1.64317i	0.0152154	−	0.999884i	$-0.495157\pi$
$432$	−2.51464e8	+	7.38366e7i	−0.150066	+	0.0440635i
$433$	−1.10876e9	+	2.42786e9i	−0.656344	+	1.43719i	0.229546	+	0.973298i	$0.426276\pi$
$433$	−1.10876e9	+	2.42786e9i	−0.656344	+	1.43719i	−0.885890	+	0.463895i	$0.846451\pi$
$434$	−3.38966e7	+	2.35756e8i	−0.0199041	+	0.138436i
$435$	8.26263e8	−	5.31007e8i	0.481289	−	0.309306i
$436$	−2.46638e8			−0.142514
$437$	3.19255e6	−	3.37727e8i	0.00183001	−	0.193589i
$438$	−6.98259e7			−0.0397061
$439$	−2.97046e9	+	1.90900e9i	−1.67571	+	1.07691i	−0.789298	+	0.614011i	$0.789555\pi$
$439$	−2.97046e9	+	1.90900e9i	−1.67571	+	1.07691i	−0.886410	+	0.462901i	$0.846808\pi$
$440$	−1.37991e8	+	9.59749e8i	−0.0772266	+	0.537123i
$441$	4.54224e8	−	9.94611e8i	0.252194	−	0.552228i
$442$	1.09372e8	−	3.21144e7i	0.0602459	−	0.0176898i
$443$	−8.83975e8	−	1.93563e9i	−0.483089	−	1.05782i	−0.981603	−	0.190935i	$-0.938848\pi$
$443$	−8.83975e8	−	1.93563e9i	−0.483089	−	1.05782i	0.498514	−	0.866882i	$-0.333879\pi$
$444$	1.94863e8	+	2.24884e8i	0.105655	+	0.121932i
$445$	2.18934e8	+	1.52272e9i	0.117775	+	0.819145i
$446$	−1.05258e9	−	3.09066e8i	−0.561803	−	0.164960i
$447$	9.76208e7	−	1.12660e8i	0.0516971	−	0.0596616i
$448$	−2.97174e9	−	1.90982e9i	−1.56148	−	1.00350i
$449$	−4.31455e8	−	2.77279e8i	−0.224944	−	0.144562i	0.423315	−	0.905982i	$-0.360866\pi$
$449$	−4.31455e8	−	2.77279e8i	−0.224944	−	0.144562i	−0.648259	+	0.761420i	$0.724503\pi$
$450$	3.28694e7	−	3.79333e7i	0.0170039	−	0.0196235i
$451$	−2.78559e8	−	8.17924e7i	−0.142988	−	0.0419851i
$452$	6.34865e7	+	4.41558e8i	0.0323368	+	0.224907i
$453$	−8.56222e8	−	9.88133e8i	−0.432756	−	0.499427i
$454$	9.72145e8	+	2.12870e9i	0.487569	+	1.06763i
$455$	1.38182e9	−	4.05738e8i	0.687718	−	0.201932i
$456$	−9.99876e7	+	2.18942e8i	−0.0493821	+	0.108132i
$457$	1.00703e7	−	7.00402e7i	0.00493553	−	0.0343274i	−0.987205	−	0.159457i	$-0.949026\pi$
$457$	1.00703e7	−	7.00402e7i	0.00493553	−	0.0343274i	0.992140	+	0.125130i	$0.0399347\pi$
$458$	−1.57940e9	+	1.01502e9i	−0.768178	+	0.493678i
$459$	6.67303e7			0.0322091
$460$	9.56332e7	+	3.37465e8i	0.0458096	+	0.161650i
$461$	4.04045e8			0.192077			0.0960387	−	0.995378i	$-0.469383\pi$
$461$	4.04045e8			0.192077			0.0960387	+	0.995378i	$0.469383\pi$
$462$	7.75680e8	−	4.98499e8i	0.365962	−	0.235189i
$463$	2.96342e8	−	2.06111e9i	0.138759	−	0.965088i	−0.794853	−	0.606802i	$-0.792452\pi$
$463$	2.96342e8	−	2.06111e9i	0.138759	−	0.965088i	0.933612	−	0.358286i	$-0.116639\pi$
$464$	−6.91086e8	+	1.51327e9i	−0.321158	+	0.703238i
$465$	−1.13752e8	+	3.34006e7i	−0.0524654	+	0.0154052i
$466$	1.36446e9	+	2.98774e9i	0.624610	+	1.36770i
$467$	1.33408e9	+	1.53961e9i	0.606140	+	0.699523i	0.973014	−	0.230748i	$-0.0741173\pi$
$467$	1.33408e9	+	1.53961e9i	0.606140	+	0.699523i	−0.366873	+	0.930271i	$0.619572\pi$
$468$	−6.95078e6	−	4.83437e7i	−0.00313453	−	0.0218012i
$469$	4.48752e9	+	1.31765e9i	2.00864	+	0.589788i
$470$	−2.40650e9	+	2.77725e9i	−1.06916	+	1.23388i
$471$	1.53758e9	+	9.88143e8i	0.678055	+	0.435759i
$472$	−2.10769e9	−	1.35453e9i	−0.922594	−	0.592915i
$473$	1.18175e9	−	1.36381e9i	0.513464	−	0.592569i
$474$	−4.27713e8	−	1.25588e8i	−0.184471	−	0.0541655i
$475$	−5.47387e6	−	3.80716e7i	−0.00234351	−	0.0162995i
$476$	6.98683e7	+	8.06323e7i	0.0296931	+	0.0342677i
$477$	1.34803e8	+	2.95177e8i	0.0568702	+	0.124528i
$478$	6.97061e8	−	2.04675e8i	0.291926	−	0.0857172i
$479$	5.76961e8	−	1.26337e9i	0.239868	−	0.525238i	−0.750963	−	0.660344i	$-0.770410\pi$
$479$	5.76961e8	−	1.26337e9i	0.239868	−	0.525238i	0.990831	+	0.135107i	$0.0431377\pi$
$480$	6.62068e7	−	4.60479e8i	0.0273249	−	0.190049i
$481$	1.45725e9	−	9.36515e8i	0.597070	−	0.383713i
$482$	−2.23338e9			−0.908442
$483$	1.31737e9	−	2.00788e9i	0.531977	−	0.810816i
$484$	3.05799e8			0.122596
$485$	−3.26871e9	+	2.10067e9i	−1.30101	+	0.836107i
$486$	−2.11582e7	+	1.47158e8i	−0.00836087	+	0.0581511i
$487$	1.42219e9	−	3.11416e9i	0.557963	−	1.22177i	−0.395000	−	0.918681i	$-0.629255\pi$
$487$	1.42219e9	−	3.11416e9i	0.557963	−	1.22177i	0.952963	−	0.303087i	$-0.0980174\pi$
$488$	−3.12171e9	+	9.16616e8i	−1.21597	+	0.357041i
$489$	3.79597e6	+	8.31203e6i	0.00146805	+	0.00321459i
$490$	−2.96306e9	−	3.41955e9i	−1.13777	−	1.31305i
$491$	8.75183e6	+	6.08703e7i	0.00333667	+	0.0232071i	0.991422	−	0.130702i	$-0.0417230\pi$
$491$	8.75183e6	+	6.08703e7i	0.00333667	+	0.0232071i	−0.988085	+	0.153909i	$0.950814\pi$
$492$	7.18121e7	+	2.10859e7i	0.0271844	+	0.00798207i
$493$	2.77388e8	−	3.20122e8i	0.104261	−	0.120324i
$494$	1.63718e8	+	1.05215e8i	0.0611015	+	0.0392675i
$495$	3.86094e8	+	2.48128e8i	0.143079	+	0.0919511i
$496$	1.31499e8	−	1.51758e8i	0.0483880	−	0.0558428i
$497$	−5.34836e9	−	1.57042e9i	−1.95422	−	0.573810i
$498$	2.81840e8	+	1.96024e9i	0.102258	+	0.711223i
$499$	2.06708e9	+	2.38554e9i	0.744743	+	0.859479i	0.994048	−	0.108946i	$-0.0347476\pi$
$499$	2.06708e9	+	2.38554e9i	0.744743	+	0.859479i	−0.249305	+	0.968425i	$0.580202\pi$
$500$	−1.78493e8	−	3.90845e8i	−0.0638596	−	0.139833i
$501$	−2.54357e9	+	7.46861e8i	−0.903675	+	0.265343i
$502$	1.94584e9	−	4.26079e9i	0.686505	−	1.50324i
$503$	2.86986e8	−	1.99603e9i	0.100548	−	0.699326i	−0.875729	−	0.482802i	$-0.839619\pi$
$503$	2.86986e8	−	1.99603e9i	0.100548	−	0.699326i	0.976277	−	0.216524i	$-0.0694719\pi$
$504$	−1.43973e9	+	9.25260e8i	−0.500928	+	0.321927i
$505$	1.10697e9			0.382487
$506$	1.19424e9	−	5.31805e8i	0.409793	−	0.182484i
$507$	1.40989e9			0.480460
$508$	2.31167e8	−	1.48562e8i	0.0782352	−	0.0502787i
$509$	1.17677e8	−	8.18458e8i	0.0395528	−	0.275096i	−0.960441	−	0.278482i	$-0.910169\pi$
$509$	1.17677e8	−	8.18458e8i	0.0395528	−	0.275096i	0.999994	+	0.00338606i	$0.00107782\pi$
$510$	1.14712e8	−	2.51184e8i	0.0382925	−	0.0838488i
$511$	−3.65049e8	+	1.07188e8i	−0.121026	+	0.0355363i
$512$	1.41777e9	+	3.10447e9i	0.466831	+	1.02222i
$513$	7.46068e7	+	8.61008e7i	0.0243987	+	0.0281577i
$514$	−3.19630e8	−	2.22308e9i	−0.103819	−	0.722077i
$515$	1.65754e9	+	4.86699e8i	0.534736	+	0.157013i
$516$	−3.04652e8	+	3.51587e8i	−0.0976180	+	0.112657i
$517$	−2.21590e9	−	1.42407e9i	−0.705233	−	0.453226i
$518$	−7.09227e9	−	4.55793e9i	−2.24198	−	1.44083i
$519$	−5.21957e8	+	6.02370e8i	−0.163889	+	0.189137i
$520$	−1.39620e9	−	4.09961e8i	−0.435447	−	0.127859i
$521$	4.58853e8	+	3.19139e9i	0.142148	+	0.988663i	0.928619	+	0.371035i	$0.120997\pi$
$521$	4.58853e8	+	3.19139e9i	0.142148	+	0.988663i	−0.786471	+	0.617628i	$0.788094\pi$
$522$	6.18005e8	+	7.13216e8i	0.190171	+	0.219469i
$523$	−3.53732e8	−	7.74565e8i	−0.108123	−	0.236756i	0.847835	−	0.530260i	$-0.177906\pi$
$523$	−3.53732e8	−	7.74565e8i	−0.108123	−	0.236756i	−0.955958	+	0.293504i	$0.905179\pi$
$524$	2.52203e8	−	7.40535e7i	0.0765757	−	0.0224847i
$525$	1.13610e8	−	2.48772e8i	0.0342657	−	0.0750315i
$526$	7.42747e8	−	5.16592e9i	0.222531	−	1.54774i
$527$	−4.30121e7	+	2.76422e7i	−0.0128013	+	0.00822688i
$528$	−7.77364e8			−0.229829
$529$	2.27793e9	−	2.53058e9i	0.669031	−	0.743235i
$530$	1.34283e9			0.391791
$531$	−9.97637e8	+	6.41143e8i	−0.289162	+	0.185833i
$532$	−2.59231e7	+	1.80299e8i	−0.00746443	+	0.0519162i
$533$	1.80993e8	−	3.96320e8i	0.0517747	−	0.113371i
$534$	−1.41826e9	+	4.16440e8i	−0.403054	+	0.118347i
$535$	8.21671e8	+	1.79921e9i	0.231985	+	0.507976i
$536$	−3.09464e9	−	3.57141e9i	−0.868027	−	1.00176i
$537$	1.49367e8	+	1.03887e9i	0.0416240	+	0.289502i
$538$	2.73854e9	+	8.04109e8i	0.758197	+	0.222627i
$539$	2.12386e9	−	2.45107e9i	0.584205	−	0.674209i
$540$	−9.95344e7	−	6.39669e7i	−0.0272016	−	0.0174814i
$541$	4.81099e8	+	3.09184e8i	0.130630	+	0.0839510i	0.604324	−	0.796739i	$-0.293443\pi$
$541$	4.81099e8	+	3.09184e8i	0.130630	+	0.0839510i	−0.473694	+	0.880690i	$0.657080\pi$
$542$	−5.12576e7	+	5.91544e7i	−0.0138280	+	0.0159584i
$543$	−1.56283e9	−	4.58887e8i	−0.418901	−	0.123000i
$544$	−2.85529e7	−	1.98589e8i	−0.00760420	−	0.0528884i
$545$	2.27770e9	+	2.62861e9i	0.602710	+	0.695565i
$546$	5.74834e8	+	1.25871e9i	0.151136	+	0.330942i
$547$	−6.27319e9	+	1.84197e9i	−1.63883	+	0.481203i	−0.965988	−	0.258587i	$-0.916743\pi$
$547$	−6.27319e9	+	1.84197e9i	−1.63883	+	0.481203i	−0.672838	+	0.739790i	$0.734925\pi$
$548$	1.85096e7	−	4.05304e7i	0.00480470	−	0.0105208i
$549$	−2.19162e8	+	1.52431e9i	−0.0565279	+	0.393160i
$550$	1.25245e8	−	8.04899e7i	0.0320989	−	0.0206287i
$551$	7.23176e8			0.184168
$552$	−2.21662e9	+	9.87080e8i	−0.560924	+	0.249785i
$553$	−2.42886e9			−0.610751
$554$	3.51714e9	−	2.26033e9i	0.878831	−	0.564791i
$555$	5.97199e8	−	4.15361e9i	0.148284	−	1.03134i
$556$	4.44283e8	−	9.72844e8i	0.109622	−	0.240039i
$557$	3.12375e9	−	9.17215e8i	0.765919	−	0.224894i	0.124640	−	0.992202i	$-0.460222\pi$
$557$	3.12375e9	−	9.17215e8i	0.765919	−	0.224894i	0.641279	+	0.767308i	$0.278404\pi$
$558$	−4.73206e7	−	1.03618e8i	−0.0115300	−	0.0252473i
$559$	1.77349e9	+	2.04672e9i	0.429425	+	0.495583i
$560$	8.40970e8	+	5.84908e9i	0.202359	+	1.40744i
$561$	1.89913e8	+	5.57635e7i	0.0454135	+	0.0133346i
$562$	−7.65536e8	+	8.83475e8i	−0.181923	+	0.209951i
$563$	3.10548e9	+	1.99577e9i	0.733414	+	0.471337i	0.853280	−	0.521453i	$-0.174610\pi$
$563$	3.10548e9	+	1.99577e9i	0.733414	+	0.471337i	−0.119865	+	0.992790i	$0.538246\pi$
$564$	5.71255e8	+	3.67123e8i	0.134077	+	0.0861658i
$565$	4.11972e9	−	4.75441e9i	0.960945	−	1.10899i
$566$	2.56820e9	+	7.54091e8i	0.595348	+	0.174810i
$567$	1.15284e8	+	8.01821e8i	0.0265601	+	0.184730i
$568$	3.68828e9	+	4.25651e9i	0.844511	+	0.974618i
$569$	−1.54585e8	−	3.38494e8i	−0.0351782	−	0.0770296i	0.891227	−	0.453557i	$-0.149845\pi$
$569$	−1.54585e8	−	3.38494e8i	−0.0351782	−	0.0770296i	−0.926405	+	0.376528i	$0.877118\pi$
$570$	4.52350e8	−	1.32822e8i	0.102309	−	0.0300405i
$571$	−2.13309e9	+	4.67081e9i	−0.479493	+	1.04994i	0.503109	+	0.864223i	$0.332189\pi$
$571$	−2.13309e9	+	4.67081e9i	−0.479493	+	1.04994i	−0.982603	+	0.185721i	$0.940538\pi$
$572$	2.06169e7	−	1.43394e8i	0.00460614	−	0.0320364i
$573$	−1.46664e9	+	9.42555e8i	−0.325674	+	0.209298i
$574$	−2.12048e9			−0.467995
$575$	2.12708e8	−	3.24201e8i	0.0466603	−	0.0711176i
$576$	1.68945e9			0.368356
$577$	5.47718e9	−	3.51997e9i	1.18698	−	0.762823i	0.210319	−	0.977633i	$-0.432550\pi$
$577$	5.47718e9	−	3.51997e9i	1.18698	−	0.762823i	0.976656	+	0.214810i	$0.0689133\pi$
$578$	−5.88117e8	+	4.09044e9i	−0.126682	+	0.881095i
$579$	−5.95908e8	+	1.30486e9i	−0.127586	+	0.279375i
$580$	−7.20615e8	+	2.11592e8i	−0.153358	+	0.0450298i
$581$	4.48256e9	+	9.81544e9i	0.948221	+	2.07632i
$582$	−2.44484e9	−	2.82149e9i	−0.514067	−	0.593264i
$583$	1.36980e8	+	9.52716e8i	0.0286297	+	0.199124i
$584$	3.68848e8	+	1.08304e8i	0.0766307	+	0.0225008i
$585$	−4.51045e8	+	5.20534e8i	−0.0931482	+	0.107499i
$586$	2.56487e7	+	1.64834e7i	0.00526530	+	0.00338380i
$587$	−3.02801e9	−	1.94598e9i	−0.617908	−	0.397105i	0.193907	−	0.981020i	$-0.437884\pi$
$587$	−3.02801e9	−	1.94598e9i	−0.617908	−	0.397105i	−0.811815	+	0.583915i	$0.801520\pi$
$588$	−5.47528e8	+	6.31881e8i	−0.111067	+	0.128178i
$589$	−8.37551e7	−	2.45927e7i	−0.0168891	−	0.00495910i
$590$	6.98392e8	+	4.85742e9i	0.139997	+	0.973697i
$591$	−1.45311e9	−	1.67698e9i	−0.289563	−	0.334174i
$592$	2.95263e9	+	6.46537e9i	0.584903	+	1.28076i
$593$	−5.69114e9	+	1.67107e9i	−1.12075	+	0.329081i	−0.789065	−	0.614310i	$-0.789434\pi$
$593$	−5.69114e9	+	1.67107e9i	−1.12075	+	0.329081i	−0.331682	+	0.943391i	$0.607616\pi$
$594$	−1.83189e8	+	4.01128e8i	−0.0358631	+	0.0785292i
$595$	2.14126e8	−	1.48928e9i	0.0416735	−	0.289845i
$596$	−9.58937e7	+	6.16271e7i	−0.0185536	+	0.0119237i
$597$	−2.91187e9			−0.560095
$598$	5.34915e8	+	1.88758e9i	0.102289	+	0.360953i
$599$	6.48297e9			1.23248			0.616240	−	0.787558i	$-0.288655\pi$
$599$	6.48297e9			1.23248			0.616240	+	0.787558i	$0.288655\pi$
$600$	−2.32466e8	+	1.49397e8i	−0.0439369	+	0.0282366i
$601$	−1.20674e9	+	8.39308e9i	−0.226753	+	1.57710i	0.484897	+	0.874571i	$0.338857\pi$
$601$	−1.20674e9	+	8.39308e9i	−0.226753	+	1.57710i	−0.711651	+	0.702533i	$0.752052\pi$
$602$	5.47538e9	−	1.19894e10i	1.02288	−	2.23981i
$603$	−2.14619e9	+	6.30178e8i	−0.398619	+	0.117045i
$604$	4.15327e8	+	9.09438e8i	0.0766938	+	0.167936i
$605$	−2.82405e9	−	3.25913e9i	−0.518476	−	0.598353i
$606$	1.51369e8	+	1.05280e9i	0.0276302	+	0.192172i
$607$	−4.88165e9	−	1.43338e9i	−0.885944	−	0.260137i	−0.193061	−	0.981187i	$-0.561842\pi$
$607$	−4.88165e9	−	1.43338e9i	−0.885944	−	0.260137i	−0.692883	+	0.721050i	$0.743660\pi$
$608$	2.24313e8	−	2.58871e8i	0.0404754	−	0.0467112i
$609$	4.32576e9	+	2.77999e9i	0.776071	+	0.498751i
$610$	5.36100e9	+	3.44531e9i	0.956294	+	0.614573i
$611$	2.58867e9	−	2.98748e9i	0.459126	−	0.529860i
$612$	−4.89593e7	−	1.43757e7i	−0.00863386	−	0.00253513i
$613$	−8.01992e8	−	5.57798e9i	−0.140624	−	0.978059i	−0.930891	−	0.365297i	$-0.880967\pi$
$613$	−8.01992e8	−	5.57798e9i	−0.140624	−	0.978059i	0.790267	−	0.612762i	$-0.209942\pi$
$614$	2.68639e9	+	3.10026e9i	0.468360	+	0.540517i
$615$	−4.38456e8	−	9.60085e8i	−0.0760087	−	0.166436i
$616$	−4.87064e9	+	1.43015e9i	−0.839564	+	0.246518i
$617$	2.81716e9	−	6.16872e9i	0.482851	−	1.05730i	−0.498818	−	0.866707i	$-0.666232\pi$
$617$	2.81716e9	−	6.16872e9i	0.482851	−	1.05730i	0.981670	−	0.190591i	$-0.0610403\pi$
$618$	−2.36225e8	+	1.64298e9i	−0.0402592	+	0.280009i
$619$	7.13685e9	−	4.58658e9i	1.20945	−	0.777269i	0.228887	−	0.973453i	$-0.426491\pi$
$619$	7.13685e9	−	4.58658e9i	1.20945	−	0.777269i	0.980567	+	0.196184i	$0.0628549\pi$
$620$	9.06539e7			0.0152762
$621$	−1.08565e7	+	1.14847e9i	−0.00181916	+	0.192441i
$622$	5.15887e9			0.859584
$623$	−6.77539e9	+	4.35428e9i	−1.12260	+	0.721454i
$624$	1.66027e8	−	1.15474e9i	0.0273548	−	0.190257i
$625$	−2.73281e9	+	5.98402e9i	−0.447744	+	0.980423i
$626$	−7.26295e8	+	2.13260e8i	−0.118332	+	0.0347455i
$627$	1.40379e8	+	3.07386e8i	0.0227439	+	0.0498022i
$628$	−9.15229e8	−	1.05623e9i	−0.147459	−	0.170177i
$629$	−2.57553e8	−	1.79132e9i	−0.0412657	−	0.287009i
$630$	3.21637e9	+	9.44410e8i	0.512476	+	0.150477i
$631$	6.11558e9	−	7.05776e9i	0.969025	−	1.11831i	−0.0239166	−	0.999714i	$-0.507614\pi$
$631$	6.11558e9	−	7.05776e9i	0.969025	−	1.11831i	0.992942	−	0.118601i	$-0.0378409\pi$
$632$	2.06455e9	+	1.32681e9i	0.325324	+	0.209073i
$633$	−4.96448e9	−	3.19048e9i	−0.777966	−	0.499968i
$634$	5.39502e9	−	6.22619e9i	0.840777	−	0.970308i
$635$	−3.71816e9	−	1.09175e9i	−0.576262	−	0.169206i
$636$	−3.53132e7	−	2.45609e8i	−0.00544299	−	0.0378568i
$637$	3.18736e9	+	3.67841e9i	0.488588	+	0.563861i
$638$	1.16283e9	+	2.54623e9i	0.177273	+	0.388174i
$639$	2.55789e9	−	7.51066e8i	0.387819	−	0.113874i
$640$	1.98805e9	−	4.35323e9i	0.299777	−	0.656420i
$641$	−7.04579e8	+	4.90045e9i	−0.105664	+	0.734908i	0.866257	+	0.499599i	$0.166519\pi$
$641$	−7.04579e8	+	4.90045e9i	−0.105664	+	0.734908i	−0.971921	+	0.235309i	$0.924390\pi$
$642$	−1.59880e9	+	1.02749e9i	−0.238463	+	0.153251i
$643$	−7.39316e9			−1.09671			−0.548355	−	0.836246i	$-0.684746\pi$
$643$	−7.39316e9			−1.09671			−0.548355	+	0.836246i	$0.684746\pi$
$644$	−1.39910e9	+	1.18936e9i	−0.206418	+	0.175473i
$645$	6.56059e9			0.962685
$646$	1.71043e8	−	1.09923e8i	0.0249628	−	0.0160426i
$647$	−1.20468e8	+	8.37871e8i	−0.0174866	+	0.121622i	−0.996695	−	0.0812350i	$-0.974114\pi$
$647$	−1.20468e8	+	8.37871e8i	−0.0174866	+	0.121622i	0.979208	+	0.202857i	$0.0650227\pi$
$648$	3.40016e8	−	7.44531e8i	0.0490893	−	0.107491i
$649$	−3.37503e9	+	9.90997e8i	−0.484642	+	0.142304i
$650$	9.28153e7	+	2.03237e8i	0.0132563	+	0.0290273i
$651$	−4.06452e8	−	4.69071e8i	−0.0577399	−	0.0666354i
$652$	−994400.	−	6.91621e6i	−0.000140506	−	0.000977240i
$653$	−7.59714e9	−	2.23072e9i	−1.06771	−	0.313509i	−0.299759	−	0.954015i	$-0.596906\pi$
$653$	−7.59714e9	−	2.23072e9i	−1.06771	−	0.313509i	−0.767953	+	0.640506i	$0.778724\pi$
$654$	−2.18851e9	+	2.52567e9i	−0.305933	+	0.353065i
$655$	−3.11834e9	−	2.00404e9i	−0.433590	−	0.278651i
$656$	1.50394e9	+	9.66520e8i	0.208001	+	0.133674i
$657$	1.19157e8	−	1.37515e8i	0.0163924	−	0.0189178i
$658$	−1.84596e10	−	5.42022e9i	−2.52599	−	0.741697i
$659$	−1.36724e8	−	9.50934e8i	−0.0186099	−	0.129435i	0.978399	−	0.206728i	$-0.0662814\pi$
$659$	−1.36724e8	−	9.50934e8i	−0.0186099	−	0.129435i	−0.997008	+	0.0772929i	$0.975372\pi$
$660$	−2.29819e8	−	2.65225e8i	−0.0311158	−	0.0359096i
$661$	1.59714e9	+	3.49726e9i	0.215099	+	0.471002i	0.986168	−	0.165750i	$-0.0530046\pi$
$661$	1.59714e9	+	3.49726e9i	0.215099	+	0.471002i	−0.771068	+	0.636752i	$0.780277\pi$
$662$	−1.99330e9	+	5.85285e8i	−0.267036	+	0.0784088i
$663$	−1.23396e8	+	2.70199e8i	−0.0164438	+	0.0360069i
$664$	1.55164e9	−	1.07919e10i	0.205685	−	1.43057i
$665$	2.16098e9	−	1.38878e9i	0.284955	−	0.183129i
$666$	4.03200e9			0.528885
$667$	5.46437e9	+	4.82609e9i	0.713016	+	0.629731i
$668$	2.02709e9			0.263121
$669$	2.40489e9	−	1.54553e9i	0.310531	−	0.199566i
$670$	−1.31729e9	+	9.16192e9i	−0.169207	+	1.17686i
$671$	−1.89752e9	+	4.15500e9i	−0.242470	+	0.530936i
$672$	2.33689e9	−	6.86172e8i	0.297061	−	0.0872250i
$673$	1.52429e8	+	3.33774e8i	0.0192760	+	0.0422084i	0.919025	−	0.394199i	$-0.128978\pi$
$673$	1.52429e8	+	3.33774e8i	0.0192760	+	0.0422084i	−0.899749	+	0.436407i	$0.856251\pi$
$674$	−1.62541e9	−	1.87582e9i	−0.204481	−	0.235984i
$675$	1.86143e7	+	1.29466e8i	0.00232962	+	0.0162028i
$676$	−1.03442e9	−	3.03733e8i	−0.128790	−	0.0378163i
$677$	−1.68348e8	+	1.94284e8i	−0.0208520	+	0.0240645i	−0.766080	−	0.642745i	$-0.777795\pi$
$677$	−1.68348e8	+	1.94284e8i	−0.0208520	+	0.0240645i	0.745228	+	0.666810i	$0.232341\pi$
$678$	5.08508e9	+	3.26798e9i	0.626605	+	0.402694i
$679$	−1.71128e10	−	1.09977e10i	−2.09786	−	1.34821i
$680$	−9.95554e8	+	1.14893e9i	−0.121418	+	0.140124i
$681$	−5.85120e9	−	1.71807e9i	−0.709954	−	0.208461i
$682$	−4.80848e7	−	3.34437e8i	−0.00580447	−	0.0403710i
$683$	−6.99461e9	−	8.07222e9i	−0.840023	−	0.969439i	0.159820	−	0.987146i	$-0.448909\pi$
$683$	−6.99461e9	−	8.07222e9i	−0.840023	−	0.969439i	−0.999843	+	0.0177077i	$0.994363\pi$
$684$	−3.61894e7	−	7.92437e7i	−0.00432399	−	0.00946823i
$685$	−6.02900e8	+	1.77027e8i	−0.0716685	+	0.0210438i
$686$	4.43739e9	−	9.71653e9i	0.524799	−	1.14915i
$687$	6.96256e8	−	4.84257e9i	0.0819257	−	0.569806i
$688$	−9.34820e9	+	6.00773e9i	−1.09438	+	0.703316i
$689$	−1.44448e9			−0.168246
$690$	4.30437e9	+	2.01513e9i	0.498813	+	0.233524i
$691$	−3.83535e9			−0.442213			−0.221107	−	0.975250i	$-0.570967\pi$
$691$	−3.83535e9			−0.442213			−0.221107	+	0.975250i	$0.570967\pi$
$692$	5.12722e8	−	3.29507e8i	0.0588181	−	0.0378001i
$693$	−3.41948e8	+	2.37830e9i	−0.0390296	+	0.271457i
$694$	−1.88107e9	+	4.11897e9i	−0.213622	+	0.467768i
$695$	−1.44713e10	+	4.24916e9i	−1.63516	+	0.480127i
$696$	−2.15831e9	−	4.72604e9i	−0.242651	−	0.531331i
$697$	−2.98085e8	−	3.44008e8i	−0.0333446	−	0.0384817i
$698$	−1.58425e9	−	1.10187e10i	−0.176332	−	1.22642i
$699$	−8.21246e9	−	2.41140e9i	−0.909501	−	0.267054i
$700$	−1.36948e8	+	1.58046e8i	−0.0150908	+	0.0174157i
$701$	1.40409e10	+	9.02355e9i	1.53951	+	0.989382i	0.987867	+	0.155301i	$0.0496349\pi$
$701$	1.40409e10	+	9.02355e9i	1.53951	+	0.989382i	0.551642	+	0.834081i	$0.314001\pi$
$702$	−5.56736e8	−	3.57793e8i	−0.0607393	−	0.0390348i
$703$	2.02335e9	−	2.33507e9i	0.219648	−	0.253487i
$704$	4.80814e9	+	1.41180e9i	0.519366	+	0.152499i
$705$	−1.36283e9	−	9.47868e9i	−0.146480	−	1.01879i
$706$	−2.33729e9	−	2.69737e9i	−0.249975	−	0.288486i
$707$	2.40748e9	+	5.27164e9i	0.256209	+	0.561019i
$708$	8.70077e8	−	2.55478e8i	0.0921385	−	0.0270543i
$709$	−2.06401e9	+	4.51956e9i	−0.217496	+	0.476249i	−0.986658	−	0.162804i	$-0.947946\pi$
$709$	−2.06401e9	+	4.51956e9i	−0.217496	+	0.476249i	0.769163	+	0.639053i	$0.220674\pi$
$710$	1.56998e9	−	1.09195e10i	0.164623	−	1.14498i
$711$	9.77218e8	−	6.28020e8i	0.101964	−	0.0655285i
$712$	8.13776e9			0.844938
$713$	−4.68741e8	−	7.44761e8i	−0.0484305	−	0.0769491i
$714$	1.44567e9			0.148637
$715$	−1.71865e9	+	1.10451e9i	−0.175839	+	0.113005i
$716$	1.14215e8	−	7.94385e8i	0.0116286	−	0.0808789i
$717$	−7.86439e8	+	1.72206e9i	−0.0796798	+	0.174474i
$718$	3.48806e9	−	1.02419e9i	0.351681	−	0.103263i
$719$	−4.24450e9	−	9.29417e9i	−0.425869	−	0.932523i	−0.993979	−	0.109570i	$-0.965053\pi$
$719$	−4.24450e9	−	9.29417e9i	−0.425869	−	0.932523i	0.568110	−	0.822953i	$-0.307675\pi$
$720$	−1.85072e9	−	2.13585e9i	−0.184790	−	0.213259i
$721$	1.28711e9	+	8.95208e9i	0.127892	+	0.889509i
$722$	−8.55335e9	−	2.51149e9i	−0.845777	−	0.248343i
$723$	3.81123e9	−	4.39840e9i	0.375043	−	0.432823i
$724$	1.04777e9	+	6.73361e8i	0.102608	+	0.0659421i
$725$	6.98456e8	+	4.48871e8i	0.0680701	+	0.0437460i
$726$	2.71346e9	−	3.13150e9i	0.263176	−	0.303721i
$727$	−3.55357e9	−	1.04342e9i	−0.343000	−	0.100714i	0.105696	−	0.994399i	$-0.466293\pi$
$727$	−3.55357e9	−	1.04342e9i	−0.343000	−	0.100714i	−0.448696	+	0.893685i	$0.648111\pi$
$728$	−1.08418e9	−	7.54061e9i	−0.104145	−	0.724347i
$729$	−2.53706e8	−	2.92793e8i	−0.0242541	−	0.0279907i
$730$	−3.12793e8	−	6.84920e8i	−0.0297596	−	0.0651644i
$731$	2.71476e9	−	7.97126e8i	0.257052	−	0.0754772i
$732$	4.89179e8	−	1.07115e9i	0.0460977	−	0.100940i
$733$	−1.18185e9	+	8.21992e9i	−0.110840	+	0.770910i	0.856266	+	0.516535i	$0.172779\pi$
$733$	−1.18185e9	+	8.21992e9i	−0.110840	+	0.770910i	−0.967106	+	0.254374i	$0.918131\pi$
$734$	1.01400e10	−	6.51660e9i	0.946462	−	0.608254i
$735$	1.17909e10			1.09532
$736$	3.42249e9	−	4.59103e8i	0.316424	−	0.0424461i
$737$	−6.63462e9			−0.610492
$738$	8.53144e8	−	5.48282e8i	0.0781313	−	0.0502120i
$739$	−2.14621e9	+	1.49272e10i	−0.195621	+	1.36058i	0.621185	+	0.783664i	$0.286652\pi$
$739$	−2.14621e9	+	1.49272e10i	−0.195621	+	1.36058i	−0.816806	+	0.576913i	$0.804257\pi$
$740$	−1.33297e9	+	2.91880e9i	−0.120923	+	0.264785i
$741$	−4.86593e8	+	1.42876e8i	−0.0439341	+	0.0129002i
$742$	2.92043e9	+	6.39484e9i	0.262442	+	0.574667i
$743$	2.00159e9	+	2.30996e9i	0.179025	+	0.206606i	0.838169	−	0.545411i	$-0.183626\pi$
$743$	2.00159e9	+	2.30996e9i	0.179025	+	0.206606i	−0.659144	+	0.752017i	$0.729081\pi$
$744$	8.92499e7	+	6.20746e8i	0.00794515	+	0.0552598i
$745$	1.54238e9	+	4.52885e8i	0.136661	+	0.0401274i
$746$	9.79280e9	−	1.13015e10i	0.863617	−	0.996667i
$747$	−4.34143e9	−	2.79007e9i	−0.381076	−	0.244902i
$748$	−1.27324e8	−	8.18261e7i	−0.0111238	−	0.00714885i
$749$	−6.78123e9	+	7.82595e9i	−0.589687	+	0.680535i
$750$	−5.58624e9	−	1.64027e9i	−0.483510	−	0.141971i
$751$	−2.16131e9	−	1.50322e10i	−0.186199	−	1.29504i	−0.841741	−	0.539882i	$-0.818469\pi$
$751$	−2.16131e9	−	1.50322e10i	−0.186199	−	1.29504i	0.655542	−	0.755159i	$-0.272440\pi$
$752$	1.06218e10	+	1.22582e10i	0.910826	+	1.05115i
$753$	5.07062e9	+	1.11031e10i	0.432792	+	0.947681i
$754$	−4.03069e9	+	1.18352e9i	−0.342436	+	0.100548i
$755$	5.85703e9	−	1.28251e10i	0.495294	−	1.08454i
$756$	8.81537e7	−	6.13122e8i	0.00742017	−	0.0516084i
$757$	−6.12822e9	+	3.93837e9i	−0.513451	+	0.329975i	−0.771577	−	0.636136i	$-0.780532\pi$
$757$	−6.12822e9	+	3.93837e9i	−0.513451	+	0.329975i	0.258126	+	0.966111i	$0.416895\pi$
$758$	−2.17596e10			−1.81472
$759$	−9.90621e8	+	3.25944e9i	−0.0822358	+	0.270581i
$760$	−2.59550e9			−0.214474
$761$	−1.97200e10	+	1.26733e10i	−1.62203	+	1.04242i	−0.667372	+	0.744724i	$0.732581\pi$
$761$	−1.97200e10	+	1.26733e10i	−1.62203	+	1.04242i	−0.954661	+	0.297694i	$0.903783\pi$
$762$	5.29893e8	−	3.68548e9i	0.0433856	−	0.301753i
$763$	−7.56438e9	+	1.65637e10i	−0.616506	+	1.34996i
$764$	1.27911e9	−	3.75582e8i	0.103773	−	0.0304704i
$765$	2.98926e8	+	6.54556e8i	0.0241406	+	0.0528606i
$766$	1.28848e10	+	1.48698e10i	1.03580	+	1.19538i
$767$	−7.51260e8	−	5.22513e9i	−0.0601183	−	0.418132i
$768$	−3.27279e9	−	9.60977e8i	−0.260708	−	0.0765506i
$769$	4.20460e9	−	4.85237e9i	0.333413	−	0.384779i	−0.564145	−	0.825676i	$-0.690794\pi$
$769$	4.20460e9	−	4.85237e9i	0.333413	−	0.384779i	0.897558	+	0.440897i	$0.145339\pi$
$770$	8.36450e9	+	5.37554e9i	0.660272	+	0.424331i
$771$	4.92355e9	+	3.16418e9i	0.386891	+	0.248640i
$772$	7.18316e8	−	8.28981e8i	0.0561895	−	0.0648461i
$773$	−1.04504e9	−	3.06851e8i	−0.0813774	−	0.0238946i	0.240790	−	0.970577i	$-0.422593\pi$
$773$	−1.04504e9	−	3.06851e8i	−0.0813774	−	0.0238946i	−0.322168	+	0.946683i	$0.604412\pi$
$774$	8.97108e8	+	6.23952e9i	0.0695427	+	0.483680i
$775$	−6.56276e7	−	7.57383e7i	−0.00506443	−	0.00584466i
$776$	8.53831e9	+	1.86963e10i	0.655928	+	1.43628i
$777$	2.10792e10	−	6.18942e9i	1.61206	−	0.473343i
$778$	5.94787e9	−	1.30240e10i	0.452827	−	0.991554i
$779$	1.10598e8	−	7.69225e8i	0.00838235	−	0.0583005i
$780$	4.43065e8	−	2.84741e8i	0.0334300	−	0.0214842i
$781$	7.90734e9			0.593953
$782$	2.02598e9	+	3.10867e8i	0.151500	+	0.0232461i
$783$	−2.45922e9			−0.183076
$784$	−1.68008e10	+	1.07972e10i	−1.24516	+	0.800214i
$785$	−2.80491e9	+	1.95086e10i	−0.206955	+	1.43940i
$786$	1.47955e9	−	3.23977e9i	0.108680	−	0.237977i
$787$	1.05060e10	−	3.08483e9i	0.768289	−	0.225590i	0.125977	−	0.992033i	$-0.459794\pi$
$787$	1.05060e10	−	3.08483e9i	0.768289	−	0.225590i	0.642312	+	0.766443i	$0.277975\pi$
$788$	7.04860e8	+	1.54343e9i	0.0513170	+	0.112369i
$789$	8.90623e9	+	1.02783e10i	0.645542	+	0.744995i
$790$	−6.84098e8	−	4.75801e9i	−0.0493655	−	0.343345i
$791$	3.16013e10	+	9.27897e9i	2.27032	+	0.666626i
$792$	1.58985e9	−	1.83478e9i	0.113715	−	0.131234i
$793$	−5.76683e9	−	3.70611e9i	−0.410658	−	0.263914i
$794$	−6.63954e9	−	4.26697e9i	−0.470724	−	0.302516i
$795$	−2.29152e9	+	2.64456e9i	−0.161748	+	0.186667i
$796$	2.13641e9	+	6.27305e8i	0.150137	+	0.0440842i
$797$	4.78049e8	+	3.32490e9i	0.0334478	+	0.232635i	0.999687	−	0.0250114i	$-0.00796220\pi$
$797$	4.78049e8	+	3.32490e9i	0.0334478	+	0.232635i	−0.966239	+	0.257646i	$0.917053\pi$
$798$	1.61631e9	+	1.86532e9i	0.112594	+	0.129940i
$799$	−1.71561e9	−	3.75667e9i	−0.118989	−	0.260549i
$800$	3.77325e8	−	1.10793e8i	0.0260556	−	0.00765060i
$801$	1.60012e9	−	3.50377e9i	0.110012	−	0.240892i
$802$	−2.21070e9	+	1.53758e10i	−0.151328	+	1.05251i
$803$	4.54033e8	−	2.91789e8i	0.0309445	−	0.0198868i
$804$	1.71039e9			0.116065
$805$	2.55965e10	+	3.92753e9i	1.72940	+	0.265359i
$806$	5.07064e8			0.0341106
$807$	−6.25690e9	+	4.02107e9i	−0.419085	+	0.269330i
$808$	8.33350e8	−	5.79607e9i	0.0555760	−	0.386540i
$809$	6.44203e9	−	1.41061e10i	0.427763	−	0.936670i	−0.565922	−	0.824459i	$-0.691479\pi$
$809$	6.44203e9	−	1.41061e10i	0.427763	−	0.936670i	0.993684	−	0.112211i	$-0.0357932\pi$
$810$	−1.53825e9	+	4.51672e8i	−0.101702	+	0.0298624i
$811$	−9.18484e9	−	2.01120e10i	−0.604643	−	1.32398i	−0.926179	−	0.377085i	$-0.876926\pi$
$811$	−9.18484e9	−	2.01120e10i	−0.604643	−	1.32398i	0.321536	−	0.946897i	$-0.395801\pi$
$812$	−2.57486e9	−	2.97155e9i	−0.168775	−	0.194777i
$813$	−2.90278e7	−	2.01893e8i	−0.00189451	−	0.0131766i
$814$	1.14750e10	+	3.36936e9i	0.745704	+	0.218959i
$815$	−6.45279e7	+	7.44692e7i	−0.00417538	+	0.00481865i
$816$	−1.02534e9	−	6.58944e8i	−0.0660619	−	0.0424554i
$817$	4.06371e9	+	2.61159e9i	0.260703	+	0.167543i
$818$	3.13377e9	−	3.61656e9i	0.200185	−	0.231025i
$819$	−3.45984e9	−	1.01590e9i	−0.220071	−	0.0646187i
$820$	1.14859e8	+	7.98860e8i	0.00727471	+	0.0505967i
$821$	−1.67093e10	−	1.92835e10i	−1.05379	−	1.21614i	−0.975680	−	0.219200i	$-0.929655\pi$
$821$	−1.67093e10	−	1.92835e10i	−1.05379	−	1.21614i	−0.0781146	−	0.996944i	$-0.524890\pi$
$822$	−2.50806e8	−	5.49188e8i	−0.0157502	−	0.0344881i
$823$	5.79500e9	−	1.70157e9i	0.362372	−	0.106402i	−0.0954781	−	0.995432i	$-0.530438\pi$
$823$	5.79500e9	−	1.70157e9i	0.362372	−	0.106402i	0.457850	+	0.889030i	$0.348620\pi$
$824$	3.79617e9	−	8.31246e9i	0.236375	−	0.517588i
$825$	−5.52125e7	+	3.84011e8i	−0.00342333	+	0.0238098i
$826$	−2.16132e10	+	1.38900e10i	−1.33441	+	0.857574i
$827$	3.19261e9			0.196281			0.0981403	−	0.995173i	$-0.468711\pi$
$827$	3.19261e9			0.196281			0.0981403	+	0.995173i	$0.468711\pi$
$828$	2.55380e8	−	8.40280e8i	0.0156344	−	0.0514420i
$829$	−5.53792e9			−0.337602			−0.168801	−	0.985650i	$-0.553990\pi$
$829$	−5.53792e9			−0.337602			−0.168801	+	0.985650i	$0.553990\pi$
$830$	−1.79654e10	+	1.15457e10i	−1.09059	+	0.700882i
$831$	−1.55048e9	+	1.07839e10i	−0.0937268	+	0.651884i
$832$	−3.12408e9	+	6.84079e9i	−0.188058	+	0.411789i
$833$	4.87903e9	−	1.43261e9i	0.292467	−	0.0858760i
$834$	−6.02004e9	−	1.31820e10i	−0.359350	−	0.786868i
$835$	−1.87201e10	−	2.16042e10i	−1.11277	−	1.28421i
$836$	−3.67738e7	−	2.55768e8i	−0.00217679	−	0.0151399i
$837$	2.84816e8	+	8.36295e7i	0.0167890	+	0.00492970i
$838$	4.38118e9	−	5.05616e9i	0.257180	−	0.296802i
$839$	1.33232e10	+	8.56232e9i	0.778830	+	0.500524i	0.868645	−	0.495435i	$-0.164991\pi$
$839$	1.33232e10	+	8.56232e9i	0.778830	+	0.500524i	−0.0898149	+	0.995958i	$0.528628\pi$
$840$	−1.55253e10	−	9.97750e9i	−0.903779	−	0.580823i
$841$	1.07367e9	−	1.23909e9i	0.0622424	−	0.0718316i
$842$	−2.95543e10	−	8.67794e9i	−1.70620	−	0.500984i
$843$	−4.33532e8	−	3.01528e9i	−0.0249244	−	0.173353i
$844$	2.95505e9	+	3.41031e9i	0.169187	+	0.195252i
$845$	6.31575e9	+	1.38296e10i	0.360103	+	0.788515i
$846$	8.82844e9	−	2.59226e9i	0.501289	−	0.147192i
$847$	9.37885e9	−	2.05368e10i	0.530344	−	1.16129i
$848$	8.43496e8	−	5.86665e9i	0.0475004	−	0.330373i
$849$	−5.86770e9	+	3.77094e9i	−0.329072	+	0.211482i
$850$	2.33425e8			0.0130371
$851$	3.08716e10	−	4.14120e9i	1.71714	−	0.230342i
$852$	−2.03850e9			−0.112920
$853$	−1.79973e10	+	1.15662e10i	−0.992857	+	0.638071i	−0.932902	−	0.360130i	$-0.882732\pi$
$853$	−1.79973e10	+	1.15662e10i	−0.992857	+	0.638071i	−0.0599555	+	0.998201i	$0.519096\pi$
$854$	−4.74802e9	+	3.30232e10i	−0.260862	+	1.81433i
$855$	−5.10351e8	+	1.11751e9i	−0.0279247	+	0.0611465i
$856$	1.00392e10	−	2.94777e9i	0.547066	−	0.160633i
$857$	1.18238e10	+	2.58904e10i	0.641686	+	1.40510i	0.898646	+	0.438675i	$0.144552\pi$
$857$	1.18238e10	+	2.58904e10i	0.641686	+	1.40510i	−0.256959	+	0.966422i	$0.582721\pi$
$858$	−1.28547e9	−	1.48351e9i	−0.0694793	−	0.0801834i
$859$	−4.44621e8	−	3.09240e9i	−0.0239339	−	0.166464i	0.974349	−	0.225043i	$-0.0722522\pi$
$859$	−4.44621e8	−	3.09240e9i	−0.0239339	−	0.166464i	−0.998283	+	0.0585788i	$0.981343\pi$
$860$	−4.81343e9	−	1.41335e9i	−0.258054	−	0.0757714i
$861$	3.61857e9	−	4.17605e9i	0.193208	−	0.222974i
$862$	2.61712e10	+	1.68192e10i	1.39171	+	0.894396i
$863$	1.94958e10	+	1.25292e10i	1.03253	+	0.663567i	0.943128	−	0.332429i	$-0.107868\pi$
$863$	1.94958e10	+	1.25292e10i	1.03253	+	0.663567i	0.0894016	+	0.995996i	$0.471505\pi$
$864$	−7.62794e8	+	8.80312e8i	−0.0402355	+	0.0464342i
$865$	−8.24679e9	−	2.42148e9i	−0.433240	−	0.127211i
$866$	−3.93565e9	−	2.73731e10i	−0.205923	−	1.43222i
$867$	−7.05207e9	−	8.13852e9i	−0.367494	−	0.424110i
$868$	1.97157e8	+	4.31714e8i	0.0102328	+	0.0224067i
$869$	3.30595e9	−	9.70714e8i	0.170894	−	0.0501790i
$870$	−4.22749e9	+	9.25692e9i	−0.217653	+	0.476595i
$871$	1.41700e9	−	9.85548e9i	0.0726620	−	0.505375i
$872$	1.54780e10	−	9.94711e9i	0.790510	−	0.508030i
$873$	9.72871e9			0.494886
$874$	1.86401e9	+	2.96164e9i	0.0944406	+	0.150052i
$875$	−3.17227e10			−1.60082
$876$	−1.17049e8	+	7.52229e7i	−0.00588306	+	0.00378082i
$877$	−3.71486e9	+	2.58374e10i	−0.185970	+	1.29345i	0.656343	+	0.754463i	$0.272103\pi$
$877$	−3.71486e9	+	2.58374e10i	−0.185970	+	1.29345i	−0.842313	+	0.538989i	$0.818806\pi$
$878$	1.51981e10	−	3.32791e10i	0.757806	−	1.65936i
$879$	−7.62314e7	+	2.23836e7i	−0.00378593	+	0.00111165i
$880$	−3.48229e9	−	7.62514e9i	−0.172256	−	0.377189i
$881$	−1.64909e9	−	1.90315e9i	−0.0812508	−	0.0937684i	0.713668	−	0.700484i	$-0.247032\pi$
$881$	−1.64909e9	−	1.90315e9i	−0.0812508	−	0.0937684i	−0.794919	+	0.606715i	$0.792487\pi$
$882$	1.61230e9	+	1.12138e10i	0.0791238	+	0.550318i
$883$	1.72946e10	+	5.07814e9i	0.845371	+	0.248223i	0.675607	−	0.737262i	$-0.263882\pi$
$883$	1.72946e10	+	5.07814e9i	0.845371	+	0.248223i	0.169763	+	0.985485i	$0.445700\pi$
$884$	1.48743e8	−	1.71659e8i	0.00724192	−	0.00835762i
$885$	−1.07580e10	−	6.91373e9i	−0.521710	−	0.335283i
$886$	1.85479e10	+	1.19200e10i	0.895934	+	0.575782i
$887$	−1.36155e10	+	1.57132e10i	−0.655091	+	0.756015i	−0.981967	−	0.189052i	$-0.939459\pi$
$887$	−1.36155e10	+	1.57132e10i	−0.655091	+	0.756015i	0.326876	+	0.945067i	$0.394004\pi$
$888$	−2.12986e10	−	6.25384e9i	−1.02072	−	0.299710i
$889$	−2.88722e9	−	2.00811e10i	−0.137824	−	0.958585i
$890$	−1.04381e10	−	1.20462e10i	−0.496315	−	0.572778i
$891$	−4.77369e8	−	1.04529e9i	−0.0226091	−	0.0495069i
$892$	−2.09740e9	+	6.15851e8i	−0.0989472	+	0.0290535i
$893$	2.92904e9	−	6.41371e9i	0.137640	−	0.301390i
$894$	−2.19813e8	+	1.52883e9i	−0.0102890	+	0.0715613i
$895$	−9.52114e9	+	6.11886e9i	−0.443923	+	0.285292i
$896$	2.50547e10			1.16362
$897$	−4.63021e9	−	2.16767e9i	−0.214204	−	0.100281i
$898$	5.31396e9			0.244879
$899$	1.58513e9	−	1.01870e9i	0.0727621	−	0.0467614i
$900$	1.42337e7	−	9.89975e7i	0.000650832	−	0.00452664i
$901$	−6.26908e8	+	1.37274e9i	−0.0285540	+	0.0625245i
$902$	2.88620e9	−	8.47466e8i	0.130950	−	0.0384503i
$903$	1.42682e10	+	3.12430e10i	0.644855	+	1.41203i
$904$	−2.17926e10	−	2.51500e10i	−0.981114	−	1.13227i
$905$	−2.49964e9	−	1.73854e10i	−0.112100	−	0.779675i
$906$	1.29984e10	+	3.81666e9i	0.580684	+	0.170504i
$907$	2.35754e10	−	2.72075e10i	1.04914	−	1.21077i	0.0721705	−	0.997392i	$-0.477007\pi$
$907$	2.35754e10	−	2.72075e10i	1.04914	−	1.21077i	0.976969	−	0.213380i	$-0.0684471\pi$
$908$	3.92284e9	+	2.52105e9i	0.173900	+	0.111759i
$909$	−2.33168e9	−	1.49848e9i	−0.102966	−	0.0661725i
$910$	−9.77163e9	+	1.12771e10i	−0.429855	+	0.496079i
$911$	1.08804e10	+	3.19479e9i	0.476796	+	0.140000i	0.511296	−	0.859405i	$-0.329166\pi$
$911$	1.08804e10	+	3.19479e9i	0.476796	+	0.140000i	−0.0344999	+	0.999405i	$0.510984\pi$
$912$	−2.96139e8	−	2.05969e9i	−0.0129275	−	0.0899125i
$913$	−1.00241e10	−	1.15684e10i	−0.435910	−	0.503067i
$914$	3.04567e8	+	6.66908e8i	0.0131938	+	0.0288904i
$915$	−1.59336e10	+	4.67854e9i	−0.687609	+	0.201900i
$916$	−1.55407e9	+	3.40294e9i	−0.0668092	+	0.146292i
$917$	2.76179e9	−	1.92087e10i	0.118276	−	0.822630i
$918$	−5.81647e8	+	3.73802e8i	−0.0248148	+	0.0159475i
$919$	−3.08227e10			−1.30999			−0.654993	−	0.755635i	$-0.727328\pi$
$919$	−3.08227e10			−1.30999			−0.654993	+	0.755635i	$0.727328\pi$
$920$	−1.96118e10	−	1.73210e10i	−0.830348	−	0.733357i
$921$	−1.06899e10			−0.450885
$922$	−3.52181e9	+	2.26333e9i	−0.147982	+	0.0951019i
$923$	−1.68883e9	+	1.17461e10i	−0.0706935	+	0.491684i
$924$	7.63242e8	−	1.67127e9i	0.0318281	−	0.0696937i
$925$	3.40355e9	−	9.99372e8i	0.141396	−	0.0415175i
$926$	8.96263e9	+	1.96254e10i	0.370934	+	0.812232i
$927$	−2.83255e9	−	3.26894e9i	−0.116788	−	0.134781i
$928$	1.05226e9	+	7.31864e9i	0.0432221	+	0.300616i
$929$	−3.40515e10	−	9.99843e9i	−1.39342	−	0.409145i	−0.503000	−	0.864287i	$-0.667770\pi$
$929$	−3.40515e10	−	9.99843e9i	−1.39342	−	0.409145i	−0.890419	+	0.455142i	$0.849589\pi$
$930$	8.04405e8	−	9.28333e8i	0.0327933	−	0.0378454i
$931$	7.30340e9	+	4.69361e9i	0.296620	+	0.190626i
$932$	5.50590e9	+	3.53843e9i	0.222778	+	0.143171i
$933$	−8.80356e9	+	1.01598e10i	−0.354873	+	0.409545i
$934$	−2.02528e10	−	5.94675e9i	−0.813336	−	0.238817i
$935$	3.03753e8	+	2.11265e9i	0.0121529	+	0.0845254i
$936$	2.38595e9	+	2.75353e9i	0.0951032	+	0.109755i
$937$	−5.84047e9	−	1.27888e10i	−0.231931	−	0.507859i	0.757505	−	0.652830i	$-0.226418\pi$
$937$	−5.84047e9	−	1.27888e10i	−0.231931	−	0.507859i	−0.989436	+	0.144971i	$0.953691\pi$
$938$	−4.64960e10	+	1.36524e10i	−1.83952	+	0.540133i
$939$	8.19423e8	−	1.79429e9i	0.0322982	−	0.0707232i
$940$	−1.04210e9	+	7.24799e9i	−0.0409226	+	0.284623i
$941$	3.22337e10	−	2.07154e10i	1.26109	−	0.810455i	0.272659	−	0.962111i	$-0.412097\pi$
$941$	3.22337e10	−	2.07154e10i	1.26109	−	0.810455i	0.988433	+	0.151656i	$0.0484605\pi$
$942$	−1.89374e10			−0.738146
$943$	5.96908e9	−	5.07425e9i	0.231802	−	0.197052i
$944$	2.16602e10			0.838030
$945$	−7.34861e9	+	4.72266e9i	−0.283265	+	0.182044i
$946$	−2.66094e9	+	1.85072e10i	−0.102192	+	0.710758i
$947$	−1.33654e10	+	2.92662e10i	−0.511396	+	1.11980i	0.461199	+	0.887297i	$0.347419\pi$
$947$	−1.33654e10	+	2.92662e10i	−0.511396	+	1.11980i	−0.972595	+	0.232505i	$0.925308\pi$
$948$	−8.52268e8	+	2.50249e8i	−0.0324898	+	0.00953987i
$949$	3.36471e8	+	7.36769e8i	0.0127796	+	0.0279833i
$950$	2.60977e8	+	3.01184e8i	0.00987575	+	0.0113972i
$951$	3.05526e9	+	2.12498e10i	0.115191	+	0.801168i
$952$	−7.63662e9	−	2.24232e9i	−0.286861	−	0.0842301i
$953$	1.76889e10	−	2.04141e10i	0.662028	−	0.764022i	−0.321079	−	0.947053i	$-0.604045\pi$
$953$	1.76889e10	−	2.04141e10i	0.662028	−	0.764022i	0.983107	+	0.183031i	$0.0585909\pi$
$954$	−2.82848e9	−	1.81775e9i	−0.105471	−	0.0677822i
$955$	−1.58155e10	−	1.01640e10i	−0.587585	−	0.377618i
$956$	9.47986e8	−	1.09403e9i	0.0350913	−	0.0404975i
$957$	−6.99888e9	−	2.05506e9i	−0.258129	−	0.0757935i
$958$	2.04797e9	+	1.42440e10i	0.0752566	+	0.523421i
$959$	−2.15425e9	−	2.48614e9i	−0.0788735	−	0.0910249i
$960$	7.56808e9	+	1.65718e10i	0.276081	+	0.604533i
$961$	2.61799e10	−	7.68712e9i	0.951561	−	0.279404i
$962$	−7.45585e9	+	1.63260e10i	−0.270013	+	0.591246i
$963$	7.04809e8	−	4.90206e9i	0.0254320	−	0.176883i
$964$	−3.74380e9	+	2.40600e9i	−0.134600	+	0.0865019i
$965$	−1.54687e10			−0.554126
$966$	−2.35201e8	+	2.48809e10i	−0.00839496	+	0.888068i
$967$	4.79563e10			1.70550			0.852752	−	0.522316i	$-0.174932\pi$
$967$	4.79563e10			1.70550			0.852752	+	0.522316i	$0.174932\pi$
$968$	−1.91907e10	+	1.23331e10i	−0.680029	+	0.437028i
$969$	−7.54022e7	+	5.24434e8i	−0.00266226	+	0.0185164i
$970$	1.67240e10	−	3.66205e10i	0.588355	−	1.28832i
$971$	−2.63895e10	+	7.74867e9i	−0.925048	+	0.271619i	−0.709362	−	0.704844i	$-0.751017\pi$
$971$	−2.63895e10	+	7.74867e9i	−0.925048	+	0.271619i	−0.215686	+	0.976463i	$0.569199\pi$
$972$	1.23065e8	+	2.69475e8i	0.00429836	+	0.00941209i
$973$	−5.17081e10	−	5.96743e10i	−1.79955	−	2.07679i
$974$	5.04817e9	+	3.51108e10i	0.175056	+	1.21754i
$975$	−5.58642e8	−	1.64032e8i	−0.0193027	−	0.00566778i
$976$	1.84196e10	−	2.12574e10i	0.634171	−	0.731872i
$977$	−1.34882e10	−	8.66834e9i	−0.462725	−	0.297375i	0.288430	−	0.957501i	$-0.406867\pi$
$977$	−1.34882e10	−	8.66834e9i	−0.462725	−	0.297375i	−0.751155	+	0.660126i	$0.770503\pi$
$978$	−7.96485e7	−	5.11870e7i	−0.00272265	−	0.00174974i
$979$	7.48184e9	−	8.63451e9i	0.254841	−	0.294102i
$980$	−8.65081e9	−	2.54011e9i	−0.293607	−	0.0862107i
$981$	−1.23938e9	−	8.62006e9i	−0.0419143	−	0.291520i
$982$	−4.17260e8	−	4.81544e8i	−0.0140610	−	0.0162273i
$983$	2.28329e10	+	4.99972e10i	0.766699	+	1.67884i	0.733789	+	0.679377i	$0.237750\pi$
$983$	2.28329e10	+	4.99972e10i	0.766699	+	1.67884i	0.0329095	+	0.999458i	$0.489523\pi$
$984$	−5.35706e9	+	1.57297e9i	−0.179244	+	0.0526307i
$985$	9.94010e9	−	2.17658e10i	0.331409	−	0.725684i
$986$	−6.24594e8	+	4.34415e9i	−0.0207505	+	0.144323i
$987$	4.21756e10	−	2.71046e10i	1.39621	−	0.897291i
$988$	3.87787e8			0.0127922
$989$	1.32773e10	+	4.68523e10i	0.436439	+	1.54008i
$990$	−4.75527e9			−0.155759
$991$	2.21413e10	−	1.42294e10i	0.722680	−	0.464438i	−0.126888	−	0.991917i	$-0.540499\pi$
$991$	2.21413e10	−	1.42294e10i	0.722680	−	0.464438i	0.849568	+	0.527479i	$0.176863\pi$
$992$	1.27013e8	−	8.83396e8i	0.00413103	−	0.0287319i
$993$	2.24888e9	−	4.92437e9i	0.0728861	−	0.159598i
$994$	5.54153e10	−	1.62714e10i	1.78969	−	0.525500i
$995$	−1.30440e10	−	2.85625e10i	−0.419789	−	0.919210i
$996$	2.58419e9	+	2.98232e9i	0.0828738	+	0.0956415i
$997$	1.15528e9	+	8.03518e9i	0.0369195	+	0.256781i	0.999919	−	0.0127222i	$-0.00404970\pi$
$997$	1.15528e9	+	8.03518e9i	0.0369195	+	0.256781i	−0.963000	+	0.269503i	$0.913141\pi$
$998$	−3.13805e10	−	9.21416e9i	−0.999318	−	0.293426i
$999$	−6.88057e9	+	7.94060e9i	−0.218346	+	0.251985i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.8.e.b.58.5	yes	140
23.2	even	11	inner	69.8.e.b.25.5	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.8.e.b.25.5	✓	140	23.2	even	11	inner
69.8.e.b.58.5	yes	140	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	69.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-8.71638 + 5.60168i) q^{2} +(3.84250 - 26.7252i) q^{3} +(-8.57661 + 18.7802i) q^{4} +(279.359 - 82.0273i) q^{5} +(116.213 + 254.471i) q^{6} +(998.192 + 1151.98i) q^{7} +(-219.186 - 1524.47i) q^{8} +(-699.470 - 205.383i) q^{9} +O(q^{10})\)	\(q+(-8.71638 + 5.60168i) q^{2} +(3.84250 - 26.7252i) q^{3} +(-8.57661 + 18.7802i) q^{4} +(279.359 - 82.0273i) q^{5} +(116.213 + 254.471i) q^{6} +(998.192 + 1151.98i) q^{7} +(-219.186 - 1524.47i) q^{8} +(-699.470 - 205.383i) q^{9} +(-1975.51 + 2279.86i) q^{10} +(-1819.05 - 1169.03i) q^{11} +(468.948 + 301.374i) q^{12} +(2125.06 - 2452.45i) q^{13} +(-15153.6 - 4449.50i) q^{14} +(-1118.76 - 7781.12i) q^{15} +(8719.52 + 10062.9i) q^{16} +(-1408.36 - 3083.88i) q^{17} +(7247.34 - 2128.01i) q^{18} +(2404.47 - 5265.06i) q^{19} +(-855.471 + 5949.93i) q^{20} +(34622.3 - 22250.4i) q^{21} +22404.0 q^{22} +(53304.6 - 23737.0i) q^{23} -41584.0 q^{24} +(5590.28 - 3592.65i) q^{25} +(-4784.99 + 33280.4i) q^{26} +(-8176.61 + 17904.3i) q^{27} +(-30195.4 + 8866.17i) q^{28} +(51902.5 + 113651. i) q^{29} +(53338.8 + 61556.3i) q^{30} +(-2146.26 - 14927.5i) q^{31} +(56781.8 + 16672.6i) q^{32} +(-38232.2 + 44122.4i) q^{33} +(29550.7 + 18991.1i) q^{34} +(373348. + 239936. i) q^{35} +(9856.21 - 11374.7i) q^{36} +(512184. + 150391. i) q^{37} +(8534.88 + 59361.4i) q^{38} +(-57376.6 - 66216.1i) q^{39} +(-186280. - 407896. i) q^{40} +(128825. - 37826.5i) q^{41} +(-177142. + 387886. i) q^{42} +(-118770. + 826066. i) q^{43} +(37555.9 - 24135.7i) q^{44} -212251. q^{45} +(-331656. + 505496. i) q^{46} +1.21816e6 q^{47} +(302437. - 194364. i) q^{48} +(-213457. + 1.48463e6i) q^{49} +(-28602.1 + 62629.8i) q^{50} +(-87828.9 + 25788.9i) q^{51} +(27831.6 + 60942.6i) q^{52} +(-291500. - 336409. i) q^{53} +(-29023.6 - 201863. i) q^{54} +(-604061. - 177368. i) q^{55} +(1.53736e6 - 1.77421e6i) q^{56} +(-131471. - 84491.0i) q^{57} +(-1.08904e6 - 699881. i) q^{58} +(1.06529e6 - 1.22941e6i) q^{59} +(155726. + 45725.2i) q^{60} +(-300634. - 2.09096e6i) q^{61} +(102327. + 118091. i) q^{62} +(-461610. - 1.01078e6i) q^{63} +(-2.22362e6 + 652913. i) q^{64} +(392487. - 859427. i) q^{65} +(86087.6 - 598752. i) q^{66} +(2.58122e6 - 1.65885e6i) q^{67} +69994.8 q^{68} +(-429553. - 1.51578e6i) q^{69} -4.59829e6 q^{70} +(-3.07638e6 + 1.97707e6i) q^{71} +(-159786. + 1.11134e6i) q^{72} +(-103687. + 227044. i) q^{73} +(-5.30683e6 + 1.55823e6i) q^{74} +(-74533.6 - 163206. i) q^{75} +(78256.5 + 90312.9i) q^{76} +(-469065. - 3.26242e6i) q^{77} +(871037. + 255760. i) q^{78} +(-1.04348e6 + 1.20425e6i) q^{79} +(3.26131e6 + 2.09592e6i) q^{80} +(447077. + 287319. i) q^{81} +(-910997. + 1.05135e6i) q^{82} +(6.79236e6 + 1.99442e6i) q^{83} +(120924. + 841046. i) q^{84} +(-646402. - 745987. i) q^{85} +(-3.59211e6 - 7.86562e6i) q^{86} +(3.23677e6 - 950401. i) q^{87} +(-1.38344e6 + 3.02932e6i) q^{88} +(-751956. + 5.22997e6i) q^{89} +(1.85006e6 - 1.18896e6i) q^{90} +4.94638e6 q^{91} +(-11387.6 + 1.20465e6i) q^{92} -407188. q^{93} +(-1.06180e7 + 6.82376e6i) q^{94} +(239833. - 1.66808e6i) q^{95} +(663763. - 1.45344e6i) q^{96} +(-1.28047e7 + 3.75980e6i) q^{97} +(-6.45582e6 - 1.41363e7i) q^{98} +(1.03227e6 + 1.19130e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 12 q^{2} + 378 q^{3} - 740 q^{4} + 2 q^{5} - 1755 q^{6} - 394 q^{7} - 1612 q^{8} - 10206 q^{9}+O(q^{10}) \) 140 * q - 12 * q^2 + 378 * q^3 - 740 * q^4 + 2 * q^5 - 1755 * q^6 - 394 * q^7 - 1612 * q^8 - 10206 * q^9	\( 140 q - 12 q^{2} + 378 q^{3} - 740 q^{4} + 2 q^{5} - 1755 q^{6} - 394 q^{7} - 1612 q^{8} - 10206 q^{9} + 9178 q^{10} - 5996 q^{11} + 19980 q^{12} - 44394 q^{13} - 9524 q^{14} - 351 q^{15} - 165236 q^{16} + 152531 q^{17} - 8748 q^{18} + 4037 q^{19} - 6167 q^{20} + 10638 q^{21} + 98494 q^{22} - 160732 q^{23} + 5508 q^{24} - 14760 q^{25} + 403412 q^{26} + 275562 q^{27} + 84152 q^{28} + 205532 q^{29} - 247806 q^{30} - 1262119 q^{31} - 1781780 q^{32} + 735399 q^{33} + 2963321 q^{34} - 955354 q^{35} - 1269189 q^{36} - 1369770 q^{37} + 3950922 q^{38} + 1198638 q^{39} - 839075 q^{40} + 4017556 q^{41} - 798390 q^{42} - 2474862 q^{43} - 5279389 q^{44} + 2006208 q^{45} - 3642508 q^{46} - 5306766 q^{47} + 1755999 q^{48} + 4554906 q^{49} + 3476227 q^{50} + 3473280 q^{51} + 15615773 q^{52} + 3269752 q^{53} + 452709 q^{54} - 7825001 q^{55} - 23842824 q^{56} - 6117309 q^{57} - 1584991 q^{58} + 1692452 q^{59} + 4240161 q^{60} + 6133200 q^{61} - 11065051 q^{62} - 287226 q^{63} + 5056548 q^{64} + 13947245 q^{65} - 7185321 q^{66} - 6003959 q^{67} + 37775092 q^{68} - 1069794 q^{69} - 27634536 q^{70} + 5868445 q^{71} - 1175148 q^{72} - 23836857 q^{73} + 8638944 q^{74} + 5583546 q^{75} - 13476319 q^{76} - 19300986 q^{77} + 16707492 q^{78} - 16058510 q^{79} - 1951148 q^{80} - 7440174 q^{81} + 47661526 q^{82} + 21531792 q^{83} + 33361956 q^{84} + 51859503 q^{85} - 20977372 q^{86} + 1565568 q^{87} - 35256744 q^{88} - 26730592 q^{89} + 6690762 q^{90} - 42532184 q^{91} - 71328833 q^{92} - 19877886 q^{93} - 70960921 q^{94} - 43191119 q^{95} + 17543196 q^{96} + 52039436 q^{97} + 98000731 q^{98} - 19855773 q^{99}+O(q^{100}) \) 140 * q - 12 * q^2 + 378 * q^3 - 740 * q^4 + 2 * q^5 - 1755 * q^6 - 394 * q^7 - 1612 * q^8 - 10206 * q^9 + 9178 * q^10 - 5996 * q^11 + 19980 * q^12 - 44394 * q^13 - 9524 * q^14 - 351 * q^15 - 165236 * q^16 + 152531 * q^17 - 8748 * q^18 + 4037 * q^19 - 6167 * q^20 + 10638 * q^21 + 98494 * q^22 - 160732 * q^23 + 5508 * q^24 - 14760 * q^25 + 403412 * q^26 + 275562 * q^27 + 84152 * q^28 + 205532 * q^29 - 247806 * q^30 - 1262119 * q^31 - 1781780 * q^32 + 735399 * q^33 + 2963321 * q^34 - 955354 * q^35 - 1269189 * q^36 - 1369770 * q^37 + 3950922 * q^38 + 1198638 * q^39 - 839075 * q^40 + 4017556 * q^41 - 798390 * q^42 - 2474862 * q^43 - 5279389 * q^44 + 2006208 * q^45 - 3642508 * q^46 - 5306766 * q^47 + 1755999 * q^48 + 4554906 * q^49 + 3476227 * q^50 + 3473280 * q^51 + 15615773 * q^52 + 3269752 * q^53 + 452709 * q^54 - 7825001 * q^55 - 23842824 * q^56 - 6117309 * q^57 - 1584991 * q^58 + 1692452 * q^59 + 4240161 * q^60 + 6133200 * q^61 - 11065051 * q^62 - 287226 * q^63 + 5056548 * q^64 + 13947245 * q^65 - 7185321 * q^66 - 6003959 * q^67 + 37775092 * q^68 - 1069794 * q^69 - 27634536 * q^70 + 5868445 * q^71 - 1175148 * q^72 - 23836857 * q^73 + 8638944 * q^74 + 5583546 * q^75 - 13476319 * q^76 - 19300986 * q^77 + 16707492 * q^78 - 16058510 * q^79 - 1951148 * q^80 - 7440174 * q^81 + 47661526 * q^82 + 21531792 * q^83 + 33361956 * q^84 + 51859503 * q^85 - 20977372 * q^86 + 1565568 * q^87 - 35256744 * q^88 - 26730592 * q^89 + 6690762 * q^90 - 42532184 * q^91 - 71328833 * q^92 - 19877886 * q^93 - 70960921 * q^94 - 43191119 * q^95 + 17543196 * q^96 + 52039436 * q^97 + 98000731 * q^98 - 19855773 * q^99

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