LMFDB - Embedded newform 69.8.e.b.58.10

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			58.10
Character	$\chi$	$=$	69.58
Dual form			69.8.e.b.25.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(7.72913 - 4.96721i) q^{2} +(3.84250 - 26.7252i) q^{3} +(-18.1068 + 39.6485i) q^{4} +(500.128 - 146.851i) q^{5} +(-103.050 - 225.649i) q^{6} +(355.198 + 409.921i) q^{7} +(224.357 + 1560.44i) q^{8} +(-699.470 - 205.383i) q^{9} +O(q^{10})$	\(q+(7.72913 - 4.96721i) q^{2} +(3.84250 - 26.7252i) q^{3} +(-18.1068 + 39.6485i) q^{4} +(500.128 - 146.851i) q^{5} +(-103.050 - 225.649i) q^{6} +(355.198 + 409.921i) q^{7} +(224.357 + 1560.44i) q^{8} +(-699.470 - 205.383i) q^{9} +(3136.12 - 3619.27i) q^{10} +(4489.99 + 2885.54i) q^{11} +(990.036 + 636.258i) q^{12} +(-7118.50 + 8215.19i) q^{13} +(4781.54 + 1403.99i) q^{14} +(-2002.87 - 13930.3i) q^{15} +(5831.51 + 6729.92i) q^{16} +(844.853 + 1849.97i) q^{17} +(-6426.48 + 1886.98i) q^{18} +(12722.7 - 27858.8i) q^{19} +(-3233.33 + 22488.3i) q^{20} +(12320.1 - 7917.62i) q^{21} +49036.8 q^{22} +(47942.4 + 33261.9i) q^{23} +42565.0 q^{24} +(162840. - 104651. i) q^{25} +(-14213.3 + 98855.4i) q^{26} +(-8176.61 + 17904.3i) q^{27} +(-22684.2 + 6660.70i) q^{28} +(-26117.5 - 57189.3i) q^{29} +(-84675.2 - 97720.3i) q^{30} +(-33606.9 - 233741. i) q^{31} +(-115114. - 33800.6i) q^{32} +(94369.4 - 108908. i) q^{33} +(15719.2 + 10102.1i) q^{34} +(237842. + 152852. i) q^{35} +(20808.3 - 24014.1i) q^{36} +(-396078. - 116299. i) q^{37} +(-40045.3 - 278521. i) q^{38} +(192200. + 221810. i) q^{39} +(341359. + 747471. i) q^{40} +(379083. - 111309. i) q^{41} +(55894.8 - 122393. i) q^{42} +(-42239.6 + 293783. i) q^{43} +(-195707. + 125773. i) q^{44} -379986. q^{45} +(535772. + 18945.5i) q^{46} -181177. q^{47} +(202266. - 129988. i) q^{48} +(75333.2 - 523954. i) q^{49} +(738789. - 1.61772e6i) q^{50} +(52687.1 - 15470.3i) q^{51} +(-196826. - 430989. i) q^{52} +(527451. + 608711. i) q^{53} +(25736.2 + 179000. i) q^{54} +(2.66931e6 + 783782. i) q^{55} +(-559964. + 646233. i) q^{56} +(-695645. - 447064. i) q^{57} +(-485937. - 312292. i) q^{58} +(-626454. + 722967. i) q^{59} +(588580. + 172823. i) q^{60} +(-197519. - 1.37378e6i) q^{61} +(-1.42079e6 - 1.63968e6i) q^{62} +(-164260. - 359679. i) q^{63} +(-2.15129e6 + 631676. i) q^{64} +(-2.35376e6 + 5.15401e6i) q^{65} +(188424. - 1.31052e6i) q^{66} +(-3.49984e6 + 2.24921e6i) q^{67} -88646.0 q^{68} +(1.07315e6 - 1.15346e6i) q^{69} +2.59756e6 q^{70} +(3.98889e6 - 2.56350e6i) q^{71} +(163556. - 1.13756e6i) q^{72} +(-1.89942e6 + 4.15916e6i) q^{73} +(-3.63902e6 + 1.06851e6i) q^{74} +(-2.17110e6 - 4.75405e6i) q^{75} +(874192. + 1.00887e6i) q^{76} +(411994. + 2.86548e6i) q^{77} +(2.58731e6 + 759704. i) q^{78} +(896819. - 1.03498e6i) q^{79} +(3.90480e6 + 2.50946e6i) q^{80} +(447077. + 287319. i) q^{81} +(2.37709e6 - 2.74330e6i) q^{82} +(-9.79416e6 - 2.87583e6i) q^{83} +(90844.1 + 631834. i) q^{84} +(694204. + 801155. i) q^{85} +(1.13281e6 + 2.48050e6i) q^{86} +(-1.62875e6 + 478244. i) q^{87} +(-3.49534e6 + 7.65373e6i) q^{88} +(-172585. + 1.20036e6i) q^{89} +(-2.93696e6 + 1.88747e6i) q^{90} -5.89606e6 q^{91} +(-2.18687e6 + 1.29857e6i) q^{92} -6.37591e6 q^{93} +(-1.40034e6 + 899945. i) q^{94} +(2.27189e6 - 1.58013e7i) q^{95} +(-1.34565e6 + 2.94657e6i) q^{96} +(-595530. + 174863. i) q^{97} +(-2.02033e6 - 4.42391e6i) q^{98} +(-2.54797e6 - 2.94052e6i) 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 $

$2$	7.72913	−	4.96721i	0.683165	−	0.439044i	−0.152485	−	0.988306i	$-0.548728\pi$
$2$	7.72913	−	4.96721i	0.683165	−	0.439044i	0.835650	+	0.549262i	$0.185091\pi$
$3$	3.84250	−	26.7252i	0.0821655	−	0.571474i
$3$	3.84250	−	26.7252i	0.0821655	−	0.571474i
$4$	−18.1068	+	39.6485i	−0.141460	+	0.309754i
$5$	500.128	−	146.851i	1.78931	−	0.525390i	0.792850	−	0.609417i	$-0.208597\pi$
$5$	500.128	−	146.851i	1.78931	−	0.525390i	0.996463	+	0.0840275i	$0.0267784\pi$
$6$	−103.050	−	225.649i	−0.194769	−	0.426485i
$7$	355.198	+	409.921i	0.391406	+	0.451707i	0.916916	−	0.399081i	$-0.130671\pi$
$7$	355.198	+	409.921i	0.391406	+	0.451707i	−0.525509	+	0.850788i	$0.676125\pi$
$8$	224.357	+	1560.44i	0.154926	+	1.07753i
$9$	−699.470	−	205.383i	−0.319831	−	0.0939109i
$10$	3136.12	−	3619.27i	0.991727	−	1.14451i
$11$	4489.99	+	2885.54i	1.01712	+	0.653661i	0.939226	−	0.343300i	$-0.111545\pi$
$11$	4489.99	+	2885.54i	1.01712	+	0.653661i	0.0778914	+	0.996962i	$0.475181\pi$
$12$	990.036	+	636.258i	0.165393	+	0.106292i
$13$	−7118.50	+	8215.19i	−0.898642	+	1.03709i	0.100469	+	0.994940i	$0.467966\pi$
$13$	−7118.50	+	8215.19i	−0.898642	+	1.03709i	−0.999111	+	0.0421483i	$0.986580\pi$
$14$	4781.54	+	1403.99i	0.465714	+	0.136746i
$15$	−2002.87	−	13930.3i	−0.153227	−	1.06571i
$16$	5831.51	+	6729.92i	0.355927	+	0.410762i
$17$	844.853	+	1849.97i	0.0417071	+	0.0913258i	0.929339	−	0.369228i	$-0.120378\pi$
$17$	844.853	+	1849.97i	0.0417071	+	0.0913258i	−0.887632	+	0.460554i	$0.847651\pi$
$18$	−6426.48	+	1886.98i	−0.259728	+	0.0762631i
$19$	12722.7	−	27858.8i	0.425541	−	0.931806i	−0.568488	−	0.822692i	$-0.692471\pi$
$19$	12722.7	−	27858.8i	0.425541	−	0.931806i	0.994029	−	0.109114i	$-0.0348014\pi$
$20$	−3233.33	+	22488.3i	−0.0903744	+	0.628568i
$21$	12320.1	−	7917.62i	0.290299	−	0.186564i
$22$	49036.8			0.981845
$23$	47942.4	+	33261.9i	0.821622	+	0.570032i
$23$	47942.4	+	33261.9i	0.821622	+	0.570032i
$24$	42565.0			0.628512
$25$	162840.	−	104651.i	2.08435	−	1.33953i
$26$	−14213.3	+	98855.4i	−0.158594	+	1.10305i
$27$	−8176.61	+	17904.3i	−0.0799467	+	0.175059i
$28$	−22684.2	+	6660.70i	−0.195286	+	0.0573412i
$29$	−26117.5	−	57189.3i	−0.198856	−	0.435433i	0.783765	−	0.621057i	$-0.213297\pi$
$29$	−26117.5	−	57189.3i	−0.198856	−	0.435433i	−0.982621	+	0.185624i	$0.940569\pi$
$30$	−84675.2	−	97720.3i	−0.572574	−	0.660786i
$31$	−33606.9	−	233741.i	−0.202611	−	1.40919i	−0.796498	−	0.604641i	$-0.793316\pi$
$31$	−33606.9	−	233741.i	−0.202611	−	1.40919i	0.593887	−	0.804548i	$-0.297593\pi$
$32$	−115114.	−	33800.6i	−0.621019	−	0.182348i
$33$	94369.4	−	108908.i	0.457122	−	0.527547i
$34$	15719.2	+	10102.1i	0.0685888	+	0.0440794i
$35$	237842.	+	152852.i	0.937671	+	0.602604i
$36$	20808.3	−	24014.1i	0.0743324	−	0.0857842i
$37$	−396078.	−	116299.i	−1.28551	−	0.377459i	−0.433578	−	0.901116i	$-0.642749\pi$
$37$	−396078.	−	116299.i	−1.28551	−	0.377459i	−0.851929	+	0.523657i	$0.824567\pi$
$38$	−40045.3	−	278521.i	−0.118388	−	0.823408i
$39$	192200.	+	221810.i	0.518831	+	0.598763i
$40$	341359.	+	747471.i	0.843336	+	1.84665i
$41$	379083.	−	111309.i	0.858995	−	0.252224i	0.177567	−	0.984109i	$-0.443177\pi$
$41$	379083.	−	111309.i	0.858995	−	0.252224i	0.681428	+	0.731885i	$0.261359\pi$
$42$	55894.8	−	122393.i	0.116412	−	0.254908i
$43$	−42239.6	+	293783.i	−0.0810178	+	0.563491i	0.908367	+	0.418173i	$0.137330\pi$
$43$	−42239.6	+	293783.i	−0.0810178	+	0.563491i	−0.989385	+	0.145318i	$0.953580\pi$
$44$	−195707.	+	125773.i	−0.346355	+	0.222589i
$45$	−379986.			−0.621618
$46$	535772.	+	18945.5i	0.811573	+	0.0286981i
$47$	−181177.			−0.254543			−0.127271	−	0.991868i	$-0.540622\pi$
$47$	−181177.			−0.254543			−0.127271	+	0.991868i	$0.540622\pi$
$48$	202266.	−	129988.i	0.263984	−	0.169653i
$49$	75333.2	−	523954.i	0.0914746	−	0.636220i
$50$	738789.	−	1.61772e6i	0.835844	−	1.83024i
$51$	52687.1	−	15470.3i	0.0556172	−	0.0163307i
$52$	−196826.	−	430989.i	−0.194120	−	0.425064i
$53$	527451.	+	608711.i	0.486650	+	0.561624i	0.944967	−	0.327164i	$-0.106093\pi$
$53$	527451.	+	608711.i	0.486650	+	0.561624i	−0.458317	+	0.888789i	$0.651548\pi$
$54$	25736.2	+	179000.i	0.0222417	+	0.154694i
$55$	2.66931e6	+	783782.i	2.16337	+	0.635222i
$56$	−559964.	+	646233.i	−0.426091	+	0.491735i
$57$	−695645.	−	447064.i	−0.497538	−	0.319748i
$58$	−485937.	−	312292.i	−0.327025	−	0.210167i
$59$	−626454.	+	722967.i	−0.397107	+	0.458286i	−0.918728	−	0.394892i	$-0.870782\pi$
$59$	−626454.	+	722967.i	−0.397107	+	0.458286i	0.521621	+	0.853177i	$0.325328\pi$
$60$	588580.	+	172823.i	0.351784	+	0.103293i
$61$	−197519.	−	1.37378e6i	−0.111418	−	0.774929i	−0.966543	−	0.256506i	$-0.917429\pi$
$61$	−197519.	−	1.37378e6i	−0.111418	−	0.774929i	0.855125	−	0.518423i	$-0.173481\pi$
$62$	−1.42079e6	−	1.63968e6i	−0.757112	−	0.873754i
$63$	−164260.	−	359679.i	−0.0827637	−	0.181227i
$64$	−2.15129e6	+	631676.i	−1.02582	+	0.301207i
$65$	−2.35376e6	+	5.15401e6i	−1.06308	+	2.32781i
$66$	188424.	−	1.31052e6i	0.0806738	−	0.561098i
$67$	−3.49984e6	+	2.24921e6i	−1.42163	+	0.913626i	−0.421653	+	0.906757i	$0.638550\pi$
$67$	−3.49984e6	+	2.24921e6i	−1.42163	+	0.913626i	−0.999976	+	0.00686818i	$0.997814\pi$
$68$	−88646.0			−0.0341884
$69$	1.07315e6	−	1.15346e6i	0.393267	−	0.422699i
$70$	2.59756e6			0.905153
$71$	3.98889e6	−	2.56350e6i	1.32266	−	0.850021i	0.327176	−	0.944963i	$-0.393903\pi$
$71$	3.98889e6	−	2.56350e6i	1.32266	−	0.850021i	0.995483	+	0.0949423i	$0.0302667\pi$
$72$	163556.	−	1.13756e6i	0.0516420	−	0.359178i
$73$	−1.89942e6	+	4.15916e6i	−0.571468	+	1.25134i	0.374545	+	0.927209i	$0.377799\pi$
$73$	−1.89942e6	+	4.15916e6i	−0.571468	+	1.25134i	−0.946012	+	0.324131i	$0.894928\pi$
$74$	−3.63902e6	+	1.06851e6i	−1.04393	+	0.306527i
$75$	−2.17110e6	−	4.75405e6i	−0.594246	−	1.30122i
$76$	874192.	+	1.00887e6i	0.228433	+	0.263626i
$77$	411994.	+	2.86548e6i	0.102843	+	0.715286i
$78$	2.58731e6	+	759704.i	0.617331	+	0.181265i
$79$	896819.	−	1.03498e6i	0.204649	−	0.236178i	−0.644142	−	0.764906i	$-0.722785\pi$
$79$	896819.	−	1.03498e6i	0.204649	−	0.236178i	0.848791	+	0.528728i	$0.177331\pi$
$80$	3.90480e6	+	2.50946e6i	0.852675	+	0.547981i
$81$	447077.	+	287319.i	0.0934726	+	0.0600712i
$82$	2.37709e6	−	2.74330e6i	0.476098	−	0.549447i
$83$	−9.79416e6	−	2.87583e6i	−1.88016	−	0.552064i	−0.996467	−	0.0839901i	$-0.973234\pi$
$83$	−9.79416e6	−	2.87583e6i	−1.88016	−	0.552064i	−0.883690	−	0.468074i	$-0.844948\pi$
$84$	90844.1	+	631834.i	0.0167232	+	0.116312i
$85$	694204.	+	801155.i	0.122609	+	0.141498i
$86$	1.13281e6	+	2.48050e6i	0.192049	+	0.420528i
$87$	−1.62875e6	+	478244.i	−0.265178	+	0.0778632i
$88$	−3.49534e6	+	7.65373e6i	−0.546765	+	1.19725i
$89$	−172585.	+	1.20036e6i	−0.0259501	+	0.180487i	−0.998674	−	0.0514787i	$-0.983607\pi$
$89$	−172585.	+	1.20036e6i	−0.0259501	+	0.180487i	0.972724	+	0.231966i	$0.0745157\pi$
$90$	−2.93696e6	+	1.88747e6i	−0.424667	+	0.272917i
$91$	−5.89606e6			−0.820194
$92$	−2.18687e6	+	1.29857e6i	−0.292796	+	0.173864i
$93$	−6.37591e6			−0.821962
$94$	−1.40034e6	+	899945.i	−0.173895	+	0.111755i
$95$	2.27189e6	−	1.58013e7i	0.271866	−	1.89087i
$96$	−1.34565e6	+	2.94657e6i	−0.155233	+	0.339913i
$97$	−595530.	+	174863.i	−0.0662526	+	0.0194535i	−0.314691	−	0.949194i	$-0.601901\pi$
$97$	−595530.	+	174863.i	−0.0662526	+	0.0194535i	0.248438	+	0.968648i	$0.420083\pi$
$98$	−2.02033e6	−	4.42391e6i	−0.216836	−	0.474804i
$99$	−2.54797e6	−	2.94052e6i	−0.263920	−	0.304580i
$100$	1.20073e6	+	8.35126e6i	0.120073	+	0.835126i
$101$	−5.24311e6	−	1.53951e6i	−0.506365	−	0.148682i	0.0185648	−	0.999828i	$-0.494090\pi$
$101$	−5.24311e6	−	1.53951e6i	−0.506365	−	0.148682i	−0.524930	+	0.851145i	$0.675908\pi$
$102$	330381.	−	381280.i	0.0308258	−	0.0355749i
$103$	−3.45796e6	−	2.22229e6i	−0.311810	−	0.200388i	0.375371	−	0.926875i	$-0.377515\pi$
$103$	−3.45796e6	−	2.22229e6i	−0.311810	−	0.200388i	−0.687180	+	0.726487i	$0.741152\pi$
$104$	−1.44164e7	−	9.26483e6i	−1.25672	−	0.807646i
$105$	4.99890e6	−	5.76904e6i	0.421417	−	0.486341i
$106$	7.10034e6	+	2.08485e6i	0.579040	+	0.170021i
$107$	−1.07360e6	−	7.46707e6i	−0.0847228	−	0.589260i	−0.987316	−	0.158766i	$-0.949248\pi$
$107$	−1.07360e6	−	7.46707e6i	−0.0847228	−	0.589260i	0.902593	−	0.430494i	$-0.141661\pi$
$108$	−561825.	−	648380.i	−0.0429158	−	0.0495275i
$109$	8.22774e6	+	1.80162e7i	0.608538	+	1.33251i	0.923570	+	0.383431i	$0.125258\pi$
$109$	8.22774e6	+	1.80162e7i	0.608538	+	1.33251i	−0.315032	+	0.949081i	$0.602015\pi$
$110$	2.45247e7	−	7.20110e6i	1.75683	−	0.515851i
$111$	−4.63004e6	+	1.01384e7i	−0.321332	+	0.703619i
$112$	−687392.	+	4.78091e6i	−0.0462318	+	0.321550i
$113$	2.24048e7	−	1.43987e7i	1.46072	−	0.938746i	0.462064	−	0.886846i	$-0.347109\pi$
$113$	2.24048e7	−	1.43987e7i	1.46072	−	0.938746i	0.998652	−	0.0518992i	$-0.0165275\pi$
$114$	−7.59740e6			−0.480284
$115$	2.88619e7	+	9.59482e6i	1.76963	+	0.588294i
$116$	2.74037e6			0.163007
$117$	6.66644e6	−	4.28426e6i	0.384808	−	0.247301i
$118$	−1.25082e6	+	8.69963e6i	−0.0700821	+	0.487432i
$119$	−458251.	+	1.00343e6i	−0.0249281	+	0.0545849i
$120$	2.12880e7	−	6.25071e6i	1.12460	−	0.330214i
$121$	3.73840e6	+	8.18595e6i	0.191839	+	0.420068i
$122$	−8.35049e6	−	9.63698e6i	−0.416344	−	0.480487i
$123$	−1.51812e6	−	1.05588e7i	−0.0735594	−	0.511617i
$124$	9.87599e6	+	2.89985e6i	0.465163	+	0.136584i
$125$	3.94056e7	−	4.54765e7i	1.80457	−	2.08258i
$126$	−3.05619e6	−	1.96409e6i	−0.136108	−	0.0874712i
$127$	−1.99755e7	−	1.28375e7i	−0.865336	−	0.556118i	0.0309866	−	0.999520i	$-0.490135\pi$
$127$	−1.99755e7	−	1.28375e7i	−0.865336	−	0.556118i	−0.896323	+	0.443402i	$0.853771\pi$
$128$	−3.43346e6	+	3.96242e6i	−0.144709	+	0.167003i
$129$	7.68910e6	+	2.25772e6i	0.315363	+	0.0925991i
$130$	7.40855e6	+	5.15276e7i	0.295755	+	2.05702i
$131$	774684.	+	894034.i	0.0301075	+	0.0347460i	0.770604	−	0.637315i	$-0.219955\pi$
$131$	774684.	+	894034.i	0.0301075	+	0.0347460i	−0.740496	+	0.672061i	$0.765409\pi$
$132$	2.60931e6	+	5.71358e6i	0.0987452	+	0.216222i
$133$	1.59390e7	−	4.68011e6i	0.587463	−	0.172495i
$134$	−1.58784e7	+	3.47689e7i	−0.570086	+	1.24831i
$135$	−1.46009e6	+	1.01552e7i	−0.0510755	+	0.355238i
$136$	−2.69721e6	+	1.73339e6i	−0.0919451	+	0.0590895i
$137$	2.50487e7			0.832269			0.416134	−	0.909303i	$-0.363385\pi$
$137$	2.50487e7			0.832269			0.416134	+	0.909303i	$0.363385\pi$
$138$	2.56503e6	−	1.42458e7i	0.0830835	−	0.461434i
$139$	−1.96313e7			−0.620009			−0.310004	−	0.950735i	$-0.600331\pi$
$139$	−1.96313e7			−0.620009			−0.310004	+	0.950735i	$0.600331\pi$
$140$	−1.03669e7	+	6.66240e6i	−0.319301	+	0.205203i
$141$	−696174.	+	4.84199e6i	−0.0209147	+	0.145465i
$142$	1.80972e7	−	3.96273e7i	0.530398	−	1.16141i
$143$	−5.56673e7	+	1.63454e7i	−1.59193	+	0.467433i
$144$	−2.69676e6	−	5.90507e6i	−0.0752615	−	0.164800i
$145$	−2.14604e7	−	2.47666e7i	−0.584587	−	0.674650i
$146$	5.97851e6	+	4.15815e7i	0.158986	+	1.10577i
$147$	−1.37133e7	−	4.02659e6i	−0.356067	−	0.104551i
$148$	1.17828e7	−	1.35981e7i	0.298767	−	0.344795i
$149$	1.39065e7	+	8.93716e6i	0.344402	+	0.221334i	0.701394	−	0.712774i	$-0.252561\pi$
$149$	1.39065e7	+	8.93716e6i	0.344402	+	0.221334i	−0.356992	+	0.934107i	$0.616198\pi$
$150$	−4.03951e7	−	2.59604e7i	−0.977259	−	0.628046i
$151$	3.03785e7	−	3.50587e7i	0.718038	−	0.828660i	−0.273031	−	0.962005i	$-0.588026\pi$
$151$	3.03785e7	−	3.50587e7i	0.718038	−	0.828660i	0.991070	+	0.133345i	$0.0425718\pi$
$152$	4.63264e7	+	1.36026e7i	1.06998	+	0.314174i
$153$	−210997.	−	1.46752e6i	−0.00476274	−	0.0331256i
$154$	1.74178e7	+	2.01012e7i	0.384300	+	0.443506i
$155$	−5.11329e7	−	1.11965e8i	−1.10291	−	2.41503i
$156$	−1.22746e7	+	3.60413e6i	−0.258863	+	0.0760090i
$157$	−3.16075e7	+	6.92108e7i	−0.651840	+	1.42733i	0.238094	+	0.971242i	$0.423477\pi$
$157$	−3.16075e7	+	6.92108e7i	−0.651840	+	1.42733i	−0.889934	+	0.456089i	$0.849250\pi$
$158$	1.79065e6	−	1.24542e7i	0.0361168	−	0.251198i
$159$	1.82947e7	−	1.17573e7i	0.360939	−	0.231962i
$160$	−6.25356e7			−1.20700
$161$	3.39432e6	+	3.14671e7i	0.0641006	+	0.594247i
$162$	4.88269e6			0.0902311
$163$	1.62697e7	−	1.04559e7i	0.294254	−	0.189106i	−0.385181	−	0.922841i	$-0.625861\pi$
$163$	1.62697e7	−	1.04559e7i	0.294254	−	0.189106i	0.679436	+	0.733735i	$0.262225\pi$
$164$	−2.45077e6	+	1.70455e7i	−0.0433860	+	0.301756i
$165$	3.12035e7	−	6.83262e7i	0.540767	−	1.18411i
$166$	−8.99852e7	+	2.64220e7i	−1.52684	+	0.448320i
$167$	3.43248e7	+	7.51609e7i	0.570297	+	1.24878i	0.946639	+	0.322295i	$0.104454\pi$
$167$	3.43248e7	+	7.51609e7i	0.570297	+	1.24878i	−0.376342	+	0.926481i	$0.622818\pi$
$168$	1.51190e7	+	1.74483e7i	0.246004	+	0.283903i
$169$	−7.88621e6	−	5.48498e7i	−0.125680	−	0.874122i
$170$	9.34510e6	+	2.74397e6i	0.145886	+	0.0428359i
$171$	−1.46209e7	+	1.68734e7i	−0.223608	+	0.258057i
$172$	−1.08832e7	−	6.99422e6i	−0.163083	−	0.104807i
$173$	−5.89821e7	−	3.79055e7i	−0.866082	−	0.556597i	0.0304697	−	0.999536i	$-0.490300\pi$
$173$	−5.89821e7	−	3.79055e7i	−0.866082	−	0.556597i	−0.896552	+	0.442938i	$0.853936\pi$
$174$	−1.02133e7	+	1.17868e7i	−0.146975	+	0.169618i
$175$	1.00739e8	+	2.95797e7i	1.42091	+	0.417215i
$176$	6.76395e6	+	4.70443e7i	0.0935204	+	0.650449i
$177$	1.69143e7	+	1.95201e7i	0.229270	+	0.264591i
$178$	4.62849e6	+	1.01350e7i	0.0615134	+	0.134696i
$179$	−4.12687e7	+	1.21176e7i	−0.537818	+	0.157918i	−0.539351	−	0.842081i	$-0.681330\pi$
$179$	−4.12687e7	+	1.21176e7i	−0.537818	+	0.157918i	0.00153283	+	0.999999i	$0.499512\pi$
$180$	6.88034e6	−	1.50658e7i	0.0879338	−	0.192548i
$181$	4.61962e6	−	3.21301e7i	0.0579070	−	0.402752i	−0.940167	−	0.340714i	$-0.889331\pi$
$181$	4.61962e6	−	3.21301e7i	0.0579070	−	0.402752i	0.998074	−	0.0620375i	$-0.0197598\pi$
$182$	−4.55714e7	+	2.92870e7i	−0.560328	+	0.360101i
$183$	−3.74734e7			−0.452006
$184$	−4.11468e7	+	8.22735e7i	−0.486938	+	0.973639i
$185$	−2.15168e8			−2.49849
$186$	−4.92803e7	+	3.16705e7i	−0.561536	+	0.360877i
$187$	−1.54478e6	+	1.07442e7i	−0.0172752	+	0.120151i
$188$	3.28055e6	−	7.18340e6i	0.0360076	−	0.0788456i
$189$	−1.02437e7	+	3.00781e6i	−0.110367	+	0.0324066i
$190$	−6.09288e7	−	1.33416e8i	−0.644444	−	1.41114i
$191$	−7.11503e7	−	8.21118e7i	−0.738856	−	0.852685i	0.254583	−	0.967051i	$-0.418062\pi$
$191$	−7.11503e7	−	8.21118e7i	−0.738856	−	0.852685i	−0.993439	+	0.114366i	$0.963516\pi$
$192$	8.61532e6	+	5.99209e7i	0.0878451	+	0.610976i
$193$	4.55856e7	+	1.33851e7i	0.456433	+	0.134021i	0.501864	−	0.864947i	$-0.332648\pi$
$193$	4.55856e7	+	1.33851e7i	0.456433	+	0.134021i	−0.0454306	+	0.998967i	$0.514466\pi$
$194$	−3.73435e6	+	4.30967e6i	−0.0367205	+	0.0423777i
$195$	1.28697e8	+	8.27088e7i	1.24294	+	0.798786i
$196$	1.94099e7	+	1.24740e7i	0.184131	+	0.118334i
$197$	6.90054e7	−	7.96365e7i	0.643060	−	0.742131i	−0.336853	−	0.941557i	$-0.609363\pi$
$197$	6.90054e7	−	7.96365e7i	0.643060	−	0.742131i	0.979913	+	0.199427i	$0.0639080\pi$
$198$	−3.42998e7	−	1.00713e7i	−0.314024	−	0.0922059i
$199$	7.07298e6	+	4.91937e7i	0.0636234	+	0.442510i	0.996588	+	0.0825413i	$0.0263036\pi$
$199$	7.07298e6	+	4.91937e7i	0.0636234	+	0.442510i	−0.932964	+	0.359969i	$0.882787\pi$
$200$	1.99835e8	+	2.30622e8i	1.76631	+	2.03843i
$201$	4.66624e7	+	1.02176e8i	0.405304	+	0.887492i
$202$	−4.81717e7	+	1.41445e7i	−0.411209	+	0.120742i
$203$	1.41662e7	−	3.10196e7i	0.118855	−	0.260256i
$204$	−340622.	+	2.36908e6i	−0.00280910	+	0.0195377i
$205$	1.73244e8	−	1.11337e8i	1.40450	−	0.902614i
$206$	−3.77656e7			−0.300996
$207$	−2.67029e7	−	3.31123e7i	−0.209248	−	0.259473i
$208$	−9.67992e7			−0.745847
$209$	1.37513e8	−	8.83740e7i	1.04191	−	0.669596i
$210$	9.98112e6	−	6.94202e7i	0.0743724	−	0.517271i
$211$	5.59406e7	−	1.22493e8i	0.409957	−	0.897682i	−0.586205	−	0.810162i	$-0.699379\pi$
$211$	5.59406e7	−	1.22493e8i	0.409957	−	0.897682i	0.996163	−	0.0875191i	$-0.0278939\pi$
$212$	−3.36849e7	+	9.89079e6i	−0.242807	+	0.0712944i
$213$	−5.31828e7	−	1.16454e8i	−0.377088	−	0.825707i
$214$	−4.53885e7	−	5.23811e7i	−0.316590	−	0.365365i
$215$	2.20171e7	+	1.53132e8i	0.151086	+	1.05083i
$216$	−2.97730e7	−	8.74213e6i	−0.201018	−	0.0590241i
$217$	8.38783e7	−	9.68007e7i	0.557238	−	0.643087i
$218$	1.53084e8	+	9.83809e7i	1.00076	+	0.643151i
$219$	1.03856e8	+	6.67440e7i	0.668153	+	0.429396i
$220$	−7.94086e7	+	9.16424e7i	−0.502792	+	0.580253i
$221$	−2.12119e7	−	6.22839e6i	−0.132193	−	0.0388153i
$222$	1.45732e7	+	1.01359e8i	0.0893966	+	0.621767i
$223$	−1.04856e8	−	1.21010e8i	−0.633176	−	0.730724i	0.344977	−	0.938611i	$-0.387887\pi$
$223$	−1.04856e8	−	1.21010e8i	−0.633176	−	0.730724i	−0.978153	+	0.207887i	$0.933341\pi$
$224$	−2.70329e7	−	5.91937e7i	−0.160703	−	0.351890i
$225$	−1.35395e8	+	3.97557e7i	−0.792437	+	0.232681i
$226$	1.01648e8	−	2.22578e8i	0.585760	−	1.28264i
$227$	−2.95736e7	+	2.05689e8i	−0.167808	+	1.16713i	0.715594	+	0.698516i	$0.246156\pi$
$227$	−2.95736e7	+	2.05689e8i	−0.167808	+	1.16713i	−0.883402	+	0.468615i	$0.844753\pi$
$228$	3.03213e7	−	1.94863e7i	0.169425	−	0.108883i
$229$	−2.32196e8			−1.27770			−0.638851	−	0.769330i	$-0.720590\pi$
$229$	−2.32196e8			−1.27770			−0.638851	+	0.769330i	$0.720590\pi$
$230$	2.70737e8	−	6.92034e7i	1.46724	−	0.375042i
$231$	7.81635e7			0.417217
$232$	8.33806e7	−	5.35854e7i	0.438386	−	0.281734i
$233$	−3.89471e7	+	2.70883e8i	−0.201711	+	1.40293i	0.597495	+	0.801873i	$0.296163\pi$
$233$	−3.89471e7	+	2.70883e8i	−0.201711	+	1.40293i	−0.799206	+	0.601057i	$0.794746\pi$
$234$	3.02450e7	−	6.62272e7i	0.154311	−	0.337895i
$235$	−9.06118e7	+	2.66060e7i	−0.455457	+	0.133734i
$236$	−1.73214e7	−	3.79286e7i	−0.0857810	−	0.187834i
$237$	−2.42141e7	−	2.79446e7i	−0.118154	−	0.136357i
$238$	1.44236e6	+	1.00319e7i	0.00693514	+	0.0482350i
$239$	−2.34381e8	−	6.88206e7i	−1.11053	−	0.326081i	−0.325502	−	0.945541i	$-0.605533\pi$
$239$	−2.34381e8	−	6.88206e7i	−1.11053	−	0.326081i	−0.785028	+	0.619460i	$0.787352\pi$
$240$	8.20700e7	−	9.47138e7i	0.383217	−	0.442256i
$241$	−1.48526e8	−	9.54517e7i	−0.683506	−	0.439262i	0.152266	−	0.988340i	$-0.451343\pi$
$241$	−1.48526e8	−	9.54517e7i	−0.683506	−	0.439262i	−0.835772	+	0.549077i	$0.814979\pi$
$242$	6.95559e7	+	4.47008e7i	0.315486	+	0.202751i
$243$	9.39654e6	−	1.08442e7i	0.0420093	−	0.0484814i
$244$	5.80446e7	+	1.70434e7i	0.255798	+	0.0751091i
$245$	−3.92669e7	−	2.73107e8i	−0.170587	−	1.18646i
$246$	−6.41814e7	−	7.40692e7i	−0.274875	−	0.317223i
$247$	1.38299e8	+	3.02833e8i	0.583955	+	1.27868i
$248$	3.57198e8	−	1.04883e8i	1.48706	−	0.436640i
$249$	−1.14491e8	+	2.50700e8i	−0.469974	+	1.02910i
$250$	7.86797e7	−	5.47229e8i	0.318473	−	2.21503i
$251$	−2.20289e8	+	1.41571e8i	−0.879297	+	0.565090i	−0.900583	−	0.434684i	$-0.856860\pi$
$251$	−2.20289e8	+	1.41571e8i	−0.879297	+	0.565090i	0.0212865	+	0.999773i	$0.493224\pi$
$252$	1.72350e7			0.0678435
$253$	1.19282e8	+	2.87685e8i	0.463078	+	1.11685i
$254$	−2.18160e8			−0.835328
$255$	2.40785e7	−	1.54743e7i	0.0909365	−	0.0584414i
$256$	3.39876e7	−	2.36389e8i	0.126614	−	0.880616i
$257$	6.29564e6	−	1.37855e7i	0.0231352	−	0.0506591i	−0.897712	−	0.440583i	$-0.854772\pi$
$257$	6.29564e6	−	1.37855e7i	0.0231352	−	0.0506591i	0.920847	+	0.389924i	$0.127499\pi$
$258$	7.06446e7	−	2.07431e7i	0.256100	−	0.0751978i
$259$	−9.30128e7	−	2.03670e8i	−0.332655	−	0.728412i
$260$	−1.61729e8	−	1.86646e8i	−0.570666	−	0.658584i
$261$	6.52269e6	+	4.53663e7i	0.0227083	+	0.157940i
$262$	1.04285e7	+	3.06208e6i	0.0358234	+	0.0105187i
$263$	−8.85337e7	+	1.02173e8i	−0.300098	+	0.346332i	−0.885692	−	0.464273i	$-0.846316\pi$
$263$	−8.85337e7	+	1.02173e8i	−0.300098	+	0.346332i	0.585594	+	0.810604i	$0.300861\pi$
$264$	1.91116e8	+	1.22823e8i	0.639270	+	0.410834i
$265$	3.53183e8	+	2.26977e8i	1.16584	+	0.749241i
$266$	9.99475e7	−	1.15346e8i	0.325601	−	0.375764i
$267$	3.14166e7	+	9.22475e6i	0.101011	+	0.0296596i
$268$	−2.58067e7	−	1.79489e8i	−0.0818955	−	0.569596i
$269$	−1.33145e8	−	1.53657e8i	−0.417052	−	0.481304i	0.507885	−	0.861425i	$-0.330428\pi$
$269$	−1.33145e8	−	1.53657e8i	−0.417052	−	0.481304i	−0.924937	+	0.380121i	$0.875882\pi$
$270$	3.91577e7	+	8.57433e7i	0.121072	+	0.265111i
$271$	−2.16015e8	+	6.34277e7i	−0.659312	+	0.193591i	−0.594238	−	0.804289i	$-0.702546\pi$
$271$	−2.16015e8	+	6.34277e7i	−0.659312	+	0.193591i	−0.0650736	+	0.997880i	$0.520728\pi$
$272$	−7.52338e6	+	1.64739e7i	−0.0226685	+	0.0496370i
$273$	−2.26556e7	+	1.57573e8i	−0.0673917	+	0.468719i
$274$	1.93605e8	−	1.24422e8i	0.568577	−	0.365402i
$275$	1.03313e9			2.99563
$276$	2.63016e7	+	6.34342e7i	0.0753009	+	0.181611i
$277$	1.64403e8			0.464763			0.232381	−	0.972625i	$-0.425348\pi$
$277$	1.64403e8			0.464763			0.232381	+	0.972625i	$0.425348\pi$
$278$	−1.51733e8	+	9.75129e7i	−0.423568	+	0.272211i
$279$	−2.44994e7	+	1.70397e8i	−0.0675370	+	0.469730i
$280$	−1.85154e8	+	4.05430e8i	−0.504057	+	1.10373i
$281$	3.55051e8	−	1.04252e8i	0.954593	−	0.280294i	0.232895	−	0.972502i	$-0.425180\pi$
$281$	3.55051e8	−	1.04252e8i	0.954593	−	0.280294i	0.721698	+	0.692208i	$0.243362\pi$
$282$	1.86704e7	+	4.08824e7i	0.0495771	+	0.108559i
$283$	1.05774e8	+	1.22070e8i	0.277413	+	0.320152i	0.877309	−	0.479926i	$-0.159337\pi$
$283$	1.05774e8	+	1.22070e8i	0.277413	+	0.320152i	−0.599896	+	0.800078i	$0.704791\pi$
$284$	2.94128e7	+	2.04570e8i	0.0761942	+	0.529942i
$285$	−4.13564e8	−	1.21433e8i	−1.05824	−	0.310728i
$286$	−3.49069e8	+	4.02847e8i	−0.882327	+	1.01826i
$287$	1.80277e8	+	1.15857e8i	0.450147	+	0.289292i
$288$	7.35770e7	+	4.72851e7i	0.181497	+	0.116641i
$289$	2.66006e8	−	3.06987e8i	0.648260	−	0.748132i
$290$	−2.88891e8	−	8.48261e7i	−0.695570	−	0.204238i
$291$	2.38493e6	+	1.65876e7i	0.00567349	+	0.0394600i
$292$	−1.30512e8	−	1.50618e8i	−0.306767	−	0.354028i
$293$	8.70237e7	+	1.90555e8i	0.202116	+	0.442573i	0.983363	−	0.181649i	$-0.0581435\pi$
$293$	8.70237e7	+	1.90555e8i	0.202116	+	0.442573i	−0.781247	+	0.624222i	$0.785416\pi$
$294$	−1.25993e8	+	3.69948e7i	−0.289155	+	0.0849034i
$295$	−2.07139e8	+	4.53571e8i	−0.469770	+	1.02865i
$296$	9.26142e7	−	6.44146e8i	0.207566	−	1.44366i
$297$	−8.83765e7	+	5.67961e7i	−0.195744	+	0.125797i
$298$	1.51878e8			0.332459
$299$	−6.14531e8	+	1.57081e8i	−1.32952	+	0.339840i
$300$	2.27803e8			0.487118
$301$	−1.35431e8	+	8.70363e7i	−0.286244	+	0.183958i
$302$	6.06557e7	−	4.21870e8i	0.126721	−	0.881362i
$303$	−6.12904e7	+	1.34207e8i	−0.126574	+	0.277158i
$304$	2.61680e8	−	7.68363e7i	0.534212	−	0.156859i
$305$	−3.00525e8	−	6.58059e8i	−0.606501	−	1.32805i
$306$	−8.92029e6	−	1.02946e7i	−0.0177973	−	0.0205392i
$307$	−4.15132e7	−	2.88731e8i	−0.0818845	−	0.569519i	−0.988918	−	0.148461i	$-0.952568\pi$
$307$	−4.15132e7	−	2.88731e8i	−0.0818845	−	0.569519i	0.907034	−	0.421058i	$-0.138341\pi$
$308$	−1.21072e8	−	3.55499e7i	−0.236110	−	0.0693283i
$309$	−7.26784e7	+	8.38754e7i	−0.140136	+	0.161726i
$310$	−9.51368e8	−	6.11407e8i	−1.81377	−	1.16564i
$311$	−1.16271e8	−	7.47229e7i	−0.219185	−	0.140862i	0.426441	−	0.904515i	$-0.359767\pi$
$311$	−1.16271e8	−	7.47229e7i	−0.219185	−	0.140862i	−0.645626	+	0.763654i	$0.723403\pi$
$312$	−3.02999e8	+	3.49680e8i	−0.564807	+	0.651822i
$313$	−6.12426e8	−	1.79825e8i	−1.12888	−	0.331470i	−0.336614	−	0.941643i	$-0.609282\pi$
$313$	−6.12426e8	−	1.79825e8i	−1.12888	−	0.331470i	−0.792268	+	0.610173i	$0.791100\pi$
$314$	9.94860e7	+	6.91940e8i	0.181346	+	1.26129i
$315$	−1.34970e8	−	1.55764e8i	−0.243305	−	0.280789i
$316$	2.47970e7	+	5.42978e7i	0.0442073	+	0.0968004i
$317$	8.49198e8	−	2.49347e8i	1.49728	−	0.439640i	0.572421	−	0.819960i	$-0.306004\pi$
$317$	8.49198e8	−	2.49347e8i	1.49728	−	0.439640i	0.924855	+	0.380320i	$0.124186\pi$
$318$	8.30010e7	−	1.81747e8i	0.144740	−	0.316936i
$319$	4.77549e7	−	3.32142e8i	0.0823664	−	0.572871i
$320$	−9.83160e8	+	6.31838e8i	−1.67726	+	1.07791i
$321$	−2.03684e8			−0.343708
$322$	1.82539e8	+	2.26353e8i	0.304692	+	0.377826i
$323$	6.22868e7			0.102846
$324$	−1.94869e7	+	1.25235e7i	−0.0318299	+	0.0204558i
$325$	−2.99450e8	+	2.08272e9i	−0.483874	+	3.36542i
$326$	7.38140e7	−	1.61630e8i	0.117999	−	0.258381i
$327$	5.13102e8	−	1.50660e8i	0.811496	−	0.238277i
$328$	2.58740e8	+	5.66562e8i	0.404860	+	0.886520i
$329$	−6.43539e7	−	7.42683e7i	−0.0996297	−	0.114979i
$330$	−9.82145e7	−	6.83097e8i	−0.150445	−	1.04637i
$331$	3.01147e8	+	8.84248e7i	0.456437	+	0.134022i	0.501866	−	0.864946i	$-0.332647\pi$
$331$	3.01147e8	+	8.84248e7i	0.456437	+	0.134022i	−0.0454286	+	0.998968i	$0.514465\pi$
$332$	2.91363e8	−	3.36251e8i	0.436970	−	0.504290i
$333$	2.53159e8	+	1.62695e8i	0.375697	+	0.241446i
$334$	6.38641e8	+	4.10430e8i	0.937874	+	0.602735i
$335$	−1.42007e9	+	1.63885e9i	−2.06373	+	2.38167i
$336$	1.25129e8	+	3.67413e7i	0.179958	+	0.0528406i
$337$	−8.39431e7	−	5.83837e8i	−0.119476	−	0.830973i	−0.958135	−	0.286316i	$-0.907569\pi$
$337$	−8.39431e7	−	5.83837e8i	−0.119476	−	0.830973i	0.838659	−	0.544656i	$-0.183340\pi$
$338$	−3.33404e8	−	3.84769e8i	−0.469637	−	0.541990i
$339$	−2.98717e8	−	6.54098e8i	−0.416448	−	0.911894i
$340$	−4.43344e7	+	1.30178e7i	−0.0611737	+	0.0179622i
$341$	5.23575e8	−	1.14647e9i	0.715054	−	1.56575i
$342$	−2.91930e7	+	2.03042e8i	−0.0394628	+	0.274469i
$343$	6.17319e8	−	3.96727e8i	0.826001	−	0.530838i
$344$	−4.67906e8			−0.619732
$345$	3.67325e8	−	7.34471e8i	0.481597	−	0.962959i
$346$	−6.44165e8			−0.836048
$347$	−6.42544e8	+	4.12938e8i	−0.825562	+	0.530556i	−0.883865	−	0.467742i	$-0.845067\pi$
$347$	−6.42544e8	+	4.12938e8i	−0.825562	+	0.530556i	0.0583028	+	0.998299i	$0.481431\pi$
$348$	1.05299e7	−	7.32369e7i	0.0133936	−	0.0931543i
$349$	−5.18118e8	+	1.13452e9i	−0.652439	+	1.42864i	0.236964	+	0.971518i	$0.423848\pi$
$349$	−5.18118e8	+	1.13452e9i	−0.652439	+	1.42864i	−0.889403	+	0.457124i	$0.848880\pi$
$350$	9.25555e8	−	2.71767e8i	1.15389	−	0.338812i
$351$	−8.88819e7	−	1.94624e8i	−0.109708	−	0.240227i
$352$	−4.19329e8	−	4.83932e8i	−0.512455	−	0.591405i
$353$	1.28533e8	+	8.93965e8i	0.155526	+	1.08171i	0.906753	+	0.421662i	$0.138553\pi$
$353$	1.28533e8	+	8.93965e8i	0.155526	+	1.08171i	−0.751228	+	0.660043i	$0.770538\pi$
$354$	2.27693e8	+	6.68567e7i	0.272796	+	0.0801002i
$355$	1.61850e9	−	1.86785e9i	1.92006	−	2.21587i
$356$	−4.44673e7	−	2.85774e7i	−0.0522355	−	0.0335697i
$357$	2.50560e7	+	1.61025e7i	0.0291456	+	0.0187307i
$358$	−2.58781e8	+	2.98649e8i	−0.298086	+	0.344009i
$359$	−1.07500e9	−	3.15649e8i	−1.22625	−	0.360059i	−0.396416	−	0.918071i	$-0.629746\pi$
$359$	−1.07500e9	−	3.15649e8i	−1.22625	−	0.360059i	−0.829833	+	0.558012i	$0.811564\pi$
$360$	−8.52523e7	−	5.92943e8i	−0.0963047	−	0.669814i
$361$	−2.88862e7	−	3.33364e7i	−0.0323158	−	0.0372944i
$362$	−1.23892e8	−	2.71285e8i	−0.137266	−	0.300570i
$363$	2.33136e8	−	6.84548e7i	0.255821	−	0.0751157i
$364$	1.06759e8	−	2.33770e8i	0.116024	−	0.254058i
$365$	−3.39179e8	+	2.35904e9i	−0.365093	+	2.53928i
$366$	−2.89637e8	+	1.86138e8i	−0.308795	+	0.198450i
$367$	2.76215e8			0.291687			0.145843	−	0.989308i	$-0.453410\pi$
$367$	2.76215e8			0.291687			0.145843	+	0.989308i	$0.453410\pi$
$368$	5.57267e7	+	5.16615e8i	0.0582902	+	0.540381i
$369$	−2.88018e8			−0.298420
$370$	−1.66306e9	+	1.06879e9i	−1.70688	+	1.09694i
$371$	−6.21736e7	+	4.32427e8i	−0.0632116	+	0.439647i
$372$	1.15448e8	−	2.52795e8i	0.116275	−	0.254606i
$373$	1.26087e9	−	3.70224e8i	1.25802	−	0.369388i	0.416263	−	0.909244i	$-0.363339\pi$
$373$	1.26087e9	−	3.70224e8i	1.25802	−	0.369388i	0.841758	+	0.539856i	$0.181521\pi$
$374$	4.14289e7	+	9.07166e7i	0.0409499	+	0.0896677i
$375$	−1.06395e9	−	1.22786e9i	−1.04187	−	1.20238i
$376$	−4.06483e7	−	2.82715e8i	−0.0394353	−	0.274279i
$377$	6.55738e8	+	1.92542e8i	0.630283	+	0.185068i
$378$	−6.42342e7	+	7.41302e7i	−0.0611709	+	0.0705950i
$379$	3.28878e8	+	2.11357e8i	0.310311	+	0.199425i	0.686522	−	0.727109i	$-0.259137\pi$
$379$	3.28878e8	+	2.11357e8i	0.310311	+	0.199425i	−0.376211	+	0.926534i	$0.622773\pi$
$380$	5.85362e8	+	3.76189e8i	0.547245	+	0.351693i
$381$	−4.19840e8	+	4.84521e8i	−0.388908	+	0.448823i
$382$	−9.57796e8	−	2.81234e8i	−0.879127	−	0.258135i
$383$	−2.60208e8	−	1.80979e9i	−0.236660	−	1.64601i	−0.668248	−	0.743938i	$-0.732956\pi$
$383$	−2.60208e8	−	1.80979e9i	−0.236660	−	1.64601i	0.431588	−	0.902071i	$-0.357954\pi$
$384$	9.27033e7	+	1.06985e8i	0.0835480	+	0.0964195i
$385$	6.26848e8	+	1.37261e9i	0.559822	+	1.22584i
$386$	4.18824e8	−	1.22978e8i	0.370660	−	0.108836i
$387$	8.98834e7	−	1.96817e8i	0.0788299	−	0.172613i
$388$	3.85011e6	−	2.67781e7i	0.00334628	−	0.0232739i
$389$	1.11055e9	−	7.13707e8i	0.956565	−	0.614747i	0.0335199	−	0.999438i	$-0.489328\pi$
$389$	1.11055e9	−	7.13707e8i	0.956565	−	0.614747i	0.923045	+	0.384691i	$0.125692\pi$
$390$	1.40555e9			1.19983
$391$	−2.10292e7	+	1.16793e8i	−0.0177912	+	0.0988097i
$392$	8.34498e8			0.699720
$393$	2.68699e7	−	1.72683e7i	0.0223302	−	0.0143507i
$394$	1.37781e8	−	9.58285e8i	0.113488	−	0.789329i
$395$	2.96536e8	−	6.49323e8i	0.242096	−	0.530116i
$396$	1.62723e8	−	4.77797e7i	0.131679	−	0.0386643i
$397$	7.64614e8	+	1.67427e9i	0.613304	+	1.34295i	0.920291	+	0.391234i	$0.127952\pi$
$397$	7.64614e8	+	1.67427e9i	0.613304	+	1.34295i	−0.306987	+	0.951714i	$0.599321\pi$
$398$	2.99023e8	+	3.45091e8i	0.237747	+	0.274374i
$399$	−6.38312e7	−	4.43956e8i	−0.0503070	−	0.349893i
$400$	1.65390e9	+	4.85628e8i	1.29211	+	0.379397i
$401$	9.15584e8	−	1.05664e9i	0.709076	−	0.818317i	−0.280873	−	0.959745i	$-0.590624\pi$
$401$	9.15584e8	−	1.05664e9i	0.709076	−	0.818317i	0.989949	+	0.141428i	$0.0451693\pi$
$402$	8.68192e8	+	5.57953e8i	0.666537	+	0.428358i
$403$	2.15946e9	+	1.38780e9i	1.64353	+	1.05623i
$404$	1.55975e8	−	1.80005e8i	0.117685	−	0.135816i
$405$	2.65789e8	+	7.80426e7i	0.198813	+	0.0583766i
$406$	−4.45887e7	−	3.10121e8i	−0.0330662	−	0.229980i
$407$	−1.44280e9	−	1.66508e9i	−1.06078	−	1.22421i
$408$	3.59612e7	+	7.87440e7i	0.0262134	+	0.0573993i
$409$	1.13184e9	−	3.32338e8i	0.818000	−	0.240186i	0.154145	−	0.988048i	$-0.450738\pi$
$409$	1.13184e9	−	3.32338e8i	0.818000	−	0.240186i	0.663854	+	0.747862i	$0.268919\pi$
$410$	7.85992e8	−	1.72108e9i	0.563215	−	1.23327i
$411$	9.62497e7	−	6.69431e8i	0.0683838	−	0.475620i
$412$	1.50723e8	−	9.68639e7i	0.106179	−	0.0682373i
$413$	−5.18875e8			−0.362441
$414$	−3.70865e8	−	1.23290e8i	−0.256871	−	0.0853940i
$415$	−5.32065e9			−3.65424
$416$	1.09712e9	−	7.05076e8i	0.747184	−	0.480186i
$417$	−7.54334e7	+	5.24651e8i	−0.0509433	+	0.354319i
$418$	6.23881e8	−	1.36611e9i	0.417816	−	0.914889i
$419$	−1.53338e8	+	4.50240e7i	−0.101836	+	0.0299016i	−0.332253	−	0.943190i	$-0.607809\pi$
$419$	−1.53338e8	+	4.50240e7i	−0.101836	+	0.0299016i	0.230418	+	0.973092i	$0.425991\pi$
$420$	1.38219e8	+	3.02658e8i	0.0910323	+	0.199333i
$421$	1.44024e9	+	1.66213e9i	0.940695	+	1.08562i	0.996194	+	0.0871614i	$0.0277796\pi$
$421$	1.44024e9	+	1.66213e9i	0.940695	+	1.08562i	−0.0554990	+	0.998459i	$0.517675\pi$
$422$	−1.76076e8	−	1.22463e9i	−0.114053	−	0.793254i
$423$	1.26728e8	+	3.72107e7i	0.0814107	+	0.0239043i
$424$	−8.31518e8	+	9.59623e8i	−0.529775	+	0.611392i
$425$	3.31177e8	+	2.12835e8i	0.209266	+	0.134487i
$426$	−9.89509e8	−	6.35919e8i	−0.620135	−	0.398536i
$427$	4.92981e8	−	5.68931e8i	0.306431	−	0.353640i
$428$	3.15497e8	+	9.26384e7i	0.194510	+	0.0571134i
$429$	2.22932e8	+	1.55052e9i	0.136324	+	0.948152i
$430$	9.30812e8	+	1.07421e9i	0.564576	+	0.651555i
$431$	6.10536e8	+	1.33689e9i	0.367317	+	0.804312i	0.999563	+	0.0295444i	$0.00940566\pi$
$431$	6.10536e8	+	1.33689e9i	0.367317	+	0.804312i	−0.632247	+	0.774767i	$0.717867\pi$
$432$	−1.68176e8	+	4.93811e7i	−0.100363	+	0.0294691i
$433$	1.17308e9	−	2.56869e9i	0.694417	−	1.52056i	−0.152195	−	0.988350i	$-0.548634\pi$
$433$	1.17308e9	−	2.56869e9i	0.694417	−	1.52056i	0.846612	−	0.532210i	$-0.178638\pi$
$434$	1.67477e8	−	1.16483e9i	0.0983423	−	0.683986i
$435$	−7.44353e8	+	4.78367e8i	−0.433578	+	0.278643i
$436$	−8.63294e8			−0.498834
$437$	1.53659e9	−	9.12438e8i	0.880794	−	0.523020i
$438$	1.13425e9			0.644982
$439$	−1.68364e9	+	1.08201e9i	−0.949779	+	0.610386i	−0.921152	−	0.389204i	$-0.872750\pi$
$439$	−1.68364e9	+	1.08201e9i	−0.949779	+	0.610386i	−0.0286279	+	0.999590i	$0.509114\pi$
$440$	−6.24162e8	+	4.34114e9i	−0.349311	+	2.42951i
$441$	−1.60305e8	+	3.51018e8i	−0.0890043	+	0.194892i
$442$	−1.94888e8	+	5.72241e7i	−0.107351	+	0.0315211i
$443$	−8.11770e8	−	1.77753e9i	−0.443629	−	0.971412i	−0.990918	−	0.134468i	$-0.957067\pi$
$443$	−8.11770e8	−	1.77753e9i	−0.443629	−	0.971412i	0.547289	−	0.836944i	$-0.315660\pi$
$444$	−3.18135e8	−	3.67148e8i	−0.172493	−	0.199067i
$445$	8.99587e7	+	6.25677e8i	0.0483931	+	0.336581i
$446$	−1.41152e9	−	4.14461e8i	−0.753383	−	0.221213i
$447$	2.92283e8	−	3.37312e8i	0.154784	−	0.178631i
$448$	−1.02307e9	−	6.57489e8i	−0.537568	−	0.345474i
$449$	−1.78393e9	−	1.14646e9i	−0.930068	−	0.597718i	−0.0145059	−	0.999895i	$-0.504618\pi$
$449$	−1.78393e9	−	1.14646e9i	−0.930068	−	0.597718i	−0.915562	+	0.402176i	$0.868254\pi$
$450$	−8.49014e8	+	9.79814e8i	−0.439209	+	0.506874i
$451$	2.02326e9	+	5.94084e8i	1.03857	+	0.304951i
$452$	1.65205e8	+	1.14903e9i	0.0841472	+	0.585257i
$453$	−8.20221e8	−	9.46585e8i	−0.414560	−	0.478427i
$454$	7.93121e8	+	1.73669e9i	0.397781	+	0.871019i
$455$	−2.94878e9	+	8.65841e8i	−1.46758	+	0.430922i
$456$	5.41542e8	−	1.18581e9i	0.267458	−	0.585651i
$457$	−7.60547e7	+	5.28972e8i	−0.0372751	+	0.259254i	−0.999934	−	0.0114621i	$-0.996351\pi$
$457$	−7.60547e7	+	5.28972e8i	−0.0372751	+	0.259254i	0.962659	+	0.270716i	$0.0872605\pi$
$458$	−1.79467e9	+	1.15336e9i	−0.872882	+	0.560967i
$459$	−4.00304e7			−0.0193217
$460$	−9.03017e8	+	9.70597e8i	−0.432557	+	0.464929i
$461$	2.11427e9			1.00509			0.502547	−	0.864550i	$-0.332396\pi$
$461$	2.11427e9			1.00509			0.502547	+	0.864550i	$0.332396\pi$
$462$	6.04136e8	−	3.88255e8i	0.285028	−	0.183177i
$463$	3.56020e8	−	2.47617e9i	0.166702	−	1.15944i	−0.718941	−	0.695071i	$-0.755373\pi$
$463$	3.56020e8	−	2.47617e9i	0.166702	−	1.15944i	0.885643	−	0.464367i	$-0.153718\pi$
$464$	2.32575e8	−	5.09268e8i	0.108081	−	0.236665i
$465$	−3.18877e9	+	9.36308e8i	−1.47075	+	0.431851i
$466$	1.04451e9	+	2.28715e9i	0.478146	+	1.04699i
$467$	−7.61174e8	−	8.78441e8i	−0.345840	−	0.399120i	0.556006	−	0.831178i	$-0.312333\pi$
$467$	−7.61174e8	−	8.78441e8i	−0.345840	−	0.399120i	−0.901846	+	0.432058i	$0.857788\pi$
$468$	4.91561e7	+	3.41889e8i	0.0221675	+	0.154179i
$469$	−2.16514e9	−	6.35741e8i	−0.969126	−	0.284561i
$470$	−5.68193e8	+	6.55730e8i	−0.252437	+	0.291328i
$471$	1.72822e9	+	1.11066e9i	0.762124	+	0.489787i
$472$	−1.26869e9	−	8.15339e8i	−0.555340	−	0.356896i
$473$	−1.03738e9	+	1.19720e9i	−0.450737	+	0.520178i
$474$	−3.25960e8	−	9.57106e7i	−0.140586	−	0.0412796i
$475$	−8.43688e8	−	5.86798e9i	−0.361205	−	2.51224i
$476$	−3.14869e7	−	3.63379e7i	−0.0133815	−	0.0154431i
$477$	−2.43918e8	−	5.34105e8i	−0.102903	−	0.225327i
$478$	−2.15341e9	+	6.32298e8i	−0.901839	+	0.264804i
$479$	−1.11666e9	+	2.44514e9i	−0.464243	+	1.01655i	0.522257	+	0.852788i	$0.325090\pi$
$479$	−1.11666e9	+	2.44514e9i	−0.464243	+	1.01655i	−0.986500	+	0.163762i	$0.947637\pi$
$480$	−2.40293e8	+	1.67128e9i	−0.0991738	+	0.689769i
$481$	3.77490e9	−	2.42598e9i	1.54667	−	0.993984i
$482$	−1.62210e9			−0.659803
$483$	8.54008e8	+	3.01987e7i	0.344863	+	0.0121948i
$484$	−3.92251e8			−0.157255
$485$	−2.72163e8	+	1.74908e8i	−0.108326	+	0.0696169i
$486$	1.87617e7	−	1.30491e8i	0.00741388	−	0.0515647i
$487$	−1.16746e9	+	2.55639e9i	−0.458028	+	1.00294i	0.529904	+	0.848058i	$0.322228\pi$
$487$	−1.16746e9	+	2.55639e9i	−0.458028	+	1.00294i	−0.987933	+	0.154885i	$0.950499\pi$
$488$	2.09938e9	−	6.16433e8i	0.817751	−	0.240113i
$489$	−2.16920e8	−	4.74988e8i	−0.0838914	−	0.183697i
$490$	−1.66008e9	−	1.91583e9i	−0.637445	−	0.735650i
$491$	−1.62063e8	−	1.12717e9i	−0.0617873	−	0.429740i	−0.997112	−	0.0759489i	$-0.975801\pi$
$491$	−1.62063e8	−	1.12717e9i	−0.0617873	−	0.429740i	0.935324	−	0.353791i	$-0.115108\pi$
$492$	4.46127e8	+	1.30995e8i	0.168881	+	0.0495879i
$493$	8.37330e7	−	9.66330e7i	0.0314726	−	0.0363213i
$494$	2.57316e9	+	1.65367e9i	0.960336	+	0.617171i
$495$	−1.70613e9	−	1.09646e9i	−0.632258	−	0.406327i
$496$	1.37708e9	−	1.58924e9i	0.506727	−	0.584794i
$497$	2.46768e9	+	7.24576e8i	0.901657	+	0.264751i
$498$	3.60365e8	+	2.50640e9i	0.130750	+	0.909384i
$499$	5.39459e8	+	6.22569e8i	0.194360	+	0.224303i	0.844562	−	0.535458i	$-0.179861\pi$
$499$	5.39459e8	+	6.22569e8i	0.194360	+	0.224303i	−0.650202	+	0.759762i	$0.725316\pi$
$500$	1.08956e9	+	2.38581e9i	0.389813	+	0.853572i
$501$	2.14058e9	−	6.28532e8i	0.760501	−	0.223303i
$502$	−9.99430e8	+	2.18845e9i	−0.352606	+	0.772099i
$503$	2.77087e8	−	1.92718e9i	0.0970796	−	0.675204i	−0.881929	−	0.471383i	$-0.843755\pi$
$503$	2.77087e8	−	1.92718e9i	0.0970796	−	0.675204i	0.979008	−	0.203821i	$-0.0653360\pi$
$504$	5.24403e8	−	3.37014e8i	0.182456	−	0.117257i
$505$	−2.84830e9			−0.984162
$506$	2.35094e9	+	1.63106e9i	0.806706	+	0.559683i
$507$	−1.49617e9			−0.509864
$508$	8.70680e8	−	5.59552e8i	0.294670	−	0.189373i
$509$	−1.94418e8	+	1.35221e9i	−0.0653468	+	0.454497i	0.930708	+	0.365762i	$0.119192\pi$
$509$	−1.94418e8	+	1.35221e9i	−0.0653468	+	0.454497i	−0.996055	+	0.0887351i	$0.971718\pi$
$510$	1.09242e8	−	2.39206e8i	0.0364664	−	0.0798502i
$511$	−2.37960e9	+	6.98712e8i	−0.788915	+	0.231646i
$512$	−1.19029e9	−	2.60636e9i	−0.391928	−	0.858203i
$513$	3.94764e8	+	4.55582e8i	0.129100	+	0.148990i
$514$	−1.98158e7	−	1.37822e8i	−0.00643636	−	0.0447659i
$515$	−2.05577e9	−	6.03628e8i	−0.663207	−	0.194735i
$516$	−2.28740e8	+	2.63981e8i	−0.0732941	+	0.0845859i
$517$	−8.13484e8	−	5.22794e8i	−0.258900	−	0.166385i
$518$	−1.73058e9	−	1.11218e9i	−0.547063	−	0.351576i
$519$	−1.23967e9	+	1.43066e9i	−0.389243	+	0.449210i
$520$	−8.57058e9	−	2.51655e9i	−2.67300	−	0.784862i
$521$	−5.57085e8	−	3.87461e9i	−0.172580	−	1.20032i	−0.873408	−	0.486989i	$-0.838095\pi$
$521$	−5.57085e8	−	3.87461e9i	−0.172580	−	1.20032i	0.700829	−	0.713330i	$-0.252814\pi$
$522$	2.75759e8	+	3.18242e8i	0.0848560	+	0.0979290i
$523$	1.69852e9	+	3.71924e9i	0.519176	+	1.13684i	0.969751	+	0.244098i	$0.0784918\pi$
$523$	1.69852e9	+	3.71924e9i	0.519176	+	1.13684i	−0.450575	+	0.892739i	$0.648781\pi$
$524$	−4.94741e7	+	1.45269e7i	−0.0150217	+	0.00441077i
$525$	1.17761e9	−	2.57861e9i	0.355177	−	0.777729i
$526$	−1.76772e8	+	1.22948e9i	−0.0529619	+	0.368358i
$527$	4.04021e8	−	2.59649e8i	0.120245	−	0.0772768i
$528$	1.28326e9			0.379398
$529$	1.19212e9	+	3.18931e9i	0.350127	+	0.936702i
$530$	3.85724e9			1.12541
$531$	5.86671e8	−	3.77031e8i	0.170045	−	0.109281i
$532$	−1.03046e8	+	7.16699e8i	−0.0296715	+	0.206370i
$533$	−1.78408e9	+	3.90659e9i	−0.510351	+	1.11751i
$534$	2.88644e8	−	8.47536e7i	0.0820292	−	0.0240859i
$535$	−1.63348e9	−	3.57683e9i	−0.461187	−	1.00986i
$536$	−4.29496e9	−	4.95665e9i	−1.20471	−	1.39031i
$537$	1.65270e8	+	1.14948e9i	0.0460557	+	0.320324i
$538$	−1.79234e9	−	5.26278e8i	−0.496229	−	0.145706i
$539$	1.85014e9	−	2.13517e9i	0.508913	−	0.587316i
$540$	−3.76200e8	−	2.41769e8i	−0.102811	−	0.0660727i
$541$	−1.48659e9	−	9.55372e8i	−0.403646	−	0.259407i	0.323029	−	0.946389i	$-0.395299\pi$
$541$	−1.48659e9	−	9.55372e8i	−0.403646	−	0.259407i	−0.726675	+	0.686982i	$0.758935\pi$
$542$	−1.35455e9	+	1.56323e9i	−0.365424	+	0.421722i
$543$	−8.40933e8	−	2.46920e8i	−0.225404	−	0.0661846i
$544$	−3.47246e7	−	2.41515e8i	−0.00924785	−	0.0643202i
$545$	6.76062e9	+	7.80217e9i	1.78895	+	2.06456i
$546$	6.07591e8	+	1.33044e9i	0.159749	+	0.349801i
$547$	6.38706e9	−	1.87541e9i	1.66857	−	0.489937i	0.695133	−	0.718881i	$-0.255345\pi$
$547$	6.38706e9	−	1.87541e9i	1.66857	−	0.489937i	0.973440	+	0.228944i	$0.0735272\pi$
$548$	−4.53553e8	+	9.93143e8i	−0.117732	+	0.257798i
$549$	−1.43992e8	+	1.00148e9i	−0.0371393	+	0.258310i
$550$	7.98516e9	−	5.13175e9i	2.04651	−	1.31521i
$551$	−1.92551e9			−0.490361
$552$	2.04067e9	+	1.41579e9i	0.516399	+	0.358272i
$553$	7.42810e8			0.186784
$554$	1.27069e9	−	8.16626e8i	0.317510	−	0.204051i
$555$	−8.26784e8	+	5.75041e9i	−0.205289	+	1.42782i
$556$	3.55461e8	−	7.78352e8i	0.0877062	−	0.192050i
$557$	−3.08091e9	+	9.04637e8i	−0.755416	+	0.221810i	−0.636693	−	0.771117i	$-0.719698\pi$
$557$	−3.08091e9	+	9.04637e8i	−0.755416	+	0.221810i	−0.118723	+	0.992927i	$0.537880\pi$
$558$	6.57040e8	+	1.43872e9i	0.160093	+	0.350555i
$559$	−2.11280e9	−	2.43830e9i	−0.511584	−	0.590399i
$560$	3.58298e8	+	2.49201e9i	0.0862156	+	0.599642i
$561$	2.81205e8	+	8.25692e7i	0.0672439	+	0.0197446i
$562$	2.22639e9	−	2.56939e9i	0.529083	−	0.610595i
$563$	3.64631e9	+	2.34334e9i	0.861141	+	0.553421i	0.895031	−	0.446004i	$-0.147153\pi$
$563$	3.64631e9	+	2.34334e9i	0.861141	+	0.553421i	−0.0338904	+	0.999426i	$0.510790\pi$
$564$	−1.79372e8	−	1.15275e8i	−0.0420996	−	0.0270558i
$565$	9.09080e9	−	1.04913e10i	2.12047	−	2.44716i
$566$	1.42389e9	+	4.18092e8i	0.330080	+	0.0969201i
$567$	4.10230e7	+	2.85321e8i	0.00945119	+	0.0657345i
$568$	4.89512e9	+	5.64927e9i	1.12084	+	1.29352i
$569$	1.15996e9	+	2.53996e9i	0.263968	+	0.578009i	0.994484	−	0.104886i	$-0.0334478\pi$
$569$	1.15996e9	+	2.53996e9i	0.263968	+	0.578009i	−0.730516	+	0.682895i	$0.760721\pi$
$570$	−3.79967e9	+	1.11568e9i	−0.859378	+	0.252336i
$571$	2.39186e8	−	5.23745e8i	0.0537663	−	0.117732i	−0.880842	−	0.473410i	$-0.843023\pi$
$571$	2.39186e8	−	5.23745e8i	0.0537663	−	0.117732i	0.934608	+	0.355678i	$0.115750\pi$
$572$	3.59889e8	−	2.50308e9i	0.0804049	−	0.559229i
$573$	−2.46785e9	+	1.58599e9i	−0.547996	+	0.352175i
$574$	1.96888e9			0.434537
$575$	1.12878e10	+	3.99151e8i	2.47613	+	0.0875587i
$576$	1.63450e9			0.356374
$577$	−5.04556e9	+	3.24258e9i	−1.09344	+	0.702710i	−0.957623	−	0.288025i	$-0.907001\pi$
$577$	−5.04556e9	+	3.24258e9i	−1.09344	+	0.702710i	−0.135814	+	0.990734i	$0.543365\pi$
$578$	5.31125e8	−	3.69405e9i	0.114406	−	0.795712i
$579$	5.32883e8	−	1.16685e9i	0.114092	−	0.249828i
$580$	1.37054e9	−	4.02426e8i	0.291671	−	0.0856422i
$581$	−2.30001e9	−	5.03632e9i	−0.486534	−	1.06536i
$582$	1.00827e8	+	1.16361e8i	0.0212006	+	0.0244668i
$583$	6.11790e8	+	4.25509e9i	0.127868	+	0.889342i
$584$	−6.91624e9	−	2.03079e9i	−1.43690	−	0.421911i
$585$	2.70493e9	−	3.12165e9i	0.558612	−	0.644672i
$586$	1.61915e9	+	1.04056e9i	0.332387	+	0.213612i
$587$	−5.00260e9	−	3.21498e9i	−1.02085	−	0.656061i	−0.0806716	−	0.996741i	$-0.525707\pi$
$587$	−5.00260e9	−	3.21498e9i	−1.02085	−	0.656061i	−0.940179	+	0.340680i	$0.889343\pi$
$588$	4.07953e8	−	4.70802e8i	0.0827540	−	0.0955032i
$589$	−6.93933e9	−	2.03757e9i	−1.39931	−	0.410875i
$590$	6.51979e8	+	4.53462e9i	0.130693	+	0.908989i
$591$	−1.86315e9	−	2.15019e9i	−0.371271	−	0.428469i
$592$	−1.52705e9	−	3.34377e9i	−0.302501	−	0.662385i
$593$	−7.47126e9	+	2.19376e9i	−1.47130	+	0.432014i	−0.916523	−	0.399982i	$-0.869016\pi$
$593$	−7.47126e9	+	2.19376e9i	−1.47130	+	0.432014i	−0.554782	+	0.831996i	$0.687198\pi$
$594$	−4.00955e8	+	8.77969e8i	−0.0784952	+	0.171881i
$595$	−8.18296e7	+	5.69138e8i	−0.0159258	+	0.110766i
$596$	−6.06147e8	+	3.89547e8i	−0.117278	+	0.0753699i
$597$	1.34189e9			0.258111
$598$	−3.96953e9	+	4.26660e9i	−0.759076	+	0.815883i
$599$	4.08082e9			0.775807			0.387903	−	0.921700i	$-0.373199\pi$
$599$	4.08082e9			0.775807			0.387903	+	0.921700i	$0.373199\pi$
$600$	6.93129e9	−	4.45447e9i	1.31004	−	0.841912i
$601$	7.13310e8	−	4.96118e9i	0.134035	−	0.932233i	−0.806185	−	0.591664i	$-0.798471\pi$
$601$	7.13310e8	−	4.96118e9i	0.134035	−	0.932233i	0.940220	−	0.340569i	$-0.110620\pi$
$602$	−6.14438e8	+	1.34543e9i	−0.114786	+	0.251347i
$603$	2.90998e9	−	8.54448e8i	0.540480	−	0.158699i
$604$	8.39964e8	+	1.83926e9i	0.155107	+	0.339637i
$605$	3.07179e9	+	3.54504e9i	0.563959	+	0.650844i
$606$	1.92914e8	+	1.34175e9i	0.0352136	+	0.244916i
$607$	6.86798e9	+	2.01662e9i	1.24643	+	0.365985i	0.837428	−	0.546547i	$-0.184058\pi$
$607$	6.86798e9	+	2.01662e9i	1.24643	+	0.365985i	0.409004	+	0.912533i	$0.365876\pi$
$608$	−2.40621e9	+	2.77692e9i	−0.434182	+	0.501072i
$609$	−7.74572e8	−	4.97787e8i	−0.138964	−	0.0893065i
$610$	−5.59152e9	−	3.59345e9i	−0.997414	−	0.640999i
$611$	1.28971e9	−	1.48841e9i	0.228743	−	0.263984i
$612$	6.20053e7	+	1.82064e7i	0.0109345	+	0.00321066i
$613$	−4.48461e7	−	3.11912e8i	−0.00786345	−	0.0546915i	0.985512	−	0.169606i	$-0.0542496\pi$
$613$	−4.48461e7	−	3.11912e8i	−0.00786345	−	0.0546915i	−0.993375	+	0.114915i	$0.963341\pi$
$614$	−1.75505e9	−	2.02543e9i	−0.305984	−	0.353125i
$615$	−2.30982e9	−	5.05780e9i	−0.400419	−	0.876796i
$616$	−4.37896e9	+	1.28578e9i	−0.754812	+	0.221633i
$617$	2.31889e9	−	5.07765e9i	0.397449	−	0.870292i	−0.600074	−	0.799945i	$-0.704862\pi$
$617$	2.31889e9	−	5.07765e9i	0.397449	−	0.870292i	0.997523	−	0.0703470i	$-0.0224107\pi$
$618$	−1.45114e8	+	1.00929e9i	−0.0247315	+	0.172011i
$619$	−6.90402e9	+	4.43695e9i	−1.17000	+	0.751912i	−0.973521	−	0.228597i	$-0.926586\pi$
$619$	−6.90402e9	+	4.43695e9i	−1.17000	+	0.751912i	−0.196477	+	0.980509i	$0.562950\pi$
$620$	5.36511e9			0.904082
$621$	−9.87537e8	+	5.86405e8i	−0.165475	+	0.0982600i
$622$	−1.26984e9			−0.211584
$623$	−5.53353e8	+	3.55619e8i	−0.0916842	+	0.0589218i
$624$	−3.71951e8	+	2.58698e9i	−0.0612829	+	0.426232i
$625$	6.74745e9	−	1.47749e10i	1.10550	−	2.42071i
$626$	−5.62675e9	+	1.65216e9i	−0.916742	+	0.269180i
$627$	−1.83342e9	−	4.01463e9i	−0.297047	−	0.650442i
$628$	−2.17179e9	−	2.50638e9i	−0.349912	−	0.403820i
$629$	−1.19478e8	−	8.30987e8i	−0.0191430	−	0.133143i
$630$	−1.81692e9	−	5.33494e8i	−0.289496	−	0.0850037i
$631$	1.57469e9	−	1.81729e9i	0.249513	−	0.287953i	−0.617152	−	0.786844i	$-0.711714\pi$
$631$	1.57469e9	−	1.81729e9i	0.249513	−	0.287953i	0.866665	+	0.498891i	$0.166259\pi$
$632$	1.81623e9	+	1.16722e9i	0.286195	+	0.183926i
$633$	−3.05869e9	−	1.96570e9i	−0.479317	−	0.308038i
$634$	5.32501e9	−	6.14538e9i	0.829865	−	0.957716i
$635$	−1.18755e10	−	3.48697e9i	−1.84054	−	0.540430i
$636$	1.34899e8	+	9.38242e8i	0.0207926	+	0.144615i
$637$	3.76812e9	+	4.34864e9i	0.577613	+	0.666601i
$638$	−1.28072e9	−	2.80438e9i	−0.195245	−	0.427528i
$639$	−3.31661e9	+	9.73845e8i	−0.502853	+	0.147651i
$640$	−1.13528e9	+	2.48592e9i	−0.171188	+	0.374850i
$641$	−1.42076e9	+	9.88158e9i	−0.213067	+	1.48192i	0.549765	+	0.835319i	$0.314717\pi$
$641$	−1.42076e9	+	9.88158e9i	−0.213067	+	1.48192i	−0.762832	+	0.646596i	$0.776192\pi$
$642$	−1.57430e9	+	1.01174e9i	−0.234809	+	0.150903i
$643$	−8.27155e9			−1.22701			−0.613505	−	0.789691i	$-0.710241\pi$
$643$	−8.27155e9			−1.22701			−0.613505	+	0.789691i	$0.710241\pi$
$644$	−1.30908e9	−	4.35191e8i	−0.193138	−	0.0642066i
$645$	4.17708e9			0.612935
$646$	4.81423e8	−	3.09392e8i	0.0702608	−	0.0451539i
$647$	−4.00693e8	+	2.78688e9i	−0.0581629	+	0.404532i	0.939853	+	0.341578i	$0.110961\pi$
$647$	−4.00693e8	+	2.78688e9i	−0.0581629	+	0.404532i	−0.998016	+	0.0629543i	$0.979948\pi$
$648$	−3.48038e8	+	7.62096e8i	−0.0502474	+	0.110026i
$649$	−4.89892e9	+	1.43845e9i	−0.703468	+	0.206557i
$650$	8.03082e9	+	1.75850e10i	1.14700	+	2.51158i
$651$	−2.26471e9	−	2.61362e9i	−0.321721	−	0.371286i
$652$	1.19967e8	+	8.34392e8i	0.0169511	+	0.117897i
$653$	9.55387e9	+	2.80527e9i	1.34271	+	0.394256i	0.872637	−	0.488370i	$-0.162408\pi$
$653$	9.55387e9	+	2.80527e9i	1.34271	+	0.394256i	0.470076	+	0.882626i	$0.344226\pi$
$654$	3.21747e9	−	3.71316e9i	0.449772	−	0.519065i
$655$	5.18731e8	+	3.33368e8i	0.0721270	+	0.0463532i
$656$	2.95972e9	+	1.90210e9i	0.409343	+	0.263069i
$657$	2.18281e9	−	2.51910e9i	0.300287	−	0.346550i
$658$	−8.66306e8	−	2.54370e8i	−0.118544	−	0.0348077i
$659$	1.57293e9	+	1.09399e10i	0.214097	+	1.48907i	0.759284	+	0.650760i	$0.225550\pi$
$659$	1.57293e9	+	1.09399e10i	0.214097	+	1.48907i	−0.545187	+	0.838314i	$0.683541\pi$
$660$	2.14403e9	+	2.47434e9i	0.290287	+	0.335009i
$661$	5.25416e9	+	1.15050e10i	0.707617	+	1.54947i	0.830484	+	0.557042i	$0.188064\pi$
$661$	5.25416e9	+	1.15050e10i	0.707617	+	1.54947i	−0.122867	+	0.992423i	$0.539209\pi$
$662$	2.76683e9	−	8.12415e8i	0.370663	−	0.108837i
$663$	−2.47962e8	+	5.42960e8i	−0.0330436	+	0.0723553i
$664$	2.29015e9	−	1.59284e10i	0.303582	−	2.11146i
$665$	7.28427e9	−	4.68131e9i	0.960528	−	0.617294i
$666$	2.76484e9			0.362669
$667$	6.50089e8	−	3.61051e9i	0.0848267	−	0.471116i
$668$	−3.60153e9			−0.467487
$669$	−3.63692e9	+	2.33730e9i	−0.469615	+	0.301803i
$670$	−2.83540e9	+	1.97207e10i	−0.364211	+	2.53314i
$671$	3.07723e9	−	6.73820e9i	0.393216	−	0.861023i
$672$	−1.68584e9	+	4.95006e8i	−0.214300	+	0.0629243i
$673$	5.50893e9	+	1.20629e10i	0.696650	+	1.52545i	0.843987	+	0.536364i	$0.180202\pi$
$673$	5.50893e9	+	1.20629e10i	0.696650	+	1.52545i	−0.147337	+	0.989086i	$0.547070\pi$
$674$	−3.54885e9	−	4.09559e9i	−0.446455	−	0.515237i
$675$	5.42221e8	+	3.77123e9i	0.0678598	+	0.471975i
$676$	2.31751e9	+	6.80481e8i	0.288541	+	0.0847232i
$677$	7.18371e8	−	8.29044e8i	0.0889792	−	0.102687i	−0.709514	−	0.704691i	$-0.751085\pi$
$677$	7.18371e8	−	8.29044e8i	0.0889792	−	0.102687i	0.798493	+	0.602004i	$0.205631\pi$
$678$	−5.55787e9	−	3.57182e9i	−0.684864	−	0.440135i
$679$	−2.83212e8	−	1.82009e8i	−0.0347190	−	0.0223125i
$680$	−1.09440e9	+	1.26301e9i	−0.133474	+	0.154037i
$681$	5.38343e9	+	1.58072e9i	0.653197	+	0.191796i
$682$	−1.64798e9	−	1.14619e10i	−0.198932	−	1.38361i
$683$	−8.71945e9	−	1.00628e10i	−1.04717	−	1.20850i	−0.977502	−	0.210926i	$-0.932352\pi$
$683$	−8.71945e9	−	1.00628e10i	−1.04717	−	1.20850i	−0.0696661	−	0.997570i	$-0.522193\pi$
$684$	−4.04266e8	−	8.85220e8i	−0.0483027	−	0.105768i
$685$	1.25276e10	−	3.67843e9i	1.48919	−	0.437265i
$686$	2.80071e9	−	6.13271e9i	0.331234	−	0.725301i
$687$	−8.92212e8	+	6.20547e9i	−0.104983	+	0.730173i
$688$	−2.22346e9	+	1.42893e9i	−0.260297	+	0.167283i
$689$	−8.75534e9			−1.01978
$690$	−8.09167e8	−	7.50140e9i	−0.0937705	−	0.869302i
$691$	5.92562e9			0.683220			0.341610	−	0.939842i	$-0.389028\pi$
$691$	5.92562e9			0.683220			0.341610	+	0.939842i	$0.389028\pi$
$692$	2.57088e9	−	1.65220e9i	0.294924	−	0.189536i
$693$	3.00343e8	−	2.08893e9i	0.0342809	−	0.238429i
$694$	−2.91516e9	+	6.38330e9i	−0.331058	+	0.724915i
$695$	−9.81818e9	+	2.88288e9i	−1.10939	+	0.325746i
$696$	−1.11169e9	−	2.43426e9i	−0.124983	−	0.273675i
$697$	5.26187e8	+	6.07252e8i	0.0588607	+	0.0679289i
$698$	1.63080e9	+	1.13425e10i	0.181513	+	1.26245i
$699$	7.08974e9	+	2.08174e9i	0.785164	+	0.230545i
$700$	−2.99686e9	+	3.45856e9i	−0.330235	+	0.381111i
$701$	−1.85332e9	−	1.19106e9i	−0.203206	−	0.130593i	0.435080	−	0.900392i	$-0.356720\pi$
$701$	−1.85332e9	−	1.19106e9i	−0.203206	−	0.130593i	−0.638286	+	0.769799i	$0.720356\pi$
$702$	−1.65372e9	−	1.06278e9i	−0.180419	−	0.115948i
$703$	−8.27913e9	+	9.55463e9i	−0.898755	+	1.03722i
$704$	−1.14820e10	−	3.37142e9i	−1.24026	−	0.364174i
$705$	3.62875e8	+	2.52385e9i	0.0390027	+	0.271270i
$706$	5.43396e9	+	6.27112e9i	0.581165	+	0.670701i
$707$	−1.23126e9	−	2.69609e9i	−0.131034	−	0.286924i
$708$	−1.08021e9	+	3.17177e8i	−0.114391	+	0.0335881i
$709$	−3.29471e8	+	7.21441e8i	−0.0347181	+	0.0760220i	−0.926196	−	0.377041i	$-0.876942\pi$
$709$	−3.29471e8	+	7.21441e8i	−0.0347181	+	0.0760220i	0.891478	+	0.453063i	$0.149669\pi$
$710$	3.23161e9	−	2.24763e10i	0.338855	−	2.35679i
$711$	−8.39866e8	+	5.39749e8i	−0.0876328	+	0.0563182i
$712$	−1.91180e9			−0.198501
$713$	6.16348e9	−	1.23239e10i	0.636814	−	1.27332i
$714$	2.73646e8			0.0281349
$715$	−2.54404e10	+	1.63496e10i	−2.60288	+	1.67277i
$716$	2.66802e8	−	1.85565e9i	0.0271640	−	0.188930i
$717$	−2.73985e9	+	5.99944e9i	−0.277594	+	0.607846i
$718$	−9.87672e9	+	2.90007e9i	−0.995812	+	0.292397i
$719$	2.66838e9	+	5.84294e9i	0.267730	+	0.586247i	0.994974	−	0.100132i	$-0.0319265\pi$
$719$	2.66838e9	+	5.84294e9i	0.267730	+	0.586247i	−0.727244	+	0.686379i	$0.759199\pi$
$720$	−2.21589e9	−	2.55727e9i	−0.221251	−	0.255337i
$721$	−3.17296e8	−	2.20684e9i	−0.0315276	−	0.219280i
$722$	−3.88854e8	−	1.14178e8i	−0.0384509	−	0.0112902i
$723$	−3.12167e9	+	3.60260e9i	−0.307188	+	0.354513i
$724$	1.19026e9	+	7.64936e8i	0.116562	+	0.0749100i
$725$	−1.02379e10	−	6.57949e9i	−0.997763	−	0.641223i
$726$	1.46191e9	−	1.68713e9i	0.141789	−	0.163633i
$727$	−6.39158e9	−	1.87674e9i	−0.616933	−	0.181148i	−0.0416903	−	0.999131i	$-0.513274\pi$
$727$	−6.39158e9	−	1.87674e9i	−0.616933	−	0.181148i	−0.575243	+	0.817983i	$0.695092\pi$
$728$	−1.32282e9	−	9.20042e9i	−0.127069	−	0.883787i
$729$	−2.53706e8	−	2.92793e8i	−0.0242541	−	0.0279907i
$730$	9.09630e9	+	1.99181e10i	0.865436	+	1.89504i
$731$	−5.79176e8	+	1.70061e8i	−0.0548403	+	0.0161026i
$732$	6.78525e8	−	1.48576e9i	0.0639407	−	0.140011i
$733$	−1.89933e9	+	1.32101e10i	−0.178130	+	1.23892i	0.682956	+	0.730460i	$0.260694\pi$
$733$	−1.89933e9	+	1.32101e10i	−0.178130	+	1.23892i	−0.861086	+	0.508460i	$0.830215\pi$
$734$	2.13490e9	−	1.37202e9i	0.199270	−	0.128063i
$735$	−7.44972e9			−0.692045
$736$	−4.39459e9	−	5.44940e9i	−0.406299	−	0.503821i
$737$	−2.22044e10			−2.04317
$738$	−2.22613e9	+	1.43065e9i	−0.203870	+	0.131019i
$739$	−5.30365e8	+	3.68877e9i	−0.0483414	+	0.336222i	0.951270	+	0.308358i	$0.0997795\pi$
$739$	−5.30365e8	+	3.68877e9i	−0.0483414	+	0.336222i	−0.999612	+	0.0278637i	$0.991130\pi$
$740$	3.89602e9	−	8.53109e9i	0.353435	−	0.773915i
$741$	8.62467e9	−	2.53243e9i	0.778715	−	0.228651i
$742$	1.66741e9	+	3.65111e9i	0.149840	+	0.328104i
$743$	6.97952e9	+	8.05480e9i	0.624259	+	0.720434i	0.976510	−	0.215472i	$-0.0691290\pi$
$743$	6.97952e9	+	8.05480e9i	0.624259	+	0.720434i	−0.352251	+	0.935906i	$0.614584\pi$
$744$	−1.43048e9	−	9.94920e9i	−0.127343	−	0.885692i
$745$	8.26746e9	+	2.42755e9i	0.732530	+	0.215090i
$746$	7.90642e9	−	9.12449e9i	0.697258	−	0.804679i
$747$	6.26008e9	+	4.02311e9i	0.549487	+	0.353134i
$748$	−3.98020e8	−	2.55792e8i	−0.0347736	−	0.0223476i
$749$	2.67957e9	−	3.09238e9i	0.233012	−	0.268910i
$750$	−1.43225e10	−	4.20546e9i	−1.23966	−	0.363998i
$751$	1.39715e9	+	9.71742e9i	0.120366	+	0.837165i	0.957142	+	0.289619i	$0.0935287\pi$
$751$	1.39715e9	+	9.71742e9i	0.120366	+	0.837165i	−0.836776	+	0.547546i	$0.815562\pi$
$752$	−1.05654e9	−	1.21931e9i	−0.0905987	−	0.104557i
$753$	2.93706e9	+	6.43126e9i	0.250686	+	0.548926i
$754$	6.02468e9	−	1.76901e9i	0.511840	−	0.150290i
$755$	1.00448e10	−	2.19950e10i	0.849426	−	1.85998i
$756$	6.62253e7	−	4.60607e8i	0.00557439	−	0.0387708i
$757$	2.44387e9	−	1.57058e9i	0.204759	−	0.131590i	−0.434243	−	0.900796i	$-0.642984\pi$
$757$	2.44387e9	−	1.57058e9i	0.204759	−	0.131590i	0.639002	+	0.769205i	$0.279348\pi$
$758$	3.59179e9			0.299550
$759$	8.14678e9	−	2.08241e9i	0.676301	−	0.172870i
$760$	2.51667e10			2.07959
$761$	−6.74525e9	+	4.33491e9i	−0.554819	+	0.356561i	−0.787810	−	0.615918i	$-0.788785\pi$
$761$	−6.74525e9	+	4.33491e9i	−0.554819	+	0.356561i	0.232991	+	0.972479i	$0.425149\pi$
$762$	−8.38279e8	+	5.83036e9i	−0.0686351	+	0.477368i
$763$	−4.46275e9	+	9.77206e9i	−0.363719	+	0.796434i
$764$	4.54391e9	−	1.33421e9i	0.368641	−	0.108243i
$765$	−3.21032e8	−	7.02962e8i	−0.0259259	−	0.0567697i
$766$	−1.10008e10	−	1.26956e10i	−0.884348	−	1.02059i
$767$	−1.47989e9	−	1.02929e10i	−0.118426	−	0.823670i
$768$	−6.18693e9	−	1.81665e9i	−0.492846	−	0.144713i
$769$	−4.09291e9	+	4.72347e9i	−0.324556	+	0.374558i	−0.894456	−	0.447157i	$-0.852437\pi$
$769$	−4.09291e9	+	4.72347e9i	−0.324556	+	0.374558i	0.569900	+	0.821714i	$0.306982\pi$
$770$	1.16630e10	+	7.49536e9i	0.920647	+	0.591664i
$771$	−3.44229e8	−	2.21223e8i	−0.0270494	−	0.0173836i
$772$	−1.35611e9	+	1.56504e9i	−0.106080	+	0.122423i
$773$	6.26626e9	+	1.83994e9i	0.487956	+	0.143277i	0.516450	−	0.856317i	$-0.327253\pi$
$773$	6.26626e9	+	1.83994e9i	0.487956	+	0.143277i	−0.0284946	+	0.999594i	$0.509071\pi$
$774$	−2.82912e8	−	1.96770e9i	−0.0219310	−	0.152533i
$775$	−2.99338e10	−	3.45455e10i	−2.30997	−	2.66585i
$776$	−4.06474e8	−	8.90055e8i	−0.0312261	−	0.0683755i
$777$	−5.80051e9	+	1.70318e9i	−0.443601	+	0.130253i
$778$	5.03845e9	−	1.10327e10i	0.383591	−	0.839948i
$779$	1.72203e9	−	1.19770e10i	0.130514	−	0.907748i
$780$	−5.60958e9	+	3.60506e9i	−0.423252	+	0.272008i
$781$	2.53072e10			1.90092
$782$	4.17600e8	+	1.00717e9i	0.0312275	+	0.0753144i
$783$	1.23749e9			0.0921243
$784$	3.96548e9	−	2.54846e9i	0.293893	−	0.188874i
$785$	−5.64414e9	+	3.92558e10i	−0.416441	+	2.89641i
$786$	1.21906e8	−	2.66937e8i	0.00895461	−	0.0196079i
$787$	7.37000e9	−	2.16403e9i	0.538959	−	0.158253i	−0.000913218	−	1.00000i	$-0.500291\pi$
$787$	7.37000e9	−	2.16403e9i	0.538959	−	0.158253i	0.539872	+	0.841747i	$0.318473\pi$
$788$	1.90799e9	+	4.17792e9i	0.138911	+	0.304172i
$789$	2.39041e9	+	2.75868e9i	0.173262	+	0.199955i
$790$	−9.33360e8	−	6.49166e9i	−0.0673526	−	0.468448i
$791$	1.38605e10	+	4.06980e9i	0.995772	+	0.292385i
$792$	4.01683e9	−	4.63567e9i	0.287307	−	0.331570i
$793$	1.26919e10	+	8.15658e9i	0.903795	+	0.580834i
$794$	1.42263e10	+	9.14266e9i	1.00860	+	0.648188i
$795$	7.42311e9	−	8.56672e9i	0.523963	−	0.604686i
$796$	−2.07852e9	−	6.10309e8i	−0.146069	−	0.0428898i
$797$	−2.46158e9	−	1.71207e10i	−0.172230	−	1.19789i	−0.874158	−	0.485641i	$-0.838586\pi$
$797$	−2.46158e9	−	1.71207e10i	−0.172230	−	1.19789i	0.701928	−	0.712248i	$-0.252323\pi$
$798$	−2.69858e9	−	3.11433e9i	−0.187986	−	0.216947i
$799$	−1.53068e8	−	3.35172e8i	−0.0106162	−	0.0232463i
$800$	−2.22825e10	+	6.54273e9i	−1.53868	+	0.451798i
$801$	3.67251e8	−	8.04168e8i	0.0252493	−	0.0552883i
$802$	1.82811e9	−	1.27148e10i	0.125139	−	0.870361i
$803$	−2.05298e10	+	1.31937e10i	−1.39920	+	0.899212i
$804$	−4.89605e9			−0.332238
$805$	6.31857e9	+	1.52391e10i	0.426907	+	1.02962i
$806$	2.35842e10			1.58653
$807$	−4.61812e9	+	2.96788e9i	−0.309320	+	0.198788i
$808$	1.22599e9	−	8.52693e9i	0.0817610	−	0.568660i
$809$	−3.93215e9	+	8.61020e9i	−0.261102	+	0.571733i	−0.994096	−	0.108501i	$-0.965395\pi$
$809$	−3.93215e9	+	8.61020e9i	−0.261102	+	0.571733i	0.732994	+	0.680235i	$0.238122\pi$
$810$	2.44197e9	−	7.17027e8i	0.161452	−	0.0474065i
$811$	−1.34483e9	−	2.94478e9i	−0.0885311	−	0.193856i	0.860187	−	0.509978i	$-0.170346\pi$
$811$	−1.34483e9	−	2.94478e9i	−0.0885311	−	0.193856i	−0.948719	+	0.316122i	$0.897619\pi$
$812$	9.73375e8	+	1.12334e9i	0.0638020	+	0.0736314i
$813$	8.65079e8	+	6.01675e9i	0.0564597	+	0.392686i
$814$	−1.94224e10	−	5.70293e9i	−1.26217	−	0.370606i
$815$	6.60148e9	−	7.61851e9i	0.427159	−	0.492968i
$816$	4.11360e8	+	2.64365e8i	0.0265037	+	0.0170329i
$817$	7.64705e9	+	4.91446e9i	0.490588	+	0.315282i
$818$	7.09734e9	−	8.19077e9i	0.453376	−	0.523224i
$819$	4.12412e9	+	1.21095e9i	0.262324	+	0.0770252i
$820$	1.27745e9	+	8.88483e9i	0.0809085	+	0.562731i
$821$	1.52725e10	+	1.76254e10i	0.963186	+	1.11158i	0.993704	+	0.112042i	$0.0357390\pi$
$821$	1.52725e10	+	1.76254e10i	0.963186	+	1.11158i	−0.0305175	+	0.999534i	$0.509716\pi$
$822$	−2.58128e9	−	5.65222e9i	−0.162100	−	0.354950i
$823$	−2.06152e10	+	6.05316e9i	−1.28910	+	0.378515i	−0.853249	−	0.521503i	$-0.825371\pi$
$823$	−2.06152e10	+	6.05316e9i	−1.28910	+	0.378515i	−0.435853	+	0.900018i	$0.643553\pi$
$824$	2.69193e9	−	5.89451e9i	0.167617	−	0.367031i
$825$	3.96978e9	−	2.76105e10i	0.246138	−	1.71193i
$826$	−4.01045e9	+	2.57736e9i	−0.247607	+	0.159127i
$827$	−1.85359e8			−0.0113958			−0.00569789	−	0.999984i	$-0.501814\pi$
$827$	−1.85359e8			−0.0113958			−0.00569789	+	0.999984i	$0.501814\pi$
$828$	1.79635e9	−	4.59168e8i	0.109973	−	0.0281103i
$829$	2.12370e10			1.29465			0.647324	−	0.762215i	$-0.275888\pi$
$829$	2.12370e10			1.29465			0.647324	+	0.762215i	$0.275888\pi$
$830$	−4.11240e10	+	2.64288e10i	−2.49645	+	1.60437i
$831$	6.31720e8	−	4.39371e9i	0.0381875	−	0.265600i
$832$	1.01246e10	−	2.21699e10i	0.609464	−	1.33454i
$833$	1.03294e9	−	3.03300e8i	0.0619184	−	0.0181809i
$834$	2.02302e9	+	4.42979e9i	0.120759	+	0.264424i
$835$	2.82043e10	+	3.25495e10i	1.67653	+	1.93482i
$836$	1.01397e9	+	7.05234e9i	0.0600212	+	0.417456i
$837$	4.45976e9	+	1.30950e9i	0.262889	+	0.0771912i
$838$	−9.61523e8	+	1.10966e9i	−0.0564424	+	0.0651380i
$839$	4.77290e9	+	3.06735e9i	0.279007	+	0.179307i	0.672659	−	0.739953i	$-0.265152\pi$
$839$	4.77290e9	+	3.06735e9i	0.279007	+	0.179307i	−0.393652	+	0.919260i	$0.628788\pi$
$840$	1.01237e10	+	6.50614e9i	0.589337	+	0.378744i
$841$	8.70777e9	−	1.00493e10i	0.504802	−	0.582573i
$842$	1.93880e10	+	5.69283e9i	1.11928	+	0.328652i
$843$	−1.42188e9	−	9.88938e9i	−0.0817459	−	0.568555i
$844$	3.84375e9	+	4.43592e9i	0.220068	+	0.253972i
$845$	−1.19989e10	−	2.62738e10i	−0.684135	−	1.49805i
$846$	1.16433e9	−	3.41879e8i	0.0661120	−	0.0194122i
$847$	−2.02772e9	+	4.44008e9i	−0.114661	+	0.251072i
$848$	−1.02074e9	+	7.09941e9i	−0.0574818	+	0.399795i
$849$	3.66878e9	−	2.35778e9i	0.205752	−	0.132229i
$850$	3.61691e9			0.202009
$851$	−1.51206e10	−	1.87499e10i	−0.841037	−	1.04291i
$852$	5.58020e9			0.309108
$853$	−1.19064e10	+	7.65177e9i	−0.656838	+	0.422124i	−0.826159	−	0.563437i	$-0.809479\pi$
$853$	−1.19064e10	+	7.65177e9i	−0.656838	+	0.422124i	0.169321	+	0.985561i	$0.445842\pi$
$854$	9.84318e8	−	6.84608e9i	0.0540795	−	0.376131i
$855$	−4.83444e9	+	1.05860e10i	−0.264524	+	0.579227i
$856$	1.14110e10	−	3.35058e9i	0.621822	−	0.182583i
$857$	7.13194e9	+	1.56168e10i	0.387057	+	0.847536i	0.998420	+	0.0561862i	$0.0178940\pi$
$857$	7.13194e9	+	1.56168e10i	0.387057	+	0.847536i	−0.611364	+	0.791350i	$0.709379\pi$
$858$	9.42485e9	+	1.08769e10i	0.509412	+	0.587893i
$859$	−2.61113e9	−	1.81608e10i	−0.140557	−	0.977595i	−0.930990	−	0.365046i	$-0.881053\pi$
$859$	−2.61113e9	−	1.81608e10i	−0.140557	−	0.977595i	0.790433	−	0.612549i	$-0.209856\pi$
$860$	−6.47011e9	−	1.89980e9i	−0.346870	−	0.101850i
$861$	3.78902e9	−	4.37276e9i	0.202309	−	0.233478i
$862$	1.13595e10	+	7.30032e9i	0.604066	+	0.388210i
$863$	−2.83050e9	−	1.81905e9i	−0.149908	−	0.0963401i	0.463537	−	0.886078i	$-0.346580\pi$
$863$	−2.83050e9	−	1.81905e9i	−0.149908	−	0.0963401i	−0.613445	+	0.789738i	$0.710217\pi$
$864$	1.54642e9	−	1.78467e9i	0.0815699	−	0.0941367i
$865$	−3.50651e10	−	1.02960e10i	−1.84212	−	0.540896i
$866$	−3.69232e9	−	2.56807e10i	−0.193191	−	1.34367i
$867$	−7.18216e9	−	8.28866e9i	−0.374273	−	0.431934i
$868$	2.31923e9	+	5.07840e9i	0.120372	+	0.263577i
$869$	7.01319e9	−	2.05926e9i	0.362532	−	0.106449i
$870$	−3.37706e9	+	7.39472e9i	−0.173868	+	0.380719i
$871$	6.43593e9	−	4.47628e10i	0.330025	−	2.29538i
$872$	−2.62672e10	+	1.68809e10i	−1.34155	+	0.862161i
$873$	4.52470e8			0.0230165
$874$	7.34427e9	−	1.46849e10i	0.372099	−	0.744016i
$875$	3.26385e10			1.64703
$876$	−4.52679e9	+	2.90919e9i	−0.227523	+	0.146220i
$877$	4.83099e8	−	3.36003e9i	0.0241845	−	0.168207i	−0.974150	−	0.225904i	$-0.927467\pi$
$877$	4.83099e8	−	3.36003e9i	0.0241845	−	0.168207i	0.998334	+	0.0576967i	$0.0183756\pi$
$878$	−7.63849e9	+	1.67260e10i	−0.380870	+	0.833989i
$879$	5.42701e9	−	1.59352e9i	0.269526	−	0.0791398i
$880$	1.02913e10	+	2.25349e10i	0.509076	+	1.11472i
$881$	1.73151e10	+	1.99827e10i	0.853117	+	0.984549i	0.999989	−	0.00460602i	$-0.00146615\pi$
$881$	1.73151e10	+	1.99827e10i	0.853117	+	0.984549i	−0.146872	+	0.989155i	$0.546921\pi$
$882$	5.04566e8	+	3.50933e9i	0.0247615	+	0.172220i
$883$	−1.97859e9	−	5.80966e8i	−0.0967149	−	0.0283980i	0.233017	−	0.972473i	$-0.425140\pi$
$883$	−1.97859e9	−	5.80966e8i	−0.0967149	−	0.0283980i	−0.329732	+	0.944075i	$0.606958\pi$
$884$	6.31027e8	−	7.28244e8i	0.0307231	−	0.0354563i
$885$	1.13258e10	+	7.27868e9i	0.549249	+	0.352981i
$886$	−1.51036e10	−	9.70652e9i	−0.729564	−	0.468862i
$887$	2.55379e10	−	2.94723e10i	1.22872	−	1.41802i	0.352700	−	0.935736i	$-0.385264\pi$
$887$	2.55379e10	−	2.94723e10i	1.22872	−	1.41802i	0.876018	−	0.482279i	$-0.160191\pi$
$888$	−1.68591e10	−	4.95026e9i	−0.807956	−	0.237237i
$889$	−1.83292e9	−	1.27482e10i	−0.0874958	−	0.608547i
$890$	3.80317e9	+	4.38909e9i	0.180834	+	0.208694i
$891$	1.17830e9	+	2.58012e9i	0.0558064	+	0.122199i
$892$	6.69645e9	−	1.96626e9i	0.315913	−	0.0927605i
$893$	−2.30506e9	+	5.04739e9i	−0.108319	+	0.237185i
$894$	5.83591e8	−	4.05896e9i	0.0273166	−	0.189991i
$895$	−1.88602e10	+	1.21207e10i	−0.879356	+	0.565128i
$896$	−2.84384e9			−0.132077
$897$	1.83668e9	+	1.70270e10i	0.0849691	+	0.787708i
$898$	−1.94829e10			−0.897815
$899$	−1.24898e10	+	8.02669e9i	−0.573318	+	0.368449i
$900$	8.75332e8	−	6.08807e9i	0.0400243	−	0.278375i
$901$	−6.80479e8	+	1.49004e9i	−0.0309940	+	0.0678674i
$902$	1.85890e10	−	5.45823e9i	0.843400	−	0.247645i
$903$	1.80567e9	+	3.95386e9i	0.0816076	+	0.178696i
$904$	2.74949e10	+	3.17308e10i	1.23783	+	1.42854i
$905$	−2.40794e9	−	1.67476e10i	−0.107988	−	0.751073i
$906$	−1.10415e10	−	3.24207e9i	−0.493263	−	0.144835i
$907$	−7.73262e8	+	8.92392e8i	−0.0344113	+	0.0397128i	−0.772694	−	0.634778i	$-0.781091\pi$
$907$	−7.73262e8	+	8.92392e8i	−0.0344113	+	0.0397128i	0.738283	+	0.674491i	$0.235637\pi$
$908$	−7.61975e9	−	4.89692e9i	−0.337785	−	0.217081i
$909$	3.35121e9	+	2.15369e9i	0.147988	+	0.0951064i
$910$	−1.84907e10	+	2.13394e10i	−0.813409	+	0.938724i
$911$	−3.60287e10	−	1.05790e10i	−1.57882	−	0.463585i	−0.629270	−	0.777187i	$-0.716646\pi$
$911$	−3.60287e10	−	1.05790e10i	−1.57882	−	0.463585i	−0.949555	+	0.313602i	$0.898464\pi$
$912$	−1.04796e9	−	7.28870e9i	−0.0457469	−	0.318176i
$913$	−3.56774e10	−	4.11739e10i	−1.55148	−	1.79050i
$914$	2.03968e9	+	4.46627e9i	0.0883588	+	0.193479i
$915$	−1.87415e10	+	5.50300e9i	−0.808781	+	0.237479i
$916$	4.20433e9	−	9.20619e9i	0.180743	−	0.395773i
$917$	−9.13163e7	+	6.35119e8i	−0.00391071	+	0.0271996i
$918$	−3.09400e8	+	1.98840e8i	−0.0131999	+	0.00848308i
$919$	3.27332e10			1.39118			0.695592	−	0.718437i	$-0.255142\pi$
$919$	3.27332e10			1.39118			0.695592	+	0.718437i	$0.255142\pi$
$920$	−8.49675e9	+	4.71898e10i	−0.359745	+	1.99798i
$921$	−7.87589e9			−0.332193
$922$	1.63415e10	−	1.05020e10i	0.686646	−	0.441280i
$923$	−7.33525e9	+	5.10178e10i	−0.307050	+	2.13558i
$924$	−1.41529e9	+	3.09906e9i	−0.0590194	+	0.129235i
$925$	−7.66681e10	+	2.25118e10i	−3.18507	+	0.935220i
$926$	−9.54795e9	−	2.09071e10i	−0.395159	−	0.865277i
$927$	1.96232e9	+	2.26463e9i	0.0809078	+	0.0933725i
$928$	1.07346e9	+	7.46610e9i	0.0440929	+	0.306673i
$929$	6.62783e9	+	1.94611e9i	0.271217	+	0.0796364i	0.414513	−	0.910043i	$-0.363952\pi$
$929$	6.62783e9	+	1.94611e9i	0.271217	+	0.0796364i	−0.143296	+	0.989680i	$0.545770\pi$
$930$	−1.99956e10	+	2.30762e10i	−0.815163	+	0.940748i
$931$	−1.36383e10	−	8.76481e9i	−0.553907	−	0.355974i
$932$	−1.00349e10	−	6.44903e9i	−0.406029	−	0.260939i
$933$	−2.44376e9	+	2.82024e9i	−0.0985081	+	0.113684i
$934$	−1.02466e10	−	3.00868e9i	−0.411497	−	0.120826i
$935$	8.05206e8	+	5.60033e9i	0.0322156	+	0.224065i
$936$	8.18098e9	+	9.44135e9i	0.326092	+	0.376330i
$937$	−6.45008e9	−	1.41237e10i	−0.256140	−	0.560868i	0.737255	−	0.675614i	$-0.236122\pi$
$937$	−6.45008e9	−	1.41237e10i	−0.256140	−	0.560868i	−0.993395	+	0.114747i	$0.963394\pi$
$938$	−1.98925e10	+	5.84096e9i	−0.787008	+	0.231086i
$939$	−7.15909e9	+	1.56762e10i	−0.282181	+	0.617891i
$940$	5.85806e8	−	4.07437e9i	0.0230042	−	0.159997i
$941$	−1.79729e10	+	1.15505e10i	−0.703160	+	0.451894i	−0.842742	−	0.538317i	$-0.819060\pi$
$941$	−1.79729e10	+	1.15505e10i	−0.703160	+	0.451894i	0.139582	+	0.990210i	$0.455424\pi$
$942$	1.88745e10			0.735694
$943$	2.18765e10	+	7.27260e9i	0.849545	+	0.282422i
$944$	−8.51868e9			−0.329587
$945$	−4.68144e9	+	3.00858e9i	−0.180455	+	0.115971i
$946$	−2.07130e9	+	1.44062e10i	−0.0795469	+	0.553261i
$947$	3.85886e9	−	8.44972e9i	0.147650	−	0.323309i	−0.821328	−	0.570457i	$-0.806766\pi$
$947$	3.85886e9	−	8.44972e9i	0.147650	−	0.323309i	0.968978	+	0.247148i	$0.0794935\pi$
$948$	1.54640e9	−	4.54064e8i	0.0589512	−	0.0173096i
$949$	−2.06472e10	−	4.52111e10i	−0.784205	−	1.71717i
$950$	−3.56685e10	−	4.11636e10i	−1.34975	−	1.55769i
$951$	−3.40080e9	−	2.36531e10i	−0.128218	−	0.891777i
$952$	−1.66860e9	−	4.89945e8i	−0.0626790	−	0.0184042i
$953$	−5.39683e9	+	6.22827e9i	−0.201982	+	0.233100i	−0.847700	−	0.530477i	$-0.822013\pi$
$953$	−5.39683e9	+	6.22827e9i	−0.201982	+	0.233100i	0.645717	+	0.763577i	$0.276558\pi$
$954$	−4.53828e9	−	2.91658e9i	−0.169228	−	0.108756i
$955$	−4.76425e10	−	3.06179e10i	−1.77004	−	1.13753i
$956$	6.97253e9	−	8.04673e9i	0.258100	−	0.297863i
$957$	−8.69307e9	−	2.55251e9i	−0.320613	−	0.0941405i
$958$	3.51473e9	+	2.44455e10i	0.129155	+	0.898295i
$959$	8.89726e9	+	1.02680e10i	0.325755	+	0.375942i
$960$	1.31082e10	+	2.87030e10i	0.478183	+	1.04707i
$961$	−2.71074e10	+	7.95945e9i	−0.985271	+	0.289302i
$962$	1.71263e10	−	3.75014e10i	0.620228	−	1.35811i
$963$	−7.82656e8	+	5.44349e9i	−0.0282409	+	0.196420i
$964$	6.47385e9	−	4.16049e9i	0.232752	−	0.149580i
$965$	2.47643e10			0.887115
$966$	6.75074e9	−	4.00863e9i	0.240953	−	0.143079i
$967$	3.30351e10			1.17485			0.587425	−	0.809279i	$-0.300142\pi$
$967$	3.30351e10			1.17485			0.587425	+	0.809279i	$0.300142\pi$
$968$	−1.19349e10	+	7.67010e9i	−0.422917	+	0.271792i
$969$	2.39337e8	−	1.66463e9i	0.00845039	−	0.0587738i
$970$	−1.23477e9	+	2.70378e9i	−0.0434397	+	0.0951196i
$971$	2.98912e10	−	8.77684e9i	1.04779	−	0.307660i	0.287868	−	0.957670i	$-0.407054\pi$
$971$	2.98912e10	−	8.77684e9i	1.04779	−	0.307660i	0.759925	+	0.650010i	$0.225235\pi$
$972$	2.59813e8	+	5.68912e8i	0.00907464	+	0.0198707i
$973$	−6.97301e9	−	8.04729e9i	−0.242675	−	0.280062i
$974$	3.67465e9	+	2.55577e10i	0.127426	+	0.886270i
$975$	5.45104e10	+	1.60057e10i	1.88349	+	0.553043i
$976$	8.09358e9	−	9.34049e9i	0.278655	−	0.321584i
$977$	5.38531e6	+	3.46093e6i	0.000184748	+	0.000118730i	0.540733	−	0.841194i	$-0.318147\pi$
$977$	5.38531e6	+	3.46093e6i	0.000184748	+	0.000118730i	−0.540548	+	0.841313i	$0.681783\pi$
$978$	−4.03596e9	−	2.59376e9i	−0.137963	−	0.0886631i
$979$	−4.23859e9	+	4.89159e9i	−0.144372	+	0.166614i
$980$	1.15393e10	+	3.38823e9i	0.391640	+	0.114996i
$981$	−2.05483e9	−	1.42917e10i	−0.0694919	−	0.483327i
$982$	−6.85152e9	−	7.90708e9i	−0.230886	−	0.266456i
$983$	1.92065e10	+	4.20564e10i	0.644928	+	1.41220i	0.895924	+	0.444208i	$0.146515\pi$
$983$	1.92065e10	+	4.20564e10i	0.644928	+	1.41220i	−0.250995	+	0.967988i	$0.580758\pi$
$984$	1.61357e10	−	4.73786e9i	0.539889	−	0.158526i
$985$	2.28169e10	−	4.99620e10i	0.760728	−	1.66576i
$986$	1.67187e8	−	1.16281e9i	0.00555434	−	0.0386313i
$987$	−2.23211e9	+	1.43449e9i	−0.0738935	+	0.0474885i
$988$	−1.45110e10			−0.478683
$989$	−1.17968e10	+	1.26797e10i	−0.387774	+	0.416794i
$990$	−1.86333e10			−0.610332
$991$	2.66665e10	−	1.71375e10i	0.870378	−	0.559358i	−0.0274900	−	0.999622i	$-0.508751\pi$
$991$	2.66665e10	−	1.71375e10i	0.870378	−	0.559358i	0.897868	+	0.440264i	$0.145115\pi$
$992$	−4.03196e9	+	2.80429e10i	−0.131137	+	0.912079i
$993$	3.52033e9	−	7.70844e9i	0.114093	−	0.249830i
$994$	2.26722e10	−	6.65714e9i	0.732218	−	0.214999i
$995$	1.07615e10	+	2.35645e10i	0.346332	+	0.758362i
$996$	−7.86681e9	−	9.07878e9i	−0.252285	−	0.291152i
$997$	8.51811e9	+	5.92447e10i	0.272214	+	1.89329i	0.425264	+	0.905069i	$0.360181\pi$
$997$	8.51811e9	+	5.92447e10i	0.272214	+	1.89329i	−0.153050	+	0.988218i	$0.548910\pi$
$998$	7.26198e9	+	2.13231e9i	0.231259	+	0.0679037i
$999$	5.32082e9	−	6.14056e9i	0.168849	−	0.194863i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.8.e.b.58.10	yes	140
23.2	even	11	inner	69.8.e.b.25.10	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.8.e.b.25.10	✓	140	23.2	even	11	inner
69.8.e.b.58.10	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)

\(f(q)\)	\(=\)	\(q+(7.72913 - 4.96721i) q^{2} +(3.84250 - 26.7252i) q^{3} +(-18.1068 + 39.6485i) q^{4} +(500.128 - 146.851i) q^{5} +(-103.050 - 225.649i) q^{6} +(355.198 + 409.921i) q^{7} +(224.357 + 1560.44i) q^{8} +(-699.470 - 205.383i) q^{9} +O(q^{10})\)	\(q+(7.72913 - 4.96721i) q^{2} +(3.84250 - 26.7252i) q^{3} +(-18.1068 + 39.6485i) q^{4} +(500.128 - 146.851i) q^{5} +(-103.050 - 225.649i) q^{6} +(355.198 + 409.921i) q^{7} +(224.357 + 1560.44i) q^{8} +(-699.470 - 205.383i) q^{9} +(3136.12 - 3619.27i) q^{10} +(4489.99 + 2885.54i) q^{11} +(990.036 + 636.258i) q^{12} +(-7118.50 + 8215.19i) q^{13} +(4781.54 + 1403.99i) q^{14} +(-2002.87 - 13930.3i) q^{15} +(5831.51 + 6729.92i) q^{16} +(844.853 + 1849.97i) q^{17} +(-6426.48 + 1886.98i) q^{18} +(12722.7 - 27858.8i) q^{19} +(-3233.33 + 22488.3i) q^{20} +(12320.1 - 7917.62i) q^{21} +49036.8 q^{22} +(47942.4 + 33261.9i) q^{23} +42565.0 q^{24} +(162840. - 104651. i) q^{25} +(-14213.3 + 98855.4i) q^{26} +(-8176.61 + 17904.3i) q^{27} +(-22684.2 + 6660.70i) q^{28} +(-26117.5 - 57189.3i) q^{29} +(-84675.2 - 97720.3i) q^{30} +(-33606.9 - 233741. i) q^{31} +(-115114. - 33800.6i) q^{32} +(94369.4 - 108908. i) q^{33} +(15719.2 + 10102.1i) q^{34} +(237842. + 152852. i) q^{35} +(20808.3 - 24014.1i) q^{36} +(-396078. - 116299. i) q^{37} +(-40045.3 - 278521. i) q^{38} +(192200. + 221810. i) q^{39} +(341359. + 747471. i) q^{40} +(379083. - 111309. i) q^{41} +(55894.8 - 122393. i) q^{42} +(-42239.6 + 293783. i) q^{43} +(-195707. + 125773. i) q^{44} -379986. q^{45} +(535772. + 18945.5i) q^{46} -181177. q^{47} +(202266. - 129988. i) q^{48} +(75333.2 - 523954. i) q^{49} +(738789. - 1.61772e6i) q^{50} +(52687.1 - 15470.3i) q^{51} +(-196826. - 430989. i) q^{52} +(527451. + 608711. i) q^{53} +(25736.2 + 179000. i) q^{54} +(2.66931e6 + 783782. i) q^{55} +(-559964. + 646233. i) q^{56} +(-695645. - 447064. i) q^{57} +(-485937. - 312292. i) q^{58} +(-626454. + 722967. i) q^{59} +(588580. + 172823. i) q^{60} +(-197519. - 1.37378e6i) q^{61} +(-1.42079e6 - 1.63968e6i) q^{62} +(-164260. - 359679. i) q^{63} +(-2.15129e6 + 631676. i) q^{64} +(-2.35376e6 + 5.15401e6i) q^{65} +(188424. - 1.31052e6i) q^{66} +(-3.49984e6 + 2.24921e6i) q^{67} -88646.0 q^{68} +(1.07315e6 - 1.15346e6i) q^{69} +2.59756e6 q^{70} +(3.98889e6 - 2.56350e6i) q^{71} +(163556. - 1.13756e6i) q^{72} +(-1.89942e6 + 4.15916e6i) q^{73} +(-3.63902e6 + 1.06851e6i) q^{74} +(-2.17110e6 - 4.75405e6i) q^{75} +(874192. + 1.00887e6i) q^{76} +(411994. + 2.86548e6i) q^{77} +(2.58731e6 + 759704. i) q^{78} +(896819. - 1.03498e6i) q^{79} +(3.90480e6 + 2.50946e6i) q^{80} +(447077. + 287319. i) q^{81} +(2.37709e6 - 2.74330e6i) q^{82} +(-9.79416e6 - 2.87583e6i) q^{83} +(90844.1 + 631834. i) q^{84} +(694204. + 801155. i) q^{85} +(1.13281e6 + 2.48050e6i) q^{86} +(-1.62875e6 + 478244. i) q^{87} +(-3.49534e6 + 7.65373e6i) q^{88} +(-172585. + 1.20036e6i) q^{89} +(-2.93696e6 + 1.88747e6i) q^{90} -5.89606e6 q^{91} +(-2.18687e6 + 1.29857e6i) q^{92} -6.37591e6 q^{93} +(-1.40034e6 + 899945. i) q^{94} +(2.27189e6 - 1.58013e7i) q^{95} +(-1.34565e6 + 2.94657e6i) q^{96} +(-595530. + 174863. i) q^{97} +(-2.02033e6 - 4.42391e6i) q^{98} +(-2.54797e6 - 2.94052e6i) 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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