LMFDB - Embedded newform 37.8.f.a.16.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,8,Mod(7,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("37.7");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	37.f (of order $9$, degree $6$, 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:	$11.5582459429$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			16.13
Character	$\chi$	$=$	37.16
Dual form			37.8.f.a.7.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.24172 + 0.815920i) q^{2} +(67.7355 - 24.6537i) q^{3} +(-93.6941 - 78.6187i) q^{4} +(-36.3337 + 206.059i) q^{5} +171.960 q^{6} +(278.285 - 1578.23i) q^{7} +(-298.567 - 517.134i) q^{8} +(2304.96 - 1934.09i) q^{9} +O(q^{10})$	\(q+(2.24172 + 0.815920i) q^{2} +(67.7355 - 24.6537i) q^{3} +(-93.6941 - 78.6187i) q^{4} +(-36.3337 + 206.059i) q^{5} +171.960 q^{6} +(278.285 - 1578.23i) q^{7} +(-298.567 - 517.134i) q^{8} +(2304.96 - 1934.09i) q^{9} +(-249.578 + 432.281i) q^{10} +(2056.02 + 3561.12i) q^{11} +(-8284.66 - 3015.37i) q^{12} +(-10957.6 - 9194.49i) q^{13} +(1911.55 - 3310.90i) q^{14} +(2619.03 + 14853.3i) q^{15} +(2471.19 + 14014.8i) q^{16} +(26139.1 - 21933.3i) q^{17} +(6745.14 - 2455.03i) q^{18} +(-13050.3 + 4749.93i) q^{19} +(19604.3 - 16450.0i) q^{20} +(-20059.5 - 113763. i) q^{21} +(1703.42 + 9660.60i) q^{22} +(18231.9 - 31578.7i) q^{23} +(-32972.9 - 27667.6i) q^{24} +(32273.4 + 11746.6i) q^{25} +(-17061.9 - 29552.0i) q^{26} +(29622.6 - 51307.9i) q^{27} +(-150152. + 125993. i) q^{28} +(-6446.71 - 11166.0i) q^{29} +(-6247.94 + 35433.8i) q^{30} +55442.1 q^{31} +(-19167.8 + 108706. i) q^{32} +(227060. + 190526. i) q^{33} +(76492.5 - 27841.0i) q^{34} +(315097. + 114686. i) q^{35} -368016. q^{36} +(-108513. + 288369. i) q^{37} -33130.8 q^{38} +(-968895. - 352649. i) q^{39} +(117408. - 42733.0i) q^{40} +(580000. + 486678. i) q^{41} +(47853.8 - 271392. i) q^{42} +197307. q^{43} +(87334.3 - 495297. i) q^{44} +(314788. + 545229. i) q^{45} +(66636.7 - 55914.8i) q^{46} +(-135317. + 234377. i) q^{47} +(512905. + 888377. i) q^{48} +(-1.63949e6 - 596727. i) q^{49} +(62763.8 + 52665.1i) q^{50} +(1.22981e6 - 2.13009e6i) q^{51} +(303801. + 1.72294e6i) q^{52} +(206888. + 1.17332e6i) q^{53} +(108269. - 90848.4i) q^{54} +(-808503. + 294271. i) q^{55} +(-899244. + 327298. i) q^{56} +(-766867. + 643478. i) q^{57} +(-5341.15 - 30291.1i) q^{58} +(253527. + 1.43783e6i) q^{59} +(922356. - 1.59757e6i) q^{60} +(735605. + 617246. i) q^{61} +(124286. + 45236.4i) q^{62} +(-2.41100e6 - 4.17598e6i) q^{63} +(779122. - 1.34948e6i) q^{64} +(2.29274e6 - 1.92383e6i) q^{65} +(353552. + 612370. i) q^{66} +(510855. - 2.89720e6i) q^{67} -4.17345e6 q^{68} +(456419. - 2.58848e6i) q^{69} +(612786. + 514188. i) q^{70} +(-2.74431e6 + 998846. i) q^{71} +(-1.68837e6 - 614516. i) q^{72} +3.69954e6 q^{73} +(-478542. + 557906. i) q^{74} +2.47565e6 q^{75} +(1.59617e6 + 580959. i) q^{76} +(6.19243e6 - 2.25386e6i) q^{77} +(-1.88426e6 - 1.58108e6i) q^{78} +(419900. - 2.38137e6i) q^{79} -2.97766e6 q^{80} +(-401114. + 2.27483e6i) q^{81} +(903109. + 1.56423e6i) q^{82} +(2.27278e6 - 1.90709e6i) q^{83} +(-7.06444e6 + 1.22360e7i) q^{84} +(3.56982e6 + 6.18312e6i) q^{85} +(442308. + 160987. i) q^{86} +(-711955. - 597401. i) q^{87} +(1.22772e6 - 2.12647e6i) q^{88} +(-520678. - 2.95291e6i) q^{89} +(260804. + 1.47909e6i) q^{90} +(-1.75604e7 + 1.47349e7i) q^{91} +(-4.19090e6 + 1.52536e6i) q^{92} +(3.75540e6 - 1.36685e6i) q^{93} +(-494577. + 414999. i) q^{94} +(-504598. - 2.86172e6i) q^{95} +(1.38166e6 + 7.83580e6i) q^{96} +(4.14322e6 - 7.17627e6i) q^{97} +(-3.18841e6 - 2.67539e6i) q^{98} +(1.16266e7 + 4.23172e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 15 q^{2} + 33 q^{3} - 279 q^{4} + 576 q^{5} - 12 q^{6} - 597 q^{7} - 3750 q^{8} - 3243 q^{9}+O(q^{10}) $ 132 * q + 15 * q^2 + 33 * q^3 - 279 * q^4 + 576 * q^5 - 12 * q^6 - 597 * q^7 - 3750 * q^8 - 3243 * q^9	\( 132 q + 15 q^{2} + 33 q^{3} - 279 q^{4} + 576 q^{5} - 12 q^{6} - 597 q^{7} - 3750 q^{8} - 3243 q^{9} - 6003 q^{10} - 15975 q^{11} - 4635 q^{12} - 15981 q^{13} - 13491 q^{14} + 38493 q^{15} - 74151 q^{16} + 37698 q^{17} - 20100 q^{18} - 66102 q^{19} - 176184 q^{20} - 142530 q^{21} + 132783 q^{22} + 140631 q^{23} - 38793 q^{24} - 544092 q^{25} - 423147 q^{26} + 130557 q^{27} + 603813 q^{28} + 22890 q^{29} - 319860 q^{30} - 1288044 q^{31} - 217866 q^{32} + 112344 q^{33} + 812019 q^{34} + 1479252 q^{35} + 8118132 q^{36} - 1664550 q^{37} + 305010 q^{38} - 1580340 q^{39} - 4681425 q^{40} - 2956593 q^{41} - 3553029 q^{42} - 1023528 q^{43} + 6409524 q^{44} + 1803336 q^{45} + 10219434 q^{46} - 2607204 q^{47} - 2984043 q^{48} - 6819531 q^{49} + 5724015 q^{50} - 1675833 q^{51} + 11768451 q^{52} + 2280177 q^{53} - 7803897 q^{54} - 3542196 q^{55} + 12168843 q^{56} - 85203 q^{57} - 12425487 q^{58} - 7014600 q^{59} + 2356788 q^{60} + 10840332 q^{61} + 6334368 q^{62} - 3331359 q^{63} - 26175624 q^{64} - 573195 q^{65} - 36720249 q^{66} + 6642918 q^{67} - 25277742 q^{68} - 1236438 q^{69} - 27401982 q^{70} + 20311041 q^{71} + 40093005 q^{72} + 38643780 q^{73} - 9531 q^{74} + 16639446 q^{75} + 5787405 q^{76} - 316971 q^{77} + 9363381 q^{78} + 17712534 q^{79} - 74410128 q^{80} - 10355109 q^{81} - 16702371 q^{82} - 31021176 q^{83} - 61626192 q^{84} + 23576445 q^{85} + 18579072 q^{86} + 104996631 q^{87} + 57279702 q^{88} - 13471320 q^{89} + 56306910 q^{90} - 2335911 q^{91} - 178133436 q^{92} + 24366258 q^{93} + 77086020 q^{94} - 26254407 q^{95} + 152523921 q^{96} + 14408415 q^{97} - 521205 q^{98} + 58375668 q^{99}+O(q^{100}) \) 132 * q + 15 * q^2 + 33 * q^3 - 279 * q^4 + 576 * q^5 - 12 * q^6 - 597 * q^7 - 3750 * q^8 - 3243 * q^9 - 6003 * q^10 - 15975 * q^11 - 4635 * q^12 - 15981 * q^13 - 13491 * q^14 + 38493 * q^15 - 74151 * q^16 + 37698 * q^17 - 20100 * q^18 - 66102 * q^19 - 176184 * q^20 - 142530 * q^21 + 132783 * q^22 + 140631 * q^23 - 38793 * q^24 - 544092 * q^25 - 423147 * q^26 + 130557 * q^27 + 603813 * q^28 + 22890 * q^29 - 319860 * q^30 - 1288044 * q^31 - 217866 * q^32 + 112344 * q^33 + 812019 * q^34 + 1479252 * q^35 + 8118132 * q^36 - 1664550 * q^37 + 305010 * q^38 - 1580340 * q^39 - 4681425 * q^40 - 2956593 * q^41 - 3553029 * q^42 - 1023528 * q^43 + 6409524 * q^44 + 1803336 * q^45 + 10219434 * q^46 - 2607204 * q^47 - 2984043 * q^48 - 6819531 * q^49 + 5724015 * q^50 - 1675833 * q^51 + 11768451 * q^52 + 2280177 * q^53 - 7803897 * q^54 - 3542196 * q^55 + 12168843 * q^56 - 85203 * q^57 - 12425487 * q^58 - 7014600 * q^59 + 2356788 * q^60 + 10840332 * q^61 + 6334368 * q^62 - 3331359 * q^63 - 26175624 * q^64 - 573195 * q^65 - 36720249 * q^66 + 6642918 * q^67 - 25277742 * q^68 - 1236438 * q^69 - 27401982 * q^70 + 20311041 * q^71 + 40093005 * q^72 + 38643780 * q^73 - 9531 * q^74 + 16639446 * q^75 + 5787405 * q^76 - 316971 * q^77 + 9363381 * q^78 + 17712534 * q^79 - 74410128 * q^80 - 10355109 * q^81 - 16702371 * q^82 - 31021176 * q^83 - 61626192 * q^84 + 23576445 * q^85 + 18579072 * q^86 + 104996631 * q^87 + 57279702 * q^88 - 13471320 * q^89 + 56306910 * q^90 - 2335911 * q^91 - 178133436 * q^92 + 24366258 * q^93 + 77086020 * q^94 - 26254407 * q^95 + 152523921 * q^96 + 14408415 * q^97 - 521205 * q^98 + 58375668 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

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 $

$2$	2.24172	+	0.815920i	0.198142	+	0.0721179i	0.439185	−	0.898397i	$-0.355267\pi$
$2$	2.24172	+	0.815920i	0.198142	+	0.0721179i	−0.241043	+	0.970514i	$0.577489\pi$
$3$	67.7355	−	24.6537i	1.44841	−	0.527179i	0.506265	−	0.862378i	$-0.331026\pi$
$3$	67.7355	−	24.6537i	1.44841	−	0.527179i	0.942147	+	0.335199i	$0.108804\pi$
$4$	−93.6941	−	78.6187i	−0.731985	−	0.614208i
$5$	−36.3337	+	206.059i	−0.129991	+	0.737218i	0.848226	+	0.529635i	$0.177671\pi$
$5$	−36.3337	+	206.059i	−0.129991	+	0.737218i	−0.978217	+	0.207584i	$0.933440\pi$
$6$	171.960			0.325011
$7$	278.285	−	1578.23i	0.306652	−	1.73911i	−0.308972	−	0.951071i	$-0.599985\pi$
$7$	278.285	−	1578.23i	0.306652	−	1.73911i	0.615624	−	0.788040i	$-0.288904\pi$
$8$	−298.567	−	517.134i	−0.206171	−	0.357099i
$9$	2304.96	−	1934.09i	1.05394	−	0.884357i
$10$	−249.578	+	432.281i	−0.0789234	+	0.136699i
$11$	2056.02	+	3561.12i	0.465749	+	0.806701i	0.999235	−	0.0391079i	$-0.0124516\pi$
$11$	2056.02	+	3561.12i	0.465749	+	0.806701i	−0.533486	+	0.845809i	$0.679118\pi$
$12$	−8284.66	−	3015.37i	−1.38401	−	0.503740i
$13$	−10957.6	−	9194.49i	−1.38329	−	1.16072i	−0.967978	−	0.251036i	$-0.919229\pi$
$13$	−10957.6	−	9194.49i	−1.38329	−	1.16072i	−0.415310	−	0.909680i	$-0.636327\pi$
$14$	1911.55	−	3310.90i	0.186182	−	0.322476i
$15$	2619.03	+	14853.3i	0.200365	+	1.13632i
$16$	2471.19	+	14014.8i	0.150830	+	0.855397i
$17$	26139.1	−	21933.3i	1.29039	−	1.08276i	0.298665	−	0.954358i	$-0.403459\pi$
$17$	26139.1	−	21933.3i	1.29039	−	1.08276i	0.991722	−	0.128405i	$-0.0409858\pi$
$18$	6745.14	−	2455.03i	0.272607	−	0.0992208i
$19$	−13050.3	+	4749.93i	−0.436499	+	0.158873i	−0.550917	−	0.834560i	$-0.685722\pi$
$19$	−13050.3	+	4749.93i	−0.436499	+	0.158873i	0.114418	+	0.993433i	$0.463500\pi$
$20$	19604.3	−	16450.0i	0.547957	−	0.459791i
$21$	−20059.5	−	113763.i	−0.472664	−	2.68061i
$22$	1703.42	+	9660.60i	0.0341070	+	0.193430i
$23$	18231.9	−	31578.7i	0.312454	−	0.541186i	−0.666439	−	0.745559i	$-0.732182\pi$
$23$	18231.9	−	31578.7i	0.312454	−	0.541186i	0.978893	+	0.204374i	$0.0655158\pi$
$24$	−32972.9	−	27667.6i	−0.486875	−	0.408537i
$25$	32273.4	+	11746.6i	0.413100	+	0.150356i
$26$	−17061.9	−	29552.0i	−0.190379	−	0.329747i
$27$	29622.6	−	51307.9i	0.289635	−	0.501662i
$28$	−150152.	+	125993.i	−1.29264	+	1.08466i
$29$	−6446.71	−	11166.0i	−0.0490846	−	0.0850170i	0.840439	−	0.541906i	$-0.182297\pi$
$29$	−6446.71	−	11166.0i	−0.0490846	−	0.0850170i	−0.889524	+	0.456889i	$0.848964\pi$
$30$	−6247.94	+	35433.8i	−0.0422486	+	0.239604i
$31$	55442.1			0.334252			0.167126	−	0.985936i	$-0.446551\pi$
$31$	55442.1			0.334252			0.167126	+	0.985936i	$0.446551\pi$
$32$	−19167.8	+	108706.i	−0.103406	+	0.586445i
$33$	227060.	+	190526.i	1.09987	+	0.922902i
$34$	76492.5	−	27841.0i	0.333767	−	0.121481i
$35$	315097.	+	114686.i	1.24224	+	0.452139i
$36$	−368016.			−1.31464
$37$	−108513.	+	288369.i	−0.352188	+	0.935929i
$37$	−108513.	+	288369.i	−0.352188	+	0.935929i
$38$	−33130.8			−0.0979465
$39$	−968895.	−	352649.i	−2.61548	−	0.951955i
$40$	117408.	−	42733.0i	0.290060	−	0.105573i
$41$	580000.	+	486678.i	1.31427	+	1.10280i	0.987486	+	0.157704i	$0.0504093\pi$
$41$	580000.	+	486678.i	1.31427	+	1.10280i	0.326784	+	0.945099i	$0.394035\pi$
$42$	47853.8	−	271392.i	0.0996652	−	0.565229i
$43$	197307.			0.378446			0.189223	−	0.981934i	$-0.439403\pi$
$43$	197307.			0.378446			0.189223	+	0.981934i	$0.439403\pi$
$44$	87334.3	−	495297.i	0.154561	−	0.876560i
$45$	314788.	+	545229.i	0.514961	+	0.891939i
$46$	66636.7	−	55914.8i	0.100939	−	0.0846982i
$47$	−135317.	+	234377.i	−0.190113	+	0.329285i	−0.945287	−	0.326239i	$-0.894219\pi$
$47$	−135317.	+	234377.i	−0.190113	+	0.329285i	0.755175	+	0.655524i	$0.227552\pi$
$48$	512905.	+	888377.i	0.669411	+	1.15945i
$49$	−1.63949e6	−	596727.i	−1.99078	−	0.724585i
$50$	62763.8	+	52665.1i	0.0710091	+	0.0595837i
$51$	1.22981e6	−	2.13009e6i	1.29820	−	2.24855i
$52$	303801.	+	1.72294e6i	0.299624	+	1.69925i
$53$	206888.	+	1.17332e6i	0.190884	+	1.08255i	0.918160	+	0.396210i	$0.129675\pi$
$53$	206888.	+	1.17332e6i	0.190884	+	1.08255i	−0.727276	+	0.686345i	$0.759214\pi$
$54$	108269.	−	90848.4i	0.0935676	−	0.0785125i
$55$	−808503.	+	294271.i	−0.655258	+	0.238494i
$56$	−899244.	+	327298.i	−0.684257	+	0.249049i
$57$	−766867.	+	643478.i	−0.548477	+	0.460227i
$58$	−5341.15	−	30291.1i	−0.00359448	−	0.0203853i
$59$	253527.	+	1.43783e6i	0.160710	+	0.911432i	0.953378	+	0.301778i	$0.0975802\pi$
$59$	253527.	+	1.43783e6i	0.160710	+	0.911432i	−0.792668	+	0.609653i	$0.791309\pi$
$60$	922356.	−	1.59757e6i	0.551276	−	0.954838i
$61$	735605.	+	617246.i	0.414945	+	0.348180i	0.826236	−	0.563324i	$-0.190478\pi$
$61$	735605.	+	617246.i	0.414945	+	0.348180i	−0.411291	+	0.911504i	$0.634922\pi$
$62$	124286.	+	45236.4i	0.0662294	+	0.0241055i
$63$	−2.41100e6	−	4.17598e6i	−1.21480	−	2.10410i
$64$	779122.	−	1.34948e6i	0.371514	−	0.643481i
$65$	2.29274e6	−	1.92383e6i	1.03552	−	0.868902i
$66$	353552.	+	612370.i	0.151373	+	0.262186i
$67$	510855.	−	2.89720e6i	0.207508	−	1.17684i	−0.685935	−	0.727663i	$-0.740607\pi$
$67$	510855.	−	2.89720e6i	0.207508	−	1.17684i	0.893443	−	0.449176i	$-0.148282\pi$
$68$	−4.17345e6			−1.60959
$69$	456419.	−	2.58848e6i	0.167260	−	0.948579i
$70$	612786.	+	514188.i	0.213533	+	0.179176i
$71$	−2.74431e6	+	998846.i	−0.909973	+	0.331203i	−0.754242	−	0.656596i	$-0.771995\pi$
$71$	−2.74431e6	+	998846.i	−0.909973	+	0.331203i	−0.155731	+	0.987800i	$0.549773\pi$
$72$	−1.68837e6	−	614516.i	−0.533094	−	0.194030i
$73$	3.69954e6			1.11306			0.556529	−	0.830828i	$-0.312133\pi$
$73$	3.69954e6			1.11306			0.556529	+	0.830828i	$0.312133\pi$
$74$	−478542.	+	557906.i	−0.137281	+	0.160048i
$75$	2.47565e6			0.677603
$76$	1.59617e6	+	580959.i	0.417092	+	0.151809i
$77$	6.19243e6	−	2.25386e6i	1.54577	−	0.562613i
$78$	−1.88426e6	−	1.58108e6i	−0.449583	−	0.377245i
$79$	419900.	−	2.38137e6i	0.0958189	−	0.543416i	−0.898674	−	0.438616i	$-0.855469\pi$
$79$	419900.	−	2.38137e6i	0.0958189	−	0.543416i	0.994493	−	0.104800i	$-0.0334201\pi$
$80$	−2.97766e6			−0.650221
$81$	−401114.	+	2.27483e6i	−0.0838631	+	0.475611i
$82$	903109.	+	1.56423e6i	0.180881	+	0.313294i
$83$	2.27278e6	−	1.90709e6i	0.436300	−	0.366099i	−0.398023	−	0.917375i	$-0.630304\pi$
$83$	2.27278e6	−	1.90709e6i	0.436300	−	0.366099i	0.834323	+	0.551277i	$0.185859\pi$
$84$	−7.06444e6	+	1.22360e7i	−1.30047	+	2.25248i
$85$	3.56982e6	+	6.18312e6i	0.630493	+	1.09205i
$86$	442308.	+	160987.i	0.0749861	+	0.0272927i
$87$	−711955.	−	597401.i	−0.115914	−	0.0972633i
$88$	1.22772e6	−	2.12647e6i	0.192048	−	0.332637i
$89$	−520678.	−	2.95291e6i	−0.0782896	−	0.444002i	−0.998604	−	0.0528227i	$-0.983178\pi$
$89$	−520678.	−	2.95291e6i	−0.0782896	−	0.444002i	0.920314	−	0.391180i	$-0.127933\pi$
$90$	260804.	+	1.47909e6i	0.0377108	+	0.213869i
$91$	−1.75604e7	+	1.47349e7i	−2.44280	+	2.04976i
$92$	−4.19090e6	+	1.52536e6i	−0.561112	+	0.204228i
$93$	3.75540e6	−	1.36685e6i	0.484134	−	0.176211i
$94$	−494577.	+	414999.i	−0.0614167	+	0.0515347i
$95$	−504598.	−	2.86172e6i	−0.0603827	−	0.342448i
$96$	1.38166e6	+	7.83580e6i	0.159387	+	0.903928i
$97$	4.14322e6	−	7.17627e6i	0.460932	−	0.798358i	−0.538075	−	0.842897i	$-0.680848\pi$
$97$	4.14322e6	−	7.17627e6i	0.460932	−	0.798358i	0.999008	+	0.0445385i	$0.0141817\pi$
$98$	−3.18841e6	−	2.67539e6i	−0.342202	−	0.287142i
$99$	1.16266e7	+	4.23172e6i	1.20428	+	0.438322i
$100$	−2.10033e6	−	3.63788e6i	−0.210033	−	0.363788i
$101$	4.74405e6	−	8.21693e6i	0.458168	−	0.793569i	−0.540697	−	0.841218i	$-0.681839\pi$
$101$	4.74405e6	−	8.21693e6i	0.458168	−	0.793569i	0.998864	+	0.0476482i	$0.0151727\pi$
$102$	4.49488e6	−	3.77165e6i	0.419389	−	0.351909i
$103$	−3.27415e6	−	5.67100e6i	−0.295236	−	0.511363i	0.679804	−	0.733394i	$-0.262065\pi$
$103$	−3.27415e6	−	5.67100e6i	−0.295236	−	0.511363i	−0.975040	+	0.222031i	$0.928731\pi$
$104$	−1.48321e6	+	8.41171e6i	−0.129296	+	0.733276i
$105$	2.41707e7			2.03764
$106$	−493549.	+	2.79906e6i	−0.0402494	+	0.228266i
$107$	−693979.	−	582318.i	−0.0547650	−	0.0459533i	0.614994	−	0.788532i	$-0.289158\pi$
$107$	−693979.	−	582318.i	−0.0547650	−	0.0459533i	−0.669759	+	0.742578i	$0.733603\pi$
$108$	−6.80922e6	+	2.47835e6i	−0.520133	+	0.189313i
$109$	−1.18487e7	−	4.31258e6i	−0.876352	−	0.318966i	−0.135615	−	0.990762i	$-0.543301\pi$
$109$	−1.18487e7	−	4.31258e6i	−0.876352	−	0.318966i	−0.740737	+	0.671796i	$0.765523\pi$
$110$	−2.05254e6			−0.147034
$111$	−240796.	+	2.22081e7i	−0.0167116	+	1.54128i
$112$	2.28063e7			1.53388
$113$	−9.27283e6	−	3.37504e6i	−0.604558	−	0.220041i	0.0215625	−	0.999768i	$-0.493136\pi$
$113$	−9.27283e6	−	3.37504e6i	−0.604558	−	0.220041i	−0.626120	+	0.779726i	$0.715358\pi$
$114$	−2.24413e6	+	816797.i	−0.141867	+	0.0516353i
$115$	5.84463e6	+	4.90422e6i	0.358356	+	0.300696i
$116$	−273840.	+	1.55302e6i	−0.0162890	+	0.0923793i
$117$	−4.30397e7			−2.48438
$118$	−604813.	+	3.43006e6i	−0.0338871	+	0.192183i
$119$	−2.73417e7	−	4.73573e7i	−1.48735	−	2.57616i
$120$	6.89917e6	−	5.78909e6i	0.364471	−	0.305827i
$121$	1.28918e6	−	2.23293e6i	0.0661556	−	0.114585i
$122$	1.14540e6	+	1.98389e6i	0.0571081	+	0.0989141i
$123$	5.12850e7	+	1.86662e7i	2.48498	+	0.904458i
$124$	−5.19460e6	−	4.35879e6i	−0.244667	−	0.205300i
$125$	−1.17664e7	+	2.03801e7i	−0.538840	+	0.933298i
$126$	−1.99753e6	−	1.13286e7i	−0.0889605	−	0.504520i
$127$	−1.11592e6	−	6.32868e6i	−0.0483414	−	0.274158i	0.951050	−	0.309037i	$-0.100007\pi$
$127$	−1.11592e6	−	6.32868e6i	−0.0483414	−	0.274158i	−0.999392	+	0.0348790i	$0.988895\pi$
$128$	1.36711e7	−	1.14714e7i	0.576193	−	0.483483i
$129$	1.33647e7	−	4.86436e6i	0.548145	−	0.199509i
$130$	6.70937e6	−	2.44201e6i	0.267843	−	0.0974868i
$131$	−2.32520e7	+	1.95108e7i	−0.903673	+	0.758272i	−0.970905	−	0.239465i	$-0.923028\pi$
$131$	−2.32520e7	+	1.95108e7i	−0.903673	+	0.758272i	0.0672316	+	0.997737i	$0.478583\pi$
$132$	−6.29529e6	−	3.57024e7i	−0.238236	−	1.35110i
$133$	3.86478e6	+	2.19183e7i	0.142444	+	0.807840i
$134$	3.50908e6	−	6.07791e6i	0.125987	−	0.218216i
$135$	9.49614e6	+	7.96821e6i	0.332184	+	0.278736i
$136$	−1.91468e7	−	6.96885e6i	−0.652694	−	0.237561i
$137$	8.51714e6	+	1.47521e7i	0.282991	+	0.490154i	0.972120	−	0.234484i	$-0.0753402\pi$
$137$	8.51714e6	+	1.47521e7i	0.282991	+	0.490154i	−0.689129	+	0.724638i	$0.742007\pi$
$138$	3.13516e6	−	5.43026e6i	0.101551	−	0.175891i
$139$	2.50919e7	−	2.10546e7i	0.792467	−	0.664959i	−0.153888	−	0.988088i	$-0.549179\pi$
$139$	2.50919e7	−	2.10546e7i	0.792467	−	0.664959i	0.946355	+	0.323130i	$0.104735\pi$
$140$	−2.05063e7	−	3.55179e7i	−0.631595	−	1.09395i
$141$	−3.38754e6	+	1.92117e7i	−0.101770	+	0.577164i
$142$	−6.96696e6			−0.204190
$143$	1.02138e7	−	5.79253e7i	0.292086	−	1.65650i
$144$	3.28019e7	+	2.75241e7i	0.915441	+	0.768146i
$145$	2.53509e6	−	922698.i	0.0690566	−	0.0251346i
$146$	8.29335e6	+	3.01853e6i	0.220544	+	0.0802714i
$147$	−1.25763e8			−3.26545
$148$	3.28382e7	−	1.84874e7i	0.832652	−	0.468769i
$149$	4.67382e7			1.15750			0.578749	−	0.815506i	$-0.303541\pi$
$149$	4.67382e7			1.15750			0.578749	+	0.815506i	$0.303541\pi$
$150$	5.54973e6	+	2.01994e6i	0.134262	+	0.0488673i
$151$	−2.64989e7	+	9.64481e6i	−0.626338	+	0.227968i	−0.635637	−	0.771988i	$-0.719262\pi$
$151$	−2.64989e7	+	9.64481e6i	−0.626338	+	0.227968i	0.00929881	+	0.999957i	$0.497040\pi$
$152$	6.35275e6	+	5.33059e6i	0.146727	+	0.123118i
$153$	1.78286e7	−	1.01111e8i	0.402435	−	2.28232i
$154$	1.57207e7			0.346856
$155$	−2.01442e6	+	1.14243e7i	−0.0434499	+	0.246417i
$156$	6.30550e7	+	1.09214e8i	1.32979	+	2.30326i
$157$	−4.37049e7	+	3.66727e7i	−0.901324	+	0.756301i	−0.970449	−	0.241308i	$-0.922424\pi$
$157$	−4.37049e7	+	3.66727e7i	−0.901324	+	0.756301i	0.0691249	+	0.997608i	$0.477979\pi$
$158$	2.88431e6	−	4.99577e6i	0.0581757	−	0.100763i
$159$	4.29403e7	+	7.43747e7i	0.847178	+	1.46736i
$160$	−2.17033e7	−	7.89937e6i	−0.418896	−	0.152466i
$161$	−4.47647e7	−	3.75621e7i	−0.845367	−	0.709348i
$162$	−2.75527e6	+	4.77227e6i	−0.0509169	+	0.0881906i
$163$	563596.	+	3.19631e6i	0.0101932	+	0.0578087i	0.989480	−	0.144669i	$-0.0462117\pi$
$163$	563596.	+	3.19631e6i	0.0101932	+	0.0578087i	−0.979287	+	0.202478i	$0.935101\pi$
$164$	−1.60806e7	−	9.11977e7i	−0.284675	−	1.61447i
$165$	−4.75095e7	+	3.98652e7i	−0.823355	+	0.690877i
$166$	6.65099e6	−	2.42076e6i	0.112852	−	0.0410746i
$167$	7.09611e6	−	2.58277e6i	0.117900	−	0.0429120i	−0.282397	−	0.959298i	$-0.591129\pi$
$167$	7.09611e6	−	2.58277e6i	0.117900	−	0.0429120i	0.400296	+	0.916386i	$0.368907\pi$
$168$	−5.28416e7	+	4.43394e7i	−0.859793	+	0.721452i
$169$	2.46335e7	+	1.39703e8i	0.392575	+	2.22640i
$170$	2.95763e6	+	1.67735e7i	0.0461713	+	0.261850i
$171$	−2.08937e7	+	3.61889e7i	−0.319542	+	0.553463i
$172$	−1.84865e7	−	1.55120e7i	−0.277017	−	0.232445i
$173$	5.50595e7	+	2.00400e7i	0.808483	+	0.294264i	0.712997	−	0.701167i	$-0.247337\pi$
$173$	5.50595e7	+	2.00400e7i	0.808483	+	0.294264i	0.0954861	+	0.995431i	$0.469559\pi$
$174$	−1.10857e6	−	1.92011e6i	−0.0159530	−	0.0276314i
$175$	2.75200e7	−	4.76660e7i	0.388164	−	0.672319i
$176$	−4.48277e7	+	3.76149e7i	−0.619801	+	0.520075i
$177$	5.26205e7	+	9.11415e7i	0.713262	+	1.23541i
$178$	1.24212e6	−	7.04444e6i	0.0165080	−	0.0936217i
$179$	−7.97142e7			−1.03884			−0.519422	−	0.854518i	$-0.673853\pi$
$179$	−7.97142e7			−1.03884			−0.519422	+	0.854518i	$0.673853\pi$
$180$	1.33714e7	−	7.58330e7i	0.170893	−	0.969180i
$181$	2.61774e7	+	2.19654e7i	0.328134	+	0.275337i	0.791939	−	0.610600i	$-0.209072\pi$
$181$	2.61774e7	+	2.19654e7i	0.328134	+	0.275337i	−0.463805	+	0.885937i	$0.653516\pi$
$182$	−5.13880e7	+	1.87037e7i	−0.631846	+	0.229973i
$183$	6.50440e7	+	2.36741e7i	0.784564	+	0.285558i
$184$	−2.17739e7			−0.257676
$185$	−5.54783e7	−	3.28375e7i	−0.644203	−	0.381302i
$186$	9.53381e6			0.108635
$187$	1.31850e8	+	4.79894e7i	1.47446	+	0.536661i
$188$	3.11048e7	−	1.13212e7i	0.341409	−	0.124263i
$189$	−7.27322e7	−	6.10295e7i	−0.783628	−	0.657542i
$190$	1.20376e6	−	6.82689e6i	0.0127322	−	0.0722080i
$191$	5.60990e7			0.582557			0.291279	−	0.956638i	$-0.405919\pi$
$191$	5.60990e7			0.582557			0.291279	+	0.956638i	$0.405919\pi$
$192$	1.95046e7	−	1.10616e8i	0.198876	−	1.12788i
$193$	−2.22235e7	−	3.84922e7i	−0.222516	−	0.385409i	0.733055	−	0.680169i	$-0.238094\pi$
$193$	−2.22235e7	−	3.84922e7i	−0.222516	−	0.385409i	−0.955571	+	0.294760i	$0.904760\pi$
$194$	1.51432e7	−	1.27067e7i	0.148906	−	0.124947i
$195$	1.07870e8	−	1.86836e8i	1.04179	−	1.80443i
$196$	1.06697e8	+	1.84804e8i	1.01218	+	1.75314i
$197$	−3.60615e7	−	1.31253e7i	−0.336056	−	0.122315i	0.168480	−	0.985705i	$-0.446114\pi$
$197$	−3.60615e7	−	1.31253e7i	−0.336056	−	0.122315i	−0.504536	+	0.863391i	$0.668336\pi$
$198$	2.26108e7	+	1.89727e7i	0.207008	+	0.173700i
$199$	−1.52341e7	+	2.63863e7i	−0.137035	+	0.237352i	−0.926373	−	0.376607i	$-0.877091\pi$
$199$	−1.52341e7	+	2.63863e7i	−0.137035	+	0.237352i	0.789338	+	0.613959i	$0.210424\pi$
$200$	−3.56124e6	−	2.01968e7i	−0.0314773	−	0.178516i
$201$	−3.68238e7	−	2.08838e8i	−0.319847	−	1.81394i
$202$	1.73392e7	−	1.45493e7i	0.148013	−	0.124198i
$203$	−1.94166e7	+	7.06706e6i	−0.162906	+	0.0592929i
$204$	−2.82691e8	+	1.02891e8i	−2.33134	+	0.848540i
$205$	−1.21358e8	+	1.01831e8i	−0.983851	+	0.825549i
$206$	−2.71266e6	−	1.53843e7i	−0.0216202	−	0.122614i
$207$	−1.90521e7	−	1.08050e8i	−0.149295	−	0.846695i
$208$	1.01781e8	−	1.76290e8i	0.784233	−	1.35833i
$209$	−4.37468e7	−	3.67079e7i	−0.331462	−	0.278130i
$210$	5.41840e7	+	1.97214e7i	0.403742	+	0.146950i
$211$	6.60211e7	+	1.14352e8i	0.483832	+	0.838021i	0.999828	−	0.0185698i	$-0.00591128\pi$
$211$	6.60211e7	+	1.14352e8i	0.483832	+	0.838021i	−0.515996	+	0.856591i	$0.672578\pi$
$212$	7.28605e7	−	1.26198e8i	0.525190	−	0.909656i
$213$	−1.61262e8	+	1.35315e8i	−1.14341	+	0.959437i
$214$	−1.08058e6	−	1.87163e6i	−0.00753721	−	0.0130548i
$215$	−7.16891e6	+	4.06569e7i	−0.0491947	+	0.278997i
$216$	−3.53774e7			−0.238857
$217$	1.54287e7	−	8.75004e7i	0.102499	−	0.581301i
$218$	−2.30428e7	−	1.93352e7i	−0.150639	−	0.126401i
$219$	2.50590e8	−	9.12075e7i	1.61217	−	0.586781i
$220$	9.88872e7	+	3.59920e7i	0.626125	+	0.227891i
$221$	−4.88087e8			−3.04176
$222$	−1.86598e7	+	4.95879e7i	−0.114465	+	0.304187i
$223$	8.53166e7			0.515189			0.257594	−	0.966253i	$-0.417070\pi$
$223$	8.53166e7			0.515189			0.257594	+	0.966253i	$0.417070\pi$
$224$	1.66229e8	+	6.05023e7i	0.988184	+	0.359670i
$225$	9.71077e7	−	3.53443e7i	0.568349	−	0.206862i
$226$	−1.80334e7	−	1.51318e7i	−0.103920	−	0.0871988i
$227$	−5.90929e7	+	3.35132e8i	−0.335309	+	1.90163i	0.0888568	+	0.996044i	$0.471679\pi$
$227$	−5.90929e7	+	3.35132e8i	−0.335309	+	1.90163i	−0.424165	+	0.905585i	$0.639432\pi$
$228$	1.22440e8			0.684152
$229$	−1.01695e7	+	5.76744e7i	−0.0559600	+	0.317365i	−0.999919	−	0.0126967i	$-0.995958\pi$
$229$	−1.01695e7	+	5.76744e7i	−0.0559600	+	0.317365i	0.943959	+	0.330062i	$0.107070\pi$
$230$	9.10058e6	+	1.57627e7i	0.0493198	+	0.0854244i
$231$	3.63882e8	−	3.05333e8i	1.94231	−	1.62979i
$232$	−3.84956e6	+	6.66763e6i	−0.0202396	+	0.0350561i
$233$	−4.64369e7	−	8.04310e7i	−0.240501	−	0.416560i	0.720356	−	0.693605i	$-0.243978\pi$
$233$	−4.64369e7	−	8.04310e7i	−0.240501	−	0.416560i	−0.960857	+	0.277044i	$0.910645\pi$
$234$	−9.64831e7	−	3.51170e7i	−0.492261	−	0.179168i
$235$	−4.33788e7	−	3.63991e7i	−0.218042	−	0.182959i
$236$	8.92859e7	−	1.54648e8i	0.442172	−	0.765864i
$237$	−3.02675e7	−	1.71656e8i	−0.147692	−	0.837604i
$238$	−2.26528e7	−	1.28471e8i	−0.108919	−	0.617710i
$239$	−1.76775e8	+	1.48332e8i	−0.837585	+	0.702818i	−0.957019	−	0.290025i	$-0.906337\pi$
$239$	−1.76775e8	+	1.48332e8i	−0.837585	+	0.702818i	0.119434	+	0.992842i	$0.461892\pi$
$240$	−2.01694e8	+	7.34105e7i	−0.941788	+	0.342783i
$241$	−3.45611e8	+	1.25792e8i	−1.59048	+	0.578887i	−0.977449	−	0.211172i	$-0.932272\pi$
$241$	−3.45611e8	+	1.25792e8i	−1.59048	+	0.578887i	−0.613031	+	0.790059i	$0.710050\pi$
$242$	4.71189e6	−	3.95375e6i	0.0213718	−	0.0179331i
$243$	5.14129e7	+	2.91577e8i	0.229853	+	1.30356i
$244$	−2.03948e7	−	1.15665e8i	−0.0898783	−	0.509725i
$245$	1.82530e8	−	3.16151e8i	0.792961	−	1.37345i
$246$	9.97367e7	+	8.36890e7i	0.427152	+	0.358423i
$247$	1.86673e8	+	6.79434e7i	0.788211	+	0.286885i
$248$	−1.65532e7	−	2.86710e7i	−0.0689130	−	0.119361i
$249$	1.06931e8	−	1.85210e8i	0.438942	−	0.760270i
$250$	−4.30056e7	+	3.60860e7i	−0.174074	+	0.146066i
$251$	−1.91377e8	−	3.31475e8i	−0.763892	−	1.32310i	−0.940830	−	0.338878i	$-0.889953\pi$
$251$	−1.91377e8	−	3.31475e8i	−0.763892	−	1.32310i	0.176938	−	0.984222i	$-0.443381\pi$
$252$	−1.02413e8	+	5.80815e8i	−0.403139	+	2.28631i
$253$	1.49941e8			0.582100
$254$	2.66212e6	−	1.50977e7i	0.0101932	−	0.0578085i
$255$	3.94241e8	+	3.30807e8i	1.48892	+	1.24935i
$256$	−1.47420e8	+	5.36565e7i	−0.549182	+	0.199886i
$257$	3.17896e8	+	1.15705e8i	1.16821	+	0.425192i	0.852022	−	0.523505i	$-0.175376\pi$
$257$	3.17896e8	+	1.15705e8i	1.16821	+	0.425192i	0.316184	+	0.948698i	$0.397598\pi$
$258$	3.39289e7			0.122999
$259$	4.24916e8	+	2.51507e8i	1.51969	+	0.899499i
$260$	−3.66065e8			−1.29167
$261$	−3.64555e7	−	1.32687e7i	−0.126917	−	0.0461941i
$262$	−6.80439e7	+	2.47659e7i	−0.233741	+	0.0850747i
$263$	−2.56142e8	−	2.14928e8i	−0.868230	−	0.728532i	0.0954946	−	0.995430i	$-0.469557\pi$
$263$	−2.56142e8	−	2.14928e8i	−0.868230	−	0.728532i	−0.963725	+	0.266898i	$0.914001\pi$
$264$	3.07348e7	−	1.74305e8i	0.102805	−	0.583039i
$265$	−2.49289e8			−0.822893
$266$	−9.21979e6	+	5.22880e7i	−0.0300355	+	0.170340i
$267$	−1.08069e8	−	1.87180e8i	−0.347464	−	0.601826i
$268$	−2.75638e8	+	2.31288e8i	−0.874717	+	0.733975i
$269$	1.53895e8	−	2.66555e8i	0.482051	−	0.834936i	−0.517737	−	0.855540i	$-0.673225\pi$
$269$	1.53895e8	−	2.66555e8i	0.482051	−	0.834936i	0.999788	+	0.0206036i	$0.00655881\pi$
$270$	1.47863e7	+	2.56106e7i	0.0457179	+	0.0791857i
$271$	−8.75365e6	−	3.18607e6i	−0.0267175	−	0.00972439i	0.328627	−	0.944460i	$-0.393414\pi$
$271$	−8.75365e6	−	3.18607e6i	−0.0267175	−	0.00972439i	−0.355344	+	0.934735i	$0.615636\pi$
$272$	3.71987e8	+	3.12134e8i	1.12082	+	0.940480i
$273$	−8.26190e8	+	1.43100e9i	−2.45760	+	4.25668i
$274$	7.05652e6	+	4.00195e7i	0.0207235	+	0.117529i
$275$	2.45237e7	+	1.39081e8i	0.0711085	+	0.403276i
$276$	−2.46267e8	+	2.06642e8i	−0.705057	+	0.591613i
$277$	−7.70644e7	+	2.80492e7i	−0.217859	+	0.0792941i	−0.448644	−	0.893711i	$-0.648093\pi$
$277$	−7.70644e7	+	2.80492e7i	−0.217859	+	0.0792941i	0.230785	+	0.973005i	$0.425871\pi$
$278$	7.34279e7	−	2.67256e7i	0.204977	−	0.0746054i
$279$	1.27792e8	−	1.07230e8i	0.352280	−	0.295598i
$280$	−3.47697e7	−	1.97189e8i	−0.0946560	−	0.536821i
$281$	9.37572e7	+	5.31724e8i	0.252077	+	1.42960i	0.803467	+	0.595350i	$0.202987\pi$
$281$	9.37572e7	+	5.31724e8i	0.252077	+	1.42960i	−0.551390	+	0.834248i	$0.685902\pi$
$282$	−2.32692e7	+	4.03034e7i	−0.0617887	+	0.107021i
$283$	−2.77052e7	−	2.32474e7i	−0.0726622	−	0.0609708i	0.605733	−	0.795668i	$-0.292880\pi$
$283$	−2.77052e7	−	2.32474e7i	−0.0726622	−	0.0609708i	−0.678395	+	0.734697i	$0.737324\pi$
$284$	3.35653e8	+	1.22168e8i	0.869514	+	0.316477i
$285$	−1.04731e8	−	1.81400e8i	−0.267990	−	0.464173i
$286$	7.01589e7	−	1.21519e8i	0.177338	−	0.307158i
$287$	9.29495e8	−	7.79939e8i	2.32092	−	1.94748i
$288$	1.66066e8	+	2.87634e8i	0.409644	+	0.709523i
$289$	1.30928e8	−	7.42532e8i	0.319074	−	1.80956i
$290$	6.43582e6			0.0154957
$291$	1.03722e8	−	5.88234e8i	0.246742	−	1.39935i
$292$	−3.46625e8	−	2.90853e8i	−0.814742	−	0.683650i
$293$	4.00550e8	−	1.45788e8i	0.930294	−	0.338599i	0.167968	−	0.985792i	$-0.446279\pi$
$293$	4.00550e8	−	1.45788e8i	0.930294	−	0.338599i	0.762326	+	0.647193i	$0.224057\pi$
$294$	−2.81927e8	−	1.02613e8i	−0.647024	−	0.235498i
$295$	−3.05488e8			−0.692815
$296$	1.81524e8	−	2.99820e7i	0.406830	−	0.0671955i
$297$	2.43618e8			0.539588
$298$	1.04774e8	+	3.81346e7i	0.229349	+	0.0834762i
$299$	−4.90128e8	+	1.78392e8i	−1.06038	+	0.385945i
$300$	−2.31954e8	−	1.94633e8i	−0.495995	−	0.416189i
$301$	5.49076e7	−	3.11397e8i	0.116051	−	0.658159i
$302$	−6.72726e7			−0.140545
$303$	1.18763e8	−	6.73537e8i	0.245262	−	1.39095i
$304$	−9.88193e7	−	1.71160e8i	−0.201736	−	0.349418i
$305$	−1.53916e8	+	1.29151e8i	−0.310624	+	0.260644i
$306$	1.22465e8	−	2.12116e8i	0.244336	−	0.423202i
$307$	1.55091e7	+	2.68626e7i	0.0305917	+	0.0529864i	0.880916	−	0.473273i	$-0.156928\pi$
$307$	1.55091e7	+	2.68626e7i	0.0305917	+	0.0529864i	−0.850324	+	0.526259i	$0.823594\pi$
$308$	−7.57390e8	−	2.75667e8i	−1.47704	−	0.537598i
$309$	−3.61588e8	−	3.03408e8i	−0.697203	−	0.585023i
$310$	−1.38371e7	+	2.39666e7i	−0.0263803	+	0.0456920i
$311$	7.72065e7	+	4.37860e8i	0.145543	+	0.825417i	0.966929	+	0.255045i	$0.0820901\pi$
$311$	7.72065e7	+	4.37860e8i	0.145543	+	0.825417i	−0.821386	+	0.570373i	$0.806799\pi$
$312$	1.06914e8	+	6.06338e8i	0.199293	+	1.13025i
$313$	2.04604e8	−	1.71683e8i	0.377145	−	0.316462i	−0.434435	−	0.900703i	$-0.643052\pi$
$313$	2.04604e8	−	1.71683e8i	0.377145	−	0.316462i	0.811581	+	0.584241i	$0.198608\pi$
$314$	−1.27896e8	+	4.65504e7i	−0.233133	+	0.0848535i
$315$	9.48098e8	−	3.45080e8i	1.70910	−	0.622060i
$316$	−2.26562e8	+	1.90108e8i	−0.403909	+	0.338919i
$317$	−1.28310e7	−	7.27681e7i	−0.0226231	−	0.128302i	0.971405	−	0.237430i	$-0.0763052\pi$
$317$	−1.28310e7	−	7.27681e7i	−0.0226231	−	0.128302i	−0.994028	+	0.109128i	$0.965194\pi$
$318$	3.55763e7	+	2.01763e8i	0.0620392	+	0.351842i
$319$	2.65091e7	−	4.59151e7i	0.0457222	−	0.0791932i
$320$	2.49763e8	+	2.09576e8i	0.426093	+	0.357534i
$321$	−6.13634e7	−	2.23344e7i	−0.103548	−	0.0376884i
$322$	−6.97025e7	−	1.20728e8i	−0.116346	−	0.201518i
$323$	−2.36942e8	+	4.10396e8i	−0.391232	+	0.677633i
$324$	2.16426e8	−	1.81603e8i	0.353511	−	0.296631i
$325$	−2.45634e8	−	4.25451e8i	−0.396915	−	0.687477i
$326$	−1.34451e6	+	7.62510e6i	−0.00214933	+	0.0121894i
$327$	−9.08900e8			−1.43747
$328$	7.85085e7	−	4.45244e8i	0.122845	−	0.696690i
$329$	3.32244e8	+	2.78786e8i	0.514365	+	0.431603i
$330$	−1.39030e8	+	5.06028e7i	−0.212966	+	0.0775132i
$331$	2.79997e8	+	1.01910e8i	0.424380	+	0.154462i	0.545376	−	0.838191i	$-0.316387\pi$
$331$	2.79997e8	+	1.01910e8i	0.424380	+	0.154462i	−0.120997	+	0.992653i	$0.538609\pi$
$332$	−3.62880e8			−0.544226
$333$	3.07614e8	+	8.74552e8i	0.456512	+	1.29787i
$334$	1.80149e7			0.0264556
$335$	5.78432e8	+	2.10532e8i	0.840613	+	0.305958i
$336$	1.54480e9	−	5.62261e8i	2.22169	−	0.808631i
$337$	5.47308e8	+	4.59246e8i	0.778981	+	0.653643i	0.942992	−	0.332816i	$-0.107999\pi$
$337$	5.47308e8	+	4.59246e8i	0.778981	+	0.653643i	−0.164011	+	0.986459i	$0.552443\pi$
$338$	−5.87654e7	+	3.33275e8i	−0.0827777	+	0.469456i
$339$	−7.11307e8			−0.991650
$340$	1.51637e8	−	8.59976e8i	0.209232	−	1.18662i
$341$	1.13990e8	+	1.97436e8i	0.155678	+	0.269641i
$342$	−7.63650e7	+	6.40779e7i	−0.103229	+	0.0866197i
$343$	−7.38122e8	+	1.27846e9i	−0.987640	+	1.71064i
$344$	−5.89096e7	−	1.02034e8i	−0.0780245	−	0.135142i
$345$	5.16796e8	+	1.88098e8i	0.677567	+	0.246614i
$346$	1.07077e8	+	8.98484e7i	0.138973	+	0.116612i
$347$	2.72773e8	−	4.72457e8i	0.350468	−	0.607029i	−0.635863	−	0.771802i	$-0.719356\pi$
$347$	2.72773e8	−	4.72457e8i	0.350468	−	0.607029i	0.986332	+	0.164773i	$0.0526891\pi$
$348$	1.97391e7	+	1.11946e8i	0.0251073	+	0.142391i
$349$	−9.68329e7	−	5.49167e8i	−0.121937	−	0.691536i	−0.983080	−	0.183175i	$-0.941363\pi$
$349$	−9.68329e7	−	5.49167e8i	−0.121937	−	0.691536i	0.861144	−	0.508361i	$-0.169749\pi$
$350$	1.00584e8	−	8.43999e7i	0.125398	−	0.105221i
$351$	−7.96342e8	+	2.89845e8i	−0.982935	+	0.357759i
$352$	−4.26524e8	+	1.55242e8i	−0.521247	+	0.189719i
$353$	−1.14812e9	+	9.63383e8i	−1.38923	+	1.16570i	−0.423579	+	0.905859i	$0.639226\pi$
$353$	−1.14812e9	+	9.63383e8i	−1.38923	+	1.16570i	−0.965651	+	0.259843i	$0.916329\pi$
$354$	4.35965e7	+	2.47248e8i	0.0522324	+	0.296225i
$355$	−1.06110e8	−	6.01780e8i	−0.125880	−	0.713902i
$356$	−1.83370e8	+	3.17605e8i	−0.215403	+	0.373089i
$357$	−3.01954e9	−	2.53370e9i	−3.51239	−	2.94724i
$358$	−1.78697e8	−	6.50404e7i	−0.205839	−	0.0749192i
$359$	−2.80444e8	−	4.85743e8i	−0.319901	−	0.554084i	0.660566	−	0.750768i	$-0.270316\pi$
$359$	−2.80444e8	−	4.85743e8i	−0.319901	−	0.554084i	−0.980467	+	0.196684i	$0.936983\pi$
$360$	1.87971e8	−	3.25575e8i	0.212340	−	0.367784i
$361$	−5.36996e8	+	4.50593e8i	−0.600753	+	0.504092i
$362$	4.07604e7	+	7.05991e7i	0.0451605	+	0.0782202i
$363$	3.22735e7	−	1.83032e8i	0.0354138	−	0.200842i
$364$	2.80374e9			3.04707
$365$	−1.34418e8	+	7.62323e8i	−0.144688	+	0.820567i
$366$	1.26494e8	+	1.06141e8i	0.134861	+	0.113162i
$367$	4.96196e8	−	1.80601e8i	0.523989	−	0.190716i	−0.0664636	−	0.997789i	$-0.521172\pi$
$367$	4.96196e8	−	1.80601e8i	0.523989	−	0.190716i	0.590452	+	0.807073i	$0.298949\pi$
$368$	4.87624e8	+	1.77481e8i	0.510056	+	0.185645i
$369$	2.27815e9			2.36043
$370$	−9.75743e7	−	1.18879e8i	−0.100145	−	0.122011i
$371$	1.90934e9			1.94122
$372$	−4.59319e8	−	1.67178e8i	−0.462609	−	0.168376i
$373$	−8.85501e8	+	3.22296e8i	−0.883503	+	0.321569i	−0.743623	−	0.668599i	$-0.766894\pi$
$373$	−8.85501e8	+	3.22296e8i	−0.883503	+	0.321569i	−0.139881	+	0.990168i	$0.544672\pi$
$374$	2.56415e8	+	2.15158e8i	0.253450	+	0.212670i
$375$	−2.94561e8	+	1.67054e9i	−0.288447	+	1.63587i
$376$	1.61606e8			0.156783
$377$	−3.20257e7	+	1.81627e8i	−0.0307825	+	0.174576i
$378$	−1.13250e8	−	1.96155e8i	−0.107849	−	0.186800i
$379$	−1.16798e9	+	9.80048e8i	−1.10204	+	0.924720i	−0.997560	−	0.0698074i	$-0.977762\pi$
$379$	−1.16798e9	+	9.80048e8i	−1.10204	+	0.924720i	−0.104478	+	0.994527i	$0.533317\pi$
$380$	−1.77707e8	+	3.07797e8i	−0.166135	+	0.287754i
$381$	−2.31613e8	−	4.01165e8i	−0.214548	−	0.371609i
$382$	1.25758e8	+	4.57723e7i	0.115429	+	0.0420128i
$383$	2.51744e8	+	2.11239e8i	0.228962	+	0.192122i	0.750050	−	0.661381i	$-0.230029\pi$
$383$	2.51744e8	+	2.11239e8i	0.228962	+	0.192122i	−0.521088	+	0.853503i	$0.674474\pi$
$384$	6.43205e8	−	1.11406e9i	0.579682	−	1.00404i
$385$	2.39434e8	+	1.35790e9i	0.213832	+	1.21270i
$386$	−1.84123e7	−	1.04421e8i	−0.0162949	−	0.0924132i
$387$	4.54785e8	−	3.81610e8i	0.398857	−	0.334681i
$388$	−9.52385e8	+	3.46640e8i	−0.827754	+	0.301278i
$389$	3.06833e8	−	1.11678e8i	0.264289	−	0.0961933i	−0.206477	−	0.978451i	$-0.566200\pi$
$389$	3.06833e8	−	1.11678e8i	0.264289	−	0.0961933i	0.470766	+	0.882258i	$0.343978\pi$
$390$	3.94258e8	−	3.30822e8i	0.336554	−	0.282402i
$391$	−2.16058e8	−	1.22533e9i	−0.182790	−	1.03665i
$392$	1.80912e8	+	1.02600e9i	0.151693	+	0.860293i
$393$	−1.09398e9	+	1.89482e9i	−0.909146	+	1.57469i
$394$	−7.01307e7	−	5.88467e7i	−0.0577659	−	0.0484714i
$395$	4.75446e8	+	1.73048e8i	0.388160	+	0.141279i
$396$	−7.56647e8	−	1.31055e9i	−0.612294	−	1.06053i
$397$	−5.65894e8	+	9.80156e8i	−0.453908	+	0.786192i	−0.998625	−	0.0524282i	$-0.983304\pi$
$397$	−5.65894e8	+	9.80156e8i	−0.453908	+	0.786192i	0.544717	+	0.838620i	$0.316637\pi$
$398$	−5.56798e7	+	4.67209e7i	−0.0442697	+	0.0371467i
$399$	8.02149e8	+	1.38936e9i	0.632194	+	1.09499i
$400$	−8.48722e7	+	4.81334e8i	−0.0663064	+	0.376042i
$401$	4.15944e8			0.322129			0.161064	−	0.986944i	$-0.448507\pi$
$401$	4.15944e8			0.322129			0.161064	+	0.986944i	$0.448507\pi$
$402$	8.78465e7	−	4.98202e8i	0.0674424	−	0.382485i
$403$	−6.07511e8	−	5.09762e8i	−0.462367	−	0.387972i
$404$	−1.09049e9	+	3.96907e8i	−0.822789	+	0.299471i
$405$	−4.54175e8	−	1.65306e8i	−0.339728	−	0.123651i
$406$	−4.92928e7			−0.0365546
$407$	−1.25002e9	+	2.06464e8i	−0.919046	+	0.151798i
$408$	−1.46872e9			−1.07061
$409$	−5.00768e8	−	1.82265e8i	−0.361914	−	0.131726i	0.154662	−	0.987967i	$-0.450571\pi$
$409$	−5.00768e8	−	1.82265e8i	−0.361914	−	0.131726i	−0.516576	+	0.856242i	$0.672793\pi$
$410$	−3.55137e8	+	1.29259e8i	−0.254479	+	0.0926228i
$411$	9.40608e8	+	7.89264e8i	0.668286	+	0.560758i
$412$	−1.39078e8	+	7.88749e8i	−0.0979755	+	0.555646i
$413$	2.33977e9			1.63436
$414$	4.54505e7	−	2.57762e8i	0.0314802	−	0.178533i
$415$	3.10394e8	+	5.37619e8i	0.213180	+	0.369238i
$416$	1.20953e9	−	1.01491e9i	0.823737	−	0.691197i
$417$	1.18054e9	−	2.04475e9i	0.797267	−	1.38091i
$418$	−6.81174e7	−	1.17983e8i	−0.0456185	−	0.0790136i
$419$	−1.61862e9	−	5.89131e8i	−1.07497	−	0.391257i	−0.256937	−	0.966428i	$-0.582713\pi$
$419$	−1.61862e9	−	5.89131e8i	−1.07497	−	0.391257i	−0.818033	+	0.575171i	$0.804936\pi$
$420$	−2.26465e9	−	1.90027e9i	−1.49152	−	1.25153i
$421$	9.75590e8	−	1.68977e9i	0.637207	−	1.10367i	−0.348837	−	0.937184i	$-0.613423\pi$
$421$	9.75590e8	−	1.68977e9i	0.637207	−	1.10367i	0.986043	−	0.166491i	$-0.0532435\pi$
$422$	5.46990e7	+	3.10213e8i	0.0354312	+	0.200940i
$423$	1.41404e8	+	8.01944e8i	0.0908389	+	0.515173i
$424$	5.44992e8	−	4.57303e8i	0.347224	−	0.291356i
$425$	1.10124e9	−	4.00819e8i	0.695858	−	0.253272i
$426$	−4.71910e8	+	1.71761e8i	−0.295751	+	0.107644i
$427$	1.17886e9	−	9.89184e8i	0.732767	−	0.614865i
$428$	1.92407e7	+	1.09120e8i	0.0118623	+	0.0672743i
$429$	−7.36237e8	−	4.17541e9i	−0.450212	−	2.55328i
$430$	−4.92435e7	+	8.52923e7i	−0.0298682	+	0.0517333i
$431$	−4.18588e6	−	3.51237e6i	−0.00251835	−	0.00211315i	0.641528	−	0.767100i	$-0.278301\pi$
$431$	−4.18588e6	−	3.51237e6i	−0.00251835	−	0.00211315i	−0.644046	+	0.764987i	$0.722745\pi$
$432$	7.92274e8	+	2.88364e8i	0.472805	+	0.172087i
$433$	6.27684e8	+	1.08718e9i	0.371564	+	0.643568i	0.989806	−	0.142420i	$-0.0454883\pi$
$433$	6.27684e8	+	1.08718e9i	0.371564	+	0.643568i	−0.618242	+	0.785987i	$0.712155\pi$
$434$	1.05980e8	−	1.83563e8i	0.0622316	−	0.107788i
$435$	1.48968e8	−	1.24999e8i	0.0867721	−	0.0728104i
$436$	7.71105e8	+	1.33559e9i	0.445565	+	0.771741i
$437$	−8.79364e7	+	4.98712e8i	−0.0504062	+	0.285868i
$438$	6.36173e8			0.361756
$439$	5.05066e8	−	2.86437e9i	0.284920	−	1.61586i	−0.420653	−	0.907222i	$-0.638199\pi$
$439$	5.05066e8	−	2.86437e9i	0.284920	−	1.61586i	0.705572	−	0.708638i	$-0.250690\pi$
$440$	3.93570e8	+	3.30245e8i	0.220261	+	0.184821i
$441$	−4.93308e9	+	1.79549e9i	−2.73894	+	0.996894i
$442$	−1.09416e9	−	3.98240e8i	−0.602700	−	0.219365i
$443$	1.75195e9			0.957433			0.478716	−	0.877970i	$-0.341102\pi$
$443$	1.75195e9			0.957433			0.478716	+	0.877970i	$0.341102\pi$
$444$	1.76853e9	−	2.06184e9i	0.958898	−	1.11793i
$445$	6.27391e8			0.337504
$446$	1.91256e8	+	6.96115e7i	0.102081	+	0.0371543i
$447$	3.16584e9	−	1.15227e9i	1.67653	−	0.610208i
$448$	−1.91297e9	−	1.60517e9i	−1.00516	−	0.843429i
$449$	3.03829e8	−	1.72310e9i	0.158404	−	0.898355i	−0.797203	−	0.603712i	$-0.793688\pi$
$449$	3.03829e8	−	1.72310e9i	0.158404	−	0.898355i	0.955607	−	0.294644i	$-0.0952010\pi$
$450$	2.46527e8			0.127532
$451$	−5.40631e8	+	3.06607e9i	−0.277513	+	1.57385i
$452$	6.03469e8	+	1.04524e9i	0.307376	+	0.532391i
$453$	−1.55714e9	+	1.30659e9i	−0.787015	+	0.660384i
$454$	−4.05911e8	+	7.03059e8i	−0.203580	+	0.352611i
$455$	−2.39822e9	−	4.15384e9i	−1.19357	−	2.06733i
$456$	5.61726e8	+	2.04452e8i	0.277426	+	0.100975i
$457$	1.35693e9	+	1.13860e9i	0.665047	+	0.558040i	0.911595	−	0.411090i	$-0.134852\pi$
$457$	1.35693e9	+	1.13860e9i	0.665047	+	0.558040i	−0.246548	+	0.969131i	$0.579296\pi$
$458$	−6.98550e7	+	1.20992e8i	−0.0339757	+	0.0588476i
$459$	−3.51043e8	−	1.99087e9i	−0.169440	−	0.960943i
$460$	−1.62043e8	−	9.18993e8i	−0.0776209	−	0.440210i
$461$	−2.70399e9	+	2.26892e9i	−1.28544	+	1.07861i	−0.292971	+	0.956121i	$0.594644\pi$
$461$	−2.70399e9	+	2.26892e9i	−1.28544	+	1.07861i	−0.992470	+	0.122492i	$0.960911\pi$
$462$	1.06485e9	−	3.87573e8i	0.502390	−	0.182855i
$463$	1.39053e9	−	5.06111e8i	0.651098	−	0.236980i	0.00470949	−	0.999989i	$-0.498501\pi$
$463$	1.39053e9	−	5.06111e8i	0.651098	−	0.236980i	0.646388	+	0.763009i	$0.276279\pi$
$464$	1.40559e8	−	1.17943e8i	0.0653199	−	0.0548099i
$465$	1.45205e8	+	8.23496e8i	0.0669723	+	0.379819i
$466$	−3.84733e7	−	2.18193e8i	−0.0176120	−	0.0998826i
$467$	−3.17082e8	+	5.49203e8i	−0.144067	+	0.249531i	−0.929024	−	0.370019i	$-0.879351\pi$
$467$	−3.17082e8	+	5.49203e8i	−0.144067	+	0.249531i	0.784958	+	0.619549i	$0.212685\pi$
$468$	4.03256e9	+	3.38372e9i	1.81853	+	1.52593i
$469$	−4.43029e9	−	1.61249e9i	−1.98302	−	0.721760i
$470$	−6.75444e7	−	1.16990e8i	−0.0300087	−	0.0519766i
$471$	−2.05625e9	+	3.56153e9i	−0.906783	+	1.57059i
$472$	6.67853e8	−	5.60395e8i	0.292337	−	0.245300i
$473$	4.05667e8	+	7.02636e8i	0.176261	+	0.305293i
$474$	7.22059e7	−	4.09500e8i	0.0311421	−	0.176616i
$475$	−4.76974e8			−0.204205
$476$	−1.16141e9	+	6.58667e9i	−0.493583	+	2.79925i
$477$	2.74617e9	+	2.30431e9i	1.15854	+	0.972134i
$478$	−5.17309e8	+	1.88285e8i	−0.216647	+	0.0788530i
$479$	−9.54541e8	−	3.47425e8i	−0.396845	−	0.144440i	0.135886	−	0.990724i	$-0.456612\pi$
$479$	−9.54541e8	−	3.47425e8i	−0.396845	−	0.144440i	−0.532731	+	0.846285i	$0.678834\pi$
$480$	−1.66484e9			−0.687111
$481$	3.84045e9	−	2.16211e9i	1.57353	−	0.885869i
$482$	−8.77401e8			−0.356889
$483$	−3.95821e9	−	1.44067e9i	−1.59839	−	0.581768i
$484$	−2.96339e8	+	1.07859e8i	−0.118804	+	0.0432411i
$485$	1.32820e9	+	1.11449e9i	0.528647	+	0.443588i
$486$	−1.22650e8	+	6.95583e8i	−0.0484664	+	0.274867i
$487$	4.32766e8			0.169786			0.0848930	−	0.996390i	$-0.472945\pi$
$487$	4.32766e8			0.169786			0.0848930	+	0.996390i	$0.472945\pi$
$488$	9.95711e7	−	5.64696e8i	0.0387850	−	0.219961i
$489$	1.16977e8	+	2.02609e8i	0.0452395	+	0.0783571i
$490$	6.67134e8	−	5.59792e8i	0.256169	−	0.214952i
$491$	1.01700e9	−	1.76150e9i	0.387736	−	0.671578i	−0.604409	−	0.796674i	$-0.706591\pi$
$491$	1.01700e9	−	1.76150e9i	0.387736	−	0.671578i	0.992145	+	0.125096i	$0.0399240\pi$
$492$	−3.33759e9	−	5.78088e9i	−1.26344	−	2.18835i
$493$	−4.13420e8	−	1.50472e8i	−0.155391	−	0.0565578i
$494$	3.63033e8	+	3.04621e8i	0.135488	+	0.113688i
$495$	−1.29442e9	+	2.24200e9i	−0.479686	+	0.830840i
$496$	1.37008e8	+	7.77011e8i	0.0504151	+	0.285918i
$497$	8.12711e8	+	4.60911e9i	0.296954	+	1.68411i
$498$	3.90827e8	−	3.27943e8i	0.141802	−	0.118986i
$499$	−5.79990e8	+	2.11099e8i	−0.208963	+	0.0760561i	−0.444381	−	0.895838i	$-0.646576\pi$
$499$	−5.79990e8	+	2.11099e8i	−0.208963	+	0.0760561i	0.235418	+	0.971894i	$0.424354\pi$
$500$	2.70470e9	−	9.84430e8i	0.967663	−	0.352200i
$501$	4.16984e8	−	3.49891e8i	0.148145	−	0.124308i
$502$	−1.58557e8	−	8.99224e8i	−0.0559401	−	0.317252i
$503$	−5.73297e8	−	3.25133e9i	−0.200859	−	1.13913i	−0.903824	−	0.427905i	$-0.859252\pi$
$503$	−5.73297e8	−	3.25133e9i	−0.200859	−	1.13913i	0.702964	−	0.711225i	$-0.251859\pi$
$504$	−1.43969e9	+	2.49362e9i	−0.500914	+	0.867609i
$505$	1.52080e9	+	1.27610e9i	0.525476	+	0.440927i
$506$	3.36125e8	+	1.22340e8i	0.115339	+	0.0419798i
$507$	5.11277e9	+	8.85558e9i	1.74232	+	3.01779i
$508$	−3.92998e8	+	6.80692e8i	−0.133005	+	0.230371i
$509$	1.39070e9	−	1.16694e9i	0.467435	−	0.392225i	−0.378423	−	0.925633i	$-0.623533\pi$
$509$	1.39070e9	−	1.16694e9i	0.467435	−	0.392225i	0.845858	+	0.533408i	$0.179089\pi$
$510$	6.13866e8	+	1.06325e9i	0.204917	+	0.354927i
$511$	1.02953e9	−	5.83873e9i	0.341322	−	1.93573i
$512$	−2.65858e9			−0.875398
$513$	−1.42876e8	+	8.10290e8i	−0.0467249	+	0.264990i
$514$	6.18230e8	+	5.18756e8i	0.200807	+	0.168497i
$515$	1.28752e9	−	4.68620e8i	0.415364	−	0.151180i
$516$	−1.63462e9	−	5.94955e8i	−0.523774	−	0.190638i
$517$	−1.11286e9			−0.354179
$518$	7.47334e8	+	9.10506e8i	0.236244	+	0.287825i
$519$	4.22355e9			1.32615
$520$	−1.67942e9	−	6.11257e8i	−0.523777	−	0.190639i
$521$	−5.55869e9	+	2.02320e9i	−1.72203	+	0.626767i	−0.998013	−	0.0630162i	$-0.979928\pi$
$521$	−5.55869e9	+	2.02320e9i	−1.72203	+	0.626767i	−0.724016	+	0.689783i	$0.757706\pi$
$522$	−7.08968e7	−	5.94895e7i	−0.0218163	−	0.0183060i
$523$	−8.47156e8	+	4.80446e9i	−0.258945	+	1.46855i	0.526795	+	0.849992i	$0.323393\pi$
$523$	−8.47156e8	+	4.80446e9i	−0.258945	+	1.46855i	−0.785740	+	0.618557i	$0.787718\pi$
$524$	3.71249e9			1.12721
$525$	6.88936e8	−	3.90715e9i	0.207788	−	1.17843i
$526$	−3.98834e8	−	6.90801e8i	−0.119493	−	0.206968i
$527$	1.44921e9	−	1.21603e9i	0.431314	−	0.361916i
$528$	−2.10908e9	+	3.65304e9i	−0.623555	+	1.08003i
$529$	1.03760e9	+	1.79718e9i	0.304745	+	0.527834i
$530$	−5.58838e8	−	2.03400e8i	−0.163050	−	0.0593452i
$531$	3.36525e9	+	2.82378e9i	0.975409	+	0.818465i
$532$	1.36108e9	−	2.35746e9i	0.391915	−	0.678817i
$533$	−1.88064e9	−	1.06656e10i	−0.537972	−	3.05099i
$534$	−8.95356e7	−	5.07782e8i	−0.0254449	−	0.144305i
$535$	1.45207e8	−	1.21843e8i	0.0409966	−	0.0344002i
$536$	−1.65077e9	+	6.00830e8i	−0.463030	+	0.168529i
$537$	−5.39948e9	+	1.96525e9i	−1.50467	+	0.547656i
$538$	5.62478e8	−	4.71975e8i	0.155728	−	0.130672i
$539$	−1.24581e9	−	7.06531e9i	−0.342681	−	1.94344i
$540$	−2.63282e8	−	1.49315e9i	−0.0719521	−	0.408061i
$541$	−1.59170e9	+	2.75691e9i	−0.432187	+	0.748569i	−0.997061	−	0.0766074i	$-0.975591\pi$
$541$	−1.59170e9	+	2.75691e9i	−0.432187	+	0.748569i	0.564875	+	0.825177i	$0.308925\pi$
$542$	−1.70237e7	−	1.42846e7i	−0.00459257	−	0.00385362i
$543$	2.31467e9	+	8.42471e8i	0.620425	+	0.225816i
$544$	1.88325e9	+	3.26189e9i	0.501547	+	0.868706i
$545$	1.31915e9	−	2.28484e9i	0.349066	−	0.604600i
$546$	−3.01967e9	+	2.53381e9i	−0.793937	+	0.666192i
$547$	1.30556e9	+	2.26129e9i	0.341068	+	0.590747i	0.984631	−	0.174646i	$-0.0558781\pi$
$547$	1.30556e9	+	2.26129e9i	0.341068	+	0.590747i	−0.643564	+	0.765393i	$0.722545\pi$
$548$	3.61787e8	−	2.05179e9i	0.0939119	−	0.532601i
$549$	2.88935e9			0.745240
$550$	−5.85035e7	+	3.31790e8i	−0.0149938	+	0.0850342i
$551$	1.37169e8	+	1.15099e8i	0.0349323	+	0.0293117i
$552$	−1.47486e9	+	5.36807e8i	−0.373220	+	0.135841i
$553$	−3.64150e9	−	1.32540e9i	−0.915677	−	0.333279i
$554$	−1.95643e8			−0.0488855
$555$	−4.56742e9	−	8.56521e8i	−1.13409	−	0.212673i
$556$	−4.00624e9			−0.988497
$557$	−6.00580e9	−	2.18593e9i	−1.47257	−	0.535973i	−0.523777	−	0.851856i	$-0.675477\pi$
$557$	−6.00580e9	−	2.18593e9i	−1.47257	−	0.535973i	−0.948798	+	0.315882i	$0.897700\pi$
$558$	3.73965e8	−	1.36112e8i	0.0911194	−	0.0331647i
$559$	−2.16201e9	−	1.81414e9i	−0.523499	−	0.439268i
$560$	−8.28638e8	+	4.69944e9i	−0.199392	+	1.13081i
$561$	1.01140e10			2.41855
$562$	−2.23666e8	+	1.26848e9i	−0.0531525	+	0.301443i
$563$	−6.96704e7	−	1.20673e8i	−0.0164539	−	0.0284990i	0.857681	−	0.514182i	$-0.171904\pi$
$563$	−6.96704e7	−	1.20673e8i	−0.0164539	−	0.0284990i	−0.874135	+	0.485683i	$0.838571\pi$
$564$	1.82779e9	−	1.53370e9i	0.428993	−	0.359968i
$565$	1.03237e9	−	1.78812e9i	0.240806	−	0.417088i
$566$	−4.31393e7	−	7.47195e7i	−0.0100004	−	0.0173211i
$567$	3.47859e9	+	1.26610e9i	0.801424	+	0.291694i
$568$	1.33590e9	+	1.12095e9i	0.305882	+	0.256666i
$569$	2.74221e9	−	4.74965e9i	0.624033	−	1.08086i	−0.364694	−	0.931127i	$-0.618826\pi$
$569$	2.74221e9	−	4.74965e9i	0.624033	−	1.08086i	0.988727	−	0.149730i	$-0.0478403\pi$
$570$	−8.67705e7	−	4.92100e8i	−0.0196250	−	0.111299i
$571$	1.41590e9	+	8.02996e9i	0.318277	+	1.80504i	0.553225	+	0.833032i	$0.313397\pi$
$571$	1.41590e9	+	8.02996e9i	0.318277	+	1.80504i	−0.234947	+	0.972008i	$0.575492\pi$
$572$	−5.51098e9	+	4.62426e9i	−1.23124	+	1.03313i
$573$	3.79990e9	−	1.38305e9i	0.843783	−	0.307112i
$574$	2.72004e9	−	9.90013e8i	0.600321	−	0.218499i
$575$	9.59348e8	−	8.04988e8i	0.210445	−	0.176584i
$576$	−8.14168e8	−	4.61738e9i	−0.177515	−	1.00674i
$577$	−1.29574e9	−	7.34850e9i	−0.280803	−	1.59252i	−0.719901	−	0.694076i	$-0.755813\pi$
$577$	−1.29574e9	−	7.34850e9i	−0.280803	−	1.59252i	0.439098	−	0.898439i	$-0.355298\pi$
$578$	8.99352e8	−	1.55772e9i	0.193724	−	0.335539i
$579$	−2.45429e9	−	2.05940e9i	−0.525474	−	0.440925i
$580$	−3.10064e8	−	1.12854e8i	−0.0659863	−	0.0240170i
$581$	−2.37735e9	−	4.11769e9i	−0.502894	−	0.871039i
$582$	7.12468e8	−	1.23403e9i	0.149808	−	0.259475i
$583$	−3.75296e9	+	3.14911e9i	−0.784394	+	0.658185i
$584$	−1.10456e9	−	1.91316e9i	−0.229480	−	0.397472i
$585$	1.56379e9	−	8.86871e9i	0.322949	−	1.83153i
$586$	1.01687e9			0.208750
$587$	1.40699e8	−	7.97942e8i	0.0287115	−	0.162831i	−0.967081	−	0.254469i	$-0.918099\pi$
$587$	1.40699e8	−	7.97942e8i	0.0287115	−	0.162831i	0.995792	+	0.0916381i	$0.0292103\pi$
$588$	1.17833e10	+	9.88735e9i	2.39026	+	2.00567i
$589$	−7.23538e8	+	2.63346e8i	−0.145901	+	0.0531035i
$590$	−6.84820e8	−	2.49254e8i	−0.137276	−	0.0499643i
$591$	−2.76623e9			−0.551230
$592$	−4.30960e9	−	8.08172e8i	−0.853711	−	0.160095i
$593$	8.80144e9			1.73326			0.866628	−	0.498956i	$-0.166283\pi$
$593$	8.80144e9			1.73326			0.866628	+	0.498956i	$0.166283\pi$
$594$	5.46125e8	+	1.98773e8i	0.106915	+	0.0389139i
$595$	1.07518e10	−	3.91334e9i	2.09253	−	0.761620i
$596$	−4.37909e9	−	3.67449e9i	−0.847271	−	0.710944i
$597$	−3.81371e8	+	2.16286e9i	−0.0733564	+	0.416025i
$598$	−1.24428e9			−0.237939
$599$	−1.49350e9	+	8.47005e9i	−0.283930	+	1.61025i	0.425154	+	0.905121i	$0.360220\pi$
$599$	−1.49350e9	+	8.47005e9i	−0.283930	+	1.61025i	−0.709084	+	0.705124i	$0.750891\pi$
$600$	−7.39149e8	−	1.28024e9i	−0.139702	−	0.241971i
$601$	−4.15829e9	+	3.48922e9i	−0.781365	+	0.655643i	−0.943592	−	0.331110i	$-0.892577\pi$
$601$	−4.15829e9	+	3.48922e9i	−0.781365	+	0.655643i	0.162227	+	0.986754i	$0.448132\pi$
$602$	3.77162e8	−	6.53265e8i	0.0704597	−	0.122040i
$603$	−4.42595e9	−	7.66596e9i	−0.822045	−	1.42382i
$604$	3.24105e9	+	1.17965e9i	0.598490	+	0.217833i
$605$	4.13275e8	+	3.46779e8i	0.0758743	+	0.0636661i
$606$	8.15785e8	−	1.41298e9i	0.148909	−	0.257918i
$607$	−6.31044e8	−	3.57883e9i	−0.114525	−	0.649502i	−0.986984	−	0.160816i	$-0.948588\pi$
$607$	−6.31044e8	−	3.57883e9i	−0.114525	−	0.649502i	0.872460	−	0.488686i	$-0.162524\pi$
$608$	−2.66199e8	−	1.50969e9i	−0.0480335	−	0.272412i
$609$	−1.14096e9	+	9.57382e8i	−0.204697	+	0.171761i
$610$	−4.50414e8	+	1.63937e8i	−0.0803448	+	0.0292431i
$611$	3.63773e9	−	1.32402e9i	0.645187	−	0.234829i
$612$	−9.61963e9	+	8.07182e9i	−1.69640	+	1.42345i
$613$	1.14707e9	+	6.50536e9i	0.201131	+	1.14067i	0.903413	+	0.428771i	$0.141053\pi$
$613$	1.14707e9	+	6.50536e9i	0.201131	+	1.14067i	−0.702282	+	0.711898i	$0.747836\pi$
$614$	1.28494e7	+	7.28728e7i	0.00224024	+	0.0127050i
$615$	−5.70972e9	+	9.88952e9i	−0.989809	+	1.71440i
$616$	−3.01441e9	−	2.52939e9i	−0.519600	−	0.435996i
$617$	−5.81739e9	−	2.11736e9i	−0.997079	−	0.362907i	−0.208622	−	0.977996i	$-0.566898\pi$
$617$	−5.81739e9	−	2.11736e9i	−0.997079	−	0.362907i	−0.788458	+	0.615089i	$0.789120\pi$
$618$	−5.63023e8	−	9.75184e8i	−0.0959547	−	0.166198i
$619$	3.11364e9	−	5.39299e9i	0.527657	−	0.913928i	−0.471824	−	0.881693i	$-0.656404\pi$
$619$	3.11364e9	−	5.39299e9i	0.527657	−	0.913928i	0.999480	−	0.0322351i	$-0.0102625\pi$
$620$	1.08691e9	−	9.12022e8i	0.183156	−	0.153686i
$621$	−1.08016e9	−	1.87089e9i	−0.180995	−	0.313492i
$622$	−1.84183e8	+	1.04455e9i	−0.0306891	+	0.174046i
$623$	−4.80527e9			−0.796177
$624$	2.54799e9	−	1.44504e10i	0.419809	−	2.38085i
$625$	−1.71654e9	−	1.44035e9i	−0.281238	−	0.235987i
$626$	5.98745e8	−	2.17925e8i	0.0975510	−	0.0355057i
$627$	−3.86820e9	−	1.40791e9i	−0.626718	−	0.228107i
$628$	6.97805e9			1.12428
$629$	3.48847e9	+	9.91777e9i	0.558931	+	1.58905i
$630$	2.40693e9			0.383506
$631$	5.90790e9	+	2.15030e9i	0.936118	+	0.340719i	0.764632	−	0.644468i	$-0.222921\pi$
$631$	5.90790e9	+	2.15030e9i	0.936118	+	0.340719i	0.171486	+	0.985187i	$0.445143\pi$
$632$	−1.35686e9	+	4.93855e8i	−0.213808	+	0.0778198i
$633$	7.29118e9	+	6.11803e9i	1.14258	+	0.958734i
$634$	3.06095e7	−	1.73595e8i	0.00477028	−	0.0270536i
$635$	1.34463e9			0.208398
$636$	1.82399e9	−	1.03444e10i	0.281140	−	1.59443i
$637$	1.24783e10	+	2.16130e10i	1.91278	+	3.31304i
$638$	9.68890e7	−	8.12995e7i	0.0147707	−	0.0123941i
$639$	−4.39365e9	+	7.61003e9i	−0.666151	+	1.15381i
$640$	1.86706e9	+	3.23384e9i	0.281532	+	0.487628i
$641$	−5.12759e9	−	1.86629e9i	−0.768971	−	0.279882i	−0.0724049	−	0.997375i	$-0.523067\pi$
$641$	−5.12759e9	−	1.86629e9i	−0.768971	−	0.279882i	−0.696566	+	0.717493i	$0.745290\pi$
$642$	−1.19337e8	−	1.00135e8i	−0.0177992	−	0.0149353i
$643$	−3.86344e9	+	6.69168e9i	−0.573107	+	0.992651i	0.423137	+	0.906066i	$0.360929\pi$
$643$	−3.86344e9	+	6.69168e9i	−0.573107	+	0.992651i	−0.996244	+	0.0865855i	$0.972404\pi$
$644$	1.24111e9	+	7.03869e9i	0.183109	+	1.03846i
$645$	5.16754e8	+	2.93066e9i	0.0758272	+	0.430037i
$646$	−8.66010e8	+	7.26669e8i	−0.126389	+	0.106053i
$647$	−7.48295e9	+	2.72357e9i	−1.08620	+	0.395343i	−0.822210	−	0.569184i	$-0.807259\pi$
$647$	−7.48295e9	+	2.72357e9i	−1.08620	+	0.395343i	−0.263985	+	0.964527i	$0.585037\pi$
$648$	1.29615e9	−	4.71761e8i	0.187130	−	0.0681098i
$649$	−4.59902e9	+	3.85903e9i	−0.660402	+	0.554143i
$650$	−2.03510e8	−	1.15416e9i	−0.0290662	−	0.164843i
$651$	−1.11214e9	−	6.30726e9i	−0.157989	−	0.895999i
$652$	1.98484e8	−	3.43785e8i	0.0280453	−	0.0485758i
$653$	1.65736e9	+	1.39069e9i	0.232928	+	0.195450i	0.751779	−	0.659415i	$-0.229196\pi$
$653$	1.65736e9	+	1.39069e9i	0.232928	+	0.195450i	−0.518852	+	0.854864i	$0.673640\pi$
$654$	−2.03750e9	−	7.41590e8i	−0.284824	−	0.103667i
$655$	−3.17553e9	−	5.50018e9i	−0.441542	−	0.764773i
$656$	−5.38741e9	+	9.33127e9i	−0.745104	+	1.29056i
$657$	8.52729e9	−	7.15524e9i	1.17309	−	0.984341i
$658$	5.17332e8	+	8.96045e8i	0.0707911	+	0.122614i
$659$	4.57417e8	−	2.59414e9i	0.0622606	−	0.353097i	−0.937723	−	0.347384i	$-0.887070\pi$
$659$	4.57417e8	−	2.59414e9i	0.0622606	−	0.353097i	0.999984	−	0.00571360i	$-0.00181871\pi$
$660$	7.58551e9			1.02703
$661$	2.44500e8	−	1.38663e9i	0.0329287	−	0.186748i	−0.963907	−	0.266240i	$-0.914219\pi$
$661$	2.44500e8	−	1.38663e9i	0.0329287	−	0.186748i	0.996835	+	0.0794921i	$0.0253298\pi$
$662$	5.44524e8	+	4.56910e8i	0.0729481	+	0.0612107i
$663$	−3.30608e10	+	1.20332e10i	−4.40572	+	1.60355i
$664$	−1.66480e9	−	6.05938e8i	−0.220686	−	0.0803230i
$665$	−4.65687e9			−0.614071
$666$	−2.39785e7	+	2.21149e9i	−0.00314531	+	0.290085i
$667$	−4.70144e8			−0.0613466
$668$	−8.67918e8	−	3.15896e8i	−0.112658	−	0.0410041i
$669$	5.77896e9	−	2.10337e9i	0.746206	−	0.271597i
$670$	1.12491e9	+	9.43910e8i	0.144496	+	0.121246i
$671$	−6.85673e8	+	3.88865e9i	−0.0876170	+	0.496901i
$672$	1.27512e10			1.62091
$673$	1.36536e9	−	7.74332e9i	0.172661	−	0.979207i	−0.768149	−	0.640271i	$-0.778822\pi$
$673$	1.36536e9	−	7.74332e9i	0.172661	−	0.979207i	0.940810	−	0.338936i	$-0.110067\pi$
$674$	8.52205e8	+	1.47606e9i	0.107210	+	0.185693i
$675$	1.55871e9	−	1.30792e9i	0.195076	−	0.163688i
$676$	8.67529e9	−	1.50260e10i	1.08012	−	1.87082i
$677$	4.24606e8	+	7.35439e8i	0.0525928	+	0.0910933i	0.891123	−	0.453761i	$-0.149918\pi$
$677$	4.24606e8	+	7.35439e8i	0.0525928	+	0.0910933i	−0.838530	+	0.544855i	$0.816585\pi$
$678$	−1.59455e9	−	5.80370e8i	−0.196488	−	0.0715157i
$679$	−1.01728e10	−	8.53601e9i	−1.24709	−	1.04643i
$680$	2.13167e9	−	3.69216e9i	0.259979	−	0.450297i
$681$	4.25957e9	+	2.41572e10i	0.516834	+	2.93111i
$682$	9.44414e7	+	5.35604e8i	0.0114003	+	0.0646545i
$683$	4.68805e9	−	3.93374e9i	0.563014	−	0.472425i	−0.316305	−	0.948658i	$-0.602442\pi$
$683$	4.68805e9	−	3.93374e9i	0.563014	−	0.472425i	0.879320	+	0.476232i	$0.157998\pi$
$684$	4.80273e9	−	1.74805e9i	0.573842	−	0.208861i
$685$	−3.34926e9	+	1.21903e9i	−0.398137	+	0.144910i
$686$	−2.69779e9	+	2.26372e9i	−0.319061	+	0.267724i
$687$	7.33048e8	+	4.15732e9i	0.0862549	+	0.489176i
$688$	4.87584e8	+	2.76523e9i	0.0570808	+	0.323721i
$689$	8.52107e9	−	1.47589e10i	0.992492	−	1.71905i
$690$	1.00504e9	+	8.43329e8i	0.116469	+	0.0977294i
$691$	−5.36436e8	−	1.95247e8i	−0.0618508	−	0.0225118i	0.310909	−	0.950440i	$-0.399366\pi$
$691$	−5.36436e8	−	1.95247e8i	−0.0618508	−	0.0225118i	−0.372760	+	0.927928i	$0.621589\pi$
$692$	−3.58323e9	−	6.20634e9i	−0.411058	−	0.711974i
$693$	9.91412e9	−	1.71718e10i	1.13159	−	1.95997i
$694$	9.96970e8	−	8.36557e8i	0.113220	−	0.0950030i
$695$	3.42680e9	+	5.93539e9i	0.387206	+	0.670660i
$696$	−9.63699e7	+	5.46541e8i	−0.0108345	+	0.0614455i
$697$	2.58352e10			2.88999
$698$	2.31004e8	−	1.31009e9i	0.0257114	−	0.145816i
$699$	−5.12835e9	−	4.30320e9i	−0.567947	−	0.476564i
$700$	−6.32590e9	+	2.30244e9i	−0.697074	+	0.253714i
$701$	−1.21882e10	−	4.43614e9i	−1.33637	−	0.486398i	−0.427701	−	0.903920i	$-0.640676\pi$
$701$	−1.21882e10	−	4.43614e9i	−1.33637	−	0.486398i	−0.908667	+	0.417522i	$0.862899\pi$
$702$	−2.02167e9			−0.220562
$703$	4.63931e7	−	4.27874e9i	0.00503628	−	0.464486i
$704$	6.40754e9			0.692129
$705$	−3.83566e9	−	1.39607e9i	−0.412267	−	0.150053i
$706$	−3.35980e9	+	1.22287e9i	−0.359333	+	0.130787i
$707$	−1.16480e10	−	9.77385e9i	−1.23961	−	1.04015i
$708$	2.23519e9	−	1.26764e10i	0.236700	−	1.34239i
$709$	−2.33352e9			−0.245895			−0.122947	−	0.992413i	$-0.539235\pi$
$709$	−2.33352e9			−0.245895			−0.122947	+	0.992413i	$0.539235\pi$
$710$	2.53135e8	−	1.43560e9i	0.0265429	−	0.150532i
$711$	−3.63793e9	−	6.30108e9i	−0.379587	−	0.657463i
$712$	−1.37159e9	+	1.15090e9i	−0.142412	+	0.119498i
$713$	1.01082e9	−	1.75079e9i	0.104438	−	0.180892i
$714$	−4.70168e9	−	8.14355e9i	−0.483403	−	0.837278i
$715$	1.15649e10	+	4.20928e9i	1.18324	+	0.430662i
$716$	7.46875e9	+	6.26703e9i	0.760418	+	0.638066i
$717$	−8.31703e9	+	1.44055e10i	−0.842658	+	1.45953i
$718$	−2.32350e8	−	1.31772e9i	−0.0234264	−	0.132858i
$719$	2.19100e9	+	1.24258e10i	0.219832	+	1.24673i	0.872322	+	0.488932i	$0.162613\pi$
$719$	2.19100e9	+	1.24258e10i	0.219832	+	1.24673i	−0.652490	+	0.757797i	$0.726276\pi$
$720$	−6.86339e9	+	5.75907e9i	−0.685291	+	0.575027i
$721$	−9.86130e9	+	3.58922e9i	−0.979852	+	0.356637i
$722$	−1.57145e9	+	5.71959e8i	−0.155389	+	0.0565568i
$723$	−2.03089e10	+	1.70412e10i	−1.99849	+	1.67693i
$724$	−7.25773e8	−	4.11606e9i	−0.0710748	−	0.403085i
$725$	−7.68949e7	−	4.36092e8i	−0.00749401	−	0.0425006i
$726$	2.21688e8	−	3.83975e8i	0.0215013	−	0.0372413i
$727$	−1.19692e10	−	1.00433e10i	−1.15530	−	0.969409i	−0.155467	−	0.987841i	$-0.549688\pi$
$727$	−1.19692e10	−	1.00433e10i	−1.15530	−	0.969409i	−0.999830	+	0.0184320i	$0.994133\pi$
$728$	1.28629e10	+	4.68170e9i	1.23560	+	0.449722i
$729$	8.14503e9	+	1.41076e10i	0.778657	+	1.34867i
$730$	−9.23323e8	+	1.59924e9i	−0.0878464	+	0.152154i
$731$	5.15744e9	−	4.32761e9i	0.488341	−	0.409767i
$732$	−4.23301e9	−	7.33179e9i	−0.398897	−	0.690910i
$733$	−3.51833e9	+	1.99534e10i	−0.329968	+	1.87134i	0.142203	+	0.989837i	$0.454581\pi$
$733$	−3.51833e9	+	1.99534e10i	−0.329968	+	1.87134i	−0.472172	+	0.881507i	$0.656530\pi$
$734$	1.25969e9			0.117578
$735$	4.56945e9	−	2.59147e10i	0.424481	−	2.40735i
$736$	3.08332e9	+	2.58721e9i	0.285066	+	0.239199i
$737$	1.13676e10	−	4.13747e9i	1.04600	−	0.380714i
$738$	5.10699e9	+	1.85879e9i	0.467700	+	0.170229i
$739$	−1.78950e10			−1.63108			−0.815542	−	0.578698i	$-0.803561\pi$
$739$	−1.78950e10			−1.63108			−0.815542	+	0.578698i	$0.803561\pi$
$740$	2.61635e9	+	7.43832e9i	0.237348	+	0.674782i
$741$	1.43195e10			1.29289
$742$	4.28021e9	+	1.55787e9i	0.384637	+	0.139997i
$743$	1.67608e10	−	6.10044e9i	1.49911	−	0.545633i	0.543283	−	0.839550i	$-0.317181\pi$
$743$	1.67608e10	−	6.10044e9i	1.49911	−	0.545633i	0.955831	+	0.293917i	$0.0949590\pi$
$744$	−1.82809e9	−	1.53395e9i	−0.162739	−	0.136554i
$745$	−1.69817e9	+	9.63081e9i	−0.150465	+	0.853328i
$746$	−2.24802e9			−0.198250
$747$	1.55018e9	−	8.79153e9i	0.136070	−	0.771689i
$748$	−8.58068e9	−	1.48622e10i	−0.749663	−	1.29845i
$749$	−1.11216e9	+	9.33210e8i	−0.0967118	+	0.0811508i
$750$	−2.02335e9	+	3.50455e9i	−0.175129	+	0.303332i
$751$	−2.63406e9	−	4.56233e9i	−0.226927	−	0.393049i	0.729969	−	0.683481i	$-0.239535\pi$
$751$	−2.63406e9	−	4.56233e9i	−0.226927	−	0.393049i	−0.956896	+	0.290431i	$0.906201\pi$
$752$	−3.61914e9	−	1.31726e9i	−0.310344	−	0.112956i
$753$	−2.11351e10	−	1.77345e10i	−1.80394	−	1.51369i
$754$	−2.19986e8	+	3.81026e8i	−0.0186894	+	0.0323709i
$755$	−1.02459e9	−	5.81076e9i	−0.0866438	−	0.491382i
$756$	2.01651e9	+	1.14362e10i	0.169736	+	0.962622i
$757$	6.42573e9	−	5.39183e9i	0.538377	−	0.451752i	−0.332605	−	0.943066i	$-0.607928\pi$
$757$	6.42573e9	−	5.39183e9i	0.538377	−	0.451752i	0.870983	+	0.491314i	$0.163483\pi$
$758$	−3.41792e9	+	1.24402e9i	−0.285049	+	0.103749i
$759$	1.01563e10	−	3.69660e9i	0.843121	−	0.306871i
$760$	−1.32923e9	+	1.11536e9i	−0.109838	+	0.0921653i
$761$	−2.92010e9	−	1.65607e10i	−0.240188	−	1.36217i	−0.831408	−	0.555663i	$-0.812465\pi$
$761$	−2.92010e9	−	1.65607e10i	−0.240188	−	1.36217i	0.591220	−	0.806510i	$-0.298647\pi$
$762$	−1.91893e8	−	1.08828e9i	−0.0157115	−	0.0891041i
$763$	−1.01036e10	+	1.74999e10i	−0.823453	+	1.42626i
$764$	−5.25615e9	−	4.41043e9i	−0.426423	−	0.357812i
$765$	2.01870e10	+	7.34746e9i	1.63026	+	0.593365i
$766$	3.91987e8	+	6.78942e8i	0.0315117	+	0.0545798i
$767$	1.04420e10	−	1.80861e10i	0.835605	−	1.44731i
$768$	−8.66274e9	+	7.26890e9i	−0.690067	+	0.579035i
$769$	9.16073e8	+	1.58669e9i	0.0726420	+	0.125820i	0.900058	−	0.435769i	$-0.143524\pi$
$769$	9.16073e8	+	1.58669e9i	0.0726420	+	0.125820i	−0.827416	+	0.561589i	$0.810190\pi$
$770$	−5.71191e8	+	3.23939e9i	−0.0450883	+	0.255708i
$771$	2.43854e10			1.91620
$772$	−9.43996e8	+	5.35367e9i	−0.0738431	+	0.418785i
$773$	1.79089e10	+	1.50274e10i	1.39457	+	1.17018i	0.963449	+	0.267892i	$0.0863269\pi$
$773$	1.79089e10	+	1.50274e10i	1.39457	+	1.17018i	0.431123	+	0.902293i	$0.358118\pi$
$774$	1.33087e9	−	4.84395e8i	0.103167	−	0.0375497i
$775$	1.78931e9	+	6.51254e8i	0.138079	+	0.0502568i
$776$	−4.94813e9			−0.380124
$777$	3.49825e10	+	6.56020e9i	2.67533	+	0.501699i
$778$	7.78956e8			0.0593040
$779$	−9.88088e9	−	3.59635e9i	−0.748884	−	0.272571i
$780$	−2.47956e10	+	9.02486e9i	−1.87087	+	0.680941i
$781$	−9.19935e9	−	7.71917e9i	−0.691001	−	0.579819i
$782$	5.15426e8	−	2.92313e9i	0.0385428	−	0.218587i
$783$	−7.63874e8			−0.0568664
$784$	4.31152e9	−	2.44518e10i	0.319539	−	1.81220i
$785$	−5.96878e9	−	1.03382e10i	−0.440394	−	0.762785i
$786$	−3.99841e9	+	3.35507e9i	−0.293703	+	0.246446i
$787$	−1.96532e9	+	3.40403e9i	−0.143721	+	0.248932i	−0.928895	−	0.370343i	$-0.879240\pi$
$787$	−1.96532e9	+	3.40403e9i	−0.143721	+	0.248932i	0.785174	+	0.619275i	$0.212574\pi$
$788$	2.34686e9	+	4.06487e9i	0.170862	+	0.295941i
$789$	−2.26487e10	−	8.24344e9i	−1.64162	−	0.597501i
$790$	9.24624e8	+	7.75852e8i	0.0667222	+	0.0559866i
$791$	−7.90707e9	+	1.36954e10i	−0.568065	+	0.983917i
$792$	−1.28294e9	−	7.27594e9i	−0.0917635	−	0.520416i
$793$	−2.38518e9	−	1.35270e10i	−0.169850	−	0.963266i
$794$	−2.06831e9	+	1.73552e9i	−0.146637	+	0.123043i
$795$	−1.68857e10	+	6.14591e9i	−1.19189	+	0.433812i
$796$	3.50180e9	−	1.27455e9i	0.246091	−	0.0895698i
$797$	−2.56474e9	+	2.15207e9i	−0.179448	+	0.150575i	−0.728087	−	0.685484i	$-0.759590\pi$
$797$	−2.56474e9	+	2.15207e9i	−0.179448	+	0.150575i	0.548639	+	0.836059i	$0.315146\pi$
$798$	6.64587e8	+	3.76906e9i	0.0462958	+	0.262556i
$799$	1.60358e9	+	9.09437e9i	0.111219	+	0.630752i
$800$	−1.89553e9	+	3.28315e9i	−0.130893	+	0.226713i
$801$	−6.91133e9	−	5.79929e9i	−0.475169	−	0.398714i
$802$	9.32431e8	+	3.39377e8i	0.0638273	+	0.0232312i
$803$	7.60632e9	+	1.31745e10i	0.518406	+	0.897906i
$804$	−1.29684e10	+	2.24619e10i	−0.880015	+	1.52423i
$805$	9.36647e9	−	7.85940e9i	0.632834	−	0.531011i
$806$	−9.45946e8	−	1.63843e9i	−0.0636346	−	0.110218i
$807$	3.85262e9	−	2.18493e10i	0.258047	−	1.46346i
$808$	−5.66567e9			−0.377843
$809$	1.33932e9	−	7.59565e9i	0.0889332	−	0.504365i	−0.907505	−	0.420041i	$-0.862016\pi$
$809$	1.33932e9	−	7.59565e9i	0.0889332	−	0.504365i	0.996438	−	0.0843243i	$-0.0268732\pi$
$810$	−8.83259e8	−	7.41142e8i	−0.0583970	−	0.0490009i
$811$	1.98606e10	−	7.22868e9i	1.30744	−	0.475868i	0.408024	−	0.912971i	$-0.366218\pi$
$811$	1.98606e10	−	7.22868e9i	1.30744	−	0.475868i	0.899411	+	0.437104i	$0.143996\pi$
$812$	2.37482e9	+	8.64365e8i	0.155663	+	0.0566567i
$813$	−6.71481e8			−0.0438245
$814$	−2.97066e9	−	5.57083e8i	−0.193049	−	0.0362022i
$815$	−6.79106e8			−0.0439426
$816$	3.28920e10	+	1.19717e10i	2.11921	+	0.771330i
$817$	−2.57493e9	+	9.37196e8i	−0.165191	+	0.0601248i
$818$	−9.73870e8	−	8.17174e8i	−0.0622106	−	0.0522009i
$819$	−1.19773e10	+	6.79266e10i	−0.761842	+	4.32062i
$820$	1.93764e10			1.22722
$821$	−1.90605e9	+	1.08098e10i	−0.120208	+	0.681735i	0.863831	+	0.503782i	$0.168059\pi$
$821$	−1.90605e9	+	1.08098e10i	−0.120208	+	0.681735i	−0.984039	+	0.177953i	$0.943053\pi$
$822$	1.46461e9	+	2.53677e9i	0.0919749	+	0.159305i
$823$	1.15310e10	−	9.67570e9i	0.721057	−	0.605038i	−0.206621	−	0.978421i	$-0.566247\pi$
$823$	1.15310e10	−	9.67570e9i	0.721057	−	0.605038i	0.927677	+	0.373383i	$0.121802\pi$
$824$	−1.95511e9	+	3.38635e9i	−0.121738	+	0.210857i
$825$	5.08998e9	+	8.81611e9i	0.315593	+	0.546623i
$826$	5.24512e9	+	1.90907e9i	0.323836	+	0.117867i
$827$	1.25225e10	+	1.05077e10i	0.769880	+	0.646006i	0.940678	−	0.339300i	$-0.110190\pi$
$827$	1.25225e10	+	1.05077e10i	0.769880	+	0.646006i	−0.170798	+	0.985306i	$0.554635\pi$
$828$	−6.70965e9	+	1.16215e10i	−0.410765	+	0.711467i
$829$	7.11939e8	+	4.03761e9i	0.0434012	+	0.246141i	0.998788	−	0.0492166i	$-0.0156725\pi$
$829$	7.11939e8	+	4.03761e9i	0.0434012	+	0.246141i	−0.955387	+	0.295357i	$0.904561\pi$
$830$	2.57164e8	+	1.45845e9i	0.0156112	+	0.0885356i
$831$	−4.52848e9	+	3.79985e9i	−0.273747	+	0.229701i
$832$	−2.09450e10	+	7.62337e9i	−1.26081	+	0.458897i
$833$	−5.59431e10	+	2.03616e10i	−3.35343	+	1.22055i
$834$	4.31479e9	−	3.62054e9i	0.257560	−	0.216119i
$835$	2.74375e8	+	1.55606e9i	0.0163095	+	0.0924960i
$836$	1.21289e9	+	6.87863e9i	0.0717957	+	0.407174i
$837$	1.64234e9	−	2.84462e9i	0.0968109	−	0.167681i
$838$	−3.14782e9	−	2.64134e9i	−0.184780	−	0.155049i
$839$	1.80860e10	+	6.58278e9i	1.05725	+	0.384806i	0.811393	−	0.584500i	$-0.198709\pi$
$839$	1.80860e10	+	6.58278e9i	1.05725	+	0.384806i	0.245854	+	0.969307i	$0.420932\pi$
$840$	−7.21659e9	−	1.24995e10i	−0.420102	−	0.727637i
$841$	8.54182e9	−	1.47949e10i	0.495181	−	0.857679i
$842$	3.56572e9	−	2.99200e9i	0.205852	−	0.172730i
$843$	1.94597e10	+	3.37051e10i	1.11876	+	1.93776i
$844$	2.80441e9	−	1.59046e10i	0.160562	−	0.910593i
$845$	−2.96821e10			−1.69238
$846$	−3.37333e8	+	1.91311e9i	−0.0191541	+	0.108629i
$847$	−3.16532e9	−	2.65602e9i	−0.178989	−	0.150190i
$848$	−1.59326e10	+	5.79898e9i	−0.897223	+	0.326563i
$849$	−2.44976e9	−	8.91640e8i	−0.137387	−	0.0500049i
$850$	2.79571e9			0.156144
$851$	7.12792e9	+	8.68422e9i	0.396469	+	0.483034i
$852$	2.57475e10			1.42626
$853$	1.49253e10	+	5.43236e9i	0.823382	+	0.299686i	0.719140	−	0.694866i	$-0.244536\pi$
$853$	1.49253e10	+	5.43236e9i	0.823382	+	0.299686i	0.104242	+	0.994552i	$0.466758\pi$
$854$	3.44978e9	−	1.25562e9i	0.189535	−	0.0689851i
$855$	−6.69789e9	−	5.62020e9i	−0.366485	−	0.307518i
$856$	−9.39367e7	+	5.32742e8i	−0.00511891	+	0.0290308i
$857$	−2.54463e10			−1.38099			−0.690496	−	0.723336i	$-0.742608\pi$
$857$	−2.54463e10			−1.38099			−0.690496	+	0.723336i	$0.742608\pi$
$858$	1.75636e9	−	9.96082e9i	0.0949310	−	0.538381i
$859$	1.40559e9	+	2.43455e9i	0.0756628	+	0.131052i	0.901374	−	0.433041i	$-0.142559\pi$
$859$	1.40559e9	+	2.43455e9i	0.0756628	+	0.131052i	−0.825711	+	0.564093i	$0.809226\pi$
$860$	3.86808e9	−	3.24570e9i	0.207372	−	0.174006i
$861$	4.37315e10	−	7.57451e10i	2.33498	−	4.04430i
$862$	−6.51777e6	−	1.12891e7i	−0.000346596	−	0.000600322i
$863$	−2.77483e10	−	1.00996e10i	−1.46960	−	0.534890i	−0.521607	−	0.853186i	$-0.674667\pi$
$863$	−2.77483e10	−	1.00996e10i	−1.46960	−	0.534890i	−0.947991	+	0.318296i	$0.896889\pi$
$864$	5.00966e9	+	4.20361e9i	0.264247	+	0.221730i
$865$	−6.12994e9	+	1.06174e10i	−0.322033	+	0.557777i
$866$	5.20041e8	+	2.94930e9i	0.0272098	+	0.154314i
$867$	−9.43767e9	−	5.35237e10i	−0.491810	−	2.78920i
$868$	−8.32475e9	+	6.98529e9i	−0.432068	+	0.362548i
$869$	9.34368e9	−	3.40082e9i	0.483002	−	0.175798i
$870$	4.35934e8	−	1.58667e8i	0.0224441	−	0.00816900i
$871$	−3.22360e10	+	2.70492e10i	−1.65302	+	1.38705i
$872$	1.30746e9	+	7.41497e9i	0.0667760	+	0.378706i
$873$	−4.32960e9	−	2.45544e10i	−0.220241	−	1.24905i
$874$	−6.04039e8	+	1.04623e9i	−0.0306038	+	0.0530073i
$875$	2.88900e10	+	2.42416e10i	1.45787	+	1.22330i
$876$	−3.06495e10	−	1.11555e10i	−1.54049	−	0.560692i
$877$	−4.13716e9	−	7.16577e9i	−0.207111	−	0.358727i	0.743692	−	0.668522i	$-0.233073\pi$
$877$	−4.13716e9	−	7.16577e9i	−0.207111	−	0.358727i	−0.950803	+	0.309795i	$0.899740\pi$
$878$	3.46932e9	−	6.00903e9i	0.172987	−	0.299622i
$879$	2.35373e10	−	1.97501e10i	1.16895	−	0.980863i
$880$	−6.12213e9	−	1.06038e10i	−0.302840	−	0.524534i
$881$	5.19862e9	−	2.94829e10i	0.256137	−	1.45263i	−0.537000	−	0.843582i	$-0.680442\pi$
$881$	5.19862e9	−	2.94829e10i	0.256137	−	1.45263i	0.793137	−	0.609043i	$-0.208447\pi$
$882$	−1.25236e10			−0.614594
$883$	4.10300e9	−	2.32693e10i	0.200558	−	1.13742i	−0.703721	−	0.710476i	$-0.748480\pi$
$883$	4.10300e9	−	2.32693e10i	0.200558	−	1.13742i	0.904279	−	0.426942i	$-0.140409\pi$
$884$	4.57309e10	+	3.83728e10i	2.22652	+	1.86827i
$885$	−2.06924e10	+	7.53142e9i	−1.00348	+	0.365237i
$886$	3.92738e9	+	1.42945e9i	0.189708	+	0.0690480i
$887$	2.72254e10			1.30991			0.654955	−	0.755667i	$-0.272687\pi$
$887$	2.72254e10			1.30991			0.654955	+	0.755667i	$0.272687\pi$
$888$	1.15565e10	−	6.50609e9i	0.553833	−	0.311799i
$889$	−1.02987e10			−0.491615
$890$	1.40644e9	+	5.11901e8i	0.0668737	+	0.0243400i
$891$	−8.92566e9	+	3.24867e9i	−0.422735	+	0.153863i
$892$	−7.99366e9	−	6.70748e9i	−0.377110	−	0.316433i
$893$	6.52664e8	−	3.70144e9i	0.0306697	−	0.173937i
$894$	8.03709e9			0.376199
$895$	2.89631e9	−	1.64258e10i	0.135041	−	0.765854i
$896$	−1.43001e10	−	2.47684e10i	−0.664140	−	1.15032i
$897$	−2.88010e10	+	2.41669e10i	−1.33240	+	1.11802i
$898$	2.08701e9	−	3.61481e9i	0.0961740	−	0.166578i
$899$	−3.57419e8	−	6.19068e8i	−0.0164066	−	0.0284171i
$900$	−1.18771e10	−	4.32293e9i	−0.543079	−	0.197665i
$901$	3.11426e10	+	2.61318e10i	1.41846	+	1.19023i
$902$	−3.71361e9	+	6.43217e9i	−0.168490	+	0.291833i
$903$	−3.95789e9	−	2.24463e10i	−0.178878	−	1.01447i
$904$	1.02322e9	+	5.80297e9i	0.0460659	+	0.261253i
$905$	−5.47729e9	+	4.59600e9i	−0.245638	+	0.206115i
$906$	−4.55674e9	+	1.65852e9i	−0.203566	+	0.0740921i
$907$	−3.65444e9	+	1.33011e9i	−0.162628	+	0.0591918i	−0.422051	−	0.906572i	$-0.638690\pi$
$907$	−3.65444e9	+	1.33011e9i	−0.162628	+	0.0591918i	0.259423	+	0.965764i	$0.416468\pi$
$908$	3.18843e10	−	2.67541e10i	1.41344	−	1.18601i
$909$	−4.95745e9	−	2.81151e10i	−0.218920	−	1.24155i
$910$	−1.98694e9	−	1.12685e10i	−0.0874058	−	0.495703i
$911$	1.15703e10	−	2.00404e10i	0.507028	−	0.878199i	−0.492939	−	0.870064i	$-0.664077\pi$
$911$	1.15703e10	−	2.00404e10i	0.507028	−	0.878199i	0.999967	−	0.00813456i	$-0.00258934\pi$
$912$	−1.09133e10	−	9.15735e9i	−0.476403	−	0.399750i
$913$	1.14643e10	+	4.17265e9i	0.498539	+	0.181453i
$914$	2.11286e9	+	3.65958e9i	0.0915291	+	0.158533i
$915$	−7.24154e9	+	1.25427e10i	−0.312505	+	0.541275i
$916$	5.48711e9	−	4.60423e9i	0.235890	−	0.197935i
$917$	2.43218e10	+	4.21266e10i	1.04161	+	1.80411i
$918$	8.37446e8	−	4.74939e9i	0.0357279	−	0.202623i
$919$	−3.05269e10			−1.29741			−0.648707	−	0.761038i	$-0.724690\pi$
$919$	−3.05269e10			−1.29741			−0.648707	+	0.761038i	$0.724690\pi$
$920$	7.91126e8	−	4.48670e9i	0.0334956	−	0.189963i
$921$	1.71278e9	+	1.43720e9i	0.0722427	+	0.0606188i
$922$	−7.91286e9	+	2.88004e9i	−0.332487	+	0.121015i
$923$	3.92548e10	+	1.42876e10i	1.64319	+	0.598071i
$924$	−5.80984e10			−2.42277
$925$	−6.88942e9	+	8.03201e9i	−0.286211	+	0.333678i
$926$	3.53012e9			0.146100
$927$	−1.85150e10	−	6.73891e9i	−0.763387	−	0.277850i
$928$	1.33738e9	−	4.86767e8i	0.0549335	−	0.0199941i
$929$	1.22436e10	+	1.02736e10i	0.501020	+	0.420405i	0.857956	−	0.513723i	$-0.171734\pi$
$929$	1.22436e10	+	1.02736e10i	0.501020	+	0.420405i	−0.356936	+	0.934129i	$0.616179\pi$
$930$	−3.46399e8	+	1.96453e9i	−0.0141217	+	0.0800880i
$931$	2.42303e10			0.984091
$932$	−1.97252e9	+	1.11867e10i	−0.0798116	+	0.452634i
$933$	1.60245e10	+	2.77552e10i	0.645949	+	1.11882i
$934$	−1.15892e9	+	9.72447e8i	−0.0465413	+	0.0390528i
$935$	−1.46792e10	+	2.54252e10i	−0.587304	+	1.01724i
$936$	1.28503e10	+	2.22573e10i	0.512208	+	0.887170i
$937$	−2.62624e10	−	9.55875e9i	−1.04291	−	0.379588i	−0.236927	−	0.971527i	$-0.576140\pi$
$937$	−2.62624e10	−	9.55875e9i	−1.04291	−	0.379588i	−0.805982	+	0.591940i	$0.798362\pi$
$938$	−8.61581e9	−	7.22953e9i	−0.340868	−	0.286022i
$939$	9.62633e9	−	1.66733e10i	0.379429	−	0.657191i
$940$	1.20269e9	+	6.82077e9i	0.0472285	+	0.267846i
$941$	3.30734e9	+	1.87569e10i	0.129394	+	0.733832i	0.978600	+	0.205770i	$0.0659699\pi$
$941$	3.30734e9	+	1.87569e10i	0.129394	+	0.733832i	−0.849206	+	0.528062i	$0.822919\pi$
$942$	−7.51548e9	+	6.30623e9i	−0.292940	+	0.245806i
$943$	2.59432e10	−	9.44254e9i	1.00747	−	0.366689i
$944$	−1.95244e10	+	7.10628e9i	−0.755396	+	0.274942i
$945$	1.52183e10	−	1.27697e10i	0.586617	−	0.492230i
$946$	3.36098e8	+	1.90611e9i	0.0129076	+	0.0732029i
$947$	−6.33794e9	−	3.59442e10i	−0.242506	−	1.37532i	−0.826213	−	0.563357i	$-0.809509\pi$
$947$	−6.33794e9	−	3.59442e10i	−0.242506	−	1.37532i	0.583707	−	0.811964i	$-0.301602\pi$
$948$	−1.06594e10	+	1.84627e10i	−0.406355	+	0.703827i
$949$	−4.05380e10	−	3.40154e10i	−1.53968	−	1.29195i
$950$	−1.06924e9	−	3.89173e8i	−0.0404617	−	0.0147268i
$951$	−2.66312e9	−	4.61265e9i	−0.100406	−	0.173908i
$952$	−1.63267e10	+	2.82787e10i	−0.613295	+	1.06226i
$953$	−6.26956e8	+	5.26079e8i	−0.0234645	+	0.0196891i	−0.654444	−	0.756110i	$-0.727097\pi$
$953$	−6.26956e8	+	5.26079e8i	−0.0234645	+	0.0196891i	0.630980	+	0.775799i	$0.282653\pi$
$954$	4.27601e9	+	7.40627e9i	0.159448	+	0.276172i
$955$	−2.03829e9	+	1.15597e10i	−0.0757275	+	0.429472i
$956$	2.82245e10			1.04478
$957$	6.63629e8	−	3.76363e9i	0.0244756	−	0.138808i
$958$	−1.85635e9	−	1.55766e9i	−0.0682150	−	0.0572392i
$959$	2.56524e10	−	9.33673e9i	0.939212	−	0.341845i
$960$	2.20847e10	+	8.03817e9i	0.805642	+	0.293230i
$961$	−2.44388e10			−0.888276
$962$	1.03733e10	−	1.71335e9i	0.375669	−	0.0620487i
$963$	−2.72585e9			−0.0983579
$964$	4.22713e10	+	1.53855e10i	1.51976	+	0.553149i
$965$	8.73911e9	−	3.18078e9i	0.313056	−	0.113943i
$966$	−7.69773e9	−	6.45917e9i	−0.274753	−	0.230545i
$967$	7.28545e8	−	4.13178e9i	0.0259098	−	0.146942i	−0.969108	−	0.246635i	$-0.920675\pi$
$967$	7.28545e8	−	4.13178e9i	0.0259098	−	0.146942i	0.995018	+	0.0996934i	$0.0317862\pi$
$968$	−1.53963e9			−0.0545574
$969$	−5.93162e9	+	3.36399e10i	−0.209431	+	1.18774i
$970$	2.06811e9	+	3.58207e9i	0.0727567	+	0.126018i
$971$	7.67842e9	−	6.44296e9i	0.269156	−	0.225849i	−0.498213	−	0.867055i	$-0.666010\pi$
$971$	7.67842e9	−	6.44296e9i	0.269156	−	0.225849i	0.767369	+	0.641206i	$0.221566\pi$
$972$	1.81063e10	−	3.13610e10i	0.632409	−	1.09536i
$973$	−2.62463e10	−	4.54599e10i	−0.913425	−	1.58210i
$974$	9.70141e8	+	3.53103e8i	0.0336418	+	0.0122446i
$975$	−2.71271e10	−	2.27624e10i	−0.937320	−	0.786505i
$976$	−6.83277e9	+	1.18347e10i	−0.235246	+	0.407458i
$977$	7.01254e9	+	3.97701e10i	0.240572	+	1.36435i	0.830556	+	0.556935i	$0.188023\pi$
$977$	7.01254e9	+	3.97701e10i	0.240572	+	1.36435i	−0.589985	+	0.807414i	$0.700866\pi$
$978$	9.69159e7	+	5.49637e8i	0.00331291	+	0.0187884i
$979$	9.44516e9	−	7.92543e9i	0.321714	−	0.269950i
$980$	−4.19573e10	+	1.52712e10i	−1.42402	+	0.518301i
$981$	−3.56517e10	+	1.29762e10i	−1.20570	+	0.438838i
$982$	3.71707e9	−	3.11899e9i	0.125260	−	0.105105i
$983$	7.90191e8	+	4.48139e9i	0.0265335	+	0.150479i	0.995196	−	0.0979012i	$-0.0312129\pi$
$983$	7.90191e8	+	4.48139e9i	0.0265335	+	0.150479i	−0.968663	+	0.248380i	$0.920102\pi$
$984$	−5.65910e9	−	3.20944e10i	−0.189350	−	1.07386i
$985$	4.01484e9	−	6.95390e9i	0.133857	−	0.231847i
$986$	−8.03999e8	−	6.74635e8i	−0.0267108	−	0.0224130i
$987$	2.93778e10	+	1.06926e10i	0.972544	+	0.353977i
$988$	−1.21485e10	−	2.10419e10i	−0.400751	−	0.694121i
$989$	3.59730e9	−	6.23070e9i	0.118247	−	0.204809i
$990$	−4.73102e9	+	3.96980e9i	−0.154964	+	0.130031i
$991$	2.83488e10	+	4.91016e10i	0.925288	+	1.60265i	0.791097	+	0.611691i	$0.209510\pi$
$991$	2.83488e10	+	4.91016e10i	0.925288	+	1.60265i	0.134191	+	0.990955i	$0.457156\pi$
$992$	−1.06270e9	+	6.02688e9i	−0.0345637	+	0.196020i
$993$	2.14782e10			0.696106
$994$	−1.93880e9	+	1.09955e10i	−0.0626152	+	0.355109i
$995$	−4.88361e9	−	4.09783e9i	−0.157167	−	0.131878i
$996$	−2.45798e10	+	8.94633e9i	−0.788263	+	0.286904i
$997$	−1.38236e9	−	5.03138e8i	−0.0441762	−	0.0160788i	0.319838	−	0.947472i	$-0.396372\pi$
$997$	−1.38236e9	−	5.03138e8i	−0.0441762	−	0.0160788i	−0.364014	+	0.931394i	$0.618594\pi$
$998$	−1.47242e9			−0.0468893
$999$	1.15812e10	+	1.41098e10i	0.367514	+	0.447757i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.8.f.a.16.13	yes	132
37.7	even	9	inner	37.8.f.a.7.13	✓	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.8.f.a.7.13	✓	132	37.7	even	9	inner
37.8.f.a.16.13	yes	132	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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	37.f (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(2.24172 + 0.815920i) q^{2} +(67.7355 - 24.6537i) q^{3} +(-93.6941 - 78.6187i) q^{4} +(-36.3337 + 206.059i) q^{5} +171.960 q^{6} +(278.285 - 1578.23i) q^{7} +(-298.567 - 517.134i) q^{8} +(2304.96 - 1934.09i) q^{9} +O(q^{10})\)	\(q+(2.24172 + 0.815920i) q^{2} +(67.7355 - 24.6537i) q^{3} +(-93.6941 - 78.6187i) q^{4} +(-36.3337 + 206.059i) q^{5} +171.960 q^{6} +(278.285 - 1578.23i) q^{7} +(-298.567 - 517.134i) q^{8} +(2304.96 - 1934.09i) q^{9} +(-249.578 + 432.281i) q^{10} +(2056.02 + 3561.12i) q^{11} +(-8284.66 - 3015.37i) q^{12} +(-10957.6 - 9194.49i) q^{13} +(1911.55 - 3310.90i) q^{14} +(2619.03 + 14853.3i) q^{15} +(2471.19 + 14014.8i) q^{16} +(26139.1 - 21933.3i) q^{17} +(6745.14 - 2455.03i) q^{18} +(-13050.3 + 4749.93i) q^{19} +(19604.3 - 16450.0i) q^{20} +(-20059.5 - 113763. i) q^{21} +(1703.42 + 9660.60i) q^{22} +(18231.9 - 31578.7i) q^{23} +(-32972.9 - 27667.6i) q^{24} +(32273.4 + 11746.6i) q^{25} +(-17061.9 - 29552.0i) q^{26} +(29622.6 - 51307.9i) q^{27} +(-150152. + 125993. i) q^{28} +(-6446.71 - 11166.0i) q^{29} +(-6247.94 + 35433.8i) q^{30} +55442.1 q^{31} +(-19167.8 + 108706. i) q^{32} +(227060. + 190526. i) q^{33} +(76492.5 - 27841.0i) q^{34} +(315097. + 114686. i) q^{35} -368016. q^{36} +(-108513. + 288369. i) q^{37} -33130.8 q^{38} +(-968895. - 352649. i) q^{39} +(117408. - 42733.0i) q^{40} +(580000. + 486678. i) q^{41} +(47853.8 - 271392. i) q^{42} +197307. q^{43} +(87334.3 - 495297. i) q^{44} +(314788. + 545229. i) q^{45} +(66636.7 - 55914.8i) q^{46} +(-135317. + 234377. i) q^{47} +(512905. + 888377. i) q^{48} +(-1.63949e6 - 596727. i) q^{49} +(62763.8 + 52665.1i) q^{50} +(1.22981e6 - 2.13009e6i) q^{51} +(303801. + 1.72294e6i) q^{52} +(206888. + 1.17332e6i) q^{53} +(108269. - 90848.4i) q^{54} +(-808503. + 294271. i) q^{55} +(-899244. + 327298. i) q^{56} +(-766867. + 643478. i) q^{57} +(-5341.15 - 30291.1i) q^{58} +(253527. + 1.43783e6i) q^{59} +(922356. - 1.59757e6i) q^{60} +(735605. + 617246. i) q^{61} +(124286. + 45236.4i) q^{62} +(-2.41100e6 - 4.17598e6i) q^{63} +(779122. - 1.34948e6i) q^{64} +(2.29274e6 - 1.92383e6i) q^{65} +(353552. + 612370. i) q^{66} +(510855. - 2.89720e6i) q^{67} -4.17345e6 q^{68} +(456419. - 2.58848e6i) q^{69} +(612786. + 514188. i) q^{70} +(-2.74431e6 + 998846. i) q^{71} +(-1.68837e6 - 614516. i) q^{72} +3.69954e6 q^{73} +(-478542. + 557906. i) q^{74} +2.47565e6 q^{75} +(1.59617e6 + 580959. i) q^{76} +(6.19243e6 - 2.25386e6i) q^{77} +(-1.88426e6 - 1.58108e6i) q^{78} +(419900. - 2.38137e6i) q^{79} -2.97766e6 q^{80} +(-401114. + 2.27483e6i) q^{81} +(903109. + 1.56423e6i) q^{82} +(2.27278e6 - 1.90709e6i) q^{83} +(-7.06444e6 + 1.22360e7i) q^{84} +(3.56982e6 + 6.18312e6i) q^{85} +(442308. + 160987. i) q^{86} +(-711955. - 597401. i) q^{87} +(1.22772e6 - 2.12647e6i) q^{88} +(-520678. - 2.95291e6i) q^{89} +(260804. + 1.47909e6i) q^{90} +(-1.75604e7 + 1.47349e7i) q^{91} +(-4.19090e6 + 1.52536e6i) q^{92} +(3.75540e6 - 1.36685e6i) q^{93} +(-494577. + 414999. i) q^{94} +(-504598. - 2.86172e6i) q^{95} +(1.38166e6 + 7.83580e6i) q^{96} +(4.14322e6 - 7.17627e6i) q^{97} +(-3.18841e6 - 2.67539e6i) q^{98} +(1.16266e7 + 4.23172e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 15 q^{2} + 33 q^{3} - 279 q^{4} + 576 q^{5} - 12 q^{6} - 597 q^{7} - 3750 q^{8} - 3243 q^{9}+O(q^{10}) \) 132 * q + 15 * q^2 + 33 * q^3 - 279 * q^4 + 576 * q^5 - 12 * q^6 - 597 * q^7 - 3750 * q^8 - 3243 * q^9	\( 132 q + 15 q^{2} + 33 q^{3} - 279 q^{4} + 576 q^{5} - 12 q^{6} - 597 q^{7} - 3750 q^{8} - 3243 q^{9} - 6003 q^{10} - 15975 q^{11} - 4635 q^{12} - 15981 q^{13} - 13491 q^{14} + 38493 q^{15} - 74151 q^{16} + 37698 q^{17} - 20100 q^{18} - 66102 q^{19} - 176184 q^{20} - 142530 q^{21} + 132783 q^{22} + 140631 q^{23} - 38793 q^{24} - 544092 q^{25} - 423147 q^{26} + 130557 q^{27} + 603813 q^{28} + 22890 q^{29} - 319860 q^{30} - 1288044 q^{31} - 217866 q^{32} + 112344 q^{33} + 812019 q^{34} + 1479252 q^{35} + 8118132 q^{36} - 1664550 q^{37} + 305010 q^{38} - 1580340 q^{39} - 4681425 q^{40} - 2956593 q^{41} - 3553029 q^{42} - 1023528 q^{43} + 6409524 q^{44} + 1803336 q^{45} + 10219434 q^{46} - 2607204 q^{47} - 2984043 q^{48} - 6819531 q^{49} + 5724015 q^{50} - 1675833 q^{51} + 11768451 q^{52} + 2280177 q^{53} - 7803897 q^{54} - 3542196 q^{55} + 12168843 q^{56} - 85203 q^{57} - 12425487 q^{58} - 7014600 q^{59} + 2356788 q^{60} + 10840332 q^{61} + 6334368 q^{62} - 3331359 q^{63} - 26175624 q^{64} - 573195 q^{65} - 36720249 q^{66} + 6642918 q^{67} - 25277742 q^{68} - 1236438 q^{69} - 27401982 q^{70} + 20311041 q^{71} + 40093005 q^{72} + 38643780 q^{73} - 9531 q^{74} + 16639446 q^{75} + 5787405 q^{76} - 316971 q^{77} + 9363381 q^{78} + 17712534 q^{79} - 74410128 q^{80} - 10355109 q^{81} - 16702371 q^{82} - 31021176 q^{83} - 61626192 q^{84} + 23576445 q^{85} + 18579072 q^{86} + 104996631 q^{87} + 57279702 q^{88} - 13471320 q^{89} + 56306910 q^{90} - 2335911 q^{91} - 178133436 q^{92} + 24366258 q^{93} + 77086020 q^{94} - 26254407 q^{95} + 152523921 q^{96} + 14408415 q^{97} - 521205 q^{98} + 58375668 q^{99}+O(q^{100}) \) 132 * q + 15 * q^2 + 33 * q^3 - 279 * q^4 + 576 * q^5 - 12 * q^6 - 597 * q^7 - 3750 * q^8 - 3243 * q^9 - 6003 * q^10 - 15975 * q^11 - 4635 * q^12 - 15981 * q^13 - 13491 * q^14 + 38493 * q^15 - 74151 * q^16 + 37698 * q^17 - 20100 * q^18 - 66102 * q^19 - 176184 * q^20 - 142530 * q^21 + 132783 * q^22 + 140631 * q^23 - 38793 * q^24 - 544092 * q^25 - 423147 * q^26 + 130557 * q^27 + 603813 * q^28 + 22890 * q^29 - 319860 * q^30 - 1288044 * q^31 - 217866 * q^32 + 112344 * q^33 + 812019 * q^34 + 1479252 * q^35 + 8118132 * q^36 - 1664550 * q^37 + 305010 * q^38 - 1580340 * q^39 - 4681425 * q^40 - 2956593 * q^41 - 3553029 * q^42 - 1023528 * q^43 + 6409524 * q^44 + 1803336 * q^45 + 10219434 * q^46 - 2607204 * q^47 - 2984043 * q^48 - 6819531 * q^49 + 5724015 * q^50 - 1675833 * q^51 + 11768451 * q^52 + 2280177 * q^53 - 7803897 * q^54 - 3542196 * q^55 + 12168843 * q^56 - 85203 * q^57 - 12425487 * q^58 - 7014600 * q^59 + 2356788 * q^60 + 10840332 * q^61 + 6334368 * q^62 - 3331359 * q^63 - 26175624 * q^64 - 573195 * q^65 - 36720249 * q^66 + 6642918 * q^67 - 25277742 * q^68 - 1236438 * q^69 - 27401982 * q^70 + 20311041 * q^71 + 40093005 * q^72 + 38643780 * q^73 - 9531 * q^74 + 16639446 * q^75 + 5787405 * q^76 - 316971 * q^77 + 9363381 * q^78 + 17712534 * q^79 - 74410128 * q^80 - 10355109 * q^81 - 16702371 * q^82 - 31021176 * q^83 - 61626192 * q^84 + 23576445 * q^85 + 18579072 * q^86 + 104996631 * q^87 + 57279702 * q^88 - 13471320 * q^89 + 56306910 * q^90 - 2335911 * q^91 - 178133436 * q^92 + 24366258 * q^93 + 77086020 * q^94 - 26254407 * q^95 + 152523921 * q^96 + 14408415 * q^97 - 521205 * q^98 + 58375668 * q^99

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