LMFDB - Embedded newform 431.3.f.a.101.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [431,3,Mod(47,431)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(431, base_ring=CyclotomicField(86))

chi = DirichletCharacter(H, H._module([63]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("431.47");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 431 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	431.f (of order $86$, degree $42$, 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:	$11.7438993939$
Analytic rank:	$0$
Dimension:	$2982$
Relative dimension:	$71$ over $\Q(\zeta_{86})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{86}]$

Embedding invariants

Embedding label			101.25
Character	$\chi$	$=$	431.101
Dual form			431.3.f.a.367.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.631139 + 1.22757i) q^{2} +(-0.189521 - 1.72242i) q^{3} +(1.21883 + 1.70362i) q^{4} +(7.67398 + 3.59741i) q^{5} +(2.23402 + 0.854440i) q^{6} +(-1.28742 - 5.77941i) q^{7} +(-8.32300 + 1.22489i) q^{8} +(5.85385 - 1.30400i) q^{9} +(-9.25944 + 7.14991i) q^{10} +(13.3343 - 7.48359i) q^{11} +(2.70336 - 2.42222i) q^{12} +(5.90011 - 3.03346i) q^{13} +(7.90719 + 2.06721i) q^{14} +(4.74190 - 13.8996i) q^{15} +(1.04395 - 3.06006i) q^{16} +(-0.957468 - 1.70603i) q^{17} +(-2.09384 + 8.00905i) q^{18} +(4.90370 - 2.29876i) q^{19} +(3.22469 + 17.4582i) q^{20} +(-9.71060 + 3.31280i) q^{21} +(0.770839 + 21.0921i) q^{22} +(-23.6587 - 24.5392i) q^{23} +(3.68717 + 14.1036i) q^{24} +(29.9567 + 35.9968i) q^{25} +9.15736i q^{26} +(-8.39091 - 24.5958i) q^{27} +(8.27675 - 9.23741i) q^{28} +(-9.17279 + 12.8212i) q^{29} +(14.0700 + 14.5936i) q^{30} +(-10.7492 - 28.1049i) q^{31} +(-20.2584 - 21.0123i) q^{32} +(-15.4170 - 21.5491i) q^{33} +(2.69857 - 0.0986230i) q^{34} +(10.9113 - 48.9824i) q^{35} +(9.35640 + 8.38337i) q^{36} +(47.1405 + 12.3241i) q^{37} +(-0.273020 + 7.47050i) q^{38} +(-6.34309 - 9.58759i) q^{39} +(-68.2770 - 20.5415i) q^{40} +(-19.6392 + 57.5673i) q^{41} +(2.06204 - 14.0113i) q^{42} +(-20.2049 + 26.1662i) q^{43} +(29.0015 + 13.5954i) q^{44} +(49.6134 + 11.0519i) q^{45} +(45.0556 - 13.5552i) q^{46} +(-3.74219 + 51.1295i) q^{47} +(-5.46857 - 1.21818i) q^{48} +(12.6229 - 5.91735i) q^{49} +(-63.0956 + 14.0551i) q^{50} +(-2.75704 + 1.97249i) q^{51} +(12.3591 + 6.35426i) q^{52} +(57.1389 - 4.18203i) q^{53} +(35.4890 + 5.22289i) q^{54} +(129.249 - 9.45980i) q^{55} +(17.7943 + 46.5251i) q^{56} +(-4.88880 - 8.01060i) q^{57} +(-9.94968 - 19.3523i) q^{58} +(-34.9789 + 68.0343i) q^{59} +(29.4593 - 8.86297i) q^{60} +(2.48789 + 5.85450i) q^{61} +(41.2851 + 4.54265i) q^{62} +(-15.0727 - 32.1530i) q^{63} +(50.9647 - 15.3330i) q^{64} +(56.1899 - 2.05354i) q^{65} +(36.1834 - 5.32509i) q^{66} +(16.4601 + 4.30323i) q^{67} +(1.73942 - 3.71052i) q^{68} +(-37.7831 + 45.4011i) q^{69} +(53.2430 + 44.3092i) q^{70} +(-0.0929731 + 1.27029i) q^{71} +(-47.1244 + 18.0235i) q^{72} +(-29.7112 - 44.9086i) q^{73} +(-44.8810 + 50.0902i) q^{74} +(56.3243 - 58.4204i) q^{75} +(9.89302 + 5.55223i) q^{76} +(-60.4176 - 67.4300i) q^{77} +(15.7729 - 1.73551i) q^{78} +(-21.9530 + 72.9687i) q^{79} +(19.0195 - 19.7273i) q^{80} +(8.09836 - 3.79636i) q^{81} +(-58.2731 - 60.4416i) q^{82} +(46.3720 - 5.10237i) q^{83} +(-17.4794 - 12.5054i) q^{84} +(-1.21031 - 16.5364i) q^{85} +(-19.3688 - 41.3175i) q^{86} +(23.8220 + 13.3696i) q^{87} +(-101.815 + 78.6190i) q^{88} +(-41.0762 + 7.58717i) q^{89} +(-44.8799 + 53.9288i) q^{90} +(-25.1275 - 30.1938i) q^{91} +(12.9693 - 70.2146i) q^{92} +(-46.3714 + 23.8412i) q^{93} +(-60.4033 - 36.8636i) q^{94} +45.9005 q^{95} +(-32.3528 + 38.8759i) q^{96} +(-20.2601 + 6.09534i) q^{97} +(-0.702794 + 19.2302i) q^{98} +(68.2986 - 61.1958i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2982 q - 43 q^{2} - 41 q^{3} - 187 q^{4} - 41 q^{5} - 33 q^{6} - 43 q^{7} - 37 q^{8} - 252 q^{9} - 23 q^{10} + 187 q^{11} + 19 q^{12} - 43 q^{13} - 43 q^{14} - 71 q^{15} - 359 q^{16} - 43 q^{17} - 93 q^{18}+ \cdots - 609 q^{99}+O(q^{100}) $ 2982 * q - 43 * q^2 - 41 * q^3 - 187 * q^4 - 41 * q^5 - 33 * q^6 - 43 * q^7 - 37 * q^8 - 252 * q^9 - 23 * q^10 + 187 * q^11 + 19 * q^12 - 43 * q^13 - 43 * q^14 - 71 * q^15 - 359 * q^16 - 43 * q^17 - 93 * q^18 - 55 * q^19 + 9 * q^20 - 172 * q^21 - 47 * q^22 + 45 * q^23 + 17 * q^24 - 436 * q^25 + 37 * q^27 - 43 * q^28 - 93 * q^29 - 911 * q^30 - 43 * q^31 + 181 * q^32 + 733 * q^33 - 43 * q^34 - 43 * q^35 - 521 * q^36 - 43 * q^37 + 691 * q^38 - 43 * q^39 + 199 * q^40 + 456 * q^41 - 43 * q^42 - 43 * q^43 - 161 * q^44 - 3 * q^45 - 279 * q^46 - 43 * q^47 + 271 * q^48 + 362 * q^49 - 21 * q^50 - 43 * q^51 - 2107 * q^52 + 53 * q^53 - 2864 * q^54 + 111 * q^55 - 1978 * q^56 + 11 * q^57 - 349 * q^58 + 59 * q^59 + 29 * q^60 - 1433 * q^61 - 43 * q^62 - 2451 * q^63 - 801 * q^64 - 43 * q^65 - 253 * q^66 + 3053 * q^67 - 43 * q^68 + 25 * q^69 - 1978 * q^70 + 2021 * q^71 - 63 * q^72 - 43 * q^73 - 43 * q^74 - 401 * q^75 - 225 * q^76 + 645 * q^77 + 344 * q^78 + 3397 * q^79 + 227 * q^80 - 1054 * q^81 - 845 * q^82 - 43 * q^83 + 6106 * q^84 - 43 * q^85 - 43 * q^86 - 1021 * q^87 + 6277 * q^88 - 43 * q^89 - 815 * q^90 - 147 * q^91 - 239 * q^92 + 2193 * q^93 - 43 * q^94 - 70 * q^95 + 129 * q^96 + 125 * q^97 + 643 * q^98 - 609 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/431\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{37}{86}\right)$

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 $

$2$	−0.631139	+	1.22757i	−0.315570	+	0.613787i	−0.992498	−	0.122262i	$-0.960985\pi$
$2$	−0.631139	+	1.22757i	−0.315570	+	0.613787i	0.676928	+	0.736049i	$0.263311\pi$
$3$	−0.189521	−	1.72242i	−0.0631735	−	0.574142i	−0.983232	−	0.182360i	$-0.941626\pi$
$3$	−0.189521	−	1.72242i	−0.0631735	−	0.574142i	0.920058	−	0.391782i	$-0.128141\pi$
$4$	1.21883	+	1.70362i	0.304709	+	0.425905i
$5$	7.67398	+	3.59741i	1.53480	+	0.719483i	0.992675	−	0.120818i	$-0.0385516\pi$
$5$	7.67398	+	3.59741i	1.53480	+	0.719483i	0.542121	+	0.840300i	$0.317621\pi$
$6$	2.23402	+	0.854440i	0.372336	+	0.142407i
$7$	−1.28742	−	5.77941i	−0.183917	−	0.825630i	−0.976440	−	0.215788i	$-0.930768\pi$
$7$	−1.28742	−	5.77941i	−0.183917	−	0.825630i	0.792523	−	0.609842i	$-0.208767\pi$
$8$	−8.32300	+	1.22489i	−1.04038	+	0.153112i
$9$	5.85385	−	1.30400i	0.650428	−	0.144889i
$10$	−9.25944	+	7.14991i	−0.925944	+	0.714991i
$11$	13.3343	−	7.48359i	1.21221	−	0.680326i	0.254227	−	0.967145i	$-0.418179\pi$
$11$	13.3343	−	7.48359i	1.21221	−	0.680326i	0.957985	+	0.286818i	$0.0925977\pi$
$12$	2.70336	−	2.42222i	0.225280	−	0.201852i
$13$	5.90011	−	3.03346i	0.453855	−	0.233343i	−0.215179	−	0.976575i	$-0.569034\pi$
$13$	5.90011	−	3.03346i	0.453855	−	0.233343i	0.669034	+	0.743232i	$0.266708\pi$
$14$	7.90719	+	2.06721i	0.564799	+	0.147658i
$15$	4.74190	−	13.8996i	0.316126	−	0.926642i
$16$	1.04395	−	3.06006i	0.0652467	−	0.191254i
$17$	−0.957468	−	1.70603i	−0.0563216	−	0.100354i	0.842444	−	0.538784i	$-0.181116\pi$
$17$	−0.957468	−	1.70603i	−0.0563216	−	0.100354i	−0.898765	+	0.438430i	$0.855535\pi$
$18$	−2.09384	+	8.00905i	−0.116324	+	0.444947i
$19$	4.90370	−	2.29876i	0.258090	−	0.120987i	−0.291079	−	0.956699i	$-0.594014\pi$
$19$	4.90370	−	2.29876i	0.258090	−	0.120987i	0.549169	+	0.835712i	$0.314944\pi$
$20$	3.22469	+	17.4582i	0.161234	+	0.872909i
$21$	−9.71060	+	3.31280i	−0.462410	+	0.157752i
$22$	0.770839	+	21.0921i	0.0350381	+	0.958730i
$23$	−23.6587	−	24.5392i	−1.02864	−	1.06692i	−0.997726	−	0.0673982i	$-0.978530\pi$
$23$	−23.6587	−	24.5392i	−1.02864	−	1.06692i	−0.0309143	−	0.999522i	$-0.509842\pi$
$24$	3.68717	+	14.1036i	0.153632	+	0.587650i
$25$	29.9567	+	35.9968i	1.19827	+	1.43987i
$26$			9.15736i			0.352206i
$27$	−8.39091	−	24.5958i	−0.310775	−	0.910955i
$28$	8.27675	−	9.23741i	0.295598	−	0.329907i
$29$	−9.17279	+	12.8212i	−0.316303	+	0.442111i	−0.940823	−	0.338898i	$-0.889946\pi$
$29$	−9.17279	+	12.8212i	−0.316303	+	0.442111i	0.624520	+	0.781009i	$0.285295\pi$
$30$	14.0700	+	14.5936i	0.469001	+	0.486455i
$31$	−10.7492	−	28.1049i	−0.346749	−	0.906609i	−0.990014	−	0.140966i	$-0.954979\pi$
$31$	−10.7492	−	28.1049i	−0.346749	−	0.906609i	0.643266	−	0.765643i	$-0.277579\pi$
$32$	−20.2584	−	21.0123i	−0.633077	−	0.656636i
$33$	−15.4170	−	21.5491i	−0.467183	−	0.653003i
$34$	2.69857	−	0.0986230i	0.0793697	−	0.00290068i
$35$	10.9113	−	48.9824i	0.311751	−	1.39950i
$36$	9.35640	+	8.38337i	0.259900	+	0.232871i
$37$	47.1405	+	12.3241i	1.27407	+	0.333085i	0.827399	−	0.561614i	$-0.189820\pi$
$37$	47.1405	+	12.3241i	1.27407	+	0.333085i	0.446669	+	0.894699i	$0.352610\pi$
$38$	−0.273020	+	7.47050i	−0.00718473	+	0.196592i
$39$	−6.34309	−	9.58759i	−0.162643	−	0.245836i
$40$	−68.2770	−	20.5415i	−1.70692	−	0.513537i
$41$	−19.6392	+	57.5673i	−0.479006	+	1.40408i	0.395231	+	0.918582i	$0.370665\pi$
$41$	−19.6392	+	57.5673i	−0.479006	+	1.40408i	−0.874237	+	0.485499i	$0.838638\pi$
$42$	2.06204	−	14.0113i	0.0490962	−	0.333603i
$43$	−20.2049	+	26.1662i	−0.469880	+	0.608515i	−0.965621	−	0.259955i	$-0.916292\pi$
$43$	−20.2049	+	26.1662i	−0.469880	+	0.608515i	0.495740	+	0.868471i	$0.334897\pi$
$44$	29.0015	+	13.5954i	0.659125	+	0.308985i
$45$	49.6134	+	11.0519i	1.10252	+	0.245597i
$46$	45.0556	−	13.5552i	0.979470	−	0.294679i
$47$	−3.74219	+	51.1295i	−0.0796211	+	1.08786i	0.796139	+	0.605114i	$0.206872\pi$
$47$	−3.74219	+	51.1295i	−0.0796211	+	1.08786i	−0.875760	+	0.482747i	$0.839639\pi$
$48$	−5.46857	−	1.21818i	−0.113929	−	0.0253787i
$49$	12.6229	−	5.91735i	0.257609	−	0.120762i
$50$	−63.0956	+	14.0551i	−1.26191	+	0.281103i
$51$	−2.75704	+	1.97249i	−0.0540596	+	0.0386763i
$52$	12.3591	+	6.35426i	0.237675	+	0.122197i
$53$	57.1389	−	4.18203i	1.07809	−	0.0789062i	0.477631	−	0.878560i	$-0.341495\pi$
$53$	57.1389	−	4.18203i	1.07809	−	0.0789062i	0.600461	+	0.799654i	$0.294984\pi$
$54$	35.4890	+	5.22289i	0.657203	+	0.0967203i
$55$	129.249	−	9.45980i	2.34998	−	0.171996i
$56$	17.7943	+	46.5251i	0.317756	+	0.830805i
$57$	−4.88880	−	8.01060i	−0.0857684	−	0.140537i
$58$	−9.94968	−	19.3523i	−0.171546	−	0.333660i
$59$	−34.9789	+	68.0343i	−0.592862	+	1.15312i	0.380699	+	0.924699i	$0.375683\pi$
$59$	−34.9789	+	68.0343i	−0.592862	+	1.15312i	−0.973561	+	0.228425i	$0.926642\pi$
$60$	29.4593	−	8.86297i	0.490988	−	0.147716i
$61$	2.48789	+	5.85450i	0.0407851	+	0.0959754i	0.939487	−	0.342585i	$-0.111302\pi$
$61$	2.48789	+	5.85450i	0.0407851	+	0.0959754i	−0.898702	+	0.438560i	$0.855489\pi$
$62$	41.2851	+	4.54265i	0.665888	+	0.0732686i
$63$	−15.0727	−	32.1530i	−0.239249	−	0.510365i
$64$	50.9647	−	15.3330i	0.796323	−	0.239578i
$65$	56.1899	−	2.05354i	0.864460	−	0.0315929i
$66$	36.1834	−	5.32509i	0.548233	−	0.0806832i
$67$	16.4601	+	4.30323i	0.245673	+	0.0642273i	0.373723	−	0.927540i	$-0.378081\pi$
$67$	16.4601	+	4.30323i	0.245673	+	0.0642273i	−0.128050	+	0.991768i	$0.540872\pi$
$68$	1.73942	−	3.71052i	0.0255797	−	0.0545665i
$69$	−37.7831	+	45.4011i	−0.547580	+	0.657986i
$70$	53.2430	+	44.3092i	0.760614	+	0.632988i
$71$	−0.0929731	+	1.27029i	−0.00130948	+	0.0178914i	−0.997947	−	0.0640467i	$-0.979599\pi$
$71$	−0.0929731	+	1.27029i	−0.00130948	+	0.0178914i	0.996637	+	0.0819381i	$0.0261110\pi$
$72$	−47.1244	+	18.0235i	−0.654505	+	0.250327i
$73$	−29.7112	−	44.9086i	−0.407003	−	0.615186i	0.571701	−	0.820462i	$-0.306284\pi$
$73$	−29.7112	−	44.9086i	−0.407003	−	0.615186i	−0.978704	+	0.205276i	$0.934191\pi$
$74$	−44.8810	+	50.0902i	−0.606500	+	0.676895i
$75$	56.3243	−	58.4204i	0.750991	−	0.778938i
$76$	9.89302	+	5.55223i	0.130171	+	0.0730556i
$77$	−60.4176	−	67.4300i	−0.784644	−	0.875714i
$78$	15.7729	−	1.73551i	0.202216	−	0.0222501i
$79$	−21.9530	+	72.9687i	−0.277886	+	0.923654i	0.699934	+	0.714208i	$0.253213\pi$
$79$	−21.9530	+	72.9687i	−0.277886	+	0.923654i	−0.977820	+	0.209447i	$0.932834\pi$
$80$	19.0195	−	19.7273i	0.237744	−	0.246591i
$81$	8.09836	−	3.79636i	0.0999798	−	0.0468686i
$82$	−58.2731	−	60.4416i	−0.710647	−	0.737093i
$83$	46.3720	−	5.10237i	0.558699	−	0.0614743i	0.174386	−	0.984677i	$-0.444206\pi$
$83$	46.3720	−	5.10237i	0.558699	−	0.0614743i	0.384313	+	0.923203i	$0.374438\pi$
$84$	−17.4794	−	12.5054i	−0.208088	−	0.148874i
$85$	−1.21031	−	16.5364i	−0.0142389	−	0.194546i
$86$	−19.3688	−	41.3175i	−0.225219	−	0.480436i
$87$	23.8220	+	13.3696i	0.273816	+	0.153673i
$88$	−101.815	+	78.6190i	−1.15699	+	0.893398i
$89$	−41.0762	+	7.58717i	−0.461531	+	0.0852490i	−0.407330	−	0.913281i	$-0.633540\pi$
$89$	−41.0762	+	7.58717i	−0.461531	+	0.0852490i	−0.0542007	+	0.998530i	$0.517261\pi$
$90$	−44.8799	+	53.9288i	−0.498666	+	0.599209i
$91$	−25.1275	−	30.1938i	−0.276126	−	0.331800i
$92$	12.9693	−	70.2146i	0.140971	−	0.763202i
$93$	−46.3714	+	23.8412i	−0.498617	+	0.256357i
$94$	−60.4033	−	36.8636i	−0.642589	−	0.392166i
$95$	45.9005			0.483163
$96$	−32.3528	+	38.8759i	−0.337008	+	0.404958i
$97$	−20.2601	+	6.09534i	−0.208867	+	0.0628386i	−0.390814	−	0.920470i	$-0.627806\pi$
$97$	−20.2601	+	6.09534i	−0.208867	+	0.0628386i	0.181947	+	0.983308i	$0.441760\pi$
$98$	−0.702794	+	19.2302i	−0.00717137	+	0.196226i
$99$	68.2986	−	61.1958i	0.689885	−	0.618140i
$100$	−24.8124	+	94.9089i	−0.248124	+	0.949089i
$101$	−25.6061	+	85.1111i	−0.253526	+	0.842684i	0.733162	+	0.680055i	$0.238044\pi$
$101$	−25.6061	+	85.1111i	−0.253526	+	0.842684i	−0.986687	+	0.162629i	$0.948003\pi$
$102$	−0.681305	−	4.62939i	−0.00667946	−	0.0453862i
$103$	−178.457	−	32.9626i	−1.73259	−	0.320025i	−0.780342	−	0.625353i	$-0.784955\pi$
$103$	−178.457	−	32.9626i	−1.73259	−	0.320025i	−0.952247	+	0.305328i	$0.901234\pi$
$104$	−45.3910	+	32.4745i	−0.436452	+	0.312254i
$105$	−86.4365	−	9.51071i	−0.823204	−	0.0905782i
$106$	−30.9289	+	72.7817i	−0.291782	+	0.686619i
$107$	51.8888	−	92.4560i	0.484942	−	0.864075i	−0.515034	−	0.857170i	$-0.672221\pi$
$107$	51.8888	−	92.4560i	0.484942	−	0.864075i	0.999976	−	0.00690521i	$-0.00219801\pi$
$108$	31.6747	−	44.2731i	0.293284	−	0.409936i
$109$	−96.4082	+	54.1069i	−0.884479	+	0.496394i	−0.864055	−	0.503398i	$-0.832083\pi$
$109$	−96.4082	+	54.1069i	−0.884479	+	0.496394i	−0.0204241	+	0.999791i	$0.506502\pi$
$110$	−69.9615	+	164.633i	−0.636013	+	1.49666i
$111$	12.2933	−	83.5317i	0.110751	−	0.752537i
$112$	−19.0293	−	2.09382i	−0.169905	−	0.0186948i
$113$	−13.8437	+	46.0144i	−0.122510	+	0.407207i	−0.996961	−	0.0779085i	$-0.975176\pi$
$113$	−13.8437	+	46.0144i	−0.122510	+	0.407207i	0.874450	+	0.485115i	$0.161222\pi$
$114$	12.9191	−	0.945558i	0.113326	−	0.00829436i
$115$	−93.2791	−	273.423i	−0.811122	−	2.37759i
$116$	−33.0226			−0.284677
$117$	30.5828	−	25.4512i	0.261391	−	0.217531i
$118$	−61.4406	−	85.8783i	−0.520683	−	0.727782i
$119$	−8.62715	+	7.72996i	−0.0724971	+	0.0649577i
$120$	−22.4413	+	121.495i	−0.187011	+	1.01246i
$121$	58.7665	−	96.2925i	0.485673	−	0.795806i
$122$	−8.75704	−	0.640933i	−0.0717790	−	0.00525355i
$123$	102.877	+	22.9169i	0.836402	+	0.186316i
$124$	34.7785	−	52.5677i	0.280472	−	0.423933i
$125$	46.7997	+	179.011i	0.374398	+	1.43209i
$126$	48.9832	+	1.79016i	0.388755	+	0.0142076i
$127$	−156.911	+	17.2651i	−1.23552	+	0.135945i	−0.703442	−	0.710753i	$-0.748355\pi$
$127$	−156.911	+	17.2651i	−1.23552	+	0.135945i	−0.532074	+	0.846698i	$0.678587\pi$
$128$	7.86283	−	42.5686i	0.0614283	−	0.332568i
$129$	48.8985	+	29.8423i	0.379058	+	0.231336i
$130$	−32.9428	+	70.2734i	−0.253406	+	0.540564i
$131$	−15.2121	+	103.364i	−0.116123	+	0.789042i	0.849217	+	0.528044i	$0.177075\pi$
$131$	−15.2121	+	103.364i	−0.116123	+	0.789042i	−0.965340	+	0.260997i	$0.915949\pi$
$132$	17.9206	−	52.5295i	0.135762	−	0.397951i
$133$	−19.5986	−	25.3810i	−0.147358	−	0.190835i
$134$	−15.6711	+	17.4900i	−0.116949	+	0.130523i
$135$	24.0895	−	218.933i	0.178441	−	1.62173i
$136$	10.0587	+	13.0265i	0.0739611	+	0.0957828i
$137$	−10.0875	−	137.825i	−0.0736315	−	1.00602i	−0.898007	−	0.439981i	$-0.854985\pi$
$137$	−10.0875	−	137.825i	−0.0736315	−	1.00602i	0.824376	−	0.566043i	$-0.191526\pi$
$138$	−31.8868	−	75.0359i	−0.231064	−	0.543738i
$139$	135.476	+	51.8151i	0.974646	+	0.372770i	0.792076	−	0.610423i	$-0.209000\pi$
$139$	135.476	+	51.8151i	0.974646	+	0.372770i	0.182570	+	0.983193i	$0.441558\pi$
$140$	96.7464	−	41.1128i	0.691046	−	0.293663i
$141$	88.7759	−	3.24444i	0.629616	−	0.0230102i
$142$	−1.50069	−	0.915860i	−0.0105683	−	0.00644972i
$143$	55.9729	−	84.6031i	0.391419	−	0.591630i
$144$	2.12079	−	19.2744i	0.0147277	−	0.133850i
$145$	−116.515	+	65.3914i	−0.803552	+	0.450975i
$146$	73.8806	−	8.12917i	0.506031	−	0.0556793i
$147$	−12.5845	−	20.6205i	−0.0856088	−	0.140275i
$148$	36.4608	+	95.3305i	0.246357	+	0.644125i
$149$	28.0340	+	13.1418i	0.188148	+	0.0882001i	0.516233	−	0.856448i	$-0.327334\pi$
$149$	28.0340	+	13.1418i	0.188148	+	0.0882001i	−0.328086	+	0.944648i	$0.606403\pi$
$150$	36.1668	+	106.014i	0.241112	+	0.706758i
$151$	−238.218	−	17.4353i	−1.57760	−	0.115466i	−0.744132	−	0.668032i	$-0.767137\pi$
$151$	−238.218	−	17.4353i	−1.57760	−	0.115466i	−0.833469	+	0.552567i	$0.813649\pi$
$152$	−37.9978	+	25.1391i	−0.249986	+	0.165389i
$153$	−7.82954	−	8.73828i	−0.0511734	−	0.0571130i
$154$	120.907	−	31.6093i	0.785112	−	0.205255i
$155$	18.6157	−	254.346i	0.120101	−	1.64094i
$156$	8.60242	−	22.4919i	0.0551437	−	0.144179i
$157$	29.8105	−	70.1500i	0.189876	−	0.446815i	−0.797881	−	0.602815i	$-0.794046\pi$
$157$	29.8105	−	70.1500i	0.189876	−	0.446815i	0.987757	+	0.155999i	$0.0498598\pi$
$158$	−75.7191	−	73.0024i	−0.479235	−	0.462040i
$159$	−18.0322	−	97.6248i	−0.113410	−	0.613993i
$160$	−79.8728	−	234.126i	−0.499205	−	1.46329i
$161$	−111.363	+	168.326i	−0.691697	+	1.04550i
$162$	−0.450887	+	12.3374i	−0.00278325	+	0.0761566i
$163$	125.487	−	47.9947i	0.769859	−	0.294446i	0.0594466	−	0.998231i	$-0.481066\pi$
$163$	125.487	−	47.9947i	0.769859	−	0.294446i	0.710413	+	0.703785i	$0.248508\pi$
$164$	−122.010	+	36.7073i	−0.743962	+	0.223825i
$165$	−40.7891	−	220.829i	−0.247207	−	1.33836i
$166$	−23.0037	+	60.1454i	−0.138576	+	0.362321i
$167$	15.6252	−	15.0646i	0.0935638	−	0.0902069i	−0.645825	−	0.763485i	$-0.723487\pi$
$167$	15.6252	−	15.0646i	0.0935638	−	0.0902069i	0.739389	+	0.673278i	$0.235114\pi$
$168$	76.7635	−	39.4669i	0.456926	−	0.234922i
$169$	−72.7247	+	101.651i	−0.430324	+	0.601482i
$170$	21.0635	+	8.95103i	0.123903	+	0.0526531i
$171$	25.7080	−	19.8511i	0.150339	−	0.116088i
$172$	−69.2035	−	2.52914i	−0.402346	−	0.0147043i
$173$	−4.89521	−	8.02110i	−0.0282960	−	0.0463648i	0.839130	−	0.543931i	$-0.183065\pi$
$173$	−4.89521	−	8.02110i	−0.0282960	−	0.0463648i	−0.867426	+	0.497566i	$0.834227\pi$
$174$	−31.4471	+	20.8052i	−0.180731	+	0.119570i
$175$	169.473	−	219.475i	0.968418	−	1.25414i
$176$	−8.97988	−	48.6163i	−0.0510221	−	0.276229i
$177$	123.813	+	47.3545i	0.699510	+	0.267540i
$178$	16.6110	−	55.2127i	0.0933203	−	0.310184i
$179$	59.3758	+	33.3233i	0.331708	+	0.186164i	0.646339	−	0.763051i	$-0.276299\pi$
$179$	59.3758	+	33.3233i	0.331708	+	0.186164i	−0.314631	+	0.949214i	$0.601881\pi$
$180$	41.6424	+	97.9926i	0.231346	+	0.544404i
$181$	54.2652	−	243.604i	0.299808	−	1.34588i	−0.557115	−	0.830435i	$-0.688092\pi$
$181$	54.2652	−	243.604i	0.299808	−	1.34588i	0.856923	−	0.515445i	$-0.172373\pi$
$182$	52.9241	−	11.7893i	0.290792	−	0.0647766i
$183$	9.61243	−	5.39476i	0.0525269	−	0.0294796i
$184$	226.969	+	175.260i	1.23353	+	0.952501i
$185$	317.420	+	264.159i	1.71578	+	1.42789i
$186$		−	71.9714i		−	0.386943i
$187$	−25.5344	−	15.5834i	−0.136547	−	0.0833337i
$188$	−91.6662	+	55.9431i	−0.487586	+	0.297569i
$189$	−131.346	+	80.1595i	−0.694954	+	0.424125i
$190$	−28.9696	+	56.3463i	−0.152472	+	0.296559i
$191$	−55.8989	+	72.3915i	−0.292664	+	0.379013i	−0.914807	−	0.403891i	$-0.867658\pi$
$191$	−55.8989	+	72.3915i	−0.292664	+	0.379013i	0.622143	+	0.782904i	$0.286262\pi$
$192$	−36.0688	−	84.8769i	−0.187858	−	0.442067i
$193$	−223.498	+	58.4301i	−1.15802	+	0.302747i	−0.781648	−	0.623720i	$-0.785620\pi$
$193$	−223.498	+	58.4301i	−1.15802	+	0.302747i	−0.376375	+	0.926467i	$0.622830\pi$
$194$	5.30443	−	28.7177i	0.0273424	−	0.148030i
$195$	−14.1862	−	96.3937i	−0.0727498	−	0.494327i
$196$	25.4661	+	14.2923i	0.129929	+	0.0729197i
$197$	−198.311	+	44.1758i	−1.00666	+	0.224242i	−0.689621	−	0.724171i	$-0.742223\pi$
$197$	−198.311	+	44.1758i	−1.00666	+	0.224242i	−0.317036	+	0.948413i	$0.602688\pi$
$198$	32.0165	+	122.465i	0.161699	+	0.618509i
$199$	−243.641	−	125.265i	−1.22433	−	0.629470i	−0.280483	−	0.959859i	$-0.590495\pi$
$199$	−243.641	−	125.265i	−1.22433	−	0.629470i	−0.943845	+	0.330388i	$0.892820\pi$
$200$	−293.422	−	262.907i	−1.46711	−	1.31454i
$201$	4.29247	−	29.1668i	0.0213556	−	0.145109i
$202$	−88.3191	−	85.1503i	−0.437223	−	0.421536i
$203$	85.9082	+	36.5070i	0.423193	+	0.179838i
$204$	−6.72075	−	2.29280i	−0.0329449	−	0.0112392i
$205$	−357.805	+	371.120i	−1.74539	+	1.81034i
$206$	153.095	−	198.265i	0.743180	−	0.962450i
$207$	−170.494	−	112.798i	−0.823642	−	0.544916i
$208$	−3.12315	−	21.2214i	−0.0150151	−	0.102026i
$209$	48.1846	−	67.3498i	0.230548	−	0.322248i
$210$	66.2286	−	100.105i	0.315374	−	0.476688i
$211$	31.7768	−	26.4448i	0.150601	−	0.125331i	−0.561296	−	0.827615i	$-0.689697\pi$
$211$	31.7768	−	26.4448i	0.150601	−	0.125331i	0.711897	+	0.702284i	$0.247836\pi$
$212$	76.7674	+	92.2456i	0.362110	+	0.435121i
$213$	2.20560	−	0.0806066i	0.0103549	−	0.000378435i
$214$	80.7476	+	122.050i	0.377325	+	0.570327i
$215$	−249.182	+	128.113i	−1.15899	+	0.595876i
$216$	99.9648	+	194.433i	0.462800	+	0.900152i
$217$	−148.591	+	98.3068i	−0.684750	+	0.453027i
$218$	−5.57323	−	152.497i	−0.0255653	−	0.699529i
$219$	−71.7208	+	59.6865i	−0.327492	+	0.272541i
$220$	173.649	+	208.661i	0.789313	+	0.948458i
$221$	−10.8243	−	7.16130i	−0.0489788	−	0.0324041i
$222$	94.7825	+	67.8111i	0.426948	+	0.305455i
$223$	213.338	−	31.3969i	0.956673	−	0.140793i	0.350884	−	0.936419i	$-0.385881\pi$
$223$	213.338	−	31.3969i	0.956673	−	0.140793i	0.605788	+	0.795626i	$0.292858\pi$
$224$	−95.3578	+	144.133i	−0.425705	+	0.643453i
$225$	222.302	+	171.656i	0.988010	+	0.762916i
$226$	−47.7488	−	46.0356i	−0.211278	−	0.203697i
$227$	−17.6993	+	51.8809i	−0.0779705	+	0.228550i	−0.978501	−	0.206243i	$-0.933876\pi$
$227$	−17.6993	+	51.8809i	−0.0779705	+	0.228550i	0.900530	+	0.434793i	$0.143179\pi$
$228$	7.68837	−	18.0922i	0.0337209	−	0.0793519i
$229$	35.2398	−	36.5512i	0.153886	−	0.159612i	−0.638524	−	0.769602i	$-0.720454\pi$
$229$	35.2398	−	36.5512i	0.153886	−	0.159612i	0.792409	+	0.609990i	$0.208827\pi$
$230$	394.519	+	58.0612i	1.71530	+	0.252440i
$231$	−104.693	+	116.844i	−0.453215	+	0.505818i
$232$	60.6406	−	117.947i	0.261382	−	0.508391i
$233$	−159.962	+	41.8195i	−0.686531	+	0.179483i	−0.579744	−	0.814799i	$-0.696847\pi$
$233$	−159.962	+	41.8195i	−0.686531	+	0.179483i	−0.106788	+	0.994282i	$0.534057\pi$
$234$	11.9412	+	53.6058i	0.0510308	+	0.229085i
$235$	−212.651	+	378.904i	−0.904899	+	1.61236i
$236$	−158.538	+	23.3319i	−0.671771	+	0.0988642i
$237$	129.844	+	23.9833i	0.547863	+	0.101195i
$238$	−4.04417	−	15.4692i	−0.0169923	−	0.0649964i
$239$	206.335	−	87.6827i	0.863325	−	0.366873i	0.0862440	−	0.996274i	$-0.472514\pi$
$239$	206.335	−	87.6827i	0.863325	−	0.366873i	0.777081	+	0.629401i	$0.216700\pi$
$240$	−37.5834	−	29.0210i	−0.156597	−	0.120921i
$241$	−123.183	−	63.3330i	−0.511135	−	0.262792i	0.182389	−	0.983226i	$-0.441617\pi$
$241$	−123.183	−	63.3330i	−0.511135	−	0.262792i	−0.693523	+	0.720434i	$0.743943\pi$
$242$	81.1163	+	132.914i	0.335191	+	0.549232i
$243$	−129.916	−	212.875i	−0.534634	−	0.876031i
$244$	−6.94151	+	11.3741i	−0.0284488	+	0.0466151i
$245$	118.155			0.482264
$246$	−93.0622	+	111.826i	−0.378302	+	0.454577i
$247$	21.9592	−	28.4381i	0.0889037	−	0.115134i
$248$	123.891	+	220.750i	0.499561	+	0.890123i
$249$	−17.5769	−	78.9053i	−0.0705899	−	0.316889i
$250$	−249.287	−	55.5311i	−0.997148	−	0.222124i
$251$	307.923	−	130.853i	1.22679	−	0.521327i	0.321815	−	0.946803i	$-0.395707\pi$
$251$	307.923	−	130.853i	1.22679	−	0.521327i	0.904970	+	0.425475i	$0.139893\pi$
$252$	36.4053	−	64.8673i	0.144466	−	0.257410i
$253$	−499.114	−	150.161i	−1.97278	−	0.593522i
$254$	77.8383	−	203.516i	0.306450	−	0.801244i
$255$	−28.2533	+	5.21866i	−0.110797	+	0.0204653i
$256$	215.791	+	166.629i	0.842935	+	0.650893i
$257$	−134.131	−	202.739i	−0.521909	−	0.788866i	0.473876	−	0.880592i	$-0.342855\pi$
$257$	−134.131	−	202.739i	−0.521909	−	0.788866i	−0.995784	+	0.0917259i	$0.970762\pi$
$258$	−67.4954	+	41.1919i	−0.261610	+	0.159658i
$259$	10.5367	−	288.311i	0.0406823	−	1.11317i
$260$	71.9846	+	93.2232i	0.276864	+	0.358551i
$261$	−36.9773	+	87.0148i	−0.141675	+	0.333390i
$262$	−117.287	−	83.9113i	−0.447659	−	0.320272i
$263$	195.178	+	379.624i	0.742121	+	1.44344i	0.890727	+	0.454539i	$0.150196\pi$
$263$	195.178	+	379.624i	0.742121	+	1.44344i	−0.148605	+	0.988897i	$0.547478\pi$
$264$	154.711	+	160.469i	0.586028	+	0.607837i
$265$	453.527	+	173.459i	1.71142	+	0.654564i
$266$	43.5266	−	8.03976i	0.163634	−	0.0302247i
$267$	20.8531	+	69.3128i	0.0781016	+	0.259599i
$268$	12.7311	+	33.2866i	0.0475039	+	0.124204i
$269$	419.253	+	15.3222i	1.55856	+	0.0569598i	0.802145	−	0.597130i	$-0.203692\pi$
$269$	419.253	+	15.3222i	1.55856	+	0.0569598i	0.756417	+	0.654090i	$0.226948\pi$
$270$	253.553	+	167.749i	0.939084	+	0.621292i
$271$	264.450	−	90.2180i	0.975832	−	0.332908i	0.211248	−	0.977432i	$-0.432247\pi$
$271$	264.450	−	90.2180i	0.975832	−	0.332908i	0.764583	+	0.644525i	$0.222945\pi$
$272$	−6.22008	+	1.14891i	−0.0228679	+	0.00422392i
$273$	−47.2444	+	49.0026i	−0.173056	+	0.179497i
$274$	175.557	+	74.6038i	0.640720	+	0.272277i
$275$	668.838	+	255.809i	2.43214	+	0.930214i
$276$	−123.397	−	9.03152i	−0.447092	−	0.0327229i
$277$	−78.4003	−	299.885i	−0.283034	−	1.08262i	−0.943395	−	0.331671i	$-0.892388\pi$
$277$	−78.4003	−	299.885i	−0.283034	−	1.08262i	0.660362	−	0.750948i	$-0.270403\pi$
$278$	−149.111	+	133.604i	−0.536370	+	0.480590i
$279$	−99.5731	−	150.505i	−0.356893	−	0.539444i
$280$	−30.8166	+	421.046i	−0.110059	+	1.50374i
$281$	−47.6955	+	16.2714i	−0.169735	+	0.0579055i	−0.406447	−	0.913674i	$-0.633232\pi$
$281$	−47.6955	+	16.2714i	−0.169735	+	0.0579055i	0.236712	+	0.971580i	$0.423930\pi$
$282$	−52.0472	+	111.027i	−0.184564	+	0.393712i
$283$	−376.595	+	144.035i	−1.33072	+	0.508958i	−0.916069	−	0.401021i	$-0.868656\pi$
$283$	−376.595	+	144.035i	−1.33072	+	0.508958i	−0.414654	+	0.909979i	$0.636097\pi$
$284$	−2.27740	+	1.38988i	−0.00801903	+	0.00489394i
$285$	−8.69910	−	79.0602i	−0.0305231	−	0.277404i
$286$	68.5299	+	122.107i	0.239615	+	0.426948i
$287$	357.989	+	39.3900i	1.24735	+	0.137247i
$288$	−145.990	−	96.5862i	−0.506910	−	0.335369i
$289$	148.558	−	243.421i	0.514041	−	0.842289i
$290$	−6.73557	−	184.302i	−0.0232261	−	0.635524i
$291$	14.3385	+	33.7412i	0.0492731	+	0.115949i
$292$	40.2940	−	105.353i	0.137993	−	0.360797i
$293$	−130.265	+	55.3565i	−0.444589	+	0.188930i	−0.601820	−	0.798632i	$-0.705557\pi$
$293$	−130.265	+	55.3565i	−0.444589	+	0.188930i	0.157230	+	0.987562i	$0.449743\pi$
$294$	33.2557	−	2.43401i	0.113115	−	0.00827893i
$295$	−513.175	+	396.261i	−1.73957	+	1.34326i
$296$	−407.446	−	44.8318i	−1.37651	−	0.151459i
$297$	−295.952	−	265.174i	−0.996471	−	0.892842i
$298$	−33.8259	+	26.1195i	−0.113510	+	0.0876494i
$299$	−214.028	−	73.0161i	−0.715811	−	0.244201i
$300$	168.176	+	24.7504i	0.560587	+	0.0825013i
$301$	177.237	+	83.0853i	0.588827	+	0.276031i
$302$	171.752	−	281.426i	0.568714	−	0.931874i
$303$	151.450	+	27.9743i	0.499836	+	0.0923244i
$304$	−1.91514	−	17.4054i	−0.00629980	−	0.0572546i
$305$	−1.96902	+	53.8773i	−0.00645581	+	0.176647i
$306$	15.6684	−	4.09626i	0.0512040	−	0.0133865i
$307$	156.649	+	103.638i	0.510256	+	0.337582i	0.780444	−	0.625225i	$-0.214993\pi$
$307$	156.649	+	103.638i	0.510256	+	0.337582i	−0.270188	+	0.962807i	$0.587086\pi$
$308$	41.2360	−	185.114i	0.133883	−	0.601021i
$309$	−22.9544	+	313.625i	−0.0742861	+	1.01497i
$310$	300.479	+	183.380i	0.969287	+	0.591547i
$311$	209.024	+	38.6086i	0.672102	+	0.124144i	0.506753	−	0.862092i	$-0.330846\pi$
$311$	209.024	+	38.6086i	0.672102	+	0.124144i	0.165349	+	0.986235i	$0.447125\pi$
$312$	64.5373	+	72.0280i	0.206850	+	0.230859i
$313$	−345.222	+	246.985i	−1.10294	+	0.789089i	−0.979134	−	0.203217i	$-0.934860\pi$
$313$	−345.222	+	246.985i	−1.10294	+	0.789089i	−0.123811	+	0.992306i	$0.539512\pi$
$314$	67.2997	+	80.8691i	0.214330	+	0.257545i
$315$		−	300.964i		−	0.955442i
$316$	−151.068	+	51.5372i	−0.478063	+	0.163092i
$317$	16.4233	+	224.390i	0.0518084	+	0.707856i	0.958324	+	0.285684i	$0.0922206\pi$
$317$	16.4233	+	224.390i	0.0518084	+	0.707856i	−0.906516	+	0.422172i	$0.861268\pi$
$318$	131.223	+	39.4790i	0.412650	+	0.124148i
$319$	−26.3643	+	239.608i	−0.0826468	+	0.751121i
$320$	446.261	+	65.6760i	1.39457	+	0.205238i
$321$	−169.083	−	71.8523i	−0.526737	−	0.223839i
$322$	−136.346	−	242.943i	−0.423436	−	0.754483i
$323$	−8.61689	−	6.16485i	−0.0266777	−	0.0190862i
$324$	16.3381	+	9.16939i	0.0504262	+	0.0283006i
$325$	285.943	+	121.512i	0.879824	+	0.373885i
$326$	−20.2827	+	184.336i	−0.0622170	+	0.565448i
$327$	111.466	+	155.802i	0.340876	+	0.476457i
$328$	92.9437	−	503.189i	0.283365	−	1.53411i
$329$	300.316	−	44.1973i	0.912814	−	0.134338i
$330$	296.827	+	89.3020i	0.899477	+	0.270612i
$331$	−184.183	−	48.1518i	−0.556445	−	0.145474i	−0.0359731	−	0.999353i	$-0.511453\pi$
$331$	−184.183	−	48.1518i	−0.556445	−	0.145474i	−0.520471	+	0.853879i	$0.674244\pi$
$332$	65.2123	+	72.7812i	0.196422	+	0.219221i
$333$	292.024	+	10.6724i	0.876950	+	0.0320494i
$334$	8.63120	+	28.6889i	0.0258419	+	0.0858948i
$335$	110.834	+	92.2367i	0.330847	+	0.275333i
$336$			33.1734i			0.0987303i
$337$	340.729	−	558.305i	1.01106	−	1.65669i	0.299465	−	0.954107i	$-0.403192\pi$
$337$	340.729	−	558.305i	1.01106	−	1.65669i	0.711600	−	0.702585i	$-0.247971\pi$
$338$	−78.8841	−	153.431i	−0.233385	−	0.453937i
$339$	81.8799	+	15.1240i	0.241534	+	0.0446135i
$340$	26.6966	−	22.2170i	0.0785193	−	0.0653443i
$341$	−353.659	−	294.317i	−1.03712	−	0.863100i
$342$	8.14333	+	44.0872i	0.0238109	+	0.128910i
$343$	−227.771	−	294.973i	−0.664055	−	0.859980i
$344$	136.114	−	242.530i	0.395681	−	0.705029i
$345$	−453.273	+	212.486i	−1.31383	+	0.615900i
$346$	12.9361	−	0.946797i	0.0373874	−	0.00273641i
$347$	−35.4671	+	49.5739i	−0.102211	+	0.142864i	−0.861252	−	0.508178i	$-0.830319\pi$
$347$	−35.4671	+	49.5739i	−0.102211	+	0.142864i	0.759041	+	0.651042i	$0.225668\pi$
$348$	6.25846	+	56.8789i	0.0179841	+	0.163445i
$349$	497.122	−	479.286i	1.42442	−	1.37331i	0.611008	−	0.791625i	$-0.290764\pi$
$349$	497.122	−	479.286i	1.42442	−	1.37331i	0.813412	−	0.581688i	$-0.197608\pi$
$350$	162.461	+	346.560i	0.464174	+	0.990172i
$351$	−124.118	−	119.664i	−0.353611	−	0.340924i
$352$	−427.381	−	128.580i	−1.21415	−	0.365283i
$353$	37.4233	+	340.115i	0.106015	+	0.963499i	0.922465	+	0.386082i	$0.126172\pi$
$353$	37.4233	+	340.115i	0.106015	+	0.963499i	−0.816450	+	0.577417i	$0.804061\pi$
$354$	−136.275	+	122.103i	−0.384957	+	0.344923i
$355$	−5.28322	+	9.41370i	−0.0148823	+	0.0265175i
$356$	−62.9908	−	60.7307i	−0.176940	−	0.170592i
$357$	14.9493	+	13.3946i	0.0418748	+	0.0375200i
$358$	−78.3812	+	51.8565i	−0.218942	+	0.144851i
$359$	−223.851	−	585.282i	−0.623542	−	1.63031i	−0.767739	−	0.640763i	$-0.778618\pi$
$359$	−223.851	−	585.282i	−0.623542	−	1.63031i	0.144197	−	0.989549i	$-0.453940\pi$
$360$	−426.470	−	31.2136i	−1.18464	−	0.0867043i
$361$	−212.160	+	254.937i	−0.587701	+	0.706196i
$362$	264.794	+	220.363i	0.731474	+	0.608737i
$363$	−176.994	−	82.9714i	−0.487587	−	0.228571i
$364$	20.8125	−	79.6089i	0.0571772	−	0.218706i
$365$	−66.4487	−	451.511i	−0.182051	−	1.23702i
$366$	0.555681	+	15.2048i	0.00151826	+	0.0415432i
$367$	157.617	+	523.898i	0.429475	+	1.42752i	0.853133	+	0.521693i	$0.174699\pi$
$367$	157.617	+	523.898i	0.429475	+	1.42752i	−0.423658	+	0.905822i	$0.639254\pi$
$368$	−99.7897	+	46.7795i	−0.271168	+	0.127118i
$369$	−39.8974	+	362.600i	−0.108123	+	0.982657i
$370$	−524.611	+	222.936i	−1.41787	+	0.602529i
$371$	−97.7313	−	324.845i	−0.263427	−	0.875593i
$372$	−97.1352	−	49.9407i	−0.261116	−	0.134249i
$373$	464.083	−	238.602i	1.24419	−	0.639683i	0.295336	−	0.955394i	$-0.404568\pi$
$373$	464.083	−	238.602i	1.24419	−	0.639683i	0.948856	+	0.315711i	$0.102243\pi$
$374$	35.2455	−	21.5100i	0.0942394	−	0.0575135i
$375$	299.464	−	114.535i	0.798572	−	0.305428i
$376$	−31.4818	−	430.134i	−0.0837281	−	1.14397i
$377$	−15.2279	+	103.472i	−0.0403923	+	0.274461i
$378$	−15.5039	−	211.829i	−0.0410156	−	0.560395i
$379$	161.554	−	314.226i	0.426265	−	0.829091i	−0.573685	−	0.819076i	$-0.694487\pi$
$379$	161.554	−	314.226i	0.426265	−	0.829091i	0.999950	−	0.0100149i	$-0.00318789\pi$
$380$	55.9451	+	78.1970i	0.147224	+	0.205781i
$381$	59.4756	+	266.994i	0.156104	+	0.700773i
$382$	−53.5859	−	114.309i	−0.140277	−	0.299239i
$383$	−79.1752	+	355.429i	−0.206724	+	0.928013i	0.755371	+	0.655298i	$0.227457\pi$
$383$	−79.1752	+	355.429i	−0.206724	+	0.928013i	−0.962095	+	0.272716i	$0.912078\pi$
$384$	−74.8115	−	5.47549i	−0.194822	−	0.0142591i
$385$	−221.069	−	734.803i	−0.574206	−	1.90858i
$386$	69.3313	−	311.238i	0.179615	−	0.806317i
$387$	−84.1556	+	179.520i	−0.217456	+	0.463876i
$388$	−35.0778	−	27.0862i	−0.0904067	−	0.0698097i
$389$	753.154	+	110.841i	1.93613	+	0.284939i	0.998100	−	0.0616168i	$-0.0196257\pi$
$389$	753.154	+	110.841i	1.93613	+	0.284939i	0.938029	+	0.346556i	$0.112649\pi$
$390$	127.284	+	43.4232i	0.326369	+	0.111342i
$391$	−19.2120	+	63.8578i	−0.0491355	+	0.163319i
$392$	−97.8120	+	64.7118i	−0.249520	+	0.165081i
$393$	180.920	+	6.61199i	0.460357	+	0.0168244i
$394$	70.9331	−	271.323i	0.180033	−	0.688637i
$395$	−430.965	+	480.986i	−1.09105	+	1.21769i
$396$	187.499	+	41.7672i	0.473482	+	0.105473i
$397$	−7.85923	−	215.048i	−0.0197966	−	0.541683i	−0.971829	−	0.235686i	$-0.924266\pi$
$397$	−7.85923	−	215.048i	−0.0197966	−	0.541683i	0.952033	−	0.305997i	$-0.0989896\pi$
$398$	307.543	−	220.028i	0.772722	−	0.552835i
$399$	−40.0026	+	38.5673i	−0.100257	+	0.0966600i
$400$	141.425	−	54.0906i	0.353564	−	0.135227i
$401$	−542.468	+	523.005i	−1.35279	+	1.30425i	−0.438758	+	0.898605i	$0.644581\pi$
$401$	−542.468	+	523.005i	−1.35279	+	1.30425i	−0.914030	+	0.405646i	$0.867047\pi$
$402$	33.0953	+	23.6776i	0.0823266	+	0.0588996i
$403$	−148.676	−	133.215i	−0.368924	−	0.330558i
$404$	−176.206	+	60.1132i	−0.436154	+	0.148795i
$405$	75.8037			0.187170
$406$	−99.0352	+	82.4177i	−0.243929	+	0.202999i
$407$	720.816	−	188.446i	1.77105	−	0.463012i
$408$	20.5308	−	19.7941i	0.0503205	−	0.0485151i
$409$	−337.539	+	12.3358i	−0.825279	+	0.0301610i	−0.445902	−	0.895082i	$-0.647117\pi$
$409$	−337.539	+	12.3358i	−0.825279	+	0.0301610i	−0.379376	+	0.925243i	$0.623861\pi$
$410$	−229.753	−	673.460i	−0.560372	−	1.64259i
$411$	−235.482	+	43.4957i	−0.572949	+	0.105829i
$412$	−161.353	−	344.198i	−0.391634	−	0.835432i
$413$	438.230	+	114.568i	1.06109	+	0.277405i
$414$	246.073	−	138.103i	0.594379	−	0.333582i
$415$	374.213	+	127.664i	0.901718	+	0.307623i
$416$	−183.267	−	62.5221i	−0.440546	−	0.150293i
$417$	63.5721	−	243.167i	0.152451	−	0.583134i
$418$	52.2656	+	101.657i	0.125037	+	0.243199i
$419$	269.804	+	301.119i	0.643923	+	0.718661i	0.974317	−	0.225182i	$-0.0722978\pi$
$419$	269.804	+	301.119i	0.643923	+	0.718661i	−0.330394	+	0.943843i	$0.607182\pi$
$420$	−89.1491	−	158.847i	−0.212260	−	0.378206i
$421$	273.722	+	354.482i	0.650172	+	0.842000i	0.995329	−	0.0965446i	$-0.0307790\pi$
$421$	273.722	+	354.482i	0.650172	+	0.842000i	−0.345157	+	0.938545i	$0.612174\pi$
$422$	12.4074	+	55.6987i	0.0294015	+	0.131987i
$423$	44.7666	+	304.184i	0.105831	+	0.719111i
$424$	−470.445	+	104.796i	−1.10954	+	0.247160i
$425$	32.7288	−	85.5727i	0.0770089	−	0.201348i
$426$	−1.29309	+	2.75841i	−0.00303542	+	0.00647513i
$427$	30.6326	−	21.9157i	0.0717391	−	0.0513249i
$428$	220.754	−	24.2898i	0.515780	−	0.0567519i
$429$	−156.330	−	80.3750i	−0.364407	−	0.187354i
$430$		−	386.747i		−	0.899412i
$431$	243.748	+	355.454i	0.565541	+	0.824720i
$431$	243.748	+	355.454i	0.565541	+	0.824720i
$432$	−84.0242			−0.194500
$433$	−41.1490	+	80.0353i	−0.0950323	+	0.184839i	−0.932043	−	0.362347i	$-0.881975\pi$
$433$	−41.1490	+	80.0353i	−0.0950323	+	0.184839i	0.837011	+	0.547186i	$0.184301\pi$
$434$	−26.8973	−	244.452i	−0.0619754	−	0.563252i
$435$	134.714	+	188.295i	0.309687	+	0.432863i
$436$	−209.683	−	98.2954i	−0.480925	−	0.225448i
$437$	−172.425	−	65.9470i	−0.394565	−	0.150909i
$438$	−28.0038	−	125.713i	−0.0639356	−	0.287016i
$439$	−438.623	+	64.5520i	−0.999142	+	0.147043i	−0.625246	−	0.780428i	$-0.715001\pi$
$439$	−438.623	+	64.5520i	−0.999142	+	0.147043i	−0.373896	+	0.927471i	$0.621978\pi$
$440$	−1064.15	+	237.050i	−2.41853	+	0.538750i
$441$	66.1761	−	51.0996i	0.150059	−	0.115872i
$442$	15.6227	−	8.76787i	0.0353454	−	0.0198368i
$443$	317.210	−	284.221i	0.716049	−	0.641583i	−0.227131	−	0.973864i	$-0.572935\pi$
$443$	317.210	−	284.221i	0.716049	−	0.641583i	0.943180	+	0.332281i	$0.107818\pi$
$444$	157.290	−	80.8681i	0.354256	−	0.182135i
$445$	−342.512	−	89.5445i	−0.769691	−	0.201223i
$446$	−96.1041	+	281.704i	−0.215480	+	0.631623i
$447$	17.3228	−	50.7771i	0.0387534	−	0.113595i
$448$	−154.228	−	274.806i	−0.344260	−	0.613406i
$449$	−225.506	+	862.574i	−0.502242	+	1.92110i	−0.135504	+	0.990777i	$0.543265\pi$
$449$	−225.506	+	862.574i	−0.502242	+	1.92110i	−0.366738	+	0.930324i	$0.619525\pi$
$450$	−351.024	+	164.553i	−0.780054	+	0.365674i
$451$	168.934	+	914.594i	0.374577	+	2.02792i
$452$	−95.2640	+	32.4996i	−0.210761	+	0.0719017i
$453$	15.1162	+	413.617i	0.0333691	+	0.913061i
$454$	−52.5169	−	54.4713i	−0.115676	−	0.119981i
$455$	−84.2081	−	322.101i	−0.185073	−	0.707914i
$456$	50.5016	+	60.6840i	0.110749	+	0.133079i
$457$		−	365.955i		−	0.800777i	−0.916345	−	0.400389i	$-0.868875\pi$
$457$		−	365.955i		−	0.800777i	0.916345	−	0.400389i	$-0.131125\pi$
$458$	22.6281	+	66.3284i	0.0494063	+	0.144822i
$459$	−33.9270	+	37.8648i	−0.0739150	+	0.0824941i
$460$	352.117	−	492.170i	0.765472	−	1.06993i
$461$	−440.151	−	456.530i	−0.954774	−	0.990305i	0.0451887	−	0.998978i	$-0.485611\pi$
$461$	−440.151	−	456.530i	−0.954774	−	0.990305i	−0.999962	+	0.00867381i	$0.997239\pi$
$462$	−77.3590	−	202.263i	−0.167444	−	0.437799i
$463$	−295.007	−	305.985i	−0.637163	−	0.660875i	0.321006	−	0.947077i	$-0.395979\pi$
$463$	−295.007	−	305.985i	−0.637163	−	0.660875i	−0.958169	+	0.286203i	$0.907607\pi$
$464$	29.6577	+	41.4539i	0.0639176	+	0.0893404i
$465$	−441.619	+	16.1396i	−0.949719	+	0.0347088i
$466$	49.6217	−	222.759i	0.106484	−	0.478023i
$467$	410.327	+	367.654i	0.878644	+	0.787268i	0.978179	−	0.207766i	$-0.0666192\pi$
$467$	410.327	+	367.654i	0.878644	+	0.787268i	−0.0995349	+	0.995034i	$0.531735\pi$
$468$	80.6344	+	21.0806i	0.172296	+	0.0450440i
$469$	3.67911	−	100.670i	0.00784459	−	0.214647i
$470$	−330.920	−	500.187i	−0.704086	−	1.06423i
$471$	−126.478	−	38.0515i	−0.268530	−	0.0807888i
$472$	207.794	−	609.095i	0.440242	−	1.29046i
$473$	−73.6014	+	500.113i	−0.155605	+	1.05732i
$474$	−111.391	+	144.256i	−0.235002	+	0.304337i
$475$	229.647	+	107.654i	0.483467	+	0.226640i
$476$	−23.6840	−	5.27583i	−0.0497562	−	0.0110837i
$477$	329.029	−	98.9902i	0.689789	−	0.207527i
$478$	−22.5889	+	308.631i	−0.0472571	+	0.645672i
$479$	6.33309	+	1.41076i	0.0132215	+	0.00294521i	0.224036	−	0.974581i	$-0.428077\pi$
$479$	6.33309	+	1.41076i	0.0132215	+	0.00294521i	−0.210814	+	0.977526i	$0.567612\pi$
$480$	−388.127	+	181.947i	−0.808599	+	0.379056i
$481$	315.519	−	70.2848i	0.655965	−	0.146122i
$482$	155.492	−	111.245i	0.322597	−	0.230799i
$483$	311.034	+	159.913i	0.643962	+	0.331084i
$484$	235.672	−	17.2490i	0.486926	−	0.0356384i
$485$	−177.403	−	26.1083i	−0.365779	−	0.0538315i
$486$	343.316	−	25.1275i	0.706411	−	0.0517026i
$487$	−292.458	−	764.662i	−0.600531	−	1.57015i	−0.806274	−	0.591542i	$-0.798519\pi$
$487$	−292.458	−	764.662i	−0.600531	−	1.57015i	0.205744	−	0.978606i	$-0.434039\pi$
$488$	−27.8779	−	45.6796i	−0.0571268	−	0.0936058i
$489$	−106.450	−	207.046i	−0.217689	−	0.423407i
$490$	−74.5721	+	145.044i	−0.152188	+	0.296008i
$491$	−748.226	+	225.108i	−1.52388	+	0.458468i	−0.936448	−	0.350805i	$-0.885908\pi$
$491$	−748.226	+	225.108i	−1.52388	+	0.458468i	−0.587433	+	0.809273i	$0.699861\pi$
$492$	86.3489	+	203.196i	0.175506	+	0.413000i
$493$	30.6560	+	3.37312i	0.0621825	+	0.00684202i
$494$	21.0506	+	44.9050i	0.0426125	+	0.0909008i
$495$	744.269	−	223.917i	1.50357	−	0.452358i
$496$	−97.2242	+	3.55319i	−0.196016	+	0.00716370i
$497$	7.46120	−	1.09806i	0.0150125	−	0.00220938i
$498$	107.956	+	28.2233i	0.216778	+	0.0566732i
$499$	338.380	−	721.830i	0.678116	−	1.44655i	−0.205650	−	0.978626i	$-0.565931\pi$
$499$	338.380	−	721.830i	0.678116	−	1.44655i	0.883767	−	0.467928i	$-0.154999\pi$
$500$	−247.926	+	297.914i	−0.495852	+	0.595828i
$501$	−28.9088	−	24.0581i	−0.0577023	−	0.0480202i
$502$	−33.7105	+	460.585i	−0.0671523	+	0.917500i
$503$	−367.829	+	140.683i	−0.731271	+	0.279687i	−0.694357	−	0.719631i	$-0.744311\pi$
$503$	−367.829	+	140.683i	−0.731271	+	0.279687i	−0.0369141	+	0.999318i	$0.511753\pi$
$504$	164.834	+	249.147i	0.327052	+	0.494340i
$505$	−502.680	+	561.025i	−0.995407	+	1.11094i
$506$	499.345	−	517.927i	0.986847	−	1.02357i
$507$	188.868	+	105.998i	0.372521	+	0.209069i
$508$	−220.661	−	246.272i	−0.434372	−	0.484788i
$509$	209.757	−	23.0798i	0.412096	−	0.0453434i	0.0990523	−	0.995082i	$-0.468419\pi$
$509$	209.757	−	23.0798i	0.412096	−	0.0453434i	0.313043	+	0.949739i	$0.398651\pi$
$510$	11.4255	−	37.9768i	0.0224030	−	0.0744643i
$511$	−221.294	+	229.529i	−0.433061	+	0.449177i
$512$	−183.961	+	86.2372i	−0.359298	+	0.168432i
$513$	−97.6864	−	101.322i	−0.190422	−	0.197508i
$514$	333.532	−	36.6989i	0.648894	−	0.0713987i
$515$	−1250.89	−	894.937i	−2.42892	−	1.73774i
$516$	8.75924	+	119.677i	0.0169753	+	0.231933i
$517$	332.732	+	709.782i	0.643582	+	1.37289i
$518$	347.272	+	194.899i	0.670410	+	0.376252i
$519$	−12.8880	+	9.95179i	−0.0248324	+	0.0191749i
$520$	−465.153	+	85.9182i	−0.894526	+	0.165227i
$521$	380.300	−	456.978i	0.729943	−	0.877118i	−0.266285	−	0.963894i	$-0.585796\pi$
$521$	380.300	−	456.978i	0.729943	−	0.877118i	0.996228	+	0.0867766i	$0.0276566\pi$
$522$	−83.4793	−	100.311i	−0.159922	−	0.192166i
$523$	−164.530	+	890.753i	−0.314590	+	1.70316i	0.334455	+	0.942412i	$0.391448\pi$
$523$	−164.530	+	890.753i	−0.314590	+	1.70316i	−0.649045	+	0.760750i	$0.724831\pi$
$524$	−194.635	+	100.069i	−0.371440	+	0.190970i
$525$	−410.148	−	250.310i	−0.781234	−	0.476780i
$526$	−589.201			−1.12015
$527$	−37.6556	+	45.2479i	−0.0714528	+	0.0858595i
$528$	−82.0360	+	24.6810i	−0.155371	+	0.0467442i
$529$	−23.1150	+	632.484i	−0.0436957	+	1.19562i
$530$	−499.173	+	447.261i	−0.941836	+	0.843889i
$531$	−116.044	+	443.875i	−0.218539	+	0.835924i
$532$	19.3521	−	64.3238i	0.0363762	−	0.120909i
$533$	58.7542	+	399.228i	0.110233	+	0.749021i
$534$	−98.2478	−	18.1473i	−0.183985	−	0.0339837i
$535$	730.797	−	522.840i	1.36597	−	0.977271i
$536$	−142.268	−	15.6540i	−0.265426	−	0.0292052i
$537$	46.1439	−	108.586i	0.0859291	−	0.202208i
$538$	−283.416	+	504.994i	−0.526796	+	0.938650i
$539$	124.034	−	173.368i	0.230119	−	0.321648i
$540$	402.339	−	225.804i	0.745073	−	0.418155i
$541$	−138.981	+	327.049i	−0.256896	+	0.604527i	−0.997743	−	0.0671470i	$-0.978610\pi$
$541$	−138.981	+	327.049i	−0.256896	+	0.604527i	0.740847	+	0.671674i	$0.234424\pi$
$542$	−56.1559	+	381.573i	−0.103609	+	0.704009i
$543$	−429.875	−	47.2997i	−0.791666	−	0.0871080i
$544$	−16.4508	+	54.6801i	−0.0302404	+	0.100515i
$545$	−934.479	+	68.3951i	−1.71464	+	0.125496i
$546$	−30.3365	−	88.9234i	−0.0555613	−	0.162863i
$547$	685.051			1.25238			0.626189	−	0.779671i	$-0.284614\pi$
$547$	685.051			1.25238			0.626189	+	0.779671i	$0.284614\pi$
$548$	222.507	−	185.171i	0.406034	−	0.337904i
$549$	22.1980	+	31.0272i	0.0404336	+	0.0565158i
$550$	−736.154	+	659.597i	−1.33846	+	1.19927i
$551$	−15.5077	+	83.9575i	−0.0281447	+	0.152373i
$552$	258.857	−	424.153i	0.468944	−	0.768394i
$553$	449.978	+	32.9342i	0.813704	+	0.0595555i
$554$	417.613	+	93.0273i	0.753814	+	0.167919i
$555$	394.837	−	596.796i	0.711417	−	1.07531i
$556$	76.8494	+	293.953i	0.138218	+	0.528692i
$557$	−142.770	−	5.21773i	−0.256319	−	0.00936755i	−0.0919393	−	0.995765i	$-0.529307\pi$
$557$	−142.770	−	5.21773i	−0.256319	−	0.00936755i	−0.164380	+	0.986397i	$0.552562\pi$
$558$	247.600	−	27.2438i	0.443728	−	0.0488240i
$559$	−39.8370	+	215.674i	−0.0712647	+	0.385821i
$560$	−138.498	−	84.5242i	−0.247318	−	0.150936i
$561$	−22.0020	+	46.9344i	−0.0392192	+	0.0836621i
$562$	10.1281	−	68.8193i	0.0180215	−	0.122454i
$563$	−308.827	+	905.244i	−0.548537	+	1.60789i	0.225148	+	0.974325i	$0.427713\pi$
$563$	−308.827	+	905.244i	−0.548537	+	1.60789i	−0.773686	+	0.633570i	$0.781589\pi$
$564$	113.730	+	147.286i	0.201650	+	0.261145i
$565$	−271.769	+	303.312i	−0.481006	+	0.536835i
$566$	60.8698	−	553.204i	0.107544	−	0.977393i
$567$	−32.3667	−	41.9162i	−0.0570841	−	0.0739263i
$568$	−0.782150	−	10.6865i	−0.00137703	−	0.0188142i
$569$	−137.678	−	323.984i	−0.241966	−	0.569393i	0.754223	−	0.656618i	$-0.228014\pi$
$569$	−137.678	−	323.984i	−0.241966	−	0.569393i	−0.996189	+	0.0872258i	$0.972200\pi$
$570$	102.543	+	39.2192i	0.179899	+	0.0688056i
$571$	−191.772	+	81.4944i	−0.335853	+	0.142722i	−0.552466	−	0.833535i	$-0.686313\pi$
$571$	−191.772	+	81.4944i	−0.335853	+	0.142722i	0.216613	+	0.976258i	$0.430499\pi$
$572$	212.353	−	7.76074i	0.371247	−	0.0135677i
$573$	135.283	+	82.5619i	0.236096	+	0.144087i
$574$	−274.295	+	414.597i	−0.477866	+	0.722295i
$575$	174.592	−	1586.75i	0.303639	−	2.75957i
$576$	278.346	−	156.215i	0.483239	−	0.271207i
$577$	−995.461	+	109.532i	−1.72524	+	0.189830i	−0.916961	−	0.398976i	$-0.869366\pi$
$577$	−995.461	+	109.532i	−1.72524	+	0.189830i	−0.808274	+	0.588806i	$0.799598\pi$
$578$	205.057	+	335.999i	0.354770	+	0.581313i
$579$	142.999	+	373.886i	0.246976	+	0.645744i
$580$	−253.414	−	118.796i	−0.436921	−	0.204820i
$581$	−89.1888	−	261.434i	−0.153509	−	0.449972i
$582$	−50.4694	−	3.69389i	−0.0867172	−	0.00634688i
$583$	730.612	−	483.368i	1.25319	−	0.829105i
$584$	302.295	+	337.381i	0.517628	+	0.577707i
$585$	326.250	−	85.2929i	0.557692	−	0.145800i
$586$	14.2610	−	194.847i	0.0243361	−	0.332504i
$587$	267.157	−	698.508i	0.455122	−	1.18996i	−0.492427	−	0.870354i	$-0.663890\pi$
$587$	267.157	−	698.508i	0.455122	−	1.18996i	0.947549	−	0.319609i	$-0.103552\pi$
$588$	19.7910	−	46.5721i	0.0336582	−	0.0792043i
$589$	−117.317	−	113.108i	−0.199181	−	0.192034i
$590$	−162.555	−	880.056i	−0.275516	−	1.49162i
$591$	113.674	+	333.204i	0.192341	+	0.563797i
$592$	86.9248	−	131.387i	0.146832	−	0.221937i
$593$	33.5163	−	917.088i	0.0565199	−	1.54652i	−0.604775	−	0.796397i	$-0.706737\pi$
$593$	33.5163	−	917.088i	0.0565199	−	1.54652i	0.661294	−	0.750126i	$-0.270007\pi$
$594$	512.308	−	195.941i	0.862471	−	0.329867i
$595$	−94.0125	+	28.2841i	−0.158004	+	0.0475364i
$596$	11.7802	+	63.7770i	0.0197654	+	0.107008i
$597$	−169.584	+	443.394i	−0.284060	+	0.742704i
$598$	224.714	−	216.651i	0.375776	−	0.362293i
$599$	−617.031	+	317.237i	−1.03010	+	0.529611i	−0.887808	−	0.460213i	$-0.847773\pi$
$599$	−617.031	+	317.237i	−1.03010	+	0.529611i	−0.142293	+	0.989825i	$0.545447\pi$
$600$	−397.229	+	555.224i	−0.662048	+	0.925373i
$601$	−99.6965	−	42.3664i	−0.165884	−	0.0704932i	0.306571	−	0.951848i	$-0.400818\pi$
$601$	−99.6965	−	42.3664i	−0.165884	−	0.0704932i	−0.472455	+	0.881355i	$0.656632\pi$
$602$	−213.855	+	165.133i	−0.355240	+	0.274308i
$603$	101.966	+	3.72650i	0.169098	+	0.00617994i
$604$	−260.645	−	427.083i	−0.431531	−	0.707091i
$605$	797.376	−	527.539i	1.31798	−	0.871966i
$606$	−129.927	+	168.261i	−0.214401	+	0.277658i
$607$	−127.344	−	689.429i	−0.209793	−	1.13580i	−0.907703	−	0.419613i	$-0.862166\pi$
$607$	−127.344	−	689.429i	−0.209793	−	1.13580i	0.697911	−	0.716185i	$-0.254113\pi$
$608$	−147.644	−	56.4690i	−0.242835	−	0.0928766i
$609$	46.5992	−	154.889i	0.0765176	−	0.254334i
$610$	−64.8957	−	36.4212i	−0.106386	−	0.0597069i
$611$	133.020	+	313.021i	0.217708	+	0.512310i
$612$	5.34379	−	23.9891i	0.00873168	−	0.0391978i
$613$	−551.843	+	122.928i	−0.900233	+	0.200535i	−0.643047	−	0.765827i	$-0.722330\pi$
$613$	−551.843	+	122.928i	−0.900233	+	0.200535i	−0.257186	+	0.966362i	$0.582795\pi$
$614$	−226.090	+	126.888i	−0.368225	+	0.206658i
$615$	707.038	+	545.957i	1.14965	+	0.887735i
$616$	585.450	+	487.215i	0.950406	+	0.790934i
$617$		−	463.958i		−	0.751958i	−0.926628	−	0.375979i	$-0.877306\pi$
$617$		−	463.958i		−	0.751958i	0.926628	−	0.375979i	$-0.122694\pi$
$618$	−370.511	−	226.120i	−0.599532	−	0.365889i
$619$	523.317	−	319.376i	0.845424	−	0.515955i	−0.0298657	−	0.999554i	$-0.509508\pi$
$619$	523.317	−	319.376i	0.845424	−	0.515955i	0.875290	+	0.483599i	$0.160671\pi$
$620$	455.997	−	278.291i	0.735479	−	0.448857i
$621$	−405.041	+	787.811i	−0.652241	+	1.26862i
$622$	−179.318	+	232.225i	−0.288293	+	0.373352i
$623$	96.7316	+	227.628i	0.155267	+	0.365375i
$624$	−35.9604	+	9.40129i	−0.0576289	+	0.0150662i
$625$	−72.1808	+	390.780i	−0.115489	+	0.625248i
$626$	−85.3093	−	579.667i	−0.136277	−	0.925986i
$627$	−125.137	−	70.2302i	−0.199580	−	0.112010i
$628$	155.843	−	34.7155i	0.248158	−	0.0552794i
$629$	−24.1102	−	92.2229i	−0.0383310	−	0.146618i
$630$	369.456	+	189.950i	0.586438	+	0.301509i
$631$	−758.212	−	679.361i	−1.20160	−	1.07664i	−0.995169	−	0.0981806i	$-0.968698\pi$
$631$	−758.212	−	679.361i	−1.20160	−	1.07664i	−0.206434	−	0.978460i	$-0.566186\pi$
$632$	93.3362	−	634.209i	0.147684	−	1.00349i
$633$	−51.5716	−	49.7213i	−0.0814717	−	0.0785486i
$634$	−285.821	−	121.461i	−0.450822	−	0.191579i
$635$	−1266.24	−	431.980i	−1.99407	−	0.680284i
$636$	144.337	−	149.709i	0.226945	−	0.235391i
$637$	56.5262	−	73.2039i	0.0887382	−	0.114920i
$638$	−277.497	−	183.590i	−0.434948	−	0.287759i
$639$	1.11221	+	7.55732i	0.00174054	+	0.0118268i
$640$	213.476	−	298.385i	0.333557	−	0.466227i
$641$	284.162	−	429.512i	0.443311	−	0.670065i	−0.542089	−	0.840321i	$-0.682366\pi$
$641$	284.162	−	429.512i	0.443311	−	0.670065i	0.985400	+	0.170256i	$0.0544595\pi$
$642$	194.919	−	162.213i	0.303612	−	0.252668i
$643$	336.351	+	404.168i	0.523096	+	0.628565i	0.963007	−	0.269476i	$-0.0868505\pi$
$643$	336.351	+	404.168i	0.523096	+	0.628565i	−0.439911	+	0.898041i	$0.644990\pi$
$644$	−422.496	+	15.4407i	−0.656049	+	0.0239762i
$645$	267.891	+	404.917i	0.415335	+	0.627779i
$646$	13.0063	−	6.68698i	0.0201335	−	0.0103514i
$647$	−165.754	−	322.394i	−0.256189	−	0.498291i	0.725636	−	0.688079i	$-0.241546\pi$
$647$	−165.754	−	322.394i	−0.256189	−	0.498291i	−0.981825	+	0.189788i	$0.939220\pi$
$648$	−62.7526	+	41.5167i	−0.0968404	+	0.0640690i
$649$	42.7213	+	1168.96i	0.0658263	+	1.80117i
$650$	−329.635	+	274.325i	−0.507131	+	0.422038i
$651$	197.487	+	237.305i	0.303360	+	0.364524i
$652$	234.713	+	155.284i	0.359989	+	0.238166i
$653$	−730.611	−	522.707i	−1.11885	−	0.800471i	−0.137086	−	0.990559i	$-0.543774\pi$
$653$	−730.611	−	522.707i	−1.11885	−	0.800471i	−0.981767	+	0.190088i	$0.939123\pi$
$654$	−261.609	+	38.5008i	−0.400013	+	0.0588698i
$655$	−488.582	+	738.492i	−0.745927	+	1.12747i
$656$	155.657	+	120.194i	0.237282	+	0.183223i
$657$	−232.486	−	224.145i	−0.353860	−	0.341164i
$658$	−135.286	+	396.554i	−0.205601	+	0.602666i
$659$	6.72646	−	15.8287i	0.0102071	−	0.0240192i	−0.915164	−	0.403081i	$-0.867939\pi$
$659$	6.72646	−	15.8287i	0.0102071	−	0.0240192i	0.925371	+	0.379062i	$0.123753\pi$
$660$	326.493	−	338.643i	0.494686	−	0.513095i
$661$	658.582	+	96.9232i	0.996342	+	0.146631i	0.623967	−	0.781451i	$-0.285520\pi$
$661$	658.582	+	96.9232i	0.996342	+	0.146631i	0.372376	+	0.928082i	$0.378543\pi$
$662$	175.355	−	195.708i	0.264887	−	0.295631i
$663$	−10.2834	+	20.0013i	−0.0155104	+	0.0301679i
$664$	−379.704	+	99.2677i	−0.571844	+	0.149500i
$665$	−59.0932	−	265.278i	−0.0888619	−	0.398914i
$666$	−197.409	+	351.746i	−0.296410	+	0.528147i
$667$	531.638	−	78.2410i	0.797059	−	0.117303i
$668$	44.7087	+	8.25812i	0.0669292	+	0.0123625i
$669$	−94.5107	−	361.508i	−0.141272	−	0.540371i
$670$	−183.179	+	77.8426i	−0.273401	+	0.116183i
$671$	76.9871	+	59.4475i	0.114735	+	0.0885953i
$672$	266.331	+	136.930i	0.396326	+	0.203765i
$673$	395.844	+	648.616i	0.588179	+	0.963768i	0.998653	+	0.0518953i	$0.0165262\pi$
$673$	395.844	+	648.616i	0.588179	+	0.963768i	−0.410474	+	0.911873i	$0.634637\pi$
$674$	470.314	+	770.638i	0.697795	+	1.14338i
$675$	634.004	−	1038.86i	0.939265	−	1.53904i
$676$	−261.813			−0.387297
$677$	−157.466	+	189.215i	−0.232594	+	0.279491i	−0.872134	−	0.489267i	$-0.837264\pi$
$677$	−157.466	+	189.215i	−0.232594	+	0.279491i	0.639540	+	0.768758i	$0.279125\pi$
$678$	−70.2435	+	90.9683i	−0.103604	+	0.134172i
$679$	61.3106	+	109.244i	0.0902955	+	0.160889i
$680$	30.3287	+	136.150i	0.0446011	+	0.200221i
$681$	92.7153	+	20.6532i	0.136146	+	0.0303278i
$682$	584.504	−	248.387i	0.857044	−	0.364204i
$683$	5.60638	−	9.98950i	0.00820846	−	0.0146259i	−0.867915	−	0.496714i	$-0.834540\pi$
$683$	5.60638	−	9.98950i	0.00820846	−	0.0146259i	0.876123	+	0.482088i	$0.160121\pi$
$684$	65.1524	+	19.6014i	0.0952520	+	0.0286571i
$685$	418.403	−	1093.96i	0.610808	−	1.59702i
$686$	505.856	−	93.4364i	0.737400	−	0.136205i
$687$	−69.6354	−	53.7707i	−0.101362	−	0.0782688i
$688$	58.9772	+	89.1441i	0.0857226	+	0.129570i
$689$	324.440	−	198.003i	0.470885	−	0.287377i
$690$	25.2365	−	690.534i	0.0365747	−	1.00077i
$691$	291.412	+	377.391i	0.421724	+	0.546151i	0.953759	−	0.300571i	$-0.0971772\pi$
$691$	291.412	+	377.391i	0.421724	+	0.546151i	−0.532035	+	0.846722i	$0.678573\pi$
$692$	7.69845	−	18.1160i	0.0111249	−	0.0261791i
$693$	−441.604	−	315.941i	−0.637236	−	0.455903i
$694$	−38.4709	−	74.8265i	−0.0554336	−	0.107819i
$695$	853.238	+	884.990i	1.22768	+	1.27337i
$696$	−214.647	−	82.0955i	−0.308401	−	0.117953i
$697$	117.015	−	21.6138i	0.167884	−	0.0310098i
$698$	274.606	+	912.751i	0.393418	+	1.30767i
$699$	102.347	+	267.597i	0.146419	+	0.382828i
$700$	580.461	+	21.2138i	0.829231	+	0.0303054i
$701$	−456.674	−	302.133i	−0.651461	−	0.431003i	0.182213	−	0.983259i	$-0.441674\pi$
$701$	−456.674	−	302.133i	−0.651461	−	0.431003i	−0.833674	+	0.552256i	$0.813767\pi$
$702$	225.232	−	76.8386i	0.320844	−	0.109457i
$703$	259.493	−	47.9309i	0.369123	−	0.0681805i
$704$	564.834	−	585.854i	0.802321	−	0.832179i
$705$	692.936	+	294.466i	0.982887	+	0.417682i
$706$	−441.136	−	168.720i	−0.624838	−	0.238980i
$707$	524.857	+	38.4146i	0.742372	+	0.0543346i
$708$	70.2337	+	268.648i	0.0992002	+	0.379446i
$709$	116.520	−	104.402i	0.164344	−	0.147252i	−0.581073	−	0.813851i	$-0.697367\pi$
$709$	116.520	−	104.402i	0.164344	−	0.147252i	0.745416	+	0.666599i	$0.232251\pi$
$710$	−8.22156	−	12.4269i	−0.0115797	−	0.0175027i
$711$	−33.3584	+	455.775i	−0.0469176	+	0.641033i
$712$	332.584	−	113.462i	0.467113	−	0.159357i
$713$	−435.358	+	928.702i	−0.610600	+	1.30253i
$714$	−25.8780	+	9.89750i	−0.0362437	+	0.0138620i
$715$	733.887	−	447.885i	1.02642	−	0.626412i
$716$	15.5990	+	141.769i	0.0217864	+	0.198002i
$717$	−190.132	−	338.778i	−0.265176	−	0.472494i
$718$	859.759	+	94.6004i	1.19744	+	0.131755i
$719$	566.979	+	375.110i	0.788567	+	0.521711i	0.880495	−	0.474055i	$-0.157210\pi$
$719$	566.979	+	375.110i	0.788567	+	0.521711i	−0.0919287	+	0.995766i	$0.529303\pi$
$720$	85.6130	−	140.282i	0.118907	−	0.194836i
$721$	39.2439	+	1073.81i	0.0544298	+	1.48933i
$722$	−179.051	−	421.343i	−0.247993	−	0.583577i
$723$	−85.7405	+	224.177i	−0.118590	+	0.310065i
$724$	481.149	−	204.466i	0.664571	−	0.282412i
$725$	−736.309	+	53.8909i	−1.01560	+	0.0743323i
$726$	213.561	−	164.907i	0.294162	−	0.227144i
$727$	−821.442	−	90.3844i	−1.12991	−	0.124325i	−0.474965	−	0.880005i	$-0.657539\pi$
$727$	−821.442	−	90.3844i	−1.12991	−	0.124325i	−0.654942	+	0.755679i	$0.727307\pi$
$728$	246.120	+	220.525i	0.338077	+	0.302919i
$729$	−278.328	+	214.918i	−0.381794	+	0.294812i
$730$	596.202	+	203.396i	0.816715	+	0.278624i
$731$	63.9856	+	9.41673i	0.0875317	+	0.0128820i
$732$	20.9066	+	9.80060i	0.0285609	+	0.0133888i
$733$	176.510	−	289.223i	0.240805	−	0.394574i	−0.710079	−	0.704122i	$-0.751341\pi$
$733$	176.510	−	289.223i	0.240805	−	0.394574i	0.950884	+	0.309548i	$0.100178\pi$
$734$	−742.602	−	137.166i	−1.01172	−	0.186874i
$735$	−22.3928	−	203.513i	−0.0304663	−	0.276888i
$736$	−36.3363	+	994.251i	−0.0493700	+	1.35088i
$737$	251.688	−	65.7998i	0.341503	−	0.0892806i
$738$	−419.938	−	277.828i	−0.569022	−	0.376461i
$739$	−218.275	+	979.866i	−0.295365	+	1.32594i	0.568696	+	0.822548i	$0.307448\pi$
$739$	−218.275	+	979.866i	−0.295365	+	1.32594i	−0.864061	+	0.503388i	$0.832087\pi$
$740$	−63.1436	+	862.729i	−0.0853292	+	1.16585i
$741$	−53.1442	−	32.4335i	−0.0717196	−	0.0437699i
$742$	460.453	+	85.0500i	0.620557	+	0.114623i
$743$	−317.070	−	353.871i	−0.426742	−	0.476273i	0.492303	−	0.870424i	$-0.336155\pi$
$743$	−317.070	−	353.871i	−0.426742	−	0.476273i	−0.919046	+	0.394151i	$0.871039\pi$
$744$	356.746	−	255.230i	0.479497	−	0.343051i
$745$	167.856	+	201.700i	0.225310	+	0.270738i
$746$			720.288i			0.965533i
$747$	264.801	−	90.3377i	0.354486	−	0.120934i
$748$	−4.57400	−	62.4944i	−0.00611498	−	0.0835487i
$749$	−601.144	−	180.857i	−0.802595	−	0.241465i
$750$	−48.4030	+	439.902i	−0.0645374	+	0.586537i
$751$	192.854	+	28.3823i	0.256797	+	0.0377927i	0.272768	−	0.962080i	$-0.412061\pi$
$751$	192.854	+	28.3823i	0.256797	+	0.0377927i	−0.0159714	+	0.999872i	$0.505084\pi$
$752$	152.552	+	64.8277i	0.202862	+	0.0862071i
$753$	−283.742	−	505.575i	−0.376816	−	0.671414i
$754$	−117.408	−	83.9985i	−0.155714	−	0.111404i
$755$	−1765.36	−	990.766i	−2.33822	−	1.31227i
$756$	−296.651	−	126.063i	−0.392395	−	0.166750i
$757$	103.229	−	938.180i	0.136366	−	1.23934i	−0.709022	−	0.705187i	$-0.750863\pi$
$757$	103.229	−	938.180i	0.136366	−	1.23934i	0.845388	−	0.534153i	$-0.179369\pi$
$758$	283.772	+	396.640i	0.374369	+	0.523272i
$759$	−164.049	+	888.145i	−0.216138	+	1.17015i
$760$	−382.030	+	56.2232i	−0.502671	+	0.0739779i
$761$	1279.79	+	385.032i	1.68172	+	0.505955i	0.978714	−	0.205228i	$-0.0657935\pi$
$761$	1279.79	+	385.032i	1.68172	+	0.505955i	0.703007	+	0.711182i	$0.251840\pi$
$762$	−365.293	−	95.5001i	−0.479387	−	0.125328i
$763$	436.823	+	487.524i	0.572508	+	0.638957i
$764$	−191.459	−	6.99714i	−0.250601	−	0.00915855i
$765$	−28.6485	−	95.2235i	−0.0374490	−	0.124475i
$766$	−386.345	−	321.519i	−0.504367	−	0.419737i
$767$			507.517i			0.661691i
$768$	246.108	−	403.264i	0.320454	−	0.525083i
$769$	157.315	+	305.980i	0.204571	+	0.397894i	0.969090	−	0.246708i	$-0.0793488\pi$
$769$	157.315	+	305.980i	0.204571	+	0.397894i	−0.764519	+	0.644602i	$0.777023\pi$
$770$	1041.55	+	192.384i	1.35266	+	0.249850i
$771$	−323.781	+	269.453i	−0.419950	+	0.349485i
$772$	−371.950	−	309.539i	−0.481801	−	0.400958i
$773$	257.952	+	1396.53i	0.333703	+	1.80664i	0.555469	+	0.831537i	$0.312539\pi$
$773$	257.952	+	1396.53i	0.333703	+	1.80664i	−0.221767	+	0.975100i	$0.571182\pi$
$774$	−167.260	−	216.609i	−0.216099	−	0.279857i
$775$	689.674	−	1228.87i	0.889902	−	1.58564i
$776$	161.158	−	75.5479i	0.207678	−	0.0973556i
$777$	−498.590	+	36.4921i	−0.641686	+	0.0469654i
$778$	−611.411	+	854.596i	−0.785876	+	1.09845i
$779$	36.0286	+	327.439i	0.0462497	+	0.420333i
$780$	146.927	−	141.656i	0.188369	−	0.181610i
$781$	8.26658	+	17.6342i	0.0105846	+	0.0225790i
$782$	−66.2648	−	63.8873i	−0.0847376	−	0.0816973i
$783$	392.316	+	118.030i	0.501042	+	0.150741i
$784$	−4.92985	−	44.8041i	−0.00628808	−	0.0571481i
$785$	481.124	−	431.089i	0.612897	−	0.549158i
$786$	−122.303	+	217.920i	−0.155601	+	0.277252i
$787$	282.352	+	272.221i	0.358770	+	0.345898i	0.851566	−	0.524247i	$-0.175653\pi$
$787$	282.352	+	272.221i	0.358770	+	0.345898i	−0.492796	+	0.870145i	$0.664025\pi$
$788$	−316.967	−	284.004i	−0.402243	−	0.360411i
$789$	616.883	−	408.126i	0.781854	−	0.517270i
$790$	−318.447	−	832.611i	−0.403097	−	1.05394i
$791$	283.758	+	20.7684i	0.358734	+	0.0262559i
$792$	−493.491	+	592.991i	−0.623095	+	0.748726i
$793$	32.4382	+	26.9953i	0.0409057	+	0.0340420i
$794$	268.948	+	126.078i	0.338725	+	0.158788i
$795$	212.818	−	814.040i	0.267696	−	1.02395i
$796$	−83.5553	−	567.749i	−0.104969	−	0.713252i
$797$	−37.8870	−	1036.68i	−0.0475371	−	1.30073i	−0.782511	−	0.622636i	$-0.786062\pi$
$797$	−37.8870	−	1036.68i	−0.0475371	−	1.30073i	0.734974	−	0.678095i	$-0.237194\pi$
$798$	−22.0971	−	73.4475i	−0.0276906	−	0.0920395i
$799$	90.8112	−	42.5705i	0.113656	−	0.0532798i
$800$	149.500	−	1358.70i	0.186874	−	1.69838i
$801$	−230.561	+	97.9776i	−0.287841	+	0.122319i
$802$	−299.654	−	996.009i	−0.373634	−	1.24191i
$803$	−732.257	−	376.479i	−0.911901	−	0.468841i
$804$	54.9209	−	28.2368i	0.0683096	−	0.0351204i
$805$	−1460.14	+	891.108i	−1.81383	+	1.10697i
$806$	257.366	−	98.4343i	0.319313	−	0.122127i
$807$	−53.0658	−	725.036i	−0.0657568	−	0.898433i
$808$	108.868	−	739.744i	0.134737	−	0.915525i
$809$	64.3762	+	879.569i	0.0795750	+	1.08723i	0.875942	+	0.482416i	$0.160241\pi$
$809$	64.3762	+	879.569i	0.0795750	+	1.08723i	−0.796367	+	0.604814i	$0.793248\pi$
$810$	−47.8427	+	93.0547i	−0.0590651	+	0.114882i
$811$	−190.833	−	266.736i	−0.235306	−	0.328898i	0.678837	−	0.734289i	$-0.262484\pi$
$811$	−190.833	−	266.736i	−0.235306	−	0.328898i	−0.914143	+	0.405391i	$0.867135\pi$
$812$	42.5138	+	190.851i	0.0523569	+	0.235038i
$813$	−205.512	−	438.398i	−0.252783	−	0.539235i
$814$	−223.604	+	1003.79i	−0.274698	+	1.23316i
$815$	1135.64	+	83.1183i	1.39343	+	0.101986i
$816$	3.15774	+	10.4959i	0.00386978	+	0.0128626i
$817$	−38.9288	+	174.757i	−0.0476485	+	0.213901i
$818$	197.891	−	422.140i	0.241921	−	0.516063i
$819$	−186.465	−	143.984i	−0.227674	−	0.175805i
$820$	−1068.35	−	157.229i	−1.30287	−	0.191742i
$821$	−228.258	−	77.8710i	−0.278025	−	0.0948489i	0.180366	−	0.983600i	$-0.442272\pi$
$821$	−228.258	−	77.8710i	−0.278025	−	0.0948489i	−0.458391	+	0.888751i	$0.651574\pi$
$822$	95.2277	−	316.523i	0.115849	−	0.385065i
$823$	891.585	−	589.867i	1.08334	−	0.716728i	0.122117	−	0.992516i	$-0.461032\pi$
$823$	891.585	−	589.867i	1.08334	−	0.716728i	0.961218	+	0.275788i	$0.0889388\pi$
$824$	1525.67	+	55.7578i	1.85154	+	0.0676672i
$825$	313.853	−	1200.50i	0.380428	−	1.45516i
$826$	−417.226	+	465.652i	−0.505116	+	0.563743i
$827$	1213.37	+	270.290i	1.46720	+	0.326832i	0.877024	−	0.480446i	$-0.159525\pi$
$827$	1213.37	+	270.290i	1.46720	+	0.326832i	0.590172	+	0.807278i	$0.299060\pi$
$828$	−15.6396	−	427.938i	−0.0188884	−	0.516833i
$829$	−1175.78	+	841.200i	−1.41831	+	1.01472i	−0.424293	+	0.905525i	$0.639477\pi$
$829$	−1175.78	+	841.200i	−1.41831	+	1.01472i	−0.994021	+	0.109191i	$0.965174\pi$
$830$	−392.897	+	378.801i	−0.473370	+	0.456386i
$831$	−501.671	+	191.873i	−0.603696	+	0.230894i
$832$	254.185	−	245.065i	0.305511	−	0.294550i
$833$	−22.1811	−	15.8692i	−0.0266280	−	0.0190507i
$834$	258.382	+	231.512i	0.309811	+	0.277592i
$835$	174.101	−	59.3949i	0.208504	−	0.0711316i
$836$	173.467			0.207497
$837$	−601.066	+	500.211i	−0.718119	+	0.597623i
$838$	−539.930	+	141.156i	−0.644307	+	0.168444i
$839$	−408.971	+	394.298i	−0.487451	+	0.469962i	−0.896813	−	0.442411i	$-0.854123\pi$
$839$	−408.971	+	394.298i	−0.487451	+	0.469962i	0.409362	+	0.912372i	$0.365751\pi$
$840$	731.060	−	26.7176i	0.870310	−	0.0318067i
$841$	191.299	+	560.743i	0.227466	+	0.666758i
$842$	−607.910	+	112.287i	−0.721983	+	0.133357i
$843$	37.0656	+	79.0681i	0.0439687	+	0.0937938i
$844$	83.7825	+	21.9036i	0.0992684	+	0.0259522i
$845$	−923.767	+	518.443i	−1.09322	+	0.613542i
$846$	−401.663	−	137.028i	−0.474778	−	0.161972i
$847$	−632.170	−	215.667i	−0.746364	−	0.254624i
$848$	46.8527	−	179.214i	0.0552508	−	0.211337i
$849$	319.462	+	621.358i	0.376281	+	0.731871i
$850$	84.3904	+	94.1853i	0.0992828	+	0.110806i
$851$	−812.860	−	1448.36i	−0.955183	−	1.70195i
$852$	2.82558	+	3.65925i	0.00331641	+	0.00429489i
$853$	210.795	+	946.289i	0.247122	+	1.10937i	0.926712	+	0.375774i	$0.122623\pi$
$853$	210.795	+	946.289i	0.247122	+	1.10937i	−0.679590	+	0.733592i	$0.737842\pi$
$854$	7.56976	+	51.4357i	0.00886389	+	0.0602291i
$855$	268.695	−	59.8544i	0.314263	−	0.0700051i
$856$	−318.622	+	833.070i	−0.372222	+	0.973213i
$857$	−278.961	+	595.078i	−0.325509	+	0.694373i	−0.998995	−	0.0448270i	$-0.985726\pi$
$857$	−278.961	+	595.078i	−0.325509	+	0.694373i	0.673486	+	0.739200i	$0.264796\pi$
$858$	197.333	−	141.179i	0.229991	−	0.164545i
$859$	3.82391	−	0.420750i	0.00445159	−	0.000489814i	−0.107145	−	0.994243i	$-0.534171\pi$
$859$	3.82391	−	0.420750i	0.00445159	−	0.000489814i	0.111597	+	0.993754i	$0.464404\pi$
$860$	−521.968	−	268.362i	−0.606940	−	0.312049i
$861$		−	624.074i		−	0.724825i
$862$	−590.186	+	74.8776i	−0.684670	+	0.0868649i
$863$	787.220			0.912190			0.456095	−	0.889931i	$-0.349248\pi$
$863$	787.220			0.912190			0.456095	+	0.889931i	$0.349248\pi$
$864$	−346.828	+	674.585i	−0.401421	+	0.780770i
$865$	−8.71050	−	79.1639i	−0.0100699	−	0.0915189i
$866$	−72.2785	−	101.027i	−0.0834625	−	0.116659i
$867$	−447.430	−	209.747i	−0.516067	−	0.241922i
$868$	−348.585	−	133.322i	−0.401595	−	0.153597i
$869$	253.339	+	1137.28i	0.291529	+	1.30872i
$870$	−316.170	+	46.5305i	−0.363413	+	0.0534834i
$871$	110.170	−	24.5414i	0.126487	−	0.0281761i
$872$	736.131	−	568.422i	0.844186	−	0.651860i
$873$	−110.651	+	62.1004i	−0.126748	+	0.0711345i
$874$	189.779	−	170.043i	0.217139	−	0.194557i
$875$	974.329	−	500.937i	1.11352	−	0.572500i
$876$	−189.099	−	49.4369i	−0.215866	−	0.0564348i
$877$	−351.819	+	1031.27i	−0.401162	+	1.17590i	0.541081	+	0.840971i	$0.318015\pi$
$877$	−351.819	+	1031.27i	−0.401162	+	1.17590i	−0.942243	+	0.334931i	$0.891287\pi$
$878$	197.590	−	579.184i	0.225046	−	0.659663i
$879$	120.035	+	213.880i	0.136559	+	0.243322i
$880$	105.981	−	405.385i	0.120433	−	0.460664i
$881$	−431.718	+	202.381i	−0.490032	+	0.229717i	−0.653637	−	0.756809i	$-0.726758\pi$
$881$	−431.718	+	202.381i	−0.490032	+	0.229717i	0.163605	+	0.986526i	$0.447688\pi$
$882$	20.9621	+	113.487i	0.0237666	+	0.128670i
$883$	238.293	−	81.2943i	0.269868	−	0.0920660i	−0.184648	−	0.982805i	$-0.559115\pi$
$883$	238.293	−	81.2943i	0.269868	−	0.0920660i	0.454516	+	0.890739i	$0.349812\pi$
$884$	−0.992927	−	27.1689i	−0.00112322	−	0.0307341i
$885$	779.786	+	808.805i	0.881114	+	0.913904i
$886$	148.699	+	568.782i	0.167832	+	0.641966i
$887$	753.856	+	905.853i	0.849894	+	1.02125i	0.999472	+	0.0325043i	$0.0103483\pi$
$887$	753.856	+	905.853i	0.849894	+	1.02125i	−0.149577	+	0.988750i	$0.547791\pi$
$888$			710.292i			0.799879i
$889$	301.791	+	884.622i	0.339473	+	0.995076i
$890$	326.095	−	363.944i	0.366399	−	0.408926i
$891$	79.5759	−	111.227i	0.0893107	−	0.124834i
$892$	313.512	+	325.179i	0.351471	+	0.364550i
$893$	99.1838	+	259.326i	0.111068	+	0.290399i
$894$	51.3996	+	53.3124i	0.0574940	+	0.0596336i
$895$	335.771	+	469.321i	0.375163	+	0.524382i
$896$	−256.144	+	9.36115i	−0.285875	+	0.0104477i
$897$	−85.2021	+	382.485i	−0.0949856	+	0.426404i
$898$	−916.548	−	821.231i	−1.02065	−	0.914511i
$899$	458.939	+	119.982i	0.510499	+	0.133462i
$900$	−21.4870	+	587.939i	−0.0238745	+	0.653265i
$901$	−61.8433	−	93.4762i	−0.0686385	−	0.103747i
$902$	−1229.35	−	369.857i	−1.36292	−	0.410041i
$903$	109.518	−	321.024i	0.121283	−	0.355508i
$904$	58.8582	−	399.935i	0.0651086	−	0.442405i
$905$	1292.78	−	1674.20i	1.42848	−	1.84995i
$906$	−517.285	−	242.493i	−0.570955	−	0.267653i
$907$	73.5035	+	16.3736i	0.0810403	+	0.0180525i	0.257763	−	0.966208i	$-0.417015\pi$
$907$	73.5035	+	16.3736i	0.0810403	+	0.0180525i	−0.176723	+	0.984261i	$0.556550\pi$
$908$	−109.958	+	33.0813i	−0.121099	+	0.0364332i
$909$	−38.9094	+	531.618i	−0.0428046	+	0.584838i
$910$	448.550	+	99.9187i	0.492912	+	0.109801i
$911$	1498.76	−	702.588i	1.64518	−	0.771227i	0.645202	−	0.764012i	$-0.276773\pi$
$911$	1498.76	−	702.588i	1.64518	−	0.771227i	0.999974	−	0.00721463i	$-0.00229651\pi$
$912$	−29.6165	+	6.59736i	−0.0324743	+	0.00723395i
$913$	580.155	−	415.066i	0.635439	−	0.454617i
$914$	449.237	+	230.969i	0.491507	+	0.252701i
$915$	93.1728	−	6.81937i	0.101828	−	0.00745286i
$916$	105.221	+	15.4853i	0.114870	+	0.0169053i
$917$	616.970	−	45.1563i	0.672813	−	0.0492436i
$918$	−25.0692	−	65.5458i	−0.0273085	−	0.0714007i
$919$	−356.406	−	583.994i	−0.387820	−	0.635467i	0.598344	−	0.801239i	$-0.295826\pi$
$919$	−356.406	−	583.994i	−0.387820	−	0.635467i	−0.986164	+	0.165772i	$0.946988\pi$
$920$	1111.28	+	2161.45i	1.20791	+	2.34940i
$921$	148.820	−	289.457i	0.161585	−	0.314285i
$922$	838.221	−	252.183i	0.909134	−	0.273518i
$923$	3.30481	+	7.77687i	0.00358051	+	0.00842564i
$924$	−326.661	−	35.9429i	−0.353529	−	0.0388992i
$925$	968.547	+	2066.10i	1.04708	+	2.23362i
$926$	561.809	−	169.023i	0.606706	−	0.182531i
$927$	−1087.64	+	39.7494i	−1.17329	+	0.0428796i
$928$	455.230	−	66.9960i	0.490550	−	0.0721940i
$929$	1547.21	+	404.494i	1.66546	+	0.435408i	0.961494	−	0.274828i	$-0.0886208\pi$
$929$	1547.21	+	404.494i	1.66546	+	0.435408i	0.703964	+	0.710235i	$0.251411\pi$
$930$	258.911	−	552.307i	0.278399	−	0.593878i
$931$	48.2962	−	58.0339i	0.0518756	−	0.0623350i
$932$	−266.211	−	221.543i	−0.285635	−	0.237707i
$933$	26.8862	−	367.345i	0.0288169	−	0.393724i
$934$	−710.296	+	271.665i	−0.760488	+	0.290862i
$935$	−139.890	−	211.444i	−0.149615	−	0.226144i
$936$	−223.365	+	249.291i	−0.238638	+	0.266336i
$937$	−671.126	+	696.101i	−0.716250	+	0.742904i	−0.974797	−	0.223094i	$-0.928384\pi$
$937$	−671.126	+	696.101i	−0.716250	+	0.742904i	0.258547	+	0.965999i	$0.416756\pi$
$938$	121.257	+	68.0529i	0.129272	+	0.0725511i
$939$	490.840	+	547.810i	0.522726	+	0.583397i
$940$	−904.695	+	99.5447i	−0.962441	+	0.105899i
$941$	−10.4021	+	34.5751i	−0.0110543	+	0.0367429i	−0.962952	−	0.269675i	$-0.913084\pi$
$941$	−10.4021	+	34.5751i	−0.0110543	+	0.0367429i	0.951897	+	0.306418i	$0.0991304\pi$
$942$	126.536	−	131.245i	0.134327	−	0.139326i
$943$	1877.29	−	880.039i	1.99077	−	0.933234i
$944$	171.673	+	178.062i	0.181857	+	0.188624i
$945$	−1296.32	+	142.635i	−1.37176	+	0.150937i
$946$	−567.473	−	405.992i	−0.599866	−	0.429167i
$947$	29.2362	+	399.453i	0.0308724	+	0.421808i	0.990214	+	0.139560i	$0.0445687\pi$
$947$	29.2362	+	399.453i	0.0308724	+	0.421808i	−0.959341	+	0.282249i	$0.908920\pi$
$948$	117.399	+	250.436i	0.123839	+	0.264173i
$949$	−311.528	−	174.838i	−0.328270	−	0.184234i
$950$	−277.093	+	213.964i	−0.291677	+	0.225225i
$951$	383.383	−	70.8144i	0.403137	−	0.0744631i
$952$	62.3354	−	74.9038i	0.0654784	−	0.0786805i
$953$	399.384	+	479.910i	0.419081	+	0.503578i	0.935778	−	0.352590i	$-0.114699\pi$
$953$	399.384	+	479.910i	0.419081	+	0.503578i	−0.516697	+	0.856168i	$0.672839\pi$
$954$	−86.1456	+	466.384i	−0.0902993	+	0.488873i
$955$	−689.389	+	354.439i	−0.721873	+	0.371141i
$956$	400.866	+	244.645i	0.419315	+	0.255905i
$957$	417.703			0.436471
$958$	−5.72887	+	6.88395i	−0.00598003	+	0.00718576i
$959$	−783.562	+	235.739i	−0.817061	+	0.245817i
$960$	28.5463	−	781.098i	0.0297358	−	0.813644i
$961$	41.3871	−	37.0830i	0.0430667	−	0.0385879i
$962$	−112.857	+	431.682i	−0.117315	+	0.448734i
$963$	183.187	−	608.887i	0.190225	−	0.632282i
$964$	−42.2450	−	287.050i	−0.0438226	−	0.297770i
$965$	−1925.32	−	355.625i	−1.99515	−	0.368523i
$966$	−392.611	+	280.889i	−0.406430	+	0.290776i
$967$	318.468	+	35.0414i	0.329336	+	0.0362372i	0.272528	−	0.962148i	$-0.412140\pi$
$967$	318.468	+	35.0414i	0.329336	+	0.0362372i	0.0568079	+	0.998385i	$0.481908\pi$
$968$	−371.165	+	873.425i	−0.383435	+	0.902299i
$969$	−8.98542	+	16.0103i	−0.00927288	+	0.0165225i
$970$	144.016	−	201.297i	0.148470	−	0.207523i
$971$	−1282.79	+	719.936i	−1.32110	+	0.741437i	−0.980077	−	0.198617i	$-0.936355\pi$
$971$	−1282.79	+	719.936i	−1.32110	+	0.741437i	−0.341023	+	0.940055i	$0.610773\pi$
$972$	204.312	−	480.787i	0.210198	−	0.494637i
$973$	125.047	−	849.677i	0.128516	−	0.873255i
$974$	1123.26	+	123.594i	1.15325	+	0.126893i
$975$	155.104	−	515.544i	0.159081	−	0.528763i
$976$	20.5123	−	1.50131i	0.0210167	−	0.00153823i
$977$	−330.890	−	969.918i	−0.338680	−	0.992752i	−0.975168	−	0.221465i	$-0.928916\pi$
$977$	−330.890	−	969.918i	−0.338680	−	0.992752i	0.636488	−	0.771286i	$-0.280386\pi$
$978$	321.349			0.328578
$979$	−490.945	+	408.567i	−0.501476	+	0.417331i
$980$	144.011	+	201.291i	0.146950	+	0.205399i
$981$	−493.804	+	442.450i	−0.503368	+	0.451020i
$982$	195.898	−	1060.58i	0.199489	−	1.08002i
$983$	−512.952	+	840.503i	−0.521823	+	0.855039i	−0.999727	−	0.0233731i	$-0.992559\pi$
$983$	−512.952	+	840.503i	−0.521823	+	0.855039i	0.477904	+	0.878412i	$0.341397\pi$
$984$	−884.320	−	64.7239i	−0.898699	−	0.0657763i
$985$	−1680.76	−	374.404i	−1.70635	−	0.380106i
$986$	−23.4889	+	35.5036i	−0.0238225	+	0.0360077i
$987$	−133.043	−	508.895i	−0.134795	−	0.515598i
$988$	75.2123	+	2.74874i	0.0761258	+	0.00278213i
$989$	1120.12	−	123.248i	1.13258	−	0.124619i
$990$	−194.862	+	1054.97i	−0.196831	+	1.06562i
$991$	722.207	+	440.757i	0.728766	+	0.444760i	0.835473	−	0.549531i	$-0.185194\pi$
$991$	722.207	+	440.757i	0.728766	+	0.444760i	−0.106707	+	0.994290i	$0.534031\pi$
$992$	−372.787	+	795.227i	−0.375794	+	0.801641i
$993$	−48.0313	+	326.367i	−0.0483699	+	0.328668i
$994$	−3.36111	+	9.85221i	−0.00338140	+	0.00991168i
$995$	−1419.07	−	1837.76i	−1.42620	−	1.84699i
$996$	113.001	−	126.117i	0.113455	−	0.126623i
$997$	98.8507	−	898.387i	0.0991481	−	0.901090i	−0.836455	−	0.548036i	$-0.815376\pi$
$997$	98.8507	−	898.387i	0.0991481	−	0.901090i	0.935603	−	0.353054i	$-0.114857\pi$
$998$	672.535	+	870.962i	0.673883	+	0.872707i
$999$	−92.4300	−	1262.87i	−0.0925226	−	1.26413i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	431.3.f.a.101.25	✓	2982
431.367	odd	86	inner	431.3.f.a.367.25	yes	2982

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
431.3.f.a.101.25	✓	2982	1.1	even	1	trivial
431.3.f.a.367.25	yes	2982	431.367	odd	86	inner

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:	\( N \)	\(=\)	\( 431 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	431.f (of order \(86\), degree \(42\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.631139 + 1.22757i) q^{2} +(-0.189521 - 1.72242i) q^{3} +(1.21883 + 1.70362i) q^{4} +(7.67398 + 3.59741i) q^{5} +(2.23402 + 0.854440i) q^{6} +(-1.28742 - 5.77941i) q^{7} +(-8.32300 + 1.22489i) q^{8} +(5.85385 - 1.30400i) q^{9} +(-9.25944 + 7.14991i) q^{10} +(13.3343 - 7.48359i) q^{11} +(2.70336 - 2.42222i) q^{12} +(5.90011 - 3.03346i) q^{13} +(7.90719 + 2.06721i) q^{14} +(4.74190 - 13.8996i) q^{15} +(1.04395 - 3.06006i) q^{16} +(-0.957468 - 1.70603i) q^{17} +(-2.09384 + 8.00905i) q^{18} +(4.90370 - 2.29876i) q^{19} +(3.22469 + 17.4582i) q^{20} +(-9.71060 + 3.31280i) q^{21} +(0.770839 + 21.0921i) q^{22} +(-23.6587 - 24.5392i) q^{23} +(3.68717 + 14.1036i) q^{24} +(29.9567 + 35.9968i) q^{25} +9.15736i q^{26} +(-8.39091 - 24.5958i) q^{27} +(8.27675 - 9.23741i) q^{28} +(-9.17279 + 12.8212i) q^{29} +(14.0700 + 14.5936i) q^{30} +(-10.7492 - 28.1049i) q^{31} +(-20.2584 - 21.0123i) q^{32} +(-15.4170 - 21.5491i) q^{33} +(2.69857 - 0.0986230i) q^{34} +(10.9113 - 48.9824i) q^{35} +(9.35640 + 8.38337i) q^{36} +(47.1405 + 12.3241i) q^{37} +(-0.273020 + 7.47050i) q^{38} +(-6.34309 - 9.58759i) q^{39} +(-68.2770 - 20.5415i) q^{40} +(-19.6392 + 57.5673i) q^{41} +(2.06204 - 14.0113i) q^{42} +(-20.2049 + 26.1662i) q^{43} +(29.0015 + 13.5954i) q^{44} +(49.6134 + 11.0519i) q^{45} +(45.0556 - 13.5552i) q^{46} +(-3.74219 + 51.1295i) q^{47} +(-5.46857 - 1.21818i) q^{48} +(12.6229 - 5.91735i) q^{49} +(-63.0956 + 14.0551i) q^{50} +(-2.75704 + 1.97249i) q^{51} +(12.3591 + 6.35426i) q^{52} +(57.1389 - 4.18203i) q^{53} +(35.4890 + 5.22289i) q^{54} +(129.249 - 9.45980i) q^{55} +(17.7943 + 46.5251i) q^{56} +(-4.88880 - 8.01060i) q^{57} +(-9.94968 - 19.3523i) q^{58} +(-34.9789 + 68.0343i) q^{59} +(29.4593 - 8.86297i) q^{60} +(2.48789 + 5.85450i) q^{61} +(41.2851 + 4.54265i) q^{62} +(-15.0727 - 32.1530i) q^{63} +(50.9647 - 15.3330i) q^{64} +(56.1899 - 2.05354i) q^{65} +(36.1834 - 5.32509i) q^{66} +(16.4601 + 4.30323i) q^{67} +(1.73942 - 3.71052i) q^{68} +(-37.7831 + 45.4011i) q^{69} +(53.2430 + 44.3092i) q^{70} +(-0.0929731 + 1.27029i) q^{71} +(-47.1244 + 18.0235i) q^{72} +(-29.7112 - 44.9086i) q^{73} +(-44.8810 + 50.0902i) q^{74} +(56.3243 - 58.4204i) q^{75} +(9.89302 + 5.55223i) q^{76} +(-60.4176 - 67.4300i) q^{77} +(15.7729 - 1.73551i) q^{78} +(-21.9530 + 72.9687i) q^{79} +(19.0195 - 19.7273i) q^{80} +(8.09836 - 3.79636i) q^{81} +(-58.2731 - 60.4416i) q^{82} +(46.3720 - 5.10237i) q^{83} +(-17.4794 - 12.5054i) q^{84} +(-1.21031 - 16.5364i) q^{85} +(-19.3688 - 41.3175i) q^{86} +(23.8220 + 13.3696i) q^{87} +(-101.815 + 78.6190i) q^{88} +(-41.0762 + 7.58717i) q^{89} +(-44.8799 + 53.9288i) q^{90} +(-25.1275 - 30.1938i) q^{91} +(12.9693 - 70.2146i) q^{92} +(-46.3714 + 23.8412i) q^{93} +(-60.4033 - 36.8636i) q^{94} +45.9005 q^{95} +(-32.3528 + 38.8759i) q^{96} +(-20.2601 + 6.09534i) q^{97} +(-0.702794 + 19.2302i) q^{98} +(68.2986 - 61.1958i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2982 q - 43 q^{2} - 41 q^{3} - 187 q^{4} - 41 q^{5} - 33 q^{6} - 43 q^{7} - 37 q^{8} - 252 q^{9} - 23 q^{10} + 187 q^{11} + 19 q^{12} - 43 q^{13} - 43 q^{14} - 71 q^{15} - 359 q^{16} - 43 q^{17} - 93 q^{18}+ \cdots - 609 q^{99}+O(q^{100}) \) 2982 * q - 43 * q^2 - 41 * q^3 - 187 * q^4 - 41 * q^5 - 33 * q^6 - 43 * q^7 - 37 * q^8 - 252 * q^9 - 23 * q^10 + 187 * q^11 + 19 * q^12 - 43 * q^13 - 43 * q^14 - 71 * q^15 - 359 * q^16 - 43 * q^17 - 93 * q^18 - 55 * q^19 + 9 * q^20 - 172 * q^21 - 47 * q^22 + 45 * q^23 + 17 * q^24 - 436 * q^25 + 37 * q^27 - 43 * q^28 - 93 * q^29 - 911 * q^30 - 43 * q^31 + 181 * q^32 + 733 * q^33 - 43 * q^34 - 43 * q^35 - 521 * q^36 - 43 * q^37 + 691 * q^38 - 43 * q^39 + 199 * q^40 + 456 * q^41 - 43 * q^42 - 43 * q^43 - 161 * q^44 - 3 * q^45 - 279 * q^46 - 43 * q^47 + 271 * q^48 + 362 * q^49 - 21 * q^50 - 43 * q^51 - 2107 * q^52 + 53 * q^53 - 2864 * q^54 + 111 * q^55 - 1978 * q^56 + 11 * q^57 - 349 * q^58 + 59 * q^59 + 29 * q^60 - 1433 * q^61 - 43 * q^62 - 2451 * q^63 - 801 * q^64 - 43 * q^65 - 253 * q^66 + 3053 * q^67 - 43 * q^68 + 25 * q^69 - 1978 * q^70 + 2021 * q^71 - 63 * q^72 - 43 * q^73 - 43 * q^74 - 401 * q^75 - 225 * q^76 + 645 * q^77 + 344 * q^78 + 3397 * q^79 + 227 * q^80 - 1054 * q^81 - 845 * q^82 - 43 * q^83 + 6106 * q^84 - 43 * q^85 - 43 * q^86 - 1021 * q^87 + 6277 * q^88 - 43 * q^89 - 815 * q^90 - 147 * q^91 - 239 * q^92 + 2193 * q^93 - 43 * q^94 - 70 * q^95 + 129 * q^96 + 125 * q^97 + 643 * q^98 - 609 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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