LMFDB - Embedded newform 429.2.bd.a.175.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(76,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 7]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("429.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bd (of order $12$, degree $4$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			175.5
Character	$\chi$	$=$	429.175
Dual form			429.2.bd.a.76.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.42470 + 0.381747i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.151984 - 0.0877479i) q^{4} +(-0.971227 + 0.971227i) q^{5} +(0.381747 - 1.42470i) q^{6} +(4.17142 + 1.11773i) q^{7} +(1.90287 - 1.90287i) q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.42470 + 0.381747i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.151984 - 0.0877479i) q^{4} +(-0.971227 + 0.971227i) q^{5} +(0.381747 - 1.42470i) q^{6} +(4.17142 + 1.11773i) q^{7} +(1.90287 - 1.90287i) q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.01294 - 1.75447i) q^{10} +(1.01743 - 3.15671i) q^{11} +0.175496i q^{12} +(3.58322 - 0.400646i) q^{13} -6.36970 q^{14} +(-0.355494 - 1.32672i) q^{15} +(-2.16010 + 3.74140i) q^{16} +(-0.301427 - 0.522088i) q^{17} +(1.04295 + 1.04295i) q^{18} +(-0.159121 + 0.593849i) q^{19} +(-0.0623876 + 0.232834i) q^{20} +(-3.05369 + 3.05369i) q^{21} +(-0.244469 + 4.88576i) q^{22} +(1.91532 + 1.10581i) q^{23} +(0.696499 + 2.59937i) q^{24} +3.11344i q^{25} +(-4.95207 + 1.93868i) q^{26} +1.00000 q^{27} +(0.732066 - 0.196156i) q^{28} +(4.74047 + 2.73691i) q^{29} +(1.01294 + 1.75447i) q^{30} +(-3.56405 + 3.56405i) q^{31} +(0.256222 - 0.956235i) q^{32} +(2.22508 + 2.45948i) q^{33} +(0.628748 + 0.628748i) q^{34} +(-5.13696 + 2.96583i) q^{35} +(-0.151984 - 0.0877479i) q^{36} +(10.4857 - 2.80963i) q^{37} -0.906800i q^{38} +(-1.44464 + 3.30348i) q^{39} +3.69624i q^{40} +(-4.48549 + 1.20188i) q^{41} +(3.18485 - 5.51632i) q^{42} +(-2.00257 - 3.46855i) q^{43} +(-0.122362 - 0.569046i) q^{44} +(1.32672 + 0.355494i) q^{45} +(-3.15090 - 0.844280i) q^{46} +(-1.15089 - 1.15089i) q^{47} +(-2.16010 - 3.74140i) q^{48} +(10.0892 + 5.82501i) q^{49} +(-1.18854 - 4.43571i) q^{50} +0.602855 q^{51} +(0.509436 - 0.375312i) q^{52} -12.3364 q^{53} +(-1.42470 + 0.381747i) q^{54} +(2.07773 + 4.05404i) q^{55} +(10.0646 - 5.81077i) q^{56} +(-0.434728 - 0.434728i) q^{57} +(-7.79855 - 2.08962i) q^{58} +(-2.37217 + 8.85304i) q^{59} +(-0.170446 - 0.170446i) q^{60} +(5.89575 - 3.40391i) q^{61} +(3.71713 - 6.43826i) q^{62} +(-1.11773 - 4.17142i) q^{63} -7.18023i q^{64} +(-3.09101 + 3.86924i) q^{65} +(-4.10896 - 2.65460i) q^{66} +(2.37464 + 8.86227i) q^{67} +(-0.0916241 - 0.0528992i) q^{68} +(-1.91532 + 1.10581i) q^{69} +(6.18642 - 6.18642i) q^{70} +(7.44392 + 1.99459i) q^{71} +(-2.59937 - 0.696499i) q^{72} +(-8.48375 + 8.48375i) q^{73} +(-13.8663 + 8.00574i) q^{74} +(-2.69631 - 1.55672i) q^{75} +(0.0279251 + 0.104218i) q^{76} +(7.77248 - 12.0307i) q^{77} +(0.797085 - 5.25796i) q^{78} -13.7568i q^{79} +(-1.53580 - 5.73169i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(5.93165 - 3.42464i) q^{82} +(5.50139 + 5.50139i) q^{83} +(-0.196156 + 0.732066i) q^{84} +(0.799820 + 0.214311i) q^{85} +(4.17717 + 4.17717i) q^{86} +(-4.74047 + 2.73691i) q^{87} +(-4.07077 - 7.94285i) q^{88} +(7.03147 - 1.88408i) q^{89} -2.02589 q^{90} +(15.3949 + 2.33381i) q^{91} +0.388131 q^{92} +(-1.30453 - 4.86858i) q^{93} +(2.07902 + 1.20032i) q^{94} +(-0.422219 - 0.731306i) q^{95} +(0.700012 + 0.700012i) q^{96} +(-12.9643 - 3.47376i) q^{97} +(-16.5978 - 4.44736i) q^{98} +(-3.24251 + 0.697234i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 28 q^{3} + 4 q^{5} - 28 q^{9}+O(q^{10}) $ 56 * q - 28 * q^3 + 4 * q^5 - 28 * q^9	$ 56 q - 28 q^{3} + 4 q^{5} - 28 q^{9} - 12 q^{11} + 24 q^{14} - 8 q^{15} + 68 q^{16} - 8 q^{20} - 10 q^{22} - 12 q^{23} - 48 q^{26} + 56 q^{27} + 4 q^{31} + 12 q^{33} + 32 q^{34} + 36 q^{37} - 12 q^{42} + 24 q^{44} + 4 q^{45} - 8 q^{47} + 68 q^{48} - 24 q^{49} - 56 q^{53} - 2 q^{55} + 72 q^{56} - 88 q^{58} + 56 q^{59} - 44 q^{60} + 20 q^{66} + 92 q^{67} + 12 q^{69} - 216 q^{70} + 72 q^{71} - 12 q^{75} - 12 q^{78} + 44 q^{80} - 28 q^{81} - 156 q^{82} - 120 q^{86} - 6 q^{88} - 56 q^{89} + 92 q^{91} + 32 q^{92} - 20 q^{93} - 44 q^{97}+O(q^{100}) $ 56 * q - 28 * q^3 + 4 * q^5 - 28 * q^9 - 12 * q^11 + 24 * q^14 - 8 * q^15 + 68 * q^16 - 8 * q^20 - 10 * q^22 - 12 * q^23 - 48 * q^26 + 56 * q^27 + 4 * q^31 + 12 * q^33 + 32 * q^34 + 36 * q^37 - 12 * q^42 + 24 * q^44 + 4 * q^45 - 8 * q^47 + 68 * q^48 - 24 * q^49 - 56 * q^53 - 2 * q^55 + 72 * q^56 - 88 * q^58 + 56 * q^59 - 44 * q^60 + 20 * q^66 + 92 * q^67 + 12 * q^69 - 216 * q^70 + 72 * q^71 - 12 * q^75 - 12 * q^78 + 44 * q^80 - 28 * q^81 - 156 * q^82 - 120 * q^86 - 6 * q^88 - 56 * q^89 + 92 * q^91 + 32 * q^92 - 20 * q^93 - 44 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.42470	+	0.381747i	−1.00741	+	0.269936i	−0.724548	−	0.689224i	$-0.757952\pi$
$2$	−1.42470	+	0.381747i	−1.00741	+	0.269936i	−0.282865	+	0.959160i	$0.591285\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.151984	−	0.0877479i	0.0759919	−	0.0438739i
$5$	−0.971227	+	0.971227i	−0.434346	+	0.434346i	−0.890104	−	0.455758i	$-0.849368\pi$
$5$	−0.971227	+	0.971227i	−0.434346	+	0.434346i	0.455758	+	0.890104i	$0.349368\pi$
$6$	0.381747	−	1.42470i	0.155847	−	0.581631i
$7$	4.17142	+	1.11773i	1.57665	+	0.422461i	0.937886	−	0.346944i	$-0.112781\pi$
$7$	4.17142	+	1.11773i	1.57665	+	0.422461i	0.638761	+	0.769405i	$0.279447\pi$
$8$	1.90287	−	1.90287i	0.672766	−	0.672766i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.01294	−	1.75447i	0.320321	−	0.554812i
$11$	1.01743	−	3.15671i	0.306767	−	0.951785i
$11$	1.01743	−	3.15671i	0.306767	−	0.951785i
$12$			0.175496i			0.0506612i
$13$	3.58322	−	0.400646i	0.993807	−	0.111119i
$13$	3.58322	−	0.400646i	0.993807	−	0.111119i
$14$	−6.36970			−1.70237
$15$	−0.355494	−	1.32672i	−0.0917881	−	0.342558i
$16$	−2.16010	+	3.74140i	−0.540024	+	0.935349i
$17$	−0.301427	−	0.522088i	−0.0731069	−	0.126625i	0.827155	−	0.561974i	$-0.189958\pi$
$17$	−0.301427	−	0.522088i	−0.0731069	−	0.126625i	−0.900261	+	0.435350i	$0.856625\pi$
$18$	1.04295	+	1.04295i	0.245826	+	0.245826i
$19$	−0.159121	+	0.593849i	−0.0365050	+	0.136238i	−0.981773	−	0.190055i	$-0.939133\pi$
$19$	−0.159121	+	0.593849i	−0.0365050	+	0.136238i	0.945268	+	0.326294i	$0.105800\pi$
$20$	−0.0623876	+	0.232834i	−0.0139503	+	0.0520632i
$21$	−3.05369	+	3.05369i	−0.666369	+	0.666369i
$22$	−0.244469	+	4.88576i	−0.0521210	+	1.04165i
$23$	1.91532	+	1.10581i	0.399372	+	0.230578i	0.686213	−	0.727401i	$-0.259272\pi$
$23$	1.91532	+	1.10581i	0.399372	+	0.230578i	−0.286841	+	0.957978i	$0.592605\pi$
$24$	0.696499	+	2.59937i	0.142172	+	0.530594i
$25$			3.11344i			0.622687i
$26$	−4.95207	+	1.93868i	−0.971180	+	0.380207i
$27$	1.00000			0.192450
$28$	0.732066	−	0.196156i	0.138347	−	0.0370701i
$29$	4.74047	+	2.73691i	0.880284	+	0.508232i	0.870752	−	0.491722i	$-0.163633\pi$
$29$	4.74047	+	2.73691i	0.880284	+	0.508232i	0.00953186	+	0.999955i	$0.496966\pi$
$30$	1.01294	+	1.75447i	0.184937	+	0.320321i
$31$	−3.56405	+	3.56405i	−0.640122	+	0.640122i	−0.950585	−	0.310464i	$-0.899516\pi$
$31$	−3.56405	+	3.56405i	−0.640122	+	0.640122i	0.310464	+	0.950585i	$0.399516\pi$
$32$	0.256222	−	0.956235i	0.0452941	−	0.169040i
$33$	2.22508	+	2.45948i	0.387336	+	0.428140i
$34$	0.628748	+	0.628748i	0.107829	+	0.107829i
$35$	−5.13696	+	2.96583i	−0.868305	+	0.501316i
$36$	−0.151984	−	0.0877479i	−0.0253306	−	0.0146246i
$37$	10.4857	−	2.80963i	1.72383	−	0.461900i	0.745086	−	0.666969i	$-0.232408\pi$
$37$	10.4857	−	2.80963i	1.72383	−	0.461900i	0.978748	+	0.205069i	$0.0657418\pi$
$38$		−	0.906800i		−	0.147102i
$39$	−1.44464	+	3.30348i	−0.231328	+	0.528981i
$40$			3.69624i			0.584426i
$41$	−4.48549	+	1.20188i	−0.700516	+	0.187703i	−0.591462	−	0.806333i	$-0.701449\pi$
$41$	−4.48549	+	1.20188i	−0.700516	+	0.187703i	−0.109054	+	0.994036i	$0.534782\pi$
$42$	3.18485	−	5.51632i	0.491433	−	0.851187i
$43$	−2.00257	−	3.46855i	−0.305389	−	0.528949i	0.671959	−	0.740588i	$-0.265453\pi$
$43$	−2.00257	−	3.46855i	−0.305389	−	0.528949i	−0.977348	+	0.211639i	$0.932120\pi$
$44$	−0.122362	−	0.569046i	−0.0184467	−	0.0857870i
$45$	1.32672	+	0.355494i	0.197776	+	0.0529939i
$46$	−3.15090	−	0.844280i	−0.464574	−	0.124482i
$47$	−1.15089	−	1.15089i	−0.167875	−	0.167875i	0.618170	−	0.786045i	$-0.287874\pi$
$47$	−1.15089	−	1.15089i	−0.167875	−	0.167875i	−0.786045	+	0.618170i	$0.787874\pi$
$48$	−2.16010	−	3.74140i	−0.311783	−	0.540024i
$49$	10.0892	+	5.82501i	1.44132	+	0.832145i
$50$	−1.18854	−	4.43571i	−0.168085	−	0.627304i
$51$	0.602855			0.0844166
$52$	0.509436	−	0.375312i	0.0706460	−	0.0520464i
$53$	−12.3364			−1.69453			−0.847266	−	0.531169i	$-0.821753\pi$
$53$	−12.3364			−1.69453			−0.847266	+	0.531169i	$0.821753\pi$
$54$	−1.42470	+	0.381747i	−0.193877	+	0.0519492i
$55$	2.07773	+	4.05404i	0.280161	+	0.546647i
$56$	10.0646	−	5.81077i	1.34493	−	0.776497i
$57$	−0.434728	−	0.434728i	−0.0575811	−	0.0575811i
$58$	−7.79855	−	2.08962i	−1.02400	−	0.274380i
$59$	−2.37217	+	8.85304i	−0.308830	+	1.15257i	0.620769	+	0.783994i	$0.286821\pi$
$59$	−2.37217	+	8.85304i	−0.308830	+	1.15257i	−0.929598	+	0.368574i	$0.879846\pi$
$60$	−0.170446	−	0.170446i	−0.0220045	−	0.0220045i
$61$	5.89575	−	3.40391i	0.754873	−	0.435826i	−0.0725787	−	0.997363i	$-0.523123\pi$
$61$	5.89575	−	3.40391i	0.754873	−	0.435826i	0.827452	+	0.561536i	$0.189790\pi$
$62$	3.71713	−	6.43826i	0.472076	−	0.817659i
$63$	−1.11773	−	4.17142i	−0.140820	−	0.525549i
$64$		−	7.18023i		−	0.897528i
$65$	−3.09101	+	3.86924i	−0.383392	+	0.479920i
$66$	−4.10896	−	2.65460i	−0.505778	−	0.326758i
$67$	2.37464	+	8.86227i	0.290108	+	1.08270i	0.945025	+	0.326998i	$0.106037\pi$
$67$	2.37464	+	8.86227i	0.290108	+	1.08270i	−0.654917	+	0.755701i	$0.727296\pi$
$68$	−0.0916241	−	0.0528992i	−0.0111111	−	0.00641497i
$69$	−1.91532	+	1.10581i	−0.230578	+	0.133124i
$70$	6.18642	−	6.18642i	0.739419	−	0.739419i
$71$	7.44392	+	1.99459i	0.883431	+	0.236715i	0.671887	−	0.740654i	$-0.265484\pi$
$71$	7.44392	+	1.99459i	0.883431	+	0.236715i	0.211544	+	0.977368i	$0.432151\pi$
$72$	−2.59937	−	0.696499i	−0.306338	−	0.0820831i
$73$	−8.48375	+	8.48375i	−0.992947	+	0.992947i	−0.999975	−	0.00702788i	$-0.997763\pi$
$73$	−8.48375	+	8.48375i	−0.992947	+	0.992947i	0.00702788	+	0.999975i	$0.497763\pi$
$74$	−13.8663	+	8.00574i	−1.61193	+	0.930648i
$75$	−2.69631	−	1.55672i	−0.311344	−	0.179754i
$76$	0.0279251	+	0.104218i	0.00320323	+	0.0119546i
$77$	7.77248	−	12.0307i	0.885756	−	1.37103i
$78$	0.797085	−	5.25796i	0.0902521	−	0.595346i
$79$		−	13.7568i		−	1.54776i	−0.633335	−	0.773878i	$-0.718314\pi$
$79$		−	13.7568i		−	1.54776i	0.633335	−	0.773878i	$-0.281686\pi$
$80$	−1.53580	−	5.73169i	−0.171708	−	0.640822i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	5.93165	−	3.42464i	0.655042	−	0.378188i
$83$	5.50139	+	5.50139i	0.603855	+	0.603855i	0.941333	−	0.337478i	$-0.109574\pi$
$83$	5.50139	+	5.50139i	0.603855	+	0.603855i	−0.337478	+	0.941333i	$0.609574\pi$
$84$	−0.196156	+	0.732066i	−0.0214024	+	0.0798749i
$85$	0.799820	+	0.214311i	0.0867527	+	0.0232453i
$86$	4.17717	+	4.17717i	0.450435	+	0.450435i
$87$	−4.74047	+	2.73691i	−0.508232	+	0.293428i
$88$	−4.07077	−	7.94285i	−0.433946	−	0.846711i
$89$	7.03147	−	1.88408i	0.745334	−	0.199712i	0.133886	−	0.990997i	$-0.457254\pi$
$89$	7.03147	−	1.88408i	0.745334	−	0.199712i	0.611447	+	0.791285i	$0.290588\pi$
$90$	−2.02589			−0.213547
$91$	15.3949	+	2.33381i	1.61383	+	0.244649i
$92$	0.388131			0.0404654
$93$	−1.30453	−	4.86858i	−0.135274	−	0.504848i
$94$	2.07902	+	1.20032i	0.214435	+	0.123804i
$95$	−0.422219	−	0.731306i	−0.0433188	−	0.0750304i
$96$	0.700012	+	0.700012i	0.0714447	+	0.0714447i
$97$	−12.9643	−	3.47376i	−1.31632	−	0.352707i	−0.468722	−	0.883346i	$-0.655285\pi$
$97$	−12.9643	−	3.47376i	−1.31632	−	0.352707i	−0.847598	+	0.530639i	$0.821952\pi$
$98$	−16.5978	−	4.44736i	−1.67663	−	0.449251i
$99$	−3.24251	+	0.697234i	−0.325884	+	0.0700747i
$100$	0.273197	+	0.473192i	0.0273197	+	0.0473192i
$101$	1.88356	−	3.26242i	0.187421	−	0.324623i	−0.756969	−	0.653451i	$-0.773320\pi$
$101$	1.88356	−	3.26242i	0.187421	−	0.324623i	0.944390	+	0.328828i	$0.106654\pi$
$102$	−0.858886	+	0.230138i	−0.0850424	+	0.0227870i
$103$		−	3.80982i		−	0.375392i	−0.982227	−	0.187696i	$-0.939898\pi$
$103$		−	3.80982i		−	0.375392i	0.982227	−	0.187696i	$-0.0601020\pi$
$104$	6.05603	−	7.58078i	0.593842	−	0.743357i
$105$		−	5.93165i		−	0.578870i
$106$	17.5756	−	4.70937i	1.70709	−	0.457415i
$107$	11.2041	+	6.46866i	1.08314	+	0.625349i	0.931741	−	0.363124i	$-0.118290\pi$
$107$	11.2041	+	6.46866i	1.08314	+	0.625349i	0.151396	+	0.988473i	$0.451623\pi$
$108$	0.151984	−	0.0877479i	0.0146246	−	0.00844354i
$109$	−0.843461	−	0.843461i	−0.0807889	−	0.0807889i	0.665558	−	0.746346i	$-0.268194\pi$
$109$	−0.843461	−	0.843461i	−0.0807889	−	0.0807889i	−0.746346	+	0.665558i	$0.768194\pi$
$110$	−4.50775	−	4.98262i	−0.429797	−	0.475074i
$111$	−2.80963	+	10.4857i	−0.266678	+	0.995256i
$112$	−13.1925	+	13.1925i	−1.24658	+	1.24658i
$113$	−2.95576	−	5.11953i	−0.278055	−	0.481605i	0.692847	−	0.721085i	$-0.256356\pi$
$113$	−2.95576	−	5.11953i	−0.278055	−	0.481605i	−0.970901	+	0.239480i	$0.923023\pi$
$114$	0.785312	+	0.453400i	0.0735512	+	0.0424648i
$115$	−2.93421	+	0.786219i	−0.273616	+	0.0733153i
$116$	0.960633			0.0891926
$117$	−2.13858	−	2.90284i	−0.197712	−	0.268368i
$118$		−	13.5185i		−	1.24448i
$119$	−0.673828	−	2.51476i	−0.0617697	−	0.230528i
$120$	−3.20104	−	1.84812i	−0.292213	−	0.168709i
$121$	−8.92966	−	6.42348i	−0.811788	−	0.583953i
$122$	−7.10023	+	7.10023i	−0.642825	+	0.642825i
$123$	1.20188	−	4.48549i	0.108370	−	0.404443i
$124$	−0.228940	+	0.854415i	−0.0205594	+	0.0767287i
$125$	−7.87999	−	7.87999i	−0.704808	−	0.704808i
$126$	3.18485	+	5.51632i	0.283729	+	0.491433i
$127$	4.85479	−	8.40874i	0.430793	−	0.746155i	−0.566149	−	0.824303i	$-0.691567\pi$
$127$	4.85479	−	8.40874i	0.430793	−	0.746155i	0.996942	+	0.0781481i	$0.0249007\pi$
$128$	3.25347	+	12.1421i	0.287569	+	1.07322i
$129$	4.00514			0.352633
$130$	2.92668	−	6.69248i	0.256687	−	0.586970i
$131$		−	7.68938i		−	0.671824i	−0.941893	−	0.335912i	$-0.890956\pi$
$131$		−	7.68938i		−	0.671824i	0.941893	−	0.335912i	$-0.109044\pi$
$132$	0.553989	+	0.178555i	0.0482186	+	0.0155412i
$133$	−1.32752	+	2.29934i	−0.115111	+	0.199378i
$134$	−6.76629	−	11.7196i	−0.584518	−	1.01242i
$135$	−0.971227	+	0.971227i	−0.0835899	+	0.0835899i
$136$	−1.56704	−	0.419888i	−0.134373	−	0.0360051i
$137$	1.18418	−	4.41942i	0.101171	−	0.377576i	−0.896711	−	0.442616i	$-0.854051\pi$
$137$	1.18418	−	4.41942i	0.101171	−	0.377576i	0.997883	+	0.0650393i	$0.0207173\pi$
$138$	2.30662	−	2.30662i	0.196352	−	0.196352i
$139$	11.0038	−	6.35304i	0.933330	−	0.538858i	0.0454665	−	0.998966i	$-0.485523\pi$
$139$	11.0038	−	6.35304i	0.933330	−	0.538858i	0.887863	+	0.460108i	$0.152189\pi$
$140$	−0.520490	+	0.901514i	−0.0439894	+	0.0761919i
$141$	1.57215	−	0.421256i	0.132399	−	0.0354761i
$142$	−11.3668			−0.953878
$143$	2.38096	−	11.7188i	0.199106	−	0.979978i
$144$	4.32019			0.360016
$145$	−7.26224	+	1.94591i	−0.603096	+	0.161599i
$146$	8.84814	−	15.3254i	0.732277	−	1.26834i
$147$	−10.0892	+	5.82501i	−0.832145	+	0.480439i
$148$	1.34711	−	1.34711i	0.110732	−	0.110732i
$149$	−3.48349	+	13.0006i	−0.285379	+	1.06505i	0.663183	+	0.748457i	$0.269205\pi$
$149$	−3.48349	+	13.0006i	−0.285379	+	1.06505i	−0.948562	+	0.316591i	$0.897462\pi$
$150$	4.43571	+	1.18854i	0.362174	+	0.0970442i
$151$	−0.616275	+	0.616275i	−0.0501517	+	0.0501517i	−0.731738	−	0.681586i	$-0.761290\pi$
$151$	−0.616275	+	0.616275i	−0.0501517	+	0.0501517i	0.681586	+	0.731738i	$0.261290\pi$
$152$	0.827230	+	1.43280i	0.0670972	+	0.116216i
$153$	−0.301427	+	0.522088i	−0.0243690	+	0.0422083i
$154$	−6.48074	+	20.1073i	−0.522233	+	1.62029i
$155$		−	6.92300i		−	0.556069i
$156$	0.0703116	+	0.628840i	0.00562943	+	0.0503475i
$157$	4.87547			0.389105			0.194552	−	0.980892i	$-0.437675\pi$
$157$	4.87547			0.389105			0.194552	+	0.980892i	$0.437675\pi$
$158$	5.25160	+	19.5992i	0.417795	+	1.55923i
$159$	6.16819	−	10.6836i	0.489169	−	0.847266i
$160$	0.679871	+	1.17757i	0.0537485	+	0.0930952i
$161$	6.75361	+	6.75361i	0.532259	+	0.532259i
$162$	0.381747	−	1.42470i	0.0299929	−	0.111935i
$163$	−4.83304	+	18.0371i	−0.378553	+	1.41278i	0.469531	+	0.882916i	$0.344423\pi$
$163$	−4.83304	+	18.0371i	−0.378553	+	1.41278i	−0.848084	+	0.529862i	$0.822244\pi$
$164$	−0.576259	+	0.576259i	−0.0449982	+	0.0449982i
$165$	−4.54977	−	0.227657i	−0.354199	−	0.0177231i
$166$	−9.93795	−	5.73768i	−0.771334	−	0.445330i
$167$	2.91807	+	10.8904i	0.225807	+	0.842722i	0.982080	+	0.188466i	$0.0603515\pi$
$167$	2.91807	+	10.8904i	0.225807	+	0.842722i	−0.756273	+	0.654256i	$0.772982\pi$
$168$			11.6215i			0.896621i
$169$	12.6790	−	2.87120i	0.975305	−	0.220862i
$170$	−1.22132			−0.0936706
$171$	0.593849	−	0.159121i	0.0454128	−	0.0121683i
$172$	−0.608716	−	0.351442i	−0.0464142	−	0.0267972i
$173$	−0.996067	−	1.72524i	−0.0757296	−	0.131167i	0.825674	−	0.564148i	$-0.190795\pi$
$173$	−0.996067	−	1.72524i	−0.0757296	−	0.131167i	−0.901403	+	0.432980i	$0.857462\pi$
$174$	5.70894	−	5.70894i	0.432793	−	0.432793i
$175$	−3.47997	+	12.9874i	−0.263061	+	0.981758i
$176$	9.61276	+	10.6254i	0.724589	+	0.800921i
$177$	−6.48088	−	6.48088i	−0.487133	−	0.487133i
$178$	−9.29848	+	5.36848i	−0.696950	+	0.402384i
$179$	18.3369	+	10.5868i	1.37056	+	0.791296i	0.990999	−	0.133869i	$-0.0427401\pi$
$179$	18.3369	+	10.5868i	1.37056	+	0.791296i	0.379566	+	0.925165i	$0.376073\pi$
$180$	0.232834	−	0.0623876i	0.0173544	−	0.00465010i
$181$			15.3435i			1.14047i	0.821481	+	0.570237i	$0.193148\pi$
$181$			15.3435i			1.14047i	−0.821481	+	0.570237i	$0.806852\pi$
$182$	−22.8240	+	2.55199i	−1.69183	+	0.189166i
$183$			6.80782i			0.503249i
$184$	5.74883	−	1.54039i	0.423809	−	0.113559i
$185$	−7.45518	+	12.9128i	−0.548116	+	0.949364i
$186$	3.71713	+	6.43826i	0.272553	+	0.472076i
$187$	−1.95476	+	0.420331i	−0.142946	+	0.0307376i
$188$	−0.275905	−	0.0739286i	−0.0201225	−	0.00539180i
$189$	4.17142	+	1.11773i	0.303426	+	0.0813027i
$190$	0.880709	+	0.880709i	0.0638933	+	0.0638933i
$191$	7.36438	+	12.7555i	0.532868	+	0.922954i	0.999263	+	0.0383778i	$0.0122190\pi$
$191$	7.36438	+	12.7555i	0.532868	+	0.922954i	−0.466395	+	0.884576i	$0.654448\pi$
$192$	6.21826	+	3.59011i	0.448764	+	0.259094i
$193$	−2.91553	−	10.8809i	−0.209864	−	0.783225i	−0.987912	−	0.155019i	$-0.950456\pi$
$193$	−2.91553	−	10.8809i	−0.209864	−	0.783225i	0.778047	−	0.628206i	$-0.216210\pi$
$194$	19.7962			1.42129
$195$	−1.80536	−	4.61151i	−0.129284	−	0.330237i
$196$	2.04453			0.146038
$197$	9.41073	−	2.52160i	0.670487	−	0.179656i	0.0925127	−	0.995712i	$-0.470510\pi$
$197$	9.41073	−	2.52160i	0.670487	−	0.179656i	0.577974	+	0.816055i	$0.303843\pi$
$198$	4.35343	−	2.23117i	0.309385	−	0.158562i
$199$	−9.96615	+	5.75396i	−0.706481	+	0.407887i	−0.809757	−	0.586766i	$-0.800401\pi$
$199$	−9.96615	+	5.75396i	−0.706481	+	0.407887i	0.103275	+	0.994653i	$0.467068\pi$
$200$	5.92446	+	5.92446i	0.418923	+	0.418923i
$201$	−8.86227	−	2.37464i	−0.625096	−	0.167494i
$202$	−1.43808	+	5.36701i	−0.101183	+	0.377621i
$203$	16.7154	+	16.7154i	1.17319	+	1.17319i
$204$	0.0916241	−	0.0528992i	0.00641497	−	0.00370369i
$205$	3.18913	−	5.52373i	0.222738	−	0.385794i
$206$	1.45438	+	5.42784i	0.101332	+	0.378175i
$207$		−	2.21162i		−	0.153719i
$208$	−6.24113	+	14.2717i	−0.432745	+	0.989564i
$209$	1.71272	+	1.10650i	0.118471	+	0.0765383i
$210$	2.26439	+	8.45081i	0.156258	+	0.583161i
$211$	−11.5406	−	6.66295i	−0.794485	−	0.458696i	0.0470539	−	0.998892i	$-0.485017\pi$
$211$	−11.5406	−	6.66295i	−0.794485	−	0.458696i	−0.841539	+	0.540196i	$0.818350\pi$
$212$	−1.87493	+	1.08249i	−0.128771	+	0.0743458i
$213$	−5.44933	+	5.44933i	−0.373382	+	0.373382i
$214$	−18.4318	−	4.93878i	−1.25997	−	0.337608i
$215$	5.31370	+	1.42380i	0.362391	+	0.0971025i
$216$	1.90287	−	1.90287i	0.129474	−	0.129474i
$217$	−18.8508	+	10.8835i	−1.27967	+	0.738819i
$218$	1.52367	+	0.879689i	0.103196	+	0.0595800i
$219$	−3.10527	−	11.5890i	−0.209834	−	0.783113i
$220$	0.671514	+	0.433832i	0.0452735	+	0.0292490i
$221$	−1.28925	−	1.74999i	−0.0867246	−	0.117717i
$222$		−	16.0115i		−	1.07462i
$223$	−5.95008	−	22.2060i	−0.398447	−	1.48702i	−0.815829	−	0.578293i	$-0.803719\pi$
$223$	−5.95008	−	22.2060i	−0.398447	−	1.48702i	0.417382	−	0.908731i	$-0.362948\pi$
$224$	2.13762	−	3.70247i	0.142826	−	0.247381i
$225$	2.69631	−	1.55672i	0.179754	−	0.103781i
$226$	6.16543	+	6.16543i	0.410118	+	0.410118i
$227$	6.20018	−	23.1394i	0.411520	−	1.53581i	−0.380185	−	0.924911i	$-0.624140\pi$
$227$	6.20018	−	23.1394i	0.411520	−	1.53581i	0.791705	−	0.610904i	$-0.209194\pi$
$228$	−0.104218	−	0.0279251i	−0.00690200	−	0.00184939i
$229$	−9.65421	−	9.65421i	−0.637968	−	0.637968i	0.312086	−	0.950054i	$-0.398972\pi$
$229$	−9.65421	−	9.65421i	−0.637968	−	0.637968i	−0.950054	+	0.312086i	$0.898972\pi$
$230$	3.88022	−	2.24025i	0.255854	−	0.147718i
$231$	6.53269	+	12.7465i	0.429820	+	0.838661i
$232$	14.2285	−	3.81251i	0.934146	−	0.250304i
$233$	−26.9246			−1.76389			−0.881944	−	0.471354i	$-0.843766\pi$
$233$	−26.9246			−1.76389			−0.881944	+	0.471354i	$0.843766\pi$
$234$	4.15498	+	3.31927i	0.271620	+	0.216988i
$235$	2.23556			0.145832
$236$	0.416305	+	1.55367i	0.0270991	+	0.101135i
$237$	11.9137	+	6.87838i	0.773878	+	0.446799i
$238$	1.92000	+	3.32554i	0.124455	+	0.215563i
$239$	8.79544	+	8.79544i	0.568930	+	0.568930i	0.931829	−	0.362899i	$-0.118213\pi$
$239$	8.79544	+	8.79544i	0.568930	+	0.568930i	−0.362899	+	0.931829i	$0.618213\pi$
$240$	5.73169	+	1.53580i	0.369979	+	0.0991356i
$241$	−20.6313	−	5.52814i	−1.32898	−	0.356099i	−0.476644	−	0.879096i	$-0.658147\pi$
$241$	−20.6313	−	5.52814i	−1.32898	−	0.356099i	−0.852334	+	0.522998i	$0.824814\pi$
$242$	15.1742	+	5.74265i	0.975436	+	0.369152i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	0.597372	−	1.03468i	0.0382428	−	0.0662385i
$245$	−15.4563	+	4.14151i	−0.987469	+	0.264592i
$246$			6.84928i			0.436694i
$247$	−0.332244	+	2.19165i	−0.0211402	+	0.139451i
$248$			13.5638i			0.861304i
$249$	−7.51503	+	2.01365i	−0.476246	+	0.127610i
$250$	14.2348	+	8.21845i	0.900286	+	0.519780i
$251$	10.2387	−	5.91130i	0.646259	−	0.373118i	−0.140763	−	0.990043i	$-0.544955\pi$
$251$	10.2387	−	5.91130i	0.646259	−	0.373118i	0.787021	+	0.616926i	$0.211622\pi$
$252$	−0.535909	−	0.535909i	−0.0337591	−	0.0337591i
$253$	5.43944	−	4.92103i	0.341975	−	0.309383i
$254$	−3.70660	+	13.8332i	−0.232573	+	0.867973i
$255$	−0.585509	+	0.585509i	−0.0366660	+	0.0366660i
$256$	−2.09021	−	3.62035i	−0.130638	−	0.226272i
$257$	−23.4522	−	13.5402i	−1.46291	−	0.844612i	−0.463766	−	0.885958i	$-0.653502\pi$
$257$	−23.4522	−	13.5402i	−1.46291	−	0.844612i	−0.999145	+	0.0413458i	$0.986835\pi$
$258$	−5.70611	+	1.52895i	−0.355247	+	0.0951882i
$259$	46.8805			2.91301
$260$	−0.130265	+	0.859291i	−0.00807869	+	0.0532910i
$261$		−	5.47383i		−	0.338821i
$262$	2.93539	+	10.9550i	0.181349	+	0.676805i
$263$	−19.0763	−	11.0137i	−1.17630	−	0.679135i	−0.221142	−	0.975242i	$-0.570978\pi$
$263$	−19.0763	−	11.0137i	−1.17630	−	0.679135i	−0.955155	+	0.296106i	$0.904312\pi$
$264$	8.91410	+	0.446035i	0.548625	+	0.0274516i
$265$	11.9814	−	11.9814i	0.736013	−	0.736013i
$266$	1.01356	−	3.78264i	0.0621451	−	0.231929i
$267$	−1.88408	+	7.03147i	−0.115304	+	0.430319i
$268$	1.13855	+	1.13855i	0.0695481	+	0.0695481i
$269$	1.09246	+	1.89220i	0.0666086	+	0.115369i	0.897406	−	0.441205i	$-0.145449\pi$
$269$	1.09246	+	1.89220i	0.0666086	+	0.115369i	−0.830798	+	0.556574i	$0.812115\pi$
$270$	1.01294	−	1.75447i	0.0616457	−	0.106774i
$271$	0.465197	+	1.73614i	0.0282587	+	0.105463i	0.978615	−	0.205702i	$-0.0659476\pi$
$271$	0.465197	+	1.73614i	0.0282587	+	0.105463i	−0.950356	+	0.311165i	$0.899281\pi$
$272$	2.60445			0.157918
$273$	−9.71860	+	12.1655i	−0.588196	+	0.736289i
$274$			6.74840i			0.407685i
$275$	9.82822	+	3.16771i	0.592664	+	0.191020i
$276$	−0.194065	+	0.336131i	−0.0116814	+	0.0202327i
$277$	−5.90148	−	10.2217i	−0.354585	−	0.614160i	0.632461	−	0.774592i	$-0.282045\pi$
$277$	−5.90148	−	10.2217i	−0.354585	−	0.614160i	−0.987047	+	0.160432i	$0.948711\pi$
$278$	−13.2518	+	13.2518i	−0.794792	+	0.794792i
$279$	4.86858	+	1.30453i	0.291474	+	0.0781003i
$280$	−4.13139	+	15.4185i	−0.246898	+	0.921434i
$281$	7.24760	−	7.24760i	0.432356	−	0.432356i	−0.457073	−	0.889429i	$-0.651102\pi$
$281$	7.24760	−	7.24760i	0.432356	−	0.432356i	0.889429	+	0.457073i	$0.151102\pi$
$282$	−2.07902	+	1.20032i	−0.123804	+	0.0714783i
$283$	−1.44242	+	2.49835i	−0.0857431	+	0.148511i	−0.905708	−	0.423903i	$-0.860660\pi$
$283$	−1.44242	+	2.49835i	−0.0857431	+	0.148511i	0.819965	+	0.572414i	$0.193993\pi$
$284$	1.30638	−	0.350042i	0.0775191	−	0.0207712i
$285$	0.844439			0.0500202
$286$	1.08147	+	17.6047i	0.0639488	+	1.04099i
$287$	−20.0542			−1.18376
$288$	−0.956235	+	0.256222i	−0.0563467	+	0.0150980i
$289$	8.31828	−	14.4077i	0.489311	−	0.847511i
$290$	9.60366	−	5.54467i	0.563946	−	0.325595i
$291$	9.49049	−	9.49049i	0.556342	−	0.556342i
$292$	−0.544961	+	2.03382i	−0.0318914	+	0.119020i
$293$	−22.2475	−	5.96119i	−1.29971	−	0.348257i	−0.458370	−	0.888761i	$-0.651567\pi$
$293$	−22.2475	−	5.96119i	−1.29971	−	0.348257i	−0.841341	+	0.540505i	$0.818233\pi$
$294$	12.1504	−	12.1504i	0.708626	−	0.708626i
$295$	−6.29440	−	10.9022i	−0.366474	−	0.634752i
$296$	14.6065	−	25.2992i	0.848986	−	1.47049i
$297$	1.01743	−	3.15671i	0.0590374	−	0.183171i
$298$		−	19.8517i		−	1.14998i
$299$	7.30607	+	3.19501i	0.422521	+	0.184772i
$300$	−0.546395			−0.0315461
$301$	−4.47665	−	16.7071i	−0.258030	−	0.962981i
$302$	0.642745	−	1.11327i	0.0369858	−	0.0640613i
$303$	1.88356	+	3.26242i	0.108208	+	0.187421i
$304$	−1.87811	−	1.87811i	−0.107717	−	0.107717i
$305$	−2.42014	+	9.03208i	−0.138577	+	0.517176i
$306$	0.230138	−	0.858886i	0.0131561	−	0.0490993i
$307$	−17.9596	+	17.9596i	−1.02501	+	1.02501i	−0.0253307	+	0.999679i	$0.508064\pi$
$307$	−17.9596	+	17.9596i	−1.02501	+	1.02501i	−0.999679	+	0.0253307i	$0.991936\pi$
$308$	0.125618	−	2.51050i	0.00715774	−	0.143049i
$309$	3.29940	+	1.90491i	0.187696	+	0.108366i
$310$	2.64283	+	9.86318i	0.150103	+	0.560191i
$311$			17.6408i			1.00032i	0.865933	+	0.500160i	$0.166725\pi$
$311$			17.6408i			1.00032i	−0.865933	+	0.500160i	$0.833275\pi$
$312$	3.53713	+	9.03507i	0.200251	+	0.511510i
$313$	−29.9083			−1.69052			−0.845259	−	0.534356i	$-0.820554\pi$
$313$	−29.9083			−1.69052			−0.845259	+	0.534356i	$0.820554\pi$
$314$	−6.94607	+	1.86119i	−0.391990	+	0.105033i
$315$	5.13696	+	2.96583i	0.289435	+	0.167105i
$316$	−1.20713	−	2.09080i	−0.0679061	−	0.117617i
$317$	6.22820	−	6.22820i	0.349810	−	0.349810i	−0.510229	−	0.860039i	$-0.670439\pi$
$317$	6.22820	−	6.22820i	0.349810	−	0.349810i	0.860039	+	0.510229i	$0.170439\pi$
$318$	−4.70937	+	17.5756i	−0.264088	+	0.985592i
$319$	13.4628	−	12.1797i	0.753770	−	0.681932i
$320$	6.97363	+	6.97363i	0.389838	+	0.389838i
$321$	−11.2041	+	6.46866i	−0.625349	+	0.361045i
$322$	−12.2000	−	7.04369i	−0.679881	−	0.392529i
$323$	0.358005	−	0.0959271i	0.0199199	−	0.00533753i
$324$			0.175496i			0.00974976i
$325$	1.24738	+	11.1561i	0.0691924	+	0.618831i
$326$		−	27.5425i		−	1.52544i
$327$	1.15219	−	0.308728i	0.0637162	−	0.0170727i
$328$	−6.24827	+	10.8223i	−0.345003	+	0.597563i
$329$	−3.51447	−	6.08723i	−0.193759	−	0.335600i
$330$	6.56895	−	1.41252i	0.361609	−	0.0777565i
$331$	18.1172	+	4.85449i	0.995811	+	0.266827i	0.719690	−	0.694296i	$-0.244284\pi$
$331$	18.1172	+	4.85449i	0.995811	+	0.266827i	0.276121	+	0.961123i	$0.410951\pi$
$332$	1.31886	+	0.353386i	0.0723816	+	0.0193946i
$333$	−7.67604	−	7.67604i	−0.420645	−	0.420645i
$334$	−8.31473	−	14.4015i	−0.454962	−	0.788016i
$335$	−10.9136	−	6.30097i	−0.596273	−	0.344259i
$336$	−4.82880	−	18.0213i	−0.263433	−	0.983144i
$337$	3.65081			0.198872			0.0994362	−	0.995044i	$-0.468296\pi$
$337$	3.65081			0.198872			0.0994362	+	0.995044i	$0.468296\pi$
$338$	−16.9676	+	8.93075i	−0.922917	+	0.485769i
$339$	5.91152			0.321070
$340$	0.140365	−	0.0376107i	0.00761236	−	0.00203973i
$341$	7.62449	+	14.8768i	0.412890	+	0.805626i
$342$	−0.785312	+	0.453400i	−0.0424648	+	0.0245171i
$343$	14.1997	+	14.1997i	0.766714	+	0.766714i
$344$	−10.4108	−	2.78957i	−0.561314	−	0.150404i
$345$	0.786219	−	2.93421i	0.0423286	−	0.157972i
$346$	2.07770	+	2.07770i	0.111698	+	0.111698i
$347$	28.5017	−	16.4555i	1.53005	−	0.883376i	0.530694	−	0.847564i	$-0.321932\pi$
$347$	28.5017	−	16.4555i	1.53005	−	0.883376i	0.999359	−	0.0358122i	$-0.0114018\pi$
$348$	−0.480317	+	0.831933i	−0.0257477	+	0.0445963i
$349$	−2.76148	−	10.3060i	−0.147818	−	0.551666i	−0.999614	−	0.0277913i	$-0.991153\pi$
$349$	−2.76148	−	10.3060i	−0.147818	−	0.551666i	0.851795	−	0.523875i	$-0.175514\pi$
$350$		−	19.8316i		−	1.06005i
$351$	3.58322	−	0.400646i	0.191258	−	0.0213849i
$352$	−2.75787	−	1.78172i	−0.146995	−	0.0949662i
$353$	−2.63681	−	9.84070i	−0.140343	−	0.523768i	−0.999919	−	0.0127589i	$-0.995939\pi$
$353$	−2.63681	−	9.84070i	−0.140343	−	0.523768i	0.859575	−	0.511009i	$-0.170728\pi$
$354$	11.7073	+	6.75924i	0.622239	+	0.359250i
$355$	−9.16694	+	5.29253i	−0.486531	+	0.280899i
$356$	0.903345	−	0.903345i	0.0478772	−	0.0478772i
$357$	2.51476	+	0.673828i	0.133095	+	0.0356627i
$358$	−30.1660	−	8.08297i	−1.59432	−	0.427198i
$359$	−10.0933	+	10.0933i	−0.532703	+	0.532703i	−0.921376	−	0.388673i	$-0.872934\pi$
$359$	−10.0933	+	10.0933i	−0.532703	+	0.532703i	0.388673	+	0.921376i	$0.372934\pi$
$360$	3.20104	−	1.84812i	0.168709	−	0.0974044i
$361$	16.1271	+	9.31101i	0.848797	+	0.490053i
$362$	−5.85733	−	21.8599i	−0.307854	−	1.14893i
$363$	10.0277	−	4.52158i	0.526319	−	0.237321i
$364$	2.54456	−	0.996171i	0.133371	−	0.0522135i
$365$		−	16.4793i		−	0.862566i
$366$	−2.59887	−	9.69910i	−0.135845	−	0.506980i
$367$	1.94841	−	3.37474i	0.101706	−	0.176160i	−0.810682	−	0.585487i	$-0.800903\pi$
$367$	1.94841	−	3.37474i	0.101706	−	0.176160i	0.912388	+	0.409327i	$0.134237\pi$
$368$	−8.27456	+	4.77732i	−0.431341	+	0.249035i
$369$	3.28361	+	3.28361i	0.170938	+	0.170938i
$370$	5.69198	−	21.2428i	0.295912	−	1.10436i
$371$	−51.4602	−	13.7887i	−2.67168	−	0.715874i
$372$	−0.625475	−	0.625475i	−0.0324294	−	0.0324294i
$373$	3.80079	−	2.19439i	0.196798	−	0.113621i	−0.398363	−	0.917228i	$-0.630422\pi$
$373$	3.80079	−	2.19439i	0.196798	−	0.113621i	0.595161	+	0.803607i	$0.297088\pi$
$374$	2.62449	−	1.34507i	0.135709	−	0.0695519i
$375$	10.7643	−	2.88428i	0.555864	−	0.148943i
$376$	−4.37999			−0.225881
$377$	18.0827	+	7.90772i	0.931307	+	0.407268i
$378$	−6.36970			−0.327622
$379$	−6.95472	−	25.9554i	−0.357240	−	1.33324i	−0.877642	−	0.479317i	$-0.840884\pi$
$379$	−6.95472	−	25.9554i	−0.357240	−	1.33324i	0.520402	−	0.853922i	$-0.325782\pi$
$380$	−0.128341	−	0.0740977i	−0.00658375	−	0.00380113i
$381$	4.85479	+	8.40874i	0.248718	+	0.430793i
$382$	−15.3614	−	15.3614i	−0.785957	−	0.785957i
$383$	−3.13216	−	0.839259i	−0.160046	−	0.0428841i	0.177906	−	0.984047i	$-0.443068\pi$
$383$	−3.13216	−	0.839259i	−0.160046	−	0.0428841i	−0.337952	+	0.941163i	$0.609734\pi$
$384$	−12.1421	−	3.25347i	−0.619625	−	0.166028i
$385$	4.13575	+	19.2334i	0.210777	+	0.980226i
$386$	8.30750	+	14.3890i	0.422841	+	0.732381i
$387$	−2.00257	+	3.46855i	−0.101796	+	0.176316i
$388$	−2.27517	+	0.609630i	−0.115504	+	0.0309493i
$389$		−	32.0226i		−	1.62361i	−0.583927	−	0.811806i	$-0.698485\pi$
$389$		−	32.0226i		−	1.62361i	0.583927	−	0.811806i	$-0.301515\pi$
$390$	4.33252	+	5.88082i	0.219386	+	0.297787i
$391$		−	1.33329i		−	0.0674273i
$392$	30.2827	−	8.11423i	1.52951	−	0.409830i
$393$	6.65920	+	3.84469i	0.335912	+	0.193939i
$394$	−12.4448	+	7.18503i	−0.626962	+	0.361977i
$395$	13.3609	+	13.3609i	0.672262	+	0.672262i
$396$	−0.431628	+	0.390491i	−0.0216901	+	0.0196229i
$397$	0.267945	−	0.999985i	0.0134478	−	0.0501878i	−0.958876	−	0.283826i	$-0.908396\pi$
$397$	0.267945	−	0.999985i	0.0134478	−	0.0501878i	0.972324	+	0.233638i	$0.0750630\pi$
$398$	12.0022	−	12.0022i	0.601616	−	0.601616i
$399$	−1.32752	−	2.29934i	−0.0664593	−	0.115111i
$400$	−11.6486	−	6.72532i	−0.582430	−	0.336266i
$401$	−14.3052	+	3.83308i	−0.714370	+	0.191415i	−0.597658	−	0.801751i	$-0.703902\pi$
$401$	−14.3052	+	3.83308i	−0.714370	+	0.191415i	−0.116712	+	0.993166i	$0.537235\pi$
$402$	13.5326			0.674943
$403$	−11.3429	+	14.1987i	−0.565028	+	0.707287i
$404$		−	0.661113i		−	0.0328916i
$405$	−0.355494	−	1.32672i	−0.0176646	−	0.0659253i
$406$	−30.1954	−	17.4333i	−1.49857	−	0.865201i
$407$	1.79927	−	35.9588i	0.0891867	−	1.78241i
$408$	1.14715	−	1.14715i	0.0567926	−	0.0567926i
$409$	−1.14958	+	4.29030i	−0.0568431	+	0.212141i	−0.988506	−	0.151183i	$-0.951692\pi$
$409$	−1.14958	+	4.29030i	−0.0568431	+	0.212141i	0.931663	+	0.363325i	$0.118358\pi$
$410$	−2.43488	+	9.08709i	−0.120250	+	0.448779i
$411$	3.23524	+	3.23524i	0.159583	+	0.159583i
$412$	−0.334303	−	0.579030i	−0.0164699	−	0.0285268i
$413$	−19.7906	+	34.2783i	−0.973831	+	1.68672i
$414$	0.844280	+	3.15090i	0.0414941	+	0.154858i
$415$	−10.6862			−0.524564
$416$	0.534990	−	3.52906i	0.0262301	−	0.173026i
$417$			12.7061i			0.622220i
$418$	−2.86251	−	0.922607i	−0.140010	−	0.0451262i
$419$	4.20883	−	7.28991i	0.205615	−	0.356135i	−0.744714	−	0.667384i	$-0.767414\pi$
$419$	4.20883	−	7.28991i	0.205615	−	0.356135i	0.950328	+	0.311249i	$0.100747\pi$
$420$	−0.520490	−	0.901514i	−0.0253973	−	0.0439894i
$421$	22.2254	−	22.2254i	1.08320	−	1.08320i	0.0869907	−	0.996209i	$-0.472275\pi$
$421$	22.2254	−	22.2254i	1.08320	−	1.08320i	0.996209	−	0.0869907i	$-0.0277250\pi$
$422$	18.9854	+	5.08712i	0.924194	+	0.247637i
$423$	−0.421256	+	1.57215i	−0.0204822	+	0.0764404i
$424$	−23.4745	+	23.4745i	−1.14002	+	1.14002i
$425$	1.62549	−	0.938475i	0.0788477	−	0.0455227i
$426$	5.68338	−	9.84391i	0.275361	−	0.476939i
$427$	28.3983	−	7.60929i	1.37429	−	0.368240i
$428$	2.27044			0.109746
$429$	8.95832	+	7.92139i	0.432512	+	0.382448i
$430$	−8.11395			−0.391290
$431$	−32.6412	+	8.74620i	−1.57227	+	0.421289i	−0.936523	−	0.350605i	$-0.885976\pi$
$431$	−32.6412	+	8.74620i	−1.57227	+	0.421289i	−0.635750	+	0.771895i	$0.719309\pi$
$432$	−2.16010	+	3.74140i	−0.103928	+	0.180008i
$433$	15.1842	−	8.76658i	0.729704	−	0.421295i	−0.0886097	−	0.996066i	$-0.528242\pi$
$433$	15.1842	−	8.76658i	0.729704	−	0.421295i	0.818314	+	0.574771i	$0.194909\pi$
$434$	22.7019	−	22.7019i	1.08973	−	1.08973i
$435$	1.94591	−	7.26224i	0.0932993	−	0.348198i
$436$	−0.202204	−	0.0541805i	−0.00968383	−	0.00259477i
$437$	−0.961454	+	0.961454i	−0.0459926	+	0.0459926i
$438$	8.84814	+	15.3254i	0.422780	+	0.732277i
$439$	17.7664	−	30.7724i	0.847946	−	1.46869i	−0.0350923	−	0.999384i	$-0.511173\pi$
$439$	17.7664	−	30.7724i	0.847946	−	1.46869i	0.883038	−	0.469301i	$-0.155494\pi$
$440$	11.6680	+	3.76067i	0.556248	+	0.179283i
$441$		−	11.6500i		−	0.554763i
$442$	2.50485	+	2.00104i	0.119144	+	0.0951798i
$443$	−15.6020			−0.741276			−0.370638	−	0.928777i	$-0.620861\pi$
$443$	−15.6020			−0.741276			−0.370638	+	0.928777i	$0.620861\pi$
$444$	0.493077	+	1.84019i	0.0234004	+	0.0873315i
$445$	−4.99929	+	8.65902i	−0.236989	+	0.410477i
$446$	16.9541	+	29.3654i	0.802802	+	1.39049i
$447$	−9.51708	−	9.51708i	−0.450142	−	0.450142i
$448$	8.02554	−	29.9517i	0.379171	−	1.41509i
$449$	6.82810	−	25.4828i	0.322238	−	1.20261i	−0.594821	−	0.803858i	$-0.702777\pi$
$449$	6.82810	−	25.4828i	0.322238	−	1.20261i	0.917059	−	0.398751i	$-0.130556\pi$
$450$	−3.24716	+	3.24716i	−0.153073	+	0.153073i
$451$	−0.769681	+	15.3822i	−0.0362429	+	0.724321i
$452$	−0.898455	−	0.518723i	−0.0422598	−	0.0243987i
$453$	−0.225572	−	0.841847i	−0.0105983	−	0.0395534i
$454$			35.3335i			1.65828i
$455$	−17.2186	+	12.6853i	−0.807222	+	0.594697i
$456$	−1.65446			−0.0774772
$457$	−2.81822	+	0.755141i	−0.131831	+	0.0353240i	−0.324131	−	0.946012i	$-0.605072\pi$
$457$	−2.81822	+	0.755141i	−0.131831	+	0.0353240i	0.192300	+	0.981336i	$0.438405\pi$
$458$	17.4398	+	10.0689i	0.814909	+	0.470488i
$459$	−0.301427	−	0.522088i	−0.0140694	−	0.0243690i
$460$	−0.376963	+	0.376963i	−0.0175760	+	0.0175760i
$461$	−6.90925	+	25.7857i	−0.321796	+	1.20096i	0.595698	+	0.803209i	$0.296876\pi$
$461$	−6.90925	+	25.7857i	−0.321796	+	1.20096i	−0.917494	+	0.397750i	$0.869791\pi$
$462$	−14.1731	−	15.6661i	−0.659391	−	0.728854i
$463$	13.0023	+	13.0023i	0.604267	+	0.604267i	0.941442	−	0.337175i	$-0.109471\pi$
$463$	13.0023	+	13.0023i	0.604267	+	0.604267i	−0.337175	+	0.941442i	$0.609471\pi$
$464$	−20.4798	+	11.8240i	−0.950749	+	0.548915i
$465$	5.99549	+	3.46150i	0.278034	+	0.160523i
$466$	38.3594	−	10.2784i	1.77697	−	0.476137i
$467$		−	37.2648i		−	1.72441i	−0.506561	−	0.862204i	$-0.669084\pi$
$467$		−	37.2648i		−	1.72441i	0.506561	−	0.862204i	$-0.330916\pi$
$468$	−0.579747	−	0.253528i	−0.0267988	−	0.0117194i
$469$			39.6224i			1.82959i
$470$	−3.18499	+	0.853416i	−0.146913	+	0.0393651i
$471$	−2.43773	+	4.22228i	−0.112325	+	0.194552i
$472$	12.3323	+	21.3601i	0.567638	+	0.983179i
$473$	−12.9867	+	2.79252i	−0.597129	+	0.128400i
$474$	−19.5992	−	5.25160i	−0.900222	−	0.241214i
$475$	−1.84891	−	0.495414i	−0.0848339	−	0.0227312i
$476$	−0.323076	−	0.323076i	−0.0148081	−	0.0148081i
$477$	6.16819	+	10.6836i	0.282422	+	0.489169i
$478$	−15.8885	−	9.17322i	−0.726722	−	0.419573i
$479$	−1.63954	−	6.11884i	−0.0749124	−	0.279577i	0.918301	−	0.395883i	$-0.129561\pi$
$479$	−1.63954	−	6.11884i	−0.0749124	−	0.279577i	−0.993213	+	0.116306i	$0.962895\pi$
$480$	−1.35974			−0.0620635
$481$	36.4468	−	14.2686i	1.66183	−	0.650590i
$482$	31.5037			1.43495
$483$	−9.22560	+	2.47199i	−0.419780	+	0.112480i
$484$	−1.92081	−	0.192706i	−0.0873096	−	0.00875936i
$485$	15.9650	−	9.21742i	0.724935	−	0.418542i
$486$	1.04295	+	1.04295i	0.0473092	+	0.0473092i
$487$	22.9832	+	6.15833i	1.04147	+	0.279060i	0.738721	−	0.674011i	$-0.235430\pi$
$487$	22.9832	+	6.15833i	1.04147	+	0.279060i	0.302746	+	0.953071i	$0.402097\pi$
$488$	4.74164	−	17.6960i	0.214644	−	0.801062i
$489$	−13.2041	−	13.2041i	−0.597110	−	0.597110i
$490$	20.4396	−	11.8008i	0.923367	−	0.533106i
$491$	2.38360	−	4.12852i	0.107570	−	0.186317i	−0.807215	−	0.590257i	$-0.799026\pi$
$491$	2.38360	−	4.12852i	0.107570	−	0.186317i	0.914785	+	0.403940i	$0.132360\pi$
$492$	−0.210925	−	0.787184i	−0.00950925	−	0.0354890i
$493$		−	3.29992i		−	0.148621i
$494$	−0.363305	−	3.24927i	−0.0163459	−	0.146191i
$495$	2.47204	−	3.82639i	0.111110	−	0.171983i
$496$	−5.63583	−	21.0332i	−0.253056	−	0.944419i
$497$	28.8223	+	16.6405i	1.29286	+	0.746430i
$498$	9.93795	−	5.73768i	0.445330	−	0.257111i
$499$	−30.3234	+	30.3234i	−1.35746	+	1.35746i	−0.480429	+	0.877034i	$0.659519\pi$
$499$	−30.3234	+	30.3234i	−1.35746	+	1.35746i	−0.877034	+	0.480429i	$0.840481\pi$
$500$	−1.88908	−	0.506178i	−0.0844823	−	0.0226370i
$501$	−10.8904	−	2.91807i	−0.486546	−	0.130370i
$502$	−12.3304	+	12.3304i	−0.550332	+	0.550332i
$503$	−20.7982	+	12.0078i	−0.927346	+	0.535404i	−0.885971	−	0.463740i	$-0.846507\pi$
$503$	−20.7982	+	12.0078i	−0.927346	+	0.535404i	−0.0413749	+	0.999144i	$0.513174\pi$
$504$	−10.0646	−	5.81077i	−0.448311	−	0.258832i
$505$	1.33919	+	4.99791i	0.0595930	+	0.222404i
$506$	−5.87097	+	9.08748i	−0.260997	+	0.403988i
$507$	−3.85295	+	12.4159i	−0.171115	+	0.551410i
$508$		−	1.70399i		−	0.0756023i
$509$	9.59521	+	35.8098i	0.425300	+	1.58724i	0.763267	+	0.646083i	$0.223594\pi$
$509$	9.59521	+	35.8098i	0.425300	+	1.58724i	−0.337967	+	0.941158i	$0.609739\pi$
$510$	0.610658	−	1.05769i	0.0270404	−	0.0468353i
$511$	−44.8718	+	25.9067i	−1.98501	+	1.14605i
$512$	−13.4173	−	13.4173i	−0.592968	−	0.592968i
$513$	−0.159121	+	0.593849i	−0.00702538	+	0.0262191i
$514$	38.5813	+	10.3378i	1.70175	+	0.455982i
$515$	3.70020	+	3.70020i	0.163050	+	0.163050i
$516$	0.608716	−	0.351442i	0.0267972	−	0.0154714i
$517$	−4.80399	+	2.46208i	−0.211279	+	0.108282i
$518$	−66.7905	+	17.8965i	−2.93461	+	0.786326i
$519$	1.99213			0.0874450
$520$	1.48088	+	13.2444i	0.0649409	+	0.580807i
$521$	−24.7847			−1.08584			−0.542918	−	0.839785i	$-0.682681\pi$
$521$	−24.7847			−1.08584			−0.542918	+	0.839785i	$0.682681\pi$
$522$	2.08962	+	7.79855i	0.0914600	+	0.341333i
$523$	−20.1497	−	11.6334i	−0.881084	−	0.508694i	−0.0100682	−	0.999949i	$-0.503205\pi$
$523$	−20.1497	−	11.6334i	−0.881084	−	0.508694i	−0.871016	+	0.491255i	$0.836538\pi$
$524$	−0.674726	−	1.16866i	−0.0294756	−	0.0510532i
$525$	−9.50746	−	9.50746i	−0.414940	−	0.414940i
$526$	31.3825	+	8.40891i	1.36834	+	0.366646i
$527$	2.93505	+	0.786443i	0.127853	+	0.0342580i
$528$	−14.0083	+	3.01219i	−0.609631	+	0.131089i
$529$	−9.05436	−	15.6826i	−0.393668	−	0.681853i
$530$	−12.4960	+	21.6438i	−0.542794	+	0.940146i
$531$	8.85304	−	2.37217i	0.384189	−	0.102943i
$532$			0.465949i			0.0202015i
$533$	−15.5910	+	6.10371i	−0.675320	+	0.264381i
$534$		−	10.7370i		−	0.464634i
$535$	−17.1642	+	4.59914i	−0.742074	+	0.198838i
$536$	21.3824	+	12.3451i	0.923578	+	0.533228i
$537$	−18.3369	+	10.5868i	−0.791296	+	0.456855i
$538$	−2.27877	−	2.27877i	−0.0982447	−	0.0982447i
$539$	28.6530	−	25.9222i	1.23417	−	1.11655i
$540$	−0.0623876	+	0.232834i	−0.00268474	+	0.0100196i
$541$	22.1057	−	22.1057i	0.950397	−	0.950397i	−0.0484299	−	0.998827i	$-0.515422\pi$
$541$	22.1057	−	22.1057i	0.950397	−	0.950397i	0.998827	+	0.0484299i	$0.0154218\pi$
$542$	−1.32553	−	2.29589i	−0.0569365	−	0.0986168i
$543$	−13.2879	−	7.67175i	−0.570237	−	0.329226i
$544$	−0.576471	+	0.154465i	−0.0247160	+	0.00662263i
$545$	1.63838			0.0701807
$546$	9.20193	−	21.0422i	0.393806	−	0.900523i
$547$		−	1.64115i		−	0.0701703i	−0.999384	−	0.0350852i	$-0.988830\pi$
$547$		−	1.64115i		−	0.0701703i	0.999384	−	0.0350852i	$-0.0111702\pi$
$548$	−0.207818	−	0.775589i	−0.00887756	−	0.0331315i
$549$	−5.89575	−	3.40391i	−0.251624	−	0.145275i
$550$	−15.2115	−	0.761139i	−0.648621	−	0.0324551i
$551$	−2.37962	+	2.37962i	−0.101375	+	0.101375i
$552$	−1.54039	+	5.74883i	−0.0655635	+	0.244686i
$553$	15.3763	−	57.3851i	0.653867	−	2.44026i
$554$	12.3099	+	12.3099i	0.522998	+	0.522998i
$555$	−7.45518	−	12.9128i	−0.316455	−	0.548116i
$556$	1.11493	−	1.93112i	0.0472836	−	0.0818977i
$557$	−2.40873	−	8.98949i	−0.102061	−	0.380897i	0.895934	−	0.444187i	$-0.146507\pi$
$557$	−2.40873	−	8.98949i	−0.102061	−	0.380897i	−0.997995	+	0.0632899i	$0.979841\pi$
$558$	−7.43426			−0.314717
$559$	−8.56531	−	11.6263i	−0.362274	−	0.491739i
$560$		−	25.6259i		−	1.08289i
$561$	0.613364	−	1.90304i	0.0258962	−	0.0803464i
$562$	−7.55890	+	13.0924i	−0.318853	+	0.552270i
$563$	3.93627	+	6.81783i	0.165894	+	0.287337i	0.936972	−	0.349403i	$-0.113616\pi$
$563$	3.93627	+	6.81783i	0.165894	+	0.287337i	−0.771078	+	0.636740i	$0.780282\pi$
$564$	0.201977	−	0.201977i	0.00850475	−	0.00850475i
$565$	7.84294	+	2.10151i	0.329955	+	0.0884112i
$566$	1.10128	−	4.11003i	0.0462902	−	0.172757i
$567$	−3.05369	+	3.05369i	−0.128243	+	0.128243i
$568$	17.9603	−	10.3694i	0.753595	−	0.435089i
$569$	−13.1458	+	22.7693i	−0.551102	+	0.954537i	0.447093	+	0.894487i	$0.352459\pi$
$569$	−13.1458	+	22.7693i	−0.551102	+	0.954537i	−0.998195	+	0.0600498i	$0.980874\pi$
$570$	−1.20307	+	0.322362i	−0.0503911	+	0.0135023i
$571$	−27.8935			−1.16731			−0.583653	−	0.812003i	$-0.698377\pi$
$571$	−27.8935			−1.16731			−0.583653	+	0.812003i	$0.698377\pi$
$572$	−0.666435	−	1.99000i	−0.0278650	−	0.0832059i
$573$	−14.7288			−0.615303
$574$	28.5712	−	7.65563i	1.19254	−	0.319540i
$575$	−3.44287	+	5.96323i	−0.143578	+	0.248684i
$576$	−6.21826	+	3.59011i	−0.259094	+	0.149588i
$577$	−12.3051	+	12.3051i	−0.512267	+	0.512267i	−0.915220	−	0.402954i	$-0.867984\pi$
$577$	−12.3051	+	12.3051i	−0.512267	+	0.512267i	0.402954	+	0.915220i	$0.367984\pi$
$578$	−6.35095	+	23.7021i	−0.264165	+	0.985877i
$579$	10.8809	+	2.91553i	0.452195	+	0.121165i
$580$	−0.932993	+	0.932993i	−0.0387404	+	0.0387404i
$581$	16.7995	+	29.0976i	0.696961	+	1.20717i
$582$	−9.89812	+	17.1441i	−0.410290	+	0.710644i
$583$	−12.5514	+	38.9424i	−0.519827	+	1.61283i
$584$			32.2869i			1.33604i
$585$	4.89636	+	0.742269i	0.202440	+	0.0306890i
$586$	33.9716			1.40335
$587$	8.41376	+	31.4006i	0.347273	+	1.29604i	0.889934	+	0.456088i	$0.150750\pi$
$587$	8.41376	+	31.4006i	0.347273	+	1.29604i	−0.542662	+	0.839951i	$0.682583\pi$
$588$	−1.02226	+	1.77061i	−0.0421575	+	0.0730189i
$589$	−1.54939	−	2.68362i	−0.0638415	−	0.110577i
$590$	13.1295	+	13.1295i	0.540534	+	0.540534i
$591$	−2.52160	+	9.41073i	−0.103725	+	0.387106i
$592$	−12.1381	+	45.3001i	−0.498874	+	1.86182i
$593$	16.5134	−	16.5134i	0.678124	−	0.678124i	−0.281451	−	0.959576i	$-0.590816\pi$
$593$	16.5134	−	16.5134i	0.678124	−	0.678124i	0.959576	+	0.281451i	$0.0908158\pi$
$594$	−0.244469	+	4.88576i	−0.0100307	+	0.200465i
$595$	3.09684	+	1.78796i	0.126958	+	0.0732993i
$596$	0.611338	+	2.28154i	0.0250414	+	0.0934557i
$597$		−	11.5079i		−	0.470988i
$598$	−11.6286	−	1.76285i	−0.475530	−	0.0720884i
$599$	16.6193			0.679046			0.339523	−	0.940598i	$-0.389734\pi$
$599$	16.6193			0.679046			0.339523	+	0.940598i	$0.389734\pi$
$600$	−8.09296	+	2.16850i	−0.330394	+	0.0885288i
$601$	−13.7223	−	7.92259i	−0.559746	−	0.323169i	0.193298	−	0.981140i	$-0.438082\pi$
$601$	−13.7223	−	7.92259i	−0.559746	−	0.323169i	−0.753043	+	0.657971i	$0.771415\pi$
$602$	12.7558	+	22.0936i	0.519886	+	0.900469i
$603$	6.48763	−	6.48763i	0.264197	−	0.264197i
$604$	−0.0395870	+	0.147741i	−0.00161077	+	0.00601148i
$605$	14.9114	−	2.43407i	0.606234	−	0.0989591i
$606$	−3.92892	−	3.92892i	−0.159601	−	0.159601i
$607$	27.4007	−	15.8198i	1.11216	−	0.642106i	0.172772	−	0.984962i	$-0.444728\pi$
$607$	27.4007	−	15.8198i	1.11216	−	0.642106i	0.939388	+	0.342856i	$0.111394\pi$
$608$	0.527089	+	0.304315i	0.0213763	+	0.0123416i
$609$	−22.8336	+	6.11825i	−0.925265	+	0.247924i
$610$		−	13.7919i		−	0.558417i
$611$	−4.58500	−	3.66280i	−0.185489	−	0.148181i
$612$			0.105798i			0.00427665i
$613$	15.8562	−	4.24865i	0.640426	−	0.171602i	0.0760294	−	0.997106i	$-0.475776\pi$
$613$	15.8562	−	4.24865i	0.640426	−	0.171602i	0.564396	+	0.825504i	$0.309109\pi$
$614$	18.7310	−	32.4431i	0.755922	−	1.30930i
$615$	3.18913	+	5.52373i	0.128598	+	0.222738i
$616$	−8.10293	−	37.6830i	−0.326477	−	1.51829i
$617$	−28.8494	−	7.73016i	−1.16143	−	0.311205i	−0.373894	−	0.927471i	$-0.621978\pi$
$617$	−28.8494	−	7.73016i	−1.16143	−	0.311205i	−0.787537	+	0.616267i	$0.788644\pi$
$618$	−5.42784	−	1.45438i	−0.218340	−	0.0585039i
$619$	28.9839	+	28.9839i	1.16496	+	1.16496i	0.983375	+	0.181588i	$0.0581237\pi$
$619$	28.9839	+	28.9839i	1.16496	+	1.16496i	0.181588	+	0.983375i	$0.441876\pi$
$620$	−0.607478	−	1.05218i	−0.0243969	−	0.0422567i
$621$	1.91532	+	1.10581i	0.0768593	+	0.0443747i
$622$	−6.73433	−	25.1329i	−0.270022	−	1.00774i
$623$	31.4371			1.25950
$624$	−9.23908	−	12.5408i	−0.369859	−	0.502035i
$625$	−0.260657			−0.0104263
$626$	42.6103	−	11.4174i	1.70305	−	0.456331i
$627$	−1.81462	+	0.930005i	−0.0724688	+	0.0371408i
$628$	0.740992	−	0.427812i	0.0295688	−	0.0170716i
$629$	−4.62754	−	4.62754i	−0.184512	−	0.184512i
$630$	−8.45081	−	2.26439i	−0.336688	−	0.0902154i
$631$	−4.02573	+	15.0242i	−0.160262	+	0.598105i	0.838335	+	0.545155i	$0.183529\pi$
$631$	−4.02573	+	15.0242i	−0.160262	+	0.598105i	−0.998597	+	0.0529502i	$0.983138\pi$
$632$	−26.1773	−	26.1773i	−1.04128	−	1.04128i
$633$	11.5406	−	6.66295i	0.458696	−	0.264828i
$634$	−6.49571	+	11.2509i	−0.257977	+	0.446830i
$635$	3.45169	+	12.8819i	0.136976	+	0.511202i
$636$		−	2.16498i		−	0.0858471i
$637$	38.4857	+	16.8301i	1.52486	+	0.666834i
$638$	−14.5308	+	22.4917i	−0.575280	+	0.890457i
$639$	−1.99459	−	7.44392i	−0.0789048	−	0.294477i
$640$	−14.9526	−	8.63290i	−0.591054	−	0.341245i
$641$	17.3216	−	10.0006i	0.684163	−	0.395002i	−0.117259	−	0.993101i	$-0.537411\pi$
$641$	17.3216	−	10.0006i	0.684163	−	0.395002i	0.801422	+	0.598100i	$0.204077\pi$
$642$	13.4930	−	13.4930i	0.532526	−	0.532526i
$643$	25.8913	+	6.93755i	1.02105	+	0.273590i	0.730241	−	0.683190i	$-0.239408\pi$
$643$	25.8913	+	6.93755i	1.02105	+	0.273590i	0.290812	+	0.956780i	$0.406075\pi$
$644$	1.61905	+	0.433824i	0.0637997	+	0.0170951i
$645$	−3.88990	+	3.88990i	−0.153165	+	0.153165i
$646$	−0.473429	+	0.273334i	−0.0186268	+	0.0107542i
$647$	−14.2389	−	8.22086i	−0.559790	−	0.323195i	0.193271	−	0.981145i	$-0.438090\pi$
$647$	−14.2389	−	8.22086i	−0.559790	−	0.323195i	−0.753061	+	0.657950i	$0.771424\pi$
$648$	0.696499	+	2.59937i	0.0273610	+	0.102113i
$649$	25.5330	+	16.4956i	1.00226	+	0.647510i
$650$	−6.03596	−	15.4179i	−0.236750	−	0.604741i
$651$		−	21.7670i		−	0.853115i
$652$	0.848177	+	3.16544i	0.0332172	+	0.123968i
$653$	−4.68516	+	8.11494i	−0.183345	+	0.317562i	−0.943017	−	0.332743i	$-0.892026\pi$
$653$	−4.68516	+	8.11494i	−0.183345	+	0.317562i	0.759673	+	0.650305i	$0.225359\pi$
$654$	−1.52367	+	0.879689i	−0.0595800	+	0.0343986i
$655$	7.46813	+	7.46813i	0.291804	+	0.291804i
$656$	5.19237	−	19.3782i	0.202728	−	0.756591i
$657$	11.5890	+	3.10527i	0.452130	+	0.121148i
$658$	7.33083	+	7.33083i	0.285786	+	0.285786i
$659$	26.6796	−	15.4035i	1.03929	−	0.600033i	0.119657	−	0.992815i	$-0.461821\pi$
$659$	26.6796	−	15.4035i	1.03929	−	0.600033i	0.919632	+	0.392782i	$0.128487\pi$
$660$	−0.711467	+	0.364632i	−0.0276938	+	0.0141933i
$661$	−26.7782	+	7.17520i	−1.04155	+	0.279083i	−0.738757	−	0.673972i	$-0.764587\pi$
$661$	−26.7782	+	7.17520i	−1.04155	+	0.279083i	−0.302796	+	0.953055i	$0.597920\pi$
$662$	−27.6647			−1.07522
$663$	2.16016	−	0.241531i	0.0838938	−	0.00938029i
$664$	20.9368			0.812507
$665$	−0.943853	−	3.52251i	−0.0366010	−	0.136597i
$666$	13.8663	+	8.00574i	0.537310	+	0.310216i
$667$	6.05302	+	10.4841i	0.234374	+	0.405948i
$668$	1.39910	+	1.39910i	0.0541330	+	0.0541330i
$669$	22.2060	+	5.95008i	0.858534	+	0.230043i
$670$	17.9539	+	4.81075i	0.693622	+	0.185855i
$671$	−4.74665	−	22.0744i	−0.183242	−	0.852174i
$672$	2.13762	+	3.70247i	0.0824605	+	0.142826i
$673$	13.5885	−	23.5359i	0.523796	−	0.907242i	−0.475820	−	0.879543i	$-0.657849\pi$
$673$	13.5885	−	23.5359i	0.523796	−	0.907242i	0.999616	−	0.0276993i	$-0.00881808\pi$
$674$	−5.20131	+	1.39369i	−0.200347	+	0.0536828i
$675$			3.11344i			0.119836i
$676$	1.67505	−	1.54893i	0.0644252	−	0.0595742i
$677$			8.32855i			0.320092i	0.987110	+	0.160046i	$0.0511643\pi$
$677$			8.32855i			0.320092i	−0.987110	+	0.160046i	$0.948836\pi$
$678$	−8.42214	+	2.25670i	−0.323450	+	0.0866682i
$679$	−50.1966	−	28.9810i	−1.92637	−	1.11219i
$680$	1.92976	−	1.11415i	0.0740029	−	0.0427256i
$681$	16.9392	+	16.9392i	0.649111	+	0.649111i
$682$	−16.5418	−	18.2844i	−0.633418	−	0.700146i
$683$	12.9730	−	48.4160i	0.496399	−	1.85259i	−0.0256521	−	0.999671i	$-0.508166\pi$
$683$	12.9730	−	48.4160i	0.496399	−	1.85259i	0.522051	−	0.852914i	$-0.325167\pi$
$684$	0.0762929	−	0.0762929i	0.00291713	−	0.00291713i
$685$	3.14215	+	5.44237i	0.120055	+	0.207942i
$686$	−25.6510	−	14.8096i	−0.979361	−	0.565434i
$687$	13.1879	−	3.53369i	0.503150	−	0.134819i
$688$	17.3030			0.659670
$689$	−44.2040	+	4.94251i	−1.68404	+	0.188295i
$690$			4.48050i			0.170570i
$691$	3.30613	+	12.3387i	0.125771	+	0.469385i	0.999866	−	0.0163709i	$-0.00521124\pi$
$691$	3.30613	+	12.3387i	0.125771	+	0.469385i	−0.874095	+	0.485755i	$0.838545\pi$
$692$	−0.302772	−	0.174805i	−0.0115097	−	0.00664511i
$693$	−14.3052	−	0.715789i	−0.543409	−	0.0271906i
$694$	−34.3245	+	34.3245i	−1.30294	+	1.30294i
$695$	−4.51694	+	16.8574i	−0.171337	+	0.639439i
$696$	−3.81251	+	14.2285i	−0.144513	+	0.539330i
$697$	1.97954	+	1.97954i	0.0749803	+	0.0749803i
$698$	7.86854	+	13.6287i	0.297829	+	0.515855i
$699$	13.4623	−	23.3174i	0.509191	−	0.881944i
$700$	0.610720	+	2.27924i	0.0230831	+	0.0861471i
$701$	−16.6520			−0.628937			−0.314469	−	0.949268i	$-0.601826\pi$
$701$	−16.6520			−0.628937			−0.314469	+	0.949268i	$0.601826\pi$
$702$	−4.95207	+	1.93868i	−0.186904	+	0.0731709i
$703$			6.67398i			0.251714i
$704$	−22.6659	−	7.30539i	−0.854254	−	0.275332i
$705$	−1.11778	+	1.93605i	−0.0420979	+	0.0729158i
$706$	7.51331	+	13.0134i	0.282767	+	0.489767i
$707$	11.5036	−	11.5036i	0.432638	−	0.432638i
$708$	−1.55367	−	0.416305i	−0.0583905	−	0.0156457i
$709$	−7.79400	+	29.0876i	−0.292710	+	1.09241i	0.650309	+	0.759670i	$0.274639\pi$
$709$	−7.79400	+	29.0876i	−0.292710	+	1.09241i	−0.943019	+	0.332738i	$0.892027\pi$
$710$	11.0397	−	11.0397i	0.414313	−	0.414313i
$711$	−11.9137	+	6.87838i	−0.446799	+	0.257959i
$712$	9.79481	−	16.9651i	0.367076	−	0.635794i
$713$	−10.7675	+	2.88513i	−0.403245	+	0.108049i
$714$	−3.84000			−0.143709
$715$	9.06919	+	13.6941i	0.339169	+	0.512130i
$716$	3.71588			0.138869
$717$	−12.0148	+	3.21935i	−0.448701	+	0.120229i
$718$	10.5268	−	18.2330i	0.392857	−	0.680448i
$719$	−14.3703	+	8.29672i	−0.535923	+	0.309415i	−0.743425	−	0.668819i	$-0.766800\pi$
$719$	−14.3703	+	8.29672i	−0.535923	+	0.309415i	0.207502	+	0.978235i	$0.433467\pi$
$720$	−4.19589	+	4.19589i	−0.156372	+	0.156372i
$721$	4.25834	−	15.8923i	0.158589	−	0.591861i
$722$	−26.5308	−	7.10890i	−0.987373	−	0.264566i
$723$	15.1032	−	15.1032i	0.561692	−	0.561692i
$724$	1.34636	+	2.33196i	0.0500370	+	0.0866667i
$725$	−8.52120	+	14.7592i	−0.316470	+	0.548141i
$726$	−12.5604	+	10.2699i	−0.466160	+	0.381153i
$727$			21.4839i			0.796794i	0.917213	+	0.398397i	$0.130433\pi$
$727$			21.4839i			0.796794i	−0.917213	+	0.398397i	$0.869567\pi$
$728$	33.7355	−	24.8536i	1.25032	−	0.921136i
$729$	1.00000			0.0370370
$730$	6.29092	+	23.4780i	0.232837	+	0.868960i
$731$	−1.20726	+	2.09103i	−0.0446521	+	0.0773397i
$732$	0.597372	+	1.03468i	0.0220795	+	0.0382428i
$733$	−33.0243	−	33.0243i	−1.21978	−	1.21978i	−0.967709	−	0.252071i	$-0.918888\pi$
$733$	−33.0243	−	33.0243i	−1.21978	−	1.21978i	−0.252071	−	0.967709i	$-0.581112\pi$
$734$	−1.48760	+	5.55179i	−0.0549082	+	0.204920i
$735$	4.14151	−	15.4563i	0.152762	−	0.570116i
$736$	1.54816	−	1.54816i	0.0570661	−	0.0570661i
$737$	30.3917	+	1.52071i	1.11949	+	0.0560161i
$738$	−5.93165	−	3.42464i	−0.218347	−	0.126063i
$739$	3.84705	+	14.3574i	0.141516	+	0.528145i	0.999886	+	0.0151134i	$0.00481091\pi$
$739$	3.84705	+	14.3574i	0.141516	+	0.528145i	−0.858370	+	0.513031i	$0.828522\pi$
$740$			2.61670i			0.0961920i
$741$	−1.73190	−	1.38355i	−0.0636229	−	0.0508262i
$742$	78.5790			2.88473
$743$	−11.6396	+	3.11883i	−0.427017	+	0.114419i	−0.465925	−	0.884824i	$-0.654278\pi$
$743$	−11.6396	+	3.11883i	−0.427017	+	0.114419i	0.0389088	+	0.999243i	$0.487612\pi$
$744$	−11.7466	−	6.78192i	−0.430652	−	0.248637i
$745$	−9.24324	−	16.0098i	−0.338646	−	0.586552i
$746$	−4.57728	+	4.57728i	−0.167586	+	0.167586i
$747$	2.01365	−	7.51503i	0.0736755	−	0.274961i
$748$	−0.260209	+	0.235410i	−0.00951418	+	0.00860743i
$749$	39.5066	+	39.5066i	1.44354	+	1.44354i
$750$	−14.2348	+	8.21845i	−0.519780	+	0.300095i
$751$	−30.7140	−	17.7328i	−1.12077	−	0.647078i	−0.179173	−	0.983817i	$-0.557342\pi$
$751$	−30.7140	−	17.7328i	−1.12077	−	0.647078i	−0.941598	+	0.336740i	$0.890676\pi$
$752$	6.79198	−	1.81991i	0.247678	−	0.0663651i
$753$			11.8226i			0.430839i
$754$	−28.7811	−	4.36310i	−1.04815	−	0.158895i
$755$		−	1.19709i		−	0.0435664i
$756$	0.732066	−	0.196156i	0.0266250	−	0.00713414i
$757$	−19.0339	+	32.9677i	−0.691800	+	1.19823i	0.279447	+	0.960161i	$0.409849\pi$
$757$	−19.0339	+	32.9677i	−0.691800	+	1.19823i	−0.971247	+	0.238072i	$0.923485\pi$
$758$	19.8168	+	34.3237i	0.719777	+	1.24669i
$759$	1.54202	+	7.17121i	0.0559718	+	0.260298i
$760$	−2.19501	−	0.588151i	−0.0796213	−	0.0213345i
$761$	37.4519	+	10.0352i	1.35763	+	0.363776i	0.862946	−	0.505297i	$-0.168617\pi$
$761$	37.4519	+	10.0352i	1.35763	+	0.363776i	0.494684	+	0.869073i	$0.335284\pi$
$762$	−10.1266	−	10.1266i	−0.366848	−	0.366848i
$763$	−2.57567	−	4.46119i	−0.0932454	−	0.161506i
$764$	2.23853	+	1.29242i	0.0809872	+	0.0467580i
$765$	−0.214311	−	0.799820i	−0.00774844	−	0.0289176i
$766$	4.78277			0.172808
$767$	−4.95307	+	32.6728i	−0.178845	+	1.17975i
$768$	4.18042			0.150848
$769$	−2.21715	+	0.594083i	−0.0799524	+	0.0214232i	−0.298574	−	0.954387i	$-0.596511\pi$
$769$	−2.21715	+	0.594083i	−0.0799524	+	0.0214232i	0.218621	+	0.975810i	$0.429844\pi$
$770$	−13.2345	−	25.8230i	−0.476938	−	0.930597i
$771$	23.4522	−	13.5402i	0.844612	−	0.487637i
$772$	−1.39789	−	1.39789i	−0.0503111	−	0.0503111i
$773$	−18.3647	−	4.92081i	−0.660533	−	0.176989i	−0.0870466	−	0.996204i	$-0.527743\pi$
$773$	−18.3647	−	4.92081i	−0.660533	−	0.176989i	−0.573487	+	0.819215i	$0.694410\pi$
$774$	1.52895	−	5.70611i	0.0549569	−	0.205102i
$775$	−11.0964	−	11.0964i	−0.398596	−	0.398596i
$776$	−31.2794	+	18.0592i	−1.12286	+	0.648286i
$777$	−23.4402	+	40.5997i	−0.840914	+	1.45651i
$778$	12.2245	+	45.6226i	0.438271	+	1.63565i
$779$		−	2.85495i		−	0.102289i
$780$	−0.679035	−	0.542458i	−0.0243134	−	0.0194231i
$781$	13.8700	−	21.4689i	0.496309	−	0.768219i
$782$	0.508979	+	1.89953i	0.0182010	+	0.0679272i
$783$	4.74047	+	2.73691i	0.169411	+	0.0978093i
$784$	−43.5874	+	25.1652i	−1.55669	+	0.898756i
$785$	−4.73519	+	4.73519i	−0.169006	+	0.169006i
$786$	−10.9550	−	2.93539i	−0.390753	−	0.104702i
$787$	3.56021	+	0.953956i	0.126908	+	0.0340049i	0.321714	−	0.946837i	$-0.395741\pi$
$787$	3.56021	+	0.953956i	0.126908	+	0.0340049i	−0.194806	+	0.980842i	$0.562408\pi$
$788$	1.20901	−	1.20901i	0.0430693	−	0.0430693i
$789$	19.0763	−	11.0137i	0.679135	−	0.392099i
$790$	−24.1358	−	13.9348i	−0.858713	−	0.495778i
$791$	−6.60747	−	24.6594i	−0.234935	−	0.876788i
$792$	−4.84333	+	7.49682i	−0.172100	+	0.266388i
$793$	19.7620	−	14.5591i	0.701770	−	0.517008i
$794$			1.52696i			0.0541899i
$795$	4.38551	+	16.3669i	0.155538	+	0.580475i
$796$	−1.00979	+	1.74902i	−0.0357912	+	0.0619922i
$797$	−16.5030	+	9.52803i	−0.584567	+	0.337500i	−0.762946	−	0.646462i	$-0.776248\pi$
$797$	−16.5030	+	9.52803i	−0.584567	+	0.337500i	0.178379	+	0.983962i	$0.442915\pi$
$798$	2.76908	+	2.76908i	0.0980245	+	0.0980245i
$799$	−0.253956	+	0.947777i	−0.00898432	+	0.0335299i
$800$	2.97718	+	0.797732i	0.105259	+	0.0282041i
$801$	−5.14739	−	5.14739i	−0.181874	−	0.181874i
$802$	18.9174	−	10.9220i	0.667996	−	0.385668i
$803$	18.1491	+	35.4124i	0.640468	+	1.24968i
$804$	−1.55529	+	0.416739i	−0.0548509	+	0.0146972i
$805$	−13.1186			−0.462369
$806$	10.7398	−	24.5590i	0.378295	−	0.865052i
$807$	−2.18492			−0.0769130
$808$	−2.62379	−	9.79212i	−0.0923047	−	0.344486i
$809$	−2.52321	−	1.45678i	−0.0887115	−	0.0512176i	0.454988	−	0.890498i	$-0.349644\pi$
$809$	−2.52321	−	1.45678i	−0.0887115	−	0.0512176i	−0.543699	+	0.839280i	$0.682977\pi$
$810$	1.01294	+	1.75447i	0.0355912	+	0.0616457i
$811$	34.9996	+	34.9996i	1.22900	+	1.22900i	0.964342	+	0.264660i	$0.0852596\pi$
$811$	34.9996	+	34.9996i	1.22900	+	1.22900i	0.264660	+	0.964342i	$0.414740\pi$
$812$	4.00720	+	1.07373i	0.140625	+	0.0376804i
$813$	−1.73614	−	0.465197i	−0.0608891	−	0.0163152i
$814$	11.1637	+	51.9174i	0.391289	+	1.81970i
$815$	−12.8242	−	22.2121i	−0.449212	−	0.778057i
$816$	−1.30222	+	2.25552i	−0.0455870	+	0.0789590i
$817$	2.37845	−	0.637303i	0.0832114	−	0.0222964i
$818$		−	6.55122i		−	0.229058i
$819$	−5.67633	−	14.4993i	−0.198347	−	0.506647i
$820$		−	1.11936i		−	0.0390896i
$821$	−13.3514	+	3.57751i	−0.465968	+	0.124856i	−0.484161	−	0.874979i	$-0.660875\pi$
$821$	−13.3514	+	3.57751i	−0.465968	+	0.124856i	0.0181932	+	0.999834i	$0.494209\pi$
$822$	−5.84428	−	3.37420i	−0.203843	−	0.117689i
$823$	−4.05633	+	2.34192i	−0.141395	+	0.0816343i	−0.569029	−	0.822318i	$-0.692681\pi$
$823$	−4.05633	+	2.34192i	−0.141395	+	0.0816343i	0.427634	+	0.903952i	$0.359347\pi$
$824$	−7.24958	−	7.24958i	−0.252551	−	0.252551i
$825$	−7.65743	+	6.92763i	−0.266597	+	0.241189i
$826$	15.1100	−	56.3912i	0.525743	−	1.96210i
$827$	29.6021	−	29.6021i	1.02937	−	1.02937i	0.0298111	−	0.999556i	$-0.490509\pi$
$827$	29.6021	−	29.6021i	1.02937	−	1.02937i	0.999556	−	0.0298111i	$-0.00949057\pi$
$828$	−0.194065	−	0.336131i	−0.00674423	−	0.0116814i
$829$	7.28722	+	4.20728i	0.253095	+	0.146125i	0.621181	−	0.783667i	$-0.286653\pi$
$829$	7.28722	+	4.20728i	0.253095	+	0.146125i	−0.368085	+	0.929792i	$0.619987\pi$
$830$	15.2246	−	4.07942i	0.528453	−	0.141599i
$831$	11.8030			0.409440
$832$	−2.87673	−	25.7284i	−0.0997325	−	0.891970i
$833$		−	7.02328i		−	0.243342i
$834$	−4.85051	−	18.1023i	−0.167959	−	0.626833i
$835$	−13.4111	−	7.74292i	−0.464111	−	0.267955i
$836$	0.357398	+	0.0178831i	0.0123609	+	0.000618501i
$837$	−3.56405	+	3.56405i	−0.123191	+	0.123191i
$838$	−3.21341	+	11.9926i	−0.111006	+	0.414278i
$839$	−2.38103	+	8.88613i	−0.0822023	+	0.306783i	−0.994770	−	0.102143i	$-0.967430\pi$
$839$	−2.38103	+	8.88613i	−0.0822023	+	0.306783i	0.912567	+	0.408926i	$0.134097\pi$
$840$	−11.2872	−	11.2872i	−0.389444	−	0.389444i
$841$	0.481394	+	0.833798i	0.0165998	+	0.0287517i
$842$	−23.1800	+	40.1490i	−0.798836	+	1.38362i
$843$	2.65281	+	9.90041i	0.0913675	+	0.340988i
$844$	−2.33864			−0.0804992
$845$	−9.52557	+	15.1027i	−0.327689	+	0.519550i
$846$		−	2.40065i		−	0.0825360i
$847$	−30.0696	−	36.7759i	−1.03321	−	1.26364i
$848$	26.6478	−	46.1553i	0.915088	−	1.58498i
$849$	−1.44242	−	2.49835i	−0.0495038	−	0.0857431i
$850$	−1.95757	+	1.95757i	−0.0671440	+	0.0671440i
$851$	23.1904	+	6.21384i	0.794955	+	0.213008i
$852$	−0.350042	+	1.30638i	−0.0119923	+	0.0447557i
$853$	6.31748	−	6.31748i	0.216306	−	0.216306i	−0.590634	−	0.806940i	$-0.701122\pi$
$853$	6.31748	−	6.31748i	0.216306	−	0.216306i	0.806940	+	0.590634i	$0.201122\pi$
$854$	−37.5541	+	21.6819i	−1.28508	+	0.741939i
$855$	−0.422219	+	0.731306i	−0.0144396	+	0.0250101i
$856$	33.6289	−	9.01083i	1.14941	−	0.307984i
$857$	11.5493			0.394516			0.197258	−	0.980352i	$-0.436796\pi$
$857$	11.5493			0.394516			0.197258	+	0.980352i	$0.436796\pi$
$858$	−15.7869	−	7.86578i	−0.538955	−	0.268533i
$859$	−20.0351			−0.683589			−0.341795	−	0.939775i	$-0.611035\pi$
$859$	−20.0351			−0.683589			−0.341795	+	0.939775i	$0.611035\pi$
$860$	0.932532	−	0.249871i	0.0317991	−	0.00852054i
$861$	10.0271	−	17.3675i	0.341723	−	0.591882i
$862$	43.1651	−	24.9214i	1.47021	−	0.848826i
$863$	3.11411	−	3.11411i	0.106005	−	0.106005i	−0.652115	−	0.758120i	$-0.726118\pi$
$863$	3.11411	−	3.11411i	0.106005	−	0.106005i	0.758120	+	0.652115i	$0.226118\pi$
$864$	0.256222	−	0.956235i	0.00871686	−	0.0325318i
$865$	2.64301	+	0.708191i	0.0898649	+	0.0240792i
$866$	−18.2862	+	18.2862i	−0.621392	+	0.621392i
$867$	8.31828	+	14.4077i	0.282504	+	0.489311i
$868$	−1.91001	+	3.30823i	−0.0648298	+	0.112289i
$869$	−43.4261	−	13.9966i	−1.47313	−	0.474801i
$870$			11.0893i			0.375964i
$871$	12.0595	+	30.8041i	0.408620	+	1.04376i
$872$	−3.20999			−0.108704
$873$	3.47376	+	12.9643i	0.117569	+	0.438773i
$874$	1.00275	−	1.73681i	0.0339185	−	0.0587486i
$875$	−24.0630	−	41.6784i	−0.813479	−	1.40899i
$876$	−1.48886	−	1.48886i	−0.0503040	−	0.0503040i
$877$	−0.305217	+	1.13909i	−0.0103065	+	0.0384642i	−0.970888	−	0.239536i	$-0.923005\pi$
$877$	−0.305217	+	1.13909i	−0.0103065	+	0.0384642i	0.960581	+	0.278000i	$0.0896715\pi$
$878$	−13.5646	+	50.6236i	−0.457782	+	1.70846i
$879$	16.2863	−	16.2863i	0.549323	−	0.549323i
$880$	−19.6559	−	0.983522i	−0.662599	−	0.0331545i
$881$	19.5851	+	11.3075i	0.659840	+	0.380959i	0.792216	−	0.610241i	$-0.208927\pi$
$881$	19.5851	+	11.3075i	0.659840	+	0.380959i	−0.132376	+	0.991200i	$0.542261\pi$
$882$	4.44736	+	16.5978i	0.149750	+	0.558876i
$883$		−	1.17978i		−	0.0397027i	−0.999803	−	0.0198514i	$-0.993681\pi$
$883$		−	1.17978i		−	0.0397027i	0.999803	−	0.0198514i	$-0.00631930\pi$
$884$	−0.349504	−	0.152841i	−0.0117551	−	0.00514060i
$885$	12.5888			0.423168
$886$	22.2282	−	5.95603i	0.746771	−	0.200097i
$887$	32.5378	+	18.7857i	1.09251	+	0.630762i	0.934244	−	0.356634i	$-0.116076\pi$
$887$	32.5378	+	18.7857i	1.09251	+	0.630762i	0.158268	+	0.987396i	$0.449409\pi$
$888$	14.6065	+	25.2992i	0.490162	+	0.848986i
$889$	29.6500	−	29.6500i	0.994429	−	0.994429i
$890$	3.81692	−	14.2449i	0.127944	−	0.477492i
$891$	2.22508	+	2.45948i	0.0745429	+	0.0823956i
$892$	−2.85284	−	2.85284i	−0.0955203	−	0.0955203i
$893$	0.866588	−	0.500325i	0.0289993	−	0.0167427i
$894$	17.1921	+	9.92585i	0.574989	+	0.331970i
$895$	−28.0915	+	7.52710i	−0.938996	+	0.251603i
$896$			54.2864i			1.81358i
$897$	−6.41999	+	4.72974i	−0.214357	+	0.157921i
$898$			38.9119i			1.29851i
$899$	−26.6498	+	7.14078i	−0.888819	+	0.238158i
$900$	0.273197	−	0.473192i	0.00910658	−	0.0157731i
$901$	3.71852	+	6.44067i	0.123882	+	0.214570i
$902$	−4.77555	−	22.2089i	−0.159009	−	0.739474i
$903$	16.7071	+	4.47665i	0.555977	+	0.148974i
$904$	−15.3662	−	4.11737i	−0.511073	−	0.136942i
$905$	−14.9020	−	14.9020i	−0.495360	−	0.495360i
$906$	0.642745	+	1.11327i	0.0213538	+	0.0369858i
$907$	6.15366	+	3.55282i	0.204329	+	0.117969i	0.598673	−	0.800994i	$-0.295695\pi$
$907$	6.15366	+	3.55282i	0.204329	+	0.117969i	−0.394344	+	0.918963i	$0.629028\pi$
$908$	−1.08810	−	4.06086i	−0.0361100	−	0.134764i
$909$	−3.76712			−0.124947
$910$	19.6888	−	24.6459i	0.652676	−	0.817004i
$911$	−12.7493			−0.422402			−0.211201	−	0.977443i	$-0.567737\pi$
$911$	−12.7493			−0.422402			−0.211201	+	0.977443i	$0.567737\pi$
$912$	2.56554	−	0.687435i	0.0849536	−	0.0227633i
$913$	22.9636	−	11.7690i	0.759983	−	0.389497i
$914$	3.72685	−	2.15170i	0.123273	−	0.0711718i
$915$	−6.61194	−	6.61194i	−0.218584	−	0.218584i
$916$	−2.31442	−	0.620147i	−0.0764706	−	0.0204902i
$917$	8.59463	−	32.0756i	0.283820	−	1.05923i
$918$	0.628748	+	0.628748i	0.0207518	+	0.0207518i
$919$	−7.72958	+	4.46267i	−0.254975	+	0.147210i	−0.622040	−	0.782985i	$-0.713696\pi$
$919$	−7.72958	+	4.46267i	−0.254975	+	0.147210i	0.367065	+	0.930195i	$0.380363\pi$
$920$	−4.08734	+	7.07949i	−0.134756	+	0.233404i
$921$	−6.57368	−	24.5333i	−0.216610	−	0.808400i
$922$		−	39.3744i		−	1.29673i
$923$	27.4723	+	4.16469i	0.904263	+	0.137083i
$924$	2.11134	+	1.36404i	0.0694581	+	0.0448735i
$925$	8.74759	+	32.6465i	0.287619	+	1.07341i
$926$	−23.4879	−	13.5607i	−0.771860	−	0.445633i
$927$	−3.29940	+	1.90491i	−0.108366	+	0.0625654i
$928$	3.83175	−	3.83175i	0.125783	−	0.125783i
$929$	8.33769	+	2.23408i	0.273551	+	0.0732977i	0.392986	−	0.919544i	$-0.371442\pi$
$929$	8.33769	+	2.23408i	0.273551	+	0.0732977i	−0.119436	+	0.992842i	$0.538109\pi$
$930$	−9.86318	−	2.64283i	−0.323427	−	0.0866619i
$931$	−5.06459	+	5.06459i	−0.165985	+	0.165985i
$932$	−4.09210	+	2.36258i	−0.134041	+	0.0773887i
$933$	−15.2774	−	8.82041i	−0.500160	−	0.288767i
$934$	14.2257	+	53.0911i	0.465479	+	1.73719i
$935$	1.49028	−	2.30676i	0.0487374	−	0.0754390i
$936$	−9.59316	−	1.45428i	−0.313562	−	0.0475348i
$937$		−	29.3584i		−	0.959098i	−0.877515	−	0.479549i	$-0.840800\pi$
$937$		−	29.3584i		−	0.959098i	0.877515	−	0.479549i	$-0.159200\pi$
$938$	−15.1257	−	56.4500i	−0.493873	−	1.84316i
$939$	14.9542	−	25.9014i	0.488011	−	0.845259i
$940$	0.339768	−	0.196165i	0.0110820	−	0.00639820i
$941$	−35.6549	−	35.6549i	−1.16232	−	1.16232i	−0.983967	−	0.178349i	$-0.942924\pi$
$941$	−35.6549	−	35.6549i	−1.16232	−	1.16232i	−0.178349	−	0.983967i	$-0.557076\pi$
$942$	1.86119	−	6.94607i	0.0606410	−	0.226315i
$943$	−9.92022	−	2.65811i	−0.323047	−	0.0865601i
$944$	−27.9986	−	27.9986i	−0.911278	−	0.911278i
$945$	−5.13696	+	2.96583i	−0.167105	+	0.0964783i
$946$	17.4361	−	8.93613i	0.566896	−	0.290539i
$947$	0.222822	−	0.0597050i	0.00724074	−	0.00194015i	−0.255197	−	0.966889i	$-0.582140\pi$
$947$	0.222822	−	0.0597050i	0.00724074	−	0.00194015i	0.262438	+	0.964949i	$0.415474\pi$
$948$	2.41425			0.0784112
$949$	−27.0002	+	33.7981i	−0.876463	+	1.09713i
$950$	2.82326			0.0915988
$951$	2.27968	+	8.50787i	0.0739236	+	0.275887i
$952$	−6.06746	−	3.50305i	−0.196648	−	0.113535i
$953$	−25.0444	−	43.3781i	−0.811266	−	1.40515i	−0.911978	−	0.410239i	$-0.865445\pi$
$953$	−25.0444	−	43.3781i	−0.811266	−	1.40515i	0.100712	−	0.994916i	$-0.467888\pi$
$954$	−12.8662	−	12.8662i	−0.416560	−	0.416560i
$955$	−19.5410	−	5.23598i	−0.632330	−	0.169432i
$956$	2.10854	+	0.564983i	0.0681952	+	0.0182729i
$957$	3.81654	+	17.7489i	0.123371	+	0.573742i
$958$	4.67169	+	8.09161i	0.150936	+	0.261428i
$959$	9.87941	−	17.1116i	0.319023	−	0.552564i
$960$	−9.52616	+	2.55253i	−0.307455	+	0.0823824i
$961$			5.59514i			0.180488i
$962$	−46.4787	+	34.2418i	−1.49854	+	1.10400i
$963$		−	12.9373i		−	0.416899i
$964$	−3.62070	+	0.970164i	−0.116615	+	0.0312469i
$965$	13.3995	+	7.73619i	0.431344	+	0.249037i
$966$	12.2000	−	7.04369i	0.392529	−	0.226627i
$967$	10.6077	+	10.6077i	0.341121	+	0.341121i	0.856789	−	0.515667i	$-0.172456\pi$
$967$	10.6077	+	10.6077i	0.341121	+	0.341121i	−0.515667	+	0.856789i	$0.672456\pi$
$968$	−29.2150	+	4.76894i	−0.939007	+	0.153280i
$969$	−0.0959271	+	0.358005i	−0.00308162	+	0.0115008i
$970$	−19.2267	+	19.2267i	−0.617331	+	0.617331i
$971$	−20.4936	−	35.4960i	−0.657671	−	1.13912i	−0.981217	−	0.192908i	$-0.938208\pi$
$971$	−20.4936	−	35.4960i	−0.657671	−	1.13912i	0.323546	−	0.946213i	$-0.395125\pi$
$972$	−0.151984	−	0.0877479i	−0.00487488	−	0.00281451i
$973$	53.0024	−	14.2019i	1.69918	−	0.455293i
$974$	−35.0950			−1.12452
$975$	−10.2852	−	4.49780i	−0.329390	−	0.144045i
$976$			29.4111i			0.941427i
$977$	11.0371	+	41.1909i	0.353107	+	1.31781i	0.882850	+	0.469655i	$0.155622\pi$
$977$	11.0371	+	41.1909i	0.353107	+	1.31781i	−0.529743	+	0.848158i	$0.677712\pi$
$978$	23.8525	+	13.7712i	0.762719	+	0.440356i
$979$	1.20655	−	24.1132i	0.0385617	−	0.770662i
$980$	−1.98570	+	1.98570i	−0.0634310	+	0.0634310i
$981$	−0.308728	+	1.15219i	−0.00985693	+	0.0367866i
$982$	−1.81986	+	6.79182i	−0.0580742	+	0.216736i
$983$	9.76556	+	9.76556i	0.311473	+	0.311473i	0.845480	−	0.534007i	$-0.179314\pi$
$983$	9.76556	+	9.76556i	0.311473	+	0.311473i	−0.534007	+	0.845480i	$0.679314\pi$
$984$	−6.24827	−	10.8223i	−0.199188	−	0.345003i
$985$	−6.69091	+	11.5890i	−0.213190	+	0.369256i
$986$	1.25974	+	4.70140i	0.0401181	+	0.149723i
$987$	7.02893			0.223733
$988$	0.141816	+	0.362248i	0.00451178	+	0.0115246i
$989$		−	8.85786i		−	0.281664i
$990$	−2.06120	+	6.39514i	−0.0655093	+	0.203251i
$991$	3.52517	−	6.10578i	0.111981	−	0.193956i	−0.804588	−	0.593833i	$-0.797614\pi$
$991$	3.52517	−	6.10578i	0.111981	−	0.193956i	0.916569	+	0.399877i	$0.130947\pi$
$992$	2.49488	+	4.32125i	0.0792124	+	0.137200i
$993$	−13.2627	+	13.2627i	−0.420879	+	0.420879i
$994$	−47.4155	−	12.7049i	−1.50393	−	0.402976i
$995$	4.09099	−	15.2678i	0.129693	−	0.484022i
$996$	−0.965469	+	0.965469i	−0.0305921	+	0.0305921i
$997$	4.82924	−	2.78816i	0.152943	−	0.0883020i	−0.421575	−	0.906793i	$-0.638523\pi$
$997$	4.82924	−	2.78816i	0.152943	−	0.0883020i	0.574519	+	0.818492i	$0.305189\pi$
$998$	31.6259	−	54.7776i	1.00110	−	1.73395i
$999$	10.4857	−	2.80963i	0.331752	−	0.0888927i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bd.a.175.5	yes	56
11.10	odd	2	inner	429.2.bd.a.175.10	yes	56
13.11	odd	12	inner	429.2.bd.a.76.10	yes	56
143.76	even	12	inner	429.2.bd.a.76.5	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bd.a.76.5	✓	56	143.76	even	12	inner
429.2.bd.a.76.10	yes	56	13.11	odd	12	inner
429.2.bd.a.175.5	yes	56	1.1	even	1	trivial
429.2.bd.a.175.10	yes	56	11.10	odd	2	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.42470 + 0.381747i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.151984 - 0.0877479i) q^{4} +(-0.971227 + 0.971227i) q^{5} +(0.381747 - 1.42470i) q^{6} +(4.17142 + 1.11773i) q^{7} +(1.90287 - 1.90287i) q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.42470 + 0.381747i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.151984 - 0.0877479i) q^{4} +(-0.971227 + 0.971227i) q^{5} +(0.381747 - 1.42470i) q^{6} +(4.17142 + 1.11773i) q^{7} +(1.90287 - 1.90287i) q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.01294 - 1.75447i) q^{10} +(1.01743 - 3.15671i) q^{11} +0.175496i q^{12} +(3.58322 - 0.400646i) q^{13} -6.36970 q^{14} +(-0.355494 - 1.32672i) q^{15} +(-2.16010 + 3.74140i) q^{16} +(-0.301427 - 0.522088i) q^{17} +(1.04295 + 1.04295i) q^{18} +(-0.159121 + 0.593849i) q^{19} +(-0.0623876 + 0.232834i) q^{20} +(-3.05369 + 3.05369i) q^{21} +(-0.244469 + 4.88576i) q^{22} +(1.91532 + 1.10581i) q^{23} +(0.696499 + 2.59937i) q^{24} +3.11344i q^{25} +(-4.95207 + 1.93868i) q^{26} +1.00000 q^{27} +(0.732066 - 0.196156i) q^{28} +(4.74047 + 2.73691i) q^{29} +(1.01294 + 1.75447i) q^{30} +(-3.56405 + 3.56405i) q^{31} +(0.256222 - 0.956235i) q^{32} +(2.22508 + 2.45948i) q^{33} +(0.628748 + 0.628748i) q^{34} +(-5.13696 + 2.96583i) q^{35} +(-0.151984 - 0.0877479i) q^{36} +(10.4857 - 2.80963i) q^{37} -0.906800i q^{38} +(-1.44464 + 3.30348i) q^{39} +3.69624i q^{40} +(-4.48549 + 1.20188i) q^{41} +(3.18485 - 5.51632i) q^{42} +(-2.00257 - 3.46855i) q^{43} +(-0.122362 - 0.569046i) q^{44} +(1.32672 + 0.355494i) q^{45} +(-3.15090 - 0.844280i) q^{46} +(-1.15089 - 1.15089i) q^{47} +(-2.16010 - 3.74140i) q^{48} +(10.0892 + 5.82501i) q^{49} +(-1.18854 - 4.43571i) q^{50} +0.602855 q^{51} +(0.509436 - 0.375312i) q^{52} -12.3364 q^{53} +(-1.42470 + 0.381747i) q^{54} +(2.07773 + 4.05404i) q^{55} +(10.0646 - 5.81077i) q^{56} +(-0.434728 - 0.434728i) q^{57} +(-7.79855 - 2.08962i) q^{58} +(-2.37217 + 8.85304i) q^{59} +(-0.170446 - 0.170446i) q^{60} +(5.89575 - 3.40391i) q^{61} +(3.71713 - 6.43826i) q^{62} +(-1.11773 - 4.17142i) q^{63} -7.18023i q^{64} +(-3.09101 + 3.86924i) q^{65} +(-4.10896 - 2.65460i) q^{66} +(2.37464 + 8.86227i) q^{67} +(-0.0916241 - 0.0528992i) q^{68} +(-1.91532 + 1.10581i) q^{69} +(6.18642 - 6.18642i) q^{70} +(7.44392 + 1.99459i) q^{71} +(-2.59937 - 0.696499i) q^{72} +(-8.48375 + 8.48375i) q^{73} +(-13.8663 + 8.00574i) q^{74} +(-2.69631 - 1.55672i) q^{75} +(0.0279251 + 0.104218i) q^{76} +(7.77248 - 12.0307i) q^{77} +(0.797085 - 5.25796i) q^{78} -13.7568i q^{79} +(-1.53580 - 5.73169i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(5.93165 - 3.42464i) q^{82} +(5.50139 + 5.50139i) q^{83} +(-0.196156 + 0.732066i) q^{84} +(0.799820 + 0.214311i) q^{85} +(4.17717 + 4.17717i) q^{86} +(-4.74047 + 2.73691i) q^{87} +(-4.07077 - 7.94285i) q^{88} +(7.03147 - 1.88408i) q^{89} -2.02589 q^{90} +(15.3949 + 2.33381i) q^{91} +0.388131 q^{92} +(-1.30453 - 4.86858i) q^{93} +(2.07902 + 1.20032i) q^{94} +(-0.422219 - 0.731306i) q^{95} +(0.700012 + 0.700012i) q^{96} +(-12.9643 - 3.47376i) q^{97} +(-16.5978 - 4.44736i) q^{98} +(-3.24251 + 0.697234i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 28 q^{3} + 4 q^{5} - 28 q^{9}+O(q^{10}) \) 56 * q - 28 * q^3 + 4 * q^5 - 28 * q^9	\( 56 q - 28 q^{3} + 4 q^{5} - 28 q^{9} - 12 q^{11} + 24 q^{14} - 8 q^{15} + 68 q^{16} - 8 q^{20} - 10 q^{22} - 12 q^{23} - 48 q^{26} + 56 q^{27} + 4 q^{31} + 12 q^{33} + 32 q^{34} + 36 q^{37} - 12 q^{42} + 24 q^{44} + 4 q^{45} - 8 q^{47} + 68 q^{48} - 24 q^{49} - 56 q^{53} - 2 q^{55} + 72 q^{56} - 88 q^{58} + 56 q^{59} - 44 q^{60} + 20 q^{66} + 92 q^{67} + 12 q^{69} - 216 q^{70} + 72 q^{71} - 12 q^{75} - 12 q^{78} + 44 q^{80} - 28 q^{81} - 156 q^{82} - 120 q^{86} - 6 q^{88} - 56 q^{89} + 92 q^{91} + 32 q^{92} - 20 q^{93} - 44 q^{97}+O(q^{100}) \) 56 * q - 28 * q^3 + 4 * q^5 - 28 * q^9 - 12 * q^11 + 24 * q^14 - 8 * q^15 + 68 * q^16 - 8 * q^20 - 10 * q^22 - 12 * q^23 - 48 * q^26 + 56 * q^27 + 4 * q^31 + 12 * q^33 + 32 * q^34 + 36 * q^37 - 12 * q^42 + 24 * q^44 + 4 * q^45 - 8 * q^47 + 68 * q^48 - 24 * q^49 - 56 * q^53 - 2 * q^55 + 72 * q^56 - 88 * q^58 + 56 * q^59 - 44 * q^60 + 20 * q^66 + 92 * q^67 + 12 * q^69 - 216 * q^70 + 72 * q^71 - 12 * q^75 - 12 * q^78 + 44 * q^80 - 28 * q^81 - 156 * q^82 - 120 * q^86 - 6 * q^88 - 56 * q^89 + 92 * q^91 + 32 * q^92 - 20 * q^93 - 44 * q^97

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