LMFDB - Embedded newform 500.2.l.f.343.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [500,2,Mod(7,500)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(500, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 17]))

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

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

chi := DirichletCharacter("500.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 500 = 2^{2} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	500.l (of order $20$, degree $8$, not 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:	$3.99252010106$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 100)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			343.12
Character	$\chi$	$=$	500.343
Dual form			500.2.l.f.207.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.41083 + 0.0976968i) q^{2} +(-0.0867473 - 0.170251i) q^{3} +(1.98091 + 0.275668i) q^{4} +(-0.105753 - 0.248671i) q^{6} +(-1.89427 - 1.89427i) q^{7} +(2.76781 + 0.582451i) q^{8} +(1.74190 - 2.39751i) q^{9} +(2.99934 + 4.12824i) q^{11} +(-0.124906 - 0.361166i) q^{12} +(-0.433317 - 2.73586i) q^{13} +(-2.48743 - 2.85756i) q^{14} +(3.84801 + 1.09215i) q^{16} +(4.16697 + 2.12318i) q^{17} +(2.69176 - 3.21232i) q^{18} +(-1.55045 - 4.77181i) q^{19} +(-0.158179 + 0.486824i) q^{21} +(3.82826 + 6.11729i) q^{22} +(-0.699923 + 4.41914i) q^{23} +(-0.140937 - 0.521748i) q^{24} +(-0.344055 - 3.90218i) q^{26} +(-1.12546 - 0.178255i) q^{27} +(-3.23018 - 4.27456i) q^{28} +(-0.211843 - 0.0688321i) q^{29} +(-7.01920 + 2.28068i) q^{31} +(5.32221 + 1.91678i) q^{32} +(0.442653 - 0.868756i) q^{33} +(5.67148 + 3.40256i) q^{34} +(4.11146 - 4.26907i) q^{36} +(-4.32186 + 0.684516i) q^{37} +(-1.72125 - 6.88371i) q^{38} +(-0.428194 + 0.311101i) q^{39} +(2.54404 + 1.84835i) q^{41} +(-0.270725 + 0.671374i) q^{42} +(-2.68807 + 2.68807i) q^{43} +(4.80341 + 9.00450i) q^{44} +(-1.41921 + 6.16630i) q^{46} +(-7.84709 + 3.99829i) q^{47} +(-0.147866 - 0.749870i) q^{48} +0.176489i q^{49} -0.893612i q^{51} +(-0.104174 - 5.53894i) q^{52} +(-1.64295 + 0.837124i) q^{53} +(-1.57042 - 0.361442i) q^{54} +(-4.13965 - 6.34628i) q^{56} +(-0.677908 + 0.677908i) q^{57} +(-0.292151 - 0.117807i) q^{58} +(-7.33328 - 5.32794i) q^{59} +(1.16375 - 0.845512i) q^{61} +(-10.1258 + 2.53191i) q^{62} +(-7.84114 + 1.24191i) q^{63} +(7.32150 + 3.22422i) q^{64} +(0.709385 - 1.18243i) q^{66} +(1.53527 - 3.01313i) q^{67} +(7.66911 + 5.35453i) q^{68} +(0.813081 - 0.264186i) q^{69} +(5.45415 + 1.77216i) q^{71} +(6.21766 - 5.62128i) q^{72} +(0.0187149 + 0.00296414i) q^{73} +(-6.16431 + 0.543507i) q^{74} +(-1.75588 - 9.87994i) q^{76} +(2.13843 - 13.5015i) q^{77} +(-0.634505 + 0.397079i) q^{78} +(-2.08434 + 6.41493i) q^{79} +(-2.68002 - 8.24826i) q^{81} +(3.40864 + 2.85627i) q^{82} +(2.99552 + 1.52629i) q^{83} +(-0.447539 + 0.920749i) q^{84} +(-4.05504 + 3.52981i) q^{86} +(0.00665810 + 0.0420376i) q^{87} +(5.89710 + 13.1731i) q^{88} +(-0.509284 - 0.700969i) q^{89} +(-4.36162 + 6.00326i) q^{91} +(-2.60470 + 8.56098i) q^{92} +(0.997185 + 0.997185i) q^{93} +(-11.4616 + 4.87429i) q^{94} +(-0.135354 - 1.07239i) q^{96} +(5.07638 + 9.96296i) q^{97} +(-0.0172424 + 0.248997i) q^{98} +15.1221 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 10 q^{2} - 10 q^{4} - 6 q^{6} + 10 q^{8} - 20 q^{9} + 10 q^{12} + 20 q^{13} - 10 q^{14} - 14 q^{16} + 20 q^{17} - 20 q^{18} - 12 q^{21} + 10 q^{22} - 12 q^{26} + 10 q^{28} - 20 q^{29} + 50 q^{32}+ \cdots + 130 q^{98}+O(q^{100}) $ 96 * q + 10 * q^2 - 10 * q^4 - 6 * q^6 + 10 * q^8 - 20 * q^9 + 10 * q^12 + 20 * q^13 - 10 * q^14 - 14 * q^16 + 20 * q^17 - 20 * q^18 - 12 * q^21 + 10 * q^22 - 12 * q^26 + 10 * q^28 - 20 * q^29 + 50 * q^32 + 20 * q^33 - 60 * q^34 - 10 * q^36 - 40 * q^37 - 20 * q^38 - 28 * q^41 - 90 * q^42 + 60 * q^44 - 6 * q^46 - 120 * q^48 - 80 * q^52 + 40 * q^53 + 120 * q^54 - 6 * q^56 + 20 * q^57 - 60 * q^58 + 12 * q^61 - 40 * q^62 + 20 * q^64 - 30 * q^66 + 10 * q^68 - 20 * q^69 + 40 * q^72 + 20 * q^73 + 20 * q^77 - 20 * q^78 - 36 * q^81 + 50 * q^82 - 90 * q^84 - 6 * q^86 + 130 * q^88 + 160 * q^89 + 110 * q^92 - 60 * q^93 - 170 * q^94 + 14 * q^96 - 180 * q^97 + 130 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/500\mathbb{Z}\right)^\times$.

$n$	$251$	$377$
$\chi(n)$	$-1$	$e\left(\frac{11}{20}\right)$

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 $

$2$	1.41083	+	0.0976968i	0.997611	+	0.0690820i
$2$	1.41083	+	0.0976968i	0.997611	+	0.0690820i
$3$	−0.0867473	−	0.170251i	−0.0500836	−	0.0982946i	0.864608	−	0.502447i	$-0.167567\pi$
$3$	−0.0867473	−	0.170251i	−0.0500836	−	0.0982946i	−0.914692	+	0.404152i	$0.867567\pi$
$4$	1.98091	+	0.275668i	0.990455	+	0.137834i
$5$		0			0
$5$		0			0
$6$	−0.105753	−	0.248671i	−0.0431735	−	0.101520i
$7$	−1.89427	−	1.89427i	−0.715965	−	0.715965i	0.251811	−	0.967776i	$-0.418974\pi$
$7$	−1.89427	−	1.89427i	−0.715965	−	0.715965i	−0.967776	+	0.251811i	$0.918974\pi$
$8$	2.76781	+	0.582451i	0.978567	+	0.205927i
$9$	1.74190	−	2.39751i	0.580632	−	0.799171i
$10$		0			0
$11$	2.99934	+	4.12824i	0.904336	+	1.24471i	0.969064	+	0.246809i	$0.0793819\pi$
$11$	2.99934	+	4.12824i	0.904336	+	1.24471i	−0.0647283	+	0.997903i	$0.520618\pi$
$12$	−0.124906	−	0.361166i	−0.0360572	−	0.104260i
$13$	−0.433317	−	2.73586i	−0.120181	−	0.758790i	−0.972005	−	0.234962i	$-0.924503\pi$
$13$	−0.433317	−	2.73586i	−0.120181	−	0.758790i	0.851824	−	0.523828i	$-0.175497\pi$
$14$	−2.48743	−	2.85756i	−0.664795	−	0.763715i
$15$		0			0
$16$	3.84801	+	1.09215i	0.962004	+	0.273037i
$17$	4.16697	+	2.12318i	1.01064	+	0.514947i	0.879238	−	0.476383i	$-0.158052\pi$
$17$	4.16697	+	2.12318i	1.01064	+	0.514947i	0.131402	+	0.991329i	$0.458052\pi$
$18$	2.69176	−	3.21232i	0.634453	−	0.757151i
$19$	−1.55045	−	4.77181i	−0.355699	−	1.09473i	−0.955603	−	0.294657i	$-0.904795\pi$
$19$	−1.55045	−	4.77181i	−0.355699	−	1.09473i	0.599905	−	0.800072i	$-0.295205\pi$
$20$		0			0
$21$	−0.158179	+	0.486824i	−0.0345174	+	0.106234i
$22$	3.82826	+	6.11729i	0.816188	+	1.30421i
$23$	−0.699923	+	4.41914i	−0.145944	+	0.921455i	0.800675	+	0.599100i	$0.204475\pi$
$23$	−0.699923	+	4.41914i	−0.145944	+	0.921455i	−0.946619	+	0.322355i	$0.895525\pi$
$24$	−0.140937	−	0.521748i	−0.0287686	−	0.106501i
$25$		0			0
$26$	−0.344055	−	3.90218i	−0.0674747	−	0.765280i
$27$	−1.12546	−	0.178255i	−0.216595	−	0.0343052i
$28$	−3.23018	−	4.27456i	−0.610447	−	0.807816i
$29$	−0.211843	−	0.0688321i	−0.0393383	−	0.0127818i	0.289282	−	0.957244i	$-0.406584\pi$
$29$	−0.211843	−	0.0688321i	−0.0393383	−	0.0127818i	−0.328620	+	0.944462i	$0.606584\pi$
$30$		0			0
$31$	−7.01920	+	2.28068i	−1.26069	+	0.409622i	−0.861739	−	0.507352i	$-0.830624\pi$
$31$	−7.01920	+	2.28068i	−1.26069	+	0.409622i	−0.398947	+	0.916974i	$0.630624\pi$
$32$	5.32221	+	1.91678i	0.940843	+	0.338842i
$33$	0.442653	−	0.868756i	0.0770560	−	0.151231i
$34$	5.67148	+	3.40256i	0.972652	+	0.583533i
$35$		0			0
$36$	4.11146	−	4.26907i	0.685243	−	0.711512i
$37$	−4.32186	+	0.684516i	−0.710510	+	0.112534i	−0.501220	−	0.865320i	$-0.667115\pi$
$37$	−4.32186	+	0.684516i	−0.710510	+	0.112534i	−0.209290	+	0.977854i	$0.567115\pi$
$38$	−1.72125	−	6.88371i	−0.279223	−	1.11669i
$39$	−0.428194	+	0.311101i	−0.0685659	+	0.0498160i
$40$		0			0
$41$	2.54404	+	1.84835i	0.397312	+	0.288664i	0.768445	−	0.639915i	$-0.221031\pi$
$41$	2.54404	+	1.84835i	0.397312	+	0.288664i	−0.371133	+	0.928580i	$0.621031\pi$
$42$	−0.270725	+	0.671374i	−0.0417738	+	0.103595i
$43$	−2.68807	+	2.68807i	−0.409927	+	0.409927i	−0.881713	−	0.471786i	$-0.843609\pi$
$43$	−2.68807	+	2.68807i	−0.409927	+	0.409927i	0.471786	+	0.881713i	$0.343609\pi$
$44$	4.80341	+	9.00450i	0.724141	+	1.35748i
$45$		0			0
$46$	−1.41921	+	6.16630i	−0.209251	+	0.909171i
$47$	−7.84709	+	3.99829i	−1.14462	+	0.583211i	−0.920264	−	0.391298i	$-0.872026\pi$
$47$	−7.84709	+	3.99829i	−1.14462	+	0.583211i	−0.224351	+	0.974508i	$0.572026\pi$
$48$	−0.147866	−	0.749870i	−0.0213425	−	0.108234i
$49$			0.176489i			0.0252127i
$50$		0			0
$51$		−	0.893612i		−	0.125131i
$52$	−0.104174	−	5.53894i	−0.0144464	−	0.768113i
$53$	−1.64295	+	0.837124i	−0.225676	+	0.114988i	−0.563173	−	0.826339i	$-0.690420\pi$
$53$	−1.64295	+	0.837124i	−0.225676	+	0.114988i	0.337497	+	0.941327i	$0.390420\pi$
$54$	−1.57042	−	0.361442i	−0.213707	−	0.0491861i
$55$		0			0
$56$	−4.13965	−	6.34628i	−0.553183	−	0.848057i
$57$	−0.677908	+	0.677908i	−0.0897912	+	0.0897912i
$58$	−0.292151	−	0.117807i	−0.0383614	−	0.0154688i
$59$	−7.33328	−	5.32794i	−0.954712	−	0.693639i	−0.00279513	−	0.999996i	$-0.500890\pi$
$59$	−7.33328	−	5.32794i	−0.954712	−	0.693639i	−0.951917	+	0.306357i	$0.900890\pi$
$60$		0			0
$61$	1.16375	−	0.845512i	0.149003	−	0.108257i	−0.510786	−	0.859708i	$-0.670646\pi$
$61$	1.16375	−	0.845512i	0.149003	−	0.108257i	0.659789	+	0.751451i	$0.270646\pi$
$62$	−10.1258	+	2.53191i	−1.28597	+	0.321552i
$63$	−7.84114	+	1.24191i	−0.987891	+	0.156467i
$64$	7.32150	+	3.22422i	0.915188	+	0.403028i
$65$		0			0
$66$	0.709385	−	1.18243i	0.0873193	−	0.145546i
$67$	1.53527	−	3.01313i	0.187563	−	0.368113i	−0.778007	−	0.628255i	$-0.783769\pi$
$67$	1.53527	−	3.01313i	0.187563	−	0.368113i	0.965570	+	0.260142i	$0.0837695\pi$
$68$	7.66911	+	5.35453i	0.930016	+	0.649332i
$69$	0.813081	−	0.264186i	0.0978834	−	0.0318043i
$70$		0			0
$71$	5.45415	+	1.77216i	0.647288	+	0.210317i	0.614218	−	0.789136i	$-0.289471\pi$
$71$	5.45415	+	1.77216i	0.647288	+	0.210317i	0.0330703	+	0.999453i	$0.489471\pi$
$72$	6.21766	−	5.62128i	0.732759	−	0.662475i
$73$	0.0187149	+	0.00296414i	0.00219041	+	0.000346927i	0.157530	−	0.987514i	$-0.449647\pi$
$73$	0.0187149	+	0.00296414i	0.00219041	+	0.000346927i	−0.155339	+	0.987861i	$0.549647\pi$
$74$	−6.16431	+	0.543507i	−0.716586	+	0.0631814i
$75$		0			0
$76$	−1.75588	−	9.87994i	−0.201413	−	1.13331i
$77$	2.13843	−	13.5015i	0.243697	−	1.53864i
$78$	−0.634505	+	0.397079i	−0.0718435	+	0.0449604i
$79$	−2.08434	+	6.41493i	−0.234506	+	0.721736i	0.762680	+	0.646776i	$0.223883\pi$
$79$	−2.08434	+	6.41493i	−0.234506	+	0.721736i	−0.997187	+	0.0749601i	$0.976117\pi$
$80$		0			0
$81$	−2.68002	−	8.24826i	−0.297780	−	0.916474i
$82$	3.40864	+	2.85627i	0.376422	+	0.315422i
$83$	2.99552	+	1.52629i	0.328801	+	0.167532i	0.610596	−	0.791942i	$-0.290930\pi$
$83$	2.99552	+	1.52629i	0.328801	+	0.167532i	−0.281795	+	0.959475i	$0.590930\pi$
$84$	−0.447539	+	0.920749i	−0.0488305	+	0.100462i
$85$		0			0
$86$	−4.05504	+	3.52981i	−0.437266	+	0.380629i
$87$	0.00665810	+	0.0420376i	0.000713823	+	0.00450690i
$88$	5.89710	+	13.1731i	0.628633	+	1.40426i
$89$	−0.509284	−	0.700969i	−0.0539840	−	0.0743026i	0.781172	−	0.624316i	$-0.214622\pi$
$89$	−0.509284	−	0.700969i	−0.0539840	−	0.0743026i	−0.835156	+	0.550014i	$0.814622\pi$
$90$		0			0
$91$	−4.36162	+	6.00326i	−0.457222	+	0.629313i
$92$	−2.60470	+	8.56098i	−0.271559	+	0.892544i
$93$	0.997185	+	0.997185i	0.103403	+	0.103403i
$94$	−11.4616	+	4.87429i	−1.18217	+	0.502745i
$95$		0			0
$96$	−0.135354	−	1.07239i	−0.0138145	−	0.109450i
$97$	5.07638	+	9.96296i	0.515428	+	1.01158i	0.991244	+	0.132040i	$0.0421528\pi$
$97$	5.07638	+	9.96296i	0.515428	+	1.01158i	−0.475816	+	0.879545i	$0.657847\pi$
$98$	−0.0172424	+	0.248997i	−0.00174175	+	0.0251525i
$99$	15.1221			1.51982
$100$		0			0
$101$	−11.8084			−1.17498			−0.587489	−	0.809232i	$-0.699884\pi$
$101$	−11.8084			−1.17498			−0.587489	+	0.809232i	$0.699884\pi$
$102$	0.0873030	−	1.26074i	0.00864429	−	0.124832i
$103$	−0.880821	−	1.72871i	−0.0867899	−	0.170335i	0.843532	−	0.537079i	$-0.180472\pi$
$103$	−0.880821	−	1.72871i	−0.0867899	−	0.170335i	−0.930322	+	0.366744i	$0.880472\pi$
$104$	0.394164	−	7.82471i	0.0386509	−	0.767276i
$105$		0			0
$106$	−2.39971	+	1.02053i	−0.233081	+	0.0991230i
$107$	−8.09772	−	8.09772i	−0.782836	−	0.782836i	0.197472	−	0.980308i	$-0.436727\pi$
$107$	−8.09772	−	8.09772i	−0.782836	−	0.782836i	−0.980308	+	0.197472i	$0.936727\pi$
$108$	−2.18029	−	0.663361i	−0.209799	−	0.0638319i
$109$	−9.13259	+	12.5699i	−0.874743	+	1.20398i	0.103106	+	0.994670i	$0.467122\pi$
$109$	−9.13259	+	12.5699i	−0.874743	+	1.20398i	−0.977849	+	0.209310i	$0.932878\pi$
$110$		0			0
$111$	0.491450	+	0.676422i	0.0466463	+	0.0642032i
$112$	−5.22035	−	9.35798i	−0.493276	−	0.884246i
$113$	1.26860	+	8.00964i	0.119340	+	0.753483i	0.972684	+	0.232135i	$0.0745710\pi$
$113$	1.26860	+	8.00964i	0.119340	+	0.753483i	−0.853344	+	0.521349i	$0.825429\pi$
$114$	−1.02265	+	0.890188i	−0.0957796	+	0.0833737i
$115$		0			0
$116$	−0.400668	−	0.194749i	−0.0372011	−	0.0180820i
$117$	−7.31405	−	3.72669i	−0.676184	−	0.344533i
$118$	−9.82552	−	8.23328i	−0.904513	−	0.757935i
$119$	−3.87149	−	11.9152i	−0.354899	−	1.09227i
$120$		0			0
$121$	−4.64713	+	14.3024i	−0.422467	+	1.30022i
$122$	1.72446	−	1.07918i	0.156125	−	0.0977047i
$123$	0.0939957	−	0.593466i	0.00847531	−	0.0535110i
$124$	−14.5331	+	2.58285i	−1.30511	+	0.231947i
$125$		0			0
$126$	−11.1839	+	0.986083i	−0.996340	+	0.0878472i
$127$	15.8543	+	2.51108i	1.40684	+	0.222822i	0.813237	−	0.581932i	$-0.197703\pi$
$127$	15.8543	+	2.51108i	1.40684	+	0.222822i	0.593608	+	0.804755i	$0.297703\pi$
$128$	10.0144	+	5.26413i	0.885159	+	0.465288i
$129$	0.690830	+	0.224464i	0.0608242	+	0.0197630i
$130$		0			0
$131$	12.9418	−	4.20505i	1.13073	−	0.367397i	0.316878	−	0.948466i	$-0.397365\pi$
$131$	12.9418	−	4.20505i	1.13073	−	0.367397i	0.813854	+	0.581069i	$0.197365\pi$
$132$	1.11634	−	1.59890i	0.0971653	−	0.139167i
$133$	−6.10210	+	11.9761i	−0.529119	+	1.03846i
$134$	2.46038	−	4.10104i	0.212545	−	0.354276i
$135$		0			0
$136$	10.2967	+	8.30361i	0.882937	+	0.712028i
$137$	−18.6626	+	2.95587i	−1.59445	+	0.252537i	−0.889575	−	0.456790i	$-0.848999\pi$
$137$	−18.6626	+	2.95587i	−1.59445	+	0.252537i	−0.704880	+	0.709327i	$0.748999\pi$
$138$	1.17293	−	0.293287i	0.0998467	−	0.0249663i
$139$	−5.89560	+	4.28340i	−0.500058	+	0.363313i	−0.809039	−	0.587755i	$-0.800012\pi$
$139$	−5.89560	+	4.28340i	−0.500058	+	0.363313i	0.308981	+	0.951068i	$0.400012\pi$
$140$		0			0
$141$	1.36143	+	0.989135i	0.114653	+	0.0833002i
$142$	7.52177	+	3.03308i	0.631213	+	0.254530i
$143$	9.99461	−	9.99461i	0.835792	−	0.835792i
$144$	9.32128	−	7.32326i	0.776773	−	0.610272i
$145$		0			0
$146$	0.0261140	+	0.00601030i	0.00216121	+	0.000497416i
$147$	0.0300475	−	0.0153100i	0.00247828	−	0.00126274i
$148$	−8.74992	+	0.164565i	−0.719239	+	0.0135272i
$149$			2.12851i			0.174375i	0.996192	+	0.0871873i	$0.0277879\pi$
$149$			2.12851i			0.174375i	−0.996192	+	0.0871873i	$0.972212\pi$
$150$		0			0
$151$		−	6.10369i		−	0.496712i	−0.968669	−	0.248356i	$-0.920110\pi$
$151$		−	6.10369i		−	0.496712i	0.968669	−	0.248356i	$-0.0798902\pi$
$152$	−1.51202	−	14.1105i	−0.122641	−	1.14451i
$153$	12.3488	−	6.29202i	0.998340	−	0.508680i
$154$	4.33603	−	18.8395i	0.349408	−	1.51813i
$155$		0			0
$156$	−0.933975	+	0.498224i	−0.0747778	+	0.0398899i
$157$	11.4802	−	11.4802i	0.916218	−	0.916218i	−0.0805335	−	0.996752i	$-0.525662\pi$
$157$	11.4802	−	11.4802i	0.916218	−	0.916218i	0.996752	+	0.0805335i	$0.0256624\pi$
$158$	−3.56737	+	8.84677i	−0.283805	+	0.703811i
$159$	0.285043	+	0.207096i	0.0226054	+	0.0164238i
$160$		0			0
$161$	9.69687	−	7.04519i	0.764221	−	0.555239i
$162$	−2.97524	−	11.8988i	−0.233757	−	0.934856i
$163$	7.81379	−	1.23758i	0.612023	−	0.0969349i	0.157275	−	0.987555i	$-0.449729\pi$
$163$	7.81379	−	1.23758i	0.612023	−	0.0969349i	0.454748	+	0.890620i	$0.349729\pi$
$164$	4.52998	+	4.36273i	0.353732	+	0.340672i
$165$		0			0
$166$	4.07707	+	2.44600i	0.316442	+	0.189846i
$167$	6.13600	−	12.0426i	0.474818	−	0.931883i	−0.522059	−	0.852910i	$-0.674836\pi$
$167$	6.13600	−	12.0426i	0.474818	−	0.931883i	0.996877	−	0.0789735i	$-0.0251643\pi$
$168$	−0.721358	+	1.25530i	−0.0556540	+	0.0968487i
$169$	5.06658	−	1.64623i	0.389737	−	0.126633i
$170$		0			0
$171$	−14.1412	−	4.59476i	−1.08141	−	0.351370i
$172$	−6.06584	+	4.58381i	−0.462516	+	0.349512i
$173$	−1.08340	−	0.171594i	−0.0823695	−	0.0130460i	0.115114	−	0.993352i	$-0.463277\pi$
$173$	−1.08340	−	0.171594i	−0.0823695	−	0.0130460i	−0.197483	+	0.980306i	$0.563277\pi$
$174$	0.00528654	+	0.0599586i	0.000400772	+	0.00454545i
$175$		0			0
$176$	7.03287	+	19.1613i	0.530122	+	1.44433i
$177$	−0.270946	+	1.71068i	−0.0203655	+	0.128583i
$178$	−0.650033	−	1.03871i	−0.0487220	−	0.0778544i
$179$	−7.45601	+	22.9472i	−0.557289	+	1.71516i	0.132533	+	0.991179i	$0.457689\pi$
$179$	−7.45601	+	22.9472i	−0.557289	+	1.71516i	−0.689822	+	0.723979i	$0.742311\pi$
$180$		0			0
$181$	−2.15964	−	6.64670i	−0.160525	−	0.494045i	0.838154	−	0.545434i	$-0.183635\pi$
$181$	−2.15964	−	6.64670i	−0.160525	−	0.494045i	−0.998679	+	0.0513890i	$0.983635\pi$
$182$	−6.74003	+	8.04349i	−0.499604	+	0.596223i
$183$	−0.244901	−	0.124784i	−0.0181036	−	0.00922426i
$184$	−4.51119	+	11.8237i	−0.332569	+	0.871652i
$185$		0			0
$186$	1.30944	+	1.50429i	0.0960130	+	0.110300i
$187$	3.73319	+	23.5704i	0.272998	+	1.72364i
$188$	−16.6466	+	5.75707i	−1.21408	+	0.419877i
$189$	1.79426	+	2.46958i	0.130513	+	0.179636i
$190$		0			0
$191$	9.26511	−	12.7523i	0.670400	−	0.922727i	−0.329369	−	0.944201i	$-0.606836\pi$
$191$	9.26511	−	12.7523i	0.670400	−	0.922727i	0.999769	+	0.0214746i	$0.00683611\pi$
$192$	−0.0861932	−	1.52619i	−0.00622046	−	0.110143i
$193$	−6.44920	−	6.44920i	−0.464223	−	0.464223i	0.435814	−	0.900037i	$-0.356461\pi$
$193$	−6.44920	−	6.44920i	−0.464223	−	0.464223i	−0.900037	+	0.435814i	$0.856461\pi$
$194$	6.18859	+	14.5520i	0.444315	+	1.04478i
$195$		0			0
$196$	−0.0486524	+	0.349609i	−0.00347517	+	0.0249721i
$197$	2.59555	+	5.09406i	0.184925	+	0.362936i	0.964794	−	0.263007i	$-0.0847142\pi$
$197$	2.59555	+	5.09406i	0.184925	+	0.362936i	−0.779869	+	0.625943i	$0.784714\pi$
$198$	21.3347	+	1.47738i	1.51619	+	0.104993i
$199$	24.6399			1.74668			0.873338	−	0.487115i	$-0.161951\pi$
$199$	24.6399			1.74668			0.873338	+	0.487115i	$0.161951\pi$
$200$		0			0
$201$	−0.646170			−0.0455773
$202$	−16.6597	−	1.15364i	−1.17217	−	0.0811699i
$203$	0.270901	+	0.531674i	0.0190136	+	0.0373162i
$204$	0.246340	−	1.77017i	0.0172473	−	0.123936i
$205$		0			0
$206$	−1.07380	−	2.52498i	−0.0748155	−	0.175923i
$207$	9.37576	+	9.37576i	0.651660	+	0.651660i
$208$	1.32055	−	11.0009i	0.0915636	−	0.762773i
$209$	15.0488	−	20.7129i	1.04095	−	1.43274i
$210$		0			0
$211$	−11.6703	−	16.0628i	−0.803419	−	1.10581i	−0.992306	−	0.123813i	$-0.960488\pi$
$211$	−11.6703	−	16.0628i	−0.803419	−	1.10581i	0.188886	−	0.981999i	$-0.439512\pi$
$212$	−3.48530	+	1.20536i	−0.239372	+	0.0827845i
$213$	−0.171420	−	1.08231i	−0.0117455	−	0.0741584i
$214$	−10.6334	−	12.2157i	−0.726886	−	0.835046i
$215$		0			0
$216$	−3.01123	−	1.14890i	−0.204888	−	0.0781728i
$217$	17.6165	+	8.97603i	1.19588	+	0.609333i
$218$	−14.1126	+	16.8419i	−0.955827	+	1.14068i
$219$	−0.00111881	−	0.00344336i	−7.56025e−5	−	0.000232681i
$220$		0			0
$221$	4.00309	−	12.3203i	0.269277	−	0.828750i
$222$	0.627270	+	1.00233i	0.0420996	+	0.0672722i
$223$	1.81060	−	11.4317i	0.121247	−	0.765524i	−0.849883	−	0.526972i	$-0.823327\pi$
$223$	1.81060	−	11.4317i	0.121247	−	0.765524i	0.971130	−	0.238552i	$-0.0766727\pi$
$224$	−6.45080	−	13.7126i	−0.431012	−	0.916210i
$225$		0			0
$226$	1.00727	+	11.4242i	0.0670028	+	0.759928i
$227$	15.3359	+	2.42897i	1.01788	+	0.161216i	0.643007	−	0.765861i	$-0.277687\pi$
$227$	15.3359	+	2.42897i	1.01788	+	0.161216i	0.374872	+	0.927077i	$0.377687\pi$
$228$	−1.52975	+	1.15600i	−0.101310	+	0.0765579i
$229$	−16.0312	−	5.20884i	−1.05937	−	0.344210i	−0.273030	−	0.962006i	$-0.588026\pi$
$229$	−16.0312	−	5.20884i	−1.05937	−	0.344210i	−0.786339	+	0.617796i	$0.788026\pi$
$230$		0			0
$231$	−2.48416	+	0.807152i	−0.163446	+	0.0531067i
$232$	−0.546250	−	0.313902i	−0.0358631	−	0.0206087i
$233$	13.2595	−	26.0233i	0.868660	−	1.70484i	0.174963	−	0.984575i	$-0.444019\pi$
$233$	13.2595	−	26.0233i	0.868660	−	1.70484i	0.693697	−	0.720267i	$-0.255981\pi$
$234$	−9.95483	−	5.97231i	−0.650768	−	0.390422i
$235$		0			0
$236$	−13.0578	−	12.5757i	−0.849992	−	0.818610i
$237$	1.27296	−	0.201617i	0.0826876	−	0.0130964i
$238$	−4.29796	−	17.1886i	−0.278595	−	1.11417i
$239$	0.369981	−	0.268807i	0.0239321	−	0.0173877i	−0.575755	−	0.817622i	$-0.695292\pi$
$239$	0.369981	−	0.268807i	0.0239321	−	0.0173877i	0.599687	+	0.800235i	$0.295292\pi$
$240$		0			0
$241$	17.6697	+	12.8378i	1.13820	+	0.826953i	0.986868	−	0.161530i	$-0.0516429\pi$
$241$	17.6697	+	12.8378i	1.13820	+	0.826953i	0.151335	+	0.988483i	$0.451643\pi$
$242$	−7.95364	+	19.7243i	−0.511279	+	1.26793i
$243$	−3.58901	+	3.58901i	−0.230235	+	0.230235i
$244$	2.53836	−	1.35408i	0.162502	−	0.0866858i
$245$		0			0
$246$	0.190592	−	0.828099i	0.0121517	−	0.0527977i
$247$	−12.3832	+	6.30953i	−0.787921	+	0.401466i
$248$	−20.7562	+	2.22413i	−1.31802	+	0.141233i
$249$		−	0.642393i		−	0.0407100i
$250$		0			0
$251$			5.42259i			0.342271i	0.985248	+	0.171135i	$0.0547436\pi$
$251$			5.42259i			0.342271i	−0.985248	+	0.171135i	$0.945256\pi$
$252$	−15.8750	+	0.298570i	−1.00003	+	0.0188082i
$253$	−20.3426	+	10.3651i	−1.27893	+	0.651647i
$254$	22.1225	+	5.09164i	1.38809	+	0.319478i
$255$		0			0
$256$	13.6144	+	8.40520i	0.850902	+	0.525325i
$257$	−8.02192	+	8.02192i	−0.500394	+	0.500394i	−0.911560	−	0.411166i	$-0.865121\pi$
$257$	−8.02192	+	8.02192i	−0.500394	+	0.500394i	0.411166	+	0.911560i	$0.365121\pi$
$258$	0.952717	+	0.384174i	0.0593136	+	0.0239176i
$259$	9.48341	+	6.89010i	0.589271	+	0.428130i
$260$		0			0
$261$	−0.534035	+	0.387999i	−0.0330559	+	0.0240165i
$262$	18.6696	−	4.66826i	1.15341	−	0.288406i
$263$	19.6441	−	3.11132i	1.21131	−	0.191852i	0.482081	−	0.876127i	$-0.339881\pi$
$263$	19.6441	−	3.11132i	1.21131	−	0.191852i	0.729224	+	0.684275i	$0.239881\pi$
$264$	1.73119	−	2.14672i	0.106547	−	0.132122i
$265$		0			0
$266$	−9.77908	+	16.3001i	−0.599594	+	0.999422i
$267$	−0.0751618	+	0.147513i	−0.00459983	+	0.00902767i
$268$	3.87185	−	5.54552i	0.236511	−	0.338747i
$269$	−9.63789	+	3.13154i	−0.587633	+	0.190933i	−0.587717	−	0.809067i	$-0.699973\pi$
$269$	−9.63789	+	3.13154i	−0.587633	+	0.190933i	8.44003e−5		1.00000i	$0.499973\pi$
$270$		0			0
$271$	1.79674	+	0.583795i	0.109144	+	0.0354630i	0.363080	−	0.931758i	$-0.381725\pi$
$271$	1.79674	+	0.583795i	0.109144	+	0.0354630i	−0.253936	+	0.967221i	$0.581725\pi$
$272$	13.7158	+	12.7210i	0.831640	+	0.771322i
$273$	1.40042	+	0.221805i	0.0847574	+	0.0134243i
$274$	−26.6186	+	2.34696i	−1.60809	+	0.141785i
$275$		0			0
$276$	1.68347	−	0.299188i	0.101333	−	0.0180090i
$277$	−1.79116	+	11.3089i	−0.107620	+	0.679488i	0.873607	+	0.486632i	$0.161775\pi$
$277$	−1.79116	+	11.3089i	−0.107620	+	0.679488i	−0.981227	+	0.192855i	$0.938225\pi$
$278$	−8.73619	+	5.46719i	−0.523962	+	0.327900i
$279$	−6.75877	+	20.8013i	−0.404637	+	1.24534i
$280$		0			0
$281$	7.15917	+	22.0337i	0.427080	+	1.31442i	0.900988	+	0.433844i	$0.142843\pi$
$281$	7.15917	+	22.0337i	0.427080	+	1.31442i	−0.473908	+	0.880574i	$0.657157\pi$
$282$	1.82411	+	1.52851i	0.108624	+	0.0910217i
$283$	−16.9779	−	8.65065i	−1.00923	−	0.514228i	−0.130449	−	0.991455i	$-0.541642\pi$
$283$	−16.9779	−	8.65065i	−1.00923	−	0.514228i	−0.878780	+	0.477227i	$0.841642\pi$
$284$	10.3157	+	5.01403i	0.612121	+	0.297528i
$285$		0			0
$286$	15.0772	−	13.1243i	0.891533	−	0.776057i
$287$	−1.31782	−	8.32036i	−0.0777882	−	0.491135i
$288$	13.8662	−	9.42125i	0.817076	−	0.555153i
$289$	2.86343	+	3.94118i	0.168437	+	0.231834i
$290$		0			0
$291$	1.25584	−	1.72852i	0.0736188	−	0.101328i
$292$	0.0362553	+	0.0110308i	0.00212168	+	0.000645528i
$293$	9.23047	+	9.23047i	0.539250	+	0.539250i	0.923309	−	0.384059i	$-0.125474\pi$
$293$	9.23047	+	9.23047i	0.539250	+	0.539250i	−0.384059	+	0.923309i	$0.625474\pi$
$294$	0.0438878	−	0.0186643i	0.00255959	−	0.00108852i
$295$		0			0
$296$	−12.3608	−	0.622665i	−0.718455	−	0.0361916i
$297$	−2.63976	−	5.18082i	−0.153174	−	0.300621i
$298$	−0.207949	+	3.00298i	−0.0120462	+	0.173958i
$299$	12.3934			0.716731
$300$		0			0
$301$	10.1838			0.586986
$302$	0.596311	−	8.61130i	0.0343138	−	0.495525i
$303$	1.02435	+	2.01039i	0.0588472	+	0.115494i
$304$	−0.754653	−	20.0553i	−0.0432823	−	1.15025i
$305$		0			0
$306$	18.0368	−	7.67056i	1.03110	−	0.438497i
$307$	−9.17187	−	9.17187i	−0.523466	−	0.523466i	0.395150	−	0.918616i	$-0.370692\pi$
$307$	−9.17187	−	9.17187i	−0.523466	−	0.523466i	−0.918616	+	0.395150i	$0.870692\pi$
$308$	7.95799	−	26.1559i	0.453449	−	1.49037i
$309$	−0.217906	+	0.299922i	−0.0123962	+	0.0170619i
$310$		0			0
$311$	2.44643	+	3.36722i	0.138724	+	0.190938i	0.872726	−	0.488209i	$-0.162350\pi$
$311$	2.44643	+	3.36722i	0.138724	+	0.190938i	−0.734002	+	0.679147i	$0.762350\pi$
$312$	−1.36636	+	0.611666i	−0.0773548	+	0.0346288i
$313$	−3.50477	−	22.1282i	−0.198101	−	1.25076i	−0.863529	−	0.504300i	$-0.831751\pi$
$313$	−3.50477	−	22.1282i	−0.198101	−	1.25076i	0.665427	−	0.746462i	$-0.268249\pi$
$314$	17.3182	−	15.0751i	0.977324	−	0.850735i
$315$		0			0
$316$	−5.89727	+	12.1328i	−0.331748	+	0.682524i
$317$	−5.61291	−	2.85992i	−0.315252	−	0.160629i	0.289204	−	0.957268i	$-0.406609\pi$
$317$	−5.61291	−	2.85992i	−0.315252	−	0.160629i	−0.604456	+	0.796639i	$0.706609\pi$
$318$	0.381916	+	0.320026i	0.0214168	+	0.0179462i
$319$	−0.351235	−	1.08099i	−0.0196654	−	0.0605239i
$320$		0			0
$321$	−0.676191	+	2.08110i	−0.0377413	+	0.116156i
$322$	14.3690	−	8.99225i	0.800752	−	0.501118i
$323$	3.67070	−	23.1759i	0.204243	−	1.28954i
$324$	−3.03510	−	17.0779i	−0.168617	−	0.948771i
$325$		0			0
$326$	11.1449	−	0.982643i	0.617257	−	0.0544235i
$327$	2.93227	+	0.464426i	0.162155	+	0.0256828i
$328$	5.96484	+	6.59766i	0.329353	+	0.364295i
$329$	22.4383	+	7.29065i	1.23706	+	0.401946i
$330$		0			0
$331$	15.4106	−	5.00720i	0.847042	−	0.275221i	0.146835	−	0.989161i	$-0.453091\pi$
$331$	15.4106	−	5.00720i	0.847042	−	0.275221i	0.700206	+	0.713940i	$0.253091\pi$
$332$	5.51311	+	3.84922i	0.302571	+	0.211253i
$333$	−5.88710	+	11.5541i	−0.322611	+	0.633159i
$334$	9.83341	−	16.3906i	0.538060	−	0.896855i
$335$		0			0
$336$	−1.14036	+	1.70055i	−0.0622116	+	0.0927726i
$337$	19.9748	−	3.16369i	1.08809	−	0.172337i	0.413484	−	0.910511i	$-0.364312\pi$
$337$	19.9748	−	3.16369i	1.08809	−	0.172337i	0.674610	+	0.738174i	$0.264312\pi$
$338$	7.30894	−	1.82757i	0.397554	−	0.0994069i
$339$	1.25360	−	0.910796i	0.0680864	−	0.0494676i
$340$		0			0
$341$	−30.4682	−	22.1364i	−1.64995	−	1.19876i
$342$	−19.5020	−	7.86399i	−1.05455	−	0.425236i
$343$	−12.9255	+	12.9255i	−0.697914	+	0.697914i
$344$	−9.00572	+	5.87439i	−0.485556	+	0.316726i
$345$		0			0
$346$	−1.51174	−	0.347935i	−0.0812714	−	0.0187051i
$347$	5.16571	−	2.63206i	0.277310	−	0.141296i	−0.309805	−	0.950800i	$-0.600264\pi$
$347$	5.16571	−	2.63206i	0.277310	−	0.141296i	0.587115	+	0.809504i	$0.300264\pi$
$348$	0.00160068	+	0.0851081i	8.58056e−5	+	0.00456227i
$349$			0.0528810i			0.00283065i	0.999999	+	0.00141533i	$0.000450513\pi$
$349$			0.0528810i			0.00283065i	−0.999999	+	0.00141533i	$0.999549\pi$
$350$		0			0
$351$			3.15634i			0.168473i
$352$	8.05022	+	27.7205i	0.429078	+	1.47751i
$353$	3.66865	−	1.86927i	0.195263	−	0.0994913i	−0.353626	−	0.935387i	$-0.615051\pi$
$353$	3.66865	−	1.86927i	0.195263	−	0.0994913i	0.548888	+	0.835896i	$0.315051\pi$
$354$	−0.549388	+	2.38702i	−0.0291996	+	0.126869i
$355$		0			0
$356$	−0.815611	−	1.52895i	−0.0432273	−	0.0810342i
$357$	−1.69274	+	1.69274i	−0.0895893	+	0.0895893i
$358$	−12.7611	+	31.6463i	−0.674444	+	1.67256i
$359$	−22.3556	−	16.2423i	−1.17989	−	0.857237i	−0.187726	−	0.982221i	$-0.560112\pi$
$359$	−22.3556	−	16.2423i	−1.17989	−	0.857237i	−0.992159	+	0.124985i	$0.960112\pi$
$360$		0			0
$361$	−4.99493	+	3.62903i	−0.262891	+	0.191002i
$362$	−2.39754	−	9.58838i	−0.126012	−	0.503954i
$363$	2.83813	−	0.449515i	0.148963	−	0.0235934i
$364$	−10.2949	+	10.6896i	−0.539599	+	0.560285i
$365$		0			0
$366$	−0.333325	−	0.199975i	−0.0174232	−	0.0104529i
$367$	3.08204	−	6.04885i	0.160881	−	0.315747i	−0.796468	−	0.604681i	$-0.793301\pi$
$367$	3.08204	−	6.04885i	0.160881	−	0.315747i	0.957349	+	0.288934i	$0.0933007\pi$
$368$	−7.51967	+	16.2405i	−0.391990	+	0.846595i
$369$	8.86290	−	2.87973i	0.461384	−	0.149913i
$370$		0			0
$371$	4.69792	+	1.52645i	0.243904	+	0.0792492i
$372$	1.70044	+	2.25023i	0.0881639	+	0.116669i
$373$	11.3458	+	1.79701i	0.587466	+	0.0930454i	0.443089	−	0.896477i	$-0.353882\pi$
$373$	11.3458	+	1.79701i	0.587466	+	0.0930454i	0.144376	+	0.989523i	$0.453882\pi$
$374$	2.96416	+	33.6187i	0.153273	+	1.73838i
$375$		0			0
$376$	−24.0480	+	6.49595i	−1.24018	+	0.335003i
$377$	−0.0965194	+	0.609399i	−0.00497100	+	0.0313857i
$378$	2.29013	+	3.65947i	0.117792	+	0.188223i
$379$	3.95657	−	12.1771i	0.203235	−	0.625494i	−0.796546	−	0.604578i	$-0.793342\pi$
$379$	3.95657	−	12.1771i	0.203235	−	0.625494i	0.999781	−	0.0209157i	$-0.00665816\pi$
$380$		0			0
$381$	−0.947807	−	2.91705i	−0.0485576	−	0.149445i
$382$	14.3174	−	17.0863i	0.732542	−	0.874210i
$383$	16.4227	+	8.36780i	0.839163	+	0.427575i	0.820084	−	0.572243i	$-0.193927\pi$
$383$	16.4227	+	8.36780i	0.839163	+	0.427575i	0.0190788	+	0.999818i	$0.493927\pi$
$384$	0.0274992	−	2.16162i	0.00140331	−	0.110310i
$385$		0			0
$386$	−8.46869	−	9.72882i	−0.431045	−	0.495184i
$387$	1.76235	+	11.1270i	0.0895851	+	0.565618i
$388$	7.30939	+	21.1351i	0.371078	+	1.07297i
$389$	−14.6199	−	20.1226i	−0.741258	−	1.02025i	−0.998545	−	0.0539190i	$-0.982829\pi$
$389$	−14.6199	−	20.1226i	−0.741258	−	1.02025i	0.257287	−	0.966335i	$-0.417171\pi$
$390$		0			0
$391$	−12.2992	+	16.9284i	−0.621997	+	0.856105i
$392$	−0.102796	+	0.488488i	−0.00519199	+	0.0246724i
$393$	−1.83858	−	1.83858i	−0.0927443	−	0.0927443i
$394$	3.16422	+	7.44045i	0.159411	+	0.374844i
$395$		0			0
$396$	29.9554	+	4.16867i	1.50532	+	0.209483i
$397$	−12.6438	−	24.8148i	−0.634574	−	1.24542i	−0.954566	−	0.298001i	$-0.903680\pi$
$397$	−12.6438	−	24.8148i	−0.634574	−	1.24542i	0.319992	−	0.947420i	$-0.396320\pi$
$398$	34.7628	+	2.40724i	1.74250	+	0.120664i
$399$	2.56828			0.128575
$400$		0			0
$401$	10.4612			0.522406			0.261203	−	0.965284i	$-0.415881\pi$
$401$	10.4612			0.522406			0.261203	+	0.965284i	$0.415881\pi$
$402$	−0.911639	−	0.0631287i	−0.0454684	−	0.00314857i
$403$	9.28115	+	18.2153i	0.462327	+	0.907368i
$404$	−23.3914	−	3.25520i	−1.16376	−	0.161952i
$405$		0			0
$406$	0.330254	+	0.776571i	0.0163903	+	0.0385405i
$407$	−15.7886	−	15.7886i	−0.782611	−	0.782611i
$408$	0.520485	−	2.47335i	0.0257679	−	0.122449i
$409$	−9.12365	+	12.5576i	−0.451136	+	0.620935i	−0.972641	−	0.232313i	$-0.925371\pi$
$409$	−9.12365	+	12.5576i	−0.451136	+	0.620935i	0.521505	+	0.853248i	$0.325371\pi$
$410$		0			0
$411$	2.12217	+	2.92092i	0.104679	+	0.144078i
$412$	−1.26828	−	3.66723i	−0.0624836	−	0.180672i
$413$	3.79865	+	23.9837i	0.186919	+	1.18016i
$414$	12.3117	+	14.1436i	0.605086	+	0.695122i
$415$		0			0
$416$	2.93783	−	15.3914i	0.144039	−	0.754625i
$417$	1.24068	+	0.632159i	0.0607564	+	0.0309569i
$418$	23.2550	−	27.7523i	1.13744	−	1.35741i
$419$	−11.1568	−	34.3371i	−0.545045	−	1.67748i	−0.720883	−	0.693056i	$-0.756264\pi$
$419$	−11.1568	−	34.3371i	−0.545045	−	1.67748i	0.175838	−	0.984419i	$-0.443736\pi$
$420$		0			0
$421$	4.95128	−	15.2385i	0.241311	−	0.742678i	−0.754911	−	0.655828i	$-0.772320\pi$
$421$	4.95128	−	15.2385i	0.241311	−	0.742678i	0.996221	−	0.0868504i	$-0.0276802\pi$
$422$	−14.8956	−	23.8022i	−0.725108	−	1.15867i
$423$	−4.08285	+	25.7781i	−0.198515	+	1.25337i
$424$	−5.03495	+	1.36006i	−0.244519	+	0.0660504i
$425$		0			0
$426$	−0.136108	−	1.54370i	−0.00659446	−	0.0747926i
$427$	−3.80607	−	0.602823i	−0.184189	−	0.0291726i
$428$	−13.8086	−	18.2731i	−0.667463	−	0.883266i
$429$	−2.56860	−	0.834589i	−0.124013	−	0.0402943i
$430$		0			0
$431$	−6.40797	+	2.08208i	−0.308661	+	0.100290i	−0.459252	−	0.888306i	$-0.651882\pi$
$431$	−6.40797	+	2.08208i	−0.308661	+	0.100290i	0.150591	+	0.988596i	$0.451882\pi$
$432$	−4.13610	−	1.91510i	−0.198998	−	0.0921401i
$433$	−4.78847	+	9.39790i	−0.230119	+	0.451634i	−0.976976	−	0.213351i	$-0.931562\pi$
$433$	−4.78847	+	9.39790i	−0.230119	+	0.451634i	0.746857	+	0.664985i	$0.231562\pi$
$434$	23.9770	+	14.3848i	1.15093	+	0.690491i
$435$		0			0
$436$	−21.5560	+	22.3823i	−1.03234	+	1.07192i
$437$	22.1725	−	3.51178i	1.06065	−	0.167991i
$438$	−0.00124206	−	0.00496732i	−5.93478e−5	−	0.000237347i
$439$	−8.47207	+	6.15532i	−0.404350	+	0.293778i	−0.771311	−	0.636459i	$-0.780398\pi$
$439$	−8.47207	+	6.15532i	−0.404350	+	0.293778i	0.366960	+	0.930237i	$0.380398\pi$
$440$		0			0
$441$	0.423135	+	0.307426i	0.0201493	+	0.0146393i
$442$	6.85136	−	16.9908i	0.325886	−	0.808168i
$443$	3.27124	−	3.27124i	0.155421	−	0.155421i	−0.625113	−	0.780534i	$-0.714947\pi$
$443$	3.27124	−	3.27124i	0.155421	−	0.155421i	0.780534	+	0.625113i	$0.214947\pi$
$444$	0.787050	+	1.47541i	0.0373517	+	0.0700198i
$445$		0			0
$446$	3.67131	−	15.9514i	0.173841	−	0.755319i
$447$	0.362382	−	0.184643i	0.0171401	−	0.00873331i
$448$	−7.76134	−	19.9764i	−0.366689	−	0.943797i
$449$			18.0931i			0.853868i	0.904283	+	0.426934i	$0.140406\pi$
$449$			18.0931i			0.853868i	−0.904283	+	0.426934i	$0.859594\pi$
$450$		0			0
$451$			16.0463i			0.755589i
$452$	0.304986	+	16.2161i	0.0143453	+	0.762741i
$453$	−1.03916	+	0.529479i	−0.0488241	+	0.0248771i
$454$	21.3991	+	4.92514i	1.00431	+	0.231148i
$455$		0			0
$456$	−2.27117	+	1.48147i	−0.106357	+	0.0693762i
$457$	−23.4612	+	23.4612i	−1.09747	+	1.09747i	−0.102764	+	0.994706i	$0.532769\pi$
$457$	−23.4612	+	23.4612i	−1.09747	+	1.09747i	−0.994706	+	0.102764i	$0.967231\pi$
$458$	−22.1084	−	8.91500i	−1.03306	−	0.416571i
$459$	−4.31129	−	3.13234i	−0.201234	−	0.146205i
$460$		0			0
$461$	−26.1799	+	19.0208i	−1.21932	+	0.885887i	−0.996043	−	0.0888686i	$-0.971675\pi$
$461$	−26.1799	+	19.0208i	−1.21932	+	0.885887i	−0.223275	+	0.974755i	$0.571675\pi$
$462$	−3.58359	+	0.896064i	−0.166724	+	0.0416887i
$463$	−30.2882	+	4.79718i	−1.40761	+	0.222944i	−0.813560	−	0.581481i	$-0.802473\pi$
$463$	−30.2882	+	4.79718i	−1.40761	+	0.222944i	−0.594054	+	0.804425i	$0.702473\pi$
$464$	−0.740002	−	0.496231i	−0.0343537	−	0.0230369i
$465$		0			0
$466$	21.2494	−	35.4191i	0.984359	−	1.64076i
$467$	7.07648	−	13.8884i	0.327460	−	0.642677i	−0.667314	−	0.744777i	$-0.732556\pi$
$467$	7.07648	−	13.8884i	0.327460	−	0.642677i	0.994774	+	0.102100i	$0.0325560\pi$
$468$	−13.4611	−	9.39850i	−0.622242	−	0.434446i
$469$	−8.61588	+	2.79947i	−0.397844	+	0.129268i
$470$		0			0
$471$	−2.95039	−	0.958640i	−0.135947	−	0.0441718i
$472$	−17.1938	−	19.0180i	−0.791410	−	0.875373i
$473$	−19.1594	−	3.03456i	−0.880952	−	0.139529i
$474$	1.81563	−	0.160084i	0.0833948	−	0.00735291i
$475$		0			0
$476$	−4.38443	−	24.6702i	−0.200960	−	1.13076i
$477$	−0.854829	+	5.39718i	−0.0391399	+	0.247120i
$478$	0.548244	−	0.343096i	0.0250761	−	0.0156929i
$479$	2.15249	−	6.62469i	0.0983498	−	0.302690i	−0.889762	−	0.456424i	$-0.849130\pi$
$479$	2.15249	−	6.62469i	0.0983498	−	0.302690i	0.988112	+	0.153734i	$0.0491300\pi$
$480$		0			0
$481$	3.74547	+	11.5274i	0.170779	+	0.525604i
$482$	23.6748	+	19.8382i	1.07836	+	0.903606i
$483$	−2.04063	−	1.03975i	−0.0928519	−	0.0473104i
$484$	−13.1483	+	27.0507i	−0.597649	+	1.22958i
$485$		0			0
$486$	−5.41414	+	4.71287i	−0.245590	+	0.213780i
$487$	3.26215	+	20.5964i	0.147822	+	0.933313i	0.944405	+	0.328784i	$0.106639\pi$
$487$	3.26215	+	20.5964i	0.147822	+	0.933313i	−0.796583	+	0.604529i	$0.793361\pi$
$488$	3.71350	−	1.66239i	0.168102	−	0.0752528i
$489$	−0.888525	−	1.22295i	−0.0401805	−	0.0553037i
$490$		0			0
$491$	2.89183	−	3.98026i	0.130506	−	0.179627i	−0.738763	−	0.673965i	$-0.764590\pi$
$491$	2.89183	−	3.98026i	0.130506	−	0.179627i	0.869269	+	0.494339i	$0.164590\pi$
$492$	0.349797	−	1.14969i	0.0157700	−	0.0518321i
$493$	−0.736603	−	0.736603i	−0.0331749	−	0.0331749i
$494$	−18.0870	+	7.69191i	−0.813773	+	0.346076i
$495$		0			0
$496$	−29.5008	+	1.11007i	−1.32463	+	0.0498438i
$497$	−6.97467	−	13.6886i	−0.312857	−	0.614016i
$498$	0.0627597	−	0.906310i	0.00281233	−	0.0406127i
$499$	−19.8140			−0.886994			−0.443497	−	0.896276i	$-0.646262\pi$
$499$	−19.8140			−0.886994			−0.443497	+	0.896276i	$0.646262\pi$
$500$		0			0
$501$	−2.58255			−0.115380
$502$	−0.529770	+	7.65038i	−0.0236448	+	0.341453i
$503$	−12.4717	−	24.4770i	−0.556084	−	1.09138i	−0.982398	−	0.186801i	$-0.940188\pi$
$503$	−12.4717	−	24.4770i	−0.556084	−	1.09138i	0.426314	−	0.904575i	$-0.359812\pi$
$504$	−22.4261	−	1.12970i	−0.998939	−	0.0503208i
$505$		0			0
$506$	−29.7127	+	12.6360i	−1.32089	+	0.561739i
$507$	−0.719785	−	0.719785i	−0.0319668	−	0.0319668i
$508$	30.7138	+	9.34476i	1.36270	+	0.414607i
$509$	−8.04575	+	11.0740i	−0.356622	+	0.490847i	−0.949204	−	0.314663i	$-0.898109\pi$
$509$	−8.04575	+	11.0740i	−0.356622	+	0.490847i	0.592582	+	0.805510i	$0.298109\pi$
$510$		0			0
$511$	−0.0298360	−	0.0410658i	−0.00131987	−	0.00181664i
$512$	18.3866	+	13.1884i	0.812578	+	0.582852i
$513$	0.894374	+	5.64685i	0.0394876	+	0.249315i
$514$	−12.1013	+	10.5339i	−0.533767	+	0.464630i
$515$		0			0
$516$	1.30659	+	0.635083i	0.0575196	+	0.0279580i
$517$	−40.0420	−	20.4024i	−1.76105	−	0.897298i
$518$	12.7064	+	10.6473i	0.558287	+	0.467815i
$519$	0.0647681	+	0.199336i	0.00284300	+	0.00874987i
$520$		0			0
$521$	1.41202	−	4.34576i	0.0618618	−	0.190391i	−0.915349	−	0.402661i	$-0.868085\pi$
$521$	1.41202	−	4.34576i	0.0618618	−	0.190391i	0.977211	+	0.212270i	$0.0680855\pi$
$522$	−0.791341	+	0.495229i	−0.0346361	+	0.0216756i
$523$	−5.67302	+	35.8180i	−0.248064	+	1.56621i	0.477859	+	0.878437i	$0.341413\pi$
$523$	−5.67302	+	35.8180i	−0.248064	+	1.56621i	−0.725923	+	0.687776i	$0.758587\pi$
$524$	26.7958	−	4.76219i	1.17058	−	0.208037i
$525$		0			0
$526$	28.0185	−	2.47039i	1.22167	−	0.107714i
$527$	−34.0911	−	5.39950i	−1.48503	−	0.235206i
$528$	2.65214	−	2.85954i	0.115420	−	0.124446i
$529$	2.83537	+	0.921267i	0.123277	+	0.0400551i
$530$		0			0
$531$	−25.5476	+	8.30092i	−1.10867	+	0.360229i
$532$	−15.3891	+	22.0413i	−0.667204	+	0.955613i
$533$	3.95446	−	7.76106i	0.171286	−	0.336169i
$534$	−0.120452	+	0.200774i	−0.00521249	+	0.00868834i
$535$		0			0
$536$	6.00433	−	7.44555i	0.259347	−	0.321599i
$537$	4.55359	−	0.721217i	0.196502	−	0.0311228i
$538$	−13.9034	+	3.47650i	−0.599419	+	0.149882i
$539$	−0.728590	+	0.529352i	−0.0313826	+	0.0228008i
$540$		0			0
$541$	−23.6895	−	17.2114i	−1.01849	−	0.739976i	−0.0525174	−	0.998620i	$-0.516724\pi$
$541$	−23.6895	−	17.2114i	−1.01849	−	0.739976i	−0.965973	+	0.258644i	$0.916724\pi$
$542$	2.47786	+	0.999174i	0.106433	+	0.0429182i
$543$	−0.944265	+	0.944265i	−0.0405223	+	0.0405223i
$544$	18.1079	+	19.2872i	0.776368	+	0.826931i
$545$		0			0
$546$	1.95409	+	0.449747i	0.0836275	+	0.0192474i
$547$	−31.1849	+	15.8895i	−1.33337	+	0.679385i	−0.967876	−	0.251429i	$-0.919100\pi$
$547$	−31.1849	+	15.8895i	−1.33337	+	0.679385i	−0.365493	+	0.930814i	$0.619100\pi$
$548$	−37.7838	+	0.710624i	−1.61404	+	0.0303563i
$549$		−	4.26289i		−	0.181936i
$550$		0			0
$551$			1.11760i			0.0476112i
$552$	2.40433	−	0.257636i	0.102335	−	0.0109657i
$553$	16.0999	−	8.20329i	0.684636	−	0.348839i
$554$	−3.63187	+	15.7800i	−0.154304	+	0.670430i
$555$		0			0
$556$	−12.8594	+	6.85981i	−0.545362	+	0.290921i
$557$	25.1416	−	25.1416i	1.06528	−	1.06528i	0.0675692	−	0.997715i	$-0.478476\pi$
$557$	25.1416	−	25.1416i	1.06528	−	1.06528i	0.997715	−	0.0675692i	$-0.0215243\pi$
$558$	−11.5677	+	28.6869i	−0.489701	+	1.21442i
$559$	8.51896	+	6.18939i	0.360314	+	0.261783i
$560$		0			0
$561$	3.68905	−	2.68025i	0.155752	−	0.113160i
$562$	7.94779	+	31.7853i	0.335257	+	1.34078i
$563$	−27.3038	+	4.32450i	−1.15072	+	0.182256i	−0.702510	−	0.711674i	$-0.747937\pi$
$563$	−27.3038	+	4.32450i	−1.15072	+	0.182256i	−0.448208	+	0.893929i	$0.647937\pi$
$564$	2.42419	+	2.33469i	0.102077	+	0.0983082i
$565$		0			0
$566$	−23.1078	−	13.8633i	−0.971294	−	0.582719i
$567$	−10.5477	+	20.7011i	−0.442963	+	0.869364i
$568$	14.0638	+	8.08177i	0.590105	+	0.339104i
$569$	8.77237	−	2.85032i	0.367757	−	0.119491i	−0.119308	−	0.992857i	$-0.538068\pi$
$569$	8.77237	−	2.85032i	0.367757	−	0.119491i	0.487065	+	0.873366i	$0.338068\pi$
$570$		0			0
$571$	17.2235	+	5.59625i	0.720780	+	0.234196i	0.646362	−	0.763031i	$-0.276290\pi$
$571$	17.2235	+	5.59625i	0.720780	+	0.234196i	0.0744189	+	0.997227i	$0.476290\pi$
$572$	22.5536	−	17.0432i	0.943015	−	0.712614i
$573$	−2.97482	−	0.471166i	−0.124275	−	0.0196832i
$574$	−1.04635	−	11.8674i	−0.0436737	−	0.495336i
$575$		0			0
$576$	20.4834	−	11.9371i	0.853475	−	0.497381i
$577$	−1.72312	+	10.8794i	−0.0717345	+	0.452914i	0.925510	+	0.378724i	$0.123637\pi$
$577$	−1.72312	+	10.8794i	−0.0717345	+	0.452914i	−0.997244	+	0.0741898i	$0.976363\pi$
$578$	3.65479	+	5.84010i	0.152019	+	0.242916i
$579$	−0.538533	+	1.65743i	−0.0223807	+	0.0688806i
$580$		0			0
$581$	−2.78310	−	8.56552i	−0.115463	−	0.355357i
$582$	1.94066	−	2.31596i	0.0804429	−	0.0959998i
$583$	−8.38362	−	4.27167i	−0.347214	−	0.176914i
$584$	0.0500726	+	0.0191047i	0.00207202	+	0.000790556i
$585$		0			0
$586$	12.1209	+	13.9245i	0.500709	+	0.575214i
$587$	−7.33025	−	46.2814i	−0.302552	−	1.91024i	−0.402825	−	0.915277i	$-0.631972\pi$
$587$	−7.33025	−	46.2814i	−0.302552	−	1.91024i	0.100273	−	0.994960i	$-0.468028\pi$
$588$	0.0637419	−	0.0220445i	0.00262867	−	0.000909101i
$589$	21.7659	+	29.9582i	0.896849	+	1.23441i
$590$		0			0
$591$	0.642112	−	0.883792i	0.0264130	−	0.0363543i
$592$	−17.3782	−	2.08608i	−0.714239	−	0.0857375i
$593$	11.5238	+	11.5238i	0.473225	+	0.473225i	0.902957	−	0.429731i	$-0.141392\pi$
$593$	11.5238	+	11.5238i	0.473225	+	0.473225i	−0.429731	+	0.902957i	$0.641392\pi$
$594$	−3.21811	−	7.56717i	−0.132041	−	0.310485i
$595$		0			0
$596$	−0.586763	+	4.21640i	−0.0240348	+	0.172710i
$597$	−2.13745	−	4.19497i	−0.0874798	−	0.171689i
$598$	17.4851	+	1.21080i	0.715019	+	0.0495132i
$599$	−7.21615			−0.294844			−0.147422	−	0.989074i	$-0.547098\pi$
$599$	−7.21615			−0.294844			−0.147422	+	0.989074i	$0.547098\pi$
$600$		0			0
$601$	−15.0642			−0.614483			−0.307241	−	0.951632i	$-0.599406\pi$
$601$	−15.0642			−0.614483			−0.307241	+	0.951632i	$0.599406\pi$
$602$	14.3677	+	0.994928i	0.585584	+	0.0405502i
$603$	−4.54975	−	8.92939i	−0.185280	−	0.363633i
$604$	1.68259	−	12.0909i	0.0684637	−	0.491971i
$605$		0			0
$606$	1.24877	+	2.93641i	0.0507280	+	0.119283i
$607$	−3.59194	−	3.59194i	−0.145792	−	0.145792i	0.630443	−	0.776235i	$-0.282873\pi$
$607$	−3.59194	−	3.59194i	−0.145792	−	0.145792i	−0.776235	+	0.630443i	$0.782873\pi$
$608$	0.894649	−	28.3685i	0.0362828	−	1.15049i
$609$	0.0670182	−	0.0922426i	0.00271571	−	0.00373786i
$610$		0			0
$611$	14.3390	+	19.7360i	0.580095	+	0.798433i
$612$	26.1963	−	9.05976i	1.05892	−	0.366219i
$613$	0.788465	+	4.97817i	0.0318458	+	0.201066i	0.998481	−	0.0550888i	$-0.0175442\pi$
$613$	0.788465	+	4.97817i	0.0318458	+	0.201066i	−0.966636	+	0.256155i	$0.917544\pi$
$614$	−12.0439	−	13.8360i	−0.486053	−	0.558378i
$615$		0			0
$616$	13.7828	−	36.1241i	0.555323	−	1.45548i
$617$	16.5627	+	8.43913i	0.666790	+	0.339746i	0.754406	−	0.656408i	$-0.227925\pi$
$617$	16.5627	+	8.43913i	0.666790	+	0.339746i	−0.0876162	+	0.996154i	$0.527925\pi$
$618$	−0.336731	+	0.401851i	−0.0135453	+	0.0161648i
$619$	6.54265	+	20.1362i	0.262971	+	0.809343i	0.992154	+	0.125024i	$0.0399006\pi$
$619$	6.54265	+	20.1362i	0.262971	+	0.809343i	−0.729182	+	0.684320i	$0.760099\pi$
$620$		0			0
$621$	1.57547	−	4.84880i	0.0632215	−	0.194576i
$622$	3.12254	+	4.98960i	0.125203	+	0.200065i
$623$	−0.363103	+	2.29254i	−0.0145474	+	0.0918487i
$624$	−1.98746	+	0.729471i	−0.0795623	+	0.0292022i
$625$		0			0
$626$	−2.78279	−	31.5617i	−0.111223	−	1.26146i
$627$	−4.83185	−	0.765290i	−0.192966	−	0.0305627i
$628$	25.9059	−	19.5765i	1.03376	−	0.781187i
$629$	−19.4624	−	6.32373i	−0.776018	−	0.252144i
$630$		0			0
$631$	−3.22756	+	1.04870i	−0.128487	+	0.0417480i	−0.372555	−	0.928010i	$-0.621518\pi$
$631$	−3.22756	+	1.04870i	−0.128487	+	0.0417480i	0.244068	+	0.969758i	$0.421518\pi$
$632$	−9.50542	+	16.5413i	−0.378105	+	0.657976i
$633$	−1.72235	+	3.38030i	−0.0684572	+	0.134355i
$634$	−7.63948	−	4.58324i	−0.303402	−	0.182024i
$635$		0			0
$636$	0.507555	+	0.488815i	0.0201259	+	0.0193828i
$637$	0.482849	−	0.0764758i	0.0191312	−	0.00303008i
$638$	−0.389926	−	1.55942i	−0.0154373	−	0.0617378i
$639$	13.7493	−	9.98948i	0.543915	−	0.395178i
$640$		0			0
$641$	31.0401	+	22.5519i	1.22601	+	0.890748i	0.996585	−	0.0825780i	$-0.0263153\pi$
$641$	31.0401	+	22.5519i	1.22601	+	0.890748i	0.229425	+	0.973326i	$0.426315\pi$
$642$	−1.15731	+	2.87003i	−0.0456754	+	0.113271i
$643$	6.79295	−	6.79295i	0.267888	−	0.267888i	−0.560361	−	0.828249i	$-0.689338\pi$
$643$	6.79295	−	6.79295i	0.267888	−	0.267888i	0.828249	+	0.560361i	$0.189338\pi$
$644$	21.1508	−	11.2828i	0.833457	−	0.444604i
$645$		0			0
$646$	7.44296	−	32.3388i	0.292840	−	1.27235i
$647$	30.3148	−	15.4461i	1.19180	−	0.607251i	0.258379	−	0.966044i	$-0.416812\pi$
$647$	30.3148	−	15.4461i	1.19180	−	0.607251i	0.933417	+	0.358793i	$0.116812\pi$
$648$	−2.61358	−	24.3906i	−0.102671	−	0.958152i
$649$		−	46.2539i		−	1.81562i
$650$		0			0
$651$		−	3.77787i		−	0.148066i
$652$	15.8196	−	0.297529i	0.619542	−	0.0116521i
$653$	−5.70477	+	2.90673i	−0.223245	+	0.113749i	−0.562036	−	0.827112i	$-0.689982\pi$
$653$	−5.70477	+	2.90673i	−0.223245	+	0.113749i	0.338791	+	0.940862i	$0.389982\pi$
$654$	4.09158	+	0.941702i	0.159993	+	0.0368235i
$655$		0			0
$656$	7.77083	+	9.89096i	0.303400	+	0.386177i
$657$	0.0397059	−	0.0397059i	0.00154907	−	0.00154907i
$658$	30.9445	+	12.4780i	1.20634	+	0.486445i
$659$	−11.5792	−	8.41281i	−0.451063	−	0.327716i	0.338952	−	0.940804i	$-0.389927\pi$
$659$	−11.5792	−	8.41281i	−0.451063	−	0.327716i	−0.790015	+	0.613087i	$0.789927\pi$
$660$		0			0
$661$	−0.382235	+	0.277710i	−0.0148672	+	0.0108017i	−0.595194	−	0.803582i	$-0.702925\pi$
$661$	−0.382235	+	0.277710i	−0.0148672	+	0.0108017i	0.580327	+	0.814384i	$0.302925\pi$
$662$	22.2310	−	5.55877i	0.864031	−	0.216048i
$663$	−2.44480	+	0.387218i	−0.0949480	+	0.0150383i
$664$	7.40203	+	5.96923i	0.287254	+	0.231651i
$665$		0			0
$666$	−9.43452	+	15.7257i	−0.365580	+	0.609360i
$667$	0.452453	−	0.887989i	0.0175190	−	0.0343831i
$668$	15.4746	−	22.1638i	0.598731	−	0.857543i
$669$	−2.10333	+	0.683413i	−0.0813193	+	0.0264223i
$670$		0			0
$671$	6.98096	+	2.26825i	0.269497	+	0.0875648i
$672$	−1.77499	+	2.28779i	−0.0684719	+	0.0882533i
$673$	21.1799	+	3.35456i	0.816424	+	0.129309i	0.550660	−	0.834729i	$-0.314376\pi$
$673$	21.1799	+	3.35456i	0.816424	+	0.129309i	0.265764	+	0.964038i	$0.414376\pi$
$674$	28.4902	−	2.51198i	1.09740	−	0.0967578i
$675$		0			0
$676$	10.4903	−	1.86434i	0.403471	−	0.0717055i
$677$	−6.95245	+	43.8961i	−0.267204	+	1.68706i	0.380191	+	0.924908i	$0.375858\pi$
$677$	−6.95245	+	43.8961i	−0.267204	+	1.68706i	−0.647395	+	0.762155i	$0.724142\pi$
$678$	1.85761	−	1.16251i	0.0713410	−	0.0446459i
$679$	9.25648	−	28.4885i	0.355231	−	1.09329i
$680$		0			0
$681$	−0.916813	−	2.82166i	−0.0351323	−	0.108126i
$682$	−40.8229	−	34.2075i	−1.56319	−	1.30987i
$683$	21.8180	+	11.1168i	0.834843	+	0.425374i	0.818510	−	0.574493i	$-0.194801\pi$
$683$	21.8180	+	11.1168i	0.834843	+	0.425374i	0.0163335	+	0.999867i	$0.494801\pi$
$684$	−26.7458	−	13.0001i	−1.02265	−	0.497071i
$685$		0			0
$686$	−19.4986	+	16.9730i	−0.744460	+	0.648033i
$687$	0.503849	+	3.18118i	0.0192230	+	0.121369i
$688$	−13.2795	+	7.40796i	−0.506276	+	0.282426i
$689$	3.00217	+	4.13213i	0.114374	+	0.157422i
$690$		0			0
$691$	−9.83947	+	13.5429i	−0.374311	+	0.515195i	−0.954066	−	0.299596i	$-0.903148\pi$
$691$	−9.83947	+	13.5429i	−0.374311	+	0.515195i	0.579755	+	0.814791i	$0.303148\pi$
$692$	−2.09882	−	0.638571i	−0.0797851	−	0.0242748i
$693$	−28.6452	−	28.6452i	−1.08814	−	1.08814i
$694$	7.54511	−	3.20873i	0.286408	−	0.121802i
$695$		0			0
$696$	−0.00605649	+	0.120230i	−0.000229571	+	0.00455730i
$697$	6.67656	+	13.1035i	0.252893	+	0.496330i
$698$	−0.00516630	+	0.0746063i	−0.000195547	+	0.00282389i
$699$	−5.58072			−0.211082
$700$		0			0
$701$	50.9450			1.92417			0.962083	−	0.272757i	$-0.0879356\pi$
$701$	50.9450			1.92417			0.962083	+	0.272757i	$0.0879356\pi$
$702$	−0.308364	+	4.45307i	−0.0116384	+	0.168070i
$703$	9.96723	+	19.5618i	0.375921	+	0.737787i
$704$	8.64933	+	39.8955i	0.325984	+	1.50362i
$705$		0			0
$706$	5.35848	−	2.27882i	0.201669	−	0.0857644i
$707$	22.3682	+	22.3682i	0.841244	+	0.841244i
$708$	−1.00830	+	3.31402i	−0.0378942	+	0.124549i
$709$	23.6335	−	32.5288i	0.887576	−	1.22164i	−0.0866885	−	0.996235i	$-0.527628\pi$
$709$	23.6335	−	32.5288i	0.887576	−	1.22164i	0.974264	−	0.225408i	$-0.0723715\pi$
$710$		0			0
$711$	11.7492	+	16.1714i	0.440629	+	0.606473i
$712$	−1.00132	−	2.23678i	−0.0375260	−	0.0838268i
$713$	−5.16574	−	32.6152i	−0.193458	−	1.22145i
$714$	−2.55355	+	2.22280i	−0.0955643	+	0.0831863i
$715$		0			0
$716$	−21.0955	+	43.4011i	−0.788376	+	1.62197i
$717$	−0.0778596	−	0.0396715i	−0.00290772	−	0.00148156i
$718$	−29.9533	−	25.0993i	−1.11785	−	0.936698i
$719$	3.14270	+	9.67223i	0.117203	+	0.360713i	0.992400	−	0.123053i	$-0.0392685\pi$
$719$	3.14270	+	9.67223i	0.117203	+	0.360713i	−0.875197	+	0.483766i	$0.839269\pi$
$720$		0			0
$721$	−1.60612	+	4.94314i	−0.0598152	+	0.184092i
$722$	−7.40157	+	4.63197i	−0.275458	+	0.172384i
$723$	0.652848	−	4.12192i	0.0242797	−	0.153296i
$724$	−2.44578	−	13.7619i	−0.0908966	−	0.511455i
$725$		0			0
$726$	4.04805	−	0.356916i	0.150237	−	0.0132464i
$727$	8.65722	+	1.37117i	0.321078	+	0.0508538i	0.314893	−	0.949127i	$-0.398031\pi$
$727$	8.65722	+	1.37117i	0.321078	+	0.0508538i	0.00618506	+	0.999981i	$0.498031\pi$
$728$	−15.5687	+	14.0754i	−0.577016	+	0.521670i
$729$	−23.8224	−	7.74037i	−0.882312	−	0.286681i
$730$		0			0
$731$	−16.9084	+	5.49386i	−0.625378	+	0.203198i
$732$	−0.450729	−	0.314697i	−0.0166594	−	0.0116315i
$733$	0.119518	−	0.234567i	0.00441450	−	0.00866394i	−0.888789	−	0.458317i	$-0.848452\pi$
$733$	0.119518	−	0.234567i	0.00441450	−	0.00866394i	0.893203	+	0.449653i	$0.148452\pi$
$734$	4.93920	−	8.23282i	0.182309	−	0.303879i
$735$		0			0
$736$	−12.1957	+	22.1780i	−0.449538	+	0.817493i
$737$	17.0437	−	2.69946i	0.627814	−	0.0994360i
$738$	12.7854	−	3.19695i	0.470638	−	0.117681i
$739$	5.97506	−	4.34113i	0.219796	−	0.159691i	−0.472439	−	0.881363i	$-0.656626\pi$
$739$	5.97506	−	4.34113i	0.219796	−	0.159691i	0.692235	+	0.721672i	$0.256626\pi$
$740$		0			0
$741$	2.14841	+	1.56091i	0.0789238	+	0.0573415i
$742$	6.47886	+	2.61254i	0.237846	+	0.0959092i
$743$	7.03452	−	7.03452i	0.258071	−	0.258071i	−0.566198	−	0.824269i	$-0.691586\pi$
$743$	7.03452	−	7.03452i	0.258071	−	0.258071i	0.824269	+	0.566198i	$0.191586\pi$
$744$	2.17920	+	3.34083i	0.0798935	+	0.122481i
$745$		0			0
$746$	15.8316	+	3.64373i	0.579634	+	0.133406i
$747$	8.87719	−	4.52315i	0.324799	−	0.165494i
$748$	0.897500	+	47.7200i	0.0328159	+	1.74482i
$749$			30.6785i			1.12097i
$750$		0			0
$751$		−	29.2029i		−	1.06563i	−0.846232	−	0.532814i	$-0.821134\pi$
$751$		−	29.2029i		−	1.06563i	0.846232	−	0.532814i	$-0.178866\pi$
$752$	−34.5624	+	6.81530i	−1.26036	+	0.248529i
$753$	0.923203	−	0.470395i	0.0336434	−	0.0171422i
$754$	−0.195709	+	0.850332i	−0.00712731	+	0.0309673i
$755$		0			0
$756$	2.87348	+	5.38664i	0.104507	+	0.195910i
$757$	20.1848	−	20.1848i	0.733630	−	0.733630i	−0.237707	−	0.971337i	$-0.576396\pi$
$757$	20.1848	−	20.1848i	0.733630	−	0.733630i	0.971337	+	0.237707i	$0.0763959\pi$
$758$	6.77172	−	16.7933i	0.245960	−	0.609959i
$759$	3.52933	+	2.56421i	0.128107	+	0.0930749i
$760$		0			0
$761$	7.93313	−	5.76375i	0.287576	−	0.208936i	−0.434639	−	0.900605i	$-0.643124\pi$
$761$	7.93313	−	5.76375i	0.287576	−	0.208936i	0.722215	+	0.691669i	$0.243124\pi$
$762$	−1.05221	−	4.20807i	−0.0381176	−	0.152442i
$763$	41.1103	−	6.51124i	1.48829	−	0.235723i
$764$	21.8688	−	22.7071i	0.791184	−	0.821516i
$765$		0			0
$766$	22.3523	+	13.4100i	0.807620	+	0.484524i
$767$	−11.3988	+	22.3715i	−0.411589	+	0.807788i
$768$	0.249980	−	3.04700i	0.00902038	−	0.109949i
$769$	17.2976	−	5.62032i	0.623766	−	0.202674i	0.0199544	−	0.999801i	$-0.493648\pi$
$769$	17.2976	−	5.62032i	0.623766	−	0.202674i	0.603812	+	0.797127i	$0.293648\pi$
$770$		0			0
$771$	2.06162	+	0.669862i	0.0742475	+	0.0241245i
$772$	−10.9974	−	14.5531i	−0.395807	−	0.523778i
$773$	−42.7233	−	6.76671i	−1.53665	−	0.243382i	−0.670025	−	0.742339i	$-0.733717\pi$
$773$	−42.7233	−	6.76671i	−1.53665	−	0.243382i	−0.866627	+	0.498957i	$0.833717\pi$
$774$	1.39931	+	15.8706i	0.0502970	+	0.570455i
$775$		0			0
$776$	8.24751	+	30.5323i	0.296068	+	1.09604i
$777$	0.350388	−	2.21226i	0.0125701	−	0.0793644i
$778$	−18.6603	−	29.8179i	−0.669006	−	1.06902i
$779$	4.87557	−	15.0055i	0.174685	−	0.537626i
$780$		0			0
$781$	9.04296	+	27.8314i	0.323582	+	0.995884i
$782$	−19.0060	+	22.6816i	−0.679653	+	0.811091i
$783$	0.226151	+	0.115230i	0.00808199	+	0.00411798i
$784$	−0.192752	+	0.679133i	−0.00688401	+	0.0242547i
$785$		0			0
$786$	−2.41432	−	2.77356i	−0.0861158	−	0.0989297i
$787$	−1.89589	−	11.9702i	−0.0675813	−	0.426691i	−0.998162	−	0.0606043i	$-0.980697\pi$
$787$	−1.89589	−	11.9702i	−0.0675813	−	0.426691i	0.930581	−	0.366087i	$-0.119303\pi$
$788$	3.73729	+	10.8064i	0.133135	+	0.384961i
$789$	−2.23378	−	3.07453i	−0.0795245	−	0.109456i
$790$		0			0
$791$	12.7693	−	17.5755i	0.454025	−	0.624911i
$792$	41.8549	+	8.80785i	1.48725	+	0.312973i
$793$	−2.81747	−	2.81747i	−0.100051	−	0.100051i
$794$	−15.4140	−	36.2449i	−0.547022	−	1.28628i
$795$		0			0
$796$	48.8094	+	6.79243i	1.73000	+	0.240751i
$797$	7.47486	+	14.6702i	0.264773	+	0.519646i	0.984668	−	0.174436i	$-0.0558103\pi$
$797$	7.47486	+	14.6702i	0.264773	+	0.519646i	−0.719895	+	0.694083i	$0.755810\pi$
$798$	3.62342	+	0.250912i	0.128268	+	0.00888221i
$799$	−41.1877			−1.45712
$800$		0			0
$801$	−2.56770			−0.0907253
$802$	14.7590	+	1.02202i	0.521158	+	0.0360889i
$803$	0.0438956	+	0.0861499i	0.00154904	+	0.00304016i
$804$	−1.28000	−	0.178128i	−0.0451423	−	0.00628210i
$805$		0			0
$806$	11.3146	+	26.6055i	0.398540	+	0.937139i
$807$	1.36921	+	1.36921i	0.0481985	+	0.0481985i
$808$	−32.6833	−	6.87780i	−1.14980	−	0.241960i
$809$	12.5671	−	17.2972i	0.441837	−	0.608136i	−0.528782	−	0.848757i	$-0.677351\pi$
$809$	12.5671	−	17.2972i	0.441837	−	0.608136i	0.970619	+	0.240621i	$0.0773512\pi$
$810$		0			0
$811$	−18.5355	−	25.5120i	−0.650871	−	0.895847i	0.348265	−	0.937396i	$-0.386771\pi$
$811$	−18.5355	−	25.5120i	−0.650871	−	0.895847i	−0.999136	+	0.0415488i	$0.986771\pi$
$812$	0.390066	+	1.12788i	0.0136886	+	0.0395807i
$813$	−0.0564703	−	0.356539i	−0.00198050	−	0.0125044i
$814$	−20.7326	−	23.8176i	−0.726677	−	0.834806i
$815$		0			0
$816$	0.975957	−	3.43863i	0.0341653	−	0.120376i
$817$	16.9947	+	8.65922i	0.594569	+	0.302948i
$818$	−14.0988	+	16.8254i	−0.492953	+	0.588286i
$819$	6.79540	+	20.9141i	0.237451	+	0.730798i
$820$		0			0
$821$	−6.22378	+	19.1548i	−0.217211	+	0.668508i	0.781778	+	0.623557i	$0.214313\pi$
$821$	−6.22378	+	19.1548i	−0.217211	+	0.668508i	−0.998989	+	0.0449507i	$0.985687\pi$
$822$	2.70867	+	4.32826i	0.0944757	+	0.150966i
$823$	6.60034	−	41.6729i	0.230073	−	1.45263i	−0.554289	−	0.832324i	$-0.687010\pi$
$823$	6.60034	−	41.6729i	0.230073	−	1.45263i	0.784363	−	0.620302i	$-0.212990\pi$
$824$	−1.43105	−	5.29776i	−0.0498531	−	0.184556i
$825$		0			0
$826$	3.01613	+	34.2082i	0.104945	+	1.19026i
$827$	−13.5996	−	2.15397i	−0.472905	−	0.0749008i	−0.0845669	−	0.996418i	$-0.526951\pi$
$827$	−13.5996	−	2.15397i	−0.472905	−	0.0749008i	−0.388338	+	0.921517i	$0.626951\pi$
$828$	15.9879	+	21.1571i	0.555620	+	0.735261i
$829$	35.5980	+	11.5665i	1.23637	+	0.401721i	0.853018	−	0.521881i	$-0.174770\pi$
$829$	35.5980	+	11.5665i	1.23637	+	0.401721i	0.383352	+	0.923602i	$0.374770\pi$
$830$		0			0
$831$	2.08074	−	0.676072i	0.0721800	−	0.0234527i
$832$	5.64848	−	21.4277i	0.195826	−	0.742872i
$833$	−0.374718	+	0.735426i	−0.0129832	+	0.0254810i
$834$	1.68864	+	1.01308i	0.0584727	+	0.0350802i
$835$		0			0
$836$	35.5203	−	36.8820i	1.22850	−	1.27559i
$837$	8.30637	−	1.31560i	0.287110	−	0.0454738i
$838$	−12.3858	−	49.5339i	−0.427859	−	1.71112i
$839$	−6.53213	+	4.74587i	−0.225514	+	0.163846i	−0.694805	−	0.719198i	$-0.744509\pi$
$839$	−6.53213	+	4.74587i	−0.225514	+	0.163846i	0.469291	+	0.883044i	$0.344509\pi$
$840$		0			0
$841$	−23.4214	−	17.0166i	−0.807633	−	0.586780i
$842$	8.47419	−	21.0153i	0.292040	−	0.724234i
$843$	3.13022	−	3.13022i	0.107810	−	0.107810i
$844$	−18.6899	−	35.0362i	−0.643332	−	1.20600i
$845$		0			0
$846$	−8.27867	+	35.9698i	−0.284626	+	1.23667i
$847$	35.8955	−	18.2897i	1.23338	−	0.628440i
$848$	−7.23635	+	1.42692i	−0.248497	+	0.0490008i
$849$			3.64092i			0.124956i
$850$		0			0
$851$		−	19.5780i		−	0.671126i
$852$	−0.0412114	−	2.19121i	−0.00141188	−	0.0750695i
$853$	31.0768	−	15.8344i	1.06405	−	0.542160i	0.167851	−	0.985812i	$-0.446317\pi$
$853$	31.0768	−	15.8344i	1.06405	−	0.542160i	0.896199	+	0.443652i	$0.146317\pi$
$854$	−5.31085	−	1.22232i	−0.181733	−	0.0418271i
$855$		0			0
$856$	−17.6964	−	27.1294i	−0.604850	−	0.927265i
$857$	−31.7738	+	31.7738i	−1.08537	+	1.08537i	−0.0893726	+	0.995998i	$0.528486\pi$
$857$	−31.7738	+	31.7738i	−1.08537	+	1.08537i	−0.995998	+	0.0893726i	$0.971514\pi$
$858$	−3.54234	−	1.42841i	−0.120933	−	0.0487652i
$859$	34.2690	+	24.8979i	1.16924	+	0.849504i	0.990918	−	0.134468i	$-0.0429325\pi$
$859$	34.2690	+	24.8979i	1.16924	+	0.849504i	0.178324	+	0.983972i	$0.442932\pi$
$860$		0			0
$861$	−1.30223	+	0.946129i	−0.0443800	+	0.0322440i
$862$	−9.24400	+	2.31143i	−0.314852	+	0.0787275i
$863$	16.4649	−	2.60778i	0.560472	−	0.0887700i	0.130230	−	0.991484i	$-0.458428\pi$
$863$	16.4649	−	2.60778i	0.560472	−	0.0887700i	0.430242	+	0.902714i	$0.358428\pi$
$864$	−5.64826	−	3.10597i	−0.192158	−	0.105667i
$865$		0			0
$866$	−7.67388	+	12.7911i	−0.260769	+	0.434658i
$867$	0.422595	−	0.829389i	0.0143521	−	0.0281675i
$868$	32.4222	+	22.6370i	1.10048	+	0.768350i
$869$	−32.7340	+	10.6359i	−1.11043	+	0.360799i
$870$		0			0
$871$	−8.90876	−	2.89463i	−0.301862	−	0.0980809i
$872$	−32.5986	+	29.4718i	−1.10393	+	0.998042i
$873$	32.7288	+	5.18374i	1.10770	+	0.175443i
$874$	31.6248	−	2.78836i	1.06973	−	0.0943177i
$875$		0			0
$876$	−0.00126705	−	0.00712941i	−4.28096e−5	−	0.000240880i
$877$	2.32444	−	14.6759i	0.0784907	−	0.495571i	−0.916856	−	0.399217i	$-0.869282\pi$
$877$	2.32444	−	14.6759i	0.0784907	−	0.495571i	0.995347	−	0.0963539i	$-0.0307181\pi$
$878$	−12.5541	+	7.85645i	−0.423679	+	0.265142i
$879$	0.770780	−	2.37222i	0.0259978	−	0.0800129i
$880$		0			0
$881$	−15.1162	−	46.5230i	−0.509279	−	1.56740i	−0.793456	−	0.608628i	$-0.791720\pi$
$881$	−15.1162	−	46.5230i	−0.509279	−	1.56740i	0.284177	−	0.958772i	$-0.408280\pi$
$882$	0.566939	+	0.475066i	0.0190898	+	0.0159963i
$883$	−1.45332	−	0.740506i	−0.0489083	−	0.0249200i	0.429365	−	0.903131i	$-0.358737\pi$
$883$	−1.45332	−	0.740506i	−0.0489083	−	0.0249200i	−0.478274	+	0.878211i	$0.658737\pi$
$884$	11.3261	−	23.3018i	0.380937	−	0.783725i
$885$		0			0
$886$	4.93478	−	4.29560i	0.165787	−	0.144313i
$887$	4.23212	+	26.7206i	0.142101	+	0.897189i	0.950989	+	0.309226i	$0.100070\pi$
$887$	4.23212	+	26.7206i	0.142101	+	0.897189i	−0.808888	+	0.587963i	$0.799930\pi$
$888$	0.966254	+	2.15845i	0.0324254	+	0.0724329i
$889$	−25.2757	−	34.7890i	−0.847719	−	1.16679i
$890$		0			0
$891$	26.0125	−	35.8032i	0.871452	−	1.19945i
$892$	6.73800	−	22.1461i	0.225605	−	0.741505i
$893$	31.2456	+	31.2456i	1.04560	+	1.04560i
$894$	0.529300	−	0.225097i	0.0177024	−	0.00752837i
$895$		0			0
$896$	−8.99834	−	28.9417i	−0.300614	−	0.966873i
$897$	−1.07510	−	2.11000i	−0.0358965	−	0.0704508i
$898$	−1.76764	+	25.5264i	−0.0589870	+	0.851828i
$899$	1.64396			0.0548290
$900$		0			0
$901$	−8.62349			−0.287290
$902$	−1.56767	+	22.6386i	−0.0521976	+	0.753784i
$903$	−0.883420	−	1.73381i	−0.0293984	−	0.0576976i
$904$	−1.15397	+	22.9080i	−0.0383806	+	0.761910i
$905$		0			0
$906$	−1.51781	+	0.645485i	−0.0504260	+	0.0214448i
$907$	35.5508	+	35.5508i	1.18045	+	1.18045i	0.979629	+	0.200818i	$0.0643600\pi$
$907$	35.5508	+	35.5508i	1.18045	+	1.18045i	0.200818	+	0.979629i	$0.435640\pi$
$908$	29.7094	+	9.03918i	0.985942	+	0.299976i
$909$	−20.5690	+	28.3108i	−0.682230	+	0.939009i
$910$		0			0
$911$	3.41319	+	4.69785i	0.113084	+	0.155647i	0.861807	−	0.507236i	$-0.169333\pi$
$911$	3.41319	+	4.69785i	0.113084	+	0.155647i	−0.748723	+	0.662883i	$0.769333\pi$
$912$	−3.34898	+	1.86823i	−0.110896	+	0.0618631i
$913$	2.68368	+	16.9441i	0.0888169	+	0.560768i
$914$	−35.3920	+	30.8078i	−1.17066	+	1.01903i
$915$		0			0
$916$	−30.3204	−	14.7375i	−1.00181	−	0.486941i
$917$	−32.4808	−	16.5498i	−1.07261	−	0.546522i
$918$	−5.77650	−	4.84041i	−0.190653	−	0.159757i
$919$	13.3369	+	41.0468i	0.439944	+	1.35401i	0.887934	+	0.459971i	$0.152140\pi$
$919$	13.3369	+	41.0468i	0.439944	+	1.35401i	−0.447990	+	0.894039i	$0.647860\pi$
$920$		0			0
$921$	−0.765886	+	2.35716i	−0.0252368	+	0.0776709i
$922$	−38.7938	+	24.2775i	−1.27760	+	0.799537i
$923$	2.48500	−	15.6897i	0.0817948	−	0.516432i
$924$	−5.14340	+	0.914093i	−0.169205	+	0.0300714i
$925$		0			0
$926$	−43.2004	+	3.80897i	−1.41965	+	0.125171i
$927$	−5.67890	−	0.899449i	−0.186520	−	0.0295418i
$928$	−0.995540	−	0.772396i	−0.0326802	−	0.0253551i
$929$	34.3019	+	11.1453i	1.12541	+	0.365667i	0.811829	−	0.583895i	$-0.198472\pi$
$929$	34.3019	+	11.1453i	1.12541	+	0.365667i	0.313578	+	0.949562i	$0.398472\pi$
$930$		0			0
$931$	0.842173	−	0.273639i	0.0276011	−	0.00896814i
$932$	33.4397	−	47.8946i	1.09535	−	1.56884i
$933$	0.361052	−	0.708605i	0.0118203	−	0.0231987i
$934$	11.3406	−	18.9028i	0.371075	−	0.618520i
$935$		0			0
$936$	−18.0733	−	14.5748i	−0.590743	−	0.476394i
$937$	−37.4056	+	5.92447i	−1.22199	+	0.193544i	−0.733905	−	0.679252i	$-0.762304\pi$
$937$	−37.4056	+	5.92447i	−1.22199	+	0.193544i	−0.488084	+	0.872796i	$0.662304\pi$
$938$	−12.4291	+	3.10785i	−0.405824	+	0.101475i
$939$	−3.46333	+	2.51626i	−0.113022	+	0.0821149i
$940$		0			0
$941$	25.8261	+	18.7637i	0.841906	+	0.611680i	0.922902	−	0.385034i	$-0.125810\pi$
$941$	25.8261	+	18.7637i	0.841906	+	0.611680i	−0.0809965	+	0.996714i	$0.525810\pi$
$942$	−4.06886	−	1.64073i	−0.132571	−	0.0534578i
$943$	−9.94877	+	9.94877i	−0.323977	+	0.323977i
$944$	−22.3997	−	28.5110i	−0.729047	−	0.927954i
$945$		0			0
$946$	−26.7343	−	6.15307i	−0.869208	−	0.200054i
$947$	3.14898	−	1.60449i	0.102328	−	0.0521388i	−0.402077	−	0.915606i	$-0.631712\pi$
$947$	3.14898	−	1.60449i	0.102328	−	0.0521388i	0.504405	+	0.863467i	$0.331712\pi$
$948$	2.57720	−	0.0484710i	0.0837035	−	0.00157426i
$949$		−	0.0524856i		−	0.00170375i
$950$		0			0
$951$			1.20369i			0.0390325i
$952$	−3.77551	−	35.2340i	−0.122365	−	1.14194i
$953$	−48.0361	+	24.4756i	−1.55604	+	0.792843i	−0.999284	−	0.0378308i	$-0.987955\pi$
$953$	−48.0361	+	24.4756i	−1.55604	+	0.792843i	−0.556759	+	0.830674i	$0.687955\pi$
$954$	−1.73331	+	7.53101i	−0.0561179	+	0.243825i
$955$		0			0
$956$	0.807001	−	0.430491i	0.0261003	−	0.0139231i
$957$	−0.153571	+	0.153571i	−0.00496426	+	0.00496426i
$958$	3.68402	−	9.13605i	0.119025	−	0.295172i
$959$	40.9512	+	29.7528i	1.32238	+	0.960767i
$960$		0			0
$961$	18.9882	−	13.7957i	0.612523	−	0.445024i
$962$	4.15806	+	16.6292i	0.134061	+	0.536146i
$963$	−33.5198	+	5.30901i	−1.08016	+	0.171080i
$964$	31.4630	+	30.3014i	1.01336	+	0.975943i
$965$		0			0
$966$	−2.77741	−	1.66628i	−0.0893618	−	0.0536118i
$967$	7.03165	−	13.8004i	0.226123	−	0.443791i	−0.749873	−	0.661582i	$-0.769885\pi$
$967$	7.03165	−	13.8004i	0.226123	−	0.443791i	0.975995	+	0.217792i	$0.0698853\pi$
$968$	−21.1928	+	36.8796i	−0.681163	+	1.18535i
$969$	−4.26415	+	1.38551i	−0.136984	+	0.0445089i
$970$		0			0
$971$	−16.7721	−	5.44959i	−0.538242	−	0.174886i	0.0272659	−	0.999628i	$-0.491320\pi$
$971$	−16.7721	−	5.44959i	−0.538242	−	0.174886i	−0.565508	+	0.824743i	$0.691320\pi$
$972$	−8.09889	+	6.12014i	−0.259772	+	0.196303i
$973$	19.2817	+	3.05393i	0.618144	+	0.0979044i
$974$	2.59016	+	29.3769i	0.0829940	+	0.941295i
$975$		0			0
$976$	5.40154	−	1.98256i	0.172899	−	0.0634602i
$977$	8.24291	−	52.0437i	0.263714	−	1.66502i	−0.399605	−	0.916687i	$-0.630853\pi$
$977$	8.24291	−	52.0437i	0.263714	−	1.66502i	0.663319	−	0.748337i	$-0.269147\pi$
$978$	−1.13408	−	1.81219i	−0.0362640	−	0.0579473i
$979$	1.36625	−	4.20489i	0.0436656	−	0.134389i
$980$		0			0
$981$	14.2286	+	43.7910i	0.454283	+	1.39814i
$982$	4.46875	−	5.33297i	0.142603	−	0.170182i
$983$	−15.6381	−	7.96803i	−0.498779	−	0.254141i	0.186455	−	0.982463i	$-0.440300\pi$
$983$	−15.6381	−	7.96803i	−0.498779	−	0.254141i	−0.685234	+	0.728323i	$0.740300\pi$
$984$	0.605826	−	1.58785i	0.0193130	−	0.0506188i
$985$		0			0
$986$	−0.967261	−	1.11119i	−0.0308039	−	0.0353875i
$987$	−0.705221	−	4.45259i	−0.0224474	−	0.141728i
$988$	−26.2693	+	9.08498i	−0.835736	+	0.289032i
$989$	−9.99752	−	13.7604i	−0.317903	−	0.437555i
$990$		0			0
$991$	−20.0939	+	27.6568i	−0.638302	+	0.878548i	−0.998524	−	0.0543192i	$-0.982701\pi$
$991$	−20.0939	+	27.6568i	−0.638302	+	0.878548i	0.360221	+	0.932867i	$0.382701\pi$
$992$	−41.7293	−	1.31600i	−1.32491	−	0.0417832i
$993$	−2.18931	−	2.18931i	−0.0694756	−	0.0694756i
$994$	−8.50278	−	19.9937i	−0.269692	−	0.634161i
$995$		0			0
$996$	0.177087	−	1.27252i	0.00561122	−	0.0403214i
$997$	−0.954518	−	1.87335i	−0.0302299	−	0.0593295i	0.875398	−	0.483404i	$-0.160600\pi$
$997$	−0.954518	−	1.87335i	−0.0302299	−	0.0593295i	−0.905628	+	0.424074i	$0.860600\pi$
$998$	−27.9542	−	1.93576i	−0.884875	−	0.0612754i
$999$	4.98610			0.157753

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	500.2.l.f.343.12		96
4.3	odd	2	inner	500.2.l.f.343.1		96
5.2	odd	4		500.2.l.d.407.5		96
5.3	odd	4		500.2.l.e.407.8		96
5.4	even	2		100.2.l.b.23.1	✓	96
15.14	odd	2		900.2.bj.d.523.12		96
20.3	even	4		500.2.l.e.407.7		96
20.7	even	4		500.2.l.d.407.6		96
20.19	odd	2		100.2.l.b.23.12	yes	96
25.9	even	10		500.2.l.e.43.7		96
25.12	odd	20	inner	500.2.l.f.207.1		96
25.13	odd	20		100.2.l.b.87.12	yes	96
25.16	even	5		500.2.l.d.43.6		96
60.59	even	2		900.2.bj.d.523.1		96
75.38	even	20		900.2.bj.d.487.1		96
100.59	odd	10		500.2.l.e.43.8		96
100.63	even	20		100.2.l.b.87.1	yes	96
100.87	even	20	inner	500.2.l.f.207.12		96
100.91	odd	10		500.2.l.d.43.5		96
300.263	odd	20		900.2.bj.d.487.12		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.2.l.b.23.1	✓	96	5.4	even	2
100.2.l.b.23.12	yes	96	20.19	odd	2
100.2.l.b.87.1	yes	96	100.63	even	20
100.2.l.b.87.12	yes	96	25.13	odd	20
500.2.l.d.43.5		96	100.91	odd	10
500.2.l.d.43.6		96	25.16	even	5
500.2.l.d.407.5		96	5.2	odd	4
500.2.l.d.407.6		96	20.7	even	4
500.2.l.e.43.7		96	25.9	even	10
500.2.l.e.43.8		96	100.59	odd	10
500.2.l.e.407.7		96	20.3	even	4
500.2.l.e.407.8		96	5.3	odd	4
500.2.l.f.207.1		96	25.12	odd	20	inner
500.2.l.f.207.12		96	100.87	even	20	inner
500.2.l.f.343.1		96	4.3	odd	2	inner
500.2.l.f.343.12		96	1.1	even	1	trivial
900.2.bj.d.487.1		96	75.38	even	20
900.2.bj.d.487.12		96	300.263	odd	20
900.2.bj.d.523.1		96	60.59	even	2
900.2.bj.d.523.12		96	15.14	odd	2

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:	\( N \)	\(=\)	\( 500 = 2^{2} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	500.l (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.41083 + 0.0976968i) q^{2} +(-0.0867473 - 0.170251i) q^{3} +(1.98091 + 0.275668i) q^{4} +(-0.105753 - 0.248671i) q^{6} +(-1.89427 - 1.89427i) q^{7} +(2.76781 + 0.582451i) q^{8} +(1.74190 - 2.39751i) q^{9} +(2.99934 + 4.12824i) q^{11} +(-0.124906 - 0.361166i) q^{12} +(-0.433317 - 2.73586i) q^{13} +(-2.48743 - 2.85756i) q^{14} +(3.84801 + 1.09215i) q^{16} +(4.16697 + 2.12318i) q^{17} +(2.69176 - 3.21232i) q^{18} +(-1.55045 - 4.77181i) q^{19} +(-0.158179 + 0.486824i) q^{21} +(3.82826 + 6.11729i) q^{22} +(-0.699923 + 4.41914i) q^{23} +(-0.140937 - 0.521748i) q^{24} +(-0.344055 - 3.90218i) q^{26} +(-1.12546 - 0.178255i) q^{27} +(-3.23018 - 4.27456i) q^{28} +(-0.211843 - 0.0688321i) q^{29} +(-7.01920 + 2.28068i) q^{31} +(5.32221 + 1.91678i) q^{32} +(0.442653 - 0.868756i) q^{33} +(5.67148 + 3.40256i) q^{34} +(4.11146 - 4.26907i) q^{36} +(-4.32186 + 0.684516i) q^{37} +(-1.72125 - 6.88371i) q^{38} +(-0.428194 + 0.311101i) q^{39} +(2.54404 + 1.84835i) q^{41} +(-0.270725 + 0.671374i) q^{42} +(-2.68807 + 2.68807i) q^{43} +(4.80341 + 9.00450i) q^{44} +(-1.41921 + 6.16630i) q^{46} +(-7.84709 + 3.99829i) q^{47} +(-0.147866 - 0.749870i) q^{48} +0.176489i q^{49} -0.893612i q^{51} +(-0.104174 - 5.53894i) q^{52} +(-1.64295 + 0.837124i) q^{53} +(-1.57042 - 0.361442i) q^{54} +(-4.13965 - 6.34628i) q^{56} +(-0.677908 + 0.677908i) q^{57} +(-0.292151 - 0.117807i) q^{58} +(-7.33328 - 5.32794i) q^{59} +(1.16375 - 0.845512i) q^{61} +(-10.1258 + 2.53191i) q^{62} +(-7.84114 + 1.24191i) q^{63} +(7.32150 + 3.22422i) q^{64} +(0.709385 - 1.18243i) q^{66} +(1.53527 - 3.01313i) q^{67} +(7.66911 + 5.35453i) q^{68} +(0.813081 - 0.264186i) q^{69} +(5.45415 + 1.77216i) q^{71} +(6.21766 - 5.62128i) q^{72} +(0.0187149 + 0.00296414i) q^{73} +(-6.16431 + 0.543507i) q^{74} +(-1.75588 - 9.87994i) q^{76} +(2.13843 - 13.5015i) q^{77} +(-0.634505 + 0.397079i) q^{78} +(-2.08434 + 6.41493i) q^{79} +(-2.68002 - 8.24826i) q^{81} +(3.40864 + 2.85627i) q^{82} +(2.99552 + 1.52629i) q^{83} +(-0.447539 + 0.920749i) q^{84} +(-4.05504 + 3.52981i) q^{86} +(0.00665810 + 0.0420376i) q^{87} +(5.89710 + 13.1731i) q^{88} +(-0.509284 - 0.700969i) q^{89} +(-4.36162 + 6.00326i) q^{91} +(-2.60470 + 8.56098i) q^{92} +(0.997185 + 0.997185i) q^{93} +(-11.4616 + 4.87429i) q^{94} +(-0.135354 - 1.07239i) q^{96} +(5.07638 + 9.96296i) q^{97} +(-0.0172424 + 0.248997i) q^{98} +15.1221 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 10 q^{2} - 10 q^{4} - 6 q^{6} + 10 q^{8} - 20 q^{9} + 10 q^{12} + 20 q^{13} - 10 q^{14} - 14 q^{16} + 20 q^{17} - 20 q^{18} - 12 q^{21} + 10 q^{22} - 12 q^{26} + 10 q^{28} - 20 q^{29} + 50 q^{32}+ \cdots + 130 q^{98}+O(q^{100}) \) 96 * q + 10 * q^2 - 10 * q^4 - 6 * q^6 + 10 * q^8 - 20 * q^9 + 10 * q^12 + 20 * q^13 - 10 * q^14 - 14 * q^16 + 20 * q^17 - 20 * q^18 - 12 * q^21 + 10 * q^22 - 12 * q^26 + 10 * q^28 - 20 * q^29 + 50 * q^32 + 20 * q^33 - 60 * q^34 - 10 * q^36 - 40 * q^37 - 20 * q^38 - 28 * q^41 - 90 * q^42 + 60 * q^44 - 6 * q^46 - 120 * q^48 - 80 * q^52 + 40 * q^53 + 120 * q^54 - 6 * q^56 + 20 * q^57 - 60 * q^58 + 12 * q^61 - 40 * q^62 + 20 * q^64 - 30 * q^66 + 10 * q^68 - 20 * q^69 + 40 * q^72 + 20 * q^73 + 20 * q^77 - 20 * q^78 - 36 * q^81 + 50 * q^82 - 90 * q^84 - 6 * q^86 + 130 * q^88 + 160 * q^89 + 110 * q^92 - 60 * q^93 - 170 * q^94 + 14 * q^96 - 180 * q^97 + 130 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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