LMFDB - Embedded newform 500.2.l.d.43.5

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			43.5
Character	$\chi$	$=$	500.43
Dual form			500.2.l.d.407.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0976968 - 1.41083i) q^{2} +(-0.170251 - 0.0867473i) q^{3} +(-1.98091 + 0.275668i) q^{4} +(-0.105753 + 0.248671i) q^{6} +(1.89427 + 1.89427i) q^{7} +(0.582451 + 2.76781i) q^{8} +(-1.74190 - 2.39751i) q^{9} +(2.99934 - 4.12824i) q^{11} +(0.361166 + 0.124906i) q^{12} +(-2.73586 - 0.433317i) q^{13} +(2.48743 - 2.85756i) q^{14} +(3.84801 - 1.09215i) q^{16} +(-2.12318 - 4.16697i) q^{17} +(-3.21232 + 2.69176i) q^{18} +(1.55045 - 4.77181i) q^{19} +(-0.158179 - 0.486824i) q^{21} +(-6.11729 - 3.82826i) q^{22} +(4.41914 - 0.699923i) q^{23} +(0.140937 - 0.521748i) q^{24} +(-0.344055 + 3.90218i) q^{26} +(0.178255 + 1.12546i) q^{27} +(-4.27456 - 3.23018i) q^{28} +(0.211843 - 0.0688321i) q^{29} +(-7.01920 - 2.28068i) q^{31} +(-1.91678 - 5.32221i) q^{32} +(-0.868756 + 0.442653i) q^{33} +(-5.67148 + 3.40256i) q^{34} +(4.11146 + 4.26907i) q^{36} +(-0.684516 + 4.32186i) q^{37} +(-6.88371 - 1.72125i) q^{38} +(0.428194 + 0.311101i) q^{39} +(2.54404 - 1.84835i) q^{41} +(-0.671374 + 0.270725i) q^{42} +(2.68807 - 2.68807i) q^{43} +(-4.80341 + 9.00450i) q^{44} +(-1.41921 - 6.16630i) q^{46} +(-3.99829 + 7.84709i) q^{47} +(-0.749870 - 0.147866i) q^{48} +0.176489i q^{49} +0.893612i q^{51} +(5.53894 + 0.104174i) q^{52} +(0.837124 - 1.64295i) q^{53} +(1.57042 - 0.361442i) q^{54} +(-4.13965 + 6.34628i) q^{56} +(-0.677908 + 0.677908i) q^{57} +(-0.117807 - 0.292151i) q^{58} +(7.33328 - 5.32794i) q^{59} +(1.16375 + 0.845512i) q^{61} +(-2.53191 + 10.1258i) q^{62} +(1.24191 - 7.84114i) q^{63} +(-7.32150 + 3.22422i) q^{64} +(0.709385 + 1.18243i) q^{66} +(3.01313 - 1.53527i) q^{67} +(5.35453 + 7.66911i) q^{68} +(-0.813081 - 0.264186i) q^{69} +(5.45415 - 1.77216i) q^{71} +(5.62128 - 6.21766i) q^{72} +(0.00296414 + 0.0187149i) q^{73} +(6.16431 + 0.543507i) q^{74} +(-1.75588 + 9.87994i) q^{76} +(13.5015 - 2.13843i) q^{77} +(0.397079 - 0.634505i) q^{78} +(2.08434 + 6.41493i) q^{79} +(-2.68002 + 8.24826i) q^{81} +(-2.85627 - 3.40864i) q^{82} +(1.52629 + 2.99552i) q^{83} +(0.447539 + 0.920749i) q^{84} +(-4.05504 - 3.52981i) q^{86} +(-0.0420376 - 0.00665810i) q^{87} +(13.1731 + 5.89710i) q^{88} +(0.509284 - 0.700969i) q^{89} +(-4.36162 - 6.00326i) q^{91} +(-8.56098 + 2.60470i) q^{92} +(0.997185 + 0.997185i) q^{93} +(11.4616 + 4.87429i) q^{94} +(-0.135354 + 1.07239i) q^{96} +(-9.96296 - 5.07638i) q^{97} +(0.248997 - 0.0172424i) q^{98} -15.1221 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 10 q^{4} - 6 q^{6} - 30 q^{8} + 20 q^{9} + 10 q^{14} - 14 q^{16} - 20 q^{18} - 12 q^{21} + 50 q^{22} - 12 q^{26} + 40 q^{28} + 20 q^{29} + 50 q^{32} + 60 q^{34} - 10 q^{36} + 40 q^{37} - 70 q^{38}+ \cdots + 70 q^{98}+O(q^{100}) $ 96 * q + 10 * q^4 - 6 * q^6 - 30 * q^8 + 20 * q^9 + 10 * q^14 - 14 * q^16 - 20 * q^18 - 12 * q^21 + 50 * q^22 - 12 * q^26 + 40 * q^28 + 20 * q^29 + 50 * q^32 + 60 * q^34 - 10 * q^36 + 40 * q^37 - 70 * q^38 - 28 * q^41 - 60 * q^42 - 60 * q^44 - 6 * q^46 + 100 * q^52 + 80 * q^53 - 120 * q^54 - 6 * q^56 + 20 * q^57 + 120 * q^58 + 12 * q^61 - 20 * q^64 - 30 * q^66 + 10 * q^68 + 20 * q^69 - 150 * q^72 - 140 * q^77 - 130 * q^78 - 36 * q^81 + 50 * q^82 + 90 * q^84 - 6 * q^86 + 110 * q^88 - 160 * q^89 + 90 * q^92 - 60 * q^93 + 170 * q^94 + 14 * q^96 + 70 * q^98

Character values

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

$n$	$251$	$377$
$\chi(n)$	$-1$	$e\left(\frac{19}{20}\right)$

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 $

$2$	−0.0976968	−	1.41083i	−0.0690820	−	0.997611i
$2$	−0.0976968	−	1.41083i	−0.0690820	−	0.997611i
$3$	−0.170251	−	0.0867473i	−0.0982946	−	0.0500836i	0.404152	−	0.914692i	$-0.367567\pi$
$3$	−0.170251	−	0.0867473i	−0.0982946	−	0.0500836i	−0.502447	+	0.864608i	$0.667567\pi$
$4$	−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	0.967776	−	0.251811i	$-0.0810262\pi$
$7$	1.89427	+	1.89427i	0.715965	+	0.715965i	−0.251811	+	0.967776i	$0.581026\pi$
$8$	0.582451	+	2.76781i	0.205927	+	0.978567i
$9$	−1.74190	−	2.39751i	−0.580632	−	0.799171i
$10$		0			0
$11$	2.99934	−	4.12824i	0.904336	−	1.24471i	−0.0647283	−	0.997903i	$-0.520618\pi$
$11$	2.99934	−	4.12824i	0.904336	−	1.24471i	0.969064	−	0.246809i	$-0.0793819\pi$
$12$	0.361166	+	0.124906i	0.104260	+	0.0360572i
$13$	−2.73586	−	0.433317i	−0.758790	−	0.120181i	−0.234962	−	0.972005i	$-0.575497\pi$
$13$	−2.73586	−	0.433317i	−0.758790	−	0.120181i	−0.523828	+	0.851824i	$0.675497\pi$
$14$	2.48743	−	2.85756i	0.664795	−	0.763715i
$15$		0			0
$16$	3.84801	−	1.09215i	0.962004	−	0.273037i
$17$	−2.12318	−	4.16697i	−0.514947	−	1.01064i	−0.991329	−	0.131402i	$-0.958052\pi$
$17$	−2.12318	−	4.16697i	−0.514947	−	1.01064i	0.476383	−	0.879238i	$-0.341948\pi$
$18$	−3.21232	+	2.69176i	−0.757151	+	0.634453i
$19$	1.55045	−	4.77181i	0.355699	−	1.09473i	−0.599905	−	0.800072i	$-0.704795\pi$
$19$	1.55045	−	4.77181i	0.355699	−	1.09473i	0.955603	−	0.294657i	$-0.0952052\pi$
$20$		0			0
$21$	−0.158179	−	0.486824i	−0.0345174	−	0.106234i
$22$	−6.11729	−	3.82826i	−1.30421	−	0.816188i
$23$	4.41914	−	0.699923i	0.921455	−	0.145944i	0.322355	−	0.946619i	$-0.395525\pi$
$23$	4.41914	−	0.699923i	0.921455	−	0.145944i	0.599100	+	0.800675i	$0.295525\pi$
$24$	0.140937	−	0.521748i	0.0287686	−	0.106501i
$25$		0			0
$26$	−0.344055	+	3.90218i	−0.0674747	+	0.765280i
$27$	0.178255	+	1.12546i	0.0343052	+	0.216595i
$28$	−4.27456	−	3.23018i	−0.807816	−	0.610447i
$29$	0.211843	−	0.0688321i	0.0393383	−	0.0127818i	−0.289282	−	0.957244i	$-0.593416\pi$
$29$	0.211843	−	0.0688321i	0.0393383	−	0.0127818i	0.328620	+	0.944462i	$0.393416\pi$
$30$		0			0
$31$	−7.01920	−	2.28068i	−1.26069	−	0.409622i	−0.398947	−	0.916974i	$-0.630624\pi$
$31$	−7.01920	−	2.28068i	−1.26069	−	0.409622i	−0.861739	+	0.507352i	$0.830624\pi$
$32$	−1.91678	−	5.32221i	−0.338842	−	0.940843i
$33$	−0.868756	+	0.442653i	−0.151231	+	0.0770560i
$34$	−5.67148	+	3.40256i	−0.972652	+	0.583533i
$35$		0			0
$36$	4.11146	+	4.26907i	0.685243	+	0.711512i
$37$	−0.684516	+	4.32186i	−0.112534	+	0.710510i	0.865320	+	0.501220i	$0.167115\pi$
$37$	−0.684516	+	4.32186i	−0.112534	+	0.710510i	−0.977854	+	0.209290i	$0.932885\pi$
$38$	−6.88371	−	1.72125i	−1.11669	−	0.279223i
$39$	0.428194	+	0.311101i	0.0685659	+	0.0498160i
$40$		0			0
$41$	2.54404	−	1.84835i	0.397312	−	0.288664i	−0.371133	−	0.928580i	$-0.621031\pi$
$41$	2.54404	−	1.84835i	0.397312	−	0.288664i	0.768445	+	0.639915i	$0.221031\pi$
$42$	−0.671374	+	0.270725i	−0.103595	+	0.0417738i
$43$	2.68807	−	2.68807i	0.409927	−	0.409927i	−0.471786	−	0.881713i	$-0.656391\pi$
$43$	2.68807	−	2.68807i	0.409927	−	0.409927i	0.881713	+	0.471786i	$0.156391\pi$
$44$	−4.80341	+	9.00450i	−0.724141	+	1.35748i
$45$		0			0
$46$	−1.41921	−	6.16630i	−0.209251	−	0.909171i
$47$	−3.99829	+	7.84709i	−0.583211	+	1.14462i	0.391298	+	0.920264i	$0.372026\pi$
$47$	−3.99829	+	7.84709i	−0.583211	+	1.14462i	−0.974508	+	0.224351i	$0.927974\pi$
$48$	−0.749870	−	0.147866i	−0.108234	−	0.0213425i
$49$			0.176489i			0.0252127i
$50$		0			0
$51$			0.893612i			0.125131i
$52$	5.53894	+	0.104174i	0.768113	+	0.0144464i
$53$	0.837124	−	1.64295i	0.114988	−	0.225676i	−0.826339	−	0.563173i	$-0.809580\pi$
$53$	0.837124	−	1.64295i	0.114988	−	0.225676i	0.941327	+	0.337497i	$0.109580\pi$
$54$	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
$58$	−0.117807	−	0.292151i	−0.0154688	−	0.0383614i
$59$	7.33328	−	5.32794i	0.954712	−	0.693639i	0.00279513	−	0.999996i	$-0.499110\pi$
$59$	7.33328	−	5.32794i	0.954712	−	0.693639i	0.951917	+	0.306357i	$0.0991103\pi$
$60$		0			0
$61$	1.16375	+	0.845512i	0.149003	+	0.108257i	0.659789	−	0.751451i	$-0.270646\pi$
$61$	1.16375	+	0.845512i	0.149003	+	0.108257i	−0.510786	+	0.859708i	$0.670646\pi$
$62$	−2.53191	+	10.1258i	−0.321552	+	1.28597i
$63$	1.24191	−	7.84114i	0.156467	−	0.987891i
$64$	−7.32150	+	3.22422i	−0.915188	+	0.403028i
$65$		0			0
$66$	0.709385	+	1.18243i	0.0873193	+	0.145546i
$67$	3.01313	−	1.53527i	0.368113	−	0.187563i	−0.260142	−	0.965570i	$-0.583769\pi$
$67$	3.01313	−	1.53527i	0.368113	−	0.187563i	0.628255	+	0.778007i	$0.283769\pi$
$68$	5.35453	+	7.66911i	0.649332	+	0.930016i
$69$	−0.813081	−	0.264186i	−0.0978834	−	0.0318043i
$70$		0			0
$71$	5.45415	−	1.77216i	0.647288	−	0.210317i	0.0330703	−	0.999453i	$-0.489471\pi$
$71$	5.45415	−	1.77216i	0.647288	−	0.210317i	0.614218	+	0.789136i	$0.289471\pi$
$72$	5.62128	−	6.21766i	0.662475	−	0.732759i
$73$	0.00296414	+	0.0187149i	0.000346927	+	0.00219041i	0.987861	−	0.155339i	$-0.0496470\pi$
$73$	0.00296414	+	0.0187149i	0.000346927	+	0.00219041i	−0.987514	+	0.157530i	$0.949647\pi$
$74$	6.16431	+	0.543507i	0.716586	+	0.0631814i
$75$		0			0
$76$	−1.75588	+	9.87994i	−0.201413	+	1.13331i
$77$	13.5015	−	2.13843i	1.53864	−	0.243697i
$78$	0.397079	−	0.634505i	0.0449604	−	0.0718435i
$79$	2.08434	+	6.41493i	0.234506	+	0.721736i	0.997187	+	0.0749601i	$0.0238830\pi$
$79$	2.08434	+	6.41493i	0.234506	+	0.721736i	−0.762680	+	0.646776i	$0.776117\pi$
$80$		0			0
$81$	−2.68002	+	8.24826i	−0.297780	+	0.916474i
$82$	−2.85627	−	3.40864i	−0.315422	−	0.376422i
$83$	1.52629	+	2.99552i	0.167532	+	0.328801i	0.959475	−	0.281795i	$-0.0909299\pi$
$83$	1.52629	+	2.99552i	0.167532	+	0.328801i	−0.791942	+	0.610596i	$0.790930\pi$
$84$	0.447539	+	0.920749i	0.0488305	+	0.100462i
$85$		0			0
$86$	−4.05504	−	3.52981i	−0.437266	−	0.380629i
$87$	−0.0420376	−	0.00665810i	−0.00450690	−	0.000713823i
$88$	13.1731	+	5.89710i	1.40426	+	0.628633i
$89$	0.509284	−	0.700969i	0.0539840	−	0.0743026i	−0.781172	−	0.624316i	$-0.785378\pi$
$89$	0.509284	−	0.700969i	0.0539840	−	0.0743026i	0.835156	+	0.550014i	$0.185378\pi$
$90$		0			0
$91$	−4.36162	−	6.00326i	−0.457222	−	0.629313i
$92$	−8.56098	+	2.60470i	−0.892544	+	0.271559i
$93$	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
$97$	−9.96296	−	5.07638i	−1.01158	−	0.515428i	−0.132040	−	0.991244i	$-0.542153\pi$
$97$	−9.96296	−	5.07638i	−1.01158	−	0.515428i	−0.879545	+	0.475816i	$0.842153\pi$
$98$	0.248997	−	0.0172424i	0.0251525	−	0.00174175i
$99$	−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	$0.699884\pi$
$102$	1.26074	−	0.0873030i	0.124832	−	0.00864429i
$103$	−1.72871	−	0.880821i	−0.170335	−	0.0867899i	0.366744	−	0.930322i	$-0.380472\pi$
$103$	−1.72871	−	0.880821i	−0.170335	−	0.0867899i	−0.537079	+	0.843532i	$0.680472\pi$
$104$	−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	0.980308	−	0.197472i	$-0.0632733\pi$
$107$	8.09772	+	8.09772i	0.782836	+	0.782836i	−0.197472	+	0.980308i	$0.563273\pi$
$108$	−0.663361	−	2.18029i	−0.0638319	−	0.209799i
$109$	9.13259	+	12.5699i	0.874743	+	1.20398i	0.977849	+	0.209310i	$0.0671219\pi$
$109$	9.13259	+	12.5699i	0.874743	+	1.20398i	−0.103106	+	0.994670i	$0.532878\pi$
$110$		0			0
$111$	0.491450	−	0.676422i	0.0466463	−	0.0642032i
$112$	9.35798	+	5.22035i	0.884246	+	0.493276i
$113$	8.00964	+	1.26860i	0.753483	+	0.119340i	0.521349	−	0.853344i	$-0.325429\pi$
$113$	8.00964	+	1.26860i	0.753483	+	0.119340i	0.232135	+	0.972684i	$0.425429\pi$
$114$	1.02265	+	0.890188i	0.0957796	+	0.0833737i
$115$		0			0
$116$	−0.400668	+	0.194749i	−0.0372011	+	0.0180820i
$117$	3.72669	+	7.31405i	0.344533	+	0.676184i
$118$	−8.23328	−	9.82552i	−0.757935	−	0.904513i
$119$	3.87149	−	11.9152i	0.354899	−	1.09227i
$120$		0			0
$121$	−4.64713	−	14.3024i	−0.422467	−	1.30022i
$122$	1.07918	−	1.72446i	0.0977047	−	0.156125i
$123$	−0.593466	+	0.0939957i	−0.0535110	+	0.00847531i
$124$	14.5331	+	2.58285i	1.30511	+	0.231947i
$125$		0			0
$126$	−11.1839	−	0.986083i	−0.996340	−	0.0878472i
$127$	−2.51108	−	15.8543i	−0.222822	−	1.40684i	−0.804755	−	0.593608i	$-0.797703\pi$
$127$	−2.51108	−	15.8543i	−0.222822	−	1.40684i	0.581932	−	0.813237i	$-0.302297\pi$
$128$	5.26413	+	10.0144i	0.465288	+	0.885159i
$129$	−0.690830	+	0.224464i	−0.0608242	+	0.0197630i
$130$		0			0
$131$	12.9418	+	4.20505i	1.13073	+	0.367397i	0.813854	−	0.581069i	$-0.197365\pi$
$131$	12.9418	+	4.20505i	1.13073	+	0.367397i	0.316878	+	0.948466i	$0.397365\pi$
$132$	1.59890	−	1.11634i	0.139167	−	0.0971653i
$133$	11.9761	−	6.10210i	1.03846	−	0.529119i
$134$	−2.46038	−	4.10104i	−0.212545	−	0.354276i
$135$		0			0
$136$	10.2967	−	8.30361i	0.882937	−	0.712028i
$137$	−2.95587	+	18.6626i	−0.252537	+	1.59445i	0.456790	+	0.889575i	$0.348999\pi$
$137$	−2.95587	+	18.6626i	−0.252537	+	1.59445i	−0.709327	+	0.704880i	$0.751001\pi$
$138$	−0.293287	+	1.17293i	−0.0249663	+	0.0998467i
$139$	5.89560	+	4.28340i	0.500058	+	0.363313i	0.809039	−	0.587755i	$-0.199988\pi$
$139$	5.89560	+	4.28340i	0.500058	+	0.363313i	−0.308981	+	0.951068i	$0.599988\pi$
$140$		0			0
$141$	1.36143	−	0.989135i	0.114653	−	0.0833002i
$142$	−3.03308	−	7.52177i	−0.254530	−	0.631213i
$143$	−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
$147$	0.0153100	−	0.0300475i	0.00126274	−	0.00247828i
$148$	0.164565	−	8.74992i	0.0135272	−	0.719239i
$149$			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	$0.0798902\pi$
$151$			6.10369i			0.496712i	−0.968669	+	0.248356i	$0.920110\pi$
$152$	14.1105	+	1.51202i	1.14451	+	0.122641i
$153$	−6.29202	+	12.3488i	−0.508680	+	0.998340i
$154$	−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	$0.0256624\pi$
$158$	8.84677	−	3.56737i	0.703811	−	0.283805i
$159$	−0.285043	+	0.207096i	−0.0226054	+	0.0164238i
$160$		0			0
$161$	9.69687	+	7.04519i	0.764221	+	0.555239i
$162$	11.8988	+	2.97524i	0.934856	+	0.233757i
$163$	−1.23758	+	7.81379i	−0.0969349	+	0.612023i	0.890620	+	0.454748i	$0.150271\pi$
$163$	−1.23758	+	7.81379i	−0.0969349	+	0.612023i	−0.987555	+	0.157275i	$0.949729\pi$
$164$	−4.52998	+	4.36273i	−0.353732	+	0.340672i
$165$		0			0
$166$	4.07707	−	2.44600i	0.316442	−	0.189846i
$167$	12.0426	−	6.13600i	0.931883	−	0.474818i	0.0789735	−	0.996877i	$-0.474836\pi$
$167$	12.0426	−	6.13600i	0.931883	−	0.474818i	0.852910	+	0.522059i	$0.174836\pi$
$168$	1.25530	−	0.721358i	0.0968487	−	0.0556540i
$169$	−5.06658	−	1.64623i	−0.389737	−	0.126633i
$170$		0			0
$171$	−14.1412	+	4.59476i	−1.08141	+	0.351370i
$172$	−4.58381	+	6.06584i	−0.349512	+	0.462516i
$173$	−0.171594	−	1.08340i	−0.0130460	−	0.0823695i	0.980306	−	0.197483i	$-0.0632768\pi$
$173$	−0.171594	−	1.08340i	−0.0130460	−	0.0823695i	−0.993352	+	0.115114i	$0.963277\pi$
$174$	−0.00528654	+	0.0599586i	−0.000400772	+	0.00454545i
$175$		0			0
$176$	7.03287	−	19.1613i	0.530122	−	1.44433i
$177$	−1.71068	+	0.270946i	−0.128583	+	0.0203655i
$178$	−1.03871	−	0.650033i	−0.0778544	−	0.0487220i
$179$	7.45601	+	22.9472i	0.557289	+	1.71516i	0.689822	+	0.723979i	$0.257689\pi$
$179$	7.45601	+	22.9472i	0.557289	+	1.71516i	−0.132533	+	0.991179i	$0.542311\pi$
$180$		0			0
$181$	−2.15964	+	6.64670i	−0.160525	+	0.494045i	−0.998679	−	0.0513890i	$-0.983635\pi$
$181$	−2.15964	+	6.64670i	−0.160525	+	0.494045i	0.838154	+	0.545434i	$0.183635\pi$
$182$	−8.04349	+	6.74003i	−0.596223	+	0.499604i
$183$	−0.124784	−	0.244901i	−0.00922426	−	0.0181036i
$184$	4.51119	+	11.8237i	0.332569	+	0.871652i
$185$		0			0
$186$	1.30944	−	1.50429i	0.0960130	−	0.110300i
$187$	−23.5704	−	3.73319i	−1.72364	−	0.272998i
$188$	5.75707	−	16.6466i	0.419877	−	1.21408i
$189$	−1.79426	+	2.46958i	−0.130513	+	0.179636i
$190$		0			0
$191$	9.26511	+	12.7523i	0.670400	+	0.922727i	0.999769	−	0.0214746i	$-0.00683611\pi$
$191$	9.26511	+	12.7523i	0.670400	+	0.922727i	−0.329369	+	0.944201i	$0.606836\pi$
$192$	1.52619	+	0.0861932i	0.110143	+	0.00622046i
$193$	−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
$197$	−5.09406	−	2.59555i	−0.362936	−	0.184925i	0.263007	−	0.964794i	$-0.415286\pi$
$197$	−5.09406	−	2.59555i	−0.362936	−	0.184925i	−0.625943	+	0.779869i	$0.715286\pi$
$198$	1.47738	+	21.3347i	0.104993	+	1.51619i
$199$	−24.6399			−1.74668			−0.873338	−	0.487115i	$-0.838049\pi$
$199$	−24.6399			−1.74668			−0.873338	+	0.487115i	$0.838049\pi$
$200$		0			0
$201$	−0.646170			−0.0455773
$202$	1.15364	+	16.6597i	0.0811699	+	1.17217i
$203$	0.531674	+	0.270901i	0.0373162	+	0.0190136i
$204$	−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
$208$	−11.0009	+	1.32055i	−0.762773	+	0.0915636i
$209$	−15.0488	−	20.7129i	−1.04095	−	1.43274i
$210$		0			0
$211$	−11.6703	+	16.0628i	−0.803419	+	1.10581i	0.188886	+	0.981999i	$0.439512\pi$
$211$	−11.6703	+	16.0628i	−0.803419	+	1.10581i	−0.992306	+	0.123813i	$0.960488\pi$
$212$	−1.20536	+	3.48530i	−0.0827845	+	0.239372i
$213$	−1.08231	−	0.171420i	−0.0741584	−	0.0117455i
$214$	10.6334	−	12.2157i	0.726886	−	0.835046i
$215$		0			0
$216$	−3.01123	+	1.14890i	−0.204888	+	0.0781728i
$217$	−8.97603	−	17.6165i	−0.609333	−	1.19588i
$218$	16.8419	−	14.1126i	1.14068	−	0.955827i
$219$	0.00111881	−	0.00344336i	7.56025e−5	−	0.000232681i
$220$		0			0
$221$	4.00309	+	12.3203i	0.269277	+	0.828750i
$222$	−1.00233	−	0.627270i	−0.0672722	−	0.0420996i
$223$	−11.4317	+	1.81060i	−0.765524	+	0.121247i	−0.526972	−	0.849883i	$-0.676673\pi$
$223$	−11.4317	+	1.81060i	−0.765524	+	0.121247i	−0.238552	+	0.971130i	$0.576673\pi$
$224$	6.45080	−	13.7126i	0.431012	−	0.916210i
$225$		0			0
$226$	1.00727	−	11.4242i	0.0670028	−	0.759928i
$227$	−2.42897	−	15.3359i	−0.161216	−	1.01788i	−0.927077	−	0.374872i	$-0.877687\pi$
$227$	−2.42897	−	15.3359i	−0.161216	−	1.01788i	0.765861	−	0.643007i	$-0.222313\pi$
$228$	1.15600	−	1.52975i	0.0765579	−	0.101310i
$229$	16.0312	−	5.20884i	1.05937	−	0.344210i	0.273030	−	0.962006i	$-0.411974\pi$
$229$	16.0312	−	5.20884i	1.05937	−	0.344210i	0.786339	+	0.617796i	$0.211974\pi$
$230$		0			0
$231$	−2.48416	−	0.807152i	−0.163446	−	0.0531067i
$232$	0.313902	+	0.546250i	0.0206087	+	0.0358631i
$233$	−26.0233	+	13.2595i	−1.70484	+	0.868660i	−0.720267	+	0.693697i	$0.755981\pi$
$233$	−26.0233	+	13.2595i	−1.70484	+	0.868660i	−0.984575	+	0.174963i	$0.944019\pi$
$234$	9.95483	−	5.97231i	0.650768	−	0.390422i
$235$		0			0
$236$	−13.0578	+	12.5757i	−0.849992	+	0.818610i
$237$	0.201617	−	1.27296i	0.0130964	−	0.0826876i
$238$	−17.1886	−	4.29796i	−1.11417	−	0.278595i
$239$	−0.369981	−	0.268807i	−0.0239321	−	0.0173877i	0.575755	−	0.817622i	$-0.304708\pi$
$239$	−0.369981	−	0.268807i	−0.0239321	−	0.0173877i	−0.599687	+	0.800235i	$0.704708\pi$
$240$		0			0
$241$	17.6697	−	12.8378i	1.13820	−	0.826953i	0.151335	−	0.988483i	$-0.451643\pi$
$241$	17.6697	−	12.8378i	1.13820	−	0.826953i	0.986868	+	0.161530i	$0.0516429\pi$
$242$	−19.7243	+	7.95364i	−1.26793	+	0.511279i
$243$	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
$247$	−6.30953	+	12.3832i	−0.401466	+	0.787921i
$248$	2.22413	−	20.7562i	0.141233	−	1.31802i
$249$		−	0.642393i		−	0.0407100i
$250$		0			0
$251$		−	5.42259i		−	0.342271i	−0.985248	−	0.171135i	$-0.945256\pi$
$251$		−	5.42259i		−	0.342271i	0.985248	−	0.171135i	$-0.0547436\pi$
$252$	−0.298570	+	15.8750i	−0.0188082	+	1.00003i
$253$	10.3651	−	20.3426i	0.651647	−	1.27893i
$254$	−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	$0.365121\pi$
$258$	0.384174	+	0.952717i	0.0239176	+	0.0593136i
$259$	−9.48341	+	6.89010i	−0.589271	+	0.428130i
$260$		0			0
$261$	−0.534035	−	0.387999i	−0.0330559	−	0.0240165i
$262$	4.66826	−	18.6696i	0.288406	−	1.15341i
$263$	−3.11132	+	19.6441i	−0.191852	+	1.21131i	0.684275	+	0.729224i	$0.260119\pi$
$263$	−3.11132	+	19.6441i	−0.191852	+	1.21131i	−0.876127	+	0.482081i	$0.839881\pi$
$264$	−1.73119	−	2.14672i	−0.106547	−	0.132122i
$265$		0			0
$266$	−9.77908	−	16.3001i	−0.599594	−	0.999422i
$267$	−0.147513	+	0.0751618i	−0.00902767	+	0.00459983i
$268$	−5.54552	+	3.87185i	−0.338747	+	0.236511i
$269$	9.63789	+	3.13154i	0.587633	+	0.190933i	0.587717	−	0.809067i	$-0.300027\pi$
$269$	9.63789	+	3.13154i	0.587633	+	0.190933i	−8.44003e−5		1.00000i	$0.500027\pi$
$270$		0			0
$271$	1.79674	−	0.583795i	0.109144	−	0.0354630i	−0.253936	−	0.967221i	$-0.581725\pi$
$271$	1.79674	−	0.583795i	0.109144	−	0.0354630i	0.363080	+	0.931758i	$0.381725\pi$
$272$	−12.7210	−	13.7158i	−0.771322	−	0.831640i
$273$	0.221805	+	1.40042i	0.0134243	+	0.0847574i
$274$	26.6186	+	2.34696i	1.60809	+	0.141785i
$275$		0			0
$276$	1.68347	+	0.299188i	0.101333	+	0.0180090i
$277$	−11.3089	+	1.79116i	−0.679488	+	0.107620i	−0.486632	−	0.873607i	$-0.661775\pi$
$277$	−11.3089	+	1.79116i	−0.679488	+	0.107620i	−0.192855	+	0.981227i	$0.561775\pi$
$278$	5.46719	−	8.73619i	0.327900	−	0.523962i
$279$	6.75877	+	20.8013i	0.404637	+	1.24534i
$280$		0			0
$281$	7.15917	−	22.0337i	0.427080	−	1.31442i	−0.473908	−	0.880574i	$-0.657157\pi$
$281$	7.15917	−	22.0337i	0.427080	−	1.31442i	0.900988	−	0.433844i	$-0.142843\pi$
$282$	−1.52851	−	1.82411i	−0.0910217	−	0.108624i
$283$	−8.65065	−	16.9779i	−0.514228	−	1.00923i	−0.991455	−	0.130449i	$-0.958358\pi$
$283$	−8.65065	−	16.9779i	−0.514228	−	1.00923i	0.477227	−	0.878780i	$-0.341642\pi$
$284$	−10.3157	+	5.01403i	−0.612121	+	0.297528i
$285$		0			0
$286$	15.0772	+	13.1243i	0.891533	+	0.776057i
$287$	8.32036	+	1.31782i	0.491135	+	0.0777882i
$288$	−9.42125	+	13.8662i	−0.555153	+	0.817076i
$289$	−2.86343	+	3.94118i	−0.168437	+	0.231834i
$290$		0			0
$291$	1.25584	+	1.72852i	0.0736188	+	0.101328i
$292$	−0.0110308	−	0.0362553i	−0.000645528	−	0.00212168i
$293$	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
$297$	5.18082	+	2.63976i	0.300621	+	0.153174i
$298$	3.00298	−	0.207949i	0.173958	−	0.0120462i
$299$	−12.3934			−0.716731
$300$		0			0
$301$	10.1838			0.586986
$302$	8.61130	−	0.596311i	0.495525	−	0.0343138i
$303$	2.01039	+	1.02435i	0.115494	+	0.0588472i
$304$	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	0.918616	−	0.395150i	$-0.129308\pi$
$307$	9.17187	+	9.17187i	0.523466	+	0.523466i	−0.395150	+	0.918616i	$0.629308\pi$
$308$	−26.1559	+	7.95799i	−1.49037	+	0.453449i
$309$	0.217906	+	0.299922i	0.0123962	+	0.0170619i
$310$		0			0
$311$	2.44643	−	3.36722i	0.138724	−	0.190938i	−0.734002	−	0.679147i	$-0.762350\pi$
$311$	2.44643	−	3.36722i	0.138724	−	0.190938i	0.872726	+	0.488209i	$0.162350\pi$
$312$	−0.611666	+	1.36636i	−0.0346288	+	0.0773548i
$313$	−22.1282	−	3.50477i	−1.25076	−	0.198101i	−0.504300	−	0.863529i	$-0.668249\pi$
$313$	−22.1282	−	3.50477i	−1.25076	−	0.198101i	−0.746462	+	0.665427i	$0.768249\pi$
$314$	−17.3182	−	15.0751i	−0.977324	−	0.850735i
$315$		0			0
$316$	−5.89727	−	12.1328i	−0.331748	−	0.682524i
$317$	2.85992	+	5.61291i	0.160629	+	0.315252i	0.957268	−	0.289204i	$-0.0933905\pi$
$317$	2.85992	+	5.61291i	0.160629	+	0.315252i	−0.796639	+	0.604456i	$0.793391\pi$
$318$	0.320026	+	0.381916i	0.0179462	+	0.0214168i
$319$	0.351235	−	1.08099i	0.0196654	−	0.0605239i
$320$		0			0
$321$	−0.676191	−	2.08110i	−0.0377413	−	0.116156i
$322$	8.99225	−	14.3690i	0.501118	−	0.800752i
$323$	−23.1759	+	3.67070i	−1.28954	+	0.204243i
$324$	3.03510	−	17.0779i	0.168617	−	0.948771i
$325$		0			0
$326$	11.1449	+	0.982643i	0.617257	+	0.0544235i
$327$	−0.464426	−	2.93227i	−0.0256828	−	0.162155i
$328$	6.59766	+	5.96484i	0.364295	+	0.329353i
$329$	−22.4383	+	7.29065i	−1.23706	+	0.401946i
$330$		0			0
$331$	15.4106	+	5.00720i	0.847042	+	0.275221i	0.700206	−	0.713940i	$-0.253091\pi$
$331$	15.4106	+	5.00720i	0.847042	+	0.275221i	0.146835	+	0.989161i	$0.453091\pi$
$332$	−3.84922	−	5.51311i	−0.211253	−	0.302571i
$333$	11.5541	−	5.88710i	0.633159	−	0.322611i
$334$	−9.83341	−	16.3906i	−0.538060	−	0.896855i
$335$		0			0
$336$	−1.14036	−	1.70055i	−0.0622116	−	0.0927726i
$337$	3.16369	−	19.9748i	0.172337	−	1.08809i	−0.738174	−	0.674610i	$-0.764312\pi$
$337$	3.16369	−	19.9748i	0.172337	−	1.08809i	0.910511	−	0.413484i	$-0.135688\pi$
$338$	−1.82757	+	7.30894i	−0.0994069	+	0.397554i
$339$	−1.25360	−	0.910796i	−0.0680864	−	0.0494676i
$340$		0			0
$341$	−30.4682	+	22.1364i	−1.64995	+	1.19876i
$342$	7.86399	+	19.5020i	0.425236	+	1.05455i
$343$	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
$347$	2.63206	−	5.16571i	0.141296	−	0.277310i	−0.809504	−	0.587115i	$-0.800264\pi$
$347$	2.63206	−	5.16571i	0.141296	−	0.277310i	0.950800	+	0.309805i	$0.100264\pi$
$348$	0.0851081	+	0.00160068i	0.00456227	+	8.58056e-5i
$349$			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
$352$	−27.7205	−	8.05022i	−1.47751	−	0.429078i
$353$	−1.86927	+	3.66865i	−0.0994913	+	0.195263i	−0.935387	−	0.353626i	$-0.884949\pi$
$353$	−1.86927	+	3.66865i	−0.0994913	+	0.195263i	0.835896	+	0.548888i	$0.184949\pi$
$354$	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
$358$	31.6463	−	12.7611i	1.67256	−	0.674444i
$359$	22.3556	−	16.2423i	1.17989	−	0.857237i	0.187726	−	0.982221i	$-0.439888\pi$
$359$	22.3556	−	16.2423i	1.17989	−	0.857237i	0.992159	+	0.124985i	$0.0398882\pi$
$360$		0			0
$361$	−4.99493	−	3.62903i	−0.262891	−	0.191002i
$362$	9.58838	+	2.39754i	0.503954	+	0.126012i
$363$	−0.449515	+	2.83813i	−0.0235934	+	0.148963i
$364$	10.2949	+	10.6896i	0.539599	+	0.560285i
$365$		0			0
$366$	−0.333325	+	0.199975i	−0.0174232	+	0.0104529i
$367$	6.04885	−	3.08204i	0.315747	−	0.160881i	−0.288934	−	0.957349i	$-0.593301\pi$
$367$	6.04885	−	3.08204i	0.315747	−	0.160881i	0.604681	+	0.796468i	$0.293301\pi$
$368$	16.2405	−	7.51967i	0.846595	−	0.391990i
$369$	−8.86290	−	2.87973i	−0.461384	−	0.149913i
$370$		0			0
$371$	4.69792	−	1.52645i	0.243904	−	0.0792492i
$372$	−2.25023	−	1.70044i	−0.116669	−	0.0881639i
$373$	1.79701	+	11.3458i	0.0930454	+	0.587466i	0.989523	+	0.144376i	$0.0461176\pi$
$373$	1.79701	+	11.3458i	0.0930454	+	0.587466i	−0.896477	+	0.443089i	$0.853882\pi$
$374$	−2.96416	+	33.6187i	−0.153273	+	1.73838i
$375$		0			0
$376$	−24.0480	−	6.49595i	−1.24018	−	0.335003i
$377$	−0.609399	+	0.0965194i	−0.0313857	+	0.00497100i
$378$	3.65947	+	2.29013i	0.188223	+	0.117792i
$379$	−3.95657	−	12.1771i	−0.203235	−	0.625494i	−0.999781	−	0.0209157i	$-0.993342\pi$
$379$	−3.95657	−	12.1771i	−0.203235	−	0.625494i	0.796546	−	0.604578i	$-0.206658\pi$
$380$		0			0
$381$	−0.947807	+	2.91705i	−0.0485576	+	0.149445i
$382$	17.0863	−	14.3174i	0.874210	−	0.732542i
$383$	8.36780	+	16.4227i	0.427575	+	0.839163i	0.999818	+	0.0190788i	$0.00607333\pi$
$383$	8.36780	+	16.4227i	0.427575	+	0.839163i	−0.572243	+	0.820084i	$0.693927\pi$
$384$	−0.0274992	−	2.16162i	−0.00140331	−	0.110310i
$385$		0			0
$386$	−8.46869	+	9.72882i	−0.431045	+	0.495184i
$387$	−11.1270	−	1.76235i	−0.565618	−	0.0895851i
$388$	21.1351	+	7.30939i	1.07297	+	0.371078i
$389$	14.6199	−	20.1226i	0.741258	−	1.02025i	−0.257287	−	0.966335i	$-0.582829\pi$
$389$	14.6199	−	20.1226i	0.741258	−	1.02025i	0.998545	−	0.0539190i	$-0.0171713\pi$
$390$		0			0
$391$	−12.2992	−	16.9284i	−0.621997	−	0.856105i
$392$	−0.488488	+	0.102796i	−0.0246724	+	0.00519199i
$393$	−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
$397$	24.8148	+	12.6438i	1.24542	+	0.634574i	0.947420	−	0.319992i	$-0.103680\pi$
$397$	24.8148	+	12.6438i	1.24542	+	0.634574i	0.298001	+	0.954566i	$0.403680\pi$
$398$	2.40724	+	34.7628i	0.120664	+	1.74250i
$399$	−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	$0.415881\pi$
$402$	0.0631287	+	0.911639i	0.00314857	+	0.0454684i
$403$	18.2153	+	9.28115i	0.907368	+	0.462327i
$404$	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
$408$	−2.47335	+	0.520485i	−0.122449	+	0.0257679i
$409$	9.12365	+	12.5576i	0.451136	+	0.620935i	0.972641	−	0.232313i	$-0.0746294\pi$
$409$	9.12365	+	12.5576i	0.451136	+	0.620935i	−0.521505	+	0.853248i	$0.674629\pi$
$410$		0			0
$411$	2.12217	−	2.92092i	0.104679	−	0.144078i
$412$	3.66723	+	1.26828i	0.180672	+	0.0624836i
$413$	23.9837	+	3.79865i	1.18016	+	0.186919i
$414$	−12.3117	+	14.1436i	−0.605086	+	0.695122i
$415$		0			0
$416$	2.93783	+	15.3914i	0.144039	+	0.754625i
$417$	−0.632159	−	1.24068i	−0.0309569	−	0.0607564i
$418$	−27.7523	+	23.2550i	−1.35741	+	1.13744i
$419$	11.1568	−	34.3371i	0.545045	−	1.67748i	−0.175838	−	0.984419i	$-0.556264\pi$
$419$	11.1568	−	34.3371i	0.545045	−	1.67748i	0.720883	−	0.693056i	$-0.243736\pi$
$420$		0			0
$421$	4.95128	+	15.2385i	0.241311	+	0.742678i	0.996221	+	0.0868504i	$0.0276802\pi$
$421$	4.95128	+	15.2385i	0.241311	+	0.742678i	−0.754911	+	0.655828i	$0.772320\pi$
$422$	23.8022	+	14.8956i	1.15867	+	0.725108i
$423$	25.7781	−	4.08285i	1.25337	−	0.198515i
$424$	5.03495	+	1.36006i	0.244519	+	0.0660504i
$425$		0			0
$426$	−0.136108	+	1.54370i	−0.00659446	+	0.0747926i
$427$	0.602823	+	3.80607i	0.0291726	+	0.184189i
$428$	−18.2731	−	13.8086i	−0.883266	−	0.667463i
$429$	2.56860	−	0.834589i	0.124013	−	0.0402943i
$430$		0			0
$431$	−6.40797	−	2.08208i	−0.308661	−	0.100290i	0.150591	−	0.988596i	$-0.451882\pi$
$431$	−6.40797	−	2.08208i	−0.308661	−	0.100290i	−0.459252	+	0.888306i	$0.651882\pi$
$432$	1.91510	+	4.13610i	0.0921401	+	0.198998i
$433$	9.39790	−	4.78847i	0.451634	−	0.230119i	−0.213351	−	0.976976i	$-0.568438\pi$
$433$	9.39790	−	4.78847i	0.451634	−	0.230119i	0.664985	+	0.746857i	$0.268438\pi$
$434$	−23.9770	+	14.3848i	−1.15093	+	0.690491i
$435$		0			0
$436$	−21.5560	−	22.3823i	−1.03234	−	1.07192i
$437$	3.51178	−	22.1725i	0.167991	−	1.06065i
$438$	−0.00496732	−	0.00124206i	−0.000237347	−	5.93478e-5i
$439$	8.47207	+	6.15532i	0.404350	+	0.293778i	0.771311	−	0.636459i	$-0.219602\pi$
$439$	8.47207	+	6.15532i	0.404350	+	0.293778i	−0.366960	+	0.930237i	$0.619602\pi$
$440$		0			0
$441$	0.423135	−	0.307426i	0.0201493	−	0.0146393i
$442$	16.9908	−	6.85136i	0.808168	−	0.325886i
$443$	−3.27124	+	3.27124i	−0.155421	+	0.155421i	−0.780534	−	0.625113i	$-0.785053\pi$
$443$	−3.27124	+	3.27124i	−0.155421	+	0.155421i	0.625113	+	0.780534i	$0.285053\pi$
$444$	−0.787050	+	1.47541i	−0.0373517	+	0.0700198i
$445$		0			0
$446$	3.67131	+	15.9514i	0.173841	+	0.755319i
$447$	0.184643	−	0.362382i	0.00873331	−	0.0171401i
$448$	−19.9764	−	7.76134i	−0.943797	−	0.366689i
$449$			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
$452$	−16.2161	−	0.304986i	−0.762741	−	0.0143453i
$453$	0.529479	−	1.03916i	0.0248771	−	0.0488241i
$454$	−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	$0.967231\pi$
$458$	−8.91500	−	22.1084i	−0.416571	−	1.03306i
$459$	4.31129	−	3.13234i	0.201234	−	0.146205i
$460$		0			0
$461$	−26.1799	−	19.0208i	−1.21932	−	0.885887i	−0.223275	−	0.974755i	$-0.571675\pi$
$461$	−26.1799	−	19.0208i	−1.21932	−	0.885887i	−0.996043	+	0.0888686i	$0.971675\pi$
$462$	−0.896064	+	3.58359i	−0.0416887	+	0.166724i
$463$	4.79718	−	30.2882i	0.222944	−	1.40761i	−0.581481	−	0.813560i	$-0.697527\pi$
$463$	4.79718	−	30.2882i	0.222944	−	1.40761i	0.804425	−	0.594054i	$-0.202473\pi$
$464$	0.740002	−	0.496231i	0.0343537	−	0.0230369i
$465$		0			0
$466$	21.2494	+	35.4191i	0.984359	+	1.64076i
$467$	13.8884	−	7.07648i	0.642677	−	0.327460i	−0.102100	−	0.994774i	$-0.532556\pi$
$467$	13.8884	−	7.07648i	0.642677	−	0.327460i	0.744777	+	0.667314i	$0.232556\pi$
$468$	−9.39850	−	13.4611i	−0.434446	−	0.622242i
$469$	8.61588	+	2.79947i	0.397844	+	0.129268i
$470$		0			0
$471$	−2.95039	+	0.958640i	−0.135947	+	0.0441718i
$472$	19.0180	+	17.1938i	0.875373	+	0.791410i
$473$	−3.03456	−	19.1594i	−0.139529	−	0.880952i
$474$	−1.81563	−	0.160084i	−0.0833948	−	0.00735291i
$475$		0			0
$476$	−4.38443	+	24.6702i	−0.200960	+	1.13076i
$477$	−5.39718	+	0.854829i	−0.247120	+	0.0391399i
$478$	−0.343096	+	0.548244i	−0.0156929	+	0.0250761i
$479$	−2.15249	−	6.62469i	−0.0983498	−	0.302690i	0.889762	−	0.456424i	$-0.150870\pi$
$479$	−2.15249	−	6.62469i	−0.0983498	−	0.302690i	−0.988112	+	0.153734i	$0.950870\pi$
$480$		0			0
$481$	3.74547	−	11.5274i	0.170779	−	0.525604i
$482$	−19.8382	−	23.6748i	−0.903606	−	1.07836i
$483$	−1.03975	−	2.04063i	−0.0473104	−	0.0928519i
$484$	13.1483	+	27.0507i	0.597649	+	1.22958i
$485$		0			0
$486$	−5.41414	−	4.71287i	−0.245590	−	0.213780i
$487$	−20.5964	−	3.26215i	−0.933313	−	0.147822i	−0.328784	−	0.944405i	$-0.606639\pi$
$487$	−20.5964	−	3.26215i	−0.933313	−	0.147822i	−0.604529	+	0.796583i	$0.706639\pi$
$488$	−1.66239	+	3.71350i	−0.0752528	+	0.168102i
$489$	0.888525	−	1.22295i	0.0401805	−	0.0553037i
$490$		0			0
$491$	2.89183	+	3.98026i	0.130506	+	0.179627i	0.869269	−	0.494339i	$-0.164590\pi$
$491$	2.89183	+	3.98026i	0.130506	+	0.179627i	−0.738763	+	0.673965i	$0.764590\pi$
$492$	1.14969	−	0.349797i	0.0518321	−	0.0157700i
$493$	−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
$497$	13.6886	+	6.97467i	0.614016	+	0.312857i
$498$	−0.906310	+	0.0627597i	−0.0406127	+	0.00281233i
$499$	19.8140			0.886994			0.443497	−	0.896276i	$-0.353738\pi$
$499$	19.8140			0.886994			0.443497	+	0.896276i	$0.353738\pi$
$500$		0			0
$501$	−2.58255			−0.115380
$502$	−7.65038	+	0.529770i	−0.341453	+	0.0236448i
$503$	−24.4770	−	12.4717i	−1.09138	−	0.556084i	−0.186801	−	0.982398i	$-0.559812\pi$
$503$	−24.4770	−	12.4717i	−1.09138	−	0.556084i	−0.904575	+	0.426314i	$0.859812\pi$
$504$	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
$508$	9.34476	+	30.7138i	0.414607	+	1.36270i
$509$	8.04575	+	11.0740i	0.356622	+	0.490847i	0.949204	−	0.314663i	$-0.101891\pi$
$509$	8.04575	+	11.0740i	0.356622	+	0.490847i	−0.592582	+	0.805510i	$0.701891\pi$
$510$		0			0
$511$	−0.0298360	+	0.0410658i	−0.00131987	+	0.00181664i
$512$	−13.1884	−	18.3866i	−0.582852	−	0.812578i
$513$	5.64685	+	0.894374i	0.249315	+	0.0394876i
$514$	12.1013	+	10.5339i	0.533767	+	0.464630i
$515$		0			0
$516$	1.30659	−	0.635083i	0.0575196	−	0.0279580i
$517$	20.4024	+	40.0420i	0.897298	+	1.76105i
$518$	10.6473	+	12.7064i	0.467815	+	0.558287i
$519$	−0.0647681	+	0.199336i	−0.00284300	+	0.00874987i
$520$		0			0
$521$	1.41202	+	4.34576i	0.0618618	+	0.190391i	0.977211	−	0.212270i	$-0.0680855\pi$
$521$	1.41202	+	4.34576i	0.0618618	+	0.190391i	−0.915349	+	0.402661i	$0.868085\pi$
$522$	−0.495229	+	0.791341i	−0.0216756	+	0.0346361i
$523$	35.8180	−	5.67302i	1.56621	−	0.248064i	0.687776	−	0.725923i	$-0.258587\pi$
$523$	35.8180	−	5.67302i	1.56621	−	0.248064i	0.878437	+	0.477859i	$0.158587\pi$
$524$	−26.7958	−	4.76219i	−1.17058	−	0.208037i
$525$		0			0
$526$	28.0185	+	2.47039i	1.22167	+	0.107714i
$527$	5.39950	+	34.0911i	0.235206	+	1.48503i
$528$	−2.85954	+	2.65214i	−0.124446	+	0.115420i
$529$	−2.83537	+	0.921267i	−0.123277	+	0.0400551i
$530$		0			0
$531$	−25.5476	−	8.30092i	−1.10867	−	0.360229i
$532$	−22.0413	+	15.3891i	−0.955613	+	0.667204i
$533$	−7.76106	+	3.95446i	−0.336169	+	0.171286i
$534$	0.120452	+	0.200774i	0.00521249	+	0.00868834i
$535$		0			0
$536$	6.00433	+	7.44555i	0.259347	+	0.321599i
$537$	0.721217	−	4.55359i	0.0311228	−	0.196502i
$538$	3.47650	−	13.9034i	0.149882	−	0.599419i
$539$	0.728590	+	0.529352i	0.0313826	+	0.0228008i
$540$		0			0
$541$	−23.6895	+	17.2114i	−1.01849	+	0.739976i	−0.965973	−	0.258644i	$-0.916724\pi$
$541$	−23.6895	+	17.2114i	−1.01849	+	0.739976i	−0.0525174	+	0.998620i	$0.516724\pi$
$542$	−0.999174	−	2.47786i	−0.0429182	−	0.106433i
$543$	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
$547$	−15.8895	+	31.1849i	−0.679385	+	1.33337i	0.251429	+	0.967876i	$0.419100\pi$
$547$	−15.8895	+	31.1849i	−0.679385	+	1.33337i	−0.930814	+	0.365493i	$0.880900\pi$
$548$	0.710624	−	37.7838i	0.0303563	−	1.61404i
$549$		−	4.26289i		−	0.181936i
$550$		0			0
$551$		−	1.11760i		−	0.0476112i
$552$	0.257636	−	2.40433i	0.0109657	−	0.102335i
$553$	−8.20329	+	16.0999i	−0.348839	+	0.684636i
$554$	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	$-0.0215243\pi$
$558$	28.6869	−	11.5677i	1.21442	−	0.489701i
$559$	−8.51896	+	6.18939i	−0.360314	+	0.261783i
$560$		0			0
$561$	3.68905	+	2.68025i	0.155752	+	0.113160i
$562$	−31.7853	−	7.94779i	−1.34078	−	0.335257i
$563$	4.32450	−	27.3038i	0.182256	−	1.15072i	−0.711674	−	0.702510i	$-0.752063\pi$
$563$	4.32450	−	27.3038i	0.182256	−	1.15072i	0.893929	−	0.448208i	$-0.147937\pi$
$564$	−2.42419	+	2.33469i	−0.102077	+	0.0983082i
$565$		0			0
$566$	−23.1078	+	13.8633i	−0.971294	+	0.582719i
$567$	−20.7011	+	10.5477i	−0.869364	+	0.442963i
$568$	8.08177	+	14.0638i	0.339104	+	0.590105i
$569$	−8.77237	−	2.85032i	−0.367757	−	0.119491i	0.119308	−	0.992857i	$-0.461932\pi$
$569$	−8.77237	−	2.85032i	−0.367757	−	0.119491i	−0.487065	+	0.873366i	$0.661932\pi$
$570$		0			0
$571$	17.2235	−	5.59625i	0.720780	−	0.234196i	0.0744189	−	0.997227i	$-0.476290\pi$
$571$	17.2235	−	5.59625i	0.720780	−	0.234196i	0.646362	+	0.763031i	$0.276290\pi$
$572$	17.0432	−	22.5536i	0.712614	−	0.943015i
$573$	−0.471166	−	2.97482i	−0.0196832	−	0.124275i
$574$	1.04635	−	11.8674i	0.0436737	−	0.495336i
$575$		0			0
$576$	20.4834	+	11.9371i	0.853475	+	0.497381i
$577$	−10.8794	+	1.72312i	−0.452914	+	0.0717345i	−0.378724	−	0.925510i	$-0.623637\pi$
$577$	−10.8794	+	1.72312i	−0.452914	+	0.0717345i	−0.0741898	+	0.997244i	$0.523637\pi$
$578$	5.84010	+	3.65479i	0.242916	+	0.152019i
$579$	0.538533	+	1.65743i	0.0223807	+	0.0688806i
$580$		0			0
$581$	−2.78310	+	8.56552i	−0.115463	+	0.355357i
$582$	2.31596	−	1.94066i	0.0959998	−	0.0804429i
$583$	−4.27167	−	8.38362i	−0.176914	−	0.347214i
$584$	−0.0500726	+	0.0191047i	−0.00207202	+	0.000790556i
$585$		0			0
$586$	12.1209	−	13.9245i	0.500709	−	0.575214i
$587$	46.2814	+	7.33025i	1.91024	+	0.302552i	0.994960	−	0.100273i	$-0.0319715\pi$
$587$	46.2814	+	7.33025i	1.91024	+	0.302552i	0.915277	+	0.402825i	$0.131972\pi$
$588$	−0.0220445	+	0.0637419i	−0.000909101	+	0.00262867i
$589$	−21.7659	+	29.9582i	−0.896849	+	1.23441i
$590$		0			0
$591$	0.642112	+	0.883792i	0.0264130	+	0.0363543i
$592$	2.08608	+	17.3782i	0.0857375	+	0.714239i
$593$	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
$597$	4.19497	+	2.13745i	0.171689	+	0.0874798i
$598$	1.21080	+	17.4851i	0.0495132	+	0.715019i
$599$	7.21615			0.294844			0.147422	−	0.989074i	$-0.452902\pi$
$599$	7.21615			0.294844			0.147422	+	0.989074i	$0.452902\pi$
$600$		0			0
$601$	−15.0642			−0.614483			−0.307241	−	0.951632i	$-0.599406\pi$
$601$	−15.0642			−0.614483			−0.307241	+	0.951632i	$0.599406\pi$
$602$	−0.994928	−	14.3677i	−0.0405502	−	0.585584i
$603$	−8.92939	−	4.54975i	−0.363633	−	0.185280i
$604$	−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	0.776235	−	0.630443i	$-0.217127\pi$
$607$	3.59194	+	3.59194i	0.145792	+	0.145792i	−0.630443	+	0.776235i	$0.717127\pi$
$608$	−28.3685	+	0.894649i	−1.15049	+	0.0362828i
$609$	−0.0670182	−	0.0922426i	−0.00271571	−	0.00373786i
$610$		0			0
$611$	14.3390	−	19.7360i	0.580095	−	0.798433i
$612$	9.05976	−	26.1963i	0.366219	−	1.05892i
$613$	4.97817	+	0.788465i	0.201066	+	0.0318458i	0.256155	−	0.966636i	$-0.417544\pi$
$613$	4.97817	+	0.788465i	0.201066	+	0.0318458i	−0.0550888	+	0.998481i	$0.517544\pi$
$614$	12.0439	−	13.8360i	0.486053	−	0.558378i
$615$		0			0
$616$	13.7828	+	36.1241i	0.555323	+	1.45548i
$617$	−8.43913	−	16.5627i	−0.339746	−	0.666790i	0.656408	−	0.754406i	$-0.272075\pi$
$617$	−8.43913	−	16.5627i	−0.339746	−	0.666790i	−0.996154	+	0.0876162i	$0.972075\pi$
$618$	0.401851	−	0.336731i	0.0161648	−	0.0135453i
$619$	−6.54265	+	20.1362i	−0.262971	+	0.809343i	0.729182	+	0.684320i	$0.239901\pi$
$619$	−6.54265	+	20.1362i	−0.262971	+	0.809343i	−0.992154	+	0.125024i	$0.960099\pi$
$620$		0			0
$621$	1.57547	+	4.84880i	0.0632215	+	0.194576i
$622$	−4.98960	−	3.12254i	−0.200065	−	0.125203i
$623$	2.29254	−	0.363103i	0.0918487	−	0.0145474i
$624$	1.98746	+	0.729471i	0.0795623	+	0.0292022i
$625$		0			0
$626$	−2.78279	+	31.5617i	−0.111223	+	1.26146i
$627$	0.765290	+	4.83185i	0.0305627	+	0.192966i
$628$	−19.5765	+	25.9059i	−0.781187	+	1.03376i
$629$	19.4624	−	6.32373i	0.776018	−	0.252144i
$630$		0			0
$631$	−3.22756	−	1.04870i	−0.128487	−	0.0417480i	0.244068	−	0.969758i	$-0.421518\pi$
$631$	−3.22756	−	1.04870i	−0.128487	−	0.0417480i	−0.372555	+	0.928010i	$0.621518\pi$
$632$	−16.5413	+	9.50542i	−0.657976	+	0.378105i
$633$	3.38030	−	1.72235i	0.134355	−	0.0684572i
$634$	7.63948	−	4.58324i	0.303402	−	0.182024i
$635$		0			0
$636$	0.507555	−	0.488815i	0.0201259	−	0.0193828i
$637$	0.0764758	−	0.482849i	0.00303008	−	0.0191312i
$638$	−1.55942	−	0.389926i	−0.0617378	−	0.0154373i
$639$	−13.7493	−	9.98948i	−0.543915	−	0.395178i
$640$		0			0
$641$	31.0401	−	22.5519i	1.22601	−	0.890748i	0.229425	−	0.973326i	$-0.426315\pi$
$641$	31.0401	−	22.5519i	1.22601	−	0.890748i	0.996585	+	0.0825780i	$0.0263153\pi$
$642$	−2.87003	+	1.15731i	−0.113271	+	0.0456754i
$643$	−6.79295	+	6.79295i	−0.267888	+	0.267888i	−0.828249	−	0.560361i	$-0.810662\pi$
$643$	−6.79295	+	6.79295i	−0.267888	+	0.267888i	0.560361	+	0.828249i	$0.310662\pi$
$644$	−21.1508	−	11.2828i	−0.833457	−	0.444604i
$645$		0			0
$646$	7.44296	+	32.3388i	0.292840	+	1.27235i
$647$	15.4461	−	30.3148i	0.607251	−	1.19180i	−0.358793	−	0.933417i	$-0.616812\pi$
$647$	15.4461	−	30.3148i	0.607251	−	1.19180i	0.966044	−	0.258379i	$-0.0831884\pi$
$648$	−24.3906	−	2.61358i	−0.958152	−	0.102671i
$649$		−	46.2539i		−	1.81562i
$650$		0			0
$651$			3.77787i			0.148066i
$652$	0.297529	−	15.8196i	0.0116521	−	0.619542i
$653$	2.90673	−	5.70477i	0.113749	−	0.223245i	−0.827112	−	0.562036i	$-0.810018\pi$
$653$	2.90673	−	5.70477i	0.113749	−	0.223245i	0.940862	+	0.338791i	$0.110018\pi$
$654$	−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
$658$	12.4780	+	30.9445i	0.486445	+	1.20634i
$659$	11.5792	−	8.41281i	0.451063	−	0.327716i	−0.338952	−	0.940804i	$-0.610073\pi$
$659$	11.5792	−	8.41281i	0.451063	−	0.327716i	0.790015	+	0.613087i	$0.210073\pi$
$660$		0			0
$661$	−0.382235	−	0.277710i	−0.0148672	−	0.0108017i	0.580327	−	0.814384i	$-0.302925\pi$
$661$	−0.382235	−	0.277710i	−0.0148672	−	0.0108017i	−0.595194	+	0.803582i	$0.702925\pi$
$662$	5.55877	−	22.2310i	0.216048	−	0.864031i
$663$	0.387218	−	2.44480i	0.0150383	−	0.0949480i
$664$	−7.40203	+	5.96923i	−0.287254	+	0.231651i
$665$		0			0
$666$	−9.43452	−	15.7257i	−0.365580	−	0.609360i
$667$	0.887989	−	0.452453i	0.0343831	−	0.0175190i
$668$	−22.1638	+	15.4746i	−0.857543	+	0.598731i
$669$	2.10333	+	0.683413i	0.0813193	+	0.0264223i
$670$		0			0
$671$	6.98096	−	2.26825i	0.269497	−	0.0875648i
$672$	−2.28779	+	1.77499i	−0.0882533	+	0.0684719i
$673$	3.35456	+	21.1799i	0.129309	+	0.816424i	0.964038	+	0.265764i	$0.0856241\pi$
$673$	3.35456	+	21.1799i	0.129309	+	0.816424i	−0.834729	+	0.550660i	$0.814376\pi$
$674$	−28.4902	−	2.51198i	−1.09740	−	0.0967578i
$675$		0			0
$676$	10.4903	+	1.86434i	0.403471	+	0.0717055i
$677$	−43.8961	+	6.95245i	−1.68706	+	0.267204i	−0.924908	−	0.380191i	$-0.875858\pi$
$677$	−43.8961	+	6.95245i	−1.68706	+	0.267204i	−0.762155	+	0.647395i	$0.775858\pi$
$678$	−1.16251	+	1.85761i	−0.0446459	+	0.0713410i
$679$	−9.25648	−	28.4885i	−0.355231	−	1.09329i
$680$		0			0
$681$	−0.916813	+	2.82166i	−0.0351323	+	0.108126i
$682$	34.2075	+	40.8229i	1.30987	+	1.56319i
$683$	11.1168	+	21.8180i	0.425374	+	0.834843i	0.999867	+	0.0163335i	$0.00519935\pi$
$683$	11.1168	+	21.8180i	0.425374	+	0.834843i	−0.574493	+	0.818510i	$0.694801\pi$
$684$	26.7458	−	13.0001i	1.02265	−	0.497071i
$685$		0			0
$686$	−19.4986	−	16.9730i	−0.744460	−	0.648033i
$687$	−3.18118	−	0.503849i	−0.121369	−	0.0192230i
$688$	7.40796	−	13.2795i	0.282426	−	0.506276i
$689$	−3.00217	+	4.13213i	−0.114374	+	0.157422i
$690$		0			0
$691$	−9.83947	−	13.5429i	−0.374311	−	0.515195i	0.579755	−	0.814791i	$-0.303148\pi$
$691$	−9.83947	−	13.5429i	−0.374311	−	0.515195i	−0.954066	+	0.299596i	$0.903148\pi$
$692$	0.638571	+	2.09882i	0.0242748	+	0.0797851i
$693$	−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
$697$	−13.1035	−	6.67656i	−0.496330	−	0.252893i
$698$	0.0746063	−	0.00516630i	0.00282389	−	0.000195547i
$699$	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	$0.0879356\pi$
$702$	−4.45307	+	0.308364i	−0.168070	+	0.0116384i
$703$	19.5618	+	9.96723i	0.737787	+	0.375921i
$704$	−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
$708$	3.31402	−	1.00830i	0.124549	−	0.0378942i
$709$	−23.6335	−	32.5288i	−0.887576	−	1.22164i	−0.974264	−	0.225408i	$-0.927628\pi$
$709$	−23.6335	−	32.5288i	−0.887576	−	1.22164i	0.0866885	−	0.996235i	$-0.472372\pi$
$710$		0			0
$711$	11.7492	−	16.1714i	0.440629	−	0.606473i
$712$	2.23678	+	1.00132i	0.0838268	+	0.0375260i
$713$	−32.6152	−	5.16574i	−1.22145	−	0.193458i
$714$	2.55355	+	2.22280i	0.0955643	+	0.0831863i
$715$		0			0
$716$	−21.0955	−	43.4011i	−0.788376	−	1.62197i
$717$	0.0396715	+	0.0778596i	0.00148156	+	0.00290772i
$718$	−25.0993	−	29.9533i	−0.936698	−	1.11785i
$719$	−3.14270	+	9.67223i	−0.117203	+	0.360713i	−0.992400	−	0.123053i	$-0.960731\pi$
$719$	−3.14270	+	9.67223i	−0.117203	+	0.360713i	0.875197	+	0.483766i	$0.160731\pi$
$720$		0			0
$721$	−1.60612	−	4.94314i	−0.0598152	−	0.184092i
$722$	−4.63197	+	7.40157i	−0.172384	+	0.275458i
$723$	−4.12192	+	0.652848i	−0.153296	+	0.0242797i
$724$	2.44578	−	13.7619i	0.0908966	−	0.511455i
$725$		0			0
$726$	4.04805	+	0.356916i	0.150237	+	0.0132464i
$727$	−1.37117	−	8.65722i	−0.0508538	−	0.321078i	−0.999981	−	0.00618506i	$-0.998031\pi$
$727$	−1.37117	−	8.65722i	−0.0508538	−	0.321078i	0.949127	−	0.314893i	$-0.101969\pi$
$728$	14.0754	−	15.5687i	0.521670	−	0.577016i
$729$	23.8224	−	7.74037i	0.882312	−	0.286681i
$730$		0			0
$731$	−16.9084	−	5.49386i	−0.625378	−	0.203198i
$732$	0.314697	+	0.450729i	0.0116315	+	0.0166594i
$733$	−0.234567	+	0.119518i	−0.00866394	+	0.00441450i	−0.458317	−	0.888789i	$-0.651548\pi$
$733$	−0.234567	+	0.119518i	−0.00866394	+	0.00441450i	0.449653	+	0.893203i	$0.351548\pi$
$734$	−4.93920	−	8.23282i	−0.182309	−	0.303879i
$735$		0			0
$736$	−12.1957	−	22.1780i	−0.449538	−	0.817493i
$737$	2.69946	−	17.0437i	0.0994360	−	0.627814i
$738$	−3.19695	+	12.7854i	−0.117681	+	0.470638i
$739$	−5.97506	−	4.34113i	−0.219796	−	0.159691i	0.472439	−	0.881363i	$-0.343374\pi$
$739$	−5.97506	−	4.34113i	−0.219796	−	0.159691i	−0.692235	+	0.721672i	$0.743374\pi$
$740$		0			0
$741$	2.14841	−	1.56091i	0.0789238	−	0.0573415i
$742$	−2.61254	−	6.47886i	−0.0959092	−	0.237846i
$743$	−7.03452	+	7.03452i	−0.258071	+	0.258071i	−0.824269	−	0.566198i	$-0.808414\pi$
$743$	−7.03452	+	7.03452i	−0.258071	+	0.258071i	0.566198	+	0.824269i	$0.308414\pi$
$744$	−2.17920	+	3.34083i	−0.0798935	+	0.122481i
$745$		0			0
$746$	15.8316	−	3.64373i	0.579634	−	0.133406i
$747$	4.52315	−	8.87719i	0.165494	−	0.324799i
$748$	47.7200	+	0.897500i	1.74482	+	0.0328159i
$749$			30.6785i			1.12097i
$750$		0			0
$751$			29.2029i			1.06563i	0.846232	+	0.532814i	$0.178866\pi$
$751$			29.2029i			1.06563i	−0.846232	+	0.532814i	$0.821134\pi$
$752$	−6.81530	+	34.5624i	−0.248529	+	1.26036i
$753$	−0.470395	+	0.923203i	−0.0171422	+	0.0336434i
$754$	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	$0.0763959\pi$
$758$	−16.7933	+	6.77172i	−0.609959	+	0.245960i
$759$	−3.52933	+	2.56421i	−0.128107	+	0.0930749i
$760$		0			0
$761$	7.93313	+	5.76375i	0.287576	+	0.208936i	0.722215	−	0.691669i	$-0.243124\pi$
$761$	7.93313	+	5.76375i	0.287576	+	0.208936i	−0.434639	+	0.900605i	$0.643124\pi$
$762$	4.20807	+	1.05221i	0.152442	+	0.0381176i
$763$	−6.51124	+	41.1103i	−0.235723	+	1.48829i
$764$	−21.8688	−	22.7071i	−0.791184	−	0.821516i
$765$		0			0
$766$	22.3523	−	13.4100i	0.807620	−	0.484524i
$767$	−22.3715	+	11.3988i	−0.807788	+	0.411589i
$768$	−3.04700	+	0.249980i	−0.109949	+	0.00902038i
$769$	−17.2976	−	5.62032i	−0.623766	−	0.202674i	−0.0199544	−	0.999801i	$-0.506352\pi$
$769$	−17.2976	−	5.62032i	−0.623766	−	0.202674i	−0.603812	+	0.797127i	$0.706352\pi$
$770$		0			0
$771$	2.06162	−	0.669862i	0.0742475	−	0.0241245i
$772$	14.5531	+	10.9974i	0.523778	+	0.395807i
$773$	−6.76671	−	42.7233i	−0.243382	−	1.53665i	−0.742339	−	0.670025i	$-0.766283\pi$
$773$	−6.76671	−	42.7233i	−0.243382	−	1.53665i	0.498957	−	0.866627i	$-0.333717\pi$
$774$	−1.39931	+	15.8706i	−0.0502970	+	0.570455i
$775$		0			0
$776$	8.24751	−	30.5323i	0.296068	−	1.09604i
$777$	2.21226	−	0.350388i	0.0793644	−	0.0125701i
$778$	−29.8179	−	18.6603i	−1.06902	−	0.669006i
$779$	−4.87557	−	15.0055i	−0.174685	−	0.537626i
$780$		0			0
$781$	9.04296	−	27.8314i	0.323582	−	0.995884i
$782$	−22.6816	+	19.0060i	−0.811091	+	0.679653i
$783$	0.115230	+	0.226151i	0.00411798	+	0.00808199i
$784$	0.192752	+	0.679133i	0.00688401	+	0.0242547i
$785$		0			0
$786$	−2.41432	+	2.77356i	−0.0861158	+	0.0989297i
$787$	11.9702	+	1.89589i	0.426691	+	0.0675813i	0.366087	−	0.930581i	$-0.380697\pi$
$787$	11.9702	+	1.89589i	0.426691	+	0.0675813i	0.0606043	+	0.998162i	$0.480697\pi$
$788$	10.8064	+	3.73729i	0.384961	+	0.133135i
$789$	2.23378	−	3.07453i	0.0795245	−	0.109456i
$790$		0			0
$791$	12.7693	+	17.5755i	0.454025	+	0.624911i
$792$	−8.80785	−	41.8549i	−0.312973	−	1.48725i
$793$	−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
$797$	−14.6702	−	7.47486i	−0.519646	−	0.264773i	0.174436	−	0.984668i	$-0.444190\pi$
$797$	−14.6702	−	7.47486i	−0.519646	−	0.264773i	−0.694083	+	0.719895i	$0.744190\pi$
$798$	0.250912	+	3.62342i	0.00888221	+	0.128268i
$799$	41.1877			1.45712
$800$		0			0
$801$	−2.56770			−0.0907253
$802$	−1.02202	−	14.7590i	−0.0360889	−	0.521158i
$803$	0.0861499	+	0.0438956i	0.00304016	+	0.00154904i
$804$	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
$808$	−6.87780	−	32.6833i	−0.241960	−	1.14980i
$809$	−12.5671	−	17.2972i	−0.441837	−	0.608136i	0.528782	−	0.848757i	$-0.322649\pi$
$809$	−12.5671	−	17.2972i	−0.441837	−	0.608136i	−0.970619	+	0.240621i	$0.922649\pi$
$810$		0			0
$811$	−18.5355	+	25.5120i	−0.650871	+	0.895847i	−0.999136	−	0.0415488i	$-0.986771\pi$
$811$	−18.5355	+	25.5120i	−0.650871	+	0.895847i	0.348265	+	0.937396i	$0.386771\pi$
$812$	−1.12788	−	0.390066i	−0.0395807	−	0.0136886i
$813$	−0.356539	−	0.0564703i	−0.0125044	−	0.00198050i
$814$	20.7326	−	23.8176i	0.726677	−	0.834806i
$815$		0			0
$816$	0.975957	+	3.43863i	0.0341653	+	0.120376i
$817$	−8.65922	−	16.9947i	−0.302948	−	0.594569i
$818$	16.8254	−	14.0988i	0.588286	−	0.492953i
$819$	−6.79540	+	20.9141i	−0.237451	+	0.730798i
$820$		0			0
$821$	−6.22378	−	19.1548i	−0.217211	−	0.668508i	−0.998989	−	0.0449507i	$-0.985687\pi$
$821$	−6.22378	−	19.1548i	−0.217211	−	0.668508i	0.781778	−	0.623557i	$-0.214313\pi$
$822$	−4.32826	−	2.70867i	−0.150966	−	0.0944757i
$823$	−41.6729	+	6.60034i	−1.45263	+	0.230073i	−0.832324	−	0.554289i	$-0.812990\pi$
$823$	−41.6729	+	6.60034i	−1.45263	+	0.230073i	−0.620302	+	0.784363i	$0.712990\pi$
$824$	1.43105	−	5.29776i	0.0498531	−	0.184556i
$825$		0			0
$826$	3.01613	−	34.2082i	0.104945	−	1.19026i
$827$	2.15397	+	13.5996i	0.0749008	+	0.472905i	0.996418	+	0.0845669i	$0.0269507\pi$
$827$	2.15397	+	13.5996i	0.0749008	+	0.472905i	−0.921517	+	0.388338i	$0.873049\pi$
$828$	21.1571	+	15.9879i	0.735261	+	0.555620i
$829$	−35.5980	+	11.5665i	−1.23637	+	0.401721i	−0.853018	−	0.521881i	$-0.825230\pi$
$829$	−35.5980	+	11.5665i	−1.23637	+	0.401721i	−0.383352	+	0.923602i	$0.625230\pi$
$830$		0			0
$831$	2.08074	+	0.676072i	0.0721800	+	0.0234527i
$832$	21.4277	−	5.64848i	0.742872	−	0.195826i
$833$	0.735426	−	0.374718i	0.0254810	−	0.0129832i
$834$	−1.68864	+	1.01308i	−0.0584727	+	0.0350802i
$835$		0			0
$836$	35.5203	+	36.8820i	1.22850	+	1.27559i
$837$	1.31560	−	8.30637i	0.0454738	−	0.287110i
$838$	−49.5339	−	12.3858i	−1.71112	−	0.427859i
$839$	6.53213	+	4.74587i	0.225514	+	0.163846i	0.694805	−	0.719198i	$-0.255491\pi$
$839$	6.53213	+	4.74587i	0.225514	+	0.163846i	−0.469291	+	0.883044i	$0.655491\pi$
$840$		0			0
$841$	−23.4214	+	17.0166i	−0.807633	+	0.586780i
$842$	21.0153	−	8.47419i	0.724234	−	0.292040i
$843$	−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
$847$	18.2897	−	35.8955i	0.628440	−	1.23338i
$848$	1.42692	−	7.23635i	0.0490008	−	0.248497i
$849$			3.64092i			0.124956i
$850$		0			0
$851$			19.5780i			0.671126i
$852$	2.19121	+	0.0412114i	0.0750695	+	0.00141188i
$853$	−15.8344	+	31.0768i	−0.542160	+	1.06405i	0.443652	+	0.896199i	$0.353683\pi$
$853$	−15.8344	+	31.0768i	−0.542160	+	1.06405i	−0.985812	+	0.167851i	$0.946317\pi$
$854$	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	$0.971514\pi$
$858$	−1.42841	−	3.54234i	−0.0487652	−	0.120933i
$859$	−34.2690	+	24.8979i	−1.16924	+	0.849504i	−0.990918	−	0.134468i	$-0.957068\pi$
$859$	−34.2690	+	24.8979i	−1.16924	+	0.849504i	−0.178324	+	0.983972i	$0.557068\pi$
$860$		0			0
$861$	−1.30223	−	0.946129i	−0.0443800	−	0.0322440i
$862$	−2.31143	+	9.24400i	−0.0787275	+	0.314852i
$863$	−2.60778	+	16.4649i	−0.0887700	+	0.560472i	0.902714	+	0.430242i	$0.141572\pi$
$863$	−2.60778	+	16.4649i	−0.0887700	+	0.560472i	−0.991484	+	0.130230i	$0.958428\pi$
$864$	5.64826	−	3.10597i	0.192158	−	0.105667i
$865$		0			0
$866$	−7.67388	−	12.7911i	−0.260769	−	0.434658i
$867$	0.829389	−	0.422595i	0.0281675	−	0.0143521i
$868$	22.6370	+	32.4222i	0.768350	+	1.10048i
$869$	32.7340	+	10.6359i	1.11043	+	0.360799i
$870$		0			0
$871$	−8.90876	+	2.89463i	−0.301862	+	0.0980809i
$872$	−29.4718	+	32.5986i	−0.998042	+	1.10393i
$873$	5.18374	+	32.7288i	0.175443	+	1.10770i
$874$	−31.6248	−	2.78836i	−1.06973	−	0.0943177i
$875$		0			0
$876$	−0.00126705	+	0.00712941i	−4.28096e−5	+	0.000240880i
$877$	14.6759	−	2.32444i	0.495571	−	0.0784907i	0.0963539	−	0.995347i	$-0.469282\pi$
$877$	14.6759	−	2.32444i	0.495571	−	0.0784907i	0.399217	+	0.916856i	$0.369282\pi$
$878$	7.85645	−	12.5541i	0.265142	−	0.423679i
$879$	−0.770780	−	2.37222i	−0.0259978	−	0.0800129i
$880$		0			0
$881$	−15.1162	+	46.5230i	−0.509279	+	1.56740i	0.284177	+	0.958772i	$0.408280\pi$
$881$	−15.1162	+	46.5230i	−0.509279	+	1.56740i	−0.793456	+	0.608628i	$0.791720\pi$
$882$	−0.475066	−	0.566939i	−0.0159963	−	0.0190898i
$883$	−0.740506	−	1.45332i	−0.0249200	−	0.0489083i	0.878211	−	0.478274i	$-0.158737\pi$
$883$	−0.740506	−	1.45332i	−0.0249200	−	0.0489083i	−0.903131	+	0.429365i	$0.858737\pi$
$884$	−11.3261	−	23.3018i	−0.380937	−	0.783725i
$885$		0			0
$886$	4.93478	+	4.29560i	0.165787	+	0.144313i
$887$	−26.7206	−	4.23212i	−0.897189	−	0.142101i	−0.309226	−	0.950989i	$-0.600070\pi$
$887$	−26.7206	−	4.23212i	−0.897189	−	0.142101i	−0.587963	+	0.808888i	$0.700070\pi$
$888$	2.15845	+	0.966254i	0.0724329	+	0.0324254i
$889$	25.2757	−	34.7890i	0.847719	−	1.16679i
$890$		0			0
$891$	26.0125	+	35.8032i	0.871452	+	1.19945i
$892$	22.1461	−	6.73800i	0.741505	−	0.225605i
$893$	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
$897$	2.11000	+	1.07510i	0.0704508	+	0.0358965i
$898$	25.5264	−	1.76764i	0.851828	−	0.0589870i
$899$	−1.64396			−0.0548290
$900$		0			0
$901$	−8.62349			−0.287290
$902$	−22.6386	+	1.56767i	−0.753784	+	0.0521976i
$903$	−1.73381	−	0.883420i	−0.0576976	−	0.0293984i
$904$	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	$-0.935640\pi$
$907$	−35.5508	−	35.5508i	−1.18045	−	1.18045i	−0.200818	−	0.979629i	$-0.564360\pi$
$908$	9.03918	+	29.7094i	0.299976	+	0.985942i
$909$	20.5690	+	28.3108i	0.682230	+	0.939009i
$910$		0			0
$911$	3.41319	−	4.69785i	0.113084	−	0.155647i	−0.748723	−	0.662883i	$-0.769333\pi$
$911$	3.41319	−	4.69785i	0.113084	−	0.155647i	0.861807	+	0.507236i	$0.169333\pi$
$912$	−1.86823	+	3.34898i	−0.0618631	+	0.110896i
$913$	16.9441	+	2.68368i	0.560768	+	0.0888169i
$914$	35.3920	+	30.8078i	1.17066	+	1.01903i
$915$		0			0
$916$	−30.3204	+	14.7375i	−1.00181	+	0.486941i
$917$	16.5498	+	32.4808i	0.546522	+	1.07261i
$918$	−4.84041	−	5.77650i	−0.159757	−	0.190653i
$919$	−13.3369	+	41.0468i	−0.439944	+	1.35401i	0.447990	+	0.894039i	$0.352140\pi$
$919$	−13.3369	+	41.0468i	−0.439944	+	1.35401i	−0.887934	+	0.459971i	$0.847860\pi$
$920$		0			0
$921$	−0.765886	−	2.35716i	−0.0252368	−	0.0776709i
$922$	−24.2775	+	38.7938i	−0.799537	+	1.27760i
$923$	−15.6897	+	2.48500i	−0.516432	+	0.0817948i
$924$	5.14340	+	0.914093i	0.169205	+	0.0300714i
$925$		0			0
$926$	−43.2004	−	3.80897i	−1.41965	−	0.125171i
$927$	0.899449	+	5.67890i	0.0295418	+	0.186520i
$928$	−0.772396	−	0.995540i	−0.0253551	−	0.0326802i
$929$	−34.3019	+	11.1453i	−1.12541	+	0.365667i	−0.811829	−	0.583895i	$-0.801528\pi$
$929$	−34.3019	+	11.1453i	−1.12541	+	0.365667i	−0.313578	+	0.949562i	$0.601528\pi$
$930$		0			0
$931$	0.842173	+	0.273639i	0.0276011	+	0.00896814i
$932$	47.8946	−	33.4397i	1.56884	−	1.09535i
$933$	−0.708605	+	0.361052i	−0.0231987	+	0.0118203i
$934$	−11.3406	−	18.9028i	−0.371075	−	0.618520i
$935$		0			0
$936$	−18.0733	+	14.5748i	−0.590743	+	0.476394i
$937$	−5.92447	+	37.4056i	−0.193544	+	1.22199i	0.679252	+	0.733905i	$0.262304\pi$
$937$	−5.92447	+	37.4056i	−0.193544	+	1.22199i	−0.872796	+	0.488084i	$0.837696\pi$
$938$	3.10785	−	12.4291i	0.101475	−	0.405824i
$939$	3.46333	+	2.51626i	0.113022	+	0.0821149i
$940$		0			0
$941$	25.8261	−	18.7637i	0.841906	−	0.611680i	−0.0809965	−	0.996714i	$-0.525810\pi$
$941$	25.8261	−	18.7637i	0.841906	−	0.611680i	0.922902	+	0.385034i	$0.125810\pi$
$942$	1.64073	+	4.06886i	0.0534578	+	0.132571i
$943$	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
$947$	1.60449	−	3.14898i	0.0521388	−	0.102328i	−0.863467	−	0.504405i	$-0.831712\pi$
$947$	1.60449	−	3.14898i	0.0521388	−	0.102328i	0.915606	+	0.402077i	$0.131712\pi$
$948$	−0.0484710	+	2.57720i	−0.00157426	+	0.0837035i
$949$		−	0.0524856i		−	0.00170375i
$950$		0			0
$951$		−	1.20369i		−	0.0390325i
$952$	35.2340	+	3.77551i	1.14194	+	0.122365i
$953$	24.4756	−	48.0361i	0.792843	−	1.55604i	−0.0378308	−	0.999284i	$-0.512045\pi$
$953$	24.4756	−	48.0361i	0.792843	−	1.55604i	0.830674	−	0.556759i	$-0.187955\pi$
$954$	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
$958$	−9.13605	+	3.68402i	−0.295172	+	0.119025i
$959$	−40.9512	+	29.7528i	−1.32238	+	0.960767i
$960$		0			0
$961$	18.9882	+	13.7957i	0.612523	+	0.445024i
$962$	−16.6292	−	4.15806i	−0.536146	−	0.134061i
$963$	5.30901	−	33.5198i	0.171080	−	1.08016i
$964$	−31.4630	+	30.3014i	−1.01336	+	0.975943i
$965$		0			0
$966$	−2.77741	+	1.66628i	−0.0893618	+	0.0536118i
$967$	13.8004	−	7.03165i	0.443791	−	0.226123i	−0.217792	−	0.975995i	$-0.569885\pi$
$967$	13.8004	−	7.03165i	0.443791	−	0.226123i	0.661582	+	0.749873i	$0.269885\pi$
$968$	36.8796	−	21.1928i	1.18535	−	0.681163i
$969$	4.26415	+	1.38551i	0.136984	+	0.0445089i
$970$		0			0
$971$	−16.7721	+	5.44959i	−0.538242	+	0.174886i	−0.565508	−	0.824743i	$-0.691320\pi$
$971$	−16.7721	+	5.44959i	−0.538242	+	0.174886i	0.0272659	+	0.999628i	$0.491320\pi$
$972$	−6.12014	+	8.09889i	−0.196303	+	0.259772i
$973$	3.05393	+	19.2817i	0.0979044	+	0.618144i
$974$	−2.59016	+	29.3769i	−0.0829940	+	0.941295i
$975$		0			0
$976$	5.40154	+	1.98256i	0.172899	+	0.0634602i
$977$	52.0437	−	8.24291i	1.66502	−	0.263714i	0.748337	−	0.663319i	$-0.230853\pi$
$977$	52.0437	−	8.24291i	1.66502	−	0.263714i	0.916687	+	0.399605i	$0.130853\pi$
$978$	−1.81219	−	1.13408i	−0.0579473	−	0.0362640i
$979$	−1.36625	−	4.20489i	−0.0436656	−	0.134389i
$980$		0			0
$981$	14.2286	−	43.7910i	0.454283	−	1.39814i
$982$	5.33297	−	4.46875i	0.170182	−	0.142603i
$983$	−7.96803	−	15.6381i	−0.254141	−	0.498779i	0.728323	−	0.685234i	$-0.240300\pi$
$983$	−7.96803	−	15.6381i	−0.254141	−	0.498779i	−0.982463	+	0.186455i	$0.940300\pi$
$984$	−0.605826	−	1.58785i	−0.0193130	−	0.0506188i
$985$		0			0
$986$	−0.967261	+	1.11119i	−0.0308039	+	0.0353875i
$987$	4.45259	+	0.705221i	0.141728	+	0.0224474i
$988$	9.08498	−	26.2693i	0.289032	−	0.835736i
$989$	9.99752	−	13.7604i	0.317903	−	0.437555i
$990$		0			0
$991$	−20.0939	−	27.6568i	−0.638302	−	0.878548i	0.360221	−	0.932867i	$-0.382701\pi$
$991$	−20.0939	−	27.6568i	−0.638302	−	0.878548i	−0.998524	+	0.0543192i	$0.982701\pi$
$992$	1.31600	+	41.7293i	0.0417832	+	1.32491i
$993$	−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
$997$	1.87335	+	0.954518i	0.0593295	+	0.0302299i	0.483404	−	0.875398i	$-0.339400\pi$
$997$	1.87335	+	0.954518i	0.0593295	+	0.0302299i	−0.424074	+	0.905628i	$0.639400\pi$
$998$	−1.93576	−	27.9542i	−0.0612754	−	0.884875i
$999$	−4.98610			−0.157753

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	500.2.l.d.43.5		96
4.3	odd	2	inner	500.2.l.d.43.6		96
5.2	odd	4		500.2.l.f.207.12		96
5.3	odd	4		100.2.l.b.87.1	yes	96
5.4	even	2		500.2.l.e.43.8		96
15.8	even	4		900.2.bj.d.487.12		96
20.3	even	4		100.2.l.b.87.12	yes	96
20.7	even	4		500.2.l.f.207.1		96
20.19	odd	2		500.2.l.e.43.7		96
25.2	odd	20	inner	500.2.l.d.407.6		96
25.11	even	5		500.2.l.f.343.1		96
25.14	even	10		100.2.l.b.23.12	yes	96
25.23	odd	20		500.2.l.e.407.7		96
60.23	odd	4		900.2.bj.d.487.1		96
75.14	odd	10		900.2.bj.d.523.1		96
100.11	odd	10		500.2.l.f.343.12		96
100.23	even	20		500.2.l.e.407.8		96
100.27	even	20	inner	500.2.l.d.407.5		96
100.39	odd	10		100.2.l.b.23.1	✓	96
300.239	even	10		900.2.bj.d.523.12		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.2.l.b.23.1	✓	96	100.39	odd	10
100.2.l.b.23.12	yes	96	25.14	even	10
100.2.l.b.87.1	yes	96	5.3	odd	4
100.2.l.b.87.12	yes	96	20.3	even	4
500.2.l.d.43.5		96	1.1	even	1	trivial
500.2.l.d.43.6		96	4.3	odd	2	inner
500.2.l.d.407.5		96	100.27	even	20	inner
500.2.l.d.407.6		96	25.2	odd	20	inner
500.2.l.e.43.7		96	20.19	odd	2
500.2.l.e.43.8		96	5.4	even	2
500.2.l.e.407.7		96	25.23	odd	20
500.2.l.e.407.8		96	100.23	even	20
500.2.l.f.207.1		96	20.7	even	4
500.2.l.f.207.12		96	5.2	odd	4
500.2.l.f.343.1		96	25.11	even	5
500.2.l.f.343.12		96	100.11	odd	10
900.2.bj.d.487.1		96	60.23	odd	4
900.2.bj.d.487.12		96	15.8	even	4
900.2.bj.d.523.1		96	75.14	odd	10
900.2.bj.d.523.12		96	300.239	even	10

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+(-0.0976968 - 1.41083i) q^{2} +(-0.170251 - 0.0867473i) q^{3} +(-1.98091 + 0.275668i) q^{4} +(-0.105753 + 0.248671i) q^{6} +(1.89427 + 1.89427i) q^{7} +(0.582451 + 2.76781i) q^{8} +(-1.74190 - 2.39751i) q^{9} +(2.99934 - 4.12824i) q^{11} +(0.361166 + 0.124906i) q^{12} +(-2.73586 - 0.433317i) q^{13} +(2.48743 - 2.85756i) q^{14} +(3.84801 - 1.09215i) q^{16} +(-2.12318 - 4.16697i) q^{17} +(-3.21232 + 2.69176i) q^{18} +(1.55045 - 4.77181i) q^{19} +(-0.158179 - 0.486824i) q^{21} +(-6.11729 - 3.82826i) q^{22} +(4.41914 - 0.699923i) q^{23} +(0.140937 - 0.521748i) q^{24} +(-0.344055 + 3.90218i) q^{26} +(0.178255 + 1.12546i) q^{27} +(-4.27456 - 3.23018i) q^{28} +(0.211843 - 0.0688321i) q^{29} +(-7.01920 - 2.28068i) q^{31} +(-1.91678 - 5.32221i) q^{32} +(-0.868756 + 0.442653i) q^{33} +(-5.67148 + 3.40256i) q^{34} +(4.11146 + 4.26907i) q^{36} +(-0.684516 + 4.32186i) q^{37} +(-6.88371 - 1.72125i) q^{38} +(0.428194 + 0.311101i) q^{39} +(2.54404 - 1.84835i) q^{41} +(-0.671374 + 0.270725i) q^{42} +(2.68807 - 2.68807i) q^{43} +(-4.80341 + 9.00450i) q^{44} +(-1.41921 - 6.16630i) q^{46} +(-3.99829 + 7.84709i) q^{47} +(-0.749870 - 0.147866i) q^{48} +0.176489i q^{49} +0.893612i q^{51} +(5.53894 + 0.104174i) q^{52} +(0.837124 - 1.64295i) q^{53} +(1.57042 - 0.361442i) q^{54} +(-4.13965 + 6.34628i) q^{56} +(-0.677908 + 0.677908i) q^{57} +(-0.117807 - 0.292151i) q^{58} +(7.33328 - 5.32794i) q^{59} +(1.16375 + 0.845512i) q^{61} +(-2.53191 + 10.1258i) q^{62} +(1.24191 - 7.84114i) q^{63} +(-7.32150 + 3.22422i) q^{64} +(0.709385 + 1.18243i) q^{66} +(3.01313 - 1.53527i) q^{67} +(5.35453 + 7.66911i) q^{68} +(-0.813081 - 0.264186i) q^{69} +(5.45415 - 1.77216i) q^{71} +(5.62128 - 6.21766i) q^{72} +(0.00296414 + 0.0187149i) q^{73} +(6.16431 + 0.543507i) q^{74} +(-1.75588 + 9.87994i) q^{76} +(13.5015 - 2.13843i) q^{77} +(0.397079 - 0.634505i) q^{78} +(2.08434 + 6.41493i) q^{79} +(-2.68002 + 8.24826i) q^{81} +(-2.85627 - 3.40864i) q^{82} +(1.52629 + 2.99552i) q^{83} +(0.447539 + 0.920749i) q^{84} +(-4.05504 - 3.52981i) q^{86} +(-0.0420376 - 0.00665810i) q^{87} +(13.1731 + 5.89710i) q^{88} +(0.509284 - 0.700969i) q^{89} +(-4.36162 - 6.00326i) q^{91} +(-8.56098 + 2.60470i) q^{92} +(0.997185 + 0.997185i) q^{93} +(11.4616 + 4.87429i) q^{94} +(-0.135354 + 1.07239i) q^{96} +(-9.96296 - 5.07638i) q^{97} +(0.248997 - 0.0172424i) q^{98} -15.1221 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 10 q^{4} - 6 q^{6} - 30 q^{8} + 20 q^{9} + 10 q^{14} - 14 q^{16} - 20 q^{18} - 12 q^{21} + 50 q^{22} - 12 q^{26} + 40 q^{28} + 20 q^{29} + 50 q^{32} + 60 q^{34} - 10 q^{36} + 40 q^{37} - 70 q^{38}+ \cdots + 70 q^{98}+O(q^{100}) \) 96 * q + 10 * q^4 - 6 * q^6 - 30 * q^8 + 20 * q^9 + 10 * q^14 - 14 * q^16 - 20 * q^18 - 12 * q^21 + 50 * q^22 - 12 * q^26 + 40 * q^28 + 20 * q^29 + 50 * q^32 + 60 * q^34 - 10 * q^36 + 40 * q^37 - 70 * q^38 - 28 * q^41 - 60 * q^42 - 60 * q^44 - 6 * q^46 + 100 * q^52 + 80 * q^53 - 120 * q^54 - 6 * q^56 + 20 * q^57 + 120 * q^58 + 12 * q^61 - 20 * q^64 - 30 * q^66 + 10 * q^68 + 20 * q^69 - 150 * q^72 - 140 * q^77 - 130 * q^78 - 36 * q^81 + 50 * q^82 + 90 * q^84 - 6 * q^86 + 110 * q^88 - 160 * q^89 + 90 * q^92 - 60 * q^93 + 170 * q^94 + 14 * q^96 + 70 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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