LMFDB - Embedded newform 500.2.l.d.407.5

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			407.5
Character	$\chi$	$=$	500.407
Dual form			500.2.l.d.43.5

$q$-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 $\left(\mathbb{Z}/500\mathbb{Z}\right)^\times$.

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

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	−0.502447	−	0.864608i	$-0.667567\pi$
$3$	−0.170251	+	0.0867473i	−0.0982946	+	0.0500836i	0.404152	+	0.914692i	$0.367567\pi$
$4$	−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	$-0.581026\pi$
$7$	1.89427	−	1.89427i	0.715965	−	0.715965i	0.967776	+	0.251811i	$0.0810262\pi$
$8$	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	0.969064	+	0.246809i	$0.0793819\pi$
$11$	2.99934	+	4.12824i	0.904336	+	1.24471i	−0.0647283	+	0.997903i	$0.520618\pi$
$12$	0.361166	−	0.124906i	0.104260	−	0.0360572i
$13$	−2.73586	+	0.433317i	−0.758790	+	0.120181i	−0.523828	−	0.851824i	$-0.675497\pi$
$13$	−2.73586	+	0.433317i	−0.758790	+	0.120181i	−0.234962	+	0.972005i	$0.575497\pi$
$14$	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	0.476383	+	0.879238i	$0.341948\pi$
$17$	−2.12318	+	4.16697i	−0.514947	+	1.01064i	−0.991329	+	0.131402i	$0.958052\pi$
$18$	−3.21232	−	2.69176i	−0.757151	−	0.634453i
$19$	1.55045	+	4.77181i	0.355699	+	1.09473i	0.955603	+	0.294657i	$0.0952052\pi$
$19$	1.55045	+	4.77181i	0.355699	+	1.09473i	−0.599905	+	0.800072i	$0.704795\pi$
$20$		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	0.599100	−	0.800675i	$-0.295525\pi$
$23$	4.41914	+	0.699923i	0.921455	+	0.145944i	0.322355	+	0.946619i	$0.395525\pi$
$24$	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	0.328620	−	0.944462i	$-0.393416\pi$
$29$	0.211843	+	0.0688321i	0.0393383	+	0.0127818i	−0.289282	+	0.957244i	$0.593416\pi$
$30$		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	$0.630624\pi$
$32$	−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	−0.977854	−	0.209290i	$-0.932885\pi$
$37$	−0.684516	−	4.32186i	−0.112534	−	0.710510i	0.865320	−	0.501220i	$-0.167115\pi$
$38$	−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	0.768445	−	0.639915i	$-0.221031\pi$
$41$	2.54404	+	1.84835i	0.397312	+	0.288664i	−0.371133	+	0.928580i	$0.621031\pi$
$42$	−0.671374	−	0.270725i	−0.103595	−	0.0417738i
$43$	2.68807	+	2.68807i	0.409927	+	0.409927i	0.881713	−	0.471786i	$-0.156391\pi$
$43$	2.68807	+	2.68807i	0.409927	+	0.409927i	−0.471786	+	0.881713i	$0.656391\pi$
$44$	−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	−0.974508	−	0.224351i	$-0.927974\pi$
$47$	−3.99829	−	7.84709i	−0.583211	−	1.14462i	0.391298	−	0.920264i	$-0.372026\pi$
$48$	−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	0.941327	−	0.337497i	$-0.109580\pi$
$53$	0.837124	+	1.64295i	0.114988	+	0.225676i	−0.826339	+	0.563173i	$0.809580\pi$
$54$	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	0.951917	−	0.306357i	$-0.0991103\pi$
$59$	7.33328	+	5.32794i	0.954712	+	0.693639i	0.00279513	+	0.999996i	$0.499110\pi$
$60$		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	$0.270646\pi$
$62$	−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	0.628255	−	0.778007i	$-0.283769\pi$
$67$	3.01313	+	1.53527i	0.368113	+	0.187563i	−0.260142	+	0.965570i	$0.583769\pi$
$68$	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	0.614218	−	0.789136i	$-0.289471\pi$
$71$	5.45415	+	1.77216i	0.647288	+	0.210317i	0.0330703	+	0.999453i	$0.489471\pi$
$72$	5.62128	+	6.21766i	0.662475	+	0.732759i
$73$	0.00296414	−	0.0187149i	0.000346927	−	0.00219041i	−0.987514	−	0.157530i	$-0.949647\pi$
$73$	0.00296414	−	0.0187149i	0.000346927	−	0.00219041i	0.987861	+	0.155339i	$0.0496470\pi$
$74$	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	−0.762680	−	0.646776i	$-0.776117\pi$
$79$	2.08434	−	6.41493i	0.234506	−	0.721736i	0.997187	−	0.0749601i	$-0.0238830\pi$
$80$		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	−0.791942	−	0.610596i	$-0.790930\pi$
$83$	1.52629	−	2.99552i	0.167532	−	0.328801i	0.959475	+	0.281795i	$0.0909299\pi$
$84$	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	0.835156	−	0.550014i	$-0.185378\pi$
$89$	0.509284	+	0.700969i	0.0539840	+	0.0743026i	−0.781172	+	0.624316i	$0.785378\pi$
$90$		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	−0.879545	−	0.475816i	$-0.842153\pi$
$97$	−9.96296	+	5.07638i	−1.01158	+	0.515428i	−0.132040	+	0.991244i	$0.542153\pi$
$98$	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	−0.537079	−	0.843532i	$-0.680472\pi$
$103$	−1.72871	+	0.880821i	−0.170335	+	0.0867899i	0.366744	+	0.930322i	$0.380472\pi$
$104$	−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	$-0.563273\pi$
$107$	8.09772	−	8.09772i	0.782836	−	0.782836i	0.980308	+	0.197472i	$0.0632733\pi$
$108$	−0.663361	+	2.18029i	−0.0638319	+	0.209799i
$109$	9.13259	−	12.5699i	0.874743	−	1.20398i	−0.103106	−	0.994670i	$-0.532878\pi$
$109$	9.13259	−	12.5699i	0.874743	−	1.20398i	0.977849	−	0.209310i	$-0.0671219\pi$
$110$		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	0.232135	−	0.972684i	$-0.425429\pi$
$113$	8.00964	−	1.26860i	0.753483	−	0.119340i	0.521349	+	0.853344i	$0.325429\pi$
$114$	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	0.581932	+	0.813237i	$0.302297\pi$
$127$	−2.51108	+	15.8543i	−0.222822	+	1.40684i	−0.804755	+	0.593608i	$0.797703\pi$
$128$	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	0.316878	−	0.948466i	$-0.397365\pi$
$131$	12.9418	−	4.20505i	1.13073	−	0.367397i	0.813854	+	0.581069i	$0.197365\pi$
$132$	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	−0.709327	−	0.704880i	$-0.751001\pi$
$137$	−2.95587	−	18.6626i	−0.252537	−	1.59445i	0.456790	−	0.889575i	$-0.348999\pi$
$138$	−0.293287	−	1.17293i	−0.0249663	−	0.0998467i
$139$	5.89560	−	4.28340i	0.500058	−	0.363313i	−0.308981	−	0.951068i	$-0.599988\pi$
$139$	5.89560	−	4.28340i	0.500058	−	0.363313i	0.809039	+	0.587755i	$0.199988\pi$
$140$		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	$-0.972212\pi$
$149$		−	2.12851i		−	0.174375i	0.996192	−	0.0871873i	$-0.0277879\pi$
$150$		0			0
$151$		−	6.10369i		−	0.496712i	−0.968669	−	0.248356i	$-0.920110\pi$
$151$		−	6.10369i		−	0.496712i	0.968669	−	0.248356i	$-0.0798902\pi$
$152$	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	0.996752	−	0.0805335i	$-0.0256624\pi$
$157$	11.4802	+	11.4802i	0.916218	+	0.916218i	−0.0805335	+	0.996752i	$0.525662\pi$
$158$	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	−0.987555	−	0.157275i	$-0.949729\pi$
$163$	−1.23758	−	7.81379i	−0.0969349	−	0.612023i	0.890620	−	0.454748i	$-0.150271\pi$
$164$	−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	0.852910	−	0.522059i	$-0.174836\pi$
$167$	12.0426	+	6.13600i	0.931883	+	0.474818i	0.0789735	+	0.996877i	$0.474836\pi$
$168$	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	−0.993352	−	0.115114i	$-0.963277\pi$
$173$	−0.171594	+	1.08340i	−0.0130460	+	0.0823695i	0.980306	+	0.197483i	$0.0632768\pi$
$174$	−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	−0.132533	−	0.991179i	$-0.542311\pi$
$179$	7.45601	−	22.9472i	0.557289	−	1.71516i	0.689822	−	0.723979i	$-0.257689\pi$
$180$		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	$0.983635\pi$
$182$	−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	−0.329369	−	0.944201i	$-0.606836\pi$
$191$	9.26511	−	12.7523i	0.670400	−	0.922727i	0.999769	+	0.0214746i	$0.00683611\pi$
$192$	1.52619	−	0.0861932i	0.110143	−	0.00622046i
$193$	−6.44920	+	6.44920i	−0.464223	+	0.464223i	−0.900037	−	0.435814i	$-0.856461\pi$
$193$	−6.44920	+	6.44920i	−0.464223	+	0.464223i	0.435814	+	0.900037i	$0.356461\pi$
$194$	−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	−0.625943	−	0.779869i	$-0.715286\pi$
$197$	−5.09406	+	2.59555i	−0.362936	+	0.184925i	0.263007	+	0.964794i	$0.415286\pi$
$198$	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	−0.992306	−	0.123813i	$-0.960488\pi$
$211$	−11.6703	−	16.0628i	−0.803419	−	1.10581i	0.188886	−	0.981999i	$-0.439512\pi$
$212$	−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	−0.238552	−	0.971130i	$-0.576673\pi$
$223$	−11.4317	−	1.81060i	−0.765524	−	0.121247i	−0.526972	+	0.849883i	$0.676673\pi$
$224$	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	0.765861	+	0.643007i	$0.222313\pi$
$227$	−2.42897	+	15.3359i	−0.161216	+	1.01788i	−0.927077	+	0.374872i	$0.877687\pi$
$228$	1.15600	+	1.52975i	0.0765579	+	0.101310i
$229$	16.0312	+	5.20884i	1.05937	+	0.344210i	0.786339	−	0.617796i	$-0.211974\pi$
$229$	16.0312	+	5.20884i	1.05937	+	0.344210i	0.273030	+	0.962006i	$0.411974\pi$
$230$		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	−0.984575	−	0.174963i	$-0.944019\pi$
$233$	−26.0233	−	13.2595i	−1.70484	−	0.868660i	−0.720267	−	0.693697i	$-0.755981\pi$
$234$	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	−0.599687	−	0.800235i	$-0.704708\pi$
$239$	−0.369981	+	0.268807i	−0.0239321	+	0.0173877i	0.575755	+	0.817622i	$0.304708\pi$
$240$		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	$0.451643\pi$
$242$	−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	$0.0547436\pi$
$251$			5.42259i			0.342271i	−0.985248	+	0.171135i	$0.945256\pi$
$252$	−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	0.411166	−	0.911560i	$-0.365121\pi$
$257$	−8.02192	−	8.02192i	−0.500394	−	0.500394i	−0.911560	+	0.411166i	$0.865121\pi$
$258$	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	−0.876127	−	0.482081i	$-0.839881\pi$
$263$	−3.11132	−	19.6441i	−0.191852	−	1.21131i	0.684275	−	0.729224i	$-0.260119\pi$
$264$	−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	−8.44003e−5	−	1.00000i	$-0.500027\pi$
$269$	9.63789	−	3.13154i	0.587633	−	0.190933i	0.587717	+	0.809067i	$0.300027\pi$
$270$		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	$0.581725\pi$
$272$	−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	−0.192855	−	0.981227i	$-0.561775\pi$
$277$	−11.3089	−	1.79116i	−0.679488	−	0.107620i	−0.486632	+	0.873607i	$0.661775\pi$
$278$	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	0.900988	+	0.433844i	$0.142843\pi$
$281$	7.15917	+	22.0337i	0.427080	+	1.31442i	−0.473908	+	0.880574i	$0.657157\pi$
$282$	−1.52851	+	1.82411i	−0.0910217	+	0.108624i
$283$	−8.65065	+	16.9779i	−0.514228	+	1.00923i	0.477227	+	0.878780i	$0.341642\pi$
$283$	−8.65065	+	16.9779i	−0.514228	+	1.00923i	−0.991455	+	0.130449i	$0.958358\pi$
$284$	−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	−0.384059	−	0.923309i	$-0.625474\pi$
$293$	9.23047	−	9.23047i	0.539250	−	0.539250i	0.923309	+	0.384059i	$0.125474\pi$
$294$	−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	−0.395150	−	0.918616i	$-0.629308\pi$
$307$	9.17187	−	9.17187i	0.523466	−	0.523466i	0.918616	+	0.395150i	$0.129308\pi$
$308$	−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	0.872726	−	0.488209i	$-0.162350\pi$
$311$	2.44643	+	3.36722i	0.138724	+	0.190938i	−0.734002	+	0.679147i	$0.762350\pi$
$312$	−0.611666	−	1.36636i	−0.0346288	−	0.0773548i
$313$	−22.1282	+	3.50477i	−1.25076	+	0.198101i	−0.746462	−	0.665427i	$-0.768249\pi$
$313$	−22.1282	+	3.50477i	−1.25076	+	0.198101i	−0.504300	+	0.863529i	$0.668249\pi$
$314$	−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	−0.796639	−	0.604456i	$-0.793391\pi$
$317$	2.85992	−	5.61291i	0.160629	−	0.315252i	0.957268	+	0.289204i	$0.0933905\pi$
$318$	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	0.146835	−	0.989161i	$-0.453091\pi$
$331$	15.4106	−	5.00720i	0.847042	−	0.275221i	0.700206	+	0.713940i	$0.253091\pi$
$332$	−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	0.910511	+	0.413484i	$0.135688\pi$
$337$	3.16369	+	19.9748i	0.172337	+	1.08809i	−0.738174	+	0.674610i	$0.764312\pi$
$338$	−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	0.950800	−	0.309805i	$-0.100264\pi$
$347$	2.63206	+	5.16571i	0.141296	+	0.277310i	−0.809504	+	0.587115i	$0.800264\pi$
$348$	0.0851081	−	0.00160068i	0.00456227	−	8.58056e-5i
$349$		−	0.0528810i		−	0.00283065i	−0.999999	−	0.00141533i	$-0.999549\pi$
$349$		−	0.0528810i		−	0.00283065i	0.999999	−	0.00141533i	$-0.000450513\pi$
$350$		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	0.835896	−	0.548888i	$-0.184949\pi$
$353$	−1.86927	−	3.66865i	−0.0994913	−	0.195263i	−0.935387	+	0.353626i	$0.884949\pi$
$354$	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	0.992159	−	0.124985i	$-0.0398882\pi$
$359$	22.3556	+	16.2423i	1.17989	+	0.857237i	0.187726	+	0.982221i	$0.439888\pi$
$360$		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	0.604681	−	0.796468i	$-0.293301\pi$
$367$	6.04885	+	3.08204i	0.315747	+	0.160881i	−0.288934	+	0.957349i	$0.593301\pi$
$368$	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	−0.896477	−	0.443089i	$-0.853882\pi$
$373$	1.79701	−	11.3458i	0.0930454	−	0.587466i	0.989523	−	0.144376i	$-0.0461176\pi$
$374$	−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	0.796546	+	0.604578i	$0.206658\pi$
$379$	−3.95657	+	12.1771i	−0.203235	+	0.625494i	−0.999781	+	0.0209157i	$0.993342\pi$
$380$		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	−0.572243	−	0.820084i	$-0.693927\pi$
$383$	8.36780	−	16.4227i	0.427575	−	0.839163i	0.999818	−	0.0190788i	$-0.00607333\pi$
$384$	−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	0.998545	+	0.0539190i	$0.0171713\pi$
$389$	14.6199	+	20.1226i	0.741258	+	1.02025i	−0.257287	+	0.966335i	$0.582829\pi$
$390$		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	0.298001	−	0.954566i	$-0.403680\pi$
$397$	24.8148	−	12.6438i	1.24542	−	0.634574i	0.947420	+	0.319992i	$0.103680\pi$
$398$	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	−0.521505	−	0.853248i	$-0.674629\pi$
$409$	9.12365	−	12.5576i	0.451136	−	0.620935i	0.972641	+	0.232313i	$0.0746294\pi$
$410$		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	0.720883	+	0.693056i	$0.243736\pi$
$419$	11.1568	+	34.3371i	0.545045	+	1.67748i	−0.175838	+	0.984419i	$0.556264\pi$
$420$		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	$-0.0276802\pi$
$422$	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	−0.459252	−	0.888306i	$-0.651882\pi$
$431$	−6.40797	+	2.08208i	−0.308661	+	0.100290i	0.150591	+	0.988596i	$0.451882\pi$
$432$	1.91510	−	4.13610i	0.0921401	−	0.198998i
$433$	9.39790	+	4.78847i	0.451634	+	0.230119i	0.664985	−	0.746857i	$-0.268438\pi$
$433$	9.39790	+	4.78847i	0.451634	+	0.230119i	−0.213351	+	0.976976i	$0.568438\pi$
$434$	−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	−0.366960	−	0.930237i	$-0.619602\pi$
$439$	8.47207	−	6.15532i	0.404350	−	0.293778i	0.771311	+	0.636459i	$0.219602\pi$
$440$		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	0.625113	−	0.780534i	$-0.285053\pi$
$443$	−3.27124	−	3.27124i	−0.155421	−	0.155421i	−0.780534	+	0.625113i	$0.785053\pi$
$444$	−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	$-0.859594\pi$
$449$		−	18.0931i		−	0.853868i	0.904283	−	0.426934i	$-0.140406\pi$
$450$		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	−0.994706	−	0.102764i	$-0.967231\pi$
$457$	−23.4612	−	23.4612i	−1.09747	−	1.09747i	−0.102764	−	0.994706i	$-0.532769\pi$
$458$	−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	−0.996043	−	0.0888686i	$-0.971675\pi$
$461$	−26.1799	+	19.0208i	−1.21932	+	0.885887i	−0.223275	+	0.974755i	$0.571675\pi$
$462$	−0.896064	−	3.58359i	−0.0416887	−	0.166724i
$463$	4.79718	+	30.2882i	0.222944	+	1.40761i	0.804425	+	0.594054i	$0.202473\pi$
$463$	4.79718	+	30.2882i	0.222944	+	1.40761i	−0.581481	+	0.813560i	$0.697527\pi$
$464$	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	0.744777	−	0.667314i	$-0.232556\pi$
$467$	13.8884	+	7.07648i	0.642677	+	0.327460i	−0.102100	+	0.994774i	$0.532556\pi$
$468$	−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	−0.988112	−	0.153734i	$-0.950870\pi$
$479$	−2.15249	+	6.62469i	−0.0983498	+	0.302690i	0.889762	+	0.456424i	$0.150870\pi$
$480$		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	−0.604529	−	0.796583i	$-0.706639\pi$
$487$	−20.5964	+	3.26215i	−0.933313	+	0.147822i	−0.328784	+	0.944405i	$0.606639\pi$
$488$	−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	−0.738763	−	0.673965i	$-0.764590\pi$
$491$	2.89183	−	3.98026i	0.130506	−	0.179627i	0.869269	+	0.494339i	$0.164590\pi$
$492$	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	−0.904575	−	0.426314i	$-0.859812\pi$
$503$	−24.4770	+	12.4717i	−1.09138	+	0.556084i	−0.186801	+	0.982398i	$0.559812\pi$
$504$	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	−0.592582	−	0.805510i	$-0.701891\pi$
$509$	8.04575	−	11.0740i	0.356622	−	0.490847i	0.949204	+	0.314663i	$0.101891\pi$
$510$		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	−0.915349	−	0.402661i	$-0.868085\pi$
$521$	1.41202	−	4.34576i	0.0618618	−	0.190391i	0.977211	+	0.212270i	$0.0680855\pi$
$522$	−0.495229	−	0.791341i	−0.0216756	−	0.0346361i
$523$	35.8180	+	5.67302i	1.56621	+	0.248064i	0.878437	−	0.477859i	$-0.158587\pi$
$523$	35.8180	+	5.67302i	1.56621	+	0.248064i	0.687776	+	0.725923i	$0.258587\pi$
$524$	−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	−0.0525174	−	0.998620i	$-0.516724\pi$
$541$	−23.6895	−	17.2114i	−1.01849	−	0.739976i	−0.965973	+	0.258644i	$0.916724\pi$
$542$	−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	−0.930814	−	0.365493i	$-0.880900\pi$
$547$	−15.8895	−	31.1849i	−0.679385	−	1.33337i	0.251429	−	0.967876i	$-0.419100\pi$
$548$	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	0.997715	+	0.0675692i	$0.0215243\pi$
$557$	25.1416	+	25.1416i	1.06528	+	1.06528i	0.0675692	+	0.997715i	$0.478476\pi$
$558$	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	0.893929	+	0.448208i	$0.147937\pi$
$563$	4.32450	+	27.3038i	0.182256	+	1.15072i	−0.711674	+	0.702510i	$0.752063\pi$
$564$	−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	−0.487065	−	0.873366i	$-0.661932\pi$
$569$	−8.77237	+	2.85032i	−0.367757	+	0.119491i	0.119308	+	0.992857i	$0.461932\pi$
$570$		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	$0.476290\pi$
$572$	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	−0.0741898	−	0.997244i	$-0.523637\pi$
$577$	−10.8794	−	1.72312i	−0.452914	−	0.0717345i	−0.378724	+	0.925510i	$0.623637\pi$
$578$	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	0.915277	−	0.402825i	$-0.131972\pi$
$587$	46.2814	−	7.33025i	1.91024	−	0.302552i	0.994960	+	0.100273i	$0.0319715\pi$
$588$	−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	−0.429731	−	0.902957i	$-0.641392\pi$
$593$	11.5238	−	11.5238i	0.473225	−	0.473225i	0.902957	+	0.429731i	$0.141392\pi$
$594$	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	−0.630443	−	0.776235i	$-0.717127\pi$
$607$	3.59194	−	3.59194i	0.145792	−	0.145792i	0.776235	+	0.630443i	$0.217127\pi$
$608$	−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	−0.0550888	−	0.998481i	$-0.517544\pi$
$613$	4.97817	−	0.788465i	0.201066	−	0.0318458i	0.256155	+	0.966636i	$0.417544\pi$
$614$	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	−0.996154	−	0.0876162i	$-0.972075\pi$
$617$	−8.43913	+	16.5627i	−0.339746	+	0.666790i	0.656408	+	0.754406i	$0.272075\pi$
$618$	0.401851	+	0.336731i	0.0161648	+	0.0135453i
$619$	−6.54265	−	20.1362i	−0.262971	−	0.809343i	−0.992154	−	0.125024i	$-0.960099\pi$
$619$	−6.54265	−	20.1362i	−0.262971	−	0.809343i	0.729182	−	0.684320i	$-0.239901\pi$
$620$		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	−0.372555	−	0.928010i	$-0.621518\pi$
$631$	−3.22756	+	1.04870i	−0.128487	+	0.0417480i	0.244068	+	0.969758i	$0.421518\pi$
$632$	−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	0.996585	−	0.0825780i	$-0.0263153\pi$
$641$	31.0401	+	22.5519i	1.22601	+	0.890748i	0.229425	+	0.973326i	$0.426315\pi$
$642$	−2.87003	−	1.15731i	−0.113271	−	0.0456754i
$643$	−6.79295	−	6.79295i	−0.267888	−	0.267888i	0.560361	−	0.828249i	$-0.310662\pi$
$643$	−6.79295	−	6.79295i	−0.267888	−	0.267888i	−0.828249	+	0.560361i	$0.810662\pi$
$644$	−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	0.966044	+	0.258379i	$0.0831884\pi$
$647$	15.4461	+	30.3148i	0.607251	+	1.19180i	−0.358793	+	0.933417i	$0.616812\pi$
$648$	−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	0.940862	−	0.338791i	$-0.110018\pi$
$653$	2.90673	+	5.70477i	0.113749	+	0.223245i	−0.827112	+	0.562036i	$0.810018\pi$
$654$	−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	0.790015	−	0.613087i	$-0.210073\pi$
$659$	11.5792	+	8.41281i	0.451063	+	0.327716i	−0.338952	+	0.940804i	$0.610073\pi$
$660$		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	$0.302925\pi$
$662$	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	−0.834729	−	0.550660i	$-0.814376\pi$
$673$	3.35456	−	21.1799i	0.129309	−	0.816424i	0.964038	−	0.265764i	$-0.0856241\pi$
$674$	−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	−0.762155	−	0.647395i	$-0.775858\pi$
$677$	−43.8961	−	6.95245i	−1.68706	−	0.267204i	−0.924908	+	0.380191i	$0.875858\pi$
$678$	−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	−0.574493	−	0.818510i	$-0.694801\pi$
$683$	11.1168	−	21.8180i	0.425374	−	0.834843i	0.999867	−	0.0163335i	$-0.00519935\pi$
$684$	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	−0.954066	−	0.299596i	$-0.903148\pi$
$691$	−9.83947	+	13.5429i	−0.374311	+	0.515195i	0.579755	+	0.814791i	$0.303148\pi$
$692$	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	0.0866885	+	0.996235i	$0.472372\pi$
$709$	−23.6335	+	32.5288i	−0.887576	+	1.22164i	−0.974264	+	0.225408i	$0.927628\pi$
$710$		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	0.875197	−	0.483766i	$-0.160731\pi$
$719$	−3.14270	−	9.67223i	−0.117203	−	0.360713i	−0.992400	+	0.123053i	$0.960731\pi$
$720$		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	0.949127	+	0.314893i	$0.101969\pi$
$727$	−1.37117	+	8.65722i	−0.0508538	+	0.321078i	−0.999981	+	0.00618506i	$0.998031\pi$
$728$	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	0.449653	−	0.893203i	$-0.351548\pi$
$733$	−0.234567	−	0.119518i	−0.00866394	−	0.00441450i	−0.458317	+	0.888789i	$0.651548\pi$
$734$	−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	−0.692235	−	0.721672i	$-0.743374\pi$
$739$	−5.97506	+	4.34113i	−0.219796	+	0.159691i	0.472439	+	0.881363i	$0.343374\pi$
$740$		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	0.566198	−	0.824269i	$-0.308414\pi$
$743$	−7.03452	−	7.03452i	−0.258071	−	0.258071i	−0.824269	+	0.566198i	$0.808414\pi$
$744$	−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	$-0.821134\pi$
$751$		−	29.2029i		−	1.06563i	0.846232	−	0.532814i	$-0.178866\pi$
$752$	−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	0.971337	−	0.237707i	$-0.0763959\pi$
$757$	20.1848	+	20.1848i	0.733630	+	0.733630i	−0.237707	+	0.971337i	$0.576396\pi$
$758$	−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	−0.434639	−	0.900605i	$-0.643124\pi$
$761$	7.93313	−	5.76375i	0.287576	−	0.208936i	0.722215	+	0.691669i	$0.243124\pi$
$762$	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	−0.603812	−	0.797127i	$-0.706352\pi$
$769$	−17.2976	+	5.62032i	−0.623766	+	0.202674i	−0.0199544	+	0.999801i	$0.506352\pi$
$770$		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	0.498957	+	0.866627i	$0.333717\pi$
$773$	−6.76671	+	42.7233i	−0.243382	+	1.53665i	−0.742339	+	0.670025i	$0.766283\pi$
$774$	−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	0.0606043	−	0.998162i	$-0.480697\pi$
$787$	11.9702	−	1.89589i	0.426691	−	0.0675813i	0.366087	+	0.930581i	$0.380697\pi$
$788$	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	−0.694083	−	0.719895i	$-0.744190\pi$
$797$	−14.6702	+	7.47486i	−0.519646	+	0.264773i	0.174436	+	0.984668i	$0.444190\pi$
$798$	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	−0.970619	−	0.240621i	$-0.922649\pi$
$809$	−12.5671	+	17.2972i	−0.441837	+	0.608136i	0.528782	+	0.848757i	$0.322649\pi$
$810$		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	$0.986771\pi$
$812$	−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	0.781778	+	0.623557i	$0.214313\pi$
$821$	−6.22378	+	19.1548i	−0.217211	+	0.668508i	−0.998989	+	0.0449507i	$0.985687\pi$
$822$	−4.32826	+	2.70867i	−0.150966	+	0.0944757i
$823$	−41.6729	−	6.60034i	−1.45263	−	0.230073i	−0.620302	−	0.784363i	$-0.712990\pi$
$823$	−41.6729	−	6.60034i	−1.45263	−	0.230073i	−0.832324	+	0.554289i	$0.812990\pi$
$824$	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	−0.921517	−	0.388338i	$-0.873049\pi$
$827$	2.15397	−	13.5996i	0.0749008	−	0.472905i	0.996418	−	0.0845669i	$-0.0269507\pi$
$828$	21.1571	−	15.9879i	0.735261	−	0.555620i
$829$	−35.5980	−	11.5665i	−1.23637	−	0.401721i	−0.383352	−	0.923602i	$-0.625230\pi$
$829$	−35.5980	−	11.5665i	−1.23637	−	0.401721i	−0.853018	+	0.521881i	$0.825230\pi$
$830$		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	−0.469291	−	0.883044i	$-0.655491\pi$
$839$	6.53213	−	4.74587i	0.225514	−	0.163846i	0.694805	+	0.719198i	$0.255491\pi$
$840$		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	−0.985812	−	0.167851i	$-0.946317\pi$
$853$	−15.8344	−	31.0768i	−0.542160	−	1.06405i	0.443652	−	0.896199i	$-0.353683\pi$
$854$	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	−0.995998	−	0.0893726i	$-0.971514\pi$
$857$	−31.7738	−	31.7738i	−1.08537	−	1.08537i	−0.0893726	−	0.995998i	$-0.528486\pi$
$858$	−1.42841	+	3.54234i	−0.0487652	+	0.120933i
$859$	−34.2690	−	24.8979i	−1.16924	−	0.849504i	−0.178324	−	0.983972i	$-0.557068\pi$
$859$	−34.2690	−	24.8979i	−1.16924	−	0.849504i	−0.990918	+	0.134468i	$0.957068\pi$
$860$		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	−0.991484	−	0.130230i	$-0.958428\pi$
$863$	−2.60778	−	16.4649i	−0.0887700	−	0.560472i	0.902714	−	0.430242i	$-0.141572\pi$
$864$	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	0.399217	−	0.916856i	$-0.369282\pi$
$877$	14.6759	+	2.32444i	0.495571	+	0.0784907i	0.0963539	+	0.995347i	$0.469282\pi$
$878$	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	−0.793456	−	0.608628i	$-0.791720\pi$
$881$	−15.1162	−	46.5230i	−0.509279	−	1.56740i	0.284177	−	0.958772i	$-0.408280\pi$
$882$	−0.475066	+	0.566939i	−0.0159963	+	0.0190898i
$883$	−0.740506	+	1.45332i	−0.0249200	+	0.0489083i	−0.903131	−	0.429365i	$-0.858737\pi$
$883$	−0.740506	+	1.45332i	−0.0249200	+	0.0489083i	0.878211	+	0.478274i	$0.158737\pi$
$884$	−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	−0.587963	−	0.808888i	$-0.700070\pi$
$887$	−26.7206	+	4.23212i	−0.897189	+	0.142101i	−0.309226	+	0.950989i	$0.600070\pi$
$888$	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	−0.200818	+	0.979629i	$0.564360\pi$
$907$	−35.5508	+	35.5508i	−1.18045	+	1.18045i	−0.979629	+	0.200818i	$0.935640\pi$
$908$	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	0.861807	−	0.507236i	$-0.169333\pi$
$911$	3.41319	+	4.69785i	0.113084	+	0.155647i	−0.748723	+	0.662883i	$0.769333\pi$
$912$	−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	−0.887934	−	0.459971i	$-0.847860\pi$
$919$	−13.3369	−	41.0468i	−0.439944	−	1.35401i	0.447990	−	0.894039i	$-0.352140\pi$
$920$		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	−0.313578	−	0.949562i	$-0.601528\pi$
$929$	−34.3019	−	11.1453i	−1.12541	−	0.365667i	−0.811829	+	0.583895i	$0.801528\pi$
$930$		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	−0.872796	−	0.488084i	$-0.837696\pi$
$937$	−5.92447	−	37.4056i	−0.193544	−	1.22199i	0.679252	−	0.733905i	$-0.262304\pi$
$938$	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	0.922902	−	0.385034i	$-0.125810\pi$
$941$	25.8261	+	18.7637i	0.841906	+	0.611680i	−0.0809965	+	0.996714i	$0.525810\pi$
$942$	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	0.915606	−	0.402077i	$-0.131712\pi$
$947$	1.60449	+	3.14898i	0.0521388	+	0.102328i	−0.863467	+	0.504405i	$0.831712\pi$
$948$	−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	0.830674	+	0.556759i	$0.187955\pi$
$953$	24.4756	+	48.0361i	0.792843	+	1.55604i	−0.0378308	+	0.999284i	$0.512045\pi$
$954$	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	0.661582	−	0.749873i	$-0.269885\pi$
$967$	13.8004	+	7.03165i	0.443791	+	0.226123i	−0.217792	+	0.975995i	$0.569885\pi$
$968$	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	0.0272659	−	0.999628i	$-0.491320\pi$
$971$	−16.7721	−	5.44959i	−0.538242	−	0.174886i	−0.565508	+	0.824743i	$0.691320\pi$
$972$	−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	0.916687	−	0.399605i	$-0.130853\pi$
$977$	52.0437	+	8.24291i	1.66502	+	0.263714i	0.748337	+	0.663319i	$0.230853\pi$
$978$	−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	−0.982463	−	0.186455i	$-0.940300\pi$
$983$	−7.96803	+	15.6381i	−0.254141	+	0.498779i	0.728323	+	0.685234i	$0.240300\pi$
$984$	−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	−0.998524	−	0.0543192i	$-0.982701\pi$
$991$	−20.0939	+	27.6568i	−0.638302	+	0.878548i	0.360221	+	0.932867i	$0.382701\pi$
$992$	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	−0.424074	−	0.905628i	$-0.639400\pi$
$997$	1.87335	−	0.954518i	0.0593295	−	0.0302299i	0.483404	+	0.875398i	$0.339400\pi$
$998$	−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.407.5		96
4.3	odd	2	inner	500.2.l.d.407.6		96
5.2	odd	4		100.2.l.b.23.1	✓	96
5.3	odd	4		500.2.l.f.343.12		96
5.4	even	2		500.2.l.e.407.8		96
15.2	even	4		900.2.bj.d.523.12		96
20.3	even	4		500.2.l.f.343.1		96
20.7	even	4		100.2.l.b.23.12	yes	96
20.19	odd	2		500.2.l.e.407.7		96
25.9	even	10		100.2.l.b.87.12	yes	96
25.12	odd	20		500.2.l.e.43.7		96
25.13	odd	20	inner	500.2.l.d.43.6		96
25.16	even	5		500.2.l.f.207.1		96
60.47	odd	4		900.2.bj.d.523.1		96
75.59	odd	10		900.2.bj.d.487.1		96
100.59	odd	10		100.2.l.b.87.1	yes	96
100.63	even	20	inner	500.2.l.d.43.5		96
100.87	even	20		500.2.l.e.43.8		96
100.91	odd	10		500.2.l.f.207.12		96
300.59	even	10		900.2.bj.d.487.12		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.2.l.b.23.1	✓	96	5.2	odd	4
100.2.l.b.23.12	yes	96	20.7	even	4
100.2.l.b.87.1	yes	96	100.59	odd	10
100.2.l.b.87.12	yes	96	25.9	even	10
500.2.l.d.43.5		96	100.63	even	20	inner
500.2.l.d.43.6		96	25.13	odd	20	inner
500.2.l.d.407.5		96	1.1	even	1	trivial
500.2.l.d.407.6		96	4.3	odd	2	inner
500.2.l.e.43.7		96	25.12	odd	20
500.2.l.e.43.8		96	100.87	even	20
500.2.l.e.407.7		96	20.19	odd	2
500.2.l.e.407.8		96	5.4	even	2
500.2.l.f.207.1		96	25.16	even	5
500.2.l.f.207.12		96	100.91	odd	10
500.2.l.f.343.1		96	20.3	even	4
500.2.l.f.343.12		96	5.3	odd	4
900.2.bj.d.487.1		96	75.59	odd	10
900.2.bj.d.487.12		96	300.59	even	10
900.2.bj.d.523.1		96	60.47	odd	4
900.2.bj.d.523.12		96	15.2	even	4

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

Properties

Related objects

Downloads

Learn more