LMFDB - Embedded newform 500.2.l.f.343.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("500.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.99252010106$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 100)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			343.1
Character	$\chi$	$=$	500.343
Dual form			500.2.l.f.207.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37197 - 0.343057i) q^{2} +(0.0867473 + 0.170251i) q^{3} +(1.76462 + 0.941330i) q^{4} +(-0.0606092 - 0.263339i) q^{6} +(1.89427 + 1.89427i) q^{7} +(-2.09809 - 1.89685i) q^{8} +(1.74190 - 2.39751i) q^{9} +O(q^{10})$	\(q+(-1.37197 - 0.343057i) q^{2} +(0.0867473 + 0.170251i) q^{3} +(1.76462 + 0.941330i) q^{4} +(-0.0606092 - 0.263339i) q^{6} +(1.89427 + 1.89427i) q^{7} +(-2.09809 - 1.89685i) q^{8} +(1.74190 - 2.39751i) q^{9} +(-2.99934 - 4.12824i) q^{11} +(-0.00718616 + 0.382087i) q^{12} +(-0.433317 - 2.73586i) q^{13} +(-1.94904 - 3.24872i) q^{14} +(2.22780 + 3.32219i) q^{16} +(4.16697 + 2.12318i) q^{17} +(-3.21232 + 2.69176i) q^{18} +(1.55045 + 4.77181i) q^{19} +(-0.158179 + 0.486824i) q^{21} +(2.69880 + 6.69278i) q^{22} +(0.699923 - 4.41914i) q^{23} +(0.140937 - 0.521748i) q^{24} +(-0.344055 + 3.90218i) q^{26} +(1.12546 + 0.178255i) q^{27} +(1.55954 + 5.12580i) q^{28} +(-0.211843 - 0.0688321i) q^{29} +(7.01920 - 2.28068i) q^{31} +(-1.91678 - 5.32221i) q^{32} +(0.442653 - 0.868756i) q^{33} +(-4.98861 - 4.34246i) q^{34} +(5.33064 - 2.59101i) q^{36} +(-4.32186 + 0.684516i) q^{37} +(-0.490182 - 7.07869i) q^{38} +(0.428194 - 0.311101i) q^{39} +(2.54404 + 1.84835i) q^{41} +(0.384025 - 0.613645i) q^{42} +(2.68807 - 2.68807i) q^{43} +(-1.40668 - 10.1082i) q^{44} +(-2.47629 + 5.82283i) q^{46} +(7.84709 - 3.99829i) q^{47} +(-0.372351 + 0.667476i) q^{48} +0.176489i q^{49} +0.893612i q^{51} +(1.81070 - 5.23565i) q^{52} +(-1.64295 + 0.837124i) q^{53} +(-1.48295 - 0.630658i) q^{54} +(-0.381206 - 7.56747i) q^{56} +(-0.677908 + 0.677908i) q^{57} +(0.267030 + 0.167110i) q^{58} +(7.33328 + 5.32794i) q^{59} +(1.16375 - 0.845512i) q^{61} +(-10.4126 + 0.721044i) q^{62} +(7.84114 - 1.24191i) q^{63} +(0.803948 + 7.95950i) q^{64} +(-0.905341 + 1.04005i) q^{66} +(-1.53527 + 3.01313i) q^{67} +(5.35453 + 7.66911i) q^{68} +(0.813081 - 0.264186i) q^{69} +(-5.45415 - 1.77216i) q^{71} +(-8.20236 + 1.72609i) q^{72} +(0.0187149 + 0.00296414i) q^{73} +(6.16431 + 0.543507i) q^{74} +(-1.75588 + 9.87994i) q^{76} +(2.13843 - 13.5015i) q^{77} +(-0.694196 + 0.279928i) q^{78} +(2.08434 - 6.41493i) q^{79} +(-2.68002 - 8.24826i) q^{81} +(-2.85627 - 3.40864i) q^{82} +(-2.99552 - 1.52629i) q^{83} +(-0.737387 + 0.710162i) q^{84} +(-4.61012 + 2.76580i) q^{86} +(-0.00665810 - 0.0420376i) q^{87} +(-1.53775 + 14.3507i) q^{88} +(-0.509284 - 0.700969i) q^{89} +(4.36162 - 6.00326i) q^{91} +(5.39497 - 7.13927i) q^{92} +(0.997185 + 0.997185i) q^{93} +(-12.1376 + 2.79355i) q^{94} +(0.739838 - 0.788022i) q^{96} +(5.07638 + 9.96296i) q^{97} +(0.0605458 - 0.242139i) q^{98} -15.1221 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 10 q^{2} - 10 q^{4} - 6 q^{6} + 10 q^{8} - 20 q^{9}+O(q^{10}) $ 96 * q + 10 * q^2 - 10 * q^4 - 6 * q^6 + 10 * q^8 - 20 * q^9	$ 96 q + 10 q^{2} - 10 q^{4} - 6 q^{6} + 10 q^{8} - 20 q^{9} + 10 q^{12} + 20 q^{13} - 10 q^{14} - 14 q^{16} + 20 q^{17} - 20 q^{18} - 12 q^{21} + 10 q^{22} - 12 q^{26} + 10 q^{28} - 20 q^{29} + 50 q^{32} + 20 q^{33} - 60 q^{34} - 10 q^{36} - 40 q^{37} - 20 q^{38} - 28 q^{41} - 90 q^{42} + 60 q^{44} - 6 q^{46} - 120 q^{48} - 80 q^{52} + 40 q^{53} + 120 q^{54} - 6 q^{56} + 20 q^{57} - 60 q^{58} + 12 q^{61} - 40 q^{62} + 20 q^{64} - 30 q^{66} + 10 q^{68} - 20 q^{69} + 40 q^{72} + 20 q^{73} + 20 q^{77} - 20 q^{78} - 36 q^{81} + 50 q^{82} - 90 q^{84} - 6 q^{86} + 130 q^{88} + 160 q^{89} + 110 q^{92} - 60 q^{93} - 170 q^{94} + 14 q^{96} - 180 q^{97} + 130 q^{98}+O(q^{100}) $ 96 * q + 10 * q^2 - 10 * q^4 - 6 * q^6 + 10 * q^8 - 20 * q^9 + 10 * q^12 + 20 * q^13 - 10 * q^14 - 14 * q^16 + 20 * q^17 - 20 * q^18 - 12 * q^21 + 10 * q^22 - 12 * q^26 + 10 * q^28 - 20 * q^29 + 50 * q^32 + 20 * q^33 - 60 * q^34 - 10 * q^36 - 40 * q^37 - 20 * q^38 - 28 * q^41 - 90 * q^42 + 60 * q^44 - 6 * q^46 - 120 * q^48 - 80 * q^52 + 40 * q^53 + 120 * q^54 - 6 * q^56 + 20 * q^57 - 60 * q^58 + 12 * q^61 - 40 * q^62 + 20 * q^64 - 30 * q^66 + 10 * q^68 - 20 * q^69 + 40 * q^72 + 20 * q^73 + 20 * q^77 - 20 * q^78 - 36 * q^81 + 50 * q^82 - 90 * q^84 - 6 * q^86 + 130 * q^88 + 160 * q^89 + 110 * q^92 - 60 * q^93 - 170 * q^94 + 14 * q^96 - 180 * q^97 + 130 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.37197	−	0.343057i	−0.970132	−	0.242578i
$2$	−1.37197	−	0.343057i	−0.970132	−	0.242578i
$3$	0.0867473	+	0.170251i	0.0500836	+	0.0982946i	0.914692	−	0.404152i	$-0.132433\pi$
$3$	0.0867473	+	0.170251i	0.0500836	+	0.0982946i	−0.864608	+	0.502447i	$0.832433\pi$
$4$	1.76462	+	0.941330i	0.882312	+	0.470665i
$5$		0			0
$5$		0			0
$6$	−0.0606092	−	0.263339i	−0.0247436	−	0.107508i
$7$	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	$0.581026\pi$
$8$	−2.09809	−	1.89685i	−0.741786	−	0.670636i
$9$	1.74190	−	2.39751i	0.580632	−	0.799171i
$10$		0			0
$11$	−2.99934	−	4.12824i	−0.904336	−	1.24471i	−0.969064	−	0.246809i	$-0.920618\pi$
$11$	−2.99934	−	4.12824i	−0.904336	−	1.24471i	0.0647283	−	0.997903i	$-0.479382\pi$
$12$	−0.00718616	+	0.382087i	−0.00207446	+	0.110299i
$13$	−0.433317	−	2.73586i	−0.120181	−	0.758790i	−0.972005	−	0.234962i	$-0.924503\pi$
$13$	−0.433317	−	2.73586i	−0.120181	−	0.758790i	0.851824	−	0.523828i	$-0.175497\pi$
$14$	−1.94904	−	3.24872i	−0.520904	−	0.868258i
$15$		0			0
$16$	2.22780	+	3.32219i	0.556949	+	0.830547i
$17$	4.16697	+	2.12318i	1.01064	+	0.514947i	0.879238	−	0.476383i	$-0.158052\pi$
$17$	4.16697	+	2.12318i	1.01064	+	0.514947i	0.131402	+	0.991329i	$0.458052\pi$
$18$	−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
$22$	2.69880	+	6.69278i	0.575386	+	1.42691i
$23$	0.699923	−	4.41914i	0.145944	−	0.921455i	−0.800675	−	0.599100i	$-0.795525\pi$
$23$	0.699923	−	4.41914i	0.145944	−	0.921455i	0.946619	−	0.322355i	$-0.104475\pi$
$24$	0.140937	−	0.521748i	0.0287686	−	0.106501i
$25$		0			0
$26$	−0.344055	+	3.90218i	−0.0674747	+	0.765280i
$27$	1.12546	+	0.178255i	0.216595	+	0.0343052i
$28$	1.55954	+	5.12580i	0.294725	+	0.968685i
$29$	−0.211843	−	0.0688321i	−0.0393383	−	0.0127818i	0.289282	−	0.957244i	$-0.406584\pi$
$29$	−0.211843	−	0.0688321i	−0.0393383	−	0.0127818i	−0.328620	+	0.944462i	$0.606584\pi$
$30$		0			0
$31$	7.01920	−	2.28068i	1.26069	−	0.409622i	0.398947	−	0.916974i	$-0.369376\pi$
$31$	7.01920	−	2.28068i	1.26069	−	0.409622i	0.861739	+	0.507352i	$0.169376\pi$
$32$	−1.91678	−	5.32221i	−0.338842	−	0.940843i
$33$	0.442653	−	0.868756i	0.0770560	−	0.151231i
$34$	−4.98861	−	4.34246i	−0.855539	−	0.744725i
$35$		0			0
$36$	5.33064	−	2.59101i	0.888440	−	0.431835i
$37$	−4.32186	+	0.684516i	−0.710510	+	0.112534i	−0.501220	−	0.865320i	$-0.667115\pi$
$37$	−4.32186	+	0.684516i	−0.710510	+	0.112534i	−0.209290	+	0.977854i	$0.567115\pi$
$38$	−0.490182	−	7.07869i	−0.0795179	−	1.14832i
$39$	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	$0.621031\pi$
$42$	0.384025	−	0.613645i	0.0592564	−	0.0946875i
$43$	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	$0.156391\pi$
$44$	−1.40668	−	10.1082i	−0.212064	−	1.52386i
$45$		0			0
$46$	−2.47629	+	5.82283i	−0.365110	+	0.858530i
$47$	7.84709	−	3.99829i	1.14462	−	0.583211i	0.224351	−	0.974508i	$-0.427974\pi$
$47$	7.84709	−	3.99829i	1.14462	−	0.583211i	0.920264	+	0.391298i	$0.127974\pi$
$48$	−0.372351	+	0.667476i	−0.0537442	+	0.0963418i
$49$			0.176489i			0.0252127i
$50$		0			0
$51$			0.893612i			0.125131i
$52$	1.81070	−	5.23565i	0.251099	−	0.726055i
$53$	−1.64295	+	0.837124i	−0.225676	+	0.114988i	−0.563173	−	0.826339i	$-0.690420\pi$
$53$	−1.64295	+	0.837124i	−0.225676	+	0.114988i	0.337497	+	0.941327i	$0.390420\pi$
$54$	−1.48295	−	0.630658i	−0.201804	−	0.0858217i
$55$		0			0
$56$	−0.381206	−	7.56747i	−0.0509407	−	1.01125i
$57$	−0.677908	+	0.677908i	−0.0897912	+	0.0897912i
$58$	0.267030	+	0.167110i	0.0350628	+	0.0219426i
$59$	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	$0.270646\pi$
$62$	−10.4126	+	0.721044i	−1.32240	+	0.0915727i
$63$	7.84114	−	1.24191i	0.987891	−	0.156467i
$64$	0.803948	+	7.95950i	0.100493	+	0.994938i
$65$		0			0
$66$	−0.905341	+	1.04005i	−0.111440	+	0.128022i
$67$	−1.53527	+	3.01313i	−0.187563	+	0.368113i	−0.965570	−	0.260142i	$-0.916231\pi$
$67$	−1.53527	+	3.01313i	−0.187563	+	0.368113i	0.778007	+	0.628255i	$0.216231\pi$
$68$	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	$-0.510529\pi$
$71$	−5.45415	−	1.77216i	−0.647288	−	0.210317i	−0.614218	+	0.789136i	$0.710529\pi$
$72$	−8.20236	+	1.72609i	−0.966658	+	0.203421i
$73$	0.0187149	+	0.00296414i	0.00219041	+	0.000346927i	0.157530	−	0.987514i	$-0.449647\pi$
$73$	0.0187149	+	0.00296414i	0.00219041	+	0.000346927i	−0.155339	+	0.987861i	$0.549647\pi$
$74$	6.16431	+	0.543507i	0.716586	+	0.0631814i
$75$		0			0
$76$	−1.75588	+	9.87994i	−0.201413	+	1.13331i
$77$	2.13843	−	13.5015i	0.243697	−	1.53864i
$78$	−0.694196	+	0.279928i	−0.0786022	+	0.0316956i
$79$	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
$83$	−2.99552	−	1.52629i	−0.328801	−	0.167532i	0.281795	−	0.959475i	$-0.409070\pi$
$83$	−2.99552	−	1.52629i	−0.328801	−	0.167532i	−0.610596	+	0.791942i	$0.709070\pi$
$84$	−0.737387	+	0.710162i	−0.0804556	+	0.0774851i
$85$		0			0
$86$	−4.61012	+	2.76580i	−0.497122	+	0.298244i
$87$	−0.00665810	−	0.0420376i	−0.000713823	−	0.00450690i
$88$	−1.53775	+	14.3507i	−0.163925	+	1.52979i
$89$	−0.509284	−	0.700969i	−0.0539840	−	0.0743026i	0.781172	−	0.624316i	$-0.214622\pi$
$89$	−0.509284	−	0.700969i	−0.0539840	−	0.0743026i	−0.835156	+	0.550014i	$0.814622\pi$
$90$		0			0
$91$	4.36162	−	6.00326i	0.457222	−	0.629313i
$92$	5.39497	−	7.13927i	0.562465	−	0.744320i
$93$	0.997185	+	0.997185i	0.103403	+	0.103403i
$94$	−12.1376	+	2.79355i	−1.25190	+	0.288133i
$95$		0			0
$96$	0.739838	−	0.788022i	0.0755094	−	0.0804271i
$97$	5.07638	+	9.96296i	0.515428	+	1.01158i	0.991244	+	0.132040i	$0.0421528\pi$
$97$	5.07638	+	9.96296i	0.515428	+	1.01158i	−0.475816	+	0.879545i	$0.657847\pi$
$98$	0.0605458	−	0.242139i	0.00611605	−	0.0244597i
$99$	−15.1221			−1.51982
$100$		0			0
$101$	−11.8084			−1.17498			−0.587489	−	0.809232i	$-0.699884\pi$
$101$	−11.8084			−1.17498			−0.587489	+	0.809232i	$0.699884\pi$
$102$	0.306560	−	1.22601i	0.0303540	−	0.121393i
$103$	0.880821	+	1.72871i	0.0867899	+	0.170335i	0.930322	−	0.366744i	$-0.119528\pi$
$103$	0.880821	+	1.72871i	0.0867899	+	0.170335i	−0.843532	+	0.537079i	$0.819528\pi$
$104$	−4.28036	+	6.56201i	−0.419724	+	0.643458i
$105$		0			0
$106$	2.54126	−	0.584888i	0.246829	−	0.0568093i
$107$	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	$0.563273\pi$
$108$	1.81822	+	1.37398i	0.174958	+	0.132211i
$109$	−9.13259	+	12.5699i	−0.874743	+	1.20398i	0.103106	+	0.994670i	$0.467122\pi$
$109$	−9.13259	+	12.5699i	−0.874743	+	1.20398i	−0.977849	+	0.209310i	$0.932878\pi$
$110$		0			0
$111$	−0.491450	−	0.676422i	−0.0466463	−	0.0642032i
$112$	−2.07307	+	10.5131i	−0.195887	+	0.993399i
$113$	1.26860	+	8.00964i	0.119340	+	0.753483i	0.972684	+	0.232135i	$0.0745710\pi$
$113$	1.26860	+	8.00964i	0.119340	+	0.753483i	−0.853344	+	0.521349i	$0.825429\pi$
$114$	1.16263	−	0.697512i	0.108891	−	0.0653279i
$115$		0			0
$116$	−0.309030	−	0.320877i	−0.0286927	−	0.0297927i
$117$	−7.31405	−	3.72669i	−0.676184	−	0.344533i
$118$	−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
$122$	−1.88669	+	0.760789i	−0.170813	+	0.0688786i
$123$	−0.0939957	+	0.593466i	−0.00847531	+	0.0535110i
$124$	14.5331	+	2.58285i	1.30511	+	0.231947i
$125$		0			0
$126$	−11.1839	−	0.986083i	−0.996340	−	0.0878472i
$127$	−15.8543	−	2.51108i	−1.40684	−	0.222822i	−0.593608	−	0.804755i	$-0.702297\pi$
$127$	−15.8543	−	2.51108i	−1.40684	−	0.222822i	−0.813237	+	0.581932i	$0.802297\pi$
$128$	1.62757	−	11.1960i	0.143858	−	0.989598i
$129$	0.690830	+	0.224464i	0.0608242	+	0.0197630i
$130$		0			0
$131$	−12.9418	+	4.20505i	−1.13073	+	0.367397i	−0.813854	−	0.581069i	$-0.802635\pi$
$131$	−12.9418	+	4.20505i	−1.13073	+	0.367397i	−0.316878	+	0.948466i	$0.602635\pi$
$132$	1.59890	−	1.11634i	0.139167	−	0.0971653i
$133$	−6.10210	+	11.9761i	−0.529119	+	1.03846i
$134$	3.14002	−	3.60726i	0.271257	−	0.311619i
$135$		0			0
$136$	−4.71533	−	12.3587i	−0.404337	−	1.05975i
$137$	−18.6626	+	2.95587i	−1.59445	+	0.252537i	−0.889575	−	0.456790i	$-0.848999\pi$
$137$	−18.6626	+	2.95587i	−1.59445	+	0.252537i	−0.704880	+	0.709327i	$0.748999\pi$
$138$	−1.20616	+	0.0835233i	−0.102675	+	0.00710998i
$139$	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
$142$	6.87500	+	4.30244i	0.576937	+	0.361053i
$143$	−9.99461	+	9.99461i	−0.835792	+	0.835792i
$144$	11.8456	+	0.445732i	0.987131	+	0.0371443i
$145$		0			0
$146$	−0.0246594	−	0.0104870i	−0.00204083	−	0.000867909i
$147$	−0.0300475	+	0.0153100i	−0.00247828	+	0.00126274i
$148$	−8.27082	−	2.86039i	−0.679857	−	0.235122i
$149$			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	$0.920110\pi$
$152$	5.79840	−	12.9527i	0.470312	−	1.05060i
$153$	12.3488	−	6.29202i	0.998340	−	0.508680i
$154$	−7.56567	+	17.7902i	−0.609659	+	1.43357i
$155$		0			0
$156$	1.04845	−	0.145905i	0.0839432	−	0.0116817i
$157$	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	$0.0256624\pi$
$158$	−5.06034	+	8.08607i	−0.402579	+	0.643293i
$159$	−0.285043	−	0.207096i	−0.0226054	−	0.0164238i
$160$		0			0
$161$	9.69687	−	7.04519i	0.764221	−	0.555239i
$162$	0.847298	+	12.2358i	0.0665701	+	0.961335i
$163$	−7.81379	+	1.23758i	−0.612023	+	0.0969349i	−0.454748	−	0.890620i	$-0.650271\pi$
$163$	−7.81379	+	1.23758i	−0.612023	+	0.0969349i	−0.157275	+	0.987555i	$0.550271\pi$
$164$	2.74936	+	5.65643i	0.214689	+	0.441693i
$165$		0			0
$166$	3.58617	+	3.12167i	0.278341	+	0.242288i
$167$	−6.13600	+	12.0426i	−0.474818	+	0.931883i	0.522059	+	0.852910i	$0.325164\pi$
$167$	−6.13600	+	12.0426i	−0.474818	+	0.931883i	−0.996877	+	0.0789735i	$0.974836\pi$
$168$	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
$172$	7.27379	−	2.21307i	0.554621	−	0.168745i
$173$	−1.08340	−	0.171594i	−0.0823695	−	0.0130460i	0.115114	−	0.993352i	$-0.463277\pi$
$173$	−1.08340	−	0.171594i	−0.0823695	−	0.0130460i	−0.197483	+	0.980306i	$0.563277\pi$
$174$	−0.00528654	+	0.0599586i	−0.000400772	+	0.00454545i
$175$		0			0
$176$	7.03287	−	19.1613i	0.530122	−	1.44433i
$177$	−0.270946	+	1.71068i	−0.0203655	+	0.128583i
$178$	0.458252	+	1.13642i	0.0343474	+	0.0851786i
$179$	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
$183$	0.244901	+	0.124784i	0.0181036	+	0.00922426i
$184$	−9.85094	+	7.94410i	−0.726221	+	0.585647i
$185$		0			0
$186$	−1.02602	−	1.71020i	−0.0752315	−	0.125398i
$187$	−3.73319	−	23.5704i	−0.272998	−	1.72364i
$188$	17.6109	+	0.331219i	1.28440	+	0.0241566i
$189$	1.79426	+	2.46958i	0.130513	+	0.179636i
$190$		0			0
$191$	−9.26511	+	12.7523i	−0.670400	+	0.922727i	−0.999769	−	0.0214746i	$-0.993164\pi$
$191$	−9.26511	+	12.7523i	−0.670400	+	0.922727i	0.329369	+	0.944201i	$0.393164\pi$
$192$	−1.28537	+	0.827339i	−0.0927639	+	0.0597080i
$193$	−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	$0.856461\pi$
$194$	−3.54680	−	15.4104i	−0.254645	−	1.10640i
$195$		0			0
$196$	−0.166135	+	0.311437i	−0.0118668	+	0.0222455i
$197$	2.59555	+	5.09406i	0.184925	+	0.362936i	0.964794	−	0.263007i	$-0.0847142\pi$
$197$	2.59555	+	5.09406i	0.184925	+	0.362936i	−0.779869	+	0.625943i	$0.784714\pi$
$198$	20.7471	+	5.18772i	1.47443	+	0.368676i
$199$	−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
$202$	16.2008	+	4.05095i	1.13988	+	0.285024i
$203$	−0.270901	−	0.531674i	−0.0190136	−	0.0373162i
$204$	−0.841184	+	1.57689i	−0.0588947	+	0.110404i
$205$		0			0
$206$	−0.615418	−	2.67391i	−0.0428782	−	0.186300i
$207$	−9.37576	−	9.37576i	−0.651660	−	0.651660i
$208$	8.12369	−	7.53449i	0.563276	−	0.522423i
$209$	15.0488	−	20.7129i	1.04095	−	1.43274i
$210$		0			0
$211$	11.6703	+	16.0628i	0.803419	+	1.10581i	0.992306	+	0.123813i	$0.0395122\pi$
$211$	11.6703	+	16.0628i	0.803419	+	1.10581i	−0.188886	+	0.981999i	$0.560488\pi$
$212$	−3.68720	−	0.0693474i	−0.253238	−	0.00476280i
$213$	−0.171420	−	1.08231i	−0.0117455	−	0.0741584i
$214$	−8.33188	−	13.8878i	−0.569556	−	0.949353i
$215$		0			0
$216$	−2.02319	−	2.50882i	−0.137661	−	0.170703i
$217$	17.6165	+	8.97603i	1.19588	+	0.609333i
$218$	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
$222$	0.442205	+	1.09663i	0.0296788	+	0.0736009i
$223$	−1.81060	+	11.4317i	−0.121247	+	0.765524i	0.849883	+	0.526972i	$0.176673\pi$
$223$	−1.81060	+	11.4317i	−0.121247	+	0.765524i	−0.971130	+	0.238552i	$0.923327\pi$
$224$	6.45080	−	13.7126i	0.431012	−	0.916210i
$225$		0			0
$226$	1.00727	−	11.4242i	0.0670028	−	0.759928i
$227$	−15.3359	−	2.42897i	−1.01788	−	0.161216i	−0.374872	−	0.927077i	$-0.622313\pi$
$227$	−15.3359	−	2.42897i	−1.01788	−	0.161216i	−0.643007	+	0.765861i	$0.722313\pi$
$228$	−1.83439	+	0.558118i	−0.121485	+	0.0369623i
$229$	−16.0312	−	5.20884i	−1.05937	−	0.344210i	−0.273030	−	0.962006i	$-0.588026\pi$
$229$	−16.0312	−	5.20884i	−1.05937	−	0.344210i	−0.786339	+	0.617796i	$0.788026\pi$
$230$		0			0
$231$	2.48416	−	0.807152i	0.163446	−	0.0531067i
$232$	0.313902	+	0.546250i	0.0206087	+	0.0358631i
$233$	13.2595	−	26.0233i	0.868660	−	1.70484i	0.174963	−	0.984575i	$-0.444019\pi$
$233$	13.2595	−	26.0233i	0.868660	−	1.70484i	0.693697	−	0.720267i	$-0.255981\pi$
$234$	8.75622	+	7.62206i	0.572412	+	0.498270i
$235$		0			0
$236$	7.92513	+	16.3048i	0.515882	+	1.06136i
$237$	1.27296	−	0.201617i	0.0826876	−	0.0130964i
$238$	−1.22399	−	17.6755i	−0.0793392	−	1.14573i
$239$	−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	$0.451643\pi$
$242$	11.2823	−	18.0283i	0.725252	−	1.15890i
$243$	3.58901	−	3.58901i	0.230235	−	0.230235i
$244$	2.84948	−	0.396541i	0.182419	−	0.0253859i
$245$		0			0
$246$	0.332552	−	0.781973i	0.0212027	−	0.0498568i
$247$	12.3832	−	6.30953i	0.787921	−	0.401466i
$248$	−19.0530	−	8.52929i	−1.20987	−	0.541610i
$249$		−	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	$-0.0547436\pi$
$252$	15.0057	+	5.18959i	0.945271	+	0.326913i
$253$	−20.3426	+	10.3651i	−1.27893	+	0.651647i
$254$	20.8903	+	8.88407i	1.31077	+	0.557436i
$255$		0			0
$256$	−6.07385	+	14.8023i	−0.379616	+	0.925144i
$257$	−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	$0.365121\pi$
$258$	−0.870796	−	0.544953i	−0.0542134	−	0.0339273i
$259$	−9.48341	−	6.89010i	−0.589271	−	0.428130i
$260$		0			0
$261$	−0.534035	+	0.387999i	−0.0330559	+	0.0240165i
$262$	19.1984	−	1.32944i	1.18608	−	0.0821332i
$263$	−19.6441	+	3.11132i	−1.21131	+	0.191852i	−0.729224	−	0.684275i	$-0.760119\pi$
$263$	−19.6441	+	3.11132i	−1.21131	+	0.191852i	−0.482081	+	0.876127i	$0.660119\pi$
$264$	−2.57662	+	0.983081i	−0.158580	+	0.0605045i
$265$		0			0
$266$	12.4804	−	14.3375i	0.765222	−	0.879086i
$267$	0.0751618	−	0.147513i	0.00459983	−	0.00902767i
$268$	−5.54552	+	3.87185i	−0.338747	+	0.236511i
$269$	−9.63789	+	3.13154i	−0.587633	+	0.190933i	−0.587717	−	0.809067i	$-0.699973\pi$
$269$	−9.63789	+	3.13154i	−0.587633	+	0.190933i	8.44003e−5		1.00000i	$0.499973\pi$
$270$		0			0
$271$	−1.79674	−	0.583795i	−0.109144	−	0.0354630i	0.253936	−	0.967221i	$-0.418275\pi$
$271$	−1.79674	−	0.583795i	−0.109144	−	0.0354630i	−0.363080	+	0.931758i	$0.618275\pi$
$272$	2.22957	+	18.5735i	0.135187	+	1.12618i
$273$	1.40042	+	0.221805i	0.0847574	+	0.0134243i
$274$	26.6186	+	2.34696i	1.60809	+	0.141785i
$275$		0			0
$276$	1.68347	+	0.299188i	0.101333	+	0.0180090i
$277$	−1.79116	+	11.3089i	−0.107620	+	0.679488i	0.873607	+	0.486632i	$0.161775\pi$
$277$	−1.79116	+	11.3089i	−0.107620	+	0.679488i	−0.981227	+	0.192855i	$0.938225\pi$
$278$	−9.55805	+	3.85419i	−0.573254	+	0.231159i
$279$	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
$283$	16.9779	+	8.65065i	1.00923	+	0.514228i	0.878780	−	0.477227i	$-0.158358\pi$
$283$	16.9779	+	8.65065i	1.00923	+	0.514228i	0.130449	+	0.991455i	$0.458358\pi$
$284$	−7.95633	−	8.26135i	−0.472122	−	0.490221i
$285$		0			0
$286$	17.1411	−	10.2836i	1.01357	−	0.608084i
$287$	1.31782	+	8.32036i	0.0777882	+	0.491135i
$288$	−16.0989	−	4.67524i	−0.948637	−	0.275491i
$289$	2.86343	+	3.94118i	0.168437	+	0.231834i
$290$		0			0
$291$	−1.25584	+	1.72852i	−0.0736188	+	0.101328i
$292$	0.0302344	+	0.0228475i	0.00176934	+	0.00133705i
$293$	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	$0.625474\pi$
$294$	0.0464766	−	0.0106969i	0.00271057	−	0.000623854i
$295$		0			0
$296$	10.3661	+	6.76173i	0.602515	+	0.393018i
$297$	−2.63976	−	5.18082i	−0.153174	−	0.300621i
$298$	0.730201	−	2.92026i	0.0422994	−	0.169166i
$299$	−12.3934			−0.716731
$300$		0			0
$301$	10.1838			0.586986
$302$	2.09391	−	8.37411i	0.120491	−	0.481876i
$303$	−1.02435	−	2.01039i	−0.0588472	−	0.115494i
$304$	−12.3987	+	15.7815i	−0.711117	+	0.905132i
$305$		0			0
$306$	−19.1007	+	4.39615i	−1.09192	+	0.251311i
$307$	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	$0.629308\pi$
$308$	16.4829	−	21.8122i	0.939203	−	1.24286i
$309$	−0.217906	+	0.299922i	−0.0123962	+	0.0170619i
$310$		0			0
$311$	−2.44643	−	3.36722i	−0.138724	−	0.190938i	0.734002	−	0.679147i	$-0.237650\pi$
$311$	−2.44643	−	3.36722i	−0.138724	−	0.190938i	−0.872726	+	0.488209i	$0.837650\pi$
$312$	−1.48850	−	0.159501i	−0.0842697	−	0.00902994i
$313$	−3.50477	−	22.1282i	−0.198101	−	1.25076i	−0.863529	−	0.504300i	$-0.831751\pi$
$313$	−3.50477	−	22.1282i	−0.198101	−	1.25076i	0.665427	−	0.746462i	$-0.268249\pi$
$314$	−19.6889	+	11.8122i	−1.11111	+	0.666598i
$315$		0			0
$316$	9.71663	−	9.35789i	0.546603	−	0.526422i
$317$	−5.61291	−	2.85992i	−0.315252	−	0.160629i	0.289204	−	0.957268i	$-0.406609\pi$
$317$	−5.61291	−	2.85992i	−0.315252	−	0.160629i	−0.604456	+	0.796639i	$0.706609\pi$
$318$	0.320026	+	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
$322$	−15.7208	+	6.33924i	−0.876084	+	0.353272i
$323$	−3.67070	+	23.1759i	−0.204243	+	1.28954i
$324$	3.03510	−	17.0779i	0.168617	−	0.948771i
$325$		0			0
$326$	11.1449	+	0.982643i	0.617257	+	0.0544235i
$327$	−2.93227	−	0.464426i	−0.162155	−	0.0256828i
$328$	−1.83158	−	8.70366i	−0.101132	−	0.480579i
$329$	22.4383	+	7.29065i	1.23706	+	0.401946i
$330$		0			0
$331$	−15.4106	+	5.00720i	−0.847042	+	0.275221i	−0.700206	−	0.713940i	$-0.746909\pi$
$331$	−15.4106	+	5.00720i	−0.847042	+	0.275221i	−0.146835	+	0.989161i	$0.546909\pi$
$332$	−3.84922	−	5.51311i	−0.211253	−	0.302571i
$333$	−5.88710	+	11.5541i	−0.322611	+	0.633159i
$334$	12.5497	−	14.4171i	0.686690	−	0.788869i
$335$		0			0
$336$	−1.96971	+	0.559045i	−0.107456	+	0.0304984i
$337$	19.9748	−	3.16369i	1.08809	−	0.172337i	0.413484	−	0.910511i	$-0.364312\pi$
$337$	19.9748	−	3.16369i	1.08809	−	0.172337i	0.674610	+	0.738174i	$0.264312\pi$
$338$	−7.51597	+	0.520462i	−0.408815	+	0.0283094i
$339$	−1.25360	+	0.910796i	−0.0680864	+	0.0494676i
$340$		0			0
$341$	−30.4682	−	22.1364i	−1.64995	−	1.19876i
$342$	−17.8251	−	11.1551i	−0.963871	−	0.603200i
$343$	12.9255	−	12.9255i	0.697914	−	0.697914i
$344$	−10.7387	+	0.540952i	−0.578990	+	0.0291662i
$345$		0			0
$346$	1.42753	+	0.607091i	0.0767446	+	0.0326374i
$347$	−5.16571	+	2.63206i	−0.277310	+	0.141296i	−0.587115	−	0.809504i	$-0.699736\pi$
$347$	−5.16571	+	2.63206i	−0.277310	+	0.141296i	0.309805	+	0.950800i	$0.399736\pi$
$348$	0.0278222	−	0.0804480i	0.00149143	−	0.00431247i
$349$			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
$352$	−16.2223	+	23.8761i	−0.864652	+	1.27260i
$353$	3.66865	−	1.86927i	0.195263	−	0.0994913i	−0.353626	−	0.935387i	$-0.615051\pi$
$353$	3.66865	−	1.86927i	0.195263	−	0.0994913i	0.548888	+	0.835896i	$0.315051\pi$
$354$	0.958592	−	2.25406i	0.0509486	−	0.119802i
$355$		0			0
$356$	−0.238851	−	1.71635i	−0.0126591	−	0.0909664i
$357$	−1.69274	+	1.69274i	−0.0895893	+	0.0895893i
$358$	−18.1017	+	28.9252i	−0.956703	+	1.52874i
$359$	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
$362$	0.682778	+	9.85997i	0.0358860	+	0.518229i
$363$	−2.83813	+	0.449515i	−0.148963	+	0.0235934i
$364$	13.3477	−	6.48777i	0.699608	−	0.340052i
$365$		0			0
$366$	−0.293191	−	0.255215i	−0.0153253	−	0.0133403i
$367$	−3.08204	+	6.04885i	−0.160881	+	0.315747i	−0.957349	−	0.288934i	$-0.906699\pi$
$367$	−3.08204	+	6.04885i	−0.160881	+	0.315747i	0.796468	+	0.604681i	$0.206699\pi$
$368$	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
$372$	0.820977	+	2.69834i	0.0425657	+	0.139902i
$373$	11.3458	+	1.79701i	0.587466	+	0.0930454i	0.443089	−	0.896477i	$-0.353882\pi$
$373$	11.3458	+	1.79701i	0.587466	+	0.0930454i	0.144376	+	0.989523i	$0.453882\pi$
$374$	−2.96416	+	33.6187i	−0.153273	+	1.73838i
$375$		0			0
$376$	−24.0480	−	6.49595i	−1.24018	−	0.335003i
$377$	−0.0965194	+	0.609399i	−0.00497100	+	0.0313857i
$378$	−1.61447	−	4.00373i	−0.0830391	−	0.205930i
$379$	−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
$383$	−16.4227	−	8.36780i	−0.839163	−	0.427575i	−0.0190788	−	0.999818i	$-0.506073\pi$
$383$	−16.4227	−	8.36780i	−0.839163	−	0.427575i	−0.820084	+	0.572243i	$0.806073\pi$
$384$	2.04732	−	0.694130i	0.104477	−	0.0354222i
$385$		0			0
$386$	6.63569	+	11.0606i	0.337748	+	0.562968i
$387$	−1.76235	−	11.1270i	−0.0895851	−	0.565618i
$388$	−0.420528	+	22.3594i	−0.0213491	+	1.13513i
$389$	−14.6199	−	20.1226i	−0.741258	−	1.02025i	−0.998545	−	0.0539190i	$-0.982829\pi$
$389$	−14.6199	−	20.1226i	−0.741258	−	1.02025i	0.257287	−	0.966335i	$-0.417171\pi$
$390$		0			0
$391$	12.2992	−	16.9284i	0.621997	−	0.856105i
$392$	0.334773	−	0.370290i	0.0169086	−	0.0187025i
$393$	−1.83858	−	1.83858i	−0.0927443	−	0.0927443i
$394$	−1.81348	−	7.87933i	−0.0913617	−	0.396955i
$395$		0			0
$396$	−26.6847	−	14.2348i	−1.34096	−	0.715328i
$397$	−12.6438	−	24.8148i	−0.634574	−	1.24542i	−0.954566	−	0.298001i	$-0.903680\pi$
$397$	−12.6438	−	24.8148i	−0.634574	−	1.24542i	0.319992	−	0.947420i	$-0.396320\pi$
$398$	33.8053	+	8.45289i	1.69451	+	0.423705i
$399$	−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	$0.415881\pi$
$402$	0.886528	+	0.221673i	0.0442160	+	0.0110560i
$403$	−9.28115	−	18.2153i	−0.462327	−	0.907368i
$404$	−20.8374	−	11.1156i	−1.03670	−	0.553021i
$405$		0			0
$406$	0.189275	+	0.822377i	0.00939357	+	0.0408139i
$407$	15.7886	+	15.7886i	0.782611	+	0.782611i
$408$	1.69505	−	1.87488i	0.0839173	−	0.0928203i
$409$	−9.12365	+	12.5576i	−0.451136	+	0.620935i	−0.972641	−	0.232313i	$-0.925371\pi$
$409$	−9.12365	+	12.5576i	−0.451136	+	0.620935i	0.521505	+	0.853248i	$0.325371\pi$
$410$		0			0
$411$	−2.12217	−	2.92092i	−0.104679	−	0.144078i
$412$	−0.0729673	+	3.87966i	−0.00359484	+	0.191137i
$413$	3.79865	+	23.9837i	0.186919	+	1.18016i
$414$	9.64688	+	16.0797i	0.474118	+	0.790275i
$415$		0			0
$416$	−13.7302	+	7.55024i	−0.673181	+	0.370181i
$417$	1.24068	+	0.632159i	0.0607564	+	0.0309569i
$418$	−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	$-0.0276802\pi$
$422$	−10.5009	−	26.0414i	−0.511177	−	1.26768i
$423$	4.08285	−	25.7781i	0.198515	−	1.25337i
$424$	5.03495	+	1.36006i	0.244519	+	0.0660504i
$425$		0			0
$426$	−0.136108	+	1.54370i	−0.00659446	+	0.0747926i
$427$	3.80607	+	0.602823i	0.184189	+	0.0291726i
$428$	6.66680	+	21.9121i	0.322252	+	1.05916i
$429$	−2.56860	−	0.834589i	−0.124013	−	0.0402943i
$430$		0			0
$431$	6.40797	−	2.08208i	0.308661	−	0.100290i	−0.150591	−	0.988596i	$-0.548118\pi$
$431$	6.40797	−	2.08208i	0.308661	−	0.100290i	0.459252	+	0.888306i	$0.348118\pi$
$432$	1.91510	+	4.13610i	0.0921401	+	0.198998i
$433$	−4.78847	+	9.39790i	−0.230119	+	0.451634i	−0.976976	−	0.213351i	$-0.931562\pi$
$433$	−4.78847	+	9.39790i	−0.230119	+	0.451634i	0.746857	+	0.664985i	$0.231562\pi$
$434$	−21.0900	−	18.3583i	−1.01235	−	0.881228i
$435$		0			0
$436$	−27.9480	+	13.5844i	−1.33847	+	0.650576i
$437$	22.1725	−	3.51178i	1.06065	−	0.167991i
$438$	−0.000353717	−	0.00510801i	−1.69013e−5	−	0.000244070i
$439$	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
$442$	−9.71869	+	15.5298i	−0.462271	+	0.738676i
$443$	−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	$0.285053\pi$
$444$	−0.230487	−	1.65625i	−0.0109384	−	0.0786020i
$445$		0			0
$446$	6.40583	−	15.0629i	0.303325	−	0.713247i
$447$	−0.362382	+	0.184643i	−0.0171401	+	0.00873331i
$448$	−13.5545	+	16.6003i	−0.640391	+	0.784291i
$449$			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
$452$	−5.30111	+	15.3282i	−0.249343	+	0.720977i
$453$	−1.03916	+	0.529479i	−0.0488241	+	0.0248771i
$454$	20.2072	+	8.59356i	0.948369	+	0.403316i
$455$		0			0
$456$	2.70820	−	0.136424i	0.126823	−	0.00638862i
$457$	−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	$0.967231\pi$
$458$	20.2074	+	12.6460i	0.944230	+	0.590908i
$459$	4.31129	+	3.13234i	0.201234	+	0.146205i
$460$		0			0
$461$	−26.1799	+	19.0208i	−1.21932	+	0.885887i	−0.996043	−	0.0888686i	$-0.971675\pi$
$461$	−26.1799	+	19.0208i	−1.21932	+	0.885887i	−0.223275	+	0.974755i	$0.571675\pi$
$462$	−3.68510	+	0.255184i	−0.171446	+	0.0118722i
$463$	30.2882	−	4.79718i	1.40761	−	0.222944i	0.594054	−	0.804425i	$-0.297527\pi$
$463$	30.2882	−	4.79718i	1.40761	−	0.222944i	0.813560	+	0.581481i	$0.197527\pi$
$464$	−0.243271	−	0.857127i	−0.0112936	−	0.0397911i
$465$		0			0
$466$	−27.1192	+	31.1545i	−1.25627	+	1.44320i
$467$	−7.07648	+	13.8884i	−0.327460	+	0.642677i	−0.994774	−	0.102100i	$-0.967444\pi$
$467$	−7.07648	+	13.8884i	−0.327460	+	0.642677i	0.667314	+	0.744777i	$0.267444\pi$
$468$	−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
$472$	−5.27958	−	25.0886i	−0.243013	−	1.15480i
$473$	−19.1594	−	3.03456i	−0.880952	−	0.139529i
$474$	−1.81563	−	0.160084i	−0.0833948	−	0.00735291i
$475$		0			0
$476$	−4.38443	+	24.6702i	−0.200960	+	1.13076i
$477$	−0.854829	+	5.39718i	−0.0391399	+	0.247120i
$478$	0.599821	−	0.241872i	0.0274352	−	0.0110630i
$479$	−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
$483$	2.04063	+	1.03975i	0.0928519	+	0.0473104i
$484$	−21.6637	+	20.8639i	−0.984715	+	0.948358i
$485$		0			0
$486$	−6.15526	+	3.69279i	−0.279208	+	0.167509i
$487$	−3.26215	−	20.5964i	−0.147822	−	0.933313i	−0.944405	−	0.328784i	$-0.893361\pi$
$487$	−3.26215	−	20.5964i	−0.147822	−	0.933313i	0.796583	−	0.604529i	$-0.206639\pi$
$488$	−4.04545	−	0.433491i	−0.183129	−	0.0196232i
$489$	−0.888525	−	1.22295i	−0.0401805	−	0.0553037i
$490$		0			0
$491$	−2.89183	+	3.98026i	−0.130506	+	0.179627i	−0.869269	−	0.494339i	$-0.835410\pi$
$491$	−2.89183	+	3.98026i	−0.130506	+	0.179627i	0.738763	+	0.673965i	$0.235410\pi$
$492$	−0.724514	+	0.958763i	−0.0326636	+	0.0432244i
$493$	−0.736603	−	0.736603i	−0.0331749	−	0.0331749i
$494$	−19.1539	+	4.40839i	−0.861774	+	0.198343i
$495$		0			0
$496$	23.2142	+	18.2382i	1.04235	+	0.818921i
$497$	−6.97467	−	13.6886i	−0.312857	−	0.614016i
$498$	−0.220377	+	0.881346i	−0.00987534	+	0.0394940i
$499$	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
$502$	−1.86026	+	7.43965i	−0.0830273	+	0.332048i
$503$	12.4717	+	24.4770i	0.556084	+	1.09138i	0.982398	+	0.186801i	$0.0598118\pi$
$503$	12.4717	+	24.4770i	0.556084	+	1.09138i	−0.426314	+	0.904575i	$0.640188\pi$
$504$	−18.8071	−	12.2678i	−0.837736	−	0.546451i
$505$		0			0
$506$	31.4653	−	7.24194i	1.39880	−	0.321943i
$507$	0.719785	+	0.719785i	0.0319668	+	0.0319668i
$508$	−25.6132	−	19.3553i	−1.13640	−	0.858751i
$509$	−8.04575	+	11.0740i	−0.356622	+	0.490847i	−0.949204	−	0.314663i	$-0.898109\pi$
$509$	−8.04575	+	11.0740i	−0.356622	+	0.490847i	0.592582	+	0.805510i	$0.298109\pi$
$510$		0			0
$511$	0.0298360	+	0.0410658i	0.00131987	+	0.00181664i
$512$	13.4112	−	18.2247i	0.592697	−	0.805426i
$513$	0.894374	+	5.64685i	0.0394876	+	0.249315i
$514$	13.7578	−	8.25389i	0.606832	−	0.364064i
$515$		0			0
$516$	1.00776	+	1.04639i	0.0443641	+	0.0460649i
$517$	−40.0420	−	20.4024i	−1.76105	−	0.897298i
$518$	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	$0.0680855\pi$
$522$	0.865787	−	0.349120i	0.0378945	−	0.0152806i
$523$	5.67302	−	35.8180i	0.248064	−	1.56621i	−0.477859	−	0.878437i	$-0.658587\pi$
$523$	5.67302	−	35.8180i	0.248064	−	1.56621i	0.725923	−	0.687776i	$-0.241413\pi$
$524$	−26.7958	−	4.76219i	−1.17058	−	0.208037i
$525$		0			0
$526$	28.0185	+	2.47039i	1.22167	+	0.107714i
$527$	34.0911	+	5.39950i	1.48503	+	0.235206i
$528$	3.87231	−	0.464834i	0.168521	−	0.0202293i
$529$	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
$533$	3.95446	−	7.76106i	0.171286	−	0.336169i
$534$	−0.153725	+	0.176600i	−0.00665235	+	0.00764222i
$535$		0			0
$536$	8.93658	−	3.40965i	0.386001	−	0.147274i
$537$	4.55359	−	0.721217i	0.196502	−	0.0311228i
$538$	14.2972	−	0.990047i	0.616397	−	0.0426840i
$539$	0.728590	−	0.529352i	0.0313826	−	0.0228008i
$540$		0			0
$541$	−23.6895	−	17.2114i	−1.01849	−	0.739976i	−0.0525174	−	0.998620i	$-0.516724\pi$
$541$	−23.6895	−	17.2114i	−1.01849	−	0.739976i	−0.965973	+	0.258644i	$0.916724\pi$
$542$	2.26480	+	1.41733i	0.0972815	+	0.0608797i
$543$	0.944265	−	0.944265i	0.0405223	−	0.0405223i
$544$	3.31285	−	26.2472i	0.142037	−	1.12534i
$545$		0			0
$546$	−1.84525	−	0.784735i	−0.0789694	−	0.0335836i
$547$	31.1849	−	15.8895i	1.33337	−	0.679385i	0.365493	−	0.930814i	$-0.380900\pi$
$547$	31.1849	−	15.8895i	1.33337	−	0.679385i	0.967876	+	0.251429i	$0.0809003\pi$
$548$	−35.7149	−	12.3517i	−1.52567	−	0.527638i
$549$		−	4.26289i		−	0.181936i
$550$		0			0
$551$		−	1.11760i		−	0.0476112i
$552$	−2.20704	−	0.988004i	−0.0939377	−	0.0420522i
$553$	16.0999	−	8.20329i	0.684636	−	0.348839i
$554$	6.33703	−	14.9011i	0.269235	−	0.633086i
$555$		0			0
$556$	14.4356	−	2.00889i	0.612206	−	0.0851960i
$557$	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	$-0.0215243\pi$
$558$	−16.4089	+	26.2203i	−0.694644	+	1.10999i
$559$	−8.51896	−	6.18939i	−0.360314	−	0.261783i
$560$		0			0
$561$	3.68905	−	2.68025i	0.155752	−	0.113160i
$562$	−2.26340	−	32.6856i	−0.0954756	−	1.37876i
$563$	27.3038	−	4.32450i	1.15072	−	0.182256i	0.448208	−	0.893929i	$-0.352063\pi$
$563$	27.3038	−	4.32450i	1.15072	−	0.182256i	0.702510	+	0.711674i	$0.252063\pi$
$564$	1.47131	+	3.02700i	0.0619531	+	0.127460i
$565$		0			0
$566$	−20.3255	−	17.6928i	−0.854345	−	0.743686i
$567$	10.5477	−	20.7011i	0.442963	−	0.869364i
$568$	8.08177	+	14.0638i	0.339104	+	0.590105i
$569$	8.77237	−	2.85032i	0.367757	−	0.119491i	−0.119308	−	0.992857i	$-0.538068\pi$
$569$	8.77237	−	2.85032i	0.367757	−	0.119491i	0.487065	+	0.873366i	$0.338068\pi$
$570$		0			0
$571$	−17.2235	−	5.59625i	−0.720780	−	0.234196i	−0.0744189	−	0.997227i	$-0.523710\pi$
$571$	−17.2235	−	5.59625i	−0.720780	−	0.234196i	−0.646362	+	0.763031i	$0.723710\pi$
$572$	−27.0450	+	8.22851i	−1.13081	+	0.344051i
$573$	−2.97482	−	0.471166i	−0.124275	−	0.0196832i
$574$	1.04635	−	11.8674i	0.0436737	−	0.495336i
$575$		0			0
$576$	20.4834	+	11.9371i	0.853475	+	0.497381i
$577$	−1.72312	+	10.8794i	−0.0717345	+	0.452914i	0.925510	+	0.378724i	$0.123637\pi$
$577$	−1.72312	+	10.8794i	−0.0717345	+	0.452914i	−0.997244	+	0.0741898i	$0.976363\pi$
$578$	−2.57651	−	6.38951i	−0.107169	−	0.265769i
$579$	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
$583$	8.38362	+	4.27167i	0.347214	+	0.176914i
$584$	−0.0336429	−	0.0417182i	−0.00139215	−	0.00172631i
$585$		0			0
$586$	−9.49738	−	15.8305i	−0.392333	−	0.653953i
$587$	7.33025	+	46.2814i	0.302552	+	1.91024i	0.402825	+	0.915277i	$0.368028\pi$
$587$	7.33025	+	46.2814i	0.302552	+	1.91024i	−0.100273	+	0.994960i	$0.531972\pi$
$588$	−0.0674343	−	0.00126828i	−0.00278094	−	5.23029e-5i
$589$	21.7659	+	29.9582i	0.896849	+	1.23441i
$590$		0			0
$591$	−0.642112	+	0.883792i	−0.0264130	+	0.0363543i
$592$	−11.9023	−	12.8331i	−0.489182	−	0.527436i
$593$	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	$0.641392\pi$
$594$	1.84436	+	8.01353i	0.0756752	+	0.328799i
$595$		0			0
$596$	−2.00363	+	3.75603i	−0.0820720	+	0.153853i
$597$	−2.13745	−	4.19497i	−0.0874798	−	0.171689i
$598$	17.0035	+	4.25165i	0.695324	+	0.173863i
$599$	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	$0.599406\pi$
$602$	−13.9720	−	3.49363i	−0.569454	−	0.142390i
$603$	4.54975	+	8.92939i	0.185280	+	0.363633i
$604$	−5.74559	+	10.7707i	−0.233785	+	0.438255i
$605$		0			0
$606$	0.715697	+	3.10962i	0.0290732	+	0.126319i
$607$	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	$0.717127\pi$
$608$	22.4247	−	17.3984i	0.909442	−	0.705596i
$609$	0.0670182	−	0.0922426i	0.00271571	−	0.00373786i
$610$		0			0
$611$	−14.3390	−	19.7360i	−0.580095	−	0.798433i
$612$	27.7138	+	0.521231i	1.12027	+	0.0210695i
$613$	0.788465	+	4.97817i	0.0318458	+	0.201066i	0.998481	−	0.0550888i	$-0.0175442\pi$
$613$	0.788465	+	4.97817i	0.0318458	+	0.201066i	−0.966636	+	0.256155i	$0.917544\pi$
$614$	−9.43709	−	15.7300i	−0.380850	−	0.634812i
$615$		0			0
$616$	−30.0970	+	24.2711i	−1.21264	+	0.977912i
$617$	16.5627	+	8.43913i	0.666790	+	0.339746i	0.754406	−	0.656408i	$-0.227925\pi$
$617$	16.5627	+	8.43913i	0.666790	+	0.339746i	−0.0876162	+	0.996154i	$0.527925\pi$
$618$	0.401851	−	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
$622$	2.20129	+	5.45901i	0.0882637	+	0.218886i
$623$	0.363103	−	2.29254i	0.0145474	−	0.0918487i
$624$	1.98746	+	0.729471i	0.0795623	+	0.0292022i
$625$		0			0
$626$	−2.78279	+	31.5617i	−0.111223	+	1.26146i
$627$	4.83185	+	0.765290i	0.192966	+	0.0305627i
$628$	31.0648	−	9.45157i	1.23962	−	0.377159i
$629$	−19.4624	−	6.32373i	−0.776018	−	0.252144i
$630$		0			0
$631$	3.22756	−	1.04870i	0.128487	−	0.0417480i	−0.244068	−	0.969758i	$-0.578482\pi$
$631$	3.22756	−	1.04870i	0.128487	−	0.0417480i	0.372555	+	0.928010i	$0.378482\pi$
$632$	−16.5413	+	9.50542i	−0.657976	+	0.378105i
$633$	−1.72235	+	3.38030i	−0.0684572	+	0.134355i
$634$	6.71965	+	5.84928i	0.266871	+	0.232305i
$635$		0			0
$636$	−0.308048	−	0.633766i	−0.0122149	−	0.0251304i
$637$	0.482849	−	0.0764758i	0.0191312	−	0.00303008i
$638$	−0.111044	−	1.60359i	−0.00439629	−	0.0634866i
$639$	−13.7493	+	9.98948i	−0.543915	+	0.395178i
$640$		0			0
$641$	31.0401	+	22.5519i	1.22601	+	0.890748i	0.996585	−	0.0825780i	$-0.0263153\pi$
$641$	31.0401	+	22.5519i	1.22601	+	0.890748i	0.229425	+	0.973326i	$0.426315\pi$
$642$	1.64165	−	2.62325i	0.0647909	−	0.103531i
$643$	−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	$0.310662\pi$
$644$	23.7432	−	3.30416i	0.935613	−	0.130202i
$645$		0			0
$646$	12.9868	−	30.5375i	0.510957	−	1.20148i
$647$	−30.3148	+	15.4461i	−1.19180	+	0.607251i	−0.933417	−	0.358793i	$-0.883188\pi$
$647$	−30.3148	+	15.4461i	−1.19180	+	0.607251i	−0.258379	+	0.966044i	$0.583188\pi$
$648$	−10.0228	+	22.3892i	−0.393731	+	0.879530i
$649$		−	46.2539i		−	1.81562i
$650$		0			0
$651$			3.77787i			0.148066i
$652$	−14.9534	−	5.17148i	−0.585619	−	0.202531i
$653$	−5.70477	+	2.90673i	−0.223245	+	0.113749i	−0.562036	−	0.827112i	$-0.689982\pi$
$653$	−5.70477	+	2.90673i	−0.223245	+	0.113749i	0.338791	+	0.940862i	$0.389982\pi$
$654$	3.86368	+	1.64312i	0.151082	+	0.0642510i
$655$		0			0
$656$	−0.472973	+	12.5695i	−0.0184665	+	0.490758i
$657$	0.0397059	−	0.0397059i	0.00154907	−	0.00154907i
$658$	−28.2837	−	17.7002i	−1.10261	−	0.690025i
$659$	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	$0.302925\pi$
$662$	22.8607	−	1.58304i	0.888505	−	0.0615267i
$663$	2.44480	−	0.387218i	0.0949480	−	0.0150383i
$664$	3.38972	+	8.88434i	0.131547	+	0.344779i
$665$		0			0
$666$	12.0406	−	13.8323i	0.466566	−	0.535990i
$667$	−0.452453	+	0.887989i	−0.0175190	+	0.0343831i
$668$	−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
$672$	2.89417	−	0.0912728i	0.111645	−	0.00352092i
$673$	21.1799	+	3.35456i	0.816424	+	0.129309i	0.550660	−	0.834729i	$-0.314376\pi$
$673$	21.1799	+	3.35456i	0.816424	+	0.129309i	0.265764	+	0.964038i	$0.414376\pi$
$674$	−28.4902	−	2.51198i	−1.09740	−	0.0967578i
$675$		0			0
$676$	10.4903	+	1.86434i	0.403471	+	0.0717055i
$677$	−6.95245	+	43.8961i	−0.267204	+	1.68706i	0.380191	+	0.924908i	$0.375858\pi$
$677$	−6.95245	+	43.8961i	−0.267204	+	1.68706i	−0.647395	+	0.762155i	$0.724142\pi$
$678$	2.03236	−	0.819531i	0.0780525	−	0.0314739i
$679$	−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
$683$	−21.8180	−	11.1168i	−0.834843	−	0.425374i	−0.0163335	−	0.999867i	$-0.505199\pi$
$683$	−21.8180	−	11.1168i	−0.834843	−	0.425374i	−0.818510	+	0.574493i	$0.805199\pi$
$684$	20.6287	+	21.4196i	0.788759	+	0.818997i
$685$		0			0
$686$	−22.1677	+	13.2993i	−0.846367	+	0.507770i
$687$	−0.503849	−	3.18118i	−0.0192230	−	0.121369i
$688$	14.9187	+	2.94180i	0.568771	+	0.112155i
$689$	3.00217	+	4.13213i	0.114374	+	0.157422i
$690$		0			0
$691$	9.83947	−	13.5429i	0.374311	−	0.515195i	−0.579755	−	0.814791i	$-0.696852\pi$
$691$	9.83947	−	13.5429i	0.374311	−	0.515195i	0.954066	+	0.299596i	$0.0968518\pi$
$692$	−1.75027	−	1.32264i	−0.0665353	−	0.0502791i
$693$	−28.6452	−	28.6452i	−1.08814	−	1.08814i
$694$	7.99017	−	1.83899i	0.303303	−	0.0698070i
$695$		0			0
$696$	−0.0657696	+	0.100828i	−0.00249299	+	0.00382187i
$697$	6.67656	+	13.1035i	0.252893	+	0.496330i
$698$	0.0181412	−	0.0725513i	0.000686654	−	0.00274611i
$699$	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	$0.0879356\pi$
$702$	−1.08280	+	4.33041i	−0.0408678	+	0.163441i
$703$	−9.96723	−	19.5618i	−0.375921	−	0.737787i
$704$	30.4474	−	27.1922i	1.14753	−	1.02484i
$705$		0			0
$706$	−5.67456	+	1.30604i	−0.213565	+	0.0491533i
$707$	−22.3682	−	22.3682i	−0.841244	−	0.841244i
$708$	−2.08844	+	2.76367i	−0.0784882	+	0.103865i
$709$	23.6335	−	32.5288i	0.887576	−	1.22164i	−0.0866885	−	0.996235i	$-0.527628\pi$
$709$	23.6335	−	32.5288i	0.887576	−	1.22164i	0.974264	−	0.225408i	$-0.0723715\pi$
$710$		0			0
$711$	−11.7492	−	16.1714i	−0.440629	−	0.606473i
$712$	−0.261108	+	2.43673i	−0.00978544	+	0.0913202i
$713$	−5.16574	−	32.6152i	−0.193458	−	1.22145i
$714$	2.90310	−	1.74169i	0.108646	−	0.0651811i
$715$		0			0
$716$	34.7580	−	33.4747i	1.29897	−	1.25101i
$717$	−0.0778596	−	0.0396715i	−0.00290772	−	0.00148156i
$718$	−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
$722$	8.09788	−	3.26539i	0.301372	−	0.121525i
$723$	−0.652848	+	4.12192i	−0.0242797	+	0.153296i
$724$	2.44578	−	13.7619i	0.0908966	−	0.511455i
$725$		0			0
$726$	4.04805	+	0.356916i	0.150237	+	0.0132464i
$727$	−8.65722	−	1.37117i	−0.321078	−	0.0508538i	−0.00618506	−	0.999981i	$-0.501969\pi$
$727$	−8.65722	−	1.37117i	−0.321078	−	0.0508538i	−0.314893	+	0.949127i	$0.601969\pi$
$728$	−20.5383	+	4.32204i	−0.761201	+	0.160185i
$729$	−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
$733$	0.119518	−	0.234567i	0.00441450	−	0.00866394i	−0.888789	−	0.458317i	$-0.848452\pi$
$733$	0.119518	−	0.234567i	0.00441450	−	0.00866394i	0.893203	+	0.449653i	$0.148452\pi$
$734$	6.30358	−	7.24154i	0.232669	−	0.267290i
$735$		0			0
$736$	−24.8612	+	4.74538i	−0.916397	+	0.174917i
$737$	17.0437	−	2.69946i	0.627814	−	0.0994360i
$738$	−13.1476	+	0.910437i	−0.483969	+	0.0335136i
$739$	−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
$742$	5.92176	+	3.70590i	0.217395	+	0.136048i
$743$	−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	$0.308414\pi$
$744$	−0.200675	−	3.98369i	−0.00735712	−	0.146049i
$745$		0			0
$746$	−14.9497	−	6.35772i	−0.547349	−	0.232772i
$747$	−8.87719	+	4.52315i	−0.324799	+	0.165494i
$748$	15.5999	−	45.1071i	0.570388	−	1.64928i
$749$			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	$0.821134\pi$
$752$	30.7648	+	17.1621i	1.12188	+	0.625838i
$753$	0.923203	−	0.470395i	0.0336434	−	0.0171422i
$754$	0.341481	−	0.802968i	0.0124360	−	0.0292424i
$755$		0			0
$756$	0.841496	+	6.04687i	0.0306049	+	0.219923i
$757$	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	$0.0763959\pi$
$758$	9.60573	−	15.3493i	0.348896	−	0.557511i
$759$	−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	$0.243124\pi$
$762$	0.299652	+	4.32727i	0.0108553	+	0.156760i
$763$	−41.1103	+	6.51124i	−1.48829	+	0.235723i
$764$	−28.3536	+	13.7815i	−1.02580	+	0.498599i
$765$		0			0
$766$	19.6609	+	17.1143i	0.710378	+	0.618366i
$767$	11.3988	−	22.3715i	0.411589	−	0.807788i
$768$	−3.04700	+	0.249980i	−0.109949	+	0.00902038i
$769$	17.2976	−	5.62032i	0.623766	−	0.202674i	0.0199544	−	0.999801i	$-0.493648\pi$
$769$	17.2976	−	5.62032i	0.623766	−	0.202674i	0.603812	+	0.797127i	$0.293648\pi$
$770$		0			0
$771$	−2.06162	−	0.669862i	−0.0742475	−	0.0241245i
$772$	−5.30959	−	17.4512i	−0.191096	−	0.628084i
$773$	−42.7233	−	6.76671i	−1.53665	−	0.243382i	−0.670025	−	0.742339i	$-0.733717\pi$
$773$	−42.7233	−	6.76671i	−1.53665	−	0.243382i	−0.866627	+	0.498957i	$0.833717\pi$
$774$	−1.39931	+	15.8706i	−0.0502970	+	0.570455i
$775$		0			0
$776$	8.24751	−	30.5323i	0.296068	−	1.09604i
$777$	0.350388	−	2.21226i	0.0125701	−	0.0793644i
$778$	13.1549	+	32.6231i	0.471627	+	1.16959i
$779$	−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
$783$	−0.226151	−	0.115230i	−0.00808199	−	0.00411798i
$784$	−0.586330	+	0.393182i	−0.0209404	+	0.0140422i
$785$		0			0
$786$	1.89175	+	3.15323i	0.0674765	+	0.112472i
$787$	1.89589	+	11.9702i	0.0675813	+	0.426691i	0.998162	+	0.0606043i	$0.0193028\pi$
$787$	1.89589	+	11.9702i	0.0675813	+	0.426691i	−0.930581	+	0.366087i	$0.880697\pi$
$788$	−0.215016	+	11.4324i	−0.00765962	+	0.407261i
$789$	−2.23378	−	3.07453i	−0.0795245	−	0.109456i
$790$		0			0
$791$	−12.7693	+	17.5755i	−0.454025	+	0.624911i
$792$	31.7274	+	28.6842i	1.12738	+	1.01925i
$793$	−2.81747	−	2.81747i	−0.100051	−	0.100051i
$794$	8.83405	+	38.3829i	0.313509	+	1.36216i
$795$		0			0
$796$	−43.4802	−	23.1943i	−1.54111	−	0.822099i
$797$	7.47486	+	14.6702i	0.264773	+	0.519646i	0.984668	−	0.174436i	$-0.0558103\pi$
$797$	7.47486	+	14.6702i	0.264773	+	0.519646i	−0.719895	+	0.694083i	$0.755810\pi$
$798$	3.52361	+	0.881065i	0.124734	+	0.0311894i
$799$	41.1877			1.45712
$800$		0			0
$801$	−2.56770			−0.0907253
$802$	−14.3525	−	3.58878i	−0.506803	−	0.126724i
$803$	−0.0438956	−	0.0861499i	−0.00154904	−	0.00304016i
$804$	−1.14025	−	0.608259i	−0.0402134	−	0.0214516i
$805$		0			0
$806$	6.48462	+	28.1749i	0.228411	+	0.992417i
$807$	−1.36921	−	1.36921i	−0.0481985	−	0.0481985i
$808$	24.7750	+	22.3987i	0.871583	+	0.787984i
$809$	12.5671	−	17.2972i	0.441837	−	0.608136i	−0.528782	−	0.848757i	$-0.677351\pi$
$809$	12.5671	−	17.2972i	0.441837	−	0.608136i	0.970619	+	0.240621i	$0.0773512\pi$
$810$		0			0
$811$	18.5355	+	25.5120i	0.650871	+	0.895847i	0.999136	−	0.0415488i	$-0.0132292\pi$
$811$	18.5355	+	25.5120i	0.650871	+	0.895847i	−0.348265	+	0.937396i	$0.613229\pi$
$812$	0.0224415	−	1.19321i	0.000787542	−	0.0418735i
$813$	−0.0564703	−	0.356539i	−0.00198050	−	0.0125044i
$814$	−16.2451	−	27.0779i	−0.569392	−	0.949080i
$815$		0			0
$816$	−2.96875	+	1.99079i	−0.103927	+	0.0696915i
$817$	16.9947	+	8.65922i	0.594569	+	0.302948i
$818$	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	$0.985687\pi$
$822$	1.90952	+	4.73545i	0.0666023	+	0.165168i
$823$	−6.60034	+	41.6729i	−0.230073	+	1.45263i	0.554289	+	0.832324i	$0.312990\pi$
$823$	−6.60034	+	41.6729i	−0.230073	+	1.45263i	−0.784363	+	0.620302i	$0.787010\pi$
$824$	1.43105	−	5.29776i	0.0498531	−	0.184556i
$825$		0			0
$826$	3.01613	−	34.2082i	0.104945	−	1.19026i
$827$	13.5996	+	2.15397i	0.472905	+	0.0749008i	0.388338	−	0.921517i	$-0.373049\pi$
$827$	13.5996	+	2.15397i	0.472905	+	0.0749008i	0.0845669	+	0.996418i	$0.473049\pi$
$828$	−7.71901	−	25.3704i	−0.268254	−	0.881682i
$829$	35.5980	+	11.5665i	1.23637	+	0.401721i	0.853018	−	0.521881i	$-0.174770\pi$
$829$	35.5980	+	11.5665i	1.23637	+	0.401721i	0.383352	+	0.923602i	$0.374770\pi$
$830$		0			0
$831$	−2.08074	+	0.676072i	−0.0721800	+	0.0234527i
$832$	21.4277	−	5.64848i	0.742872	−	0.195826i
$833$	−0.374718	+	0.735426i	−0.0129832	+	0.0254810i
$834$	−1.48532	−	1.29293i	−0.0514323	−	0.0447705i
$835$		0			0
$836$	46.0533	−	22.3846i	1.59279	−	0.774189i
$837$	8.30637	−	1.31560i	0.287110	−	0.0454738i
$838$	−3.52726	−	50.9370i	−0.121847	−	1.75959i
$839$	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
$842$	−12.0207	+	19.2082i	−0.414260	+	0.661959i
$843$	−3.13022	+	3.13022i	−0.107810	+	0.107810i
$844$	5.47332	+	39.3305i	0.188400	+	1.35381i
$845$		0			0
$846$	−14.4449	+	33.9662i	−0.496627	+	1.16778i
$847$	−35.8955	+	18.2897i	−1.23338	+	0.628440i
$848$	−6.44124	−	3.59324i	−0.221193	−	0.123392i
$849$			3.64092i			0.124956i
$850$		0			0
$851$			19.5780i			0.671126i
$852$	0.716314	−	2.07123i	0.0245405	−	0.0709590i
$853$	31.0768	−	15.8344i	1.06405	−	0.542160i	0.167851	−	0.985812i	$-0.446317\pi$
$853$	31.0768	−	15.8344i	1.06405	−	0.542160i	0.896199	+	0.443652i	$0.146317\pi$
$854$	−5.01503	−	2.13276i	−0.171611	−	0.0729814i
$855$		0			0
$856$	−1.62960	−	32.3499i	−0.0556986	−	1.10570i
$857$	−31.7738	+	31.7738i	−1.08537	+	1.08537i	−0.0893726	+	0.995998i	$0.528486\pi$
$857$	−31.7738	+	31.7738i	−1.08537	+	1.08537i	−0.995998	+	0.0893726i	$0.971514\pi$
$858$	3.23774	+	2.02621i	0.110535	+	0.0691737i
$859$	−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
$862$	−9.50584	+	0.658255i	−0.323770	+	0.0224203i
$863$	−16.4649	+	2.60778i	−0.560472	+	0.0887700i	−0.430242	−	0.902714i	$-0.641572\pi$
$863$	−16.4649	+	2.60778i	−0.560472	+	0.0887700i	−0.130230	+	0.991484i	$0.541572\pi$
$864$	−1.20854	−	6.33161i	−0.0411155	−	0.215406i
$865$		0			0
$866$	9.79367	−	11.2510i	0.332802	−	0.382323i
$867$	−0.422595	+	0.829389i	−0.0143521	+	0.0281675i
$868$	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
$872$	43.0042	−	9.04970i	1.45631	−	0.306462i
$873$	32.7288	+	5.18374i	1.10770	+	0.175443i
$874$	−31.6248	−	2.78836i	−1.06973	−	0.0943177i
$875$		0			0
$876$	−0.00126705	+	0.00712941i	−4.28096e−5	+	0.000240880i
$877$	2.32444	−	14.6759i	0.0784907	−	0.495571i	−0.916856	−	0.399217i	$-0.869282\pi$
$877$	2.32444	−	14.6759i	0.0784907	−	0.495571i	0.995347	−	0.0963539i	$-0.0307181\pi$
$878$	−13.7351	+	5.53854i	−0.463537	+	0.186917i
$879$	−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
$883$	1.45332	+	0.740506i	0.0489083	+	0.0249200i	0.478274	−	0.878211i	$-0.341263\pi$
$883$	1.45332	+	0.740506i	0.0489083	+	0.0249200i	−0.429365	+	0.903131i	$0.641263\pi$
$884$	18.6614	−	17.9724i	0.627650	−	0.604477i
$885$		0			0
$886$	5.61028	−	3.36584i	0.188481	−	0.113078i
$887$	−4.23212	−	26.7206i	−0.142101	−	0.897189i	−0.950989	−	0.309226i	$-0.899930\pi$
$887$	−4.23212	−	26.7206i	−0.142101	−	0.897189i	0.808888	−	0.587963i	$-0.200070\pi$
$888$	−0.251965	+	2.35140i	−0.00845538	+	0.0789077i
$889$	−25.2757	−	34.7890i	−0.847719	−	1.16679i
$890$		0			0
$891$	−26.0125	+	35.8032i	−0.871452	+	1.19945i
$892$	−13.9560	+	18.4683i	−0.467283	+	0.618364i
$893$	31.2456	+	31.2456i	1.04560	+	1.04560i
$894$	0.560522	−	0.129008i	0.0187466	−	0.00431466i
$895$		0			0
$896$	24.2913	−	18.1252i	0.811515	−	0.605521i
$897$	−1.07510	−	2.11000i	−0.0358965	−	0.0704508i
$898$	6.20698	−	24.8233i	0.207130	−	0.828365i
$899$	−1.64396			−0.0548290
$900$		0			0
$901$	−8.62349			−0.287290
$902$	−5.50478	+	22.0150i	−0.183289	+	0.733021i
$903$	0.883420	+	1.73381i	0.0293984	+	0.0576976i
$904$	12.5314	−	19.2113i	0.416789	−	0.638957i
$905$		0			0
$906$	1.60734	−	0.369940i	0.0534004	−	0.0122904i
$907$	−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	$-0.564360\pi$
$908$	−24.7756	−	18.7223i	−0.822208	−	0.621323i
$909$	−20.5690	+	28.3108i	−0.682230	+	0.939009i
$910$		0			0
$911$	−3.41319	−	4.69785i	−0.113084	−	0.155647i	0.748723	−	0.662883i	$-0.230667\pi$
$911$	−3.41319	−	4.69785i	−0.113084	−	0.155647i	−0.861807	+	0.507236i	$0.830667\pi$
$912$	−3.76238	−	0.741897i	−0.124585	−	0.0245667i
$913$	2.68368	+	16.9441i	0.0888169	+	0.560768i
$914$	40.2367	−	24.1397i	1.33091	−	0.798469i
$915$		0			0
$916$	−23.3857	−	24.2822i	−0.772686	−	0.802308i
$917$	−32.4808	−	16.5498i	−1.07261	−	0.546522i
$918$	−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
$922$	42.4433	−	17.1148i	1.39780	−	0.563647i
$923$	−2.48500	+	15.6897i	−0.0817948	+	0.516432i
$924$	5.14340	+	0.914093i	0.169205	+	0.0300714i
$925$		0			0
$926$	−43.2004	−	3.80897i	−1.41965	−	0.125171i
$927$	5.67890	+	0.899449i	0.186520	+	0.0295418i
$928$	0.0397177	+	1.25941i	0.00130380	+	0.0413422i
$929$	34.3019	+	11.1453i	1.12541	+	0.365667i	0.811829	−	0.583895i	$-0.198472\pi$
$929$	34.3019	+	11.1453i	1.12541	+	0.365667i	0.313578	+	0.949562i	$0.398472\pi$
$930$		0			0
$931$	−0.842173	+	0.273639i	−0.0276011	+	0.00896814i
$932$	47.8946	−	33.4397i	1.56884	−	1.09535i
$933$	0.361052	−	0.708605i	0.0118203	−	0.0231987i
$934$	14.4732	−	16.6268i	0.473579	−	0.544047i
$935$		0			0
$936$	8.27655	+	21.6926i	0.270528	+	0.709043i
$937$	−37.4056	+	5.92447i	−1.22199	+	0.193544i	−0.733905	−	0.679252i	$-0.762304\pi$
$937$	−37.4056	+	5.92447i	−1.22199	+	0.193544i	−0.488084	+	0.872796i	$0.662304\pi$
$938$	12.7811	−	0.885062i	0.417319	−	0.0288983i
$939$	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	$0.525810\pi$
$942$	−3.71899	−	2.32738i	−0.121171	−	0.0758302i
$943$	9.94877	−	9.94877i	0.323977	−	0.323977i
$944$	−1.36336	+	36.2321i	−0.0443736	+	1.17925i
$945$		0			0
$946$	25.2452	+	10.7361i	0.820793	+	0.349061i
$947$	−3.14898	+	1.60449i	−0.102328	+	0.0521388i	−0.504405	−	0.863467i	$-0.668288\pi$
$947$	−3.14898	+	1.60449i	−0.102328	+	0.0521388i	0.402077	+	0.915606i	$0.368288\pi$
$948$	2.43608	+	0.842497i	0.0791203	+	0.0273630i
$949$		−	0.0524856i		−	0.00170375i
$950$		0			0
$951$		−	1.20369i		−	0.0390325i
$952$	14.4786	−	32.3428i	0.469255	−	1.04824i
$953$	−48.0361	+	24.4756i	−1.55604	+	0.792843i	−0.999284	−	0.0378308i	$-0.987955\pi$
$953$	−48.0361	+	24.4756i	−1.55604	+	0.792843i	−0.556759	+	0.830674i	$0.687955\pi$
$954$	3.02434	−	7.11153i	0.0979166	−	0.230244i
$955$		0			0
$956$	−0.905914	+	0.126069i	−0.0292994	+	0.00407736i
$957$	−0.153571	+	0.153571i	−0.00496426	+	0.00496426i
$958$	5.22581	−	8.35047i	0.168838	−	0.269791i
$959$	−40.9512	−	29.7528i	−1.32238	−	0.960767i
$960$		0			0
$961$	18.9882	−	13.7957i	0.612523	−	0.445024i
$962$	−1.18414	−	17.1002i	−0.0381783	−	0.551332i
$963$	33.5198	−	5.30901i	1.08016	−	0.171080i
$964$	19.0957	+	39.2868i	0.615032	+	1.26534i
$965$		0			0
$966$	−2.44300	−	2.12657i	−0.0786021	−	0.0684211i
$967$	−7.03165	+	13.8004i	−0.226123	+	0.443791i	−0.975995	−	0.217792i	$-0.930115\pi$
$967$	−7.03165	+	13.8004i	−0.226123	+	0.443791i	0.749873	+	0.661582i	$0.230115\pi$
$968$	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	$-0.308680\pi$
$971$	16.7721	+	5.44959i	0.538242	+	0.174886i	−0.0272659	+	0.999628i	$0.508680\pi$
$972$	9.71170	−	2.95481i	0.311503	−	0.0947756i
$973$	19.2817	+	3.05393i	0.618144	+	0.0979044i
$974$	−2.59016	+	29.3769i	−0.0829940	+	0.941295i
$975$		0			0
$976$	5.40154	+	1.98256i	0.172899	+	0.0634602i
$977$	8.24291	−	52.0437i	0.263714	−	1.66502i	−0.399605	−	0.916687i	$-0.630853\pi$
$977$	8.24291	−	52.0437i	0.263714	−	1.66502i	0.663319	−	0.748337i	$-0.269147\pi$
$978$	0.799492	+	1.98267i	0.0255649	+	0.0633988i
$979$	−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
$983$	15.6381	+	7.96803i	0.498779	+	0.254141i	0.685234	−	0.728323i	$-0.259700\pi$
$983$	15.6381	+	7.96803i	0.498779	+	0.254141i	−0.186455	+	0.982463i	$0.559700\pi$
$984$	1.32292	−	1.06685i	0.0421733	−	0.0340099i
$985$		0			0
$986$	0.757903	+	1.26330i	0.0241366	+	0.0402316i
$987$	0.705221	+	4.45259i	0.0224474	+	0.141728i
$988$	27.7910	+	0.522682i	0.884148	+	0.0166287i
$989$	−9.99752	−	13.7604i	−0.317903	−	0.437555i
$990$		0			0
$991$	20.0939	−	27.6568i	0.638302	−	0.878548i	−0.360221	−	0.932867i	$-0.617299\pi$
$991$	20.0939	−	27.6568i	0.638302	−	0.878548i	0.998524	+	0.0543192i	$0.0172988\pi$
$992$	−25.5925	−	32.9862i	−0.812563	−	1.04731i
$993$	−2.18931	−	2.18931i	−0.0694756	−	0.0694756i
$994$	4.87311	+	21.1730i	0.154566	+	0.671568i
$995$		0			0
$996$	0.604703	−	1.13358i	0.0191608	−	0.0359189i
$997$	−0.954518	−	1.87335i	−0.0302299	−	0.0593295i	0.875398	−	0.483404i	$-0.160600\pi$
$997$	−0.954518	−	1.87335i	−0.0302299	−	0.0593295i	−0.905628	+	0.424074i	$0.860600\pi$
$998$	−27.1842	−	6.79731i	−0.860502	−	0.215165i
$999$	−4.98610			−0.157753

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.37197 - 0.343057i) q^{2} +(0.0867473 + 0.170251i) q^{3} +(1.76462 + 0.941330i) q^{4} +(-0.0606092 - 0.263339i) q^{6} +(1.89427 + 1.89427i) q^{7} +(-2.09809 - 1.89685i) q^{8} +(1.74190 - 2.39751i) q^{9} +O(q^{10})\)	\(q+(-1.37197 - 0.343057i) q^{2} +(0.0867473 + 0.170251i) q^{3} +(1.76462 + 0.941330i) q^{4} +(-0.0606092 - 0.263339i) q^{6} +(1.89427 + 1.89427i) q^{7} +(-2.09809 - 1.89685i) q^{8} +(1.74190 - 2.39751i) q^{9} +(-2.99934 - 4.12824i) q^{11} +(-0.00718616 + 0.382087i) q^{12} +(-0.433317 - 2.73586i) q^{13} +(-1.94904 - 3.24872i) q^{14} +(2.22780 + 3.32219i) q^{16} +(4.16697 + 2.12318i) q^{17} +(-3.21232 + 2.69176i) q^{18} +(1.55045 + 4.77181i) q^{19} +(-0.158179 + 0.486824i) q^{21} +(2.69880 + 6.69278i) q^{22} +(0.699923 - 4.41914i) q^{23} +(0.140937 - 0.521748i) q^{24} +(-0.344055 + 3.90218i) q^{26} +(1.12546 + 0.178255i) q^{27} +(1.55954 + 5.12580i) q^{28} +(-0.211843 - 0.0688321i) q^{29} +(7.01920 - 2.28068i) q^{31} +(-1.91678 - 5.32221i) q^{32} +(0.442653 - 0.868756i) q^{33} +(-4.98861 - 4.34246i) q^{34} +(5.33064 - 2.59101i) q^{36} +(-4.32186 + 0.684516i) q^{37} +(-0.490182 - 7.07869i) q^{38} +(0.428194 - 0.311101i) q^{39} +(2.54404 + 1.84835i) q^{41} +(0.384025 - 0.613645i) q^{42} +(2.68807 - 2.68807i) q^{43} +(-1.40668 - 10.1082i) q^{44} +(-2.47629 + 5.82283i) q^{46} +(7.84709 - 3.99829i) q^{47} +(-0.372351 + 0.667476i) q^{48} +0.176489i q^{49} +0.893612i q^{51} +(1.81070 - 5.23565i) q^{52} +(-1.64295 + 0.837124i) q^{53} +(-1.48295 - 0.630658i) q^{54} +(-0.381206 - 7.56747i) q^{56} +(-0.677908 + 0.677908i) q^{57} +(0.267030 + 0.167110i) q^{58} +(7.33328 + 5.32794i) q^{59} +(1.16375 - 0.845512i) q^{61} +(-10.4126 + 0.721044i) q^{62} +(7.84114 - 1.24191i) q^{63} +(0.803948 + 7.95950i) q^{64} +(-0.905341 + 1.04005i) q^{66} +(-1.53527 + 3.01313i) q^{67} +(5.35453 + 7.66911i) q^{68} +(0.813081 - 0.264186i) q^{69} +(-5.45415 - 1.77216i) q^{71} +(-8.20236 + 1.72609i) q^{72} +(0.0187149 + 0.00296414i) q^{73} +(6.16431 + 0.543507i) q^{74} +(-1.75588 + 9.87994i) q^{76} +(2.13843 - 13.5015i) q^{77} +(-0.694196 + 0.279928i) q^{78} +(2.08434 - 6.41493i) q^{79} +(-2.68002 - 8.24826i) q^{81} +(-2.85627 - 3.40864i) q^{82} +(-2.99552 - 1.52629i) q^{83} +(-0.737387 + 0.710162i) q^{84} +(-4.61012 + 2.76580i) q^{86} +(-0.00665810 - 0.0420376i) q^{87} +(-1.53775 + 14.3507i) q^{88} +(-0.509284 - 0.700969i) q^{89} +(4.36162 - 6.00326i) q^{91} +(5.39497 - 7.13927i) q^{92} +(0.997185 + 0.997185i) q^{93} +(-12.1376 + 2.79355i) q^{94} +(0.739838 - 0.788022i) q^{96} +(5.07638 + 9.96296i) q^{97} +(0.0605458 - 0.242139i) q^{98} -15.1221 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 10 q^{2} - 10 q^{4} - 6 q^{6} + 10 q^{8} - 20 q^{9}+O(q^{10}) \) 96 * q + 10 * q^2 - 10 * q^4 - 6 * q^6 + 10 * q^8 - 20 * q^9	\( 96 q + 10 q^{2} - 10 q^{4} - 6 q^{6} + 10 q^{8} - 20 q^{9} + 10 q^{12} + 20 q^{13} - 10 q^{14} - 14 q^{16} + 20 q^{17} - 20 q^{18} - 12 q^{21} + 10 q^{22} - 12 q^{26} + 10 q^{28} - 20 q^{29} + 50 q^{32} + 20 q^{33} - 60 q^{34} - 10 q^{36} - 40 q^{37} - 20 q^{38} - 28 q^{41} - 90 q^{42} + 60 q^{44} - 6 q^{46} - 120 q^{48} - 80 q^{52} + 40 q^{53} + 120 q^{54} - 6 q^{56} + 20 q^{57} - 60 q^{58} + 12 q^{61} - 40 q^{62} + 20 q^{64} - 30 q^{66} + 10 q^{68} - 20 q^{69} + 40 q^{72} + 20 q^{73} + 20 q^{77} - 20 q^{78} - 36 q^{81} + 50 q^{82} - 90 q^{84} - 6 q^{86} + 130 q^{88} + 160 q^{89} + 110 q^{92} - 60 q^{93} - 170 q^{94} + 14 q^{96} - 180 q^{97} + 130 q^{98}+O(q^{100}) \) 96 * q + 10 * q^2 - 10 * q^4 - 6 * q^6 + 10 * q^8 - 20 * q^9 + 10 * q^12 + 20 * q^13 - 10 * q^14 - 14 * q^16 + 20 * q^17 - 20 * q^18 - 12 * q^21 + 10 * q^22 - 12 * q^26 + 10 * q^28 - 20 * q^29 + 50 * q^32 + 20 * q^33 - 60 * q^34 - 10 * q^36 - 40 * q^37 - 20 * q^38 - 28 * q^41 - 90 * q^42 + 60 * q^44 - 6 * q^46 - 120 * q^48 - 80 * q^52 + 40 * q^53 + 120 * q^54 - 6 * q^56 + 20 * q^57 - 60 * q^58 + 12 * q^61 - 40 * q^62 + 20 * q^64 - 30 * q^66 + 10 * q^68 - 20 * q^69 + 40 * q^72 + 20 * q^73 + 20 * q^77 - 20 * q^78 - 36 * q^81 + 50 * q^82 - 90 * q^84 - 6 * q^86 + 130 * q^88 + 160 * q^89 + 110 * q^92 - 60 * q^93 - 170 * q^94 + 14 * q^96 - 180 * q^97 + 130 * q^98

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