LMFDB - Embedded newform 500.2.l.e.407.7

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			407.7
Character	$\chi$	$=$	500.407
Dual form			500.2.l.e.43.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.343057	+	1.37197i	−0.242578	+	0.970132i
$2$	−0.343057	+	1.37197i	−0.242578	+	0.970132i
$3$	−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	$0.367567\pi$
$4$	−1.76462	−	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	−0.251811	−	0.967776i	$-0.581026\pi$
$7$	1.89427	−	1.89427i	0.715965	−	0.715965i	0.967776	+	0.251811i	$0.0810262\pi$
$8$	1.89685	−	2.09809i	0.670636	−	0.741786i
$9$	−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	$-0.479382\pi$
$12$	0.382087	+	0.00718616i	0.110299	+	0.00207446i
$13$	2.73586	−	0.433317i	0.758790	−	0.120181i	0.234962	−	0.972005i	$-0.424503\pi$
$13$	2.73586	−	0.433317i	0.758790	−	0.120181i	0.523828	+	0.851824i	$0.324503\pi$
$14$	1.94904	+	3.24872i	0.520904	+	0.868258i
$15$		0			0
$16$	2.22780	+	3.32219i	0.556949	+	0.830547i
$17$	2.12318	−	4.16697i	0.514947	−	1.01064i	−0.476383	−	0.879238i	$-0.658052\pi$
$17$	2.12318	−	4.16697i	0.514947	−	1.01064i	0.991329	−	0.131402i	$-0.0419477\pi$
$18$	−2.69176	−	3.21232i	−0.634453	−	0.757151i
$19$	−1.55045	−	4.77181i	−0.355699	−	1.09473i	−0.955603	−	0.294657i	$-0.904795\pi$
$19$	−1.55045	−	4.77181i	−0.355699	−	1.09473i	0.599905	−	0.800072i	$-0.295205\pi$
$20$		0			0
$21$	−0.158179	+	0.486824i	−0.0345174	+	0.106234i
$22$	6.69278	−	2.69880i	1.42691	−	0.575386i
$23$	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
$28$	−5.12580	+	1.55954i	−0.968685	+	0.294725i
$29$	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	0.398947	−	0.916974i	$-0.369376\pi$
$31$	7.01920	−	2.28068i	1.26069	−	0.409622i	0.861739	+	0.507352i	$0.169376\pi$
$32$	−5.32221	+	1.91678i	−0.940843	+	0.338842i
$33$	0.868756	+	0.442653i	0.151231	+	0.0770560i
$34$	4.98861	+	4.34246i	0.855539	+	0.744725i
$35$		0			0
$36$	5.33064	−	2.59101i	0.888440	−	0.431835i
$37$	0.684516	+	4.32186i	0.112534	+	0.710510i	0.977854	+	0.209290i	$0.0671152\pi$
$37$	0.684516	+	4.32186i	0.112534	+	0.710510i	−0.865320	+	0.501220i	$0.832885\pi$
$38$	7.07869	−	0.490182i	1.14832	−	0.0795179i
$39$	−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	$0.621031\pi$
$42$	−0.613645	−	0.384025i	−0.0946875	−	0.0592564i
$43$	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	$0.656391\pi$
$44$	1.40668	+	10.1082i	0.212064	+	1.52386i
$45$		0			0
$46$	−2.47629	+	5.82283i	−0.365110	+	0.858530i
$47$	−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	$-0.372026\pi$
$48$	−0.667476	−	0.372351i	−0.0963418	−	0.0537442i
$49$		−	0.176489i		−	0.0252127i
$50$		0			0
$51$			0.893612i			0.125131i
$52$	−5.23565	−	1.81070i	−0.726055	−	0.251099i
$53$	−0.837124	−	1.64295i	−0.114988	−	0.225676i	0.826339	−	0.563173i	$-0.190420\pi$
$53$	−0.837124	−	1.64295i	−0.114988	−	0.225676i	−0.941327	+	0.337497i	$0.890420\pi$
$54$	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
$58$	−0.167110	+	0.267030i	−0.0219426	+	0.0350628i
$59$	−7.33328	−	5.32794i	−0.954712	−	0.693639i	−0.00279513	−	0.999996i	$-0.500890\pi$
$59$	−7.33328	−	5.32794i	−0.954712	−	0.693639i	−0.951917	+	0.306357i	$0.900890\pi$
$60$		0			0
$61$	1.16375	−	0.845512i	0.149003	−	0.108257i	−0.510786	−	0.859708i	$-0.670646\pi$
$61$	1.16375	−	0.845512i	0.149003	−	0.108257i	0.659789	+	0.751451i	$0.270646\pi$
$62$	0.721044	+	10.4126i	0.0915727	+	1.32240i
$63$	1.24191	+	7.84114i	0.156467	+	0.987891i
$64$	−0.803948	−	7.95950i	−0.100493	−	0.994938i
$65$		0			0
$66$	−0.905341	+	1.04005i	−0.111440	+	0.128022i
$67$	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	$0.583769\pi$
$68$	−7.66911	+	5.35453i	−0.930016	+	0.649332i
$69$	−0.813081	+	0.264186i	−0.0978834	+	0.0318043i
$70$		0			0
$71$	−5.45415	−	1.77216i	−0.647288	−	0.210317i	−0.0330703	−	0.999453i	$-0.510529\pi$
$71$	−5.45415	−	1.77216i	−0.647288	−	0.210317i	−0.614218	+	0.789136i	$0.710529\pi$
$72$	1.72609	+	8.20236i	0.203421	+	0.966658i
$73$	−0.00296414	+	0.0187149i	−0.000346927	+	0.00219041i	−0.987861	−	0.155339i	$-0.950353\pi$
$73$	−0.00296414	+	0.0187149i	−0.000346927	+	0.00219041i	0.987514	+	0.157530i	$0.0503530\pi$
$74$	−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
$78$	−0.279928	−	0.694196i	−0.0316956	−	0.0786022i
$79$	−2.08434	+	6.41493i	−0.234506	+	0.721736i	0.762680	+	0.646776i	$0.223883\pi$
$79$	−2.08434	+	6.41493i	−0.234506	+	0.721736i	−0.997187	+	0.0749601i	$0.976117\pi$
$80$		0			0
$81$	−2.68002	−	8.24826i	−0.297780	−	0.916474i
$82$	−3.40864	+	2.85627i	−0.376422	+	0.315422i
$83$	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	$0.0909299\pi$
$84$	0.737387	−	0.710162i	0.0804556	−	0.0774851i
$85$		0			0
$86$	−4.61012	+	2.76580i	−0.497122	+	0.298244i
$87$	−0.0420376	+	0.00665810i	−0.00450690	+	0.000713823i
$88$	−14.3507	−	1.53775i	−1.52979	−	0.163925i
$89$	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
$92$	−7.13927	−	5.39497i	−0.744320	−	0.562465i
$93$	−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
$97$	9.96296	−	5.07638i	1.01158	−	0.515428i	0.132040	−	0.991244i	$-0.457847\pi$
$97$	9.96296	−	5.07638i	1.01158	−	0.515428i	0.879545	+	0.475816i	$0.157847\pi$
$98$	0.242139	+	0.0605458i	0.0244597	+	0.00611605i
$99$	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	$0.699884\pi$
$102$	−1.22601	−	0.306560i	−0.121393	−	0.0303540i
$103$	−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	$0.380472\pi$
$104$	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	−0.197472	−	0.980308i	$-0.563273\pi$
$107$	8.09772	−	8.09772i	0.782836	−	0.782836i	0.980308	+	0.197472i	$0.0632733\pi$
$108$	−1.37398	+	1.81822i	−0.132211	+	0.174958i
$109$	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
$112$	10.5131	+	2.07307i	0.993399	+	0.195887i
$113$	−8.00964	+	1.26860i	−0.753483	+	0.119340i	−0.521349	−	0.853344i	$-0.674571\pi$
$113$	−8.00964	+	1.26860i	−0.753483	+	0.119340i	−0.232135	+	0.972684i	$0.574571\pi$
$114$	−1.16263	+	0.697512i	−0.108891	+	0.0653279i
$115$		0			0
$116$	−0.309030	−	0.320877i	−0.0286927	−	0.0297927i
$117$	−3.72669	+	7.31405i	−0.344533	+	0.676184i
$118$	9.82552	−	8.23328i	0.904513	−	0.757935i
$119$	−3.87149	−	11.9152i	−0.354899	−	1.09227i
$120$		0			0
$121$	−4.64713	+	14.3024i	−0.422467	+	1.30022i
$122$	0.760789	+	1.88669i	0.0688786	+	0.170813i
$123$	−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	$0.797703\pi$
$128$	11.1960	+	1.62757i	0.989598	+	0.143858i
$129$	−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	$0.602635\pi$
$132$	−1.11634	−	1.59890i	−0.0971653	−	0.139167i
$133$	−11.9761	−	6.10210i	−1.03846	−	0.529119i
$134$	−3.14002	+	3.60726i	−0.271257	+	0.311619i
$135$		0			0
$136$	−4.71533	−	12.3587i	−0.404337	−	1.05975i
$137$	2.95587	+	18.6626i	0.252537	+	1.59445i	0.709327	+	0.704880i	$0.248999\pi$
$137$	2.95587	+	18.6626i	0.252537	+	1.59445i	−0.456790	+	0.889575i	$0.651001\pi$
$138$	−0.0835233	−	1.20616i	−0.00710998	−	0.102675i
$139$	−5.89560	+	4.28340i	−0.500058	+	0.363313i	−0.809039	−	0.587755i	$-0.800012\pi$
$139$	−5.89560	+	4.28340i	−0.500058	+	0.363313i	0.308981	+	0.951068i	$0.400012\pi$
$140$		0			0
$141$	1.36143	+	0.989135i	0.114653	+	0.0833002i
$142$	4.30244	−	6.87500i	0.361053	−	0.576937i
$143$	−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
$147$	0.0153100	+	0.0300475i	0.00126274	+	0.00247828i
$148$	2.86039	−	8.27082i	0.235122	−	0.679857i
$149$		−	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	$0.0798902\pi$
$151$			6.10369i			0.496712i	−0.968669	+	0.248356i	$0.920110\pi$
$152$	−12.9527	−	5.79840i	−1.05060	−	0.470312i
$153$	6.29202	+	12.3488i	0.508680	+	0.998340i
$154$	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	$-0.474338\pi$
$157$	−11.4802	−	11.4802i	−0.916218	−	0.916218i	−0.996752	+	0.0805335i	$0.974338\pi$
$158$	−8.08607	−	5.06034i	−0.643293	−	0.402579i
$159$	0.285043	+	0.207096i	0.0226054	+	0.0164238i
$160$		0			0
$161$	9.69687	−	7.04519i	0.764221	−	0.555239i
$162$	12.2358	−	0.847298i	0.961335	−	0.0665701i
$163$	−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	$-0.150271\pi$
$164$	−2.74936	−	5.65643i	−0.214689	−	0.441693i
$165$		0			0
$166$	3.58617	+	3.12167i	0.278341	+	0.242288i
$167$	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	$0.474836\pi$
$168$	0.721358	+	1.25530i	0.0556540	+	0.0968487i
$169$	−5.06658	+	1.64623i	−0.389737	+	0.126633i
$170$		0			0
$171$	14.1412	+	4.59476i	1.08141	+	0.351370i
$172$	−2.21307	−	7.27379i	−0.168745	−	0.554621i
$173$	0.171594	−	1.08340i	0.0130460	−	0.0823695i	−0.980306	−	0.197483i	$-0.936723\pi$
$173$	0.171594	−	1.08340i	0.0130460	−	0.0823695i	0.993352	+	0.115114i	$0.0367232\pi$
$174$	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
$178$	−1.13642	+	0.458252i	−0.0851786	+	0.0343474i
$179$	−7.45601	+	22.9472i	−0.557289	+	1.71516i	0.132533	+	0.991179i	$0.457689\pi$
$179$	−7.45601	+	22.9472i	−0.557289	+	1.71516i	−0.689822	+	0.723979i	$0.742311\pi$
$180$		0			0
$181$	−2.15964	−	6.64670i	−0.160525	−	0.494045i	0.838154	−	0.545434i	$-0.183635\pi$
$181$	−2.15964	−	6.64670i	−0.160525	−	0.494045i	−0.998679	+	0.0513890i	$0.983635\pi$
$182$	6.74003	+	8.04349i	0.499604	+	0.596223i
$183$	−0.124784	+	0.244901i	−0.00922426	+	0.0181036i
$184$	9.85094	−	7.94410i	0.726221	−	0.585647i
$185$		0			0
$186$	−1.02602	−	1.71020i	−0.0752315	−	0.125398i
$187$	−23.5704	+	3.73319i	−1.72364	+	0.272998i
$188$	−0.331219	+	17.6109i	−0.0241566	+	1.28440i
$189$	−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	$0.393164\pi$
$192$	0.827339	+	1.28537i	0.0597080	+	0.0927639i
$193$	6.44920	−	6.44920i	0.464223	−	0.464223i	−0.435814	−	0.900037i	$-0.643539\pi$
$193$	6.44920	−	6.44920i	0.464223	−	0.464223i	0.900037	+	0.435814i	$0.143539\pi$
$194$	3.54680	+	15.4104i	0.254645	+	1.10640i
$195$		0			0
$196$	−0.166135	+	0.311437i	−0.0118668	+	0.0222455i
$197$	5.09406	−	2.59555i	0.362936	−	0.184925i	−0.263007	−	0.964794i	$-0.584714\pi$
$197$	5.09406	−	2.59555i	0.362936	−	0.184925i	0.625943	+	0.779869i	$0.284714\pi$
$198$	−5.18772	+	20.7471i	−0.368676	+	1.47443i
$199$	24.6399			1.74668			0.873338	−	0.487115i	$-0.161951\pi$
$199$	24.6399			1.74668			0.873338	+	0.487115i	$0.161951\pi$
$200$		0			0
$201$	−0.646170			−0.0455773
$202$	4.05095	−	16.2008i	0.285024	−	1.13988i
$203$	0.531674	−	0.270901i	0.0373162	−	0.0190136i
$204$	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
$208$	7.53449	+	8.12369i	0.522423	+	0.563276i
$209$	−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	$0.560488\pi$
$212$	−0.0693474	+	3.68720i	−0.00476280	+	0.253238i
$213$	1.08231	−	0.171420i	0.0741584	−	0.0117455i
$214$	8.33188	+	13.8878i	0.569556	+	0.949353i
$215$		0			0
$216$	−2.02319	−	2.50882i	−0.137661	−	0.170703i
$217$	8.97603	−	17.6165i	0.609333	−	1.19588i
$218$	14.1126	+	16.8419i	0.955827	+	1.14068i
$219$	−0.00111881	−	0.00344336i	−7.56025e−5	−	0.000232681i
$220$		0			0
$221$	4.00309	−	12.3203i	0.269277	−	0.828750i
$222$	1.09663	−	0.442205i	0.0736009	−	0.0296788i
$223$	−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	$0.877687\pi$
$228$	−0.558118	−	1.83439i	−0.0369623	−	0.121485i
$229$	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
$232$	0.546250	−	0.313902i	0.0358631	−	0.0206087i
$233$	26.0233	+	13.2595i	1.70484	+	0.868660i	0.984575	+	0.174963i	$0.0559806\pi$
$233$	26.0233	+	13.2595i	1.70484	+	0.868660i	0.720267	+	0.693697i	$0.244019\pi$
$234$	−8.75622	−	7.62206i	−0.572412	−	0.498270i
$235$		0			0
$236$	7.92513	+	16.3048i	0.515882	+	1.06136i
$237$	−0.201617	−	1.27296i	−0.0130964	−	0.0826876i
$238$	17.6755	−	1.22399i	1.14573	−	0.0793392i
$239$	0.369981	−	0.268807i	0.0239321	−	0.0173877i	−0.575755	−	0.817622i	$-0.695292\pi$
$239$	0.369981	−	0.268807i	0.0239321	−	0.0173877i	0.599687	+	0.800235i	$0.295292\pi$
$240$		0			0
$241$	17.6697	+	12.8378i	1.13820	+	0.826953i	0.986868	−	0.161530i	$-0.0516429\pi$
$241$	17.6697	+	12.8378i	1.13820	+	0.826953i	0.151335	+	0.988483i	$0.451643\pi$
$242$	−18.0283	−	11.2823i	−1.15890	−	0.725252i
$243$	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
$247$	−6.30953	−	12.3832i	−0.401466	−	0.787921i
$248$	8.52929	−	19.0530i	0.541610	−	1.20987i
$249$			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	$-0.0547436\pi$
$252$	5.18959	−	15.0057i	0.326913	−	0.945271i
$253$	−10.3651	−	20.3426i	−0.651647	−	1.27893i
$254$	−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	$-0.134879\pi$
$257$	8.02192	+	8.02192i	0.500394	+	0.500394i	−0.411166	+	0.911560i	$0.634879\pi$
$258$	0.544953	−	0.870796i	0.0339273	−	0.0542134i
$259$	9.48341	+	6.89010i	0.589271	+	0.428130i
$260$		0			0
$261$	−0.534035	+	0.387999i	−0.0330559	+	0.0240165i
$262$	−1.32944	−	19.1984i	−0.0821332	−	1.18608i
$263$	−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	$-0.260119\pi$
$264$	2.57662	−	0.983081i	0.158580	−	0.0605045i
$265$		0			0
$266$	12.4804	−	14.3375i	0.765222	−	0.879086i
$267$	−0.147513	−	0.0751618i	−0.00902767	−	0.00459983i
$268$	−3.87185	−	5.54552i	−0.236511	−	0.338747i
$269$	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	0.253936	−	0.967221i	$-0.418275\pi$
$271$	−1.79674	−	0.583795i	−0.109144	−	0.0354630i	−0.363080	+	0.931758i	$0.618275\pi$
$272$	18.5735	−	2.22957i	1.12618	−	0.135187i
$273$	−0.221805	+	1.40042i	−0.0134243	+	0.0847574i
$274$	−26.6186	−	2.34696i	−1.60809	−	0.141785i
$275$		0			0
$276$	1.68347	+	0.299188i	0.101333	+	0.0180090i
$277$	11.3089	+	1.79116i	0.679488	+	0.107620i	0.486632	−	0.873607i	$-0.338225\pi$
$277$	11.3089	+	1.79116i	0.679488	+	0.107620i	0.192855	+	0.981227i	$0.438225\pi$
$278$	−3.85419	−	9.55805i	−0.231159	−	0.573254i
$279$	−6.75877	+	20.8013i	−0.404637	+	1.24534i
$280$		0			0
$281$	7.15917	+	22.0337i	0.427080	+	1.31442i	0.900988	+	0.433844i	$0.142843\pi$
$281$	7.15917	+	22.0337i	0.427080	+	1.31442i	−0.473908	+	0.880574i	$0.657157\pi$
$282$	−1.82411	+	1.52851i	−0.108624	+	0.0910217i
$283$	−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	$0.958358\pi$
$284$	7.95633	+	8.26135i	0.472122	+	0.490221i
$285$		0			0
$286$	17.1411	−	10.2836i	1.01357	−	0.608084i
$287$	8.32036	−	1.31782i	0.491135	−	0.0777882i
$288$	4.67524	−	16.0989i	0.275491	−	0.948637i
$289$	−2.86343	−	3.94118i	−0.168437	−	0.231834i
$290$		0			0
$291$	−1.25584	+	1.72852i	−0.0736188	+	0.101328i
$292$	0.0228475	−	0.0302344i	0.00133705	−	0.00176934i
$293$	−9.23047	+	9.23047i	−0.539250	+	0.539250i	−0.923309	−	0.384059i	$-0.874526\pi$
$293$	−9.23047	+	9.23047i	−0.539250	+	0.539250i	0.384059	+	0.923309i	$0.374526\pi$
$294$	−0.0464766	+	0.0106969i	−0.00271057	+	0.000623854i
$295$		0			0
$296$	10.3661	+	6.76173i	0.602515	+	0.393018i
$297$	−5.18082	+	2.63976i	−0.300621	+	0.153174i
$298$	2.92026	+	0.730201i	0.169166	+	0.0422994i
$299$	12.3934			0.716731
$300$		0			0
$301$	10.1838			0.586986
$302$	−8.37411	−	2.09391i	−0.481876	−	0.120491i
$303$	2.01039	−	1.02435i	0.115494	−	0.0588472i
$304$	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	−0.395150	−	0.918616i	$-0.629308\pi$
$307$	9.17187	−	9.17187i	0.523466	−	0.523466i	0.918616	+	0.395150i	$0.129308\pi$
$308$	21.8122	+	16.4829i	1.24286	+	0.939203i
$309$	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	$0.837650\pi$
$312$	−0.159501	+	1.48850i	−0.00902994	+	0.0842697i
$313$	22.1282	−	3.50477i	1.25076	−	0.198101i	0.504300	−	0.863529i	$-0.331751\pi$
$313$	22.1282	−	3.50477i	1.25076	−	0.198101i	0.746462	+	0.665427i	$0.231751\pi$
$314$	19.6889	−	11.8122i	1.11111	−	0.666598i
$315$		0			0
$316$	9.71663	−	9.35789i	0.546603	−	0.526422i
$317$	−2.85992	+	5.61291i	−0.160629	+	0.315252i	−0.957268	−	0.289204i	$-0.906609\pi$
$317$	−2.85992	+	5.61291i	−0.160629	+	0.315252i	0.796639	+	0.604456i	$0.206609\pi$
$318$	−0.381916	+	0.320026i	−0.0214168	+	0.0179462i
$319$	−0.351235	−	1.08099i	−0.0196654	−	0.0605239i
$320$		0			0
$321$	−0.676191	+	2.08110i	−0.0377413	+	0.116156i
$322$	6.33924	+	15.7208i	0.353272	+	0.876084i
$323$	−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
$328$	8.70366	−	1.83158i	0.480579	−	0.101132i
$329$	−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	$0.546909\pi$
$332$	−5.51311	+	3.84922i	−0.302571	+	0.211253i
$333$	−11.5541	−	5.88710i	−0.633159	−	0.322611i
$334$	−12.5497	+	14.4171i	−0.686690	+	0.788869i
$335$		0			0
$336$	−1.96971	+	0.559045i	−0.107456	+	0.0304984i
$337$	−3.16369	−	19.9748i	−0.172337	−	1.08809i	−0.910511	−	0.413484i	$-0.864312\pi$
$337$	−3.16369	−	19.9748i	−0.172337	−	1.08809i	0.738174	−	0.674610i	$-0.235688\pi$
$338$	−0.520462	−	7.51597i	−0.0283094	−	0.408815i
$339$	1.25360	−	0.910796i	0.0680864	−	0.0494676i
$340$		0			0
$341$	−30.4682	−	22.1364i	−1.64995	−	1.19876i
$342$	−11.1551	+	17.8251i	−0.603200	+	0.963871i
$343$	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
$347$	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	$0.800264\pi$
$348$	0.0804480	+	0.0278222i	0.00431247	+	0.00149143i
$349$		−	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
$352$	23.8761	+	16.2223i	1.27260	+	0.864652i
$353$	1.86927	+	3.66865i	0.0994913	+	0.195263i	0.935387	−	0.353626i	$-0.115051\pi$
$353$	1.86927	+	3.66865i	0.0994913	+	0.195263i	−0.835896	+	0.548888i	$0.815051\pi$
$354$	−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
$358$	−28.9252	−	18.1017i	−1.52874	−	0.956703i
$359$	−22.3556	−	16.2423i	−1.17989	−	0.857237i	−0.187726	−	0.982221i	$-0.560112\pi$
$359$	−22.3556	−	16.2423i	−1.17989	−	0.857237i	−0.992159	+	0.124985i	$0.960112\pi$
$360$		0			0
$361$	−4.99493	+	3.62903i	−0.262891	+	0.191002i
$362$	9.85997	−	0.682778i	0.518229	−	0.0358860i
$363$	−0.449515	−	2.83813i	−0.0235934	−	0.148963i
$364$	−13.3477	+	6.48777i	−0.699608	+	0.340052i
$365$		0			0
$366$	−0.293191	−	0.255215i	−0.0153253	−	0.0133403i
$367$	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	$0.593301\pi$
$368$	7.51967	+	16.2405i	0.391990	+	0.846595i
$369$	−8.86290	+	2.87973i	−0.461384	+	0.149913i
$370$		0			0
$371$	−4.69792	−	1.52645i	−0.243904	−	0.0792492i
$372$	2.69834	−	0.820977i	0.139902	−	0.0425657i
$373$	−1.79701	+	11.3458i	−0.0930454	+	0.587466i	0.896477	+	0.443089i	$0.146118\pi$
$373$	−1.79701	+	11.3458i	−0.0930454	+	0.587466i	−0.989523	+	0.144376i	$0.953882\pi$
$374$	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
$378$	4.00373	−	1.61447i	0.205930	−	0.0830391i
$379$	3.95657	−	12.1771i	0.203235	−	0.625494i	−0.796546	−	0.604578i	$-0.793342\pi$
$379$	3.95657	−	12.1771i	0.203235	−	0.625494i	0.999781	−	0.0209157i	$-0.00665816\pi$
$380$		0			0
$381$	−0.947807	−	2.91705i	−0.0485576	−	0.149445i
$382$	−14.3174	−	17.0863i	−0.732542	−	0.874210i
$383$	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	$-0.00607333\pi$
$384$	−2.04732	+	0.694130i	−0.104477	+	0.0354222i
$385$		0			0
$386$	6.63569	+	11.0606i	0.337748	+	0.562968i
$387$	−11.1270	+	1.76235i	−0.565618	+	0.0895851i
$388$	−22.3594	−	0.420528i	−1.13513	−	0.0213491i
$389$	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
$392$	−0.370290	−	0.334773i	−0.0187025	−	0.0169086i
$393$	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
$397$	−24.8148	+	12.6438i	−1.24542	+	0.634574i	−0.947420	−	0.319992i	$-0.896320\pi$
$397$	−24.8148	+	12.6438i	−1.24542	+	0.634574i	−0.298001	+	0.954566i	$0.596320\pi$
$398$	−8.45289	+	33.8053i	−0.423705	+	1.69451i
$399$	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	$0.415881\pi$
$402$	0.221673	−	0.886528i	0.0110560	−	0.0442160i
$403$	18.2153	−	9.28115i	0.907368	−	0.462327i
$404$	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
$408$	1.87488	+	1.69505i	0.0928203	+	0.0839173i
$409$	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
$412$	3.87966	+	0.0729673i	0.191137	+	0.00359484i
$413$	−23.9837	+	3.79865i	−1.18016	+	0.186919i
$414$	−9.64688	−	16.0797i	−0.474118	−	0.790275i
$415$		0			0
$416$	−13.7302	+	7.55024i	−0.673181	+	0.370181i
$417$	0.632159	−	1.24068i	0.0309569	−	0.0607564i
$418$	−23.2550	−	27.7523i	−1.13744	−	1.35741i
$419$	−11.1568	−	34.3371i	−0.545045	−	1.67748i	−0.720883	−	0.693056i	$-0.756264\pi$
$419$	−11.1568	−	34.3371i	−0.545045	−	1.67748i	0.175838	−	0.984419i	$-0.443736\pi$
$420$		0			0
$421$	4.95128	−	15.2385i	0.241311	−	0.742678i	−0.754911	−	0.655828i	$-0.772320\pi$
$421$	4.95128	−	15.2385i	0.241311	−	0.742678i	0.996221	−	0.0868504i	$-0.0276802\pi$
$422$	−26.0414	+	10.5009i	−1.26768	+	0.511177i
$423$	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
$428$	−21.9121	+	6.66680i	−1.05916	+	0.322252i
$429$	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	$0.348118\pi$
$432$	4.13610	−	1.91510i	0.198998	−	0.0921401i
$433$	−9.39790	−	4.78847i	−0.451634	−	0.230119i	0.213351	−	0.976976i	$-0.431562\pi$
$433$	−9.39790	−	4.78847i	−0.451634	−	0.230119i	−0.664985	+	0.746857i	$0.731562\pi$
$434$	21.0900	+	18.3583i	1.01235	+	0.881228i
$435$		0			0
$436$	−27.9480	+	13.5844i	−1.33847	+	0.650576i
$437$	−3.51178	−	22.1725i	−0.167991	−	1.06065i
$438$	0.00510801		0.000353717i	0.000244070		1.69013e-5i
$439$	−8.47207	+	6.15532i	−0.404350	+	0.293778i	−0.771311	−	0.636459i	$-0.780398\pi$
$439$	−8.47207	+	6.15532i	−0.404350	+	0.293778i	0.366960	+	0.930237i	$0.380398\pi$
$440$		0			0
$441$	0.423135	+	0.307426i	0.0201493	+	0.0146393i
$442$	15.5298	+	9.71869i	0.738676	+	0.462271i
$443$	−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	$0.785053\pi$
$444$	0.230487	+	1.65625i	0.0109384	+	0.0786020i
$445$		0			0
$446$	6.40583	−	15.0629i	0.303325	−	0.713247i
$447$	0.184643	+	0.362382i	0.00873331	+	0.0171401i
$448$	−16.6003	−	13.5545i	−0.784291	−	0.640391i
$449$		−	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
$452$	15.3282	+	5.30111i	0.720977	+	0.249343i
$453$	−0.529479	−	1.03916i	−0.0248771	−	0.0488241i
$454$	−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	0.994706	+	0.102764i	$0.0327687\pi$
$457$	23.4612	+	23.4612i	1.09747	+	1.09747i	0.102764	+	0.994706i	$0.467231\pi$
$458$	−12.6460	+	20.2074i	−0.590908	+	0.944230i
$459$	−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	$0.571675\pi$
$462$	0.255184	+	3.68510i	0.0118722	+	0.171446i
$463$	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	$0.697527\pi$
$464$	0.243271	+	0.857127i	0.0112936	+	0.0397911i
$465$		0			0
$466$	−27.1192	+	31.1545i	−1.25627	+	1.44320i
$467$	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	$0.532556\pi$
$468$	13.4611	−	9.39850i	0.622242	−	0.434446i
$469$	8.61588	−	2.79947i	0.397844	−	0.129268i
$470$		0			0
$471$	2.95039	+	0.958640i	0.135947	+	0.0441718i
$472$	−25.0886	+	5.27958i	−1.15480	+	0.243013i
$473$	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
$478$	0.241872	+	0.599821i	0.0110630	+	0.0274352i
$479$	2.15249	−	6.62469i	0.0983498	−	0.302690i	−0.889762	−	0.456424i	$-0.849130\pi$
$479$	2.15249	−	6.62469i	0.0983498	−	0.302690i	0.988112	+	0.153734i	$0.0491300\pi$
$480$		0			0
$481$	3.74547	+	11.5274i	0.170779	+	0.525604i
$482$	−23.6748	+	19.8382i	−1.07836	+	0.903606i
$483$	−1.03975	+	2.04063i	−0.0473104	+	0.0928519i
$484$	21.6637	−	20.8639i	0.984715	−	0.948358i
$485$		0			0
$486$	−6.15526	+	3.69279i	−0.279208	+	0.167509i
$487$	−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	$0.606639\pi$
$488$	0.433491	−	4.04545i	0.0196232	−	0.183129i
$489$	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	$0.235410\pi$
$492$	0.958763	+	0.724514i	0.0432244	+	0.0326636i
$493$	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
$497$	−13.6886	+	6.97467i	−0.614016	+	0.312857i
$498$	−0.881346	−	0.220377i	−0.0394940	−	0.00987534i
$499$	−19.8140			−0.886994			−0.443497	−	0.896276i	$-0.646262\pi$
$499$	−19.8140			−0.886994			−0.443497	+	0.896276i	$0.646262\pi$
$500$		0			0
$501$	−2.58255			−0.115380
$502$	7.43965	+	1.86026i	0.332048	+	0.0830273i
$503$	−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	$0.559812\pi$
$504$	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
$508$	19.3553	−	25.6132i	0.858751	−	1.13640i
$509$	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
$512$	−18.2247	−	13.4112i	−0.805426	−	0.592697i
$513$	−5.64685	+	0.894374i	−0.249315	+	0.0394876i
$514$	−13.7578	+	8.25389i	−0.606832	+	0.364064i
$515$		0			0
$516$	1.00776	+	1.04639i	0.0443641	+	0.0460649i
$517$	−20.4024	+	40.0420i	−0.897298	+	1.76105i
$518$	−12.7064	+	10.6473i	−0.558287	+	0.467815i
$519$	0.0647681	+	0.199336i	0.00284300	+	0.00874987i
$520$		0			0
$521$	1.41202	−	4.34576i	0.0618618	−	0.190391i	−0.915349	−	0.402661i	$-0.868085\pi$
$521$	1.41202	−	4.34576i	0.0618618	−	0.190391i	0.977211	+	0.212270i	$0.0680855\pi$
$522$	−0.349120	−	0.865787i	−0.0152806	−	0.0378945i
$523$	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
$528$	0.464834	+	3.87231i	0.0202293	+	0.168521i
$529$	−2.83537	−	0.921267i	−0.123277	−	0.0400551i
$530$		0			0
$531$	25.5476	−	8.30092i	1.10867	−	0.360229i
$532$	15.3891	+	22.0413i	0.667204	+	0.955613i
$533$	7.76106	+	3.95446i	0.336169	+	0.171286i
$534$	0.153725	−	0.176600i	0.00665235	−	0.00764222i
$535$		0			0
$536$	8.93658	−	3.40965i	0.386001	−	0.147274i
$537$	−0.721217	−	4.55359i	−0.0311228	−	0.196502i
$538$	0.990047	+	14.2972i	0.0426840	+	0.616397i
$539$	−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	$0.916724\pi$
$542$	1.41733	−	2.26480i	0.0608797	−	0.0972815i
$543$	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
$547$	−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	$-0.419100\pi$
$548$	12.3517	−	35.7149i	0.527638	−	1.52567i
$549$			4.26289i			0.181936i
$550$		0			0
$551$		−	1.11760i		−	0.0476112i
$552$	−0.988004	+	2.20704i	−0.0420522	+	0.0939377i
$553$	8.20329	+	16.0999i	0.348839	+	0.684636i
$554$	−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	−0.997715	−	0.0675692i	$-0.978476\pi$
$557$	−25.1416	−	25.1416i	−1.06528	−	1.06528i	−0.0675692	−	0.997715i	$-0.521524\pi$
$558$	−26.2203	−	16.4089i	−1.10999	−	0.694644i
$559$	8.51896	+	6.18939i	0.360314	+	0.261783i
$560$		0			0
$561$	3.68905	−	2.68025i	0.155752	−	0.113160i
$562$	−32.6856	+	2.26340i	−1.37876	+	0.0954756i
$563$	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	$0.752063\pi$
$564$	−1.47131	−	3.02700i	−0.0619531	−	0.127460i
$565$		0			0
$566$	−20.3255	−	17.6928i	−0.854345	−	0.743686i
$567$	−20.7011	−	10.5477i	−0.869364	−	0.442963i
$568$	−14.0638	+	8.08177i	−0.590105	+	0.339104i
$569$	−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	−0.0744189	−	0.997227i	$-0.523710\pi$
$571$	−17.2235	−	5.59625i	−0.720780	−	0.234196i	−0.646362	+	0.763031i	$0.723710\pi$
$572$	8.22851	+	27.0450i	0.344051	+	1.13081i
$573$	0.471166	−	2.97482i	0.0196832	−	0.124275i
$574$	−1.04635	+	11.8674i	−0.0436737	+	0.495336i
$575$		0			0
$576$	20.4834	+	11.9371i	0.853475	+	0.497381i
$577$	10.8794	+	1.72312i	0.452914	+	0.0717345i	0.378724	−	0.925510i	$-0.376363\pi$
$577$	10.8794	+	1.72312i	0.452914	+	0.0717345i	0.0741898	+	0.997244i	$0.476363\pi$
$578$	6.38951	−	2.57651i	0.265769	−	0.107169i
$579$	−0.538533	+	1.65743i	−0.0223807	+	0.0688806i
$580$		0			0
$581$	−2.78310	−	8.56552i	−0.115463	−	0.355357i
$582$	−1.94066	−	2.31596i	−0.0804429	−	0.0959998i
$583$	−4.27167	+	8.38362i	−0.176914	+	0.347214i
$584$	0.0336429	+	0.0417182i	0.00139215	+	0.00172631i
$585$		0			0
$586$	−9.49738	−	15.8305i	−0.392333	−	0.653953i
$587$	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	$0.0319715\pi$
$588$	0.00126828	−	0.0674343i	5.23029e−5	−	0.00278094i
$589$	−21.7659	−	29.9582i	−0.896849	−	1.23441i
$590$		0			0
$591$	−0.642112	+	0.883792i	−0.0264130	+	0.0363543i
$592$	−12.8331	+	11.9023i	−0.527436	+	0.489182i
$593$	−11.5238	+	11.5238i	−0.473225	+	0.473225i	−0.902957	−	0.429731i	$-0.858608\pi$
$593$	−11.5238	+	11.5238i	−0.473225	+	0.473225i	0.429731	+	0.902957i	$0.358608\pi$
$594$	−1.84436	−	8.01353i	−0.0756752	−	0.328799i
$595$		0			0
$596$	−2.00363	+	3.75603i	−0.0820720	+	0.153853i
$597$	−4.19497	+	2.13745i	−0.171689	+	0.0874798i
$598$	−4.25165	+	17.0035i	−0.173863	+	0.695324i
$599$	−7.21615			−0.294844			−0.147422	−	0.989074i	$-0.547098\pi$
$599$	−7.21615			−0.294844			−0.147422	+	0.989074i	$0.547098\pi$
$600$		0			0
$601$	−15.0642			−0.614483			−0.307241	−	0.951632i	$-0.599406\pi$
$601$	−15.0642			−0.614483			−0.307241	+	0.951632i	$0.599406\pi$
$602$	−3.49363	+	13.9720i	−0.142390	+	0.569454i
$603$	−8.92939	+	4.54975i	−0.363633	+	0.185280i
$604$	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	−0.630443	−	0.776235i	$-0.717127\pi$
$607$	3.59194	−	3.59194i	0.145792	−	0.145792i	0.776235	+	0.630443i	$0.217127\pi$
$608$	17.3984	+	22.4247i	0.705596	+	0.909442i
$609$	−0.0670182	+	0.0922426i	−0.00271571	+	0.00373786i
$610$		0			0
$611$	−14.3390	−	19.7360i	−0.580095	−	0.798433i
$612$	0.521231	−	27.7138i	0.0210695	−	1.12027i
$613$	−4.97817	+	0.788465i	−0.201066	+	0.0318458i	−0.256155	−	0.966636i	$-0.582456\pi$
$613$	−4.97817	+	0.788465i	−0.201066	+	0.0318458i	0.0550888	+	0.998481i	$0.482456\pi$
$614$	9.43709	+	15.7300i	0.380850	+	0.634812i
$615$		0			0
$616$	−30.0970	+	24.2711i	−1.21264	+	0.977912i
$617$	8.43913	−	16.5627i	0.339746	−	0.666790i	−0.656408	−	0.754406i	$-0.727925\pi$
$617$	8.43913	−	16.5627i	0.339746	−	0.666790i	0.996154	+	0.0876162i	$0.0279249\pi$
$618$	0.336731	+	0.401851i	0.0135453	+	0.0161648i
$619$	6.54265	+	20.1362i	0.262971	+	0.809343i	0.992154	+	0.125024i	$0.0399006\pi$
$619$	6.54265	+	20.1362i	0.262971	+	0.809343i	−0.729182	+	0.684320i	$0.760099\pi$
$620$		0			0
$621$	1.57547	−	4.84880i	0.0632215	−	0.194576i
$622$	5.45901	−	2.20129i	0.218886	−	0.0882637i
$623$	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
$628$	9.45157	+	31.0648i	0.377159	+	1.23962i
$629$	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	$0.378482\pi$
$632$	9.50542	+	16.5413i	0.378105	+	0.657976i
$633$	−3.38030	−	1.72235i	−0.134355	−	0.0684572i
$634$	−6.71965	−	5.84928i	−0.266871	−	0.232305i
$635$		0			0
$636$	−0.308048	−	0.633766i	−0.0122149	−	0.0251304i
$637$	−0.0764758	−	0.482849i	−0.00303008	−	0.0191312i
$638$	1.60359	−	0.111044i	0.0634866	−	0.00439629i
$639$	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	$0.426315\pi$
$642$	−2.62325	−	1.64165i	−0.103531	−	0.0647909i
$643$	−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	$0.810662\pi$
$644$	−23.7432	+	3.30416i	−0.935613	+	0.130202i
$645$		0			0
$646$	12.9868	−	30.5375i	0.510957	−	1.20148i
$647$	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	$0.616812\pi$
$648$	−22.3892	−	10.0228i	−0.879530	−	0.393731i
$649$			46.2539i			1.81562i
$650$		0			0
$651$			3.77787i			0.148066i
$652$	−5.17148	+	14.9534i	−0.202531	+	0.585619i
$653$	−2.90673	−	5.70477i	−0.113749	−	0.223245i	0.827112	−	0.562036i	$-0.189982\pi$
$653$	−2.90673	−	5.70477i	−0.113749	−	0.223245i	−0.940862	+	0.338791i	$0.889982\pi$
$654$	−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
$658$	17.7002	−	28.2837i	0.690025	−	1.10261i
$659$	−11.5792	−	8.41281i	−0.451063	−	0.327716i	0.338952	−	0.940804i	$-0.389927\pi$
$659$	−11.5792	−	8.41281i	−0.451063	−	0.327716i	−0.790015	+	0.613087i	$0.789927\pi$
$660$		0			0
$661$	−0.382235	+	0.277710i	−0.0148672	+	0.0108017i	−0.595194	−	0.803582i	$-0.702925\pi$
$661$	−0.382235	+	0.277710i	−0.0148672	+	0.0108017i	0.580327	+	0.814384i	$0.302925\pi$
$662$	−1.58304	−	22.8607i	−0.0615267	−	0.888505i
$663$	0.387218	+	2.44480i	0.0150383	+	0.0949480i
$664$	−3.38972	−	8.88434i	−0.131547	−	0.344779i
$665$		0			0
$666$	12.0406	−	13.8323i	0.466566	−	0.535990i
$667$	0.887989	+	0.452453i	0.0343831	+	0.0175190i
$668$	−15.4746	−	22.1638i	−0.598731	−	0.857543i
$669$	2.10333	−	0.683413i	0.0813193	−	0.0264223i
$670$		0			0
$671$	−6.98096	−	2.26825i	−0.269497	−	0.0875648i
$672$	−0.0912728	−	2.89417i	−0.00352092	−	0.111645i
$673$	−3.35456	+	21.1799i	−0.129309	+	0.816424i	0.834729	+	0.550660i	$0.185624\pi$
$673$	−3.35456	+	21.1799i	−0.129309	+	0.816424i	−0.964038	+	0.265764i	$0.914376\pi$
$674$	28.4902	+	2.51198i	1.09740	+	0.0967578i
$675$		0			0
$676$	10.4903	+	1.86434i	0.403471	+	0.0717055i
$677$	43.8961	+	6.95245i	1.68706	+	0.267204i	0.924908	−	0.380191i	$-0.124142\pi$
$677$	43.8961	+	6.95245i	1.68706	+	0.267204i	0.762155	+	0.647395i	$0.224142\pi$
$678$	0.819531	+	2.03236i	0.0314739	+	0.0780525i
$679$	9.25648	−	28.4885i	0.355231	−	1.09329i
$680$		0			0
$681$	−0.916813	−	2.82166i	−0.0351323	−	0.108126i
$682$	40.8229	−	34.2075i	1.56319	−	1.30987i
$683$	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	$-0.00519935\pi$
$684$	−20.6287	−	21.4196i	−0.788759	−	0.818997i
$685$		0			0
$686$	−22.1677	+	13.2993i	−0.846367	+	0.507770i
$687$	−3.18118	+	0.503849i	−0.121369	+	0.0192230i
$688$	−2.94180	+	14.9187i	−0.112155	+	0.568771i
$689$	−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	$0.0968518\pi$
$692$	−1.32264	+	1.75027i	−0.0502791	+	0.0665353i
$693$	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
$697$	13.1035	−	6.67656i	0.496330	−	0.252893i
$698$	0.0725513	+	0.0181412i	0.00274611	+	0.000686654i
$699$	−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	$0.0879356\pi$
$702$	4.33041	+	1.08280i	0.163441	+	0.0408678i
$703$	19.5618	−	9.96723i	0.737787	−	0.375921i
$704$	−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
$708$	−2.76367	−	2.08844i	−0.103865	−	0.0784882i
$709$	−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
$712$	2.43673	+	0.261108i	0.0913202	+	0.00978544i
$713$	32.6152	−	5.16574i	1.22145	−	0.193458i
$714$	−2.90310	+	1.74169i	−0.108646	+	0.0651811i
$715$		0			0
$716$	34.7580	−	33.4747i	1.29897	−	1.25101i
$717$	−0.0396715	+	0.0778596i	−0.00148156	+	0.00290772i
$718$	29.9533	−	25.0993i	1.11785	−	0.936698i
$719$	3.14270	+	9.67223i	0.117203	+	0.360713i	0.992400	−	0.123053i	$-0.0392685\pi$
$719$	3.14270	+	9.67223i	0.117203	+	0.360713i	−0.875197	+	0.483766i	$0.839269\pi$
$720$		0			0
$721$	−1.60612	+	4.94314i	−0.0598152	+	0.184092i
$722$	−3.26539	−	8.09788i	−0.121525	−	0.301372i
$723$	−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	$0.998031\pi$
$728$	−4.32204	−	20.5383i	−0.160185	−	0.761201i
$729$	23.8224	+	7.74037i	0.882312	+	0.286681i
$730$		0			0
$731$	16.9084	−	5.49386i	0.625378	−	0.203198i
$732$	0.450729	−	0.314697i	0.0166594	−	0.0116315i
$733$	0.234567	+	0.119518i	0.00866394	+	0.00441450i	0.458317	−	0.888789i	$-0.348452\pi$
$733$	0.234567	+	0.119518i	0.00866394	+	0.00441450i	−0.449653	+	0.893203i	$0.648452\pi$
$734$	−6.30358	+	7.24154i	−0.232669	+	0.267290i
$735$		0			0
$736$	−24.8612	+	4.74538i	−0.916397	+	0.174917i
$737$	−2.69946	−	17.0437i	−0.0994360	−	0.627814i
$738$	−0.910437	−	13.1476i	−0.0335136	−	0.483969i
$739$	5.97506	−	4.34113i	0.219796	−	0.159691i	−0.472439	−	0.881363i	$-0.656626\pi$
$739$	5.97506	−	4.34113i	0.219796	−	0.159691i	0.692235	+	0.721672i	$0.256626\pi$
$740$		0			0
$741$	2.14841	+	1.56091i	0.0789238	+	0.0573415i
$742$	3.70590	−	5.92176i	0.136048	−	0.217395i
$743$	−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	$0.808414\pi$
$744$	0.200675	+	3.98369i	0.00735712	+	0.146049i
$745$		0			0
$746$	−14.9497	−	6.35772i	−0.547349	−	0.232772i
$747$	4.52315	+	8.87719i	0.165494	+	0.324799i
$748$	45.1071	+	15.5999i	1.64928	+	0.570388i
$749$		−	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	$0.821134\pi$
$752$	17.1621	−	30.7648i	0.625838	−	1.12188i
$753$	0.470395	+	0.923203i	0.0171422	+	0.0336434i
$754$	−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	$-0.423604\pi$
$757$	−20.1848	−	20.1848i	−0.733630	−	0.733630i	−0.971337	+	0.237707i	$0.923604\pi$
$758$	15.3493	+	9.60573i	0.557511	+	0.348896i
$759$	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	$0.243124\pi$
$762$	4.32727	−	0.299652i	0.156760	−	0.0108553i
$763$	−6.51124	−	41.1103i	−0.235723	−	1.48829i
$764$	28.3536	−	13.7815i	1.02580	−	0.498599i
$765$		0			0
$766$	19.6609	+	17.1143i	0.710378	+	0.618366i
$767$	−22.3715	−	11.3988i	−0.807788	−	0.411589i
$768$	−0.249980	−	3.04700i	−0.00902038	−	0.109949i
$769$	−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
$772$	−17.4512	+	5.30959i	−0.628084	+	0.191096i
$773$	6.76671	−	42.7233i	0.243382	−	1.53665i	−0.498957	−	0.866627i	$-0.666283\pi$
$773$	6.76671	−	42.7233i	0.243382	−	1.53665i	0.742339	−	0.670025i	$-0.233717\pi$
$774$	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
$778$	−32.6231	+	13.1549i	−1.16959	+	0.471627i
$779$	4.87557	−	15.0055i	0.174685	−	0.537626i
$780$		0			0
$781$	9.04296	+	27.8314i	0.323582	+	0.995884i
$782$	19.0060	+	22.6816i	0.679653	+	0.811091i
$783$	0.115230	−	0.226151i	0.00411798	−	0.00808199i
$784$	0.586330	−	0.393182i	0.0209404	−	0.0140422i
$785$		0			0
$786$	1.89175	+	3.15323i	0.0674765	+	0.112472i
$787$	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	$0.380697\pi$
$788$	−11.4324	−	0.215016i	−0.407261	−	0.00765962i
$789$	2.23378	+	3.07453i	0.0795245	+	0.109456i
$790$		0			0
$791$	−12.7693	+	17.5755i	−0.454025	+	0.624911i
$792$	28.6842	−	31.7274i	1.01925	−	1.12738i
$793$	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
$797$	14.6702	−	7.47486i	0.519646	−	0.264773i	−0.174436	−	0.984668i	$-0.555810\pi$
$797$	14.6702	−	7.47486i	0.519646	−	0.264773i	0.694083	+	0.719895i	$0.255810\pi$
$798$	−0.881065	+	3.52361i	−0.0311894	+	0.124734i
$799$	−41.1877			−1.45712
$800$		0			0
$801$	−2.56770			−0.0907253
$802$	−3.58878	+	14.3525i	−0.126724	+	0.506803i
$803$	0.0861499	−	0.0438956i	0.00304016	−	0.00154904i
$804$	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
$808$	−22.3987	+	24.7750i	−0.787984	+	0.871583i
$809$	−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	0.999136	−	0.0415488i	$-0.0132292\pi$
$811$	18.5355	+	25.5120i	0.650871	+	0.895847i	−0.348265	+	0.937396i	$0.613229\pi$
$812$	−1.19321	−	0.0224415i	−0.0418735	−	0.000787542i
$813$	0.356539	−	0.0564703i	0.0125044	−	0.00198050i
$814$	16.2451	+	27.0779i	0.569392	+	0.949080i
$815$		0			0
$816$	−2.96875	+	1.99079i	−0.103927	+	0.0696915i
$817$	8.65922	−	16.9947i	0.302948	−	0.594569i
$818$	14.0988	+	16.8254i	0.492953	+	0.588286i
$819$	6.79540	+	20.9141i	0.237451	+	0.730798i
$820$		0			0
$821$	−6.22378	+	19.1548i	−0.217211	+	0.668508i	0.781778	+	0.623557i	$0.214313\pi$
$821$	−6.22378	+	19.1548i	−0.217211	+	0.668508i	−0.998989	+	0.0449507i	$0.985687\pi$
$822$	4.73545	−	1.90952i	0.165168	−	0.0666023i
$823$	−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	$-0.0269507\pi$
$828$	25.3704	−	7.71901i	0.881682	−	0.268254i
$829$	−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
$832$	−5.64848	−	21.4277i	−0.195826	−	0.742872i
$833$	−0.735426	−	0.374718i	−0.0254810	−	0.0129832i
$834$	1.48532	+	1.29293i	0.0514323	+	0.0447705i
$835$		0			0
$836$	46.0533	−	22.3846i	1.59279	−	0.774189i
$837$	−1.31560	−	8.30637i	−0.0454738	−	0.287110i
$838$	50.9370	−	3.52726i	1.75959	−	0.121847i
$839$	−6.53213	+	4.74587i	−0.225514	+	0.163846i	−0.694805	−	0.719198i	$-0.744509\pi$
$839$	−6.53213	+	4.74587i	−0.225514	+	0.163846i	0.469291	+	0.883044i	$0.344509\pi$
$840$		0			0
$841$	−23.4214	−	17.0166i	−0.807633	−	0.586780i
$842$	19.2082	+	12.0207i	0.661959	+	0.414260i
$843$	−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
$847$	18.2897	+	35.8955i	0.628440	+	1.23338i
$848$	3.59324	−	6.44124i	0.123392	−	0.221193i
$849$		−	3.64092i		−	0.124956i
$850$		0			0
$851$			19.5780i			0.671126i
$852$	−2.07123	−	0.716314i	−0.0709590	−	0.0245405i
$853$	15.8344	+	31.0768i	0.542160	+	1.06405i	0.985812	+	0.167851i	$0.0536826\pi$
$853$	15.8344	+	31.0768i	0.542160	+	1.06405i	−0.443652	+	0.896199i	$0.646317\pi$
$854$	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	0.995998	+	0.0893726i	$0.0284862\pi$
$857$	31.7738	+	31.7738i	1.08537	+	1.08537i	0.0893726	+	0.995998i	$0.471514\pi$
$858$	−2.02621	+	3.23774i	−0.0691737	+	0.110535i
$859$	34.2690	+	24.8979i	1.16924	+	0.849504i	0.990918	−	0.134468i	$-0.0429325\pi$
$859$	34.2690	+	24.8979i	1.16924	+	0.849504i	0.178324	+	0.983972i	$0.442932\pi$
$860$		0			0
$861$	−1.30223	+	0.946129i	−0.0443800	+	0.0322440i
$862$	0.658255	+	9.50584i	0.0224203	+	0.323770i
$863$	−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	$-0.141572\pi$
$864$	1.20854	+	6.33161i	0.0411155	+	0.215406i
$865$		0			0
$866$	9.79367	−	11.2510i	0.332802	−	0.382323i
$867$	0.829389	+	0.422595i	0.0281675	+	0.0143521i
$868$	−32.4222	+	22.6370i	−1.10048	+	0.768350i
$869$	32.7340	−	10.6359i	1.11043	−	0.360799i
$870$		0			0
$871$	8.90876	+	2.89463i	0.301862	+	0.0980809i
$872$	−9.04970	−	43.0042i	−0.306462	−	1.45631i
$873$	−5.18374	+	32.7288i	−0.175443	+	1.10770i
$874$	31.6248	+	2.78836i	1.06973	+	0.0943177i
$875$		0			0
$876$	−0.00126705	+	0.00712941i	−4.28096e−5	+	0.000240880i
$877$	−14.6759	−	2.32444i	−0.495571	−	0.0784907i	−0.0963539	−	0.995347i	$-0.530718\pi$
$877$	−14.6759	−	2.32444i	−0.495571	−	0.0784907i	−0.399217	+	0.916856i	$0.630718\pi$
$878$	−5.53854	−	13.7351i	−0.186917	−	0.463537i
$879$	0.770780	−	2.37222i	0.0259978	−	0.0800129i
$880$		0			0
$881$	−15.1162	−	46.5230i	−0.509279	−	1.56740i	−0.793456	−	0.608628i	$-0.791720\pi$
$881$	−15.1162	−	46.5230i	−0.509279	−	1.56740i	0.284177	−	0.958772i	$-0.408280\pi$
$882$	−0.566939	+	0.475066i	−0.0190898	+	0.0159963i
$883$	−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	$0.158737\pi$
$884$	−18.6614	+	17.9724i	−0.627650	+	0.604477i
$885$		0			0
$886$	5.61028	−	3.36584i	0.188481	−	0.113078i
$887$	−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	$0.600070\pi$
$888$	−2.35140	−	0.251965i	−0.0789077	−	0.00845538i
$889$	25.2757	+	34.7890i	0.847719	+	1.16679i
$890$		0			0
$891$	−26.0125	+	35.8032i	−0.871452	+	1.19945i
$892$	18.4683	+	13.9560i	0.618364	+	0.467283i
$893$	−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
$897$	−2.11000	+	1.07510i	−0.0704508	+	0.0358965i
$898$	24.8233	+	6.20698i	0.828365	+	0.207130i
$899$	1.64396			0.0548290
$900$		0			0
$901$	−8.62349			−0.287290
$902$	22.0150	+	5.50478i	0.733021	+	0.183289i
$903$	−1.73381	+	0.883420i	−0.0576976	+	0.0293984i
$904$	−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	−0.200818	+	0.979629i	$0.564360\pi$
$907$	−35.5508	+	35.5508i	−1.18045	+	1.18045i	−0.979629	+	0.200818i	$0.935640\pi$
$908$	18.7223	−	24.7756i	0.621323	−	0.822208i
$909$	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	$0.830667\pi$
$912$	−0.741897	+	3.76238i	−0.0245667	+	0.124585i
$913$	−16.9441	+	2.68368i	−0.560768	+	0.0888169i
$914$	−40.2367	+	24.1397i	−1.33091	+	0.798469i
$915$		0			0
$916$	−23.3857	−	24.2822i	−0.772686	−	0.802308i
$917$	−16.5498	+	32.4808i	−0.546522	+	1.07261i
$918$	5.77650	−	4.84041i	0.190653	−	0.159757i
$919$	13.3369	+	41.0468i	0.439944	+	1.35401i	0.887934	+	0.459971i	$0.152140\pi$
$919$	13.3369	+	41.0468i	0.439944	+	1.35401i	−0.447990	+	0.894039i	$0.647860\pi$
$920$		0			0
$921$	−0.765886	+	2.35716i	−0.0252368	+	0.0776709i
$922$	−17.1148	−	42.4433i	−0.563647	−	1.39780i
$923$	−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
$928$	−1.25941	+	0.0397177i	−0.0413422	+	0.00130380i
$929$	−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
$932$	−33.4397	−	47.8946i	−1.09535	−	1.56884i
$933$	0.708605	+	0.361052i	0.0231987	+	0.0118203i
$934$	−14.4732	+	16.6268i	−0.473579	+	0.544047i
$935$		0			0
$936$	8.27655	+	21.6926i	0.270528	+	0.709043i
$937$	5.92447	+	37.4056i	0.193544	+	1.22199i	0.872796	+	0.488084i	$0.162304\pi$
$937$	5.92447	+	37.4056i	0.193544	+	1.22199i	−0.679252	+	0.733905i	$0.737696\pi$
$938$	0.885062	+	12.7811i	0.0288983	+	0.417319i
$939$	−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	$0.525810\pi$
$942$	−2.32738	+	3.71899i	−0.0758302	+	0.121171i
$943$	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
$947$	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	$0.831712\pi$
$948$	−0.842497	+	2.43608i	−0.0273630	+	0.0791203i
$949$			0.0524856i			0.00170375i
$950$		0			0
$951$		−	1.20369i		−	0.0390325i
$952$	−32.3428	−	14.4786i	−1.04824	−	0.469255i
$953$	−24.4756	−	48.0361i	−0.792843	−	1.55604i	−0.830674	−	0.556759i	$-0.812045\pi$
$953$	−24.4756	−	48.0361i	−0.792843	−	1.55604i	0.0378308	−	0.999284i	$-0.487955\pi$
$954$	−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
$958$	8.35047	+	5.22581i	0.269791	+	0.168838i
$959$	40.9512	+	29.7528i	1.32238	+	0.960767i
$960$		0			0
$961$	18.9882	−	13.7957i	0.612523	−	0.445024i
$962$	−17.1002	+	1.18414i	−0.551332	+	0.0381783i
$963$	5.30901	+	33.5198i	0.171080	+	1.08016i
$964$	−19.0957	−	39.2868i	−0.615032	−	1.26534i
$965$		0			0
$966$	−2.44300	−	2.12657i	−0.0786021	−	0.0684211i
$967$	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	$0.569885\pi$
$968$	21.1928	+	36.8796i	0.681163	+	1.18535i
$969$	4.26415	−	1.38551i	0.136984	−	0.0445089i
$970$		0			0
$971$	16.7721	+	5.44959i	0.538242	+	0.174886i	0.565508	−	0.824743i	$-0.308680\pi$
$971$	16.7721	+	5.44959i	0.538242	+	0.174886i	−0.0272659	+	0.999628i	$0.508680\pi$
$972$	−2.95481	−	9.71170i	−0.0947756	−	0.311503i
$973$	−3.05393	+	19.2817i	−0.0979044	+	0.618144i
$974$	2.59016	−	29.3769i	0.0829940	−	0.941295i
$975$		0			0
$976$	5.40154	+	1.98256i	0.172899	+	0.0634602i
$977$	−52.0437	−	8.24291i	−1.66502	−	0.263714i	−0.748337	−	0.663319i	$-0.769147\pi$
$977$	−52.0437	−	8.24291i	−1.66502	−	0.263714i	−0.916687	+	0.399605i	$0.869147\pi$
$978$	−1.98267	+	0.799492i	−0.0633988	+	0.0255649i
$979$	1.36625	−	4.20489i	0.0436656	−	0.134389i
$980$		0			0
$981$	14.2286	+	43.7910i	0.454283	+	1.39814i
$982$	−4.46875	−	5.33297i	−0.142603	−	0.170182i
$983$	−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	$0.240300\pi$
$984$	−1.32292	+	1.06685i	−0.0421733	+	0.0340099i
$985$		0			0
$986$	0.757903	+	1.26330i	0.0241366	+	0.0402316i
$987$	4.45259	−	0.705221i	0.141728	−	0.0224474i
$988$	−0.522682	+	27.7910i	−0.0166287	+	0.884148i
$989$	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	$0.0172988\pi$
$992$	−32.9862	+	25.5925i	−1.04731	+	0.812563i
$993$	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
$997$	−1.87335	+	0.954518i	−0.0593295	+	0.0302299i	−0.483404	−	0.875398i	$-0.660600\pi$
$997$	−1.87335	+	0.954518i	−0.0593295	+	0.0302299i	0.424074	+	0.905628i	$0.360600\pi$
$998$	6.79731	−	27.1842i	0.215165	−	0.860502i
$999$	4.98610			0.157753

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.2.l.b.23.1	✓	96	20.3	even	4
100.2.l.b.23.12	yes	96	5.3	odd	4
100.2.l.b.87.1	yes	96	25.16	even	5
100.2.l.b.87.12	yes	96	100.91	odd	10
500.2.l.d.43.5		96	25.12	odd	20
500.2.l.d.43.6		96	100.87	even	20
500.2.l.d.407.5		96	20.19	odd	2
500.2.l.d.407.6		96	5.4	even	2
500.2.l.e.43.7		96	100.63	even	20	inner
500.2.l.e.43.8		96	25.13	odd	20	inner
500.2.l.e.407.7		96	1.1	even	1	trivial
500.2.l.e.407.8		96	4.3	odd	2	inner
500.2.l.f.207.1		96	100.59	odd	10
500.2.l.f.207.12		96	25.9	even	10
500.2.l.f.343.1		96	5.2	odd	4
500.2.l.f.343.12		96	20.7	even	4
900.2.bj.d.487.1		96	300.191	even	10
900.2.bj.d.487.12		96	75.41	odd	10
900.2.bj.d.523.1		96	15.8	even	4
900.2.bj.d.523.12		96	60.23	odd	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)

\(f(q)\)	\(=\)	\(q+(-0.343057 + 1.37197i) q^{2} +(-0.170251 + 0.0867473i) q^{3} +(-1.76462 - 0.941330i) q^{4} +(-0.0606092 - 0.263339i) q^{6} +(1.89427 - 1.89427i) q^{7} +(1.89685 - 2.09809i) q^{8} +(-1.74190 + 2.39751i) q^{9} +O(q^{10})\)	\(q+(-0.343057 + 1.37197i) q^{2} +(-0.170251 + 0.0867473i) q^{3} +(-1.76462 - 0.941330i) q^{4} +(-0.0606092 - 0.263339i) q^{6} +(1.89427 - 1.89427i) q^{7} +(1.89685 - 2.09809i) q^{8} +(-1.74190 + 2.39751i) q^{9} +(-2.99934 - 4.12824i) q^{11} +(0.382087 + 0.00718616i) q^{12} +(2.73586 - 0.433317i) q^{13} +(1.94904 + 3.24872i) q^{14} +(2.22780 + 3.32219i) q^{16} +(2.12318 - 4.16697i) q^{17} +(-2.69176 - 3.21232i) q^{18} +(-1.55045 - 4.77181i) q^{19} +(-0.158179 + 0.486824i) q^{21} +(6.69278 - 2.69880i) 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} +(-5.12580 + 1.55954i) q^{28} +(0.211843 + 0.0688321i) q^{29} +(7.01920 - 2.28068i) q^{31} +(-5.32221 + 1.91678i) q^{32} +(0.868756 + 0.442653i) q^{33} +(4.98861 + 4.34246i) q^{34} +(5.33064 - 2.59101i) q^{36} +(0.684516 + 4.32186i) q^{37} +(7.07869 - 0.490182i) q^{38} +(-0.428194 + 0.311101i) q^{39} +(2.54404 + 1.84835i) q^{41} +(-0.613645 - 0.384025i) q^{42} +(2.68807 + 2.68807i) q^{43} +(1.40668 + 10.1082i) q^{44} +(-2.47629 + 5.82283i) q^{46} +(-3.99829 - 7.84709i) q^{47} +(-0.667476 - 0.372351i) q^{48} -0.176489i q^{49} +0.893612i q^{51} +(-5.23565 - 1.81070i) q^{52} +(-0.837124 - 1.64295i) q^{53} +(1.48295 + 0.630658i) q^{54} +(-0.381206 - 7.56747i) q^{56} +(0.677908 + 0.677908i) q^{57} +(-0.167110 + 0.267030i) q^{58} +(-7.33328 - 5.32794i) q^{59} +(1.16375 - 0.845512i) q^{61} +(0.721044 + 10.4126i) q^{62} +(1.24191 + 7.84114i) q^{63} +(-0.803948 - 7.95950i) q^{64} +(-0.905341 + 1.04005i) q^{66} +(3.01313 + 1.53527i) q^{67} +(-7.66911 + 5.35453i) q^{68} +(-0.813081 + 0.264186i) q^{69} +(-5.45415 - 1.77216i) q^{71} +(1.72609 + 8.20236i) 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} +(-0.279928 - 0.694196i) q^{78} +(-2.08434 + 6.41493i) q^{79} +(-2.68002 - 8.24826i) q^{81} +(-3.40864 + 2.85627i) q^{82} +(1.52629 - 2.99552i) q^{83} +(0.737387 - 0.710162i) q^{84} +(-4.61012 + 2.76580i) q^{86} +(-0.0420376 + 0.00665810i) q^{87} +(-14.3507 - 1.53775i) q^{88} +(0.509284 + 0.700969i) q^{89} +(4.36162 - 6.00326i) q^{91} +(-7.13927 - 5.39497i) q^{92} +(-0.997185 + 0.997185i) q^{93} +(12.1376 - 2.79355i) q^{94} +(0.739838 - 0.788022i) q^{96} +(9.96296 - 5.07638i) q^{97} +(0.242139 + 0.0605458i) q^{98} +15.1221 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 10 q^{4} - 6 q^{6} + 30 q^{8} + 20 q^{9}+O(q^{10}) \) 96 * q + 10 * q^4 - 6 * q^6 + 30 * q^8 + 20 * q^9	\( 96 q + 10 q^{4} - 6 q^{6} + 30 q^{8} + 20 q^{9} + 10 q^{14} - 14 q^{16} + 20 q^{18} - 12 q^{21} - 50 q^{22} - 12 q^{26} - 40 q^{28} + 20 q^{29} - 50 q^{32} + 60 q^{34} - 10 q^{36} - 40 q^{37} + 70 q^{38} - 28 q^{41} + 60 q^{42} - 60 q^{44} - 6 q^{46} - 100 q^{52} - 80 q^{53} - 120 q^{54} - 6 q^{56} - 20 q^{57} - 120 q^{58} + 12 q^{61} - 20 q^{64} - 30 q^{66} - 10 q^{68} + 20 q^{69} + 150 q^{72} + 140 q^{77} + 130 q^{78} - 36 q^{81} - 50 q^{82} + 90 q^{84} - 6 q^{86} - 110 q^{88} - 160 q^{89} - 90 q^{92} + 60 q^{93} + 170 q^{94} + 14 q^{96} - 70 q^{98}+O(q^{100}) \) 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

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