LMFDB - Embedded newform 500.2.l.d.43.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("500.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			43.6
Character	$\chi$	$=$	500.43
Dual form			500.2.l.d.407.6

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

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

Coefficient data

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

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

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

$2$	0.343057	+	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	$-0.332433\pi$
$3$	0.170251	+	0.0867473i	0.0982946	+	0.0500836i	−0.404152	+	0.914692i	$0.632433\pi$
$4$	−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	$-0.418974\pi$
$7$	−1.89427	−	1.89427i	−0.715965	−	0.715965i	−0.967776	+	0.251811i	$0.918974\pi$
$8$	−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	0.0647283	+	0.997903i	$0.479382\pi$
$11$	−2.99934	+	4.12824i	−0.904336	+	1.24471i	−0.969064	+	0.246809i	$0.920618\pi$
$12$	−0.382087	+	0.00718616i	−0.110299	+	0.00207446i
$13$	−2.73586	−	0.433317i	−0.758790	−	0.120181i	−0.234962	−	0.972005i	$-0.575497\pi$
$13$	−2.73586	−	0.433317i	−0.758790	−	0.120181i	−0.523828	+	0.851824i	$0.675497\pi$
$14$	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	−0.991329	−	0.131402i	$-0.958052\pi$
$17$	−2.12318	−	4.16697i	−0.514947	−	1.01064i	0.476383	−	0.879238i	$-0.341948\pi$
$18$	2.69176	−	3.21232i	0.634453	−	0.757151i
$19$	−1.55045	+	4.77181i	−0.355699	+	1.09473i	0.599905	+	0.800072i	$0.295205\pi$
$19$	−1.55045	+	4.77181i	−0.355699	+	1.09473i	−0.955603	+	0.294657i	$0.904795\pi$
$20$		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	$-0.704475\pi$
$23$	−4.41914	+	0.699923i	−0.921455	+	0.145944i	−0.322355	+	0.946619i	$0.604475\pi$
$24$	−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	−0.289282	−	0.957244i	$-0.593416\pi$
$29$	0.211843	−	0.0688321i	0.0393383	−	0.0127818i	0.328620	+	0.944462i	$0.393416\pi$
$30$		0			0
$31$	7.01920	+	2.28068i	1.26069	+	0.409622i	0.861739	−	0.507352i	$-0.169376\pi$
$31$	7.01920	+	2.28068i	1.26069	+	0.409622i	0.398947	+	0.916974i	$0.369376\pi$
$32$	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	0.865320	+	0.501220i	$0.167115\pi$
$37$	−0.684516	+	4.32186i	−0.112534	+	0.710510i	−0.977854	+	0.209290i	$0.932885\pi$
$38$	−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	−0.371133	−	0.928580i	$-0.621031\pi$
$41$	2.54404	−	1.84835i	0.397312	−	0.288664i	0.768445	+	0.639915i	$0.221031\pi$
$42$	0.613645	−	0.384025i	0.0946875	−	0.0592564i
$43$	−2.68807	+	2.68807i	−0.409927	+	0.409927i	−0.881713	−	0.471786i	$-0.843609\pi$
$43$	−2.68807	+	2.68807i	−0.409927	+	0.409927i	0.471786	+	0.881713i	$0.343609\pi$
$44$	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	−0.391298	−	0.920264i	$-0.627974\pi$
$47$	3.99829	−	7.84709i	0.583211	−	1.14462i	0.974508	−	0.224351i	$-0.0720263\pi$
$48$	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	$-0.809580\pi$
$53$	0.837124	−	1.64295i	0.114988	−	0.225676i	0.941327	+	0.337497i	$0.109580\pi$
$54$	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	−0.951917	−	0.306357i	$-0.900890\pi$
$59$	−7.33328	+	5.32794i	−0.954712	+	0.693639i	−0.00279513	+	0.999996i	$0.500890\pi$
$60$		0			0
$61$	1.16375	+	0.845512i	0.149003	+	0.108257i	0.659789	−	0.751451i	$-0.270646\pi$
$61$	1.16375	+	0.845512i	0.149003	+	0.108257i	−0.510786	+	0.859708i	$0.670646\pi$
$62$	−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	$-0.716231\pi$
$67$	−3.01313	+	1.53527i	−0.368113	+	0.187563i	0.260142	+	0.965570i	$0.416231\pi$
$68$	7.66911	+	5.35453i	0.930016	+	0.649332i
$69$	−0.813081	−	0.264186i	−0.0978834	−	0.0318043i
$70$		0			0
$71$	−5.45415	+	1.77216i	−0.647288	+	0.210317i	−0.614218	−	0.789136i	$-0.710529\pi$
$71$	−5.45415	+	1.77216i	−0.647288	+	0.210317i	−0.0330703	+	0.999453i	$0.510529\pi$
$72$	−1.72609	+	8.20236i	−0.203421	+	0.966658i
$73$	0.00296414	+	0.0187149i	0.000346927	+	0.00219041i	0.987861	−	0.155339i	$-0.0496470\pi$
$73$	0.00296414	+	0.0187149i	0.000346927	+	0.00219041i	−0.987514	+	0.157530i	$0.949647\pi$
$74$	−6.16431	+	0.543507i	−0.716586	+	0.0631814i
$75$		0			0
$76$	−1.75588	−	9.87994i	−0.201413	−	1.13331i
$77$	13.5015	−	2.13843i	1.53864	−	0.243697i
$78$	0.279928	−	0.694196i	0.0316956	−	0.0786022i
$79$	−2.08434	−	6.41493i	−0.234506	−	0.721736i	−0.997187	−	0.0749601i	$-0.976117\pi$
$79$	−2.08434	−	6.41493i	−0.234506	−	0.721736i	0.762680	−	0.646776i	$-0.223883\pi$
$80$		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	$-0.209070\pi$
$83$	−1.52629	−	2.99552i	−0.167532	−	0.328801i	−0.959475	+	0.281795i	$0.909070\pi$
$84$	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	−0.781172	−	0.624316i	$-0.785378\pi$
$89$	0.509284	−	0.700969i	0.0539840	−	0.0743026i	0.835156	+	0.550014i	$0.185378\pi$
$90$		0			0
$91$	4.36162	+	6.00326i	0.457222	+	0.629313i
$92$	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	$-0.542153\pi$
$97$	−9.96296	−	5.07638i	−1.01158	−	0.515428i	−0.879545	+	0.475816i	$0.842153\pi$
$98$	−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	$-0.319528\pi$
$103$	1.72871	+	0.880821i	0.170335	+	0.0867899i	−0.366744	+	0.930322i	$0.619528\pi$
$104$	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	$-0.436727\pi$
$107$	−8.09772	−	8.09772i	−0.782836	−	0.782836i	−0.980308	+	0.197472i	$0.936727\pi$
$108$	1.37398	+	1.81822i	0.132211	+	0.174958i
$109$	9.13259	+	12.5699i	0.874743	+	1.20398i	0.977849	+	0.209310i	$0.0671219\pi$
$109$	9.13259	+	12.5699i	0.874743	+	1.20398i	−0.103106	+	0.994670i	$0.532878\pi$
$110$		0			0
$111$	−0.491450	+	0.676422i	−0.0466463	+	0.0642032i
$112$	−10.5131	+	2.07307i	−0.993399	+	0.195887i
$113$	8.00964	+	1.26860i	0.753483	+	0.119340i	0.521349	−	0.853344i	$-0.325429\pi$
$113$	8.00964	+	1.26860i	0.753483	+	0.119340i	0.232135	+	0.972684i	$0.425429\pi$
$114$	−1.16263	−	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	0.804755	+	0.593608i	$0.202297\pi$
$127$	2.51108	+	15.8543i	0.222822	+	1.40684i	−0.581932	+	0.813237i	$0.697703\pi$
$128$	−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	−0.316878	−	0.948466i	$-0.602635\pi$
$131$	−12.9418	−	4.20505i	−1.13073	−	0.367397i	−0.813854	+	0.581069i	$0.802635\pi$
$132$	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	0.456790	+	0.889575i	$0.348999\pi$
$137$	−2.95587	+	18.6626i	−0.252537	+	1.59445i	−0.709327	+	0.704880i	$0.751001\pi$
$138$	0.0835233	−	1.20616i	0.00710998	−	0.102675i
$139$	−5.89560	−	4.28340i	−0.500058	−	0.363313i	0.308981	−	0.951068i	$-0.400012\pi$
$139$	−5.89560	−	4.28340i	−0.500058	−	0.363313i	−0.809039	+	0.587755i	$0.800012\pi$
$140$		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	$0.0277879\pi$
$149$			2.12851i			0.174375i	−0.996192	+	0.0871873i	$0.972212\pi$
$150$		0			0
$151$		−	6.10369i		−	0.496712i	−0.968669	−	0.248356i	$-0.920110\pi$
$151$		−	6.10369i		−	0.496712i	0.968669	−	0.248356i	$-0.0798902\pi$
$152$	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	$-0.525662\pi$
$157$	11.4802	−	11.4802i	0.916218	−	0.916218i	0.996752	+	0.0805335i	$0.0256624\pi$
$158$	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	−0.890620	−	0.454748i	$-0.849729\pi$
$163$	1.23758	−	7.81379i	0.0969349	−	0.612023i	0.987555	−	0.157275i	$-0.0502708\pi$
$164$	−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	$-0.825164\pi$
$167$	−12.0426	+	6.13600i	−0.931883	+	0.474818i	−0.0789735	+	0.996877i	$0.525164\pi$
$168$	−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	$-0.0632768\pi$
$173$	−0.171594	−	1.08340i	−0.0130460	−	0.0823695i	−0.993352	+	0.115114i	$0.963277\pi$
$174$	0.00528654	+	0.0599586i	0.000400772	+	0.00454545i
$175$		0			0
$176$	7.03287	+	19.1613i	0.530122	+	1.44433i
$177$	−1.71068	+	0.270946i	−0.128583	+	0.0203655i
$178$	1.13642	+	0.458252i	0.0851786	+	0.0343474i
$179$	−7.45601	−	22.9472i	−0.557289	−	1.71516i	−0.689822	−	0.723979i	$-0.742311\pi$
$179$	−7.45601	−	22.9472i	−0.557289	−	1.71516i	0.132533	−	0.991179i	$-0.457689\pi$
$180$		0			0
$181$	−2.15964	+	6.64670i	−0.160525	+	0.494045i	−0.998679	−	0.0513890i	$-0.983635\pi$
$181$	−2.15964	+	6.64670i	−0.160525	+	0.494045i	0.838154	+	0.545434i	$0.183635\pi$
$182$	−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	0.329369	−	0.944201i	$-0.393164\pi$
$191$	−9.26511	−	12.7523i	−0.670400	−	0.922727i	−0.999769	+	0.0214746i	$0.993164\pi$
$192$	−0.827339	+	1.28537i	−0.0597080	+	0.0927639i
$193$	−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
$197$	−5.09406	−	2.59555i	−0.362936	−	0.184925i	0.263007	−	0.964794i	$-0.415286\pi$
$197$	−5.09406	−	2.59555i	−0.362936	−	0.184925i	−0.625943	+	0.779869i	$0.715286\pi$
$198$	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	−0.188886	−	0.981999i	$-0.560488\pi$
$211$	11.6703	−	16.0628i	0.803419	−	1.10581i	0.992306	−	0.123813i	$-0.0395122\pi$
$212$	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	$-0.423327\pi$
$223$	11.4317	−	1.81060i	0.765524	−	0.121247i	0.526972	+	0.849883i	$0.323327\pi$
$224$	−6.45080	−	13.7126i	−0.431012	−	0.916210i
$225$		0			0
$226$	1.00727	+	11.4242i	0.0670028	+	0.759928i
$227$	2.42897	+	15.3359i	0.161216	+	1.01788i	0.927077	+	0.374872i	$0.122313\pi$
$227$	2.42897	+	15.3359i	0.161216	+	1.01788i	−0.765861	+	0.643007i	$0.777687\pi$
$228$	0.558118	−	1.83439i	0.0369623	−	0.121485i
$229$	16.0312	−	5.20884i	1.05937	−	0.344210i	0.273030	−	0.962006i	$-0.411974\pi$
$229$	16.0312	−	5.20884i	1.05937	−	0.344210i	0.786339	+	0.617796i	$0.211974\pi$
$230$		0			0
$231$	2.48416	+	0.807152i	0.163446	+	0.0531067i
$232$	−0.546250	−	0.313902i	−0.0358631	−	0.0206087i
$233$	−26.0233	+	13.2595i	−1.70484	+	0.868660i	−0.720267	+	0.693697i	$0.755981\pi$
$233$	−26.0233	+	13.2595i	−1.70484	+	0.868660i	−0.984575	+	0.174963i	$0.944019\pi$
$234$	−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	0.599687	−	0.800235i	$-0.295292\pi$
$239$	0.369981	+	0.268807i	0.0239321	+	0.0173877i	−0.575755	+	0.817622i	$0.695292\pi$
$240$		0			0
$241$	17.6697	−	12.8378i	1.13820	−	0.826953i	0.151335	−	0.988483i	$-0.451643\pi$
$241$	17.6697	−	12.8378i	1.13820	−	0.826953i	0.986868	+	0.161530i	$0.0516429\pi$
$242$	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	$0.0547436\pi$
$251$			5.42259i			0.342271i	−0.985248	+	0.171135i	$0.945256\pi$
$252$	−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	$-0.865121\pi$
$257$	−8.02192	+	8.02192i	−0.500394	+	0.500394i	0.411166	+	0.911560i	$0.365121\pi$
$258$	−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	−0.684275	−	0.729224i	$-0.739881\pi$
$263$	3.11132	−	19.6441i	0.191852	−	1.21131i	0.876127	−	0.482081i	$-0.160119\pi$
$264$	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	0.587717	−	0.809067i	$-0.300027\pi$
$269$	9.63789	+	3.13154i	0.587633	+	0.190933i	−8.44003e−5		1.00000i	$0.500027\pi$
$270$		0			0
$271$	−1.79674	+	0.583795i	−0.109144	+	0.0354630i	−0.363080	−	0.931758i	$-0.618275\pi$
$271$	−1.79674	+	0.583795i	−0.109144	+	0.0354630i	0.253936	+	0.967221i	$0.418275\pi$
$272$	−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	$-0.661775\pi$
$277$	−11.3089	+	1.79116i	−0.679488	+	0.107620i	−0.192855	+	0.981227i	$0.561775\pi$
$278$	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	−0.473908	−	0.880574i	$-0.657157\pi$
$281$	7.15917	−	22.0337i	0.427080	−	1.31442i	0.900988	−	0.433844i	$-0.142843\pi$
$282$	1.82411	+	1.52851i	0.108624	+	0.0910217i
$283$	8.65065	+	16.9779i	0.514228	+	1.00923i	0.991455	+	0.130449i	$0.0416420\pi$
$283$	8.65065	+	16.9779i	0.514228	+	1.00923i	−0.477227	+	0.878780i	$0.658358\pi$
$284$	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	$-0.125474\pi$
$293$	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
$297$	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	$-0.370692\pi$
$307$	−9.17187	−	9.17187i	−0.523466	−	0.523466i	−0.918616	+	0.395150i	$0.870692\pi$
$308$	−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	−0.872726	−	0.488209i	$-0.837650\pi$
$311$	−2.44643	+	3.36722i	−0.138724	+	0.190938i	0.734002	+	0.679147i	$0.237650\pi$
$312$	0.159501	+	1.48850i	0.00902994	+	0.0842697i
$313$	−22.1282	−	3.50477i	−1.25076	−	0.198101i	−0.504300	−	0.863529i	$-0.668249\pi$
$313$	−22.1282	−	3.50477i	−1.25076	−	0.198101i	−0.746462	+	0.665427i	$0.768249\pi$
$314$	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	$-0.0933905\pi$
$317$	2.85992	+	5.61291i	0.160629	+	0.315252i	−0.796639	+	0.604456i	$0.793391\pi$
$318$	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	−0.146835	−	0.989161i	$-0.546909\pi$
$331$	−15.4106	−	5.00720i	−0.847042	−	0.275221i	−0.700206	+	0.713940i	$0.746909\pi$
$332$	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	−0.738174	−	0.674610i	$-0.764312\pi$
$337$	3.16369	−	19.9748i	0.172337	−	1.08809i	0.910511	−	0.413484i	$-0.135688\pi$
$338$	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	$-0.899736\pi$
$347$	−2.63206	+	5.16571i	−0.141296	+	0.277310i	0.809504	+	0.587115i	$0.199736\pi$
$348$	−0.0804480	+	0.0278222i	−0.00431247	+	0.00149143i
$349$			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
$352$	−23.8761	+	16.2223i	−1.27260	+	0.864652i
$353$	−1.86927	+	3.66865i	−0.0994913	+	0.195263i	−0.935387	−	0.353626i	$-0.884949\pi$
$353$	−1.86927	+	3.66865i	−0.0994913	+	0.195263i	0.835896	+	0.548888i	$0.184949\pi$
$354$	−0.958592	−	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	−0.992159	−	0.124985i	$-0.960112\pi$
$359$	−22.3556	+	16.2423i	−1.17989	+	0.857237i	−0.187726	+	0.982221i	$0.560112\pi$
$360$		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	$-0.706699\pi$
$367$	−6.04885	+	3.08204i	−0.315747	+	0.160881i	0.288934	+	0.957349i	$0.406699\pi$
$368$	−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	0.989523	+	0.144376i	$0.0461176\pi$
$373$	1.79701	+	11.3458i	0.0930454	+	0.587466i	−0.896477	+	0.443089i	$0.853882\pi$
$374$	2.96416	+	33.6187i	0.153273	+	1.73838i
$375$		0			0
$376$	−24.0480	+	6.49595i	−1.24018	+	0.335003i
$377$	−0.609399	+	0.0965194i	−0.0313857	+	0.00497100i
$378$	−4.00373	−	1.61447i	−0.205930	−	0.0830391i
$379$	3.95657	+	12.1771i	0.203235	+	0.625494i	0.999781	+	0.0209157i	$0.00665816\pi$
$379$	3.95657	+	12.1771i	0.203235	+	0.625494i	−0.796546	+	0.604578i	$0.793342\pi$
$380$		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	−0.999818	−	0.0190788i	$-0.993927\pi$
$383$	−8.36780	−	16.4227i	−0.427575	−	0.839163i	0.572243	−	0.820084i	$-0.306073\pi$
$384$	−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	−0.257287	−	0.966335i	$-0.582829\pi$
$389$	14.6199	−	20.1226i	0.741258	−	1.02025i	0.998545	−	0.0539190i	$-0.0171713\pi$
$390$		0			0
$391$	12.2992	+	16.9284i	0.621997	+	0.856105i
$392$	0.370290	−	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	$-0.103680\pi$
$397$	24.8148	+	12.6438i	1.24542	+	0.634574i	0.298001	+	0.954566i	$0.403680\pi$
$398$	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	0.972641	−	0.232313i	$-0.0746294\pi$
$409$	9.12365	+	12.5576i	0.451136	+	0.620935i	−0.521505	+	0.853248i	$0.674629\pi$
$410$		0			0
$411$	−2.12217	+	2.92092i	−0.104679	+	0.144078i
$412$	−3.87966	+	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	0.175838	+	0.984419i	$0.443736\pi$
$419$	−11.1568	+	34.3371i	−0.545045	+	1.67748i	−0.720883	+	0.693056i	$0.756264\pi$
$420$		0			0
$421$	4.95128	+	15.2385i	0.241311	+	0.742678i	0.996221	+	0.0868504i	$0.0276802\pi$
$421$	4.95128	+	15.2385i	0.241311	+	0.742678i	−0.754911	+	0.655828i	$0.772320\pi$
$422$	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	0.459252	−	0.888306i	$-0.348118\pi$
$431$	6.40797	+	2.08208i	0.308661	+	0.100290i	−0.150591	+	0.988596i	$0.548118\pi$
$432$	−4.13610	−	1.91510i	−0.198998	−	0.0921401i
$433$	9.39790	−	4.78847i	0.451634	−	0.230119i	−0.213351	−	0.976976i	$-0.568438\pi$
$433$	9.39790	−	4.78847i	0.451634	−	0.230119i	0.664985	+	0.746857i	$0.268438\pi$
$434$	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	0.366960	−	0.930237i	$-0.380398\pi$
$439$	−8.47207	−	6.15532i	−0.404350	−	0.293778i	−0.771311	+	0.636459i	$0.780398\pi$
$440$		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	$-0.714947\pi$
$443$	3.27124	−	3.27124i	0.155421	−	0.155421i	0.780534	+	0.625113i	$0.214947\pi$
$444$	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	$0.140406\pi$
$449$			18.0931i			0.853868i	−0.904283	+	0.426934i	$0.859594\pi$
$450$		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	−0.102764	+	0.994706i	$0.532769\pi$
$457$	−23.4612	+	23.4612i	−1.09747	+	1.09747i	−0.994706	+	0.102764i	$0.967231\pi$
$458$	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	−0.223275	−	0.974755i	$-0.571675\pi$
$461$	−26.1799	−	19.0208i	−1.21932	−	0.885887i	−0.996043	+	0.0888686i	$0.971675\pi$
$462$	−0.255184	+	3.68510i	−0.0118722	+	0.171446i
$463$	−4.79718	+	30.2882i	−0.222944	+	1.40761i	0.581481	+	0.813560i	$0.302473\pi$
$463$	−4.79718	+	30.2882i	−0.222944	+	1.40761i	−0.804425	+	0.594054i	$0.797527\pi$
$464$	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	$-0.767444\pi$
$467$	−13.8884	+	7.07648i	−0.642677	+	0.327460i	0.102100	+	0.994774i	$0.467444\pi$
$468$	−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	0.988112	−	0.153734i	$-0.0491300\pi$
$479$	2.15249	+	6.62469i	0.0983498	+	0.302690i	−0.889762	+	0.456424i	$0.849130\pi$
$480$		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	$-0.293361\pi$
$487$	20.5964	+	3.26215i	0.933313	+	0.147822i	0.328784	+	0.944405i	$0.393361\pi$
$488$	−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	0.738763	−	0.673965i	$-0.235410\pi$
$491$	−2.89183	−	3.98026i	−0.130506	−	0.179627i	−0.869269	+	0.494339i	$0.835410\pi$
$492$	−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	$-0.140188\pi$
$503$	24.4770	+	12.4717i	1.09138	+	0.556084i	0.186801	+	0.982398i	$0.440188\pi$
$504$	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	0.949204	−	0.314663i	$-0.101891\pi$
$509$	8.04575	+	11.0740i	0.356622	+	0.490847i	−0.592582	+	0.805510i	$0.701891\pi$
$510$		0			0
$511$	0.0298360	−	0.0410658i	0.00131987	−	0.00181664i
$512$	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	0.977211	−	0.212270i	$-0.0680855\pi$
$521$	1.41202	+	4.34576i	0.0618618	+	0.190391i	−0.915349	+	0.402661i	$0.868085\pi$
$522$	0.349120	−	0.865787i	0.0152806	−	0.0378945i
$523$	−35.8180	+	5.67302i	−1.56621	+	0.248064i	−0.878437	−	0.477859i	$-0.841413\pi$
$523$	−35.8180	+	5.67302i	−1.56621	+	0.248064i	−0.687776	+	0.725923i	$0.741413\pi$
$524$	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	−0.965973	−	0.258644i	$-0.916724\pi$
$541$	−23.6895	+	17.2114i	−1.01849	+	0.739976i	−0.0525174	+	0.998620i	$0.516724\pi$
$542$	−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	−0.251429	−	0.967876i	$-0.580900\pi$
$547$	15.8895	−	31.1849i	0.679385	−	1.33337i	0.930814	−	0.365493i	$-0.119100\pi$
$548$	−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	0.0675692	−	0.997715i	$-0.478476\pi$
$557$	25.1416	−	25.1416i	1.06528	−	1.06528i	0.997715	−	0.0675692i	$-0.0215243\pi$
$558$	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	0.711674	+	0.702510i	$0.247937\pi$
$563$	−4.32450	+	27.3038i	−0.182256	+	1.15072i	−0.893929	+	0.448208i	$0.852063\pi$
$564$	−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	0.119308	−	0.992857i	$-0.461932\pi$
$569$	−8.77237	−	2.85032i	−0.367757	−	0.119491i	−0.487065	+	0.873366i	$0.661932\pi$
$570$		0			0
$571$	−17.2235	+	5.59625i	−0.720780	+	0.234196i	−0.646362	−	0.763031i	$-0.723710\pi$
$571$	−17.2235	+	5.59625i	−0.720780	+	0.234196i	−0.0744189	+	0.997227i	$0.523710\pi$
$572$	−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	$-0.623637\pi$
$577$	−10.8794	+	1.72312i	−0.452914	+	0.0717345i	−0.0741898	+	0.997244i	$0.523637\pi$
$578$	−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	$-0.868028\pi$
$587$	−46.2814	−	7.33025i	−1.91024	−	0.302552i	−0.994960	+	0.100273i	$0.968028\pi$
$588$	−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	$-0.141392\pi$
$593$	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
$597$	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	$-0.282873\pi$
$607$	−3.59194	−	3.59194i	−0.145792	−	0.145792i	−0.776235	+	0.630443i	$0.782873\pi$
$608$	−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	$-0.417544\pi$
$613$	4.97817	+	0.788465i	0.201066	+	0.0318458i	−0.0550888	+	0.998481i	$0.517544\pi$
$614$	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	$-0.272075\pi$
$617$	−8.43913	−	16.5627i	−0.339746	−	0.666790i	−0.996154	+	0.0876162i	$0.972075\pi$
$618$	−0.336731	+	0.401851i	−0.0135453	+	0.0161648i
$619$	6.54265	−	20.1362i	0.262971	−	0.809343i	−0.729182	−	0.684320i	$-0.760099\pi$
$619$	6.54265	−	20.1362i	0.262971	−	0.809343i	0.992154	−	0.125024i	$-0.0399006\pi$
$620$		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	0.372555	−	0.928010i	$-0.378482\pi$
$631$	3.22756	+	1.04870i	0.128487	+	0.0417480i	−0.244068	+	0.969758i	$0.578482\pi$
$632$	−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	0.229425	−	0.973326i	$-0.426315\pi$
$641$	31.0401	−	22.5519i	1.22601	−	0.890748i	0.996585	+	0.0825780i	$0.0263153\pi$
$642$	2.62325	−	1.64165i	0.103531	−	0.0647909i
$643$	6.79295	−	6.79295i	0.267888	−	0.267888i	−0.560361	−	0.828249i	$-0.689338\pi$
$643$	6.79295	−	6.79295i	0.267888	−	0.267888i	0.828249	+	0.560361i	$0.189338\pi$
$644$	−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	0.358793	+	0.933417i	$0.383188\pi$
$647$	−15.4461	+	30.3148i	−0.607251	+	1.19180i	−0.966044	+	0.258379i	$0.916812\pi$
$648$	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	$-0.810018\pi$
$653$	2.90673	−	5.70477i	0.113749	−	0.223245i	0.940862	+	0.338791i	$0.110018\pi$
$654$	−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	−0.790015	−	0.613087i	$-0.789927\pi$
$659$	−11.5792	+	8.41281i	−0.451063	+	0.327716i	0.338952	+	0.940804i	$0.389927\pi$
$660$		0			0
$661$	−0.382235	−	0.277710i	−0.0148672	−	0.0108017i	0.580327	−	0.814384i	$-0.302925\pi$
$661$	−0.382235	−	0.277710i	−0.0148672	−	0.0108017i	−0.595194	+	0.803582i	$0.702925\pi$
$662$	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	0.964038	+	0.265764i	$0.0856241\pi$
$673$	3.35456	+	21.1799i	0.129309	+	0.816424i	−0.834729	+	0.550660i	$0.814376\pi$
$674$	28.4902	−	2.51198i	1.09740	−	0.0967578i
$675$		0			0
$676$	10.4903	−	1.86434i	0.403471	−	0.0717055i
$677$	−43.8961	+	6.95245i	−1.68706	+	0.267204i	−0.924908	−	0.380191i	$-0.875858\pi$
$677$	−43.8961	+	6.95245i	−1.68706	+	0.267204i	−0.762155	+	0.647395i	$0.775858\pi$
$678$	−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	−0.999867	−	0.0163335i	$-0.994801\pi$
$683$	−11.1168	−	21.8180i	−0.425374	−	0.834843i	0.574493	−	0.818510i	$-0.305199\pi$
$684$	−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	0.954066	−	0.299596i	$-0.0968518\pi$
$691$	9.83947	+	13.5429i	0.374311	+	0.515195i	−0.579755	+	0.814791i	$0.696852\pi$
$692$	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	−0.974264	−	0.225408i	$-0.927628\pi$
$709$	−23.6335	−	32.5288i	−0.887576	−	1.22164i	0.0866885	−	0.996235i	$-0.472372\pi$
$710$		0			0
$711$	−11.7492	+	16.1714i	−0.440629	+	0.606473i
$712$	−2.43673	+	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	−0.875197	−	0.483766i	$-0.839269\pi$
$719$	3.14270	−	9.67223i	0.117203	−	0.360713i	0.992400	+	0.123053i	$0.0392685\pi$
$720$		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	0.999981	+	0.00618506i	$0.00196878\pi$
$727$	1.37117	+	8.65722i	0.0508538	+	0.321078i	−0.949127	+	0.314893i	$0.898031\pi$
$728$	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	$-0.651548\pi$
$733$	−0.234567	+	0.119518i	−0.00866394	+	0.00441450i	0.449653	+	0.893203i	$0.351548\pi$
$734$	−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	0.692235	−	0.721672i	$-0.256626\pi$
$739$	5.97506	+	4.34113i	0.219796	+	0.159691i	−0.472439	+	0.881363i	$0.656626\pi$
$740$		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	$-0.691586\pi$
$743$	7.03452	−	7.03452i	0.258071	−	0.258071i	0.824269	+	0.566198i	$0.191586\pi$
$744$	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	$-0.821134\pi$
$751$		−	29.2029i		−	1.06563i	0.846232	−	0.532814i	$-0.178866\pi$
$752$	−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	$-0.576396\pi$
$757$	20.1848	−	20.1848i	0.733630	−	0.733630i	0.971337	+	0.237707i	$0.0763959\pi$
$758$	−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	0.722215	−	0.691669i	$-0.243124\pi$
$761$	7.93313	+	5.76375i	0.287576	+	0.208936i	−0.434639	+	0.900605i	$0.643124\pi$
$762$	−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	−0.0199544	−	0.999801i	$-0.506352\pi$
$769$	−17.2976	−	5.62032i	−0.623766	−	0.202674i	−0.603812	+	0.797127i	$0.706352\pi$
$770$		0			0
$771$	−2.06162	+	0.669862i	−0.0742475	+	0.0241245i
$772$	17.4512	+	5.30959i	0.628084	+	0.191096i
$773$	−6.76671	−	42.7233i	−0.243382	−	1.53665i	−0.742339	−	0.670025i	$-0.766283\pi$
$773$	−6.76671	−	42.7233i	−0.243382	−	1.53665i	0.498957	−	0.866627i	$-0.333717\pi$
$774$	1.39931	+	15.8706i	0.0502970	+	0.570455i
$775$		0			0
$776$	8.24751	+	30.5323i	0.296068	+	1.09604i
$777$	2.21226	−	0.350388i	0.0793644	−	0.0125701i
$778$	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	$-0.519303\pi$
$787$	−11.9702	−	1.89589i	−0.426691	−	0.0675813i	−0.366087	+	0.930581i	$0.619303\pi$
$788$	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	$-0.444190\pi$
$797$	−14.6702	−	7.47486i	−0.519646	−	0.264773i	−0.694083	+	0.719895i	$0.744190\pi$
$798$	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	0.528782	−	0.848757i	$-0.322649\pi$
$809$	−12.5671	−	17.2972i	−0.441837	−	0.608136i	−0.970619	+	0.240621i	$0.922649\pi$
$810$		0			0
$811$	18.5355	−	25.5120i	0.650871	−	0.895847i	−0.348265	−	0.937396i	$-0.613229\pi$
$811$	18.5355	−	25.5120i	0.650871	−	0.895847i	0.999136	+	0.0415488i	$0.0132292\pi$
$812$	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	−0.998989	−	0.0449507i	$-0.985687\pi$
$821$	−6.22378	−	19.1548i	−0.217211	−	0.668508i	0.781778	−	0.623557i	$-0.214313\pi$
$822$	−4.73545	−	1.90952i	−0.165168	−	0.0666023i
$823$	41.6729	−	6.60034i	1.45263	−	0.230073i	0.620302	−	0.784363i	$-0.287010\pi$
$823$	41.6729	−	6.60034i	1.45263	−	0.230073i	0.832324	+	0.554289i	$0.187010\pi$
$824$	−1.43105	−	5.29776i	−0.0498531	−	0.184556i
$825$		0			0
$826$	3.01613	+	34.2082i	0.104945	+	1.19026i
$827$	−2.15397	−	13.5996i	−0.0749008	−	0.472905i	−0.996418	−	0.0845669i	$-0.973049\pi$
$827$	−2.15397	−	13.5996i	−0.0749008	−	0.472905i	0.921517	−	0.388338i	$-0.126951\pi$
$828$	−25.3704	−	7.71901i	−0.881682	−	0.268254i
$829$	−35.5980	+	11.5665i	−1.23637	+	0.401721i	−0.853018	−	0.521881i	$-0.825230\pi$
$829$	−35.5980	+	11.5665i	−1.23637	+	0.401721i	−0.383352	+	0.923602i	$0.625230\pi$
$830$		0			0
$831$	−2.08074	−	0.676072i	−0.0721800	−	0.0234527i
$832$	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	0.469291	−	0.883044i	$-0.344509\pi$
$839$	−6.53213	−	4.74587i	−0.225514	−	0.163846i	−0.694805	+	0.719198i	$0.744509\pi$
$840$		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	0.443652	+	0.896199i	$0.353683\pi$
$853$	−15.8344	+	31.0768i	−0.542160	+	1.06405i	−0.985812	+	0.167851i	$0.946317\pi$
$854$	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	$0.971514\pi$
$858$	2.02621	+	3.23774i	0.0691737	+	0.110535i
$859$	34.2690	−	24.8979i	1.16924	−	0.849504i	0.178324	−	0.983972i	$-0.442932\pi$
$859$	34.2690	−	24.8979i	1.16924	−	0.849504i	0.990918	+	0.134468i	$0.0429325\pi$
$860$		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	−0.902714	−	0.430242i	$-0.858428\pi$
$863$	2.60778	−	16.4649i	0.0887700	−	0.560472i	0.991484	−	0.130230i	$-0.0415716\pi$
$864$	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	$-0.469282\pi$
$877$	14.6759	−	2.32444i	0.495571	−	0.0784907i	0.399217	+	0.916856i	$0.369282\pi$
$878$	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	0.284177	+	0.958772i	$0.408280\pi$
$881$	−15.1162	+	46.5230i	−0.509279	+	1.56740i	−0.793456	+	0.608628i	$0.791720\pi$
$882$	0.566939	+	0.475066i	0.0190898	+	0.0159963i
$883$	0.740506	+	1.45332i	0.0249200	+	0.0489083i	0.903131	−	0.429365i	$-0.141263\pi$
$883$	0.740506	+	1.45332i	0.0249200	+	0.0489083i	−0.878211	+	0.478274i	$0.841263\pi$
$884$	−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	$-0.299930\pi$
$887$	26.7206	+	4.23212i	0.897189	+	0.142101i	0.309226	+	0.950989i	$0.399930\pi$
$888$	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	0.979629	+	0.200818i	$0.0643600\pi$
$907$	35.5508	+	35.5508i	1.18045	+	1.18045i	0.200818	+	0.979629i	$0.435640\pi$
$908$	−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	−0.861807	−	0.507236i	$-0.830667\pi$
$911$	−3.41319	+	4.69785i	−0.113084	+	0.155647i	0.748723	+	0.662883i	$0.230667\pi$
$912$	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	−0.447990	−	0.894039i	$-0.647860\pi$
$919$	13.3369	−	41.0468i	0.439944	−	1.35401i	0.887934	−	0.459971i	$-0.152140\pi$
$920$		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	−0.811829	−	0.583895i	$-0.801528\pi$
$929$	−34.3019	+	11.1453i	−1.12541	+	0.365667i	−0.313578	+	0.949562i	$0.601528\pi$
$930$		0			0
$931$	−0.842173	−	0.273639i	−0.0276011	−	0.00896814i
$932$	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	0.679252	+	0.733905i	$0.262304\pi$
$937$	−5.92447	+	37.4056i	−0.193544	+	1.22199i	−0.872796	+	0.488084i	$0.837696\pi$
$938$	−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	−0.0809965	−	0.996714i	$-0.525810\pi$
$941$	25.8261	−	18.7637i	0.841906	−	0.611680i	0.922902	+	0.385034i	$0.125810\pi$
$942$	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	$-0.868288\pi$
$947$	−1.60449	+	3.14898i	−0.0521388	+	0.102328i	0.863467	+	0.504405i	$0.168288\pi$
$948$	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	−0.0378308	−	0.999284i	$-0.512045\pi$
$953$	24.4756	−	48.0361i	0.792843	−	1.55604i	0.830674	−	0.556759i	$-0.187955\pi$
$954$	−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	$-0.730115\pi$
$967$	−13.8004	+	7.03165i	−0.443791	+	0.226123i	0.217792	+	0.975995i	$0.430115\pi$
$968$	−21.1928	+	36.8796i	−0.681163	+	1.18535i
$969$	4.26415	+	1.38551i	0.136984	+	0.0445089i
$970$		0			0
$971$	16.7721	−	5.44959i	0.538242	−	0.174886i	−0.0272659	−	0.999628i	$-0.508680\pi$
$971$	16.7721	−	5.44959i	0.538242	−	0.174886i	0.565508	+	0.824743i	$0.308680\pi$
$972$	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	$-0.230853\pi$
$977$	52.0437	−	8.24291i	1.66502	−	0.263714i	0.916687	+	0.399605i	$0.130853\pi$
$978$	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	$-0.0596999\pi$
$983$	7.96803	+	15.6381i	0.254141	+	0.498779i	−0.728323	+	0.685234i	$0.759700\pi$
$984$	−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	0.998524	−	0.0543192i	$-0.0172988\pi$
$991$	20.0939	+	27.6568i	0.638302	+	0.878548i	−0.360221	+	0.932867i	$0.617299\pi$
$992$	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	$-0.339400\pi$
$997$	1.87335	+	0.954518i	0.0593295	+	0.0302299i	−0.424074	+	0.905628i	$0.639400\pi$
$998$	−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.d.43.6		96
4.3	odd	2	inner	500.2.l.d.43.5		96
5.2	odd	4		500.2.l.f.207.1		96
5.3	odd	4		100.2.l.b.87.12	yes	96
5.4	even	2		500.2.l.e.43.7		96
15.8	even	4		900.2.bj.d.487.1		96
20.3	even	4		100.2.l.b.87.1	yes	96
20.7	even	4		500.2.l.f.207.12		96
20.19	odd	2		500.2.l.e.43.8		96
25.2	odd	20	inner	500.2.l.d.407.5		96
25.11	even	5		500.2.l.f.343.12		96
25.14	even	10		100.2.l.b.23.1	✓	96
25.23	odd	20		500.2.l.e.407.8		96
60.23	odd	4		900.2.bj.d.487.12		96
75.14	odd	10		900.2.bj.d.523.12		96
100.11	odd	10		500.2.l.f.343.1		96
100.23	even	20		500.2.l.e.407.7		96
100.27	even	20	inner	500.2.l.d.407.6		96
100.39	odd	10		100.2.l.b.23.12	yes	96
300.239	even	10		900.2.bj.d.523.1		96

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.343057 + 1.37197i) q^{2} +(0.170251 + 0.0867473i) q^{3} +(-1.76462 + 0.941330i) q^{4} +(-0.0606092 + 0.263339i) q^{6} +(-1.89427 - 1.89427i) q^{7} +(-1.89685 - 2.09809i) q^{8} +(-1.74190 - 2.39751i) q^{9} +O(q^{10})\)	\(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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