LMFDB - Embedded newform 900.2.bj.d.523.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,2,Mod(127,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 1]))

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

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

chi := DirichletCharacter("900.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.bj (of order $20$, degree $8$, 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:	$7.18653618192$
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			523.12
Character	$\chi$	$=$	900.523
Dual form			900.2.bj.d.487.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41083 + 0.0976968i) q^{2} +(1.98091 + 0.275668i) q^{4} +(1.18066 - 1.89896i) q^{5} +(1.89427 + 1.89427i) q^{7} +(2.76781 + 0.582451i) q^{8} +O(q^{10})$	\(q+(1.41083 + 0.0976968i) q^{2} +(1.98091 + 0.275668i) q^{4} +(1.18066 - 1.89896i) q^{5} +(1.89427 + 1.89427i) q^{7} +(2.76781 + 0.582451i) q^{8} +(1.85124 - 2.56377i) q^{10} +(-2.99934 - 4.12824i) q^{11} +(0.433317 + 2.73586i) q^{13} +(2.48743 + 2.85756i) q^{14} +(3.84801 + 1.09215i) q^{16} +(4.16697 + 2.12318i) q^{17} +(-1.55045 - 4.77181i) q^{19} +(2.86226 - 3.43620i) q^{20} +(-3.82826 - 6.11729i) q^{22} +(-0.699923 + 4.41914i) q^{23} +(-2.21209 - 4.48404i) q^{25} +(0.344055 + 3.90218i) q^{26} +(3.23018 + 4.27456i) q^{28} +(0.211843 + 0.0688321i) q^{29} +(-7.01920 + 2.28068i) q^{31} +(5.32221 + 1.91678i) q^{32} +(5.67148 + 3.40256i) q^{34} +(5.83362 - 1.36065i) q^{35} +(4.32186 - 0.684516i) q^{37} +(-1.72125 - 6.88371i) q^{38} +(4.37388 - 4.56828i) q^{40} +(-2.54404 - 1.84835i) q^{41} +(2.68807 - 2.68807i) q^{43} +(-4.80341 - 9.00450i) q^{44} +(-1.41921 + 6.16630i) q^{46} +(-7.84709 + 3.99829i) q^{47} +0.176489i q^{49} +(-2.68282 - 6.54236i) q^{50} +(0.104174 + 5.53894i) q^{52} +(-1.64295 + 0.837124i) q^{53} +(-11.3806 + 0.821587i) q^{55} +(4.13965 + 6.34628i) q^{56} +(0.292151 + 0.117807i) q^{58} +(7.33328 + 5.32794i) q^{59} +(1.16375 - 0.845512i) q^{61} +(-10.1258 + 2.53191i) q^{62} +(7.32150 + 3.22422i) q^{64} +(5.70688 + 2.40726i) q^{65} +(-1.53527 + 3.01313i) q^{67} +(7.66911 + 5.35453i) q^{68} +(8.36320 - 1.34973i) q^{70} +(-5.45415 - 1.77216i) q^{71} +(-0.0187149 - 0.00296414i) q^{73} +(6.16431 - 0.543507i) q^{74} +(-1.75588 - 9.87994i) q^{76} +(2.13843 - 13.5015i) q^{77} +(-2.08434 + 6.41493i) q^{79} +(6.61713 - 6.01777i) q^{80} +(-3.40864 - 2.85627i) q^{82} +(2.99552 + 1.52629i) q^{83} +(8.95160 - 5.40616i) q^{85} +(4.05504 - 3.52981i) q^{86} +(-5.89710 - 13.1731i) q^{88} +(0.509284 + 0.700969i) q^{89} +(-4.36162 + 6.00326i) q^{91} +(-2.60470 + 8.56098i) q^{92} +(-11.4616 + 4.87429i) q^{94} +(-10.8920 - 2.68963i) q^{95} +(-5.07638 - 9.96296i) q^{97} +(-0.0172424 + 0.248997i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 10 q^{2} - 10 q^{4} + 20 q^{5} + 10 q^{8}+O(q^{10}) $ 96 * q + 10 * q^2 - 10 * q^4 + 20 * q^5 + 10 * q^8	$ 96 q + 10 q^{2} - 10 q^{4} + 20 q^{5} + 10 q^{8} - 10 q^{10} - 20 q^{13} + 10 q^{14} - 14 q^{16} + 20 q^{17} - 10 q^{20} - 10 q^{22} - 20 q^{25} + 12 q^{26} - 10 q^{28} + 20 q^{29} + 50 q^{32} - 60 q^{34} + 40 q^{37} - 20 q^{38} + 40 q^{40} + 28 q^{41} - 60 q^{44} - 6 q^{46} - 80 q^{50} + 80 q^{52} + 40 q^{53} + 6 q^{56} + 60 q^{58} + 12 q^{61} - 40 q^{62} + 20 q^{64} + 100 q^{65} + 10 q^{68} - 10 q^{70} - 20 q^{73} + 20 q^{77} + 10 q^{80} - 50 q^{82} + 100 q^{85} + 6 q^{86} - 130 q^{88} - 160 q^{89} + 110 q^{92} - 170 q^{94} + 180 q^{97} + 130 q^{98}+O(q^{100}) $ 96 * q + 10 * q^2 - 10 * q^4 + 20 * q^5 + 10 * q^8 - 10 * q^10 - 20 * q^13 + 10 * q^14 - 14 * q^16 + 20 * q^17 - 10 * q^20 - 10 * q^22 - 20 * q^25 + 12 * q^26 - 10 * q^28 + 20 * q^29 + 50 * q^32 - 60 * q^34 + 40 * q^37 - 20 * q^38 + 40 * q^40 + 28 * q^41 - 60 * q^44 - 6 * q^46 - 80 * q^50 + 80 * q^52 + 40 * q^53 + 6 * q^56 + 60 * q^58 + 12 * q^61 - 40 * q^62 + 20 * q^64 + 100 * q^65 + 10 * q^68 - 10 * q^70 - 20 * q^73 + 20 * q^77 + 10 * q^80 - 50 * q^82 + 100 * q^85 + 6 * q^86 - 130 * q^88 - 160 * q^89 + 110 * q^92 - 170 * q^94 + 180 * q^97 + 130 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{20}\right)$

Coefficient data

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

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

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

$2$	1.41083	+	0.0976968i	0.997611	+	0.0690820i
$2$	1.41083	+	0.0976968i	0.997611	+	0.0690820i
$3$		0			0
$3$		0			0
$4$	1.98091	+	0.275668i	0.990455	+	0.137834i
$5$	1.18066	−	1.89896i	0.528006	−	0.849240i
$5$	1.18066	−	1.89896i	0.528006	−	0.849240i
$6$		0			0
$7$	1.89427	+	1.89427i	0.715965	+	0.715965i	0.967776	−	0.251811i	$-0.0810262\pi$
$7$	1.89427	+	1.89427i	0.715965	+	0.715965i	−0.251811	+	0.967776i	$0.581026\pi$
$8$	2.76781	+	0.582451i	0.978567	+	0.205927i
$9$		0			0
$10$	1.85124	−	2.56377i	0.585412	−	0.810736i
$11$	−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			0
$13$	0.433317	+	2.73586i	0.120181	+	0.758790i	0.972005	+	0.234962i	$0.0754966\pi$
$13$	0.433317	+	2.73586i	0.120181	+	0.758790i	−0.851824	+	0.523828i	$0.824503\pi$
$14$	2.48743	+	2.85756i	0.664795	+	0.763715i
$15$		0			0
$16$	3.84801	+	1.09215i	0.962004	+	0.273037i
$17$	4.16697	+	2.12318i	1.01064	+	0.514947i	0.879238	−	0.476383i	$-0.158052\pi$
$17$	4.16697	+	2.12318i	1.01064	+	0.514947i	0.131402	+	0.991329i	$0.458052\pi$
$18$		0			0
$19$	−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	$-0.295205\pi$
$20$	2.86226	−	3.43620i	0.640021	−	0.768357i
$21$		0			0
$22$	−3.82826	−	6.11729i	−0.816188	−	1.30421i
$23$	−0.699923	+	4.41914i	−0.145944	+	0.921455i	0.800675	+	0.599100i	$0.204475\pi$
$23$	−0.699923	+	4.41914i	−0.145944	+	0.921455i	−0.946619	+	0.322355i	$0.895525\pi$
$24$		0			0
$25$	−2.21209	−	4.48404i	−0.442418	−	0.896809i
$26$	0.344055	+	3.90218i	0.0674747	+	0.765280i
$27$		0			0
$28$	3.23018	+	4.27456i	0.610447	+	0.807816i
$29$	0.211843	+	0.0688321i	0.0393383	+	0.0127818i	0.328620	−	0.944462i	$-0.393416\pi$
$29$	0.211843	+	0.0688321i	0.0393383	+	0.0127818i	−0.289282	+	0.957244i	$0.593416\pi$
$30$		0			0
$31$	−7.01920	+	2.28068i	−1.26069	+	0.409622i	−0.861739	−	0.507352i	$-0.830624\pi$
$31$	−7.01920	+	2.28068i	−1.26069	+	0.409622i	−0.398947	+	0.916974i	$0.630624\pi$
$32$	5.32221	+	1.91678i	0.940843	+	0.338842i
$33$		0			0
$34$	5.67148	+	3.40256i	0.972652	+	0.583533i
$35$	5.83362	−	1.36065i	0.986061	−	0.229992i
$36$		0			0
$37$	4.32186	−	0.684516i	0.710510	−	0.112534i	0.209290	−	0.977854i	$-0.432885\pi$
$37$	4.32186	−	0.684516i	0.710510	−	0.112534i	0.501220	+	0.865320i	$0.332885\pi$
$38$	−1.72125	−	6.88371i	−0.279223	−	1.11669i
$39$		0			0
$40$	4.37388	−	4.56828i	0.691572	−	0.722308i
$41$	−2.54404	−	1.84835i	−0.397312	−	0.288664i	0.371133	−	0.928580i	$-0.378969\pi$
$41$	−2.54404	−	1.84835i	−0.397312	−	0.288664i	−0.768445	+	0.639915i	$0.778969\pi$
$42$		0			0
$43$	2.68807	−	2.68807i	0.409927	−	0.409927i	−0.471786	−	0.881713i	$-0.656391\pi$
$43$	2.68807	−	2.68807i	0.409927	−	0.409927i	0.881713	+	0.471786i	$0.156391\pi$
$44$	−4.80341	−	9.00450i	−0.724141	−	1.35748i
$45$		0			0
$46$	−1.41921	+	6.16630i	−0.209251	+	0.909171i
$47$	−7.84709	+	3.99829i	−1.14462	+	0.583211i	−0.920264	−	0.391298i	$-0.872026\pi$
$47$	−7.84709	+	3.99829i	−1.14462	+	0.583211i	−0.224351	+	0.974508i	$0.572026\pi$
$48$		0			0
$49$			0.176489i			0.0252127i
$50$	−2.68282	−	6.54236i	−0.379408	−	0.925229i
$51$		0			0
$52$	0.104174	+	5.53894i	0.0144464	+	0.768113i
$53$	−1.64295	+	0.837124i	−0.225676	+	0.114988i	−0.563173	−	0.826339i	$-0.690420\pi$
$53$	−1.64295	+	0.837124i	−0.225676	+	0.114988i	0.337497	+	0.941327i	$0.390420\pi$
$54$		0			0
$55$	−11.3806	+	0.821587i	−1.53455	+	0.110783i
$56$	4.13965	+	6.34628i	0.553183	+	0.848057i
$57$		0			0
$58$	0.292151	+	0.117807i	0.0383614	+	0.0154688i
$59$	7.33328	+	5.32794i	0.954712	+	0.693639i	0.951917	−	0.306357i	$-0.0991103\pi$
$59$	7.33328	+	5.32794i	0.954712	+	0.693639i	0.00279513	+	0.999996i	$0.499110\pi$
$60$		0			0
$61$	1.16375	−	0.845512i	0.149003	−	0.108257i	−0.510786	−	0.859708i	$-0.670646\pi$
$61$	1.16375	−	0.845512i	0.149003	−	0.108257i	0.659789	+	0.751451i	$0.270646\pi$
$62$	−10.1258	+	2.53191i	−1.28597	+	0.321552i
$63$		0			0
$64$	7.32150	+	3.22422i	0.915188	+	0.403028i
$65$	5.70688	+	2.40726i	0.707852	+	0.298584i
$66$		0			0
$67$	−1.53527	+	3.01313i	−0.187563	+	0.368113i	−0.965570	−	0.260142i	$-0.916231\pi$
$67$	−1.53527	+	3.01313i	−0.187563	+	0.368113i	0.778007	+	0.628255i	$0.216231\pi$
$68$	7.66911	+	5.35453i	0.930016	+	0.649332i
$69$		0			0
$70$	8.36320	−	1.34973i	0.999594	−	0.161324i
$71$	−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	$0.710529\pi$
$72$		0			0
$73$	−0.0187149	−	0.00296414i	−0.00219041	−	0.000346927i	0.155339	−	0.987861i	$-0.450353\pi$
$73$	−0.0187149	−	0.00296414i	−0.00219041	−	0.000346927i	−0.157530	+	0.987514i	$0.550353\pi$
$74$	6.16431	−	0.543507i	0.716586	−	0.0631814i
$75$		0			0
$76$	−1.75588	−	9.87994i	−0.201413	−	1.13331i
$77$	2.13843	−	13.5015i	0.243697	−	1.53864i
$78$		0			0
$79$	−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	$0.976117\pi$
$80$	6.61713	−	6.01777i	0.739818	−	0.672807i
$81$		0			0
$82$	−3.40864	−	2.85627i	−0.376422	−	0.315422i
$83$	2.99552	+	1.52629i	0.328801	+	0.167532i	0.610596	−	0.791942i	$-0.290930\pi$
$83$	2.99552	+	1.52629i	0.328801	+	0.167532i	−0.281795	+	0.959475i	$0.590930\pi$
$84$		0			0
$85$	8.95160	−	5.40616i	0.970938	−	0.586381i
$86$	4.05504	−	3.52981i	0.437266	−	0.380629i
$87$		0			0
$88$	−5.89710	−	13.1731i	−0.628633	−	1.40426i
$89$	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
$92$	−2.60470	+	8.56098i	−0.271559	+	0.892544i
$93$		0			0
$94$	−11.4616	+	4.87429i	−1.18217	+	0.502745i
$95$	−10.8920	−	2.68963i	−1.11750	−	0.275950i
$96$		0			0
$97$	−5.07638	−	9.96296i	−0.515428	−	1.01158i	−0.991244	−	0.132040i	$-0.957847\pi$
$97$	−5.07638	−	9.96296i	−0.515428	−	1.01158i	0.475816	−	0.879545i	$-0.342153\pi$
$98$	−0.0172424	+	0.248997i	−0.00174175	+	0.0251525i
$99$		0			0
$100$	−3.14585	−	9.49229i	−0.314585	−	0.949229i
$101$	11.8084			1.17498			0.587489	−	0.809232i	$-0.300116\pi$
$101$	11.8084			1.17498			0.587489	+	0.809232i	$0.300116\pi$
$102$		0			0
$103$	0.880821	+	1.72871i	0.0867899	+	0.170335i	0.930322	−	0.366744i	$-0.119528\pi$
$103$	0.880821	+	1.72871i	0.0867899	+	0.170335i	−0.843532	+	0.537079i	$0.819528\pi$
$104$	−0.394164	+	7.82471i	−0.0386509	+	0.767276i
$105$		0			0
$106$	−2.39971	+	1.02053i	−0.233081	+	0.0991230i
$107$	−8.09772	−	8.09772i	−0.782836	−	0.782836i	0.197472	−	0.980308i	$-0.436727\pi$
$107$	−8.09772	−	8.09772i	−0.782836	−	0.782836i	−0.980308	+	0.197472i	$0.936727\pi$
$108$		0			0
$109$	−9.13259	+	12.5699i	−0.874743	+	1.20398i	0.103106	+	0.994670i	$0.467122\pi$
$109$	−9.13259	+	12.5699i	−0.874743	+	1.20398i	−0.977849	+	0.209310i	$0.932878\pi$
$110$	−16.1364	+	0.0472801i	−1.53854	+	0.00450798i
$111$		0			0
$112$	5.22035	+	9.35798i	0.493276	+	0.884246i
$113$	1.26860	+	8.00964i	0.119340	+	0.753483i	0.972684	+	0.232135i	$0.0745710\pi$
$113$	1.26860	+	8.00964i	0.119340	+	0.753483i	−0.853344	+	0.521349i	$0.825429\pi$
$114$		0			0
$115$	7.56540	+	6.54662i	0.705477	+	0.610476i
$116$	0.400668	+	0.194749i	0.0372011	+	0.0180820i
$117$		0			0
$118$	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
$122$	1.72446	−	1.07918i	0.156125	−	0.0977047i
$123$		0			0
$124$	−14.5331	+	2.58285i	−1.30511	+	0.231947i
$125$	−11.1267	−	1.09345i	−0.995206	−	0.0978013i
$126$		0			0
$127$	−15.8543	−	2.51108i	−1.40684	−	0.222822i	−0.593608	−	0.804755i	$-0.702297\pi$
$127$	−15.8543	−	2.51108i	−1.40684	−	0.222822i	−0.813237	+	0.581932i	$0.802297\pi$
$128$	10.0144	+	5.26413i	0.885159	+	0.465288i
$129$		0			0
$130$	7.81629	+	3.95379i	0.685534	+	0.346771i
$131$	−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	$0.602635\pi$
$132$		0			0
$133$	6.10210	−	11.9761i	0.529119	−	1.03846i
$134$	−2.46038	+	4.10104i	−0.212545	+	0.354276i
$135$		0			0
$136$	10.2967	+	8.30361i	0.882937	+	0.712028i
$137$	−18.6626	+	2.95587i	−1.59445	+	0.252537i	−0.889575	−	0.456790i	$-0.848999\pi$
$137$	−18.6626	+	2.95587i	−1.59445	+	0.252537i	−0.704880	+	0.709327i	$0.748999\pi$
$138$		0			0
$139$	−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	$0.400012\pi$
$140$	11.9310	−	1.08719i	1.00835	−	0.0918844i
$141$		0			0
$142$	−7.52177	−	3.03308i	−0.631213	−	0.254530i
$143$	9.99461	−	9.99461i	0.835792	−	0.835792i
$144$		0			0
$145$	0.380824	−	0.321015i	0.0316257	−	0.0266588i
$146$	−0.0261140	−	0.00601030i	−0.00216121	−	0.000497416i
$147$		0			0
$148$	8.74992	−	0.164565i	0.719239	−	0.0135272i
$149$		−	2.12851i		−	0.174375i	−0.996192	−	0.0871873i	$-0.972212\pi$
$149$		−	2.12851i		−	0.174375i	0.996192	−	0.0871873i	$-0.0277879\pi$
$150$		0			0
$151$		−	6.10369i		−	0.496712i	−0.968669	−	0.248356i	$-0.920110\pi$
$151$		−	6.10369i		−	0.496712i	0.968669	−	0.248356i	$-0.0798902\pi$
$152$	−1.51202	−	14.1105i	−0.122641	−	1.14451i
$153$		0			0
$154$	4.33603	−	18.8395i	0.349408	−	1.51813i
$155$	−3.95637	+	16.0219i	−0.317783	+	1.28691i
$156$		0			0
$157$	−11.4802	+	11.4802i	−0.916218	+	0.916218i	−0.996752	−	0.0805335i	$-0.974338\pi$
$157$	−11.4802	+	11.4802i	−0.916218	+	0.916218i	0.0805335	+	0.996752i	$0.474338\pi$
$158$	−3.56737	+	8.84677i	−0.283805	+	0.703811i
$159$		0			0
$160$	9.92360	−	7.84361i	0.784529	−	0.620092i
$161$	−9.69687	+	7.04519i	−0.764221	+	0.555239i
$162$		0			0
$163$	−7.81379	+	1.23758i	−0.612023	+	0.0969349i	−0.454748	−	0.890620i	$-0.650271\pi$
$163$	−7.81379	+	1.23758i	−0.612023	+	0.0969349i	−0.157275	+	0.987555i	$0.550271\pi$
$164$	−4.52998	−	4.36273i	−0.353732	−	0.340672i
$165$		0			0
$166$	4.07707	+	2.44600i	0.316442	+	0.189846i
$167$	6.13600	−	12.0426i	0.474818	−	0.931883i	−0.522059	−	0.852910i	$-0.674836\pi$
$167$	6.13600	−	12.0426i	0.474818	−	0.931883i	0.996877	−	0.0789735i	$-0.0251643\pi$
$168$		0			0
$169$	5.06658	−	1.64623i	0.389737	−	0.126633i
$170$	13.1574	−	6.75266i	1.00913	−	0.517906i
$171$		0			0
$172$	6.06584	−	4.58381i	0.462516	−	0.349512i
$173$	−1.08340	−	0.171594i	−0.0823695	−	0.0130460i	0.115114	−	0.993352i	$-0.463277\pi$
$173$	−1.08340	−	0.171594i	−0.0823695	−	0.0130460i	−0.197483	+	0.980306i	$0.563277\pi$
$174$		0			0
$175$	4.30368	−	12.6843i	0.325328	−	0.958840i
$176$	−7.03287	−	19.1613i	−0.530122	−	1.44433i
$177$		0			0
$178$	0.650033	+	1.03871i	0.0487220	+	0.0778544i
$179$	7.45601	−	22.9472i	0.557289	−	1.71516i	−0.132533	−	0.991179i	$-0.542311\pi$
$179$	7.45601	−	22.9472i	0.557289	−	1.71516i	0.689822	−	0.723979i	$-0.257689\pi$
$180$		0			0
$181$	−2.15964	−	6.64670i	−0.160525	−	0.494045i	0.838154	−	0.545434i	$-0.183635\pi$
$181$	−2.15964	−	6.64670i	−0.160525	−	0.494045i	−0.998679	+	0.0513890i	$0.983635\pi$
$182$	−6.74003	+	8.04349i	−0.499604	+	0.596223i
$183$		0			0
$184$	−4.51119	+	11.8237i	−0.332569	+	0.871652i
$185$	3.80277	−	9.01522i	0.279586	−	0.662812i
$186$		0			0
$187$	−3.73319	−	23.5704i	−0.272998	−	1.72364i
$188$	−16.6466	+	5.75707i	−1.21408	+	0.419877i
$189$		0			0
$190$	−15.1041	−	4.85873i	−1.09577	−	0.352490i
$191$	−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			0
$193$	6.44920	+	6.44920i	0.464223	+	0.464223i	0.900037	−	0.435814i	$-0.143539\pi$
$193$	6.44920	+	6.44920i	0.464223	+	0.464223i	−0.435814	+	0.900037i	$0.643539\pi$
$194$	−6.18859	−	14.5520i	−0.444315	−	1.04478i
$195$		0			0
$196$	−0.0486524	+	0.349609i	−0.00347517	+	0.0249721i
$197$	2.59555	+	5.09406i	0.184925	+	0.362936i	0.964794	−	0.263007i	$-0.0847142\pi$
$197$	2.59555	+	5.09406i	0.184925	+	0.362936i	−0.779869	+	0.625943i	$0.784714\pi$
$198$		0			0
$199$	24.6399			1.74668			0.873338	−	0.487115i	$-0.161951\pi$
$199$	24.6399			1.74668			0.873338	+	0.487115i	$0.161951\pi$
$200$	−3.51091	−	13.6994i	−0.248259	−	0.968694i
$201$		0			0
$202$	16.6597	+	1.15364i	1.17217	+	0.0811699i
$203$	0.270901	+	0.531674i	0.0190136	+	0.0373162i
$204$		0			0
$205$	−6.51359	+	2.64875i	−0.454929	+	0.184997i
$206$	1.07380	+	2.52498i	0.0748155	+	0.175923i
$207$		0			0
$208$	−1.32055	+	11.0009i	−0.0915636	+	0.762773i
$209$	−15.0488	+	20.7129i	−1.04095	+	1.43274i
$210$		0			0
$211$	−11.6703	−	16.0628i	−0.803419	−	1.10581i	−0.992306	−	0.123813i	$-0.960488\pi$
$211$	−11.6703	−	16.0628i	−0.803419	−	1.10581i	0.188886	−	0.981999i	$-0.439512\pi$
$212$	−3.48530	+	1.20536i	−0.239372	+	0.0827845i
$213$		0			0
$214$	−10.6334	−	12.2157i	−0.726886	−	0.835046i
$215$	−1.93084	−	8.27822i	−0.131682	−	0.564570i
$216$		0			0
$217$	−17.6165	−	8.97603i	−1.19588	−	0.609333i
$218$	−14.1126	+	16.8419i	−0.955827	+	1.14068i
$219$		0			0
$220$	−22.7704	−	1.50977i	−1.53518	−	0.101788i
$221$	−4.00309	+	12.3203i	−0.269277	+	0.828750i
$222$		0			0
$223$	−1.81060	+	11.4317i	−0.121247	+	0.765524i	0.849883	+	0.526972i	$0.176673\pi$
$223$	−1.81060	+	11.4317i	−0.121247	+	0.765524i	−0.971130	+	0.238552i	$0.923327\pi$
$224$	6.45080	+	13.7126i	0.431012	+	0.916210i
$225$		0			0
$226$	1.00727	+	11.4242i	0.0670028	+	0.759928i
$227$	15.3359	+	2.42897i	1.01788	+	0.161216i	0.643007	−	0.765861i	$-0.277687\pi$
$227$	15.3359	+	2.42897i	1.01788	+	0.161216i	0.374872	+	0.927077i	$0.377687\pi$
$228$		0			0
$229$	−16.0312	−	5.20884i	−1.05937	−	0.344210i	−0.273030	−	0.962006i	$-0.588026\pi$
$229$	−16.0312	−	5.20884i	−1.05937	−	0.344210i	−0.786339	+	0.617796i	$0.788026\pi$
$230$	10.0339	+	9.97532i	0.661619	+	0.657753i
$231$		0			0
$232$	0.546250	+	0.313902i	0.0358631	+	0.0206087i
$233$	13.2595	−	26.0233i	0.868660	−	1.70484i	0.174963	−	0.984575i	$-0.444019\pi$
$233$	13.2595	−	26.0233i	0.868660	−	1.70484i	0.693697	−	0.720267i	$-0.255981\pi$
$234$		0			0
$235$	−1.67214	+	19.6219i	−0.109078	+	1.27999i
$236$	13.0578	+	12.5757i	0.849992	+	0.818610i
$237$		0			0
$238$	4.29796	+	17.1886i	0.278595	+	1.11417i
$239$	−0.369981	+	0.268807i	−0.0239321	+	0.0173877i	−0.599687	−	0.800235i	$-0.704708\pi$
$239$	−0.369981	+	0.268807i	−0.0239321	+	0.0173877i	0.575755	+	0.817622i	$0.304708\pi$
$240$		0			0
$241$	17.6697	+	12.8378i	1.13820	+	0.826953i	0.986868	−	0.161530i	$-0.0516429\pi$
$241$	17.6697	+	12.8378i	1.13820	+	0.826953i	0.151335	+	0.988483i	$0.451643\pi$
$242$	−7.95364	+	19.7243i	−0.511279	+	1.26793i
$243$		0			0
$244$	2.53836	−	1.35408i	0.162502	−	0.0866858i
$245$	0.335146	+	0.208373i	0.0214117	+	0.0133125i
$246$		0			0
$247$	12.3832	−	6.30953i	0.787921	−	0.401466i
$248$	−20.7562	+	2.22413i	−1.31802	+	0.141233i
$249$		0			0
$250$	−15.5912	−	2.62973i	−0.986072	−	0.166318i
$251$		−	5.42259i		−	0.342271i	−0.985248	−	0.171135i	$-0.945256\pi$
$251$		−	5.42259i		−	0.342271i	0.985248	−	0.171135i	$-0.0547436\pi$
$252$		0			0
$253$	20.3426	−	10.3651i	1.27893	−	0.651647i
$254$	−22.1225	−	5.09164i	−1.38809	−	0.319478i
$255$		0			0
$256$	13.6144	+	8.40520i	0.850902	+	0.525325i
$257$	−8.02192	+	8.02192i	−0.500394	+	0.500394i	−0.911560	−	0.411166i	$-0.865121\pi$
$257$	−8.02192	+	8.02192i	−0.500394	+	0.500394i	0.411166	+	0.911560i	$0.365121\pi$
$258$		0			0
$259$	9.48341	+	6.89010i	0.589271	+	0.428130i
$260$	10.6412	+	6.34177i	0.659940	+	0.393300i
$261$		0			0
$262$	−18.6696	+	4.66826i	−1.15341	+	0.288406i
$263$	19.6441	−	3.11132i	1.21131	−	0.191852i	0.482081	−	0.876127i	$-0.339881\pi$
$263$	19.6441	−	3.11132i	1.21131	−	0.191852i	0.729224	+	0.684275i	$0.239881\pi$
$264$		0			0
$265$	−0.350096	+	4.10825i	−0.0215063	+	0.252368i
$266$	9.77908	−	16.3001i	0.599594	−	0.999422i
$267$		0			0
$268$	−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	0.363080	−	0.931758i	$-0.381725\pi$
$271$	1.79674	+	0.583795i	0.109144	+	0.0354630i	−0.253936	+	0.967221i	$0.581725\pi$
$272$	13.7158	+	12.7210i	0.831640	+	0.771322i
$273$		0			0
$274$	−26.6186	+	2.34696i	−1.60809	+	0.141785i
$275$	−11.8764	+	22.5812i	−0.716173	+	1.36170i
$276$		0			0
$277$	1.79116	−	11.3089i	0.107620	−	0.679488i	−0.873607	−	0.486632i	$-0.838225\pi$
$277$	1.79116	−	11.3089i	0.107620	−	0.679488i	0.981227	−	0.192855i	$-0.0617748\pi$
$278$	−8.73619	+	5.46719i	−0.523962	+	0.327900i
$279$		0			0
$280$	16.9388	−	0.368231i	1.01229	−	0.0220060i
$281$	−7.15917	−	22.0337i	−0.427080	−	1.31442i	−0.900988	−	0.433844i	$-0.857157\pi$
$281$	−7.15917	−	22.0337i	−0.427080	−	1.31442i	0.473908	−	0.880574i	$-0.342843\pi$
$282$		0			0
$283$	16.9779	+	8.65065i	1.00923	+	0.514228i	0.878780	−	0.477227i	$-0.158358\pi$
$283$	16.9779	+	8.65065i	1.00923	+	0.514228i	0.130449	+	0.991455i	$0.458358\pi$
$284$	−10.3157	−	5.01403i	−0.612121	−	0.297528i
$285$		0			0
$286$	15.0772	−	13.1243i	0.891533	−	0.776057i
$287$	−1.31782	−	8.32036i	−0.0777882	−	0.491135i
$288$		0			0
$289$	2.86343	+	3.94118i	0.168437	+	0.231834i
$290$	0.568642	−	0.415694i	0.0333918	−	0.0244104i
$291$		0			0
$292$	−0.0362553	−	0.0110308i	−0.00212168	−	0.000645528i
$293$	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			0
$295$	18.7756	−	7.63512i	1.09316	−	0.444534i
$296$	12.3608	+	0.622665i	0.718455	+	0.0361916i
$297$		0			0
$298$	0.207949	−	3.00298i	0.0120462	−	0.173958i
$299$	−12.3934			−0.716731
$300$		0			0
$301$	10.1838			0.586986
$302$	0.596311	−	8.61130i	0.0343138	−	0.495525i
$303$		0			0
$304$	−0.754653	−	20.0553i	−0.0432823	−	1.15025i
$305$	−0.231605	−	3.20817i	−0.0132616	−	0.183699i
$306$		0			0
$307$	9.17187	+	9.17187i	0.523466	+	0.523466i	0.918616	−	0.395150i	$-0.129308\pi$
$307$	9.17187	+	9.17187i	0.523466	+	0.523466i	−0.395150	+	0.918616i	$0.629308\pi$
$308$	7.95799	−	26.1559i	0.453449	−	1.49037i
$309$		0			0
$310$	−7.14707	+	22.2177i	−0.405926	+	1.26188i
$311$	−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			0
$313$	3.50477	+	22.1282i	0.198101	+	1.25076i	0.863529	+	0.504300i	$0.168249\pi$
$313$	3.50477	+	22.1282i	0.198101	+	1.25076i	−0.665427	+	0.746462i	$0.731751\pi$
$314$	−17.3182	+	15.0751i	−0.977324	+	0.850735i
$315$		0			0
$316$	−5.89727	+	12.1328i	−0.331748	+	0.682524i
$317$	−5.61291	−	2.85992i	−0.315252	−	0.160629i	0.289204	−	0.957268i	$-0.406609\pi$
$317$	−5.61291	−	2.85992i	−0.315252	−	0.160629i	−0.604456	+	0.796639i	$0.706609\pi$
$318$		0			0
$319$	−0.351235	−	1.08099i	−0.0196654	−	0.0605239i
$320$	14.7669	−	10.0965i	0.825492	−	0.564413i
$321$		0			0
$322$	−14.3690	+	8.99225i	−0.800752	+	0.501118i
$323$	3.67070	−	23.1759i	0.204243	−	1.28954i
$324$		0			0
$325$	11.3092	−	7.99498i	0.627320	−	0.443482i
$326$	−11.1449	+	0.982643i	−0.617257	+	0.0544235i
$327$		0			0
$328$	−5.96484	−	6.59766i	−0.329353	−	0.364295i
$329$	−22.4383	−	7.29065i	−1.23706	−	0.401946i
$330$		0			0
$331$	15.4106	−	5.00720i	0.847042	−	0.275221i	0.146835	−	0.989161i	$-0.453091\pi$
$331$	15.4106	−	5.00720i	0.847042	−	0.275221i	0.700206	+	0.713940i	$0.253091\pi$
$332$	5.51311	+	3.84922i	0.302571	+	0.211253i
$333$		0			0
$334$	9.83341	−	16.3906i	0.538060	−	0.896855i
$335$	3.90919	+	6.47289i	0.213582	+	0.353652i
$336$		0			0
$337$	−19.9748	+	3.16369i	−1.08809	+	0.172337i	−0.674610	−	0.738174i	$-0.735688\pi$
$337$	−19.9748	+	3.16369i	−1.08809	+	0.172337i	−0.413484	+	0.910511i	$0.635688\pi$
$338$	7.30894	−	1.82757i	0.397554	−	0.0994069i
$339$		0			0
$340$	19.2226	−	8.24146i	1.04249	−	0.446956i
$341$	30.4682	+	22.1364i	1.64995	+	1.19876i
$342$		0			0
$343$	12.9255	−	12.9255i	0.697914	−	0.697914i
$344$	9.00572	−	5.87439i	0.485556	−	0.316726i
$345$		0			0
$346$	−1.51174	−	0.347935i	−0.0812714	−	0.0187051i
$347$	5.16571	−	2.63206i	0.277310	−	0.141296i	−0.309805	−	0.950800i	$-0.600264\pi$
$347$	5.16571	−	2.63206i	0.277310	−	0.141296i	0.587115	+	0.809504i	$0.300264\pi$
$348$		0			0
$349$			0.0528810i			0.00283065i	0.999999	+	0.00141533i	$0.000450513\pi$
$349$			0.0528810i			0.00283065i	−0.999999	+	0.00141533i	$0.999549\pi$
$350$	7.31100	−	17.4749i	0.390789	−	0.934075i
$351$		0			0
$352$	−8.05022	−	27.7205i	−0.429078	−	1.47751i
$353$	3.66865	−	1.86927i	0.195263	−	0.0994913i	−0.353626	−	0.935387i	$-0.615051\pi$
$353$	3.66865	−	1.86927i	0.195263	−	0.0994913i	0.548888	+	0.835896i	$0.315051\pi$
$354$		0			0
$355$	−9.80475	+	8.26489i	−0.520382	+	0.438655i
$356$	0.815611	+	1.52895i	0.0432273	+	0.0810342i
$357$		0			0
$358$	12.7611	−	31.6463i	0.674444	−	1.67256i
$359$	22.3556	+	16.2423i	1.17989	+	0.857237i	0.992159	−	0.124985i	$-0.0398882\pi$
$359$	22.3556	+	16.2423i	1.17989	+	0.857237i	0.187726	+	0.982221i	$0.439888\pi$
$360$		0			0
$361$	−4.99493	+	3.62903i	−0.262891	+	0.191002i
$362$	−2.39754	−	9.58838i	−0.126012	−	0.503954i
$363$		0			0
$364$	−10.2949	+	10.6896i	−0.539599	+	0.560285i
$365$	−0.0277246	+	0.0320391i	−0.00145117	+	0.00167700i
$366$		0			0
$367$	−3.08204	+	6.04885i	−0.160881	+	0.315747i	−0.957349	−	0.288934i	$-0.906699\pi$
$367$	−3.08204	+	6.04885i	−0.160881	+	0.315747i	0.796468	+	0.604681i	$0.206699\pi$
$368$	−7.51967	+	16.2405i	−0.391990	+	0.846595i
$369$		0			0
$370$	6.24584	−	12.3475i	0.324706	−	0.641914i
$371$	−4.69792	−	1.52645i	−0.243904	−	0.0792492i
$372$		0			0
$373$	−11.3458	−	1.79701i	−0.587466	−	0.0930454i	−0.144376	−	0.989523i	$-0.546118\pi$
$373$	−11.3458	−	1.79701i	−0.587466	−	0.0930454i	−0.443089	+	0.896477i	$0.646118\pi$
$374$	−2.96416	−	33.6187i	−0.153273	−	1.73838i
$375$		0			0
$376$	−24.0480	+	6.49595i	−1.24018	+	0.335003i
$377$	−0.0965194	+	0.609399i	−0.00497100	+	0.0313857i
$378$		0			0
$379$	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	$-0.00665816\pi$
$380$	−20.8347	−	8.33049i	−1.06880	−	0.427345i
$381$		0			0
$382$	−14.3174	+	17.0863i	−0.732542	+	0.874210i
$383$	16.4227	+	8.36780i	0.839163	+	0.427575i	0.820084	−	0.572243i	$-0.193927\pi$
$383$	16.4227	+	8.36780i	0.839163	+	0.427575i	0.0190788	+	0.999818i	$0.493927\pi$
$384$		0			0
$385$	−23.1141	−	20.0015i	−1.17800	−	1.01937i
$386$	8.46869	+	9.72882i	0.431045	+	0.495184i
$387$		0			0
$388$	−7.30939	−	21.1351i	−0.371078	−	1.07297i
$389$	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
$392$	−0.102796	+	0.488488i	−0.00519199	+	0.0246724i
$393$		0			0
$394$	3.16422	+	7.44045i	0.159411	+	0.374844i
$395$	9.72080	+	11.5319i	0.489106	+	0.580233i
$396$		0			0
$397$	12.6438	+	24.8148i	0.634574	+	1.24542i	0.954566	+	0.298001i	$0.0963199\pi$
$397$	12.6438	+	24.8148i	0.634574	+	1.24542i	−0.319992	+	0.947420i	$0.603680\pi$
$398$	34.7628	+	2.40724i	1.74250	+	0.120664i
$399$		0			0
$400$	−3.61492	−	19.6706i	−0.180746	−	0.983530i
$401$	−10.4612			−0.522406			−0.261203	−	0.965284i	$-0.584119\pi$
$401$	−10.4612			−0.522406			−0.261203	+	0.965284i	$0.584119\pi$
$402$		0			0
$403$	−9.28115	−	18.2153i	−0.462327	−	0.907368i
$404$	23.3914	+	3.25520i	1.16376	+	0.161952i
$405$		0			0
$406$	0.330254	+	0.776571i	0.0163903	+	0.0385405i
$407$	−15.7886	−	15.7886i	−0.782611	−	0.782611i
$408$		0			0
$409$	−9.12365	+	12.5576i	−0.451136	+	0.620935i	−0.972641	−	0.232313i	$-0.925371\pi$
$409$	−9.12365	+	12.5576i	−0.451136	+	0.620935i	0.521505	+	0.853248i	$0.325371\pi$
$410$	−9.44837	+	3.10060i	−0.466622	+	0.153128i
$411$		0			0
$412$	1.26828	+	3.66723i	0.0624836	+	0.180672i
$413$	3.79865	+	23.9837i	0.186919	+	1.18016i
$414$		0			0
$415$	6.43505	−	3.88634i	0.315884	−	0.190773i
$416$	−2.93783	+	15.3914i	−0.144039	+	0.754625i
$417$		0			0
$418$	−23.2550	+	27.7523i	−1.13744	+	1.35741i
$419$	11.1568	+	34.3371i	0.545045	+	1.67748i	0.720883	+	0.693056i	$0.243736\pi$
$419$	11.1568	+	34.3371i	0.545045	+	1.67748i	−0.175838	+	0.984419i	$0.556264\pi$
$420$		0			0
$421$	4.95128	−	15.2385i	0.241311	−	0.742678i	−0.754911	−	0.655828i	$-0.772320\pi$
$421$	4.95128	−	15.2385i	0.241311	−	0.742678i	0.996221	−	0.0868504i	$-0.0276802\pi$
$422$	−14.8956	−	23.8022i	−0.725108	−	1.15867i
$423$		0			0
$424$	−5.03495	+	1.36006i	−0.244519	+	0.0660504i
$425$	0.302700	−	23.3816i	0.0146831	−	1.13417i
$426$		0			0
$427$	3.80607	+	0.602823i	0.184189	+	0.0291726i
$428$	−13.8086	−	18.2731i	−0.667463	−	0.883266i
$429$		0			0
$430$	−1.91534	−	11.8678i	−0.0923661	−	0.572318i
$431$	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	$0.348118\pi$
$432$		0			0
$433$	4.78847	−	9.39790i	0.230119	−	0.451634i	−0.746857	−	0.664985i	$-0.768438\pi$
$433$	4.78847	−	9.39790i	0.230119	−	0.451634i	0.976976	+	0.213351i	$0.0684378\pi$
$434$	−23.9770	−	14.3848i	−1.15093	−	0.690491i
$435$		0			0
$436$	−21.5560	+	22.3823i	−1.03234	+	1.07192i
$437$	22.1725	−	3.51178i	1.06065	−	0.167991i
$438$		0			0
$439$	−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	$0.380398\pi$
$440$	−31.9777	−	4.35462i	−1.52448	−	0.207598i
$441$		0			0
$442$	−6.85136	+	16.9908i	−0.325886	+	0.808168i
$443$	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			0
$445$	1.93240	−	0.139504i	0.0916046	−	0.00661314i
$446$	−3.67131	+	15.9514i	−0.173841	+	0.755319i
$447$		0			0
$448$	7.76134	+	19.9764i	0.366689	+	0.943797i
$449$		−	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
$452$	0.304986	+	16.2161i	0.0143453	+	0.762741i
$453$		0			0
$454$	21.3991	+	4.92514i	1.00431	+	0.231148i
$455$	6.25036	+	15.3703i	0.293021	+	0.720573i
$456$		0			0
$457$	23.4612	−	23.4612i	1.09747	−	1.09747i	0.102764	−	0.994706i	$-0.467231\pi$
$457$	23.4612	−	23.4612i	1.09747	−	1.09747i	0.994706	−	0.102764i	$-0.0327687\pi$
$458$	−22.1084	−	8.91500i	−1.03306	−	0.416571i
$459$		0			0
$460$	13.1817	+	15.0538i	0.614599	+	0.701888i
$461$	26.1799	−	19.0208i	1.21932	−	0.885887i	0.223275	−	0.974755i	$-0.428325\pi$
$461$	26.1799	−	19.0208i	1.21932	−	0.885887i	0.996043	+	0.0888686i	$0.0283251\pi$
$462$		0			0
$463$	30.2882	−	4.79718i	1.40761	−	0.222944i	0.594054	−	0.804425i	$-0.297527\pi$
$463$	30.2882	−	4.79718i	1.40761	−	0.222944i	0.813560	+	0.581481i	$0.197527\pi$
$464$	0.740002	+	0.496231i	0.0343537	+	0.0230369i
$465$		0			0
$466$	21.2494	−	35.4191i	0.984359	−	1.64076i
$467$	7.07648	−	13.8884i	0.327460	−	0.642677i	−0.667314	−	0.744777i	$-0.732556\pi$
$467$	7.07648	−	13.8884i	0.327460	−	0.642677i	0.994774	+	0.102100i	$0.0325560\pi$
$468$		0			0
$469$	−8.61588	+	2.79947i	−0.397844	+	0.129268i
$470$	−4.27611	+	27.5199i	−0.197242	+	1.26940i
$471$		0			0
$472$	17.1938	+	19.0180i	0.791410	+	0.875373i
$473$	−19.1594	−	3.03456i	−0.880952	−	0.139529i
$474$		0			0
$475$	−17.9673	+	17.5080i	−0.824394	+	0.803322i
$476$	4.38443	+	24.6702i	0.200960	+	1.13076i
$477$		0			0
$478$	−0.548244	+	0.343096i	−0.0250761	+	0.0156929i
$479$	−2.15249	+	6.62469i	−0.0983498	+	0.302690i	−0.988112	−	0.153734i	$-0.950870\pi$
$479$	−2.15249	+	6.62469i	−0.0983498	+	0.302690i	0.889762	+	0.456424i	$0.150870\pi$
$480$		0			0
$481$	3.74547	+	11.5274i	0.170779	+	0.525604i
$482$	23.6748	+	19.8382i	1.07836	+	0.903606i
$483$		0			0
$484$	−13.1483	+	27.0507i	−0.597649	+	1.22958i
$485$	−24.9127	−	2.12301i	−1.13123	−	0.0964009i
$486$		0			0
$487$	−3.26215	−	20.5964i	−0.147822	−	0.933313i	−0.944405	−	0.328784i	$-0.893361\pi$
$487$	−3.26215	−	20.5964i	−0.147822	−	0.933313i	0.796583	−	0.604529i	$-0.206639\pi$
$488$	3.71350	−	1.66239i	0.168102	−	0.0752528i
$489$		0			0
$490$	0.452478	+	0.326723i	0.0204409	+	0.0147598i
$491$	−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			0
$493$	0.736603	+	0.736603i	0.0331749	+	0.0331749i
$494$	18.0870	−	7.69191i	0.813773	−	0.346076i
$495$		0			0
$496$	−29.5008	+	1.11007i	−1.32463	+	0.0498438i
$497$	−6.97467	−	13.6886i	−0.312857	−	0.614016i
$498$		0			0
$499$	−19.8140			−0.886994			−0.443497	−	0.896276i	$-0.646262\pi$
$499$	−19.8140			−0.886994			−0.443497	+	0.896276i	$0.646262\pi$
$500$	−21.7397	−	5.23332i	−0.972227	−	0.234041i
$501$		0			0
$502$	0.529770	−	7.65038i	0.0236448	−	0.341453i
$503$	−12.4717	−	24.4770i	−0.556084	−	1.09138i	−0.982398	−	0.186801i	$-0.940188\pi$
$503$	−12.4717	−	24.4770i	−0.556084	−	1.09138i	0.426314	−	0.904575i	$-0.359812\pi$
$504$		0			0
$505$	13.9417	−	22.4237i	0.620396	−	0.997839i
$506$	29.7127	−	12.6360i	1.32089	−	0.561739i
$507$		0			0
$508$	−30.7138	−	9.34476i	−1.36270	−	0.414607i
$509$	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
$512$	18.3866	+	13.1884i	0.812578	+	0.582852i
$513$		0			0
$514$	−12.1013	+	10.5339i	−0.533767	+	0.464630i
$515$	4.32270	+	0.368371i	0.190481	+	0.0162324i
$516$		0			0
$517$	40.0420	+	20.4024i	1.76105	+	0.897298i
$518$	12.7064	+	10.6473i	0.558287	+	0.467815i
$519$		0			0
$520$	14.3934	+	9.98681i	0.631194	+	0.437951i
$521$	−1.41202	+	4.34576i	−0.0618618	+	0.190391i	−0.977211	−	0.212270i	$-0.931915\pi$
$521$	−1.41202	+	4.34576i	−0.0618618	+	0.190391i	0.915349	+	0.402661i	$0.131915\pi$
$522$		0			0
$523$	5.67302	−	35.8180i	0.248064	−	1.56621i	−0.477859	−	0.878437i	$-0.658587\pi$
$523$	5.67302	−	35.8180i	0.248064	−	1.56621i	0.725923	−	0.687776i	$-0.241413\pi$
$524$	−26.7958	+	4.76219i	−1.17058	+	0.208037i
$525$		0			0
$526$	28.0185	−	2.47039i	1.22167	−	0.107714i
$527$	−34.0911	−	5.39950i	−1.48503	−	0.235206i
$528$		0			0
$529$	2.83537	+	0.921267i	0.123277	+	0.0400551i
$530$	−0.895291	+	5.76186i	−0.0388890	+	0.250279i
$531$		0			0
$532$	15.3891	−	22.0413i	0.667204	−	0.955613i
$533$	3.95446	−	7.76106i	0.171286	−	0.336169i
$534$		0			0
$535$	−24.9379	+	5.81660i	−1.07816	+	0.251473i
$536$	−6.00433	+	7.44555i	−0.259347	+	0.321599i
$537$		0			0
$538$	13.9034	−	3.47650i	0.599419	−	0.149882i
$539$	0.728590	−	0.529352i	0.0313826	−	0.0228008i
$540$		0			0
$541$	−23.6895	−	17.2114i	−1.01849	−	0.739976i	−0.0525174	−	0.998620i	$-0.516724\pi$
$541$	−23.6895	−	17.2114i	−1.01849	−	0.739976i	−0.965973	+	0.258644i	$0.916724\pi$
$542$	2.47786	+	0.999174i	0.106433	+	0.0429182i
$543$		0			0
$544$	18.1079	+	19.2872i	0.776368	+	0.826931i
$545$	13.0873	+	32.1832i	0.560599	+	1.37858i
$546$		0			0
$547$	31.1849	−	15.8895i	1.33337	−	0.679385i	0.365493	−	0.930814i	$-0.380900\pi$
$547$	31.1849	−	15.8895i	1.33337	−	0.679385i	0.967876	+	0.251429i	$0.0809003\pi$
$548$	−37.7838	+	0.710624i	−1.61404	+	0.0303563i
$549$		0			0
$550$	−18.9617	+	30.6981i	−0.808532	+	1.30897i
$551$		−	1.11760i		−	0.0476112i
$552$		0			0
$553$	−16.0999	+	8.20329i	−0.684636	+	0.348839i
$554$	3.63187	−	15.7800i	0.154304	−	0.670430i
$555$		0			0
$556$	−12.8594	+	6.85981i	−0.545362	+	0.290921i
$557$	25.1416	−	25.1416i	1.06528	−	1.06528i	0.0675692	−	0.997715i	$-0.478476\pi$
$557$	25.1416	−	25.1416i	1.06528	−	1.06528i	0.997715	−	0.0675692i	$-0.0215243\pi$
$558$		0			0
$559$	8.51896	+	6.18939i	0.360314	+	0.261783i
$560$	23.9339	+	1.13536i	1.01139	+	0.0479775i
$561$		0			0
$562$	−7.94779	−	31.7853i	−0.335257	−	1.34078i
$563$	−27.3038	+	4.32450i	−1.15072	+	0.182256i	−0.702510	−	0.711674i	$-0.747937\pi$
$563$	−27.3038	+	4.32450i	−1.15072	+	0.182256i	−0.448208	+	0.893929i	$0.647937\pi$
$564$		0			0
$565$	16.7078	+	7.04762i	0.702901	+	0.296496i
$566$	23.1078	+	13.8633i	0.971294	+	0.582719i
$567$		0			0
$568$	−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	0.646362	−	0.763031i	$-0.276290\pi$
$571$	17.2235	+	5.59625i	0.720780	+	0.234196i	0.0744189	+	0.997227i	$0.476290\pi$
$572$	22.5536	−	17.0432i	0.943015	−	0.712614i
$573$		0			0
$574$	−1.04635	−	11.8674i	−0.0436737	−	0.495336i
$575$	21.3639	−	6.63706i	0.890937	−	0.276785i
$576$		0			0
$577$	1.72312	−	10.8794i	0.0717345	−	0.452914i	−0.925510	−	0.378724i	$-0.876363\pi$
$577$	1.72312	−	10.8794i	0.0717345	−	0.452914i	0.997244	−	0.0741898i	$-0.0236371\pi$
$578$	3.65479	+	5.84010i	0.152019	+	0.242916i
$579$		0			0
$580$	0.842872	−	0.530921i	0.0349983	−	0.0220453i
$581$	2.78310	+	8.56552i	0.115463	+	0.355357i
$582$		0			0
$583$	8.38362	+	4.27167i	0.347214	+	0.176914i
$584$	−0.0500726	−	0.0191047i	−0.00207202	−	0.000790556i
$585$		0			0
$586$	12.1209	+	13.9245i	0.500709	+	0.575214i
$587$	−7.33025	−	46.2814i	−0.302552	−	1.91024i	−0.402825	−	0.915277i	$-0.631972\pi$
$587$	−7.33025	−	46.2814i	−0.302552	−	1.91024i	0.100273	−	0.994960i	$-0.468028\pi$
$588$		0			0
$589$	21.7659	+	29.9582i	0.896849	+	1.23441i
$590$	27.2353	−	8.93758i	1.12126	−	0.367954i
$591$		0			0
$592$	17.3782	+	2.08608i	0.714239	+	0.0857375i
$593$	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	$0.641392\pi$
$594$		0			0
$595$	27.1974	+	6.71601i	1.11499	+	0.275329i
$596$	0.586763	−	4.21640i	0.0240348	−	0.172710i
$597$		0			0
$598$	−17.4851	−	1.21080i	−0.715019	−	0.0495132i
$599$	7.21615			0.294844			0.147422	−	0.989074i	$-0.452902\pi$
$599$	7.21615			0.294844			0.147422	+	0.989074i	$0.452902\pi$
$600$		0			0
$601$	−15.0642			−0.614483			−0.307241	−	0.951632i	$-0.599406\pi$
$601$	−15.0642			−0.614483			−0.307241	+	0.951632i	$0.599406\pi$
$602$	14.3677	+	0.994928i	0.585584	+	0.0405502i
$603$		0			0
$604$	1.68259	−	12.0909i	0.0684637	−	0.491971i
$605$	21.6730	+	25.7110i	0.881133	+	1.04530i
$606$		0			0
$607$	3.59194	+	3.59194i	0.145792	+	0.145792i	0.776235	−	0.630443i	$-0.217127\pi$
$607$	3.59194	+	3.59194i	0.145792	+	0.145792i	−0.630443	+	0.776235i	$0.717127\pi$
$608$	0.894649	−	28.3685i	0.0362828	−	1.15049i
$609$		0			0
$610$	−0.0133282	−	4.54883i	−0.000539644	−	0.184177i
$611$	−14.3390	−	19.7360i	−0.580095	−	0.798433i
$612$		0			0
$613$	−0.788465	−	4.97817i	−0.0318458	−	0.201066i	0.966636	−	0.256155i	$-0.0824558\pi$
$613$	−0.788465	−	4.97817i	−0.0318458	−	0.201066i	−0.998481	+	0.0550888i	$0.982456\pi$
$614$	12.0439	+	13.8360i	0.486053	+	0.558378i
$615$		0			0
$616$	13.7828	−	36.1241i	0.555323	−	1.45548i
$617$	16.5627	+	8.43913i	0.666790	+	0.339746i	0.754406	−	0.656408i	$-0.227925\pi$
$617$	16.5627	+	8.43913i	0.666790	+	0.339746i	−0.0876162	+	0.996154i	$0.527925\pi$
$618$		0			0
$619$	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	$0.760099\pi$
$620$	−12.2539	+	30.6473i	−0.492130	+	1.23082i
$621$		0			0
$622$	−3.12254	−	4.98960i	−0.125203	−	0.200065i
$623$	−0.363103	+	2.29254i	−0.0145474	+	0.0918487i
$624$		0			0
$625$	−15.2133	+	19.8382i	−0.608532	+	0.793529i
$626$	2.78279	+	31.5617i	0.111223	+	1.26146i
$627$		0			0
$628$	−25.9059	+	19.5765i	−1.03376	+	0.781187i
$629$	19.4624	+	6.32373i	0.776018	+	0.252144i
$630$		0			0
$631$	−3.22756	+	1.04870i	−0.128487	+	0.0417480i	−0.372555	−	0.928010i	$-0.621518\pi$
$631$	−3.22756	+	1.04870i	−0.128487	+	0.0417480i	0.244068	+	0.969758i	$0.421518\pi$
$632$	−9.50542	+	16.5413i	−0.378105	+	0.657976i
$633$		0			0
$634$	−7.63948	−	4.58324i	−0.303402	−	0.182024i
$635$	−23.4870	+	27.1420i	−0.932053	+	1.07710i
$636$		0			0
$637$	−0.482849	+	0.0764758i	−0.0191312	+	0.00303008i
$638$	−0.389926	−	1.55942i	−0.0154373	−	0.0617378i
$639$		0			0
$640$	21.8200	−	12.8019i	0.862511	−	0.506038i
$641$	−31.0401	−	22.5519i	−1.22601	−	0.890748i	−0.229425	−	0.973326i	$-0.573685\pi$
$641$	−31.0401	−	22.5519i	−1.22601	−	0.890748i	−0.996585	+	0.0825780i	$0.973685\pi$
$642$		0			0
$643$	−6.79295	+	6.79295i	−0.267888	+	0.267888i	−0.828249	−	0.560361i	$-0.810662\pi$
$643$	−6.79295	+	6.79295i	−0.267888	+	0.267888i	0.560361	+	0.828249i	$0.310662\pi$
$644$	−21.1508	+	11.2828i	−0.833457	+	0.444604i
$645$		0			0
$646$	7.44296	−	32.3388i	0.292840	−	1.27235i
$647$	30.3148	−	15.4461i	1.19180	−	0.607251i	0.258379	−	0.966044i	$-0.416812\pi$
$647$	30.3148	−	15.4461i	1.19180	−	0.607251i	0.933417	+	0.358793i	$0.116812\pi$
$648$		0			0
$649$		−	46.2539i		−	1.81562i
$650$	16.7365	−	10.1747i	0.656458	−	0.399086i
$651$		0			0
$652$	−15.8196	+	0.297529i	−0.619542	+	0.0116521i
$653$	−5.70477	+	2.90673i	−0.223245	+	0.113749i	−0.562036	−	0.827112i	$-0.689982\pi$
$653$	−5.70477	+	2.90673i	−0.223245	+	0.113749i	0.338791	+	0.940862i	$0.389982\pi$
$654$		0			0
$655$	−7.29465	+	29.5407i	−0.285025	+	1.15425i
$656$	−7.77083	−	9.89096i	−0.303400	−	0.386177i
$657$		0			0
$658$	−30.9445	−	12.4780i	−1.20634	−	0.486445i
$659$	11.5792	+	8.41281i	0.451063	+	0.327716i	0.790015	−	0.613087i	$-0.210073\pi$
$659$	11.5792	+	8.41281i	0.451063	+	0.327716i	−0.338952	+	0.940804i	$0.610073\pi$
$660$		0			0
$661$	−0.382235	+	0.277710i	−0.0148672	+	0.0108017i	−0.595194	−	0.803582i	$-0.702925\pi$
$661$	−0.382235	+	0.277710i	−0.0148672	+	0.0108017i	0.580327	+	0.814384i	$0.302925\pi$
$662$	22.2310	−	5.55877i	0.864031	−	0.216048i
$663$		0			0
$664$	7.40203	+	5.96923i	0.287254	+	0.231651i
$665$	−15.5375	−	25.7273i	−0.602520	−	0.997661i
$666$		0			0
$667$	−0.452453	+	0.887989i	−0.0175190	+	0.0343831i
$668$	15.4746	−	22.1638i	0.598731	−	0.857543i
$669$		0			0
$670$	4.88284	+	9.51410i	0.188641	+	0.367562i
$671$	−6.98096	−	2.26825i	−0.269497	−	0.0875648i
$672$		0			0
$673$	−21.1799	−	3.35456i	−0.816424	−	0.129309i	−0.265764	−	0.964038i	$-0.585624\pi$
$673$	−21.1799	−	3.35456i	−0.816424	−	0.129309i	−0.550660	+	0.834729i	$0.685624\pi$
$674$	−28.4902	+	2.51198i	−1.09740	+	0.0967578i
$675$		0			0
$676$	10.4903	−	1.86434i	0.403471	−	0.0717055i
$677$	−6.95245	+	43.8961i	−0.267204	+	1.68706i	0.380191	+	0.924908i	$0.375858\pi$
$677$	−6.95245	+	43.8961i	−0.267204	+	1.68706i	−0.647395	+	0.762155i	$0.724142\pi$
$678$		0			0
$679$	9.25648	−	28.4885i	0.355231	−	1.09329i
$680$	27.9251	−	9.74935i	1.07088	−	0.373870i
$681$		0			0
$682$	40.8229	+	34.2075i	1.56319	+	1.30987i
$683$	21.8180	+	11.1168i	0.834843	+	0.425374i	0.818510	−	0.574493i	$-0.194801\pi$
$683$	21.8180	+	11.1168i	0.834843	+	0.425374i	0.0163335	+	0.999867i	$0.494801\pi$
$684$		0			0
$685$	−16.4211	+	38.9294i	−0.627418	+	1.48742i
$686$	19.4986	−	16.9730i	0.744460	−	0.648033i
$687$		0			0
$688$	13.2795	−	7.40796i	0.506276	−	0.282426i
$689$	−3.00217	−	4.13213i	−0.114374	−	0.157422i
$690$		0			0
$691$	−9.83947	+	13.5429i	−0.374311	+	0.515195i	−0.954066	−	0.299596i	$-0.903148\pi$
$691$	−9.83947	+	13.5429i	−0.374311	+	0.515195i	0.579755	+	0.814791i	$0.303148\pi$
$692$	−2.09882	−	0.638571i	−0.0797851	−	0.0242748i
$693$		0			0
$694$	7.54511	−	3.20873i	0.286408	−	0.121802i
$695$	1.17332	+	16.2527i	0.0445065	+	0.616501i
$696$		0			0
$697$	−6.67656	−	13.1035i	−0.252893	−	0.496330i
$698$	−0.00516630	+	0.0746063i	−0.000195547	+	0.00282389i
$699$		0			0
$700$	12.0219	−	23.9400i	0.454383	−	0.904847i
$701$	−50.9450			−1.92417			−0.962083	−	0.272757i	$-0.912064\pi$
$701$	−50.9450			−1.92417			−0.962083	+	0.272757i	$0.912064\pi$
$702$		0			0
$703$	−9.96723	−	19.5618i	−0.375921	−	0.737787i
$704$	−8.64933	−	39.8955i	−0.325984	−	1.50362i
$705$		0			0
$706$	5.35848	−	2.27882i	0.201669	−	0.0857644i
$707$	22.3682	+	22.3682i	0.841244	+	0.841244i
$708$		0			0
$709$	23.6335	−	32.5288i	0.887576	−	1.22164i	−0.0866885	−	0.996235i	$-0.527628\pi$
$709$	23.6335	−	32.5288i	0.887576	−	1.22164i	0.974264	−	0.225408i	$-0.0723715\pi$
$710$	−14.6403	+	10.7025i	−0.549442	+	0.401658i
$711$		0			0
$712$	1.00132	+	2.23678i	0.0375260	+	0.0838268i
$713$	−5.16574	−	32.6152i	−0.193458	−	1.22145i
$714$		0			0
$715$	−7.17914	−	30.7796i	−0.268485	−	1.15109i
$716$	21.0955	−	43.4011i	0.788376	−	1.62197i
$717$		0			0
$718$	29.9533	+	25.0993i	1.11785	+	0.936698i
$719$	−3.14270	−	9.67223i	−0.117203	−	0.360713i	0.875197	−	0.483766i	$-0.160731\pi$
$719$	−3.14270	−	9.67223i	−0.117203	−	0.360713i	−0.992400	+	0.123053i	$0.960731\pi$
$720$		0			0
$721$	−1.60612	+	4.94314i	−0.0598152	+	0.184092i
$722$	−7.40157	+	4.63197i	−0.275458	+	0.172384i
$723$		0			0
$724$	−2.44578	−	13.7619i	−0.0908966	−	0.511455i
$725$	−0.159971	−	1.10218i	−0.00594117	−	0.0409339i
$726$		0			0
$727$	−8.65722	−	1.37117i	−0.321078	−	0.0508538i	−0.00618506	−	0.999981i	$-0.501969\pi$
$727$	−8.65722	−	1.37117i	−0.321078	−	0.0508538i	−0.314893	+	0.949127i	$0.601969\pi$
$728$	−15.5687	+	14.0754i	−0.577016	+	0.521670i
$729$		0			0
$730$	−0.0422450	+	0.0424933i	−0.00156356	+	0.00157275i
$731$	16.9084	−	5.49386i	0.625378	−	0.203198i
$732$		0			0
$733$	−0.119518	+	0.234567i	−0.00441450	+	0.00866394i	−0.893203	−	0.449653i	$-0.851548\pi$
$733$	−0.119518	+	0.234567i	−0.00441450	+	0.00866394i	0.888789	+	0.458317i	$0.151548\pi$
$734$	−4.93920	+	8.23282i	−0.182309	+	0.303879i
$735$		0			0
$736$	−12.1957	+	22.1780i	−0.449538	+	0.817493i
$737$	17.0437	−	2.69946i	0.627814	−	0.0994360i
$738$		0			0
$739$	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	$0.256626\pi$
$740$	10.0182	−	16.8100i	0.368275	−	0.617949i
$741$		0			0
$742$	−6.47886	−	2.61254i	−0.237846	−	0.0959092i
$743$	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			0
$745$	−4.04196	−	2.51305i	−0.148086	−	0.0920709i
$746$	−15.8316	−	3.64373i	−0.579634	−	0.133406i
$747$		0			0
$748$	−0.897500	−	47.7200i	−0.0328159	−	1.74482i
$749$		−	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	$-0.178866\pi$
$752$	−34.5624	+	6.81530i	−1.26036	+	0.248529i
$753$		0			0
$754$	−0.195709	+	0.850332i	−0.00712731	+	0.0309673i
$755$	−11.5907	−	7.20638i	−0.421827	−	0.262267i
$756$		0			0
$757$	−20.1848	+	20.1848i	−0.733630	+	0.733630i	−0.971337	−	0.237707i	$-0.923604\pi$
$757$	−20.1848	+	20.1848i	−0.733630	+	0.733630i	0.237707	+	0.971337i	$0.423604\pi$
$758$	6.77172	−	16.7933i	0.245960	−	0.609959i
$759$		0			0
$760$	−28.5804	−	13.7884i	−1.03672	−	0.500159i
$761$	−7.93313	+	5.76375i	−0.287576	+	0.208936i	−0.722215	−	0.691669i	$-0.756876\pi$
$761$	−7.93313	+	5.76375i	−0.287576	+	0.208936i	0.434639	+	0.900605i	$0.356876\pi$
$762$		0			0
$763$	−41.1103	+	6.51124i	−1.48829	+	0.235723i
$764$	−21.8688	+	22.7071i	−0.791184	+	0.821516i
$765$		0			0
$766$	22.3523	+	13.4100i	0.807620	+	0.484524i
$767$	−11.3988	+	22.3715i	−0.411589	+	0.807788i
$768$		0			0
$769$	17.2976	−	5.62032i	0.623766	−	0.202674i	0.0199544	−	0.999801i	$-0.493648\pi$
$769$	17.2976	−	5.62032i	0.623766	−	0.202674i	0.603812	+	0.797127i	$0.293648\pi$
$770$	−30.6561	−	30.4770i	−1.10477	−	1.09831i
$771$		0			0
$772$	10.9974	+	14.5531i	0.395807	+	0.523778i
$773$	−42.7233	−	6.76671i	−1.53665	−	0.243382i	−0.670025	−	0.742339i	$-0.733717\pi$
$773$	−42.7233	−	6.76671i	−1.53665	−	0.243382i	−0.866627	+	0.498957i	$0.833717\pi$
$774$		0			0
$775$	25.7538	+	26.4294i	0.925103	+	0.949370i
$776$	−8.24751	−	30.5323i	−0.296068	−	1.09604i
$777$		0			0
$778$	18.6603	+	29.8179i	0.669006	+	1.06902i
$779$	−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			0
$784$	−0.192752	+	0.679133i	−0.00688401	+	0.0242547i
$785$	8.24623	+	35.3546i	0.294320	+	1.26186i
$786$		0			0
$787$	1.89589	+	11.9702i	0.0675813	+	0.426691i	0.998162	+	0.0606043i	$0.0193028\pi$
$787$	1.89589	+	11.9702i	0.0675813	+	0.426691i	−0.930581	+	0.366087i	$0.880697\pi$
$788$	3.73729	+	10.8064i	0.133135	+	0.384961i
$789$		0			0
$790$	12.5878	+	17.2193i	0.447854	+	0.612635i
$791$	−12.7693	+	17.5755i	−0.454025	+	0.624911i
$792$		0			0
$793$	2.81747	+	2.81747i	0.100051	+	0.100051i
$794$	15.4140	+	36.2449i	0.547022	+	1.28628i
$795$		0			0
$796$	48.8094	+	6.79243i	1.73000	+	0.240751i
$797$	7.47486	+	14.6702i	0.264773	+	0.519646i	0.984668	−	0.174436i	$-0.0558103\pi$
$797$	7.47486	+	14.6702i	0.264773	+	0.519646i	−0.719895	+	0.694083i	$0.755810\pi$
$798$		0			0
$799$	−41.1877			−1.45712
$800$	−3.17831	−	28.1051i	−0.112370	−	0.993666i
$801$		0			0
$802$	−14.7590	−	1.02202i	−0.521158	−	0.0360889i
$803$	0.0438956	+	0.0861499i	0.00154904	+	0.00304016i
$804$		0			0
$805$	1.92984	+	26.7319i	0.0680178	+	0.942177i
$806$	−11.3146	−	26.6055i	−0.398540	−	0.937139i
$807$		0			0
$808$	32.6833	+	6.87780i	1.14980	+	0.241960i
$809$	−12.5671	+	17.2972i	−0.441837	+	0.608136i	−0.970619	−	0.240621i	$-0.922649\pi$
$809$	−12.5671	+	17.2972i	−0.441837	+	0.608136i	0.528782	+	0.848757i	$0.322649\pi$
$810$		0			0
$811$	−18.5355	−	25.5120i	−0.650871	−	0.895847i	0.348265	−	0.937396i	$-0.386771\pi$
$811$	−18.5355	−	25.5120i	−0.650871	−	0.895847i	−0.999136	+	0.0415488i	$0.986771\pi$
$812$	0.390066	+	1.12788i	0.0136886	+	0.0395807i
$813$		0			0
$814$	−20.7326	−	23.8176i	−0.726677	−	0.834806i
$815$	−6.87529	+	16.2992i	−0.240831	+	0.570937i
$816$		0			0
$817$	−16.9947	−	8.65922i	−0.594569	−	0.302948i
$818$	−14.0988	+	16.8254i	−0.492953	+	0.588286i
$819$		0			0
$820$	−13.6330	+	3.45136i	−0.476086	+	0.120527i
$821$	6.22378	−	19.1548i	0.217211	−	0.668508i	−0.781778	−	0.623557i	$-0.785687\pi$
$821$	6.22378	−	19.1548i	0.217211	−	0.668508i	0.998989	−	0.0449507i	$-0.0143131\pi$
$822$		0			0
$823$	−6.60034	+	41.6729i	−0.230073	+	1.45263i	0.554289	+	0.832324i	$0.312990\pi$
$823$	−6.60034	+	41.6729i	−0.230073	+	1.45263i	−0.784363	+	0.620302i	$0.787010\pi$
$824$	1.43105	+	5.29776i	0.0498531	+	0.184556i
$825$		0			0
$826$	3.01613	+	34.2082i	0.104945	+	1.19026i
$827$	−13.5996	−	2.15397i	−0.472905	−	0.0749008i	−0.0845669	−	0.996418i	$-0.526951\pi$
$827$	−13.5996	−	2.15397i	−0.472905	−	0.0749008i	−0.388338	+	0.921517i	$0.626951\pi$
$828$		0			0
$829$	35.5980	+	11.5665i	1.23637	+	0.401721i	0.853018	−	0.521881i	$-0.174770\pi$
$829$	35.5980	+	11.5665i	1.23637	+	0.401721i	0.383352	+	0.923602i	$0.374770\pi$
$830$	9.45848	−	4.85430i	0.328309	−	0.168495i
$831$		0			0
$832$	−5.64848	+	21.4277i	−0.195826	+	0.742872i
$833$	−0.374718	+	0.735426i	−0.0129832	+	0.0254810i
$834$		0			0
$835$	−15.6239	−	25.8702i	−0.540686	−	0.895275i
$836$	−35.5203	+	36.8820i	−1.22850	+	1.27559i
$837$		0			0
$838$	12.3858	+	49.5339i	0.427859	+	1.71112i
$839$	6.53213	−	4.74587i	0.225514	−	0.163846i	−0.469291	−	0.883044i	$-0.655491\pi$
$839$	6.53213	−	4.74587i	0.225514	−	0.163846i	0.694805	+	0.719198i	$0.255491\pi$
$840$		0			0
$841$	−23.4214	−	17.0166i	−0.807633	−	0.586780i
$842$	8.47419	−	21.0153i	0.292040	−	0.724234i
$843$		0			0
$844$	−18.6899	−	35.0362i	−0.643332	−	1.20600i
$845$	2.85577	−	11.5649i	0.0982416	−	0.397844i
$846$		0			0
$847$	−35.8955	+	18.2897i	−1.23338	+	0.628440i
$848$	−7.23635	+	1.42692i	−0.248497	+	0.0490008i
$849$		0			0
$850$	2.71136	−	32.9580i	0.0929990	−	1.13045i
$851$			19.5780i			0.671126i
$852$		0			0
$853$	−31.0768	+	15.8344i	−1.06405	+	0.542160i	−0.896199	−	0.443652i	$-0.853683\pi$
$853$	−31.0768	+	15.8344i	−1.06405	+	0.542160i	−0.167851	+	0.985812i	$0.553683\pi$
$854$	5.31085	+	1.22232i	0.181733	+	0.0418271i
$855$		0			0
$856$	−17.6964	−	27.1294i	−0.604850	−	0.927265i
$857$	−31.7738	+	31.7738i	−1.08537	+	1.08537i	−0.0893726	+	0.995998i	$0.528486\pi$
$857$	−31.7738	+	31.7738i	−1.08537	+	1.08537i	−0.995998	+	0.0893726i	$0.971514\pi$
$858$		0			0
$859$	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	$0.442932\pi$
$860$	−1.54278	−	16.9307i	−0.0526085	−	0.577332i
$861$		0			0
$862$	9.24400	−	2.31143i	0.314852	−	0.0787275i
$863$	16.4649	−	2.60778i	0.560472	−	0.0887700i	0.130230	−	0.991484i	$-0.458428\pi$
$863$	16.4649	−	2.60778i	0.560472	−	0.0887700i	0.430242	+	0.902714i	$0.358428\pi$
$864$		0			0
$865$	−1.60498	+	1.85474i	−0.0545708	+	0.0630631i
$866$	7.67388	−	12.7911i	0.260769	−	0.434658i
$867$		0			0
$868$	−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
$872$	−32.5986	+	29.4718i	−1.10393	+	0.998042i
$873$		0			0
$874$	31.6248	−	2.78836i	1.06973	−	0.0943177i
$875$	−19.0057	−	23.1483i	−0.642511	−	0.782555i
$876$		0			0
$877$	−2.32444	+	14.6759i	−0.0784907	+	0.495571i	0.916856	+	0.399217i	$0.130718\pi$
$877$	−2.32444	+	14.6759i	−0.0784907	+	0.495571i	−0.995347	+	0.0963539i	$0.969282\pi$
$878$	−12.5541	+	7.85645i	−0.423679	+	0.265142i
$879$		0			0
$880$	−44.6899	−	9.26777i	−1.50649	−	0.312417i
$881$	15.1162	+	46.5230i	0.509279	+	1.56740i	0.793456	+	0.608628i	$0.208280\pi$
$881$	15.1162	+	46.5230i	0.509279	+	1.56740i	−0.284177	+	0.958772i	$0.591720\pi$
$882$		0			0
$883$	1.45332	+	0.740506i	0.0489083	+	0.0249200i	0.478274	−	0.878211i	$-0.341263\pi$
$883$	1.45332	+	0.740506i	0.0489083	+	0.0249200i	−0.429365	+	0.903131i	$0.641263\pi$
$884$	−11.3261	+	23.3018i	−0.380937	+	0.783725i
$885$		0			0
$886$	4.93478	−	4.29560i	0.165787	−	0.144313i
$887$	4.23212	+	26.7206i	0.142101	+	0.897189i	0.950989	+	0.309226i	$0.100070\pi$
$887$	4.23212	+	26.7206i	0.142101	+	0.897189i	−0.808888	+	0.587963i	$0.799930\pi$
$888$		0			0
$889$	−25.2757	−	34.7890i	−0.847719	−	1.16679i
$890$	2.73993	−	0.00802808i	0.0918426	−	0.000269102i
$891$		0			0
$892$	−6.73800	+	22.1461i	−0.225605	+	0.741505i
$893$	31.2456	+	31.2456i	1.04560	+	1.04560i
$894$		0			0
$895$	−34.7729	−	41.2515i	−1.16233	−	1.37889i
$896$	8.99834	+	28.9417i	0.300614	+	0.966873i
$897$		0			0
$898$	1.76764	−	25.5264i	0.0589870	−	0.851828i
$899$	−1.64396			−0.0548290
$900$		0			0
$901$	−8.62349			−0.287290
$902$	−1.56767	+	22.6386i	−0.0521976	+	0.753784i
$903$		0			0
$904$	−1.15397	+	22.9080i	−0.0383806	+	0.761910i
$905$	−15.1716	−	3.74640i	−0.504321	−	0.124535i
$906$		0			0
$907$	−35.5508	−	35.5508i	−1.18045	−	1.18045i	−0.979629	−	0.200818i	$-0.935640\pi$
$907$	−35.5508	−	35.5508i	−1.18045	−	1.18045i	−0.200818	−	0.979629i	$-0.564360\pi$
$908$	29.7094	+	9.03918i	0.985942	+	0.299976i
$909$		0			0
$910$	7.31659	+	22.2957i	0.242543	+	0.739094i
$911$	−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			0
$913$	−2.68368	−	16.9441i	−0.0888169	−	0.560768i
$914$	35.3920	−	30.8078i	1.17066	−	1.01903i
$915$		0			0
$916$	−30.3204	−	14.7375i	−1.00181	−	0.486941i
$917$	−32.4808	−	16.5498i	−1.07261	−	0.546522i
$918$		0			0
$919$	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	$0.647860\pi$
$920$	17.1265	+	22.5263i	0.564643	+	0.742669i
$921$		0			0
$922$	38.7938	−	24.2775i	1.27760	−	0.799537i
$923$	2.48500	−	15.6897i	0.0817948	−	0.516432i
$924$		0			0
$925$	−12.6298	−	17.8652i	−0.415264	−	0.587404i
$926$	43.2004	−	3.80897i	1.41965	−	0.125171i
$927$		0			0
$928$	0.995540	+	0.772396i	0.0326802	+	0.0253551i
$929$	−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			0
$934$	11.3406	−	18.9028i	0.371075	−	0.618520i
$935$	−49.1669	−	20.7394i	−1.60793	−	0.678252i
$936$		0			0
$937$	37.4056	−	5.92447i	1.22199	−	0.193544i	0.488084	−	0.872796i	$-0.337696\pi$
$937$	37.4056	−	5.92447i	1.22199	−	0.193544i	0.733905	+	0.679252i	$0.237696\pi$
$938$	−12.4291	+	3.10785i	−0.405824	+	0.101475i
$939$		0			0
$940$	−8.72149	+	38.4083i	−0.284464	+	1.25274i
$941$	−25.8261	−	18.7637i	−0.841906	−	0.611680i	0.0809965	−	0.996714i	$-0.474190\pi$
$941$	−25.8261	−	18.7637i	−0.841906	−	0.611680i	−0.922902	+	0.385034i	$0.874190\pi$
$942$		0			0
$943$	9.94877	−	9.94877i	0.323977	−	0.323977i
$944$	22.3997	+	28.5110i	0.729047	+	0.927954i
$945$		0			0
$946$	−26.7343	−	6.15307i	−0.869208	−	0.200054i
$947$	3.14898	−	1.60449i	0.102328	−	0.0521388i	−0.402077	−	0.915606i	$-0.631712\pi$
$947$	3.14898	−	1.60449i	0.102328	−	0.0521388i	0.504405	+	0.863467i	$0.331712\pi$
$948$		0			0
$949$		−	0.0524856i		−	0.00170375i
$950$	−27.0593	+	22.9455i	−0.877920	+	0.744452i
$951$		0			0
$952$	3.77551	+	35.2340i	0.122365	+	1.14194i
$953$	−48.0361	+	24.4756i	−1.55604	+	0.792843i	−0.999284	−	0.0378308i	$-0.987955\pi$
$953$	−48.0361	+	24.4756i	−1.55604	+	0.792843i	−0.556759	+	0.830674i	$0.687955\pi$
$954$		0			0
$955$	13.2772	+	32.6502i	0.429641	+	1.05654i
$956$	−0.807001	+	0.430491i	−0.0261003	+	0.0139231i
$957$		0			0
$958$	−3.68402	+	9.13605i	−0.119025	+	0.295172i
$959$	−40.9512	−	29.7528i	−1.32238	−	0.960767i
$960$		0			0
$961$	18.9882	−	13.7957i	0.612523	−	0.445024i
$962$	4.15806	+	16.6292i	0.134061	+	0.536146i
$963$		0			0
$964$	31.4630	+	30.3014i	1.01336	+	0.975943i
$965$	19.8611	−	4.63246i	0.639350	−	0.149124i
$966$		0			0
$967$	−7.03165	+	13.8004i	−0.226123	+	0.443791i	−0.975995	−	0.217792i	$-0.930115\pi$
$967$	−7.03165	+	13.8004i	−0.226123	+	0.443791i	0.749873	+	0.661582i	$0.230115\pi$
$968$	−21.1928	+	36.8796i	−0.681163	+	1.18535i
$969$		0			0
$970$	−34.9403	−	5.42911i	−1.12187	−	0.174318i
$971$	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	$0.508680\pi$
$972$		0			0
$973$	−19.2817	−	3.05393i	−0.618144	−	0.0979044i
$974$	−2.59016	−	29.3769i	−0.0829940	−	0.941295i
$975$		0			0
$976$	5.40154	−	1.98256i	0.172899	−	0.0634602i
$977$	8.24291	−	52.0437i	0.263714	−	1.66502i	−0.399605	−	0.916687i	$-0.630853\pi$
$977$	8.24291	−	52.0437i	0.263714	−	1.66502i	0.663319	−	0.748337i	$-0.269147\pi$
$978$		0			0
$979$	1.36625	−	4.20489i	0.0436656	−	0.134389i
$980$	0.606452	+	0.505158i	0.0193724	+	0.0161367i
$981$		0			0
$982$	−4.46875	+	5.33297i	−0.142603	+	0.170182i
$983$	−15.6381	−	7.96803i	−0.498779	−	0.254141i	0.186455	−	0.982463i	$-0.440300\pi$
$983$	−15.6381	−	7.96803i	−0.498779	−	0.254141i	−0.685234	+	0.728323i	$0.740300\pi$
$984$		0			0
$985$	12.7379	+	1.08549i	0.405862	+	0.0345867i
$986$	0.967261	+	1.11119i	0.0308039	+	0.0353875i
$987$		0			0
$988$	26.2693	−	9.08498i	0.835736	−	0.289032i
$989$	9.99752	+	13.7604i	0.317903	+	0.437555i
$990$		0			0
$991$	−20.0939	+	27.6568i	−0.638302	+	0.878548i	−0.998524	−	0.0543192i	$-0.982701\pi$
$991$	−20.0939	+	27.6568i	−0.638302	+	0.878548i	0.360221	+	0.932867i	$0.382701\pi$
$992$	−41.7293	−	1.31600i	−1.32491	−	0.0417832i
$993$		0			0
$994$	−8.50278	−	19.9937i	−0.269692	−	0.634161i
$995$	29.0913	−	46.7902i	0.922256	−	1.48335i
$996$		0			0
$997$	0.954518	+	1.87335i	0.0302299	+	0.0593295i	0.905628	−	0.424074i	$-0.139400\pi$
$997$	0.954518	+	1.87335i	0.0302299	+	0.0593295i	−0.875398	+	0.483404i	$0.839400\pi$
$998$	−27.9542	−	1.93576i	−0.884875	−	0.0612754i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.bj.d.523.12		96
3.2	odd	2		100.2.l.b.23.1	✓	96
4.3	odd	2	inner	900.2.bj.d.523.1		96
12.11	even	2		100.2.l.b.23.12	yes	96
15.2	even	4		500.2.l.e.407.8		96
15.8	even	4		500.2.l.d.407.5		96
15.14	odd	2		500.2.l.f.343.12		96
25.12	odd	20	inner	900.2.bj.d.487.1		96
60.23	odd	4		500.2.l.d.407.6		96
60.47	odd	4		500.2.l.e.407.7		96
60.59	even	2		500.2.l.f.343.1		96
75.38	even	20		500.2.l.f.207.1		96
75.41	odd	10		500.2.l.e.43.7		96
75.59	odd	10		500.2.l.d.43.6		96
75.62	even	20		100.2.l.b.87.12	yes	96
100.87	even	20	inner	900.2.bj.d.487.12		96
300.59	even	10		500.2.l.d.43.5		96
300.191	even	10		500.2.l.e.43.8		96
300.263	odd	20		500.2.l.f.207.12		96
300.287	odd	20		100.2.l.b.87.1	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.2.l.b.23.1	✓	96	3.2	odd	2
100.2.l.b.23.12	yes	96	12.11	even	2
100.2.l.b.87.1	yes	96	300.287	odd	20
100.2.l.b.87.12	yes	96	75.62	even	20
500.2.l.d.43.5		96	300.59	even	10
500.2.l.d.43.6		96	75.59	odd	10
500.2.l.d.407.5		96	15.8	even	4
500.2.l.d.407.6		96	60.23	odd	4
500.2.l.e.43.7		96	75.41	odd	10
500.2.l.e.43.8		96	300.191	even	10
500.2.l.e.407.7		96	60.47	odd	4
500.2.l.e.407.8		96	15.2	even	4
500.2.l.f.207.1		96	75.38	even	20
500.2.l.f.207.12		96	300.263	odd	20
500.2.l.f.343.1		96	60.59	even	2
500.2.l.f.343.12		96	15.14	odd	2
900.2.bj.d.487.1		96	25.12	odd	20	inner
900.2.bj.d.487.12		96	100.87	even	20	inner
900.2.bj.d.523.1		96	4.3	odd	2	inner
900.2.bj.d.523.12		96	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41083 + 0.0976968i) q^{2} +(1.98091 + 0.275668i) q^{4} +(1.18066 - 1.89896i) q^{5} +(1.89427 + 1.89427i) q^{7} +(2.76781 + 0.582451i) q^{8} +O(q^{10})\)	\(q+(1.41083 + 0.0976968i) q^{2} +(1.98091 + 0.275668i) q^{4} +(1.18066 - 1.89896i) q^{5} +(1.89427 + 1.89427i) q^{7} +(2.76781 + 0.582451i) q^{8} +(1.85124 - 2.56377i) q^{10} +(-2.99934 - 4.12824i) q^{11} +(0.433317 + 2.73586i) q^{13} +(2.48743 + 2.85756i) q^{14} +(3.84801 + 1.09215i) q^{16} +(4.16697 + 2.12318i) q^{17} +(-1.55045 - 4.77181i) q^{19} +(2.86226 - 3.43620i) q^{20} +(-3.82826 - 6.11729i) q^{22} +(-0.699923 + 4.41914i) q^{23} +(-2.21209 - 4.48404i) q^{25} +(0.344055 + 3.90218i) q^{26} +(3.23018 + 4.27456i) q^{28} +(0.211843 + 0.0688321i) q^{29} +(-7.01920 + 2.28068i) q^{31} +(5.32221 + 1.91678i) q^{32} +(5.67148 + 3.40256i) q^{34} +(5.83362 - 1.36065i) q^{35} +(4.32186 - 0.684516i) q^{37} +(-1.72125 - 6.88371i) q^{38} +(4.37388 - 4.56828i) q^{40} +(-2.54404 - 1.84835i) q^{41} +(2.68807 - 2.68807i) q^{43} +(-4.80341 - 9.00450i) q^{44} +(-1.41921 + 6.16630i) q^{46} +(-7.84709 + 3.99829i) q^{47} +0.176489i q^{49} +(-2.68282 - 6.54236i) q^{50} +(0.104174 + 5.53894i) q^{52} +(-1.64295 + 0.837124i) q^{53} +(-11.3806 + 0.821587i) q^{55} +(4.13965 + 6.34628i) q^{56} +(0.292151 + 0.117807i) q^{58} +(7.33328 + 5.32794i) q^{59} +(1.16375 - 0.845512i) q^{61} +(-10.1258 + 2.53191i) q^{62} +(7.32150 + 3.22422i) q^{64} +(5.70688 + 2.40726i) q^{65} +(-1.53527 + 3.01313i) q^{67} +(7.66911 + 5.35453i) q^{68} +(8.36320 - 1.34973i) q^{70} +(-5.45415 - 1.77216i) q^{71} +(-0.0187149 - 0.00296414i) q^{73} +(6.16431 - 0.543507i) q^{74} +(-1.75588 - 9.87994i) q^{76} +(2.13843 - 13.5015i) q^{77} +(-2.08434 + 6.41493i) q^{79} +(6.61713 - 6.01777i) q^{80} +(-3.40864 - 2.85627i) q^{82} +(2.99552 + 1.52629i) q^{83} +(8.95160 - 5.40616i) q^{85} +(4.05504 - 3.52981i) q^{86} +(-5.89710 - 13.1731i) q^{88} +(0.509284 + 0.700969i) q^{89} +(-4.36162 + 6.00326i) q^{91} +(-2.60470 + 8.56098i) q^{92} +(-11.4616 + 4.87429i) q^{94} +(-10.8920 - 2.68963i) q^{95} +(-5.07638 - 9.96296i) q^{97} +(-0.0172424 + 0.248997i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 10 q^{2} - 10 q^{4} + 20 q^{5} + 10 q^{8}+O(q^{10}) \) 96 * q + 10 * q^2 - 10 * q^4 + 20 * q^5 + 10 * q^8	\( 96 q + 10 q^{2} - 10 q^{4} + 20 q^{5} + 10 q^{8} - 10 q^{10} - 20 q^{13} + 10 q^{14} - 14 q^{16} + 20 q^{17} - 10 q^{20} - 10 q^{22} - 20 q^{25} + 12 q^{26} - 10 q^{28} + 20 q^{29} + 50 q^{32} - 60 q^{34} + 40 q^{37} - 20 q^{38} + 40 q^{40} + 28 q^{41} - 60 q^{44} - 6 q^{46} - 80 q^{50} + 80 q^{52} + 40 q^{53} + 6 q^{56} + 60 q^{58} + 12 q^{61} - 40 q^{62} + 20 q^{64} + 100 q^{65} + 10 q^{68} - 10 q^{70} - 20 q^{73} + 20 q^{77} + 10 q^{80} - 50 q^{82} + 100 q^{85} + 6 q^{86} - 130 q^{88} - 160 q^{89} + 110 q^{92} - 170 q^{94} + 180 q^{97} + 130 q^{98}+O(q^{100}) \) 96 * q + 10 * q^2 - 10 * q^4 + 20 * q^5 + 10 * q^8 - 10 * q^10 - 20 * q^13 + 10 * q^14 - 14 * q^16 + 20 * q^17 - 10 * q^20 - 10 * q^22 - 20 * q^25 + 12 * q^26 - 10 * q^28 + 20 * q^29 + 50 * q^32 - 60 * q^34 + 40 * q^37 - 20 * q^38 + 40 * q^40 + 28 * q^41 - 60 * q^44 - 6 * q^46 - 80 * q^50 + 80 * q^52 + 40 * q^53 + 6 * q^56 + 60 * q^58 + 12 * q^61 - 40 * q^62 + 20 * q^64 + 100 * q^65 + 10 * q^68 - 10 * q^70 - 20 * q^73 + 20 * q^77 + 10 * q^80 - 50 * q^82 + 100 * q^85 + 6 * q^86 - 130 * q^88 - 160 * q^89 + 110 * q^92 - 170 * q^94 + 180 * q^97 + 130 * q^98

Introduction

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