LMFDB - Embedded newform 900.2.bj.d.487.12

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			487.12
Character	$\chi$	$=$	900.487
Dual form			900.2.bj.d.523.12

$q$-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 $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$-1$	$e\left(\frac{9}{20}\right)$

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	−0.251811	−	0.967776i	$-0.581026\pi$
$7$	1.89427	−	1.89427i	0.715965	−	0.715965i	0.967776	+	0.251811i	$0.0810262\pi$
$8$	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	0.0647283	+	0.997903i	$0.479382\pi$
$11$	−2.99934	+	4.12824i	−0.904336	+	1.24471i	−0.969064	+	0.246809i	$0.920618\pi$
$12$		0			0
$13$	0.433317	−	2.73586i	0.120181	−	0.758790i	−0.851824	−	0.523828i	$-0.824503\pi$
$13$	0.433317	−	2.73586i	0.120181	−	0.758790i	0.972005	−	0.234962i	$-0.0754966\pi$
$14$	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	0.131402	−	0.991329i	$-0.458052\pi$
$17$	4.16697	−	2.12318i	1.01064	−	0.514947i	0.879238	+	0.476383i	$0.158052\pi$
$18$		0			0
$19$	−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	$0.904795\pi$
$20$	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	−0.946619	−	0.322355i	$-0.895525\pi$
$23$	−0.699923	−	4.41914i	−0.145944	−	0.921455i	0.800675	−	0.599100i	$-0.204475\pi$
$24$		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	−0.289282	−	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	−0.398947	−	0.916974i	$-0.630624\pi$
$31$	−7.01920	−	2.28068i	−1.26069	−	0.409622i	−0.861739	+	0.507352i	$0.830624\pi$
$32$	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	0.501220	−	0.865320i	$-0.332885\pi$
$37$	4.32186	+	0.684516i	0.710510	+	0.112534i	0.209290	+	0.977854i	$0.432885\pi$
$38$	−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	−0.768445	−	0.639915i	$-0.778969\pi$
$41$	−2.54404	+	1.84835i	−0.397312	+	0.288664i	0.371133	+	0.928580i	$0.378969\pi$
$42$		0			0
$43$	2.68807	+	2.68807i	0.409927	+	0.409927i	0.881713	−	0.471786i	$-0.156391\pi$
$43$	2.68807	+	2.68807i	0.409927	+	0.409927i	−0.471786	+	0.881713i	$0.656391\pi$
$44$	−4.80341	+	9.00450i	−0.724141	+	1.35748i
$45$		0			0
$46$	−1.41921	−	6.16630i	−0.209251	−	0.909171i
$47$	−7.84709	−	3.99829i	−1.14462	−	0.583211i	−0.224351	−	0.974508i	$-0.572026\pi$
$47$	−7.84709	−	3.99829i	−1.14462	−	0.583211i	−0.920264	+	0.391298i	$0.872026\pi$
$48$		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	0.337497	−	0.941327i	$-0.390420\pi$
$53$	−1.64295	−	0.837124i	−0.225676	−	0.114988i	−0.563173	+	0.826339i	$0.690420\pi$
$54$		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	0.00279513	−	0.999996i	$-0.499110\pi$
$59$	7.33328	−	5.32794i	0.954712	−	0.693639i	0.951917	+	0.306357i	$0.0991103\pi$
$60$		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	$0.670646\pi$
$62$	−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	0.778007	−	0.628255i	$-0.216231\pi$
$67$	−1.53527	−	3.01313i	−0.187563	−	0.368113i	−0.965570	+	0.260142i	$0.916231\pi$
$68$	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	−0.614218	−	0.789136i	$-0.710529\pi$
$71$	−5.45415	+	1.77216i	−0.647288	+	0.210317i	−0.0330703	+	0.999453i	$0.510529\pi$
$72$		0			0
$73$	−0.0187149	+	0.00296414i	−0.00219041	+	0.000346927i	−0.157530	−	0.987514i	$-0.550353\pi$
$73$	−0.0187149	+	0.00296414i	−0.00219041	+	0.000346927i	0.155339	+	0.987861i	$0.450353\pi$
$74$	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	−0.997187	−	0.0749601i	$-0.976117\pi$
$79$	−2.08434	−	6.41493i	−0.234506	−	0.721736i	0.762680	−	0.646776i	$-0.223883\pi$
$80$	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	−0.281795	−	0.959475i	$-0.590930\pi$
$83$	2.99552	−	1.52629i	0.328801	−	0.167532i	0.610596	+	0.791942i	$0.290930\pi$
$84$		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	−0.781172	−	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
$92$	−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	0.475816	+	0.879545i	$0.342153\pi$
$97$	−5.07638	+	9.96296i	−0.515428	+	1.01158i	−0.991244	+	0.132040i	$0.957847\pi$
$98$	−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	−0.843532	−	0.537079i	$-0.819528\pi$
$103$	0.880821	−	1.72871i	0.0867899	−	0.170335i	0.930322	+	0.366744i	$0.119528\pi$
$104$	−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	−0.980308	−	0.197472i	$-0.936727\pi$
$107$	−8.09772	+	8.09772i	−0.782836	+	0.782836i	0.197472	+	0.980308i	$0.436727\pi$
$108$		0			0
$109$	−9.13259	−	12.5699i	−0.874743	−	1.20398i	−0.977849	−	0.209310i	$-0.932878\pi$
$109$	−9.13259	−	12.5699i	−0.874743	−	1.20398i	0.103106	−	0.994670i	$-0.467122\pi$
$110$	−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	−0.853344	−	0.521349i	$-0.825429\pi$
$113$	1.26860	−	8.00964i	0.119340	−	0.753483i	0.972684	−	0.232135i	$-0.0745710\pi$
$114$		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	−0.813237	−	0.581932i	$-0.802297\pi$
$127$	−15.8543	+	2.51108i	−1.40684	+	0.222822i	−0.593608	+	0.804755i	$0.702297\pi$
$128$	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	−0.316878	−	0.948466i	$-0.602635\pi$
$131$	−12.9418	−	4.20505i	−1.13073	−	0.367397i	−0.813854	+	0.581069i	$0.802635\pi$
$132$		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	−0.704880	−	0.709327i	$-0.748999\pi$
$137$	−18.6626	−	2.95587i	−1.59445	−	0.252537i	−0.889575	+	0.456790i	$0.848999\pi$
$138$		0			0
$139$	−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	$0.800012\pi$
$140$	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	$0.0277879\pi$
$149$			2.12851i			0.174375i	−0.996192	+	0.0871873i	$0.972212\pi$
$150$		0			0
$151$			6.10369i			0.496712i	0.968669	+	0.248356i	$0.0798902\pi$
$151$			6.10369i			0.496712i	−0.968669	+	0.248356i	$0.920110\pi$
$152$	−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	0.0805335	−	0.996752i	$-0.474338\pi$
$157$	−11.4802	−	11.4802i	−0.916218	−	0.916218i	−0.996752	+	0.0805335i	$0.974338\pi$
$158$	−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	−0.157275	−	0.987555i	$-0.550271\pi$
$163$	−7.81379	−	1.23758i	−0.612023	−	0.0969349i	−0.454748	+	0.890620i	$0.650271\pi$
$164$	−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	0.996877	+	0.0789735i	$0.0251643\pi$
$167$	6.13600	+	12.0426i	0.474818	+	0.931883i	−0.522059	+	0.852910i	$0.674836\pi$
$168$		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	−0.197483	−	0.980306i	$-0.563277\pi$
$173$	−1.08340	+	0.171594i	−0.0823695	+	0.0130460i	0.115114	+	0.993352i	$0.463277\pi$
$174$		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	0.689822	+	0.723979i	$0.257689\pi$
$179$	7.45601	+	22.9472i	0.557289	+	1.71516i	−0.132533	+	0.991179i	$0.542311\pi$
$180$		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			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	0.329369	−	0.944201i	$-0.393164\pi$
$191$	−9.26511	−	12.7523i	−0.670400	−	0.922727i	−0.999769	+	0.0214746i	$0.993164\pi$
$192$		0			0
$193$	6.44920	−	6.44920i	0.464223	−	0.464223i	−0.435814	−	0.900037i	$-0.643539\pi$
$193$	6.44920	−	6.44920i	0.464223	−	0.464223i	0.900037	+	0.435814i	$0.143539\pi$
$194$	−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	−0.779869	−	0.625943i	$-0.784714\pi$
$197$	2.59555	−	5.09406i	0.184925	−	0.362936i	0.964794	+	0.263007i	$0.0847142\pi$
$198$		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	0.188886	+	0.981999i	$0.439512\pi$
$211$	−11.6703	+	16.0628i	−0.803419	+	1.10581i	−0.992306	+	0.123813i	$0.960488\pi$
$212$	−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	−0.971130	−	0.238552i	$-0.923327\pi$
$223$	−1.81060	−	11.4317i	−0.121247	−	0.765524i	0.849883	−	0.526972i	$-0.176673\pi$
$224$	6.45080	−	13.7126i	0.431012	−	0.916210i
$225$		0			0
$226$	1.00727	−	11.4242i	0.0670028	−	0.759928i
$227$	15.3359	−	2.42897i	1.01788	−	0.161216i	0.374872	−	0.927077i	$-0.377687\pi$
$227$	15.3359	−	2.42897i	1.01788	−	0.161216i	0.643007	+	0.765861i	$0.277687\pi$
$228$		0			0
$229$	−16.0312	+	5.20884i	−1.05937	+	0.344210i	−0.786339	−	0.617796i	$-0.788026\pi$
$229$	−16.0312	+	5.20884i	−1.05937	+	0.344210i	−0.273030	+	0.962006i	$0.588026\pi$
$230$	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	0.693697	+	0.720267i	$0.255981\pi$
$233$	13.2595	+	26.0233i	0.868660	+	1.70484i	0.174963	+	0.984575i	$0.444019\pi$
$234$		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	0.575755	−	0.817622i	$-0.304708\pi$
$239$	−0.369981	−	0.268807i	−0.0239321	−	0.0173877i	−0.599687	+	0.800235i	$0.704708\pi$
$240$		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	$0.0516429\pi$
$242$	−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	$0.0547436\pi$
$251$			5.42259i			0.342271i	−0.985248	+	0.171135i	$0.945256\pi$
$252$		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	0.411166	−	0.911560i	$-0.365121\pi$
$257$	−8.02192	−	8.02192i	−0.500394	−	0.500394i	−0.911560	+	0.411166i	$0.865121\pi$
$258$		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	0.729224	−	0.684275i	$-0.239881\pi$
$263$	19.6441	+	3.11132i	1.21131	+	0.191852i	0.482081	+	0.876127i	$0.339881\pi$
$264$		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	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	−0.253936	−	0.967221i	$-0.581725\pi$
$271$	1.79674	−	0.583795i	0.109144	−	0.0354630i	0.363080	+	0.931758i	$0.381725\pi$
$272$	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	0.981227	+	0.192855i	$0.0617748\pi$
$277$	1.79116	+	11.3089i	0.107620	+	0.679488i	−0.873607	+	0.486632i	$0.838225\pi$
$278$	−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	0.473908	+	0.880574i	$0.342843\pi$
$281$	−7.15917	+	22.0337i	−0.427080	+	1.31442i	−0.900988	+	0.433844i	$0.857157\pi$
$282$		0			0
$283$	16.9779	−	8.65065i	1.00923	−	0.514228i	0.130449	−	0.991455i	$-0.458358\pi$
$283$	16.9779	−	8.65065i	1.00923	−	0.514228i	0.878780	+	0.477227i	$0.158358\pi$
$284$	−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	−0.384059	−	0.923309i	$-0.625474\pi$
$293$	9.23047	−	9.23047i	0.539250	−	0.539250i	0.923309	+	0.384059i	$0.125474\pi$
$294$		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	−0.395150	−	0.918616i	$-0.629308\pi$
$307$	9.17187	−	9.17187i	0.523466	−	0.523466i	0.918616	+	0.395150i	$0.129308\pi$
$308$	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	−0.872726	−	0.488209i	$-0.837650\pi$
$311$	−2.44643	+	3.36722i	−0.138724	+	0.190938i	0.734002	+	0.679147i	$0.237650\pi$
$312$		0			0
$313$	3.50477	−	22.1282i	0.198101	−	1.25076i	−0.665427	−	0.746462i	$-0.731751\pi$
$313$	3.50477	−	22.1282i	0.198101	−	1.25076i	0.863529	−	0.504300i	$-0.168249\pi$
$314$	−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	−0.604456	−	0.796639i	$-0.706609\pi$
$317$	−5.61291	+	2.85992i	−0.315252	+	0.160629i	0.289204	+	0.957268i	$0.406609\pi$
$318$		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	0.700206	−	0.713940i	$-0.253091\pi$
$331$	15.4106	+	5.00720i	0.847042	+	0.275221i	0.146835	+	0.989161i	$0.453091\pi$
$332$	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	−0.413484	−	0.910511i	$-0.635688\pi$
$337$	−19.9748	−	3.16369i	−1.08809	−	0.172337i	−0.674610	+	0.738174i	$0.735688\pi$
$338$	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	0.587115	−	0.809504i	$-0.300264\pi$
$347$	5.16571	+	2.63206i	0.277310	+	0.141296i	−0.309805	+	0.950800i	$0.600264\pi$
$348$		0			0
$349$		−	0.0528810i		−	0.00283065i	−0.999999	−	0.00141533i	$-0.999549\pi$
$349$		−	0.0528810i		−	0.00283065i	0.999999	−	0.00141533i	$-0.000450513\pi$
$350$	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	0.548888	−	0.835896i	$-0.315051\pi$
$353$	3.66865	+	1.86927i	0.195263	+	0.0994913i	−0.353626	+	0.935387i	$0.615051\pi$
$354$		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	0.187726	−	0.982221i	$-0.439888\pi$
$359$	22.3556	−	16.2423i	1.17989	−	0.857237i	0.992159	+	0.124985i	$0.0398882\pi$
$360$		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	0.796468	−	0.604681i	$-0.206699\pi$
$367$	−3.08204	−	6.04885i	−0.160881	−	0.315747i	−0.957349	+	0.288934i	$0.906699\pi$
$368$	−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	−0.443089	−	0.896477i	$-0.646118\pi$
$373$	−11.3458	+	1.79701i	−0.587466	+	0.0930454i	−0.144376	+	0.989523i	$0.546118\pi$
$374$	−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	0.999781	+	0.0209157i	$0.00665816\pi$
$379$	3.95657	+	12.1771i	0.203235	+	0.625494i	−0.796546	+	0.604578i	$0.793342\pi$
$380$	−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	0.0190788	−	0.999818i	$-0.493927\pi$
$383$	16.4227	−	8.36780i	0.839163	−	0.427575i	0.820084	+	0.572243i	$0.193927\pi$
$384$		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	−0.257287	−	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
$392$	−0.102796	−	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	−0.319992	−	0.947420i	$-0.603680\pi$
$397$	12.6438	−	24.8148i	0.634574	−	1.24542i	0.954566	−	0.298001i	$-0.0963199\pi$
$398$	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	0.521505	−	0.853248i	$-0.325371\pi$
$409$	−9.12365	−	12.5576i	−0.451136	−	0.620935i	−0.972641	+	0.232313i	$0.925371\pi$
$410$	−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	−0.175838	−	0.984419i	$-0.556264\pi$
$419$	11.1568	−	34.3371i	0.545045	−	1.67748i	0.720883	−	0.693056i	$-0.243736\pi$
$420$		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	$0.772320\pi$
$422$	−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	0.459252	−	0.888306i	$-0.348118\pi$
$431$	6.40797	+	2.08208i	0.308661	+	0.100290i	−0.150591	+	0.988596i	$0.548118\pi$
$432$		0			0
$433$	4.78847	+	9.39790i	0.230119	+	0.451634i	0.976976	−	0.213351i	$-0.0684378\pi$
$433$	4.78847	+	9.39790i	0.230119	+	0.451634i	−0.746857	+	0.664985i	$0.768438\pi$
$434$	−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	0.366960	−	0.930237i	$-0.380398\pi$
$439$	−8.47207	−	6.15532i	−0.404350	−	0.293778i	−0.771311	+	0.636459i	$0.780398\pi$
$440$	−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	0.780534	−	0.625113i	$-0.214947\pi$
$443$	3.27124	+	3.27124i	0.155421	+	0.155421i	−0.625113	+	0.780534i	$0.714947\pi$
$444$		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	$0.140406\pi$
$449$			18.0931i			0.853868i	−0.904283	+	0.426934i	$0.859594\pi$
$450$		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	0.994706	+	0.102764i	$0.0327687\pi$
$457$	23.4612	+	23.4612i	1.09747	+	1.09747i	0.102764	+	0.994706i	$0.467231\pi$
$458$	−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	0.996043	−	0.0888686i	$-0.0283251\pi$
$461$	26.1799	+	19.0208i	1.21932	+	0.885887i	0.223275	+	0.974755i	$0.428325\pi$
$462$		0			0
$463$	30.2882	+	4.79718i	1.40761	+	0.222944i	0.813560	−	0.581481i	$-0.197527\pi$
$463$	30.2882	+	4.79718i	1.40761	+	0.222944i	0.594054	+	0.804425i	$0.297527\pi$
$464$	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	0.994774	−	0.102100i	$-0.0325560\pi$
$467$	7.07648	+	13.8884i	0.327460	+	0.642677i	−0.667314	+	0.744777i	$0.732556\pi$
$468$		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	0.889762	−	0.456424i	$-0.150870\pi$
$479$	−2.15249	−	6.62469i	−0.0983498	−	0.302690i	−0.988112	+	0.153734i	$0.950870\pi$
$480$		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	0.796583	+	0.604529i	$0.206639\pi$
$487$	−3.26215	+	20.5964i	−0.147822	+	0.933313i	−0.944405	+	0.328784i	$0.893361\pi$
$488$	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	0.738763	−	0.673965i	$-0.235410\pi$
$491$	−2.89183	−	3.98026i	−0.130506	−	0.179627i	−0.869269	+	0.494339i	$0.835410\pi$
$492$		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	0.426314	+	0.904575i	$0.359812\pi$
$503$	−12.4717	+	24.4770i	−0.556084	+	1.09138i	−0.982398	+	0.186801i	$0.940188\pi$
$504$		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	0.949204	−	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
$512$	18.3866	−	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	0.915349	−	0.402661i	$-0.131915\pi$
$521$	−1.41202	−	4.34576i	−0.0618618	−	0.190391i	−0.977211	+	0.212270i	$0.931915\pi$
$522$		0			0
$523$	5.67302	+	35.8180i	0.248064	+	1.56621i	0.725923	+	0.687776i	$0.241413\pi$
$523$	5.67302	+	35.8180i	0.248064	+	1.56621i	−0.477859	+	0.878437i	$0.658587\pi$
$524$	−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	−0.965973	−	0.258644i	$-0.916724\pi$
$541$	−23.6895	+	17.2114i	−1.01849	+	0.739976i	−0.0525174	+	0.998620i	$0.516724\pi$
$542$	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	0.967876	−	0.251429i	$-0.0809003\pi$
$547$	31.1849	+	15.8895i	1.33337	+	0.679385i	0.365493	+	0.930814i	$0.380900\pi$
$548$	−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	0.997715	+	0.0675692i	$0.0215243\pi$
$557$	25.1416	+	25.1416i	1.06528	+	1.06528i	0.0675692	+	0.997715i	$0.478476\pi$
$558$		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	−0.448208	−	0.893929i	$-0.647937\pi$
$563$	−27.3038	−	4.32450i	−1.15072	−	0.182256i	−0.702510	+	0.711674i	$0.747937\pi$
$564$		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	0.119308	−	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	0.0744189	−	0.997227i	$-0.476290\pi$
$571$	17.2235	−	5.59625i	0.720780	−	0.234196i	0.646362	+	0.763031i	$0.276290\pi$
$572$	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	0.997244	+	0.0741898i	$0.0236371\pi$
$577$	1.72312	+	10.8794i	0.0717345	+	0.452914i	−0.925510	+	0.378724i	$0.876363\pi$
$578$	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	0.100273	+	0.994960i	$0.468028\pi$
$587$	−7.33025	+	46.2814i	−0.302552	+	1.91024i	−0.402825	+	0.915277i	$0.631972\pi$
$588$		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	−0.429731	−	0.902957i	$-0.641392\pi$
$593$	11.5238	−	11.5238i	0.473225	−	0.473225i	0.902957	+	0.429731i	$0.141392\pi$
$594$		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	−0.630443	−	0.776235i	$-0.717127\pi$
$607$	3.59194	−	3.59194i	0.145792	−	0.145792i	0.776235	+	0.630443i	$0.217127\pi$
$608$	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	−0.998481	−	0.0550888i	$-0.982456\pi$
$613$	−0.788465	+	4.97817i	−0.0318458	+	0.201066i	0.966636	+	0.256155i	$0.0824558\pi$
$614$	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	−0.0876162	−	0.996154i	$-0.527925\pi$
$617$	16.5627	−	8.43913i	0.666790	−	0.339746i	0.754406	+	0.656408i	$0.227925\pi$
$618$		0			0
$619$	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	$-0.0399006\pi$
$620$	−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	0.244068	−	0.969758i	$-0.421518\pi$
$631$	−3.22756	−	1.04870i	−0.128487	−	0.0417480i	−0.372555	+	0.928010i	$0.621518\pi$
$632$	−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	−0.996585	−	0.0825780i	$-0.973685\pi$
$641$	−31.0401	+	22.5519i	−1.22601	+	0.890748i	−0.229425	+	0.973326i	$0.573685\pi$
$642$		0			0
$643$	−6.79295	−	6.79295i	−0.267888	−	0.267888i	0.560361	−	0.828249i	$-0.310662\pi$
$643$	−6.79295	−	6.79295i	−0.267888	−	0.267888i	−0.828249	+	0.560361i	$0.810662\pi$
$644$	−21.1508	−	11.2828i	−0.833457	−	0.444604i
$645$		0			0
$646$	7.44296	+	32.3388i	0.292840	+	1.27235i
$647$	30.3148	+	15.4461i	1.19180	+	0.607251i	0.933417	−	0.358793i	$-0.116812\pi$
$647$	30.3148	+	15.4461i	1.19180	+	0.607251i	0.258379	+	0.966044i	$0.416812\pi$
$648$		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	0.338791	−	0.940862i	$-0.389982\pi$
$653$	−5.70477	−	2.90673i	−0.223245	−	0.113749i	−0.562036	+	0.827112i	$0.689982\pi$
$654$		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	−0.338952	−	0.940804i	$-0.610073\pi$
$659$	11.5792	−	8.41281i	0.451063	−	0.327716i	0.790015	+	0.613087i	$0.210073\pi$
$660$		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	$0.702925\pi$
$662$	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	−0.550660	−	0.834729i	$-0.685624\pi$
$673$	−21.1799	+	3.35456i	−0.816424	+	0.129309i	−0.265764	+	0.964038i	$0.585624\pi$
$674$	−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	−0.647395	−	0.762155i	$-0.724142\pi$
$677$	−6.95245	−	43.8961i	−0.267204	−	1.68706i	0.380191	−	0.924908i	$-0.375858\pi$
$678$		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	0.0163335	−	0.999867i	$-0.494801\pi$
$683$	21.8180	−	11.1168i	0.834843	−	0.425374i	0.818510	+	0.574493i	$0.194801\pi$
$684$		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	0.579755	−	0.814791i	$-0.303148\pi$
$691$	−9.83947	−	13.5429i	−0.374311	−	0.515195i	−0.954066	+	0.299596i	$0.903148\pi$
$692$	−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	0.974264	+	0.225408i	$0.0723715\pi$
$709$	23.6335	+	32.5288i	0.887576	+	1.22164i	−0.0866885	+	0.996235i	$0.527628\pi$
$710$	−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	−0.992400	−	0.123053i	$-0.960731\pi$
$719$	−3.14270	+	9.67223i	−0.117203	+	0.360713i	0.875197	+	0.483766i	$0.160731\pi$
$720$		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	−0.314893	−	0.949127i	$-0.601969\pi$
$727$	−8.65722	+	1.37117i	−0.321078	+	0.0508538i	−0.00618506	+	0.999981i	$0.501969\pi$
$728$	−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	0.888789	−	0.458317i	$-0.151548\pi$
$733$	−0.119518	−	0.234567i	−0.00441450	−	0.00866394i	−0.893203	+	0.449653i	$0.851548\pi$
$734$	−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	0.692235	−	0.721672i	$-0.256626\pi$
$739$	5.97506	+	4.34113i	0.219796	+	0.159691i	−0.472439	+	0.881363i	$0.656626\pi$
$740$	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	0.824269	−	0.566198i	$-0.191586\pi$
$743$	7.03452	+	7.03452i	0.258071	+	0.258071i	−0.566198	+	0.824269i	$0.691586\pi$
$744$		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	$0.178866\pi$
$751$			29.2029i			1.06563i	−0.846232	+	0.532814i	$0.821134\pi$
$752$	−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	0.237707	−	0.971337i	$-0.423604\pi$
$757$	−20.1848	−	20.1848i	−0.733630	−	0.733630i	−0.971337	+	0.237707i	$0.923604\pi$
$758$	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	0.434639	−	0.900605i	$-0.356876\pi$
$761$	−7.93313	−	5.76375i	−0.287576	−	0.208936i	−0.722215	+	0.691669i	$0.756876\pi$
$762$		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	0.603812	−	0.797127i	$-0.293648\pi$
$769$	17.2976	+	5.62032i	0.623766	+	0.202674i	0.0199544	+	0.999801i	$0.493648\pi$
$770$	−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	−0.866627	−	0.498957i	$-0.833717\pi$
$773$	−42.7233	+	6.76671i	−1.53665	+	0.243382i	−0.670025	+	0.742339i	$0.733717\pi$
$774$		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	−0.930581	−	0.366087i	$-0.880697\pi$
$787$	1.89589	−	11.9702i	0.0675813	−	0.426691i	0.998162	−	0.0606043i	$-0.0193028\pi$
$788$	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	−0.719895	−	0.694083i	$-0.755810\pi$
$797$	7.47486	−	14.6702i	0.264773	−	0.519646i	0.984668	+	0.174436i	$0.0558103\pi$
$798$		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	0.528782	−	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	−0.999136	−	0.0415488i	$-0.986771\pi$
$811$	−18.5355	+	25.5120i	−0.650871	+	0.895847i	0.348265	+	0.937396i	$0.386771\pi$
$812$	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	0.998989	+	0.0449507i	$0.0143131\pi$
$821$	6.22378	+	19.1548i	0.217211	+	0.668508i	−0.781778	+	0.623557i	$0.785687\pi$
$822$		0			0
$823$	−6.60034	−	41.6729i	−0.230073	−	1.45263i	−0.784363	−	0.620302i	$-0.787010\pi$
$823$	−6.60034	−	41.6729i	−0.230073	−	1.45263i	0.554289	−	0.832324i	$-0.312990\pi$
$824$	1.43105	−	5.29776i	0.0498531	−	0.184556i
$825$		0			0
$826$	3.01613	−	34.2082i	0.104945	−	1.19026i
$827$	−13.5996	+	2.15397i	−0.472905	+	0.0749008i	−0.388338	−	0.921517i	$-0.626951\pi$
$827$	−13.5996	+	2.15397i	−0.472905	+	0.0749008i	−0.0845669	+	0.996418i	$0.526951\pi$
$828$		0			0
$829$	35.5980	−	11.5665i	1.23637	−	0.401721i	0.383352	−	0.923602i	$-0.374770\pi$
$829$	35.5980	−	11.5665i	1.23637	−	0.401721i	0.853018	+	0.521881i	$0.174770\pi$
$830$	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	0.694805	−	0.719198i	$-0.255491\pi$
$839$	6.53213	+	4.74587i	0.225514	+	0.163846i	−0.469291	+	0.883044i	$0.655491\pi$
$840$		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	−0.167851	−	0.985812i	$-0.553683\pi$
$853$	−31.0768	−	15.8344i	−1.06405	−	0.542160i	−0.896199	+	0.443652i	$0.853683\pi$
$854$	5.31085	−	1.22232i	0.181733	−	0.0418271i
$855$		0			0
$856$	−17.6964	+	27.1294i	−0.604850	+	0.927265i
$857$	−31.7738	−	31.7738i	−1.08537	−	1.08537i	−0.995998	−	0.0893726i	$-0.971514\pi$
$857$	−31.7738	−	31.7738i	−1.08537	−	1.08537i	−0.0893726	−	0.995998i	$-0.528486\pi$
$858$		0			0
$859$	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	$0.0429325\pi$
$860$	−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	0.430242	−	0.902714i	$-0.358428\pi$
$863$	16.4649	+	2.60778i	0.560472	+	0.0887700i	0.130230	+	0.991484i	$0.458428\pi$
$864$		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	−0.995347	−	0.0963539i	$-0.969282\pi$
$877$	−2.32444	−	14.6759i	−0.0784907	−	0.495571i	0.916856	−	0.399217i	$-0.130718\pi$
$878$	−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	−0.284177	−	0.958772i	$-0.591720\pi$
$881$	15.1162	−	46.5230i	0.509279	−	1.56740i	0.793456	−	0.608628i	$-0.208280\pi$
$882$		0			0
$883$	1.45332	−	0.740506i	0.0489083	−	0.0249200i	−0.429365	−	0.903131i	$-0.641263\pi$
$883$	1.45332	−	0.740506i	0.0489083	−	0.0249200i	0.478274	+	0.878211i	$0.341263\pi$
$884$	−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	−0.808888	−	0.587963i	$-0.799930\pi$
$887$	4.23212	−	26.7206i	0.142101	−	0.897189i	0.950989	−	0.309226i	$-0.100070\pi$
$888$		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	−0.200818	+	0.979629i	$0.564360\pi$
$907$	−35.5508	+	35.5508i	−1.18045	+	1.18045i	−0.979629	+	0.200818i	$0.935640\pi$
$908$	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	−0.861807	−	0.507236i	$-0.830667\pi$
$911$	−3.41319	+	4.69785i	−0.113084	+	0.155647i	0.748723	+	0.662883i	$0.230667\pi$
$912$		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	−0.447990	−	0.894039i	$-0.647860\pi$
$919$	13.3369	−	41.0468i	0.439944	−	1.35401i	0.887934	−	0.459971i	$-0.152140\pi$
$920$	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	−0.811829	−	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			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	0.733905	−	0.679252i	$-0.237696\pi$
$937$	37.4056	+	5.92447i	1.22199	+	0.193544i	0.488084	+	0.872796i	$0.337696\pi$
$938$	−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	−0.922902	−	0.385034i	$-0.874190\pi$
$941$	−25.8261	+	18.7637i	−0.841906	+	0.611680i	0.0809965	+	0.996714i	$0.474190\pi$
$942$		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	0.504405	−	0.863467i	$-0.331712\pi$
$947$	3.14898	+	1.60449i	0.102328	+	0.0521388i	−0.402077	+	0.915606i	$0.631712\pi$
$948$		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	−0.556759	−	0.830674i	$-0.687955\pi$
$953$	−48.0361	−	24.4756i	−1.55604	−	0.792843i	−0.999284	+	0.0378308i	$0.987955\pi$
$954$		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	0.749873	−	0.661582i	$-0.230115\pi$
$967$	−7.03165	−	13.8004i	−0.226123	−	0.443791i	−0.975995	+	0.217792i	$0.930115\pi$
$968$	−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	−0.0272659	−	0.999628i	$-0.508680\pi$
$971$	16.7721	−	5.44959i	0.538242	−	0.174886i	0.565508	+	0.824743i	$0.308680\pi$
$972$		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	0.663319	+	0.748337i	$0.269147\pi$
$977$	8.24291	+	52.0437i	0.263714	+	1.66502i	−0.399605	+	0.916687i	$0.630853\pi$
$978$		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	−0.685234	−	0.728323i	$-0.740300\pi$
$983$	−15.6381	+	7.96803i	−0.498779	+	0.254141i	0.186455	+	0.982463i	$0.440300\pi$
$984$		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	0.360221	−	0.932867i	$-0.382701\pi$
$991$	−20.0939	−	27.6568i	−0.638302	−	0.878548i	−0.998524	+	0.0543192i	$0.982701\pi$
$992$	−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	−0.875398	−	0.483404i	$-0.839400\pi$
$997$	0.954518	−	1.87335i	0.0302299	−	0.0593295i	0.905628	+	0.424074i	$0.139400\pi$
$998$	−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.487.12		96
3.2	odd	2		100.2.l.b.87.1	yes	96
4.3	odd	2	inner	900.2.bj.d.487.1		96
12.11	even	2		100.2.l.b.87.12	yes	96
15.2	even	4		500.2.l.d.43.5		96
15.8	even	4		500.2.l.e.43.8		96
15.14	odd	2		500.2.l.f.207.12		96
25.23	odd	20	inner	900.2.bj.d.523.1		96
60.23	odd	4		500.2.l.e.43.7		96
60.47	odd	4		500.2.l.d.43.6		96
60.59	even	2		500.2.l.f.207.1		96
75.2	even	20		500.2.l.f.343.1		96
75.11	odd	10		500.2.l.e.407.7		96
75.14	odd	10		500.2.l.d.407.6		96
75.23	even	20		100.2.l.b.23.12	yes	96
100.23	even	20	inner	900.2.bj.d.523.12		96
300.11	even	10		500.2.l.e.407.8		96
300.23	odd	20		100.2.l.b.23.1	✓	96
300.227	odd	20		500.2.l.f.343.12		96
300.239	even	10		500.2.l.d.407.5		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.2.l.b.23.1	✓	96	300.23	odd	20
100.2.l.b.23.12	yes	96	75.23	even	20
100.2.l.b.87.1	yes	96	3.2	odd	2
100.2.l.b.87.12	yes	96	12.11	even	2
500.2.l.d.43.5		96	15.2	even	4
500.2.l.d.43.6		96	60.47	odd	4
500.2.l.d.407.5		96	300.239	even	10
500.2.l.d.407.6		96	75.14	odd	10
500.2.l.e.43.7		96	60.23	odd	4
500.2.l.e.43.8		96	15.8	even	4
500.2.l.e.407.7		96	75.11	odd	10
500.2.l.e.407.8		96	300.11	even	10
500.2.l.f.207.1		96	60.59	even	2
500.2.l.f.207.12		96	15.14	odd	2
500.2.l.f.343.1		96	75.2	even	20
500.2.l.f.343.12		96	300.227	odd	20
900.2.bj.d.487.1		96	4.3	odd	2	inner
900.2.bj.d.487.12		96	1.1	even	1	trivial
900.2.bj.d.523.1		96	25.23	odd	20	inner
900.2.bj.d.523.12		96	100.23	even	20	inner

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

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