LMFDB - Embedded newform 900.2.bj.d.487.1

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			487.1
Character	$\chi$	$=$	900.487
Dual form			900.2.bj.d.523.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37197 + 0.343057i) q^{2} +(1.76462 - 0.941330i) q^{4} +(1.18066 + 1.89896i) q^{5} +(-1.89427 + 1.89427i) q^{7} +(-2.09809 + 1.89685i) q^{8} +O(q^{10})$	\(q+(-1.37197 + 0.343057i) q^{2} +(1.76462 - 0.941330i) q^{4} +(1.18066 + 1.89896i) q^{5} +(-1.89427 + 1.89427i) q^{7} +(-2.09809 + 1.89685i) q^{8} +(-2.27128 - 2.20029i) q^{10} +(2.99934 - 4.12824i) q^{11} +(0.433317 - 2.73586i) q^{13} +(1.94904 - 3.24872i) q^{14} +(2.22780 - 3.32219i) q^{16} +(4.16697 - 2.12318i) q^{17} +(1.55045 - 4.77181i) q^{19} +(3.87097 + 2.23956i) q^{20} +(-2.69880 + 6.69278i) q^{22} +(0.699923 + 4.41914i) q^{23} +(-2.21209 + 4.48404i) q^{25} +(0.344055 + 3.90218i) q^{26} +(-1.55954 + 5.12580i) q^{28} +(0.211843 - 0.0688321i) q^{29} +(7.01920 + 2.28068i) q^{31} +(-1.91678 + 5.32221i) q^{32} +(-4.98861 + 4.34246i) q^{34} +(-5.83362 - 1.36065i) q^{35} +(4.32186 + 0.684516i) q^{37} +(-0.490182 + 7.07869i) q^{38} +(-6.07916 - 1.74466i) q^{40} +(-2.54404 + 1.84835i) q^{41} +(-2.68807 - 2.68807i) q^{43} +(1.40668 - 10.1082i) q^{44} +(-2.47629 - 5.82283i) q^{46} +(7.84709 + 3.99829i) q^{47} -0.176489i q^{49} +(1.49665 - 6.91086i) q^{50} +(-1.81070 - 5.23565i) q^{52} +(-1.64295 - 0.837124i) q^{53} +(11.3806 + 0.821587i) q^{55} +(0.381206 - 7.56747i) q^{56} +(-0.267030 + 0.167110i) q^{58} +(-7.33328 + 5.32794i) q^{59} +(1.16375 + 0.845512i) q^{61} +(-10.4126 - 0.721044i) q^{62} +(0.803948 - 7.95950i) q^{64} +(5.70688 - 2.40726i) q^{65} +(1.53527 + 3.01313i) q^{67} +(5.35453 - 7.66911i) q^{68} +(8.47035 - 0.134481i) q^{70} +(5.45415 - 1.77216i) q^{71} +(-0.0187149 + 0.00296414i) q^{73} +(-6.16431 + 0.543507i) q^{74} +(-1.75588 - 9.87994i) q^{76} +(2.13843 + 13.5015i) q^{77} +(2.08434 + 6.41493i) q^{79} +(8.93896 + 0.308126i) q^{80} +(2.85627 - 3.40864i) q^{82} +(-2.99552 + 1.52629i) q^{83} +(8.95160 + 5.40616i) q^{85} +(4.61012 + 2.76580i) q^{86} +(1.53775 + 14.3507i) q^{88} +(0.509284 - 0.700969i) q^{89} +(4.36162 + 6.00326i) q^{91} +(5.39497 + 7.13927i) q^{92} +(-12.1376 - 2.79355i) q^{94} +(10.8920 - 2.68963i) q^{95} +(-5.07638 + 9.96296i) q^{97} +(0.0605458 + 0.242139i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.37197	+	0.343057i	−0.970132	+	0.242578i
$2$	−1.37197	+	0.343057i	−0.970132	+	0.242578i
$3$		0			0
$3$		0			0
$4$	1.76462	−	0.941330i	0.882312	−	0.470665i
$5$	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	$-0.918974\pi$
$7$	−1.89427	+	1.89427i	−0.715965	+	0.715965i	0.251811	+	0.967776i	$0.418974\pi$
$8$	−2.09809	+	1.89685i	−0.741786	+	0.670636i
$9$		0			0
$10$	−2.27128	−	2.20029i	−0.718243	−	0.695793i
$11$	2.99934	−	4.12824i	0.904336	−	1.24471i	−0.0647283	−	0.997903i	$-0.520618\pi$
$11$	2.99934	−	4.12824i	0.904336	−	1.24471i	0.969064	−	0.246809i	$-0.0793819\pi$
$12$		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	$-0.0754966\pi$
$14$	1.94904	−	3.24872i	0.520904	−	0.868258i
$15$		0			0
$16$	2.22780	−	3.32219i	0.556949	−	0.830547i
$17$	4.16697	−	2.12318i	1.01064	−	0.514947i	0.131402	−	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	$-0.704795\pi$
$19$	1.55045	−	4.77181i	0.355699	−	1.09473i	0.955603	−	0.294657i	$-0.0952052\pi$
$20$	3.87097	+	2.23956i	0.865574	+	0.500781i
$21$		0			0
$22$	−2.69880	+	6.69278i	−0.575386	+	1.42691i
$23$	0.699923	+	4.41914i	0.145944	+	0.921455i	0.946619	+	0.322355i	$0.104475\pi$
$23$	0.699923	+	4.41914i	0.145944	+	0.921455i	−0.800675	+	0.599100i	$0.795525\pi$
$24$		0			0
$25$	−2.21209	+	4.48404i	−0.442418	+	0.896809i
$26$	0.344055	+	3.90218i	0.0674747	+	0.765280i
$27$		0			0
$28$	−1.55954	+	5.12580i	−0.294725	+	0.968685i
$29$	0.211843	−	0.0688321i	0.0393383	−	0.0127818i	−0.289282	−	0.957244i	$-0.593416\pi$
$29$	0.211843	−	0.0688321i	0.0393383	−	0.0127818i	0.328620	+	0.944462i	$0.393416\pi$
$30$		0			0
$31$	7.01920	+	2.28068i	1.26069	+	0.409622i	0.861739	−	0.507352i	$-0.169376\pi$
$31$	7.01920	+	2.28068i	1.26069	+	0.409622i	0.398947	+	0.916974i	$0.369376\pi$
$32$	−1.91678	+	5.32221i	−0.338842	+	0.940843i
$33$		0			0
$34$	−4.98861	+	4.34246i	−0.855539	+	0.744725i
$35$	−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	$0.432885\pi$
$38$	−0.490182	+	7.07869i	−0.0795179	+	1.14832i
$39$		0			0
$40$	−6.07916	−	1.74466i	−0.961199	−	0.275854i
$41$	−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	0.471786	−	0.881713i	$-0.343609\pi$
$43$	−2.68807	−	2.68807i	−0.409927	−	0.409927i	−0.881713	+	0.471786i	$0.843609\pi$
$44$	1.40668	−	10.1082i	0.212064	−	1.52386i
$45$		0			0
$46$	−2.47629	−	5.82283i	−0.365110	−	0.858530i
$47$	7.84709	+	3.99829i	1.14462	+	0.583211i	0.920264	−	0.391298i	$-0.127974\pi$
$47$	7.84709	+	3.99829i	1.14462	+	0.583211i	0.224351	+	0.974508i	$0.427974\pi$
$48$		0			0
$49$		−	0.176489i		−	0.0252127i
$50$	1.49665	−	6.91086i	0.211658	−	0.977344i
$51$		0			0
$52$	−1.81070	−	5.23565i	−0.251099	−	0.726055i
$53$	−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
$56$	0.381206	−	7.56747i	0.0509407	−	1.01125i
$57$		0			0
$58$	−0.267030	+	0.167110i	−0.0350628	+	0.0219426i
$59$	−7.33328	+	5.32794i	−0.954712	+	0.693639i	−0.951917	−	0.306357i	$-0.900890\pi$
$59$	−7.33328	+	5.32794i	−0.954712	+	0.693639i	−0.00279513	+	0.999996i	$0.500890\pi$
$60$		0			0
$61$	1.16375	+	0.845512i	0.149003	+	0.108257i	0.659789	−	0.751451i	$-0.270646\pi$
$61$	1.16375	+	0.845512i	0.149003	+	0.108257i	−0.510786	+	0.859708i	$0.670646\pi$
$62$	−10.4126	−	0.721044i	−1.32240	−	0.0915727i
$63$		0			0
$64$	0.803948	−	7.95950i	0.100493	−	0.994938i
$65$	5.70688	−	2.40726i	0.707852	−	0.298584i
$66$		0			0
$67$	1.53527	+	3.01313i	0.187563	+	0.368113i	0.965570	−	0.260142i	$-0.0837695\pi$
$67$	1.53527	+	3.01313i	0.187563	+	0.368113i	−0.778007	+	0.628255i	$0.783769\pi$
$68$	5.35453	−	7.66911i	0.649332	−	0.930016i
$69$		0			0
$70$	8.47035	−	0.134481i	1.01240	−	0.0160736i
$71$	5.45415	−	1.77216i	0.647288	−	0.210317i	0.0330703	−	0.999453i	$-0.489471\pi$
$71$	5.45415	−	1.77216i	0.647288	−	0.210317i	0.614218	+	0.789136i	$0.289471\pi$
$72$		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	$0.0238830\pi$
$79$	2.08434	+	6.41493i	0.234506	+	0.721736i	−0.762680	+	0.646776i	$0.776117\pi$
$80$	8.93896	+	0.308126i	0.999406	+	0.0344495i
$81$		0			0
$82$	2.85627	−	3.40864i	0.315422	−	0.376422i
$83$	−2.99552	+	1.52629i	−0.328801	+	0.167532i	−0.610596	−	0.791942i	$-0.709070\pi$
$83$	−2.99552	+	1.52629i	−0.328801	+	0.167532i	0.281795	+	0.959475i	$0.409070\pi$
$84$		0			0
$85$	8.95160	+	5.40616i	0.970938	+	0.586381i
$86$	4.61012	+	2.76580i	0.497122	+	0.298244i
$87$		0			0
$88$	1.53775	+	14.3507i	0.163925	+	1.52979i
$89$	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
$92$	5.39497	+	7.13927i	0.562465	+	0.744320i
$93$		0			0
$94$	−12.1376	−	2.79355i	−1.25190	−	0.288133i
$95$	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	$0.957847\pi$
$98$	0.0605458	+	0.242139i	0.00611605	+	0.0244597i
$99$		0			0
$100$	0.317454	+	9.99496i	0.0317454	+	0.999496i
$101$	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	$-0.880472\pi$
$103$	−0.880821	+	1.72871i	−0.0867899	+	0.170335i	0.843532	+	0.537079i	$0.180472\pi$
$104$	4.28036	+	6.56201i	0.419724	+	0.643458i
$105$		0			0
$106$	2.54126	+	0.584888i	0.246829	+	0.0568093i
$107$	8.09772	−	8.09772i	0.782836	−	0.782836i	−0.197472	−	0.980308i	$-0.563273\pi$
$107$	8.09772	−	8.09772i	0.782836	−	0.782836i	0.980308	+	0.197472i	$0.0632733\pi$
$108$		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	$-0.467122\pi$
$110$	−15.8957	+	2.77698i	−1.51559	+	0.264775i
$111$		0			0
$112$	2.07307	+	10.5131i	0.195887	+	0.993399i
$113$	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
$116$	0.309030	−	0.320877i	0.0286927	−	0.0297927i
$117$		0			0
$118$	8.23328	−	9.82552i	0.757935	−	0.904513i
$119$	−3.87149	+	11.9152i	−0.354899	+	1.09227i
$120$		0			0
$121$	−4.64713	−	14.3024i	−0.422467	−	1.30022i
$122$	−1.88669	−	0.760789i	−0.170813	−	0.0688786i
$123$		0			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	$-0.297703\pi$
$127$	15.8543	−	2.51108i	1.40684	−	0.222822i	0.813237	+	0.581932i	$0.197703\pi$
$128$	1.62757	+	11.1960i	0.143858	+	0.989598i
$129$		0			0
$130$	−7.00386	+	5.26048i	−0.614280	+	0.461375i
$131$	12.9418	+	4.20505i	1.13073	+	0.367397i	0.813854	−	0.581069i	$-0.197365\pi$
$131$	12.9418	+	4.20505i	1.13073	+	0.367397i	0.316878	+	0.948466i	$0.397365\pi$
$132$		0			0
$133$	6.10210	+	11.9761i	0.529119	+	1.03846i
$134$	−3.14002	−	3.60726i	−0.271257	−	0.311619i
$135$		0			0
$136$	−4.71533	+	12.3587i	−0.404337	+	1.05975i
$137$	−18.6626	−	2.95587i	−1.59445	−	0.252537i	−0.704880	−	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	0.809039	−	0.587755i	$-0.199988\pi$
$139$	5.89560	+	4.28340i	0.500058	+	0.363313i	−0.308981	+	0.951068i	$0.599988\pi$
$140$	−11.5750	+	3.09032i	−0.978263	+	0.261179i
$141$		0			0
$142$	−6.87500	+	4.30244i	−0.576937	+	0.361053i
$143$	−9.99461	−	9.99461i	−0.835792	−	0.835792i
$144$		0			0
$145$	0.380824	+	0.321015i	0.0316257	+	0.0266588i
$146$	0.0246594	−	0.0104870i	0.00204083	−	0.000867909i
$147$		0			0
$148$	8.27082	−	2.86039i	0.679857	−	0.235122i
$149$			2.12851i			0.174375i	0.996192	+	0.0871873i	$0.0277879\pi$
$149$			2.12851i			0.174375i	−0.996192	+	0.0871873i	$0.972212\pi$
$150$		0			0
$151$		−	6.10369i		−	0.496712i	−0.968669	−	0.248356i	$-0.920110\pi$
$151$		−	6.10369i		−	0.496712i	0.968669	−	0.248356i	$-0.0798902\pi$
$152$	5.79840	+	12.9527i	0.470312	+	1.05060i
$153$		0			0
$154$	−7.56567	−	17.7902i	−0.609659	−	1.43357i
$155$	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	$0.974338\pi$
$158$	−5.06034	−	8.08607i	−0.402579	−	0.643293i
$159$		0			0
$160$	−12.3697	+	2.64383i	−0.977913	+	0.209013i
$161$	−9.69687	−	7.04519i	−0.764221	−	0.555239i
$162$		0			0
$163$	7.81379	+	1.23758i	0.612023	+	0.0969349i	0.454748	−	0.890620i	$-0.349729\pi$
$163$	7.81379	+	1.23758i	0.612023	+	0.0969349i	0.157275	+	0.987555i	$0.449729\pi$
$164$	−2.74936	+	5.65643i	−0.214689	+	0.441693i
$165$		0			0
$166$	3.58617	−	3.12167i	0.278341	−	0.242288i
$167$	−6.13600	−	12.0426i	−0.474818	−	0.931883i	−0.996877	−	0.0789735i	$-0.974836\pi$
$167$	−6.13600	−	12.0426i	−0.474818	−	0.931883i	0.522059	−	0.852910i	$-0.325164\pi$
$168$		0			0
$169$	5.06658	+	1.64623i	0.389737	+	0.126633i
$170$	−14.1360	−	4.34621i	−1.08418	−	0.333339i
$171$		0			0
$172$	−7.27379	−	2.21307i	−0.554621	−	0.168745i
$173$	−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
$178$	−0.458252	+	1.13642i	−0.0343474	+	0.0851786i
$179$	−7.45601	−	22.9472i	−0.557289	−	1.71516i	−0.689822	−	0.723979i	$-0.742311\pi$
$179$	−7.45601	−	22.9472i	−0.557289	−	1.71516i	0.132533	−	0.991179i	$-0.457689\pi$
$180$		0			0
$181$	−2.15964	+	6.64670i	−0.160525	+	0.494045i	−0.998679	−	0.0513890i	$-0.983635\pi$
$181$	−2.15964	+	6.64670i	−0.160525	+	0.494045i	0.838154	+	0.545434i	$0.183635\pi$
$182$	−8.04349	−	6.74003i	−0.596223	−	0.499604i
$183$		0			0
$184$	−9.85094	−	7.94410i	−0.726221	−	0.585647i
$185$	3.80277	+	9.01522i	0.279586	+	0.662812i
$186$		0			0
$187$	3.73319	−	23.5704i	0.272998	−	1.72364i
$188$	17.6109	−	0.331219i	1.28440	−	0.0241566i
$189$		0			0
$190$	−14.0209	+	7.42668i	−1.01718	+	0.538788i
$191$	9.26511	+	12.7523i	0.670400	+	0.922727i	0.999769	−	0.0214746i	$-0.00683611\pi$
$191$	9.26511	+	12.7523i	0.670400	+	0.922727i	−0.329369	+	0.944201i	$0.606836\pi$
$192$		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	$0.143539\pi$
$194$	3.54680	−	15.4104i	0.254645	−	1.10640i
$195$		0			0
$196$	−0.166135	−	0.311437i	−0.0118668	−	0.0222455i
$197$	2.59555	−	5.09406i	0.184925	−	0.362936i	−0.779869	−	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	$-0.838049\pi$
$199$	−24.6399			−1.74668			−0.873338	+	0.487115i	$0.838049\pi$
$200$	−3.86438	−	13.6039i	−0.273253	−	0.961942i
$201$		0			0
$202$	−16.2008	+	4.05095i	−1.13988	+	0.285024i
$203$	−0.270901	+	0.531674i	−0.0190136	+	0.0373162i
$204$		0			0
$205$	−6.51359	−	2.64875i	−0.454929	−	0.184997i
$206$	0.615418	−	2.67391i	0.0428782	−	0.186300i
$207$		0			0
$208$	−8.12369	−	7.53449i	−0.563276	−	0.522423i
$209$	−15.0488	−	20.7129i	−1.04095	−	1.43274i
$210$		0			0
$211$	11.6703	−	16.0628i	0.803419	−	1.10581i	−0.188886	−	0.981999i	$-0.560488\pi$
$211$	11.6703	−	16.0628i	0.803419	−	1.10581i	0.992306	−	0.123813i	$-0.0395122\pi$
$212$	−3.68720	+	0.0693474i	−0.253238	+	0.00476280i
$213$		0			0
$214$	−8.33188	+	13.8878i	−0.569556	+	0.949353i
$215$	1.93084	−	8.27822i	0.131682	−	0.564570i
$216$		0			0
$217$	−17.6165	+	8.97603i	−1.19588	+	0.609333i
$218$	16.8419	+	14.1126i	1.14068	+	0.955827i
$219$		0			0
$220$	20.8558	−	9.26307i	1.40610	−	0.624516i
$221$	−4.00309	−	12.3203i	−0.269277	−	0.828750i
$222$		0			0
$223$	1.81060	+	11.4317i	0.121247	+	0.765524i	0.971130	+	0.238552i	$0.0766727\pi$
$223$	1.81060	+	11.4317i	0.121247	+	0.765524i	−0.849883	+	0.526972i	$0.823327\pi$
$224$	−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	$-0.722313\pi$
$227$	−15.3359	+	2.42897i	−1.01788	+	0.161216i	−0.374872	+	0.927077i	$0.622313\pi$
$228$		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	$0.588026\pi$
$230$	8.13367	−	11.5772i	0.536318	−	0.763375i
$231$		0			0
$232$	−0.313902	+	0.546250i	−0.0206087	+	0.0358631i
$233$	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
$236$	−7.92513	+	16.3048i	−0.515882	+	1.06136i
$237$		0			0
$238$	1.22399	−	17.6755i	0.0793392	−	1.14573i
$239$	0.369981	+	0.268807i	0.0239321	+	0.0173877i	0.599687	−	0.800235i	$-0.295292\pi$
$239$	0.369981	+	0.268807i	0.0239321	+	0.0173877i	−0.575755	+	0.817622i	$0.695292\pi$
$240$		0			0
$241$	17.6697	−	12.8378i	1.13820	−	0.826953i	0.151335	−	0.988483i	$-0.451643\pi$
$241$	17.6697	−	12.8378i	1.13820	−	0.826953i	0.986868	+	0.161530i	$0.0516429\pi$
$242$	11.2823	+	18.0283i	0.725252	+	1.15890i
$243$		0			0
$244$	2.84948	+	0.396541i	0.182419	+	0.0253859i
$245$	0.335146	−	0.208373i	0.0214117	−	0.0133125i
$246$		0			0
$247$	−12.3832	−	6.30953i	−0.787921	−	0.401466i
$248$	−19.0530	+	8.52929i	−1.20987	+	0.541610i
$249$		0			0
$250$	14.8905	−	5.31729i	0.941757	−	0.336295i
$251$		−	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
$254$	−20.8903	+	8.88407i	−1.31077	+	0.557436i
$255$		0			0
$256$	−6.07385	−	14.8023i	−0.379616	−	0.925144i
$257$	−8.02192	−	8.02192i	−0.500394	−	0.500394i	0.411166	−	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
$260$	7.80447	−	9.61997i	0.484013	−	0.596605i
$261$		0			0
$262$	−19.1984	−	1.32944i	−1.18608	−	0.0821332i
$263$	−19.6441	−	3.11132i	−1.21131	−	0.191852i	−0.482081	−	0.876127i	$-0.660119\pi$
$263$	−19.6441	−	3.11132i	−1.21131	−	0.191852i	−0.729224	+	0.684275i	$0.760119\pi$
$264$		0			0
$265$	−0.350096	−	4.10825i	−0.0215063	−	0.252368i
$266$	−12.4804	−	14.3375i	−0.765222	−	0.879086i
$267$		0			0
$268$	5.54552	+	3.87185i	0.338747	+	0.236511i
$269$	9.63789	+	3.13154i	0.587633	+	0.190933i	0.587717	−	0.809067i	$-0.300027\pi$
$269$	9.63789	+	3.13154i	0.587633	+	0.190933i	−8.44003e−5		1.00000i	$0.500027\pi$
$270$		0			0
$271$	−1.79674	+	0.583795i	−0.109144	+	0.0354630i	−0.363080	−	0.931758i	$-0.618275\pi$
$271$	−1.79674	+	0.583795i	−0.109144	+	0.0354630i	0.253936	+	0.967221i	$0.418275\pi$
$272$	2.22957	−	18.5735i	0.135187	−	1.12618i
$273$		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	$0.838225\pi$
$278$	−9.55805	−	3.85419i	−0.573254	−	0.231159i
$279$		0			0
$280$	14.8204	−	8.21070i	0.885688	−	0.490683i
$281$	−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	−0.878780	−	0.477227i	$-0.841642\pi$
$283$	−16.9779	+	8.65065i	−1.00923	+	0.514228i	−0.130449	+	0.991455i	$0.541642\pi$
$284$	7.95633	−	8.26135i	0.472122	−	0.490221i
$285$		0			0
$286$	17.1411	+	10.2836i	1.01357	+	0.608084i
$287$	1.31782	−	8.32036i	0.0777882	−	0.491135i
$288$		0			0
$289$	2.86343	−	3.94118i	0.168437	−	0.231834i
$290$	−0.632607	−	0.309780i	−0.0371479	−	0.0181909i
$291$		0			0
$292$	−0.0302344	+	0.0228475i	−0.00176934	+	0.00133705i
$293$	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
$296$	−10.3661	+	6.76173i	−0.602515	+	0.393018i
$297$		0			0
$298$	−0.730201	−	2.92026i	−0.0422994	−	0.169166i
$299$	12.3934			0.716731
$300$		0			0
$301$	10.1838			0.586986
$302$	2.09391	+	8.37411i	0.120491	+	0.481876i
$303$		0			0
$304$	−12.3987	−	15.7815i	−0.711117	−	0.905132i
$305$	−0.231605	+	3.20817i	−0.0132616	+	0.183699i
$306$		0			0
$307$	−9.17187	+	9.17187i	−0.523466	+	0.523466i	−0.918616	−	0.395150i	$-0.870692\pi$
$307$	−9.17187	+	9.17187i	−0.523466	+	0.523466i	0.395150	+	0.918616i	$0.370692\pi$
$308$	16.4829	+	21.8122i	0.939203	+	1.24286i
$309$		0			0
$310$	−10.9245	−	20.6243i	−0.620467	−	1.17138i
$311$	2.44643	−	3.36722i	0.138724	−	0.190938i	−0.734002	−	0.679147i	$-0.762350\pi$
$311$	2.44643	−	3.36722i	0.138724	−	0.190938i	0.872726	+	0.488209i	$0.162350\pi$
$312$		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	$-0.168249\pi$
$314$	19.6889	+	11.8122i	1.11111	+	0.666598i
$315$		0			0
$316$	9.71663	+	9.35789i	0.546603	+	0.526422i
$317$	−5.61291	+	2.85992i	−0.315252	+	0.160629i	−0.604456	−	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
$320$	16.0640	−	7.87079i	0.898002	−	0.439990i
$321$		0			0
$322$	15.7208	+	6.33924i	0.876084	+	0.353272i
$323$	−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
$328$	1.83158	−	8.70366i	0.101132	−	0.480579i
$329$	−22.4383	+	7.29065i	−1.23706	+	0.401946i
$330$		0			0
$331$	−15.4106	−	5.00720i	−0.847042	−	0.275221i	−0.146835	−	0.989161i	$-0.546909\pi$
$331$	−15.4106	−	5.00720i	−0.847042	−	0.275221i	−0.700206	+	0.713940i	$0.746909\pi$
$332$	−3.84922	+	5.51311i	−0.211253	+	0.302571i
$333$		0			0
$334$	12.5497	+	14.4171i	0.686690	+	0.788869i
$335$	−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	$0.735688\pi$
$338$	−7.51597	−	0.520462i	−0.408815	−	0.0283094i
$339$		0			0
$340$	20.8852	+	1.11343i	1.13266	+	0.0603845i
$341$	30.4682	−	22.1364i	1.64995	−	1.19876i
$342$		0			0
$343$	−12.9255	−	12.9255i	−0.697914	−	0.697914i
$344$	10.7387	+	0.540952i	0.578990	+	0.0291662i
$345$		0			0
$346$	1.42753	−	0.607091i	0.0767446	−	0.0326374i
$347$	−5.16571	−	2.63206i	−0.277310	−	0.141296i	0.309805	−	0.950800i	$-0.399736\pi$
$347$	−5.16571	−	2.63206i	−0.277310	−	0.141296i	−0.587115	+	0.809504i	$0.699736\pi$
$348$		0			0
$349$		−	0.0528810i		−	0.00283065i	−0.999999	−	0.00141533i	$-0.999549\pi$
$349$		−	0.0528810i		−	0.00283065i	0.999999	−	0.00141533i	$-0.000450513\pi$
$350$	10.2560	+	15.9261i	0.548204	+	0.851284i
$351$		0			0
$352$	16.2223	+	23.8761i	0.864652	+	1.27260i
$353$	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
$356$	0.238851	−	1.71635i	0.0126591	−	0.0909664i
$357$		0			0
$358$	18.1017	+	28.9252i	0.956703	+	1.52874i
$359$	−22.3556	+	16.2423i	−1.17989	+	0.857237i	−0.992159	−	0.124985i	$-0.960112\pi$
$359$	−22.3556	+	16.2423i	−1.17989	+	0.857237i	−0.187726	+	0.982221i	$0.560112\pi$
$360$		0			0
$361$	−4.99493	−	3.62903i	−0.262891	−	0.191002i
$362$	0.682778	−	9.85997i	0.0358860	−	0.518229i
$363$		0			0
$364$	13.3477	+	6.48777i	0.699608	+	0.340052i
$365$	−0.0277246	−	0.0320391i	−0.00145117	−	0.00167700i
$366$		0			0
$367$	3.08204	+	6.04885i	0.160881	+	0.315747i	0.957349	−	0.288934i	$-0.0933007\pi$
$367$	3.08204	+	6.04885i	0.160881	+	0.315747i	−0.796468	+	0.604681i	$0.793301\pi$
$368$	16.2405	+	7.51967i	0.846595	+	0.391990i
$369$		0			0
$370$	−8.31004	−	11.0641i	−0.432018	−	0.575194i
$371$	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	$-0.993342\pi$
$379$	−3.95657	−	12.1771i	−0.203235	−	0.625494i	0.796546	−	0.604578i	$-0.206658\pi$
$380$	16.6885	−	14.9992i	0.856102	−	0.769441i
$381$		0			0
$382$	−17.0863	−	14.3174i	−0.874210	−	0.732542i
$383$	−16.4227	+	8.36780i	−0.839163	+	0.427575i	−0.820084	−	0.572243i	$-0.806073\pi$
$383$	−16.4227	+	8.36780i	−0.839163	+	0.427575i	−0.0190788	+	0.999818i	$0.506073\pi$
$384$		0			0
$385$	−23.1141	+	20.0015i	−1.17800	+	1.01937i
$386$	−6.63569	+	11.0606i	−0.337748	+	0.562968i
$387$		0			0
$388$	0.420528	+	22.3594i	0.0213491	+	1.13513i
$389$	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
$392$	0.334773	+	0.370290i	0.0169086	+	0.0187025i
$393$		0			0
$394$	−1.81348	+	7.87933i	−0.0913617	+	0.396955i
$395$	−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	$-0.0963199\pi$
$398$	33.8053	−	8.45289i	1.69451	−	0.423705i
$399$		0			0
$400$	9.96874	+	17.3385i	0.498437	+	0.866926i
$401$	−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
$404$	20.8374	−	11.1156i	1.03670	−	0.553021i
$405$		0			0
$406$	0.189275	−	0.822377i	0.00939357	−	0.0408139i
$407$	15.7886	−	15.7886i	0.782611	−	0.782611i
$408$		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	$0.925371\pi$
$410$	9.84515	+	1.39949i	0.486217	+	0.0691159i
$411$		0			0
$412$	0.0729673	+	3.87966i	0.00359484	+	0.191137i
$413$	3.79865	−	23.9837i	0.186919	−	1.18016i
$414$		0			0
$415$	−6.43505	−	3.88634i	−0.315884	−	0.190773i
$416$	13.7302	+	7.55024i	0.673181	+	0.370181i
$417$		0			0
$418$	27.7523	+	23.2550i	1.35741	+	1.13744i
$419$	−11.1568	+	34.3371i	−0.545045	+	1.67748i	0.175838	+	0.984419i	$0.443736\pi$
$419$	−11.1568	+	34.3371i	−0.545045	+	1.67748i	−0.720883	+	0.693056i	$0.756264\pi$
$420$		0			0
$421$	4.95128	+	15.2385i	0.241311	+	0.742678i	0.996221	+	0.0868504i	$0.0276802\pi$
$421$	4.95128	+	15.2385i	0.241311	+	0.742678i	−0.754911	+	0.655828i	$0.772320\pi$
$422$	−10.5009	+	26.0414i	−0.511177	+	1.26768i
$423$		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
$428$	6.66680	−	21.9121i	0.322252	−	1.05916i
$429$		0			0
$430$	0.190836	+	12.0199i	0.00920295	+	0.579651i
$431$	−6.40797	−	2.08208i	−0.308661	−	0.100290i	0.150591	−	0.988596i	$-0.451882\pi$
$431$	−6.40797	−	2.08208i	−0.308661	−	0.100290i	−0.459252	+	0.888306i	$0.651882\pi$
$432$		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	$0.768438\pi$
$434$	21.0900	−	18.3583i	1.01235	−	0.881228i
$435$		0			0
$436$	−27.9480	−	13.5844i	−1.33847	−	0.650576i
$437$	22.1725	+	3.51178i	1.06065	+	0.167991i
$438$		0			0
$439$	8.47207	+	6.15532i	0.404350	+	0.293778i	0.771311	−	0.636459i	$-0.219602\pi$
$439$	8.47207	+	6.15532i	0.404350	+	0.293778i	−0.366960	+	0.930237i	$0.619602\pi$
$440$	−25.4358	+	19.8634i	−1.21261	+	0.946951i
$441$		0			0
$442$	9.71869	+	15.5298i	0.462271	+	0.738676i
$443$	−3.27124	−	3.27124i	−0.155421	−	0.155421i	0.625113	−	0.780534i	$-0.285053\pi$
$443$	−3.27124	−	3.27124i	−0.155421	−	0.155421i	−0.780534	+	0.625113i	$0.785053\pi$
$444$		0			0
$445$	1.93240	+	0.139504i	0.0916046	+	0.00661314i
$446$	−6.40583	−	15.0629i	−0.303325	−	0.713247i
$447$		0			0
$448$	13.5545	+	16.6003i	0.640391	+	0.784291i
$449$			18.0931i			0.853868i	0.904283	+	0.426934i	$0.140406\pi$
$449$			18.0931i			0.853868i	−0.904283	+	0.426934i	$0.859594\pi$
$450$		0			0
$451$			16.0463i			0.755589i
$452$	−5.30111	−	15.3282i	−0.249343	−	0.720977i
$453$		0			0
$454$	20.2072	−	8.59356i	0.948369	−	0.403316i
$455$	−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	$0.467231\pi$
$458$	20.2074	−	12.6460i	0.944230	−	0.590908i
$459$		0			0
$460$	−7.18756	+	18.6739i	−0.335122	+	0.870674i
$461$	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	−0.594054	−	0.804425i	$-0.702473\pi$
$463$	−30.2882	−	4.79718i	−1.40761	−	0.222944i	−0.813560	+	0.581481i	$0.802473\pi$
$464$	0.243271	−	0.857127i	0.0112936	−	0.0397911i
$465$		0			0
$466$	−27.1192	−	31.1545i	−1.25627	−	1.44320i
$467$	−7.07648	−	13.8884i	−0.327460	−	0.642677i	0.667314	−	0.744777i	$-0.267444\pi$
$467$	−7.07648	−	13.8884i	−0.327460	−	0.642677i	−0.994774	+	0.102100i	$0.967444\pi$
$468$		0			0
$469$	−8.61588	−	2.79947i	−0.397844	−	0.129268i
$470$	−9.02556	−	26.3471i	−0.416318	−	1.21530i
$471$		0			0
$472$	5.27958	−	25.0886i	0.243013	−	1.15480i
$473$	−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
$478$	−0.599821	−	0.241872i	−0.0274352	−	0.0110630i
$479$	2.15249	+	6.62469i	0.0983498	+	0.302690i	0.988112	−	0.153734i	$-0.0491300\pi$
$479$	2.15249	+	6.62469i	0.0983498	+	0.302690i	−0.889762	+	0.456424i	$0.849130\pi$
$480$		0			0
$481$	3.74547	−	11.5274i	0.170779	−	0.525604i
$482$	−19.8382	+	23.6748i	−0.903606	+	1.07836i
$483$		0			0
$484$	−21.6637	−	20.8639i	−0.984715	−	0.948358i
$485$	−24.9127	+	2.12301i	−1.13123	+	0.0964009i
$486$		0			0
$487$	3.26215	−	20.5964i	0.147822	−	0.933313i	−0.796583	−	0.604529i	$-0.793361\pi$
$487$	3.26215	−	20.5964i	0.147822	−	0.933313i	0.944405	−	0.328784i	$-0.106639\pi$
$488$	−4.04545	+	0.433491i	−0.183129	+	0.0196232i
$489$		0			0
$490$	−0.388327	+	0.400857i	−0.0175428	+	0.0181089i
$491$	2.89183	+	3.98026i	0.130506	+	0.179627i	0.869269	−	0.494339i	$-0.164590\pi$
$491$	2.89183	+	3.98026i	0.130506	+	0.179627i	−0.738763	+	0.673965i	$0.764590\pi$
$492$		0			0
$493$	0.736603	−	0.736603i	0.0331749	−	0.0331749i
$494$	19.1539	+	4.40839i	0.861774	+	0.198343i
$495$		0			0
$496$	23.2142	−	18.2382i	1.04235	−	0.818921i
$497$	−6.97467	+	13.6886i	−0.312857	+	0.614016i
$498$		0			0
$499$	19.8140			0.886994			0.443497	−	0.896276i	$-0.353738\pi$
$499$	19.8140			0.886994			0.443497	+	0.896276i	$0.353738\pi$
$500$	−18.6052	+	12.4035i	−0.832051	+	0.554700i
$501$		0			0
$502$	1.86026	+	7.43965i	0.0830273	+	0.332048i
$503$	12.4717	−	24.4770i	0.556084	−	1.09138i	−0.426314	−	0.904575i	$-0.640188\pi$
$503$	12.4717	−	24.4770i	0.556084	−	1.09138i	0.982398	−	0.186801i	$-0.0598118\pi$
$504$		0			0
$505$	13.9417	+	22.4237i	0.620396	+	0.997839i
$506$	−31.4653	−	7.24194i	−1.39880	−	0.321943i
$507$		0			0
$508$	25.6132	−	19.3553i	1.13640	−	0.858751i
$509$	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
$512$	13.4112	+	18.2247i	0.592697	+	0.805426i
$513$		0			0
$514$	13.7578	+	8.25389i	0.606832	+	0.364064i
$515$	−4.32270	+	0.368371i	−0.190481	+	0.0162324i
$516$		0			0
$517$	40.0420	−	20.4024i	1.76105	−	0.897298i
$518$	10.6473	−	12.7064i	0.467815	−	0.558287i
$519$		0			0
$520$	−7.40734	+	15.8757i	−0.324833	+	0.696197i
$521$	−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	$-0.758587\pi$
$523$	−5.67302	−	35.8180i	−0.248064	−	1.56621i	0.477859	−	0.878437i	$-0.341413\pi$
$524$	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
$530$	1.88969	+	5.51631i	0.0820828	+	0.239613i
$531$		0			0
$532$	22.0413	+	15.3891i	0.955613	+	0.667204i
$533$	3.95446	+	7.76106i	0.171286	+	0.336169i
$534$		0			0
$535$	24.9379	+	5.81660i	1.07816	+	0.251473i
$536$	−8.93658	−	3.40965i	−0.386001	−	0.147274i
$537$		0			0
$538$	−14.2972	−	0.990047i	−0.616397	−	0.0426840i
$539$	−0.728590	−	0.529352i	−0.0313826	−	0.0228008i
$540$		0			0
$541$	−23.6895	+	17.2114i	−1.01849	+	0.739976i	−0.965973	−	0.258644i	$-0.916724\pi$
$541$	−23.6895	+	17.2114i	−1.01849	+	0.739976i	−0.0525174	+	0.998620i	$0.516724\pi$
$542$	2.26480	−	1.41733i	0.0972815	−	0.0608797i
$543$		0			0
$544$	3.31285	+	26.2472i	0.142037	+	1.12534i
$545$	13.0873	−	32.1832i	0.560599	−	1.37858i
$546$		0			0
$547$	−31.1849	−	15.8895i	−1.33337	−	0.679385i	−0.365493	−	0.930814i	$-0.619100\pi$
$547$	−31.1849	−	15.8895i	−1.33337	−	0.679385i	−0.967876	+	0.251429i	$0.919100\pi$
$548$	−35.7149	+	12.3517i	−1.52567	+	0.527638i
$549$		0			0
$550$	−24.0407	−	26.9066i	−1.02510	−	1.14730i
$551$		−	1.11760i		−	0.0476112i
$552$		0			0
$553$	−16.0999	−	8.20329i	−0.684636	−	0.348839i
$554$	−6.33703	−	14.9011i	−0.269235	−	0.633086i
$555$		0			0
$556$	14.4356	+	2.00889i	0.612206	+	0.0851960i
$557$	25.1416	+	25.1416i	1.06528	+	1.06528i	0.997715	+	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
$560$	−17.5164	+	16.3491i	−0.740205	+	0.690876i
$561$		0			0
$562$	2.26340	−	32.6856i	0.0954756	−	1.37876i
$563$	27.3038	+	4.32450i	1.15072	+	0.182256i	0.702510	−	0.711674i	$-0.252063\pi$
$563$	27.3038	+	4.32450i	1.15072	+	0.182256i	0.448208	+	0.893929i	$0.352063\pi$
$564$		0			0
$565$	16.7078	−	7.04762i	0.702901	−	0.296496i
$566$	20.3255	−	17.6928i	0.854345	−	0.743686i
$567$		0			0
$568$	−8.08177	+	14.0638i	−0.339104	+	0.590105i
$569$	−8.77237	−	2.85032i	−0.367757	−	0.119491i	0.119308	−	0.992857i	$-0.461932\pi$
$569$	−8.77237	−	2.85032i	−0.367757	−	0.119491i	−0.487065	+	0.873366i	$0.661932\pi$
$570$		0			0
$571$	−17.2235	+	5.59625i	−0.720780	+	0.234196i	−0.646362	−	0.763031i	$-0.723710\pi$
$571$	−17.2235	+	5.59625i	−0.720780	+	0.234196i	−0.0744189	+	0.997227i	$0.523710\pi$
$572$	−27.0450	−	8.22851i	−1.13081	−	0.344051i
$573$		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	$0.876363\pi$
$578$	−2.57651	+	6.38951i	−0.107169	+	0.265769i
$579$		0			0
$580$	0.974192	+	0.207989i	0.0404511	+	0.00863629i
$581$	2.78310	−	8.56552i	0.115463	−	0.355357i
$582$		0			0
$583$	−8.38362	+	4.27167i	−0.347214	+	0.176914i
$584$	0.0336429	−	0.0417182i	0.00139215	−	0.00172631i
$585$		0			0
$586$	−9.49738	+	15.8305i	−0.392333	+	0.653953i
$587$	7.33025	−	46.2814i	0.302552	−	1.91024i	−0.100273	−	0.994960i	$-0.531972\pi$
$587$	7.33025	−	46.2814i	0.302552	−	1.91024i	0.402825	−	0.915277i	$-0.368028\pi$
$588$		0			0
$589$	21.7659	−	29.9582i	0.896849	−	1.23441i
$590$	28.3790	+	4.03408i	1.16834	+	0.166080i
$591$		0			0
$592$	11.9023	−	12.8331i	0.489182	−	0.527436i
$593$	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
$596$	2.00363	+	3.75603i	0.0820720	+	0.153853i
$597$		0			0
$598$	−17.0035	+	4.25165i	−0.695324	+	0.173863i
$599$	−7.21615			−0.294844			−0.147422	−	0.989074i	$-0.547098\pi$
$599$	−7.21615			−0.294844			−0.147422	+	0.989074i	$0.547098\pi$
$600$		0			0
$601$	−15.0642			−0.614483			−0.307241	−	0.951632i	$-0.599406\pi$
$601$	−15.0642			−0.614483			−0.307241	+	0.951632i	$0.599406\pi$
$602$	−13.9720	+	3.49363i	−0.569454	+	0.142390i
$603$		0			0
$604$	−5.74559	−	10.7707i	−0.233785	−	0.438255i
$605$	21.6730	−	25.7110i	0.881133	−	1.04530i
$606$		0			0
$607$	−3.59194	+	3.59194i	−0.145792	+	0.145792i	−0.776235	−	0.630443i	$-0.782873\pi$
$607$	−3.59194	+	3.59194i	−0.145792	+	0.145792i	0.630443	+	0.776235i	$0.282873\pi$
$608$	22.4247	+	17.3984i	0.909442	+	0.705596i
$609$		0			0
$610$	−0.782829	−	4.48098i	−0.0316958	−	0.181430i
$611$	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	$0.0824558\pi$
$614$	9.43709	−	15.7300i	0.380850	−	0.634812i
$615$		0			0
$616$	−30.0970	−	24.2711i	−1.21264	−	0.977912i
$617$	16.5627	−	8.43913i	0.666790	−	0.339746i	−0.0876162	−	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	$0.239901\pi$
$619$	−6.54265	+	20.1362i	−0.262971	+	0.809343i	−0.992154	+	0.125024i	$0.960099\pi$
$620$	22.0634	+	24.5484i	0.886087	+	0.985886i
$621$		0			0
$622$	−2.20129	+	5.45901i	−0.0882637	+	0.218886i
$623$	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
$628$	−31.0648	−	9.45157i	−1.23962	−	0.377159i
$629$	19.4624	−	6.32373i	0.776018	−	0.252144i
$630$		0			0
$631$	3.22756	+	1.04870i	0.128487	+	0.0417480i	0.372555	−	0.928010i	$-0.378482\pi$
$631$	3.22756	+	1.04870i	0.128487	+	0.0417480i	−0.244068	+	0.969758i	$0.578482\pi$
$632$	−16.5413	−	9.50542i	−0.657976	−	0.378105i
$633$		0			0
$634$	6.71965	−	5.84928i	0.266871	−	0.232305i
$635$	23.4870	+	27.1420i	0.932053	+	1.07710i
$636$		0			0
$637$	−0.482849	−	0.0764758i	−0.0191312	−	0.00303008i
$638$	−0.111044	+	1.60359i	−0.00439629	+	0.0634866i
$639$		0			0
$640$	−19.3392	+	16.3094i	−0.764449	+	0.644684i
$641$	−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	0.828249	−	0.560361i	$-0.189338\pi$
$643$	6.79295	+	6.79295i	0.267888	+	0.267888i	−0.560361	+	0.828249i	$0.689338\pi$
$644$	−23.7432	−	3.30416i	−0.935613	−	0.130202i
$645$		0			0
$646$	12.9868	+	30.5375i	0.510957	+	1.20148i
$647$	−30.3148	−	15.4461i	−1.19180	−	0.607251i	−0.258379	−	0.966044i	$-0.583188\pi$
$647$	−30.3148	−	15.4461i	−1.19180	−	0.607251i	−0.933417	+	0.358793i	$0.883188\pi$
$648$		0			0
$649$			46.2539i			1.81562i
$650$	−18.2586	−	7.08922i	−0.716162	−	0.278062i
$651$		0			0
$652$	14.9534	−	5.17148i	0.585619	−	0.202531i
$653$	−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
$656$	0.472973	+	12.5695i	0.0184665	+	0.490758i
$657$		0			0
$658$	28.2837	−	17.7002i	1.10261	−	0.690025i
$659$	−11.5792	+	8.41281i	−0.451063	+	0.327716i	−0.790015	−	0.613087i	$-0.789927\pi$
$659$	−11.5792	+	8.41281i	−0.451063	+	0.327716i	0.338952	+	0.940804i	$0.389927\pi$
$660$		0			0
$661$	−0.382235	−	0.277710i	−0.0148672	−	0.0108017i	0.580327	−	0.814384i	$-0.302925\pi$
$661$	−0.382235	−	0.277710i	−0.0148672	−	0.0108017i	−0.595194	+	0.803582i	$0.702925\pi$
$662$	22.8607	+	1.58304i	0.888505	+	0.0615267i
$663$		0			0
$664$	3.38972	−	8.88434i	0.131547	−	0.344779i
$665$	−15.5375	+	25.7273i	−0.602520	+	0.997661i
$666$		0			0
$667$	0.452453	+	0.887989i	0.0175190	+	0.0343831i
$668$	−22.1638	−	15.4746i	−0.857543	−	0.598731i
$669$		0			0
$670$	3.14274	−	10.2217i	0.121414	−	0.394899i
$671$	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
$680$	−29.0359	+	5.63721i	−1.11348	+	0.216177i
$681$		0			0
$682$	−34.2075	+	40.8229i	−1.30987	+	1.56319i
$683$	−21.8180	+	11.1168i	−0.834843	+	0.425374i	−0.818510	−	0.574493i	$-0.805199\pi$
$683$	−21.8180	+	11.1168i	−0.834843	+	0.425374i	−0.0163335	+	0.999867i	$0.505199\pi$
$684$		0			0
$685$	−16.4211	−	38.9294i	−0.627418	−	1.48742i
$686$	22.1677	+	13.2993i	0.846367	+	0.507770i
$687$		0			0
$688$	−14.9187	+	2.94180i	−0.568771	+	0.112155i
$689$	−3.00217	+	4.13213i	−0.114374	+	0.157422i
$690$		0			0
$691$	9.83947	+	13.5429i	0.374311	+	0.515195i	0.954066	−	0.299596i	$-0.0968518\pi$
$691$	9.83947	+	13.5429i	0.374311	+	0.515195i	−0.579755	+	0.814791i	$0.696852\pi$
$692$	−1.75027	+	1.32264i	−0.0665353	+	0.0502791i
$693$		0			0
$694$	7.99017	+	1.83899i	0.303303	+	0.0698070i
$695$	−1.17332	+	16.2527i	−0.0445065	+	0.616501i
$696$		0			0
$697$	−6.67656	+	13.1035i	−0.252893	+	0.496330i
$698$	0.0181412	+	0.0725513i	0.000686654	+	0.00274611i
$699$		0			0
$700$	−19.5345	−	18.3318i	−0.738333	−	0.692876i
$701$	−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
$704$	−30.4474	−	27.1922i	−1.14753	−	1.02484i
$705$		0			0
$706$	−5.67456	−	1.30604i	−0.213565	−	0.0491533i
$707$	−22.3682	+	22.3682i	−0.841244	+	0.841244i
$708$		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	$0.527628\pi$
$710$	−16.2872	−	7.97563i	−0.611247	−	0.299320i
$711$		0			0
$712$	0.261108	+	2.43673i	0.00978544	+	0.0913202i
$713$	−5.16574	+	32.6152i	−0.193458	+	1.22145i
$714$		0			0
$715$	7.17914	−	30.7796i	0.268485	−	1.15109i
$716$	−34.7580	−	33.4747i	−1.29897	−	1.25101i
$717$		0			0
$718$	25.0993	−	29.9533i	0.936698	−	1.11785i
$719$	3.14270	−	9.67223i	0.117203	−	0.360713i	−0.875197	−	0.483766i	$-0.839269\pi$
$719$	3.14270	−	9.67223i	0.117203	−	0.360713i	0.992400	+	0.123053i	$0.0392685\pi$
$720$		0			0
$721$	−1.60612	−	4.94314i	−0.0598152	−	0.184092i
$722$	8.09788	+	3.26539i	0.301372	+	0.121525i
$723$		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	$-0.498031\pi$
$727$	8.65722	−	1.37117i	0.321078	−	0.0508538i	0.314893	+	0.949127i	$0.398031\pi$
$728$	−20.5383	−	4.32204i	−0.761201	−	0.160185i
$729$		0			0
$730$	0.0490287	+	0.0344457i	0.00181463	+	0.00127489i
$731$	−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	$0.851548\pi$
$734$	−6.30358	−	7.24154i	−0.232669	−	0.267290i
$735$		0			0
$736$	−24.8612	−	4.74538i	−0.916397	−	0.174917i
$737$	17.0437	+	2.69946i	0.627814	+	0.0994360i
$738$		0			0
$739$	−5.97506	−	4.34113i	−0.219796	−	0.159691i	0.472439	−	0.881363i	$-0.343374\pi$
$739$	−5.97506	−	4.34113i	−0.219796	−	0.159691i	−0.692235	+	0.721672i	$0.743374\pi$
$740$	15.1968	+	12.3288i	0.558644	+	0.453216i
$741$		0			0
$742$	−5.92176	+	3.70590i	−0.217395	+	0.136048i
$743$	−7.03452	−	7.03452i	−0.258071	−	0.258071i	0.566198	−	0.824269i	$-0.308414\pi$
$743$	−7.03452	−	7.03452i	−0.258071	−	0.258071i	−0.824269	+	0.566198i	$0.808414\pi$
$744$		0			0
$745$	−4.04196	+	2.51305i	−0.148086	+	0.0920709i
$746$	14.9497	−	6.35772i	0.547349	−	0.232772i
$747$		0			0
$748$	−15.5999	−	45.1071i	−0.570388	−	1.64928i
$749$			30.6785i			1.12097i
$750$		0			0
$751$		−	29.2029i		−	1.06563i	−0.846232	−	0.532814i	$-0.821134\pi$
$751$		−	29.2029i		−	1.06563i	0.846232	−	0.532814i	$-0.178866\pi$
$752$	30.7648	−	17.1621i	1.12188	−	0.625838i
$753$		0			0
$754$	0.341481	+	0.802968i	0.0124360	+	0.0292424i
$755$	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	$0.923604\pi$
$758$	9.60573	+	15.3493i	0.348896	+	0.557511i
$759$		0			0
$760$	−17.7506	+	26.3036i	−0.643883	+	0.954131i
$761$	−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
$764$	28.3536	+	13.7815i	1.02580	+	0.498599i
$765$		0			0
$766$	19.6609	−	17.1143i	0.710378	−	0.618366i
$767$	11.3988	+	22.3715i	0.411589	+	0.807788i
$768$		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	$0.493648\pi$
$770$	24.8503	−	35.3710i	0.895543	−	1.27468i
$771$		0			0
$772$	5.30959	−	17.4512i	0.191096	−	0.628084i
$773$	−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
$778$	−13.1549	+	32.6231i	−0.471627	+	1.16959i
$779$	4.87557	+	15.0055i	0.174685	+	0.537626i
$780$		0			0
$781$	9.04296	−	27.8314i	0.323582	−	0.995884i
$782$	−22.6816	−	19.0060i	−0.811091	−	0.679653i
$783$		0			0
$784$	−0.586330	−	0.393182i	−0.0209404	−	0.0140422i
$785$	8.24623	−	35.3546i	0.294320	−	1.26186i
$786$		0			0
$787$	−1.89589	+	11.9702i	−0.0675813	+	0.426691i	0.930581	+	0.366087i	$0.119303\pi$
$787$	−1.89589	+	11.9702i	−0.0675813	+	0.426691i	−0.998162	+	0.0606043i	$0.980697\pi$
$788$	−0.215016	−	11.4324i	−0.00765962	−	0.407261i
$789$		0			0
$790$	9.38058	−	19.1563i	0.333746	−	0.681549i
$791$	12.7693	+	17.5755i	0.454025	+	0.624911i
$792$		0			0
$793$	2.81747	−	2.81747i	0.100051	−	0.100051i
$794$	−8.83405	+	38.3829i	−0.313509	+	1.36216i
$795$		0			0
$796$	−43.4802	+	23.1943i	−1.54111	+	0.822099i
$797$	7.47486	−	14.6702i	0.264773	−	0.519646i	−0.719895	−	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
$800$	−19.6250	−	20.3681i	−0.693847	−	0.720123i
$801$		0			0
$802$	14.3525	−	3.58878i	0.506803	−	0.126724i
$803$	−0.0438956	+	0.0861499i	−0.00154904	+	0.00304016i
$804$		0			0
$805$	1.92984	−	26.7319i	0.0680178	−	0.942177i
$806$	−6.48462	+	28.1749i	−0.228411	+	0.992417i
$807$		0			0
$808$	−24.7750	+	22.3987i	−0.871583	+	0.787984i
$809$	−12.5671	−	17.2972i	−0.441837	−	0.608136i	0.528782	−	0.848757i	$-0.322649\pi$
$809$	−12.5671	−	17.2972i	−0.441837	−	0.608136i	−0.970619	+	0.240621i	$0.922649\pi$
$810$		0			0
$811$	18.5355	−	25.5120i	0.650871	−	0.895847i	−0.348265	−	0.937396i	$-0.613229\pi$
$811$	18.5355	−	25.5120i	0.650871	−	0.895847i	0.999136	+	0.0415488i	$0.0132292\pi$
$812$	0.0224415	+	1.19321i	0.000787542	+	0.0418735i
$813$		0			0
$814$	−16.2451	+	27.0779i	−0.569392	+	0.949080i
$815$	6.87529	+	16.2992i	0.240831	+	0.570937i
$816$		0			0
$817$	−16.9947	+	8.65922i	−0.594569	+	0.302948i
$818$	16.8254	+	14.0988i	0.588286	+	0.492953i
$819$		0			0
$820$	−13.9874	+	1.45738i	−0.488461	+	0.0508940i
$821$	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	$0.212990\pi$
$823$	6.60034	+	41.6729i	0.230073	+	1.45263i	−0.554289	+	0.832324i	$0.687010\pi$
$824$	−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	$-0.473049\pi$
$827$	13.5996	−	2.15397i	0.472905	−	0.0749008i	0.388338	+	0.921517i	$0.373049\pi$
$828$		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	$0.174770\pi$
$830$	10.1620	+	3.12436i	0.352727	+	0.108448i
$831$		0			0
$832$	−21.4277	−	5.64848i	−0.742872	−	0.195826i
$833$	−0.374718	−	0.735426i	−0.0129832	−	0.0254810i
$834$		0			0
$835$	15.6239	−	25.8702i	0.540686	−	0.895275i
$836$	−46.0533	−	22.3846i	−1.59279	−	0.774189i
$837$		0			0
$838$	3.52726	−	50.9370i	0.121847	−	1.75959i
$839$	−6.53213	−	4.74587i	−0.225514	−	0.163846i	0.469291	−	0.883044i	$-0.344509\pi$
$839$	−6.53213	−	4.74587i	−0.225514	−	0.163846i	−0.694805	+	0.719198i	$0.744509\pi$
$840$		0			0
$841$	−23.4214	+	17.0166i	−0.807633	+	0.586780i
$842$	−12.0207	−	19.2082i	−0.414260	−	0.661959i
$843$		0			0
$844$	5.47332	−	39.3305i	0.188400	−	1.35381i
$845$	2.85577	+	11.5649i	0.0982416	+	0.397844i
$846$		0			0
$847$	35.8955	+	18.2897i	1.23338	+	0.628440i
$848$	−6.44124	+	3.59324i	−0.221193	+	0.123392i
$849$		0			0
$850$	−8.43650	−	31.9750i	−0.289370	−	1.09674i
$851$			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	$0.853683\pi$
$854$	5.01503	−	2.13276i	0.171611	−	0.0729814i
$855$		0			0
$856$	−1.62960	+	32.3499i	−0.0556986	+	1.10570i
$857$	−31.7738	−	31.7738i	−1.08537	−	1.08537i	−0.995998	−	0.0893726i	$-0.971514\pi$
$857$	−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	−0.990918	−	0.134468i	$-0.957068\pi$
$859$	−34.2690	+	24.8979i	−1.16924	+	0.849504i	−0.178324	+	0.983972i	$0.557068\pi$
$860$	−4.38533	−	16.4255i	−0.149538	−	0.560105i
$861$		0			0
$862$	9.50584	+	0.658255i	0.323770	+	0.0224203i
$863$	−16.4649	−	2.60778i	−0.560472	−	0.0887700i	−0.130230	−	0.991484i	$-0.541572\pi$
$863$	−16.4649	−	2.60778i	−0.560472	−	0.0887700i	−0.430242	+	0.902714i	$0.641572\pi$
$864$		0			0
$865$	−1.60498	−	1.85474i	−0.0545708	−	0.0630631i
$866$	−9.79367	−	11.2510i	−0.332802	−	0.382323i
$867$		0			0
$868$	−22.6370	+	32.4222i	−0.768350	+	1.10048i
$869$	32.7340	+	10.6359i	1.11043	+	0.360799i
$870$		0			0
$871$	8.90876	−	2.89463i	0.301862	−	0.0980809i
$872$	43.0042	+	9.04970i	1.45631	+	0.306462i
$873$		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	$-0.130718\pi$
$878$	−13.7351	−	5.53854i	−0.463537	−	0.186917i
$879$		0			0
$880$	28.0830	−	35.9780i	0.946679	−	1.21282i
$881$	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	−0.478274	−	0.878211i	$-0.658737\pi$
$883$	−1.45332	+	0.740506i	−0.0489083	+	0.0249200i	0.429365	+	0.903131i	$0.358737\pi$
$884$	−18.6614	−	17.9724i	−0.627650	−	0.604477i
$885$		0			0
$886$	5.61028	+	3.36584i	0.188481	+	0.113078i
$887$	−4.23212	+	26.7206i	−0.142101	+	0.897189i	0.808888	+	0.587963i	$0.200070\pi$
$887$	−4.23212	+	26.7206i	−0.142101	+	0.897189i	−0.950989	+	0.309226i	$0.899930\pi$
$888$		0			0
$889$	−25.2757	+	34.7890i	−0.847719	+	1.16679i
$890$	−2.69906	+	0.471527i	−0.0904728	+	0.0158056i
$891$		0			0
$892$	13.9560	+	18.4683i	0.467283	+	0.618364i
$893$	31.2456	−	31.2456i	1.04560	−	1.04560i
$894$		0			0
$895$	34.7729	−	41.2515i	1.16233	−	1.37889i
$896$	−24.2913	−	18.1252i	−0.811515	−	0.605521i
$897$		0			0
$898$	−6.20698	−	24.8233i	−0.207130	−	0.828365i
$899$	1.64396			0.0548290
$900$		0			0
$901$	−8.62349			−0.287290
$902$	−5.50478	−	22.0150i	−0.183289	−	0.733021i
$903$		0			0
$904$	12.5314	+	19.2113i	0.416789	+	0.638957i
$905$	−15.1716	+	3.74640i	−0.504321	+	0.124535i
$906$		0			0
$907$	35.5508	−	35.5508i	1.18045	−	1.18045i	0.200818	−	0.979629i	$-0.435640\pi$
$907$	35.5508	−	35.5508i	1.18045	−	1.18045i	0.979629	−	0.200818i	$-0.0643600\pi$
$908$	−24.7756	+	18.7223i	−0.822208	+	0.621323i
$909$		0			0
$910$	3.30243	−	23.2319i	0.109474	−	0.770131i
$911$	3.41319	−	4.69785i	0.113084	−	0.155647i	−0.748723	−	0.662883i	$-0.769333\pi$
$911$	3.41319	−	4.69785i	0.113084	−	0.155647i	0.861807	+	0.507236i	$0.169333\pi$
$912$		0			0
$913$	−2.68368	+	16.9441i	−0.0888169	+	0.560768i
$914$	−40.2367	−	24.1397i	−1.33091	−	0.798469i
$915$		0			0
$916$	−23.3857	+	24.2822i	−0.772686	+	0.802308i
$917$	−32.4808	+	16.5498i	−1.07261	+	0.546522i
$918$		0			0
$919$	−13.3369	+	41.0468i	−0.439944	+	1.35401i	0.447990	+	0.894039i	$0.352140\pi$
$919$	−13.3369	+	41.0468i	−0.439944	+	1.35401i	−0.887934	+	0.459971i	$0.847860\pi$
$920$	3.45494	−	28.0858i	0.113906	−	0.925961i
$921$		0			0
$922$	−42.4433	−	17.1148i	−1.39780	−	0.563647i
$923$	−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
$928$	−0.0397177	+	1.25941i	−0.00130380	+	0.0413422i
$929$	−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
$932$	47.8946	+	33.4397i	1.56884	+	1.09535i
$933$		0			0
$934$	14.4732	+	16.6268i	0.473579	+	0.544047i
$935$	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	$0.337696\pi$
$938$	12.7811	+	0.885062i	0.417319	+	0.0288983i
$939$		0			0
$940$	21.4214	+	33.0513i	0.698689	+	1.07801i
$941$	−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
$944$	1.36336	+	36.2321i	0.0443736	+	1.17925i
$945$		0			0
$946$	25.2452	−	10.7361i	0.820793	−	0.349061i
$947$	−3.14898	−	1.60449i	−0.102328	−	0.0521388i	0.402077	−	0.915606i	$-0.368288\pi$
$947$	−3.14898	−	1.60449i	−0.102328	−	0.0521388i	−0.504405	+	0.863467i	$0.668288\pi$
$948$		0			0
$949$			0.0524856i			0.00170375i
$950$	−30.6568	−	17.8567i	−0.994639	−	0.579348i
$951$		0			0
$952$	−14.4786	−	32.3428i	−0.469255	−	1.04824i
$953$	−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
$956$	0.905914	+	0.126069i	0.0292994	+	0.00407736i
$957$		0			0
$958$	−5.22581	−	8.35047i	−0.168838	−	0.269791i
$959$	40.9512	−	29.7528i	1.32238	−	0.960767i
$960$		0			0
$961$	18.9882	+	13.7957i	0.612523	+	0.445024i
$962$	−1.18414	+	17.1002i	−0.0381783	+	0.551332i
$963$		0			0
$964$	19.0957	−	39.2868i	0.615032	−	1.26534i
$965$	19.8611	+	4.63246i	0.639350	+	0.149124i
$966$		0			0
$967$	7.03165	+	13.8004i	0.226123	+	0.443791i	0.975995	−	0.217792i	$-0.0698853\pi$
$967$	7.03165	+	13.8004i	0.226123	+	0.443791i	−0.749873	+	0.661582i	$0.769885\pi$
$968$	36.8796	+	21.1928i	1.18535	+	0.681163i
$969$		0			0
$970$	33.4513	−	11.4592i	1.07406	−	0.367932i
$971$	−16.7721	+	5.44959i	−0.538242	+	0.174886i	−0.565508	−	0.824743i	$-0.691320\pi$
$971$	−16.7721	+	5.44959i	−0.538242	+	0.174886i	0.0272659	+	0.999628i	$0.491320\pi$
$972$		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
$980$	0.395258	−	0.683183i	0.0126261	−	0.0218235i
$981$		0			0
$982$	−5.33297	−	4.46875i	−0.170182	−	0.142603i
$983$	15.6381	−	7.96803i	0.498779	−	0.254141i	−0.186455	−	0.982463i	$-0.559700\pi$
$983$	15.6381	−	7.96803i	0.498779	−	0.254141i	0.685234	+	0.728323i	$0.259700\pi$
$984$		0			0
$985$	12.7379	−	1.08549i	0.405862	−	0.0345867i
$986$	−0.757903	+	1.26330i	−0.0241366	+	0.0402316i
$987$		0			0
$988$	−27.7910	+	0.522682i	−0.884148	+	0.0166287i
$989$	9.99752	−	13.7604i	0.317903	−	0.437555i
$990$		0			0
$991$	20.0939	+	27.6568i	0.638302	+	0.878548i	0.998524	−	0.0543192i	$-0.0172988\pi$
$991$	20.0939	+	27.6568i	0.638302	+	0.878548i	−0.360221	+	0.932867i	$0.617299\pi$
$992$	−25.5925	+	32.9862i	−0.812563	+	1.04731i
$993$		0			0
$994$	4.87311	−	21.1730i	0.154566	−	0.671568i
$995$	−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	$0.139400\pi$
$998$	−27.1842	+	6.79731i	−0.860502	+	0.215165i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-1.37197 + 0.343057i) q^{2} +(1.76462 - 0.941330i) q^{4} +(1.18066 + 1.89896i) q^{5} +(-1.89427 + 1.89427i) q^{7} +(-2.09809 + 1.89685i) q^{8} +O(q^{10})\)	\(q+(-1.37197 + 0.343057i) q^{2} +(1.76462 - 0.941330i) q^{4} +(1.18066 + 1.89896i) q^{5} +(-1.89427 + 1.89427i) q^{7} +(-2.09809 + 1.89685i) q^{8} +(-2.27128 - 2.20029i) q^{10} +(2.99934 - 4.12824i) q^{11} +(0.433317 - 2.73586i) q^{13} +(1.94904 - 3.24872i) q^{14} +(2.22780 - 3.32219i) q^{16} +(4.16697 - 2.12318i) q^{17} +(1.55045 - 4.77181i) q^{19} +(3.87097 + 2.23956i) q^{20} +(-2.69880 + 6.69278i) q^{22} +(0.699923 + 4.41914i) q^{23} +(-2.21209 + 4.48404i) q^{25} +(0.344055 + 3.90218i) q^{26} +(-1.55954 + 5.12580i) q^{28} +(0.211843 - 0.0688321i) q^{29} +(7.01920 + 2.28068i) q^{31} +(-1.91678 + 5.32221i) q^{32} +(-4.98861 + 4.34246i) q^{34} +(-5.83362 - 1.36065i) q^{35} +(4.32186 + 0.684516i) q^{37} +(-0.490182 + 7.07869i) q^{38} +(-6.07916 - 1.74466i) q^{40} +(-2.54404 + 1.84835i) q^{41} +(-2.68807 - 2.68807i) q^{43} +(1.40668 - 10.1082i) q^{44} +(-2.47629 - 5.82283i) q^{46} +(7.84709 + 3.99829i) q^{47} -0.176489i q^{49} +(1.49665 - 6.91086i) q^{50} +(-1.81070 - 5.23565i) q^{52} +(-1.64295 - 0.837124i) q^{53} +(11.3806 + 0.821587i) q^{55} +(0.381206 - 7.56747i) q^{56} +(-0.267030 + 0.167110i) q^{58} +(-7.33328 + 5.32794i) q^{59} +(1.16375 + 0.845512i) q^{61} +(-10.4126 - 0.721044i) q^{62} +(0.803948 - 7.95950i) q^{64} +(5.70688 - 2.40726i) q^{65} +(1.53527 + 3.01313i) q^{67} +(5.35453 - 7.66911i) q^{68} +(8.47035 - 0.134481i) q^{70} +(5.45415 - 1.77216i) q^{71} +(-0.0187149 + 0.00296414i) q^{73} +(-6.16431 + 0.543507i) q^{74} +(-1.75588 - 9.87994i) q^{76} +(2.13843 + 13.5015i) q^{77} +(2.08434 + 6.41493i) q^{79} +(8.93896 + 0.308126i) q^{80} +(2.85627 - 3.40864i) q^{82} +(-2.99552 + 1.52629i) q^{83} +(8.95160 + 5.40616i) q^{85} +(4.61012 + 2.76580i) q^{86} +(1.53775 + 14.3507i) q^{88} +(0.509284 - 0.700969i) q^{89} +(4.36162 + 6.00326i) q^{91} +(5.39497 + 7.13927i) q^{92} +(-12.1376 - 2.79355i) q^{94} +(10.8920 - 2.68963i) q^{95} +(-5.07638 + 9.96296i) q^{97} +(0.0605458 + 0.242139i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 10 q^{2} - 10 q^{4} + 20 q^{5} + 10 q^{8}+O(q^{10}) \) 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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