LMFDB - Embedded newform 888.2.br.a.569.32

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [888,2,Mod(473,888)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("888.473"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(888, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 0, 6, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 888 = 2^{3} \cdot 3 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	888.br (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$7.09071569949$
Analytic rank:	$0$
Dimension:	$152$
Relative dimension:	$38$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			569.32
Character	$\chi$	$=$	888.569
Dual form			888.2.br.a.785.32

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.36692 + 1.06373i) q^{3} +(0.356362 - 1.32996i) q^{5} +(0.659764 + 1.14274i) q^{7} +(0.736949 + 2.90808i) q^{9} -0.353852 q^{11} +(-0.106594 - 0.0285618i) q^{13} +(1.90184 - 1.43888i) q^{15} +(-0.268822 + 0.0720307i) q^{17} +(7.97106 + 2.13584i) q^{19} +(-0.313728 + 2.26385i) q^{21} +(-0.593239 - 0.593239i) q^{23} +(2.68832 + 1.55210i) q^{25} +(-2.08606 + 4.75903i) q^{27} +(-1.88653 + 1.88653i) q^{29} +(3.87869 + 3.87869i) q^{31} +(-0.483688 - 0.376404i) q^{33} +(1.75492 - 0.470230i) q^{35} +(-5.93717 - 1.32288i) q^{37} +(-0.115324 - 0.152430i) q^{39} +(0.379388 + 0.657119i) q^{41} +(4.16777 - 4.16777i) q^{43} +(4.13025 + 0.0562150i) q^{45} -6.18133i q^{47} +(2.62942 - 4.55430i) q^{49} +(-0.444080 - 0.187494i) q^{51} +(-3.52233 - 2.03362i) q^{53} +(-0.126100 + 0.470610i) q^{55} +(8.62385 + 11.3986i) q^{57} +(-5.80978 + 1.55673i) q^{59} +(-1.41803 + 5.29217i) q^{61} +(-2.83697 + 2.76079i) q^{63} +(-0.0759724 + 0.131588i) q^{65} +(4.53482 - 2.61818i) q^{67} +(-0.179864 - 1.44196i) q^{69} +(5.08729 - 2.93715i) q^{71} -1.03868i q^{73} +(2.02370 + 4.98125i) q^{75} +(-0.233459 - 0.404363i) q^{77} +(0.472722 + 0.126665i) q^{79} +(-7.91381 + 4.28620i) q^{81} +(-11.5472 - 6.66677i) q^{83} +0.383192i q^{85} +(-4.58550 + 0.571976i) q^{87} +(4.27017 + 15.9365i) q^{89} +(-0.0376881 - 0.140654i) q^{91} +(1.17598 + 9.42774i) q^{93} +(5.68117 - 9.84008i) q^{95} +(-7.97830 + 7.97830i) q^{97} +(-0.260771 - 1.02903i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q + 4 q^{13} - 12 q^{15} + 4 q^{19} - 44 q^{31} - 12 q^{39} + 28 q^{43} + 20 q^{45} - 80 q^{49} - 12 q^{51} - 8 q^{55} - 40 q^{57} - 28 q^{61} + 48 q^{63} + 56 q^{69} + 64 q^{75} + 20 q^{79} + 16 q^{81}+ \cdots - 20 q^{97}+O(q^{100}) $ 152 * q + 4 * q^13 - 12 * q^15 + 4 * q^19 - 44 * q^31 - 12 * q^39 + 28 * q^43 + 20 * q^45 - 80 * q^49 - 12 * q^51 - 8 * q^55 - 40 * q^57 - 28 * q^61 + 48 * q^63 + 56 * q^69 + 64 * q^75 + 20 * q^79 + 16 * q^81 + 56 * q^87 + 52 * q^91 + 40 * q^93 - 20 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/888\mathbb{Z}\right)^\times$.

$n$	$223$	$409$	$445$	$593$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.36692	+	1.06373i	0.789192	+	0.614146i
$3$	1.36692	+	1.06373i	0.789192	+	0.614146i
$4$		0			0
$5$	0.356362	−	1.32996i	0.159370	−	0.594777i	−0.839321	−	0.543636i	$-0.817047\pi$
$5$	0.356362	−	1.32996i	0.159370	−	0.594777i	0.998691	−	0.0511417i	$-0.0162860\pi$
$6$		0			0
$7$	0.659764	+	1.14274i	0.249367	+	0.431917i	0.963350	−	0.268246i	$-0.0864441\pi$
$7$	0.659764	+	1.14274i	0.249367	+	0.431917i	−0.713983	+	0.700163i	$0.753111\pi$
$8$		0			0
$9$	0.736949	+	2.90808i	0.245650	+	0.969359i
$10$		0			0
$11$	−0.353852			−0.106690			−0.0533452	−	0.998576i	$-0.516988\pi$
$11$	−0.353852			−0.106690			−0.0533452	+	0.998576i	$0.516988\pi$
$12$		0			0
$13$	−0.106594	−	0.0285618i	−0.0295639	−	0.00792163i	0.244007	−	0.969774i	$-0.421538\pi$
$13$	−0.106594	−	0.0285618i	−0.0295639	−	0.00792163i	−0.273571	+	0.961852i	$0.588205\pi$
$14$		0			0
$15$	1.90184	−	1.43888i	0.491054	−	0.371517i
$16$		0			0
$17$	−0.268822	+	0.0720307i	−0.0651989	+	0.0174700i	−0.291271	−	0.956641i	$-0.594078\pi$
$17$	−0.268822	+	0.0720307i	−0.0651989	+	0.0174700i	0.226072	+	0.974111i	$0.427411\pi$
$18$		0			0
$19$	7.97106	+	2.13584i	1.82869	+	0.489995i	0.997791	−	0.0664333i	$-0.0211620\pi$
$19$	7.97106	+	2.13584i	1.82869	+	0.489995i	0.830896	+	0.556428i	$0.187829\pi$
$20$		0			0
$21$	−0.313728	+	2.26385i	−0.0684611	+	0.494013i
$22$		0			0
$23$	−0.593239	−	0.593239i	−0.123699	−	0.123699i	0.642547	−	0.766246i	$-0.277878\pi$
$23$	−0.593239	−	0.593239i	−0.123699	−	0.123699i	−0.766246	+	0.642547i	$0.777878\pi$
$24$		0			0
$25$	2.68832	+	1.55210i	0.537664	+	0.310420i
$26$		0			0
$27$	−2.08606	+	4.75903i	−0.401463	+	0.915875i
$28$		0			0
$29$	−1.88653	+	1.88653i	−0.350320	+	0.350320i	−0.860229	−	0.509909i	$-0.829679\pi$
$29$	−1.88653	+	1.88653i	−0.350320	+	0.350320i	0.509909	+	0.860229i	$0.329679\pi$
$30$		0			0
$31$	3.87869	+	3.87869i	0.696633	+	0.696633i	0.963683	−	0.267050i	$-0.0860489\pi$
$31$	3.87869	+	3.87869i	0.696633	+	0.696633i	−0.267050	+	0.963683i	$0.586049\pi$
$32$		0			0
$33$	−0.483688	−	0.376404i	−0.0841993	−	0.0655235i
$34$		0			0
$35$	1.75492	−	0.470230i	0.296636	−	0.0794834i
$36$		0			0
$37$	−5.93717	−	1.32288i	−0.976065	−	0.217481i
$37$	−5.93717	−	1.32288i	−0.976065	−	0.217481i
$38$		0			0
$39$	−0.115324	−	0.152430i	−0.0184666	−	0.0244083i
$40$		0			0
$41$	0.379388	+	0.657119i	0.0592504	+	0.102625i	0.894129	−	0.447809i	$-0.147796\pi$
$41$	0.379388	+	0.657119i	0.0592504	+	0.102625i	−0.834879	+	0.550434i	$0.814462\pi$
$42$		0			0
$43$	4.16777	−	4.16777i	0.635579	−	0.635579i	−0.313883	−	0.949462i	$-0.601630\pi$
$43$	4.16777	−	4.16777i	0.635579	−	0.635579i	0.949462	+	0.313883i	$0.101630\pi$
$44$		0			0
$45$	4.13025	+	0.0562150i	0.615702	+	0.00838004i
$46$		0			0
$47$		−	6.18133i		−	0.901639i	−0.892615	−	0.450820i	$-0.851132\pi$
$47$		−	6.18133i		−	0.901639i	0.892615	−	0.450820i	$-0.148868\pi$
$48$		0			0
$49$	2.62942	−	4.55430i	0.375632	−	0.650614i
$50$		0			0
$51$	−0.444080	−	0.187494i	−0.0621836	−	0.0262545i
$52$		0			0
$53$	−3.52233	−	2.03362i	−0.483829	−	0.279339i	0.238182	−	0.971221i	$-0.423449\pi$
$53$	−3.52233	−	2.03362i	−0.483829	−	0.279339i	−0.722011	+	0.691882i	$0.756782\pi$
$54$		0			0
$55$	−0.126100	+	0.470610i	−0.0170033	+	0.0634571i
$56$		0			0
$57$	8.62385	+	11.3986i	1.14226	+	1.50978i
$58$		0			0
$59$	−5.80978	+	1.55673i	−0.756369	+	0.202669i	−0.616341	−	0.787479i	$-0.711386\pi$
$59$	−5.80978	+	1.55673i	−0.756369	+	0.202669i	−0.140028	+	0.990148i	$0.544719\pi$
$60$		0			0
$61$	−1.41803	+	5.29217i	−0.181561	+	0.677593i	0.813780	+	0.581173i	$0.197406\pi$
$61$	−1.41803	+	5.29217i	−0.181561	+	0.677593i	−0.995341	+	0.0964204i	$0.969261\pi$
$62$		0			0
$63$	−2.83697	+	2.76079i	−0.357425	+	0.347826i
$64$		0			0
$65$	−0.0759724	+	0.131588i	−0.00942321	+	0.0163215i
$66$		0			0
$67$	4.53482	−	2.61818i	0.554016	−	0.319861i	−0.196724	−	0.980459i	$-0.563030\pi$
$67$	4.53482	−	2.61818i	0.554016	−	0.319861i	0.750740	+	0.660598i	$0.229697\pi$
$68$		0			0
$69$	−0.179864	−	1.44196i	−0.0216531	−	0.173592i
$70$		0			0
$71$	5.08729	−	2.93715i	0.603750	−	0.348575i	−0.166765	−	0.985997i	$-0.553332\pi$
$71$	5.08729	−	2.93715i	0.603750	−	0.348575i	0.770516	+	0.637421i	$0.219999\pi$
$72$		0			0
$73$		−	1.03868i		−	0.121568i	−0.998151	−	0.0607842i	$-0.980640\pi$
$73$		−	1.03868i		−	0.121568i	0.998151	−	0.0607842i	$-0.0193601\pi$
$74$		0			0
$75$	2.02370	+	4.98125i	0.233677	+	0.575186i
$76$		0			0
$77$	−0.233459	−	0.404363i	−0.0266051	−	0.0460814i
$78$		0			0
$79$	0.472722	+	0.126665i	0.0531853	+	0.0142510i	0.285314	−	0.958434i	$-0.407902\pi$
$79$	0.472722	+	0.126665i	0.0531853	+	0.0142510i	−0.232128	+	0.972685i	$0.574569\pi$
$80$		0			0
$81$	−7.91381	+	4.28620i	−0.879313	+	0.476245i
$82$		0			0
$83$	−11.5472	−	6.66677i	−1.26747	−	0.731773i	−0.292960	−	0.956125i	$-0.594640\pi$
$83$	−11.5472	−	6.66677i	−1.26747	−	0.731773i	−0.974508	+	0.224351i	$0.927974\pi$
$84$		0			0
$85$			0.383192i			0.0415631i
$86$		0			0
$87$	−4.58550	+	0.571976i	−0.491617	+	0.0613223i
$88$		0			0
$89$	4.27017	+	15.9365i	0.452637	+	1.68927i	0.694942	+	0.719065i	$0.255430\pi$
$89$	4.27017	+	15.9365i	0.452637	+	1.68927i	−0.242305	+	0.970200i	$0.577904\pi$
$90$		0			0
$91$	−0.0376881	−	0.140654i	−0.00395079	−	0.0147445i
$92$		0			0
$93$	1.17598	+	9.42774i	0.121943	+	0.977611i
$94$		0			0
$95$	5.68117	−	9.84008i	0.582876	−	1.00957i
$96$		0			0
$97$	−7.97830	+	7.97830i	−0.810074	+	0.810074i	−0.984645	−	0.174571i	$-0.944146\pi$
$97$	−7.97830	+	7.97830i	−0.810074	+	0.810074i	0.174571	+	0.984645i	$0.444146\pi$
$98$		0			0
$99$	−0.260771	−	1.02903i	−0.0262085	−	0.103421i
$100$		0			0
$101$	−12.2653			−1.22044			−0.610222	−	0.792230i	$-0.708920\pi$
$101$	−12.2653			−1.22044			−0.610222	+	0.792230i	$0.708920\pi$
$102$		0			0
$103$	−7.56087	−	7.56087i	−0.744995	−	0.744995i	0.228540	−	0.973535i	$-0.426605\pi$
$103$	−7.56087	−	7.56087i	−0.744995	−	0.744995i	−0.973535	+	0.228540i	$0.926605\pi$
$104$		0			0
$105$	2.89904	+	1.22400i	0.282917	+	0.119450i
$106$		0			0
$107$	9.71460	−	5.60873i	0.939146	−	0.542216i	0.0494537	−	0.998776i	$-0.484252\pi$
$107$	9.71460	−	5.60873i	0.939146	−	0.542216i	0.889693	+	0.456560i	$0.150919\pi$
$108$		0			0
$109$	−0.346478	−	1.29307i	−0.0331866	−	0.123854i	0.947345	−	0.320214i	$-0.103755\pi$
$109$	−0.346478	−	1.29307i	−0.0331866	−	0.123854i	−0.980532	+	0.196360i	$0.937088\pi$
$110$		0			0
$111$	−6.70845	−	8.12384i	−0.636738	−	0.771080i
$112$		0			0
$113$	−0.205514	−	0.766990i	−0.0193332	−	0.0721523i	0.955585	−	0.294715i	$-0.0952246\pi$
$113$	−0.205514	−	0.766990i	−0.0193332	−	0.0721523i	−0.974918	+	0.222562i	$0.928558\pi$
$114$		0			0
$115$	−1.00039	+	0.577578i	−0.0932873	+	0.0538594i
$116$		0			0
$117$	0.00450554	−	0.331033i	0.000416537	−	0.0306040i
$118$		0			0
$119$	−0.259672	−	0.259672i	−0.0238041	−	0.0238041i
$120$		0			0
$121$	−10.8748			−0.988617
$122$		0			0
$123$	−0.180405	+	1.30180i	−0.0162666	+	0.117379i
$124$		0			0
$125$	7.89026	−	7.89026i	0.705726	−	0.705726i
$126$		0			0
$127$	−0.547971	+	0.949114i	−0.0486246	+	0.0842202i	−0.889313	−	0.457298i	$-0.848817\pi$
$127$	−0.547971	+	0.949114i	−0.0486246	+	0.0842202i	0.840689	+	0.541519i	$0.182150\pi$
$128$		0			0
$129$	10.1304	−	1.26362i	0.891933	−	0.111256i
$130$		0			0
$131$	−0.646234	−	2.41178i	−0.0564617	−	0.210718i	0.931932	−	0.362634i	$-0.118122\pi$
$131$	−0.646234	−	2.41178i	−0.0564617	−	0.210718i	−0.988393	+	0.151916i	$0.951456\pi$
$132$		0			0
$133$	2.81830	+	10.5180i	0.244377	+	0.912029i
$134$		0			0
$135$	5.58593	+	4.47032i	0.480761	+	0.384744i
$136$		0			0
$137$			1.00031i			0.0854620i	0.999087	+	0.0427310i	$0.0136058\pi$
$137$			1.00031i			0.0854620i	−0.999087	+	0.0427310i	$0.986394\pi$
$138$		0			0
$139$	−2.63719	−	1.52258i	−0.223684	−	0.129144i	0.383971	−	0.923345i	$-0.374556\pi$
$139$	−2.63719	−	1.52258i	−0.223684	−	0.129144i	−0.607655	+	0.794201i	$0.707890\pi$
$140$		0			0
$141$	6.57528	−	8.44939i	0.553738	−	0.711567i
$142$		0			0
$143$	0.0377186	+	0.0101067i	0.00315419	+	0.000845163i
$144$		0			0
$145$	1.83673	+	3.18130i	0.152532	+	0.264193i
$146$		0			0
$147$	8.43877	−	3.42836i	0.696018	−	0.282767i
$148$		0			0
$149$		−	14.9878i		−	1.22785i	−0.789366	−	0.613923i	$-0.789591\pi$
$149$		−	14.9878i		−	1.22785i	0.789366	−	0.613923i	$-0.210409\pi$
$150$		0			0
$151$	0.883659	−	0.510181i	0.0719111	−	0.0415179i	−0.463613	−	0.886038i	$-0.653447\pi$
$151$	0.883659	−	0.510181i	0.0719111	−	0.0415179i	0.535524	+	0.844520i	$0.320114\pi$
$152$		0			0
$153$	−0.407579	−	0.728672i	−0.0329508	−	0.0589097i
$154$		0			0
$155$	6.54073	−	3.77629i	0.525364	−	0.303319i
$156$		0			0
$157$	1.47706	−	2.55835i	0.117883	−	0.204179i	−0.801046	−	0.598603i	$-0.795723\pi$
$157$	1.47706	−	2.55835i	0.117883	−	0.204179i	0.918928	+	0.394424i	$0.129056\pi$
$158$		0			0
$159$	−2.65152	−	6.52660i	−0.210279	−	0.517593i
$160$		0			0
$161$	0.286523	−	1.06932i	0.0225812	−	0.0842741i
$162$		0			0
$163$	5.78959	−	1.55132i	0.453476	−	0.121509i	−0.0248494	−	0.999691i	$-0.507911\pi$
$163$	5.78959	−	1.55132i	0.453476	−	0.121509i	0.478325	+	0.878183i	$0.341244\pi$
$164$		0			0
$165$	−0.672972	+	0.509151i	−0.0523908	+	0.0396374i
$166$		0			0
$167$	5.57534	−	20.8075i	0.431433	−	1.61013i	−0.318029	−	0.948081i	$-0.603021\pi$
$167$	5.57534	−	20.8075i	0.431433	−	1.61013i	0.749461	−	0.662048i	$-0.230313\pi$
$168$		0			0
$169$	−11.2478	−	6.49391i	−0.865214	−	0.499532i
$170$		0			0
$171$	−0.336922	+	24.7545i	−0.0257650	+	1.89302i
$172$		0			0
$173$	6.15811	−	10.6662i	0.468192	−	0.810933i	−0.531147	−	0.847280i	$-0.678239\pi$
$173$	6.15811	−	10.6662i	0.468192	−	0.810933i	0.999339	+	0.0363470i	$0.0115721\pi$
$174$		0			0
$175$			4.09608i			0.309635i
$176$		0			0
$177$	−9.59746	−	4.05213i	−0.721389	−	0.304577i
$178$		0			0
$179$	3.20372	−	3.20372i	0.239457	−	0.239457i	−0.577168	−	0.816625i	$-0.695842\pi$
$179$	3.20372	−	3.20372i	0.239457	−	0.239457i	0.816625	+	0.577168i	$0.195842\pi$
$180$		0			0
$181$	−5.63591	−	9.76169i	−0.418914	−	0.725580i	0.576916	−	0.816803i	$-0.304256\pi$
$181$	−5.63591	−	9.76169i	−0.418914	−	0.725580i	−0.995831	+	0.0912228i	$0.970922\pi$
$182$		0			0
$183$	−7.56779	+	5.72558i	−0.559427	+	0.423247i
$184$		0			0
$185$	−3.87517	+	7.42479i	−0.284908	+	0.545881i
$186$		0			0
$187$	0.0951233	−	0.0254882i	0.00695611	−	0.00186388i
$188$		0			0
$189$	−6.81466	+	0.755997i	−0.495693	+	0.0549907i
$190$		0			0
$191$	−5.79529	−	5.79529i	−0.419333	−	0.419333i	0.465641	−	0.884974i	$-0.345824\pi$
$191$	−5.79529	−	5.79529i	−0.419333	−	0.419333i	−0.884974	+	0.465641i	$0.845824\pi$
$192$		0			0
$193$	−10.6254	+	10.6254i	−0.764834	+	0.764834i	−0.977192	−	0.212358i	$-0.931886\pi$
$193$	−10.6254	+	10.6254i	−0.764834	+	0.764834i	0.212358	+	0.977192i	$0.431886\pi$
$194$		0			0
$195$	−0.243823	+	0.0990562i	−0.0174605	+	0.00709357i
$196$		0			0
$197$	−4.04485	−	2.33529i	−0.288183	−	0.166383i	0.348939	−	0.937145i	$-0.386542\pi$
$197$	−4.04485	−	2.33529i	−0.288183	−	0.166383i	−0.637122	+	0.770763i	$0.719875\pi$
$198$		0			0
$199$	−14.1171	−	14.1171i	−1.00074	−	1.00074i	−1.00000		0.000735341i	$-0.999766\pi$
$199$	−14.1171	−	14.1171i	−1.00074	−	1.00074i	−0.000735341	−	1.00000i	$-0.500234\pi$
$200$		0			0
$201$	8.98378	+	1.24499i	0.633667	+	0.0878146i
$202$		0			0
$203$	−3.40048	−	0.911157i	−0.238667	−	0.0639507i
$204$		0			0
$205$	1.00914	−	0.270399i	0.0704817	−	0.0188855i
$206$		0			0
$207$	1.28800	−	2.16237i	0.0895221	−	0.150295i
$208$		0			0
$209$	−2.82058	−	0.755772i	−0.195103	−	0.0522778i
$210$		0			0
$211$	21.8962			1.50740			0.753699	−	0.657220i	$-0.228268\pi$
$211$	21.8962			1.50740			0.753699	+	0.657220i	$0.228268\pi$
$212$		0			0
$213$	10.0783	+	1.39666i	0.690551	+	0.0956977i
$214$		0			0
$215$	−4.05774	−	7.02822i	−0.276736	−	0.479321i
$216$		0			0
$217$	−1.87333	+	6.99136i	−0.127170	+	0.474605i
$218$		0			0
$219$	1.10488	−	1.41979i	0.0746607	−	0.0959408i
$220$		0			0
$221$	0.0307122			0.00206593
$222$		0			0
$223$	3.05720			0.204725			0.102363	−	0.994747i	$-0.467360\pi$
$223$	3.05720			0.204725			0.102363	+	0.994747i	$0.467360\pi$
$224$		0			0
$225$	−2.53248	+	8.96166i	−0.168832	+	0.597444i
$226$		0			0
$227$	−1.06703	+	3.98222i	−0.0708214	+	0.264309i	−0.992253	−	0.124231i	$-0.960354\pi$
$227$	−1.06703	+	3.98222i	−0.0708214	+	0.264309i	0.921432	+	0.388540i	$0.127020\pi$
$228$		0			0
$229$	−7.28814	−	12.6234i	−0.481614	−	0.834180i	0.518163	−	0.855282i	$-0.326616\pi$
$229$	−7.28814	−	12.6234i	−0.481614	−	0.834180i	−0.999777	+	0.0211018i	$0.993283\pi$
$230$		0			0
$231$	0.111014	−	0.801070i	0.00730415	−	0.0527065i
$232$		0			0
$233$	−1.04695			−0.0685879			−0.0342940	−	0.999412i	$-0.510918\pi$
$233$	−1.04695			−0.0685879			−0.0342940	+	0.999412i	$0.510918\pi$
$234$		0			0
$235$	−8.22094	−	2.20279i	−0.536275	−	0.143694i
$236$		0			0
$237$	0.511435	+	0.675991i	0.0332213	+	0.0439103i
$238$		0			0
$239$	−18.4282	+	4.93783i	−1.19202	+	0.319401i	−0.799685	−	0.600420i	$-0.795000\pi$
$239$	−18.4282	+	4.93783i	−1.19202	+	0.319401i	−0.392338	+	0.919821i	$0.628333\pi$
$240$		0			0
$241$	−13.1248	−	3.51678i	−0.845443	−	0.226536i	−0.190004	−	0.981783i	$-0.560850\pi$
$241$	−13.1248	−	3.51678i	−0.845443	−	0.226536i	−0.655440	+	0.755247i	$0.727517\pi$
$242$		0			0
$243$	−15.3769	−	2.55927i	−0.986431	−	0.164177i
$244$		0			0
$245$	−5.12002	−	5.12002i	−0.327106	−	0.327106i
$246$		0			0
$247$	−0.788666	−	0.455336i	−0.0501816	−	0.0289724i
$248$		0			0
$249$	−8.69244	−	21.3961i	−0.550861	−	1.35592i
$250$		0			0
$251$	−12.8801	+	12.8801i	−0.812988	+	0.812988i	−0.985081	−	0.172093i	$-0.944947\pi$
$251$	−12.8801	+	12.8801i	−0.812988	+	0.812988i	0.172093	+	0.985081i	$0.444947\pi$
$252$		0			0
$253$	0.209919	+	0.209919i	0.0131975	+	0.0131975i
$254$		0			0
$255$	−0.407614	+	0.523794i	−0.0255258	+	0.0328012i
$256$		0			0
$257$	24.7058	−	6.61991i	1.54111	−	0.412939i	0.614484	−	0.788929i	$-0.289364\pi$
$257$	24.7058	−	6.61991i	1.54111	−	0.412939i	0.926623	+	0.375991i	$0.122698\pi$
$258$		0			0
$259$	−2.40541	−	7.65746i	−0.149465	−	0.475811i
$260$		0			0
$261$	−6.87645	−	4.09590i	−0.425641	−	0.253530i
$262$		0			0
$263$	11.2712	+	19.5223i	0.695013	+	1.20380i	0.970176	+	0.242401i	$0.0779348\pi$
$263$	11.2712	+	19.5223i	0.695013	+	1.20380i	−0.275163	+	0.961398i	$0.588732\pi$
$264$		0			0
$265$	−3.95986	+	3.95986i	−0.243252	+	0.243252i
$266$		0			0
$267$	−11.1152	+	26.3263i	−0.680238	+	1.61114i
$268$		0			0
$269$		−	8.01206i		−	0.488504i	−0.969712	−	0.244252i	$-0.921458\pi$
$269$		−	8.01206i		−	0.488504i	0.969712	−	0.244252i	$-0.0785424\pi$
$270$		0			0
$271$	−1.20711	+	2.09078i	−0.0733270	+	0.127006i	−0.900358	−	0.435151i	$-0.856695\pi$
$271$	−1.20711	+	2.09078i	−0.0733270	+	0.127006i	0.827031	+	0.562157i	$0.190028\pi$
$272$		0			0
$273$	0.0981015	−	0.232353i	0.00593737	−	0.0140626i
$274$		0			0
$275$	−0.951268	−	0.549215i	−0.0573636	−	0.0331189i
$276$		0			0
$277$	1.12495	−	4.19837i	0.0675917	−	0.252256i	−0.923860	−	0.382731i	$-0.874984\pi$
$277$	1.12495	−	4.19837i	0.0675917	−	0.252256i	0.991452	+	0.130475i	$0.0416503\pi$
$278$		0			0
$279$	−8.42112	+	14.1379i	−0.504159	+	0.846414i
$280$		0			0
$281$	−6.78700	+	1.81857i	−0.404879	+	0.108487i	−0.455510	−	0.890230i	$-0.650543\pi$
$281$	−6.78700	+	1.81857i	−0.404879	+	0.108487i	0.0506317	+	0.998717i	$0.483877\pi$
$282$		0			0
$283$	4.58114	−	17.0971i	0.272321	−	1.01631i	−0.685295	−	0.728266i	$-0.740327\pi$
$283$	4.58114	−	17.0971i	0.272321	−	1.01631i	0.957616	−	0.288049i	$-0.0930067\pi$
$284$		0			0
$285$	18.2329	−	7.40737i	1.08003	−	0.438775i
$286$		0			0
$287$	−0.500613	+	0.867087i	−0.0295502	+	0.0511825i
$288$		0			0
$289$	−14.6554	+	8.46127i	−0.862080	+	0.497722i
$290$		0			0
$291$	−19.3925	+	2.41894i	−1.13681	+	0.141801i
$292$		0			0
$293$	−4.52457	+	2.61226i	−0.264328	+	0.152610i	−0.626307	−	0.779576i	$-0.715434\pi$
$293$	−4.52457	+	2.61226i	−0.264328	+	0.152610i	0.361979	+	0.932186i	$0.382101\pi$
$294$		0			0
$295$			8.28155i			0.482171i
$296$		0			0
$297$	0.738158	−	1.68399i	0.0428323	−	0.0977152i
$298$		0			0
$299$	0.0462919	+	0.0801799i	0.00267713	+	0.00463693i
$300$		0			0
$301$	7.51244	+	2.01295i	0.433010	+	0.116025i
$302$		0			0
$303$	−16.7657	−	13.0470i	−0.963165	−	0.749531i
$304$		0			0
$305$	6.53306	+	3.77186i	0.374082	+	0.215976i
$306$		0			0
$307$		−	15.0090i		−	0.856610i	−0.903634	−	0.428305i	$-0.859111\pi$
$307$		−	15.0090i		−	0.856610i	0.903634	−	0.428305i	$-0.140889\pi$
$308$		0			0
$309$	−2.29238	−	18.3779i	−0.130409	−	1.04548i
$310$		0			0
$311$	7.68506	+	28.6810i	0.435780	+	1.62635i	0.739193	+	0.673494i	$0.235207\pi$
$311$	7.68506	+	28.6810i	0.435780	+	1.62635i	−0.303413	+	0.952859i	$0.598126\pi$
$312$		0			0
$313$	−2.12274	−	7.92219i	−0.119985	−	0.447789i	0.879627	−	0.475664i	$-0.157792\pi$
$313$	−2.12274	−	7.92219i	−0.119985	−	0.447789i	−0.999611	+	0.0278759i	$0.991126\pi$
$314$		0			0
$315$	2.66075	+	4.75691i	0.149916	+	0.268022i
$316$		0			0
$317$	1.50907	−	2.61378i	0.0847576	−	0.146804i	−0.820530	−	0.571603i	$-0.806322\pi$
$317$	1.50907	−	2.61378i	0.0847576	−	0.146804i	0.905288	+	0.424799i	$0.139655\pi$
$318$		0			0
$319$	0.667553	−	0.667553i	0.0373758	−	0.0373758i
$320$		0			0
$321$	19.2453	+	2.66704i	1.07417	+	0.148860i
$322$		0			0
$323$	−2.29664			−0.127789
$324$		0			0
$325$	−0.242229	−	0.242229i	−0.0134364	−	0.0134364i
$326$		0			0
$327$	0.901876	−	2.13609i	0.0498739	−	0.118126i
$328$		0			0
$329$	7.06368	−	4.07822i	0.389433	−	0.224839i
$330$		0			0
$331$	5.35290	+	19.9773i	0.294222	+	1.09805i	0.941833	+	0.336081i	$0.109102\pi$
$331$	5.35290	+	19.9773i	0.294222	+	1.09805i	−0.647611	+	0.761971i	$0.724232\pi$
$332$		0			0
$333$	−0.528341	−	18.2406i	−0.0289529	−	0.999581i
$334$		0			0
$335$	−1.86604	−	6.96416i	−0.101953	−	0.380493i
$336$		0			0
$337$	−10.8203	+	6.24709i	−0.589418	+	0.340301i	−0.764867	−	0.644188i	$-0.777196\pi$
$337$	−10.8203	+	6.24709i	−0.589418	+	0.340301i	0.175449	+	0.984488i	$0.443862\pi$
$338$		0			0
$339$	0.534949	−	1.26703i	0.0290545	−	0.0688154i
$340$		0			0
$341$	−1.37248	−	1.37248i	−0.0743241	−	0.0743241i
$342$		0			0
$343$	16.1759			0.873416
$344$		0			0
$345$	−1.98185	−	0.274648i	−0.106699	−	0.0147865i
$346$		0			0
$347$	−1.03403	+	1.03403i	−0.0555098	+	0.0555098i	−0.734317	−	0.678807i	$-0.762497\pi$
$347$	−1.03403	+	1.03403i	−0.0555098	+	0.0555098i	0.678807	+	0.734317i	$0.262497\pi$
$348$		0			0
$349$	13.1887	−	22.8436i	0.705977	−	1.22279i	−0.260361	−	0.965511i	$-0.583842\pi$
$349$	13.1887	−	22.8436i	0.705977	−	1.22279i	0.966338	−	0.257276i	$-0.0828251\pi$
$350$		0			0
$351$	0.358289	−	0.447703i	0.0191240	−	0.0238966i
$352$		0			0
$353$	4.72097	+	17.6189i	0.251272	+	0.937759i	0.970127	+	0.242599i	$0.0779999\pi$
$353$	4.72097	+	17.6189i	0.251272	+	0.937759i	−0.718855	+	0.695160i	$0.755333\pi$
$354$		0			0
$355$	−2.09338	−	7.81260i	−0.111105	−	0.414650i
$356$		0			0
$357$	−0.0787297	−	0.631172i	−0.00416682	−	0.0334052i
$358$		0			0
$359$			35.0852i			1.85172i	0.377862	+	0.925862i	$0.376659\pi$
$359$			35.0852i			1.85172i	−0.377862	+	0.925862i	$0.623341\pi$
$360$		0			0
$361$	42.5215	+	24.5498i	2.23797	+	1.29209i
$362$		0			0
$363$	−14.8650	−	11.5679i	−0.780209	−	0.607155i
$364$		0			0
$365$	−1.38141	−	0.370147i	−0.0723061	−	0.0193744i
$366$		0			0
$367$	13.3791	+	23.1732i	0.698381	+	1.20963i	0.969028	+	0.246952i	$0.0794291\pi$
$367$	13.3791	+	23.1732i	0.698381	+	1.20963i	−0.270647	+	0.962679i	$0.587238\pi$
$368$		0			0
$369$	−1.63136	+	1.58755i	−0.0849254	+	0.0826447i
$370$		0			0
$371$		−	5.36682i		−	0.278632i
$372$		0			0
$373$	−9.26611	+	5.34979i	−0.479781	+	0.277002i	−0.720325	−	0.693637i	$-0.756007\pi$
$373$	−9.26611	+	5.34979i	−0.479781	+	0.277002i	0.240544	+	0.970638i	$0.422674\pi$
$374$		0			0
$375$	19.1785	−	2.39224i	0.990372	−	0.123535i
$376$		0			0
$377$	0.254976	−	0.147210i	0.0131319	−	0.00758173i
$378$		0			0
$379$	6.24669	−	10.8196i	0.320871	−	0.555765i	−0.659797	−	0.751444i	$-0.729358\pi$
$379$	6.24669	−	10.8196i	0.320871	−	0.555765i	0.980668	+	0.195679i	$0.0626911\pi$
$380$		0			0
$381$	−1.75864	+	0.714469i	−0.0900976	+	0.0366034i
$382$		0			0
$383$	−2.40828	+	8.98784i	−0.123058	+	0.459257i	−0.999763	−	0.0217706i	$-0.993070\pi$
$383$	−2.40828	+	8.98784i	−0.123058	+	0.459257i	0.876705	+	0.481028i	$0.159736\pi$
$384$		0			0
$385$	−0.620983	+	0.166392i	−0.0316482	+	0.00848012i
$386$		0			0
$387$	15.1916	+	9.04876i	0.772234	+	0.459975i
$388$		0			0
$389$	7.70642	−	28.7608i	0.390731	−	1.45823i	−0.438200	−	0.898877i	$-0.644384\pi$
$389$	7.70642	−	28.7608i	0.390731	−	1.45823i	0.828931	−	0.559351i	$-0.188949\pi$
$390$		0			0
$391$	0.202207	+	0.116744i	0.0102261	+	0.00590402i
$392$		0			0
$393$	1.68213	−	3.98413i	0.0848524	−	0.200973i
$394$		0			0
$395$	0.336920	−	0.583563i	0.0169523	−	0.0293623i
$396$		0			0
$397$		−	14.7534i		−	0.740453i	−0.928942	−	0.370226i	$-0.879280\pi$
$397$		−	14.7534i		−	0.740453i	0.928942	−	0.370226i	$-0.120720\pi$
$398$		0			0
$399$	−7.33597	+	17.3752i	−0.367258	+	0.869850i
$400$		0			0
$401$	−5.29030	+	5.29030i	−0.264185	+	0.264185i	−0.826752	−	0.562567i	$-0.809814\pi$
$401$	−5.29030	+	5.29030i	−0.264185	+	0.264185i	0.562567	+	0.826752i	$0.309814\pi$
$402$		0			0
$403$	−0.302663	−	0.524228i	−0.0150767	−	0.0261137i
$404$		0			0
$405$	2.88031	+	12.0525i	0.143124	+	0.598895i
$406$		0			0
$407$	2.10088	+	0.468106i	0.104137	+	0.0232031i
$408$		0			0
$409$	11.5636	−	3.09845i	0.571781	−	0.153208i	0.0386678	−	0.999252i	$-0.487689\pi$
$409$	11.5636	−	3.09845i	0.571781	−	0.153208i	0.533113	+	0.846044i	$0.321022\pi$
$410$		0			0
$411$	−1.06406	+	1.36734i	−0.0524861	+	0.0674459i
$412$		0			0
$413$	−5.61202	−	5.61202i	−0.276150	−	0.276150i
$414$		0			0
$415$	−12.9815	+	12.9815i	−0.637239	+	0.637239i
$416$		0			0
$417$	−1.98522	−	4.88652i	−0.0972164	−	0.239294i
$418$		0			0
$419$	−19.5424	−	11.2828i	−0.954709	−	0.551202i	−0.0601686	−	0.998188i	$-0.519164\pi$
$419$	−19.5424	−	11.2828i	−0.954709	−	0.551202i	−0.894541	+	0.446987i	$0.852497\pi$
$420$		0			0
$421$	16.6835	+	16.6835i	0.813104	+	0.813104i	0.985098	−	0.171994i	$-0.0550210\pi$
$421$	16.6835	+	16.6835i	0.813104	+	0.813104i	−0.171994	+	0.985098i	$0.555021\pi$
$422$		0			0
$423$	17.9758	−	4.55532i	0.874012	−	0.221487i
$424$		0			0
$425$	−0.834479	−	0.223598i	−0.0404782	−	0.0108461i
$426$		0			0
$427$	−6.98317	+	1.87113i	−0.337939	+	0.0905505i
$428$		0			0
$429$	0.0408076	+	0.0539375i	0.00197021	+	0.00260413i
$430$		0			0
$431$	17.0880	+	4.57873i	0.823102	+	0.220550i	0.645702	−	0.763589i	$-0.276565\pi$
$431$	17.0880	+	4.57873i	0.823102	+	0.220550i	0.177400	+	0.984139i	$0.443231\pi$
$432$		0			0
$433$	10.9188			0.524725			0.262362	−	0.964969i	$-0.415498\pi$
$433$	10.9188			0.524725			0.262362	+	0.964969i	$0.415498\pi$
$434$		0			0
$435$	−0.873393	+	6.30238i	−0.0418760	+	0.302176i
$436$		0			0
$437$	−3.46168	−	5.99581i	−0.165595	−	0.286819i
$438$		0			0
$439$	−8.93434	+	33.3434i	−0.426413	+	1.59139i	0.334406	+	0.942429i	$0.391464\pi$
$439$	−8.93434	+	33.3434i	−0.426413	+	1.59139i	−0.760819	+	0.648965i	$0.775202\pi$
$440$		0			0
$441$	15.1820	+	4.29028i	0.722952	+	0.204299i
$442$		0			0
$443$	22.5313			1.07049			0.535246	−	0.844696i	$-0.320219\pi$
$443$	22.5313			1.07049			0.535246	+	0.844696i	$0.320219\pi$
$444$		0			0
$445$	22.7167			1.07687
$446$		0			0
$447$	15.9430	−	20.4871i	0.754077	−	0.969007i
$448$		0			0
$449$	3.95126	−	14.7463i	0.186472	−	0.695921i	−0.807839	−	0.589403i	$-0.799363\pi$
$449$	3.95126	−	14.7463i	0.186472	−	0.695921i	0.994311	−	0.106518i	$-0.0339703\pi$
$450$		0			0
$451$	−0.134247	−	0.232523i	−0.00632146	−	0.0109491i
$452$		0			0
$453$	1.75059	+	0.242599i	0.0822498	+	0.0113983i
$454$		0			0
$455$	−0.200495			−0.00939936
$456$		0			0
$457$	−15.9508	−	4.27399i	−0.746145	−	0.199929i	−0.134338	−	0.990936i	$-0.542891\pi$
$457$	−15.9508	−	4.27399i	−0.746145	−	0.199929i	−0.611808	+	0.791007i	$0.709557\pi$
$458$		0			0
$459$	0.217984	−	1.42959i	0.0101746	−	0.0667277i
$460$		0			0
$461$	−21.4125	+	5.73746i	−0.997279	+	0.267220i	−0.720305	−	0.693657i	$-0.755998\pi$
$461$	−21.4125	+	5.73746i	−0.997279	+	0.267220i	−0.276974	+	0.960877i	$0.589332\pi$
$462$		0			0
$463$	12.7671	+	3.42093i	0.593337	+	0.158984i	0.542978	−	0.839747i	$-0.317297\pi$
$463$	12.7671	+	3.42093i	0.593337	+	0.158984i	0.0503590	+	0.998731i	$0.483963\pi$
$464$		0			0
$465$	12.9576	+	1.79569i	0.600895	+	0.0832730i
$466$		0			0
$467$	28.7974	+	28.7974i	1.33258	+	1.33258i	0.903052	+	0.429532i	$0.141321\pi$
$467$	28.7974	+	28.7974i	1.33258	+	1.33258i	0.429532	+	0.903052i	$0.358679\pi$
$468$		0			0
$469$	5.98381	+	3.45476i	0.276307	+	0.159526i
$470$		0			0
$471$	4.74043	−	1.92586i	0.218427	−	0.0887391i
$472$		0			0
$473$	−1.47478	+	1.47478i	−0.0678103	+	0.0678103i
$474$		0			0
$475$	18.1137	+	18.1137i	0.831114	+	0.831114i
$476$		0			0
$477$	3.31814	−	11.7419i	0.151927	−	0.537623i
$478$		0			0
$479$	−31.4390	+	8.42405i	−1.43648	+	0.384905i	−0.891301	−	0.453412i	$-0.850207\pi$
$479$	−31.4390	+	8.42405i	−1.43648	+	0.384905i	−0.545183	+	0.838317i	$0.683540\pi$
$480$		0			0
$481$	0.595084	+	0.310588i	0.0271335	+	0.0141616i
$482$		0			0
$483$	1.52912	−	1.15689i	0.0695775	−	0.0526404i
$484$		0			0
$485$	7.76767	+	13.4540i	0.352712	+	0.610915i
$486$		0			0
$487$	14.8376	−	14.8376i	0.672356	−	0.672356i	−0.285903	−	0.958259i	$-0.592293\pi$
$487$	14.8376	−	14.8376i	0.672356	−	0.672356i	0.958259	+	0.285903i	$0.0922935\pi$
$488$		0			0
$489$	9.56410	+	4.03805i	0.432504	+	0.182607i
$490$		0			0
$491$			39.3272i			1.77481i	0.460988	+	0.887406i	$0.347495\pi$
$491$			39.3272i			1.77481i	−0.460988	+	0.887406i	$0.652505\pi$
$492$		0			0
$493$	0.371253	−	0.643029i	0.0167204	−	0.0289606i
$494$		0			0
$495$	−1.46150	−	0.0198918i	−0.0656895	−	0.000894070i
$496$		0			0
$497$	6.71282	+	3.87565i	0.301111	+	0.173847i
$498$		0			0
$499$	−2.15680	+	8.04929i	−0.0965517	+	0.360336i	−0.997250	−	0.0741090i	$-0.976389\pi$
$499$	−2.15680	+	8.04929i	−0.0965517	+	0.360336i	0.900698	+	0.434445i	$0.143055\pi$
$500$		0			0
$501$	29.7546	−	22.5115i	1.32934	−	1.00574i
$502$		0			0
$503$	34.4722	−	9.23680i	1.53704	−	0.411848i	0.611732	−	0.791065i	$-0.290473\pi$
$503$	34.4722	−	9.23680i	1.53704	−	0.411848i	0.925308	+	0.379217i	$0.123807\pi$
$504$		0			0
$505$	−4.37090	+	16.3124i	−0.194502	+	0.725893i
$506$		0			0
$507$	−8.46706	−	20.8413i	−0.376035	−	0.925594i
$508$		0			0
$509$	−0.880811	+	1.52561i	−0.0390412	+	0.0676214i	−0.884886	−	0.465808i	$-0.845764\pi$
$509$	−0.880811	+	1.52561i	−0.0390412	+	0.0676214i	0.845845	+	0.533430i	$0.179097\pi$
$510$		0			0
$511$	1.18695	−	0.685284i	0.0525074	−	0.0303152i
$512$		0			0
$513$	−26.7926	+	33.4790i	−1.18292	+	1.47813i
$514$		0			0
$515$	−12.7501	+	7.36127i	−0.561836	+	0.324376i
$516$		0			0
$517$			2.18728i			0.0961964i
$518$		0			0
$519$	19.7636	−	8.02922i	0.867525	−	0.352444i
$520$		0			0
$521$	16.2122	+	28.0803i	0.710268	+	1.23022i	0.964757	+	0.263144i	$0.0847594\pi$
$521$	16.2122	+	28.0803i	0.710268	+	1.23022i	−0.254489	+	0.967076i	$0.581907\pi$
$522$		0			0
$523$	1.12456	+	0.301324i	0.0491734	+	0.0131760i	0.283322	−	0.959025i	$-0.408564\pi$
$523$	1.12456	+	0.301324i	0.0491734	+	0.0131760i	−0.234149	+	0.972201i	$0.575230\pi$
$524$		0			0
$525$	−4.35713	+	5.59902i	−0.190161	+	0.244361i
$526$		0			0
$527$	−1.32206	−	0.763292i	−0.0575899	−	0.0332495i
$528$		0			0
$529$		−	22.2961i		−	0.969397i
$530$		0			0
$531$	−8.80859	−	15.7481i	−0.382260	−	0.683408i
$532$		0			0
$533$	−0.0216720	−	0.0808812i	−0.000938720	−	0.00350335i
$534$		0			0
$535$	−3.99748	−	14.9188i	−0.172826	−	0.644996i
$536$		0			0
$537$	7.78712	−	0.971333i	0.336039	−	0.0419161i
$538$		0			0
$539$	−0.930428	+	1.61155i	−0.0400764	+	0.0694143i
$540$		0			0
$541$	−31.4789	+	31.4789i	−1.35338	+	1.35338i	−0.471538	+	0.881846i	$0.656301\pi$
$541$	−31.4789	+	31.4789i	−1.35338	+	1.35338i	−0.881846	+	0.471538i	$0.843699\pi$
$542$		0			0
$543$	2.67997	−	19.3386i	0.115008	−	0.829897i
$544$		0			0
$545$	−1.84321			−0.0789546
$546$		0			0
$547$	−26.3554	−	26.3554i	−1.12687	−	1.12687i	−0.990682	−	0.136193i	$-0.956513\pi$
$547$	−26.3554	−	26.3554i	−1.12687	−	1.12687i	−0.136193	−	0.990682i	$-0.543487\pi$
$548$		0			0
$549$	−16.4351	−	0.223690i	−0.701431	−	0.00954686i
$550$		0			0
$551$	−19.0670	+	11.0083i	−0.812280	+	0.468970i
$552$		0			0
$553$	0.167138	+	0.623769i	0.00710745	+	0.0265254i
$554$		0			0
$555$	−13.1950	+	6.02696i	−0.560098	+	0.255830i
$556$		0			0
$557$	7.46768	+	27.8698i	0.316416	+	1.18088i	0.922664	+	0.385604i	$0.126007\pi$
$557$	7.46768	+	27.8698i	0.316416	+	1.18088i	−0.606248	+	0.795275i	$0.707326\pi$
$558$		0			0
$559$	−0.563300	+	0.325221i	−0.0238250	+	0.0137554i
$560$		0			0
$561$	0.157139	+	0.0663453i	0.00663440	+	0.00280110i
$562$		0			0
$563$	−9.50686	−	9.50686i	−0.400666	−	0.400666i	0.477801	−	0.878468i	$-0.341434\pi$
$563$	−9.50686	−	9.50686i	−0.400666	−	0.400666i	−0.878468	+	0.477801i	$0.841434\pi$
$564$		0			0
$565$	−1.09331			−0.0459957
$566$		0			0
$567$	−10.1193	−	6.21558i	−0.424970	−	0.261030i
$568$		0			0
$569$	−8.56472	+	8.56472i	−0.359052	+	0.359052i	−0.863463	−	0.504412i	$-0.831709\pi$
$569$	−8.56472	+	8.56472i	−0.359052	+	0.359052i	0.504412	+	0.863463i	$0.331709\pi$
$570$		0			0
$571$	10.7544	−	18.6271i	0.450057	−	0.779521i	−0.548332	−	0.836261i	$-0.684737\pi$
$571$	10.7544	−	18.6271i	0.450057	−	0.779521i	0.998389	+	0.0567394i	$0.0180704\pi$
$572$		0			0
$573$	−1.75707	−	14.0864i	−0.0734027	−	0.588466i
$574$		0			0
$575$	−0.674049	−	2.51559i	−0.0281098	−	0.104907i
$576$		0			0
$577$	2.86567	+	10.6948i	0.119300	+	0.445232i	0.999573	−	0.0292356i	$-0.00930732\pi$
$577$	2.86567	+	10.6948i	0.119300	+	0.445232i	−0.880273	+	0.474467i	$0.842641\pi$
$578$		0			0
$579$	−25.8267	+	3.22151i	−1.07332	+	0.133882i
$580$		0			0
$581$		−	17.5940i		−	0.729921i
$582$		0			0
$583$	1.24638	+	0.719600i	0.0516199	+	0.0298028i
$584$		0			0
$585$	−0.438656	−	0.123960i	−0.0181362	−	0.00512511i
$586$		0			0
$587$	1.34730	+	0.361008i	0.0556091	+	0.0149004i	0.286516	−	0.958075i	$-0.407503\pi$
$587$	1.34730	+	0.361008i	0.0556091	+	0.0149004i	−0.230907	+	0.972976i	$0.574169\pi$
$588$		0			0
$589$	22.6330	+	39.2015i	0.932576	+	1.61527i
$590$		0			0
$591$	−3.04486	−	7.49479i	−0.125249	−	0.308295i
$592$		0			0
$593$			18.2476i			0.749339i	0.927158	+	0.374670i	$0.122244\pi$
$593$			18.2476i			0.749339i	−0.927158	+	0.374670i	$0.877756\pi$
$594$		0			0
$595$	−0.437891	+	0.252816i	−0.0179518	+	0.0103645i
$596$		0			0
$597$	−4.28016	−	34.3138i	−0.175175	−	1.40437i
$598$		0			0
$599$	−15.0264	+	8.67547i	−0.613960	+	0.354470i	−0.774514	−	0.632557i	$-0.782005\pi$
$599$	−15.0264	+	8.67547i	−0.613960	+	0.354470i	0.160554	+	0.987027i	$0.448672\pi$
$600$		0			0
$601$	17.3013	−	29.9667i	0.705734	−	1.22237i	−0.260692	−	0.965422i	$-0.583951\pi$
$601$	17.3013	−	29.9667i	0.705734	−	1.22237i	0.966426	−	0.256946i	$-0.0827161\pi$
$602$		0			0
$603$	10.9558	+	11.2581i	0.446154	+	0.458466i
$604$		0			0
$605$	−3.87537	+	14.4631i	−0.157556	+	0.588007i
$606$		0			0
$607$	10.6773	−	2.86098i	0.433380	−	0.116124i	−0.0355325	−	0.999369i	$-0.511313\pi$
$607$	10.6773	−	2.86098i	0.433380	−	0.116124i	0.468912	+	0.883245i	$0.344646\pi$
$608$		0			0
$609$	−3.67897	−	4.86268i	−0.149079	−	0.197046i
$610$		0			0
$611$	−0.176550	+	0.658894i	−0.00714246	+	0.0266560i
$612$		0			0
$613$	−7.63602	−	4.40866i	−0.308416	−	0.178064i	0.337801	−	0.941217i	$-0.390317\pi$
$613$	−7.63602	−	4.40866i	−0.308416	−	0.178064i	−0.646217	+	0.763153i	$0.723650\pi$
$614$		0			0
$615$	1.66705	+	0.703844i	0.0672220	+	0.0283817i
$616$		0			0
$617$	−14.4287	+	24.9912i	−0.580876	+	1.00611i	0.414500	+	0.910049i	$0.363957\pi$
$617$	−14.4287	+	24.9912i	−0.580876	+	1.00611i	−0.995376	+	0.0960575i	$0.969377\pi$
$618$		0			0
$619$		−	6.28062i		−	0.252439i	−0.992002	−	0.126220i	$-0.959716\pi$
$619$		−	6.28062i		−	0.252439i	0.992002	−	0.126220i	$-0.0402844\pi$
$620$		0			0
$621$	4.06078	−	1.58571i	0.162953	−	0.0636323i
$622$		0			0
$623$	−15.3940	+	15.3940i	−0.616749	+	0.616749i
$624$		0			0
$625$	0.0785562	+	0.136063i	0.00314225	+	0.00544253i
$626$		0			0
$627$	−3.05157	−	4.03342i	−0.121868	−	0.161079i
$628$		0			0
$629$	1.69133	−	0.0720378i	0.0674378	−	0.00287234i
$630$		0			0
$631$	3.56689	−	0.955745i	0.141996	−	0.0380476i	−0.187121	−	0.982337i	$-0.559916\pi$
$631$	3.56689	−	0.955745i	0.141996	−	0.0380476i	0.329117	+	0.944289i	$0.393249\pi$
$632$		0			0
$633$	29.9304	+	23.2917i	1.18963	+	0.925762i
$634$		0			0
$635$	1.06701	+	1.06701i	0.0423430	+	0.0423430i
$636$		0			0
$637$	−0.410361	+	0.410361i	−0.0162591	+	0.0162591i
$638$		0			0
$639$	12.2905	+	12.6297i	0.486206	+	0.499623i
$640$		0			0
$641$	−30.5896	−	17.6609i	−1.20822	−	0.697565i	−0.245848	−	0.969308i	$-0.579066\pi$
$641$	−30.5896	−	17.6609i	−1.20822	−	0.697565i	−0.962370	+	0.271744i	$0.912400\pi$
$642$		0			0
$643$	−21.1770	−	21.1770i	−0.835141	−	0.835141i	0.153074	−	0.988215i	$-0.451083\pi$
$643$	−21.1770	−	21.1770i	−0.835141	−	0.835141i	−0.988215	+	0.153074i	$0.951083\pi$
$644$		0			0
$645$	1.92952	−	13.9234i	0.0759749	−	0.548232i
$646$		0			0
$647$	38.5461	+	10.3284i	1.51540	+	0.406051i	0.918226	−	0.396057i	$-0.129622\pi$
$647$	38.5461	+	10.3284i	1.51540	+	0.406051i	0.597178	+	0.802109i	$0.296289\pi$
$648$		0			0
$649$	2.05581	−	0.550851i	0.0806974	−	0.0216228i
$650$		0			0
$651$	−9.99763	+	7.56392i	−0.391838	+	0.296453i
$652$		0			0
$653$	−14.5652	−	3.90274i	−0.569981	−	0.152726i	−0.0376934	−	0.999289i	$-0.512001\pi$
$653$	−14.5652	−	3.90274i	−0.569981	−	0.152726i	−0.532288	+	0.846563i	$0.678668\pi$
$654$		0			0
$655$	−3.43787			−0.134329
$656$		0			0
$657$	3.02056	−	0.765454i	0.117843	−	0.0298632i
$658$		0			0
$659$	−17.4986	−	30.3085i	−0.681649	−	1.18065i	−0.974477	−	0.224486i	$-0.927930\pi$
$659$	−17.4986	−	30.3085i	−0.681649	−	1.18065i	0.292828	−	0.956165i	$-0.405404\pi$
$660$		0			0
$661$	−5.18024	+	19.3329i	−0.201488	+	0.751963i	0.789003	+	0.614389i	$0.210597\pi$
$661$	−5.18024	+	19.3329i	−0.201488	+	0.751963i	−0.990491	+	0.137575i	$0.956069\pi$
$662$		0			0
$663$	0.0419812	+	0.0326696i	0.00163041	+	0.00126878i
$664$		0			0
$665$	14.9929			0.581401
$666$		0			0
$667$	2.23833			0.0866684
$668$		0			0
$669$	4.17895	+	3.25204i	0.161567	+	0.125731i
$670$		0			0
$671$	0.501774	−	1.87265i	0.0193708	−	0.0722928i
$672$		0			0
$673$	−14.6165	−	25.3164i	−0.563423	−	0.975877i	−0.997194	−	0.0748542i	$-0.976151\pi$
$673$	−14.6165	−	25.3164i	−0.563423	−	0.975877i	0.433772	−	0.901023i	$-0.357182\pi$
$674$		0			0
$675$	−12.9945	+	9.55601i	−0.500159	+	0.367811i
$676$		0			0
$677$	−40.0961			−1.54102			−0.770508	−	0.637430i	$-0.779998\pi$
$677$	−40.0961			−1.54102			−0.770508	+	0.637430i	$0.779998\pi$
$678$		0			0
$679$	−14.3809	−	3.85336i	−0.551890	−	0.147878i
$680$		0			0
$681$	−5.69456	+	4.30834i	−0.218216	+	0.165096i
$682$		0			0
$683$	35.4427	−	9.49685i	1.35618	−	0.363387i	0.493767	−	0.869595i	$-0.335620\pi$
$683$	35.4427	−	9.49685i	1.35618	−	0.363387i	0.862412	+	0.506208i	$0.168953\pi$
$684$		0			0
$685$	1.33037	+	0.356472i	0.0508309	+	0.0136201i
$686$		0			0
$687$	3.46563	−	25.0079i	0.132222	−	0.954110i
$688$		0			0
$689$	0.317376	+	0.317376i	0.0120911	+	0.0120911i
$690$		0			0
$691$	20.2063	+	11.6661i	0.768684	+	0.443800i	0.832405	−	0.554168i	$-0.186964\pi$
$691$	20.2063	+	11.6661i	0.768684	+	0.443800i	−0.0637212	+	0.997968i	$0.520297\pi$
$692$		0			0
$693$	1.00387	−	0.976911i	0.0381339	−	0.0371098i
$694$		0			0
$695$	−2.96478	+	2.96478i	−0.112460	+	0.112460i
$696$		0			0
$697$	−0.149321	−	0.149321i	−0.00565592	−	0.00565592i
$698$		0			0
$699$	−1.43110	−	1.11367i	−0.0541291	−	0.0421230i
$700$		0			0
$701$	47.2764	−	12.6677i	1.78561	−	0.478452i	0.794020	−	0.607892i	$-0.207985\pi$
$701$	47.2764	−	12.6677i	1.78561	−	0.478452i	0.991587	+	0.129440i	$0.0413180\pi$
$702$		0			0
$703$	−44.5001	−	23.2256i	−1.67835	−	0.875971i
$704$		0			0
$705$	−8.89419	−	11.7559i	−0.334975	−	0.442754i
$706$		0			0
$707$	−8.09221	−	14.0161i	−0.304339	−	0.527130i
$708$		0			0
$709$	−2.43280	+	2.43280i	−0.0913657	+	0.0913657i	−0.751312	−	0.659947i	$-0.770579\pi$
$709$	−2.43280	+	2.43280i	−0.0913657	+	0.0913657i	0.659947	+	0.751312i	$0.270579\pi$
$710$		0			0
$711$	−0.0199810	+	1.46806i	−0.000749348	+	0.0550564i
$712$		0			0
$713$		−	4.60198i		−	0.172345i
$714$		0			0
$715$	0.0268830	−	0.0465627i	0.00100537	−	0.00174135i
$716$		0			0
$717$	−30.4425	−	12.8531i	−1.13689	−	0.480007i
$718$		0			0
$719$	28.5477	+	16.4820i	1.06465	+	0.614676i	0.926715	−	0.375765i	$-0.122620\pi$
$719$	28.5477	+	16.4820i	1.06465	+	0.614676i	0.137935	+	0.990441i	$0.455953\pi$
$720$		0			0
$721$	3.65175	−	13.6285i	0.135998	−	0.507553i
$722$		0			0
$723$	−14.1997	−	18.7684i	−0.528092	−	0.698006i
$724$		0			0
$725$	−7.99968	+	2.14351i	−0.297101	+	0.0796079i
$726$		0			0
$727$	−11.8100	+	44.0754i	−0.438007	+	1.63467i	0.295758	+	0.955263i	$0.404428\pi$
$727$	−11.8100	+	44.0754i	−0.438007	+	1.63467i	−0.733765	+	0.679403i	$0.762239\pi$
$728$		0			0
$729$	−18.2967	−	19.8553i	−0.677655	−	0.735380i
$730$		0			0
$731$	−0.820182	+	1.42060i	−0.0303355	+	0.0525427i
$732$		0			0
$733$	−1.48991	+	0.860199i	−0.0550310	+	0.0317722i	−0.527263	−	0.849702i	$-0.676782\pi$
$733$	−1.48991	+	0.860199i	−0.0550310	+	0.0317722i	0.472232	+	0.881474i	$0.343448\pi$
$734$		0			0
$735$	−1.55233	−	12.4450i	−0.0572587	−	0.459040i
$736$		0			0
$737$	−1.60466	+	0.926448i	−0.0591082	+	0.0341262i
$738$		0			0
$739$		−	33.1098i		−	1.21796i	−0.793185	−	0.608981i	$-0.791579\pi$
$739$		−	33.1098i		−	1.21796i	0.793185	−	0.608981i	$-0.208421\pi$
$740$		0			0
$741$	−0.593688	−	1.46134i	−0.0218097	−	0.0536836i
$742$		0			0
$743$	−14.5143	−	25.1395i	−0.532477	−	0.922278i	−0.999281	−	0.0379168i	$-0.987928\pi$
$743$	−14.5143	−	25.1395i	−0.532477	−	0.922278i	0.466804	−	0.884361i	$-0.345406\pi$
$744$		0			0
$745$	−19.9332	−	5.34108i	−0.730295	−	0.195682i
$746$		0			0
$747$	10.8778	−	38.4932i	0.397998	−	1.40839i
$748$		0			0
$749$	12.8187	+	7.40087i	0.468385	+	0.270422i
$750$		0			0
$751$			12.5828i			0.459151i	0.973291	+	0.229576i	$0.0737339\pi$
$751$			12.5828i			0.459151i	−0.973291	+	0.229576i	$0.926266\pi$
$752$		0			0
$753$	−31.3072	+	3.90512i	−1.14090	+	0.142311i
$754$		0			0
$755$	−0.363618	−	1.35704i	−0.0132334	−	0.0493878i
$756$		0			0
$757$	−9.30044	−	34.7097i	−0.338030	−	1.26155i	−0.900546	−	0.434760i	$-0.856833\pi$
$757$	−9.30044	−	34.7097i	−0.338030	−	1.26155i	0.562516	−	0.826786i	$-0.309833\pi$
$758$		0			0
$759$	0.0636453	+	0.510241i	0.00231018	+	0.0185206i
$760$		0			0
$761$	−0.843001	+	1.46012i	−0.0305588	+	0.0529293i	−0.880900	−	0.473302i	$-0.843062\pi$
$761$	−0.843001	+	1.46012i	−0.0305588	+	0.0529293i	0.850342	+	0.526231i	$0.176395\pi$
$762$		0			0
$763$	1.24906	−	1.24906i	0.0452190	−	0.0452190i
$764$		0			0
$765$	−1.11435	+	0.282393i	−0.0402895	+	0.0102099i
$766$		0			0
$767$	0.663752			0.0239667
$768$		0			0
$769$	−21.9973	−	21.9973i	−0.793243	−	0.793243i	0.188777	−	0.982020i	$-0.439548\pi$
$769$	−21.9973	−	21.9973i	−0.793243	−	0.793243i	−0.982020	+	0.188777i	$0.939548\pi$
$770$		0			0
$771$	40.8127	+	17.2315i	1.46984	+	0.620577i
$772$		0			0
$773$	27.8188	−	16.0612i	1.00057	−	0.577682i	0.0921561	−	0.995745i	$-0.470624\pi$
$773$	27.8188	−	16.0612i	1.00057	−	0.577682i	0.908418	+	0.418063i	$0.137291\pi$
$774$		0			0
$775$	4.40703	+	16.4473i	0.158305	+	0.590803i
$776$		0			0
$777$	4.85747	−	13.0259i	0.174261	−	0.467300i
$778$		0			0
$779$	1.62062	+	6.04825i	0.0580649	+	0.216701i
$780$		0			0
$781$	−1.80015	+	1.03932i	−0.0644144	+	0.0371897i
$782$		0			0
$783$	−5.04263	−	12.9135i	−0.180209	−	0.461490i
$784$		0			0
$785$	−2.87614	−	2.87614i	−0.102654	−	0.102654i
$786$		0			0
$787$	12.4988			0.445533			0.222766	−	0.974872i	$-0.428491\pi$
$787$	12.4988			0.445533			0.222766	+	0.974872i	$0.428491\pi$
$788$		0			0
$789$	−5.35965	+	38.6750i	−0.190809	+	1.37687i
$790$		0			0
$791$	0.740882	−	0.740882i	0.0263427	−	0.0263427i
$792$		0			0
$793$	0.302308	−	0.523614i	0.0107353	−	0.0185941i
$794$		0			0
$795$	−9.62504	+	1.20059i	−0.341365	+	0.0425804i
$796$		0			0
$797$	8.92787	+	33.3193i	0.316241	+	1.18023i	0.922828	+	0.385211i	$0.125871\pi$
$797$	8.92787	+	33.3193i	0.316241	+	1.18023i	−0.606587	+	0.795017i	$0.707462\pi$
$798$		0			0
$799$	0.445245	+	1.66168i	0.0157516	+	0.0587859i
$800$		0			0
$801$	−43.1977	+	24.1624i	−1.52631	+	0.853735i
$802$		0			0
$803$			0.367540i			0.0129702i
$804$		0			0
$805$	−1.32005	−	0.762130i	−0.0465256	−	0.0268616i
$806$		0			0
$807$	8.52269	−	10.9519i	0.300013	−	0.385524i
$808$		0			0
$809$	21.6388	+	5.79811i	0.760781	+	0.203851i	0.618295	−	0.785946i	$-0.287824\pi$
$809$	21.6388	+	5.79811i	0.760781	+	0.203851i	0.142486	+	0.989797i	$0.454490\pi$
$810$		0			0
$811$	15.7540	+	27.2867i	0.553196	+	0.958164i	0.998041	+	0.0625566i	$0.0199254\pi$
$811$	15.7540	+	27.2867i	0.553196	+	0.958164i	−0.444845	+	0.895608i	$0.646741\pi$
$812$		0			0
$813$	−3.87406	+	1.57389i	−0.135869	+	0.0551987i
$814$		0			0
$815$		−	8.25277i		−	0.289082i
$816$		0			0
$817$	42.1232	−	24.3199i	1.47371	−	0.850844i
$818$		0			0
$819$	0.381258	−	0.213255i	0.0133222	−	0.00745172i
$820$		0			0
$821$	−31.9875	+	18.4680i	−1.11637	+	0.644537i	−0.940472	−	0.339872i	$-0.889616\pi$
$821$	−31.9875	+	18.4680i	−1.11637	+	0.644537i	−0.175898	+	0.984408i	$0.556283\pi$
$822$		0			0
$823$	−20.7728	+	35.9796i	−0.724095	+	1.25417i	0.235251	+	0.971935i	$0.424409\pi$
$823$	−20.7728	+	35.9796i	−0.724095	+	1.25417i	−0.959345	+	0.282234i	$0.908924\pi$
$824$		0			0
$825$	−0.716092	−	1.76263i	−0.0249311	−	0.0613668i
$826$		0			0
$827$	7.59493	−	28.3447i	0.264102	−	0.985641i	−0.698696	−	0.715418i	$-0.746236\pi$
$827$	7.59493	−	28.3447i	0.264102	−	0.985641i	0.962798	−	0.270222i	$-0.0870972\pi$
$828$		0			0
$829$	13.9771	−	3.74516i	0.485446	−	0.130075i	−0.00779119	−	0.999970i	$-0.502480\pi$
$829$	13.9771	−	3.74516i	0.485446	−	0.130075i	0.493237	+	0.869895i	$0.335813\pi$
$830$		0			0
$831$	6.00366	−	4.54220i	0.208265	−	0.157567i
$832$		0			0
$833$	−0.378798	+	1.41369i	−0.0131246	+	0.0489816i
$834$		0			0
$835$	−25.6863	−	14.8300i	−0.888911	−	0.513213i
$836$		0			0
$837$	−26.5500	+	10.3676i	−0.917701	+	0.358356i
$838$		0			0
$839$	7.80837	−	13.5245i	0.269575	−	0.466918i	−0.699177	−	0.714948i	$-0.746450\pi$
$839$	7.80837	−	13.5245i	0.269575	−	0.466918i	0.968752	+	0.248031i	$0.0797835\pi$
$840$		0			0
$841$			21.8820i			0.754552i
$842$		0			0
$843$	−11.2118	−	4.73371i	−0.386154	−	0.163038i
$844$		0			0
$845$	−12.6449	+	12.6449i	−0.434999	+	0.434999i
$846$		0			0
$847$	−7.17479	−	12.4271i	−0.246529	−	0.427000i
$848$		0			0
$849$	24.4488	−	18.4972i	0.839079	−	0.634823i
$850$		0			0
$851$	2.73738	+	4.30695i	0.0938360	+	0.147640i
$852$		0			0
$853$	6.26475	−	1.67863i	0.214501	−	0.0574753i	−0.149968	−	0.988691i	$-0.547917\pi$
$853$	6.26475	−	1.67863i	0.214501	−	0.0574753i	0.364469	+	0.931215i	$0.381250\pi$
$854$		0			0
$855$	32.8024	+	9.26965i	1.12182	+	0.317015i
$856$		0			0
$857$	25.1123	+	25.1123i	0.857820	+	0.857820i	0.991081	−	0.133261i	$-0.0425447\pi$
$857$	25.1123	+	25.1123i	0.857820	+	0.857820i	−0.133261	+	0.991081i	$0.542545\pi$
$858$		0			0
$859$	−15.0815	+	15.0815i	−0.514573	+	0.514573i	−0.915924	−	0.401351i	$-0.868541\pi$
$859$	−15.0815	+	15.0815i	−0.514573	+	0.514573i	0.401351	+	0.915924i	$0.368541\pi$
$860$		0			0
$861$	−1.60665	+	0.652722i	−0.0547544	+	0.0222447i
$862$		0			0
$863$	−19.6968	−	11.3720i	−0.670488	−	0.387106i	0.125773	−	0.992059i	$-0.459859\pi$
$863$	−19.6968	−	11.3720i	−0.670488	−	0.387106i	−0.796262	+	0.604953i	$0.793192\pi$
$864$		0			0
$865$	−11.9911	−	11.9911i	−0.407709	−	0.407709i
$866$		0			0
$867$	−29.0332	−	4.02347i	−0.986021	−	0.136644i
$868$		0			0
$869$	−0.167274	−	0.0448208i	−0.00567437	−	0.00152044i
$870$		0			0
$871$	−0.558165	+	0.149560i	−0.0189127	+	0.00506765i
$872$		0			0
$873$	−29.0811	−	17.3219i	−0.984246	−	0.586258i
$874$		0			0
$875$	14.2222	+	3.81084i	0.480800	+	0.128830i
$876$		0			0
$877$	−16.7425			−0.565355			−0.282677	−	0.959215i	$-0.591223\pi$
$877$	−16.7425			−0.565355			−0.282677	+	0.959215i	$0.591223\pi$
$878$		0			0
$879$	−8.96347	−	1.24217i	−0.302330	−	0.0418974i
$880$		0			0
$881$	19.1733	+	33.2092i	0.645966	+	1.11885i	0.984077	+	0.177740i	$0.0568786\pi$
$881$	19.1733	+	33.2092i	0.645966	+	1.11885i	−0.338111	+	0.941106i	$0.609788\pi$
$882$		0			0
$883$	−2.82950	+	10.5598i	−0.0952202	+	0.355367i	−0.997053	−	0.0767190i	$-0.975556\pi$
$883$	−2.82950	+	10.5598i	−0.0952202	+	0.355367i	0.901833	+	0.432086i	$0.142222\pi$
$884$		0			0
$885$	−8.80935	+	11.3202i	−0.296123	+	0.380525i
$886$		0			0
$887$	8.12593			0.272842			0.136421	−	0.990651i	$-0.456440\pi$
$887$	8.12593			0.272842			0.136421	+	0.990651i	$0.456440\pi$
$888$		0			0
$889$	−1.44613			−0.0485015
$890$		0			0
$891$	2.80032	−	1.51668i	0.0938143	−	0.0508108i
$892$		0			0
$893$	13.2023	−	49.2717i	0.441799	−	1.64882i
$894$		0			0
$895$	−3.11914	−	5.40251i	−0.104261	−	0.180586i
$896$		0			0
$897$	−0.0220126	+	0.158842i	−0.000734978	+	0.00530358i
$898$		0			0
$899$	−14.6345			−0.488088
$900$		0			0
$901$	1.09336	+	0.292965i	0.0364252	+	0.00976009i
$902$		0			0
$903$	8.12767	+	10.7428i	0.270472	+	0.357497i
$904$		0			0
$905$	−14.9911	+	4.01685i	−0.498321	+	0.133525i
$906$		0			0
$907$	0.865810	+	0.231993i	0.0287488	+	0.00770321i	0.273165	−	0.961967i	$-0.411930\pi$
$907$	0.865810	+	0.231993i	0.0287488	+	0.00770321i	−0.244416	+	0.969670i	$0.578596\pi$
$908$		0			0
$909$	−9.03890	−	35.6685i	−0.299802	−	1.18305i
$910$		0			0
$911$	−27.9706	−	27.9706i	−0.926708	−	0.926708i	0.0707840	−	0.997492i	$-0.477450\pi$
$911$	−27.9706	−	27.9706i	−0.926708	−	0.926708i	−0.997492	+	0.0707840i	$0.977450\pi$
$912$		0			0
$913$	4.08600	+	2.35905i	0.135227	+	0.0780733i
$914$		0			0
$915$	4.91793	+	12.1053i	0.162582	+	0.400188i
$916$		0			0
$917$	2.32968	−	2.32968i	0.0769329	−	0.0769329i
$918$		0			0
$919$	5.88949	+	5.88949i	0.194276	+	0.194276i	0.797541	−	0.603265i	$-0.206134\pi$
$919$	5.88949	+	5.88949i	0.194276	+	0.194276i	−0.603265	+	0.797541i	$0.706134\pi$
$920$		0			0
$921$	15.9656	−	20.5162i	0.526084	−	0.676030i
$922$		0			0
$923$	−0.626166	+	0.167781i	−0.0206105	+	0.00552257i
$924$		0			0
$925$	−13.9078	−	12.7714i	−0.457284	−	0.419922i
$926$		0			0
$927$	16.4156	−	27.5596i	0.539160	−	0.905175i
$928$		0			0
$929$	−16.6994	−	28.9243i	−0.547891	−	0.948975i	−0.998419	−	0.0562128i	$-0.982097\pi$
$929$	−16.6994	−	28.9243i	−0.547891	−	0.948975i	0.450528	−	0.892762i	$-0.351236\pi$
$930$		0			0
$931$	30.6865	−	30.6865i	1.00571	−	1.00571i
$932$		0			0
$933$	−20.0041	+	47.3796i	−0.654904	+	1.55114i
$934$		0			0
$935$		−	0.135594i		−	0.00443438i
$936$		0			0
$937$	−12.9027	+	22.3481i	−0.421512	+	0.730080i	−0.996088	−	0.0883712i	$-0.971834\pi$
$937$	−12.9027	+	22.3481i	−0.421512	+	0.730080i	0.574576	+	0.818452i	$0.305167\pi$
$938$		0			0
$939$	5.52546	−	13.0870i	0.180317	−	0.427079i
$940$		0			0
$941$	26.3820	+	15.2317i	0.860029	+	0.496538i	0.864022	−	0.503454i	$-0.167938\pi$
$941$	26.3820	+	15.2317i	0.860029	+	0.496538i	−0.00399314	+	0.999992i	$0.501271\pi$
$942$		0			0
$943$	0.164761	−	0.614897i	0.00536536	−	0.0200238i
$944$		0			0
$945$	−1.42304	+	9.33265i	−0.0462915	+	0.303591i
$946$		0			0
$947$	14.0237	−	3.75764i	0.455709	−	0.122107i	−0.0236604	−	0.999720i	$-0.507532\pi$
$947$	14.0237	−	3.75764i	0.455709	−	0.122107i	0.479369	+	0.877613i	$0.340865\pi$
$948$		0			0
$949$	−0.0296666	+	0.110717i	−0.000963020	+	0.00359404i
$950$		0			0
$951$	4.84314	−	1.96759i	0.157049	−	0.0638034i
$952$		0			0
$953$	18.6963	−	32.3830i	0.605634	−	1.04899i	−0.386317	−	0.922366i	$-0.626253\pi$
$953$	18.6963	−	32.3830i	0.605634	−	1.04899i	0.991951	−	0.126623i	$-0.0404137\pi$
$954$		0			0
$955$	−9.77275	+	5.64230i	−0.316239	+	0.182581i
$956$		0			0
$957$	1.62259	−	0.202395i	0.0524509	−	0.00654250i
$958$		0			0
$959$	−1.14309	+	0.659966i	−0.0369125	+	0.0213114i
$960$		0			0
$961$		−	0.911590i		−	0.0294061i
$962$		0			0
$963$	23.4698	+	24.1175i	0.756303	+	0.777174i
$964$		0			0
$965$	10.3449	+	17.9179i	0.333014	+	0.576798i
$966$		0			0
$967$	−52.6273	−	14.1015i	−1.69238	−	0.453472i	−0.721378	−	0.692541i	$-0.756491\pi$
$967$	−52.6273	−	14.1015i	−1.69238	−	0.453472i	−0.971003	+	0.239069i	$0.923158\pi$
$968$		0			0
$969$	−3.13933	−	2.44301i	−0.100850	−	0.0784809i
$970$		0			0
$971$	40.9589	+	23.6476i	1.31443	+	0.758889i	0.982827	−	0.184529i	$-0.0590759\pi$
$971$	40.9589	+	23.6476i	1.31443	+	0.758889i	0.331607	+	0.943418i	$0.392409\pi$
$972$		0			0
$973$		−	4.01818i		−	0.128817i
$974$		0			0
$975$	−0.0734412	−	0.588774i	−0.00235200	−	0.0188559i
$976$		0			0
$977$	−0.203767	−	0.760470i	−0.00651909	−	0.0243296i	0.962590	−	0.270963i	$-0.0873422\pi$
$977$	−0.203767	−	0.760470i	−0.00651909	−	0.0243296i	−0.969109	+	0.246634i	$0.920676\pi$
$978$		0			0
$979$	−1.51101	−	5.63917i	−0.0482921	−	0.180229i
$980$		0			0
$981$	3.50502	−	1.96052i	0.111907	−	0.0625944i
$982$		0			0
$983$	7.03602	−	12.1868i	0.224414	−	0.388697i	−0.731729	−	0.681595i	$-0.761286\pi$
$983$	7.03602	−	12.1868i	0.224414	−	0.388697i	0.956144	+	0.292898i	$0.0946198\pi$
$984$		0			0
$985$	−4.54728	+	4.54728i	−0.144889	+	0.144889i
$986$		0			0
$987$	13.9936	+	1.93926i	0.445422	+	0.0617273i
$988$		0			0
$989$	−4.94497			−0.157241
$990$		0			0
$991$	11.2483	+	11.2483i	0.357315	+	0.357315i	0.862822	−	0.505507i	$-0.168695\pi$
$991$	11.2483	+	11.2483i	0.357315	+	0.357315i	−0.505507	+	0.862822i	$0.668695\pi$
$992$		0			0
$993$	−13.9335	+	33.0015i	−0.442166	+	1.04727i
$994$		0			0
$995$	−23.8060	+	13.7444i	−0.754702	+	0.435727i
$996$		0			0
$997$	−14.4003	−	53.7428i	−0.456063	−	1.70205i	−0.684943	−	0.728597i	$-0.740173\pi$
$997$	−14.4003	−	53.7428i	−0.456063	−	1.70205i	0.228880	−	0.973455i	$-0.426494\pi$
$998$		0			0
$999$	18.6809	−	25.4955i	0.591039	−	0.806643i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	888.2.br.a.569.32	yes	152
3.2	odd	2	inner	888.2.br.a.569.19	✓	152
37.8	odd	12	inner	888.2.br.a.785.19	yes	152
111.8	even	12	inner	888.2.br.a.785.32	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
888.2.br.a.569.19	✓	152	3.2	odd	2	inner
888.2.br.a.569.32	yes	152	1.1	even	1	trivial
888.2.br.a.785.19	yes	152	37.8	odd	12	inner
888.2.br.a.785.32	yes	152	111.8	even	12	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 888 = 2^{3} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	888.br (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36692 + 1.06373i) q^{3} +(0.356362 - 1.32996i) q^{5} +(0.659764 + 1.14274i) q^{7} +(0.736949 + 2.90808i) q^{9} -0.353852 q^{11} +(-0.106594 - 0.0285618i) q^{13} +(1.90184 - 1.43888i) q^{15} +(-0.268822 + 0.0720307i) q^{17} +(7.97106 + 2.13584i) q^{19} +(-0.313728 + 2.26385i) q^{21} +(-0.593239 - 0.593239i) q^{23} +(2.68832 + 1.55210i) q^{25} +(-2.08606 + 4.75903i) q^{27} +(-1.88653 + 1.88653i) q^{29} +(3.87869 + 3.87869i) q^{31} +(-0.483688 - 0.376404i) q^{33} +(1.75492 - 0.470230i) q^{35} +(-5.93717 - 1.32288i) q^{37} +(-0.115324 - 0.152430i) q^{39} +(0.379388 + 0.657119i) q^{41} +(4.16777 - 4.16777i) q^{43} +(4.13025 + 0.0562150i) q^{45} -6.18133i q^{47} +(2.62942 - 4.55430i) q^{49} +(-0.444080 - 0.187494i) q^{51} +(-3.52233 - 2.03362i) q^{53} +(-0.126100 + 0.470610i) q^{55} +(8.62385 + 11.3986i) q^{57} +(-5.80978 + 1.55673i) q^{59} +(-1.41803 + 5.29217i) q^{61} +(-2.83697 + 2.76079i) q^{63} +(-0.0759724 + 0.131588i) q^{65} +(4.53482 - 2.61818i) q^{67} +(-0.179864 - 1.44196i) q^{69} +(5.08729 - 2.93715i) q^{71} -1.03868i q^{73} +(2.02370 + 4.98125i) q^{75} +(-0.233459 - 0.404363i) q^{77} +(0.472722 + 0.126665i) q^{79} +(-7.91381 + 4.28620i) q^{81} +(-11.5472 - 6.66677i) q^{83} +0.383192i q^{85} +(-4.58550 + 0.571976i) q^{87} +(4.27017 + 15.9365i) q^{89} +(-0.0376881 - 0.140654i) q^{91} +(1.17598 + 9.42774i) q^{93} +(5.68117 - 9.84008i) q^{95} +(-7.97830 + 7.97830i) q^{97} +(-0.260771 - 1.02903i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 4 q^{13} - 12 q^{15} + 4 q^{19} - 44 q^{31} - 12 q^{39} + 28 q^{43} + 20 q^{45} - 80 q^{49} - 12 q^{51} - 8 q^{55} - 40 q^{57} - 28 q^{61} + 48 q^{63} + 56 q^{69} + 64 q^{75} + 20 q^{79} + 16 q^{81}+ \cdots - 20 q^{97}+O(q^{100}) \) 152 * q + 4 * q^13 - 12 * q^15 + 4 * q^19 - 44 * q^31 - 12 * q^39 + 28 * q^43 + 20 * q^45 - 80 * q^49 - 12 * q^51 - 8 * q^55 - 40 * q^57 - 28 * q^61 + 48 * q^63 + 56 * q^69 + 64 * q^75 + 20 * q^79 + 16 * q^81 + 56 * q^87 + 52 * q^91 + 40 * q^93 - 20 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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