LMFDB - Embedded newform 891.2.u.c.755.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(107,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([5, 9]))

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

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

chi := DirichletCharacter("891.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.u (of order $30$, degree $8$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			755.3
Character	$\chi$	$=$	891.755
Dual form			891.2.u.c.701.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.231744 - 0.103179i) q^{2} +(-1.29520 + 1.43847i) q^{4} +(-1.18837 + 2.66913i) q^{5} +(-0.565298 + 2.65952i) q^{7} +(-0.308515 + 0.949513i) q^{8} +0.741170i q^{10} +(-3.00358 + 1.40659i) q^{11} +(2.84032 + 0.298529i) q^{13} +(0.143402 + 0.674654i) q^{14} +(-0.378188 - 3.59821i) q^{16} +(3.60998 - 2.62280i) q^{17} +(-1.81761 - 0.590579i) q^{19} +(-2.30027 - 5.16650i) q^{20} +(-0.550930 + 0.635876i) q^{22} +(-0.706997 + 0.408185i) q^{23} +(-2.36637 - 2.62812i) q^{25} +(0.689029 - 0.223879i) q^{26} +(-3.09345 - 4.25777i) q^{28} +(-9.33798 - 1.98485i) q^{29} +(0.625712 - 5.95326i) q^{31} +(-1.45728 - 2.52408i) q^{32} +(0.565973 - 0.980294i) q^{34} +(-6.42681 - 4.66935i) q^{35} +(1.83750 + 5.65524i) q^{37} +(-0.482157 + 0.0506767i) q^{38} +(-2.16774 - 1.95184i) q^{40} +(-8.24905 + 1.75339i) q^{41} +(10.2852 + 5.93817i) q^{43} +(1.86690 - 6.14238i) q^{44} +(-0.121726 + 0.167542i) q^{46} +(5.73571 - 5.16446i) q^{47} +(-0.358652 - 0.159682i) q^{49} +(-0.819560 - 0.364891i) q^{50} +(-4.10821 + 3.69905i) q^{52} +(-6.14564 + 8.45874i) q^{53} +(-0.185009 - 9.68851i) q^{55} +(-2.35084 - 1.35726i) q^{56} +(-2.36882 + 0.503507i) q^{58} +(-0.0693351 - 0.0624296i) q^{59} +(-2.13230 + 0.224114i) q^{61} +(-0.469246 - 1.44419i) q^{62} +(5.25595 + 3.81867i) q^{64} +(-4.17217 + 7.22641i) q^{65} +(0.703892 + 1.21918i) q^{67} +(-0.902835 + 8.58990i) q^{68} +(-1.97115 - 0.418982i) q^{70} +(-2.12141 - 2.91987i) q^{71} +(-1.67338 + 0.543714i) q^{73} +(1.00933 + 1.12098i) q^{74} +(3.20371 - 1.84966i) q^{76} +(-2.04294 - 8.78322i) q^{77} +(-2.90121 - 6.51621i) q^{79} +(10.0535 + 3.26659i) q^{80} +(-1.73075 + 1.25747i) q^{82} +(-0.818907 - 7.79138i) q^{83} +(2.71060 + 12.7524i) q^{85} +(2.99623 + 0.314916i) q^{86} +(-0.408929 - 3.28589i) q^{88} +2.06830i q^{89} +(-2.39957 + 7.38512i) q^{91} +(0.328543 - 1.54567i) q^{92} +(0.796353 - 1.78864i) q^{94} +(3.73634 - 4.14962i) q^{95} +(1.52602 - 0.679428i) q^{97} -0.0995913 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{4} + 20 q^{16} + 48 q^{22} + 32 q^{25} + 80 q^{28} - 16 q^{31} - 40 q^{34} - 24 q^{37} - 60 q^{40} - 80 q^{46} + 24 q^{49} + 40 q^{52} + 32 q^{55} - 12 q^{58} + 72 q^{64} - 96 q^{67} - 76 q^{70}+ \cdots - 60 q^{97}+O(q^{100}) $ 32 * q + 4 * q^4 + 20 * q^16 + 48 * q^22 + 32 * q^25 + 80 * q^28 - 16 * q^31 - 40 * q^34 - 24 * q^37 - 60 * q^40 - 80 * q^46 + 24 * q^49 + 40 * q^52 + 32 * q^55 - 12 * q^58 + 72 * q^64 - 96 * q^67 - 76 * q^70 - 40 * q^73 - 24 * q^82 + 100 * q^85 + 12 * q^88 - 144 * q^91 + 80 * q^94 - 60 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.231744	−	0.103179i	0.163868	−	0.0729586i	−0.323164	−	0.946343i	$-0.604746\pi$
$2$	0.231744	−	0.103179i	0.163868	−	0.0729586i	0.487031	+	0.873384i	$0.338080\pi$
$3$		0			0
$3$		0			0
$4$	−1.29520	+	1.43847i	−0.647601	+	0.719234i
$5$	−1.18837	+	2.66913i	−0.531457	+	1.19367i	0.425902	+	0.904769i	$0.359957\pi$
$5$	−1.18837	+	2.66913i	−0.531457	+	1.19367i	−0.957359	+	0.288902i	$0.906710\pi$
$6$		0			0
$7$	−0.565298	+	2.65952i	−0.213662	+	1.00520i	0.732314	+	0.680967i	$0.238440\pi$
$7$	−0.565298	+	2.65952i	−0.213662	+	1.00520i	−0.945976	+	0.324236i	$0.894893\pi$
$8$	−0.308515	+	0.949513i	−0.109077	+	0.335704i
$9$		0			0
$10$			0.741170i			0.234379i
$11$	−3.00358	+	1.40659i	−0.905613	+	0.424104i
$11$	−3.00358	+	1.40659i	−0.905613	+	0.424104i
$12$		0			0
$13$	2.84032	+	0.298529i	0.787762	+	0.0827972i	0.489862	−	0.871800i	$-0.337047\pi$
$13$	2.84032	+	0.298529i	0.787762	+	0.0827972i	0.297900	+	0.954597i	$0.403714\pi$
$14$	0.143402	+	0.674654i	0.0383258	+	0.180309i
$15$		0			0
$16$	−0.378188	−	3.59821i	−0.0945469	−	0.899554i
$17$	3.60998	−	2.62280i	0.875549	−	0.636124i	−0.0565211	−	0.998401i	$-0.518001\pi$
$17$	3.60998	−	2.62280i	0.875549	−	0.636124i	0.932070	+	0.362278i	$0.118001\pi$
$18$		0			0
$19$	−1.81761	−	0.590579i	−0.416989	−	0.135488i	0.0930053	−	0.995666i	$-0.470353\pi$
$19$	−1.81761	−	0.590579i	−0.416989	−	0.135488i	−0.509995	+	0.860178i	$0.670353\pi$
$20$	−2.30027	−	5.16650i	−0.514357	−	1.15526i
$21$		0			0
$22$	−0.550930	+	0.635876i	−0.117459	+	0.135569i
$23$	−0.706997	+	0.408185i	−0.147419	+	0.0851124i	−0.571895	−	0.820327i	$-0.693792\pi$
$23$	−0.706997	+	0.408185i	−0.147419	+	0.0851124i	0.424476	+	0.905439i	$0.360458\pi$
$24$		0			0
$25$	−2.36637	−	2.62812i	−0.473274	−	0.525624i
$26$	0.689029	−	0.223879i	0.135130	−	0.0439063i
$27$		0			0
$28$	−3.09345	−	4.25777i	−0.584608	−	0.804644i
$29$	−9.33798	−	1.98485i	−1.73402	−	0.368577i	−0.770755	−	0.637131i	$-0.780121\pi$
$29$	−9.33798	−	1.98485i	−1.73402	−	0.368577i	−0.963265	+	0.268554i	$0.913454\pi$
$30$		0			0
$31$	0.625712	−	5.95326i	0.112381	−	1.06924i	−0.782414	−	0.622759i	$-0.786012\pi$
$31$	0.625712	−	5.95326i	0.112381	−	1.06924i	0.894795	−	0.446477i	$-0.147322\pi$
$32$	−1.45728	−	2.52408i	−0.257613	−	0.446199i
$33$		0			0
$34$	0.565973	−	0.980294i	0.0970635	−	0.168119i
$35$	−6.42681	−	4.66935i	−1.08633	−	0.789265i
$36$		0			0
$37$	1.83750	+	5.65524i	0.302083	+	0.929717i	0.980750	+	0.195270i	$0.0625583\pi$
$37$	1.83750	+	5.65524i	0.302083	+	0.929717i	−0.678666	+	0.734447i	$0.737442\pi$
$38$	−0.482157	+	0.0506767i	−0.0782161	+	0.00822085i
$39$		0			0
$40$	−2.16774	−	1.95184i	−0.342750	−	0.308614i
$41$	−8.24905	+	1.75339i	−1.28829	+	0.273833i	−0.800607	−	0.599190i	$-0.795489\pi$
$41$	−8.24905	+	1.75339i	−1.28829	+	0.273833i	−0.487678	+	0.873023i	$0.662156\pi$
$42$		0			0
$43$	10.2852	+	5.93817i	1.56848	+	0.905562i	0.996347	+	0.0854008i	$0.0272171\pi$
$43$	10.2852	+	5.93817i	1.56848	+	0.905562i	0.572133	+	0.820161i	$0.306116\pi$
$44$	1.86690	−	6.14238i	0.281446	−	0.925998i
$45$		0			0
$46$	−0.121726	+	0.167542i	−0.0179475	+	0.0247027i
$47$	5.73571	−	5.16446i	0.836640	−	0.753314i	−0.134731	−	0.990882i	$-0.543017\pi$
$47$	5.73571	−	5.16446i	0.836640	−	0.753314i	0.971371	+	0.237569i	$0.0763504\pi$
$48$		0			0
$49$	−0.358652	−	0.159682i	−0.0512360	−	0.0228117i
$50$	−0.819560	−	0.364891i	−0.115903	−	0.0516034i
$51$		0			0
$52$	−4.10821	+	3.69905i	−0.569706	+	0.512966i
$53$	−6.14564	+	8.45874i	−0.844168	+	1.16190i	0.140950	+	0.990017i	$0.454984\pi$
$53$	−6.14564	+	8.45874i	−0.844168	+	1.16190i	−0.985118	+	0.171881i	$0.945016\pi$
$54$		0			0
$55$	−0.185009	−	9.68851i	−0.0249466	−	1.30640i
$56$	−2.35084	−	1.35726i	−0.314145	−	0.181371i
$57$		0			0
$58$	−2.36882	+	0.503507i	−0.311041	+	0.0661138i
$59$	−0.0693351	−	0.0624296i	−0.00902666	−	0.00812765i	0.664605	−	0.747195i	$-0.268600\pi$
$59$	−0.0693351	−	0.0624296i	−0.00902666	−	0.00812765i	−0.673632	+	0.739067i	$0.735267\pi$
$60$		0			0
$61$	−2.13230	+	0.224114i	−0.273013	+	0.0286949i	−0.240046	−	0.970762i	$-0.577162\pi$
$61$	−2.13230	+	0.224114i	−0.273013	+	0.0286949i	−0.0329676	+	0.999456i	$0.510496\pi$
$62$	−0.469246	−	1.44419i	−0.0595943	−	0.183412i
$63$		0			0
$64$	5.25595	+	3.81867i	0.656994	+	0.477334i
$65$	−4.17217	+	7.22641i	−0.517494	+	0.896326i
$66$		0			0
$67$	0.703892	+	1.21918i	0.0859941	+	0.148946i	0.905814	−	0.423675i	$-0.139260\pi$
$67$	0.703892	+	1.21918i	0.0859941	+	0.148946i	−0.819820	+	0.572621i	$0.805927\pi$
$68$	−0.902835	+	8.58990i	−0.109485	+	1.04168i
$69$		0			0
$70$	−1.97115	−	0.418982i	−0.235598	−	0.0500779i
$71$	−2.12141	−	2.91987i	−0.251765	−	0.346525i	0.664363	−	0.747410i	$-0.268703\pi$
$71$	−2.12141	−	2.91987i	−0.251765	−	0.346525i	−0.916128	+	0.400885i	$0.868703\pi$
$72$		0			0
$73$	−1.67338	+	0.543714i	−0.195854	+	0.0636369i	−0.405302	−	0.914183i	$-0.632833\pi$
$73$	−1.67338	+	0.543714i	−0.195854	+	0.0636369i	0.209447	+	0.977820i	$0.432833\pi$
$74$	1.00933	+	1.12098i	0.117333	+	0.130311i
$75$		0			0
$76$	3.20371	−	1.84966i	0.367490	−	0.212171i
$77$	−2.04294	−	8.78322i	−0.232815	−	1.00094i
$78$		0			0
$79$	−2.90121	−	6.51621i	−0.326411	−	0.733131i	0.673571	−	0.739123i	$-0.264760\pi$
$79$	−2.90121	−	6.51621i	−0.326411	−	0.733131i	−0.999982	+	0.00599118i	$0.998093\pi$
$80$	10.0535	+	3.26659i	1.12402	+	0.365216i
$81$		0			0
$82$	−1.73075	+	1.25747i	−0.191130	+	0.138864i
$83$	−0.818907	−	7.79138i	−0.0898867	−	0.855215i	−0.942844	−	0.333234i	$-0.891860\pi$
$83$	−0.818907	−	7.79138i	−0.0898867	−	0.855215i	0.852957	−	0.521981i	$-0.174807\pi$
$84$		0			0
$85$	2.71060	+	12.7524i	0.294006	+	1.38319i
$86$	2.99623	+	0.314916i	0.323092	+	0.0339583i
$87$		0			0
$88$	−0.408929	−	3.28589i	−0.0435919	−	0.350278i
$89$			2.06830i			0.219240i	0.993974	+	0.109620i	$0.0349633\pi$
$89$			2.06830i			0.219240i	−0.993974	+	0.109620i	$0.965037\pi$
$90$		0			0
$91$	−2.39957	+	7.38512i	−0.251543	+	0.774171i
$92$	0.328543	−	1.54567i	0.0342530	−	0.161148i
$93$		0			0
$94$	0.796353	−	1.78864i	0.0821375	−	0.184484i
$95$	3.73634	−	4.14962i	0.383340	−	0.425742i
$96$		0			0
$97$	1.52602	−	0.679428i	0.154944	−	0.0689855i	−0.327800	−	0.944747i	$-0.606307\pi$
$97$	1.52602	−	0.679428i	0.154944	−	0.0689855i	0.482743	+	0.875762i	$0.339640\pi$
$98$	−0.0995913			−0.0100602
$99$		0			0
$100$	6.84540			0.684540
$101$	−8.26546	+	3.68002i	−0.822444	+	0.366176i	−0.774421	−	0.632671i	$-0.781959\pi$
$101$	−8.26546	+	3.68002i	−0.822444	+	0.366176i	−0.0480230	+	0.998846i	$0.515292\pi$
$102$		0			0
$103$	−11.0895	+	12.3161i	−1.09268	+	1.21354i	−0.117276	+	0.993099i	$0.537416\pi$
$103$	−11.0895	+	12.3161i	−1.09268	+	1.21354i	−0.975400	+	0.220441i	$0.929250\pi$
$104$	−1.15974	+	2.60482i	−0.113722	+	0.255423i
$105$		0			0
$106$	−0.551449	+	2.59436i	−0.0535615	+	0.251987i
$107$	−2.19803	+	6.76484i	−0.212492	+	0.653982i	0.786830	+	0.617169i	$0.211721\pi$
$107$	−2.19803	+	6.76484i	−0.212492	+	0.653982i	−0.999322	+	0.0368130i	$0.988279\pi$
$108$		0			0
$109$			8.62045i			0.825690i	0.910801	+	0.412845i	$0.135465\pi$
$109$			8.62045i			0.825690i	−0.910801	+	0.412845i	$0.864535\pi$
$110$	−1.04253	−	2.22616i	−0.0994009	−	0.212256i
$111$		0			0
$112$	9.78330	+	1.02827i	0.924435	+	0.0971620i
$113$	2.37183	+	11.1586i	0.223123	+	1.04971i	0.936970	+	0.349410i	$0.113618\pi$
$113$	2.37183	+	11.1586i	0.223123	+	1.04971i	−0.713847	+	0.700302i	$0.753049\pi$
$114$		0			0
$115$	−0.249322	−	2.37214i	−0.0232494	−	0.221203i
$116$	14.9497	−	10.8616i	1.38805	−	1.00847i
$117$		0			0
$118$	−0.0225094	−	0.00731376i	−0.00207216	−	0.000673286i
$119$	4.93468	+	11.0835i	0.452361	+	1.01602i
$120$		0			0
$121$	7.04299	−	8.44964i	0.640271	−	0.768149i
$122$	−0.471024	+	0.271946i	−0.0426445	+	0.0246208i
$123$		0			0
$124$	7.75314	+	8.61073i	0.696253	+	0.773267i
$125$	−4.06670	+	1.32135i	−0.363737	+	0.118185i
$126$		0			0
$127$	−1.69463	−	2.33246i	−0.150374	−	0.206973i	0.727184	−	0.686443i	$-0.240829\pi$
$127$	−1.69463	−	2.33246i	−0.150374	−	0.206973i	−0.877558	+	0.479470i	$0.840829\pi$
$128$	7.31378	+	1.55459i	0.646453	+	0.137408i
$129$		0			0
$130$	−0.221261	+	2.10516i	−0.0194059	+	0.184635i
$131$	1.05078	+	1.82000i	0.0918067	+	0.159014i	0.908271	−	0.418382i	$-0.137402\pi$
$131$	1.05078	+	1.82000i	0.0918067	+	0.159014i	−0.816465	+	0.577395i	$0.804069\pi$
$132$		0			0
$133$	2.59815	−	4.50013i	0.225288	−	0.390210i
$134$	0.288916	+	0.209910i	0.0249586	+	0.0181335i
$135$		0			0
$136$	1.37665	+	4.23690i	0.118047	+	0.363311i
$137$	5.04624	−	0.530382i	0.431130	−	0.0453136i	0.113521	−	0.993536i	$-0.463787\pi$
$137$	5.04624	−	0.530382i	0.431130	−	0.0453136i	0.317608	+	0.948222i	$0.397120\pi$
$138$		0			0
$139$	−12.9931	−	11.6990i	−1.10206	−	0.992299i	−0.102063	−	0.994778i	$-0.532544\pi$
$139$	−12.9931	−	11.6990i	−1.10206	−	0.992299i	−0.999997	+	0.00247849i	$0.999211\pi$
$140$	15.0407	−	3.19701i	1.27117	−	0.270196i
$141$		0			0
$142$	−0.792894	−	0.457777i	−0.0665382	−	0.0384158i
$143$	−8.95103	+	3.09852i	−0.748523	+	0.259111i
$144$		0			0
$145$	16.3948	−	22.5656i	1.36152	−	1.87397i
$146$	−0.331696	+	0.298660i	−0.0274513	+	0.0247173i
$147$		0			0
$148$	−10.5148	−	4.68150i	−0.864313	−	0.384817i
$149$	5.16750	+	2.30072i	0.423338	+	0.188482i	0.607337	−	0.794444i	$-0.292238\pi$
$149$	5.16750	+	2.30072i	0.423338	+	0.188482i	−0.183999	+	0.982926i	$0.558904\pi$
$150$		0			0
$151$	−6.81871	+	6.13960i	−0.554899	+	0.499633i	−0.898197	−	0.439593i	$-0.855123\pi$
$151$	−6.81871	+	6.13960i	−0.554899	+	0.499633i	0.343298	+	0.939227i	$0.388456\pi$
$152$	1.12152	−	1.54365i	0.0909677	−	0.125206i
$153$		0			0
$154$	−1.37968	−	1.82467i	−0.111178	−	0.147036i
$155$	15.1464	+	8.74480i	1.21659	+	0.702399i
$156$		0			0
$157$	2.98699	−	0.634905i	0.238388	−	0.0506709i	−0.0871683	−	0.996194i	$-0.527782\pi$
$157$	2.98699	−	0.634905i	0.238388	−	0.0506709i	0.325556	+	0.945523i	$0.394448\pi$
$158$	−1.34467	−	1.21075i	−0.106977	−	0.0963221i
$159$		0			0
$160$	8.46890	−	0.890117i	0.669525	−	0.0703699i
$161$	−0.685911	−	2.11102i	−0.0540573	−	0.166371i
$162$		0			0
$163$	−6.39488	−	4.64615i	−0.500885	−	0.363914i	0.308470	−	0.951234i	$-0.400183\pi$
$163$	−6.39488	−	4.64615i	−0.500885	−	0.363914i	−0.809355	+	0.587320i	$0.800183\pi$
$164$	8.16199	−	14.1370i	0.637344	−	1.10391i
$165$		0			0
$166$	−0.993684	−	1.72111i	−0.0771248	−	0.133584i
$167$	1.71926	−	16.3577i	0.133041	−	1.26580i	−0.700626	−	0.713529i	$-0.747096\pi$
$167$	1.71926	−	16.3577i	0.133041	−	1.26580i	0.833667	−	0.552268i	$-0.186237\pi$
$168$		0			0
$169$	−4.73763	−	1.00701i	−0.364433	−	0.0774627i
$170$	1.94394	+	2.67561i	0.149094	+	0.205210i
$171$		0			0
$172$	−21.8633	+	7.10381i	−1.66706	+	0.541660i
$173$	10.3865	+	11.5354i	0.789673	+	0.877020i	0.994814	−	0.101712i	$-0.0324321\pi$
$173$	10.3865	+	11.5354i	0.789673	+	0.877020i	−0.205141	+	0.978732i	$0.565765\pi$
$174$		0			0
$175$	8.32724	−	4.80773i	0.629480	−	0.363431i
$176$	6.19714	+	10.2756i	0.467127	+	0.774550i
$177$		0			0
$178$	0.213405	+	0.479317i	0.0159954	+	0.0359263i
$179$	4.93538	+	1.60360i	0.368888	+	0.119859i	0.487594	−	0.873071i	$-0.337875\pi$
$179$	4.93538	+	1.60360i	0.368888	+	0.119859i	−0.118706	+	0.992929i	$0.537875\pi$
$180$		0			0
$181$	−4.29773	+	3.12248i	−0.319448	+	0.232092i	−0.735940	−	0.677047i	$-0.763259\pi$
$181$	−4.29773	+	3.12248i	−0.319448	+	0.232092i	0.416492	+	0.909139i	$0.363259\pi$
$182$	0.205904	+	1.95904i	0.0152626	+	0.145214i
$183$		0			0
$184$	−0.169457	−	0.797234i	−0.0124926	−	0.0587729i
$185$	−17.2782	−	1.81601i	−1.27032	−	0.133516i
$186$		0			0
$187$	−7.15364	+	12.9556i	−0.523126	+	0.947406i
$188$			14.9396i			1.08959i
$189$		0			0
$190$	0.437719	−	1.34716i	0.0317555	−	0.0977334i
$191$	−2.26616	+	10.6614i	−0.163974	+	0.771435i	0.816898	+	0.576782i	$0.195692\pi$
$191$	−2.26616	+	10.6614i	−0.163974	+	0.771435i	−0.980872	+	0.194654i	$0.937642\pi$
$192$		0			0
$193$	6.25009	−	14.0379i	0.449891	−	1.01047i	−0.536173	−	0.844108i	$-0.680131\pi$
$193$	6.25009	−	14.0379i	0.449891	−	1.01047i	0.986064	−	0.166364i	$-0.0532028\pi$
$194$	0.283543	−	0.314907i	0.0203572	−	0.0226090i
$195$		0			0
$196$	0.694224	−	0.309089i	0.0495875	−	0.0220778i
$197$	−7.24149			−0.515935			−0.257967	−	0.966154i	$-0.583053\pi$
$197$	−7.24149			−0.515935			−0.257967	+	0.966154i	$0.583053\pi$
$198$		0			0
$199$	−11.3726			−0.806181			−0.403090	−	0.915160i	$-0.632064\pi$
$199$	−11.3726			−0.806181			−0.403090	+	0.915160i	$0.632064\pi$
$200$	3.22550	−	1.43608i	0.228077	−	0.101547i
$201$		0			0
$202$	−1.53577	+	1.70564i	−0.108056	+	0.120009i
$203$	10.5575	−	23.7125i	0.740990	−	1.66429i
$204$		0			0
$205$	5.12293	−	24.1015i	0.357801	−	1.68332i
$206$	−1.29915	+	3.99838i	−0.0905162	+	0.278580i
$207$		0			0
$208$		−	10.3330i		−	0.716463i
$209$	6.29006	−	0.782796i	0.435092	−	0.0541471i
$210$		0			0
$211$	3.67797	+	0.386570i	0.253202	+	0.0266126i	0.230279	−	0.973125i	$-0.426036\pi$
$211$	3.67797	+	0.386570i	0.253202	+	0.0266126i	0.0229227	+	0.999737i	$0.492703\pi$
$212$	−4.20779	−	19.7961i	−0.288992	−	1.35960i
$213$		0			0
$214$	0.188610	+	1.79450i	0.0128931	+	0.122670i
$215$	−28.0724	+	20.3958i	−1.91452	+	1.39098i
$216$		0			0
$217$	15.4791	+	5.02946i	1.05079	+	0.341422i
$218$	0.889450	+	1.99774i	0.0602412	+	0.135304i
$219$		0			0
$220$	14.1762	+	12.2824i	0.955761	+	0.828082i
$221$	11.0365	−	6.37191i	0.742394	−	0.428621i
$222$		0			0
$223$	−0.189514	−	0.210476i	−0.0126908	−	0.0140945i	0.736766	−	0.676148i	$-0.236352\pi$
$223$	−0.189514	−	0.210476i	−0.0126908	−	0.0140945i	−0.749457	+	0.662053i	$0.769685\pi$
$224$	7.53664	−	2.44880i	0.503563	−	0.163618i
$225$		0			0
$226$	1.70099	+	2.34121i	0.113148	+	0.155735i
$227$	17.8570	+	3.79563i	1.18521	+	0.251925i	0.758017	−	0.652235i	$-0.226168\pi$
$227$	17.8570	+	3.79563i	1.18521	+	0.251925i	0.427195	+	0.904159i	$0.359502\pi$
$228$		0			0
$229$	−2.75702	+	26.2313i	−0.182189	+	1.73342i	0.396647	+	0.917971i	$0.370174\pi$
$229$	−2.75702	+	26.2313i	−0.182189	+	1.73342i	−0.578836	+	0.815444i	$0.696493\pi$
$230$	−0.302534	−	0.524005i	−0.0199485	−	0.0345519i
$231$		0			0
$232$	4.76555	−	8.25418i	0.312874	−	0.541914i
$233$	8.73916	+	6.34937i	0.572521	+	0.415961i	0.836020	−	0.548699i	$-0.184877\pi$
$233$	8.73916	+	6.34937i	0.572521	+	0.415961i	−0.263499	+	0.964660i	$0.584877\pi$
$234$		0			0
$235$	6.96844	+	21.4467i	0.454571	+	1.39903i
$236$	0.179606	−	0.0188773i	0.0116914	−	0.00122881i
$237$		0			0
$238$	2.28716	+	2.05937i	0.148255	+	0.133489i
$239$	−7.26110	+	1.54340i	−0.469682	+	0.0998339i	−0.436671	−	0.899621i	$-0.643843\pi$
$239$	−7.26110	+	1.54340i	−0.469682	+	0.0998339i	−0.0330103	+	0.999455i	$0.510509\pi$
$240$		0			0
$241$	−2.31118	−	1.33436i	−0.148876	−	0.0859539i	0.423711	−	0.905797i	$-0.360727\pi$
$241$	−2.31118	−	1.33436i	−0.148876	−	0.0859539i	−0.572588	+	0.819843i	$0.694060\pi$
$242$	0.760344	−	2.68484i	0.0488767	−	0.172588i
$243$		0			0
$244$	2.43938	−	3.35752i	0.156165	−	0.214943i
$245$	0.852425	−	0.767527i	0.0544594	−	0.0490355i
$246$		0			0
$247$	−4.98630	−	2.22004i	−0.317271	−	0.141258i
$248$	5.45965	+	2.43079i	0.346688	+	0.154356i
$249$		0			0
$250$	−0.806098	+	0.725814i	−0.0509821	+	0.0459045i
$251$	14.2630	−	19.6313i	0.900271	−	1.23912i	−0.0701107	−	0.997539i	$-0.522335\pi$
$251$	14.2630	−	19.6313i	0.900271	−	1.23912i	0.970382	−	0.241577i	$-0.0776647\pi$
$252$		0			0
$253$	1.54937	−	2.22047i	0.0974081	−	0.139600i
$254$	−0.633383	−	0.365684i	−0.0397420	−	0.0229450i
$255$		0			0
$256$	−10.8542	+	2.30712i	−0.678385	+	0.144195i
$257$	12.4522	+	11.2120i	0.776747	+	0.699386i	0.958856	−	0.283892i	$-0.0916259\pi$
$257$	12.4522	+	11.2120i	0.776747	+	0.699386i	−0.182110	+	0.983278i	$0.558293\pi$
$258$		0			0
$259$	−16.0790	+	1.68997i	−0.999098	+	0.105009i
$260$	−4.99116	−	15.3612i	−0.309538	−	0.952661i
$261$		0			0
$262$	0.431296	+	0.313355i	0.0266456	+	0.0193591i
$263$	−5.45728	+	9.45229i	−0.336511	+	0.582853i	−0.983774	−	0.179413i	$-0.942580\pi$
$263$	−5.45728	+	9.45229i	−0.336511	+	0.582853i	0.647263	+	0.762267i	$0.275913\pi$
$264$		0			0
$265$	−15.2742	−	26.4557i	−0.938285	−	1.62516i
$266$	0.137787	−	1.31095i	0.00844823	−	0.0803796i
$267$		0			0
$268$	−2.66543	−	0.566555i	−0.162817	−	0.0346078i
$269$	9.22041	+	12.6908i	0.562178	+	0.773772i	0.991601	−	0.129331i	$-0.0412830\pi$
$269$	9.22041	+	12.6908i	0.562178	+	0.773772i	−0.429423	+	0.903103i	$0.641283\pi$
$270$		0			0
$271$	−2.76289	+	0.897717i	−0.167834	+	0.0545324i	−0.391728	−	0.920081i	$-0.628123\pi$
$271$	−2.76289	+	0.897717i	−0.167834	+	0.0545324i	0.223895	+	0.974613i	$0.428123\pi$
$272$	−10.8027	−	11.9976i	−0.655008	−	0.727460i
$273$		0			0
$274$	1.11471	−	0.643579i	0.0673422	−	0.0388801i
$275$	10.8043	+	4.56525i	0.651523	+	0.275295i
$276$		0			0
$277$	8.58823	+	19.2895i	0.516017	+	1.15899i	0.964230	+	0.265066i	$0.0853938\pi$
$277$	8.58823	+	19.2895i	0.516017	+	1.15899i	−0.448213	+	0.893927i	$0.647939\pi$
$278$	−4.21817	−	1.37057i	−0.252989	−	0.0822011i
$279$		0			0
$280$	6.41638	−	4.66177i	0.383452	−	0.278594i
$281$	−0.323031	−	3.07343i	−0.0192704	−	0.183346i	0.980653	−	0.195756i	$-0.0627161\pi$
$281$	−0.323031	−	3.07343i	−0.0192704	−	0.183346i	−0.999923	+	0.0124107i	$0.996049\pi$
$282$		0			0
$283$	4.66236	+	21.9347i	0.277148	+	1.30388i	0.867784	+	0.496942i	$0.165544\pi$
$283$	4.66236	+	21.9347i	0.277148	+	1.30388i	−0.590635	+	0.806939i	$0.701123\pi$
$284$	6.94780	+	0.730243i	0.412276	+	0.0433319i
$285$		0			0
$286$	−1.75465	+	1.64162i	−0.103754	+	0.0970711i
$287$		−	22.9297i		−	1.35350i
$288$		0			0
$289$	0.899570	−	2.76859i	0.0529159	−	0.162858i
$290$	1.47111	−	6.92103i	0.0863866	−	0.406417i
$291$		0			0
$292$	1.38525	−	3.11132i	0.0810656	−	0.182076i
$293$	−13.8784	+	15.4135i	−0.810784	+	0.900467i	−0.996623	−	0.0821129i	$-0.973833\pi$
$293$	−13.8784	+	15.4135i	−0.810784	+	0.900467i	0.185839	+	0.982580i	$0.440500\pi$
$294$		0			0
$295$	0.249029	−	0.110875i	0.0144990	−	0.00645538i
$296$	−5.93663			−0.345059
$297$		0			0
$298$	1.43492			0.0831229
$299$	−2.12995	+	0.948315i	−0.123178	+	0.0548425i
$300$		0			0
$301$	−21.6069	+	23.9969i	−1.24540	+	1.38316i
$302$	−0.946718	+	2.12636i	−0.0544775	+	0.122358i
$303$		0			0
$304$	−1.43763	+	6.76352i	−0.0824537	+	0.387914i
$305$	1.93578	−	5.95772i	0.110843	−	0.341138i
$306$		0			0
$307$		−	15.0077i		−	0.856533i	−0.903652	−	0.428267i	$-0.859124\pi$
$307$		−	15.0077i		−	0.856533i	0.903652	−	0.428267i	$-0.140876\pi$
$308$	15.2804	+	8.43733i	0.870681	+	0.480762i
$309$		0			0
$310$	4.41237	+	0.463759i	0.250606	+	0.0263398i
$311$	−0.428093	−	2.01402i	−0.0242749	−	0.114205i	0.964342	−	0.264659i	$-0.0852595\pi$
$311$	−0.428093	−	2.01402i	−0.0242749	−	0.114205i	−0.988617	+	0.150455i	$0.951926\pi$
$312$		0			0
$313$	2.59989	+	24.7363i	0.146954	+	1.39818i	0.780831	+	0.624743i	$0.214796\pi$
$313$	2.59989	+	24.7363i	0.146954	+	1.39818i	−0.633876	+	0.773435i	$0.718537\pi$
$314$	0.626709	−	0.455330i	0.0353672	−	0.0256958i
$315$		0			0
$316$	13.1310	+	4.26652i	0.738677	+	0.240011i
$317$	−0.176006	−	0.395317i	−0.00988551	−	0.0222032i	0.908535	−	0.417808i	$-0.137202\pi$
$317$	−0.176006	−	0.395317i	−0.00988551	−	0.0222032i	−0.918421	+	0.395605i	$0.870535\pi$
$318$		0			0
$319$	30.8393	−	7.17310i	1.72667	−	0.401617i
$320$	−16.4386	+	9.49081i	−0.918944	+	0.530553i
$321$		0			0
$322$	−0.376768	−	0.418444i	−0.0209965	−	0.0233190i
$323$	−8.11053	+	2.63527i	−0.451282	+	0.146630i
$324$		0			0
$325$	−5.93668	−	8.17113i	−0.329308	−	0.453253i
$326$	−1.96136	−	0.416900i	−0.108630	−	0.0230899i
$327$		0			0
$328$	0.880093	−	8.37353i	0.0485950	−	0.462351i
$329$	10.4926	+	18.1737i	0.578475	+	1.00195i
$330$		0			0
$331$	8.65452	−	14.9901i	0.475696	−	0.823929i	−0.523917	−	0.851769i	$-0.675530\pi$
$331$	8.65452	−	14.9901i	0.475696	−	0.823929i	0.999612	+	0.0278406i	$0.00886309\pi$
$332$	12.2683	+	8.91344i	0.673310	+	0.489189i
$333$		0			0
$334$	−1.28934	−	3.96819i	−0.0705497	−	0.217130i
$335$	−4.09063	+	0.429943i	−0.223495	+	0.0234903i
$336$		0			0
$337$	−18.6269	−	16.7717i	−1.01467	−	0.913613i	−0.0183933	−	0.999831i	$-0.505855\pi$
$337$	−18.6269	−	16.7717i	−1.01467	−	0.913613i	−0.996276	+	0.0862182i	$0.972522\pi$
$338$	−1.20182	+	0.255455i	−0.0653704	+	0.0138949i
$339$		0			0
$340$	−21.8547	−	12.6178i	−1.18524	−	0.684296i
$341$	6.49444	+	18.7612i	0.351694	+	1.01598i
$342$		0			0
$343$	−10.5596	+	14.5341i	−0.570166	+	0.784766i
$344$	−8.81151	+	7.93392i	−0.475085	+	0.427768i
$345$		0			0
$346$	3.59723	+	1.60159i	0.193388	+	0.0861019i
$347$	−19.0684	−	8.48980i	−1.02365	−	0.455756i	−0.174916	−	0.984583i	$-0.555965\pi$
$347$	−19.0684	−	8.48980i	−1.02365	−	0.455756i	−0.848730	+	0.528827i	$0.822632\pi$
$348$		0			0
$349$	13.3919	−	12.0581i	0.716850	−	0.645455i	−0.227734	−	0.973723i	$-0.573132\pi$
$349$	13.3919	−	12.0581i	0.716850	−	0.645455i	0.944584	+	0.328269i	$0.106465\pi$
$350$	1.43373	−	1.97336i	0.0766361	−	0.105481i
$351$		0			0
$352$	7.92742	+	5.53148i	0.422533	+	0.294829i
$353$	−14.1122	−	8.14766i	−0.751115	−	0.433656i	0.0749818	−	0.997185i	$-0.476110\pi$
$353$	−14.1122	−	8.14766i	−0.751115	−	0.433656i	−0.826097	+	0.563529i	$0.809443\pi$
$354$		0			0
$355$	10.3145	−	2.19242i	0.547439	−	0.116362i
$356$	−2.97519	−	2.67887i	−0.157685	−	0.141980i
$357$		0			0
$358$	1.30920	−	0.137603i	0.0691935	−	0.00727253i
$359$	7.65875	+	23.5712i	0.404213	+	1.24404i	0.921550	+	0.388259i	$0.126923\pi$
$359$	7.65875	+	23.5712i	0.404213	+	1.24404i	−0.517337	+	0.855782i	$0.673077\pi$
$360$		0			0
$361$	−12.4164	−	9.02103i	−0.653494	−	0.474791i
$362$	−0.673798	+	1.16705i	−0.0354140	+	0.0613389i
$363$		0			0
$364$	−7.51532	−	13.0169i	−0.393910	−	0.682272i
$365$	0.537356	−	5.11260i	0.0281265	−	0.267606i
$366$		0			0
$367$	−8.75800	−	1.86157i	−0.457164	−	0.0971732i	−0.0264271	−	0.999651i	$-0.508413\pi$
$367$	−8.75800	−	1.86157i	−0.457164	−	0.0971732i	−0.430737	+	0.902478i	$0.641746\pi$
$368$	1.73611	+	2.38956i	0.0905012	+	0.124564i
$369$		0			0
$370$	−4.19150	+	1.36190i	−0.217906	+	0.0708018i
$371$	−19.0221	−	21.1261i	−0.987576	−	1.09681i
$372$		0			0
$373$	14.6365	−	8.45037i	0.757848	−	0.437544i	−0.0706745	−	0.997499i	$-0.522515\pi$
$373$	14.6365	−	8.45037i	0.757848	−	0.437544i	0.828523	+	0.559956i	$0.189182\pi$
$374$	−0.321069	+	3.74048i	−0.0166021	+	0.193416i
$375$		0			0
$376$	3.13416	+	7.03945i	0.161632	+	0.363032i
$377$	−25.9303	−	8.42527i	−1.33548	−	0.433923i
$378$		0			0
$379$	−15.9625	+	11.5975i	−0.819940	+	0.595722i	−0.916695	−	0.399587i	$-0.869154\pi$
$379$	−15.9625	+	11.5975i	−0.819940	+	0.595722i	0.0967550	+	0.995308i	$0.469154\pi$
$380$	1.12979	+	10.7492i	0.0579568	+	0.551422i
$381$		0			0
$382$	0.574869	+	2.70455i	0.0294129	+	0.138377i
$383$	4.97254	+	0.522635i	0.254085	+	0.0267054i	0.230715	−	0.973021i	$-0.425894\pi$
$383$	4.97254	+	0.522635i	0.254085	+	0.0267054i	0.0233704	+	0.999727i	$0.492560\pi$
$384$		0			0
$385$	25.8713	+	4.98486i	1.31853	+	0.254052i
$386$		−	3.89808i		−	0.198407i
$387$		0			0
$388$	−0.999169	+	3.07513i	−0.0507251	+	0.156116i
$389$	−2.04864	+	9.63809i	−0.103870	+	0.488671i	0.895204	+	0.445656i	$0.147030\pi$
$389$	−2.04864	+	9.63809i	−0.103870	+	0.488671i	−0.999074	+	0.0430147i	$0.986304\pi$
$390$		0			0
$391$	−1.48166	+	3.32785i	−0.0749306	+	0.168297i
$392$	0.262270	−	0.291280i	0.0132466	−	0.0147119i
$393$		0			0
$394$	−1.67817	+	0.747170i	−0.0845451	+	0.0376419i
$395$	20.8403			1.04859
$396$		0			0
$397$	−19.0245			−0.954812			−0.477406	−	0.878683i	$-0.658423\pi$
$397$	−19.0245			−0.954812			−0.477406	+	0.878683i	$0.658423\pi$
$398$	−2.63553	+	1.17341i	−0.132107	+	0.0588178i
$399$		0			0
$400$	−8.56161	+	9.50864i	−0.428081	+	0.475432i
$401$	−12.4891	+	28.0509i	−0.623673	+	1.40079i	0.274687	+	0.961534i	$0.411426\pi$
$401$	−12.4891	+	28.0509i	−0.623673	+	1.40079i	−0.898360	+	0.439260i	$0.855241\pi$
$402$		0			0
$403$	3.55444	−	16.7223i	0.177059	−	0.832999i
$404$	5.41185	−	16.6560i	0.269250	−	0.828665i
$405$		0			0
$406$		−	6.58454i		−	0.326785i
$407$	−13.4737	−	14.4014i	−0.667867	−	0.713849i
$408$		0			0
$409$	11.8084	+	1.24111i	0.583889	+	0.0613692i	0.391868	−	0.920022i	$-0.371829\pi$
$409$	11.8084	+	1.24111i	0.583889	+	0.0613692i	0.192021	+	0.981391i	$0.438496\pi$
$410$	−1.29956	−	6.11395i	−0.0641807	−	0.301946i
$411$		0			0
$412$	−3.35321	−	31.9036i	−0.165201	−	1.57178i
$413$	0.205228	−	0.149107i	0.0100986	−	0.00733706i
$414$		0			0
$415$	21.7694	+	7.07330i	1.06862	+	0.347215i
$416$	−3.38563	−	7.60424i	−0.165994	−	0.372829i
$417$		0			0
$418$	1.37691	−	0.830410i	0.0673471	−	0.0406167i
$419$	8.71474	−	5.03146i	0.425743	−	0.245803i	−0.271788	−	0.962357i	$-0.587615\pi$
$419$	8.71474	−	5.03146i	0.425743	−	0.245803i	0.697531	+	0.716554i	$0.254282\pi$
$420$		0			0
$421$	−4.18642	−	4.64949i	−0.204034	−	0.226602i	0.632440	−	0.774609i	$-0.282053\pi$
$421$	−4.18642	−	4.64949i	−0.204034	−	0.226602i	−0.836474	+	0.548007i	$0.815387\pi$
$422$	0.892232	−	0.289904i	0.0434332	−	0.0141123i
$423$		0			0
$424$	−6.13566	−	8.44502i	−0.297974	−	0.410126i
$425$	−15.4356	−	3.28094i	−0.748737	−	0.159149i
$426$		0			0
$427$	0.609351	−	5.79759i	0.0294886	−	0.280565i
$428$	−6.88411	−	11.9236i	−0.332756	−	0.576351i
$429$		0			0
$430$	−4.40119	+	7.62309i	−0.212244	+	0.367618i
$431$	−15.8885	−	11.5436i	−0.765321	−	0.556038i	0.135217	−	0.990816i	$-0.456827\pi$
$431$	−15.8885	−	11.5436i	−0.765321	−	0.556038i	−0.900538	+	0.434778i	$0.856827\pi$
$432$		0			0
$433$	9.66882	+	29.7576i	0.464654	+	1.43006i	0.859418	+	0.511274i	$0.170826\pi$
$433$	9.66882	+	29.7576i	0.464654	+	1.43006i	−0.394764	+	0.918783i	$0.629174\pi$
$434$	4.10612	−	0.431570i	0.197100	−	0.0207160i
$435$		0			0
$436$	−12.4002	−	11.1652i	−0.593864	−	0.534717i
$437$	1.52611	−	0.324385i	0.0730039	−	0.0155175i
$438$		0			0
$439$	17.4881	+	10.0967i	0.834659	+	0.481891i	0.855445	−	0.517893i	$-0.173283\pi$
$439$	17.4881	+	10.0967i	0.834659	+	0.481891i	−0.0207859	+	0.999784i	$0.506617\pi$
$440$	9.25644	+	2.81339i	0.441283	+	0.134123i
$441$		0			0
$442$	1.90019	−	2.61539i	0.0903828	−	0.124401i
$443$	−18.1089	+	16.3053i	−0.860378	+	0.774688i	−0.975808	−	0.218628i	$-0.929842\pi$
$443$	−18.1089	+	16.3053i	−0.860378	+	0.774688i	0.115430	+	0.993316i	$0.463175\pi$
$444$		0			0
$445$	−5.52057	−	2.45792i	−0.261700	−	0.116516i
$446$	−0.0656353	−	0.0292227i	−0.00310792	−	0.00138374i
$447$		0			0
$448$	−13.1270	+	11.8196i	−0.620193	+	0.558424i
$449$	1.94082	−	2.67131i	0.0915930	−	0.126067i	−0.760761	−	0.649032i	$-0.775174\pi$
$449$	1.94082	−	2.67131i	0.0915930	−	0.126067i	0.852354	+	0.522965i	$0.175174\pi$
$450$		0			0
$451$	22.3104	−	16.8695i	1.05055	−	0.794354i
$452$	−19.1233	−	11.0408i	−0.899483	−	0.519317i
$453$		0			0
$454$	4.52989	−	0.962857i	0.212598	−	0.0451891i
$455$	−16.8603	−	15.1810i	−0.790421	−	0.711698i
$456$		0			0
$457$	15.5319	−	1.63246i	0.726549	−	0.0763634i	0.265969	−	0.963982i	$-0.414308\pi$
$457$	15.5319	−	1.63246i	0.726549	−	0.0763634i	0.460580	+	0.887618i	$0.347641\pi$
$458$	2.06760	+	6.36342i	0.0966126	+	0.297343i
$459$		0			0
$460$	3.73517	+	2.71376i	0.174153	+	0.126530i
$461$	18.2842	−	31.6692i	0.851582	−	1.47498i	−0.0281979	−	0.999602i	$-0.508977\pi$
$461$	18.2842	−	31.6692i	0.851582	−	1.47498i	0.879780	−	0.475381i	$-0.157690\pi$
$462$		0			0
$463$	−2.22766	−	3.85841i	−0.103528	−	0.179316i	0.809608	−	0.586971i	$-0.199680\pi$
$463$	−2.22766	−	3.85841i	−0.103528	−	0.179316i	−0.913136	+	0.407655i	$0.866346\pi$
$464$	−3.61041	+	34.3507i	−0.167609	+	1.59469i
$465$		0			0
$466$	2.68037	+	0.569730i	0.124166	+	0.0263922i
$467$	−24.4676	−	33.6768i	−1.13223	−	1.55838i	−0.783769	−	0.621052i	$-0.786706\pi$
$467$	−24.4676	−	33.6768i	−1.13223	−	1.55838i	−0.348458	−	0.937325i	$-0.613294\pi$
$468$		0			0
$469$	−3.64033	+	1.18282i	−0.168095	+	0.0546173i
$470$	3.82774	+	4.25114i	0.176561	+	0.196090i
$471$		0			0
$472$	0.0806687	−	0.0465741i	0.00371308	−	0.00214375i
$473$	−39.2450	−	3.36865i	−1.80449	−	0.154891i
$474$		0			0
$475$	2.74904	+	6.17444i	0.126135	+	0.283303i
$476$	−22.3346	−	7.25696i	−1.02371	−	0.332622i
$477$		0			0
$478$	−1.52347	+	1.10687i	−0.0696819	+	0.0506269i
$479$	0.368097	+	3.50221i	0.0168188	+	0.160020i	0.999708	−	0.0241796i	$-0.00769735\pi$
$479$	0.368097	+	3.50221i	0.0168188	+	0.160020i	−0.982889	+	0.184200i	$0.941031\pi$
$480$		0			0
$481$	3.53083	+	16.6112i	0.160992	+	0.757407i
$482$	−0.673281	−	0.0707647i	−0.0306671	−	0.00322324i
$483$		0			0
$484$	3.03244	+	21.0751i	0.137838	+	0.957959i
$485$			4.88056i			0.221615i
$486$		0			0
$487$	9.85775	−	30.3390i	0.446697	−	1.37479i	−0.433914	−	0.900954i	$-0.642868\pi$
$487$	9.85775	−	30.3390i	0.446697	−	1.37479i	0.880611	−	0.473839i	$-0.157132\pi$
$488$	0.445049	−	2.09379i	0.0201464	−	0.0947815i
$489$		0			0
$490$	0.118352	−	0.265822i	0.00534658	−	0.0120086i
$491$	16.3396	−	18.1470i	0.737398	−	0.818963i	−0.251453	−	0.967869i	$-0.580909\pi$
$491$	16.3396	−	18.1470i	0.737398	−	0.818963i	0.988851	+	0.148906i	$0.0475752\pi$
$492$		0			0
$493$	−38.9158	+	17.3264i	−1.75268	+	0.780344i
$494$	−1.38461			−0.0622964
$495$		0			0
$496$	−21.6577			−0.972460
$497$	8.96468	−	3.99133i	0.402121	−	0.179036i
$498$		0			0
$499$	−15.5701	+	17.2924i	−0.697015	+	0.774113i	−0.982898	−	0.184151i	$-0.941046\pi$
$499$	−15.5701	+	17.2924i	−0.697015	+	0.774113i	0.285883	+	0.958264i	$0.407713\pi$
$500$	3.36648	−	7.56124i	0.150554	−	0.338149i
$501$		0			0
$502$	1.27982	−	6.02107i	0.0571211	−	0.268734i
$503$	11.2856	−	34.7334i	0.503199	−	1.54869i	−0.300579	−	0.953757i	$-0.597180\pi$
$503$	11.2856	−	34.7334i	0.503199	−	1.54869i	0.803778	−	0.594930i	$-0.202820\pi$
$504$		0			0
$505$		−	26.4348i		−	1.17633i
$506$	0.129951	−	0.674444i	0.00577703	−	0.0299827i
$507$		0			0
$508$	5.55007	+	0.583336i	0.246244	+	0.0258813i
$509$	5.16681	+	24.3080i	0.229015	+	1.07743i	0.930938	+	0.365178i	$0.118992\pi$
$509$	5.16681	+	24.3080i	0.229015	+	1.07743i	−0.701923	+	0.712253i	$0.747675\pi$
$510$		0			0
$511$	−0.500059	−	4.75774i	−0.0221213	−	0.210470i
$512$	−14.3757	+	10.4445i	−0.635321	+	0.461588i
$513$		0			0
$514$	4.04257	+	1.31351i	0.178310	+	0.0579364i
$515$	−19.6948	−	44.2353i	−0.867858	−	1.94924i
$516$		0			0
$517$	−9.96337	+	23.5797i	−0.438189	+	1.03703i
$518$	−3.55183	+	2.05065i	−0.156059	+	0.0901004i
$519$		0			0
$520$	−5.57439	−	6.19099i	−0.244453	−	0.271493i
$521$	9.26334	−	3.00984i	0.405834	−	0.131864i	−0.0989844	−	0.995089i	$-0.531559\pi$
$521$	9.26334	−	3.00984i	0.405834	−	0.131864i	0.504819	+	0.863225i	$0.331559\pi$
$522$		0			0
$523$	19.5526	+	26.9118i	0.854975	+	1.17677i	0.982744	+	0.184968i	$0.0592182\pi$
$523$	19.5526	+	26.9118i	0.854975	+	1.17677i	−0.127769	+	0.991804i	$0.540782\pi$
$524$	−3.97897	−	0.845757i	−0.173822	−	0.0369471i
$525$		0			0
$526$	−0.289414	+	2.75359i	−0.0126190	+	0.120062i
$527$	−13.3554	−	23.1323i	−0.581771	−	1.00766i
$528$		0			0
$529$	−11.1668	+	19.3414i	−0.485512	+	0.840931i
$530$	−6.26937	−	4.55496i	−0.272324	−	0.197855i
$531$		0			0
$532$	3.10816	+	9.56592i	0.134756	+	0.414735i
$533$	−23.9534	+	2.51760i	−1.03754	+	0.109049i
$534$		0			0
$535$	−15.4442	−	13.9060i	−0.667710	−	0.601208i
$536$	−1.37479	+	0.292220i	−0.0593817	+	0.0126220i
$537$		0			0
$538$	3.44620	+	1.98966i	0.148576	+	0.0857805i
$539$	1.30185	−	0.0248597i	0.0560746	−	0.00107078i
$540$		0			0
$541$	−6.85075	+	9.42925i	−0.294537	+	0.405395i	−0.930481	−	0.366340i	$-0.880611\pi$
$541$	−6.85075	+	9.42925i	−0.294537	+	0.405395i	0.635944	+	0.771735i	$0.280611\pi$
$542$	−0.547657	+	0.493113i	−0.0235239	+	0.0211810i
$543$		0			0
$544$	−11.8809	−	5.28973i	−0.509391	−	0.226795i
$545$	−23.0091	−	10.2443i	−0.985602	−	0.438818i
$546$		0			0
$547$	−0.604017	+	0.543859i	−0.0258259	+	0.0232537i	−0.681943	−	0.731406i	$-0.738865\pi$
$547$	−0.604017	+	0.543859i	−0.0258259	+	0.0232537i	0.656117	+	0.754659i	$0.272198\pi$
$548$	−5.77297	+	7.94581i	−0.246609	+	0.339428i
$549$		0			0
$550$	2.97487	−	0.0568072i	0.126849	−	0.00242227i
$551$	15.8006	+	9.12251i	0.673130	+	0.388632i
$552$		0			0
$553$	18.9700	−	4.03220i	0.806688	−	0.171467i
$554$	3.98054	+	3.58410i	0.169117	+	0.152274i
$555$		0			0
$556$	33.6574	−	3.53753i	1.42739	−	0.150025i
$557$	2.14843	+	6.61219i	0.0910320	+	0.280168i	0.986199	−	0.165563i	$-0.0529440\pi$
$557$	2.14843	+	6.61219i	0.0910320	+	0.280168i	−0.895167	+	0.445730i	$0.852944\pi$
$558$		0			0
$559$	27.4405	+	19.9367i	1.16061	+	0.843233i
$560$	−14.3708	+	24.8909i	−0.607277	+	1.05183i
$561$		0			0
$562$	−0.391974	−	0.678919i	−0.0165344	−	0.0286385i
$563$	−3.00599	+	28.6000i	−0.126687	+	1.20535i	0.727768	+	0.685823i	$0.240558\pi$
$563$	−3.00599	+	28.6000i	−0.126687	+	1.20535i	−0.854455	+	0.519525i	$0.826109\pi$
$564$		0			0
$565$	−32.6024	−	6.92985i	−1.37159	−	0.291541i
$566$	3.34367	+	4.60217i	0.140545	+	0.193444i
$567$		0			0
$568$	3.42694	−	1.11348i	0.143791	−	0.0467207i
$569$	−6.99170	−	7.76507i	−0.293107	−	0.325528i	0.578548	−	0.815648i	$-0.303620\pi$
$569$	−6.99170	−	7.76507i	−0.293107	−	0.325528i	−0.871655	+	0.490120i	$0.836953\pi$
$570$		0			0
$571$	18.4056	−	10.6265i	0.770251	−	0.444704i	−0.0627134	−	0.998032i	$-0.519975\pi$
$571$	18.4056	−	10.6265i	0.770251	−	0.444704i	0.832964	+	0.553327i	$0.186642\pi$
$572$	7.13628	−	16.8890i	0.298383	−	0.706163i
$573$		0			0
$574$	−2.36586	−	5.31381i	−0.0987492	−	0.221794i
$575$	2.74578	+	0.892157i	0.114507	+	0.0372055i
$576$		0			0
$577$	−12.6856	+	9.21665i	−0.528110	+	0.383694i	−0.819650	−	0.572864i	$-0.805832\pi$
$577$	−12.6856	+	9.21665i	−0.528110	+	0.383694i	0.291541	+	0.956558i	$0.405832\pi$
$578$	−0.0771908	−	0.734421i	−0.00321071	−	0.0305479i
$579$		0			0
$580$	11.2252	+	52.8104i	0.466101	+	2.19283i
$581$	21.1842	+	2.22655i	0.878870	+	0.0923730i
$582$		0			0
$583$	6.56089	−	34.0509i	0.271724	−	1.41025i
$584$		−	1.75664i		−	0.0726903i
$585$		0			0
$586$	−1.62588	+	5.00395i	−0.0671646	+	0.206711i
$587$	4.19059	−	19.7152i	0.172964	−	0.813732i	−0.803030	−	0.595938i	$-0.796780\pi$
$587$	4.19059	−	19.7152i	0.172964	−	0.813732i	0.975995	−	0.217794i	$-0.0698863\pi$
$588$		0			0
$589$	−4.65317	+	10.4512i	−0.191731	+	0.430634i
$590$	0.0462710	−	0.0513891i	0.00190495	−	0.00211566i
$591$		0			0
$592$	19.6539	−	8.75046i	0.807769	−	0.359642i
$593$	40.5694			1.66599			0.832993	−	0.553284i	$-0.186626\pi$
$593$	40.5694			1.66599			0.832993	+	0.553284i	$0.186626\pi$
$594$		0			0
$595$	−35.4475			−1.45320
$596$	−10.0025	+	4.45339i	−0.409717	+	0.182418i
$597$		0			0
$598$	−0.395757	+	0.439533i	−0.0161837	+	0.0179738i
$599$	−4.44868	+	9.99189i	−0.181768	+	0.408258i	−0.981331	−	0.192324i	$-0.938398\pi$
$599$	−4.44868	+	9.99189i	−0.181768	+	0.408258i	0.799563	+	0.600582i	$0.205064\pi$
$600$		0			0
$601$	−3.40064	+	15.9987i	−0.138715	+	0.652602i	0.852760	+	0.522303i	$0.174927\pi$
$601$	−3.40064	+	15.9987i	−0.138715	+	0.652602i	−0.991475	+	0.130299i	$0.958406\pi$
$602$	−2.53129	+	7.79050i	−0.103168	+	0.317517i
$603$		0			0
$604$		−	17.7605i		−	0.722665i
$605$	14.1835	+	28.8400i	0.576641	+	1.17251i
$606$		0			0
$607$	23.7338	+	2.49453i	0.963327	+	0.101250i	0.573115	−	0.819475i	$-0.305735\pi$
$607$	23.7338	+	2.49453i	0.963327	+	0.101250i	0.390212	+	0.920725i	$0.372402\pi$
$608$	1.15810	+	5.44845i	0.0469673	+	0.220964i
$609$		0			0
$610$	−0.166107	−	1.58040i	−0.00672546	−	0.0639885i
$611$	17.8330	−	12.9564i	0.721445	−	0.524161i
$612$		0			0
$613$	0.0461533	+	0.0149961i	0.00186411	+	0.000605687i	0.309949	−	0.950753i	$-0.399688\pi$
$613$	0.0461533	+	0.0149961i	0.00186411	+	0.000605687i	−0.308085	+	0.951359i	$0.599688\pi$
$614$	−1.54848	−	3.47794i	−0.0624915	−	0.140358i
$615$		0			0
$616$	8.97006	+	0.769956i	0.361414	+	0.0310224i
$617$	7.14090	−	4.12280i	0.287482	−	0.165978i	−0.349324	−	0.937002i	$-0.613589\pi$
$617$	7.14090	−	4.12280i	0.287482	−	0.165978i	0.636806	+	0.771024i	$0.280255\pi$
$618$		0			0
$619$	−1.16380	−	1.29253i	−0.0467770	−	0.0519512i	0.719302	−	0.694697i	$-0.244462\pi$
$619$	−1.16380	−	1.29253i	−0.0467770	−	0.0519512i	−0.766079	+	0.642746i	$0.777795\pi$
$620$	−32.1968	+	10.4614i	−1.29305	+	0.420139i
$621$		0			0
$622$	−0.307013	−	0.422567i	−0.0123101	−	0.0169434i
$623$	−5.50069	−	1.16921i	−0.220380	−	0.0468433i
$624$		0			0
$625$	3.15422	−	30.0104i	0.126169	−	1.20042i
$626$	3.15477	+	5.46423i	0.126090	+	0.218395i
$627$		0			0
$628$	−2.95547	+	5.11902i	−0.117936	+	0.204271i
$629$	21.4659	+	15.5959i	0.855903	+	0.621850i
$630$		0			0
$631$	−8.14182	−	25.0580i	−0.324121	−	0.997541i	−0.971836	−	0.235659i	$-0.924275\pi$
$631$	−8.14182	−	25.0580i	−0.324121	−	0.997541i	0.647715	−	0.761883i	$-0.275725\pi$
$632$	7.08230	−	0.744379i	0.281719	−	0.0296098i
$633$		0			0
$634$	−0.0815769	−	0.0734521i	−0.00323983	−	0.00291716i
$635$	8.23951	−	1.75136i	0.326975	−	0.0695007i
$636$		0			0
$637$	−0.971016	−	0.560616i	−0.0384731	−	0.0222124i
$638$	6.40670	−	4.84429i	0.253644	−	0.191787i
$639$		0			0
$640$	−12.8409	+	17.6740i	−0.507582	+	0.698626i
$641$	6.46222	−	5.81861i	0.255242	−	0.229821i	−0.531569	−	0.847015i	$-0.678397\pi$
$641$	6.46222	−	5.81861i	0.255242	−	0.229821i	0.786811	+	0.617194i	$0.211731\pi$
$642$		0			0
$643$	−19.7472	−	8.79200i	−0.778752	−	0.346723i	−0.0214348	−	0.999770i	$-0.506823\pi$
$643$	−19.7472	−	8.79200i	−0.778752	−	0.346723i	−0.757317	+	0.653048i	$0.773490\pi$
$644$	3.92502	+	1.74753i	0.154668	+	0.0688624i
$645$		0			0
$646$	−1.60766	+	1.44754i	−0.0632526	+	0.0569529i
$647$	−17.2616	+	23.7586i	−0.678625	+	0.934048i	−0.999916	−	0.0129330i	$-0.995883\pi$
$647$	−17.2616	+	23.7586i	−0.678625	+	0.934048i	0.321291	+	0.946980i	$0.395883\pi$
$648$		0			0
$649$	0.296067	+	0.0899860i	0.0116216	+	0.00353226i
$650$	−2.21888	−	1.28107i	−0.0870316	−	0.0502477i
$651$		0			0
$652$	14.9660	−	3.18112i	0.586113	−	0.124582i
$653$	17.6077	+	15.8541i	0.689043	+	0.620417i	0.937401	−	0.348251i	$-0.113224\pi$
$653$	17.6077	+	15.8541i	0.689043	+	0.620417i	−0.248358	+	0.968668i	$0.579891\pi$
$654$		0			0
$655$	−6.10652	+	0.641821i	−0.238602	+	0.0250780i
$656$	9.42876	+	29.0187i	0.368131	+	1.13299i
$657$		0			0
$658$	4.30674	+	3.12903i	0.167894	+	0.121982i
$659$	−17.2970	+	29.9594i	−0.673797	+	1.16705i	0.303022	+	0.952984i	$0.402004\pi$
$659$	−17.2970	+	29.9594i	−0.673797	+	1.16705i	−0.976819	+	0.214067i	$0.931329\pi$
$660$		0			0
$661$	−17.7456	−	30.7363i	−0.690225	−	1.19550i	−0.971764	−	0.235955i	$-0.924178\pi$
$661$	−17.7456	−	30.7363i	−0.690225	−	1.19550i	0.281539	−	0.959550i	$-0.409155\pi$
$662$	0.458972	−	4.36682i	0.0178384	−	0.169721i
$663$		0			0
$664$	7.65066	+	1.62620i	0.296903	+	0.0631087i
$665$	8.92385	+	12.2826i	0.346052	+	0.476300i
$666$		0			0
$667$	7.41211	−	2.40834i	0.286998	−	0.0932513i
$668$	21.3032	+	23.6596i	0.824246	+	0.915418i
$669$		0			0
$670$	−0.903618	+	0.521704i	−0.0349098	+	0.0201552i
$671$	6.08930	−	3.67243i	0.235075	−	0.141773i
$672$		0			0
$673$	−8.50131	−	19.0942i	−0.327701	−	0.736029i	0.672290	−	0.740288i	$-0.265311\pi$
$673$	−8.50131	−	19.0942i	−0.327701	−	0.736029i	−0.999991	+	0.00425911i	$0.998644\pi$
$674$	−6.04715	−	1.96484i	−0.232928	−	0.0756827i
$675$		0			0
$676$	7.58475	−	5.51064i	0.291721	−	0.211948i
$677$	2.53356	+	24.1052i	0.0973728	+	0.926440i	0.928744	+	0.370722i	$0.120890\pi$
$677$	2.53356	+	24.1052i	0.0973728	+	0.926440i	−0.831371	+	0.555718i	$0.812444\pi$
$678$		0			0
$679$	0.944294	+	4.44256i	0.0362387	+	0.170490i
$680$	−12.9448	−	1.36055i	−0.496411	−	0.0521749i
$681$		0			0
$682$	3.44081	+	3.67771i	0.131755	+	0.140827i
$683$		−	17.6311i		−	0.674636i	−0.941391	−	0.337318i	$-0.890480\pi$
$683$		−	17.6311i		−	0.674636i	0.941391	−	0.337318i	$-0.109520\pi$
$684$		0			0
$685$	−4.58116	+	14.0994i	−0.175037	+	0.538709i
$686$	−0.947516	+	4.45771i	−0.0361763	+	0.170196i
$687$		0			0
$688$	17.4771	−	39.2541i	0.666307	−	1.49655i
$689$	−19.9807	+	22.1909i	−0.761206	+	0.845405i
$690$		0			0
$691$	26.6174	−	11.8508i	1.01257	−	0.450826i	0.167725	−	0.985834i	$-0.446358\pi$
$691$	26.6174	−	11.8508i	1.01257	−	0.450826i	0.844847	+	0.535007i	$0.179691\pi$
$692$	−30.0459			−1.14218
$693$		0			0
$694$	−5.29496			−0.200994
$695$	46.6669	−	20.7774i	1.77018	−	0.788133i
$696$		0			0
$697$	−25.1801	+	27.9653i	−0.953765	+	1.05926i
$698$	1.85934	−	4.17615i	0.0703771	−	0.158070i
$699$		0			0
$700$	−3.86969	+	18.2055i	−0.146260	+	0.688101i
$701$	−4.54301	+	13.9820i	−0.171587	+	0.528091i	−0.999461	−	0.0328229i	$-0.989550\pi$
$701$	−4.54301	+	13.9820i	−0.171587	+	0.528091i	0.827874	+	0.560914i	$0.189550\pi$
$702$		0			0
$703$		−	11.3642i		−	0.428611i
$704$	−21.1580	−	4.07670i	−0.797422	−	0.153646i
$705$		0			0
$706$	−4.11108	−	0.432092i	−0.154722	−	0.0162620i
$707$	−5.11463	−	24.0624i	−0.192355	−	0.904961i
$708$		0			0
$709$	−1.12706	−	10.7233i	−0.0423278	−	0.402722i	−0.995088	−	0.0989975i	$-0.968436\pi$
$709$	−1.12706	−	10.7233i	−0.0423278	−	0.402722i	0.952760	−	0.303724i	$-0.0982302\pi$
$710$	2.16412	−	1.57233i	0.0812180	−	0.0590083i
$711$		0			0
$712$	−1.96388	−	0.638103i	−0.0735995	−	0.0239139i
$713$	1.98765	+	4.46434i	0.0744382	+	0.167191i
$714$		0			0
$715$	2.36682	−	27.5737i	0.0885140	−	1.03120i
$716$	−8.69904	+	5.02239i	−0.325098	+	0.187696i
$717$		0			0
$718$	4.20692	+	4.67226i	0.157001	+	0.174367i
$719$	30.1960	−	9.81128i	1.12612	−	0.365899i	0.314020	−	0.949416i	$-0.398324\pi$
$719$	30.1960	−	9.81128i	1.12612	−	0.365899i	0.812101	+	0.583517i	$0.198324\pi$
$720$		0			0
$721$	−26.4860	−	36.4549i	−0.986390	−	1.35765i
$722$	−3.80820	−	0.809459i	−0.141727	−	0.0301249i
$723$		0			0
$724$	1.07484	−	10.2264i	0.0399460	−	0.380061i
$725$	16.8807	+	29.2383i	0.626934	+	1.08588i
$726$		0			0
$727$	−11.8209	+	20.4744i	−0.438414	+	0.759355i	−0.997567	−	0.0697091i	$-0.977793\pi$
$727$	−11.8209	+	20.4744i	−0.438414	+	0.759355i	0.559154	+	0.829064i	$0.311126\pi$
$728$	−6.27196	−	4.55685i	−0.232454	−	0.168888i
$729$		0			0
$730$	−0.402984	−	1.24026i	−0.0149151	−	0.0459040i
$731$	52.7041	−	5.53942i	1.94933	−	0.204883i
$732$		0			0
$733$	−12.2057	−	10.9901i	−0.450829	−	0.405929i	0.412191	−	0.911097i	$-0.364764\pi$
$733$	−12.2057	−	10.9901i	−0.450829	−	0.405929i	−0.863021	+	0.505169i	$0.831430\pi$
$734$	−2.22169	+	0.472235i	−0.0820040	+	0.0174305i
$735$		0			0
$736$	2.06059	+	1.18968i	0.0759542	+	0.0438522i
$737$	−3.82908	−	2.67181i	−0.141046	−	0.0984172i
$738$		0			0
$739$	20.4813	−	28.1901i	0.753417	−	1.03699i	−0.244316	−	0.969696i	$-0.578563\pi$
$739$	20.4813	−	28.1901i	0.753417	−	1.03699i	0.997733	−	0.0672942i	$-0.0214366\pi$
$740$	24.9911	−	22.5021i	0.918690	−	0.827192i
$741$		0			0
$742$	−6.58802	−	2.93318i	−0.241854	−	0.107680i
$743$	48.2284	+	21.4727i	1.76933	+	0.787756i	0.986128	+	0.165987i	$0.0530808\pi$
$743$	48.2284	+	21.4727i	1.76933	+	0.787756i	0.783201	+	0.621769i	$0.213586\pi$
$744$		0			0
$745$	−12.2818	+	11.0586i	−0.449972	+	0.405157i
$746$	2.52001	−	3.46850i	0.0922643	−	0.126991i
$747$		0			0
$748$	−9.37077	−	27.0704i	−0.342629	−	0.989791i
$749$	−16.7487	−	9.66985i	−0.611983	−	0.353329i
$750$		0			0
$751$	−50.2550	+	10.6820i	−1.83383	+	0.389793i	−0.989322	−	0.145749i	$-0.953441\pi$
$751$	−50.2550	+	10.6820i	−1.83383	+	0.389793i	−0.844509	+	0.535542i	$0.820108\pi$
$752$	−20.7520	−	18.6852i	−0.756748	−	0.681379i
$753$		0			0
$754$	−6.87850	+	0.722960i	−0.250500	+	0.0263286i
$755$	−8.28421	−	25.4962i	−0.301493	−	0.927900i
$756$		0			0
$757$	5.71877	+	4.15493i	0.207852	+	0.151013i	0.686841	−	0.726807i	$-0.258997\pi$
$757$	5.71877	+	4.15493i	0.207852	+	0.151013i	−0.478989	+	0.877821i	$0.658997\pi$
$758$	−2.50261	+	4.33464i	−0.0908987	+	0.157441i
$759$		0			0
$760$	2.78740	+	4.82792i	0.101110	+	0.175127i
$761$	3.04520	−	28.9731i	0.110388	−	1.05027i	−0.789380	−	0.613905i	$-0.789598\pi$
$761$	3.04520	−	28.9731i	0.110388	−	1.05027i	0.899768	−	0.436369i	$-0.143736\pi$
$762$		0			0
$763$	−22.9262	−	4.87312i	−0.829986	−	0.176419i
$764$	−12.4010	−	17.0685i	−0.448653	−	0.617517i
$765$		0			0
$766$	1.20628	−	0.391945i	0.0435847	−	0.0141615i
$767$	−0.178297	−	0.198019i	−0.00643792	−	0.00715004i
$768$		0			0
$769$	38.3136	−	22.1204i	1.38162	−	0.797682i	0.389273	−	0.921122i	$-0.372726\pi$
$769$	38.3136	−	22.1204i	1.38162	−	0.797682i	0.992352	+	0.123441i	$0.0393929\pi$
$770$	6.50986	−	1.51417i	0.234599	−	0.0545669i
$771$		0			0
$772$	12.0980	+	27.1725i	0.435416	+	0.977960i
$773$	38.0786	+	12.3725i	1.36959	+	0.445007i	0.899234	−	0.437468i	$-0.144125\pi$
$773$	38.0786	+	12.3725i	1.36959	+	0.445007i	0.470358	+	0.882476i	$0.344125\pi$
$774$		0			0
$775$	−17.1266	+	12.4432i	−0.615204	+	0.446972i
$776$	0.174325	+	1.65859i	0.00625790	+	0.0595399i
$777$		0			0
$778$	0.519689	+	2.44495i	0.0186318	+	0.0876556i
$779$	16.0291	+	1.68473i	0.574302	+	0.0603616i
$780$		0			0
$781$	10.4789	+	5.78610i	0.374965	+	0.207043i
$782$			0.924086i			0.0330453i
$783$		0			0
$784$	−0.438933	+	1.35090i	−0.0156762	+	0.0482463i
$785$	−1.85502	+	8.72718i	−0.0662084	+	0.311486i
$786$		0			0
$787$	−11.5367	+	25.9119i	−0.411239	+	0.923659i	0.582593	+	0.812764i	$0.302038\pi$
$787$	−11.5367	+	25.9119i	−0.411239	+	0.923659i	−0.993832	+	0.110895i	$0.964628\pi$
$788$	9.37919	−	10.4167i	0.334120	−	0.371078i
$789$		0			0
$790$	4.82962	−	2.15029i	0.171830	−	0.0765038i
$791$	−31.0173			−1.10285
$792$		0			0
$793$	−6.12332			−0.217446
$794$	−4.40881	+	1.96293i	−0.156463	+	0.0696618i
$795$		0			0
$796$	14.7298	−	16.3591i	0.522083	−	0.579832i
$797$	6.07817	−	13.6518i	0.215300	−	0.483571i	−0.773318	−	0.634018i	$-0.781405\pi$
$797$	6.07817	−	13.6518i	0.215300	−	0.483571i	0.988618	+	0.150447i	$0.0480712\pi$
$798$		0			0
$799$	7.16045	−	33.6872i	0.253318	−	1.19177i
$800$	−3.18513	+	9.80283i	−0.112611	+	0.346582i
$801$		0			0
$802$			7.78923i			0.275047i
$803$	4.26134	−	3.98685i	0.150380	−	0.140693i
$804$		0			0
$805$	6.44970	+	0.677890i	0.227322	+	0.0238925i
$806$	−0.901675	−	4.24205i	−0.0317601	−	0.149420i
$807$		0			0
$808$	−0.944204	−	8.98351i	−0.0332170	−	0.316039i
$809$	24.0892	−	17.5019i	0.846933	−	0.615333i	−0.0773660	−	0.997003i	$-0.524651\pi$
$809$	24.0892	−	17.5019i	0.846933	−	0.615333i	0.924299	+	0.381670i	$0.124651\pi$
$810$		0			0
$811$	41.9856	+	13.6420i	1.47432	+	0.479034i	0.932409	−	0.361405i	$-0.117703\pi$
$811$	41.9856	+	13.6420i	1.47432	+	0.479034i	0.541906	+	0.840439i	$0.317703\pi$
$812$	20.4356	+	45.8991i	0.717148	+	1.61074i
$813$		0			0
$814$	−4.60837	−	1.94722i	−0.161523	−	0.0682502i
$815$	20.0007	−	11.5474i	0.700593	−	0.404488i
$816$		0			0
$817$	−15.1876	−	16.8675i	−0.531346	−	0.590120i
$818$	2.86459	−	0.930761i	0.100158	−	0.0325433i
$819$		0			0
$820$	28.0340	+	38.5854i	0.978988	+	1.34746i
$821$	3.91743	+	0.832676i	0.136719	+	0.0290606i	0.275763	−	0.961226i	$-0.411070\pi$
$821$	3.91743	+	0.832676i	0.136719	+	0.0290606i	−0.139044	+	0.990286i	$0.544403\pi$
$822$		0			0
$823$	−4.40925	+	41.9512i	−0.153697	+	1.46233i	0.597299	+	0.802019i	$0.296241\pi$
$823$	−4.40925	+	41.9512i	−0.153697	+	1.46233i	−0.750995	+	0.660307i	$0.770426\pi$
$824$	−8.27302	−	14.3293i	−0.288204	−	0.499184i
$825$		0			0
$826$	0.0321756	−	0.0557298i	0.00111953	−	0.00193909i
$827$	−21.5183	−	15.6340i	−0.748266	−	0.543647i	0.147023	−	0.989133i	$-0.453031\pi$
$827$	−21.5183	−	15.6340i	−0.748266	−	0.543647i	−0.895289	+	0.445486i	$0.853031\pi$
$828$		0			0
$829$	3.77976	+	11.6329i	0.131276	+	0.404027i	0.994992	−	0.0999518i	$-0.0318689\pi$
$829$	3.77976	+	11.6329i	0.131276	+	0.404027i	−0.863716	+	0.503979i	$0.831869\pi$
$830$	5.77474	−	0.606949i	0.200444	−	0.0210675i
$831$		0			0
$832$	13.7886	+	12.4153i	0.478033	+	0.430423i
$833$	−1.71354	+	0.364225i	−0.0593707	+	0.0126196i
$834$		0			0
$835$	41.6177	+	24.0280i	1.44024	+	0.831523i
$836$	−7.02087	+	10.0619i	−0.242822	+	0.347999i
$837$		0			0
$838$	1.50045	−	2.06519i	0.0518321	−	0.0713408i
$839$	7.16872	−	6.45475i	0.247492	−	0.222843i	−0.536043	−	0.844191i	$-0.680081\pi$
$839$	7.16872	−	6.45475i	0.247492	−	0.222843i	0.783535	+	0.621348i	$0.213415\pi$
$840$		0			0
$841$	56.7655	+	25.2736i	1.95743	+	0.871505i
$842$	−1.44991	−	0.645540i	−0.0499671	−	0.0222468i
$843$		0			0
$844$	−5.31978	+	4.78995i	−0.183114	+	0.164877i
$845$	8.31793	−	11.4486i	0.286146	−	0.393846i
$846$		0			0
$847$	18.4906	+	23.5075i	0.635344	+	0.807727i
$848$	32.7606	+	18.9143i	1.12500	+	0.649521i
$849$		0			0
$850$	−3.91563	+	0.832294i	−0.134305	+	0.0285474i
$851$	−3.60749	−	3.24820i	−0.123663	−	0.111347i
$852$		0			0
$853$	11.6743	−	1.22701i	0.399719	−	0.0420122i	0.0974635	−	0.995239i	$-0.468927\pi$
$853$	11.6743	−	1.22701i	0.399719	−	0.0420122i	0.302256	+	0.953227i	$0.402260\pi$
$854$	−0.456976	−	1.40643i	−0.0156374	−	0.0481270i
$855$		0			0
$856$	−5.74518	−	4.17412i	−0.196366	−	0.142668i
$857$	24.3869	−	42.2393i	0.833041	−	1.44287i	−0.0625753	−	0.998040i	$-0.519931\pi$
$857$	24.3869	−	42.2393i	0.833041	−	1.44287i	0.895616	−	0.444828i	$-0.146735\pi$
$858$		0			0
$859$	15.5440	+	26.9230i	0.530355	+	0.918602i	0.999373	+	0.0354131i	$0.0112747\pi$
$859$	15.5440	+	26.9230i	0.530355	+	0.918602i	−0.469018	+	0.883189i	$0.655392\pi$
$860$	7.02074	−	66.7979i	0.239405	−	2.27779i
$861$		0			0
$862$	−4.87312	−	1.03581i	−0.165979	−	0.0352800i
$863$	30.6459	+	42.1805i	1.04320	+	1.43584i	0.894559	+	0.446950i	$0.147490\pi$
$863$	30.6459	+	42.1805i	1.04320	+	1.43584i	0.148641	+	0.988891i	$0.452510\pi$
$864$		0			0
$865$	−43.1325	+	14.0146i	−1.46655	+	0.476511i
$866$	5.31105	+	5.89851i	0.180477	+	0.200440i
$867$		0			0
$868$	−27.2832	+	15.7520i	−0.926053	+	0.534657i
$869$	17.8797	+	15.4912i	0.606526	+	0.525501i
$870$		0			0
$871$	1.63532	+	3.67298i	0.0554106	+	0.124454i
$872$	−8.18523	−	2.65954i	−0.277187	−	0.0900635i
$873$		0			0
$874$	0.320198	−	0.232637i	0.0108309	−	0.00786907i
$875$	−1.21526	−	11.5624i	−0.0410833	−	0.390881i
$876$		0			0
$877$	−3.53196	−	16.6166i	−0.119266	−	0.561102i	−0.996684	−	0.0813746i	$-0.974069\pi$
$877$	−3.53196	−	16.6166i	−0.119266	−	0.561102i	0.877418	−	0.479727i	$-0.159264\pi$
$878$	5.09452	+	0.535456i	0.171932	+	0.0180708i
$879$		0			0
$880$	−34.7913	+	4.32977i	−1.17282	+	0.145957i
$881$			50.3115i			1.69504i	0.530765	+	0.847519i	$0.321905\pi$
$881$			50.3115i			1.69504i	−0.530765	+	0.847519i	$0.678095\pi$
$882$		0			0
$883$	4.44037	−	13.6660i	0.149430	−	0.459899i	−0.848124	−	0.529798i	$-0.822268\pi$
$883$	4.44037	−	13.6660i	0.149430	−	0.459899i	0.997554	+	0.0698990i	$0.0222677\pi$
$884$	−5.12868	+	24.1285i	−0.172496	+	0.811530i
$885$		0			0
$886$	−2.51425	+	5.64711i	−0.0844680	+	0.189718i
$887$	27.6353	−	30.6921i	0.927903	−	1.03054i	−0.0715485	−	0.997437i	$-0.522794\pi$
$887$	27.6353	−	30.6921i	0.927903	−	1.03054i	0.999452	−	0.0331040i	$-0.0105393\pi$
$888$		0			0
$889$	7.16120	−	3.18837i	0.240179	−	0.106935i
$890$	−1.53296			−0.0513851
$891$		0			0
$892$	0.548221			0.0183558
$893$	−13.4753	+	5.99961i	−0.450935	+	0.200769i
$894$		0			0
$895$	−10.1453	+	11.2675i	−0.339120	+	0.376631i
$896$	−8.26893	+	18.5723i	−0.276246	+	0.620458i
$897$		0			0
$898$	0.174150	−	0.819312i	0.00581147	−	0.0273408i
$899$	−17.6592	+	54.3495i	−0.588968	+	1.81266i
$900$		0			0
$901$			46.6547i			1.55429i
$902$	3.42971	−	6.21137i	0.114197	−	0.206816i
$903$		0			0
$904$	−11.3270	−	1.19051i	−0.376730	−	0.0395959i
$905$	−3.22701	−	15.1819i	−0.107269	−	0.504663i
$906$		0			0
$907$	2.72994	+	25.9736i	0.0906460	+	0.862439i	0.941495	+	0.337028i	$0.109422\pi$
$907$	2.72994	+	25.9736i	0.0906460	+	0.862439i	−0.850849	+	0.525411i	$0.823912\pi$
$908$	−28.5883	+	20.7706i	−0.948738	+	0.689298i
$909$		0			0
$910$	−5.47363	−	1.77849i	−0.181449	−	0.0589563i
$911$	18.4710	+	41.4866i	0.611972	+	1.37451i	0.907853	+	0.419288i	$0.137720\pi$
$911$	18.4710	+	41.4866i	0.611972	+	1.37451i	−0.295881	+	0.955225i	$0.595613\pi$
$912$		0			0
$913$	13.4190	+	22.2502i	0.444103	+	0.736373i
$914$	3.43098	−	1.98088i	0.113487	−	0.0655215i
$915$		0			0
$916$	−34.1620	−	37.9408i	−1.12874	−	1.25360i
$917$	−5.43431	+	1.76572i	−0.179457	+	0.0583091i
$918$		0			0
$919$	−16.3737	−	22.5365i	−0.540119	−	0.743410i	0.448511	−	0.893777i	$-0.351954\pi$
$919$	−16.3737	−	22.5365i	−0.540119	−	0.743410i	−0.988630	+	0.150367i	$0.951954\pi$
$920$	2.32930	+	0.495108i	0.0767948	+	0.0163232i
$921$		0			0
$922$	0.969661	−	9.22571i	0.0319341	−	0.303832i
$923$	−5.15381	−	8.92667i	−0.169640	−	0.293825i
$924$		0			0
$925$	10.5145	−	18.2116i	0.345713	−	0.598793i
$926$	−0.914353	−	0.664317i	−0.0300475	−	0.0218308i
$927$		0			0
$928$	8.59813	+	26.4623i	0.282248	+	0.868669i
$929$	−49.4820	+	5.20076i	−1.62345	+	0.170632i	−0.872119	−	0.489293i	$-0.837255\pi$
$929$	−49.4820	+	5.20076i	−1.62345	+	0.170632i	−0.751331	+	0.659925i	$0.770588\pi$
$930$		0			0
$931$	0.557586	+	0.502053i	0.0182742	+	0.0164541i
$932$	−20.4523	+	4.34728i	−0.669938	+	0.142400i
$933$		0			0
$934$	−9.14497	−	5.27985i	−0.299232	−	0.172762i
$935$	−26.0789	−	34.4901i	−0.852872	−	1.12795i
$936$		0			0
$937$	11.9943	−	16.5087i	0.391837	−	0.539317i	−0.566835	−	0.823831i	$-0.691832\pi$
$937$	11.9943	−	16.5087i	0.391837	−	0.539317i	0.958672	+	0.284514i	$0.0918323\pi$
$938$	−0.721583	+	0.649716i	−0.0235605	+	0.0212140i
$939$		0			0
$940$	−39.8759	−	17.7539i	−1.30061	−	0.579068i
$941$	−16.0267	−	7.13554i	−0.522455	−	0.232612i	0.128526	−	0.991706i	$-0.458976\pi$
$941$	−16.0267	−	7.13554i	−0.522455	−	0.232612i	−0.650981	+	0.759094i	$0.725642\pi$
$942$		0			0
$943$	5.11635	−	4.60678i	0.166611	−	0.150017i
$944$	−0.198413	+	0.273093i	−0.00645781	+	0.00888841i
$945$		0			0
$946$	−9.44237	+	3.26860i	−0.306998	+	0.106271i
$947$	40.7614	+	23.5336i	1.32457	+	0.764739i	0.984453	−	0.175646i	$-0.0562013\pi$
$947$	40.7614	+	23.5336i	1.32457	+	0.764739i	0.340113	+	0.940385i	$0.389535\pi$
$948$		0			0
$949$	−4.91524	+	1.04477i	−0.159556	+	0.0339146i
$950$	1.27415	+	1.14725i	0.0413388	+	0.0372216i
$951$		0			0
$952$	−12.0463	+	1.26612i	−0.390424	+	0.0410352i
$953$	−15.9545	−	49.1029i	−0.516817	−	1.59060i	−0.779952	−	0.625839i	$-0.784757\pi$
$953$	−15.9545	−	49.1029i	−0.516817	−	1.59060i	0.263136	−	0.964759i	$-0.415243\pi$
$954$		0			0
$955$	−25.7637	−	18.7185i	−0.833695	−	0.605715i
$956$	7.18447	−	12.4439i	0.232362	−	0.402463i
$957$		0			0
$958$	0.446659	+	0.773636i	0.0144309	+	0.0249951i
$959$	−1.44207	+	13.7204i	−0.0465669	+	0.443055i
$960$		0			0
$961$	−4.72716	−	1.00479i	−0.152489	−	0.0324125i
$962$	2.53218	+	3.48525i	0.0816408	+	0.112369i
$963$		0			0
$964$	4.91289	−	1.59629i	0.158233	−	0.0514132i
$965$	30.0416	+	33.3646i	0.967074	+	1.07404i
$966$		0			0
$967$	29.1820	−	16.8482i	0.938429	−	0.541802i	0.0489615	−	0.998801i	$-0.484409\pi$
$967$	29.1820	−	16.8482i	0.938429	−	0.541802i	0.889467	+	0.456998i	$0.151076\pi$
$968$	5.85017	+	9.29425i	0.188032	+	0.298729i
$969$		0			0
$970$	0.503572	+	1.13104i	0.0161687	+	0.0363155i
$971$	53.1467	+	17.2684i	1.70556	+	0.554170i	0.989584	−	0.143955i	$-0.0459822\pi$
$971$	53.1467	+	17.2684i	1.70556	+	0.554170i	0.715976	+	0.698125i	$0.245982\pi$
$972$		0			0
$973$	38.4588	−	27.9419i	1.23293	−	0.895777i
$974$	−0.845879	−	8.04800i	−0.0271037	−	0.257875i
$975$		0			0
$976$	1.61282	+	7.58772i	0.0516251	+	0.242877i
$977$	−20.5461	−	2.15948i	−0.657329	−	0.0690880i	−0.230009	−	0.973189i	$-0.573875\pi$
$977$	−20.5461	−	2.15948i	−0.657329	−	0.0690880i	−0.427320	+	0.904101i	$0.640542\pi$
$978$		0			0
$979$	−2.90926	−	6.21231i	−0.0929804	−	0.198546i
$980$			2.22029i			0.0709245i
$981$		0			0
$982$	1.91422	−	5.89137i	0.0610853	−	0.188001i
$983$	10.4221	−	49.0320i	0.332412	−	1.56388i	−0.421454	−	0.906850i	$-0.638480\pi$
$983$	10.4221	−	49.0320i	0.332412	−	1.56388i	0.753866	−	0.657028i	$-0.228187\pi$
$984$		0			0
$985$	8.60560	−	19.3285i	0.274197	−	0.615857i
$986$	−7.23078	+	8.03060i	−0.230275	+	0.255746i
$987$		0			0
$988$	9.65172	−	4.29722i	0.307062	−	0.136713i
$989$	−9.69548			−0.308298
$990$		0			0
$991$	45.3068			1.43922			0.719609	−	0.694379i	$-0.244321\pi$
$991$	45.3068			1.43922			0.719609	+	0.694379i	$0.244321\pi$
$992$	−15.9383	+	7.09621i	−0.506043	+	0.225305i
$993$		0			0
$994$	1.66569	−	1.84993i	0.0528324	−	0.0586763i
$995$	13.5149	−	30.3549i	0.428450	−	0.962315i
$996$		0			0
$997$	−2.13731	+	10.0553i	−0.0676893	+	0.318453i	−0.998945	−	0.0459120i	$-0.985381\pi$
$997$	−2.13731	+	10.0553i	−0.0676893	+	0.318453i	0.931256	+	0.364365i	$0.118714\pi$
$998$	−1.82407	+	5.61392i	−0.0577400	+	0.177705i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.u.c.755.3		32
3.2	odd	2	inner	891.2.u.c.755.2		32
9.2	odd	6		99.2.j.a.62.3	yes	16
9.4	even	3	inner	891.2.u.c.458.2		32
9.5	odd	6	inner	891.2.u.c.458.3		32
9.7	even	3		99.2.j.a.62.2	yes	16
11.8	odd	10	inner	891.2.u.c.107.3		32
33.8	even	10	inner	891.2.u.c.107.2		32
36.7	odd	6		1584.2.cd.c.161.2		16
36.11	even	6		1584.2.cd.c.161.3		16
99.16	even	15		1089.2.d.g.1088.10		16
99.38	odd	30		1089.2.d.g.1088.7		16
99.41	even	30	inner	891.2.u.c.701.3		32
99.52	odd	30		99.2.j.a.8.3	yes	16
99.61	odd	30		1089.2.d.g.1088.8		16
99.74	even	30		99.2.j.a.8.2	✓	16
99.83	even	30		1089.2.d.g.1088.9		16
99.85	odd	30	inner	891.2.u.c.701.2		32
396.151	even	30		1584.2.cd.c.305.3		16
396.371	odd	30		1584.2.cd.c.305.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.j.a.8.2	✓	16	99.74	even	30
99.2.j.a.8.3	yes	16	99.52	odd	30
99.2.j.a.62.2	yes	16	9.7	even	3
99.2.j.a.62.3	yes	16	9.2	odd	6
891.2.u.c.107.2		32	33.8	even	10	inner
891.2.u.c.107.3		32	11.8	odd	10	inner
891.2.u.c.458.2		32	9.4	even	3	inner
891.2.u.c.458.3		32	9.5	odd	6	inner
891.2.u.c.701.2		32	99.85	odd	30	inner
891.2.u.c.701.3		32	99.41	even	30	inner
891.2.u.c.755.2		32	3.2	odd	2	inner
891.2.u.c.755.3		32	1.1	even	1	trivial
1089.2.d.g.1088.7		16	99.38	odd	30
1089.2.d.g.1088.8		16	99.61	odd	30
1089.2.d.g.1088.9		16	99.83	even	30
1089.2.d.g.1088.10		16	99.16	even	15
1584.2.cd.c.161.2		16	36.7	odd	6
1584.2.cd.c.161.3		16	36.11	even	6
1584.2.cd.c.305.2		16	396.371	odd	30
1584.2.cd.c.305.3		16	396.151	even	30

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:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.u (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.231744 - 0.103179i) q^{2} +(-1.29520 + 1.43847i) q^{4} +(-1.18837 + 2.66913i) q^{5} +(-0.565298 + 2.65952i) q^{7} +(-0.308515 + 0.949513i) q^{8} +0.741170i q^{10} +(-3.00358 + 1.40659i) q^{11} +(2.84032 + 0.298529i) q^{13} +(0.143402 + 0.674654i) q^{14} +(-0.378188 - 3.59821i) q^{16} +(3.60998 - 2.62280i) q^{17} +(-1.81761 - 0.590579i) q^{19} +(-2.30027 - 5.16650i) q^{20} +(-0.550930 + 0.635876i) q^{22} +(-0.706997 + 0.408185i) q^{23} +(-2.36637 - 2.62812i) q^{25} +(0.689029 - 0.223879i) q^{26} +(-3.09345 - 4.25777i) q^{28} +(-9.33798 - 1.98485i) q^{29} +(0.625712 - 5.95326i) q^{31} +(-1.45728 - 2.52408i) q^{32} +(0.565973 - 0.980294i) q^{34} +(-6.42681 - 4.66935i) q^{35} +(1.83750 + 5.65524i) q^{37} +(-0.482157 + 0.0506767i) q^{38} +(-2.16774 - 1.95184i) q^{40} +(-8.24905 + 1.75339i) q^{41} +(10.2852 + 5.93817i) q^{43} +(1.86690 - 6.14238i) q^{44} +(-0.121726 + 0.167542i) q^{46} +(5.73571 - 5.16446i) q^{47} +(-0.358652 - 0.159682i) q^{49} +(-0.819560 - 0.364891i) q^{50} +(-4.10821 + 3.69905i) q^{52} +(-6.14564 + 8.45874i) q^{53} +(-0.185009 - 9.68851i) q^{55} +(-2.35084 - 1.35726i) q^{56} +(-2.36882 + 0.503507i) q^{58} +(-0.0693351 - 0.0624296i) q^{59} +(-2.13230 + 0.224114i) q^{61} +(-0.469246 - 1.44419i) q^{62} +(5.25595 + 3.81867i) q^{64} +(-4.17217 + 7.22641i) q^{65} +(0.703892 + 1.21918i) q^{67} +(-0.902835 + 8.58990i) q^{68} +(-1.97115 - 0.418982i) q^{70} +(-2.12141 - 2.91987i) q^{71} +(-1.67338 + 0.543714i) q^{73} +(1.00933 + 1.12098i) q^{74} +(3.20371 - 1.84966i) q^{76} +(-2.04294 - 8.78322i) q^{77} +(-2.90121 - 6.51621i) q^{79} +(10.0535 + 3.26659i) q^{80} +(-1.73075 + 1.25747i) q^{82} +(-0.818907 - 7.79138i) q^{83} +(2.71060 + 12.7524i) q^{85} +(2.99623 + 0.314916i) q^{86} +(-0.408929 - 3.28589i) q^{88} +2.06830i q^{89} +(-2.39957 + 7.38512i) q^{91} +(0.328543 - 1.54567i) q^{92} +(0.796353 - 1.78864i) q^{94} +(3.73634 - 4.14962i) q^{95} +(1.52602 - 0.679428i) q^{97} -0.0995913 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{4} + 20 q^{16} + 48 q^{22} + 32 q^{25} + 80 q^{28} - 16 q^{31} - 40 q^{34} - 24 q^{37} - 60 q^{40} - 80 q^{46} + 24 q^{49} + 40 q^{52} + 32 q^{55} - 12 q^{58} + 72 q^{64} - 96 q^{67} - 76 q^{70}+ \cdots - 60 q^{97}+O(q^{100}) \) 32 * q + 4 * q^4 + 20 * q^16 + 48 * q^22 + 32 * q^25 + 80 * q^28 - 16 * q^31 - 40 * q^34 - 24 * q^37 - 60 * q^40 - 80 * q^46 + 24 * q^49 + 40 * q^52 + 32 * q^55 - 12 * q^58 + 72 * q^64 - 96 * q^67 - 76 * q^70 - 40 * q^73 - 24 * q^82 + 100 * q^85 + 12 * q^88 - 144 * q^91 + 80 * q^94 - 60 * q^97

Introduction

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