LMFDB - Embedded newform 405.2.r.a.233.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,2,Mod(8,405)] 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("405.8"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([2, 27])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.r (of order $36$, degree $12$, not 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:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			233.4
Character	$\chi$	$=$	405.233
Dual form			405.2.r.a.332.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866263 + 1.23715i) q^{2} +(-0.0960923 - 0.264011i) q^{4} +(-0.525423 - 2.17346i) q^{5} +(1.45360 - 0.677826i) q^{7} +(-2.50778 - 0.671958i) q^{8} +(3.14405 + 1.23276i) q^{10} +(1.78545 + 2.12782i) q^{11} +(-0.251952 + 0.176418i) q^{13} +(-0.420628 + 2.38550i) q^{14} +(3.43416 - 2.88160i) q^{16} +(7.02145 - 1.88139i) q^{17} +(5.07203 - 2.92834i) q^{19} +(-0.523329 + 0.347571i) q^{20} +(-4.17910 + 0.365624i) q^{22} +(0.0543910 - 0.116642i) q^{23} +(-4.44786 + 2.28397i) q^{25} -0.464527i q^{26} +(-0.318634 - 0.318634i) q^{28} +(1.51659 + 8.60103i) q^{29} +(4.22026 - 1.53605i) q^{31} +(0.137538 + 1.57207i) q^{32} +(-3.75485 + 10.3164i) q^{34} +(-2.23699 - 2.80320i) q^{35} +(-0.558369 - 2.08386i) q^{37} +(-0.770913 + 8.81158i) q^{38} +(-0.142827 + 5.80362i) q^{40} +(4.62442 + 0.815410i) q^{41} +(-4.90494 - 0.429127i) q^{43} +(0.390200 - 0.675847i) q^{44} +(0.0971868 + 0.168333i) q^{46} +(-3.58654 - 7.69135i) q^{47} +(-2.84600 + 3.39173i) q^{49} +(1.02740 - 7.48120i) q^{50} +(0.0707870 + 0.0495656i) q^{52} +(0.483003 - 0.483003i) q^{53} +(3.68661 - 4.99861i) q^{55} +(-4.10079 + 0.723079i) q^{56} +(-11.9546 - 5.57450i) q^{58} +(7.43127 + 6.23558i) q^{59} +(2.50049 + 0.910105i) q^{61} +(-1.75553 + 6.55173i) q^{62} +(5.70071 + 3.29131i) q^{64} +(0.515819 + 0.454912i) q^{65} +(0.619257 + 0.884390i) q^{67} +(-1.17142 - 1.67295i) q^{68} +(5.40580 - 0.339179i) q^{70} +(-9.03942 - 5.21891i) q^{71} +(1.78199 - 6.65047i) q^{73} +(3.06175 + 1.11439i) q^{74} +(-1.26050 - 1.05768i) q^{76} +(4.03763 + 1.88278i) q^{77} +(-2.04188 + 0.360038i) q^{79} +(-8.06743 - 5.94995i) q^{80} +(-5.01475 + 5.01475i) q^{82} +(-10.7962 - 7.55956i) q^{83} +(-7.77836 - 14.2723i) q^{85} +(4.77986 - 5.69642i) q^{86} +(-3.04772 - 6.53585i) q^{88} +(-5.58181 - 9.66798i) q^{89} +(-0.246656 + 0.427222i) q^{91} +(-0.0360214 - 0.00315146i) q^{92} +(12.6222 + 2.22564i) q^{94} +(-9.02959 - 9.48524i) q^{95} +(-1.03291 + 11.8062i) q^{97} +(-1.73070 - 6.45906i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	−0.866263	+	1.23715i	−0.612540	+	0.874798i	−0.998868	−	0.0475633i	$-0.984854\pi$
$2$	−0.866263	+	1.23715i	−0.612540	+	0.874798i	0.386328	+	0.922361i	$0.373743\pi$
$3$		0			0
$3$		0			0
$4$	−0.0960923	−	0.264011i	−0.0480461	−	0.132006i
$5$	−0.525423	−	2.17346i	−0.234976	−	0.972001i
$5$	−0.525423	−	2.17346i	−0.234976	−	0.972001i
$6$		0			0
$7$	1.45360	−	0.677826i	0.549410	−	0.256194i	−0.128032	−	0.991770i	$-0.540866\pi$
$7$	1.45360	−	0.677826i	0.549410	−	0.256194i	0.677442	+	0.735576i	$0.263088\pi$
$8$	−2.50778	−	0.671958i	−0.886634	−	0.237573i
$9$		0			0
$10$	3.14405	+	1.23276i	0.994237	+	0.389833i
$11$	1.78545	+	2.12782i	0.538334	+	0.641561i	0.964813	−	0.262936i	$-0.0846908\pi$
$11$	1.78545	+	2.12782i	0.538334	+	0.641561i	−0.426479	+	0.904497i	$0.640246\pi$
$12$		0			0
$13$	−0.251952	+	0.176418i	−0.0698788	+	0.0489296i	−0.607994	−	0.793942i	$-0.708025\pi$
$13$	−0.251952	+	0.176418i	−0.0698788	+	0.0489296i	0.538115	+	0.842871i	$0.319137\pi$
$14$	−0.420628	+	2.38550i	−0.112418	+	0.637552i
$15$		0			0
$16$	3.43416	−	2.88160i	0.858539	−	0.720400i
$17$	7.02145	−	1.88139i	1.70295	−	0.456304i	0.729271	−	0.684225i	$-0.239859\pi$
$17$	7.02145	−	1.88139i	1.70295	−	0.456304i	0.973680	+	0.227921i	$0.0731927\pi$
$18$		0			0
$19$	5.07203	−	2.92834i	1.16360	−	0.671807i	0.211439	−	0.977391i	$-0.432185\pi$
$19$	5.07203	−	2.92834i	1.16360	−	0.671807i	0.952165	+	0.305584i	$0.0988518\pi$
$20$	−0.523329	+	0.347571i	−0.117020	+	0.0777191i
$21$		0			0
$22$	−4.17910	+	0.365624i	−0.890988	+	0.0779514i
$23$	0.0543910	−	0.116642i	0.0113413	−	0.0243215i	−0.900556	−	0.434741i	$-0.856840\pi$
$23$	0.0543910	−	0.116642i	0.0113413	−	0.0243215i	0.911897	+	0.410419i	$0.134618\pi$
$24$		0			0
$25$	−4.44786	+	2.28397i	−0.889572	+	0.456795i
$26$		−	0.464527i		−	0.0911012i
$27$		0			0
$28$	−0.318634	−	0.318634i	−0.0602161	−	0.0602161i
$29$	1.51659	+	8.60103i	0.281625	+	1.59717i	0.717099	+	0.696971i	$0.245469\pi$
$29$	1.51659	+	8.60103i	0.281625	+	1.59717i	−0.435475	+	0.900201i	$0.643419\pi$
$30$		0			0
$31$	4.22026	−	1.53605i	0.757981	−	0.275883i	0.0660211	−	0.997818i	$-0.478970\pi$
$31$	4.22026	−	1.53605i	0.757981	−	0.275883i	0.691960	+	0.721936i	$0.256747\pi$
$32$	0.137538	+	1.57207i	0.0243135	+	0.277905i
$33$		0			0
$34$	−3.75485	+	10.3164i	−0.643952	+	1.76924i
$35$	−2.23699	−	2.80320i	−0.378119	−	0.473828i
$36$		0			0
$37$	−0.558369	−	2.08386i	−0.0917953	−	0.342585i	0.904719	−	0.426009i	$-0.140081\pi$
$37$	−0.558369	−	2.08386i	−0.0917953	−	0.342585i	−0.996514	+	0.0834245i	$0.973414\pi$
$38$	−0.770913	+	8.81158i	−0.125059	+	1.42943i
$39$		0			0
$40$	−0.142827	+	5.80362i	−0.0225830	+	0.917633i
$41$	4.62442	+	0.815410i	0.722213	+	0.127346i	0.522660	−	0.852541i	$-0.324940\pi$
$41$	4.62442	+	0.815410i	0.722213	+	0.127346i	0.199553	+	0.979887i	$0.436051\pi$
$42$		0			0
$43$	−4.90494	−	0.429127i	−0.747997	−	0.0654412i	−0.293218	−	0.956046i	$-0.594726\pi$
$43$	−4.90494	−	0.429127i	−0.747997	−	0.0654412i	−0.454779	+	0.890604i	$0.650282\pi$
$44$	0.390200	−	0.675847i	0.0588249	−	0.101888i
$45$		0			0
$46$	0.0971868	+	0.168333i	0.0143294	+	0.0248193i
$47$	−3.58654	−	7.69135i	−0.523150	−	1.12190i	−0.973424	−	0.229009i	$-0.926452\pi$
$47$	−3.58654	−	7.69135i	−0.523150	−	1.12190i	0.450274	−	0.892890i	$-0.351326\pi$
$48$		0			0
$49$	−2.84600	+	3.39173i	−0.406571	+	0.484533i
$50$	1.02740	−	7.48120i	0.145296	−	1.05800i
$51$		0			0
$52$	0.0707870	+	0.0495656i	0.00981640	+	0.00687352i
$53$	0.483003	−	0.483003i	0.0663456	−	0.0663456i	−0.673155	−	0.739501i	$-0.735062\pi$
$53$	0.483003	−	0.483003i	0.0663456	−	0.0663456i	0.739501	+	0.673155i	$0.235062\pi$
$54$		0			0
$55$	3.68661	−	4.99861i	0.497103	−	0.674013i
$56$	−4.10079	+	0.723079i	−0.547991	+	0.0966255i
$57$		0			0
$58$	−11.9546	−	5.57450i	−1.56971	−	0.731968i
$59$	7.43127	+	6.23558i	0.967469	+	0.811803i	0.982152	−	0.188089i	$-0.0602295\pi$
$59$	7.43127	+	6.23558i	0.967469	+	0.811803i	−0.0146830	+	0.999892i	$0.504674\pi$
$60$		0			0
$61$	2.50049	+	0.910105i	0.320155	+	0.116527i	0.497099	−	0.867694i	$-0.334399\pi$
$61$	2.50049	+	0.910105i	0.320155	+	0.116527i	−0.176943	+	0.984221i	$0.556621\pi$
$62$	−1.75553	+	6.55173i	−0.222952	+	0.832070i
$63$		0			0
$64$	5.70071	+	3.29131i	0.712589	+	0.411413i
$65$	0.515819	+	0.454912i	0.0639795	+	0.0564249i
$66$		0			0
$67$	0.619257	+	0.884390i	0.0756543	+	0.108045i	0.855196	−	0.518305i	$-0.173437\pi$
$67$	0.619257	+	0.884390i	0.0756543	+	0.108045i	−0.779542	+	0.626350i	$0.784548\pi$
$68$	−1.17142	−	1.67295i	−0.142055	−	0.202876i
$69$		0			0
$70$	5.40580	−	0.339179i	0.646117	−	0.0405397i
$71$	−9.03942	−	5.21891i	−1.07278	−	0.619371i	−0.143842	−	0.989601i	$-0.545946\pi$
$71$	−9.03942	−	5.21891i	−1.07278	−	0.619371i	−0.928940	+	0.370230i	$0.879279\pi$
$72$		0			0
$73$	1.78199	−	6.65047i	0.208566	−	0.778378i	−0.779767	−	0.626070i	$-0.784663\pi$
$73$	1.78199	−	6.65047i	0.208566	−	0.778378i	0.988333	−	0.152309i	$-0.0486707\pi$
$74$	3.06175	+	1.11439i	0.355921	+	0.129545i
$75$		0			0
$76$	−1.26050	−	1.05768i	−0.144589	−	0.121325i
$77$	4.03763	+	1.88278i	0.460130	+	0.214562i
$78$		0			0
$79$	−2.04188	+	0.360038i	−0.229729	+	0.0405074i	−0.287327	−	0.957832i	$-0.592767\pi$
$79$	−2.04188	+	0.360038i	−0.229729	+	0.0405074i	0.0575985	+	0.998340i	$0.481656\pi$
$80$	−8.06743	−	5.94995i	−0.901966	−	0.665224i
$81$		0			0
$82$	−5.01475	+	5.01475i	−0.553787	+	0.553787i
$83$	−10.7962	−	7.55956i	−1.18503	−	0.829770i	−0.196461	−	0.980512i	$-0.562945\pi$
$83$	−10.7962	−	7.55956i	−1.18503	−	0.829770i	−0.988573	+	0.150742i	$0.951834\pi$
$84$		0			0
$85$	−7.77836	−	14.2723i	−0.843681	−	1.54805i
$86$	4.77986	−	5.69642i	0.515426	−	0.614261i
$87$		0			0
$88$	−3.04772	−	6.53585i	−0.324888	−	0.696724i
$89$	−5.58181	−	9.66798i	−0.591671	−	1.02480i	−0.994007	−	0.109312i	$-0.965135\pi$
$89$	−5.58181	−	9.66798i	−0.591671	−	1.02480i	0.402337	−	0.915492i	$-0.368198\pi$
$90$		0			0
$91$	−0.246656	+	0.427222i	−0.0258566	+	0.0447850i
$92$	−0.0360214	−	0.00315146i	−0.00375549	−	0.000328562i
$93$		0			0
$94$	12.6222	+	2.22564i	1.30189	+	0.229558i
$95$	−9.02959	−	9.48524i	−0.926416	−	0.973165i
$96$		0			0
$97$	−1.03291	+	11.8062i	−0.104876	+	1.19874i	0.743275	+	0.668986i	$0.233271\pi$
$97$	−1.03291	+	11.8062i	−0.104876	+	1.19874i	−0.848151	+	0.529754i	$0.822284\pi$
$98$	−1.73070	−	6.45906i	−0.174827	−	0.652464i
$99$		0			0
$100$	1.03040	+	0.954814i	0.103040	+	0.0954814i
$101$	4.61138	−	12.6697i	0.458850	−	1.26068i	−0.467493	−	0.883997i	$-0.654843\pi$
$101$	4.61138	−	12.6697i	0.458850	−	1.26068i	0.926343	−	0.376682i	$-0.122935\pi$
$102$		0			0
$103$	0.259260	+	2.96335i	0.0255456	+	0.291988i	0.998212	+	0.0597791i	$0.0190396\pi$
$103$	0.259260	+	2.96335i	0.0255456	+	0.291988i	−0.972666	+	0.232209i	$0.925405\pi$
$104$	0.750384	−	0.273118i	0.0735813	−	0.0267814i
$105$		0			0
$106$	0.179140	+	1.01596i	0.0173997	+	0.0986783i
$107$	7.80800	+	7.80800i	0.754828	+	0.754828i	0.975376	−	0.220548i	$-0.0707846\pi$
$107$	7.80800	+	7.80800i	0.754828	+	0.754828i	−0.220548	+	0.975376i	$0.570785\pi$
$108$		0			0
$109$			0.464359i			0.0444775i	0.999753	+	0.0222388i	$0.00707940\pi$
$109$			0.464359i			0.0444775i	−0.999753	+	0.0222388i	$0.992921\pi$
$110$	2.99047	+	8.89101i	0.285130	+	0.847725i
$111$		0			0
$112$	3.03868	−	6.51646i	0.287128	−	0.615748i
$113$	0.477053	−	0.0417367i	0.0448774	−	0.00392626i	−0.0646950	−	0.997905i	$-0.520607\pi$
$113$	0.477053	−	0.0417367i	0.0448774	−	0.00392626i	0.109572	+	0.993979i	$0.465052\pi$
$114$		0			0
$115$	−0.282095	−	0.0569304i	−0.0263055	−	0.00530878i
$116$	2.12504	−	1.22689i	0.197305	−	0.113914i
$117$		0			0
$118$	−14.1518	+	3.79196i	−1.30278	+	0.349078i
$119$	8.93114	−	7.49411i	0.818716	−	0.686984i
$120$		0			0
$121$	0.570356	−	3.23465i	0.0518506	−	0.294059i
$122$	−3.29202	+	2.30510i	−0.298046	+	0.208694i
$123$		0			0
$124$	−0.811069	−	0.966595i	−0.0728362	−	0.0868028i
$125$	7.30114	+	8.46720i	0.653033	+	0.757329i
$126$		0			0
$127$	−12.9954	−	3.48210i	−1.15315	−	0.308987i	−0.368925	−	0.929459i	$-0.620274\pi$
$127$	−12.9954	−	3.48210i	−1.15315	−	0.308987i	−0.784228	+	0.620473i	$0.786941\pi$
$128$	−11.8706	+	5.53535i	−1.04922	+	0.489260i
$129$		0			0
$130$	−1.00963	+	0.244073i	−0.0885505	+	0.0214066i
$131$	2.11500	+	5.81092i	0.184788	+	0.507702i	0.997149	−	0.0754528i	$-0.0240402\pi$
$131$	2.11500	+	5.81092i	0.184788	+	0.507702i	−0.812361	+	0.583155i	$0.801818\pi$
$132$		0			0
$133$	5.38781	−	7.69460i	0.467183	−	0.667206i
$134$	−1.63056			−0.140859
$135$		0			0
$136$	−18.8725			−1.61830
$137$	4.23537	−	6.04873i	0.361852	−	0.516778i	−0.596406	−	0.802683i	$-0.703405\pi$
$137$	4.23537	−	6.04873i	0.361852	−	0.516778i	0.958258	+	0.285905i	$0.0922942\pi$
$138$		0			0
$139$	−3.50715	−	9.63582i	−0.297473	−	0.817299i	−0.994921	−	0.100664i	$-0.967903\pi$
$139$	−3.50715	−	9.63582i	−0.297473	−	0.817299i	0.697448	−	0.716635i	$-0.254319\pi$
$140$	−0.525120	+	0.859956i	−0.0443808	+	0.0726795i
$141$		0			0
$142$	14.2871	−	6.66218i	1.19895	−	0.559078i
$143$	−0.825233	−	0.221121i	−0.0690095	−	0.0184910i
$144$		0			0
$145$	17.8972	−	7.81544i	1.48628	−	0.649037i
$146$	6.68396	+	7.96564i	0.553169	+	0.659241i
$147$		0			0
$148$	−0.496508	+	0.347659i	−0.0408127	+	0.0285774i
$149$	−0.210055	+	1.19128i	−0.0172084	+	0.0975937i	−0.992202	−	0.124638i	$-0.960223\pi$
$149$	−0.210055	+	1.19128i	−0.0172084	+	0.0975937i	0.974994	+	0.222232i	$0.0713341\pi$
$150$		0			0
$151$	−12.3858	+	10.3930i	−1.00795	+	0.845766i	−0.988065	−	0.154036i	$-0.950773\pi$
$151$	−12.3858	+	10.3930i	−1.00795	+	0.845766i	−0.0198800	+	0.999802i	$0.506328\pi$
$152$	−14.6873	+	3.93544i	−1.19129	+	0.319206i
$153$		0			0
$154$	−5.82693	+	3.36418i	−0.469547	+	0.271093i
$155$	−5.55597	−	8.36550i	−0.446266	−	0.671933i
$156$		0			0
$157$	−20.6680	+	1.80822i	−1.64949	+	0.144311i	−0.873627	−	0.486596i	$-0.838238\pi$
$157$	−20.6680	+	1.80822i	−1.64949	+	0.144311i	−0.775858	+	0.630907i	$0.782683\pi$
$158$	1.32338	−	2.83800i	0.105282	−	0.225779i
$159$		0			0
$160$	3.34456	−	1.12493i	0.264411	−	0.0889338i
$161$		−	0.206419i		−	0.0162681i
$162$		0			0
$163$	9.24417	+	9.24417i	0.724060	+	0.724060i	0.969430	−	0.245370i	$-0.0789094\pi$
$163$	9.24417	+	9.24417i	0.724060	+	0.724060i	−0.245370	+	0.969430i	$0.578909\pi$
$164$	−0.229094	−	1.29925i	−0.0178892	−	0.101455i
$165$		0			0
$166$	18.7046	−	6.80794i	1.45176	−	0.528398i
$167$	1.40245	+	16.0301i	0.108525	+	1.24044i	0.833832	+	0.552018i	$0.186142\pi$
$167$	1.40245	+	16.0301i	0.108525	+	1.24044i	−0.725307	+	0.688425i	$0.758302\pi$
$168$		0			0
$169$	−4.41391	+	12.1271i	−0.339531	+	0.932854i
$170$	24.3951	+	2.74056i	1.87102	+	0.210191i
$171$		0			0
$172$	0.358033	+	1.33620i	0.0272997	+	0.101884i
$173$	−0.231197	+	2.64260i	−0.0175776	+	0.200913i	0.982328	+	0.187168i	$0.0599308\pi$
$173$	−0.231197	+	2.64260i	−0.0175776	+	0.200913i	−0.999906	+	0.0137449i	$0.995625\pi$
$174$		0			0
$175$	−4.91729	+	6.33487i	−0.371712	+	0.478871i
$176$	12.2630	+	2.16231i	0.924362	+	0.162990i
$177$		0			0
$178$	16.7961	+	1.46947i	1.25892	+	0.110141i
$179$	−3.43088	+	5.94245i	−0.256436	+	0.444160i	−0.965284	−	0.261201i	$-0.915882\pi$
$179$	−3.43088	+	5.94245i	−0.256436	+	0.444160i	0.708849	+	0.705360i	$0.249215\pi$
$180$		0			0
$181$	10.0120	+	17.3412i	0.744183	+	1.28896i	0.950575	+	0.310494i	$0.100494\pi$
$181$	10.0120	+	17.3412i	0.744183	+	1.28896i	−0.206392	+	0.978469i	$0.566172\pi$
$182$	−0.314868	−	0.675238i	−0.0233396	−	0.0500519i
$183$		0			0
$184$	−0.214779	+	0.255964i	−0.0158337	+	0.0188699i
$185$	−4.23581	+	2.30850i	−0.311423	+	0.169725i
$186$		0			0
$187$	16.5397	+	11.5812i	1.20950	+	0.846903i
$188$	−1.68597	+	1.68597i	−0.122962	+	0.122962i
$189$		0			0
$190$	19.5567	−	2.95426i	1.41879	−	0.214325i
$191$	−9.22577	+	1.62675i	−0.667553	+	0.117708i	−0.497147	−	0.867666i	$-0.665619\pi$
$191$	−9.22577	+	1.62675i	−0.667553	+	0.117708i	−0.170406	+	0.985374i	$0.554508\pi$
$192$		0			0
$193$	19.1014	+	8.90711i	1.37495	+	0.641148i	0.962861	−	0.269998i	$-0.0870230\pi$
$193$	19.1014	+	8.90711i	1.37495	+	0.641148i	0.412085	+	0.911146i	$0.364801\pi$
$194$	−13.7113	−	11.5052i	−0.984414	−	0.826022i
$195$		0			0
$196$	1.16893	+	0.425457i	0.0834953	+	0.0303898i
$197$	−1.90191	+	7.09801i	−0.135505	+	0.505712i	0.864490	+	0.502650i	$0.167642\pi$
$197$	−1.90191	+	7.09801i	−0.135505	+	0.505712i	−0.999995	+	0.00306257i	$0.999025\pi$
$198$		0			0
$199$	−22.3449	−	12.9008i	−1.58399	−	0.914516i	−0.994269	−	0.106906i	$-0.965905\pi$
$199$	−22.3449	−	12.9008i	−1.58399	−	0.914516i	−0.589718	−	0.807609i	$-0.700761\pi$
$200$	12.6890	−	2.73893i	0.897247	−	0.193671i
$201$		0			0
$202$	11.6796	+	16.6802i	0.821776	+	1.17362i
$203$	8.03453	+	11.4745i	0.563914	+	0.805352i
$204$		0			0
$205$	−0.657517	−	10.4794i	−0.0459230	−	0.731915i
$206$	−3.89070	−	2.24630i	−0.271078	−	0.156507i
$207$		0			0
$208$	−0.356874	+	1.33187i	−0.0247448	+	0.0923487i
$209$	15.2868	+	5.56395i	1.05741	+	0.384867i
$210$		0			0
$211$	−0.268205	−	0.225051i	−0.0184640	−	0.0154932i	0.633509	−	0.773735i	$-0.281614\pi$
$211$	−0.268205	−	0.225051i	−0.0184640	−	0.0154932i	−0.651973	+	0.758242i	$0.726058\pi$
$212$	−0.173931	−	0.0811054i	−0.0119456	−	0.00557035i
$213$		0			0
$214$	−16.4235	+	2.89590i	−1.12268	+	0.197960i
$215$	1.64448	+	10.8862i	0.112153	+	0.742431i
$216$		0			0
$217$	5.09341	−	5.09341i	0.345763	−	0.345763i
$218$	−0.574483	−	0.402257i	−0.0389089	−	0.0272443i
$219$		0			0
$220$	−1.67395	−	0.492979i	−0.112857	−	0.0332366i
$221$	−1.43715	+	1.71273i	−0.0966733	+	0.115211i
$222$		0			0
$223$	−6.64028	−	14.2401i	−0.444666	−	0.953590i	−0.993086	−	0.117387i	$-0.962548\pi$
$223$	−6.64028	−	14.2401i	−0.444666	−	0.953590i	0.548420	−	0.836203i	$-0.315230\pi$
$224$	1.26551	+	2.19193i	0.0845557	+	0.146455i
$225$		0			0
$226$	−0.361618	+	0.626342i	−0.0240545	+	0.0416636i
$227$	−23.4570	−	2.05222i	−1.55690	−	0.136211i	−0.724064	−	0.689733i	$-0.757728\pi$
$227$	−23.4570	−	2.05222i	−1.55690	−	0.136211i	−0.832834	+	0.553522i	$0.813283\pi$
$228$		0			0
$229$	22.8004	+	4.02032i	1.50669	+	0.265671i	0.865188	−	0.501448i	$-0.167199\pi$
$229$	22.8004	+	4.02032i	1.50669	+	0.265671i	0.641505	+	0.767119i	$0.278310\pi$
$230$	0.314800	−	0.299678i	0.0207573	−	0.0197602i
$231$		0			0
$232$	1.97625	−	22.5886i	0.129747	−	1.48301i
$233$	5.59828	+	20.8931i	0.366755	+	1.36875i	0.865026	+	0.501728i	$0.167302\pi$
$233$	5.59828	+	20.8931i	0.366755	+	1.36875i	−0.498270	+	0.867022i	$0.666031\pi$
$234$		0			0
$235$	−14.8324	+	11.8364i	−0.967559	+	0.772122i
$236$	0.932175	−	2.56113i	0.0606794	−	0.166715i
$237$		0			0
$238$	1.53464	+	17.5410i	0.0994761	+	1.13702i
$239$	−13.3597	+	4.86252i	−0.864165	+	0.314530i	−0.735802	−	0.677197i	$-0.763195\pi$
$239$	−13.3597	+	4.86252i	−0.864165	+	0.314530i	−0.128363	+	0.991727i	$0.540972\pi$
$240$		0			0
$241$	−1.44826	−	8.21348i	−0.0932905	−	0.529077i	−0.995258	−	0.0972724i	$-0.968988\pi$
$241$	−1.44826	−	8.21348i	−0.0932905	−	0.529077i	0.901967	−	0.431804i	$-0.142123\pi$
$242$	3.50767	+	3.50767i	0.225482	+	0.225482i
$243$		0			0
$244$		−	0.747612i		−	0.0478610i
$245$	8.86715	+	4.40357i	0.566501	+	0.281334i
$246$		0			0
$247$	−0.761293	+	1.63260i	−0.0484399	+	0.103880i
$248$	−11.6156	+	1.01624i	−0.737594	+	0.0645311i
$249$		0			0
$250$	−16.7999	+	1.69779i	−1.06252	+	0.107378i
$251$	−4.13040	+	2.38469i	−0.260708	+	0.150520i	−0.624658	−	0.780899i	$-0.714761\pi$
$251$	−4.13040	+	2.38469i	−0.260708	+	0.150520i	0.363949	+	0.931419i	$0.381428\pi$
$252$		0			0
$253$	0.345305	−	0.0925243i	0.0217092	−	0.00581695i
$254$	15.5653	−	13.0608i	0.976654	−	0.819510i
$255$		0			0
$256$	1.14887	−	6.51557i	0.0718045	−	0.407223i
$257$	3.86684	−	2.70759i	0.241207	−	0.168895i	−0.446722	−	0.894673i	$-0.647409\pi$
$257$	3.86684	−	2.70759i	0.241207	−	0.168895i	0.687929	+	0.725778i	$0.258520\pi$
$258$		0			0
$259$	−2.22414	−	2.65063i	−0.138202	−	0.164702i
$260$	0.0705358	−	0.179896i	0.00437444	−	0.0111567i
$261$		0			0
$262$	−9.02113	−	2.41720i	−0.557327	−	0.149335i
$263$	3.01862	−	1.40761i	0.186136	−	0.0867967i	−0.327316	−	0.944915i	$-0.606144\pi$
$263$	3.01862	−	1.40761i	0.186136	−	0.0867967i	0.513452	+	0.858118i	$0.328366\pi$
$264$		0			0
$265$	−1.30357	−	0.796007i	−0.0800776	−	0.0488983i
$266$	4.85212	+	13.3311i	0.297502	+	0.817381i
$267$		0			0
$268$	0.173983	−	0.248474i	0.0106277	−	0.0151780i
$269$	−8.37429			−0.510589			−0.255295	−	0.966863i	$-0.582172\pi$
$269$	−8.37429			−0.510589			−0.255295	+	0.966863i	$0.582172\pi$
$270$		0			0
$271$	−13.7893			−0.837641			−0.418821	−	0.908069i	$-0.637556\pi$
$271$	−13.7893			−0.837641			−0.418821	+	0.908069i	$0.637556\pi$
$272$	18.6913	−	26.6940i	1.13333	−	1.61856i
$273$		0			0
$274$	3.81425	+	10.4796i	0.230428	+	0.633094i
$275$	−12.8013	−	5.38632i	−0.771949	−	0.324807i
$276$		0			0
$277$	0.111462	−	0.0519757i	0.00669711	−	0.00312292i	−0.419267	−	0.907863i	$-0.637713\pi$
$277$	0.111462	−	0.0519757i	0.00669711	−	0.00312292i	0.425964	+	0.904740i	$0.359935\pi$
$278$	14.9591	+	4.00827i	0.897186	+	0.240400i
$279$		0			0
$280$	3.72623	+	8.53297i	0.222685	+	0.509943i
$281$	−15.4444	−	18.4059i	−0.921334	−	1.09800i	−0.994915	−	0.100714i	$-0.967887\pi$
$281$	−15.4444	−	18.4059i	−0.921334	−	1.09800i	0.0735813	−	0.997289i	$-0.476557\pi$
$282$		0			0
$283$	13.0589	−	9.14396i	0.776273	−	0.543552i	−0.116965	−	0.993136i	$-0.537317\pi$
$283$	13.0589	−	9.14396i	0.776273	−	0.543552i	0.893238	+	0.449584i	$0.148428\pi$
$284$	−0.509233	+	2.88801i	−0.0302174	+	0.171372i
$285$		0			0
$286$	0.988429	−	0.829390i	0.0584470	−	0.0490429i
$287$	7.27478	−	1.94927i	0.429417	−	0.115062i
$288$		0			0
$289$	31.0386	−	17.9202i	1.82580	−	1.05413i
$290$	−5.83475	+	28.9117i	−0.342629	+	1.69775i
$291$		0			0
$292$	−1.92703	+	0.168594i	−0.112771	+	0.00986619i
$293$	−2.22735	+	4.77657i	−0.130123	+	0.279050i	−0.960565	−	0.278055i	$-0.910310\pi$
$293$	−2.22735	+	4.77657i	−0.130123	+	0.279050i	0.830442	+	0.557105i	$0.188088\pi$
$294$		0			0
$295$	9.64822	−	19.4279i	0.561741	−	1.13114i
$296$			5.60107i			0.325555i
$297$		0			0
$298$	−1.29183	−	1.29183i	−0.0748340	−	0.0748340i
$299$	0.00687388	+	0.0389837i	0.000397526	+	0.00225448i
$300$		0			0
$301$	−7.42071	+	2.70092i	−0.427723	+	0.155678i
$302$	−2.12827	−	24.3262i	−0.122468	−	1.39981i
$303$		0			0
$304$	8.97985	−	24.6719i	0.515030	−	1.41503i
$305$	0.664260	−	5.91291i	0.0380354	−	0.338572i
$306$		0			0
$307$	5.72834	+	21.3785i	0.326934	+	1.22013i	0.912353	+	0.409403i	$0.134263\pi$
$307$	5.72834	+	21.3785i	0.326934	+	1.22013i	−0.585420	+	0.810730i	$0.699070\pi$
$308$	0.109090	−	1.24690i	0.00621596	−	0.0710487i
$309$		0			0
$310$	15.1623	+	0.373145i	0.861161	+	0.0211932i
$311$	−14.1711	−	2.49874i	−0.803567	−	0.141691i	−0.243244	−	0.969965i	$-0.578212\pi$
$311$	−14.1711	−	2.49874i	−0.803567	−	0.141691i	−0.560322	+	0.828275i	$0.689323\pi$
$312$		0			0
$313$	−21.1736	−	1.85245i	−1.19680	−	0.104707i	−0.528722	−	0.848795i	$-0.677329\pi$
$313$	−21.1736	−	1.85245i	−1.19680	−	0.104707i	−0.668081	+	0.744088i	$0.732884\pi$
$314$	15.6669	−	27.1358i	0.884133	−	1.53136i
$315$		0			0
$316$	0.291263	+	0.504482i	0.0163848	+	0.0283793i
$317$	9.71542	+	20.8348i	0.545672	+	1.17020i	0.964973	+	0.262350i	$0.0844976\pi$
$317$	9.71542	+	20.8348i	0.545672	+	1.17020i	−0.419300	+	0.907848i	$0.637725\pi$
$318$		0			0
$319$	−15.5936	+	18.5838i	−0.873076	+	1.04049i
$320$	4.15824	−	14.1196i	0.232453	−	0.789310i
$321$		0			0
$322$	0.255371	+	0.178813i	0.0142313	+	0.00996485i
$323$	30.1036	−	30.1036i	1.67501	−	1.67501i
$324$		0			0
$325$	0.717710	−	1.36013i	0.0398114	−	0.0754467i
$326$	−19.4443	+	3.42856i	−1.07692	+	0.189890i
$327$		0			0
$328$	−11.0491	−	5.15228i	−0.610085	−	0.284487i
$329$	−10.4268	−	8.74912i	−0.574848	−	0.482355i
$330$		0			0
$331$	13.1133	+	4.77285i	0.720772	+	0.262340i	0.676253	−	0.736669i	$-0.263602\pi$
$331$	13.1133	+	4.77285i	0.720772	+	0.262340i	0.0445184	+	0.999009i	$0.485825\pi$
$332$	−0.958382	+	3.57673i	−0.0525980	+	0.196298i
$333$		0			0
$334$	−21.0465	−	12.1512i	−1.15161	−	0.664884i
$335$	1.59682	−	1.81061i	0.0872434	−	0.0989242i
$336$		0			0
$337$	−8.31162	−	11.8702i	−0.452763	−	0.646612i	0.526269	−	0.850318i	$-0.323590\pi$
$337$	−8.31162	−	11.8702i	−0.452763	−	0.646612i	−0.979032	+	0.203705i	$0.934701\pi$
$338$	−11.1795	−	15.9659i	−0.608083	−	0.868432i
$339$		0			0
$340$	−3.02061	+	3.42503i	−0.163816	+	0.185749i
$341$	10.8035	+	6.23741i	0.585043	+	0.337775i
$342$		0			0
$343$	−4.74374	+	17.7039i	−0.256138	+	0.955920i
$344$	12.0122	+	4.37207i	0.647652	+	0.235726i
$345$		0			0
$346$	−3.06901	−	2.57521i	−0.164991	−	0.138444i
$347$	−8.22815	−	3.83685i	−0.441710	−	0.205973i	0.189023	−	0.981973i	$-0.439468\pi$
$347$	−8.22815	−	3.83685i	−0.441710	−	0.205973i	−0.630733	+	0.776000i	$0.717246\pi$
$348$		0			0
$349$	−8.20842	+	1.44737i	−0.439387	+	0.0774757i	−0.388966	−	0.921252i	$-0.627167\pi$
$349$	−8.20842	+	1.44737i	−0.439387	+	0.0774757i	−0.0504212	+	0.998728i	$0.516056\pi$
$350$	−3.57753	−	11.5711i	−0.191227	−	0.618501i
$351$		0			0
$352$	−3.09950	+	3.09950i	−0.165204	+	0.165204i
$353$	2.16366	+	1.51501i	0.115160	+	0.0806358i	0.629738	−	0.776808i	$-0.283162\pi$
$353$	2.16366	+	1.51501i	0.115160	+	0.0806358i	−0.514578	+	0.857444i	$0.672051\pi$
$354$		0			0
$355$	−6.59358	+	22.3890i	−0.349951	+	1.18828i
$356$	−2.01609	+	2.40268i	−0.106852	+	0.127342i
$357$		0			0
$358$	−4.37967	−	9.39224i	−0.231473	−	0.496395i
$359$	−7.06131	−	12.2306i	−0.372682	−	0.645504i	0.617295	−	0.786732i	$-0.288228\pi$
$359$	−7.06131	−	12.2306i	−0.372682	−	0.645504i	−0.989977	+	0.141228i	$0.954895\pi$
$360$		0			0
$361$	7.65033	−	13.2508i	0.402649	−	0.697408i
$362$	−30.1267	−	2.63575i	−1.58342	−	0.138532i
$363$		0			0
$364$	0.136493	+	0.0240674i	0.00715418	+	0.00126148i
$365$	−15.3908	−	0.378769i	−0.805592	−	0.0198257i
$366$		0			0
$367$	−1.20011	+	13.7173i	−0.0626451	+	0.716037i	0.898315	+	0.439351i	$0.144792\pi$
$367$	−1.20011	+	13.7173i	−0.0626451	+	0.716037i	−0.960961	+	0.276686i	$0.910764\pi$
$368$	−0.149328	−	0.557300i	−0.00778426	−	0.0290513i
$369$		0			0
$370$	0.813358	−	7.24011i	0.0422845	−	0.376396i
$371$	0.374703	−	1.02949i	0.0194536	−	0.0534483i
$372$		0			0
$373$	−1.77048	−	20.2366i	−0.0916718	−	1.04781i	−0.893141	−	0.449777i	$-0.851503\pi$
$373$	−1.77048	−	20.2366i	−0.0916718	−	1.04781i	0.801469	−	0.598036i	$-0.204052\pi$
$374$	−28.6555	+	10.4297i	−1.48174	+	0.539309i
$375$		0			0
$376$	3.82598	+	21.6982i	0.197310	+	1.11900i
$377$	−1.89949	−	1.89949i	−0.0978286	−	0.0978286i
$378$		0			0
$379$		−	20.8542i		−	1.07121i	−0.844469	−	0.535605i	$-0.820084\pi$
$379$		−	20.8542i		−	1.07121i	0.844469	−	0.535605i	$-0.179916\pi$
$380$	−1.63654	+	3.29537i	−0.0839526	+	0.169049i
$381$		0			0
$382$	5.97940	−	12.8229i	0.305933	−	0.656075i
$383$	14.6116	−	1.27835i	0.746618	−	0.0653206i	0.292504	−	0.956264i	$-0.405512\pi$
$383$	14.6116	−	1.27835i	0.746618	−	0.0653206i	0.454114	+	0.890944i	$0.349956\pi$
$384$		0			0
$385$	1.97068	−	9.76488i	0.100435	−	0.497664i
$386$	−27.5662	+	15.9154i	−1.40308	+	0.810071i
$387$		0			0
$388$	3.21623	−	0.861786i	0.163279	−	0.0437506i
$389$	−4.79561	+	4.02400i	−0.243147	+	0.204025i	−0.756215	−	0.654323i	$-0.772953\pi$
$389$	−4.79561	+	4.02400i	−0.243147	+	0.204025i	0.513067	+	0.858348i	$0.328509\pi$
$390$		0			0
$391$	0.162455	−	0.921326i	0.00821568	−	0.0465934i
$392$	9.41624	−	6.59332i	0.475592	−	0.333013i
$393$		0			0
$394$	−7.13377	−	8.50169i	−0.359394	−	0.428309i
$395$	1.85538	+	4.24876i	0.0933541	+	0.213779i
$396$		0			0
$397$	−0.450577	−	0.120732i	−0.0226138	−	0.00605935i	0.247494	−	0.968889i	$-0.420393\pi$
$397$	−0.450577	−	0.120732i	−0.0226138	−	0.00605935i	−0.270108	+	0.962830i	$0.587059\pi$
$398$	35.3168	−	16.4685i	1.77027	−	0.825492i
$399$		0			0
$400$	−8.69316	+	20.6605i	−0.434658	+	1.03302i
$401$	−3.19304	−	8.77280i	−0.159453	−	0.438093i	0.834079	−	0.551644i	$-0.185999\pi$
$401$	−3.19304	−	8.77280i	−0.159453	−	0.438093i	−0.993532	+	0.113552i	$0.963777\pi$
$402$		0			0
$403$	−0.792314	+	1.13154i	−0.0394680	+	0.0563661i
$404$	−3.78805			−0.188463
$405$		0			0
$406$	−21.1557			−1.04994
$407$	3.43714	−	4.90874i	0.170373	−	0.243317i
$408$		0			0
$409$	0.240362	+	0.660389i	0.0118851	+	0.0326541i	0.945493	−	0.325641i	$-0.105580\pi$
$409$	0.240362	+	0.660389i	0.0118851	+	0.0326541i	−0.933608	+	0.358296i	$0.883358\pi$
$410$	13.5342	+	8.26450i	0.668408	+	0.408154i
$411$		0			0
$412$	0.757446	−	0.353203i	0.0373167	−	0.0174010i
$413$	15.0288	+	4.02694i	0.739517	+	0.198153i
$414$		0			0
$415$	−10.7578	+	27.4370i	−0.528082	+	1.34683i
$416$	−0.311994	−	0.371820i	−0.0152968	−	0.0182300i
$417$		0			0
$418$	−20.1259	+	14.0923i	−0.984389	+	0.689276i
$419$	−3.72329	+	21.1158i	−0.181894	+	1.03157i	0.747986	+	0.663714i	$0.231021\pi$
$419$	−3.72329	+	21.1158i	−0.181894	+	1.03157i	−0.929881	+	0.367861i	$0.880090\pi$
$420$		0			0
$421$	13.6486	−	11.4526i	0.665194	−	0.558164i	−0.246445	−	0.969157i	$-0.579262\pi$
$421$	13.6486	−	11.4526i	0.665194	−	0.558164i	0.911638	+	0.410993i	$0.134818\pi$
$422$	0.510759	−	0.136857i	0.0248633	−	0.00666211i
$423$		0			0
$424$	−1.53582	+	0.886708i	−0.0745862	+	0.0430623i
$425$	−26.9334	+	24.4050i	−1.30646	+	1.18381i
$426$		0			0
$427$	4.25162	−	0.371968i	0.205750	−	0.0180008i
$428$	1.31111	−	2.81169i	0.0633750	−	0.135908i
$429$		0			0
$430$	−14.8924	−	7.39581i	−0.718175	−	0.356658i
$431$		−	13.6942i		−	0.659624i	−0.944047	−	0.329812i	$-0.893015\pi$
$431$		−	13.6942i		−	0.659624i	0.944047	−	0.329812i	$-0.106985\pi$
$432$		0			0
$433$	22.8337	+	22.8337i	1.09732	+	1.09732i	0.994723	+	0.102594i	$0.0327142\pi$
$433$	22.8337	+	22.8337i	1.09732	+	1.09732i	0.102594	+	0.994723i	$0.467286\pi$
$434$	1.88909	+	10.7136i	0.0906791	+	0.514267i
$435$		0			0
$436$	0.122596	−	0.0446213i	0.00587129	−	0.00213697i
$437$	−0.0656941	−	0.750887i	−0.00314257	−	0.0359198i
$438$		0			0
$439$	−3.85214	+	10.5837i	−0.183852	+	0.505130i	−0.997041	−	0.0768697i	$-0.975507\pi$
$439$	−3.85214	+	10.5837i	−0.183852	+	0.505130i	0.813189	+	0.582000i	$0.197730\pi$
$440$	−12.6041	+	10.0582i	−0.600875	+	0.479505i
$441$		0			0
$442$	−0.873956	−	3.26165i	−0.0415699	−	0.155141i
$443$	0.588927	−	6.73147i	0.0279808	−	0.319822i	−0.969286	−	0.245936i	$-0.920905\pi$
$443$	0.588927	−	6.73147i	0.0279808	−	0.319822i	0.997267	−	0.0738853i	$-0.0235399\pi$
$444$		0			0
$445$	−18.0802	+	17.2116i	−0.857082	+	0.815910i
$446$	23.3694	+	4.12066i	1.10657	+	0.195119i
$447$		0			0
$448$	10.5175	+	0.920162i	0.496905	+	0.0434736i
$449$	−5.70190	+	9.87598i	−0.269089	+	0.466076i	−0.968627	−	0.248519i	$-0.920056\pi$
$449$	−5.70190	+	9.87598i	−0.269089	+	0.466076i	0.699538	+	0.714596i	$0.253389\pi$
$450$		0			0
$451$	6.52164	+	11.2958i	0.307092	+	0.531899i
$452$	−0.0568601	−	0.121937i	−0.00267447	−	0.00573542i
$453$		0			0
$454$	22.8589	−	27.2421i	1.07282	−	1.27854i
$455$	1.05815	+	0.311626i	0.0496067	+	0.0146092i
$456$		0			0
$457$	6.07605	+	4.25450i	0.284226	+	0.199017i	0.706992	−	0.707222i	$-0.250052\pi$
$457$	6.07605	+	4.25450i	0.284226	+	0.199017i	−0.422766	+	0.906239i	$0.638941\pi$
$458$	−24.7249	+	24.7249i	−1.15532	+	1.15532i
$459$		0			0
$460$	0.0120769	+	0.0799468i	0.000563088	+	0.00372754i
$461$	41.0458	−	7.23749i	1.91170	−	0.337083i	0.914046	−	0.405611i	$-0.132941\pi$
$461$	41.0458	−	7.23749i	1.91170	−	0.337083i	0.997649	+	0.0685275i	$0.0218301\pi$
$462$		0			0
$463$	3.01669	+	1.40671i	0.140198	+	0.0653752i	0.491451	−	0.870905i	$-0.336467\pi$
$463$	3.01669	+	1.40671i	0.140198	+	0.0653752i	−0.351253	+	0.936280i	$0.614244\pi$
$464$	29.9930	+	25.1671i	1.39239	+	1.16835i
$465$		0			0
$466$	−30.6975	−	11.1730i	−1.42203	−	0.517577i
$467$	1.15789	−	4.32129i	0.0535806	−	0.199966i	−0.933947	−	0.357412i	$-0.883659\pi$
$467$	1.15789	−	4.32129i	0.0535806	−	0.199966i	0.987528	+	0.157446i	$0.0503260\pi$
$468$		0			0
$469$	1.49962	+	0.865804i	0.0692458	+	0.0399791i
$470$	−1.79468	−	28.6034i	−0.0827822	−	1.31937i
$471$		0			0
$472$	−14.4459	−	20.6309i	−0.664929	−	0.949616i
$473$	−7.84443	−	11.2030i	−0.360687	−	0.515115i
$474$		0			0
$475$	−15.8714	+	24.6092i	−0.728232	+	1.12915i
$476$	−2.83674	−	1.63780i	−0.130022	−	0.0750682i
$477$		0			0
$478$	5.55731	−	20.7402i	0.254185	−	0.948632i
$479$	−34.5314	−	12.5684i	−1.57778	−	0.574264i	−0.603059	−	0.797697i	$-0.706052\pi$
$479$	−34.5314	−	12.5684i	−1.57778	−	0.574264i	−0.974719	+	0.223432i	$0.928274\pi$
$480$		0			0
$481$	0.508314	+	0.426526i	0.0231771	+	0.0194479i
$482$	11.4159	+	5.32332i	0.519980	+	0.242470i
$483$		0			0
$484$	−0.908792	+	0.160244i	−0.0413087	+	0.00728384i
$485$	26.2031	−	3.95827i	1.18982	−	0.179736i
$486$		0			0
$487$	9.05628	−	9.05628i	0.410379	−	0.410379i	−0.471492	−	0.881871i	$-0.656284\pi$
$487$	9.05628	−	9.05628i	0.410379	−	0.410379i	0.881871	+	0.471492i	$0.156284\pi$
$488$	−5.65913	−	3.96257i	−0.256177	−	0.179377i
$489$		0			0
$490$	−13.1292	+	7.15535i	−0.593115	+	0.323246i
$491$	−14.7648	+	17.5960i	−0.666326	+	0.794096i	−0.988279	−	0.152660i	$-0.951216\pi$
$491$	−14.7648	+	17.5960i	−0.666326	+	0.794096i	0.321953	+	0.946756i	$0.395661\pi$
$492$		0			0
$493$	26.8306	+	57.5384i	1.20839	+	2.59140i
$494$	−1.36029	−	2.35609i	−0.0612024	−	0.106006i
$495$		0			0
$496$	10.0668	−	17.4361i	0.452011	−	0.782906i
$497$	−16.6772	−	1.45907i	−0.748076	−	0.0654482i
$498$		0			0
$499$	9.11992	+	1.60809i	0.408264	+	0.0719879i	0.374009	−	0.927425i	$-0.377983\pi$
$499$	9.11992	+	1.60809i	0.408264	+	0.0719879i	0.0342550	+	0.999413i	$0.489094\pi$
$500$	1.53385	−	2.74122i	0.0685960	−	0.122591i
$501$		0			0
$502$	0.627792	−	7.17569i	0.0280197	−	0.320267i
$503$	−2.22875	−	8.31780i	−0.0993750	−	0.370873i	0.898271	−	0.439441i	$-0.144823\pi$
$503$	−2.22875	−	8.31780i	−0.0993750	−	0.370873i	−0.997646	+	0.0685686i	$0.978157\pi$
$504$		0			0
$505$	−29.9599	−	3.36572i	−1.33320	−	0.149772i
$506$	−0.184659	+	0.507345i	−0.00820908	+	0.0225543i
$507$		0			0
$508$	0.329441	+	3.76553i	0.0146166	+	0.167068i
$509$	20.6614	−	7.52013i	0.915799	−	0.333324i	0.159233	−	0.987241i	$-0.449098\pi$
$509$	20.6614	−	7.52013i	0.915799	−	0.333324i	0.756566	+	0.653917i	$0.226876\pi$
$510$		0			0
$511$	−1.91756	−	10.8750i	−0.0848278	−	0.481082i
$512$	−11.4575	−	11.4575i	−0.506354	−	0.506354i
$513$		0			0
$514$			7.12936i			0.314463i
$515$	6.30451	−	2.12050i	0.277810	−	0.0934406i
$516$		0			0
$517$	9.96221	−	21.3640i	0.438138	−	0.939589i
$518$	5.20593	−	0.455459i	0.228735	−	0.0200117i
$519$		0			0
$520$	−0.987880	−	1.48743i	−0.0433214	−	0.0652281i
$521$	4.43677	−	2.56157i	0.194378	−	0.112224i	−0.399652	−	0.916667i	$-0.630869\pi$
$521$	4.43677	−	2.56157i	0.194378	−	0.112224i	0.594031	+	0.804442i	$0.297536\pi$
$522$		0			0
$523$	−7.57196	+	2.02890i	−0.331099	+	0.0887177i	−0.420539	−	0.907275i	$-0.638159\pi$
$523$	−7.57196	+	2.02890i	−0.331099	+	0.0887177i	0.0894400	+	0.995992i	$0.471492\pi$
$524$	1.33091	−	1.11677i	0.0581412	−	0.0487863i
$525$		0			0
$526$	−0.873497	+	4.95385i	−0.0380863	+	0.215998i
$527$	26.7424	−	18.7252i	1.16492	−	0.815685i
$528$		0			0
$529$	14.7735	+	17.6063i	0.642325	+	0.765493i
$530$	2.11401	−	0.923161i	0.0918269	−	0.0400996i
$531$		0			0
$532$	−2.54919	−	0.683053i	−0.110521	−	0.0296141i
$533$	−1.30898	+	0.610389i	−0.0566984	+	0.0264389i
$534$		0			0
$535$	12.8679	−	21.0729i	0.556327	−	0.911060i
$536$	−0.958687	−	2.63397i	−0.0414090	−	0.113770i
$537$		0			0
$538$	7.25433	−	10.3603i	0.312757	−	0.446663i
$539$	−12.2984			−0.529729
$540$		0			0
$541$	−12.2903			−0.528401			−0.264200	−	0.964468i	$-0.585108\pi$
$541$	−12.2903			−0.528401			−0.264200	+	0.964468i	$0.585108\pi$
$542$	11.9452	−	17.0595i	0.513089	−	0.732767i
$543$		0			0
$544$	3.92339	+	10.7794i	0.168214	+	0.462164i
$545$	1.00927	−	0.243985i	0.0432322	−	0.0104512i
$546$		0			0
$547$	−0.472172	+	0.220177i	−0.0201886	+	0.00941410i	−0.432686	−	0.901545i	$-0.642434\pi$
$547$	−0.472172	+	0.220177i	−0.0201886	+	0.00941410i	0.412498	+	0.910959i	$0.364656\pi$
$548$	−2.00392	−	0.536948i	−0.0856032	−	0.0229373i
$549$		0			0
$550$	17.7530	−	11.1712i	0.756990	−	0.476342i
$551$	32.8789	+	39.1836i	1.40069	+	1.66928i
$552$		0			0
$553$	−2.72403	+	1.90739i	−0.115838	+	0.0811104i
$554$	−0.0322538	+	0.182920i	−0.00137033	+	0.00777153i
$555$		0			0
$556$	−2.20695	+	1.85185i	−0.0935957	+	0.0785361i
$557$	−22.5239	+	6.03527i	−0.954370	+	0.255723i	−0.702216	−	0.711964i	$-0.747806\pi$
$557$	−22.5239	+	6.03527i	−0.954370	+	0.255723i	−0.252155	+	0.967687i	$0.581139\pi$
$558$		0			0
$559$	1.31151	−	0.757203i	0.0554711	−	0.0320263i
$560$	−15.7599	−	3.18054i	−0.665976	−	0.134402i
$561$		0			0
$562$	36.1498	−	3.16269i	1.52489	−	0.133410i
$563$	14.5231	−	31.1449i	0.612076	−	1.31260i	−0.318993	−	0.947757i	$-0.603344\pi$
$563$	14.5231	−	31.1449i	0.612076	−	1.31260i	0.931069	−	0.364844i	$-0.118878\pi$
$564$		0			0
$565$	−0.341368	−	1.01493i	−0.0143614	−	0.0426983i
$566$			24.0770i			1.01203i
$567$		0			0
$568$	19.1620	+	19.1620i	0.804019	+	0.804019i
$569$	0.227444	+	1.28990i	0.00953495	+	0.0540754i	0.989204	−	0.146545i	$-0.0468153\pi$
$569$	0.227444	+	1.28990i	0.00953495	+	0.0540754i	−0.979669	+	0.200620i	$0.935704\pi$
$570$		0			0
$571$	−17.9969	+	6.55033i	−0.753146	+	0.274123i	−0.689929	−	0.723877i	$-0.742358\pi$
$571$	−17.9969	+	6.55033i	−0.753146	+	0.274123i	−0.0632171	+	0.998000i	$0.520136\pi$
$572$	0.0209202	+	0.239119i	0.000874718	+	0.00999807i
$573$		0			0
$574$	−3.89033	+	10.6886i	−0.162379	+	0.446133i
$575$	0.0244834	+	0.643035i	0.00102103	+	0.0268164i
$576$		0			0
$577$	3.38883	+	12.6473i	0.141079	+	0.526514i	0.999899	+	0.0142358i	$0.00453155\pi$
$577$	3.38883	+	12.6473i	0.141079	+	0.526514i	−0.858820	+	0.512278i	$0.828802\pi$
$578$	−4.71766	+	53.9231i	−0.196229	+	2.24290i
$579$		0			0
$580$	−3.78314	−	3.97405i	−0.157087	−	0.165013i
$581$	−20.8174	−	3.67067i	−0.863652	−	0.152285i
$582$		0			0
$583$	1.89012	+	0.165364i	0.0782808	+	0.00684869i
$584$	−8.93766	+	15.4805i	−0.369843	+	0.640587i
$585$		0			0
$586$	−3.97987	−	6.89333i	−0.164407	−	0.284761i
$587$	12.2703	+	26.3137i	0.506449	+	1.08608i	0.978827	+	0.204687i	$0.0656177\pi$
$587$	12.2703	+	26.3137i	0.506449	+	1.08608i	−0.472379	+	0.881396i	$0.656605\pi$
$588$		0			0
$589$	16.9072	−	20.1492i	0.696650	−	0.830235i
$590$	15.6774	+	28.7660i	0.645426	+	1.18428i
$591$		0			0
$592$	−7.92239	−	5.54732i	−0.325608	−	0.227993i
$593$	−18.8092	+	18.8092i	−0.772402	+	0.772402i	−0.978526	−	0.206124i	$-0.933915\pi$
$593$	−18.8092	+	18.8092i	−0.772402	+	0.772402i	0.206124	+	0.978526i	$0.433915\pi$
$594$		0			0
$595$	−20.9808	−	15.4739i	−0.860128	−	0.634368i
$596$	0.334697	−	0.0590161i	0.0137097	−	0.00241739i
$597$		0			0
$598$	−0.0541833	−	0.0252661i	−0.00221572	−	0.00103321i
$599$	3.51169	+	2.94665i	0.143484	+	0.120397i	0.711704	−	0.702479i	$-0.247924\pi$
$599$	3.51169	+	2.94665i	0.143484	+	0.120397i	−0.568221	+	0.822876i	$0.692368\pi$
$600$		0			0
$601$	25.1131	+	9.14041i	1.02438	+	0.372845i	0.798940	−	0.601411i	$-0.205395\pi$
$601$	25.1131	+	9.14041i	1.02438	+	0.372845i	0.225443	+	0.974256i	$0.427617\pi$
$602$	3.08684	−	11.5202i	0.125810	−	0.469530i
$603$		0			0
$604$	3.93404	+	2.27132i	0.160074	+	0.0924187i
$605$	−7.33006	+	0.459914i	−0.298009	+	0.0186982i
$606$		0			0
$607$	−20.5023	−	29.2803i	−0.832163	−	1.18845i	−0.979913	−	0.199428i	$-0.936092\pi$
$607$	−20.5023	−	29.2803i	−0.832163	−	1.18845i	0.147749	−	0.989025i	$-0.452797\pi$
$608$	5.30114	+	7.57081i	0.214990	+	0.307037i
$609$		0			0
$610$	6.73974	+	5.94392i	0.272884	+	0.240662i
$611$	2.26053	+	1.30512i	0.0914512	+	0.0527994i
$612$		0			0
$613$	9.61085	−	35.8682i	0.388179	−	1.44870i	−0.444916	−	0.895572i	$-0.646767\pi$
$613$	9.61085	−	35.8682i	0.388179	−	1.44870i	0.833095	−	0.553130i	$-0.186567\pi$
$614$	−31.4107	−	11.4325i	−1.26763	−	0.461380i
$615$		0			0
$616$	−8.86034	−	7.43471i	−0.356993	−	0.299553i
$617$	42.1491	+	19.6545i	1.69686	+	0.791258i	0.997036	+	0.0769428i	$0.0245159\pi$
$617$	42.1491	+	19.6545i	1.69686	+	0.791258i	0.699824	+	0.714316i	$0.253262\pi$
$618$		0			0
$619$	13.9352	−	2.45716i	0.560104	−	0.0987615i	0.113573	−	0.993530i	$-0.463770\pi$
$619$	13.9352	−	2.45716i	0.560104	−	0.0987615i	0.446531	+	0.894768i	$0.352659\pi$
$620$	−1.67470	+	2.27070i	−0.0672576	+	0.0911934i
$621$		0			0
$622$	15.3672	−	15.3672i	0.616168	−	0.616168i
$623$	−14.6669	−	10.2699i	−0.587619	−	0.411455i
$624$		0			0
$625$	14.5669	−	20.3176i	0.582677	−	0.812704i
$626$	20.6337	−	24.5903i	0.824687	−	0.982824i
$627$		0			0
$628$	2.46342	+	5.28283i	0.0983013	+	0.210808i
$629$	−7.84112	−	13.5812i	−0.312646	−	0.541519i
$630$		0			0
$631$	16.2979	−	28.2288i	0.648810	−	1.12377i	−0.334597	−	0.942361i	$-0.608600\pi$
$631$	16.2979	−	28.2288i	0.648810	−	1.12377i	0.983407	−	0.181411i	$-0.0580664\pi$
$632$	5.36250	+	0.469158i	0.213309	+	0.0186621i
$633$		0			0
$634$	−34.1919	−	6.02895i	−1.35793	−	0.239440i
$635$	−0.740135	+	30.0745i	−0.0293714	+	1.19347i
$636$		0			0
$637$	0.118690	−	1.35664i	0.00470269	−	0.0537520i
$638$	−9.48275	−	35.3901i	−0.375426	−	1.40111i
$639$		0			0
$640$	18.2680	+	22.8919i	0.722104	+	0.904881i
$641$	11.8689	−	32.6096i	0.468794	−	1.28800i	−0.449916	−	0.893071i	$-0.648546\pi$
$641$	11.8689	−	32.6096i	0.468794	−	1.28800i	0.918711	−	0.394931i	$-0.129232\pi$
$642$		0			0
$643$	0.772198	+	8.82626i	0.0304525	+	0.348074i	0.996101	+	0.0882215i	$0.0281183\pi$
$643$	0.772198	+	8.82626i	0.0304525	+	0.348074i	−0.965648	+	0.259852i	$0.916326\pi$
$644$	−0.0544969	+	0.0198352i	−0.00214748	+	0.000781618i
$645$		0			0
$646$	11.1651	+	63.3204i	0.439285	+	2.49131i
$647$	−14.1426	−	14.1426i	−0.556003	−	0.556003i	0.372164	−	0.928167i	$-0.378616\pi$
$647$	−14.1426	−	14.1426i	−0.556003	−	0.556003i	−0.928167	+	0.372164i	$0.878616\pi$
$648$		0			0
$649$			26.9457i			1.05771i
$650$	1.06097	+	2.06615i	0.0416145	+	0.0810411i
$651$		0			0
$652$	1.55227	−	3.32886i	0.0607917	−	0.130368i
$653$	−1.98004	+	0.173231i	−0.0774848	+	0.00677904i	−0.125832	−	0.992052i	$-0.540160\pi$
$653$	−1.98004	+	0.173231i	−0.0774848	+	0.00677904i	0.0483474	+	0.998831i	$0.484605\pi$
$654$		0			0
$655$	11.5185	−	7.65006i	0.450066	−	0.298913i
$656$	18.2307	−	10.5255i	0.711788	−	0.410951i
$657$		0			0
$658$	19.8563	−	5.32049i	0.774081	−	0.207414i
$659$	−9.93910	+	8.33989i	−0.387172	+	0.324876i	−0.815510	−	0.578742i	$-0.803544\pi$
$659$	−9.93910	+	8.33989i	−0.387172	+	0.324876i	0.428338	+	0.903619i	$0.359099\pi$
$660$		0			0
$661$	2.91716	−	16.5440i	0.113464	−	0.643489i	−0.874035	−	0.485864i	$-0.838505\pi$
$661$	2.91716	−	16.5440i	0.113464	−	0.643489i	0.987499	−	0.157625i	$-0.0503837\pi$
$662$	−17.2643	+	12.0886i	−0.670996	+	0.469836i
$663$		0			0
$664$	21.9947	+	26.2123i	0.853561	+	1.01723i
$665$	−19.5548	−	7.66728i	−0.758302	−	0.297324i
$666$		0			0
$667$	1.08573	+	0.290921i	0.0420396	+	0.0112645i
$668$	4.09735	−	1.91063i	0.158531	−	0.0739244i
$669$		0			0
$670$	0.856736	+	3.54397i	0.0330986	+	0.136915i
$671$	2.52797	+	6.94554i	0.0975912	+	0.268130i
$672$		0			0
$673$	−5.24028	+	7.48390i	−0.201998	+	0.288483i	−0.907352	−	0.420373i	$-0.861899\pi$
$673$	−5.24028	+	7.48390i	−0.201998	+	0.288483i	0.705353	+	0.708856i	$0.250788\pi$
$674$	21.8853			0.842991
$675$		0			0
$676$	3.62584			0.139455
$677$	0.0694054	−	0.0991212i	0.00266747	−	0.00380954i	−0.817816	−	0.575480i	$-0.804815\pi$
$677$	0.0694054	−	0.0991212i	0.00266747	−	0.00380954i	0.820484	+	0.571670i	$0.193704\pi$
$678$		0			0
$679$	6.50112	+	17.8617i	0.249490	+	0.685468i
$680$	9.91603	+	41.0185i	0.380262	+	1.57299i
$681$		0			0
$682$	−17.0753	+	7.96234i	−0.653847	+	0.304894i
$683$	−13.3758	−	3.58403i	−0.511810	−	0.137139i	−0.00633429	−	0.999980i	$-0.502016\pi$
$683$	−13.3758	−	3.58403i	−0.511810	−	0.137139i	−0.505476	+	0.862841i	$0.668683\pi$
$684$		0			0
$685$	−15.3720	−	6.02726i	−0.587335	−	0.230290i
$686$	−17.7931	−	21.2049i	−0.679342	−	0.809608i
$687$		0			0
$688$	−18.0809	+	12.6604i	−0.689329	+	0.482673i
$689$	−0.0364828	+	0.206904i	−0.00138988	+	0.00788241i
$690$		0			0
$691$	17.4891	−	14.6751i	0.665315	−	0.558266i	−0.246359	−	0.969179i	$-0.579234\pi$
$691$	17.4891	−	14.6751i	0.665315	−	0.558266i	0.911675	+	0.410913i	$0.134790\pi$
$692$	0.719892	−	0.192894i	0.0273662	−	0.00733274i
$693$		0			0
$694$	11.8745	−	6.85575i	0.450750	−	0.260241i
$695$	−19.1003	+	12.6855i	−0.724517	+	0.481190i
$696$		0			0
$697$	34.0042	−	2.97498i	1.28800	−	0.112686i
$698$	5.32004	−	11.4089i	0.201366	−	0.431832i
$699$		0			0
$700$	2.14499	+	0.689488i	0.0810730	+	0.0260602i
$701$			15.6693i			0.591821i	0.955216	+	0.295910i	$0.0956230\pi$
$701$			15.6693i			0.591821i	−0.955216	+	0.295910i	$0.904377\pi$
$702$		0			0
$703$	−8.93432	−	8.93432i	−0.336964	−	0.336964i
$704$	3.17504	+	18.0065i	0.119664	+	0.678647i
$705$		0			0
$706$	−3.74859	+	1.36438i	−0.141080	+	0.0513490i
$707$	−1.88471	−	21.5424i	−0.0708820	−	0.810184i
$708$		0			0
$709$	2.91839	−	8.01821i	0.109602	−	0.301130i	−0.872751	−	0.488166i	$-0.837666\pi$
$709$	2.91839	−	8.01821i	0.109602	−	0.301130i	0.982353	+	0.187036i	$0.0598882\pi$
$710$	−21.9868	−	27.5520i	−0.825148	−	1.03401i
$711$		0			0
$712$	7.50148	+	27.9959i	0.281130	+	1.04919i
$713$	0.0503766	−	0.575807i	0.00188662	−	0.0215641i
$714$		0			0
$715$	−0.0470001	+	1.90979i	−0.00175770	+	0.0714223i
$716$	1.89856	+	0.334767i	0.0709523	+	0.0125108i
$717$		0			0
$718$	21.2480	+	1.85896i	0.792968	+	0.0693758i
$719$	19.9277	−	34.5157i	0.743176	−	1.28722i	−0.207866	−	0.978157i	$-0.566652\pi$
$719$	19.9277	−	34.5157i	0.743176	−	1.28722i	0.951042	−	0.309062i	$-0.100015\pi$
$720$		0			0
$721$	2.38550	+	4.13180i	0.0888406	+	0.153876i
$722$	9.76600	+	20.9433i	0.363453	+	0.779427i
$723$		0			0
$724$	3.61621	−	4.30963i	0.134395	−	0.160166i
$725$	−26.3901	−	34.7923i	−0.980105	−	1.29216i
$726$		0			0
$727$	−37.5210	−	26.2725i	−1.39158	−	0.974393i	−0.998492	−	0.0548911i	$-0.982519\pi$
$727$	−37.5210	−	26.2725i	−1.39158	−	0.974393i	−0.393085	−	0.919502i	$-0.628592\pi$
$728$	0.905635	−	0.905635i	0.0335651	−	0.0335651i
$729$		0			0
$730$	13.8011	−	18.7127i	0.510801	−	0.692587i
$731$	−35.2471	+	6.21502i	−1.30366	+	0.229871i
$732$		0			0
$733$	−33.5325	−	15.6365i	−1.23855	−	0.577546i	−0.310704	−	0.950507i	$-0.600565\pi$
$733$	−33.5325	−	15.6365i	−1.23855	−	0.577546i	−0.927847	+	0.372961i	$0.878343\pi$
$734$	−15.9308	−	13.3675i	−0.588015	−	0.493403i
$735$		0			0
$736$	0.190850	+	0.0694636i	0.00703481	+	0.00256046i
$737$	−0.776169	+	2.89670i	−0.0285906	+	0.106701i
$738$		0			0
$739$	9.45965	+	5.46153i	0.347979	+	0.200906i	0.663795	−	0.747915i	$-0.268945\pi$
$739$	9.45965	+	5.46153i	0.347979	+	0.200906i	−0.315816	+	0.948820i	$0.602278\pi$
$740$	1.01650	+	0.896473i	0.0373673	+	0.0329550i
$741$		0			0
$742$	0.949040	+	1.35537i	0.0348404	+	0.0497572i
$743$	4.75185	+	6.78635i	0.174329	+	0.248967i	0.896802	−	0.442431i	$-0.145884\pi$
$743$	4.75185	+	6.78635i	0.174329	+	0.248967i	−0.722474	+	0.691398i	$0.756995\pi$
$744$		0			0
$745$	2.69957	−	0.169381i	0.0989047	−	0.00620563i
$746$	26.5695	+	15.3399i	0.972778	+	0.561633i
$747$		0			0
$748$	1.46824	−	5.47954i	0.0536841	−	0.200352i
$749$	16.6422	+	6.05726i	0.608093	+	0.221328i
$750$		0			0
$751$	1.01418	+	0.851000i	0.0370080	+	0.0310534i	0.661104	−	0.750294i	$-0.270088\pi$
$751$	1.01418	+	0.851000i	0.0370080	+	0.0310534i	−0.624096	+	0.781348i	$0.714533\pi$
$752$	−34.4801	−	16.0783i	−1.25736	−	0.586317i
$753$		0			0
$754$	3.99541	−	0.704499i	0.145504	−	0.0256563i
$755$	29.0965	+	21.4594i	1.05893	+	0.780989i
$756$		0			0
$757$	−26.5719	+	26.5719i	−0.965772	+	0.965772i	−0.999433	−	0.0336615i	$-0.989283\pi$
$757$	−26.5719	+	26.5719i	−0.965772	+	0.965772i	0.0336615	+	0.999433i	$0.489283\pi$
$758$	25.7998	+	18.0652i	0.937092	+	0.656159i
$759$		0			0
$760$	16.2705	+	29.8544i	0.590195	+	1.08293i
$761$	−6.97127	+	8.30804i	−0.252708	+	0.301166i	−0.877453	−	0.479663i	$-0.840759\pi$
$761$	−6.97127	+	8.30804i	−0.252708	+	0.301166i	0.624744	+	0.780829i	$0.285203\pi$
$762$		0			0
$763$	0.314755	+	0.674994i	0.0113949	+	0.0244364i
$764$	1.31601	+	2.27939i	0.0476114	+	0.0824654i
$765$		0			0
$766$	−11.0760	+	19.1841i	−0.400191	+	0.693151i
$767$	−2.97239	−	0.260050i	−0.107327	−	0.00938988i
$768$		0			0
$769$	−44.1842	−	7.79087i	−1.59332	−	0.280946i	−0.694579	−	0.719417i	$-0.744409\pi$
$769$	−44.1842	−	7.79087i	−1.59332	−	0.280946i	−0.898745	+	0.438471i	$0.855520\pi$
$770$	10.3735	+	10.8970i	0.373835	+	0.392700i
$771$		0			0
$772$	0.516085	−	5.89888i	0.0185743	−	0.212305i
$773$	8.13915	+	30.3757i	0.292745	+	1.09254i	0.942992	+	0.332816i	$0.107999\pi$
$773$	8.13915	+	30.3757i	0.292745	+	1.09254i	−0.650247	+	0.759723i	$0.725334\pi$
$774$		0			0
$775$	−15.2628	+	16.4711i	−0.548257	+	0.591659i
$776$	10.5236	−	28.9133i	0.377775	−	1.03793i
$777$		0			0
$778$	−0.824033	−	9.41874i	−0.0295430	−	0.337678i
$779$	25.8430	−	9.40608i	0.925922	−	0.337008i
$780$		0			0
$781$	−5.03455	−	28.5524i	−0.180150	−	1.02168i
$782$	0.999091	+	0.999091i	0.0357274	+	0.0357274i
$783$		0			0
$784$			19.8488i			0.708885i
$785$	14.7895	+	43.9710i	0.527861	+	1.56939i
$786$		0			0
$787$	−13.3215	+	28.5680i	−0.474860	+	1.01834i	0.512330	+	0.858789i	$0.328783\pi$
$787$	−13.3215	+	28.5680i	−0.474860	+	1.01834i	−0.987190	+	0.159552i	$0.948995\pi$
$788$	2.05671	−	0.179939i	0.0732674	−	0.00641007i
$789$		0			0
$790$	−6.86361	−	1.38516i	−0.244196	−	0.0492819i
$791$	0.665155	−	0.384027i	0.0236502	−	0.0136544i
$792$		0			0
$793$	−0.790562	+	0.211830i	−0.0280737	+	0.00752232i
$794$	0.539681	−	0.452846i	0.0191526	−	0.0160709i
$795$		0			0
$796$	−1.25879	+	7.13898i	−0.0446168	+	0.253034i
$797$	5.33729	−	3.73721i	0.189057	−	0.132379i	−0.475216	−	0.879869i	$-0.657630\pi$
$797$	5.33729	−	3.73721i	0.189057	−	0.132379i	0.664273	+	0.747490i	$0.268741\pi$
$798$		0			0
$799$	−39.6531	−	47.2567i	−1.40283	−	1.67182i
$800$	−4.20231	−	6.67820i	−0.148574	−	0.236110i
$801$		0			0
$802$	13.6193	+	3.64928i	0.480914	+	0.128860i
$803$	17.3326	−	8.08234i	0.611655	−	0.285220i
$804$		0			0
$805$	−0.448643	+	0.108457i	−0.0158126	+	0.00382261i
$806$	−0.713536	−	1.96042i	−0.0251332	−	0.0690530i
$807$		0			0
$808$	−20.0778	+	28.6741i	−0.706335	+	1.00875i
$809$	−21.5117			−0.756312			−0.378156	−	0.925742i	$-0.623442\pi$
$809$	−21.5117			−0.756312			−0.378156	+	0.925742i	$0.623442\pi$
$810$		0			0
$811$	15.2216			0.534502			0.267251	−	0.963627i	$-0.413885\pi$
$811$	15.2216			0.534502			0.267251	+	0.963627i	$0.413885\pi$
$812$	2.25734	−	3.22382i	0.0792172	−	0.113134i
$813$		0			0
$814$	3.09539	+	8.50453i	0.108494	+	0.298083i
$815$	15.2347	−	24.9489i	0.533650	−	0.873924i
$816$		0			0
$817$	−26.1346	+	12.1868i	−0.914335	+	0.426362i
$818$	−1.02522	−	0.274706i	−0.0358459	−	0.00960488i
$819$		0			0
$820$	−2.70351	+	1.18058i	−0.0944106	+	0.0412278i
$821$	32.2494	+	38.4334i	1.12551	+	1.34133i	0.932932	+	0.360053i	$0.117242\pi$
$821$	32.2494	+	38.4334i	1.12551	+	1.34133i	0.192581	+	0.981281i	$0.438314\pi$
$822$		0			0
$823$	−2.87349	+	2.01204i	−0.100164	+	0.0701354i	−0.622585	−	0.782552i	$-0.713918\pi$
$823$	−2.87349	+	2.01204i	−0.100164	+	0.0701354i	0.522422	+	0.852687i	$0.325029\pi$
$824$	1.34108	−	7.60564i	0.0467187	−	0.264955i
$825$		0			0
$826$	−18.0008	+	15.1045i	−0.626327	+	0.525551i
$827$	−2.56281	+	0.686704i	−0.0891178	+	0.0238790i	−0.303102	−	0.952958i	$-0.598022\pi$
$827$	−2.56281	+	0.686704i	−0.0891178	+	0.0238790i	0.213985	+	0.976837i	$0.431356\pi$
$828$		0			0
$829$	−13.2911	+	7.67359i	−0.461617	+	0.266515i	−0.712724	−	0.701444i	$-0.752539\pi$
$829$	−13.2911	+	7.67359i	−0.461617	+	0.266515i	0.251107	+	0.967959i	$0.419206\pi$
$830$	−24.6246	−	37.0768i	−0.854734	−	1.28695i
$831$		0			0
$832$	−2.01695	+	0.176460i	−0.0699251	+	0.00611766i
$833$	−13.6019	+	29.1693i	−0.471277	+	1.01066i
$834$		0			0
$835$	34.1038	−	11.4707i	1.18021	−	0.396961i
$836$		−	4.57055i		−	0.158076i
$837$		0			0
$838$	−22.8981	−	22.8981i	−0.791002	−	0.791002i
$839$	−2.05282	−	11.6421i	−0.0708712	−	0.401931i	−0.999520	−	0.0309713i	$-0.990140\pi$
$839$	−2.05282	−	11.6421i	−0.0708712	−	0.401931i	0.928649	−	0.370960i	$-0.120971\pi$
$840$		0			0
$841$	−44.4266	+	16.1700i	−1.53195	+	0.557585i
$842$	2.34525	+	26.8064i	0.0808227	+	0.923808i
$843$		0			0
$844$	−0.0336436	+	0.0924350i	−0.00115806	+	0.00318174i
$845$	28.6770	+	3.22159i	0.986517	+	0.110826i
$846$		0			0
$847$	−1.36346	−	5.08850i	−0.0468490	−	0.174843i
$848$	0.266887	−	3.05053i	0.00916493	−	0.104756i
$849$		0			0
$850$	−6.86126	−	54.4618i	−0.235339	−	1.86802i
$851$	−0.273436	−	0.0482142i	−0.00937327	−	0.00165276i
$852$		0			0
$853$	−33.5308	−	2.93357i	−1.14807	−	0.100443i	−0.502805	−	0.864400i	$-0.667699\pi$
$853$	−33.5308	−	2.93357i	−1.14807	−	0.100443i	−0.645268	+	0.763956i	$0.723254\pi$
$854$	−3.22284	+	5.58211i	−0.110283	+	0.191016i
$855$		0			0
$856$	−14.3341	−	24.8274i	−0.489929	−	0.848583i
$857$	15.6821	+	33.6303i	0.535689	+	1.14879i	0.968890	+	0.247491i	$0.0796062\pi$
$857$	15.6821	+	33.6303i	0.535689	+	1.14879i	−0.433201	+	0.901297i	$0.642616\pi$
$858$		0			0
$859$	−18.6876	+	22.2710i	−0.637613	+	0.759878i	−0.983991	−	0.178217i	$-0.942967\pi$
$859$	−18.6876	+	22.2710i	−0.637613	+	0.759878i	0.346378	+	0.938095i	$0.387412\pi$
$860$	2.71605	−	1.48024i	0.0926166	−	0.0504757i
$861$		0			0
$862$	16.9417	+	11.8627i	0.577038	+	0.404046i
$863$	9.57951	−	9.57951i	0.326090	−	0.326090i	−0.525007	−	0.851098i	$-0.675937\pi$
$863$	9.57951	−	9.57951i	0.326090	−	0.326090i	0.851098	+	0.525007i	$0.175937\pi$
$864$		0			0
$865$	5.86505	−	0.885983i	0.199418	−	0.0301243i
$866$	−48.0287	+	8.46876i	−1.63208	+	0.287780i
$867$		0			0
$868$	−1.83416	−	0.855281i	−0.0622553	−	0.0290301i
$869$	−4.41177	−	3.70191i	−0.149659	−	0.125579i
$870$		0			0
$871$	−0.312045	−	0.113575i	−0.0105733	−	0.00384835i
$872$	0.312030	−	1.16451i	0.0105667	−	0.0394353i
$873$		0			0
$874$	0.985869	+	0.569192i	0.0333475	+	0.0192532i
$875$	16.3522	+	7.35904i	0.552807	+	0.248781i
$876$		0			0
$877$	12.6973	+	18.1337i	0.428759	+	0.612331i	0.974164	−	0.225842i	$-0.0725132\pi$
$877$	12.6973	+	18.1337i	0.428759	+	0.612331i	−0.545405	+	0.838172i	$0.683624\pi$
$878$	−9.75663	−	13.9339i	−0.329270	−	0.470247i
$879$		0			0
$880$	−1.74360	−	27.7894i	−0.0587769	−	0.936779i
$881$	−38.5171	−	22.2379i	−1.29768	−	0.749213i	−0.317673	−	0.948200i	$-0.602902\pi$
$881$	−38.5171	−	22.2379i	−1.29768	−	0.749213i	−0.980002	+	0.198987i	$0.936235\pi$
$882$		0			0
$883$	4.08387	−	15.2412i	0.137433	−	0.512907i	−0.862543	−	0.505984i	$-0.831130\pi$
$883$	4.08387	−	15.2412i	0.137433	−	0.512907i	0.999976	−	0.00692327i	$-0.00220376\pi$
$884$	0.590280	+	0.214844i	0.0198533	+	0.00722599i
$885$		0			0
$886$	7.81768	+	6.55981i	0.262640	+	0.220381i
$887$	−25.0117	−	11.6632i	−0.839811	−	0.391610i	−0.0453839	−	0.998970i	$-0.514451\pi$
$887$	−25.0117	−	11.6632i	−0.839811	−	0.391610i	−0.794427	+	0.607359i	$0.792229\pi$
$888$		0			0
$889$	−21.2504	+	3.74702i	−0.712715	+	0.125671i
$890$	−5.63122	−	37.2777i	−0.188759	−	1.24955i
$891$		0			0
$892$	−3.12148	+	3.12148i	−0.104515	+	0.104515i
$893$	−40.7139	−	28.5082i	−1.36244	−	0.953990i
$894$		0			0
$895$	14.7183	+	4.33457i	0.491980	+	0.144889i
$896$	−13.5031	+	16.0924i	−0.451108	+	0.537609i
$897$		0			0
$898$	−7.27874	−	15.6093i	−0.242895	−	0.520890i
$899$	19.6120	+	33.9690i	0.654098	+	1.13293i
$900$		0			0
$901$	2.48266	−	4.30010i	0.0827095	−	0.143257i
$902$	−19.6241	−	1.71688i	−0.653410	−	0.0571660i
$903$		0			0
$904$	−1.22439	−	0.215893i	−0.0407226	−	0.00718049i
$905$	32.4299	−	30.8721i	1.07801	−	1.02622i
$906$		0			0
$907$	−0.325298	+	3.71818i	−0.0108014	+	0.123460i	−0.999681	−	0.0252582i	$-0.991959\pi$
$907$	−0.325298	+	3.71818i	−0.0108014	+	0.123460i	0.988880	+	0.148718i	$0.0475148\pi$
$908$	1.71223	+	6.39013i	0.0568223	+	0.212064i
$909$		0			0
$910$	−1.30216	+	1.03914i	−0.0431663	+	0.0344471i
$911$	8.20345	−	22.5388i	0.271792	−	0.746743i	−0.726435	−	0.687235i	$-0.758824\pi$
$911$	8.20345	−	22.5388i	0.271792	−	0.746743i	0.998228	−	0.0595086i	$-0.0189534\pi$
$912$		0			0
$913$	−3.19067	−	36.4695i	−0.105596	−	1.20697i
$914$	−10.5269	+	3.83148i	−0.348199	+	0.126734i
$915$		0			0
$916$	−1.12953	−	6.40589i	−0.0373207	−	0.211656i
$917$	7.01316	+	7.01316i	0.231595	+	0.231595i
$918$		0			0
$919$		−	55.8452i		−	1.84216i	−0.389370	−	0.921081i	$-0.627307\pi$
$919$		−	55.8452i		−	1.84216i	0.389370	−	0.921081i	$-0.372693\pi$
$920$	0.669177	+	0.332325i	0.0220621	+	0.0109564i
$921$		0			0
$922$	−26.6026	+	57.0495i	−0.876110	+	1.87882i
$923$	3.19821	−	0.279807i	0.105270	−	0.00920995i
$924$		0			0
$925$	7.24304	+	7.99343i	0.238150	+	0.262822i
$926$	−4.35356	+	2.51353i	−0.143067	+	0.0825997i
$927$		0			0
$928$	−13.3128	+	3.56716i	−0.437014	+	0.117098i
$929$	43.9037	−	36.8395i	1.44043	−	1.20867i	0.501224	−	0.865317i	$-0.332883\pi$
$929$	43.9037	−	36.8395i	1.44043	−	1.20867i	0.939208	−	0.343349i	$-0.111561\pi$
$930$		0			0
$931$	−4.50286	+	25.5370i	−0.147575	+	0.836942i
$932$	4.97805	−	3.48567i	0.163062	−	0.114177i
$933$		0			0
$934$	4.34306	+	5.17586i	0.142109	+	0.169359i
$935$	16.4810	−	42.0335i	0.538986	−	1.37464i
$936$		0			0
$937$	54.7688	+	14.6753i	1.78922	+	0.479420i	0.992213	−	0.124551i	$-0.0397491\pi$
$937$	54.7688	+	14.6753i	1.78922	+	0.479420i	0.797006	+	0.603971i	$0.206416\pi$
$938$	−2.37019	+	1.10524i	−0.0773895	+	0.0360873i
$939$		0			0
$940$	4.55023	+	2.77853i	0.148412	+	0.0906258i
$941$	−13.7044	−	37.6526i	−0.446751	−	1.22744i	−0.934973	−	0.354719i	$-0.884577\pi$
$941$	−13.7044	−	37.6526i	−0.446751	−	1.22744i	0.488222	−	0.872719i	$-0.337646\pi$
$942$		0			0
$943$	0.346638	−	0.495050i	0.0112881	−	0.0161211i
$944$	43.4886			1.41543
$945$		0			0
$946$	20.6552			0.671557
$947$	−26.6669	+	38.0843i	−0.866557	+	1.23757i	0.103484	+	0.994631i	$0.467001\pi$
$947$	−26.6669	+	38.0843i	−0.866557	+	1.23757i	−0.970041	+	0.242941i	$0.921888\pi$
$948$		0			0
$949$	0.724290	+	1.98997i	0.0235114	+	0.0645972i
$950$	−16.6965	−	40.9534i	−0.541706	−	1.32870i
$951$		0			0
$952$	−27.4331	+	12.7922i	−0.889110	+	0.414599i
$953$	−55.6950	−	14.9234i	−1.80414	−	0.483417i	−0.809526	−	0.587085i	$-0.800276\pi$
$953$	−55.6950	−	14.9234i	−1.80414	−	0.483417i	−0.994612	+	0.103668i	$0.966942\pi$
$954$		0			0
$955$	8.38311	+	19.1971i	0.271271	+	0.621204i
$956$	2.56752	+	3.05985i	0.0830396	+	0.0989627i
$957$		0			0
$958$	45.4622	−	31.8330i	1.46882	−	1.02848i
$959$	2.05655	−	11.6633i	0.0664095	−	0.376627i
$960$		0			0
$961$	−8.29622	+	6.96135i	−0.267620	+	0.224560i
$962$	−0.968010	+	0.259378i	−0.0312099	+	0.00836267i
$963$		0			0
$964$	−2.02929	+	1.17161i	−0.0653589	+	0.0377350i
$965$	9.32295	−	46.1960i	0.300116	−	1.48710i
$966$		0			0
$967$	25.9600	−	2.27121i	0.834818	−	0.0730371i	0.338273	−	0.941048i	$-0.390157\pi$
$967$	25.9600	−	2.27121i	0.834818	−	0.0730371i	0.496545	+	0.868011i	$0.334602\pi$
$968$	−3.60388	+	7.72854i	−0.115833	+	0.248405i
$969$		0			0
$970$	−17.8018	+	35.8461i	−0.571580	+	1.15095i
$971$		−	24.3222i		−	0.780536i	−0.920701	−	0.390268i	$-0.872382\pi$
$971$		−	24.3222i		−	0.780536i	0.920701	−	0.390268i	$-0.127618\pi$
$972$		0			0
$973$	−11.6294	−	11.6294i	−0.372822	−	0.372822i
$974$	3.35887	+	19.0491i	0.107625	+	0.610372i
$975$		0			0
$976$	11.2096	−	4.07998i	0.358812	−	0.130597i
$977$	−0.384646	−	4.39652i	−0.0123059	−	0.140657i	0.987556	−	0.157267i	$-0.0502683\pi$
$977$	−0.384646	−	4.39652i	−0.0123059	−	0.140657i	−0.999862	+	0.0166097i	$0.994713\pi$
$978$		0			0
$979$	10.6057	−	29.1388i	0.338958	−	0.931280i
$980$	0.310529	−	2.76418i	0.00991949	−	0.0882984i
$981$		0			0
$982$	−8.97872	−	33.5090i	−0.286522	−	1.06932i
$983$	0.550651	−	6.29396i	0.0175630	−	0.200746i	−0.982344	−	0.187085i	$-0.940096\pi$
$983$	0.550651	−	6.29396i	0.0175630	−	0.200746i	0.999907	−	0.0136609i	$-0.00434854\pi$
$984$		0			0
$985$	16.4266	+	0.404258i	0.523394	+	0.0128807i
$986$	−94.4260	−	16.6499i	−3.00714	−	0.530240i
$987$		0			0
$988$	0.504179	+	0.0441099i	0.0160401	+	0.00140332i
$989$	−0.316839	+	0.548781i	−0.0100749	+	0.0174502i
$990$		0			0
$991$	3.28793	+	5.69486i	0.104445	+	0.180903i	0.913511	−	0.406814i	$-0.133360\pi$
$991$	3.28793	+	5.69486i	0.104445	+	0.180903i	−0.809067	+	0.587717i	$0.800027\pi$
$992$	2.99522	+	6.42327i	0.0950983	+	0.203939i
$993$		0			0
$994$	16.2520	−	19.3683i	0.515481	−	0.614326i
$995$	−16.2989	+	55.3441i	−0.516710	+	1.75453i
$996$		0			0
$997$	−16.4219	−	11.4987i	−0.520086	−	0.364168i	0.283864	−	0.958864i	$-0.408383\pi$
$997$	−16.4219	−	11.4987i	−0.520086	−	0.364168i	−0.803951	+	0.594696i	$0.797272\pi$
$998$	−9.88969	+	9.88969i	−0.313053	+	0.313053i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.r.a.233.4		192
3.2	odd	2		135.2.q.a.68.13	yes	192
5.2	odd	4	inner	405.2.r.a.152.4		192
15.2	even	4		135.2.q.a.122.13	yes	192
15.8	even	4		675.2.ba.b.257.4		192
15.14	odd	2		675.2.ba.b.68.4		192
27.2	odd	18	inner	405.2.r.a.8.4		192
27.25	even	9		135.2.q.a.83.13	yes	192
135.2	even	36	inner	405.2.r.a.332.4		192
135.52	odd	36		135.2.q.a.2.13	✓	192
135.79	even	18		675.2.ba.b.218.4		192
135.133	odd	36		675.2.ba.b.407.4		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.13	✓	192	135.52	odd	36
135.2.q.a.68.13	yes	192	3.2	odd	2
135.2.q.a.83.13	yes	192	27.25	even	9
135.2.q.a.122.13	yes	192	15.2	even	4
405.2.r.a.8.4		192	27.2	odd	18	inner
405.2.r.a.152.4		192	5.2	odd	4	inner
405.2.r.a.233.4		192	1.1	even	1	trivial
405.2.r.a.332.4		192	135.2	even	36	inner
675.2.ba.b.68.4		192	15.14	odd	2
675.2.ba.b.218.4		192	135.79	even	18
675.2.ba.b.257.4		192	15.8	even	4
675.2.ba.b.407.4		192	135.133	odd	36

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.r (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866263 + 1.23715i) q^{2} +(-0.0960923 - 0.264011i) q^{4} +(-0.525423 - 2.17346i) q^{5} +(1.45360 - 0.677826i) q^{7} +(-2.50778 - 0.671958i) q^{8} +(3.14405 + 1.23276i) q^{10} +(1.78545 + 2.12782i) q^{11} +(-0.251952 + 0.176418i) q^{13} +(-0.420628 + 2.38550i) q^{14} +(3.43416 - 2.88160i) q^{16} +(7.02145 - 1.88139i) q^{17} +(5.07203 - 2.92834i) q^{19} +(-0.523329 + 0.347571i) q^{20} +(-4.17910 + 0.365624i) q^{22} +(0.0543910 - 0.116642i) q^{23} +(-4.44786 + 2.28397i) q^{25} -0.464527i q^{26} +(-0.318634 - 0.318634i) q^{28} +(1.51659 + 8.60103i) q^{29} +(4.22026 - 1.53605i) q^{31} +(0.137538 + 1.57207i) q^{32} +(-3.75485 + 10.3164i) q^{34} +(-2.23699 - 2.80320i) q^{35} +(-0.558369 - 2.08386i) q^{37} +(-0.770913 + 8.81158i) q^{38} +(-0.142827 + 5.80362i) q^{40} +(4.62442 + 0.815410i) q^{41} +(-4.90494 - 0.429127i) q^{43} +(0.390200 - 0.675847i) q^{44} +(0.0971868 + 0.168333i) q^{46} +(-3.58654 - 7.69135i) q^{47} +(-2.84600 + 3.39173i) q^{49} +(1.02740 - 7.48120i) q^{50} +(0.0707870 + 0.0495656i) q^{52} +(0.483003 - 0.483003i) q^{53} +(3.68661 - 4.99861i) q^{55} +(-4.10079 + 0.723079i) q^{56} +(-11.9546 - 5.57450i) q^{58} +(7.43127 + 6.23558i) q^{59} +(2.50049 + 0.910105i) q^{61} +(-1.75553 + 6.55173i) q^{62} +(5.70071 + 3.29131i) q^{64} +(0.515819 + 0.454912i) q^{65} +(0.619257 + 0.884390i) q^{67} +(-1.17142 - 1.67295i) q^{68} +(5.40580 - 0.339179i) q^{70} +(-9.03942 - 5.21891i) q^{71} +(1.78199 - 6.65047i) q^{73} +(3.06175 + 1.11439i) q^{74} +(-1.26050 - 1.05768i) q^{76} +(4.03763 + 1.88278i) q^{77} +(-2.04188 + 0.360038i) q^{79} +(-8.06743 - 5.94995i) q^{80} +(-5.01475 + 5.01475i) q^{82} +(-10.7962 - 7.55956i) q^{83} +(-7.77836 - 14.2723i) q^{85} +(4.77986 - 5.69642i) q^{86} +(-3.04772 - 6.53585i) q^{88} +(-5.58181 - 9.66798i) q^{89} +(-0.246656 + 0.427222i) q^{91} +(-0.0360214 - 0.00315146i) q^{92} +(12.6222 + 2.22564i) q^{94} +(-9.02959 - 9.48524i) q^{95} +(-1.03291 + 11.8062i) q^{97} +(-1.73070 - 6.45906i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Introduction

L-functions

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