LMFDB - Embedded newform 405.2.r.a.8.4

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			8.4
Character	$\chi$	$=$	405.8
Dual form			405.2.r.a.152.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.23715 + 0.866263i) q^{2} +(0.0960923 - 0.264011i) q^{4} +(2.23168 - 0.140023i) q^{5} +(0.677826 - 1.45360i) q^{7} +(-0.671958 - 2.50778i) q^{8} +(-2.63963 + 2.10645i) q^{10} +(1.78545 - 2.12782i) q^{11} +(0.176418 - 0.251952i) q^{13} +(0.420628 + 2.38550i) q^{14} +(3.43416 + 2.88160i) q^{16} +(1.88139 - 7.02145i) q^{17} +(-5.07203 - 2.92834i) q^{19} +(0.177479 - 0.602644i) q^{20} +(-0.365624 + 4.17910i) q^{22} +(-0.116642 + 0.0543910i) q^{23} +(4.96079 - 0.624975i) q^{25} +0.464527i q^{26} +(-0.318634 - 0.318634i) q^{28} +(-1.51659 + 8.60103i) q^{29} +(4.22026 + 1.53605i) q^{31} +(-1.57207 - 0.137538i) q^{32} +(3.75485 + 10.3164i) q^{34} +(1.30915 - 3.33889i) q^{35} +(2.08386 + 0.558369i) q^{37} +(8.81158 - 0.770913i) q^{38} +(-1.85074 - 5.50247i) q^{40} +(4.62442 - 0.815410i) q^{41} +(-0.429127 - 4.90494i) q^{43} +(-0.390200 - 0.675847i) q^{44} +(0.0971868 - 0.168333i) q^{46} +(7.69135 + 3.58654i) q^{47} +(2.84600 + 3.39173i) q^{49} +(-5.59585 + 5.07053i) q^{50} +(-0.0495656 - 0.0707870i) q^{52} +(-0.483003 + 0.483003i) q^{53} +(3.68661 - 4.99861i) q^{55} +(-4.10079 - 0.723079i) q^{56} +(-5.57450 - 11.9546i) q^{58} +(-7.43127 + 6.23558i) q^{59} +(2.50049 - 0.910105i) q^{61} +(-6.55173 + 1.75553i) q^{62} +(-5.70071 + 3.29131i) q^{64} +(0.358430 - 0.586978i) q^{65} +(-0.884390 - 0.619257i) q^{67} +(-1.67295 - 1.17142i) q^{68} +(1.27273 + 5.26478i) q^{70} +(-9.03942 + 5.21891i) q^{71} +(-6.65047 + 1.78199i) q^{73} +(-3.06175 + 1.11439i) q^{74} +(-1.26050 + 1.05768i) q^{76} +(-1.88278 - 4.03763i) q^{77} +(2.04188 + 0.360038i) q^{79} +(8.06743 + 5.94995i) q^{80} +(-5.01475 + 5.01475i) q^{82} +(-7.55956 - 10.7962i) q^{83} +(3.21549 - 15.9331i) q^{85} +(4.77986 + 5.69642i) q^{86} +(-6.53585 - 3.04772i) q^{88} +(5.58181 - 9.66798i) q^{89} +(-0.246656 - 0.427222i) q^{91} +(0.00315146 + 0.0360214i) q^{92} +(-12.6222 + 2.22564i) q^{94} +(-11.7292 - 5.82491i) q^{95} +(-11.8062 + 1.03291i) q^{97} +(-6.45906 - 1.73070i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{18}\right)$

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 $

$2$	−1.23715	+	0.866263i	−0.874798	+	0.612540i	−0.922361	−	0.386328i	$-0.873743\pi$
$2$	−1.23715	+	0.866263i	−0.874798	+	0.612540i	0.0475633	+	0.998868i	$0.484854\pi$
$3$		0			0
$3$		0			0
$4$	0.0960923	−	0.264011i	0.0480461	−	0.132006i
$5$	2.23168	−	0.140023i	0.998037	−	0.0626204i
$5$	2.23168	−	0.140023i	0.998037	−	0.0626204i
$6$		0			0
$7$	0.677826	−	1.45360i	0.256194	−	0.549410i	−0.735576	−	0.677442i	$-0.763088\pi$
$7$	0.677826	−	1.45360i	0.256194	−	0.549410i	0.991770	+	0.128032i	$0.0408661\pi$
$8$	−0.671958	−	2.50778i	−0.237573	−	0.886634i
$9$		0			0
$10$	−2.63963	+	2.10645i	−0.834724	+	0.666118i
$11$	1.78545	−	2.12782i	0.538334	−	0.641561i	−0.426479	−	0.904497i	$-0.640246\pi$
$11$	1.78545	−	2.12782i	0.538334	−	0.641561i	0.964813	+	0.262936i	$0.0846908\pi$
$12$		0			0
$13$	0.176418	−	0.251952i	0.0489296	−	0.0698788i	−0.793942	−	0.607994i	$-0.791975\pi$
$13$	0.176418	−	0.251952i	0.0489296	−	0.0698788i	0.842871	+	0.538115i	$0.180863\pi$
$14$	0.420628	+	2.38550i	0.112418	+	0.637552i
$15$		0			0
$16$	3.43416	+	2.88160i	0.858539	+	0.720400i
$17$	1.88139	−	7.02145i	0.456304	−	1.70295i	−0.227921	−	0.973680i	$-0.573193\pi$
$17$	1.88139	−	7.02145i	0.456304	−	1.70295i	0.684225	−	0.729271i	$-0.260141\pi$
$18$		0			0
$19$	−5.07203	−	2.92834i	−1.16360	−	0.671807i	−0.211439	−	0.977391i	$-0.567815\pi$
$19$	−5.07203	−	2.92834i	−1.16360	−	0.671807i	−0.952165	+	0.305584i	$0.901148\pi$
$20$	0.177479	−	0.602644i	0.0396856	−	0.134755i
$21$		0			0
$22$	−0.365624	+	4.17910i	−0.0779514	+	0.890988i
$23$	−0.116642	+	0.0543910i	−0.0243215	+	0.0113413i	−0.434741	−	0.900556i	$-0.643160\pi$
$23$	−0.116642	+	0.0543910i	−0.0243215	+	0.0113413i	0.410419	+	0.911897i	$0.365382\pi$
$24$		0			0
$25$	4.96079	−	0.624975i	0.992157	−	0.124995i
$26$			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	0.435475	+	0.900201i	$0.356581\pi$
$29$	−1.51659	+	8.60103i	−0.281625	+	1.59717i	−0.717099	+	0.696971i	$0.754531\pi$
$30$		0			0
$31$	4.22026	+	1.53605i	0.757981	+	0.275883i	0.691960	−	0.721936i	$-0.256747\pi$
$31$	4.22026	+	1.53605i	0.757981	+	0.275883i	0.0660211	+	0.997818i	$0.478970\pi$
$32$	−1.57207	−	0.137538i	−0.277905	−	0.0243135i
$33$		0			0
$34$	3.75485	+	10.3164i	0.643952	+	1.76924i
$35$	1.30915	−	3.33889i	0.221287	−	0.564375i
$36$		0			0
$37$	2.08386	+	0.558369i	0.342585	+	0.0917953i	0.426009	−	0.904719i	$-0.359919\pi$
$37$	2.08386	+	0.558369i	0.342585	+	0.0917953i	−0.0834245	+	0.996514i	$0.526586\pi$
$38$	8.81158	−	0.770913i	1.42943	−	0.125059i
$39$		0			0
$40$	−1.85074	−	5.50247i	−0.292628	−	0.870017i
$41$	4.62442	−	0.815410i	0.722213	−	0.127346i	0.199553	−	0.979887i	$-0.436051\pi$
$41$	4.62442	−	0.815410i	0.722213	−	0.127346i	0.522660	+	0.852541i	$0.324940\pi$
$42$		0			0
$43$	−0.429127	−	4.90494i	−0.0654412	−	0.747997i	−0.956046	−	0.293218i	$-0.905274\pi$
$43$	−0.429127	−	4.90494i	−0.0654412	−	0.747997i	0.890604	−	0.454779i	$-0.150282\pi$
$44$	−0.390200	−	0.675847i	−0.0588249	−	0.101888i
$45$		0			0
$46$	0.0971868	−	0.168333i	0.0143294	−	0.0248193i
$47$	7.69135	+	3.58654i	1.12190	+	0.523150i	0.892890	−	0.450274i	$-0.148674\pi$
$47$	7.69135	+	3.58654i	1.12190	+	0.523150i	0.229009	+	0.973424i	$0.426452\pi$
$48$		0			0
$49$	2.84600	+	3.39173i	0.406571	+	0.484533i
$50$	−5.59585	+	5.07053i	−0.791373	+	0.717082i
$51$		0			0
$52$	−0.0495656	−	0.0707870i	−0.00687352	−	0.00981640i
$53$	−0.483003	+	0.483003i	−0.0663456	+	0.0663456i	−0.739501	−	0.673155i	$-0.764938\pi$
$53$	−0.483003	+	0.483003i	−0.0663456	+	0.0663456i	0.673155	+	0.739501i	$0.264938\pi$
$54$		0			0
$55$	3.68661	−	4.99861i	0.497103	−	0.674013i
$56$	−4.10079	−	0.723079i	−0.547991	−	0.0966255i
$57$		0			0
$58$	−5.57450	−	11.9546i	−0.731968	−	1.56971i
$59$	−7.43127	+	6.23558i	−0.967469	+	0.811803i	−0.982152	−	0.188089i	$-0.939771\pi$
$59$	−7.43127	+	6.23558i	−0.967469	+	0.811803i	0.0146830	+	0.999892i	$0.495326\pi$
$60$		0			0
$61$	2.50049	−	0.910105i	0.320155	−	0.116527i	−0.176943	−	0.984221i	$-0.556621\pi$
$61$	2.50049	−	0.910105i	0.320155	−	0.116527i	0.497099	+	0.867694i	$0.334399\pi$
$62$	−6.55173	+	1.75553i	−0.832070	+	0.222952i
$63$		0			0
$64$	−5.70071	+	3.29131i	−0.712589	+	0.411413i
$65$	0.358430	−	0.586978i	0.0444578	−	0.0728056i
$66$		0			0
$67$	−0.884390	−	0.619257i	−0.108045	−	0.0756543i	0.518305	−	0.855196i	$-0.326563\pi$
$67$	−0.884390	−	0.619257i	−0.108045	−	0.0756543i	−0.626350	+	0.779542i	$0.715452\pi$
$68$	−1.67295	−	1.17142i	−0.202876	−	0.142055i
$69$		0			0
$70$	1.27273	+	5.26478i	0.152121	+	0.629261i
$71$	−9.03942	+	5.21891i	−1.07278	+	0.619371i	−0.928940	−	0.370230i	$-0.879279\pi$
$71$	−9.03942	+	5.21891i	−1.07278	+	0.619371i	−0.143842	+	0.989601i	$0.545946\pi$
$72$		0			0
$73$	−6.65047	+	1.78199i	−0.778378	+	0.208566i	−0.626070	−	0.779767i	$-0.715337\pi$
$73$	−6.65047	+	1.78199i	−0.778378	+	0.208566i	−0.152309	+	0.988333i	$0.548671\pi$
$74$	−3.06175	+	1.11439i	−0.355921	+	0.129545i
$75$		0			0
$76$	−1.26050	+	1.05768i	−0.144589	+	0.121325i
$77$	−1.88278	−	4.03763i	−0.214562	−	0.460130i
$78$		0			0
$79$	2.04188	+	0.360038i	0.229729	+	0.0405074i	0.287327	−	0.957832i	$-0.407233\pi$
$79$	2.04188	+	0.360038i	0.229729	+	0.0405074i	−0.0575985	+	0.998340i	$0.518344\pi$
$80$	8.06743	+	5.94995i	0.901966	+	0.665224i
$81$		0			0
$82$	−5.01475	+	5.01475i	−0.553787	+	0.553787i
$83$	−7.55956	−	10.7962i	−0.829770	−	1.18503i	−0.980512	−	0.196461i	$-0.937055\pi$
$83$	−7.55956	−	10.7962i	−0.829770	−	1.18503i	0.150742	−	0.988573i	$-0.451834\pi$
$84$		0			0
$85$	3.21549	−	15.9331i	0.348769	−	1.72818i
$86$	4.77986	+	5.69642i	0.515426	+	0.614261i
$87$		0			0
$88$	−6.53585	−	3.04772i	−0.696724	−	0.324888i
$89$	5.58181	−	9.66798i	0.591671	−	1.02480i	−0.402337	−	0.915492i	$-0.631802\pi$
$89$	5.58181	−	9.66798i	0.591671	−	1.02480i	0.994007	−	0.109312i	$-0.0348648\pi$
$90$		0			0
$91$	−0.246656	−	0.427222i	−0.0258566	−	0.0447850i
$92$	0.00315146	+	0.0360214i	0.000328562	+	0.00375549i
$93$		0			0
$94$	−12.6222	+	2.22564i	−1.30189	+	0.229558i
$95$	−11.7292	−	5.82491i	−1.20339	−	0.597623i
$96$		0			0
$97$	−11.8062	+	1.03291i	−1.19874	+	0.104876i	−0.668986	−	0.743275i	$-0.733271\pi$
$97$	−11.8062	+	1.03291i	−1.19874	+	0.104876i	−0.529754	+	0.848151i	$0.677716\pi$
$98$	−6.45906	−	1.73070i	−0.652464	−	0.174827i
$99$		0			0
$100$	0.311693	−	1.36976i	0.0311693	−	0.136976i
$101$	4.61138	+	12.6697i	0.458850	+	1.26068i	0.926343	+	0.376682i	$0.122935\pi$
$101$	4.61138	+	12.6697i	0.458850	+	1.26068i	−0.467493	+	0.883997i	$0.654843\pi$
$102$		0			0
$103$	2.96335	+	0.259260i	0.291988	+	0.0255456i	0.232209	−	0.972666i	$-0.425405\pi$
$103$	2.96335	+	0.259260i	0.291988	+	0.0255456i	0.0597791	+	0.998212i	$0.480960\pi$
$104$	−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	0.220548	−	0.975376i	$-0.429215\pi$
$107$	−7.80800	−	7.80800i	−0.754828	−	0.754828i	−0.975376	+	0.220548i	$0.929215\pi$
$108$		0			0
$109$			0.464359i			0.0444775i	0.999753	+	0.0222388i	$0.00707940\pi$
$109$			0.464359i			0.0444775i	−0.999753	+	0.0222388i	$0.992921\pi$
$110$	−0.230783	+	9.37762i	−0.0220043	+	0.894121i
$111$		0			0
$112$	6.51646	−	3.03868i	0.615748	−	0.287128i
$113$	−0.0417367	+	0.477053i	−0.00392626	+	0.0448774i	−0.997905	−	0.0646950i	$-0.979393\pi$
$113$	−0.0417367	+	0.477053i	−0.00392626	+	0.0448774i	0.993979	+	0.109572i	$0.0349481\pi$
$114$		0			0
$115$	−0.252691	+	0.137716i	−0.0235636	+	0.0128421i
$116$	2.12504	+	1.22689i	0.197305	+	0.113914i
$117$		0			0
$118$	3.79196	−	14.1518i	0.349078	−	1.30278i
$119$	−8.93114	−	7.49411i	−0.818716	−	0.686984i
$120$		0			0
$121$	0.570356	+	3.23465i	0.0518506	+	0.294059i
$122$	−2.30510	+	3.29202i	−0.208694	+	0.298046i
$123$		0			0
$124$	0.811069	−	0.966595i	0.0728362	−	0.0868028i
$125$	10.9834	−	2.08937i	0.982383	−	0.186879i
$126$		0			0
$127$	3.48210	+	12.9954i	0.308987	+	1.15315i	0.929459	+	0.368925i	$0.120274\pi$
$127$	3.48210	+	12.9954i	0.308987	+	1.15315i	−0.620473	+	0.784228i	$0.713059\pi$
$128$	5.53535	−	11.8706i	0.489260	−	1.04922i
$129$		0			0
$130$	0.0650447	+	1.03667i	0.00570479	+	0.0909224i
$131$	2.11500	−	5.81092i	0.184788	−	0.507702i	−0.812361	−	0.583155i	$-0.801818\pi$
$131$	2.11500	−	5.81092i	0.184788	−	0.507702i	0.997149	+	0.0754528i	$0.0240402\pi$
$132$		0			0
$133$	−7.69460	+	5.38781i	−0.667206	+	0.467183i
$134$	1.63056			0.140859
$135$		0			0
$136$	−18.8725			−1.61830
$137$	6.04873	−	4.23537i	0.516778	−	0.361852i	−0.285905	−	0.958258i	$-0.592294\pi$
$137$	6.04873	−	4.23537i	0.516778	−	0.361852i	0.802683	+	0.596406i	$0.203405\pi$
$138$		0			0
$139$	3.50715	−	9.63582i	0.297473	−	0.817299i	−0.697448	−	0.716635i	$-0.745681\pi$
$139$	3.50715	−	9.63582i	0.297473	−	0.817299i	0.994921	−	0.100664i	$-0.0320966\pi$
$140$	−0.755705	−	0.666472i	−0.0638687	−	0.0563272i
$141$		0			0
$142$	6.66218	−	14.2871i	0.559078	−	1.19895i
$143$	−0.221121	−	0.825233i	−0.0184910	−	0.0690095i
$144$		0			0
$145$	−2.18021	+	19.4071i	−0.181056	+	1.61167i
$146$	6.68396	−	7.96564i	0.553169	−	0.659241i
$147$		0			0
$148$	0.347659	−	0.496508i	0.0285774	−	0.0408127i
$149$	0.210055	+	1.19128i	0.0172084	+	0.0975937i	0.992202	−	0.124638i	$-0.0397770\pi$
$149$	0.210055	+	1.19128i	0.0172084	+	0.0975937i	−0.974994	+	0.222232i	$0.928666\pi$
$150$		0			0
$151$	−12.3858	−	10.3930i	−1.00795	−	0.845766i	−0.0198800	−	0.999802i	$-0.506328\pi$
$151$	−12.3858	−	10.3930i	−1.00795	−	0.845766i	−0.988065	+	0.154036i	$0.950773\pi$
$152$	−3.93544	+	14.6873i	−0.319206	+	1.19129i
$153$		0			0
$154$	5.82693	+	3.36418i	0.469547	+	0.271093i
$155$	9.63335	+	2.83703i	0.773770	+	0.227876i
$156$		0			0
$157$	−1.80822	+	20.6680i	−0.144311	+	1.64949i	0.486596	+	0.873627i	$0.338238\pi$
$157$	−1.80822	+	20.6680i	−0.144311	+	1.64949i	−0.630907	+	0.775858i	$0.717317\pi$
$158$	−2.83800	+	1.32338i	−0.225779	+	0.105282i
$159$		0			0
$160$	−3.52761	−	0.0868145i	−0.278882	−	0.00686329i
$161$			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
$167$	−16.0301	−	1.40245i	−1.24044	−	0.108525i	−0.552018	−	0.833832i	$-0.686142\pi$
$167$	−16.0301	−	1.40245i	−1.24044	−	0.108525i	−0.688425	+	0.725307i	$0.741698\pi$
$168$		0			0
$169$	4.41391	+	12.1271i	0.339531	+	0.932854i
$170$	9.82416	+	22.4971i	0.753479	+	1.72545i
$171$		0			0
$172$	−1.33620	−	0.358033i	−0.101884	−	0.0272997i
$173$	2.64260	−	0.231197i	0.200913	−	0.0175776i	0.0137449	−	0.999906i	$-0.495625\pi$
$173$	2.64260	−	0.231197i	0.200913	−	0.0175776i	0.187168	+	0.982328i	$0.440069\pi$
$174$		0			0
$175$	2.45409	−	7.63464i	0.185511	−	0.577124i
$176$	12.2630	−	2.16231i	0.924362	−	0.162990i
$177$		0			0
$178$	1.46947	+	16.7961i	0.110141	+	1.25892i
$179$	3.43088	+	5.94245i	0.256436	+	0.444160i	0.965284	−	0.261201i	$-0.0841185\pi$
$179$	3.43088	+	5.94245i	0.256436	+	0.444160i	−0.708849	+	0.705360i	$0.750785\pi$
$180$		0			0
$181$	10.0120	−	17.3412i	0.744183	−	1.28896i	−0.206392	−	0.978469i	$-0.566172\pi$
$181$	10.0120	−	17.3412i	0.744183	−	1.28896i	0.950575	−	0.310494i	$-0.100494\pi$
$182$	0.675238	+	0.314868i	0.0500519	+	0.0233396i
$183$		0			0
$184$	0.214779	+	0.255964i	0.0158337	+	0.0188699i
$185$	4.72870	+	0.954312i	0.347661	+	0.0701624i
$186$		0			0
$187$	−11.5812	−	16.5397i	−0.846903	−	1.20950i
$188$	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	−0.170406	−	0.985374i	$-0.554508\pi$
$191$	−9.22577	−	1.62675i	−0.667553	−	0.117708i	−0.497147	+	0.867666i	$0.665619\pi$
$192$		0			0
$193$	8.90711	+	19.1014i	0.641148	+	1.37495i	0.911146	+	0.412085i	$0.135199\pi$
$193$	8.90711	+	19.1014i	0.641148	+	1.37495i	−0.269998	+	0.962861i	$0.587023\pi$
$194$	13.7113	−	11.5052i	0.984414	−	0.826022i
$195$		0			0
$196$	1.16893	−	0.425457i	0.0834953	−	0.0303898i
$197$	−7.09801	+	1.90191i	−0.505712	+	0.135505i	−0.502650	−	0.864490i	$-0.667642\pi$
$197$	−7.09801	+	1.90191i	−0.505712	+	0.135505i	−0.00306257	+	0.999995i	$0.500975\pi$
$198$		0			0
$199$	22.3449	−	12.9008i	1.58399	−	0.914516i	0.589718	−	0.807609i	$-0.299239\pi$
$199$	22.3449	−	12.9008i	1.58399	−	0.914516i	0.994269	−	0.106906i	$-0.0340945\pi$
$200$	−4.90074	−	12.0206i	−0.346534	−	0.849985i
$201$		0			0
$202$	−16.6802	−	11.6796i	−1.17362	−	0.821776i
$203$	11.4745	+	8.03453i	0.805352	+	0.563914i
$204$		0			0
$205$	10.2061	−	2.46726i	0.712821	−	0.172321i
$206$	−3.89070	+	2.24630i	−0.271078	+	0.156507i
$207$		0			0
$208$	1.33187	−	0.356874i	0.0923487	−	0.0247448i
$209$	−15.2868	+	5.56395i	−1.05741	+	0.384867i
$210$		0			0
$211$	−0.268205	+	0.225051i	−0.0184640	+	0.0154932i	−0.651973	−	0.758242i	$-0.726058\pi$
$211$	−0.268205	+	0.225051i	−0.0184640	+	0.0154932i	0.633509	+	0.773735i	$0.281614\pi$
$212$	0.0811054	+	0.173931i	0.00557035	+	0.0119456i
$213$		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
$218$	−0.402257	−	0.574483i	−0.0272443	−	0.0389089i
$219$		0			0
$220$	−0.965436	−	1.45364i	−0.0650897	−	0.0980041i
$221$	−1.43715	−	1.71273i	−0.0966733	−	0.115211i
$222$		0			0
$223$	−14.2401	−	6.64028i	−0.953590	−	0.444666i	−0.117387	−	0.993086i	$-0.537452\pi$
$223$	−14.2401	−	6.64028i	−0.953590	−	0.444666i	−0.836203	+	0.548420i	$0.815230\pi$
$224$	−1.26551	+	2.19193i	−0.0845557	+	0.146455i
$225$		0			0
$226$	−0.361618	−	0.626342i	−0.0240545	−	0.0416636i
$227$	2.05222	+	23.4570i	0.136211	+	1.55690i	0.689733	+	0.724064i	$0.257728\pi$
$227$	2.05222	+	23.4570i	0.136211	+	1.55690i	−0.553522	+	0.832834i	$0.686717\pi$
$228$		0			0
$229$	−22.8004	+	4.02032i	−1.50669	+	0.265671i	−0.865188	−	0.501448i	$-0.832801\pi$
$229$	−22.8004	+	4.02032i	−1.50669	+	0.265671i	−0.641505	+	0.767119i	$0.721690\pi$
$230$	0.193319	−	0.389273i	0.0127471	−	0.0256679i
$231$		0			0
$232$	22.5886	−	1.97625i	1.48301	−	0.129747i
$233$	20.8931	+	5.59828i	1.36875	+	0.366755i	0.867022	−	0.498270i	$-0.166031\pi$
$233$	20.8931	+	5.59828i	1.36875	+	0.366755i	0.501728	+	0.865026i	$0.332698\pi$
$234$		0			0
$235$	17.6668	+	6.92703i	1.15246	+	0.451870i
$236$	0.932175	+	2.56113i	0.0606794	+	0.166715i
$237$		0			0
$238$	17.5410	+	1.53464i	1.13702	+	0.0994761i
$239$	13.3597	+	4.86252i	0.864165	+	0.314530i	0.735802	−	0.677197i	$-0.236805\pi$
$239$	13.3597	+	4.86252i	0.864165	+	0.314530i	0.128363	+	0.991727i	$0.459028\pi$
$240$		0			0
$241$	−1.44826	+	8.21348i	−0.0932905	+	0.529077i	0.901967	+	0.431804i	$0.142123\pi$
$241$	−1.44826	+	8.21348i	−0.0932905	+	0.529077i	−0.995258	+	0.0972724i	$0.968988\pi$
$242$	−3.50767	−	3.50767i	−0.225482	−	0.225482i
$243$		0			0
$244$		−	0.747612i		−	0.0478610i
$245$	6.82628	+	7.17075i	0.436115	+	0.458122i
$246$		0			0
$247$	−1.63260	+	0.761293i	−0.103880	+	0.0484399i
$248$	1.01624	−	11.6156i	0.0645311	−	0.737594i
$249$		0			0
$250$	−11.7782	+	12.0994i	−0.744916	+	0.765231i
$251$	−4.13040	−	2.38469i	−0.260708	−	0.150520i	0.363949	−	0.931419i	$-0.381428\pi$
$251$	−4.13040	−	2.38469i	−0.260708	−	0.150520i	−0.624658	+	0.780899i	$0.714761\pi$
$252$		0			0
$253$	−0.0925243	+	0.345305i	−0.00581695	+	0.0217092i
$254$	−15.5653	−	13.0608i	−0.976654	−	0.819510i
$255$		0			0
$256$	1.14887	+	6.51557i	0.0718045	+	0.407223i
$257$	2.70759	−	3.86684i	0.168895	−	0.241207i	−0.725778	−	0.687929i	$-0.758520\pi$
$257$	2.70759	−	3.86684i	0.168895	−	0.241207i	0.894673	+	0.446722i	$0.147409\pi$
$258$		0			0
$259$	2.22414	−	2.65063i	0.138202	−	0.164702i
$260$	−0.120526	−	0.151034i	−0.00747473	−	0.00936671i
$261$		0			0
$262$	2.41720	+	9.02113i	0.149335	+	0.557327i
$263$	−1.40761	+	3.01862i	−0.0867967	+	0.186136i	−0.944915	−	0.327316i	$-0.893856\pi$
$263$	−1.40761	+	3.01862i	−0.0867967	+	0.186136i	0.858118	+	0.513452i	$0.171634\pi$
$264$		0			0
$265$	−1.01028	+	1.14554i	−0.0620608	+	0.0703700i
$266$	4.85212	−	13.3311i	0.297502	−	0.817381i
$267$		0			0
$268$	−0.248474	+	0.173983i	−0.0151780	+	0.0106277i
$269$	8.37429			0.510589			0.255295	−	0.966863i	$-0.417828\pi$
$269$	8.37429			0.510589			0.255295	+	0.966863i	$0.417828\pi$
$270$		0			0
$271$	−13.7893			−0.837641			−0.418821	−	0.908069i	$-0.637556\pi$
$271$	−13.7893			−0.837641			−0.418821	+	0.908069i	$0.637556\pi$
$272$	26.6940	−	18.6913i	1.61856	−	1.13333i
$273$		0			0
$274$	−3.81425	+	10.4796i	−0.230428	+	0.633094i
$275$	7.52741	−	11.6715i	0.453920	−	0.703819i
$276$		0			0
$277$	0.0519757	−	0.111462i	0.00312292	−	0.00669711i	−0.904740	−	0.425964i	$-0.859935\pi$
$277$	0.0519757	−	0.111462i	0.00312292	−	0.00669711i	0.907863	+	0.419267i	$0.137713\pi$
$278$	4.00827	+	14.9591i	0.240400	+	0.897186i
$279$		0			0
$280$	−9.25289	−	1.03947i	−0.552966	−	0.0621205i
$281$	−15.4444	+	18.4059i	−0.921334	+	1.09800i	0.0735813	+	0.997289i	$0.476557\pi$
$281$	−15.4444	+	18.4059i	−0.921334	+	1.09800i	−0.994915	+	0.100714i	$0.967887\pi$
$282$		0			0
$283$	−9.14396	+	13.0589i	−0.543552	+	0.776273i	−0.993136	−	0.116965i	$-0.962683\pi$
$283$	−9.14396	+	13.0589i	−0.543552	+	0.776273i	0.449584	+	0.893238i	$0.351572\pi$
$284$	0.509233	+	2.88801i	0.0302174	+	0.171372i
$285$		0			0
$286$	0.988429	+	0.829390i	0.0584470	+	0.0490429i
$287$	1.94927	−	7.27478i	0.115062	−	0.429417i
$288$		0			0
$289$	−31.0386	−	17.9202i	−1.82580	−	1.05413i
$290$	−14.1144	−	25.8982i	−0.828827	−	1.52079i
$291$		0			0
$292$	−0.168594	+	1.92703i	−0.00986619	+	0.112771i
$293$	4.77657	−	2.22735i	0.279050	−	0.130123i	−0.278055	−	0.960565i	$-0.589690\pi$
$293$	4.77657	−	2.22735i	0.279050	−	0.130123i	0.557105	+	0.830442i	$0.311912\pi$
$294$		0			0
$295$	−15.7111	+	14.9564i	−0.914735	+	0.870793i
$296$		−	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
$302$	24.3262	+	2.12827i	1.39981	+	0.122468i
$303$		0			0
$304$	−8.97985	−	24.6719i	−0.515030	−	1.41503i
$305$	5.45286	−	2.38119i	0.312230	−	0.136347i
$306$		0			0
$307$	−21.3785	−	5.72834i	−1.22013	−	0.326934i	−0.409403	−	0.912353i	$-0.634263\pi$
$307$	−21.3785	−	5.72834i	−1.22013	−	0.326934i	−0.810730	+	0.585420i	$0.800930\pi$
$308$	−1.24690	+	0.109090i	−0.0710487	+	0.00621596i
$309$		0			0
$310$	−14.3755	+	4.83517i	−0.816476	+	0.274619i
$311$	−14.1711	+	2.49874i	−0.803567	+	0.141691i	−0.560322	−	0.828275i	$-0.689323\pi$
$311$	−14.1711	+	2.49874i	−0.803567	+	0.141691i	−0.243244	+	0.969965i	$0.578212\pi$
$312$		0			0
$313$	−1.85245	−	21.1736i	−0.104707	−	1.19680i	−0.848795	−	0.528722i	$-0.822671\pi$
$313$	−1.85245	−	21.1736i	−0.104707	−	1.19680i	0.744088	−	0.668081i	$-0.232884\pi$
$314$	−15.6669	−	27.1358i	−0.884133	−	1.53136i
$315$		0			0
$316$	0.291263	−	0.504482i	0.0163848	−	0.0283793i
$317$	−20.8348	−	9.71542i	−1.17020	−	0.545672i	−0.262350	−	0.964973i	$-0.584498\pi$
$317$	−20.8348	−	9.71542i	−1.17020	−	0.545672i	−0.907848	+	0.419300i	$0.862275\pi$
$318$		0			0
$319$	15.5936	+	18.5838i	0.873076	+	1.04049i
$320$	−12.2613	+	8.14338i	−0.685428	+	0.455229i
$321$		0			0
$322$	−0.178813	−	0.255371i	−0.00996485	−	0.0142313i
$323$	−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
$328$	−5.15228	−	11.0491i	−0.284487	−	0.610085i
$329$	10.4268	−	8.74912i	0.574848	−	0.482355i
$330$		0			0
$331$	13.1133	−	4.77285i	0.720772	−	0.262340i	0.0445184	−	0.999009i	$-0.485825\pi$
$331$	13.1133	−	4.77285i	0.720772	−	0.262340i	0.676253	+	0.736669i	$0.263602\pi$
$332$	−3.57673	+	0.958382i	−0.196298	+	0.0525980i
$333$		0			0
$334$	21.0465	−	12.1512i	1.15161	−	0.664884i
$335$	−2.06039	−	1.25815i	−0.112571	−	0.0687399i
$336$		0			0
$337$	11.8702	+	8.31162i	0.646612	+	0.452763i	0.850318	−	0.526269i	$-0.176410\pi$
$337$	11.8702	+	8.31162i	0.646612	+	0.452763i	−0.203705	+	0.979032i	$0.565299\pi$
$338$	−15.9659	−	11.1795i	−0.868432	−	0.608083i
$339$		0			0
$340$	−3.89752	−	2.37997i	−0.211373	−	0.129072i
$341$	10.8035	−	6.23741i	0.585043	−	0.337775i
$342$		0			0
$343$	17.7039	−	4.74374i	0.955920	−	0.256138i
$344$	−12.0122	+	4.37207i	−0.647652	+	0.235726i
$345$		0			0
$346$	−3.06901	+	2.57521i	−0.164991	+	0.138444i
$347$	3.83685	+	8.22815i	0.205973	+	0.441710i	0.981973	−	0.189023i	$-0.0605320\pi$
$347$	3.83685	+	8.22815i	0.205973	+	0.441710i	−0.776000	+	0.630733i	$0.782754\pi$
$348$		0			0
$349$	8.20842	+	1.44737i	0.439387	+	0.0774757i	0.388966	−	0.921252i	$-0.372833\pi$
$349$	8.20842	+	1.44737i	0.439387	+	0.0774757i	0.0504212	+	0.998728i	$0.483944\pi$
$350$	3.57753	+	11.5711i	0.191227	+	0.618501i
$351$		0			0
$352$	−3.09950	+	3.09950i	−0.165204	+	0.165204i
$353$	1.51501	+	2.16366i	0.0806358	+	0.115160i	0.857444	−	0.514578i	$-0.172051\pi$
$353$	1.51501	+	2.16366i	0.0806358	+	0.115160i	−0.776808	+	0.629738i	$0.783162\pi$
$354$		0			0
$355$	−19.4423	+	12.9127i	−1.03189	+	0.685333i
$356$	−2.01609	−	2.40268i	−0.106852	−	0.127342i
$357$		0			0
$358$	−9.39224	−	4.37967i	−0.496395	−	0.231473i
$359$	7.06131	−	12.2306i	0.372682	−	0.645504i	−0.617295	−	0.786732i	$-0.711772\pi$
$359$	7.06131	−	12.2306i	0.372682	−	0.645504i	0.989977	+	0.141228i	$0.0451049\pi$
$360$		0			0
$361$	7.65033	+	13.2508i	0.402649	+	0.697408i
$362$	2.63575	+	30.1267i	0.138532	+	1.58342i
$363$		0			0
$364$	−0.136493	+	0.0240674i	−0.00715418	+	0.00126148i
$365$	−14.5922	+	4.90804i	−0.763790	+	0.256899i
$366$		0			0
$367$	−13.7173	+	1.20011i	−0.716037	+	0.0626451i	−0.439351	−	0.898315i	$-0.644792\pi$
$367$	−13.7173	+	1.20011i	−0.716037	+	0.0626451i	−0.276686	+	0.960961i	$0.589236\pi$
$368$	−0.557300	−	0.149328i	−0.0290513	−	0.00778426i
$369$		0			0
$370$	−6.67680	+	2.91567i	−0.347110	+	0.151578i
$371$	0.374703	+	1.02949i	0.0194536	+	0.0534483i
$372$		0			0
$373$	−20.2366	−	1.77048i	−1.04781	−	0.0916718i	−0.449777	−	0.893141i	$-0.648497\pi$
$373$	−20.2366	−	1.77048i	−1.04781	−	0.0916718i	−0.598036	+	0.801469i	$0.704052\pi$
$374$	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	$-0.179916\pi$
$380$	−2.66493	+	2.53691i	−0.136708	+	0.130141i
$381$		0			0
$382$	12.8229	−	5.97940i	0.656075	−	0.305933i
$383$	−1.27835	+	14.6116i	−0.0653206	+	0.746618i	0.890944	+	0.454114i	$0.150044\pi$
$383$	−1.27835	+	14.6116i	−0.0653206	+	0.746618i	−0.956264	+	0.292504i	$0.905512\pi$
$384$		0			0
$385$	−4.76712	−	8.74706i	−0.242955	−	0.445791i
$386$	−27.5662	−	15.9154i	−1.40308	−	0.810071i
$387$		0			0
$388$	−0.861786	+	3.21623i	−0.0437506	+	0.163279i
$389$	4.79561	+	4.02400i	0.243147	+	0.204025i	0.756215	−	0.654323i	$-0.227047\pi$
$389$	4.79561	+	4.02400i	0.243147	+	0.204025i	−0.513067	+	0.858348i	$0.671491\pi$
$390$		0			0
$391$	0.162455	+	0.921326i	0.00821568	+	0.0465934i
$392$	6.59332	−	9.41624i	0.333013	−	0.475592i
$393$		0			0
$394$	7.13377	−	8.50169i	0.359394	−	0.428309i
$395$	4.60723	+	0.517578i	0.231815	+	0.0260422i
$396$		0			0
$397$	0.120732	+	0.450577i	0.00605935	+	0.0226138i	0.968889	−	0.247494i	$-0.0796072\pi$
$397$	0.120732	+	0.450577i	0.00605935	+	0.0226138i	−0.962830	+	0.270108i	$0.912941\pi$
$398$	−16.4685	+	35.3168i	−0.825492	+	1.77027i
$399$		0			0
$400$	18.8371	+	12.1487i	0.941853	+	0.607437i
$401$	−3.19304	+	8.77280i	−0.159453	+	0.438093i	−0.993532	−	0.113552i	$-0.963777\pi$
$401$	−3.19304	+	8.77280i	−0.159453	+	0.438093i	0.834079	+	0.551644i	$0.185999\pi$
$402$		0			0
$403$	1.13154	−	0.792314i	0.0563661	−	0.0394680i
$404$	3.78805			0.188463
$405$		0			0
$406$	−21.1557			−1.04994
$407$	4.90874	−	3.43714i	0.243317	−	0.170373i
$408$		0			0
$409$	−0.240362	+	0.660389i	−0.0118851	+	0.0326541i	−0.945493	−	0.325641i	$-0.894420\pi$
$409$	−0.240362	+	0.660389i	−0.0118851	+	0.0326541i	0.933608	+	0.358296i	$0.116642\pi$
$410$	−10.4891	+	11.8935i	−0.518021	+	0.587378i
$411$		0			0
$412$	0.353203	−	0.757446i	0.0174010	−	0.0373167i
$413$	4.02694	+	15.0288i	0.198153	+	0.739517i
$414$		0			0
$415$	−18.3822	−	23.0351i	−0.902349	−	1.13075i
$416$	−0.311994	+	0.371820i	−0.0152968	+	0.0182300i
$417$		0			0
$418$	14.0923	−	20.1259i	0.689276	−	0.984389i
$419$	3.72329	+	21.1158i	0.181894	+	1.03157i	0.929881	+	0.367861i	$0.119910\pi$
$419$	3.72329	+	21.1158i	0.181894	+	1.03157i	−0.747986	+	0.663714i	$0.768979\pi$
$420$		0			0
$421$	13.6486	+	11.4526i	0.665194	+	0.558164i	0.911638	−	0.410993i	$-0.134818\pi$
$421$	13.6486	+	11.4526i	0.665194	+	0.558164i	−0.246445	+	0.969157i	$0.579262\pi$
$422$	0.136857	−	0.510759i	0.00666211	−	0.0248633i
$423$		0			0
$424$	1.53582	+	0.886708i	0.0745862	+	0.0430623i
$425$	4.94495	−	36.0077i	0.239865	−	1.74663i
$426$		0			0
$427$	0.371968	−	4.25162i	0.0180008	−	0.205750i
$428$	−2.81169	+	1.31111i	−0.135908	+	0.0633750i
$429$		0			0
$430$	11.4648	+	12.0433i	0.552880	+	0.580779i
$431$			13.6942i			0.659624i	0.944047	+	0.329812i	$0.106985\pi$
$431$			13.6942i			0.659624i	−0.944047	+	0.329812i	$0.893015\pi$
$432$		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
$437$	0.750887	+	0.0656941i	0.0359198	+	0.00314257i
$438$		0			0
$439$	3.85214	+	10.5837i	0.183852	+	0.505130i	0.997041	−	0.0768697i	$-0.0244925\pi$
$439$	3.85214	+	10.5837i	0.183852	+	0.505130i	−0.813189	+	0.582000i	$0.802270\pi$
$440$	−15.0127	−	5.88635i	−0.715701	−	0.280621i
$441$		0			0
$442$	3.26165	+	0.873956i	0.155141	+	0.0415699i
$443$	−6.73147	+	0.588927i	−0.319822	+	0.0279808i	−0.245936	−	0.969286i	$-0.579095\pi$
$443$	−6.73147	+	0.588927i	−0.319822	+	0.0279808i	−0.0738853	+	0.997267i	$0.523540\pi$
$444$		0			0
$445$	11.1031	−	22.3574i	0.526336	−	1.05984i
$446$	23.3694	−	4.12066i	1.10657	−	0.195119i
$447$		0			0
$448$	0.920162	+	10.5175i	0.0434736	+	0.496905i
$449$	5.70190	+	9.87598i	0.269089	+	0.466076i	0.968627	−	0.248519i	$-0.0799440\pi$
$449$	5.70190	+	9.87598i	0.269089	+	0.466076i	−0.699538	+	0.714596i	$0.746611\pi$
$450$		0			0
$451$	6.52164	−	11.2958i	0.307092	−	0.531899i
$452$	0.121937	+	0.0568601i	0.00573542	+	0.00267447i
$453$		0			0
$454$	−22.8589	−	27.2421i	−1.07282	−	1.27854i
$455$	−0.610279	−	0.918884i	−0.0286103	−	0.0430779i
$456$		0			0
$457$	−4.25450	−	6.07605i	−0.199017	−	0.284226i	0.707222	−	0.706992i	$-0.249948\pi$
$457$	−4.25450	−	6.07605i	−0.199017	−	0.284226i	−0.906239	+	0.422766i	$0.861059\pi$
$458$	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	0.997649	−	0.0685275i	$-0.0218301\pi$
$461$	41.0458	+	7.23749i	1.91170	+	0.337083i	0.914046	+	0.405611i	$0.132941\pi$
$462$		0			0
$463$	1.40671	+	3.01669i	0.0653752	+	0.140198i	0.936280	−	0.351253i	$-0.114244\pi$
$463$	1.40671	+	3.01669i	0.0653752	+	0.140198i	−0.870905	+	0.491451i	$0.836467\pi$
$464$	−29.9930	+	25.1671i	−1.39239	+	1.16835i
$465$		0			0
$466$	−30.6975	+	11.1730i	−1.42203	+	0.517577i
$467$	4.32129	−	1.15789i	0.199966	−	0.0535806i	−0.157446	−	0.987528i	$-0.550326\pi$
$467$	4.32129	−	1.15789i	0.199966	−	0.0535806i	0.357412	+	0.933947i	$0.383659\pi$
$468$		0			0
$469$	−1.49962	+	0.865804i	−0.0692458	+	0.0399791i
$470$	−27.8572	+	6.73433i	−1.28496	+	0.310632i
$471$		0			0
$472$	20.6309	+	14.4459i	0.949616	+	0.664929i
$473$	−11.2030	−	7.84443i	−0.515115	−	0.360687i
$474$		0			0
$475$	−26.9914	−	11.3570i	−1.23845	−	0.521093i
$476$	−2.83674	+	1.63780i	−0.130022	+	0.0750682i
$477$		0			0
$478$	−20.7402	+	5.55731i	−0.948632	+	0.254185i
$479$	34.5314	−	12.5684i	1.57778	−	0.574264i	0.603059	−	0.797697i	$-0.293948\pi$
$479$	34.5314	−	12.5684i	1.57778	−	0.574264i	0.974719	+	0.223432i	$0.0717262\pi$
$480$		0			0
$481$	0.508314	−	0.426526i	0.0231771	−	0.0194479i
$482$	−5.32332	−	11.4159i	−0.242470	−	0.519980i
$483$		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	$0.156284\pi$
$488$	−3.96257	−	5.65913i	−0.179377	−	0.256177i
$489$		0			0
$490$	−14.6569	−	2.95795i	−0.662131	−	0.133627i
$491$	−14.7648	−	17.5960i	−0.666326	−	0.794096i	0.321953	−	0.946756i	$-0.395661\pi$
$491$	−14.7648	−	17.5960i	−0.666326	−	0.794096i	−0.988279	+	0.152660i	$0.951216\pi$
$492$		0			0
$493$	57.5384	+	26.8306i	2.59140	+	1.20839i
$494$	1.36029	−	2.35609i	0.0612024	−	0.106006i
$495$		0			0
$496$	10.0668	+	17.4361i	0.452011	+	0.782906i
$497$	1.45907	+	16.6772i	0.0654482	+	0.748076i
$498$		0			0
$499$	−9.11992	+	1.60809i	−0.408264	+	0.0719879i	−0.374009	−	0.927425i	$-0.622017\pi$
$499$	−9.11992	+	1.60809i	−0.408264	+	0.0719879i	−0.0342550	+	0.999413i	$0.510906\pi$
$500$	0.503800	−	3.10051i	0.0225306	−	0.138659i
$501$		0			0
$502$	7.17569	−	0.627792i	0.320267	−	0.0280197i
$503$	−8.31780	−	2.22875i	−0.370873	−	0.0993750i	0.0685686	−	0.997646i	$-0.478157\pi$
$503$	−8.31780	−	2.22875i	−0.370873	−	0.0993750i	−0.439441	+	0.898271i	$0.644823\pi$
$504$		0			0
$505$	12.0652	+	27.6289i	0.536893	+	1.22947i
$506$	−0.184659	−	0.507345i	−0.00820908	−	0.0225543i
$507$		0			0
$508$	3.76553	+	0.329441i	0.167068	+	0.0146166i
$509$	−20.6614	−	7.52013i	−0.915799	−	0.333324i	−0.159233	−	0.987241i	$-0.550902\pi$
$509$	−20.6614	−	7.52013i	−0.915799	−	0.333324i	−0.756566	+	0.653917i	$0.773124\pi$
$510$		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
$515$	6.64955	+	0.163646i	0.293014	+	0.00721109i
$516$		0			0
$517$	21.3640	−	9.96221i	0.939589	−	0.438138i
$518$	−0.455459	+	5.20593i	−0.0200117	+	0.228735i
$519$		0			0
$520$	−1.71286	−	0.504440i	−0.0751139	−	0.0221211i
$521$	4.43677	+	2.56157i	0.194378	+	0.112224i	0.594031	−	0.804442i	$-0.297536\pi$
$521$	4.43677	+	2.56157i	0.194378	+	0.112224i	−0.399652	+	0.916667i	$0.630869\pi$
$522$		0			0
$523$	2.02890	−	7.57196i	0.0887177	−	0.331099i	−0.907275	−	0.420539i	$-0.861841\pi$
$523$	2.02890	−	7.57196i	0.0887177	−	0.331099i	0.995992	+	0.0894400i	$0.0285077\pi$
$524$	−1.33091	−	1.11677i	−0.0581412	−	0.0487863i
$525$		0			0
$526$	−0.873497	−	4.95385i	−0.0380863	−	0.215998i
$527$	18.7252	−	26.7424i	0.815685	−	1.16492i
$528$		0			0
$529$	−14.7735	+	17.6063i	−0.642325	+	0.765493i
$530$	0.257526	−	2.29237i	0.0111862	−	0.0995742i
$531$		0			0
$532$	0.683053	+	2.54919i	0.0296141	+	0.110521i
$533$	0.610389	−	1.30898i	0.0264389	−	0.0566984i
$534$		0			0
$535$	−18.5183	−	16.3317i	−0.800614	−	0.706079i
$536$	−0.958687	+	2.63397i	−0.0414090	+	0.113770i
$537$		0			0
$538$	−10.3603	+	7.25433i	−0.446663	+	0.312757i
$539$	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	$0.585108\pi$
$542$	17.0595	−	11.9452i	0.732767	−	0.513089i
$543$		0			0
$544$	−3.92339	+	10.7794i	−0.168214	+	0.462164i
$545$	0.0650212	+	1.03630i	0.00278520	+	0.0443903i
$546$		0			0
$547$	−0.220177	+	0.472172i	−0.00941410	+	0.0201886i	−0.910959	−	0.412498i	$-0.864656\pi$
$547$	−0.220177	+	0.472172i	−0.00941410	+	0.0201886i	0.901545	+	0.432686i	$0.142434\pi$
$548$	−0.536948	−	2.00392i	−0.0229373	−	0.0856032i
$549$		0			0
$550$	0.798052	+	20.9602i	0.0340290	+	0.893744i
$551$	32.8789	−	39.1836i	1.40069	−	1.66928i
$552$		0			0
$553$	1.90739	−	2.72403i	0.0811104	−	0.115838i
$554$	0.0322538	+	0.182920i	0.00137033	+	0.00777153i
$555$		0			0
$556$	−2.20695	−	1.85185i	−0.0935957	−	0.0785361i
$557$	−6.03527	+	22.5239i	−0.255723	+	0.954370i	0.711964	+	0.702216i	$0.247806\pi$
$557$	−6.03527	+	22.5239i	−0.255723	+	0.954370i	−0.967687	+	0.252155i	$0.918861\pi$
$558$		0			0
$559$	−1.31151	−	0.757203i	−0.0554711	−	0.0320263i
$560$	14.1172	−	7.69381i	0.596559	−	0.325123i
$561$		0			0
$562$	3.16269	−	36.1498i	0.133410	−	1.52489i
$563$	−31.1449	+	14.5231i	−1.31260	+	0.612076i	−0.947757	−	0.318993i	$-0.896656\pi$
$563$	−31.1449	+	14.5231i	−1.31260	+	0.612076i	−0.364844	+	0.931069i	$0.618878\pi$
$564$		0			0
$565$	−0.0263444	+	1.07047i	−0.00110832	+	0.0450351i
$566$		−	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	$-0.953185\pi$
$569$	−0.227444	+	1.28990i	−0.00953495	+	0.0540754i	0.979669	+	0.200620i	$0.0642958\pi$
$570$		0			0
$571$	−17.9969	−	6.55033i	−0.753146	−	0.274123i	−0.0632171	−	0.998000i	$-0.520136\pi$
$571$	−17.9969	−	6.55033i	−0.753146	−	0.274123i	−0.689929	+	0.723877i	$0.742358\pi$
$572$	−0.239119	−	0.0209202i	−0.00999807	−	0.000874718i
$573$		0			0
$574$	3.89033	+	10.6886i	0.162379	+	0.446133i
$575$	−0.544643	+	0.342721i	−0.0227132	+	0.0142924i
$576$		0			0
$577$	−12.6473	−	3.38883i	−0.526514	−	0.141079i	−0.0142358	−	0.999899i	$-0.504532\pi$
$577$	−12.6473	−	3.38883i	−0.526514	−	0.141079i	−0.512278	+	0.858820i	$0.671198\pi$
$578$	53.9231	−	4.71766i	2.24290	−	0.196229i
$579$		0			0
$580$	4.91420	+	2.44047i	0.204051	+	0.101335i
$581$	−20.8174	+	3.67067i	−0.863652	+	0.152285i
$582$		0			0
$583$	0.165364	+	1.89012i	0.00684869	+	0.0782808i
$584$	8.93766	+	15.4805i	0.369843	+	0.640587i
$585$		0			0
$586$	−3.97987	+	6.89333i	−0.164407	+	0.284761i
$587$	−26.3137	−	12.2703i	−1.08608	−	0.506449i	−0.204687	−	0.978827i	$-0.565618\pi$
$587$	−26.3137	−	12.2703i	−1.08608	−	0.506449i	−0.881396	+	0.472379i	$0.843395\pi$
$588$		0			0
$589$	−16.9072	−	20.1492i	−0.696650	−	0.830235i
$590$	6.48086	−	32.1132i	0.266813	−	1.32208i
$591$		0			0
$592$	5.54732	+	7.92239i	0.227993	+	0.325608i
$593$	18.8092	−	18.8092i	0.772402	−	0.772402i	−0.206124	−	0.978526i	$-0.566085\pi$
$593$	18.8092	−	18.8092i	0.772402	−	0.772402i	0.978526	+	0.206124i	$0.0660851\pi$
$594$		0			0
$595$	−20.9808	−	15.4739i	−0.860128	−	0.634368i
$596$	0.334697	+	0.0590161i	0.0137097	+	0.00241739i
$597$		0			0
$598$	−0.0252661	−	0.0541833i	−0.00103321	−	0.00221572i
$599$	−3.51169	+	2.94665i	−0.143484	+	0.120397i	−0.711704	−	0.702479i	$-0.752076\pi$
$599$	−3.51169	+	2.94665i	−0.143484	+	0.120397i	0.568221	+	0.822876i	$0.307632\pi$
$600$		0			0
$601$	25.1131	−	9.14041i	1.02438	−	0.372845i	0.225443	−	0.974256i	$-0.427617\pi$
$601$	25.1131	−	9.14041i	1.02438	−	0.372845i	0.798940	+	0.601411i	$0.205395\pi$
$602$	11.5202	−	3.08684i	0.469530	−	0.125810i
$603$		0			0
$604$	−3.93404	+	2.27132i	−0.160074	+	0.0924187i
$605$	1.72578	+	7.13884i	0.0701629	+	0.290235i
$606$		0			0
$607$	29.2803	+	20.5023i	1.18845	+	0.832163i	0.989025	−	0.147749i	$-0.0472028\pi$
$607$	29.2803	+	20.5023i	1.18845	+	0.832163i	0.199428	+	0.979913i	$0.436092\pi$
$608$	7.57081	+	5.30114i	0.307037	+	0.214990i
$609$		0			0
$610$	−4.68328	+	7.66950i	−0.189620	+	0.310529i
$611$	2.26053	−	1.30512i	0.0914512	−	0.0527994i
$612$		0			0
$613$	−35.8682	+	9.61085i	−1.44870	+	0.388179i	−0.895572	−	0.444916i	$-0.853233\pi$
$613$	−35.8682	+	9.61085i	−1.44870	+	0.388179i	−0.553130	+	0.833095i	$0.686567\pi$
$614$	31.4107	−	11.4325i	1.26763	−	0.461380i
$615$		0			0
$616$	−8.86034	+	7.43471i	−0.356993	+	0.299553i
$617$	−19.6545	−	42.1491i	−0.791258	−	1.69686i	−0.714316	−	0.699824i	$-0.753262\pi$
$617$	−19.6545	−	42.1491i	−0.791258	−	1.69686i	−0.0769428	−	0.997036i	$-0.524516\pi$
$618$		0			0
$619$	−13.9352	−	2.45716i	−0.560104	−	0.0987615i	−0.113573	−	0.993530i	$-0.536230\pi$
$619$	−13.9352	−	2.45716i	−0.560104	−	0.0987615i	−0.446531	+	0.894768i	$0.647341\pi$
$620$	1.67470	−	2.27070i	0.0672576	−	0.0911934i
$621$		0			0
$622$	15.3672	−	15.3672i	0.616168	−	0.616168i
$623$	−10.2699	−	14.6669i	−0.411455	−	0.587619i
$624$		0			0
$625$	24.2188	−	6.20074i	0.968752	−	0.248029i
$626$	20.6337	+	24.5903i	0.824687	+	0.982824i
$627$		0			0
$628$	5.28283	+	2.46342i	0.210808	+	0.0983013i
$629$	7.84112	−	13.5812i	0.312646	−	0.541519i
$630$		0			0
$631$	16.2979	+	28.2288i	0.648810	+	1.12377i	0.983407	+	0.181411i	$0.0580664\pi$
$631$	16.2979	+	28.2288i	0.648810	+	1.12377i	−0.334597	+	0.942361i	$0.608600\pi$
$632$	−0.469158	−	5.36250i	−0.0186621	−	0.213309i
$633$		0			0
$634$	34.1919	−	6.02895i	1.35793	−	0.239440i
$635$	9.59059	+	28.5139i	0.380591	+	1.13154i
$636$		0			0
$637$	1.35664	−	0.118690i	0.0537520	−	0.00470269i
$638$	−35.3901	−	9.48275i	−1.40111	−	0.375426i
$639$		0			0
$640$	10.6910	−	27.2664i	0.422597	−	1.07780i
$641$	11.8689	+	32.6096i	0.468794	+	1.28800i	0.918711	+	0.394931i	$0.129232\pi$
$641$	11.8689	+	32.6096i	0.468794	+	1.28800i	−0.449916	+	0.893071i	$0.648546\pi$
$642$		0			0
$643$	8.82626	+	0.772198i	0.348074	+	0.0304525i	0.259852	−	0.965648i	$-0.416326\pi$
$643$	8.82626	+	0.772198i	0.348074	+	0.0304525i	0.0882215	+	0.996101i	$0.471882\pi$
$644$	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	0.928167	−	0.372164i	$-0.121384\pi$
$647$	14.1426	+	14.1426i	0.556003	+	0.556003i	−0.372164	+	0.928167i	$0.621384\pi$
$648$		0			0
$649$			26.9457i			1.05771i
$650$	0.290318	+	2.30442i	0.0113872	+	0.0903867i
$651$		0			0
$652$	3.32886	−	1.55227i	0.130368	−	0.0607917i
$653$	0.173231	−	1.98004i	0.00677904	−	0.0774848i	−0.992052	−	0.125832i	$-0.959840\pi$
$653$	0.173231	−	1.98004i	0.00677904	−	0.0774848i	0.998831	+	0.0483474i	$0.0153955\pi$
$654$		0			0
$655$	3.90634	−	13.2643i	0.152633	−	0.518277i
$656$	18.2307	+	10.5255i	0.711788	+	0.410951i
$657$		0			0
$658$	−5.32049	+	19.8563i	−0.207414	+	0.774081i
$659$	9.93910	+	8.33989i	0.387172	+	0.324876i	0.815510	−	0.578742i	$-0.196456\pi$
$659$	9.93910	+	8.33989i	0.387172	+	0.324876i	−0.428338	+	0.903619i	$0.640901\pi$
$660$		0			0
$661$	2.91716	+	16.5440i	0.113464	+	0.643489i	0.987499	+	0.157625i	$0.0503837\pi$
$661$	2.91716	+	16.5440i	0.113464	+	0.643489i	−0.874035	+	0.485864i	$0.838505\pi$
$662$	−12.0886	+	17.2643i	−0.469836	+	0.670996i
$663$		0			0
$664$	−21.9947	+	26.2123i	−0.853561	+	1.01723i
$665$	−16.4174	+	13.1013i	−0.636641	+	0.508047i
$666$		0			0
$667$	−0.290921	−	1.08573i	−0.0112645	−	0.0420396i
$668$	−1.91063	+	4.09735i	−0.0739244	+	0.158531i
$669$		0			0
$670$	3.63890	−	0.228317i	0.140583	−	0.00882066i
$671$	2.52797	−	6.94554i	0.0975912	−	0.268130i
$672$		0			0
$673$	7.48390	−	5.24028i	0.288483	−	0.201998i	−0.420373	−	0.907352i	$-0.638101\pi$
$673$	7.48390	−	5.24028i	0.288483	−	0.201998i	0.708856	+	0.705353i	$0.249212\pi$
$674$	−21.8853			−0.842991
$675$		0			0
$676$	3.62584			0.139455
$677$	0.0991212	−	0.0694054i	0.00380954	−	0.00266747i	−0.571670	−	0.820484i	$-0.693704\pi$
$677$	0.0991212	−	0.0694054i	0.00380954	−	0.00266747i	0.575480	+	0.817816i	$0.304815\pi$
$678$		0			0
$679$	−6.50112	+	17.8617i	−0.249490	+	0.685468i
$680$	−42.1173	+	2.64259i	−1.61512	+	0.101339i
$681$		0			0
$682$	−7.96234	+	17.0753i	−0.304894	+	0.653847i
$683$	−3.58403	−	13.3758i	−0.137139	−	0.511810i	−0.999980	−	0.00633429i	$-0.997984\pi$
$683$	−3.58403	−	13.3758i	−0.137139	−	0.511810i	0.862841	−	0.505476i	$-0.168683\pi$
$684$		0			0
$685$	12.9058	−	10.2989i	0.493104	−	0.393502i
$686$	−17.7931	+	21.2049i	−0.679342	+	0.809608i
$687$		0			0
$688$	12.6604	−	18.0809i	0.482673	−	0.689329i
$689$	0.0364828	+	0.206904i	0.00138988	+	0.00788241i
$690$		0			0
$691$	17.4891	+	14.6751i	0.665315	+	0.558266i	0.911675	−	0.410913i	$-0.134790\pi$
$691$	17.4891	+	14.6751i	0.665315	+	0.558266i	−0.246359	+	0.969179i	$0.579234\pi$
$692$	0.192894	−	0.719892i	0.00733274	−	0.0273662i
$693$		0			0
$694$	−11.8745	−	6.85575i	−0.450750	−	0.260241i
$695$	6.47759	−	21.9951i	0.245709	−	0.834323i
$696$		0			0
$697$	2.97498	−	34.0042i	0.112686	−	1.28800i
$698$	−11.4089	+	5.32004i	−0.431832	+	0.201366i
$699$		0			0
$700$	−1.77981	−	1.38154i	−0.0672706	−	0.0522172i
$701$		−	15.6693i		−	0.591821i	−0.955216	−	0.295910i	$-0.904377\pi$
$701$		−	15.6693i		−	0.591821i	0.955216	−	0.295910i	$-0.0956230\pi$
$702$		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
$707$	21.5424	+	1.88471i	0.810184	+	0.0708820i
$708$		0			0
$709$	−2.91839	−	8.01821i	−0.109602	−	0.301130i	0.872751	−	0.488166i	$-0.162334\pi$
$709$	−2.91839	−	8.01821i	−0.109602	−	0.301130i	−0.982353	+	0.187036i	$0.940112\pi$
$710$	12.8673	−	32.8171i	0.482902	−	1.23160i
$711$		0			0
$712$	−27.9959	−	7.50148i	−1.04919	−	0.281130i
$713$	−0.575807	+	0.0503766i	−0.0215641	+	0.00188662i
$714$		0			0
$715$	−0.609022	−	1.81069i	−0.0227761	−	0.0677161i
$716$	1.89856	−	0.334767i	0.0709523	−	0.0125108i
$717$		0			0
$718$	1.85896	+	21.2480i	0.0693758	+	0.792968i
$719$	−19.9277	−	34.5157i	−0.743176	−	1.28722i	−0.951042	−	0.309062i	$-0.899985\pi$
$719$	−19.9277	−	34.5157i	−0.743176	−	1.28722i	0.207866	−	0.978157i	$-0.433348\pi$
$720$		0			0
$721$	2.38550	−	4.13180i	0.0888406	−	0.153876i
$722$	−20.9433	−	9.76600i	−0.779427	−	0.363453i
$723$		0			0
$724$	−3.61621	−	4.30963i	−0.134395	−	0.160166i
$725$	−2.14807	+	43.6157i	−0.0797773	+	1.61985i
$726$		0			0
$727$	26.2725	+	37.5210i	0.974393	+	1.39158i	0.919502	+	0.393085i	$0.128592\pi$
$727$	26.2725	+	37.5210i	0.974393	+	1.39158i	0.0548911	+	0.998492i	$0.482519\pi$
$728$	−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
$733$	−15.6365	−	33.5325i	−0.577546	−	1.23855i	−0.950507	−	0.310704i	$-0.899435\pi$
$733$	−15.6365	−	33.5325i	−0.577546	−	1.23855i	0.372961	−	0.927847i	$-0.378343\pi$
$734$	15.9308	−	13.3675i	0.588015	−	0.493403i
$735$		0			0
$736$	0.190850	−	0.0694636i	0.00703481	−	0.00256046i
$737$	−2.89670	+	0.776169i	−0.106701	+	0.0285906i
$738$		0			0
$739$	−9.45965	+	5.46153i	−0.347979	+	0.200906i	−0.663795	−	0.747915i	$-0.731055\pi$
$739$	−9.45965	+	5.46153i	−0.347979	+	0.200906i	0.315816	+	0.948820i	$0.397722\pi$
$740$	0.706341	−	1.15673i	0.0259656	−	0.0425222i
$741$		0			0
$742$	−1.35537	−	0.949040i	−0.0497572	−	0.0348404i
$743$	6.78635	+	4.75185i	0.248967	+	0.174329i	0.691398	−	0.722474i	$-0.256995\pi$
$743$	6.78635	+	4.75185i	0.248967	+	0.174329i	−0.442431	+	0.896802i	$0.645884\pi$
$744$		0			0
$745$	0.635584	+	2.62915i	0.0232860	+	0.0963246i
$746$	26.5695	−	15.3399i	0.972778	−	0.561633i
$747$		0			0
$748$	−5.47954	+	1.46824i	−0.200352	+	0.0536841i
$749$	−16.6422	+	6.05726i	−0.608093	+	0.221328i
$750$		0			0
$751$	1.01418	−	0.851000i	0.0370080	−	0.0310534i	−0.624096	−	0.781348i	$-0.714533\pi$
$751$	1.01418	−	0.851000i	0.0370080	−	0.0310534i	0.661104	+	0.750294i	$0.270088\pi$
$752$	16.0783	+	34.4801i	0.586317	+	1.25736i
$753$		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	$0.489283\pi$
$758$	18.0652	+	25.7998i	0.656159	+	0.937092i
$759$		0			0
$760$	−6.72608	+	33.3283i	−0.243980	+	1.20894i
$761$	−6.97127	−	8.30804i	−0.252708	−	0.301166i	0.624744	−	0.780829i	$-0.285203\pi$
$761$	−6.97127	−	8.30804i	−0.252708	−	0.301166i	−0.877453	+	0.479663i	$0.840759\pi$
$762$		0			0
$763$	0.674994	+	0.314755i	0.0244364	+	0.0113949i
$764$	−1.31601	+	2.27939i	−0.0476114	+	0.0824654i
$765$		0			0
$766$	−11.0760	−	19.1841i	−0.400191	−	0.693151i
$767$	0.260050	+	2.97239i	0.00938988	+	0.107327i
$768$		0			0
$769$	44.1842	−	7.79087i	1.59332	−	0.280946i	0.694579	−	0.719417i	$-0.255591\pi$
$769$	44.1842	−	7.79087i	1.59332	−	0.280946i	0.898745	+	0.438471i	$0.144480\pi$
$770$	13.4749	+	6.69186i	0.485602	+	0.241158i
$771$		0			0
$772$	5.89888	−	0.516085i	0.212305	−	0.0185743i
$773$	30.3757	+	8.13915i	1.09254	+	0.292745i	0.759723	−	0.650247i	$-0.225334\pi$
$773$	30.3757	+	8.13915i	1.09254	+	0.292745i	0.332816	+	0.942992i	$0.392001\pi$
$774$		0			0
$775$	21.8958	+	4.98246i	0.786521	+	0.178975i
$776$	10.5236	+	28.9133i	0.377775	+	1.03793i
$777$		0			0
$778$	−9.41874	−	0.824033i	−0.337678	−	0.0295430i
$779$	−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
$785$	−1.14135	+	46.3775i	−0.0407366	+	1.65529i
$786$		0			0
$787$	−28.5680	+	13.3215i	−1.01834	+	0.474860i	−0.858789	−	0.512330i	$-0.828783\pi$
$787$	−28.5680	+	13.3215i	−1.01834	+	0.474860i	−0.159552	+	0.987190i	$0.551005\pi$
$788$	−0.179939	+	2.05671i	−0.00641007	+	0.0732674i
$789$		0			0
$790$	−6.14820	+	3.35075i	−0.218743	+	0.119214i
$791$	0.665155	+	0.384027i	0.0236502	+	0.0136544i
$792$		0			0
$793$	0.211830	−	0.790562i	0.00752232	−	0.0280737i
$794$	−0.539681	−	0.452846i	−0.0191526	−	0.0160709i
$795$		0			0
$796$	−1.25879	−	7.13898i	−0.0446168	−	0.253034i
$797$	3.73721	−	5.33729i	0.132379	−	0.189057i	−0.747490	−	0.664273i	$-0.768741\pi$
$797$	3.73721	−	5.33729i	0.132379	−	0.189057i	0.879869	+	0.475216i	$0.157630\pi$
$798$		0			0
$799$	39.6531	−	47.2567i	1.40283	−	1.67182i
$800$	−7.88464	+	0.300206i	−0.278764	+	0.0106139i
$801$		0			0
$802$	−3.64928	−	13.6193i	−0.128860	−	0.480914i
$803$	−8.08234	+	17.3326i	−0.285220	+	0.611655i
$804$		0			0
$805$	0.0289035	+	0.460660i	0.00101871	+	0.0162361i
$806$	−0.713536	+	1.96042i	−0.0251332	+	0.0690530i
$807$		0			0
$808$	28.6741	−	20.0778i	1.00875	−	0.706335i
$809$	21.5117			0.756312			0.378156	−	0.925742i	$-0.376558\pi$
$809$	21.5117			0.756312			0.378156	+	0.925742i	$0.376558\pi$
$810$		0			0
$811$	15.2216			0.534502			0.267251	−	0.963627i	$-0.413885\pi$
$811$	15.2216			0.534502			0.267251	+	0.963627i	$0.413885\pi$
$812$	3.22382	−	2.25734i	0.113134	−	0.0792172i
$813$		0			0
$814$	−3.09539	+	8.50453i	−0.108494	+	0.298083i
$815$	21.9244	+	19.3356i	0.767979	+	0.677298i
$816$		0			0
$817$	−12.1868	+	26.1346i	−0.426362	+	0.914335i
$818$	−0.274706	−	1.02522i	−0.00960488	−	0.0358459i
$819$		0			0
$820$	0.329337	−	2.93160i	0.0115010	−	0.102376i
$821$	32.2494	−	38.4334i	1.12551	−	1.34133i	0.192581	−	0.981281i	$-0.438314\pi$
$821$	32.2494	−	38.4334i	1.12551	−	1.34133i	0.932932	−	0.360053i	$-0.117242\pi$
$822$		0			0
$823$	2.01204	−	2.87349i	0.0701354	−	0.100164i	−0.782552	−	0.622585i	$-0.786082\pi$
$823$	2.01204	−	2.87349i	0.0701354	−	0.100164i	0.852687	+	0.522422i	$0.174971\pi$
$824$	−1.34108	−	7.60564i	−0.0467187	−	0.264955i
$825$		0			0
$826$	−18.0008	−	15.1045i	−0.626327	−	0.525551i
$827$	−0.686704	+	2.56281i	−0.0238790	+	0.0891178i	−0.976837	−	0.213985i	$-0.931356\pi$
$827$	−0.686704	+	2.56281i	−0.0238790	+	0.0891178i	0.952958	+	0.303102i	$0.0980224\pi$
$828$		0			0
$829$	13.2911	+	7.67359i	0.461617	+	0.266515i	0.712724	−	0.701444i	$-0.247461\pi$
$829$	13.2911	+	7.67359i	0.461617	+	0.266515i	−0.251107	+	0.967959i	$0.580794\pi$
$830$	42.6960	+	12.5740i	1.48200	+	0.436451i
$831$		0			0
$832$	−0.176460	+	2.01695i	−0.00611766	+	0.0699251i
$833$	29.1693	−	13.6019i	1.01066	−	0.471277i
$834$		0			0
$835$	−35.9703	−	0.885231i	−1.24480	−	0.0306347i
$836$			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	−0.928649	−	0.370960i	$-0.879029\pi$
$839$	2.05282	−	11.6421i	0.0708712	−	0.401931i	0.999520	−	0.0309713i	$-0.00986003\pi$
$840$		0			0
$841$	−44.4266	−	16.1700i	−1.53195	−	0.557585i
$842$	−26.8064	−	2.34525i	−0.923808	−	0.0808227i
$843$		0			0
$844$	0.0336436	+	0.0924350i	0.00115806	+	0.00318174i
$845$	11.5485	+	26.4458i	0.397281	+	0.909762i
$846$		0			0
$847$	5.08850	+	1.36346i	0.174843	+	0.0468490i
$848$	−3.05053	+	0.266887i	−0.104756	+	0.00916493i
$849$		0			0
$850$	25.0745	+	48.8306i	0.860048	+	1.67488i
$851$	−0.273436	+	0.0482142i	−0.00937327	+	0.00165276i
$852$		0			0
$853$	−2.93357	−	33.5308i	−0.100443	−	1.14807i	−0.864400	−	0.502805i	$-0.832301\pi$
$853$	−2.93357	−	33.5308i	−0.100443	−	1.14807i	0.763956	−	0.645268i	$-0.223254\pi$
$854$	3.22284	+	5.58211i	0.110283	+	0.191016i
$855$		0			0
$856$	−14.3341	+	24.8274i	−0.489929	+	0.848583i
$857$	−33.6303	−	15.6821i	−1.14879	−	0.535689i	−0.247491	−	0.968890i	$-0.579606\pi$
$857$	−33.6303	−	15.6821i	−1.14879	−	0.535689i	−0.901297	+	0.433201i	$0.857384\pi$
$858$		0			0
$859$	18.6876	+	22.2710i	0.637613	+	0.759878i	0.983991	−	0.178217i	$-0.0570329\pi$
$859$	18.6876	+	22.2710i	0.637613	+	0.759878i	−0.346378	+	0.938095i	$0.612588\pi$
$860$	−3.03210	−	0.611915i	−0.103394	−	0.0208661i
$861$		0			0
$862$	−11.8627	−	16.9417i	−0.404046	−	0.577038i
$863$	−9.57951	+	9.57951i	−0.326090	+	0.326090i	−0.851098	−	0.525007i	$-0.824063\pi$
$863$	−9.57951	+	9.57951i	−0.326090	+	0.326090i	0.525007	+	0.851098i	$0.324063\pi$
$864$		0			0
$865$	5.86505	−	0.885983i	0.199418	−	0.0301243i
$866$	−48.0287	−	8.46876i	−1.63208	−	0.287780i
$867$		0			0
$868$	−0.855281	−	1.83416i	−0.0290301	−	0.0622553i
$869$	4.41177	−	3.70191i	0.149659	−	0.125579i
$870$		0			0
$871$	−0.312045	+	0.113575i	−0.0105733	+	0.00384835i
$872$	1.16451	−	0.312030i	0.0394353	−	0.0105667i
$873$		0			0
$874$	−0.985869	+	0.569192i	−0.0333475	+	0.0192532i
$875$	4.40770	−	17.3817i	0.149008	−	0.587609i
$876$		0			0
$877$	−18.1337	−	12.6973i	−0.612331	−	0.428759i	0.225842	−	0.974164i	$-0.427487\pi$
$877$	−18.1337	−	12.6973i	−0.612331	−	0.428759i	−0.838172	+	0.545405i	$0.816376\pi$
$878$	−13.9339	−	9.75663i	−0.470247	−	0.329270i
$879$		0			0
$880$	27.0644	−	6.54269i	0.912341	−	0.220554i
$881$	−38.5171	+	22.2379i	−1.29768	+	0.749213i	−0.980002	−	0.198987i	$-0.936235\pi$
$881$	−38.5171	+	22.2379i	−1.29768	+	0.749213i	−0.317673	+	0.948200i	$0.602902\pi$
$882$		0			0
$883$	−15.2412	+	4.08387i	−0.512907	+	0.137433i	−0.505984	−	0.862543i	$-0.668870\pi$
$883$	−15.2412	+	4.08387i	−0.512907	+	0.137433i	−0.00692327	+	0.999976i	$0.502204\pi$
$884$	−0.590280	+	0.214844i	−0.0198533	+	0.00722599i
$885$		0			0
$886$	7.81768	−	6.55981i	0.262640	−	0.220381i
$887$	11.6632	+	25.0117i	0.391610	+	0.839811i	0.998970	+	0.0453839i	$0.0144511\pi$
$887$	11.6632	+	25.0117i	0.391610	+	0.839811i	−0.607359	+	0.794427i	$0.707771\pi$
$888$		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
$893$	−28.5082	−	40.7139i	−0.953990	−	1.36244i
$894$		0			0
$895$	8.48870	+	12.7812i	0.283746	+	0.427230i
$896$	−13.5031	−	16.0924i	−0.451108	−	0.537609i
$897$		0			0
$898$	−15.6093	−	7.27874i	−0.520890	−	0.242895i
$899$	−19.6120	+	33.9690i	−0.654098	+	1.13293i
$900$		0			0
$901$	2.48266	+	4.30010i	0.0827095	+	0.143257i
$902$	1.71688	+	19.6241i	0.0571660	+	0.653410i
$903$		0			0
$904$	1.22439	−	0.215893i	0.0407226	−	0.00718049i
$905$	19.9153	−	40.1020i	0.662007	−	1.33303i
$906$		0			0
$907$	−3.71818	+	0.325298i	−0.123460	+	0.0108014i	−0.148718	−	0.988880i	$-0.547515\pi$
$907$	−3.71818	+	0.325298i	−0.123460	+	0.0108014i	0.0252582	+	0.999681i	$0.491959\pi$
$908$	6.39013	+	1.71223i	0.212064	+	0.0568223i
$909$		0			0
$910$	1.55100	+	0.608136i	0.0514152	+	0.0201595i
$911$	8.20345	+	22.5388i	0.271792	+	0.746743i	0.998228	+	0.0595086i	$0.0189534\pi$
$911$	8.20345	+	22.5388i	0.271792	+	0.746743i	−0.726435	+	0.687235i	$0.758824\pi$
$912$		0			0
$913$	−36.4695	−	3.19067i	−1.20697	−	0.105596i
$914$	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	$-0.372693\pi$
$920$	0.515159	+	0.541155i	0.0169843	+	0.0178414i
$921$		0			0
$922$	−57.0495	+	26.6026i	−1.87882	+	0.876110i
$923$	−0.279807	+	3.19821i	−0.00920995	+	0.105270i
$924$		0			0
$925$	10.6866	+	1.46759i	0.351372	+	0.0482540i
$926$	−4.35356	−	2.51353i	−0.143067	−	0.0825997i
$927$		0			0
$928$	3.56716	−	13.3128i	0.117098	−	0.437014i
$929$	−43.9037	−	36.8395i	−1.44043	−	1.20867i	−0.939208	−	0.343349i	$-0.888439\pi$
$929$	−43.9037	−	36.8395i	−1.44043	−	1.20867i	−0.501224	−	0.865317i	$-0.667117\pi$
$930$		0			0
$931$	−4.50286	−	25.5370i	−0.147575	−	0.836942i
$932$	3.48567	−	4.97805i	0.114177	−	0.163062i
$933$		0			0
$934$	−4.34306	+	5.17586i	−0.142109	+	0.169359i
$935$	−28.1615	−	35.2897i	−0.920981	−	1.15410i
$936$		0			0
$937$	−14.6753	−	54.7688i	−0.479420	−	1.78922i	−0.603971	−	0.797006i	$-0.706416\pi$
$937$	−14.6753	−	54.7688i	−0.479420	−	1.78922i	0.124551	−	0.992213i	$-0.460251\pi$
$938$	1.10524	−	2.37019i	0.0360873	−	0.0773895i
$939$		0			0
$940$	3.52646	−	3.99861i	0.115020	−	0.130420i
$941$	−13.7044	+	37.6526i	−0.446751	+	1.22744i	0.488222	+	0.872719i	$0.337646\pi$
$941$	−13.7044	+	37.6526i	−0.446751	+	1.22744i	−0.934973	+	0.354719i	$0.884577\pi$
$942$		0			0
$943$	−0.495050	+	0.346638i	−0.0161211	+	0.0112881i
$944$	−43.4886			−1.41543
$945$		0			0
$946$	20.6552			0.671557
$947$	−38.0843	+	26.6669i	−1.23757	+	0.866557i	−0.994631	−	0.103484i	$-0.967001\pi$
$947$	−38.0843	+	26.6669i	−1.23757	+	0.866557i	−0.242941	+	0.970041i	$0.578112\pi$
$948$		0			0
$949$	−0.724290	+	1.98997i	−0.0235114	+	0.0645972i
$950$	43.2306	−	9.33135i	1.40258	−	0.302749i
$951$		0			0
$952$	−12.7922	+	27.4331i	−0.414599	+	0.889110i
$953$	−14.9234	−	55.6950i	−0.483417	−	1.80414i	−0.587085	−	0.809526i	$-0.699724\pi$
$953$	−14.9234	−	55.6950i	−0.483417	−	1.80414i	0.103668	−	0.994612i	$-0.466942\pi$
$954$		0			0
$955$	−20.8167	−	2.33856i	−0.673614	−	0.0756742i
$956$	2.56752	−	3.05985i	0.0830396	−	0.0989627i
$957$		0			0
$958$	−31.8330	+	45.4622i	−1.02848	+	1.46882i
$959$	−2.05655	−	11.6633i	−0.0664095	−	0.376627i
$960$		0			0
$961$	−8.29622	−	6.96135i	−0.267620	−	0.224560i
$962$	−0.259378	+	0.968010i	−0.00836267	+	0.0312099i
$963$		0			0
$964$	2.02929	+	1.17161i	0.0653589	+	0.0377350i
$965$	22.5524	+	41.3809i	0.725989	+	1.33210i
$966$		0			0
$967$	2.27121	−	25.9600i	0.0730371	−	0.834818i	−0.868011	−	0.496545i	$-0.834602\pi$
$967$	2.27121	−	25.9600i	0.0730371	−	0.834818i	0.941048	−	0.338273i	$-0.109843\pi$
$968$	7.72854	−	3.60388i	0.248405	−	0.115833i
$969$		0			0
$970$	28.9882	−	27.5957i	0.930757	−	0.886045i
$971$			24.3222i			0.780536i	0.920701	+	0.390268i	$0.127618\pi$
$971$			24.3222i			0.780536i	−0.920701	+	0.390268i	$0.872382\pi$
$972$		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
$977$	4.39652	+	0.384646i	0.140657	+	0.0123059i	0.157267	−	0.987556i	$-0.449732\pi$
$977$	4.39652	+	0.384646i	0.140657	+	0.0123059i	−0.0166097	+	0.999862i	$0.505287\pi$
$978$		0			0
$979$	−10.6057	−	29.1388i	−0.338958	−	0.931280i
$980$	2.54911	−	1.11316i	0.0814284	−	0.0355587i
$981$		0			0
$982$	33.5090	+	8.97872i	1.06932	+	0.286522i
$983$	−6.29396	+	0.550651i	−0.200746	+	0.0175630i	−0.187085	−	0.982344i	$-0.559904\pi$
$983$	−6.29396	+	0.550651i	−0.200746	+	0.0175630i	−0.0136609	+	0.999907i	$0.504349\pi$
$984$		0			0
$985$	−15.5742	+	5.23833i	−0.496235	+	0.166907i
$986$	−94.4260	+	16.6499i	−3.00714	+	0.530240i
$987$		0			0
$988$	0.0441099	+	0.504179i	0.00140332	+	0.0160401i
$989$	0.316839	+	0.548781i	0.0100749	+	0.0174502i
$990$		0			0
$991$	3.28793	−	5.69486i	0.104445	−	0.180903i	−0.809067	−	0.587717i	$-0.800027\pi$
$991$	3.28793	−	5.69486i	0.104445	−	0.180903i	0.913511	+	0.406814i	$0.133360\pi$
$992$	−6.42327	−	2.99522i	−0.203939	−	0.0950983i
$993$		0			0
$994$	−16.2520	−	19.3683i	−0.515481	−	0.614326i
$995$	48.0602	−	31.9193i	1.52361	−	1.01191i
$996$		0			0
$997$	11.4987	+	16.4219i	0.364168	+	0.520086i	0.958864	−	0.283864i	$-0.0916165\pi$
$997$	11.4987	+	16.4219i	0.364168	+	0.520086i	−0.594696	+	0.803951i	$0.702728\pi$
$998$	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.8.4		192
3.2	odd	2		135.2.q.a.83.13	yes	192
5.2	odd	4	inner	405.2.r.a.332.4		192
15.2	even	4		135.2.q.a.2.13	✓	192
15.8	even	4		675.2.ba.b.407.4		192
15.14	odd	2		675.2.ba.b.218.4		192
27.13	even	9		135.2.q.a.68.13	yes	192
27.14	odd	18	inner	405.2.r.a.233.4		192
135.13	odd	36		675.2.ba.b.257.4		192
135.67	odd	36		135.2.q.a.122.13	yes	192
135.94	even	18		675.2.ba.b.68.4		192
135.122	even	36	inner	405.2.r.a.152.4		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.13	✓	192	15.2	even	4
135.2.q.a.68.13	yes	192	27.13	even	9
135.2.q.a.83.13	yes	192	3.2	odd	2
135.2.q.a.122.13	yes	192	135.67	odd	36
405.2.r.a.8.4		192	1.1	even	1	trivial
405.2.r.a.152.4		192	135.122	even	36	inner
405.2.r.a.233.4		192	27.14	odd	18	inner
405.2.r.a.332.4		192	5.2	odd	4	inner
675.2.ba.b.68.4		192	135.94	even	18
675.2.ba.b.218.4		192	15.14	odd	2
675.2.ba.b.257.4		192	135.13	odd	36
675.2.ba.b.407.4		192	15.8	even	4

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)

\(f(q)\)	\(=\)	\(q+(-1.23715 + 0.866263i) q^{2} +(0.0960923 - 0.264011i) q^{4} +(2.23168 - 0.140023i) q^{5} +(0.677826 - 1.45360i) q^{7} +(-0.671958 - 2.50778i) q^{8} +(-2.63963 + 2.10645i) q^{10} +(1.78545 - 2.12782i) q^{11} +(0.176418 - 0.251952i) q^{13} +(0.420628 + 2.38550i) q^{14} +(3.43416 + 2.88160i) q^{16} +(1.88139 - 7.02145i) q^{17} +(-5.07203 - 2.92834i) q^{19} +(0.177479 - 0.602644i) q^{20} +(-0.365624 + 4.17910i) q^{22} +(-0.116642 + 0.0543910i) q^{23} +(4.96079 - 0.624975i) q^{25} +0.464527i q^{26} +(-0.318634 - 0.318634i) q^{28} +(-1.51659 + 8.60103i) q^{29} +(4.22026 + 1.53605i) q^{31} +(-1.57207 - 0.137538i) q^{32} +(3.75485 + 10.3164i) q^{34} +(1.30915 - 3.33889i) q^{35} +(2.08386 + 0.558369i) q^{37} +(8.81158 - 0.770913i) q^{38} +(-1.85074 - 5.50247i) q^{40} +(4.62442 - 0.815410i) q^{41} +(-0.429127 - 4.90494i) q^{43} +(-0.390200 - 0.675847i) q^{44} +(0.0971868 - 0.168333i) q^{46} +(7.69135 + 3.58654i) q^{47} +(2.84600 + 3.39173i) q^{49} +(-5.59585 + 5.07053i) q^{50} +(-0.0495656 - 0.0707870i) q^{52} +(-0.483003 + 0.483003i) q^{53} +(3.68661 - 4.99861i) q^{55} +(-4.10079 - 0.723079i) q^{56} +(-5.57450 - 11.9546i) q^{58} +(-7.43127 + 6.23558i) q^{59} +(2.50049 - 0.910105i) q^{61} +(-6.55173 + 1.75553i) q^{62} +(-5.70071 + 3.29131i) q^{64} +(0.358430 - 0.586978i) q^{65} +(-0.884390 - 0.619257i) q^{67} +(-1.67295 - 1.17142i) q^{68} +(1.27273 + 5.26478i) q^{70} +(-9.03942 + 5.21891i) q^{71} +(-6.65047 + 1.78199i) q^{73} +(-3.06175 + 1.11439i) q^{74} +(-1.26050 + 1.05768i) q^{76} +(-1.88278 - 4.03763i) q^{77} +(2.04188 + 0.360038i) q^{79} +(8.06743 + 5.94995i) q^{80} +(-5.01475 + 5.01475i) q^{82} +(-7.55956 - 10.7962i) q^{83} +(3.21549 - 15.9331i) q^{85} +(4.77986 + 5.69642i) q^{86} +(-6.53585 - 3.04772i) q^{88} +(5.58181 - 9.66798i) q^{89} +(-0.246656 - 0.427222i) q^{91} +(0.00315146 + 0.0360214i) q^{92} +(-12.6222 + 2.22564i) q^{94} +(-11.7292 - 5.82491i) q^{95} +(-11.8062 + 1.03291i) q^{97} +(-6.45906 - 1.73070i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100}) \) 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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Database

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