LMFDB - Embedded newform 405.2.r.a.8.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,2,Mod(8,405)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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			8.13
Character	$\chi$	$=$	405.8
Dual form			405.2.r.a.152.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.42277 - 0.996232i) q^{2} +(0.347747 - 0.955427i) q^{4} +(0.893670 + 2.04972i) q^{5} +(0.429055 - 0.920112i) q^{7} +(0.442010 + 1.64960i) q^{8} +O(q^{10})$	\(q+(1.42277 - 0.996232i) q^{2} +(0.347747 - 0.955427i) q^{4} +(0.893670 + 2.04972i) q^{5} +(0.429055 - 0.920112i) q^{7} +(0.442010 + 1.64960i) q^{8} +(3.31348 + 2.02597i) q^{10} +(0.759141 - 0.904709i) q^{11} +(2.21505 - 3.16342i) q^{13} +(-0.306200 - 1.73654i) q^{14} +(3.83001 + 3.21376i) q^{16} +(-0.144887 + 0.540727i) q^{17} +(3.83587 + 2.21464i) q^{19} +(2.26913 - 0.141052i) q^{20} +(0.178781 - 2.04347i) q^{22} +(-4.21975 + 1.96770i) q^{23} +(-3.40271 + 3.66355i) q^{25} -6.70752i q^{26} +(-0.729897 - 0.729897i) q^{28} +(1.44060 - 8.17007i) q^{29} +(-7.51688 - 2.73592i) q^{31} +(5.24827 + 0.459164i) q^{32} +(0.332549 + 0.913671i) q^{34} +(2.26941 + 0.0571670i) q^{35} +(-5.30076 - 1.42034i) q^{37} +(7.66385 - 0.670500i) q^{38} +(-2.98621 + 2.38020i) q^{40} +(-5.46773 + 0.964109i) q^{41} +(0.0660161 + 0.754568i) q^{43} +(-0.600395 - 1.03991i) q^{44} +(-4.04344 + 7.00343i) q^{46} +(-11.1364 - 5.19301i) q^{47} +(3.83700 + 4.57275i) q^{49} +(-1.19152 + 8.60226i) q^{50} +(-2.25214 - 3.21639i) q^{52} +(5.40763 - 5.40763i) q^{53} +(2.53282 + 0.747516i) q^{55} +(1.70747 + 0.301072i) q^{56} +(-6.08964 - 13.0593i) q^{58} +(-6.20310 + 5.20502i) q^{59} +(10.5365 - 3.83498i) q^{61} +(-13.4204 + 3.59598i) q^{62} +(-0.735277 + 0.424512i) q^{64} +(8.46365 + 1.71318i) q^{65} +(-1.29416 - 0.906180i) q^{67} +(0.466241 + 0.326466i) q^{68} +(3.28579 - 2.17952i) q^{70} +(-6.95937 + 4.01800i) q^{71} +(-5.11087 + 1.36945i) q^{73} +(-8.95674 + 3.25999i) q^{74} +(3.44984 - 2.89476i) q^{76} +(-0.506721 - 1.08667i) q^{77} +(6.62789 + 1.16868i) q^{79} +(-3.16454 + 10.7225i) q^{80} +(-6.81884 + 6.81884i) q^{82} +(-0.172108 - 0.245796i) q^{83} +(-1.23782 + 0.186253i) q^{85} +(0.845650 + 1.00781i) q^{86} +(1.82796 + 0.852391i) q^{88} +(5.41601 - 9.38081i) q^{89} +(-1.96032 - 3.39538i) q^{91} +(0.412590 + 4.71593i) q^{92} +(-21.0180 + 3.70604i) q^{94} +(-1.11139 + 9.84163i) q^{95} +(-5.10194 + 0.446362i) q^{97} +(10.0147 + 2.68342i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8	$ 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}+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

Display 100 coefficients 10 coefficients

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 $

$2$	1.42277	−	0.996232i	1.00605	−	0.704443i	0.0503320	−	0.998733i	$-0.483972\pi$
$2$	1.42277	−	0.996232i	1.00605	−	0.704443i	0.955716	+	0.294290i	$0.0950832\pi$
$3$		0			0
$3$		0			0
$4$	0.347747	−	0.955427i	0.173874	−	0.477714i
$5$	0.893670	+	2.04972i	0.399661	+	0.916663i
$5$	0.893670	+	2.04972i	0.399661	+	0.916663i
$6$		0			0
$7$	0.429055	−	0.920112i	0.162168	−	0.347770i	−0.808387	−	0.588652i	$-0.799659\pi$
$7$	0.429055	−	0.920112i	0.162168	−	0.347770i	0.970554	+	0.240882i	$0.0774367\pi$
$8$	0.442010	+	1.64960i	0.156274	+	0.583223i
$9$		0			0
$10$	3.31348	+	2.02597i	1.04781	+	0.640669i
$11$	0.759141	−	0.904709i	0.228890	−	0.272780i	−0.639360	−	0.768908i	$-0.720801\pi$
$11$	0.759141	−	0.904709i	0.228890	−	0.272780i	0.868250	+	0.496127i	$0.165245\pi$
$12$		0			0
$13$	2.21505	−	3.16342i	0.614345	−	0.877375i	−0.384610	−	0.923079i	$-0.625664\pi$
$13$	2.21505	−	3.16342i	0.614345	−	0.877375i	0.998955	+	0.0457040i	$0.0145531\pi$
$14$	−0.306200	−	1.73654i	−0.0818353	−	0.464111i
$15$		0			0
$16$	3.83001	+	3.21376i	0.957502	+	0.803439i
$17$	−0.144887	+	0.540727i	−0.0351404	+	0.131146i	−0.981268	−	0.192649i	$-0.938292\pi$
$17$	−0.144887	+	0.540727i	−0.0351404	+	0.131146i	0.946127	+	0.323795i	$0.104959\pi$
$18$		0			0
$19$	3.83587	+	2.21464i	0.880010	+	0.508074i	0.870662	−	0.491882i	$-0.163691\pi$
$19$	3.83587	+	2.21464i	0.880010	+	0.508074i	0.00934815	+	0.999956i	$0.497024\pi$
$20$	2.26913	−	0.141052i	0.507393	−	0.0315402i
$21$		0			0
$22$	0.178781	−	2.04347i	0.0381162	−	0.435670i
$23$	−4.21975	+	1.96770i	−0.879879	+	0.410294i	−0.809427	−	0.587221i	$-0.800222\pi$
$23$	−4.21975	+	1.96770i	−0.879879	+	0.410294i	−0.0704523	+	0.997515i	$0.522444\pi$
$24$		0			0
$25$	−3.40271	+	3.66355i	−0.680542	+	0.732709i
$26$		−	6.70752i		−	1.31545i
$27$		0			0
$28$	−0.729897	−	0.729897i	−0.137938	−	0.137938i
$29$	1.44060	−	8.17007i	0.267513	−	1.51714i	−0.494268	−	0.869309i	$-0.664564\pi$
$29$	1.44060	−	8.17007i	0.267513	−	1.51714i	0.761782	−	0.647834i	$-0.224325\pi$
$30$		0			0
$31$	−7.51688	−	2.73592i	−1.35007	−	0.491386i	−0.437102	−	0.899412i	$-0.643995\pi$
$31$	−7.51688	−	2.73592i	−1.35007	−	0.491386i	−0.912970	+	0.408026i	$0.866217\pi$
$32$	5.24827	+	0.459164i	0.927771	+	0.0811694i
$33$		0			0
$34$	0.332549	+	0.913671i	0.0570317	+	0.156693i
$35$	2.26941	+	0.0571670i	0.383600	+	0.00966299i
$36$		0			0
$37$	−5.30076	−	1.42034i	−0.871440	−	0.233502i	−0.204730	−	0.978819i	$-0.565632\pi$
$37$	−5.30076	−	1.42034i	−0.871440	−	0.233502i	−0.666710	+	0.745317i	$0.732298\pi$
$38$	7.66385	−	0.670500i	1.24324	−	0.108770i
$39$		0			0
$40$	−2.98621	+	2.38020i	−0.472162	+	0.376342i
$41$	−5.46773	+	0.964109i	−0.853917	+	0.150569i	−0.583438	−	0.812157i	$-0.698293\pi$
$41$	−5.46773	+	0.964109i	−0.853917	+	0.150569i	−0.270478	+	0.962726i	$0.587182\pi$
$42$		0			0
$43$	0.0660161	+	0.754568i	0.0100674	+	0.115070i	0.999566	−	0.0294750i	$-0.00938355\pi$
$43$	0.0660161	+	0.754568i	0.0100674	+	0.115070i	−0.989498	+	0.144546i	$0.953828\pi$
$44$	−0.600395	−	1.03991i	−0.0905129	−	0.156773i
$45$		0			0
$46$	−4.04344	+	7.00343i	−0.596172	+	1.03260i
$47$	−11.1364	−	5.19301i	−1.62442	−	0.757478i	−0.624691	−	0.780872i	$-0.714775\pi$
$47$	−11.1364	−	5.19301i	−1.62442	−	0.757478i	−0.999726	+	0.0233932i	$0.992553\pi$
$48$		0			0
$49$	3.83700	+	4.57275i	0.548142	+	0.653250i
$50$	−1.19152	+	8.60226i	−0.168506	+	1.21654i
$51$		0			0
$52$	−2.25214	−	3.21639i	−0.312316	−	0.446033i
$53$	5.40763	−	5.40763i	0.742795	−	0.742795i	−0.230320	−	0.973115i	$-0.573977\pi$
$53$	5.40763	−	5.40763i	0.742795	−	0.742795i	0.973115	+	0.230320i	$0.0739772\pi$
$54$		0			0
$55$	2.53282	+	0.747516i	0.341526	+	0.100795i
$56$	1.70747	+	0.301072i	0.228170	+	0.0402325i
$57$		0			0
$58$	−6.08964	−	13.0593i	−0.799609	−	1.71477i
$59$	−6.20310	+	5.20502i	−0.807575	+	0.677636i	−0.950028	−	0.312166i	$-0.898946\pi$
$59$	−6.20310	+	5.20502i	−0.807575	+	0.677636i	0.142453	+	0.989802i	$0.454501\pi$
$60$		0			0
$61$	10.5365	−	3.83498i	1.34906	−	0.491018i	0.436407	−	0.899749i	$-0.356251\pi$
$61$	10.5365	−	3.83498i	1.34906	−	0.491018i	0.912655	+	0.408731i	$0.134029\pi$
$62$	−13.4204	+	3.59598i	−1.70439	+	0.456690i
$63$		0			0
$64$	−0.735277	+	0.424512i	−0.0919096	+	0.0530640i
$65$	8.46365	+	1.71318i	1.04979	+	0.212494i
$66$		0			0
$67$	−1.29416	−	0.906180i	−0.158107	−	0.110707i	0.491846	−	0.870682i	$-0.336322\pi$
$67$	−1.29416	−	0.906180i	−0.158107	−	0.110707i	−0.649953	+	0.759975i	$0.725211\pi$
$68$	0.466241	+	0.326466i	0.0565401	+	0.0395898i
$69$		0			0
$70$	3.28579	−	2.17952i	0.392727	−	0.260503i
$71$	−6.95937	+	4.01800i	−0.825926	+	0.476849i	−0.852456	−	0.522800i	$-0.824888\pi$
$71$	−6.95937	+	4.01800i	−0.825926	+	0.476849i	0.0265298	+	0.999648i	$0.491554\pi$
$72$		0			0
$73$	−5.11087	+	1.36945i	−0.598182	+	0.160282i	−0.545190	−	0.838312i	$-0.683543\pi$
$73$	−5.11087	+	1.36945i	−0.598182	+	0.160282i	−0.0529922	+	0.998595i	$0.516876\pi$
$74$	−8.95674	+	3.25999i	−1.04120	+	0.378966i
$75$		0			0
$76$	3.44984	−	2.89476i	0.395724	−	0.332052i
$77$	−0.506721	−	1.08667i	−0.0577462	−	0.123837i
$78$		0			0
$79$	6.62789	+	1.16868i	0.745696	+	0.131486i	0.533570	−	0.845756i	$-0.320850\pi$
$79$	6.62789	+	1.16868i	0.745696	+	0.131486i	0.212126	+	0.977242i	$0.431961\pi$
$80$	−3.16454	+	10.7225i	−0.353807	+	1.19881i
$81$		0			0
$82$	−6.81884	+	6.81884i	−0.753014	+	0.753014i
$83$	−0.172108	−	0.245796i	−0.0188913	−	0.0269796i	0.809595	−	0.586988i	$-0.199687\pi$
$83$	−0.172108	−	0.245796i	−0.0188913	−	0.0269796i	−0.828487	+	0.560009i	$0.810798\pi$
$84$		0			0
$85$	−1.23782	+	0.186253i	−0.134261	+	0.0202020i
$86$	0.845650	+	1.00781i	0.0911888	+	0.108675i
$87$		0			0
$88$	1.82796	+	0.852391i	0.194861	+	0.0908652i
$89$	5.41601	−	9.38081i	0.574096	−	0.994364i	−0.422043	−	0.906576i	$-0.638687\pi$
$89$	5.41601	−	9.38081i	0.574096	−	0.994364i	0.996139	−	0.0877879i	$-0.0279798\pi$
$90$		0			0
$91$	−1.96032	−	3.39538i	−0.205498	−	0.355932i
$92$	0.412590	+	4.71593i	0.0430155	+	0.491670i
$93$		0			0
$94$	−21.0180	+	3.70604i	−2.16784	+	0.382249i
$95$	−1.11139	+	9.84163i	−0.114027	+	1.00973i
$96$		0			0
$97$	−5.10194	+	0.446362i	−0.518023	+	0.0453212i	−0.343170	−	0.939273i	$-0.611501\pi$
$97$	−5.10194	+	0.446362i	−0.518023	+	0.0453212i	−0.174853	+	0.984595i	$0.555945\pi$
$98$	10.0147	+	2.68342i	1.01163	+	0.271067i
$99$		0			0
$100$	2.31697	+	4.52503i	0.231697	+	0.452503i
$101$	6.63190	+	18.2210i	0.659899	+	1.81306i	0.577393	+	0.816467i	$0.304070\pi$
$101$	6.63190	+	18.2210i	0.659899	+	1.81306i	0.0825062	+	0.996591i	$0.473708\pi$
$102$		0			0
$103$	14.8525	+	1.29943i	1.46346	+	0.128036i	0.790873	−	0.611980i	$-0.209627\pi$
$103$	14.8525	+	1.29943i	1.46346	+	0.128036i	0.672589	+	0.740016i	$0.265182\pi$
$104$	6.19746	+	2.25569i	0.607711	+	0.221189i
$105$		0			0
$106$	2.30654	−	13.0811i	0.224031	−	1.27054i
$107$	−3.20052	−	3.20052i	−0.309406	−	0.309406i	0.535273	−	0.844679i	$-0.320209\pi$
$107$	−3.20052	−	3.20052i	−0.309406	−	0.309406i	−0.844679	+	0.535273i	$0.820209\pi$
$108$		0			0
$109$		−	10.7258i		−	1.02735i	−0.857986	−	0.513673i	$-0.828284\pi$
$109$		−	10.7258i		−	1.02735i	0.857986	−	0.513673i	$-0.171716\pi$
$110$	4.34832	−	1.45974i	0.414596	−	0.139181i
$111$		0			0
$112$	4.60030	−	2.14516i	0.434688	−	0.202698i
$113$	1.10011	−	12.5744i	0.103490	−	1.18290i	−0.749874	−	0.661581i	$-0.769886\pi$
$113$	1.10011	−	12.5744i	0.103490	−	1.18290i	0.853364	−	0.521316i	$-0.174559\pi$
$114$		0			0
$115$	−7.80431	−	6.89084i	−0.727755	−	0.642574i
$116$	−7.30494	−	4.21751i	−0.678247	−	0.391586i
$117$		0			0
$118$	−3.64016	+	13.5853i	−0.335104	+	1.25062i
$119$	0.435365	+	0.365315i	0.0399099	+	0.0334883i
$120$		0			0
$121$	1.66793	+	9.45928i	0.151630	+	0.859935i
$122$	11.1705	−	15.9531i	1.01133	−	1.44432i
$123$		0			0
$124$	−5.22795	+	6.23043i	−0.469484	+	0.559509i
$125$	−10.5501	−	3.70060i	−0.943634	−	0.330992i
$126$		0			0
$127$	−4.56717	−	17.0449i	−0.405270	−	1.51249i	−0.803556	−	0.595229i	$-0.797061\pi$
$127$	−4.56717	−	17.0449i	−0.405270	−	1.51249i	0.398286	−	0.917261i	$-0.369605\pi$
$128$	−5.07618	+	10.8859i	−0.448676	+	0.962188i
$129$		0			0
$130$	13.7485	−	5.99430i	1.20583	−	0.525735i
$131$	0.988469	−	2.71580i	0.0863629	−	0.237280i	−0.888992	−	0.457923i	$-0.848593\pi$
$131$	0.988469	−	2.71580i	0.0863629	−	0.237280i	0.975355	+	0.220643i	$0.0708156\pi$
$132$		0			0
$133$	3.68352	−	2.57923i	0.319402	−	0.223648i
$134$	−2.74405			−0.237050
$135$		0			0
$136$	−0.956027			−0.0819787
$137$	6.89836	−	4.83028i	0.589367	−	0.412679i	−0.240493	−	0.970651i	$-0.577309\pi$
$137$	6.89836	−	4.83028i	0.589367	−	0.412679i	0.829860	+	0.557972i	$0.188420\pi$
$138$		0			0
$139$	−3.42050	+	9.39775i	−0.290123	+	0.797107i	0.705925	+	0.708287i	$0.250532\pi$
$139$	−3.42050	+	9.39775i	−0.290123	+	0.797107i	−0.996048	+	0.0888198i	$0.971690\pi$
$140$	0.843798	−	2.14837i	0.0713140	−	0.181571i
$141$		0			0
$142$	−5.89871	+	12.6498i	−0.495009	+	1.06155i
$143$	−1.18044	−	4.40546i	−0.0987133	−	0.368403i
$144$		0			0
$145$	18.0338	−	4.34851i	1.49762	−	0.361124i
$146$	−5.90728	+	7.04003i	−0.488890	+	0.582637i
$147$		0			0
$148$	−3.20035	+	4.57058i	−0.263067	+	0.375699i
$149$	2.48868	+	14.1140i	0.203881	+	1.15626i	0.899191	+	0.437555i	$0.144156\pi$
$149$	2.48868	+	14.1140i	0.203881	+	1.15626i	−0.695311	+	0.718709i	$0.744733\pi$
$150$		0			0
$151$	4.12708	+	3.46303i	0.335857	+	0.281818i	0.795081	−	0.606503i	$-0.207428\pi$
$151$	4.12708	+	3.46303i	0.335857	+	0.281818i	−0.459224	+	0.888320i	$0.651873\pi$
$152$	−1.95779	+	7.30656i	−0.158798	+	0.592640i
$153$		0			0
$154$	−1.80352	−	1.04126i	−0.145332	−	0.0839072i
$155$	−1.10974	−	17.8525i	−0.0891362	−	1.43395i
$156$		0			0
$157$	−0.694063	+	7.93317i	−0.0553922	+	0.633136i	0.916861	+	0.399206i	$0.130714\pi$
$157$	−0.694063	+	7.93317i	−0.0553922	+	0.633136i	−0.972253	+	0.233930i	$0.924841\pi$
$158$	10.5942	−	4.94016i	0.842831	−	0.393018i
$159$		0			0
$160$	3.74906	+	11.1678i	0.296389	+	0.882893i
$161$			4.72690i			0.372532i
$162$		0			0
$163$	−11.3432	−	11.3432i	−0.888466	−	0.888466i	0.105910	−	0.994376i	$-0.466224\pi$
$163$	−11.3432	−	11.3432i	−0.888466	−	0.888466i	−0.994376	+	0.105910i	$0.966224\pi$
$164$	−0.980253	+	5.55929i	−0.0765449	+	0.434108i
$165$		0			0
$166$	−0.489740	−	0.178251i	−0.0380112	−	0.0138349i
$167$	0.422026	+	0.0369225i	0.0326574	+	0.00285715i	0.103473	−	0.994632i	$-0.467005\pi$
$167$	0.422026	+	0.0369225i	0.0326574	+	0.00285715i	−0.0708153	+	0.997489i	$0.522560\pi$
$168$		0			0
$169$	−0.654517	−	1.79827i	−0.0503475	−	0.138329i
$170$	−1.57558	+	1.49815i	−0.120842	+	0.114903i
$171$		0			0
$172$	0.743891	+	0.199325i	0.0567212	+	0.0151984i
$173$	8.04840	−	0.704144i	0.611909	−	0.0535351i	0.223011	−	0.974816i	$-0.428411\pi$
$173$	8.04840	−	0.704144i	0.611909	−	0.0535351i	0.388898	+	0.921281i	$0.372856\pi$
$174$		0			0
$175$	1.91092	+	4.70274i	0.144452	+	0.355494i
$176$	5.81503	−	1.02535i	0.438325	−	0.0772885i
$177$		0			0
$178$	−1.63974	−	18.7423i	−0.122904	−	1.40480i
$179$	−6.38218	−	11.0543i	−0.477026	−	0.826234i	0.522627	−	0.852561i	$-0.324952\pi$
$179$	−6.38218	−	11.0543i	−0.477026	−	0.826234i	−0.999653	+	0.0263277i	$0.991619\pi$
$180$		0			0
$181$	−9.24880	+	16.0194i	−0.687458	+	1.19071i	0.285199	+	0.958468i	$0.407940\pi$
$181$	−9.24880	+	16.0194i	−0.687458	+	1.19071i	−0.972657	+	0.232244i	$0.925393\pi$
$182$	−6.17167	−	2.87790i	−0.457474	−	0.213324i
$183$		0			0
$184$	−5.11110	−	6.09117i	−0.376795	−	0.449047i
$185$	−1.82584	−	12.1344i	−0.134239	−	0.892139i
$186$		0			0
$187$	0.379211	+	0.541570i	0.0277307	+	0.0396035i
$188$	−8.83421	+	8.83421i	−0.644301	+	0.644301i
$189$		0			0
$190$	8.22329	+	15.1096i	0.596580	+	1.09616i
$191$	−4.20349	−	0.741189i	−0.304154	−	0.0536306i	0.0194882	−	0.999810i	$-0.493796\pi$
$191$	−4.20349	−	0.741189i	−0.304154	−	0.0536306i	−0.323642	+	0.946180i	$0.604907\pi$
$192$		0			0
$193$	−4.28212	−	9.18304i	−0.308234	−	0.661010i	0.689779	−	0.724020i	$-0.257708\pi$
$193$	−4.28212	−	9.18304i	−0.308234	−	0.661010i	−0.998013	+	0.0630104i	$0.979930\pi$
$194$	−6.81419	+	5.71778i	−0.489230	+	0.410513i
$195$		0			0
$196$	5.70324	−	2.07581i	0.407374	−	0.148272i
$197$	11.4519	−	3.06853i	0.815916	−	0.218624i	0.173356	−	0.984859i	$-0.444539\pi$
$197$	11.4519	−	3.06853i	0.815916	−	0.218624i	0.642560	+	0.766235i	$0.277872\pi$
$198$		0			0
$199$	5.06551	−	2.92457i	0.359084	−	0.207317i	−0.309595	−	0.950869i	$-0.600193\pi$
$199$	5.06551	−	2.92457i	0.359084	−	0.207317i	0.668679	+	0.743551i	$0.266860\pi$
$200$	−7.54743	−	3.99379i	−0.533684	−	0.282404i
$201$		0			0
$202$	27.5880	+	19.3173i	1.94108	+	1.35916i
$203$	−6.89928	−	4.83093i	−0.484234	−	0.339065i
$204$		0			0
$205$	−6.86250	−	10.3457i	−0.479298	−	0.722577i
$206$	22.4262	−	12.9478i	1.56251	−	0.902114i
$207$		0			0
$208$	18.6501	−	4.99729i	1.29315	−	0.346500i
$209$	4.91558	−	1.78912i	0.340018	−	0.123756i
$210$		0			0
$211$	−5.44373	+	4.56783i	−0.374762	+	0.314462i	−0.810642	−	0.585542i	$-0.800882\pi$
$211$	−5.44373	+	4.56783i	−0.374762	+	0.314462i	0.435880	+	0.900005i	$0.356437\pi$
$212$	−3.28611	−	7.04709i	−0.225691	−	0.483996i
$213$		0			0
$214$	−7.74205	−	1.36513i	−0.529236	−	0.0933186i
$215$	−1.48766	+	0.809649i	−0.101457	+	0.0552176i
$216$		0			0
$217$	−5.74251	+	5.74251i	−0.389827	+	0.389827i
$218$	−10.6854	−	15.2603i	−0.723707	−	1.03356i
$219$		0			0
$220$	1.59498	−	2.15998i	0.107533	−	0.145626i
$221$	1.38961	+	1.65608i	0.0934756	+	0.111400i
$222$		0			0
$223$	2.00892	+	0.936774i	0.134527	+	0.0627310i	0.488716	−	0.872443i	$-0.337465\pi$
$223$	2.00892	+	0.936774i	0.134527	+	0.0627310i	−0.354189	+	0.935174i	$0.615243\pi$
$224$	2.67428	−	4.63199i	0.178683	−	0.309488i
$225$		0			0
$226$	−10.9618	−	18.9864i	−0.729167	−	1.26295i
$227$	0.837726	+	9.57526i	0.0556018	+	0.635532i	0.971956	+	0.235163i	$0.0755624\pi$
$227$	0.837726	+	9.57526i	0.0556018	+	0.635532i	−0.916354	+	0.400369i	$0.868882\pi$
$228$		0			0
$229$	−9.88832	+	1.74358i	−0.653438	+	0.115219i	−0.490533	−	0.871423i	$-0.663198\pi$
$229$	−9.88832	+	1.74358i	−0.653438	+	0.115219i	−0.162906	+	0.986642i	$0.552087\pi$
$230$	−17.9686	−	2.02915i	−1.18481	−	0.133798i
$231$		0			0
$232$	14.1141	−	1.23483i	0.926638	−	0.0810703i
$233$	11.6282	+	3.11576i	0.761788	+	0.204120i	0.618741	−	0.785595i	$-0.287643\pi$
$233$	11.6282	+	3.11576i	0.761788	+	0.204120i	0.143047	+	0.989716i	$0.454310\pi$
$234$		0			0
$235$	0.691913	−	27.4674i	0.0451354	−	1.79178i
$236$	2.81591	+	7.73664i	0.183300	+	0.503613i
$237$		0			0
$238$	0.983361	+	0.0860330i	0.0637418	+	0.00557669i
$239$	1.69787	+	0.617976i	0.109826	+	0.0399735i	0.396349	−	0.918100i	$-0.370277\pi$
$239$	1.69787	+	0.617976i	0.109826	+	0.0399735i	−0.286522	+	0.958074i	$0.592499\pi$
$240$		0			0
$241$	−2.79425	+	15.8470i	−0.179994	+	1.02079i	0.752227	+	0.658904i	$0.228980\pi$
$241$	−2.79425	+	15.8470i	−0.179994	+	1.02079i	−0.932221	+	0.361890i	$0.882131\pi$
$242$	11.7967	+	11.7967i	0.758321	+	0.758321i
$243$		0			0
$244$		−	11.4005i		−	0.729840i
$245$	−5.94386	+	11.9513i	−0.379739	+	0.763541i
$246$		0			0
$247$	15.5025	−	7.22894i	0.986401	−	0.459966i
$248$	1.19065	−	13.6092i	0.0756063	−	0.864184i
$249$		0			0
$250$	−18.6971	+	5.24530i	−1.18251	+	0.331742i
$251$	15.8224	+	9.13506i	0.998700	+	0.576600i	0.907863	−	0.419266i	$-0.137713\pi$
$251$	15.8224	+	9.13506i	0.998700	+	0.576600i	0.0908365	+	0.995866i	$0.471046\pi$
$252$		0			0
$253$	−1.42319	+	5.31141i	−0.0894751	+	0.333926i
$254$	−23.4787	−	19.7010i	−1.47318	−	1.23615i
$255$		0			0
$256$	3.32781	+	18.8729i	0.207988	+	1.17956i
$257$	8.13228	−	11.6141i	0.507278	−	0.724468i	−0.481070	−	0.876682i	$-0.659752\pi$
$257$	8.13228	−	11.6141i	0.507278	−	0.724468i	0.988347	+	0.152215i	$0.0486405\pi$
$258$		0			0
$259$	−3.58119	+	4.26790i	−0.222524	+	0.265194i
$260$	4.58003	−	7.49065i	0.284041	−	0.464550i
$261$		0			0
$262$	−1.29920	−	4.84869i	−0.0802650	−	0.299553i
$263$	1.55072	−	3.32553i	0.0956215	−	0.205061i	−0.852679	−	0.522436i	$-0.825023\pi$
$263$	1.55072	−	3.32553i	0.0956215	−	0.205061i	0.948300	+	0.317375i	$0.102801\pi$
$264$		0			0
$265$	15.9168	+	6.25149i	0.977759	+	0.384026i
$266$	2.67128	−	7.33929i	0.163787	−	0.450000i
$267$		0			0
$268$	−1.31583	+	0.921353i	−0.0803770	+	0.0562806i
$269$	11.1677			0.680904			0.340452	−	0.940262i	$-0.389420\pi$
$269$	11.1677			0.680904			0.340452	+	0.940262i	$0.389420\pi$
$270$		0			0
$271$	23.0328			1.39914			0.699572	−	0.714562i	$-0.253374\pi$
$271$	23.0328			1.39914			0.699572	+	0.714562i	$0.253374\pi$
$272$	−2.29269	+	1.60536i	−0.139015	+	0.0973390i
$273$		0			0
$274$	5.00267	−	13.7447i	0.302223	−	0.830350i
$275$	0.731309	+	5.85961i	0.0440996	+	0.353348i
$276$		0			0
$277$	5.25770	−	11.2752i	0.315905	−	0.677460i	−0.682676	−	0.730721i	$-0.739184\pi$
$277$	5.25770	−	11.2752i	0.315905	−	0.677460i	0.998581	+	0.0532613i	$0.0169616\pi$
$278$	4.49577	+	16.7784i	0.269638	+	1.00630i
$279$		0			0
$280$	0.908797	+	3.76889i	0.0543110	+	0.225234i
$281$	−5.39196	+	6.42589i	−0.321657	+	0.383336i	−0.902507	−	0.430674i	$-0.858276\pi$
$281$	−5.39196	+	6.42589i	−0.321657	+	0.383336i	0.580850	+	0.814011i	$0.302720\pi$
$282$		0			0
$283$	−6.92088	+	9.88404i	−0.411404	+	0.587545i	−0.970364	−	0.241649i	$-0.922312\pi$
$283$	−6.92088	+	9.88404i	−0.411404	+	0.587545i	0.558960	+	0.829195i	$0.311201\pi$
$284$	1.41880	+	8.04642i	0.0841904	+	0.477467i
$285$		0			0
$286$	−6.06835	−	5.09195i	−0.358829	−	0.301093i
$287$	−1.45887	+	5.44459i	−0.0861145	+	0.321384i
$288$		0			0
$289$	14.4510	+	8.34331i	0.850061	+	0.490783i
$290$	21.3257	−	24.1527i	1.25229	−	1.41830i
$291$		0			0
$292$	−0.468877	+	5.35929i	−0.0274390	+	0.313629i
$293$	−19.4978	+	9.09195i	−1.13907	+	0.531157i	−0.898282	−	0.439420i	$-0.855184\pi$
$293$	−19.4978	+	9.09195i	−1.13907	+	0.531157i	−0.240789	+	0.970577i	$0.577406\pi$
$294$		0			0
$295$	−16.2124	−	8.06305i	−0.943920	−	0.469449i
$296$		−	9.37196i		−	0.544734i
$297$		0			0
$298$	17.6016	+	17.6016i	1.01964	+	1.01964i
$299$	−3.12229	+	17.7074i	−0.180567	+	1.02405i
$300$		0			0
$301$	0.722611	+	0.263009i	0.0416506	+	0.0151596i
$302$	9.32186	+	0.815557i	0.536413	+	0.0469301i
$303$		0			0
$304$	7.57410	+	20.8097i	0.434404	+	1.19352i
$305$	17.2768	+	18.1697i	0.989266	+	1.04039i
$306$		0			0
$307$	−11.9453	−	3.20074i	−0.681757	−	0.182676i	−0.0987117	−	0.995116i	$-0.531472\pi$
$307$	−11.9453	−	3.20074i	−0.681757	−	0.182676i	−0.583045	+	0.812440i	$0.698139\pi$
$308$	−1.21444	+	0.106250i	−0.0691992	+	0.00605414i
$309$		0			0
$310$	−19.3642	−	24.2944i	−1.09981	−	1.37983i
$311$	13.5294	−	2.38560i	0.767181	−	0.135275i	0.223656	−	0.974668i	$-0.428201\pi$
$311$	13.5294	−	2.38560i	0.767181	−	0.135275i	0.543524	+	0.839393i	$0.317090\pi$
$312$		0			0
$313$	2.60145	+	29.7347i	0.147043	+	1.68071i	0.608507	+	0.793548i	$0.291769\pi$
$313$	2.60145	+	29.7347i	0.147043	+	1.68071i	−0.461465	+	0.887159i	$0.652676\pi$
$314$	6.91579	+	11.9785i	0.390281	+	0.675986i
$315$		0			0
$316$	3.42141	−	5.92606i	0.192470	−	0.333367i
$317$	19.3873	+	9.04044i	1.08890	+	0.507762i	0.882311	−	0.470666i	$-0.155986\pi$
$317$	19.3873	+	9.04044i	1.08890	+	0.507762i	0.206588	+	0.978428i	$0.433764\pi$
$318$		0			0
$319$	−6.29792	−	7.50556i	−0.352616	−	0.420231i
$320$	−1.52723	−	1.12774i	−0.0853745	−	0.0630425i
$321$		0			0
$322$	4.70909	+	6.72527i	0.262427	+	0.374785i
$323$	−1.75329	+	1.75329i	−0.0975556	+	0.0975556i
$324$		0			0
$325$	4.05217	+	18.8791i	0.224774	+	1.04723i
$326$	−27.4391	−	4.83826i	−1.51971	−	0.267966i
$327$		0			0
$328$	−4.00719	−	8.59345i	−0.221260	−	0.474494i
$329$	−9.55630	+	8.01869i	−0.526856	+	0.442085i
$330$		0			0
$331$	−24.1329	+	8.78365i	−1.32646	+	0.482793i	−0.905524	−	0.424296i	$-0.860522\pi$
$331$	−24.1329	+	8.78365i	−1.32646	+	0.482793i	−0.420939	+	0.907089i	$0.638299\pi$
$332$	−0.294691	+	0.0789621i	−0.0161732	+	0.00433361i
$333$		0			0
$334$	0.637228	−	0.367904i	0.0348676	−	0.0201308i
$335$	0.700864	−	3.46249i	0.0382923	−	0.189176i
$336$		0			0
$337$	−0.778831	−	0.545344i	−0.0424256	−	0.0297068i	0.552171	−	0.833731i	$-0.313799\pi$
$337$	−0.778831	−	0.545344i	−0.0424256	−	0.0297068i	−0.594597	+	0.804024i	$0.702688\pi$
$338$	−2.72272	−	1.90647i	−0.148096	−	0.103698i
$339$		0			0
$340$	−0.252498	+	1.24742i	−0.0136936	+	0.0676507i
$341$	−8.18159	+	4.72364i	−0.443058	+	0.255800i
$342$		0			0
$343$	12.7182	−	3.40783i	0.686718	−	0.184006i
$344$	−1.21556	+	0.442427i	−0.0655385	+	0.0238540i
$345$		0			0
$346$	10.7495	−	9.01991i	0.577897	−	0.484913i
$347$	−0.861237	−	1.84693i	−0.0462336	−	0.0991483i	0.881834	−	0.471560i	$-0.156309\pi$
$347$	−0.861237	−	1.84693i	−0.0462336	−	0.0991483i	−0.928068	+	0.372411i	$0.878531\pi$
$348$		0			0
$349$	13.3172	+	2.34817i	0.712851	+	0.125695i	0.518302	−	0.855198i	$-0.326564\pi$
$349$	13.3172	+	2.34817i	0.712851	+	0.125695i	0.194549	+	0.980893i	$0.437676\pi$
$350$	7.40382	+	4.78718i	0.395751	+	0.255885i
$351$		0			0
$352$	4.39958	−	4.39958i	0.234499	−	0.234499i
$353$	4.28254	+	6.11610i	0.227936	+	0.325527i	0.916787	−	0.399376i	$-0.130773\pi$
$353$	4.28254	+	6.11610i	0.227936	+	0.325527i	−0.688851	+	0.724903i	$0.741884\pi$
$354$		0			0
$355$	−14.4552	−	10.6740i	−0.767200	−	0.566518i
$356$	−7.07928	−	8.43675i	−0.375201	−	0.447147i
$357$		0			0
$358$	−20.0930	−	9.36950i	−1.06195	−	0.495193i
$359$	−4.40107	+	7.62287i	−0.232279	+	0.402320i	−0.958479	−	0.285165i	$-0.907952\pi$
$359$	−4.40107	+	7.62287i	−0.232279	+	0.402320i	0.726199	+	0.687484i	$0.241285\pi$
$360$		0			0
$361$	0.309285	+	0.535697i	0.0162782	+	0.0281946i
$362$	2.80015	+	32.0058i	0.147172	+	1.68219i
$363$		0			0
$364$	−3.92573	+	0.692213i	−0.205764	+	0.0362818i
$365$	−7.37443	−	9.25202i	−0.385995	−	0.484273i
$366$		0			0
$367$	−27.1913	+	2.37893i	−1.41938	+	0.124179i	−0.770852	−	0.637015i	$-0.780169\pi$
$367$	−27.1913	+	2.37893i	−1.41938	+	0.124179i	−0.648524	+	0.761194i	$0.724613\pi$
$368$	−22.4854	−	6.02494i	−1.17213	−	0.314072i
$369$		0			0
$370$	−14.6864	−	15.4455i	−0.763511	−	0.802971i
$371$	−2.65545	−	7.29580i	−0.137864	−	0.378779i
$372$		0			0
$373$	12.1103	+	1.05951i	0.627046	+	0.0548594i	0.396250	−	0.918143i	$-0.370311\pi$
$373$	12.1103	+	1.05951i	0.627046	+	0.0548594i	0.230796	+	0.973002i	$0.425867\pi$
$374$	1.07906	+	0.392745i	0.0557968	+	0.0203084i
$375$		0			0
$376$	3.64399	−	20.6661i	0.187924	−	1.06577i
$377$	−22.6543	−	22.6543i	−1.16676	−	1.16676i
$378$		0			0
$379$		−	22.6602i		−	1.16398i	−0.813198	−	0.581988i	$-0.802275\pi$
$379$		−	22.6602i		−	1.16398i	0.813198	−	0.581988i	$-0.197725\pi$
$380$	9.01648	+	4.48425i	0.462535	+	0.230037i
$381$		0			0
$382$	−6.71899	+	3.13312i	−0.343773	+	0.160304i
$383$	−1.66185	+	18.9950i	−0.0849166	+	0.970601i	0.827534	+	0.561415i	$0.189743\pi$
$383$	−1.66185	+	18.9950i	−0.0849166	+	0.970601i	−0.912451	+	0.409186i	$0.865813\pi$
$384$		0			0
$385$	1.77452	−	2.00976i	0.0904379	−	0.102427i
$386$	−15.2409	−	8.79934i	−0.775741	−	0.447874i
$387$		0			0
$388$	−1.34772	+	5.02975i	−0.0684200	+	0.255347i
$389$	−11.9485	−	10.0260i	−0.605814	−	0.508338i	0.287495	−	0.957782i	$-0.407178\pi$
$389$	−11.9485	−	10.0260i	−0.605814	−	0.508338i	−0.893309	+	0.449444i	$0.851622\pi$
$390$		0			0
$391$	−0.452602	−	2.56683i	−0.0228890	−	0.129810i
$392$	−5.84724	+	8.35072i	−0.295330	+	0.421775i
$393$		0			0
$394$	13.2364	−	15.7746i	0.666842	−	0.794712i
$395$	3.52769	+	14.6297i	0.177497	+	0.736102i
$396$		0			0
$397$	2.30277	+	8.59405i	0.115573	+	0.431323i	0.999329	−	0.0366240i	$-0.0116604\pi$
$397$	2.30277	+	8.59405i	0.115573	+	0.431323i	−0.883756	+	0.467947i	$0.844994\pi$
$398$	4.29348	−	9.20740i	0.215213	−	0.461525i
$399$		0			0
$400$	−24.8062	+	3.09593i	−1.24031	+	0.154797i
$401$	0.377837	−	1.03810i	0.0188683	−	0.0518401i	−0.929901	−	0.367810i	$-0.880108\pi$
$401$	0.377837	−	1.03810i	0.0188683	−	0.0518401i	0.948769	+	0.315970i	$0.102330\pi$
$402$		0			0
$403$	−25.3051	+	17.7189i	−1.26054	+	0.882639i
$404$	19.7151			0.980861
$405$		0			0
$406$	−14.6288			−0.726015
$407$	−5.30902	+	3.71742i	−0.263158	+	0.184265i
$408$		0			0
$409$	−0.248916	+	0.683891i	−0.0123081	+	0.0338162i	−0.945695	−	0.325057i	$-0.894617\pi$
$409$	−0.248916	+	0.683891i	−0.0123081	+	0.0338162i	0.933386	+	0.358873i	$0.116839\pi$
$410$	−20.0705	−	7.88292i	−0.991211	−	0.389310i
$411$		0			0
$412$	6.40643	−	13.7386i	0.315622	−	0.676854i
$413$	2.12773	+	7.94079i	0.104699	+	0.390741i
$414$		0			0
$415$	0.350005	−	0.572435i	0.0171811	−	0.0280997i
$416$	13.0777	−	15.5854i	0.641187	−	0.764137i
$417$		0			0
$418$	5.21134	−	7.44256i	0.254895	−	0.364028i
$419$	3.40845	+	19.3303i	0.166514	+	0.944347i	0.947490	+	0.319786i	$0.103611\pi$
$419$	3.40845	+	19.3303i	0.166514	+	0.944347i	−0.780976	+	0.624561i	$0.785278\pi$
$420$		0			0
$421$	−8.09926	−	6.79608i	−0.394734	−	0.331221i	0.423720	−	0.905793i	$-0.360724\pi$
$421$	−8.09926	−	6.79608i	−0.394734	−	0.331221i	−0.818454	+	0.574572i	$0.805168\pi$
$422$	−3.19454	+	11.9222i	−0.155508	+	0.580362i
$423$		0			0
$424$	11.3107	+	6.53022i	0.549295	+	0.317135i
$425$	−1.48797	−	2.37074i	−0.0721772	−	0.114998i
$426$		0			0
$427$	0.992138	−	11.3402i	0.0480129	−	0.548790i
$428$	−4.17083	+	1.94489i	−0.201605	+	0.0940099i
$429$		0			0
$430$	−1.30999	+	2.63399i	−0.0631733	+	0.127022i
$431$		−	16.6095i		−	0.800052i	−0.916504	−	0.400026i	$-0.869001\pi$
$431$		−	16.6095i		−	0.800052i	0.916504	−	0.400026i	$-0.130999\pi$
$432$		0			0
$433$	−14.3203	−	14.3203i	−0.688189	−	0.688189i	0.273643	−	0.961831i	$-0.411771\pi$
$433$	−14.3203	−	14.3203i	−0.688189	−	0.688189i	−0.961831	+	0.273643i	$0.911771\pi$
$434$	−2.44938	+	13.8911i	−0.117574	+	0.666796i
$435$		0			0
$436$	−10.2477	−	3.72987i	−0.490778	−	0.178628i
$437$	−20.5442	−	1.79738i	−0.982762	−	0.0859805i
$438$		0			0
$439$	4.05583	+	11.1433i	0.193574	+	0.531840i	0.998069	−	0.0621195i	$-0.0197860\pi$
$439$	4.05583	+	11.1433i	0.193574	+	0.531840i	−0.804495	+	0.593960i	$0.797564\pi$
$440$	−0.113572	+	4.50856i	−0.00541434	+	0.214937i
$441$		0			0
$442$	3.62694	+	0.971835i	0.172516	+	0.0462255i
$443$	−22.1937	+	1.94169i	−1.05445	+	0.0922527i	−0.601176	−	0.799117i	$-0.705301\pi$
$443$	−22.1937	+	1.94169i	−1.05445	+	0.0922527i	−0.453277	+	0.891369i	$0.649745\pi$
$444$		0			0
$445$	24.0682	+	2.71797i	1.14094	+	0.128844i
$446$	3.79147	−	0.668538i	0.179531	−	0.0316562i
$447$		0			0
$448$	0.0751244	+	0.858676i	0.00354930	+	0.0405686i
$449$	−2.63657	−	4.56667i	−0.124427	−	0.215514i	0.797082	−	0.603872i	$-0.206376\pi$
$449$	−2.63657	−	4.56667i	−0.124427	−	0.215514i	−0.921509	+	0.388357i	$0.873043\pi$
$450$		0			0
$451$	−3.27855	+	5.67861i	−0.154381	+	0.267395i
$452$	−11.6313	−	5.42378i	−0.547092	−	0.255113i
$453$		0			0
$454$	10.7311	+	12.7888i	0.503634	+	0.600208i
$455$	5.20769	−	7.05246i	0.244140	−	0.330624i
$456$		0			0
$457$	−5.51211	−	7.87211i	−0.257846	−	0.368242i	0.669269	−	0.743021i	$-0.266608\pi$
$457$	−5.51211	−	7.87211i	−0.257846	−	0.368242i	−0.927114	+	0.374779i	$0.877719\pi$
$458$	−12.3318	+	12.3318i	−0.576225	+	0.576225i
$459$		0			0
$460$	−9.29762	+	5.06018i	−0.433504	+	0.235932i
$461$	−10.5760	−	1.86484i	−0.492575	−	0.0868543i	−0.0781574	−	0.996941i	$-0.524904\pi$
$461$	−10.5760	−	1.86484i	−0.492575	−	0.0868543i	−0.414418	+	0.910087i	$0.636015\pi$
$462$		0			0
$463$	15.1325	+	32.4518i	0.703268	+	1.50816i	0.854381	+	0.519647i	$0.173936\pi$
$463$	15.1325	+	32.4518i	0.703268	+	1.50816i	−0.151113	+	0.988516i	$0.548286\pi$
$464$	31.7741	−	26.6617i	1.47508	−	1.23774i
$465$		0			0
$466$	19.6482	−	7.15137i	0.910187	−	0.331281i
$467$	−23.5963	+	6.32261i	−1.09191	+	0.292575i	−0.759465	−	0.650549i	$-0.774539\pi$
$467$	−23.5963	+	6.32261i	−1.09191	+	0.292575i	−0.332441	+	0.943124i	$0.607872\pi$
$468$		0			0
$469$	−1.38905	+	0.801970i	−0.0641405	+	0.0370315i
$470$	−26.3795	−	39.7691i	−1.21680	−	1.83441i
$471$		0			0
$472$	−11.3280	−	7.93199i	−0.521416	−	0.365099i
$473$	0.732780	+	0.513098i	0.0336933	+	0.0235923i
$474$		0			0
$475$	−21.1658	+	6.51712i	−0.971154	+	0.299026i
$476$	0.500429	−	0.288923i	0.0229371	−	0.0132427i
$477$		0			0
$478$	3.03133	−	0.812242i	0.138650	−	0.0371511i
$479$	38.3549	−	13.9601i	1.75248	−	0.637851i	0.752692	−	0.658373i	$-0.228755\pi$
$479$	38.3549	−	13.9601i	1.75248	−	0.637851i	0.999789	+	0.0205215i	$0.00653265\pi$
$480$		0			0
$481$	−16.2346	+	13.6224i	−0.740233	+	0.621129i
$482$	11.8117	+	25.3303i	0.538009	+	1.15376i
$483$		0			0
$484$	9.61767	+	1.69585i	0.437167	+	0.0770843i
$485$	−5.47436	−	10.0586i	−0.248578	−	0.456739i
$486$		0			0
$487$	−23.5238	+	23.5238i	−1.06596	+	1.06596i	−0.0682997	+	0.997665i	$0.521757\pi$
$487$	−23.5238	+	23.5238i	−1.06596	+	1.06596i	−0.997665	+	0.0682997i	$0.978243\pi$
$488$	10.9834	+	15.6860i	0.497196	+	0.710070i
$489$		0			0
$490$	3.44954	+	22.9254i	0.155834	+	1.03566i
$491$	3.19936	+	3.81285i	0.144385	+	0.172071i	0.833390	−	0.552685i	$-0.186397\pi$
$491$	3.19936	+	3.81285i	0.144385	+	0.172071i	−0.689005	+	0.724756i	$0.741952\pi$
$492$		0			0
$493$	4.20905	+	1.96271i	0.189566	+	0.0883962i
$494$	14.8548	−	25.7292i	0.668347	−	1.15761i
$495$		0			0
$496$	−19.9971	−	34.6360i	−0.897897	−	1.55520i
$497$	0.711051	+	8.12735i	0.0318950	+	0.364561i
$498$		0			0
$499$	6.36453	−	1.12224i	0.284916	−	0.0502383i	−0.0293640	−	0.999569i	$-0.509348\pi$
$499$	6.36453	−	1.12224i	0.284916	−	0.0502383i	0.314280	+	0.949330i	$0.398237\pi$
$500$	−7.20444	+	8.79302i	−0.322192	+	0.393236i
$501$		0			0
$502$	31.6122	−	2.76571i	1.41092	−	0.123440i
$503$	−24.7077	−	6.62040i	−1.10166	−	0.295189i	−0.338220	−	0.941067i	$-0.609825\pi$
$503$	−24.7077	−	6.62040i	−1.10166	−	0.295189i	−0.763441	+	0.645878i	$0.776491\pi$
$504$		0			0
$505$	−31.4212	+	29.8771i	−1.39823	+	1.32951i
$506$	3.26654	+	8.97473i	0.145215	+	0.398975i
$507$		0			0
$508$	−17.8734	−	1.56372i	−0.793003	−	0.0693788i
$509$	22.5637	+	8.21250i	1.00012	+	0.364013i	0.789630	−	0.613584i	$-0.210273\pi$
$509$	22.5637	+	8.21250i	1.00012	+	0.364013i	0.210487	+	0.977597i	$0.432495\pi$
$510$		0			0
$511$	−0.932796	+	5.29015i	−0.0412644	+	0.234022i
$512$	6.55000	+	6.55000i	0.289472	+	0.289472i
$513$		0			0
$514$		−	24.6258i		−	1.08620i
$515$	10.6098	+	31.6048i	0.467523	+	1.39267i
$516$		0			0
$517$	−13.1523	+	6.13302i	−0.578438	+	0.269730i
$518$	−0.843383	+	9.63992i	−0.0370561	+	0.423554i
$519$		0			0
$520$	0.914947	+	14.7189i	0.0401231	+	0.645467i
$521$	−10.1059	−	5.83464i	−0.442747	−	0.255620i	0.262015	−	0.965064i	$-0.415613\pi$
$521$	−10.1059	−	5.83464i	−0.442747	−	0.255620i	−0.704762	+	0.709444i	$0.748946\pi$
$522$		0			0
$523$	−9.07224	+	33.8581i	−0.396701	+	1.48051i	0.422162	+	0.906521i	$0.361272\pi$
$523$	−9.07224	+	33.8581i	−0.396701	+	1.48051i	−0.818863	+	0.573989i	$0.805395\pi$
$524$	−2.25101	−	1.88882i	−0.0983358	−	0.0825135i
$525$		0			0
$526$	−1.10669	−	6.27633i	−0.0482539	−	0.273661i
$527$	2.56849	−	3.66818i	0.111885	−	0.159789i
$528$		0			0
$529$	−0.849663	+	1.01259i	−0.0369419	+	0.0440256i
$530$	28.8738	−	6.96238i	1.25420	−	0.302426i
$531$		0			0
$532$	−1.18333	−	4.41626i	−0.0513040	−	0.191469i
$533$	−9.06143	+	19.4323i	−0.392494	+	0.841706i
$534$		0			0
$535$	3.69996	−	9.42038i	0.159963	−	0.407278i
$536$	0.922806	−	2.53539i	0.0398591	−	0.109512i
$537$		0			0
$538$	15.8890	−	11.1256i	0.685022	−	0.479658i
$539$	7.04983			0.303658
$540$		0			0
$541$	32.8530			1.41246			0.706230	−	0.707983i	$-0.250394\pi$
$541$	32.8530			1.41246			0.706230	+	0.707983i	$0.250394\pi$
$542$	32.7703	−	22.9460i	1.40761	−	0.985617i
$543$		0			0
$544$	−1.00869	+	2.77135i	−0.0432472	+	0.118821i
$545$	21.9849	−	9.58534i	0.941731	−	0.410591i
$546$		0			0
$547$	18.7126	−	40.1294i	0.800094	−	1.71581i	0.107823	−	0.994170i	$-0.465612\pi$
$547$	18.7126	−	40.1294i	0.800094	−	1.71581i	0.692271	−	0.721638i	$-0.256610\pi$
$548$	−2.21610	−	8.27060i	−0.0946671	−	0.353302i
$549$		0			0
$550$	6.87802	+	7.60831i	0.293280	+	0.324419i
$551$	23.6198	−	28.1489i	1.00624	−	1.19918i
$552$		0			0
$553$	3.91904	−	5.59698i	0.166655	−	0.238008i
$554$	−3.75221	−	21.2799i	−0.159416	−	0.904094i
$555$		0			0
$556$	7.78940	+	6.53608i	0.330344	+	0.277192i
$557$	9.87492	−	36.8537i	0.418414	−	1.56154i	−0.359484	−	0.933151i	$-0.617047\pi$
$557$	9.87492	−	36.8537i	0.418414	−	1.56154i	0.777898	−	0.628391i	$-0.216286\pi$
$558$		0			0
$559$	2.53324	+	1.46257i	0.107145	+	0.0618601i
$560$	8.50812	+	7.51227i	0.359534	+	0.317451i
$561$		0			0
$562$	−1.26983	+	14.5142i	−0.0535644	+	0.612244i
$563$	−7.65616	+	3.57013i	−0.322669	+	0.150463i	−0.577203	−	0.816601i	$-0.695856\pi$
$563$	−7.65616	+	3.57013i	−0.322669	+	0.150463i	0.254534	+	0.967064i	$0.418078\pi$
$564$		0			0
$565$	26.7571	−	8.98241i	1.12568	−	0.377893i
$566$			20.9575i			0.880909i
$567$		0			0
$568$	−9.70421	−	9.70421i	−0.407180	−	0.407180i
$569$	−0.364320	+	2.06616i	−0.0152731	+	0.0866180i	−0.991492	−	0.130171i	$-0.958447\pi$
$569$	−0.364320	+	2.06616i	−0.0152731	+	0.0866180i	0.976218	+	0.216789i	$0.0695584\pi$
$570$		0			0
$571$	39.5609	+	14.3990i	1.65557	+	0.602578i	0.989657	−	0.143451i	$-0.0458200\pi$
$571$	39.5609	+	14.3990i	1.65557	+	0.602578i	0.665913	+	0.746029i	$0.268042\pi$
$572$	−4.61959	−	0.404162i	−0.193155	−	0.0168989i
$573$		0			0
$574$	3.34844	+	9.19975i	0.139761	+	0.383990i
$575$	7.14981	−	22.1548i	0.298168	−	0.923918i
$576$		0			0
$577$	39.4191	+	10.5623i	1.64104	+	0.439715i	0.957084	−	0.289810i	$-0.0935920\pi$
$577$	39.4191	+	10.5623i	1.64104	+	0.439715i	0.683955	+	0.729525i	$0.260259\pi$
$578$	28.8723	−	2.52600i	1.20093	−	0.105068i
$579$		0			0
$580$	2.11651	−	18.7421i	0.0878833	−	0.778225i
$581$	−0.300004	+	0.0528988i	−0.0124463	+	0.00219461i
$582$		0			0
$583$	−0.787178	−	8.99749i	−0.0326016	−	0.372638i
$584$	−4.51811	−	7.82560i	−0.186961	−	0.323825i
$585$		0			0
$586$	−18.6831	+	32.3600i	−0.771790	+	1.33678i
$587$	−11.5098	−	5.36709i	−0.475059	−	0.221524i	0.170316	−	0.985389i	$-0.445521\pi$
$587$	−11.5098	−	5.36709i	−0.475059	−	0.221524i	−0.645375	+	0.763866i	$0.723299\pi$
$588$		0			0
$589$	−22.7747	−	27.1419i	−0.938416	−	1.11836i
$590$	−31.0991	+	4.67943i	−1.28033	+	0.192649i
$591$		0			0
$592$	−15.7374	−	22.4753i	−0.646801	−	0.923728i
$593$	6.50749	−	6.50749i	0.267230	−	0.267230i	−0.560753	−	0.827983i	$-0.689488\pi$
$593$	6.50749	−	6.50749i	0.267230	−	0.267230i	0.827983	+	0.560753i	$0.189488\pi$
$594$		0			0
$595$	−0.359720	+	1.21885i	−0.0147471	+	0.0499679i
$596$	14.3503	+	2.53035i	0.587813	+	0.103647i
$597$		0			0
$598$	13.1984	+	28.3041i	0.539723	+	1.15744i
$599$	7.62396	−	6.39726i	0.311507	−	0.261385i	−0.473608	−	0.880736i	$-0.657049\pi$
$599$	7.62396	−	6.39726i	0.311507	−	0.261385i	0.785114	+	0.619351i	$0.212604\pi$
$600$		0			0
$601$	24.7845	−	9.02082i	1.01098	−	0.367967i	0.217171	−	0.976134i	$-0.430317\pi$
$601$	24.7845	−	9.02082i	1.01098	−	0.367967i	0.793809	+	0.608167i	$0.208095\pi$
$602$	1.29013	−	0.345688i	0.0525816	−	0.0140892i
$603$		0			0
$604$	4.74386	−	2.73887i	0.193025	−	0.111443i
$605$	−17.8983	+	11.8723i	−0.727670	+	0.482676i
$606$		0			0
$607$	−5.73315	−	4.01440i	−0.232701	−	0.162939i	0.451410	−	0.892316i	$-0.350921\pi$
$607$	−5.73315	−	4.01440i	−0.232701	−	0.162939i	−0.684112	+	0.729377i	$0.739810\pi$
$608$	19.1148	+	13.3843i	0.775207	+	0.542806i
$609$		0			0
$610$	42.6821	+	8.63955i	1.72815	+	0.349805i
$611$	−41.0955	+	23.7265i	−1.66254	+	0.959871i
$612$		0			0
$613$	−3.76248	+	1.00815i	−0.151965	+	0.0407189i	−0.334000	−	0.942573i	$-0.608398\pi$
$613$	−3.76248	+	1.00815i	−0.151965	+	0.0407189i	0.182034	+	0.983292i	$0.441732\pi$
$614$	−20.1841	+	7.34642i	−0.814565	+	0.296477i
$615$		0			0
$616$	1.56859	−	1.31620i	0.0632004	−	0.0530314i
$617$	1.85144	+	3.97043i	0.0745363	+	0.159844i	0.940045	−	0.341050i	$-0.110783\pi$
$617$	1.85144	+	3.97043i	0.0745363	+	0.159844i	−0.865509	+	0.500894i	$0.833005\pi$
$618$		0			0
$619$	33.2378	+	5.86071i	1.33594	+	0.235562i	0.795567	−	0.605865i	$-0.207173\pi$
$619$	33.2378	+	5.86071i	1.33594	+	0.235562i	0.540371	+	0.841427i	$0.318284\pi$
$620$	−17.4427	−	5.14789i	−0.700515	−	0.206744i
$621$		0			0
$622$	16.8726	−	16.8726i	0.676528	−	0.676528i
$623$	−6.30763	−	9.00822i	−0.252710	−	0.360907i
$624$		0			0
$625$	−1.84315	−	24.9320i	−0.0737261	−	0.997279i
$626$	33.3240	+	39.7140i	1.33189	+	1.58729i
$627$		0			0
$628$	7.33821	+	3.42186i	0.292827	+	0.136547i
$629$	1.53603	−	2.66048i	0.0612455	−	0.106080i
$630$		0			0
$631$	−17.7304	−	30.7100i	−0.705837	−	1.22255i	−0.966389	−	0.257086i	$-0.917238\pi$
$631$	−17.7304	−	30.7100i	−0.705837	−	1.22255i	0.260552	−	0.965460i	$-0.416096\pi$
$632$	1.00174	+	11.4500i	0.0398471	+	0.455455i
$633$		0			0
$634$	36.5900	−	6.45180i	1.45317	−	0.256234i
$635$	30.8557	−	24.5939i	1.22447	−	0.975980i
$636$		0			0
$637$	22.9647	−	2.00915i	0.909894	−	0.0796054i
$638$	−16.4377	−	4.40448i	−0.650777	−	0.174375i
$639$		0			0
$640$	−26.8495	−	0.676347i	−1.06132	−	0.0267350i
$641$	9.20207	+	25.2825i	0.363460	+	0.998598i	0.977797	+	0.209554i	$0.0672013\pi$
$641$	9.20207	+	25.2825i	0.363460	+	0.998598i	−0.614337	+	0.789044i	$0.710577\pi$
$642$		0			0
$643$	−16.3427	−	1.42980i	−0.644495	−	0.0563860i	−0.239778	−	0.970828i	$-0.577075\pi$
$643$	−16.3427	−	1.42980i	−0.644495	−	0.0563860i	−0.404717	+	0.914442i	$0.632630\pi$
$644$	4.51621	+	1.64377i	0.177964	+	0.0647734i
$645$		0			0
$646$	−0.747838	+	4.24120i	−0.0294233	+	0.166868i
$647$	−6.34739	−	6.34739i	−0.249542	−	0.249542i	0.571241	−	0.820783i	$-0.306462\pi$
$647$	−6.34739	−	6.34739i	−0.249542	−	0.249542i	−0.820783	+	0.571241i	$0.806462\pi$
$648$		0			0
$649$			9.56335i			0.375394i
$650$	24.5733	+	22.8237i	0.963844	+	0.895220i
$651$		0			0
$652$	−14.7821	+	6.89302i	−0.578913	+	0.269951i
$653$	−1.09427	+	12.5076i	−0.0428222	+	0.489460i	0.944255	+	0.329215i	$0.106784\pi$
$653$	−1.09427	+	12.5076i	−0.0428222	+	0.489460i	−0.987077	+	0.160245i	$0.948772\pi$
$654$		0			0
$655$	6.44999	−	0.400940i	0.252022	−	0.0156660i
$656$	−24.0399	−	13.8794i	−0.938600	−	0.541901i
$657$		0			0
$658$	−5.60792	+	20.9290i	−0.218619	+	0.815898i
$659$	−7.46847	−	6.26679i	−0.290930	−	0.244120i	0.485627	−	0.874166i	$-0.338591\pi$
$659$	−7.46847	−	6.26679i	−0.290930	−	0.244120i	−0.776557	+	0.630047i	$0.783036\pi$
$660$		0			0
$661$	−7.28597	−	41.3208i	−0.283391	−	1.60719i	−0.710975	−	0.703217i	$-0.751746\pi$
$661$	−7.28597	−	41.3208i	−0.283391	−	1.60719i	0.427584	−	0.903976i	$-0.359365\pi$
$662$	−25.5849	+	36.5390i	−0.994386	+	1.42013i
$663$		0			0
$664$	0.329393	−	0.392555i	0.0127829	−	0.0152341i
$665$	8.57855	+	5.24521i	0.332662	+	0.203401i
$666$		0			0
$667$	9.99727	+	37.3103i	0.387096	+	1.44466i
$668$	0.182035	−	0.390376i	0.00704315	−	0.0151041i
$669$		0			0
$670$	−2.45228	−	5.62454i	−0.0947397	−	0.217295i
$671$	4.52916	−	12.4438i	0.174846	−	0.480386i
$672$		0			0
$673$	7.99252	−	5.59642i	0.308089	−	0.215726i	−0.409299	−	0.912401i	$-0.634227\pi$
$673$	7.99252	−	5.59642i	0.308089	−	0.215726i	0.717388	+	0.696674i	$0.245338\pi$
$674$	−1.65138			−0.0636089
$675$		0			0
$676$	−1.94572			−0.0748355
$677$	34.3309	−	24.0388i	1.31944	−	0.923885i	0.319724	−	0.947511i	$-0.396410\pi$
$677$	34.3309	−	24.0388i	1.31944	−	0.923885i	0.999721	+	0.0236257i	$0.00752099\pi$
$678$		0			0
$679$	−1.77831	+	4.88587i	−0.0682453	+	0.187502i
$680$	−0.854373	−	1.95959i	−0.0327637	−	0.0751468i
$681$		0			0
$682$	−6.93465	+	14.8714i	−0.265542	+	0.569456i
$683$	−5.59914	−	20.8963i	−0.214245	−	0.799574i	−0.986431	−	0.164177i	$-0.947503\pi$
$683$	−5.59914	−	20.8963i	−0.214245	−	0.799574i	0.772186	−	0.635397i	$-0.219163\pi$
$684$		0			0
$685$	16.0656	+	9.82303i	0.613835	+	0.375319i
$686$	14.7000	−	17.5188i	0.561250	−	0.668872i
$687$		0			0
$688$	−2.17216	+	3.10216i	−0.0828127	+	0.118269i
$689$	−5.12843	−	29.0848i	−0.195378	−	1.10804i
$690$		0			0
$691$	−19.0033	−	15.9457i	−0.722921	−	0.606603i	0.205270	−	0.978705i	$-0.434193\pi$
$691$	−19.0033	−	15.9457i	−0.722921	−	0.606603i	−0.928192	+	0.372102i	$0.878637\pi$
$692$	2.12605	−	7.93453i	0.0808203	−	0.301625i
$693$		0			0
$694$	−3.06531	−	1.76976i	−0.116358	−	0.0671791i
$695$	−22.3196	+	1.38741i	−0.846629	+	0.0526276i
$696$		0			0
$697$	0.270886	−	3.09624i	0.0102605	−	0.117279i
$698$	21.2865	−	9.92607i	0.805707	−	0.375707i
$699$		0			0
$700$	5.15764	−	0.190385i	0.194941	−	0.00719589i
$701$			3.89640i			0.147165i	0.997289	+	0.0735825i	$0.0234432\pi$
$701$			3.89640i			0.147165i	−0.997289	+	0.0735825i	$0.976557\pi$
$702$		0			0
$703$	−17.1875	−	17.1875i	−0.648240	−	0.648240i
$704$	−0.174119	+	0.987476i	−0.00656235	+	0.0372169i
$705$		0			0
$706$	12.1861	+	4.43538i	0.458630	+	0.166928i
$707$	19.6108	+	1.71572i	0.737541	+	0.0645264i
$708$		0			0
$709$	−7.07809	−	19.4469i	−0.265823	−	0.730343i	−0.998748	−	0.0500331i	$-0.984067\pi$
$709$	−7.07809	−	19.4469i	−0.265823	−	0.730343i	0.732924	−	0.680310i	$-0.238155\pi$
$710$	−31.2001	−	0.785940i	−1.17092	−	0.0294958i
$711$		0			0
$712$	17.8685	+	4.78786i	0.669652	+	0.179433i
$713$	37.1029	−	3.24608i	1.38951	−	0.121567i
$714$		0			0
$715$	7.97504	−	6.35660i	0.298250	−	0.237723i
$716$	−12.7809	+	2.25362i	−0.477645	+	0.0842218i
$717$		0			0
$718$	1.33246	+	15.2301i	0.0497269	+	0.568381i
$719$	23.2328	+	40.2403i	0.866436	+	1.50071i	0.865614	+	0.500712i	$0.166928\pi$
$719$	23.2328	+	40.2403i	0.866436	+	1.50071i	0.000822468		1.00000i	$0.499738\pi$
$720$		0			0
$721$	7.56817	−	13.1085i	0.281853	−	0.488185i
$722$	0.973719	+	0.454053i	0.0362381	+	0.0168981i
$723$		0			0
$724$	12.0891	+	14.4073i	0.449289	+	0.535442i
$725$	25.0295	+	33.0781i	0.929571	+	1.22849i
$726$		0			0
$727$	14.7105	+	21.0088i	0.545584	+	0.779175i	0.993369	−	0.114966i	$-0.0366760\pi$
$727$	14.7105	+	21.0088i	0.545584	+	0.779175i	−0.447785	+	0.894141i	$0.647787\pi$
$728$	4.73454	−	4.73454i	0.175474	−	0.175474i
$729$		0			0
$730$	−19.7093	−	5.81682i	−0.729472	−	0.215290i
$731$	−0.417580	−	0.0736307i	−0.0154448	−	0.00272333i
$732$		0			0
$733$	1.12205	+	2.40624i	0.0414438	+	0.0888766i	0.925940	−	0.377672i	$-0.123275\pi$
$733$	1.12205	+	2.40624i	0.0414438	+	0.0888766i	−0.884496	+	0.466548i	$0.845497\pi$
$734$	−36.3169	+	30.4735i	−1.34048	+	1.12480i
$735$		0			0
$736$	−23.0499	+	8.38947i	−0.849630	+	0.309240i
$737$	−1.80228	+	0.482919i	−0.0663878	+	0.0177886i
$738$		0			0
$739$	−19.4519	+	11.2305i	−0.715548	+	0.413122i	−0.813112	−	0.582107i	$-0.802228\pi$
$739$	−19.4519	+	11.2305i	−0.715548	+	0.413122i	0.0975639	+	0.995229i	$0.468895\pi$
$740$	−12.2285	−	2.47524i	−0.449527	−	0.0909917i
$741$		0			0
$742$	−11.0464	−	7.73477i	−0.405526	−	0.283952i
$743$	−25.2126	−	17.6540i	−0.924960	−	0.647664i	0.0109359	−	0.999940i	$-0.496519\pi$
$743$	−25.2126	−	17.6540i	−0.924960	−	0.647664i	−0.935896	+	0.352276i	$0.885408\pi$
$744$		0			0
$745$	−26.7057	+	17.7144i	−0.978422	+	0.649004i
$746$	18.2856	−	10.5572i	0.669484	−	0.386527i
$747$		0			0
$748$	0.649300	−	0.173979i	0.0237408	−	0.00636132i
$749$	−4.31804	+	1.57164i	−0.157778	+	0.0574264i
$750$		0			0
$751$	5.77858	−	4.84881i	0.210864	−	0.176936i	−0.531239	−	0.847222i	$-0.678273\pi$
$751$	5.77858	−	4.84881i	0.210864	−	0.176936i	0.742102	+	0.670287i	$0.233829\pi$
$752$	−25.9636	−	55.6791i	−0.946795	−	2.03041i
$753$		0			0
$754$	−54.8008	−	9.66287i	−1.99573	−	0.351901i
$755$	−3.41000	+	11.5542i	−0.124103	+	0.420499i
$756$		0			0
$757$	−18.1781	+	18.1781i	−0.660696	+	0.660696i	−0.955544	−	0.294848i	$-0.904731\pi$
$757$	−18.1781	+	18.1781i	−0.660696	+	0.660696i	0.294848	+	0.955544i	$0.404731\pi$
$758$	−22.5748	−	32.2402i	−0.819954	−	1.17102i
$759$		0			0
$760$	−16.7260	+	2.51674i	−0.606717	+	0.0912917i
$761$	−19.2569	−	22.9494i	−0.698061	−	0.831916i	0.294245	−	0.955730i	$-0.404932\pi$
$761$	−19.2569	−	22.9494i	−0.698061	−	0.831916i	−0.992305	+	0.123814i	$0.960487\pi$
$762$		0			0
$763$	−9.86895	−	4.60197i	−0.357280	−	0.166602i
$764$	−2.16991	+	3.75839i	−0.0785044	+	0.135974i
$765$		0			0
$766$	16.5590	+	28.6811i	0.598302	+	1.03629i
$767$	2.72548	+	31.1524i	0.0984115	+	1.12485i
$768$		0			0
$769$	4.02410	−	0.709557i	0.145113	−	0.0255873i	−0.100620	−	0.994925i	$-0.532083\pi$
$769$	4.02410	−	0.709557i	0.145113	−	0.0255873i	0.245733	+	0.969338i	$0.420971\pi$
$770$	0.522545	−	4.62725i	0.0188312	−	0.166754i
$771$		0			0
$772$	−10.2628	+	0.897880i	−0.369367	+	0.0323154i
$773$	38.4073	+	10.2912i	1.38141	+	0.370149i	0.871635	−	0.490156i	$-0.163060\pi$
$773$	38.4073	+	10.2912i	1.38141	+	0.370149i	0.509780	+	0.860305i	$0.329727\pi$
$774$		0			0
$775$	35.6009	−	18.2289i	1.27882	−	0.654802i
$776$	−2.99143	−	8.21887i	−0.107386	−	0.295040i
$777$		0			0
$778$	−26.9882	−	2.36116i	−0.967573	−	0.0846517i
$779$	−23.1087	−	8.41088i	−0.827955	−	0.301351i
$780$		0			0
$781$	−1.64803	+	9.34644i	−0.0589711	+	0.334442i
$782$	−3.20111	−	3.20111i	−0.114471	−	0.114471i
$783$		0			0
$784$			29.8449i			1.06589i
$785$	−16.8811	+	5.66700i	−0.602511	+	0.202264i
$786$		0			0
$787$	4.88315	−	2.27705i	0.174066	−	0.0811681i	−0.333632	−	0.942703i	$-0.608274\pi$
$787$	4.88315	−	2.27705i	0.174066	−	0.0811681i	0.507698	+	0.861535i	$0.330497\pi$
$788$	1.05061	−	12.0086i	0.0374265	−	0.427787i
$789$		0			0
$790$	19.5937	+	17.3003i	0.697112	+	0.615517i
$791$	−11.0978	−	6.40733i	−0.394593	−	0.227818i
$792$		0			0
$793$	11.2073	−	41.8261i	0.397982	−	1.48529i
$794$	11.8380	+	9.93324i	0.420114	+	0.352518i
$795$		0			0
$796$	−1.03270	−	5.85673i	−0.0366031	−	0.207586i
$797$	−17.9597	+	25.6491i	−0.636165	+	0.908538i	−0.999735	−	0.0230287i	$-0.992669\pi$
$797$	−17.9597	+	25.6491i	−0.636165	+	0.908538i	0.363569	+	0.931567i	$0.381558\pi$
$798$		0			0
$799$	4.42153	−	5.26938i	0.156423	−	0.186417i
$800$	−19.5405	+	17.6649i	−0.690860	+	0.624547i
$801$		0			0
$802$	−0.496613	−	1.85338i	−0.0175360	−	0.0654453i
$803$	−2.64092	+	5.66346i	−0.0931959	+	0.199859i
$804$		0			0
$805$	−9.68882	+	4.22429i	−0.341486	+	0.148887i
$806$	−18.3512	+	50.4196i	−0.646395	+	1.77595i
$807$		0			0
$808$	−27.1260	+	18.9939i	−0.954291	+	0.668202i
$809$	−4.86947			−0.171202			−0.0856008	−	0.996330i	$-0.527281\pi$
$809$	−4.86947			−0.171202			−0.0856008	+	0.996330i	$0.527281\pi$
$810$		0			0
$811$	−14.9764			−0.525893			−0.262947	−	0.964810i	$-0.584694\pi$
$811$	−14.9764			−0.525893			−0.262947	+	0.964810i	$0.584694\pi$
$812$	−7.01480	+	4.91182i	−0.246171	+	0.172371i
$813$		0			0
$814$	−3.85009	+	10.5780i	−0.134946	+	0.370760i
$815$	13.1133	−	33.3874i	0.459338	−	1.16951i
$816$		0			0
$817$	−1.41787	+	3.04063i	−0.0496049	+	0.106378i
$818$	0.327165	+	1.22100i	0.0114391	+	0.0426911i
$819$		0			0
$820$	−12.2710	+	2.95893i	−0.428522	+	0.103330i
$821$	−2.55907	+	3.04978i	−0.0893122	+	0.106438i	−0.808850	−	0.588015i	$-0.799909\pi$
$821$	−2.55907	+	3.04978i	−0.0893122	+	0.106438i	0.719537	+	0.694454i	$0.244354\pi$
$822$		0			0
$823$	9.33088	−	13.3259i	0.325254	−	0.464511i	−0.622909	−	0.782294i	$-0.714049\pi$
$823$	9.33088	−	13.3259i	0.325254	−	0.464511i	0.948163	+	0.317783i	$0.102938\pi$
$824$	4.42142	+	25.0751i	0.154027	+	0.873533i
$825$		0			0
$826$	10.9381	+	9.17818i	0.380586	+	0.319350i
$827$	5.10757	−	19.0617i	0.177608	−	0.662841i	−0.818485	−	0.574528i	$-0.805186\pi$
$827$	5.10757	−	19.0617i	0.177608	−	0.662841i	0.996093	−	0.0883130i	$-0.0281476\pi$
$828$		0			0
$829$	−32.1618	−	18.5687i	−1.11703	−	0.644916i	−0.176387	−	0.984321i	$-0.556441\pi$
$829$	−32.1618	−	18.5687i	−1.11703	−	0.644916i	−0.940640	+	0.339405i	$0.889774\pi$
$830$	−0.0723016	−	1.16313i	−0.00250963	−	0.0403727i
$831$		0			0
$832$	−0.285765	+	3.26630i	−0.00990711	+	0.113239i
$833$	−3.02855	+	1.41223i	−0.104933	+	0.0489310i
$834$		0			0
$835$	0.301471	+	0.898032i	0.0104328	+	0.0310777i
$836$		−	5.31864i		−	0.183949i
$837$		0			0
$838$	24.1069	+	24.1069i	0.832759	+	0.832759i
$839$	6.68205	−	37.8958i	0.230690	−	1.30831i	−0.620813	−	0.783958i	$-0.713198\pi$
$839$	6.68205	−	37.8958i	0.230690	−	1.30831i	0.851503	−	0.524349i	$-0.175691\pi$
$840$		0			0
$841$	−37.4236	−	13.6211i	−1.29047	−	0.469692i
$842$	−18.2938	−	1.60050i	−0.630447	−	0.0551570i
$843$		0			0
$844$	2.47119	+	6.78953i	0.0850618	+	0.233705i
$845$	3.10103	−	2.94864i	0.106679	−	0.101436i
$846$		0			0
$847$	9.41923	+	2.52388i	0.323649	+	0.0867214i
$848$	38.0901	−	3.33245i	1.30802	−	0.114437i
$849$		0			0
$850$	−4.47884	−	1.89065i	−0.153623	−	0.0648486i
$851$	25.1627	−	4.43686i	0.862567	−	0.152094i
$852$		0			0
$853$	−3.27769	−	37.4642i	−0.112226	−	1.28275i	−0.818374	−	0.574685i	$-0.805124\pi$
$853$	−3.27769	−	37.4642i	−0.112226	−	1.28275i	0.706148	−	0.708064i	$-0.250431\pi$
$854$	−9.88588	−	17.1228i	−0.338288	−	0.585932i
$855$		0			0
$856$	3.86493	−	6.69425i	0.132100	−	0.228805i
$857$	−17.6382	−	8.22482i	−0.602509	−	0.280954i	0.0973336	−	0.995252i	$-0.468969\pi$
$857$	−17.6382	−	8.22482i	−0.602509	−	0.280954i	−0.699842	+	0.714297i	$0.746746\pi$
$858$		0			0
$859$	−13.2902	−	15.8386i	−0.453454	−	0.540406i	0.490081	−	0.871677i	$-0.336967\pi$
$859$	−13.2902	−	15.8386i	−0.453454	−	0.540406i	−0.943536	+	0.331271i	$0.892523\pi$
$860$	0.256233	+	1.70290i	0.00873746	+	0.0580684i
$861$		0			0
$862$	−16.5469	−	23.6315i	−0.563590	−	0.804891i
$863$	1.02957	−	1.02957i	0.0350471	−	0.0350471i	−0.689366	−	0.724413i	$-0.742111\pi$
$863$	1.02957	−	1.02957i	0.0350471	−	0.0350471i	0.724413	+	0.689366i	$0.242111\pi$
$864$		0			0
$865$	8.63591	+	15.8677i	0.293630	+	0.539518i
$866$	−34.6408	−	6.10810i	−1.17714	−	0.207562i
$867$		0			0
$868$	3.48961	+	7.48350i	0.118445	+	0.254006i
$869$	6.08882	−	5.10913i	0.206549	−	0.173315i
$870$		0			0
$871$	−5.73325	+	2.08673i	−0.194264	+	0.0707063i
$872$	17.6933	−	4.74092i	0.599172	−	0.160548i
$873$		0			0
$874$	−31.0202	+	17.9095i	−1.04927	+	0.605799i
$875$	−7.93156	+	8.11955i	−0.268136	+	0.274491i
$876$		0			0
$877$	−47.3607	−	33.1623i	−1.59926	−	1.11981i	−0.924110	−	0.382126i	$-0.875192\pi$
$877$	−47.3607	−	33.1623i	−1.59926	−	1.11981i	−0.675145	−	0.737685i	$-0.735919\pi$
$878$	16.8718	+	11.8138i	0.569396	+	0.398695i
$879$		0			0
$880$	7.29840	+	11.0029i	0.246029	+	0.370907i
$881$	−6.00946	+	3.46956i	−0.202464	+	0.116893i	−0.597804	−	0.801642i	$-0.703960\pi$
$881$	−6.00946	+	3.46956i	−0.202464	+	0.116893i	0.395340	+	0.918535i	$0.370627\pi$
$882$		0			0
$883$	14.9527	−	4.00657i	0.503199	−	0.134832i	0.00171481	−	0.999999i	$-0.499454\pi$
$883$	14.9527	−	4.00657i	0.503199	−	0.134832i	0.501484	+	0.865167i	$0.332787\pi$
$884$	2.06550	−	0.751779i	0.0694702	−	0.0252851i
$885$		0			0
$886$	−29.6420	+	24.8726i	−0.995844	+	0.835612i
$887$	16.6122	+	35.6250i	0.557783	+	1.19617i	0.959838	+	0.280554i	$0.0905181\pi$
$887$	16.6122	+	35.6250i	0.557783	+	1.19617i	−0.402055	+	0.915615i	$0.631704\pi$
$888$		0			0
$889$	−17.6428	−	3.11090i	−0.591720	−	0.104336i
$890$	36.9511	−	20.1104i	1.23860	−	0.674104i
$891$		0			0
$892$	1.59361	−	1.59361i	0.0533582	−	0.0533582i
$893$	−31.2173	−	44.5830i	−1.04465	−	1.49191i
$894$		0			0
$895$	16.9546	−	22.9605i	0.566729	−	0.767486i
$896$	7.83830	+	9.34132i	0.261859	+	0.312072i
$897$		0			0
$898$	−8.30068	−	3.87067i	−0.276997	−	0.129166i
$899$	−33.1815	+	57.4721i	−1.10667	+	1.91680i
$900$		0			0
$901$	2.14056	+	3.70755i	0.0713123	+	0.123516i
$902$	0.992605	+	11.3455i	0.0330501	+	0.377765i
$903$		0			0
$904$	21.2290	−	3.74324i	0.706065	−	0.124498i
$905$	−41.1007	−	4.64141i	−1.36623	−	0.154286i
$906$		0			0
$907$	−16.6313	+	1.45505i	−0.552232	+	0.0483140i	−0.359857	−	0.933008i	$-0.617174\pi$
$907$	−16.6313	+	1.45505i	−0.552232	+	0.0483140i	−0.192375	+	0.981322i	$0.561619\pi$
$908$	9.43978	+	2.52938i	0.313270	+	0.0839404i
$909$		0			0
$910$	0.383449	−	15.2221i	0.0127112	−	0.504607i
$911$	−15.5855	−	42.8207i	−0.516369	−	1.41871i	−0.874493	−	0.485038i	$-0.838806\pi$
$911$	−15.5855	−	42.8207i	−0.516369	−	1.41871i	0.358124	−	0.933674i	$-0.383417\pi$
$912$		0			0
$913$	−0.353029	−	0.0308860i	−0.0116835	−	0.00102218i
$914$	−15.6849	−	5.70884i	−0.518810	−	0.188831i
$915$		0			0
$916$	−1.77277	+	10.0539i	−0.0585740	+	0.332190i
$917$	−2.07473	−	2.07473i	−0.0685136	−	0.0685136i
$918$		0			0
$919$			3.56037i			0.117446i	0.998274	+	0.0587228i	$0.0187028\pi$
$919$			3.56037i			0.117446i	−0.998274	+	0.0587228i	$0.981297\pi$
$920$	7.91756	−	15.9198i	0.261034	−	0.524861i
$921$		0			0
$922$	−16.9051	+	7.88296i	−0.556738	+	0.259611i
$923$	−2.70476	+	30.9155i	−0.0890281	+	1.01760i
$924$		0			0
$925$	23.2404	−	14.5866i	0.764140	−	0.479605i
$926$	53.8596	+	31.0958i	1.76994	+	1.02187i
$927$		0			0
$928$	11.3121	−	42.2172i	0.371337	−	1.38585i
$929$	9.72612	+	8.16118i	0.319104	+	0.267760i	0.788243	−	0.615365i	$-0.210991\pi$
$929$	9.72612	+	8.16118i	0.319104	+	0.267760i	−0.469139	+	0.883124i	$0.655436\pi$
$930$		0			0
$931$	4.59122	+	26.0381i	0.150471	+	0.853364i
$932$	7.02055	−	10.0264i	0.229966	−	0.328425i
$933$		0			0
$934$	−27.2732	+	32.5030i	−0.892407	+	1.06353i
$935$	−0.771177	+	1.26126i	−0.0252202	+	0.0412477i
$936$		0			0
$937$	−6.23661	−	23.2753i	−0.203741	−	0.760372i	−0.989830	−	0.142258i	$-0.954564\pi$
$937$	−6.23661	−	23.2753i	−0.203741	−	0.760372i	0.786089	−	0.618114i	$-0.212103\pi$
$938$	−1.17735	+	2.52484i	−0.0384418	+	0.0824388i
$939$		0			0
$940$	−26.0025	−	10.2128i	−0.848109	−	0.333105i
$941$	2.96478	−	8.14566i	0.0966490	−	0.265541i	−0.881941	−	0.471359i	$-0.843763\pi$
$941$	2.96478	−	8.14566i	0.0966490	−	0.265541i	0.978590	+	0.205819i	$0.0659857\pi$
$942$		0			0
$943$	21.1754	−	14.8272i	0.689566	−	0.482839i
$944$	−40.4856			−1.31769
$945$		0			0
$946$	1.55374			0.0505165
$947$	23.3157	−	16.3258i	0.757658	−	0.530518i	−0.129726	−	0.991550i	$-0.541410\pi$
$947$	23.3157	−	16.3258i	0.757658	−	0.530518i	0.887383	+	0.461032i	$0.152521\pi$
$948$		0			0
$949$	−6.98868	+	19.2012i	−0.226862	+	0.623299i
$950$	−23.6214	+	30.3584i	−0.766381	+	0.984957i
$951$		0			0
$952$	−0.410189	+	0.879652i	−0.0132943	+	0.0285097i
$953$	3.74136	+	13.9629i	0.121194	+	0.452304i	0.999675	−	0.0254735i	$-0.00810933\pi$
$953$	3.74136	+	13.9629i	0.121194	+	0.452304i	−0.878481	+	0.477777i	$0.841443\pi$
$954$		0			0
$955$	−2.23730	−	9.27837i	−0.0723975	−	0.300241i
$956$	1.18086	−	1.40730i	0.0381918	−	0.0455152i
$957$		0			0
$958$	40.6627	−	58.0723i	1.31375	−	1.87623i
$959$	−1.48462	−	8.41972i	−0.0479410	−	0.271887i
$960$		0			0
$961$	25.2709	+	21.2048i	0.815190	+	0.684025i
$962$	−9.52692	+	35.5550i	−0.307160	+	1.14634i
$963$		0			0
$964$	14.1690	+	8.18045i	0.456351	+	0.263474i
$965$	14.9959	−	16.9838i	0.482734	−	0.546726i
$966$		0			0
$967$	−2.08098	+	23.7858i	−0.0669199	+	0.764898i	0.886397	+	0.462926i	$0.153201\pi$
$967$	−2.08098	+	23.7858i	−0.0669199	+	0.764898i	−0.953317	+	0.301972i	$0.902355\pi$
$968$	−14.8668	+	6.93251i	−0.477838	+	0.222819i
$969$		0			0
$970$	−17.8095	−	8.85737i	−0.571828	−	0.284393i
$971$			55.0723i			1.76735i	0.468098	+	0.883676i	$0.344939\pi$
$971$			55.0723i			1.76735i	−0.468098	+	0.883676i	$0.655061\pi$
$972$		0			0
$973$	7.17940	+	7.17940i	0.230161	+	0.230161i
$974$	−10.0337	+	56.9040i	−0.321501	+	1.82332i
$975$		0			0
$976$	52.6796	+	19.1738i	1.68623	+	0.613738i
$977$	12.7178	+	1.11266i	0.406878	+	0.0355972i	0.288758	−	0.957402i	$-0.406758\pi$
$977$	12.7178	+	1.11266i	0.406878	+	0.0355972i	0.118120	+	0.992999i	$0.462313\pi$
$978$		0			0
$979$	−4.37539	−	12.0213i	−0.139838	−	0.384202i
$980$	9.35164	+	9.83495i	0.298727	+	0.314166i
$981$		0			0
$982$	8.35043	+	2.23749i	0.266473	+	0.0714012i
$983$	−7.16081	+	0.626489i	−0.228394	+	0.0199819i	−0.200778	−	0.979637i	$-0.564347\pi$
$983$	−7.16081	+	0.626489i	−0.228394	+	0.0199819i	−0.0276159	+	0.999619i	$0.508792\pi$
$984$		0			0
$985$	16.5239	+	20.7310i	0.526494	+	0.660544i
$986$	7.94382	−	1.40071i	0.252983	−	0.0446077i
$987$		0			0
$988$	−1.51577	−	17.3254i	−0.0482231	−	0.551193i
$989$	−1.76334	−	3.05419i	−0.0560708	−	0.0971175i
$990$		0			0
$991$	18.6356	−	32.2778i	0.591979	−	1.02534i	−0.401987	−	0.915645i	$-0.631680\pi$
$991$	18.6356	−	32.2778i	0.591979	−	1.02534i	0.993966	−	0.109692i	$-0.0349863\pi$
$992$	−38.1944	−	17.8103i	−1.21267	−	0.565478i
$993$		0			0
$994$	9.10839	+	10.8550i	0.288900	+	0.344298i
$995$	10.5214	+	7.76927i	0.333552	+	0.246302i
$996$		0			0
$997$	18.5746	+	26.5272i	0.588262	+	0.840126i	0.997379	−	0.0723564i	$-0.0230519\pi$
$997$	18.5746	+	26.5272i	0.588262	+	0.840126i	−0.409116	+	0.912482i	$0.634163\pi$
$998$	7.93723	−	7.93723i	0.251249	−	0.251249i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.r.a.8.13		192
3.2	odd	2		135.2.q.a.83.4	yes	192
5.2	odd	4	inner	405.2.r.a.332.13		192
15.2	even	4		135.2.q.a.2.4	✓	192
15.8	even	4		675.2.ba.b.407.13		192
15.14	odd	2		675.2.ba.b.218.13		192
27.13	even	9		135.2.q.a.68.4	yes	192
27.14	odd	18	inner	405.2.r.a.233.13		192
135.13	odd	36		675.2.ba.b.257.13		192
135.67	odd	36		135.2.q.a.122.4	yes	192
135.94	even	18		675.2.ba.b.68.13		192
135.122	even	36	inner	405.2.r.a.152.13		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.4	✓	192	15.2	even	4
135.2.q.a.68.4	yes	192	27.13	even	9
135.2.q.a.83.4	yes	192	3.2	odd	2
135.2.q.a.122.4	yes	192	135.67	odd	36
405.2.r.a.8.13		192	1.1	even	1	trivial
405.2.r.a.152.13		192	135.122	even	36	inner
405.2.r.a.233.13		192	27.14	odd	18	inner
405.2.r.a.332.13		192	5.2	odd	4	inner
675.2.ba.b.68.13		192	135.94	even	18
675.2.ba.b.218.13		192	15.14	odd	2
675.2.ba.b.257.13		192	135.13	odd	36
675.2.ba.b.407.13		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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.42277 - 0.996232i) q^{2} +(0.347747 - 0.955427i) q^{4} +(0.893670 + 2.04972i) q^{5} +(0.429055 - 0.920112i) q^{7} +(0.442010 + 1.64960i) q^{8} +O(q^{10})\)	\(q+(1.42277 - 0.996232i) q^{2} +(0.347747 - 0.955427i) q^{4} +(0.893670 + 2.04972i) q^{5} +(0.429055 - 0.920112i) q^{7} +(0.442010 + 1.64960i) q^{8} +(3.31348 + 2.02597i) q^{10} +(0.759141 - 0.904709i) q^{11} +(2.21505 - 3.16342i) q^{13} +(-0.306200 - 1.73654i) q^{14} +(3.83001 + 3.21376i) q^{16} +(-0.144887 + 0.540727i) q^{17} +(3.83587 + 2.21464i) q^{19} +(2.26913 - 0.141052i) q^{20} +(0.178781 - 2.04347i) q^{22} +(-4.21975 + 1.96770i) q^{23} +(-3.40271 + 3.66355i) q^{25} -6.70752i q^{26} +(-0.729897 - 0.729897i) q^{28} +(1.44060 - 8.17007i) q^{29} +(-7.51688 - 2.73592i) q^{31} +(5.24827 + 0.459164i) q^{32} +(0.332549 + 0.913671i) q^{34} +(2.26941 + 0.0571670i) q^{35} +(-5.30076 - 1.42034i) q^{37} +(7.66385 - 0.670500i) q^{38} +(-2.98621 + 2.38020i) q^{40} +(-5.46773 + 0.964109i) q^{41} +(0.0660161 + 0.754568i) q^{43} +(-0.600395 - 1.03991i) q^{44} +(-4.04344 + 7.00343i) q^{46} +(-11.1364 - 5.19301i) q^{47} +(3.83700 + 4.57275i) q^{49} +(-1.19152 + 8.60226i) q^{50} +(-2.25214 - 3.21639i) q^{52} +(5.40763 - 5.40763i) q^{53} +(2.53282 + 0.747516i) q^{55} +(1.70747 + 0.301072i) q^{56} +(-6.08964 - 13.0593i) q^{58} +(-6.20310 + 5.20502i) q^{59} +(10.5365 - 3.83498i) q^{61} +(-13.4204 + 3.59598i) q^{62} +(-0.735277 + 0.424512i) q^{64} +(8.46365 + 1.71318i) q^{65} +(-1.29416 - 0.906180i) q^{67} +(0.466241 + 0.326466i) q^{68} +(3.28579 - 2.17952i) q^{70} +(-6.95937 + 4.01800i) q^{71} +(-5.11087 + 1.36945i) q^{73} +(-8.95674 + 3.25999i) q^{74} +(3.44984 - 2.89476i) q^{76} +(-0.506721 - 1.08667i) q^{77} +(6.62789 + 1.16868i) q^{79} +(-3.16454 + 10.7225i) q^{80} +(-6.81884 + 6.81884i) q^{82} +(-0.172108 - 0.245796i) q^{83} +(-1.23782 + 0.186253i) q^{85} +(0.845650 + 1.00781i) q^{86} +(1.82796 + 0.852391i) q^{88} +(5.41601 - 9.38081i) q^{89} +(-1.96032 - 3.39538i) q^{91} +(0.412590 + 4.71593i) q^{92} +(-21.0180 + 3.70604i) q^{94} +(-1.11139 + 9.84163i) q^{95} +(-5.10194 + 0.446362i) q^{97} +(10.0147 + 2.68342i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) \) 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

Modular forms

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