LMFDB - Embedded newform 405.2.r.a.17.1

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			17.1
Character	$\chi$	$=$	405.17
Dual form			405.2.r.a.143.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.47401 + 1.15365i) q^{2} +(3.50423 - 4.17618i) q^{4} +(1.69173 - 1.46221i) q^{5} +(-0.0671403 - 0.00587402i) q^{7} +(-2.43862 + 9.10104i) q^{8} +O(q^{10})$	\(q+(-2.47401 + 1.15365i) q^{2} +(3.50423 - 4.17618i) q^{4} +(1.69173 - 1.46221i) q^{5} +(-0.0671403 - 0.00587402i) q^{7} +(-2.43862 + 9.10104i) q^{8} +(-2.49848 + 5.56917i) q^{10} +(2.84658 - 0.501928i) q^{11} +(-0.668569 + 1.43375i) q^{13} +(0.172882 - 0.0629240i) q^{14} +(-2.57292 - 14.5918i) q^{16} +(0.0710153 + 0.265033i) q^{17} +(1.42429 - 0.822315i) q^{19} +(-0.178226 - 12.1889i) q^{20} +(-6.46340 + 4.52572i) q^{22} +(-0.635912 - 7.26851i) q^{23} +(0.723902 - 4.94732i) q^{25} -4.31840i q^{26} +(-0.259806 + 0.259806i) q^{28} +(-0.282115 - 0.102681i) q^{29} +(-0.140950 - 0.118271i) q^{31} +(12.3906 + 17.6956i) q^{32} +(-0.481447 - 0.573766i) q^{34} +(-0.122172 + 0.0882358i) q^{35} +(9.18868 - 2.46210i) q^{37} +(-2.57504 + 3.67754i) q^{38} +(9.18212 + 18.9623i) q^{40} +(1.74933 + 4.80625i) q^{41} +(4.44406 + 3.11177i) q^{43} +(7.87892 - 13.6467i) q^{44} +(9.95855 + 17.2487i) q^{46} +(-0.164477 + 1.87998i) q^{47} +(-6.88918 - 1.21475i) q^{49} +(3.91653 + 13.0748i) q^{50} +(3.64478 + 7.81625i) q^{52} +(1.58658 + 1.58658i) q^{53} +(4.08172 - 5.01141i) q^{55} +(0.217189 - 0.596722i) q^{56} +(0.816413 - 0.0714269i) q^{58} +(2.10453 - 11.9354i) q^{59} +(3.42343 - 2.87260i) q^{61} +(0.485153 + 0.129996i) q^{62} +(-25.4054 - 14.6678i) q^{64} +(0.965402 + 3.40311i) q^{65} +(2.24913 + 1.04879i) q^{67} +(1.35568 + 0.632163i) q^{68} +(0.200462 - 0.359240i) q^{70} +(4.91000 + 2.83479i) q^{71} +(-8.72199 - 2.33705i) q^{73} +(-19.8925 + 16.6918i) q^{74} +(1.55691 - 8.82967i) q^{76} +(-0.194068 + 0.0169788i) q^{77} +(2.57857 - 7.08457i) q^{79} +(-25.6889 - 20.9232i) q^{80} +(-9.87258 - 9.87258i) q^{82} +(-5.20307 - 11.1580i) q^{83} +(0.507671 + 0.344525i) q^{85} +(-14.5845 - 2.57164i) q^{86} +(-2.37364 + 27.1308i) q^{88} +(6.33320 + 10.9694i) q^{89} +(0.0533098 - 0.0923353i) q^{91} +(-32.5830 - 22.8148i) q^{92} +(-1.76192 - 4.84082i) q^{94} +(1.20712 - 3.47374i) q^{95} +(1.11896 - 1.59804i) q^{97} +(18.4453 - 4.94240i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	−2.47401	+	1.15365i	−1.74939	+	0.815752i	−0.764045	+	0.645163i	$0.776789\pi$
$2$	−2.47401	+	1.15365i	−1.74939	+	0.815752i	−0.985342	+	0.170589i	$0.945433\pi$
$3$		0			0
$3$		0			0
$4$	3.50423	−	4.17618i	1.75211	−	2.08809i
$5$	1.69173	−	1.46221i	0.756565	−	0.653919i
$5$	1.69173	−	1.46221i	0.756565	−	0.653919i
$6$		0			0
$7$	−0.0671403	−	0.00587402i	−0.0253767	−	0.00222017i	0.0744603	−	0.997224i	$-0.476277\pi$
$7$	−0.0671403	−	0.00587402i	−0.0253767	−	0.00222017i	−0.0998370	+	0.995004i	$0.531832\pi$
$8$	−2.43862	+	9.10104i	−0.862181	+	3.21770i
$9$		0			0
$10$	−2.49848	+	5.56917i	−0.790088	+	1.76113i
$11$	2.84658	−	0.501928i	0.858275	−	0.151337i	0.272843	−	0.962059i	$-0.412036\pi$
$11$	2.84658	−	0.501928i	0.858275	−	0.151337i	0.585432	+	0.810721i	$0.300925\pi$
$12$		0			0
$13$	−0.668569	+	1.43375i	−0.185428	+	0.397651i	−0.976944	−	0.213498i	$-0.931514\pi$
$13$	−0.668569	+	1.43375i	−0.185428	+	0.397651i	0.791516	+	0.611149i	$0.209292\pi$
$14$	0.172882	−	0.0629240i	0.0462047	−	0.0168171i
$15$		0			0
$16$	−2.57292	−	14.5918i	−0.643230	−	3.64794i
$17$	0.0710153	+	0.265033i	0.0172237	+	0.0642799i	0.974003	−	0.226536i	$-0.0727400\pi$
$17$	0.0710153	+	0.265033i	0.0172237	+	0.0642799i	−0.956779	+	0.290816i	$0.906073\pi$
$18$		0			0
$19$	1.42429	−	0.822315i	0.326755	−	0.188652i	−0.327645	−	0.944801i	$-0.606255\pi$
$19$	1.42429	−	0.822315i	0.326755	−	0.188652i	0.654399	+	0.756149i	$0.272922\pi$
$20$	−0.178226	−	12.1889i	−0.0398526	−	2.72552i
$21$		0			0
$22$	−6.46340	+	4.52572i	−1.37800	+	0.964887i
$23$	−0.635912	−	7.26851i	−0.132597	−	1.51559i	−0.712945	−	0.701220i	$-0.752639\pi$
$23$	−0.635912	−	7.26851i	−0.132597	−	1.51559i	0.580348	−	0.814368i	$-0.302916\pi$
$24$		0			0
$25$	0.723902	−	4.94732i	0.144780	−	0.989464i
$26$		−	4.31840i		−	0.846908i
$27$		0			0
$28$	−0.259806	+	0.259806i	−0.0490987	+	0.0490987i
$29$	−0.282115	−	0.102681i	−0.0523874	−	0.0190675i	0.315694	−	0.948861i	$-0.397763\pi$
$29$	−0.282115	−	0.102681i	−0.0523874	−	0.0190675i	−0.368081	+	0.929794i	$0.619985\pi$
$30$		0			0
$31$	−0.140950	−	0.118271i	−0.0253153	−	0.0212421i	0.630042	−	0.776561i	$-0.283038\pi$
$31$	−0.140950	−	0.118271i	−0.0253153	−	0.0212421i	−0.655358	+	0.755319i	$0.727482\pi$
$32$	12.3906	+	17.6956i	2.19037	+	3.12817i
$33$		0			0
$34$	−0.481447	−	0.573766i	−0.0825675	−	0.0984001i
$35$	−0.122172	+	0.0882358i	−0.0206509	+	0.0149146i
$36$		0			0
$37$	9.18868	−	2.46210i	1.51061	−	0.404767i	0.593972	−	0.804485i	$-0.297559\pi$
$37$	9.18868	−	2.46210i	1.51061	−	0.404767i	0.916638	+	0.399719i	$0.130892\pi$
$38$	−2.57504	+	3.67754i	−0.417727	+	0.596576i
$39$		0			0
$40$	9.18212	+	18.9623i	1.45182	+	2.99820i
$41$	1.74933	+	4.80625i	0.273200	+	0.750610i	0.998092	+	0.0617475i	$0.0196674\pi$
$41$	1.74933	+	4.80625i	0.273200	+	0.750610i	−0.724892	+	0.688862i	$0.758110\pi$
$42$		0			0
$43$	4.44406	+	3.11177i	0.677713	+	0.474540i	0.861057	−	0.508509i	$-0.169803\pi$
$43$	4.44406	+	3.11177i	0.677713	+	0.474540i	−0.183344	+	0.983049i	$0.558692\pi$
$44$	7.87892	−	13.6467i	1.18779	−	2.05731i
$45$		0			0
$46$	9.95855	+	17.2487i	1.46831	+	2.54318i
$47$	−0.164477	+	1.87998i	−0.0239914	+	0.274223i	0.974718	+	0.223438i	$0.0717279\pi$
$47$	−0.164477	+	1.87998i	−0.0239914	+	0.274223i	−0.998710	+	0.0507851i	$0.983828\pi$
$48$		0			0
$49$	−6.88918	−	1.21475i	−0.984169	−	0.173535i
$50$	3.91653	+	13.0748i	0.553881	+	1.84906i
$51$		0			0
$52$	3.64478	+	7.81625i	0.505440	+	1.08392i
$53$	1.58658	+	1.58658i	0.217933	+	0.217933i	0.807627	−	0.589694i	$-0.200752\pi$
$53$	1.58658	+	1.58658i	0.217933	+	0.217933i	−0.589694	+	0.807627i	$0.700752\pi$
$54$		0			0
$55$	4.08172	−	5.01141i	0.550379	−	0.675739i
$56$	0.217189	−	0.596722i	0.0290231	−	0.0797404i
$57$		0			0
$58$	0.816413	−	0.0714269i	0.107200	−	0.00937881i
$59$	2.10453	−	11.9354i	0.273987	−	1.55386i	−0.468175	−	0.883636i	$-0.655088\pi$
$59$	2.10453	−	11.9354i	0.273987	−	1.55386i	0.742162	−	0.670221i	$-0.233801\pi$
$60$		0			0
$61$	3.42343	−	2.87260i	0.438325	−	0.367799i	−0.396757	−	0.917924i	$-0.629864\pi$
$61$	3.42343	−	2.87260i	0.438325	−	0.367799i	0.835082	+	0.550125i	$0.185420\pi$
$62$	0.485153	+	0.129996i	0.0616146	+	0.0165096i
$63$		0			0
$64$	−25.4054	−	14.6678i	−3.17567	−	1.83348i
$65$	0.965402	+	3.40311i	0.119743	+	0.422103i
$66$		0			0
$67$	2.24913	+	1.04879i	0.274775	+	0.128130i	0.555122	−	0.831769i	$-0.312672\pi$
$67$	2.24913	+	1.04879i	0.274775	+	0.128130i	−0.280347	+	0.959899i	$0.590450\pi$
$68$	1.35568	+	0.632163i	0.164400	+	0.0766610i
$69$		0			0
$70$	0.200462	−	0.359240i	0.0239598	−	0.0429374i
$71$	4.91000	+	2.83479i	0.582710	+	0.336427i	0.762209	−	0.647330i	$-0.224115\pi$
$71$	4.91000	+	2.83479i	0.582710	+	0.336427i	−0.179500	+	0.983758i	$0.557448\pi$
$72$		0			0
$73$	−8.72199	−	2.33705i	−1.02083	−	0.273531i	−0.290683	−	0.956819i	$-0.593883\pi$
$73$	−8.72199	−	2.33705i	−1.02083	−	0.273531i	−0.730149	+	0.683288i	$0.760549\pi$
$74$	−19.8925	+	16.6918i	−2.31245	+	1.94038i
$75$		0			0
$76$	1.55691	−	8.82967i	0.178590	−	1.01283i
$77$	−0.194068	+	0.0169788i	−0.0221161	+	0.00193491i
$78$		0			0
$79$	2.57857	−	7.08457i	0.290112	−	0.797076i	−0.705937	−	0.708274i	$-0.749474\pi$
$79$	2.57857	−	7.08457i	0.290112	−	0.797076i	0.996049	−	0.0888020i	$-0.0283038\pi$
$80$	−25.6889	−	20.9232i	−2.87210	−	2.33928i
$81$		0			0
$82$	−9.87258	−	9.87258i	−1.09024	−	1.09024i
$83$	−5.20307	−	11.1580i	−0.571111	−	1.22475i	−0.953679	−	0.300825i	$-0.902738\pi$
$83$	−5.20307	−	11.1580i	−0.571111	−	1.22475i	0.382568	−	0.923927i	$-0.375040\pi$
$84$		0			0
$85$	0.507671	+	0.344525i	0.0550647	+	0.0373690i
$86$	−14.5845	−	2.57164i	−1.57269	−	0.277308i
$87$		0			0
$88$	−2.37364	+	27.1308i	−0.253031	+	2.89216i
$89$	6.33320	+	10.9694i	0.671318	+	1.16276i	0.977530	+	0.210794i	$0.0676050\pi$
$89$	6.33320	+	10.9694i	0.671318	+	1.16276i	−0.306212	+	0.951963i	$0.599062\pi$
$90$		0			0
$91$	0.0533098	−	0.0923353i	0.00558839	−	0.00967937i
$92$	−32.5830	−	22.8148i	−3.39701	−	2.37861i
$93$		0			0
$94$	−1.76192	−	4.84082i	−0.181728	−	0.499293i
$95$	1.20712	−	3.47374i	0.123848	−	0.356398i
$96$		0			0
$97$	1.11896	−	1.59804i	0.113613	−	0.162256i	−0.758318	−	0.651885i	$-0.773979\pi$
$97$	1.11896	−	1.59804i	0.113613	−	0.162256i	0.871931	+	0.489628i	$0.162868\pi$
$98$	18.4453	−	4.94240i	1.86325	−	0.499257i
$99$		0			0
$100$	−18.1242	−	20.3597i	−1.81242	−	2.03597i
$101$	7.95401	+	9.47922i	0.791454	+	0.943218i	0.999390	−	0.0349247i	$-0.0111191\pi$
$101$	7.95401	+	9.47922i	0.791454	+	0.943218i	−0.207936	+	0.978142i	$0.566675\pi$
$102$		0			0
$103$	1.90393	+	2.71909i	0.187600	+	0.267920i	0.901924	−	0.431895i	$-0.142155\pi$
$103$	1.90393	+	2.71909i	0.187600	+	0.267920i	−0.714324	+	0.699815i	$0.753266\pi$
$104$	−11.4182	−	9.58104i	−1.11965	−	0.939498i
$105$		0			0
$106$	−5.75556	−	2.09485i	−0.559029	−	0.203470i
$107$	6.13426	−	6.13426i	0.593021	−	0.593021i	−0.345425	−	0.938446i	$-0.612265\pi$
$107$	6.13426	−	6.13426i	0.593021	−	0.593021i	0.938446	+	0.345425i	$0.112265\pi$
$108$		0			0
$109$			14.6291i			1.40122i	0.713547	+	0.700608i	$0.247088\pi$
$109$			14.6291i			1.40122i	−0.713547	+	0.700608i	$0.752912\pi$
$110$	−4.31679	+	17.1071i	−0.411590	+	1.63110i
$111$		0			0
$112$	0.0870345	+	0.994809i	0.00822398	+	0.0940006i
$113$	−6.10616	+	4.27558i	−0.574419	+	0.402212i	−0.824374	−	0.566045i	$-0.808473\pi$
$113$	−6.10616	+	4.27558i	−0.574419	+	0.402212i	0.249956	+	0.968257i	$0.419584\pi$
$114$		0			0
$115$	−11.7039	−	11.3665i	−1.09139	−	1.05993i
$116$	−1.41741	+	0.818343i	−0.131603	+	0.0759813i
$117$		0			0
$118$	8.56263	+	31.9562i	0.788254	+	2.94180i
$119$	−0.00321118	−	0.0182115i	−0.000294369	−	0.00166945i
$120$		0			0
$121$	−2.48555	+	0.904666i	−0.225959	+	0.0822424i
$122$	−5.15562	+	11.0563i	−0.466768	+	1.00099i
$123$		0			0
$124$	−0.987840	+	0.174183i	−0.0887107	+	0.0156421i
$125$	−6.00936	−	9.42802i	−0.537493	−	0.843268i
$126$		0			0
$127$	1.54001	−	5.74740i	0.136654	−	0.509999i	−0.863332	−	0.504637i	$-0.831626\pi$
$127$	1.54001	−	5.74740i	0.136654	−	0.509999i	0.999986	−	0.00536222i	$-0.00170686\pi$
$128$	36.7343	+	3.21383i	3.24688	+	0.284065i
$129$		0			0
$130$	−6.31440	−	7.30557i	−0.553809	−	0.640741i
$131$	2.94865	−	3.51407i	0.257625	−	0.307025i	−0.621693	−	0.783261i	$-0.713555\pi$
$131$	2.94865	−	3.51407i	0.257625	−	0.307025i	0.879318	+	0.476236i	$0.157999\pi$
$132$		0			0
$133$	−0.100458	+	0.0468442i	−0.00871078	+	0.00406190i
$134$	−6.77429			−0.585209
$135$		0			0
$136$	−2.58525			−0.221684
$137$	8.08399	−	3.76963i	0.690662	−	0.322061i	−0.0454058	−	0.998969i	$-0.514458\pi$
$137$	8.08399	−	3.76963i	0.690662	−	0.322061i	0.736068	+	0.676908i	$0.236680\pi$
$138$		0			0
$139$	−9.70032	+	11.5604i	−0.822771	+	0.980540i	−0.999993	−	0.00363092i	$-0.998844\pi$
$139$	−9.70032	+	11.5604i	−0.822771	+	0.980540i	0.177223	+	0.984171i	$0.443289\pi$
$140$	−0.0596315	+	0.819412i	−0.00503978	+	0.0692529i
$141$		0			0
$142$	−15.4177	−	1.34888i	−1.29383	−	0.113195i
$143$	−1.18349	+	4.41686i	−0.0989686	+	0.369356i
$144$		0			0
$145$	−0.627404	+	0.238801i	−0.0521031	+	0.0198314i
$146$	24.2744	−	4.28023i	2.00896	−	0.354234i
$147$		0			0
$148$	21.9171	−	47.0013i	1.80157	−	3.86349i
$149$	−13.5292	+	4.92423i	−1.10836	+	0.403409i	−0.830390	−	0.557182i	$-0.811882\pi$
$149$	−13.5292	+	4.92423i	−1.10836	+	0.403409i	−0.277966	+	0.960591i	$0.589660\pi$
$150$		0			0
$151$	−0.377952	−	2.14347i	−0.0307573	−	0.174433i	0.965559	−	0.260182i	$-0.0837827\pi$
$151$	−0.377952	−	2.14347i	−0.0307573	−	0.174433i	−0.996317	+	0.0857493i	$0.972672\pi$
$152$	4.01062	+	14.9678i	0.325304	+	1.21405i
$153$		0			0
$154$	0.460539	−	0.265892i	0.0371113	−	0.0214262i
$155$	−0.411385	+	0.00601529i	−0.0330433	+	0.000483160i
$156$		0			0
$157$	−4.98020	+	3.48717i	−0.397463	+	0.278307i	−0.755172	−	0.655526i	$-0.772447\pi$
$157$	−4.98020	+	3.48717i	−0.397463	+	0.278307i	0.357709	+	0.933833i	$0.383558\pi$
$158$	1.79370	+	20.5020i	0.142699	+	1.63105i
$159$		0			0
$160$	46.8362	+	11.8186i	3.70273	+	0.934340i
$161$			0.491745i			0.0387549i
$162$		0			0
$163$	−8.83178	+	8.83178i	−0.691758	+	0.691758i	−0.962619	−	0.270860i	$-0.912692\pi$
$163$	−8.83178	+	8.83178i	−0.691758	+	0.691758i	0.270860	+	0.962619i	$0.412692\pi$
$164$	26.2018	+	9.53668i	2.04602	+	0.744689i
$165$		0			0
$166$	25.7449	+	21.6025i	1.99819	+	1.67668i
$167$	−12.7854	−	18.2595i	−0.989367	−	1.41296i	−0.909285	−	0.416174i	$-0.863371\pi$
$167$	−12.7854	−	18.2595i	−0.989367	−	1.41296i	−0.0800820	−	0.996788i	$-0.525518\pi$
$168$		0			0
$169$	6.74758	+	8.04146i	0.519045	+	0.618573i
$170$	−1.65344	−	0.266682i	−0.126813	−	0.0204536i
$171$		0			0
$172$	28.5683	−	7.65485i	2.17831	−	0.583677i
$173$	−7.10715	+	10.1501i	−0.540347	+	0.771695i	−0.992760	−	0.120113i	$-0.961674\pi$
$173$	−7.10715	+	10.1501i	−0.540347	+	0.771695i	0.452413	+	0.891808i	$0.350563\pi$
$174$		0			0
$175$	−0.0776636	+	0.327912i	−0.00587082	+	0.0247878i
$176$	−14.6480	−	40.2451i	−1.10414	−	3.03359i
$177$		0			0
$178$	−28.3233	−	19.8322i	−2.12292	−	1.48648i
$179$	−7.35758	+	12.7437i	−0.549932	+	0.952510i	0.448347	+	0.893860i	$0.352013\pi$
$179$	−7.35758	+	12.7437i	−0.549932	+	0.952510i	−0.998279	+	0.0586499i	$0.981320\pi$
$180$		0			0
$181$	1.50284	+	2.60299i	0.111705	+	0.193479i	0.916458	−	0.400131i	$-0.131035\pi$
$181$	1.50284	+	2.60299i	0.111705	+	0.193479i	−0.804753	+	0.593610i	$0.797702\pi$
$182$	−0.0253664	+	0.289939i	−0.00188028	+	0.0214917i
$183$		0			0
$184$	67.7017	+	11.9376i	4.99104	+	0.880054i
$185$	11.9447	−	17.6010i	0.878190	−	1.29405i
$186$		0			0
$187$	0.335178	+	0.718791i	0.0245106	+	0.0525632i
$188$	7.27475	+	7.27475i	0.530566	+	0.530566i
$189$		0			0
$190$	1.02105	+	9.98666i	0.0740748	+	0.724508i
$191$	−7.98174	+	21.9296i	−0.577538	+	1.58677i	0.214778	+	0.976663i	$0.431097\pi$
$191$	−7.98174	+	21.9296i	−0.577538	+	1.58677i	−0.792316	+	0.610110i	$0.791125\pi$
$192$		0			0
$193$	−19.3299	+	1.69115i	−1.39140	+	0.121731i	−0.758079	−	0.652162i	$-0.773862\pi$
$193$	−19.3299	+	1.69115i	−1.39140	+	0.121731i	−0.633316	+	0.773893i	$0.718307\pi$
$194$	−0.924736	+	5.24444i	−0.0663922	+	0.376529i
$195$		0			0
$196$	−29.2143	+	24.5137i	−2.08673	+	1.75098i
$197$	15.5702	+	4.17203i	1.10933	+	0.297245i	0.766560	−	0.642173i	$-0.221967\pi$
$197$	15.5702	+	4.17203i	1.10933	+	0.297245i	0.342774	+	0.939418i	$0.388634\pi$
$198$		0			0
$199$	−10.7021	−	6.17889i	−0.758655	−	0.438010i	0.0701576	−	0.997536i	$-0.477650\pi$
$199$	−10.7021	−	6.17889i	−0.758655	−	0.438010i	−0.828813	+	0.559526i	$0.810983\pi$
$200$	43.2604	+	18.6529i	3.05897	+	1.31896i
$201$		0			0
$202$	−30.6140	−	14.2755i	−2.15399	−	1.00442i
$203$	0.0183381	+	0.00855122i	0.00128709	+	0.000600178i
$204$		0			0
$205$	9.98713	+	5.57299i	0.697531	+	0.389235i
$206$	−7.84721	−	4.53059i	−0.546741	−	0.315661i
$207$		0			0
$208$	22.6411	+	6.06667i	1.56988	+	0.420648i
$209$	3.64161	−	3.05567i	0.251895	−	0.211365i
$210$		0			0
$211$	2.28006	−	12.9309i	0.156966	−	0.890199i	−0.800000	−	0.600000i	$-0.795167\pi$
$211$	2.28006	−	12.9309i	0.156966	−	0.890199i	0.956966	−	0.290199i	$-0.0937216\pi$
$212$	12.1856	−	1.06610i	0.836908	−	0.0732199i
$213$		0			0
$214$	−8.09942	+	22.2530i	−0.553665	+	1.52118i
$215$	12.0682	−	1.23387i	0.823044	−	0.0841493i
$216$		0			0
$217$	0.00876868	+	0.00876868i	0.000595257	+	0.000595257i
$218$	−16.8769	−	36.1925i	−1.14304	−	2.45127i
$219$		0			0
$220$	−6.62528	−	34.6071i	−0.446676	−	2.33321i
$221$	−0.427470	−	0.0753744i	−0.0287547	−	0.00507023i
$222$		0			0
$223$	1.06292	−	12.1492i	0.0711782	−	0.813571i	−0.873768	−	0.486344i	$-0.838330\pi$
$223$	1.06292	−	12.1492i	0.0711782	−	0.813571i	0.944946	−	0.327227i	$-0.106114\pi$
$224$	−0.727964	−	1.26087i	−0.0486392	−	0.0842455i
$225$		0			0
$226$	10.1742	−	17.6222i	0.676775	−	1.17221i
$227$	4.46369	+	3.12551i	0.296265	+	0.207447i	0.712253	−	0.701923i	$-0.247675\pi$
$227$	4.46369	+	3.12551i	0.296265	+	0.207447i	−0.415987	+	0.909370i	$0.636564\pi$
$228$		0			0
$229$	0.0613439	+	0.168541i	0.00405372	+	0.0111375i	0.941703	−	0.336445i	$-0.109225\pi$
$229$	0.0613439	+	0.168541i	0.00405372	+	0.0111375i	−0.937649	+	0.347583i	$0.887003\pi$
$230$	42.0684	+	14.6187i	2.77391	+	0.963929i
$231$		0			0
$232$	1.62248	−	2.31714i	0.106521	−	0.152128i
$233$	−7.78593	+	2.08623i	−0.510073	+	0.136674i	−0.504671	−	0.863312i	$-0.668386\pi$
$233$	−7.78593	+	2.08623i	−0.510073	+	0.136674i	−0.00540204	+	0.999985i	$0.501720\pi$
$234$		0			0
$235$	2.47066	+	3.42091i	0.161168	+	0.223156i
$236$	−42.4696	−	50.6133i	−2.76454	−	3.29464i
$237$		0			0
$238$	0.0289542	+	0.0413509i	0.00187682	+	0.00268038i
$239$	−2.31718	−	1.94434i	−0.149886	−	0.125769i	0.564761	−	0.825254i	$-0.308968\pi$
$239$	−2.31718	−	1.94434i	−0.149886	−	0.125769i	−0.714647	+	0.699485i	$0.753413\pi$
$240$		0			0
$241$	10.3835	+	3.77929i	0.668861	+	0.243446i	0.654057	−	0.756445i	$-0.273065\pi$
$241$	10.3835	+	3.77929i	0.668861	+	0.243446i	0.0148037	+	0.999890i	$0.495288\pi$
$242$	5.10560	−	5.10560i	0.328200	−	0.328200i
$243$		0			0
$244$		−	24.3631i		−	1.55969i
$245$	−13.4308	+	8.01838i	−0.858065	+	0.512276i
$246$		0			0
$247$	0.226758	+	2.59185i	0.0144282	+	0.164916i
$248$	1.42011	−	0.994372i	0.0901771	−	0.0631427i
$249$		0			0
$250$	25.7438	+	16.3923i	1.62818	+	1.03674i
$251$	−21.4342	+	12.3751i	−1.35292	+	0.781107i	−0.988657	−	0.150191i	$-0.952011\pi$
$251$	−21.4342	+	12.3751i	−1.35292	+	0.781107i	−0.364259	+	0.931298i	$0.618678\pi$
$252$		0			0
$253$	−5.45844	−	20.3712i	−0.343169	−	1.28073i
$254$	2.82048	+	15.9957i	0.176973	+	1.00366i
$255$		0			0
$256$	−39.4556	+	14.3607i	−2.46597	+	0.897541i
$257$	−10.1456	+	21.7573i	−0.632865	+	1.35718i	0.284324	+	0.958728i	$0.408231\pi$
$257$	−10.1456	+	21.7573i	−0.632865	+	1.35718i	−0.917188	+	0.398454i	$0.869547\pi$
$258$		0			0
$259$	−0.631394	+	0.111332i	−0.0392329	+	0.00691782i
$260$	17.5950	+	7.89357i	1.09119	+	0.489538i
$261$		0			0
$262$	−3.24099	+	12.0955i	−0.200229	+	0.747264i
$263$	4.03359	+	0.352894i	0.248722	+	0.0217604i	0.210835	−	0.977522i	$-0.432382\pi$
$263$	4.03359	+	0.352894i	0.248722	+	0.0217604i	0.0378870	+	0.999282i	$0.487937\pi$
$264$		0			0
$265$	5.00397	+	0.364156i	0.307391	+	0.0223699i
$266$	0.194491	−	0.231786i	0.0119250	−	0.0142117i
$267$		0			0
$268$	12.2614	−	5.71757i	0.748983	−	0.349256i
$269$	−17.0798			−1.04137			−0.520686	−	0.853748i	$-0.674324\pi$
$269$	−17.0798			−1.04137			−0.520686	+	0.853748i	$0.674324\pi$
$270$		0			0
$271$	8.56847			0.520497			0.260249	−	0.965542i	$-0.416195\pi$
$271$	8.56847			0.520497			0.260249	+	0.965542i	$0.416195\pi$
$272$	3.68458	−	1.71815i	0.223410	−	0.104178i
$273$		0			0
$274$	−15.6510	+	18.6522i	−0.945513	+	1.12682i
$275$	−0.422558	−	14.4463i	−0.0254812	−	0.871143i
$276$		0			0
$277$	10.8871	+	0.952498i	0.654142	+	0.0572300i	0.409396	−	0.912357i	$-0.365740\pi$
$277$	10.8871	+	0.952498i	0.654142	+	0.0572300i	0.244747	+	0.969587i	$0.421295\pi$
$278$	10.6620	−	39.7913i	0.639466	−	2.38652i
$279$		0			0
$280$	−0.505106	−	1.32707i	−0.0301859	−	0.0793075i
$281$	−13.8445	+	2.44116i	−0.825893	+	0.145627i	−0.570591	−	0.821234i	$-0.693286\pi$
$281$	−13.8445	+	2.44116i	−0.825893	+	0.145627i	−0.255302	+	0.966861i	$0.582175\pi$
$282$		0			0
$283$	−10.6416	+	22.8211i	−0.632580	+	1.35657i	0.284810	+	0.958584i	$0.408070\pi$
$283$	−10.6416	+	22.8211i	−0.632580	+	1.35657i	−0.917390	+	0.397989i	$0.869708\pi$
$284$	29.0443	−	10.5713i	1.72346	−	0.627290i
$285$		0			0
$286$	−2.16753	−	12.2927i	−0.128169	−	0.726880i
$287$	−0.0892187	−	0.332969i	−0.00526641	−	0.0196545i
$288$		0			0
$289$	14.6572	−	8.46236i	0.862190	−	0.497786i
$290$	1.27671	−	1.31460i	0.0749710	−	0.0771959i
$291$		0			0
$292$	−40.3238	+	28.2350i	−2.35977	+	1.65233i
$293$	1.94195	+	22.1966i	0.113450	+	1.29674i	0.813046	+	0.582199i	$0.197807\pi$
$293$	1.94195	+	22.1966i	0.113450	+	1.29674i	−0.699597	+	0.714538i	$0.746637\pi$
$294$		0			0
$295$	−13.8917	−	23.2687i	−0.808808	−	1.35476i
$296$			89.6307i			5.20968i
$297$		0			0
$298$	27.7905	−	27.7905i	1.60986	−	1.60986i
$299$	10.8464	+	3.94776i	0.627262	+	0.228305i
$300$		0			0
$301$	−0.280097	−	0.235029i	−0.0161445	−	0.0135469i
$302$	3.40786	+	4.86693i	0.196101	+	0.280061i
$303$		0			0
$304$	−15.6636	−	18.6672i	−0.898369	−	1.07063i
$305$	1.59119	−	9.86542i	0.0911110	−	0.564892i
$306$		0			0
$307$	−25.7655	+	6.90384i	−1.47051	+	0.394023i	−0.903108	−	0.429414i	$-0.858720\pi$
$307$	−25.7655	+	6.90384i	−1.47051	+	0.394023i	−0.567407	+	0.823437i	$0.692053\pi$
$308$	−0.609154	+	0.869962i	−0.0347098	+	0.0495707i
$309$		0			0
$310$	1.01083	−	0.489476i	0.0574113	−	0.0278004i
$311$	3.92967	+	10.7967i	0.222831	+	0.612223i	0.999851	−	0.0172526i	$-0.00549193\pi$
$311$	3.92967	+	10.7967i	0.222831	+	0.612223i	−0.777020	+	0.629476i	$0.783270\pi$
$312$		0			0
$313$	16.6608	+	11.6660i	0.941726	+	0.659404i	0.940210	−	0.340595i	$-0.110628\pi$
$313$	16.6608	+	11.6660i	0.941726	+	0.659404i	0.00151626	+	0.999999i	$0.499517\pi$
$314$	8.29807	−	14.3727i	0.468287	−	0.811097i
$315$		0			0
$316$	−20.5505	−	35.5945i	−1.15606	−	2.00235i
$317$	0.601241	−	6.87221i	0.0337690	−	0.385982i	−0.960438	−	0.278496i	$-0.910164\pi$
$317$	0.601241	−	6.87221i	0.0337690	−	0.385982i	0.994207	−	0.107486i	$-0.0342802\pi$
$318$		0			0
$319$	−0.854601	−	0.150689i	−0.0478485	−	0.00843698i
$320$	−64.4264	+	12.3340i	−3.60155	+	0.689489i
$321$		0			0
$322$	−0.567301	−	1.21658i	−0.0316144	−	0.0677974i
$323$	0.319087	+	0.319087i	0.0177545	+	0.0177545i
$324$		0			0
$325$	6.60924	+	4.34552i	0.366615	+	0.241046i
$326$	11.6611	−	32.0386i	0.645849	−	1.77446i
$327$		0			0
$328$	−48.0078	+	4.20014i	−2.65079	+	0.231914i
$329$	0.0220860	−	0.125256i	0.00121764	−	0.00690559i
$330$		0			0
$331$	−8.89164	+	7.46097i	−0.488729	+	0.410092i	−0.853570	−	0.520977i	$-0.825568\pi$
$331$	−8.89164	+	7.46097i	−0.488729	+	0.410092i	0.364842	+	0.931070i	$0.381123\pi$
$332$	−64.8306	−	17.3713i	−3.55804	−	0.953375i
$333$		0			0
$334$	52.6963	+	30.4242i	2.88341	+	1.66474i
$335$	5.33846	−	1.51443i	0.291671	−	0.0827421i
$336$		0			0
$337$	−8.79051	−	4.09908i	−0.478849	−	0.223291i	0.168180	−	0.985756i	$-0.446211\pi$
$337$	−8.79051	−	4.09908i	−0.478849	−	0.223291i	−0.647029	+	0.762465i	$0.723989\pi$
$338$	−25.9706	−	12.1103i	−1.41261	−	0.658712i
$339$		0			0
$340$	3.21779	−	0.912832i	0.174509	−	0.0495053i
$341$	−0.460588	−	0.265920i	−0.0249422	−	0.0144004i
$342$		0			0
$343$	0.911108	+	0.244131i	0.0491952	+	0.0131818i
$344$	−39.1577	+	32.8572i	−2.11124	+	1.77154i
$345$		0			0
$346$	5.87354	−	33.3105i	0.315763	−	1.79078i
$347$	23.5905	−	2.06390i	1.26640	−	0.110796i	0.565918	−	0.824462i	$-0.308522\pi$
$347$	23.5905	−	2.06390i	1.26640	−	0.110796i	0.700487	+	0.713666i	$0.252966\pi$
$348$		0			0
$349$	−0.840919	+	2.31040i	−0.0450133	+	0.123673i	−0.960163	−	0.279442i	$-0.909850\pi$
$349$	−0.840919	+	2.31040i	−0.0450133	+	0.123673i	0.915149	+	0.403115i	$0.132073\pi$
$350$	−0.186155	−	0.900854i	−0.00995042	−	0.0481527i
$351$		0			0
$352$	44.1527	+	44.1527i	2.35335	+	2.35335i
$353$	0.186556	+	0.400070i	0.00992935	+	0.0212936i	0.911210	−	0.411942i	$-0.135149\pi$
$353$	0.186556	+	0.400070i	0.00992935	+	0.0212936i	−0.901281	+	0.433236i	$0.857372\pi$
$354$		0			0
$355$	12.4514	−	2.38374i	0.660854	−	0.126516i
$356$	68.0033	+	11.9908i	3.60417	+	0.635512i
$357$		0			0
$358$	3.50095	−	40.0161i	0.185031	−	2.11492i
$359$	−10.2203	−	17.7022i	−0.539409	−	0.934284i	−0.998936	−	0.0461203i	$-0.985314\pi$
$359$	−10.2203	−	17.7022i	−0.539409	−	0.934284i	0.459527	−	0.888164i	$-0.348019\pi$
$360$		0			0
$361$	−8.14760	+	14.1121i	−0.428821	+	0.742740i
$362$	−6.72096	−	4.70607i	−0.353246	−	0.247346i
$363$		0			0
$364$	−0.198799	−	0.546195i	−0.0104199	−	0.0286284i
$365$	−18.1725	+	8.79970i	−0.951192	+	0.460597i
$366$		0			0
$367$	−6.42120	+	9.17042i	−0.335184	+	0.478692i	−0.950997	−	0.309200i	$-0.899939\pi$
$367$	−6.42120	+	9.17042i	−0.335184	+	0.478692i	0.615813	+	0.787892i	$0.288828\pi$
$368$	−104.424	+	27.9804i	−5.44348	+	1.45858i
$369$		0			0
$370$	−9.24587	+	57.3249i	−0.480670	+	2.98018i
$371$	−0.0972037	−	0.115843i	−0.00504657	−	0.00601426i
$372$		0			0
$373$	21.8665	+	31.2287i	1.13221	+	1.61696i	0.697903	+	0.716192i	$0.254116\pi$
$373$	21.8665	+	31.2287i	1.13221	+	1.61696i	0.434303	+	0.900767i	$0.356995\pi$
$374$	−1.65847	−	1.39162i	−0.0857572	−	0.0719588i
$375$		0			0
$376$	−16.7086	−	6.08145i	−0.861683	−	0.313627i
$377$	0.335833	−	0.335833i	0.0172963	−	0.0172963i
$378$		0			0
$379$		−	4.11755i		−	0.211504i	−0.994393	−	0.105752i	$-0.966275\pi$
$379$		−	4.11755i		−	0.211504i	0.994393	−	0.105752i	$-0.0337250\pi$
$380$	−10.2769	−	17.2139i	−0.527196	−	0.883057i
$381$		0			0
$382$	−5.55222	−	63.4622i	−0.284076	−	3.24701i
$383$	−6.96702	+	4.87836i	−0.355998	+	0.249273i	−0.737870	−	0.674943i	$-0.764168\pi$
$383$	−6.96702	+	4.87836i	−0.355998	+	0.249273i	0.381872	+	0.924215i	$0.375279\pi$
$384$		0			0
$385$	−0.303485	+	0.312492i	−0.0154670	+	0.0159261i
$386$	45.8713	−	26.4838i	2.33479	−	1.34799i
$387$		0			0
$388$	−2.75260	−	10.2729i	−0.139742	−	0.521525i
$389$	−5.58151	−	31.6543i	−0.282994	−	1.60494i	−0.712365	−	0.701809i	$-0.752376\pi$
$389$	−5.58151	−	31.6543i	−0.282994	−	1.60494i	0.429371	−	0.903128i	$-0.358735\pi$
$390$		0			0
$391$	1.88123	−	0.684713i	0.0951380	−	0.0346274i
$392$	27.8555	−	59.7364i	1.40692	−	3.01714i
$393$		0			0
$394$	−43.3339	+	7.64094i	−2.18313	+	0.384945i
$395$	−5.99686	−	15.7556i	−0.301735	−	0.792750i
$396$		0			0
$397$	7.17628	−	26.7823i	0.360167	−	1.34416i	−0.513688	−	0.857977i	$-0.671721\pi$
$397$	7.17628	−	26.7823i	0.360167	−	1.34416i	0.873855	−	0.486186i	$-0.161612\pi$
$398$	33.6054	+	2.94010i	1.68449	+	0.147374i
$399$		0			0
$400$	−74.0526	+	2.16606i	−3.70263	+	0.108303i
$401$	21.1044	−	25.1513i	1.05390	−	1.25599i	0.0882682	−	0.996097i	$-0.471867\pi$
$401$	21.1044	−	25.1513i	1.05390	−	1.25599i	0.965636	−	0.259898i	$-0.0836888\pi$
$402$		0			0
$403$	0.263806	−	0.123015i	0.0131411	−	0.00612779i
$404$	67.4596			3.35624
$405$		0			0
$406$	−0.0552338			−0.00274121
$407$	24.9205	−	11.6206i	1.23526	−	0.576013i
$408$		0			0
$409$	17.7773	−	21.1861i	0.879029	−	1.04759i	−0.119472	−	0.992838i	$-0.538120\pi$
$409$	17.7773	−	21.1861i	0.879029	−	1.04759i	0.998500	−	0.0547479i	$-0.0174355\pi$
$410$	−31.1375	−	2.26599i	−1.53777	−	0.111909i
$411$		0			0
$412$	18.0272	+	1.57718i	0.888137	+	0.0777019i
$413$	−0.211408	+	0.788985i	−0.0104027	+	0.0388234i
$414$		0			0
$415$	−25.1175	−	11.2684i	−1.23297	−	0.553144i
$416$	−33.6551	+	5.93430i	−1.65008	+	0.290953i
$417$		0			0
$418$	−5.48420	+	11.7609i	−0.268241	+	0.575244i
$419$	−6.15194	+	2.23912i	−0.300542	+	0.109388i	−0.487890	−	0.872905i	$-0.662233\pi$
$419$	−6.15194	+	2.23912i	−0.300542	+	0.109388i	0.187348	+	0.982294i	$0.440011\pi$
$420$		0			0
$421$	0.0842371	+	0.477733i	0.00410547	+	0.0232833i	0.986792	−	0.161994i	$-0.0517927\pi$
$421$	0.0842371	+	0.477733i	0.00410547	+	0.0232833i	−0.982686	+	0.185278i	$0.940682\pi$
$422$	9.27680	+	34.6215i	0.451588	+	1.68535i
$423$		0			0
$424$	−18.3086	+	10.5705i	−0.889142	+	0.513346i
$425$	1.36261	−	0.159478i	0.0660963	−	0.00773581i
$426$		0			0
$427$	−0.246724	+	0.172758i	−0.0119398	+	0.00836034i
$428$	−4.12191	−	47.1136i	−0.199240	−	2.27732i
$429$		0			0
$430$	−28.4333	+	16.9751i	−1.37118	+	0.818610i
$431$			16.2782i			0.784091i	0.919946	+	0.392046i	$0.128232\pi$
$431$			16.2782i			0.784091i	−0.919946	+	0.392046i	$0.871768\pi$
$432$		0			0
$433$	−18.2154	+	18.2154i	−0.875374	+	0.875374i	−0.993052	−	0.117677i	$-0.962455\pi$
$433$	−18.2154	+	18.2154i	−0.875374	+	0.875374i	0.117677	+	0.993052i	$0.462455\pi$
$434$	−0.0318098	−	0.0115778i	−0.00152692	−	0.000555752i
$435$		0			0
$436$	61.0938	+	51.2638i	2.92586	+	2.45509i
$437$	−6.88272	−	9.82955i	−0.329245	−	0.470211i
$438$		0			0
$439$	17.5389	+	20.9020i	0.837085	+	0.997599i	0.999940	+	0.0109489i	$0.00348521\pi$
$439$	17.5389	+	20.9020i	0.837085	+	0.997599i	−0.162855	+	0.986650i	$0.552070\pi$
$440$	35.6553	+	49.3688i	1.69980	+	2.35356i
$441$		0			0
$442$	1.14452	−	0.306673i	0.0544392	−	0.0145869i
$443$	14.3930	−	20.5553i	0.683832	−	0.976613i	−0.315782	−	0.948832i	$-0.602267\pi$
$443$	14.3930	−	20.5553i	0.683832	−	0.976613i	0.999614	−	0.0277815i	$-0.00884425\pi$
$444$		0			0
$445$	26.7537	+	9.29686i	1.26824	+	0.440714i
$446$	11.3862	+	31.2834i	0.539154	+	1.48131i
$447$		0			0
$448$	1.61957	+	1.13403i	0.0765173	+	0.0535780i
$449$	−13.1545	+	22.7842i	−0.620798	+	1.07525i	0.368540	+	0.929612i	$0.379858\pi$
$449$	−13.1545	+	22.7842i	−0.620798	+	1.07525i	−0.989338	+	0.145641i	$0.953476\pi$
$450$		0			0
$451$	7.39200	+	12.8033i	0.348076	+	0.602885i
$452$	−3.54180	+	40.4830i	−0.166592	+	1.90416i
$453$		0			0
$454$	−14.6489	−	2.58300i	−0.687508	−	0.121226i
$455$	−0.0448275	−	0.234156i	−0.00210155	−	0.0109774i
$456$		0			0
$457$	16.4957	+	35.3751i	0.771635	+	1.65478i	0.755713	+	0.654903i	$0.227290\pi$
$457$	16.4957	+	35.3751i	0.771635	+	1.65478i	0.0159216	+	0.999873i	$0.494932\pi$
$458$	−0.346202	−	0.346202i	−0.0161770	−	0.0161770i
$459$		0			0
$460$	−88.4816	+	9.04649i	−4.12547	+	0.421795i
$461$	1.05017	−	2.88532i	0.0489113	−	0.134383i	−0.912832	−	0.408336i	$-0.866109\pi$
$461$	1.05017	−	2.88532i	0.0489113	−	0.134383i	0.961743	+	0.273953i	$0.0883314\pi$
$462$		0			0
$463$	40.3952	−	3.53412i	1.87732	−	0.164244i	0.909471	−	0.415767i	$-0.136487\pi$
$463$	40.3952	−	3.53412i	1.87732	−	0.164244i	0.967851	+	0.251523i	$0.0809313\pi$
$464$	−0.772444	+	4.38075i	−0.0358598	+	0.203371i
$465$		0			0
$466$	16.8557	−	14.1436i	0.780823	−	0.655188i
$467$	4.40748	+	1.18098i	0.203954	+	0.0546493i	0.359350	−	0.933203i	$-0.382999\pi$
$467$	4.40748	+	1.18098i	0.203954	+	0.0546493i	−0.155396	+	0.987852i	$0.549665\pi$
$468$		0			0
$469$	−0.144847	−	0.0836272i	−0.00668839	−	0.00386155i
$470$	−10.0590	−	5.61308i	−0.463986	−	0.258912i
$471$		0			0
$472$	103.492	+	48.2593i	4.76362	+	2.22131i
$473$	14.2122	+	6.62728i	0.653480	+	0.304723i
$474$		0			0
$475$	−3.03721	−	7.64170i	−0.139357	−	0.350625i
$476$	−0.0873073	−	0.0504069i	−0.00400172	−	0.00231040i
$477$		0			0
$478$	7.97581	+	2.13711i	0.364805	+	0.0977492i
$479$	19.9896	−	16.7733i	0.913349	−	0.766391i	−0.0594042	−	0.998234i	$-0.518920\pi$
$479$	19.9896	−	16.7733i	0.913349	−	0.766391i	0.972753	+	0.231843i	$0.0744756\pi$
$480$		0			0
$481$	−2.61323	+	14.8204i	−0.119153	+	0.675750i
$482$	−30.0489	+	2.62893i	−1.36869	+	0.119745i
$483$		0			0
$484$	−4.93189	+	13.5503i	−0.224177	+	0.615921i
$485$	−0.443687	−	4.33959i	−0.0201468	−	0.197051i
$486$		0			0
$487$	10.3340	+	10.3340i	0.468280	+	0.468280i	0.901357	−	0.433077i	$-0.142572\pi$
$487$	10.3340	+	10.3340i	0.468280	+	0.468280i	−0.433077	+	0.901357i	$0.642572\pi$
$488$	17.7952	+	38.1619i	0.805551	+	1.72751i
$489$		0			0
$490$	23.9776	−	35.3320i	1.08320	−	1.59614i
$491$	−21.2487	−	3.74671i	−0.958939	−	0.169087i	−0.327792	−	0.944750i	$-0.606304\pi$
$491$	−21.2487	−	3.74671i	−0.958939	−	0.169087i	−0.631147	+	0.775663i	$0.717416\pi$
$492$		0			0
$493$	0.00717947	−	0.0820617i	0.000323347	−	0.00369587i
$494$	−3.55109	−	6.15066i	−0.159771	−	0.276731i
$495$		0			0
$496$	−1.36313	+	2.36101i	−0.0612062	+	0.106012i
$497$	−0.313007	−	0.219170i	−0.0140403	−	0.00983112i
$498$		0			0
$499$	−8.93292	−	24.5430i	−0.399892	−	1.09870i	−0.962337	−	0.271860i	$-0.912361\pi$
$499$	−8.93292	−	24.5430i	−0.399892	−	1.09870i	0.562444	−	0.826835i	$-0.309861\pi$
$500$	−60.4313	−	7.94180i	−2.70257	−	0.355168i
$501$		0			0
$502$	38.7520	−	55.3435i	1.72958	−	2.47010i
$503$	25.8163	−	6.91747i	1.15109	−	0.308435i	0.367690	−	0.929948i	$-0.380149\pi$
$503$	25.8163	−	6.91747i	1.15109	−	0.308435i	0.783403	+	0.621514i	$0.213482\pi$
$504$		0			0
$505$	27.3166	+	4.40587i	1.21557	+	0.196059i
$506$	37.0054	+	44.1013i	1.64509	+	1.96054i
$507$		0			0
$508$	−18.6056	−	26.5715i	−0.825490	−	1.17892i
$509$	12.1514	+	10.1962i	0.538601	+	0.451940i	0.871059	−	0.491178i	$-0.163434\pi$
$509$	12.1514	+	10.1962i	0.538601	+	0.451940i	−0.332458	+	0.943118i	$0.607878\pi$
$510$		0			0
$511$	0.571869	+	0.208143i	0.0252980	+	0.00920772i
$512$	28.8976	−	28.8976i	1.27711	−	1.27711i
$513$		0			0
$514$		−	65.5321i		−	2.89050i
$515$	7.19681	+	1.81603i	0.317129	+	0.0800239i
$516$		0			0
$517$	0.475418	+	5.43405i	0.0209089	+	0.238989i
$518$	1.43363	−	1.00384i	0.0629903	−	0.0441063i
$519$		0			0
$520$	−33.3260	+	0.487295i	−1.46144	+	0.0213693i
$521$	4.16523	−	2.40480i	0.182482	−	0.105356i	−0.405976	−	0.913884i	$-0.633068\pi$
$521$	4.16523	−	2.40480i	0.182482	−	0.105356i	0.588458	+	0.808528i	$0.299735\pi$
$522$		0			0
$523$	−7.09977	−	26.4967i	−0.310451	−	1.15862i	−0.928150	−	0.372206i	$-0.878602\pi$
$523$	−7.09977	−	26.4967i	−0.310451	−	1.15862i	0.617699	−	0.786415i	$-0.288065\pi$
$524$	−4.34261	−	24.6282i	−0.189708	−	1.07589i
$525$		0			0
$526$	−10.3862	+	3.78029i	−0.452862	+	0.164828i
$527$	0.0213361	−	0.0457553i	0.000929413	−	0.00199313i
$528$		0			0
$529$	−29.7762	+	5.25035i	−1.29462	+	0.228276i
$530$	−12.8000	+	4.87189i	−0.555994	+	0.211621i
$531$		0			0
$532$	−0.156397	+	0.583682i	−0.00678067	+	0.0253058i
$533$	−8.06051	−	0.705203i	−0.349140	−	0.0305457i
$534$		0			0
$535$	1.40795	−	19.3471i	0.0608712	−	0.836447i
$536$	−15.0298	+	17.9118i	−0.649188	+	0.773673i
$537$		0			0
$538$	42.2555	−	19.7041i	1.82176	−	0.849502i
$539$	−20.2203			−0.870950
$540$		0			0
$541$	6.59325			0.283466			0.141733	−	0.989905i	$-0.454733\pi$
$541$	6.59325			0.283466			0.141733	+	0.989905i	$0.454733\pi$
$542$	−21.1984	+	9.88500i	−0.910551	+	0.424597i
$543$		0			0
$544$	−3.80999	+	4.54057i	−0.163352	+	0.194675i
$545$	21.3908	+	24.7485i	0.916281	+	1.06011i
$546$		0			0
$547$	−21.6365	−	1.89295i	−0.925110	−	0.0809366i	−0.385364	−	0.922765i	$-0.625924\pi$
$547$	−21.6365	−	1.89295i	−0.925110	−	0.0809366i	−0.539746	+	0.841828i	$0.681480\pi$
$548$	12.5855	−	46.9698i	0.537627	−	2.00645i
$549$		0			0
$550$	17.7113	+	35.2527i	0.755214	+	1.50318i
$551$	−0.486250	+	0.0857391i	−0.0207150	+	0.00365261i
$552$		0			0
$553$	−0.214741	+	0.460514i	−0.00913172	+	0.0195830i
$554$	−28.0336	+	10.2034i	−1.19103	+	0.433501i
$555$		0			0
$556$	14.2861	+	81.0205i	0.605866	+	3.43604i
$557$	−4.22003	−	15.7494i	−0.178809	−	0.667323i	−0.995871	−	0.0907742i	$-0.971066\pi$
$557$	−4.22003	−	15.7494i	−0.178809	−	0.667323i	0.817063	−	0.576549i	$-0.195601\pi$
$558$		0			0
$559$	−7.43266	+	4.29125i	−0.314368	+	0.181500i
$560$	1.60185	+	1.55569i	0.0676907	+	0.0657397i
$561$		0			0
$562$	31.4351	−	22.0111i	1.32601	−	0.928483i
$563$	1.71719	+	19.6276i	0.0723710	+	0.827204i	0.942462	+	0.334313i	$0.108504\pi$
$563$	1.71719	+	19.6276i	0.0723710	+	0.827204i	−0.870091	+	0.492891i	$0.835940\pi$
$564$		0			0
$565$	−4.07819	+	16.1616i	−0.171571	+	0.679923i
$566$		−	68.7362i		−	2.88920i
$567$		0			0
$568$	−37.7731	+	37.7731i	−1.58493	+	1.58493i
$569$	4.06034	+	1.47784i	0.170218	+	0.0619544i	0.425724	−	0.904853i	$-0.360020\pi$
$569$	4.06034	+	1.47784i	0.170218	+	0.0619544i	−0.255505	+	0.966808i	$0.582242\pi$
$570$		0			0
$571$	−17.9249	−	15.0408i	−0.750135	−	0.629438i	0.185404	−	0.982662i	$-0.440641\pi$
$571$	−17.9249	−	15.0408i	−0.750135	−	0.629438i	−0.935539	+	0.353224i	$0.885085\pi$
$572$	14.2983	+	20.4202i	0.597844	+	0.853809i
$573$		0			0
$574$	0.604856	+	0.720840i	0.0252462	+	0.0300873i
$575$	−36.4200	−	2.11562i	−1.51882	−	0.0882276i
$576$		0			0
$577$	10.2491	−	2.74624i	0.426677	−	0.114328i	−0.0390891	−	0.999236i	$-0.512446\pi$
$577$	10.2491	−	2.74624i	0.426677	−	0.114328i	0.465766	+	0.884908i	$0.345779\pi$
$578$	−26.4995	+	37.8452i	−1.10223	+	1.57415i
$579$		0			0
$580$	−1.20129	+	3.45697i	−0.0498809	+	0.143543i
$581$	0.283793	+	0.779716i	0.0117737	+	0.0323481i
$582$		0			0
$583$	5.31266	+	3.71997i	0.220028	+	0.154065i
$584$	42.5392	−	73.6800i	1.76028	−	3.04890i
$585$		0			0
$586$	−30.4114	−	52.6741i	−1.25628	−	2.17595i
$587$	1.68557	−	19.2661i	0.0695708	−	0.795197i	−0.878625	−	0.477512i	$-0.841539\pi$
$587$	1.68557	−	19.2661i	0.0695708	−	0.795197i	0.948196	−	0.317686i	$-0.102906\pi$
$588$		0			0
$589$	−0.298009	−	0.0525471i	−0.0122793	−	0.00216516i
$590$	61.2122	+	41.5409i	2.52006	+	1.71021i
$591$		0			0
$592$	−59.5681	−	127.744i	−2.44823	−	5.25026i
$593$	−0.516721	−	0.516721i	−0.0212192	−	0.0212192i	0.696418	−	0.717637i	$-0.254776\pi$
$593$	−0.516721	−	0.516721i	−0.0212192	−	0.0212192i	−0.717637	+	0.696418i	$0.754776\pi$
$594$		0			0
$595$	−0.0320615	−	0.0261136i	−0.00131439	−	0.00107055i
$596$	−26.8450	+	73.7560i	−1.09961	+	3.02116i
$597$		0			0
$598$	−31.3883	+	2.74612i	−1.28356	+	0.112297i
$599$	1.33236	−	7.55620i	0.0544389	−	0.308738i	−0.945414	−	0.325871i	$-0.894343\pi$
$599$	1.33236	−	7.55620i	0.0544389	−	0.308738i	0.999853	+	0.0171325i	$0.00545372\pi$
$600$		0			0
$601$	−13.5931	+	11.4060i	−0.554475	+	0.465260i	−0.876453	−	0.481488i	$-0.840097\pi$
$601$	−13.5931	+	11.4060i	−0.554475	+	0.465260i	0.321978	+	0.946747i	$0.395652\pi$
$602$	0.964103	+	0.258331i	0.0392939	+	0.0105288i
$603$		0			0
$604$	−10.2759	−	5.93282i	−0.418122	−	0.241403i
$605$	−2.88207	+	5.16484i	−0.117173	+	0.209981i
$606$		0			0
$607$	24.1847	+	11.2775i	0.981627	+	0.457740i	0.846095	−	0.533033i	$-0.178948\pi$
$607$	24.1847	+	11.2775i	0.981627	+	0.457740i	0.135532	+	0.990773i	$0.456726\pi$
$608$	32.1992	+	15.0147i	1.30585	+	0.608927i
$609$		0			0
$610$	7.44463	+	26.2428i	0.301424	+	1.06254i
$611$	−2.58545	−	1.49271i	−0.104596	−	0.0603887i
$612$		0			0
$613$	−39.1590	−	10.4926i	−1.58162	−	0.423793i	−0.642192	−	0.766544i	$-0.721975\pi$
$613$	−39.1590	−	10.4926i	−1.58162	−	0.423793i	−0.939427	+	0.342750i	$0.888642\pi$
$614$	55.7794	−	46.8045i	2.25107	−	1.88888i
$615$		0			0
$616$	0.318734	−	1.80763i	0.0128422	−	0.0728315i
$617$	−18.3464	+	1.60510i	−0.738597	+	0.0646189i	−0.450244	−	0.892905i	$-0.648663\pi$
$617$	−18.3464	+	1.60510i	−0.738597	+	0.0646189i	−0.288353	+	0.957524i	$0.593108\pi$
$618$		0			0
$619$	3.93502	−	10.8114i	0.158162	−	0.434546i	−0.835148	−	0.550025i	$-0.814618\pi$
$619$	3.93502	−	10.8114i	0.158162	−	0.434546i	0.993310	+	0.115479i	$0.0368403\pi$
$620$	−1.41647	+	1.73910i	−0.0568867	+	0.0698438i
$621$		0			0
$622$	−22.1776	−	22.1776i	−0.889240	−	0.889240i
$623$	−0.360779	−	0.773692i	−0.0144543	−	0.0309973i
$624$		0			0
$625$	−23.9519	−	7.16274i	−0.958077	−	0.286510i
$626$	−54.6775	−	9.64113i	−2.18535	−	0.385337i
$627$		0			0
$628$	−2.88870	+	33.0180i	−0.115272	+	1.31756i
$629$	1.30507	+	2.26045i	0.0520367	+	0.0901302i
$630$		0			0
$631$	−8.72085	+	15.1050i	−0.347172	+	0.601319i	−0.985746	−	0.168241i	$-0.946191\pi$
$631$	−8.72085	+	15.1050i	−0.347172	+	0.601319i	0.638574	+	0.769560i	$0.279525\pi$
$632$	58.1888	+	40.7442i	2.31463	+	1.62072i
$633$		0			0
$634$	6.44064	+	17.6955i	0.255791	+	0.702779i
$635$	−5.79860	−	11.9749i	−0.230110	−	0.475208i
$636$		0			0
$637$	6.34754	−	9.06523i	0.251499	−	0.359177i
$638$	2.28813	−	0.613103i	0.0905880	−	0.0242730i
$639$		0			0
$640$	66.8438	−	48.2762i	2.64223	−	1.90828i
$641$	−13.6102	−	16.2200i	−0.537569	−	0.640650i	0.427072	−	0.904218i	$-0.359545\pi$
$641$	−13.6102	−	16.2200i	−0.537569	−	0.640650i	−0.964641	+	0.263568i	$0.915101\pi$
$642$		0			0
$643$	3.01183	+	4.30134i	0.118775	+	0.169628i	0.874137	−	0.485680i	$-0.161428\pi$
$643$	3.01183	+	4.30134i	0.118775	+	0.169628i	−0.755362	+	0.655308i	$0.772539\pi$
$644$	2.05362	+	1.72319i	0.0809238	+	0.0679031i
$645$		0			0
$646$	−1.15754	−	0.421309i	−0.0455427	−	0.0165762i
$647$	−25.4612	+	25.4612i	−1.00098	+	1.00098i	−0.000982063		1.00000i	$0.500313\pi$
$647$	−25.4612	+	25.4612i	−1.00098	+	1.00098i	−1.00000		0.000982063i	$0.999687\pi$
$648$		0			0
$649$		−	35.0314i		−	1.37510i
$650$	−21.3645	−	3.12610i	−0.837985	−	0.122616i
$651$		0			0
$652$	5.93450	+	67.8317i	0.232413	+	2.65649i
$653$	−31.5335	+	22.0800i	−1.23400	+	0.864056i	−0.994282	−	0.106787i	$-0.965944\pi$
$653$	−31.5335	+	22.0800i	−1.23400	+	0.864056i	−0.239718	+	0.970843i	$0.577055\pi$
$654$		0			0
$655$	−0.149969	−	10.2564i	−0.00585979	−	0.400750i
$656$	65.6307	−	37.8919i	2.56245	−	1.47943i
$657$		0			0
$658$	0.0898605	+	0.335364i	0.00350313	+	0.0130738i
$659$	4.48911	+	25.4590i	0.174871	+	0.991742i	0.938293	+	0.345842i	$0.112407\pi$
$659$	4.48911	+	25.4590i	0.174871	+	0.991742i	−0.763422	+	0.645900i	$0.776482\pi$
$660$		0			0
$661$	−30.7185	+	11.1806i	−1.19481	+	0.434875i	−0.861410	−	0.507910i	$-0.830418\pi$
$661$	−30.7185	+	11.1806i	−1.19481	+	0.434875i	−0.333400	+	0.942786i	$0.608196\pi$
$662$	13.3906	−	28.7163i	0.520442	−	1.11609i
$663$		0			0
$664$	114.238	−	20.1432i	4.43329	−	0.781709i
$665$	−0.101451	+	0.226138i	−0.00393411	+	0.00876924i
$666$		0			0
$667$	−0.566941	+	2.11585i	−0.0219520	+	0.0819261i
$668$	−121.058	−	10.5912i	−4.68388	−	0.409786i
$669$		0			0
$670$	−11.4603	+	9.90541i	−0.442749	+	0.382679i
$671$	8.30322	−	9.89539i	0.320542	−	0.382007i
$672$		0			0
$673$	−19.6407	+	9.15859i	−0.757092	+	0.353038i	−0.762534	−	0.646948i	$-0.776045\pi$
$673$	−19.6407	+	9.15859i	−0.757092	+	0.353038i	0.00544291	+	0.999985i	$0.498267\pi$
$674$	26.4767			1.01984
$675$		0			0
$676$	57.2276			2.20106
$677$	−11.1454	+	5.19717i	−0.428351	+	0.199743i	−0.624824	−	0.780766i	$-0.714829\pi$
$677$	−11.1454	+	5.19717i	−0.428351	+	0.199743i	0.196473	+	0.980509i	$0.437051\pi$
$678$		0			0
$679$	−0.0845141	+	0.100720i	−0.00324335	+	0.00386528i
$680$	−4.37355	+	3.78017i	−0.167718	+	0.144963i
$681$		0			0
$682$	1.44628	+	0.126533i	0.0553808	+	0.00484519i
$683$	8.97660	−	33.5011i	0.343480	−	1.28188i	−0.550898	−	0.834573i	$-0.685715\pi$
$683$	8.97660	−	33.5011i	0.343480	−	1.28188i	0.894378	−	0.447312i	$-0.147619\pi$
$684$		0			0
$685$	8.16396	−	18.1977i	0.311929	−	0.695297i
$686$	−2.53573	+	0.447117i	−0.0968146	+	0.0170710i
$687$		0			0
$688$	33.9719	−	72.8530i	1.29517	−	2.77749i
$689$	−3.33549	+	1.21402i	−0.127072	+	0.0462505i
$690$		0			0
$691$	−8.06781	−	45.7548i	−0.306914	−	1.74060i	−0.614356	−	0.789029i	$-0.710584\pi$
$691$	−8.06781	−	45.7548i	−0.306914	−	1.74060i	0.307442	−	0.951567i	$-0.400527\pi$
$692$	17.4834	+	65.2489i	0.664619	+	2.48039i
$693$		0			0
$694$	−55.9820	+	32.3212i	−2.12505	+	1.22690i
$695$	0.493361	+	33.7409i	0.0187143	+	1.27987i
$696$		0			0
$697$	−1.14958	+	0.804947i	−0.0435436	+	0.0304896i
$698$	−0.584956	−	6.68608i	−0.0221409	−	0.253072i
$699$		0			0
$700$	1.09727	+	1.47342i	0.0414729	+	0.0556899i
$701$		−	23.7132i		−	0.895637i	−0.894125	−	0.447818i	$-0.852201\pi$
$701$		−	23.7132i		−	0.895637i	0.894125	−	0.447818i	$-0.147799\pi$
$702$		0			0
$703$	11.0627	−	11.0627i	0.417239	−	0.417239i
$704$	−79.6806	−	29.0014i	−3.00307	−	1.09303i
$705$		0			0
$706$	−0.923079	−	0.774556i	−0.0347406	−	0.0291508i
$707$	−0.478354	−	0.683160i	−0.0179903	−	0.0256929i
$708$		0			0
$709$	17.8373	+	21.2576i	0.669892	+	0.798346i	0.988769	−	0.149450i	$-0.0477502\pi$
$709$	17.8373	+	21.2576i	0.669892	+	0.798346i	−0.318877	+	0.947796i	$0.603306\pi$
$710$	−28.0549	+	20.2620i	−1.05288	+	0.760418i
$711$		0			0
$712$	−115.277	+	30.8885i	−4.32021	+	1.15760i
$713$	−0.770021	+	1.09970i	−0.0288375	+	0.0411842i
$714$		0			0
$715$	4.45621	+	9.20264i	0.166653	+	0.344159i
$716$	27.4373	+	75.3835i	1.02538	+	2.81721i
$717$		0			0
$718$	45.7073	+	32.0046i	1.70578	+	1.19440i
$719$	−13.3000	+	23.0362i	−0.496005	+	0.859105i	−0.999989	−	0.00460740i	$-0.998533\pi$
$719$	−13.3000	+	23.0362i	−0.496005	+	0.859105i	0.503985	+	0.863713i	$0.331867\pi$
$720$		0			0
$721$	−0.111858	−	0.193744i	−0.00416582	−	0.00721542i
$722$	3.87687	−	44.3128i	0.144282	−	1.64915i
$723$		0			0
$724$	16.1368	+	2.84536i	0.599721	+	0.105747i
$725$	−0.712222	+	1.32138i	−0.0264512	+	0.0490749i
$726$		0			0
$727$	14.5395	+	31.1801i	0.539240	+	1.15640i	0.967528	+	0.252762i	$0.0813390\pi$
$727$	14.5395	+	31.1801i	0.539240	+	1.15640i	−0.428288	+	0.903642i	$0.640883\pi$
$728$	0.710345	+	0.710345i	0.0263271	+	0.0263271i
$729$		0			0
$730$	34.8071	−	42.7352i	1.28827	−	1.58170i
$731$	−0.509123	+	1.39880i	−0.0188306	+	0.0517367i
$732$		0			0
$733$	−2.37945	+	0.208175i	−0.0878868	+	0.00768910i	−0.131014	−	0.991380i	$-0.541823\pi$
$733$	−2.37945	+	0.208175i	−0.0878868	+	0.00768910i	0.0431275	+	0.999070i	$0.486268\pi$
$734$	5.30665	−	30.0955i	0.195872	−	1.11085i
$735$		0			0
$736$	120.741	−	101.314i	4.45058	−	3.73448i
$737$	6.92873	+	1.85655i	0.255223	+	0.0683868i
$738$		0			0
$739$	−4.08269	−	2.35714i	−0.150184	−	0.0867088i	0.423025	−	0.906118i	$-0.360968\pi$
$739$	−4.08269	−	2.35714i	−0.150184	−	0.0867088i	−0.573209	+	0.819409i	$0.694302\pi$
$740$	−31.6479	−	111.561i	−1.16340	−	4.10106i
$741$		0			0
$742$	0.374125	+	0.174457i	0.0137345	+	0.00640452i
$743$	42.8072	+	19.9613i	1.57044	+	0.732310i	0.996259	−	0.0864151i	$-0.0275411\pi$
$743$	42.8072	+	19.9613i	1.57044	+	0.732310i	0.574185	+	0.818725i	$0.305319\pi$
$744$		0			0
$745$	−15.6875	+	28.1130i	−0.574747	+	1.02998i
$746$	−90.1249	−	52.0336i	−3.29971	−	1.90509i
$747$		0			0
$748$	4.17634	+	1.11905i	0.152702	+	0.0409164i
$749$	−0.447889	+	0.375823i	−0.0163655	+	0.0137323i
$750$		0			0
$751$	8.23787	−	46.7193i	0.300604	−	1.70481i	−0.342904	−	0.939371i	$-0.611410\pi$
$751$	8.23787	−	46.7193i	0.300604	−	1.70481i	0.643508	−	0.765440i	$-0.277478\pi$
$752$	27.8553	−	2.43703i	1.01578	−	0.0888692i
$753$		0			0
$754$	−0.443420	+	1.21829i	−0.0161484	+	0.0443674i
$755$	−3.77359	−	3.07353i	−0.137335	−	0.111857i
$756$		0			0
$757$	4.48441	+	4.48441i	0.162989	+	0.162989i	0.783889	−	0.620901i	$-0.213233\pi$
$757$	4.48441	+	4.48441i	0.162989	+	0.162989i	−0.620901	+	0.783889i	$0.713233\pi$
$758$	4.75020	+	10.1868i	0.172535	+	0.370003i
$759$		0			0
$760$	28.6710	+	19.4572i	1.04001	+	0.705786i
$761$	35.8871	+	6.32786i	1.30091	+	0.229385i	0.780834	−	0.624738i	$-0.214794\pi$
$761$	35.8871	+	6.32786i	1.30091	+	0.229385i	0.520071	+	0.854123i	$0.325905\pi$
$762$		0			0
$763$	0.0859317	−	0.982204i	0.00311094	−	0.0355582i
$764$	63.6122	+	110.180i	2.30141	+	3.98616i
$765$		0			0
$766$	11.6085	−	20.1066i	0.419434	−	0.726480i
$767$	15.7054	+	10.9970i	0.567088	+	0.397079i
$768$		0			0
$769$	−12.5047	−	34.3564i	−0.450931	−	1.23892i	−0.932070	−	0.362279i	$-0.881999\pi$
$769$	−12.5047	−	34.3564i	−0.450931	−	1.23892i	0.481139	−	0.876645i	$-0.340223\pi$
$770$	0.390318	−	1.12322i	0.0140661	−	0.0404781i
$771$		0			0
$772$	−60.6738	+	86.6512i	−2.18370	+	3.11864i
$773$	33.4533	−	8.96378i	1.20323	−	0.322405i	0.399128	−	0.916895i	$-0.369313\pi$
$773$	33.4533	−	8.96378i	1.20323	−	0.322405i	0.804103	+	0.594491i	$0.202646\pi$
$774$		0			0
$775$	−0.687157	+	0.611707i	−0.0246834	+	0.0219732i
$776$	11.8151	+	14.0807i	0.424137	+	0.505467i
$777$		0			0
$778$	50.3266	+	71.8739i	1.80430	+	2.57680i
$779$	6.44381	+	5.40700i	0.230873	+	0.193726i
$780$		0			0
$781$	15.3995	+	5.60498i	0.551039	+	0.200562i
$782$	−3.86426	+	3.86426i	−0.138186	+	0.138186i
$783$		0			0
$784$			103.651i			3.70181i
$785$	−3.32618	+	13.1814i	−0.118717	+	0.470465i
$786$		0			0
$787$	0.967441	+	11.0579i	0.0344855	+	0.394172i	0.993747	+	0.111653i	$0.0356144\pi$
$787$	0.967441	+	11.0579i	0.0344855	+	0.394172i	−0.959262	+	0.282519i	$0.908830\pi$
$788$	71.9848	−	50.4043i	2.56435	−	1.79558i
$789$		0			0
$790$	33.0127	+	32.0612i	1.17454	+	1.14068i
$791$	0.435084	−	0.251196i	0.0154698	−	0.00893150i
$792$		0			0
$793$	1.82979	+	6.82887i	0.0649778	+	0.242500i
$794$	13.1431	+	74.5384i	0.466432	+	2.64527i
$795$		0			0
$796$	−63.3069	+	23.0418i	−2.24385	+	0.816696i
$797$	−9.25041	+	19.8376i	−0.327666	+	0.702683i	−0.999269	−	0.0382286i	$-0.987828\pi$
$797$	−9.25041	+	19.8376i	−0.327666	+	0.702683i	0.671603	+	0.740912i	$0.265606\pi$
$798$		0			0
$799$	−0.509936	+	0.0899154i	−0.0180402	+	0.00318098i
$800$	96.5154	−	48.4904i	3.41233	−	1.71439i
$801$		0			0
$802$	−23.1968	+	86.5715i	−0.819106	+	3.05695i
$803$	−26.0008	−	2.27478i	−0.917550	−	0.0802752i
$804$		0			0
$805$	0.719033	+	0.831900i	0.0253426	+	0.0293206i
$806$	−0.510741	+	0.608678i	−0.0179901	+	0.0214398i
$807$		0			0
$808$	−105.668	+	49.2736i	−3.71737	+	1.73344i
$809$	27.2653			0.958598			0.479299	−	0.877652i	$-0.340891\pi$
$809$	27.2653			0.958598			0.479299	+	0.877652i	$0.340891\pi$
$810$		0			0
$811$	−36.1569			−1.26964			−0.634820	−	0.772660i	$-0.718926\pi$
$811$	−36.1569			−1.26964			−0.634820	+	0.772660i	$0.718926\pi$
$812$	0.0999725	−	0.0466179i	0.00350835	−	0.00163597i
$813$		0			0
$814$	−48.2474	+	57.4990i	−1.69107	+	2.01534i
$815$	−2.02710	+	27.8549i	−0.0710061	+	0.975714i
$816$		0			0
$817$	8.88849	+	0.777642i	0.310969	+	0.0272062i
$818$	−19.5397	+	72.9233i	−0.683191	+	2.54970i
$819$		0			0
$820$	58.2710	−	22.1790i	2.03491	−	0.774524i
$821$	0.864071	−	0.152359i	0.0301563	−	0.00531736i	−0.158550	−	0.987351i	$-0.550682\pi$
$821$	0.864071	−	0.152359i	0.0301563	−	0.00531736i	0.188706	+	0.982034i	$0.439571\pi$
$822$		0			0
$823$	10.0357	−	21.5215i	0.349821	−	0.750194i	−0.650132	−	0.759821i	$-0.725287\pi$
$823$	10.0357	−	21.5215i	0.349821	−	0.750194i	0.999954	+	0.00962693i	$0.00306439\pi$
$824$	−29.3895	+	10.6969i	−1.02383	+	0.372644i
$825$		0			0
$826$	−0.387186	−	2.19584i	−0.0134719	−	0.0764032i
$827$	9.02850	+	33.6948i	0.313952	+	1.17168i	0.924961	+	0.380061i	$0.124097\pi$
$827$	9.02850	+	33.6948i	0.313952	+	1.17168i	−0.611010	+	0.791623i	$0.709236\pi$
$828$		0			0
$829$	30.9073	−	17.8443i	1.07345	−	0.619759i	0.144330	−	0.989530i	$-0.453897\pi$
$829$	30.9073	−	17.8443i	1.07345	−	0.619759i	0.929123	+	0.369771i	$0.120564\pi$
$830$	75.1407	−	1.09871i	2.60817	−	0.0381368i
$831$		0			0
$832$	38.0152	−	26.6185i	1.31794	−	0.922832i
$833$	−0.167289	−	1.91212i	−0.00579623	−	0.0662512i
$834$		0			0
$835$	−48.3287	−	12.1952i	−1.67248	−	0.422032i
$836$		−	25.9158i		−	0.896317i
$837$		0			0
$838$	12.6368	−	12.6368i	0.436530	−	0.436530i
$839$	9.08974	+	3.30839i	0.313813	+	0.114218i	0.494125	−	0.869391i	$-0.335489\pi$
$839$	9.08974	+	3.30839i	0.313813	+	0.114218i	−0.180312	+	0.983609i	$0.557711\pi$
$840$		0			0
$841$	−22.1462	−	18.5829i	−0.763664	−	0.640790i
$842$	−0.759539	−	1.08473i	−0.0261754	−	0.0373824i
$843$		0			0
$844$	−46.0118	−	54.8347i	−1.58379	−	1.88749i
$845$	23.1734	+	3.73761i	0.797188	+	0.128578i
$846$		0			0
$847$	0.172195	−	0.0461394i	0.00591668	−	0.00158537i
$848$	19.0688	−	27.2331i	0.654826	−	0.935188i
$849$		0			0
$850$	−3.18712	+	1.96652i	−0.109317	+	0.0674511i
$851$	−23.7390	−	65.2223i	−0.813762	−	2.23579i
$852$		0			0
$853$	−22.9607	−	16.0773i	−0.786161	−	0.550476i	0.110143	−	0.993916i	$-0.464869\pi$
$853$	−22.9607	−	16.0773i	−0.786161	−	0.550476i	−0.896304	+	0.443440i	$0.853758\pi$
$854$	0.411095	−	0.712037i	0.0140674	−	0.0243654i
$855$		0			0
$856$	40.8690	+	70.7872i	1.39687	+	2.41946i
$857$	0.867353	−	9.91389i	0.0296282	−	0.338652i	−0.966885	−	0.255214i	$-0.917854\pi$
$857$	0.867353	−	9.91389i	0.0296282	−	0.338652i	0.996513	−	0.0834385i	$-0.0265902\pi$
$858$		0			0
$859$	4.41290	+	0.778113i	0.150566	+	0.0265489i	0.248423	−	0.968652i	$-0.420088\pi$
$859$	4.41290	+	0.778113i	0.150566	+	0.0265489i	−0.0978570	+	0.995200i	$0.531199\pi$
$860$	37.1369	−	54.7227i	1.26636	−	1.86603i
$861$		0			0
$862$	−18.7793	−	40.2723i	−0.639624	−	1.37168i
$863$	−9.71940	−	9.71940i	−0.330852	−	0.330852i	0.522058	−	0.852910i	$-0.325165\pi$
$863$	−9.71940	−	9.71940i	−0.330852	−	0.330852i	−0.852910	+	0.522058i	$0.825165\pi$
$864$		0			0
$865$	2.81811	+	27.5633i	0.0958187	+	0.937180i
$866$	24.0508	−	66.0790i	0.817280	−	2.24546i
$867$		0			0
$868$	0.0673471	−	0.00589210i	0.00228591	−	0.000199991i
$869$	3.78416	−	21.4610i	0.128369	−	0.728016i
$870$		0			0
$871$	−3.00739	+	2.52350i	−0.101902	+	0.0855056i
$872$	−133.140	−	35.6748i	−4.50870	−	1.20810i
$873$		0			0
$874$	28.3677	+	16.3781i	0.959553	+	0.553998i
$875$	0.348090	+	0.668299i	0.0117676	+	0.0225926i
$876$		0			0
$877$	−10.0621	−	4.69203i	−0.339772	−	0.158438i	0.245241	−	0.969462i	$-0.421133\pi$
$877$	−10.0621	−	4.69203i	−0.339772	−	0.158438i	−0.585013	+	0.811024i	$0.698911\pi$
$878$	−67.5049	−	31.4780i	−2.27818	−	1.06233i
$879$		0			0
$880$	−83.6272	−	46.6655i	−2.81907	−	1.57309i
$881$	−6.04019	−	3.48730i	−0.203499	−	0.117490i	0.394787	−	0.918772i	$-0.370818\pi$
$881$	−6.04019	−	3.48730i	−0.203499	−	0.117490i	−0.598287	+	0.801282i	$0.704152\pi$
$882$		0			0
$883$	−6.34719	−	1.70073i	−0.213600	−	0.0572340i	0.150432	−	0.988620i	$-0.451934\pi$
$883$	−6.34719	−	1.70073i	−0.213600	−	0.0572340i	−0.364032	+	0.931386i	$0.618600\pi$
$884$	−1.81273	+	1.52106i	−0.0609686	+	0.0511588i
$885$		0			0
$886$	−11.8947	+	67.4585i	−0.399612	+	2.26631i
$887$	10.1701	−	0.889770i	0.341479	−	0.0298756i	0.0848735	−	0.996392i	$-0.472951\pi$
$887$	10.1701	−	0.889770i	0.341479	−	0.0298756i	0.256606	+	0.966516i	$0.417396\pi$
$888$		0			0
$889$	−0.137157	+	0.376836i	−0.00460010	+	0.0126387i
$890$	−76.9140	+	7.86380i	−2.57816	+	0.263595i
$891$		0			0
$892$	−47.0125	−	47.0125i	−1.57410	−	1.57410i
$893$	1.31167	+	2.81288i	0.0438934	+	0.0941296i
$894$		0			0
$895$	6.18689	+	32.3172i	0.206805	+	1.08025i
$896$	−2.44747	−	0.431556i	−0.0817643	−	0.0144173i
$897$		0			0
$898$	6.25928	−	71.5439i	0.208875	−	2.38745i
$899$	0.0276198	+	0.0478389i	0.000921172	+	0.00159552i
$900$		0			0
$901$	−0.307824	+	0.533166i	−0.0102551	+	0.0177623i
$902$	−33.0584	−	23.1477i	−1.10072	−	0.770735i
$903$		0			0
$904$	−24.0216	−	65.9989i	−0.798947	−	2.19509i
$905$	6.34851	+	2.20610i	0.211031	+	0.0733332i
$906$		0			0
$907$	12.2531	−	17.4992i	0.406858	−	0.581053i	−0.562472	−	0.826816i	$-0.690150\pi$
$907$	12.2531	−	17.4992i	0.406858	−	0.581053i	0.969330	+	0.245763i	$0.0790386\pi$
$908$	28.6945	−	7.68866i	0.952259	−	0.255157i
$909$		0			0
$910$	0.381038	+	0.527589i	0.0126313	+	0.0174894i
$911$	1.27365	+	1.51788i	0.0421979	+	0.0502895i	0.786731	−	0.617296i	$-0.211772\pi$
$911$	1.27365	+	1.51788i	0.0421979	+	0.0502895i	−0.744533	+	0.667586i	$0.767328\pi$
$912$		0			0
$913$	−20.4115	−	29.1506i	−0.675521	−	0.964744i
$914$	−81.6208	−	68.4880i	−2.69978	−	2.26538i
$915$		0			0
$916$	0.918820	+	0.334423i	0.0303587	+	0.0110497i
$917$	−0.218615	+	0.218615i	−0.00721930	+	0.00721930i
$918$		0			0
$919$			49.9403i			1.64738i	0.567042	+	0.823689i	$0.308088\pi$
$919$			49.9403i			1.64738i	−0.567042	+	0.823689i	$0.691912\pi$
$920$	131.988	−	78.7986i	4.35153	−	2.59791i
$921$		0			0
$922$	0.730515	+	8.34983i	0.0240582	+	0.274987i
$923$	−7.34705	+	5.14446i	−0.241831	+	0.169332i
$924$		0			0
$925$	−5.52909	−	47.2417i	−0.181795	−	1.55330i
$926$	−95.8608	+	55.3452i	−3.15018	+	1.81876i
$927$		0			0
$928$	−1.67856	−	6.26448i	−0.0551015	−	0.205642i
$929$	−4.34439	−	24.6383i	−0.142535	−	0.808355i	−0.969314	−	0.245828i	$-0.920940\pi$
$929$	−4.34439	−	24.6383i	−0.142535	−	0.808355i	0.826779	−	0.562527i	$-0.190171\pi$
$930$		0			0
$931$	−10.8111	+	3.93492i	−0.354320	+	0.128962i
$932$	−18.5712	+	39.8261i	−0.608320	+	1.30455i
$933$		0			0
$934$	−12.2666	+	2.16293i	−0.401374	+	0.0707731i
$935$	1.61805	+	0.725902i	0.0529160	+	0.0237395i
$936$		0			0
$937$	8.09111	−	30.1964i	0.264325	−	0.986475i	−0.698337	−	0.715769i	$-0.746076\pi$
$937$	8.09111	−	30.1964i	0.264325	−	0.986475i	0.962662	−	0.270706i	$-0.0872570\pi$
$938$	0.454828	+	0.0397923i	0.0148507	+	0.00129926i
$939$		0			0
$940$	22.9441	+	1.66972i	0.748354	+	0.0544604i
$941$	−20.9973	+	25.0236i	−0.684491	+	0.815745i	−0.990678	−	0.136227i	$-0.956502\pi$
$941$	−20.9973	+	25.0236i	−0.684491	+	0.815745i	0.306186	+	0.951972i	$0.400947\pi$
$942$		0			0
$943$	33.8218	−	15.7714i	1.10139	−	0.513587i
$944$	−179.573			−5.84461
$945$		0			0
$946$	−42.8067			−1.39177
$947$	20.6175	−	9.61412i	0.669980	−	0.312417i	−0.0576996	−	0.998334i	$-0.518377\pi$
$947$	20.6175	−	9.61412i	0.669980	−	0.312417i	0.727680	+	0.685917i	$0.240599\pi$
$948$		0			0
$949$	9.18200	−	10.9427i	0.298060	−	0.355214i
$950$	16.3299	+	15.4017i	0.529812	+	0.499698i
$951$		0			0
$952$	0.173575	+	0.0151858i	0.00562559	+	0.000492175i
$953$	−8.22034	+	30.6787i	−0.266283	+	0.993781i	0.695178	+	0.718838i	$0.255326\pi$
$953$	−8.22034	+	30.6787i	−0.266283	+	0.993781i	−0.961461	+	0.274943i	$0.911341\pi$
$954$		0			0
$955$	18.5627	+	48.7700i	0.600676	+	1.57816i
$956$	−16.2399	+	2.86352i	−0.525235	+	0.0926130i
$957$		0			0
$958$	−30.1040	+	64.5582i	−0.972615	+	2.08578i
$959$	−0.564905	+	0.205609i	−0.0182417	+	0.00663945i
$960$		0			0
$961$	−5.37721	−	30.4957i	−0.173459	−	0.983732i
$962$	−10.6323	−	39.6804i	−0.342800	−	1.27935i
$963$		0			0
$964$	52.1692	−	30.1199i	1.68026	−	0.970097i
$965$	−30.2281	+	31.1252i	−0.973078	+	1.00196i
$966$		0			0
$967$	9.35397	−	6.54972i	0.300803	−	0.210625i	−0.413424	−	0.910539i	$-0.635667\pi$
$967$	9.35397	−	6.54972i	0.300803	−	0.210625i	0.714227	+	0.699914i	$0.246778\pi$
$968$	−2.17210	−	24.8272i	−0.0698140	−	0.797977i
$969$		0			0
$970$	6.10405	+	10.2243i	0.195989	+	0.328283i
$971$			1.87641i			0.0602168i	0.999547	+	0.0301084i	$0.00958525\pi$
$971$			1.87641i			0.0602168i	−0.999547	+	0.0301084i	$0.990415\pi$
$972$		0			0
$973$	0.719189	−	0.719189i	0.0230561	−	0.0230561i
$974$	−37.4883	−	13.6446i	−1.20120	−	0.437202i
$975$		0			0
$976$	−50.7245	−	42.5629i	−1.62365	−	1.36240i
$977$	−5.93121	−	8.47065i	−0.189756	−	0.271000i	0.712989	−	0.701175i	$-0.247341\pi$
$977$	−5.93121	−	8.47065i	−0.189756	−	0.271000i	−0.902746	+	0.430175i	$0.858452\pi$
$978$		0			0
$979$	23.5338	+	28.0465i	0.752144	+	0.896371i
$980$	−13.5786	+	84.1879i	−0.433752	+	2.68928i
$981$		0			0
$982$	56.8917	−	15.2441i	1.81549	−	0.486459i
$983$	22.1970	−	31.7007i	0.707976	−	1.01109i	−0.290552	−	0.956859i	$-0.593839\pi$
$983$	22.1970	−	31.7007i	0.707976	−	1.01109i	0.998528	−	0.0542350i	$-0.0172720\pi$
$984$		0			0
$985$	32.4410	−	15.7090i	1.03366	−	0.500529i
$986$	0.0769083	+	0.211304i	0.00244926	+	0.00672928i
$987$		0			0
$988$	11.6186	+	8.13546i	0.369638	+	0.258824i
$989$	19.7919	−	34.2805i	0.629344	−	1.09006i
$990$		0			0
$991$	22.3137	+	38.6485i	0.708818	+	1.22771i	0.965296	+	0.261159i	$0.0841048\pi$
$991$	22.3137	+	38.6485i	0.708818	+	1.22771i	−0.256477	+	0.966550i	$0.582562\pi$
$992$	0.346423	−	3.95964i	0.0109990	−	0.125719i
$993$		0			0
$994$	1.02723	+	0.181128i	0.0325817	+	0.00574503i
$995$	−27.1400	+	5.19574i	−0.860394	+	0.164716i
$996$		0			0
$997$	−6.20488	−	13.3064i	−0.196511	−	0.421418i	0.783218	−	0.621747i	$-0.213577\pi$
$997$	−6.20488	−	13.3064i	−0.196511	−	0.421418i	−0.979729	+	0.200329i	$0.935799\pi$
$998$	50.4141	+	50.4141i	1.59583	+	1.59583i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.r.a.17.1		192
3.2	odd	2		135.2.q.a.77.16	yes	192
5.3	odd	4	inner	405.2.r.a.98.16		192
15.2	even	4		675.2.ba.b.293.16		192
15.8	even	4		135.2.q.a.23.1	✓	192
15.14	odd	2		675.2.ba.b.482.1		192
27.7	even	9		135.2.q.a.47.1	yes	192
27.20	odd	18	inner	405.2.r.a.62.16		192
135.7	odd	36		675.2.ba.b.668.1		192
135.34	even	18		675.2.ba.b.182.16		192
135.88	odd	36		135.2.q.a.128.16	yes	192
135.128	even	36	inner	405.2.r.a.143.1		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.23.1	✓	192	15.8	even	4
135.2.q.a.47.1	yes	192	27.7	even	9
135.2.q.a.77.16	yes	192	3.2	odd	2
135.2.q.a.128.16	yes	192	135.88	odd	36
405.2.r.a.17.1		192	1.1	even	1	trivial
405.2.r.a.62.16		192	27.20	odd	18	inner
405.2.r.a.98.16		192	5.3	odd	4	inner
405.2.r.a.143.1		192	135.128	even	36	inner
675.2.ba.b.182.16		192	135.34	even	18
675.2.ba.b.293.16		192	15.2	even	4
675.2.ba.b.482.1		192	15.14	odd	2
675.2.ba.b.668.1		192	135.7	odd	36

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-2.47401 + 1.15365i) q^{2} +(3.50423 - 4.17618i) q^{4} +(1.69173 - 1.46221i) q^{5} +(-0.0671403 - 0.00587402i) q^{7} +(-2.43862 + 9.10104i) q^{8} +O(q^{10})\)	\(q+(-2.47401 + 1.15365i) q^{2} +(3.50423 - 4.17618i) q^{4} +(1.69173 - 1.46221i) q^{5} +(-0.0671403 - 0.00587402i) q^{7} +(-2.43862 + 9.10104i) q^{8} +(-2.49848 + 5.56917i) q^{10} +(2.84658 - 0.501928i) q^{11} +(-0.668569 + 1.43375i) q^{13} +(0.172882 - 0.0629240i) q^{14} +(-2.57292 - 14.5918i) q^{16} +(0.0710153 + 0.265033i) q^{17} +(1.42429 - 0.822315i) q^{19} +(-0.178226 - 12.1889i) q^{20} +(-6.46340 + 4.52572i) q^{22} +(-0.635912 - 7.26851i) q^{23} +(0.723902 - 4.94732i) q^{25} -4.31840i q^{26} +(-0.259806 + 0.259806i) q^{28} +(-0.282115 - 0.102681i) q^{29} +(-0.140950 - 0.118271i) q^{31} +(12.3906 + 17.6956i) q^{32} +(-0.481447 - 0.573766i) q^{34} +(-0.122172 + 0.0882358i) q^{35} +(9.18868 - 2.46210i) q^{37} +(-2.57504 + 3.67754i) q^{38} +(9.18212 + 18.9623i) q^{40} +(1.74933 + 4.80625i) q^{41} +(4.44406 + 3.11177i) q^{43} +(7.87892 - 13.6467i) q^{44} +(9.95855 + 17.2487i) q^{46} +(-0.164477 + 1.87998i) q^{47} +(-6.88918 - 1.21475i) q^{49} +(3.91653 + 13.0748i) q^{50} +(3.64478 + 7.81625i) q^{52} +(1.58658 + 1.58658i) q^{53} +(4.08172 - 5.01141i) q^{55} +(0.217189 - 0.596722i) q^{56} +(0.816413 - 0.0714269i) q^{58} +(2.10453 - 11.9354i) q^{59} +(3.42343 - 2.87260i) q^{61} +(0.485153 + 0.129996i) q^{62} +(-25.4054 - 14.6678i) q^{64} +(0.965402 + 3.40311i) q^{65} +(2.24913 + 1.04879i) q^{67} +(1.35568 + 0.632163i) q^{68} +(0.200462 - 0.359240i) q^{70} +(4.91000 + 2.83479i) q^{71} +(-8.72199 - 2.33705i) q^{73} +(-19.8925 + 16.6918i) q^{74} +(1.55691 - 8.82967i) q^{76} +(-0.194068 + 0.0169788i) q^{77} +(2.57857 - 7.08457i) q^{79} +(-25.6889 - 20.9232i) q^{80} +(-9.87258 - 9.87258i) q^{82} +(-5.20307 - 11.1580i) q^{83} +(0.507671 + 0.344525i) q^{85} +(-14.5845 - 2.57164i) q^{86} +(-2.37364 + 27.1308i) q^{88} +(6.33320 + 10.9694i) q^{89} +(0.0533098 - 0.0923353i) q^{91} +(-32.5830 - 22.8148i) q^{92} +(-1.76192 - 4.84082i) q^{94} +(1.20712 - 3.47374i) q^{95} +(1.11896 - 1.59804i) q^{97} +(18.4453 - 4.94240i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) 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

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