LMFDB - Embedded newform 495.2.bj.a.118.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [495,2,Mod(28,495)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(495, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([0, 15, 18])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("495.28"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.bj (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,10,0,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			118.4
Character	$\chi$	$=$	495.118
Dual form			495.2.bj.a.172.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.40264 + 0.380541i) q^{2} +(3.72576 + 1.21057i) q^{4} +(-1.85044 + 1.25533i) q^{5} +(2.30033 - 1.17208i) q^{7} +(4.15610 + 2.11764i) q^{8} +(-4.92366 + 2.31195i) q^{10} +(2.55440 + 2.11543i) q^{11} +(-0.439393 + 2.77422i) q^{13} +(5.97289 - 1.94071i) q^{14} +(2.84111 + 2.06419i) q^{16} +(-0.147723 - 0.932684i) q^{17} +(-1.28236 - 3.94669i) q^{19} +(-8.41399 + 2.43698i) q^{20} +(5.33231 + 6.05467i) q^{22} +(-0.104710 - 0.104710i) q^{23} +(1.84827 - 4.64585i) q^{25} +(-2.11141 + 6.49824i) q^{26} +(9.98937 - 1.58216i) q^{28} +(2.14459 - 6.60038i) q^{29} +(-7.33171 + 5.32680i) q^{31} +(-0.555921 - 0.555921i) q^{32} -2.29712i q^{34} +(-2.78528 + 5.05654i) q^{35} +(-3.44950 - 6.77002i) q^{37} +(-1.57917 - 9.97047i) q^{38} +(-10.3490 + 1.29873i) q^{40} +(-3.27880 + 1.06535i) q^{41} +(-3.91833 + 3.91833i) q^{43} +(6.95623 + 10.9739i) q^{44} +(-0.211733 - 0.291426i) q^{46} +(0.942051 + 0.479999i) q^{47} +(-0.196744 + 0.270795i) q^{49} +(6.20867 - 10.4590i) q^{50} +(-4.99547 + 9.80416i) q^{52} +(4.07187 + 0.644920i) q^{53} +(-7.38234 - 0.707841i) q^{55} +12.0424 q^{56} +(7.66441 - 15.0422i) q^{58} +(-6.16460 - 2.00300i) q^{59} +(5.59880 - 7.70609i) q^{61} +(-19.6426 + 10.0084i) q^{62} +(-5.25251 - 7.22946i) q^{64} +(-2.66950 - 5.68511i) q^{65} +(2.94509 - 2.94509i) q^{67} +(0.578703 - 3.65379i) q^{68} +(-8.61625 + 11.0891i) q^{70} +(1.02426 + 0.744171i) q^{71} +(0.804189 + 1.57831i) q^{73} +(-5.71163 - 17.5786i) q^{74} -16.2568i q^{76} +(8.35541 + 1.87222i) q^{77} +(3.51271 - 2.55214i) q^{79} +(-7.84857 - 0.253115i) q^{80} +(-8.28320 + 1.31193i) q^{82} +(8.18939 - 1.29707i) q^{83} +(1.44418 + 1.54044i) q^{85} +(-10.9054 + 7.92326i) q^{86} +(6.13664 + 14.2012i) q^{88} +4.23092i q^{89} +(2.24084 + 6.89661i) q^{91} +(-0.263364 - 0.516882i) q^{92} +(2.08075 + 1.51175i) q^{94} +(7.32735 + 5.69333i) q^{95} +(-2.25634 + 14.2460i) q^{97} +(-0.575755 + 0.575755i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 10 q^{2} + 2 q^{5} + 10 q^{8} + 24 q^{11} - 10 q^{13} - 8 q^{16} - 16 q^{20} + 10 q^{22} + 24 q^{23} + 16 q^{25} - 20 q^{26} + 50 q^{28} - 28 q^{31} + 10 q^{35} - 8 q^{37} - 10 q^{38} - 50 q^{40}+ \cdots - 8 q^{97}+O(q^{100}) $ 32 * q + 10 * q^2 + 2 * q^5 + 10 * q^8 + 24 * q^11 - 10 * q^13 - 8 * q^16 - 16 * q^20 + 10 * q^22 + 24 * q^23 + 16 * q^25 - 20 * q^26 + 50 * q^28 - 28 * q^31 + 10 * q^35 - 8 * q^37 - 10 * q^38 - 50 * q^40 - 40 * q^41 + 60 * q^46 + 28 * q^47 + 50 * q^50 - 50 * q^52 + 24 * q^53 - 64 * q^55 + 80 * q^56 - 50 * q^58 - 60 * q^61 - 100 * q^62 - 8 * q^67 + 30 * q^68 + 30 * q^70 - 24 * q^71 + 50 * q^73 - 70 * q^77 - 98 * q^80 - 10 * q^82 - 90 * q^83 + 30 * q^85 - 100 * q^86 + 170 * q^88 + 20 * q^91 + 68 * q^92 + 40 * q^95 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	2.40264	+	0.380541i	1.69892	+	0.269083i	0.929276	−	0.369385i	$-0.120432\pi$
$2$	2.40264	+	0.380541i	1.69892	+	0.269083i	0.769648	+	0.638468i	$0.220432\pi$
$3$		0			0
$3$		0			0
$4$	3.72576	+	1.21057i	1.86288	+	0.605287i
$5$	−1.85044	+	1.25533i	−0.827543	+	0.561403i
$5$	−1.85044	+	1.25533i	−0.827543	+	0.561403i
$6$		0			0
$7$	2.30033	−	1.17208i	0.869443	−	0.443003i	0.0384331	−	0.999261i	$-0.487763\pi$
$7$	2.30033	−	1.17208i	0.869443	−	0.443003i	0.831010	+	0.556258i	$0.187763\pi$
$8$	4.15610	+	2.11764i	1.46940	+	0.748698i
$9$		0			0
$10$	−4.92366	+	2.31195i	−1.55700	+	0.731103i
$11$	2.55440	+	2.11543i	0.770182	+	0.637825i
$11$	2.55440	+	2.11543i	0.770182	+	0.637825i
$12$		0			0
$13$	−0.439393	+	2.77422i	−0.121866	+	0.769429i	0.848750	+	0.528794i	$0.177356\pi$
$13$	−0.439393	+	2.77422i	−0.121866	+	0.769429i	−0.970616	+	0.240635i	$0.922644\pi$
$14$	5.97289	−	1.94071i	1.59632	−	0.518677i
$15$		0			0
$16$	2.84111	+	2.06419i	0.710279	+	0.516048i
$17$	−0.147723	−	0.932684i	−0.0358280	−	0.226209i	0.963277	−	0.268510i	$-0.0865312\pi$
$17$	−0.147723	−	0.932684i	−0.0358280	−	0.226209i	−0.999105	+	0.0423009i	$0.986531\pi$
$18$		0			0
$19$	−1.28236	−	3.94669i	−0.294193	−	0.905433i	−0.983491	−	0.180955i	$-0.942081\pi$
$19$	−1.28236	−	3.94669i	−0.294193	−	0.905433i	0.689298	−	0.724478i	$-0.257919\pi$
$20$	−8.41399	+	2.43698i	−1.88142	+	0.544926i
$21$		0			0
$22$	5.33231	+	6.05467i	1.13685	+	1.29086i
$23$	−0.104710	−	0.104710i	−0.0218334	−	0.0218334i	0.696106	−	0.717939i	$-0.254914\pi$
$23$	−0.104710	−	0.104710i	−0.0218334	−	0.0218334i	−0.717939	+	0.696106i	$0.754914\pi$
$24$		0			0
$25$	1.84827	−	4.64585i	0.369654	−	0.929169i
$26$	−2.11141	+	6.49824i	−0.414081	+	1.27441i
$27$		0			0
$28$	9.98937	−	1.58216i	1.88781	−	0.299000i
$29$	2.14459	−	6.60038i	0.398241	−	1.22566i	−0.528168	−	0.849140i	$-0.677121\pi$
$29$	2.14459	−	6.60038i	0.398241	−	1.22566i	0.926409	−	0.376520i	$-0.122879\pi$
$30$		0			0
$31$	−7.33171	+	5.32680i	−1.31681	+	0.956722i	−0.316849	+	0.948476i	$0.602625\pi$
$31$	−7.33171	+	5.32680i	−1.31681	+	0.956722i	−0.999966	+	0.00824590i	$0.997375\pi$
$32$	−0.555921	−	0.555921i	−0.0982739	−	0.0982739i
$33$		0			0
$34$		−	2.29712i		−	0.393953i
$35$	−2.78528	+	5.05654i	−0.470798	+	0.854712i
$36$		0			0
$37$	−3.44950	−	6.77002i	−0.567094	−	1.11298i	−0.979398	−	0.201938i	$-0.935276\pi$
$37$	−3.44950	−	6.77002i	−0.567094	−	1.11298i	0.412305	−	0.911046i	$-0.364724\pi$
$38$	−1.57917	−	9.97047i	−0.256175	−	1.61742i
$39$		0			0
$40$	−10.3490	+	1.29873i	−1.63631	+	0.205347i
$41$	−3.27880	+	1.06535i	−0.512063	+	0.166379i	−0.553640	−	0.832756i	$-0.686762\pi$
$41$	−3.27880	+	1.06535i	−0.512063	+	0.166379i	0.0415772	+	0.999135i	$0.486762\pi$
$42$		0			0
$43$	−3.91833	+	3.91833i	−0.597540	+	0.597540i	−0.939657	−	0.342117i	$-0.888856\pi$
$43$	−3.91833	+	3.91833i	−0.597540	+	0.597540i	0.342117	+	0.939657i	$0.388856\pi$
$44$	6.95623	+	10.9739i	1.04869	+	1.65437i
$45$		0			0
$46$	−0.211733	−	0.291426i	−0.0312184	−	0.0429684i
$47$	0.942051	+	0.479999i	0.137412	+	0.0700150i	0.521345	−	0.853346i	$-0.325431\pi$
$47$	0.942051	+	0.479999i	0.137412	+	0.0700150i	−0.383933	+	0.923361i	$0.625431\pi$
$48$		0			0
$49$	−0.196744	+	0.270795i	−0.0281063	+	0.0386850i
$50$	6.20867	−	10.4590i	0.878038	−	1.47912i
$51$		0			0
$52$	−4.99547	+	9.80416i	−0.692747	+	1.35959i
$53$	4.07187	+	0.644920i	0.559314	+	0.0885866i	0.429690	−	0.902977i	$-0.358623\pi$
$53$	4.07187	+	0.644920i	0.559314	+	0.0885866i	0.129624	+	0.991563i	$0.458623\pi$
$54$		0			0
$55$	−7.38234	−	0.707841i	−0.995435	−	0.0954452i
$56$	12.0424			1.60924
$57$		0			0
$58$	7.66441	−	15.0422i	1.00639	−	1.97514i
$59$	−6.16460	−	2.00300i	−0.802563	−	0.260768i	−0.121118	−	0.992638i	$-0.538648\pi$
$59$	−6.16460	−	2.00300i	−0.802563	−	0.260768i	−0.681445	+	0.731870i	$0.738648\pi$
$60$		0			0
$61$	5.59880	−	7.70609i	0.716853	−	0.986663i	−0.282769	−	0.959188i	$-0.591253\pi$
$61$	5.59880	−	7.70609i	0.716853	−	0.986663i	0.999622	−	0.0274756i	$-0.00874685\pi$
$62$	−19.6426	+	10.0084i	−2.49461	+	1.27107i
$63$		0			0
$64$	−5.25251	−	7.22946i	−0.656564	−	0.903682i
$65$	−2.66950	−	5.68511i	−0.331111	−	0.705151i
$66$		0			0
$67$	2.94509	−	2.94509i	0.359801	−	0.359801i	−0.503939	−	0.863739i	$-0.668116\pi$
$67$	2.94509	−	2.94509i	0.359801	−	0.359801i	0.863739	+	0.503939i	$0.168116\pi$
$68$	0.578703	−	3.65379i	0.0701781	−	0.443087i
$69$		0			0
$70$	−8.61625	+	11.0891i	−1.02984	+	1.32541i
$71$	1.02426	+	0.744171i	0.121558	+	0.0883168i	0.646903	−	0.762572i	$-0.276064\pi$
$71$	1.02426	+	0.744171i	0.121558	+	0.0883168i	−0.525345	+	0.850889i	$0.676064\pi$
$72$		0			0
$73$	0.804189	+	1.57831i	0.0941232	+	0.184727i	0.933268	−	0.359181i	$-0.116944\pi$
$73$	0.804189	+	1.57831i	0.0941232	+	0.184727i	−0.839145	+	0.543908i	$0.816944\pi$
$74$	−5.71163	−	17.5786i	−0.663964	−	2.04347i
$75$		0			0
$76$		−	16.2568i		−	1.86479i
$77$	8.35541	+	1.87222i	0.952187	+	0.213359i
$78$		0			0
$79$	3.51271	−	2.55214i	0.395211	−	0.287138i	−0.372376	−	0.928082i	$-0.621457\pi$
$79$	3.51271	−	2.55214i	0.395211	−	0.287138i	0.767588	+	0.640944i	$0.221457\pi$
$80$	−7.84857	−	0.253115i	−0.877497	−	0.0282991i
$81$		0			0
$82$	−8.28320	+	1.31193i	−0.914726	+	0.144878i
$83$	8.18939	−	1.29707i	0.898902	−	0.142372i	0.310152	−	0.950687i	$-0.399620\pi$
$83$	8.18939	−	1.29707i	0.898902	−	0.142372i	0.588750	+	0.808315i	$0.299620\pi$
$84$		0			0
$85$	1.44418	+	1.54044i	0.156644	+	0.167084i
$86$	−10.9054	+	7.92326i	−1.17596	+	0.854388i
$87$		0			0
$88$	6.13664	+	14.2012i	0.654168	+	1.51385i
$89$			4.23092i			0.448477i	0.974534	+	0.224238i	$0.0719894\pi$
$89$			4.23092i			0.448477i	−0.974534	+	0.224238i	$0.928011\pi$
$90$		0			0
$91$	2.24084	+	6.89661i	0.234904	+	0.722961i
$92$	−0.263364	−	0.516882i	−0.0274576	−	0.0538886i
$93$		0			0
$94$	2.08075	+	1.51175i	0.214613	+	0.155926i
$95$	7.32735	+	5.69333i	0.751770	+	0.584124i
$96$		0			0
$97$	−2.25634	+	14.2460i	−0.229097	+	1.44646i	0.558109	+	0.829768i	$0.311527\pi$
$97$	−2.25634	+	14.2460i	−0.229097	+	1.44646i	−0.787205	+	0.616691i	$0.788473\pi$
$98$	−0.575755	+	0.575755i	−0.0581600	+	0.0581600i
$99$		0			0
$100$	12.5104	−	15.0719i	1.25104	−	1.50719i
$101$	−1.13747	−	1.56559i	−0.113182	−	0.155782i	0.748668	−	0.662946i	$-0.230694\pi$
$101$	−1.13747	−	1.56559i	−0.113182	−	0.155782i	−0.861850	+	0.507164i	$0.830694\pi$
$102$		0			0
$103$	1.53187	−	0.780525i	0.150939	−	0.0769075i	−0.376889	−	0.926258i	$-0.623006\pi$
$103$	1.53187	−	0.780525i	0.150939	−	0.0769075i	0.527829	+	0.849351i	$0.323006\pi$
$104$	−7.70094	+	10.5994i	−0.755139	+	1.03936i
$105$		0			0
$106$	9.53782	+	3.09903i	0.926395	+	0.301004i
$107$	−1.88816	+	3.70571i	−0.182535	+	0.358245i	−0.964083	−	0.265600i	$-0.914430\pi$
$107$	−1.88816	+	3.70571i	−0.182535	+	0.358245i	0.781549	+	0.623844i	$0.214430\pi$
$108$		0			0
$109$	3.22321			0.308728			0.154364	−	0.988014i	$-0.450667\pi$
$109$	3.22321			0.308728			0.154364	+	0.988014i	$0.450667\pi$
$110$	−17.4678	−	4.50997i	−1.66549	−	0.430009i
$111$		0			0
$112$	8.95489	+	1.41832i	0.846157	+	0.134018i
$113$	−5.06345	+	9.93758i	−0.476329	+	0.934849i	0.520391	+	0.853928i	$0.325786\pi$
$113$	−5.06345	+	9.93758i	−0.476329	+	0.934849i	−0.996721	+	0.0809210i	$0.974214\pi$
$114$		0			0
$115$	0.325204	+	0.0623134i	0.0303255	+	0.00581075i
$116$	15.9805	−	21.9953i	1.48375	−	2.04221i
$117$		0			0
$118$	−14.0491	−	7.15838i	−1.29333	−	0.658982i
$119$	−1.43299	−	1.97234i	−0.131362	−	0.180804i
$120$		0			0
$121$	2.04995	+	10.8073i	0.186359	+	0.982482i
$122$	16.3844	−	16.3844i	1.48337	−	1.48337i
$123$		0			0
$124$	−33.7647	+	10.9708i	−3.03216	+	0.985209i
$125$	2.41198	+	10.9171i	0.215734	+	0.976452i
$126$		0			0
$127$	0.371538	+	2.34580i	0.0329687	+	0.208156i	0.998674	−	0.0514856i	$-0.0163956\pi$
$127$	0.371538	+	2.34580i	0.0329687	+	0.208156i	−0.965705	+	0.259641i	$0.916396\pi$
$128$	−9.15495	−	17.9676i	−0.809191	−	1.58813i
$129$		0			0
$130$	−4.25043	−	14.6751i	−0.372788	−	1.28709i
$131$		−	3.12466i		−	0.273003i	−0.990640	−	0.136501i	$-0.956414\pi$
$131$		−	3.12466i		−	0.273003i	0.990640	−	0.136501i	$-0.0435858\pi$
$132$		0			0
$133$	−7.57567	−	7.57567i	−0.656894	−	0.656894i
$134$	8.19674	−	5.95528i	0.708090	−	0.514458i
$135$		0			0
$136$	1.36114	−	4.18915i	0.116716	−	0.359216i
$137$	−16.3323	+	2.58679i	−1.39537	+	0.221004i	−0.808412	−	0.588617i	$-0.799673\pi$
$137$	−16.3323	+	2.58679i	−1.39537	+	0.221004i	−0.586953	+	0.809621i	$0.699673\pi$
$138$		0			0
$139$	−1.33510	+	4.10901i	−0.113242	+	0.348522i	−0.991576	−	0.129524i	$-0.958655\pi$
$139$	−1.33510	+	4.10901i	−0.113242	+	0.348522i	0.878335	+	0.478046i	$0.158655\pi$
$140$	−16.4986	+	15.4677i	−1.39439	+	1.30726i
$141$		0			0
$142$	2.17775	+	2.17775i	0.182753	+	0.182753i
$143$	−6.99103	+	6.15696i	−0.584619	+	0.514871i
$144$		0			0
$145$	4.31724	+	14.9058i	0.358527	+	1.23786i
$146$	1.33157	+	4.09814i	0.110201	+	0.339164i
$147$		0			0
$148$	−4.65640	−	29.3994i	−0.382754	−	2.41661i
$149$	6.83188	+	4.96365i	0.559689	+	0.406638i	0.831345	−	0.555756i	$-0.187571\pi$
$149$	6.83188	+	4.96365i	0.559689	+	0.406638i	−0.271656	+	0.962394i	$0.587571\pi$
$150$		0			0
$151$	11.3483	−	3.68729i	0.923513	−	0.300068i	0.191606	−	0.981472i	$-0.438630\pi$
$151$	11.3483	−	3.68729i	0.923513	−	0.300068i	0.731907	+	0.681404i	$0.238630\pi$
$152$	3.02806	−	19.1184i	0.245608	−	1.55071i
$153$		0			0
$154$	19.3626	+	7.67785i	1.56028	+	0.618699i
$155$	6.87999	−	19.0607i	0.552614	−	1.53099i
$156$		0			0
$157$	−1.21312	−	0.618117i	−0.0968177	−	0.0493311i	0.404911	−	0.914356i	$-0.367302\pi$
$157$	−1.21312	−	0.618117i	−0.0968177	−	0.0493311i	−0.501729	+	0.865025i	$0.667302\pi$
$158$	9.41098	−	4.79514i	0.748698	−	0.381481i
$159$		0			0
$160$	1.72657	+	0.330833i	0.136497	+	0.0261546i
$161$	−0.363594	−	0.118139i	−0.0286552	−	0.00931064i
$162$		0			0
$163$	22.6610	+	3.58914i	1.77494	+	0.281123i	0.956131	−	0.292939i	$-0.0946333\pi$
$163$	22.6610	+	3.58914i	1.77494	+	0.281123i	0.818812	+	0.574062i	$0.194633\pi$
$164$	−13.5057			−1.05462
$165$		0			0
$166$	20.1698			1.56548
$167$	−14.1836	−	2.24646i	−1.09756	−	0.173836i	−0.418714	−	0.908118i	$-0.637519\pi$
$167$	−14.1836	−	2.24646i	−1.09756	−	0.173836i	−0.678845	+	0.734282i	$0.737519\pi$
$168$		0			0
$169$	4.86053	+	1.57928i	0.373887	+	0.121483i
$170$	2.88365	+	4.25069i	0.221166	+	0.326013i
$171$		0			0
$172$	−19.3422	+	9.85535i	−1.47483	+	0.751464i
$173$	19.8708	+	10.1247i	1.51075	+	0.769766i	0.996150	−	0.0876641i	$-0.0279402\pi$
$173$	19.8708	+	10.1247i	1.51075	+	0.769766i	0.514601	+	0.857430i	$0.327940\pi$
$174$		0			0
$175$	−1.19366	−	12.8533i	−0.0902321	−	0.971618i
$176$	2.89071	+	11.2829i	0.217896	+	0.850484i
$177$		0			0
$178$	−1.61004	+	10.1654i	−0.120678	+	0.761928i
$179$	−4.15441	+	1.34985i	−0.310516	+	0.100893i	−0.460129	−	0.887852i	$-0.652197\pi$
$179$	−4.15441	+	1.34985i	−0.310516	+	0.100893i	0.149614	+	0.988745i	$0.452197\pi$
$180$		0			0
$181$	−7.63694	−	5.54857i	−0.567650	−	0.412422i	0.266601	−	0.963807i	$-0.414099\pi$
$181$	−7.63694	−	5.54857i	−0.567650	−	0.412422i	−0.834251	+	0.551385i	$0.814099\pi$
$182$	2.75950	+	17.4228i	0.204548	+	1.29147i
$183$		0			0
$184$	−0.213446	−	0.656920i	−0.0157355	−	0.0484287i
$185$	14.8817	+	8.19725i	1.09413	+	0.602674i
$186$		0			0
$187$	1.59568	−	2.69495i	0.116688	−	0.197074i
$188$	2.92879	+	2.92879i	0.213604	+	0.213604i
$189$		0			0
$190$	15.4384	+	16.4674i	1.12002	+	1.19467i
$191$	2.00020	−	6.15597i	0.144729	−	0.445430i	−0.852247	−	0.523140i	$-0.824761\pi$
$191$	2.00020	−	6.15597i	0.144729	−	0.445430i	0.996976	+	0.0777092i	$0.0247606\pi$
$192$		0			0
$193$	−0.994245	+	0.157473i	−0.0715674	+	0.0113352i	−0.192115	−	0.981372i	$-0.561535\pi$
$193$	−0.994245	+	0.157473i	−0.0715674	+	0.0113352i	0.120548	+	0.992707i	$0.461535\pi$
$194$	−10.8424	+	33.3693i	−0.778436	+	2.39578i
$195$		0			0
$196$	−1.06084	+	0.770746i	−0.0757744	+	0.0550533i
$197$	17.3425	+	17.3425i	1.23560	+	1.23560i	0.961781	+	0.273821i	$0.0882874\pi$
$197$	17.3425	+	17.3425i	1.23560	+	1.23560i	0.273821	+	0.961781i	$0.411713\pi$
$198$		0			0
$199$			3.25580i			0.230797i	0.993319	+	0.115399i	$0.0368146\pi$
$199$			3.25580i			0.230797i	−0.993319	+	0.115399i	$0.963185\pi$
$200$	17.5198	−	15.3946i	1.23884	−	1.08856i
$201$		0			0
$202$	−2.13715	−	4.19440i	−0.150370	−	0.295117i
$203$	−2.80288	−	17.6967i	−0.196723	−	1.24206i
$204$		0			0
$205$	4.72987	−	6.08736i	0.330348	−	0.425160i
$206$	3.97755	−	1.29238i	0.277129	−	0.0900447i
$207$		0			0
$208$	−6.97487	+	6.97487i	−0.483621	+	0.483621i
$209$	5.07327	−	12.7942i	0.350926	−	0.884991i
$210$		0			0
$211$	−14.6014	−	20.0971i	−1.00520	−	1.38354i	−0.922080	−	0.387000i	$-0.873511\pi$
$211$	−14.6014	−	20.0971i	−1.00520	−	1.38354i	−0.0831208	−	0.996539i	$-0.526489\pi$
$212$	14.3901	+	7.33212i	0.988316	+	0.503572i
$213$		0			0
$214$	−5.94674	+	8.18498i	−0.406511	+	0.559514i
$215$	2.33183	−	12.1695i	0.159029	−	0.829951i
$216$		0			0
$217$	−10.6219	+	20.8467i	−0.721064	+	1.41517i
$218$	7.74423	+	1.22657i	0.524505	+	0.0830735i
$219$		0			0
$220$	−26.6480	−	11.5741i	−1.79661	−	0.780327i
$221$	2.65237			0.178418
$222$		0			0
$223$	−8.89368	+	17.4548i	−0.595565	+	1.16886i	0.374774	+	0.927116i	$0.377720\pi$
$223$	−8.89368	+	17.4548i	−0.595565	+	1.16886i	−0.970339	+	0.241746i	$0.922280\pi$
$224$	−1.93038	−	0.627220i	−0.128979	−	0.0419079i
$225$		0			0
$226$	−15.9473	+	21.9496i	−1.06080	+	1.46007i
$227$	−0.911427	+	0.464395i	−0.0604935	+	0.0308230i	−0.483976	−	0.875081i	$-0.660808\pi$
$227$	−0.911427	+	0.464395i	−0.0604935	+	0.0308230i	0.423482	+	0.905904i	$0.360808\pi$
$228$		0			0
$229$	−0.0598653	−	0.0823975i	−0.00395601	−	0.00544498i	0.807034	−	0.590504i	$-0.201071\pi$
$229$	−0.0598653	−	0.0823975i	−0.00395601	−	0.00544498i	−0.810990	+	0.585059i	$0.801071\pi$
$230$	0.757637	+	0.273470i	0.0499571	+	0.0180321i
$231$		0			0
$232$	22.8903	−	22.8903i	1.50282	−	1.50282i
$233$	−3.34771	+	21.1366i	−0.219316	+	1.38470i	0.594740	+	0.803918i	$0.297255\pi$
$233$	−3.34771	+	21.1366i	−0.219316	+	1.38470i	−0.814056	+	0.580786i	$0.802745\pi$
$234$		0			0
$235$	−2.34577	+	0.294379i	−0.153021	+	0.0192032i
$236$	−20.5431	−	14.9254i	−1.33724	−	0.971562i
$237$		0			0
$238$	−2.69240	−	5.28413i	−0.174522	−	0.342519i
$239$	−2.67723	−	8.23966i	−0.173175	−	0.532979i	0.826370	−	0.563128i	$-0.190402\pi$
$239$	−2.67723	−	8.23966i	−0.173175	−	0.532979i	−0.999545	+	0.0301483i	$0.990402\pi$
$240$		0			0
$241$		−	10.6492i		−	0.685976i	−0.939340	−	0.342988i	$-0.888561\pi$
$241$		−	10.6492i		−	0.685976i	0.939340	−	0.342988i	$-0.111439\pi$
$242$	0.812677	+	26.7462i	0.0522408	+	1.71931i
$243$		0			0
$244$	30.1886	−	21.9333i	1.93263	−	1.40414i
$245$	0.0241252	−	0.748071i	0.00154130	−	0.0477925i
$246$		0			0
$247$	11.5124	−	1.82339i	0.732518	−	0.116020i
$248$	−41.7515	+	6.61279i	−2.65123	+	0.419913i
$249$		0			0
$250$	1.64072	+	27.1477i	0.103769	+	1.71697i
$251$	−7.59915	+	5.52110i	−0.479654	+	0.348489i	−0.801192	−	0.598408i	$-0.795800\pi$
$251$	−7.59915	+	5.52110i	−0.479654	+	0.348489i	0.321538	+	0.946897i	$0.395800\pi$
$252$		0			0
$253$	−0.0459651	−	0.488975i	−0.00288980	−	0.0307416i
$254$			5.77750i			0.362513i
$255$		0			0
$256$	−9.63584	−	29.6561i	−0.602240	−	1.85350i
$257$	−8.37149	−	16.4300i	−0.522199	−	1.02487i	−0.990004	−	0.141042i	$-0.954955\pi$
$257$	−8.37149	−	16.4300i	−0.522199	−	1.02487i	0.467804	−	0.883832i	$-0.345045\pi$
$258$		0			0
$259$	−15.8700	−	11.5302i	−0.986111	−	0.716451i
$260$	−3.06368	−	24.4130i	−0.190001	−	1.51403i
$261$		0			0
$262$	1.18906	−	7.50744i	0.0734605	−	0.463811i
$263$	−11.8928	+	11.8928i	−0.733342	+	0.733342i	−0.971280	−	0.237938i	$-0.923528\pi$
$263$	−11.8928	+	11.8928i	−0.733342	+	0.733342i	0.237938	+	0.971280i	$0.423528\pi$
$264$		0			0
$265$	−8.34434	+	3.91817i	−0.512589	+	0.240691i
$266$	−15.3188	−	21.0845i	−0.939254	−	1.29277i
$267$		0			0
$268$	14.5380	−	7.40747i	0.888049	−	0.452483i
$269$	16.7264	−	23.0219i	1.01983	−	1.40367i	0.107502	−	0.994205i	$-0.465715\pi$
$269$	16.7264	−	23.0219i	1.01983	−	1.40367i	0.912325	−	0.409467i	$-0.134285\pi$
$270$		0			0
$271$	−28.2295	−	9.17232i	−1.71482	−	0.557179i	−0.723696	−	0.690118i	$-0.757558\pi$
$271$	−28.2295	−	9.17232i	−1.71482	−	0.557179i	−0.991124	+	0.132939i	$0.957558\pi$
$272$	1.50554	−	2.95479i	0.0912868	−	0.179160i
$273$		0			0
$274$	−40.2251			−2.43009
$275$	14.5492	−	7.95749i	0.877348	−	0.479855i
$276$		0			0
$277$	12.2668	+	1.94287i	0.737041	+	0.116736i	0.513658	−	0.857995i	$-0.328290\pi$
$277$	12.2668	+	1.94287i	0.737041	+	0.116736i	0.223383	+	0.974731i	$0.428290\pi$
$278$	−4.77141	+	9.36443i	−0.286170	+	0.561641i
$279$		0			0
$280$	−22.2838	+	15.1173i	−1.33171	+	0.903430i
$281$	−12.8578	+	17.6972i	−0.767032	+	1.05573i	0.229564	+	0.973294i	$0.426270\pi$
$281$	−12.8578	+	17.6972i	−0.767032	+	1.05573i	−0.996596	+	0.0824357i	$0.973730\pi$
$282$		0			0
$283$	24.2332	+	12.3474i	1.44051	+	0.733978i	0.987514	−	0.157532i	$-0.0503538\pi$
$283$	24.2332	+	12.3474i	1.44051	+	0.733978i	0.453000	+	0.891511i	$0.350354\pi$
$284$	2.91529	+	4.01255i	0.172991	+	0.238101i
$285$		0			0
$286$	−19.1399	+	12.1326i	−1.13177	+	0.717416i
$287$	−6.29366	+	6.29366i	−0.371503	+	0.371503i
$288$		0			0
$289$	15.3199	−	4.97773i	0.901170	−	0.292808i
$290$	4.70051	+	37.4562i	0.276024	+	2.19950i
$291$		0			0
$292$	1.08556	+	6.85394i	0.0635274	+	0.401096i
$293$	−9.13077	−	17.9201i	−0.533425	−	1.04691i	−0.987746	−	0.156068i	$-0.950118\pi$
$293$	−9.13077	−	17.9201i	−0.533425	−	1.04691i	0.454321	−	0.890838i	$-0.349882\pi$
$294$		0			0
$295$	13.9217	−	4.03220i	0.810551	−	0.234764i
$296$		−	35.4416i		−	2.06000i
$297$		0			0
$298$	14.5257	+	14.5257i	0.841450	+	0.841450i
$299$	0.336495	−	0.244478i	0.0194600	−	0.0141385i
$300$		0			0
$301$	−4.42087	+	13.6060i	−0.254815	+	0.784239i
$302$	28.6691	−	4.54074i	1.64972	−	0.261290i
$303$		0			0
$304$	4.50340	−	13.8600i	0.258288	−	0.794927i
$305$	−0.686536	+	21.2880i	−0.0393109	+	1.21895i
$306$		0			0
$307$	14.6921	+	14.6921i	0.838520	+	0.838520i	0.988664	−	0.150144i	$-0.0479738\pi$
$307$	14.6921	+	14.6921i	0.838520	+	0.838520i	−0.150144	+	0.988664i	$0.547974\pi$
$308$	28.8638	+	17.0903i	1.64467	+	0.973810i
$309$		0			0
$310$	23.7835	−	43.1779i	1.35081	−	2.45234i
$311$	−7.19358	−	22.1396i	−0.407911	−	1.25542i	−0.918440	−	0.395560i	$-0.870551\pi$
$311$	−7.19358	−	22.1396i	−0.407911	−	1.25542i	0.510530	−	0.859860i	$-0.329449\pi$
$312$		0			0
$313$	2.19289	+	13.8454i	0.123950	+	0.782587i	0.968847	+	0.247659i	$0.0796612\pi$
$313$	2.19289	+	13.8454i	0.123950	+	0.782587i	−0.844898	+	0.534928i	$0.820339\pi$
$314$	−2.67948	−	1.94676i	−0.151212	−	0.109862i
$315$		0			0
$316$	16.1771	−	5.25626i	0.910032	−	0.295687i
$317$	−4.61482	+	29.1369i	−0.259194	+	1.63649i	0.423580	+	0.905859i	$0.360773\pi$
$317$	−4.61482	+	29.1369i	−0.259194	+	1.63649i	−0.682774	+	0.730630i	$0.739227\pi$
$318$		0			0
$319$	19.4408	−	12.3233i	1.08847	−	0.689972i
$320$	18.7949	+	6.78404i	1.05066	+	0.379239i
$321$		0			0
$322$	−0.828629	−	0.422208i	−0.0461777	−	0.0235287i
$323$	−3.49158	+	1.77905i	−0.194277	+	0.0989889i
$324$		0			0
$325$	12.0765	+	7.16885i	0.669882	+	0.397656i
$326$	53.0803	+	17.2468i	2.93985	+	0.955215i
$327$		0			0
$328$	−15.8830	−	2.51563i	−0.876994	−	0.138902i
$329$	2.72962			0.150489
$330$		0			0
$331$	2.18560			0.120131			0.0600657	−	0.998194i	$-0.480869\pi$
$331$	2.18560			0.120131			0.0600657	+	0.998194i	$0.480869\pi$
$332$	32.0819	+	5.08128i	1.76072	+	0.278871i
$333$		0			0
$334$	−33.2232	−	10.7949i	−1.81789	−	0.590670i
$335$	−1.75265	+	9.14681i	−0.0957573	+	0.499743i
$336$		0			0
$337$	−1.60560	+	0.818095i	−0.0874627	+	0.0445645i	−0.497175	−	0.867650i	$-0.665629\pi$
$337$	−1.60560	+	0.818095i	−0.0874627	+	0.0445645i	0.409712	+	0.912215i	$0.365629\pi$
$338$	11.0771	+	5.64408i	0.602516	+	0.306997i
$339$		0			0
$340$	3.51587	+	7.48759i	0.190675	+	0.406072i
$341$	−29.9966	−	1.90289i	−1.62441	−	0.103047i
$342$		0			0
$343$	−2.96227	+	18.7031i	−0.159948	+	1.00987i
$344$	−24.5826	+	7.98736i	−1.32540	+	0.430650i
$345$		0			0
$346$	43.8896	+	31.8877i	2.35952	+	1.71429i
$347$	−3.35900	−	21.2079i	−0.180321	−	1.13850i	−0.897305	−	0.441411i	$-0.854478\pi$
$347$	−3.35900	−	21.2079i	−0.180321	−	1.13850i	0.716984	−	0.697090i	$-0.245522\pi$
$348$		0			0
$349$	−3.29300	−	10.1348i	−0.176270	−	0.542505i	0.823419	−	0.567434i	$-0.192064\pi$
$349$	−3.29300	−	10.1348i	−0.176270	−	0.542505i	−0.999689	+	0.0249295i	$0.992064\pi$
$350$	2.02327	−	31.3361i	0.108148	−	1.67498i
$351$		0			0
$352$	−0.244037	−	2.59606i	−0.0130072	−	0.138370i
$353$	7.73857	+	7.73857i	0.411883	+	0.411883i	0.882394	−	0.470511i	$-0.155931\pi$
$353$	7.73857	+	7.73857i	0.411883	+	0.411883i	−0.470511	+	0.882394i	$0.655931\pi$
$354$		0			0
$355$	−2.82952	−	0.0912516i	−0.150175	−	0.00484313i
$356$	−5.12185	+	15.7634i	−0.271457	+	0.835460i
$357$		0			0
$358$	−10.4952	+	1.66228i	−0.554691	+	0.0878544i
$359$	1.01178	−	3.11394i	0.0533997	−	0.164347i	−0.920800	−	0.390035i	$-0.872463\pi$
$359$	1.01178	−	3.11394i	0.0533997	−	0.164347i	0.974200	+	0.225688i	$0.0724629\pi$
$360$		0			0
$361$	1.43940	−	1.04578i	0.0757578	−	0.0550412i
$362$	−16.2374	−	16.2374i	−0.853418	−	0.853418i
$363$		0			0
$364$			28.4079i			1.48898i
$365$	−3.46941	−	1.91104i	−0.181597	−	0.100029i
$366$		0			0
$367$	−8.27615	−	16.2428i	−0.432011	−	0.847870i	−0.999697	−	0.0246243i	$-0.992161\pi$
$367$	−8.27615	−	16.2428i	−0.432011	−	0.847870i	0.567686	−	0.823246i	$-0.307839\pi$
$368$	−0.0813513	−	0.513632i	−0.00424073	−	0.0267749i
$369$		0			0
$370$	32.6361	+	25.3582i	1.69667	+	1.31831i
$371$	10.1225	−	3.28901i	0.525536	−	0.170757i
$372$		0			0
$373$	−12.4917	+	12.4917i	−0.646795	+	0.646795i	−0.952217	−	0.305422i	$-0.901202\pi$
$373$	−12.4917	+	12.4917i	−0.646795	+	0.646795i	0.305422	+	0.952217i	$0.401202\pi$
$374$	4.85939	−	5.86777i	0.251273	−	0.303415i
$375$		0			0
$376$	2.89879	+	3.98984i	0.149494	+	0.205760i
$377$	17.3686	+	8.84972i	0.894526	+	0.455784i
$378$		0			0
$379$	12.9685	−	17.8496i	0.666146	−	0.916872i	−0.333519	−	0.942743i	$-0.608236\pi$
$379$	12.9685	−	17.8496i	0.666146	−	0.916872i	0.999665	+	0.0258717i	$0.00823614\pi$
$380$	20.4078	+	30.0823i	1.04690	+	1.54319i
$381$		0			0
$382$	7.14836	−	14.0294i	0.365742	−	0.717809i
$383$	19.4473	+	3.08015i	0.993712	+	0.157389i	0.632056	−	0.774923i	$-0.282211\pi$
$383$	19.4473	+	3.08015i	0.993712	+	0.157389i	0.361656	+	0.932311i	$0.382211\pi$
$384$		0			0
$385$	−17.8115	+	7.02440i	−0.907756	+	0.357997i
$386$	−2.44874			−0.124638
$387$		0			0
$388$	−25.6524	+	50.3457i	−1.30230	+	2.55591i
$389$	−16.2827	−	5.29057i	−0.825565	−	0.268242i	−0.134389	−	0.990929i	$-0.542907\pi$
$389$	−16.2827	−	5.29057i	−0.825565	−	0.268242i	−0.691176	+	0.722686i	$0.742907\pi$
$390$		0			0
$391$	−0.0821929	+	0.113129i	−0.00415667	+	0.00572117i
$392$	−1.39113	+	0.708818i	−0.0702629	+	0.0358007i
$393$		0			0
$394$	35.0683	+	48.2673i	1.76671	+	2.43167i
$395$	−3.29629	+	9.13221i	−0.165854	+	0.459491i
$396$		0			0
$397$	5.24887	−	5.24887i	0.263433	−	0.263433i	−0.563014	−	0.826447i	$-0.690358\pi$
$397$	5.24887	−	5.24887i	0.263433	−	0.263433i	0.826447	+	0.563014i	$0.190358\pi$
$398$	−1.23896	+	7.82252i	−0.0621037	+	0.392107i
$399$		0			0
$400$	14.8411	−	9.38420i	0.742053	−	0.469210i
$401$	9.93091	+	7.21523i	0.495926	+	0.360311i	0.807459	−	0.589924i	$-0.200842\pi$
$401$	9.93091	+	7.21523i	0.495926	+	0.360311i	−0.311533	+	0.950235i	$0.600842\pi$
$402$		0			0
$403$	−11.5562	−	22.6803i	−0.575655	−	1.12979i
$404$	−2.34267	−	7.21000i	−0.116552	−	0.358711i
$405$		0			0
$406$		−	43.5854i		−	2.16311i
$407$	5.51006	−	24.5905i	0.273124	−	1.21891i
$408$		0			0
$409$	−21.6485	+	15.7286i	−1.07045	+	0.777727i	−0.975993	−	0.217802i	$-0.930111\pi$
$409$	−21.6485	+	15.7286i	−1.07045	+	0.777727i	−0.0944563	+	0.995529i	$0.530111\pi$
$410$	13.6807	−	12.8258i	0.675640	−	0.633423i
$411$		0			0
$412$	6.65226	−	1.05361i	0.327733	−	0.0519079i
$413$	−16.5283	+	2.61782i	−0.813304	+	0.128815i
$414$		0			0
$415$	−13.5257	+	12.6806i	−0.663952	+	0.622465i
$416$	1.78651	−	1.29798i	0.0875910	−	0.0636386i
$417$		0			0
$418$	17.0580	−	28.8092i	0.834332	−	1.40911i
$419$		−	14.2401i		−	0.695676i	−0.937555	−	0.347838i	$-0.886916\pi$
$419$		−	14.2401i		−	0.695676i	0.937555	−	0.347838i	$-0.113084\pi$
$420$		0			0
$421$	−2.13413	−	6.56818i	−0.104011	−	0.320113i	0.885486	−	0.464666i	$-0.153826\pi$
$421$	−2.13413	−	6.56818i	−0.104011	−	0.320113i	−0.989497	+	0.144553i	$0.953826\pi$
$422$	−27.4341	−	53.8425i	−1.33547	−	2.62101i
$423$		0			0
$424$	15.5574	+	11.3031i	0.755532	+	0.548926i
$425$	−4.60614	−	1.03755i	−0.223430	−	0.0503288i
$426$		0			0
$427$	3.84696	−	24.2888i	0.186168	−	1.17542i
$428$	−11.5209	+	11.5209i	−0.556882	+	0.556882i
$429$		0			0
$430$	10.2335	−	28.3515i	0.493505	−	1.36723i
$431$	4.19638	+	5.77582i	0.202132	+	0.278211i	0.898034	−	0.439926i	$-0.144995\pi$
$431$	4.19638	+	5.77582i	0.202132	+	0.278211i	−0.695902	+	0.718137i	$0.744995\pi$
$432$		0			0
$433$	14.9712	−	7.62822i	0.719471	−	0.366589i	−0.0556084	−	0.998453i	$-0.517710\pi$
$433$	14.9712	−	7.62822i	0.719471	−	0.366589i	0.775079	+	0.631864i	$0.217710\pi$
$434$	−33.4538	+	46.0451i	−1.60583	+	2.21024i
$435$		0			0
$436$	12.0089	+	3.90194i	0.575124	+	0.186869i
$437$	−0.278981	+	0.547531i	−0.0133455	+	0.0261920i
$438$		0			0
$439$	−0.772934			−0.0368901			−0.0184451	−	0.999830i	$-0.505872\pi$
$439$	−0.772934			−0.0368901			−0.0184451	+	0.999830i	$0.505872\pi$
$440$	−29.1828	−	18.5750i	−1.39123	−	0.885527i
$441$		0			0
$442$	6.37271	+	1.00934i	0.303119	+	0.0480093i
$443$	8.53040	−	16.7419i	0.405292	−	0.795430i	−0.594672	−	0.803968i	$-0.702718\pi$
$443$	8.53040	−	16.7419i	0.405292	−	0.795430i	0.999964	+	0.00853887i	$0.00271804\pi$
$444$		0			0
$445$	−5.31122	−	7.82908i	−0.251776	−	0.371134i
$446$	−28.0106	+	38.5533i	−1.32634	+	1.82555i
$447$		0			0
$448$	−20.5560	−	10.4738i	−0.971179	−	0.494840i
$449$	−0.419317	−	0.577140i	−0.0197888	−	0.0272369i	0.799008	−	0.601320i	$-0.205358\pi$
$449$	−0.419317	−	0.577140i	−0.0197888	−	0.0272369i	−0.818797	+	0.574084i	$0.805358\pi$
$450$		0			0
$451$	−10.6291	−	4.21474i	−0.500502	−	0.198464i
$452$	−30.8954	+	30.8954i	−1.45320	+	1.45320i
$453$		0			0
$454$	−2.36655	+	0.768940i	−0.111068	+	0.0360882i
$455$	−12.8041	−	9.94877i	−0.600266	−	0.466405i
$456$		0			0
$457$	3.02622	+	19.1068i	0.141561	+	0.893780i	0.951586	+	0.307384i	$0.0994536\pi$
$457$	3.02622	+	19.1068i	0.141561	+	0.893780i	−0.810025	+	0.586396i	$0.800546\pi$
$458$	−0.112479	−	0.220753i	−0.00525581	−	0.0103151i
$459$		0			0
$460$	1.13620	+	0.625849i	0.0529756	+	0.0291804i
$461$		−	36.5277i		−	1.70126i	−0.525761	−	0.850632i	$-0.676219\pi$
$461$		−	36.5277i		−	1.70126i	0.525761	−	0.850632i	$-0.323781\pi$
$462$		0			0
$463$	−17.1422	−	17.1422i	−0.796664	−	0.796664i	0.185904	−	0.982568i	$-0.440479\pi$
$463$	−17.1422	−	17.1422i	−0.796664	−	0.796664i	−0.982568	+	0.185904i	$0.940479\pi$
$464$	19.7175	−	14.3256i	0.915361	−	0.665049i
$465$		0			0
$466$	−16.0867	+	49.5097i	−0.745201	+	2.29349i
$467$	14.6373	−	2.31832i	0.677333	−	0.107279i	0.191715	−	0.981451i	$-0.438595\pi$
$467$	14.6373	−	2.31832i	0.677333	−	0.107279i	0.485617	+	0.874172i	$0.338595\pi$
$468$		0			0
$469$	3.32281	−	10.2266i	0.153433	−	0.472219i
$470$	−5.74807	−	0.185374i	−0.265139	−	0.00855068i
$471$		0			0
$472$	−21.3791	−	21.3791i	−0.984051	−	0.984051i
$473$	−18.2979	+	1.72006i	−0.841340	+	0.0790885i
$474$		0			0
$475$	−20.7059	−	1.33691i	−0.950050	−	0.0613417i
$476$	−2.95131	−	9.08320i	−0.135273	−	0.416328i
$477$		0			0
$478$	−3.29689	−	20.8157i	−0.150796	−	0.952090i
$479$	22.3176	+	16.2146i	1.01971	+	0.740866i	0.966224	−	0.257702i	$-0.0829653\pi$
$479$	22.3176	+	16.2146i	1.01971	+	0.740866i	0.0534905	+	0.998568i	$0.482965\pi$
$480$		0			0
$481$	20.2972	−	6.59495i	0.925471	−	0.300704i
$482$	4.05246	−	25.5862i	0.184585	−	1.16542i
$483$		0			0
$484$	−5.44540	+	42.7471i	−0.247518	+	1.94305i
$485$	−13.7082	−	29.1938i	−0.622459	−	1.32562i
$486$		0			0
$487$	−34.6563	−	17.6583i	−1.57043	−	0.800174i	−0.570650	−	0.821193i	$-0.693309\pi$
$487$	−34.6563	−	17.6583i	−1.57043	−	0.800174i	−0.999779	+	0.0210198i	$0.993309\pi$
$488$	39.5879	−	20.1710i	1.79206	−	0.913099i
$489$		0			0
$490$	0.342636	−	1.78817i	0.0154787	−	0.0807811i
$491$	−17.8811	−	5.80992i	−0.806962	−	0.262198i	−0.123652	−	0.992326i	$-0.539461\pi$
$491$	−17.8811	−	5.80992i	−0.806962	−	0.262198i	−0.683311	+	0.730128i	$0.739461\pi$
$492$		0			0
$493$	−6.47287	−	1.02520i	−0.291523	−	0.0461728i
$494$	28.3541			1.27571
$495$		0			0
$496$	−31.8258			−1.42902
$497$	3.22837	+	0.511323i	0.144812	+	0.0229360i
$498$		0			0
$499$	4.98327	+	1.61916i	0.223082	+	0.0724837i	0.418425	−	0.908251i	$-0.362582\pi$
$499$	4.98327	+	1.61916i	0.223082	+	0.0724837i	−0.195343	+	0.980735i	$0.562582\pi$
$500$	−4.22946	+	43.5943i	−0.189147	+	1.94960i
$501$		0			0
$502$	−20.3590	+	10.3734i	−0.908668	+	0.462990i
$503$	−11.7545	−	5.98921i	−0.524106	−	0.267046i	0.171858	−	0.985122i	$-0.445023\pi$
$503$	−11.7545	−	5.98921i	−0.524106	−	0.267046i	−0.695965	+	0.718076i	$0.745023\pi$
$504$		0			0
$505$	4.07015	+	1.46913i	0.181119	+	0.0653754i
$506$	0.0756375	−	1.19232i	0.00336250	−	0.0530053i
$507$		0			0
$508$	−1.45550	+	9.18967i	−0.0645774	+	0.407726i
$509$	−5.32193	+	1.72920i	−0.235890	+	0.0766454i	−0.424577	−	0.905392i	$-0.639577\pi$
$509$	−5.32193	+	1.72920i	−0.235890	+	0.0766454i	0.188686	+	0.982037i	$0.439577\pi$
$510$		0			0
$511$	3.69980	+	2.68806i	0.163669	+	0.118913i
$512$	−5.55696	−	35.0853i	−0.245585	−	1.55056i
$513$		0			0
$514$	−13.8614	−	42.6611i	−0.611401	−	1.88170i
$515$	−1.85481	+	3.36732i	−0.0817327	+	0.148382i
$516$		0			0
$517$	1.39098	+	3.21895i	0.0611751	+	0.141569i
$518$	−33.7421	−	33.7421i	−1.48254	−	1.48254i
$519$		0			0
$520$	0.944304	−	29.2809i	0.0414105	−	1.28405i
$521$	−5.89515	+	18.1434i	−0.258271	+	0.794877i	0.734896	+	0.678179i	$0.237231\pi$
$521$	−5.89515	+	18.1434i	−0.258271	+	0.794877i	−0.993168	+	0.116697i	$0.962769\pi$
$522$		0			0
$523$	−34.6664	+	5.49061i	−1.51585	+	0.240088i	−0.858233	−	0.513261i	$-0.828437\pi$
$523$	−34.6664	+	5.49061i	−1.51585	+	0.240088i	−0.657621	+	0.753349i	$0.728437\pi$
$524$	3.78263	−	11.6417i	0.165245	−	0.508572i
$525$		0			0
$526$	−33.0999	+	24.0485i	−1.44322	+	1.04856i
$527$	6.05128	+	6.05128i	0.263598	+	0.263598i
$528$		0			0
$529$		−	22.9781i		−	0.999047i
$530$	−21.5395	+	6.23859i	−0.935616	+	0.270987i
$531$		0			0
$532$	−19.0542	−	37.3961i	−0.826106	−	1.62132i
$533$	−1.51482	−	9.56421i	−0.0656143	−	0.414272i
$534$		0			0
$535$	−1.15799	−	9.22747i	−0.0500642	−	0.398938i
$536$	18.4767	−	6.00346i	0.798074	−	0.259310i
$537$		0			0
$538$	48.9484	−	48.9484i	2.11031	−	2.11031i
$539$	−1.07541	+	0.275523i	−0.0463213	+	0.0118676i
$540$		0			0
$541$	−1.49345	−	2.05556i	−0.0642084	−	0.0883752i	0.775705	−	0.631095i	$-0.217394\pi$
$541$	−1.49345	−	2.05556i	−0.0642084	−	0.0883752i	−0.839914	+	0.542720i	$0.817394\pi$
$542$	−64.3350	−	32.7803i	−2.76342	−	1.40803i
$543$		0			0
$544$	−0.436376	+	0.600621i	−0.0187095	+	0.0257514i
$545$	−5.96437	+	4.04621i	−0.255486	+	0.173321i
$546$		0			0
$547$	6.73017	−	13.2087i	0.287761	−	0.564764i	−0.701195	−	0.712969i	$-0.747350\pi$
$547$	6.73017	−	13.2087i	0.287761	−	0.564764i	0.988957	+	0.148206i	$0.0473498\pi$
$548$	−63.9819	−	10.1337i	−2.73317	−	0.432892i
$549$		0			0
$550$	37.9846	−	13.5824i	1.61967	−	0.579157i
$551$	−28.7998			−1.22691
$552$		0			0
$553$	5.08910	−	9.98792i	0.216411	−	0.424730i
$554$	28.7334	+	9.33604i	1.22076	+	0.396650i
$555$		0			0
$556$	−9.94853	+	13.6930i	−0.421912	+	0.580712i
$557$	−11.3704	+	5.79353i	−0.481781	+	0.245480i	−0.677974	−	0.735086i	$-0.737142\pi$
$557$	−11.3704	+	5.79353i	−0.481781	+	0.245480i	0.196194	+	0.980565i	$0.437142\pi$
$558$		0			0
$559$	−9.14861	−	12.5920i	−0.386945	−	0.532584i
$560$	−18.3510	+	8.61687i	−0.775470	+	0.364129i
$561$		0			0
$562$	−37.6272	+	37.6272i	−1.58721	+	1.58721i
$563$	−5.24553	+	33.1190i	−0.221073	+	1.39580i	0.588367	+	0.808594i	$0.299771\pi$
$563$	−5.24553	+	33.1190i	−0.221073	+	1.39580i	−0.809439	+	0.587204i	$0.800229\pi$
$564$		0			0
$565$	−3.10537	−	24.7452i	−0.130644	−	1.04104i
$566$	53.5250	+	38.8882i	2.24982	+	1.63459i
$567$		0			0
$568$	2.68105	+	5.26186i	0.112494	+	0.220783i
$569$	2.57065	+	7.91165i	0.107767	+	0.331674i	0.990370	−	0.138446i	$-0.0442107\pi$
$569$	2.57065	+	7.91165i	0.107767	+	0.331674i	−0.882603	+	0.470120i	$0.844211\pi$
$570$		0			0
$571$			45.2601i			1.89408i	0.321118	+	0.947039i	$0.395941\pi$
$571$			45.2601i			1.89408i	−0.321118	+	0.947039i	$0.604059\pi$
$572$	−33.5004	+	14.4762i	−1.40072	+	0.605282i
$573$		0			0
$574$	−17.5164	+	12.7264i	−0.731121	+	0.531190i
$575$	−0.679996	+	0.292933i	−0.0283578	+	0.0122161i
$576$		0			0
$577$	−22.6517	+	3.58768i	−0.943005	+	0.149357i	−0.608961	−	0.793200i	$-0.708413\pi$
$577$	−22.6517	+	3.58768i	−0.943005	+	0.149357i	−0.334044	+	0.942558i	$0.608413\pi$
$578$	38.7024	−	6.12986i	1.60981	−	0.254969i
$579$		0			0
$580$	−1.95956	+	60.7618i	−0.0813663	+	2.52300i
$581$	17.3180	−	12.5823i	0.718472	−	0.522001i
$582$		0			0
$583$	9.03691	+	10.2611i	0.374270	+	0.424972i
$584$			8.26259i			0.341908i
$585$		0			0
$586$	−15.1186	−	46.5303i	−0.624545	−	1.92215i
$587$	4.58380	+	8.99622i	0.189194	+	0.371314i	0.966046	−	0.258369i	$-0.0831850\pi$
$587$	4.58380	+	8.99622i	0.189194	+	0.371314i	−0.776853	+	0.629683i	$0.783185\pi$
$588$		0			0
$589$	30.4251	+	22.1051i	1.25365	+	0.910827i
$590$	34.9832	−	4.39017i	1.44024	−	0.180740i
$591$		0			0
$592$	4.17419	−	26.3548i	0.171558	−	1.08318i
$593$	9.47168	−	9.47168i	0.388955	−	0.388955i	−0.485359	−	0.874315i	$-0.661311\pi$
$593$	9.47168	−	9.47168i	0.388955	−	0.388955i	0.874315	+	0.485359i	$0.161311\pi$
$594$		0			0
$595$	5.12760	+	1.85082i	0.210211	+	0.0758761i
$596$	19.4451	+	26.7639i	0.796503	+	1.09629i
$597$		0			0
$598$	0.901512	−	0.459343i	0.0368656	−	0.0187839i
$599$	23.5167	−	32.3680i	0.960866	−	1.32252i	0.0143383	−	0.999897i	$-0.495436\pi$
$599$	23.5167	−	32.3680i	0.960866	−	1.32252i	0.946528	−	0.322622i	$-0.104564\pi$
$600$		0			0
$601$	34.5805	+	11.2359i	1.41057	+	0.458322i	0.912593	−	0.408869i	$-0.134077\pi$
$601$	34.5805	+	11.2359i	1.41057	+	0.458322i	0.497976	+	0.867191i	$0.334077\pi$
$602$	−15.7994	+	31.0081i	−0.643937	+	1.26380i
$603$		0			0
$604$	46.7449			1.90202
$605$	−17.3601	−	17.4249i	−0.705788	−	0.708423i
$606$		0			0
$607$	24.6231	+	3.89991i	0.999420	+	0.158293i	0.634646	−	0.772803i	$-0.281146\pi$
$607$	24.6231	+	3.89991i	0.999420	+	0.158293i	0.364774	+	0.931096i	$0.381146\pi$
$608$	−1.48116	+	2.90694i	−0.0600689	+	0.117892i
$609$		0			0
$610$	−9.75047	+	50.8863i	−0.394785	+	2.06033i
$611$	−1.74555	+	2.40254i	−0.0706174	+	0.0971965i
$612$		0			0
$613$	−10.4167	−	5.30759i	−0.420728	−	0.214372i	0.230792	−	0.973003i	$-0.425868\pi$
$613$	−10.4167	−	5.30759i	−0.420728	−	0.214372i	−0.651520	+	0.758632i	$0.725868\pi$
$614$	29.7088	+	40.8907i	1.19895	+	1.65021i
$615$		0			0
$616$	30.7612	+	25.4748i	1.23940	+	1.02641i
$617$	−6.18386	+	6.18386i	−0.248953	+	0.248953i	−0.820541	−	0.571588i	$-0.806328\pi$
$617$	−6.18386	+	6.18386i	−0.248953	+	0.248953i	0.571588	+	0.820541i	$0.306328\pi$
$618$		0			0
$619$	1.04489	−	0.339504i	0.0419975	−	0.0136458i	−0.287943	−	0.957648i	$-0.592971\pi$
$619$	1.04489	−	0.339504i	0.0419975	−	0.0136458i	0.329940	+	0.944002i	$0.392971\pi$
$620$	48.7076	−	62.6869i	1.95614	−	2.51757i
$621$		0			0
$622$	−8.85859	−	55.9309i	−0.355197	−	2.24263i
$623$	4.95896	+	9.73251i	0.198677	+	0.389925i
$624$		0			0
$625$	−18.1678	−	17.1736i	−0.726712	−	0.686942i
$626$			34.1000i			1.36291i
$627$		0			0
$628$	−3.77153	−	3.77153i	−0.150501	−	0.150501i
$629$	−5.80472	+	4.21737i	−0.231449	+	0.168158i
$630$		0			0
$631$	−1.00765	+	3.10124i	−0.0401140	+	0.123458i	−0.969108	−	0.246636i	$-0.920675\pi$
$631$	−1.00765	+	3.10124i	−0.0401140	+	0.123458i	0.928994	+	0.370095i	$0.120675\pi$
$632$	20.0037	−	3.16827i	0.795703	−	0.126027i
$633$		0			0
$634$	−22.1755	+	68.2493i	−0.880703	+	2.71053i
$635$	−3.63227	−	3.87436i	−0.144142	−	0.153749i
$636$		0			0
$637$	−0.664797	−	0.664797i	−0.0263402	−	0.0263402i
$638$	51.3987	−	22.2105i	2.03490	−	0.879321i
$639$		0			0
$640$	39.4960	+	21.7555i	1.56122	+	0.859960i
$641$	2.75407	+	8.47616i	0.108779	+	0.334788i	0.990599	−	0.136799i	$-0.0436814\pi$
$641$	2.75407	+	8.47616i	0.108779	+	0.334788i	−0.881820	+	0.471587i	$0.843681\pi$
$642$		0			0
$643$	−5.80382	−	36.6439i	−0.228880	−	1.44509i	−0.787830	−	0.615893i	$-0.788796\pi$
$643$	−5.80382	−	36.6439i	−0.228880	−	1.44509i	0.558950	−	0.829202i	$-0.311204\pi$
$644$	−1.21165	−	0.880315i	−0.0477457	−	0.0346893i
$645$		0			0
$646$	−9.06602	+	2.94573i	−0.356698	+	0.115898i
$647$	3.44966	−	21.7803i	0.135620	−	0.856273i	−0.822262	−	0.569110i	$-0.807288\pi$
$647$	3.44966	−	21.7803i	0.135620	−	0.856273i	0.957882	−	0.287163i	$-0.0927121\pi$
$648$		0			0
$649$	−11.5097	−	18.1572i	−0.451794	−	0.712734i
$650$	26.2874	+	21.8198i	1.03108	+	0.855842i
$651$		0			0
$652$	80.0844	+	40.8051i	3.13635	+	1.59805i
$653$	43.2861	−	22.0554i	1.69392	−	0.863093i	0.705980	−	0.708232i	$-0.250507\pi$
$653$	43.2861	−	22.0554i	1.69392	−	0.863093i	0.987936	−	0.154861i	$-0.0494930\pi$
$654$		0			0
$655$	3.92249	+	5.78200i	0.153265	+	0.225921i
$656$	−11.5145	−	3.74130i	−0.449567	−	0.146073i
$657$		0			0
$658$	6.55831	+	1.03873i	0.255669	+	0.0404941i
$659$	−47.3029			−1.84266			−0.921329	−	0.388783i	$-0.872896\pi$
$659$	−47.3029			−1.84266			−0.921329	+	0.388783i	$0.872896\pi$
$660$		0			0
$661$	−26.7159			−1.03913			−0.519564	−	0.854432i	$-0.673906\pi$
$661$	−26.7159			−1.03913			−0.519564	+	0.854432i	$0.673906\pi$
$662$	5.25121	+	0.831711i	0.204094	+	0.0323254i
$663$		0			0
$664$	36.7826	+	11.9514i	1.42744	+	0.463804i
$665$	23.5283	+	4.50833i	0.912389	+	0.174826i
$666$		0			0
$667$	−0.915682	+	0.466563i	−0.0354553	+	0.0180654i
$668$	−50.1252	−	25.5401i	−1.93940	−	0.988175i
$669$		0			0
$670$	−7.69172	+	21.3095i	−0.297157	+	0.823260i
$671$	30.6032	−	7.84061i	1.18143	−	0.302683i
$672$		0			0
$673$	−2.07046	+	13.0723i	−0.0798102	+	0.503902i	0.915107	+	0.403210i	$0.132106\pi$
$673$	−2.07046	+	13.0723i	−0.0798102	+	0.503902i	−0.994918	+	0.100692i	$0.967894\pi$
$674$	−4.16900	+	1.35459i	−0.160584	+	0.0521769i
$675$		0			0
$676$	16.1973	+	11.7681i	0.622975	+	0.452618i
$677$	5.37982	+	33.9668i	0.206763	+	1.30545i	0.844649	+	0.535321i	$0.179809\pi$
$677$	5.37982	+	33.9668i	0.206763	+	1.30545i	−0.637885	+	0.770131i	$0.720191\pi$
$678$		0			0
$679$	11.5070	+	35.4150i	0.441600	+	1.35910i
$680$	2.74008	+	9.46045i	0.105077	+	0.362792i
$681$		0			0
$682$	−71.3470	−	15.9869i	−2.73202	−	0.612171i
$683$	−27.9495	−	27.9495i	−1.06946	−	1.06946i	−0.997401	−	0.0720555i	$-0.977044\pi$
$683$	−27.9495	−	27.9495i	−1.06946	−	1.06946i	−0.0720555	−	0.997401i	$-0.522956\pi$
$684$		0			0
$685$	26.9747	−	25.2892i	1.03065	−	0.966252i
$686$	−14.2346	+	43.8095i	−0.543478	+	1.67265i
$687$		0			0
$688$	−19.2206	+	3.04425i	−0.732779	+	0.116061i
$689$	−3.57830	+	11.0129i	−0.136322	+	0.419557i
$690$		0			0
$691$	−2.64892	+	1.92455i	−0.100770	+	0.0732134i	−0.637029	−	0.770840i	$-0.719837\pi$
$691$	−2.64892	+	1.92455i	−0.100770	+	0.0732134i	0.536259	+	0.844053i	$0.319837\pi$
$692$	61.7773	+	61.7773i	2.34842	+	2.34842i
$693$		0			0
$694$		−	52.2333i		−	1.98275i
$695$	−2.68766	−	9.27949i	−0.101949	−	0.351991i
$696$		0			0
$697$	1.47799	+	2.90071i	0.0559827	+	0.109872i
$698$	−4.05519	−	25.6035i	−0.153491	−	0.969106i
$699$		0			0
$700$	11.1126	−	49.3334i	0.420016	−	1.86463i
$701$	5.55696	−	1.80557i	0.209883	−	0.0681953i	−0.202188	−	0.979347i	$-0.564805\pi$
$701$	5.55696	−	1.80557i	0.209883	−	0.0681953i	0.412072	+	0.911151i	$0.364805\pi$
$702$		0			0
$703$	−22.2957	+	22.2957i	−0.840897	+	0.840897i
$704$	1.87635	−	29.5782i	0.0707178	−	1.11477i
$705$		0			0
$706$	15.6482	+	21.5379i	0.588927	+	0.810588i
$707$	−4.45154	−	2.26817i	−0.167417	−	0.0853034i
$708$		0			0
$709$	23.5016	−	32.3472i	0.882623	−	1.21483i	−0.0930647	−	0.995660i	$-0.529666\pi$
$709$	23.5016	−	32.3472i	0.882623	−	1.21483i	0.975688	−	0.219166i	$-0.0703337\pi$
$710$	−6.76360	−	1.29599i	−0.253834	−	0.0486378i
$711$		0			0
$712$	−8.95956	+	17.5841i	−0.335774	+	0.658993i
$713$	1.32547	+	0.209933i	0.0496391	+	0.00786207i
$714$		0			0
$715$	5.20745	−	20.1692i	0.194748	−	0.754285i
$716$	−17.1125			−0.639523
$717$		0			0
$718$	3.61592	−	7.09665i	0.134945	−	0.264845i
$719$	−19.2106	−	6.24190i	−0.716434	−	0.232784i	−0.0719577	−	0.997408i	$-0.522925\pi$
$719$	−19.2106	−	6.24190i	−0.716434	−	0.232784i	−0.644477	+	0.764624i	$0.722925\pi$
$720$		0			0
$721$	2.60896	−	3.59093i	0.0971629	−	0.133733i
$722$	3.85632	−	1.96489i	0.143517	−	0.0731258i
$723$		0			0
$724$	−21.7365	−	29.9177i	−0.807831	−	1.11188i
$725$	−26.7006	−	22.1627i	−0.991634	−	0.823103i
$726$		0			0
$727$	26.5141	−	26.5141i	0.983354	−	0.983354i	−0.0165102	−	0.999864i	$-0.505256\pi$
$727$	26.5141	−	26.5141i	0.983354	−	0.983354i	0.999864	+	0.0165102i	$0.00525558\pi$
$728$	−5.29135	+	33.4083i	−0.196111	+	1.23819i
$729$		0			0
$730$	−7.60852	−	5.91181i	−0.281604	−	0.218806i
$731$	4.23339	+	3.07574i	0.156578	+	0.113760i
$732$		0			0
$733$	14.4811	+	28.4208i	0.534873	+	1.04975i	0.987437	+	0.158015i	$0.0505096\pi$
$733$	14.4811	+	28.4208i	0.534873	+	1.04975i	−0.452563	+	0.891732i	$0.649490\pi$
$734$	−13.7035	−	42.1752i	−0.505807	−	1.55671i
$735$		0			0
$736$			0.116420i			0.00429131i
$737$	13.7531	−	1.29283i	0.506601	−	0.0476220i
$738$		0			0
$739$	−31.6871	+	23.0220i	−1.16563	+	0.846879i	−0.990479	−	0.137662i	$-0.956041\pi$
$739$	−31.6871	+	23.0220i	−1.16563	+	0.846879i	−0.175150	+	0.984542i	$0.556041\pi$
$740$	45.5224	+	48.5565i	1.67344	+	1.78497i
$741$		0			0
$742$	25.5724	−	4.05027i	0.938793	−	0.148690i
$743$	6.70139	−	1.06140i	0.245850	−	0.0389389i	−0.0322930	−	0.999478i	$-0.510281\pi$
$743$	6.70139	−	1.06140i	0.245850	−	0.0389389i	0.278143	+	0.960540i	$0.410281\pi$
$744$		0			0
$745$	−18.8730	−	0.608652i	−0.691455	−	0.0222993i
$746$	−34.7666	+	25.2594i	−1.27290	+	0.924814i
$747$		0			0
$748$	9.20756	−	8.10905i	0.336662	−	0.296496i
$749$			10.7374i			0.392337i
$750$		0			0
$751$	−6.82703	−	21.0114i	−0.249122	−	0.766718i	−0.994931	−	0.100559i	$-0.967937\pi$
$751$	−6.82703	−	21.0114i	−0.249122	−	0.766718i	0.745809	−	0.666160i	$-0.232063\pi$
$752$	1.68567	+	3.30830i	0.0614699	+	0.120641i
$753$		0			0
$754$	38.3627	+	27.8722i	1.39709	+	1.01504i
$755$	−16.3706	+	21.0691i	−0.595788	+	0.766782i
$756$		0			0
$757$	−5.23341	+	33.0425i	−0.190212	+	1.20095i	0.689087	+	0.724678i	$0.258012\pi$
$757$	−5.23341	+	33.0425i	−0.190212	+	1.20095i	−0.879299	+	0.476271i	$0.841988\pi$
$758$	37.9511	−	37.9511i	1.37845	−	1.37845i
$759$		0			0
$760$	18.3967	+	39.1787i	0.667320	+	1.42116i
$761$	15.3149	+	21.0791i	0.555163	+	0.764117i	0.990701	−	0.136054i	$-0.0434419\pi$
$761$	15.3149	+	21.0791i	0.555163	+	0.764117i	−0.435538	+	0.900170i	$0.643442\pi$
$762$		0			0
$763$	7.41445	−	3.77785i	0.268421	−	0.136767i
$764$	14.9045	−	20.5143i	0.539227	−	0.742182i
$765$		0			0
$766$	45.5528	+	14.8010i	1.64589	+	0.534782i
$767$	8.26544	−	16.2218i	0.298448	−	0.585736i
$768$		0			0
$769$	−51.2907			−1.84959			−0.924794	−	0.380468i	$-0.875763\pi$
$769$	−51.2907			−1.84959			−0.924794	+	0.380468i	$0.875763\pi$
$770$	−45.4676	+	10.0991i	−1.63854	+	0.363947i
$771$		0			0
$772$	−3.89496	−	0.616901i	−0.140183	−	0.0222027i
$773$	7.49740	−	14.7145i	0.269663	−	0.529243i	−0.715973	−	0.698128i	$-0.754017\pi$
$773$	7.49740	−	14.7145i	0.269663	−	0.529243i	0.985636	+	0.168885i	$0.0540167\pi$
$774$		0			0
$775$	11.1965	+	43.9074i	0.402191	+	1.57720i
$776$	−39.5453	+	54.4295i	−1.41960	+	1.95391i
$777$		0			0
$778$	−37.1082	−	18.9076i	−1.33039	−	0.677869i
$779$	8.40920	+	11.5743i	0.301291	+	0.414691i
$780$		0			0
$781$	1.04214	+	4.06766i	0.0372908	+	0.145552i
$782$	−0.240530	+	0.240530i	−0.00860135	+	0.00860135i
$783$		0			0
$784$	−1.11795	+	0.363243i	−0.0399267	+	0.0129730i
$785$	3.02076	−	0.379085i	0.107815	−	0.0135301i
$786$		0			0
$787$	−0.692641	−	4.37316i	−0.0246900	−	0.155886i	0.972263	−	0.233890i	$-0.0751455\pi$
$787$	−0.692641	−	4.37316i	−0.0246900	−	0.155886i	−0.996953	+	0.0780034i	$0.975146\pi$
$788$	43.6197	+	85.6084i	1.55389	+	3.04967i
$789$		0			0
$790$	−11.3950	+	20.6871i	−0.405415	+	0.736012i
$791$			28.7945i			1.02381i
$792$		0			0
$793$	18.9183	+	18.9183i	0.671808	+	0.671808i
$794$	14.6086	−	10.6137i	0.518438	−	0.376667i
$795$		0			0
$796$	−3.94138	+	12.1303i	−0.139699	+	0.429948i
$797$	−18.9850	+	3.00692i	−0.672482	+	0.106511i	−0.483331	−	0.875437i	$-0.660573\pi$
$797$	−18.9850	+	3.00692i	−0.672482	+	0.106511i	−0.189150	+	0.981948i	$0.560573\pi$
$798$		0			0
$799$	0.308525	−	0.949542i	0.0109148	−	0.0335924i
$800$	−3.61022	+	1.55523i	−0.127640	+	0.0549858i
$801$		0			0
$802$	21.1147	+	21.1147i	0.745587	+	0.745587i
$803$	−1.28457	+	5.73284i	−0.0453316	+	0.202308i
$804$		0			0
$805$	0.821113	−	0.237823i	0.0289404	−	0.00838216i
$806$	−19.1346	−	58.8903i	−0.673988	−	2.07432i
$807$		0			0
$808$	−1.41207	−	8.91548i	−0.0496765	−	0.313645i
$809$	24.9923	+	18.1580i	0.878683	+	0.638401i	0.932903	−	0.360128i	$-0.117267\pi$
$809$	24.9923	+	18.1580i	0.878683	+	0.638401i	−0.0542197	+	0.998529i	$0.517267\pi$
$810$		0			0
$811$	23.8090	−	7.73601i	0.836047	−	0.271648i	0.140456	−	0.990087i	$-0.455143\pi$
$811$	23.8090	−	7.73601i	0.836047	−	0.271648i	0.695590	+	0.718439i	$0.255143\pi$
$812$	10.9803	−	69.3267i	0.385332	−	2.43289i
$813$		0			0
$814$	22.5964	−	56.9854i	0.792004	−	1.99734i
$815$	−46.4383	+	21.8056i	−1.62666	+	0.763816i
$816$		0			0
$817$	20.4891	+	10.4397i	0.716825	+	0.365240i
$818$	−57.9990	+	29.5519i	−2.02789	+	1.03326i
$819$		0			0
$820$	24.9916	−	16.9542i	0.872744	−	0.592067i
$821$	21.6750	+	7.04264i	0.756463	+	0.245790i	0.661760	−	0.749716i	$-0.269810\pi$
$821$	21.6750	+	7.04264i	0.756463	+	0.245790i	0.0947032	+	0.995506i	$0.469810\pi$
$822$		0			0
$823$	17.4278	+	2.76029i	0.607495	+	0.0962177i	0.452601	−	0.891713i	$-0.350496\pi$
$823$	17.4278	+	2.76029i	0.607495	+	0.0962177i	0.154894	+	0.987931i	$0.450496\pi$
$824$	8.01946			0.279371
$825$		0			0
$826$	−40.7077			−1.41640
$827$	−16.4544	−	2.60613i	−0.572177	−	0.0906239i	−0.136360	−	0.990659i	$-0.543540\pi$
$827$	−16.4544	−	2.60613i	−0.572177	−	0.0906239i	−0.435817	+	0.900035i	$0.643540\pi$
$828$		0			0
$829$	39.7855	+	12.9271i	1.38181	+	0.448976i	0.903263	−	0.429087i	$-0.141165\pi$
$829$	39.7855	+	12.9271i	1.38181	+	0.448976i	0.478544	+	0.878064i	$0.341165\pi$
$830$	−37.3230	+	25.3198i	−1.29550	+	0.878863i
$831$		0			0
$832$	22.3640	−	11.3950i	0.775332	−	0.395051i
$833$	0.281630	+	0.143498i	0.00975790	+	0.00497190i
$834$		0			0
$835$	29.0660	−	13.6482i	1.00587	−	0.472316i
$836$	34.3901	−	41.5265i	1.18941	−	1.43622i
$837$		0			0
$838$	5.41895	−	34.2139i	0.187195	−	1.18190i
$839$	49.3818	−	16.0451i	1.70485	−	0.553939i	0.715388	−	0.698728i	$-0.246250\pi$
$839$	49.3818	−	16.0451i	1.70485	−	0.553939i	0.989463	+	0.144788i	$0.0462501\pi$
$840$		0			0
$841$	−15.5042	−	11.2645i	−0.534629	−	0.388431i
$842$	−2.62809	−	16.5931i	−0.0905699	−	0.571836i
$843$		0			0
$844$	−30.0723	−	92.5530i	−1.03513	−	3.18581i
$845$	−10.9767	+	3.17922i	−0.377608	+	0.109369i
$846$		0			0
$847$	17.3825	+	22.4576i	0.597271	+	0.771654i
$848$	10.2374	+	10.2374i	0.351554	+	0.351554i
$849$		0			0
$850$	−10.6721	−	4.24570i	−0.366049	−	0.145626i
$851$	−0.347690	+	1.07008i	−0.0119187	+	0.0366819i
$852$		0			0
$853$	13.8327	−	2.19089i	0.473623	−	0.0750145i	0.0849401	−	0.996386i	$-0.472930\pi$
$853$	13.8327	−	2.19089i	0.473623	−	0.0750145i	0.388683	+	0.921372i	$0.372930\pi$
$854$	18.4857	−	56.8933i	0.632569	−	1.94685i
$855$		0			0
$856$	−15.6947	+	11.4029i	−0.536434	+	0.389742i
$857$	−10.2364	−	10.2364i	−0.349669	−	0.349669i	0.510317	−	0.859986i	$-0.329528\pi$
$857$	−10.2364	−	10.2364i	−0.349669	−	0.349669i	−0.859986	+	0.510317i	$0.829528\pi$
$858$		0			0
$859$			56.0426i			1.91215i	0.293125	+	0.956074i	$0.405305\pi$
$859$			56.0426i			1.91215i	−0.293125	+	0.956074i	$0.594695\pi$
$860$	23.4199	−	42.5177i	0.798611	−	1.44984i
$861$		0			0
$862$	7.88446	+	15.4741i	0.268546	+	0.527050i
$863$	2.69640	+	17.0244i	0.0917867	+	0.579518i	0.990122	+	0.140208i	$0.0447771\pi$
$863$	2.69640	+	17.0244i	0.0917867	+	0.579518i	−0.898335	+	0.439310i	$0.855223\pi$
$864$		0			0
$865$	−49.4797	+	6.20938i	−1.68236	+	0.211125i
$866$	38.8733	−	12.6307i	1.32097	−	0.429209i
$867$		0			0
$868$	−64.8114	+	64.8114i	−2.19984	+	2.19984i
$869$	14.3717	+	0.911700i	0.487528	+	0.0309273i
$870$		0			0
$871$	6.87628	+	9.46438i	0.232994	+	0.320688i
$872$	13.3960	+	6.82560i	0.453645	+	0.231144i
$873$		0			0
$874$	−0.878650	+	1.20936i	−0.0297208	+	0.0409071i
$875$	18.3440	+	22.2858i	0.620140	+	0.753399i
$876$		0			0
$877$	3.20066	−	6.28165i	0.108079	−	0.212116i	−0.830633	−	0.556821i	$-0.812021\pi$
$877$	3.20066	−	6.28165i	0.108079	−	0.212116i	0.938711	+	0.344705i	$0.112021\pi$
$878$	−1.85708	−	0.294133i	−0.0626735	−	0.00992651i
$879$		0			0
$880$	−19.5130	−	17.2496i	−0.657782	−	0.581484i
$881$	46.6330			1.57111			0.785553	−	0.618794i	$-0.212378\pi$
$881$	46.6330			1.57111			0.785553	+	0.618794i	$0.212378\pi$
$882$		0			0
$883$	−4.99714	+	9.80743i	−0.168167	+	0.330046i	−0.959675	−	0.281113i	$-0.909296\pi$
$883$	−4.99714	+	9.80743i	−0.168167	+	0.330046i	0.791508	+	0.611159i	$0.209296\pi$
$884$	9.88212	+	3.21090i	0.332372	+	0.107994i
$885$		0			0
$886$	26.8665	−	36.9785i	0.902597	−	1.24232i
$887$	34.7292	−	17.6954i	1.16609	−	0.594154i	0.239750	−	0.970835i	$-0.422934\pi$
$887$	34.7292	−	17.6954i	1.16609	−	0.594154i	0.926343	+	0.376680i	$0.122934\pi$
$888$		0			0
$889$	3.60411	+	4.96064i	0.120878	+	0.166374i
$890$	−9.78168	−	20.8316i	−0.327883	−	0.698277i
$891$		0			0
$892$	−54.2662	+	54.2662i	−1.81697	+	1.81697i
$893$	0.686361	−	4.33351i	0.0229682	−	0.145016i
$894$		0			0
$895$	5.99299	−	7.71300i	0.200323	−	0.257817i
$896$	−42.1188	−	30.6011i	−1.40709	−	1.02231i
$897$		0			0
$898$	−0.787843	−	1.54623i	−0.0262906	−	0.0515983i
$899$	19.4354	+	59.8159i	0.648206	+	1.99497i
$900$		0			0
$901$		−	3.89303i		−	0.129696i
$902$	−23.9339	−	14.1713i	−0.796912	−	0.471852i
$903$		0			0
$904$	−42.0884	+	30.5790i	−1.39984	+	1.01704i
$905$	21.0970	+	0.680376i	0.701289	+	0.0226165i
$906$		0			0
$907$	−27.7688	+	4.39815i	−0.922049	+	0.146038i	−0.599372	−	0.800471i	$-0.704583\pi$
$907$	−27.7688	+	4.39815i	−0.922049	+	0.146038i	−0.322677	+	0.946509i	$0.604583\pi$
$908$	−3.95795	+	0.626877i	−0.131349	+	0.0208037i
$909$		0			0
$910$	−26.9778	−	28.7758i	−0.894305	−	0.953909i
$911$	−23.8530	+	17.3302i	−0.790285	+	0.574175i	−0.908048	−	0.418866i	$-0.862428\pi$
$911$	−23.8530	+	17.3302i	−0.790285	+	0.574175i	0.117763	+	0.993042i	$0.462428\pi$
$912$		0			0
$913$	23.6628	+	14.0108i	0.783126	+	0.463689i
$914$			47.0585i			1.55656i
$915$		0			0
$916$	−0.123296	−	0.379465i	−0.00407380	−	0.0125379i
$917$	−3.66234	−	7.18775i	−0.120941	−	0.237360i
$918$		0			0
$919$	32.9943	+	23.9718i	1.08838	+	0.790755i	0.979125	−	0.203258i	$-0.0651532\pi$
$919$	32.9943	+	23.9718i	1.08838	+	0.790755i	0.109256	+	0.994014i	$0.465153\pi$
$920$	1.21962	+	0.947645i	0.0402098	+	0.0312429i
$921$		0			0
$922$	13.9003	−	87.7630i	0.457782	−	2.89032i
$923$	−2.51454	+	2.51454i	−0.0827672	+	0.0827672i
$924$		0			0
$925$	−37.8281	+	3.51301i	−1.24378	+	0.115507i
$926$	−34.6632	−	47.7098i	−1.13910	−	1.56784i
$927$		0			0
$928$	−4.86151	+	2.47706i	−0.159587	+	0.0813136i
$929$	−30.1380	+	41.4814i	−0.988795	+	1.36096i	−0.0568413	+	0.998383i	$0.518103\pi$
$929$	−30.1380	+	41.4814i	−0.988795	+	1.36096i	−0.931954	+	0.362577i	$0.881897\pi$
$930$		0			0
$931$	1.32104	+	0.429233i	0.0432954	+	0.0140675i
$932$	−38.0602	+	74.6973i	−1.24670	+	2.44679i
$933$		0			0
$934$	36.0504			1.17960
$935$	0.430347	+	6.98995i	0.0140738	+	0.228596i
$936$		0			0
$937$	−3.04254	−	0.481891i	−0.0993955	−	0.0157427i	0.106539	−	0.994309i	$-0.466023\pi$
$937$	−3.04254	−	0.481891i	−0.0993955	−	0.0157427i	−0.205934	+	0.978566i	$0.566023\pi$
$938$	11.8752	−	23.3063i	0.387738	−	0.760978i
$939$		0			0
$940$	−9.09615	−	1.74294i	−0.296684	−	0.0568485i
$941$	16.7138	−	23.0045i	0.544854	−	0.749927i	−0.444449	−	0.895804i	$-0.646601\pi$
$941$	16.7138	−	23.0045i	0.544854	−	0.749927i	0.989303	+	0.145877i	$0.0466005\pi$
$942$		0			0
$943$	0.454874	+	0.231770i	0.0148127	+	0.00754747i
$944$	−13.3798	−	18.4157i	−0.435474	−	0.599379i
$945$		0			0
$946$	−44.6180	−	2.83043i	−1.45065	−	0.0920252i
$947$	40.6526	−	40.6526i	1.32103	−	1.32103i	0.408091	−	0.912941i	$-0.366195\pi$
$947$	40.6526	−	40.6526i	1.32103	−	1.32103i	0.912941	−	0.408091i	$-0.133805\pi$
$948$		0			0
$949$	−4.73193	+	1.53750i	−0.153605	+	0.0499092i
$950$	−49.2400	−	11.0916i	−1.59756	−	0.359858i
$951$		0			0
$952$	−1.77894	−	11.2318i	−0.0576557	−	0.364024i
$953$	8.68746	+	17.0501i	0.281414	+	0.552307i	0.987839	−	0.155482i	$-0.0496930\pi$
$953$	8.68746	+	17.0501i	0.281414	+	0.552307i	−0.706424	+	0.707788i	$0.749693\pi$
$954$		0			0
$955$	4.02656	+	13.9022i	0.130296	+	0.449864i
$956$		−	33.9400i		−	1.09770i
$957$		0			0
$958$	47.4507	+	47.4507i	1.53306	+	1.53306i
$959$	−34.5378	+	25.0932i	−1.11528	+	0.810302i
$960$		0			0
$961$	15.7997	−	48.6264i	0.509667	−	1.56859i
$962$	51.2765	−	8.12140i	1.65322	−	0.261844i
$963$		0			0
$964$	12.8917	−	39.6764i	0.415212	−	1.27789i
$965$	1.64211	−	1.53951i	0.0528615	−	0.0495584i
$966$		0			0
$967$	−12.6930	−	12.6930i	−0.408178	−	0.408178i	0.472925	−	0.881103i	$-0.343198\pi$
$967$	−12.6930	−	12.6930i	−0.408178	−	0.408178i	−0.881103	+	0.472925i	$0.843198\pi$
$968$	−14.3661	+	49.2572i	−0.461745	+	1.58319i
$969$		0			0
$970$	−21.8265	−	75.3588i	−0.700808	−	2.41962i
$971$	1.07721	+	3.31533i	0.0345695	+	0.106394i	0.966852	−	0.255336i	$-0.0821862\pi$
$971$	1.07721	+	3.31533i	0.0345695	+	0.106394i	−0.932283	+	0.361730i	$0.882186\pi$
$972$		0			0
$973$	1.74491	+	11.0169i	0.0559392	+	0.353186i
$974$	−76.5471	−	55.6147i	−2.45273	−	1.78201i
$975$		0			0
$976$	31.8137	−	10.3369i	1.01833	−	0.330876i
$977$	−4.04170	+	25.5183i	−0.129305	+	0.816402i	0.834736	+	0.550650i	$0.185620\pi$
$977$	−4.04170	+	25.5183i	−0.129305	+	0.816402i	−0.964042	+	0.265752i	$0.914380\pi$
$978$		0			0
$979$	−8.95020	+	10.8075i	−0.286050	+	0.345409i
$980$	0.995480	−	2.75793i	0.0317994	−	0.0880989i
$981$		0			0
$982$	−40.7509	−	20.7636i	−1.30042	−	0.662595i
$983$	−27.8228	+	14.1764i	−0.887409	+	0.452158i	−0.837400	−	0.546591i	$-0.815925\pi$
$983$	−27.8228	+	14.1764i	−0.887409	+	0.452158i	−0.0500096	+	0.998749i	$0.515925\pi$
$984$		0			0
$985$	−53.8619	−	10.3206i	−1.71618	−	0.328843i
$986$	−15.1619	−	4.92639i	−0.482852	−	0.156888i
$987$		0			0
$988$	45.1000	+	7.14313i	1.43482	+	0.227253i
$989$	0.820573			0.0260927
$990$		0			0
$991$	−19.5868			−0.622196			−0.311098	−	0.950378i	$-0.600697\pi$
$991$	−19.5868			−0.622196			−0.311098	+	0.950378i	$0.600697\pi$
$992$	7.03714	+	1.11457i	0.223429	+	0.0353877i
$993$		0			0
$994$	7.56203	+	2.45705i	0.239853	+	0.0779330i
$995$	−4.08712	−	6.02466i	−0.129570	−	0.190995i
$996$		0			0
$997$	25.2279	−	12.8543i	0.798976	−	0.407098i	−0.00631392	−	0.999980i	$-0.502010\pi$
$997$	25.2279	−	12.8543i	0.798976	−	0.407098i	0.805290	+	0.592882i	$0.202010\pi$
$998$	11.3569	+	5.78661i	0.359495	+	0.183172i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.bj.a.118.4		32
3.2	odd	2		55.2.l.a.8.1	yes	32
5.2	odd	4	inner	495.2.bj.a.217.1		32
11.7	odd	10	inner	495.2.bj.a.73.1		32
12.11	even	2		880.2.cm.a.833.3		32
15.2	even	4		55.2.l.a.52.4	yes	32
15.8	even	4		275.2.bm.b.107.1		32
15.14	odd	2		275.2.bm.b.118.4		32
33.2	even	10		605.2.e.b.483.2		32
33.5	odd	10		605.2.m.d.233.4		32
33.8	even	10		605.2.m.d.578.4		32
33.14	odd	10		605.2.m.c.578.1		32
33.17	even	10		605.2.m.c.233.1		32
33.20	odd	10		605.2.e.b.483.15		32
33.26	odd	10		605.2.m.e.403.1		32
33.29	even	10		55.2.l.a.18.4	yes	32
33.32	even	2		605.2.m.e.118.4		32
55.7	even	20	inner	495.2.bj.a.172.4		32
60.47	odd	4		880.2.cm.a.657.2		32
132.95	odd	10		880.2.cm.a.513.2		32
165.2	odd	20		605.2.e.b.362.15		32
165.17	odd	20		605.2.m.c.112.1		32
165.29	even	10		275.2.bm.b.18.1		32
165.32	odd	4		605.2.m.e.602.1		32
165.47	even	20		605.2.m.c.457.1		32
165.62	odd	20		55.2.l.a.7.1	✓	32
165.92	even	20		605.2.m.e.282.4		32
165.107	odd	20		605.2.m.d.457.4		32
165.128	odd	20		275.2.bm.b.7.4		32
165.137	even	20		605.2.m.d.112.4		32
165.152	even	20		605.2.e.b.362.2		32
660.227	even	20		880.2.cm.a.337.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.7.1	✓	32	165.62	odd	20
55.2.l.a.8.1	yes	32	3.2	odd	2
55.2.l.a.18.4	yes	32	33.29	even	10
55.2.l.a.52.4	yes	32	15.2	even	4
275.2.bm.b.7.4		32	165.128	odd	20
275.2.bm.b.18.1		32	165.29	even	10
275.2.bm.b.107.1		32	15.8	even	4
275.2.bm.b.118.4		32	15.14	odd	2
495.2.bj.a.73.1		32	11.7	odd	10	inner
495.2.bj.a.118.4		32	1.1	even	1	trivial
495.2.bj.a.172.4		32	55.7	even	20	inner
495.2.bj.a.217.1		32	5.2	odd	4	inner
605.2.e.b.362.2		32	165.152	even	20
605.2.e.b.362.15		32	165.2	odd	20
605.2.e.b.483.2		32	33.2	even	10
605.2.e.b.483.15		32	33.20	odd	10
605.2.m.c.112.1		32	165.17	odd	20
605.2.m.c.233.1		32	33.17	even	10
605.2.m.c.457.1		32	165.47	even	20
605.2.m.c.578.1		32	33.14	odd	10
605.2.m.d.112.4		32	165.137	even	20
605.2.m.d.233.4		32	33.5	odd	10
605.2.m.d.457.4		32	165.107	odd	20
605.2.m.d.578.4		32	33.8	even	10
605.2.m.e.118.4		32	33.32	even	2
605.2.m.e.282.4		32	165.92	even	20
605.2.m.e.403.1		32	33.26	odd	10
605.2.m.e.602.1		32	165.32	odd	4
880.2.cm.a.337.3		32	660.227	even	20
880.2.cm.a.513.2		32	132.95	odd	10
880.2.cm.a.657.2		32	60.47	odd	4
880.2.cm.a.833.3		32	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(2.40264 + 0.380541i) q^{2} +(3.72576 + 1.21057i) q^{4} +(-1.85044 + 1.25533i) q^{5} +(2.30033 - 1.17208i) q^{7} +(4.15610 + 2.11764i) q^{8} +(-4.92366 + 2.31195i) q^{10} +(2.55440 + 2.11543i) q^{11} +(-0.439393 + 2.77422i) q^{13} +(5.97289 - 1.94071i) q^{14} +(2.84111 + 2.06419i) q^{16} +(-0.147723 - 0.932684i) q^{17} +(-1.28236 - 3.94669i) q^{19} +(-8.41399 + 2.43698i) q^{20} +(5.33231 + 6.05467i) q^{22} +(-0.104710 - 0.104710i) q^{23} +(1.84827 - 4.64585i) q^{25} +(-2.11141 + 6.49824i) q^{26} +(9.98937 - 1.58216i) q^{28} +(2.14459 - 6.60038i) q^{29} +(-7.33171 + 5.32680i) q^{31} +(-0.555921 - 0.555921i) q^{32} -2.29712i q^{34} +(-2.78528 + 5.05654i) q^{35} +(-3.44950 - 6.77002i) q^{37} +(-1.57917 - 9.97047i) q^{38} +(-10.3490 + 1.29873i) q^{40} +(-3.27880 + 1.06535i) q^{41} +(-3.91833 + 3.91833i) q^{43} +(6.95623 + 10.9739i) q^{44} +(-0.211733 - 0.291426i) q^{46} +(0.942051 + 0.479999i) q^{47} +(-0.196744 + 0.270795i) q^{49} +(6.20867 - 10.4590i) q^{50} +(-4.99547 + 9.80416i) q^{52} +(4.07187 + 0.644920i) q^{53} +(-7.38234 - 0.707841i) q^{55} +12.0424 q^{56} +(7.66441 - 15.0422i) q^{58} +(-6.16460 - 2.00300i) q^{59} +(5.59880 - 7.70609i) q^{61} +(-19.6426 + 10.0084i) q^{62} +(-5.25251 - 7.22946i) q^{64} +(-2.66950 - 5.68511i) q^{65} +(2.94509 - 2.94509i) q^{67} +(0.578703 - 3.65379i) q^{68} +(-8.61625 + 11.0891i) q^{70} +(1.02426 + 0.744171i) q^{71} +(0.804189 + 1.57831i) q^{73} +(-5.71163 - 17.5786i) q^{74} -16.2568i q^{76} +(8.35541 + 1.87222i) q^{77} +(3.51271 - 2.55214i) q^{79} +(-7.84857 - 0.253115i) q^{80} +(-8.28320 + 1.31193i) q^{82} +(8.18939 - 1.29707i) q^{83} +(1.44418 + 1.54044i) q^{85} +(-10.9054 + 7.92326i) q^{86} +(6.13664 + 14.2012i) q^{88} +4.23092i q^{89} +(2.24084 + 6.89661i) q^{91} +(-0.263364 - 0.516882i) q^{92} +(2.08075 + 1.51175i) q^{94} +(7.32735 + 5.69333i) q^{95} +(-2.25634 + 14.2460i) q^{97} +(-0.575755 + 0.575755i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 10 q^{2} + 2 q^{5} + 10 q^{8} + 24 q^{11} - 10 q^{13} - 8 q^{16} - 16 q^{20} + 10 q^{22} + 24 q^{23} + 16 q^{25} - 20 q^{26} + 50 q^{28} - 28 q^{31} + 10 q^{35} - 8 q^{37} - 10 q^{38} - 50 q^{40}+ \cdots - 8 q^{97}+O(q^{100}) \) 32 * q + 10 * q^2 + 2 * q^5 + 10 * q^8 + 24 * q^11 - 10 * q^13 - 8 * q^16 - 16 * q^20 + 10 * q^22 + 24 * q^23 + 16 * q^25 - 20 * q^26 + 50 * q^28 - 28 * q^31 + 10 * q^35 - 8 * q^37 - 10 * q^38 - 50 * q^40 - 40 * q^41 + 60 * q^46 + 28 * q^47 + 50 * q^50 - 50 * q^52 + 24 * q^53 - 64 * q^55 + 80 * q^56 - 50 * q^58 - 60 * q^61 - 100 * q^62 - 8 * q^67 + 30 * q^68 + 30 * q^70 - 24 * q^71 + 50 * q^73 - 70 * q^77 - 98 * q^80 - 10 * q^82 - 90 * q^83 + 30 * q^85 - 100 * q^86 + 170 * q^88 + 20 * q^91 + 68 * q^92 + 40 * q^95 - 8 * q^97

Introduction

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