LMFDB - Embedded newform 630.2.bv.c.73.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(73,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("630.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bv (of order $12$, degree $4$, 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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 $ x^16 + 10x^14 + 61x^12 + 266x^10 + 852x^8 + 1438x^6 + 1933x^4 + 3038*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			73.3
Root			$1.01089 - 0.750919i$ of defining polynomial
Character	$\chi$	$=$	630.73
Dual form			630.2.bv.c.397.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(-2.20382 - 0.378409i) q^{5} +(0.126334 - 2.64273i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(-2.20382 - 0.378409i) q^{5} +(0.126334 - 2.64273i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.03078 - 0.935904i) q^{10} +(2.81288 - 4.87205i) q^{11} +(-1.42962 + 1.42962i) q^{13} +(0.806019 - 2.51999i) q^{14} +(0.500000 + 0.866025i) q^{16} +(5.12784 - 1.37400i) q^{17} +(-1.94590 - 3.37040i) q^{19} +(-1.71936 - 1.42962i) q^{20} +(3.97801 - 3.97801i) q^{22} +(0.290892 - 1.08562i) q^{23} +(4.71361 + 1.66789i) q^{25} +(-1.75092 + 1.01089i) q^{26} +(1.43078 - 2.22551i) q^{28} -3.15502i q^{29} +(-3.33287 - 1.92423i) q^{31} +(0.258819 + 0.965926i) q^{32} +5.30873 q^{34} +(-1.27845 + 5.77629i) q^{35} +(4.86824 + 1.30444i) q^{37} +(-1.00727 - 3.75919i) q^{38} +(-1.29076 - 1.82591i) q^{40} +7.21050i q^{41} +(1.85669 + 1.85669i) q^{43} +(4.87205 - 2.81288i) q^{44} +(0.561961 - 0.973344i) q^{46} +(1.52590 - 5.69475i) q^{47} +(-6.96808 - 0.667734i) q^{49} +(4.12132 + 2.83103i) q^{50} +(-1.95290 + 0.523277i) q^{52} +(-1.33599 + 0.357978i) q^{53} +(-8.04270 + 9.67269i) q^{55} +(1.95803 - 1.77936i) q^{56} +(0.816578 - 3.04751i) q^{58} +(-2.73923 + 4.74448i) q^{59} +(-3.99172 + 2.30462i) q^{61} +(-2.72127 - 2.72127i) q^{62} +1.00000i q^{64} +(3.69160 - 2.60964i) q^{65} +(0.218698 + 0.816193i) q^{67} +(5.12784 + 1.37400i) q^{68} +(-2.72990 + 5.24858i) q^{70} -4.77710 q^{71} +(1.45256 + 5.42104i) q^{73} +(4.36475 + 2.51999i) q^{74} -3.89180i q^{76} +(-12.5202 - 8.04920i) q^{77} +(5.41079 - 3.12392i) q^{79} +(-0.774197 - 2.09777i) q^{80} +(-1.86622 + 6.96481i) q^{82} +(-5.67281 + 5.67281i) q^{83} +(-11.8207 + 1.08763i) q^{85} +(1.31288 + 2.27397i) q^{86} +(5.43407 - 1.45605i) q^{88} +(5.96090 + 10.3246i) q^{89} +(3.59749 + 3.95871i) q^{91} +(0.794732 - 0.794732i) q^{92} +(2.94782 - 5.10577i) q^{94} +(3.01302 + 8.16409i) q^{95} +(-6.63103 - 6.63103i) q^{97} +(-6.55783 - 2.44845i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{5} + 8 q^{7}+O(q^{10}) $ 16 * q + 12 * q^5 + 8 * q^7	$ 16 q + 12 q^{5} + 8 q^{7} - 12 q^{10} + 12 q^{11} + 8 q^{16} + 36 q^{17} - 8 q^{22} + 4 q^{23} + 12 q^{25} - 12 q^{26} + 4 q^{28} + 24 q^{31} - 8 q^{35} + 4 q^{37} - 24 q^{38} - 8 q^{43} - 8 q^{46} - 12 q^{47} + 32 q^{50} + 28 q^{53} + 4 q^{56} - 32 q^{58} - 12 q^{61} + 8 q^{65} + 32 q^{67} + 36 q^{68} - 12 q^{70} - 16 q^{71} - 12 q^{73} - 16 q^{77} + 12 q^{80} - 48 q^{82} + 24 q^{85} - 12 q^{86} - 4 q^{88} - 16 q^{91} - 8 q^{92} - 20 q^{95} - 40 q^{98}+O(q^{100}) $ 16 * q + 12 * q^5 + 8 * q^7 - 12 * q^10 + 12 * q^11 + 8 * q^16 + 36 * q^17 - 8 * q^22 + 4 * q^23 + 12 * q^25 - 12 * q^26 + 4 * q^28 + 24 * q^31 - 8 * q^35 + 4 * q^37 - 24 * q^38 - 8 * q^43 - 8 * q^46 - 12 * q^47 + 32 * q^50 + 28 * q^53 + 4 * q^56 - 32 * q^58 - 12 * q^61 + 8 * q^65 + 32 * q^67 + 36 * q^68 - 12 * q^70 - 16 * q^71 - 12 * q^73 - 16 * q^77 + 12 * q^80 - 48 * q^82 + 24 * q^85 - 12 * q^86 - 4 * q^88 - 16 * q^91 - 8 * q^92 - 20 * q^95 - 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$		0			0
$3$		0			0
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−2.20382	−	0.378409i	−0.985577	−	0.169230i
$5$	−2.20382	−	0.378409i	−0.985577	−	0.169230i
$6$		0			0
$7$	0.126334	−	2.64273i	0.0477497	−	0.998859i
$7$	0.126334	−	2.64273i	0.0477497	−	0.998859i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	−2.03078	−	0.935904i	−0.642190	−	0.295959i
$11$	2.81288	−	4.87205i	0.848115	−	1.46898i	−0.0347729	−	0.999395i	$-0.511071\pi$
$11$	2.81288	−	4.87205i	0.848115	−	1.46898i	0.882888	−	0.469583i	$-0.155596\pi$
$12$		0			0
$13$	−1.42962	+	1.42962i	−0.396505	+	0.396505i	−0.876998	−	0.480493i	$-0.840458\pi$
$13$	−1.42962	+	1.42962i	−0.396505	+	0.396505i	0.480493	+	0.876998i	$0.340458\pi$
$14$	0.806019	−	2.51999i	0.215418	−	0.673495i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	5.12784	−	1.37400i	1.24368	−	0.333244i	0.423790	−	0.905760i	$-0.360699\pi$
$17$	5.12784	−	1.37400i	1.24368	−	0.333244i	0.819893	+	0.572516i	$0.194033\pi$
$18$		0			0
$19$	−1.94590	−	3.37040i	−0.446420	−	0.773223i	0.551729	−	0.834023i	$-0.313968\pi$
$19$	−1.94590	−	3.37040i	−0.446420	−	0.773223i	−0.998150	+	0.0608002i	$0.980635\pi$
$20$	−1.71936	−	1.42962i	−0.384460	−	0.319673i
$21$		0			0
$22$	3.97801	−	3.97801i	0.848115	−	0.848115i
$23$	0.290892	−	1.08562i	0.0606552	−	0.226368i	−0.928944	−	0.370220i	$-0.879282\pi$
$23$	0.290892	−	1.08562i	0.0606552	−	0.226368i	0.989599	+	0.143852i	$0.0459489\pi$
$24$		0			0
$25$	4.71361	+	1.66789i	0.942723	+	0.333577i
$26$	−1.75092	+	1.01089i	−0.343384	+	0.198253i
$27$		0			0
$28$	1.43078	−	2.22551i	0.270391	−	0.420581i
$29$		−	3.15502i		−	0.585872i	−0.956132	−	0.292936i	$-0.905368\pi$
$29$		−	3.15502i		−	0.585872i	0.956132	−	0.292936i	$-0.0946322\pi$
$30$		0			0
$31$	−3.33287	−	1.92423i	−0.598601	−	0.345602i	0.169890	−	0.985463i	$-0.445659\pi$
$31$	−3.33287	−	1.92423i	−0.598601	−	0.345602i	−0.768491	+	0.639861i	$0.778992\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$		0			0
$34$	5.30873			0.910440
$35$	−1.27845	+	5.77629i	−0.216098	+	0.976372i
$36$		0			0
$37$	4.86824	+	1.30444i	0.800334	+	0.214449i	0.635731	−	0.771911i	$-0.280699\pi$
$37$	4.86824	+	1.30444i	0.800334	+	0.214449i	0.164603	+	0.986360i	$0.447366\pi$
$38$	−1.00727	−	3.75919i	−0.163401	−	0.609822i
$39$		0			0
$40$	−1.29076	−	1.82591i	−0.204087	−	0.288702i
$41$			7.21050i			1.12609i	0.826426	+	0.563046i	$0.190371\pi$
$41$			7.21050i			1.12609i	−0.826426	+	0.563046i	$0.809629\pi$
$42$		0			0
$43$	1.85669	+	1.85669i	0.283143	+	0.283143i	0.834361	−	0.551218i	$-0.185837\pi$
$43$	1.85669	+	1.85669i	0.283143	+	0.283143i	−0.551218	+	0.834361i	$0.685837\pi$
$44$	4.87205	−	2.81288i	0.734489	−	0.424058i
$45$		0			0
$46$	0.561961	−	0.973344i	0.0828566	−	0.143512i
$47$	1.52590	−	5.69475i	0.222576	−	0.830665i	−0.760785	−	0.649004i	$-0.775186\pi$
$47$	1.52590	−	5.69475i	0.222576	−	0.830665i	0.983361	−	0.181661i	$-0.0581474\pi$
$48$		0			0
$49$	−6.96808	−	0.667734i	−0.995440	−	0.0953905i
$50$	4.12132	+	2.83103i	0.582843	+	0.400368i
$51$		0			0
$52$	−1.95290	+	0.523277i	−0.270818	+	0.0725655i
$53$	−1.33599	+	0.357978i	−0.183512	+	0.0491720i	−0.349405	−	0.936972i	$-0.613616\pi$
$53$	−1.33599	+	0.357978i	−0.183512	+	0.0491720i	0.165892	+	0.986144i	$0.446950\pi$
$54$		0			0
$55$	−8.04270	+	9.67269i	−1.08448	+	1.30426i
$56$	1.95803	−	1.77936i	0.261652	−	0.237777i
$57$		0			0
$58$	0.816578	−	3.04751i	0.107222	−	0.400158i
$59$	−2.73923	+	4.74448i	−0.356617	+	0.617679i	−0.987393	−	0.158286i	$-0.949403\pi$
$59$	−2.73923	+	4.74448i	−0.356617	+	0.617679i	0.630776	+	0.775965i	$0.282737\pi$
$60$		0			0
$61$	−3.99172	+	2.30462i	−0.511088	+	0.295077i	−0.733281	−	0.679926i	$-0.762012\pi$
$61$	−3.99172	+	2.30462i	−0.511088	+	0.295077i	0.222193	+	0.975003i	$0.428678\pi$
$62$	−2.72127	−	2.72127i	−0.345602	−	0.345602i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	3.69160	−	2.60964i	0.457887	−	0.323686i
$66$		0			0
$67$	0.218698	+	0.816193i	0.0267182	+	0.0997138i	0.977997	−	0.208617i	$-0.0668963\pi$
$67$	0.218698	+	0.816193i	0.0267182	+	0.0997138i	−0.951279	+	0.308331i	$0.900230\pi$
$68$	5.12784	+	1.37400i	0.621842	+	0.166622i
$69$		0			0
$70$	−2.72990	+	5.24858i	−0.326286	+	0.627326i
$71$	−4.77710			−0.566937			−0.283469	−	0.958982i	$-0.591485\pi$
$71$	−4.77710			−0.566937			−0.283469	+	0.958982i	$0.591485\pi$
$72$		0			0
$73$	1.45256	+	5.42104i	0.170010	+	0.634485i	0.997348	+	0.0727807i	$0.0231873\pi$
$73$	1.45256	+	5.42104i	0.170010	+	0.634485i	−0.827338	+	0.561704i	$0.810146\pi$
$74$	4.36475	+	2.51999i	0.507391	+	0.292943i
$75$		0			0
$76$		−	3.89180i		−	0.446420i
$77$	−12.5202	−	8.04920i	−1.42681	−	0.917291i
$78$		0			0
$79$	5.41079	−	3.12392i	0.608761	−	0.351469i	−0.163719	−	0.986507i	$-0.552349\pi$
$79$	5.41079	−	3.12392i	0.608761	−	0.351469i	0.772481	+	0.635038i	$0.219016\pi$
$80$	−0.774197	−	2.09777i	−0.0865578	−	0.234537i
$81$		0			0
$82$	−1.86622	+	6.96481i	−0.206089	+	0.769135i
$83$	−5.67281	+	5.67281i	−0.622672	+	0.622672i	−0.946214	−	0.323542i	$-0.895126\pi$
$83$	−5.67281	+	5.67281i	−0.622672	+	0.622672i	0.323542	+	0.946214i	$0.395126\pi$
$84$		0			0
$85$	−11.8207	+	1.08763i	−1.28214	+	0.117970i
$86$	1.31288	+	2.27397i	0.141571	+	0.245209i
$87$		0			0
$88$	5.43407	−	1.45605i	0.579273	−	0.155216i
$89$	5.96090	+	10.3246i	0.631855	+	1.09440i	0.987172	+	0.159659i	$0.0510393\pi$
$89$	5.96090	+	10.3246i	0.631855	+	1.09440i	−0.355318	+	0.934746i	$0.615627\pi$
$90$		0			0
$91$	3.59749	+	3.95871i	0.377120	+	0.414986i
$92$	0.794732	−	0.794732i	0.0828566	−	0.0828566i
$93$		0			0
$94$	2.94782	−	5.10577i	0.304044	−	0.526620i
$95$	3.01302	+	8.16409i	0.309129	+	0.837618i
$96$		0			0
$97$	−6.63103	−	6.63103i	−0.673279	−	0.673279i	0.285191	−	0.958471i	$-0.407943\pi$
$97$	−6.63103	−	6.63103i	−0.673279	−	0.673279i	−0.958471	+	0.285191i	$0.907943\pi$
$98$	−6.55783	−	2.44845i	−0.662440	−	0.247331i
$99$		0			0
$100$	3.24817	+	3.80124i	0.324817	+	0.380124i
$101$	−13.9423	−	8.04960i	−1.38731	−	0.800965i	−0.394301	−	0.918981i	$-0.629013\pi$
$101$	−13.9423	−	8.04960i	−1.38731	−	0.800965i	−0.993012	+	0.118016i	$0.962347\pi$
$102$		0			0
$103$	18.9993	+	5.09084i	1.87206	+	0.501616i	0.999924	+	0.0123445i	$0.00392947\pi$
$103$	18.9993	+	5.09084i	1.87206	+	0.501616i	0.872132	+	0.489271i	$0.162737\pi$
$104$	−2.02179			−0.198253
$105$		0			0
$106$	−1.38312			−0.134340
$107$	2.70557	+	0.724955i	0.261557	+	0.0700840i	0.387214	−	0.921990i	$-0.373437\pi$
$107$	2.70557	+	0.724955i	0.261557	+	0.0700840i	−0.125657	+	0.992074i	$0.540104\pi$
$108$		0			0
$109$	−5.11895	−	2.95543i	−0.490306	−	0.283078i	0.234395	−	0.972141i	$-0.424689\pi$
$109$	−5.11895	−	2.95543i	−0.490306	−	0.283078i	−0.724701	+	0.689063i	$0.758022\pi$
$110$	−10.2721	+	7.26150i	−0.979409	+	0.692356i
$111$		0			0
$112$	2.35184	−	1.21196i	0.222228	−	0.114519i
$113$	13.5818	+	13.5818i	1.27767	+	1.27767i	0.941970	+	0.335697i	$0.108972\pi$
$113$	13.5818	+	13.5818i	1.27767	+	1.27767i	0.335697	+	0.941970i	$0.391028\pi$
$114$		0			0
$115$	−1.05188	+	2.28244i	−0.0980886	+	0.212839i
$116$	1.57751	−	2.73232i	0.146468	−	0.253690i
$117$		0			0
$118$	−3.87385	+	3.87385i	−0.356617	+	0.356617i
$119$	−2.98330	−	13.7251i	−0.273478	−	1.25818i
$120$		0			0
$121$	−10.3246	−	17.8827i	−0.938599	−	1.62570i
$122$	−4.45219	+	1.19296i	−0.403082	+	0.108006i
$123$		0			0
$124$	−1.92423	−	3.33287i	−0.172801	−	0.299300i
$125$	−9.75680	−	5.45939i	−0.872674	−	0.488303i
$126$		0			0
$127$	4.63487	−	4.63487i	0.411278	−	0.411278i	−0.470906	−	0.882184i	$-0.656073\pi$
$127$	4.63487	−	4.63487i	0.411278	−	0.411278i	0.882184	+	0.470906i	$0.156073\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$		0			0
$130$	4.24124	−	1.56526i	0.371981	−	0.137282i
$131$	6.66437	−	3.84768i	0.582269	−	0.336173i	−0.179766	−	0.983709i	$-0.557534\pi$
$131$	6.66437	−	3.84768i	0.582269	−	0.336173i	0.762035	+	0.647536i	$0.224201\pi$
$132$		0			0
$133$	−9.15290	+	4.71670i	−0.793657	+	0.408990i
$134$			0.844985i			0.0729956i
$135$		0			0
$136$	4.59749	+	2.65436i	0.394232	+	0.227610i
$137$	2.28687	+	8.53471i	0.195380	+	0.729170i	0.992168	+	0.124910i	$0.0398643\pi$
$137$	2.28687	+	8.53471i	0.195380	+	0.729170i	−0.796788	+	0.604259i	$0.793469\pi$
$138$		0			0
$139$	11.0631			0.938361			0.469180	−	0.883102i	$-0.344549\pi$
$139$	11.0631			0.938361			0.469180	+	0.883102i	$0.344549\pi$
$140$	−3.99532	+	4.36319i	−0.337666	+	0.368757i
$141$		0			0
$142$	−4.61432	−	1.23640i	−0.387225	−	0.103757i
$143$	2.94383	+	10.9865i	0.246176	+	0.918740i
$144$		0			0
$145$	−1.19389	+	6.95307i	−0.0991468	+	0.577421i
$146$			5.61227i			0.464475i
$147$		0			0
$148$	3.56380	+	3.56380i	0.292943	+	0.292943i
$149$	4.37243	−	2.52443i	0.358204	−	0.206809i	−0.310089	−	0.950708i	$-0.600359\pi$
$149$	4.37243	−	2.52443i	0.358204	−	0.206809i	0.668293	+	0.743899i	$0.267025\pi$
$150$		0			0
$151$	−6.72142	+	11.6418i	−0.546981	+	0.947399i	0.451498	+	0.892272i	$0.350890\pi$
$151$	−6.72142	+	11.6418i	−0.546981	+	0.947399i	−0.998479	+	0.0551270i	$0.982444\pi$
$152$	1.00727	−	3.75919i	0.0817006	−	0.304911i
$153$		0			0
$154$	−10.0103	−	11.0154i	−0.806651	−	0.887645i
$155$	6.61688	+	5.50184i	0.531481	+	0.441918i
$156$		0			0
$157$	−1.06529	+	0.285443i	−0.0850191	+	0.0227808i	−0.301078	−	0.953600i	$-0.597346\pi$
$157$	−1.06529	+	0.285443i	−0.0850191	+	0.0227808i	0.216059	+	0.976380i	$0.430680\pi$
$158$	6.03495	−	1.61706i	0.480115	−	0.128646i
$159$		0			0
$160$	−0.204875	−	2.22666i	−0.0161968	−	0.176033i
$161$	−2.83227	−	0.905902i	−0.223214	−	0.0713951i
$162$		0			0
$163$	−3.42705	+	12.7899i	−0.268428	+	1.00179i	0.691691	+	0.722193i	$0.256866\pi$
$163$	−3.42705	+	12.7899i	−0.268428	+	1.00179i	−0.960119	+	0.279592i	$0.909801\pi$
$164$	−3.60525	+	6.24448i	−0.281523	+	0.487612i
$165$		0			0
$166$	−6.94775	+	4.01128i	−0.539250	+	0.311336i
$167$	4.70680	+	4.70680i	0.364223	+	0.364223i	0.865365	−	0.501142i	$-0.167087\pi$
$167$	4.70680	+	4.70680i	0.364223	+	0.364223i	−0.501142	+	0.865365i	$0.667087\pi$
$168$		0			0
$169$			8.91237i			0.685567i
$170$	−11.6995	−	2.00887i	−0.897308	−	0.154073i
$171$		0			0
$172$	0.679597	+	2.53629i	0.0518188	+	0.193390i
$173$	6.81421	+	1.82586i	0.518075	+	0.138818i	0.508376	−	0.861135i	$-0.330246\pi$
$173$	6.81421	+	1.82586i	0.518075	+	0.138818i	0.00969875	+	0.999953i	$0.496913\pi$
$174$		0			0
$175$	5.00327	−	12.2461i	0.378212	−	0.925719i
$176$	5.62576			0.424058
$177$		0			0
$178$	3.08559	+	11.5156i	0.231275	+	0.863129i
$179$	−1.91075	−	1.10317i	−0.142816	−	0.0824550i	0.426889	−	0.904304i	$-0.359609\pi$
$179$	−1.91075	−	1.10317i	−0.142816	−	0.0824550i	−0.569706	+	0.821849i	$0.692943\pi$
$180$		0			0
$181$			4.11867i			0.306139i	0.988215	+	0.153069i	$0.0489158\pi$
$181$			4.11867i			0.306139i	−0.988215	+	0.153069i	$0.951084\pi$
$182$	2.45032	+	4.75492i	0.181630	+	0.352458i
$183$		0			0
$184$	0.973344	−	0.561961i	0.0717559	−	0.0414283i
$185$	−10.2351	−	4.71693i	−0.752499	−	0.346796i
$186$		0			0
$187$	7.72980	−	28.8480i	0.565259	−	2.10957i
$188$	4.16885	−	4.16885i	0.304044	−	0.304044i
$189$		0			0
$190$	0.797333	+	8.66573i	0.0578446	+	0.628678i
$191$	−8.60117	−	14.8977i	−0.622359	−	1.07796i	−0.989045	−	0.147613i	$-0.952841\pi$
$191$	−8.60117	−	14.8977i	−0.622359	−	1.07796i	0.366686	−	0.930345i	$-0.380492\pi$
$192$		0			0
$193$	11.6562	−	3.12327i	0.839032	−	0.224818i	0.186382	−	0.982477i	$-0.440324\pi$
$193$	11.6562	−	3.12327i	0.839032	−	0.224818i	0.652650	+	0.757659i	$0.273657\pi$
$194$	−4.68885	−	8.12132i	−0.336640	−	0.583077i
$195$		0			0
$196$	−5.70067	−	4.06231i	−0.407190	−	0.290165i
$197$	−14.3135	+	14.3135i	−1.01979	+	1.01979i	−0.0199932	+	0.999800i	$0.506364\pi$
$197$	−14.3135	+	14.3135i	−1.01979	+	1.01979i	−0.999800	+	0.0199932i	$0.993636\pi$
$198$		0			0
$199$	−3.76653	+	6.52383i	−0.267002	+	0.462462i	−0.968086	−	0.250617i	$-0.919367\pi$
$199$	−3.76653	+	6.52383i	−0.267002	+	0.462462i	0.701084	+	0.713079i	$0.252700\pi$
$200$	2.15365	+	4.51240i	0.152286	+	0.319075i
$201$		0			0
$202$	−11.3839	−	11.3839i	−0.800965	−	0.800965i
$203$	−8.33786	−	0.398585i	−0.585203	−	0.0279752i
$204$		0			0
$205$	2.72852	−	15.8906i	0.190568	−	1.10985i
$206$	17.0343	+	9.83476i	1.18684	+	0.685220i
$207$		0			0
$208$	−1.95290	−	0.523277i	−0.135409	−	0.0362827i
$209$	−21.8944			−1.51446
$210$		0			0
$211$	19.5766			1.34771			0.673854	−	0.738865i	$-0.264638\pi$
$211$	19.5766			1.34771			0.673854	+	0.738865i	$0.264638\pi$
$212$	−1.33599	−	0.357978i	−0.0917562	−	0.0245860i
$213$		0			0
$214$	2.42575	+	1.40051i	0.165821	+	0.0957366i
$215$	−3.38922	−	4.79440i	−0.231143	−	0.326975i
$216$		0			0
$217$	−5.50629	+	8.56478i	−0.373791	+	0.581415i
$218$	−4.17960	−	4.17960i	−0.283078	−	0.283078i
$219$		0			0
$220$	−11.8015	+	4.35544i	−0.795659	+	0.293644i
$221$	−5.36656	+	9.29516i	−0.360994	+	0.625260i
$222$		0			0
$223$	1.46027	−	1.46027i	0.0977867	−	0.0977867i	−0.656521	−	0.754308i	$-0.727973\pi$
$223$	1.46027	−	1.46027i	0.0977867	−	0.0977867i	0.754308	+	0.656521i	$0.227973\pi$
$224$	2.58538	−	0.561961i	0.172743	−	0.0375476i
$225$		0			0
$226$	9.60377	+	16.6342i	0.638833	+	1.10649i
$227$	18.0081	−	4.82525i	1.19524	−	0.320263i	0.394283	−	0.918989i	$-0.370993\pi$
$227$	18.0081	−	4.82525i	1.19524	−	0.320263i	0.800954	+	0.598726i	$0.204326\pi$
$228$		0			0
$229$	−2.00384	−	3.47074i	−0.132417	−	0.229353i	0.792191	−	0.610274i	$-0.208941\pi$
$229$	−2.00384	−	3.47074i	−0.132417	−	0.229353i	−0.924608	+	0.380920i	$0.875607\pi$
$230$	−1.60678	+	1.93242i	−0.105948	+	0.127420i
$231$		0			0
$232$	2.23093	−	2.23093i	0.146468	−	0.146468i
$233$	3.55400	−	13.2637i	0.232830	−	0.868934i	−0.746285	−	0.665627i	$-0.768164\pi$
$233$	3.55400	−	13.2637i	0.232830	−	0.868934i	0.979115	−	0.203307i	$-0.0651691\pi$
$234$		0			0
$235$	−5.51775	+	11.9728i	−0.359939	+	0.781017i
$236$	−4.74448	+	2.73923i	−0.308839	+	0.178308i
$237$		0			0
$238$	0.670673	−	14.0296i	0.0434732	−	0.909401i
$239$			19.6621i			1.27183i	0.771758	+	0.635916i	$0.219378\pi$
$239$			19.6621i			1.27183i	−0.771758	+	0.635916i	$0.780622\pi$
$240$		0			0
$241$	−5.09667	−	2.94256i	−0.328305	−	0.189547i	0.326783	−	0.945099i	$-0.394035\pi$
$241$	−5.09667	−	2.94256i	−0.328305	−	0.189547i	−0.655088	+	0.755552i	$0.727369\pi$
$242$	−5.34440	−	19.9456i	−0.343551	−	1.28215i
$243$		0			0
$244$	−4.60924			−0.295077
$245$	15.1037	+	4.10834i	0.964939	+	0.262473i
$246$		0			0
$247$	7.60029	+	2.03649i	0.483595	+	0.129579i
$248$	−0.996056	−	3.71733i	−0.0632496	−	0.236051i
$249$		0			0
$250$	−8.01135	−	7.79861i	−0.506682	−	0.493227i
$251$		−	7.09950i		−	0.448116i	−0.974576	−	0.224058i	$-0.928069\pi$
$251$		−	7.09950i		−	0.448116i	0.974576	−	0.224058i	$-0.0719306\pi$
$252$		0			0
$253$	−4.47097	−	4.47097i	−0.281088	−	0.281088i
$254$	5.67653	−	3.27735i	0.356177	−	0.205639i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	2.55891	−	9.54998i	0.159620	−	0.595711i	−0.839045	−	0.544062i	$-0.816886\pi$
$257$	2.55891	−	9.54998i	0.159620	−	0.595711i	0.998665	−	0.0516491i	$-0.0164478\pi$
$258$		0			0
$259$	4.06231	−	12.7007i	0.252420	−	0.789181i
$260$	4.50184	−	0.414214i	0.279192	−	0.0256884i
$261$		0			0
$262$	7.43314	−	1.99170i	0.459221	−	0.123048i
$263$	13.2797	−	3.55829i	0.818861	−	0.219413i	0.175013	−	0.984566i	$-0.444003\pi$
$263$	13.2797	−	3.55829i	0.818861	−	0.219413i	0.643849	+	0.765153i	$0.277337\pi$
$264$		0			0
$265$	3.07974	−	0.283366i	0.189187	−	0.0174071i
$266$	−10.0618	+	2.18704i	−0.616929	+	0.134096i
$267$		0			0
$268$	−0.218698	+	0.816193i	−0.0133591	+	0.0498569i
$269$	13.2510	−	22.9514i	0.807928	−	1.39937i	−0.106368	−	0.994327i	$-0.533922\pi$
$269$	13.2510	−	22.9514i	0.807928	−	1.39937i	0.914296	−	0.405046i	$-0.132745\pi$
$270$		0			0
$271$	−11.0824	+	6.39844i	−0.673209	+	0.388678i	−0.797292	−	0.603594i	$-0.793735\pi$
$271$	−11.0824	+	6.39844i	−0.673209	+	0.388678i	0.124082	+	0.992272i	$0.460401\pi$
$272$	3.75384	+	3.75384i	0.227610	+	0.227610i
$273$		0			0
$274$			8.83578i			0.533789i
$275$	21.3849	−	18.2734i	1.28956	−	1.10193i
$276$		0			0
$277$	5.20313	+	19.4184i	0.312626	+	1.16674i	0.926180	+	0.377083i	$0.123073\pi$
$277$	5.20313	+	19.4184i	0.312626	+	1.16674i	−0.613554	+	0.789653i	$0.710261\pi$
$278$	10.6861	+	2.86334i	0.640912	+	0.171732i
$279$		0			0
$280$	−4.98846	+	3.18046i	−0.298117	+	0.190069i
$281$	14.1498			0.844107			0.422054	−	0.906571i	$-0.361309\pi$
$281$	14.1498			0.844107			0.422054	+	0.906571i	$0.361309\pi$
$282$		0			0
$283$	−7.00563	−	26.1454i	−0.416442	−	1.55418i	−0.781930	−	0.623366i	$-0.785765\pi$
$283$	−7.00563	−	26.1454i	−0.416442	−	1.55418i	0.365489	−	0.930816i	$-0.380902\pi$
$284$	−4.13709	−	2.38855i	−0.245491	−	0.141734i
$285$		0			0
$286$			11.3741i			0.672564i
$287$	19.0554	+	0.910931i	1.12481	+	0.0537706i
$288$		0			0
$289$	9.68442	−	5.59130i	0.569672	−	0.328900i
$290$	−2.95279	+	6.40715i	−0.173394	+	0.376241i
$291$		0			0
$292$	−1.45256	+	5.42104i	−0.0850048	+	0.317242i
$293$	−17.1191	+	17.1191i	−1.00011	+	1.00011i	−0.000106876		1.00000i	$0.500034\pi$
$293$	−17.1191	+	17.1191i	−1.00011	+	1.00011i	−1.00000		0.000106876i	$0.999966\pi$
$294$		0			0
$295$	7.83211	−	9.41941i	0.456003	−	0.548420i
$296$	2.51999	+	4.36475i	0.146471	+	0.253696i
$297$		0			0
$298$	4.87682	−	1.30674i	0.282506	−	0.0756974i
$299$	1.13616	+	1.96790i	0.0657061	+	0.113806i
$300$		0			0
$301$	5.14131	−	4.67218i	0.296340	−	0.269300i
$302$	−9.50552	+	9.50552i	−0.546981	+	0.546981i
$303$		0			0
$304$	1.94590	−	3.37040i	0.111605	−	0.193306i
$305$	9.66911	−	3.56846i	0.553652	−	0.204329i
$306$		0			0
$307$	17.2974	+	17.2974i	0.987217	+	0.987217i	0.999919	−	0.0127019i	$-0.00404326\pi$
$307$	17.2974	+	17.2974i	0.987217	+	0.987217i	−0.0127019	+	0.999919i	$0.504043\pi$
$308$	−6.81819	−	13.2309i	−0.388502	−	0.753900i
$309$		0			0
$310$	4.96744	+	7.02694i	0.282131	+	0.399104i
$311$	9.51095	+	5.49115i	0.539316	+	0.311374i	0.744802	−	0.667286i	$-0.232544\pi$
$311$	9.51095	+	5.49115i	0.539316	+	0.311374i	−0.205486	+	0.978660i	$0.565877\pi$
$312$		0			0
$313$	28.4088	+	7.61212i	1.60576	+	0.430262i	0.946776	−	0.321893i	$-0.104319\pi$
$313$	28.4088	+	7.61212i	1.60576	+	0.430262i	0.658985	+	0.752156i	$0.270986\pi$
$314$	−1.10287			−0.0622383
$315$		0			0
$316$	6.24784			0.351469
$317$	4.14766	+	1.11136i	0.232956	+	0.0624203i	0.373408	−	0.927667i	$-0.378189\pi$
$317$	4.14766	+	1.11136i	0.232956	+	0.0624203i	−0.140453	+	0.990087i	$0.544856\pi$
$318$		0			0
$319$	−15.3714	−	8.87468i	−0.860633	−	0.496887i
$320$	0.378409	−	2.20382i	0.0211537	−	0.123197i
$321$		0			0
$322$	−2.50129	−	1.60808i	−0.139392	−	0.0896147i
$323$	−14.6092	−	14.6092i	−0.812878	−	0.812878i
$324$		0			0
$325$	−9.12312	+	4.35423i	−0.506060	+	0.241529i
$326$	−6.62056	+	11.4671i	−0.366679	+	0.635106i
$327$		0			0
$328$	−5.09860	+	5.09860i	−0.281523	+	0.281523i
$329$	−14.8569	−	4.75200i	−0.819089	−	0.261986i
$330$		0			0
$331$	−17.7249	−	30.7005i	−0.974250	−	1.68745i	−0.682387	−	0.730991i	$-0.739058\pi$
$331$	−17.7249	−	30.7005i	−0.974250	−	1.68745i	−0.291863	−	0.956460i	$-0.594275\pi$
$332$	−7.74921	+	2.07639i	−0.425293	+	0.113957i
$333$		0			0
$334$	3.32821	+	5.76463i	0.182112	+	0.315426i
$335$	−0.173116	−	1.88150i	−0.00945835	−	0.102797i
$336$		0			0
$337$	−12.1473	+	12.1473i	−0.661708	+	0.661708i	−0.955782	−	0.294075i	$-0.904989\pi$
$337$	−12.1473	+	12.1473i	−0.661708	+	0.661708i	0.294075	+	0.955782i	$0.404989\pi$
$338$	−2.30669	+	8.60869i	−0.125468	+	0.468251i
$339$		0			0
$340$	−10.7809	−	4.96846i	−0.584675	−	0.269453i
$341$	−18.7499	+	10.8253i	−1.01536	+	0.586221i
$342$		0			0
$343$	−2.64495	+	18.3304i	−0.142814	+	0.989750i
$344$			2.62576i			0.141571i
$345$		0			0
$346$	6.10945	+	3.52729i	0.328446	+	0.189628i
$347$	−2.32323	−	8.67040i	−0.124717	−	0.465452i	0.875112	−	0.483920i	$-0.160788\pi$
$347$	−2.32323	−	8.67040i	−0.124717	−	0.465452i	−0.999829	+	0.0184687i	$0.994121\pi$
$348$		0			0
$349$	−26.0251			−1.39309			−0.696546	−	0.717512i	$-0.745281\pi$
$349$	−26.0251			−1.39309			−0.696546	+	0.717512i	$0.745281\pi$
$350$	8.00231	−	10.5339i	0.427742	−	0.563060i
$351$		0			0
$352$	5.43407	+	1.45605i	0.289637	+	0.0776079i
$353$	−2.57944	−	9.62659i	−0.137290	−	0.512372i	−0.999978	−	0.00663577i	$-0.997888\pi$
$353$	−2.57944	−	9.62659i	−0.137290	−	0.512372i	0.862688	−	0.505736i	$-0.168779\pi$
$354$		0			0
$355$	10.5278	+	1.80770i	0.558760	+	0.0959425i
$356$			11.9218i			0.631855i
$357$		0			0
$358$	−1.56012	−	1.56012i	−0.0824550	−	0.0824550i
$359$	−10.0235	+	5.78705i	−0.529019	+	0.305429i	−0.740617	−	0.671928i	$-0.765467\pi$
$359$	−10.0235	+	5.78705i	−0.529019	+	0.305429i	0.211598	+	0.977357i	$0.432133\pi$
$360$		0			0
$361$	1.92693	−	3.33754i	0.101417	−	0.175660i
$362$	−1.06599	+	3.97833i	−0.0560273	+	0.209097i
$363$		0			0
$364$	1.13616	+	5.22709i	0.0595512	+	0.273974i
$365$	−1.14981	−	12.4966i	−0.0601840	−	0.654104i
$366$		0			0
$367$	16.1256	−	4.32083i	0.841747	−	0.225545i	0.187915	−	0.982185i	$-0.439827\pi$
$367$	16.1256	−	4.32083i	0.841747	−	0.225545i	0.653832	+	0.756640i	$0.273160\pi$
$368$	1.08562	−	0.290892i	0.0565921	−	0.0151638i
$369$		0			0
$370$	−8.66551	−	7.20525i	−0.450499	−	0.374583i
$371$	0.777258	+	3.57589i	0.0403532	+	0.185651i
$372$		0			0
$373$	0.822767	−	3.07061i	0.0426013	−	0.158990i	−0.941348	−	0.337436i	$-0.890440\pi$
$373$	0.822767	−	3.07061i	0.0426013	−	0.158990i	0.983950	+	0.178446i	$0.0571070\pi$
$374$	14.9328	−	25.8644i	0.772158	−	1.33742i
$375$		0			0
$376$	5.10577	−	2.94782i	0.263310	−	0.152022i
$377$	4.51047	+	4.51047i	0.232301	+	0.232301i
$378$		0			0
$379$		−	7.15349i		−	0.367450i	−0.982978	−	0.183725i	$-0.941184\pi$
$379$		−	7.15349i		−	0.367450i	0.982978	−	0.183725i	$-0.0588156\pi$
$380$	−1.47269	+	8.57682i	−0.0755475	+	0.439982i
$381$		0			0
$382$	−4.45229	−	16.6162i	−0.227799	−	0.850158i
$383$	14.0961	+	3.77704i	0.720278	+	0.192998i	0.600296	−	0.799778i	$-0.295050\pi$
$383$	14.0961	+	3.77704i	0.720278	+	0.192998i	0.119982	+	0.992776i	$0.461716\pi$
$384$		0			0
$385$	24.5463	+	22.4767i	1.25099	+	1.14552i
$386$	12.0674			0.614214
$387$		0			0
$388$	−2.42713	−	9.05816i	−0.123219	−	0.459858i
$389$	−5.36634	−	3.09826i	−0.272084	−	0.157088i	0.357750	−	0.933817i	$-0.383544\pi$
$389$	−5.36634	−	3.09826i	−0.272084	−	0.157088i	−0.629834	+	0.776729i	$0.716877\pi$
$390$		0			0
$391$		−	5.96659i		−	0.301744i
$392$	−4.45502	−	5.39934i	−0.225012	−	0.272708i
$393$		0			0
$394$	−17.5304	+	10.1212i	−0.883167	+	0.509897i
$395$	−13.1065	+	4.83706i	−0.659460	+	0.243379i
$396$		0			0
$397$	0.754685	−	2.81652i	0.0378766	−	0.141357i	−0.944398	−	0.328804i	$-0.893354\pi$
$397$	0.754685	−	2.81652i	0.0378766	−	0.141357i	0.982275	+	0.187447i	$0.0600212\pi$
$398$	−5.32668	+	5.32668i	−0.267002	+	0.267002i
$399$		0			0
$400$	0.912375	+	4.91605i	0.0456187	+	0.245803i
$401$	−9.98528	−	17.2950i	−0.498641	−	0.863672i	0.501358	−	0.865240i	$-0.332834\pi$
$401$	−9.98528	−	17.2950i	−0.498641	−	0.863672i	−0.999999	+	0.00156835i	$0.999501\pi$
$402$		0			0
$403$	7.51565	−	2.01381i	0.374381	−	0.100315i
$404$	−8.04960	−	13.9423i	−0.400483	−	0.693656i
$405$		0			0
$406$	−7.95060	−	2.54300i	−0.394581	−	0.126207i
$407$	20.0491	−	20.0491i	0.993796	−	0.993796i
$408$		0			0
$409$	17.1791	−	29.7550i	0.849451	−	1.47129i	−0.0322484	−	0.999480i	$-0.510267\pi$
$409$	17.1791	−	29.7550i	0.849451	−	1.47129i	0.881699	−	0.471812i	$-0.156400\pi$
$410$	6.74834	−	14.6430i	0.333277	−	0.723165i
$411$		0			0
$412$	13.9084	+	13.9084i	0.685220	+	0.685220i
$413$	12.1923	+	7.83843i	0.599946	+	0.385704i
$414$		0			0
$415$	14.6485	−	10.3552i	0.719065	−	0.508317i
$416$	−1.75092	−	1.01089i	−0.0858459	−	0.0495631i
$417$		0			0
$418$	−21.1483	−	5.66668i	−1.03440	−	0.277166i
$419$	31.1360			1.52109			0.760547	−	0.649283i	$-0.224931\pi$
$419$	31.1360			1.52109			0.760547	+	0.649283i	$0.224931\pi$
$420$		0			0
$421$	−33.6728			−1.64111			−0.820555	−	0.571567i	$-0.806336\pi$
$421$	−33.6728			−1.64111			−0.820555	+	0.571567i	$0.806336\pi$
$422$	18.9095	+	5.06679i	0.920501	+	0.246648i
$423$		0			0
$424$	−1.19782	−	0.691560i	−0.0581711	−	0.0335851i
$425$	26.4623	+	2.07615i	1.28361	+	0.100708i
$426$		0			0
$427$	5.58621	+	10.8402i	0.270336	+	0.524594i
$428$	1.98061	+	1.98061i	0.0957366	+	0.0957366i
$429$		0			0
$430$	−2.03285	−	5.50823i	−0.0980330	−	0.265630i
$431$	−7.37284	+	12.7701i	−0.355137	+	0.615116i	−0.987141	−	0.159849i	$-0.948899\pi$
$431$	−7.37284	+	12.7701i	−0.355137	+	0.615116i	0.632004	+	0.774965i	$0.282233\pi$
$432$		0			0
$433$	−9.98256	+	9.98256i	−0.479731	+	0.479731i	−0.905046	−	0.425315i	$-0.860163\pi$
$433$	−9.98256	+	9.98256i	−0.479731	+	0.479731i	0.425315	+	0.905046i	$0.360163\pi$
$434$	−7.53539	+	6.84781i	−0.361710	+	0.328706i
$435$		0			0
$436$	−2.95543	−	5.11895i	−0.141539	−	0.245153i
$437$	−4.22504	+	1.13210i	−0.202111	+	0.0541555i
$438$		0			0
$439$	19.2142	+	33.2800i	0.917046	+	1.58837i	0.803878	+	0.594794i	$0.202766\pi$
$439$	19.2142	+	33.2800i	0.917046	+	1.58837i	0.113167	+	0.993576i	$0.463900\pi$
$440$	−12.5267	+	1.15258i	−0.597186	+	0.0549470i
$441$		0			0
$442$	−7.58946	+	7.58946i	−0.360994	+	0.360994i
$443$	−1.48448	+	5.54016i	−0.0705299	+	0.263221i	−0.992183	−	0.124795i	$-0.960173\pi$
$443$	−1.48448	+	5.54016i	−0.0705299	+	0.263221i	0.921653	+	0.388016i	$0.126839\pi$
$444$		0			0
$445$	−9.22982	−	25.0092i	−0.437536	−	1.18555i
$446$	1.78845	−	1.03256i	0.0846857	−	0.0488933i
$447$		0			0
$448$	2.64273	+	0.126334i	0.124857	+	0.00596872i
$449$			7.30267i			0.344635i	0.985042	+	0.172317i	$0.0551254\pi$
$449$			7.30267i			0.344635i	−0.985042	+	0.172317i	$0.944875\pi$
$450$		0			0
$451$	35.1299	+	20.2823i	1.65420	+	0.955055i
$452$	4.97128	+	18.5531i	0.233829	+	0.872663i
$453$		0			0
$454$	18.6433			0.874974
$455$	−6.43021	−	10.0856i	−0.301453	−	0.472820i
$456$		0			0
$457$	−4.97047	−	1.33183i	−0.232509	−	0.0623006i	0.140683	−	0.990055i	$-0.455070\pi$
$457$	−4.97047	−	1.33183i	−0.232509	−	0.0623006i	−0.373192	+	0.927754i	$0.621737\pi$
$458$	−1.03726	−	3.87111i	−0.0484680	−	0.180885i
$459$		0			0
$460$	−2.05218	+	1.45071i	−0.0956833	+	0.0676397i
$461$		−	29.4110i		−	1.36981i	−0.728634	−	0.684903i	$-0.759845\pi$
$461$		−	29.4110i		−	1.36981i	0.728634	−	0.684903i	$-0.240155\pi$
$462$		0			0
$463$	−4.04625	−	4.04625i	−0.188045	−	0.188045i	0.606805	−	0.794851i	$-0.292451\pi$
$463$	−4.04625	−	4.04625i	−0.188045	−	0.188045i	−0.794851	+	0.606805i	$0.792451\pi$
$464$	2.73232	−	1.57751i	0.126845	−	0.0732340i
$465$		0			0
$466$	6.86580	−	11.8919i	0.318052	−	0.550882i
$467$	−4.30747	+	16.0757i	−0.199326	+	0.743894i	0.791779	+	0.610808i	$0.209155\pi$
$467$	−4.30747	+	16.0757i	−0.199326	+	0.743894i	−0.991105	+	0.133086i	$0.957511\pi$
$468$		0			0
$469$	2.18461	−	0.474848i	0.100876	−	0.0219264i
$470$	−8.42852	+	10.1367i	−0.388779	+	0.467571i
$471$		0			0
$472$	−5.29178	+	1.41793i	−0.243574	+	0.0652654i
$473$	14.2686	−	3.82325i	0.656069	−	0.175793i
$474$		0			0
$475$	−3.55078	−	19.1323i	−0.162921	−	0.877851i
$476$	4.27894	−	13.3779i	0.196125	−	0.613176i
$477$		0			0
$478$	−5.08891	+	18.9921i	−0.232762	+	0.868678i
$479$	−7.69460	+	13.3274i	−0.351575	+	0.608946i	−0.986526	−	0.163607i	$-0.947687\pi$
$479$	−7.69460	+	13.3274i	−0.351575	+	0.608946i	0.634950	+	0.772553i	$0.281021\pi$
$480$		0			0
$481$	−8.82459	+	5.09488i	−0.402367	+	0.232306i
$482$	−4.16141	−	4.16141i	−0.189547	−	0.189547i
$483$		0			0
$484$		−	20.6492i		−	0.938599i
$485$	12.1043	+	17.1228i	0.549629	+	0.777507i
$486$		0			0
$487$	−9.31541	−	34.7656i	−0.422122	−	1.57538i	−0.770129	−	0.637888i	$-0.779808\pi$
$487$	−9.31541	−	34.7656i	−0.422122	−	1.57538i	0.348007	−	0.937492i	$-0.386858\pi$
$488$	−4.45219	−	1.19296i	−0.201541	−	0.0540028i
$489$		0			0
$490$	13.5257	+	7.87748i	0.611030	+	0.355868i
$491$	15.2823			0.689680			0.344840	−	0.938661i	$-0.387933\pi$
$491$	15.2823			0.689680			0.344840	+	0.938661i	$0.387933\pi$
$492$		0			0
$493$	−4.33499	−	16.1784i	−0.195238	−	0.728639i
$494$	6.81423	+	3.93420i	0.306587	+	0.177008i
$495$		0			0
$496$		−	3.84846i		−	0.172801i
$497$	−0.603509	+	12.6246i	−0.0270711	+	0.566290i
$498$		0			0
$499$	−27.3534	+	15.7925i	−1.22451	+	0.706969i	−0.965875	−	0.259008i	$-0.916604\pi$
$499$	−27.3534	+	15.7925i	−1.22451	+	0.706969i	−0.258630	+	0.965976i	$0.583271\pi$
$500$	−5.71994	−	9.60637i	−0.255803	−	0.429610i
$501$		0			0
$502$	1.83749	−	6.85759i	0.0820110	−	0.306069i
$503$	−16.9777	+	16.9777i	−0.756997	+	0.756997i	−0.975775	−	0.218778i	$-0.929793\pi$
$503$	−16.9777	+	16.9777i	−0.756997	+	0.756997i	0.218778	+	0.975775i	$0.429793\pi$
$504$		0			0
$505$	27.6803	+	23.0157i	1.23176	+	1.02419i
$506$	−3.16146	−	5.47580i	−0.140544	−	0.243429i
$507$		0			0
$508$	6.33135	−	1.69648i	0.280908	−	0.0752691i
$509$	−10.7571	−	18.6318i	−0.476799	−	0.825840i	0.522848	−	0.852426i	$-0.324870\pi$
$509$	−10.7571	−	18.6318i	−0.476799	−	0.825840i	−0.999647	+	0.0265865i	$0.991536\pi$
$510$		0			0
$511$	14.5099	−	3.15388i	0.641879	−	0.139519i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$	4.94343	−	8.56228i	0.218045	−	0.377666i
$515$	−39.9445	−	18.4088i	−1.76017	−	0.811188i
$516$		0			0
$517$	−23.4529	−	23.4529i	−1.03146	−	1.03146i
$518$	7.21107	−	11.2165i	0.316836	−	0.492825i
$519$		0			0
$520$	4.45565	+	0.765062i	0.195393	+	0.0335502i
$521$	−11.4657	−	6.61973i	−0.502322	−	0.290016i	0.227350	−	0.973813i	$-0.426994\pi$
$521$	−11.4657	−	6.61973i	−0.502322	−	0.290016i	−0.729672	+	0.683798i	$0.760327\pi$
$522$		0			0
$523$	−26.0126	−	6.97006i	−1.13745	−	0.304779i	−0.359526	−	0.933135i	$-0.617062\pi$
$523$	−26.0126	−	6.97006i	−1.13745	−	0.304779i	−0.777926	+	0.628356i	$0.783728\pi$
$524$	7.69535			0.336173
$525$		0			0
$526$	13.7482			0.599448
$527$	−19.7343	−	5.28779i	−0.859640	−	0.230340i
$528$		0			0
$529$	18.8246	+	10.8684i	0.818462	+	0.472539i
$530$	3.04814	+	0.523384i	0.132403	+	0.0227344i
$531$		0			0
$532$	−10.2850	−	0.491667i	−0.445911	−	0.0213165i
$533$	−10.3083	−	10.3083i	−0.446501	−	0.446501i
$534$		0			0
$535$	−5.68825	−	2.62148i	−0.245924	−	0.113336i
$536$	−0.422492	+	0.731778i	−0.0182489	+	0.0316080i
$537$		0			0
$538$	18.7398	−	18.7398i	0.807928	−	0.807928i
$539$	−22.8536	+	32.0706i	−0.984374	+	1.38138i
$540$		0			0
$541$	5.66491	+	9.81190i	0.243553	+	0.421847i	0.961724	−	0.274020i	$-0.0883536\pi$
$541$	5.66491	+	9.81190i	0.243553	+	0.421847i	−0.718171	+	0.695867i	$0.755020\pi$
$542$	−12.3608	+	3.31208i	−0.530943	+	0.142266i
$543$		0			0
$544$	2.65436	+	4.59749i	0.113805	+	0.197116i
$545$	10.1629	+	8.45027i	0.435329	+	0.361970i
$546$		0			0
$547$	−30.9149	+	30.9149i	−1.32182	+	1.32182i	−0.409527	+	0.912298i	$0.634306\pi$
$547$	−30.9149	+	30.9149i	−1.32182	+	1.32182i	−0.912298	+	0.409527i	$0.865694\pi$
$548$	−2.28687	+	8.53471i	−0.0976902	+	0.364585i
$549$		0			0
$550$	25.3857	−	12.1159i	1.08245	−	0.516625i
$551$	−10.6337	+	6.13935i	−0.453009	+	0.261545i
$552$		0			0
$553$	−7.57212	−	14.6939i	−0.321999	−	0.624850i
$554$			20.1034i			0.854110i
$555$		0			0
$556$	9.58094	+	5.53156i	0.406322	+	0.234590i
$557$	6.83277	+	25.5003i	0.289514	+	1.08048i	0.945477	+	0.325688i	$0.105596\pi$
$557$	6.83277	+	25.5003i	0.289514	+	1.08048i	−0.655963	+	0.754793i	$0.727737\pi$
$558$		0			0
$559$	−5.30873			−0.224535
$560$	−5.64164	+	1.78098i	−0.238403	+	0.0752600i
$561$		0			0
$562$	13.6677	+	3.66224i	0.576536	+	0.154482i
$563$	−5.22648	−	19.5055i	−0.220270	−	0.822058i	−0.984245	−	0.176812i	$-0.943422\pi$
$563$	−5.22648	−	19.5055i	−0.220270	−	0.822058i	0.763975	−	0.645246i	$-0.223245\pi$
$564$		0			0
$565$	−24.7923	−	35.0712i	−1.04302	−	1.47546i
$566$		−	27.0677i		−	1.13774i
$567$		0			0
$568$	−3.37792	−	3.37792i	−0.141734	−	0.141734i
$569$	−21.4890	+	12.4067i	−0.900867	+	0.520116i	−0.877481	−	0.479611i	$-0.840778\pi$
$569$	−21.4890	+	12.4067i	−0.900867	+	0.520116i	−0.0233856	+	0.999727i	$0.507445\pi$
$570$		0			0
$571$	−2.29029	+	3.96690i	−0.0958458	+	0.166010i	−0.909961	−	0.414693i	$-0.863889\pi$
$571$	−2.29029	+	3.96690i	−0.0958458	+	0.166010i	0.814116	+	0.580703i	$0.197222\pi$
$572$	−2.94383	+	10.9865i	−0.123088	+	0.459370i
$573$		0			0
$574$	18.1704	+	5.81180i	0.758417	+	0.242580i
$575$	3.18185	−	4.63204i	0.132692	−	0.193169i
$576$		0			0
$577$	−19.1065	+	5.11957i	−0.795414	+	0.213131i	−0.633570	−	0.773686i	$-0.718411\pi$
$577$	−19.1065	+	5.11957i	−0.795414	+	0.213131i	−0.161845	+	0.986816i	$0.551744\pi$
$578$	10.8016	−	2.89427i	0.449286	−	0.120386i
$579$		0			0
$580$	−4.51047	+	5.42460i	−0.187287	+	0.225244i
$581$	14.2751	+	15.7084i	0.592229	+	0.651694i
$582$		0			0
$583$	−2.01390	+	7.51596i	−0.0834071	+	0.311279i
$584$	−2.80614	+	4.86037i	−0.116119	+	0.201124i
$585$		0			0
$586$	−20.9665	+	12.1050i	−0.866118	+	0.500053i
$587$	−19.3782	−	19.3782i	−0.799824	−	0.799824i	0.183244	−	0.983068i	$-0.441340\pi$
$587$	−19.3782	−	19.3782i	−0.799824	−	0.799824i	−0.983068	+	0.183244i	$0.941340\pi$
$588$		0			0
$589$			14.9775i			0.617136i
$590$	10.0032	−	7.07136i	0.411823	−	0.291123i
$591$		0			0
$592$	1.30444	+	4.86824i	0.0536122	+	0.200083i
$593$	−3.12741	−	0.837988i	−0.128428	−	0.0344121i	0.194033	−	0.980995i	$-0.437843\pi$
$593$	−3.12741	−	0.837988i	−0.128428	−	0.0344121i	−0.322460	+	0.946583i	$0.604510\pi$
$594$		0			0
$595$	1.38094	+	31.3765i	0.0566131	+	1.28631i
$596$	5.04885			0.206809
$597$		0			0
$598$	0.588122	+	2.19490i	0.0240501	+	0.0897562i
$599$	−6.75802	−	3.90174i	−0.276125	−	0.159421i	0.355543	−	0.934660i	$-0.384296\pi$
$599$	−6.75802	−	3.90174i	−0.276125	−	0.159421i	−0.631668	+	0.775239i	$0.717629\pi$
$600$		0			0
$601$			31.7170i			1.29377i	0.762590	+	0.646883i	$0.223928\pi$
$601$			31.7170i			1.29377i	−0.762590	+	0.646883i	$0.776072\pi$
$602$	6.17537	−	3.18231i	0.251689	−	0.129701i
$603$		0			0
$604$	−11.6418	+	6.72142i	−0.473699	+	0.273491i
$605$	15.9865	+	43.3171i	0.649945	+	1.76109i
$606$		0			0
$607$	0.199219	−	0.743495i	0.00808604	−	0.0301775i	−0.961765	−	0.273876i	$-0.911694\pi$
$607$	0.199219	−	0.743495i	0.00808604	−	0.0301775i	0.969851	+	0.243699i	$0.0783608\pi$
$608$	2.75192	−	2.75192i	0.111605	−	0.111605i
$609$		0			0
$610$	10.2632	−	0.944318i	0.415546	−	0.0382343i
$611$	5.95987	+	10.3228i	0.241110	+	0.417615i
$612$		0			0
$613$	−33.8086	+	9.05898i	−1.36552	+	0.365889i	−0.865839	−	0.500323i	$-0.833214\pi$
$613$	−33.8086	+	9.05898i	−1.36552	+	0.365889i	−0.499676	+	0.866212i	$0.666548\pi$
$614$	12.2311	+	21.1850i	0.493609	+	0.854955i
$615$		0			0
$616$	−3.16146	−	14.5447i	−0.127379	−	0.586024i
$617$	−21.5403	+	21.5403i	−0.867179	+	0.867179i	−0.992159	−	0.124980i	$-0.960113\pi$
$617$	−21.5403	+	21.5403i	−0.867179	+	0.867179i	0.124980	+	0.992159i	$0.460113\pi$
$618$		0			0
$619$	−21.6707	+	37.5348i	−0.871021	+	1.50865i	−0.0100783	+	0.999949i	$0.503208\pi$
$619$	−21.6707	+	37.5348i	−0.871021	+	1.50865i	−0.860942	+	0.508703i	$0.830125\pi$
$620$	2.97947	+	8.07317i	0.119658	+	0.324226i
$621$		0			0
$622$	7.76566	+	7.76566i	0.311374	+	0.311374i
$623$	28.0382	−	14.4487i	1.12333	−	0.578876i
$624$		0			0
$625$	19.4363	+	15.7235i	0.777452	+	0.628942i
$626$	25.4707	+	14.7055i	1.01801	+	0.587749i
$627$		0			0
$628$	−1.06529	−	0.285443i	−0.0425096	−	0.0113904i
$629$	26.7559			1.06683
$630$		0			0
$631$	7.53463			0.299949			0.149974	−	0.988690i	$-0.452081\pi$
$631$	7.53463			0.299949			0.149974	+	0.988690i	$0.452081\pi$
$632$	6.03495	+	1.61706i	0.240058	+	0.0643232i
$633$		0			0
$634$	3.71869	+	2.14699i	0.147688	+	0.0852677i
$635$	−11.9683	+	8.46052i	−0.474946	+	0.335746i
$636$		0			0
$637$	10.9163	−	9.00710i	0.432520	−	0.356874i
$638$	−12.5507	−	12.5507i	−0.496887	−	0.496887i
$639$		0			0
$640$	0.935904	−	2.03078i	0.0369949	−	0.0802738i
$641$	12.1657	−	21.0717i	0.480518	−	0.832281i	−0.519233	−	0.854633i	$-0.673782\pi$
$641$	12.1657	−	21.0717i	0.480518	−	0.832281i	0.999750	+	0.0223521i	$0.00711549\pi$
$642$		0			0
$643$	−6.21713	+	6.21713i	−0.245180	+	0.245180i	−0.818989	−	0.573809i	$-0.805465\pi$
$643$	−6.21713	+	6.21713i	−0.245180	+	0.245180i	0.573809	+	0.818989i	$0.305465\pi$
$644$	−1.99986	−	2.20067i	−0.0788057	−	0.0867184i
$645$		0			0
$646$	−10.3303	−	17.8925i	−0.406439	−	0.703973i
$647$	−19.9243	+	5.33869i	−0.783304	+	0.209886i	−0.628241	−	0.778019i	$-0.716225\pi$
$647$	−19.9243	+	5.33869i	−0.783304	+	0.209886i	−0.155063	+	0.987905i	$0.549558\pi$
$648$		0			0
$649$	15.4102	+	26.6913i	0.604905	+	1.04773i
$650$	−9.93921	+	1.84463i	−0.389848	+	0.0723523i
$651$		0			0
$652$	−9.36288	+	9.36288i	−0.366679	+	0.366679i
$653$	−6.76544	+	25.2490i	−0.264752	+	0.988069i	0.697650	+	0.716439i	$0.254229\pi$
$653$	−6.76544	+	25.2490i	−0.264752	+	0.988069i	−0.962402	+	0.271630i	$0.912437\pi$
$654$		0			0
$655$	−16.1430	+	5.95772i	−0.630761	+	0.232787i
$656$	−6.24448	+	3.60525i	−0.243806	+	0.140761i
$657$		0			0
$658$	−13.1208	−	8.43533i	−0.511502	−	0.328844i
$659$			24.2448i			0.944443i	0.881480	+	0.472222i	$0.156548\pi$
$659$			24.2448i			0.944443i	−0.881480	+	0.472222i	$0.843452\pi$
$660$		0			0
$661$	15.5301	+	8.96630i	0.604050	+	0.348749i	0.770633	−	0.637279i	$-0.219940\pi$
$661$	15.5301	+	8.96630i	0.604050	+	0.348749i	−0.166583	+	0.986027i	$0.553273\pi$
$662$	−9.17510	−	34.2419i	−0.356600	−	1.33085i
$663$		0			0
$664$	−8.02257			−0.311336
$665$	21.9562	−	6.93121i	0.851423	−	0.268781i
$666$		0			0
$667$	−3.42516	−	0.917769i	−0.132623	−	0.0355362i
$668$	1.72281	+	6.42961i	0.0666574	+	0.248769i
$669$		0			0
$670$	0.319750	−	1.86219i	0.0123530	−	0.0719427i
$671$			25.9305i			1.00104i
$672$		0			0
$673$	−4.85386	−	4.85386i	−0.187103	−	0.187103i	0.607340	−	0.794442i	$-0.292237\pi$
$673$	−4.85386	−	4.85386i	−0.187103	−	0.187103i	−0.794442	+	0.607340i	$0.792237\pi$
$674$	−14.8774	+	8.58946i	−0.573056	+	0.330854i
$675$		0			0
$676$	−4.45619	+	7.71834i	−0.171392	+	0.296859i
$677$	4.78306	−	17.8506i	0.183828	−	0.686055i	−0.811051	−	0.584976i	$-0.801104\pi$
$677$	4.78306	−	17.8506i	0.183828	−	0.686055i	0.994878	−	0.101079i	$-0.0322294\pi$
$678$		0			0
$679$	−18.3618	+	16.6863i	−0.704660	+	0.640362i
$680$	−9.12760	−	7.58946i	−0.350027	−	0.291043i
$681$		0			0
$682$	−20.9128	+	5.60357i	−0.800793	+	0.214572i
$683$	−25.8878	+	6.93661i	−0.990569	+	0.265422i	−0.717489	−	0.696569i	$-0.754709\pi$
$683$	−25.8878	+	6.93661i	−0.990569	+	0.265422i	−0.273079	+	0.961992i	$0.588042\pi$
$684$		0			0
$685$	−1.81023	−	19.6743i	−0.0691653	−	0.751717i
$686$	−7.29908	+	17.0213i	−0.278680	+	0.649875i
$687$		0			0
$688$	−0.679597	+	2.53629i	−0.0259094	+	0.0966951i
$689$	1.39819	−	2.42173i	0.0532667	−	0.0922606i
$690$		0			0
$691$	25.1773	−	14.5361i	0.957790	−	0.552980i	0.0622976	−	0.998058i	$-0.480157\pi$
$691$	25.1773	−	14.5361i	0.957790	−	0.552980i	0.895492	+	0.445077i	$0.146824\pi$
$692$	4.98835	+	4.98835i	0.189628	+	0.189628i
$693$		0			0
$694$		−	8.97626i		−	0.340734i
$695$	−24.3811	−	4.18638i	−0.924827	−	0.158798i
$696$		0			0
$697$	9.90723	+	36.9743i	0.375263	+	1.40050i
$698$	−25.1383	−	6.73580i	−0.951500	−	0.254954i
$699$		0			0
$700$	10.4560	−	8.10381i	0.395200	−	0.306295i
$701$	−25.4462			−0.961089			−0.480545	−	0.876970i	$-0.659561\pi$
$701$	−25.4462			−0.961089			−0.480545	+	0.876970i	$0.659561\pi$
$702$		0			0
$703$	−5.07663	−	18.9462i	−0.191469	−	0.714571i
$704$	4.87205	+	2.81288i	0.183622	+	0.106014i
$705$		0			0
$706$		−	9.96618i		−	0.375082i
$707$	−23.0343	+	35.8289i	−0.866295	+	1.34748i
$708$		0			0
$709$	−27.1994	+	15.7036i	−1.02150	+	0.589760i	−0.914537	−	0.404503i	$-0.867445\pi$
$709$	−27.1994	+	15.7036i	−1.02150	+	0.589760i	−0.106958	+	0.994263i	$0.534111\pi$
$710$	9.70125	+	4.47091i	0.364081	+	0.167790i
$711$		0			0
$712$	−3.08559	+	11.5156i	−0.115637	+	0.431565i
$713$	−3.05850	+	3.05850i	−0.114542	+	0.114542i
$714$		0			0
$715$	−2.33027	−	25.3263i	−0.0871470	−	0.947149i
$716$	−1.10317	−	1.91075i	−0.0412275	−	0.0714081i
$717$		0			0
$718$	−11.1797	+	2.99560i	−0.417224	+	0.111795i
$719$	5.40214	+	9.35678i	0.201466	+	0.348949i	0.949001	−	0.315273i	$-0.102096\pi$
$719$	5.40214	+	9.35678i	0.201466	+	0.348949i	−0.747535	+	0.664222i	$0.768763\pi$
$720$		0			0
$721$	15.8540	−	49.5669i	0.590434	−	1.84597i
$722$	2.72509	−	2.72509i	0.101417	−	0.101417i
$723$		0			0
$724$	−2.05934	+	3.56688i	−0.0765347	+	0.132562i
$725$	5.26221	−	14.8715i	0.195433	−	0.552315i
$726$		0			0
$727$	33.6108	+	33.6108i	1.24656	+	1.24656i	0.957231	+	0.289326i	$0.0934311\pi$
$727$	33.6108	+	33.6108i	1.24656	+	1.24656i	0.289326	+	0.957231i	$0.406569\pi$
$728$	−0.255420	+	5.34305i	−0.00946651	+	0.198026i
$729$		0			0
$730$	2.12373	−	12.3684i	0.0786029	−	0.457776i
$731$	12.0719	+	6.96972i	0.446496	+	0.257785i
$732$		0			0
$733$	24.8800	+	6.66658i	0.918964	+	0.246236i	0.687143	−	0.726523i	$-0.258865\pi$
$733$	24.8800	+	6.66658i	0.918964	+	0.246236i	0.231822	+	0.972758i	$0.425531\pi$
$734$	16.6944			0.616202
$735$		0			0
$736$	1.12392			0.0414283
$737$	4.59170	+	1.23034i	0.169138	+	0.0453203i
$738$		0			0
$739$	10.4948	+	6.05920i	0.386059	+	0.222891i	0.680451	−	0.732793i	$-0.261784\pi$
$739$	10.4948	+	6.05920i	0.386059	+	0.222891i	−0.294392	+	0.955685i	$0.595117\pi$
$740$	−6.50539	−	9.20253i	−0.239143	−	0.338292i
$741$		0			0
$742$	−0.174735	+	3.65522i	−0.00641472	+	0.134187i
$743$	−23.2618	−	23.2618i	−0.853393	−	0.853393i	0.137157	−	0.990549i	$-0.456204\pi$
$743$	−23.2618	−	23.2618i	−0.853393	−	0.853393i	−0.990549	+	0.137157i	$0.956204\pi$
$744$		0			0
$745$	−10.5913	+	3.90881i	−0.388036	+	0.143208i
$746$	1.58946	−	2.75303i	0.0581944	−	0.100796i
$747$		0			0
$748$	21.1182	−	21.1182i	0.772158	−	0.772158i
$749$	2.25767	−	7.05851i	0.0824934	−	0.257912i
$750$		0			0
$751$	−6.98887	−	12.1051i	−0.255028	−	0.441721i	0.709875	−	0.704327i	$-0.248751\pi$
$751$	−6.98887	−	12.1051i	−0.255028	−	0.441721i	−0.964903	+	0.262607i	$0.915418\pi$
$752$	5.69475	−	1.52590i	0.207666	−	0.0556440i
$753$		0			0
$754$	3.18939	+	5.52418i	0.116151	+	0.201179i
$755$	19.2181	−	23.1130i	0.699420	−	0.841169i
$756$		0			0
$757$	17.5547	−	17.5547i	0.638036	−	0.638036i	−0.312035	−	0.950071i	$-0.601010\pi$
$757$	17.5547	−	17.5547i	0.638036	−	0.638036i	0.950071	+	0.312035i	$0.101010\pi$
$758$	1.85146	−	6.90974i	0.0672481	−	0.250973i
$759$		0			0
$760$	−3.64236	+	7.90341i	−0.132122	+	0.286687i
$761$	−18.9372	+	10.9334i	−0.686471	+	0.396334i	−0.802289	−	0.596936i	$-0.796385\pi$
$761$	−18.9372	+	10.9334i	−0.686471	+	0.396334i	0.115817	+	0.993271i	$0.463051\pi$
$762$		0			0
$763$	−8.45710	+	13.1546i	−0.306168	+	0.476230i
$764$		−	17.2023i		−	0.622359i
$765$		0			0
$766$	12.6382	+	7.29669i	0.456638	+	0.263640i
$767$	−2.86675	−	10.6989i	−0.103512	−	0.386313i
$768$		0			0
$769$	31.0506			1.11971			0.559857	−	0.828589i	$-0.310856\pi$
$769$	31.0506			1.11971			0.559857	+	0.828589i	$0.310856\pi$
$770$	17.8925	+	28.0639i	0.644800	+	1.01135i
$771$		0			0
$772$	11.6562	+	3.12327i	0.419516	+	0.112409i
$773$	1.57065	+	5.86173i	0.0564922	+	0.210832i	0.988402	−	0.151857i	$-0.0485254\pi$
$773$	1.57065	+	5.86173i	0.0564922	+	0.210832i	−0.931910	+	0.362689i	$0.881859\pi$
$774$		0			0
$775$	−12.5004	−	14.6289i	−0.449029	−	0.525487i
$776$		−	9.37769i		−	0.336640i
$777$		0			0
$778$	−4.38160	−	4.38160i	−0.157088	−	0.157088i
$779$	24.3023	−	14.0309i	0.870720	−	0.502710i
$780$		0			0
$781$	−13.4374	+	23.2743i	−0.480828	+	0.832819i
$782$	1.54427	−	5.76329i	0.0552229	−	0.206095i
$783$		0			0
$784$	−2.90577	−	6.36840i	−0.103777	−	0.227443i
$785$	2.45571	−	0.225950i	0.0876481	−	0.00806449i
$786$		0			0
$787$	−21.5993	+	5.78752i	−0.769932	+	0.206303i	−0.622342	−	0.782746i	$-0.713818\pi$
$787$	−21.5993	+	5.78752i	−0.769932	+	0.206303i	−0.147591	+	0.989049i	$0.547152\pi$
$788$	−19.5526	+	5.23910i	−0.696532	+	0.186635i
$789$		0			0
$790$	−13.9118	+	1.28003i	−0.494961	+	0.0455413i
$791$	37.6089	−	34.1772i	1.33722	−	1.21520i
$792$		0			0
$793$	2.41191	−	9.00138i	0.0856495	−	0.319648i
$794$	1.45794	−	2.52523i	0.0517403	−	0.0896169i
$795$		0			0
$796$	−6.52383	+	3.76653i	−0.231231	+	0.133501i
$797$	−16.5528	−	16.5528i	−0.586330	−	0.586330i	0.350305	−	0.936636i	$-0.386078\pi$
$797$	−16.5528	−	16.5528i	−0.586330	−	0.586330i	−0.936636	+	0.350305i	$0.886078\pi$
$798$		0			0
$799$		−	31.2984i		−	1.10726i
$800$	−0.391082	+	4.98468i	−0.0138268	+	0.176235i
$801$		0			0
$802$	−5.16876	−	19.2901i	−0.182515	−	0.681156i
$803$	30.4975	+	8.17177i	1.07623	+	0.288376i
$804$		0			0
$805$	5.89899	+	3.06820i	0.207912	+	0.108140i
$806$	7.78078			0.274066
$807$		0			0
$808$	−4.16678	−	15.5506i	−0.146587	−	0.547069i
$809$	−2.84139	−	1.64048i	−0.0998980	−	0.0576762i	0.449219	−	0.893422i	$-0.351702\pi$
$809$	−2.84139	−	1.64048i	−0.0998980	−	0.0576762i	−0.549117	+	0.835746i	$0.685036\pi$
$810$		0			0
$811$		−	17.8693i		−	0.627476i	−0.949510	−	0.313738i	$-0.898419\pi$
$811$		−	17.8693i		−	0.627476i	0.949510	−	0.313738i	$-0.101581\pi$
$812$	−7.02151	−	4.51412i	−0.246407	−	0.158414i
$813$		0			0
$814$	24.5550	−	14.1768i	0.860653	−	0.496898i
$815$	12.3924	−	26.8898i	0.434088	−	0.941910i
$816$		0			0
$817$	2.64486	−	9.87074i	0.0925318	−	0.345333i
$818$	24.2949	−	24.2949i	0.849451	−	0.849451i
$819$		0			0
$820$	10.3083	−	12.3974i	0.359981	−	0.432937i
$821$	−5.90837	−	10.2336i	−0.206204	−	0.357155i	0.744312	−	0.667832i	$-0.232778\pi$
$821$	−5.90837	−	10.2336i	−0.206204	−	0.357155i	−0.950516	+	0.310677i	$0.899444\pi$
$822$		0			0
$823$	−34.0995	+	9.13692i	−1.18863	+	0.318493i	−0.798345	−	0.602200i	$-0.794291\pi$
$823$	−34.0995	+	9.13692i	−1.18863	+	0.318493i	−0.390287	+	0.920693i	$0.627624\pi$
$824$	9.83476	+	17.0343i	0.342610	+	0.593418i
$825$		0			0
$826$	9.74816	+	10.7270i	0.339182	+	0.373239i
$827$	17.2835	−	17.2835i	0.601005	−	0.601005i	−0.339574	−	0.940579i	$-0.610283\pi$
$827$	17.2835	−	17.2835i	0.601005	−	0.601005i	0.940579	+	0.339574i	$0.110283\pi$
$828$		0			0
$829$	17.2877	−	29.9431i	0.600426	−	1.03997i	−0.392330	−	0.919824i	$-0.628331\pi$
$829$	17.2877	−	29.9431i	0.600426	−	1.03997i	0.992756	−	0.120144i	$-0.0383357\pi$
$830$	16.8295	−	6.21104i	0.584159	−	0.215589i
$831$		0			0
$832$	−1.42962	−	1.42962i	−0.0495631	−	0.0495631i
$833$	−36.6487	+	6.15011i	−1.26980	+	0.213089i
$834$		0			0
$835$	−8.59183	−	12.1540i	−0.297332	−	0.420607i
$836$	−18.9611	−	10.9472i	−0.655782	−	0.378616i
$837$		0			0
$838$	30.0751	+	8.05859i	1.03893	+	0.278379i
$839$	50.1328			1.73078			0.865388	−	0.501102i	$-0.167072\pi$
$839$	50.1328			1.73078			0.865388	+	0.501102i	$0.167072\pi$
$840$		0			0
$841$	19.0459			0.656754
$842$	−32.5254	−	8.71515i	−1.12090	−	0.300344i
$843$		0			0
$844$	16.9538	+	9.78829i	0.583575	+	0.336927i
$845$	3.37252	−	19.6412i	0.116018	−	0.675679i
$846$		0			0
$847$	−48.5636	+	25.0259i	−1.66866	+	0.859901i
$848$	−0.978013	−	0.978013i	−0.0335851	−	0.0335851i
$849$		0			0
$850$	25.0233	+	8.85436i	0.858292	+	0.303702i
$851$	2.83227	−	4.90563i	0.0970888	−	0.168163i
$852$		0			0
$853$	−2.37500	+	2.37500i	−0.0813183	+	0.0813183i	−0.746596	−	0.665278i	$-0.768313\pi$
$853$	−2.37500	+	2.37500i	−0.0813183	+	0.0813183i	0.665278	+	0.746596i	$0.268313\pi$
$854$	2.59021	+	11.9167i	0.0886352	+	0.407779i
$855$		0			0
$856$	1.40051	+	2.42575i	0.0478683	+	0.0829103i
$857$	40.5097	−	10.8545i	1.38378	−	0.370784i	0.511290	−	0.859408i	$-0.329168\pi$
$857$	40.5097	−	10.8545i	1.38378	−	0.370784i	0.872494	+	0.488624i	$0.162501\pi$
$858$		0			0
$859$	−1.17847	−	2.04117i	−0.0402090	−	0.0696440i	0.845221	−	0.534418i	$-0.179469\pi$
$859$	−1.17847	−	2.04117i	−0.0402090	−	0.0696440i	−0.885430	+	0.464774i	$0.846136\pi$
$860$	−0.537952	−	5.84668i	−0.0183440	−	0.199370i
$861$		0			0
$862$	−10.4268	+	10.4268i	−0.355137	+	0.355137i
$863$	−12.5138	+	46.7022i	−0.425975	+	1.58976i	0.335808	+	0.941930i	$0.390991\pi$
$863$	−12.5138	+	46.7022i	−0.425975	+	1.58976i	−0.761784	+	0.647831i	$0.775676\pi$
$864$		0			0
$865$	−14.3263	−	6.60242i	−0.487110	−	0.224489i
$866$	−12.2261	+	7.05873i	−0.415459	+	0.239865i
$867$		0			0
$868$	−9.05097	+	4.66418i	−0.307210	+	0.158312i
$869$		−	35.1489i		−	1.19234i
$870$		0			0
$871$	−1.47950	−	0.854190i	−0.0501310	−	0.0289431i
$872$	−1.52984	−	5.70944i	−0.0518069	−	0.193346i
$873$		0			0
$874$	−4.37408			−0.147955
$875$	−15.6603	+	25.0949i	−0.529416	+	0.848363i
$876$		0			0
$877$	13.3115	+	3.56681i	0.449498	+	0.120443i	0.476465	−	0.879194i	$-0.341918\pi$
$877$	13.3115	+	3.56681i	0.449498	+	0.120443i	−0.0269665	+	0.999636i	$0.508585\pi$
$878$	9.94602	+	37.1191i	0.335662	+	1.25271i
$879$		0			0
$880$	−12.3981	−	2.12884i	−0.417941	−	0.0717631i
$881$			3.32542i			0.112036i	0.998430	+	0.0560181i	$0.0178405\pi$
$881$			3.32542i			0.112036i	−0.998430	+	0.0560181i	$0.982160\pi$
$882$		0			0
$883$	−36.8930	−	36.8930i	−1.24155	−	1.24155i	−0.959358	−	0.282191i	$-0.908939\pi$
$883$	−36.8930	−	36.8930i	−1.24155	−	1.24155i	−0.282191	−	0.959358i	$-0.591061\pi$
$884$	−9.29516	+	5.36656i	−0.312630	+	0.180497i
$885$		0			0
$886$	−2.86780	+	4.96718i	−0.0963456	+	0.166876i
$887$	9.27107	−	34.6001i	0.311292	−	1.16176i	−0.616101	−	0.787668i	$-0.711289\pi$
$887$	9.27107	−	34.6001i	0.311292	−	1.16176i	0.927392	−	0.374090i	$-0.122045\pi$
$888$		0			0
$889$	−11.6632	−	12.8343i	−0.391170	−	0.430447i
$890$	−2.44248	−	26.5458i	−0.0818721	−	0.889819i
$891$		0			0
$892$	1.99476	−	0.534495i	0.0667895	−	0.0178962i
$893$	−22.1628	+	5.93852i	−0.741651	+	0.198725i
$894$		0			0
$895$	3.79349	+	3.15423i	0.126803	+	0.105434i
$896$	2.51999	+	0.806019i	0.0841869	+	0.0269272i
$897$		0			0
$898$	−1.89007	+	7.05384i	−0.0630725	+	0.235390i
$899$	−6.07098	+	10.5152i	−0.202479	+	0.350703i
$900$		0			0
$901$	−6.35888	+	3.67130i	−0.211845	+	0.122309i
$902$	28.6835	+	28.6835i	0.955055	+	0.955055i
$903$		0			0
$904$			19.2075i			0.638833i
$905$	1.55854	−	9.07680i	0.0518077	−	0.301723i
$906$		0			0
$907$	−4.46661	−	16.6696i	−0.148312	−	0.553506i	−0.999586	−	0.0287849i	$-0.990836\pi$
$907$	−4.46661	−	16.6696i	−0.148312	−	0.553506i	0.851274	−	0.524721i	$-0.175830\pi$
$908$	18.0081	+	4.82525i	0.597618	+	0.160131i
$909$		0			0
$910$	−3.60076	−	11.4062i	−0.119364	−	0.378112i
$911$	−5.56820			−0.184483			−0.0922414	−	0.995737i	$-0.529403\pi$
$911$	−5.56820			−0.184483			−0.0922414	+	0.995737i	$0.529403\pi$
$912$		0			0
$913$	11.6813	+	43.5952i	0.386594	+	1.44279i
$914$	−4.45641	−	2.57291i	−0.147405	−	0.0851042i
$915$		0			0
$916$		−	4.00767i		−	0.132417i
$917$	−9.32645	−	18.0982i	−0.307986	−	0.597657i
$918$		0			0
$919$	5.37964	−	3.10593i	0.177458	−	0.102455i	−0.408640	−	0.912696i	$-0.633997\pi$
$919$	5.37964	−	3.10593i	0.177458	−	0.102455i	0.586098	+	0.810240i	$0.300663\pi$
$920$	−2.35772	+	0.870136i	−0.0777318	+	0.0286875i
$921$		0			0
$922$	7.61212	−	28.4088i	0.250692	−	0.935595i
$923$	6.82943	−	6.82943i	0.224794	−	0.224794i
$924$		0			0
$925$	20.7713	+	14.2683i	0.682958	+	0.469139i
$926$	−2.86113	−	4.95563i	−0.0940226	−	0.162852i
$927$		0			0
$928$	3.04751	−	0.816578i	0.100039	−	0.0268055i
$929$	−0.0947297	−	0.164077i	−0.00310798	−	0.00538318i	0.864467	−	0.502689i	$-0.167656\pi$
$929$	−0.0947297	−	0.164077i	−0.00310798	−	0.00538318i	−0.867575	+	0.497306i	$0.834323\pi$
$930$		0			0
$931$	11.3087	+	24.7846i	0.370627	+	0.812281i
$932$	9.70971	−	9.70971i	0.318052	−	0.318052i
$933$		0			0
$934$	−8.32139	+	14.4131i	−0.272284	+	0.471610i
$935$	−27.9514	+	60.6507i	−0.914108	+	1.98349i
$936$		0			0
$937$	−34.2022	−	34.2022i	−1.11734	−	1.11734i	−0.992131	−	0.125208i	$-0.960040\pi$
$937$	−34.2022	−	34.2022i	−1.11734	−	1.11734i	−0.125208	−	0.992131i	$-0.539960\pi$
$938$	2.23307	+	0.106750i	0.0729123	+	0.00348552i
$939$		0			0
$940$	−10.7649	+	7.60984i	−0.351112	+	0.248206i
$941$	16.3826	+	9.45851i	0.534058	+	0.308339i	0.742667	−	0.669660i	$-0.233560\pi$
$941$	16.3826	+	9.45851i	0.534058	+	0.308339i	−0.208609	+	0.977999i	$0.566894\pi$
$942$		0			0
$943$	7.82790	+	2.09748i	0.254911	+	0.0683033i
$944$	−5.47845			−0.178308
$945$		0			0
$946$	14.7719			0.480276
$947$	45.5435	+	12.2033i	1.47996	+	0.396555i	0.906335	−	0.422560i	$-0.138869\pi$
$947$	45.5435	+	12.2033i	1.47996	+	0.396555i	0.573629	+	0.819115i	$0.305535\pi$
$948$		0			0
$949$	−9.82664	−	5.67341i	−0.318986	−	0.184167i
$950$	1.52201	−	19.3994i	0.0493806	−	0.629400i
$951$		0			0
$952$	7.59560	−	11.8146i	0.246175	−	0.382914i
$953$	−18.8431	−	18.8431i	−0.610389	−	0.610389i	0.332658	−	0.943047i	$-0.392054\pi$
$953$	−18.8431	−	18.8431i	−0.610389	−	0.610389i	−0.943047	+	0.332658i	$0.892054\pi$
$954$		0			0
$955$	13.3180	+	36.0865i	0.430960	+	1.16773i
$956$	−9.83103	+	17.0278i	−0.317958	+	0.550720i
$957$		0			0
$958$	−10.8818	+	10.8818i	−0.351575	+	0.351575i
$959$	22.8439	−	4.96536i	0.737667	−	0.160340i
$960$		0			0
$961$	−8.09467	−	14.0204i	−0.261118	−	0.452270i
$962$	−9.84255	+	2.63730i	−0.317337	+	0.0850301i
$963$		0			0
$964$	−2.94256	−	5.09667i	−0.0947735	−	0.164153i
$965$	−26.8700	+	2.47231i	−0.864976	+	0.0795863i
$966$		0			0
$967$	27.3703	−	27.3703i	0.880169	−	0.880169i	−0.113383	−	0.993551i	$-0.536169\pi$
$967$	27.3703	−	27.3703i	0.880169	−	0.880169i	0.993551	+	0.113383i	$0.0361687\pi$
$968$	5.34440	−	19.9456i	0.171776	−	0.641075i
$969$		0			0
$970$	7.26018	+	19.6722i	0.233110	+	0.631636i
$971$	27.8750	−	16.0936i	0.894550	−	0.516469i	0.0191221	−	0.999817i	$-0.493913\pi$
$971$	27.8750	−	16.0936i	0.894550	−	0.516469i	0.875428	+	0.483348i	$0.160580\pi$
$972$		0			0
$973$	1.39765	−	29.2369i	0.0448065	−	0.937291i
$974$		−	35.9920i		−	1.15326i
$975$		0			0
$976$	−3.99172	−	2.30462i	−0.127772	−	0.0737691i
$977$	6.02479	+	22.4848i	0.192750	+	0.719353i	0.992838	+	0.119470i	$0.0381195\pi$
$977$	6.02479	+	22.4848i	0.192750	+	0.719353i	−0.800088	+	0.599883i	$0.795214\pi$
$978$		0			0
$979$	67.0692			2.14354
$980$	11.0260	+	11.1098i	0.352213	+	0.354889i
$981$		0			0
$982$	14.7616	+	3.95535i	0.471060	+	0.126220i
$983$	−14.7630	−	55.0964i	−0.470868	−	1.75730i	−0.636662	−	0.771143i	$-0.719685\pi$
$983$	−14.7630	−	55.0964i	−0.470868	−	1.75730i	0.165793	−	0.986160i	$-0.446981\pi$
$984$		0			0
$985$	36.9606	−	26.1279i	1.17766	−	0.832505i
$986$		−	16.7491i		−	0.533401i
$987$		0			0
$988$	5.56380	+	5.56380i	0.177008	+	0.177008i
$989$	2.55577	−	1.47557i	0.0812687	−	0.0469205i
$990$		0			0
$991$	28.7703	−	49.8316i	0.913918	−	1.58295i	0.105440	−	0.994426i	$-0.466375\pi$
$991$	28.7703	−	49.8316i	0.913918	−	1.58295i	0.808478	−	0.588526i	$-0.200292\pi$
$992$	0.996056	−	3.71733i	0.0316248	−	0.118025i
$993$		0			0
$994$	−3.85043	+	12.0382i	−0.122128	+	0.381829i
$995$	10.7694	−	12.9520i	0.341414	−	0.410607i
$996$		0			0
$997$	23.4284	−	6.27762i	0.741985	−	0.198814i	0.132025	−	0.991246i	$-0.457852\pi$
$997$	23.4284	−	6.27762i	0.741985	−	0.198814i	0.609960	+	0.792432i	$0.291185\pi$
$998$	−30.5087	+	8.17479i	−0.965737	+	0.258768i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bv.c.73.3		16
3.2	odd	2		70.2.k.a.3.1	✓	16
5.2	odd	4	inner	630.2.bv.c.577.1		16
7.5	odd	6	inner	630.2.bv.c.523.1		16
12.11	even	2		560.2.ci.c.353.3		16
15.2	even	4		70.2.k.a.17.3	yes	16
15.8	even	4		350.2.o.c.157.2		16
15.14	odd	2		350.2.o.c.143.4		16
21.2	odd	6		490.2.l.c.313.4		16
21.5	even	6		70.2.k.a.33.3	yes	16
21.11	odd	6		490.2.g.c.293.6		16
21.17	even	6		490.2.g.c.293.7		16
21.20	even	2		490.2.l.c.423.2		16
35.12	even	12	inner	630.2.bv.c.397.3		16
60.47	odd	4		560.2.ci.c.17.3		16
84.47	odd	6		560.2.ci.c.33.3		16
105.2	even	12		490.2.l.c.117.2		16
105.17	odd	12		490.2.g.c.97.6		16
105.32	even	12		490.2.g.c.97.7		16
105.47	odd	12		70.2.k.a.47.1	yes	16
105.62	odd	4		490.2.l.c.227.4		16
105.68	odd	12		350.2.o.c.257.4		16
105.89	even	6		350.2.o.c.243.2		16
420.47	even	12		560.2.ci.c.257.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.k.a.3.1	✓	16	3.2	odd	2
70.2.k.a.17.3	yes	16	15.2	even	4
70.2.k.a.33.3	yes	16	21.5	even	6
70.2.k.a.47.1	yes	16	105.47	odd	12
350.2.o.c.143.4		16	15.14	odd	2
350.2.o.c.157.2		16	15.8	even	4
350.2.o.c.243.2		16	105.89	even	6
350.2.o.c.257.4		16	105.68	odd	12
490.2.g.c.97.6		16	105.17	odd	12
490.2.g.c.97.7		16	105.32	even	12
490.2.g.c.293.6		16	21.11	odd	6
490.2.g.c.293.7		16	21.17	even	6
490.2.l.c.117.2		16	105.2	even	12
490.2.l.c.227.4		16	105.62	odd	4
490.2.l.c.313.4		16	21.2	odd	6
490.2.l.c.423.2		16	21.20	even	2
560.2.ci.c.17.3		16	60.47	odd	4
560.2.ci.c.33.3		16	84.47	odd	6
560.2.ci.c.257.3		16	420.47	even	12
560.2.ci.c.353.3		16	12.11	even	2
630.2.bv.c.73.3		16	1.1	even	1	trivial
630.2.bv.c.397.3		16	35.12	even	12	inner
630.2.bv.c.523.1		16	7.5	odd	6	inner
630.2.bv.c.577.1		16	5.2	odd	4	inner

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(-2.20382 - 0.378409i) q^{5} +(0.126334 - 2.64273i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(-2.20382 - 0.378409i) q^{5} +(0.126334 - 2.64273i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.03078 - 0.935904i) q^{10} +(2.81288 - 4.87205i) q^{11} +(-1.42962 + 1.42962i) q^{13} +(0.806019 - 2.51999i) q^{14} +(0.500000 + 0.866025i) q^{16} +(5.12784 - 1.37400i) q^{17} +(-1.94590 - 3.37040i) q^{19} +(-1.71936 - 1.42962i) q^{20} +(3.97801 - 3.97801i) q^{22} +(0.290892 - 1.08562i) q^{23} +(4.71361 + 1.66789i) q^{25} +(-1.75092 + 1.01089i) q^{26} +(1.43078 - 2.22551i) q^{28} -3.15502i q^{29} +(-3.33287 - 1.92423i) q^{31} +(0.258819 + 0.965926i) q^{32} +5.30873 q^{34} +(-1.27845 + 5.77629i) q^{35} +(4.86824 + 1.30444i) q^{37} +(-1.00727 - 3.75919i) q^{38} +(-1.29076 - 1.82591i) q^{40} +7.21050i q^{41} +(1.85669 + 1.85669i) q^{43} +(4.87205 - 2.81288i) q^{44} +(0.561961 - 0.973344i) q^{46} +(1.52590 - 5.69475i) q^{47} +(-6.96808 - 0.667734i) q^{49} +(4.12132 + 2.83103i) q^{50} +(-1.95290 + 0.523277i) q^{52} +(-1.33599 + 0.357978i) q^{53} +(-8.04270 + 9.67269i) q^{55} +(1.95803 - 1.77936i) q^{56} +(0.816578 - 3.04751i) q^{58} +(-2.73923 + 4.74448i) q^{59} +(-3.99172 + 2.30462i) q^{61} +(-2.72127 - 2.72127i) q^{62} +1.00000i q^{64} +(3.69160 - 2.60964i) q^{65} +(0.218698 + 0.816193i) q^{67} +(5.12784 + 1.37400i) q^{68} +(-2.72990 + 5.24858i) q^{70} -4.77710 q^{71} +(1.45256 + 5.42104i) q^{73} +(4.36475 + 2.51999i) q^{74} -3.89180i q^{76} +(-12.5202 - 8.04920i) q^{77} +(5.41079 - 3.12392i) q^{79} +(-0.774197 - 2.09777i) q^{80} +(-1.86622 + 6.96481i) q^{82} +(-5.67281 + 5.67281i) q^{83} +(-11.8207 + 1.08763i) q^{85} +(1.31288 + 2.27397i) q^{86} +(5.43407 - 1.45605i) q^{88} +(5.96090 + 10.3246i) q^{89} +(3.59749 + 3.95871i) q^{91} +(0.794732 - 0.794732i) q^{92} +(2.94782 - 5.10577i) q^{94} +(3.01302 + 8.16409i) q^{95} +(-6.63103 - 6.63103i) q^{97} +(-6.55783 - 2.44845i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{5} + 8 q^{7}+O(q^{10}) \) 16 * q + 12 * q^5 + 8 * q^7	\( 16 q + 12 q^{5} + 8 q^{7} - 12 q^{10} + 12 q^{11} + 8 q^{16} + 36 q^{17} - 8 q^{22} + 4 q^{23} + 12 q^{25} - 12 q^{26} + 4 q^{28} + 24 q^{31} - 8 q^{35} + 4 q^{37} - 24 q^{38} - 8 q^{43} - 8 q^{46} - 12 q^{47} + 32 q^{50} + 28 q^{53} + 4 q^{56} - 32 q^{58} - 12 q^{61} + 8 q^{65} + 32 q^{67} + 36 q^{68} - 12 q^{70} - 16 q^{71} - 12 q^{73} - 16 q^{77} + 12 q^{80} - 48 q^{82} + 24 q^{85} - 12 q^{86} - 4 q^{88} - 16 q^{91} - 8 q^{92} - 20 q^{95} - 40 q^{98}+O(q^{100}) \) 16 * q + 12 * q^5 + 8 * q^7 - 12 * q^10 + 12 * q^11 + 8 * q^16 + 36 * q^17 - 8 * q^22 + 4 * q^23 + 12 * q^25 - 12 * q^26 + 4 * q^28 + 24 * q^31 - 8 * q^35 + 4 * q^37 - 24 * q^38 - 8 * q^43 - 8 * q^46 - 12 * q^47 + 32 * q^50 + 28 * q^53 + 4 * q^56 - 32 * q^58 - 12 * q^61 + 8 * q^65 + 32 * q^67 + 36 * q^68 - 12 * q^70 - 16 * q^71 - 12 * q^73 - 16 * q^77 + 12 * q^80 - 48 * q^82 + 24 * q^85 - 12 * q^86 - 4 * q^88 - 16 * q^91 - 8 * q^92 - 20 * q^95 - 40 * q^98

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