LMFDB - Embedded newform 630.2.bv.c.523.1

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			523.1
Root			$-1.01089 - 0.750919i$ of defining polynomial
Character	$\chi$	$=$	630.523
Dual form			630.2.bv.c.577.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-0.774197 - 2.09777i) q^{5} +(2.64273 - 0.126334i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-0.774197 - 2.09777i) q^{5} +(2.64273 - 0.126334i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.82591 + 1.29076i) q^{10} +(2.81288 + 4.87205i) q^{11} +(1.42962 - 1.42962i) q^{13} +(-0.806019 - 2.51999i) q^{14} +(0.500000 - 0.866025i) q^{16} +(1.37400 - 5.12784i) q^{17} +(1.94590 - 3.37040i) q^{19} +(1.71936 + 1.42962i) q^{20} +(3.97801 - 3.97801i) q^{22} +(-1.08562 + 0.290892i) q^{23} +(-3.80124 + 3.24817i) q^{25} +(-1.75092 - 1.01089i) q^{26} +(-2.22551 + 1.43078i) q^{28} -3.15502i q^{29} +(-3.33287 + 1.92423i) q^{31} +(-0.965926 - 0.258819i) q^{32} -5.30873 q^{34} +(-2.31101 - 5.44603i) q^{35} +(-1.30444 - 4.86824i) q^{37} +(-3.75919 - 1.00727i) q^{38} +(0.935904 - 2.03078i) q^{40} -7.21050i q^{41} +(1.85669 + 1.85669i) q^{43} +(-4.87205 - 2.81288i) q^{44} +(0.561961 + 0.973344i) q^{46} +(5.69475 - 1.52590i) q^{47} +(6.96808 - 0.667734i) q^{49} +(4.12132 + 2.83103i) q^{50} +(-0.523277 + 1.95290i) q^{52} +(0.357978 - 1.33599i) q^{53} +(8.04270 - 9.67269i) q^{55} +(1.95803 + 1.77936i) q^{56} +(-3.04751 + 0.816578i) q^{58} +(2.73923 + 4.74448i) q^{59} +(-3.99172 - 2.30462i) q^{61} +(2.72127 + 2.72127i) q^{62} +1.00000i q^{64} +(-4.10581 - 1.89220i) q^{65} +(-0.816193 - 0.218698i) q^{67} +(1.37400 + 5.12784i) q^{68} +(-4.66232 + 3.64180i) q^{70} -4.77710 q^{71} +(5.42104 + 1.45256i) q^{73} +(-4.36475 + 2.51999i) q^{74} +3.89180i q^{76} +(8.04920 + 12.5202i) q^{77} +(-5.41079 - 3.12392i) q^{79} +(-2.20382 - 0.378409i) q^{80} +(-6.96481 + 1.86622i) q^{82} +(5.67281 - 5.67281i) q^{83} +(-11.8207 + 1.08763i) q^{85} +(1.31288 - 2.27397i) q^{86} +(-1.45605 + 5.43407i) q^{88} +(-5.96090 + 10.3246i) q^{89} +(3.59749 - 3.95871i) q^{91} +(0.794732 - 0.794732i) q^{92} +(-2.94782 - 5.10577i) q^{94} +(-8.57682 - 1.47269i) q^{95} +(6.63103 + 6.63103i) q^{97} +(-2.44845 - 6.55783i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	−0.774197	−	2.09777i	−0.346231	−	0.938149i
$5$	−0.774197	−	2.09777i	−0.346231	−	0.938149i
$6$		0			0
$7$	2.64273	−	0.126334i	0.998859	−	0.0477497i
$7$	2.64273	−	0.126334i	0.998859	−	0.0477497i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	−1.82591	+	1.29076i	−0.577403	+	0.408174i
$11$	2.81288	+	4.87205i	0.848115	+	1.46898i	0.882888	+	0.469583i	$0.155596\pi$
$11$	2.81288	+	4.87205i	0.848115	+	1.46898i	−0.0347729	+	0.999395i	$0.511071\pi$
$12$		0			0
$13$	1.42962	−	1.42962i	0.396505	−	0.396505i	−0.480493	−	0.876998i	$-0.659542\pi$
$13$	1.42962	−	1.42962i	0.396505	−	0.396505i	0.876998	+	0.480493i	$0.159542\pi$
$14$	−0.806019	−	2.51999i	−0.215418	−	0.673495i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	1.37400	−	5.12784i	0.333244	−	1.24368i	−0.572516	−	0.819893i	$-0.694033\pi$
$17$	1.37400	−	5.12784i	0.333244	−	1.24368i	0.905760	−	0.423790i	$-0.139301\pi$
$18$		0			0
$19$	1.94590	−	3.37040i	0.446420	−	0.773223i	−0.551729	−	0.834023i	$-0.686032\pi$
$19$	1.94590	−	3.37040i	0.446420	−	0.773223i	0.998150	+	0.0608002i	$0.0193652\pi$
$20$	1.71936	+	1.42962i	0.384460	+	0.319673i
$21$		0			0
$22$	3.97801	−	3.97801i	0.848115	−	0.848115i
$23$	−1.08562	+	0.290892i	−0.226368	+	0.0606552i	−0.370220	−	0.928944i	$-0.620718\pi$
$23$	−1.08562	+	0.290892i	−0.226368	+	0.0606552i	0.143852	+	0.989599i	$0.454051\pi$
$24$		0			0
$25$	−3.80124	+	3.24817i	−0.760248	+	0.649633i
$26$	−1.75092	−	1.01089i	−0.343384	−	0.198253i
$27$		0			0
$28$	−2.22551	+	1.43078i	−0.420581	+	0.270391i
$29$		−	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	−0.768491	−	0.639861i	$-0.778992\pi$
$31$	−3.33287	+	1.92423i	−0.598601	+	0.345602i	0.169890	+	0.985463i	$0.445659\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$		0			0
$34$	−5.30873			−0.910440
$35$	−2.31101	−	5.44603i	−0.390633	−	0.920547i
$36$		0			0
$37$	−1.30444	−	4.86824i	−0.214449	−	0.800334i	−0.986360	−	0.164603i	$-0.947366\pi$
$37$	−1.30444	−	4.86824i	−0.214449	−	0.800334i	0.771911	−	0.635731i	$-0.219301\pi$
$38$	−3.75919	−	1.00727i	−0.609822	−	0.163401i
$39$		0			0
$40$	0.935904	−	2.03078i	0.147979	−	0.321095i
$41$		−	7.21050i		−	1.12609i	−0.826426	−	0.563046i	$-0.809629\pi$
$41$		−	7.21050i		−	1.12609i	0.826426	−	0.563046i	$-0.190371\pi$
$42$		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
$47$	5.69475	−	1.52590i	0.830665	−	0.222576i	0.181661	−	0.983361i	$-0.441853\pi$
$47$	5.69475	−	1.52590i	0.830665	−	0.222576i	0.649004	+	0.760785i	$0.275186\pi$
$48$		0			0
$49$	6.96808	−	0.667734i	0.995440	−	0.0953905i
$50$	4.12132	+	2.83103i	0.582843	+	0.400368i
$51$		0			0
$52$	−0.523277	+	1.95290i	−0.0725655	+	0.270818i
$53$	0.357978	−	1.33599i	0.0491720	−	0.183512i	−0.936972	−	0.349405i	$-0.886384\pi$
$53$	0.357978	−	1.33599i	0.0491720	−	0.183512i	0.986144	+	0.165892i	$0.0530505\pi$
$54$		0			0
$55$	8.04270	−	9.67269i	1.08448	−	1.30426i
$56$	1.95803	+	1.77936i	0.261652	+	0.237777i
$57$		0			0
$58$	−3.04751	+	0.816578i	−0.400158	+	0.107222i
$59$	2.73923	+	4.74448i	0.356617	+	0.617679i	0.987393	−	0.158286i	$-0.0505968\pi$
$59$	2.73923	+	4.74448i	0.356617	+	0.617679i	−0.630776	+	0.775965i	$0.717263\pi$
$60$		0			0
$61$	−3.99172	−	2.30462i	−0.511088	−	0.295077i	0.222193	−	0.975003i	$-0.428678\pi$
$61$	−3.99172	−	2.30462i	−0.511088	−	0.295077i	−0.733281	+	0.679926i	$0.762012\pi$
$62$	2.72127	+	2.72127i	0.345602	+	0.345602i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−4.10581	−	1.89220i	−0.509264	−	0.234699i
$66$		0			0
$67$	−0.816193	−	0.218698i	−0.0997138	−	0.0267182i	0.208617	−	0.977997i	$-0.433104\pi$
$67$	−0.816193	−	0.218698i	−0.0997138	−	0.0267182i	−0.308331	+	0.951279i	$0.599770\pi$
$68$	1.37400	+	5.12784i	0.166622	+	0.621842i
$69$		0			0
$70$	−4.66232	+	3.64180i	−0.557254	+	0.435279i
$71$	−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
$73$	5.42104	+	1.45256i	0.634485	+	0.170010i	0.561704	−	0.827338i	$-0.310146\pi$
$73$	5.42104	+	1.45256i	0.634485	+	0.170010i	0.0727807	+	0.997348i	$0.476813\pi$
$74$	−4.36475	+	2.51999i	−0.507391	+	0.292943i
$75$		0			0
$76$			3.89180i			0.446420i
$77$	8.04920	+	12.5202i	0.917291	+	1.42681i
$78$		0			0
$79$	−5.41079	−	3.12392i	−0.608761	−	0.351469i	0.163719	−	0.986507i	$-0.447651\pi$
$79$	−5.41079	−	3.12392i	−0.608761	−	0.351469i	−0.772481	+	0.635038i	$0.780984\pi$
$80$	−2.20382	−	0.378409i	−0.246394	−	0.0423074i
$81$		0			0
$82$	−6.96481	+	1.86622i	−0.769135	+	0.206089i
$83$	5.67281	−	5.67281i	0.622672	−	0.622672i	−0.323542	−	0.946214i	$-0.604874\pi$
$83$	5.67281	−	5.67281i	0.622672	−	0.622672i	0.946214	+	0.323542i	$0.104874\pi$
$84$		0			0
$85$	−11.8207	+	1.08763i	−1.28214	+	0.117970i
$86$	1.31288	−	2.27397i	0.141571	−	0.245209i
$87$		0			0
$88$	−1.45605	+	5.43407i	−0.155216	+	0.579273i
$89$	−5.96090	+	10.3246i	−0.631855	+	1.09440i	0.355318	+	0.934746i	$0.384373\pi$
$89$	−5.96090	+	10.3246i	−0.631855	+	1.09440i	−0.987172	+	0.159659i	$0.948961\pi$
$90$		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
$95$	−8.57682	−	1.47269i	−0.879963	−	0.151095i
$96$		0			0
$97$	6.63103	+	6.63103i	0.673279	+	0.673279i	0.958471	−	0.285191i	$-0.0920572\pi$
$97$	6.63103	+	6.63103i	0.673279	+	0.673279i	−0.285191	+	0.958471i	$0.592057\pi$
$98$	−2.44845	−	6.55783i	−0.247331	−	0.662440i
$99$		0			0
$100$	1.66789	−	4.71361i	0.166789	−	0.471361i
$101$	−13.9423	+	8.04960i	−1.38731	+	0.800965i	−0.993012	−	0.118016i	$-0.962347\pi$
$101$	−13.9423	+	8.04960i	−1.38731	+	0.800965i	−0.394301	+	0.918981i	$0.629013\pi$
$102$		0			0
$103$	5.09084	+	18.9993i	0.501616	+	1.87206i	0.489271	+	0.872132i	$0.337263\pi$
$103$	5.09084	+	18.9993i	0.501616	+	1.87206i	0.0123445	+	0.999924i	$0.496071\pi$
$104$	2.02179			0.198253
$105$		0			0
$106$	−1.38312			−0.134340
$107$	−0.724955	−	2.70557i	−0.0700840	−	0.261557i	0.921990	−	0.387214i	$-0.126563\pi$
$107$	−0.724955	−	2.70557i	−0.0700840	−	0.261557i	−0.992074	+	0.125657i	$0.959896\pi$
$108$		0			0
$109$	5.11895	−	2.95543i	0.490306	−	0.283078i	−0.234395	−	0.972141i	$-0.575311\pi$
$109$	5.11895	−	2.95543i	0.490306	−	0.283078i	0.724701	+	0.689063i	$0.241978\pi$
$110$	−11.4247	−	5.26517i	−1.08930	−	0.502015i
$111$		0			0
$112$	1.21196	−	2.35184i	0.114519	−	0.222228i
$113$	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
$115$	1.45071	+	2.05218i	0.135279	+	0.191367i
$116$	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
$122$	−1.19296	+	4.45219i	−0.108006	+	0.403082i
$123$		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	$0.156073\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$		0			0
$130$	−0.765062	+	4.45565i	−0.0671004	+	0.390786i
$131$	6.66437	+	3.84768i	0.582269	+	0.336173i	0.762035	−	0.647536i	$-0.224201\pi$
$131$	6.66437	+	3.84768i	0.582269	+	0.336173i	−0.179766	+	0.983709i	$0.557534\pi$
$132$		0			0
$133$	4.71670	−	9.15290i	0.408990	−	0.793657i
$134$			0.844985i			0.0729956i
$135$		0			0
$136$	4.59749	−	2.65436i	0.394232	−	0.227610i
$137$	−8.53471	−	2.28687i	−0.729170	−	0.195380i	−0.124910	−	0.992168i	$-0.539864\pi$
$137$	−8.53471	−	2.28687i	−0.729170	−	0.195380i	−0.604259	+	0.796788i	$0.706531\pi$
$138$		0			0
$139$	−11.0631			−0.938361			−0.469180	−	0.883102i	$-0.655451\pi$
$139$	−11.0631			−0.938361			−0.469180	+	0.883102i	$0.655451\pi$
$140$	4.72441	+	3.56089i	0.399286	+	0.300950i
$141$		0			0
$142$	1.23640	+	4.61432i	0.103757	+	0.387225i
$143$	10.9865	+	2.94383i	0.918740	+	0.246176i
$144$		0			0
$145$	−6.61848	+	2.44260i	−0.549635	+	0.202847i
$146$		−	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	$-0.399641\pi$
$149$	−4.37243	−	2.52443i	−0.358204	−	0.206809i	−0.668293	+	0.743899i	$0.732975\pi$
$150$		0			0
$151$	−6.72142	−	11.6418i	−0.546981	−	0.947399i	−0.998479	−	0.0551270i	$-0.982444\pi$
$151$	−6.72142	−	11.6418i	−0.546981	−	0.947399i	0.451498	−	0.892272i	$-0.350890\pi$
$152$	3.75919	−	1.00727i	0.304911	−	0.0817006i
$153$		0			0
$154$	10.0103	−	11.0154i	0.806651	−	0.887645i
$155$	6.61688	+	5.50184i	0.531481	+	0.441918i
$156$		0			0
$157$	−0.285443	+	1.06529i	−0.0227808	+	0.0850191i	−0.976380	−	0.216059i	$-0.930680\pi$
$157$	−0.285443	+	1.06529i	−0.0227808	+	0.0850191i	0.953600	+	0.301078i	$0.0973464\pi$
$158$	−1.61706	+	6.03495i	−0.128646	+	0.480115i
$159$		0			0
$160$	0.204875	+	2.22666i	0.0161968	+	0.176033i
$161$	−2.83227	+	0.905902i	−0.223214	+	0.0713951i
$162$		0			0
$163$	12.7899	−	3.42705i	1.00179	−	0.268428i	0.279592	−	0.960119i	$-0.409801\pi$
$163$	12.7899	−	3.42705i	1.00179	−	0.268428i	0.722193	+	0.691691i	$0.243134\pi$
$164$	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	0.501142	−	0.865365i	$-0.332913\pi$
$167$	−4.70680	−	4.70680i	−0.364223	−	0.364223i	−0.865365	+	0.501142i	$0.832913\pi$
$168$		0			0
$169$			8.91237i			0.685567i
$170$	4.11000	+	11.1365i	0.315223	+	0.854128i
$171$		0			0
$172$	−2.53629	−	0.679597i	−0.193390	−	0.0518188i
$173$	1.82586	+	6.81421i	0.138818	+	0.518075i	0.999953	+	0.00969875i	$0.00308726\pi$
$173$	1.82586	+	6.81421i	0.138818	+	0.518075i	−0.861135	+	0.508376i	$0.830246\pi$
$174$		0			0
$175$	−9.63531	+	9.06426i	−0.728361	+	0.685194i
$176$	5.62576			0.424058
$177$		0			0
$178$	11.5156	+	3.08559i	0.863129	+	0.231275i
$179$	1.91075	−	1.10317i	0.142816	−	0.0824550i	−0.426889	−	0.904304i	$-0.640391\pi$
$179$	1.91075	−	1.10317i	0.142816	−	0.0824550i	0.569706	+	0.821849i	$0.307057\pi$
$180$		0			0
$181$		−	4.11867i		−	0.306139i	−0.988215	−	0.153069i	$-0.951084\pi$
$181$		−	4.11867i		−	0.306139i	0.988215	−	0.153069i	$-0.0489158\pi$
$182$	−4.75492	−	2.45032i	−0.352458	−	0.181630i
$183$		0			0
$184$	−0.973344	−	0.561961i	−0.0717559	−	0.0414283i
$185$	−9.20253	+	6.50539i	−0.676584	+	0.478286i
$186$		0			0
$187$	28.8480	−	7.72980i	2.10957	−	0.565259i
$188$	−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	0.366686	+	0.930345i	$0.380492\pi$
$191$	−8.60117	+	14.8977i	−0.622359	+	1.07796i	−0.989045	+	0.147613i	$0.952841\pi$
$192$		0			0
$193$	−3.12327	+	11.6562i	−0.224818	+	0.839032i	0.757659	+	0.652650i	$0.226343\pi$
$193$	−3.12327	+	11.6562i	−0.224818	+	0.839032i	−0.982477	+	0.186382i	$0.940324\pi$
$194$	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	$-0.0806335\pi$
$199$	3.76653	+	6.52383i	0.267002	+	0.462462i	−0.701084	+	0.713079i	$0.747300\pi$
$200$	−4.98468	−	0.391082i	−0.352470	−	0.0276537i
$201$		0			0
$202$	11.3839	+	11.3839i	0.800965	+	0.800965i
$203$	−0.398585	−	8.33786i	−0.0279752	−	0.585203i
$204$		0			0
$205$	−15.1259	+	5.58235i	−1.05644	+	0.389888i
$206$	17.0343	−	9.83476i	1.18684	−	0.685220i
$207$		0			0
$208$	−0.523277	−	1.95290i	−0.0362827	−	0.135409i
$209$	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	$0.264638\pi$
$212$	0.357978	+	1.33599i	0.0245860	+	0.0917562i
$213$		0			0
$214$	−2.42575	+	1.40051i	−0.165821	+	0.0957366i
$215$	2.45746	−	5.33235i	0.167597	−	0.363663i
$216$		0			0
$217$	−8.56478	+	5.50629i	−0.581415	+	0.373791i
$218$	−4.17960	−	4.17960i	−0.283078	−	0.283078i
$219$		0			0
$220$	−2.12884	+	12.3981i	−0.143526	+	0.835883i
$221$	−5.36656	−	9.29516i	−0.360994	−	0.625260i
$222$		0			0
$223$	−1.46027	+	1.46027i	−0.0977867	+	0.0977867i	−0.754308	−	0.656521i	$-0.772027\pi$
$223$	−1.46027	+	1.46027i	−0.0977867	+	0.0977867i	0.656521	+	0.754308i	$0.272027\pi$
$224$	−2.58538	−	0.561961i	−0.172743	−	0.0375476i
$225$		0			0
$226$	9.60377	−	16.6342i	0.638833	−	1.10649i
$227$	4.82525	−	18.0081i	0.320263	−	1.19524i	−0.598726	−	0.800954i	$-0.704326\pi$
$227$	4.82525	−	18.0081i	0.320263	−	1.19524i	0.918989	−	0.394283i	$-0.129007\pi$
$228$		0			0
$229$	2.00384	−	3.47074i	0.132417	−	0.229353i	−0.792191	−	0.610274i	$-0.791059\pi$
$229$	2.00384	−	3.47074i	0.132417	−	0.229353i	0.924608	+	0.380920i	$0.124393\pi$
$230$	1.60678	−	1.93242i	0.105948	−	0.127420i
$231$		0			0
$232$	2.23093	−	2.23093i	0.146468	−	0.146468i
$233$	−13.2637	+	3.55400i	−0.868934	+	0.232830i	−0.665627	−	0.746285i	$-0.731836\pi$
$233$	−13.2637	+	3.55400i	−0.868934	+	0.232830i	−0.203307	+	0.979115i	$0.565169\pi$
$234$		0			0
$235$	−7.60984	−	10.7649i	−0.496412	−	0.702225i
$236$	−4.74448	−	2.73923i	−0.308839	−	0.178308i
$237$		0			0
$238$	−14.0296	+	0.670673i	−0.909401	+	0.0434732i
$239$			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	−0.655088	−	0.755552i	$-0.727369\pi$
$241$	−5.09667	+	2.94256i	−0.328305	+	0.189547i	0.326783	+	0.945099i	$0.394035\pi$
$242$	19.9456	+	5.34440i	1.28215	+	0.343551i
$243$		0			0
$244$	4.60924			0.295077
$245$	−6.79541	−	14.1004i	−0.434143	−	0.900844i
$246$		0			0
$247$	−2.03649	−	7.60029i	−0.129579	−	0.483595i
$248$	−3.71733	−	0.996056i	−0.236051	−	0.0632496i
$249$		0			0
$250$	2.74812	−	10.8373i	0.173806	−	0.685413i
$251$			7.09950i			0.448116i	0.974576	+	0.224058i	$0.0719306\pi$
$251$			7.09950i			0.448116i	−0.974576	+	0.224058i	$0.928069\pi$
$252$		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
$257$	9.54998	−	2.55891i	0.595711	−	0.159620i	0.0516491	−	0.998665i	$-0.483552\pi$
$257$	9.54998	−	2.55891i	0.595711	−	0.159620i	0.544062	+	0.839045i	$0.316886\pi$
$258$		0			0
$259$	−4.06231	−	12.7007i	−0.252420	−	0.789181i
$260$	4.50184	−	0.414214i	0.279192	−	0.0256884i
$261$		0			0
$262$	1.99170	−	7.43314i	0.123048	−	0.459221i
$263$	−3.55829	+	13.2797i	−0.219413	+	0.818861i	0.765153	+	0.643849i	$0.222663\pi$
$263$	−3.55829	+	13.2797i	−0.219413	+	0.818861i	−0.984566	+	0.175013i	$0.944003\pi$
$264$		0			0
$265$	−3.07974	+	0.283366i	−0.189187	+	0.0174071i
$266$	−10.0618	−	2.18704i	−0.616929	−	0.134096i
$267$		0			0
$268$	0.816193	−	0.218698i	0.0498569	−	0.0133591i
$269$	−13.2510	−	22.9514i	−0.807928	−	1.39937i	−0.914296	−	0.405046i	$-0.867255\pi$
$269$	−13.2510	−	22.9514i	−0.807928	−	1.39937i	0.106368	−	0.994327i	$-0.466078\pi$
$270$		0			0
$271$	−11.0824	−	6.39844i	−0.673209	−	0.388678i	0.124082	−	0.992272i	$-0.460401\pi$
$271$	−11.0824	−	6.39844i	−0.673209	−	0.388678i	−0.797292	+	0.603594i	$0.793735\pi$
$272$	−3.75384	−	3.75384i	−0.227610	−	0.227610i
$273$		0			0
$274$			8.83578i			0.533789i
$275$	−26.5177	−	9.38313i	−1.59908	−	0.565824i
$276$		0			0
$277$	−19.4184	−	5.20313i	−1.16674	−	0.312626i	−0.377083	−	0.926180i	$-0.623073\pi$
$277$	−19.4184	−	5.20313i	−1.16674	−	0.312626i	−0.789653	+	0.613554i	$0.789739\pi$
$278$	2.86334	+	10.6861i	0.171732	+	0.640912i
$279$		0			0
$280$	2.21679	−	5.48506i	0.132478	−	0.327795i
$281$	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
$283$	−26.1454	−	7.00563i	−1.55418	−	0.416442i	−0.623366	−	0.781930i	$-0.714235\pi$
$283$	−26.1454	−	7.00563i	−1.55418	−	0.416442i	−0.930816	+	0.365489i	$0.880902\pi$
$284$	4.13709	−	2.38855i	0.245491	−	0.141734i
$285$		0			0
$286$		−	11.3741i		−	0.672564i
$287$	−0.910931	−	19.0554i	−0.0537706	−	1.12481i
$288$		0			0
$289$	−9.68442	−	5.59130i	−0.569672	−	0.328900i
$290$	4.07236	+	5.76077i	0.239137	+	0.338284i
$291$		0			0
$292$	−5.42104	+	1.45256i	−0.317242	+	0.0850048i
$293$	17.1191	−	17.1191i	1.00011	−	1.00011i	0.000106876	−	1.00000i	$-0.499966\pi$
$293$	17.1191	−	17.1191i	1.00011	−	1.00011i	1.00000		0.000106876i	$-3.40197e-5\pi$
$294$		0			0
$295$	7.83211	−	9.41941i	0.456003	−	0.548420i
$296$	2.51999	−	4.36475i	0.146471	−	0.253696i
$297$		0			0
$298$	−1.30674	+	4.87682i	−0.0756974	+	0.282506i
$299$	−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
$305$	−1.74418	+	10.1579i	−0.0998713	+	0.581641i
$306$		0			0
$307$	−17.2974	−	17.2974i	−0.987217	−	0.987217i	0.0127019	−	0.999919i	$-0.495957\pi$
$307$	−17.2974	−	17.2974i	−0.987217	−	0.987217i	−0.999919	+	0.0127019i	$0.995957\pi$
$308$	−13.2309	−	6.81819i	−0.753900	−	0.388502i
$309$		0			0
$310$	3.60179	−	7.81540i	0.204568	−	0.443885i
$311$	9.51095	−	5.49115i	0.539316	−	0.311374i	−0.205486	−	0.978660i	$-0.565877\pi$
$311$	9.51095	−	5.49115i	0.539316	−	0.311374i	0.744802	+	0.667286i	$0.232544\pi$
$312$		0			0
$313$	7.61212	+	28.4088i	0.430262	+	1.60576i	0.752156	+	0.658985i	$0.229014\pi$
$313$	7.61212	+	28.4088i	0.430262	+	1.60576i	−0.321893	+	0.946776i	$0.604319\pi$
$314$	1.10287			0.0622383
$315$		0			0
$316$	6.24784			0.351469
$317$	−1.11136	−	4.14766i	−0.0624203	−	0.232956i	0.927667	−	0.373408i	$-0.121811\pi$
$317$	−1.11136	−	4.14766i	−0.0624203	−	0.232956i	−0.990087	+	0.140453i	$0.955144\pi$
$318$		0			0
$319$	15.3714	−	8.87468i	0.860633	−	0.496887i
$320$	2.09777	−	0.774197i	0.117269	−	0.0432789i
$321$		0			0
$322$	1.60808	+	2.50129i	0.0896147	+	0.139392i
$323$	−14.6092	−	14.6092i	−0.812878	−	0.812878i
$324$		0			0
$325$	−0.790684	+	10.0780i	−0.0438593	+	0.559025i
$326$	−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	−0.291863	+	0.956460i	$0.594275\pi$
$331$	−17.7249	+	30.7005i	−0.974250	+	1.68745i	−0.682387	+	0.730991i	$0.739058\pi$
$332$	−2.07639	+	7.74921i	−0.113957	+	0.425293i
$333$		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	$0.404989\pi$
$338$	8.60869	−	2.30669i	0.468251	−	0.125468i
$339$		0			0
$340$	9.69326	−	6.85229i	0.525691	−	0.371617i
$341$	−18.7499	−	10.8253i	−1.01536	−	0.586221i
$342$		0			0
$343$	18.3304	−	2.64495i	0.989750	−	0.142814i
$344$			2.62576i			0.141571i
$345$		0			0
$346$	6.10945	−	3.52729i	0.328446	−	0.189628i
$347$	8.67040	+	2.32323i	0.465452	+	0.124717i	0.483920	−	0.875112i	$-0.339212\pi$
$347$	8.67040	+	2.32323i	0.465452	+	0.124717i	−0.0184687	+	0.999829i	$0.505879\pi$
$348$		0			0
$349$	26.0251			1.39309			0.696546	−	0.717512i	$-0.254719\pi$
$349$	26.0251			1.39309			0.696546	+	0.717512i	$0.254719\pi$
$350$	11.2492	+	6.96099i	0.601295	+	0.372081i
$351$		0			0
$352$	−1.45605	−	5.43407i	−0.0776079	−	0.289637i
$353$	−9.62659	−	2.57944i	−0.512372	−	0.137290i	−0.00663577	−	0.999978i	$-0.502112\pi$
$353$	−9.62659	−	2.57944i	−0.512372	−	0.137290i	−0.505736	+	0.862688i	$0.668779\pi$
$354$		0			0
$355$	3.69841	+	10.0212i	0.196291	+	0.531872i
$356$		−	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	$-0.234533\pi$
$359$	10.0235	+	5.78705i	0.529019	+	0.305429i	−0.211598	+	0.977357i	$0.567867\pi$
$360$		0			0
$361$	1.92693	+	3.33754i	0.101417	+	0.175660i
$362$	−3.97833	+	1.06599i	−0.209097	+	0.0560273i
$363$		0			0
$364$	−1.13616	+	5.22709i	−0.0595512	+	0.273974i
$365$	−1.14981	−	12.4966i	−0.0601840	−	0.654104i
$366$		0			0
$367$	4.32083	−	16.1256i	0.225545	−	0.841747i	−0.756640	−	0.653832i	$-0.773160\pi$
$367$	4.32083	−	16.1256i	0.225545	−	0.841747i	0.982185	−	0.187915i	$-0.0601730\pi$
$368$	−0.290892	+	1.08562i	−0.0151638	+	0.0565921i
$369$		0			0
$370$	8.66551	+	7.20525i	0.450499	+	0.374583i
$371$	0.777258	−	3.57589i	0.0403532	−	0.185651i
$372$		0			0
$373$	−3.07061	+	0.822767i	−0.158990	+	0.0426013i	−0.337436	−	0.941348i	$-0.609560\pi$
$373$	−3.07061	+	0.822767i	−0.158990	+	0.0426013i	0.178446	+	0.983950i	$0.442893\pi$
$374$	−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	$-0.0588156\pi$
$380$	8.16409	−	3.01302i	0.418809	−	0.154565i
$381$		0			0
$382$	16.6162	+	4.45229i	0.850158	+	0.227799i
$383$	3.77704	+	14.0961i	0.192998	+	0.720278i	0.992776	+	0.119982i	$0.0382837\pi$
$383$	3.77704	+	14.0961i	0.192998	+	0.720278i	−0.799778	+	0.600296i	$0.795050\pi$
$384$		0			0
$385$	20.0327	−	26.5784i	1.02096	−	1.35456i
$386$	12.0674			0.614214
$387$		0			0
$388$	−9.05816	−	2.42713i	−0.459858	−	0.123219i
$389$	5.36634	−	3.09826i	0.272084	−	0.157088i	−0.357750	−	0.933817i	$-0.616456\pi$
$389$	5.36634	−	3.09826i	0.272084	−	0.157088i	0.629834	+	0.776729i	$0.283123\pi$
$390$		0			0
$391$			5.96659i			0.301744i
$392$	5.39934	+	4.45502i	0.272708	+	0.225012i
$393$		0			0
$394$	17.5304	+	10.1212i	0.883167	+	0.509897i
$395$	−2.36424	+	13.7691i	−0.118958	+	0.692798i
$396$		0			0
$397$	2.81652	−	0.754685i	0.141357	−	0.0378766i	−0.187447	−	0.982275i	$-0.560021\pi$
$397$	2.81652	−	0.754685i	0.141357	−	0.0378766i	0.328804	+	0.944398i	$0.393354\pi$
$398$	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	−0.999999	−	0.00156835i	$-0.999501\pi$
$401$	−9.98528	+	17.2950i	−0.498641	+	0.863672i	0.501358	+	0.865240i	$0.332834\pi$
$402$		0			0
$403$	−2.01381	+	7.51565i	−0.100315	+	0.374381i
$404$	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	−0.881699	−	0.471812i	$-0.843600\pi$
$409$	−17.1791	−	29.7550i	−0.849451	−	1.47129i	0.0322484	−	0.999480i	$-0.489733\pi$
$410$	9.30702	+	13.1657i	0.459641	+	0.650209i
$411$		0			0
$412$	−13.9084	−	13.9084i	−0.685220	−	0.685220i
$413$	7.83843	+	12.1923i	0.385704	+	0.599946i
$414$		0			0
$415$	−16.2921	−	7.50836i	−0.799748	−	0.368571i
$416$	−1.75092	+	1.01089i	−0.0858459	+	0.0495631i
$417$		0			0
$418$	−5.66668	−	21.1483i	−0.277166	−	1.03440i
$419$	−31.1360			−1.52109			−0.760547	−	0.649283i	$-0.775069\pi$
$419$	−31.1360			−1.52109			−0.760547	+	0.649283i	$0.775069\pi$
$420$		0			0
$421$	−33.6728			−1.64111			−0.820555	−	0.571567i	$-0.806336\pi$
$421$	−33.6728			−1.64111			−0.820555	+	0.571567i	$0.806336\pi$
$422$	−5.06679	−	18.9095i	−0.246648	−	0.920501i
$423$		0			0
$424$	1.19782	−	0.691560i	0.0581711	−	0.0335851i
$425$	11.4332	+	23.9551i	0.554590	+	1.16199i
$426$		0			0
$427$	−10.8402	−	5.58621i	−0.524594	−	0.270336i
$428$	1.98061	+	1.98061i	0.0957366	+	0.0957366i
$429$		0			0
$430$	−5.78669	−	0.993610i	−0.279059	−	0.0479162i
$431$	−7.37284	−	12.7701i	−0.355137	−	0.615116i	0.632004	−	0.774965i	$-0.282233\pi$
$431$	−7.37284	−	12.7701i	−0.355137	−	0.615116i	−0.987141	+	0.159849i	$0.948899\pi$
$432$		0			0
$433$	9.98256	−	9.98256i	0.479731	−	0.479731i	−0.425315	−	0.905046i	$-0.639837\pi$
$433$	9.98256	−	9.98256i	0.479731	−	0.479731i	0.905046	+	0.425315i	$0.139837\pi$
$434$	7.53539	+	6.84781i	0.361710	+	0.328706i
$435$		0			0
$436$	−2.95543	+	5.11895i	−0.141539	+	0.245153i
$437$	−1.13210	+	4.22504i	−0.0541555	+	0.202111i
$438$		0			0
$439$	−19.2142	+	33.2800i	−0.917046	+	1.58837i	−0.113167	+	0.993576i	$0.536100\pi$
$439$	−19.2142	+	33.2800i	−0.917046	+	1.58837i	−0.803878	+	0.594794i	$0.797234\pi$
$440$	12.5267	−	1.15258i	0.597186	−	0.0549470i
$441$		0			0
$442$	−7.58946	+	7.58946i	−0.360994	+	0.360994i
$443$	5.54016	−	1.48448i	0.263221	−	0.0705299i	−0.124795	−	0.992183i	$-0.539827\pi$
$443$	5.54016	−	1.48448i	0.263221	−	0.0705299i	0.388016	+	0.921653i	$0.373161\pi$
$444$		0			0
$445$	26.2735	+	4.51132i	1.24548	+	0.213857i
$446$	1.78845	+	1.03256i	0.0846857	+	0.0488933i
$447$		0			0
$448$	0.126334	+	2.64273i	0.00596872	+	0.124857i
$449$			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
$452$	−18.5531	−	4.97128i	−0.872663	−	0.233829i
$453$		0			0
$454$	−18.6433			−0.874974
$455$	−11.0896	−	4.48188i	−0.519889	−	0.210114i
$456$		0			0
$457$	1.33183	+	4.97047i	0.0623006	+	0.232509i	0.990055	−	0.140683i	$-0.0449299\pi$
$457$	1.33183	+	4.97047i	0.0623006	+	0.232509i	−0.927754	+	0.373192i	$0.878263\pi$
$458$	−3.87111	−	1.03726i	−0.180885	−	0.0484680i
$459$		0			0
$460$	−2.28244	−	1.05188i	−0.106419	−	0.0490443i
$461$			29.4110i			1.36981i	0.728634	+	0.684903i	$0.240155\pi$
$461$			29.4110i			1.36981i	−0.728634	+	0.684903i	$0.759845\pi$
$462$		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
$467$	−16.0757	+	4.30747i	−0.743894	+	0.199326i	−0.610808	−	0.791779i	$-0.709155\pi$
$467$	−16.0757	+	4.30747i	−0.743894	+	0.199326i	−0.133086	+	0.991105i	$0.542489\pi$
$468$		0			0
$469$	−2.18461	−	0.474848i	−0.100876	−	0.0219264i
$470$	−8.42852	+	10.1367i	−0.388779	+	0.467571i
$471$		0			0
$472$	−1.41793	+	5.29178i	−0.0652654	+	0.243574i
$473$	−3.82325	+	14.2686i	−0.175793	+	0.656069i
$474$		0			0
$475$	3.55078	+	19.1323i	0.162921	+	0.877851i
$476$	4.27894	+	13.3779i	0.196125	+	0.613176i
$477$		0			0
$478$	18.9921	−	5.08891i	0.868678	−	0.232762i
$479$	7.69460	+	13.3274i	0.351575	+	0.608946i	0.986526	−	0.163607i	$-0.0523128\pi$
$479$	7.69460	+	13.3274i	0.351575	+	0.608946i	−0.634950	+	0.772553i	$0.718979\pi$
$480$		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
$485$	8.77662	−	19.0441i	0.398526	−	0.864747i
$486$		0			0
$487$	34.7656	+	9.31541i	1.57538	+	0.422122i	0.937492	−	0.348007i	$-0.113142\pi$
$487$	34.7656	+	9.31541i	1.57538	+	0.422122i	0.637888	+	0.770129i	$0.279808\pi$
$488$	−1.19296	−	4.45219i	−0.0540028	−	0.201541i
$489$		0			0
$490$	−11.8612	+	10.2133i	−0.535834	+	0.461391i
$491$	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
$493$	−16.1784	−	4.33499i	−0.728639	−	0.195238i
$494$	−6.81423	+	3.93420i	−0.306587	+	0.177008i
$495$		0			0
$496$			3.84846i			0.172801i
$497$	−12.6246	+	0.603509i	−0.566290	+	0.0270711i
$498$		0			0
$499$	27.3534	+	15.7925i	1.22451	+	0.706969i	0.965875	−	0.259008i	$-0.0833955\pi$
$499$	27.3534	+	15.7925i	1.22451	+	0.706969i	0.258630	+	0.965976i	$0.416729\pi$
$500$	−11.1793	+	0.150429i	−0.499955	+	0.00672739i
$501$		0			0
$502$	6.85759	−	1.83749i	0.306069	−	0.0820110i
$503$	16.9777	−	16.9777i	0.756997	−	0.756997i	−0.218778	−	0.975775i	$-0.570207\pi$
$503$	16.9777	−	16.9777i	0.756997	−	0.756997i	0.975775	+	0.218778i	$0.0702070\pi$
$504$		0			0
$505$	27.6803	+	23.0157i	1.23176	+	1.02419i
$506$	−3.16146	+	5.47580i	−0.140544	+	0.243429i
$507$		0			0
$508$	−1.69648	+	6.33135i	−0.0752691	+	0.280908i
$509$	10.7571	−	18.6318i	0.476799	−	0.825840i	−0.522848	−	0.852426i	$-0.675130\pi$
$509$	10.7571	−	18.6318i	0.476799	−	0.825840i	0.999647	+	0.0265865i	$0.00846373\pi$
$510$		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
$515$	35.9147	−	25.3886i	1.58259	−	1.11875i
$516$		0			0
$517$	23.4529	+	23.4529i	1.03146	+	1.03146i
$518$	−11.2165	+	7.21107i	−0.492825	+	0.316836i
$519$		0			0
$520$	−1.56526	−	4.24124i	−0.0686412	−	0.185991i
$521$	−11.4657	+	6.61973i	−0.502322	+	0.290016i	−0.729672	−	0.683798i	$-0.760327\pi$
$521$	−11.4657	+	6.61973i	−0.502322	+	0.290016i	0.227350	+	0.973813i	$0.426994\pi$
$522$		0			0
$523$	−6.97006	−	26.0126i	−0.304779	−	1.13745i	−0.933135	−	0.359526i	$-0.882938\pi$
$523$	−6.97006	−	26.0126i	−0.304779	−	1.13745i	0.628356	−	0.777926i	$-0.283728\pi$
$524$	−7.69535			−0.336173
$525$		0			0
$526$	13.7482			0.599448
$527$	5.28779	+	19.7343i	0.230340	+	0.859640i
$528$		0			0
$529$	−18.8246	+	10.8684i	−0.818462	+	0.472539i
$530$	1.07081	+	2.90146i	0.0465129	+	0.126031i
$531$		0			0
$532$	0.491667	+	10.2850i	0.0213165	+	0.445911i
$533$	−10.3083	−	10.3083i	−0.446501	−	0.446501i
$534$		0			0
$535$	−5.11439	+	3.61543i	−0.221114	+	0.156309i
$536$	−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	−0.718171	−	0.695867i	$-0.755020\pi$
$541$	5.66491	−	9.81190i	0.243553	−	0.421847i	0.961724	+	0.274020i	$0.0883536\pi$
$542$	−3.31208	+	12.3608i	−0.142266	+	0.530943i
$543$		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	$0.865694\pi$
$548$	8.53471	−	2.28687i	0.364585	−	0.0976902i
$549$		0			0
$550$	−2.20013	+	28.0426i	−0.0938140	+	1.19574i
$551$	−10.6337	−	6.13935i	−0.453009	−	0.261545i
$552$		0			0
$553$	−14.6939	−	7.57212i	−0.624850	−	0.321999i
$554$			20.1034i			0.854110i
$555$		0			0
$556$	9.58094	−	5.53156i	0.406322	−	0.234590i
$557$	−25.5003	−	6.83277i	−1.08048	−	0.289514i	−0.325688	−	0.945477i	$-0.605596\pi$
$557$	−25.5003	−	6.83277i	−1.08048	−	0.289514i	−0.754793	+	0.655963i	$0.772263\pi$
$558$		0			0
$559$	5.30873			0.224535
$560$	−5.87191	−	0.721617i	−0.248133	−	0.0304939i
$561$		0			0
$562$	−3.66224	−	13.6677i	−0.154482	−	0.576536i
$563$	−19.5055	−	5.22648i	−0.822058	−	0.220270i	−0.176812	−	0.984245i	$-0.556578\pi$
$563$	−19.5055	−	5.22648i	−0.822058	−	0.220270i	−0.645246	+	0.763975i	$0.723245\pi$
$564$		0			0
$565$	17.9764	−	39.0064i	0.756274	−	1.64101i
$566$			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	$-0.159222\pi$
$569$	21.4890	+	12.4067i	0.900867	+	0.520116i	0.0233856	+	0.999727i	$0.492555\pi$
$570$		0			0
$571$	−2.29029	−	3.96690i	−0.0958458	−	0.166010i	0.814116	−	0.580703i	$-0.197222\pi$
$571$	−2.29029	−	3.96690i	−0.0958458	−	0.166010i	−0.909961	+	0.414693i	$0.863889\pi$
$572$	−10.9865	+	2.94383i	−0.459370	+	0.123088i
$573$		0			0
$574$	−18.1704	+	5.81180i	−0.758417	+	0.242580i
$575$	3.18185	−	4.63204i	0.132692	−	0.193169i
$576$		0			0
$577$	−5.11957	+	19.1065i	−0.213131	+	0.795414i	0.773686	+	0.633570i	$0.218411\pi$
$577$	−5.11957	+	19.1065i	−0.213131	+	0.795414i	−0.986816	+	0.161845i	$0.948256\pi$
$578$	−2.89427	+	10.8016i	−0.120386	+	0.449286i
$579$		0			0
$580$	4.51047	−	5.42460i	0.187287	−	0.225244i
$581$	14.2751	−	15.7084i	0.592229	−	0.651694i
$582$		0			0
$583$	7.51596	−	2.01390i	0.311279	−	0.0834071i
$584$	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	0.983068	−	0.183244i	$-0.0586597\pi$
$587$	19.3782	+	19.3782i	0.799824	+	0.799824i	−0.183244	+	0.983068i	$0.558660\pi$
$588$		0			0
$589$			14.9775i			0.617136i
$590$	−11.1256	−	5.12731i	−0.458032	−	0.211088i
$591$		0			0
$592$	−4.86824	−	1.30444i	−0.200083	−	0.0536122i
$593$	−0.837988	−	3.12741i	−0.0344121	−	0.128428i	0.946583	−	0.322460i	$-0.104510\pi$
$593$	−0.837988	−	3.12741i	−0.0344121	−	0.128428i	−0.980995	+	0.194033i	$0.937843\pi$
$594$		0			0
$595$	−31.1017	+	4.36767i	−1.27504	+	0.179057i
$596$	5.04885			0.206809
$597$		0			0
$598$	2.19490	+	0.588122i	0.0897562	+	0.0240501i
$599$	6.75802	−	3.90174i	0.276125	−	0.159421i	−0.355543	−	0.934660i	$-0.615704\pi$
$599$	6.75802	−	3.90174i	0.276125	−	0.159421i	0.631668	+	0.775239i	$0.282371\pi$
$600$		0			0
$601$		−	31.7170i		−	1.29377i	−0.762590	−	0.646883i	$-0.776072\pi$
$601$		−	31.7170i		−	1.29377i	0.762590	−	0.646883i	$-0.223928\pi$
$602$	3.18231	−	6.17537i	0.129701	−	0.251689i
$603$		0			0
$604$	11.6418	+	6.72142i	0.473699	+	0.273491i
$605$	45.5070	+	7.81383i	1.85012	+	0.317677i
$606$		0			0
$607$	0.743495	−	0.199219i	0.0301775	−	0.00808604i	−0.243699	−	0.969851i	$-0.578361\pi$
$607$	0.743495	−	0.199219i	0.0301775	−	0.00808604i	0.273876	+	0.961765i	$0.411694\pi$
$608$	−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
$613$	9.05898	−	33.8086i	0.365889	−	1.36552i	−0.500323	−	0.865839i	$-0.666786\pi$
$613$	9.05898	−	33.8086i	0.365889	−	1.36552i	0.866212	−	0.499676i	$-0.166548\pi$
$614$	−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	0.860942	+	0.508703i	$0.169875\pi$
$619$	21.6707	+	37.5348i	0.871021	+	1.50865i	0.0100783	+	0.999949i	$0.496792\pi$
$620$	−8.48131	−	1.45629i	−0.340617	−	0.0584861i
$621$		0			0
$622$	−7.76566	−	7.76566i	−0.311374	−	0.311374i
$623$	−14.4487	+	28.0382i	−0.578876	+	1.12333i
$624$		0			0
$625$	3.89884	−	24.6941i	0.155953	−	0.987764i
$626$	25.4707	−	14.7055i	1.01801	−	0.587749i
$627$		0			0
$628$	−0.285443	−	1.06529i	−0.0113904	−	0.0425096i
$629$	−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	$0.452081\pi$
$632$	−1.61706	−	6.03495i	−0.0643232	−	0.240058i
$633$		0			0
$634$	−3.71869	+	2.14699i	−0.147688	+	0.0852677i
$635$	−13.3112	−	6.13457i	−0.528237	−	0.243443i
$636$		0			0
$637$	9.00710	−	10.9163i	0.356874	−	0.432520i
$638$	−12.5507	−	12.5507i	−0.496887	−	0.496887i
$639$		0			0
$640$	−1.29076	−	1.82591i	−0.0510217	−	0.0721754i
$641$	12.1657	+	21.0717i	0.480518	+	0.832281i	0.999750	−	0.0223521i	$-0.00711549\pi$
$641$	12.1657	+	21.0717i	0.480518	+	0.832281i	−0.519233	+	0.854633i	$0.673782\pi$
$642$		0			0
$643$	6.21713	−	6.21713i	0.245180	−	0.245180i	−0.573809	−	0.818989i	$-0.694535\pi$
$643$	6.21713	−	6.21713i	0.245180	−	0.245180i	0.818989	+	0.573809i	$0.194535\pi$
$644$	1.99986	−	2.20067i	0.0788057	−	0.0867184i
$645$		0			0
$646$	−10.3303	+	17.8925i	−0.406439	+	0.703973i
$647$	−5.33869	+	19.9243i	−0.209886	+	0.783304i	0.778019	+	0.628241i	$0.216225\pi$
$647$	−5.33869	+	19.9243i	−0.209886	+	0.783304i	−0.987905	+	0.155063i	$0.950442\pi$
$648$		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
$653$	25.2490	−	6.76544i	0.988069	−	0.264752i	0.271630	−	0.962402i	$-0.412437\pi$
$653$	25.2490	−	6.76544i	0.988069	−	0.264752i	0.716439	+	0.697650i	$0.245771\pi$
$654$		0			0
$655$	2.91199	−	16.9591i	0.113781	−	0.662649i
$656$	−6.24448	−	3.60525i	−0.243806	−	0.140761i
$657$		0			0
$658$	−8.43533	−	13.1208i	−0.328844	−	0.511502i
$659$			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	−0.166583	−	0.986027i	$-0.553273\pi$
$661$	15.5301	−	8.96630i	0.604050	−	0.348749i	0.770633	+	0.637279i	$0.219940\pi$
$662$	34.2419	+	9.17510i	1.33085	+	0.356600i
$663$		0			0
$664$	8.02257			0.311336
$665$	−22.8523	−	2.80839i	−0.886174	−	0.108905i
$666$		0			0
$667$	0.917769	+	3.42516i	0.0355362	+	0.132623i
$668$	6.42961	+	1.72281i	0.248769	+	0.0666574i
$669$		0			0
$670$	1.77258	−	0.654184i	0.0684807	−	0.0252733i
$671$		−	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
$677$	17.8506	−	4.78306i	0.686055	−	0.183828i	0.101079	−	0.994878i	$-0.467771\pi$
$677$	17.8506	−	4.78306i	0.686055	−	0.183828i	0.584976	+	0.811051i	$0.301104\pi$
$678$		0			0
$679$	18.3618	+	16.6863i	0.704660	+	0.640362i
$680$	−9.12760	−	7.58946i	−0.350027	−	0.291043i
$681$		0			0
$682$	−5.60357	+	20.9128i	−0.214572	+	0.800793i
$683$	6.93661	−	25.8878i	0.265422	−	0.990569i	−0.696569	−	0.717489i	$-0.745291\pi$
$683$	6.93661	−	25.8878i	0.265422	−	0.990569i	0.961992	−	0.273079i	$-0.0880421\pi$
$684$		0			0
$685$	1.81023	+	19.6743i	0.0691653	+	0.751717i
$686$	−7.29908	−	17.0213i	−0.278680	−	0.649875i
$687$		0			0
$688$	2.53629	−	0.679597i	0.0966951	−	0.0259094i
$689$	−1.39819	−	2.42173i	−0.0532667	−	0.0922606i
$690$		0			0
$691$	25.1773	+	14.5361i	0.957790	+	0.552980i	0.895492	−	0.445077i	$-0.146824\pi$
$691$	25.1773	+	14.5361i	0.957790	+	0.552980i	0.0622976	+	0.998058i	$0.480157\pi$
$692$	−4.98835	−	4.98835i	−0.189628	−	0.189628i
$693$		0			0
$694$		−	8.97626i		−	0.340734i
$695$	8.56502	+	23.2078i	0.324890	+	0.880323i
$696$		0			0
$697$	−36.9743	−	9.90723i	−1.40050	−	0.375263i
$698$	−6.73580	−	25.1383i	−0.254954	−	0.951500i
$699$		0			0
$700$	3.81229	−	12.6675i	0.144091	−	0.478788i
$701$	−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
$703$	−18.9462	−	5.07663i	−0.714571	−	0.191469i
$704$	−4.87205	+	2.81288i	−0.183622	+	0.106014i
$705$		0			0
$706$			9.96618i			0.375082i
$707$	−35.8289	+	23.0343i	−1.34748	+	0.866295i
$708$		0			0
$709$	27.1994	+	15.7036i	1.02150	+	0.589760i	0.914537	−	0.404503i	$-0.132555\pi$
$709$	27.1994	+	15.7036i	1.02150	+	0.589760i	0.106958	+	0.994263i	$0.465889\pi$
$710$	8.72254	−	6.16608i	0.327351	−	0.231409i
$711$		0			0
$712$	−11.5156	+	3.08559i	−0.431565	+	0.115637i
$713$	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
$718$	2.99560	−	11.1797i	0.111795	−	0.417224i
$719$	−5.40214	+	9.35678i	−0.201466	+	0.348949i	−0.949001	−	0.315273i	$-0.897904\pi$
$719$	−5.40214	+	9.35678i	−0.201466	+	0.348949i	0.747535	+	0.664222i	$0.231237\pi$
$720$		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
$725$	10.2480	+	11.9930i	0.380602	+	0.445408i
$726$		0			0
$727$	−33.6108	−	33.6108i	−1.24656	−	1.24656i	−0.957231	−	0.289326i	$-0.906569\pi$
$727$	−33.6108	−	33.6108i	−1.24656	−	1.24656i	−0.289326	−	0.957231i	$-0.593431\pi$
$728$	5.34305	−	0.255420i	0.198026	−	0.00946651i
$729$		0			0
$730$	−11.7732	+	4.34500i	−0.435747	+	0.160816i
$731$	12.0719	−	6.96972i	0.446496	−	0.257785i
$732$		0			0
$733$	6.66658	+	24.8800i	0.246236	+	0.918964i	0.972758	+	0.231822i	$0.0744686\pi$
$733$	6.66658	+	24.8800i	0.246236	+	0.918964i	−0.726523	+	0.687143i	$0.758865\pi$
$734$	−16.6944			−0.616202
$735$		0			0
$736$	1.12392			0.0414283
$737$	−1.23034	−	4.59170i	−0.0453203	−	0.169138i
$738$		0			0
$739$	−10.4948	+	6.05920i	−0.386059	+	0.222891i	−0.680451	−	0.732793i	$-0.738216\pi$
$739$	−10.4948	+	6.05920i	−0.386059	+	0.222891i	0.294392	+	0.955685i	$0.404883\pi$
$740$	4.71693	−	10.2351i	0.173398	−	0.376250i
$741$		0			0
$742$	−3.65522	+	0.174735i	−0.134187	+	0.00641472i
$743$	−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
$745$	−1.91053	+	11.1267i	−0.0699964	+	0.407652i
$746$	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	−0.964903	−	0.262607i	$-0.915418\pi$
$751$	−6.98887	+	12.1051i	−0.255028	+	0.441721i	0.709875	+	0.704327i	$0.248751\pi$
$752$	1.52590	−	5.69475i	0.0556440	−	0.207666i
$753$		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	$0.101010\pi$
$758$	−6.90974	+	1.85146i	−0.250973	+	0.0672481i
$759$		0			0
$760$	−5.02338	−	7.10608i	−0.182217	−	0.257765i
$761$	−18.9372	−	10.9334i	−0.686471	−	0.396334i	0.115817	−	0.993271i	$-0.463051\pi$
$761$	−18.9372	−	10.9334i	−0.686471	−	0.396334i	−0.802289	+	0.596936i	$0.796385\pi$
$762$		0			0
$763$	13.1546	−	8.45710i	0.476230	−	0.306168i
$764$		−	17.2023i		−	0.622359i
$765$		0			0
$766$	12.6382	−	7.29669i	0.456638	−	0.263640i
$767$	10.6989	+	2.86675i	0.386313	+	0.103512i
$768$		0			0
$769$	−31.0506			−1.11971			−0.559857	−	0.828589i	$-0.689144\pi$
$769$	−31.0506			−1.11971			−0.559857	+	0.828589i	$0.689144\pi$
$770$	−30.8576	−	12.4711i	−1.11203	−	0.449428i
$771$		0			0
$772$	−3.12327	−	11.6562i	−0.112409	−	0.419516i
$773$	5.86173	+	1.57065i	0.210832	+	0.0564922i	0.362689	−	0.931910i	$-0.381859\pi$
$773$	5.86173	+	1.57065i	0.210832	+	0.0564922i	−0.151857	+	0.988402i	$0.548525\pi$
$774$		0			0
$775$	6.41880	−	18.1402i	0.230570	−	0.651614i
$776$			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
$782$	5.76329	−	1.54427i	0.206095	−	0.0552229i
$783$		0			0
$784$	2.90577	−	6.36840i	0.103777	−	0.227443i
$785$	2.45571	−	0.225950i	0.0876481	−	0.00806449i
$786$		0			0
$787$	−5.78752	+	21.5993i	−0.206303	+	0.769932i	0.782746	+	0.622342i	$0.213818\pi$
$787$	−5.78752	+	21.5993i	−0.206303	+	0.769932i	−0.989049	+	0.147591i	$0.952848\pi$
$788$	5.23910	−	19.5526i	0.186635	−	0.696532i
$789$		0			0
$790$	13.9118	−	1.28003i	0.494961	−	0.0455413i
$791$	37.6089	+	34.1772i	1.33722	+	1.21520i
$792$		0			0
$793$	−9.00138	+	2.41191i	−0.319648	+	0.0856495i
$794$	−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	0.936636	−	0.350305i	$-0.113922\pi$
$797$	16.5528	+	16.5528i	0.586330	+	0.586330i	−0.350305	+	0.936636i	$0.613922\pi$
$798$		0			0
$799$		−	31.2984i		−	1.10726i
$800$	4.51240	−	2.15365i	0.159538	−	0.0761432i
$801$		0			0
$802$	19.2901	+	5.16876i	0.681156	+	0.182515i
$803$	8.17177	+	30.4975i	0.288376	+	1.07623i
$804$		0			0
$805$	4.09310	+	5.24008i	0.144263	+	0.184689i
$806$	7.78078			0.274066
$807$		0			0
$808$	−15.5506	−	4.16678i	−0.547069	−	0.146587i
$809$	2.84139	−	1.64048i	0.0998980	−	0.0576762i	−0.449219	−	0.893422i	$-0.648298\pi$
$809$	2.84139	−	1.64048i	0.0998980	−	0.0576762i	0.549117	+	0.835746i	$0.314964\pi$
$810$		0			0
$811$			17.8693i			0.627476i	0.949510	+	0.313738i	$0.101581\pi$
$811$			17.8693i			0.627476i	−0.949510	+	0.313738i	$0.898419\pi$
$812$	4.51412	+	7.02151i	0.158414	+	0.246407i
$813$		0			0
$814$	−24.5550	−	14.1768i	−0.860653	−	0.496898i
$815$	−17.0911	−	24.1771i	−0.598674	−	0.846886i
$816$		0			0
$817$	9.87074	−	2.64486i	0.345333	−	0.0925318i
$818$	−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	−0.950516	−	0.310677i	$-0.899444\pi$
$821$	−5.90837	+	10.2336i	−0.206204	+	0.357155i	0.744312	+	0.667832i	$0.232778\pi$
$822$		0			0
$823$	9.13692	−	34.0995i	0.318493	−	1.18863i	−0.602200	−	0.798345i	$-0.705709\pi$
$823$	9.13692	−	34.0995i	0.318493	−	1.18863i	0.920693	−	0.390287i	$-0.127624\pi$
$824$	−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	−0.992756	−	0.120144i	$-0.961664\pi$
$829$	−17.2877	−	29.9431i	−0.600426	−	1.03997i	0.392330	−	0.919824i	$-0.371669\pi$
$830$	−3.03581	+	17.6803i	−0.105374	+	0.613691i
$831$		0			0
$832$	1.42962	+	1.42962i	0.0495631	+	0.0495631i
$833$	6.15011	−	36.6487i	0.213089	−	1.26980i
$834$		0			0
$835$	−6.22977	+	13.5177i	−0.215590	+	0.467801i
$836$	−18.9611	+	10.9472i	−0.655782	+	0.378616i
$837$		0			0
$838$	8.05859	+	30.0751i	0.278379	+	1.03893i
$839$	−50.1328			−1.73078			−0.865388	−	0.501102i	$-0.832928\pi$
$839$	−50.1328			−1.73078			−0.865388	+	0.501102i	$0.832928\pi$
$840$		0			0
$841$	19.0459			0.656754
$842$	8.71515	+	32.5254i	0.300344	+	1.12090i
$843$		0			0
$844$	−16.9538	+	9.78829i	−0.583575	+	0.336927i
$845$	18.6961	−	6.89993i	0.643164	−	0.237365i
$846$		0			0
$847$	−25.0259	+	48.5636i	−0.859901	+	1.66866i
$848$	−0.978013	−	0.978013i	−0.0335851	−	0.0335851i
$849$		0			0
$850$	20.1797	−	17.2436i	0.692160	−	0.591452i
$851$	2.83227	+	4.90563i	0.0970888	+	0.168163i
$852$		0			0
$853$	2.37500	−	2.37500i	0.0813183	−	0.0813183i	−0.665278	−	0.746596i	$-0.731687\pi$
$853$	2.37500	−	2.37500i	0.0813183	−	0.0813183i	0.746596	+	0.665278i	$0.231687\pi$
$854$	−2.59021	+	11.9167i	−0.0886352	+	0.407779i
$855$		0			0
$856$	1.40051	−	2.42575i	0.0478683	−	0.0829103i
$857$	10.8545	−	40.5097i	0.370784	−	1.38378i	−0.488624	−	0.872494i	$-0.662501\pi$
$857$	10.8545	−	40.5097i	0.370784	−	1.38378i	0.859408	−	0.511290i	$-0.170832\pi$
$858$		0			0
$859$	1.17847	−	2.04117i	0.0402090	−	0.0696440i	−0.845221	−	0.534418i	$-0.820531\pi$
$859$	1.17847	−	2.04117i	0.0402090	−	0.0696440i	0.885430	+	0.464774i	$0.153864\pi$
$860$	0.537952	+	5.84668i	0.0183440	+	0.199370i
$861$		0			0
$862$	−10.4268	+	10.4268i	−0.355137	+	0.355137i
$863$	46.7022	−	12.5138i	1.58976	−	0.425975i	0.647831	−	0.761784i	$-0.275676\pi$
$863$	46.7022	−	12.5138i	1.58976	−	0.425975i	0.941930	+	0.335808i	$0.109009\pi$
$864$		0			0
$865$	12.8810	−	9.10577i	0.437968	−	0.309605i
$866$	−12.2261	−	7.05873i	−0.415459	−	0.239865i
$867$		0			0
$868$	4.66418	−	9.05097i	0.158312	−	0.307210i
$869$		−	35.1489i		−	1.19234i
$870$		0			0
$871$	−1.47950	+	0.854190i	−0.0501310	+	0.0289431i
$872$	5.70944	+	1.52984i	0.193346	+	0.0518069i
$873$		0			0
$874$	4.37408			0.147955
$875$	26.4743	+	13.1951i	0.894995	+	0.446076i
$876$		0			0
$877$	−3.56681	−	13.3115i	−0.120443	−	0.449498i	0.879194	−	0.476465i	$-0.158082\pi$
$877$	−3.56681	−	13.3115i	−0.120443	−	0.449498i	−0.999636	+	0.0269665i	$0.991415\pi$
$878$	37.1191	+	9.94602i	1.25271	+	0.335662i
$879$		0			0
$880$	−4.35544	−	11.8015i	−0.146822	−	0.397829i
$881$		−	3.32542i		−	0.112036i	−0.998430	−	0.0560181i	$-0.982160\pi$
$881$		−	3.32542i		−	0.112036i	0.998430	−	0.0560181i	$-0.0178405\pi$
$882$		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
$887$	34.6001	−	9.27107i	1.16176	−	0.311292i	0.374090	−	0.927392i	$-0.377955\pi$
$887$	34.6001	−	9.27107i	1.16176	−	0.311292i	0.787668	+	0.616101i	$0.211289\pi$
$888$		0			0
$889$	11.6632	−	12.8343i	0.391170	−	0.430447i
$890$	−2.44248	−	26.5458i	−0.0818721	−	0.889819i
$891$		0			0
$892$	0.534495	−	1.99476i	0.0178962	−	0.0667895i
$893$	5.93852	−	22.1628i	0.198725	−	0.741651i
$894$		0			0
$895$	−3.79349	−	3.15423i	−0.126803	−	0.105434i
$896$	2.51999	−	0.806019i	0.0841869	−	0.0269272i
$897$		0			0
$898$	7.05384	−	1.89007i	0.235390	−	0.0630725i
$899$	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
$905$	−8.64001	+	3.18866i	−0.287204	+	0.105995i
$906$		0			0
$907$	16.6696	+	4.46661i	0.553506	+	0.148312i	0.524721	−	0.851274i	$-0.324170\pi$
$907$	16.6696	+	4.46661i	0.553506	+	0.148312i	0.0287849	+	0.999586i	$0.490836\pi$
$908$	4.82525	+	18.0081i	0.160131	+	0.597618i
$909$		0			0
$910$	−1.45896	+	11.8717i	−0.0483639	+	0.393545i
$911$	−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
$913$	43.5952	+	11.6813i	1.44279	+	0.386594i
$914$	4.45641	−	2.57291i	0.147405	−	0.0851042i
$915$		0			0
$916$			4.00767i			0.132417i
$917$	18.0982	+	9.32645i	0.597657	+	0.307986i
$918$		0			0
$919$	−5.37964	−	3.10593i	−0.177458	−	0.102455i	0.408640	−	0.912696i	$-0.366003\pi$
$919$	−5.37964	−	3.10593i	−0.177458	−	0.102455i	−0.586098	+	0.810240i	$0.699337\pi$
$920$	−0.425302	+	2.47692i	−0.0140218	+	0.0816615i
$921$		0			0
$922$	28.4088	−	7.61212i	0.935595	−	0.250692i
$923$	−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
$928$	−0.816578	+	3.04751i	−0.0268055	+	0.100039i
$929$	0.0947297	−	0.164077i	0.00310798	−	0.00538318i	−0.864467	−	0.502689i	$-0.832344\pi$
$929$	0.0947297	−	0.164077i	0.00310798	−	0.00538318i	0.867575	+	0.497306i	$0.165677\pi$
$930$		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
$935$	−38.5493	−	54.5319i	−1.26070	−	1.78338i
$936$		0			0
$937$	34.2022	+	34.2022i	1.11734	+	1.11734i	0.992131	+	0.125208i	$0.0399598\pi$
$937$	34.2022	+	34.2022i	1.11734	+	1.11734i	0.125208	+	0.992131i	$0.460040\pi$
$938$	0.106750	+	2.23307i	0.00348552	+	0.0729123i
$939$		0			0
$940$	11.9728	+	5.51775i	0.390509	+	0.179969i
$941$	16.3826	−	9.45851i	0.534058	−	0.308339i	−0.208609	−	0.977999i	$-0.566894\pi$
$941$	16.3826	−	9.45851i	0.534058	−	0.308339i	0.742667	+	0.669660i	$0.233560\pi$
$942$		0			0
$943$	2.09748	+	7.82790i	0.0683033	+	0.254911i
$944$	5.47845			0.178308
$945$		0			0
$946$	14.7719			0.480276
$947$	−12.2033	−	45.5435i	−0.396555	−	1.47996i	−0.819115	−	0.573629i	$-0.805535\pi$
$947$	−12.2033	−	45.5435i	−0.396555	−	1.47996i	0.422560	−	0.906335i	$-0.361131\pi$
$948$		0			0
$949$	9.82664	−	5.67341i	0.318986	−	0.184167i
$950$	17.5614	−	8.38160i	0.569767	−	0.271935i
$951$		0			0
$952$	11.8146	−	7.59560i	0.382914	−	0.246175i
$953$	−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
$955$	37.9108	+	6.50952i	1.22677	+	0.210643i
$956$	−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
$962$	−2.63730	+	9.84255i	−0.0850301	+	0.317337i
$963$		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	$0.0361687\pi$
$968$	−19.9456	+	5.34440i	−0.641075	+	0.171776i
$969$		0			0
$970$	−20.6667	−	3.54860i	−0.663568	−	0.113939i
$971$	27.8750	+	16.0936i	0.894550	+	0.516469i	0.875428	−	0.483348i	$-0.160580\pi$
$971$	27.8750	+	16.0936i	0.894550	+	0.516469i	0.0191221	+	0.999817i	$0.493913\pi$
$972$		0			0
$973$	−29.2369	+	1.39765i	−0.937291	+	0.0448065i
$974$		−	35.9920i		−	1.15326i
$975$		0			0
$976$	−3.99172	+	2.30462i	−0.127772	+	0.0737691i
$977$	−22.4848	−	6.02479i	−0.719353	−	0.192750i	−0.119470	−	0.992838i	$-0.538119\pi$
$977$	−22.4848	−	6.02479i	−0.719353	−	0.192750i	−0.599883	+	0.800088i	$0.704786\pi$
$978$		0			0
$979$	−67.0692			−2.14354
$980$	12.9352	+	8.81363i	0.413200	+	0.281541i
$981$		0			0
$982$	−3.95535	−	14.7616i	−0.126220	−	0.471060i
$983$	−55.0964	−	14.7630i	−1.75730	−	0.470868i	−0.771143	−	0.636662i	$-0.780315\pi$
$983$	−55.0964	−	14.7630i	−1.75730	−	0.470868i	−0.986160	+	0.165793i	$0.946981\pi$
$984$		0			0
$985$	41.1078	+	18.9449i	1.30980	+	0.603634i
$986$			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	0.808478	+	0.588526i	$0.200292\pi$
$991$	28.7703	+	49.8316i	0.913918	+	1.58295i	0.105440	+	0.994426i	$0.466375\pi$
$992$	3.71733	−	0.996056i	0.118025	−	0.0316248i
$993$		0			0
$994$	3.85043	+	12.0382i	0.122128	+	0.381829i
$995$	10.7694	−	12.9520i	0.341414	−	0.410607i
$996$		0			0
$997$	6.27762	−	23.4284i	0.198814	−	0.741985i	−0.792432	−	0.609960i	$-0.791185\pi$
$997$	6.27762	−	23.4284i	0.198814	−	0.741985i	0.991246	−	0.132025i	$-0.0421479\pi$
$998$	8.17479	−	30.5087i	0.258768	−	0.965737i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.k.a.3.1	✓	16	21.17	even	6
70.2.k.a.17.3	yes	16	105.17	odd	12
70.2.k.a.33.3	yes	16	3.2	odd	2
70.2.k.a.47.1	yes	16	15.2	even	4
350.2.o.c.143.4		16	105.59	even	6
350.2.o.c.157.2		16	105.38	odd	12
350.2.o.c.243.2		16	15.14	odd	2
350.2.o.c.257.4		16	15.8	even	4
490.2.g.c.97.6		16	105.2	even	12
490.2.g.c.97.7		16	105.47	odd	12
490.2.g.c.293.6		16	21.5	even	6
490.2.g.c.293.7		16	21.2	odd	6
490.2.l.c.117.2		16	105.62	odd	4
490.2.l.c.227.4		16	105.32	even	12
490.2.l.c.313.4		16	21.20	even	2
490.2.l.c.423.2		16	21.11	odd	6
560.2.ci.c.17.3		16	420.227	even	12
560.2.ci.c.33.3		16	12.11	even	2
560.2.ci.c.257.3		16	60.47	odd	4
560.2.ci.c.353.3		16	84.59	odd	6
630.2.bv.c.73.3		16	7.3	odd	6	inner
630.2.bv.c.397.3		16	5.2	odd	4	inner
630.2.bv.c.523.1		16	1.1	even	1	trivial
630.2.bv.c.577.1		16	35.17	even	12	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)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-0.774197 - 2.09777i) q^{5} +(2.64273 - 0.126334i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-0.774197 - 2.09777i) q^{5} +(2.64273 - 0.126334i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.82591 + 1.29076i) q^{10} +(2.81288 + 4.87205i) q^{11} +(1.42962 - 1.42962i) q^{13} +(-0.806019 - 2.51999i) q^{14} +(0.500000 - 0.866025i) q^{16} +(1.37400 - 5.12784i) q^{17} +(1.94590 - 3.37040i) q^{19} +(1.71936 + 1.42962i) q^{20} +(3.97801 - 3.97801i) q^{22} +(-1.08562 + 0.290892i) q^{23} +(-3.80124 + 3.24817i) q^{25} +(-1.75092 - 1.01089i) q^{26} +(-2.22551 + 1.43078i) q^{28} -3.15502i q^{29} +(-3.33287 + 1.92423i) q^{31} +(-0.965926 - 0.258819i) q^{32} -5.30873 q^{34} +(-2.31101 - 5.44603i) q^{35} +(-1.30444 - 4.86824i) q^{37} +(-3.75919 - 1.00727i) q^{38} +(0.935904 - 2.03078i) q^{40} -7.21050i q^{41} +(1.85669 + 1.85669i) q^{43} +(-4.87205 - 2.81288i) q^{44} +(0.561961 + 0.973344i) q^{46} +(5.69475 - 1.52590i) q^{47} +(6.96808 - 0.667734i) q^{49} +(4.12132 + 2.83103i) q^{50} +(-0.523277 + 1.95290i) q^{52} +(0.357978 - 1.33599i) q^{53} +(8.04270 - 9.67269i) q^{55} +(1.95803 + 1.77936i) q^{56} +(-3.04751 + 0.816578i) q^{58} +(2.73923 + 4.74448i) q^{59} +(-3.99172 - 2.30462i) q^{61} +(2.72127 + 2.72127i) q^{62} +1.00000i q^{64} +(-4.10581 - 1.89220i) q^{65} +(-0.816193 - 0.218698i) q^{67} +(1.37400 + 5.12784i) q^{68} +(-4.66232 + 3.64180i) q^{70} -4.77710 q^{71} +(5.42104 + 1.45256i) q^{73} +(-4.36475 + 2.51999i) q^{74} +3.89180i q^{76} +(8.04920 + 12.5202i) q^{77} +(-5.41079 - 3.12392i) q^{79} +(-2.20382 - 0.378409i) q^{80} +(-6.96481 + 1.86622i) q^{82} +(5.67281 - 5.67281i) q^{83} +(-11.8207 + 1.08763i) q^{85} +(1.31288 - 2.27397i) q^{86} +(-1.45605 + 5.43407i) q^{88} +(-5.96090 + 10.3246i) q^{89} +(3.59749 - 3.95871i) q^{91} +(0.794732 - 0.794732i) q^{92} +(-2.94782 - 5.10577i) q^{94} +(-8.57682 - 1.47269i) q^{95} +(6.63103 + 6.63103i) q^{97} +(-2.44845 - 6.55783i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{5} + 8 q^{7}+O(q^{10}) \) 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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