LMFDB - Embedded newform 630.2.bv.c.73.4

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			73.4
Root			$-0.144868 + 1.25092i$ of defining polynomial
Character	$\chi$	$=$	630.73
Dual form			630.2.bv.c.397.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(2.03078 - 0.935904i) q^{5} +(1.83959 + 1.90155i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(2.03078 - 0.935904i) q^{5} +(1.83959 + 1.90155i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.20382 - 0.378409i) q^{10} +(-2.01999 + 3.49872i) q^{11} +(0.204875 - 0.204875i) q^{13} +(1.28475 + 2.31288i) q^{14} +(0.500000 + 0.866025i) q^{16} +(1.97024 - 0.527924i) q^{17} +(-3.10166 - 5.37224i) q^{19} +(2.22666 + 0.204875i) q^{20} +(-2.85669 + 2.85669i) q^{22} +(-1.17456 + 4.38350i) q^{23} +(3.24817 - 3.80124i) q^{25} +(0.250919 - 0.144868i) q^{26} +(0.642357 + 2.56659i) q^{28} -7.15869i q^{29} +(6.33287 + 3.65628i) q^{31} +(0.258819 + 0.965926i) q^{32} +2.03974 q^{34} +(5.51548 + 2.13996i) q^{35} +(-4.46814 - 1.19723i) q^{37} +(-1.60554 - 5.99195i) q^{38} +(2.09777 + 0.774197i) q^{40} +2.58745i q^{41} +(-4.97801 - 4.97801i) q^{43} +(-3.49872 + 2.01999i) q^{44} +(-2.26907 + 3.93014i) q^{46} +(0.0815604 - 0.304388i) q^{47} +(-0.231803 + 6.99616i) q^{49} +(4.12132 - 2.83103i) q^{50} +(0.279864 - 0.0749894i) q^{52} +(8.00039 - 2.14370i) q^{53} +(-0.827689 + 8.99566i) q^{55} +(-0.0438127 + 2.64539i) q^{56} +(1.85281 - 6.91477i) q^{58} +(-0.427702 + 0.740802i) q^{59} +(-5.99356 + 3.46038i) q^{61} +(5.17076 + 5.17076i) q^{62} +1.00000i q^{64} +(0.224313 - 0.607800i) q^{65} +(-0.817530 - 3.05106i) q^{67} +(1.97024 + 0.527924i) q^{68} +(4.77369 + 3.49455i) q^{70} -7.12240 q^{71} +(-2.98311 - 11.1331i) q^{73} +(-4.00603 - 2.31288i) q^{74} -6.20333i q^{76} +(-10.3690 + 2.59511i) q^{77} +(-4.39618 + 2.53813i) q^{79} +(1.82591 + 1.29076i) q^{80} +(-0.669683 + 2.49929i) q^{82} +(3.85372 - 3.85372i) q^{83} +(3.50704 - 2.91605i) q^{85} +(-3.51999 - 6.09680i) q^{86} +(-3.90231 + 1.04562i) q^{88} +(1.53615 + 2.66069i) q^{89} +(0.766467 + 0.0126942i) q^{91} +(-3.20895 + 3.20895i) q^{92} +(0.157563 - 0.272906i) q^{94} +(-11.3267 - 8.00700i) q^{95} +(-6.63103 - 6.63103i) q^{97} +(-2.03464 + 6.69778i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	2.03078	−	0.935904i	0.908194	−	0.418549i
$5$	2.03078	−	0.935904i	0.908194	−	0.418549i
$6$		0			0
$7$	1.83959	+	1.90155i	0.695300	+	0.718719i
$7$	1.83959	+	1.90155i	0.695300	+	0.718719i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	2.20382	−	0.378409i	0.696908	−	0.119663i
$11$	−2.01999	+	3.49872i	−0.609049	+	1.05490i	0.382349	+	0.924018i	$0.375115\pi$
$11$	−2.01999	+	3.49872i	−0.609049	+	1.05490i	−0.991397	+	0.130886i	$0.958218\pi$
$12$		0			0
$13$	0.204875	−	0.204875i	0.0568221	−	0.0568221i	−0.678125	−	0.734947i	$-0.737207\pi$
$13$	0.204875	−	0.204875i	0.0568221	−	0.0568221i	0.734947	+	0.678125i	$0.237207\pi$
$14$	1.28475	+	2.31288i	0.343364	+	0.618143i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.97024	−	0.527924i	0.477853	−	0.128040i	−0.0118498	−	0.999930i	$-0.503772\pi$
$17$	1.97024	−	0.527924i	0.477853	−	0.128040i	0.489703	+	0.871890i	$0.337105\pi$
$18$		0			0
$19$	−3.10166	−	5.37224i	−0.711571	−	1.23248i	−0.964267	−	0.264931i	$-0.914651\pi$
$19$	−3.10166	−	5.37224i	−0.711571	−	1.23248i	0.252697	−	0.967545i	$-0.418682\pi$
$20$	2.22666	+	0.204875i	0.497897	+	0.0458114i
$21$		0			0
$22$	−2.85669	+	2.85669i	−0.609049	+	0.609049i
$23$	−1.17456	+	4.38350i	−0.244912	+	0.914023i	0.728516	+	0.685029i	$0.240210\pi$
$23$	−1.17456	+	4.38350i	−0.244912	+	0.914023i	−0.973428	+	0.228994i	$0.926456\pi$
$24$		0			0
$25$	3.24817	−	3.80124i	0.649633	−	0.760248i
$26$	0.250919	−	0.144868i	0.0492094	−	0.0284110i
$27$		0			0
$28$	0.642357	+	2.56659i	0.121394	+	0.485040i
$29$		−	7.15869i		−	1.32934i	−0.747139	−	0.664668i	$-0.768573\pi$
$29$		−	7.15869i		−	1.32934i	0.747139	−	0.664668i	$-0.231427\pi$
$30$		0			0
$31$	6.33287	+	3.65628i	1.13742	+	0.656688i	0.945790	−	0.324780i	$-0.105290\pi$
$31$	6.33287	+	3.65628i	1.13742	+	0.656688i	0.191627	+	0.981468i	$0.438624\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$		0			0
$34$	2.03974			0.349813
$35$	5.51548	+	2.13996i	0.932287	+	0.361719i
$36$		0			0
$37$	−4.46814	−	1.19723i	−0.734558	−	0.196824i	−0.127900	−	0.991787i	$-0.540824\pi$
$37$	−4.46814	−	1.19723i	−0.734558	−	0.196824i	−0.606658	+	0.794963i	$0.707490\pi$
$38$	−1.60554	−	5.99195i	−0.260453	−	0.972023i
$39$		0			0
$40$	2.09777	+	0.774197i	0.331686	+	0.122411i
$41$			2.58745i			0.404093i	0.979376	+	0.202046i	$0.0647591\pi$
$41$			2.58745i			0.404093i	−0.979376	+	0.202046i	$0.935241\pi$
$42$		0			0
$43$	−4.97801	−	4.97801i	−0.759140	−	0.759140i	0.217026	−	0.976166i	$-0.430364\pi$
$43$	−4.97801	−	4.97801i	−0.759140	−	0.759140i	−0.976166	+	0.217026i	$0.930364\pi$
$44$	−3.49872	+	2.01999i	−0.527452	+	0.304524i
$45$		0			0
$46$	−2.26907	+	3.93014i	−0.334556	+	0.579468i
$47$	0.0815604	−	0.304388i	0.0118968	−	0.0443995i	−0.959722	−	0.280950i	$-0.909350\pi$
$47$	0.0815604	−	0.304388i	0.0118968	−	0.0443995i	0.971619	+	0.236551i	$0.0760170\pi$
$48$		0			0
$49$	−0.231803	+	6.99616i	−0.0331148	+	0.999452i
$50$	4.12132	−	2.83103i	0.582843	−	0.400368i
$51$		0			0
$52$	0.279864	−	0.0749894i	0.0388102	−	0.0103992i
$53$	8.00039	−	2.14370i	1.09894	−	0.294460i	0.336606	−	0.941646i	$-0.390721\pi$
$53$	8.00039	−	2.14370i	1.09894	−	0.294460i	0.762332	+	0.647186i	$0.224054\pi$
$54$		0			0
$55$	−0.827689	+	8.99566i	−0.111606	+	1.21297i
$56$	−0.0438127	+	2.64539i	−0.00585472	+	0.353505i
$57$		0			0
$58$	1.85281	−	6.91477i	0.243285	−	0.907953i
$59$	−0.427702	+	0.740802i	−0.0556821	+	0.0964442i	−0.892523	−	0.451002i	$-0.851067\pi$
$59$	−0.427702	+	0.740802i	−0.0556821	+	0.0964442i	0.836841	+	0.547446i	$0.184400\pi$
$60$		0			0
$61$	−5.99356	+	3.46038i	−0.767397	+	0.443057i	−0.831945	−	0.554858i	$-0.812773\pi$
$61$	−5.99356	+	3.46038i	−0.767397	+	0.443057i	0.0645484	+	0.997915i	$0.479439\pi$
$62$	5.17076	+	5.17076i	0.656688	+	0.656688i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	0.224313	−	0.607800i	0.0278226	−	0.0753883i
$66$		0			0
$67$	−0.817530	−	3.05106i	−0.0998772	−	0.372747i	0.897837	−	0.440329i	$-0.145138\pi$
$67$	−0.817530	−	3.05106i	−0.0998772	−	0.372747i	−0.997714	+	0.0675822i	$0.978472\pi$
$68$	1.97024	+	0.527924i	0.238926	+	0.0640201i
$69$		0			0
$70$	4.77369	+	3.49455i	0.570565	+	0.417679i
$71$	−7.12240			−0.845273			−0.422637	−	0.906299i	$-0.638895\pi$
$71$	−7.12240			−0.845273			−0.422637	+	0.906299i	$0.638895\pi$
$72$		0			0
$73$	−2.98311	−	11.1331i	−0.349147	−	1.30303i	−0.887692	−	0.460438i	$-0.847693\pi$
$73$	−2.98311	−	11.1331i	−0.349147	−	1.30303i	0.538545	−	0.842597i	$-0.318974\pi$
$74$	−4.00603	−	2.31288i	−0.465691	−	0.268867i
$75$		0			0
$76$		−	6.20333i		−	0.711571i
$77$	−10.3690	+	2.59511i	−1.18165	+	0.295740i
$78$		0			0
$79$	−4.39618	+	2.53813i	−0.494609	+	0.285562i	−0.726484	−	0.687183i	$-0.758847\pi$
$79$	−4.39618	+	2.53813i	−0.494609	+	0.285562i	0.231876	+	0.972745i	$0.425514\pi$
$80$	1.82591	+	1.29076i	0.204143	+	0.144311i
$81$		0			0
$82$	−0.669683	+	2.49929i	−0.0739541	+	0.276000i
$83$	3.85372	−	3.85372i	0.423001	−	0.423001i	−0.463235	−	0.886236i	$-0.653311\pi$
$83$	3.85372	−	3.85372i	0.423001	−	0.423001i	0.886236	+	0.463235i	$0.153311\pi$
$84$		0			0
$85$	3.50704	−	2.91605i	0.380392	−	0.316290i
$86$	−3.51999	−	6.09680i	−0.379570	−	0.657434i
$87$		0			0
$88$	−3.90231	+	1.04562i	−0.415988	+	0.111464i
$89$	1.53615	+	2.66069i	0.162832	+	0.282033i	0.935883	−	0.352310i	$-0.114604\pi$
$89$	1.53615	+	2.66069i	0.162832	+	0.282033i	−0.773051	+	0.634343i	$0.781271\pi$
$90$		0			0
$91$	0.766467	+	0.0126942i	0.0803475	+	0.00133071i
$92$	−3.20895	+	3.20895i	−0.334556	+	0.334556i
$93$		0			0
$94$	0.157563	−	0.272906i	0.0162513	−	0.0281481i
$95$	−11.3267	−	8.00700i	−1.16210	−	0.821501i
$96$		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	$0.907943\pi$
$98$	−2.03464	+	6.69778i	−0.205530	+	0.676578i
$99$		0			0
$100$	4.71361	−	1.66789i	0.471361	−	0.166789i
$101$	8.56364	+	4.94422i	0.852114	+	0.491968i	0.861364	−	0.507989i	$-0.169611\pi$
$101$	8.56364	+	4.94422i	0.852114	+	0.491968i	−0.00924966	+	0.999957i	$0.502944\pi$
$102$		0			0
$103$	4.13612	+	1.10827i	0.407544	+	0.109201i	0.456766	−	0.889587i	$-0.349008\pi$
$103$	4.13612	+	1.10827i	0.407544	+	0.109201i	−0.0492221	+	0.998788i	$0.515674\pi$
$104$	0.289737			0.0284110
$105$		0			0
$106$	8.28261			0.804479
$107$	−14.3653	−	3.84918i	−1.38875	−	0.372114i	−0.514457	−	0.857516i	$-0.672007\pi$
$107$	−14.3653	−	3.84918i	−1.38875	−	0.372114i	−0.874291	+	0.485402i	$0.838673\pi$
$108$		0			0
$109$	−11.4586	−	6.61564i	−1.09754	−	0.633664i	−0.161964	−	0.986797i	$-0.551783\pi$
$109$	−11.4586	−	6.61564i	−1.09754	−	0.633664i	−0.935573	+	0.353133i	$0.885116\pi$
$110$	−3.12773	+	8.47492i	−0.298218	+	0.808052i
$111$		0			0
$112$	−0.726997	+	2.54391i	−0.0686947	+	0.240377i
$113$	−9.75336	−	9.75336i	−0.917519	−	0.917519i	0.0793296	−	0.996848i	$-0.474722\pi$
$113$	−9.75336	−	9.75336i	−0.917519	−	0.917519i	−0.996848	+	0.0793296i	$0.974722\pi$
$114$		0			0
$115$	1.71727	+	10.0012i	0.160136	+	0.932618i
$116$	3.57935	−	6.19961i	0.332334	−	0.575619i
$117$		0			0
$118$	−0.604862	+	0.604862i	−0.0556821	+	0.0556821i
$119$	4.62831	+	2.77535i	0.424276	+	0.254416i
$120$		0			0
$121$	−2.66069	−	4.60846i	−0.241881	−	0.418951i
$122$	−6.68495	+	1.79123i	−0.605227	+	0.162170i
$123$		0			0
$124$	3.65628	+	6.33287i	0.328344	+	0.568708i
$125$	3.03873	−	10.7595i	0.271792	−	0.962356i
$126$		0			0
$127$	−2.19984	+	2.19984i	−0.195204	+	0.195204i	−0.797940	−	0.602736i	$-0.794077\pi$
$127$	−2.19984	+	2.19984i	−0.195204	+	0.195204i	0.602736	+	0.797940i	$0.294077\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$		0			0
$130$	0.373980	−	0.529033i	0.0328002	−	0.0463993i
$131$	6.32091	−	3.64938i	0.552260	−	0.318848i	−0.197773	−	0.980248i	$-0.563371\pi$
$131$	6.32091	−	3.64938i	0.552260	−	0.318848i	0.750033	+	0.661400i	$0.230037\pi$
$132$		0			0
$133$	4.50980	−	15.7807i	0.391049	−	1.36836i
$134$		−	3.15869i		−	0.272870i
$135$		0			0
$136$	1.76647	+	1.01987i	0.151473	+	0.0874531i
$137$	−1.85804	−	6.93431i	−0.158743	−	0.592438i	−0.998756	−	0.0498710i	$-0.984119\pi$
$137$	−1.85804	−	6.93431i	−0.158743	−	0.592438i	0.840012	−	0.542567i	$-0.182548\pi$
$138$		0			0
$139$	12.4172			1.05321			0.526605	−	0.850110i	$-0.323465\pi$
$139$	12.4172			1.05321			0.526605	+	0.850110i	$0.323465\pi$
$140$	3.70657	+	4.61100i	0.313262	+	0.389701i
$141$		0			0
$142$	−6.87971	−	1.84341i	−0.577332	−	0.154696i
$143$	0.302955	+	1.13064i	0.0253344	+	0.0945492i
$144$		0			0
$145$	−6.69985	−	14.5378i	−0.556392	−	1.20730i
$146$		−	11.5259i		−	0.953887i
$147$		0			0
$148$	−3.27091	−	3.27091i	−0.268867	−	0.268867i
$149$	−20.7399	+	11.9742i	−1.69908	+	0.980963i	−0.752440	+	0.658661i	$0.771123\pi$
$149$	−20.7399	+	11.9742i	−1.69908	+	0.980963i	−0.946637	+	0.322302i	$0.895543\pi$
$150$		0			0
$151$	1.77167	−	3.06862i	0.144176	−	0.249721i	−0.784889	−	0.619636i	$-0.787280\pi$
$151$	1.77167	−	3.06862i	0.144176	−	0.249721i	0.929065	+	0.369916i	$0.120613\pi$
$152$	1.60554	−	5.99195i	0.130226	−	0.486012i
$153$		0			0
$154$	−10.6873	−	0.177002i	−0.861207	−	0.0142632i
$155$	16.2826	+	1.49816i	1.30785	+	0.120335i
$156$		0			0
$157$	−5.91389	+	1.58462i	−0.471980	+	0.126467i	−0.486966	−	0.873421i	$-0.661896\pi$
$157$	−5.91389	+	1.58462i	−0.471980	+	0.126467i	0.0149859	+	0.999888i	$0.495230\pi$
$158$	−4.90330	+	1.31384i	−0.390086	+	0.104523i
$159$		0			0
$160$	1.42962	+	1.71936i	0.113021	+	0.135927i
$161$	−10.4962	+	5.83037i	−0.827213	+	0.459498i
$162$		0			0
$163$	−4.28549	+	15.9937i	−0.335666	+	1.25272i	0.567480	+	0.823387i	$0.307918\pi$
$163$	−4.28549	+	15.9937i	−0.335666	+	1.25272i	−0.903146	+	0.429334i	$0.858748\pi$
$164$	−1.29373	+	2.24080i	−0.101023	+	0.174977i
$165$		0			0
$166$	4.71983	−	2.72499i	0.366329	−	0.211500i
$167$	10.2873	+	10.2873i	0.796056	+	0.796056i	0.982471	−	0.186415i	$-0.0596869\pi$
$167$	10.2873	+	10.2873i	0.796056	+	0.796056i	−0.186415	+	0.982471i	$0.559687\pi$
$168$		0			0
$169$			12.9161i			0.993543i
$170$	4.14227	−	1.90900i	0.317698	−	0.146414i
$171$		0			0
$172$	−1.82208	−	6.80009i	−0.138932	−	0.518502i
$173$	−7.50720	−	2.01155i	−0.570762	−	0.152935i	−0.0381159	−	0.999273i	$-0.512136\pi$
$173$	−7.50720	−	2.01155i	−0.570762	−	0.152935i	−0.532646	+	0.846338i	$0.678802\pi$
$174$		0			0
$175$	13.2036	−	0.816171i	0.998095	−	0.0616967i
$176$	−4.03997			−0.304524
$177$		0			0
$178$	0.795171	+	2.96762i	0.0596006	+	0.222432i
$179$	−3.34695	−	1.93236i	−0.250163	−	0.144431i	0.369676	−	0.929161i	$-0.379469\pi$
$179$	−3.34695	−	1.93236i	−0.250163	−	0.144431i	−0.619839	+	0.784729i	$0.712802\pi$
$180$		0			0
$181$			6.99107i			0.519642i	0.965657	+	0.259821i	$0.0836636\pi$
$181$			6.99107i			0.519642i	−0.965657	+	0.259821i	$0.916336\pi$
$182$	0.737064	+	0.210638i	0.0546348	+	0.0156135i
$183$		0			0
$184$	−3.93014	+	2.26907i	−0.289734	+	0.167278i
$185$	−10.1943	+	1.75043i	−0.749502	+	0.128694i
$186$		0			0
$187$	−2.13280	+	7.95971i	−0.155966	+	0.582071i
$188$	0.222827	−	0.222827i	0.0162513	−	0.0162513i
$189$		0			0
$190$	−8.86840	−	10.6657i	−0.643381	−	0.773774i
$191$	2.23721	+	3.87496i	0.161879	+	0.280383i	0.935543	−	0.353214i	$-0.114911\pi$
$191$	2.23721	+	3.87496i	0.161879	+	0.280383i	−0.773664	+	0.633597i	$0.781578\pi$
$192$		0			0
$193$	19.3907	−	5.19573i	1.39577	−	0.373997i	0.518949	−	0.854805i	$-0.326324\pi$
$193$	19.3907	−	5.19573i	1.39577	−	0.373997i	0.876825	+	0.480809i	$0.159657\pi$
$194$	−4.68885	−	8.12132i	−0.336640	−	0.583077i
$195$		0			0
$196$	−3.69883	+	5.94295i	−0.264202	+	0.424497i
$197$	7.84901	−	7.84901i	0.559219	−	0.559219i	−0.369866	−	0.929085i	$-0.620596\pi$
$197$	7.84901	−	7.84901i	0.559219	−	0.559219i	0.929085	+	0.369866i	$0.120596\pi$
$198$		0			0
$199$	−5.40103	+	9.35485i	−0.382869	+	0.663148i	−0.991471	−	0.130327i	$-0.958397\pi$
$199$	−5.40103	+	9.35485i	−0.382869	+	0.663148i	0.608602	+	0.793475i	$0.291730\pi$
$200$	4.98468	−	0.391082i	0.352470	−	0.0276537i
$201$		0			0
$202$	6.99218	+	6.99218i	0.491968	+	0.491968i
$203$	13.6126	−	13.1691i	0.955419	−	0.924288i
$204$		0			0
$205$	2.42161	+	5.25456i	0.169133	+	0.366995i
$206$	3.70835	+	2.14101i	0.258373	+	0.149172i
$207$		0			0
$208$	0.279864	+	0.0749894i	0.0194051	+	0.00519958i
$209$	25.0613			1.73353
$210$		0			0
$211$	7.56555			0.520834			0.260417	−	0.965496i	$-0.416140\pi$
$211$	7.56555			0.520834			0.260417	+	0.965496i	$0.416140\pi$
$212$	8.00039	+	2.14370i	0.549469	+	0.147230i
$213$		0			0
$214$	−12.8796	−	7.43604i	−0.880431	−	0.508317i
$215$	−14.7682	−	5.45032i	−1.00718	−	0.371709i
$216$		0			0
$217$	4.69728	+	18.7683i	0.318872	+	1.27408i
$218$	−9.35593	−	9.35593i	−0.633664	−	0.633664i
$219$		0			0
$220$	−5.21463	+	7.37662i	−0.351570	+	0.497332i
$221$	0.295494	−	0.511811i	0.0198771	−	0.0344281i
$222$		0			0
$223$	9.35230	−	9.35230i	0.626277	−	0.626277i	−0.320853	−	0.947129i	$-0.603969\pi$
$223$	9.35230	−	9.35230i	0.626277	−	0.626277i	0.947129	+	0.320853i	$0.103969\pi$
$224$	−1.36064	+	2.26907i	−0.0909114	+	0.151608i
$225$		0			0
$226$	−6.89667	−	11.9454i	−0.458759	−	0.794595i
$227$	−15.6420	+	4.19127i	−1.03820	+	0.278184i	−0.737367	−	0.675493i	$-0.763931\pi$
$227$	−15.6420	+	4.19127i	−1.03820	+	0.278184i	−0.300832	+	0.953677i	$0.597264\pi$
$228$		0			0
$229$	5.88820	+	10.1987i	0.389103	+	0.673947i	0.992329	−	0.123624i	$-0.0394515\pi$
$229$	5.88820	+	10.1987i	0.389103	+	0.673947i	−0.603226	+	0.797570i	$0.706118\pi$
$230$	−0.929750	+	10.1049i	−0.0613059	+	0.666297i
$231$		0			0
$232$	5.06196	−	5.06196i	0.332334	−	0.332334i
$233$	1.48154	−	5.52920i	0.0970591	−	0.362230i	−0.900264	−	0.435343i	$-0.856627\pi$
$233$	1.48154	−	5.52920i	0.0970591	−	0.362230i	0.997324	+	0.0731138i	$0.0232936\pi$
$234$		0			0
$235$	−0.119246	−	0.694478i	−0.00777876	−	0.0453028i
$236$	−0.740802	+	0.427702i	−0.0482221	+	0.0278410i
$237$		0			0
$238$	3.75229	+	3.87867i	0.243225	+	0.251417i
$239$			8.33794i			0.539337i	0.962953	+	0.269668i	$0.0869141\pi$
$239$			8.33794i			0.539337i	−0.962953	+	0.269668i	$0.913086\pi$
$240$		0			0
$241$	2.56723	+	1.48219i	0.165370	+	0.0954763i	0.580401	−	0.814331i	$-0.302896\pi$
$241$	2.56723	+	1.48219i	0.165370	+	0.0954763i	−0.415031	+	0.909807i	$0.636229\pi$
$242$	−1.37728	−	5.14006i	−0.0885347	−	0.330416i
$243$		0			0
$244$	−6.92077			−0.443057
$245$	6.07700	+	14.4246i	0.388245	+	0.921556i
$246$		0			0
$247$	−1.73609	−	0.465184i	−0.110465	−	0.0295989i
$248$	1.89263	+	7.06340i	0.120182	+	0.448526i
$249$		0			0
$250$	5.71994	−	9.60637i	0.361761	−	0.607560i
$251$			16.1800i			1.02127i	0.859796	+	0.510637i	$0.170590\pi$
$251$			16.1800i			1.02127i	−0.859796	+	0.510637i	$0.829410\pi$
$252$		0			0
$253$	−12.9641	−	12.9641i	−0.815043	−	0.815043i
$254$	−2.69424	+	1.55552i	−0.169052	+	0.0976020i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.50754	−	5.62621i	0.0940377	−	0.350954i	−0.902834	−	0.429989i	$-0.858517\pi$
$257$	1.50754	−	5.62621i	0.0940377	−	0.350954i	0.996872	+	0.0790355i	$0.0251841\pi$
$258$		0			0
$259$	−5.94295	−	10.6988i	−0.369277	−	0.664793i
$260$	0.498161	−	0.414214i	0.0308946	−	0.0256884i
$261$		0			0
$262$	7.05006	−	1.88906i	0.435554	−	0.116706i
$263$	1.67793	−	0.449601i	0.103466	−	0.0277236i	−0.206715	−	0.978401i	$-0.566277\pi$
$263$	1.67793	−	0.449601i	0.103466	−	0.0277236i	0.310180	+	0.950678i	$0.399611\pi$
$264$		0			0
$265$	14.2408	−	11.8410i	0.874803	−	0.727386i
$266$	8.44048	−	14.0758i	0.517519	−	0.863041i
$267$		0			0
$268$	0.817530	−	3.05106i	0.0499386	−	0.186373i
$269$	1.89169	−	3.27650i	0.115338	−	0.199772i	−0.802577	−	0.596549i	$-0.796538\pi$
$269$	1.89169	−	3.27650i	0.115338	−	0.199772i	0.917915	+	0.396777i	$0.129872\pi$
$270$		0			0
$271$	−18.4029	+	10.6249i	−1.11789	+	0.645416i	−0.940862	−	0.338789i	$-0.889983\pi$
$271$	−18.4029	+	10.6249i	−1.11789	+	0.645416i	−0.177032	+	0.984205i	$0.556649\pi$
$272$	1.44231	+	1.44231i	0.0874531	+	0.0874531i
$273$		0			0
$274$		−	7.17893i		−	0.433695i
$275$	6.73822	+	19.0429i	0.406330	+	1.14833i
$276$		0			0
$277$	−1.26567	−	4.72353i	−0.0760465	−	0.283810i	0.917422	−	0.397916i	$-0.130266\pi$
$277$	−1.26567	−	4.72353i	−0.0760465	−	0.283810i	−0.993469	+	0.114106i	$0.963600\pi$
$278$	11.9941	+	3.21380i	0.719356	+	0.192751i
$279$		0			0
$280$	2.38686	+	5.41322i	0.142642	+	0.323502i
$281$	29.4776			1.75849			0.879243	−	0.476373i	$-0.158049\pi$
$281$	29.4776			1.75849			0.879243	+	0.476373i	$0.158049\pi$
$282$		0			0
$283$	−2.92041	−	10.8991i	−0.173601	−	0.647886i	−0.996786	−	0.0801133i	$-0.974472\pi$
$283$	−2.92041	−	10.8991i	−0.173601	−	0.647886i	0.823185	−	0.567773i	$-0.192195\pi$
$284$	−6.16818	−	3.56120i	−0.366014	−	0.211318i
$285$		0			0
$286$			1.17053i			0.0692148i
$287$	−4.92018	+	4.75986i	−0.290429	+	0.280966i
$288$		0			0
$289$	−11.1193	+	6.41973i	−0.654076	+	0.377631i
$290$	−2.70891	−	15.7764i	−0.159073	−	0.926425i
$291$		0			0
$292$	2.98311	−	11.1331i	0.174573	−	0.651517i
$293$	7.23407	−	7.23407i	0.422619	−	0.422619i	−0.463485	−	0.886105i	$-0.653401\pi$
$293$	7.23407	−	7.23407i	0.422619	−	0.422619i	0.886105	+	0.463485i	$0.153401\pi$
$294$		0			0
$295$	−0.175251	+	1.90470i	−0.0102035	+	0.110896i
$296$	−2.31288	−	4.00603i	−0.134433	−	0.232846i
$297$		0			0
$298$	−23.1323	+	6.19829i	−1.34002	+	0.359057i
$299$	0.657432	+	1.13871i	0.0380203	+	0.0658531i
$300$		0			0
$301$	0.308440	−	18.6235i	0.0177782	−	1.07344i
$302$	2.50552	−	2.50552i	0.144176	−	0.144176i
$303$		0			0
$304$	3.10166	−	5.37224i	0.177893	−	0.308119i
$305$	−8.93304	+	12.6367i	−0.511504	+	0.723575i
$306$		0			0
$307$	−1.07859	−	1.07859i	−0.0615584	−	0.0615584i	0.675657	−	0.737216i	$-0.263860\pi$
$307$	−1.07859	−	1.07859i	−0.0615584	−	0.0615584i	−0.737216	+	0.675657i	$0.763860\pi$
$308$	−10.2773	−	2.93705i	−0.585605	−	0.167354i
$309$		0			0
$310$	15.3400	+	5.66136i	0.871256	+	0.321544i
$311$	8.33830	+	4.81412i	0.472821	+	0.272984i	0.717420	−	0.696641i	$-0.245323\pi$
$311$	8.33830	+	4.81412i	0.472821	+	0.272984i	−0.244599	+	0.969624i	$0.578656\pi$
$312$		0			0
$313$	2.92361	+	0.783378i	0.165252	+	0.0442791i	0.340496	−	0.940246i	$-0.389405\pi$
$313$	2.92361	+	0.783378i	0.165252	+	0.0442791i	−0.175244	+	0.984525i	$0.556072\pi$
$314$	−6.12251			−0.345513
$315$		0			0
$316$	−5.07627			−0.285562
$317$	1.88227	+	0.504353i	0.105719	+	0.0283273i	0.311291	−	0.950315i	$-0.399239\pi$
$317$	1.88227	+	0.504353i	0.105719	+	0.0283273i	−0.205572	+	0.978642i	$0.565905\pi$
$318$		0			0
$319$	25.0463	+	14.4605i	1.40232	+	0.809631i
$320$	0.935904	+	2.03078i	0.0523186	+	0.113524i
$321$		0			0
$322$	−11.6475	+	2.91510i	−0.649091	+	0.162452i
$323$	−8.94715	−	8.94715i	−0.497833	−	0.497833i
$324$		0			0
$325$	−0.113311	−	1.44425i	−0.00628535	−	0.0801124i
$326$	−8.27894	+	14.3395i	−0.458528	+	0.794194i
$327$		0			0
$328$	−1.82961	+	1.82961i	−0.101023	+	0.101023i
$329$	0.728847	−	0.404858i	0.0401826	−	0.0223205i
$330$		0			0
$331$	14.4468	+	25.0225i	0.794066	+	1.37536i	0.923431	+	0.383765i	$0.125373\pi$
$331$	14.4468	+	25.0225i	0.794066	+	1.37536i	−0.129365	+	0.991597i	$0.541294\pi$
$332$	5.26428	−	1.41056i	0.288915	−	0.0774145i
$333$		0			0
$334$	7.27423	+	12.5993i	0.398028	+	0.689405i
$335$	−4.51573	−	5.43092i	−0.246721	−	0.296723i
$336$		0			0
$337$	−0.823226	+	0.823226i	−0.0448440	+	0.0448440i	−0.729173	−	0.684329i	$-0.760095\pi$
$337$	−0.823226	+	0.823226i	−0.0448440	+	0.0448440i	0.684329	+	0.729173i	$0.260095\pi$
$338$	−3.34292	+	12.4759i	−0.181831	+	0.678602i
$339$		0			0
$340$	4.49521	−	0.771855i	0.243787	−	0.0418597i
$341$	−25.5846	+	14.7713i	−1.38548	+	0.799910i
$342$		0			0
$343$	−13.7300	+	12.4293i	−0.741350	+	0.671119i
$344$		−	7.03997i		−	0.379570i
$345$		0			0
$346$	−6.73077	−	3.88601i	−0.361849	−	0.208913i
$347$	4.32336	+	16.1350i	0.232090	+	0.866172i	0.979439	+	0.201740i	$0.0646597\pi$
$347$	4.32336	+	16.1350i	0.232090	+	0.866172i	−0.747349	+	0.664432i	$0.768674\pi$
$348$		0			0
$349$	36.7146			1.96529			0.982644	−	0.185503i	$-0.0593916\pi$
$349$	36.7146			1.96529			0.982644	+	0.185503i	$0.0593916\pi$
$350$	12.9649	+	2.62897i	0.693003	+	0.140524i
$351$		0			0
$352$	−3.90231	−	1.04562i	−0.207994	−	0.0557318i
$353$	3.69356	+	13.7845i	0.196588	+	0.733677i	0.991850	+	0.127411i	$0.0406667\pi$
$353$	3.69356	+	13.7845i	0.196588	+	0.733677i	−0.795262	+	0.606266i	$0.792667\pi$
$354$		0			0
$355$	−14.4640	+	6.66588i	−0.767672	+	0.353788i
$356$			3.07230i			0.162832i
$357$		0			0
$358$	−2.73277	−	2.73277i	−0.144431	−	0.144431i
$359$	23.4596	−	13.5444i	1.23815	−	0.714847i	0.269435	−	0.963019i	$-0.413163\pi$
$359$	23.4596	−	13.5444i	1.23815	−	0.714847i	0.968716	+	0.248172i	$0.0798298\pi$
$360$		0			0
$361$	−9.74064	+	16.8713i	−0.512665	+	0.887962i
$362$	−1.80942	+	6.75285i	−0.0951011	+	0.354922i
$363$		0			0
$364$	0.657432	+	0.394227i	0.0344588	+	0.0206631i
$365$	−16.4776	−	19.8171i	−0.862477	−	1.03727i
$366$		0			0
$367$	21.8990	−	5.86782i	1.14312	−	0.306298i	0.362914	−	0.931823i	$-0.381782\pi$
$367$	21.8990	−	5.86782i	1.14312	−	0.306298i	0.780204	+	0.625525i	$0.215115\pi$
$368$	−4.38350	+	1.17456i	−0.228506	+	0.0612279i
$369$		0			0
$370$	−10.3000	−	0.947702i	−0.535472	−	0.0492687i
$371$	18.7938	+	11.2696i	0.975726	+	0.585090i
$372$		0			0
$373$	−3.32215	+	12.3984i	−0.172014	+	0.641966i	0.825027	+	0.565094i	$0.191160\pi$
$373$	−3.32215	+	12.3984i	−0.172014	+	0.641966i	−0.997041	+	0.0768720i	$0.975507\pi$
$374$	−4.12025	+	7.13648i	−0.213053	+	0.369019i
$375$		0			0
$376$	0.272906	−	0.157563i	0.0140741	−	0.00812567i
$377$	−1.46664	−	1.46664i	−0.0755356	−	0.0755356i
$378$		0			0
$379$		−	14.4739i		−	0.743476i	−0.928338	−	0.371738i	$-0.878762\pi$
$379$		−	14.4739i		−	0.743476i	0.928338	−	0.371738i	$-0.121238\pi$
$380$	−5.80572	−	12.5976i	−0.297827	−	0.646244i
$381$		0			0
$382$	1.15807	+	4.32196i	0.0592518	+	0.221131i
$383$	−1.69189	−	0.453341i	−0.0864517	−	0.0231647i	0.215334	−	0.976540i	$-0.430916\pi$
$383$	−1.69189	−	0.453341i	−0.0864517	−	0.0231647i	−0.301786	+	0.953376i	$0.597583\pi$
$384$		0			0
$385$	−18.6283	+	14.9744i	−0.949387	+	0.763168i
$386$	20.0747			1.02178
$387$		0			0
$388$	−2.42713	−	9.05816i	−0.123219	−	0.459858i
$389$	2.40954	+	1.39115i	0.122169	+	0.0705341i	0.559839	−	0.828601i	$-0.310863\pi$
$389$	2.40954	+	1.39115i	0.122169	+	0.0705341i	−0.437670	+	0.899135i	$0.644196\pi$
$390$		0			0
$391$			9.25661i			0.468127i
$392$	−5.11094	+	4.78312i	−0.258142	+	0.241584i
$393$		0			0
$394$	9.61304	−	5.55009i	0.484298	−	0.279610i
$395$	−6.55224	+	9.26881i	−0.329679	+	0.466364i
$396$		0			0
$397$	10.2668	−	38.3163i	0.515277	−	1.92304i	0.165486	−	0.986212i	$-0.447081\pi$
$397$	10.2668	−	38.3163i	0.515277	−	1.92304i	0.349791	−	0.936828i	$-0.386253\pi$
$398$	−7.63821	+	7.63821i	−0.382869	+	0.382869i
$399$		0			0
$400$	4.91605	+	0.912375i	0.245803	+	0.0456187i
$401$	−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
$403$	2.04653	−	0.548365i	0.101945	−	0.0273160i
$404$	4.94422	+	8.56364i	0.245984	+	0.426057i
$405$		0			0
$406$	16.5572	−	9.19714i	0.821720	−	0.456446i
$407$	13.2144	−	13.2144i	0.655012	−	0.655012i
$408$		0			0
$409$	−7.65280	+	13.2550i	−0.378407	+	0.655419i	−0.990831	−	0.135110i	$-0.956861\pi$
$409$	−7.65280	+	13.2550i	−0.378407	+	0.655419i	0.612424	+	0.790529i	$0.290195\pi$
$410$	0.979116	+	5.70228i	0.0483551	+	0.281615i
$411$		0			0
$412$	3.02785	+	3.02785i	0.149172	+	0.149172i
$413$	−2.19547	+	0.549475i	−0.108032	+	0.0270379i
$414$		0			0
$415$	4.21936	−	11.4328i	0.207120	−	0.561214i
$416$	0.250919	+	0.144868i	0.0123023	+	0.00710276i
$417$		0			0
$418$	24.2073	+	6.48634i	1.18402	+	0.317257i
$419$	27.7027			1.35337			0.676684	−	0.736274i	$-0.263416\pi$
$419$	27.7027			1.35337			0.676684	+	0.736274i	$0.263416\pi$
$420$		0			0
$421$	33.0159			1.60910			0.804549	−	0.593887i	$-0.202407\pi$
$421$	33.0159			1.60910			0.804549	+	0.593887i	$0.202407\pi$
$422$	7.30776	+	1.95811i	0.355736	+	0.0953192i
$423$		0			0
$424$	7.17295	+	4.14131i	0.348349	+	0.201120i
$425$	4.39289	−	9.20413i	0.213087	−	0.446466i
$426$		0			0
$427$	−17.6058	−	5.03138i	−0.852005	−	0.243485i
$428$	−10.5161	−	10.5161i	−0.508317	−	0.508317i
$429$		0			0
$430$	−12.8544	−	9.08690i	−0.619892	−	0.438209i
$431$	11.9586	−	20.7129i	0.576027	−	0.997708i	−0.419902	−	0.907569i	$-0.637936\pi$
$431$	11.9586	−	20.7129i	0.576027	−	0.997708i	0.995929	−	0.0901384i	$-0.0287309\pi$
$432$		0			0
$433$	−13.2515	+	13.2515i	−0.636829	+	0.636829i	−0.949772	−	0.312943i	$-0.898685\pi$
$433$	−13.2515	+	13.2515i	−0.636829	+	0.636829i	0.312943	+	0.949772i	$0.398685\pi$
$434$	−0.320383	+	19.3446i	−0.0153789	+	0.928569i
$435$		0			0
$436$	−6.61564	−	11.4586i	−0.316832	−	0.548769i
$437$	27.1923	−	7.28615i	1.30078	−	0.348544i
$438$		0			0
$439$	−7.05383	−	12.2176i	−0.336661	−	0.583114i	0.647141	−	0.762370i	$-0.275964\pi$
$439$	−7.05383	−	12.2176i	−0.336661	−	0.583114i	−0.983802	+	0.179256i	$0.942631\pi$
$440$	−6.94616	+	5.77563i	−0.331145	+	0.275342i
$441$		0			0
$442$	0.417892	−	0.417892i	0.0198771	−	0.0198771i
$443$	−5.45161	+	20.3457i	−0.259014	+	0.966652i	0.706800	+	0.707414i	$0.250138\pi$
$443$	−5.45161	+	20.3457i	−0.259014	+	0.966652i	−0.965813	+	0.259238i	$0.916528\pi$
$444$		0			0
$445$	5.60975	+	3.96560i	0.265928	+	0.187988i
$446$	11.4542	−	6.61308i	0.542371	−	0.313138i
$447$		0			0
$448$	−1.90155	+	1.83959i	−0.0898399	+	0.0869125i
$449$			31.3247i			1.47831i	0.673538	+	0.739153i	$0.264774\pi$
$449$			31.3247i			1.47831i	−0.673538	+	0.739153i	$0.735226\pi$
$450$		0			0
$451$	−9.05278	−	5.22662i	−0.426279	−	0.246112i
$452$	−3.56998	−	13.3233i	−0.167918	−	0.626677i
$453$		0			0
$454$	−16.1938			−0.760014
$455$	1.56841	−	0.691560i	0.0735281	−	0.0324209i
$456$		0			0
$457$	2.76404	+	0.740622i	0.129296	+	0.0346448i	0.322887	−	0.946438i	$-0.395347\pi$
$457$	2.76404	+	0.740622i	0.129296	+	0.0346448i	−0.193591	+	0.981082i	$0.562013\pi$
$458$	3.04796	+	11.3751i	0.142422	+	0.531525i
$459$		0			0
$460$	−3.51341	+	9.51994i	−0.163814	+	0.443870i
$461$		−	3.02674i		−	0.140969i	−0.997513	−	0.0704846i	$-0.977545\pi$
$461$		−	3.02674i		−	0.140969i	0.997513	−	0.0704846i	$-0.0224546\pi$
$462$		0			0
$463$	19.2889	+	19.2889i	0.896431	+	0.896431i	0.995118	−	0.0986876i	$-0.0314644\pi$
$463$	19.2889	+	19.2889i	0.896431	+	0.896431i	−0.0986876	+	0.995118i	$0.531464\pi$
$464$	6.19961	−	3.57935i	0.287810	−	0.166167i
$465$		0			0
$466$	2.86212	−	4.95734i	0.132585	−	0.229644i
$467$	6.50385	−	24.2727i	0.300962	−	1.12321i	−0.635403	−	0.772180i	$-0.719166\pi$
$467$	6.50385	−	24.2727i	0.300962	−	1.12321i	0.936366	−	0.351026i	$-0.114167\pi$
$468$		0			0
$469$	4.29784	−	7.16729i	0.198456	−	0.330955i
$470$	0.0645612	−	0.701677i	0.00297799	−	0.0323660i
$471$		0			0
$472$	−0.826257	+	0.221395i	−0.0380316	+	0.0101905i
$473$	27.4722	−	7.36115i	1.26317	−	0.338466i
$474$		0			0
$475$	−30.4959	−	5.65976i	−1.39925	−	0.259688i
$476$	2.62056	+	4.71767i	0.120113	+	0.216234i
$477$		0			0
$478$	−2.15802	+	8.05384i	−0.0987055	+	0.368374i
$479$	4.14346	−	7.17668i	0.189319	−	0.327911i	−0.755704	−	0.654913i	$-0.772705\pi$
$479$	4.14346	−	7.17668i	0.189319	−	0.327911i	0.945024	+	0.327002i	$0.106039\pi$
$480$		0			0
$481$	−1.16069	+	0.670127i	−0.0529231	+	0.0305551i
$482$	2.09613	+	2.09613i	0.0954763	+	0.0954763i
$483$		0			0
$484$		−	5.32139i		−	0.241881i
$485$	−19.6722	−	7.26018i	−0.893269	−	0.329668i
$486$		0			0
$487$	2.76375	+	10.3144i	0.125237	+	0.467392i	0.999848	−	0.0174340i	$-0.00554969\pi$
$487$	2.76375	+	10.3144i	0.125237	+	0.467392i	−0.874611	+	0.484826i	$0.838883\pi$
$488$	−6.68495	−	1.79123i	−0.302613	−	0.0810850i
$489$		0			0
$490$	2.13656	+	15.5060i	0.0965198	+	0.700488i
$491$	−25.7259			−1.16100			−0.580498	−	0.814262i	$-0.697142\pi$
$491$	−25.7259			−1.16100			−0.580498	+	0.814262i	$0.697142\pi$
$492$		0			0
$493$	−3.77924	−	14.1043i	−0.170209	−	0.635227i
$494$	−1.55654	−	0.898666i	−0.0700319	−	0.0404329i
$495$		0			0
$496$			7.31256i			0.328344i
$497$	−13.1023	−	13.5436i	−0.587719	−	0.607514i
$498$		0			0
$499$	−12.6429	+	7.29940i	−0.565975	+	0.326766i	−0.755540	−	0.655102i	$-0.772626\pi$
$499$	−12.6429	+	7.29940i	−0.565975	+	0.326766i	0.189565	+	0.981868i	$0.439292\pi$
$500$	8.01135	−	7.79861i	0.358278	−	0.348764i
$501$		0			0
$502$	−4.18770	+	15.6287i	−0.186906	+	0.697543i
$503$	−13.9891	+	13.9891i	−0.623744	+	0.623744i	−0.946487	−	0.322743i	$-0.895395\pi$
$503$	−13.9891	+	13.9891i	−0.623744	+	0.623744i	0.322743	+	0.946487i	$0.395395\pi$
$504$		0			0
$505$	22.0182	+	2.02589i	0.979798	+	0.0901510i
$506$	−9.16697	−	15.8777i	−0.407522	−	0.705848i
$507$		0			0
$508$	−3.00504	+	0.805197i	−0.133327	+	0.0357248i
$509$	−1.42883	−	2.47481i	−0.0633319	−	0.109694i	0.832621	−	0.553843i	$-0.186839\pi$
$509$	−1.42883	−	2.47481i	−0.0633319	−	0.109694i	−0.895953	+	0.444149i	$0.853506\pi$
$510$		0			0
$511$	15.6825	−	26.1530i	0.693754	−	1.15694i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$	2.91234	−	5.04433i	0.128458	−	0.222496i
$515$	9.43680	−	1.62036i	0.415835	−	0.0714015i
$516$		0			0
$517$	0.900216	+	0.900216i	0.0395914	+	0.0395914i
$518$	−2.97139	−	11.8724i	−0.130555	−	0.521644i
$519$		0			0
$520$	0.588393	−	0.271166i	0.0258027	−	0.0118914i
$521$	−24.7917	−	14.3135i	−1.08614	−	0.627084i	−0.153595	−	0.988134i	$-0.549085\pi$
$521$	−24.7917	−	14.3135i	−1.08614	−	0.627084i	−0.932547	+	0.361049i	$0.882419\pi$
$522$		0			0
$523$	30.5069	+	8.17429i	1.33397	+	0.357437i	0.854195	−	0.519954i	$-0.174051\pi$
$523$	30.5069	+	8.17429i	1.33397	+	0.357437i	0.479777	+	0.877390i	$0.340717\pi$
$524$	7.29876			0.318848
$525$		0			0
$526$	1.73712			0.0757422
$527$	14.4075	+	3.86048i	0.627600	+	0.168165i
$528$		0			0
$529$	2.08308	+	1.20267i	0.0905687	+	0.0522899i
$530$	16.8202	−	7.75174i	0.730623	−	0.336714i
$531$		0			0
$532$	11.7960	−	11.4116i	0.511419	−	0.494755i
$533$	0.530105	+	0.530105i	0.0229614	+	0.0229614i
$534$		0			0
$535$	−32.7753	+	5.62772i	−1.41700	+	0.243308i
$536$	1.57935	−	2.73551i	0.0682174	−	0.118156i
$537$		0			0
$538$	2.67525	−	2.67525i	0.115338	−	0.115338i
$539$	−24.0094	−	14.9432i	−1.03416	−	0.643648i
$540$		0			0
$541$	−18.4994	−	32.0420i	−0.795353	−	1.37759i	−0.922615	−	0.385722i	$-0.873952\pi$
$541$	−18.4994	−	32.0420i	−0.795353	−	1.37759i	0.127262	−	0.991869i	$-0.459381\pi$
$542$	−20.5257	+	5.49985i	−0.881655	+	0.236239i
$543$		0			0
$544$	1.01987	+	1.76647i	0.0437266	+	0.0757366i
$545$	−29.4616	−	2.71076i	−1.26200	−	0.116116i
$546$		0			0
$547$	−20.0765	+	20.0765i	−0.858409	+	0.858409i	−0.991151	−	0.132742i	$-0.957622\pi$
$547$	−20.0765	+	20.0765i	−0.858409	+	0.858409i	0.132742	+	0.991151i	$0.457622\pi$
$548$	1.85804	−	6.93431i	0.0793717	−	0.296219i
$549$		0			0
$550$	1.57996	+	20.1380i	0.0673697	+	0.858687i
$551$	−38.4582	+	22.2039i	−1.63838	+	0.945916i
$552$		0			0
$553$	−12.9136	−	3.69043i	−0.549141	−	0.156933i
$554$		−	4.89016i		−	0.207763i
$555$		0			0
$556$	10.7536	+	6.20859i	0.456054	+	0.263303i
$557$	6.65499	+	24.8367i	0.281981	+	1.05237i	0.951017	+	0.309137i	$0.100040\pi$
$557$	6.65499	+	24.8367i	0.281981	+	1.05237i	−0.669037	+	0.743229i	$0.733293\pi$
$558$		0			0
$559$	−2.03974			−0.0862718
$560$	0.904483	+	5.84653i	0.0382214	+	0.247061i
$561$		0			0
$562$	28.4732	+	7.62937i	1.20107	+	0.321825i
$563$	−1.38907	−	5.18407i	−0.0585422	−	0.218482i	0.930458	−	0.366400i	$-0.119410\pi$
$563$	−1.38907	−	5.18407i	−0.0585422	−	0.218482i	−0.989000	+	0.147917i	$0.952743\pi$
$564$		0			0
$565$	−28.9352	−	10.6788i	−1.21731	−	0.449258i
$566$		−	11.2836i		−	0.474286i
$567$		0			0
$568$	−5.03630	−	5.03630i	−0.211318	−	0.211318i
$569$	−22.0839	+	12.7502i	−0.925806	+	0.534514i	−0.885483	−	0.464672i	$-0.846172\pi$
$569$	−22.0839	+	12.7502i	−0.925806	+	0.534514i	−0.0403234	+	0.999187i	$0.512839\pi$
$570$		0			0
$571$	−7.95235	+	13.7739i	−0.332795	+	0.576419i	−0.983059	−	0.183290i	$-0.941325\pi$
$571$	−7.95235	+	13.7739i	−0.332795	+	0.576419i	0.650263	+	0.759709i	$0.274659\pi$
$572$	−0.302955	+	1.13064i	−0.0126672	+	0.0472746i
$573$		0			0
$574$	−5.98447	+	3.32424i	−0.249787	+	0.138751i
$575$	12.8476	+	18.7031i	0.535781	+	0.779973i
$576$		0			0
$577$	−22.2641	+	5.96565i	−0.926867	+	0.248353i	−0.690518	−	0.723315i	$-0.742617\pi$
$577$	−22.2641	+	5.96565i	−0.926867	+	0.248353i	−0.236349	+	0.971668i	$0.575951\pi$
$578$	−12.4020	+	3.32310i	−0.515854	+	0.138223i
$579$		0			0
$580$	1.46664	−	15.9400i	0.0608988	−	0.661872i
$581$	14.4173	+	0.238779i	0.598132	+	0.00990621i
$582$		0			0
$583$	−8.66048	+	32.3214i	−0.358681	+	1.33861i
$584$	5.76293	−	9.98169i	0.238472	−	0.413045i
$585$		0			0
$586$	8.85989	−	5.11526i	0.365999	−	0.211310i
$587$	−28.2277	−	28.2277i	−1.16508	−	1.16508i	−0.983348	−	0.181734i	$-0.941829\pi$
$587$	−28.2277	−	28.2277i	−1.16508	−	1.16508i	−0.181734	−	0.983348i	$-0.558171\pi$
$588$		0			0
$589$		−	45.3622i		−	1.86912i
$590$	−0.662251	+	1.79444i	−0.0272644	+	0.0738758i
$591$		0			0
$592$	−1.19723	−	4.46814i	−0.0492060	−	0.183639i
$593$	34.2220	+	9.16977i	1.40533	+	0.376557i	0.880256	−	0.474499i	$-0.157371\pi$
$593$	34.2220	+	9.16977i	1.40533	+	0.376557i	0.525075	+	0.851056i	$0.324037\pi$
$594$		0			0
$595$	11.9965	+	1.30447i	0.491811	+	0.0534782i
$596$	−23.9483			−0.980963
$597$		0			0
$598$	0.340312	+	1.27006i	0.0139164	+	0.0519367i
$599$	−14.5339	−	8.39115i	−0.593839	−	0.342853i	0.172775	−	0.984961i	$-0.444727\pi$
$599$	−14.5339	−	8.39115i	−0.593839	−	0.342853i	−0.766614	+	0.642108i	$0.778060\pi$
$600$		0			0
$601$			1.73528i			0.0707833i	0.999374	+	0.0353917i	$0.0112679\pi$
$601$			1.73528i			0.0707833i	−0.999374	+	0.0353917i	$0.988732\pi$
$602$	5.11804	−	17.9091i	0.208596	−	0.729919i
$603$		0			0
$604$	3.06862	−	1.77167i	0.124860	−	0.0720881i
$605$	−9.71637	−	6.86862i	−0.395027	−	0.279249i
$606$		0			0
$607$	10.2070	−	38.0930i	0.414288	−	1.54615i	−0.371968	−	0.928245i	$-0.621317\pi$
$607$	10.2070	−	38.0930i	0.414288	−	1.54615i	0.786257	−	0.617900i	$-0.212016\pi$
$608$	4.38642	−	4.38642i	0.177893	−	0.177893i
$609$		0			0
$610$	−11.8993	+	9.89407i	−0.481787	+	0.400599i
$611$	−0.0456517	−	0.0790711i	−0.00184687	−	0.00319887i
$612$		0			0
$613$	−0.330293	+	0.0885018i	−0.0133404	+	0.00357455i	−0.265483	−	0.964116i	$-0.585531\pi$
$613$	−0.330293	+	0.0885018i	−0.0133404	+	0.00357455i	0.252143	+	0.967690i	$0.418865\pi$
$614$	−0.762678	−	1.32100i	−0.0307792	−	0.0533111i
$615$		0			0
$616$	−9.16697	−	5.49694i	−0.369348	−	0.221478i
$617$	−11.1876	+	11.1876i	−0.450397	+	0.450397i	−0.895486	−	0.445089i	$-0.853172\pi$
$617$	−11.1876	+	11.1876i	−0.450397	+	0.450397i	0.445089	+	0.895486i	$0.353172\pi$
$618$		0			0
$619$	18.2682	−	31.6414i	0.734260	−	1.27178i	−0.220787	−	0.975322i	$-0.570862\pi$
$619$	18.2682	−	31.6414i	0.734260	−	1.27178i	0.955047	−	0.296454i	$-0.0958042\pi$
$620$	13.3521	+	9.43875i	0.536232	+	0.379069i
$621$		0			0
$622$	6.80819	+	6.80819i	0.272984	+	0.272984i
$623$	−2.23356	+	7.81566i	−0.0894855	+	0.313128i
$624$		0			0
$625$	−3.89884	−	24.6941i	−0.155953	−	0.987764i
$626$	2.62123	+	1.51337i	0.104766	+	0.0604864i
$627$		0			0
$628$	−5.91389	−	1.58462i	−0.235990	−	0.0632333i
$629$	−9.43535			−0.376212
$630$		0			0
$631$	−35.8189			−1.42593			−0.712964	−	0.701201i	$-0.752648\pi$
$631$	−35.8189			−1.42593			−0.712964	+	0.701201i	$0.752648\pi$
$632$	−4.90330	−	1.31384i	−0.195043	−	0.0522616i
$633$		0			0
$634$	1.68760	+	0.974335i	0.0670231	+	0.0386958i
$635$	−2.40856	+	6.52623i	−0.0955807	+	0.258986i
$636$		0			0
$637$	1.38585	+	1.48083i	0.0549093	+	0.0586726i
$638$	20.4502	+	20.4502i	0.809631	+	0.809631i
$639$		0			0
$640$	0.378409	+	2.20382i	0.0149579	+	0.0871135i
$641$	−7.16573	+	12.4114i	−0.283029	+	0.490221i	−0.972129	−	0.234445i	$-0.924673\pi$
$641$	−7.16573	+	12.4114i	−0.283029	+	0.490221i	0.689100	+	0.724666i	$0.258006\pi$
$642$		0			0
$643$	7.65201	−	7.65201i	0.301766	−	0.301766i	−0.539939	−	0.841704i	$-0.681553\pi$
$643$	7.65201	−	7.65201i	0.301766	−	0.301766i	0.841704	+	0.539939i	$0.181553\pi$
$644$	−12.0051	−	0.198828i	−0.473068	−	0.00783492i
$645$		0			0
$646$	−6.32659	−	10.9580i	−0.248916	−	0.431136i
$647$	−31.2468	+	8.37254i	−1.22844	+	0.329159i	−0.813971	−	0.580906i	$-0.802698\pi$
$647$	−31.2468	+	8.37254i	−1.22844	+	0.329159i	−0.414466	+	0.910065i	$0.636032\pi$
$648$		0			0
$649$	−1.72791	−	2.99282i	−0.0678262	−	0.117478i
$650$	0.264349	−	1.42436i	0.0103686	−	0.0558681i
$651$		0			0
$652$	−11.7082	+	11.7082i	−0.458528	+	0.458528i
$653$	0.132578	−	0.494788i	0.00518818	−	0.0193625i	−0.963283	−	0.268487i	$-0.913476\pi$
$653$	0.132578	−	0.494788i	0.00518818	−	0.0193625i	0.968471	+	0.249125i	$0.0801429\pi$
$654$		0			0
$655$	9.42093	−	13.3269i	0.368106	−	0.520724i
$656$	−2.24080	+	1.29373i	−0.0874886	+	0.0505116i
$657$		0			0
$658$	0.808797	−	0.202423i	0.0315302	−	0.00789127i
$659$			19.5542i			0.761723i	0.924632	+	0.380862i	$0.124373\pi$
$659$			19.5542i			0.761723i	−0.924632	+	0.380862i	$0.875627\pi$
$660$		0			0
$661$	34.0324	+	19.6486i	1.32371	+	0.764242i	0.984318	−	0.176405i	$-0.0564468\pi$
$661$	34.0324	+	19.6486i	1.32371	+	0.764242i	0.339388	+	0.940647i	$0.389780\pi$
$662$	7.47819	+	27.9090i	0.290648	+	1.08471i
$663$		0			0
$664$	5.44998			0.211500
$665$	−5.61080	−	36.2679i	−0.217578	−	1.40641i
$666$		0			0
$667$	31.3801	+	8.40828i	1.21504	+	0.325570i
$668$	3.76542	+	14.0527i	0.145688	+	0.543716i
$669$		0			0
$670$	−2.95623	−	6.41462i	−0.114209	−	0.247819i
$671$		−	27.9597i		−	1.07937i
$672$		0			0
$673$	18.4813	+	18.4813i	0.712401	+	0.712401i	0.967037	−	0.254636i	$-0.0819556\pi$
$673$	18.4813	+	18.4813i	0.712401	+	0.712401i	−0.254636	+	0.967037i	$0.581956\pi$
$674$	−1.00824	+	0.582108i	−0.0388360	+	0.0224220i
$675$		0			0
$676$	−6.45803	+	11.1856i	−0.248386	+	0.430217i
$677$	10.6631	−	39.7951i	0.409815	−	1.52945i	−0.385183	−	0.922840i	$-0.625862\pi$
$677$	10.6631	−	39.7951i	0.409815	−	1.52945i	0.794999	−	0.606611i	$-0.207472\pi$
$678$		0			0
$679$	0.410862	−	24.8076i	0.0157674	−	0.952030i
$680$	4.54181	+	0.417892i	0.174171	+	0.0160254i
$681$		0			0
$682$	−28.5359	+	7.64618i	−1.09270	+	0.292787i
$683$	−8.81689	+	2.36248i	−0.337369	+	0.0903978i	−0.423526	−	0.905884i	$-0.639208\pi$
$683$	−8.81689	+	2.36248i	−0.337369	+	0.0903978i	0.0861573	+	0.996282i	$0.472541\pi$
$684$		0			0
$685$	−10.2631	−	12.3431i	−0.392134	−	0.471607i
$686$	−16.4791	+	8.45219i	−0.629175	+	0.322706i
$687$		0			0
$688$	1.82208	−	6.80009i	0.0694661	−	0.259251i
$689$	1.19989	−	2.07827i	0.0457121	−	0.0791758i
$690$		0			0
$691$	−41.9971	+	24.2470i	−1.59765	+	0.922401i	−0.605706	+	0.795689i	$0.707109\pi$
$691$	−41.9971	+	24.2470i	−1.59765	+	0.922401i	−0.991940	+	0.126712i	$0.959558\pi$
$692$	−5.49565	−	5.49565i	−0.208913	−	0.208913i
$693$		0			0
$694$			16.7042i			0.634082i
$695$	25.2166	−	11.6213i	0.956520	−	0.440821i
$696$		0			0
$697$	1.36598	+	5.09790i	0.0517401	+	0.193097i
$698$	35.4636	+	9.50244i	1.34232	+	0.359673i
$699$		0			0
$700$	11.8427	+	5.89495i	0.447612	+	0.222808i
$701$	30.8898			1.16669			0.583347	−	0.812223i	$-0.301743\pi$
$701$	30.8898			1.16669			0.583347	+	0.812223i	$0.301743\pi$
$702$		0			0
$703$	7.42684	+	27.7173i	0.280109	+	1.04538i
$704$	−3.49872	−	2.01999i	−0.131863	−	0.0761311i
$705$		0			0
$706$			14.2708i			0.537089i
$707$	6.35191	+	25.3796i	0.238888	+	0.954496i
$708$		0			0
$709$	−12.7354	+	7.35277i	−0.478287	+	0.276139i	−0.719702	−	0.694283i	$-0.755722\pi$
$709$	−12.7354	+	7.35277i	−0.478287	+	0.276139i	0.241416	+	0.970422i	$0.422388\pi$
$710$	−15.6965	+	2.69518i	−0.589078	+	0.101148i
$711$		0			0
$712$	−0.795171	+	2.96762i	−0.0298003	+	0.111216i
$713$	−23.4656	+	23.4656i	−0.878795	+	0.878795i
$714$		0			0
$715$	1.67341	+	2.01256i	0.0625821	+	0.0752654i
$716$	−1.93236	−	3.34695i	−0.0722157	−	0.125081i
$717$		0			0
$718$	26.1658	−	7.01110i	0.976499	−	0.261652i
$719$	−11.7360	−	20.3273i	−0.437679	−	0.758082i	0.559831	−	0.828607i	$-0.310866\pi$
$719$	−11.7360	−	20.3273i	−0.437679	−	0.758082i	−0.997510	+	0.0705247i	$0.977533\pi$
$720$		0			0
$721$	5.50134	+	9.90382i	0.204881	+	0.368837i
$722$	−13.7753	+	13.7753i	−0.512665	+	0.512665i
$723$		0			0
$724$	−3.49553	+	6.05444i	−0.129911	+	0.225012i
$725$	−27.2119	−	23.2526i	−1.01062	−	0.863581i
$726$		0			0
$727$	−14.1380	−	14.1380i	−0.524349	−	0.524349i	0.394533	−	0.918882i	$-0.370907\pi$
$727$	−14.1380	−	14.1380i	−0.524349	−	0.524349i	−0.918882	+	0.394533i	$0.870907\pi$
$728$	0.532998	+	0.550950i	0.0197542	+	0.0204196i
$729$		0			0
$730$	−10.7871	−	23.4065i	−0.399249	−	0.866315i
$731$	−12.4359	−	7.17986i	−0.459958	−	0.265557i
$732$		0			0
$733$	−26.7908	−	7.17859i	−0.989543	−	0.265147i	−0.272484	−	0.962160i	$-0.587845\pi$
$733$	−26.7908	−	7.17859i	−0.989543	−	0.265147i	−0.717058	+	0.697013i	$0.754512\pi$
$734$	22.6715			0.836821
$735$		0			0
$736$	−4.53813			−0.167278
$737$	12.3262	+	3.30280i	0.454042	+	0.121660i
$738$		0			0
$739$	−11.7451	−	6.78102i	−0.432050	−	0.249444i	0.268170	−	0.963372i	$-0.413581\pi$
$739$	−11.7451	−	6.78102i	−0.432050	−	0.249444i	−0.700219	+	0.713928i	$0.746915\pi$
$740$	−9.70376	−	3.58125i	−0.356717	−	0.131649i
$741$		0			0
$742$	15.2366	+	15.7498i	0.559354	+	0.578194i
$743$	−13.5961	−	13.5961i	−0.498791	−	0.498791i	0.412270	−	0.911062i	$-0.364736\pi$
$743$	−13.5961	−	13.5961i	−0.498791	−	0.498791i	−0.911062	+	0.412270i	$0.864736\pi$
$744$		0			0
$745$	−30.9115	+	43.7275i	−1.13251	+	1.60205i
$746$	−6.41789	+	11.1161i	−0.234976	+	0.406990i
$747$		0			0
$748$	−5.82691	+	5.82691i	−0.213053	+	0.213053i
$749$	−19.1069	−	34.3973i	−0.698152	−	1.25685i
$750$		0			0
$751$	−21.8309	−	37.8123i	−0.796622	−	1.37979i	−0.921804	−	0.387656i	$-0.873285\pi$
$751$	−21.8309	−	37.8123i	−0.796622	−	1.37979i	0.125182	−	0.992134i	$-0.460049\pi$
$752$	0.304388	−	0.0815604i	0.0110999	−	0.00297420i
$753$		0			0
$754$	−1.03707	−	1.79626i	−0.0377678	−	0.0654158i
$755$	0.725941	−	7.88981i	0.0264197	−	0.287140i
$756$		0			0
$757$	7.88896	−	7.88896i	0.286729	−	0.286729i	−0.549056	−	0.835785i	$-0.685013\pi$
$757$	7.88896	−	7.88896i	0.286729	−	0.286729i	0.835785	+	0.549056i	$0.185013\pi$
$758$	3.74613	−	13.9807i	0.136065	−	0.507803i
$759$		0			0
$760$	−2.34739	−	13.6710i	−0.0851489	−	0.495899i
$761$	1.70923	−	0.986825i	0.0619596	−	0.0357724i	−0.468700	−	0.883357i	$-0.655278\pi$
$761$	1.70923	−	0.986825i	0.0619596	−	0.0357724i	0.530660	+	0.847585i	$0.321944\pi$
$762$		0			0
$763$	−8.49921	−	33.9593i	−0.307692	−	1.22941i
$764$			4.47442i			0.161879i
$765$		0			0
$766$	−1.51691	−	0.875788i	−0.0548082	−	0.0316435i
$767$	0.0641463	+	0.239397i	0.00231619	+	0.00864413i
$768$		0			0
$769$	−17.4914			−0.630756			−0.315378	−	0.948966i	$-0.602131\pi$
$769$	−17.4914			−0.630756			−0.315378	+	0.948966i	$0.602131\pi$
$770$	−21.8693	+	9.64284i	−0.788113	+	0.347504i
$771$		0			0
$772$	19.3907	+	5.19573i	0.697887	+	0.186998i
$773$	−11.5736	−	43.1933i	−0.416274	−	1.55355i	−0.782271	−	0.622939i	$-0.785939\pi$
$773$	−11.5736	−	43.1933i	−0.416274	−	1.55355i	0.365997	−	0.930616i	$-0.380728\pi$
$774$		0			0
$775$	34.4686	−	12.1965i	1.23815	−	0.438112i
$776$		−	9.37769i		−	0.336640i
$777$		0			0
$778$	1.96738	+	1.96738i	0.0705341	+	0.0705341i
$779$	13.9004	−	8.02542i	0.498035	−	0.287540i
$780$		0			0
$781$	14.3871	−	24.9193i	0.514813	−	0.891682i
$782$	−2.39579	+	8.94120i	−0.0856732	+	0.319737i
$783$		0			0
$784$	−6.17475	+	3.29733i	−0.220527	+	0.117762i
$785$	−10.5268	+	8.75286i	−0.375717	+	0.312403i
$786$		0			0
$787$	25.0643	−	6.71595i	0.893445	−	0.239398i	0.217246	−	0.976117i	$-0.430293\pi$
$787$	25.0643	−	6.71595i	0.893445	−	0.239398i	0.676199	+	0.736719i	$0.263626\pi$
$788$	10.7220	−	2.87294i	0.381954	−	0.102344i
$789$		0			0
$790$	−8.72792	+	7.25713i	−0.310525	+	0.258197i
$791$	0.604323	−	36.4887i	0.0214873	−	1.29739i
$792$		0			0
$793$	−0.518984	+	1.93688i	−0.0184297	+	0.0687805i
$794$	19.8340	−	34.3535i	0.703881	−	1.21916i
$795$		0			0
$796$	−9.35485	+	5.40103i	−0.331574	+	0.191434i
$797$	37.3374	+	37.3374i	1.32256	+	1.32256i	0.911698	+	0.410861i	$0.134772\pi$
$797$	37.3374	+	37.3374i	1.32256	+	1.32256i	0.410861	+	0.911698i	$0.365228\pi$
$798$		0			0
$799$		−	0.642773i		−	0.0227397i
$800$	4.51240	+	2.15365i	0.159538	+	0.0761432i
$801$		0			0
$802$	−5.16876	−	19.2901i	−0.182515	−	0.681156i
$803$	44.9776	+	12.0517i	1.58722	+	0.425295i
$804$		0			0
$805$	−15.8588	+	21.6636i	−0.558948	+	0.763543i
$806$	2.11872			0.0746287
$807$		0			0
$808$	2.55932	+	9.55150i	0.0900364	+	0.336021i
$809$	13.9001	+	8.02525i	0.488703	+	0.282153i	0.724036	−	0.689762i	$-0.242285\pi$
$809$	13.9001	+	8.02525i	0.488703	+	0.282153i	−0.235333	+	0.971915i	$0.575618\pi$
$810$		0			0
$811$		−	35.4040i		−	1.24320i	−0.783334	−	0.621602i	$-0.786482\pi$
$811$		−	35.4040i		−	1.24320i	0.783334	−	0.621602i	$-0.213518\pi$
$812$	18.3734	−	4.59844i	0.644781	−	0.161374i
$813$		0			0
$814$	16.1842	−	9.34397i	0.567257	−	0.327506i
$815$	6.26564	+	36.4905i	0.219476	+	1.27821i
$816$		0			0
$817$	−11.3030	+	42.1832i	−0.395440	+	1.47580i
$818$	−10.8227	+	10.8227i	−0.378407	+	0.378407i
$819$		0			0
$820$	−0.530105	+	5.76139i	−0.0185121	+	0.201196i
$821$	13.4231	+	23.2495i	0.468469	+	0.811412i	0.999351	−	0.0360337i	$-0.0114724\pi$
$821$	13.4231	+	23.2495i	0.468469	+	0.811412i	−0.530881	+	0.847446i	$0.678139\pi$
$822$		0			0
$823$	−27.0285	+	7.24225i	−0.942153	+	0.252449i	−0.697029	−	0.717043i	$-0.745495\pi$
$823$	−27.0285	+	7.24225i	−0.942153	+	0.252449i	−0.245124	+	0.969492i	$0.578829\pi$
$824$	2.14101	+	3.70835i	0.0745858	+	0.129186i
$825$		0			0
$826$	−2.26288	−	0.0374776i	−0.0787355	−	0.00130401i
$827$	−16.8901	+	16.8901i	−0.587325	+	0.587325i	−0.936906	−	0.349581i	$-0.886324\pi$
$827$	−16.8901	+	16.8901i	−0.587325	+	0.587325i	0.349581	+	0.936906i	$0.386324\pi$
$828$		0			0
$829$	7.08412	−	12.2701i	0.246042	−	0.426157i	−0.716382	−	0.697708i	$-0.754203\pi$
$829$	7.08412	−	12.2701i	0.246042	−	0.426157i	0.962424	+	0.271551i	$0.0875367\pi$
$830$	7.03461	−	9.95118i	0.244175	−	0.345410i
$831$		0			0
$832$	0.204875	+	0.204875i	0.00710276	+	0.00710276i
$833$	3.23673	+	13.9065i	0.112146	+	0.481831i
$834$		0			0
$835$	30.5192	+	11.2634i	1.05616	+	0.389785i
$836$	21.7037	+	12.5306i	0.750638	+	0.433381i
$837$		0			0
$838$	26.7588	+	7.17000i	0.924367	+	0.247683i
$839$	−18.1874			−0.627900			−0.313950	−	0.949439i	$-0.601652\pi$
$839$	−18.1874			−0.627900			−0.313950	+	0.949439i	$0.601652\pi$
$840$		0			0
$841$	−22.2469			−0.767134
$842$	31.8909	+	8.54515i	1.09903	+	0.294485i
$843$		0			0
$844$	6.55196	+	3.78278i	0.225528	+	0.130209i
$845$	12.0882	+	26.2297i	0.415846	+	0.902329i
$846$		0			0
$847$	3.86863	−	13.5371i	0.132928	−	0.465141i
$848$	5.85669	+	5.85669i	0.201120	+	0.201120i
$849$		0			0
$850$	6.62541	−	7.75354i	0.227250	−	0.265944i
$851$	10.4962	−	18.1799i	0.359804	−	0.623198i
$852$		0			0
$853$	−17.4820	+	17.4820i	−0.598574	+	0.598574i	−0.939933	−	0.341359i	$-0.889113\pi$
$853$	−17.4820	+	17.4820i	−0.598574	+	0.598574i	0.341359	+	0.939933i	$0.389113\pi$
$854$	−15.7037	−	9.41665i	−0.537369	−	0.322231i
$855$		0			0
$856$	−7.43604	−	12.8796i	−0.254159	−	0.440216i
$857$	25.2634	−	6.76932i	0.862982	−	0.231235i	0.199932	−	0.979810i	$-0.435928\pi$
$857$	25.2634	−	6.76932i	0.862982	−	0.231235i	0.663051	+	0.748574i	$0.269261\pi$
$858$		0			0
$859$	24.4126	+	42.2838i	0.832946	+	1.44271i	0.895692	+	0.444676i	$0.146681\pi$
$859$	24.4126	+	42.2838i	0.832946	+	1.44271i	−0.0627455	+	0.998030i	$0.519986\pi$
$860$	−10.0645	−	12.1042i	−0.343196	−	0.412751i
$861$		0			0
$862$	16.9121	−	16.9121i	0.576027	−	0.576027i
$863$	−3.97256	+	14.8258i	−0.135228	+	0.504676i	0.864769	+	0.502169i	$0.167465\pi$
$863$	−3.97256	+	14.8258i	−0.135228	+	0.504676i	−0.999997	+	0.00250685i	$0.999202\pi$
$864$		0			0
$865$	−17.1281	+	2.94100i	−0.582373	+	0.0999971i
$866$	−16.2298	+	9.37026i	−0.551510	+	0.318414i
$867$		0			0
$868$	−5.31621	+	18.6025i	−0.180444	+	0.631410i
$869$		−	20.5080i		−	0.695686i
$870$		0			0
$871$	−0.792578	−	0.457595i	−0.0268555	−	0.0155050i
$872$	−3.42451	−	12.7804i	−0.115968	−	0.432800i
$873$		0			0
$874$	28.1515			0.952240
$875$	26.0497	−	14.0147i	0.880641	−	0.473784i
$876$		0			0
$877$	38.1169	+	10.2134i	1.28712	+	0.344882i	0.836565	−	0.547868i	$-0.184560\pi$
$877$	38.1169	+	10.2134i	1.28712	+	0.344882i	0.450552	+	0.892750i	$0.351227\pi$
$878$	−3.65133	−	13.6270i	−0.123227	−	0.459888i
$879$		0			0
$880$	−8.20431	+	3.78103i	−0.276567	+	0.127458i
$881$			52.5926i			1.77189i	0.463791	+	0.885945i	$0.346489\pi$
$881$			52.5926i			1.77189i	−0.463791	+	0.885945i	$0.653511\pi$
$882$		0			0
$883$	13.0940	+	13.0940i	0.440649	+	0.440649i	0.892230	−	0.451581i	$-0.149140\pi$
$883$	13.0940	+	13.0940i	0.440649	+	0.440649i	−0.451581	+	0.892230i	$0.649140\pi$
$884$	0.511811	−	0.295494i	0.0172141	−	0.00993854i
$885$		0			0
$886$	−10.5317	+	18.2414i	−0.353819	+	0.612833i
$887$	−9.56553	+	35.6990i	−0.321179	+	1.19866i	0.596919	+	0.802302i	$0.296391\pi$
$887$	−9.56553	+	35.6990i	−0.321179	+	1.19866i	−0.918098	+	0.396354i	$0.870275\pi$
$888$		0			0
$889$	−8.22991	−	0.136303i	−0.276022	−	0.00457146i
$890$	4.39223	+	5.28239i	0.147228	+	0.177066i
$891$		0			0
$892$	12.7755	−	3.42318i	0.427755	−	0.114617i
$893$	−1.88822	+	0.505946i	−0.0631867	+	0.0169308i
$894$		0			0
$895$	−8.60543	−	0.791785i	−0.287648	−	0.0264664i
$896$	−2.31288	+	1.28475i	−0.0772679	+	0.0429205i
$897$		0			0
$898$	−8.10744	+	30.2574i	−0.270549	+	1.00970i
$899$	26.1742	−	45.3351i	0.872959	−	1.51201i
$900$		0			0
$901$	14.6310	−	8.44719i	0.487428	−	0.281417i
$902$	−7.39156	−	7.39156i	−0.246112	−	0.246112i
$903$		0			0
$904$		−	13.7933i		−	0.458759i
$905$	6.54297	+	14.1974i	0.217496	+	0.471936i
$906$		0			0
$907$	−4.28883	−	16.0061i	−0.142408	−	0.531474i	−0.999857	−	0.0169054i	$-0.994619\pi$
$907$	−4.28883	−	16.0061i	−0.142408	−	0.531474i	0.857449	−	0.514569i	$-0.172048\pi$
$908$	−15.6420	−	4.19127i	−0.519099	−	0.139092i
$909$		0			0
$910$	1.69396	−	0.262062i	0.0561541	−	0.00868727i
$911$	1.46770			0.0486270			0.0243135	−	0.999704i	$-0.492260\pi$
$911$	1.46770			0.0486270			0.0243135	+	0.999704i	$0.492260\pi$
$912$		0			0
$913$	5.69862	+	21.2676i	0.188597	+	0.703853i
$914$	2.47817	+	1.43077i	0.0819705	+	0.0473257i
$915$		0			0
$916$			11.7764i			0.389103i
$917$	18.5674	+	5.30617i	0.613149	+	0.175225i
$918$		0			0
$919$	24.1523	−	13.9443i	0.796710	−	0.459981i	−0.0456096	−	0.998959i	$-0.514523\pi$
$919$	24.1523	−	13.9443i	0.796710	−	0.459981i	0.842319	+	0.538979i	$0.181190\pi$
$920$	−5.85763	+	8.28622i	−0.193120	+	0.273189i
$921$		0			0
$922$	0.783378	−	2.92361i	0.0257992	−	0.0962838i
$923$	−1.45920	+	1.45920i	−0.0480302	+	0.0480302i
$924$		0			0
$925$	−19.0642	+	13.0957i	−0.626828	+	0.430582i
$926$	13.6393	+	23.6240i	0.448215	+	0.776332i
$927$		0			0
$928$	6.91477	−	1.85281i	0.226988	−	0.0608213i
$929$	16.6468	+	28.8331i	0.546164	+	0.945984i	0.998533	+	0.0541530i	$0.0172459\pi$
$929$	16.6468	+	28.8331i	0.546164	+	0.945984i	−0.452368	+	0.891831i	$0.649421\pi$
$930$		0			0
$931$	38.3040	−	20.4544i	1.25536	−	0.670367i
$932$	4.04765	−	4.04765i	0.132585	−	0.132585i
$933$		0			0
$934$	12.5645	−	21.7623i	0.411122	−	0.712084i
$935$	3.11828	+	18.1605i	0.101979	+	0.593913i
$936$		0			0
$937$	25.6651	+	25.6651i	0.838442	+	0.838442i	0.988654	−	0.150212i	$-0.0479957\pi$
$937$	25.6651	+	25.6651i	0.838442	+	0.838442i	−0.150212	+	0.988654i	$0.547996\pi$
$938$	6.00642	−	5.81071i	0.196117	−	0.189726i
$939$		0			0
$940$	0.243969	−	0.661059i	0.00795739	−	0.0215614i
$941$	21.0732	+	12.1666i	0.686967	+	0.396621i	0.802475	−	0.596686i	$-0.203516\pi$
$941$	21.0732	+	12.1666i	0.686967	+	0.396621i	−0.115508	+	0.993307i	$0.536849\pi$
$942$		0			0
$943$	−11.3421	−	3.03911i	−0.369350	−	0.0989670i
$944$	−0.855404			−0.0278410
$945$		0			0
$946$	28.4413			0.924707
$947$	−2.07680	−	0.556477i	−0.0674869	−	0.0180831i	0.224918	−	0.974378i	$-0.427789\pi$
$947$	−2.07680	−	0.556477i	−0.0674869	−	0.0180831i	−0.292405	+	0.956295i	$0.594455\pi$
$948$		0			0
$949$	−2.89206	−	1.66973i	−0.0938804	−	0.0542019i
$950$	−27.9919	−	13.3598i	−0.908178	−	0.433450i
$951$		0			0
$952$	1.31024	+	5.23517i	0.0424652	+	0.169673i
$953$	13.1863	+	13.1863i	0.427146	+	0.427146i	0.887655	−	0.460509i	$-0.152333\pi$
$953$	13.1863	+	13.1863i	0.427146	+	0.427146i	−0.460509	+	0.887655i	$0.652333\pi$
$954$		0			0
$955$	8.16989	+	5.77540i	0.264371	+	0.186887i
$956$	−4.16897	+	7.22087i	−0.134834	+	0.233540i
$957$		0			0
$958$	5.85973	−	5.85973i	0.189319	−	0.189319i
$959$	9.76792	−	16.2895i	0.315423	−	0.526015i
$960$		0			0
$961$	11.2368	+	19.4627i	0.362477	+	0.627829i
$962$	−1.29459	+	0.346883i	−0.0417391	+	0.0111840i
$963$		0			0
$964$	1.48219	+	2.56723i	0.0477381	+	0.0826849i
$965$	34.5156	−	28.6993i	1.11110	−	0.923862i
$966$		0			0
$967$	−27.7931	+	27.7931i	−0.893766	+	0.893766i	−0.994875	−	0.101109i	$-0.967761\pi$
$967$	−27.7931	+	27.7931i	−0.893766	+	0.893766i	0.101109	+	0.994875i	$0.467761\pi$
$968$	1.37728	−	5.14006i	0.0442673	−	0.165208i
$969$		0			0
$970$	−17.1228	−	12.1043i	−0.549780	−	0.388647i
$971$	−12.1029	+	6.98760i	−0.388400	+	0.224243i	−0.681467	−	0.731849i	$-0.738658\pi$
$971$	−12.1029	+	6.98760i	−0.388400	+	0.224243i	0.293067	+	0.956092i	$0.405324\pi$
$972$		0			0
$973$	22.8425	+	23.6119i	0.732298	+	0.756963i
$974$			10.6783i			0.342155i
$975$		0			0
$976$	−5.99356	−	3.46038i	−0.191849	−	0.110764i
$977$	−2.16089	−	8.06456i	−0.0691331	−	0.258008i	0.922706	−	0.385505i	$-0.125973\pi$
$977$	−2.16089	−	8.06456i	−0.0691331	−	0.258008i	−0.991839	+	0.127496i	$0.959306\pi$
$978$		0			0
$979$	−12.4120			−0.396690
$980$	−1.94949	+	15.5306i	−0.0622740	+	0.496107i
$981$		0			0
$982$	−24.8494	−	6.65836i	−0.792975	−	0.212477i
$983$	6.30383	+	23.5262i	0.201061	+	0.750370i	0.990614	+	0.136688i	$0.0436457\pi$
$983$	6.30383	+	23.5262i	0.201061	+	0.750370i	−0.789553	+	0.613682i	$0.789688\pi$
$984$		0			0
$985$	8.59372	−	23.2856i	0.273819	−	0.741940i
$986$		−	14.6019i		−	0.465018i
$987$		0			0
$988$	−1.27091	−	1.27091i	−0.0404329	−	0.0404329i
$989$	27.6681	−	15.9742i	0.879794	−	0.507949i
$990$		0			0
$991$	−8.72002	+	15.1035i	−0.277000	+	0.479779i	−0.970638	−	0.240545i	$-0.922674\pi$
$991$	−8.72002	+	15.1035i	−0.277000	+	0.479779i	0.693637	+	0.720324i	$0.256007\pi$
$992$	−1.89263	+	7.06340i	−0.0600911	+	0.224263i
$993$		0			0
$994$	−9.15051	−	16.4733i	−0.290237	−	0.522500i
$995$	−2.21307	+	24.0525i	−0.0701590	+	0.762516i
$996$		0			0
$997$	25.2781	−	6.77324i	0.800565	−	0.214511i	0.164733	−	0.986338i	$-0.447324\pi$
$997$	25.2781	−	6.77324i	0.800565	−	0.214511i	0.635832	+	0.771827i	$0.280657\pi$
$998$	−14.1014	+	3.77845i	−0.446371	+	0.119605i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bv.c.73.4		16
3.2	odd	2		70.2.k.a.3.2	✓	16
5.2	odd	4	inner	630.2.bv.c.577.2		16
7.5	odd	6	inner	630.2.bv.c.523.2		16
12.11	even	2		560.2.ci.c.353.1		16
15.2	even	4		70.2.k.a.17.4	yes	16
15.8	even	4		350.2.o.c.157.1		16
15.14	odd	2		350.2.o.c.143.3		16
21.2	odd	6		490.2.l.c.313.3		16
21.5	even	6		70.2.k.a.33.4	yes	16
21.11	odd	6		490.2.g.c.293.8		16
21.17	even	6		490.2.g.c.293.5		16
21.20	even	2		490.2.l.c.423.1		16
35.12	even	12	inner	630.2.bv.c.397.4		16
60.47	odd	4		560.2.ci.c.17.1		16
84.47	odd	6		560.2.ci.c.33.1		16
105.2	even	12		490.2.l.c.117.1		16
105.17	odd	12		490.2.g.c.97.8		16
105.32	even	12		490.2.g.c.97.5		16
105.47	odd	12		70.2.k.a.47.2	yes	16
105.62	odd	4		490.2.l.c.227.3		16
105.68	odd	12		350.2.o.c.257.3		16
105.89	even	6		350.2.o.c.243.1		16
420.47	even	12		560.2.ci.c.257.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.k.a.3.2	✓	16	3.2	odd	2
70.2.k.a.17.4	yes	16	15.2	even	4
70.2.k.a.33.4	yes	16	21.5	even	6
70.2.k.a.47.2	yes	16	105.47	odd	12
350.2.o.c.143.3		16	15.14	odd	2
350.2.o.c.157.1		16	15.8	even	4
350.2.o.c.243.1		16	105.89	even	6
350.2.o.c.257.3		16	105.68	odd	12
490.2.g.c.97.5		16	105.32	even	12
490.2.g.c.97.8		16	105.17	odd	12
490.2.g.c.293.5		16	21.17	even	6
490.2.g.c.293.8		16	21.11	odd	6
490.2.l.c.117.1		16	105.2	even	12
490.2.l.c.227.3		16	105.62	odd	4
490.2.l.c.313.3		16	21.2	odd	6
490.2.l.c.423.1		16	21.20	even	2
560.2.ci.c.17.1		16	60.47	odd	4
560.2.ci.c.33.1		16	84.47	odd	6
560.2.ci.c.257.1		16	420.47	even	12
560.2.ci.c.353.1		16	12.11	even	2
630.2.bv.c.73.4		16	1.1	even	1	trivial
630.2.bv.c.397.4		16	35.12	even	12	inner
630.2.bv.c.523.2		16	7.5	odd	6	inner
630.2.bv.c.577.2		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)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(2.03078 - 0.935904i) q^{5} +(1.83959 + 1.90155i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(2.03078 - 0.935904i) q^{5} +(1.83959 + 1.90155i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.20382 - 0.378409i) q^{10} +(-2.01999 + 3.49872i) q^{11} +(0.204875 - 0.204875i) q^{13} +(1.28475 + 2.31288i) q^{14} +(0.500000 + 0.866025i) q^{16} +(1.97024 - 0.527924i) q^{17} +(-3.10166 - 5.37224i) q^{19} +(2.22666 + 0.204875i) q^{20} +(-2.85669 + 2.85669i) q^{22} +(-1.17456 + 4.38350i) q^{23} +(3.24817 - 3.80124i) q^{25} +(0.250919 - 0.144868i) q^{26} +(0.642357 + 2.56659i) q^{28} -7.15869i q^{29} +(6.33287 + 3.65628i) q^{31} +(0.258819 + 0.965926i) q^{32} +2.03974 q^{34} +(5.51548 + 2.13996i) q^{35} +(-4.46814 - 1.19723i) q^{37} +(-1.60554 - 5.99195i) q^{38} +(2.09777 + 0.774197i) q^{40} +2.58745i q^{41} +(-4.97801 - 4.97801i) q^{43} +(-3.49872 + 2.01999i) q^{44} +(-2.26907 + 3.93014i) q^{46} +(0.0815604 - 0.304388i) q^{47} +(-0.231803 + 6.99616i) q^{49} +(4.12132 - 2.83103i) q^{50} +(0.279864 - 0.0749894i) q^{52} +(8.00039 - 2.14370i) q^{53} +(-0.827689 + 8.99566i) q^{55} +(-0.0438127 + 2.64539i) q^{56} +(1.85281 - 6.91477i) q^{58} +(-0.427702 + 0.740802i) q^{59} +(-5.99356 + 3.46038i) q^{61} +(5.17076 + 5.17076i) q^{62} +1.00000i q^{64} +(0.224313 - 0.607800i) q^{65} +(-0.817530 - 3.05106i) q^{67} +(1.97024 + 0.527924i) q^{68} +(4.77369 + 3.49455i) q^{70} -7.12240 q^{71} +(-2.98311 - 11.1331i) q^{73} +(-4.00603 - 2.31288i) q^{74} -6.20333i q^{76} +(-10.3690 + 2.59511i) q^{77} +(-4.39618 + 2.53813i) q^{79} +(1.82591 + 1.29076i) q^{80} +(-0.669683 + 2.49929i) q^{82} +(3.85372 - 3.85372i) q^{83} +(3.50704 - 2.91605i) q^{85} +(-3.51999 - 6.09680i) q^{86} +(-3.90231 + 1.04562i) q^{88} +(1.53615 + 2.66069i) q^{89} +(0.766467 + 0.0126942i) q^{91} +(-3.20895 + 3.20895i) q^{92} +(0.157563 - 0.272906i) q^{94} +(-11.3267 - 8.00700i) q^{95} +(-6.63103 - 6.63103i) q^{97} +(-2.03464 + 6.69778i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{5} + 8 q^{7}+O(q^{10}) \) 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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