LMFDB - Embedded newform 315.2.bz.d.208.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(73,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, 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("315.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bz (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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			208.3
Character	$\chi$	$=$	315.208
Dual form			315.2.bz.d.262.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.259789 - 0.969545i) q^{2} +(0.859523 - 0.496246i) q^{4} +(1.40510 - 1.73945i) q^{5} +(-1.06195 - 2.42328i) q^{7} +(-2.12394 - 2.12394i) q^{8} +O(q^{10})$	\(q+(-0.259789 - 0.969545i) q^{2} +(0.859523 - 0.496246i) q^{4} +(1.40510 - 1.73945i) q^{5} +(-1.06195 - 2.42328i) q^{7} +(-2.12394 - 2.12394i) q^{8} +(-2.05151 - 0.910421i) q^{10} +(1.78283 + 3.08796i) q^{11} +(-2.78368 + 2.78368i) q^{13} +(-2.07359 + 1.65915i) q^{14} +(-0.514988 + 0.891986i) q^{16} +(0.135713 - 0.506489i) q^{17} +(2.06188 - 3.57128i) q^{19} +(0.344523 - 2.19237i) q^{20} +(2.53075 - 2.53075i) q^{22} +(2.49427 - 0.668338i) q^{23} +(-1.05137 - 4.88821i) q^{25} +(3.42207 + 1.97574i) q^{26} +(-2.11531 - 1.55587i) q^{28} +6.14396i q^{29} +(-1.71173 + 0.988266i) q^{31} +(-4.80410 - 1.28726i) q^{32} -0.526321 q^{34} +(-5.70731 - 1.55774i) q^{35} +(-0.0409435 - 0.152803i) q^{37} +(-3.99817 - 1.07131i) q^{38} +(-6.67884 + 0.710134i) q^{40} -8.28475i q^{41} +(9.01253 + 9.01253i) q^{43} +(3.06477 + 1.76945i) q^{44} +(-1.29597 - 2.24468i) q^{46} +(5.19095 - 1.39091i) q^{47} +(-4.74453 + 5.14679i) q^{49} +(-4.46621 + 2.28926i) q^{50} +(-1.01125 + 3.77403i) q^{52} +(1.48765 - 5.55200i) q^{53} +(7.87641 + 1.23775i) q^{55} +(-2.89138 + 7.40241i) q^{56} +(5.95685 - 1.59613i) q^{58} +(1.30044 + 2.25243i) q^{59} +(8.67653 + 5.00940i) q^{61} +(1.40286 + 1.40286i) q^{62} +7.05216i q^{64} +(0.930716 + 8.75343i) q^{65} +(5.32418 + 1.42661i) q^{67} +(-0.134694 - 0.502686i) q^{68} +(-0.0276056 + 5.93818i) q^{70} +7.23274 q^{71} +(-14.8625 - 3.98240i) q^{73} +(-0.137513 + 0.0793931i) q^{74} -4.09280i q^{76} +(5.58969 - 7.59955i) q^{77} +(13.1146 + 7.57171i) q^{79} +(0.827954 + 2.14913i) q^{80} +(-8.03244 + 2.15229i) q^{82} +(-9.42372 + 9.42372i) q^{83} +(-0.690321 - 0.947735i) q^{85} +(6.39670 - 11.0794i) q^{86} +(2.77201 - 10.3453i) q^{88} +(-5.52672 + 9.57257i) q^{89} +(9.70175 + 3.78950i) q^{91} +(1.81222 - 1.81222i) q^{92} +(-2.69710 - 4.67152i) q^{94} +(-3.31491 - 8.60455i) q^{95} +(-2.48828 - 2.48828i) q^{97} +(6.22262 + 3.26295i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 12 q^{5} + 8 q^{7} + 24 q^{8}+O(q^{10}) $ 32 * q + 12 * q^5 + 8 * q^7 + 24 * q^8	$ 32 q + 12 q^{5} + 8 q^{7} + 24 q^{8} - 12 q^{10} + 8 q^{11} - 8 q^{22} + 8 q^{23} + 12 q^{25} - 24 q^{26} - 24 q^{28} + 24 q^{31} - 24 q^{32} - 44 q^{35} + 4 q^{37} - 12 q^{38} + 12 q^{40} + 40 q^{43} - 40 q^{46} + 60 q^{47} - 72 q^{50} - 108 q^{52} + 24 q^{53} + 48 q^{56} + 4 q^{58} - 24 q^{61} + 4 q^{65} + 8 q^{67} - 132 q^{68} + 4 q^{70} + 16 q^{71} + 36 q^{73} - 60 q^{77} + 12 q^{80} + 12 q^{82} - 72 q^{85} + 16 q^{86} - 32 q^{88} - 24 q^{91} + 56 q^{92} + 12 q^{95} + 72 q^{98}+O(q^{100}) $ 32 * q + 12 * q^5 + 8 * q^7 + 24 * q^8 - 12 * q^10 + 8 * q^11 - 8 * q^22 + 8 * q^23 + 12 * q^25 - 24 * q^26 - 24 * q^28 + 24 * q^31 - 24 * q^32 - 44 * q^35 + 4 * q^37 - 12 * q^38 + 12 * q^40 + 40 * q^43 - 40 * q^46 + 60 * q^47 - 72 * q^50 - 108 * q^52 + 24 * q^53 + 48 * q^56 + 4 * q^58 - 24 * q^61 + 4 * q^65 + 8 * q^67 - 132 * q^68 + 4 * q^70 + 16 * q^71 + 36 * q^73 - 60 * q^77 + 12 * q^80 + 12 * q^82 - 72 * q^85 + 16 * q^86 - 32 * q^88 - 24 * q^91 + 56 * q^92 + 12 * q^95 + 72 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−0.259789	−	0.969545i	−0.183698	−	0.685572i	−0.994905	−	0.100813i	$-0.967856\pi$
$2$	−0.259789	−	0.969545i	−0.183698	−	0.685572i	0.811207	−	0.584759i	$-0.198811\pi$
$3$		0			0
$3$		0			0
$4$	0.859523	−	0.496246i	0.429762	−	0.248123i
$5$	1.40510	−	1.73945i	0.628381	−	0.777906i
$5$	1.40510	−	1.73945i	0.628381	−	0.777906i
$6$		0			0
$7$	−1.06195	−	2.42328i	−0.401379	−	0.915912i
$7$	−1.06195	−	2.42328i	−0.401379	−	0.915912i
$8$	−2.12394	−	2.12394i	−0.750926	−	0.750926i
$9$		0			0
$10$	−2.05151	−	0.910421i	−0.648743	−	0.287900i
$11$	1.78283	+	3.08796i	0.537545	+	0.931054i	0.999036	+	0.0439095i	$0.0139813\pi$
$11$	1.78283	+	3.08796i	0.537545	+	0.931054i	−0.461491	+	0.887145i	$0.652685\pi$
$12$		0			0
$13$	−2.78368	+	2.78368i	−0.772054	+	0.772054i	−0.978465	−	0.206411i	$-0.933822\pi$
$13$	−2.78368	+	2.78368i	−0.772054	+	0.772054i	0.206411	+	0.978465i	$0.433822\pi$
$14$	−2.07359	+	1.65915i	−0.554191	+	0.443426i
$15$		0			0
$16$	−0.514988	+	0.891986i	−0.128747	+	0.222997i
$17$	0.135713	−	0.506489i	0.0329153	−	0.122842i	−0.947513	−	0.319716i	$-0.896412\pi$
$17$	0.135713	−	0.506489i	0.0329153	−	0.122842i	0.980429	+	0.196874i	$0.0630791\pi$
$18$		0			0
$19$	2.06188	−	3.57128i	0.473028	−	0.819308i	−0.526496	−	0.850178i	$-0.676494\pi$
$19$	2.06188	−	3.57128i	0.473028	−	0.819308i	0.999523	+	0.0308699i	$0.00982775\pi$
$20$	0.344523	−	2.19237i	0.0770377	−	0.490230i
$21$		0			0
$22$	2.53075	−	2.53075i	0.539559	−	0.539559i
$23$	2.49427	−	0.668338i	0.520092	−	0.139358i	0.0107826	−	0.999942i	$-0.496568\pi$
$23$	2.49427	−	0.668338i	0.520092	−	0.139358i	0.509309	+	0.860584i	$0.329901\pi$
$24$		0			0
$25$	−1.05137	−	4.88821i	−0.210275	−	0.977642i
$26$	3.42207	+	1.97574i	0.671124	+	0.387474i
$27$		0			0
$28$	−2.11531	−	1.55587i	−0.399756	−	0.294032i
$29$			6.14396i			1.14091i	0.821331	+	0.570453i	$0.193232\pi$
$29$			6.14396i			1.14091i	−0.821331	+	0.570453i	$0.806768\pi$
$30$		0			0
$31$	−1.71173	+	0.988266i	−0.307435	+	0.177498i	−0.645778	−	0.763525i	$-0.723467\pi$
$31$	−1.71173	+	0.988266i	−0.307435	+	0.177498i	0.338343	+	0.941023i	$0.390134\pi$
$32$	−4.80410	−	1.28726i	−0.849253	−	0.227557i
$33$		0			0
$34$	−0.526321			−0.0902633
$35$	−5.70731	−	1.55774i	−0.964712	−	0.263307i
$36$		0			0
$37$	−0.0409435	−	0.152803i	−0.00673106	−	0.0251207i	0.962479	−	0.271357i	$-0.0874726\pi$
$37$	−0.0409435	−	0.152803i	−0.00673106	−	0.0251207i	−0.969210	+	0.246237i	$0.920806\pi$
$38$	−3.99817	−	1.07131i	−0.648589	−	0.173789i
$39$		0			0
$40$	−6.67884	+	0.710134i	−1.05602	+	0.112282i
$41$		−	8.28475i		−	1.29386i	−0.762549	−	0.646930i	$-0.776052\pi$
$41$		−	8.28475i		−	1.29386i	0.762549	−	0.646930i	$-0.223948\pi$
$42$		0			0
$43$	9.01253	+	9.01253i	1.37440	+	1.37440i	0.853805	+	0.520594i	$0.174289\pi$
$43$	9.01253	+	9.01253i	1.37440	+	1.37440i	0.520594	+	0.853805i	$0.325711\pi$
$44$	3.06477	+	1.76945i	0.462032	+	0.266754i
$45$		0			0
$46$	−1.29597	−	2.24468i	−0.191080	−	0.330960i
$47$	5.19095	−	1.39091i	0.757178	−	0.202885i	0.140478	−	0.990084i	$-0.455136\pi$
$47$	5.19095	−	1.39091i	0.757178	−	0.202885i	0.616700	+	0.787198i	$0.288469\pi$
$48$		0			0
$49$	−4.74453	+	5.14679i	−0.677790	+	0.735256i
$50$	−4.46621	+	2.28926i	−0.631617	+	0.323750i
$51$		0			0
$52$	−1.01125	+	3.77403i	−0.140235	+	0.523363i
$53$	1.48765	−	5.55200i	0.204345	−	0.762626i	−0.785303	−	0.619111i	$-0.787493\pi$
$53$	1.48765	−	5.55200i	0.204345	−	0.762626i	0.989648	−	0.143514i	$-0.0458404\pi$
$54$		0			0
$55$	7.87641	+	1.23775i	1.06206	+	0.166898i
$56$	−2.89138	+	7.40241i	−0.386376	+	0.989188i
$57$		0			0
$58$	5.95685	−	1.59613i	0.782173	−	0.209583i
$59$	1.30044	+	2.25243i	0.169303	+	0.293242i	0.938175	−	0.346161i	$-0.112515\pi$
$59$	1.30044	+	2.25243i	0.169303	+	0.293242i	−0.768872	+	0.639403i	$0.779182\pi$
$60$		0			0
$61$	8.67653	+	5.00940i	1.11092	+	0.641387i	0.939066	−	0.343736i	$-0.111692\pi$
$61$	8.67653	+	5.00940i	1.11092	+	0.641387i	0.171849	+	0.985123i	$0.445026\pi$
$62$	1.40286	+	1.40286i	0.178163	+	0.178163i
$63$		0			0
$64$			7.05216i			0.881521i
$65$	0.930716	+	8.75343i	0.115441	+	1.08573i
$66$		0			0
$67$	5.32418	+	1.42661i	0.650452	+	0.174288i	0.568933	−	0.822384i	$-0.307356\pi$
$67$	5.32418	+	1.42661i	0.650452	+	0.174288i	0.0815189	+	0.996672i	$0.474023\pi$
$68$	−0.134694	−	0.502686i	−0.0163341	−	0.0609596i
$69$		0			0
$70$	−0.0276056	+	5.93818i	−0.00329950	+	0.709749i
$71$	7.23274			0.858369			0.429184	−	0.903217i	$-0.358801\pi$
$71$	7.23274			0.858369			0.429184	+	0.903217i	$0.358801\pi$
$72$		0			0
$73$	−14.8625	−	3.98240i	−1.73953	−	0.466105i	−0.757185	−	0.653201i	$-0.773426\pi$
$73$	−14.8625	−	3.98240i	−1.73953	−	0.466105i	−0.982342	+	0.187096i	$0.940092\pi$
$74$	−0.137513	+	0.0793931i	−0.0159855	+	0.00922926i
$75$		0			0
$76$		−	4.09280i		−	0.469476i
$77$	5.58969	−	7.59955i	0.637005	−	0.866049i
$78$		0			0
$79$	13.1146	+	7.57171i	1.47551	+	0.851884i	0.999618	−	0.0276214i	$-0.00879330\pi$
$79$	13.1146	+	7.57171i	1.47551	+	0.851884i	0.475888	+	0.879506i	$0.342127\pi$
$80$	0.827954	+	2.14913i	0.0925680	+	0.240280i
$81$		0			0
$82$	−8.03244	+	2.15229i	−0.887035	+	0.237680i
$83$	−9.42372	+	9.42372i	−1.03439	+	1.03439i	−0.0350007	+	0.999387i	$0.511143\pi$
$83$	−9.42372	+	9.42372i	−1.03439	+	1.03439i	−0.999387	+	0.0350007i	$0.988857\pi$
$84$		0			0
$85$	−0.690321	−	0.947735i	−0.0748758	−	0.102796i
$86$	6.39670	−	11.0794i	0.689774	−	1.19472i
$87$		0			0
$88$	2.77201	−	10.3453i	0.295497	−	1.10281i
$89$	−5.52672	+	9.57257i	−0.585831	+	1.01469i	0.408940	+	0.912561i	$0.365899\pi$
$89$	−5.52672	+	9.57257i	−0.585831	+	1.01469i	−0.994771	+	0.102128i	$0.967435\pi$
$90$		0			0
$91$	9.70175	+	3.78950i	1.01702	+	0.397247i
$92$	1.81222	−	1.81222i	0.188937	−	0.188937i
$93$		0			0
$94$	−2.69710	−	4.67152i	−0.278185	−	0.481830i
$95$	−3.31491	−	8.60455i	−0.340103	−	0.882808i
$96$		0			0
$97$	−2.48828	−	2.48828i	−0.252647	−	0.252647i	0.569408	−	0.822055i	$-0.307172\pi$
$97$	−2.48828	−	2.48828i	−0.252647	−	0.252647i	−0.822055	+	0.569408i	$0.807172\pi$
$98$	6.22262	+	3.26295i	0.628580	+	0.329608i
$99$		0			0
$100$	−3.32943	−	3.67979i	−0.332943	−	0.367979i
$101$	−0.739502	+	0.426952i	−0.0735832	+	0.0424833i	−0.536340	−	0.844002i	$-0.680194\pi$
$101$	−0.739502	+	0.426952i	−0.0735832	+	0.0424833i	0.462757	+	0.886485i	$0.346860\pi$
$102$		0			0
$103$	−1.57114	−	5.86357i	−0.154809	−	0.577755i	−0.999122	−	0.0419040i	$-0.986658\pi$
$103$	−1.57114	−	5.86357i	−0.154809	−	0.577755i	0.844313	−	0.535851i	$-0.180009\pi$
$104$	11.8247			1.15951
$105$		0			0
$106$	−5.76939			−0.560373
$107$	3.02740	+	11.2984i	0.292670	+	1.09226i	0.943051	+	0.332650i	$0.107943\pi$
$107$	3.02740	+	11.2984i	0.292670	+	1.09226i	−0.650381	+	0.759608i	$0.725391\pi$
$108$		0			0
$109$	−10.8565	+	6.26802i	−1.03987	+	0.600367i	−0.919796	−	0.392398i	$-0.871646\pi$
$109$	−10.8565	+	6.26802i	−1.03987	+	0.600367i	−0.120071	+	0.992765i	$0.538312\pi$
$110$	−0.846151	−	7.95809i	−0.0806773	−	0.758774i
$111$		0			0
$112$	2.70842	+	0.300715i	0.255922	+	0.0284149i
$113$	7.25767	+	7.25767i	0.682744	+	0.682744i	0.960618	−	0.277874i	$-0.0896296\pi$
$113$	7.25767	+	7.25767i	0.682744	+	0.682744i	−0.277874	+	0.960618i	$0.589630\pi$
$114$		0			0
$115$	2.34217	−	5.27774i	0.218408	−	0.492152i
$116$	3.04892	+	5.28088i	0.283085	+	0.490317i
$117$		0			0
$118$	1.84600	−	1.84600i	0.169938	−	0.169938i
$119$	−1.37148	+	0.208995i	−0.125724	+	0.0191585i
$120$		0			0
$121$	−0.856990	+	1.48435i	−0.0779082	+	0.134941i
$122$	2.60277	−	9.71367i	0.235644	−	0.879435i
$123$		0			0
$124$	−0.980846	+	1.69887i	−0.0880825	+	0.152563i
$125$	−9.98009	−	5.03963i	−0.892646	−	0.450758i
$126$		0			0
$127$	−1.06249	+	1.06249i	−0.0942804	+	0.0942804i	−0.752674	−	0.658393i	$-0.771236\pi$
$127$	−1.06249	+	1.06249i	−0.0942804	+	0.0942804i	0.658393	+	0.752674i	$0.271236\pi$
$128$	−2.77081	+	0.742437i	−0.244908	+	0.0656228i
$129$		0			0
$130$	8.24506	−	3.17642i	0.723139	−	0.278590i
$131$	−10.3808	−	5.99337i	−0.906976	−	0.523643i	−0.0275190	−	0.999621i	$-0.508761\pi$
$131$	−10.3808	−	5.99337i	−0.906976	−	0.523643i	−0.879457	+	0.475979i	$0.842094\pi$
$132$		0			0
$133$	−10.8438	−	1.20398i	−0.940277	−	0.104399i
$134$		−	5.53265i		−	0.477948i
$135$		0			0
$136$	−1.36400	+	0.787505i	−0.116962	+	0.0675280i
$137$	6.10553	+	1.63597i	0.521630	+	0.139770i	0.510021	−	0.860162i	$-0.329638\pi$
$137$	6.10553	+	1.63597i	0.521630	+	0.139770i	0.0116098	+	0.999933i	$0.496304\pi$
$138$		0			0
$139$	5.07872			0.430772			0.215386	−	0.976529i	$-0.430899\pi$
$139$	5.07872			0.430772			0.215386	+	0.976529i	$0.430899\pi$
$140$	−5.67859	+	1.49332i	−0.479929	+	0.126208i
$141$		0			0
$142$	−1.87899	−	7.01247i	−0.157681	−	0.588474i
$143$	−13.5587	−	3.63305i	−1.13384	−	0.303811i
$144$		0			0
$145$	10.6871	+	8.63290i	0.887517	+	0.716923i
$146$			15.4445i			1.27819i
$147$		0			0
$148$	−0.111020	−	0.111020i	−0.00912577	−	0.00912577i
$149$	−13.1991	−	7.62048i	−1.08131	−	0.624294i	−0.150060	−	0.988677i	$-0.547947\pi$
$149$	−13.1991	−	7.62048i	−1.08131	−	0.624294i	−0.931249	+	0.364383i	$0.881280\pi$
$150$		0			0
$151$	−7.46500	−	12.9298i	−0.607493	−	1.05221i	−0.991652	−	0.128942i	$-0.958842\pi$
$151$	−7.46500	−	12.9298i	−0.607493	−	1.05221i	0.384159	−	0.923267i	$-0.374491\pi$
$152$	−11.9645	+	3.20588i	−0.970449	+	0.260031i
$153$		0			0
$154$	−8.82025	−	3.44518i	−0.710756	−	0.277621i
$155$	−0.686113	+	4.36608i	−0.0551099	+	0.350692i
$156$		0			0
$157$	1.70656	−	6.36897i	0.136198	−	0.508299i	−0.863792	−	0.503849i	$-0.831917\pi$
$157$	1.70656	−	6.36897i	0.136198	−	0.508299i	0.999990	−	0.00445019i	$-0.00141654\pi$
$158$	3.93409	−	14.6822i	0.312980	−	1.16806i
$159$		0			0
$160$	−8.98937	+	6.54777i	−0.710672	+	0.517647i
$161$	−4.26836	−	5.33457i	−0.336394	−	0.420423i
$162$		0			0
$163$	−1.35039	+	0.361835i	−0.105770	+	0.0283411i	−0.311316	−	0.950306i	$-0.600770\pi$
$163$	−1.35039	+	0.361835i	−0.105770	+	0.0283411i	0.205546	+	0.978648i	$0.434103\pi$
$164$	−4.11127	−	7.12093i	−0.321036	−	0.556051i
$165$		0			0
$166$	11.5849	+	6.68855i	0.899163	+	0.519132i
$167$	4.18179	+	4.18179i	0.323597	+	0.323597i	0.850145	−	0.526548i	$-0.176514\pi$
$167$	4.18179	+	4.18179i	0.323597	+	0.323597i	−0.526548	+	0.850145i	$0.676514\pi$
$168$		0			0
$169$		−	2.49776i		−	0.192135i
$170$	−0.739535	+	0.915509i	−0.0567197	+	0.0702163i
$171$		0			0
$172$	12.2189	+	3.27405i	0.931683	+	0.249644i
$173$	0.619668	+	2.31263i	0.0471125	+	0.175826i	0.985473	−	0.169832i	$-0.0543224\pi$
$173$	0.619668	+	2.31263i	0.0471125	+	0.175826i	−0.938361	+	0.345658i	$0.887656\pi$
$174$		0			0
$175$	−10.7290	+	7.73880i	−0.811035	+	0.584998i
$176$	−3.67255			−0.276829
$177$		0			0
$178$	10.7168	+	2.87156i	0.803259	+	0.215233i
$179$	−1.63071	+	0.941493i	−0.121885	+	0.0703705i	−0.559703	−	0.828693i	$-0.689085\pi$
$179$	−1.63071	+	0.941493i	−0.121885	+	0.0703705i	0.437818	+	0.899064i	$0.355751\pi$
$180$		0			0
$181$		−	17.7439i		−	1.31889i	−0.751751	−	0.659447i	$-0.770791\pi$
$181$		−	17.7439i		−	1.31889i	0.751751	−	0.659447i	$-0.229209\pi$
$182$	1.15368	−	10.3908i	0.0855166	−	0.770214i
$183$		0			0
$184$	−6.71719	−	3.87817i	−0.495198	−	0.285903i
$185$	−0.323323	−	0.143485i	−0.0237712	−	0.0105492i
$186$		0			0
$187$	1.80597	−	0.483908i	0.132066	−	0.0353869i
$188$	3.77151	−	3.77151i	0.275066	−	0.275066i
$189$		0			0
$190$	−7.48133	+	5.44932i	−0.542752	+	0.395335i
$191$	5.37301	−	9.30633i	0.388778	−	0.673382i	−0.603508	−	0.797357i	$-0.706231\pi$
$191$	5.37301	−	9.30633i	0.388778	−	0.673382i	0.992285	+	0.123975i	$0.0395641\pi$
$192$		0			0
$193$	−0.833614	+	3.11109i	−0.0600049	+	0.223941i	−0.989416	−	0.145104i	$-0.953648\pi$
$193$	−0.833614	+	3.11109i	−0.0600049	+	0.223941i	0.929412	+	0.369045i	$0.120315\pi$
$194$	−1.76607	+	3.05893i	−0.126797	+	0.219618i
$195$		0			0
$196$	−1.52396	+	6.77824i	−0.108854	+	0.484160i
$197$	10.9317	−	10.9317i	0.778852	−	0.778852i	−0.200784	−	0.979636i	$-0.564349\pi$
$197$	10.9317	−	10.9317i	0.778852	−	0.778852i	0.979636	+	0.200784i	$0.0643489\pi$
$198$		0			0
$199$	−6.19974	−	10.7383i	−0.439488	−	0.761215i	0.558162	−	0.829732i	$-0.311507\pi$
$199$	−6.19974	−	10.7383i	−0.439488	−	0.761215i	−0.997650	+	0.0685166i	$0.978173\pi$
$200$	−8.14922	+	12.6153i	−0.576237	+	0.892038i
$201$		0			0
$202$	0.606063	+	0.606063i	0.0426425	+	0.0426425i
$203$	14.8885	−	6.52458i	1.04497	−	0.457935i
$204$		0			0
$205$	−14.4109	−	11.6409i	−1.00650	−	0.813037i
$206$	−5.27683	+	3.04658i	−0.367654	+	0.212265i
$207$		0			0
$208$	−1.04944	−	3.91657i	−0.0727657	−	0.271565i
$209$	14.7040			1.01709
$210$		0			0
$211$	−13.4216			−0.923982			−0.461991	−	0.886885i	$-0.652865\pi$
$211$	−13.4216			−0.923982			−0.461991	+	0.886885i	$0.652865\pi$
$212$	−1.47648	−	5.51031i	−0.101405	−	0.378450i
$213$		0			0
$214$	10.1678	−	5.87040i	0.695058	−	0.401292i
$215$	28.3404	−	3.01332i	1.93280	−	0.205506i
$216$		0			0
$217$	4.21261	+	3.09850i	0.285970	+	0.210340i
$218$	8.89753	+	8.89753i	0.602617	+	0.602617i
$219$		0			0
$220$	7.38419	−	2.84476i	0.497842	−	0.191794i
$221$	1.03212	+	1.78769i	0.0694280	+	0.120253i
$222$		0			0
$223$	1.60905	−	1.60905i	0.107750	−	0.107750i	−0.651176	−	0.758927i	$-0.725724\pi$
$223$	1.60905	−	1.60905i	0.107750	−	0.107750i	0.758927	+	0.651176i	$0.225724\pi$
$224$	1.98234	+	13.0087i	0.132451	+	0.869178i
$225$		0			0
$226$	5.15118	−	8.92210i	0.342651	−	0.593489i
$227$	−6.67262	+	24.9026i	−0.442878	+	1.65284i	0.278603	+	0.960407i	$0.410129\pi$
$227$	−6.67262	+	24.9026i	−0.442878	+	1.65284i	−0.721480	+	0.692435i	$0.756538\pi$
$228$		0			0
$229$	−0.669566	+	1.15972i	−0.0442462	+	0.0766366i	−0.887300	−	0.461192i	$-0.847422\pi$
$229$	−0.669566	+	1.15972i	−0.0442462	+	0.0766366i	0.843054	+	0.537829i	$0.180755\pi$
$230$	−5.72548	−	0.899738i	−0.377527	−	0.0593270i
$231$		0			0
$232$	13.0494	−	13.0494i	0.856736	−	0.856736i
$233$	−20.7283	+	5.55413i	−1.35796	+	0.363863i	−0.863065	−	0.505093i	$-0.831458\pi$
$233$	−20.7283	+	5.55413i	−1.35796	+	0.363863i	−0.494890	+	0.868956i	$0.664792\pi$
$234$		0			0
$235$	4.87440	−	10.9838i	0.317971	−	0.716502i
$236$	2.23552	+	1.29068i	0.145520	+	0.0840161i
$237$		0			0
$238$	0.558926	+	1.27542i	0.0362298	+	0.0826732i
$239$		−	12.8433i		−	0.830767i	−0.909646	−	0.415384i	$-0.863647\pi$
$239$		−	12.8433i		−	0.830767i	0.909646	−	0.415384i	$-0.136353\pi$
$240$		0			0
$241$	−22.0766	+	12.7459i	−1.42208	+	0.821036i	−0.996476	−	0.0838747i	$-0.973270\pi$
$241$	−22.0766	+	12.7459i	−1.42208	+	0.821036i	−0.425601	+	0.904911i	$0.639937\pi$
$242$	1.66178	+	0.445273i	0.106823	+	0.0286232i
$243$		0			0
$244$	9.94357			0.636572
$245$	2.28604	+	15.4846i	0.146050	+	0.989277i
$246$		0			0
$247$	4.20169	+	15.6809i	0.267347	+	0.997753i
$248$	5.73462	+	1.53659i	0.364149	+	0.0975734i
$249$		0			0
$250$	−2.29343	+	10.9854i	−0.145049	+	0.694777i
$251$		−	12.0858i		−	0.762849i	−0.924400	−	0.381425i	$-0.875434\pi$
$251$		−	12.0858i		−	0.762849i	0.924400	−	0.381425i	$-0.124566\pi$
$252$		0			0
$253$	6.51067	+	6.51067i	0.409322	+	0.409322i
$254$	1.30615	+	0.754106i	0.0819552	+	0.0473168i
$255$		0			0
$256$	8.49182	+	14.7083i	0.530739	+	0.919266i
$257$	−10.0104	+	2.68228i	−0.624431	+	0.167316i	−0.557141	−	0.830418i	$-0.688102\pi$
$257$	−10.0104	+	2.68228i	−0.624431	+	0.167316i	−0.0672896	+	0.997733i	$0.521435\pi$
$258$		0			0
$259$	−0.326804	+	0.261486i	−0.0203066	+	0.0162480i
$260$	5.14383	+	7.06191i	0.319007	+	0.437961i
$261$		0			0
$262$	−3.11402	+	11.6217i	−0.192385	+	0.717990i
$263$	2.05827	−	7.68155i	0.126918	−	0.473665i	−0.872983	−	0.487751i	$-0.837817\pi$
$263$	2.05827	−	7.68155i	0.126918	−	0.473665i	0.999901	+	0.0140863i	$0.00448397\pi$
$264$		0			0
$265$	−7.56712	−	10.3888i	−0.464844	−	0.638181i
$266$	1.64978	+	10.8263i	0.101155	+	0.663806i
$267$		0			0
$268$	5.28421	−	1.41590i	0.322784	−	0.0864898i
$269$	0.857638	+	1.48547i	0.0522911	+	0.0905709i	0.890986	−	0.454030i	$-0.150014\pi$
$269$	0.857638	+	1.48547i	0.0522911	+	0.0905709i	−0.838695	+	0.544601i	$0.816681\pi$
$270$		0			0
$271$	−10.0645	−	5.81076i	−0.611377	−	0.352979i	0.162127	−	0.986770i	$-0.448164\pi$
$271$	−10.0645	−	5.81076i	−0.611377	−	0.352979i	−0.773504	+	0.633791i	$0.781498\pi$
$272$	0.381890	+	0.381890i	0.0231555	+	0.0231555i
$273$		0			0
$274$		−	6.34459i		−	0.383291i
$275$	13.2202	−	11.9615i	0.797206	−	0.721303i
$276$		0			0
$277$	−8.83410	−	2.36709i	−0.530790	−	0.142225i	−0.0165369	−	0.999863i	$-0.505264\pi$
$277$	−8.83410	−	2.36709i	−0.530790	−	0.142225i	−0.514253	+	0.857639i	$0.671931\pi$
$278$	−1.31940	−	4.92405i	−0.0791321	−	0.295325i
$279$		0			0
$280$	8.81344	+	15.4305i	0.526704	+	0.922152i
$281$	−15.0644			−0.898669			−0.449334	−	0.893364i	$-0.648339\pi$
$281$	−15.0644			−0.898669			−0.449334	+	0.893364i	$0.648339\pi$
$282$		0			0
$283$	15.4679	+	4.14461i	0.919470	+	0.246371i	0.687359	−	0.726318i	$-0.258770\pi$
$283$	15.4679	+	4.14461i	0.919470	+	0.246371i	0.232111	+	0.972689i	$0.425437\pi$
$284$	6.21671	−	3.58922i	0.368894	−	0.212981i
$285$		0			0
$286$			14.0896i			0.833137i
$287$	−20.0762	+	8.79798i	−1.18506	+	0.519329i
$288$		0			0
$289$	14.4843	+	8.36253i	0.852019	+	0.491913i
$290$	5.59359	−	12.6044i	0.328467	−	0.740154i
$291$		0			0
$292$	−14.7509	+	3.95250i	−0.863233	+	0.231302i
$293$	−6.20477	+	6.20477i	−0.362487	+	0.362487i	−0.864728	−	0.502241i	$-0.832509\pi$
$293$	−6.20477	+	6.20477i	−0.362487	+	0.362487i	0.502241	+	0.864728i	$0.332509\pi$
$294$		0			0
$295$	5.74525	+	0.902845i	0.334502	+	0.0525657i
$296$	−0.237583	+	0.411506i	−0.0138092	+	0.0239183i
$297$		0			0
$298$	−3.95943	+	14.7768i	−0.229364	+	0.855997i
$299$	−5.08282	+	8.80370i	−0.293947	+	0.509131i
$300$		0			0
$301$	12.2690	−	31.4107i	0.707173	−	1.81048i
$302$	−10.5967	+	10.5967i	−0.609769	+	0.609769i
$303$		0			0
$304$	2.12369	+	3.67834i	0.121802	+	0.210967i
$305$	20.9050	−	8.05367i	1.19702	−	0.461152i
$306$		0			0
$307$	6.26397	+	6.26397i	0.357504	+	0.357504i	0.862892	−	0.505388i	$-0.168651\pi$
$307$	6.26397	+	6.26397i	0.357504	+	0.357504i	−0.505388	+	0.862892i	$0.668651\pi$
$308$	1.03322	−	9.30585i	0.0588735	−	0.530250i
$309$		0			0
$310$	4.41135	−	0.469041i	0.250548	−	0.0266397i
$311$	5.78463	−	3.33976i	0.328016	−	0.189380i	−0.326944	−	0.945044i	$-0.606019\pi$
$311$	5.78463	−	3.33976i	0.328016	−	0.189380i	0.654960	+	0.755664i	$0.272685\pi$
$312$		0			0
$313$	−0.480011	−	1.79143i	−0.0271318	−	0.101257i	0.951032	−	0.309092i	$-0.100025\pi$
$313$	−0.480011	−	1.79143i	−0.0271318	−	0.101257i	−0.978164	+	0.207835i	$0.933358\pi$
$314$	−6.61835			−0.373495
$315$		0			0
$316$	15.0297			0.845488
$317$	0.446453	+	1.66619i	0.0250753	+	0.0935824i	0.977329	−	0.211724i	$-0.0679078\pi$
$317$	0.446453	+	1.66619i	0.0250753	+	0.0935824i	−0.952254	+	0.305306i	$0.901241\pi$
$318$		0			0
$319$	−18.9723	+	10.9537i	−1.06224	+	0.613287i
$320$	12.2669	+	9.90901i	0.685740	+	0.553931i
$321$		0			0
$322$	−4.06323	+	5.52423i	−0.226435	+	0.307853i
$323$	−1.52899	−	1.52899i	−0.0850752	−	0.0850752i
$324$		0			0
$325$	16.5339	+	10.6805i	0.917136	+	0.592450i
$326$	0.701630	+	1.21526i	0.0388597	+	0.0673070i
$327$		0			0
$328$	−17.5963	+	17.5963i	−0.971594	+	0.971594i
$329$	−8.88309	−	11.1020i	−0.489741	−	0.612075i
$330$		0			0
$331$	−13.0089	+	22.5320i	−0.715032	+	1.23847i	0.247915	+	0.968782i	$0.420255\pi$
$331$	−13.0089	+	22.5320i	−0.715032	+	1.23847i	−0.962947	+	0.269690i	$0.913079\pi$
$332$	−3.42342	+	12.7764i	−0.187885	+	0.701196i
$333$		0			0
$334$	2.96806	−	5.14082i	0.162405	−	0.281293i
$335$	9.96254	−	7.25661i	0.544312	−	0.396471i
$336$		0			0
$337$	−14.7150	+	14.7150i	−0.801579	+	0.801579i	−0.983342	−	0.181763i	$-0.941820\pi$
$337$	−14.7150	+	14.7150i	−0.801579	+	0.801579i	0.181763	+	0.983342i	$0.441820\pi$
$338$	−2.42169	+	0.648890i	−0.131723	+	0.0352950i
$339$		0			0
$340$	−1.06366	−	0.472031i	−0.0576849	−	0.0255995i
$341$	−6.10345	−	3.52383i	−0.330520	−	0.190826i
$342$		0			0
$343$	17.5105	+	6.03166i	0.945480	+	0.325679i
$344$		−	38.2842i		−	2.06414i
$345$		0			0
$346$	2.08122	−	1.20159i	0.111887	−	0.0645980i
$347$	−12.3723	−	3.31515i	−0.664181	−	0.177967i	−0.0890489	−	0.996027i	$-0.528383\pi$
$347$	−12.3723	−	3.31515i	−0.664181	−	0.177967i	−0.575132	+	0.818060i	$0.695049\pi$
$348$		0			0
$349$	12.7510			0.682546			0.341273	−	0.939964i	$-0.389142\pi$
$349$	12.7510			0.682546			0.341273	+	0.939964i	$0.389142\pi$
$350$	10.2904	+	8.39178i	0.550044	+	0.448559i
$351$		0			0
$352$	−4.58992	−	17.1298i	−0.244644	−	0.913023i
$353$	16.6743	+	4.46786i	0.887483	+	0.237800i	0.673633	−	0.739066i	$-0.264733\pi$
$353$	16.6743	+	4.46786i	0.887483	+	0.237800i	0.213850	+	0.976866i	$0.431400\pi$
$354$		0			0
$355$	10.1627	−	12.5810i	0.539383	−	0.667730i
$356$			10.9705i			0.581433i
$357$		0			0
$358$	1.33646	+	1.33646i	0.0706342	+	0.0706342i
$359$	6.50719	+	3.75693i	0.343437	+	0.198283i	0.661791	−	0.749689i	$-0.269797\pi$
$359$	6.50719	+	3.75693i	0.343437	+	0.198283i	−0.318354	+	0.947972i	$0.603130\pi$
$360$		0			0
$361$	0.997305	+	1.72738i	0.0524897	+	0.0909149i
$362$	−17.2035	+	4.60967i	−0.904197	+	0.242279i
$363$		0			0
$364$	10.2194	−	1.55729i	0.535642	−	0.0816244i
$365$	−27.8105	+	20.2569i	−1.45567	+	1.06030i
$366$		0			0
$367$	−1.78295	+	6.65407i	−0.0930693	+	0.347340i	−0.996720	−	0.0809315i	$-0.974210\pi$
$367$	−1.78295	+	6.65407i	−0.0930693	+	0.347340i	0.903650	+	0.428271i	$0.140877\pi$
$368$	−0.688373	+	2.56904i	−0.0358839	+	0.133921i
$369$		0			0
$370$	−0.0551194	+	0.350752i	−0.00286552	+	0.0182347i
$371$	−15.0338	+	2.29095i	−0.780518	+	0.118940i
$372$		0			0
$373$	−6.50499	+	1.74301i	−0.336816	+	0.0902494i	−0.423263	−	0.906007i	$-0.639115\pi$
$373$	−6.50499	+	1.74301i	−0.336816	+	0.0902494i	0.0864472	+	0.996256i	$0.472449\pi$
$374$	−0.938342	−	1.62526i	−0.0485205	−	0.0840400i
$375$		0			0
$376$	−13.9795	−	8.07106i	−0.720937	−	0.416233i
$377$	−17.1028	−	17.1028i	−0.880840	−	0.880840i
$378$		0			0
$379$		−	37.6021i		−	1.93149i	−0.259496	−	0.965744i	$-0.583556\pi$
$379$		−	37.6021i		−	1.93149i	0.259496	−	0.965744i	$-0.416444\pi$
$380$	−7.11922	−	5.75080i	−0.365208	−	0.295010i
$381$		0			0
$382$	−10.4188	−	2.79170i	−0.533070	−	0.142836i
$383$	4.00163	+	14.9343i	0.204474	+	0.763106i	0.989609	+	0.143782i	$0.0459265\pi$
$383$	4.00163	+	14.9343i	0.204474	+	0.763106i	−0.785136	+	0.619324i	$0.787407\pi$
$384$		0			0
$385$	−5.36495	−	20.4011i	−0.273423	−	1.03974i
$386$	3.23291			0.164551
$387$		0			0
$388$	−3.37353	−	0.903935i	−0.171265	−	0.0458904i
$389$	−16.0657	+	9.27555i	−0.814565	+	0.470289i	−0.848539	−	0.529134i	$-0.822517\pi$
$389$	−16.0657	+	9.27555i	−0.814565	+	0.470289i	0.0339739	+	0.999423i	$0.489184\pi$
$390$		0			0
$391$		−	1.35402i		−	0.0684759i
$392$	21.0086	−	0.854385i	1.06109	−	0.0431530i
$393$		0			0
$394$	−13.4387	−	7.75885i	−0.677033	−	0.390885i
$395$	31.5980	−	12.1731i	1.58987	−	0.612497i
$396$		0			0
$397$	−4.39567	+	1.17781i	−0.220612	+	0.0591128i	−0.367432	−	0.930050i	$-0.619763\pi$
$397$	−4.39567	+	1.17781i	−0.220612	+	0.0591128i	0.146820	+	0.989163i	$0.453096\pi$
$398$	−8.80061	+	8.80061i	−0.441135	+	0.441135i
$399$		0			0
$400$	4.90166	+	1.57956i	0.245083	+	0.0789781i
$401$	−11.1701	+	19.3471i	−0.557806	+	0.966148i	0.439873	+	0.898060i	$0.355023\pi$
$401$	−11.1701	+	19.3471i	−0.557806	+	0.966148i	−0.997679	+	0.0680885i	$0.978310\pi$
$402$		0			0
$403$	2.01388	−	7.51592i	0.100319	−	0.374395i
$404$	−0.423746	+	0.733949i	−0.0210821	+	0.0365153i
$405$		0			0
$406$	−10.1937	−	12.7401i	−0.505907	−	0.632279i
$407$	0.398854	−	0.398854i	0.0197705	−	0.0197705i
$408$		0			0
$409$	3.04693	+	5.27744i	0.150661	+	0.260953i	0.931471	−	0.363816i	$-0.118526\pi$
$409$	3.04693	+	5.27744i	0.150661	+	0.260953i	−0.780810	+	0.624769i	$0.785193\pi$
$410$	−7.54261	+	16.9962i	−0.372503	+	0.839383i
$411$		0			0
$412$	−4.26020	−	4.26020i	−0.209885	−	0.209885i
$413$	4.07726	−	5.54331i	0.200629	−	0.272768i
$414$		0			0
$415$	3.15080	+	29.6334i	0.154667	+	1.45465i
$416$	16.9564	−	9.78978i	0.831356	−	0.479984i
$417$		0			0
$418$	−3.81992	−	14.2561i	−0.186839	−	0.697291i
$419$	23.3177			1.13914			0.569572	−	0.821942i	$-0.307109\pi$
$419$	23.3177			1.13914			0.569572	+	0.821942i	$0.307109\pi$
$420$		0			0
$421$	−0.0119079			−0.000580356			−0.000290178	−	1.00000i	$-0.500092\pi$
$421$	−0.0119079			−0.000580356			−0.000290178		1.00000i	$0.500092\pi$
$422$	3.48679	+	13.0129i	0.169734	+	0.633456i
$423$		0			0
$424$	−14.9518	+	8.63243i	−0.726124	+	0.419228i
$425$	−2.61851	−	0.130887i	−0.127016	−	0.00634894i
$426$		0			0
$427$	2.92511	−	26.3453i	0.141556	−	1.27494i
$428$	8.20890	+	8.20890i	0.396792	+	0.396792i
$429$		0			0
$430$	−10.2841	−	26.6945i	−0.495942	−	1.28732i
$431$	9.44866	+	16.3656i	0.455126	+	0.788301i	0.998695	−	0.0510628i	$-0.0162609\pi$
$431$	9.44866	+	16.3656i	0.455126	+	0.788301i	−0.543569	+	0.839364i	$0.682928\pi$
$432$		0			0
$433$	−18.7716	+	18.7716i	−0.902105	+	0.902105i	−0.995618	−	0.0935133i	$-0.970190\pi$
$433$	−18.7716	+	18.7716i	−0.902105	+	0.902105i	0.0935133	+	0.995618i	$0.470190\pi$
$434$	1.90974	−	4.88927i	0.0916707	−	0.234692i
$435$		0			0
$436$	−6.22096	+	10.7750i	−0.297930	+	0.516029i
$437$	2.75607	−	10.2858i	0.131840	−	0.492035i
$438$		0			0
$439$	3.40990	−	5.90612i	0.162746	−	0.281884i	−0.773107	−	0.634276i	$-0.781298\pi$
$439$	3.40990	−	5.90612i	0.162746	−	0.281884i	0.935852	+	0.352392i	$0.114632\pi$
$440$	−14.1001	−	19.3579i	−0.672197	−	0.922853i
$441$		0			0
$442$	1.46511	−	1.46511i	0.0696881	−	0.0696881i
$443$	6.66435	−	1.78571i	0.316633	−	0.0848415i	−0.0970026	−	0.995284i	$-0.530926\pi$
$443$	6.66435	−	1.78571i	0.316633	−	0.0848415i	0.413635	+	0.910443i	$0.364259\pi$
$444$		0			0
$445$	8.88539	+	23.0639i	0.421208	+	1.09333i
$446$	−1.97807	−	1.14204i	−0.0936641	−	0.0540770i
$447$		0			0
$448$	17.0893	−	7.48904i	0.807395	−	0.353824i
$449$		−	27.2653i		−	1.28673i	−0.765560	−	0.643365i	$-0.777538\pi$
$449$		−	27.2653i		−	1.28673i	0.765560	−	0.643365i	$-0.222462\pi$
$450$		0			0
$451$	25.5830	−	14.7703i	1.20465	−	0.695508i
$452$	9.83972	+	2.63655i	0.462822	+	0.124013i
$453$		0			0
$454$	25.8776			1.21450
$455$	20.2236	−	11.5511i	0.948097	−	0.541523i
$456$		0			0
$457$	−4.49326	−	16.7691i	−0.210186	−	0.784425i	−0.987806	−	0.155690i	$-0.950240\pi$
$457$	−4.49326	−	16.7691i	−0.210186	−	0.784425i	0.777620	−	0.628735i	$-0.216427\pi$
$458$	1.29835	+	0.347892i	0.0606679	+	0.0162559i
$459$		0			0
$460$	−0.605912	−	5.69863i	−0.0282508	−	0.265700i
$461$		−	41.8808i		−	1.95058i	−0.220920	−	0.975292i	$-0.570906\pi$
$461$		−	41.8808i		−	1.95058i	0.220920	−	0.975292i	$-0.429094\pi$
$462$		0			0
$463$	−15.4654	−	15.4654i	−0.718740	−	0.718740i	0.249607	−	0.968347i	$-0.419698\pi$
$463$	−15.4654	−	15.4654i	−0.718740	−	0.718740i	−0.968347	+	0.249607i	$0.919698\pi$
$464$	−5.48033	−	3.16407i	−0.254418	−	0.146888i
$465$		0			0
$466$	10.7700	+	18.6541i	0.498909	+	0.864135i
$467$	32.4120	−	8.68477i	1.49985	−	0.401883i	0.586800	−	0.809732i	$-0.300388\pi$
$467$	32.4120	−	8.68477i	1.49985	−	0.401883i	0.913049	+	0.407849i	$0.133721\pi$
$468$		0			0
$469$	−2.19694	−	14.4169i	−0.101445	−	0.665713i
$470$	−11.9156	−	1.87249i	−0.549625	−	0.0863715i
$471$		0			0
$472$	2.02197	−	7.54610i	0.0930688	−	0.347337i
$473$	−11.7625	+	43.8982i	−0.540839	+	2.01844i
$474$		0			0
$475$	−19.6250	−	6.32416i	−0.900456	−	0.290172i
$476$	−1.07511	+	0.860229i	−0.0492775	+	0.0394285i
$477$		0			0
$478$	−12.4522	+	3.33656i	−0.569551	+	0.152611i
$479$	−8.19191	−	14.1888i	−0.374298	−	0.648303i	0.615924	−	0.787806i	$-0.288783\pi$
$479$	−8.19191	−	14.1888i	−0.374298	−	0.648303i	−0.990222	+	0.139503i	$0.955450\pi$
$480$		0			0
$481$	0.539329	+	0.311381i	0.0245913	+	0.0141978i
$482$	18.0930	+	18.0930i	0.824113	+	0.824113i
$483$		0			0
$484$			1.70111i			0.0773232i
$485$	−7.82453	+	0.831950i	−0.355293	+	0.0377769i
$486$		0			0
$487$	4.22392	+	1.13179i	0.191404	+	0.0512865i	0.353248	−	0.935530i	$-0.385077\pi$
$487$	4.22392	+	1.13179i	0.191404	+	0.0512865i	−0.161844	+	0.986816i	$0.551744\pi$
$488$	−7.78877	−	29.0681i	−0.352581	−	1.31585i
$489$		0			0
$490$	14.4192	−	6.23915i	0.651392	−	0.281856i
$491$	−33.8633			−1.52823			−0.764116	−	0.645079i	$-0.776824\pi$
$491$	−33.8633			−1.52823			−0.764116	+	0.645079i	$0.776824\pi$
$492$		0			0
$493$	3.11185	+	0.833817i	0.140151	+	0.0375532i
$494$	14.1118	−	8.14746i	0.634920	−	0.366571i
$495$		0			0
$496$		−	2.03578i		−	0.0914093i
$497$	−7.68081	−	17.5269i	−0.344531	−	0.786190i
$498$		0			0
$499$	−15.2390	−	8.79824i	−0.682192	−	0.393864i	0.118489	−	0.992955i	$-0.462195\pi$
$499$	−15.2390	−	8.79824i	−0.682192	−	0.393864i	−0.800680	+	0.599092i	$0.795528\pi$
$500$	−11.0790	+	0.620899i	−0.495468	+	0.0277675i
$501$		0			0
$502$	−11.7177	+	3.13976i	−0.522988	+	0.140134i
$503$	−9.37063	+	9.37063i	−0.417816	+	0.417816i	−0.884450	−	0.466635i	$-0.845466\pi$
$503$	−9.37063	+	9.37063i	−0.417816	+	0.417816i	0.466635	+	0.884450i	$0.345466\pi$
$504$		0			0
$505$	−0.296415	+	1.88624i	−0.0131903	+	0.0839365i
$506$	4.62099	−	8.00379i	0.205428	−	0.355812i
$507$		0			0
$508$	−0.385977	+	1.44049i	−0.0171250	+	0.0639112i
$509$	13.8907	−	24.0594i	0.615695	−	1.06641i	−0.374567	−	0.927200i	$-0.622209\pi$
$509$	13.8907	−	24.0594i	0.615695	−	1.06641i	0.990262	−	0.139215i	$-0.0444580\pi$
$510$		0			0
$511$	6.13279	+	40.2451i	0.271299	+	1.78034i
$512$	7.99749	−	7.99749i	0.353442	−	0.353442i
$513$		0			0
$514$	5.20118	+	9.00870i	0.229414	+	0.397357i
$515$	−12.4070	−	5.50600i	−0.546718	−	0.242623i
$516$		0			0
$517$	13.5497	+	13.5497i	0.595914	+	0.595914i
$518$	0.338423	+	0.248920i	0.0148695	+	0.0109369i
$519$		0			0
$520$	16.6150	−	20.5685i	0.728615	−	0.901991i
$521$	−15.2942	+	8.83010i	−0.670050	+	0.386854i	−0.796096	−	0.605171i	$-0.793105\pi$
$521$	−15.2942	+	8.83010i	−0.670050	+	0.386854i	0.126045	+	0.992024i	$0.459772\pi$
$522$		0			0
$523$	1.08429	+	4.04661i	0.0474125	+	0.176946i	0.985572	−	0.169258i	$-0.0541371\pi$
$523$	1.08429	+	4.04661i	0.0474125	+	0.176946i	−0.938159	+	0.346204i	$0.887470\pi$
$524$	−11.8967			−0.519711
$525$		0			0
$526$	−7.98233			−0.348046
$527$	0.268242	+	1.00109i	0.0116848	+	0.0436082i
$528$		0			0
$529$	−14.1439	+	8.16597i	−0.614951	+	0.355042i
$530$	−8.10659	+	10.0356i	−0.352128	+	0.435917i
$531$		0			0
$532$	−9.91797	+	4.34634i	−0.429999	+	0.188438i
$533$	23.0621	+	23.0621i	0.998930	+	0.998930i
$534$		0			0
$535$	23.9068	+	10.6094i	1.03358	+	0.458685i
$536$	−8.27821	−	14.3383i	−0.357564	−	0.619319i
$537$		0			0
$538$	1.21743	−	1.21743i	0.0524871	−	0.0524871i
$539$	−24.3518	−	5.47503i	−1.04891	−	0.235826i
$540$		0			0
$541$	9.49606	−	16.4477i	0.408267	−	0.707140i	−0.586428	−	0.810001i	$-0.699466\pi$
$541$	9.49606	−	16.4477i	0.408267	−	0.707140i	0.994696	+	0.102861i	$0.0327998\pi$
$542$	−3.01914	+	11.2676i	−0.129683	+	0.483984i
$543$		0			0
$544$	−1.30396	+	2.25853i	−0.0559069	+	0.0968336i
$545$	−4.35163	+	27.6916i	−0.186403	+	1.18618i
$546$		0			0
$547$	−4.10986	+	4.10986i	−0.175725	+	0.175725i	−0.789489	−	0.613764i	$-0.789655\pi$
$547$	−4.10986	+	4.10986i	−0.175725	+	0.175725i	0.613764	+	0.789489i	$0.289655\pi$
$548$	6.05969	−	1.62369i	0.258857	−	0.0693605i
$549$		0			0
$550$	−15.0316	−	9.71010i	−0.640951	−	0.414040i
$551$	21.9418	+	12.6681i	0.934752	+	0.539680i
$552$		0			0
$553$	4.42131	−	39.8210i	0.188013	−	1.69336i
$554$			9.18001i			0.390021i
$555$		0			0
$556$	4.36528	−	2.52029i	0.185129	−	0.106884i
$557$	−27.2967	−	7.31412i	−1.15660	−	0.309909i	−0.370991	−	0.928637i	$-0.620982\pi$
$557$	−27.2967	−	7.31412i	−1.15660	−	0.309909i	−0.785606	+	0.618727i	$0.787649\pi$
$558$		0			0
$559$	−50.1760			−2.12222
$560$	4.32869	−	4.28863i	0.182920	−	0.181228i
$561$		0			0
$562$	3.91357	+	14.6057i	0.165084	+	0.616102i
$563$	−23.8998	−	6.40394i	−1.00726	−	0.269894i	−0.282775	−	0.959186i	$-0.591255\pi$
$563$	−23.8998	−	6.40394i	−1.00726	−	0.269894i	−0.724483	+	0.689292i	$0.757922\pi$
$564$		0			0
$565$	22.8221	−	2.42658i	0.960134	−	0.102087i
$566$		−	16.0735i		−	0.675621i
$567$		0			0
$568$	−15.3619	−	15.3619i	−0.644572	−	0.644572i
$569$	31.0893	+	17.9494i	1.30333	+	0.752479i	0.980974	−	0.194140i	$-0.0621914\pi$
$569$	31.0893	+	17.9494i	1.30333	+	0.752479i	0.322357	+	0.946618i	$0.395525\pi$
$570$		0			0
$571$	3.51101	+	6.08125i	0.146931	+	0.254492i	0.930092	−	0.367327i	$-0.119727\pi$
$571$	3.51101	+	6.08125i	0.146931	+	0.254492i	−0.783161	+	0.621820i	$0.786394\pi$
$572$	−13.4569	+	3.60577i	−0.562662	+	0.150765i
$573$		0			0
$574$	13.7456	+	17.1792i	0.573731	+	0.717046i
$575$	−5.88939	−	11.4899i	−0.245604	−	0.479160i
$576$		0			0
$577$	−6.47806	+	24.1765i	−0.269685	+	1.00648i	0.689635	+	0.724157i	$0.257771\pi$
$577$	−6.47806	+	24.1765i	−0.269685	+	1.00648i	−0.959320	+	0.282321i	$0.908896\pi$
$578$	4.34498	−	16.2157i	0.180727	−	0.674484i
$579$		0			0
$580$	13.4699	+	2.11674i	0.559305	+	0.0878927i
$581$	32.8438	+	12.8288i	1.36259	+	0.532227i
$582$		0			0
$583$	19.7966	−	5.30448i	0.819891	−	0.219689i
$584$	23.1087	+	40.0255i	0.956246	+	1.65627i
$585$		0			0
$586$	7.62774	+	4.40388i	0.315099	+	0.181923i
$587$	22.0509	+	22.0509i	0.910139	+	0.910139i	0.996283	−	0.0861436i	$-0.0274544\pi$
$587$	22.0509	+	22.0509i	0.910139	+	0.910139i	−0.0861436	+	0.996283i	$0.527454\pi$
$588$		0			0
$589$			8.15074i			0.335845i
$590$	−0.617204	−	5.80483i	−0.0254099	−	0.238981i
$591$		0			0
$592$	0.157384	+	0.0421708i	0.00646843	+	0.00173321i
$593$	−11.1621	−	41.6575i	−0.458372	−	1.71067i	−0.677981	−	0.735079i	$-0.737145\pi$
$593$	−11.1621	−	41.6575i	−0.458372	−	1.71067i	0.219609	−	0.975588i	$-0.429522\pi$
$594$		0			0
$595$	−1.56354	+	2.67928i	−0.0640988	+	0.109840i
$596$	−15.1265			−0.619607
$597$		0			0
$598$	9.85604	+	2.64092i	0.403043	+	0.107995i
$599$	−23.6940	+	13.6797i	−0.968111	+	0.558939i	−0.898660	−	0.438646i	$-0.855458\pi$
$599$	−23.6940	+	13.6797i	−0.968111	+	0.558939i	−0.0694514	+	0.997585i	$0.522125\pi$
$600$		0			0
$601$		−	7.61565i		−	0.310649i	−0.987864	−	0.155324i	$-0.950358\pi$
$601$		−	7.61565i		−	0.310649i	0.987864	−	0.155324i	$-0.0496423\pi$
$602$	−33.6414	−	3.73520i	−1.37112	−	0.152235i
$603$		0			0
$604$	−12.8327	−	7.40895i	−0.522154	−	0.301466i
$605$	1.37779	+	3.57636i	0.0560153	+	0.145400i
$606$		0			0
$607$	15.0249	−	4.02590i	0.609840	−	0.163406i	0.0593354	−	0.998238i	$-0.481102\pi$
$607$	15.0249	−	4.02590i	0.609840	−	0.163406i	0.550505	+	0.834832i	$0.314435\pi$
$608$	−14.5026	+	14.5026i	−0.588159	+	0.588159i
$609$		0			0
$610$	−13.2393	−	18.1761i	−0.536043	−	0.735929i
$611$	−10.5781	+	18.3218i	−0.427944	+	0.741221i
$612$		0			0
$613$	0.880848	−	3.28737i	0.0355771	−	0.132776i	−0.945853	−	0.324595i	$-0.894772\pi$
$613$	0.880848	−	3.28737i	0.0355771	−	0.132776i	0.981430	+	0.191819i	$0.0614387\pi$
$614$	4.44590	−	7.70052i	0.179422	−	0.310768i
$615$		0			0
$616$	−28.0132	+	4.26882i	−1.12868	+	0.171996i
$617$	19.3906	−	19.3906i	0.780637	−	0.780637i	−0.199301	−	0.979938i	$-0.563867\pi$
$617$	19.3906	−	19.3906i	0.780637	−	0.780637i	0.979938	+	0.199301i	$0.0638671\pi$
$618$		0			0
$619$	15.4314	+	26.7280i	0.620240	+	1.07429i	0.989441	+	0.144938i	$0.0462982\pi$
$619$	15.4314	+	26.7280i	0.620240	+	1.07429i	−0.369200	+	0.929350i	$0.620368\pi$
$620$	1.57692	+	4.09323i	0.0633306	+	0.164388i
$621$		0			0
$622$	−4.74083	−	4.74083i	−0.190090	−	0.190090i
$623$	29.0661	+	3.22719i	1.16451	+	0.129295i
$624$		0			0
$625$	−22.7892	+	10.2787i	−0.911569	+	0.411147i
$626$	−1.61217	+	0.930785i	−0.0644351	+	0.0372016i
$627$		0			0
$628$	−1.69375	−	6.32115i	−0.0675879	−	0.252241i
$629$	−0.0829496			−0.00330742
$630$		0			0
$631$	−19.0017			−0.756446			−0.378223	−	0.925714i	$-0.623465\pi$
$631$	−19.0017			−0.756446			−0.378223	+	0.925714i	$0.623465\pi$
$632$	−11.7727	−	43.9365i	−0.468295	−	1.74770i
$633$		0			0
$634$	1.49946	−	0.865713i	0.0595512	−	0.0343819i
$635$	0.355239	+	3.34104i	0.0140972	+	0.132585i
$636$		0			0
$637$	−1.11978	−	27.5343i	−0.0443671	−	1.09095i
$638$	15.5489	+	15.5489i	0.615585	+	0.615585i
$639$		0			0
$640$	−2.60185	+	5.86289i	−0.102847	+	0.231751i
$641$	−8.84861	−	15.3262i	−0.349499	−	0.605350i	0.636661	−	0.771143i	$-0.280315\pi$
$641$	−8.84861	−	15.3262i	−0.349499	−	0.605350i	−0.986161	+	0.165793i	$0.946982\pi$
$642$		0			0
$643$	−1.20751	+	1.20751i	−0.0476194	+	0.0476194i	−0.730516	−	0.682896i	$-0.760720\pi$
$643$	−1.20751	+	1.20751i	−0.0476194	+	0.0476194i	0.682896	+	0.730516i	$0.260720\pi$
$644$	−6.31601	−	2.46703i	−0.248886	−	0.0972145i
$645$		0			0
$646$	−1.08521	+	1.87964i	−0.0426970	+	0.0739534i
$647$	−0.977939	+	3.64972i	−0.0384468	+	0.143485i	−0.982481	−	0.186362i	$-0.940330\pi$
$647$	−0.977939	+	3.64972i	−0.0384468	+	0.143485i	0.944034	+	0.329847i	$0.106997\pi$
$648$		0			0
$649$	−4.63695	+	8.03143i	−0.182016	+	0.315261i
$650$	6.05994	−	18.8051i	0.237690	−	0.737595i
$651$		0			0
$652$	−0.981129	+	0.981129i	−0.0384240	+	0.0384240i
$653$	8.72296	−	2.33731i	0.341356	−	0.0914660i	−0.0840686	−	0.996460i	$-0.526791\pi$
$653$	8.72296	−	2.33731i	0.341356	−	0.0914660i	0.425424	+	0.904994i	$0.360125\pi$
$654$		0			0
$655$	−25.0113	+	9.63561i	−0.977271	+	0.376495i
$656$	7.38988	+	4.26655i	0.288526	+	0.166581i
$657$		0			0
$658$	−8.45619	+	11.4967i	−0.329657	+	0.448190i
$659$			40.3378i			1.57134i	0.618648	+	0.785668i	$0.287681\pi$
$659$			40.3378i			1.57134i	−0.618648	+	0.785668i	$0.712319\pi$
$660$		0			0
$661$	23.8392	−	13.7636i	0.927238	−	0.535341i	0.0413010	−	0.999147i	$-0.486850\pi$
$661$	23.8392	−	13.7636i	0.927238	−	0.535341i	0.885937	+	0.463806i	$0.153516\pi$
$662$	25.2254	+	6.75912i	0.980412	+	0.262701i
$663$		0			0
$664$	40.0308			1.55350
$665$	−17.3309	+	17.1705i	−0.672065	+	0.665845i
$666$		0			0
$667$	4.10624	+	15.3247i	0.158994	+	0.593375i
$668$	5.66955	+	1.51915i	0.219361	+	0.0587777i
$669$		0			0
$670$	−9.62377	−	7.77394i	−0.371799	−	0.300334i
$671$			35.7237i			1.37910i
$672$		0			0
$673$	22.5966	+	22.5966i	0.871035	+	0.871035i	0.992585	−	0.121550i	$-0.0387866\pi$
$673$	22.5966	+	22.5966i	0.871035	+	0.871035i	−0.121550	+	0.992585i	$0.538787\pi$
$674$	18.0897	+	10.4441i	0.696789	+	0.402291i
$675$		0			0
$676$	−1.23950	−	2.14688i	−0.0476732	−	0.0825723i
$677$	−8.93720	+	2.39472i	−0.343484	+	0.0920364i	−0.426437	−	0.904517i	$-0.640232\pi$
$677$	−8.93720	+	2.39472i	−0.343484	+	0.0920364i	0.0829529	+	0.996553i	$0.473565\pi$
$678$		0			0
$679$	−3.38736	+	8.67221i	−0.129995	+	0.332809i
$680$	−0.546733	+	3.47913i	−0.0209662	+	0.133419i
$681$		0			0
$682$	−1.83090	+	6.83302i	−0.0701089	+	0.261650i
$683$	−1.20450	+	4.49527i	−0.0460891	+	0.172007i	−0.985134	−	0.171788i	$-0.945046\pi$
$683$	−1.20450	+	4.49527i	−0.0460891	+	0.172007i	0.939045	+	0.343794i	$0.111712\pi$
$684$		0			0
$685$	11.4246	−	8.32155i	0.436511	−	0.317950i
$686$	1.29893	−	18.5442i	0.0495933	−	0.708022i
$687$		0			0
$688$	−12.6804	+	3.39770i	−0.483436	+	0.129536i
$689$	11.3138	+	19.5961i	0.431023	+	0.746554i
$690$		0			0
$691$	−6.52332	−	3.76624i	−0.248159	−	0.143275i	0.370762	−	0.928728i	$-0.379097\pi$
$691$	−6.52332	−	3.76624i	−0.248159	−	0.143275i	−0.618921	+	0.785453i	$0.712430\pi$
$692$	1.68025	+	1.68025i	0.0638736	+	0.0638736i
$693$		0			0
$694$			12.8568i			0.488036i
$695$	7.13613	−	8.83418i	0.270689	−	0.335100i
$696$		0			0
$697$	−4.19613	−	1.12435i	−0.158940	−	0.0425878i
$698$	−3.31257	−	12.3627i	−0.125383	−	0.467934i
$699$		0			0
$700$	−5.38146	+	11.9759i	−0.203400	+	0.452646i
$701$	45.2736			1.70996			0.854981	−	0.518660i	$-0.173569\pi$
$701$	45.2736			1.70996			0.854981	+	0.518660i	$0.173569\pi$
$702$		0			0
$703$	−0.630123	−	0.168841i	−0.0237655	−	0.00636796i
$704$	−21.7768	+	12.5728i	−0.820744	+	0.473857i
$705$		0			0
$706$		−	17.3272i		−	0.652117i
$707$	1.81993	+	1.33862i	0.0684457	+	0.0503438i
$708$		0			0
$709$	27.8909	+	16.1028i	1.04747	+	0.604754i	0.921939	−	0.387336i	$-0.126605\pi$
$709$	27.8909	+	16.1028i	1.04747	+	0.604754i	0.125527	+	0.992090i	$0.459938\pi$
$710$	−14.8380	−	6.58484i	−0.556861	−	0.247125i
$711$		0			0
$712$	32.0700	−	8.59313i	1.20187	−	0.322041i
$713$	−3.60902	+	3.60902i	−0.135159	+	0.135159i
$714$		0			0
$715$	−25.3709	+	18.4799i	−0.948818	+	0.691110i
$716$	−0.934424	+	1.61847i	−0.0349211	+	0.0604851i
$717$		0			0
$718$	1.95202	−	7.28503i	0.0728486	−	0.271875i
$719$	−14.8623	+	25.7422i	−0.554270	+	0.960023i	0.443690	+	0.896180i	$0.353669\pi$
$719$	−14.8623	+	25.7422i	−0.554270	+	0.960023i	−0.997960	+	0.0638430i	$0.979664\pi$
$720$		0			0
$721$	−12.5406	+	10.0341i	−0.467036	+	0.373690i
$722$	1.41569	−	1.41569i	0.0526864	−	0.0526864i
$723$		0			0
$724$	−8.80534	−	15.2513i	−0.327248	−	0.566810i
$725$	30.0330	−	6.45959i	1.11540	−	0.239903i
$726$		0			0
$727$	8.03461	+	8.03461i	0.297987	+	0.297987i	0.840225	−	0.542238i	$-0.182423\pi$
$727$	8.03461	+	8.03461i	0.297987	+	0.297987i	−0.542238	+	0.840225i	$0.682423\pi$
$728$	−12.5573	−	28.6546i	−0.465404	−	1.06201i
$729$		0			0
$730$	26.8649	+	21.7011i	0.994314	+	0.803192i
$731$	5.78787	−	3.34163i	0.214072	−	0.123595i
$732$		0			0
$733$	7.77556	+	29.0188i	0.287197	+	1.07183i	0.947219	+	0.320587i	$0.103880\pi$
$733$	7.77556	+	29.0188i	0.287197	+	1.07183i	−0.660022	+	0.751246i	$0.729453\pi$
$734$	6.91461			0.255223
$735$		0			0
$736$	−12.8431			−0.473401
$737$	5.08682	+	18.9843i	0.187375	+	0.699294i
$738$		0			0
$739$	35.8813	−	20.7161i	1.31992	−	0.762054i	0.336202	−	0.941790i	$-0.390858\pi$
$739$	35.8813	−	20.7161i	1.31992	−	0.762054i	0.983715	+	0.179736i	$0.0575243\pi$
$740$	−0.349107	+	0.0371192i	−0.0128334	+	0.00136453i
$741$		0			0
$742$	6.12680	+	13.9808i	0.224922	+	0.513252i
$743$	−10.5103	−	10.5103i	−0.385585	−	0.385585i	0.487525	−	0.873109i	$-0.337900\pi$
$743$	−10.5103	−	10.5103i	−0.385585	−	0.385585i	−0.873109	+	0.487525i	$0.837900\pi$
$744$		0			0
$745$	−31.8015	+	12.2515i	−1.16512	+	0.448862i
$746$	3.37985	+	5.85407i	0.123745	+	0.214333i
$747$		0			0
$748$	1.31214	−	1.31214i	0.0479764	−	0.0479764i
$749$	24.1642	−	19.3346i	0.882941	−	0.706469i
$750$		0			0
$751$	21.0235	−	36.4138i	0.767159	−	1.32876i	−0.171938	−	0.985108i	$-0.555003\pi$
$751$	21.0235	−	36.4138i	0.767159	−	1.32876i	0.939097	−	0.343651i	$-0.111664\pi$
$752$	−1.43261	+	5.34656i	−0.0522418	+	0.194969i
$753$		0			0
$754$	−12.1388	+	21.0251i	−0.442071	+	0.765689i
$755$	−32.9798	−	5.18264i	−1.20026	−	0.188616i
$756$		0			0
$757$	12.0838	−	12.0838i	0.439193	−	0.439193i	−0.452547	−	0.891740i	$-0.649485\pi$
$757$	12.0838	−	12.0838i	0.439193	−	0.439193i	0.891740	+	0.452547i	$0.149485\pi$
$758$	−36.4569	+	9.76860i	−1.32417	+	0.354811i
$759$		0			0
$760$	−11.2349	+	25.3162i	−0.407532	+	0.918316i
$761$	12.6620	+	7.31041i	0.458997	+	0.265002i	0.711623	−	0.702562i	$-0.247961\pi$
$761$	12.6620	+	7.31041i	0.458997	+	0.265002i	−0.252625	+	0.967564i	$0.581294\pi$
$762$		0			0
$763$	26.7182	+	19.6520i	0.967264	+	0.711451i
$764$		−	10.6653i		−	0.385858i
$765$		0			0
$766$	13.4399	−	7.75952i	0.485603	−	0.280363i
$767$	−9.89008	−	2.65004i	−0.357110	−	0.0956874i
$768$		0			0
$769$	−5.95109			−0.214602			−0.107301	−	0.994227i	$-0.534221\pi$
$769$	−5.95109			−0.214602			−0.107301	+	0.994227i	$0.534221\pi$
$770$	−18.3861	+	10.5015i	−0.662588	+	0.378450i
$771$		0			0
$772$	0.827355	+	3.08773i	0.0297772	+	0.111130i
$773$	−4.58677	−	1.22902i	−0.164975	−	0.0442049i	0.175386	−	0.984500i	$-0.443883\pi$
$773$	−4.58677	−	1.22902i	−0.164975	−	0.0442049i	−0.340361	+	0.940295i	$0.610549\pi$
$774$		0			0
$775$	6.63052	+	7.32825i	0.238175	+	0.263238i
$776$			10.5699i			0.379438i
$777$		0			0
$778$	13.1668	+	13.1668i	0.472051	+	0.472051i
$779$	−29.5872	−	17.0822i	−1.06007	−	0.612032i
$780$		0			0
$781$	12.8948	+	22.3344i	0.461411	+	0.799188i
$782$	−1.31279	+	0.351760i	−0.0469452	+	0.0125789i
$783$		0			0
$784$	−2.14749	−	6.88259i	−0.0766961	−	0.245807i
$785$	−8.68061	−	11.9175i	−0.309824	−	0.425355i
$786$		0			0
$787$	4.26300	−	15.9097i	0.151959	−	0.567120i	−0.847387	−	0.530976i	$-0.821826\pi$
$787$	4.26300	−	15.9097i	0.151959	−	0.567120i	0.999347	−	0.0361447i	$-0.0115077\pi$
$788$	3.97124	−	14.8209i	0.141470	−	0.527971i
$789$		0			0
$790$	−20.0112	−	27.4732i	−0.711967	−	0.977453i
$791$	9.88005	−	25.2946i	0.351294	−	0.899373i
$792$		0			0
$793$	−38.0972	+	10.2081i	−1.35287	+	0.362501i
$794$	2.28389	+	3.95581i	0.0810522	+	0.140387i
$795$		0			0
$796$	−10.6576	−	6.15319i	−0.377750	−	0.218094i
$797$	33.5483	+	33.5483i	1.18834	+	1.18834i	0.977525	+	0.210818i	$0.0676127\pi$
$797$	33.5483	+	33.5483i	1.18834	+	1.18834i	0.210818	+	0.977525i	$0.432387\pi$
$798$		0			0
$799$		−	2.81792i		−	0.0996910i
$800$	−1.24147	+	24.8369i	−0.0438927	+	0.878116i
$801$		0			0
$802$	21.6598	+	5.80371i	0.764832	+	0.204936i
$803$	−14.1999	−	52.9948i	−0.501104	−	1.87015i
$804$		0			0
$805$	−15.2767	−	0.0710187i	−0.538433	−	0.00250308i
$806$	−7.81021			−0.275103
$807$		0			0
$808$	2.47748	+	0.663838i	0.0871573	+	0.0233537i
$809$	−5.58195	+	3.22274i	−0.196251	+	0.113306i	−0.594906	−	0.803796i	$-0.702811\pi$
$809$	−5.58195	+	3.22274i	−0.196251	+	0.113306i	0.398655	+	0.917101i	$0.369477\pi$
$810$		0			0
$811$			0.116404i			0.00408751i	0.999998	+	0.00204375i	$0.000650547\pi$
$811$			0.116404i			0.00408751i	−0.999998	+	0.00204375i	$0.999349\pi$
$812$	9.55922	−	12.9964i	0.335463	−	0.456084i
$813$		0			0
$814$	−0.490325	−	0.283089i	−0.0171859	−	0.00992227i
$815$	−1.26804	+	2.85734i	−0.0444174	+	0.100088i
$816$		0			0
$817$	50.7690	−	13.6035i	1.77618	−	0.475927i
$818$	4.32516	−	4.32516i	0.151226	−	0.151226i
$819$		0			0
$820$	−18.1633	−	2.85429i	−0.634289	−	0.0996761i
$821$	−0.698986	+	1.21068i	−0.0243948	+	0.0422530i	−0.877965	−	0.478725i	$-0.841099\pi$
$821$	−0.698986	+	1.21068i	−0.0243948	+	0.0422530i	0.853570	+	0.520978i	$0.174433\pi$
$822$		0			0
$823$	−4.22216	+	15.7573i	−0.147175	+	0.549265i	0.852474	+	0.522770i	$0.175101\pi$
$823$	−4.22216	+	15.7573i	−0.147175	+	0.549265i	−0.999649	+	0.0264952i	$0.991565\pi$
$824$	−9.11687	+	15.7909i	−0.317601	+	0.550101i
$825$		0			0
$826$	−6.43371	−	2.51300i	−0.223858	−	0.0874386i
$827$	29.7712	−	29.7712i	1.03524	−	1.03524i	0.0358886	−	0.999356i	$-0.488574\pi$
$827$	29.7712	−	29.7712i	1.03524	−	1.03524i	0.999356	−	0.0358886i	$-0.0114262\pi$
$828$		0			0
$829$	−3.31772	−	5.74647i	−0.115229	−	0.199583i	0.802642	−	0.596461i	$-0.203427\pi$
$829$	−3.31772	−	5.74647i	−0.115229	−	0.199583i	−0.917871	+	0.396878i	$0.870094\pi$
$830$	27.9124	−	10.7533i	0.968853	−	0.373251i
$831$		0			0
$832$	−19.6310	−	19.6310i	−0.680582	−	0.680582i
$833$	1.96290	+	3.10154i	0.0680104	+	0.107462i
$834$		0			0
$835$	13.1499	−	1.39817i	0.455070	−	0.0483857i
$836$	12.6384	−	7.29677i	0.437108	−	0.252364i
$837$		0			0
$838$	−6.05768	−	22.6076i	−0.209259	−	0.780965i
$839$	−18.1682			−0.627234			−0.313617	−	0.949550i	$-0.601541\pi$
$839$	−18.1682			−0.627234			−0.313617	+	0.949550i	$0.601541\pi$
$840$		0			0
$841$	−8.74827			−0.301664
$842$	0.00309354	+	0.0115453i	0.000106610	+	0.000397876i
$843$		0			0
$844$	−11.5362	+	6.66042i	−0.397092	+	0.229261i
$845$	−4.34473	−	3.50961i	−0.149463	−	0.120734i
$846$		0			0
$847$	4.50707	+	0.500418i	0.154865	+	0.0171946i
$848$	4.18618	+	4.18618i	0.143754	+	0.143754i
$849$		0			0
$850$	0.553359	+	2.57277i	0.0189801	+	0.0882452i
$851$	−0.204248	−	0.353768i	−0.00700154	−	0.0121270i
$852$		0			0
$853$	34.0703	−	34.0703i	1.16654	−	1.16654i	0.183530	−	0.983014i	$-0.441248\pi$
$853$	34.0703	−	34.0703i	1.16654	−	1.16654i	0.983014	−	0.183530i	$-0.0587523\pi$
$854$	−26.3029	+	4.00820i	−0.900067	+	0.137158i
$855$		0			0
$856$	17.5671	−	30.4271i	0.600432	−	1.03998i
$857$	9.53874	−	35.5991i	0.325837	−	1.21604i	−0.587631	−	0.809129i	$-0.699939\pi$
$857$	9.53874	−	35.5991i	0.325837	−	1.21604i	0.913468	−	0.406911i	$-0.133394\pi$
$858$		0			0
$859$	−6.11471	+	10.5910i	−0.208631	+	0.361360i	−0.951284	−	0.308317i	$-0.900234\pi$
$859$	−6.11471	+	10.5910i	−0.208631	+	0.361360i	0.742652	+	0.669677i	$0.233567\pi$
$860$	22.8639	−	16.6538i	0.779651	−	0.567890i
$861$		0			0
$862$	13.4125	−	13.4125i	0.456831	−	0.456831i
$863$	40.1292	−	10.7526i	1.36601	−	0.366022i	0.499993	−	0.866030i	$-0.333336\pi$
$863$	40.1292	−	10.7526i	1.36601	−	0.366022i	0.866021	+	0.500007i	$0.166669\pi$
$864$		0			0
$865$	4.89340	+	2.17160i	0.166381	+	0.0738367i
$866$	23.0765	+	13.3233i	0.784173	+	0.452743i
$867$		0			0
$868$	5.15845	+	0.572740i	0.175089	+	0.0194401i
$869$			53.9964i			1.83170i
$870$		0			0
$871$	−18.7920	+	10.8496i	−0.636744	+	0.367624i
$872$	36.3715	+	9.74572i	1.23169	+	0.330032i
$873$		0			0
$874$	−10.6885			−0.361545
$875$	−1.61406	+	29.5363i	−0.0545653	+	0.998510i
$876$		0			0
$877$	0.648098	+	2.41873i	0.0218847	+	0.0816748i	0.976005	−	0.217750i	$-0.0698718\pi$
$877$	0.648098	+	2.41873i	0.0218847	+	0.0816748i	−0.954120	+	0.299425i	$0.903205\pi$
$878$	−6.61211	−	1.77171i	−0.223148	−	0.0597923i
$879$		0			0
$880$	−5.16032	+	6.38823i	−0.173954	+	0.215347i
$881$		−	48.7030i		−	1.64084i	−0.571758	−	0.820422i	$-0.693738\pi$
$881$		−	48.7030i		−	1.64084i	0.571758	−	0.820422i	$-0.306262\pi$
$882$		0			0
$883$	−5.87749	−	5.87749i	−0.197793	−	0.197793i	0.601260	−	0.799053i	$-0.294666\pi$
$883$	−5.87749	−	5.87749i	−0.197793	−	0.197793i	−0.799053	+	0.601260i	$0.794666\pi$
$884$	1.77426	+	1.02437i	0.0596749	+	0.0344533i
$885$		0			0
$886$	−3.46265	−	5.99748i	−0.116330	−	0.201489i
$887$	−9.36397	+	2.50907i	−0.314411	+	0.0842463i	−0.412574	−	0.910924i	$-0.635370\pi$
$887$	−9.36397	+	2.50907i	−0.314411	+	0.0842463i	0.0981626	+	0.995170i	$0.468703\pi$
$888$		0			0
$889$	3.70300	+	1.44639i	0.124195	+	0.0485104i
$890$	20.0532	−	14.6065i	0.672184	−	0.489612i
$891$		0			0
$892$	0.584533	−	2.18151i	0.0195716	−	0.0730422i
$893$	5.73578	−	21.4062i	0.191941	−	0.716332i
$894$		0			0
$895$	−0.653640	+	4.15944i	−0.0218488	+	0.139035i
$896$	4.74159	+	5.92601i	0.158406	+	0.197974i
$897$		0			0
$898$	−26.4350	+	7.08322i	−0.882146	+	0.236370i
$899$	−6.07187	−	10.5168i	−0.202508	−	0.350754i
$900$		0			0
$901$	−2.61013	−	1.50696i	−0.0869561	−	0.0502041i
$902$	−20.9667	−	20.9667i	−0.698114	−	0.698114i
$903$		0			0
$904$		−	30.8297i		−	1.02538i
$905$	−30.8646	−	24.9320i	−1.02598	−	0.828768i
$906$		0			0
$907$	−31.8869	−	8.54407i	−1.05879	−	0.283701i	−0.312909	−	0.949783i	$-0.601303\pi$
$907$	−31.8869	−	8.54407i	−1.05879	−	0.283701i	−0.745878	+	0.666082i	$0.767970\pi$
$908$	6.62252	+	24.7156i	0.219776	+	0.820216i
$909$		0			0
$910$	−16.4532	−	16.6069i	−0.545417	−	0.550512i
$911$	−33.1445			−1.09813			−0.549064	−	0.835781i	$-0.685016\pi$
$911$	−33.1445			−1.09813			−0.549064	+	0.835781i	$0.685016\pi$
$912$		0			0
$913$	−45.9010	−	12.2991i	−1.51910	−	0.407042i
$914$	−15.0911	+	8.71284i	−0.499169	+	0.288195i
$915$		0			0
$916$			1.32908i			0.0439140i
$917$	−3.49968	+	31.5202i	−0.115570	+	1.04089i
$918$		0			0
$919$	−27.8600	−	16.0850i	−0.919015	−	0.530594i	−0.0356945	−	0.999363i	$-0.511364\pi$
$919$	−27.8600	−	16.0850i	−0.919015	−	0.530594i	−0.883321	+	0.468769i	$0.844698\pi$
$920$	−16.1842	+	6.23499i	−0.533578	+	0.205562i
$921$		0			0
$922$	−40.6053	+	10.8802i	−1.33727	+	0.358319i
$923$	−20.1336	+	20.1336i	−0.662707	+	0.662707i
$924$		0			0
$925$	−0.703887	+	0.360793i	−0.0231437	+	0.0118628i
$926$	−10.9767	+	19.0122i	−0.360716	+	0.624779i
$927$		0			0
$928$	7.90885	−	29.5162i	0.259621	−	0.968918i
$929$	−20.2533	+	35.0798i	−0.664490	+	1.15093i	0.314934	+	0.949114i	$0.398018\pi$
$929$	−20.2533	+	35.0798i	−0.664490	+	1.15093i	−0.979423	+	0.201816i	$0.935316\pi$
$930$		0			0
$931$	8.59799	+	27.5561i	0.281788	+	0.903115i
$932$	−15.0602	+	15.0602i	−0.493314	+	0.493314i
$933$		0			0
$934$	−16.8406	−	29.1687i	−0.551040	−	0.954429i
$935$	1.69584	−	3.82134i	0.0554599	−	0.124971i
$936$		0			0
$937$	10.0291	+	10.0291i	0.327637	+	0.327637i	0.851687	−	0.524050i	$-0.175580\pi$
$937$	10.0291	+	10.0291i	0.327637	+	0.327637i	−0.524050	+	0.851687i	$0.675580\pi$
$938$	−13.4071	+	5.87540i	−0.437759	+	0.191838i
$939$		0			0
$940$	−1.26099	−	11.8597i	−0.0411291	−	0.386821i
$941$	32.3581	−	18.6820i	1.05485	−	0.609015i	0.130843	−	0.991403i	$-0.458232\pi$
$941$	32.3581	−	18.6820i	1.05485	−	0.609015i	0.924002	+	0.382388i	$0.124898\pi$
$942$		0			0
$943$	−5.53701	−	20.6644i	−0.180310	−	0.672926i
$944$	−2.67885			−0.0871893
$945$		0			0
$946$	45.6170			1.48314
$947$	−0.500489	−	1.86785i	−0.0162637	−	0.0606970i	0.957317	−	0.289040i	$-0.0933360\pi$
$947$	−0.500489	−	1.86785i	−0.0162637	−	0.0606970i	−0.973581	+	0.228343i	$0.926669\pi$
$948$		0			0
$949$	52.4582	−	30.2868i	1.70287	−	0.983150i
$950$	−1.03321	+	20.6703i	−0.0335216	+	0.670631i
$951$		0			0
$952$	3.35684	+	2.46905i	0.108796	+	0.0800225i
$953$	−14.5970	−	14.5970i	−0.472845	−	0.472845i	0.429989	−	0.902834i	$-0.358517\pi$
$953$	−14.5970	−	14.5970i	−0.472845	−	0.472845i	−0.902834	+	0.429989i	$0.858517\pi$
$954$		0			0
$955$	−8.63826	−	22.4224i	−0.279528	−	0.725573i
$956$	−6.37346	−	11.0392i	−0.206132	−	0.357032i
$957$		0			0
$958$	−11.6285	+	11.6285i	−0.375700	+	0.375700i
$959$	−2.51935	−	16.5327i	−0.0813541	−	0.533869i
$960$		0			0
$961$	−13.5467	+	23.4635i	−0.436989	+	0.756887i
$962$	0.161787	−	0.603797i	0.00521622	−	0.0194672i
$963$		0			0
$964$	−12.6502	+	21.9108i	−0.407436	+	0.705700i
$965$	4.24027	+	5.82143i	0.136499	+	0.187399i
$966$		0			0
$967$	34.5723	−	34.5723i	1.11177	−	1.11177i	0.118858	−	0.992911i	$-0.462077\pi$
$967$	34.5723	−	34.5723i	1.11177	−	1.11177i	0.992911	−	0.118858i	$-0.0379234\pi$
$968$	4.97287	−	1.33248i	0.159834	−	0.0428274i
$969$		0			0
$970$	2.83934	+	7.37010i	0.0911656	+	0.236640i
$971$	2.45937	+	1.41992i	0.0789251	+	0.0455674i	0.538943	−	0.842342i	$-0.318824\pi$
$971$	2.45937	+	1.41992i	0.0789251	+	0.0455674i	−0.460018	+	0.887910i	$0.652157\pi$
$972$		0			0
$973$	−5.39334	−	12.3071i	−0.172903	−	0.394549i
$974$		−	4.38930i		−	0.140642i
$975$		0			0
$976$	−8.93662	+	5.15956i	−0.286054	+	0.165154i
$977$	−36.0763	−	9.66661i	−1.15418	−	0.309262i	−0.369543	−	0.929214i	$-0.620486\pi$
$977$	−36.0763	−	9.66661i	−1.15418	−	0.309262i	−0.784640	+	0.619951i	$0.787152\pi$
$978$		0			0
$979$	−39.4129			−1.25964
$980$	9.64909	+	12.1750i	0.308229	+	0.388915i
$981$		0			0
$982$	8.79732	+	32.8320i	0.280734	+	1.04771i
$983$	−30.9698	−	8.29834i	−0.987784	−	0.264676i	−0.271465	−	0.962448i	$-0.587508\pi$
$983$	−30.9698	−	8.29834i	−0.987784	−	0.264676i	−0.716320	+	0.697772i	$0.754175\pi$
$984$		0			0
$985$	−3.65499	−	34.3753i	−0.116458	−	1.09529i
$986$		−	3.23369i		−	0.102982i
$987$		0			0
$988$	11.3930	+	11.3930i	0.362461	+	0.362461i
$989$	28.5031	+	16.4563i	0.906346	+	0.523279i
$990$		0			0
$991$	−20.9999	−	36.3729i	−0.667084	−	1.15542i	−0.978716	−	0.205221i	$-0.934209\pi$
$991$	−20.9999	−	36.3729i	−0.667084	−	1.15542i	0.311632	−	0.950203i	$-0.399125\pi$
$992$	9.49546	−	2.54430i	0.301481	−	0.0807817i
$993$		0			0
$994$	−14.9978	+	12.0002i	−0.475700	+	0.380623i
$995$	−27.3899	−	4.30423i	−0.868320	−	0.136453i
$996$		0			0
$997$	5.68114	−	21.2023i	0.179924	−	0.671484i	−0.815737	−	0.578423i	$-0.803668\pi$
$997$	5.68114	−	21.2023i	0.179924	−	0.671484i	0.995660	−	0.0930609i	$-0.0296651\pi$
$998$	−4.57137	+	17.0606i	−0.144704	+	0.540044i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bz.d.208.3		32
3.2	odd	2		105.2.u.a.103.6	yes	32
5.2	odd	4	inner	315.2.bz.d.82.6		32
7.3	odd	6	inner	315.2.bz.d.73.6		32
15.2	even	4		105.2.u.a.82.3	yes	32
15.8	even	4		525.2.bc.e.82.6		32
15.14	odd	2		525.2.bc.e.418.3		32
21.2	odd	6		735.2.m.c.538.11		32
21.5	even	6		735.2.m.c.538.12		32
21.11	odd	6		735.2.v.b.178.3		32
21.17	even	6		105.2.u.a.73.3	yes	32
21.20	even	2		735.2.v.b.313.6		32
35.17	even	12	inner	315.2.bz.d.262.3		32
105.2	even	12		735.2.m.c.97.12		32
105.17	odd	12		105.2.u.a.52.6	✓	32
105.32	even	12		735.2.v.b.472.6		32
105.38	odd	12		525.2.bc.e.157.3		32
105.47	odd	12		735.2.m.c.97.11		32
105.59	even	6		525.2.bc.e.493.6		32
105.62	odd	4		735.2.v.b.607.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.u.a.52.6	✓	32	105.17	odd	12
105.2.u.a.73.3	yes	32	21.17	even	6
105.2.u.a.82.3	yes	32	15.2	even	4
105.2.u.a.103.6	yes	32	3.2	odd	2
315.2.bz.d.73.6		32	7.3	odd	6	inner
315.2.bz.d.82.6		32	5.2	odd	4	inner
315.2.bz.d.208.3		32	1.1	even	1	trivial
315.2.bz.d.262.3		32	35.17	even	12	inner
525.2.bc.e.82.6		32	15.8	even	4
525.2.bc.e.157.3		32	105.38	odd	12
525.2.bc.e.418.3		32	15.14	odd	2
525.2.bc.e.493.6		32	105.59	even	6
735.2.m.c.97.11		32	105.47	odd	12
735.2.m.c.97.12		32	105.2	even	12
735.2.m.c.538.11		32	21.2	odd	6
735.2.m.c.538.12		32	21.5	even	6
735.2.v.b.178.3		32	21.11	odd	6
735.2.v.b.313.6		32	21.20	even	2
735.2.v.b.472.6		32	105.32	even	12
735.2.v.b.607.3		32	105.62	odd	4

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bz (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.259789 - 0.969545i) q^{2} +(0.859523 - 0.496246i) q^{4} +(1.40510 - 1.73945i) q^{5} +(-1.06195 - 2.42328i) q^{7} +(-2.12394 - 2.12394i) q^{8} +O(q^{10})\)	\(q+(-0.259789 - 0.969545i) q^{2} +(0.859523 - 0.496246i) q^{4} +(1.40510 - 1.73945i) q^{5} +(-1.06195 - 2.42328i) q^{7} +(-2.12394 - 2.12394i) q^{8} +(-2.05151 - 0.910421i) q^{10} +(1.78283 + 3.08796i) q^{11} +(-2.78368 + 2.78368i) q^{13} +(-2.07359 + 1.65915i) q^{14} +(-0.514988 + 0.891986i) q^{16} +(0.135713 - 0.506489i) q^{17} +(2.06188 - 3.57128i) q^{19} +(0.344523 - 2.19237i) q^{20} +(2.53075 - 2.53075i) q^{22} +(2.49427 - 0.668338i) q^{23} +(-1.05137 - 4.88821i) q^{25} +(3.42207 + 1.97574i) q^{26} +(-2.11531 - 1.55587i) q^{28} +6.14396i q^{29} +(-1.71173 + 0.988266i) q^{31} +(-4.80410 - 1.28726i) q^{32} -0.526321 q^{34} +(-5.70731 - 1.55774i) q^{35} +(-0.0409435 - 0.152803i) q^{37} +(-3.99817 - 1.07131i) q^{38} +(-6.67884 + 0.710134i) q^{40} -8.28475i q^{41} +(9.01253 + 9.01253i) q^{43} +(3.06477 + 1.76945i) q^{44} +(-1.29597 - 2.24468i) q^{46} +(5.19095 - 1.39091i) q^{47} +(-4.74453 + 5.14679i) q^{49} +(-4.46621 + 2.28926i) q^{50} +(-1.01125 + 3.77403i) q^{52} +(1.48765 - 5.55200i) q^{53} +(7.87641 + 1.23775i) q^{55} +(-2.89138 + 7.40241i) q^{56} +(5.95685 - 1.59613i) q^{58} +(1.30044 + 2.25243i) q^{59} +(8.67653 + 5.00940i) q^{61} +(1.40286 + 1.40286i) q^{62} +7.05216i q^{64} +(0.930716 + 8.75343i) q^{65} +(5.32418 + 1.42661i) q^{67} +(-0.134694 - 0.502686i) q^{68} +(-0.0276056 + 5.93818i) q^{70} +7.23274 q^{71} +(-14.8625 - 3.98240i) q^{73} +(-0.137513 + 0.0793931i) q^{74} -4.09280i q^{76} +(5.58969 - 7.59955i) q^{77} +(13.1146 + 7.57171i) q^{79} +(0.827954 + 2.14913i) q^{80} +(-8.03244 + 2.15229i) q^{82} +(-9.42372 + 9.42372i) q^{83} +(-0.690321 - 0.947735i) q^{85} +(6.39670 - 11.0794i) q^{86} +(2.77201 - 10.3453i) q^{88} +(-5.52672 + 9.57257i) q^{89} +(9.70175 + 3.78950i) q^{91} +(1.81222 - 1.81222i) q^{92} +(-2.69710 - 4.67152i) q^{94} +(-3.31491 - 8.60455i) q^{95} +(-2.48828 - 2.48828i) q^{97} +(6.22262 + 3.26295i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 12 q^{5} + 8 q^{7} + 24 q^{8}+O(q^{10}) \) 32 * q + 12 * q^5 + 8 * q^7 + 24 * q^8	\( 32 q + 12 q^{5} + 8 q^{7} + 24 q^{8} - 12 q^{10} + 8 q^{11} - 8 q^{22} + 8 q^{23} + 12 q^{25} - 24 q^{26} - 24 q^{28} + 24 q^{31} - 24 q^{32} - 44 q^{35} + 4 q^{37} - 12 q^{38} + 12 q^{40} + 40 q^{43} - 40 q^{46} + 60 q^{47} - 72 q^{50} - 108 q^{52} + 24 q^{53} + 48 q^{56} + 4 q^{58} - 24 q^{61} + 4 q^{65} + 8 q^{67} - 132 q^{68} + 4 q^{70} + 16 q^{71} + 36 q^{73} - 60 q^{77} + 12 q^{80} + 12 q^{82} - 72 q^{85} + 16 q^{86} - 32 q^{88} - 24 q^{91} + 56 q^{92} + 12 q^{95} + 72 q^{98}+O(q^{100}) \) 32 * q + 12 * q^5 + 8 * q^7 + 24 * q^8 - 12 * q^10 + 8 * q^11 - 8 * q^22 + 8 * q^23 + 12 * q^25 - 24 * q^26 - 24 * q^28 + 24 * q^31 - 24 * q^32 - 44 * q^35 + 4 * q^37 - 12 * q^38 + 12 * q^40 + 40 * q^43 - 40 * q^46 + 60 * q^47 - 72 * q^50 - 108 * q^52 + 24 * q^53 + 48 * q^56 + 4 * q^58 - 24 * q^61 + 4 * q^65 + 8 * q^67 - 132 * q^68 + 4 * q^70 + 16 * q^71 + 36 * q^73 - 60 * q^77 + 12 * q^80 + 12 * q^82 - 72 * q^85 + 16 * q^86 - 32 * q^88 - 24 * q^91 + 56 * q^92 + 12 * q^95 + 72 * q^98

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