LMFDB - Embedded newform 936.2.ed.d.379.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [936,2,Mod(19,936)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(936, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 6, 0, 5]))

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

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

chi := DirichletCharacter("936.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.ed (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:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			379.8
Character	$\chi$	$=$	936.379
Dual form			936.2.ed.d.163.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.829865 + 1.14513i) q^{2} +(-0.622649 + 1.90061i) q^{4} +(1.40823 + 1.40823i) q^{5} +(1.02175 + 3.81323i) q^{7} +(-2.69316 + 0.864233i) q^{8} +O(q^{10})$	\(q+(0.829865 + 1.14513i) q^{2} +(-0.622649 + 1.90061i) q^{4} +(1.40823 + 1.40823i) q^{5} +(1.02175 + 3.81323i) q^{7} +(-2.69316 + 0.864233i) q^{8} +(-0.443968 + 2.78126i) q^{10} +(-0.756644 + 2.82384i) q^{11} +(2.47643 - 2.62055i) q^{13} +(-3.51873 + 4.33450i) q^{14} +(-3.22462 - 2.36682i) q^{16} +(-0.373696 - 0.215754i) q^{17} +(-0.960219 - 3.58359i) q^{19} +(-3.55334 + 1.79966i) q^{20} +(-3.86157 + 1.47694i) q^{22} +(0.264259 + 0.457711i) q^{23} -1.03375i q^{25} +(5.05598 + 0.661127i) q^{26} +(-7.88364 - 0.432354i) q^{28} +(1.96425 - 1.13406i) q^{29} +(0.525538 + 0.525538i) q^{31} +(0.0343246 - 5.65675i) q^{32} +(-0.0630513 - 0.606978i) q^{34} +(-3.93105 + 6.80878i) q^{35} +(-4.50702 - 1.20765i) q^{37} +(3.30682 - 4.07347i) q^{38} +(-5.00964 - 2.57556i) q^{40} +(1.02295 + 0.274098i) q^{41} +(5.78795 + 3.34168i) q^{43} +(-4.89588 - 3.19634i) q^{44} +(-0.304839 + 0.682450i) q^{46} +(-3.10880 + 3.10880i) q^{47} +(-7.43454 + 4.29233i) q^{49} +(1.18378 - 0.857876i) q^{50} +(3.43870 + 6.33840i) q^{52} +5.89363i q^{53} +(-5.04215 + 2.91109i) q^{55} +(-6.04725 - 9.38659i) q^{56} +(2.92871 + 1.30821i) q^{58} +(5.50874 - 1.47606i) q^{59} +(4.67379 + 2.69841i) q^{61} +(-0.165684 + 1.03793i) q^{62} +(6.50620 - 4.65503i) q^{64} +(7.17774 - 0.202965i) q^{65} +(1.76688 + 0.473433i) q^{67} +(0.642745 - 0.575911i) q^{68} +(-11.0592 + 1.14880i) q^{70} +(-4.80671 + 1.28795i) q^{71} +(-8.61849 - 8.61849i) q^{73} +(-2.35730 - 6.16332i) q^{74} +(7.40887 + 0.406316i) q^{76} -11.5410 q^{77} +17.5395i q^{79} +(-1.20798 - 7.87405i) q^{80} +(0.535030 + 1.39887i) q^{82} +(9.64657 - 9.64657i) q^{83} +(-0.222420 - 0.830084i) q^{85} +(0.976562 + 9.40110i) q^{86} +(-0.402688 - 8.25895i) q^{88} +(2.41190 - 9.00133i) q^{89} +(12.5231 + 6.76562i) q^{91} +(-1.03447 + 0.217260i) q^{92} +(-6.13986 - 0.980098i) q^{94} +(3.69432 - 6.39874i) q^{95} +(0.871452 + 3.25230i) q^{97} +(-11.0849 - 4.95147i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{2} - 6 q^{4} + 10 q^{8}+O(q^{10}) $ 48 * q + 4 * q^2 - 6 * q^4 + 10 * q^8	$ 48 q + 4 q^{2} - 6 q^{4} + 10 q^{8} - 6 q^{10} + 8 q^{11} - 8 q^{14} - 10 q^{16} + 12 q^{17} - 8 q^{19} - 10 q^{20} - 20 q^{22} + 2 q^{26} + 12 q^{28} - 16 q^{32} - 46 q^{34} + 4 q^{35} - 32 q^{40} - 12 q^{43} + 16 q^{44} + 34 q^{46} - 60 q^{49} - 86 q^{50} + 12 q^{52} - 48 q^{56} + 30 q^{58} + 64 q^{59} - 42 q^{62} + 16 q^{65} - 8 q^{67} + 32 q^{68} + 36 q^{70} - 12 q^{73} - 38 q^{74} - 94 q^{76} + 108 q^{80} + 54 q^{82} + 48 q^{83} - 80 q^{86} - 108 q^{88} - 12 q^{89} + 104 q^{91} + 20 q^{92} + 26 q^{94} + 4 q^{97} + 16 q^{98}+O(q^{100}) $ 48 * q + 4 * q^2 - 6 * q^4 + 10 * q^8 - 6 * q^10 + 8 * q^11 - 8 * q^14 - 10 * q^16 + 12 * q^17 - 8 * q^19 - 10 * q^20 - 20 * q^22 + 2 * q^26 + 12 * q^28 - 16 * q^32 - 46 * q^34 + 4 * q^35 - 32 * q^40 - 12 * q^43 + 16 * q^44 + 34 * q^46 - 60 * q^49 - 86 * q^50 + 12 * q^52 - 48 * q^56 + 30 * q^58 + 64 * q^59 - 42 * q^62 + 16 * q^65 - 8 * q^67 + 32 * q^68 + 36 * q^70 - 12 * q^73 - 38 * q^74 - 94 * q^76 + 108 * q^80 + 54 * q^82 + 48 * q^83 - 80 * q^86 - 108 * q^88 - 12 * q^89 + 104 * q^91 + 20 * q^92 + 26 * q^94 + 4 * q^97 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$1$	$-1$	$-1$

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 $

$2$	0.829865	+	1.14513i	0.586803	+	0.809730i
$2$	0.829865	+	1.14513i	0.586803	+	0.809730i
$3$		0			0
$3$		0			0
$4$	−0.622649	+	1.90061i	−0.311324	+	0.950304i
$5$	1.40823	+	1.40823i	0.629781	+	0.629781i	0.948013	−	0.318232i	$-0.103089\pi$
$5$	1.40823	+	1.40823i	0.629781	+	0.629781i	−0.318232	+	0.948013i	$0.603089\pi$
$6$		0			0
$7$	1.02175	+	3.81323i	0.386186	+	1.44126i	0.836290	+	0.548288i	$0.184720\pi$
$7$	1.02175	+	3.81323i	0.386186	+	1.44126i	−0.450104	+	0.892976i	$0.648613\pi$
$8$	−2.69316	+	0.864233i	−0.952175	+	0.305552i
$9$		0			0
$10$	−0.443968	+	2.78126i	−0.140395	+	0.879510i
$11$	−0.756644	+	2.82384i	−0.228137	+	0.851418i	0.752987	+	0.658036i	$0.228612\pi$
$11$	−0.756644	+	2.82384i	−0.228137	+	0.851418i	−0.981123	+	0.193382i	$0.938054\pi$
$12$		0			0
$13$	2.47643	−	2.62055i	0.686837	−	0.726811i
$13$	2.47643	−	2.62055i	0.686837	−	0.726811i
$14$	−3.51873	+	4.33450i	−0.940419	+	1.15844i
$15$		0			0
$16$	−3.22462	−	2.36682i	−0.806154	−	0.591705i
$17$	−0.373696	−	0.215754i	−0.0906347	−	0.0523280i	0.453998	−	0.891003i	$-0.349997\pi$
$17$	−0.373696	−	0.215754i	−0.0906347	−	0.0523280i	−0.544632	+	0.838675i	$0.683331\pi$
$18$		0			0
$19$	−0.960219	−	3.58359i	−0.220289	−	0.822131i	−0.984237	−	0.176853i	$-0.943408\pi$
$19$	−0.960219	−	3.58359i	−0.220289	−	0.822131i	0.763948	−	0.645278i	$-0.223258\pi$
$20$	−3.55334	+	1.79966i	−0.794550	+	0.402417i
$21$		0			0
$22$	−3.86157	+	1.47694i	−0.823290	+	0.314886i
$23$	0.264259	+	0.457711i	0.0551019	+	0.0954393i	0.892261	−	0.451521i	$-0.149118\pi$
$23$	0.264259	+	0.457711i	0.0551019	+	0.0954393i	−0.837159	+	0.546960i	$0.815785\pi$
$24$		0			0
$25$		−	1.03375i		−	0.206751i
$26$	5.05598	+	0.661127i	0.991559	+	0.129658i
$27$		0			0
$28$	−7.88364	−	0.432354i	−1.48987	−	0.0817072i
$29$	1.96425	−	1.13406i	0.364752	−	0.210590i	−0.306411	−	0.951899i	$-0.599128\pi$
$29$	1.96425	−	1.13406i	0.364752	−	0.210590i	0.671163	+	0.741310i	$0.265795\pi$
$30$		0			0
$31$	0.525538	+	0.525538i	0.0943894	+	0.0943894i	0.752725	−	0.658335i	$-0.228739\pi$
$31$	0.525538	+	0.525538i	0.0943894	+	0.0943894i	−0.658335	+	0.752725i	$0.728739\pi$
$32$	0.0343246	−	5.65675i	0.00606778	−	0.999982i
$33$		0			0
$34$	−0.0630513	−	0.606978i	−0.0108132	−	0.104096i
$35$	−3.93105	+	6.80878i	−0.664469	+	1.15089i
$36$		0			0
$37$	−4.50702	−	1.20765i	−0.740950	−	0.198537i	−0.131450	−	0.991323i	$-0.541963\pi$
$37$	−4.50702	−	1.20765i	−0.740950	−	0.198537i	−0.609500	+	0.792786i	$0.708630\pi$
$38$	3.30682	−	4.07347i	0.536437	−	0.660804i
$39$		0			0
$40$	−5.00964	−	2.57556i	−0.792094	−	0.407231i
$41$	1.02295	+	0.274098i	0.159757	+	0.0428069i	0.337811	−	0.941214i	$-0.390313\pi$
$41$	1.02295	+	0.274098i	0.159757	+	0.0428069i	−0.178054	+	0.984021i	$0.556980\pi$
$42$		0			0
$43$	5.78795	+	3.34168i	0.882654	+	0.509601i	0.871533	−	0.490337i	$-0.163126\pi$
$43$	5.78795	+	3.34168i	0.882654	+	0.509601i	0.0111217	+	0.999938i	$0.496460\pi$
$44$	−4.89588	−	3.19634i	−0.738081	−	0.481867i
$45$		0			0
$46$	−0.304839	+	0.682450i	−0.0449461	+	0.100622i
$47$	−3.10880	+	3.10880i	−0.453465	+	0.453465i	−0.896503	−	0.443038i	$-0.853901\pi$
$47$	−3.10880	+	3.10880i	−0.453465	+	0.453465i	0.443038	+	0.896503i	$0.353901\pi$
$48$		0			0
$49$	−7.43454	+	4.29233i	−1.06208	+	0.613191i
$50$	1.18378	−	0.857876i	0.167412	−	0.121322i
$51$		0			0
$52$	3.43870	+	6.33840i	0.476862	+	0.878978i
$53$			5.89363i			0.809552i	0.914416	+	0.404776i	$0.132650\pi$
$53$			5.89363i			0.809552i	−0.914416	+	0.404776i	$0.867350\pi$
$54$		0			0
$55$	−5.04215	+	2.91109i	−0.679884	+	0.392531i
$56$	−6.04725	−	9.38659i	−0.808098	−	1.25434i
$57$		0			0
$58$	2.92871	+	1.30821i	0.384558	+	0.171776i
$59$	5.50874	−	1.47606i	0.717176	−	0.192167i	0.118265	−	0.992982i	$-0.462267\pi$
$59$	5.50874	−	1.47606i	0.717176	−	0.192167i	0.598911	+	0.800815i	$0.295600\pi$
$60$		0			0
$61$	4.67379	+	2.69841i	0.598417	+	0.345496i	0.768419	−	0.639948i	$-0.221044\pi$
$61$	4.67379	+	2.69841i	0.598417	+	0.345496i	−0.170002	+	0.985444i	$0.554377\pi$
$62$	−0.165684	+	1.03793i	−0.0210419	+	0.131818i
$63$		0			0
$64$	6.50620	−	4.65503i	0.813275	−	0.581879i
$65$	7.17774	−	0.202965i	0.890290	−	0.0251747i
$66$		0			0
$67$	1.76688	+	0.473433i	0.215858	+	0.0578391i	0.365127	−	0.930958i	$-0.381025\pi$
$67$	1.76688	+	0.473433i	0.215858	+	0.0578391i	−0.149269	+	0.988797i	$0.547692\pi$
$68$	0.642745	−	0.575911i	0.0779443	−	0.0698395i
$69$		0			0
$70$	−11.0592	+	1.14880i	−1.32183	+	0.137308i
$71$	−4.80671	+	1.28795i	−0.570452	+	0.152852i	−0.532504	−	0.846428i	$-0.678749\pi$
$71$	−4.80671	+	1.28795i	−0.570452	+	0.152852i	−0.0379481	+	0.999280i	$0.512082\pi$
$72$		0			0
$73$	−8.61849	−	8.61849i	−1.00872	−	1.00872i	−0.999962	−	0.00875645i	$-0.997213\pi$
$73$	−8.61849	−	8.61849i	−1.00872	−	1.00872i	−0.00875645	−	0.999962i	$-0.502787\pi$
$74$	−2.35730	−	6.16332i	−0.274031	−	0.716472i
$75$		0			0
$76$	7.40887	+	0.406316i	0.849856	+	0.0466077i
$77$	−11.5410			−1.31522
$78$		0			0
$79$			17.5395i			1.97334i	0.162727	+	0.986671i	$0.447971\pi$
$79$			17.5395i			1.97334i	−0.162727	+	0.986671i	$0.552029\pi$
$80$	−1.20798	−	7.87405i	−0.135056	−	0.880346i
$81$		0			0
$82$	0.535030	+	1.39887i	0.0590841	+	0.154480i
$83$	9.64657	−	9.64657i	1.05885	−	1.05885i	0.0606926	−	0.998157i	$-0.480669\pi$
$83$	9.64657	−	9.64657i	1.05885	−	1.05885i	0.998157	−	0.0606926i	$-0.0193309\pi$
$84$		0			0
$85$	−0.222420	−	0.830084i	−0.0241249	−	0.0900352i
$86$	0.976562	+	9.40110i	0.105305	+	1.01375i
$87$		0			0
$88$	−0.402688	−	8.25895i	−0.0429267	−	0.880407i
$89$	2.41190	−	9.00133i	0.255661	−	0.954139i	−0.712061	−	0.702118i	$-0.752238\pi$
$89$	2.41190	−	9.00133i	0.255661	−	0.954139i	0.967722	−	0.252022i	$-0.0810954\pi$
$90$		0			0
$91$	12.5231	+	6.76562i	1.31277	+	0.709230i
$92$	−1.03447	+	0.217260i	−0.107851	+	0.0226510i
$93$		0			0
$94$	−6.13986	−	0.980098i	−0.633278	−	0.101089i
$95$	3.69432	−	6.39874i	0.379029	−	0.656497i
$96$		0			0
$97$	0.871452	+	3.25230i	0.0884825	+	0.330221i	0.995951	−	0.0898992i	$-0.0286545\pi$
$97$	0.871452	+	3.25230i	0.0884825	+	0.330221i	−0.907468	+	0.420120i	$0.861988\pi$
$98$	−11.0849	−	4.95147i	−1.11975	−	0.500173i
$99$		0			0
$100$	1.96476	+	0.643665i	0.196476	+	0.0643665i
$101$	0.895975	+	1.55187i	0.0891529	+	0.154417i	0.907153	−	0.420800i	$-0.138251\pi$
$101$	0.895975	+	1.55187i	0.0891529	+	0.154417i	−0.818000	+	0.575218i	$0.804917\pi$
$102$		0			0
$103$	6.26322			0.617133			0.308567	−	0.951203i	$-0.400151\pi$
$103$	6.26322			0.617133			0.308567	+	0.951203i	$0.400151\pi$
$104$	−4.40464	+	9.19778i	−0.431911	+	0.901916i
$105$		0			0
$106$	−6.74897	+	4.89091i	−0.655518	+	0.475047i
$107$	3.81015	+	6.59937i	0.368341	+	0.637985i	0.989306	−	0.145853i	$-0.0465926\pi$
$107$	3.81015	+	6.59937i	0.368341	+	0.637985i	−0.620965	+	0.783838i	$0.713259\pi$
$108$		0			0
$109$	−12.4705	−	12.4705i	−1.19445	−	1.19445i	−0.975803	−	0.218650i	$-0.929835\pi$
$109$	−12.4705	−	12.4705i	−1.19445	−	1.19445i	−0.218650	−	0.975803i	$-0.570165\pi$
$110$	−7.51788	−	3.35811i	−0.716802	−	0.320184i
$111$		0			0
$112$	5.73047	−	14.7145i	0.541479	−	1.39039i
$113$	−5.82301	+	10.0857i	−0.547783	+	0.948787i	0.450643	+	0.892704i	$0.351195\pi$
$113$	−5.82301	+	10.0857i	−0.547783	+	0.948787i	−0.998426	+	0.0560833i	$0.982139\pi$
$114$		0			0
$115$	−0.272425	+	1.01670i	−0.0254037	+	0.0948080i
$116$	0.932365	+	4.43939i	0.0865679	+	0.412187i
$117$		0			0
$118$	6.26179	+	5.08329i	0.576444	+	0.467955i
$119$	0.440893	−	1.64544i	0.0404166	−	0.150837i
$120$		0			0
$121$	2.12474	+	1.22672i	0.193159	+	0.111520i
$122$	0.788576	+	7.59141i	0.0713943	+	0.687294i
$123$		0			0
$124$	−1.32607	+	0.671615i	−0.119084	+	0.0603128i
$125$	8.49694	−	8.49694i	0.759989	−	0.759989i
$126$		0			0
$127$	−9.77681	−	16.9339i	−0.867552	−	1.50264i	−0.864491	−	0.502648i	$-0.832359\pi$
$127$	−9.77681	−	16.9339i	−0.867552	−	1.50264i	−0.00306091	−	0.999995i	$-0.500974\pi$
$128$	10.7299	+	3.58741i	0.948397	+	0.317085i
$129$		0			0
$130$	6.18898	+	8.05102i	0.542809	+	0.706121i
$131$	16.1468			1.41075			0.705375	−	0.708834i	$-0.250778\pi$
$131$	16.1468			1.41075			0.705375	+	0.708834i	$0.250778\pi$
$132$		0			0
$133$	12.6839	−	7.32306i	1.09984	−	0.634990i
$134$	0.924126	+	2.41619i	0.0798323	+	0.208727i
$135$		0			0
$136$	1.19289	+	0.258098i	0.102289	+	0.0221317i
$137$	12.8147	−	3.43369i	1.09483	−	0.293360i	0.334175	−	0.942511i	$-0.391542\pi$
$137$	12.8147	−	3.43369i	1.09483	−	0.293360i	0.760660	+	0.649151i	$0.224876\pi$
$138$		0			0
$139$	−6.07441	+	10.5212i	−0.515225	+	0.892396i	0.484619	+	0.874725i	$0.338958\pi$
$139$	−6.07441	+	10.5212i	−0.515225	+	0.892396i	−0.999844	+	0.0176705i	$0.994375\pi$
$140$	−10.4932	−	11.7109i	−0.886833	−	0.989749i
$141$		0			0
$142$	−5.46380	−	4.43549i	−0.458512	−	0.372218i
$143$	5.52624	+	8.97585i	0.462127	+	0.750598i
$144$		0			0
$145$	4.36315	+	1.16910i	0.362340	+	0.0970886i
$146$	2.71712	−	17.0215i	0.224870	−	1.40871i
$147$		0			0
$148$	5.10157	−	7.81414i	0.419346	−	0.642318i
$149$	11.0487	−	2.96049i	0.905146	−	0.242533i	0.223921	−	0.974607i	$-0.428114\pi$
$149$	11.0487	−	2.96049i	0.905146	−	0.242533i	0.681225	+	0.732074i	$0.261448\pi$
$150$		0			0
$151$	−4.47584	+	4.47584i	−0.364239	+	0.364239i	−0.865371	−	0.501132i	$-0.832917\pi$
$151$	−4.47584	+	4.47584i	−0.364239	+	0.364239i	0.501132	+	0.865371i	$0.332917\pi$
$152$	5.68307	+	8.82131i	0.460958	+	0.715503i
$153$		0			0
$154$	−9.57749	−	13.2160i	−0.771776	−	1.06497i
$155$			1.48016i			0.118889i
$156$		0			0
$157$		−	2.29073i		−	0.182820i	−0.995813	−	0.0914101i	$-0.970863\pi$
$157$		−	2.29073i		−	0.182820i	0.995813	−	0.0914101i	$-0.0291374\pi$
$158$	−20.0850	+	14.5554i	−1.59787	+	1.15796i
$159$		0			0
$160$	8.01437	−	7.91769i	0.633591	−	0.625948i
$161$	−1.47535	+	1.47535i	−0.116274	+	0.116274i
$162$		0			0
$163$	18.8514	−	5.05123i	1.47656	−	0.395643i	0.571385	−	0.820682i	$-0.306406\pi$
$163$	18.8514	−	5.05123i	1.47656	−	0.395643i	0.905175	+	0.425040i	$0.139740\pi$
$164$	−1.15789	+	1.77355i	−0.0904159	+	0.138491i
$165$		0			0
$166$	19.0519	+	3.04124i	1.47872	+	0.236046i
$167$	−19.6986	−	5.27823i	−1.52433	−	0.408442i	−0.603162	−	0.797618i	$-0.706093\pi$
$167$	−19.6986	−	5.27823i	−1.52433	−	0.408442i	−0.921163	+	0.389177i	$0.872760\pi$
$168$		0			0
$169$	−0.734614	−	12.9792i	−0.0565087	−	0.998402i
$170$	0.765976	−	0.943558i	0.0587477	−	0.0723676i
$171$		0			0
$172$	−9.95508	+	8.91993i	−0.759067	+	0.680139i
$173$	11.5483	−	20.0022i	0.877999	−	1.52074i	0.0244651	−	0.999701i	$-0.492212\pi$
$173$	11.5483	−	20.0022i	0.877999	−	1.52074i	0.853534	−	0.521038i	$-0.174455\pi$
$174$		0			0
$175$	3.94194	−	1.05624i	0.297982	−	0.0798441i
$176$	9.12340	−	7.31494i	0.687702	−	0.551385i
$177$		0			0
$178$	12.3093	−	4.70795i	0.922618	−	0.352876i
$179$	−8.55591	+	4.93976i	−0.639499	+	0.369215i	−0.784421	−	0.620228i	$-0.787040\pi$
$179$	−8.55591	+	4.93976i	−0.639499	+	0.369215i	0.144923	+	0.989443i	$0.453707\pi$
$180$		0			0
$181$	14.6104			1.08598			0.542991	−	0.839738i	$-0.317292\pi$
$181$	14.6104			1.08598			0.542991	+	0.839738i	$0.317292\pi$
$182$	2.64492	+	19.9551i	0.196055	+	1.47917i
$183$		0			0
$184$	−1.10726	−	1.00431i	−0.0816284	−	0.0740384i
$185$	−4.64629	−	8.04760i	−0.341602	−	0.591672i
$186$		0			0
$187$	0.892008	−	0.892008i	0.0652301	−	0.0652301i
$188$	−3.97291	−	7.84429i	−0.289755	−	0.572104i
$189$		0			0
$190$	10.3932	−	1.07962i	0.754000	−	0.0783236i
$191$	9.51822	+	5.49535i	0.688714	+	0.397629i	0.803130	−	0.595804i	$-0.203166\pi$
$191$	9.51822	+	5.49535i	0.688714	+	0.397629i	−0.114416	+	0.993433i	$0.536500\pi$
$192$		0			0
$193$	−1.07308	+	4.00480i	−0.0772422	+	0.288272i	−0.993732	−	0.111785i	$-0.964343\pi$
$193$	−1.07308	+	4.00480i	−0.0772422	+	0.288272i	0.916490	+	0.400057i	$0.131010\pi$
$194$	−3.00112	+	3.69690i	−0.215468	+	0.265422i
$195$		0			0
$196$	−3.52893	−	16.8028i	−0.252067	−	1.20020i
$197$	−3.39832	+	12.6827i	−0.242120	+	0.903606i	0.732688	+	0.680564i	$0.238265\pi$
$197$	−3.39832	+	12.6827i	−0.242120	+	0.903606i	−0.974809	+	0.223042i	$0.928401\pi$
$198$		0			0
$199$	−6.83125	+	11.8321i	−0.484255	+	0.838754i	−0.999836	−	0.0180866i	$-0.994243\pi$
$199$	−6.83125	+	11.8321i	−0.484255	+	0.838754i	0.515582	+	0.856840i	$0.327576\pi$
$200$	0.893404	+	2.78406i	0.0631732	+	0.196863i
$201$		0			0
$202$	−1.03356	+	2.31385i	−0.0727211	+	0.162802i
$203$	6.33140	+	6.33140i	0.444377	+	0.444377i
$204$		0			0
$205$	1.05455	+	1.82654i	0.0736533	+	0.127571i
$206$	5.19762	+	7.17220i	0.362136	+	0.499711i
$207$		0			0
$208$	−14.1879	+	2.58902i	−0.983755	+	0.179516i
$209$	10.8460			0.750234
$210$		0			0
$211$	4.28662	+	7.42464i	0.295103	+	0.511133i	0.975009	−	0.222166i	$-0.0713127\pi$
$211$	4.28662	+	7.42464i	0.295103	+	0.511133i	−0.679906	+	0.733299i	$0.737979\pi$
$212$	−11.2015	−	3.66966i	−0.769320	−	0.252033i
$213$		0			0
$214$	−4.39523	+	9.83971i	−0.300452	+	0.672628i
$215$	3.44493	+	12.8567i	0.234942	+	0.876816i
$216$		0			0
$217$	−1.46703	+	2.54096i	−0.0995882	+	0.172492i
$218$	3.93151	−	24.6291i	0.266276	−	1.66809i
$219$		0			0
$220$	−2.39335	−	11.3957i	−0.161359	−	0.768301i
$221$	−1.49083	+	0.444993i	−0.100284	+	0.0299335i
$222$		0			0
$223$	0.481305	−	1.79626i	0.0322306	−	0.120286i	−0.947936	−	0.318460i	$-0.896834\pi$
$223$	0.481305	−	1.79626i	0.0322306	−	0.120286i	0.980167	+	0.198174i	$0.0635010\pi$
$224$	21.6055	−	5.64890i	1.44358	−	0.377433i
$225$		0			0
$226$	−16.3818	+	1.70170i	−1.08970	+	0.113195i
$227$	−5.15967	−	19.2561i	−0.342459	−	1.27808i	−0.895552	−	0.444956i	$-0.853219\pi$
$227$	−5.15967	−	19.2561i	−0.342459	−	1.27808i	0.553093	−	0.833119i	$-0.313447\pi$
$228$		0			0
$229$	5.88318	−	5.88318i	0.388772	−	0.388772i	−0.485478	−	0.874249i	$-0.661354\pi$
$229$	5.88318	−	5.88318i	0.388772	−	0.388772i	0.874249	+	0.485478i	$0.161354\pi$
$230$	−1.39033	+	0.531764i	−0.0916759	+	0.0350635i
$231$		0			0
$232$	−4.30994	+	4.75177i	−0.282962	+	0.311969i
$233$			14.9520i			0.979537i	0.871853	+	0.489768i	$0.162919\pi$
$233$			14.9520i			0.979537i	−0.871853	+	0.489768i	$0.837081\pi$
$234$		0			0
$235$	−8.75583			−0.571167
$236$	−0.624595	+	11.3890i	−0.0406577	+	0.741362i
$237$		0			0
$238$	2.25012	−	0.860609i	0.145854	−	0.0557850i
$239$	2.11437	+	2.11437i	0.136767	+	0.136767i	0.772176	−	0.635409i	$-0.219168\pi$
$239$	2.11437	+	2.11437i	0.136767	+	0.136767i	−0.635409	+	0.772176i	$0.719168\pi$
$240$		0			0
$241$	13.8151	−	3.70175i	0.889911	−	0.238451i	0.215233	−	0.976563i	$-0.430949\pi$
$241$	13.8151	−	3.70175i	0.889911	−	0.238451i	0.674678	+	0.738112i	$0.264282\pi$
$242$	0.358494	+	3.45112i	0.0230449	+	0.221847i
$243$		0			0
$244$	−8.03875	+	7.20287i	−0.514628	+	0.461116i
$245$	−16.5142	−	4.42496i	−1.05505	−	0.282701i
$246$		0			0
$247$	−11.7689	−	6.35819i	−0.748837	−	0.404562i
$248$	−1.86954	−	0.961169i	−0.118716	−	0.0610343i
$249$		0			0
$250$	16.7814	+	2.67880i	1.06135	+	0.169422i
$251$	−4.77498	−	2.75684i	−0.301394	−	0.174010i	0.341675	−	0.939818i	$-0.389006\pi$
$251$	−4.77498	−	2.75684i	−0.301394	−	0.174010i	−0.643069	+	0.765808i	$0.722339\pi$
$252$		0			0
$253$	−1.49245	+	0.399901i	−0.0938295	+	0.0251415i
$254$	11.2781	−	25.2486i	0.707653	−	1.58424i
$255$		0			0
$256$	4.79631	+	15.2642i	0.299769	+	0.954012i
$257$	−24.7355	+	14.2811i	−1.54296	+	0.890828i	−0.544310	+	0.838884i	$0.683208\pi$
$257$	−24.7355	+	14.2811i	−1.54296	+	0.890828i	−0.998650	+	0.0519442i	$0.983458\pi$
$258$		0			0
$259$		−	18.4202i		−	1.14458i
$260$	−4.08346	+	13.7684i	−0.253245	+	0.853883i
$261$		0			0
$262$	13.3996	+	18.4902i	0.827833	+	1.14233i
$263$	−22.3279	+	12.8910i	−1.37680	+	0.794896i	−0.991773	−	0.128009i	$-0.959141\pi$
$263$	−22.3279	+	12.8910i	−1.37680	+	0.794896i	−0.385027	+	0.922905i	$0.625808\pi$
$264$		0			0
$265$	−8.29960	+	8.29960i	−0.509841	+	0.509841i
$266$	18.9118	+	8.44759i	1.15956	+	0.517955i
$267$		0			0
$268$	−1.99995	+	3.06336i	−0.122167	+	0.187124i
$269$	13.1981	+	7.61995i	0.804704	+	0.464596i	0.845113	−	0.534587i	$-0.179533\pi$
$269$	13.1981	+	7.61995i	0.804704	+	0.464596i	−0.0404091	+	0.999183i	$0.512866\pi$
$270$		0			0
$271$	−2.30836	−	0.618524i	−0.140223	−	0.0375727i	0.188025	−	0.982164i	$-0.439791\pi$
$271$	−2.30836	−	0.618524i	−0.140223	−	0.0375727i	−0.328248	+	0.944592i	$0.606458\pi$
$272$	0.694377	+	1.58020i	0.0421028	+	0.0958135i
$273$		0			0
$274$	14.5665	+	11.8250i	0.879995	+	0.714375i
$275$	2.91915	+	0.782184i	0.176031	+	0.0471675i
$276$		0			0
$277$	9.66247	−	16.7359i	0.580561	−	1.00556i	−0.414852	−	0.909889i	$-0.636166\pi$
$277$	9.66247	−	16.7359i	0.580561	−	1.00556i	0.995413	−	0.0956726i	$-0.0305002\pi$
$278$	−17.0891	+	1.77517i	−1.02494	+	0.106468i
$279$		0			0
$280$	4.70257	−	21.7345i	0.281032	−	1.29888i
$281$	−21.9119	−	21.9119i	−1.30715	−	1.30715i	−0.923462	−	0.383691i	$-0.874653\pi$
$281$	−21.9119	−	21.9119i	−1.30715	−	1.30715i	−0.383691	−	0.923462i	$-0.625347\pi$
$282$		0			0
$283$	−9.50892	+	5.48998i	−0.565247	+	0.326345i	−0.755249	−	0.655438i	$-0.772484\pi$
$283$	−9.50892	+	5.48998i	−0.565247	+	0.326345i	0.190002	+	0.981784i	$0.439151\pi$
$284$	0.544998	−	9.93762i	0.0323397	−	0.589689i
$285$		0			0
$286$	−5.69249	+	13.7770i	−0.336604	+	0.814652i
$287$			4.18079i			0.246784i
$288$		0			0
$289$	−8.40690	−	14.5612i	−0.494524	−	0.856540i
$290$	2.28205	+	5.96657i	0.134006	+	0.350369i
$291$		0			0
$292$	21.7467	−	11.0141i	1.27263	−	0.644550i
$293$	−1.28916	−	4.81120i	−0.0753133	−	0.281073i	0.917991	−	0.396601i	$-0.129811\pi$
$293$	−1.28916	−	4.81120i	−0.0753133	−	0.281073i	−0.993304	+	0.115528i	$0.963144\pi$
$294$		0			0
$295$	9.83623	+	5.67895i	0.572687	+	0.330641i
$296$	13.1818	−	0.642716i	0.766178	−	0.0373571i
$297$		0			0
$298$	12.5591	+	10.1954i	0.727529	+	0.590605i
$299$	1.85388	+	0.440981i	0.107212	+	0.0255026i
$300$		0			0
$301$	−6.82872	+	25.4851i	−0.393601	+	1.46894i
$302$	−8.83976	−	1.41108i	−0.508671	−	0.0811985i
$303$		0			0
$304$	−5.38537	+	13.8284i	−0.308872	+	0.793111i
$305$	2.78179	+	10.3818i	0.159285	+	0.594459i
$306$		0			0
$307$	9.32161	+	9.32161i	0.532013	+	0.532013i	0.921171	−	0.389158i	$-0.127234\pi$
$307$	9.32161	+	9.32161i	0.532013	+	0.532013i	−0.389158	+	0.921171i	$0.627234\pi$
$308$	7.18601	−	21.9350i	0.409461	−	1.24986i
$309$		0			0
$310$	−1.69498	+	1.22833i	−0.0962682	+	0.0697646i
$311$	7.84329			0.444752			0.222376	−	0.974961i	$-0.428619\pi$
$311$	7.84329			0.444752			0.222376	+	0.974961i	$0.428619\pi$
$312$		0			0
$313$	17.5938			0.994462			0.497231	−	0.867618i	$-0.334350\pi$
$313$	17.5938			0.994462			0.497231	+	0.867618i	$0.334350\pi$
$314$	2.62319	−	1.90100i	0.148035	−	0.107279i
$315$		0			0
$316$	−33.3356	−	10.9209i	−1.87527	−	0.614350i
$317$	−14.7327	−	14.7327i	−0.827472	−	0.827472i	0.159695	−	0.987166i	$-0.448949\pi$
$317$	−14.7327	−	14.7327i	−0.827472	−	0.827472i	−0.987166	+	0.159695i	$0.948949\pi$
$318$		0			0
$319$	1.71616	+	6.40480i	0.0960865	+	0.358600i
$320$	15.7176	+	2.60688i	0.878642	+	0.145729i
$321$		0			0
$322$	−2.91380	−	0.465127i	−0.162380	−	0.0259205i
$323$	−0.414342	+	1.54634i	−0.0230546	+	0.0860409i
$324$		0			0
$325$	−2.70901	−	2.56002i	−0.150269	−	0.142004i
$326$	21.4285	+	17.3955i	1.18681	+	0.963450i
$327$		0			0
$328$	−2.99184	+	0.145876i	−0.165197	+	0.00805463i
$329$	−15.0310	−	8.67813i	−0.828684	−	0.478441i
$330$		0			0
$331$	−2.45117	−	9.14790i	−0.134729	−	0.502814i	−0.999999	−	0.00150826i	$-0.999520\pi$
$331$	−2.45117	−	9.14790i	−0.134729	−	0.502814i	0.865270	−	0.501306i	$-0.167147\pi$
$332$	12.3279	+	24.3408i	0.676583	+	1.33587i
$333$		0			0
$334$	−10.3029	−	26.9377i	−0.563751	−	1.47397i
$335$	1.82147	+	3.15488i	0.0995176	+	0.172370i
$336$		0			0
$337$			21.1551i			1.15239i	0.817312	+	0.576196i	$0.195463\pi$
$337$			21.1551i			1.15239i	−0.817312	+	0.576196i	$0.804537\pi$
$338$	14.2533	−	11.6122i	0.775276	−	0.631622i
$339$		0			0
$340$	1.71615	+	0.0941171i	0.0930715	+	0.00510422i
$341$	−1.88168	+	1.08639i	−0.101899	+	0.0588311i
$342$		0			0
$343$	−4.42357	−	4.42357i	−0.238850	−	0.238850i
$344$	−18.4759	−	3.99752i	−0.996151	−	0.215532i
$345$		0			0
$346$	32.4886	−	3.37483i	1.74660	−	0.181432i
$347$	8.19610	−	14.1961i	0.439990	−	0.762085i	−0.557698	−	0.830044i	$-0.688315\pi$
$347$	8.19610	−	14.1961i	0.439990	−	0.762085i	0.997688	+	0.0679589i	$0.0216487\pi$
$348$		0			0
$349$	5.13248	+	1.37525i	0.274736	+	0.0736152i	0.393556	−	0.919301i	$-0.371245\pi$
$349$	5.13248	+	1.37525i	0.274736	+	0.0736152i	−0.118821	+	0.992916i	$0.537911\pi$
$350$	4.48081	+	3.63750i	0.239509	+	0.194432i
$351$		0			0
$352$	15.9478	+	4.37708i	0.850018	+	0.233299i
$353$	−6.04366	−	1.61939i	−0.321671	−	0.0861916i	0.0943702	−	0.995537i	$-0.469916\pi$
$353$	−6.04366	−	1.61939i	−0.321671	−	0.0861916i	−0.416042	+	0.909346i	$0.636583\pi$
$354$		0			0
$355$	−8.58272	−	4.95524i	−0.455523	−	0.262997i
$356$	15.6062	+	10.1887i	0.827129	+	0.540002i
$357$		0			0
$358$	−12.7569	−	5.69831i	−0.674224	−	0.301165i
$359$	9.28036	−	9.28036i	0.489799	−	0.489799i	−0.418444	−	0.908243i	$-0.637424\pi$
$359$	9.28036	−	9.28036i	0.489799	−	0.489799i	0.908243	+	0.418444i	$0.137424\pi$
$360$		0			0
$361$	4.53441	−	2.61794i	0.238653	−	0.137787i
$362$	12.1247	+	16.7308i	0.637258	+	0.879352i
$363$		0			0
$364$	−20.6563	+	19.5888i	−1.08268	+	1.02673i
$365$		−	24.2737i		−	1.27054i
$366$		0			0
$367$	−21.4767	+	12.3996i	−1.12107	+	0.647252i	−0.941675	−	0.336524i	$-0.890749\pi$
$367$	−21.4767	+	12.3996i	−1.12107	+	0.647252i	−0.179399	+	0.983776i	$0.557415\pi$
$368$	0.231184	−	2.10140i	0.0120513	−	0.109543i
$369$		0			0
$370$	5.35977	−	11.9990i	0.278641	−	0.623800i
$371$	−22.4737	+	6.02182i	−1.16678	+	0.312637i
$372$		0			0
$373$	−1.91414	−	1.10513i	−0.0991107	−	0.0572216i	0.449625	−	0.893217i	$-0.351557\pi$
$373$	−1.91414	−	1.10513i	−0.0991107	−	0.0572216i	−0.548736	+	0.835996i	$0.684891\pi$
$374$	1.76171	+	0.281220i	0.0910960	+	0.0145415i
$375$		0			0
$376$	5.68576	−	11.0592i	0.293221	−	0.570335i
$377$	1.89246	−	7.95584i	0.0974664	−	0.409747i
$378$		0			0
$379$	−11.5125	−	3.08477i	−0.591358	−	0.158454i	−0.0492842	−	0.998785i	$-0.515694\pi$
$379$	−11.5125	−	3.08477i	−0.591358	−	0.158454i	−0.542074	+	0.840331i	$0.682361\pi$
$380$	9.86123	+	11.0056i	0.505871	+	0.564576i
$381$		0			0
$382$	1.60594	+	15.4600i	0.0821673	+	0.791002i
$383$	23.5153	−	6.30090i	1.20158	−	0.321961i	0.398124	−	0.917332i	$-0.369661\pi$
$383$	23.5153	−	6.30090i	1.20158	−	0.321961i	0.803451	+	0.595370i	$0.202995\pi$
$384$		0			0
$385$	−16.2525	−	16.2525i	−0.828302	−	0.828302i
$386$	−5.47653	+	2.09462i	−0.278748	+	0.106613i
$387$		0			0
$388$	−6.72396	−	0.368754i	−0.341357	−	0.0187207i
$389$	−20.5350			−1.04117			−0.520584	−	0.853811i	$-0.674286\pi$
$389$	−20.5350			−1.04117			−0.520584	+	0.853811i	$0.674286\pi$
$390$		0			0
$391$		−	0.228060i		−	0.0115335i
$392$	16.3128	−	17.9851i	0.823922	−	0.908385i
$393$		0			0
$394$	−17.3435	+	6.63341i	−0.873753	+	0.334186i
$395$	−24.6997	+	24.6997i	−1.24277	+	1.24277i
$396$		0			0
$397$	7.08669	+	26.4479i	0.355671	+	1.32738i	0.879638	+	0.475643i	$0.157785\pi$
$397$	7.08669	+	26.4479i	0.355671	+	1.32738i	−0.523967	+	0.851738i	$0.675549\pi$
$398$	−19.2183	+	1.99635i	−0.963326	+	0.100068i
$399$		0			0
$400$	−2.44671	+	3.33346i	−0.122336	+	0.166673i
$401$	−1.38519	+	5.16959i	−0.0691729	+	0.258157i	−0.991849	−	0.127419i	$-0.959331\pi$
$401$	−1.38519	+	5.16959i	−0.0691729	+	0.258157i	0.922676	+	0.385576i	$0.125997\pi$
$402$		0			0
$403$	2.67866	−	0.0757443i	0.133433	−	0.00377309i
$404$	−3.50738	+	0.736624i	−0.174499	+	0.0366484i
$405$		0			0
$406$	−1.99608	+	12.5045i	−0.0990636	+	0.620587i
$407$	6.82043	−	11.8133i	0.338076	−	0.585565i
$408$		0			0
$409$	−8.27483	−	30.8821i	−0.409164	−	1.52702i	−0.796245	−	0.604974i	$-0.793183\pi$
$409$	−8.27483	−	30.8821i	−0.409164	−	1.52702i	0.387081	−	0.922046i	$-0.373483\pi$
$410$	−1.21649	+	2.72339i	−0.0600782	+	0.134498i
$411$		0			0
$412$	−3.89979	+	11.9039i	−0.192129	+	0.586464i
$413$	11.2571	+	19.4979i	0.553926	+	0.959428i
$414$		0			0
$415$	27.1693			1.33369
$416$	−14.7388	−	14.0985i	−0.722630	−	0.691235i
$417$		0			0
$418$	9.00071	+	12.4201i	0.440239	+	0.607486i
$419$	−4.06151	−	7.03474i	−0.198418	−	0.343670i	0.749598	−	0.661894i	$-0.230247\pi$
$419$	−4.06151	−	7.03474i	−0.198418	−	0.343670i	−0.948016	+	0.318224i	$0.896914\pi$
$420$		0			0
$421$	−23.7134	−	23.7134i	−1.15572	−	1.15572i	−0.985387	−	0.170333i	$-0.945516\pi$
$421$	−23.7134	−	23.7134i	−1.15572	−	1.15572i	−0.170333	−	0.985387i	$-0.554484\pi$
$422$	−4.94487	+	11.0702i	−0.240713	+	0.538888i
$423$		0			0
$424$	−5.09346	−	15.8725i	−0.247361	−	0.770835i
$425$	−0.223036	+	0.386310i	−0.0108188	+	0.0187388i
$426$		0			0
$427$	−5.51421	+	20.5793i	−0.266851	+	0.995902i
$428$	−14.9152	+	3.13251i	−0.720953	+	0.151415i
$429$		0			0
$430$	−11.8637	+	14.6142i	−0.572120	+	0.704758i
$431$	8.20438	−	30.6192i	0.395191	−	1.47487i	−0.426263	−	0.904599i	$-0.640170\pi$
$431$	8.20438	−	30.6192i	0.395191	−	1.47487i	0.821455	−	0.570274i	$-0.193163\pi$
$432$		0			0
$433$	−16.7664	−	9.68007i	−0.805740	−	0.465194i	0.0397341	−	0.999210i	$-0.487349\pi$
$433$	−16.7664	−	9.68007i	−0.805740	−	0.465194i	−0.845474	+	0.534016i	$0.820682\pi$
$434$	−4.12717	+	0.428719i	−0.198110	+	0.0205792i
$435$		0			0
$436$	31.4662	−	15.9367i	1.50696	−	0.763231i
$437$	1.38650	−	1.38650i	0.0663252	−	0.0663252i
$438$		0			0
$439$	−9.29759	−	16.1039i	−0.443750	−	0.768597i	0.554214	−	0.832374i	$-0.313019\pi$
$439$	−9.29759	−	16.1039i	−0.443750	−	0.768597i	−0.997964	+	0.0637766i	$0.979685\pi$
$440$	11.0635	−	12.1976i	0.527430	−	0.581499i
$441$		0			0
$442$	−1.74676	−	1.33791i	−0.0830849	−	0.0636377i
$443$	3.81566			0.181288			0.0906439	−	0.995883i	$-0.471108\pi$
$443$	3.81566			0.181288			0.0906439	+	0.995883i	$0.471108\pi$
$444$		0			0
$445$	16.0725	−	9.27946i	0.761910	−	0.439889i
$446$	2.45637	−	0.939492i	0.116312	−	0.0444862i
$447$		0			0
$448$	24.3984	+	20.0533i	1.15272	+	0.947431i
$449$	7.39494	−	1.98147i	0.348989	−	0.0935112i	−0.0800665	−	0.996790i	$-0.525513\pi$
$449$	7.39494	−	1.98147i	0.348989	−	0.0935112i	0.429055	+	0.903278i	$0.358847\pi$
$450$		0			0
$451$	−1.54801	+	2.68124i	−0.0728931	+	0.126255i
$452$	−15.5434	−	17.3471i	−0.731098	−	0.815940i
$453$		0			0
$454$	17.7690	−	21.8885i	0.833939	−	1.02728i
$455$	8.10782	+	27.1630i	0.380100	+	1.27342i
$456$		0			0
$457$	17.5841	+	4.71165i	0.822550	+	0.220402i	0.645461	−	0.763793i	$-0.276665\pi$
$457$	17.5841	+	4.71165i	0.822550	+	0.220402i	0.177089	+	0.984195i	$0.443332\pi$
$458$	11.6193	+	1.85477i	0.542932	+	0.0866676i
$459$		0			0
$460$	−1.76273	−	1.15082i	−0.0821876	−	0.0536573i
$461$	3.90436	−	1.04617i	0.181844	−	0.0487250i	−0.166748	−	0.986000i	$-0.553327\pi$
$461$	3.90436	−	1.04617i	0.181844	−	0.0487250i	0.348592	+	0.937275i	$0.386660\pi$
$462$		0			0
$463$	0.0778804	−	0.0778804i	0.00361941	−	0.00361941i	−0.705295	−	0.708914i	$-0.749185\pi$
$463$	0.0778804	−	0.0778804i	0.00361941	−	0.00361941i	0.708914	+	0.705295i	$0.249185\pi$
$464$	−9.01807	−	0.992120i	−0.418653	−	0.0460580i
$465$		0			0
$466$	−17.1220	+	12.4081i	−0.793160	+	0.574795i
$467$			0.605322i			0.0280110i	0.999902	+	0.0140055i	$0.00445823\pi$
$467$			0.605322i			0.0280110i	−0.999902	+	0.0140055i	$0.995542\pi$
$468$		0			0
$469$			7.22123i			0.333445i
$470$	−7.26616	−	10.0266i	−0.335163	−	0.462491i
$471$		0			0
$472$	−13.5602	+	8.73610i	−0.624161	+	0.402111i
$473$	−13.8158	+	13.8158i	−0.635249	+	0.635249i
$474$		0			0
$475$	−3.70455	+	0.992630i	−0.169976	+	0.0455450i
$476$	2.85281	+	1.86249i	0.130758	+	0.0853672i
$477$		0			0
$478$	−0.666587	+	4.17586i	−0.0304890	+	0.190999i
$479$	−15.3267	−	4.10679i	−0.700297	−	0.187644i	−0.108933	−	0.994049i	$-0.534743\pi$
$479$	−15.3267	−	4.10679i	−0.700297	−	0.187644i	−0.591364	+	0.806405i	$0.701410\pi$
$480$		0			0
$481$	−14.3260	+	8.82024i	−0.653211	+	0.402168i
$482$	15.7037	+	12.7482i	0.715283	+	0.580663i
$483$		0			0
$484$	−3.65449	+	3.27449i	−0.166113	+	0.148840i
$485$	−3.35279	+	5.80721i	−0.152243	+	0.263692i
$486$		0			0
$487$	1.60788	−	0.430831i	0.0728601	−	0.0195228i	−0.222205	−	0.975000i	$-0.571325\pi$
$487$	1.60788	−	0.430831i	0.0728601	−	0.0195228i	0.295065	+	0.955477i	$0.404659\pi$
$488$	−14.9193	−	3.22801i	−0.675365	−	0.146125i
$489$		0			0
$490$	−8.63738	−	22.5830i	−0.390197	−	1.02020i
$491$	−19.1677	+	11.0665i	−0.865026	+	0.499423i	−0.865692	−	0.500577i	$-0.833121\pi$
$491$	−19.1677	+	11.0665i	−0.865026	+	0.499423i	0.000666399		1.00000i	$0.499788\pi$
$492$		0			0
$493$	−0.978711			−0.0440789
$494$	−2.48564	−	18.7534i	−0.111834	−	0.843754i
$495$		0			0
$496$	−0.450804	−	2.93851i	−0.0202417	−	0.131943i
$497$	−9.82253	−	17.0131i	−0.440601	−	0.763143i
$498$		0			0
$499$	−5.15371	+	5.15371i	−0.230712	+	0.230712i	−0.812990	−	0.582278i	$-0.802162\pi$
$499$	−5.15371	+	5.15371i	−0.230712	+	0.230712i	0.582278	+	0.812990i	$0.302162\pi$
$500$	10.8587	+	21.4400i	0.485617	+	0.958824i
$501$		0			0
$502$	−0.805650	−	7.75578i	−0.0359579	−	0.346157i
$503$	−37.9365	−	21.9026i	−1.69150	−	0.976590i	−0.953307	−	0.302003i	$-0.902345\pi$
$503$	−37.9365	−	21.9026i	−1.69150	−	0.976590i	−0.738196	−	0.674586i	$-0.764322\pi$
$504$		0			0
$505$	−0.923660	+	3.44715i	−0.0411023	+	0.153396i
$506$	−1.69647	−	1.37719i	−0.0754173	−	0.0612234i
$507$		0			0
$508$	38.2723	−	8.03799i	1.69806	−	0.356628i
$509$	−1.64040	+	6.12207i	−0.0727096	+	0.271356i	−0.992704	−	0.120575i	$-0.961526\pi$
$509$	−1.64040	+	6.12207i	−0.0727096	+	0.271356i	0.919995	+	0.391931i	$0.128193\pi$
$510$		0			0
$511$	24.0583	−	41.6702i	1.06428	−	1.84338i
$512$	−13.4992	+	18.1596i	−0.596586	+	0.802549i
$513$		0			0
$514$	−36.8808	−	16.4741i	−1.62674	−	0.726640i
$515$	8.82008	+	8.82008i	0.388659	+	0.388659i
$516$		0			0
$517$	−6.42648	−	11.1310i	−0.282636	−	0.489540i
$518$	21.0936	−	15.2863i	0.926798	−	0.671641i
$519$		0			0
$520$	−19.1554	+	6.74986i	−0.840020	+	0.296001i
$521$	−23.1087			−1.01241			−0.506206	−	0.862413i	$-0.668952\pi$
$521$	−23.1087			−1.01241			−0.506206	+	0.862413i	$0.668952\pi$
$522$		0			0
$523$	−10.4715	−	18.1372i	−0.457887	−	0.793083i	0.540962	−	0.841047i	$-0.318060\pi$
$523$	−10.4715	−	18.1372i	−0.457887	−	0.793083i	−0.998849	+	0.0479636i	$0.984727\pi$
$524$	−10.0538	+	30.6887i	−0.439201	+	1.34064i
$525$		0			0
$526$	−33.2911	−	14.8706i	−1.45156	−	0.648389i
$527$	−0.0830048	−	0.309778i	−0.00361575	−	0.0134942i
$528$		0			0
$529$	11.3603	−	19.6767i	0.493928	−	0.855508i
$530$	−16.3917	−	2.61658i	−0.712009	−	0.113657i
$531$		0			0
$532$	6.02064	+	28.6669i	0.261028	+	1.24287i
$533$	3.25154	−	2.00190i	0.140840	−	0.0867121i
$534$		0			0
$535$	−3.92788	+	14.6590i	−0.169817	+	0.633766i
$536$	−5.16763	+	0.251962i	−0.223208	+	0.0108831i
$537$		0			0
$538$	2.22683	+	21.4371i	0.0960055	+	0.924219i
$539$	−6.49554	−	24.2417i	−0.279783	−	1.04416i
$540$		0			0
$541$	−22.4938	+	22.4938i	−0.967084	+	0.967084i	−0.999475	−	0.0323917i	$-0.989688\pi$
$541$	−22.4938	+	22.4938i	−0.967084	+	0.967084i	0.0323917	+	0.999475i	$0.489688\pi$
$542$	−1.20734	−	3.15667i	−0.0518597	−	0.135591i
$543$		0			0
$544$	−1.23329	+	2.10650i	−0.0528770	+	0.0903155i
$545$		−	35.1227i		−	1.50449i
$546$		0			0
$547$	−14.1772			−0.606172			−0.303086	−	0.952963i	$-0.598017\pi$
$547$	−14.1772			−0.606172			−0.303086	+	0.952963i	$0.598017\pi$
$548$	−1.45297	+	26.4937i	−0.0620676	+	1.13176i
$549$		0			0
$550$	1.52680	+	3.99191i	0.0651028	+	0.170216i
$551$	−5.95011	−	5.95011i	−0.253483	−	0.253483i
$552$		0			0
$553$	−66.8819	+	17.9209i	−2.84411	+	0.762076i
$554$	27.1833	−	2.82373i	1.15491	−	0.119969i
$555$		0			0
$556$	−16.2144	−	18.0961i	−0.687645	−	0.767445i
$557$	−11.2083	−	3.00327i	−0.474913	−	0.127253i	0.0134200	−	0.999910i	$-0.495728\pi$
$557$	−11.2083	−	3.00327i	−0.474913	−	0.127253i	−0.488333	+	0.872657i	$0.662395\pi$
$558$		0			0
$559$	23.0905	−	6.89223i	0.976624	−	0.291510i
$560$	28.7913	−	12.6516i	1.21665	−	0.534628i
$561$		0			0
$562$	6.90807	−	43.2758i	0.291399	−	1.82548i
$563$	8.60923	+	4.97054i	0.362836	+	0.209483i	0.670324	−	0.742069i	$-0.266155\pi$
$563$	8.60923	+	4.97054i	0.362836	+	0.209483i	−0.307488	+	0.951552i	$0.599488\pi$
$564$		0			0
$565$	−22.4033	+	6.00293i	−0.942512	+	0.252545i
$566$	−14.1779	−	6.33302i	−0.595940	−	0.266197i
$567$		0			0
$568$	11.8321	−	7.62279i	0.496466	−	0.319845i
$569$	31.2898	−	18.0652i	1.31174	−	0.757332i	0.329353	−	0.944207i	$-0.393169\pi$
$569$	31.2898	−	18.0652i	1.31174	−	0.757332i	0.982384	+	0.186875i	$0.0598360\pi$
$570$		0			0
$571$		−	3.28225i		−	0.137358i	−0.997639	−	0.0686790i	$-0.978122\pi$
$571$		−	3.28225i		−	0.137358i	0.997639	−	0.0686790i	$-0.0218784\pi$
$572$	−20.5005	+	4.91441i	−0.857168	+	0.205482i
$573$		0			0
$574$	−4.78755	+	3.46949i	−0.199828	+	0.144814i
$575$	0.473160	−	0.273179i	0.0197321	−	0.0113924i
$576$		0			0
$577$	−7.55694	+	7.55694i	−0.314600	+	0.314600i	−0.846689	−	0.532089i	$-0.821407\pi$
$577$	−7.55694	+	7.55694i	−0.314600	+	0.314600i	0.532089	+	0.846689i	$0.321407\pi$
$578$	9.69786	−	21.7108i	0.403378	−	0.903051i
$579$		0			0
$580$	−4.93871	+	7.56469i	−0.205069	+	0.314107i
$581$	46.6410	+	26.9282i	1.93499	+	1.11717i
$582$		0			0
$583$	−16.6426	−	4.45938i	−0.689267	−	0.184689i
$584$	30.6593	+	15.7626i	1.26869	+	0.652260i
$585$		0			0
$586$	4.43962	−	5.46889i	0.183399	−	0.225918i
$587$	−14.0208	−	3.75688i	−0.578702	−	0.155063i	−0.0424176	−	0.999100i	$-0.513506\pi$
$587$	−14.0208	−	3.75688i	−0.578702	−	0.155063i	−0.536285	+	0.844037i	$0.680173\pi$
$588$		0			0
$589$	1.37868	−	2.38794i	0.0568075	−	0.0983934i
$590$	1.65960	+	15.9765i	0.0683247	+	0.657743i
$591$		0			0
$592$	11.6751	+	14.5615i	0.479845	+	0.598476i
$593$	2.71248	+	2.71248i	0.111388	+	0.111388i	0.760604	−	0.649216i	$-0.224903\pi$
$593$	2.71248	+	2.71248i	0.111388	+	0.111388i	−0.649216	+	0.760604i	$0.724903\pi$
$594$		0			0
$595$	2.93804	−	1.69628i	0.120448	−	0.0695406i
$596$	−1.25273	+	22.8426i	−0.0513139	+	0.935670i
$597$		0			0
$598$	1.03348	+	2.48888i	0.0422623	+	0.101778i
$599$			20.2262i			0.826421i	0.910635	+	0.413211i	$0.135593\pi$
$599$			20.2262i			0.826421i	−0.910635	+	0.413211i	$0.864407\pi$
$600$		0			0
$601$	20.9818	+	36.3415i	0.855865	+	1.48240i	0.875840	+	0.482601i	$0.160308\pi$
$601$	20.9818	+	36.3415i	0.855865	+	1.48240i	−0.0199752	+	0.999800i	$0.506359\pi$
$602$	−34.8507	+	13.3294i	−1.42041	+	0.543267i
$603$		0			0
$604$	−5.71994	−	11.2937i	−0.232741	−	0.459534i
$605$	1.26463	+	4.71965i	0.0514144	+	0.191881i
$606$		0			0
$607$	14.4059	+	8.31726i	0.584718	+	0.337587i	0.763006	−	0.646391i	$-0.223723\pi$
$607$	14.4059	+	8.31726i	0.584718	+	0.337587i	−0.178288	+	0.983978i	$0.557056\pi$
$608$	−20.3044	+	5.30871i	−0.823453	+	0.215297i
$609$		0			0
$610$	−9.57999	+	11.8010i	−0.387882	+	0.477808i
$611$	0.448062	+	15.8455i	0.0181267	+	0.641040i
$612$		0			0
$613$	0.326274	−	1.21767i	0.0131781	−	0.0491812i	−0.959024	−	0.283326i	$-0.908562\pi$
$613$	0.326274	−	1.21767i	0.0131781	−	0.0491812i	0.972202	+	0.234145i	$0.0752289\pi$
$614$	−2.93879	+	18.4101i	−0.118600	+	0.742973i
$615$		0			0
$616$	31.0818	−	9.97413i	1.25232	−	0.401869i
$617$	6.14320	+	22.9267i	0.247316	+	0.922995i	0.972205	+	0.234130i	$0.0752242\pi$
$617$	6.14320	+	22.9267i	0.247316	+	0.922995i	−0.724889	+	0.688865i	$0.758109\pi$
$618$		0			0
$619$	7.13833	+	7.13833i	0.286914	+	0.286914i	0.835859	−	0.548945i	$-0.184970\pi$
$619$	7.13833	+	7.13833i	0.286914	+	0.286914i	−0.548945	+	0.835859i	$0.684970\pi$
$620$	−2.81320	−	0.921620i	−0.112981	−	0.0370131i
$621$		0			0
$622$	6.50887	+	8.98159i	0.260982	+	0.360129i
$623$	36.7885			1.47390
$624$		0			0
$625$	18.7626			0.750503
$626$	14.6005	+	20.1472i	0.583553	+	0.805245i
$627$		0			0
$628$	4.35378	+	1.42632i	0.173735	+	0.0569164i
$629$	1.42370	+	1.42370i	0.0567668	+	0.0567668i
$630$		0			0
$631$	0.0485313	+	0.181121i	0.00193200	+	0.00721032i	0.966885	−	0.255212i	$-0.0821453\pi$
$631$	0.0485313	+	0.181121i	0.00193200	+	0.00721032i	−0.964953	+	0.262422i	$0.915479\pi$
$632$	−15.1582	−	47.2365i	−0.602960	−	1.87897i
$633$		0			0
$634$	4.64472	−	29.0970i	0.184466	−	1.15559i
$635$	10.0789	−	37.6150i	0.399969	−	1.49271i
$636$		0			0
$637$	−7.16281	+	30.1123i	−0.283801	+	1.19309i
$638$	−5.91015	+	7.28034i	−0.233985	+	0.288232i
$639$		0			0
$640$	10.0583	+	20.1621i	0.397589	+	0.796977i
$641$	11.5562	+	6.67195i	0.456441	+	0.263526i	0.710546	−	0.703650i	$-0.248448\pi$
$641$	11.5562	+	6.67195i	0.456441	+	0.263526i	−0.254106	+	0.967176i	$0.581781\pi$
$642$		0			0
$643$	−3.41461	−	12.7435i	−0.134659	−	0.502554i	−0.999999	−	0.00136906i	$-0.999564\pi$
$643$	−3.41461	−	12.7435i	−0.134659	−	0.502554i	0.865340	−	0.501185i	$-0.167102\pi$
$644$	−1.88543	−	3.72268i	−0.0742964	−	0.146694i
$645$		0			0
$646$	−2.11461	+	0.808781i	−0.0831984	+	0.0318211i
$647$	−4.24409	−	7.35098i	−0.166852	−	0.288997i	0.770459	−	0.637489i	$-0.220027\pi$
$647$	−4.24409	−	7.35098i	−0.166852	−	0.288997i	−0.937312	+	0.348492i	$0.886694\pi$
$648$		0			0
$649$			16.6726i			0.654457i
$650$	0.683443	−	5.22664i	0.0268068	−	0.205005i
$651$		0			0
$652$	−2.13743	+	38.9743i	−0.0837081	+	1.52635i
$653$	−39.7745	+	22.9638i	−1.55649	+	0.898643i	−0.558907	+	0.829230i	$0.688779\pi$
$653$	−39.7745	+	22.9638i	−1.55649	+	0.898643i	−0.997588	+	0.0694122i	$0.977888\pi$
$654$		0			0
$655$	22.7384	+	22.7384i	0.888464	+	0.888464i
$656$	−2.64987	−	3.30499i	−0.103460	−	0.129038i
$657$		0			0
$658$	−2.53607	−	24.4141i	−0.0988664	−	0.951761i
$659$	12.3199	−	21.3386i	0.479913	−	0.831234i	−0.519821	−	0.854275i	$-0.674001\pi$
$659$	12.3199	−	21.3386i	0.479913	−	0.831234i	0.999735	+	0.0230408i	$0.00733476\pi$
$660$		0			0
$661$	−4.80194	−	1.28668i	−0.186774	−	0.0500459i	0.164220	−	0.986424i	$-0.447489\pi$
$661$	−4.80194	−	1.28668i	−0.186774	−	0.0500459i	−0.350993	+	0.936378i	$0.614156\pi$
$662$	8.44140	−	10.3984i	0.328084	−	0.404146i
$663$		0			0
$664$	−17.6429	+	34.3166i	−0.684676	+	1.33174i
$665$	28.1745	+	7.54934i	1.09256	+	0.292751i
$666$		0			0
$667$	1.03814	+	0.599372i	0.0401971	+	0.0232078i
$668$	22.2972	−	34.1529i	0.862704	−	1.32141i
$669$		0			0
$670$	−2.10118	+	4.70395i	−0.0811755	+	0.181729i
$671$	−11.1563	+	11.1563i	−0.430683	+	0.430683i
$672$		0			0
$673$	−18.9947	+	10.9666i	−0.732193	+	0.422732i	−0.819224	−	0.573474i	$-0.805596\pi$
$673$	−18.9947	+	10.9666i	−0.732193	+	0.422732i	0.0870306	+	0.996206i	$0.472262\pi$
$674$	−24.2254	+	17.5559i	−0.933126	+	0.676227i
$675$		0			0
$676$	25.1258	+	6.68529i	0.966378	+	0.257126i
$677$			27.2466i			1.04717i	0.851972	+	0.523587i	$0.175406\pi$
$677$			27.2466i			1.04717i	−0.851972	+	0.523587i	$0.824594\pi$
$678$		0			0
$679$	−11.5114	+	6.64608i	−0.441765	+	0.255053i
$680$	1.31640	+	2.04332i	0.0504816	+	0.0783579i
$681$		0			0
$682$	−2.80559	−	1.25321i	−0.107432	−	0.0479880i
$683$	−36.4710	+	9.77237i	−1.39552	+	0.373929i	−0.876735	−	0.480974i	$-0.840283\pi$
$683$	−36.4710	+	9.77237i	−1.39552	+	0.373929i	−0.518788	+	0.854903i	$0.673617\pi$
$684$		0			0
$685$	22.8816	+	13.2107i	0.874259	+	0.504754i
$686$	1.39460	−	8.73652i	0.0532461	−	0.333562i
$687$		0			0
$688$	−10.7548	−	24.4747i	−0.410022	−	0.933088i
$689$	15.4446	+	14.5951i	0.588391	+	0.556030i
$690$		0			0
$691$	2.76976	+	0.742154i	0.105367	+	0.0282329i	0.311117	−	0.950372i	$-0.399297\pi$
$691$	2.76976	+	0.742154i	0.105367	+	0.0282329i	−0.205751	+	0.978604i	$0.565964\pi$
$692$	30.8258	+	34.4031i	1.17182	+	1.30781i
$693$		0			0
$694$	23.0580	−	2.39521i	0.875270	−	0.0909208i
$695$	−23.3705	+	6.26211i	−0.886494	+	0.237535i
$696$		0			0
$697$	−0.323134	−	0.323134i	−0.0122396	−	0.0122396i
$698$	2.68443	+	7.01863i	0.101607	+	0.265659i
$699$		0			0
$700$	−0.446947	+	8.14974i	−0.0168930	+	0.308031i
$701$	39.5968			1.49555			0.747775	−	0.663952i	$-0.231122\pi$
$701$	39.5968			1.49555			0.747775	+	0.663952i	$0.231122\pi$
$702$		0			0
$703$			17.3109i			0.652894i
$704$	8.22216	+	21.8946i	0.309884	+	0.825186i
$705$		0			0
$706$	−3.16100	−	8.26466i	−0.118966	−	0.311044i
$707$	−5.00219	+	5.00219i	−0.188127	+	0.188127i
$708$		0			0
$709$	0.979951	+	3.65723i	0.0368028	+	0.137350i	0.981883	−	0.189489i	$-0.0606831\pi$
$709$	0.979951	+	3.65723i	0.0368028	+	0.137350i	−0.945080	+	0.326839i	$0.894016\pi$
$710$	−1.44810	−	13.9405i	−0.0543464	−	0.523178i
$711$		0			0
$712$	1.28362	+	26.3265i	0.0481057	+	0.986626i
$713$	−0.101666	+	0.379422i	−0.00380742	+	0.0142095i
$714$		0			0
$715$	−4.85786	+	20.4223i	−0.181674	+	0.763752i
$716$	−4.06121	−	19.3372i	−0.151775	−	0.722664i
$717$		0			0
$718$	18.3287	+	2.92578i	0.684020	+	0.109189i
$719$	19.2355	−	33.3168i	0.717363	−	1.24251i	−0.244678	−	0.969604i	$-0.578682\pi$
$719$	19.2355	−	33.3168i	0.717363	−	1.24251i	0.962041	−	0.272904i	$-0.0879843\pi$
$720$		0			0
$721$	6.39945	+	23.8831i	0.238328	+	0.889452i
$722$	6.76084	+	3.01996i	0.251612	+	0.112391i
$723$		0			0
$724$	−9.09715	+	27.7686i	−0.338093	+	1.03201i
$725$	−1.17234	−	2.03055i	−0.0435396	−	0.0754127i
$726$		0			0
$727$	4.98457			0.184867			0.0924337	−	0.995719i	$-0.470535\pi$
$727$	4.98457			0.184867			0.0924337	+	0.995719i	$0.470535\pi$
$728$	−39.5737	−	7.39806i	−1.46670	−	0.274190i
$729$		0			0
$730$	27.7966	−	20.1439i	1.02880	−	0.745559i
$731$	−1.44196	−	2.49754i	−0.0533327	−	0.0923750i
$732$		0			0
$733$	−7.68903	−	7.68903i	−0.284001	−	0.284001i	0.550701	−	0.834702i	$-0.314360\pi$
$733$	−7.68903	−	7.68903i	−0.284001	−	0.284001i	−0.834702	+	0.550701i	$0.814360\pi$
$734$	−32.0219	−	14.3036i	−1.18195	−	0.527957i
$735$		0			0
$736$	2.59823	−	1.47914i	0.0957719	−	0.0545218i
$737$	−2.67379	+	4.63115i	−0.0984905	+	0.170591i
$738$		0			0
$739$	3.25679	−	12.1545i	0.119803	−	0.447111i	−0.879798	−	0.475347i	$-0.842322\pi$
$739$	3.25679	−	12.1545i	0.119803	−	0.447111i	0.999601	+	0.0282364i	$0.00898913\pi$
$740$	18.1883	−	3.81993i	0.668617	−	0.140424i
$741$		0			0
$742$	−25.5459	−	20.7381i	−0.937820	−	0.761318i
$743$	−1.24991	+	4.66472i	−0.0458547	+	0.171132i	−0.985056	−	0.172235i	$-0.944901\pi$
$743$	−1.24991	+	4.66472i	−0.0458547	+	0.171132i	0.939201	+	0.343368i	$0.111568\pi$
$744$		0			0
$745$	19.7282	+	11.3901i	0.722787	+	0.417301i
$746$	−0.322961	−	3.10906i	−0.0118244	−	0.113831i
$747$		0			0
$748$	1.13995	+	2.25077i	0.0416807	+	0.0822961i
$749$	−21.2719	+	21.2719i	−0.777257	+	0.777257i
$750$		0			0
$751$	−16.3389	−	28.2997i	−0.596213	−	1.03267i	−0.993374	−	0.114923i	$-0.963338\pi$
$751$	−16.3389	−	28.2997i	−0.596213	−	1.03267i	0.397161	−	0.917749i	$-0.369995\pi$
$752$	17.3827	−	2.66671i	0.633880	−	0.0972449i
$753$		0			0
$754$	10.6810	−	4.43516i	0.388978	−	0.161519i
$755$	−12.6061			−0.458781
$756$		0			0
$757$	21.9250	−	12.6584i	0.796879	−	0.460079i	−0.0454994	−	0.998964i	$-0.514488\pi$
$757$	21.9250	−	12.6584i	0.796879	−	0.460079i	0.842379	+	0.538886i	$0.181155\pi$
$758$	−6.02137	−	15.7433i	−0.218706	−	0.571821i
$759$		0			0
$760$	−4.41937	+	20.4256i	−0.160308	+	0.740913i
$761$	12.5595	−	3.36531i	0.455282	−	0.121993i	−0.0238877	−	0.999715i	$-0.507604\pi$
$761$	12.5595	−	3.36531i	0.455282	−	0.121993i	0.479170	+	0.877722i	$0.340938\pi$
$762$		0			0
$763$	34.8110	−	60.2944i	1.26024	−	2.18280i
$764$	−16.3710	+	14.6687i	−0.592282	+	0.530696i
$765$		0			0
$766$	26.7299	+	21.6992i	0.965790	+	0.784024i
$767$	9.77389	−	18.0913i	0.352915	−	0.653239i
$768$		0			0
$769$	47.5222	+	12.7335i	1.71369	+	0.459183i	0.976325	−	0.216308i	$-0.0694014\pi$
$769$	47.5222	+	12.7335i	1.71369	+	0.459183i	0.737369	+	0.675490i	$0.236068\pi$
$770$	5.12385	−	32.0985i	0.184651	−	1.15675i
$771$		0			0
$772$	−6.94340	−	4.53309i	−0.249898	−	0.163150i
$773$	−4.85399	+	1.30062i	−0.174586	+	0.0467802i	−0.345053	−	0.938583i	$-0.612139\pi$
$773$	−4.85399	+	1.30062i	−0.174586	+	0.0467802i	0.170467	+	0.985363i	$0.445472\pi$
$774$		0			0
$775$	0.543276	−	0.543276i	0.0195151	−	0.0195151i
$776$	−5.15770	−	8.00583i	−0.185151	−	0.287392i
$777$		0			0
$778$	−17.0413	−	23.5153i	−0.610960	−	0.843064i
$779$		−	3.92901i		−	0.140771i
$780$		0			0
$781$		−	14.5479i		−	0.520564i
$782$	0.261158	−	0.189259i	0.00933900	−	0.00676788i
$783$		0			0
$784$	34.1327	+	3.75510i	1.21903	+	0.134111i
$785$	3.22588	−	3.22588i	0.115137	−	0.115137i
$786$		0			0
$787$	−45.4229	+	12.1710i	−1.61915	+	0.433851i	−0.950752	−	0.309951i	$-0.899687\pi$
$787$	−45.4229	+	12.1710i	−1.61915	+	0.433851i	−0.668400	+	0.743802i	$0.733021\pi$
$788$	−21.9889	−	14.3558i	−0.783322	−	0.511402i
$789$		0			0
$790$	−48.7817	−	7.78696i	−1.73558	−	0.277048i
$791$	−44.4089	−	11.8993i	−1.57900	−	0.423091i
$792$		0			0
$793$	18.6456	−	5.56549i	0.662126	−	0.197636i
$794$	−24.4053	+	30.0634i	−0.866112	+	1.06691i
$795$		0			0
$796$	−18.2347	−	20.3508i	−0.646311	−	0.721314i
$797$	23.4500	−	40.6165i	0.830641	−	1.43871i	−0.0668904	−	0.997760i	$-0.521308\pi$
$797$	23.4500	−	40.6165i	0.830641	−	1.43871i	0.897531	−	0.440951i	$-0.145359\pi$
$798$		0			0
$799$	1.83248	−	0.491012i	0.0648285	−	0.0173708i
$800$	−5.84769	−	0.0354831i	−0.206747	−	0.00125452i
$801$		0			0
$802$	−7.06937	+	2.70384i	−0.249628	+	0.0954758i
$803$	30.8583	−	17.8161i	1.08897	−	0.628715i
$804$		0			0
$805$	−4.15527			−0.146454
$806$	2.30966	+	3.00455i	0.0813543	+	0.105831i
$807$		0			0
$808$	−3.75418	−	3.40511i	−0.132072	−	0.119791i
$809$	5.37324	+	9.30673i	0.188913	+	0.327207i	0.944888	−	0.327393i	$-0.106170\pi$
$809$	5.37324	+	9.30673i	0.188913	+	0.327207i	−0.755975	+	0.654600i	$0.772837\pi$
$810$		0			0
$811$	−13.3668	+	13.3668i	−0.469372	+	0.469372i	−0.901711	−	0.432339i	$-0.857688\pi$
$811$	−13.3668	+	13.3668i	−0.469372	+	0.469372i	0.432339	+	0.901711i	$0.357688\pi$
$812$	−15.9757	+	8.09127i	−0.560639	+	0.283948i
$813$		0			0
$814$	19.1878	−	1.99318i	0.672533	−	0.0698610i
$815$	33.6606	+	19.4339i	1.17908	+	0.680741i
$816$		0			0
$817$	6.41748	−	23.9504i	0.224519	−	0.837917i
$818$	28.4970	−	35.1037i	0.996375	−	1.22737i
$819$		0			0
$820$	−4.12816	+	0.867000i	−0.144161	+	0.0302769i
$821$	3.83338	−	14.3064i	0.133786	−	0.499295i	−0.866214	−	0.499673i	$-0.833454\pi$
$821$	3.83338	−	14.3064i	0.133786	−	0.499295i	1.00000		0.000377692i	$0.000120223\pi$
$822$		0			0
$823$	18.8317	−	32.6174i	0.656431	−	1.13697i	−0.325102	−	0.945679i	$-0.605399\pi$
$823$	18.8317	−	32.6174i	0.656431	−	1.13697i	0.981533	−	0.191292i	$-0.0612679\pi$
$824$	−16.8678	+	5.41288i	−0.587619	+	0.188567i
$825$		0			0
$826$	−12.9858	+	29.0715i	−0.451832	+	1.01153i
$827$	2.55841	+	2.55841i	0.0889646	+	0.0889646i	0.750189	−	0.661224i	$-0.229963\pi$
$827$	2.55841	+	2.55841i	0.0889646	+	0.0889646i	−0.661224	+	0.750189i	$0.729963\pi$
$828$		0			0
$829$	−3.90712	−	6.76733i	−0.135700	−	0.235039i	0.790165	−	0.612895i	$-0.209995\pi$
$829$	−3.90712	−	6.76733i	−0.135700	−	0.235039i	−0.925865	+	0.377855i	$0.876662\pi$
$830$	22.5468	+	31.1124i	0.782612	+	1.07993i
$831$		0			0
$832$	3.91338	−	28.5777i	0.135672	−	0.990754i
$833$	3.70435			0.128348
$834$		0			0
$835$	−20.3073	−	35.1733i	−0.702763	−	1.21722i
$836$	−6.75325	+	20.6140i	−0.233566	+	0.712950i
$837$		0			0
$838$	4.68519	−	10.4888i	0.161847	−	0.362331i
$839$	7.70458	+	28.7539i	0.265991	+	0.992694i	0.961641	+	0.274312i	$0.0884501\pi$
$839$	7.70458	+	28.7539i	0.265991	+	0.992694i	−0.695649	+	0.718382i	$0.744883\pi$
$840$		0			0
$841$	−11.9278	+	20.6596i	−0.411304	+	0.712399i
$842$	7.47602	−	46.8338i	0.257641	−	1.61400i
$843$		0			0
$844$	−16.7804	+	3.52423i	−0.577605	+	0.121309i
$845$	17.2433	−	19.3123i	0.593187	−	0.664363i
$846$		0			0
$847$	−2.50681	+	9.35554i	−0.0861349	+	0.321460i
$848$	13.9492	−	19.0047i	0.479016	−	0.652624i
$849$		0			0
$850$	−0.627465	+	0.0651795i	−0.0215219	+	0.00223564i
$851$	−0.638268	−	2.38205i	−0.0218795	−	0.0816555i
$852$		0			0
$853$	−7.62369	+	7.62369i	−0.261030	+	0.261030i	−0.825473	−	0.564442i	$-0.809091\pi$
$853$	−7.62369	+	7.62369i	−0.261030	+	0.261030i	0.564442	+	0.825473i	$0.309091\pi$
$854$	−28.1420	+	10.7636i	−0.963001	+	0.368321i
$855$		0			0
$856$	−15.9647	−	14.4803i	−0.545663	−	0.494926i
$857$			56.9565i			1.94560i	0.231650	+	0.972799i	$0.425588\pi$
$857$			56.9565i			1.94560i	−0.231650	+	0.972799i	$0.574412\pi$
$858$		0			0
$859$	−12.7259			−0.434201			−0.217101	−	0.976149i	$-0.569660\pi$
$859$	−12.7259			−0.434201			−0.217101	+	0.976149i	$0.569660\pi$
$860$	−26.5804	−	1.45772i	−0.906385	−	0.0497079i
$861$		0			0
$862$	41.8715	−	16.0147i	1.42615	−	0.545462i
$863$	−28.5737	−	28.5737i	−0.972660	−	0.972660i	0.0269758	−	0.999636i	$-0.491412\pi$
$863$	−28.5737	−	28.5737i	−0.972660	−	0.972660i	−0.999636	+	0.0269758i	$0.991412\pi$
$864$		0			0
$865$	44.4304	−	11.9051i	1.51068	−	0.404786i
$866$	−2.82888	−	27.2328i	−0.0961291	−	0.925409i
$867$		0			0
$868$	−3.91593	−	4.37037i	−0.132915	−	0.148340i
$869$	−49.5285	−	13.2711i	−1.68014	−	0.450192i
$870$		0			0
$871$	5.61620	−	3.45777i	0.190298	−	0.117162i
$872$	44.3623	+	22.8075i	1.50230	+	0.772361i
$873$		0			0
$874$	2.73833	+	0.437116i	0.0926254	+	0.0147857i
$875$	41.0825	+	23.7190i	1.38884	+	0.801848i
$876$		0			0
$877$	−7.32275	+	1.96212i	−0.247272	+	0.0662562i	−0.380326	−	0.924853i	$-0.624188\pi$
$877$	−7.32275	+	1.96212i	−0.247272	+	0.0662562i	0.133054	+	0.991109i	$0.457522\pi$
$878$	10.7253	−	24.0110i	0.361962	−	0.810333i
$879$		0			0
$880$	23.1490	+	2.54673i	0.780354	+	0.0858504i
$881$	29.2464	−	16.8854i	0.985336	−	0.568884i	0.0814588	−	0.996677i	$-0.474042\pi$
$881$	29.2464	−	16.8854i	0.985336	−	0.568884i	0.903877	+	0.427793i	$0.140709\pi$
$882$		0			0
$883$		−	33.0864i		−	1.11345i	−0.830698	−	0.556723i	$-0.812058\pi$
$883$		−	33.0864i		−	1.11345i	0.830698	−	0.556723i	$-0.187942\pi$
$884$	0.0825036	−	3.11055i	0.00277490	−	0.104619i
$885$		0			0
$886$	3.16649	+	4.36944i	0.106380	+	0.146794i
$887$	5.41849	−	3.12837i	0.181935	−	0.105040i	−0.406266	−	0.913755i	$-0.633169\pi$
$887$	5.41849	−	3.12837i	0.181935	−	0.105040i	0.588202	+	0.808714i	$0.299836\pi$
$888$		0			0
$889$	54.5835	−	54.5835i	1.83067	−	1.83067i
$890$	23.9642	+	10.7044i	0.803282	+	0.358813i
$891$		0			0
$892$	3.11429	+	2.03321i	0.104274	+	0.0680769i
$893$	14.1258	+	8.15552i	0.472701	+	0.272914i
$894$		0			0
$895$	−19.0051	−	5.09239i	−0.635269	−	0.170220i
$896$	−2.71632	+	44.5809i	−0.0907458	+	1.48934i
$897$		0			0
$898$	8.40584	+	6.82382i	0.280506	+	0.227714i
$899$	1.62828	+	0.436296i	0.0543061	+	0.0145513i
$900$		0			0
$901$	1.27157	−	2.20243i	0.0423622	−	0.0733735i
$902$	−4.35501	+	0.452387i	−0.145006	+	0.0150628i
$903$		0			0
$904$	6.96585	−	32.1949i	0.231681	−	1.07079i
$905$	20.5749	+	20.5749i	0.683932	+	0.683932i
$906$		0			0
$907$	39.7698	−	22.9611i	1.32053	−	0.762410i	0.336719	−	0.941605i	$-0.390683\pi$
$907$	39.7698	−	22.9611i	1.32053	−	0.762410i	0.983814	+	0.179195i	$0.0573493\pi$
$908$	39.8110	+	2.18331i	1.32118	+	0.0724558i
$909$		0			0
$910$	−24.3768	+	31.8261i	−0.808082	+	1.05503i
$911$		−	40.9298i		−	1.35607i	−0.735032	−	0.678033i	$-0.762833\pi$
$911$		−	40.9298i		−	1.35607i	0.735032	−	0.678033i	$-0.237167\pi$
$912$		0			0
$913$	19.9413	+	34.5394i	0.659961	+	1.14309i
$914$	9.19698	+	24.0461i	0.304209	+	0.795375i
$915$		0			0
$916$	7.51846	+	14.8448i	0.248417	+	0.490485i
$917$	16.4980	+	61.5713i	0.544811	+	2.03326i
$918$		0			0
$919$	−6.79881	−	3.92529i	−0.224272	−	0.129484i	0.383655	−	0.923477i	$-0.374665\pi$
$919$	−6.79881	−	3.92529i	−0.224272	−	0.129484i	−0.607927	+	0.793993i	$0.707999\pi$
$920$	−0.144985	−	2.97358i	−0.00478002	−	0.0980360i
$921$		0			0
$922$	4.43809	+	3.60282i	0.146161	+	0.118653i
$923$	−8.52832	+	15.7858i	−0.280713	+	0.519595i
$924$		0			0
$925$	−1.24842	+	4.65915i	−0.0410477	+	0.153192i
$926$	0.153813	+	0.0245530i	0.00505462	+	0.000806863i
$927$		0			0
$928$	−6.34767	−	11.1502i	−0.208373	−	0.366023i
$929$	−5.88675	−	21.9696i	−0.193138	−	0.720800i	−0.992741	−	0.120272i	$-0.961623\pi$
$929$	−5.88675	−	21.9696i	−0.193138	−	0.720800i	0.799603	−	0.600529i	$-0.205043\pi$
$930$		0			0
$931$	22.5207	+	22.5207i	0.738087	+	0.738087i
$932$	−28.4178	−	9.30983i	−0.930857	−	0.304954i
$933$		0			0
$934$	−0.693173	+	0.502336i	−0.0226813	+	0.0164369i
$935$	2.51231			0.0821614
$936$		0			0
$937$	35.1246			1.14747			0.573735	−	0.819041i	$-0.305494\pi$
$937$	35.1246			1.14747			0.573735	+	0.819041i	$0.305494\pi$
$938$	−8.26925	+	5.99264i	−0.270001	+	0.195667i
$939$		0			0
$940$	5.45181	−	16.6414i	0.177818	−	0.542782i
$941$	−33.4717	−	33.4717i	−1.09115	−	1.09115i	−0.995406	−	0.0957410i	$-0.969478\pi$
$941$	−33.4717	−	33.4717i	−1.09115	−	1.09115i	−0.0957410	−	0.995406i	$-0.530522\pi$
$942$		0			0
$943$	0.144866	+	0.540646i	0.00471748	+	0.0176059i
$944$	−21.2571	−	8.27846i	−0.691861	−	0.269441i
$945$		0			0
$946$	−27.2861	−	4.35564i	−0.887147	−	0.141614i
$947$	−6.87571	+	25.6605i	−0.223430	+	0.833854i	0.759597	+	0.650394i	$0.225396\pi$
$947$	−6.87571	+	25.6605i	−0.223430	+	0.833854i	−0.983027	+	0.183460i	$0.941270\pi$
$948$		0			0
$949$	−43.9283	+	1.24216i	−1.42597	+	0.0403222i
$950$	−4.21096	−	3.41844i	−0.136622	−	0.110909i
$951$		0			0
$952$	0.234644	+	4.81245i	0.00760487	+	0.155973i
$953$	18.5794	+	10.7268i	0.601845	+	0.347475i	0.769767	−	0.638325i	$-0.220372\pi$
$953$	18.5794	+	10.7268i	0.601845	+	0.347475i	−0.167922	+	0.985800i	$0.553706\pi$
$954$		0			0
$955$	5.66515	+	21.1426i	0.183320	+	0.684159i
$956$	−5.33508	+	2.70207i	−0.172549	+	0.0873912i
$957$		0			0
$958$	−8.01632	−	20.9592i	−0.258995	−	0.677161i
$959$	26.1869	+	45.3570i	0.845618	+	1.46465i
$960$		0			0
$961$		−	30.4476i		−	0.982181i
$962$	−21.9890	−	9.08559i	−0.708954	−	0.292931i
$963$		0			0
$964$	−1.56640	+	28.5620i	−0.0504502	+	0.919921i
$965$	−7.15085	+	4.12854i	−0.230194	+	0.132903i
$966$		0			0
$967$	−28.4651	−	28.4651i	−0.915375	−	0.915375i	0.0813132	−	0.996689i	$-0.474089\pi$
$967$	−28.4651	−	28.4651i	−0.915375	−	0.915375i	−0.996689	+	0.0813132i	$0.974089\pi$
$968$	−6.78245	−	1.46748i	−0.217996	−	0.0471667i
$969$		0			0
$970$	−9.43238	+	0.979811i	−0.302855	+	0.0314598i
$971$	2.57471	−	4.45954i	0.0826265	−	0.143113i	−0.821751	−	0.569847i	$-0.807002\pi$
$971$	2.57471	−	4.45954i	0.0826265	−	0.143113i	0.904377	+	0.426734i	$0.140336\pi$
$972$		0			0
$973$	−46.3262	−	12.4131i	−1.48515	−	0.397945i
$974$	1.82768	+	1.48370i	0.0585627	+	0.0475409i
$975$		0			0
$976$	−8.68451	−	19.7634i	−0.277984	−	0.632610i
$977$	12.7613	+	3.41938i	0.408270	+	0.109396i	0.457108	−	0.889411i	$-0.348885\pi$
$977$	12.7613	+	3.41938i	0.408270	+	0.109396i	−0.0488381	+	0.998807i	$0.515552\pi$
$978$		0			0
$979$	23.5933	+	13.6216i	0.754046	+	0.435349i
$980$	18.6927	−	28.6318i	0.597115	−	0.914609i
$981$		0			0
$982$	−28.5791	−	12.7658i	−0.911997	−	0.407374i
$983$	−6.17750	+	6.17750i	−0.197032	+	0.197032i	−0.798726	−	0.601695i	$-0.794492\pi$
$983$	−6.17750	+	6.17750i	−0.197032	+	0.197032i	0.601695	+	0.798726i	$0.294492\pi$
$984$		0			0
$985$	−22.6459	+	13.0746i	−0.721557	+	0.416591i
$986$	−0.812198	−	1.12075i	−0.0258656	−	0.0356920i
$987$		0			0
$988$	19.4123	−	18.4091i	0.617588	−	0.585673i
$989$			3.53228i			0.112320i
$990$		0			0
$991$	23.9402	−	13.8219i	0.760486	−	0.439067i	−0.0689844	−	0.997618i	$-0.521976\pi$
$991$	23.9402	−	13.8219i	0.760486	−	0.439067i	0.829470	+	0.558551i	$0.188643\pi$
$992$	2.99087	−	2.95480i	0.0949604	−	0.0938149i
$993$		0			0
$994$	11.3309	−	25.3667i	0.359393	−	0.804582i
$995$	−26.2823	+	7.04233i	−0.833206	+	0.223257i
$996$		0			0
$997$	52.0747	+	30.0653i	1.64922	+	0.952179i	0.977382	+	0.211483i	$0.0678292\pi$
$997$	52.0747	+	30.0653i	1.64922	+	0.952179i	0.671840	+	0.740696i	$0.265504\pi$
$998$	−10.1786	−	1.62479i	−0.322196	−	0.0514318i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.ed.d.379.8		48
3.2	odd	2		104.2.u.a.67.5	yes	48
8.3	odd	2	inner	936.2.ed.d.379.11		48
12.11	even	2		416.2.bk.a.15.1		48
13.7	odd	12	inner	936.2.ed.d.163.11		48
24.5	odd	2		416.2.bk.a.15.2		48
24.11	even	2		104.2.u.a.67.2	yes	48
39.20	even	12		104.2.u.a.59.2	✓	48
104.59	even	12	inner	936.2.ed.d.163.8		48
156.59	odd	12		416.2.bk.a.111.2		48
312.59	odd	12		104.2.u.a.59.5	yes	48
312.293	even	12		416.2.bk.a.111.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.u.a.59.2	✓	48	39.20	even	12
104.2.u.a.59.5	yes	48	312.59	odd	12
104.2.u.a.67.2	yes	48	24.11	even	2
104.2.u.a.67.5	yes	48	3.2	odd	2
416.2.bk.a.15.1		48	12.11	even	2
416.2.bk.a.15.2		48	24.5	odd	2
416.2.bk.a.111.1		48	312.293	even	12
416.2.bk.a.111.2		48	156.59	odd	12
936.2.ed.d.163.8		48	104.59	even	12	inner
936.2.ed.d.163.11		48	13.7	odd	12	inner
936.2.ed.d.379.8		48	1.1	even	1	trivial
936.2.ed.d.379.11		48	8.3	odd	2	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:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.ed (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.829865 + 1.14513i) q^{2} +(-0.622649 + 1.90061i) q^{4} +(1.40823 + 1.40823i) q^{5} +(1.02175 + 3.81323i) q^{7} +(-2.69316 + 0.864233i) q^{8} +O(q^{10})\)	\(q+(0.829865 + 1.14513i) q^{2} +(-0.622649 + 1.90061i) q^{4} +(1.40823 + 1.40823i) q^{5} +(1.02175 + 3.81323i) q^{7} +(-2.69316 + 0.864233i) q^{8} +(-0.443968 + 2.78126i) q^{10} +(-0.756644 + 2.82384i) q^{11} +(2.47643 - 2.62055i) q^{13} +(-3.51873 + 4.33450i) q^{14} +(-3.22462 - 2.36682i) q^{16} +(-0.373696 - 0.215754i) q^{17} +(-0.960219 - 3.58359i) q^{19} +(-3.55334 + 1.79966i) q^{20} +(-3.86157 + 1.47694i) q^{22} +(0.264259 + 0.457711i) q^{23} -1.03375i q^{25} +(5.05598 + 0.661127i) q^{26} +(-7.88364 - 0.432354i) q^{28} +(1.96425 - 1.13406i) q^{29} +(0.525538 + 0.525538i) q^{31} +(0.0343246 - 5.65675i) q^{32} +(-0.0630513 - 0.606978i) q^{34} +(-3.93105 + 6.80878i) q^{35} +(-4.50702 - 1.20765i) q^{37} +(3.30682 - 4.07347i) q^{38} +(-5.00964 - 2.57556i) q^{40} +(1.02295 + 0.274098i) q^{41} +(5.78795 + 3.34168i) q^{43} +(-4.89588 - 3.19634i) q^{44} +(-0.304839 + 0.682450i) q^{46} +(-3.10880 + 3.10880i) q^{47} +(-7.43454 + 4.29233i) q^{49} +(1.18378 - 0.857876i) q^{50} +(3.43870 + 6.33840i) q^{52} +5.89363i q^{53} +(-5.04215 + 2.91109i) q^{55} +(-6.04725 - 9.38659i) q^{56} +(2.92871 + 1.30821i) q^{58} +(5.50874 - 1.47606i) q^{59} +(4.67379 + 2.69841i) q^{61} +(-0.165684 + 1.03793i) q^{62} +(6.50620 - 4.65503i) q^{64} +(7.17774 - 0.202965i) q^{65} +(1.76688 + 0.473433i) q^{67} +(0.642745 - 0.575911i) q^{68} +(-11.0592 + 1.14880i) q^{70} +(-4.80671 + 1.28795i) q^{71} +(-8.61849 - 8.61849i) q^{73} +(-2.35730 - 6.16332i) q^{74} +(7.40887 + 0.406316i) q^{76} -11.5410 q^{77} +17.5395i q^{79} +(-1.20798 - 7.87405i) q^{80} +(0.535030 + 1.39887i) q^{82} +(9.64657 - 9.64657i) q^{83} +(-0.222420 - 0.830084i) q^{85} +(0.976562 + 9.40110i) q^{86} +(-0.402688 - 8.25895i) q^{88} +(2.41190 - 9.00133i) q^{89} +(12.5231 + 6.76562i) q^{91} +(-1.03447 + 0.217260i) q^{92} +(-6.13986 - 0.980098i) q^{94} +(3.69432 - 6.39874i) q^{95} +(0.871452 + 3.25230i) q^{97} +(-11.0849 - 4.95147i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{2} - 6 q^{4} + 10 q^{8}+O(q^{10}) \) 48 * q + 4 * q^2 - 6 * q^4 + 10 * q^8	\( 48 q + 4 q^{2} - 6 q^{4} + 10 q^{8} - 6 q^{10} + 8 q^{11} - 8 q^{14} - 10 q^{16} + 12 q^{17} - 8 q^{19} - 10 q^{20} - 20 q^{22} + 2 q^{26} + 12 q^{28} - 16 q^{32} - 46 q^{34} + 4 q^{35} - 32 q^{40} - 12 q^{43} + 16 q^{44} + 34 q^{46} - 60 q^{49} - 86 q^{50} + 12 q^{52} - 48 q^{56} + 30 q^{58} + 64 q^{59} - 42 q^{62} + 16 q^{65} - 8 q^{67} + 32 q^{68} + 36 q^{70} - 12 q^{73} - 38 q^{74} - 94 q^{76} + 108 q^{80} + 54 q^{82} + 48 q^{83} - 80 q^{86} - 108 q^{88} - 12 q^{89} + 104 q^{91} + 20 q^{92} + 26 q^{94} + 4 q^{97} + 16 q^{98}+O(q^{100}) \) 48 * q + 4 * q^2 - 6 * q^4 + 10 * q^8 - 6 * q^10 + 8 * q^11 - 8 * q^14 - 10 * q^16 + 12 * q^17 - 8 * q^19 - 10 * q^20 - 20 * q^22 + 2 * q^26 + 12 * q^28 - 16 * q^32 - 46 * q^34 + 4 * q^35 - 32 * q^40 - 12 * q^43 + 16 * q^44 + 34 * q^46 - 60 * q^49 - 86 * q^50 + 12 * q^52 - 48 * q^56 + 30 * q^58 + 64 * q^59 - 42 * q^62 + 16 * q^65 - 8 * q^67 + 32 * q^68 + 36 * q^70 - 12 * q^73 - 38 * q^74 - 94 * q^76 + 108 * q^80 + 54 * q^82 + 48 * q^83 - 80 * q^86 - 108 * q^88 - 12 * q^89 + 104 * q^91 + 20 * q^92 + 26 * q^94 + 4 * q^97 + 16 * q^98

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