LMFDB - Embedded newform 405.2.r.a.17.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,2,Mod(8,405)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("405.8"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([2, 27])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.r (of order $36$, degree $12$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			17.3
Character	$\chi$	$=$	405.17
Dual form			405.2.r.a.143.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.81626 + 0.846935i) q^{2} +(1.29592 - 1.54442i) q^{4} +(-0.828498 - 2.07692i) q^{5} +(-2.21198 - 0.193523i) q^{7} +(-0.00834683 + 0.0311508i) q^{8} +(3.26378 + 3.07054i) q^{10} +(-1.09616 + 0.193283i) q^{11} +(-1.28211 + 2.74949i) q^{13} +(4.18143 - 1.52192i) q^{14} +(0.688959 + 3.90728i) q^{16} +(1.56207 + 5.82972i) q^{17} +(3.84801 - 2.22165i) q^{19} +(-4.28129 - 1.41197i) q^{20} +(1.82722 - 1.27943i) q^{22} +(0.293046 + 3.34953i) q^{23} +(-3.62718 + 3.44145i) q^{25} -6.07964i q^{26} +(-3.16543 + 3.16543i) q^{28} +(1.74671 + 0.635749i) q^{29} +(7.13252 + 5.98490i) q^{31} +(-4.59753 - 6.56596i) q^{32} +(-7.77451 - 9.26530i) q^{34} +(1.43069 + 4.75444i) q^{35} +(-4.53439 + 1.21499i) q^{37} +(-5.10738 + 7.29410i) q^{38} +(0.0716130 - 0.00847269i) q^{40} +(1.07377 + 2.95017i) q^{41} +(-5.86507 - 4.10676i) q^{43} +(-1.12203 + 1.94341i) q^{44} +(-3.36908 - 5.83541i) q^{46} +(-1.10183 + 12.5940i) q^{47} +(-2.03824 - 0.359397i) q^{49} +(3.67322 - 9.32254i) q^{50} +(2.58485 + 5.54322i) q^{52} +(-6.34457 - 6.34457i) q^{53} +(1.30960 + 2.11651i) q^{55} +(0.0244914 - 0.0672897i) q^{56} +(-3.71091 + 0.324662i) q^{58} +(-0.242616 + 1.37594i) q^{59} +(-2.30056 + 1.93040i) q^{61} +(-18.0233 - 4.82933i) q^{62} +(7.03924 + 4.06411i) q^{64} +(6.77268 + 0.384887i) q^{65} +(8.07622 + 3.76600i) q^{67} +(11.0278 + 5.14236i) q^{68} +(-6.62521 - 7.42359i) q^{70} +(6.78702 + 3.91849i) q^{71} +(-0.167045 - 0.0447595i) q^{73} +(7.20661 - 6.04707i) q^{74} +(1.55556 - 8.82200i) q^{76} +(2.46210 - 0.215406i) q^{77} +(-0.697324 + 1.91588i) q^{79} +(7.54430 - 4.66809i) q^{80} +(-4.44885 - 4.44885i) q^{82} +(2.27031 + 4.86870i) q^{83} +(10.8137 - 8.07420i) q^{85} +(14.1306 + 2.49161i) q^{86} +(0.00312857 - 0.0357597i) q^{88} +(-6.70700 - 11.6169i) q^{89} +(3.36809 - 5.83370i) q^{91} +(5.55283 + 3.88813i) q^{92} +(-8.66507 - 23.8071i) q^{94} +(-7.80225 - 6.15137i) q^{95} +(9.92914 - 14.1803i) q^{97} +(4.00635 - 1.07350i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{11}{18}\right)$

Coefficient data

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

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

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

$2$	−1.81626	+	0.846935i	−1.28429	+	0.598874i	−0.940379	−	0.340129i	$-0.889529\pi$
$2$	−1.81626	+	0.846935i	−1.28429	+	0.598874i	−0.343910	+	0.939003i	$0.611751\pi$
$3$		0			0
$3$		0			0
$4$	1.29592	−	1.54442i	0.647960	−	0.772208i
$5$	−0.828498	−	2.07692i	−0.370516	−	0.928826i
$5$	−0.828498	−	2.07692i	−0.370516	−	0.928826i
$6$		0			0
$7$	−2.21198	−	0.193523i	−0.836051	−	0.0731450i	−0.338914	−	0.940817i	$-0.610060\pi$
$7$	−2.21198	−	0.193523i	−0.836051	−	0.0731450i	−0.497137	+	0.867672i	$0.665615\pi$
$8$	−0.00834683	+	0.0311508i	−0.00295105	+	0.0110135i
$9$		0			0
$10$	3.26378	+	3.07054i	1.03210	+	0.970989i
$11$	−1.09616	+	0.193283i	−0.330506	+	0.0582771i	−0.336439	−	0.941705i	$-0.609223\pi$
$11$	−1.09616	+	0.193283i	−0.330506	+	0.0582771i	0.00593305	+	0.999982i	$0.498111\pi$
$12$		0			0
$13$	−1.28211	+	2.74949i	−0.355592	+	0.762570i	−0.999998	−	0.00211367i	$-0.999327\pi$
$13$	−1.28211	+	2.74949i	−0.355592	+	0.762570i	0.644405	+	0.764684i	$0.277105\pi$
$14$	4.18143	−	1.52192i	1.11753	−	0.406749i
$15$		0			0
$16$	0.688959	+	3.90728i	0.172240	+	0.976820i
$17$	1.56207	+	5.82972i	0.378857	+	1.41391i	0.847626	+	0.530594i	$0.178031\pi$
$17$	1.56207	+	5.82972i	0.378857	+	1.41391i	−0.468769	+	0.883321i	$0.655302\pi$
$18$		0			0
$19$	3.84801	−	2.22165i	0.882794	−	0.509681i	0.0112151	−	0.999937i	$-0.496430\pi$
$19$	3.84801	−	2.22165i	0.882794	−	0.509681i	0.871578	+	0.490256i	$0.163097\pi$
$20$	−4.28129	−	1.41197i	−0.957326	−	0.315727i
$21$		0			0
$22$	1.82722	−	1.27943i	0.389564	−	0.272776i
$23$	0.293046	+	3.34953i	0.0611042	+	0.698425i	0.963534	+	0.267587i	$0.0862263\pi$
$23$	0.293046	+	3.34953i	0.0611042	+	0.698425i	−0.902429	+	0.430838i	$0.858218\pi$
$24$		0			0
$25$	−3.62718	+	3.44145i	−0.725436	+	0.688289i
$26$		−	6.07964i		−	1.19232i
$27$		0			0
$28$	−3.16543	+	3.16543i	−0.598210	+	0.598210i
$29$	1.74671	+	0.635749i	0.324355	+	0.118056i	0.499066	−	0.866564i	$-0.333677\pi$
$29$	1.74671	+	0.635749i	0.324355	+	0.118056i	−0.174710	+	0.984620i	$0.555899\pi$
$30$		0			0
$31$	7.13252	+	5.98490i	1.28104	+	1.07492i	0.993100	+	0.117270i	$0.0374144\pi$
$31$	7.13252	+	5.98490i	1.28104	+	1.07492i	0.287939	+	0.957649i	$0.407030\pi$
$32$	−4.59753	−	6.56596i	−0.812737	−	1.16071i
$33$		0			0
$34$	−7.77451	−	9.26530i	−1.33332	−	1.58899i
$35$	1.43069	+	4.75444i	0.241831	+	0.803647i
$36$		0			0
$37$	−4.53439	+	1.21499i	−0.745450	+	0.199743i	−0.611499	−	0.791245i	$-0.709433\pi$
$37$	−4.53439	+	1.21499i	−0.745450	+	0.199743i	−0.133951	+	0.990988i	$0.542766\pi$
$38$	−5.10738	+	7.29410i	−0.828527	+	1.18326i
$39$		0			0
$40$	0.0716130	−	0.00847269i	0.0113230	−	0.00133965i
$41$	1.07377	+	2.95017i	0.167695	+	0.460739i	0.994865	−	0.101214i	$-0.0322726\pi$
$41$	1.07377	+	2.95017i	0.167695	+	0.460739i	−0.827169	+	0.561953i	$0.810050\pi$
$42$		0			0
$43$	−5.86507	−	4.10676i	−0.894414	−	0.626276i	0.0333495	−	0.999444i	$-0.489383\pi$
$43$	−5.86507	−	4.10676i	−0.894414	−	0.626276i	−0.927764	+	0.373168i	$0.878271\pi$
$44$	−1.12203	+	1.94341i	−0.169152	+	0.292981i
$45$		0			0
$46$	−3.36908	−	5.83541i	−0.496743	−	0.860385i
$47$	−1.10183	+	12.5940i	−0.160718	+	1.83702i	0.305313	+	0.952252i	$0.401239\pi$
$47$	−1.10183	+	12.5940i	−0.160718	+	1.83702i	−0.466031	+	0.884768i	$0.654317\pi$
$48$		0			0
$49$	−2.03824	−	0.359397i	−0.291177	−	0.0513424i
$50$	3.67322	−	9.32254i	0.519471	−	1.31841i
$51$		0			0
$52$	2.58485	+	5.54322i	0.358454	+	0.768706i
$53$	−6.34457	−	6.34457i	−0.871494	−	0.871494i	0.121142	−	0.992635i	$-0.461344\pi$
$53$	−6.34457	−	6.34457i	−0.871494	−	0.871494i	−0.992635	+	0.121142i	$0.961344\pi$
$54$		0			0
$55$	1.30960	+	2.11651i	0.176587	+	0.285390i
$56$	0.0244914	−	0.0672897i	0.00327281	−	0.00899196i
$57$		0			0
$58$	−3.71091	+	0.324662i	−0.487266	+	0.0426303i
$59$	−0.242616	+	1.37594i	−0.0315859	+	0.179132i	−0.996519	−	0.0833623i	$-0.973434\pi$
$59$	−0.242616	+	1.37594i	−0.0315859	+	0.179132i	0.964933	+	0.262495i	$0.0845452\pi$
$60$		0			0
$61$	−2.30056	+	1.93040i	−0.294557	+	0.247163i	−0.778075	−	0.628172i	$-0.783803\pi$
$61$	−2.30056	+	1.93040i	−0.294557	+	0.247163i	0.483517	+	0.875335i	$0.339359\pi$
$62$	−18.0233	−	4.82933i	−2.28896	−	0.613326i
$63$		0			0
$64$	7.03924	+	4.06411i	0.879905	+	0.508014i
$65$	6.77268	+	0.384887i	0.840048	+	0.0477393i
$66$		0			0
$67$	8.07622	+	3.76600i	0.986667	+	0.460090i	0.847855	−	0.530228i	$-0.177894\pi$
$67$	8.07622	+	3.76600i	0.986667	+	0.460090i	0.138812	+	0.990319i	$0.455672\pi$
$68$	11.0278	+	5.14236i	1.33732	+	0.623603i
$69$		0			0
$70$	−6.62521	−	7.42359i	−0.791864	−	0.887289i
$71$	6.78702	+	3.91849i	0.805471	+	0.465039i	0.845380	−	0.534165i	$-0.179374\pi$
$71$	6.78702	+	3.91849i	0.805471	+	0.465039i	−0.0399099	+	0.999203i	$0.512707\pi$
$72$		0			0
$73$	−0.167045	−	0.0447595i	−0.0195511	−	0.00523870i	0.249030	−	0.968496i	$-0.419888\pi$
$73$	−0.167045	−	0.0447595i	−0.0195511	−	0.00523870i	−0.268581	+	0.963257i	$0.586555\pi$
$74$	7.20661	−	6.04707i	0.837752	−	0.702957i
$75$		0			0
$76$	1.55556	−	8.82200i	0.178435	−	1.01195i
$77$	2.46210	−	0.215406i	0.280582	−	0.0245478i
$78$		0			0
$79$	−0.697324	+	1.91588i	−0.0784551	+	0.215554i	−0.972719	−	0.231986i	$-0.925478\pi$
$79$	−0.697324	+	1.91588i	−0.0784551	+	0.215554i	0.894264	+	0.447540i	$0.147700\pi$
$80$	7.54430	−	4.66809i	0.843479	−	0.521908i
$81$		0			0
$82$	−4.44885	−	4.44885i	−0.491293	−	0.491293i
$83$	2.27031	+	4.86870i	0.249199	+	0.534409i	0.990622	−	0.136629i	$-0.0436267\pi$
$83$	2.27031	+	4.86870i	0.249199	+	0.534409i	−0.741423	+	0.671038i	$0.765849\pi$
$84$		0			0
$85$	10.8137	−	8.07420i	1.17291	−	0.875770i
$86$	14.1306	+	2.49161i	1.52375	+	0.268677i
$87$		0			0
$88$	0.00312857	−	0.0357597i	0.000333506	−	0.00381199i
$89$	−6.70700	−	11.6169i	−0.710941	−	1.23139i	−0.964504	−	0.264067i	$-0.914936\pi$
$89$	−6.70700	−	11.6169i	−0.710941	−	1.23139i	0.253563	−	0.967319i	$-0.418397\pi$
$90$		0			0
$91$	3.36809	−	5.83370i	0.353072	−	0.611538i
$92$	5.55283	+	3.88813i	0.578922	+	0.405366i
$93$		0			0
$94$	−8.66507	−	23.8071i	−0.893734	−	2.45551i
$95$	−7.80225	−	6.15137i	−0.800494	−	0.631117i
$96$		0			0
$97$	9.92914	−	14.1803i	1.00815	−	1.43979i	0.113229	−	0.993569i	$-0.463881\pi$
$97$	9.92914	−	14.1803i	1.00815	−	1.43979i	0.894923	−	0.446221i	$-0.147231\pi$
$98$	4.00635	−	1.07350i	0.404703	−	0.108440i
$99$		0			0
$100$	0.614492	+	10.0617i	0.0614492	+	1.00617i
$101$	−4.92991	−	5.87523i	−0.490544	−	0.584608i	0.462812	−	0.886457i	$-0.346841\pi$
$101$	−4.92991	−	5.87523i	−0.490544	−	0.584608i	−0.953356	+	0.301849i	$0.902396\pi$
$102$		0			0
$103$	6.03654	+	8.62107i	0.594798	+	0.849460i	0.997838	−	0.0657227i	$-0.0209353\pi$
$103$	6.03654	+	8.62107i	0.594798	+	0.849460i	−0.403040	+	0.915182i	$0.632046\pi$
$104$	−0.0749472	−	0.0628881i	−0.00734917	−	0.00616669i
$105$		0			0
$106$	16.8968	+	6.14994i	1.64116	+	0.597335i
$107$	4.95248	−	4.95248i	0.478774	−	0.478774i	−0.425965	−	0.904740i	$-0.640065\pi$
$107$	4.95248	−	4.95248i	0.478774	−	0.478774i	0.904740	+	0.425965i	$0.140065\pi$
$108$		0			0
$109$			9.40170i			0.900520i	0.892898	+	0.450260i	$0.148669\pi$
$109$			9.40170i			0.900520i	−0.892898	+	0.450260i	$0.851331\pi$
$110$	−4.17112	−	2.73498i	−0.397701	−	0.260770i
$111$		0			0
$112$	−0.767815	−	8.77616i	−0.0725517	−	0.829270i
$113$	1.10249	−	0.771969i	0.103713	−	0.0726207i	−0.520569	−	0.853819i	$-0.674280\pi$
$113$	1.10249	−	0.771969i	0.103713	−	0.0726207i	0.624283	+	0.781199i	$0.285391\pi$
$114$		0			0
$115$	6.71391	−	3.38371i	0.626075	−	0.315532i
$116$	3.24545	−	1.87376i	0.301333	−	0.173974i
$117$		0			0
$118$	−0.724681	−	2.70455i	−0.0667123	−	0.248974i
$119$	−2.32708	−	13.1975i	−0.213323	−	1.20982i
$120$		0			0
$121$	−9.17240	+	3.33848i	−0.833855	+	0.303498i
$122$	2.54349	−	5.45454i	0.230277	−	0.493831i
$123$		0			0
$124$	18.4863	−	3.25964i	1.66012	−	0.292724i
$125$	10.1527	+	4.68213i	0.908087	+	0.418782i
$126$		0			0
$127$	−3.93996	+	14.7041i	−0.349615	+	1.30478i	0.537513	+	0.843256i	$0.319364\pi$
$127$	−3.93996	+	14.7041i	−0.349615	+	1.30478i	−0.887127	+	0.461525i	$0.847303\pi$
$128$	−0.257007	−	0.0224852i	−0.0227165	−	0.00198743i
$129$		0			0
$130$	−12.6269	+	5.03697i	−1.10745	+	0.441771i
$131$	−12.8204	+	15.2788i	−1.12013	+	1.33491i	−0.184131	+	0.982902i	$0.558947\pi$
$131$	−12.8204	+	15.2788i	−1.12013	+	1.33491i	−0.935995	+	0.352013i	$0.885497\pi$
$132$		0			0
$133$	−8.94167	+	4.16957i	−0.775341	+	0.361547i
$134$	−17.8581			−1.54270
$135$		0			0
$136$	−0.194639			−0.0166901
$137$	14.7130	−	6.86076i	1.25701	−	0.586155i	0.324020	−	0.946050i	$-0.394966\pi$
$137$	14.7130	−	6.86076i	1.25701	−	0.586155i	0.932993	+	0.359896i	$0.117188\pi$
$138$		0			0
$139$	−1.79469	+	2.13883i	−0.152223	+	0.181413i	−0.836767	−	0.547559i	$-0.815557\pi$
$139$	−1.79469	+	2.13883i	−0.152223	+	0.181413i	0.684544	+	0.728972i	$0.260002\pi$
$140$	9.19690	+	3.95179i	0.777280	+	0.333987i
$141$		0			0
$142$	−15.6457	−	1.36882i	−1.31296	−	0.114869i
$143$	0.873969	−	3.26170i	0.0730850	−	0.272757i
$144$		0			0
$145$	−0.126744	−	4.15448i	−0.0105255	−	0.345011i
$146$	0.341305	−	0.0601812i	0.0282466	−	0.00498063i
$147$		0			0
$148$	−3.99976	+	8.57752i	−0.328778	+	0.705068i
$149$	−18.9187	+	6.88585i	−1.54988	+	0.564111i	−0.968390	−	0.249441i	$-0.919753\pi$
$149$	−18.9187	+	6.88585i	−1.54988	+	0.564111i	−0.581492	+	0.813552i	$0.697531\pi$
$150$		0			0
$151$	0.0907569	+	0.514708i	0.00738569	+	0.0418864i	0.988278	−	0.152666i	$-0.0487858\pi$
$151$	0.0907569	+	0.514708i	0.00738569	+	0.0418864i	−0.980892	+	0.194552i	$0.937675\pi$
$152$	0.0370874	+	0.138412i	0.00300819	+	0.0112267i
$153$		0			0
$154$	−4.28937	+	2.47647i	−0.345648	+	0.199560i
$155$	6.52086	−	19.7721i	0.523768	−	1.58814i
$156$		0			0
$157$	0.765462	−	0.535982i	0.0610905	−	0.0427760i	−0.542632	−	0.839970i	$-0.682572\pi$
$157$	0.765462	−	0.535982i	0.0610905	−	0.0427760i	0.603723	+	0.797194i	$0.293683\pi$
$158$	−0.356107	−	4.07033i	−0.0283304	−	0.323818i
$159$		0			0
$160$	−9.82792	+	14.9886i	−0.776965	+	1.18495i
$161$		−	7.46581i		−	0.588388i
$162$		0			0
$163$	4.24897	−	4.24897i	0.332805	−	0.332805i	−0.520846	−	0.853651i	$-0.674383\pi$
$163$	4.24897	−	4.24897i	0.332805	−	0.332805i	0.853651	+	0.520846i	$0.174383\pi$
$164$	5.94781	+	2.16483i	0.464446	+	0.169045i
$165$		0			0
$166$	−8.24694	−	6.92001i	−0.640087	−	0.537097i
$167$	−4.66589	−	6.66358i	−0.361057	−	0.515643i	0.596992	−	0.802247i	$-0.296362\pi$
$167$	−4.66589	−	6.66358i	−0.361057	−	0.515643i	−0.958049	+	0.286604i	$0.907474\pi$
$168$		0			0
$169$	2.44036	+	2.90831i	0.187720	+	0.223716i
$170$	−12.8021	+	23.8233i	−0.981877	+	1.82716i
$171$		0			0
$172$	−13.9432	+	3.73607i	−1.06316	+	0.284873i
$173$	−9.39399	+	13.4160i	−0.714212	+	1.02000i	0.283917	+	0.958849i	$0.408366\pi$
$173$	−9.39399	+	13.4160i	−0.714212	+	1.02000i	−0.998129	+	0.0611509i	$0.980523\pi$
$174$		0			0
$175$	8.68926	−	6.91047i	0.656846	−	0.522383i
$176$	−1.51042	−	4.14985i	−0.113852	−	0.312807i
$177$		0			0
$178$	22.0204	+	15.4188i	1.65050	+	1.15569i
$179$	−0.436647	+	0.756295i	−0.0326365	+	0.0565281i	−0.881882	−	0.471470i	$-0.843724\pi$
$179$	−0.436647	+	0.756295i	−0.0326365	+	0.0565281i	0.849246	+	0.527998i	$0.177057\pi$
$180$		0			0
$181$	−0.367901	−	0.637223i	−0.0273459	−	0.0473644i	0.852029	−	0.523495i	$-0.175372\pi$
$181$	−0.367901	−	0.637223i	−0.0273459	−	0.0473644i	−0.879374	+	0.476131i	$0.842039\pi$
$182$	−1.17655	+	13.4481i	−0.0872119	+	0.996836i
$183$		0			0
$184$	−0.106786	−	0.0188293i	−0.00787240	−	0.00138812i
$185$	6.28017	+	8.41095i	0.461727	+	0.618385i
$186$		0			0
$187$	−2.83907	−	6.08840i	−0.207613	−	0.445228i
$188$	18.0225	+	18.0225i	1.31442	+	1.31442i
$189$		0			0
$190$	19.3807	+	4.56447i	1.40602	+	0.331142i
$191$	−2.16218	+	5.94054i	−0.156450	+	0.429842i	−0.993010	−	0.118033i	$-0.962341\pi$
$191$	−2.16218	+	5.94054i	−0.156450	+	0.429842i	0.836560	+	0.547876i	$0.184563\pi$
$192$		0			0
$193$	−26.3618	+	2.30636i	−1.89756	+	0.166015i	−0.975349	−	0.220667i	$-0.929176\pi$
$193$	−26.3618	+	2.30636i	−1.89756	+	0.166015i	−0.922213	+	0.386683i	$0.873621\pi$
$194$	−6.02411	+	34.1644i	−0.432506	+	2.45286i
$195$		0			0
$196$	−3.19645	+	2.68214i	−0.228318	+	0.191582i
$197$	0.424090	+	0.113635i	0.0302152	+	0.00809613i	0.273895	−	0.961760i	$-0.411688\pi$
$197$	0.424090	+	0.113635i	0.0302152	+	0.00809613i	−0.243680	+	0.969856i	$0.578355\pi$
$198$		0			0
$199$	−2.06085	−	1.18983i	−0.146090	−	0.0843452i	0.425173	−	0.905112i	$-0.360213\pi$
$199$	−2.06085	−	1.18983i	−0.146090	−	0.0843452i	−0.571263	+	0.820767i	$0.693546\pi$
$200$	−0.0769283	−	0.141715i	−0.00543965	−	0.0100207i
$201$		0			0
$202$	13.9299	+	6.49563i	0.980106	+	0.457031i
$203$	−3.74065	−	1.74429i	−0.262542	−	0.122425i
$204$		0			0
$205$	5.23764	−	4.67435i	0.365813	−	0.326471i
$206$	−18.2654	−	10.5455i	−1.27261	−	0.734742i
$207$		0			0
$208$	−11.6263	−	3.11527i	−0.806141	−	0.216005i
$209$	−3.78864	+	3.17905i	−0.262066	+	0.219899i
$210$		0			0
$211$	1.83079	−	10.3830i	0.126037	−	0.714792i	−0.854649	−	0.519206i	$-0.826228\pi$
$211$	1.83079	−	10.3830i	0.126037	−	0.714792i	0.980686	−	0.195586i	$-0.0626610\pi$
$212$	−18.0207	+	1.57661i	−1.23767	+	0.108282i
$213$		0			0
$214$	−4.80055	+	13.1894i	−0.328159	+	0.901610i
$215$	−3.67022	+	15.5837i	−0.250307	+	1.06280i
$216$		0			0
$217$	−14.6188	−	14.6188i	−0.992389	−	0.992389i
$218$	−7.96263	−	17.0759i	−0.539297	−	1.15653i
$219$		0			0
$220$	4.96591	+	0.720251i	0.334802	+	0.0485593i
$221$	−18.0315	−	3.17944i	−1.21293	−	0.213872i
$222$		0			0
$223$	0.713099	−	8.15076i	0.0477527	−	0.545815i	−0.934208	−	0.356729i	$-0.883892\pi$
$223$	0.713099	−	8.15076i	0.0477527	−	0.545815i	0.981960	−	0.189086i	$-0.0605525\pi$
$224$	8.89900	+	15.4135i	0.594589	+	1.02986i
$225$		0			0
$226$	−1.34859	+	2.33583i	−0.0897069	+	0.155377i
$227$	3.90472	+	2.73411i	0.259165	+	0.181469i	0.695937	−	0.718103i	$-0.254989\pi$
$227$	3.90472	+	2.73411i	0.259165	+	0.181469i	−0.436772	+	0.899572i	$0.643878\pi$
$228$		0			0
$229$	2.44592	+	6.72010i	0.161631	+	0.444077i	0.993899	−	0.110297i	$-0.0351801\pi$
$229$	2.44592	+	6.72010i	0.161631	+	0.444077i	−0.832268	+	0.554374i	$0.812958\pi$
$230$	−9.32841	+	11.8319i	−0.615097	+	0.780174i
$231$		0			0
$232$	−0.0343835	+	0.0491048i	−0.00225739	+	0.00322389i
$233$	−8.72938	+	2.33903i	−0.571881	+	0.153235i	−0.533159	−	0.846015i	$-0.678995\pi$
$233$	−8.72938	+	2.33903i	−0.571881	+	0.153235i	−0.0387217	+	0.999250i	$0.512329\pi$
$234$		0			0
$235$	27.0695	−	8.14568i	1.76582	−	0.531365i
$236$	1.81062	+	2.15781i	0.117861	+	0.140461i
$237$		0			0
$238$	15.4040	+	21.9992i	0.998495	+	1.42600i
$239$	3.14736	+	2.64095i	0.203586	+	0.170829i	0.738880	−	0.673837i	$-0.235355\pi$
$239$	3.14736	+	2.64095i	0.203586	+	0.170829i	−0.535295	+	0.844665i	$0.679799\pi$
$240$		0			0
$241$	5.80277	+	2.11203i	0.373789	+	0.136048i	0.522082	−	0.852895i	$-0.325156\pi$
$241$	5.80277	+	2.11203i	0.373789	+	0.136048i	−0.148293	+	0.988944i	$0.547378\pi$
$242$	13.8320	−	13.8320i	0.889153	−	0.889153i
$243$		0			0
$244$			6.05468i			0.387611i
$245$	0.942240	+	4.53102i	0.0601975	+	0.289476i
$246$		0			0
$247$	1.17484	+	13.4284i	0.0747530	+	0.854431i
$248$	−0.245968	+	0.172229i	−0.0156190	+	0.0109365i
$249$		0			0
$250$	−22.4054	+	0.0947372i	−1.41704	+	0.00599171i
$251$	15.6657	−	9.04459i	0.988810	−	0.570890i	0.0838914	−	0.996475i	$-0.473265\pi$
$251$	15.6657	−	9.04459i	0.988810	−	0.570890i	0.904918	+	0.425585i	$0.139932\pi$
$252$		0			0
$253$	−0.968633	−	3.61499i	−0.0608975	−	0.227272i
$254$	−5.29746	−	30.0434i	−0.332392	−	1.88509i
$255$		0			0
$256$	−14.7902	+	5.38320i	−0.924389	+	0.336450i
$257$	4.90513	−	10.5191i	0.305974	−	0.656163i	−0.691854	−	0.722037i	$-0.743206\pi$
$257$	4.90513	−	10.5191i	0.305974	−	0.656163i	0.997828	+	0.0658743i	$0.0209837\pi$
$258$		0			0
$259$	10.2651	−	1.81002i	0.637844	−	0.112469i
$260$	9.37128	−	9.96106i	0.581182	−	0.617759i
$261$		0			0
$262$	10.3451	−	38.6083i	0.639120	−	2.38523i
$263$	2.21755	+	0.194010i	0.136740	+	0.0119632i	0.155320	−	0.987864i	$-0.450359\pi$
$263$	2.21755	+	0.194010i	0.136740	+	0.0119632i	−0.0185804	+	0.999827i	$0.505915\pi$
$264$		0			0
$265$	−7.92069	+	18.4336i	−0.486564	+	1.13237i
$266$	12.7090	−	15.1460i	0.779240	−	0.928662i
$267$		0			0
$268$	16.2824	−	7.59261i	0.994606	−	0.463792i
$269$	2.60637			0.158913			0.0794565	−	0.996838i	$-0.474682\pi$
$269$	2.60637			0.158913			0.0794565	+	0.996838i	$0.474682\pi$
$270$		0			0
$271$	−22.2817			−1.35352			−0.676759	−	0.736205i	$-0.736616\pi$
$271$	−22.2817			−1.35352			−0.676759	+	0.736205i	$0.736616\pi$
$272$	−21.7021	+	10.1199i	−1.31589	+	0.613608i
$273$		0			0
$274$	−20.9119	+	24.9218i	−1.26333	+	1.50558i
$275$	3.31081	−	4.47346i	0.199649	−	0.269760i
$276$		0			0
$277$	−8.27992	−	0.724399i	−0.497492	−	0.0435249i	−0.164351	−	0.986402i	$-0.552553\pi$
$277$	−8.27992	−	0.724399i	−0.497492	−	0.0435249i	−0.333141	+	0.942877i	$0.608109\pi$
$278$	1.44817	−	5.40464i	0.0868555	−	0.324149i
$279$		0			0
$280$	−0.160046	+	0.00488265i	−0.00956460	+	0.000291794i
$281$	6.04432	−	1.06578i	0.360574	−	0.0635790i	0.00957353	−	0.999954i	$-0.496953\pi$
$281$	6.04432	−	1.06578i	0.360574	−	0.0635790i	0.351001	+	0.936375i	$0.385841\pi$
$282$		0			0
$283$	12.9205	−	27.7081i	0.768044	−	1.64708i	0.00563108	−	0.999984i	$-0.498208\pi$
$283$	12.9205	−	27.7081i	0.768044	−	1.64708i	0.762413	−	0.647091i	$-0.224015\pi$
$284$	14.8472	−	5.40394i	0.881019	−	0.320665i
$285$		0			0
$286$	1.17509	+	6.66428i	0.0694847	+	0.394067i
$287$	−1.80424	−	6.73352i	−0.106501	−	0.397467i
$288$		0			0
$289$	−16.8231	+	9.71284i	−0.989596	+	0.571343i
$290$	3.74878	+	7.43827i	0.220136	+	0.436790i
$291$		0			0
$292$	−0.285604	+	0.199982i	−0.0167137	+	0.0117031i
$293$	−0.657015	−	7.50972i	−0.0383833	−	0.438723i	−0.990935	−	0.134345i	$-0.957107\pi$
$293$	−0.657015	−	7.50972i	−0.0383833	−	0.438723i	0.952551	−	0.304378i	$-0.0984485\pi$
$294$		0			0
$295$	3.05873	−	0.636072i	0.178086	−	0.0370336i
$296$		−	0.151391i		−	0.00879944i
$297$		0			0
$298$	28.5294	−	28.5294i	1.65266	−	1.65266i
$299$	−9.58520	−	3.48873i	−0.554326	−	0.201758i
$300$		0			0
$301$	12.1787	+	10.2191i	0.701967	+	0.589020i
$302$	−0.600762	−	0.857978i	−0.0345700	−	0.0493711i
$303$		0			0
$304$	11.3317	+	13.5046i	0.649919	+	0.774543i
$305$	5.91530	+	3.17875i	0.338709	+	0.182015i
$306$		0			0
$307$	−12.7384	+	3.41325i	−0.727021	+	0.194805i	−0.603302	−	0.797513i	$-0.706149\pi$
$307$	−12.7384	+	3.41325i	−0.727021	+	0.194805i	−0.123719	+	0.992317i	$0.539482\pi$
$308$	2.85801	−	4.08166i	0.162850	−	0.232574i
$309$		0			0
$310$	4.90215	+	41.4341i	0.278424	+	2.35330i
$311$	0.0958399	+	0.263318i	0.00543458	+	0.0149314i	0.942380	−	0.334544i	$-0.108582\pi$
$311$	0.0958399	+	0.263318i	0.00543458	+	0.0149314i	−0.936946	+	0.349475i	$0.886360\pi$
$312$		0			0
$313$	−7.80530	−	5.46533i	−0.441182	−	0.308919i	0.331797	−	0.943351i	$-0.392345\pi$
$313$	−7.80530	−	5.46533i	−0.441182	−	0.308919i	−0.772979	+	0.634432i	$0.781234\pi$
$314$	−0.936334	+	1.62178i	−0.0528404	+	0.0915223i
$315$		0			0
$316$	2.05524	+	3.55979i	0.115617	+	0.200254i
$317$	0.318142	−	3.63638i	0.0178686	−	0.204239i	−0.982012	−	0.188816i	$-0.939535\pi$
$317$	0.318142	−	3.63638i	0.0178686	−	0.204239i	0.999881	−	0.0154231i	$-0.00490952\pi$
$318$		0			0
$319$	−2.03756	−	0.359276i	−0.114081	−	0.0201156i
$320$	2.60882	−	17.9870i	0.145838	−	1.00551i
$321$		0			0
$322$	6.32305	+	13.5598i	0.352370	+	0.755660i
$323$	18.9624	+	18.9624i	1.05510	+	1.05510i
$324$		0			0
$325$	−4.81178	−	14.3852i	−0.266909	−	0.797947i
$326$	−4.11862	+	11.3158i	−0.228109	+	0.626725i
$327$		0			0
$328$	−0.100863	+	0.00882434i	−0.00556921	+	0.000487243i
$329$	4.87446	−	27.6444i	0.268738	−	1.52409i
$330$		0			0
$331$	−6.76703	+	5.67821i	−0.371950	+	0.312103i	−0.809532	−	0.587075i	$-0.800279\pi$
$331$	−6.76703	+	5.67821i	−0.371950	+	0.312103i	0.437583	+	0.899178i	$0.355835\pi$
$332$	10.4614	+	2.80313i	0.574146	+	0.153842i
$333$		0			0
$334$	14.1181	+	8.15107i	0.772506	+	0.446007i
$335$	1.13055	−	19.8938i	0.0617685	−	1.08691i
$336$		0			0
$337$	21.7951	+	10.1632i	1.18726	+	0.553627i	0.912972	−	0.408022i	$-0.133781\pi$
$337$	21.7951	+	10.1632i	1.18726	+	0.553627i	0.274284	+	0.961649i	$0.411559\pi$
$338$	−6.89547	−	3.21541i	−0.375064	−	0.174895i
$339$		0			0
$340$	1.54373	−	27.1643i	0.0837205	−	1.47319i
$341$	−8.97519	−	5.18183i	−0.486034	−	0.280612i
$342$		0			0
$343$	19.4524	+	5.21226i	1.05033	+	0.281435i
$344$	0.176884	−	0.148423i	0.00953693	−	0.00800243i
$345$		0			0
$346$	5.69942	−	32.3230i	0.306403	−	1.73770i
$347$	16.7440	−	1.46491i	0.898867	−	0.0786406i	0.371651	−	0.928372i	$-0.378792\pi$
$347$	16.7440	−	1.46491i	0.898867	−	0.0786406i	0.527215	+	0.849732i	$0.323236\pi$
$348$		0			0
$349$	11.7112	−	32.1764i	0.626888	−	1.72236i	−0.0625752	−	0.998040i	$-0.519931\pi$
$349$	11.7112	−	32.1764i	0.626888	−	1.72236i	0.689463	−	0.724321i	$-0.257846\pi$
$350$	−9.92922	+	19.9104i	−0.530739	+	1.06426i
$351$		0			0
$352$	6.30874	+	6.30874i	0.336257	+	0.336257i
$353$	−9.55751	−	20.4961i	−0.508695	−	1.09090i	−0.978142	−	0.207939i	$-0.933324\pi$
$353$	−9.55751	−	20.4961i	−0.508695	−	1.09090i	0.469447	−	0.882961i	$-0.344453\pi$
$354$		0			0
$355$	2.51535	−	17.3425i	0.133501	−	0.920446i
$356$	−26.6330	−	4.69612i	−1.41155	−	0.248894i
$357$		0			0
$358$	0.152531	−	1.74344i	0.00806152	−	0.0921436i
$359$	15.4051	+	26.6824i	0.813050	+	1.40824i	0.910720	+	0.413025i	$0.135528\pi$
$359$	15.4051	+	26.6824i	0.813050	+	1.40824i	−0.0976695	+	0.995219i	$0.531139\pi$
$360$		0			0
$361$	0.371443	−	0.643357i	0.0195496	−	0.0338609i
$362$	1.20789	+	0.845774i	0.0634853	+	0.0444529i
$363$		0			0
$364$	−4.64489	−	12.7617i	−0.243458	−	0.668897i
$365$	0.0454344	+	0.384021i	0.00237814	+	0.0201006i
$366$		0			0
$367$	−8.33253	+	11.9001i	−0.434955	+	0.621179i	−0.975464	−	0.220158i	$-0.929343\pi$
$367$	−8.33253	+	11.9001i	−0.434955	+	0.621179i	0.540510	+	0.841338i	$0.318231\pi$
$368$	−12.8856	+	3.45270i	−0.671711	+	0.179984i
$369$		0			0
$370$	−18.5299	−	9.95757i	−0.963325	−	0.517669i
$371$	12.8063	+	15.2619i	0.664868	+	0.792358i
$372$		0			0
$373$	−9.77090	−	13.9543i	−0.505918	−	0.722526i	0.482227	−	0.876046i	$-0.339828\pi$
$373$	−9.77090	−	13.9543i	−0.505918	−	0.722526i	−0.988146	+	0.153520i	$0.950939\pi$
$374$	10.3130	+	8.65361i	0.533271	+	0.447467i
$375$		0			0
$376$	−0.383116	−	0.139443i	−0.0197577	−	0.00719121i
$377$	−3.98745	+	3.98745i	−0.205364	+	0.205364i
$378$		0			0
$379$			1.06208i			0.0545552i	0.999628	+	0.0272776i	$0.00868381\pi$
$379$			1.06208i			0.0545552i	−0.999628	+	0.0272776i	$0.991316\pi$
$380$	−19.6114	+	4.07825i	−1.00604	+	0.209210i
$381$		0			0
$382$	−1.10417	−	12.6208i	−0.0564945	−	0.645735i
$383$	18.5741	−	13.0057i	0.949090	−	0.664560i	0.00701991	−	0.999975i	$-0.497765\pi$
$383$	18.5741	−	13.0057i	0.949090	−	0.664560i	0.942070	+	0.335415i	$0.108877\pi$
$384$		0			0
$385$	−2.48723	−	4.93512i	−0.126761	−	0.251517i
$386$	45.9265	−	26.5156i	2.33759	−	1.34961i
$387$		0			0
$388$	−9.03290	−	33.7112i	−0.458576	−	1.71143i
$389$	0.536388	+	3.04201i	0.0271960	+	0.154236i	0.995382	−	0.0959969i	$-0.0306039\pi$
$389$	0.536388	+	3.04201i	0.0271960	+	0.154236i	−0.968186	+	0.250233i	$0.919493\pi$
$390$		0			0
$391$	−19.0690	+	6.94056i	−0.964363	+	0.350999i
$392$	0.0282083	−	0.0604930i	0.00142474	−	0.00305536i
$393$		0			0
$394$	−0.866498	+	0.152787i	−0.0436535	+	0.00769729i
$395$	4.55686	−	0.139019i	0.229281	−	0.00699483i
$396$		0			0
$397$	−3.92165	+	14.6358i	−0.196822	+	0.734549i	0.794966	+	0.606654i	$0.207489\pi$
$397$	−3.92165	+	14.6358i	−0.196822	+	0.734549i	−0.991788	+	0.127895i	$0.959178\pi$
$398$	4.75076	+	0.415637i	0.238134	+	0.0208340i
$399$		0			0
$400$	−15.9457	−	11.8014i	−0.797284	−	0.590070i
$401$	−15.1491	+	18.0540i	−0.756509	+	0.901573i	−0.997622	−	0.0689246i	$-0.978043\pi$
$401$	−15.1491	+	18.0540i	−0.756509	+	0.901573i	0.241113	+	0.970497i	$0.422488\pi$
$402$		0			0
$403$	−25.6001	+	11.9375i	−1.27523	+	0.594649i
$404$	−15.4626			−0.769292
$405$		0			0
$406$	8.27129			0.410497
$407$	4.73560	−	2.20825i	0.234735	−	0.109459i
$408$		0			0
$409$	−9.99118	+	11.9070i	−0.494032	+	0.588764i	−0.954238	−	0.299048i	$-0.903331\pi$
$409$	−9.99118	+	11.9070i	−0.494032	+	0.588764i	0.460206	+	0.887812i	$0.347775\pi$
$410$	−5.55404	+	12.9258i	−0.274294	+	0.638358i
$411$		0			0
$412$	21.1374	+	1.84928i	1.04136	+	0.0911076i
$413$	0.802939	−	2.99661i	0.0395100	−	0.147453i
$414$		0			0
$415$	8.23094	−	8.74896i	0.404041	−	0.429469i
$416$	23.9476	−	4.22260i	1.17413	−	0.207030i
$417$		0			0
$418$	4.18870	−	8.98270i	0.204876	−	0.439358i
$419$	−7.24231	+	2.63599i	−0.353810	+	0.128776i	−0.512810	−	0.858502i	$-0.671395\pi$
$419$	−7.24231	+	2.63599i	−0.353810	+	0.128776i	0.159000	+	0.987279i	$0.449173\pi$
$420$		0			0
$421$	−0.219552	−	1.24514i	−0.0107003	−	0.0606845i	0.978990	−	0.203908i	$-0.0653643\pi$
$421$	−0.219552	−	1.24514i	−0.0107003	−	0.0606845i	−0.989690	+	0.143223i	$0.954253\pi$
$422$	5.46849	+	20.4087i	0.266202	+	0.993479i
$423$		0			0
$424$	0.250595	−	0.144681i	0.0121700	−	0.00702635i
$425$	−25.7286	−	15.7697i	−1.24802	−	0.764942i
$426$		0			0
$427$	5.46239	−	3.82480i	0.264343	−	0.185095i
$428$	−1.23068	−	14.0667i	−0.0594871	−	0.679940i
$429$		0			0
$430$	−6.53233	−	31.4125i	−0.315017	−	1.51484i
$431$			31.3833i			1.51168i	0.654755	+	0.755841i	$0.272772\pi$
$431$			31.3833i			1.51168i	−0.654755	+	0.755841i	$0.727228\pi$
$432$		0			0
$433$	−24.8304	+	24.8304i	−1.19327	+	1.19327i	−0.217127	+	0.976143i	$0.569669\pi$
$433$	−24.8304	+	24.8304i	−1.19327	+	1.19327i	−0.976143	+	0.217127i	$0.930331\pi$
$434$	38.9327	+	14.1703i	1.86883	+	0.680198i
$435$		0			0
$436$	14.5201	+	12.1838i	0.695389	+	0.583500i
$437$	8.56911	+	12.2380i	0.409916	+	0.585421i
$438$		0			0
$439$	−13.0944	−	15.6053i	−0.624962	−	0.744800i	0.356953	−	0.934122i	$-0.383815\pi$
$439$	−13.0944	−	15.6053i	−0.624962	−	0.744800i	−0.981915	+	0.189322i	$0.939371\pi$
$440$	−0.0768619	+	0.0231290i	−0.00366425	+	0.00110263i
$441$		0			0
$442$	35.4426	−	9.49681i	1.68583	−	0.451717i
$443$	−1.58059	+	2.25731i	−0.0750960	+	0.107248i	−0.854943	−	0.518722i	$-0.826408\pi$
$443$	−1.58059	+	2.25731i	−0.0750960	+	0.107248i	0.779847	+	0.625970i	$0.215297\pi$
$444$		0			0
$445$	−18.5706	+	23.5545i	−0.880329	+	1.11659i
$446$	5.60799	+	15.4078i	0.265546	+	0.729582i
$447$		0			0
$448$	−14.7842	−	10.3520i	−0.698487	−	0.489086i
$449$	14.4725	−	25.0672i	0.683001	−	1.18299i	−0.291059	−	0.956705i	$-0.594008\pi$
$449$	14.4725	−	25.0672i	0.683001	−	1.18299i	0.974060	−	0.226288i	$-0.0726590\pi$
$450$		0			0
$451$	−1.74725	−	3.02633i	−0.0822748	−	0.142504i
$452$	0.236491	−	2.70311i	0.0111236	−	0.127143i
$453$		0			0
$454$	−9.40759	−	1.65881i	−0.441520	−	0.0778519i
$455$	−14.9066	−	2.16204i	−0.698831	−	0.101358i
$456$		0			0
$457$	10.0414	+	21.5339i	0.469718	+	1.00731i	0.988333	+	0.152305i	$0.0486697\pi$
$457$	10.0414	+	21.5339i	0.469718	+	1.00731i	−0.518616	+	0.855007i	$0.673553\pi$
$458$	−10.1339	−	10.1339i	−0.473527	−	0.473527i
$459$		0			0
$460$	3.47483	−	14.7541i	0.162015	−	0.687913i
$461$	3.22783	−	8.86840i	0.150335	−	0.413043i	−0.841550	−	0.540179i	$-0.818356\pi$
$461$	3.22783	−	8.86840i	0.150335	−	0.413043i	0.991885	+	0.127137i	$0.0405786\pi$
$462$		0			0
$463$	18.4116	−	1.61081i	0.855659	−	0.0748605i	0.349121	−	0.937078i	$-0.386480\pi$
$463$	18.4116	−	1.61081i	0.855659	−	0.0748605i	0.506538	+	0.862217i	$0.330925\pi$
$464$	−1.28064	+	7.26288i	−0.0594523	+	0.337171i
$465$		0			0
$466$	13.8738	−	11.6415i	0.642691	−	0.539282i
$467$	12.3653	+	3.31326i	0.572196	+	0.153320i	0.533304	−	0.845924i	$-0.320950\pi$
$467$	12.3653	+	3.31326i	0.572196	+	0.153320i	0.0388925	+	0.999243i	$0.487617\pi$
$468$		0			0
$469$	−17.1356	−	9.89327i	−0.791250	−	0.456829i
$470$	−42.2664	+	37.7208i	−1.94960	+	1.73993i
$471$		0			0
$472$	−0.0408366	−	0.0190424i	−0.00187966	−	0.000876499i
$473$	7.22284	+	3.36807i	0.332107	+	0.154864i
$474$		0			0
$475$	−6.31174	+	21.3010i	−0.289602	+	0.977358i
$476$	−23.3982	−	13.5090i	−1.07245	−	0.619182i
$477$		0			0
$478$	−7.95312	−	2.13103i	−0.363767	−	0.0974712i
$479$	6.23949	−	5.23555i	0.285090	−	0.239219i	−0.489016	−	0.872275i	$-0.662644\pi$
$479$	6.23949	−	5.23555i	0.285090	−	0.239219i	0.774106	+	0.633056i	$0.218200\pi$
$480$		0			0
$481$	2.47299	−	14.0250i	0.112758	−	0.639485i
$482$	−12.3281	+	1.07857i	−0.561529	+	0.0491274i
$483$		0			0
$484$	−6.73069	+	18.4924i	−0.305940	+	0.840564i
$485$	−37.6776	−	8.87368i	−1.71085	−	0.402933i
$486$		0			0
$487$	11.3243	+	11.3243i	0.513154	+	0.513154i	0.915492	−	0.402337i	$-0.131802\pi$
$487$	11.3243	+	11.3243i	0.513154	+	0.513154i	−0.402337	+	0.915492i	$0.631802\pi$
$488$	−0.0409312	−	0.0877772i	−0.00185287	−	0.00397349i
$489$		0			0
$490$	−5.54883	−	7.43148i	−0.250671	−	0.335720i
$491$	−3.22425	−	0.568523i	−0.145508	−	0.0256571i	0.100419	−	0.994945i	$-0.467982\pi$
$491$	−3.22425	−	0.568523i	−0.145508	−	0.0256571i	−0.245928	+	0.969288i	$0.579093\pi$
$492$		0			0
$493$	−0.977764	+	11.1759i	−0.0440363	+	0.503337i
$494$	−13.5068	−	23.3945i	−0.607701	−	1.05257i
$495$		0			0
$496$	−18.4707	+	31.9921i	−0.829357	+	1.43649i
$497$	−14.2544	−	9.98107i	−0.639399	−	0.447712i
$498$		0			0
$499$	−10.4633	−	28.7478i	−0.468404	−	1.28693i	−0.919020	−	0.394211i	$-0.871018\pi$
$499$	−10.4633	−	28.7478i	−0.468404	−	1.28693i	0.450616	−	0.892718i	$-0.351204\pi$
$500$	20.3883	−	9.61236i	0.911791	−	0.429878i
$501$		0			0
$502$	−20.7928	+	29.6951i	−0.928026	+	1.32536i
$503$	−12.3296	+	3.30370i	−0.549749	+	0.147305i	−0.522993	−	0.852337i	$-0.675184\pi$
$503$	−12.3296	+	3.30370i	−0.549749	+	0.147305i	−0.0267563	+	0.999642i	$0.508518\pi$
$504$		0			0
$505$	−8.11796	+	15.1066i	−0.361245	+	0.672236i
$506$	4.82095	+	5.74538i	0.214317	+	0.255413i
$507$		0			0
$508$	17.6034	+	25.1403i	0.781026	+	1.11542i
$509$	25.3418	+	21.2643i	1.12326	+	0.942525i	0.998764	−	0.0496958i	$-0.0158252\pi$
$509$	25.3418	+	21.2643i	1.12326	+	0.942525i	0.124493	+	0.992221i	$0.460270\pi$
$510$		0			0
$511$	0.360838	+	0.131334i	0.0159625	+	0.00580988i
$512$	22.6685	−	22.6685i	1.00181	−	1.00181i
$513$		0			0
$514$			23.2597i			1.02594i
$515$	12.9040	−	19.6799i	0.568618	−	0.867202i
$516$		0			0
$517$	−1.22642	−	14.0180i	−0.0539378	−	0.616512i
$518$	−17.1112	+	11.9814i	−0.751821	+	0.526431i
$519$		0			0
$520$	−0.0685200	+	0.207762i	−0.00300480	+	0.00911096i
$521$	−25.0460	+	14.4603i	−1.09728	+	0.633518i	−0.935507	−	0.353309i	$-0.885056\pi$
$521$	−25.0460	+	14.4603i	−1.09728	+	0.633518i	−0.161778	+	0.986827i	$0.551723\pi$
$522$		0			0
$523$	6.53051	+	24.3722i	0.285559	+	1.06572i	0.948430	+	0.316987i	$0.102671\pi$
$523$	6.53051	+	24.3722i	0.285559	+	1.06572i	−0.662871	+	0.748734i	$0.730662\pi$
$524$	6.98258	+	39.6002i	0.305035	+	1.72994i
$525$		0			0
$526$	−4.19195	+	1.52575i	−0.182778	+	0.0665257i
$527$	−23.7488	+	50.9294i	−1.03451	+	2.21852i
$528$		0			0
$529$	11.5171	−	2.03078i	0.500745	−	0.0882948i
$530$	−1.22606	−	40.1885i	−0.0532566	−	1.74568i
$531$		0			0
$532$	−5.14813	+	19.2131i	−0.223200	+	0.832993i
$533$	−9.48814	−	0.830105i	−0.410977	−	0.0359558i
$534$		0			0
$535$	−14.3890	−	6.18278i	−0.622092	−	0.267305i
$536$	−0.184725	+	0.220146i	−0.00797889	+	0.00950888i
$537$		0			0
$538$	−4.73383	+	2.20742i	−0.204090	+	0.0951687i
$539$	2.30371			0.0992278
$540$		0			0
$541$	−5.37883			−0.231254			−0.115627	−	0.993293i	$-0.536888\pi$
$541$	−5.37883			−0.231254			−0.115627	+	0.993293i	$0.536888\pi$
$542$	40.4693	−	18.8712i	1.73831	−	0.810586i
$543$		0			0
$544$	31.0960	−	37.0588i	1.33323	−	1.58888i
$545$	19.5266	−	7.78929i	0.836426	−	0.333657i
$546$		0			0
$547$	18.2031	+	1.59256i	0.778308	+	0.0680931i	0.469384	−	0.882994i	$-0.344476\pi$
$547$	18.2031	+	1.59256i	0.778308	+	0.0680931i	0.308923	+	0.951087i	$0.400031\pi$
$548$	8.47092	−	31.6139i	0.361860	−	1.35048i
$549$		0			0
$550$	−2.22456	+	10.9290i	−0.0948554	+	0.466014i
$551$	8.13375	−	1.43420i	0.346509	−	0.0610990i
$552$		0			0
$553$	1.91324	−	4.10295i	0.0813591	−	0.174475i
$554$	15.6520	−	5.69686i	0.664990	−	0.242036i
$555$		0			0
$556$	0.977467	+	5.54349i	0.0414538	+	0.235096i
$557$	1.10675	+	4.13045i	0.0468945	+	0.175013i	0.985401	−	0.170248i	$-0.0544570\pi$
$557$	1.10675	+	4.13045i	0.0468945	+	0.175013i	−0.938507	+	0.345261i	$0.887790\pi$
$558$		0			0
$559$	18.8111	−	10.8606i	0.795626	−	0.459355i
$560$	−17.5912	+	8.86572i	−0.743366	+	0.374645i
$561$		0			0
$562$	−10.0754	+	7.05488i	−0.425005	+	0.297592i
$563$	−2.00004	−	22.8606i	−0.0842918	−	0.963459i	−0.914121	−	0.405442i	$-0.867118\pi$
$563$	−2.00004	−	22.8606i	−0.0842918	−	0.963459i	0.829829	−	0.558018i	$-0.188438\pi$
$564$		0			0
$565$	−2.51672	−	1.65020i	−0.105879	−	0.0694244i
$566$			61.2679i			2.57528i
$567$		0			0
$568$	−0.178714	+	0.178714i	−0.00749867	+	0.00749867i
$569$	−4.11183	−	1.49658i	−0.172377	−	0.0627400i	0.254390	−	0.967102i	$-0.418125\pi$
$569$	−4.11183	−	1.49658i	−0.172377	−	0.0627400i	−0.426767	+	0.904362i	$0.640348\pi$
$570$		0			0
$571$	16.1524	+	13.5535i	0.675958	+	0.567196i	0.914822	−	0.403857i	$-0.132331\pi$
$571$	16.1524	+	13.5535i	0.675958	+	0.567196i	−0.238864	+	0.971053i	$0.576775\pi$
$572$	−3.90483	−	5.57667i	−0.163269	−	0.233172i
$573$		0			0
$574$	8.97982	+	10.7017i	0.374811	+	0.446682i
$575$	−12.5901	−	11.1408i	−0.525045	−	0.464605i
$576$		0			0
$577$	11.7007	−	3.13518i	0.487105	−	0.130519i	−0.00690397	−	0.999976i	$-0.502198\pi$
$577$	11.7007	−	3.13518i	0.487105	−	0.130519i	0.494009	+	0.869457i	$0.335531\pi$
$578$	22.3290	−	31.8891i	0.928764	−	1.32641i
$579$		0			0
$580$	−6.58050	−	5.18813i	−0.273241	−	0.215425i
$581$	−4.07968	−	11.2088i	−0.169254	−	0.465021i
$582$		0			0
$583$	8.18099	+	5.72839i	0.338822	+	0.237246i
$584$	0.00278859	−	0.00482997i	0.000115393	−	0.000199866i
$585$		0			0
$586$	7.55356	+	13.0831i	0.312034	+	0.540460i
$587$	1.25428	−	14.3364i	0.0517695	−	0.591728i	−0.925361	−	0.379087i	$-0.876238\pi$
$587$	1.25428	−	14.3364i	0.0517695	−	0.591728i	0.977130	−	0.212641i	$-0.0682064\pi$
$588$		0			0
$589$	40.7423	+	7.18397i	1.67876	+	0.296010i
$590$	−5.01672	+	3.74581i	−0.206535	+	0.154213i
$591$		0			0
$592$	−7.87131	−	16.8801i	−0.323509	−	0.693767i
$593$	0.209120	+	0.209120i	0.00858753	+	0.00858753i	0.711388	−	0.702800i	$-0.248067\pi$
$593$	0.209120	+	0.209120i	0.00858753	+	0.00858753i	−0.702800	+	0.711388i	$0.748067\pi$
$594$		0			0
$595$	−25.4822	+	15.7673i	−1.04467	+	0.646396i
$596$	−13.8825	+	38.1419i	−0.568650	+	1.56235i
$597$		0			0
$598$	20.3639	−	1.78161i	0.832742	−	0.0728555i
$599$	−1.58777	+	9.00467i	−0.0648743	+	0.367921i	0.935036	+	0.354552i	$0.115367\pi$
$599$	−1.58777	+	9.00467i	−0.0648743	+	0.367921i	−0.999911	+	0.0133687i	$0.995744\pi$
$600$		0			0
$601$	−4.24577	+	3.56262i	−0.173188	+	0.145322i	−0.725262	−	0.688473i	$-0.758281\pi$
$601$	−4.24577	+	3.56262i	−0.173188	+	0.145322i	0.552073	+	0.833796i	$0.313837\pi$
$602$	−30.7745	−	8.24601i	−1.25428	−	0.336082i
$603$		0			0
$604$	0.912537	+	0.526854i	0.0371306	+	0.0214374i
$605$	14.5331	+	16.2844i	0.590853	+	0.662055i
$606$		0			0
$607$	−33.1493	−	15.4578i	−1.34549	−	0.627412i	−0.389559	−	0.921002i	$-0.627372\pi$
$607$	−33.1493	−	15.4578i	−1.34549	−	0.627412i	−0.955932	+	0.293589i	$0.905150\pi$
$608$	−32.2786	−	15.0518i	−1.30907	−	0.610429i
$609$		0			0
$610$	−13.4359	−	0.763553i	−0.544004	−	0.0309154i
$611$	−33.2143	−	19.1763i	−1.34371	−	0.775790i
$612$		0			0
$613$	25.3096	+	6.78170i	1.02225	+	0.273910i	0.730738	−	0.682658i	$-0.239176\pi$
$613$	25.3096	+	6.78170i	1.02225	+	0.273910i	0.291509	+	0.956568i	$0.405843\pi$
$614$	20.2455	−	16.9880i	0.817041	−	0.685579i
$615$		0			0
$616$	−0.0138407	+	0.0784943i	−0.000557656	+	0.00316263i
$617$	11.4338	−	1.00033i	0.460309	−	0.0402718i	0.145356	−	0.989379i	$-0.453567\pi$
$617$	11.4338	−	1.00033i	0.460309	−	0.0402718i	0.314952	+	0.949108i	$0.398012\pi$
$618$		0			0
$619$	9.29363	−	25.5340i	0.373542	−	1.02630i	−0.600439	−	0.799671i	$-0.705007\pi$
$619$	9.29363	−	25.5340i	0.373542	−	1.02630i	0.973981	−	0.226629i	$-0.0727704\pi$
$620$	−22.0859	−	35.6940i	−0.886992	−	1.43351i
$621$		0			0
$622$	−0.397083	−	0.397083i	−0.0159216	−	0.0159216i
$623$	12.5876	+	26.9943i	0.504313	+	1.08150i
$624$		0			0
$625$	1.31289	−	24.9655i	0.0525157	−	0.998620i
$626$	18.8052	+	3.31587i	0.751608	+	0.132529i
$627$		0			0
$628$	0.164197	−	1.87678i	0.00655218	−	0.0748917i
$629$	−14.1661	−	24.5363i	−0.564838	−	0.978328i
$630$		0			0
$631$	7.42122	−	12.8539i	0.295434	−	0.511707i	−0.679652	−	0.733535i	$-0.737869\pi$
$631$	7.42122	−	12.8539i	0.295434	−	0.511707i	0.975086	+	0.221828i	$0.0712024\pi$
$632$	−0.0538608	−	0.0377137i	−0.00214247	−	0.00150017i
$633$		0			0
$634$	2.50195	+	6.87405i	0.0993651	+	0.273003i
$635$	33.8035	−	3.99937i	1.34145	−	0.158710i
$636$		0			0
$637$	3.60140	−	5.14333i	0.142693	−	0.203786i
$638$	4.00501	−	1.07314i	0.158560	−	0.0424860i
$639$		0			0
$640$	0.166230	+	0.552412i	0.00657082	+	0.0218360i
$641$	2.24280	+	2.67286i	0.0885851	+	0.105572i	0.808516	−	0.588474i	$-0.200271\pi$
$641$	2.24280	+	2.67286i	0.0885851	+	0.105572i	−0.719931	+	0.694046i	$0.755827\pi$
$642$		0			0
$643$	−1.30898	−	1.86941i	−0.0516210	−	0.0737225i	0.792512	−	0.609857i	$-0.208773\pi$
$643$	−1.30898	−	1.86941i	−0.0516210	−	0.0737225i	−0.844133	+	0.536134i	$0.819884\pi$
$644$	−11.5303	−	9.67508i	−0.454358	−	0.381252i
$645$		0			0
$646$	−50.5006	−	18.3807i	−1.98692	−	0.723180i
$647$	8.56365	−	8.56365i	0.336672	−	0.336672i	−0.518441	−	0.855113i	$-0.673488\pi$
$647$	8.56365	−	8.56365i	0.336672	−	0.336672i	0.855113	+	0.518441i	$0.173488\pi$
$648$		0			0
$649$		−	1.55515i		−	0.0610450i
$650$	20.9228	+	22.0520i	0.820658	+	0.864949i
$651$		0			0
$652$	−1.05586	−	12.0685i	−0.0413505	−	0.472638i
$653$	20.3999	−	14.2842i	0.798311	−	0.558984i	−0.101718	−	0.994813i	$-0.532434\pi$
$653$	20.3999	−	14.2842i	0.798311	−	0.558984i	0.900029	+	0.435830i	$0.143545\pi$
$654$		0			0
$655$	42.3545	+	13.9685i	1.65493	+	0.545796i
$656$	−10.7873	+	6.22808i	−0.421175	+	0.243166i
$657$		0			0
$658$	14.5598	+	54.3378i	0.567599	+	2.11831i
$659$	5.36362	+	30.4186i	0.208937	+	1.18494i	0.891123	+	0.453762i	$0.149918\pi$
$659$	5.36362	+	30.4186i	0.208937	+	1.18494i	−0.682186	+	0.731179i	$0.738970\pi$
$660$		0			0
$661$	33.9585	−	12.3599i	1.32083	−	0.480744i	0.417109	−	0.908857i	$-0.363043\pi$
$661$	33.9585	−	12.3599i	1.32083	−	0.480744i	0.903726	+	0.428112i	$0.140821\pi$
$662$	7.48160	−	16.0443i	0.290780	−	0.623581i
$663$		0			0
$664$	−0.170614	+	0.0300838i	−0.00662109	+	0.00116748i
$665$	16.0680	+	15.1166i	0.623091	+	0.586198i
$666$		0			0
$667$	−1.61759	+	6.03694i	−0.0626335	+	0.233751i
$668$	−16.3379	−	1.42939i	−0.632134	−	0.0553046i
$669$		0			0
$670$	14.7954	+	37.0897i	0.571595	+	1.43290i
$671$	2.14868	−	2.56070i	0.0829489	−	0.0988547i
$672$		0			0
$673$	33.5440	−	15.6418i	1.29303	−	0.602949i	0.350339	−	0.936623i	$-0.386066\pi$
$673$	33.5440	−	15.6418i	1.29303	−	0.602949i	0.942689	+	0.333674i	$0.108288\pi$
$674$	−48.1932			−1.85633
$675$		0			0
$676$	7.65415			0.294390
$677$	−41.5346	+	19.3679i	−1.59630	+	0.744368i	−0.998364	−	0.0571738i	$-0.981791\pi$
$677$	−41.5346	+	19.3679i	−1.59630	+	0.744368i	−0.597938	+	0.801542i	$0.704013\pi$
$678$		0			0
$679$	−24.7073	+	29.4450i	−0.948179	+	1.13000i
$680$	0.161258	+	0.404249i	0.00618395	+	0.0155022i
$681$		0			0
$682$	20.6899	+	1.81014i	0.792259	+	0.0693137i
$683$	−4.46063	+	16.6473i	−0.170681	+	0.636992i	0.826566	+	0.562840i	$0.190291\pi$
$683$	−4.46063	+	16.6473i	−0.170681	+	0.636992i	−0.997247	+	0.0741513i	$0.976375\pi$
$684$		0			0
$685$	−26.4389	−	24.8735i	−1.01018	−	0.950367i
$686$	−39.7450	+	7.00812i	−1.51747	+	0.267571i
$687$		0			0
$688$	12.0055	−	25.7458i	0.457705	−	0.981551i
$689$	25.5787	−	9.30989i	0.974472	−	0.354679i
$690$		0			0
$691$	−6.05103	−	34.3171i	−0.230192	−	1.30548i	−0.852506	−	0.522717i	$-0.824918\pi$
$691$	−6.05103	−	34.3171i	−0.230192	−	1.30548i	0.622314	−	0.782768i	$-0.286193\pi$
$692$	8.54605	+	31.8943i	0.324872	+	1.21244i
$693$		0			0
$694$	−29.1708	+	16.8418i	−1.10731	+	0.639305i
$695$	5.92906	+	1.95541i	0.224902	+	0.0741728i
$696$		0			0
$697$	−15.5213	+	10.8682i	−0.587913	+	0.411661i
$698$	5.98066	+	68.3592i	0.226371	+	2.58743i
$699$		0			0
$700$	0.587932	−	22.3753i	0.0222218	−	0.845705i
$701$		−	27.2979i		−	1.03103i	−0.856881	−	0.515515i	$-0.827601\pi$
$701$		−	27.2979i		−	1.03103i	0.856881	−	0.515515i	$-0.172399\pi$
$702$		0			0
$703$	−14.7491	+	14.7491i	−0.556273	+	0.556273i
$704$	−8.50169	−	3.09436i	−0.320419	−	0.116623i
$705$		0			0
$706$	34.7178	+	29.1317i	1.30662	+	1.09639i
$707$	9.76787	+	13.9500i	0.367359	+	0.524642i
$708$		0			0
$709$	16.4826	+	19.6432i	0.619018	+	0.737717i	0.980901	−	0.194506i	$-0.0623105\pi$
$709$	16.4826	+	19.6432i	0.619018	+	0.737717i	−0.361883	+	0.932223i	$0.617866\pi$
$710$	10.1195	+	33.6289i	0.379778	+	1.26207i
$711$		0			0
$712$	0.417857	−	0.111964i	0.0156598	−	0.00419604i
$713$	−17.9564	+	25.6444i	−0.672473	+	0.960391i
$714$		0			0
$715$	−7.49836	+	0.887147i	−0.280423	+	0.0331774i
$716$	0.602175	+	1.65446i	0.0225043	+	0.0618302i
$717$		0			0
$718$	−50.5779	−	35.4150i	−1.88755	−	1.32168i
$719$	−0.729141	+	1.26291i	−0.0271924	+	0.0470986i	−0.879301	−	0.476266i	$-0.841990\pi$
$719$	−0.729141	+	1.26291i	−0.0271924	+	0.0470986i	0.852109	+	0.523364i	$0.175323\pi$
$720$		0			0
$721$	−11.6843	−	20.2379i	−0.435148	−	0.753698i
$722$	−0.129754	+	1.48309i	−0.00482893	+	0.0551949i
$723$		0			0
$724$	−1.46091	−	0.257598i	−0.0542942	−	0.00957354i
$725$	−8.52352	+	3.70522i	−0.316555	+	0.137608i
$726$		0			0
$727$	19.8194	+	42.5029i	0.735062	+	1.57634i	0.814944	+	0.579540i	$0.196768\pi$
$727$	19.8194	+	42.5029i	0.735062	+	1.57634i	−0.0798819	+	0.996804i	$0.525454\pi$
$728$	0.153611	+	0.153611i	0.00569322	+	0.00569322i
$729$		0			0
$730$	−0.407762	−	0.659002i	−0.0150919	−	0.0243908i
$731$	14.7796	−	40.6067i	0.546645	−	1.50189i
$732$		0			0
$733$	−24.4678	+	2.14066i	−0.903740	+	0.0790670i	−0.529544	−	0.848283i	$-0.677637\pi$
$733$	−24.4678	+	2.14066i	−0.903740	+	0.0790670i	−0.374196	+	0.927350i	$0.622081\pi$
$734$	5.05543	−	28.6707i	0.186599	−	1.05826i
$735$		0			0
$736$	20.6456	−	17.3237i	0.761006	−	0.638560i
$737$	−9.58076	−	2.56716i	−0.352912	−	0.0945625i
$738$		0			0
$739$	18.0486	+	10.4204i	0.663928	+	0.383319i	0.793772	−	0.608215i	$-0.208114\pi$
$739$	18.0486	+	10.4204i	0.663928	+	0.383319i	−0.129844	+	0.991534i	$0.541448\pi$
$740$	21.1286	+	1.20072i	0.776703	+	0.0441395i
$741$		0			0
$742$	−36.1853	−	16.8735i	−1.32840	−	0.619445i
$743$	−38.5547	−	17.9783i	−1.41443	−	0.659561i	−0.442923	−	0.896559i	$-0.646059\pi$
$743$	−38.5547	−	17.9783i	−1.41443	−	0.659561i	−0.971510	+	0.236998i	$0.923836\pi$
$744$		0			0
$745$	29.9755	+	33.5877i	1.09822	+	1.23056i
$746$	29.5649	+	17.0693i	1.08245	+	0.624951i
$747$		0			0
$748$	−13.0822	−	3.50537i	−0.478334	−	0.128169i
$749$	−11.9132	+	9.99638i	−0.435300	+	0.365260i
$750$		0			0
$751$	3.51433	−	19.9308i	0.128240	−	0.727284i	−0.851091	−	0.525018i	$-0.824059\pi$
$751$	3.51433	−	19.9308i	0.128240	−	0.727284i	0.979331	−	0.202265i	$-0.0648304\pi$
$752$	−49.9673	+	4.37157i	−1.82212	+	0.159415i
$753$		0			0
$754$	3.86512	−	10.6193i	0.140760	−	0.386734i
$755$	0.993815	−	0.614929i	0.0361686	−	0.0223796i
$756$		0			0
$757$	10.9992	+	10.9992i	0.399771	+	0.399771i	0.878152	−	0.478381i	$-0.158776\pi$
$757$	10.9992	+	10.9992i	0.399771	+	0.399771i	−0.478381	+	0.878152i	$0.658776\pi$
$758$	−0.899510	−	1.92901i	−0.0326717	−	0.0700647i
$759$		0			0
$760$	0.256744	−	0.191702i	0.00931308	−	0.00695376i
$761$	12.7782	+	2.25313i	0.463208	+	0.0816761i	0.400382	−	0.916348i	$-0.368878\pi$
$761$	12.7782	+	2.25313i	0.463208	+	0.0816761i	0.0628262	+	0.998024i	$0.479989\pi$
$762$		0			0
$763$	1.81945	−	20.7964i	0.0658685	−	0.752880i
$764$	6.37266	+	11.0378i	0.230555	+	0.399332i
$765$		0			0
$766$	−22.7203	+	39.3527i	−0.820918	+	1.42187i
$767$	−3.47208	−	2.43117i	−0.125369	−	0.0877846i
$768$		0			0
$769$	10.6865	+	29.3608i	0.385364	+	1.05878i	0.969064	+	0.246810i	$0.0793822\pi$
$769$	10.6865	+	29.3608i	0.385364	+	1.05878i	−0.583700	+	0.811969i	$0.698396\pi$
$770$	8.69717	+	6.85693i	0.313424	+	0.247107i
$771$		0			0
$772$	−30.6008	+	43.7024i	−1.10135	+	1.57288i
$773$	−35.0964	+	9.40406i	−1.26233	+	0.338241i	−0.827088	−	0.562072i	$-0.810004\pi$
$773$	−35.0964	+	9.40406i	−1.26233	+	0.338241i	−0.435243	+	0.900313i	$0.643338\pi$
$774$		0			0
$775$	−46.4677	+	2.83789i	−1.66917	+	0.101940i
$776$	0.358850	+	0.427661i	0.0128820	+	0.0153521i
$777$		0			0
$778$	−3.55061	−	5.07079i	−0.127295	−	0.181797i
$779$	10.6861	+	8.96672i	0.382870	+	0.321266i
$780$		0			0
$781$	−8.19706	−	2.98349i	−0.293314	−	0.106758i
$782$	28.7561	−	28.7561i	1.02832	−	1.02832i
$783$		0			0
$784$		−	8.21158i		−	0.293271i
$785$	−1.74738	−	1.14574i	−0.0623665	−	0.0408933i
$786$		0			0
$787$	−3.06442	−	35.0265i	−0.109235	−	1.24856i	−0.830942	−	0.556360i	$-0.812198\pi$
$787$	−3.06442	−	35.0265i	−0.109235	−	1.24856i	0.721707	−	0.692199i	$-0.243358\pi$
$788$	0.725085	−	0.507710i	0.0258301	−	0.0180864i
$789$		0			0
$790$	−8.15870	+	4.11186i	−0.290274	+	0.146294i
$791$	−2.58807	+	1.49422i	−0.0920213	+	0.0531285i
$792$		0			0
$793$	−2.35805	−	8.80036i	−0.0837367	−	0.312510i
$794$	−5.27284	−	29.9037i	−0.187126	−	1.06124i
$795$		0			0
$796$	−4.50830	+	1.64089i	−0.159793	+	0.0581597i
$797$	10.8830	−	23.3386i	0.385495	−	0.826696i	−0.613811	−	0.789453i	$-0.710364\pi$
$797$	10.8830	−	23.3386i	0.385495	−	0.826696i	0.999306	−	0.0372435i	$-0.0118577\pi$
$798$		0			0
$799$	−75.1405	+	13.2493i	−2.65828	+	0.468726i
$800$	39.2725	+	7.99376i	1.38849	+	0.282622i
$801$		0			0
$802$	12.2241	−	45.6210i	0.431648	−	1.61093i
$803$	0.191760	+	0.0167768i	0.00676705	+	0.000592040i
$804$		0			0
$805$	−15.5059	+	6.18541i	−0.546510	+	0.218007i
$806$	36.3860	−	43.3632i	1.28164	−	1.52740i
$807$		0			0
$808$	0.224167	−	0.104531i	0.00788618	−	0.00367739i
$809$	14.9511			0.525654			0.262827	−	0.964843i	$-0.415345\pi$
$809$	14.9511			0.525654			0.262827	+	0.964843i	$0.415345\pi$
$810$		0			0
$811$	14.0980			0.495049			0.247525	−	0.968882i	$-0.420383\pi$
$811$	14.0980			0.495049			0.247525	+	0.968882i	$0.420383\pi$
$812$	−7.54150	+	3.51666i	−0.264655	+	0.123411i
$813$		0			0
$814$	−6.73083	+	8.02149i	−0.235916	+	0.281153i
$815$	−12.3450	−	5.30449i	−0.432427	−	0.185808i
$816$		0			0
$817$	−31.6926	−	2.77274i	−1.10878	−	0.0970060i
$818$	8.06208	−	30.0881i	0.281884	−	1.05201i
$819$		0			0
$820$	−0.431583	−	14.1467i	−0.0150715	−	0.494023i
$821$	−6.53467	+	1.15224i	−0.228061	+	0.0402134i	−0.286511	−	0.958077i	$-0.592495\pi$
$821$	−6.53467	+	1.15224i	−0.228061	+	0.0402134i	0.0584494	+	0.998290i	$0.481384\pi$
$822$		0			0
$823$	9.68030	−	20.7595i	0.337434	−	0.723630i	−0.662236	−	0.749295i	$-0.730393\pi$
$823$	9.68030	−	20.7595i	0.337434	−	0.723630i	0.999671	+	0.0256651i	$0.00817034\pi$
$824$	−0.318939	+	0.116084i	−0.0111108	+	0.00404399i
$825$		0			0
$826$	1.07959	+	6.12265i	0.0375637	+	0.213034i
$827$	6.34894	+	23.6946i	0.220774	+	0.823941i	0.984054	+	0.177872i	$0.0569213\pi$
$827$	6.34894	+	23.6946i	0.220774	+	0.823941i	−0.763279	+	0.646069i	$0.776412\pi$
$828$		0			0
$829$	24.8714	−	14.3595i	0.863821	−	0.498727i	−0.00146915	−	0.999999i	$-0.500468\pi$
$829$	24.8714	−	14.3595i	0.863821	−	0.498727i	0.865290	+	0.501272i	$0.167134\pi$
$830$	−7.53971	+	22.8614i	−0.261707	+	0.793532i
$831$		0			0
$832$	−20.1993	+	14.1437i	−0.700284	+	0.490344i
$833$	−1.08869	−	12.4438i	−0.0377208	−	0.431151i
$834$		0			0
$835$	−9.97403	+	15.2114i	−0.345165	+	0.526413i
$836$			9.97102i			0.344855i
$837$		0			0
$838$	10.9214	−	10.9214i	0.377273	−	0.377273i
$839$	−29.6410	−	10.7884i	−1.02332	−	0.372458i	−0.224787	−	0.974408i	$-0.572169\pi$
$839$	−29.6410	−	10.7884i	−1.02332	−	0.372458i	−0.798534	+	0.601950i	$0.794391\pi$
$840$		0			0
$841$	−19.5685	−	16.4199i	−0.674775	−	0.566204i
$842$	1.45332	+	2.07555i	0.0500846	+	0.0715282i
$843$		0			0
$844$	−13.6630	−	16.2830i	−0.470301	−	0.560483i
$845$	4.01848	−	7.47795i	0.138240	−	0.257249i
$846$		0			0
$847$	20.9353	−	5.60959i	0.719344	−	0.192748i
$848$	20.4189	−	29.1612i	0.701187	−	1.00140i
$849$		0			0
$850$	60.0856	+	6.85137i	2.06092	+	0.235000i
$851$	−5.39842	−	14.8320i	−0.185055	−	0.508435i
$852$		0			0
$853$	−18.5060	−	12.9580i	−0.633632	−	0.443674i	0.212125	−	0.977243i	$-0.431962\pi$
$853$	−18.5060	−	12.9580i	−0.633632	−	0.443674i	−0.845757	+	0.533569i	$0.820851\pi$
$854$	−6.68174	+	11.5731i	−0.228645	+	0.396024i
$855$		0			0
$856$	0.112936	+	0.195611i	0.00386008	+	0.00668586i
$857$	−0.720788	+	8.23864i	−0.0246216	+	0.281427i	0.973896	+	0.226995i	$0.0728902\pi$
$857$	−0.720788	+	8.23864i	−0.0246216	+	0.281427i	−0.998518	+	0.0544314i	$0.982665\pi$
$858$		0			0
$859$	11.2675	+	1.98676i	0.384442	+	0.0677875i	0.362529	−	0.931972i	$-0.381913\pi$
$859$	11.2675	+	1.98676i	0.384442	+	0.0677875i	0.0219126	+	0.999760i	$0.493024\pi$
$860$	19.3114	+	25.8636i	0.658514	+	0.881941i
$861$		0			0
$862$	−26.5797	−	57.0002i	−0.905306	−	1.94144i
$863$	9.18912	+	9.18912i	0.312801	+	0.312801i	0.845994	−	0.533193i	$-0.179008\pi$
$863$	9.18912	+	9.18912i	0.312801	+	0.312801i	−0.533193	+	0.845994i	$0.679008\pi$
$864$		0			0
$865$	35.6468	+	8.39541i	1.21203	+	0.285453i
$866$	24.0686	−	66.1280i	0.817886	−	2.24712i
$867$		0			0
$868$	−41.5223	+	3.63273i	−1.40936	+	0.123303i
$869$	0.394074	−	2.23490i	0.0133680	−	0.0758139i
$870$		0			0
$871$	−20.7091	+	17.3770i	−0.701703	+	0.588798i
$872$	−0.292870	−	0.0784744i	−0.00991784	−	0.00265748i
$873$		0			0
$874$	−25.9285	−	14.9698i	−0.877044	−	0.506362i
$875$	−21.5515	−	12.3216i	−0.728575	−	0.416545i
$876$		0			0
$877$	48.3756	+	22.5579i	1.63353	+	0.761726i	0.999929	−	0.0119368i	$-0.00379970\pi$
$877$	48.3756	+	22.5579i	1.63353	+	0.761726i	0.633598	+	0.773663i	$0.281577\pi$
$878$	36.9995	+	17.2531i	1.24867	+	0.582265i
$879$		0			0
$880$	−7.36753	+	6.57517i	−0.248359	+	0.221649i
$881$	34.2794	+	19.7912i	1.15490	+	0.666782i	0.950077	−	0.312016i	$-0.101004\pi$
$881$	34.2794	+	19.7912i	1.15490	+	0.666782i	0.204824	+	0.978799i	$0.434338\pi$
$882$		0			0
$883$	48.7707	+	13.0681i	1.64127	+	0.439776i	0.957149	−	0.289597i	$-0.0935213\pi$
$883$	48.7707	+	13.0681i	1.64127	+	0.439776i	0.684116	+	0.729373i	$0.260188\pi$
$884$	−28.2777	+	23.7278i	−0.951082	+	0.798053i
$885$		0			0
$886$	0.958958	−	5.43852i	0.0322168	−	0.182711i
$887$	11.8379	−	1.03569i	0.397479	−	0.0347749i	0.113336	−	0.993557i	$-0.463846\pi$
$887$	11.8379	−	1.03569i	0.397479	−	0.0347749i	0.284143	+	0.958782i	$0.408291\pi$
$888$		0			0
$889$	11.5607	−	31.7628i	0.387734	−	1.06529i
$890$	13.7798	−	58.5090i	0.461901	−	1.96123i
$891$		0			0
$892$	−11.6641	−	11.6641i	−0.390541	−	0.390541i
$893$	23.7395	+	50.9096i	0.794413	+	1.70362i
$894$		0			0
$895$	1.93252	+	0.280292i	0.0645972	+	0.00936911i
$896$	0.564144	+	0.0994738i	0.0188467	+	0.00332319i
$897$		0			0
$898$	−5.05560	+	57.7858i	−0.168708	+	1.92834i
$899$	8.65353	+	14.9884i	0.288611	+	0.499890i
$900$		0			0
$901$	27.0764	−	46.8977i	0.902046	−	1.56239i
$902$	5.73656	+	4.01678i	0.191006	+	0.133744i
$903$		0			0
$904$	0.0148452	+	0.0407868i	0.000493743	+	0.00135655i
$905$	−1.01866	+	1.29204i	−0.0338613	+	0.0429488i
$906$		0			0
$907$	0.725418	−	1.03600i	0.0240871	−	0.0343999i	−0.806928	−	0.590650i	$-0.798871\pi$
$907$	0.725418	−	1.03600i	0.0240871	−	0.0343999i	0.831015	+	0.556250i	$0.187760\pi$
$908$	9.28280	−	2.48732i	0.308061	−	0.0825446i
$909$		0			0
$910$	28.9053	−	8.69808i	0.958201	−	0.288339i
$911$	−0.894909	−	1.06651i	−0.0296497	−	0.0353351i	0.751016	−	0.660284i	$-0.229564\pi$
$911$	−0.894909	−	1.06651i	−0.0296497	−	0.0353351i	−0.780666	+	0.624949i	$0.785120\pi$
$912$		0			0
$913$	−3.42967	−	4.89808i	−0.113506	−	0.162103i
$914$	−36.4756	−	30.6067i	−1.20651	−	1.01238i
$915$		0			0
$916$	13.5484	+	4.93120i	0.447650	+	0.162931i
$917$	31.3154	−	31.3154i	1.03412	−	1.03412i
$918$		0			0
$919$			3.33325i			0.109954i	0.998488	+	0.0549769i	$0.0175085\pi$
$919$			3.33325i			0.109954i	−0.998488	+	0.0549769i	$0.982491\pi$
$920$	0.0493654	+	0.237387i	0.00162753	+	0.00782641i
$921$		0			0
$922$	1.64838	+	18.8411i	0.0542865	+	0.620498i
$923$	−19.4755	+	13.6369i	−0.641044	+	0.448864i
$924$		0			0
$925$	12.2658	−	20.0119i	0.403296	−	0.657986i
$926$	−32.0759	+	18.5191i	−1.05408	+	0.608574i
$927$		0			0
$928$	−3.85624	−	14.3917i	−0.126587	−	0.472430i
$929$	5.78861	+	32.8289i	0.189918	+	1.07708i	0.919472	+	0.393156i	$0.128617\pi$
$929$	5.78861	+	32.8289i	0.189918	+	1.07708i	−0.729554	+	0.683924i	$0.760272\pi$
$930$		0			0
$931$	−8.64161	+	3.14529i	−0.283217	+	0.103083i
$932$	−7.70014	+	16.5130i	−0.252226	+	0.540901i
$933$		0			0
$934$	−25.2646	+	4.45484i	−0.826684	+	0.145767i
$935$	−10.2930	+	10.9407i	−0.336616	+	0.357801i
$936$		0			0
$937$	11.0023	−	41.0610i	0.359428	−	1.34140i	−0.515392	−	0.856955i	$-0.672353\pi$
$937$	11.0023	−	41.0610i	0.359428	−	1.34140i	0.874820	−	0.484449i	$-0.160980\pi$
$938$	39.5017	+	3.45595i	1.28978	+	0.112841i
$939$		0			0
$940$	22.4996	−	52.3628i	0.733856	−	1.70789i
$941$	1.20131	−	1.43167i	0.0391617	−	0.0466711i	−0.746108	−	0.665825i	$-0.768080\pi$
$941$	1.20131	−	1.43167i	0.0391617	−	0.0466711i	0.785270	+	0.619154i	$0.212524\pi$
$942$		0			0
$943$	−9.56700	+	4.46117i	−0.311544	+	0.145276i
$944$	−5.54334			−0.180420
$945$		0			0
$946$	−15.9711			−0.519265
$947$	−28.3806	+	13.2341i	−0.922246	+	0.430050i	−0.824950	−	0.565205i	$-0.808797\pi$
$947$	−28.3806	+	13.2341i	−0.922246	+	0.430050i	−0.0972956	+	0.995256i	$0.531019\pi$
$948$		0			0
$949$	0.337235	−	0.401901i	0.0109471	−	0.0130462i
$950$	−6.57684	−	44.0338i	−0.213381	−	1.42865i
$951$		0			0
$952$	0.430537	+	0.0376671i	0.0139538	+	0.00122080i
$953$	−3.16696	+	11.8193i	−0.102588	+	0.382864i	−0.998060	−	0.0622534i	$-0.980171\pi$
$953$	−3.16696	+	11.8193i	−0.102588	+	0.382864i	0.895472	+	0.445117i	$0.146838\pi$
$954$		0			0
$955$	14.1294	−	0.431055i	0.457216	−	0.0139486i
$956$	8.15744	−	1.43838i	0.263830	−	0.0465204i
$957$		0			0
$958$	−6.89835	+	14.7936i	−0.222876	+	0.477958i
$959$	−33.8725	+	12.3286i	−1.09380	+	0.398111i
$960$		0			0
$961$	9.67079	+	54.8458i	0.311961	+	1.76922i
$962$	7.38668	+	27.5675i	0.238156	+	0.888811i
$963$		0			0
$964$	10.7818	−	6.22486i	0.347258	−	0.200489i
$965$	26.6308	+	52.8404i	0.857276	+	1.70099i
$966$		0			0
$967$	8.91754	−	6.24413i	0.286769	−	0.200798i	−0.421337	−	0.906904i	$-0.638439\pi$
$967$	8.91754	−	6.24413i	0.286769	−	0.200798i	0.708106	+	0.706107i	$0.249550\pi$
$968$	−0.0274359	−	0.313593i	−0.000881822	−	0.0100793i
$969$		0			0
$970$	75.9476	−	15.7936i	2.43853	−	0.507101i
$971$		−	17.9235i		−	0.575194i	−0.957752	−	0.287597i	$-0.907144\pi$
$971$		−	17.9235i		−	0.575194i	0.957752	−	0.287597i	$-0.0928563\pi$
$972$		0			0
$973$	4.38373	−	4.38373i	0.140536	−	0.140536i
$974$	−30.1589	−	10.9769i	−0.966353	−	0.351724i
$975$		0			0
$976$	−9.12762	−	7.65898i	−0.292168	−	0.245158i
$977$	−2.92108	−	4.17173i	−0.0934536	−	0.133466i	0.769702	−	0.638403i	$-0.220405\pi$
$977$	−2.92108	−	4.17173i	−0.0934536	−	0.133466i	−0.863156	+	0.504937i	$0.831516\pi$
$978$		0			0
$979$	9.59732	+	11.4376i	0.306732	+	0.365549i
$980$	8.21884	+	4.41662i	0.262541	+	0.141084i
$981$		0			0
$982$	6.33758	−	1.69815i	0.202240	−	0.0541901i
$983$	31.6427	−	45.1905i	1.00925	−	1.44135i	0.115220	−	0.993340i	$-0.463243\pi$
$983$	31.6427	−	45.1905i	1.00925	−	1.44135i	0.894027	−	0.448014i	$-0.147868\pi$
$984$		0			0
$985$	−0.115348	−	0.974946i	−0.00367529	−	0.0310644i
$986$	−7.68938	−	21.1264i	−0.244880	−	0.672802i
$987$		0			0
$988$	22.2616	+	15.5877i	0.708236	+	0.495912i
$989$	12.0370	−	20.8487i	0.382754	−	0.662949i
$990$		0			0
$991$	4.20341	+	7.28053i	0.133526	+	0.231274i	0.925033	−	0.379886i	$-0.124037\pi$
$991$	4.20341	+	7.28053i	0.133526	+	0.231274i	−0.791508	+	0.611159i	$0.790703\pi$
$992$	6.50458	−	74.3476i	0.206520	−	2.36054i
$993$		0			0
$994$	34.3431	+	6.05561i	1.08930	+	0.192072i
$995$	−0.763776	+	5.26600i	−0.0242133	+	0.166944i
$996$		0			0
$997$	−15.9928	−	34.2966i	−0.506496	−	1.08618i	−0.978813	−	0.204756i	$-0.934360\pi$
$997$	−15.9928	−	34.2966i	−0.506496	−	1.08618i	0.472317	−	0.881429i	$-0.343418\pi$
$998$	43.3517	+	43.3517i	1.37227	+	1.37227i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.r.a.17.3		192
3.2	odd	2		135.2.q.a.77.14	yes	192
5.3	odd	4	inner	405.2.r.a.98.14		192
15.2	even	4		675.2.ba.b.293.14		192
15.8	even	4		135.2.q.a.23.3	✓	192
15.14	odd	2		675.2.ba.b.482.3		192
27.7	even	9		135.2.q.a.47.3	yes	192
27.20	odd	18	inner	405.2.r.a.62.14		192
135.7	odd	36		675.2.ba.b.668.3		192
135.34	even	18		675.2.ba.b.182.14		192
135.88	odd	36		135.2.q.a.128.14	yes	192
135.128	even	36	inner	405.2.r.a.143.3		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.23.3	✓	192	15.8	even	4
135.2.q.a.47.3	yes	192	27.7	even	9
135.2.q.a.77.14	yes	192	3.2	odd	2
135.2.q.a.128.14	yes	192	135.88	odd	36
405.2.r.a.17.3		192	1.1	even	1	trivial
405.2.r.a.62.14		192	27.20	odd	18	inner
405.2.r.a.98.14		192	5.3	odd	4	inner
405.2.r.a.143.3		192	135.128	even	36	inner
675.2.ba.b.182.14		192	135.34	even	18
675.2.ba.b.293.14		192	15.2	even	4
675.2.ba.b.482.3		192	15.14	odd	2
675.2.ba.b.668.3		192	135.7	odd	36

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.r (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.81626 + 0.846935i) q^{2} +(1.29592 - 1.54442i) q^{4} +(-0.828498 - 2.07692i) q^{5} +(-2.21198 - 0.193523i) q^{7} +(-0.00834683 + 0.0311508i) q^{8} +(3.26378 + 3.07054i) q^{10} +(-1.09616 + 0.193283i) q^{11} +(-1.28211 + 2.74949i) q^{13} +(4.18143 - 1.52192i) q^{14} +(0.688959 + 3.90728i) q^{16} +(1.56207 + 5.82972i) q^{17} +(3.84801 - 2.22165i) q^{19} +(-4.28129 - 1.41197i) q^{20} +(1.82722 - 1.27943i) q^{22} +(0.293046 + 3.34953i) q^{23} +(-3.62718 + 3.44145i) q^{25} -6.07964i q^{26} +(-3.16543 + 3.16543i) q^{28} +(1.74671 + 0.635749i) q^{29} +(7.13252 + 5.98490i) q^{31} +(-4.59753 - 6.56596i) q^{32} +(-7.77451 - 9.26530i) q^{34} +(1.43069 + 4.75444i) q^{35} +(-4.53439 + 1.21499i) q^{37} +(-5.10738 + 7.29410i) q^{38} +(0.0716130 - 0.00847269i) q^{40} +(1.07377 + 2.95017i) q^{41} +(-5.86507 - 4.10676i) q^{43} +(-1.12203 + 1.94341i) q^{44} +(-3.36908 - 5.83541i) q^{46} +(-1.10183 + 12.5940i) q^{47} +(-2.03824 - 0.359397i) q^{49} +(3.67322 - 9.32254i) q^{50} +(2.58485 + 5.54322i) q^{52} +(-6.34457 - 6.34457i) q^{53} +(1.30960 + 2.11651i) q^{55} +(0.0244914 - 0.0672897i) q^{56} +(-3.71091 + 0.324662i) q^{58} +(-0.242616 + 1.37594i) q^{59} +(-2.30056 + 1.93040i) q^{61} +(-18.0233 - 4.82933i) q^{62} +(7.03924 + 4.06411i) q^{64} +(6.77268 + 0.384887i) q^{65} +(8.07622 + 3.76600i) q^{67} +(11.0278 + 5.14236i) q^{68} +(-6.62521 - 7.42359i) q^{70} +(6.78702 + 3.91849i) q^{71} +(-0.167045 - 0.0447595i) q^{73} +(7.20661 - 6.04707i) q^{74} +(1.55556 - 8.82200i) q^{76} +(2.46210 - 0.215406i) q^{77} +(-0.697324 + 1.91588i) q^{79} +(7.54430 - 4.66809i) q^{80} +(-4.44885 - 4.44885i) q^{82} +(2.27031 + 4.86870i) q^{83} +(10.8137 - 8.07420i) q^{85} +(14.1306 + 2.49161i) q^{86} +(0.00312857 - 0.0357597i) q^{88} +(-6.70700 - 11.6169i) q^{89} +(3.36809 - 5.83370i) q^{91} +(5.55283 + 3.88813i) q^{92} +(-8.66507 - 23.8071i) q^{94} +(-7.80225 - 6.15137i) q^{95} +(9.92914 - 14.1803i) q^{97} +(4.00635 - 1.07350i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Introduction

L-functions

Modular forms

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Database

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