LMFDB - Embedded newform 405.2.r.a.143.3

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			143.3
Character	$\chi$	$=$	405.143
Dual form			405.2.r.a.17.3

$q$-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 $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{7}{18}\right)$

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	−0.343910	−	0.939003i	$-0.611751\pi$
$2$	−1.81626	−	0.846935i	−1.28429	−	0.598874i	−0.940379	+	0.340129i	$0.889529\pi$
$3$		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	−0.497137	−	0.867672i	$-0.665615\pi$
$7$	−2.21198	+	0.193523i	−0.836051	+	0.0731450i	−0.338914	+	0.940817i	$0.610060\pi$
$8$	−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	0.00593305	−	0.999982i	$-0.498111\pi$
$11$	−1.09616	−	0.193283i	−0.330506	−	0.0582771i	−0.336439	+	0.941705i	$0.609223\pi$
$12$		0			0
$13$	−1.28211	−	2.74949i	−0.355592	−	0.762570i	0.644405	−	0.764684i	$-0.277105\pi$
$13$	−1.28211	−	2.74949i	−0.355592	−	0.762570i	−0.999998	+	0.00211367i	$0.999327\pi$
$14$	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	−0.468769	−	0.883321i	$-0.655302\pi$
$17$	1.56207	−	5.82972i	0.378857	−	1.41391i	0.847626	−	0.530594i	$-0.178031\pi$
$18$		0			0
$19$	3.84801	+	2.22165i	0.882794	+	0.509681i	0.871578	−	0.490256i	$-0.163097\pi$
$19$	3.84801	+	2.22165i	0.882794	+	0.509681i	0.0112151	+	0.999937i	$0.496430\pi$
$20$	−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	−0.902429	−	0.430838i	$-0.858218\pi$
$23$	0.293046	−	3.34953i	0.0611042	−	0.698425i	0.963534	−	0.267587i	$-0.0862263\pi$
$24$		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	−0.174710	−	0.984620i	$-0.555899\pi$
$29$	1.74671	−	0.635749i	0.324355	−	0.118056i	0.499066	+	0.866564i	$0.333677\pi$
$30$		0			0
$31$	7.13252	−	5.98490i	1.28104	−	1.07492i	0.287939	−	0.957649i	$-0.407030\pi$
$31$	7.13252	−	5.98490i	1.28104	−	1.07492i	0.993100	−	0.117270i	$-0.0374144\pi$
$32$	−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	−0.133951	−	0.990988i	$-0.542766\pi$
$37$	−4.53439	−	1.21499i	−0.745450	−	0.199743i	−0.611499	+	0.791245i	$0.709433\pi$
$38$	−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	−0.827169	−	0.561953i	$-0.810050\pi$
$41$	1.07377	−	2.95017i	0.167695	−	0.460739i	0.994865	+	0.101214i	$0.0322726\pi$
$42$		0			0
$43$	−5.86507	+	4.10676i	−0.894414	+	0.626276i	−0.927764	−	0.373168i	$-0.878271\pi$
$43$	−5.86507	+	4.10676i	−0.894414	+	0.626276i	0.0333495	+	0.999444i	$0.489383\pi$
$44$	−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	−0.466031	−	0.884768i	$-0.654317\pi$
$47$	−1.10183	−	12.5940i	−0.160718	−	1.83702i	0.305313	−	0.952252i	$-0.401239\pi$
$48$		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	−0.992635	−	0.121142i	$-0.961344\pi$
$53$	−6.34457	+	6.34457i	−0.871494	+	0.871494i	0.121142	+	0.992635i	$0.461344\pi$
$54$		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	0.964933	−	0.262495i	$-0.0845452\pi$
$59$	−0.242616	−	1.37594i	−0.0315859	−	0.179132i	−0.996519	+	0.0833623i	$0.973434\pi$
$60$		0			0
$61$	−2.30056	−	1.93040i	−0.294557	−	0.247163i	0.483517	−	0.875335i	$-0.339359\pi$
$61$	−2.30056	−	1.93040i	−0.294557	−	0.247163i	−0.778075	+	0.628172i	$0.783803\pi$
$62$	−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	0.138812	−	0.990319i	$-0.455672\pi$
$67$	8.07622	−	3.76600i	0.986667	−	0.460090i	0.847855	+	0.530228i	$0.177894\pi$
$68$	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	−0.0399099	−	0.999203i	$-0.512707\pi$
$71$	6.78702	−	3.91849i	0.805471	−	0.465039i	0.845380	+	0.534165i	$0.179374\pi$
$72$		0			0
$73$	−0.167045	+	0.0447595i	−0.0195511	+	0.00523870i	−0.268581	−	0.963257i	$-0.586555\pi$
$73$	−0.167045	+	0.0447595i	−0.0195511	+	0.00523870i	0.249030	+	0.968496i	$0.419888\pi$
$74$	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	0.894264	−	0.447540i	$-0.147700\pi$
$79$	−0.697324	−	1.91588i	−0.0784551	−	0.215554i	−0.972719	+	0.231986i	$0.925478\pi$
$80$	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	−0.741423	−	0.671038i	$-0.765849\pi$
$83$	2.27031	−	4.86870i	0.249199	−	0.534409i	0.990622	+	0.136629i	$0.0436267\pi$
$84$		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	0.253563	+	0.967319i	$0.418397\pi$
$89$	−6.70700	+	11.6169i	−0.710941	+	1.23139i	−0.964504	+	0.264067i	$0.914936\pi$
$90$		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	0.894923	+	0.446221i	$0.147231\pi$
$97$	9.92914	+	14.1803i	1.00815	+	1.43979i	0.113229	+	0.993569i	$0.463881\pi$
$98$	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	−0.953356	−	0.301849i	$-0.902396\pi$
$101$	−4.92991	+	5.87523i	−0.490544	+	0.584608i	0.462812	+	0.886457i	$0.346841\pi$
$102$		0			0
$103$	6.03654	−	8.62107i	0.594798	−	0.849460i	−0.403040	−	0.915182i	$-0.632046\pi$
$103$	6.03654	−	8.62107i	0.594798	−	0.849460i	0.997838	+	0.0657227i	$0.0209353\pi$
$104$	−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	0.904740	−	0.425965i	$-0.140065\pi$
$107$	4.95248	+	4.95248i	0.478774	+	0.478774i	−0.425965	+	0.904740i	$0.640065\pi$
$108$		0			0
$109$		−	9.40170i		−	0.900520i	−0.892898	−	0.450260i	$-0.851331\pi$
$109$		−	9.40170i		−	0.900520i	0.892898	−	0.450260i	$-0.148669\pi$
$110$	−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	0.624283	−	0.781199i	$-0.285391\pi$
$113$	1.10249	+	0.771969i	0.103713	+	0.0726207i	−0.520569	+	0.853819i	$0.674280\pi$
$114$		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	−0.887127	−	0.461525i	$-0.847303\pi$
$127$	−3.93996	−	14.7041i	−0.349615	−	1.30478i	0.537513	−	0.843256i	$-0.319364\pi$
$128$	−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	−0.935995	−	0.352013i	$-0.885497\pi$
$131$	−12.8204	−	15.2788i	−1.12013	−	1.33491i	−0.184131	−	0.982902i	$-0.558947\pi$
$132$		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	0.932993	−	0.359896i	$-0.117188\pi$
$137$	14.7130	+	6.86076i	1.25701	+	0.586155i	0.324020	+	0.946050i	$0.394966\pi$
$138$		0			0
$139$	−1.79469	−	2.13883i	−0.152223	−	0.181413i	0.684544	−	0.728972i	$-0.260002\pi$
$139$	−1.79469	−	2.13883i	−0.152223	−	0.181413i	−0.836767	+	0.547559i	$0.815557\pi$
$140$	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	−0.581492	−	0.813552i	$-0.697531\pi$
$149$	−18.9187	−	6.88585i	−1.54988	−	0.564111i	−0.968390	+	0.249441i	$0.919753\pi$
$150$		0			0
$151$	0.0907569	−	0.514708i	0.00738569	−	0.0418864i	−0.980892	−	0.194552i	$-0.937675\pi$
$151$	0.0907569	−	0.514708i	0.00738569	−	0.0418864i	0.988278	+	0.152666i	$0.0487858\pi$
$152$	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	0.603723	−	0.797194i	$-0.293683\pi$
$157$	0.765462	+	0.535982i	0.0610905	+	0.0427760i	−0.542632	+	0.839970i	$0.682572\pi$
$158$	−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	0.853651	−	0.520846i	$-0.174383\pi$
$163$	4.24897	+	4.24897i	0.332805	+	0.332805i	−0.520846	+	0.853651i	$0.674383\pi$
$164$	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	−0.958049	−	0.286604i	$-0.907474\pi$
$167$	−4.66589	+	6.66358i	−0.361057	+	0.515643i	0.596992	+	0.802247i	$0.296362\pi$
$168$		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	−0.998129	−	0.0611509i	$-0.980523\pi$
$173$	−9.39399	−	13.4160i	−0.714212	−	1.02000i	0.283917	−	0.958849i	$-0.408366\pi$
$174$		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	0.849246	−	0.527998i	$-0.177057\pi$
$179$	−0.436647	−	0.756295i	−0.0326365	−	0.0565281i	−0.881882	+	0.471470i	$0.843724\pi$
$180$		0			0
$181$	−0.367901	+	0.637223i	−0.0273459	+	0.0473644i	−0.879374	−	0.476131i	$-0.842039\pi$
$181$	−0.367901	+	0.637223i	−0.0273459	+	0.0473644i	0.852029	+	0.523495i	$0.175372\pi$
$182$	−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	0.836560	−	0.547876i	$-0.184563\pi$
$191$	−2.16218	−	5.94054i	−0.156450	−	0.429842i	−0.993010	+	0.118033i	$0.962341\pi$
$192$		0			0
$193$	−26.3618	−	2.30636i	−1.89756	−	0.166015i	−0.922213	−	0.386683i	$-0.873621\pi$
$193$	−26.3618	−	2.30636i	−1.89756	−	0.166015i	−0.975349	+	0.220667i	$0.929176\pi$
$194$	−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	−0.243680	−	0.969856i	$-0.578355\pi$
$197$	0.424090	−	0.113635i	0.0302152	−	0.00809613i	0.273895	+	0.961760i	$0.411688\pi$
$198$		0			0
$199$	−2.06085	+	1.18983i	−0.146090	+	0.0843452i	−0.571263	−	0.820767i	$-0.693546\pi$
$199$	−2.06085	+	1.18983i	−0.146090	+	0.0843452i	0.425173	+	0.905112i	$0.360213\pi$
$200$	−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	0.980686	+	0.195586i	$0.0626610\pi$
$211$	1.83079	+	10.3830i	0.126037	+	0.714792i	−0.854649	+	0.519206i	$0.826228\pi$
$212$	−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	0.981960	+	0.189086i	$0.0605525\pi$
$223$	0.713099	+	8.15076i	0.0477527	+	0.545815i	−0.934208	+	0.356729i	$0.883892\pi$
$224$	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	−0.436772	−	0.899572i	$-0.643878\pi$
$227$	3.90472	−	2.73411i	0.259165	−	0.181469i	0.695937	+	0.718103i	$0.254989\pi$
$228$		0			0
$229$	2.44592	−	6.72010i	0.161631	−	0.444077i	−0.832268	−	0.554374i	$-0.812958\pi$
$229$	2.44592	−	6.72010i	0.161631	−	0.444077i	0.993899	+	0.110297i	$0.0351801\pi$
$230$	−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	−0.0387217	−	0.999250i	$-0.512329\pi$
$233$	−8.72938	−	2.33903i	−0.571881	−	0.153235i	−0.533159	+	0.846015i	$0.678995\pi$
$234$		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	−0.535295	−	0.844665i	$-0.679799\pi$
$239$	3.14736	−	2.64095i	0.203586	−	0.170829i	0.738880	+	0.673837i	$0.235355\pi$
$240$		0			0
$241$	5.80277	−	2.11203i	0.373789	−	0.136048i	−0.148293	−	0.988944i	$-0.547378\pi$
$241$	5.80277	−	2.11203i	0.373789	−	0.136048i	0.522082	+	0.852895i	$0.325156\pi$
$242$	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	0.904918	−	0.425585i	$-0.139932\pi$
$251$	15.6657	+	9.04459i	0.988810	+	0.570890i	0.0838914	+	0.996475i	$0.473265\pi$
$252$		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	0.997828	−	0.0658743i	$-0.0209837\pi$
$257$	4.90513	+	10.5191i	0.305974	+	0.656163i	−0.691854	+	0.722037i	$0.743206\pi$
$258$		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	−0.0185804	−	0.999827i	$-0.505915\pi$
$263$	2.21755	−	0.194010i	0.136740	−	0.0119632i	0.155320	+	0.987864i	$0.450359\pi$
$264$		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	−0.333141	−	0.942877i	$-0.608109\pi$
$277$	−8.27992	+	0.724399i	−0.497492	+	0.0435249i	−0.164351	+	0.986402i	$0.552553\pi$
$278$	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	0.351001	−	0.936375i	$-0.385841\pi$
$281$	6.04432	+	1.06578i	0.360574	+	0.0635790i	0.00957353	+	0.999954i	$0.496953\pi$
$282$		0			0
$283$	12.9205	+	27.7081i	0.768044	+	1.64708i	0.762413	+	0.647091i	$0.224015\pi$
$283$	12.9205	+	27.7081i	0.768044	+	1.64708i	0.00563108	+	0.999984i	$0.498208\pi$
$284$	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	0.952551	+	0.304378i	$0.0984485\pi$
$293$	−0.657015	+	7.50972i	−0.0383833	+	0.438723i	−0.990935	+	0.134345i	$0.957107\pi$
$294$		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	−0.123719	−	0.992317i	$-0.539482\pi$
$307$	−12.7384	−	3.41325i	−0.727021	−	0.194805i	−0.603302	+	0.797513i	$0.706149\pi$
$308$	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	−0.936946	−	0.349475i	$-0.886360\pi$
$311$	0.0958399	−	0.263318i	0.00543458	−	0.0149314i	0.942380	+	0.334544i	$0.108582\pi$
$312$		0			0
$313$	−7.80530	+	5.46533i	−0.441182	+	0.308919i	−0.772979	−	0.634432i	$-0.781234\pi$
$313$	−7.80530	+	5.46533i	−0.441182	+	0.308919i	0.331797	+	0.943351i	$0.392345\pi$
$314$	−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	0.999881	+	0.0154231i	$0.00490952\pi$
$317$	0.318142	+	3.63638i	0.0178686	+	0.204239i	−0.982012	+	0.188816i	$0.939535\pi$
$318$		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	0.437583	−	0.899178i	$-0.355835\pi$
$331$	−6.76703	−	5.67821i	−0.371950	−	0.312103i	−0.809532	+	0.587075i	$0.800279\pi$
$332$	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	0.274284	−	0.961649i	$-0.411559\pi$
$337$	21.7951	−	10.1632i	1.18726	−	0.553627i	0.912972	+	0.408022i	$0.133781\pi$
$338$	−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	0.527215	−	0.849732i	$-0.323236\pi$
$347$	16.7440	+	1.46491i	0.898867	+	0.0786406i	0.371651	+	0.928372i	$0.378792\pi$
$348$		0			0
$349$	11.7112	+	32.1764i	0.626888	+	1.72236i	0.689463	+	0.724321i	$0.257846\pi$
$349$	11.7112	+	32.1764i	0.626888	+	1.72236i	−0.0625752	+	0.998040i	$0.519931\pi$
$350$	−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	0.469447	+	0.882961i	$0.344453\pi$
$353$	−9.55751	+	20.4961i	−0.508695	+	1.09090i	−0.978142	+	0.207939i	$0.933324\pi$
$354$		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	−0.0976695	−	0.995219i	$-0.531139\pi$
$359$	15.4051	−	26.6824i	0.813050	−	1.40824i	0.910720	−	0.413025i	$-0.135528\pi$
$360$		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	0.540510	−	0.841338i	$-0.318231\pi$
$367$	−8.33253	−	11.9001i	−0.434955	−	0.621179i	−0.975464	+	0.220158i	$0.929343\pi$
$368$	−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	−0.988146	−	0.153520i	$-0.950939\pi$
$373$	−9.77090	+	13.9543i	−0.505918	+	0.722526i	0.482227	+	0.876046i	$0.339828\pi$
$374$	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	$-0.991316\pi$
$379$		−	1.06208i		−	0.0545552i	0.999628	−	0.0272776i	$-0.00868381\pi$
$380$	−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	0.942070	−	0.335415i	$-0.108877\pi$
$383$	18.5741	+	13.0057i	0.949090	+	0.664560i	0.00701991	+	0.999975i	$0.497765\pi$
$384$		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	−0.968186	−	0.250233i	$-0.919493\pi$
$389$	0.536388	−	3.04201i	0.0271960	−	0.154236i	0.995382	+	0.0959969i	$0.0306039\pi$
$390$		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	−0.991788	−	0.127895i	$-0.959178\pi$
$397$	−3.92165	−	14.6358i	−0.196822	−	0.734549i	0.794966	−	0.606654i	$-0.207489\pi$
$398$	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	0.241113	−	0.970497i	$-0.422488\pi$
$401$	−15.1491	−	18.0540i	−0.756509	−	0.901573i	−0.997622	+	0.0689246i	$0.978043\pi$
$402$		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	0.460206	−	0.887812i	$-0.347775\pi$
$409$	−9.99118	−	11.9070i	−0.494032	−	0.588764i	−0.954238	+	0.299048i	$0.903331\pi$
$410$	−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	0.159000	−	0.987279i	$-0.449173\pi$
$419$	−7.24231	−	2.63599i	−0.353810	−	0.128776i	−0.512810	+	0.858502i	$0.671395\pi$
$420$		0			0
$421$	−0.219552	+	1.24514i	−0.0107003	+	0.0606845i	−0.989690	−	0.143223i	$-0.954253\pi$
$421$	−0.219552	+	1.24514i	−0.0107003	+	0.0606845i	0.978990	+	0.203908i	$0.0653643\pi$
$422$	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	$-0.727228\pi$
$431$		−	31.3833i		−	1.51168i	0.654755	−	0.755841i	$-0.272772\pi$
$432$		0			0
$433$	−24.8304	−	24.8304i	−1.19327	−	1.19327i	−0.976143	−	0.217127i	$-0.930331\pi$
$433$	−24.8304	−	24.8304i	−1.19327	−	1.19327i	−0.217127	−	0.976143i	$-0.569669\pi$
$434$	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	−0.981915	−	0.189322i	$-0.939371\pi$
$439$	−13.0944	+	15.6053i	−0.624962	+	0.744800i	0.356953	+	0.934122i	$0.383815\pi$
$440$	−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	0.779847	−	0.625970i	$-0.215297\pi$
$443$	−1.58059	−	2.25731i	−0.0750960	−	0.107248i	−0.854943	+	0.518722i	$0.826408\pi$
$444$		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	0.974060	+	0.226288i	$0.0726590\pi$
$449$	14.4725	+	25.0672i	0.683001	+	1.18299i	−0.291059	+	0.956705i	$0.594008\pi$
$450$		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	−0.518616	−	0.855007i	$-0.673553\pi$
$457$	10.0414	−	21.5339i	0.469718	−	1.00731i	0.988333	−	0.152305i	$-0.0486697\pi$
$458$	−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	0.991885	−	0.127137i	$-0.0405786\pi$
$461$	3.22783	+	8.86840i	0.150335	+	0.413043i	−0.841550	+	0.540179i	$0.818356\pi$
$462$		0			0
$463$	18.4116	+	1.61081i	0.855659	+	0.0748605i	0.506538	−	0.862217i	$-0.330925\pi$
$463$	18.4116	+	1.61081i	0.855659	+	0.0748605i	0.349121	+	0.937078i	$0.386480\pi$
$464$	−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	0.0388925	−	0.999243i	$-0.487617\pi$
$467$	12.3653	−	3.31326i	0.572196	−	0.153320i	0.533304	+	0.845924i	$0.320950\pi$
$468$		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	0.774106	−	0.633056i	$-0.218200\pi$
$479$	6.23949	+	5.23555i	0.285090	+	0.239219i	−0.489016	+	0.872275i	$0.662644\pi$
$480$		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	−0.402337	−	0.915492i	$-0.631802\pi$
$487$	11.3243	−	11.3243i	0.513154	−	0.513154i	0.915492	+	0.402337i	$0.131802\pi$
$488$	−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	−0.245928	−	0.969288i	$-0.579093\pi$
$491$	−3.22425	+	0.568523i	−0.145508	+	0.0256571i	0.100419	+	0.994945i	$0.467982\pi$
$492$		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	0.450616	+	0.892718i	$0.351204\pi$
$499$	−10.4633	+	28.7478i	−0.468404	+	1.28693i	−0.919020	+	0.394211i	$0.871018\pi$
$500$	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	−0.0267563	−	0.999642i	$-0.508518\pi$
$503$	−12.3296	−	3.30370i	−0.549749	−	0.147305i	−0.522993	+	0.852337i	$0.675184\pi$
$504$		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	0.124493	−	0.992221i	$-0.460270\pi$
$509$	25.3418	−	21.2643i	1.12326	−	0.942525i	0.998764	+	0.0496958i	$0.0158252\pi$
$510$		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	−0.161778	−	0.986827i	$-0.551723\pi$
$521$	−25.0460	−	14.4603i	−1.09728	−	0.633518i	−0.935507	+	0.353309i	$0.885056\pi$
$522$		0			0
$523$	6.53051	−	24.3722i	0.285559	−	1.06572i	−0.662871	−	0.748734i	$-0.730662\pi$
$523$	6.53051	−	24.3722i	0.285559	−	1.06572i	0.948430	−	0.316987i	$-0.102671\pi$
$524$	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	0.308923	−	0.951087i	$-0.400031\pi$
$547$	18.2031	−	1.59256i	0.778308	−	0.0680931i	0.469384	+	0.882994i	$0.344476\pi$
$548$	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	−0.938507	−	0.345261i	$-0.887790\pi$
$557$	1.10675	−	4.13045i	0.0468945	−	0.175013i	0.985401	+	0.170248i	$0.0544570\pi$
$558$		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	0.829829	+	0.558018i	$0.188438\pi$
$563$	−2.00004	+	22.8606i	−0.0842918	+	0.963459i	−0.914121	+	0.405442i	$0.867118\pi$
$564$		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	−0.426767	−	0.904362i	$-0.640348\pi$
$569$	−4.11183	+	1.49658i	−0.172377	+	0.0627400i	0.254390	+	0.967102i	$0.418125\pi$
$570$		0			0
$571$	16.1524	−	13.5535i	0.675958	−	0.567196i	−0.238864	−	0.971053i	$-0.576775\pi$
$571$	16.1524	−	13.5535i	0.675958	−	0.567196i	0.914822	+	0.403857i	$0.132331\pi$
$572$	−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	0.494009	−	0.869457i	$-0.335531\pi$
$577$	11.7007	+	3.13518i	0.487105	+	0.130519i	−0.00690397	+	0.999976i	$0.502198\pi$
$578$	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	0.977130	+	0.212641i	$0.0682064\pi$
$587$	1.25428	+	14.3364i	0.0517695	+	0.591728i	−0.925361	+	0.379087i	$0.876238\pi$
$588$		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	−0.702800	−	0.711388i	$-0.748067\pi$
$593$	0.209120	−	0.209120i	0.00858753	−	0.00858753i	0.711388	+	0.702800i	$0.248067\pi$
$594$		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	−0.999911	−	0.0133687i	$-0.995744\pi$
$599$	−1.58777	−	9.00467i	−0.0648743	−	0.367921i	0.935036	−	0.354552i	$-0.115367\pi$
$600$		0			0
$601$	−4.24577	−	3.56262i	−0.173188	−	0.145322i	0.552073	−	0.833796i	$-0.313837\pi$
$601$	−4.24577	−	3.56262i	−0.173188	−	0.145322i	−0.725262	+	0.688473i	$0.758281\pi$
$602$	−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	−0.955932	−	0.293589i	$-0.905150\pi$
$607$	−33.1493	+	15.4578i	−1.34549	+	0.627412i	−0.389559	+	0.921002i	$0.627372\pi$
$608$	−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	0.291509	−	0.956568i	$-0.405843\pi$
$613$	25.3096	−	6.78170i	1.02225	−	0.273910i	0.730738	+	0.682658i	$0.239176\pi$
$614$	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	0.314952	−	0.949108i	$-0.398012\pi$
$617$	11.4338	+	1.00033i	0.460309	+	0.0402718i	0.145356	+	0.989379i	$0.453567\pi$
$618$		0			0
$619$	9.29363	+	25.5340i	0.373542	+	1.02630i	0.973981	+	0.226629i	$0.0727704\pi$
$619$	9.29363	+	25.5340i	0.373542	+	1.02630i	−0.600439	+	0.799671i	$0.705007\pi$
$620$	−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	0.975086	−	0.221828i	$-0.0712024\pi$
$631$	7.42122	+	12.8539i	0.295434	+	0.511707i	−0.679652	+	0.733535i	$0.737869\pi$
$632$	−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	−0.719931	−	0.694046i	$-0.755827\pi$
$641$	2.24280	−	2.67286i	0.0885851	−	0.105572i	0.808516	+	0.588474i	$0.200271\pi$
$642$		0			0
$643$	−1.30898	+	1.86941i	−0.0516210	+	0.0737225i	−0.844133	−	0.536134i	$-0.819884\pi$
$643$	−1.30898	+	1.86941i	−0.0516210	+	0.0737225i	0.792512	+	0.609857i	$0.208773\pi$
$644$	−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	0.855113	−	0.518441i	$-0.173488\pi$
$647$	8.56365	+	8.56365i	0.336672	+	0.336672i	−0.518441	+	0.855113i	$0.673488\pi$
$648$		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	0.900029	−	0.435830i	$-0.143545\pi$
$653$	20.3999	+	14.2842i	0.798311	+	0.558984i	−0.101718	+	0.994813i	$0.532434\pi$
$654$		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	−0.682186	−	0.731179i	$-0.738970\pi$
$659$	5.36362	−	30.4186i	0.208937	−	1.18494i	0.891123	−	0.453762i	$-0.149918\pi$
$660$		0			0
$661$	33.9585	+	12.3599i	1.32083	+	0.480744i	0.903726	−	0.428112i	$-0.140821\pi$
$661$	33.9585	+	12.3599i	1.32083	+	0.480744i	0.417109	+	0.908857i	$0.363043\pi$
$662$	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	0.942689	−	0.333674i	$-0.108288\pi$
$673$	33.5440	+	15.6418i	1.29303	+	0.602949i	0.350339	+	0.936623i	$0.386066\pi$
$674$	−48.1932			−1.85633
$675$		0			0
$676$	7.65415			0.294390
$677$	−41.5346	−	19.3679i	−1.59630	−	0.744368i	−0.597938	−	0.801542i	$-0.704013\pi$
$677$	−41.5346	−	19.3679i	−1.59630	−	0.744368i	−0.998364	+	0.0571738i	$0.981791\pi$
$678$		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	−0.997247	−	0.0741513i	$-0.976375\pi$
$683$	−4.46063	−	16.6473i	−0.170681	−	0.636992i	0.826566	−	0.562840i	$-0.190291\pi$
$684$		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	0.622314	+	0.782768i	$0.286193\pi$
$691$	−6.05103	+	34.3171i	−0.230192	+	1.30548i	−0.852506	+	0.522717i	$0.824918\pi$
$692$	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	$0.172399\pi$
$701$			27.2979i			1.03103i	−0.856881	+	0.515515i	$0.827601\pi$
$702$		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	−0.361883	−	0.932223i	$-0.617866\pi$
$709$	16.4826	−	19.6432i	0.619018	−	0.737717i	0.980901	+	0.194506i	$0.0623105\pi$
$710$	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	0.852109	−	0.523364i	$-0.175323\pi$
$719$	−0.729141	−	1.26291i	−0.0271924	−	0.0470986i	−0.879301	+	0.476266i	$0.841990\pi$
$720$		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	−0.0798819	−	0.996804i	$-0.525454\pi$
$727$	19.8194	−	42.5029i	0.735062	−	1.57634i	0.814944	−	0.579540i	$-0.196768\pi$
$728$	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	−0.374196	−	0.927350i	$-0.622081\pi$
$733$	−24.4678	−	2.14066i	−0.903740	−	0.0790670i	−0.529544	+	0.848283i	$0.677637\pi$
$734$	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	−0.129844	−	0.991534i	$-0.541448\pi$
$739$	18.0486	−	10.4204i	0.663928	−	0.383319i	0.793772	+	0.608215i	$0.208114\pi$
$740$	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	−0.971510	−	0.236998i	$-0.923836\pi$
$743$	−38.5547	+	17.9783i	−1.41443	+	0.659561i	−0.442923	+	0.896559i	$0.646059\pi$
$744$		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	0.979331	+	0.202265i	$0.0648304\pi$
$751$	3.51433	+	19.9308i	0.128240	+	0.727284i	−0.851091	+	0.525018i	$0.824059\pi$
$752$	−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	−0.478381	−	0.878152i	$-0.658776\pi$
$757$	10.9992	−	10.9992i	0.399771	−	0.399771i	0.878152	+	0.478381i	$0.158776\pi$
$758$	−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	0.0628262	−	0.998024i	$-0.479989\pi$
$761$	12.7782	−	2.25313i	0.463208	−	0.0816761i	0.400382	+	0.916348i	$0.368878\pi$
$762$		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	−0.583700	−	0.811969i	$-0.698396\pi$
$769$	10.6865	−	29.3608i	0.385364	−	1.05878i	0.969064	−	0.246810i	$-0.0793822\pi$
$770$	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	−0.435243	−	0.900313i	$-0.643338\pi$
$773$	−35.0964	−	9.40406i	−1.26233	−	0.338241i	−0.827088	+	0.562072i	$0.810004\pi$
$774$		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	0.721707	+	0.692199i	$0.243358\pi$
$787$	−3.06442	+	35.0265i	−0.109235	+	1.24856i	−0.830942	+	0.556360i	$0.812198\pi$
$788$	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	0.999306	+	0.0372435i	$0.0118577\pi$
$797$	10.8830	+	23.3386i	0.385495	+	0.826696i	−0.613811	+	0.789453i	$0.710364\pi$
$798$		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	0.0584494	−	0.998290i	$-0.481384\pi$
$821$	−6.53467	−	1.15224i	−0.228061	−	0.0402134i	−0.286511	+	0.958077i	$0.592495\pi$
$822$		0			0
$823$	9.68030	+	20.7595i	0.337434	+	0.723630i	0.999671	−	0.0256651i	$-0.00817034\pi$
$823$	9.68030	+	20.7595i	0.337434	+	0.723630i	−0.662236	+	0.749295i	$0.730393\pi$
$824$	−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	−0.763279	−	0.646069i	$-0.776412\pi$
$827$	6.34894	−	23.6946i	0.220774	−	0.823941i	0.984054	−	0.177872i	$-0.0569213\pi$
$828$		0			0
$829$	24.8714	+	14.3595i	0.863821	+	0.498727i	0.865290	−	0.501272i	$-0.167134\pi$
$829$	24.8714	+	14.3595i	0.863821	+	0.498727i	−0.00146915	+	0.999999i	$0.500468\pi$
$830$	−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	−0.798534	−	0.601950i	$-0.794391\pi$
$839$	−29.6410	+	10.7884i	−1.02332	+	0.372458i	−0.224787	+	0.974408i	$0.572169\pi$
$840$		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	−0.845757	−	0.533569i	$-0.820851\pi$
$853$	−18.5060	+	12.9580i	−0.633632	+	0.443674i	0.212125	+	0.977243i	$0.431962\pi$
$854$	−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	−0.998518	−	0.0544314i	$-0.982665\pi$
$857$	−0.720788	−	8.23864i	−0.0246216	−	0.281427i	0.973896	−	0.226995i	$-0.0728902\pi$
$858$		0			0
$859$	11.2675	−	1.98676i	0.384442	−	0.0677875i	0.0219126	−	0.999760i	$-0.493024\pi$
$859$	11.2675	−	1.98676i	0.384442	−	0.0677875i	0.362529	+	0.931972i	$0.381913\pi$
$860$	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	−0.533193	−	0.845994i	$-0.679008\pi$
$863$	9.18912	−	9.18912i	0.312801	−	0.312801i	0.845994	+	0.533193i	$0.179008\pi$
$864$		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	0.633598	−	0.773663i	$-0.281577\pi$
$877$	48.3756	−	22.5579i	1.63353	−	0.761726i	0.999929	+	0.0119368i	$0.00379970\pi$
$878$	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	0.204824	−	0.978799i	$-0.434338\pi$
$881$	34.2794	−	19.7912i	1.15490	−	0.666782i	0.950077	+	0.312016i	$0.101004\pi$
$882$		0			0
$883$	48.7707	−	13.0681i	1.64127	−	0.439776i	0.684116	−	0.729373i	$-0.260188\pi$
$883$	48.7707	−	13.0681i	1.64127	−	0.439776i	0.957149	+	0.289597i	$0.0935213\pi$
$884$	−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	0.284143	−	0.958782i	$-0.408291\pi$
$887$	11.8379	+	1.03569i	0.397479	+	0.0347749i	0.113336	+	0.993557i	$0.463846\pi$
$888$		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	0.831015	−	0.556250i	$-0.187760\pi$
$907$	0.725418	+	1.03600i	0.0240871	+	0.0343999i	−0.806928	+	0.590650i	$0.798871\pi$
$908$	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	−0.780666	−	0.624949i	$-0.785120\pi$
$911$	−0.894909	+	1.06651i	−0.0296497	+	0.0353351i	0.751016	+	0.660284i	$0.229564\pi$
$912$		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	$-0.982491\pi$
$919$		−	3.33325i		−	0.109954i	0.998488	−	0.0549769i	$-0.0175085\pi$
$920$	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	−0.729554	−	0.683924i	$-0.760272\pi$
$929$	5.78861	−	32.8289i	0.189918	−	1.07708i	0.919472	−	0.393156i	$-0.128617\pi$
$930$		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	0.874820	+	0.484449i	$0.160980\pi$
$937$	11.0023	+	41.0610i	0.359428	+	1.34140i	−0.515392	+	0.856955i	$0.672353\pi$
$938$	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	0.785270	−	0.619154i	$-0.212524\pi$
$941$	1.20131	+	1.43167i	0.0391617	+	0.0466711i	−0.746108	+	0.665825i	$0.768080\pi$
$942$		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	−0.0972956	−	0.995256i	$-0.531019\pi$
$947$	−28.3806	−	13.2341i	−0.922246	−	0.430050i	−0.824950	+	0.565205i	$0.808797\pi$
$948$		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	0.895472	−	0.445117i	$-0.146838\pi$
$953$	−3.16696	−	11.8193i	−0.102588	−	0.382864i	−0.998060	+	0.0622534i	$0.980171\pi$
$954$		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	0.708106	−	0.706107i	$-0.249550\pi$
$967$	8.91754	+	6.24413i	0.286769	+	0.200798i	−0.421337	+	0.906904i	$0.638439\pi$
$968$	−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	$0.0928563\pi$
$971$			17.9235i			0.575194i	−0.957752	+	0.287597i	$0.907144\pi$
$972$		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	−0.863156	−	0.504937i	$-0.831516\pi$
$977$	−2.92108	+	4.17173i	−0.0934536	+	0.133466i	0.769702	+	0.638403i	$0.220405\pi$
$978$		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	0.894027	+	0.448014i	$0.147868\pi$
$983$	31.6427	+	45.1905i	1.00925	+	1.44135i	0.115220	+	0.993340i	$0.463243\pi$
$984$		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	−0.791508	−	0.611159i	$-0.790703\pi$
$991$	4.20341	−	7.28053i	0.133526	−	0.231274i	0.925033	+	0.379886i	$0.124037\pi$
$992$	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	0.472317	+	0.881429i	$0.343418\pi$
$997$	−15.9928	+	34.2966i	−0.506496	+	1.08618i	−0.978813	+	0.204756i	$0.934360\pi$
$998$	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.143.3		192
3.2	odd	2		135.2.q.a.128.14	yes	192
5.2	odd	4	inner	405.2.r.a.62.14		192
15.2	even	4		135.2.q.a.47.3	yes	192
15.8	even	4		675.2.ba.b.182.14		192
15.14	odd	2		675.2.ba.b.668.3		192
27.4	even	9		135.2.q.a.23.3	✓	192
27.23	odd	18	inner	405.2.r.a.98.14		192
135.4	even	18		675.2.ba.b.293.14		192
135.58	odd	36		675.2.ba.b.482.3		192
135.77	even	36	inner	405.2.r.a.17.3		192
135.112	odd	36		135.2.q.a.77.14	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.23.3	✓	192	27.4	even	9
135.2.q.a.47.3	yes	192	15.2	even	4
135.2.q.a.77.14	yes	192	135.112	odd	36
135.2.q.a.128.14	yes	192	3.2	odd	2
405.2.r.a.17.3		192	135.77	even	36	inner
405.2.r.a.62.14		192	5.2	odd	4	inner
405.2.r.a.98.14		192	27.23	odd	18	inner
405.2.r.a.143.3		192	1.1	even	1	trivial
675.2.ba.b.182.14		192	15.8	even	4
675.2.ba.b.293.14		192	135.4	even	18
675.2.ba.b.482.3		192	135.58	odd	36
675.2.ba.b.668.3		192	15.14	odd	2

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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