LMFDB - Embedded newform 484.2.i.a.221.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [484,2,Mod(45,484)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(484, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("484.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 484 = 2^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	484.i (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.86475945783$
Analytic rank:	$0$
Dimension:	$110$
Relative dimension:	$11$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			221.3
Character	$\chi$	$=$	484.221
Dual form			484.2.i.a.265.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.94110 q^{3} +(-1.34270 + 0.394253i) q^{5} +(0.322293 - 2.24160i) q^{7} +0.767885 q^{9} +(2.67636 + 1.95885i) q^{11} +(0.525392 - 0.606334i) q^{13} +(2.60632 - 0.765286i) q^{15} +(-4.15823 + 2.67233i) q^{17} +(3.69032 + 2.37163i) q^{19} +(-0.625604 + 4.35117i) q^{21} +(1.01927 + 7.08917i) q^{23} +(-2.55886 + 1.64448i) q^{25} +4.33277 q^{27} +(4.12817 + 2.65301i) q^{29} +(4.22508 + 4.87600i) q^{31} +(-5.19509 - 3.80233i) q^{33} +(0.451012 + 3.13686i) q^{35} +(-0.881378 - 1.01716i) q^{37} +(-1.01984 + 1.17696i) q^{39} +(-1.27440 - 2.79054i) q^{41} +(-2.44916 - 0.719138i) q^{43} +(-1.03104 + 0.302741i) q^{45} +(-1.56156 + 3.41934i) q^{47} +(1.79556 + 0.527225i) q^{49} +(8.07156 - 5.18727i) q^{51} +(-1.58008 + 10.9897i) q^{53} +(-4.36583 - 1.57499i) q^{55} +(-7.16330 - 4.60357i) q^{57} +(4.69769 - 10.2865i) q^{59} +(2.44950 - 5.36366i) q^{61} +(0.247484 - 1.72129i) q^{63} +(-0.466395 + 1.02126i) q^{65} +(2.49248 + 5.45778i) q^{67} +(-1.97851 - 13.7608i) q^{69} +(8.30838 + 5.33947i) q^{71} +(-1.01447 - 7.05578i) q^{73} +(4.96701 - 3.19210i) q^{75} +(5.25353 - 5.36800i) q^{77} +(-12.4996 + 3.67021i) q^{79} -10.7140 q^{81} +(-0.180094 + 1.25258i) q^{83} +(4.52969 - 5.22754i) q^{85} +(-8.01321 - 5.14978i) q^{87} +(-2.79587 + 1.79680i) q^{89} +(-1.18983 - 1.37313i) q^{91} +(-8.20132 - 9.46483i) q^{93} +(-5.89002 - 1.72947i) q^{95} +(0.636620 + 0.186928i) q^{97} +(2.05514 + 1.50417i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 110 q - 2 q^{3} + 2 q^{5} - 2 q^{7} + 112 q^{9} - 10 q^{11} - 29 q^{13} - 18 q^{15} - 6 q^{17} - 8 q^{19} - 2 q^{21} + 4 q^{23} - 17 q^{25} + 4 q^{27} - 28 q^{31} + q^{33} + 6 q^{35} - 31 q^{37} + 4 q^{39}+ \cdots - 57 q^{99}+O(q^{100}) $ 110 * q - 2 * q^3 + 2 * q^5 - 2 * q^7 + 112 * q^9 - 10 * q^11 - 29 * q^13 - 18 * q^15 - 6 * q^17 - 8 * q^19 - 2 * q^21 + 4 * q^23 - 17 * q^25 + 4 * q^27 - 28 * q^31 + q^33 + 6 * q^35 - 31 * q^37 + 4 * q^39 + 10 * q^43 - 8 * q^45 + 2 * q^47 - 49 * q^49 + 115 * q^51 + 72 * q^53 + 41 * q^55 + 3 * q^57 - 6 * q^59 + 4 * q^61 - 51 * q^63 - 45 * q^65 - 51 * q^67 + 4 * q^69 + 26 * q^71 - 18 * q^73 + 46 * q^77 - 24 * q^79 + 110 * q^81 - 6 * q^83 - 92 * q^85 - 7 * q^89 - 91 * q^91 - 37 * q^93 - 64 * q^95 - 31 * q^97 - 57 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/484\mathbb{Z}\right)^\times$.

$n$	$243$	$365$
$\chi(n)$	$1$	$e\left(\frac{4}{11}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.94110			−1.12070			−0.560349	−	0.828257i	$-0.689333\pi$
$3$	−1.94110			−1.12070			−0.560349	+	0.828257i	$0.689333\pi$
$4$		0			0
$5$	−1.34270	+	0.394253i	−0.600474	+	0.176315i	−0.567822	−	0.823152i	$-0.692214\pi$
$5$	−1.34270	+	0.394253i	−0.600474	+	0.176315i	−0.0326526	+	0.999467i	$0.510396\pi$
$6$		0			0
$7$	0.322293	−	2.24160i	0.121815	−	0.847244i	−0.833682	−	0.552245i	$-0.813771\pi$
$7$	0.322293	−	2.24160i	0.121815	−	0.847244i	0.955497	−	0.295000i	$-0.0953195\pi$
$8$		0			0
$9$	0.767885			0.255962
$10$		0			0
$11$	2.67636	+	1.95885i	0.806953	+	0.590616i
$11$	2.67636	+	1.95885i	0.806953	+	0.590616i
$12$		0			0
$13$	0.525392	−	0.606334i	0.145717	−	0.168167i	−0.678199	−	0.734878i	$-0.737239\pi$
$13$	0.525392	−	0.606334i	0.145717	−	0.168167i	0.823916	+	0.566712i	$0.191785\pi$
$14$		0			0
$15$	2.60632	−	0.765286i	0.672950	−	0.197596i
$16$		0			0
$17$	−4.15823	+	2.67233i	−1.00852	+	0.648136i	−0.937009	−	0.349304i	$-0.886418\pi$
$17$	−4.15823	+	2.67233i	−1.00852	+	0.648136i	−0.0715095	+	0.997440i	$0.522782\pi$
$18$		0			0
$19$	3.69032	+	2.37163i	0.846618	+	0.544088i	0.890518	−	0.454948i	$-0.150342\pi$
$19$	3.69032	+	2.37163i	0.846618	+	0.544088i	−0.0439002	+	0.999036i	$0.513978\pi$
$20$		0			0
$21$	−0.625604	+	4.35117i	−0.136518	+	0.949504i
$22$		0			0
$23$	1.01927	+	7.08917i	0.212532	+	1.47820i	0.764659	+	0.644435i	$0.222907\pi$
$23$	1.01927	+	7.08917i	0.212532	+	1.47820i	−0.552127	+	0.833760i	$0.686184\pi$
$24$		0			0
$25$	−2.55886	+	1.64448i	−0.511771	+	0.328895i
$26$		0			0
$27$	4.33277			0.833841
$28$		0			0
$29$	4.12817	+	2.65301i	0.766582	+	0.492652i	0.864556	−	0.502537i	$-0.167600\pi$
$29$	4.12817	+	2.65301i	0.766582	+	0.492652i	−0.0979739	+	0.995189i	$0.531236\pi$
$30$		0			0
$31$	4.22508	+	4.87600i	0.758847	+	0.875756i	0.995394	−	0.0958641i	$-0.0305614\pi$
$31$	4.22508	+	4.87600i	0.758847	+	0.875756i	−0.236548	+	0.971620i	$0.576016\pi$
$32$		0			0
$33$	−5.19509	−	3.80233i	−0.904350	−	0.661902i
$34$		0			0
$35$	0.451012	+	3.13686i	0.0762350	+	0.530226i
$36$		0			0
$37$	−0.881378	−	1.01716i	−0.144898	−	0.167221i	0.678662	−	0.734451i	$-0.262560\pi$
$37$	−0.881378	−	1.01716i	−0.144898	−	0.167221i	−0.823559	+	0.567230i	$0.808015\pi$
$38$		0			0
$39$	−1.01984	+	1.17696i	−0.163305	+	0.188464i
$40$		0			0
$41$	−1.27440	−	2.79054i	−0.199027	−	0.435809i	0.783633	−	0.621224i	$-0.213364\pi$
$41$	−1.27440	−	2.79054i	−0.199027	−	0.435809i	−0.982660	+	0.185415i	$0.940637\pi$
$42$		0			0
$43$	−2.44916	−	0.719138i	−0.373493	−	0.109667i	0.0895983	−	0.995978i	$-0.471442\pi$
$43$	−2.44916	−	0.719138i	−0.373493	−	0.109667i	−0.463091	+	0.886311i	$0.653260\pi$
$44$		0			0
$45$	−1.03104	+	0.302741i	−0.153698	+	0.0451299i
$46$		0			0
$47$	−1.56156	+	3.41934i	−0.227777	+	0.498762i	−0.988668	−	0.150117i	$-0.952035\pi$
$47$	−1.56156	+	3.41934i	−0.227777	+	0.498762i	0.760891	+	0.648880i	$0.224762\pi$
$48$		0			0
$49$	1.79556	+	0.527225i	0.256509	+	0.0753179i
$50$		0			0
$51$	8.07156	−	5.18727i	1.13024	−	0.726364i
$52$		0			0
$53$	−1.58008	+	10.9897i	−0.217041	+	1.50955i	0.531837	+	0.846847i	$0.321502\pi$
$53$	−1.58008	+	10.9897i	−0.217041	+	1.50955i	−0.748878	+	0.662708i	$0.769407\pi$
$54$		0			0
$55$	−4.36583	−	1.57499i	−0.588689	−	0.212372i
$56$		0			0
$57$	−7.16330	−	4.60357i	−0.948802	−	0.609758i
$58$		0			0
$59$	4.69769	−	10.2865i	0.611587	−	1.33919i	−0.309895	−	0.950771i	$-0.600294\pi$
$59$	4.69769	−	10.2865i	0.611587	−	1.33919i	0.921483	−	0.388419i	$-0.126979\pi$
$60$		0			0
$61$	2.44950	−	5.36366i	0.313627	−	0.686747i	−0.685520	−	0.728054i	$-0.740425\pi$
$61$	2.44950	−	5.36366i	0.313627	−	0.686747i	0.999146	+	0.0413072i	$0.0131522\pi$
$62$		0			0
$63$	0.247484	−	1.72129i	0.0311801	−	0.216862i
$64$		0			0
$65$	−0.466395	+	1.02126i	−0.0578492	+	0.126672i
$66$		0			0
$67$	2.49248	+	5.45778i	0.304505	+	0.666773i	0.998588	−	0.0531217i	$-0.0169171\pi$
$67$	2.49248	+	5.45778i	0.304505	+	0.666773i	−0.694083	+	0.719895i	$0.744190\pi$
$68$		0			0
$69$	−1.97851	−	13.7608i	−0.238184	−	1.65661i
$70$		0			0
$71$	8.30838	+	5.33947i	0.986023	+	0.633679i	0.931082	−	0.364811i	$-0.118866\pi$
$71$	8.30838	+	5.33947i	0.986023	+	0.633679i	0.0549414	+	0.998490i	$0.482503\pi$
$72$		0			0
$73$	−1.01447	−	7.05578i	−0.118734	−	0.825817i	−0.958952	−	0.283567i	$-0.908482\pi$
$73$	−1.01447	−	7.05578i	−0.118734	−	0.825817i	0.840218	−	0.542249i	$-0.182427\pi$
$74$		0			0
$75$	4.96701	−	3.19210i	0.573540	−	0.368592i
$76$		0			0
$77$	5.25353	−	5.36800i	0.598695	−	0.611740i
$78$		0			0
$79$	−12.4996	+	3.67021i	−1.40631	+	0.412931i	−0.894847	−	0.446373i	$-0.852716\pi$
$79$	−12.4996	+	3.67021i	−1.40631	+	0.412931i	−0.511466	+	0.859304i	$0.670897\pi$
$80$		0			0
$81$	−10.7140			−1.19045
$82$		0			0
$83$	−0.180094	+	1.25258i	−0.0197679	+	0.137489i	−0.997315	−	0.0732267i	$-0.976670\pi$
$83$	−0.180094	+	1.25258i	−0.0197679	+	0.137489i	0.977547	+	0.210716i	$0.0675794\pi$
$84$		0			0
$85$	4.52969	−	5.22754i	0.491314	−	0.567006i
$86$		0			0
$87$	−8.01321	−	5.14978i	−0.859106	−	0.552114i
$88$		0			0
$89$	−2.79587	+	1.79680i	−0.296362	+	0.190460i	−0.680368	−	0.732870i	$-0.738180\pi$
$89$	−2.79587	+	1.79680i	−0.296362	+	0.190460i	0.384007	+	0.923330i	$0.374544\pi$
$90$		0			0
$91$	−1.18983	−	1.37313i	−0.124728	−	0.143944i
$92$		0			0
$93$	−8.20132	−	9.46483i	−0.850437	−	0.981457i
$94$		0			0
$95$	−5.89002	−	1.72947i	−0.604303	−	0.177439i
$96$		0			0
$97$	0.636620	+	0.186928i	0.0646390	+	0.0189797i	0.313892	−	0.949459i	$-0.398367\pi$
$97$	0.636620	+	0.186928i	0.0646390	+	0.0189797i	−0.249253	+	0.968438i	$0.580185\pi$
$98$		0			0
$99$	2.05514	+	1.50417i	0.206549	+	0.151175i
$100$		0			0
$101$	−3.09923	+	6.78636i	−0.308385	+	0.675268i	−0.998842	−	0.0481045i	$-0.984682\pi$
$101$	−3.09923	+	6.78636i	−0.308385	+	0.675268i	0.690458	+	0.723373i	$0.257409\pi$
$102$		0			0
$103$	−4.44554	−	9.73438i	−0.438032	−	0.959157i	−0.991955	−	0.126589i	$-0.959597\pi$
$103$	−4.44554	−	9.73438i	−0.438032	−	0.959157i	0.553923	−	0.832568i	$-0.313130\pi$
$104$		0			0
$105$	−0.875462	−	6.08897i	−0.0854364	−	0.594223i
$106$		0			0
$107$	13.2811	−	3.89970i	1.28394	−	0.376998i	0.432585	−	0.901593i	$-0.357602\pi$
$107$	13.2811	−	3.89970i	1.28394	−	0.376998i	0.851352	+	0.524595i	$0.175783\pi$
$108$		0			0
$109$	−3.79803	+	4.38316i	−0.363786	+	0.419831i	−0.907904	−	0.419177i	$-0.862319\pi$
$109$	−3.79803	+	4.38316i	−0.363786	+	0.419831i	0.544119	+	0.839008i	$0.316864\pi$
$110$		0			0
$111$	1.71085	+	1.97442i	0.162386	+	0.187404i
$112$		0			0
$113$	−15.5490	−	4.56559i	−1.46273	−	0.429495i	−0.548999	−	0.835823i	$-0.684991\pi$
$113$	−15.5490	−	4.56559i	−1.46273	−	0.429495i	−0.913727	+	0.406328i	$0.866809\pi$
$114$		0			0
$115$	−4.16350	−	9.11679i	−0.388248	−	0.850145i
$116$		0			0
$117$	0.403441	−	0.465595i	0.0372981	−	0.0430443i
$118$		0			0
$119$	4.65012	+	10.1824i	0.426276	+	0.933415i
$120$		0			0
$121$	3.32580	+	10.4852i	0.302346	+	0.953198i
$122$		0			0
$123$	2.47374	+	5.41672i	0.223049	+	0.488410i
$124$		0			0
$125$	7.36946	−	8.50481i	0.659144	−	0.760693i
$126$		0			0
$127$	−6.44789	−	14.1189i	−0.572158	−	1.25285i	−0.945641	−	0.325214i	$-0.894564\pi$
$127$	−6.44789	−	14.1189i	−0.572158	−	1.25285i	0.373483	−	0.927637i	$-0.378164\pi$
$128$		0			0
$129$	4.75407	+	1.39592i	0.418573	+	0.122904i
$130$		0			0
$131$	11.6661	+	13.4634i	1.01928	+	1.17631i	0.984225	+	0.176921i	$0.0566137\pi$
$131$	11.6661	+	13.4634i	1.01928	+	1.17631i	0.0350505	+	0.999386i	$0.488841\pi$
$132$		0			0
$133$	6.50560	−	7.50786i	0.564107	−	0.651014i
$134$		0			0
$135$	−5.81761	+	1.70821i	−0.500700	+	0.147019i
$136$		0			0
$137$	1.82404	+	12.6865i	0.155838	+	1.08388i	0.906200	+	0.422850i	$0.138970\pi$
$137$	1.82404	+	12.6865i	0.155838	+	1.08388i	−0.750362	+	0.661028i	$0.770121\pi$
$138$		0			0
$139$	−7.61916	−	16.6836i	−0.646249	−	1.41509i	−0.894800	−	0.446468i	$-0.852682\pi$
$139$	−7.61916	−	16.6836i	−0.646249	−	1.41509i	0.248551	−	0.968619i	$-0.420046\pi$
$140$		0			0
$141$	3.03115	−	6.63730i	0.255269	−	0.558961i
$142$		0			0
$143$	2.59386	−	0.593604i	0.216909	−	0.0496397i
$144$		0			0
$145$	−6.58886	−	1.93466i	−0.547175	−	0.160665i
$146$		0			0
$147$	−3.48538	−	1.02340i	−0.287469	−	0.0844085i
$148$		0			0
$149$	−2.47934	−	2.86131i	−0.203116	−	0.234408i	0.645048	−	0.764142i	$-0.276837\pi$
$149$	−2.47934	−	2.86131i	−0.203116	−	0.234408i	−0.848164	+	0.529734i	$0.822292\pi$
$150$		0			0
$151$	13.4226	+	15.4905i	1.09231	+	1.26060i	0.963147	+	0.268976i	$0.0866852\pi$
$151$	13.4226	+	15.4905i	1.09231	+	1.26060i	0.129168	+	0.991623i	$0.458769\pi$
$152$		0			0
$153$	−3.19304	+	2.05204i	−0.258142	+	0.165898i
$154$		0			0
$155$	−7.59540	−	4.88127i	−0.610077	−	0.392073i
$156$		0			0
$157$	−1.20817	+	1.39430i	−0.0964222	+	0.111277i	−0.801910	−	0.597445i	$-0.796183\pi$
$157$	−1.20817	+	1.39430i	−0.0964222	+	0.111277i	0.705488	+	0.708722i	$0.250728\pi$
$158$		0			0
$159$	3.06711	−	21.3322i	0.243237	−	1.69175i
$160$		0			0
$161$	16.2196			1.27828
$162$		0			0
$163$	3.16808	−	0.930232i	0.248143	−	0.0728614i	−0.155296	−	0.987868i	$-0.549633\pi$
$163$	3.16808	−	0.930232i	0.248143	−	0.0728614i	0.403439	+	0.915007i	$0.367815\pi$
$164$		0			0
$165$	8.47454	+	3.05722i	0.659742	+	0.238004i
$166$		0			0
$167$	−8.59562	+	5.52407i	−0.665149	+	0.427465i	−0.829174	−	0.558991i	$-0.811189\pi$
$167$	−8.59562	+	5.52407i	−0.665149	+	0.427465i	0.164025	+	0.986456i	$0.447552\pi$
$168$		0			0
$169$	1.75849	+	12.2306i	0.135268	+	0.940812i
$170$		0			0
$171$	2.83374	+	1.82114i	0.216702	+	0.139266i
$172$		0			0
$173$	1.83708	+	12.7772i	0.139671	+	0.971431i	0.932289	+	0.361713i	$0.117808\pi$
$173$	1.83708	+	12.7772i	0.139671	+	0.971431i	−0.792619	+	0.609718i	$0.791283\pi$
$174$		0			0
$175$	2.86155	+	6.26593i	0.216313	+	0.473660i
$176$		0			0
$177$	−9.11871	+	19.9672i	−0.685404	+	1.50083i
$178$		0			0
$179$	0.308660	−	2.14677i	0.0230703	−	0.160457i	−0.975030	−	0.222075i	$-0.928717\pi$
$179$	0.308660	−	2.14677i	0.0230703	−	0.160457i	0.998100	+	0.0616178i	$0.0196260\pi$
$180$		0			0
$181$	−2.58817	+	5.66730i	−0.192377	+	0.421247i	−0.981100	−	0.193502i	$-0.938015\pi$
$181$	−2.58817	+	5.66730i	−0.192377	+	0.421247i	0.788723	+	0.614749i	$0.210743\pi$
$182$		0			0
$183$	−4.75474	+	10.4114i	−0.351481	+	0.769635i
$184$		0			0
$185$	1.58445	+	1.01826i	0.116491	+	0.0748641i
$186$		0			0
$187$	−16.3636	−	0.993233i	−1.19663	−	0.0726324i
$188$		0			0
$189$	1.39642	−	9.71232i	0.101575	−	0.706467i
$190$		0			0
$191$	6.59287	−	4.23698i	0.477043	−	0.306577i	−0.279933	−	0.960020i	$-0.590312\pi$
$191$	6.59287	−	4.23698i	0.477043	−	0.306577i	0.756976	+	0.653442i	$0.226676\pi$
$192$		0			0
$193$	14.2804	+	4.19312i	1.02793	+	0.301827i	0.751868	−	0.659313i	$-0.229153\pi$
$193$	14.2804	+	4.19312i	1.02793	+	0.301827i	0.276060	+	0.961140i	$0.410971\pi$
$194$		0			0
$195$	0.905322	−	1.98238i	0.0648314	−	0.141961i
$196$		0			0
$197$	−4.03281	+	1.18414i	−0.287326	+	0.0843666i	−0.422220	−	0.906494i	$-0.638749\pi$
$197$	−4.03281	+	1.18414i	−0.287326	+	0.0843666i	0.134894	+	0.990860i	$0.456931\pi$
$198$		0			0
$199$	−26.0167	−	7.63918i	−1.84427	−	0.541527i	−0.999984	−	0.00563676i	$-0.998206\pi$
$199$	−26.0167	−	7.63918i	−1.84427	−	0.541527i	−0.844288	−	0.535890i	$-0.819976\pi$
$200$		0			0
$201$	−4.83817	−	10.5941i	−0.341258	−	0.747251i
$202$		0			0
$203$	7.27747	−	8.39865i	0.510778	−	0.589470i
$204$		0			0
$205$	2.81131	+	3.24442i	0.196350	+	0.226600i
$206$		0			0
$207$	0.782682	+	5.44367i	0.0544002	+	0.378361i
$208$		0			0
$209$	5.23097	+	13.5761i	0.361834	+	0.939080i
$210$		0			0
$211$	15.9706	+	18.4310i	1.09946	+	1.26884i	0.960419	+	0.278558i	$0.0898566\pi$
$211$	15.9706	+	18.4310i	1.09946	+	1.26884i	0.139041	+	0.990287i	$0.455598\pi$
$212$		0			0
$213$	−16.1274	−	10.3645i	−1.10503	−	0.710162i
$214$		0			0
$215$	3.57201			0.243609
$216$		0			0
$217$	12.2917	−	7.89943i	0.834418	−	0.536248i
$218$		0			0
$219$	1.96919	+	13.6960i	0.133065	+	0.925490i
$220$		0			0
$221$	−0.564373	+	3.92530i	−0.0379638	+	0.264044i
$222$		0			0
$223$	1.50919	+	0.969895i	0.101063	+	0.0649489i	0.590196	−	0.807260i	$-0.299051\pi$
$223$	1.50919	+	0.969895i	0.101063	+	0.0649489i	−0.489133	+	0.872209i	$0.662687\pi$
$224$		0			0
$225$	−1.96491	+	1.26277i	−0.130994	+	0.0841846i
$226$		0			0
$227$	4.61608	−	1.35540i	0.306380	−	0.0899614i	−0.124929	−	0.992166i	$-0.539870\pi$
$227$	4.61608	−	1.35540i	0.306380	−	0.0899614i	0.431309	+	0.902204i	$0.358052\pi$
$228$		0			0
$229$	1.63334	−	1.88498i	0.107934	−	0.124563i	−0.699212	−	0.714915i	$-0.746465\pi$
$229$	1.63334	−	1.88498i	0.107934	−	0.124563i	0.807146	+	0.590352i	$0.201011\pi$
$230$		0			0
$231$	−10.1976	+	10.4198i	−0.670956	+	0.685575i
$232$		0			0
$233$	−14.0926			−0.923236			−0.461618	−	0.887079i	$-0.652731\pi$
$233$	−14.0926			−0.923236			−0.461618	+	0.887079i	$0.652731\pi$
$234$		0			0
$235$	0.748625	−	5.20680i	0.0488349	−	0.339654i
$236$		0			0
$237$	24.2630	−	7.12426i	1.57605	−	0.462770i
$238$		0			0
$239$	−2.60603			−0.168570			−0.0842852	−	0.996442i	$-0.526861\pi$
$239$	−2.60603			−0.168570			−0.0842852	+	0.996442i	$0.526861\pi$
$240$		0			0
$241$	13.9475			0.898438			0.449219	−	0.893422i	$-0.351702\pi$
$241$	13.9475			0.898438			0.449219	+	0.893422i	$0.351702\pi$
$242$		0			0
$243$	7.79870			0.500287
$244$		0			0
$245$	−2.61877			−0.167307
$246$		0			0
$247$	3.37686	−	0.991537i	0.214865	−	0.0630900i
$248$		0			0
$249$	0.349582	−	2.43140i	0.0221539	−	0.154084i
$250$		0			0
$251$	−2.85978			−0.180508			−0.0902540	−	0.995919i	$-0.528768\pi$
$251$	−2.85978			−0.180508			−0.0902540	+	0.995919i	$0.528768\pi$
$252$		0			0
$253$	−11.1587	+	20.9698i	−0.701542	+	1.31836i
$254$		0			0
$255$	−8.79259	+	10.1472i	−0.550614	+	0.635442i
$256$		0			0
$257$	−12.1968	+	3.58131i	−0.760817	+	0.223396i	−0.639053	−	0.769163i	$-0.720673\pi$
$257$	−12.1968	+	3.58131i	−0.760817	+	0.223396i	−0.121764	+	0.992559i	$0.538855\pi$
$258$		0			0
$259$	−2.56414	+	1.64787i	−0.159328	+	0.102394i
$260$		0			0
$261$	3.16996	+	2.03721i	0.196216	+	0.126100i
$262$		0			0
$263$	−0.587027	+	4.08286i	−0.0361976	+	0.251760i	−0.999883	−	0.0152793i	$-0.995136\pi$
$263$	−0.587027	+	4.08286i	−0.0361976	+	0.251760i	0.963686	+	0.267039i	$0.0860453\pi$
$264$		0			0
$265$	−2.21115	−	15.3789i	−0.135830	−	0.944716i
$266$		0			0
$267$	5.42707	−	3.48777i	0.332132	−	0.213448i
$268$		0			0
$269$	−6.55668			−0.399768			−0.199884	−	0.979820i	$-0.564056\pi$
$269$	−6.55668			−0.399768			−0.199884	+	0.979820i	$0.564056\pi$
$270$		0			0
$271$	10.8102	+	6.94729i	0.656673	+	0.422018i	0.826099	−	0.563525i	$-0.190555\pi$
$271$	10.8102	+	6.94729i	0.656673	+	0.422018i	−0.169426	+	0.985543i	$0.554192\pi$
$272$		0			0
$273$	2.30958	+	2.66540i	0.139782	+	0.161317i
$274$		0			0
$275$	−10.0697	−	0.611207i	−0.607226	−	0.0368572i
$276$		0			0
$277$	−2.71453	−	18.8800i	−0.163100	−	1.13439i	−0.892745	−	0.450562i	$-0.851224\pi$
$277$	−2.71453	−	18.8800i	−0.163100	−	1.13439i	0.729645	−	0.683826i	$-0.239685\pi$
$278$		0			0
$279$	3.24438	+	3.74421i	0.194236	+	0.224160i
$280$		0			0
$281$	14.0767	−	16.2453i	0.839743	−	0.969115i	−0.160095	−	0.987102i	$-0.551180\pi$
$281$	14.0767	−	16.2453i	0.839743	−	0.969115i	0.999838	+	0.0179864i	$0.00572557\pi$
$282$		0			0
$283$	−5.82158	−	12.7475i	−0.346057	−	0.757759i	−0.999999	−	0.00121452i	$-0.999613\pi$
$283$	−5.82158	−	12.7475i	−0.346057	−	0.757759i	0.653942	−	0.756544i	$-0.273114\pi$
$284$		0			0
$285$	11.4331	+	3.35707i	0.677241	+	0.198856i
$286$		0			0
$287$	−6.66599	+	1.95731i	−0.393481	+	0.115536i
$288$		0			0
$289$	3.08746	−	6.76060i	0.181615	−	0.397682i
$290$		0			0
$291$	−1.23575	−	0.362848i	−0.0724407	−	0.0212705i
$292$		0			0
$293$	19.8579	−	12.7619i	1.16011	−	0.745558i	0.188484	−	0.982076i	$-0.439643\pi$
$293$	19.8579	−	12.7619i	1.16011	−	0.745558i	0.971627	+	0.236518i	$0.0760063\pi$
$294$		0			0
$295$	−2.25211	+	15.6638i	−0.131123	+	0.911981i
$296$		0			0
$297$	11.5960	+	8.48725i	0.672871	+	0.492480i
$298$		0			0
$299$	4.83393	+	3.10658i	0.279553	+	0.179658i
$300$		0			0
$301$	−2.40136	+	5.25825i	−0.138412	+	0.303081i
$302$		0			0
$303$	6.01593	−	13.1730i	0.345606	−	0.756771i
$304$		0			0
$305$	−1.17431	+	8.16752i	−0.0672409	+	0.467671i
$306$		0			0
$307$	6.89971	−	15.1082i	0.393787	−	0.862273i	−0.604076	−	0.796927i	$-0.706458\pi$
$307$	6.89971	−	15.1082i	0.393787	−	0.862273i	0.997863	−	0.0653463i	$-0.0208152\pi$
$308$		0			0
$309$	8.62926	+	18.8954i	0.490901	+	1.07492i
$310$		0			0
$311$	3.12474	+	21.7331i	0.177188	+	1.23237i	0.863232	+	0.504808i	$0.168437\pi$
$311$	3.12474	+	21.7331i	0.177188	+	1.23237i	−0.686044	+	0.727560i	$0.740654\pi$
$312$		0			0
$313$	−19.6678	−	12.6397i	−1.11169	−	0.714438i	−0.150027	−	0.988682i	$-0.547936\pi$
$313$	−19.6678	−	12.6397i	−1.11169	−	0.714438i	−0.961660	+	0.274244i	$0.911572\pi$
$314$		0			0
$315$	0.346326	+	2.40875i	0.0195133	+	0.135718i
$316$		0			0
$317$	−9.28818	+	5.96915i	−0.521676	+	0.335261i	−0.774835	−	0.632164i	$-0.782167\pi$
$317$	−9.28818	+	5.96915i	−0.521676	+	0.335261i	0.253158	+	0.967425i	$0.418531\pi$
$318$		0			0
$319$	5.85161	+	15.1869i	0.327627	+	0.850303i
$320$		0			0
$321$	−25.7801	+	7.56971i	−1.43890	+	0.422500i
$322$		0			0
$323$	−21.6830			−1.20647
$324$		0			0
$325$	−0.347299	+	2.41552i	−0.0192647	+	0.133989i
$326$		0			0
$327$	7.37238	−	8.50818i	0.407693	−	0.470503i
$328$		0			0
$329$	7.16151	+	4.60242i	0.394827	+	0.253740i
$330$		0			0
$331$	−2.38293	+	1.53142i	−0.130978	+	0.0841743i	−0.604489	−	0.796613i	$-0.706623\pi$
$331$	−2.38293	+	1.53142i	−0.130978	+	0.0841743i	0.473511	+	0.880788i	$0.342986\pi$
$332$		0			0
$333$	−0.676797	−	0.781066i	−0.0370883	−	0.0428021i
$334$		0			0
$335$	−5.49840	−	6.34550i	−0.300410	−	0.346691i
$336$		0			0
$337$	−2.03363	−	0.597127i	−0.110779	−	0.0325276i	0.225873	−	0.974157i	$-0.427476\pi$
$337$	−2.03363	−	0.597127i	−0.110779	−	0.0325276i	−0.336652	+	0.941629i	$0.609295\pi$
$338$		0			0
$339$	30.1822	+	8.86230i	1.63927	+	0.481334i
$340$		0			0
$341$	1.75647	+	21.3262i	0.0951181	+	1.15488i
$342$		0			0
$343$	8.34591	−	18.2750i	0.450637	−	0.986757i
$344$		0			0
$345$	8.08179	+	17.6966i	0.435109	+	0.952755i
$346$		0			0
$347$	3.88660	+	27.0319i	0.208644	+	1.45115i	0.777589	+	0.628773i	$0.216442\pi$
$347$	3.88660	+	27.0319i	0.208644	+	1.45115i	−0.568945	+	0.822375i	$0.692648\pi$
$348$		0			0
$349$	−10.2262	+	3.00269i	−0.547398	+	0.160731i	−0.543726	−	0.839263i	$-0.682987\pi$
$349$	−10.2262	+	3.00269i	−0.547398	+	0.160731i	−0.00367189	+	0.999993i	$0.501169\pi$
$350$		0			0
$351$	2.27640	−	2.62711i	0.121505	−	0.140225i
$352$		0			0
$353$	11.1276	+	12.8419i	0.592260	+	0.683504i	0.970194	−	0.242328i	$-0.0779110\pi$
$353$	11.1276	+	12.8419i	0.592260	+	0.683504i	−0.377935	+	0.925832i	$0.623366\pi$
$354$		0			0
$355$	−13.2608	−	3.89371i	−0.703809	−	0.206657i
$356$		0			0
$357$	−9.02638	−	19.7650i	−0.477726	−	1.04608i
$358$		0			0
$359$	−13.0852	+	15.1011i	−0.690611	+	0.797007i	−0.987452	−	0.157920i	$-0.949521\pi$
$359$	−13.0852	+	15.1011i	−0.690611	+	0.797007i	0.296841	+	0.954927i	$0.404067\pi$
$360$		0			0
$361$	0.100983	+	0.221123i	0.00531492	+	0.0116381i
$362$		0			0
$363$	−6.45573	−	20.3528i	−0.338838	−	1.06825i
$364$		0			0
$365$	4.14389	+	9.07385i	0.216901	+	0.474947i
$366$		0			0
$367$	1.20429	−	1.38983i	0.0628635	−	0.0725484i	−0.723447	−	0.690380i	$-0.757443\pi$
$367$	1.20429	−	1.38983i	0.0628635	−	0.0725484i	0.786310	+	0.617832i	$0.211989\pi$
$368$		0			0
$369$	−0.978590	−	2.14281i	−0.0509434	−	0.111550i
$370$		0			0
$371$	24.1253	+	7.08382i	1.25252	+	0.367774i
$372$		0			0
$373$	4.02649	+	4.64681i	0.208484	+	0.240603i	0.850355	−	0.526209i	$-0.176387\pi$
$373$	4.02649	+	4.64681i	0.208484	+	0.240603i	−0.641871	+	0.766812i	$0.721842\pi$
$374$		0			0
$375$	−14.3049	+	16.5087i	−0.738701	+	0.852506i
$376$		0			0
$377$	3.77752	−	1.10918i	0.194552	−	0.0571257i
$378$		0			0
$379$	−2.14290	−	14.9042i	−0.110073	−	0.765577i	−0.967845	−	0.251546i	$-0.919061\pi$
$379$	−2.14290	−	14.9042i	−0.110073	−	0.765577i	0.857772	−	0.514030i	$-0.171848\pi$
$380$		0			0
$381$	12.5160	+	27.4063i	0.641216	+	1.40407i
$382$		0			0
$383$	7.41155	−	16.2290i	0.378713	−	0.829265i	−0.620280	−	0.784381i	$-0.712981\pi$
$383$	7.41155	−	16.2290i	0.378713	−	0.829265i	0.998992	−	0.0448841i	$-0.0142919\pi$
$384$		0			0
$385$	−4.93757	+	9.27883i	−0.251642	+	0.472893i
$386$		0			0
$387$	−1.88067	−	0.552215i	−0.0956000	−	0.0280707i
$388$		0			0
$389$	−8.01821	−	2.35436i	−0.406540	−	0.119371i	0.0720680	−	0.997400i	$-0.477040\pi$
$389$	−8.01821	−	2.35436i	−0.406540	−	0.119371i	−0.478608	+	0.878029i	$0.658858\pi$
$390$		0			0
$391$	−23.1830	−	26.7546i	−1.17241	−	1.35304i
$392$		0			0
$393$	−22.6452	−	26.1339i	−1.14230	−	1.31828i
$394$		0			0
$395$	15.3362	−	9.85599i	0.771649	−	0.495909i
$396$		0			0
$397$	−22.6533	−	14.5584i	−1.13694	−	0.730665i	−0.169940	−	0.985454i	$-0.554357\pi$
$397$	−22.6533	−	14.5584i	−1.13694	−	0.730665i	−0.966996	+	0.254790i	$0.917994\pi$
$398$		0			0
$399$	−12.6280	+	14.5735i	−0.632193	+	0.729589i
$400$		0			0
$401$	3.58247	−	24.9166i	0.178900	−	1.24428i	−0.680414	−	0.732828i	$-0.738200\pi$
$401$	3.58247	−	24.9166i	0.178900	−	1.24428i	0.859314	−	0.511448i	$-0.170891\pi$
$402$		0			0
$403$	5.17631			0.257850
$404$		0			0
$405$	14.3857	−	4.22403i	0.714832	−	0.209894i
$406$		0			0
$407$	−0.366410	−	4.44879i	−0.0181623	−	0.220518i
$408$		0			0
$409$	31.2224	−	20.0654i	1.54385	−	0.992170i	0.556999	−	0.830513i	$-0.311953\pi$
$409$	31.2224	−	20.0654i	1.54385	−	0.992170i	0.986847	−	0.161657i	$-0.0516838\pi$
$410$		0			0
$411$	−3.54065	−	24.6257i	−0.174647	−	1.21470i
$412$		0			0
$413$	−21.5442	−	13.8456i	−1.06012	−	0.681298i
$414$		0			0
$415$	−0.252022	−	1.75285i	−0.0123713	−	0.0860440i
$416$		0			0
$417$	14.7896	+	32.3847i	0.724249	+	1.58588i
$418$		0			0
$419$	−7.29573	+	15.9754i	−0.356420	+	0.780451i	0.643468	+	0.765473i	$0.277495\pi$
$419$	−7.29573	+	15.9754i	−0.356420	+	0.780451i	−0.999888	+	0.0149777i	$0.995232\pi$
$420$		0			0
$421$	1.03951	−	7.22997i	0.0506627	−	0.352367i	−0.948684	−	0.316226i	$-0.897584\pi$
$421$	1.03951	−	7.22997i	0.0506627	−	0.352367i	0.999347	−	0.0361413i	$-0.0115066\pi$
$422$		0			0
$423$	−1.19910	+	2.62566i	−0.0583022	+	0.127664i
$424$		0			0
$425$	6.24572	−	13.6762i	0.302962	−	0.663394i
$426$		0			0
$427$	−11.2337	−	7.21947i	−0.543638	−	0.349375i
$428$		0			0
$429$	−5.03494	+	1.15225i	−0.243089	+	0.0556311i
$430$		0			0
$431$	1.73749	−	12.0845i	0.0836919	−	0.582090i	−0.904219	−	0.427069i	$-0.859546\pi$
$431$	1.73749	−	12.0845i	0.0836919	−	0.582090i	0.987911	−	0.155021i	$-0.0495447\pi$
$432$		0			0
$433$	−4.75648	+	3.05681i	−0.228582	+	0.146901i	−0.649919	−	0.760003i	$-0.725197\pi$
$433$	−4.75648	+	3.05681i	−0.228582	+	0.146901i	0.421337	+	0.906904i	$0.361561\pi$
$434$		0			0
$435$	12.7897	+	3.75538i	0.613217	+	0.180057i
$436$		0			0
$437$	−13.0514	+	28.5787i	−0.624335	+	1.36710i
$438$		0			0
$439$	−2.88593	+	0.847384i	−0.137738	+	0.0404434i	−0.349875	−	0.936796i	$-0.613776\pi$
$439$	−2.88593	+	0.847384i	−0.137738	+	0.0404434i	0.212137	+	0.977240i	$0.431958\pi$
$440$		0			0
$441$	1.37879	+	0.404849i	0.0656566	+	0.0192785i
$442$		0			0
$443$	−1.33152	−	2.91562i	−0.0632624	−	0.138525i	0.875360	−	0.483472i	$-0.160624\pi$
$443$	−1.33152	−	2.91562i	−0.0632624	−	0.138525i	−0.938622	+	0.344946i	$0.887897\pi$
$444$		0			0
$445$	3.04563	−	3.51484i	0.144377	−	0.166619i
$446$		0			0
$447$	4.81266	+	5.55411i	0.227631	+	0.262700i
$448$		0			0
$449$	−5.99693	−	41.7095i	−0.283012	−	1.96840i	−0.246871	−	0.969048i	$-0.579402\pi$
$449$	−5.99693	−	41.7095i	−0.283012	−	1.96840i	−0.0361418	−	0.999347i	$-0.511507\pi$
$450$		0			0
$451$	2.05551	−	9.96484i	0.0967901	−	0.469226i
$452$		0			0
$453$	−26.0546	−	30.0687i	−1.22415	−	1.41275i
$454$		0			0
$455$	2.13894	+	1.37462i	0.100275	+	0.0644430i
$456$		0			0
$457$	41.1562			1.92521			0.962603	−	0.270917i	$-0.0873269\pi$
$457$	41.1562			1.92521			0.962603	+	0.270917i	$0.0873269\pi$
$458$		0			0
$459$	−18.0166	+	11.5786i	−0.840945	+	0.540442i
$460$		0			0
$461$	−0.116553	−	0.810645i	−0.00542842	−	0.0377555i	0.986927	−	0.161167i	$-0.0515257\pi$
$461$	−0.116553	−	0.810645i	−0.00542842	−	0.0377555i	−0.992356	+	0.123411i	$0.960617\pi$
$462$		0			0
$463$	4.59317	−	31.9462i	0.213463	−	1.48466i	−0.548012	−	0.836470i	$-0.684615\pi$
$463$	4.59317	−	31.9462i	0.213463	−	1.48466i	0.761475	−	0.648195i	$-0.224476\pi$
$464$		0			0
$465$	14.7435	+	9.47504i	0.683711	+	0.439395i
$466$		0			0
$467$	21.6749	−	13.9296i	1.00300	−	0.644587i	0.0674251	−	0.997724i	$-0.478522\pi$
$467$	21.6749	−	13.9296i	1.00300	−	0.644587i	0.935571	+	0.353138i	$0.114885\pi$
$468$		0			0
$469$	13.0374	−	3.82814i	0.602013	−	0.176767i
$470$		0			0
$471$	2.34518	−	2.70648i	0.108060	−	0.124708i
$472$		0			0
$473$	−5.14614	−	6.72221i	−0.236620	−	0.309087i
$474$		0			0
$475$	−13.3431			−0.612223
$476$		0			0
$477$	−1.21332	+	8.43885i	−0.0555542	+	0.386388i
$478$		0			0
$479$	−25.0269	+	7.34857i	−1.14351	+	0.335765i	−0.798004	−	0.602652i	$-0.794111\pi$
$479$	−25.0269	+	7.34857i	−1.14351	+	0.335765i	−0.345506	+	0.938417i	$0.612293\pi$
$480$		0			0
$481$	−1.07981			−0.0492351
$482$		0			0
$483$	−31.4839			−1.43257
$484$		0			0
$485$	−0.928488			−0.0421604
$486$		0			0
$487$	−34.0054			−1.54093			−0.770465	−	0.637482i	$-0.779976\pi$
$487$	−34.0054			−1.54093			−0.770465	+	0.637482i	$0.779976\pi$
$488$		0			0
$489$	−6.14957	+	1.80568i	−0.278093	+	0.0816556i
$490$		0			0
$491$	5.04518	−	35.0900i	0.227686	−	1.58359i	−0.480133	−	0.877196i	$-0.659412\pi$
$491$	5.04518	−	35.0900i	0.227686	−	1.58359i	0.707819	−	0.706394i	$-0.249679\pi$
$492$		0			0
$493$	−24.2556			−1.09242
$494$		0			0
$495$	−3.35246	−	1.20941i	−0.150682	−	0.0543590i
$496$		0			0
$497$	14.6467	−	16.9032i	0.656993	−	0.758211i
$498$		0			0
$499$	10.1274	−	2.97368i	0.453366	−	0.133120i	−0.0470740	−	0.998891i	$-0.514990\pi$
$499$	10.1274	−	2.97368i	0.453366	−	0.133120i	0.500440	+	0.865771i	$0.333171\pi$
$500$		0			0
$501$	16.6850	−	10.7228i	0.745430	−	0.479059i
$502$		0			0
$503$	−14.4978	−	9.31716i	−0.646424	−	0.415432i	0.175934	−	0.984402i	$-0.443706\pi$
$503$	−14.4978	−	9.31716i	−0.646424	−	0.415432i	−0.822358	+	0.568970i	$0.807342\pi$
$504$		0			0
$505$	1.48580	−	10.3339i	0.0661171	−	0.459854i
$506$		0			0
$507$	−3.41341	−	23.7408i	−0.151595	−	1.05436i
$508$		0			0
$509$	2.22262	−	1.42839i	0.0985160	−	0.0633124i	−0.490455	−	0.871466i	$-0.663169\pi$
$509$	2.22262	−	1.42839i	0.0985160	−	0.0633124i	0.588971	+	0.808154i	$0.299533\pi$
$510$		0			0
$511$	−16.1432			−0.714132
$512$		0			0
$513$	15.9893	+	10.2757i	0.705945	+	0.453683i
$514$		0			0
$515$	9.80684	+	11.3177i	0.432141	+	0.498717i
$516$		0			0
$517$	−10.8773	+	6.09252i	−0.478382	+	0.267949i
$518$		0			0
$519$	−3.56597	−	24.8018i	−0.156529	−	1.08868i
$520$		0			0
$521$	−8.56034	−	9.87916i	−0.375035	−	0.432814i	0.536586	−	0.843846i	$-0.319714\pi$
$521$	−8.56034	−	9.87916i	−0.375035	−	0.432814i	−0.911621	+	0.411032i	$0.865168\pi$
$522$		0			0
$523$	7.07618	−	8.16635i	0.309420	−	0.357089i	−0.579646	−	0.814868i	$-0.696809\pi$
$523$	7.07618	−	8.16635i	0.309420	−	0.357089i	0.889066	+	0.457779i	$0.151355\pi$
$524$		0			0
$525$	−5.55457	−	12.1628i	−0.242421	−	0.530829i
$526$		0			0
$527$	−30.5991	−	8.98472i	−1.33292	−	0.391381i
$528$		0			0
$529$	−27.1491	+	7.97171i	−1.18040	+	0.346596i
$530$		0			0
$531$	3.60729	−	7.89886i	0.156543	−	0.342781i
$532$		0			0
$533$	−2.36156	−	0.693415i	−0.102290	−	0.0300352i
$534$		0			0
$535$	−16.2951	+	10.4723i	−0.704500	+	0.452755i
$536$		0			0
$537$	−0.599141	+	4.16711i	−0.0258548	+	0.179824i
$538$		0			0
$539$	3.77282	+	4.92829i	0.162507	+	0.212276i
$540$		0			0
$541$	32.9466	+	21.1735i	1.41649	+	0.910321i	0.999999	+	0.00117887i	$0.000375245\pi$
$541$	32.9466	+	21.1735i	1.41649	+	0.910321i	0.416487	+	0.909142i	$0.363261\pi$
$542$		0			0
$543$	5.02391	−	11.0008i	0.215597	−	0.472091i
$544$		0			0
$545$	3.37155	−	7.38266i	0.144421	−	0.316239i
$546$		0			0
$547$	−0.993787	+	6.91194i	−0.0424913	+	0.295533i	0.957484	+	0.288487i	$0.0931521\pi$
$547$	−0.993787	+	6.91194i	−0.0424913	+	0.295533i	−0.999975	+	0.00704651i	$0.997757\pi$
$548$		0			0
$549$	1.88094	−	4.11868i	0.0802765	−	0.175781i
$550$		0			0
$551$	8.94232	+	19.5810i	0.380956	+	0.834177i
$552$		0			0
$553$	4.19860	+	29.2019i	0.178543	+	1.24179i
$554$		0			0
$555$	−3.07558	−	1.97655i	−0.130551	−	0.0839000i
$556$		0			0
$557$	0.402600	+	2.80014i	0.0170587	+	0.118646i	0.996571	−	0.0827361i	$-0.0263658\pi$
$557$	0.402600	+	2.80014i	0.0170587	+	0.118646i	−0.979513	+	0.201382i	$0.935457\pi$
$558$		0			0
$559$	−1.72281	+	1.10718i	−0.0728669	+	0.0468287i
$560$		0			0
$561$	31.7635	+	1.92797i	1.34106	+	0.0813989i
$562$		0			0
$563$	−30.6530	+	9.00053i	−1.29187	+	0.379327i	−0.854264	−	0.519840i	$-0.825992\pi$
$563$	−30.6530	+	9.00053i	−1.29187	+	0.379327i	−0.437606	+	0.899167i	$0.644173\pi$
$564$		0			0
$565$	22.6776			0.954056
$566$		0			0
$567$	−3.45305	+	24.0165i	−0.145014	+	1.00860i
$568$		0			0
$569$	−0.240924	+	0.278041i	−0.0101001	+	0.0116561i	−0.760777	−	0.649013i	$-0.775182\pi$
$569$	−0.240924	+	0.278041i	−0.0101001	+	0.0116561i	0.750677	+	0.660669i	$0.229727\pi$
$570$		0			0
$571$	37.5728	+	24.1466i	1.57237	+	1.01050i	0.978575	+	0.205891i	$0.0660092\pi$
$571$	37.5728	+	24.1466i	1.57237	+	1.01050i	0.593800	+	0.804613i	$0.297627\pi$
$572$		0			0
$573$	−12.7974	+	8.22442i	−0.534621	+	0.343580i
$574$		0			0
$575$	−14.2661	−	16.4640i	−0.594939	−	0.686597i
$576$		0			0
$577$	17.6123	+	20.3256i	0.733209	+	0.846168i	0.992829	−	0.119543i	$-0.0381429\pi$
$577$	17.6123	+	20.3256i	0.733209	+	0.846168i	−0.259621	+	0.965711i	$0.583597\pi$
$578$		0			0
$579$	−27.7198	−	8.13927i	−1.15200	−	0.338257i
$580$		0			0
$581$	2.74975	+	0.807399i	0.114079	+	0.0334965i
$582$		0			0
$583$	−25.7561	+	26.3173i	−1.06671	+	1.08995i
$584$		0			0
$585$	−0.358138	+	0.784213i	−0.0148072	+	0.0324232i
$586$		0			0
$587$	−1.87122	−	4.09741i	−0.0772336	−	0.169118i	0.867076	−	0.498175i	$-0.165996\pi$
$587$	−1.87122	−	4.09741i	−0.0772336	−	0.169118i	−0.944310	+	0.329057i	$0.893269\pi$
$588$		0			0
$589$	4.02785	+	28.0143i	0.165965	+	1.15431i
$590$		0			0
$591$	7.82811	−	2.29854i	0.322006	−	0.0945493i
$592$		0			0
$593$	8.91760	−	10.2915i	0.366202	−	0.422619i	−0.542506	−	0.840052i	$-0.682524\pi$
$593$	8.91760	−	10.2915i	0.366202	−	0.422619i	0.908708	+	0.417432i	$0.137070\pi$
$594$		0			0
$595$	−10.2581	−	11.8385i	−0.420543	−	0.485333i
$596$		0			0
$597$	50.5010	+	14.8284i	2.06687	+	0.606888i
$598$		0			0
$599$	16.7682	+	36.7171i	0.685128	+	1.50022i	0.857117	+	0.515123i	$0.172254\pi$
$599$	16.7682	+	36.7171i	0.685128	+	1.50022i	−0.171988	+	0.985099i	$0.555019\pi$
$600$		0			0
$601$	18.6967	−	21.5772i	0.762656	−	0.880152i	−0.233075	−	0.972459i	$-0.574879\pi$
$601$	18.6967	−	21.5772i	0.762656	−	0.880152i	0.995731	+	0.0923070i	$0.0294241\pi$
$602$		0			0
$603$	1.91394	+	4.19095i	0.0779417	+	0.170669i
$604$		0			0
$605$	−8.59937	−	12.7673i	−0.349614	−	0.519063i
$606$		0			0
$607$	19.6201	+	42.9620i	0.796356	+	1.74378i	0.657489	+	0.753465i	$0.271619\pi$
$607$	19.6201	+	42.9620i	0.796356	+	1.74378i	0.138867	+	0.990311i	$0.455654\pi$
$608$		0			0
$609$	−14.1263	+	16.3027i	−0.572428	+	0.660617i
$610$		0			0
$611$	1.25283	+	2.74332i	0.0506842	+	0.110983i
$612$		0			0
$613$	19.4437	+	5.70917i	0.785322	+	0.230591i	0.649721	−	0.760172i	$-0.274886\pi$
$613$	19.4437	+	5.70917i	0.785322	+	0.230591i	0.135600	+	0.990764i	$0.456704\pi$
$614$		0			0
$615$	−5.45705	−	6.29777i	−0.220049	−	0.253950i
$616$		0			0
$617$	19.3152	−	22.2909i	0.777599	−	0.897397i	−0.219335	−	0.975650i	$-0.570389\pi$
$617$	19.3152	−	22.2909i	0.777599	−	0.897397i	0.996934	+	0.0782526i	$0.0249341\pi$
$618$		0			0
$619$	37.7818	−	11.0937i	1.51858	−	0.445895i	0.587046	−	0.809554i	$-0.300291\pi$
$619$	37.7818	−	11.0937i	1.51858	−	0.445895i	0.931532	+	0.363659i	$0.118473\pi$
$620$		0			0
$621$	4.41626	+	30.7157i	0.177218	+	1.23258i
$622$		0			0
$623$	3.12660	+	6.84631i	0.125265	+	0.274292i
$624$		0			0
$625$	−0.224059	+	0.490621i	−0.00896237	+	0.0196249i
$626$		0			0
$627$	−10.1539	−	26.3527i	−0.405506	−	1.05242i
$628$		0			0
$629$	6.38317	+	1.87427i	0.254514	+	0.0747320i
$630$		0			0
$631$	−23.3870	−	6.86704i	−0.931021	−	0.273372i	−0.219157	−	0.975690i	$-0.570331\pi$
$631$	−23.3870	−	6.86704i	−0.931021	−	0.273372i	−0.711864	+	0.702317i	$0.752149\pi$
$632$		0			0
$633$	−31.0006	−	35.7766i	−1.23216	−	1.42199i
$634$		0			0
$635$	14.2240	+	16.4154i	0.564463	+	0.651425i
$636$		0			0
$637$	1.26305	−	0.811713i	0.0500438	−	0.0321612i
$638$		0			0
$639$	6.37988	+	4.10010i	0.252384	+	0.162197i
$640$		0			0
$641$	−19.9396	+	23.0115i	−0.787566	+	0.908899i	−0.997631	−	0.0687880i	$-0.978087\pi$
$641$	−19.9396	+	23.0115i	−0.787566	+	0.908899i	0.210066	+	0.977687i	$0.432632\pi$
$642$		0			0
$643$	0.440400	−	3.06305i	0.0173677	−	0.120795i	−0.979293	−	0.202447i	$-0.935111\pi$
$643$	0.440400	−	3.06305i	0.0173677	−	0.120795i	0.996661	+	0.0816523i	$0.0260197\pi$
$644$		0			0
$645$	−6.93364			−0.273012
$646$		0			0
$647$	36.4746	−	10.7099i	1.43396	−	0.421050i	0.529759	−	0.848148i	$-0.322282\pi$
$647$	36.4746	−	10.7099i	1.43396	−	0.421050i	0.904205	+	0.427098i	$0.140464\pi$
$648$		0			0
$649$	32.7225	−	18.3283i	1.28447	−	0.719450i
$650$		0			0
$651$	−23.8596	+	15.3336i	−0.935130	+	0.600972i
$652$		0			0
$653$	2.59857	+	18.0735i	0.101690	+	0.707270i	0.975339	+	0.220713i	$0.0708383\pi$
$653$	2.59857	+	18.0735i	0.101690	+	0.707270i	−0.873649	+	0.486557i	$0.838253\pi$
$654$		0			0
$655$	−20.9721	−	13.4780i	−0.819449	−	0.526628i
$656$		0			0
$657$	−0.778995	−	5.41803i	−0.0303915	−	0.211377i
$658$		0			0
$659$	0.661943	+	1.44945i	0.0257856	+	0.0564627i	0.922087	−	0.386984i	$-0.126483\pi$
$659$	0.661943	+	1.44945i	0.0257856	+	0.0564627i	−0.896301	+	0.443446i	$0.853756\pi$
$660$		0			0
$661$	−15.4975	+	33.9348i	−0.602782	+	1.31991i	0.324620	+	0.945845i	$0.394764\pi$
$661$	−15.4975	+	33.9348i	−0.602782	+	1.31991i	−0.927402	+	0.374065i	$0.877964\pi$
$662$		0			0
$663$	1.09551	−	7.61941i	0.0425459	−	0.295914i
$664$		0			0
$665$	−5.77508	+	12.6457i	−0.223948	+	0.490378i
$666$		0			0
$667$	−14.6000	+	31.9695i	−0.565313	+	1.23786i
$668$		0			0
$669$	−2.92949	−	1.88267i	−0.113260	−	0.0727881i
$670$		0			0
$671$	17.0624	−	9.55688i	0.658686	−	0.368939i
$672$		0			0
$673$	−1.12071	+	7.79469i	−0.0432001	+	0.300463i	0.956754	+	0.290898i	$0.0939539\pi$
$673$	−1.12071	+	7.79469i	−0.0432001	+	0.300463i	−0.999954	+	0.00956555i	$0.996955\pi$
$674$		0			0
$675$	−11.0869	+	7.12514i	−0.426736	+	0.274247i
$676$		0			0
$677$	−13.2080	−	3.87821i	−0.507624	−	0.149052i	0.0178849	−	0.999840i	$-0.494307\pi$
$677$	−13.2080	−	3.87821i	−0.507624	−	0.149052i	−0.525509	+	0.850788i	$0.676125\pi$
$678$		0			0
$679$	0.624197	−	1.36680i	0.0239545	−	0.0524530i
$680$		0			0
$681$	−8.96030	+	2.63098i	−0.343359	+	0.100819i
$682$		0			0
$683$	30.1375	+	8.84918i	1.15318	+	0.338605i	0.801779	−	0.597620i	$-0.203887\pi$
$683$	30.1375	+	8.84918i	1.15318	+	0.338605i	0.351402	+	0.936225i	$0.385705\pi$
$684$		0			0
$685$	−7.45081	−	16.3150i	−0.284681	−	0.623364i
$686$		0			0
$687$	−3.17049	+	3.65894i	−0.120962	+	0.139597i
$688$		0			0
$689$	5.83328	+	6.73197i	0.222230	+	0.256468i
$690$		0			0
$691$	2.93603	+	20.4205i	0.111692	+	0.776833i	0.966274	+	0.257517i	$0.0829042\pi$
$691$	2.93603	+	20.4205i	0.111692	+	0.776833i	−0.854582	+	0.519316i	$0.826187\pi$
$692$		0			0
$693$	4.03411	−	4.12201i	0.153243	−	0.156582i
$694$		0			0
$695$	16.8078	+	19.3973i	0.637557	+	0.735780i
$696$		0			0
$697$	12.7565	+	8.19809i	0.483186	+	0.310525i
$698$		0			0
$699$	27.3552			1.03467
$700$		0			0
$701$	−5.03625	+	3.23660i	−0.190216	+	0.122245i	−0.632283	−	0.774738i	$-0.717882\pi$
$701$	−5.03625	+	3.23660i	−0.190216	+	0.122245i	0.442066	+	0.896982i	$0.354246\pi$
$702$		0			0
$703$	−0.840235	−	5.84396i	−0.0316901	−	0.220409i
$704$		0			0
$705$	−1.45316	+	10.1069i	−0.0547292	+	0.380650i
$706$		0			0
$707$	14.2134	+	9.13442i	0.534551	+	0.343535i
$708$		0			0
$709$	−6.33775	+	4.07303i	−0.238019	+	0.152966i	−0.654213	−	0.756310i	$-0.727000\pi$
$709$	−6.33775	+	4.07303i	−0.238019	+	0.152966i	0.416194	+	0.909276i	$0.363364\pi$
$710$		0			0
$711$	−9.59825	+	2.81830i	−0.359962	+	0.105695i
$712$		0			0
$713$	−30.2603	+	34.9223i	−1.13326	+	1.30785i
$714$		0			0
$715$	−3.24874	+	1.81967i	−0.121496	+	0.0680517i
$716$		0			0
$717$	5.05858			0.188916
$718$		0			0
$719$	3.99442	−	27.7818i	0.148967	−	1.03609i	−0.768949	−	0.639310i	$-0.779220\pi$
$719$	3.99442	−	27.7818i	0.148967	−	1.03609i	0.917916	−	0.396776i	$-0.129871\pi$
$720$		0			0
$721$	−23.2533	+	6.82779i	−0.865999	+	0.254280i
$722$		0			0
$723$	−27.0736			−1.00688
$724$		0			0
$725$	−14.9262			−0.554346
$726$		0			0
$727$	45.9212			1.70312			0.851562	−	0.524254i	$-0.175656\pi$
$727$	45.9212			1.70312			0.851562	+	0.524254i	$0.175656\pi$
$728$		0			0
$729$	17.0039			0.629775
$730$		0			0
$731$	12.1059	−	3.55462i	0.447754	−	0.131473i
$732$		0			0
$733$	−3.20224	+	22.2721i	−0.118277	+	0.822638i	0.841174	+	0.540764i	$0.181865\pi$
$733$	−3.20224	+	22.2721i	−0.118277	+	0.822638i	−0.959452	+	0.281874i	$0.909044\pi$
$734$		0			0
$735$	5.08330			0.187500
$736$		0			0
$737$	−4.02019	+	19.4894i	−0.148086	+	0.717900i
$738$		0			0
$739$	−11.6042	+	13.3920i	−0.426868	+	0.492632i	−0.927917	−	0.372787i	$-0.878402\pi$
$739$	−11.6042	+	13.3920i	−0.426868	+	0.492632i	0.501049	+	0.865419i	$0.332948\pi$
$740$		0			0
$741$	−6.55484	+	1.92468i	−0.240798	+	0.0707047i
$742$		0			0
$743$	−2.09490	+	1.34631i	−0.0768545	+	0.0493914i	−0.578504	−	0.815680i	$-0.696363\pi$
$743$	−2.09490	+	1.34631i	−0.0768545	+	0.0493914i	0.501649	+	0.865071i	$0.332727\pi$
$744$		0			0
$745$	4.45710	+	2.86440i	0.163295	+	0.104944i
$746$		0			0
$747$	−0.138292	+	0.961841i	−0.00505984	+	0.0351919i
$748$		0			0
$749$	−4.46113	−	31.0278i	−0.163006	−	1.13373i
$750$		0			0
$751$	−29.5275	+	18.9762i	−1.07748	+	0.692451i	−0.953973	−	0.299893i	$-0.903049\pi$
$751$	−29.5275	+	18.9762i	−1.07748	+	0.692451i	−0.123502	+	0.992344i	$0.539413\pi$
$752$		0			0
$753$	5.55114			0.202295
$754$		0			0
$755$	−24.1297	−	15.5072i	−0.878170	−	0.564365i
$756$		0			0
$757$	−23.5993	−	27.2351i	−0.857731	−	0.989875i	−1.00000		4.67994e-5i	$-0.999985\pi$
$757$	−23.5993	−	27.2351i	−0.857731	−	0.989875i	0.142269	−	0.989828i	$-0.454560\pi$
$758$		0			0
$759$	21.6602	−	40.7045i	0.786216	−	1.47748i
$760$		0			0
$761$	−6.98020	−	48.5484i	−0.253032	−	1.75988i	−0.579788	−	0.814768i	$-0.696864\pi$
$761$	−6.98020	−	48.5484i	−0.253032	−	1.75988i	0.326756	−	0.945109i	$-0.394045\pi$
$762$		0			0
$763$	8.60121	+	9.92632i	0.311385	+	0.359357i
$764$		0			0
$765$	3.47828	−	4.01415i	0.125757	−	0.145132i
$766$		0			0
$767$	−3.76894	−	8.25282i	−0.136088	−	0.297992i
$768$		0			0
$769$	1.73675	+	0.509956i	0.0626288	+	0.0183895i	0.312897	−	0.949787i	$-0.398701\pi$
$769$	1.73675	+	0.509956i	0.0626288	+	0.0183895i	−0.250268	+	0.968177i	$0.580519\pi$
$770$		0			0
$771$	23.6753	−	6.95170i	0.852645	−	0.250359i
$772$		0			0
$773$	19.4210	−	42.5261i	0.698526	−	1.52956i	−0.143223	−	0.989690i	$-0.545747\pi$
$773$	19.4210	−	42.5261i	0.698526	−	1.52956i	0.841749	−	0.539868i	$-0.181526\pi$
$774$		0			0
$775$	−18.8298	−	5.52894i	−0.676388	−	0.198605i
$776$		0			0
$777$	4.97725	−	3.19869i	0.178558	−	0.114752i
$778$		0			0
$779$	1.91518	−	13.3204i	0.0686185	−	0.477252i
$780$		0			0
$781$	11.7770	+	30.5652i	0.421413	+	1.09371i
$782$		0			0
$783$	17.8864	+	11.4949i	0.639208	+	0.410794i
$784$		0			0
$785$	1.07250	−	2.34845i	0.0382792	−	0.0838198i
$786$		0			0
$787$	−19.0790	+	41.7772i	−0.680093	+	1.48920i	0.182451	+	0.983215i	$0.441597\pi$
$787$	−19.0790	+	41.7772i	−0.680093	+	1.48920i	−0.862544	+	0.505982i	$0.831130\pi$
$788$		0			0
$789$	1.13948	−	7.92526i	0.0405666	−	0.282147i
$790$		0			0
$791$	−15.2456	+	33.3831i	−0.542070	+	1.18697i
$792$		0			0
$793$	−1.96523	−	4.30324i	−0.0697872	−	0.152813i
$794$		0			0
$795$	4.29207	+	29.8520i	0.152224	+	1.05874i
$796$		0			0
$797$	41.3654	+	26.5839i	1.46524	+	0.941651i	0.998355	+	0.0573320i	$0.0182594\pi$
$797$	41.3654	+	26.5839i	1.46524	+	0.941651i	0.466883	+	0.884319i	$0.345377\pi$
$798$		0			0
$799$	−2.64429	−	18.3914i	−0.0935481	−	0.650642i
$800$		0			0
$801$	−2.14691	+	1.37973i	−0.0758572	+	0.0487505i
$802$		0			0
$803$	11.1061	−	20.8710i	0.391927	−	0.736521i
$804$		0			0
$805$	−21.7780	+	6.39461i	−0.767575	+	0.225380i
$806$		0			0
$807$	12.7272			0.448019
$808$		0			0
$809$	−2.50368	+	17.4135i	−0.0880247	+	0.612225i	0.897285	+	0.441451i	$0.145536\pi$
$809$	−2.50368	+	17.4135i	−0.0880247	+	0.612225i	−0.985310	+	0.170774i	$0.945373\pi$
$810$		0			0
$811$	35.1683	−	40.5864i	1.23493	−	1.42518i	0.365726	−	0.930722i	$-0.380821\pi$
$811$	35.1683	−	40.5864i	1.23493	−	1.42518i	0.869201	−	0.494459i	$-0.164634\pi$
$812$		0			0
$813$	−20.9837	−	13.4854i	−0.735931	−	0.472954i
$814$		0			0
$815$	−3.88704	+	2.49805i	−0.136157	+	0.0875028i
$816$		0			0
$817$	−7.33266	−	8.46234i	−0.256537	−	0.296060i
$818$		0			0
$819$	−0.913651	−	1.05441i	−0.0319256	−	0.0368441i
$820$		0			0
$821$	−29.8965	−	8.77840i	−1.04339	−	0.306368i	−0.285249	−	0.958453i	$-0.592076\pi$
$821$	−29.8965	−	8.77840i	−1.04339	−	0.306368i	−0.758146	+	0.652085i	$0.773895\pi$
$822$		0			0
$823$	27.7646	+	8.15243i	0.967813	+	0.284176i	0.727185	−	0.686442i	$-0.240828\pi$
$823$	27.7646	+	8.15243i	0.967813	+	0.284176i	0.240629	+	0.970617i	$0.422646\pi$
$824$		0			0
$825$	19.5463	+	1.18642i	0.680516	+	0.0413057i
$826$		0			0
$827$	14.9880	−	32.8191i	0.521183	−	1.14123i	−0.447807	−	0.894130i	$-0.647795\pi$
$827$	14.9880	−	32.8191i	0.521183	−	1.14123i	0.968990	−	0.247101i	$-0.0794778\pi$
$828$		0			0
$829$	10.9742	+	24.0301i	0.381149	+	0.834600i	0.998839	+	0.0481782i	$0.0153416\pi$
$829$	10.9742	+	24.0301i	0.381149	+	0.834600i	−0.617690	+	0.786422i	$0.711931\pi$
$830$		0			0
$831$	5.26919	+	36.6480i	0.182786	+	1.27130i
$832$		0			0
$833$	−8.87529	+	2.60602i	−0.307511	+	0.0902933i
$834$		0			0
$835$	9.36347	−	10.8060i	0.324036	−	0.373958i
$836$		0			0
$837$	18.3063	+	21.1266i	0.632758	+	0.730241i
$838$		0			0
$839$	−26.3392	−	7.73389i	−0.909330	−	0.267003i	−0.206571	−	0.978432i	$-0.566231\pi$
$839$	−26.3392	−	7.73389i	−0.909330	−	0.267003i	−0.702759	+	0.711428i	$0.748049\pi$
$840$		0			0
$841$	−2.04373	−	4.47514i	−0.0704733	−	0.154315i
$842$		0			0
$843$	−27.3243	+	31.5339i	−0.941098	+	1.08608i
$844$		0			0
$845$	−7.18305	−	15.7287i	−0.247105	−	0.541083i
$846$		0			0
$847$	24.5754	−	4.07581i	0.844422	−	0.140046i
$848$		0			0
$849$	11.3003	+	24.7442i	0.387825	+	0.849218i
$850$		0			0
$851$	6.31249	−	7.28501i	0.216390	−	0.249727i
$852$		0			0
$853$	5.31865	+	11.6462i	0.182107	+	0.398759i	0.978566	−	0.205934i	$-0.0660231\pi$
$853$	5.31865	+	11.6462i	0.182107	+	0.398759i	−0.796459	+	0.604693i	$0.793296\pi$
$854$		0			0
$855$	−4.52286	−	1.32803i	−0.154679	−	0.0454177i
$856$		0			0
$857$	−30.5661	−	35.2752i	−1.04412	−	1.20498i	−0.978310	−	0.207146i	$-0.933583\pi$
$857$	−30.5661	−	35.2752i	−1.04412	−	1.20498i	−0.0658091	−	0.997832i	$-0.520963\pi$
$858$		0			0
$859$	28.4127	−	32.7900i	0.969429	−	1.11878i	−0.0234587	−	0.999725i	$-0.507468\pi$
$859$	28.4127	−	32.7900i	0.969429	−	1.11878i	0.992888	−	0.119056i	$-0.0379867\pi$
$860$		0			0
$861$	12.9394	−	3.79935i	0.440973	−	0.129481i
$862$		0			0
$863$	6.53824	+	45.4744i	0.222564	+	1.54797i	0.728287	+	0.685272i	$0.240317\pi$
$863$	6.53824	+	45.4744i	0.222564	+	1.54797i	−0.505723	+	0.862696i	$0.668774\pi$
$864$		0			0
$865$	−7.50409	−	16.4317i	−0.255147	−	0.558693i
$866$		0			0
$867$	−5.99309	+	13.1230i	−0.203536	+	0.445681i
$868$		0			0
$869$	−40.6428	−	14.6620i	−1.37871	−	0.497375i
$870$		0			0
$871$	4.61877	+	1.35619i	0.156501	+	0.0459528i
$872$		0			0
$873$	0.488851	+	0.143540i	0.0165451	+	0.00485808i
$874$		0			0
$875$	−16.6892	−	19.2604i	−0.564199	−	0.651120i
$876$		0			0
$877$	23.1882	+	26.7606i	0.783008	+	0.903640i	0.997323	−	0.0731249i	$-0.0232972\pi$
$877$	23.1882	+	26.7606i	0.783008	+	0.903640i	−0.214314	+	0.976765i	$0.568752\pi$
$878$		0			0
$879$	−38.5462	+	24.7722i	−1.30013	+	0.835545i
$880$		0			0
$881$	−16.2548	−	10.4463i	−0.547639	−	0.351946i	0.237381	−	0.971417i	$-0.423711\pi$
$881$	−16.2548	−	10.4463i	−0.547639	−	0.351946i	−0.785020	+	0.619470i	$0.787347\pi$
$882$		0			0
$883$	17.6081	−	20.3208i	0.592559	−	0.683850i	−0.377697	−	0.925929i	$-0.623284\pi$
$883$	17.6081	−	20.3208i	0.592559	−	0.683850i	0.970256	+	0.242079i	$0.0778294\pi$
$884$		0			0
$885$	4.37159	−	30.4050i	0.146949	−	1.02205i
$886$		0			0
$887$	9.45310			0.317404			0.158702	−	0.987327i	$-0.449269\pi$
$887$	9.45310			0.317404			0.158702	+	0.987327i	$0.449269\pi$
$888$		0			0
$889$	−33.7270	+	9.90315i	−1.13117	+	0.332141i
$890$		0			0
$891$	−28.6745	−	20.9872i	−0.960633	−	0.703096i
$892$		0			0
$893$	−13.8721	+	8.91503i	−0.464211	+	0.298330i
$894$		0			0
$895$	0.431934	+	3.00417i	0.0144380	+	0.100418i
$896$		0			0
$897$	−9.38315	−	6.03019i	−0.313294	−	0.201342i
$898$		0			0
$899$	4.50575	+	31.3382i	0.150275	+	1.04519i
$900$		0			0
$901$	−22.7978	−	49.9203i	−0.759506	−	1.66309i
$902$		0			0
$903$	4.66130	−	10.2068i	0.155118	−	0.339662i
$904$		0			0
$905$	1.24079	−	8.62989i	0.0412453	−	0.286867i
$906$		0			0
$907$	−17.5475	+	38.4236i	−0.582654	+	1.27583i	0.357126	+	0.934056i	$0.383757\pi$
$907$	−17.5475	+	38.4236i	−0.582654	+	1.27583i	−0.939781	+	0.341778i	$0.888971\pi$
$908$		0			0
$909$	−2.37985	+	5.21115i	−0.0789347	+	0.172843i
$910$		0			0
$911$	−13.8801	−	8.92020i	−0.459868	−	0.295539i	0.290120	−	0.956990i	$-0.406305\pi$
$911$	−13.8801	−	8.92020i	−0.459868	−	0.295539i	−0.749988	+	0.661451i	$0.769941\pi$
$912$		0			0
$913$	−2.93562	+	2.99959i	−0.0971550	+	0.0992719i
$914$		0			0
$915$	2.27946	−	15.8540i	0.0753567	−	0.524117i
$916$		0			0
$917$	33.9395	−	21.8116i	1.12078	−	0.720283i
$918$		0			0
$919$	55.4253	+	16.2743i	1.82831	+	0.536841i	0.999735	−	0.0230340i	$-0.00733259\pi$
$919$	55.4253	+	16.2743i	1.82831	+	0.536841i	0.828577	+	0.559875i	$0.189151\pi$
$920$		0			0
$921$	−13.3930	+	29.3267i	−0.441316	+	0.966347i
$922$		0			0
$923$	7.60266	−	2.23234i	0.250245	−	0.0734784i
$924$		0			0
$925$	3.92802	+	1.15337i	0.129153	+	0.0379226i
$926$		0			0
$927$	−3.41367	−	7.47488i	−0.112119	−	0.245507i
$928$		0			0
$929$	−16.0335	+	18.5036i	−0.526040	+	0.607083i	−0.955133	−	0.296178i	$-0.904288\pi$
$929$	−16.0335	+	18.5036i	−0.526040	+	0.607083i	0.429092	+	0.903261i	$0.358833\pi$
$930$		0			0
$931$	5.37583	+	6.20404i	0.176186	+	0.203329i
$932$		0			0
$933$	−6.06545	−	42.1861i	−0.198574	−	1.38111i
$934$		0			0
$935$	22.3630	−	5.11779i	0.731350	−	0.167369i
$936$		0			0
$937$	19.1319	+	22.0793i	0.625010	+	0.721300i	0.976650	−	0.214835i	$-0.0689213\pi$
$937$	19.1319	+	22.0793i	0.625010	+	0.721300i	−0.351640	+	0.936135i	$0.614376\pi$
$938$		0			0
$939$	38.1772	+	24.5350i	1.24586	+	0.800669i
$940$		0			0
$941$	−21.2853			−0.693882			−0.346941	−	0.937887i	$-0.612780\pi$
$941$	−21.2853			−0.693882			−0.346941	+	0.937887i	$0.612780\pi$
$942$		0			0
$943$	18.4837	−	11.8787i	0.601911	−	0.386824i
$944$		0			0
$945$	1.95413	+	13.5913i	0.0635679	+	0.442125i
$946$		0			0
$947$	1.47258	−	10.2420i	0.0478525	−	0.332822i	−0.951806	−	0.306700i	$-0.900775\pi$
$947$	1.47258	−	10.2420i	0.0478525	−	0.332822i	0.999659	−	0.0261217i	$-0.00831575\pi$
$948$		0			0
$949$	−4.81115	−	3.09194i	−0.156177	−	0.100369i
$950$		0			0
$951$	18.0293	−	11.5867i	0.584641	−	0.375726i
$952$		0			0
$953$	−17.2732	+	5.07187i	−0.559534	+	0.164294i	−0.549257	−	0.835653i	$-0.685089\pi$
$953$	−17.2732	+	5.07187i	−0.559534	+	0.164294i	−0.0102763	+	0.999947i	$0.503271\pi$
$954$		0			0
$955$	−7.18181	+	8.28826i	−0.232398	+	0.268202i
$956$		0			0
$957$	−11.3586	−	29.4793i	−0.367171	−	0.952932i
$958$		0			0
$959$	29.0258			0.937293
$960$		0			0
$961$	−1.51234	+	10.5185i	−0.0487850	+	0.339307i
$962$		0			0
$963$	10.1984	−	2.99452i	0.328639	−	0.0964970i
$964$		0			0
$965$	−20.8275			−0.670461
$966$		0			0
$967$	−10.1076			−0.325037			−0.162519	−	0.986705i	$-0.551962\pi$
$967$	−10.1076			−0.325037			−0.162519	+	0.986705i	$0.551962\pi$
$968$		0			0
$969$	42.0889			1.35209
$970$		0			0
$971$	−13.7583			−0.441524			−0.220762	−	0.975328i	$-0.570854\pi$
$971$	−13.7583			−0.441524			−0.220762	+	0.975328i	$0.570854\pi$
$972$		0			0
$973$	−39.8536	+	11.7021i	−1.27765	+	0.375151i
$974$		0			0
$975$	0.674143	−	4.68877i	0.0215899	−	0.150161i
$976$		0			0
$977$	−49.7309			−1.59103			−0.795516	−	0.605932i	$-0.792800\pi$
$977$	−49.7309			−1.59103			−0.795516	+	0.605932i	$0.792800\pi$
$978$		0			0
$979$	−11.0024	−	0.667820i	−0.351639	−	0.0213436i
$980$		0			0
$981$	−2.91645	+	3.36577i	−0.0931152	+	0.107461i
$982$		0			0
$983$	17.0156	−	4.99623i	0.542713	−	0.159355i	0.00112562	−	0.999999i	$-0.499642\pi$
$983$	17.0156	−	4.99623i	0.542713	−	0.159355i	0.541587	+	0.840644i	$0.317824\pi$
$984$		0			0
$985$	4.94801	−	3.17990i	0.157657	−	0.101320i
$986$		0			0
$987$	−13.9012	−	8.93378i	−0.442481	−	0.284365i
$988$		0			0
$989$	2.60174	−	18.0955i	0.0827305	−	0.575404i
$990$		0			0
$991$	−2.96362	−	20.6124i	−0.0941425	−	0.654775i	−0.981182	−	0.193083i	$-0.938151\pi$
$991$	−2.96362	−	20.6124i	−0.0941425	−	0.654775i	0.887040	−	0.461693i	$-0.152758\pi$
$992$		0			0
$993$	4.62552	−	2.97264i	0.146786	−	0.0943339i
$994$		0			0
$995$	37.9444			1.20292
$996$		0			0
$997$	−21.4326	−	13.7739i	−0.678777	−	0.436224i	0.155303	−	0.987867i	$-0.450365\pi$
$997$	−21.4326	−	13.7739i	−0.678777	−	0.436224i	−0.834080	+	0.551643i	$0.814001\pi$
$998$		0			0
$999$	−3.81881	−	4.40714i	−0.120822	−	0.139436i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	484.2.i.a.221.3	✓	110
121.23	even	11	inner	484.2.i.a.265.3	yes	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
484.2.i.a.221.3	✓	110	1.1	even	1	trivial
484.2.i.a.265.3	yes	110	121.23	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 484 = 2^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	484.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q-1.94110 q^{3} +(-1.34270 + 0.394253i) q^{5} +(0.322293 - 2.24160i) q^{7} +0.767885 q^{9} +(2.67636 + 1.95885i) q^{11} +(0.525392 - 0.606334i) q^{13} +(2.60632 - 0.765286i) q^{15} +(-4.15823 + 2.67233i) q^{17} +(3.69032 + 2.37163i) q^{19} +(-0.625604 + 4.35117i) q^{21} +(1.01927 + 7.08917i) q^{23} +(-2.55886 + 1.64448i) q^{25} +4.33277 q^{27} +(4.12817 + 2.65301i) q^{29} +(4.22508 + 4.87600i) q^{31} +(-5.19509 - 3.80233i) q^{33} +(0.451012 + 3.13686i) q^{35} +(-0.881378 - 1.01716i) q^{37} +(-1.01984 + 1.17696i) q^{39} +(-1.27440 - 2.79054i) q^{41} +(-2.44916 - 0.719138i) q^{43} +(-1.03104 + 0.302741i) q^{45} +(-1.56156 + 3.41934i) q^{47} +(1.79556 + 0.527225i) q^{49} +(8.07156 - 5.18727i) q^{51} +(-1.58008 + 10.9897i) q^{53} +(-4.36583 - 1.57499i) q^{55} +(-7.16330 - 4.60357i) q^{57} +(4.69769 - 10.2865i) q^{59} +(2.44950 - 5.36366i) q^{61} +(0.247484 - 1.72129i) q^{63} +(-0.466395 + 1.02126i) q^{65} +(2.49248 + 5.45778i) q^{67} +(-1.97851 - 13.7608i) q^{69} +(8.30838 + 5.33947i) q^{71} +(-1.01447 - 7.05578i) q^{73} +(4.96701 - 3.19210i) q^{75} +(5.25353 - 5.36800i) q^{77} +(-12.4996 + 3.67021i) q^{79} -10.7140 q^{81} +(-0.180094 + 1.25258i) q^{83} +(4.52969 - 5.22754i) q^{85} +(-8.01321 - 5.14978i) q^{87} +(-2.79587 + 1.79680i) q^{89} +(-1.18983 - 1.37313i) q^{91} +(-8.20132 - 9.46483i) q^{93} +(-5.89002 - 1.72947i) q^{95} +(0.636620 + 0.186928i) q^{97} +(2.05514 + 1.50417i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q - 2 q^{3} + 2 q^{5} - 2 q^{7} + 112 q^{9} - 10 q^{11} - 29 q^{13} - 18 q^{15} - 6 q^{17} - 8 q^{19} - 2 q^{21} + 4 q^{23} - 17 q^{25} + 4 q^{27} - 28 q^{31} + q^{33} + 6 q^{35} - 31 q^{37} + 4 q^{39}+ \cdots - 57 q^{99}+O(q^{100}) \) 110 * q - 2 * q^3 + 2 * q^5 - 2 * q^7 + 112 * q^9 - 10 * q^11 - 29 * q^13 - 18 * q^15 - 6 * q^17 - 8 * q^19 - 2 * q^21 + 4 * q^23 - 17 * q^25 + 4 * q^27 - 28 * q^31 + q^33 + 6 * q^35 - 31 * q^37 + 4 * q^39 + 10 * q^43 - 8 * q^45 + 2 * q^47 - 49 * q^49 + 115 * q^51 + 72 * q^53 + 41 * q^55 + 3 * q^57 - 6 * q^59 + 4 * q^61 - 51 * q^63 - 45 * q^65 - 51 * q^67 + 4 * q^69 + 26 * q^71 - 18 * q^73 + 46 * q^77 - 24 * q^79 + 110 * q^81 - 6 * q^83 - 92 * q^85 - 7 * q^89 - 91 * q^91 - 37 * q^93 - 64 * q^95 - 31 * q^97 - 57 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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