LMFDB - Embedded newform 2070.2.j.i.737.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2070,2,Mod(323,2070)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2070, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("2070.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2070.j (of order $4$, degree $2$, 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:	$16.5290332184$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 28x^{14} + 290x^{12} + 1396x^{10} + 3263x^{8} + 3508x^{6} + 1442x^{4} + 128x^{2} + 1 $ x^16 + 28x^14 + 290x^12 + 1396x^10 + 3263x^8 + 3508x^6 + 1442x^4 + 128*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			737.7
Root			$-0.822192i$ of defining polynomial
Character	$\chi$	$=$	2070.737
Dual form			2070.2.j.i.323.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(0.226546 - 2.22456i) q^{5} +(-2.57697 - 2.57697i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(0.226546 - 2.22456i) q^{5} +(-2.57697 - 2.57697i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.41281 - 1.73320i) q^{10} -4.44912i q^{11} +(2.00000 - 2.00000i) q^{13} -3.64438 q^{14} -1.00000 q^{16} +(-4.09748 + 4.09748i) q^{17} +0.825621i q^{19} +(-2.22456 - 0.226546i) q^{20} +(-3.14601 - 3.14601i) q^{22} +(0.707107 + 0.707107i) q^{23} +(-4.89735 - 1.00793i) q^{25} -2.82843i q^{26} +(-2.57697 + 2.57697i) q^{28} -1.25783 q^{29} +5.79471 q^{31} +(-0.707107 + 0.707107i) q^{32} +5.79471i q^{34} +(-6.31643 + 5.14883i) q^{35} +(1.43096 + 1.43096i) q^{37} +(0.583802 + 0.583802i) q^{38} +(-1.73320 + 1.41281i) q^{40} +3.57823i q^{41} +(-0.569037 + 0.569037i) q^{43} -4.44912 q^{44} +1.00000 q^{46} +(1.86731 - 1.86731i) q^{47} +6.28154i q^{49} +(-4.17567 + 2.75024i) q^{50} +(-2.00000 - 2.00000i) q^{52} +(-2.80276 - 2.80276i) q^{53} +(-9.89735 - 1.00793i) q^{55} +3.64438i q^{56} +(-0.889422 + 0.889422i) q^{58} +5.30521 q^{59} +0.328317 q^{61} +(4.09748 - 4.09748i) q^{62} +1.00000i q^{64} +(-3.99603 - 4.90222i) q^{65} +(9.53812 + 9.53812i) q^{67} +(4.09748 + 4.09748i) q^{68} +(-0.825621 + 8.10716i) q^{70} -10.6252i q^{71} +(-3.90529 + 3.90529i) q^{73} +2.02369 q^{74} +0.825621 q^{76} +(-11.4653 + 11.4653i) q^{77} +15.8814i q^{79} +(-0.226546 + 2.22456i) q^{80} +(2.53019 + 2.53019i) q^{82} +(-9.36579 - 9.36579i) q^{83} +(8.18682 + 10.0434i) q^{85} +0.804740i q^{86} +(-3.14601 + 3.14601i) q^{88} -8.63683 q^{89} -10.3079 q^{91} +(0.707107 - 0.707107i) q^{92} -2.64077i q^{94} +(1.83665 + 0.187041i) q^{95} +(-6.39212 - 6.39212i) q^{97} +(4.44172 + 4.44172i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 4 q^{10} + 32 q^{13} - 16 q^{16} - 24 q^{25} - 16 q^{31} + 32 q^{37} + 4 q^{40} + 16 q^{46} - 32 q^{52} - 104 q^{55} + 8 q^{58} - 40 q^{61} + 72 q^{67} + 24 q^{70} + 24 q^{73} - 24 q^{76} - 8 q^{82} - 8 q^{85} - 72 q^{97}+O(q^{100}) $ 16 * q - 4 * q^10 + 32 * q^13 - 16 * q^16 - 24 * q^25 - 16 * q^31 + 32 * q^37 + 4 * q^40 + 16 * q^46 - 32 * q^52 - 104 * q^55 + 8 * q^58 - 40 * q^61 + 72 * q^67 + 24 * q^70 + 24 * q^73 - 24 * q^76 - 8 * q^82 - 8 * q^85 - 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times$.

$n$	$461$	$1657$	$1891$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	0.226546	−	2.22456i	0.101315	−	0.994854i
$5$	0.226546	−	2.22456i	0.101315	−	0.994854i
$6$		0			0
$7$	−2.57697	−	2.57697i	−0.974003	−	0.974003i	0.0256678	−	0.999671i	$-0.491829\pi$
$7$	−2.57697	−	2.57697i	−0.974003	−	0.974003i	−0.999671	+	0.0256678i	$0.991829\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	−1.41281	−	1.73320i	−0.446770	−	0.548084i
$11$		−	4.44912i		−	1.34146i	−0.741701	−	0.670731i	$-0.765981\pi$
$11$		−	4.44912i		−	1.34146i	0.741701	−	0.670731i	$-0.234019\pi$
$12$		0			0
$13$	2.00000	−	2.00000i	0.554700	−	0.554700i	−0.373094	−	0.927794i	$-0.621703\pi$
$13$	2.00000	−	2.00000i	0.554700	−	0.554700i	0.927794	+	0.373094i	$0.121703\pi$
$14$	−3.64438			−0.974003
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−4.09748	+	4.09748i	−0.993784	+	0.993784i	−0.999981	−	0.00619669i	$-0.998028\pi$
$17$	−4.09748	+	4.09748i	−0.993784	+	0.993784i	0.00619669	+	0.999981i	$0.498028\pi$
$18$		0			0
$19$			0.825621i			0.189411i	0.995505	+	0.0947053i	$0.0301909\pi$
$19$			0.825621i			0.189411i	−0.995505	+	0.0947053i	$0.969809\pi$
$20$	−2.22456	−	0.226546i	−0.497427	−	0.0506573i
$21$		0			0
$22$	−3.14601	−	3.14601i	−0.670731	−	0.670731i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$24$		0			0
$25$	−4.89735	−	1.00793i	−0.979471	−	0.201586i
$26$		−	2.82843i		−	0.554700i
$27$		0			0
$28$	−2.57697	+	2.57697i	−0.487001	+	0.487001i
$29$	−1.25783			−0.233574			−0.116787	−	0.993157i	$-0.537259\pi$
$29$	−1.25783			−0.233574			−0.116787	+	0.993157i	$0.537259\pi$
$30$		0			0
$31$	5.79471			1.04076			0.520380	−	0.853935i	$-0.325790\pi$
$31$	5.79471			1.04076			0.520380	+	0.853935i	$0.325790\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$			5.79471i			0.993784i
$35$	−6.31643	+	5.14883i	−1.06767	+	0.870310i
$36$		0			0
$37$	1.43096	+	1.43096i	0.235249	+	0.235249i	0.814879	−	0.579631i	$-0.196803\pi$
$37$	1.43096	+	1.43096i	0.235249	+	0.235249i	−0.579631	+	0.814879i	$0.696803\pi$
$38$	0.583802	+	0.583802i	0.0947053	+	0.0947053i
$39$		0			0
$40$	−1.73320	+	1.41281i	−0.274042	+	0.223385i
$41$			3.57823i			0.558826i	0.960171	+	0.279413i	$0.0901398\pi$
$41$			3.57823i			0.558826i	−0.960171	+	0.279413i	$0.909860\pi$
$42$		0			0
$43$	−0.569037	+	0.569037i	−0.0867773	+	0.0867773i	−0.749163	−	0.662386i	$-0.769544\pi$
$43$	−0.569037	+	0.569037i	−0.0867773	+	0.0867773i	0.662386	+	0.749163i	$0.269544\pi$
$44$	−4.44912			−0.670731
$45$		0			0
$46$	1.00000			0.147442
$47$	1.86731	−	1.86731i	0.272375	−	0.272375i	−0.557681	−	0.830055i	$-0.688309\pi$
$47$	1.86731	−	1.86731i	0.272375	−	0.272375i	0.830055	+	0.557681i	$0.188309\pi$
$48$		0			0
$49$			6.28154i			0.897363i
$50$	−4.17567	+	2.75024i	−0.590529	+	0.388942i
$51$		0			0
$52$	−2.00000	−	2.00000i	−0.277350	−	0.277350i
$53$	−2.80276	−	2.80276i	−0.384988	−	0.384988i	0.487907	−	0.872895i	$-0.337760\pi$
$53$	−2.80276	−	2.80276i	−0.384988	−	0.384988i	−0.872895	+	0.487907i	$0.837760\pi$
$54$		0			0
$55$	−9.89735	−	1.00793i	−1.33456	−	0.135910i
$56$			3.64438i			0.487001i
$57$		0			0
$58$	−0.889422	+	0.889422i	−0.116787	+	0.116787i
$59$	5.30521			0.690679			0.345340	−	0.938478i	$-0.387764\pi$
$59$	5.30521			0.690679			0.345340	+	0.938478i	$0.387764\pi$
$60$		0			0
$61$	0.328317			0.0420366			0.0210183	−	0.999779i	$-0.493309\pi$
$61$	0.328317			0.0420366			0.0210183	+	0.999779i	$0.493309\pi$
$62$	4.09748	−	4.09748i	0.520380	−	0.520380i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−3.99603	−	4.90222i	−0.495647	−	0.608045i
$66$		0			0
$67$	9.53812	+	9.53812i	1.16527	+	1.16527i	0.983306	+	0.181962i	$0.0582446\pi$
$67$	9.53812	+	9.53812i	1.16527	+	1.16527i	0.181962	+	0.983306i	$0.441755\pi$
$68$	4.09748	+	4.09748i	0.496892	+	0.496892i
$69$		0			0
$70$	−0.825621	+	8.10716i	−0.0986806	+	0.968991i
$71$		−	10.6252i		−	1.26098i	−0.776196	−	0.630491i	$-0.782854\pi$
$71$		−	10.6252i		−	1.26098i	0.776196	−	0.630491i	$-0.217146\pi$
$72$		0			0
$73$	−3.90529	+	3.90529i	−0.457079	+	0.457079i	−0.897695	−	0.440616i	$-0.854760\pi$
$73$	−3.90529	+	3.90529i	−0.457079	+	0.457079i	0.440616	+	0.897695i	$0.354760\pi$
$74$	2.02369			0.235249
$75$		0			0
$76$	0.825621			0.0947053
$77$	−11.4653	+	11.4653i	−1.30659	+	1.30659i
$78$		0			0
$79$			15.8814i			1.78680i	0.449262	+	0.893400i	$0.351687\pi$
$79$			15.8814i			1.78680i	−0.449262	+	0.893400i	$0.648313\pi$
$80$	−0.226546	+	2.22456i	−0.0253286	+	0.248714i
$81$		0			0
$82$	2.53019	+	2.53019i	0.279413	+	0.279413i
$83$	−9.36579	−	9.36579i	−1.02803	−	1.02803i	−0.999596	−	0.0284338i	$-0.990948\pi$
$83$	−9.36579	−	9.36579i	−1.02803	−	1.02803i	−0.0284338	−	0.999596i	$-0.509052\pi$
$84$		0			0
$85$	8.18682	+	10.0434i	0.887986	+	1.08936i
$86$			0.804740i			0.0867773i
$87$		0			0
$88$	−3.14601	+	3.14601i	−0.335365	+	0.335365i
$89$	−8.63683			−0.915502			−0.457751	−	0.889080i	$-0.651345\pi$
$89$	−8.63683			−0.915502			−0.457751	+	0.889080i	$0.651345\pi$
$90$		0			0
$91$	−10.3079			−1.08056
$92$	0.707107	−	0.707107i	0.0737210	−	0.0737210i
$93$		0			0
$94$		−	2.64077i		−	0.272375i
$95$	1.83665	+	0.187041i	0.188436	+	0.0191900i
$96$		0			0
$97$	−6.39212	−	6.39212i	−0.649021	−	0.649021i	0.303735	−	0.952756i	$-0.401766\pi$
$97$	−6.39212	−	6.39212i	−0.649021	−	0.649021i	−0.952756	+	0.303735i	$0.901766\pi$
$98$	4.44172	+	4.44172i	0.448681	+	0.448681i
$99$		0			0
$100$	−1.00793	+	4.89735i	−0.100793	+	0.489735i
$101$		−	12.5940i		−	1.25315i	−0.779362	−	0.626574i	$-0.784457\pi$
$101$		−	12.5940i		−	1.25315i	0.779362	−	0.626574i	$-0.215543\pi$
$102$		0			0
$103$	2.57697	−	2.57697i	0.253916	−	0.253916i	−0.568658	−	0.822574i	$-0.692537\pi$
$103$	2.57697	−	2.57697i	0.253916	−	0.253916i	0.822574	+	0.568658i	$0.192537\pi$
$104$	−2.82843			−0.277350
$105$		0			0
$106$	−3.96370			−0.384988
$107$	−7.30322	+	7.30322i	−0.706029	+	0.706029i	−0.965698	−	0.259669i	$-0.916387\pi$
$107$	−7.30322	+	7.30322i	−0.706029	+	0.706029i	0.259669	+	0.965698i	$0.416387\pi$
$108$		0			0
$109$		−	19.4046i		−	1.85862i	−0.369301	−	0.929310i	$-0.620403\pi$
$109$		−	19.4046i		−	1.85862i	0.369301	−	0.929310i	$-0.379597\pi$
$110$	−7.71120	+	6.28577i	−0.735234	+	0.599325i
$111$		0			0
$112$	2.57697	+	2.57697i	0.243501	+	0.243501i
$113$	−9.66410	−	9.66410i	−0.909122	−	0.909122i	0.0870790	−	0.996201i	$-0.472247\pi$
$113$	−9.66410	−	9.66410i	−0.909122	−	0.909122i	−0.996201	+	0.0870790i	$0.972247\pi$
$114$		0			0
$115$	1.73320	−	1.41281i	0.161621	−	0.131745i
$116$			1.25783i			0.116787i
$117$		0			0
$118$	3.75135	−	3.75135i	0.345340	−	0.345340i
$119$	21.1181			1.93590
$120$		0			0
$121$	−8.79471			−0.799519
$122$	0.232155	−	0.232155i	0.0210183	−	0.0210183i
$123$		0			0
$124$		−	5.79471i		−	0.520380i
$125$	−3.35168	+	10.6661i	−0.299784	+	0.954007i
$126$		0			0
$127$	7.30788	+	7.30788i	0.648469	+	0.648469i	0.952623	−	0.304154i	$-0.0983737\pi$
$127$	7.30788	+	7.30788i	0.648469	+	0.648469i	−0.304154	+	0.952623i	$0.598374\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$	−6.29201	−	0.640769i	−0.551846	−	0.0561992i
$131$		−	17.6253i		−	1.53993i	−0.638086	−	0.769965i	$-0.720274\pi$
$131$		−	17.6253i		−	1.53993i	0.638086	−	0.769965i	$-0.279726\pi$
$132$		0			0
$133$	2.12760	−	2.12760i	0.184486	−	0.184486i
$134$	13.4889			1.16527
$135$		0			0
$136$	5.79471			0.496892
$137$	−7.36778	+	7.36778i	−0.629472	+	0.629472i	−0.947935	−	0.318463i	$-0.896833\pi$
$137$	−7.36778	+	7.36778i	−0.629472	+	0.629472i	0.318463	+	0.947935i	$0.396833\pi$
$138$		0			0
$139$		−	0.784234i		−	0.0665179i	−0.999447	−	0.0332589i	$-0.989411\pi$
$139$		−	0.784234i		−	0.0665179i	0.999447	−	0.0332589i	$-0.0105886\pi$
$140$	5.14883	+	6.31643i	0.435155	+	0.533836i
$141$		0			0
$142$	−7.51317	−	7.51317i	−0.630491	−	0.630491i
$143$	−8.89825	−	8.89825i	−0.744109	−	0.744109i
$144$		0			0
$145$	−0.284957	+	2.79813i	−0.0236644	+	0.232372i
$146$			5.52291i			0.457079i
$147$		0			0
$148$	1.43096	−	1.43096i	0.117624	−	0.117624i
$149$	3.12997			0.256417			0.128209	−	0.991747i	$-0.459077\pi$
$149$	3.12997			0.256417			0.128209	+	0.991747i	$0.459077\pi$
$150$		0			0
$151$	−3.01047			−0.244989			−0.122494	−	0.992469i	$-0.539089\pi$
$151$	−3.01047			−0.244989			−0.122494	+	0.992469i	$0.539089\pi$
$152$	0.583802	−	0.583802i	0.0473526	−	0.0473526i
$153$		0			0
$154$			16.2143i			1.30659i
$155$	1.31277	−	12.8907i	0.105444	−	1.03540i
$156$		0			0
$157$	−4.08760	−	4.08760i	−0.326226	−	0.326226i	0.524924	−	0.851149i	$-0.324094\pi$
$157$	−4.08760	−	4.08760i	−0.326226	−	0.326226i	−0.851149	+	0.524924i	$0.824094\pi$
$158$	11.2299	+	11.2299i	0.893400	+	0.893400i
$159$		0			0
$160$	1.41281	+	1.73320i	0.111692	+	0.137021i
$161$		−	3.64438i		−	0.287218i
$162$		0			0
$163$	9.28154	−	9.28154i	0.726986	−	0.726986i	−0.243032	−	0.970018i	$-0.578142\pi$
$163$	9.28154	−	9.28154i	0.726986	−	0.726986i	0.970018	+	0.243032i	$0.0781420\pi$
$164$	3.57823			0.279413
$165$		0			0
$166$	−13.2452			−1.02803
$167$	−6.10995	+	6.10995i	−0.472802	+	0.472802i	−0.902820	−	0.430018i	$-0.858507\pi$
$167$	−6.10995	+	6.10995i	−0.472802	+	0.472802i	0.430018	+	0.902820i	$0.358507\pi$
$168$		0			0
$169$			5.00000i			0.384615i
$170$	12.8907	+	1.31277i	0.988671	+	0.100685i
$171$		0			0
$172$	0.569037	+	0.569037i	0.0433887	+	0.0433887i
$173$	−2.23017	−	2.23017i	−0.169557	−	0.169557i	0.617228	−	0.786785i	$-0.288256\pi$
$173$	−2.23017	−	2.23017i	−0.169557	−	0.169557i	−0.786785	+	0.617228i	$0.788256\pi$
$174$		0			0
$175$	10.0229	+	15.2177i	0.757661	+	1.15035i
$176$			4.44912i			0.335365i
$177$		0			0
$178$	−6.10716	+	6.10716i	−0.457751	+	0.457751i
$179$	16.8514			1.25953			0.629767	−	0.776784i	$-0.283150\pi$
$179$	16.8514			1.25953			0.629767	+	0.776784i	$0.283150\pi$
$180$		0			0
$181$	−6.10716			−0.453942			−0.226971	−	0.973902i	$-0.572882\pi$
$181$	−6.10716			−0.453942			−0.226971	+	0.973902i	$0.572882\pi$
$182$	−7.28877	+	7.28877i	−0.540280	+	0.540280i
$183$		0			0
$184$		−	1.00000i		−	0.0737210i
$185$	3.50745	−	2.85909i	0.257873	−	0.210204i
$186$		0			0
$187$	18.2302	+	18.2302i	1.33312	+	1.33312i
$188$	−1.86731	−	1.86731i	−0.136187	−	0.136187i
$189$		0			0
$190$	1.43096	−	1.16645i	0.103813	−	0.0846229i
$191$		−	25.9690i		−	1.87905i	−0.342478	−	0.939526i	$-0.611266\pi$
$191$		−	25.9690i		−	1.87905i	0.342478	−	0.939526i	$-0.388734\pi$
$192$		0			0
$193$	−1.94865	+	1.94865i	−0.140267	+	0.140267i	−0.773753	−	0.633487i	$-0.781623\pi$
$193$	−1.94865	+	1.94865i	−0.140267	+	0.140267i	0.633487	+	0.773753i	$0.281623\pi$
$194$	−9.03982			−0.649021
$195$		0			0
$196$	6.28154			0.448681
$197$	15.3049	−	15.3049i	1.09043	−	1.09043i	0.0949471	−	0.995482i	$-0.469732\pi$
$197$	15.3049	−	15.3049i	1.09043	−	1.09043i	0.995482	−	0.0949471i	$-0.0302682\pi$
$198$		0			0
$199$			17.0762i			1.21050i	0.796034	+	0.605251i	$0.206927\pi$
$199$			17.0762i			1.21050i	−0.796034	+	0.605251i	$0.793073\pi$
$200$	2.75024	+	4.17567i	0.194471	+	0.295264i
$201$		0			0
$202$	−8.90529	−	8.90529i	−0.626574	−	0.626574i
$203$	3.24139	+	3.24139i	0.227501	+	0.227501i
$204$		0			0
$205$	7.96000	+	0.810634i	0.555950	+	0.0566172i
$206$		−	3.64438i		−	0.253916i
$207$		0			0
$208$	−2.00000	+	2.00000i	−0.138675	+	0.138675i
$209$	3.67329			0.254087
$210$		0			0
$211$	24.7983			1.70719			0.853594	−	0.520939i	$-0.174418\pi$
$211$	24.7983			1.70719			0.853594	+	0.520939i	$0.174418\pi$
$212$	−2.80276	+	2.80276i	−0.192494	+	0.192494i
$213$		0			0
$214$			10.3283i			0.706029i
$215$	1.13694	+	1.39477i	0.0775390	+	0.0951226i
$216$		0			0
$217$	−14.9328	−	14.9328i	−1.01370	−	1.01370i
$218$	−13.7211	−	13.7211i	−0.929310	−	0.929310i
$219$		0			0
$220$	−1.00793	+	9.89735i	−0.0679548	+	0.667279i
$221$			16.3899i			1.10250i
$222$		0			0
$223$	−5.52480	+	5.52480i	−0.369968	+	0.369968i	−0.867465	−	0.497497i	$-0.834252\pi$
$223$	−5.52480	+	5.52480i	−0.369968	+	0.369968i	0.497497	+	0.867465i	$0.334252\pi$
$224$	3.64438			0.243501
$225$		0			0
$226$	−13.6671			−0.909122
$227$	−18.2364	+	18.2364i	−1.21039	+	1.21039i	−0.239493	+	0.970898i	$0.576981\pi$
$227$	−18.2364	+	18.2364i	−1.21039	+	1.21039i	−0.970898	+	0.239493i	$0.923019\pi$
$228$		0			0
$229$		−	28.4150i		−	1.87772i	−0.344301	−	0.938859i	$-0.611884\pi$
$229$		−	28.4150i		−	1.87772i	0.344301	−	0.938859i	$-0.388116\pi$
$230$	0.226546	−	2.22456i	0.0149380	−	0.146683i
$231$		0			0
$232$	0.889422	+	0.889422i	0.0583934	+	0.0583934i
$233$	−19.3122	−	19.3122i	−1.26518	−	1.26518i	−0.948548	−	0.316633i	$-0.897448\pi$
$233$	−19.3122	−	19.3122i	−1.26518	−	1.26518i	−0.316633	−	0.948548i	$-0.602552\pi$
$234$		0			0
$235$	−3.73091	−	4.57697i	−0.243378	−	0.298569i
$236$		−	5.30521i		−	0.345340i
$237$		0			0
$238$	14.9328	−	14.9328i	0.967948	−	0.967948i
$239$	−9.98325			−0.645763			−0.322881	−	0.946439i	$-0.604651\pi$
$239$	−9.98325			−0.645763			−0.322881	+	0.946439i	$0.604651\pi$
$240$		0			0
$241$	−10.0867			−0.649743			−0.324871	−	0.945758i	$-0.605321\pi$
$241$	−10.0867			−0.649743			−0.324871	+	0.945758i	$0.605321\pi$
$242$	−6.21880	+	6.21880i	−0.399759	+	0.399759i
$243$		0			0
$244$		−	0.328317i		−	0.0210183i
$245$	13.9737	+	1.42306i	0.892745	+	0.0909159i
$246$		0			0
$247$	1.65124	+	1.65124i	0.105066	+	0.105066i
$248$	−4.09748	−	4.09748i	−0.260190	−	0.260190i
$249$		0			0
$250$	5.17209	+	9.91209i	0.327112	+	0.626895i
$251$		−	1.59826i		−	0.100881i	−0.998727	−	0.0504407i	$-0.983937\pi$
$251$		−	1.59826i		−	0.100881i	0.998727	−	0.0504407i	$-0.0160626\pi$
$252$		0			0
$253$	3.14601	−	3.14601i	0.197788	−	0.197788i
$254$	10.3349			0.648469
$255$		0			0
$256$	1.00000			0.0625000
$257$	11.5779	−	11.5779i	0.722211	−	0.722211i	−0.246844	−	0.969055i	$-0.579394\pi$
$257$	11.5779	−	11.5779i	0.722211	−	0.722211i	0.969055	+	0.246844i	$0.0793937\pi$
$258$		0			0
$259$		−	7.37509i		−	0.458266i
$260$	−4.90222	+	3.99603i	−0.304023	+	0.247823i
$261$		0			0
$262$	−12.4630	−	12.4630i	−0.769965	−	0.769965i
$263$	−1.77348	−	1.77348i	−0.109358	−	0.109358i	0.650311	−	0.759668i	$-0.274639\pi$
$263$	−1.77348	−	1.77348i	−0.109358	−	0.109358i	−0.759668	+	0.650311i	$0.774639\pi$
$264$		0			0
$265$	−6.86986	+	5.59995i	−0.422012	+	0.344002i
$266$		−	3.00888i		−	0.184486i
$267$		0			0
$268$	9.53812	−	9.53812i	0.582634	−	0.582634i
$269$	9.95319			0.606857			0.303428	−	0.952854i	$-0.401869\pi$
$269$	9.95319			0.606857			0.303428	+	0.952854i	$0.401869\pi$
$270$		0			0
$271$	−8.28693			−0.503395			−0.251698	−	0.967806i	$-0.580989\pi$
$271$	−8.28693			−0.503395			−0.251698	+	0.967806i	$0.580989\pi$
$272$	4.09748	−	4.09748i	0.248446	−	0.248446i
$273$		0			0
$274$			10.4196i			0.629472i
$275$	−4.48441	+	21.7889i	−0.270420	+	1.31392i
$276$		0			0
$277$	0.419613	+	0.419613i	0.0252121	+	0.0252121i	0.719600	−	0.694388i	$-0.244325\pi$
$277$	0.419613	+	0.419613i	0.0252121	+	0.0252121i	−0.694388	+	0.719600i	$0.744325\pi$
$278$	−0.554537	−	0.554537i	−0.0332589	−	0.0332589i
$279$		0			0
$280$	8.10716	+	0.825621i	0.484495	+	0.0493403i
$281$		−	4.77958i		−	0.285126i	−0.989786	−	0.142563i	$-0.954466\pi$
$281$		−	4.77958i		−	0.285126i	0.989786	−	0.142563i	$-0.0455343\pi$
$282$		0			0
$283$	6.25658	−	6.25658i	0.371915	−	0.371915i	−0.496259	−	0.868174i	$-0.665293\pi$
$283$	6.25658	−	6.25658i	0.371915	−	0.371915i	0.868174	+	0.496259i	$0.165293\pi$
$284$	−10.6252			−0.630491
$285$		0			0
$286$	−12.5840			−0.744109
$287$	9.22099	−	9.22099i	0.544298	−	0.544298i
$288$		0			0
$289$		−	16.5786i		−	0.975214i
$290$	1.77708	+	2.18007i	0.104354	+	0.128018i
$291$		0			0
$292$	3.90529	+	3.90529i	0.228540	+	0.228540i
$293$	4.62634	+	4.62634i	0.270274	+	0.270274i	0.829210	−	0.558937i	$-0.188790\pi$
$293$	4.62634	+	4.62634i	0.270274	+	0.270274i	−0.558937	+	0.829210i	$0.688790\pi$
$294$		0			0
$295$	1.20187	−	11.8018i	0.0699758	−	0.687125i
$296$		−	2.02369i		−	0.117624i
$297$		0			0
$298$	2.21322	−	2.21322i	0.128209	−	0.128209i
$299$	2.82843			0.163572
$300$		0			0
$301$	2.93278			0.169043
$302$	−2.12873	+	2.12873i	−0.122494	+	0.122494i
$303$		0			0
$304$		−	0.825621i		−	0.0473526i
$305$	0.0743789	−	0.730361i	0.00425892	−	0.0418203i
$306$		0			0
$307$	19.7380	+	19.7380i	1.12650	+	1.12650i	0.990741	+	0.135764i	$0.0433488\pi$
$307$	19.7380	+	19.7380i	1.12650	+	1.12650i	0.135764	+	0.990741i	$0.456651\pi$
$308$	11.4653	+	11.4653i	0.653294	+	0.653294i
$309$		0			0
$310$	−8.18682	−	10.0434i	−0.464980	−	0.570424i
$311$			11.9833i			0.679508i	0.940514	+	0.339754i	$0.110344\pi$
$311$			11.9833i			0.679508i	−0.940514	+	0.339754i	$0.889656\pi$
$312$		0			0
$313$	−9.96567	+	9.96567i	−0.563293	+	0.563293i	−0.930241	−	0.366948i	$-0.880403\pi$
$313$	−9.96567	+	9.96567i	−0.563293	+	0.563293i	0.366948	+	0.930241i	$0.380403\pi$
$314$	−5.78073			−0.326226
$315$		0			0
$316$	15.8814			0.893400
$317$	−7.86459	+	7.86459i	−0.441719	+	0.441719i	−0.892590	−	0.450870i	$-0.851114\pi$
$317$	−7.86459	+	7.86459i	−0.441719	+	0.441719i	0.450870	+	0.892590i	$0.351114\pi$
$318$		0			0
$319$			5.59625i			0.313330i
$320$	2.22456	+	0.226546i	0.124357	+	0.0126643i
$321$		0			0
$322$	−2.57697	−	2.57697i	−0.143609	−	0.143609i
$323$	−3.38296	−	3.38296i	−0.188233	−	0.188233i
$324$		0			0
$325$	−11.8106	+	7.77884i	−0.655133	+	0.431493i
$326$		−	13.1261i		−	0.726986i
$327$		0			0
$328$	2.53019	−	2.53019i	0.139706	−	0.139706i
$329$	−9.62398			−0.530587
$330$		0			0
$331$	1.56452			0.0859940			0.0429970	−	0.999075i	$-0.486309\pi$
$331$	1.56452			0.0859940			0.0429970	+	0.999075i	$0.486309\pi$
$332$	−9.36579	+	9.36579i	−0.514015	+	0.514015i
$333$		0			0
$334$			8.64077i			0.472802i
$335$	23.3790	−	19.0573i	1.27733	−	1.04121i
$336$		0			0
$337$	13.9158	+	13.9158i	0.758040	+	0.758040i	0.975965	−	0.217926i	$-0.0699290\pi$
$337$	13.9158	+	13.9158i	0.758040	+	0.758040i	−0.217926	+	0.975965i	$0.569929\pi$
$338$	3.53553	+	3.53553i	0.192308	+	0.192308i
$339$		0			0
$340$	10.0434	−	8.18682i	0.544678	−	0.443993i
$341$		−	25.7814i		−	1.39614i
$342$		0			0
$343$	−1.85145	+	1.85145i	−0.0999690	+	0.0999690i
$344$	0.804740			0.0433887
$345$		0			0
$346$	−3.15394			−0.169557
$347$	−2.30280	+	2.30280i	−0.123621	+	0.123621i	−0.766210	−	0.642590i	$-0.777860\pi$
$347$	−2.30280	+	2.30280i	−0.123621	+	0.123621i	0.642590	+	0.766210i	$0.277860\pi$
$348$		0			0
$349$		−	0.221157i		−	0.0118382i	−0.999982	−	0.00591912i	$-0.998116\pi$
$349$		−	0.221157i		−	0.0118382i	0.999982	−	0.00591912i	$-0.00188413\pi$
$350$	17.8478	+	3.67329i	0.954007	+	0.196346i
$351$		0			0
$352$	3.14601	+	3.14601i	0.167683	+	0.167683i
$353$	16.6012	+	16.6012i	0.883594	+	0.883594i	0.993898	−	0.110304i	$-0.0351824\pi$
$353$	16.6012	+	16.6012i	0.883594	+	0.883594i	−0.110304	+	0.993898i	$0.535182\pi$
$354$		0			0
$355$	−23.6365	−	2.40710i	−1.25449	−	0.127756i
$356$			8.63683i			0.457751i
$357$		0			0
$358$	11.9158	−	11.9158i	0.629767	−	0.629767i
$359$	−8.68817			−0.458544			−0.229272	−	0.973362i	$-0.573635\pi$
$359$	−8.68817			−0.458544			−0.229272	+	0.973362i	$0.573635\pi$
$360$		0			0
$361$	18.3183			0.964124
$362$	−4.31841	+	4.31841i	−0.226971	+	0.226971i
$363$		0			0
$364$			10.3079i			0.540280i
$365$	7.80282	+	9.57228i	0.408418	+	0.501036i
$366$		0			0
$367$	−14.4267	−	14.4267i	−0.753066	−	0.753066i	0.221984	−	0.975050i	$-0.428747\pi$
$367$	−14.4267	−	14.4267i	−0.753066	−	0.753066i	−0.975050	+	0.221984i	$0.928747\pi$
$368$	−0.707107	−	0.707107i	−0.0368605	−	0.0368605i
$369$		0			0
$370$	0.458459	−	4.50182i	0.0238341	−	0.234038i
$371$			14.4452i			0.749959i
$372$		0			0
$373$	17.6662	−	17.6662i	0.914723	−	0.914723i	−0.0819165	−	0.996639i	$-0.526104\pi$
$373$	17.6662	−	17.6662i	0.914723	−	0.914723i	0.996639	+	0.0819165i	$0.0261041\pi$
$374$	25.7814			1.33312
$375$		0			0
$376$	−2.64077			−0.136187
$377$	−2.51566	+	2.51566i	−0.129563	+	0.129563i
$378$		0			0
$379$		−	17.3110i		−	0.889207i	−0.895728	−	0.444603i	$-0.853345\pi$
$379$		−	17.3110i		−	0.889207i	0.895728	−	0.444603i	$-0.146655\pi$
$380$	0.187041	−	1.83665i	0.00959502	−	0.0942180i
$381$		0			0
$382$	−18.3629	−	18.3629i	−0.939526	−	0.939526i
$383$	20.3859	+	20.3859i	1.04167	+	1.04167i	0.999093	+	0.0425798i	$0.0135577\pi$
$383$	20.3859	+	20.3859i	1.04167	+	1.04167i	0.0425798	+	0.999093i	$0.486442\pi$
$384$		0			0
$385$	22.9078	+	28.1026i	1.16749	+	1.43224i
$386$			2.75580i			0.140267i
$387$		0			0
$388$	−6.39212	+	6.39212i	−0.324511	+	0.324511i
$389$	29.8689			1.51441			0.757206	−	0.653176i	$-0.226564\pi$
$389$	29.8689			1.51441			0.757206	+	0.653176i	$0.226564\pi$
$390$		0			0
$391$	−5.79471			−0.293051
$392$	4.44172	−	4.44172i	0.224341	−	0.224341i
$393$		0			0
$394$		−	21.6444i		−	1.09043i
$395$	35.3292	+	3.59788i	1.77761	+	0.181029i
$396$		0			0
$397$	−8.58402	−	8.58402i	−0.430820	−	0.430820i	0.458087	−	0.888907i	$-0.348535\pi$
$397$	−8.58402	−	8.58402i	−0.430820	−	0.430820i	−0.888907	+	0.458087i	$0.848535\pi$
$398$	12.0747	+	12.0747i	0.605251	+	0.605251i
$399$		0			0
$400$	4.89735	+	1.00793i	0.244868	+	0.0503966i
$401$			13.6128i			0.679792i	0.940463	+	0.339896i	$0.110392\pi$
$401$			13.6128i			0.679792i	−0.940463	+	0.339896i	$0.889608\pi$
$402$		0			0
$403$	11.5894	−	11.5894i	0.577310	−	0.577310i
$404$	−12.5940			−0.626574
$405$		0			0
$406$	4.58402			0.227501
$407$	6.36653	−	6.36653i	0.315577	−	0.315577i
$408$		0			0
$409$		−	37.7311i		−	1.86568i	−0.360286	−	0.932842i	$-0.617321\pi$
$409$		−	37.7311i		−	1.86568i	0.360286	−	0.932842i	$-0.382679\pi$
$410$	6.20177	−	5.05536i	0.306284	−	0.249667i
$411$		0			0
$412$	−2.57697	−	2.57697i	−0.126958	−	0.126958i
$413$	−13.6714	−	13.6714i	−0.672723	−	0.672723i
$414$		0			0
$415$	−22.9566	+	18.7130i	−1.12689	+	0.918585i
$416$			2.82843i			0.138675i
$417$		0			0
$418$	2.59741	−	2.59741i	0.127043	−	0.127043i
$419$	−21.0780			−1.02973			−0.514864	−	0.857272i	$-0.672158\pi$
$419$	−21.0780			−1.02973			−0.514864	+	0.857272i	$0.672158\pi$
$420$		0			0
$421$	31.9569			1.55748			0.778741	−	0.627346i	$-0.215859\pi$
$421$	31.9569			1.55748			0.778741	+	0.627346i	$0.215859\pi$
$422$	17.5351	−	17.5351i	0.853594	−	0.853594i
$423$		0			0
$424$			3.96370i			0.192494i
$425$	24.1968	−	15.9368i	1.17372	−	0.773049i
$426$		0			0
$427$	−0.846062	−	0.846062i	−0.0409438	−	0.0409438i
$428$	7.30322	+	7.30322i	0.353015	+	0.353015i
$429$		0			0
$430$	1.79019	+	0.182311i	0.0863308	+	0.00879180i
$431$			10.4300i			0.502393i	0.967936	+	0.251197i	$0.0808241\pi$
$431$			10.4300i			0.502393i	−0.967936	+	0.251197i	$0.919176\pi$
$432$		0			0
$433$	24.6274	−	24.6274i	1.18352	−	1.18352i	0.204690	−	0.978827i	$-0.434382\pi$
$433$	24.6274	−	24.6274i	1.18352	−	1.18352i	0.978827	−	0.204690i	$-0.0656185\pi$
$434$	−21.1181			−1.01370
$435$		0			0
$436$	−19.4046			−0.929310
$437$	−0.583802	+	0.583802i	−0.0279271	+	0.0279271i
$438$		0			0
$439$			22.7575i			1.08615i	0.839683	+	0.543077i	$0.182741\pi$
$439$			22.7575i			1.08615i	−0.839683	+	0.543077i	$0.817259\pi$
$440$	6.28577	+	7.71120i	0.299662	+	0.367617i
$441$		0			0
$442$	11.5894	+	11.5894i	0.551252	+	0.551252i
$443$	−15.9769	−	15.9769i	−0.759087	−	0.759087i	0.217069	−	0.976156i	$-0.430350\pi$
$443$	−15.9769	−	15.9769i	−0.759087	−	0.759087i	−0.976156	+	0.217069i	$0.930350\pi$
$444$		0			0
$445$	−1.95664	+	19.2132i	−0.0927536	+	0.910791i
$446$			7.81325i			0.369968i
$447$		0			0
$448$	2.57697	−	2.57697i	0.121750	−	0.121750i
$449$	7.80606			0.368391			0.184195	−	0.982890i	$-0.441032\pi$
$449$	7.80606			0.368391			0.184195	+	0.982890i	$0.441032\pi$
$450$		0			0
$451$	15.9200			0.749643
$452$	−9.66410	+	9.66410i	−0.454561	+	0.454561i
$453$		0			0
$454$			25.7901i			1.21039i
$455$	−2.33521	+	22.9305i	−0.109476	+	1.07500i
$456$		0			0
$457$	−21.6169	−	21.6169i	−1.01120	−	1.01120i	−0.999937	−	0.0112598i	$-0.996416\pi$
$457$	−21.6169	−	21.6169i	−1.01120	−	1.01120i	−0.0112598	−	0.999937i	$-0.503584\pi$
$458$	−20.0925	−	20.0925i	−0.938859	−	0.938859i
$459$		0			0
$460$	−1.41281	−	1.73320i	−0.0658726	−	0.0808106i
$461$			33.0160i			1.53771i	0.639424	+	0.768854i	$0.279173\pi$
$461$			33.0160i			1.53771i	−0.639424	+	0.768854i	$0.720827\pi$
$462$		0			0
$463$	7.59989	−	7.59989i	0.353197	−	0.353197i	−0.508101	−	0.861298i	$-0.669652\pi$
$463$	7.59989	−	7.59989i	0.353197	−	0.353197i	0.861298	+	0.508101i	$0.169652\pi$
$464$	1.25783			0.0583934
$465$		0			0
$466$	−27.3115			−1.26518
$467$	18.6670	−	18.6670i	0.863807	−	0.863807i	−0.127971	−	0.991778i	$-0.540846\pi$
$467$	18.6670	−	18.6670i	0.863807	−	0.863807i	0.991778	+	0.127971i	$0.0408463\pi$
$468$		0			0
$469$		−	49.1589i		−	2.26995i
$470$	−5.87456	−	0.598256i	−0.270973	−	0.0275955i
$471$		0			0
$472$	−3.75135	−	3.75135i	−0.172670	−	0.172670i
$473$	2.53172	+	2.53172i	0.116408	+	0.116408i
$474$		0			0
$475$	0.832170	−	4.04336i	0.0381826	−	0.185522i
$476$		−	21.1181i		−	0.967948i
$477$		0			0
$478$	−7.05922	+	7.05922i	−0.322881	+	0.322881i
$479$	22.2344			1.01592			0.507958	−	0.861382i	$-0.330401\pi$
$479$	22.2344			1.01592			0.507958	+	0.861382i	$0.330401\pi$
$480$		0			0
$481$	5.72385			0.260985
$482$	−7.13239	+	7.13239i	−0.324871	+	0.324871i
$483$		0			0
$484$			8.79471i			0.399759i
$485$	−15.6678	+	12.7716i	−0.711437	+	0.579926i
$486$		0			0
$487$	−17.2460	−	17.2460i	−0.781493	−	0.781493i	0.198590	−	0.980083i	$-0.436364\pi$
$487$	−17.2460	−	17.2460i	−0.781493	−	0.781493i	−0.980083	+	0.198590i	$0.936364\pi$
$488$	−0.232155	−	0.232155i	−0.0105092	−	0.0105092i
$489$		0			0
$490$	10.8871	−	8.87462i	0.491831	−	0.400915i
$491$		−	27.3744i		−	1.23539i	−0.786418	−	0.617695i	$-0.788067\pi$
$491$		−	27.3744i		−	1.23539i	0.786418	−	0.617695i	$-0.211933\pi$
$492$		0			0
$493$	5.15394	−	5.15394i	0.232122	−	0.232122i
$494$	2.33521			0.105066
$495$		0			0
$496$	−5.79471			−0.260190
$497$	−27.3809	+	27.3809i	−1.22820	+	1.22820i
$498$		0			0
$499$		−	0.369704i		−	0.0165502i	−0.999966	−	0.00827511i	$-0.997366\pi$
$499$		−	0.369704i		−	0.0165502i	0.999966	−	0.00827511i	$-0.00263408\pi$
$500$	10.6661	+	3.35168i	0.477004	+	0.149892i
$501$		0			0
$502$	−1.13014	−	1.13014i	−0.0504407	−	0.0504407i
$503$	21.2019	+	21.2019i	0.945346	+	0.945346i	0.998582	−	0.0532361i	$-0.0169536\pi$
$503$	21.2019	+	21.2019i	0.945346	+	0.945346i	−0.0532361	+	0.998582i	$0.516954\pi$
$504$		0			0
$505$	−28.0161	−	2.85312i	−1.24670	−	0.126962i
$506$		−	4.44912i		−	0.197788i
$507$		0			0
$508$	7.30788	−	7.30788i	0.324235	−	0.324235i
$509$	−17.9453			−0.795409			−0.397705	−	0.917513i	$-0.630193\pi$
$509$	−17.9453			−0.795409			−0.397705	+	0.917513i	$0.630193\pi$
$510$		0			0
$511$	20.1276			0.890393
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$		−	16.3736i		−	0.722211i
$515$	−5.14883	−	6.31643i	−0.226884	−	0.278335i
$516$		0			0
$517$	−8.30788	−	8.30788i	−0.365380	−	0.365380i
$518$	−5.21498	−	5.21498i	−0.229133	−	0.229133i
$519$		0			0
$520$	−0.640769	+	6.29201i	−0.0280996	+	0.275923i
$521$		−	38.1400i		−	1.67095i	−0.549532	−	0.835473i	$-0.685194\pi$
$521$		−	38.1400i		−	1.67095i	0.549532	−	0.835473i	$-0.314806\pi$
$522$		0			0
$523$	16.5781	−	16.5781i	0.724908	−	0.724908i	−0.244693	−	0.969601i	$-0.578687\pi$
$523$	16.5781	−	16.5781i	0.724908	−	0.724908i	0.969601	+	0.244693i	$0.0786870\pi$
$524$	−17.6253			−0.769965
$525$		0			0
$526$	−2.50809			−0.109358
$527$	−23.7437	+	23.7437i	−1.03429	+	1.03429i
$528$		0			0
$529$			1.00000i			0.0434783i
$530$	−0.897960	+	8.81749i	−0.0390049	+	0.383007i
$531$		0			0
$532$	−2.12760	−	2.12760i	−0.0922432	−	0.0922432i
$533$	7.15646	+	7.15646i	0.309981	+	0.309981i
$534$		0			0
$535$	14.5920	+	17.9010i	0.630865	+	0.773927i
$536$		−	13.4889i		−	0.582634i
$537$		0			0
$538$	7.03797	−	7.03797i	0.303428	−	0.303428i
$539$	27.9473			1.20378
$540$		0			0
$541$	22.0000			0.945854			0.472927	−	0.881102i	$-0.343197\pi$
$541$	22.0000			0.945854			0.472927	+	0.881102i	$0.343197\pi$
$542$	−5.85974	+	5.85974i	−0.251698	+	0.251698i
$543$		0			0
$544$		−	5.79471i		−	0.248446i
$545$	−43.1667	−	4.39603i	−1.84906	−	0.188305i
$546$		0			0
$547$	−28.6657	−	28.6657i	−1.22566	−	1.22566i	−0.965591	−	0.260064i	$-0.916256\pi$
$547$	−28.6657	−	28.6657i	−1.22566	−	1.22566i	−0.260064	−	0.965591i	$-0.583744\pi$
$548$	7.36778	+	7.36778i	0.314736	+	0.314736i
$549$		0			0
$550$	12.2361	+	18.5781i	0.521751	+	0.792171i
$551$		−	1.03849i		−	0.0442413i
$552$		0			0
$553$	40.9259	−	40.9259i	1.74035	−	1.74035i
$554$	0.593422			0.0252121
$555$		0			0
$556$	−0.784234			−0.0332589
$557$	−29.6627	+	29.6627i	−1.25685	+	1.25685i	−0.304263	+	0.952588i	$0.598410\pi$
$557$	−29.6627	+	29.6627i	−1.25685	+	1.25685i	−0.952588	+	0.304263i	$0.901590\pi$
$558$		0			0
$559$			2.27615i			0.0962708i
$560$	6.31643	−	5.14883i	0.266918	−	0.217578i
$561$		0			0
$562$	−3.37967	−	3.37967i	−0.142563	−	0.142563i
$563$	6.82122	+	6.82122i	0.287480	+	0.287480i	0.836083	−	0.548603i	$-0.184840\pi$
$563$	6.82122	+	6.82122i	0.287480	+	0.287480i	−0.548603	+	0.836083i	$0.684840\pi$
$564$		0			0
$565$	−23.6878	+	19.3090i	−0.996552	+	0.812337i
$566$		−	8.84815i		−	0.371915i
$567$		0			0
$568$	−7.51317	+	7.51317i	−0.315246	+	0.315246i
$569$	−25.5200			−1.06985			−0.534926	−	0.844899i	$-0.679661\pi$
$569$	−25.5200			−1.06985			−0.534926	+	0.844899i	$0.679661\pi$
$570$		0			0
$571$	25.4488			1.06500			0.532499	−	0.846431i	$-0.321253\pi$
$571$	25.4488			1.06500			0.532499	+	0.846431i	$0.321253\pi$
$572$	−8.89825	+	8.89825i	−0.372054	+	0.372054i
$573$		0			0
$574$		−	13.0404i		−	0.544298i
$575$	−2.75024	−	4.17567i	−0.114693	−	0.174137i
$576$		0			0
$577$	19.2027	+	19.2027i	0.799418	+	0.799418i	0.983004	−	0.183585i	$-0.0587704\pi$
$577$	19.2027	+	19.2027i	0.799418	+	0.799418i	−0.183585	+	0.983004i	$0.558770\pi$
$578$	−11.7229	−	11.7229i	−0.487607	−	0.487607i
$579$		0			0
$580$	2.79813	+	0.284957i	0.116186	+	0.0118322i
$581$			48.2707i			2.00261i
$582$		0			0
$583$	−12.4698	+	12.4698i	−0.516447	+	0.516447i
$584$	5.52291			0.228540
$585$		0			0
$586$	6.54264			0.270274
$587$	2.62833	−	2.62833i	0.108483	−	0.108483i	−0.650782	−	0.759265i	$-0.725559\pi$
$587$	2.62833	−	2.62833i	0.108483	−	0.108483i	0.759265	+	0.650782i	$0.225559\pi$
$588$		0			0
$589$			4.78423i			0.197131i
$590$	−7.49525	−	9.19496i	−0.308575	−	0.378550i
$591$		0			0
$592$	−1.43096	−	1.43096i	−0.0588122	−	0.0588122i
$593$	−27.8748	−	27.8748i	−1.14468	−	1.14468i	−0.987583	−	0.157098i	$-0.949786\pi$
$593$	−27.8748	−	27.8748i	−1.14468	−	1.14468i	−0.157098	−	0.987583i	$-0.550214\pi$
$594$		0			0
$595$	4.78423	−	46.9786i	0.196134	−	1.92594i
$596$		−	3.12997i		−	0.128209i
$597$		0			0
$598$	2.00000	−	2.00000i	0.0817861	−	0.0817861i
$599$	34.8136			1.42244			0.711222	−	0.702968i	$-0.248142\pi$
$599$	34.8136			1.42244			0.711222	+	0.702968i	$0.248142\pi$
$600$		0			0
$601$	−2.27107			−0.0926387			−0.0463193	−	0.998927i	$-0.514749\pi$
$601$	−2.27107			−0.0926387			−0.0463193	+	0.998927i	$0.514749\pi$
$602$	2.07379	−	2.07379i	0.0845214	−	0.0845214i
$603$		0			0
$604$			3.01047i			0.122494i
$605$	−1.99241	+	19.5644i	−0.0810029	+	0.795405i
$606$		0			0
$607$	−23.0751	−	23.0751i	−0.936589	−	0.936589i	0.0615171	−	0.998106i	$-0.480406\pi$
$607$	−23.0751	−	23.0751i	−0.936589	−	0.936589i	−0.998106	+	0.0615171i	$0.980406\pi$
$608$	−0.583802	−	0.583802i	−0.0236763	−	0.0236763i
$609$		0			0
$610$	−0.463849	−	0.569037i	−0.0187807	−	0.0230396i
$611$		−	7.46922i		−	0.302172i
$612$		0			0
$613$	−17.0181	+	17.0181i	−0.687355	+	0.687355i	−0.961647	−	0.274291i	$-0.911557\pi$
$613$	−17.0181	+	17.0181i	−0.687355	+	0.687355i	0.274291	+	0.961647i	$0.411557\pi$
$614$	27.9137			1.12650
$615$		0			0
$616$	16.2143			0.653294
$617$	−23.4646	+	23.4646i	−0.944648	+	0.944648i	−0.998546	−	0.0538984i	$-0.982835\pi$
$617$	−23.4646	+	23.4646i	−0.944648	+	0.944648i	0.0538984	+	0.998546i	$0.482835\pi$
$618$		0			0
$619$		−	42.8188i		−	1.72103i	−0.509423	−	0.860516i	$-0.670141\pi$
$619$		−	42.8188i		−	1.72103i	0.509423	−	0.860516i	$-0.329859\pi$
$620$	−12.8907	−	1.31277i	−0.517702	−	0.0527221i
$621$		0			0
$622$	8.47345	+	8.47345i	0.339754	+	0.339754i
$623$	22.2568	+	22.2568i	0.891701	+	0.891701i
$624$		0			0
$625$	22.9681	+	9.87240i	0.918726	+	0.394896i
$626$			14.0936i			0.563293i
$627$		0			0
$628$	−4.08760	+	4.08760i	−0.163113	+	0.163113i
$629$	−11.7267			−0.467573
$630$		0			0
$631$	30.3856			1.20963			0.604815	−	0.796366i	$-0.293247\pi$
$631$	30.3856			1.20963			0.604815	+	0.796366i	$0.293247\pi$
$632$	11.2299	−	11.2299i	0.446700	−	0.446700i
$633$		0			0
$634$			11.1222i			0.441719i
$635$	17.9124	−	14.6013i	0.710832	−	0.579433i
$636$		0			0
$637$	12.5631	+	12.5631i	0.497767	+	0.497767i
$638$	3.95715	+	3.95715i	0.156665	+	0.156665i
$639$		0			0
$640$	1.73320	−	1.41281i	0.0685106	−	0.0558462i
$641$		−	27.4718i		−	1.08507i	−0.840033	−	0.542536i	$-0.817464\pi$
$641$		−	27.4718i		−	1.08507i	0.840033	−	0.542536i	$-0.182536\pi$
$642$		0			0
$643$	−3.33283	+	3.33283i	−0.131434	+	0.131434i	−0.769763	−	0.638329i	$-0.779626\pi$
$643$	−3.33283	+	3.33283i	−0.131434	+	0.131434i	0.638329	+	0.769763i	$0.279626\pi$
$644$	−3.64438			−0.143609
$645$		0			0
$646$	−4.78423			−0.188233
$647$	−3.37534	+	3.37534i	−0.132698	+	0.132698i	−0.770336	−	0.637638i	$-0.779912\pi$
$647$	−3.37534	+	3.37534i	−0.132698	+	0.132698i	0.637638	+	0.770336i	$0.279912\pi$
$648$		0			0
$649$		−	23.6035i		−	0.926519i
$650$	−2.85086	+	13.8518i	−0.111820	+	0.543313i
$651$		0			0
$652$	−9.28154	−	9.28154i	−0.363493	−	0.363493i
$653$	−14.1859	−	14.1859i	−0.555135	−	0.555135i	0.372783	−	0.927919i	$-0.378404\pi$
$653$	−14.1859	−	14.1859i	−0.555135	−	0.555135i	−0.927919	+	0.372783i	$0.878404\pi$
$654$		0			0
$655$	−39.2086	−	3.99295i	−1.53201	−	0.156017i
$656$		−	3.57823i		−	0.139706i
$657$		0			0
$658$	−6.80518	+	6.80518i	−0.265294	+	0.265294i
$659$	−13.7242			−0.534621			−0.267310	−	0.963610i	$-0.586135\pi$
$659$	−13.7242			−0.534621			−0.267310	+	0.963610i	$0.586135\pi$
$660$		0			0
$661$	17.3388			0.674401			0.337200	−	0.941433i	$-0.390520\pi$
$661$	17.3388			0.674401			0.337200	+	0.941433i	$0.390520\pi$
$662$	1.10629	−	1.10629i	0.0429970	−	0.0429970i
$663$		0			0
$664$			13.2452i			0.514015i
$665$	−4.25098	−	5.21498i	−0.164846	−	0.202228i
$666$		0			0
$667$	−0.889422	−	0.889422i	−0.0344385	−	0.0344385i
$668$	6.10995	+	6.10995i	0.236401	+	0.236401i
$669$		0			0
$670$	3.05587	−	30.0070i	0.118058	−	1.15927i
$671$		−	1.46072i		−	0.0563905i
$672$		0			0
$673$	−18.6737	+	18.6737i	−0.719817	+	0.719817i	−0.968567	−	0.248751i	$-0.919980\pi$
$673$	−18.6737	+	18.6737i	−0.719817	+	0.719817i	0.248751	+	0.968567i	$0.419980\pi$
$674$	19.6799			0.758040
$675$		0			0
$676$	5.00000			0.192308
$677$	−21.8583	+	21.8583i	−0.840084	+	0.840084i	−0.988869	−	0.148786i	$-0.952464\pi$
$677$	−21.8583	+	21.8583i	−0.840084	+	0.840084i	0.148786	+	0.988869i	$0.452464\pi$
$678$		0			0
$679$			32.9446i			1.26430i
$680$	1.31277	−	12.8907i	0.0503424	−	0.494335i
$681$		0			0
$682$	−18.2302	−	18.2302i	−0.698070	−	0.698070i
$683$	0.0196459	+	0.0196459i	0.000751731	+	0.000751731i	0.707483	−	0.706731i	$-0.249831\pi$
$683$	0.0196459	+	0.0196459i	0.000751731	+	0.000751731i	−0.706731	+	0.707483i	$0.749831\pi$
$684$		0			0
$685$	14.7209	+	18.0592i	0.562458	+	0.690007i
$686$			2.61835i			0.0999690i
$687$		0			0
$688$	0.569037	−	0.569037i	0.0216943	−	0.0216943i
$689$	−11.2110			−0.427106
$690$		0			0
$691$	−15.9591			−0.607113			−0.303557	−	0.952813i	$-0.598174\pi$
$691$	−15.9591			−0.607113			−0.303557	+	0.952813i	$0.598174\pi$
$692$	−2.23017	+	2.23017i	−0.0847784	+	0.0847784i
$693$		0			0
$694$			3.25665i			0.123621i
$695$	−1.74458	−	0.177665i	−0.0661756	−	0.00673923i
$696$		0			0
$697$	−14.6617	−	14.6617i	−0.555352	−	0.555352i
$698$	−0.156381	−	0.156381i	−0.00591912	−	0.00591912i
$699$		0			0
$700$	15.2177	−	10.0229i	0.575176	−	0.378831i
$701$		−	42.2603i		−	1.59615i	−0.602559	−	0.798074i	$-0.705852\pi$
$701$		−	42.2603i		−	1.59615i	0.602559	−	0.798074i	$-0.294148\pi$
$702$		0			0
$703$	−1.18143	+	1.18143i	−0.0445586	+	0.0445586i
$704$	4.44912			0.167683
$705$		0			0
$706$	23.4777			0.883594
$707$	−32.4543	+	32.4543i	−1.22057	+	1.22057i
$708$		0			0
$709$			32.0912i			1.20521i	0.798040	+	0.602605i	$0.205870\pi$
$709$			32.0912i			1.20521i	−0.798040	+	0.602605i	$0.794130\pi$
$710$	−18.4156	+	15.0114i	−0.691125	+	0.563369i
$711$		0			0
$712$	6.10716	+	6.10716i	0.228875	+	0.228875i
$713$	4.09748	+	4.09748i	0.153452	+	0.153452i
$714$		0			0
$715$	−21.8106	+	17.7788i	−0.815669	+	0.664891i
$716$		−	16.8514i		−	0.629767i
$717$		0			0
$718$	−6.14346	+	6.14346i	−0.229272	+	0.229272i
$719$	34.0076			1.26827			0.634135	−	0.773223i	$-0.281357\pi$
$719$	34.0076			1.26827			0.634135	+	0.773223i	$0.281357\pi$
$720$		0			0
$721$	−13.2815			−0.494630
$722$	12.9530	−	12.9530i	0.482062	−	0.482062i
$723$		0			0
$724$			6.10716i			0.226971i
$725$	6.16005	+	1.26781i	0.228778	+	0.0470853i
$726$		0			0
$727$	−4.73235	−	4.73235i	−0.175513	−	0.175513i	0.613883	−	0.789397i	$-0.289606\pi$
$727$	−4.73235	−	4.73235i	−0.175513	−	0.175513i	−0.789397	+	0.613883i	$0.789606\pi$
$728$	7.28877	+	7.28877i	0.270140	+	0.270140i
$729$		0			0
$730$	12.2861	+	1.25119i	0.454727	+	0.0463088i
$731$		−	4.66323i		−	0.172476i
$732$		0			0
$733$	−6.82474	+	6.82474i	−0.252078	+	0.252078i	−0.821822	−	0.569744i	$-0.807042\pi$
$733$	−6.82474	+	6.82474i	−0.252078	+	0.252078i	0.569744	+	0.821822i	$0.307042\pi$
$734$	−20.4024			−0.753066
$735$		0			0
$736$	−1.00000			−0.0368605
$737$	42.4363	−	42.4363i	1.56316	−	1.56316i
$738$		0			0
$739$			3.26059i			0.119943i	0.998200	+	0.0599714i	$0.0191010\pi$
$739$			3.26059i			0.119943i	−0.998200	+	0.0599714i	$0.980899\pi$
$740$	−2.85909	−	3.50745i	−0.105102	−	0.128936i
$741$		0			0
$742$	10.2143	+	10.2143i	0.374979	+	0.374979i
$743$	−21.3948	−	21.3948i	−0.784899	−	0.784899i	0.195754	−	0.980653i	$-0.437285\pi$
$743$	−21.3948	−	21.3948i	−0.784899	−	0.784899i	−0.980653	+	0.195754i	$0.937285\pi$
$744$		0			0
$745$	0.709083	−	6.96282i	0.0259788	−	0.255098i
$746$		−	24.9838i		−	0.914723i
$747$		0			0
$748$	18.2302	−	18.2302i	0.666562	−	0.666562i
$749$	37.6404			1.37535
$750$		0			0
$751$	−14.5682			−0.531600			−0.265800	−	0.964028i	$-0.585636\pi$
$751$	−14.5682			−0.531600			−0.265800	+	0.964028i	$0.585636\pi$
$752$	−1.86731	+	1.86731i	−0.0680936	+	0.0680936i
$753$		0			0
$754$			3.55769i			0.129563i
$755$	−0.682011	+	6.69699i	−0.0248209	+	0.243728i
$756$		0			0
$757$	−29.2143	−	29.2143i	−1.06181	−	1.06181i	−0.997959	−	0.0638508i	$-0.979662\pi$
$757$	−29.2143	−	29.2143i	−1.06181	−	1.06181i	−0.0638508	−	0.997959i	$-0.520338\pi$
$758$	−12.2407	−	12.2407i	−0.444603	−	0.444603i
$759$		0			0
$760$	−1.16645	−	1.43096i	−0.0423115	−	0.0519065i
$761$			8.59311i			0.311500i	0.987797	+	0.155750i	$0.0497794\pi$
$761$			8.59311i			0.311500i	−0.987797	+	0.155750i	$0.950221\pi$
$762$		0			0
$763$	−50.0050	+	50.0050i	−1.81030	+	1.81030i
$764$	−25.9690			−0.939526
$765$		0			0
$766$	28.8301			1.04167
$767$	10.6104	−	10.6104i	0.383120	−	0.383120i
$768$		0			0
$769$			38.8710i			1.40172i	0.713298	+	0.700861i	$0.247201\pi$
$769$			38.8710i			1.40172i	−0.713298	+	0.700861i	$0.752799\pi$
$770$	36.0698	+	3.67329i	1.29986	+	0.132376i
$771$		0			0
$772$	1.94865	+	1.94865i	0.0701333	+	0.0701333i
$773$	9.58833	+	9.58833i	0.344868	+	0.344868i	0.858194	−	0.513326i	$-0.171587\pi$
$773$	9.58833	+	9.58833i	0.344868	+	0.344868i	−0.513326	+	0.858194i	$0.671587\pi$
$774$		0			0
$775$	−28.3787	−	5.84067i	−1.01939	−	0.209803i
$776$			9.03982i			0.324511i
$777$		0			0
$778$	21.1205	−	21.1205i	0.757206	−	0.757206i
$779$	−2.95426			−0.105847
$780$		0			0
$781$	−47.2729			−1.69156
$782$	−4.09748	+	4.09748i	−0.146525	+	0.146525i
$783$		0			0
$784$		−	6.28154i		−	0.224341i
$785$	−10.0191	+	8.16708i	−0.357599	+	0.291496i
$786$		0			0
$787$	21.8460	+	21.8460i	0.778726	+	0.778726i	0.979614	−	0.200888i	$-0.0643829\pi$
$787$	21.8460	+	21.8460i	0.778726	+	0.778726i	−0.200888	+	0.979614i	$0.564383\pi$
$788$	−15.3049	−	15.3049i	−0.545215	−	0.545215i
$789$		0			0
$790$	27.5256	−	22.4374i	0.979317	−	0.798289i
$791$			49.8082i			1.77098i
$792$		0			0
$793$	0.656633	−	0.656633i	0.0233177	−	0.0233177i
$794$	−12.1396			−0.430820
$795$		0			0
$796$	17.0762			0.605251
$797$	−36.0894	+	36.0894i	−1.27835	+	1.27835i	−0.336765	+	0.941589i	$0.609333\pi$
$797$	−36.0894	+	36.0894i	−1.27835	+	1.27835i	−0.941589	+	0.336765i	$0.890667\pi$
$798$		0			0
$799$			15.3025i			0.541363i
$800$	4.17567	−	2.75024i	0.147632	−	0.0972355i
$801$		0			0
$802$	9.62572	+	9.62572i	0.339896	+	0.339896i
$803$	17.3751	+	17.3751i	0.613154	+	0.613154i
$804$		0			0
$805$	−8.10716	−	0.825621i	−0.285740	−	0.0290993i
$806$		−	16.3899i		−	0.577310i
$807$		0			0
$808$	−8.90529	+	8.90529i	−0.313287	+	0.313287i
$809$	−12.7207			−0.447237			−0.223619	−	0.974677i	$-0.571787\pi$
$809$	−12.7207			−0.447237			−0.223619	+	0.974677i	$0.571787\pi$
$810$		0			0
$811$	28.0039			0.983351			0.491676	−	0.870778i	$-0.336385\pi$
$811$	28.0039			0.983351			0.491676	+	0.870778i	$0.336385\pi$
$812$	3.24139	−	3.24139i	0.113751	−	0.113751i
$813$		0			0
$814$		−	9.00364i		−	0.315577i
$815$	−18.5447	−	22.7501i	−0.649591	−	0.796900i
$816$		0			0
$817$	−0.469809	−	0.469809i	−0.0164365	−	0.0164365i
$818$	−26.6799	−	26.6799i	−0.932842	−	0.932842i
$819$		0			0
$820$	0.810634	−	7.96000i	0.0283086	−	0.277975i
$821$		−	24.0151i		−	0.838132i	−0.907956	−	0.419066i	$-0.862358\pi$
$821$		−	24.0151i		−	0.838132i	0.907956	−	0.419066i	$-0.137642\pi$
$822$		0			0
$823$	4.31587	−	4.31587i	0.150442	−	0.150442i	−0.627874	−	0.778315i	$-0.716075\pi$
$823$	4.31587	−	4.31587i	0.150442	−	0.150442i	0.778315	+	0.627874i	$0.216075\pi$
$824$	−3.64438			−0.126958
$825$		0			0
$826$	−19.3342			−0.672723
$827$	29.1471	−	29.1471i	1.01354	−	1.01354i	0.0136368	−	0.999907i	$-0.495659\pi$
$827$	29.1471	−	29.1471i	1.01354	−	1.01354i	0.999907	−	0.0136368i	$-0.00434086\pi$
$828$		0			0
$829$			22.4286i			0.778979i	0.921031	+	0.389489i	$0.127349\pi$
$829$			22.4286i			0.778979i	−0.921031	+	0.389489i	$0.872651\pi$
$830$	−3.00066	+	29.4648i	−0.104154	+	1.02274i
$831$		0			0
$832$	2.00000	+	2.00000i	0.0693375	+	0.0693375i
$833$	−25.7385	−	25.7385i	−0.891785	−	0.891785i
$834$		0			0
$835$	12.2078	+	14.9761i	0.422467	+	0.518271i
$836$		−	3.67329i		−	0.127043i
$837$		0			0
$838$	−14.9044	+	14.9044i	−0.514864	+	0.514864i
$839$	48.5162			1.67496			0.837482	−	0.546464i	$-0.184027\pi$
$839$	48.5162			1.67496			0.837482	+	0.546464i	$0.184027\pi$
$840$		0			0
$841$	−27.4179			−0.945443
$842$	22.5969	−	22.5969i	0.778741	−	0.778741i
$843$		0			0
$844$		−	24.7983i		−	0.853594i
$845$	11.1228	+	1.13273i	0.382636	+	0.0389671i
$846$		0			0
$847$	22.6637	+	22.6637i	0.778734	+	0.778734i
$848$	2.80276	+	2.80276i	0.0962470	+	0.0962470i
$849$		0			0
$850$	5.84067	−	28.3787i	0.200333	−	0.973382i
$851$			2.02369i			0.0693711i
$852$		0			0
$853$	−30.3629	+	30.3629i	−1.03960	+	1.03960i	−0.0404221	+	0.999183i	$0.512870\pi$
$853$	−30.3629	+	30.3629i	−1.03960	+	1.03960i	−0.999183	+	0.0404221i	$0.987130\pi$
$854$	−1.19651			−0.0409438
$855$		0			0
$856$	10.3283			0.353015
$857$	6.76469	−	6.76469i	0.231077	−	0.231077i	−0.582065	−	0.813142i	$-0.697755\pi$
$857$	6.76469	−	6.76469i	0.231077	−	0.231077i	0.813142	+	0.582065i	$0.197755\pi$
$858$		0			0
$859$			38.2176i			1.30397i	0.758232	+	0.651985i	$0.226063\pi$
$859$			38.2176i			1.30397i	−0.758232	+	0.651985i	$0.773937\pi$
$860$	1.39477	−	1.13694i	0.0475613	−	0.0387695i
$861$		0			0
$862$	7.37509	+	7.37509i	0.251197	+	0.251197i
$863$	23.4445	+	23.4445i	0.798061	+	0.798061i	0.982790	−	0.184729i	$-0.0591406\pi$
$863$	23.4445	+	23.4445i	0.798061	+	0.798061i	−0.184729	+	0.982790i	$0.559141\pi$
$864$		0			0
$865$	−5.46639	+	4.45592i	−0.185863	+	0.151506i
$866$		−	34.8284i		−	1.18352i
$867$		0			0
$868$	−14.9328	+	14.9328i	−0.506852	+	0.506852i
$869$	70.6584			2.39692
$870$		0			0
$871$	38.1525			1.29275
$872$	−13.7211	+	13.7211i	−0.464655	+	0.464655i
$873$		0			0
$874$			0.825621i			0.0279271i
$875$	36.1235	−	18.8491i	1.22120	−	0.637215i
$876$		0			0
$877$	−27.5667	−	27.5667i	−0.930862	−	0.930862i	0.0668980	−	0.997760i	$-0.478690\pi$
$877$	−27.5667	−	27.5667i	−0.930862	−	0.930862i	−0.997760	+	0.0668980i	$0.978690\pi$
$878$	16.0920	+	16.0920i	0.543077	+	0.543077i
$879$		0			0
$880$	9.89735	+	1.00793i	0.333640	+	0.0339774i
$881$			9.10761i			0.306843i	0.988161	+	0.153422i	$0.0490293\pi$
$881$			9.10761i			0.306843i	−0.988161	+	0.153422i	$0.950971\pi$
$882$		0			0
$883$	−39.1221	+	39.1221i	−1.31656	+	1.31656i	−0.400085	+	0.916478i	$0.631019\pi$
$883$	−39.1221	+	39.1221i	−1.31656	+	1.31656i	−0.916478	+	0.400085i	$0.868981\pi$
$884$	16.3899			0.551252
$885$		0			0
$886$	−22.5948			−0.759087
$887$	−8.56265	+	8.56265i	−0.287506	+	0.287506i	−0.836093	−	0.548587i	$-0.815166\pi$
$887$	−8.56265	+	8.56265i	−0.287506	+	0.287506i	0.548587	+	0.836093i	$0.315166\pi$
$888$		0			0
$889$		−	37.6643i		−	1.26322i
$890$	12.2022	+	14.9693i	0.409019	+	0.501772i
$891$		0			0
$892$	5.52480	+	5.52480i	0.184984	+	0.184984i
$893$	1.54169	+	1.54169i	0.0515906	+	0.0515906i
$894$		0			0
$895$	3.81763	−	37.4870i	0.127609	−	1.25305i
$896$		−	3.64438i		−	0.121750i
$897$		0			0
$898$	5.51972	−	5.51972i	0.184195	−	0.184195i
$899$	−7.28877			−0.243094
$900$		0			0
$901$	22.9685			0.765190
$902$	11.2571	−	11.2571i	0.374822	−	0.374822i
$903$		0			0
$904$			13.6671i			0.454561i
$905$	−1.38355	+	13.5858i	−0.0459909	+	0.451606i
$906$		0			0
$907$	−31.0255	−	31.0255i	−1.03018	−	1.03018i	−0.999530	−	0.0306534i	$-0.990241\pi$
$907$	−31.0255	−	31.0255i	−1.03018	−	1.03018i	−0.0306534	−	0.999530i	$-0.509759\pi$
$908$	18.2364	+	18.2364i	0.605195	+	0.605195i
$909$		0			0
$910$	14.5631	+	17.8656i	0.482761	+	0.592238i
$911$		−	50.5467i		−	1.67469i	−0.546677	−	0.837343i	$-0.684108\pi$
$911$		−	50.5467i		−	1.67469i	0.546677	−	0.837343i	$-0.315892\pi$
$912$		0			0
$913$	−41.6696	+	41.6696i	−1.37906	+	1.37906i
$914$	−30.5709			−1.01120
$915$		0			0
$916$	−28.4150			−0.938859
$917$	−45.4199	+	45.4199i	−1.49990	+	1.49990i
$918$		0			0
$919$		−	22.6827i		−	0.748232i	−0.927382	−	0.374116i	$-0.877946\pi$
$919$		−	22.6827i		−	0.748232i	0.927382	−	0.374116i	$-0.122054\pi$
$920$	−2.22456	−	0.226546i	−0.0733416	−	0.00746901i
$921$		0			0
$922$	23.3458	+	23.3458i	0.768854	+	0.768854i
$923$	−21.2505	−	21.2505i	−0.699467	−	0.699467i
$924$		0			0
$925$	−5.56562	−	8.45025i	−0.182996	−	0.277842i
$926$		−	10.7479i		−	0.353197i
$927$		0			0
$928$	0.889422	−	0.889422i	0.0291967	−	0.0291967i
$929$	−47.8016			−1.56832			−0.784160	−	0.620559i	$-0.786906\pi$
$929$	−47.8016			−1.56832			−0.784160	+	0.620559i	$0.786906\pi$
$930$		0			0
$931$	−5.18617			−0.169970
$932$	−19.3122	+	19.3122i	−0.632591	+	0.632591i
$933$		0			0
$934$		−	26.3992i		−	0.863807i
$935$	44.6842	−	36.4242i	1.46133	−	1.19120i
$936$		0			0
$937$	38.2786	+	38.2786i	1.25051	+	1.25051i	0.955492	+	0.295016i	$0.0953249\pi$
$937$	38.2786	+	38.2786i	1.25051	+	1.25051i	0.295016	+	0.955492i	$0.404675\pi$
$938$	−34.7606	−	34.7606i	−1.13497	−	1.13497i
$939$		0			0
$940$	−4.57697	+	3.73091i	−0.149284	+	0.121689i
$941$			43.2250i			1.40909i	0.709657	+	0.704547i	$0.248850\pi$
$941$			43.2250i			1.40909i	−0.709657	+	0.704547i	$0.751150\pi$
$942$		0			0
$943$	−2.53019	+	2.53019i	−0.0823944	+	0.0823944i
$944$	−5.30521			−0.172670
$945$		0			0
$946$	3.58039			0.116408
$947$	−12.5130	+	12.5130i	−0.406618	+	0.406618i	−0.880558	−	0.473939i	$-0.842832\pi$
$947$	−12.5130	+	12.5130i	−0.406618	+	0.406618i	0.473939	+	0.880558i	$0.342832\pi$
$948$		0			0
$949$			15.6211i			0.507084i
$950$	−2.27065	−	3.44752i	−0.0736697	−	0.111852i
$951$		0			0
$952$	−14.9328	−	14.9328i	−0.483974	−	0.483974i
$953$	15.2696	+	15.2696i	0.494631	+	0.494631i	0.909762	−	0.415131i	$-0.136264\pi$
$953$	15.2696	+	15.2696i	0.494631	+	0.494631i	−0.415131	+	0.909762i	$0.636264\pi$
$954$		0			0
$955$	−57.7697	−	5.88318i	−1.86938	−	0.190375i
$956$			9.98325i			0.322881i
$957$		0			0
$958$	15.7221	−	15.7221i	0.507958	−	0.507958i
$959$	37.9731			1.22621
$960$		0			0
$961$	2.57863			0.0831817
$962$	4.04737	−	4.04737i	0.130493	−	0.130493i
$963$		0			0
$964$			10.0867i			0.324871i
$965$	3.89342	+	4.77634i	0.125334	+	0.153756i
$966$		0			0
$967$	−0.531945	−	0.531945i	−0.0171062	−	0.0171062i	0.698502	−	0.715608i	$-0.253850\pi$
$967$	−0.531945	−	0.531945i	−0.0171062	−	0.0171062i	−0.715608	+	0.698502i	$0.753850\pi$
$968$	6.21880	+	6.21880i	0.199880	+	0.199880i
$969$		0			0
$970$	−2.04794	+	20.1096i	−0.0657553	+	0.645682i
$971$			25.6964i			0.824636i	0.911040	+	0.412318i	$0.135281\pi$
$971$			25.6964i			0.824636i	−0.911040	+	0.412318i	$0.864719\pi$
$972$		0			0
$973$	−2.02095	+	2.02095i	−0.0647886	+	0.0647886i
$974$	−24.3896			−0.781493
$975$		0			0
$976$	−0.328317			−0.0105092
$977$	37.5357	−	37.5357i	1.20087	−	1.20087i	0.226973	−	0.973901i	$-0.427117\pi$
$977$	37.5357	−	37.5357i	1.20087	−	1.20087i	0.973901	−	0.226973i	$-0.0728829\pi$
$978$		0			0
$979$			38.4263i			1.22811i
$980$	1.42306	−	13.9737i	0.0454579	−	0.446373i
$981$		0			0
$982$	−19.3566	−	19.3566i	−0.617695	−	0.617695i
$983$	−10.0948	−	10.0948i	−0.321973	−	0.321973i	0.527551	−	0.849524i	$-0.323110\pi$
$983$	−10.0948	−	10.0948i	−0.321973	−	0.321973i	−0.849524	+	0.527551i	$0.823110\pi$
$984$		0			0
$985$	−30.5794	−	37.5140i	−0.974342	−	1.19529i
$986$		−	7.28877i		−	0.232122i
$987$		0			0
$988$	1.65124	−	1.65124i	0.0525330	−	0.0525330i
$989$	−0.804740			−0.0255892
$990$		0			0
$991$	25.4499			0.808443			0.404221	−	0.914661i	$-0.367543\pi$
$991$	25.4499			0.808443			0.404221	+	0.914661i	$0.367543\pi$
$992$	−4.09748	+	4.09748i	−0.130095	+	0.130095i
$993$		0			0
$994$			38.7224i			1.22820i
$995$	37.9872	+	3.86856i	1.20427	+	0.122642i
$996$		0			0
$997$	17.9364	+	17.9364i	0.568052	+	0.568052i	0.931582	−	0.363530i	$-0.118429\pi$
$997$	17.9364	+	17.9364i	0.568052	+	0.568052i	−0.363530	+	0.931582i	$0.618429\pi$
$998$	−0.261420	−	0.261420i	−0.00827511	−	0.00827511i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2070.2.j.i.737.7	yes	16
3.2	odd	2	inner	2070.2.j.i.737.2	yes	16
5.3	odd	4	inner	2070.2.j.i.323.2	✓	16
15.8	even	4	inner	2070.2.j.i.323.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2070.2.j.i.323.2	✓	16	5.3	odd	4	inner
2070.2.j.i.323.7	yes	16	15.8	even	4	inner
2070.2.j.i.737.2	yes	16	3.2	odd	2	inner
2070.2.j.i.737.7	yes	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2070.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(0.226546 - 2.22456i) q^{5} +(-2.57697 - 2.57697i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(0.226546 - 2.22456i) q^{5} +(-2.57697 - 2.57697i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.41281 - 1.73320i) q^{10} -4.44912i q^{11} +(2.00000 - 2.00000i) q^{13} -3.64438 q^{14} -1.00000 q^{16} +(-4.09748 + 4.09748i) q^{17} +0.825621i q^{19} +(-2.22456 - 0.226546i) q^{20} +(-3.14601 - 3.14601i) q^{22} +(0.707107 + 0.707107i) q^{23} +(-4.89735 - 1.00793i) q^{25} -2.82843i q^{26} +(-2.57697 + 2.57697i) q^{28} -1.25783 q^{29} +5.79471 q^{31} +(-0.707107 + 0.707107i) q^{32} +5.79471i q^{34} +(-6.31643 + 5.14883i) q^{35} +(1.43096 + 1.43096i) q^{37} +(0.583802 + 0.583802i) q^{38} +(-1.73320 + 1.41281i) q^{40} +3.57823i q^{41} +(-0.569037 + 0.569037i) q^{43} -4.44912 q^{44} +1.00000 q^{46} +(1.86731 - 1.86731i) q^{47} +6.28154i q^{49} +(-4.17567 + 2.75024i) q^{50} +(-2.00000 - 2.00000i) q^{52} +(-2.80276 - 2.80276i) q^{53} +(-9.89735 - 1.00793i) q^{55} +3.64438i q^{56} +(-0.889422 + 0.889422i) q^{58} +5.30521 q^{59} +0.328317 q^{61} +(4.09748 - 4.09748i) q^{62} +1.00000i q^{64} +(-3.99603 - 4.90222i) q^{65} +(9.53812 + 9.53812i) q^{67} +(4.09748 + 4.09748i) q^{68} +(-0.825621 + 8.10716i) q^{70} -10.6252i q^{71} +(-3.90529 + 3.90529i) q^{73} +2.02369 q^{74} +0.825621 q^{76} +(-11.4653 + 11.4653i) q^{77} +15.8814i q^{79} +(-0.226546 + 2.22456i) q^{80} +(2.53019 + 2.53019i) q^{82} +(-9.36579 - 9.36579i) q^{83} +(8.18682 + 10.0434i) q^{85} +0.804740i q^{86} +(-3.14601 + 3.14601i) q^{88} -8.63683 q^{89} -10.3079 q^{91} +(0.707107 - 0.707107i) q^{92} -2.64077i q^{94} +(1.83665 + 0.187041i) q^{95} +(-6.39212 - 6.39212i) q^{97} +(4.44172 + 4.44172i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 4 q^{10} + 32 q^{13} - 16 q^{16} - 24 q^{25} - 16 q^{31} + 32 q^{37} + 4 q^{40} + 16 q^{46} - 32 q^{52} - 104 q^{55} + 8 q^{58} - 40 q^{61} + 72 q^{67} + 24 q^{70} + 24 q^{73} - 24 q^{76} - 8 q^{82} - 8 q^{85} - 72 q^{97}+O(q^{100}) \) 16 * q - 4 * q^10 + 32 * q^13 - 16 * q^16 - 24 * q^25 - 16 * q^31 + 32 * q^37 + 4 * q^40 + 16 * q^46 - 32 * q^52 - 104 * q^55 + 8 * q^58 - 40 * q^61 + 72 * q^67 + 24 * q^70 + 24 * q^73 - 24 * q^76 - 8 * q^82 - 8 * q^85 - 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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