LMFDB - Embedded newform 2070.2.j.i.737.2

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			737.2
Root			$2.82219i$ of defining polynomial
Character	$\chi$	$=$	2070.737
Dual form			2070.2.j.i.323.2

$q$-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	$0.234019\pi$
$11$			4.44912i			1.34146i	−0.741701	+	0.670731i	$0.765981\pi$
$12$		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	−0.00619669	−	0.999981i	$-0.501972\pi$
$17$	4.09748	−	4.09748i	0.993784	−	0.993784i	0.999981	+	0.00619669i	$0.00197248\pi$
$18$		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	$-0.462741\pi$
$29$	1.25783			0.233574			0.116787	+	0.993157i	$0.462741\pi$
$30$		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	$-0.909860\pi$
$41$		−	3.57823i		−	0.558826i	0.960171	−	0.279413i	$-0.0901398\pi$
$42$		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	−0.830055	−	0.557681i	$-0.811691\pi$
$47$	−1.86731	+	1.86731i	−0.272375	+	0.272375i	0.557681	+	0.830055i	$0.311691\pi$
$48$		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	0.872895	−	0.487907i	$-0.162240\pi$
$53$	2.80276	+	2.80276i	0.384988	+	0.384988i	−0.487907	+	0.872895i	$0.662240\pi$
$54$		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	$-0.612236\pi$
$59$	−5.30521			−0.690679			−0.345340	+	0.938478i	$0.612236\pi$
$60$		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	$0.217146\pi$
$71$			10.6252i			1.26098i	−0.776196	+	0.630491i	$0.782854\pi$
$72$		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	$0.00905200\pi$
$83$	9.36579	+	9.36579i	1.02803	+	1.02803i	0.0284338	+	0.999596i	$0.490948\pi$
$84$		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	$-0.348655\pi$
$89$	8.63683			0.915502			0.457751	+	0.889080i	$0.348655\pi$
$90$		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	$0.215543\pi$
$101$			12.5940i			1.25315i	−0.779362	+	0.626574i	$0.784457\pi$
$102$		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	−0.259669	−	0.965698i	$-0.583613\pi$
$107$	7.30322	−	7.30322i	0.706029	−	0.706029i	0.965698	+	0.259669i	$0.0836133\pi$
$108$		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	0.996201	−	0.0870790i	$-0.0277533\pi$
$113$	9.66410	+	9.66410i	0.909122	+	0.909122i	−0.0870790	+	0.996201i	$0.527753\pi$
$114$		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	$0.279726\pi$
$131$			17.6253i			1.53993i	−0.638086	+	0.769965i	$0.720274\pi$
$132$		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	−0.318463	−	0.947935i	$-0.603167\pi$
$137$	7.36778	−	7.36778i	0.629472	−	0.629472i	0.947935	+	0.318463i	$0.103167\pi$
$138$		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	$-0.540923\pi$
$149$	−3.12997			−0.256417			−0.128209	+	0.991747i	$0.540923\pi$
$150$		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	−0.430018	−	0.902820i	$-0.641493\pi$
$167$	6.10995	−	6.10995i	0.472802	−	0.472802i	0.902820	+	0.430018i	$0.141493\pi$
$168$		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	0.786785	−	0.617228i	$-0.211744\pi$
$173$	2.23017	+	2.23017i	0.169557	+	0.169557i	−0.617228	+	0.786785i	$0.711744\pi$
$174$		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	$-0.716850\pi$
$179$	−16.8514			−1.25953			−0.629767	+	0.776784i	$0.716850\pi$
$180$		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	$0.388734\pi$
$191$			25.9690i			1.87905i	−0.342478	+	0.939526i	$0.611266\pi$
$192$		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	$0.530268\pi$
$197$	−15.3049	+	15.3049i	−1.09043	+	1.09043i	−0.995482	+	0.0949471i	$0.969732\pi$
$198$		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	$-0.423019\pi$
$227$	18.2364	−	18.2364i	1.21039	−	1.21039i	0.970898	−	0.239493i	$-0.0769811\pi$
$228$		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	$0.102552\pi$
$233$	19.3122	+	19.3122i	1.26518	+	1.26518i	0.316633	+	0.948548i	$0.397448\pi$
$234$		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	$-0.395349\pi$
$239$	9.98325			0.645763			0.322881	+	0.946439i	$0.395349\pi$
$240$		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	$0.0160626\pi$
$251$			1.59826i			0.100881i	−0.998727	+	0.0504407i	$0.983937\pi$
$252$		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	−0.969055	−	0.246844i	$-0.920606\pi$
$257$	−11.5779	+	11.5779i	−0.722211	+	0.722211i	0.246844	+	0.969055i	$0.420606\pi$
$258$		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	0.759668	−	0.650311i	$-0.225361\pi$
$263$	1.77348	+	1.77348i	0.109358	+	0.109358i	−0.650311	+	0.759668i	$0.725361\pi$
$264$		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	$-0.598131\pi$
$269$	−9.95319			−0.606857			−0.303428	+	0.952854i	$0.598131\pi$
$270$		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	$0.0455343\pi$
$281$			4.77958i			0.285126i	−0.989786	+	0.142563i	$0.954466\pi$
$282$		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	0.558937	−	0.829210i	$-0.311210\pi$
$293$	−4.62634	−	4.62634i	−0.270274	−	0.270274i	−0.829210	+	0.558937i	$0.811210\pi$
$294$		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	$-0.889656\pi$
$311$		−	11.9833i		−	0.679508i	0.940514	−	0.339754i	$-0.110344\pi$
$312$		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	−0.450870	−	0.892590i	$-0.648886\pi$
$317$	7.86459	−	7.86459i	0.441719	−	0.441719i	0.892590	+	0.450870i	$0.148886\pi$
$318$		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	−0.642590	−	0.766210i	$-0.722140\pi$
$347$	2.30280	−	2.30280i	0.123621	−	0.123621i	0.766210	+	0.642590i	$0.222140\pi$
$348$		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	0.110304	−	0.993898i	$-0.464818\pi$
$353$	−16.6012	−	16.6012i	−0.883594	−	0.883594i	−0.993898	+	0.110304i	$0.964818\pi$
$354$		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	$-0.426365\pi$
$359$	8.68817			0.458544			0.229272	+	0.973362i	$0.426365\pi$
$360$		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	$-0.986442\pi$
$383$	−20.3859	−	20.3859i	−1.04167	−	1.04167i	−0.0425798	−	0.999093i	$-0.513558\pi$
$384$		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	$-0.773436\pi$
$389$	−29.8689			−1.51441			−0.757206	+	0.653176i	$0.773436\pi$
$390$		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	$-0.889608\pi$
$401$		−	13.6128i		−	0.679792i	0.940463	−	0.339896i	$-0.110392\pi$
$402$		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	$-0.327842\pi$
$419$	21.0780			1.02973			0.514864	+	0.857272i	$0.327842\pi$
$420$		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	$-0.919176\pi$
$431$		−	10.4300i		−	0.502393i	0.967936	−	0.251197i	$-0.0808241\pi$
$432$		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	0.976156	−	0.217069i	$-0.0696496\pi$
$443$	15.9769	+	15.9769i	0.759087	+	0.759087i	−0.217069	+	0.976156i	$0.569650\pi$
$444$		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	$-0.558968\pi$
$449$	−7.80606			−0.368391			−0.184195	+	0.982890i	$0.558968\pi$
$450$		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	$-0.720827\pi$
$461$		−	33.0160i		−	1.53771i	0.639424	−	0.768854i	$-0.279173\pi$
$462$		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	−0.991778	−	0.127971i	$-0.959154\pi$
$467$	−18.6670	+	18.6670i	−0.863807	+	0.863807i	0.127971	+	0.991778i	$0.459154\pi$
$468$		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	$-0.669599\pi$
$479$	−22.2344			−1.01592			−0.507958	+	0.861382i	$0.669599\pi$
$480$		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	$0.211933\pi$
$491$			27.3744i			1.23539i	−0.786418	+	0.617695i	$0.788067\pi$
$492$		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	0.0532361	−	0.998582i	$-0.483046\pi$
$503$	−21.2019	−	21.2019i	−0.945346	−	0.945346i	−0.998582	+	0.0532361i	$0.983046\pi$
$504$		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	$-0.369807\pi$
$509$	17.9453			0.795409			0.397705	+	0.917513i	$0.369807\pi$
$510$		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	$0.314806\pi$
$521$			38.1400i			1.67095i	−0.549532	+	0.835473i	$0.685194\pi$
$522$		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	$-0.401590\pi$
$557$	29.6627	−	29.6627i	1.25685	−	1.25685i	0.952588	−	0.304263i	$-0.0984101\pi$
$558$		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	0.548603	−	0.836083i	$-0.315160\pi$
$563$	−6.82122	−	6.82122i	−0.287480	−	0.287480i	−0.836083	+	0.548603i	$0.815160\pi$
$564$		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	$-0.320339\pi$
$569$	25.5200			1.06985			0.534926	+	0.844899i	$0.320339\pi$
$570$		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	−0.759265	−	0.650782i	$-0.774441\pi$
$587$	−2.62833	+	2.62833i	−0.108483	+	0.108483i	0.650782	+	0.759265i	$0.274441\pi$
$588$		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	$0.0502139\pi$
$593$	27.8748	+	27.8748i	1.14468	+	1.14468i	0.157098	+	0.987583i	$0.449786\pi$
$594$		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	$-0.751858\pi$
$599$	−34.8136			−1.42244			−0.711222	+	0.702968i	$0.751858\pi$
$600$		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	−0.0538984	−	0.998546i	$-0.517165\pi$
$617$	23.4646	−	23.4646i	0.944648	−	0.944648i	0.998546	+	0.0538984i	$0.0171647\pi$
$618$		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	$0.182536\pi$
$641$			27.4718i			1.08507i	−0.840033	+	0.542536i	$0.817464\pi$
$642$		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	−0.637638	−	0.770336i	$-0.720088\pi$
$647$	3.37534	−	3.37534i	0.132698	−	0.132698i	0.770336	+	0.637638i	$0.220088\pi$
$648$		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	0.927919	−	0.372783i	$-0.121596\pi$
$653$	14.1859	+	14.1859i	0.555135	+	0.555135i	−0.372783	+	0.927919i	$0.621596\pi$
$654$		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	$-0.413865\pi$
$659$	13.7242			0.534621			0.267310	+	0.963610i	$0.413865\pi$
$660$		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	−0.148786	−	0.988869i	$-0.547536\pi$
$677$	21.8583	−	21.8583i	0.840084	−	0.840084i	0.988869	+	0.148786i	$0.0475365\pi$
$678$		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	0.706731	−	0.707483i	$-0.250169\pi$
$683$	−0.0196459	−	0.0196459i	−0.000751731	−	0.000751731i	−0.707483	+	0.706731i	$0.750169\pi$
$684$		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	$0.294148\pi$
$701$			42.2603i			1.59615i	−0.602559	+	0.798074i	$0.705852\pi$
$702$		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	$-0.718643\pi$
$719$	−34.0076			−1.26827			−0.634135	+	0.773223i	$0.718643\pi$
$720$		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	0.980653	−	0.195754i	$-0.0627153\pi$
$743$	21.3948	+	21.3948i	0.784899	+	0.784899i	−0.195754	+	0.980653i	$0.562715\pi$
$744$		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	$-0.950221\pi$
$761$		−	8.59311i		−	0.311500i	0.987797	−	0.155750i	$-0.0497794\pi$
$762$		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	0.513326	−	0.858194i	$-0.328413\pi$
$773$	−9.58833	−	9.58833i	−0.344868	−	0.344868i	−0.858194	+	0.513326i	$0.828413\pi$
$774$		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	$-0.390667\pi$
$797$	36.0894	−	36.0894i	1.27835	−	1.27835i	0.941589	−	0.336765i	$-0.109333\pi$
$798$		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	$-0.428213\pi$
$809$	12.7207			0.447237			0.223619	+	0.974677i	$0.428213\pi$
$810$		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	$0.137642\pi$
$821$			24.0151i			0.838132i	−0.907956	+	0.419066i	$0.862358\pi$
$822$		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	$0.504341\pi$
$827$	−29.1471	+	29.1471i	−1.01354	+	1.01354i	−0.999907	+	0.0136368i	$0.995659\pi$
$828$		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	$-0.815973\pi$
$839$	−48.5162			−1.67496			−0.837482	+	0.546464i	$0.815973\pi$
$840$		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	−0.813142	−	0.582065i	$-0.802245\pi$
$857$	−6.76469	+	6.76469i	−0.231077	+	0.231077i	0.582065	+	0.813142i	$0.302245\pi$
$858$		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	0.184729	−	0.982790i	$-0.440859\pi$
$863$	−23.4445	−	23.4445i	−0.798061	−	0.798061i	−0.982790	+	0.184729i	$0.940859\pi$
$864$		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	$-0.950971\pi$
$881$		−	9.10761i		−	0.306843i	0.988161	−	0.153422i	$-0.0490293\pi$
$882$		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	−0.548587	−	0.836093i	$-0.684834\pi$
$887$	8.56265	−	8.56265i	0.287506	−	0.287506i	0.836093	+	0.548587i	$0.184834\pi$
$888$		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	$0.315892\pi$
$911$			50.5467i			1.67469i	−0.546677	+	0.837343i	$0.684108\pi$
$912$		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	$-0.213094\pi$
$929$	47.8016			1.56832			0.784160	+	0.620559i	$0.213094\pi$
$930$		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	$-0.751150\pi$
$941$		−	43.2250i		−	1.40909i	0.709657	−	0.704547i	$-0.248850\pi$
$942$		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	−0.473939	−	0.880558i	$-0.657168\pi$
$947$	12.5130	−	12.5130i	0.406618	−	0.406618i	0.880558	+	0.473939i	$0.157168\pi$
$948$		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	0.415131	−	0.909762i	$-0.363736\pi$
$953$	−15.2696	−	15.2696i	−0.494631	−	0.494631i	−0.909762	+	0.415131i	$0.863736\pi$
$954$		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	$-0.864719\pi$
$971$		−	25.6964i		−	0.824636i	0.911040	−	0.412318i	$-0.135281\pi$
$972$		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	$0.572883\pi$
$977$	−37.5357	+	37.5357i	−1.20087	+	1.20087i	−0.973901	+	0.226973i	$0.927117\pi$
$978$		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	0.849524	−	0.527551i	$-0.176890\pi$
$983$	10.0948	+	10.0948i	0.321973	+	0.321973i	−0.527551	+	0.849524i	$0.676890\pi$
$984$		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.737.2	yes	16
3.2	odd	2	inner	2070.2.j.i.737.7	yes	16
5.3	odd	4	inner	2070.2.j.i.323.7	yes	16
15.8	even	4	inner	2070.2.j.i.323.2	✓	16

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
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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