LMFDB - Embedded newform 832.2.ba.b.225.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [832,2,Mod(225,832)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(832, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("832.225");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 832 = 2^{6} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	832.ba (of order $6$, 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:	$6.64355344817$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			225.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	832.225
Dual form			832.2.ba.b.673.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.36603 - 1.36603i) q^{3} -1.73205 q^{5} +(1.73205 - 1.00000i) q^{7} +(2.23205 + 3.86603i) q^{9} +(1.73205 - 3.00000i) q^{11} +(3.59808 - 0.232051i) q^{13} +(4.09808 + 2.36603i) q^{15} +(0.232051 + 0.401924i) q^{17} +(-2.36603 - 4.09808i) q^{19} -5.46410 q^{21} +(2.36603 - 4.09808i) q^{23} -2.00000 q^{25} -4.00000i q^{27} +(0.401924 + 0.232051i) q^{29} -0.196152i q^{31} +(-8.19615 + 4.73205i) q^{33} +(-3.00000 + 1.73205i) q^{35} +(-4.59808 + 7.96410i) q^{37} +(-8.83013 - 4.36603i) q^{39} +(-4.50000 - 2.59808i) q^{41} +(-10.7321 + 6.19615i) q^{43} +(-3.86603 - 6.69615i) q^{45} -11.6603i q^{47} +(-1.50000 + 2.59808i) q^{49} -1.26795i q^{51} -12.4641i q^{53} +(-3.00000 + 5.19615i) q^{55} +12.9282i q^{57} +(0.464102 + 0.803848i) q^{59} +(11.5981 - 6.69615i) q^{61} +(7.73205 + 4.46410i) q^{63} +(-6.23205 + 0.401924i) q^{65} +(-4.09808 + 7.09808i) q^{67} +(-11.1962 + 6.46410i) q^{69} +(-10.0981 + 5.83013i) q^{71} -5.19615i q^{73} +(4.73205 + 2.73205i) q^{75} -6.92820i q^{77} +6.00000 q^{79} +(1.23205 - 2.13397i) q^{81} -2.53590 q^{83} +(-0.401924 - 0.696152i) q^{85} +(-0.633975 - 1.09808i) q^{87} +(-13.3923 - 7.73205i) q^{89} +(6.00000 - 4.00000i) q^{91} +(-0.267949 + 0.464102i) q^{93} +(4.09808 + 7.09808i) q^{95} +(5.19615 - 3.00000i) q^{97} +15.4641 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{3} + 2 q^{9} + 4 q^{13} + 6 q^{15} - 6 q^{17} - 6 q^{19} - 8 q^{21} + 6 q^{23} - 8 q^{25} + 12 q^{29} - 12 q^{33} - 12 q^{35} - 8 q^{37} - 18 q^{39} - 18 q^{41} - 36 q^{43} - 12 q^{45} - 6 q^{49}+ \cdots + 48 q^{99}+O(q^{100}) $ 4 * q - 6 * q^3 + 2 * q^9 + 4 * q^13 + 6 * q^15 - 6 * q^17 - 6 * q^19 - 8 * q^21 + 6 * q^23 - 8 * q^25 + 12 * q^29 - 12 * q^33 - 12 * q^35 - 8 * q^37 - 18 * q^39 - 18 * q^41 - 36 * q^43 - 12 * q^45 - 6 * q^49 - 12 * q^55 - 12 * q^59 + 36 * q^61 + 24 * q^63 - 18 * q^65 - 6 * q^67 - 24 * q^69 - 30 * q^71 + 12 * q^75 + 24 * q^79 - 2 * q^81 - 24 * q^83 - 12 * q^85 - 6 * q^87 - 12 * q^89 + 24 * q^91 - 8 * q^93 + 6 * q^95 + 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/832\mathbb{Z}\right)^\times$.

$n$	$261$	$703$	$769$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.36603	−	1.36603i	−1.36603	−	0.788675i	−0.375608	−	0.926779i	$-0.622566\pi$
$3$	−2.36603	−	1.36603i	−1.36603	−	0.788675i	−0.990418	+	0.138104i	$0.955899\pi$
$4$		0			0
$5$	−1.73205			−0.774597			−0.387298	−	0.921954i	$-0.626592\pi$
$5$	−1.73205			−0.774597			−0.387298	+	0.921954i	$0.626592\pi$
$6$		0			0
$7$	1.73205	−	1.00000i	0.654654	−	0.377964i	−0.135583	−	0.990766i	$-0.543291\pi$
$7$	1.73205	−	1.00000i	0.654654	−	0.377964i	0.790237	+	0.612801i	$0.209957\pi$
$8$		0			0
$9$	2.23205	+	3.86603i	0.744017	+	1.28868i
$10$		0			0
$11$	1.73205	−	3.00000i	0.522233	−	0.904534i	−0.477432	−	0.878668i	$-0.658432\pi$
$11$	1.73205	−	3.00000i	0.522233	−	0.904534i	0.999665	−	0.0258656i	$-0.00823419\pi$
$12$		0			0
$13$	3.59808	−	0.232051i	0.997927	−	0.0643593i
$13$	3.59808	−	0.232051i	0.997927	−	0.0643593i
$14$		0			0
$15$	4.09808	+	2.36603i	1.05812	+	0.610905i
$16$		0			0
$17$	0.232051	+	0.401924i	0.0562806	+	0.0974808i	0.892793	−	0.450467i	$-0.148743\pi$
$17$	0.232051	+	0.401924i	0.0562806	+	0.0974808i	−0.836512	+	0.547948i	$0.815409\pi$
$18$		0			0
$19$	−2.36603	−	4.09808i	−0.542803	−	0.940163i	−0.998742	−	0.0501517i	$-0.984030\pi$
$19$	−2.36603	−	4.09808i	−0.542803	−	0.940163i	0.455938	−	0.890011i	$-0.349304\pi$
$20$		0			0
$21$	−5.46410			−1.19236
$22$		0			0
$23$	2.36603	−	4.09808i	0.493350	−	0.854508i	−0.506620	−	0.862169i	$-0.669105\pi$
$23$	2.36603	−	4.09808i	0.493350	−	0.854508i	0.999971	+	0.00766135i	$0.00243871\pi$
$24$		0			0
$25$	−2.00000			−0.400000
$26$		0			0
$27$		−	4.00000i		−	0.769800i
$28$		0			0
$29$	0.401924	+	0.232051i	0.0746354	+	0.0430908i	0.536853	−	0.843676i	$-0.319613\pi$
$29$	0.401924	+	0.232051i	0.0746354	+	0.0430908i	−0.462218	+	0.886766i	$0.652946\pi$
$30$		0			0
$31$		−	0.196152i		−	0.0352300i	−0.999845	−	0.0176150i	$-0.994393\pi$
$31$		−	0.196152i		−	0.0352300i	0.999845	−	0.0176150i	$-0.00560732\pi$
$32$		0			0
$33$	−8.19615	+	4.73205i	−1.42677	+	0.823744i
$34$		0			0
$35$	−3.00000	+	1.73205i	−0.507093	+	0.292770i
$36$		0			0
$37$	−4.59808	+	7.96410i	−0.755919	+	1.30929i	0.188997	+	0.981978i	$0.439476\pi$
$37$	−4.59808	+	7.96410i	−0.755919	+	1.30929i	−0.944916	+	0.327313i	$0.893857\pi$
$38$		0			0
$39$	−8.83013	−	4.36603i	−1.41395	−	0.699124i
$40$		0			0
$41$	−4.50000	−	2.59808i	−0.702782	−	0.405751i	0.105601	−	0.994409i	$-0.466323\pi$
$41$	−4.50000	−	2.59808i	−0.702782	−	0.405751i	−0.808383	+	0.588657i	$0.799657\pi$
$42$		0			0
$43$	−10.7321	+	6.19615i	−1.63662	+	0.944904i	−0.654638	+	0.755943i	$0.727179\pi$
$43$	−10.7321	+	6.19615i	−1.63662	+	0.944904i	−0.981984	+	0.188962i	$0.939488\pi$
$44$		0			0
$45$	−3.86603	−	6.69615i	−0.576313	−	0.998203i
$46$		0			0
$47$		−	11.6603i		−	1.70082i	−0.526118	−	0.850411i	$-0.676353\pi$
$47$		−	11.6603i		−	1.70082i	0.526118	−	0.850411i	$-0.323647\pi$
$48$		0			0
$49$	−1.50000	+	2.59808i	−0.214286	+	0.371154i
$50$		0			0
$51$		−	1.26795i		−	0.177548i
$52$		0			0
$53$		−	12.4641i		−	1.71208i	−0.516913	−	0.856038i	$-0.672919\pi$
$53$		−	12.4641i		−	1.71208i	0.516913	−	0.856038i	$-0.327081\pi$
$54$		0			0
$55$	−3.00000	+	5.19615i	−0.404520	+	0.700649i
$56$		0			0
$57$			12.9282i			1.71238i
$58$		0			0
$59$	0.464102	+	0.803848i	0.0604209	+	0.104652i	0.894654	−	0.446760i	$-0.147422\pi$
$59$	0.464102	+	0.803848i	0.0604209	+	0.104652i	−0.834233	+	0.551413i	$0.814089\pi$
$60$		0			0
$61$	11.5981	−	6.69615i	1.48498	−	0.857354i	0.485128	−	0.874443i	$-0.338773\pi$
$61$	11.5981	−	6.69615i	1.48498	−	0.857354i	0.999854	+	0.0170890i	$0.00543985\pi$
$62$		0			0
$63$	7.73205	+	4.46410i	0.974147	+	0.562424i
$64$		0			0
$65$	−6.23205	+	0.401924i	−0.772991	+	0.0498525i
$66$		0			0
$67$	−4.09808	+	7.09808i	−0.500660	+	0.867168i	0.499340	+	0.866406i	$0.333576\pi$
$67$	−4.09808	+	7.09808i	−0.500660	+	0.867168i	−1.00000		0.000761916i	$0.999757\pi$
$68$		0			0
$69$	−11.1962	+	6.46410i	−1.34786	+	0.778186i
$70$		0			0
$71$	−10.0981	+	5.83013i	−1.19842	+	0.691909i	−0.960203	−	0.279303i	$-0.909897\pi$
$71$	−10.0981	+	5.83013i	−1.19842	+	0.691909i	−0.238218	+	0.971212i	$0.576563\pi$
$72$		0			0
$73$		−	5.19615i		−	0.608164i	−0.952646	−	0.304082i	$-0.901650\pi$
$73$		−	5.19615i		−	0.608164i	0.952646	−	0.304082i	$-0.0983496\pi$
$74$		0			0
$75$	4.73205	+	2.73205i	0.546410	+	0.315470i
$76$		0			0
$77$		−	6.92820i		−	0.789542i
$78$		0			0
$79$	6.00000			0.675053			0.337526	−	0.941316i	$-0.390410\pi$
$79$	6.00000			0.675053			0.337526	+	0.941316i	$0.390410\pi$
$80$		0			0
$81$	1.23205	−	2.13397i	0.136895	−	0.237108i
$82$		0			0
$83$	−2.53590			−0.278351			−0.139176	−	0.990268i	$-0.544445\pi$
$83$	−2.53590			−0.278351			−0.139176	+	0.990268i	$0.544445\pi$
$84$		0			0
$85$	−0.401924	−	0.696152i	−0.0435948	−	0.0755083i
$86$		0			0
$87$	−0.633975	−	1.09808i	−0.0679692	−	0.117726i
$88$		0			0
$89$	−13.3923	−	7.73205i	−1.41958	−	0.819596i	−0.423320	−	0.905980i	$-0.639135\pi$
$89$	−13.3923	−	7.73205i	−1.41958	−	0.819596i	−0.996262	+	0.0863847i	$0.972469\pi$
$90$		0			0
$91$	6.00000	−	4.00000i	0.628971	−	0.419314i
$92$		0			0
$93$	−0.267949	+	0.464102i	−0.0277850	+	0.0481251i
$94$		0			0
$95$	4.09808	+	7.09808i	0.420454	+	0.728247i
$96$		0			0
$97$	5.19615	−	3.00000i	0.527589	−	0.304604i	−0.212445	−	0.977173i	$-0.568143\pi$
$97$	5.19615	−	3.00000i	0.527589	−	0.304604i	0.740034	+	0.672569i	$0.234809\pi$
$98$		0			0
$99$	15.4641			1.55420
$100$		0			0
$101$	8.59808	+	4.96410i	0.855541	+	0.493947i	0.862516	−	0.506029i	$-0.168887\pi$
$101$	8.59808	+	4.96410i	0.855541	+	0.493947i	−0.00697585	+	0.999976i	$0.502220\pi$
$102$		0			0
$103$	−13.2679			−1.30733			−0.653665	−	0.756784i	$-0.726769\pi$
$103$	−13.2679			−1.30733			−0.653665	+	0.756784i	$0.726769\pi$
$104$		0			0
$105$	9.46410			0.923602
$106$		0			0
$107$	−12.2942	−	7.09808i	−1.18853	−	0.686197i	−0.230556	−	0.973059i	$-0.574055\pi$
$107$	−12.2942	−	7.09808i	−1.18853	−	0.686197i	−0.957972	+	0.286862i	$0.907388\pi$
$108$		0			0
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$		0			0
$111$	21.7583	−	12.5622i	2.06521	−	1.19235i
$112$		0			0
$113$	1.50000	+	2.59808i	0.141108	+	0.244406i	0.927914	−	0.372794i	$-0.121600\pi$
$113$	1.50000	+	2.59808i	0.141108	+	0.244406i	−0.786806	+	0.617200i	$0.788267\pi$
$114$		0			0
$115$	−4.09808	+	7.09808i	−0.382148	+	0.661899i
$116$		0			0
$117$	8.92820	+	13.3923i	0.825413	+	1.23812i
$118$		0			0
$119$	0.803848	+	0.464102i	0.0736886	+	0.0425441i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$		0			0
$123$	7.09808	+	12.2942i	0.640012	+	1.10853i
$124$		0			0
$125$	12.1244			1.08444
$126$		0			0
$127$	−2.83013	+	4.90192i	−0.251133	+	0.434975i	−0.963838	−	0.266489i	$-0.914137\pi$
$127$	−2.83013	+	4.90192i	−0.251133	+	0.434975i	0.712705	+	0.701464i	$0.247470\pi$
$128$		0			0
$129$	33.8564			2.98089
$130$		0			0
$131$		−	21.1244i		−	1.84564i	−0.385227	−	0.922822i	$-0.625877\pi$
$131$		−	21.1244i		−	1.84564i	0.385227	−	0.922822i	$-0.374123\pi$
$132$		0			0
$133$	−8.19615	−	4.73205i	−0.710697	−	0.410321i
$134$		0			0
$135$			6.92820i			0.596285i
$136$		0			0
$137$	5.30385	−	3.06218i	0.453138	−	0.261620i	−0.256016	−	0.966672i	$-0.582410\pi$
$137$	5.30385	−	3.06218i	0.453138	−	0.261620i	0.709155	+	0.705053i	$0.249077\pi$
$138$		0			0
$139$	0.339746	−	0.196152i	0.0288169	−	0.0166374i	−0.485522	−	0.874224i	$-0.661371\pi$
$139$	0.339746	−	0.196152i	0.0288169	−	0.0166374i	0.514339	+	0.857587i	$0.328037\pi$
$140$		0			0
$141$	−15.9282	+	27.5885i	−1.34140	+	2.32337i
$142$		0			0
$143$	5.53590	−	11.1962i	0.462935	−	0.936269i
$144$		0			0
$145$	−0.696152	−	0.401924i	−0.0578123	−	0.0333780i
$146$		0			0
$147$	7.09808	−	4.09808i	0.585439	−	0.338004i
$148$		0			0
$149$	−2.59808	−	4.50000i	−0.212843	−	0.368654i	0.739760	−	0.672870i	$-0.234939\pi$
$149$	−2.59808	−	4.50000i	−0.212843	−	0.368654i	−0.952603	+	0.304216i	$0.901606\pi$
$150$		0			0
$151$		−	11.8038i		−	0.960583i	−0.877109	−	0.480292i	$-0.840531\pi$
$151$		−	11.8038i		−	0.960583i	0.877109	−	0.480292i	$-0.159469\pi$
$152$		0			0
$153$	−1.03590	+	1.79423i	−0.0837474	+	0.145055i
$154$		0			0
$155$			0.339746i			0.0272891i
$156$		0			0
$157$			14.3205i			1.14290i	0.820637	+	0.571450i	$0.193619\pi$
$157$			14.3205i			1.14290i	−0.820637	+	0.571450i	$0.806381\pi$
$158$		0			0
$159$	−17.0263	+	29.4904i	−1.35027	+	2.33874i
$160$		0			0
$161$		−	9.46410i		−	0.745876i
$162$		0			0
$163$	4.73205	+	8.19615i	0.370643	+	0.641972i	0.989665	−	0.143402i	$-0.0458041\pi$
$163$	4.73205	+	8.19615i	0.370643	+	0.641972i	−0.619022	+	0.785374i	$0.712471\pi$
$164$		0			0
$165$	14.1962	−	8.19615i	1.10517	−	0.638070i
$166$		0			0
$167$	9.00000	+	5.19615i	0.696441	+	0.402090i	0.806020	−	0.591888i	$-0.201617\pi$
$167$	9.00000	+	5.19615i	0.696441	+	0.402090i	−0.109580	+	0.993978i	$0.534950\pi$
$168$		0			0
$169$	12.8923	−	1.66987i	0.991716	−	0.128452i
$170$		0			0
$171$	10.5622	−	18.2942i	0.807710	−	1.39899i
$172$		0			0
$173$	−10.3923	+	6.00000i	−0.790112	+	0.456172i	−0.840002	−	0.542583i	$-0.817446\pi$
$173$	−10.3923	+	6.00000i	−0.790112	+	0.456172i	0.0498898	+	0.998755i	$0.484113\pi$
$174$		0			0
$175$	−3.46410	+	2.00000i	−0.261861	+	0.151186i
$176$		0			0
$177$		−	2.53590i		−	0.190610i
$178$		0			0
$179$	12.0000	+	6.92820i	0.896922	+	0.517838i	0.876200	−	0.481947i	$-0.160070\pi$
$179$	12.0000	+	6.92820i	0.896922	+	0.517838i	0.0207218	+	0.999785i	$0.493404\pi$
$180$		0			0
$181$		−	9.92820i		−	0.737958i	−0.929438	−	0.368979i	$-0.879708\pi$
$181$		−	9.92820i		−	0.737958i	0.929438	−	0.368979i	$-0.120292\pi$
$182$		0			0
$183$	−36.5885			−2.70470
$184$		0			0
$185$	7.96410	−	13.7942i	0.585532	−	1.01417i
$186$		0			0
$187$	1.60770			0.117566
$188$		0			0
$189$	−4.00000	−	6.92820i	−0.290957	−	0.503953i
$190$		0			0
$191$	8.02628	+	13.9019i	0.580761	+	1.00591i	0.995389	+	0.0959170i	$0.0305783\pi$
$191$	8.02628	+	13.9019i	0.580761	+	1.00591i	−0.414628	+	0.909991i	$0.636088\pi$
$192$		0			0
$193$	−12.6962	−	7.33013i	−0.913889	−	0.527634i	−0.0322086	−	0.999481i	$-0.510254\pi$
$193$	−12.6962	−	7.33013i	−0.913889	−	0.527634i	−0.881680	+	0.471847i	$0.843587\pi$
$194$		0			0
$195$	15.2942	+	7.56218i	1.09524	+	0.541539i
$196$		0			0
$197$	−1.73205	+	3.00000i	−0.123404	+	0.213741i	−0.921108	−	0.389308i	$-0.872714\pi$
$197$	−1.73205	+	3.00000i	−0.123404	+	0.213741i	0.797704	+	0.603049i	$0.206048\pi$
$198$		0			0
$199$	−3.29423	−	5.70577i	−0.233522	−	0.404471i	0.725320	−	0.688412i	$-0.241692\pi$
$199$	−3.29423	−	5.70577i	−0.233522	−	0.404471i	−0.958842	+	0.283940i	$0.908358\pi$
$200$		0			0
$201$	19.3923	−	11.1962i	1.36783	−	0.789716i
$202$		0			0
$203$	0.928203			0.0651471
$204$		0			0
$205$	7.79423	+	4.50000i	0.544373	+	0.314294i
$206$		0			0
$207$	21.1244			1.46824
$208$		0			0
$209$	−16.3923			−1.13388
$210$		0			0
$211$	5.36603	+	3.09808i	0.369412	+	0.213280i	0.673202	−	0.739459i	$-0.264919\pi$
$211$	5.36603	+	3.09808i	0.369412	+	0.213280i	−0.303789	+	0.952739i	$0.598252\pi$
$212$		0			0
$213$	31.8564			2.18277
$214$		0			0
$215$	18.5885	−	10.7321i	1.26772	−	0.731920i
$216$		0			0
$217$	−0.196152	−	0.339746i	−0.0133157	−	0.0230635i
$218$		0			0
$219$	−7.09808	+	12.2942i	−0.479644	+	0.830767i
$220$		0			0
$221$	0.928203	+	1.39230i	0.0624377	+	0.0936566i
$222$		0			0
$223$	−10.5622	−	6.09808i	−0.707296	−	0.408357i	0.102763	−	0.994706i	$-0.467232\pi$
$223$	−10.5622	−	6.09808i	−0.707296	−	0.408357i	−0.810059	+	0.586348i	$0.800565\pi$
$224$		0			0
$225$	−4.46410	−	7.73205i	−0.297607	−	0.515470i
$226$		0			0
$227$	−4.90192	−	8.49038i	−0.325352	−	0.563526i	0.656231	−	0.754560i	$-0.272149\pi$
$227$	−4.90192	−	8.49038i	−0.325352	−	0.563526i	−0.981584	+	0.191033i	$0.938816\pi$
$228$		0			0
$229$	22.7846			1.50565			0.752825	−	0.658221i	$-0.228691\pi$
$229$	22.7846			1.50565			0.752825	+	0.658221i	$0.228691\pi$
$230$		0			0
$231$	−9.46410	+	16.3923i	−0.622692	+	1.07853i
$232$		0			0
$233$	−25.8564			−1.69391			−0.846955	−	0.531665i	$-0.821567\pi$
$233$	−25.8564			−1.69391			−0.846955	+	0.531665i	$0.821567\pi$
$234$		0			0
$235$			20.1962i			1.31745i
$236$		0			0
$237$	−14.1962	−	8.19615i	−0.922139	−	0.532397i
$238$		0			0
$239$		−	0.928203i		−	0.0600405i	−0.999549	−	0.0300202i	$-0.990443\pi$
$239$		−	0.928203i		−	0.0600405i	0.999549	−	0.0300202i	$-0.00955717\pi$
$240$		0			0
$241$	15.6962	−	9.06218i	1.01108	−	0.583746i	0.0995709	−	0.995030i	$-0.468253\pi$
$241$	15.6962	−	9.06218i	1.01108	−	0.583746i	0.911507	+	0.411284i	$0.134920\pi$
$242$		0			0
$243$	−16.2224	+	9.36603i	−1.04067	+	0.600831i
$244$		0			0
$245$	2.59808	−	4.50000i	0.165985	−	0.287494i
$246$		0			0
$247$	−9.46410	−	14.1962i	−0.602186	−	0.903280i
$248$		0			0
$249$	6.00000	+	3.46410i	0.380235	+	0.219529i
$250$		0			0
$251$	−1.90192	+	1.09808i	−0.120048	+	0.0693100i	−0.558822	−	0.829288i	$-0.688746\pi$
$251$	−1.90192	+	1.09808i	−0.120048	+	0.0693100i	0.438773	+	0.898598i	$0.355413\pi$
$252$		0			0
$253$	−8.19615	−	14.1962i	−0.515288	−	0.892504i
$254$		0			0
$255$			2.19615i			0.137528i
$256$		0			0
$257$	−5.42820	+	9.40192i	−0.338602	+	0.586476i	−0.984170	−	0.177227i	$-0.943287\pi$
$257$	−5.42820	+	9.40192i	−0.338602	+	0.586476i	0.645568	+	0.763703i	$0.276621\pi$
$258$		0			0
$259$			18.3923i			1.14284i
$260$		0			0
$261$			2.07180i			0.128241i
$262$		0			0
$263$	−9.12436	+	15.8038i	−0.562632	+	0.974507i	0.434634	+	0.900607i	$0.356878\pi$
$263$	−9.12436	+	15.8038i	−0.562632	+	0.974507i	−0.997266	+	0.0738997i	$0.976456\pi$
$264$		0			0
$265$			21.5885i			1.32617i
$266$		0			0
$267$	21.1244	+	36.5885i	1.29279	+	2.23918i
$268$		0			0
$269$	−2.19615	+	1.26795i	−0.133902	+	0.0773082i	−0.565455	−	0.824779i	$-0.691299\pi$
$269$	−2.19615	+	1.26795i	−0.133902	+	0.0773082i	0.431553	+	0.902088i	$0.357966\pi$
$270$		0			0
$271$	16.2679	+	9.39230i	0.988208	+	0.570542i	0.904738	−	0.425968i	$-0.140067\pi$
$271$	16.2679	+	9.39230i	0.988208	+	0.570542i	0.0834695	+	0.996510i	$0.473400\pi$
$272$		0			0
$273$	−19.6603	+	1.26795i	−1.18989	+	0.0767398i
$274$		0			0
$275$	−3.46410	+	6.00000i	−0.208893	+	0.361814i
$276$		0			0
$277$	−15.4019	+	8.89230i	−0.925412	+	0.534287i	−0.885358	−	0.464911i	$-0.846086\pi$
$277$	−15.4019	+	8.89230i	−0.925412	+	0.534287i	−0.0400543	+	0.999198i	$0.512753\pi$
$278$		0			0
$279$	0.758330	−	0.437822i	0.0454000	−	0.0262117i
$280$		0			0
$281$			16.2679i			0.970464i	0.874385	+	0.485232i	$0.161265\pi$
$281$			16.2679i			0.970464i	−0.874385	+	0.485232i	$0.838735\pi$
$282$		0			0
$283$	−12.4641	−	7.19615i	−0.740914	−	0.427767i	0.0814876	−	0.996674i	$-0.474033\pi$
$283$	−12.4641	−	7.19615i	−0.740914	−	0.427767i	−0.822402	+	0.568907i	$0.807366\pi$
$284$		0			0
$285$		−	22.3923i		−	1.32641i
$286$		0			0
$287$	−10.3923			−0.613438
$288$		0			0
$289$	8.39230	−	14.5359i	0.493665	−	0.855053i
$290$		0			0
$291$	−16.3923			−0.960934
$292$		0			0
$293$	−15.8660	−	27.4808i	−0.926903	−	1.60544i	−0.788472	−	0.615071i	$-0.789127\pi$
$293$	−15.8660	−	27.4808i	−0.926903	−	1.60544i	−0.138432	−	0.990372i	$-0.544206\pi$
$294$		0			0
$295$	−0.803848	−	1.39230i	−0.0468018	−	0.0810631i
$296$		0			0
$297$	−12.0000	−	6.92820i	−0.696311	−	0.402015i
$298$		0			0
$299$	7.56218	−	15.2942i	0.437332	−	0.884488i
$300$		0			0
$301$	−12.3923	+	21.4641i	−0.714281	+	1.23717i
$302$		0			0
$303$	−13.5622	−	23.4904i	−0.779127	−	1.34949i
$304$		0			0
$305$	−20.0885	+	11.5981i	−1.15026	+	0.664104i
$306$		0			0
$307$	5.66025			0.323048			0.161524	−	0.986869i	$-0.448359\pi$
$307$	5.66025			0.323048			0.161524	+	0.986869i	$0.448359\pi$
$308$		0			0
$309$	31.3923	+	18.1244i	1.78585	+	1.03106i
$310$		0			0
$311$	10.7321			0.608559			0.304279	−	0.952583i	$-0.401584\pi$
$311$	10.7321			0.608559			0.304279	+	0.952583i	$0.401584\pi$
$312$		0			0
$313$	−11.6077			−0.656106			−0.328053	−	0.944659i	$-0.606392\pi$
$313$	−11.6077			−0.656106			−0.328053	+	0.944659i	$0.606392\pi$
$314$		0			0
$315$	−13.3923	−	7.73205i	−0.754571	−	0.435652i
$316$		0			0
$317$	24.8038			1.39312			0.696561	−	0.717497i	$-0.254712\pi$
$317$	24.8038			1.39312			0.696561	+	0.717497i	$0.254712\pi$
$318$		0			0
$319$	1.39230	−	0.803848i	0.0779541	−	0.0450068i
$320$		0			0
$321$	19.3923	+	33.5885i	1.08237	+	1.87472i
$322$		0			0
$323$	1.09808	−	1.90192i	0.0610986	−	0.105826i
$324$		0			0
$325$	−7.19615	+	0.464102i	−0.399171	+	0.0257437i
$326$		0			0
$327$	−4.73205	−	2.73205i	−0.261683	−	0.151083i
$328$		0			0
$329$	−11.6603	−	20.1962i	−0.642851	−	1.11345i
$330$		0			0
$331$	−10.3923	−	18.0000i	−0.571213	−	0.989369i	−0.996442	−	0.0842837i	$-0.973140\pi$
$331$	−10.3923	−	18.0000i	−0.571213	−	0.989369i	0.425229	−	0.905086i	$-0.360194\pi$
$332$		0			0
$333$	−41.0526			−2.24967
$334$		0			0
$335$	7.09808	−	12.2942i	0.387809	−	0.671705i
$336$		0			0
$337$	21.3923			1.16531			0.582657	−	0.812718i	$-0.302013\pi$
$337$	21.3923			1.16531			0.582657	+	0.812718i	$0.302013\pi$
$338$		0			0
$339$		−	8.19615i		−	0.445154i
$340$		0			0
$341$	−0.588457	−	0.339746i	−0.0318667	−	0.0183983i
$342$		0			0
$343$			20.0000i			1.07990i
$344$		0			0
$345$	19.3923	−	11.1962i	1.04405	−	0.602781i
$346$		0			0
$347$	24.8827	−	14.3660i	1.33577	−	0.771209i	0.349595	−	0.936901i	$-0.386319\pi$
$347$	24.8827	−	14.3660i	1.33577	−	0.771209i	0.986178	+	0.165692i	$0.0529858\pi$
$348$		0			0
$349$	−4.80385	+	8.32051i	−0.257144	+	0.445387i	−0.965476	−	0.260493i	$-0.916115\pi$
$349$	−4.80385	+	8.32051i	−0.257144	+	0.445387i	0.708332	+	0.705880i	$0.249448\pi$
$350$		0			0
$351$	−0.928203	−	14.3923i	−0.0495438	−	0.768204i
$352$		0			0
$353$	−26.8923	−	15.5263i	−1.43133	−	0.826380i	−0.434110	−	0.900860i	$-0.642937\pi$
$353$	−26.8923	−	15.5263i	−1.43133	−	0.826380i	−0.997223	+	0.0744792i	$0.976271\pi$
$354$		0			0
$355$	17.4904	−	10.0981i	0.928293	−	0.535950i
$356$		0			0
$357$	−1.26795	−	2.19615i	−0.0671070	−	0.116233i
$358$		0			0
$359$		0			0		1.00000			$0$
$359$		0			0		−1.00000			$\pi$
$360$		0			0
$361$	−1.69615	+	2.93782i	−0.0892712	+	0.154622i
$362$		0			0
$363$			2.73205i			0.143395i
$364$		0			0
$365$			9.00000i			0.471082i
$366$		0			0
$367$	1.09808	−	1.90192i	0.0573191	−	0.0992796i	−0.835942	−	0.548818i	$-0.815078\pi$
$367$	1.09808	−	1.90192i	0.0573191	−	0.0992796i	0.893261	+	0.449538i	$0.148411\pi$
$368$		0			0
$369$		−	23.1962i		−	1.20754i
$370$		0			0
$371$	−12.4641	−	21.5885i	−0.647104	−	1.12082i
$372$		0			0
$373$	7.20577	−	4.16025i	0.373101	−	0.215410i	−0.301712	−	0.953399i	$-0.597558\pi$
$373$	7.20577	−	4.16025i	0.373101	−	0.215410i	0.674812	+	0.737989i	$0.264225\pi$
$374$		0			0
$375$	−28.6865	−	16.5622i	−1.48137	−	0.855267i
$376$		0			0
$377$	1.50000	+	0.741670i	0.0772539	+	0.0381979i
$378$		0			0
$379$	3.29423	−	5.70577i	0.169213	−	0.293086i	−0.768930	−	0.639333i	$-0.779211\pi$
$379$	3.29423	−	5.70577i	0.169213	−	0.293086i	0.938143	+	0.346247i	$0.112544\pi$
$380$		0			0
$381$	13.3923	−	7.73205i	0.686109	−	0.396125i
$382$		0			0
$383$	22.3923	−	12.9282i	1.14419	−	0.660600i	0.196728	−	0.980458i	$-0.436968\pi$
$383$	22.3923	−	12.9282i	1.14419	−	0.660600i	0.947466	+	0.319858i	$0.103635\pi$
$384$		0			0
$385$			12.0000i			0.611577i
$386$		0			0
$387$	−47.9090	−	27.6603i	−2.43535	−	1.40605i
$388$		0			0
$389$		−	19.3923i		−	0.983229i	−0.870813	−	0.491614i	$-0.836407\pi$
$389$		−	19.3923i		−	0.983229i	0.870813	−	0.491614i	$-0.163593\pi$
$390$		0			0
$391$	2.19615			0.111064
$392$		0			0
$393$	−28.8564	+	49.9808i	−1.45561	+	2.52120i
$394$		0			0
$395$	−10.3923			−0.522894
$396$		0			0
$397$	−2.80385	−	4.85641i	−0.140721	−	0.243736i	0.787047	−	0.616893i	$-0.211609\pi$
$397$	−2.80385	−	4.85641i	−0.140721	−	0.243736i	−0.927768	+	0.373157i	$0.878275\pi$
$398$		0			0
$399$	12.9282	+	22.3923i	0.647220	+	1.12102i
$400$		0			0
$401$	32.6769	+	18.8660i	1.63181	+	0.942124i	0.983535	+	0.180715i	$0.0578413\pi$
$401$	32.6769	+	18.8660i	1.63181	+	0.942124i	0.648272	+	0.761409i	$0.275492\pi$
$402$		0			0
$403$	−0.0455173	−	0.705771i	−0.00226738	−	0.0351570i
$404$		0			0
$405$	−2.13397	+	3.69615i	−0.106038	+	0.183663i
$406$		0			0
$407$	15.9282	+	27.5885i	0.789532	+	1.36751i
$408$		0			0
$409$	24.6962	−	14.2583i	1.22115	−	0.705029i	0.255984	−	0.966681i	$-0.417601\pi$
$409$	24.6962	−	14.2583i	1.22115	−	0.705029i	0.965162	+	0.261652i	$0.0842673\pi$
$410$		0			0
$411$	−16.7321			−0.825331
$412$		0			0
$413$	1.60770	+	0.928203i	0.0791095	+	0.0456739i
$414$		0			0
$415$	4.39230			0.215610
$416$		0			0
$417$	−1.07180			−0.0524861
$418$		0			0
$419$	−10.0981	−	5.83013i	−0.493323	−	0.284820i	0.232629	−	0.972566i	$-0.425267\pi$
$419$	−10.0981	−	5.83013i	−0.493323	−	0.284820i	−0.725952	+	0.687745i	$0.758601\pi$
$420$		0			0
$421$	−23.5885			−1.14963			−0.574816	−	0.818283i	$-0.694926\pi$
$421$	−23.5885			−1.14963			−0.574816	+	0.818283i	$0.694926\pi$
$422$		0			0
$423$	45.0788	−	26.0263i	2.19181	−	1.26544i
$424$		0			0
$425$	−0.464102	−	0.803848i	−0.0225122	−	0.0389923i
$426$		0			0
$427$	13.3923	−	23.1962i	0.648099	−	1.12254i
$428$		0			0
$429$	−28.3923	+	18.9282i	−1.37079	+	0.913862i
$430$		0			0
$431$	−1.60770	−	0.928203i	−0.0774400	−	0.0447100i	0.460780	−	0.887514i	$-0.347570\pi$
$431$	−1.60770	−	0.928203i	−0.0774400	−	0.0447100i	−0.538220	+	0.842804i	$0.680903\pi$
$432$		0			0
$433$	7.89230	+	13.6699i	0.379280	+	0.656932i	0.990958	−	0.134175i	$-0.0428384\pi$
$433$	7.89230	+	13.6699i	0.379280	+	0.656932i	−0.611678	+	0.791107i	$0.709505\pi$
$434$		0			0
$435$	1.09808	+	1.90192i	0.0526487	+	0.0911903i
$436$		0			0
$437$	−22.3923			−1.07117
$438$		0			0
$439$	7.26795	−	12.5885i	0.346880	−	0.600814i	−0.638813	−	0.769362i	$-0.720574\pi$
$439$	7.26795	−	12.5885i	0.346880	−	0.600814i	0.985694	+	0.168548i	$0.0539077\pi$
$440$		0			0
$441$	−13.3923			−0.637729
$442$		0			0
$443$		−	5.07180i		−	0.240968i	−0.992715	−	0.120484i	$-0.961555\pi$
$443$		−	5.07180i		−	0.240968i	0.992715	−	0.120484i	$-0.0384447\pi$
$444$		0			0
$445$	23.1962	+	13.3923i	1.09960	+	0.634856i
$446$		0			0
$447$			14.1962i			0.671455i
$448$		0			0
$449$	−1.39230	+	0.803848i	−0.0657069	+	0.0379359i	−0.532494	−	0.846434i	$-0.678745\pi$
$449$	−1.39230	+	0.803848i	−0.0657069	+	0.0379359i	0.466787	+	0.884370i	$0.345412\pi$
$450$		0			0
$451$	−15.5885	+	9.00000i	−0.734032	+	0.423793i
$452$		0			0
$453$	−16.1244	+	27.9282i	−0.757588	+	1.31218i
$454$		0			0
$455$	−10.3923	+	6.92820i	−0.487199	+	0.324799i
$456$		0			0
$457$	27.4808	+	15.8660i	1.28550	+	0.742181i	0.977847	−	0.209319i	$-0.0671246\pi$
$457$	27.4808	+	15.8660i	1.28550	+	0.742181i	0.307648	+	0.951500i	$0.400458\pi$
$458$		0			0
$459$	1.60770	−	0.928203i	0.0750408	−	0.0433248i
$460$		0			0
$461$	1.33013	+	2.30385i	0.0619502	+	0.107301i	0.895337	−	0.445389i	$-0.146935\pi$
$461$	1.33013	+	2.30385i	0.0619502	+	0.107301i	−0.833387	+	0.552690i	$0.813601\pi$
$462$		0			0
$463$		−	20.3923i		−	0.947711i	−0.880603	−	0.473855i	$-0.842862\pi$
$463$		−	20.3923i		−	0.947711i	0.880603	−	0.473855i	$-0.157138\pi$
$464$		0			0
$465$	0.464102	−	0.803848i	0.0215222	−	0.0372775i
$466$		0			0
$467$		−	26.7846i		−	1.23944i	−0.784821	−	0.619722i	$-0.787245\pi$
$467$		−	26.7846i		−	1.23944i	0.784821	−	0.619722i	$-0.212755\pi$
$468$		0			0
$469$			16.3923i			0.756926i
$470$		0			0
$471$	19.5622	−	33.8827i	0.901378	−	1.56123i
$472$		0			0
$473$			42.9282i			1.97384i
$474$		0			0
$475$	4.73205	+	8.19615i	0.217121	+	0.376065i
$476$		0			0
$477$	48.1865	−	27.8205i	2.20631	−	1.27381i
$478$		0			0
$479$	−24.2942	−	14.0263i	−1.11003	−	0.640877i	−0.171194	−	0.985237i	$-0.554763\pi$
$479$	−24.2942	−	14.0263i	−1.11003	−	0.640877i	−0.938838	+	0.344360i	$0.888096\pi$
$480$		0			0
$481$	−14.6962	+	29.7224i	−0.670087	+	1.35523i
$482$		0			0
$483$	−12.9282	+	22.3923i	−0.588254	+	1.01889i
$484$		0			0
$485$	−9.00000	+	5.19615i	−0.408669	+	0.235945i
$486$		0			0
$487$	7.26795	−	4.19615i	0.329342	−	0.190146i	−0.326207	−	0.945298i	$-0.605771\pi$
$487$	7.26795	−	4.19615i	0.329342	−	0.190146i	0.655549	+	0.755153i	$0.272437\pi$
$488$		0			0
$489$		−	25.8564i		−	1.16927i
$490$		0			0
$491$	0.588457	+	0.339746i	0.0265567	+	0.0153325i	0.513220	−	0.858257i	$-0.328453\pi$
$491$	0.588457	+	0.339746i	0.0265567	+	0.0153325i	−0.486663	+	0.873590i	$0.661786\pi$
$492$		0			0
$493$			0.215390i			0.00970069i
$494$		0			0
$495$	−26.7846			−1.20388
$496$		0			0
$497$	−11.6603	+	20.1962i	−0.523034	+	0.905921i
$498$		0			0
$499$	9.80385			0.438880			0.219440	−	0.975626i	$-0.429577\pi$
$499$	9.80385			0.438880			0.219440	+	0.975626i	$0.429577\pi$
$500$		0			0
$501$	−14.1962	−	24.5885i	−0.634237	−	1.09853i
$502$		0			0
$503$	13.8564	+	24.0000i	0.617827	+	1.07011i	0.989882	+	0.141896i	$0.0453200\pi$
$503$	13.8564	+	24.0000i	0.617827	+	1.07011i	−0.372055	+	0.928211i	$0.621347\pi$
$504$		0			0
$505$	−14.8923	−	8.59808i	−0.662699	−	0.382609i
$506$		0			0
$507$	−32.7846	−	13.6603i	−1.45602	−	0.606673i
$508$		0			0
$509$	9.99038	−	17.3038i	0.442816	−	0.766980i	−0.555081	−	0.831796i	$-0.687313\pi$
$509$	9.99038	−	17.3038i	0.442816	−	0.766980i	0.997897	+	0.0648165i	$0.0206462\pi$
$510$		0			0
$511$	−5.19615	−	9.00000i	−0.229864	−	0.398137i
$512$		0			0
$513$	−16.3923	+	9.46410i	−0.723738	+	0.417850i
$514$		0			0
$515$	22.9808			1.01265
$516$		0			0
$517$	−34.9808	−	20.1962i	−1.53845	−	0.888226i
$518$		0			0
$519$	32.7846			1.43908
$520$		0			0
$521$	5.53590			0.242532			0.121266	−	0.992620i	$-0.461305\pi$
$521$	5.53590			0.242532			0.121266	+	0.992620i	$0.461305\pi$
$522$		0			0
$523$	−2.07180	−	1.19615i	−0.0905933	−	0.0523041i	0.454019	−	0.890992i	$-0.349990\pi$
$523$	−2.07180	−	1.19615i	−0.0905933	−	0.0523041i	−0.544612	+	0.838688i	$0.683323\pi$
$524$		0			0
$525$	10.9282			0.476946
$526$		0			0
$527$	0.0788383	−	0.0455173i	0.00343425	−	0.00198277i
$528$		0			0
$529$	0.303848	+	0.526279i	0.0132108	+	0.0228817i
$530$		0			0
$531$	−2.07180	+	3.58846i	−0.0899083	+	0.155726i
$532$		0			0
$533$	−16.7942	−	8.30385i	−0.727439	−	0.359680i
$534$		0			0
$535$	21.2942	+	12.2942i	0.920630	+	0.531526i
$536$		0			0
$537$	−18.9282	−	32.7846i	−0.816812	−	1.41476i
$538$		0			0
$539$	5.19615	+	9.00000i	0.223814	+	0.387657i
$540$		0			0
$541$	−2.80385			−0.120547			−0.0602734	−	0.998182i	$-0.519197\pi$
$541$	−2.80385			−0.120547			−0.0602734	+	0.998182i	$0.519197\pi$
$542$		0			0
$543$	−13.5622	+	23.4904i	−0.582009	+	1.00807i
$544$		0			0
$545$	−3.46410			−0.148386
$546$		0			0
$547$			12.9808i			0.555017i	0.960723	+	0.277509i	$0.0895087\pi$
$547$			12.9808i			0.555017i	−0.960723	+	0.277509i	$0.910491\pi$
$548$		0			0
$549$	51.7750	+	29.8923i	2.20970	+	1.27577i
$550$		0			0
$551$		−	2.19615i		−	0.0935592i
$552$		0			0
$553$	10.3923	−	6.00000i	0.441926	−	0.255146i
$554$		0			0
$555$	−37.6865	+	21.7583i	−1.59970	+	0.923590i
$556$		0			0
$557$	18.8660	−	32.6769i	0.799379	−	1.38457i	−0.120642	−	0.992696i	$-0.538495\pi$
$557$	18.8660	−	32.6769i	0.799379	−	1.38457i	0.920021	−	0.391869i	$-0.128171\pi$
$558$		0			0
$559$	−37.1769	+	24.7846i	−1.57242	+	1.04828i
$560$		0			0
$561$	−3.80385	−	2.19615i	−0.160599	−	0.0927216i
$562$		0			0
$563$	13.3923	−	7.73205i	0.564418	−	0.325867i	−0.190499	−	0.981687i	$-0.561010\pi$
$563$	13.3923	−	7.73205i	0.564418	−	0.325867i	0.754917	+	0.655820i	$0.227677\pi$
$564$		0			0
$565$	−2.59808	−	4.50000i	−0.109302	−	0.189316i
$566$		0			0
$567$		−	4.92820i		−	0.206965i
$568$		0			0
$569$	0.928203	−	1.60770i	0.0389123	−	0.0673981i	−0.845913	−	0.533320i	$-0.820944\pi$
$569$	0.928203	−	1.60770i	0.0389123	−	0.0673981i	0.884826	+	0.465922i	$0.154277\pi$
$570$		0			0
$571$			22.0000i			0.920671i	0.887745	+	0.460336i	$0.152271\pi$
$571$			22.0000i			0.920671i	−0.887745	+	0.460336i	$0.847729\pi$
$572$		0			0
$573$		−	43.8564i		−	1.83213i
$574$		0			0
$575$	−4.73205	+	8.19615i	−0.197340	+	0.341803i
$576$		0			0
$577$		−	44.6603i		−	1.85923i	−0.368531	−	0.929615i	$-0.620139\pi$
$577$		−	44.6603i		−	1.85923i	0.368531	−	0.929615i	$-0.379861\pi$
$578$		0			0
$579$	20.0263	+	34.6865i	0.832264	+	1.44152i
$580$		0			0
$581$	−4.39230	+	2.53590i	−0.182224	+	0.105207i
$582$		0			0
$583$	−37.3923	−	21.5885i	−1.54863	−	0.894103i
$584$		0			0
$585$	−15.4641	−	23.1962i	−0.639362	−	0.959043i
$586$		0			0
$587$	5.66025	−	9.80385i	0.233624	−	0.404648i	−0.725248	−	0.688488i	$-0.758275\pi$
$587$	5.66025	−	9.80385i	0.233624	−	0.404648i	0.958872	+	0.283839i	$0.0916083\pi$
$588$		0			0
$589$	−0.803848	+	0.464102i	−0.0331220	+	0.0191230i
$590$		0			0
$591$	8.19615	−	4.73205i	0.337145	−	0.194651i
$592$		0			0
$593$		−	28.5167i		−	1.17104i	−0.810658	−	0.585519i	$-0.800891\pi$
$593$		−	28.5167i		−	1.17104i	0.810658	−	0.585519i	$-0.199109\pi$
$594$		0			0
$595$	−1.39230	−	0.803848i	−0.0570789	−	0.0329545i
$596$		0			0
$597$			18.0000i			0.736691i
$598$		0			0
$599$	33.8038			1.38119			0.690594	−	0.723243i	$-0.257349\pi$
$599$	33.8038			1.38119			0.690594	+	0.723243i	$0.257349\pi$
$600$		0			0
$601$	−16.8923	+	29.2583i	−0.689051	+	1.19347i	0.283094	+	0.959092i	$0.408639\pi$
$601$	−16.8923	+	29.2583i	−0.689051	+	1.19347i	−0.972145	+	0.234380i	$0.924694\pi$
$602$		0			0
$603$	−36.5885			−1.49000
$604$		0			0
$605$	0.866025	+	1.50000i	0.0352089	+	0.0609837i
$606$		0			0
$607$	14.8301	+	25.6865i	0.601936	+	1.04258i	0.992528	+	0.122020i	$0.0389372\pi$
$607$	14.8301	+	25.6865i	0.601936	+	1.04258i	−0.390591	+	0.920564i	$0.627729\pi$
$608$		0			0
$609$	−2.19615	−	1.26795i	−0.0889926	−	0.0513799i
$610$		0			0
$611$	−2.70577	−	41.9545i	−0.109464	−	1.69730i
$612$		0			0
$613$	0.598076	−	1.03590i	0.0241561	−	0.0418395i	−0.853695	−	0.520774i	$-0.825643\pi$
$613$	0.598076	−	1.03590i	0.0241561	−	0.0418395i	0.877851	+	0.478934i	$0.158977\pi$
$614$		0			0
$615$	−12.2942	−	21.2942i	−0.495751	−	0.858666i
$616$		0			0
$617$	−22.5000	+	12.9904i	−0.905816	+	0.522973i	−0.879083	−	0.476670i	$-0.841844\pi$
$617$	−22.5000	+	12.9904i	−0.905816	+	0.522973i	−0.0267333	+	0.999643i	$0.508510\pi$
$618$		0			0
$619$	16.1436			0.648866			0.324433	−	0.945909i	$-0.394827\pi$
$619$	16.1436			0.648866			0.324433	+	0.945909i	$0.394827\pi$
$620$		0			0
$621$	−16.3923	−	9.46410i	−0.657801	−	0.379781i
$622$		0			0
$623$	−30.9282			−1.23911
$624$		0			0
$625$	−11.0000			−0.440000
$626$		0			0
$627$	38.7846	+	22.3923i	1.54891	+	0.894263i
$628$		0			0
$629$	−4.26795			−0.170174
$630$		0			0
$631$	−24.9282	+	14.3923i	−0.992376	+	0.572949i	−0.905984	−	0.423313i	$-0.860867\pi$
$631$	−24.9282	+	14.3923i	−0.992376	+	0.572949i	−0.0863924	+	0.996261i	$0.527534\pi$
$632$		0			0
$633$	−8.46410	−	14.6603i	−0.336418	−	0.582693i
$634$		0			0
$635$	4.90192	−	8.49038i	0.194527	−	0.336930i
$636$		0			0
$637$	−4.79423	+	9.69615i	−0.189954	+	0.384176i
$638$		0			0
$639$	−45.0788	−	26.0263i	−1.78329	−	1.02958i
$640$		0			0
$641$	10.5000	+	18.1865i	0.414725	+	0.718325i	0.995400	−	0.0958109i	$-0.0305444\pi$
$641$	10.5000	+	18.1865i	0.414725	+	0.718325i	−0.580674	+	0.814136i	$0.697211\pi$
$642$		0			0
$643$	18.1244	+	31.3923i	0.714755	+	1.23799i	0.963054	+	0.269308i	$0.0867950\pi$
$643$	18.1244	+	31.3923i	0.714755	+	1.23799i	−0.248299	+	0.968683i	$0.579872\pi$
$644$		0			0
$645$	−58.6410			−2.30899
$646$		0			0
$647$	−6.75833	+	11.7058i	−0.265697	+	0.460201i	−0.967746	−	0.251928i	$-0.918936\pi$
$647$	−6.75833	+	11.7058i	−0.265697	+	0.460201i	0.702049	+	0.712129i	$0.252269\pi$
$648$		0			0
$649$	3.21539			0.126215
$650$		0			0
$651$			1.07180i			0.0420070i
$652$		0			0
$653$	28.3923	+	16.3923i	1.11108	+	0.641480i	0.939108	−	0.343622i	$-0.111654\pi$
$653$	28.3923	+	16.3923i	1.11108	+	0.641480i	0.171969	+	0.985102i	$0.444987\pi$
$654$		0			0
$655$			36.5885i			1.42963i
$656$		0			0
$657$	20.0885	−	11.5981i	0.783725	−	0.452484i
$658$		0			0
$659$	−2.78461	+	1.60770i	−0.108473	+	0.0626269i	−0.553255	−	0.833012i	$-0.686614\pi$
$659$	−2.78461	+	1.60770i	−0.108473	+	0.0626269i	0.444782	+	0.895639i	$0.353281\pi$
$660$		0			0
$661$	11.1865	−	19.3756i	0.435106	−	0.753625i	−0.562199	−	0.827002i	$-0.690044\pi$
$661$	11.1865	−	19.3756i	0.435106	−	0.753625i	0.997304	+	0.0733771i	$0.0233777\pi$
$662$		0			0
$663$	−0.294229	−	4.56218i	−0.0114269	−	0.177180i
$664$		0			0
$665$	14.1962	+	8.19615i	0.550503	+	0.317833i
$666$		0			0
$667$	1.90192	−	1.09808i	0.0736428	−	0.0425177i
$668$		0			0
$669$	16.6603	+	28.8564i	0.644123	+	1.11565i
$670$		0			0
$671$		−	46.3923i		−	1.79096i
$672$		0			0
$673$	−22.8923	+	39.6506i	−0.882434	+	1.52842i	−0.0338062	+	0.999428i	$0.510763\pi$
$673$	−22.8923	+	39.6506i	−0.882434	+	1.52842i	−0.848627	+	0.528991i	$0.822570\pi$
$674$		0			0
$675$			8.00000i			0.307920i
$676$		0			0
$677$			47.5692i			1.82823i	0.405451	+	0.914117i	$0.367115\pi$
$677$			47.5692i			1.82823i	−0.405451	+	0.914117i	$0.632885\pi$
$678$		0			0
$679$	6.00000	−	10.3923i	0.230259	−	0.398820i
$680$		0			0
$681$			26.7846i			1.02639i
$682$		0			0
$683$	3.75833	+	6.50962i	0.143809	+	0.249084i	0.928928	−	0.370261i	$-0.120732\pi$
$683$	3.75833	+	6.50962i	0.143809	+	0.249084i	−0.785119	+	0.619345i	$0.787398\pi$
$684$		0			0
$685$	−9.18653	+	5.30385i	−0.350999	+	0.202650i
$686$		0			0
$687$	−53.9090	−	31.1244i	−2.05676	−	1.18747i
$688$		0			0
$689$	−2.89230	−	44.8468i	−0.110188	−	1.70853i
$690$		0			0
$691$	−12.1244	+	21.0000i	−0.461232	+	0.798878i	−0.999023	−	0.0442009i	$-0.985926\pi$
$691$	−12.1244	+	21.0000i	−0.461232	+	0.798878i	0.537790	+	0.843079i	$0.319259\pi$
$692$		0			0
$693$	26.7846	−	15.4641i	1.01746	−	0.587433i
$694$		0			0
$695$	−0.588457	+	0.339746i	−0.0223215	+	0.0128873i
$696$		0			0
$697$		−	2.41154i		−	0.0913437i
$698$		0			0
$699$	61.1769	+	35.3205i	2.31392	+	1.33594i
$700$		0			0
$701$		−	12.0000i		−	0.453234i	−0.973984	−	0.226617i	$-0.927233\pi$
$701$		−	12.0000i		−	0.453234i	0.973984	−	0.226617i	$-0.0727665\pi$
$702$		0			0
$703$	43.5167			1.64126
$704$		0			0
$705$	27.5885	−	47.7846i	1.03904	−	1.79967i
$706$		0			0
$707$	19.8564			0.746777
$708$		0			0
$709$	−3.20577	−	5.55256i	−0.120395	−	0.208531i	0.799528	−	0.600628i	$-0.205083\pi$
$709$	−3.20577	−	5.55256i	−0.120395	−	0.208531i	−0.919924	+	0.392098i	$0.871750\pi$
$710$		0			0
$711$	13.3923	+	23.1962i	0.502251	+	0.869924i
$712$		0			0
$713$	−0.803848	−	0.464102i	−0.0301043	−	0.0173807i
$714$		0			0
$715$	−9.58846	+	19.3923i	−0.358588	+	0.725231i
$716$		0			0
$717$	−1.26795	+	2.19615i	−0.0473524	+	0.0820168i
$718$		0			0
$719$	−1.73205	−	3.00000i	−0.0645946	−	0.111881i	0.831919	−	0.554896i	$-0.187242\pi$
$719$	−1.73205	−	3.00000i	−0.0645946	−	0.111881i	−0.896514	+	0.443015i	$0.853909\pi$
$720$		0			0
$721$	−22.9808	+	13.2679i	−0.855848	+	0.494124i
$722$		0			0
$723$	−49.5167			−1.84154
$724$		0			0
$725$	−0.803848	−	0.464102i	−0.0298541	−	0.0172363i
$726$		0			0
$727$	40.6410			1.50729			0.753646	−	0.657281i	$-0.228293\pi$
$727$	40.6410			1.50729			0.753646	+	0.657281i	$0.228293\pi$
$728$		0			0
$729$	43.7846			1.62165
$730$		0			0
$731$	−4.98076	−	2.87564i	−0.184220	−	0.106360i
$732$		0			0
$733$	35.9808			1.32898			0.664490	−	0.747297i	$-0.268649\pi$
$733$	35.9808			1.32898			0.664490	+	0.747297i	$0.268649\pi$
$734$		0			0
$735$	−12.2942	+	7.09808i	−0.453479	+	0.261816i
$736$		0			0
$737$	14.1962	+	24.5885i	0.522922	+	0.905727i
$738$		0			0
$739$	24.0000	−	41.5692i	0.882854	−	1.52915i	0.0347009	−	0.999398i	$-0.488952\pi$
$739$	24.0000	−	41.5692i	0.882854	−	1.52915i	0.848153	−	0.529751i	$-0.177715\pi$
$740$		0			0
$741$	3.00000	+	46.5167i	0.110208	+	1.70883i
$742$		0			0
$743$	44.1962	+	25.5167i	1.62140	+	0.936115i	0.986546	+	0.163483i	$0.0522728\pi$
$743$	44.1962	+	25.5167i	1.62140	+	0.936115i	0.634853	+	0.772633i	$0.281060\pi$
$744$		0			0
$745$	4.50000	+	7.79423i	0.164867	+	0.285558i
$746$		0			0
$747$	−5.66025	−	9.80385i	−0.207098	−	0.358704i
$748$		0			0
$749$	−28.3923			−1.03743
$750$		0			0
$751$	−17.6603	+	30.5885i	−0.644432	+	1.11619i	0.340001	+	0.940425i	$0.389573\pi$
$751$	−17.6603	+	30.5885i	−0.644432	+	1.11619i	−0.984432	+	0.175763i	$0.943761\pi$
$752$		0			0
$753$	6.00000			0.218652
$754$		0			0
$755$			20.4449i			0.744065i
$756$		0			0
$757$	2.19615	+	1.26795i	0.0798205	+	0.0460844i	0.539379	−	0.842063i	$-0.318659\pi$
$757$	2.19615	+	1.26795i	0.0798205	+	0.0460844i	−0.459559	+	0.888147i	$0.651992\pi$
$758$		0			0
$759$			44.7846i			1.62558i
$760$		0			0
$761$	21.0000	−	12.1244i	0.761249	−	0.439508i	−0.0684947	−	0.997651i	$-0.521820\pi$
$761$	21.0000	−	12.1244i	0.761249	−	0.439508i	0.829744	+	0.558144i	$0.188486\pi$
$762$		0			0
$763$	3.46410	−	2.00000i	0.125409	−	0.0724049i
$764$		0			0
$765$	1.79423	−	3.10770i	0.0648705	−	0.112359i
$766$		0			0
$767$	1.85641	+	2.78461i	0.0670310	+	0.100546i
$768$		0			0
$769$	−7.39230	−	4.26795i	−0.266573	−	0.153906i	0.360756	−	0.932660i	$-0.382519\pi$
$769$	−7.39230	−	4.26795i	−0.266573	−	0.153906i	−0.627329	+	0.778754i	$0.715852\pi$
$770$		0			0
$771$	25.6865	−	14.8301i	0.925078	−	0.534094i
$772$		0			0
$773$	6.92820	+	12.0000i	0.249190	+	0.431610i	0.963301	−	0.268422i	$-0.0865023\pi$
$773$	6.92820	+	12.0000i	0.249190	+	0.431610i	−0.714111	+	0.700032i	$0.753169\pi$
$774$		0			0
$775$			0.392305i			0.0140920i
$776$		0			0
$777$	25.1244	−	43.5167i	0.901331	−	1.56115i
$778$		0			0
$779$			24.5885i			0.880973i
$780$		0			0
$781$			40.3923i			1.44535i
$782$		0			0
$783$	0.928203	−	1.60770i	0.0331713	−	0.0574543i
$784$		0			0
$785$		−	24.8038i		−	0.885287i
$786$		0			0
$787$	−16.0981	−	27.8827i	−0.573834	−	0.993910i	−0.996167	−	0.0874695i	$-0.972122\pi$
$787$	−16.0981	−	27.8827i	−0.573834	−	0.993910i	0.422333	−	0.906441i	$-0.361211\pi$
$788$		0			0
$789$	43.1769	−	24.9282i	1.53714	−	0.887468i
$790$		0			0
$791$	5.19615	+	3.00000i	0.184754	+	0.106668i
$792$		0			0
$793$	40.1769	−	26.7846i	1.42672	−	0.951149i
$794$		0			0
$795$	29.4904	−	51.0788i	1.04592	−	1.81158i
$796$		0			0
$797$	22.9808	−	13.2679i	0.814020	−	0.469975i	−0.0343297	−	0.999411i	$-0.510930\pi$
$797$	22.9808	−	13.2679i	0.814020	−	0.469975i	0.848350	+	0.529436i	$0.177596\pi$
$798$		0			0
$799$	4.68653	−	2.70577i	0.165798	−	0.0957233i
$800$		0			0
$801$		−	69.0333i		−	2.43917i
$802$		0			0
$803$	−15.5885	−	9.00000i	−0.550105	−	0.317603i
$804$		0			0
$805$			16.3923i			0.577753i
$806$		0			0
$807$	6.92820			0.243884
$808$		0			0
$809$	−4.03590	+	6.99038i	−0.141895	+	0.245769i	−0.928210	−	0.372057i	$-0.878653\pi$
$809$	−4.03590	+	6.99038i	−0.141895	+	0.245769i	0.786315	+	0.617825i	$0.211986\pi$
$810$		0			0
$811$	1.26795			0.0445237			0.0222619	−	0.999752i	$-0.492913\pi$
$811$	1.26795			0.0445237			0.0222619	+	0.999752i	$0.492913\pi$
$812$		0			0
$813$	−25.6603	−	44.4449i	−0.899944	−	1.55875i
$814$		0			0
$815$	−8.19615	−	14.1962i	−0.287099	−	0.497270i
$816$		0			0
$817$	50.7846	+	29.3205i	1.77673	+	1.02579i
$818$		0			0
$819$	28.8564	+	14.2679i	1.00832	+	0.498562i
$820$		0			0
$821$	2.07180	−	3.58846i	0.0723062	−	0.125238i	−0.827605	−	0.561310i	$-0.810297\pi$
$821$	2.07180	−	3.58846i	0.0723062	−	0.125238i	0.899912	+	0.436072i	$0.143631\pi$
$822$		0			0
$823$	−7.73205	−	13.3923i	−0.269522	−	0.466826i	0.699216	−	0.714910i	$-0.253532\pi$
$823$	−7.73205	−	13.3923i	−0.269522	−	0.466826i	−0.968739	+	0.248084i	$0.920199\pi$
$824$		0			0
$825$	16.3923	−	9.46410i	0.570707	−	0.329498i
$826$		0			0
$827$	29.3205			1.01957			0.509787	−	0.860301i	$-0.329724\pi$
$827$	29.3205			1.01957			0.509787	+	0.860301i	$0.329724\pi$
$828$		0			0
$829$	34.7942	+	20.0885i	1.20845	+	0.697701i	0.962421	−	0.271561i	$-0.0875398\pi$
$829$	34.7942	+	20.0885i	1.20845	+	0.697701i	0.246032	+	0.969262i	$0.420873\pi$
$830$		0			0
$831$	48.5885			1.68551
$832$		0			0
$833$	−1.39230			−0.0482405
$834$		0			0
$835$	−15.5885	−	9.00000i	−0.539461	−	0.311458i
$836$		0			0
$837$	−0.784610			−0.0271201
$838$		0			0
$839$	1.90192	−	1.09808i	0.0656617	−	0.0379098i	−0.466810	−	0.884358i	$-0.654597\pi$
$839$	1.90192	−	1.09808i	0.0656617	−	0.0379098i	0.532471	+	0.846448i	$0.321263\pi$
$840$		0			0
$841$	−14.3923	−	24.9282i	−0.496286	−	0.859593i
$842$		0			0
$843$	22.2224	−	38.4904i	0.765381	−	1.32568i
$844$		0			0
$845$	−22.3301	+	2.89230i	−0.768180	+	0.0994983i
$846$		0			0
$847$	−1.73205	−	1.00000i	−0.0595140	−	0.0343604i
$848$		0			0
$849$	19.6603	+	34.0526i	0.674738	+	1.16868i
$850$		0			0
$851$	21.7583	+	37.6865i	0.745866	+	1.29188i
$852$		0			0
$853$	25.1962			0.862700			0.431350	−	0.902185i	$-0.358037\pi$
$853$	25.1962			0.862700			0.431350	+	0.902185i	$0.358037\pi$
$854$		0			0
$855$	−18.2942	+	31.6865i	−0.625649	+	1.08366i
$856$		0			0
$857$	−1.39230			−0.0475602			−0.0237801	−	0.999717i	$-0.507570\pi$
$857$	−1.39230			−0.0475602			−0.0237801	+	0.999717i	$0.507570\pi$
$858$		0			0
$859$			17.8038i			0.607459i	0.952758	+	0.303730i	$0.0982320\pi$
$859$			17.8038i			0.607459i	−0.952758	+	0.303730i	$0.901768\pi$
$860$		0			0
$861$	24.5885	+	14.1962i	0.837972	+	0.483804i
$862$		0			0
$863$		−	31.8564i		−	1.08440i	−0.840248	−	0.542202i	$-0.817591\pi$
$863$		−	31.8564i		−	1.08440i	0.840248	−	0.542202i	$-0.182409\pi$
$864$		0			0
$865$	18.0000	−	10.3923i	0.612018	−	0.353349i
$866$		0			0
$867$	−39.7128	+	22.9282i	−1.34872	+	0.778683i
$868$		0			0
$869$	10.3923	−	18.0000i	0.352535	−	0.610608i
$870$		0			0
$871$	−13.0981	+	26.4904i	−0.443811	+	0.897592i
$872$		0			0
$873$	23.1962	+	13.3923i	0.785071	+	0.453261i
$874$		0			0
$875$	21.0000	−	12.1244i	0.709930	−	0.409878i
$876$		0			0
$877$	2.79423	+	4.83975i	0.0943544	+	0.163427i	0.909339	−	0.416056i	$-0.136588\pi$
$877$	2.79423	+	4.83975i	0.0943544	+	0.163427i	−0.814985	+	0.579483i	$0.803255\pi$
$878$		0			0
$879$			86.6936i			2.92410i
$880$		0			0
$881$	1.16025	−	2.00962i	0.0390900	−	0.0677058i	−0.845819	−	0.533471i	$-0.820887\pi$
$881$	1.16025	−	2.00962i	0.0390900	−	0.0677058i	0.884908	+	0.465765i	$0.154221\pi$
$882$		0			0
$883$		−	40.1962i		−	1.35271i	−0.736577	−	0.676354i	$-0.763559\pi$
$883$		−	40.1962i		−	1.35271i	0.736577	−	0.676354i	$-0.236441\pi$
$884$		0			0
$885$			4.39230i			0.147646i
$886$		0			0
$887$	−4.85641	+	8.41154i	−0.163062	+	0.282432i	−0.935965	−	0.352092i	$-0.885470\pi$
$887$	−4.85641	+	8.41154i	−0.163062	+	0.282432i	0.772903	+	0.634524i	$0.218804\pi$
$888$		0			0
$889$			11.3205i			0.379678i
$890$		0			0
$891$	−4.26795	−	7.39230i	−0.142982	−	0.247652i
$892$		0			0
$893$	−47.7846	+	27.5885i	−1.59905	+	0.923213i
$894$		0			0
$895$	−20.7846	−	12.0000i	−0.694753	−	0.401116i
$896$		0			0
$897$	−38.7846	+	25.8564i	−1.29498	+	0.863320i
$898$		0			0
$899$	0.0455173	−	0.0788383i	0.00151809	−	0.00262941i
$900$		0			0
$901$	5.00962	−	2.89230i	0.166895	−	0.0963566i
$902$		0			0
$903$	58.6410	−	33.8564i	1.95145	−	1.12667i
$904$		0			0
$905$			17.1962i			0.571619i
$906$		0			0
$907$	−0.339746	−	0.196152i	−0.0112811	−	0.00651313i	0.494349	−	0.869264i	$-0.335407\pi$
$907$	−0.339746	−	0.196152i	−0.0112811	−	0.00651313i	−0.505630	+	0.862750i	$0.668740\pi$
$908$		0			0
$909$			44.3205i			1.47002i
$910$		0			0
$911$	−8.53590			−0.282807			−0.141403	−	0.989952i	$-0.545161\pi$
$911$	−8.53590			−0.282807			−0.141403	+	0.989952i	$0.545161\pi$
$912$		0			0
$913$	−4.39230	+	7.60770i	−0.145364	+	0.251778i
$914$		0			0
$915$	63.3731			2.09505
$916$		0			0
$917$	−21.1244	−	36.5885i	−0.697588	−	1.20826i
$918$		0			0
$919$	10.0981	+	17.4904i	0.333105	+	0.576954i	0.983119	−	0.182968i	$-0.0585704\pi$
$919$	10.0981	+	17.4904i	0.333105	+	0.576954i	−0.650014	+	0.759922i	$0.725237\pi$
$920$		0			0
$921$	−13.3923	−	7.73205i	−0.441291	−	0.254780i
$922$		0			0
$923$	−34.9808	+	23.3205i	−1.15141	+	0.767604i
$924$		0			0
$925$	9.19615	−	15.9282i	0.302368	−	0.523716i
$926$		0			0
$927$	−29.6147	−	51.2942i	−0.972676	−	1.68472i
$928$		0			0
$929$	32.6769	−	18.8660i	1.07209	−	0.618974i	0.143342	−	0.989673i	$-0.454215\pi$
$929$	32.6769	−	18.8660i	1.07209	−	0.618974i	0.928753	+	0.370699i	$0.120882\pi$
$930$		0			0
$931$	14.1962			0.465260
$932$		0			0
$933$	−25.3923	−	14.6603i	−0.831307	−	0.479955i
$934$		0			0
$935$	−2.78461			−0.0910665
$936$		0			0
$937$	−9.78461			−0.319649			−0.159825	−	0.987145i	$-0.551093\pi$
$937$	−9.78461			−0.319649			−0.159825	+	0.987145i	$0.551093\pi$
$938$		0			0
$939$	27.4641	+	15.8564i	0.896257	+	0.517454i
$940$		0			0
$941$	−27.7128			−0.903412			−0.451706	−	0.892167i	$-0.649184\pi$
$941$	−27.7128			−0.903412			−0.451706	+	0.892167i	$0.649184\pi$
$942$		0			0
$943$	−21.2942	+	12.2942i	−0.693435	+	0.400355i
$944$		0			0
$945$	6.92820	+	12.0000i	0.225374	+	0.390360i
$946$		0			0
$947$	−18.7583	+	32.4904i	−0.609564	+	1.05580i	0.381748	+	0.924266i	$0.375322\pi$
$947$	−18.7583	+	32.4904i	−0.609564	+	1.05580i	−0.991312	+	0.131529i	$0.958011\pi$
$948$		0			0
$949$	−1.20577	−	18.6962i	−0.0391410	−	0.606903i
$950$		0			0
$951$	−58.6865	−	33.8827i	−1.90304	−	1.09872i
$952$		0			0
$953$	−5.53590	−	9.58846i	−0.179325	−	0.310601i	0.762324	−	0.647195i	$-0.224058\pi$
$953$	−5.53590	−	9.58846i	−0.179325	−	0.310601i	−0.941650	+	0.336595i	$0.890725\pi$
$954$		0			0
$955$	−13.9019	−	24.0788i	−0.449856	−	0.779173i
$956$		0			0
$957$	−4.39230			−0.141983
$958$		0			0
$959$	6.12436	−	10.6077i	0.197766	−	0.342540i
$960$		0			0
$961$	30.9615			0.998759
$962$		0			0
$963$		−	63.3731i		−	2.04217i
$964$		0			0
$965$	21.9904	+	12.6962i	0.707895	+	0.408704i
$966$		0			0
$967$		−	26.9808i		−	0.867643i	−0.900999	−	0.433821i	$-0.857165\pi$
$967$		−	26.9808i		−	0.867643i	0.900999	−	0.433821i	$-0.142835\pi$
$968$		0			0
$969$	−5.19615	+	3.00000i	−0.166924	+	0.0963739i
$970$		0			0
$971$	−16.9019	+	9.75833i	−0.542409	+	0.313160i	−0.746055	−	0.665885i	$-0.768054\pi$
$971$	−16.9019	+	9.75833i	−0.542409	+	0.313160i	0.203646	+	0.979045i	$0.434721\pi$
$972$		0			0
$973$	0.392305	−	0.679492i	0.0125767	−	0.0217835i
$974$		0			0
$975$	17.6603	+	8.73205i	0.565581	+	0.279649i
$976$		0			0
$977$	−36.4808	−	21.0622i	−1.16712	−	0.673839i	−0.214122	−	0.976807i	$-0.568689\pi$
$977$	−36.4808	−	21.0622i	−1.16712	−	0.673839i	−0.953001	+	0.302968i	$0.902022\pi$
$978$		0			0
$979$	−46.3923	+	26.7846i	−1.48270	+	0.856040i
$980$		0			0
$981$	4.46410	+	7.73205i	0.142528	+	0.246865i
$982$		0			0
$983$			17.6603i			0.563275i	0.959521	+	0.281637i	$0.0908775\pi$
$983$			17.6603i			0.563275i	−0.959521	+	0.281637i	$0.909123\pi$
$984$		0			0
$985$	3.00000	−	5.19615i	0.0955879	−	0.165563i
$986$		0			0
$987$			63.7128i			2.02800i
$988$		0			0
$989$			58.6410i			1.86468i
$990$		0			0
$991$	6.97372	−	12.0788i	0.221528	−	0.383697i	−0.733744	−	0.679426i	$-0.762229\pi$
$991$	6.97372	−	12.0788i	0.221528	−	0.383697i	0.955272	+	0.295729i	$0.0955624\pi$
$992$		0			0
$993$			56.7846i			1.80201i
$994$		0			0
$995$	5.70577	+	9.88269i	0.180885	+	0.313302i
$996$		0			0
$997$	−1.79423	+	1.03590i	−0.0568238	+	0.0328072i	−0.528143	−	0.849156i	$-0.677111\pi$
$997$	−1.79423	+	1.03590i	−0.0568238	+	0.0328072i	0.471319	+	0.881963i	$0.343778\pi$
$998$		0			0
$999$	31.8564	+	18.3923i	1.00789	+	0.581907i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	832.2.ba.b.225.1	yes	4
4.3	odd	2		832.2.ba.f.225.2	yes	4
8.3	odd	2		832.2.ba.a.225.1	✓	4
8.5	even	2		832.2.ba.e.225.2	yes	4
13.10	even	6		832.2.ba.e.673.2	yes	4
52.23	odd	6		832.2.ba.a.673.1	yes	4
104.75	odd	6		832.2.ba.f.673.2	yes	4
104.101	even	6	inner	832.2.ba.b.673.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
832.2.ba.a.225.1	✓	4	8.3	odd	2
832.2.ba.a.673.1	yes	4	52.23	odd	6
832.2.ba.b.225.1	yes	4	1.1	even	1	trivial
832.2.ba.b.673.1	yes	4	104.101	even	6	inner
832.2.ba.e.225.2	yes	4	8.5	even	2
832.2.ba.e.673.2	yes	4	13.10	even	6
832.2.ba.f.225.2	yes	4	4.3	odd	2
832.2.ba.f.673.2	yes	4	104.75	odd	6

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:	\( N \)	\(=\)	\( 832 = 2^{6} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	832.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.36603 - 1.36603i) q^{3} -1.73205 q^{5} +(1.73205 - 1.00000i) q^{7} +(2.23205 + 3.86603i) q^{9} +(1.73205 - 3.00000i) q^{11} +(3.59808 - 0.232051i) q^{13} +(4.09808 + 2.36603i) q^{15} +(0.232051 + 0.401924i) q^{17} +(-2.36603 - 4.09808i) q^{19} -5.46410 q^{21} +(2.36603 - 4.09808i) q^{23} -2.00000 q^{25} -4.00000i q^{27} +(0.401924 + 0.232051i) q^{29} -0.196152i q^{31} +(-8.19615 + 4.73205i) q^{33} +(-3.00000 + 1.73205i) q^{35} +(-4.59808 + 7.96410i) q^{37} +(-8.83013 - 4.36603i) q^{39} +(-4.50000 - 2.59808i) q^{41} +(-10.7321 + 6.19615i) q^{43} +(-3.86603 - 6.69615i) q^{45} -11.6603i q^{47} +(-1.50000 + 2.59808i) q^{49} -1.26795i q^{51} -12.4641i q^{53} +(-3.00000 + 5.19615i) q^{55} +12.9282i q^{57} +(0.464102 + 0.803848i) q^{59} +(11.5981 - 6.69615i) q^{61} +(7.73205 + 4.46410i) q^{63} +(-6.23205 + 0.401924i) q^{65} +(-4.09808 + 7.09808i) q^{67} +(-11.1962 + 6.46410i) q^{69} +(-10.0981 + 5.83013i) q^{71} -5.19615i q^{73} +(4.73205 + 2.73205i) q^{75} -6.92820i q^{77} +6.00000 q^{79} +(1.23205 - 2.13397i) q^{81} -2.53590 q^{83} +(-0.401924 - 0.696152i) q^{85} +(-0.633975 - 1.09808i) q^{87} +(-13.3923 - 7.73205i) q^{89} +(6.00000 - 4.00000i) q^{91} +(-0.267949 + 0.464102i) q^{93} +(4.09808 + 7.09808i) q^{95} +(5.19615 - 3.00000i) q^{97} +15.4641 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{3} + 2 q^{9} + 4 q^{13} + 6 q^{15} - 6 q^{17} - 6 q^{19} - 8 q^{21} + 6 q^{23} - 8 q^{25} + 12 q^{29} - 12 q^{33} - 12 q^{35} - 8 q^{37} - 18 q^{39} - 18 q^{41} - 36 q^{43} - 12 q^{45} - 6 q^{49}+ \cdots + 48 q^{99}+O(q^{100}) \) 4 * q - 6 * q^3 + 2 * q^9 + 4 * q^13 + 6 * q^15 - 6 * q^17 - 6 * q^19 - 8 * q^21 + 6 * q^23 - 8 * q^25 + 12 * q^29 - 12 * q^33 - 12 * q^35 - 8 * q^37 - 18 * q^39 - 18 * q^41 - 36 * q^43 - 12 * q^45 - 6 * q^49 - 12 * q^55 - 12 * q^59 + 36 * q^61 + 24 * q^63 - 18 * q^65 - 6 * q^67 - 24 * q^69 - 30 * q^71 + 12 * q^75 + 24 * q^79 - 2 * q^81 - 24 * q^83 - 12 * q^85 - 6 * q^87 - 12 * q^89 + 24 * q^91 - 8 * q^93 + 6 * q^95 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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