LMFDB - Embedded newform 832.2.ba.d.673.2

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:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			673.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	832.673
Dual form			832.2.ba.d.225.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.73205 - 1.00000i) q^{3} +3.00000 q^{5} +(1.73205 + 1.00000i) q^{7} +(0.500000 - 0.866025i) q^{9} +(-1.73205 - 3.00000i) q^{11} +(2.50000 - 2.59808i) q^{13} +(5.19615 - 3.00000i) q^{15} +(-1.50000 + 2.59808i) q^{17} +(-1.73205 + 3.00000i) q^{19} +4.00000 q^{21} +(-3.46410 - 6.00000i) q^{23} +4.00000 q^{25} +4.00000i q^{27} +(1.50000 - 0.866025i) q^{29} +4.00000i q^{31} +(-6.00000 - 3.46410i) q^{33} +(5.19615 + 3.00000i) q^{35} +(5.50000 + 9.52628i) q^{37} +(1.73205 - 7.00000i) q^{39} +(-4.50000 + 2.59808i) q^{41} +(-6.92820 - 4.00000i) q^{43} +(1.50000 - 2.59808i) q^{45} -6.00000i q^{47} +(-1.50000 - 2.59808i) q^{49} +6.00000i q^{51} +12.1244i q^{53} +(-5.19615 - 9.00000i) q^{55} +6.92820i q^{57} +(1.73205 - 3.00000i) q^{59} +(1.50000 + 0.866025i) q^{61} +(1.73205 - 1.00000i) q^{63} +(7.50000 - 7.79423i) q^{65} +(-3.46410 - 6.00000i) q^{67} +(-12.0000 - 6.92820i) q^{69} +(-5.19615 - 3.00000i) q^{71} -12.1244i q^{73} +(6.92820 - 4.00000i) q^{75} -6.92820i q^{77} +3.46410 q^{79} +(5.50000 + 9.52628i) q^{81} +6.92820 q^{83} +(-4.50000 + 7.79423i) q^{85} +(1.73205 - 3.00000i) q^{87} +(-6.00000 + 3.46410i) q^{89} +(6.92820 - 2.00000i) q^{91} +(4.00000 + 6.92820i) q^{93} +(-5.19615 + 9.00000i) q^{95} +(12.0000 + 6.92820i) q^{97} -3.46410 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 12 q^{5} + 2 q^{9} + 10 q^{13} - 6 q^{17} + 16 q^{21} + 16 q^{25} + 6 q^{29} - 24 q^{33} + 22 q^{37} - 18 q^{41} + 6 q^{45} - 6 q^{49} + 6 q^{61} + 30 q^{65} - 48 q^{69} + 22 q^{81} - 18 q^{85} - 24 q^{89}+ \cdots + 48 q^{97}+O(q^{100}) $ 4 * q + 12 * q^5 + 2 * q^9 + 10 * q^13 - 6 * q^17 + 16 * q^21 + 16 * q^25 + 6 * q^29 - 24 * q^33 + 22 * q^37 - 18 * q^41 + 6 * q^45 - 6 * q^49 + 6 * q^61 + 30 * q^65 - 48 * q^69 + 22 * q^81 - 18 * q^85 - 24 * q^89 + 16 * q^93 + 48 * q^97

Character values

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

$n$	$261$	$703$	$769$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	1.73205	−	1.00000i	1.00000	−	0.577350i	0.0917517	−	0.995782i	$-0.470753\pi$
$3$	1.73205	−	1.00000i	1.00000	−	0.577350i	0.908248	+	0.418432i	$0.137420\pi$
$4$		0			0
$5$	3.00000			1.34164			0.670820	−	0.741620i	$-0.265942\pi$
$5$	3.00000			1.34164			0.670820	+	0.741620i	$0.265942\pi$
$6$		0			0
$7$	1.73205	+	1.00000i	0.654654	+	0.377964i	0.790237	−	0.612801i	$-0.209957\pi$
$7$	1.73205	+	1.00000i	0.654654	+	0.377964i	−0.135583	+	0.990766i	$0.543291\pi$
$8$		0			0
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	−1.73205	−	3.00000i	−0.522233	−	0.904534i	−0.999665	−	0.0258656i	$-0.991766\pi$
$11$	−1.73205	−	3.00000i	−0.522233	−	0.904534i	0.477432	−	0.878668i	$-0.341568\pi$
$12$		0			0
$13$	2.50000	−	2.59808i	0.693375	−	0.720577i
$13$	2.50000	−	2.59808i	0.693375	−	0.720577i
$14$		0			0
$15$	5.19615	−	3.00000i	1.34164	−	0.774597i
$16$		0			0
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$		0			0
$19$	−1.73205	+	3.00000i	−0.397360	+	0.688247i	−0.993399	−	0.114708i	$-0.963407\pi$
$19$	−1.73205	+	3.00000i	−0.397360	+	0.688247i	0.596040	+	0.802955i	$0.296740\pi$
$20$		0			0
$21$	4.00000			0.872872
$22$		0			0
$23$	−3.46410	−	6.00000i	−0.722315	−	1.25109i	−0.960070	−	0.279761i	$-0.909745\pi$
$23$	−3.46410	−	6.00000i	−0.722315	−	1.25109i	0.237754	−	0.971325i	$-0.423589\pi$
$24$		0			0
$25$	4.00000			0.800000
$26$		0			0
$27$			4.00000i			0.769800i
$28$		0			0
$29$	1.50000	−	0.866025i	0.278543	−	0.160817i	−0.354221	−	0.935162i	$-0.615254\pi$
$29$	1.50000	−	0.866025i	0.278543	−	0.160817i	0.632764	+	0.774345i	$0.281920\pi$
$30$		0			0
$31$			4.00000i			0.718421i	0.933257	+	0.359211i	$0.116954\pi$
$31$			4.00000i			0.718421i	−0.933257	+	0.359211i	$0.883046\pi$
$32$		0			0
$33$	−6.00000	−	3.46410i	−1.04447	−	0.603023i
$34$		0			0
$35$	5.19615	+	3.00000i	0.878310	+	0.507093i
$36$		0			0
$37$	5.50000	+	9.52628i	0.904194	+	1.56611i	0.821995	+	0.569495i	$0.192861\pi$
$37$	5.50000	+	9.52628i	0.904194	+	1.56611i	0.0821995	+	0.996616i	$0.473806\pi$
$38$		0			0
$39$	1.73205	−	7.00000i	0.277350	−	1.12090i
$40$		0			0
$41$	−4.50000	+	2.59808i	−0.702782	+	0.405751i	−0.808383	−	0.588657i	$-0.799657\pi$
$41$	−4.50000	+	2.59808i	−0.702782	+	0.405751i	0.105601	+	0.994409i	$0.466323\pi$
$42$		0			0
$43$	−6.92820	−	4.00000i	−1.05654	−	0.609994i	−0.132068	−	0.991241i	$-0.542162\pi$
$43$	−6.92820	−	4.00000i	−1.05654	−	0.609994i	−0.924473	+	0.381246i	$0.875495\pi$
$44$		0			0
$45$	1.50000	−	2.59808i	0.223607	−	0.387298i
$46$		0			0
$47$		−	6.00000i		−	0.875190i	−0.899172	−	0.437595i	$-0.855830\pi$
$47$		−	6.00000i		−	0.875190i	0.899172	−	0.437595i	$-0.144170\pi$
$48$		0			0
$49$	−1.50000	−	2.59808i	−0.214286	−	0.371154i
$50$		0			0
$51$			6.00000i			0.840168i
$52$		0			0
$53$			12.1244i			1.66541i	0.553718	+	0.832704i	$0.313209\pi$
$53$			12.1244i			1.66541i	−0.553718	+	0.832704i	$0.686791\pi$
$54$		0			0
$55$	−5.19615	−	9.00000i	−0.700649	−	1.21356i
$56$		0			0
$57$			6.92820i			0.917663i
$58$		0			0
$59$	1.73205	−	3.00000i	0.225494	−	0.390567i	−0.730974	−	0.682406i	$-0.760934\pi$
$59$	1.73205	−	3.00000i	0.225494	−	0.390567i	0.956467	+	0.291839i	$0.0942671\pi$
$60$		0			0
$61$	1.50000	+	0.866025i	0.192055	+	0.110883i	0.592944	−	0.805243i	$-0.297965\pi$
$61$	1.50000	+	0.866025i	0.192055	+	0.110883i	−0.400889	+	0.916127i	$0.631299\pi$
$62$		0			0
$63$	1.73205	−	1.00000i	0.218218	−	0.125988i
$64$		0			0
$65$	7.50000	−	7.79423i	0.930261	−	0.966755i
$66$		0			0
$67$	−3.46410	−	6.00000i	−0.423207	−	0.733017i	0.573044	−	0.819525i	$-0.305762\pi$
$67$	−3.46410	−	6.00000i	−0.423207	−	0.733017i	−0.996251	+	0.0865081i	$0.972429\pi$
$68$		0			0
$69$	−12.0000	−	6.92820i	−1.44463	−	0.834058i
$70$		0			0
$71$	−5.19615	−	3.00000i	−0.616670	−	0.356034i	0.158901	−	0.987294i	$-0.449205\pi$
$71$	−5.19615	−	3.00000i	−0.616670	−	0.356034i	−0.775571	+	0.631260i	$0.782538\pi$
$72$		0			0
$73$		−	12.1244i		−	1.41905i	−0.704681	−	0.709524i	$-0.748910\pi$
$73$		−	12.1244i		−	1.41905i	0.704681	−	0.709524i	$-0.251090\pi$
$74$		0			0
$75$	6.92820	−	4.00000i	0.800000	−	0.461880i
$76$		0			0
$77$		−	6.92820i		−	0.789542i
$78$		0			0
$79$	3.46410			0.389742			0.194871	−	0.980829i	$-0.437571\pi$
$79$	3.46410			0.389742			0.194871	+	0.980829i	$0.437571\pi$
$80$		0			0
$81$	5.50000	+	9.52628i	0.611111	+	1.05848i
$82$		0			0
$83$	6.92820			0.760469			0.380235	−	0.924890i	$-0.375843\pi$
$83$	6.92820			0.760469			0.380235	+	0.924890i	$0.375843\pi$
$84$		0			0
$85$	−4.50000	+	7.79423i	−0.488094	+	0.845403i
$86$		0			0
$87$	1.73205	−	3.00000i	0.185695	−	0.321634i
$88$		0			0
$89$	−6.00000	+	3.46410i	−0.635999	+	0.367194i	−0.783072	−	0.621932i	$-0.786348\pi$
$89$	−6.00000	+	3.46410i	−0.635999	+	0.367194i	0.147073	+	0.989126i	$0.453015\pi$
$90$		0			0
$91$	6.92820	−	2.00000i	0.726273	−	0.209657i
$92$		0			0
$93$	4.00000	+	6.92820i	0.414781	+	0.718421i
$94$		0			0
$95$	−5.19615	+	9.00000i	−0.533114	+	0.923381i
$96$		0			0
$97$	12.0000	+	6.92820i	1.21842	+	0.703452i	0.964579	−	0.263795i	$-0.0849741\pi$
$97$	12.0000	+	6.92820i	1.21842	+	0.703452i	0.253837	+	0.967247i	$0.418307\pi$
$98$		0			0
$99$	−3.46410			−0.348155
$100$		0			0
$101$	16.5000	−	9.52628i	1.64181	−	0.947900i	0.661622	−	0.749838i	$-0.269868\pi$
$101$	16.5000	−	9.52628i	1.64181	−	0.947900i	0.980189	−	0.198063i	$-0.0634650\pi$
$102$		0			0
$103$	−10.3923			−1.02398			−0.511992	−	0.858990i	$-0.671092\pi$
$103$	−10.3923			−1.02398			−0.511992	+	0.858990i	$0.671092\pi$
$104$		0			0
$105$	12.0000			1.17108
$106$		0			0
$107$	−10.3923	+	6.00000i	−1.00466	+	0.580042i	−0.909624	−	0.415432i	$-0.863630\pi$
$107$	−10.3923	+	6.00000i	−1.00466	+	0.580042i	−0.0950377	+	0.995474i	$0.530297\pi$
$108$		0			0
$109$	−10.0000			−0.957826			−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000			−0.957826			−0.478913	+	0.877862i	$0.658969\pi$
$110$		0			0
$111$	19.0526	+	11.0000i	1.80839	+	1.04407i
$112$		0			0
$113$	−4.50000	+	7.79423i	−0.423324	+	0.733219i	−0.996262	−	0.0863794i	$-0.972470\pi$
$113$	−4.50000	+	7.79423i	−0.423324	+	0.733219i	0.572938	+	0.819599i	$0.305804\pi$
$114$		0			0
$115$	−10.3923	−	18.0000i	−0.969087	−	1.67851i
$116$		0			0
$117$	−1.00000	−	3.46410i	−0.0924500	−	0.320256i
$118$		0			0
$119$	−5.19615	+	3.00000i	−0.476331	+	0.275010i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$		0			0
$123$	−5.19615	+	9.00000i	−0.468521	+	0.811503i
$124$		0			0
$125$	−3.00000			−0.268328
$126$		0			0
$127$	8.66025	+	15.0000i	0.768473	+	1.33103i	0.938391	+	0.345576i	$0.112317\pi$
$127$	8.66025	+	15.0000i	0.768473	+	1.33103i	−0.169917	+	0.985458i	$0.554350\pi$
$128$		0			0
$129$	−16.0000			−1.40872
$130$		0			0
$131$		0			0		1.00000			$0$
$131$		0			0		−1.00000			$\pi$
$132$		0			0
$133$	−6.00000	+	3.46410i	−0.520266	+	0.300376i
$134$		0			0
$135$			12.0000i			1.03280i
$136$		0			0
$137$	−19.5000	−	11.2583i	−1.66600	−	0.961864i	−0.969763	−	0.244050i	$-0.921524\pi$
$137$	−19.5000	−	11.2583i	−1.66600	−	0.961864i	−0.696235	−	0.717814i	$-0.745143\pi$
$138$		0			0
$139$	17.3205	+	10.0000i	1.46911	+	0.848189i	0.999400	−	0.0346338i	$-0.0110265\pi$
$139$	17.3205	+	10.0000i	1.46911	+	0.848189i	0.469706	+	0.882823i	$0.344360\pi$
$140$		0			0
$141$	−6.00000	−	10.3923i	−0.505291	−	0.875190i
$142$		0			0
$143$	−12.1244	−	3.00000i	−1.01389	−	0.250873i
$144$		0			0
$145$	4.50000	−	2.59808i	0.373705	−	0.215758i
$146$		0			0
$147$	−5.19615	−	3.00000i	−0.428571	−	0.247436i
$148$		0			0
$149$	7.50000	−	12.9904i	0.614424	−	1.06421i	−0.376061	−	0.926595i	$-0.622722\pi$
$149$	7.50000	−	12.9904i	0.614424	−	1.06421i	0.990485	−	0.137619i	$-0.0439449\pi$
$150$		0			0
$151$		−	4.00000i		−	0.325515i	−0.986666	−	0.162758i	$-0.947961\pi$
$151$		−	4.00000i		−	0.325515i	0.986666	−	0.162758i	$-0.0520389\pi$
$152$		0			0
$153$	1.50000	+	2.59808i	0.121268	+	0.210042i
$154$		0			0
$155$			12.0000i			0.963863i
$156$		0			0
$157$		−	1.73205i		−	0.138233i	−0.997609	−	0.0691164i	$-0.977982\pi$
$157$		−	1.73205i		−	0.138233i	0.997609	−	0.0691164i	$-0.0220180\pi$
$158$		0			0
$159$	12.1244	+	21.0000i	0.961524	+	1.66541i
$160$		0			0
$161$		−	13.8564i		−	1.09204i
$162$		0			0
$163$	−10.3923	+	18.0000i	−0.813988	+	1.40987i	0.0960641	+	0.995375i	$0.469375\pi$
$163$	−10.3923	+	18.0000i	−0.813988	+	1.40987i	−0.910052	+	0.414494i	$0.863959\pi$
$164$		0			0
$165$	−18.0000	−	10.3923i	−1.40130	−	0.809040i
$166$		0			0
$167$	5.19615	−	3.00000i	0.402090	−	0.232147i	−0.285295	−	0.958440i	$-0.592092\pi$
$167$	5.19615	−	3.00000i	0.402090	−	0.232147i	0.687386	+	0.726293i	$0.258758\pi$
$168$		0			0
$169$	−0.500000	−	12.9904i	−0.0384615	−	0.999260i
$170$		0			0
$171$	1.73205	+	3.00000i	0.132453	+	0.229416i
$172$		0			0
$173$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$173$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$174$		0			0
$175$	6.92820	+	4.00000i	0.523723	+	0.302372i
$176$		0			0
$177$		−	6.92820i		−	0.520756i
$178$		0			0
$179$	10.3923	−	6.00000i	0.776757	−	0.448461i	−0.0585225	−	0.998286i	$-0.518639\pi$
$179$	10.3923	−	6.00000i	0.776757	−	0.448461i	0.835280	+	0.549825i	$0.185306\pi$
$180$		0			0
$181$		−	1.73205i		−	0.128742i	−0.997926	−	0.0643712i	$-0.979496\pi$
$181$		−	1.73205i		−	0.128742i	0.997926	−	0.0643712i	$-0.0205042\pi$
$182$		0			0
$183$	3.46410			0.256074
$184$		0			0
$185$	16.5000	+	28.5788i	1.21310	+	2.10116i
$186$		0			0
$187$	10.3923			0.759961
$188$		0			0
$189$	−4.00000	+	6.92820i	−0.290957	+	0.503953i
$190$		0			0
$191$	−6.92820	+	12.0000i	−0.501307	+	0.868290i	0.498692	+	0.866779i	$0.333814\pi$
$191$	−6.92820	+	12.0000i	−0.501307	+	0.868290i	−0.999999	+	0.00151007i	$0.999519\pi$
$192$		0			0
$193$	−13.5000	+	7.79423i	−0.971751	+	0.561041i	−0.899770	−	0.436365i	$-0.856266\pi$
$193$	−13.5000	+	7.79423i	−0.971751	+	0.561041i	−0.0719816	+	0.997406i	$0.522932\pi$
$194$		0			0
$195$	5.19615	−	21.0000i	0.372104	−	1.50384i
$196$		0			0
$197$	−3.00000	−	5.19615i	−0.213741	−	0.370211i	0.739141	−	0.673550i	$-0.235232\pi$
$197$	−3.00000	−	5.19615i	−0.213741	−	0.370211i	−0.952882	+	0.303340i	$0.901898\pi$
$198$		0			0
$199$	−13.8564	+	24.0000i	−0.982255	+	1.70131i	−0.328702	+	0.944434i	$0.606611\pi$
$199$	−13.8564	+	24.0000i	−0.982255	+	1.70131i	−0.653552	+	0.756881i	$0.726722\pi$
$200$		0			0
$201$	−12.0000	−	6.92820i	−0.846415	−	0.488678i
$202$		0			0
$203$	3.46410			0.243132
$204$		0			0
$205$	−13.5000	+	7.79423i	−0.942881	+	0.544373i
$206$		0			0
$207$	−6.92820			−0.481543
$208$		0			0
$209$	12.0000			0.830057
$210$		0			0
$211$	−6.92820	+	4.00000i	−0.476957	+	0.275371i	−0.719148	−	0.694857i	$-0.755467\pi$
$211$	−6.92820	+	4.00000i	−0.476957	+	0.275371i	0.242190	+	0.970229i	$0.422134\pi$
$212$		0			0
$213$	−12.0000			−0.822226
$214$		0			0
$215$	−20.7846	−	12.0000i	−1.41750	−	0.818393i
$216$		0			0
$217$	−4.00000	+	6.92820i	−0.271538	+	0.470317i
$218$		0			0
$219$	−12.1244	−	21.0000i	−0.819288	−	1.41905i
$220$		0			0
$221$	3.00000	+	10.3923i	0.201802	+	0.699062i
$222$		0			0
$223$	6.92820	−	4.00000i	0.463947	−	0.267860i	−0.249756	−	0.968309i	$-0.580350\pi$
$223$	6.92820	−	4.00000i	0.463947	−	0.267860i	0.713702	+	0.700449i	$0.247017\pi$
$224$		0			0
$225$	2.00000	−	3.46410i	0.133333	−	0.230940i
$226$		0			0
$227$	−5.19615	+	9.00000i	−0.344881	+	0.597351i	−0.985332	−	0.170648i	$-0.945414\pi$
$227$	−5.19615	+	9.00000i	−0.344881	+	0.597351i	0.640451	+	0.767999i	$0.278747\pi$
$228$		0			0
$229$	−10.0000			−0.660819			−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000			−0.660819			−0.330409	+	0.943838i	$0.607187\pi$
$230$		0			0
$231$	−6.92820	−	12.0000i	−0.455842	−	0.789542i
$232$		0			0
$233$	18.0000			1.17922			0.589610	−	0.807688i	$-0.299282\pi$
$233$	18.0000			1.17922			0.589610	+	0.807688i	$0.299282\pi$
$234$		0			0
$235$		−	18.0000i		−	1.17419i
$236$		0			0
$237$	6.00000	−	3.46410i	0.389742	−	0.225018i
$238$		0			0
$239$		−	6.00000i		−	0.388108i	−0.980991	−	0.194054i	$-0.937836\pi$
$239$		−	6.00000i		−	0.388108i	0.980991	−	0.194054i	$-0.0621637\pi$
$240$		0			0
$241$	−10.5000	−	6.06218i	−0.676364	−	0.390499i	0.122119	−	0.992515i	$-0.461031\pi$
$241$	−10.5000	−	6.06218i	−0.676364	−	0.390499i	−0.798484	+	0.602016i	$0.794364\pi$
$242$		0			0
$243$	8.66025	+	5.00000i	0.555556	+	0.320750i
$244$		0			0
$245$	−4.50000	−	7.79423i	−0.287494	−	0.497955i
$246$		0			0
$247$	3.46410	+	12.0000i	0.220416	+	0.763542i
$248$		0			0
$249$	12.0000	−	6.92820i	0.760469	−	0.439057i
$250$		0			0
$251$	−10.3923	−	6.00000i	−0.655956	−	0.378717i	0.134778	−	0.990876i	$-0.456968\pi$
$251$	−10.3923	−	6.00000i	−0.655956	−	0.378717i	−0.790735	+	0.612159i	$0.790301\pi$
$252$		0			0
$253$	−12.0000	+	20.7846i	−0.754434	+	1.30672i
$254$		0			0
$255$			18.0000i			1.12720i
$256$		0			0
$257$	4.50000	+	7.79423i	0.280702	+	0.486191i	0.971558	−	0.236802i	$-0.0760993\pi$
$257$	4.50000	+	7.79423i	0.280702	+	0.486191i	−0.690856	+	0.722993i	$0.742766\pi$
$258$		0			0
$259$			22.0000i			1.36701i
$260$		0			0
$261$		−	1.73205i		−	0.107211i
$262$		0			0
$263$	−13.8564	−	24.0000i	−0.854423	−	1.47990i	−0.877180	−	0.480162i	$-0.840578\pi$
$263$	−13.8564	−	24.0000i	−0.854423	−	1.47990i	0.0227570	−	0.999741i	$-0.492756\pi$
$264$		0			0
$265$			36.3731i			2.23438i
$266$		0			0
$267$	−6.92820	+	12.0000i	−0.423999	+	0.734388i
$268$		0			0
$269$	6.00000	+	3.46410i	0.365826	+	0.211210i	0.671634	−	0.740883i	$-0.265593\pi$
$269$	6.00000	+	3.46410i	0.365826	+	0.211210i	−0.305807	+	0.952093i	$0.598926\pi$
$270$		0			0
$271$	−1.73205	+	1.00000i	−0.105215	+	0.0607457i	−0.551684	−	0.834053i	$-0.686015\pi$
$271$	−1.73205	+	1.00000i	−0.105215	+	0.0607457i	0.446469	+	0.894799i	$0.352681\pi$
$272$		0			0
$273$	10.0000	−	10.3923i	0.605228	−	0.628971i
$274$		0			0
$275$	−6.92820	−	12.0000i	−0.417786	−	0.723627i
$276$		0			0
$277$	−4.50000	−	2.59808i	−0.270379	−	0.156103i	0.358681	−	0.933460i	$-0.383227\pi$
$277$	−4.50000	−	2.59808i	−0.270379	−	0.156103i	−0.629060	+	0.777357i	$0.716560\pi$
$278$		0			0
$279$	3.46410	+	2.00000i	0.207390	+	0.119737i
$280$		0			0
$281$		−	22.5167i		−	1.34323i	−0.740900	−	0.671616i	$-0.765601\pi$
$281$		−	22.5167i		−	1.34323i	0.740900	−	0.671616i	$-0.234399\pi$
$282$		0			0
$283$	12.1244	−	7.00000i	0.720718	−	0.416107i	−0.0942988	−	0.995544i	$-0.530061\pi$
$283$	12.1244	−	7.00000i	0.720718	−	0.416107i	0.815017	+	0.579437i	$0.196728\pi$
$284$		0			0
$285$			20.7846i			1.23117i
$286$		0			0
$287$	−10.3923			−0.613438
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$	27.7128			1.62455
$292$		0			0
$293$	1.50000	−	2.59808i	0.0876309	−	0.151781i	−0.818878	−	0.573967i	$-0.805404\pi$
$293$	1.50000	−	2.59808i	0.0876309	−	0.151781i	0.906509	+	0.422186i	$0.138737\pi$
$294$		0			0
$295$	5.19615	−	9.00000i	0.302532	−	0.524000i
$296$		0			0
$297$	12.0000	−	6.92820i	0.696311	−	0.402015i
$298$		0			0
$299$	−24.2487	−	6.00000i	−1.40234	−	0.346989i
$300$		0			0
$301$	−8.00000	−	13.8564i	−0.461112	−	0.798670i
$302$		0			0
$303$	19.0526	−	33.0000i	1.09454	−	1.89580i
$304$		0			0
$305$	4.50000	+	2.59808i	0.257669	+	0.148765i
$306$		0			0
$307$	13.8564			0.790827			0.395413	−	0.918503i	$-0.370601\pi$
$307$	13.8564			0.790827			0.395413	+	0.918503i	$0.370601\pi$
$308$		0			0
$309$	−18.0000	+	10.3923i	−1.02398	+	0.591198i
$310$		0			0
$311$	24.2487			1.37502			0.687509	−	0.726176i	$-0.258704\pi$
$311$	24.2487			1.37502			0.687509	+	0.726176i	$0.258704\pi$
$312$		0			0
$313$	−10.0000			−0.565233			−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000			−0.565233			−0.282617	+	0.959233i	$0.591202\pi$
$314$		0			0
$315$	5.19615	−	3.00000i	0.292770	−	0.169031i
$316$		0			0
$317$	15.0000			0.842484			0.421242	−	0.906948i	$-0.361594\pi$
$317$	15.0000			0.842484			0.421242	+	0.906948i	$0.361594\pi$
$318$		0			0
$319$	−5.19615	−	3.00000i	−0.290929	−	0.167968i
$320$		0			0
$321$	−12.0000	+	20.7846i	−0.669775	+	1.16008i
$322$		0			0
$323$	−5.19615	−	9.00000i	−0.289122	−	0.500773i
$324$		0			0
$325$	10.0000	−	10.3923i	0.554700	−	0.576461i
$326$		0			0
$327$	−17.3205	+	10.0000i	−0.957826	+	0.553001i
$328$		0			0
$329$	6.00000	−	10.3923i	0.330791	−	0.572946i
$330$		0			0
$331$	−3.46410	+	6.00000i	−0.190404	+	0.329790i	−0.945384	−	0.325958i	$-0.894313\pi$
$331$	−3.46410	+	6.00000i	−0.190404	+	0.329790i	0.754980	+	0.655748i	$0.227647\pi$
$332$		0			0
$333$	11.0000			0.602796
$334$		0			0
$335$	−10.3923	−	18.0000i	−0.567792	−	0.983445i
$336$		0			0
$337$	−31.0000			−1.68868			−0.844339	−	0.535810i	$-0.820006\pi$
$337$	−31.0000			−1.68868			−0.844339	+	0.535810i	$0.820006\pi$
$338$		0			0
$339$			18.0000i			0.977626i
$340$		0			0
$341$	12.0000	−	6.92820i	0.649836	−	0.375183i
$342$		0			0
$343$		−	20.0000i		−	1.07990i
$344$		0			0
$345$	−36.0000	−	20.7846i	−1.93817	−	1.11901i
$346$		0			0
$347$	10.3923	+	6.00000i	0.557888	+	0.322097i	0.752297	−	0.658824i	$-0.228946\pi$
$347$	10.3923	+	6.00000i	0.557888	+	0.322097i	−0.194409	+	0.980921i	$0.562279\pi$
$348$		0			0
$349$	11.0000	+	19.0526i	0.588817	+	1.01986i	0.994388	+	0.105797i	$0.0337393\pi$
$349$	11.0000	+	19.0526i	0.588817	+	1.01986i	−0.405571	+	0.914063i	$0.632927\pi$
$350$		0			0
$351$	10.3923	+	10.0000i	0.554700	+	0.533761i
$352$		0			0
$353$	−1.50000	+	0.866025i	−0.0798369	+	0.0460939i	−0.539387	−	0.842058i	$-0.681344\pi$
$353$	−1.50000	+	0.866025i	−0.0798369	+	0.0460939i	0.459550	+	0.888152i	$0.348011\pi$
$354$		0			0
$355$	−15.5885	−	9.00000i	−0.827349	−	0.477670i
$356$		0			0
$357$	−6.00000	+	10.3923i	−0.317554	+	0.550019i
$358$		0			0
$359$			12.0000i			0.633336i	0.948536	+	0.316668i	$0.102564\pi$
$359$			12.0000i			0.633336i	−0.948536	+	0.316668i	$0.897436\pi$
$360$		0			0
$361$	3.50000	+	6.06218i	0.184211	+	0.319062i
$362$		0			0
$363$			2.00000i			0.104973i
$364$		0			0
$365$		−	36.3731i		−	1.90385i
$366$		0			0
$367$	13.8564	+	24.0000i	0.723299	+	1.25279i	0.959671	+	0.281127i	$0.0907083\pi$
$367$	13.8564	+	24.0000i	0.723299	+	1.25279i	−0.236372	+	0.971663i	$0.575958\pi$
$368$		0			0
$369$			5.19615i			0.270501i
$370$		0			0
$371$	−12.1244	+	21.0000i	−0.629465	+	1.09027i
$372$		0			0
$373$	31.5000	+	18.1865i	1.63101	+	0.941663i	0.983783	+	0.179364i	$0.0574041\pi$
$373$	31.5000	+	18.1865i	1.63101	+	0.941663i	0.647225	+	0.762299i	$0.275929\pi$
$374$		0			0
$375$	−5.19615	+	3.00000i	−0.268328	+	0.154919i
$376$		0			0
$377$	1.50000	−	6.06218i	0.0772539	−	0.312218i
$378$		0			0
$379$	8.66025	+	15.0000i	0.444847	+	0.770498i	0.998042	−	0.0625541i	$-0.0199246\pi$
$379$	8.66025	+	15.0000i	0.444847	+	0.770498i	−0.553194	+	0.833052i	$0.686591\pi$
$380$		0			0
$381$	30.0000	+	17.3205i	1.53695	+	0.887357i
$382$		0			0
$383$	−20.7846	−	12.0000i	−1.06204	−	0.613171i	−0.136047	−	0.990702i	$-0.543440\pi$
$383$	−20.7846	−	12.0000i	−1.06204	−	0.613171i	−0.925997	+	0.377531i	$0.876773\pi$
$384$		0			0
$385$		−	20.7846i		−	1.05928i
$386$		0			0
$387$	−6.92820	+	4.00000i	−0.352180	+	0.203331i
$388$		0			0
$389$		−	25.9808i		−	1.31728i	−0.752460	−	0.658638i	$-0.771133\pi$
$389$		−	25.9808i		−	1.31728i	0.752460	−	0.658638i	$-0.228867\pi$
$390$		0			0
$391$	20.7846			1.05112
$392$		0			0
$393$		0			0
$394$		0			0
$395$	10.3923			0.522894
$396$		0			0
$397$	19.0000	−	32.9090i	0.953583	−	1.65165i	0.216004	−	0.976392i	$-0.430698\pi$
$397$	19.0000	−	32.9090i	0.953583	−	1.65165i	0.737579	−	0.675261i	$-0.235969\pi$
$398$		0			0
$399$	−6.92820	+	12.0000i	−0.346844	+	0.600751i
$400$		0			0
$401$	7.50000	−	4.33013i	0.374532	−	0.216236i	−0.300904	−	0.953654i	$-0.597289\pi$
$401$	7.50000	−	4.33013i	0.374532	−	0.216236i	0.675437	+	0.737418i	$0.263955\pi$
$402$		0			0
$403$	10.3923	+	10.0000i	0.517678	+	0.498135i
$404$		0			0
$405$	16.5000	+	28.5788i	0.819892	+	1.42009i
$406$		0			0
$407$	19.0526	−	33.0000i	0.944400	−	1.63575i
$408$		0			0
$409$	−4.50000	−	2.59808i	−0.222511	−	0.128467i	0.384602	−	0.923083i	$-0.374339\pi$
$409$	−4.50000	−	2.59808i	−0.222511	−	0.128467i	−0.607112	+	0.794616i	$0.707672\pi$
$410$		0			0
$411$	−45.0333			−2.22133
$412$		0			0
$413$	6.00000	−	3.46410i	0.295241	−	0.170457i
$414$		0			0
$415$	20.7846			1.02028
$416$		0			0
$417$	40.0000			1.95881
$418$		0			0
$419$	31.1769	−	18.0000i	1.52309	−	0.879358i	0.523465	−	0.852047i	$-0.324639\pi$
$419$	31.1769	−	18.0000i	1.52309	−	0.879358i	0.999627	−	0.0273103i	$-0.00869423\pi$
$420$		0			0
$421$	19.0000			0.926003			0.463002	−	0.886357i	$-0.346772\pi$
$421$	19.0000			0.926003			0.463002	+	0.886357i	$0.346772\pi$
$422$		0			0
$423$	−5.19615	−	3.00000i	−0.252646	−	0.145865i
$424$		0			0
$425$	−6.00000	+	10.3923i	−0.291043	+	0.504101i
$426$		0			0
$427$	1.73205	+	3.00000i	0.0838198	+	0.145180i
$428$		0			0
$429$	−24.0000	+	6.92820i	−1.15873	+	0.334497i
$430$		0			0
$431$	20.7846	−	12.0000i	1.00116	−	0.578020i	0.0925683	−	0.995706i	$-0.470492\pi$
$431$	20.7846	−	12.0000i	1.00116	−	0.578020i	0.908591	+	0.417687i	$0.137159\pi$
$432$		0			0
$433$	3.50000	−	6.06218i	0.168199	−	0.291330i	−0.769588	−	0.638541i	$-0.779538\pi$
$433$	3.50000	−	6.06218i	0.168199	−	0.291330i	0.937787	+	0.347212i	$0.112871\pi$
$434$		0			0
$435$	5.19615	−	9.00000i	0.249136	−	0.431517i
$436$		0			0
$437$	24.0000			1.14808
$438$		0			0
$439$	13.8564	+	24.0000i	0.661330	+	1.14546i	0.980266	+	0.197681i	$0.0633411\pi$
$439$	13.8564	+	24.0000i	0.661330	+	1.14546i	−0.318936	+	0.947776i	$0.603326\pi$
$440$		0			0
$441$	−3.00000			−0.142857
$442$		0			0
$443$		−	24.0000i		−	1.14027i	−0.821549	−	0.570137i	$-0.806890\pi$
$443$		−	24.0000i		−	1.14027i	0.821549	−	0.570137i	$-0.193110\pi$
$444$		0			0
$445$	−18.0000	+	10.3923i	−0.853282	+	0.492642i
$446$		0			0
$447$		−	30.0000i		−	1.41895i
$448$		0			0
$449$	−18.0000	−	10.3923i	−0.849473	−	0.490443i	0.0110003	−	0.999939i	$-0.496498\pi$
$449$	−18.0000	−	10.3923i	−0.849473	−	0.490443i	−0.860473	+	0.509496i	$0.829832\pi$
$450$		0			0
$451$	15.5885	+	9.00000i	0.734032	+	0.423793i
$452$		0			0
$453$	−4.00000	−	6.92820i	−0.187936	−	0.325515i
$454$		0			0
$455$	20.7846	−	6.00000i	0.974398	−	0.281284i
$456$		0			0
$457$	−16.5000	+	9.52628i	−0.771837	+	0.445621i	−0.833530	−	0.552475i	$-0.813684\pi$
$457$	−16.5000	+	9.52628i	−0.771837	+	0.445621i	0.0616922	+	0.998095i	$0.480350\pi$
$458$		0			0
$459$	−10.3923	−	6.00000i	−0.485071	−	0.280056i
$460$		0			0
$461$	7.50000	−	12.9904i	0.349310	−	0.605022i	−0.636817	−	0.771015i	$-0.719749\pi$
$461$	7.50000	−	12.9904i	0.349310	−	0.605022i	0.986127	+	0.165992i	$0.0530827\pi$
$462$		0			0
$463$		−	32.0000i		−	1.48717i	−0.668644	−	0.743583i	$-0.733125\pi$
$463$		−	32.0000i		−	1.48717i	0.668644	−	0.743583i	$-0.266875\pi$
$464$		0			0
$465$	12.0000	+	20.7846i	0.556487	+	0.963863i
$466$		0			0
$467$			6.00000i			0.277647i	0.990317	+	0.138823i	$0.0443321\pi$
$467$			6.00000i			0.277647i	−0.990317	+	0.138823i	$0.955668\pi$
$468$		0			0
$469$		−	13.8564i		−	0.639829i
$470$		0			0
$471$	−1.73205	−	3.00000i	−0.0798087	−	0.138233i
$472$		0			0
$473$			27.7128i			1.27424i
$474$		0			0
$475$	−6.92820	+	12.0000i	−0.317888	+	0.550598i
$476$		0			0
$477$	10.5000	+	6.06218i	0.480762	+	0.277568i
$478$		0			0
$479$	−25.9808	+	15.0000i	−1.18709	+	0.685367i	−0.957644	−	0.287954i	$-0.907025\pi$
$479$	−25.9808	+	15.0000i	−1.18709	+	0.685367i	−0.229447	+	0.973321i	$0.573692\pi$
$480$		0			0
$481$	38.5000	+	9.52628i	1.75545	+	0.434361i
$482$		0			0
$483$	−13.8564	−	24.0000i	−0.630488	−	1.09204i
$484$		0			0
$485$	36.0000	+	20.7846i	1.63468	+	0.943781i
$486$		0			0
$487$	13.8564	+	8.00000i	0.627894	+	0.362515i	0.779936	−	0.625859i	$-0.215252\pi$
$487$	13.8564	+	8.00000i	0.627894	+	0.362515i	−0.152042	+	0.988374i	$0.548585\pi$
$488$		0			0
$489$			41.5692i			1.87983i
$490$		0			0
$491$	20.7846	−	12.0000i	0.937996	−	0.541552i	0.0486647	−	0.998815i	$-0.484503\pi$
$491$	20.7846	−	12.0000i	0.937996	−	0.541552i	0.889332	+	0.457263i	$0.151170\pi$
$492$		0			0
$493$			5.19615i			0.234023i
$494$		0			0
$495$	−10.3923			−0.467099
$496$		0			0
$497$	−6.00000	−	10.3923i	−0.269137	−	0.466159i
$498$		0			0
$499$	−10.3923			−0.465223			−0.232612	−	0.972570i	$-0.574727\pi$
$499$	−10.3923			−0.465223			−0.232612	+	0.972570i	$0.574727\pi$
$500$		0			0
$501$	6.00000	−	10.3923i	0.268060	−	0.464294i
$502$		0			0
$503$	6.92820	−	12.0000i	0.308913	−	0.535054i	−0.669212	−	0.743072i	$-0.733368\pi$
$503$	6.92820	−	12.0000i	0.308913	−	0.535054i	0.978125	+	0.208018i	$0.0667014\pi$
$504$		0			0
$505$	49.5000	−	28.5788i	2.20272	−	1.27174i
$506$		0			0
$507$	−13.8564	−	22.0000i	−0.615385	−	0.977054i
$508$		0			0
$509$	−7.50000	−	12.9904i	−0.332432	−	0.575789i	0.650556	−	0.759458i	$-0.274536\pi$
$509$	−7.50000	−	12.9904i	−0.332432	−	0.575789i	−0.982988	+	0.183669i	$0.941202\pi$
$510$		0			0
$511$	12.1244	−	21.0000i	0.536350	−	0.928985i
$512$		0			0
$513$	−12.0000	−	6.92820i	−0.529813	−	0.305888i
$514$		0			0
$515$	−31.1769			−1.37382
$516$		0			0
$517$	−18.0000	+	10.3923i	−0.791639	+	0.457053i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−3.00000			−0.131432			−0.0657162	−	0.997838i	$-0.520933\pi$
$521$	−3.00000			−0.131432			−0.0657162	+	0.997838i	$0.520933\pi$
$522$		0			0
$523$	22.5167	−	13.0000i	0.984585	−	0.568450i	0.0809336	−	0.996719i	$-0.474210\pi$
$523$	22.5167	−	13.0000i	0.984585	−	0.568450i	0.903651	+	0.428269i	$0.140876\pi$
$524$		0			0
$525$	16.0000			0.698297
$526$		0			0
$527$	−10.3923	−	6.00000i	−0.452696	−	0.261364i
$528$		0			0
$529$	−12.5000	+	21.6506i	−0.543478	+	0.941332i
$530$		0			0
$531$	−1.73205	−	3.00000i	−0.0751646	−	0.130189i
$532$		0			0
$533$	−4.50000	+	18.1865i	−0.194917	+	0.787746i
$534$		0			0
$535$	−31.1769	+	18.0000i	−1.34790	+	0.778208i
$536$		0			0
$537$	12.0000	−	20.7846i	0.517838	−	0.896922i
$538$		0			0
$539$	−5.19615	+	9.00000i	−0.223814	+	0.387657i
$540$		0			0
$541$	−11.0000			−0.472927			−0.236463	−	0.971640i	$-0.575988\pi$
$541$	−11.0000			−0.472927			−0.236463	+	0.971640i	$0.575988\pi$
$542$		0			0
$543$	−1.73205	−	3.00000i	−0.0743294	−	0.128742i
$544$		0			0
$545$	−30.0000			−1.28506
$546$		0			0
$547$		−	26.0000i		−	1.11168i	−0.831289	−	0.555840i	$-0.812397\pi$
$547$		−	26.0000i		−	1.11168i	0.831289	−	0.555840i	$-0.187603\pi$
$548$		0			0
$549$	1.50000	−	0.866025i	0.0640184	−	0.0369611i
$550$		0			0
$551$			6.00000i			0.255609i
$552$		0			0
$553$	6.00000	+	3.46410i	0.255146	+	0.147309i
$554$		0			0
$555$	57.1577	+	33.0000i	2.42621	+	1.40077i
$556$		0			0
$557$	−16.5000	−	28.5788i	−0.699127	−	1.21092i	−0.968769	−	0.247964i	$-0.920239\pi$
$557$	−16.5000	−	28.5788i	−0.699127	−	1.21092i	0.269642	−	0.962961i	$-0.413095\pi$
$558$		0			0
$559$	−27.7128	+	8.00000i	−1.17213	+	0.338364i
$560$		0			0
$561$	18.0000	−	10.3923i	0.759961	−	0.438763i
$562$		0			0
$563$	25.9808	+	15.0000i	1.09496	+	0.632175i	0.934892	−	0.354932i	$-0.115496\pi$
$563$	25.9808	+	15.0000i	1.09496	+	0.632175i	0.160066	+	0.987106i	$0.448829\pi$
$564$		0			0
$565$	−13.5000	+	23.3827i	−0.567949	+	0.983717i
$566$		0			0
$567$			22.0000i			0.923913i
$568$		0			0
$569$	−15.0000	−	25.9808i	−0.628833	−	1.08917i	−0.987786	−	0.155815i	$-0.950200\pi$
$569$	−15.0000	−	25.9808i	−0.628833	−	1.08917i	0.358954	−	0.933355i	$-0.383134\pi$
$570$		0			0
$571$			2.00000i			0.0836974i	0.999124	+	0.0418487i	$0.0133247\pi$
$571$			2.00000i			0.0836974i	−0.999124	+	0.0418487i	$0.986675\pi$
$572$		0			0
$573$			27.7128i			1.15772i
$574$		0			0
$575$	−13.8564	−	24.0000i	−0.577852	−	1.00087i
$576$		0			0
$577$		−	8.66025i		−	0.360531i	−0.983618	−	0.180266i	$-0.942304\pi$
$577$		−	8.66025i		−	0.360531i	0.983618	−	0.180266i	$-0.0576957\pi$
$578$		0			0
$579$	−15.5885	+	27.0000i	−0.647834	+	1.12208i
$580$		0			0
$581$	12.0000	+	6.92820i	0.497844	+	0.287430i
$582$		0			0
$583$	36.3731	−	21.0000i	1.50642	−	0.869731i
$584$		0			0
$585$	−3.00000	−	10.3923i	−0.124035	−	0.429669i
$586$		0			0
$587$	−3.46410	−	6.00000i	−0.142979	−	0.247647i	0.785638	−	0.618686i	$-0.212335\pi$
$587$	−3.46410	−	6.00000i	−0.142979	−	0.247647i	−0.928617	+	0.371040i	$0.879001\pi$
$588$		0			0
$589$	−12.0000	−	6.92820i	−0.494451	−	0.285472i
$590$		0			0
$591$	−10.3923	−	6.00000i	−0.427482	−	0.246807i
$592$		0			0
$593$		−	22.5167i		−	0.924648i	−0.886711	−	0.462324i	$-0.847016\pi$
$593$		−	22.5167i		−	0.924648i	0.886711	−	0.462324i	$-0.152984\pi$
$594$		0			0
$595$	−15.5885	+	9.00000i	−0.639064	+	0.368964i
$596$		0			0
$597$			55.4256i			2.26842i
$598$		0			0
$599$	−20.7846			−0.849236			−0.424618	−	0.905373i	$-0.639592\pi$
$599$	−20.7846			−0.849236			−0.424618	+	0.905373i	$0.639592\pi$
$600$		0			0
$601$	−3.50000	−	6.06218i	−0.142768	−	0.247281i	0.785770	−	0.618519i	$-0.212267\pi$
$601$	−3.50000	−	6.06218i	−0.142768	−	0.247281i	−0.928538	+	0.371237i	$0.878934\pi$
$602$		0			0
$603$	−6.92820			−0.282138
$604$		0			0
$605$	−1.50000	+	2.59808i	−0.0609837	+	0.105627i
$606$		0			0
$607$	19.0526	−	33.0000i	0.773320	−	1.33943i	−0.162415	−	0.986723i	$-0.551928\pi$
$607$	19.0526	−	33.0000i	0.773320	−	1.33943i	0.935734	−	0.352706i	$-0.114738\pi$
$608$		0			0
$609$	6.00000	−	3.46410i	0.243132	−	0.140372i
$610$		0			0
$611$	−15.5885	−	15.0000i	−0.630641	−	0.606835i
$612$		0			0
$613$	−12.5000	−	21.6506i	−0.504870	−	0.874461i	−0.999984	−	0.00563283i	$-0.998207\pi$
$613$	−12.5000	−	21.6506i	−0.504870	−	0.874461i	0.495114	−	0.868828i	$-0.335126\pi$
$614$		0			0
$615$	−15.5885	+	27.0000i	−0.628587	+	1.08875i
$616$		0			0
$617$	−4.50000	−	2.59808i	−0.181163	−	0.104595i	0.406676	−	0.913573i	$-0.366688\pi$
$617$	−4.50000	−	2.59808i	−0.181163	−	0.104595i	−0.587839	+	0.808978i	$0.700021\pi$
$618$		0			0
$619$	−10.3923			−0.417702			−0.208851	−	0.977947i	$-0.566972\pi$
$619$	−10.3923			−0.417702			−0.208851	+	0.977947i	$0.566972\pi$
$620$		0			0
$621$	24.0000	−	13.8564i	0.963087	−	0.556038i
$622$		0			0
$623$	−13.8564			−0.555145
$624$		0			0
$625$	−29.0000			−1.16000
$626$		0			0
$627$	20.7846	−	12.0000i	0.830057	−	0.479234i
$628$		0			0
$629$	−33.0000			−1.31580
$630$		0			0
$631$	−17.3205	−	10.0000i	−0.689519	−	0.398094i	0.113913	−	0.993491i	$-0.463661\pi$
$631$	−17.3205	−	10.0000i	−0.689519	−	0.398094i	−0.803432	+	0.595397i	$0.796995\pi$
$632$		0			0
$633$	−8.00000	+	13.8564i	−0.317971	+	0.550743i
$634$		0			0
$635$	25.9808	+	45.0000i	1.03102	+	1.78577i
$636$		0			0
$637$	−10.5000	−	2.59808i	−0.416025	−	0.102940i
$638$		0			0
$639$	−5.19615	+	3.00000i	−0.205557	+	0.118678i
$640$		0			0
$641$	−13.5000	+	23.3827i	−0.533218	+	0.923561i	0.466029	+	0.884769i	$0.345684\pi$
$641$	−13.5000	+	23.3827i	−0.533218	+	0.923561i	−0.999247	+	0.0387913i	$0.987649\pi$
$642$		0			0
$643$	1.73205	−	3.00000i	0.0683054	−	0.118308i	−0.829850	−	0.557986i	$-0.811574\pi$
$643$	1.73205	−	3.00000i	0.0683054	−	0.118308i	0.898155	+	0.439678i	$0.144907\pi$
$644$		0			0
$645$	−48.0000			−1.89000
$646$		0			0
$647$	3.46410	+	6.00000i	0.136188	+	0.235884i	0.926051	−	0.377399i	$-0.123182\pi$
$647$	3.46410	+	6.00000i	0.136188	+	0.235884i	−0.789863	+	0.613284i	$0.789848\pi$
$648$		0			0
$649$	−12.0000			−0.471041
$650$		0			0
$651$			16.0000i			0.627089i
$652$		0			0
$653$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$653$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−10.5000	−	6.06218i	−0.409644	−	0.236508i
$658$		0			0
$659$	−31.1769	−	18.0000i	−1.21448	−	0.701180i	−0.250748	−	0.968052i	$-0.580677\pi$
$659$	−31.1769	−	18.0000i	−1.21448	−	0.701180i	−0.963732	+	0.266872i	$0.914010\pi$
$660$		0			0
$661$	0.500000	+	0.866025i	0.0194477	+	0.0336845i	0.875585	−	0.483063i	$-0.160476\pi$
$661$	0.500000	+	0.866025i	0.0194477	+	0.0336845i	−0.856138	+	0.516748i	$0.827143\pi$
$662$		0			0
$663$	15.5885	+	15.0000i	0.605406	+	0.582552i
$664$		0			0
$665$	−18.0000	+	10.3923i	−0.698010	+	0.402996i
$666$		0			0
$667$	−10.3923	−	6.00000i	−0.402392	−	0.232321i
$668$		0			0
$669$	8.00000	−	13.8564i	0.309298	−	0.535720i
$670$		0			0
$671$		−	6.00000i		−	0.231627i
$672$		0			0
$673$	20.5000	+	35.5070i	0.790217	+	1.36870i	0.925832	+	0.377934i	$0.123365\pi$
$673$	20.5000	+	35.5070i	0.790217	+	1.36870i	−0.135615	+	0.990762i	$0.543301\pi$
$674$		0			0
$675$			16.0000i			0.615840i
$676$		0			0
$677$		0			0		1.00000			$0$
$677$		0			0		−1.00000			$\pi$
$678$		0			0
$679$	13.8564	+	24.0000i	0.531760	+	0.921035i
$680$		0			0
$681$			20.7846i			0.796468i
$682$		0			0
$683$	−24.2487	+	42.0000i	−0.927851	+	1.60709i	−0.140941	+	0.990018i	$0.545013\pi$
$683$	−24.2487	+	42.0000i	−0.927851	+	1.60709i	−0.786910	+	0.617067i	$0.788321\pi$
$684$		0			0
$685$	−58.5000	−	33.7750i	−2.23517	−	1.29048i
$686$		0			0
$687$	−17.3205	+	10.0000i	−0.660819	+	0.381524i
$688$		0			0
$689$	31.5000	+	30.3109i	1.20005	+	1.15475i
$690$		0			0
$691$	−12.1244	−	21.0000i	−0.461232	−	0.798878i	0.537790	−	0.843079i	$-0.319259\pi$
$691$	−12.1244	−	21.0000i	−0.461232	−	0.798878i	−0.999023	+	0.0442009i	$0.985926\pi$
$692$		0			0
$693$	−6.00000	−	3.46410i	−0.227921	−	0.131590i
$694$		0			0
$695$	51.9615	+	30.0000i	1.97101	+	1.13796i
$696$		0			0
$697$		−	15.5885i		−	0.590455i
$698$		0			0
$699$	31.1769	−	18.0000i	1.17922	−	0.680823i
$700$		0			0
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$		0			0
$703$	−38.1051			−1.43716
$704$		0			0
$705$	−18.0000	−	31.1769i	−0.677919	−	1.17419i
$706$		0			0
$707$	38.1051			1.43309
$708$		0			0
$709$	−9.50000	+	16.4545i	−0.356780	+	0.617961i	−0.987421	−	0.158114i	$-0.949459\pi$
$709$	−9.50000	+	16.4545i	−0.356780	+	0.617961i	0.630641	+	0.776075i	$0.282792\pi$
$710$		0			0
$711$	1.73205	−	3.00000i	0.0649570	−	0.112509i
$712$		0			0
$713$	24.0000	−	13.8564i	0.898807	−	0.518927i
$714$		0			0
$715$	−36.3731	−	9.00000i	−1.36028	−	0.336581i
$716$		0			0
$717$	−6.00000	−	10.3923i	−0.224074	−	0.388108i
$718$		0			0
$719$	−8.66025	+	15.0000i	−0.322973	+	0.559406i	−0.981100	−	0.193501i	$-0.938016\pi$
$719$	−8.66025	+	15.0000i	−0.322973	+	0.559406i	0.658127	+	0.752907i	$0.271349\pi$
$720$		0			0
$721$	−18.0000	−	10.3923i	−0.670355	−	0.387030i
$722$		0			0
$723$	−24.2487			−0.901819
$724$		0			0
$725$	6.00000	−	3.46410i	0.222834	−	0.128654i
$726$		0			0
$727$	−17.3205			−0.642382			−0.321191	−	0.947014i	$-0.604083\pi$
$727$	−17.3205			−0.642382			−0.321191	+	0.947014i	$0.604083\pi$
$728$		0			0
$729$	−13.0000			−0.481481
$730$		0			0
$731$	20.7846	−	12.0000i	0.768747	−	0.443836i
$732$		0			0
$733$	31.0000			1.14501			0.572506	−	0.819901i	$-0.305971\pi$
$733$	31.0000			1.14501			0.572506	+	0.819901i	$0.305971\pi$
$734$		0			0
$735$	−15.5885	−	9.00000i	−0.574989	−	0.331970i
$736$		0			0
$737$	−12.0000	+	20.7846i	−0.442026	+	0.765611i
$738$		0			0
$739$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$739$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$740$		0			0
$741$	18.0000	+	17.3205i	0.661247	+	0.636285i
$742$		0			0
$743$	20.7846	−	12.0000i	0.762513	−	0.440237i	−0.0676840	−	0.997707i	$-0.521561\pi$
$743$	20.7846	−	12.0000i	0.762513	−	0.440237i	0.830197	+	0.557470i	$0.188228\pi$
$744$		0			0
$745$	22.5000	−	38.9711i	0.824336	−	1.42779i
$746$		0			0
$747$	3.46410	−	6.00000i	0.126745	−	0.219529i
$748$		0			0
$749$	−24.0000			−0.876941
$750$		0			0
$751$	24.2487	+	42.0000i	0.884848	+	1.53260i	0.845888	+	0.533361i	$0.179071\pi$
$751$	24.2487	+	42.0000i	0.884848	+	1.53260i	0.0389603	+	0.999241i	$0.487595\pi$
$752$		0			0
$753$	−24.0000			−0.874609
$754$		0			0
$755$		−	12.0000i		−	0.436725i
$756$		0			0
$757$	12.0000	−	6.92820i	0.436147	−	0.251810i	−0.265815	−	0.964024i	$-0.585641\pi$
$757$	12.0000	−	6.92820i	0.436147	−	0.251810i	0.701962	+	0.712214i	$0.252308\pi$
$758$		0			0
$759$			48.0000i			1.74229i
$760$		0			0
$761$	6.00000	+	3.46410i	0.217500	+	0.125574i	0.604792	−	0.796383i	$-0.293256\pi$
$761$	6.00000	+	3.46410i	0.217500	+	0.125574i	−0.387292	+	0.921957i	$0.626590\pi$
$762$		0			0
$763$	−17.3205	−	10.0000i	−0.627044	−	0.362024i
$764$		0			0
$765$	4.50000	+	7.79423i	0.162698	+	0.281801i
$766$		0			0
$767$	−3.46410	−	12.0000i	−0.125081	−	0.433295i
$768$		0			0
$769$	42.0000	−	24.2487i	1.51456	−	0.874431i	0.514704	−	0.857368i	$-0.327902\pi$
$769$	42.0000	−	24.2487i	1.51456	−	0.874431i	0.999854	−	0.0170631i	$-0.00543163\pi$
$770$		0			0
$771$	15.5885	+	9.00000i	0.561405	+	0.324127i
$772$		0			0
$773$	15.0000	−	25.9808i	0.539513	−	0.934463i	−0.459418	−	0.888220i	$-0.651942\pi$
$773$	15.0000	−	25.9808i	0.539513	−	0.934463i	0.998930	−	0.0462427i	$-0.0147248\pi$
$774$		0			0
$775$			16.0000i			0.574737i
$776$		0			0
$777$	22.0000	+	38.1051i	0.789246	+	1.36701i
$778$		0			0
$779$		−	18.0000i		−	0.644917i
$780$		0			0
$781$			20.7846i			0.743732i
$782$		0			0
$783$	3.46410	+	6.00000i	0.123797	+	0.214423i
$784$		0			0
$785$		−	5.19615i		−	0.185459i
$786$		0			0
$787$	−6.92820	+	12.0000i	−0.246964	+	0.427754i	−0.962682	−	0.270635i	$-0.912766\pi$
$787$	−6.92820	+	12.0000i	−0.246964	+	0.427754i	0.715718	+	0.698389i	$0.246100\pi$
$788$		0			0
$789$	−48.0000	−	27.7128i	−1.70885	−	0.986602i
$790$		0			0
$791$	−15.5885	+	9.00000i	−0.554262	+	0.320003i
$792$		0			0
$793$	6.00000	−	1.73205i	0.213066	−	0.0615069i
$794$		0			0
$795$	36.3731	+	63.0000i	1.29002	+	2.23438i
$796$		0			0
$797$	−6.00000	−	3.46410i	−0.212531	−	0.122705i	0.389956	−	0.920833i	$-0.372490\pi$
$797$	−6.00000	−	3.46410i	−0.212531	−	0.122705i	−0.602487	+	0.798129i	$0.705823\pi$
$798$		0			0
$799$	15.5885	+	9.00000i	0.551480	+	0.318397i
$800$		0			0
$801$			6.92820i			0.244796i
$802$		0			0
$803$	−36.3731	+	21.0000i	−1.28358	+	0.741074i
$804$		0			0
$805$		−	41.5692i		−	1.46512i
$806$		0			0
$807$	13.8564			0.487769
$808$		0			0
$809$	19.5000	+	33.7750i	0.685583	+	1.18747i	0.973253	+	0.229736i	$0.0737862\pi$
$809$	19.5000	+	33.7750i	0.685583	+	1.18747i	−0.287670	+	0.957730i	$0.592880\pi$
$810$		0			0
$811$	−6.92820			−0.243282			−0.121641	−	0.992574i	$-0.538816\pi$
$811$	−6.92820			−0.243282			−0.121641	+	0.992574i	$0.538816\pi$
$812$		0			0
$813$	−2.00000	+	3.46410i	−0.0701431	+	0.121491i
$814$		0			0
$815$	−31.1769	+	54.0000i	−1.09208	+	1.89154i
$816$		0			0
$817$	24.0000	−	13.8564i	0.839654	−	0.484774i
$818$		0			0
$819$	1.73205	−	7.00000i	0.0605228	−	0.244600i
$820$		0			0
$821$	3.00000	+	5.19615i	0.104701	+	0.181347i	0.913616	−	0.406578i	$-0.133278\pi$
$821$	3.00000	+	5.19615i	0.104701	+	0.181347i	−0.808915	+	0.587925i	$0.799945\pi$
$822$		0			0
$823$	−8.66025	+	15.0000i	−0.301877	+	0.522867i	−0.976561	−	0.215240i	$-0.930947\pi$
$823$	−8.66025	+	15.0000i	−0.301877	+	0.522867i	0.674684	+	0.738107i	$0.264280\pi$
$824$		0			0
$825$	−24.0000	−	13.8564i	−0.835573	−	0.482418i
$826$		0			0
$827$	3.46410			0.120459			0.0602293	−	0.998185i	$-0.480817\pi$
$827$	3.46410			0.120459			0.0602293	+	0.998185i	$0.480817\pi$
$828$		0			0
$829$	−19.5000	+	11.2583i	−0.677263	+	0.391018i	−0.798823	−	0.601566i	$-0.794544\pi$
$829$	−19.5000	+	11.2583i	−0.677263	+	0.391018i	0.121560	+	0.992584i	$0.461210\pi$
$830$		0			0
$831$	−10.3923			−0.360505
$832$		0			0
$833$	9.00000			0.311832
$834$		0			0
$835$	15.5885	−	9.00000i	0.539461	−	0.311458i
$836$		0			0
$837$	−16.0000			−0.553041
$838$		0			0
$839$	46.7654	+	27.0000i	1.61452	+	0.932144i	0.988304	+	0.152493i	$0.0487303\pi$
$839$	46.7654	+	27.0000i	1.61452	+	0.932144i	0.626215	+	0.779650i	$0.284603\pi$
$840$		0			0
$841$	−13.0000	+	22.5167i	−0.448276	+	0.776437i
$842$		0			0
$843$	−22.5167	−	39.0000i	−0.775515	−	1.34323i
$844$		0			0
$845$	−1.50000	−	38.9711i	−0.0516016	−	1.34065i
$846$		0			0
$847$	−1.73205	+	1.00000i	−0.0595140	+	0.0343604i
$848$		0			0
$849$	14.0000	−	24.2487i	0.480479	−	0.832214i
$850$		0			0
$851$	38.1051	−	66.0000i	1.30623	−	2.26245i
$852$		0			0
$853$	47.0000			1.60925			0.804625	−	0.593784i	$-0.202367\pi$
$853$	47.0000			1.60925			0.804625	+	0.593784i	$0.202367\pi$
$854$		0			0
$855$	5.19615	+	9.00000i	0.177705	+	0.307794i
$856$		0			0
$857$	3.00000			0.102478			0.0512390	−	0.998686i	$-0.483683\pi$
$857$	3.00000			0.102478			0.0512390	+	0.998686i	$0.483683\pi$
$858$		0			0
$859$		−	44.0000i		−	1.50126i	−0.660722	−	0.750630i	$-0.729750\pi$
$859$		−	44.0000i		−	1.50126i	0.660722	−	0.750630i	$-0.270250\pi$
$860$		0			0
$861$	−18.0000	+	10.3923i	−0.613438	+	0.354169i
$862$		0			0
$863$			6.00000i			0.204242i	0.994772	+	0.102121i	$0.0325630\pi$
$863$			6.00000i			0.204242i	−0.994772	+	0.102121i	$0.967437\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	13.8564	+	8.00000i	0.470588	+	0.271694i
$868$		0			0
$869$	−6.00000	−	10.3923i	−0.203536	−	0.352535i
$870$		0			0
$871$	−24.2487	−	6.00000i	−0.821636	−	0.203302i
$872$		0			0
$873$	12.0000	−	6.92820i	0.406138	−	0.234484i
$874$		0			0
$875$	−5.19615	−	3.00000i	−0.175662	−	0.101419i
$876$		0			0
$877$	2.50000	−	4.33013i	0.0844190	−	0.146218i	−0.820724	−	0.571324i	$-0.806430\pi$
$877$	2.50000	−	4.33013i	0.0844190	−	0.146218i	0.905143	+	0.425106i	$0.139763\pi$
$878$		0			0
$879$		−	6.00000i		−	0.202375i
$880$		0			0
$881$	−1.50000	−	2.59808i	−0.0505363	−	0.0875314i	0.839651	−	0.543127i	$-0.182760\pi$
$881$	−1.50000	−	2.59808i	−0.0505363	−	0.0875314i	−0.890187	+	0.455595i	$0.849426\pi$
$882$		0			0
$883$			2.00000i			0.0673054i	0.999434	+	0.0336527i	$0.0107140\pi$
$883$			2.00000i			0.0673054i	−0.999434	+	0.0336527i	$0.989286\pi$
$884$		0			0
$885$		−	20.7846i		−	0.698667i
$886$		0			0
$887$	8.66025	+	15.0000i	0.290783	+	0.503651i	0.973995	−	0.226569i	$-0.0727509\pi$
$887$	8.66025	+	15.0000i	0.290783	+	0.503651i	−0.683212	+	0.730220i	$0.739418\pi$
$888$		0			0
$889$			34.6410i			1.16182i
$890$		0			0
$891$	19.0526	−	33.0000i	0.638285	−	1.10554i
$892$		0			0
$893$	18.0000	+	10.3923i	0.602347	+	0.347765i
$894$		0			0
$895$	31.1769	−	18.0000i	1.04213	−	0.601674i
$896$		0			0
$897$	−48.0000	+	13.8564i	−1.60267	+	0.462652i
$898$		0			0
$899$	3.46410	+	6.00000i	0.115534	+	0.200111i
$900$		0			0
$901$	−31.5000	−	18.1865i	−1.04942	−	0.605881i
$902$		0			0
$903$	−27.7128	−	16.0000i	−0.922225	−	0.532447i
$904$		0			0
$905$		−	5.19615i		−	0.172726i
$906$		0			0
$907$	3.46410	−	2.00000i	0.115024	−	0.0664089i	−0.441384	−	0.897318i	$-0.645512\pi$
$907$	3.46410	−	2.00000i	0.115024	−	0.0664089i	0.556408	+	0.830909i	$0.312179\pi$
$908$		0			0
$909$		−	19.0526i		−	0.631933i
$910$		0			0
$911$	−3.46410			−0.114771			−0.0573854	−	0.998352i	$-0.518276\pi$
$911$	−3.46410			−0.114771			−0.0573854	+	0.998352i	$0.518276\pi$
$912$		0			0
$913$	−12.0000	−	20.7846i	−0.397142	−	0.687870i
$914$		0			0
$915$	10.3923			0.343559
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−5.19615	+	9.00000i	−0.171405	+	0.296883i	−0.938911	−	0.344159i	$-0.888164\pi$
$919$	−5.19615	+	9.00000i	−0.171405	+	0.296883i	0.767506	+	0.641042i	$0.221497\pi$
$920$		0			0
$921$	24.0000	−	13.8564i	0.790827	−	0.456584i
$922$		0			0
$923$	−20.7846	+	6.00000i	−0.684134	+	0.197492i
$924$		0			0
$925$	22.0000	+	38.1051i	0.723356	+	1.25289i
$926$		0			0
$927$	−5.19615	+	9.00000i	−0.170664	+	0.295599i
$928$		0			0
$929$	−1.50000	−	0.866025i	−0.0492134	−	0.0284134i	0.475191	−	0.879882i	$-0.342379\pi$
$929$	−1.50000	−	0.866025i	−0.0492134	−	0.0284134i	−0.524405	+	0.851469i	$0.675712\pi$
$930$		0			0
$931$	10.3923			0.340594
$932$		0			0
$933$	42.0000	−	24.2487i	1.37502	−	0.793867i
$934$		0			0
$935$	31.1769			1.01959
$936$		0			0
$937$	−7.00000			−0.228680			−0.114340	−	0.993442i	$-0.536475\pi$
$937$	−7.00000			−0.228680			−0.114340	+	0.993442i	$0.536475\pi$
$938$		0			0
$939$	−17.3205	+	10.0000i	−0.565233	+	0.326338i
$940$		0			0
$941$	−30.0000			−0.977972			−0.488986	−	0.872292i	$-0.662633\pi$
$941$	−30.0000			−0.977972			−0.488986	+	0.872292i	$0.662633\pi$
$942$		0			0
$943$	31.1769	+	18.0000i	1.01526	+	0.586161i
$944$		0			0
$945$	−12.0000	+	20.7846i	−0.390360	+	0.676123i
$946$		0			0
$947$	29.4449	+	51.0000i	0.956830	+	1.65728i	0.730125	+	0.683314i	$0.239462\pi$
$947$	29.4449	+	51.0000i	0.956830	+	1.65728i	0.226705	+	0.973964i	$0.427205\pi$
$948$		0			0
$949$	−31.5000	−	30.3109i	−1.02253	−	0.983933i
$950$		0			0
$951$	25.9808	−	15.0000i	0.842484	−	0.486408i
$952$		0			0
$953$	9.00000	−	15.5885i	0.291539	−	0.504960i	−0.682635	−	0.730759i	$-0.739166\pi$
$953$	9.00000	−	15.5885i	0.291539	−	0.504960i	0.974174	+	0.225800i	$0.0724995\pi$
$954$		0			0
$955$	−20.7846	+	36.0000i	−0.672574	+	1.16493i
$956$		0			0
$957$	−12.0000			−0.387905
$958$		0			0
$959$	−22.5167	−	39.0000i	−0.727101	−	1.25938i
$960$		0			0
$961$	15.0000			0.483871
$962$		0			0
$963$			12.0000i			0.386695i
$964$		0			0
$965$	−40.5000	+	23.3827i	−1.30374	+	0.752715i
$966$		0			0
$967$			22.0000i			0.707472i	0.935345	+	0.353736i	$0.115089\pi$
$967$			22.0000i			0.707472i	−0.935345	+	0.353736i	$0.884911\pi$
$968$		0			0
$969$	−18.0000	−	10.3923i	−0.578243	−	0.333849i
$970$		0			0
$971$	5.19615	+	3.00000i	0.166752	+	0.0962746i	0.581054	−	0.813865i	$-0.302641\pi$
$971$	5.19615	+	3.00000i	0.166752	+	0.0962746i	−0.414301	+	0.910140i	$0.635974\pi$
$972$		0			0
$973$	20.0000	+	34.6410i	0.641171	+	1.11054i
$974$		0			0
$975$	6.92820	−	28.0000i	0.221880	−	0.896718i
$976$		0			0
$977$	10.5000	−	6.06218i	0.335925	−	0.193946i	−0.322544	−	0.946555i	$-0.604538\pi$
$977$	10.5000	−	6.06218i	0.335925	−	0.193946i	0.658468	+	0.752608i	$0.271205\pi$
$978$		0			0
$979$	20.7846	+	12.0000i	0.664279	+	0.383522i
$980$		0			0
$981$	−5.00000	+	8.66025i	−0.159638	+	0.276501i
$982$		0			0
$983$		0			0		1.00000			$0$
$983$		0			0		−1.00000			$\pi$
$984$		0			0
$985$	−9.00000	−	15.5885i	−0.286764	−	0.496690i
$986$		0			0
$987$		−	24.0000i		−	0.763928i
$988$		0			0
$989$			55.4256i			1.76243i
$990$		0			0
$991$	−19.0526	−	33.0000i	−0.605224	−	1.04828i	−0.992016	−	0.126112i	$-0.959750\pi$
$991$	−19.0526	−	33.0000i	−0.605224	−	1.04828i	0.386791	−	0.922167i	$-0.373583\pi$
$992$		0			0
$993$			13.8564i			0.439720i
$994$		0			0
$995$	−41.5692	+	72.0000i	−1.31783	+	2.28255i
$996$		0			0
$997$	37.5000	+	21.6506i	1.18764	+	0.685682i	0.957769	−	0.287539i	$-0.0928372\pi$
$997$	37.5000	+	21.6506i	1.18764	+	0.685682i	0.229868	+	0.973222i	$0.426171\pi$
$998$		0			0
$999$	−38.1051	+	22.0000i	−1.20559	+	0.696049i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	832.2.ba.d.673.2	yes	4
4.3	odd	2	inner	832.2.ba.d.673.1	yes	4
8.3	odd	2		832.2.ba.c.673.2	yes	4
8.5	even	2		832.2.ba.c.673.1	yes	4
13.4	even	6		832.2.ba.c.225.1	✓	4
52.43	odd	6		832.2.ba.c.225.2	yes	4
104.43	odd	6	inner	832.2.ba.d.225.1	yes	4
104.69	even	6	inner	832.2.ba.d.225.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
832.2.ba.c.225.1	✓	4	13.4	even	6
832.2.ba.c.225.2	yes	4	52.43	odd	6
832.2.ba.c.673.1	yes	4	8.5	even	2
832.2.ba.c.673.2	yes	4	8.3	odd	2
832.2.ba.d.225.1	yes	4	104.43	odd	6	inner
832.2.ba.d.225.2	yes	4	104.69	even	6	inner
832.2.ba.d.673.1	yes	4	4.3	odd	2	inner
832.2.ba.d.673.2	yes	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.73205 - 1.00000i) q^{3} +3.00000 q^{5} +(1.73205 + 1.00000i) q^{7} +(0.500000 - 0.866025i) q^{9} +(-1.73205 - 3.00000i) q^{11} +(2.50000 - 2.59808i) q^{13} +(5.19615 - 3.00000i) q^{15} +(-1.50000 + 2.59808i) q^{17} +(-1.73205 + 3.00000i) q^{19} +4.00000 q^{21} +(-3.46410 - 6.00000i) q^{23} +4.00000 q^{25} +4.00000i q^{27} +(1.50000 - 0.866025i) q^{29} +4.00000i q^{31} +(-6.00000 - 3.46410i) q^{33} +(5.19615 + 3.00000i) q^{35} +(5.50000 + 9.52628i) q^{37} +(1.73205 - 7.00000i) q^{39} +(-4.50000 + 2.59808i) q^{41} +(-6.92820 - 4.00000i) q^{43} +(1.50000 - 2.59808i) q^{45} -6.00000i q^{47} +(-1.50000 - 2.59808i) q^{49} +6.00000i q^{51} +12.1244i q^{53} +(-5.19615 - 9.00000i) q^{55} +6.92820i q^{57} +(1.73205 - 3.00000i) q^{59} +(1.50000 + 0.866025i) q^{61} +(1.73205 - 1.00000i) q^{63} +(7.50000 - 7.79423i) q^{65} +(-3.46410 - 6.00000i) q^{67} +(-12.0000 - 6.92820i) q^{69} +(-5.19615 - 3.00000i) q^{71} -12.1244i q^{73} +(6.92820 - 4.00000i) q^{75} -6.92820i q^{77} +3.46410 q^{79} +(5.50000 + 9.52628i) q^{81} +6.92820 q^{83} +(-4.50000 + 7.79423i) q^{85} +(1.73205 - 3.00000i) q^{87} +(-6.00000 + 3.46410i) q^{89} +(6.92820 - 2.00000i) q^{91} +(4.00000 + 6.92820i) q^{93} +(-5.19615 + 9.00000i) q^{95} +(12.0000 + 6.92820i) q^{97} -3.46410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 12 q^{5} + 2 q^{9} + 10 q^{13} - 6 q^{17} + 16 q^{21} + 16 q^{25} + 6 q^{29} - 24 q^{33} + 22 q^{37} - 18 q^{41} + 6 q^{45} - 6 q^{49} + 6 q^{61} + 30 q^{65} - 48 q^{69} + 22 q^{81} - 18 q^{85} - 24 q^{89}+ \cdots + 48 q^{97}+O(q^{100}) \) 4 * q + 12 * q^5 + 2 * q^9 + 10 * q^13 - 6 * q^17 + 16 * q^21 + 16 * q^25 + 6 * q^29 - 24 * q^33 + 22 * q^37 - 18 * q^41 + 6 * q^45 - 6 * q^49 + 6 * q^61 + 30 * q^65 - 48 * q^69 + 22 * q^81 - 18 * q^85 - 24 * q^89 + 16 * q^93 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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