LMFDB - Embedded newform 1170.2.bs.b.901.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,2,Mod(361,1170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1170, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("1170.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.bs (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:	$9.34249703649$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1170.901
Dual form			1170.2.bs.b.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000i q^{5} +1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000i q^{5} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{10} +(2.59808 + 1.50000i) q^{11} +(-1.00000 + 3.46410i) q^{13} +(-0.500000 + 0.866025i) q^{16} +(-3.00000 + 1.73205i) q^{19} +(-0.866025 + 0.500000i) q^{20} +(1.50000 + 2.59808i) q^{22} +(0.866025 - 1.50000i) q^{23} -1.00000 q^{25} +(-2.59808 + 2.50000i) q^{26} +(0.866025 - 1.50000i) q^{29} +5.19615i q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.50000 + 0.866025i) q^{37} -3.46410 q^{38} -1.00000 q^{40} +(5.19615 + 3.00000i) q^{41} +(0.500000 + 0.866025i) q^{43} +3.00000i q^{44} +(1.50000 - 0.866025i) q^{46} +3.00000i q^{47} +(-3.50000 + 6.06218i) q^{49} +(-0.866025 - 0.500000i) q^{50} +(-3.50000 + 0.866025i) q^{52} -6.92820 q^{53} +(-1.50000 + 2.59808i) q^{55} +(1.50000 - 0.866025i) q^{58} +(7.79423 - 4.50000i) q^{59} +(4.00000 + 6.92820i) q^{61} +(-2.59808 + 4.50000i) q^{62} -1.00000 q^{64} +(-3.46410 - 1.00000i) q^{65} +(-3.00000 - 1.73205i) q^{67} +(5.19615 - 3.00000i) q^{71} +(0.866025 + 1.50000i) q^{74} +(-3.00000 - 1.73205i) q^{76} -11.0000 q^{79} +(-0.866025 - 0.500000i) q^{80} +(3.00000 + 5.19615i) q^{82} -6.00000i q^{83} +1.00000i q^{86} +(-1.50000 + 2.59808i) q^{88} +1.73205 q^{92} +(-1.50000 + 2.59808i) q^{94} +(-1.73205 - 3.00000i) q^{95} +(-3.00000 + 1.73205i) q^{97} +(-6.06218 + 3.50000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4}+O(q^{10}) $ 4 * q + 2 * q^4	$ 4 q + 2 q^{4} - 2 q^{10} - 4 q^{13} - 2 q^{16} - 12 q^{19} + 6 q^{22} - 4 q^{25} + 6 q^{37} - 4 q^{40} + 2 q^{43} + 6 q^{46} - 14 q^{49} - 14 q^{52} - 6 q^{55} + 6 q^{58} + 16 q^{61} - 4 q^{64} - 12 q^{67} - 12 q^{76} - 44 q^{79} + 12 q^{82} - 6 q^{88} - 6 q^{94} - 12 q^{97}+O(q^{100}) $ 4 * q + 2 * q^4 - 2 * q^10 - 4 * q^13 - 2 * q^16 - 12 * q^19 + 6 * q^22 - 4 * q^25 + 6 * q^37 - 4 * q^40 + 2 * q^43 + 6 * q^46 - 14 * q^49 - 14 * q^52 - 6 * q^55 + 6 * q^58 + 16 * q^61 - 4 * q^64 - 12 * q^67 - 12 * q^76 - 44 * q^79 + 12 * q^82 - 6 * q^88 - 6 * q^94 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		0			0
$7$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$7$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	2.59808	+	1.50000i	0.783349	+	0.452267i	0.837616	−	0.546259i	$-0.183949\pi$
$11$	2.59808	+	1.50000i	0.783349	+	0.452267i	−0.0542666	+	0.998526i	$0.517282\pi$
$12$		0			0
$13$	−1.00000	+	3.46410i	−0.277350	+	0.960769i
$13$	−1.00000	+	3.46410i	−0.277350	+	0.960769i
$14$		0			0
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$		0			0
$19$	−3.00000	+	1.73205i	−0.688247	+	0.397360i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	−3.00000	+	1.73205i	−0.688247	+	0.397360i	0.114708	+	0.993399i	$0.463407\pi$
$20$	−0.866025	+	0.500000i	−0.193649	+	0.111803i
$21$		0			0
$22$	1.50000	+	2.59808i	0.319801	+	0.553912i
$23$	0.866025	−	1.50000i	0.180579	−	0.312772i	−0.761499	−	0.648166i	$-0.775536\pi$
$23$	0.866025	−	1.50000i	0.180579	−	0.312772i	0.942078	+	0.335394i	$0.108870\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−2.59808	+	2.50000i	−0.509525	+	0.490290i
$27$		0			0
$28$		0			0
$29$	0.866025	−	1.50000i	0.160817	−	0.278543i	−0.774345	−	0.632764i	$-0.781920\pi$
$29$	0.866025	−	1.50000i	0.160817	−	0.278543i	0.935162	+	0.354221i	$0.115254\pi$
$30$		0			0
$31$			5.19615i			0.933257i	0.884454	+	0.466628i	$0.154531\pi$
$31$			5.19615i			0.933257i	−0.884454	+	0.466628i	$0.845469\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.50000	+	0.866025i	0.246598	+	0.142374i	0.618206	−	0.786016i	$-0.287860\pi$
$37$	1.50000	+	0.866025i	0.246598	+	0.142374i	−0.371607	+	0.928390i	$0.621193\pi$
$38$	−3.46410			−0.561951
$39$		0			0
$40$	−1.00000			−0.158114
$41$	5.19615	+	3.00000i	0.811503	+	0.468521i	0.847477	−	0.530831i	$-0.178120\pi$
$41$	5.19615	+	3.00000i	0.811503	+	0.468521i	−0.0359748	+	0.999353i	$0.511454\pi$
$42$		0			0
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	0.901629	−	0.432511i	$-0.142372\pi$
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	−0.825380	+	0.564578i	$0.809039\pi$
$44$			3.00000i			0.452267i
$45$		0			0
$46$	1.50000	−	0.866025i	0.221163	−	0.127688i
$47$			3.00000i			0.437595i	0.975770	+	0.218797i	$0.0702134\pi$
$47$			3.00000i			0.437595i	−0.975770	+	0.218797i	$0.929787\pi$
$48$		0			0
$49$	−3.50000	+	6.06218i	−0.500000	+	0.866025i
$50$	−0.866025	−	0.500000i	−0.122474	−	0.0707107i
$51$		0			0
$52$	−3.50000	+	0.866025i	−0.485363	+	0.120096i
$53$	−6.92820			−0.951662			−0.475831	−	0.879537i	$-0.657853\pi$
$53$	−6.92820			−0.951662			−0.475831	+	0.879537i	$0.657853\pi$
$54$		0			0
$55$	−1.50000	+	2.59808i	−0.202260	+	0.350325i
$56$		0			0
$57$		0			0
$58$	1.50000	−	0.866025i	0.196960	−	0.113715i
$59$	7.79423	−	4.50000i	1.01472	−	0.585850i	0.102151	−	0.994769i	$-0.467427\pi$
$59$	7.79423	−	4.50000i	1.01472	−	0.585850i	0.912571	+	0.408919i	$0.134094\pi$
$60$		0			0
$61$	4.00000	+	6.92820i	0.512148	+	0.887066i	0.999901	+	0.0140840i	$0.00448323\pi$
$61$	4.00000	+	6.92820i	0.512148	+	0.887066i	−0.487753	+	0.872982i	$0.662183\pi$
$62$	−2.59808	+	4.50000i	−0.329956	+	0.571501i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−3.46410	−	1.00000i	−0.429669	−	0.124035i
$66$		0			0
$67$	−3.00000	−	1.73205i	−0.366508	−	0.211604i	0.305424	−	0.952217i	$-0.401202\pi$
$67$	−3.00000	−	1.73205i	−0.366508	−	0.211604i	−0.671932	+	0.740613i	$0.734535\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	5.19615	−	3.00000i	0.616670	−	0.356034i	−0.158901	−	0.987294i	$-0.550795\pi$
$71$	5.19615	−	3.00000i	0.616670	−	0.356034i	0.775571	+	0.631260i	$0.217462\pi$
$72$		0			0
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$	0.866025	+	1.50000i	0.100673	+	0.174371i
$75$		0			0
$76$	−3.00000	−	1.73205i	−0.344124	−	0.198680i
$77$		0			0
$78$		0			0
$79$	−11.0000			−1.23760			−0.618798	−	0.785550i	$-0.712380\pi$
$79$	−11.0000			−1.23760			−0.618798	+	0.785550i	$0.712380\pi$
$80$	−0.866025	−	0.500000i	−0.0968246	−	0.0559017i
$81$		0			0
$82$	3.00000	+	5.19615i	0.331295	+	0.573819i
$83$		−	6.00000i		−	0.658586i	−0.944228	−	0.329293i	$-0.893190\pi$
$83$		−	6.00000i		−	0.658586i	0.944228	−	0.329293i	$-0.106810\pi$
$84$		0			0
$85$		0			0
$86$			1.00000i			0.107833i
$87$		0			0
$88$	−1.50000	+	2.59808i	−0.159901	+	0.276956i
$89$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$89$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$90$		0			0
$91$		0			0
$92$	1.73205			0.180579
$93$		0			0
$94$	−1.50000	+	2.59808i	−0.154713	+	0.267971i
$95$	−1.73205	−	3.00000i	−0.177705	−	0.307794i
$96$		0			0
$97$	−3.00000	+	1.73205i	−0.304604	+	0.175863i	−0.644509	−	0.764597i	$-0.722938\pi$
$97$	−3.00000	+	1.73205i	−0.304604	+	0.175863i	0.339905	+	0.940460i	$0.389605\pi$
$98$	−6.06218	+	3.50000i	−0.612372	+	0.353553i
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	6.92820	−	12.0000i	0.689382	−	1.19404i	−0.282656	−	0.959221i	$-0.591216\pi$
$101$	6.92820	−	12.0000i	0.689382	−	1.19404i	0.972038	−	0.234823i	$-0.0754512\pi$
$102$		0			0
$103$	14.0000			1.37946			0.689730	−	0.724066i	$-0.257729\pi$
$103$	14.0000			1.37946			0.689730	+	0.724066i	$0.257729\pi$
$104$	−3.46410	−	1.00000i	−0.339683	−	0.0980581i
$105$		0			0
$106$	−6.00000	−	3.46410i	−0.582772	−	0.336463i
$107$	3.46410	−	6.00000i	0.334887	−	0.580042i	−0.648576	−	0.761150i	$-0.724635\pi$
$107$	3.46410	−	6.00000i	0.334887	−	0.580042i	0.983463	+	0.181108i	$0.0579684\pi$
$108$		0			0
$109$		0			0		1.00000			$0$
$109$		0			0		−1.00000			$\pi$
$110$	−2.59808	+	1.50000i	−0.247717	+	0.143019i
$111$		0			0
$112$		0			0
$113$	−6.06218	−	10.5000i	−0.570282	−	0.987757i	−0.996537	−	0.0831539i	$-0.973501\pi$
$113$	−6.06218	−	10.5000i	−0.570282	−	0.987757i	0.426255	−	0.904603i	$-0.359833\pi$
$114$		0			0
$115$	1.50000	+	0.866025i	0.139876	+	0.0807573i
$116$	1.73205			0.160817
$117$		0			0
$118$	9.00000			0.828517
$119$		0			0
$120$		0			0
$121$	−1.00000	−	1.73205i	−0.0909091	−	0.157459i
$122$			8.00000i			0.724286i
$123$		0			0
$124$	−4.50000	+	2.59808i	−0.404112	+	0.233314i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$	1.00000	−	1.73205i	0.0887357	−	0.153695i	−0.818241	−	0.574875i	$-0.805051\pi$
$127$	1.00000	−	1.73205i	0.0887357	−	0.153695i	0.906977	+	0.421180i	$0.138384\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	−2.50000	−	2.59808i	−0.219265	−	0.227866i
$131$	12.1244			1.05931			0.529655	−	0.848213i	$-0.322321\pi$
$131$	12.1244			1.05931			0.529655	+	0.848213i	$0.322321\pi$
$132$		0			0
$133$		0			0
$134$	−1.73205	−	3.00000i	−0.149626	−	0.259161i
$135$		0			0
$136$		0			0
$137$	2.59808	−	1.50000i	0.221969	−	0.128154i	−0.384893	−	0.922961i	$-0.625762\pi$
$137$	2.59808	−	1.50000i	0.221969	−	0.128154i	0.606861	+	0.794808i	$0.292428\pi$
$138$		0			0
$139$	5.00000	+	8.66025i	0.424094	+	0.734553i	0.996335	−	0.0855324i	$-0.0272591\pi$
$139$	5.00000	+	8.66025i	0.424094	+	0.734553i	−0.572241	+	0.820086i	$0.693926\pi$
$140$		0			0
$141$		0			0
$142$	6.00000			0.503509
$143$	−7.79423	+	7.50000i	−0.651786	+	0.627182i
$144$		0			0
$145$	1.50000	+	0.866025i	0.124568	+	0.0719195i
$146$		0			0
$147$		0			0
$148$			1.73205i			0.142374i
$149$	2.59808	−	1.50000i	0.212843	−	0.122885i	−0.389789	−	0.920904i	$-0.627452\pi$
$149$	2.59808	−	1.50000i	0.212843	−	0.122885i	0.602632	+	0.798019i	$0.294119\pi$
$150$		0			0
$151$		−	3.46410i		−	0.281905i	−0.990016	−	0.140952i	$-0.954984\pi$
$151$		−	3.46410i		−	0.281905i	0.990016	−	0.140952i	$-0.0450164\pi$
$152$	−1.73205	−	3.00000i	−0.140488	−	0.243332i
$153$		0			0
$154$		0			0
$155$	−5.19615			−0.417365
$156$		0			0
$157$	−7.00000			−0.558661			−0.279330	−	0.960195i	$-0.590112\pi$
$157$	−7.00000			−0.558661			−0.279330	+	0.960195i	$0.590112\pi$
$158$	−9.52628	−	5.50000i	−0.757870	−	0.437557i
$159$		0			0
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$		0			0
$162$		0			0
$163$	19.5000	−	11.2583i	1.52736	−	0.881820i	0.527886	−	0.849315i	$-0.322985\pi$
$163$	19.5000	−	11.2583i	1.52736	−	0.881820i	0.999472	−	0.0325054i	$-0.0103486\pi$
$164$			6.00000i			0.468521i
$165$		0			0
$166$	3.00000	−	5.19615i	0.232845	−	0.403300i
$167$	18.1865	+	10.5000i	1.40732	+	0.812514i	0.995129	−	0.0985846i	$-0.0314315\pi$
$167$	18.1865	+	10.5000i	1.40732	+	0.812514i	0.412188	+	0.911099i	$0.364765\pi$
$168$		0			0
$169$	−11.0000	−	6.92820i	−0.846154	−	0.532939i
$170$		0			0
$171$		0			0
$172$	−0.500000	+	0.866025i	−0.0381246	+	0.0660338i
$173$	−10.3923	−	18.0000i	−0.790112	−	1.36851i	−0.925897	−	0.377776i	$-0.876689\pi$
$173$	−10.3923	−	18.0000i	−0.790112	−	1.36851i	0.135785	−	0.990738i	$-0.456644\pi$
$174$		0			0
$175$		0			0
$176$	−2.59808	+	1.50000i	−0.195837	+	0.113067i
$177$		0			0
$178$		0			0
$179$	4.33013	−	7.50000i	0.323649	−	0.560576i	−0.657589	−	0.753377i	$-0.728424\pi$
$179$	4.33013	−	7.50000i	0.323649	−	0.560576i	0.981238	+	0.192800i	$0.0617570\pi$
$180$		0			0
$181$	20.0000			1.48659			0.743294	−	0.668965i	$-0.233262\pi$
$181$	20.0000			1.48659			0.743294	+	0.668965i	$0.233262\pi$
$182$		0			0
$183$		0			0
$184$	1.50000	+	0.866025i	0.110581	+	0.0638442i
$185$	−0.866025	+	1.50000i	−0.0636715	+	0.110282i
$186$		0			0
$187$		0			0
$188$	−2.59808	+	1.50000i	−0.189484	+	0.109399i
$189$		0			0
$190$		−	3.46410i		−	0.251312i
$191$	8.66025	+	15.0000i	0.626634	+	1.08536i	0.988222	+	0.153024i	$0.0489012\pi$
$191$	8.66025	+	15.0000i	0.626634	+	1.08536i	−0.361588	+	0.932338i	$0.617765\pi$
$192$		0			0
$193$	−9.00000	−	5.19615i	−0.647834	−	0.374027i	0.139792	−	0.990181i	$-0.455357\pi$
$193$	−9.00000	−	5.19615i	−0.647834	−	0.374027i	−0.787626	+	0.616154i	$0.788690\pi$
$194$	−3.46410			−0.248708
$195$		0			0
$196$	−7.00000			−0.500000
$197$	−5.19615	−	3.00000i	−0.370211	−	0.213741i	0.303340	−	0.952882i	$-0.401898\pi$
$197$	−5.19615	−	3.00000i	−0.370211	−	0.213741i	−0.673550	+	0.739141i	$0.735232\pi$
$198$		0			0
$199$	−8.00000	−	13.8564i	−0.567105	−	0.982255i	−0.996850	−	0.0793045i	$-0.974730\pi$
$199$	−8.00000	−	13.8564i	−0.567105	−	0.982255i	0.429745	−	0.902950i	$-0.358603\pi$
$200$		−	1.00000i		−	0.0707107i
$201$		0			0
$202$	12.0000	−	6.92820i	0.844317	−	0.487467i
$203$		0			0
$204$		0			0
$205$	−3.00000	+	5.19615i	−0.209529	+	0.362915i
$206$	12.1244	+	7.00000i	0.844744	+	0.487713i
$207$		0			0
$208$	−2.50000	−	2.59808i	−0.173344	−	0.180144i
$209$	−10.3923			−0.718851
$210$		0			0
$211$	1.00000	−	1.73205i	0.0688428	−	0.119239i	−0.829549	−	0.558433i	$-0.811403\pi$
$211$	1.00000	−	1.73205i	0.0688428	−	0.119239i	0.898392	+	0.439194i	$0.144736\pi$
$212$	−3.46410	−	6.00000i	−0.237915	−	0.412082i
$213$		0			0
$214$	6.00000	−	3.46410i	0.410152	−	0.236801i
$215$	−0.866025	+	0.500000i	−0.0590624	+	0.0340997i
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$	−3.00000			−0.202260
$221$		0			0
$222$		0			0
$223$	−15.0000	−	8.66025i	−1.00447	−	0.579934i	−0.0949052	−	0.995486i	$-0.530255\pi$
$223$	−15.0000	−	8.66025i	−1.00447	−	0.579934i	−0.909569	+	0.415553i	$0.863588\pi$
$224$		0			0
$225$		0			0
$226$		−	12.1244i		−	0.806500i
$227$	15.5885	−	9.00000i	1.03464	−	0.597351i	0.116331	−	0.993210i	$-0.462887\pi$
$227$	15.5885	−	9.00000i	1.03464	−	0.597351i	0.918311	+	0.395860i	$0.129553\pi$
$228$		0			0
$229$		−	6.92820i		−	0.457829i	−0.973447	−	0.228914i	$-0.926482\pi$
$229$		−	6.92820i		−	0.457829i	0.973447	−	0.228914i	$-0.0735176\pi$
$230$	0.866025	+	1.50000i	0.0571040	+	0.0989071i
$231$		0			0
$232$	1.50000	+	0.866025i	0.0984798	+	0.0568574i
$233$	−19.0526			−1.24817			−0.624087	−	0.781355i	$-0.714529\pi$
$233$	−19.0526			−1.24817			−0.624087	+	0.781355i	$0.714529\pi$
$234$		0			0
$235$	−3.00000			−0.195698
$236$	7.79423	+	4.50000i	0.507361	+	0.292925i
$237$		0			0
$238$		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
$241$	13.5000	−	7.79423i	0.869611	−	0.502070i	0.00239235	−	0.999997i	$-0.499238\pi$
$241$	13.5000	−	7.79423i	0.869611	−	0.502070i	0.867219	+	0.497927i	$0.165905\pi$
$242$		−	2.00000i		−	0.128565i
$243$		0			0
$244$	−4.00000	+	6.92820i	−0.256074	+	0.443533i
$245$	−6.06218	−	3.50000i	−0.387298	−	0.223607i
$246$		0			0
$247$	−3.00000	−	12.1244i	−0.190885	−	0.771454i
$248$	−5.19615			−0.329956
$249$		0			0
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	2.59808	+	4.50000i	0.163989	+	0.284037i	0.936296	−	0.351212i	$-0.114230\pi$
$251$	2.59808	+	4.50000i	0.163989	+	0.284037i	−0.772307	+	0.635250i	$0.780897\pi$
$252$		0			0
$253$	4.50000	−	2.59808i	0.282913	−	0.163340i
$254$	1.73205	−	1.00000i	0.108679	−	0.0627456i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	4.33013	−	7.50000i	0.270106	−	0.467837i	−0.698783	−	0.715334i	$-0.746275\pi$
$257$	4.33013	−	7.50000i	0.270106	−	0.467837i	0.968889	+	0.247497i	$0.0796080\pi$
$258$		0			0
$259$		0			0
$260$	−0.866025	−	3.50000i	−0.0537086	−	0.217061i
$261$		0			0
$262$	10.5000	+	6.06218i	0.648692	+	0.374523i
$263$	−7.79423	+	13.5000i	−0.480613	+	0.832446i	−0.999753	−	0.0222436i	$-0.992919\pi$
$263$	−7.79423	+	13.5000i	−0.480613	+	0.832446i	0.519140	+	0.854689i	$0.326252\pi$
$264$		0			0
$265$		−	6.92820i		−	0.425596i
$266$		0			0
$267$		0			0
$268$		−	3.46410i		−	0.211604i
$269$	13.8564	+	24.0000i	0.844840	+	1.46331i	0.885760	+	0.464143i	$0.153638\pi$
$269$	13.8564	+	24.0000i	0.844840	+	1.46331i	−0.0409201	+	0.999162i	$0.513029\pi$
$270$		0			0
$271$	10.5000	+	6.06218i	0.637830	+	0.368251i	0.783778	−	0.621041i	$-0.213290\pi$
$271$	10.5000	+	6.06218i	0.637830	+	0.368251i	−0.145948	+	0.989292i	$0.546623\pi$
$272$		0			0
$273$		0			0
$274$	3.00000			0.181237
$275$	−2.59808	−	1.50000i	−0.156670	−	0.0904534i
$276$		0			0
$277$	−8.50000	−	14.7224i	−0.510716	−	0.884585i	−0.999923	−	0.0124177i	$-0.996047\pi$
$277$	−8.50000	−	14.7224i	−0.510716	−	0.884585i	0.489207	−	0.872167i	$-0.337286\pi$
$278$			10.0000i			0.599760i
$279$		0			0
$280$		0			0
$281$			6.00000i			0.357930i	0.983855	+	0.178965i	$0.0572749\pi$
$281$			6.00000i			0.357930i	−0.983855	+	0.178965i	$0.942725\pi$
$282$		0			0
$283$	2.50000	−	4.33013i	0.148610	−	0.257399i	−0.782104	−	0.623148i	$-0.785854\pi$
$283$	2.50000	−	4.33013i	0.148610	−	0.257399i	0.930714	+	0.365748i	$0.119187\pi$
$284$	5.19615	+	3.00000i	0.308335	+	0.178017i
$285$		0			0
$286$	−10.5000	+	2.59808i	−0.620878	+	0.153627i
$287$		0			0
$288$		0			0
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$	0.866025	+	1.50000i	0.0508548	+	0.0880830i
$291$		0			0
$292$		0			0
$293$	−15.5885	+	9.00000i	−0.910687	+	0.525786i	−0.880652	−	0.473763i	$-0.842895\pi$
$293$	−15.5885	+	9.00000i	−0.910687	+	0.525786i	−0.0300351	+	0.999549i	$0.509562\pi$
$294$		0			0
$295$	4.50000	+	7.79423i	0.262000	+	0.453798i
$296$	−0.866025	+	1.50000i	−0.0503367	+	0.0871857i
$297$		0			0
$298$	3.00000			0.173785
$299$	4.33013	+	4.50000i	0.250418	+	0.260242i
$300$		0			0
$301$		0			0
$302$	1.73205	−	3.00000i	0.0996683	−	0.172631i
$303$		0			0
$304$		−	3.46410i		−	0.198680i
$305$	−6.92820	+	4.00000i	−0.396708	+	0.229039i
$306$		0			0
$307$		−	31.1769i		−	1.77936i	−0.456584	−	0.889680i	$-0.650927\pi$
$307$		−	31.1769i		−	1.77936i	0.456584	−	0.889680i	$-0.349073\pi$
$308$		0			0
$309$		0			0
$310$	−4.50000	−	2.59808i	−0.255583	−	0.147561i
$311$	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
$313$	−8.00000			−0.452187			−0.226093	−	0.974106i	$-0.572595\pi$
$313$	−8.00000			−0.452187			−0.226093	+	0.974106i	$0.572595\pi$
$314$	−6.06218	−	3.50000i	−0.342108	−	0.197516i
$315$		0			0
$316$	−5.50000	−	9.52628i	−0.309399	−	0.535895i
$317$			6.00000i			0.336994i	0.985702	+	0.168497i	$0.0538913\pi$
$317$			6.00000i			0.336994i	−0.985702	+	0.168497i	$0.946109\pi$
$318$		0			0
$319$	4.50000	−	2.59808i	0.251952	−	0.145464i
$320$		−	1.00000i		−	0.0559017i
$321$		0			0
$322$		0			0
$323$		0			0
$324$		0			0
$325$	1.00000	−	3.46410i	0.0554700	−	0.192154i
$326$	22.5167			1.24708
$327$		0			0
$328$	−3.00000	+	5.19615i	−0.165647	+	0.286910i
$329$		0			0
$330$		0			0
$331$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$331$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$332$	5.19615	−	3.00000i	0.285176	−	0.164646i
$333$		0			0
$334$	10.5000	+	18.1865i	0.574534	+	0.995123i
$335$	1.73205	−	3.00000i	0.0946320	−	0.163908i
$336$		0			0
$337$	4.00000			0.217894			0.108947	−	0.994048i	$-0.465252\pi$
$337$	4.00000			0.217894			0.108947	+	0.994048i	$0.465252\pi$
$338$	−6.06218	−	11.5000i	−0.329739	−	0.625518i
$339$		0			0
$340$		0			0
$341$	−7.79423	+	13.5000i	−0.422081	+	0.731066i
$342$		0			0
$343$		0			0
$344$	−0.866025	+	0.500000i	−0.0466930	+	0.0269582i
$345$		0			0
$346$		−	20.7846i		−	1.11739i
$347$	8.66025	+	15.0000i	0.464907	+	0.805242i	0.999197	−	0.0400587i	$-0.0127545\pi$
$347$	8.66025	+	15.0000i	0.464907	+	0.805242i	−0.534291	+	0.845301i	$0.679421\pi$
$348$		0			0
$349$	−27.0000	−	15.5885i	−1.44528	−	0.834431i	−0.447082	−	0.894493i	$-0.647537\pi$
$349$	−27.0000	−	15.5885i	−1.44528	−	0.834431i	−0.998195	+	0.0600619i	$0.980870\pi$
$350$		0			0
$351$		0			0
$352$	−3.00000			−0.159901
$353$	−15.5885	−	9.00000i	−0.829690	−	0.479022i	0.0240566	−	0.999711i	$-0.492342\pi$
$353$	−15.5885	−	9.00000i	−0.829690	−	0.479022i	−0.853746	+	0.520689i	$0.825675\pi$
$354$		0			0
$355$	3.00000	+	5.19615i	0.159223	+	0.275783i
$356$		0			0
$357$		0			0
$358$	7.50000	−	4.33013i	0.396387	−	0.228854i
$359$			24.0000i			1.26667i	0.773877	+	0.633336i	$0.218315\pi$
$359$			24.0000i			1.26667i	−0.773877	+	0.633336i	$0.781685\pi$
$360$		0			0
$361$	−3.50000	+	6.06218i	−0.184211	+	0.319062i
$362$	17.3205	+	10.0000i	0.910346	+	0.525588i
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−13.0000	+	22.5167i	−0.678594	+	1.17536i	0.296810	+	0.954937i	$0.404077\pi$
$367$	−13.0000	+	22.5167i	−0.678594	+	1.17536i	−0.975404	+	0.220423i	$0.929256\pi$
$368$	0.866025	+	1.50000i	0.0451447	+	0.0781929i
$369$		0			0
$370$	−1.50000	+	0.866025i	−0.0779813	+	0.0450225i
$371$		0			0
$372$		0			0
$373$	8.50000	+	14.7224i	0.440113	+	0.762299i	0.997697	−	0.0678218i	$-0.0216049\pi$
$373$	8.50000	+	14.7224i	0.440113	+	0.762299i	−0.557584	+	0.830120i	$0.688272\pi$
$374$		0			0
$375$		0			0
$376$	−3.00000			−0.154713
$377$	4.33013	+	4.50000i	0.223013	+	0.231762i
$378$		0			0
$379$	12.0000	+	6.92820i	0.616399	+	0.355878i	0.775466	−	0.631390i	$-0.217515\pi$
$379$	12.0000	+	6.92820i	0.616399	+	0.355878i	−0.159067	+	0.987268i	$0.550849\pi$
$380$	1.73205	−	3.00000i	0.0888523	−	0.153897i
$381$		0			0
$382$			17.3205i			0.886194i
$383$	7.79423	−	4.50000i	0.398266	−	0.229939i	−0.287469	−	0.957790i	$-0.592814\pi$
$383$	7.79423	−	4.50000i	0.398266	−	0.229939i	0.685736	+	0.727851i	$0.259481\pi$
$384$		0			0
$385$		0			0
$386$	−5.19615	−	9.00000i	−0.264477	−	0.458088i
$387$		0			0
$388$	−3.00000	−	1.73205i	−0.152302	−	0.0879316i
$389$	−29.4449			−1.49291			−0.746457	−	0.665434i	$-0.768247\pi$
$389$	−29.4449			−1.49291			−0.746457	+	0.665434i	$0.768247\pi$
$390$		0			0
$391$		0			0
$392$	−6.06218	−	3.50000i	−0.306186	−	0.176777i
$393$		0			0
$394$	−3.00000	−	5.19615i	−0.151138	−	0.261778i
$395$		−	11.0000i		−	0.553470i
$396$		0			0
$397$	25.5000	−	14.7224i	1.27981	−	0.738898i	0.302995	−	0.952992i	$-0.402013\pi$
$397$	25.5000	−	14.7224i	1.27981	−	0.738898i	0.976813	+	0.214094i	$0.0686800\pi$
$398$		−	16.0000i		−	0.802008i
$399$		0			0
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$401$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$402$		0			0
$403$	−18.0000	−	5.19615i	−0.896644	−	0.258839i
$404$	13.8564			0.689382
$405$		0			0
$406$		0			0
$407$	2.59808	+	4.50000i	0.128782	+	0.223057i
$408$		0			0
$409$	30.0000	−	17.3205i	1.48340	−	0.856444i	0.483582	−	0.875299i	$-0.339335\pi$
$409$	30.0000	−	17.3205i	1.48340	−	0.856444i	0.999822	+	0.0188549i	$0.00600205\pi$
$410$	−5.19615	+	3.00000i	−0.256620	+	0.148159i
$411$		0			0
$412$	7.00000	+	12.1244i	0.344865	+	0.597324i
$413$		0			0
$414$		0			0
$415$	6.00000			0.294528
$416$	−0.866025	−	3.50000i	−0.0424604	−	0.171602i
$417$		0			0
$418$	−9.00000	−	5.19615i	−0.440204	−	0.254152i
$419$	8.66025	−	15.0000i	0.423081	−	0.732798i	−0.573158	−	0.819445i	$-0.694282\pi$
$419$	8.66025	−	15.0000i	0.423081	−	0.732798i	0.996239	+	0.0866469i	$0.0276152\pi$
$420$		0			0
$421$			38.1051i			1.85713i	0.371170	+	0.928565i	$0.378957\pi$
$421$			38.1051i			1.85713i	−0.371170	+	0.928565i	$0.621043\pi$
$422$	1.73205	−	1.00000i	0.0843149	−	0.0486792i
$423$		0			0
$424$		−	6.92820i		−	0.336463i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	6.92820			0.334887
$429$		0			0
$430$	−1.00000			−0.0482243
$431$	15.5885	+	9.00000i	0.750870	+	0.433515i	0.826008	−	0.563658i	$-0.190607\pi$
$431$	15.5885	+	9.00000i	0.750870	+	0.433515i	−0.0751385	+	0.997173i	$0.523940\pi$
$432$		0			0
$433$	7.00000	+	12.1244i	0.336399	+	0.582659i	0.983752	−	0.179530i	$-0.0574578\pi$
$433$	7.00000	+	12.1244i	0.336399	+	0.582659i	−0.647354	+	0.762190i	$0.724124\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$			6.00000i			0.287019i
$438$		0			0
$439$	−16.0000	+	27.7128i	−0.763638	+	1.32266i	0.177325	+	0.984152i	$0.443256\pi$
$439$	−16.0000	+	27.7128i	−0.763638	+	1.32266i	−0.940963	+	0.338508i	$0.890078\pi$
$440$	−2.59808	−	1.50000i	−0.123858	−	0.0715097i
$441$		0			0
$442$		0			0
$443$	−31.1769			−1.48126			−0.740630	−	0.671913i	$-0.765473\pi$
$443$	−31.1769			−1.48126			−0.740630	+	0.671913i	$0.765473\pi$
$444$		0			0
$445$		0			0
$446$	−8.66025	−	15.0000i	−0.410075	−	0.710271i
$447$		0			0
$448$		0			0
$449$	−10.3923	+	6.00000i	−0.490443	+	0.283158i	−0.724758	−	0.689003i	$-0.758049\pi$
$449$	−10.3923	+	6.00000i	−0.490443	+	0.283158i	0.234315	+	0.972161i	$0.424715\pi$
$450$		0			0
$451$	9.00000	+	15.5885i	0.423793	+	0.734032i
$452$	6.06218	−	10.5000i	0.285141	−	0.493878i
$453$		0			0
$454$	18.0000			0.844782
$455$		0			0
$456$		0			0
$457$	−21.0000	−	12.1244i	−0.982339	−	0.567153i	−0.0793632	−	0.996846i	$-0.525289\pi$
$457$	−21.0000	−	12.1244i	−0.982339	−	0.567153i	−0.902975	+	0.429692i	$0.858622\pi$
$458$	3.46410	−	6.00000i	0.161867	−	0.280362i
$459$		0			0
$460$			1.73205i			0.0807573i
$461$	18.1865	−	10.5000i	0.847031	−	0.489034i	−0.0126168	−	0.999920i	$-0.504016\pi$
$461$	18.1865	−	10.5000i	0.847031	−	0.489034i	0.859648	+	0.510887i	$0.170683\pi$
$462$		0			0
$463$		0			0		1.00000			$0$
$463$		0			0		−1.00000			$\pi$
$464$	0.866025	+	1.50000i	0.0402042	+	0.0696358i
$465$		0			0
$466$	−16.5000	−	9.52628i	−0.764348	−	0.441296i
$467$	−13.8564			−0.641198			−0.320599	−	0.947215i	$-0.603884\pi$
$467$	−13.8564			−0.641198			−0.320599	+	0.947215i	$0.603884\pi$
$468$		0			0
$469$		0			0
$470$	−2.59808	−	1.50000i	−0.119840	−	0.0691898i
$471$		0			0
$472$	4.50000	+	7.79423i	0.207129	+	0.358758i
$473$			3.00000i			0.137940i
$474$		0			0
$475$	3.00000	−	1.73205i	0.137649	−	0.0794719i
$476$		0			0
$477$		0			0
$478$	3.00000	−	5.19615i	0.137217	−	0.237666i
$479$	5.19615	+	3.00000i	0.237418	+	0.137073i	0.613990	−	0.789314i	$-0.289564\pi$
$479$	5.19615	+	3.00000i	0.237418	+	0.137073i	−0.376571	+	0.926388i	$0.622897\pi$
$480$		0			0
$481$	−4.50000	+	4.33013i	−0.205182	+	0.197437i
$482$	15.5885			0.710035
$483$		0			0
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$	−1.73205	−	3.00000i	−0.0786484	−	0.136223i
$486$		0			0
$487$	−9.00000	+	5.19615i	−0.407829	+	0.235460i	−0.689856	−	0.723946i	$-0.742326\pi$
$487$	−9.00000	+	5.19615i	−0.407829	+	0.235460i	0.282028	+	0.959406i	$0.408993\pi$
$488$	−6.92820	+	4.00000i	−0.313625	+	0.181071i
$489$		0			0
$490$	−3.50000	−	6.06218i	−0.158114	−	0.273861i
$491$	8.66025	−	15.0000i	0.390832	−	0.676941i	−0.601728	−	0.798701i	$-0.705521\pi$
$491$	8.66025	−	15.0000i	0.390832	−	0.676941i	0.992559	+	0.121761i	$0.0388541\pi$
$492$		0			0
$493$		0			0
$494$	3.46410	−	12.0000i	0.155857	−	0.539906i
$495$		0			0
$496$	−4.50000	−	2.59808i	−0.202056	−	0.116657i
$497$		0			0
$498$		0			0
$499$			17.3205i			0.775372i	0.921791	+	0.387686i	$0.126726\pi$
$499$			17.3205i			0.775372i	−0.921791	+	0.387686i	$0.873274\pi$
$500$	0.866025	−	0.500000i	0.0387298	−	0.0223607i
$501$		0			0
$502$			5.19615i			0.231916i
$503$	1.73205	+	3.00000i	0.0772283	+	0.133763i	0.902053	−	0.431625i	$-0.142060\pi$
$503$	1.73205	+	3.00000i	0.0772283	+	0.133763i	−0.824825	+	0.565388i	$0.808726\pi$
$504$		0			0
$505$	12.0000	+	6.92820i	0.533993	+	0.308301i
$506$	5.19615			0.230997
$507$		0			0
$508$	2.00000			0.0887357
$509$	−18.1865	−	10.5000i	−0.806104	−	0.465404i	0.0394971	−	0.999220i	$-0.487424\pi$
$509$	−18.1865	−	10.5000i	−0.806104	−	0.465404i	−0.845601	+	0.533815i	$0.820758\pi$
$510$		0			0
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	7.50000	−	4.33013i	0.330811	−	0.190994i
$515$			14.0000i			0.616914i
$516$		0			0
$517$	−4.50000	+	7.79423i	−0.197910	+	0.342790i
$518$		0			0
$519$		0			0
$520$	1.00000	−	3.46410i	0.0438529	−	0.151911i
$521$	−38.1051			−1.66942			−0.834708	−	0.550693i	$-0.814363\pi$
$521$	−38.1051			−1.66942			−0.834708	+	0.550693i	$0.814363\pi$
$522$		0			0
$523$	−8.50000	+	14.7224i	−0.371679	+	0.643767i	−0.989824	−	0.142297i	$-0.954551\pi$
$523$	−8.50000	+	14.7224i	−0.371679	+	0.643767i	0.618145	+	0.786064i	$0.287884\pi$
$524$	6.06218	+	10.5000i	0.264827	+	0.458695i
$525$		0			0
$526$	−13.5000	+	7.79423i	−0.588628	+	0.339845i
$527$		0			0
$528$		0			0
$529$	10.0000	+	17.3205i	0.434783	+	0.753066i
$530$	3.46410	−	6.00000i	0.150471	−	0.260623i
$531$		0			0
$532$		0			0
$533$	−15.5885	+	15.0000i	−0.675211	+	0.649722i
$534$		0			0
$535$	6.00000	+	3.46410i	0.259403	+	0.149766i
$536$	1.73205	−	3.00000i	0.0748132	−	0.129580i
$537$		0			0
$538$			27.7128i			1.19478i
$539$	−18.1865	+	10.5000i	−0.783349	+	0.452267i
$540$		0			0
$541$			13.8564i			0.595733i	0.954607	+	0.297867i	$0.0962751\pi$
$541$			13.8564i			0.595733i	−0.954607	+	0.297867i	$0.903725\pi$
$542$	6.06218	+	10.5000i	0.260393	+	0.451014i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−28.0000			−1.19719			−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000			−1.19719			−0.598597	+	0.801050i	$0.704275\pi$
$548$	2.59808	+	1.50000i	0.110984	+	0.0640768i
$549$		0			0
$550$	−1.50000	−	2.59808i	−0.0639602	−	0.110782i
$551$			6.00000i			0.255609i
$552$		0			0
$553$		0			0
$554$		−	17.0000i		−	0.722261i
$555$		0			0
$556$	−5.00000	+	8.66025i	−0.212047	+	0.367277i
$557$	−25.9808	−	15.0000i	−1.10084	−	0.635570i	−0.164399	−	0.986394i	$-0.552568\pi$
$557$	−25.9808	−	15.0000i	−1.10084	−	0.635570i	−0.936442	+	0.350824i	$0.885902\pi$
$558$		0			0
$559$	−3.50000	+	0.866025i	−0.148034	+	0.0366290i
$560$		0			0
$561$		0			0
$562$	−3.00000	+	5.19615i	−0.126547	+	0.219186i
$563$	−8.66025	−	15.0000i	−0.364986	−	0.632175i	0.623788	−	0.781594i	$-0.285593\pi$
$563$	−8.66025	−	15.0000i	−0.364986	−	0.632175i	−0.988774	+	0.149419i	$0.952260\pi$
$564$		0			0
$565$	10.5000	−	6.06218i	0.441738	−	0.255038i
$566$	4.33013	−	2.50000i	0.182009	−	0.105083i
$567$		0			0
$568$	3.00000	+	5.19615i	0.125877	+	0.218026i
$569$	12.1244	−	21.0000i	0.508279	−	0.880366i	−0.491675	−	0.870779i	$-0.663615\pi$
$569$	12.1244	−	21.0000i	0.508279	−	0.880366i	0.999954	−	0.00958679i	$-0.00305162\pi$
$570$		0			0
$571$	−2.00000			−0.0836974			−0.0418487	−	0.999124i	$-0.513325\pi$
$571$	−2.00000			−0.0836974			−0.0418487	+	0.999124i	$0.513325\pi$
$572$	−10.3923	−	3.00000i	−0.434524	−	0.125436i
$573$		0			0
$574$		0			0
$575$	−0.866025	+	1.50000i	−0.0361158	+	0.0625543i
$576$		0			0
$577$			6.92820i			0.288425i	0.989547	+	0.144212i	$0.0460649\pi$
$577$			6.92820i			0.288425i	−0.989547	+	0.144212i	$0.953935\pi$
$578$	14.7224	−	8.50000i	0.612372	−	0.353553i
$579$		0			0
$580$			1.73205i			0.0719195i
$581$		0			0
$582$		0			0
$583$	−18.0000	−	10.3923i	−0.745484	−	0.430405i
$584$		0			0
$585$		0			0
$586$	−18.0000			−0.743573
$587$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$587$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$588$		0			0
$589$	−9.00000	−	15.5885i	−0.370839	−	0.642311i
$590$			9.00000i			0.370524i
$591$		0			0
$592$	−1.50000	+	0.866025i	−0.0616496	+	0.0355934i
$593$		−	3.00000i		−	0.123195i	−0.998101	−	0.0615976i	$-0.980380\pi$
$593$		−	3.00000i		−	0.123195i	0.998101	−	0.0615976i	$-0.0196196\pi$
$594$		0			0
$595$		0			0
$596$	2.59808	+	1.50000i	0.106421	+	0.0614424i
$597$		0			0
$598$	1.50000	+	6.06218i	0.0613396	+	0.247901i
$599$	17.3205			0.707697			0.353848	−	0.935303i	$-0.384873\pi$
$599$	17.3205			0.707697			0.353848	+	0.935303i	$0.384873\pi$
$600$		0			0
$601$	−18.5000	+	32.0429i	−0.754631	+	1.30706i	0.190927	+	0.981604i	$0.438851\pi$
$601$	−18.5000	+	32.0429i	−0.754631	+	1.30706i	−0.945558	+	0.325455i	$0.894483\pi$
$602$		0			0
$603$		0			0
$604$	3.00000	−	1.73205i	0.122068	−	0.0704761i
$605$	1.73205	−	1.00000i	0.0704179	−	0.0406558i
$606$		0			0
$607$	8.00000	+	13.8564i	0.324710	+	0.562414i	0.981454	−	0.191700i	$-0.0614000\pi$
$607$	8.00000	+	13.8564i	0.324710	+	0.562414i	−0.656744	+	0.754114i	$0.728067\pi$
$608$	1.73205	−	3.00000i	0.0702439	−	0.121666i
$609$		0			0
$610$	−8.00000			−0.323911
$611$	−10.3923	−	3.00000i	−0.420428	−	0.121367i
$612$		0			0
$613$	−13.5000	−	7.79423i	−0.545260	−	0.314806i	0.201948	−	0.979396i	$-0.435273\pi$
$613$	−13.5000	−	7.79423i	−0.545260	−	0.314806i	−0.747208	+	0.664590i	$0.768606\pi$
$614$	15.5885	−	27.0000i	0.629099	−	1.08963i
$615$		0			0
$616$		0			0
$617$	2.59808	−	1.50000i	0.104595	−	0.0603877i	−0.446790	−	0.894639i	$-0.647433\pi$
$617$	2.59808	−	1.50000i	0.104595	−	0.0603877i	0.551385	+	0.834251i	$0.314100\pi$
$618$		0			0
$619$			10.3923i			0.417702i	0.977947	+	0.208851i	$0.0669724\pi$
$619$			10.3923i			0.417702i	−0.977947	+	0.208851i	$0.933028\pi$
$620$	−2.59808	−	4.50000i	−0.104341	−	0.180724i
$621$		0			0
$622$	21.0000	+	12.1244i	0.842023	+	0.486142i
$623$		0			0
$624$		0			0
$625$	1.00000			0.0400000
$626$	−6.92820	−	4.00000i	−0.276907	−	0.159872i
$627$		0			0
$628$	−3.50000	−	6.06218i	−0.139665	−	0.241907i
$629$		0			0
$630$		0			0
$631$	33.0000	−	19.0526i	1.31371	−	0.758470i	0.331001	−	0.943630i	$-0.392614\pi$
$631$	33.0000	−	19.0526i	1.31371	−	0.758470i	0.982708	+	0.185160i	$0.0592804\pi$
$632$		−	11.0000i		−	0.437557i
$633$		0			0
$634$	−3.00000	+	5.19615i	−0.119145	+	0.206366i
$635$	1.73205	+	1.00000i	0.0687343	+	0.0396838i
$636$		0			0
$637$	−17.5000	−	18.1865i	−0.693375	−	0.720577i
$638$	5.19615			0.205718
$639$		0			0
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	3.46410	+	6.00000i	0.136824	+	0.236986i	0.926293	−	0.376805i	$-0.122977\pi$
$641$	3.46410	+	6.00000i	0.136824	+	0.236986i	−0.789469	+	0.613791i	$0.789644\pi$
$642$		0			0
$643$	3.00000	−	1.73205i	0.118308	−	0.0683054i	−0.439678	−	0.898155i	$-0.644907\pi$
$643$	3.00000	−	1.73205i	0.118308	−	0.0683054i	0.557986	+	0.829850i	$0.311574\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	5.19615	−	9.00000i	0.204282	−	0.353827i	−0.745622	−	0.666369i	$-0.767847\pi$
$647$	5.19615	−	9.00000i	0.204282	−	0.353827i	0.949904	+	0.312543i	$0.101181\pi$
$648$		0			0
$649$	27.0000			1.05984
$650$	2.59808	−	2.50000i	0.101905	−	0.0980581i
$651$		0			0
$652$	19.5000	+	11.2583i	0.763679	+	0.440910i
$653$	−5.19615	+	9.00000i	−0.203341	+	0.352197i	−0.949603	−	0.313455i	$-0.898513\pi$
$653$	−5.19615	+	9.00000i	−0.203341	+	0.352197i	0.746262	+	0.665653i	$0.231847\pi$
$654$		0			0
$655$			12.1244i			0.473738i
$656$	−5.19615	+	3.00000i	−0.202876	+	0.117130i
$657$		0			0
$658$		0			0
$659$	6.06218	+	10.5000i	0.236149	+	0.409022i	0.959606	−	0.281347i	$-0.0907813\pi$
$659$	6.06218	+	10.5000i	0.236149	+	0.409022i	−0.723457	+	0.690369i	$0.757448\pi$
$660$		0			0
$661$	−33.0000	−	19.0526i	−1.28355	−	0.741059i	−0.306055	−	0.952014i	$-0.599009\pi$
$661$	−33.0000	−	19.0526i	−1.28355	−	0.741059i	−0.977496	+	0.210955i	$0.932343\pi$
$662$		0			0
$663$		0			0
$664$	6.00000			0.232845
$665$		0			0
$666$		0			0
$667$	−1.50000	−	2.59808i	−0.0580802	−	0.100598i
$668$			21.0000i			0.812514i
$669$		0			0
$670$	3.00000	−	1.73205i	0.115900	−	0.0669150i
$671$			24.0000i			0.926510i
$672$		0			0
$673$	−22.0000	+	38.1051i	−0.848038	+	1.46884i	0.0349191	+	0.999390i	$0.488883\pi$
$673$	−22.0000	+	38.1051i	−0.848038	+	1.46884i	−0.882957	+	0.469454i	$0.844451\pi$
$674$	3.46410	+	2.00000i	0.133432	+	0.0770371i
$675$		0			0
$676$	0.500000	−	12.9904i	0.0192308	−	0.499630i
$677$	−45.0333			−1.73077			−0.865386	−	0.501107i	$-0.832926\pi$
$677$	−45.0333			−1.73077			−0.865386	+	0.501107i	$0.832926\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$	−13.5000	+	7.79423i	−0.516942	+	0.298456i
$683$	31.1769	−	18.0000i	1.19295	−	0.688751i	0.233977	−	0.972242i	$-0.424826\pi$
$683$	31.1769	−	18.0000i	1.19295	−	0.688751i	0.958975	+	0.283491i	$0.0914927\pi$
$684$		0			0
$685$	1.50000	+	2.59808i	0.0573121	+	0.0992674i
$686$		0			0
$687$		0			0
$688$	−1.00000			−0.0381246
$689$	6.92820	−	24.0000i	0.263944	−	0.914327i
$690$		0			0
$691$	21.0000	+	12.1244i	0.798878	+	0.461232i	0.843079	−	0.537790i	$-0.180741\pi$
$691$	21.0000	+	12.1244i	0.798878	+	0.461232i	−0.0442009	+	0.999023i	$0.514074\pi$
$692$	10.3923	−	18.0000i	0.395056	−	0.684257i
$693$		0			0
$694$			17.3205i			0.657477i
$695$	−8.66025	+	5.00000i	−0.328502	+	0.189661i
$696$		0			0
$697$		0			0
$698$	−15.5885	−	27.0000i	−0.590032	−	1.02197i
$699$		0			0
$700$		0			0
$701$	22.5167			0.850443			0.425221	−	0.905089i	$-0.360196\pi$
$701$	22.5167			0.850443			0.425221	+	0.905089i	$0.360196\pi$
$702$		0			0
$703$	−6.00000			−0.226294
$704$	−2.59808	−	1.50000i	−0.0979187	−	0.0565334i
$705$		0			0
$706$	−9.00000	−	15.5885i	−0.338719	−	0.586679i
$707$		0			0
$708$		0			0
$709$	18.0000	−	10.3923i	0.676004	−	0.390291i	−0.122344	−	0.992488i	$-0.539041\pi$
$709$	18.0000	−	10.3923i	0.676004	−	0.390291i	0.798348	+	0.602197i	$0.205708\pi$
$710$			6.00000i			0.225176i
$711$		0			0
$712$		0			0
$713$	7.79423	+	4.50000i	0.291896	+	0.168526i
$714$		0			0
$715$	−7.50000	−	7.79423i	−0.280484	−	0.291488i
$716$	8.66025			0.323649
$717$		0			0
$718$	−12.0000	+	20.7846i	−0.447836	+	0.775675i
$719$	13.8564	+	24.0000i	0.516757	+	0.895049i	0.999811	+	0.0194584i	$0.00619418\pi$
$719$	13.8564	+	24.0000i	0.516757	+	0.895049i	−0.483054	+	0.875591i	$0.660472\pi$
$720$		0			0
$721$		0			0
$722$	−6.06218	+	3.50000i	−0.225611	+	0.130257i
$723$		0			0
$724$	10.0000	+	17.3205i	0.371647	+	0.643712i
$725$	−0.866025	+	1.50000i	−0.0321634	+	0.0557086i
$726$		0			0
$727$	−8.00000			−0.296704			−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000			−0.296704			−0.148352	+	0.988935i	$0.547397\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$		0			0
$732$		0			0
$733$			27.7128i			1.02360i	0.859106	+	0.511798i	$0.171020\pi$
$733$			27.7128i			1.02360i	−0.859106	+	0.511798i	$0.828980\pi$
$734$	−22.5167	+	13.0000i	−0.831105	+	0.479839i
$735$		0			0
$736$			1.73205i			0.0638442i
$737$	−5.19615	−	9.00000i	−0.191403	−	0.331519i
$738$		0			0
$739$	−9.00000	−	5.19615i	−0.331070	−	0.191144i	0.325246	−	0.945629i	$-0.394553\pi$
$739$	−9.00000	−	5.19615i	−0.331070	−	0.191144i	−0.656316	+	0.754486i	$0.727886\pi$
$740$	−1.73205			−0.0636715
$741$		0			0
$742$		0			0
$743$	38.9711	+	22.5000i	1.42971	+	0.825445i	0.997098	−	0.0761338i	$-0.0242576\pi$
$743$	38.9711	+	22.5000i	1.42971	+	0.825445i	0.432615	+	0.901579i	$0.357591\pi$
$744$		0			0
$745$	1.50000	+	2.59808i	0.0549557	+	0.0951861i
$746$			17.0000i			0.622414i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−2.50000	+	4.33013i	−0.0912263	+	0.158009i	−0.908027	−	0.418911i	$-0.862412\pi$
$751$	−2.50000	+	4.33013i	−0.0912263	+	0.158009i	0.816801	+	0.576919i	$0.195745\pi$
$752$	−2.59808	−	1.50000i	−0.0947421	−	0.0546994i
$753$		0			0
$754$	1.50000	+	6.06218i	0.0546268	+	0.220771i
$755$	3.46410			0.126072
$756$		0			0
$757$	−23.0000	+	39.8372i	−0.835949	+	1.44791i	0.0573060	+	0.998357i	$0.481749\pi$
$757$	−23.0000	+	39.8372i	−0.835949	+	1.44791i	−0.893255	+	0.449550i	$0.851584\pi$
$758$	6.92820	+	12.0000i	0.251644	+	0.435860i
$759$		0			0
$760$	3.00000	−	1.73205i	0.108821	−	0.0628281i
$761$	−31.1769	+	18.0000i	−1.13016	+	0.652499i	−0.943976	−	0.330015i	$-0.892946\pi$
$761$	−31.1769	+	18.0000i	−1.13016	+	0.652499i	−0.186187	+	0.982514i	$0.559613\pi$
$762$		0			0
$763$		0			0
$764$	−8.66025	+	15.0000i	−0.313317	+	0.542681i
$765$		0			0
$766$	9.00000			0.325183
$767$	7.79423	+	31.5000i	0.281433	+	1.13740i
$768$		0			0
$769$	−13.5000	−	7.79423i	−0.486822	−	0.281067i	0.236433	−	0.971648i	$-0.424022\pi$
$769$	−13.5000	−	7.79423i	−0.486822	−	0.281067i	−0.723255	+	0.690581i	$0.757355\pi$
$770$		0			0
$771$		0			0
$772$		−	10.3923i		−	0.374027i
$773$	20.7846	−	12.0000i	0.747570	−	0.431610i	−0.0772449	−	0.997012i	$-0.524612\pi$
$773$	20.7846	−	12.0000i	0.747570	−	0.431610i	0.824815	+	0.565402i	$0.191279\pi$
$774$		0			0
$775$		−	5.19615i		−	0.186651i
$776$	−1.73205	−	3.00000i	−0.0621770	−	0.107694i
$777$		0			0
$778$	−25.5000	−	14.7224i	−0.914219	−	0.527825i
$779$	−20.7846			−0.744686
$780$		0			0
$781$	18.0000			0.644091
$782$		0			0
$783$		0			0
$784$	−3.50000	−	6.06218i	−0.125000	−	0.216506i
$785$		−	7.00000i		−	0.249841i
$786$		0			0
$787$	28.5000	−	16.4545i	1.01592	−	0.586539i	0.102997	−	0.994682i	$-0.467157\pi$
$787$	28.5000	−	16.4545i	1.01592	−	0.586539i	0.912918	+	0.408143i	$0.133823\pi$
$788$		−	6.00000i		−	0.213741i
$789$		0			0
$790$	5.50000	−	9.52628i	0.195681	−	0.338930i
$791$		0			0
$792$		0			0
$793$	−28.0000	+	6.92820i	−0.994309	+	0.246028i
$794$	29.4449			1.04496
$795$		0			0
$796$	8.00000	−	13.8564i	0.283552	−	0.491127i
$797$	24.2487	+	42.0000i	0.858933	+	1.48772i	0.872947	+	0.487815i	$0.162206\pi$
$797$	24.2487	+	42.0000i	0.858933	+	1.48772i	−0.0140139	+	0.999902i	$0.504461\pi$
$798$		0			0
$799$		0			0
$800$	0.866025	−	0.500000i	0.0306186	−	0.0176777i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	−12.9904	−	13.5000i	−0.457567	−	0.475517i
$807$		0			0
$808$	12.0000	+	6.92820i	0.422159	+	0.243733i
$809$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$809$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$810$		0			0
$811$			27.7128i			0.973128i	0.873645	+	0.486564i	$0.161750\pi$
$811$			27.7128i			0.973128i	−0.873645	+	0.486564i	$0.838250\pi$
$812$		0			0
$813$		0			0
$814$			5.19615i			0.182125i
$815$	11.2583	+	19.5000i	0.394362	+	0.683055i
$816$		0			0
$817$	−3.00000	−	1.73205i	−0.104957	−	0.0605968i
$818$	34.6410			1.21119
$819$		0			0
$820$	−6.00000			−0.209529
$821$	−12.9904	−	7.50000i	−0.453367	−	0.261752i	0.255884	−	0.966708i	$-0.417634\pi$
$821$	−12.9904	−	7.50000i	−0.453367	−	0.261752i	−0.709251	+	0.704956i	$0.750967\pi$
$822$		0			0
$823$	−22.0000	−	38.1051i	−0.766872	−	1.32826i	−0.939251	−	0.343230i	$-0.888479\pi$
$823$	−22.0000	−	38.1051i	−0.766872	−	1.32826i	0.172379	−	0.985031i	$-0.444854\pi$
$824$			14.0000i			0.487713i
$825$		0			0
$826$		0			0
$827$		−	36.0000i		−	1.25184i	−0.779886	−	0.625921i	$-0.784723\pi$
$827$		−	36.0000i		−	1.25184i	0.779886	−	0.625921i	$-0.215277\pi$
$828$		0			0
$829$	16.0000	−	27.7128i	0.555703	−	0.962506i	−0.442145	−	0.896943i	$-0.645783\pi$
$829$	16.0000	−	27.7128i	0.555703	−	0.962506i	0.997848	−	0.0655624i	$-0.0208842\pi$
$830$	5.19615	+	3.00000i	0.180361	+	0.104132i
$831$		0			0
$832$	1.00000	−	3.46410i	0.0346688	−	0.120096i
$833$		0			0
$834$		0			0
$835$	−10.5000	+	18.1865i	−0.363367	+	0.629371i
$836$	−5.19615	−	9.00000i	−0.179713	−	0.311272i
$837$		0			0
$838$	15.0000	−	8.66025i	0.518166	−	0.299164i
$839$	15.5885	−	9.00000i	0.538173	−	0.310715i	−0.206165	−	0.978517i	$-0.566098\pi$
$839$	15.5885	−	9.00000i	0.538173	−	0.310715i	0.744338	+	0.667803i	$0.232765\pi$
$840$		0			0
$841$	13.0000	+	22.5167i	0.448276	+	0.776437i
$842$	−19.0526	+	33.0000i	−0.656595	+	1.13726i
$843$		0			0
$844$	2.00000			0.0688428
$845$	6.92820	−	11.0000i	0.238337	−	0.378412i
$846$		0			0
$847$		0			0
$848$	3.46410	−	6.00000i	0.118958	−	0.206041i
$849$		0			0
$850$		0			0
$851$	2.59808	−	1.50000i	0.0890609	−	0.0514193i
$852$		0			0
$853$			1.73205i			0.0593043i	0.999560	+	0.0296521i	$0.00943995\pi$
$853$			1.73205i			0.0593043i	−0.999560	+	0.0296521i	$0.990560\pi$
$854$		0			0
$855$		0			0
$856$	6.00000	+	3.46410i	0.205076	+	0.118401i
$857$	−22.5167			−0.769154			−0.384577	−	0.923093i	$-0.625653\pi$
$857$	−22.5167			−0.769154			−0.384577	+	0.923093i	$0.625653\pi$
$858$		0			0
$859$	16.0000			0.545913			0.272956	−	0.962026i	$-0.411998\pi$
$859$	16.0000			0.545913			0.272956	+	0.962026i	$0.411998\pi$
$860$	−0.866025	−	0.500000i	−0.0295312	−	0.0170499i
$861$		0			0
$862$	9.00000	+	15.5885i	0.306541	+	0.530945i
$863$		−	3.00000i		−	0.102121i	−0.998696	−	0.0510606i	$-0.983740\pi$
$863$		−	3.00000i		−	0.102121i	0.998696	−	0.0510606i	$-0.0162602\pi$
$864$		0			0
$865$	18.0000	−	10.3923i	0.612018	−	0.353349i
$866$			14.0000i			0.475739i
$867$		0			0
$868$		0			0
$869$	−28.5788	−	16.5000i	−0.969471	−	0.559724i
$870$		0			0
$871$	9.00000	−	8.66025i	0.304953	−	0.293442i
$872$		0			0
$873$		0			0
$874$	−3.00000	+	5.19615i	−0.101477	+	0.175762i
$875$		0			0
$876$		0			0
$877$	1.50000	−	0.866025i	0.0506514	−	0.0292436i	−0.474460	−	0.880277i	$-0.657357\pi$
$877$	1.50000	−	0.866025i	0.0506514	−	0.0292436i	0.525112	+	0.851033i	$0.324023\pi$
$878$	−27.7128	+	16.0000i	−0.935262	+	0.539974i
$879$		0			0
$880$	−1.50000	−	2.59808i	−0.0505650	−	0.0875811i
$881$	6.92820	−	12.0000i	0.233417	−	0.404290i	−0.725394	−	0.688333i	$-0.758343\pi$
$881$	6.92820	−	12.0000i	0.233417	−	0.404290i	0.958811	+	0.284043i	$0.0916759\pi$
$882$		0			0
$883$	25.0000			0.841317			0.420658	−	0.907219i	$-0.361799\pi$
$883$	25.0000			0.841317			0.420658	+	0.907219i	$0.361799\pi$
$884$		0			0
$885$		0			0
$886$	−27.0000	−	15.5885i	−0.907083	−	0.523704i
$887$	−18.1865	+	31.5000i	−0.610644	+	1.05767i	0.380488	+	0.924786i	$0.375756\pi$
$887$	−18.1865	+	31.5000i	−0.610644	+	1.05767i	−0.991132	+	0.132881i	$0.957577\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		−	17.3205i		−	0.579934i
$893$	−5.19615	−	9.00000i	−0.173883	−	0.301174i
$894$		0			0
$895$	7.50000	+	4.33013i	0.250697	+	0.144740i
$896$		0			0
$897$		0			0
$898$	−12.0000			−0.400445
$899$	7.79423	+	4.50000i	0.259952	+	0.150083i
$900$		0			0
$901$		0			0
$902$			18.0000i			0.599334i
$903$		0			0
$904$	10.5000	−	6.06218i	0.349225	−	0.201625i
$905$			20.0000i			0.664822i
$906$		0			0
$907$	8.50000	−	14.7224i	0.282238	−	0.488850i	−0.689698	−	0.724097i	$-0.742257\pi$
$907$	8.50000	−	14.7224i	0.282238	−	0.488850i	0.971936	+	0.235247i	$0.0755899\pi$
$908$	15.5885	+	9.00000i	0.517321	+	0.298675i
$909$		0			0
$910$		0			0
$911$	−45.0333			−1.49202			−0.746010	−	0.665934i	$-0.768033\pi$
$911$	−45.0333			−1.49202			−0.746010	+	0.665934i	$0.768033\pi$
$912$		0			0
$913$	9.00000	−	15.5885i	0.297857	−	0.515903i
$914$	−12.1244	−	21.0000i	−0.401038	−	0.694618i
$915$		0			0
$916$	6.00000	−	3.46410i	0.198246	−	0.114457i
$917$		0			0
$918$		0			0
$919$	4.00000	+	6.92820i	0.131948	+	0.228540i	0.924427	−	0.381358i	$-0.124544\pi$
$919$	4.00000	+	6.92820i	0.131948	+	0.228540i	−0.792480	+	0.609898i	$0.791210\pi$
$920$	−0.866025	+	1.50000i	−0.0285520	+	0.0494535i
$921$		0			0
$922$	21.0000			0.691598
$923$	5.19615	+	21.0000i	0.171033	+	0.691223i
$924$		0			0
$925$	−1.50000	−	0.866025i	−0.0493197	−	0.0284747i
$926$		0			0
$927$		0			0
$928$			1.73205i			0.0568574i
$929$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$929$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$930$		0			0
$931$		−	24.2487i		−	0.794719i
$932$	−9.52628	−	16.5000i	−0.312044	−	0.540475i
$933$		0			0
$934$	−12.0000	−	6.92820i	−0.392652	−	0.226698i
$935$		0			0
$936$		0			0
$937$	−2.00000			−0.0653372			−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000			−0.0653372			−0.0326686	+	0.999466i	$0.510401\pi$
$938$		0			0
$939$		0			0
$940$	−1.50000	−	2.59808i	−0.0489246	−	0.0847399i
$941$		−	18.0000i		−	0.586783i	−0.955992	−	0.293392i	$-0.905216\pi$
$941$		−	18.0000i		−	0.586783i	0.955992	−	0.293392i	$-0.0947840\pi$
$942$		0			0
$943$	9.00000	−	5.19615i	0.293080	−	0.169210i
$944$			9.00000i			0.292925i
$945$		0			0
$946$	−1.50000	+	2.59808i	−0.0487692	+	0.0844707i
$947$	−5.19615	−	3.00000i	−0.168852	−	0.0974869i	0.413192	−	0.910644i	$-0.364414\pi$
$947$	−5.19615	−	3.00000i	−0.168852	−	0.0974869i	−0.582045	+	0.813157i	$0.697747\pi$
$948$		0			0
$949$		0			0
$950$	3.46410			0.112390
$951$		0			0
$952$		0			0
$953$	18.1865	+	31.5000i	0.589120	+	1.02039i	0.994348	+	0.106170i	$0.0338587\pi$
$953$	18.1865	+	31.5000i	0.589120	+	1.02039i	−0.405228	+	0.914215i	$0.632808\pi$
$954$		0			0
$955$	−15.0000	+	8.66025i	−0.485389	+	0.280239i
$956$	5.19615	−	3.00000i	0.168056	−	0.0970269i
$957$		0			0
$958$	3.00000	+	5.19615i	0.0969256	+	0.167880i
$959$		0			0
$960$		0			0
$961$	4.00000			0.129032
$962$	−6.06218	+	1.50000i	−0.195452	+	0.0483619i
$963$		0			0
$964$	13.5000	+	7.79423i	0.434806	+	0.251035i
$965$	5.19615	−	9.00000i	0.167270	−	0.289720i
$966$		0			0
$967$			24.2487i			0.779786i	0.920860	+	0.389893i	$0.127488\pi$
$967$			24.2487i			0.779786i	−0.920860	+	0.389893i	$0.872512\pi$
$968$	1.73205	−	1.00000i	0.0556702	−	0.0321412i
$969$		0			0
$970$		−	3.46410i		−	0.111226i
$971$	−25.9808	−	45.0000i	−0.833762	−	1.44412i	−0.895034	−	0.445998i	$-0.852849\pi$
$971$	−25.9808	−	45.0000i	−0.833762	−	1.44412i	0.0612718	−	0.998121i	$-0.480484\pi$
$972$		0			0
$973$		0			0
$974$	−10.3923			−0.332991
$975$		0			0
$976$	−8.00000			−0.256074
$977$	28.5788	+	16.5000i	0.914318	+	0.527882i	0.881818	−	0.471590i	$-0.156320\pi$
$977$	28.5788	+	16.5000i	0.914318	+	0.527882i	0.0325001	+	0.999472i	$0.489653\pi$
$978$		0			0
$979$		0			0
$980$		−	7.00000i		−	0.223607i
$981$		0			0
$982$	15.0000	−	8.66025i	0.478669	−	0.276360i
$983$		−	9.00000i		−	0.287055i	−0.989646	−	0.143528i	$-0.954155\pi$
$983$		−	9.00000i		−	0.287055i	0.989646	−	0.143528i	$-0.0458446\pi$
$984$		0			0
$985$	3.00000	−	5.19615i	0.0955879	−	0.165563i
$986$		0			0
$987$		0			0
$988$	9.00000	−	8.66025i	0.286328	−	0.275519i
$989$	1.73205			0.0550760
$990$		0			0
$991$	3.50000	−	6.06218i	0.111181	−	0.192571i	−0.805066	−	0.593186i	$-0.797870\pi$
$991$	3.50000	−	6.06218i	0.111181	−	0.192571i	0.916247	+	0.400614i	$0.131203\pi$
$992$	−2.59808	−	4.50000i	−0.0824890	−	0.142875i
$993$		0			0
$994$		0			0
$995$	13.8564	−	8.00000i	0.439278	−	0.253617i
$996$		0			0
$997$	−13.0000	−	22.5167i	−0.411714	−	0.713110i	0.583363	−	0.812211i	$-0.301736\pi$
$997$	−13.0000	−	22.5167i	−0.411714	−	0.713110i	−0.995077	+	0.0991016i	$0.968403\pi$
$998$	−8.66025	+	15.0000i	−0.274136	+	0.474817i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.bs.b.901.2	yes	4
3.2	odd	2	inner	1170.2.bs.b.901.1	yes	4
13.10	even	6	inner	1170.2.bs.b.361.2	yes	4
39.23	odd	6	inner	1170.2.bs.b.361.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1170.2.bs.b.361.1	✓	4	39.23	odd	6	inner
1170.2.bs.b.361.2	yes	4	13.10	even	6	inner
1170.2.bs.b.901.1	yes	4	3.2	odd	2	inner
1170.2.bs.b.901.2	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:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.bs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000i q^{5} +1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000i q^{5} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{10} +(2.59808 + 1.50000i) q^{11} +(-1.00000 + 3.46410i) q^{13} +(-0.500000 + 0.866025i) q^{16} +(-3.00000 + 1.73205i) q^{19} +(-0.866025 + 0.500000i) q^{20} +(1.50000 + 2.59808i) q^{22} +(0.866025 - 1.50000i) q^{23} -1.00000 q^{25} +(-2.59808 + 2.50000i) q^{26} +(0.866025 - 1.50000i) q^{29} +5.19615i q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.50000 + 0.866025i) q^{37} -3.46410 q^{38} -1.00000 q^{40} +(5.19615 + 3.00000i) q^{41} +(0.500000 + 0.866025i) q^{43} +3.00000i q^{44} +(1.50000 - 0.866025i) q^{46} +3.00000i q^{47} +(-3.50000 + 6.06218i) q^{49} +(-0.866025 - 0.500000i) q^{50} +(-3.50000 + 0.866025i) q^{52} -6.92820 q^{53} +(-1.50000 + 2.59808i) q^{55} +(1.50000 - 0.866025i) q^{58} +(7.79423 - 4.50000i) q^{59} +(4.00000 + 6.92820i) q^{61} +(-2.59808 + 4.50000i) q^{62} -1.00000 q^{64} +(-3.46410 - 1.00000i) q^{65} +(-3.00000 - 1.73205i) q^{67} +(5.19615 - 3.00000i) q^{71} +(0.866025 + 1.50000i) q^{74} +(-3.00000 - 1.73205i) q^{76} -11.0000 q^{79} +(-0.866025 - 0.500000i) q^{80} +(3.00000 + 5.19615i) q^{82} -6.00000i q^{83} +1.00000i q^{86} +(-1.50000 + 2.59808i) q^{88} +1.73205 q^{92} +(-1.50000 + 2.59808i) q^{94} +(-1.73205 - 3.00000i) q^{95} +(-3.00000 + 1.73205i) q^{97} +(-6.06218 + 3.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4}+O(q^{10}) \) 4 * q + 2 * q^4	\( 4 q + 2 q^{4} - 2 q^{10} - 4 q^{13} - 2 q^{16} - 12 q^{19} + 6 q^{22} - 4 q^{25} + 6 q^{37} - 4 q^{40} + 2 q^{43} + 6 q^{46} - 14 q^{49} - 14 q^{52} - 6 q^{55} + 6 q^{58} + 16 q^{61} - 4 q^{64} - 12 q^{67} - 12 q^{76} - 44 q^{79} + 12 q^{82} - 6 q^{88} - 6 q^{94} - 12 q^{97}+O(q^{100}) \) 4 * q + 2 * q^4 - 2 * q^10 - 4 * q^13 - 2 * q^16 - 12 * q^19 + 6 * q^22 - 4 * q^25 + 6 * q^37 - 4 * q^40 + 2 * q^43 + 6 * q^46 - 14 * q^49 - 14 * q^52 - 6 * q^55 + 6 * q^58 + 16 * q^61 - 4 * q^64 - 12 * q^67 - 12 * q^76 - 44 * q^79 + 12 * q^82 - 6 * q^88 - 6 * q^94 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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