LMFDB - Embedded newform 2646.2.f.f.883.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2646,2,Mod(883,2646)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2646, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2646.883"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.f (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,1,0,-1,-1,0,0,-2,0,-2,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 882)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			883.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	2646.883
Dual form			2646.2.f.f.1765.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.00000 q^{8} -1.00000 q^{10} +(-1.00000 + 1.73205i) q^{11} +(1.00000 + 1.73205i) q^{13} +(-0.500000 + 0.866025i) q^{16} +7.00000 q^{19} +(-0.500000 + 0.866025i) q^{20} +(1.00000 + 1.73205i) q^{22} +(1.50000 + 2.59808i) q^{23} +(2.00000 - 3.46410i) q^{25} +2.00000 q^{26} +(-4.00000 + 6.92820i) q^{29} +(2.00000 + 3.46410i) q^{31} +(0.500000 + 0.866025i) q^{32} -6.00000 q^{37} +(3.50000 - 6.06218i) q^{38} +(0.500000 + 0.866025i) q^{40} +(6.00000 + 10.3923i) q^{41} +(4.00000 - 6.92820i) q^{43} +2.00000 q^{44} +3.00000 q^{46} +(4.00000 - 6.92820i) q^{47} +(-2.00000 - 3.46410i) q^{50} +(1.00000 - 1.73205i) q^{52} -4.00000 q^{53} +2.00000 q^{55} +(4.00000 + 6.92820i) q^{58} +(-2.00000 - 3.46410i) q^{59} +(6.50000 - 11.2583i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(1.00000 - 1.73205i) q^{65} +(1.00000 + 1.73205i) q^{67} +5.00000 q^{71} +14.0000 q^{73} +(-3.00000 + 5.19615i) q^{74} +(-3.50000 - 6.06218i) q^{76} +(5.50000 - 9.52628i) q^{79} +1.00000 q^{80} +12.0000 q^{82} +(-6.00000 + 10.3923i) q^{83} +(-4.00000 - 6.92820i) q^{86} +(1.00000 - 1.73205i) q^{88} +14.0000 q^{89} +(1.50000 - 2.59808i) q^{92} +(-4.00000 - 6.92820i) q^{94} +(-3.50000 - 6.06218i) q^{95} +(-1.00000 + 1.73205i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} - q^{5} - 2 q^{8} - 2 q^{10} - 2 q^{11} + 2 q^{13} - q^{16} + 14 q^{19} - q^{20} + 2 q^{22} + 3 q^{23} + 4 q^{25} + 4 q^{26} - 8 q^{29} + 4 q^{31} + q^{32} - 12 q^{37} + 7 q^{38}+ \cdots - 2 q^{97}+O(q^{100}) $ 2 * q + q^2 - q^4 - q^5 - 2 * q^8 - 2 * q^10 - 2 * q^11 + 2 * q^13 - q^16 + 14 * q^19 - q^20 + 2 * q^22 + 3 * q^23 + 4 * q^25 + 4 * q^26 - 8 * q^29 + 4 * q^31 + q^32 - 12 * q^37 + 7 * q^38 + q^40 + 12 * q^41 + 8 * q^43 + 4 * q^44 + 6 * q^46 + 8 * q^47 - 4 * q^50 + 2 * q^52 - 8 * q^53 + 4 * q^55 + 8 * q^58 - 4 * q^59 + 13 * q^61 + 8 * q^62 + 2 * q^64 + 2 * q^65 + 2 * q^67 + 10 * q^71 + 28 * q^73 - 6 * q^74 - 7 * q^76 + 11 * q^79 + 2 * q^80 + 24 * q^82 - 12 * q^83 - 8 * q^86 + 2 * q^88 + 28 * q^89 + 3 * q^92 - 8 * q^94 - 7 * q^95 - 2 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	0.732294	−	0.680989i	$-0.238450\pi$
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	−0.955901	+	0.293691i	$0.905116\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−1.00000			−0.316228
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	−0.976478	−	0.215615i	$-0.930824\pi$
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$12$		0			0
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	0.970725	−	0.240192i	$-0.0772105\pi$
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	−0.693375	+	0.720577i	$0.743877\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		0			0			−	1.00000i	$-0.5\pi$
$17$		0			0				1.00000i	$0.5\pi$
$18$		0			0
$19$	7.00000			1.60591			0.802955	−	0.596040i	$-0.203260\pi$
$19$	7.00000			1.60591			0.802955	+	0.596040i	$0.203260\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$		0			0
$22$	1.00000	+	1.73205i	0.213201	+	0.369274i
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	0.978961	−	0.204046i	$-0.0654092\pi$
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	−0.666190	+	0.745782i	$0.732076\pi$
$24$		0			0
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$	2.00000			0.392232
$27$		0			0
$28$		0			0
$29$	−4.00000	+	6.92820i	−0.742781	+	1.28654i	0.208443	+	0.978035i	$0.433160\pi$
$29$	−4.00000	+	6.92820i	−0.742781	+	1.28654i	−0.951224	+	0.308500i	$0.900173\pi$
$30$		0			0
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	0.987829	−	0.155543i	$-0.0497126\pi$
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	−0.628619	+	0.777714i	$0.716379\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−6.00000			−0.986394			−0.493197	−	0.869918i	$-0.664172\pi$
$37$	−6.00000			−0.986394			−0.493197	+	0.869918i	$0.664172\pi$
$38$	3.50000	−	6.06218i	0.567775	−	0.983415i
$39$		0			0
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	6.00000	+	10.3923i	0.937043	+	1.62301i	0.770950	+	0.636895i	$0.219782\pi$
$41$	6.00000	+	10.3923i	0.937043	+	1.62301i	0.166092	+	0.986110i	$0.446885\pi$
$42$		0			0
$43$	4.00000	−	6.92820i	0.609994	−	1.05654i	−0.381246	−	0.924473i	$-0.624505\pi$
$43$	4.00000	−	6.92820i	0.609994	−	1.05654i	0.991241	−	0.132068i	$-0.0421616\pi$
$44$	2.00000			0.301511
$45$		0			0
$46$	3.00000			0.442326
$47$	4.00000	−	6.92820i	0.583460	−	1.01058i	−0.411606	−	0.911362i	$-0.635032\pi$
$47$	4.00000	−	6.92820i	0.583460	−	1.01058i	0.995066	−	0.0992202i	$-0.0316348\pi$
$48$		0			0
$49$		0			0
$50$	−2.00000	−	3.46410i	−0.282843	−	0.489898i
$51$		0			0
$52$	1.00000	−	1.73205i	0.138675	−	0.240192i
$53$	−4.00000			−0.549442			−0.274721	−	0.961524i	$-0.588586\pi$
$53$	−4.00000			−0.549442			−0.274721	+	0.961524i	$0.588586\pi$
$54$		0			0
$55$	2.00000			0.269680
$56$		0			0
$57$		0			0
$58$	4.00000	+	6.92820i	0.525226	+	0.909718i
$59$	−2.00000	−	3.46410i	−0.260378	−	0.450988i	0.705965	−	0.708247i	$-0.250514\pi$
$59$	−2.00000	−	3.46410i	−0.260378	−	0.450988i	−0.966342	+	0.257260i	$0.917180\pi$
$60$		0			0
$61$	6.50000	−	11.2583i	0.832240	−	1.44148i	−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	6.50000	−	11.2583i	0.832240	−	1.44148i	0.896258	−	0.443533i	$-0.146275\pi$
$62$	4.00000			0.508001
$63$		0			0
$64$	1.00000			0.125000
$65$	1.00000	−	1.73205i	0.124035	−	0.214834i
$66$		0			0
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	0.920623	−	0.390453i	$-0.127682\pi$
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	−0.798454	+	0.602056i	$0.794348\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	5.00000			0.593391			0.296695	−	0.954972i	$-0.404115\pi$
$71$	5.00000			0.593391			0.296695	+	0.954972i	$0.404115\pi$
$72$		0			0
$73$	14.0000			1.63858			0.819288	−	0.573382i	$-0.194369\pi$
$73$	14.0000			1.63858			0.819288	+	0.573382i	$0.194369\pi$
$74$	−3.00000	+	5.19615i	−0.348743	+	0.604040i
$75$		0			0
$76$	−3.50000	−	6.06218i	−0.401478	−	0.695379i
$77$		0			0
$78$		0			0
$79$	5.50000	−	9.52628i	0.618798	−	1.07179i	−0.370907	−	0.928670i	$-0.620953\pi$
$79$	5.50000	−	9.52628i	0.618798	−	1.07179i	0.989705	−	0.143120i	$-0.0457135\pi$
$80$	1.00000			0.111803
$81$		0			0
$82$	12.0000			1.32518
$83$	−6.00000	+	10.3923i	−0.658586	+	1.14070i	0.322396	+	0.946605i	$0.395512\pi$
$83$	−6.00000	+	10.3923i	−0.658586	+	1.14070i	−0.980982	+	0.194099i	$0.937822\pi$
$84$		0			0
$85$		0			0
$86$	−4.00000	−	6.92820i	−0.431331	−	0.747087i
$87$		0			0
$88$	1.00000	−	1.73205i	0.106600	−	0.184637i
$89$	14.0000			1.48400			0.741999	−	0.670402i	$-0.233878\pi$
$89$	14.0000			1.48400			0.741999	+	0.670402i	$0.233878\pi$
$90$		0			0
$91$		0			0
$92$	1.50000	−	2.59808i	0.156386	−	0.270868i
$93$		0			0
$94$	−4.00000	−	6.92820i	−0.412568	−	0.714590i
$95$	−3.50000	−	6.06218i	−0.359092	−	0.621966i
$96$		0			0
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	−0.912317	−	0.409484i	$-0.865709\pi$
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	0.810782	+	0.585348i	$0.199042\pi$
$98$		0			0
$99$		0			0
$100$	−4.00000			−0.400000
$101$	5.50000	−	9.52628i	0.547270	−	0.947900i	−0.451190	−	0.892428i	$-0.649000\pi$
$101$	5.50000	−	9.52628i	0.547270	−	0.947900i	0.998460	−	0.0554722i	$-0.0176664\pi$
$102$		0			0
$103$	4.00000	+	6.92820i	0.394132	+	0.682656i	0.992990	−	0.118199i	$-0.0377120\pi$
$103$	4.00000	+	6.92820i	0.394132	+	0.682656i	−0.598858	+	0.800855i	$0.704379\pi$
$104$	−1.00000	−	1.73205i	−0.0980581	−	0.169842i
$105$		0			0
$106$	−2.00000	+	3.46410i	−0.194257	+	0.336463i
$107$	−8.00000			−0.773389			−0.386695	−	0.922208i	$-0.626383\pi$
$107$	−8.00000			−0.773389			−0.386695	+	0.922208i	$0.626383\pi$
$108$		0			0
$109$	4.00000			0.383131			0.191565	−	0.981480i	$-0.438644\pi$
$109$	4.00000			0.383131			0.191565	+	0.981480i	$0.438644\pi$
$110$	1.00000	−	1.73205i	0.0953463	−	0.165145i
$111$		0			0
$112$		0			0
$113$	−0.500000	−	0.866025i	−0.0470360	−	0.0814688i	0.841549	−	0.540181i	$-0.181644\pi$
$113$	−0.500000	−	0.866025i	−0.0470360	−	0.0814688i	−0.888585	+	0.458712i	$0.848311\pi$
$114$		0			0
$115$	1.50000	−	2.59808i	0.139876	−	0.242272i
$116$	8.00000			0.742781
$117$		0			0
$118$	−4.00000			−0.368230
$119$		0			0
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	−6.50000	−	11.2583i	−0.588482	−	1.01928i
$123$		0			0
$124$	2.00000	−	3.46410i	0.179605	−	0.311086i
$125$	−9.00000			−0.804984
$126$		0			0
$127$	−19.0000			−1.68598			−0.842989	−	0.537931i	$-0.819206\pi$
$127$	−19.0000			−1.68598			−0.842989	+	0.537931i	$0.819206\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−1.00000	−	1.73205i	−0.0877058	−	0.151911i
$131$	−7.50000	−	12.9904i	−0.655278	−	1.13497i	−0.981824	−	0.189794i	$-0.939218\pi$
$131$	−7.50000	−	12.9904i	−0.655278	−	1.13497i	0.326546	−	0.945181i	$-0.394115\pi$
$132$		0			0
$133$		0			0
$134$	2.00000			0.172774
$135$		0			0
$136$		0			0
$137$	−1.00000	+	1.73205i	−0.0854358	+	0.147979i	−0.905577	−	0.424182i	$-0.860562\pi$
$137$	−1.00000	+	1.73205i	−0.0854358	+	0.147979i	0.820141	+	0.572161i	$0.193895\pi$
$138$		0			0
$139$	4.50000	+	7.79423i	0.381685	+	0.661098i	0.991303	−	0.131597i	$-0.0420106\pi$
$139$	4.50000	+	7.79423i	0.381685	+	0.661098i	−0.609618	+	0.792695i	$0.708677\pi$
$140$		0			0
$141$		0			0
$142$	2.50000	−	4.33013i	0.209795	−	0.363376i
$143$	−4.00000			−0.334497
$144$		0			0
$145$	8.00000			0.664364
$146$	7.00000	−	12.1244i	0.579324	−	1.00342i
$147$		0			0
$148$	3.00000	+	5.19615i	0.246598	+	0.427121i
$149$	5.00000	+	8.66025i	0.409616	+	0.709476i	0.994847	−	0.101391i	$-0.0323294\pi$
$149$	5.00000	+	8.66025i	0.409616	+	0.709476i	−0.585231	+	0.810867i	$0.698996\pi$
$150$		0			0
$151$	−9.50000	+	16.4545i	−0.773099	+	1.33905i	0.162758	+	0.986666i	$0.447961\pi$
$151$	−9.50000	+	16.4545i	−0.773099	+	1.33905i	−0.935857	+	0.352381i	$0.885372\pi$
$152$	−7.00000			−0.567775
$153$		0			0
$154$		0			0
$155$	2.00000	−	3.46410i	0.160644	−	0.278243i
$156$		0			0
$157$	5.50000	+	9.52628i	0.438948	+	0.760280i	0.997609	−	0.0691164i	$-0.0220180\pi$
$157$	5.50000	+	9.52628i	0.438948	+	0.760280i	−0.558661	+	0.829396i	$0.688685\pi$
$158$	−5.50000	−	9.52628i	−0.437557	−	0.757870i
$159$		0			0
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$		0			0
$162$		0			0
$163$	−6.00000			−0.469956			−0.234978	−	0.972001i	$-0.575502\pi$
$163$	−6.00000			−0.469956			−0.234978	+	0.972001i	$0.575502\pi$
$164$	6.00000	−	10.3923i	0.468521	−	0.811503i
$165$		0			0
$166$	6.00000	+	10.3923i	0.465690	+	0.806599i
$167$	−1.00000	−	1.73205i	−0.0773823	−	0.134030i	0.824737	−	0.565516i	$-0.191323\pi$
$167$	−1.00000	−	1.73205i	−0.0773823	−	0.134030i	−0.902120	+	0.431486i	$0.857990\pi$
$168$		0			0
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$		0			0
$171$		0			0
$172$	−8.00000			−0.609994
$173$	11.0000	−	19.0526i	0.836315	−	1.44854i	−0.0566411	−	0.998395i	$-0.518039\pi$
$173$	11.0000	−	19.0526i	0.836315	−	1.44854i	0.892956	−	0.450145i	$-0.148628\pi$
$174$		0			0
$175$		0			0
$176$	−1.00000	−	1.73205i	−0.0753778	−	0.130558i
$177$		0			0
$178$	7.00000	−	12.1244i	0.524672	−	0.908759i
$179$	24.0000			1.79384			0.896922	−	0.442189i	$-0.145798\pi$
$179$	24.0000			1.79384			0.896922	+	0.442189i	$0.145798\pi$
$180$		0			0
$181$	−7.00000			−0.520306			−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000			−0.520306			−0.260153	+	0.965567i	$0.583773\pi$
$182$		0			0
$183$		0			0
$184$	−1.50000	−	2.59808i	−0.110581	−	0.191533i
$185$	3.00000	+	5.19615i	0.220564	+	0.382029i
$186$		0			0
$187$		0			0
$188$	−8.00000			−0.583460
$189$		0			0
$190$	−7.00000			−0.507833
$191$	1.50000	−	2.59808i	0.108536	−	0.187990i	−0.806641	−	0.591041i	$-0.798717\pi$
$191$	1.50000	−	2.59808i	0.108536	−	0.187990i	0.915177	+	0.403051i	$0.132050\pi$
$192$		0			0
$193$	−2.50000	−	4.33013i	−0.179954	−	0.311689i	0.761911	−	0.647682i	$-0.224262\pi$
$193$	−2.50000	−	4.33013i	−0.179954	−	0.311689i	−0.941865	+	0.335993i	$0.890928\pi$
$194$	1.00000	+	1.73205i	0.0717958	+	0.124354i
$195$		0			0
$196$		0			0
$197$	12.0000			0.854965			0.427482	−	0.904024i	$-0.359401\pi$
$197$	12.0000			0.854965			0.427482	+	0.904024i	$0.359401\pi$
$198$		0			0
$199$	14.0000			0.992434			0.496217	−	0.868199i	$-0.334722\pi$
$199$	14.0000			0.992434			0.496217	+	0.868199i	$0.334722\pi$
$200$	−2.00000	+	3.46410i	−0.141421	+	0.244949i
$201$		0			0
$202$	−5.50000	−	9.52628i	−0.386979	−	0.670267i
$203$		0			0
$204$		0			0
$205$	6.00000	−	10.3923i	0.419058	−	0.725830i
$206$	8.00000			0.557386
$207$		0			0
$208$	−2.00000			−0.138675
$209$	−7.00000	+	12.1244i	−0.484200	+	0.838659i
$210$		0			0
$211$	11.0000	+	19.0526i	0.757271	+	1.31163i	0.944237	+	0.329266i	$0.106801\pi$
$211$	11.0000	+	19.0526i	0.757271	+	1.31163i	−0.186966	+	0.982366i	$0.559865\pi$
$212$	2.00000	+	3.46410i	0.137361	+	0.237915i
$213$		0			0
$214$	−4.00000	+	6.92820i	−0.273434	+	0.473602i
$215$	−8.00000			−0.545595
$216$		0			0
$217$		0			0
$218$	2.00000	−	3.46410i	0.135457	−	0.234619i
$219$		0			0
$220$	−1.00000	−	1.73205i	−0.0674200	−	0.116775i
$221$		0			0
$222$		0			0
$223$	−1.00000	+	1.73205i	−0.0669650	+	0.115987i	−0.897564	−	0.440884i	$-0.854665\pi$
$223$	−1.00000	+	1.73205i	−0.0669650	+	0.115987i	0.830599	+	0.556871i	$0.187998\pi$
$224$		0			0
$225$		0			0
$226$	−1.00000			−0.0665190
$227$	−8.50000	+	14.7224i	−0.564165	+	0.977162i	0.432962	+	0.901412i	$0.357468\pi$
$227$	−8.50000	+	14.7224i	−0.564165	+	0.977162i	−0.997127	+	0.0757500i	$0.975865\pi$
$228$		0			0
$229$	−6.50000	−	11.2583i	−0.429532	−	0.743971i	0.567300	−	0.823511i	$-0.307988\pi$
$229$	−6.50000	−	11.2583i	−0.429532	−	0.743971i	−0.996832	+	0.0795401i	$0.974655\pi$
$230$	−1.50000	−	2.59808i	−0.0989071	−	0.171312i
$231$		0			0
$232$	4.00000	−	6.92820i	0.262613	−	0.454859i
$233$	−1.00000			−0.0655122			−0.0327561	−	0.999463i	$-0.510428\pi$
$233$	−1.00000			−0.0655122			−0.0327561	+	0.999463i	$0.510428\pi$
$234$		0			0
$235$	−8.00000			−0.521862
$236$	−2.00000	+	3.46410i	−0.130189	+	0.225494i
$237$		0			0
$238$		0			0
$239$	−7.50000	−	12.9904i	−0.485135	−	0.840278i	0.514719	−	0.857359i	$-0.327896\pi$
$239$	−7.50000	−	12.9904i	−0.485135	−	0.840278i	−0.999854	+	0.0170808i	$0.994563\pi$
$240$		0			0
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	−0.658838	−	0.752285i	$-0.728952\pi$
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	0.980917	+	0.194429i	$0.0622852\pi$
$242$	7.00000			0.449977
$243$		0			0
$244$	−13.0000			−0.832240
$245$		0			0
$246$		0			0
$247$	7.00000	+	12.1244i	0.445399	+	0.771454i
$248$	−2.00000	−	3.46410i	−0.127000	−	0.219971i
$249$		0			0
$250$	−4.50000	+	7.79423i	−0.284605	+	0.492950i
$251$	7.00000			0.441836			0.220918	−	0.975292i	$-0.429095\pi$
$251$	7.00000			0.441836			0.220918	+	0.975292i	$0.429095\pi$
$252$		0			0
$253$	−6.00000			−0.377217
$254$	−9.50000	+	16.4545i	−0.596083	+	1.03245i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.00000	−	6.92820i	−0.249513	−	0.432169i	0.713878	−	0.700270i	$-0.246937\pi$
$257$	−4.00000	−	6.92820i	−0.249513	−	0.432169i	−0.963391	+	0.268101i	$0.913604\pi$
$258$		0			0
$259$		0			0
$260$	−2.00000			−0.124035
$261$		0			0
$262$	−15.0000			−0.926703
$263$	9.50000	−	16.4545i	0.585795	−	1.01463i	−0.408981	−	0.912543i	$-0.634116\pi$
$263$	9.50000	−	16.4545i	0.585795	−	1.01463i	0.994776	−	0.102084i	$-0.0325510\pi$
$264$		0			0
$265$	2.00000	+	3.46410i	0.122859	+	0.212798i
$266$		0			0
$267$		0			0
$268$	1.00000	−	1.73205i	0.0610847	−	0.105802i
$269$	7.00000			0.426798			0.213399	−	0.976965i	$-0.431547\pi$
$269$	7.00000			0.426798			0.213399	+	0.976965i	$0.431547\pi$
$270$		0			0
$271$	−14.0000			−0.850439			−0.425220	−	0.905090i	$-0.639803\pi$
$271$	−14.0000			−0.850439			−0.425220	+	0.905090i	$0.639803\pi$
$272$		0			0
$273$		0			0
$274$	1.00000	+	1.73205i	0.0604122	+	0.104637i
$275$	4.00000	+	6.92820i	0.241209	+	0.417786i
$276$		0			0
$277$	1.00000	−	1.73205i	0.0600842	−	0.104069i	−0.834419	−	0.551131i	$-0.814196\pi$
$277$	1.00000	−	1.73205i	0.0600842	−	0.104069i	0.894503	+	0.447062i	$0.147530\pi$
$278$	9.00000			0.539784
$279$		0			0
$280$		0			0
$281$	−7.50000	+	12.9904i	−0.447412	+	0.774941i	−0.998217	−	0.0596933i	$-0.980988\pi$
$281$	−7.50000	+	12.9904i	−0.447412	+	0.774941i	0.550804	+	0.834634i	$0.314321\pi$
$282$		0			0
$283$	12.5000	+	21.6506i	0.743048	+	1.28700i	0.951101	+	0.308879i	$0.0999539\pi$
$283$	12.5000	+	21.6506i	0.743048	+	1.28700i	−0.208053	+	0.978117i	$0.566713\pi$
$284$	−2.50000	−	4.33013i	−0.148348	−	0.256946i
$285$		0			0
$286$	−2.00000	+	3.46410i	−0.118262	+	0.204837i
$287$		0			0
$288$		0			0
$289$	−17.0000			−1.00000
$290$	4.00000	−	6.92820i	0.234888	−	0.406838i
$291$		0			0
$292$	−7.00000	−	12.1244i	−0.409644	−	0.709524i
$293$	−4.50000	−	7.79423i	−0.262893	−	0.455344i	0.704117	−	0.710084i	$-0.251343\pi$
$293$	−4.50000	−	7.79423i	−0.262893	−	0.455344i	−0.967009	+	0.254741i	$0.918010\pi$
$294$		0			0
$295$	−2.00000	+	3.46410i	−0.116445	+	0.201688i
$296$	6.00000			0.348743
$297$		0			0
$298$	10.0000			0.579284
$299$	−3.00000	+	5.19615i	−0.173494	+	0.300501i
$300$		0			0
$301$		0			0
$302$	9.50000	+	16.4545i	0.546664	+	0.946849i
$303$		0			0
$304$	−3.50000	+	6.06218i	−0.200739	+	0.347690i
$305$	−13.0000			−0.744378
$306$		0			0
$307$	−7.00000			−0.399511			−0.199756	−	0.979846i	$-0.564015\pi$
$307$	−7.00000			−0.399511			−0.199756	+	0.979846i	$0.564015\pi$
$308$		0			0
$309$		0			0
$310$	−2.00000	−	3.46410i	−0.113592	−	0.196748i
$311$	5.00000	+	8.66025i	0.283524	+	0.491078i	0.972250	−	0.233944i	$-0.0751631\pi$
$311$	5.00000	+	8.66025i	0.283524	+	0.491078i	−0.688726	+	0.725022i	$0.741830\pi$
$312$		0			0
$313$	3.00000	−	5.19615i	0.169570	−	0.293704i	−0.768699	−	0.639611i	$-0.779095\pi$
$313$	3.00000	−	5.19615i	0.169570	−	0.293704i	0.938269	+	0.345907i	$0.112429\pi$
$314$	11.0000			0.620766
$315$		0			0
$316$	−11.0000			−0.618798
$317$	12.0000	−	20.7846i	0.673987	−	1.16738i	−0.302777	−	0.953062i	$-0.597914\pi$
$317$	12.0000	−	20.7846i	0.673987	−	1.16738i	0.976764	−	0.214318i	$-0.0687530\pi$
$318$		0			0
$319$	−8.00000	−	13.8564i	−0.447914	−	0.775810i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$		0			0
$322$		0			0
$323$		0			0
$324$		0			0
$325$	8.00000			0.443760
$326$	−3.00000	+	5.19615i	−0.166155	+	0.287788i
$327$		0			0
$328$	−6.00000	−	10.3923i	−0.331295	−	0.573819i
$329$		0			0
$330$		0			0
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	−0.805812	−	0.592172i	$-0.798271\pi$
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	0.915742	+	0.401768i	$0.131604\pi$
$332$	12.0000			0.658586
$333$		0			0
$334$	−2.00000			−0.109435
$335$	1.00000	−	1.73205i	0.0546358	−	0.0946320i
$336$		0			0
$337$	11.0000	+	19.0526i	0.599208	+	1.03786i	0.992938	+	0.118633i	$0.0378512\pi$
$337$	11.0000	+	19.0526i	0.599208	+	1.03786i	−0.393730	+	0.919226i	$0.628816\pi$
$338$	−4.50000	−	7.79423i	−0.244768	−	0.423950i
$339$		0			0
$340$		0			0
$341$	−8.00000			−0.433224
$342$		0			0
$343$		0			0
$344$	−4.00000	+	6.92820i	−0.215666	+	0.373544i
$345$		0			0
$346$	−11.0000	−	19.0526i	−0.591364	−	1.02427i
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	0.980921	−	0.194409i	$-0.0622790\pi$
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	−0.658824	+	0.752297i	$0.728946\pi$
$348$		0			0
$349$	−15.0000	+	25.9808i	−0.802932	+	1.39072i	0.114747	+	0.993395i	$0.463394\pi$
$349$	−15.0000	+	25.9808i	−0.802932	+	1.39072i	−0.917679	+	0.397324i	$0.869939\pi$
$350$		0			0
$351$		0			0
$352$	−2.00000			−0.106600
$353$	−12.0000	+	20.7846i	−0.638696	+	1.10625i	0.347024	+	0.937856i	$0.387192\pi$
$353$	−12.0000	+	20.7846i	−0.638696	+	1.10625i	−0.985719	+	0.168397i	$0.946141\pi$
$354$		0			0
$355$	−2.50000	−	4.33013i	−0.132686	−	0.229819i
$356$	−7.00000	−	12.1244i	−0.370999	−	0.642590i
$357$		0			0
$358$	12.0000	−	20.7846i	0.634220	−	1.09850i
$359$	−29.0000			−1.53056			−0.765281	−	0.643697i	$-0.777400\pi$
$359$	−29.0000			−1.53056			−0.765281	+	0.643697i	$0.777400\pi$
$360$		0			0
$361$	30.0000			1.57895
$362$	−3.50000	+	6.06218i	−0.183956	+	0.318621i
$363$		0			0
$364$		0			0
$365$	−7.00000	−	12.1244i	−0.366397	−	0.634618i
$366$		0			0
$367$	−16.0000	+	27.7128i	−0.835193	+	1.44660i	0.0586798	+	0.998277i	$0.481311\pi$
$367$	−16.0000	+	27.7128i	−0.835193	+	1.44660i	−0.893873	+	0.448320i	$0.852022\pi$
$368$	−3.00000			−0.156386
$369$		0			0
$370$	6.00000			0.311925
$371$		0			0
$372$		0			0
$373$	16.0000	+	27.7128i	0.828449	+	1.43492i	0.899255	+	0.437425i	$0.144109\pi$
$373$	16.0000	+	27.7128i	0.828449	+	1.43492i	−0.0708063	+	0.997490i	$0.522557\pi$
$374$		0			0
$375$		0			0
$376$	−4.00000	+	6.92820i	−0.206284	+	0.357295i
$377$	−16.0000			−0.824042
$378$		0			0
$379$	−12.0000			−0.616399			−0.308199	−	0.951322i	$-0.599726\pi$
$379$	−12.0000			−0.616399			−0.308199	+	0.951322i	$0.599726\pi$
$380$	−3.50000	+	6.06218i	−0.179546	+	0.310983i
$381$		0			0
$382$	−1.50000	−	2.59808i	−0.0767467	−	0.132929i
$383$	3.00000	+	5.19615i	0.153293	+	0.265511i	0.932436	−	0.361335i	$-0.117679\pi$
$383$	3.00000	+	5.19615i	0.153293	+	0.265511i	−0.779143	+	0.626846i	$0.784346\pi$
$384$		0			0
$385$		0			0
$386$	−5.00000			−0.254493
$387$		0			0
$388$	2.00000			0.101535
$389$	−15.0000	+	25.9808i	−0.760530	+	1.31728i	0.182047	+	0.983290i	$0.441728\pi$
$389$	−15.0000	+	25.9808i	−0.760530	+	1.31728i	−0.942578	+	0.333987i	$0.891606\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$	6.00000	−	10.3923i	0.302276	−	0.523557i
$395$	−11.0000			−0.553470
$396$		0			0
$397$	−14.0000			−0.702640			−0.351320	−	0.936255i	$-0.614267\pi$
$397$	−14.0000			−0.702640			−0.351320	+	0.936255i	$0.614267\pi$
$398$	7.00000	−	12.1244i	0.350878	−	0.607739i
$399$		0			0
$400$	2.00000	+	3.46410i	0.100000	+	0.173205i
$401$	1.50000	+	2.59808i	0.0749064	+	0.129742i	0.901046	−	0.433724i	$-0.142801\pi$
$401$	1.50000	+	2.59808i	0.0749064	+	0.129742i	−0.826139	+	0.563466i	$0.809468\pi$
$402$		0			0
$403$	−4.00000	+	6.92820i	−0.199254	+	0.345118i
$404$	−11.0000			−0.547270
$405$		0			0
$406$		0			0
$407$	6.00000	−	10.3923i	0.297409	−	0.515127i
$408$		0			0
$409$	−12.0000	−	20.7846i	−0.593362	−	1.02773i	−0.993776	−	0.111398i	$-0.964467\pi$
$409$	−12.0000	−	20.7846i	−0.593362	−	1.02773i	0.400414	−	0.916334i	$-0.368866\pi$
$410$	−6.00000	−	10.3923i	−0.296319	−	0.513239i
$411$		0			0
$412$	4.00000	−	6.92820i	0.197066	−	0.341328i
$413$		0			0
$414$		0			0
$415$	12.0000			0.589057
$416$	−1.00000	+	1.73205i	−0.0490290	+	0.0849208i
$417$		0			0
$418$	7.00000	+	12.1244i	0.342381	+	0.593022i
$419$	2.50000	+	4.33013i	0.122133	+	0.211541i	0.920609	−	0.390487i	$-0.127693\pi$
$419$	2.50000	+	4.33013i	0.122133	+	0.211541i	−0.798476	+	0.602027i	$0.794360\pi$
$420$		0			0
$421$	18.0000	−	31.1769i	0.877266	−	1.51947i	0.0229375	−	0.999737i	$-0.492698\pi$
$421$	18.0000	−	31.1769i	0.877266	−	1.51947i	0.854329	−	0.519733i	$-0.173969\pi$
$422$	22.0000			1.07094
$423$		0			0
$424$	4.00000			0.194257
$425$		0			0
$426$		0			0
$427$		0			0
$428$	4.00000	+	6.92820i	0.193347	+	0.334887i
$429$		0			0
$430$	−4.00000	+	6.92820i	−0.192897	+	0.334108i
$431$	−32.0000			−1.54139			−0.770693	−	0.637207i	$-0.780090\pi$
$431$	−32.0000			−1.54139			−0.770693	+	0.637207i	$0.780090\pi$
$432$		0			0
$433$	28.0000			1.34559			0.672797	−	0.739827i	$-0.265093\pi$
$433$	28.0000			1.34559			0.672797	+	0.739827i	$0.265093\pi$
$434$		0			0
$435$		0			0
$436$	−2.00000	−	3.46410i	−0.0957826	−	0.165900i
$437$	10.5000	+	18.1865i	0.502283	+	0.869980i
$438$		0			0
$439$	−18.0000	+	31.1769i	−0.859093	+	1.48799i	0.0137020	+	0.999906i	$0.495638\pi$
$439$	−18.0000	+	31.1769i	−0.859093	+	1.48799i	−0.872795	+	0.488087i	$0.837695\pi$
$440$	−2.00000			−0.0953463
$441$		0			0
$442$		0			0
$443$	12.0000	−	20.7846i	0.570137	−	0.987507i	−0.426414	−	0.904528i	$-0.640223\pi$
$443$	12.0000	−	20.7846i	0.570137	−	0.987507i	0.996551	−	0.0829786i	$-0.0264433\pi$
$444$		0			0
$445$	−7.00000	−	12.1244i	−0.331832	−	0.574750i
$446$	1.00000	+	1.73205i	0.0473514	+	0.0820150i
$447$		0			0
$448$		0			0
$449$	−9.00000			−0.424736			−0.212368	−	0.977190i	$-0.568118\pi$
$449$	−9.00000			−0.424736			−0.212368	+	0.977190i	$0.568118\pi$
$450$		0			0
$451$	−24.0000			−1.13012
$452$	−0.500000	+	0.866025i	−0.0235180	+	0.0407344i
$453$		0			0
$454$	8.50000	+	14.7224i	0.398925	+	0.690958i
$455$		0			0
$456$		0			0
$457$	−8.50000	+	14.7224i	−0.397613	+	0.688686i	−0.993431	−	0.114433i	$-0.963495\pi$
$457$	−8.50000	+	14.7224i	−0.397613	+	0.688686i	0.595818	+	0.803120i	$0.296828\pi$
$458$	−13.0000			−0.607450
$459$		0			0
$460$	−3.00000			−0.139876
$461$	4.50000	−	7.79423i	0.209586	−	0.363013i	−0.741998	−	0.670402i	$-0.766122\pi$
$461$	4.50000	−	7.79423i	0.209586	−	0.363013i	0.951584	+	0.307388i	$0.0994551\pi$
$462$		0			0
$463$	0.500000	+	0.866025i	0.0232370	+	0.0402476i	0.877410	−	0.479741i	$-0.159269\pi$
$463$	0.500000	+	0.866025i	0.0232370	+	0.0402476i	−0.854173	+	0.519989i	$0.825936\pi$
$464$	−4.00000	−	6.92820i	−0.185695	−	0.321634i
$465$		0			0
$466$	−0.500000	+	0.866025i	−0.0231621	+	0.0401179i
$467$	−28.0000			−1.29569			−0.647843	−	0.761774i	$-0.724329\pi$
$467$	−28.0000			−1.29569			−0.647843	+	0.761774i	$0.724329\pi$
$468$		0			0
$469$		0			0
$470$	−4.00000	+	6.92820i	−0.184506	+	0.319574i
$471$		0			0
$472$	2.00000	+	3.46410i	0.0920575	+	0.159448i
$473$	8.00000	+	13.8564i	0.367840	+	0.637118i
$474$		0			0
$475$	14.0000	−	24.2487i	0.642364	−	1.11261i
$476$		0			0
$477$		0			0
$478$	−15.0000			−0.686084
$479$	−12.0000	+	20.7846i	−0.548294	+	0.949673i	0.450098	+	0.892979i	$0.351389\pi$
$479$	−12.0000	+	20.7846i	−0.548294	+	0.949673i	−0.998392	+	0.0566937i	$0.981944\pi$
$480$		0			0
$481$	−6.00000	−	10.3923i	−0.273576	−	0.473848i
$482$	−5.00000	−	8.66025i	−0.227744	−	0.394464i
$483$		0			0
$484$	3.50000	−	6.06218i	0.159091	−	0.275554i
$485$	2.00000			0.0908153
$486$		0			0
$487$	25.0000			1.13286			0.566429	−	0.824110i	$-0.308325\pi$
$487$	25.0000			1.13286			0.566429	+	0.824110i	$0.308325\pi$
$488$	−6.50000	+	11.2583i	−0.294241	+	0.509641i
$489$		0			0
$490$		0			0
$491$	3.00000	+	5.19615i	0.135388	+	0.234499i	0.925746	−	0.378147i	$-0.123439\pi$
$491$	3.00000	+	5.19615i	0.135388	+	0.234499i	−0.790358	+	0.612646i	$0.790105\pi$
$492$		0			0
$493$		0			0
$494$	14.0000			0.629890
$495$		0			0
$496$	−4.00000			−0.179605
$497$		0			0
$498$		0			0
$499$	−12.0000	−	20.7846i	−0.537194	−	0.930447i	−0.999054	−	0.0434940i	$-0.986151\pi$
$499$	−12.0000	−	20.7846i	−0.537194	−	0.930447i	0.461860	−	0.886953i	$-0.347182\pi$
$500$	4.50000	+	7.79423i	0.201246	+	0.348569i
$501$		0			0
$502$	3.50000	−	6.06218i	0.156213	−	0.270568i
$503$	14.0000			0.624229			0.312115	−	0.950044i	$-0.398963\pi$
$503$	14.0000			0.624229			0.312115	+	0.950044i	$0.398963\pi$
$504$		0			0
$505$	−11.0000			−0.489494
$506$	−3.00000	+	5.19615i	−0.133366	+	0.230997i
$507$		0			0
$508$	9.50000	+	16.4545i	0.421494	+	0.730050i
$509$	17.0000	+	29.4449i	0.753512	+	1.30512i	0.946111	+	0.323843i	$0.104975\pi$
$509$	17.0000	+	29.4449i	0.753512	+	1.30512i	−0.192599	+	0.981278i	$0.561692\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−8.00000			−0.352865
$515$	4.00000	−	6.92820i	0.176261	−	0.305293i
$516$		0			0
$517$	8.00000	+	13.8564i	0.351840	+	0.609404i
$518$		0			0
$519$		0			0
$520$	−1.00000	+	1.73205i	−0.0438529	+	0.0759555i
$521$	14.0000			0.613351			0.306676	−	0.951814i	$-0.400783\pi$
$521$	14.0000			0.613351			0.306676	+	0.951814i	$0.400783\pi$
$522$		0			0
$523$	−35.0000			−1.53044			−0.765222	−	0.643767i	$-0.777371\pi$
$523$	−35.0000			−1.53044			−0.765222	+	0.643767i	$0.777371\pi$
$524$	−7.50000	+	12.9904i	−0.327639	+	0.567487i
$525$		0			0
$526$	−9.50000	−	16.4545i	−0.414220	−	0.717450i
$527$		0			0
$528$		0			0
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$	4.00000			0.173749
$531$		0			0
$532$		0			0
$533$	−12.0000	+	20.7846i	−0.519778	+	0.900281i
$534$		0			0
$535$	4.00000	+	6.92820i	0.172935	+	0.299532i
$536$	−1.00000	−	1.73205i	−0.0431934	−	0.0748132i
$537$		0			0
$538$	3.50000	−	6.06218i	0.150896	−	0.261359i
$539$		0			0
$540$		0			0
$541$	−20.0000			−0.859867			−0.429934	−	0.902861i	$-0.641463\pi$
$541$	−20.0000			−0.859867			−0.429934	+	0.902861i	$0.641463\pi$
$542$	−7.00000	+	12.1244i	−0.300676	+	0.520786i
$543$		0			0
$544$		0			0
$545$	−2.00000	−	3.46410i	−0.0856706	−	0.148386i
$546$		0			0
$547$	4.00000	−	6.92820i	0.171028	−	0.296229i	−0.767752	−	0.640747i	$-0.778625\pi$
$547$	4.00000	−	6.92820i	0.171028	−	0.296229i	0.938779	+	0.344519i	$0.111958\pi$
$548$	2.00000			0.0854358
$549$		0			0
$550$	8.00000			0.341121
$551$	−28.0000	+	48.4974i	−1.19284	+	2.06606i
$552$		0			0
$553$		0			0
$554$	−1.00000	−	1.73205i	−0.0424859	−	0.0735878i
$555$		0			0
$556$	4.50000	−	7.79423i	0.190843	−	0.330549i
$557$	−18.0000			−0.762684			−0.381342	−	0.924434i	$-0.624538\pi$
$557$	−18.0000			−0.762684			−0.381342	+	0.924434i	$0.624538\pi$
$558$		0			0
$559$	16.0000			0.676728
$560$		0			0
$561$		0			0
$562$	7.50000	+	12.9904i	0.316368	+	0.547966i
$563$	−5.50000	−	9.52628i	−0.231797	−	0.401485i	0.726540	−	0.687124i	$-0.241127\pi$
$563$	−5.50000	−	9.52628i	−0.231797	−	0.401485i	−0.958337	+	0.285640i	$0.907794\pi$
$564$		0			0
$565$	−0.500000	+	0.866025i	−0.0210352	+	0.0364340i
$566$	25.0000			1.05083
$567$		0			0
$568$	−5.00000			−0.209795
$569$	−9.00000	+	15.5885i	−0.377300	+	0.653502i	−0.990668	−	0.136295i	$-0.956481\pi$
$569$	−9.00000	+	15.5885i	−0.377300	+	0.653502i	0.613369	+	0.789797i	$0.289814\pi$
$570$		0			0
$571$	−6.00000	−	10.3923i	−0.251092	−	0.434904i	0.712735	−	0.701434i	$-0.247456\pi$
$571$	−6.00000	−	10.3923i	−0.251092	−	0.434904i	−0.963827	+	0.266529i	$0.914123\pi$
$572$	2.00000	+	3.46410i	0.0836242	+	0.144841i
$573$		0			0
$574$		0			0
$575$	12.0000			0.500435
$576$		0			0
$577$	−28.0000			−1.16566			−0.582828	−	0.812596i	$-0.698054\pi$
$577$	−28.0000			−1.16566			−0.582828	+	0.812596i	$0.698054\pi$
$578$	−8.50000	+	14.7224i	−0.353553	+	0.612372i
$579$		0			0
$580$	−4.00000	−	6.92820i	−0.166091	−	0.287678i
$581$		0			0
$582$		0			0
$583$	4.00000	−	6.92820i	0.165663	−	0.286937i
$584$	−14.0000			−0.579324
$585$		0			0
$586$	−9.00000			−0.371787
$587$	11.5000	−	19.9186i	0.474656	−	0.822128i	−0.524923	−	0.851150i	$-0.675906\pi$
$587$	11.5000	−	19.9186i	0.474656	−	0.822128i	0.999579	+	0.0290218i	$0.00923921\pi$
$588$		0			0
$589$	14.0000	+	24.2487i	0.576860	+	0.999151i
$590$	2.00000	+	3.46410i	0.0823387	+	0.142615i
$591$		0			0
$592$	3.00000	−	5.19615i	0.123299	−	0.213561i
$593$	42.0000			1.72473			0.862367	−	0.506284i	$-0.168981\pi$
$593$	42.0000			1.72473			0.862367	+	0.506284i	$0.168981\pi$
$594$		0			0
$595$		0			0
$596$	5.00000	−	8.66025i	0.204808	−	0.354738i
$597$		0			0
$598$	3.00000	+	5.19615i	0.122679	+	0.212486i
$599$	6.00000	+	10.3923i	0.245153	+	0.424618i	0.962175	−	0.272433i	$-0.0878284\pi$
$599$	6.00000	+	10.3923i	0.245153	+	0.424618i	−0.717021	+	0.697051i	$0.754495\pi$
$600$		0			0
$601$	13.0000	−	22.5167i	0.530281	−	0.918474i	−0.469095	−	0.883148i	$-0.655420\pi$
$601$	13.0000	−	22.5167i	0.530281	−	0.918474i	0.999376	−	0.0353259i	$-0.0112469\pi$
$602$		0			0
$603$		0			0
$604$	19.0000			0.773099
$605$	3.50000	−	6.06218i	0.142295	−	0.246463i
$606$		0			0
$607$	−3.00000	−	5.19615i	−0.121766	−	0.210905i	0.798698	−	0.601732i	$-0.205522\pi$
$607$	−3.00000	−	5.19615i	−0.121766	−	0.210905i	−0.920464	+	0.390827i	$0.872189\pi$
$608$	3.50000	+	6.06218i	0.141944	+	0.245854i
$609$		0			0
$610$	−6.50000	+	11.2583i	−0.263177	+	0.455836i
$611$	16.0000			0.647291
$612$		0			0
$613$	−10.0000			−0.403896			−0.201948	−	0.979396i	$-0.564727\pi$
$613$	−10.0000			−0.403896			−0.201948	+	0.979396i	$0.564727\pi$
$614$	−3.50000	+	6.06218i	−0.141249	+	0.244650i
$615$		0			0
$616$		0			0
$617$	−11.0000	−	19.0526i	−0.442843	−	0.767027i	0.555056	−	0.831813i	$-0.312697\pi$
$617$	−11.0000	−	19.0526i	−0.442843	−	0.767027i	−0.997899	+	0.0647859i	$0.979364\pi$
$618$		0			0
$619$	−5.50000	+	9.52628i	−0.221064	+	0.382893i	−0.955131	−	0.296183i	$-0.904286\pi$
$619$	−5.50000	+	9.52628i	−0.221064	+	0.382893i	0.734068	+	0.679076i	$0.237620\pi$
$620$	−4.00000			−0.160644
$621$		0			0
$622$	10.0000			0.400963
$623$		0			0
$624$		0			0
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$	−3.00000	−	5.19615i	−0.119904	−	0.207680i
$627$		0			0
$628$	5.50000	−	9.52628i	0.219474	−	0.380140i
$629$		0			0
$630$		0			0
$631$	9.00000			0.358284			0.179142	−	0.983823i	$-0.442668\pi$
$631$	9.00000			0.358284			0.179142	+	0.983823i	$0.442668\pi$
$632$	−5.50000	+	9.52628i	−0.218778	+	0.378935i
$633$		0			0
$634$	−12.0000	−	20.7846i	−0.476581	−	0.825462i
$635$	9.50000	+	16.4545i	0.376996	+	0.652976i
$636$		0			0
$637$		0			0
$638$	−16.0000			−0.633446
$639$		0			0
$640$	−1.00000			−0.0395285
$641$	23.5000	−	40.7032i	0.928194	−	1.60768i	0.141852	−	0.989888i	$-0.454694\pi$
$641$	23.5000	−	40.7032i	0.928194	−	1.60768i	0.786342	−	0.617792i	$-0.211973\pi$
$642$		0			0
$643$	−6.00000	−	10.3923i	−0.236617	−	0.409832i	0.723124	−	0.690718i	$-0.242705\pi$
$643$	−6.00000	−	10.3923i	−0.236617	−	0.409832i	−0.959741	+	0.280885i	$0.909372\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−42.0000			−1.65119			−0.825595	−	0.564263i	$-0.809160\pi$
$647$	−42.0000			−1.65119			−0.825595	+	0.564263i	$0.809160\pi$
$648$		0			0
$649$	8.00000			0.314027
$650$	4.00000	−	6.92820i	0.156893	−	0.271746i
$651$		0			0
$652$	3.00000	+	5.19615i	0.117489	+	0.203497i
$653$	−16.0000	−	27.7128i	−0.626128	−	1.08449i	−0.988322	−	0.152383i	$-0.951305\pi$
$653$	−16.0000	−	27.7128i	−0.626128	−	1.08449i	0.362193	−	0.932103i	$-0.382028\pi$
$654$		0			0
$655$	−7.50000	+	12.9904i	−0.293049	+	0.507576i
$656$	−12.0000			−0.468521
$657$		0			0
$658$		0			0
$659$	10.0000	−	17.3205i	0.389545	−	0.674711i	−0.602844	−	0.797859i	$-0.705966\pi$
$659$	10.0000	−	17.3205i	0.389545	−	0.674711i	0.992388	+	0.123148i	$0.0392990\pi$
$660$		0			0
$661$	−15.5000	−	26.8468i	−0.602880	−	1.04422i	−0.992383	−	0.123194i	$-0.960686\pi$
$661$	−15.5000	−	26.8468i	−0.602880	−	1.04422i	0.389503	−	0.921025i	$-0.372647\pi$
$662$	−2.00000	−	3.46410i	−0.0777322	−	0.134636i
$663$		0			0
$664$	6.00000	−	10.3923i	0.232845	−	0.403300i
$665$		0			0
$666$		0			0
$667$	−24.0000			−0.929284
$668$	−1.00000	+	1.73205i	−0.0386912	+	0.0670151i
$669$		0			0
$670$	−1.00000	−	1.73205i	−0.0386334	−	0.0669150i
$671$	13.0000	+	22.5167i	0.501859	+	0.869246i
$672$		0			0
$673$	0.500000	−	0.866025i	0.0192736	−	0.0333828i	−0.856228	−	0.516599i	$-0.827198\pi$
$673$	0.500000	−	0.866025i	0.0192736	−	0.0333828i	0.875501	+	0.483216i	$0.160531\pi$
$674$	22.0000			0.847408
$675$		0			0
$676$	−9.00000			−0.346154
$677$	−3.00000	+	5.19615i	−0.115299	+	0.199704i	−0.917899	−	0.396813i	$-0.870116\pi$
$677$	−3.00000	+	5.19615i	−0.115299	+	0.199704i	0.802600	+	0.596518i	$0.203449\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$	−4.00000	+	6.92820i	−0.153168	+	0.265295i
$683$	10.0000			0.382639			0.191320	−	0.981528i	$-0.438723\pi$
$683$	10.0000			0.382639			0.191320	+	0.981528i	$0.438723\pi$
$684$		0			0
$685$	2.00000			0.0764161
$686$		0			0
$687$		0			0
$688$	4.00000	+	6.92820i	0.152499	+	0.264135i
$689$	−4.00000	−	6.92820i	−0.152388	−	0.263944i
$690$		0			0
$691$	−14.5000	+	25.1147i	−0.551606	+	0.955410i	0.446553	+	0.894757i	$0.352651\pi$
$691$	−14.5000	+	25.1147i	−0.551606	+	0.955410i	−0.998159	+	0.0606524i	$0.980682\pi$
$692$	−22.0000			−0.836315
$693$		0			0
$694$	12.0000			0.455514
$695$	4.50000	−	7.79423i	0.170695	−	0.295652i
$696$		0			0
$697$		0			0
$698$	15.0000	+	25.9808i	0.567758	+	0.983386i
$699$		0			0
$700$		0			0
$701$	−2.00000			−0.0755390			−0.0377695	−	0.999286i	$-0.512025\pi$
$701$	−2.00000			−0.0755390			−0.0377695	+	0.999286i	$0.512025\pi$
$702$		0			0
$703$	−42.0000			−1.58406
$704$	−1.00000	+	1.73205i	−0.0376889	+	0.0652791i
$705$		0			0
$706$	12.0000	+	20.7846i	0.451626	+	0.782239i
$707$		0			0
$708$		0			0
$709$	16.0000	−	27.7128i	0.600893	−	1.04078i	−0.391794	−	0.920053i	$-0.628145\pi$
$709$	16.0000	−	27.7128i	0.600893	−	1.04078i	0.992686	−	0.120723i	$-0.0385214\pi$
$710$	−5.00000			−0.187647
$711$		0			0
$712$	−14.0000			−0.524672
$713$	−6.00000	+	10.3923i	−0.224702	+	0.389195i
$714$		0			0
$715$	2.00000	+	3.46410i	0.0747958	+	0.129550i
$716$	−12.0000	−	20.7846i	−0.448461	−	0.776757i
$717$		0			0
$718$	−14.5000	+	25.1147i	−0.541135	+	0.937274i
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$		0			0
$721$		0			0
$722$	15.0000	−	25.9808i	0.558242	−	0.966904i
$723$		0			0
$724$	3.50000	+	6.06218i	0.130076	+	0.225299i
$725$	16.0000	+	27.7128i	0.594225	+	1.02923i
$726$		0			0
$727$	13.0000	−	22.5167i	0.482143	−	0.835097i	−0.517647	−	0.855595i	$-0.673192\pi$
$727$	13.0000	−	22.5167i	0.482143	−	0.835097i	0.999790	+	0.0204978i	$0.00652512\pi$
$728$		0			0
$729$		0			0
$730$	−14.0000			−0.518163
$731$		0			0
$732$		0			0
$733$	0.500000	+	0.866025i	0.0184679	+	0.0319874i	0.875112	−	0.483921i	$-0.160788\pi$
$733$	0.500000	+	0.866025i	0.0184679	+	0.0319874i	−0.856644	+	0.515908i	$0.827454\pi$
$734$	16.0000	+	27.7128i	0.590571	+	1.02290i
$735$		0			0
$736$	−1.50000	+	2.59808i	−0.0552907	+	0.0957664i
$737$	−4.00000			−0.147342
$738$		0			0
$739$	−38.0000			−1.39785			−0.698926	−	0.715194i	$-0.746338\pi$
$739$	−38.0000			−1.39785			−0.698926	+	0.715194i	$0.746338\pi$
$740$	3.00000	−	5.19615i	0.110282	−	0.191014i
$741$		0			0
$742$		0			0
$743$	24.0000	+	41.5692i	0.880475	+	1.52503i	0.850814	+	0.525467i	$0.176109\pi$
$743$	24.0000	+	41.5692i	0.880475	+	1.52503i	0.0296605	+	0.999560i	$0.490557\pi$
$744$		0			0
$745$	5.00000	−	8.66025i	0.183186	−	0.317287i
$746$	32.0000			1.17160
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	19.5000	+	33.7750i	0.711565	+	1.23247i	0.964269	+	0.264923i	$0.0853467\pi$
$751$	19.5000	+	33.7750i	0.711565	+	1.23247i	−0.252704	+	0.967544i	$0.581320\pi$
$752$	4.00000	+	6.92820i	0.145865	+	0.252646i
$753$		0			0
$754$	−8.00000	+	13.8564i	−0.291343	+	0.504621i
$755$	19.0000			0.691481
$756$		0			0
$757$	−26.0000			−0.944986			−0.472493	−	0.881334i	$-0.656646\pi$
$757$	−26.0000			−0.944986			−0.472493	+	0.881334i	$0.656646\pi$
$758$	−6.00000	+	10.3923i	−0.217930	+	0.377466i
$759$		0			0
$760$	3.50000	+	6.06218i	0.126958	+	0.219898i
$761$	10.0000	+	17.3205i	0.362500	+	0.627868i	0.988372	−	0.152058i	$-0.0485900\pi$
$761$	10.0000	+	17.3205i	0.362500	+	0.627868i	−0.625872	+	0.779926i	$0.715257\pi$
$762$		0			0
$763$		0			0
$764$	−3.00000			−0.108536
$765$		0			0
$766$	6.00000			0.216789
$767$	4.00000	−	6.92820i	0.144432	−	0.250163i
$768$		0			0
$769$	1.00000	+	1.73205i	0.0360609	+	0.0624593i	0.883493	−	0.468445i	$-0.155186\pi$
$769$	1.00000	+	1.73205i	0.0360609	+	0.0624593i	−0.847432	+	0.530904i	$0.821852\pi$
$770$		0			0
$771$		0			0
$772$	−2.50000	+	4.33013i	−0.0899770	+	0.155845i
$773$	21.0000			0.755318			0.377659	−	0.925945i	$-0.376729\pi$
$773$	21.0000			0.755318			0.377659	+	0.925945i	$0.376729\pi$
$774$		0			0
$775$	16.0000			0.574737
$776$	1.00000	−	1.73205i	0.0358979	−	0.0621770i
$777$		0			0
$778$	15.0000	+	25.9808i	0.537776	+	0.931455i
$779$	42.0000	+	72.7461i	1.50481	+	2.60640i
$780$		0			0
$781$	−5.00000	+	8.66025i	−0.178914	+	0.309888i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	5.50000	−	9.52628i	0.196303	−	0.340007i
$786$		0			0
$787$	2.00000	+	3.46410i	0.0712923	+	0.123482i	0.899468	−	0.436987i	$-0.143954\pi$
$787$	2.00000	+	3.46410i	0.0712923	+	0.123482i	−0.828176	+	0.560469i	$0.810621\pi$
$788$	−6.00000	−	10.3923i	−0.213741	−	0.370211i
$789$		0			0
$790$	−5.50000	+	9.52628i	−0.195681	+	0.338930i
$791$		0			0
$792$		0			0
$793$	26.0000			0.923287
$794$	−7.00000	+	12.1244i	−0.248421	+	0.430277i
$795$		0			0
$796$	−7.00000	−	12.1244i	−0.248108	−	0.429736i
$797$	−25.5000	−	44.1673i	−0.903256	−	1.56449i	−0.823241	−	0.567692i	$-0.807836\pi$
$797$	−25.5000	−	44.1673i	−0.903256	−	1.56449i	−0.0800155	−	0.996794i	$-0.525497\pi$
$798$		0			0
$799$		0			0
$800$	4.00000			0.141421
$801$		0			0
$802$	3.00000			0.105934
$803$	−14.0000	+	24.2487i	−0.494049	+	0.855718i
$804$		0			0
$805$		0			0
$806$	4.00000	+	6.92820i	0.140894	+	0.244036i
$807$		0			0
$808$	−5.50000	+	9.52628i	−0.193489	+	0.335133i
$809$	−18.0000			−0.632846			−0.316423	−	0.948618i	$-0.602482\pi$
$809$	−18.0000			−0.632846			−0.316423	+	0.948618i	$0.602482\pi$
$810$		0			0
$811$	28.0000			0.983213			0.491606	−	0.870817i	$-0.336410\pi$
$811$	28.0000			0.983213			0.491606	+	0.870817i	$0.336410\pi$
$812$		0			0
$813$		0			0
$814$	−6.00000	−	10.3923i	−0.210300	−	0.364250i
$815$	3.00000	+	5.19615i	0.105085	+	0.182013i
$816$		0			0
$817$	28.0000	−	48.4974i	0.979596	−	1.69671i
$818$	−24.0000			−0.839140
$819$		0			0
$820$	−12.0000			−0.419058
$821$	−16.0000	+	27.7128i	−0.558404	+	0.967184i	0.439226	+	0.898377i	$0.355253\pi$
$821$	−16.0000	+	27.7128i	−0.558404	+	0.967184i	−0.997630	+	0.0688073i	$0.978081\pi$
$822$		0			0
$823$	22.0000	+	38.1051i	0.766872	+	1.32826i	0.939251	+	0.343230i	$0.111521\pi$
$823$	22.0000	+	38.1051i	0.766872	+	1.32826i	−0.172379	+	0.985031i	$0.555146\pi$
$824$	−4.00000	−	6.92820i	−0.139347	−	0.241355i
$825$		0			0
$826$		0			0
$827$	−30.0000			−1.04320			−0.521601	−	0.853189i	$-0.674665\pi$
$827$	−30.0000			−1.04320			−0.521601	+	0.853189i	$0.674665\pi$
$828$		0			0
$829$	14.0000			0.486240			0.243120	−	0.969996i	$-0.421829\pi$
$829$	14.0000			0.486240			0.243120	+	0.969996i	$0.421829\pi$
$830$	6.00000	−	10.3923i	0.208263	−	0.360722i
$831$		0			0
$832$	1.00000	+	1.73205i	0.0346688	+	0.0600481i
$833$		0			0
$834$		0			0
$835$	−1.00000	+	1.73205i	−0.0346064	+	0.0599401i
$836$	14.0000			0.484200
$837$		0			0
$838$	5.00000			0.172722
$839$	15.0000	−	25.9808i	0.517858	−	0.896956i	−0.481927	−	0.876211i	$-0.660063\pi$
$839$	15.0000	−	25.9808i	0.517858	−	0.896956i	0.999785	−	0.0207443i	$-0.00660359\pi$
$840$		0			0
$841$	−17.5000	−	30.3109i	−0.603448	−	1.04520i
$842$	−18.0000	−	31.1769i	−0.620321	−	1.07443i
$843$		0			0
$844$	11.0000	−	19.0526i	0.378636	−	0.655816i
$845$	−9.00000			−0.309609
$846$		0			0
$847$		0			0
$848$	2.00000	−	3.46410i	0.0686803	−	0.118958i
$849$		0			0
$850$		0			0
$851$	−9.00000	−	15.5885i	−0.308516	−	0.534365i
$852$		0			0
$853$	−18.5000	+	32.0429i	−0.633428	+	1.09713i	0.353418	+	0.935466i	$0.385019\pi$
$853$	−18.5000	+	32.0429i	−0.633428	+	1.09713i	−0.986846	+	0.161664i	$0.948314\pi$
$854$		0			0
$855$		0			0
$856$	8.00000			0.273434
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	−0.670366	−	0.742030i	$-0.733863\pi$
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	0.977800	+	0.209539i	$0.0671963\pi$
$858$		0			0
$859$	18.0000	+	31.1769i	0.614152	+	1.06374i	0.990533	+	0.137277i	$0.0438352\pi$
$859$	18.0000	+	31.1769i	0.614152	+	1.06374i	−0.376381	+	0.926465i	$0.622831\pi$
$860$	4.00000	+	6.92820i	0.136399	+	0.236250i
$861$		0			0
$862$	−16.0000	+	27.7128i	−0.544962	+	0.943902i
$863$	−57.0000			−1.94030			−0.970151	−	0.242500i	$-0.922032\pi$
$863$	−57.0000			−1.94030			−0.970151	+	0.242500i	$0.922032\pi$
$864$		0			0
$865$	−22.0000			−0.748022
$866$	14.0000	−	24.2487i	0.475739	−	0.824005i
$867$		0			0
$868$		0			0
$869$	11.0000	+	19.0526i	0.373149	+	0.646314i
$870$		0			0
$871$	−2.00000	+	3.46410i	−0.0677674	+	0.117377i
$872$	−4.00000			−0.135457
$873$		0			0
$874$	21.0000			0.710336
$875$		0			0
$876$		0			0
$877$	−12.0000	−	20.7846i	−0.405211	−	0.701846i	0.589135	−	0.808035i	$-0.299469\pi$
$877$	−12.0000	−	20.7846i	−0.405211	−	0.701846i	−0.994346	+	0.106188i	$0.966135\pi$
$878$	18.0000	+	31.1769i	0.607471	+	1.05217i
$879$		0			0
$880$	−1.00000	+	1.73205i	−0.0337100	+	0.0583874i
$881$	28.0000			0.943344			0.471672	−	0.881774i	$-0.343651\pi$
$881$	28.0000			0.943344			0.471672	+	0.881774i	$0.343651\pi$
$882$		0			0
$883$	−26.0000			−0.874970			−0.437485	−	0.899226i	$-0.644131\pi$
$883$	−26.0000			−0.874970			−0.437485	+	0.899226i	$0.644131\pi$
$884$		0			0
$885$		0			0
$886$	−12.0000	−	20.7846i	−0.403148	−	0.698273i
$887$	−18.0000	−	31.1769i	−0.604381	−	1.04682i	−0.992149	−	0.125061i	$-0.960087\pi$
$887$	−18.0000	−	31.1769i	−0.604381	−	1.04682i	0.387768	−	0.921757i	$-0.373246\pi$
$888$		0			0
$889$		0			0
$890$	−14.0000			−0.469281
$891$		0			0
$892$	2.00000			0.0669650
$893$	28.0000	−	48.4974i	0.936984	−	1.62290i
$894$		0			0
$895$	−12.0000	−	20.7846i	−0.401116	−	0.694753i
$896$		0			0
$897$		0			0
$898$	−4.50000	+	7.79423i	−0.150167	+	0.260097i
$899$	−32.0000			−1.06726
$900$		0			0
$901$		0			0
$902$	−12.0000	+	20.7846i	−0.399556	+	0.692052i
$903$		0			0
$904$	0.500000	+	0.866025i	0.0166298	+	0.0288036i
$905$	3.50000	+	6.06218i	0.116344	+	0.201514i
$906$		0			0
$907$	1.00000	−	1.73205i	0.0332045	−	0.0575118i	−0.848946	−	0.528480i	$-0.822762\pi$
$907$	1.00000	−	1.73205i	0.0332045	−	0.0575118i	0.882150	+	0.470968i	$0.156095\pi$
$908$	17.0000			0.564165
$909$		0			0
$910$		0			0
$911$	−0.500000	+	0.866025i	−0.0165657	+	0.0286927i	−0.874189	−	0.485585i	$-0.838607\pi$
$911$	−0.500000	+	0.866025i	−0.0165657	+	0.0286927i	0.857624	+	0.514278i	$0.171940\pi$
$912$		0			0
$913$	−12.0000	−	20.7846i	−0.397142	−	0.687870i
$914$	8.50000	+	14.7224i	0.281155	+	0.486975i
$915$		0			0
$916$	−6.50000	+	11.2583i	−0.214766	+	0.371986i
$917$		0			0
$918$		0			0
$919$	15.0000			0.494804			0.247402	−	0.968913i	$-0.420423\pi$
$919$	15.0000			0.494804			0.247402	+	0.968913i	$0.420423\pi$
$920$	−1.50000	+	2.59808i	−0.0494535	+	0.0856560i
$921$		0			0
$922$	−4.50000	−	7.79423i	−0.148200	−	0.256689i
$923$	5.00000	+	8.66025i	0.164577	+	0.285056i
$924$		0			0
$925$	−12.0000	+	20.7846i	−0.394558	+	0.683394i
$926$	1.00000			0.0328620
$927$		0			0
$928$	−8.00000			−0.262613
$929$	−3.00000	+	5.19615i	−0.0984268	+	0.170480i	−0.911034	−	0.412332i	$-0.864714\pi$
$929$	−3.00000	+	5.19615i	−0.0984268	+	0.170480i	0.812607	+	0.582812i	$0.198048\pi$
$930$		0			0
$931$		0			0
$932$	0.500000	+	0.866025i	0.0163780	+	0.0283676i
$933$		0			0
$934$	−14.0000	+	24.2487i	−0.458094	+	0.793442i
$935$		0			0
$936$		0			0
$937$		0			0			−	1.00000i	$-0.5\pi$
$937$		0			0				1.00000i	$0.5\pi$
$938$		0			0
$939$		0			0
$940$	4.00000	+	6.92820i	0.130466	+	0.225973i
$941$	1.50000	+	2.59808i	0.0488986	+	0.0846949i	0.889439	−	0.457054i	$-0.151096\pi$
$941$	1.50000	+	2.59808i	0.0488986	+	0.0846949i	−0.840540	+	0.541749i	$0.817762\pi$
$942$		0			0
$943$	−18.0000	+	31.1769i	−0.586161	+	1.01526i
$944$	4.00000			0.130189
$945$		0			0
$946$	16.0000			0.520205
$947$	5.00000	−	8.66025i	0.162478	−	0.281420i	−0.773279	−	0.634066i	$-0.781385\pi$
$947$	5.00000	−	8.66025i	0.162478	−	0.281420i	0.935757	+	0.352646i	$0.114718\pi$
$948$		0			0
$949$	14.0000	+	24.2487i	0.454459	+	0.787146i
$950$	−14.0000	−	24.2487i	−0.454220	−	0.786732i
$951$		0			0
$952$		0			0
$953$	54.0000			1.74923			0.874616	−	0.484817i	$-0.161114\pi$
$953$	54.0000			1.74923			0.874616	+	0.484817i	$0.161114\pi$
$954$		0			0
$955$	−3.00000			−0.0970777
$956$	−7.50000	+	12.9904i	−0.242567	+	0.420139i
$957$		0			0
$958$	12.0000	+	20.7846i	0.387702	+	0.671520i
$959$		0			0
$960$		0			0
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$	−12.0000			−0.386896
$963$		0			0
$964$	−10.0000			−0.322078
$965$	−2.50000	+	4.33013i	−0.0804778	+	0.139392i
$966$		0			0
$967$	−6.50000	−	11.2583i	−0.209026	−	0.362043i	0.742382	−	0.669977i	$-0.233696\pi$
$967$	−6.50000	−	11.2583i	−0.209026	−	0.362043i	−0.951408	+	0.307933i	$0.900363\pi$
$968$	−3.50000	−	6.06218i	−0.112494	−	0.194846i
$969$		0			0
$970$	1.00000	−	1.73205i	0.0321081	−	0.0556128i
$971$	−35.0000			−1.12320			−0.561602	−	0.827408i	$-0.689815\pi$
$971$	−35.0000			−1.12320			−0.561602	+	0.827408i	$0.689815\pi$
$972$		0			0
$973$		0			0
$974$	12.5000	−	21.6506i	0.400526	−	0.693731i
$975$		0			0
$976$	6.50000	+	11.2583i	0.208060	+	0.360370i
$977$	−1.00000	−	1.73205i	−0.0319928	−	0.0554132i	0.849586	−	0.527451i	$-0.176852\pi$
$977$	−1.00000	−	1.73205i	−0.0319928	−	0.0554132i	−0.881579	+	0.472037i	$0.843519\pi$
$978$		0			0
$979$	−14.0000	+	24.2487i	−0.447442	+	0.774992i
$980$		0			0
$981$		0			0
$982$	6.00000			0.191468
$983$	16.0000	−	27.7128i	0.510321	−	0.883901i	−0.489608	−	0.871943i	$-0.662860\pi$
$983$	16.0000	−	27.7128i	0.510321	−	0.883901i	0.999928	−	0.0119587i	$-0.00380665\pi$
$984$		0			0
$985$	−6.00000	−	10.3923i	−0.191176	−	0.331126i
$986$		0			0
$987$		0			0
$988$	7.00000	−	12.1244i	0.222700	−	0.385727i
$989$	24.0000			0.763156
$990$		0			0
$991$	32.0000			1.01651			0.508257	−	0.861206i	$-0.330290\pi$
$991$	32.0000			1.01651			0.508257	+	0.861206i	$0.330290\pi$
$992$	−2.00000	+	3.46410i	−0.0635001	+	0.109985i
$993$		0			0
$994$		0			0
$995$	−7.00000	−	12.1244i	−0.221915	−	0.384368i
$996$		0			0
$997$	8.50000	−	14.7224i	0.269198	−	0.466264i	−0.699457	−	0.714675i	$-0.746575\pi$
$997$	8.50000	−	14.7224i	0.269198	−	0.466264i	0.968655	+	0.248410i	$0.0799082\pi$
$998$	−24.0000			−0.759707
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.f.f.883.1		2
3.2	odd	2		882.2.f.c.295.1	yes	2
7.2	even	3		2646.2.e.a.2125.1		2
7.3	odd	6		2646.2.h.g.667.1		2
7.4	even	3		2646.2.h.j.667.1		2
7.5	odd	6		2646.2.e.d.2125.1		2
7.6	odd	2		2646.2.f.h.883.1		2
9.2	odd	6		7938.2.a.v.1.1		1
9.4	even	3	inner	2646.2.f.f.1765.1		2
9.5	odd	6		882.2.f.c.589.1	yes	2
9.7	even	3		7938.2.a.k.1.1		1
21.2	odd	6		882.2.e.j.655.1		2
21.5	even	6		882.2.e.f.655.1		2
21.11	odd	6		882.2.h.a.79.1		2
21.17	even	6		882.2.h.d.79.1		2
21.20	even	2		882.2.f.b.295.1	✓	2
63.4	even	3		2646.2.e.a.1549.1		2
63.5	even	6		882.2.h.d.67.1		2
63.13	odd	6		2646.2.f.h.1765.1		2
63.20	even	6		7938.2.a.ba.1.1		1
63.23	odd	6		882.2.h.a.67.1		2
63.31	odd	6		2646.2.e.d.1549.1		2
63.32	odd	6		882.2.e.j.373.1		2
63.34	odd	6		7938.2.a.f.1.1		1
63.40	odd	6		2646.2.h.g.361.1		2
63.41	even	6		882.2.f.b.589.1	yes	2
63.58	even	3		2646.2.h.j.361.1		2
63.59	even	6		882.2.e.f.373.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.e.f.373.1		2	63.59	even	6
882.2.e.f.655.1		2	21.5	even	6
882.2.e.j.373.1		2	63.32	odd	6
882.2.e.j.655.1		2	21.2	odd	6
882.2.f.b.295.1	✓	2	21.20	even	2
882.2.f.b.589.1	yes	2	63.41	even	6
882.2.f.c.295.1	yes	2	3.2	odd	2
882.2.f.c.589.1	yes	2	9.5	odd	6
882.2.h.a.67.1		2	63.23	odd	6
882.2.h.a.79.1		2	21.11	odd	6
882.2.h.d.67.1		2	63.5	even	6
882.2.h.d.79.1		2	21.17	even	6
2646.2.e.a.1549.1		2	63.4	even	3
2646.2.e.a.2125.1		2	7.2	even	3
2646.2.e.d.1549.1		2	63.31	odd	6
2646.2.e.d.2125.1		2	7.5	odd	6
2646.2.f.f.883.1		2	1.1	even	1	trivial
2646.2.f.f.1765.1		2	9.4	even	3	inner
2646.2.f.h.883.1		2	7.6	odd	2
2646.2.f.h.1765.1		2	63.13	odd	6
2646.2.h.g.361.1		2	63.40	odd	6
2646.2.h.g.667.1		2	7.3	odd	6
2646.2.h.j.361.1		2	63.58	even	3
2646.2.h.j.667.1		2	7.4	even	3
7938.2.a.f.1.1		1	63.34	odd	6
7938.2.a.k.1.1		1	9.7	even	3
7938.2.a.v.1.1		1	9.2	odd	6
7938.2.a.ba.1.1		1	63.20	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.00000 q^{8} -1.00000 q^{10} +(-1.00000 + 1.73205i) q^{11} +(1.00000 + 1.73205i) q^{13} +(-0.500000 + 0.866025i) q^{16} +7.00000 q^{19} +(-0.500000 + 0.866025i) q^{20} +(1.00000 + 1.73205i) q^{22} +(1.50000 + 2.59808i) q^{23} +(2.00000 - 3.46410i) q^{25} +2.00000 q^{26} +(-4.00000 + 6.92820i) q^{29} +(2.00000 + 3.46410i) q^{31} +(0.500000 + 0.866025i) q^{32} -6.00000 q^{37} +(3.50000 - 6.06218i) q^{38} +(0.500000 + 0.866025i) q^{40} +(6.00000 + 10.3923i) q^{41} +(4.00000 - 6.92820i) q^{43} +2.00000 q^{44} +3.00000 q^{46} +(4.00000 - 6.92820i) q^{47} +(-2.00000 - 3.46410i) q^{50} +(1.00000 - 1.73205i) q^{52} -4.00000 q^{53} +2.00000 q^{55} +(4.00000 + 6.92820i) q^{58} +(-2.00000 - 3.46410i) q^{59} +(6.50000 - 11.2583i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(1.00000 - 1.73205i) q^{65} +(1.00000 + 1.73205i) q^{67} +5.00000 q^{71} +14.0000 q^{73} +(-3.00000 + 5.19615i) q^{74} +(-3.50000 - 6.06218i) q^{76} +(5.50000 - 9.52628i) q^{79} +1.00000 q^{80} +12.0000 q^{82} +(-6.00000 + 10.3923i) q^{83} +(-4.00000 - 6.92820i) q^{86} +(1.00000 - 1.73205i) q^{88} +14.0000 q^{89} +(1.50000 - 2.59808i) q^{92} +(-4.00000 - 6.92820i) q^{94} +(-3.50000 - 6.06218i) q^{95} +(-1.00000 + 1.73205i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} - q^{5} - 2 q^{8} - 2 q^{10} - 2 q^{11} + 2 q^{13} - q^{16} + 14 q^{19} - q^{20} + 2 q^{22} + 3 q^{23} + 4 q^{25} + 4 q^{26} - 8 q^{29} + 4 q^{31} + q^{32} - 12 q^{37} + 7 q^{38}+ \cdots - 2 q^{97}+O(q^{100}) \) 2 * q + q^2 - q^4 - q^5 - 2 * q^8 - 2 * q^10 - 2 * q^11 + 2 * q^13 - q^16 + 14 * q^19 - q^20 + 2 * q^22 + 3 * q^23 + 4 * q^25 + 4 * q^26 - 8 * q^29 + 4 * q^31 + q^32 - 12 * q^37 + 7 * q^38 + q^40 + 12 * q^41 + 8 * q^43 + 4 * q^44 + 6 * q^46 + 8 * q^47 - 4 * q^50 + 2 * q^52 - 8 * q^53 + 4 * q^55 + 8 * q^58 - 4 * q^59 + 13 * q^61 + 8 * q^62 + 2 * q^64 + 2 * q^65 + 2 * q^67 + 10 * q^71 + 28 * q^73 - 6 * q^74 - 7 * q^76 + 11 * q^79 + 2 * q^80 + 24 * q^82 - 12 * q^83 - 8 * q^86 + 2 * q^88 + 28 * q^89 + 3 * q^92 - 8 * q^94 - 7 * q^95 - 2 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more