LMFDB - Embedded newform 351.2.q.f.244.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [351,2,Mod(82,351)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("351.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(351, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	351.q (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,0,0,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$2.80274911095$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			244.1
Root			$-1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	351.244
Dual form			351.2.q.f.82.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.22474 + 0.707107i) q^{2} -1.41421i q^{5} +(1.50000 + 0.866025i) q^{7} -2.82843i q^{8} +(1.00000 + 1.73205i) q^{10} +(-1.22474 + 0.707107i) q^{11} +(2.50000 - 2.59808i) q^{13} -2.44949 q^{14} +(2.00000 + 3.46410i) q^{16} +(2.44949 - 4.24264i) q^{17} +(1.50000 + 0.866025i) q^{19} +(1.00000 - 1.73205i) q^{22} +(1.22474 + 2.12132i) q^{23} +3.00000 q^{25} +(-1.22474 + 4.94975i) q^{26} +(4.89898 + 8.48528i) q^{29} -5.19615i q^{31} +6.92820i q^{34} +(1.22474 - 2.12132i) q^{35} +(1.50000 - 0.866025i) q^{37} -2.44949 q^{38} -4.00000 q^{40} +(6.12372 - 3.53553i) q^{41} +(-2.50000 + 4.33013i) q^{43} +(-3.00000 - 1.73205i) q^{46} +2.82843i q^{47} +(-2.00000 - 3.46410i) q^{49} +(-3.67423 + 2.12132i) q^{50} +(1.00000 + 1.73205i) q^{55} +(2.44949 - 4.24264i) q^{56} +(-12.0000 - 6.92820i) q^{58} +(4.89898 + 2.82843i) q^{59} +(2.00000 - 3.46410i) q^{61} +(3.67423 + 6.36396i) q^{62} -8.00000 q^{64} +(-3.67423 - 3.53553i) q^{65} +(6.00000 - 3.46410i) q^{67} +3.46410i q^{70} +(-13.4722 - 7.77817i) q^{71} +(-1.22474 + 2.12132i) q^{74} -2.44949 q^{77} -10.0000 q^{79} +(4.89898 - 2.82843i) q^{80} +(-5.00000 + 8.66025i) q^{82} -9.89949i q^{83} +(-6.00000 - 3.46410i) q^{85} -7.07107i q^{86} +(2.00000 + 3.46410i) q^{88} +(-8.57321 + 4.94975i) q^{89} +(6.00000 - 1.73205i) q^{91} +(-2.00000 - 3.46410i) q^{94} +(1.22474 - 2.12132i) q^{95} +(-12.0000 - 6.92820i) q^{97} +(4.89898 + 2.82843i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{7} + 4 q^{10} + 10 q^{13} + 8 q^{16} + 6 q^{19} + 4 q^{22} + 12 q^{25} + 6 q^{37} - 16 q^{40} - 10 q^{43} - 12 q^{46} - 8 q^{49} + 4 q^{55} - 48 q^{58} + 8 q^{61} - 32 q^{64} + 24 q^{67} - 40 q^{79}+ \cdots - 48 q^{97}+O(q^{100}) $ 4 * q + 6 * q^7 + 4 * q^10 + 10 * q^13 + 8 * q^16 + 6 * q^19 + 4 * q^22 + 12 * q^25 + 6 * q^37 - 16 * q^40 - 10 * q^43 - 12 * q^46 - 8 * q^49 + 4 * q^55 - 48 * q^58 + 8 * q^61 - 32 * q^64 + 24 * q^67 - 40 * q^79 - 20 * q^82 - 24 * q^85 + 8 * q^88 + 24 * q^91 - 8 * q^94 - 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/351\mathbb{Z}\right)^\times$.

$n$	$28$	$326$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−1.22474	+	0.707107i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$2$	−1.22474	+	0.707107i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$3$		0			0
$3$		0			0
$4$		0			0
$5$		−	1.41421i		−	0.632456i	−0.948683	−	0.316228i	$-0.897584\pi$
$5$		−	1.41421i		−	0.632456i	0.948683	−	0.316228i	$-0.102416\pi$
$6$		0			0
$7$	1.50000	+	0.866025i	0.566947	+	0.327327i	0.755929	−	0.654654i	$-0.227186\pi$
$7$	1.50000	+	0.866025i	0.566947	+	0.327327i	−0.188982	+	0.981981i	$0.560519\pi$
$8$		−	2.82843i		−	1.00000i
$9$		0			0
$10$	1.00000	+	1.73205i	0.316228	+	0.547723i
$11$	−1.22474	+	0.707107i	−0.369274	+	0.213201i	−0.673141	−	0.739514i	$-0.735055\pi$
$11$	−1.22474	+	0.707107i	−0.369274	+	0.213201i	0.303867	+	0.952714i	$0.401722\pi$
$12$		0			0
$13$	2.50000	−	2.59808i	0.693375	−	0.720577i
$13$	2.50000	−	2.59808i	0.693375	−	0.720577i
$14$	−2.44949			−0.654654
$15$		0			0
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	2.44949	−	4.24264i	0.594089	−	1.02899i	−0.399586	−	0.916696i	$-0.630846\pi$
$17$	2.44949	−	4.24264i	0.594089	−	1.02899i	0.993675	−	0.112296i	$-0.0358205\pi$
$18$		0			0
$19$	1.50000	+	0.866025i	0.344124	+	0.198680i	0.662094	−	0.749421i	$-0.269668\pi$
$19$	1.50000	+	0.866025i	0.344124	+	0.198680i	−0.317970	+	0.948101i	$0.603001\pi$
$20$		0			0
$21$		0			0
$22$	1.00000	−	1.73205i	0.213201	−	0.369274i
$23$	1.22474	+	2.12132i	0.255377	+	0.442326i	0.964998	−	0.262258i	$-0.0844671\pi$
$23$	1.22474	+	2.12132i	0.255377	+	0.442326i	−0.709621	+	0.704584i	$0.751134\pi$
$24$		0			0
$25$	3.00000			0.600000
$26$	−1.22474	+	4.94975i	−0.240192	+	0.970725i
$27$		0			0
$28$		0			0
$29$	4.89898	+	8.48528i	0.909718	+	1.57568i	0.814456	+	0.580225i	$0.197035\pi$
$29$	4.89898	+	8.48528i	0.909718	+	1.57568i	0.0952614	+	0.995452i	$0.469631\pi$
$30$		0			0
$31$		−	5.19615i		−	0.933257i	−0.884454	−	0.466628i	$-0.845469\pi$
$31$		−	5.19615i		−	0.933257i	0.884454	−	0.466628i	$-0.154531\pi$
$32$		0			0
$33$		0			0
$34$			6.92820i			1.18818i
$35$	1.22474	−	2.12132i	0.207020	−	0.358569i
$36$		0			0
$37$	1.50000	−	0.866025i	0.246598	−	0.142374i	−0.371607	−	0.928390i	$-0.621193\pi$
$37$	1.50000	−	0.866025i	0.246598	−	0.142374i	0.618206	+	0.786016i	$0.287860\pi$
$38$	−2.44949			−0.397360
$39$		0			0
$40$	−4.00000			−0.632456
$41$	6.12372	−	3.53553i	0.956365	−	0.552158i	0.0613127	−	0.998119i	$-0.480471\pi$
$41$	6.12372	−	3.53553i	0.956365	−	0.552158i	0.895052	+	0.445961i	$0.147138\pi$
$42$		0			0
$43$	−2.50000	+	4.33013i	−0.381246	+	0.660338i	−0.991241	−	0.132068i	$-0.957838\pi$
$43$	−2.50000	+	4.33013i	−0.381246	+	0.660338i	0.609994	+	0.792406i	$0.291172\pi$
$44$		0			0
$45$		0			0
$46$	−3.00000	−	1.73205i	−0.442326	−	0.255377i
$47$			2.82843i			0.412568i	0.978492	+	0.206284i	$0.0661372\pi$
$47$			2.82843i			0.412568i	−0.978492	+	0.206284i	$0.933863\pi$
$48$		0			0
$49$	−2.00000	−	3.46410i	−0.285714	−	0.494872i
$50$	−3.67423	+	2.12132i	−0.519615	+	0.300000i
$51$		0			0
$52$		0			0
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$		0			0
$55$	1.00000	+	1.73205i	0.134840	+	0.233550i
$56$	2.44949	−	4.24264i	0.327327	−	0.566947i
$57$		0			0
$58$	−12.0000	−	6.92820i	−1.57568	−	0.909718i
$59$	4.89898	+	2.82843i	0.637793	+	0.368230i	0.783764	−	0.621059i	$-0.213297\pi$
$59$	4.89898	+	2.82843i	0.637793	+	0.368230i	−0.145971	+	0.989289i	$0.546631\pi$
$60$		0			0
$61$	2.00000	−	3.46410i	0.256074	−	0.443533i	−0.709113	−	0.705095i	$-0.750904\pi$
$61$	2.00000	−	3.46410i	0.256074	−	0.443533i	0.965187	+	0.261562i	$0.0842377\pi$
$62$	3.67423	+	6.36396i	0.466628	+	0.808224i
$63$		0			0
$64$	−8.00000			−1.00000
$65$	−3.67423	−	3.53553i	−0.455733	−	0.438529i
$66$		0			0
$67$	6.00000	−	3.46410i	0.733017	−	0.423207i	−0.0865081	−	0.996251i	$-0.527571\pi$
$67$	6.00000	−	3.46410i	0.733017	−	0.423207i	0.819525	+	0.573044i	$0.194238\pi$
$68$		0			0
$69$		0			0
$70$			3.46410i			0.414039i
$71$	−13.4722	−	7.77817i	−1.59886	−	0.923099i	−0.991708	−	0.128510i	$-0.958981\pi$
$71$	−13.4722	−	7.77817i	−1.59886	−	0.923099i	−0.607147	−	0.794590i	$-0.707686\pi$
$72$		0			0
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$	−1.22474	+	2.12132i	−0.142374	+	0.246598i
$75$		0			0
$76$		0			0
$77$	−2.44949			−0.279145
$78$		0			0
$79$	−10.0000			−1.12509			−0.562544	−	0.826767i	$-0.690177\pi$
$79$	−10.0000			−1.12509			−0.562544	+	0.826767i	$0.690177\pi$
$80$	4.89898	−	2.82843i	0.547723	−	0.316228i
$81$		0			0
$82$	−5.00000	+	8.66025i	−0.552158	+	0.956365i
$83$		−	9.89949i		−	1.08661i	−0.839535	−	0.543305i	$-0.817173\pi$
$83$		−	9.89949i		−	1.08661i	0.839535	−	0.543305i	$-0.182827\pi$
$84$		0			0
$85$	−6.00000	−	3.46410i	−0.650791	−	0.375735i
$86$		−	7.07107i		−	0.762493i
$87$		0			0
$88$	2.00000	+	3.46410i	0.213201	+	0.369274i
$89$	−8.57321	+	4.94975i	−0.908759	+	0.524672i	−0.880032	−	0.474915i	$-0.842479\pi$
$89$	−8.57321	+	4.94975i	−0.908759	+	0.524672i	−0.0287273	+	0.999587i	$0.509145\pi$
$90$		0			0
$91$	6.00000	−	1.73205i	0.628971	−	0.181568i
$92$		0			0
$93$		0			0
$94$	−2.00000	−	3.46410i	−0.206284	−	0.357295i
$95$	1.22474	−	2.12132i	0.125656	−	0.217643i
$96$		0			0
$97$	−12.0000	−	6.92820i	−1.21842	−	0.703452i	−0.253837	−	0.967247i	$-0.581693\pi$
$97$	−12.0000	−	6.92820i	−1.21842	−	0.703452i	−0.964579	+	0.263795i	$0.915026\pi$
$98$	4.89898	+	2.82843i	0.494872	+	0.285714i
$99$		0			0
$100$		0			0
$101$	−6.12372	−	10.6066i	−0.609333	−	1.05540i	−0.991350	−	0.131241i	$-0.958104\pi$
$101$	−6.12372	−	10.6066i	−0.609333	−	1.05540i	0.382017	−	0.924155i	$-0.375230\pi$
$102$		0			0
$103$	5.00000			0.492665			0.246332	−	0.969185i	$-0.420775\pi$
$103$	5.00000			0.492665			0.246332	+	0.969185i	$0.420775\pi$
$104$	−7.34847	−	7.07107i	−0.720577	−	0.693375i
$105$		0			0
$106$		0			0
$107$	8.57321	+	14.8492i	0.828804	+	1.43553i	0.898977	+	0.437996i	$0.144311\pi$
$107$	8.57321	+	14.8492i	0.828804	+	1.43553i	−0.0701732	+	0.997535i	$0.522355\pi$
$108$		0			0
$109$		−	15.5885i		−	1.49310i	−0.665327	−	0.746552i	$-0.731708\pi$
$109$		−	15.5885i		−	1.49310i	0.665327	−	0.746552i	$-0.268292\pi$
$110$	−2.44949	−	1.41421i	−0.233550	−	0.134840i
$111$		0			0
$112$			6.92820i			0.654654i
$113$	−8.57321	+	14.8492i	−0.806500	+	1.39690i	0.108774	+	0.994067i	$0.465308\pi$
$113$	−8.57321	+	14.8492i	−0.806500	+	1.39690i	−0.915274	+	0.402833i	$0.868026\pi$
$114$		0			0
$115$	3.00000	−	1.73205i	0.279751	−	0.161515i
$116$		0			0
$117$		0			0
$118$	−8.00000			−0.736460
$119$	7.34847	−	4.24264i	0.673633	−	0.388922i
$120$		0			0
$121$	−4.50000	+	7.79423i	−0.409091	+	0.708566i
$122$			5.65685i			0.512148i
$123$		0			0
$124$		0			0
$125$		−	11.3137i		−	1.01193i
$126$		0			0
$127$	9.50000	+	16.4545i	0.842989	+	1.46010i	0.887357	+	0.461084i	$0.152539\pi$
$127$	9.50000	+	16.4545i	0.842989	+	1.46010i	−0.0443678	+	0.999015i	$0.514127\pi$
$128$	9.79796	−	5.65685i	0.866025	−	0.500000i
$129$		0			0
$130$	7.00000	+	1.73205i	0.613941	+	0.151911i
$131$	−14.6969			−1.28408			−0.642039	−	0.766672i	$-0.721911\pi$
$131$	−14.6969			−1.28408			−0.642039	+	0.766672i	$0.721911\pi$
$132$		0			0
$133$	1.50000	+	2.59808i	0.130066	+	0.225282i
$134$	−4.89898	+	8.48528i	−0.423207	+	0.733017i
$135$		0			0
$136$	−12.0000	−	6.92820i	−1.02899	−	0.594089i
$137$	12.2474	+	7.07107i	1.04637	+	0.604122i	0.921631	−	0.388067i	$-0.126857\pi$
$137$	12.2474	+	7.07107i	1.04637	+	0.604122i	0.124739	+	0.992190i	$0.460191\pi$
$138$		0			0
$139$	−1.00000	+	1.73205i	−0.0848189	+	0.146911i	−0.905314	−	0.424743i	$-0.860365\pi$
$139$	−1.00000	+	1.73205i	−0.0848189	+	0.146911i	0.820495	+	0.571654i	$0.193698\pi$
$140$		0			0
$141$		0			0
$142$	22.0000			1.84620
$143$	−1.22474	+	4.94975i	−0.102418	+	0.413919i
$144$		0			0
$145$	12.0000	−	6.92820i	0.996546	−	0.575356i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	15.9217	+	9.19239i	1.30436	+	0.753070i	0.981148	−	0.193258i	$-0.0619056\pi$
$149$	15.9217	+	9.19239i	1.30436	+	0.753070i	0.323207	+	0.946328i	$0.395239\pi$
$150$		0			0
$151$			5.19615i			0.422857i	0.977393	+	0.211428i	$0.0678115\pi$
$151$			5.19615i			0.422857i	−0.977393	+	0.211428i	$0.932188\pi$
$152$	2.44949	−	4.24264i	0.198680	−	0.344124i
$153$		0			0
$154$	3.00000	−	1.73205i	0.241747	−	0.139573i
$155$	−7.34847			−0.590243
$156$		0			0
$157$	5.00000			0.399043			0.199522	−	0.979893i	$-0.436061\pi$
$157$	5.00000			0.399043			0.199522	+	0.979893i	$0.436061\pi$
$158$	12.2474	−	7.07107i	0.974355	−	0.562544i
$159$		0			0
$160$		0			0
$161$			4.24264i			0.334367i
$162$		0			0
$163$	1.50000	+	0.866025i	0.117489	+	0.0678323i	0.557593	−	0.830115i	$-0.311725\pi$
$163$	1.50000	+	0.866025i	0.117489	+	0.0678323i	−0.440104	+	0.897947i	$0.645058\pi$
$164$		0			0
$165$		0			0
$166$	7.00000	+	12.1244i	0.543305	+	0.941033i
$167$	6.12372	−	3.53553i	0.473868	−	0.273588i	−0.243990	−	0.969778i	$-0.578456\pi$
$167$	6.12372	−	3.53553i	0.473868	−	0.273588i	0.717858	+	0.696190i	$0.245123\pi$
$168$		0			0
$169$	−0.500000	−	12.9904i	−0.0384615	−	0.999260i
$170$	9.79796			0.751469
$171$		0			0
$172$		0			0
$173$	2.44949	−	4.24264i	0.186231	−	0.322562i	−0.757759	−	0.652534i	$-0.773706\pi$
$173$	2.44949	−	4.24264i	0.186231	−	0.322562i	0.943991	+	0.329972i	$0.107039\pi$
$174$		0			0
$175$	4.50000	+	2.59808i	0.340168	+	0.196396i
$176$	−4.89898	−	2.82843i	−0.369274	−	0.213201i
$177$		0			0
$178$	7.00000	−	12.1244i	0.524672	−	0.908759i
$179$	−2.44949	−	4.24264i	−0.183083	−	0.317110i	0.759846	−	0.650104i	$-0.225275\pi$
$179$	−2.44949	−	4.24264i	−0.183083	−	0.317110i	−0.942929	+	0.332994i	$0.891941\pi$
$180$		0			0
$181$	11.0000			0.817624			0.408812	−	0.912619i	$-0.365943\pi$
$181$	11.0000			0.817624			0.408812	+	0.912619i	$0.365943\pi$
$182$	−6.12372	+	6.36396i	−0.453921	+	0.471728i
$183$		0			0
$184$	6.00000	−	3.46410i	0.442326	−	0.255377i
$185$	−1.22474	−	2.12132i	−0.0900450	−	0.155963i
$186$		0			0
$187$			6.92820i			0.506640i
$188$		0			0
$189$		0			0
$190$			3.46410i			0.251312i
$191$	−8.57321	+	14.8492i	−0.620336	+	1.07445i	0.369087	+	0.929395i	$0.379670\pi$
$191$	−8.57321	+	14.8492i	−0.620336	+	1.07445i	−0.989423	+	0.145059i	$0.953663\pi$
$192$		0			0
$193$	−7.50000	+	4.33013i	−0.539862	+	0.311689i	−0.745023	−	0.667039i	$-0.767561\pi$
$193$	−7.50000	+	4.33013i	−0.539862	+	0.311689i	0.205161	+	0.978728i	$0.434228\pi$
$194$	19.5959			1.40690
$195$		0			0
$196$		0			0
$197$	−8.57321	+	4.94975i	−0.610816	+	0.352655i	−0.773285	−	0.634059i	$-0.781388\pi$
$197$	−8.57321	+	4.94975i	−0.610816	+	0.352655i	0.162469	+	0.986714i	$0.448054\pi$
$198$		0			0
$199$	−13.0000	+	22.5167i	−0.921546	+	1.59616i	−0.124521	+	0.992217i	$0.539739\pi$
$199$	−13.0000	+	22.5167i	−0.921546	+	1.59616i	−0.797025	+	0.603947i	$0.793594\pi$
$200$		−	8.48528i		−	0.600000i
$201$		0			0
$202$	15.0000	+	8.66025i	1.05540	+	0.609333i
$203$			16.9706i			1.19110i
$204$		0			0
$205$	−5.00000	−	8.66025i	−0.349215	−	0.604858i
$206$	−6.12372	+	3.53553i	−0.426660	+	0.246332i
$207$		0			0
$208$	14.0000	+	3.46410i	0.970725	+	0.240192i
$209$	−2.44949			−0.169435
$210$		0			0
$211$	12.5000	+	21.6506i	0.860535	+	1.49049i	0.871413	+	0.490550i	$0.163204\pi$
$211$	12.5000	+	21.6506i	0.860535	+	1.49049i	−0.0108774	+	0.999941i	$0.503462\pi$
$212$		0			0
$213$		0			0
$214$	−21.0000	−	12.1244i	−1.43553	−	0.828804i
$215$	6.12372	+	3.53553i	0.417635	+	0.241121i
$216$		0			0
$217$	4.50000	−	7.79423i	0.305480	−	0.529107i
$218$	11.0227	+	19.0919i	0.746552	+	1.29307i
$219$		0			0
$220$		0			0
$221$	−4.89898	−	16.9706i	−0.329541	−	1.14156i
$222$		0			0
$223$	−3.00000	+	1.73205i	−0.200895	+	0.115987i	−0.597073	−	0.802187i	$-0.703670\pi$
$223$	−3.00000	+	1.73205i	−0.200895	+	0.115987i	0.396178	+	0.918174i	$0.370336\pi$
$224$		0			0
$225$		0			0
$226$		−	24.2487i		−	1.61300i
$227$	1.22474	+	0.707107i	0.0812892	+	0.0469323i	0.540094	−	0.841605i	$-0.318389\pi$
$227$	1.22474	+	0.707107i	0.0812892	+	0.0469323i	−0.458804	+	0.888537i	$0.651722\pi$
$228$		0			0
$229$			10.3923i			0.686743i	0.939200	+	0.343371i	$0.111569\pi$
$229$			10.3923i			0.686743i	−0.939200	+	0.343371i	$0.888431\pi$
$230$	−2.44949	+	4.24264i	−0.161515	+	0.279751i
$231$		0			0
$232$	24.0000	−	13.8564i	1.57568	−	0.909718i
$233$	−22.0454			−1.44424			−0.722121	−	0.691766i	$-0.756833\pi$
$233$	−22.0454			−1.44424			−0.722121	+	0.691766i	$0.756833\pi$
$234$		0			0
$235$	4.00000			0.260931
$236$		0			0
$237$		0			0
$238$	−6.00000	+	10.3923i	−0.388922	+	0.673633i
$239$		−	14.1421i		−	0.914779i	−0.889267	−	0.457389i	$-0.848785\pi$
$239$		−	14.1421i		−	0.914779i	0.889267	−	0.457389i	$-0.151215\pi$
$240$		0			0
$241$	−25.5000	−	14.7224i	−1.64260	−	0.948355i	−0.979905	−	0.199465i	$-0.936079\pi$
$241$	−25.5000	−	14.7224i	−1.64260	−	0.948355i	−0.662695	−	0.748890i	$-0.730587\pi$
$242$		−	12.7279i		−	0.818182i
$243$		0			0
$244$		0			0
$245$	−4.89898	+	2.82843i	−0.312984	+	0.180702i
$246$		0			0
$247$	6.00000	−	1.73205i	0.381771	−	0.110208i
$248$	−14.6969			−0.933257
$249$		0			0
$250$	8.00000	+	13.8564i	0.505964	+	0.876356i
$251$	13.4722	−	23.3345i	0.850357	−	1.47286i	−0.0305288	−	0.999534i	$-0.509719\pi$
$251$	13.4722	−	23.3345i	0.850357	−	1.47286i	0.880886	−	0.473328i	$-0.156948\pi$
$252$		0			0
$253$	−3.00000	−	1.73205i	−0.188608	−	0.108893i
$254$	−23.2702	−	13.4350i	−1.46010	−	0.842989i
$255$		0			0
$256$		0			0
$257$	1.22474	+	2.12132i	0.0763975	+	0.132324i	0.901693	−	0.432377i	$-0.142325\pi$
$257$	1.22474	+	2.12132i	0.0763975	+	0.132324i	−0.825296	+	0.564701i	$0.808992\pi$
$258$		0			0
$259$	3.00000			0.186411
$260$		0			0
$261$		0			0
$262$	18.0000	−	10.3923i	1.11204	−	0.642039i
$263$	−6.12372	−	10.6066i	−0.377605	−	0.654031i	0.613108	−	0.789999i	$-0.289919\pi$
$263$	−6.12372	−	10.6066i	−0.377605	−	0.654031i	−0.990713	+	0.135968i	$0.956586\pi$
$264$		0			0
$265$		0			0
$266$	−3.67423	−	2.12132i	−0.225282	−	0.130066i
$267$		0			0
$268$		0			0
$269$	13.4722	−	23.3345i	0.821414	−	1.42273i	−0.0832151	−	0.996532i	$-0.526519\pi$
$269$	13.4722	−	23.3345i	0.821414	−	1.42273i	0.904629	−	0.426199i	$-0.140148\pi$
$270$		0			0
$271$	−25.5000	+	14.7224i	−1.54901	+	0.894324i	−0.550797	+	0.834639i	$0.685676\pi$
$271$	−25.5000	+	14.7224i	−1.54901	+	0.894324i	−0.998217	+	0.0596851i	$0.980990\pi$
$272$	19.5959			1.18818
$273$		0			0
$274$	−20.0000			−1.20824
$275$	−3.67423	+	2.12132i	−0.221565	+	0.127920i
$276$		0			0
$277$	2.00000	−	3.46410i	0.120168	−	0.208138i	−0.799666	−	0.600446i	$-0.794990\pi$
$277$	2.00000	−	3.46410i	0.120168	−	0.208138i	0.919834	+	0.392308i	$0.128323\pi$
$278$		−	2.82843i		−	0.169638i
$279$		0			0
$280$	−6.00000	−	3.46410i	−0.358569	−	0.207020i
$281$			15.5563i			0.928014i	0.885832	+	0.464007i	$0.153589\pi$
$281$			15.5563i			0.928014i	−0.885832	+	0.464007i	$0.846411\pi$
$282$		0			0
$283$	3.50000	+	6.06218i	0.208053	+	0.360359i	0.951101	−	0.308879i	$-0.0999539\pi$
$283$	3.50000	+	6.06218i	0.208053	+	0.360359i	−0.743048	+	0.669238i	$0.766621\pi$
$284$		0			0
$285$		0			0
$286$	−2.00000	−	6.92820i	−0.118262	−	0.409673i
$287$	12.2474			0.722944
$288$		0			0
$289$	−3.50000	−	6.06218i	−0.205882	−	0.356599i
$290$	−9.79796	+	16.9706i	−0.575356	+	0.996546i
$291$		0			0
$292$		0			0
$293$	−17.1464	−	9.89949i	−1.00171	−	0.578335i	−0.0929527	−	0.995671i	$-0.529631\pi$
$293$	−17.1464	−	9.89949i	−1.00171	−	0.578335i	−0.908752	+	0.417336i	$0.862964\pi$
$294$		0			0
$295$	4.00000	−	6.92820i	0.232889	−	0.403376i
$296$	−2.44949	−	4.24264i	−0.142374	−	0.246598i
$297$		0			0
$298$	−26.0000			−1.50614
$299$	8.57321	+	2.12132i	0.495802	+	0.122679i
$300$		0			0
$301$	−7.50000	+	4.33013i	−0.432293	+	0.249584i
$302$	−3.67423	−	6.36396i	−0.211428	−	0.366205i
$303$		0			0
$304$			6.92820i			0.397360i
$305$	−4.89898	−	2.82843i	−0.280515	−	0.161955i
$306$		0			0
$307$			15.5885i			0.889680i	0.895610	+	0.444840i	$0.146740\pi$
$307$			15.5885i			0.889680i	−0.895610	+	0.444840i	$0.853260\pi$
$308$		0			0
$309$		0			0
$310$	9.00000	−	5.19615i	0.511166	−	0.295122i
$311$	7.34847			0.416693			0.208347	−	0.978055i	$-0.433192\pi$
$311$	7.34847			0.416693			0.208347	+	0.978055i	$0.433192\pi$
$312$		0			0
$313$	−28.0000			−1.58265			−0.791327	−	0.611393i	$-0.790609\pi$
$313$	−28.0000			−1.58265			−0.791327	+	0.611393i	$0.790609\pi$
$314$	−6.12372	+	3.53553i	−0.345582	+	0.199522i
$315$		0			0
$316$		0			0
$317$			15.5563i			0.873732i	0.899527	+	0.436866i	$0.143912\pi$
$317$			15.5563i			0.873732i	−0.899527	+	0.436866i	$0.856088\pi$
$318$		0			0
$319$	−12.0000	−	6.92820i	−0.671871	−	0.387905i
$320$			11.3137i			0.632456i
$321$		0			0
$322$	−3.00000	−	5.19615i	−0.167183	−	0.289570i
$323$	7.34847	−	4.24264i	0.408880	−	0.236067i
$324$		0			0
$325$	7.50000	−	7.79423i	0.416025	−	0.432346i
$326$	−2.44949			−0.135665
$327$		0			0
$328$	−10.0000	−	17.3205i	−0.552158	−	0.956365i
$329$	−2.44949	+	4.24264i	−0.135045	+	0.233904i
$330$		0			0
$331$	−12.0000	−	6.92820i	−0.659580	−	0.380808i	0.132537	−	0.991178i	$-0.457688\pi$
$331$	−12.0000	−	6.92820i	−0.659580	−	0.380808i	−0.792117	+	0.610370i	$0.791021\pi$
$332$		0			0
$333$		0			0
$334$	−5.00000	+	8.66025i	−0.273588	+	0.473868i
$335$	−4.89898	−	8.48528i	−0.267660	−	0.463600i
$336$		0			0
$337$	−4.00000			−0.217894			−0.108947	−	0.994048i	$-0.534748\pi$
$337$	−4.00000			−0.217894			−0.108947	+	0.994048i	$0.534748\pi$
$338$	9.79796	+	15.5563i	0.532939	+	0.846154i
$339$		0			0
$340$		0			0
$341$	3.67423	+	6.36396i	0.198971	+	0.344628i
$342$		0			0
$343$		−	19.0526i		−	1.02874i
$344$	12.2474	+	7.07107i	0.660338	+	0.381246i
$345$		0			0
$346$			6.92820i			0.372463i
$347$	2.44949	−	4.24264i	0.131495	−	0.227757i	−0.792758	−	0.609537i	$-0.791355\pi$
$347$	2.44949	−	4.24264i	0.131495	−	0.227757i	0.924253	+	0.381780i	$0.124689\pi$
$348$		0			0
$349$	−3.00000	+	1.73205i	−0.160586	+	0.0927146i	−0.578140	−	0.815938i	$-0.696221\pi$
$349$	−3.00000	+	1.73205i	−0.160586	+	0.0927146i	0.417553	+	0.908652i	$0.362888\pi$
$350$	−7.34847			−0.392792
$351$		0			0
$352$		0			0
$353$	−1.22474	+	0.707107i	−0.0651866	+	0.0376355i	−0.532239	−	0.846594i	$-0.678649\pi$
$353$	−1.22474	+	0.707107i	−0.0651866	+	0.0376355i	0.467052	+	0.884230i	$0.345316\pi$
$354$		0			0
$355$	−11.0000	+	19.0526i	−0.583819	+	1.01120i
$356$		0			0
$357$		0			0
$358$	6.00000	+	3.46410i	0.317110	+	0.183083i
$359$			19.7990i			1.04495i	0.852654	+	0.522475i	$0.174991\pi$
$359$			19.7990i			1.04495i	−0.852654	+	0.522475i	$0.825009\pi$
$360$		0			0
$361$	−8.00000	−	13.8564i	−0.421053	−	0.729285i
$362$	−13.4722	+	7.77817i	−0.708083	+	0.408812i
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$	11.0000	+	19.0526i	0.574195	+	0.994535i	0.996129	+	0.0879086i	$0.0280183\pi$
$367$	11.0000	+	19.0526i	0.574195	+	0.994535i	−0.421933	+	0.906627i	$0.638648\pi$
$368$	−4.89898	+	8.48528i	−0.255377	+	0.442326i
$369$		0			0
$370$	3.00000	+	1.73205i	0.155963	+	0.0900450i
$371$		0			0
$372$		0			0
$373$	3.50000	−	6.06218i	0.181223	−	0.313888i	−0.761074	−	0.648665i	$-0.775328\pi$
$373$	3.50000	−	6.06218i	0.181223	−	0.313888i	0.942297	+	0.334777i	$0.108661\pi$
$374$	−4.89898	−	8.48528i	−0.253320	−	0.438763i
$375$		0			0
$376$	8.00000			0.412568
$377$	34.2929	+	8.48528i	1.76617	+	0.437014i
$378$		0			0
$379$	−12.0000	+	6.92820i	−0.616399	+	0.355878i	−0.775466	−	0.631390i	$-0.782485\pi$
$379$	−12.0000	+	6.92820i	−0.616399	+	0.355878i	0.159067	+	0.987268i	$0.449151\pi$
$380$		0			0
$381$		0			0
$382$		−	24.2487i		−	1.24067i
$383$	26.9444	+	15.5563i	1.37679	+	0.794892i	0.991772	−	0.128015i	$-0.0408606\pi$
$383$	26.9444	+	15.5563i	1.37679	+	0.794892i	0.385022	+	0.922908i	$0.374194\pi$
$384$		0			0
$385$			3.46410i			0.176547i
$386$	6.12372	−	10.6066i	0.311689	−	0.539862i
$387$		0			0
$388$		0			0
$389$	14.6969			0.745164			0.372582	−	0.927999i	$-0.378472\pi$
$389$	14.6969			0.745164			0.372582	+	0.927999i	$0.378472\pi$
$390$		0			0
$391$	12.0000			0.606866
$392$	−9.79796	+	5.65685i	−0.494872	+	0.285714i
$393$		0			0
$394$	7.00000	−	12.1244i	0.352655	−	0.610816i
$395$			14.1421i			0.711568i
$396$		0			0
$397$	28.5000	+	16.4545i	1.43037	+	0.825827i	0.997149	−	0.0754589i	$-0.0240422\pi$
$397$	28.5000	+	16.4545i	1.43037	+	0.825827i	0.433225	+	0.901286i	$0.357376\pi$
$398$		−	36.7696i		−	1.84309i
$399$		0			0
$400$	6.00000	+	10.3923i	0.300000	+	0.519615i
$401$	17.1464	−	9.89949i	0.856252	−	0.494357i	−0.00650355	−	0.999979i	$-0.502070\pi$
$401$	17.1464	−	9.89949i	0.856252	−	0.494357i	0.862755	+	0.505622i	$0.168737\pi$
$402$		0			0
$403$	−13.5000	−	12.9904i	−0.672483	−	0.647097i
$404$		0			0
$405$		0			0
$406$	−12.0000	−	20.7846i	−0.595550	−	1.03152i
$407$	−1.22474	+	2.12132i	−0.0607083	+	0.105150i
$408$		0			0
$409$	−25.5000	−	14.7224i	−1.26089	−	0.727977i	−0.287646	−	0.957737i	$-0.592873\pi$
$409$	−25.5000	−	14.7224i	−1.26089	−	0.727977i	−0.973247	+	0.229759i	$0.926206\pi$
$410$	12.2474	+	7.07107i	0.604858	+	0.349215i
$411$		0			0
$412$		0			0
$413$	4.89898	+	8.48528i	0.241063	+	0.417533i
$414$		0			0
$415$	−14.0000			−0.687233
$416$		0			0
$417$		0			0
$418$	3.00000	−	1.73205i	0.146735	−	0.0847174i
$419$	−9.79796	−	16.9706i	−0.478662	−	0.829066i	0.521039	−	0.853533i	$-0.325545\pi$
$419$	−9.79796	−	16.9706i	−0.478662	−	0.829066i	−0.999701	+	0.0244666i	$0.992211\pi$
$420$		0			0
$421$			36.3731i			1.77271i	0.463002	+	0.886357i	$0.346772\pi$
$421$			36.3731i			1.77271i	−0.463002	+	0.886357i	$0.653228\pi$
$422$	−30.6186	−	17.6777i	−1.49049	−	0.860535i
$423$		0			0
$424$		0			0
$425$	7.34847	−	12.7279i	0.356453	−	0.617395i
$426$		0			0
$427$	6.00000	−	3.46410i	0.290360	−	0.167640i
$428$		0			0
$429$		0			0
$430$	−10.0000			−0.482243
$431$	−30.6186	+	17.6777i	−1.47485	+	0.851503i	−0.999598	−	0.0283480i	$-0.990975\pi$
$431$	−30.6186	+	17.6777i	−1.47485	+	0.851503i	−0.475249	+	0.879851i	$0.657642\pi$
$432$		0			0
$433$	0.500000	−	0.866025i	0.0240285	−	0.0416185i	−0.853761	−	0.520665i	$-0.825684\pi$
$433$	0.500000	−	0.866025i	0.0240285	−	0.0416185i	0.877790	+	0.479046i	$0.159017\pi$
$434$			12.7279i			0.610960i
$435$		0			0
$436$		0			0
$437$			4.24264i			0.202953i
$438$		0			0
$439$	6.50000	+	11.2583i	0.310228	+	0.537331i	0.978412	−	0.206666i	$-0.0662612\pi$
$439$	6.50000	+	11.2583i	0.310228	+	0.537331i	−0.668184	+	0.743996i	$0.732928\pi$
$440$	4.89898	−	2.82843i	0.233550	−	0.134840i
$441$		0			0
$442$	18.0000	+	17.3205i	0.856173	+	0.823853i
$443$	14.6969			0.698273			0.349136	−	0.937072i	$-0.386475\pi$
$443$	14.6969			0.698273			0.349136	+	0.937072i	$0.386475\pi$
$444$		0			0
$445$	7.00000	+	12.1244i	0.331832	+	0.574750i
$446$	2.44949	−	4.24264i	0.115987	−	0.200895i
$447$		0			0
$448$	−12.0000	−	6.92820i	−0.566947	−	0.327327i
$449$	19.5959	+	11.3137i	0.924789	+	0.533927i	0.885160	−	0.465288i	$-0.154049\pi$
$449$	19.5959	+	11.3137i	0.924789	+	0.533927i	0.0396290	+	0.999214i	$0.487382\pi$
$450$		0			0
$451$	−5.00000	+	8.66025i	−0.235441	+	0.407795i
$452$		0			0
$453$		0			0
$454$	−2.00000			−0.0938647
$455$	−2.44949	−	8.48528i	−0.114834	−	0.397796i
$456$		0			0
$457$	−16.5000	+	9.52628i	−0.771837	+	0.445621i	−0.833530	−	0.552475i	$-0.813684\pi$
$457$	−16.5000	+	9.52628i	−0.771837	+	0.445621i	0.0616922	+	0.998095i	$0.480350\pi$
$458$	−7.34847	−	12.7279i	−0.343371	−	0.594737i
$459$		0			0
$460$		0			0
$461$	−9.79796	−	5.65685i	−0.456336	−	0.263466i	0.254166	−	0.967161i	$-0.418199\pi$
$461$	−9.79796	−	5.65685i	−0.456336	−	0.263466i	−0.710503	+	0.703695i	$0.751532\pi$
$462$		0			0
$463$		−	20.7846i		−	0.965943i	−0.875636	−	0.482971i	$-0.839558\pi$
$463$		−	20.7846i		−	0.965943i	0.875636	−	0.482971i	$-0.160442\pi$
$464$	−19.5959	+	33.9411i	−0.909718	+	1.57568i
$465$		0			0
$466$	27.0000	−	15.5885i	1.25075	−	0.722121i
$467$	−22.0454			−1.02014			−0.510070	−	0.860133i	$-0.670380\pi$
$467$	−22.0454			−1.02014			−0.510070	+	0.860133i	$0.670380\pi$
$468$		0			0
$469$	12.0000			0.554109
$470$	−4.89898	+	2.82843i	−0.225973	+	0.130466i
$471$		0			0
$472$	8.00000	−	13.8564i	0.368230	−	0.637793i
$473$		−	7.07107i		−	0.325128i
$474$		0			0
$475$	4.50000	+	2.59808i	0.206474	+	0.119208i
$476$		0			0
$477$		0			0
$478$	10.0000	+	17.3205i	0.457389	+	0.792222i
$479$	9.79796	−	5.65685i	0.447680	−	0.258468i	−0.259170	−	0.965832i	$-0.583449\pi$
$479$	9.79796	−	5.65685i	0.447680	−	0.258468i	0.706850	+	0.707364i	$0.250116\pi$
$480$		0			0
$481$	1.50000	−	6.06218i	0.0683941	−	0.276412i
$482$	41.6413			1.89671
$483$		0			0
$484$		0			0
$485$	−9.79796	+	16.9706i	−0.444902	+	0.770594i
$486$		0			0
$487$	28.5000	+	16.4545i	1.29146	+	0.745624i	0.978913	−	0.204279i	$-0.0654850\pi$
$487$	28.5000	+	16.4545i	1.29146	+	0.745624i	0.312546	+	0.949903i	$0.398818\pi$
$488$	−9.79796	−	5.65685i	−0.443533	−	0.256074i
$489$		0			0
$490$	4.00000	−	6.92820i	0.180702	−	0.312984i
$491$	−9.79796	−	16.9706i	−0.442176	−	0.765871i	0.555675	−	0.831400i	$-0.312460\pi$
$491$	−9.79796	−	16.9706i	−0.442176	−	0.765871i	−0.997851	+	0.0655288i	$0.979127\pi$
$492$		0			0
$493$	48.0000			2.16181
$494$	−6.12372	+	6.36396i	−0.275519	+	0.286328i
$495$		0			0
$496$	18.0000	−	10.3923i	0.808224	−	0.466628i
$497$	−13.4722	−	23.3345i	−0.604310	−	1.04670i
$498$		0			0
$499$		−	20.7846i		−	0.930447i	−0.885193	−	0.465223i	$-0.845974\pi$
$499$		−	20.7846i		−	0.930447i	0.885193	−	0.465223i	$-0.154026\pi$
$500$		0			0
$501$		0			0
$502$			38.1051i			1.70071i
$503$	13.4722	−	23.3345i	0.600695	−	1.04043i	−0.392021	−	0.919956i	$-0.628224\pi$
$503$	13.4722	−	23.3345i	0.600695	−	1.04043i	0.992716	−	0.120479i	$-0.0384429\pi$
$504$		0			0
$505$	−15.0000	+	8.66025i	−0.667491	+	0.385376i
$506$	4.89898			0.217786
$507$		0			0
$508$		0			0
$509$	−15.9217	+	9.19239i	−0.705716	+	0.407445i	−0.809473	−	0.587157i	$-0.800247\pi$
$509$	−15.9217	+	9.19239i	−0.705716	+	0.407445i	0.103757	+	0.994603i	$0.466914\pi$
$510$		0			0
$511$		0			0
$512$			22.6274i			1.00000i
$513$		0			0
$514$	−3.00000	−	1.73205i	−0.132324	−	0.0763975i
$515$		−	7.07107i		−	0.311588i
$516$		0			0
$517$	−2.00000	−	3.46410i	−0.0879599	−	0.152351i
$518$	−3.67423	+	2.12132i	−0.161437	+	0.0932055i
$519$		0			0
$520$	−10.0000	+	10.3923i	−0.438529	+	0.455733i
$521$		0			0			−	1.00000i	$-0.5\pi$
$521$		0			0				1.00000i	$0.5\pi$
$522$		0			0
$523$	0.500000	+	0.866025i	0.0218635	+	0.0378686i	0.876750	−	0.480946i	$-0.159707\pi$
$523$	0.500000	+	0.866025i	0.0218635	+	0.0378686i	−0.854887	+	0.518815i	$0.826373\pi$
$524$		0			0
$525$		0			0
$526$	15.0000	+	8.66025i	0.654031	+	0.377605i
$527$	−22.0454	−	12.7279i	−0.960313	−	0.554437i
$528$		0			0
$529$	8.50000	−	14.7224i	0.369565	−	0.640106i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	6.12372	−	24.7487i	0.265248	−	1.07199i
$534$		0			0
$535$	21.0000	−	12.1244i	0.907909	−	0.524182i
$536$	−9.79796	−	16.9706i	−0.423207	−	0.733017i
$537$		0			0
$538$			38.1051i			1.64283i
$539$	4.89898	+	2.82843i	0.211014	+	0.121829i
$540$		0			0
$541$		−	31.1769i		−	1.34040i	−0.742180	−	0.670200i	$-0.766208\pi$
$541$		−	31.1769i		−	1.34040i	0.742180	−	0.670200i	$-0.233792\pi$
$542$	20.8207	−	36.0624i	0.894324	−	1.54901i
$543$		0			0
$544$		0			0
$545$	−22.0454			−0.944322
$546$		0			0
$547$	26.0000			1.11168			0.555840	−	0.831289i	$-0.312397\pi$
$547$	26.0000			1.11168			0.555840	+	0.831289i	$0.312397\pi$
$548$		0			0
$549$		0			0
$550$	3.00000	−	5.19615i	0.127920	−	0.221565i
$551$			16.9706i			0.722970i
$552$		0			0
$553$	−15.0000	−	8.66025i	−0.637865	−	0.368271i
$554$			5.65685i			0.240337i
$555$		0			0
$556$		0			0
$557$	−8.57321	+	4.94975i	−0.363259	+	0.209728i	−0.670509	−	0.741901i	$-0.733924\pi$
$557$	−8.57321	+	4.94975i	−0.363259	+	0.209728i	0.307251	+	0.951629i	$0.400591\pi$
$558$		0			0
$559$	5.00000	+	17.3205i	0.211477	+	0.732579i
$560$	9.79796			0.414039
$561$		0			0
$562$	−11.0000	−	19.0526i	−0.464007	−	0.803684i
$563$	−19.5959	+	33.9411i	−0.825869	+	1.43045i	0.0753835	+	0.997155i	$0.475982\pi$
$563$	−19.5959	+	33.9411i	−0.825869	+	1.43045i	−0.901253	+	0.433293i	$0.857351\pi$
$564$		0			0
$565$	21.0000	+	12.1244i	0.883477	+	0.510075i
$566$	−8.57321	−	4.94975i	−0.360359	−	0.208053i
$567$		0			0
$568$	−22.0000	+	38.1051i	−0.923099	+	1.59886i
$569$	−6.12372	−	10.6066i	−0.256720	−	0.444652i	0.708641	−	0.705569i	$-0.249308\pi$
$569$	−6.12372	−	10.6066i	−0.256720	−	0.444652i	−0.965361	+	0.260917i	$0.915975\pi$
$570$		0			0
$571$	−13.0000			−0.544033			−0.272017	−	0.962293i	$-0.587691\pi$
$571$	−13.0000			−0.544033			−0.272017	+	0.962293i	$0.587691\pi$
$572$		0			0
$573$		0			0
$574$	−15.0000	+	8.66025i	−0.626088	+	0.361472i
$575$	3.67423	+	6.36396i	0.153226	+	0.265396i
$576$		0			0
$577$		−	15.5885i		−	0.648956i	−0.945893	−	0.324478i	$-0.894811\pi$
$577$		−	15.5885i		−	0.648956i	0.945893	−	0.324478i	$-0.105189\pi$
$578$	8.57321	+	4.94975i	0.356599	+	0.205882i
$579$		0			0
$580$		0			0
$581$	8.57321	−	14.8492i	0.355677	−	0.616050i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	28.0000			1.15667
$587$	−12.2474	+	7.07107i	−0.505506	+	0.291854i	−0.730985	−	0.682394i	$-0.760939\pi$
$587$	−12.2474	+	7.07107i	−0.505506	+	0.291854i	0.225478	+	0.974248i	$0.427606\pi$
$588$		0			0
$589$	4.50000	−	7.79423i	0.185419	−	0.321156i
$590$			11.3137i			0.465778i
$591$		0			0
$592$	6.00000	+	3.46410i	0.246598	+	0.142374i
$593$			7.07107i			0.290374i	0.989404	+	0.145187i	$0.0463784\pi$
$593$			7.07107i			0.290374i	−0.989404	+	0.145187i	$0.953622\pi$
$594$		0			0
$595$	−6.00000	−	10.3923i	−0.245976	−	0.426043i
$596$		0			0
$597$		0			0
$598$	−12.0000	+	3.46410i	−0.490716	+	0.141658i
$599$	7.34847			0.300250			0.150125	−	0.988667i	$-0.452032\pi$
$599$	7.34847			0.300250			0.150125	+	0.988667i	$0.452032\pi$
$600$		0			0
$601$	20.0000	+	34.6410i	0.815817	+	1.41304i	0.908740	+	0.417363i	$0.137046\pi$
$601$	20.0000	+	34.6410i	0.815817	+	1.41304i	−0.0929227	+	0.995673i	$0.529621\pi$
$602$	6.12372	−	10.6066i	0.249584	−	0.432293i
$603$		0			0
$604$		0			0
$605$	11.0227	+	6.36396i	0.448137	+	0.258732i
$606$		0			0
$607$	3.50000	−	6.06218i	0.142061	−	0.246056i	−0.786212	−	0.617957i	$-0.787961\pi$
$607$	3.50000	−	6.06218i	0.142061	−	0.246056i	0.928272	+	0.371901i	$0.121294\pi$
$608$		0			0
$609$		0			0
$610$	8.00000			0.323911
$611$	7.34847	+	7.07107i	0.297287	+	0.286065i
$612$		0			0
$613$	15.0000	−	8.66025i	0.605844	−	0.349784i	−0.165493	−	0.986211i	$-0.552922\pi$
$613$	15.0000	−	8.66025i	0.605844	−	0.349784i	0.771337	+	0.636427i	$0.219588\pi$
$614$	−11.0227	−	19.0919i	−0.444840	−	0.770486i
$615$		0			0
$616$			6.92820i			0.279145i
$617$	−6.12372	−	3.53553i	−0.246532	−	0.142335i	0.371643	−	0.928376i	$-0.378794\pi$
$617$	−6.12372	−	3.53553i	−0.246532	−	0.142335i	−0.618175	+	0.786040i	$0.712128\pi$
$618$		0			0
$619$		−	25.9808i		−	1.04425i	−0.852867	−	0.522127i	$-0.825139\pi$
$619$		−	25.9808i		−	1.04425i	0.852867	−	0.522127i	$-0.174861\pi$
$620$		0			0
$621$		0			0
$622$	−9.00000	+	5.19615i	−0.360867	+	0.208347i
$623$	−17.1464			−0.686957
$624$		0			0
$625$	−1.00000			−0.0400000
$626$	34.2929	−	19.7990i	1.37062	−	0.791327i
$627$		0			0
$628$		0			0
$629$		−	8.48528i		−	0.338330i
$630$		0			0
$631$	−12.0000	−	6.92820i	−0.477712	−	0.275807i	0.241750	−	0.970339i	$-0.422279\pi$
$631$	−12.0000	−	6.92820i	−0.477712	−	0.275807i	−0.719463	+	0.694531i	$0.755612\pi$
$632$			28.2843i			1.12509i
$633$		0			0
$634$	−11.0000	−	19.0526i	−0.436866	−	0.756674i
$635$	23.2702	−	13.4350i	0.923448	−	0.533153i
$636$		0			0
$637$	−14.0000	−	3.46410i	−0.554700	−	0.137253i
$638$	19.5959			0.775810
$639$		0			0
$640$	−8.00000	−	13.8564i	−0.316228	−	0.547723i
$641$	−8.57321	+	14.8492i	−0.338622	+	0.586510i	−0.984174	−	0.177206i	$-0.943294\pi$
$641$	−8.57321	+	14.8492i	−0.338622	+	0.586510i	0.645552	+	0.763716i	$0.276627\pi$
$642$		0			0
$643$	28.5000	+	16.4545i	1.12393	+	0.648901i	0.942401	−	0.334484i	$-0.108562\pi$
$643$	28.5000	+	16.4545i	1.12393	+	0.648901i	0.181529	+	0.983386i	$0.441895\pi$
$644$		0			0
$645$		0			0
$646$	−6.00000	+	10.3923i	−0.236067	+	0.408880i
$647$	−2.44949	−	4.24264i	−0.0962994	−	0.166795i	0.813851	−	0.581074i	$-0.197367\pi$
$647$	−2.44949	−	4.24264i	−0.0962994	−	0.166795i	−0.910150	+	0.414278i	$0.864034\pi$
$648$		0			0
$649$	−8.00000			−0.314027
$650$	−3.67423	+	14.8492i	−0.144115	+	0.582435i
$651$		0			0
$652$		0			0
$653$	12.2474	+	21.2132i	0.479280	+	0.830137i	0.999718	−	0.0237627i	$-0.00756462\pi$
$653$	12.2474	+	21.2132i	0.479280	+	0.830137i	−0.520438	+	0.853900i	$0.674231\pi$
$654$		0			0
$655$			20.7846i			0.812122i
$656$	24.4949	+	14.1421i	0.956365	+	0.552158i
$657$		0			0
$658$		−	6.92820i		−	0.270089i
$659$	−8.57321	+	14.8492i	−0.333965	+	0.578444i	−0.983285	−	0.182071i	$-0.941720\pi$
$659$	−8.57321	+	14.8492i	−0.333965	+	0.578444i	0.649320	+	0.760515i	$0.275053\pi$
$660$		0			0
$661$	−7.50000	+	4.33013i	−0.291716	+	0.168422i	−0.638716	−	0.769443i	$-0.720534\pi$
$661$	−7.50000	+	4.33013i	−0.291716	+	0.168422i	0.346999	+	0.937865i	$0.387201\pi$
$662$	19.5959			0.761617
$663$		0			0
$664$	−28.0000			−1.08661
$665$	3.67423	−	2.12132i	0.142481	−	0.0822613i
$666$		0			0
$667$	−12.0000	+	20.7846i	−0.464642	+	0.804783i
$668$		0			0
$669$		0			0
$670$	12.0000	+	6.92820i	0.463600	+	0.267660i
$671$			5.65685i			0.218380i
$672$		0			0
$673$	−16.0000	−	27.7128i	−0.616755	−	1.06825i	−0.990074	−	0.140548i	$-0.955114\pi$
$673$	−16.0000	−	27.7128i	−0.616755	−	1.06825i	0.373319	−	0.927703i	$-0.378220\pi$
$674$	4.89898	−	2.82843i	0.188702	−	0.108947i
$675$		0			0
$676$		0			0
$677$	−29.3939			−1.12970			−0.564849	−	0.825194i	$-0.691066\pi$
$677$	−29.3939			−1.12970			−0.564849	+	0.825194i	$0.691066\pi$
$678$		0			0
$679$	−12.0000	−	20.7846i	−0.460518	−	0.797640i
$680$	−9.79796	+	16.9706i	−0.375735	+	0.650791i
$681$		0			0
$682$	−9.00000	−	5.19615i	−0.344628	−	0.198971i
$683$	−24.4949	−	14.1421i	−0.937271	−	0.541134i	−0.0481673	−	0.998839i	$-0.515338\pi$
$683$	−24.4949	−	14.1421i	−0.937271	−	0.541134i	−0.889104	+	0.457705i	$0.848671\pi$
$684$		0			0
$685$	10.0000	−	17.3205i	0.382080	−	0.661783i
$686$	13.4722	+	23.3345i	0.514371	+	0.890916i
$687$		0			0
$688$	−20.0000			−0.762493
$689$		0			0
$690$		0			0
$691$	−16.5000	+	9.52628i	−0.627690	+	0.362397i	−0.779857	−	0.625958i	$-0.784708\pi$
$691$	−16.5000	+	9.52628i	−0.627690	+	0.362397i	0.152167	+	0.988355i	$0.451375\pi$
$692$		0			0
$693$		0			0
$694$			6.92820i			0.262991i
$695$	2.44949	+	1.41421i	0.0929144	+	0.0536442i
$696$		0			0
$697$		−	34.6410i		−	1.31212i
$698$	2.44949	−	4.24264i	0.0927146	−	0.160586i
$699$		0			0
$700$		0			0
$701$	22.0454			0.832644			0.416322	−	0.909217i	$-0.363319\pi$
$701$	22.0454			0.832644			0.416322	+	0.909217i	$0.363319\pi$
$702$		0			0
$703$	3.00000			0.113147
$704$	9.79796	−	5.65685i	0.369274	−	0.213201i
$705$		0			0
$706$	1.00000	−	1.73205i	0.0376355	−	0.0651866i
$707$		−	21.2132i		−	0.797805i
$708$		0			0
$709$	1.50000	+	0.866025i	0.0563337	+	0.0325243i	0.527902	−	0.849305i	$-0.322979\pi$
$709$	1.50000	+	0.866025i	0.0563337	+	0.0325243i	−0.471569	+	0.881829i	$0.656312\pi$
$710$		−	31.1127i		−	1.16764i
$711$		0			0
$712$	14.0000	+	24.2487i	0.524672	+	0.908759i
$713$	11.0227	−	6.36396i	0.412804	−	0.238332i
$714$		0			0
$715$	7.00000	+	1.73205i	0.261785	+	0.0647750i
$716$		0			0
$717$		0			0
$718$	−14.0000	−	24.2487i	−0.522475	−	0.904954i
$719$	2.44949	−	4.24264i	0.0913506	−	0.158224i	−0.816729	−	0.577021i	$-0.804215\pi$
$719$	2.44949	−	4.24264i	0.0913506	−	0.158224i	0.908080	+	0.418797i	$0.137548\pi$
$720$		0			0
$721$	7.50000	+	4.33013i	0.279315	+	0.161262i
$722$	19.5959	+	11.3137i	0.729285	+	0.421053i
$723$		0			0
$724$		0			0
$725$	14.6969	+	25.4558i	0.545831	+	0.945406i
$726$		0			0
$727$	17.0000			0.630495			0.315248	−	0.949009i	$-0.397912\pi$
$727$	17.0000			0.630495			0.315248	+	0.949009i	$0.397912\pi$
$728$	−4.89898	−	16.9706i	−0.181568	−	0.628971i
$729$		0			0
$730$		0			0
$731$	12.2474	+	21.2132i	0.452988	+	0.784599i
$732$		0			0
$733$			25.9808i			0.959621i	0.877372	+	0.479811i	$0.159295\pi$
$733$			25.9808i			0.959621i	−0.877372	+	0.479811i	$0.840705\pi$
$734$	−26.9444	−	15.5563i	−0.994535	−	0.574195i
$735$		0			0
$736$		0			0
$737$	−4.89898	+	8.48528i	−0.180456	+	0.312559i
$738$		0			0
$739$	−39.0000	+	22.5167i	−1.43464	+	0.828289i	−0.997470	−	0.0710909i	$-0.977352\pi$
$739$	−39.0000	+	22.5167i	−1.43464	+	0.828289i	−0.437168	+	0.899380i	$0.644019\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−37.9671	+	21.9203i	−1.39288	+	0.804178i	−0.993633	−	0.112666i	$-0.964061\pi$
$743$	−37.9671	+	21.9203i	−1.39288	+	0.804178i	−0.399245	+	0.916844i	$0.630728\pi$
$744$		0			0
$745$	13.0000	−	22.5167i	0.476283	−	0.824947i
$746$			9.89949i			0.362446i
$747$		0			0
$748$		0			0
$749$			29.6985i			1.08516i
$750$		0			0
$751$	−5.50000	−	9.52628i	−0.200698	−	0.347619i	0.748056	−	0.663636i	$-0.230988\pi$
$751$	−5.50000	−	9.52628i	−0.200698	−	0.347619i	−0.948753	+	0.316017i	$0.897654\pi$
$752$	−9.79796	+	5.65685i	−0.357295	+	0.206284i
$753$		0			0
$754$	−48.0000	+	13.8564i	−1.74806	+	0.504621i
$755$	7.34847			0.267438
$756$		0			0
$757$	0.500000	+	0.866025i	0.0181728	+	0.0314762i	0.874969	−	0.484179i	$-0.160882\pi$
$757$	0.500000	+	0.866025i	0.0181728	+	0.0314762i	−0.856796	+	0.515656i	$0.827548\pi$
$758$	9.79796	−	16.9706i	0.355878	−	0.616399i
$759$		0			0
$760$	−6.00000	−	3.46410i	−0.217643	−	0.125656i
$761$	4.89898	+	2.82843i	0.177588	+	0.102530i	0.586159	−	0.810196i	$-0.300639\pi$
$761$	4.89898	+	2.82843i	0.177588	+	0.102530i	−0.408571	+	0.912727i	$0.633973\pi$
$762$		0			0
$763$	13.5000	−	23.3827i	0.488733	−	0.846510i
$764$		0			0
$765$		0			0
$766$	−44.0000			−1.58978
$767$	19.5959	−	5.65685i	0.707568	−	0.204257i
$768$		0			0
$769$	−34.5000	+	19.9186i	−1.24410	+	0.718283i	−0.969927	−	0.243397i	$-0.921738\pi$
$769$	−34.5000	+	19.9186i	−1.24410	+	0.718283i	−0.274175	+	0.961680i	$0.588405\pi$
$770$	−2.44949	−	4.24264i	−0.0882735	−	0.152894i
$771$		0			0
$772$		0			0
$773$	19.5959	+	11.3137i	0.704816	+	0.406926i	0.809139	−	0.587618i	$-0.199934\pi$
$773$	19.5959	+	11.3137i	0.704816	+	0.406926i	−0.104323	+	0.994544i	$0.533267\pi$
$774$		0			0
$775$		−	15.5885i		−	0.559954i
$776$	−19.5959	+	33.9411i	−0.703452	+	1.21842i
$777$		0			0
$778$	−18.0000	+	10.3923i	−0.645331	+	0.372582i
$779$	12.2474			0.438810
$780$		0			0
$781$	22.0000			0.787222
$782$	−14.6969	+	8.48528i	−0.525561	+	0.303433i
$783$		0			0
$784$	8.00000	−	13.8564i	0.285714	−	0.494872i
$785$		−	7.07107i		−	0.252377i
$786$		0			0
$787$	−12.0000	−	6.92820i	−0.427754	−	0.246964i	0.270635	−	0.962682i	$-0.412766\pi$
$787$	−12.0000	−	6.92820i	−0.427754	−	0.246964i	−0.698389	+	0.715718i	$0.746100\pi$
$788$		0			0
$789$		0			0
$790$	−10.0000	−	17.3205i	−0.355784	−	0.616236i
$791$	−25.7196	+	14.8492i	−0.914485	+	0.527978i
$792$		0			0
$793$	−4.00000	−	13.8564i	−0.142044	−	0.492055i
$794$	−46.5403			−1.65165
$795$		0			0
$796$		0			0
$797$	13.4722	−	23.3345i	0.477210	−	0.826551i	−0.522449	−	0.852670i	$-0.674982\pi$
$797$	13.4722	−	23.3345i	0.477210	−	0.826551i	0.999659	+	0.0261191i	$0.00831493\pi$
$798$		0			0
$799$	12.0000	+	6.92820i	0.424529	+	0.245102i
$800$		0			0
$801$		0			0
$802$	−14.0000	+	24.2487i	−0.494357	+	0.856252i
$803$		0			0
$804$		0			0
$805$	6.00000			0.211472
$806$	25.7196	+	6.36396i	0.905936	+	0.224161i
$807$		0			0
$808$	−30.0000	+	17.3205i	−1.05540	+	0.609333i
$809$	−24.4949	−	42.4264i	−0.861195	−	1.49163i	−0.870777	−	0.491679i	$-0.836383\pi$
$809$	−24.4949	−	42.4264i	−0.861195	−	1.49163i	0.00958183	−	0.999954i	$-0.496950\pi$
$810$		0			0
$811$		−	46.7654i		−	1.64215i	−0.570817	−	0.821077i	$-0.693374\pi$
$811$		−	46.7654i		−	1.64215i	0.570817	−	0.821077i	$-0.306626\pi$
$812$		0			0
$813$		0			0
$814$		−	3.46410i		−	0.121417i
$815$	1.22474	−	2.12132i	0.0429009	−	0.0743066i
$816$		0			0
$817$	−7.50000	+	4.33013i	−0.262392	+	0.151492i
$818$	41.6413			1.45595
$819$		0			0
$820$		0			0
$821$	−1.22474	+	0.707107i	−0.0427439	+	0.0246782i	−0.521220	−	0.853423i	$-0.674523\pi$
$821$	−1.22474	+	0.707107i	−0.0427439	+	0.0246782i	0.478476	+	0.878101i	$0.341189\pi$
$822$		0			0
$823$	21.5000	−	37.2391i	0.749443	−	1.29807i	−0.198647	−	0.980071i	$-0.563655\pi$
$823$	21.5000	−	37.2391i	0.749443	−	1.29807i	0.948090	−	0.318002i	$-0.103012\pi$
$824$		−	14.1421i		−	0.492665i
$825$		0			0
$826$	−12.0000	−	6.92820i	−0.417533	−	0.241063i
$827$		−	18.3848i		−	0.639301i	−0.947535	−	0.319651i	$-0.896434\pi$
$827$		−	18.3848i		−	0.639301i	0.947535	−	0.319651i	$-0.103566\pi$
$828$		0			0
$829$	−4.00000	−	6.92820i	−0.138926	−	0.240626i	0.788165	−	0.615465i	$-0.211032\pi$
$829$	−4.00000	−	6.92820i	−0.138926	−	0.240626i	−0.927090	+	0.374838i	$0.877698\pi$
$830$	17.1464	−	9.89949i	0.595161	−	0.343616i
$831$		0			0
$832$	−20.0000	+	20.7846i	−0.693375	+	0.720577i
$833$	−19.5959			−0.678958
$834$		0			0
$835$	−5.00000	−	8.66025i	−0.173032	−	0.299700i
$836$		0			0
$837$		0			0
$838$	24.0000	+	13.8564i	0.829066	+	0.478662i
$839$	−9.79796	−	5.65685i	−0.338263	−	0.195296i	0.321241	−	0.946998i	$-0.395900\pi$
$839$	−9.79796	−	5.65685i	−0.338263	−	0.195296i	−0.659504	+	0.751701i	$0.729234\pi$
$840$		0			0
$841$	−33.5000	+	58.0237i	−1.15517	+	2.00082i
$842$	−25.7196	−	44.5477i	−0.886357	−	1.53522i
$843$		0			0
$844$		0			0
$845$	−18.3712	+	0.707107i	−0.631988	+	0.0243252i
$846$		0			0
$847$	−13.5000	+	7.79423i	−0.463865	+	0.267813i
$848$		0			0
$849$		0			0
$850$			20.7846i			0.712906i
$851$	3.67423	+	2.12132i	0.125951	+	0.0727179i
$852$		0			0
$853$			5.19615i			0.177913i	0.996036	+	0.0889564i	$0.0283532\pi$
$853$			5.19615i			0.177913i	−0.996036	+	0.0889564i	$0.971647\pi$
$854$	−4.89898	+	8.48528i	−0.167640	+	0.290360i
$855$		0			0
$856$	42.0000	−	24.2487i	1.43553	−	0.828804i
$857$	−29.3939			−1.00408			−0.502038	−	0.864846i	$-0.667416\pi$
$857$	−29.3939			−1.00408			−0.502038	+	0.864846i	$0.667416\pi$
$858$		0			0
$859$	41.0000			1.39890			0.699451	−	0.714681i	$-0.253428\pi$
$859$	41.0000			1.39890			0.699451	+	0.714681i	$0.253428\pi$
$860$		0			0
$861$		0			0
$862$	25.0000	−	43.3013i	0.851503	−	1.47485i
$863$		−	43.8406i		−	1.49235i	−0.665749	−	0.746176i	$-0.731888\pi$
$863$		−	43.8406i		−	1.49235i	0.665749	−	0.746176i	$-0.268112\pi$
$864$		0			0
$865$	−6.00000	−	3.46410i	−0.204006	−	0.117783i
$866$			1.41421i			0.0480569i
$867$		0			0
$868$		0			0
$869$	12.2474	−	7.07107i	0.415466	−	0.239870i
$870$		0			0
$871$	6.00000	−	24.2487i	0.203302	−	0.821636i
$872$	−44.0908			−1.49310
$873$		0			0
$874$	−3.00000	−	5.19615i	−0.101477	−	0.175762i
$875$	9.79796	−	16.9706i	0.331231	−	0.573710i
$876$		0			0
$877$	28.5000	+	16.4545i	0.962377	+	0.555628i	0.896904	−	0.442226i	$-0.145811\pi$
$877$	28.5000	+	16.4545i	0.962377	+	0.555628i	0.0654729	+	0.997854i	$0.479144\pi$
$878$	−15.9217	−	9.19239i	−0.537331	−	0.310228i
$879$		0			0
$880$	−4.00000	+	6.92820i	−0.134840	+	0.233550i
$881$	−2.44949	−	4.24264i	−0.0825254	−	0.142938i	0.821809	−	0.569764i	$-0.192965\pi$
$881$	−2.44949	−	4.24264i	−0.0825254	−	0.142938i	−0.904334	+	0.426825i	$0.859632\pi$
$882$		0			0
$883$	−34.0000			−1.14419			−0.572096	−	0.820187i	$-0.693869\pi$
$883$	−34.0000			−1.14419			−0.572096	+	0.820187i	$0.693869\pi$
$884$		0			0
$885$		0			0
$886$	−18.0000	+	10.3923i	−0.604722	+	0.349136i
$887$	12.2474	+	21.2132i	0.411229	+	0.712270i	0.995024	−	0.0996312i	$-0.0317663\pi$
$887$	12.2474	+	21.2132i	0.411229	+	0.712270i	−0.583795	+	0.811901i	$0.698433\pi$
$888$		0			0
$889$			32.9090i			1.10373i
$890$	−17.1464	−	9.89949i	−0.574750	−	0.331832i
$891$		0			0
$892$		0			0
$893$	−2.44949	+	4.24264i	−0.0819690	+	0.141975i
$894$		0			0
$895$	−6.00000	+	3.46410i	−0.200558	+	0.115792i
$896$	19.5959			0.654654
$897$		0			0
$898$	−32.0000			−1.06785
$899$	44.0908	−	25.4558i	1.47051	−	0.849000i
$900$		0			0
$901$		0			0
$902$		−	14.1421i		−	0.470882i
$903$		0			0
$904$	42.0000	+	24.2487i	1.39690	+	0.806500i
$905$		−	15.5563i		−	0.517111i
$906$		0			0
$907$	−11.5000	−	19.9186i	−0.381851	−	0.661386i	0.609476	−	0.792805i	$-0.291380\pi$
$907$	−11.5000	−	19.9186i	−0.381851	−	0.661386i	−0.991327	+	0.131419i	$0.958047\pi$
$908$		0			0
$909$		0			0
$910$	9.00000	+	8.66025i	0.298347	+	0.287085i
$911$	36.7423			1.21733			0.608664	−	0.793428i	$-0.291706\pi$
$911$	36.7423			1.21733			0.608664	+	0.793428i	$0.291706\pi$
$912$		0			0
$913$	7.00000	+	12.1244i	0.231666	+	0.401258i
$914$	13.4722	−	23.3345i	0.445621	−	0.771837i
$915$		0			0
$916$		0			0
$917$	−22.0454	−	12.7279i	−0.728003	−	0.420313i
$918$		0			0
$919$	5.00000	−	8.66025i	0.164935	−	0.285675i	−0.771697	−	0.635990i	$-0.780592\pi$
$919$	5.00000	−	8.66025i	0.164935	−	0.285675i	0.936632	+	0.350315i	$0.113925\pi$
$920$	−4.89898	−	8.48528i	−0.161515	−	0.279751i
$921$		0			0
$922$	16.0000			0.526932
$923$	−53.8888	+	15.5563i	−1.77377	+	0.512043i
$924$		0			0
$925$	4.50000	−	2.59808i	0.147959	−	0.0854242i
$926$	14.6969	+	25.4558i	0.482971	+	0.836531i
$927$		0			0
$928$		0			0
$929$	23.2702	+	13.4350i	0.763469	+	0.440789i	0.830540	−	0.556959i	$-0.188032\pi$
$929$	23.2702	+	13.4350i	0.763469	+	0.440789i	−0.0670709	+	0.997748i	$0.521365\pi$
$930$		0			0
$931$		−	6.92820i		−	0.227063i
$932$		0			0
$933$		0			0
$934$	27.0000	−	15.5885i	0.883467	−	0.510070i
$935$	9.79796			0.320428
$936$		0			0
$937$	11.0000			0.359354			0.179677	−	0.983726i	$-0.442495\pi$
$937$	11.0000			0.359354			0.179677	+	0.983726i	$0.442495\pi$
$938$	−14.6969	+	8.48528i	−0.479872	+	0.277054i
$939$		0			0
$940$		0			0
$941$			24.0416i			0.783735i	0.920022	+	0.391867i	$0.128171\pi$
$941$			24.0416i			0.783735i	−0.920022	+	0.391867i	$0.871829\pi$
$942$		0			0
$943$	15.0000	+	8.66025i	0.488467	+	0.282017i
$944$			22.6274i			0.736460i
$945$		0			0
$946$	5.00000	+	8.66025i	0.162564	+	0.281569i
$947$	−34.2929	+	19.7990i	−1.11437	+	0.643381i	−0.939957	−	0.341292i	$-0.889135\pi$
$947$	−34.2929	+	19.7990i	−1.11437	+	0.643381i	−0.174411	+	0.984673i	$0.555802\pi$
$948$		0			0
$949$		0			0
$950$	−7.34847			−0.238416
$951$		0			0
$952$	−12.0000	−	20.7846i	−0.388922	−	0.673633i
$953$	2.44949	−	4.24264i	0.0793468	−	0.137433i	−0.823622	−	0.567140i	$-0.808050\pi$
$953$	2.44949	−	4.24264i	0.0793468	−	0.137433i	0.902968	+	0.429707i	$0.141383\pi$
$954$		0			0
$955$	21.0000	+	12.1244i	0.679544	+	0.392335i
$956$		0			0
$957$		0			0
$958$	−8.00000	+	13.8564i	−0.258468	+	0.447680i
$959$	12.2474	+	21.2132i	0.395491	+	0.685010i
$960$		0			0
$961$	4.00000			0.129032
$962$	2.44949	+	8.48528i	0.0789747	+	0.273576i
$963$		0			0
$964$		0			0
$965$	6.12372	+	10.6066i	0.197130	+	0.341439i
$966$		0			0
$967$		−	5.19615i		−	0.167097i	−0.996504	−	0.0835485i	$-0.973375\pi$
$967$		−	5.19615i		−	0.167097i	0.996504	−	0.0835485i	$-0.0266254\pi$
$968$	22.0454	+	12.7279i	0.708566	+	0.409091i
$969$		0			0
$970$		−	27.7128i		−	0.889805i
$971$	−19.5959	+	33.9411i	−0.628863	+	1.08922i	0.358917	+	0.933369i	$0.383146\pi$
$971$	−19.5959	+	33.9411i	−0.628863	+	1.08922i	−0.987780	+	0.155853i	$0.950187\pi$
$972$		0			0
$973$	−3.00000	+	1.73205i	−0.0961756	+	0.0555270i
$974$	−46.5403			−1.49125
$975$		0			0
$976$	16.0000			0.512148
$977$	39.1918	−	22.6274i	1.25386	−	0.723915i	0.281984	−	0.959419i	$-0.409007\pi$
$977$	39.1918	−	22.6274i	1.25386	−	0.723915i	0.971873	+	0.235504i	$0.0756740\pi$
$978$		0			0
$979$	7.00000	−	12.1244i	0.223721	−	0.387496i
$980$		0			0
$981$		0			0
$982$	24.0000	+	13.8564i	0.765871	+	0.442176i
$983$		−	9.89949i		−	0.315745i	−0.987460	−	0.157872i	$-0.949537\pi$
$983$		−	9.89949i		−	0.315745i	0.987460	−	0.157872i	$-0.0504635\pi$
$984$		0			0
$985$	7.00000	+	12.1244i	0.223039	+	0.386314i
$986$	−58.7878	+	33.9411i	−1.87218	+	1.08091i
$987$		0			0
$988$		0			0
$989$	−12.2474			−0.389446
$990$		0			0
$991$	−17.5000	−	30.3109i	−0.555906	−	0.962857i	−0.997832	−	0.0658059i	$-0.979038\pi$
$991$	−17.5000	−	30.3109i	−0.555906	−	0.962857i	0.441927	−	0.897051i	$-0.354295\pi$
$992$		0			0
$993$		0			0
$994$	33.0000	+	19.0526i	1.04670	+	0.604310i
$995$	31.8434	+	18.3848i	1.00950	+	0.582837i
$996$		0			0
$997$	6.50000	−	11.2583i	0.205857	−	0.356555i	−0.744548	−	0.667568i	$-0.767335\pi$
$997$	6.50000	−	11.2583i	0.205857	−	0.356555i	0.950405	+	0.311014i	$0.100668\pi$
$998$	14.6969	+	25.4558i	0.465223	+	0.805791i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.2.q.f.244.1	yes	4
3.2	odd	2	inner	351.2.q.f.244.2	yes	4
13.2	odd	12		4563.2.a.v.1.2		4
13.4	even	6	inner	351.2.q.f.82.1	✓	4
13.11	odd	12		4563.2.a.v.1.3		4
39.2	even	12		4563.2.a.v.1.4		4
39.11	even	12		4563.2.a.v.1.1		4
39.17	odd	6	inner	351.2.q.f.82.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
351.2.q.f.82.1	✓	4	13.4	even	6	inner
351.2.q.f.82.2	yes	4	39.17	odd	6	inner
351.2.q.f.244.1	yes	4	1.1	even	1	trivial
351.2.q.f.244.2	yes	4	3.2	odd	2	inner
4563.2.a.v.1.1		4	39.11	even	12
4563.2.a.v.1.2		4	13.2	odd	12
4563.2.a.v.1.3		4	13.11	odd	12
4563.2.a.v.1.4		4	39.2	even	12

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:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	351.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 0.707107i) q^{2} -1.41421i q^{5} +(1.50000 + 0.866025i) q^{7} -2.82843i q^{8} +(1.00000 + 1.73205i) q^{10} +(-1.22474 + 0.707107i) q^{11} +(2.50000 - 2.59808i) q^{13} -2.44949 q^{14} +(2.00000 + 3.46410i) q^{16} +(2.44949 - 4.24264i) q^{17} +(1.50000 + 0.866025i) q^{19} +(1.00000 - 1.73205i) q^{22} +(1.22474 + 2.12132i) q^{23} +3.00000 q^{25} +(-1.22474 + 4.94975i) q^{26} +(4.89898 + 8.48528i) q^{29} -5.19615i q^{31} +6.92820i q^{34} +(1.22474 - 2.12132i) q^{35} +(1.50000 - 0.866025i) q^{37} -2.44949 q^{38} -4.00000 q^{40} +(6.12372 - 3.53553i) q^{41} +(-2.50000 + 4.33013i) q^{43} +(-3.00000 - 1.73205i) q^{46} +2.82843i q^{47} +(-2.00000 - 3.46410i) q^{49} +(-3.67423 + 2.12132i) q^{50} +(1.00000 + 1.73205i) q^{55} +(2.44949 - 4.24264i) q^{56} +(-12.0000 - 6.92820i) q^{58} +(4.89898 + 2.82843i) q^{59} +(2.00000 - 3.46410i) q^{61} +(3.67423 + 6.36396i) q^{62} -8.00000 q^{64} +(-3.67423 - 3.53553i) q^{65} +(6.00000 - 3.46410i) q^{67} +3.46410i q^{70} +(-13.4722 - 7.77817i) q^{71} +(-1.22474 + 2.12132i) q^{74} -2.44949 q^{77} -10.0000 q^{79} +(4.89898 - 2.82843i) q^{80} +(-5.00000 + 8.66025i) q^{82} -9.89949i q^{83} +(-6.00000 - 3.46410i) q^{85} -7.07107i q^{86} +(2.00000 + 3.46410i) q^{88} +(-8.57321 + 4.94975i) q^{89} +(6.00000 - 1.73205i) q^{91} +(-2.00000 - 3.46410i) q^{94} +(1.22474 - 2.12132i) q^{95} +(-12.0000 - 6.92820i) q^{97} +(4.89898 + 2.82843i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{7} + 4 q^{10} + 10 q^{13} + 8 q^{16} + 6 q^{19} + 4 q^{22} + 12 q^{25} + 6 q^{37} - 16 q^{40} - 10 q^{43} - 12 q^{46} - 8 q^{49} + 4 q^{55} - 48 q^{58} + 8 q^{61} - 32 q^{64} + 24 q^{67} - 40 q^{79}+ \cdots - 48 q^{97}+O(q^{100}) \) 4 * q + 6 * q^7 + 4 * q^10 + 10 * q^13 + 8 * q^16 + 6 * q^19 + 4 * q^22 + 12 * q^25 + 6 * q^37 - 16 * q^40 - 10 * q^43 - 12 * q^46 - 8 * q^49 + 4 * q^55 - 48 * q^58 + 8 * q^61 - 32 * q^64 + 24 * q^67 - 40 * q^79 - 20 * q^82 - 24 * q^85 + 8 * q^88 + 24 * q^91 - 8 * q^94 - 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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