LMFDB - Embedded newform 840.2.bg.h.361.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(121,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.121"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.bg (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-2,0,2,0,0] 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:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{7})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 49 $ x^4 + 7*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$1.32288 - 2.29129i$ of defining polynomial
Character	$\chi$	$=$	840.361
Dual form			840.2.bg.h.121.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-1.32288 - 2.29129i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(0.822876 - 1.42526i) q^{11} +0.645751 q^{13} -1.00000 q^{15} +(2.82288 - 4.88936i) q^{17} +(-0.500000 - 0.866025i) q^{19} +2.64575 q^{21} +(-0.822876 - 1.42526i) q^{23} +(-0.500000 + 0.866025i) q^{25} +1.00000 q^{27} +3.64575 q^{29} +(2.50000 - 4.33013i) q^{31} +(0.822876 + 1.42526i) q^{33} +(1.32288 - 2.29129i) q^{35} +(1.32288 + 2.29129i) q^{37} +(-0.322876 + 0.559237i) q^{39} +8.93725 q^{41} +0.645751 q^{43} +(0.500000 - 0.866025i) q^{45} +(-4.29150 - 7.43310i) q^{47} +(-3.50000 + 6.06218i) q^{49} +(2.82288 + 4.88936i) q^{51} +(-0.354249 + 0.613577i) q^{53} +1.64575 q^{55} +1.00000 q^{57} +(3.82288 - 6.62141i) q^{59} +(7.29150 + 12.6293i) q^{61} +(-1.32288 + 2.29129i) q^{63} +(0.322876 + 0.559237i) q^{65} +(2.96863 - 5.14181i) q^{67} +1.64575 q^{69} -6.35425 q^{71} +(6.32288 - 10.9515i) q^{73} +(-0.500000 - 0.866025i) q^{75} -4.35425 q^{77} +(6.50000 + 11.2583i) q^{79} +(-0.500000 + 0.866025i) q^{81} -2.93725 q^{83} +5.64575 q^{85} +(-1.82288 + 3.15731i) q^{87} +(-5.46863 - 9.47194i) q^{89} +(-0.854249 - 1.47960i) q^{91} +(2.50000 + 4.33013i) q^{93} +(0.500000 - 0.866025i) q^{95} -14.5830 q^{97} -1.64575 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 2 q^{5} - 2 q^{9} - 2 q^{11} - 8 q^{13} - 4 q^{15} + 6 q^{17} - 2 q^{19} + 2 q^{23} - 2 q^{25} + 4 q^{27} + 4 q^{29} + 10 q^{31} - 2 q^{33} + 4 q^{39} + 4 q^{41} - 8 q^{43} + 2 q^{45} + 4 q^{47}+ \cdots + 4 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 + 2 * q^5 - 2 * q^9 - 2 * q^11 - 8 * q^13 - 4 * q^15 + 6 * q^17 - 2 * q^19 + 2 * q^23 - 2 * q^25 + 4 * q^27 + 4 * q^29 + 10 * q^31 - 2 * q^33 + 4 * q^39 + 4 * q^41 - 8 * q^43 + 2 * q^45 + 4 * q^47 - 14 * q^49 + 6 * q^51 - 12 * q^53 - 4 * q^55 + 4 * q^57 + 10 * q^59 + 8 * q^61 - 4 * q^65 - 4 * q^67 - 4 * q^69 - 36 * q^71 + 20 * q^73 - 2 * q^75 - 28 * q^77 + 26 * q^79 - 2 * q^81 + 20 * q^83 + 12 * q^85 - 2 * q^87 - 6 * q^89 - 14 * q^91 + 10 * q^93 + 2 * q^95 - 16 * q^97 + 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$	$1$

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			0
$2$		0			0
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	−1.32288	−	2.29129i	−0.500000	−	0.866025i
$7$	−1.32288	−	2.29129i	−0.500000	−	0.866025i
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	0.822876	−	1.42526i	0.248106	−	0.429733i	−0.714894	−	0.699233i	$-0.753525\pi$
$11$	0.822876	−	1.42526i	0.248106	−	0.429733i	0.963000	+	0.269500i	$0.0868584\pi$
$12$		0			0
$13$	0.645751			0.179099			0.0895496	−	0.995982i	$-0.471457\pi$
$13$	0.645751			0.179099			0.0895496	+	0.995982i	$0.471457\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$		0			0
$17$	2.82288	−	4.88936i	0.684648	−	1.18584i	−0.288899	−	0.957359i	$-0.593289\pi$
$17$	2.82288	−	4.88936i	0.684648	−	1.18584i	0.973547	−	0.228486i	$-0.0733774\pi$
$18$		0			0
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	0.802955	−	0.596040i	$-0.203260\pi$
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	−0.917663	+	0.397360i	$0.869927\pi$
$20$		0			0
$21$	2.64575			0.577350
$22$		0			0
$23$	−0.822876	−	1.42526i	−0.171581	−	0.297188i	0.767391	−	0.641179i	$-0.221554\pi$
$23$	−0.822876	−	1.42526i	−0.171581	−	0.297188i	−0.938973	+	0.343991i	$0.888221\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	3.64575			0.676999			0.338500	−	0.940967i	$-0.390081\pi$
$29$	3.64575			0.676999			0.338500	+	0.940967i	$0.390081\pi$
$30$		0			0
$31$	2.50000	−	4.33013i	0.449013	−	0.777714i	−0.549309	−	0.835619i	$-0.685109\pi$
$31$	2.50000	−	4.33013i	0.449013	−	0.777714i	0.998322	+	0.0579057i	$0.0184423\pi$
$32$		0			0
$33$	0.822876	+	1.42526i	0.143244	+	0.248106i
$34$		0			0
$35$	1.32288	−	2.29129i	0.223607	−	0.387298i
$36$		0			0
$37$	1.32288	+	2.29129i	0.217479	+	0.376685i	0.954037	−	0.299690i	$-0.0968832\pi$
$37$	1.32288	+	2.29129i	0.217479	+	0.376685i	−0.736557	+	0.676375i	$0.763550\pi$
$38$		0			0
$39$	−0.322876	+	0.559237i	−0.0517015	+	0.0895496i
$40$		0			0
$41$	8.93725			1.39576			0.697882	−	0.716212i	$-0.254126\pi$
$41$	8.93725			1.39576			0.697882	+	0.716212i	$0.254126\pi$
$42$		0			0
$43$	0.645751			0.0984762			0.0492381	−	0.998787i	$-0.484321\pi$
$43$	0.645751			0.0984762			0.0492381	+	0.998787i	$0.484321\pi$
$44$		0			0
$45$	0.500000	−	0.866025i	0.0745356	−	0.129099i
$46$		0			0
$47$	−4.29150	−	7.43310i	−0.625980	−	1.08423i	−0.988350	−	0.152195i	$-0.951366\pi$
$47$	−4.29150	−	7.43310i	−0.625980	−	1.08423i	0.362370	−	0.932034i	$-0.381968\pi$
$48$		0			0
$49$	−3.50000	+	6.06218i	−0.500000	+	0.866025i
$50$		0			0
$51$	2.82288	+	4.88936i	0.395282	+	0.684648i
$52$		0			0
$53$	−0.354249	+	0.613577i	−0.0486598	+	0.0842812i	−0.889329	−	0.457267i	$-0.848828\pi$
$53$	−0.354249	+	0.613577i	−0.0486598	+	0.0842812i	0.840670	+	0.541548i	$0.182162\pi$
$54$		0			0
$55$	1.64575			0.221913
$56$		0			0
$57$	1.00000			0.132453
$58$		0			0
$59$	3.82288	−	6.62141i	0.497696	−	0.862035i	−0.502300	−	0.864693i	$-0.667513\pi$
$59$	3.82288	−	6.62141i	0.497696	−	0.862035i	0.999996	+	0.00265837i	$0.000846186\pi$
$60$		0			0
$61$	7.29150	+	12.6293i	0.933581	+	1.61701i	0.777145	+	0.629322i	$0.216667\pi$
$61$	7.29150	+	12.6293i	0.933581	+	1.61701i	0.156437	+	0.987688i	$0.449999\pi$
$62$		0			0
$63$	−1.32288	+	2.29129i	−0.166667	+	0.288675i
$64$		0			0
$65$	0.322876	+	0.559237i	0.0400478	+	0.0693648i
$66$		0			0
$67$	2.96863	−	5.14181i	0.362676	−	0.628172i	−0.625725	−	0.780044i	$-0.715197\pi$
$67$	2.96863	−	5.14181i	0.362676	−	0.628172i	0.988400	+	0.151872i	$0.0485300\pi$
$68$		0			0
$69$	1.64575			0.198125
$70$		0			0
$71$	−6.35425			−0.754111			−0.377055	−	0.926191i	$-0.623063\pi$
$71$	−6.35425			−0.754111			−0.377055	+	0.926191i	$0.623063\pi$
$72$		0			0
$73$	6.32288	−	10.9515i	0.740037	−	1.28178i	−0.212441	−	0.977174i	$-0.568141\pi$
$73$	6.32288	−	10.9515i	0.740037	−	1.28178i	0.952478	−	0.304607i	$-0.0985252\pi$
$74$		0			0
$75$	−0.500000	−	0.866025i	−0.0577350	−	0.100000i
$76$		0			0
$77$	−4.35425			−0.496213
$78$		0			0
$79$	6.50000	+	11.2583i	0.731307	+	1.26666i	0.956325	+	0.292306i	$0.0944227\pi$
$79$	6.50000	+	11.2583i	0.731307	+	1.26666i	−0.225018	+	0.974355i	$0.572244\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−2.93725			−0.322406			−0.161203	−	0.986921i	$-0.551537\pi$
$83$	−2.93725			−0.322406			−0.161203	+	0.986921i	$0.551537\pi$
$84$		0			0
$85$	5.64575			0.612368
$86$		0			0
$87$	−1.82288	+	3.15731i	−0.195433	+	0.338500i
$88$		0			0
$89$	−5.46863	−	9.47194i	−0.579673	−	1.00402i	−0.995517	−	0.0945873i	$-0.969847\pi$
$89$	−5.46863	−	9.47194i	−0.579673	−	1.00402i	0.415843	−	0.909436i	$-0.363486\pi$
$90$		0			0
$91$	−0.854249	−	1.47960i	−0.0895496	−	0.155104i
$92$		0			0
$93$	2.50000	+	4.33013i	0.259238	+	0.449013i
$94$		0			0
$95$	0.500000	−	0.866025i	0.0512989	−	0.0888523i
$96$		0			0
$97$	−14.5830			−1.48068			−0.740340	−	0.672233i	$-0.765335\pi$
$97$	−14.5830			−1.48068			−0.740340	+	0.672233i	$0.765335\pi$
$98$		0			0
$99$	−1.64575			−0.165404
$100$		0			0
$101$	8.46863	−	14.6681i	0.842660	−	1.45953i	−0.0449782	−	0.998988i	$-0.514322\pi$
$101$	8.46863	−	14.6681i	0.842660	−	1.45953i	0.887638	−	0.460542i	$-0.152345\pi$
$102$		0			0
$103$	−0.677124	−	1.17281i	−0.0667190	−	0.115561i	0.830736	−	0.556666i	$-0.187920\pi$
$103$	−0.677124	−	1.17281i	−0.0667190	−	0.115561i	−0.897455	+	0.441106i	$0.854586\pi$
$104$		0			0
$105$	1.32288	+	2.29129i	0.129099	+	0.223607i
$106$		0			0
$107$	−6.11438	−	10.5904i	−0.591099	−	1.02381i	−0.994085	−	0.108608i	$-0.965361\pi$
$107$	−6.11438	−	10.5904i	−0.591099	−	1.02381i	0.402985	−	0.915206i	$-0.367973\pi$
$108$		0			0
$109$	−0.791503	+	1.37092i	−0.0758122	+	0.131311i	−0.901439	−	0.432906i	$-0.857488\pi$
$109$	−0.791503	+	1.37092i	−0.0758122	+	0.131311i	0.825627	+	0.564216i	$0.190822\pi$
$110$		0			0
$111$	−2.64575			−0.251124
$112$		0			0
$113$	2.00000			0.188144			0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000			0.188144			0.0940721	+	0.995565i	$0.470012\pi$
$114$		0			0
$115$	0.822876	−	1.42526i	0.0767336	−	0.132906i
$116$		0			0
$117$	−0.322876	−	0.559237i	−0.0298499	−	0.0517015i
$118$		0			0
$119$	−14.9373			−1.36930
$120$		0			0
$121$	4.14575	+	7.18065i	0.376886	+	0.652787i
$122$		0			0
$123$	−4.46863	+	7.73989i	−0.402923	+	0.697882i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−7.22876			−0.641448			−0.320724	−	0.947173i	$-0.603926\pi$
$127$	−7.22876			−0.641448			−0.320724	+	0.947173i	$0.603926\pi$
$128$		0			0
$129$	−0.322876	+	0.559237i	−0.0284276	+	0.0492381i
$130$		0			0
$131$	4.64575	+	8.04668i	0.405901	+	0.703041i	0.994426	−	0.105438i	$-0.0336244\pi$
$131$	4.64575	+	8.04668i	0.405901	+	0.703041i	−0.588525	+	0.808479i	$0.700291\pi$
$132$		0			0
$133$	−1.32288	+	2.29129i	−0.114708	+	0.198680i
$134$		0			0
$135$	0.500000	+	0.866025i	0.0430331	+	0.0745356i
$136$		0			0
$137$	−1.17712	+	2.03884i	−0.100569	+	0.174190i	−0.911919	−	0.410370i	$-0.865399\pi$
$137$	−1.17712	+	2.03884i	−0.100569	+	0.174190i	0.811351	+	0.584560i	$0.198733\pi$
$138$		0			0
$139$	−3.70850			−0.314551			−0.157275	−	0.987555i	$-0.550271\pi$
$139$	−3.70850			−0.314551			−0.157275	+	0.987555i	$0.550271\pi$
$140$		0			0
$141$	8.58301			0.722819
$142$		0			0
$143$	0.531373	−	0.920365i	0.0444356	−	0.0769648i
$144$		0			0
$145$	1.82288	+	3.15731i	0.151382	+	0.262201i
$146$		0			0
$147$	−3.50000	−	6.06218i	−0.288675	−	0.500000i
$148$		0			0
$149$	−3.29150	−	5.70105i	−0.269650	−	0.467048i	0.699121	−	0.715003i	$-0.253575\pi$
$149$	−3.29150	−	5.70105i	−0.269650	−	0.467048i	−0.968772	+	0.247955i	$0.920241\pi$
$150$		0			0
$151$	−8.29150	+	14.3613i	−0.674753	+	1.16871i	0.301788	+	0.953375i	$0.402416\pi$
$151$	−8.29150	+	14.3613i	−0.674753	+	1.16871i	−0.976541	+	0.215331i	$0.930917\pi$
$152$		0			0
$153$	−5.64575			−0.456432
$154$		0			0
$155$	5.00000			0.401610
$156$		0			0
$157$	−5.93725	+	10.2836i	−0.473844	+	0.820723i	−0.999552	−	0.0299429i	$-0.990467\pi$
$157$	−5.93725	+	10.2836i	−0.473844	+	0.820723i	0.525707	+	0.850666i	$0.323801\pi$
$158$		0			0
$159$	−0.354249	−	0.613577i	−0.0280937	−	0.0486598i
$160$		0			0
$161$	−2.17712	+	3.77089i	−0.171581	+	0.297188i
$162$		0			0
$163$	4.00000	+	6.92820i	0.313304	+	0.542659i	0.979076	−	0.203497i	$-0.0652307\pi$
$163$	4.00000	+	6.92820i	0.313304	+	0.542659i	−0.665771	+	0.746156i	$0.731897\pi$
$164$		0			0
$165$	−0.822876	+	1.42526i	−0.0640608	+	0.110957i
$166$		0			0
$167$	−17.5203			−1.35576			−0.677879	−	0.735173i	$-0.737101\pi$
$167$	−17.5203			−1.35576			−0.677879	+	0.735173i	$0.737101\pi$
$168$		0			0
$169$	−12.5830			−0.967923
$170$		0			0
$171$	−0.500000	+	0.866025i	−0.0382360	+	0.0662266i
$172$		0			0
$173$	0.354249	+	0.613577i	0.0269330	+	0.0466494i	0.879178	−	0.476494i	$-0.158093\pi$
$173$	0.354249	+	0.613577i	0.0269330	+	0.0466494i	−0.852245	+	0.523143i	$0.824759\pi$
$174$		0			0
$175$	2.64575			0.200000
$176$		0			0
$177$	3.82288	+	6.62141i	0.287345	+	0.497696i
$178$		0			0
$179$	−3.00000	+	5.19615i	−0.224231	+	0.388379i	−0.956088	−	0.293079i	$-0.905320\pi$
$179$	−3.00000	+	5.19615i	−0.224231	+	0.388379i	0.731858	+	0.681457i	$0.238654\pi$
$180$		0			0
$181$	−20.2915			−1.50826			−0.754128	−	0.656728i	$-0.771940\pi$
$181$	−20.2915			−1.50826			−0.754128	+	0.656728i	$0.771940\pi$
$182$		0			0
$183$	−14.5830			−1.07801
$184$		0			0
$185$	−1.32288	+	2.29129i	−0.0972598	+	0.168459i
$186$		0			0
$187$	−4.64575	−	8.04668i	−0.339731	−	0.588431i
$188$		0			0
$189$	−1.32288	−	2.29129i	−0.0962250	−	0.166667i
$190$		0			0
$191$	10.2915	+	17.8254i	0.744667	+	1.28980i	0.950350	+	0.311182i	$0.100725\pi$
$191$	10.2915	+	17.8254i	0.744667	+	1.28980i	−0.205683	+	0.978619i	$0.565942\pi$
$192$		0			0
$193$	4.96863	−	8.60591i	0.357650	−	0.619467i	−0.629918	−	0.776662i	$-0.716912\pi$
$193$	4.96863	−	8.60591i	0.357650	−	0.619467i	0.987568	+	0.157194i	$0.0502449\pi$
$194$		0			0
$195$	−0.645751			−0.0462432
$196$		0			0
$197$	7.06275			0.503200			0.251600	−	0.967831i	$-0.419043\pi$
$197$	7.06275			0.503200			0.251600	+	0.967831i	$0.419043\pi$
$198$		0			0
$199$	−2.29150	+	3.96900i	−0.162440	+	0.281355i	−0.935743	−	0.352682i	$-0.885270\pi$
$199$	−2.29150	+	3.96900i	−0.162440	+	0.281355i	0.773303	+	0.634037i	$0.218603\pi$
$200$		0			0
$201$	2.96863	+	5.14181i	0.209391	+	0.362676i
$202$		0			0
$203$	−4.82288	−	8.35347i	−0.338500	−	0.586298i
$204$		0			0
$205$	4.46863	+	7.73989i	0.312102	+	0.540577i
$206$		0			0
$207$	−0.822876	+	1.42526i	−0.0571938	+	0.0990626i
$208$		0			0
$209$	−1.64575			−0.113839
$210$		0			0
$211$	16.5830			1.14162			0.570811	−	0.821082i	$-0.306629\pi$
$211$	16.5830			1.14162			0.570811	+	0.821082i	$0.306629\pi$
$212$		0			0
$213$	3.17712	−	5.50294i	0.217693	−	0.377055i
$214$		0			0
$215$	0.322876	+	0.559237i	0.0220199	+	0.0381396i
$216$		0			0
$217$	−13.2288			−0.898027
$218$		0			0
$219$	6.32288	+	10.9515i	0.427260	+	0.740037i
$220$		0			0
$221$	1.82288	−	3.15731i	0.122620	−	0.212384i
$222$		0			0
$223$	3.29150			0.220415			0.110208	−	0.993909i	$-0.464848\pi$
$223$	3.29150			0.220415			0.110208	+	0.993909i	$0.464848\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	3.46863	−	6.00784i	0.230221	−	0.398754i	−0.727652	−	0.685946i	$-0.759388\pi$
$227$	3.46863	−	6.00784i	0.230221	−	0.398754i	0.957873	+	0.287192i	$0.0927218\pi$
$228$		0			0
$229$	−3.79150	−	6.56708i	−0.250550	−	0.433965i	0.713128	−	0.701034i	$-0.247278\pi$
$229$	−3.79150	−	6.56708i	−0.250550	−	0.433965i	−0.963677	+	0.267070i	$0.913945\pi$
$230$		0			0
$231$	2.17712	−	3.77089i	0.143244	−	0.248106i
$232$		0			0
$233$	−4.64575	−	8.04668i	−0.304353	−	0.527155i	0.672764	−	0.739857i	$-0.265107\pi$
$233$	−4.64575	−	8.04668i	−0.304353	−	0.527155i	−0.977117	+	0.212702i	$0.931774\pi$
$234$		0			0
$235$	4.29150	−	7.43310i	0.279947	−	0.484882i
$236$		0			0
$237$	−13.0000			−0.844441
$238$		0			0
$239$	−8.58301			−0.555188			−0.277594	−	0.960698i	$-0.589537\pi$
$239$	−8.58301			−0.555188			−0.277594	+	0.960698i	$0.589537\pi$
$240$		0			0
$241$	−8.93725	+	15.4798i	−0.575699	+	0.997140i	0.420266	+	0.907401i	$0.361937\pi$
$241$	−8.93725	+	15.4798i	−0.575699	+	0.997140i	−0.995965	+	0.0897393i	$0.971397\pi$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$		0			0
$245$	−7.00000			−0.447214
$246$		0			0
$247$	−0.322876	−	0.559237i	−0.0205441	−	0.0355834i
$248$		0			0
$249$	1.46863	−	2.54374i	0.0930705	−	0.161203i
$250$		0			0
$251$	28.8118			1.81858			0.909291	−	0.416161i	$-0.136625\pi$
$251$	28.8118			1.81858			0.909291	+	0.416161i	$0.136625\pi$
$252$		0			0
$253$	−2.70850			−0.170282
$254$		0			0
$255$	−2.82288	+	4.88936i	−0.176775	+	0.306184i
$256$		0			0
$257$	9.11438	+	15.7866i	0.568539	+	0.984739i	0.996711	+	0.0810414i	$0.0258246\pi$
$257$	9.11438	+	15.7866i	0.568539	+	0.984739i	−0.428171	+	0.903698i	$0.640842\pi$
$258$		0			0
$259$	3.50000	−	6.06218i	0.217479	−	0.376685i
$260$		0			0
$261$	−1.82288	−	3.15731i	−0.112833	−	0.195433i
$262$		0			0
$263$	−14.9373	+	25.8721i	−0.921071	+	1.59534i	−0.123309	+	0.992368i	$0.539351\pi$
$263$	−14.9373	+	25.8721i	−0.921071	+	1.59534i	−0.797762	+	0.602973i	$0.793983\pi$
$264$		0			0
$265$	−0.708497			−0.0435226
$266$		0			0
$267$	10.9373			0.669349
$268$		0			0
$269$	12.6458	−	21.9031i	0.771025	−	1.33545i	−0.165977	−	0.986130i	$-0.553078\pi$
$269$	12.6458	−	21.9031i	0.771025	−	1.33545i	0.937002	−	0.349325i	$-0.113589\pi$
$270$		0			0
$271$	1.00000	+	1.73205i	0.0607457	+	0.105215i	0.894799	−	0.446469i	$-0.147319\pi$
$271$	1.00000	+	1.73205i	0.0607457	+	0.105215i	−0.834053	+	0.551684i	$0.813985\pi$
$272$		0			0
$273$	1.70850			0.103403
$274$		0			0
$275$	0.822876	+	1.42526i	0.0496213	+	0.0859466i
$276$		0			0
$277$	−9.90588	+	17.1575i	−0.595187	+	1.03089i	0.398334	+	0.917241i	$0.369589\pi$
$277$	−9.90588	+	17.1575i	−0.595187	+	1.03089i	−0.993520	+	0.113653i	$0.963745\pi$
$278$		0			0
$279$	−5.00000			−0.299342
$280$		0			0
$281$	12.0000			0.715860			0.357930	−	0.933748i	$-0.383483\pi$
$281$	12.0000			0.715860			0.357930	+	0.933748i	$0.383483\pi$
$282$		0			0
$283$	13.9059	−	24.0857i	0.826619	−	1.43175i	−0.0740570	−	0.997254i	$-0.523595\pi$
$283$	13.9059	−	24.0857i	0.826619	−	1.43175i	0.900676	−	0.434492i	$-0.143072\pi$
$284$		0			0
$285$	0.500000	+	0.866025i	0.0296174	+	0.0512989i
$286$		0			0
$287$	−11.8229	−	20.4778i	−0.697882	−	1.20877i
$288$		0			0
$289$	−7.43725	−	12.8817i	−0.437486	−	0.757747i
$290$		0			0
$291$	7.29150	−	12.6293i	0.427435	−	0.740340i
$292$		0			0
$293$	−24.0000			−1.40209			−0.701047	−	0.713115i	$-0.747284\pi$
$293$	−24.0000			−1.40209			−0.701047	+	0.713115i	$0.747284\pi$
$294$		0			0
$295$	7.64575			0.445153
$296$		0			0
$297$	0.822876	−	1.42526i	0.0477481	−	0.0827021i
$298$		0			0
$299$	−0.531373	−	0.920365i	−0.0307301	−	0.0532261i
$300$		0			0
$301$	−0.854249	−	1.47960i	−0.0492381	−	0.0852828i
$302$		0			0
$303$	8.46863	+	14.6681i	0.486510	+	0.842660i
$304$		0			0
$305$	−7.29150	+	12.6293i	−0.417510	+	0.723149i
$306$		0			0
$307$	−4.06275			−0.231873			−0.115937	−	0.993257i	$-0.536987\pi$
$307$	−4.06275			−0.231873			−0.115937	+	0.993257i	$0.536987\pi$
$308$		0			0
$309$	1.35425			0.0770405
$310$		0			0
$311$	9.17712	−	15.8952i	0.520387	−	0.901337i	−0.479332	−	0.877634i	$-0.659121\pi$
$311$	9.17712	−	15.8952i	0.520387	−	0.901337i	0.999719	−	0.0237031i	$-0.00754563\pi$
$312$		0			0
$313$	2.38562	+	4.13202i	0.134843	+	0.233555i	0.925538	−	0.378656i	$-0.123614\pi$
$313$	2.38562	+	4.13202i	0.134843	+	0.233555i	−0.790694	+	0.612211i	$0.790280\pi$
$314$		0			0
$315$	−2.64575			−0.149071
$316$		0			0
$317$	2.11438	+	3.66221i	0.118755	+	0.205690i	0.919275	−	0.393617i	$-0.128776\pi$
$317$	2.11438	+	3.66221i	0.118755	+	0.205690i	−0.800519	+	0.599307i	$0.795443\pi$
$318$		0			0
$319$	3.00000	−	5.19615i	0.167968	−	0.290929i
$320$		0			0
$321$	12.2288			0.682543
$322$		0			0
$323$	−5.64575			−0.314138
$324$		0			0
$325$	−0.322876	+	0.559237i	−0.0179099	+	0.0310209i
$326$		0			0
$327$	−0.791503	−	1.37092i	−0.0437702	−	0.0758122i
$328$		0			0
$329$	−11.3542	+	19.6661i	−0.625980	+	1.08423i
$330$		0			0
$331$	11.1458	+	19.3050i	0.612626	+	1.06110i	0.990796	+	0.135363i	$0.0432201\pi$
$331$	11.1458	+	19.3050i	0.612626	+	1.06110i	−0.378170	+	0.925736i	$0.623447\pi$
$332$		0			0
$333$	1.32288	−	2.29129i	0.0724931	−	0.125562i
$334$		0			0
$335$	5.93725			0.324387
$336$		0			0
$337$	2.06275			0.112365			0.0561825	−	0.998421i	$-0.482107\pi$
$337$	2.06275			0.112365			0.0561825	+	0.998421i	$0.482107\pi$
$338$		0			0
$339$	−1.00000	+	1.73205i	−0.0543125	+	0.0940721i
$340$		0			0
$341$	−4.11438	−	7.12631i	−0.222806	−	0.385911i
$342$		0			0
$343$	18.5203			1.00000
$344$		0			0
$345$	0.822876	+	1.42526i	0.0443021	+	0.0767336i
$346$		0			0
$347$	−2.70850	+	4.69126i	−0.145400	+	0.251840i	−0.929522	−	0.368767i	$-0.879780\pi$
$347$	−2.70850	+	4.69126i	−0.145400	+	0.251840i	0.784122	+	0.620606i	$0.213113\pi$
$348$		0			0
$349$	−15.1660			−0.811818			−0.405909	−	0.913914i	$-0.633045\pi$
$349$	−15.1660			−0.811818			−0.405909	+	0.913914i	$0.633045\pi$
$350$		0			0
$351$	0.645751			0.0344677
$352$		0			0
$353$	6.17712	−	10.6991i	0.328775	−	0.569455i	−0.653494	−	0.756932i	$-0.726698\pi$
$353$	6.17712	−	10.6991i	0.328775	−	0.569455i	0.982269	+	0.187476i	$0.0600308\pi$
$354$		0			0
$355$	−3.17712	−	5.50294i	−0.168624	−	0.292066i
$356$		0			0
$357$	7.46863	−	12.9360i	0.395282	−	0.684648i
$358$		0			0
$359$	15.1144	+	26.1789i	0.797706	+	1.38167i	0.921106	+	0.389311i	$0.127287\pi$
$359$	15.1144	+	26.1789i	0.797706	+	1.38167i	−0.123400	+	0.992357i	$0.539380\pi$
$360$		0			0
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$		0			0
$363$	−8.29150			−0.435191
$364$		0			0
$365$	12.6458			0.661909
$366$		0			0
$367$	−1.03137	+	1.78639i	−0.0538372	+	0.0932488i	−0.891688	−	0.452650i	$-0.850479\pi$
$367$	−1.03137	+	1.78639i	−0.0538372	+	0.0932488i	0.837851	+	0.545899i	$0.183812\pi$
$368$		0			0
$369$	−4.46863	−	7.73989i	−0.232627	−	0.402923i
$370$		0			0
$371$	1.87451			0.0973196
$372$		0			0
$373$	7.03137	+	12.1787i	0.364071	+	0.630589i	0.988627	−	0.150391i	$-0.0480533\pi$
$373$	7.03137	+	12.1787i	0.364071	+	0.630589i	−0.624556	+	0.780980i	$0.714720\pi$
$374$		0			0
$375$	0.500000	−	0.866025i	0.0258199	−	0.0447214i
$376$		0			0
$377$	2.35425			0.121250
$378$		0			0
$379$	14.1660			0.727659			0.363830	−	0.931466i	$-0.381469\pi$
$379$	14.1660			0.727659			0.363830	+	0.931466i	$0.381469\pi$
$380$		0			0
$381$	3.61438	−	6.26029i	0.185170	−	0.320724i
$382$		0			0
$383$	10.9373	+	18.9439i	0.558868	+	0.967987i	0.997591	+	0.0693651i	$0.0220973\pi$
$383$	10.9373	+	18.9439i	0.558868	+	0.967987i	−0.438724	+	0.898622i	$0.644569\pi$
$384$		0			0
$385$	−2.17712	−	3.77089i	−0.110957	−	0.192182i
$386$		0			0
$387$	−0.322876	−	0.559237i	−0.0164127	−	0.0284276i
$388$		0			0
$389$	9.40588	−	16.2915i	0.476897	−	0.826010i	−0.522752	−	0.852485i	$-0.675095\pi$
$389$	9.40588	−	16.2915i	0.476897	−	0.826010i	0.999649	+	0.0264746i	$0.00842810\pi$
$390$		0			0
$391$	−9.29150			−0.469891
$392$		0			0
$393$	−9.29150			−0.468694
$394$		0			0
$395$	−6.50000	+	11.2583i	−0.327050	+	0.566468i
$396$		0			0
$397$	15.3229	+	26.5400i	0.769033	+	1.33200i	0.938088	+	0.346398i	$0.112595\pi$
$397$	15.3229	+	26.5400i	0.769033	+	1.33200i	−0.169055	+	0.985607i	$0.554071\pi$
$398$		0			0
$399$	−1.32288	−	2.29129i	−0.0662266	−	0.114708i
$400$		0			0
$401$	−10.3542	−	17.9341i	−0.517067	−	0.895585i	−0.999804	−	0.0198201i	$-0.993691\pi$
$401$	−10.3542	−	17.9341i	−0.517067	−	0.895585i	0.482737	−	0.875765i	$-0.339643\pi$
$402$		0			0
$403$	1.61438	−	2.79619i	0.0804179	−	0.139288i
$404$		0			0
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	4.35425			0.215832
$408$		0			0
$409$	17.3745	−	30.0935i	0.859114	−	1.48803i	−0.0136609	−	0.999907i	$-0.504349\pi$
$409$	17.3745	−	30.0935i	0.859114	−	1.48803i	0.872775	−	0.488123i	$-0.162318\pi$
$410$		0			0
$411$	−1.17712	−	2.03884i	−0.0580633	−	0.100569i
$412$		0			0
$413$	−20.2288			−0.995392
$414$		0			0
$415$	−1.46863	−	2.54374i	−0.0720921	−	0.124867i
$416$		0			0
$417$	1.85425	−	3.21165i	0.0908029	−	0.157275i
$418$		0			0
$419$	14.7085			0.718557			0.359279	−	0.933230i	$-0.383023\pi$
$419$	14.7085			0.718557			0.359279	+	0.933230i	$0.383023\pi$
$420$		0			0
$421$	−11.5830			−0.564521			−0.282261	−	0.959338i	$-0.591084\pi$
$421$	−11.5830			−0.564521			−0.282261	+	0.959338i	$0.591084\pi$
$422$		0			0
$423$	−4.29150	+	7.43310i	−0.208660	+	0.361410i
$424$		0			0
$425$	2.82288	+	4.88936i	0.136930	+	0.237169i
$426$		0			0
$427$	19.2915	−	33.4139i	0.933581	−	1.61701i
$428$		0			0
$429$	0.531373	+	0.920365i	0.0256549	+	0.0444356i
$430$		0			0
$431$	−10.6458	+	18.4390i	−0.512788	+	0.888175i	0.487102	+	0.873345i	$0.338054\pi$
$431$	−10.6458	+	18.4390i	−0.512788	+	0.888175i	−0.999890	+	0.0148296i	$0.995279\pi$
$432$		0			0
$433$	−2.77124			−0.133177			−0.0665887	−	0.997781i	$-0.521212\pi$
$433$	−2.77124			−0.133177			−0.0665887	+	0.997781i	$0.521212\pi$
$434$		0			0
$435$	−3.64575			−0.174800
$436$		0			0
$437$	−0.822876	+	1.42526i	−0.0393635	+	0.0681795i
$438$		0			0
$439$	−15.3542	−	26.5943i	−0.732818	−	1.26928i	−0.955674	−	0.294427i	$-0.904871\pi$
$439$	−15.3542	−	26.5943i	−0.732818	−	1.26928i	0.222856	−	0.974851i	$-0.428462\pi$
$440$		0			0
$441$	7.00000			0.333333
$442$		0			0
$443$	−11.6458	−	20.1710i	−0.553306	−	0.958355i	−0.998033	−	0.0626884i	$-0.980033\pi$
$443$	−11.6458	−	20.1710i	−0.553306	−	0.958355i	0.444727	−	0.895666i	$-0.353301\pi$
$444$		0			0
$445$	5.46863	−	9.47194i	0.259238	−	0.449013i
$446$		0			0
$447$	6.58301			0.311365
$448$		0			0
$449$	12.5830			0.593829			0.296914	−	0.954904i	$-0.404042\pi$
$449$	12.5830			0.593829			0.296914	+	0.954904i	$0.404042\pi$
$450$		0			0
$451$	7.35425	−	12.7379i	0.346298	−	0.599806i
$452$		0			0
$453$	−8.29150	−	14.3613i	−0.389569	−	0.674753i
$454$		0			0
$455$	0.854249	−	1.47960i	0.0400478	−	0.0693648i
$456$		0			0
$457$	−17.6144	−	30.5090i	−0.823966	−	1.42715i	−0.902707	−	0.430256i	$-0.858423\pi$
$457$	−17.6144	−	30.5090i	−0.823966	−	1.42715i	0.0787412	−	0.996895i	$-0.474910\pi$
$458$		0			0
$459$	2.82288	−	4.88936i	0.131761	−	0.228216i
$460$		0			0
$461$	−7.64575			−0.356098			−0.178049	−	0.984022i	$-0.556979\pi$
$461$	−7.64575			−0.356098			−0.178049	+	0.984022i	$0.556979\pi$
$462$		0			0
$463$	25.1033			1.16665			0.583324	−	0.812240i	$-0.301752\pi$
$463$	25.1033			1.16665			0.583324	+	0.812240i	$0.301752\pi$
$464$		0			0
$465$	−2.50000	+	4.33013i	−0.115935	+	0.200805i
$466$		0			0
$467$	11.0000	+	19.0526i	0.509019	+	0.881647i	0.999945	+	0.0104461i	$0.00332515\pi$
$467$	11.0000	+	19.0526i	0.509019	+	0.881647i	−0.490926	+	0.871201i	$0.663342\pi$
$468$		0			0
$469$	−15.7085			−0.725351
$470$		0			0
$471$	−5.93725	−	10.2836i	−0.273574	−	0.473844i
$472$		0			0
$473$	0.531373	−	0.920365i	0.0244326	−	0.0423184i
$474$		0			0
$475$	1.00000			0.0458831
$476$		0			0
$477$	0.708497			0.0324399
$478$		0			0
$479$	−5.29150	+	9.16515i	−0.241775	+	0.418766i	−0.961220	−	0.275783i	$-0.911063\pi$
$479$	−5.29150	+	9.16515i	−0.241775	+	0.418766i	0.719445	+	0.694549i	$0.244396\pi$
$480$		0			0
$481$	0.854249	+	1.47960i	0.0389504	+	0.0674641i
$482$		0			0
$483$	−2.17712	−	3.77089i	−0.0990626	−	0.171581i
$484$		0			0
$485$	−7.29150	−	12.6293i	−0.331090	−	0.573465i
$486$		0			0
$487$	−10.6771	+	18.4933i	−0.483827	+	0.838012i	−0.999827	−	0.0185757i	$-0.994087\pi$
$487$	−10.6771	+	18.4933i	−0.483827	+	0.838012i	0.516001	+	0.856588i	$0.327420\pi$
$488$		0			0
$489$	−8.00000			−0.361773
$490$		0			0
$491$	28.4575			1.28427			0.642135	−	0.766592i	$-0.278049\pi$
$491$	28.4575			1.28427			0.642135	+	0.766592i	$0.278049\pi$
$492$		0			0
$493$	10.2915	−	17.8254i	0.463506	−	0.802816i
$494$		0			0
$495$	−0.822876	−	1.42526i	−0.0369855	−	0.0640608i
$496$		0			0
$497$	8.40588	+	14.5594i	0.377055	+	0.653079i
$498$		0			0
$499$	15.7915	+	27.3517i	0.706925	+	1.22443i	0.965992	+	0.258570i	$0.0832514\pi$
$499$	15.7915	+	27.3517i	0.706925	+	1.22443i	−0.259068	+	0.965859i	$0.583415\pi$
$500$		0			0
$501$	8.76013	−	15.1730i	0.391374	−	0.677879i
$502$		0			0
$503$	41.2915			1.84110			0.920549	−	0.390628i	$-0.127742\pi$
$503$	41.2915			1.84110			0.920549	+	0.390628i	$0.127742\pi$
$504$		0			0
$505$	16.9373			0.753698
$506$		0			0
$507$	6.29150	−	10.8972i	0.279415	−	0.483962i
$508$		0			0
$509$	7.93725	+	13.7477i	0.351813	+	0.609357i	0.986567	−	0.163357i	$-0.0522321\pi$
$509$	7.93725	+	13.7477i	0.351813	+	0.609357i	−0.634754	+	0.772714i	$0.718899\pi$
$510$		0			0
$511$	−33.4575			−1.48007
$512$		0			0
$513$	−0.500000	−	0.866025i	−0.0220755	−	0.0382360i
$514$		0			0
$515$	0.677124	−	1.17281i	0.0298377	−	0.0516803i
$516$		0			0
$517$	−14.1255			−0.621238
$518$		0			0
$519$	−0.708497			−0.0310996
$520$		0			0
$521$	−8.35425	+	14.4700i	−0.366006	+	0.633941i	−0.988937	−	0.148335i	$-0.952608\pi$
$521$	−8.35425	+	14.4700i	−0.366006	+	0.633941i	0.622931	+	0.782277i	$0.285942\pi$
$522$		0			0
$523$	−3.61438	−	6.26029i	−0.158046	−	0.273743i	0.776118	−	0.630588i	$-0.217186\pi$
$523$	−3.61438	−	6.26029i	−0.158046	−	0.273743i	−0.934164	+	0.356844i	$0.883853\pi$
$524$		0			0
$525$	−1.32288	+	2.29129i	−0.0577350	+	0.100000i
$526$		0			0
$527$	−14.1144	−	24.4468i	−0.614832	−	1.06492i
$528$		0			0
$529$	10.1458	−	17.5730i	0.441120	−	0.764042i
$530$		0			0
$531$	−7.64575			−0.331797
$532$		0			0
$533$	5.77124			0.249980
$534$		0			0
$535$	6.11438	−	10.5904i	0.264348	−	0.457864i
$536$		0			0
$537$	−3.00000	−	5.19615i	−0.129460	−	0.224231i
$538$		0			0
$539$	5.76013	+	9.97684i	0.248106	+	0.429733i
$540$		0			0
$541$	15.5000	+	26.8468i	0.666397	+	1.15423i	0.978905	+	0.204318i	$0.0654977\pi$
$541$	15.5000	+	26.8468i	0.666397	+	1.15423i	−0.312507	+	0.949915i	$0.601169\pi$
$542$		0			0
$543$	10.1458	−	17.5730i	0.435396	−	0.754128i
$544$		0			0
$545$	−1.58301			−0.0678085
$546$		0			0
$547$	35.2915			1.50896			0.754478	−	0.656326i	$-0.227890\pi$
$547$	35.2915			1.50896			0.754478	+	0.656326i	$0.227890\pi$
$548$		0			0
$549$	7.29150	−	12.6293i	0.311194	−	0.539003i
$550$		0			0
$551$	−1.82288	−	3.15731i	−0.0776571	−	0.134506i
$552$		0			0
$553$	17.1974	−	29.7867i	0.731307	−	1.26666i
$554$		0			0
$555$	−1.32288	−	2.29129i	−0.0561529	−	0.0972598i
$556$		0			0
$557$	−10.2915	+	17.8254i	−0.436065	+	0.755287i	−0.997382	−	0.0723143i	$-0.976962\pi$
$557$	−10.2915	+	17.8254i	−0.436065	+	0.755287i	0.561317	+	0.827601i	$0.310295\pi$
$558$		0			0
$559$	0.416995			0.0176370
$560$		0			0
$561$	9.29150			0.392288
$562$		0			0
$563$	−5.58301	+	9.67005i	−0.235296	+	0.407544i	−0.959359	−	0.282190i	$-0.908939\pi$
$563$	−5.58301	+	9.67005i	−0.235296	+	0.407544i	0.724063	+	0.689734i	$0.242272\pi$
$564$		0			0
$565$	1.00000	+	1.73205i	0.0420703	+	0.0728679i
$566$		0			0
$567$	2.64575			0.111111
$568$		0			0
$569$	−5.53137	−	9.58062i	−0.231887	−	0.401640i	0.726476	−	0.687192i	$-0.241157\pi$
$569$	−5.53137	−	9.58062i	−0.231887	−	0.401640i	−0.958363	+	0.285551i	$0.907823\pi$
$570$		0			0
$571$	−18.5000	+	32.0429i	−0.774201	+	1.34096i	0.161042	+	0.986948i	$0.448515\pi$
$571$	−18.5000	+	32.0429i	−0.774201	+	1.34096i	−0.935243	+	0.354008i	$0.884819\pi$
$572$		0			0
$573$	−20.5830			−0.859867
$574$		0			0
$575$	1.64575			0.0686326
$576$		0			0
$577$	−22.9686	+	39.7828i	−0.956196	+	1.65618i	−0.224590	+	0.974453i	$0.572104\pi$
$577$	−22.9686	+	39.7828i	−0.956196	+	1.65618i	−0.731606	+	0.681728i	$0.761229\pi$
$578$		0			0
$579$	4.96863	+	8.60591i	0.206489	+	0.357650i
$580$		0			0
$581$	3.88562	+	6.73009i	0.161203	+	0.279211i
$582$		0			0
$583$	0.583005	+	1.00979i	0.0241456	+	0.0418214i
$584$		0			0
$585$	0.322876	−	0.559237i	0.0133493	−	0.0231216i
$586$		0			0
$587$	19.5203			0.805687			0.402844	−	0.915269i	$-0.368022\pi$
$587$	19.5203			0.805687			0.402844	+	0.915269i	$0.368022\pi$
$588$		0			0
$589$	−5.00000			−0.206021
$590$		0			0
$591$	−3.53137	+	6.11652i	−0.145261	+	0.251600i
$592$		0			0
$593$	15.1144	+	26.1789i	0.620673	+	1.07504i	0.989361	+	0.145484i	$0.0464739\pi$
$593$	15.1144	+	26.1789i	0.620673	+	1.07504i	−0.368687	+	0.929553i	$0.620193\pi$
$594$		0			0
$595$	−7.46863	−	12.9360i	−0.306184	−	0.530326i
$596$		0			0
$597$	−2.29150	−	3.96900i	−0.0937850	−	0.162440i
$598$		0			0
$599$	−11.6458	+	20.1710i	−0.475832	+	0.824166i	−0.999617	−	0.0276849i	$-0.991186\pi$
$599$	−11.6458	+	20.1710i	−0.475832	+	0.824166i	0.523784	+	0.851851i	$0.324520\pi$
$600$		0			0
$601$	−28.1660			−1.14892			−0.574458	−	0.818534i	$-0.694787\pi$
$601$	−28.1660			−1.14892			−0.574458	+	0.818534i	$0.694787\pi$
$602$		0			0
$603$	−5.93725			−0.241784
$604$		0			0
$605$	−4.14575	+	7.18065i	−0.168549	+	0.291935i
$606$		0			0
$607$	−5.03137	−	8.71459i	−0.204217	−	0.353714i	0.745666	−	0.666320i	$-0.232132\pi$
$607$	−5.03137	−	8.71459i	−0.204217	−	0.353714i	−0.949883	+	0.312606i	$0.898798\pi$
$608$		0			0
$609$	9.64575			0.390866
$610$		0			0
$611$	−2.77124	−	4.79993i	−0.112113	−	0.194185i
$612$		0			0
$613$	17.2915	−	29.9498i	0.698397	−	1.20966i	−0.270625	−	0.962685i	$-0.587230\pi$
$613$	17.2915	−	29.9498i	0.698397	−	1.20966i	0.969022	−	0.246975i	$-0.0794364\pi$
$614$		0			0
$615$	−8.93725			−0.360385
$616$		0			0
$617$	45.0405			1.81326			0.906631	−	0.421923i	$-0.138645\pi$
$617$	45.0405			1.81326			0.906631	+	0.421923i	$0.138645\pi$
$618$		0			0
$619$	−13.4373	+	23.2740i	−0.540089	+	0.935461i	0.458810	+	0.888535i	$0.348276\pi$
$619$	−13.4373	+	23.2740i	−0.540089	+	0.935461i	−0.998898	+	0.0469266i	$0.985057\pi$
$620$		0			0
$621$	−0.822876	−	1.42526i	−0.0330209	−	0.0571938i
$622$		0			0
$623$	−14.4686	+	25.0604i	−0.579673	+	1.00402i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	0.822876	−	1.42526i	0.0328625	−	0.0569195i
$628$		0			0
$629$	14.9373			0.595587
$630$		0			0
$631$	−42.3320			−1.68521			−0.842606	−	0.538531i	$-0.818979\pi$
$631$	−42.3320			−1.68521			−0.842606	+	0.538531i	$0.818979\pi$
$632$		0			0
$633$	−8.29150	+	14.3613i	−0.329558	+	0.570811i
$634$		0			0
$635$	−3.61438	−	6.26029i	−0.143432	−	0.248432i
$636$		0			0
$637$	−2.26013	+	3.91466i	−0.0895496	+	0.155104i
$638$		0			0
$639$	3.17712	+	5.50294i	0.125685	+	0.217693i
$640$		0			0
$641$	−7.11438	+	12.3225i	−0.281001	+	0.486708i	−0.971632	−	0.236500i	$-0.924000\pi$
$641$	−7.11438	+	12.3225i	−0.281001	+	0.486708i	0.690631	+	0.723208i	$0.257333\pi$
$642$		0			0
$643$	36.5203			1.44022			0.720109	−	0.693861i	$-0.244092\pi$
$643$	36.5203			1.44022			0.720109	+	0.693861i	$0.244092\pi$
$644$		0			0
$645$	−0.645751			−0.0254264
$646$		0			0
$647$	9.82288	−	17.0137i	0.386177	−	0.668878i	−0.605755	−	0.795652i	$-0.707129\pi$
$647$	9.82288	−	17.0137i	0.386177	−	0.668878i	0.991932	+	0.126773i	$0.0404620\pi$
$648$		0			0
$649$	−6.29150	−	10.8972i	−0.246963	−	0.427753i
$650$		0			0
$651$	6.61438	−	11.4564i	0.259238	−	0.449013i
$652$		0			0
$653$	16.4059	+	28.4158i	0.642012	+	1.11200i	0.984983	+	0.172651i	$0.0552333\pi$
$653$	16.4059	+	28.4158i	0.642012	+	1.11200i	−0.342971	+	0.939346i	$0.611433\pi$
$654$		0			0
$655$	−4.64575	+	8.04668i	−0.181525	+	0.314410i
$656$		0			0
$657$	−12.6458			−0.493358
$658$		0			0
$659$	−33.1660			−1.29196			−0.645982	−	0.763352i	$-0.723552\pi$
$659$	−33.1660			−1.29196			−0.645982	+	0.763352i	$0.723552\pi$
$660$		0			0
$661$	9.85425	−	17.0681i	0.383286	−	0.663871i	−0.608244	−	0.793750i	$-0.708126\pi$
$661$	9.85425	−	17.0681i	0.383286	−	0.663871i	0.991530	+	0.129880i	$0.0414591\pi$
$662$		0			0
$663$	1.82288	+	3.15731i	0.0707946	+	0.122620i
$664$		0			0
$665$	−2.64575			−0.102598
$666$		0			0
$667$	−3.00000	−	5.19615i	−0.116160	−	0.201196i
$668$		0			0
$669$	−1.64575	+	2.85052i	−0.0636284	+	0.110208i
$670$		0			0
$671$	24.0000			0.926510
$672$		0			0
$673$	−24.6458			−0.950024			−0.475012	−	0.879979i	$-0.657556\pi$
$673$	−24.6458			−0.950024			−0.475012	+	0.879979i	$0.657556\pi$
$674$		0			0
$675$	−0.500000	+	0.866025i	−0.0192450	+	0.0333333i
$676$		0			0
$677$	17.0516	+	29.5343i	0.655347	+	1.13510i	0.981807	+	0.189884i	$0.0608111\pi$
$677$	17.0516	+	29.5343i	0.655347	+	1.13510i	−0.326459	+	0.945211i	$0.605856\pi$
$678$		0			0
$679$	19.2915	+	33.4139i	0.740340	+	1.28231i
$680$		0			0
$681$	3.46863	+	6.00784i	0.132918	+	0.230221i
$682$		0			0
$683$	−14.4686	+	25.0604i	−0.553627	+	0.958909i	0.444382	+	0.895837i	$0.353423\pi$
$683$	−14.4686	+	25.0604i	−0.553627	+	0.958909i	−0.998009	+	0.0630722i	$0.979910\pi$
$684$		0			0
$685$	−2.35425			−0.0899512
$686$		0			0
$687$	7.58301			0.289310
$688$		0			0
$689$	−0.228757	+	0.396218i	−0.00871493	+	0.0150947i
$690$		0			0
$691$	−12.1458	−	21.0371i	−0.462046	−	0.800287i	0.537017	−	0.843572i	$-0.319551\pi$
$691$	−12.1458	−	21.0371i	−0.462046	−	0.800287i	−0.999063	+	0.0432842i	$0.986218\pi$
$692$		0			0
$693$	2.17712	+	3.77089i	0.0827021	+	0.143244i
$694$		0			0
$695$	−1.85425	−	3.21165i	−0.0703357	−	0.121825i
$696$		0			0
$697$	25.2288	−	43.6975i	0.955607	−	1.65516i
$698$		0			0
$699$	9.29150			0.351437
$700$		0			0
$701$	−47.3948			−1.79008			−0.895038	−	0.445990i	$-0.852852\pi$
$701$	−47.3948			−1.79008			−0.895038	+	0.445990i	$0.852852\pi$
$702$		0			0
$703$	1.32288	−	2.29129i	0.0498932	−	0.0864176i
$704$		0			0
$705$	4.29150	+	7.43310i	0.161627	+	0.279947i
$706$		0			0
$707$	−44.8118			−1.68532
$708$		0			0
$709$	14.5830	+	25.2585i	0.547676	+	0.948603i	0.998433	+	0.0559564i	$0.0178208\pi$
$709$	14.5830	+	25.2585i	0.547676	+	0.948603i	−0.450757	+	0.892647i	$0.648846\pi$
$710$		0			0
$711$	6.50000	−	11.2583i	0.243769	−	0.422220i
$712$		0			0
$713$	−8.22876			−0.308169
$714$		0			0
$715$	1.06275			0.0397444
$716$		0			0
$717$	4.29150	−	7.43310i	0.160269	−	0.277594i
$718$		0			0
$719$	−5.35425	−	9.27383i	−0.199680	−	0.345856i	0.748745	−	0.662858i	$-0.230657\pi$
$719$	−5.35425	−	9.27383i	−0.199680	−	0.345856i	−0.948425	+	0.317003i	$0.897324\pi$
$720$		0			0
$721$	−1.79150	+	3.10297i	−0.0667190	+	0.115561i
$722$		0			0
$723$	−8.93725	−	15.4798i	−0.332380	−	0.575699i
$724$		0			0
$725$	−1.82288	+	3.15731i	−0.0676999	+	0.117260i
$726$		0			0
$727$	−9.81176			−0.363898			−0.181949	−	0.983308i	$-0.558241\pi$
$727$	−9.81176			−0.363898			−0.181949	+	0.983308i	$0.558241\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	1.82288	−	3.15731i	0.0674215	−	0.116777i
$732$		0			0
$733$	3.90588	+	6.76518i	0.144267	+	0.249878i	0.929099	−	0.369831i	$-0.120584\pi$
$733$	3.90588	+	6.76518i	0.144267	+	0.249878i	−0.784832	+	0.619708i	$0.787251\pi$
$734$		0			0
$735$	3.50000	−	6.06218i	0.129099	−	0.223607i
$736$		0			0
$737$	−4.88562	−	8.46215i	−0.179964	−	0.311707i
$738$		0			0
$739$	−5.43725	+	9.41760i	−0.200013	+	0.346432i	−0.948532	−	0.316681i	$-0.897432\pi$
$739$	−5.43725	+	9.41760i	−0.200013	+	0.346432i	0.748520	+	0.663113i	$0.230765\pi$
$740$		0			0
$741$	0.645751			0.0237223
$742$		0			0
$743$	−39.6458			−1.45446			−0.727231	−	0.686393i	$-0.759193\pi$
$743$	−39.6458			−1.45446			−0.727231	+	0.686393i	$0.759193\pi$
$744$		0			0
$745$	3.29150	−	5.70105i	0.120591	−	0.208870i
$746$		0			0
$747$	1.46863	+	2.54374i	0.0537343	+	0.0930705i
$748$		0			0
$749$	−16.1771	+	28.0196i	−0.591099	+	1.02381i
$750$		0			0
$751$	−22.3118	−	38.6451i	−0.814168	−	1.41018i	−0.909924	−	0.414775i	$-0.863860\pi$
$751$	−22.3118	−	38.6451i	−0.814168	−	1.41018i	0.0957562	−	0.995405i	$-0.469473\pi$
$752$		0			0
$753$	−14.4059	+	24.9517i	−0.524979	+	0.909291i
$754$		0			0
$755$	−16.5830			−0.603517
$756$		0			0
$757$	3.41699			0.124193			0.0620964	−	0.998070i	$-0.480221\pi$
$757$	3.41699			0.124193			0.0620964	+	0.998070i	$0.480221\pi$
$758$		0			0
$759$	1.35425	−	2.34563i	0.0491561	−	0.0851409i
$760$		0			0
$761$	−3.11438	−	5.39426i	−0.112896	−	0.195542i	0.804041	−	0.594574i	$-0.202679\pi$
$761$	−3.11438	−	5.39426i	−0.112896	−	0.195542i	−0.916937	+	0.399032i	$0.869346\pi$
$762$		0			0
$763$	4.18824			0.151624
$764$		0			0
$765$	−2.82288	−	4.88936i	−0.102061	−	0.176775i
$766$		0			0
$767$	2.46863	−	4.27579i	0.0891370	−	0.154390i
$768$		0			0
$769$	49.4575			1.78348			0.891742	−	0.452545i	$-0.149484\pi$
$769$	49.4575			1.78348			0.891742	+	0.452545i	$0.149484\pi$
$770$		0			0
$771$	−18.2288			−0.656493
$772$		0			0
$773$	8.88562	−	15.3903i	0.319594	−	0.553552i	−0.660810	−	0.750554i	$-0.729787\pi$
$773$	8.88562	−	15.3903i	0.319594	−	0.553552i	0.980403	+	0.197001i	$0.0631203\pi$
$774$		0			0
$775$	2.50000	+	4.33013i	0.0898027	+	0.155543i
$776$		0			0
$777$	3.50000	+	6.06218i	0.125562	+	0.217479i
$778$		0			0
$779$	−4.46863	−	7.73989i	−0.160105	−	0.277310i
$780$		0			0
$781$	−5.22876	+	9.05647i	−0.187100	+	0.324066i
$782$		0			0
$783$	3.64575			0.130289
$784$		0			0
$785$	−11.8745			−0.423819
$786$		0			0
$787$	−20.3542	+	35.2546i	−0.725551	+	1.25669i	0.233196	+	0.972430i	$0.425082\pi$
$787$	−20.3542	+	35.2546i	−0.725551	+	1.25669i	−0.958747	+	0.284261i	$0.908252\pi$
$788$		0			0
$789$	−14.9373	−	25.8721i	−0.531780	−	0.921071i
$790$		0			0
$791$	−2.64575	−	4.58258i	−0.0940721	−	0.162938i
$792$		0			0
$793$	4.70850	+	8.15536i	0.167204	+	0.289605i
$794$		0			0
$795$	0.354249	−	0.613577i	0.0125639	−	0.0217613i
$796$		0			0
$797$	6.10326			0.216189			0.108094	−	0.994141i	$-0.465525\pi$
$797$	6.10326			0.216189			0.108094	+	0.994141i	$0.465525\pi$
$798$		0			0
$799$	−48.4575			−1.71430
$800$		0			0
$801$	−5.46863	+	9.47194i	−0.193224	+	0.334675i
$802$		0			0
$803$	−10.4059	−	18.0235i	−0.367216	−	0.636036i
$804$		0			0
$805$	−4.35425			−0.153467
$806$		0			0
$807$	12.6458	+	21.9031i	0.445152	+	0.771025i
$808$		0			0
$809$	−7.58301	+	13.1342i	−0.266604	+	0.461772i	−0.967983	−	0.251017i	$-0.919235\pi$
$809$	−7.58301	+	13.1342i	−0.266604	+	0.461772i	0.701378	+	0.712789i	$0.252568\pi$
$810$		0			0
$811$	−41.0405			−1.44113			−0.720564	−	0.693389i	$-0.756117\pi$
$811$	−41.0405			−1.44113			−0.720564	+	0.693389i	$0.756117\pi$
$812$		0			0
$813$	−2.00000			−0.0701431
$814$		0			0
$815$	−4.00000	+	6.92820i	−0.140114	+	0.242684i
$816$		0			0
$817$	−0.322876	−	0.559237i	−0.0112960	−	0.0195652i
$818$		0			0
$819$	−0.854249	+	1.47960i	−0.0298499	+	0.0517015i
$820$		0			0
$821$	−24.3431	−	42.1635i	−0.849581	−	1.47152i	−0.881582	−	0.472030i	$-0.843521\pi$
$821$	−24.3431	−	42.1635i	−0.849581	−	1.47152i	0.0320012	−	0.999488i	$-0.489812\pi$
$822$		0			0
$823$	−0.0627461	+	0.108679i	−0.00218719	+	0.00378832i	−0.867117	−	0.498105i	$-0.834030\pi$
$823$	−0.0627461	+	0.108679i	−0.00218719	+	0.00378832i	0.864930	+	0.501893i	$0.167363\pi$
$824$		0			0
$825$	−1.64575			−0.0572977
$826$		0			0
$827$	38.7085			1.34603			0.673013	−	0.739630i	$-0.265000\pi$
$827$	38.7085			1.34603			0.673013	+	0.739630i	$0.265000\pi$
$828$		0			0
$829$	−11.7288	+	20.3148i	−0.407357	+	0.705562i	−0.994593	−	0.103853i	$-0.966883\pi$
$829$	−11.7288	+	20.3148i	−0.407357	+	0.705562i	0.587236	+	0.809416i	$0.300216\pi$
$830$		0			0
$831$	−9.90588	−	17.1575i	−0.343631	−	0.595187i
$832$		0			0
$833$	19.7601	+	34.2255i	0.684648	+	1.18584i
$834$		0			0
$835$	−8.76013	−	15.1730i	−0.303157	−	0.525083i
$836$		0			0
$837$	2.50000	−	4.33013i	0.0864126	−	0.149671i
$838$		0			0
$839$	9.77124			0.337341			0.168670	−	0.985673i	$-0.446053\pi$
$839$	9.77124			0.337341			0.168670	+	0.985673i	$0.446053\pi$
$840$		0			0
$841$	−15.7085			−0.541672
$842$		0			0
$843$	−6.00000	+	10.3923i	−0.206651	+	0.357930i
$844$		0			0
$845$	−6.29150	−	10.8972i	−0.216434	−	0.374875i
$846$		0			0
$847$	10.9686	−	18.9982i	0.376886	−	0.652787i
$848$		0			0
$849$	13.9059	+	24.0857i	0.477249	+	0.826619i
$850$		0			0
$851$	2.17712	−	3.77089i	0.0746309	−	0.129264i
$852$		0			0
$853$	−8.06275			−0.276063			−0.138032	−	0.990428i	$-0.544078\pi$
$853$	−8.06275			−0.276063			−0.138032	+	0.990428i	$0.544078\pi$
$854$		0			0
$855$	−1.00000			−0.0341993
$856$		0			0
$857$	−20.4686	+	35.4527i	−0.699195	+	1.21104i	0.269551	+	0.962986i	$0.413125\pi$
$857$	−20.4686	+	35.4527i	−0.699195	+	1.21104i	−0.968746	+	0.248055i	$0.920209\pi$
$858$		0			0
$859$	−8.64575	−	14.9749i	−0.294989	−	0.510936i	0.679993	−	0.733218i	$-0.261983\pi$
$859$	−8.64575	−	14.9749i	−0.294989	−	0.510936i	−0.974982	+	0.222282i	$0.928649\pi$
$860$		0			0
$861$	23.6458			0.805845
$862$		0			0
$863$	5.22876	+	9.05647i	0.177989	+	0.308286i	0.941192	−	0.337873i	$-0.109708\pi$
$863$	5.22876	+	9.05647i	0.177989	+	0.308286i	−0.763203	+	0.646159i	$0.776374\pi$
$864$		0			0
$865$	−0.354249	+	0.613577i	−0.0120448	+	0.0208622i
$866$		0			0
$867$	14.8745			0.505165
$868$		0			0
$869$	21.3948			0.725768
$870$		0			0
$871$	1.91699	−	3.32033i	0.0649549	−	0.112505i
$872$		0			0
$873$	7.29150	+	12.6293i	0.246780	+	0.427435i
$874$		0			0
$875$	1.32288	+	2.29129i	0.0447214	+	0.0774597i
$876$		0			0
$877$	6.87451	+	11.9070i	0.232136	+	0.402071i	0.958436	−	0.285306i	$-0.0920953\pi$
$877$	6.87451	+	11.9070i	0.232136	+	0.402071i	−0.726301	+	0.687377i	$0.758762\pi$
$878$		0			0
$879$	12.0000	−	20.7846i	0.404750	−	0.701047i
$880$		0			0
$881$	−21.1660			−0.713101			−0.356551	−	0.934276i	$-0.616047\pi$
$881$	−21.1660			−0.713101			−0.356551	+	0.934276i	$0.616047\pi$
$882$		0			0
$883$	−45.8118			−1.54169			−0.770844	−	0.637024i	$-0.780165\pi$
$883$	−45.8118			−1.54169			−0.770844	+	0.637024i	$0.780165\pi$
$884$		0			0
$885$	−3.82288	+	6.62141i	−0.128505	+	0.222576i
$886$		0			0
$887$	−2.05163	−	3.55353i	−0.0688871	−	0.119316i	0.829525	−	0.558470i	$-0.188611\pi$
$887$	−2.05163	−	3.55353i	−0.0688871	−	0.119316i	−0.898412	+	0.439154i	$0.855278\pi$
$888$		0			0
$889$	9.56275	+	16.5632i	0.320724	+	0.555511i
$890$		0			0
$891$	0.822876	+	1.42526i	0.0275674	+	0.0477481i
$892$		0			0
$893$	−4.29150	+	7.43310i	−0.143610	+	0.248739i
$894$		0			0
$895$	−6.00000			−0.200558
$896$		0			0
$897$	1.06275			0.0354841
$898$		0			0
$899$	9.11438	−	15.7866i	0.303982	−	0.526511i
$900$		0			0
$901$	2.00000	+	3.46410i	0.0666297	+	0.115406i
$902$		0			0
$903$	1.70850			0.0568552
$904$		0			0
$905$	−10.1458	−	17.5730i	−0.337256	−	0.584145i
$906$		0			0
$907$	−18.8431	+	32.6373i	−0.625676	+	1.08370i	0.362734	+	0.931893i	$0.381843\pi$
$907$	−18.8431	+	32.6373i	−0.625676	+	1.08370i	−0.988410	+	0.151810i	$0.951490\pi$
$908$		0			0
$909$	−16.9373			−0.561773
$910$		0			0
$911$	−10.9373			−0.362367			−0.181184	−	0.983449i	$-0.557993\pi$
$911$	−10.9373			−0.362367			−0.181184	+	0.983449i	$0.557993\pi$
$912$		0			0
$913$	−2.41699	+	4.18636i	−0.0799909	+	0.138548i
$914$		0			0
$915$	−7.29150	−	12.6293i	−0.241050	−	0.417510i
$916$		0			0
$917$	12.2915	−	21.2895i	0.405901	−	0.703041i
$918$		0			0
$919$	18.4373	+	31.9343i	0.608189	+	1.05341i	0.991539	+	0.129811i	$0.0414370\pi$
$919$	18.4373	+	31.9343i	0.608189	+	1.05341i	−0.383350	+	0.923603i	$0.625230\pi$
$920$		0			0
$921$	2.03137	−	3.51844i	0.0669360	−	0.115937i
$922$		0			0
$923$	−4.10326			−0.135061
$924$		0			0
$925$	−2.64575			−0.0869918
$926$		0			0
$927$	−0.677124	+	1.17281i	−0.0222397	+	0.0385203i
$928$		0			0
$929$	0.822876	+	1.42526i	0.0269977	+	0.0467613i	0.879209	−	0.476437i	$-0.158072\pi$
$929$	0.822876	+	1.42526i	0.0269977	+	0.0467613i	−0.852211	+	0.523198i	$0.824739\pi$
$930$		0			0
$931$	7.00000			0.229416
$932$		0			0
$933$	9.17712	+	15.8952i	0.300446	+	0.520387i
$934$		0			0
$935$	4.64575	−	8.04668i	0.151932	−	0.263154i
$936$		0			0
$937$	47.9373			1.56604			0.783021	−	0.621995i	$-0.213678\pi$
$937$	47.9373			1.56604			0.783021	+	0.621995i	$0.213678\pi$
$938$		0			0
$939$	−4.77124			−0.155704
$940$		0			0
$941$	2.88562	−	4.99804i	0.0940686	−	0.162932i	−0.815151	−	0.579249i	$-0.803346\pi$
$941$	2.88562	−	4.99804i	0.0940686	−	0.162932i	0.909219	+	0.416317i	$0.136679\pi$
$942$		0			0
$943$	−7.35425	−	12.7379i	−0.239487	−	0.414804i
$944$		0			0
$945$	1.32288	−	2.29129i	0.0430331	−	0.0745356i
$946$		0			0
$947$	−10.5314	−	18.2409i	−0.342224	−	0.592749i	0.642622	−	0.766184i	$-0.277847\pi$
$947$	−10.5314	−	18.2409i	−0.342224	−	0.592749i	−0.984845	+	0.173435i	$0.944513\pi$
$948$		0			0
$949$	4.08301	−	7.07197i	0.132540	−	0.229566i
$950$		0			0
$951$	−4.22876			−0.137127
$952$		0			0
$953$	−36.7085			−1.18910			−0.594552	−	0.804057i	$-0.702671\pi$
$953$	−36.7085			−1.18910			−0.594552	+	0.804057i	$0.702671\pi$
$954$		0			0
$955$	−10.2915	+	17.8254i	−0.333025	+	0.576817i
$956$		0			0
$957$	3.00000	+	5.19615i	0.0969762	+	0.167968i
$958$		0			0
$959$	6.22876			0.201137
$960$		0			0
$961$	3.00000	+	5.19615i	0.0967742	+	0.167618i
$962$		0			0
$963$	−6.11438	+	10.5904i	−0.197033	+	0.341271i
$964$		0			0
$965$	9.93725			0.319892
$966$		0			0
$967$	20.5203			0.659887			0.329944	−	0.944001i	$-0.392970\pi$
$967$	20.5203			0.659887			0.329944	+	0.944001i	$0.392970\pi$
$968$		0			0
$969$	2.82288	−	4.88936i	0.0906838	−	0.157069i
$970$		0			0
$971$	24.5830	+	42.5790i	0.788906	+	1.36643i	0.926638	+	0.375956i	$0.122686\pi$
$971$	24.5830	+	42.5790i	0.788906	+	1.36643i	−0.137731	+	0.990470i	$0.543981\pi$
$972$		0			0
$973$	4.90588	+	8.49723i	0.157275	+	0.272409i
$974$		0			0
$975$	−0.322876	−	0.559237i	−0.0103403	−	0.0179099i
$976$		0			0
$977$	−11.4686	+	19.8642i	−0.366914	+	0.635513i	−0.989081	−	0.147371i	$-0.952919\pi$
$977$	−11.4686	+	19.8642i	−0.366914	+	0.635513i	0.622167	+	0.782884i	$0.286252\pi$
$978$		0			0
$979$	−18.0000			−0.575282
$980$		0			0
$981$	1.58301			0.0505415
$982$		0			0
$983$	7.40588	−	12.8274i	0.236211	−	0.409129i	−0.723413	−	0.690416i	$-0.757428\pi$
$983$	7.40588	−	12.8274i	0.236211	−	0.409129i	0.959624	+	0.281286i	$0.0907610\pi$
$984$		0			0
$985$	3.53137	+	6.11652i	0.112519	+	0.194888i
$986$		0			0
$987$	−11.3542	−	19.6661i	−0.361410	−	0.625980i
$988$		0			0
$989$	−0.531373	−	0.920365i	−0.0168967	−	0.0292659i
$990$		0			0
$991$	−9.79150	+	16.9594i	−0.311037	+	0.538732i	−0.978587	−	0.205833i	$-0.934010\pi$
$991$	−9.79150	+	16.9594i	−0.311037	+	0.538732i	0.667550	+	0.744565i	$0.267343\pi$
$992$		0			0
$993$	−22.2915			−0.707399
$994$		0			0
$995$	−4.58301			−0.145291
$996$		0			0
$997$	−23.9686	+	41.5149i	−0.759094	+	1.31479i	0.184219	+	0.982885i	$0.441024\pi$
$997$	−23.9686	+	41.5149i	−0.759094	+	1.31479i	−0.943313	+	0.331904i	$0.892309\pi$
$998$		0			0
$999$	1.32288	+	2.29129i	0.0418539	+	0.0724931i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.bg.h.361.1	yes	4
3.2	odd	2		2520.2.bi.j.361.1		4
4.3	odd	2		1680.2.bg.s.1201.2		4
7.2	even	3	inner	840.2.bg.h.121.1	✓	4
7.3	odd	6		5880.2.a.bo.1.1		2
7.4	even	3		5880.2.a.bq.1.1		2
21.2	odd	6		2520.2.bi.j.1801.1		4
28.23	odd	6		1680.2.bg.s.961.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.bg.h.121.1	✓	4	7.2	even	3	inner
840.2.bg.h.361.1	yes	4	1.1	even	1	trivial
1680.2.bg.s.961.2		4	28.23	odd	6
1680.2.bg.s.1201.2		4	4.3	odd	2
2520.2.bi.j.361.1		4	3.2	odd	2
2520.2.bi.j.1801.1		4	21.2	odd	6
5880.2.a.bo.1.1		2	7.3	odd	6
5880.2.a.bq.1.1		2	7.4	even	3

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:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.bg (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-1.32288 - 2.29129i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(0.822876 - 1.42526i) q^{11} +0.645751 q^{13} -1.00000 q^{15} +(2.82288 - 4.88936i) q^{17} +(-0.500000 - 0.866025i) q^{19} +2.64575 q^{21} +(-0.822876 - 1.42526i) q^{23} +(-0.500000 + 0.866025i) q^{25} +1.00000 q^{27} +3.64575 q^{29} +(2.50000 - 4.33013i) q^{31} +(0.822876 + 1.42526i) q^{33} +(1.32288 - 2.29129i) q^{35} +(1.32288 + 2.29129i) q^{37} +(-0.322876 + 0.559237i) q^{39} +8.93725 q^{41} +0.645751 q^{43} +(0.500000 - 0.866025i) q^{45} +(-4.29150 - 7.43310i) q^{47} +(-3.50000 + 6.06218i) q^{49} +(2.82288 + 4.88936i) q^{51} +(-0.354249 + 0.613577i) q^{53} +1.64575 q^{55} +1.00000 q^{57} +(3.82288 - 6.62141i) q^{59} +(7.29150 + 12.6293i) q^{61} +(-1.32288 + 2.29129i) q^{63} +(0.322876 + 0.559237i) q^{65} +(2.96863 - 5.14181i) q^{67} +1.64575 q^{69} -6.35425 q^{71} +(6.32288 - 10.9515i) q^{73} +(-0.500000 - 0.866025i) q^{75} -4.35425 q^{77} +(6.50000 + 11.2583i) q^{79} +(-0.500000 + 0.866025i) q^{81} -2.93725 q^{83} +5.64575 q^{85} +(-1.82288 + 3.15731i) q^{87} +(-5.46863 - 9.47194i) q^{89} +(-0.854249 - 1.47960i) q^{91} +(2.50000 + 4.33013i) q^{93} +(0.500000 - 0.866025i) q^{95} -14.5830 q^{97} -1.64575 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 2 q^{5} - 2 q^{9} - 2 q^{11} - 8 q^{13} - 4 q^{15} + 6 q^{17} - 2 q^{19} + 2 q^{23} - 2 q^{25} + 4 q^{27} + 4 q^{29} + 10 q^{31} - 2 q^{33} + 4 q^{39} + 4 q^{41} - 8 q^{43} + 2 q^{45} + 4 q^{47}+ \cdots + 4 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 + 2 * q^5 - 2 * q^9 - 2 * q^11 - 8 * q^13 - 4 * q^15 + 6 * q^17 - 2 * q^19 + 2 * q^23 - 2 * q^25 + 4 * q^27 + 4 * q^29 + 10 * q^31 - 2 * q^33 + 4 * q^39 + 4 * q^41 - 8 * q^43 + 2 * q^45 + 4 * q^47 - 14 * q^49 + 6 * q^51 - 12 * q^53 - 4 * q^55 + 4 * q^57 + 10 * q^59 + 8 * q^61 - 4 * q^65 - 4 * q^67 - 4 * q^69 - 36 * q^71 + 20 * q^73 - 2 * q^75 - 28 * q^77 + 26 * q^79 - 2 * q^81 + 20 * q^83 + 12 * q^85 - 2 * q^87 - 6 * q^89 - 14 * q^91 + 10 * q^93 + 2 * q^95 - 16 * q^97 + 4 * q^99

Introduction

L-functions

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Representations

Groups

Database

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