LMFDB - Embedded newform 567.2.f.i.379.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [567,2,Mod(190,567)] 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("567.190"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(567, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.f (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,-10,0,0,2,0,0,-28] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$4.52751779461$
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:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			379.2
Root			$1.32288 - 2.29129i$ of defining polynomial
Character	$\chi$	$=$	567.379
Dual form			567.2.f.i.190.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.32288 - 2.29129i) q^{2} +(-2.50000 - 4.33013i) q^{4} +(-1.32288 - 2.29129i) q^{5} +(0.500000 - 0.866025i) q^{7} -7.93725 q^{8} -7.00000 q^{10} +(-1.32288 + 2.29129i) q^{11} +(1.00000 + 1.73205i) q^{13} +(-1.32288 - 2.29129i) q^{14} +(-5.50000 + 9.52628i) q^{16} +7.00000 q^{19} +(-6.61438 + 11.4564i) q^{20} +(3.50000 + 6.06218i) q^{22} +(-3.96863 - 6.87386i) q^{23} +(-1.00000 + 1.73205i) q^{25} +5.29150 q^{26} -5.00000 q^{28} +(2.64575 - 4.58258i) q^{29} +(-1.50000 - 2.59808i) q^{31} +(6.61438 + 11.4564i) q^{32} -2.64575 q^{35} -3.00000 q^{37} +(9.26013 - 16.0390i) q^{38} +(10.5000 + 18.1865i) q^{40} +(1.32288 + 2.29129i) q^{41} +(-4.00000 + 6.92820i) q^{43} +13.2288 q^{44} -21.0000 q^{46} +(-0.500000 - 0.866025i) q^{49} +(2.64575 + 4.58258i) q^{50} +(5.00000 - 8.66025i) q^{52} +7.00000 q^{55} +(-3.96863 + 6.87386i) q^{56} +(-7.00000 - 12.1244i) q^{58} +(4.00000 - 6.92820i) q^{61} -7.93725 q^{62} +13.0000 q^{64} +(2.64575 - 4.58258i) q^{65} +(1.00000 + 1.73205i) q^{67} +(-3.50000 + 6.06218i) q^{70} -7.93725 q^{71} +(-3.96863 + 6.87386i) q^{74} +(-17.5000 - 30.3109i) q^{76} +(1.32288 + 2.29129i) q^{77} +(2.00000 - 3.46410i) q^{79} +29.1033 q^{80} +7.00000 q^{82} +(7.93725 - 13.7477i) q^{83} +(10.5830 + 18.3303i) q^{86} +(10.5000 - 18.1865i) q^{88} +18.5203 q^{89} +2.00000 q^{91} +(-19.8431 + 34.3693i) q^{92} +(-9.26013 - 16.0390i) q^{95} +(6.00000 - 10.3923i) q^{97} -2.64575 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 10 q^{4} + 2 q^{7} - 28 q^{10} + 4 q^{13} - 22 q^{16} + 28 q^{19} + 14 q^{22} - 4 q^{25} - 20 q^{28} - 6 q^{31} - 12 q^{37} + 42 q^{40} - 16 q^{43} - 84 q^{46} - 2 q^{49} + 20 q^{52} + 28 q^{55} - 28 q^{58}+ \cdots + 24 q^{97}+O(q^{100}) $ 4 * q - 10 * q^4 + 2 * q^7 - 28 * q^10 + 4 * q^13 - 22 * q^16 + 28 * q^19 + 14 * q^22 - 4 * q^25 - 20 * q^28 - 6 * q^31 - 12 * q^37 + 42 * q^40 - 16 * q^43 - 84 * q^46 - 2 * q^49 + 20 * q^52 + 28 * q^55 - 28 * q^58 + 16 * q^61 + 52 * q^64 + 4 * q^67 - 14 * q^70 - 70 * q^76 + 8 * q^79 + 28 * q^82 + 42 * q^88 + 8 * q^91 + 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.32288	−	2.29129i	0.935414	−	1.62019i	0.161521	−	0.986869i	$-0.448360\pi$
$2$	1.32288	−	2.29129i	0.935414	−	1.62019i	0.773893	−	0.633316i	$-0.218307\pi$
$3$		0			0
$3$		0			0
$4$	−2.50000	−	4.33013i	−1.25000	−	2.16506i
$5$	−1.32288	−	2.29129i	−0.591608	−	1.02470i	−0.994016	−	0.109235i	$-0.965160\pi$
$5$	−1.32288	−	2.29129i	−0.591608	−	1.02470i	0.402408	−	0.915460i	$-0.368173\pi$
$6$		0			0
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$	−7.93725			−2.80624
$9$		0			0
$10$	−7.00000			−2.21359
$11$	−1.32288	+	2.29129i	−0.398862	+	0.690849i	−0.993586	−	0.113081i	$-0.963928\pi$
$11$	−1.32288	+	2.29129i	−0.398862	+	0.690849i	0.594724	+	0.803930i	$0.297261\pi$
$12$		0			0
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	0.970725	−	0.240192i	$-0.0772105\pi$
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	−0.693375	+	0.720577i	$0.743877\pi$
$14$	−1.32288	−	2.29129i	−0.353553	−	0.612372i
$15$		0			0
$16$	−5.50000	+	9.52628i	−1.37500	+	2.38157i
$17$		0			0			−	1.00000i	$-0.5\pi$
$17$		0			0				1.00000i	$0.5\pi$
$18$		0			0
$19$	7.00000			1.60591			0.802955	−	0.596040i	$-0.203260\pi$
$19$	7.00000			1.60591			0.802955	+	0.596040i	$0.203260\pi$
$20$	−6.61438	+	11.4564i	−1.47902	+	2.56174i
$21$		0			0
$22$	3.50000	+	6.06218i	0.746203	+	1.29246i
$23$	−3.96863	−	6.87386i	−0.827516	−	1.43330i	−0.899981	−	0.435929i	$-0.856420\pi$
$23$	−3.96863	−	6.87386i	−0.827516	−	1.43330i	0.0724653	−	0.997371i	$-0.476913\pi$
$24$		0			0
$25$	−1.00000	+	1.73205i	−0.200000	+	0.346410i
$26$	5.29150			1.03775
$27$		0			0
$28$	−5.00000			−0.944911
$29$	2.64575	−	4.58258i	0.491304	−	0.850963i	−0.508646	−	0.860976i	$-0.669854\pi$
$29$	2.64575	−	4.58258i	0.491304	−	0.850963i	0.999950	+	0.0100127i	$0.00318719\pi$
$30$		0			0
$31$	−1.50000	−	2.59808i	−0.269408	−	0.466628i	0.699301	−	0.714827i	$-0.253495\pi$
$31$	−1.50000	−	2.59808i	−0.269408	−	0.466628i	−0.968709	+	0.248199i	$0.920161\pi$
$32$	6.61438	+	11.4564i	1.16927	+	2.02523i
$33$		0			0
$34$		0			0
$35$	−2.64575			−0.447214
$36$		0			0
$37$	−3.00000			−0.493197			−0.246598	−	0.969118i	$-0.579313\pi$
$37$	−3.00000			−0.493197			−0.246598	+	0.969118i	$0.579313\pi$
$38$	9.26013	−	16.0390i	1.50219	−	2.60187i
$39$		0			0
$40$	10.5000	+	18.1865i	1.66020	+	2.87554i
$41$	1.32288	+	2.29129i	0.206598	+	0.357839i	0.950641	−	0.310293i	$-0.100427\pi$
$41$	1.32288	+	2.29129i	0.206598	+	0.357839i	−0.744042	+	0.668132i	$0.767094\pi$
$42$		0			0
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	0.381246	+	0.924473i	$0.375495\pi$
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	−0.991241	+	0.132068i	$0.957838\pi$
$44$	13.2288			1.99431
$45$		0			0
$46$	−21.0000			−3.09628
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	2.64575	+	4.58258i	0.374166	+	0.648074i
$51$		0			0
$52$	5.00000	−	8.66025i	0.693375	−	1.20096i
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$		0			0
$55$	7.00000			0.943880
$56$	−3.96863	+	6.87386i	−0.530330	+	0.918559i
$57$		0			0
$58$	−7.00000	−	12.1244i	−0.919145	−	1.59201i
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$		0			0
$61$	4.00000	−	6.92820i	0.512148	−	0.887066i	−0.487753	−	0.872982i	$-0.662183\pi$
$61$	4.00000	−	6.92820i	0.512148	−	0.887066i	0.999901	−	0.0140840i	$-0.00448323\pi$
$62$	−7.93725			−1.00803
$63$		0			0
$64$	13.0000			1.62500
$65$	2.64575	−	4.58258i	0.328165	−	0.568399i
$66$		0			0
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	0.920623	−	0.390453i	$-0.127682\pi$
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	−0.798454	+	0.602056i	$0.794348\pi$
$68$		0			0
$69$		0			0
$70$	−3.50000	+	6.06218i	−0.418330	+	0.724569i
$71$	−7.93725			−0.941979			−0.470989	−	0.882139i	$-0.656103\pi$
$71$	−7.93725			−0.941979			−0.470989	+	0.882139i	$0.656103\pi$
$72$		0			0
$73$		0			0			−	1.00000i	$-0.5\pi$
$73$		0			0				1.00000i	$0.5\pi$
$74$	−3.96863	+	6.87386i	−0.461344	+	0.799070i
$75$		0			0
$76$	−17.5000	−	30.3109i	−2.00739	−	3.47690i
$77$	1.32288	+	2.29129i	0.150756	+	0.261116i
$78$		0			0
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	−0.731307	−	0.682048i	$-0.761089\pi$
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	0.956325	+	0.292306i	$0.0944227\pi$
$80$	29.1033			3.25384
$81$		0			0
$82$	7.00000			0.773021
$83$	7.93725	−	13.7477i	0.871227	−	1.50901i	0.0104983	−	0.999945i	$-0.496658\pi$
$83$	7.93725	−	13.7477i	0.871227	−	1.50901i	0.860729	−	0.509064i	$-0.170008\pi$
$84$		0			0
$85$		0			0
$86$	10.5830	+	18.3303i	1.14119	+	1.97661i
$87$		0			0
$88$	10.5000	−	18.1865i	1.11930	−	1.93869i
$89$	18.5203			1.96314			0.981572	−	0.191094i	$-0.0612035\pi$
$89$	18.5203			1.96314			0.981572	+	0.191094i	$0.0612035\pi$
$90$		0			0
$91$	2.00000			0.209657
$92$	−19.8431	+	34.3693i	−2.06879	+	3.58325i
$93$		0			0
$94$		0			0
$95$	−9.26013	−	16.0390i	−0.950069	−	1.64557i
$96$		0			0
$97$	6.00000	−	10.3923i	0.609208	−	1.05518i	−0.382164	−	0.924095i	$-0.624821\pi$
$97$	6.00000	−	10.3923i	0.609208	−	1.05518i	0.991371	−	0.131084i	$-0.0418458\pi$
$98$	−2.64575			−0.267261
$99$		0			0
$100$	10.0000			1.00000
$101$	5.29150	−	9.16515i	0.526524	−	0.911967i	−0.472998	−	0.881063i	$-0.656828\pi$
$101$	5.29150	−	9.16515i	0.526524	−	0.911967i	0.999522	−	0.0309033i	$-0.00983838\pi$
$102$		0			0
$103$	6.50000	+	11.2583i	0.640464	+	1.10932i	0.985329	+	0.170664i	$0.0545913\pi$
$103$	6.50000	+	11.2583i	0.640464	+	1.10932i	−0.344865	+	0.938652i	$0.612075\pi$
$104$	−7.93725	−	13.7477i	−0.778312	−	1.34808i
$105$		0			0
$106$		0			0
$107$	−5.29150			−0.511549			−0.255774	−	0.966736i	$-0.582330\pi$
$107$	−5.29150			−0.511549			−0.255774	+	0.966736i	$0.582330\pi$
$108$		0			0
$109$	9.00000			0.862044			0.431022	−	0.902342i	$-0.358153\pi$
$109$	9.00000			0.862044			0.431022	+	0.902342i	$0.358153\pi$
$110$	9.26013	−	16.0390i	0.882919	−	1.52926i
$111$		0			0
$112$	5.50000	+	9.52628i	0.519701	+	0.900149i
$113$	2.64575	+	4.58258i	0.248891	+	0.431092i	0.963218	−	0.268719i	$-0.0866005\pi$
$113$	2.64575	+	4.58258i	0.248891	+	0.431092i	−0.714327	+	0.699812i	$0.753267\pi$
$114$		0			0
$115$	−10.5000	+	18.1865i	−0.979130	+	1.69590i
$116$	−26.4575			−2.45652
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	2.00000	+	3.46410i	0.181818	+	0.314918i
$122$	−10.5830	−	18.3303i	−0.958140	−	1.65955i
$123$		0			0
$124$	−7.50000	+	12.9904i	−0.673520	+	1.16657i
$125$	−7.93725			−0.709930
$126$		0			0
$127$	6.00000			0.532414			0.266207	−	0.963916i	$-0.414230\pi$
$127$	6.00000			0.532414			0.266207	+	0.963916i	$0.414230\pi$
$128$	3.96863	−	6.87386i	0.350780	−	0.607569i
$129$		0			0
$130$	−7.00000	−	12.1244i	−0.613941	−	1.06338i
$131$	10.5830	+	18.3303i	0.924641	+	1.60153i	0.792137	+	0.610344i	$0.208969\pi$
$131$	10.5830	+	18.3303i	0.924641	+	1.60153i	0.132505	+	0.991182i	$0.457698\pi$
$132$		0			0
$133$	3.50000	−	6.06218i	0.303488	−	0.525657i
$134$	5.29150			0.457116
$135$		0			0
$136$		0			0
$137$	−7.93725	+	13.7477i	−0.678125	+	1.17455i	0.297419	+	0.954747i	$0.403874\pi$
$137$	−7.93725	+	13.7477i	−0.678125	+	1.17455i	−0.975545	+	0.219801i	$0.929459\pi$
$138$		0			0
$139$	6.00000	+	10.3923i	0.508913	+	0.881464i	0.999947	+	0.0103230i	$0.00328598\pi$
$139$	6.00000	+	10.3923i	0.508913	+	0.881464i	−0.491033	+	0.871141i	$0.663381\pi$
$140$	6.61438	+	11.4564i	0.559017	+	0.968246i
$141$		0			0
$142$	−10.5000	+	18.1865i	−0.881140	+	1.52618i
$143$	−5.29150			−0.442498
$144$		0			0
$145$	−14.0000			−1.16264
$146$		0			0
$147$		0			0
$148$	7.50000	+	12.9904i	0.616496	+	1.06780i
$149$	−7.93725	−	13.7477i	−0.650245	−	1.12626i	−0.983063	−	0.183267i	$-0.941333\pi$
$149$	−7.93725	−	13.7477i	−0.650245	−	1.12626i	0.332818	−	0.942991i	$-0.392000\pi$
$150$		0			0
$151$	−1.00000	+	1.73205i	−0.0813788	+	0.140952i	−0.903842	−	0.427865i	$-0.859266\pi$
$151$	−1.00000	+	1.73205i	−0.0813788	+	0.140952i	0.822464	+	0.568818i	$0.192599\pi$
$152$	−55.5608			−4.50657
$153$		0			0
$154$	7.00000			0.564076
$155$	−3.96863	+	6.87386i	−0.318768	+	0.552122i
$156$		0			0
$157$	7.00000	+	12.1244i	0.558661	+	0.967629i	0.997609	+	0.0691164i	$0.0220180\pi$
$157$	7.00000	+	12.1244i	0.558661	+	0.967629i	−0.438948	+	0.898513i	$0.644649\pi$
$158$	−5.29150	−	9.16515i	−0.420969	−	0.729140i
$159$		0			0
$160$	17.5000	−	30.3109i	1.38350	−	2.39629i
$161$	−7.93725			−0.625543
$162$		0			0
$163$	10.0000			0.783260			0.391630	−	0.920123i	$-0.371911\pi$
$163$	10.0000			0.783260			0.391630	+	0.920123i	$0.371911\pi$
$164$	6.61438	−	11.4564i	0.516496	−	0.894598i
$165$		0			0
$166$	−21.0000	−	36.3731i	−1.62992	−	2.82310i
$167$	2.64575	+	4.58258i	0.204734	+	0.354610i	0.950048	−	0.312104i	$-0.101034\pi$
$167$	2.64575	+	4.58258i	0.204734	+	0.354610i	−0.745314	+	0.666714i	$0.767700\pi$
$168$		0			0
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$		0			0
$171$		0			0
$172$	40.0000			3.04997
$173$	−6.61438	+	11.4564i	−0.502882	+	0.871017i	0.497113	+	0.867686i	$0.334394\pi$
$173$	−6.61438	+	11.4564i	−0.502882	+	0.871017i	−0.999994	+	0.00333090i	$0.998940\pi$
$174$		0			0
$175$	1.00000	+	1.73205i	0.0755929	+	0.130931i
$176$	−14.5516	−	25.2042i	−1.09687	−	1.89984i
$177$		0			0
$178$	24.5000	−	42.4352i	1.83635	−	3.18066i
$179$	5.29150			0.395505			0.197753	−	0.980252i	$-0.436636\pi$
$179$	5.29150			0.395505			0.197753	+	0.980252i	$0.436636\pi$
$180$		0			0
$181$	−14.0000			−1.04061			−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000			−1.04061			−0.520306	+	0.853980i	$0.674182\pi$
$182$	2.64575	−	4.58258i	0.196116	−	0.339683i
$183$		0			0
$184$	31.5000	+	54.5596i	2.32221	+	4.02219i
$185$	3.96863	+	6.87386i	0.291779	+	0.505376i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	−49.0000			−3.55483
$191$	−1.32288	+	2.29129i	−0.0957199	+	0.165792i	−0.909909	−	0.414808i	$-0.863849\pi$
$191$	−1.32288	+	2.29129i	−0.0957199	+	0.165792i	0.814189	+	0.580600i	$0.197182\pi$
$192$		0			0
$193$	−1.00000	−	1.73205i	−0.0719816	−	0.124676i	0.827788	−	0.561041i	$-0.189599\pi$
$193$	−1.00000	−	1.73205i	−0.0719816	−	0.124676i	−0.899770	+	0.436365i	$0.856266\pi$
$194$	−15.8745	−	27.4955i	−1.13972	−	1.97406i
$195$		0			0
$196$	−2.50000	+	4.33013i	−0.178571	+	0.309295i
$197$	26.4575			1.88502			0.942510	−	0.334178i	$-0.108459\pi$
$197$	26.4575			1.88502			0.942510	+	0.334178i	$0.108459\pi$
$198$		0			0
$199$	−3.00000			−0.212664			−0.106332	−	0.994331i	$-0.533911\pi$
$199$	−3.00000			−0.212664			−0.106332	+	0.994331i	$0.533911\pi$
$200$	7.93725	−	13.7477i	0.561249	−	0.972111i
$201$		0			0
$202$	−14.0000	−	24.2487i	−0.985037	−	1.70613i
$203$	−2.64575	−	4.58258i	−0.185695	−	0.321634i
$204$		0			0
$205$	3.50000	−	6.06218i	0.244451	−	0.423401i
$206$	34.3948			2.39640
$207$		0			0
$208$	−22.0000			−1.52543
$209$	−9.26013	+	16.0390i	−0.640537	+	1.10944i
$210$		0			0
$211$	−11.0000	−	19.0526i	−0.757271	−	1.31163i	−0.944237	−	0.329266i	$-0.893199\pi$
$211$	−11.0000	−	19.0526i	−0.757271	−	1.31163i	0.186966	−	0.982366i	$-0.440135\pi$
$212$		0			0
$213$		0			0
$214$	−7.00000	+	12.1244i	−0.478510	+	0.828804i
$215$	21.1660			1.44351
$216$		0			0
$217$	−3.00000			−0.203653
$218$	11.9059	−	20.6216i	0.806368	−	1.39667i
$219$		0			0
$220$	−17.5000	−	30.3109i	−1.17985	−	2.04356i
$221$		0			0
$222$		0			0
$223$	−3.50000	+	6.06218i	−0.234377	+	0.405953i	−0.959092	−	0.283096i	$-0.908638\pi$
$223$	−3.50000	+	6.06218i	−0.234377	+	0.405953i	0.724714	+	0.689050i	$0.241972\pi$
$224$	13.2288			0.883883
$225$		0			0
$226$	14.0000			0.931266
$227$	−7.93725	+	13.7477i	−0.526814	+	0.912469i	0.472698	+	0.881225i	$0.343280\pi$
$227$	−7.93725	+	13.7477i	−0.526814	+	0.912469i	−0.999512	+	0.0312441i	$0.990053\pi$
$228$		0			0
$229$	−10.0000	−	17.3205i	−0.660819	−	1.14457i	−0.980401	−	0.197013i	$-0.936876\pi$
$229$	−10.0000	−	17.3205i	−0.660819	−	1.14457i	0.319582	−	0.947559i	$-0.396457\pi$
$230$	27.7804	+	48.1170i	1.83178	+	3.17274i
$231$		0			0
$232$	−21.0000	+	36.3731i	−1.37872	+	2.38801i
$233$	−15.8745			−1.03997			−0.519987	−	0.854174i	$-0.674063\pi$
$233$	−15.8745			−1.03997			−0.519987	+	0.854174i	$0.674063\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	7.93725	+	13.7477i	0.513418	+	0.889267i	0.999879	+	0.0155640i	$0.00495438\pi$
$239$	7.93725	+	13.7477i	0.513418	+	0.889267i	−0.486461	+	0.873703i	$0.661712\pi$
$240$		0			0
$241$	2.00000	−	3.46410i	0.128831	−	0.223142i	−0.794393	−	0.607404i	$-0.792211\pi$
$241$	2.00000	−	3.46410i	0.128831	−	0.223142i	0.923224	+	0.384262i	$0.125544\pi$
$242$	10.5830			0.680301
$243$		0			0
$244$	−40.0000			−2.56074
$245$	−1.32288	+	2.29129i	−0.0845154	+	0.146385i
$246$		0			0
$247$	7.00000	+	12.1244i	0.445399	+	0.771454i
$248$	11.9059	+	20.6216i	0.756024	+	1.30947i
$249$		0			0
$250$	−10.5000	+	18.1865i	−0.664078	+	1.15022i
$251$	10.5830			0.667993			0.333997	−	0.942574i	$-0.391603\pi$
$251$	10.5830			0.667993			0.333997	+	0.942574i	$0.391603\pi$
$252$		0			0
$253$	21.0000			1.32026
$254$	7.93725	−	13.7477i	0.498028	−	0.862609i
$255$		0			0
$256$	2.50000	+	4.33013i	0.156250	+	0.270633i
$257$	9.26013	+	16.0390i	0.577631	+	1.00049i	0.995750	+	0.0920941i	$0.0293561\pi$
$257$	9.26013	+	16.0390i	0.577631	+	1.00049i	−0.418119	+	0.908392i	$0.637311\pi$
$258$		0			0
$259$	−1.50000	+	2.59808i	−0.0932055	+	0.161437i
$260$	−26.4575			−1.64083
$261$		0			0
$262$	56.0000			3.45969
$263$	−9.26013	+	16.0390i	−0.571004	+	0.989008i	0.425459	+	0.904978i	$0.360113\pi$
$263$	−9.26013	+	16.0390i	−0.571004	+	0.989008i	−0.996463	+	0.0840304i	$0.973221\pi$
$264$		0			0
$265$		0			0
$266$	−9.26013	−	16.0390i	−0.567775	−	0.983415i
$267$		0			0
$268$	5.00000	−	8.66025i	0.305424	−	0.529009i
$269$	−23.8118			−1.45183			−0.725914	−	0.687785i	$-0.758583\pi$
$269$	−23.8118			−1.45183			−0.725914	+	0.687785i	$0.758583\pi$
$270$		0			0
$271$	−20.0000			−1.21491			−0.607457	−	0.794353i	$-0.707810\pi$
$271$	−20.0000			−1.21491			−0.607457	+	0.794353i	$0.707810\pi$
$272$		0			0
$273$		0			0
$274$	21.0000	+	36.3731i	1.26866	+	2.19738i
$275$	−2.64575	−	4.58258i	−0.159545	−	0.276340i
$276$		0			0
$277$	11.5000	−	19.9186i	0.690968	−	1.19679i	−0.280553	−	0.959839i	$-0.590518\pi$
$277$	11.5000	−	19.9186i	0.690968	−	1.19679i	0.971521	−	0.236953i	$-0.0761488\pi$
$278$	31.7490			1.90418
$279$		0			0
$280$	21.0000			1.25499
$281$	5.29150	−	9.16515i	0.315665	−	0.546747i	−0.663914	−	0.747809i	$-0.731106\pi$
$281$	5.29150	−	9.16515i	0.315665	−	0.546747i	0.979579	+	0.201062i	$0.0644392\pi$
$282$		0			0
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	0.800439	−	0.599414i	$-0.204600\pi$
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	−0.919327	+	0.393494i	$0.871266\pi$
$284$	19.8431	+	34.3693i	1.17747	+	2.03944i
$285$		0			0
$286$	−7.00000	+	12.1244i	−0.413919	+	0.716928i
$287$	2.64575			0.156174
$288$		0			0
$289$	−17.0000			−1.00000
$290$	−18.5203	+	32.0780i	−1.08755	+	1.88369i
$291$		0			0
$292$		0			0
$293$	5.29150	+	9.16515i	0.309133	+	0.535434i	0.978173	−	0.207792i	$-0.0666279\pi$
$293$	5.29150	+	9.16515i	0.309133	+	0.535434i	−0.669040	+	0.743226i	$0.733295\pi$
$294$		0			0
$295$		0			0
$296$	23.8118			1.38403
$297$		0			0
$298$	−42.0000			−2.43299
$299$	7.93725	−	13.7477i	0.459023	−	0.795052i
$300$		0			0
$301$	4.00000	+	6.92820i	0.230556	+	0.399335i
$302$	2.64575	+	4.58258i	0.152246	+	0.263698i
$303$		0			0
$304$	−38.5000	+	66.6840i	−2.20813	+	3.82459i
$305$	−21.1660			−1.21196
$306$		0			0
$307$	19.0000			1.08439			0.542194	−	0.840254i	$-0.317594\pi$
$307$	19.0000			1.08439			0.542194	+	0.840254i	$0.317594\pi$
$308$	6.61438	−	11.4564i	0.376889	−	0.652791i
$309$		0			0
$310$	10.5000	+	18.1865i	0.596360	+	1.03293i
$311$	7.93725	+	13.7477i	0.450080	+	0.779562i	0.998391	−	0.0567130i	$-0.0180620\pi$
$311$	7.93725	+	13.7477i	0.450080	+	0.779562i	−0.548310	+	0.836275i	$0.684729\pi$
$312$		0			0
$313$	−7.00000	+	12.1244i	−0.395663	+	0.685309i	−0.993186	−	0.116543i	$-0.962819\pi$
$313$	−7.00000	+	12.1244i	−0.395663	+	0.685309i	0.597522	+	0.801852i	$0.296152\pi$
$314$	37.0405			2.09032
$315$		0			0
$316$	−20.0000			−1.12509
$317$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$317$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$318$		0			0
$319$	7.00000	+	12.1244i	0.391925	+	0.678834i
$320$	−17.1974	−	29.7867i	−0.961363	−	1.66513i
$321$		0			0
$322$	−10.5000	+	18.1865i	−0.585142	+	1.01350i
$323$		0			0
$324$		0			0
$325$	−4.00000			−0.221880
$326$	13.2288	−	22.9129i	0.732673	−	1.26903i
$327$		0			0
$328$	−10.5000	−	18.1865i	−0.579766	−	1.00418i
$329$		0			0
$330$		0			0
$331$	−10.0000	+	17.3205i	−0.549650	+	0.952021i	0.448649	+	0.893708i	$0.351905\pi$
$331$	−10.0000	+	17.3205i	−0.549650	+	0.952021i	−0.998298	+	0.0583130i	$0.981428\pi$
$332$	−79.3725			−4.35613
$333$		0			0
$334$	14.0000			0.766046
$335$	2.64575	−	4.58258i	0.144553	−	0.250373i
$336$		0			0
$337$	−9.50000	−	16.4545i	−0.517498	−	0.896333i	−0.999793	−	0.0203242i	$-0.993530\pi$
$337$	−9.50000	−	16.4545i	−0.517498	−	0.896333i	0.482295	−	0.876009i	$-0.339803\pi$
$338$	−11.9059	−	20.6216i	−0.647595	−	1.12167i
$339$		0			0
$340$		0			0
$341$	7.93725			0.429826
$342$		0			0
$343$	−1.00000			−0.0539949
$344$	31.7490	−	54.9909i	1.71179	−	2.96491i
$345$		0			0
$346$	17.5000	+	30.3109i	0.940806	+	1.62952i
$347$	1.32288	+	2.29129i	0.0710157	+	0.123003i	0.899347	−	0.437236i	$-0.144043\pi$
$347$	1.32288	+	2.29129i	0.0710157	+	0.123003i	−0.828331	+	0.560239i	$0.810709\pi$
$348$		0			0
$349$	1.00000	−	1.73205i	0.0535288	−	0.0927146i	−0.838019	−	0.545640i	$-0.816286\pi$
$349$	1.00000	−	1.73205i	0.0535288	−	0.0927146i	0.891548	+	0.452926i	$0.149620\pi$
$350$	5.29150			0.282843
$351$		0			0
$352$	−35.0000			−1.86551
$353$	−1.32288	+	2.29129i	−0.0704096	+	0.121953i	−0.899081	−	0.437783i	$-0.855764\pi$
$353$	−1.32288	+	2.29129i	−0.0704096	+	0.121953i	0.828671	+	0.559736i	$0.189097\pi$
$354$		0			0
$355$	10.5000	+	18.1865i	0.557282	+	0.965241i
$356$	−46.3006	−	80.1951i	−2.45393	−	4.25033i
$357$		0			0
$358$	7.00000	−	12.1244i	0.369961	−	0.640792i
$359$	5.29150			0.279275			0.139637	−	0.990203i	$-0.455406\pi$
$359$	5.29150			0.279275			0.139637	+	0.990203i	$0.455406\pi$
$360$		0			0
$361$	30.0000			1.57895
$362$	−18.5203	+	32.0780i	−0.973403	+	1.68598i
$363$		0			0
$364$	−5.00000	−	8.66025i	−0.262071	−	0.453921i
$365$		0			0
$366$		0			0
$367$	−10.5000	+	18.1865i	−0.548096	+	0.949329i	0.450310	+	0.892873i	$0.351314\pi$
$367$	−10.5000	+	18.1865i	−0.548096	+	0.949329i	−0.998405	+	0.0564568i	$0.982020\pi$
$368$	87.3098			4.55134
$369$		0			0
$370$	21.0000			1.09174
$371$		0			0
$372$		0			0
$373$	−14.5000	−	25.1147i	−0.750782	−	1.30039i	−0.947444	−	0.319921i	$-0.896344\pi$
$373$	−14.5000	−	25.1147i	−0.750782	−	1.30039i	0.196663	−	0.980471i	$-0.436990\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	10.5830			0.545053
$378$		0			0
$379$	36.0000			1.84920			0.924598	−	0.380945i	$-0.124401\pi$
$379$	36.0000			1.84920			0.924598	+	0.380945i	$0.124401\pi$
$380$	−46.3006	+	80.1951i	−2.37517	+	4.11392i
$381$		0			0
$382$	3.50000	+	6.06218i	0.179076	+	0.310168i
$383$	7.93725	+	13.7477i	0.405575	+	0.702476i	0.994388	−	0.105793i	$-0.0337381\pi$
$383$	7.93725	+	13.7477i	0.405575	+	0.702476i	−0.588813	+	0.808269i	$0.700405\pi$
$384$		0			0
$385$	3.50000	−	6.06218i	0.178377	−	0.308957i
$386$	−5.29150			−0.269330
$387$		0			0
$388$	−60.0000			−3.04604
$389$	15.8745	−	27.4955i	0.804869	−	1.39407i	−0.111510	−	0.993763i	$-0.535569\pi$
$389$	15.8745	−	27.4955i	0.804869	−	1.39407i	0.916379	−	0.400312i	$-0.131098\pi$
$390$		0			0
$391$		0			0
$392$	3.96863	+	6.87386i	0.200446	+	0.347183i
$393$		0			0
$394$	35.0000	−	60.6218i	1.76327	−	3.05408i
$395$	−10.5830			−0.532489
$396$		0			0
$397$	−6.00000			−0.301131			−0.150566	−	0.988600i	$-0.548110\pi$
$397$	−6.00000			−0.301131			−0.150566	+	0.988600i	$0.548110\pi$
$398$	−3.96863	+	6.87386i	−0.198929	+	0.344556i
$399$		0			0
$400$	−11.0000	−	19.0526i	−0.550000	−	0.952628i
$401$	7.93725	+	13.7477i	0.396368	+	0.686529i	0.993275	−	0.115782i	$-0.0369373\pi$
$401$	7.93725	+	13.7477i	0.396368	+	0.686529i	−0.596907	+	0.802310i	$0.703604\pi$
$402$		0			0
$403$	3.00000	−	5.19615i	0.149441	−	0.258839i
$404$	−52.9150			−2.63262
$405$		0			0
$406$	−14.0000			−0.694808
$407$	3.96863	−	6.87386i	0.196718	−	0.340725i
$408$		0			0
$409$	−16.0000	−	27.7128i	−0.791149	−	1.37031i	−0.925256	−	0.379344i	$-0.876150\pi$
$409$	−16.0000	−	27.7128i	−0.791149	−	1.37031i	0.134107	−	0.990967i	$-0.457183\pi$
$410$	−9.26013	−	16.0390i	−0.457325	−	0.792110i
$411$		0			0
$412$	32.5000	−	56.2917i	1.60116	−	2.77329i
$413$		0			0
$414$		0			0
$415$	−42.0000			−2.06170
$416$	−13.2288	+	22.9129i	−0.648593	+	1.12340i
$417$		0			0
$418$	24.5000	+	42.4352i	1.19833	+	2.07558i
$419$	−7.93725	−	13.7477i	−0.387760	−	0.671620i	0.604388	−	0.796690i	$-0.293418\pi$
$419$	−7.93725	−	13.7477i	−0.387760	−	0.671620i	−0.992148	+	0.125070i	$0.960084\pi$
$420$		0			0
$421$	9.50000	−	16.4545i	0.463002	−	0.801942i	−0.536107	−	0.844150i	$-0.680106\pi$
$421$	9.50000	−	16.4545i	0.463002	−	0.801942i	0.999109	+	0.0422075i	$0.0134391\pi$
$422$	−58.2065			−2.83345
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−4.00000	−	6.92820i	−0.193574	−	0.335279i
$428$	13.2288	+	22.9129i	0.639436	+	1.10754i
$429$		0			0
$430$	28.0000	−	48.4974i	1.35028	−	2.33875i
$431$	−39.6863			−1.91162			−0.955810	−	0.293985i	$-0.905019\pi$
$431$	−39.6863			−1.91162			−0.955810	+	0.293985i	$0.905019\pi$
$432$		0			0
$433$	−26.0000			−1.24948			−0.624740	−	0.780833i	$-0.714795\pi$
$433$	−26.0000			−1.24948			−0.624740	+	0.780833i	$0.714795\pi$
$434$	−3.96863	+	6.87386i	−0.190500	+	0.329956i
$435$		0			0
$436$	−22.5000	−	38.9711i	−1.07755	−	1.86638i
$437$	−27.7804	−	48.1170i	−1.32892	−	2.30175i
$438$		0			0
$439$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$439$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$440$	−55.5608			−2.64876
$441$		0			0
$442$		0			0
$443$	−3.96863	+	6.87386i	−0.188555	+	0.326587i	−0.944769	−	0.327738i	$-0.893714\pi$
$443$	−3.96863	+	6.87386i	−0.188555	+	0.326587i	0.756214	+	0.654325i	$0.227047\pi$
$444$		0			0
$445$	−24.5000	−	42.4352i	−1.16141	−	2.01162i
$446$	9.26013	+	16.0390i	0.438480	+	0.759469i
$447$		0			0
$448$	6.50000	−	11.2583i	0.307096	−	0.531906i
$449$	15.8745			0.749164			0.374582	−	0.927194i	$-0.377786\pi$
$449$	15.8745			0.749164			0.374582	+	0.927194i	$0.377786\pi$
$450$		0			0
$451$	−7.00000			−0.329617
$452$	13.2288	−	22.9129i	0.622228	−	1.07773i
$453$		0			0
$454$	21.0000	+	36.3731i	0.985579	+	1.70707i
$455$	−2.64575	−	4.58258i	−0.124035	−	0.214834i
$456$		0			0
$457$	−12.5000	+	21.6506i	−0.584725	+	1.01277i	0.410184	+	0.912003i	$0.365464\pi$
$457$	−12.5000	+	21.6506i	−0.584725	+	1.01277i	−0.994910	+	0.100771i	$0.967869\pi$
$458$	−52.9150			−2.47256
$459$		0			0
$460$	105.000			4.89565
$461$	9.26013	−	16.0390i	0.431287	−	0.747011i	−0.565697	−	0.824613i	$-0.691393\pi$
$461$	9.26013	−	16.0390i	0.431287	−	0.747011i	0.996984	+	0.0776016i	$0.0247262\pi$
$462$		0			0
$463$	13.0000	+	22.5167i	0.604161	+	1.04644i	0.992183	+	0.124788i	$0.0398251\pi$
$463$	13.0000	+	22.5167i	0.604161	+	1.04644i	−0.388022	+	0.921650i	$0.626842\pi$
$464$	29.1033	+	50.4083i	1.35109	+	2.34015i
$465$		0			0
$466$	−21.0000	+	36.3731i	−0.972806	+	1.68495i
$467$	31.7490			1.46917			0.734585	−	0.678517i	$-0.237377\pi$
$467$	31.7490			1.46917			0.734585	+	0.678517i	$0.237377\pi$
$468$		0			0
$469$	2.00000			0.0923514
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−10.5830	−	18.3303i	−0.486607	−	0.842828i
$474$		0			0
$475$	−7.00000	+	12.1244i	−0.321182	+	0.556304i
$476$		0			0
$477$		0			0
$478$	42.0000			1.92104
$479$	−10.5830	+	18.3303i	−0.483550	+	0.837533i	−0.999822	−	0.0188920i	$-0.993986\pi$
$479$	−10.5830	+	18.3303i	−0.483550	+	0.837533i	0.516272	+	0.856425i	$0.327319\pi$
$480$		0			0
$481$	−3.00000	−	5.19615i	−0.136788	−	0.236924i
$482$	−5.29150	−	9.16515i	−0.241021	−	0.417461i
$483$		0			0
$484$	10.0000	−	17.3205i	0.454545	−	0.787296i
$485$	−31.7490			−1.44165
$486$		0			0
$487$	−32.0000			−1.45006			−0.725029	−	0.688718i	$-0.758174\pi$
$487$	−32.0000			−1.45006			−0.725029	+	0.688718i	$0.758174\pi$
$488$	−31.7490	+	54.9909i	−1.43721	+	2.48932i
$489$		0			0
$490$	3.50000	+	6.06218i	0.158114	+	0.273861i
$491$	1.32288	+	2.29129i	0.0597005	+	0.103404i	0.894331	−	0.447406i	$-0.147652\pi$
$491$	1.32288	+	2.29129i	0.0597005	+	0.103404i	−0.834630	+	0.550810i	$0.814319\pi$
$492$		0			0
$493$		0			0
$494$	37.0405			1.66653
$495$		0			0
$496$	33.0000			1.48174
$497$	−3.96863	+	6.87386i	−0.178017	+	0.308335i
$498$		0			0
$499$	−2.00000	−	3.46410i	−0.0895323	−	0.155074i	0.817781	−	0.575529i	$-0.195204\pi$
$499$	−2.00000	−	3.46410i	−0.0895323	−	0.155074i	−0.907314	+	0.420455i	$0.861871\pi$
$500$	19.8431	+	34.3693i	0.887412	+	1.53704i
$501$		0			0
$502$	14.0000	−	24.2487i	0.624851	−	1.08227i
$503$	15.8745			0.707809			0.353905	−	0.935282i	$-0.384854\pi$
$503$	15.8745			0.707809			0.353905	+	0.935282i	$0.384854\pi$
$504$		0			0
$505$	−28.0000			−1.24598
$506$	27.7804	−	48.1170i	1.23499	−	2.13906i
$507$		0			0
$508$	−15.0000	−	25.9808i	−0.665517	−	1.15271i
$509$	5.29150	+	9.16515i	0.234542	+	0.406238i	0.959139	−	0.282934i	$-0.0913077\pi$
$509$	5.29150	+	9.16515i	0.234542	+	0.406238i	−0.724598	+	0.689172i	$0.757974\pi$
$510$		0			0
$511$		0			0
$512$	29.1033			1.28619
$513$		0			0
$514$	49.0000			2.16130
$515$	17.1974	−	29.7867i	0.757807	−	1.31256i
$516$		0			0
$517$		0			0
$518$	3.96863	+	6.87386i	0.174371	+	0.302020i
$519$		0			0
$520$	−21.0000	+	36.3731i	−0.920911	+	1.59506i
$521$	39.6863			1.73869			0.869344	−	0.494208i	$-0.164542\pi$
$521$	39.6863			1.73869			0.869344	+	0.494208i	$0.164542\pi$
$522$		0			0
$523$	13.0000			0.568450			0.284225	−	0.958758i	$-0.408264\pi$
$523$	13.0000			0.568450			0.284225	+	0.958758i	$0.408264\pi$
$524$	52.9150	−	91.6515i	2.31160	−	4.00381i
$525$		0			0
$526$	24.5000	+	42.4352i	1.06825	+	1.85026i
$527$		0			0
$528$		0			0
$529$	−20.0000	+	34.6410i	−0.869565	+	1.50613i
$530$		0			0
$531$		0			0
$532$	−35.0000			−1.51744
$533$	−2.64575	+	4.58258i	−0.114600	+	0.198493i
$534$		0			0
$535$	7.00000	+	12.1244i	0.302636	+	0.524182i
$536$	−7.93725	−	13.7477i	−0.342837	−	0.593811i
$537$		0			0
$538$	−31.5000	+	54.5596i	−1.35806	+	2.35223i
$539$	2.64575			0.113961
$540$		0			0
$541$	29.0000			1.24681			0.623404	−	0.781900i	$-0.285749\pi$
$541$	29.0000			1.24681			0.623404	+	0.781900i	$0.285749\pi$
$542$	−26.4575	+	45.8258i	−1.13645	+	1.96838i
$543$		0			0
$544$		0			0
$545$	−11.9059	−	20.6216i	−0.509992	−	0.883332i
$546$		0			0
$547$	4.00000	−	6.92820i	0.171028	−	0.296229i	−0.767752	−	0.640747i	$-0.778625\pi$
$547$	4.00000	−	6.92820i	0.171028	−	0.296229i	0.938779	+	0.344519i	$0.111958\pi$
$548$	79.3725			3.39063
$549$		0			0
$550$	−14.0000			−0.596962
$551$	18.5203	−	32.0780i	0.788990	−	1.36657i
$552$		0			0
$553$	−2.00000	−	3.46410i	−0.0850487	−	0.147309i
$554$	−30.4261	−	52.6996i	−1.29268	−	2.23899i
$555$		0			0
$556$	30.0000	−	51.9615i	1.27228	−	2.20366i
$557$	−5.29150			−0.224208			−0.112104	−	0.993696i	$-0.535759\pi$
$557$	−5.29150			−0.224208			−0.112104	+	0.993696i	$0.535759\pi$
$558$		0			0
$559$	−16.0000			−0.676728
$560$	14.5516	−	25.2042i	0.614919	−	1.06507i
$561$		0			0
$562$	−14.0000	−	24.2487i	−0.590554	−	1.02287i
$563$	−13.2288	−	22.9129i	−0.557526	−	0.965663i	−0.997702	−	0.0677515i	$-0.978418\pi$
$563$	−13.2288	−	22.9129i	−0.557526	−	0.965663i	0.440177	−	0.897911i	$-0.354916\pi$
$564$		0			0
$565$	7.00000	−	12.1244i	0.294492	−	0.510075i
$566$	−10.5830			−0.444837
$567$		0			0
$568$	63.0000			2.64342
$569$	−13.2288	+	22.9129i	−0.554578	+	0.960558i	0.443358	+	0.896345i	$0.353787\pi$
$569$	−13.2288	+	22.9129i	−0.554578	+	0.960558i	−0.997936	+	0.0642132i	$0.979546\pi$
$570$		0			0
$571$	5.00000	+	8.66025i	0.209243	+	0.362420i	0.951476	−	0.307722i	$-0.0995665\pi$
$571$	5.00000	+	8.66025i	0.209243	+	0.362420i	−0.742233	+	0.670142i	$0.766233\pi$
$572$	13.2288	+	22.9129i	0.553122	+	0.958036i
$573$		0			0
$574$	3.50000	−	6.06218i	0.146087	−	0.253030i
$575$	15.8745			0.662013
$576$		0			0
$577$	−38.0000			−1.58196			−0.790980	−	0.611842i	$-0.790429\pi$
$577$	−38.0000			−1.58196			−0.790980	+	0.611842i	$0.790429\pi$
$578$	−22.4889	+	38.9519i	−0.935414	+	1.62019i
$579$		0			0
$580$	35.0000	+	60.6218i	1.45330	+	2.51718i
$581$	−7.93725	−	13.7477i	−0.329293	−	0.570352i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	28.0000			1.15667
$587$	−13.2288	+	22.9129i	−0.546009	+	0.945716i	0.452533	+	0.891747i	$0.350520\pi$
$587$	−13.2288	+	22.9129i	−0.546009	+	0.945716i	−0.998543	+	0.0539683i	$0.982813\pi$
$588$		0			0
$589$	−10.5000	−	18.1865i	−0.432645	−	0.749363i
$590$		0			0
$591$		0			0
$592$	16.5000	−	28.5788i	0.678146	−	1.17458i
$593$	−23.8118			−0.977832			−0.488916	−	0.872331i	$-0.662608\pi$
$593$	−23.8118			−0.977832			−0.488916	+	0.872331i	$0.662608\pi$
$594$		0			0
$595$		0			0
$596$	−39.6863	+	68.7386i	−1.62561	+	2.81564i
$597$		0			0
$598$	−21.0000	−	36.3731i	−0.858754	−	1.48741i
$599$	3.96863	+	6.87386i	0.162154	+	0.280858i	0.935641	−	0.352954i	$-0.114823\pi$
$599$	3.96863	+	6.87386i	0.162154	+	0.280858i	−0.773487	+	0.633812i	$0.781489\pi$
$600$		0			0
$601$	15.0000	−	25.9808i	0.611863	−	1.05978i	−0.379063	−	0.925371i	$-0.623754\pi$
$601$	15.0000	−	25.9808i	0.611863	−	1.05978i	0.990926	−	0.134407i	$-0.0429129\pi$
$602$	21.1660			0.862662
$603$		0			0
$604$	10.0000			0.406894
$605$	5.29150	−	9.16515i	0.215130	−	0.372616i
$606$		0			0
$607$	14.0000	+	24.2487i	0.568242	+	0.984225i	0.996740	+	0.0806818i	$0.0257098\pi$
$607$	14.0000	+	24.2487i	0.568242	+	0.984225i	−0.428497	+	0.903543i	$0.640957\pi$
$608$	46.3006	+	80.1951i	1.87774	+	3.25234i
$609$		0			0
$610$	−28.0000	+	48.4974i	−1.13369	+	1.96360i
$611$		0			0
$612$		0			0
$613$	19.0000			0.767403			0.383701	−	0.923457i	$-0.374649\pi$
$613$	19.0000			0.767403			0.383701	+	0.923457i	$0.374649\pi$
$614$	25.1346	−	43.5345i	1.01435	−	1.75691i
$615$		0			0
$616$	−10.5000	−	18.1865i	−0.423057	−	0.732756i
$617$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$617$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$618$		0			0
$619$	−15.5000	+	26.8468i	−0.622998	+	1.07906i	0.365927	+	0.930644i	$0.380752\pi$
$619$	−15.5000	+	26.8468i	−0.622998	+	1.07906i	−0.988924	+	0.148420i	$0.952581\pi$
$620$	39.6863			1.59384
$621$		0			0
$622$	42.0000			1.68405
$623$	9.26013	−	16.0390i	0.370999	−	0.642590i
$624$		0			0
$625$	15.5000	+	26.8468i	0.620000	+	1.07387i
$626$	18.5203	+	32.0780i	0.740218	+	1.28210i
$627$		0			0
$628$	35.0000	−	60.6218i	1.39665	−	2.41907i
$629$		0			0
$630$		0			0
$631$	20.0000			0.796187			0.398094	−	0.917345i	$-0.369672\pi$
$631$	20.0000			0.796187			0.398094	+	0.917345i	$0.369672\pi$
$632$	−15.8745	+	27.4955i	−0.631454	+	1.09371i
$633$		0			0
$634$		0			0
$635$	−7.93725	−	13.7477i	−0.314980	−	0.545562i
$636$		0			0
$637$	1.00000	−	1.73205i	0.0396214	−	0.0686264i
$638$	37.0405			1.46645
$639$		0			0
$640$	−21.0000			−0.830098
$641$	7.93725	−	13.7477i	0.313503	−	0.543003i	−0.665615	−	0.746295i	$-0.731831\pi$
$641$	7.93725	−	13.7477i	0.313503	−	0.543003i	0.979118	+	0.203292i	$0.0651642\pi$
$642$		0			0
$643$	−11.5000	−	19.9186i	−0.453516	−	0.785512i	0.545086	−	0.838380i	$-0.316497\pi$
$643$	−11.5000	−	19.9186i	−0.453516	−	0.785512i	−0.998602	+	0.0528680i	$0.983164\pi$
$644$	19.8431	+	34.3693i	0.781929	+	1.35434i
$645$		0			0
$646$		0			0
$647$	−10.5830			−0.416061			−0.208030	−	0.978122i	$-0.566705\pi$
$647$	−10.5830			−0.416061			−0.208030	+	0.978122i	$0.566705\pi$
$648$		0			0
$649$		0			0
$650$	−5.29150	+	9.16515i	−0.207550	+	0.359487i
$651$		0			0
$652$	−25.0000	−	43.3013i	−0.979076	−	1.69581i
$653$	−15.8745	−	27.4955i	−0.621217	−	1.07598i	−0.989259	−	0.146171i	$-0.953305\pi$
$653$	−15.8745	−	27.4955i	−0.621217	−	1.07598i	0.368042	−	0.929809i	$-0.380028\pi$
$654$		0			0
$655$	28.0000	−	48.4974i	1.09405	−	1.89495i
$656$	−29.1033			−1.13629
$657$		0			0
$658$		0			0
$659$	−11.9059	+	20.6216i	−0.463787	+	0.803303i	−0.999146	−	0.0413217i	$-0.986843\pi$
$659$	−11.9059	+	20.6216i	−0.463787	+	0.803303i	0.535359	+	0.844625i	$0.320176\pi$
$660$		0			0
$661$	7.00000	+	12.1244i	0.272268	+	0.471583i	0.969442	−	0.245319i	$-0.0788928\pi$
$661$	7.00000	+	12.1244i	0.272268	+	0.471583i	−0.697174	+	0.716902i	$0.745559\pi$
$662$	26.4575	+	45.8258i	1.02830	+	1.78107i
$663$		0			0
$664$	−63.0000	+	109.119i	−2.44487	+	4.23465i
$665$	−18.5203			−0.718185
$666$		0			0
$667$	−42.0000			−1.62625
$668$	13.2288	−	22.9129i	0.511836	−	0.886526i
$669$		0			0
$670$	−7.00000	−	12.1244i	−0.270434	−	0.468405i
$671$	10.5830	+	18.3303i	0.408552	+	0.707633i
$672$		0			0
$673$	1.00000	−	1.73205i	0.0385472	−	0.0667657i	−0.846108	−	0.533011i	$-0.821060\pi$
$673$	1.00000	−	1.73205i	0.0385472	−	0.0667657i	0.884655	+	0.466246i	$0.154394\pi$
$674$	−50.2693			−1.93630
$675$		0			0
$676$	−45.0000			−1.73077
$677$	−3.96863	+	6.87386i	−0.152527	+	0.264184i	−0.932156	−	0.362058i	$-0.882074\pi$
$677$	−3.96863	+	6.87386i	−0.152527	+	0.264184i	0.779629	+	0.626242i	$0.215408\pi$
$678$		0			0
$679$	−6.00000	−	10.3923i	−0.230259	−	0.398820i
$680$		0			0
$681$		0			0
$682$	10.5000	−	18.1865i	0.402066	−	0.696398i
$683$	−23.8118			−0.911132			−0.455566	−	0.890202i	$-0.650563\pi$
$683$	−23.8118			−0.911132			−0.455566	+	0.890202i	$0.650563\pi$
$684$		0			0
$685$	42.0000			1.60474
$686$	−1.32288	+	2.29129i	−0.0505076	+	0.0874818i
$687$		0			0
$688$	−44.0000	−	76.2102i	−1.67748	−	2.90549i
$689$		0			0
$690$		0			0
$691$	−4.00000	+	6.92820i	−0.152167	+	0.263561i	−0.932024	−	0.362397i	$-0.881959\pi$
$691$	−4.00000	+	6.92820i	−0.152167	+	0.263561i	0.779857	+	0.625958i	$0.215292\pi$
$692$	66.1438			2.51441
$693$		0			0
$694$	7.00000			0.265716
$695$	15.8745	−	27.4955i	0.602154	−	1.04296i
$696$		0			0
$697$		0			0
$698$	−2.64575	−	4.58258i	−0.100143	−	0.173453i
$699$		0			0
$700$	5.00000	−	8.66025i	0.188982	−	0.327327i
$701$	15.8745			0.599572			0.299786	−	0.954006i	$-0.403085\pi$
$701$	15.8745			0.599572			0.299786	+	0.954006i	$0.403085\pi$
$702$		0			0
$703$	−21.0000			−0.792030
$704$	−17.1974	+	29.7867i	−0.648151	+	1.12263i
$705$		0			0
$706$	3.50000	+	6.06218i	0.131724	+	0.228153i
$707$	−5.29150	−	9.16515i	−0.199007	−	0.344691i
$708$		0			0
$709$	1.50000	−	2.59808i	0.0563337	−	0.0975728i	−0.836483	−	0.547992i	$-0.815392\pi$
$709$	1.50000	−	2.59808i	0.0563337	−	0.0975728i	0.892817	+	0.450420i	$0.148726\pi$
$710$	55.5608			2.08516
$711$		0			0
$712$	−147.000			−5.50906
$713$	−11.9059	+	20.6216i	−0.445879	+	0.772285i
$714$		0			0
$715$	7.00000	+	12.1244i	0.261785	+	0.453425i
$716$	−13.2288	−	22.9129i	−0.494382	−	0.856294i
$717$		0			0
$718$	7.00000	−	12.1244i	0.261238	−	0.452477i
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$		0			0
$721$	13.0000			0.484145
$722$	39.6863	−	68.7386i	1.47697	−	2.55819i
$723$		0			0
$724$	35.0000	+	60.6218i	1.30076	+	2.25299i
$725$	5.29150	+	9.16515i	0.196521	+	0.340385i
$726$		0			0
$727$	20.0000	−	34.6410i	0.741759	−	1.28476i	−0.209935	−	0.977715i	$-0.567325\pi$
$727$	20.0000	−	34.6410i	0.741759	−	1.28476i	0.951694	−	0.307049i	$-0.0993415\pi$
$728$	−15.8745			−0.588348
$729$		0			0
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−18.0000	−	31.1769i	−0.664845	−	1.15155i	−0.979327	−	0.202282i	$-0.935164\pi$
$733$	−18.0000	−	31.1769i	−0.664845	−	1.15155i	0.314482	−	0.949263i	$-0.398169\pi$
$734$	27.7804	+	48.1170i	1.02539	+	1.77603i
$735$		0			0
$736$	52.5000	−	90.9327i	1.93518	−	3.35182i
$737$	−5.29150			−0.194915
$738$		0			0
$739$	−30.0000			−1.10357			−0.551784	−	0.833987i	$-0.686053\pi$
$739$	−30.0000			−1.10357			−0.551784	+	0.833987i	$0.686053\pi$
$740$	19.8431	−	34.3693i	0.729448	−	1.26344i
$741$		0			0
$742$		0			0
$743$	−11.9059	−	20.6216i	−0.436784	−	0.756533i	0.560655	−	0.828050i	$-0.310549\pi$
$743$	−11.9059	−	20.6216i	−0.436784	−	0.756533i	−0.997439	+	0.0715167i	$0.977216\pi$
$744$		0			0
$745$	−21.0000	+	36.3731i	−0.769380	+	1.33261i
$746$	−76.7268			−2.80917
$747$		0			0
$748$		0			0
$749$	−2.64575	+	4.58258i	−0.0966736	+	0.167444i
$750$		0			0
$751$	4.00000	+	6.92820i	0.145962	+	0.252814i	0.929731	−	0.368238i	$-0.120039\pi$
$751$	4.00000	+	6.92820i	0.145962	+	0.252814i	−0.783769	+	0.621052i	$0.786706\pi$
$752$		0			0
$753$		0			0
$754$	14.0000	−	24.2487i	0.509850	−	0.883086i
$755$	5.29150			0.192577
$756$		0			0
$757$	−34.0000			−1.23575			−0.617876	−	0.786276i	$-0.712006\pi$
$757$	−34.0000			−1.23575			−0.617876	+	0.786276i	$0.712006\pi$
$758$	47.6235	−	82.4864i	1.72976	−	2.99604i
$759$		0			0
$760$	73.5000	+	127.306i	2.66613	+	4.61786i
$761$	15.8745	+	27.4955i	0.575450	+	0.996709i	0.995993	+	0.0894364i	$0.0285066\pi$
$761$	15.8745	+	27.4955i	0.575450	+	0.996709i	−0.420542	+	0.907273i	$0.638160\pi$
$762$		0			0
$763$	4.50000	−	7.79423i	0.162911	−	0.282170i
$764$	13.2288			0.478600
$765$		0			0
$766$	42.0000			1.51752
$767$		0			0
$768$		0			0
$769$	−7.00000	−	12.1244i	−0.252426	−	0.437215i	0.711767	−	0.702416i	$-0.247895\pi$
$769$	−7.00000	−	12.1244i	−0.252426	−	0.437215i	−0.964193	+	0.265200i	$0.914562\pi$
$770$	−9.26013	−	16.0390i	−0.333712	−	0.578006i
$771$		0			0
$772$	−5.00000	+	8.66025i	−0.179954	+	0.311689i
$773$	−2.64575			−0.0951611			−0.0475805	−	0.998867i	$-0.515151\pi$
$773$	−2.64575			−0.0951611			−0.0475805	+	0.998867i	$0.515151\pi$
$774$		0			0
$775$	6.00000			0.215526
$776$	−47.6235	+	82.4864i	−1.70958	+	2.96109i
$777$		0			0
$778$	−42.0000	−	72.7461i	−1.50577	−	2.60808i
$779$	9.26013	+	16.0390i	0.331779	+	0.574657i
$780$		0			0
$781$	10.5000	−	18.1865i	0.375720	−	0.650765i
$782$		0			0
$783$		0			0
$784$	11.0000			0.392857
$785$	18.5203	−	32.0780i	0.661016	−	1.14491i
$786$		0			0
$787$	−2.00000	−	3.46410i	−0.0712923	−	0.123482i	0.828176	−	0.560469i	$-0.189379\pi$
$787$	−2.00000	−	3.46410i	−0.0712923	−	0.123482i	−0.899468	+	0.436987i	$0.856046\pi$
$788$	−66.1438	−	114.564i	−2.35627	−	4.08119i
$789$		0			0
$790$	−14.0000	+	24.2487i	−0.498098	+	0.862730i
$791$	5.29150			0.188144
$792$		0			0
$793$	16.0000			0.568177
$794$	−7.93725	+	13.7477i	−0.281683	+	0.487889i
$795$		0			0
$796$	7.50000	+	12.9904i	0.265830	+	0.460432i
$797$	22.4889	+	38.9519i	0.796597	+	1.37975i	0.921820	+	0.387618i	$0.126702\pi$
$797$	22.4889	+	38.9519i	0.796597	+	1.37975i	−0.125223	+	0.992129i	$0.539965\pi$
$798$		0			0
$799$		0			0
$800$	−26.4575			−0.935414
$801$		0			0
$802$	42.0000			1.48307
$803$		0			0
$804$		0			0
$805$	10.5000	+	18.1865i	0.370076	+	0.640991i
$806$	−7.93725	−	13.7477i	−0.279578	−	0.484243i
$807$		0			0
$808$	−42.0000	+	72.7461i	−1.47755	+	2.55920i
$809$	15.8745			0.558118			0.279059	−	0.960274i	$-0.409977\pi$
$809$	15.8745			0.558118			0.279059	+	0.960274i	$0.409977\pi$
$810$		0			0
$811$	35.0000			1.22902			0.614508	−	0.788911i	$-0.289355\pi$
$811$	35.0000			1.22902			0.614508	+	0.788911i	$0.289355\pi$
$812$	−13.2288	+	22.9129i	−0.464238	+	0.804084i
$813$		0			0
$814$	−10.5000	−	18.1865i	−0.368025	−	0.637438i
$815$	−13.2288	−	22.9129i	−0.463383	−	0.802603i
$816$		0			0
$817$	−28.0000	+	48.4974i	−0.979596	+	1.69671i
$818$	−84.6640			−2.96021
$819$		0			0
$820$	−35.0000			−1.22225
$821$	−10.5830	+	18.3303i	−0.369349	+	0.639732i	−0.989464	−	0.144779i	$-0.953753\pi$
$821$	−10.5830	+	18.3303i	−0.369349	+	0.639732i	0.620115	+	0.784511i	$0.287086\pi$
$822$		0			0
$823$	15.0000	+	25.9808i	0.522867	+	0.905632i	0.999646	+	0.0266091i	$0.00847095\pi$
$823$	15.0000	+	25.9808i	0.522867	+	0.905632i	−0.476779	+	0.879023i	$0.658196\pi$
$824$	−51.5922	−	89.3602i	−1.79730	−	3.11301i
$825$		0			0
$826$		0			0
$827$	−39.6863			−1.38003			−0.690013	−	0.723797i	$-0.742395\pi$
$827$	−39.6863			−1.38003			−0.690013	+	0.723797i	$0.742395\pi$
$828$		0			0
$829$	−28.0000			−0.972480			−0.486240	−	0.873825i	$-0.661632\pi$
$829$	−28.0000			−0.972480			−0.486240	+	0.873825i	$0.661632\pi$
$830$	−55.5608	+	96.2341i	−1.92854	+	3.34033i
$831$		0			0
$832$	13.0000	+	22.5167i	0.450694	+	0.780625i
$833$		0			0
$834$		0			0
$835$	7.00000	−	12.1244i	0.242245	−	0.419581i
$836$	92.6013			3.20268
$837$		0			0
$838$	−42.0000			−1.45087
$839$	2.64575	−	4.58258i	0.0913415	−	0.158208i	−0.816734	−	0.577014i	$-0.804218\pi$
$839$	2.64575	−	4.58258i	0.0913415	−	0.158208i	0.908076	+	0.418806i	$0.137551\pi$
$840$		0			0
$841$	0.500000	+	0.866025i	0.0172414	+	0.0298629i
$842$	−25.1346	−	43.5345i	−0.866197	−	1.50030i
$843$		0			0
$844$	−55.0000	+	95.2628i	−1.89318	+	3.27908i
$845$	−23.8118			−0.819150
$846$		0			0
$847$	4.00000			0.137442
$848$		0			0
$849$		0			0
$850$		0			0
$851$	11.9059	+	20.6216i	0.408128	+	0.706899i
$852$		0			0
$853$	14.0000	−	24.2487i	0.479351	−	0.830260i	−0.520369	−	0.853942i	$-0.674205\pi$
$853$	14.0000	−	24.2487i	0.479351	−	0.830260i	0.999720	+	0.0236816i	$0.00753881\pi$
$854$	−21.1660			−0.724286
$855$		0			0
$856$	42.0000			1.43553
$857$	6.61438	−	11.4564i	0.225943	−	0.391345i	−0.730659	−	0.682743i	$-0.760787\pi$
$857$	6.61438	−	11.4564i	0.225943	−	0.391345i	0.956602	+	0.291398i	$0.0941204\pi$
$858$		0			0
$859$	6.50000	+	11.2583i	0.221777	+	0.384129i	0.955348	−	0.295484i	$-0.0954809\pi$
$859$	6.50000	+	11.2583i	0.221777	+	0.384129i	−0.733571	+	0.679613i	$0.762148\pi$
$860$	−52.9150	−	91.6515i	−1.80439	−	3.12529i
$861$		0			0
$862$	−52.5000	+	90.9327i	−1.78816	+	3.09718i
$863$	−15.8745			−0.540375			−0.270187	−	0.962808i	$-0.587086\pi$
$863$	−15.8745			−0.540375			−0.270187	+	0.962808i	$0.587086\pi$
$864$		0			0
$865$	35.0000			1.19004
$866$	−34.3948	+	59.5735i	−1.16878	+	2.02439i
$867$		0			0
$868$	7.50000	+	12.9904i	0.254567	+	0.440922i
$869$	5.29150	+	9.16515i	0.179502	+	0.310906i
$870$		0			0
$871$	−2.00000	+	3.46410i	−0.0677674	+	0.117377i
$872$	−71.4353			−2.41910
$873$		0			0
$874$	−147.000			−4.97235
$875$	−3.96863	+	6.87386i	−0.134164	+	0.232379i
$876$		0			0
$877$	−5.00000	−	8.66025i	−0.168838	−	0.292436i	0.769174	−	0.639040i	$-0.220668\pi$
$877$	−5.00000	−	8.66025i	−0.168838	−	0.292436i	−0.938012	+	0.346604i	$0.887335\pi$
$878$		0			0
$879$		0			0
$880$	−38.5000	+	66.6840i	−1.29783	+	2.24792i
$881$	23.8118			0.802239			0.401119	−	0.916026i	$-0.368621\pi$
$881$	23.8118			0.802239			0.401119	+	0.916026i	$0.368621\pi$
$882$		0			0
$883$	−16.0000			−0.538443			−0.269221	−	0.963078i	$-0.586766\pi$
$883$	−16.0000			−0.538443			−0.269221	+	0.963078i	$0.586766\pi$
$884$		0			0
$885$		0			0
$886$	10.5000	+	18.1865i	0.352754	+	0.610989i
$887$	−18.5203	−	32.0780i	−0.621849	−	1.07707i	−0.989141	−	0.146969i	$-0.953048\pi$
$887$	−18.5203	−	32.0780i	−0.621849	−	1.07707i	0.367292	−	0.930106i	$-0.380285\pi$
$888$		0			0
$889$	3.00000	−	5.19615i	0.100617	−	0.174273i
$890$	−129.642			−4.34560
$891$		0			0
$892$	35.0000			1.17189
$893$		0			0
$894$		0			0
$895$	−7.00000	−	12.1244i	−0.233984	−	0.405273i
$896$	−3.96863	−	6.87386i	−0.132583	−	0.229640i
$897$		0			0
$898$	21.0000	−	36.3731i	0.700779	−	1.21378i
$899$	−15.8745			−0.529444
$900$		0			0
$901$		0			0
$902$	−9.26013	+	16.0390i	−0.308329	+	0.534041i
$903$		0			0
$904$	−21.0000	−	36.3731i	−0.698450	−	1.20975i
$905$	18.5203	+	32.0780i	0.615634	+	1.06631i
$906$		0			0
$907$	−1.00000	+	1.73205i	−0.0332045	+	0.0575118i	−0.882150	−	0.470968i	$-0.843905\pi$
$907$	−1.00000	+	1.73205i	−0.0332045	+	0.0575118i	0.848946	+	0.528480i	$0.177238\pi$
$908$	79.3725			2.63407
$909$		0			0
$910$	−14.0000			−0.464095
$911$	−23.8118	+	41.2432i	−0.788919	+	1.36645i	0.137711	+	0.990472i	$0.456026\pi$
$911$	−23.8118	+	41.2432i	−0.788919	+	1.36645i	−0.926630	+	0.375975i	$0.877308\pi$
$912$		0			0
$913$	21.0000	+	36.3731i	0.694999	+	1.20377i
$914$	33.0719	+	57.2822i	1.09392	+	1.89473i
$915$		0			0
$916$	−50.0000	+	86.6025i	−1.65205	+	2.86143i
$917$	21.1660			0.698963
$918$		0			0
$919$	32.0000			1.05558			0.527791	−	0.849374i	$-0.323020\pi$
$919$	32.0000			1.05558			0.527791	+	0.849374i	$0.323020\pi$
$920$	83.3412	−	144.351i	2.74768	−	4.75912i
$921$		0			0
$922$	−24.5000	−	42.4352i	−0.806865	−	1.39753i
$923$	−7.93725	−	13.7477i	−0.261258	−	0.452512i
$924$		0			0
$925$	3.00000	−	5.19615i	0.0986394	−	0.170848i
$926$	68.7895			2.26056
$927$		0			0
$928$	70.0000			2.29786
$929$	21.1660	−	36.6606i	0.694434	−	1.20280i	−0.275937	−	0.961176i	$-0.588988\pi$
$929$	21.1660	−	36.6606i	0.694434	−	1.20280i	0.970371	−	0.241620i	$-0.0776786\pi$
$930$		0			0
$931$	−3.50000	−	6.06218i	−0.114708	−	0.198680i
$932$	39.6863	+	68.7386i	1.29997	+	2.25161i
$933$		0			0
$934$	42.0000	−	72.7461i	1.37428	−	2.38033i
$935$		0			0
$936$		0			0
$937$	−12.0000			−0.392023			−0.196011	−	0.980602i	$-0.562799\pi$
$937$	−12.0000			−0.392023			−0.196011	+	0.980602i	$0.562799\pi$
$938$	2.64575	−	4.58258i	0.0863868	−	0.149626i
$939$		0			0
$940$		0			0
$941$	25.1346	+	43.5345i	0.819366	+	1.41918i	0.906150	+	0.422956i	$0.139008\pi$
$941$	25.1346	+	43.5345i	0.819366	+	1.41918i	−0.0867844	+	0.996227i	$0.527659\pi$
$942$		0			0
$943$	10.5000	−	18.1865i	0.341927	−	0.592235i
$944$		0			0
$945$		0			0
$946$	−56.0000			−1.82072
$947$	9.26013	−	16.0390i	0.300914	−	0.521198i	−0.675429	−	0.737425i	$-0.736042\pi$
$947$	9.26013	−	16.0390i	0.300914	−	0.521198i	0.976343	+	0.216227i	$0.0693750\pi$
$948$		0			0
$949$		0			0
$950$	18.5203	+	32.0780i	0.600877	+	1.04075i
$951$		0			0
$952$		0			0
$953$	−26.4575			−0.857043			−0.428521	−	0.903532i	$-0.640965\pi$
$953$	−26.4575			−0.857043			−0.428521	+	0.903532i	$0.640965\pi$
$954$		0			0
$955$	7.00000			0.226515
$956$	39.6863	−	68.7386i	1.28355	−	2.22317i
$957$		0			0
$958$	28.0000	+	48.4974i	0.904639	+	1.56688i
$959$	7.93725	+	13.7477i	0.256307	+	0.443937i
$960$		0			0
$961$	11.0000	−	19.0526i	0.354839	−	0.614599i
$962$	−15.8745			−0.511815
$963$		0			0
$964$	−20.0000			−0.644157
$965$	−2.64575	+	4.58258i	−0.0851697	+	0.147518i
$966$		0			0
$967$	25.0000	+	43.3013i	0.803946	+	1.39247i	0.917000	+	0.398886i	$0.130603\pi$
$967$	25.0000	+	43.3013i	0.803946	+	1.39247i	−0.113055	+	0.993589i	$0.536064\pi$
$968$	−15.8745	−	27.4955i	−0.510226	−	0.883737i
$969$		0			0
$970$	−42.0000	+	72.7461i	−1.34854	+	2.33574i
$971$	15.8745			0.509437			0.254719	−	0.967015i	$-0.418017\pi$
$971$	15.8745			0.509437			0.254719	+	0.967015i	$0.418017\pi$
$972$		0			0
$973$	12.0000			0.384702
$974$	−42.3320	+	73.3212i	−1.35641	+	2.34936i
$975$		0			0
$976$	44.0000	+	76.2102i	1.40841	+	2.43943i
$977$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$977$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$978$		0			0
$979$	−24.5000	+	42.4352i	−0.783023	+	1.35624i
$980$	13.2288			0.422577
$981$		0			0
$982$	7.00000			0.223379
$983$	15.8745	−	27.4955i	0.506318	−	0.876969i	−0.493655	−	0.869658i	$-0.664339\pi$
$983$	15.8745	−	27.4955i	0.506318	−	0.876969i	0.999973	−	0.00731102i	$-0.00232719\pi$
$984$		0			0
$985$	−35.0000	−	60.6218i	−1.11519	−	1.93157i
$986$		0			0
$987$		0			0
$988$	35.0000	−	60.6218i	1.11350	−	1.92864i
$989$	63.4980			2.01912
$990$		0			0
$991$	2.00000			0.0635321			0.0317660	−	0.999495i	$-0.489887\pi$
$991$	2.00000			0.0635321			0.0317660	+	0.999495i	$0.489887\pi$
$992$	19.8431	−	34.3693i	0.630020	−	1.09123i
$993$		0			0
$994$	10.5000	+	18.1865i	0.333040	+	0.576842i
$995$	3.96863	+	6.87386i	0.125814	+	0.217916i
$996$		0			0
$997$	19.0000	−	32.9090i	0.601736	−	1.04224i	−0.390822	−	0.920466i	$-0.627809\pi$
$997$	19.0000	−	32.9090i	0.601736	−	1.04224i	0.992558	−	0.121771i	$-0.0388574\pi$
$998$	−10.5830			−0.334999
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.f.i.379.2		4
3.2	odd	2	inner	567.2.f.i.379.1		4
9.2	odd	6		189.2.a.f.1.2	yes	2
9.4	even	3	inner	567.2.f.i.190.2		4
9.5	odd	6	inner	567.2.f.i.190.1		4
9.7	even	3		189.2.a.f.1.1	✓	2
36.7	odd	6		3024.2.a.bi.1.2		2
36.11	even	6		3024.2.a.bi.1.1		2
45.29	odd	6		4725.2.a.bb.1.1		2
45.34	even	6		4725.2.a.bb.1.2		2
63.20	even	6		1323.2.a.w.1.2		2
63.34	odd	6		1323.2.a.w.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.a.f.1.1	✓	2	9.7	even	3
189.2.a.f.1.2	yes	2	9.2	odd	6
567.2.f.i.190.1		4	9.5	odd	6	inner
567.2.f.i.190.2		4	9.4	even	3	inner
567.2.f.i.379.1		4	3.2	odd	2	inner
567.2.f.i.379.2		4	1.1	even	1	trivial
1323.2.a.w.1.1		2	63.34	odd	6
1323.2.a.w.1.2		2	63.20	even	6
3024.2.a.bi.1.1		2	36.11	even	6
3024.2.a.bi.1.2		2	36.7	odd	6
4725.2.a.bb.1.1		2	45.29	odd	6
4725.2.a.bb.1.2		2	45.34	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.32288 - 2.29129i) q^{2} +(-2.50000 - 4.33013i) q^{4} +(-1.32288 - 2.29129i) q^{5} +(0.500000 - 0.866025i) q^{7} -7.93725 q^{8} -7.00000 q^{10} +(-1.32288 + 2.29129i) q^{11} +(1.00000 + 1.73205i) q^{13} +(-1.32288 - 2.29129i) q^{14} +(-5.50000 + 9.52628i) q^{16} +7.00000 q^{19} +(-6.61438 + 11.4564i) q^{20} +(3.50000 + 6.06218i) q^{22} +(-3.96863 - 6.87386i) q^{23} +(-1.00000 + 1.73205i) q^{25} +5.29150 q^{26} -5.00000 q^{28} +(2.64575 - 4.58258i) q^{29} +(-1.50000 - 2.59808i) q^{31} +(6.61438 + 11.4564i) q^{32} -2.64575 q^{35} -3.00000 q^{37} +(9.26013 - 16.0390i) q^{38} +(10.5000 + 18.1865i) q^{40} +(1.32288 + 2.29129i) q^{41} +(-4.00000 + 6.92820i) q^{43} +13.2288 q^{44} -21.0000 q^{46} +(-0.500000 - 0.866025i) q^{49} +(2.64575 + 4.58258i) q^{50} +(5.00000 - 8.66025i) q^{52} +7.00000 q^{55} +(-3.96863 + 6.87386i) q^{56} +(-7.00000 - 12.1244i) q^{58} +(4.00000 - 6.92820i) q^{61} -7.93725 q^{62} +13.0000 q^{64} +(2.64575 - 4.58258i) q^{65} +(1.00000 + 1.73205i) q^{67} +(-3.50000 + 6.06218i) q^{70} -7.93725 q^{71} +(-3.96863 + 6.87386i) q^{74} +(-17.5000 - 30.3109i) q^{76} +(1.32288 + 2.29129i) q^{77} +(2.00000 - 3.46410i) q^{79} +29.1033 q^{80} +7.00000 q^{82} +(7.93725 - 13.7477i) q^{83} +(10.5830 + 18.3303i) q^{86} +(10.5000 - 18.1865i) q^{88} +18.5203 q^{89} +2.00000 q^{91} +(-19.8431 + 34.3693i) q^{92} +(-9.26013 - 16.0390i) q^{95} +(6.00000 - 10.3923i) q^{97} -2.64575 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 10 q^{4} + 2 q^{7} - 28 q^{10} + 4 q^{13} - 22 q^{16} + 28 q^{19} + 14 q^{22} - 4 q^{25} - 20 q^{28} - 6 q^{31} - 12 q^{37} + 42 q^{40} - 16 q^{43} - 84 q^{46} - 2 q^{49} + 20 q^{52} + 28 q^{55} - 28 q^{58}+ \cdots + 24 q^{97}+O(q^{100}) \) 4 * q - 10 * q^4 + 2 * q^7 - 28 * q^10 + 4 * q^13 - 22 * q^16 + 28 * q^19 + 14 * q^22 - 4 * q^25 - 20 * q^28 - 6 * q^31 - 12 * q^37 + 42 * q^40 - 16 * q^43 - 84 * q^46 - 2 * q^49 + 20 * q^52 + 28 * q^55 - 28 * q^58 + 16 * q^61 + 52 * q^64 + 4 * q^67 - 14 * q^70 - 70 * q^76 + 8 * q^79 + 28 * q^82 + 42 * q^88 + 8 * q^91 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more