LMFDB - Embedded newform 252.4.bm.a.173.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(173,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 5]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("252.173");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.bm (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			173.6
Character	$\chi$	$=$	252.173
Dual form			252.4.bm.a.185.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.93325 - 3.39552i) q^{3} -12.5831 q^{5} +(-6.65587 - 17.2829i) q^{7} +(3.94093 + 26.7108i) q^{9} +O(q^{10})$	\(q+(-3.93325 - 3.39552i) q^{3} -12.5831 q^{5} +(-6.65587 - 17.2829i) q^{7} +(3.94093 + 26.7108i) q^{9} -68.7640i q^{11} +(-34.1431 + 19.7125i) q^{13} +(49.4923 + 42.7260i) q^{15} +(38.3848 + 66.4844i) q^{17} +(-69.3139 - 40.0184i) q^{19} +(-32.5053 + 90.5782i) q^{21} +155.420i q^{23} +33.3333 q^{25} +(75.1964 - 118.442i) q^{27} +(197.862 + 114.236i) q^{29} +(126.001 + 72.7467i) q^{31} +(-233.489 + 270.466i) q^{33} +(83.7511 + 217.472i) q^{35} +(74.1910 - 128.503i) q^{37} +(201.227 + 38.3991i) q^{39} +(-27.9434 - 48.3994i) q^{41} +(-109.056 + 188.891i) q^{43} +(-49.5890 - 336.104i) q^{45} +(54.9765 + 95.2222i) q^{47} +(-254.399 + 230.066i) q^{49} +(74.7719 - 391.836i) q^{51} +(257.488 - 148.661i) q^{53} +865.262i q^{55} +(136.746 + 392.759i) q^{57} +(-89.5529 + 155.110i) q^{59} +(-275.950 + 159.320i) q^{61} +(435.411 - 245.895i) q^{63} +(429.624 - 248.044i) q^{65} +(326.911 - 566.226i) q^{67} +(527.732 - 611.307i) q^{69} +157.634i q^{71} +(-1055.68 + 609.495i) q^{73} +(-131.108 - 113.184i) q^{75} +(-1188.44 + 457.684i) q^{77} +(-409.401 - 709.103i) q^{79} +(-697.938 + 210.531i) q^{81} +(-404.460 + 700.546i) q^{83} +(-482.998 - 836.577i) q^{85} +(-390.352 - 1121.16i) q^{87} +(-20.9797 + 36.3379i) q^{89} +(567.941 + 458.888i) q^{91} +(-248.581 - 713.969i) q^{93} +(872.181 + 503.554i) q^{95} +(161.296 + 93.1244i) q^{97} +(1836.74 - 270.994i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{7} - 30 q^{9}+O(q^{10}) $ 48 * q + 6 * q^7 - 30 * q^9	$ 48 q + 6 q^{7} - 30 q^{9} + 36 q^{13} + 66 q^{15} + 72 q^{17} + 126 q^{21} + 1200 q^{25} + 396 q^{27} + 42 q^{29} - 90 q^{31} + 108 q^{33} - 390 q^{35} + 84 q^{37} + 1014 q^{39} + 618 q^{41} - 42 q^{43} - 1014 q^{45} + 198 q^{47} - 276 q^{49} + 408 q^{51} + 1620 q^{53} + 492 q^{57} + 750 q^{59} - 1314 q^{61} + 1542 q^{63} + 564 q^{65} + 294 q^{67} + 924 q^{69} - 1410 q^{75} - 2448 q^{77} - 804 q^{79} - 666 q^{81} - 360 q^{85} + 1788 q^{87} - 1722 q^{89} + 540 q^{91} + 1128 q^{93} - 2946 q^{95} + 792 q^{97} - 54 q^{99}+O(q^{100}) $ 48 * q + 6 * q^7 - 30 * q^9 + 36 * q^13 + 66 * q^15 + 72 * q^17 + 126 * q^21 + 1200 * q^25 + 396 * q^27 + 42 * q^29 - 90 * q^31 + 108 * q^33 - 390 * q^35 + 84 * q^37 + 1014 * q^39 + 618 * q^41 - 42 * q^43 - 1014 * q^45 + 198 * q^47 - 276 * q^49 + 408 * q^51 + 1620 * q^53 + 492 * q^57 + 750 * q^59 - 1314 * q^61 + 1542 * q^63 + 564 * q^65 + 294 * q^67 + 924 * q^69 - 1410 * q^75 - 2448 * q^77 - 804 * q^79 - 666 * q^81 - 360 * q^85 + 1788 * q^87 - 1722 * q^89 + 540 * q^91 + 1128 * q^93 - 2946 * q^95 + 792 * q^97 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−3.93325	−	3.39552i	−0.756955	−	0.653467i
$3$	−3.93325	−	3.39552i	−0.756955	−	0.653467i
$4$		0			0
$5$	−12.5831			−1.12546			−0.562731	−	0.826640i	$-0.690249\pi$
$5$	−12.5831			−1.12546			−0.562731	+	0.826640i	$0.690249\pi$
$6$		0			0
$7$	−6.65587	−	17.2829i	−0.359383	−	0.933190i
$7$	−6.65587	−	17.2829i	−0.359383	−	0.933190i
$8$		0			0
$9$	3.94093	+	26.7108i	0.145961	+	0.989290i
$10$		0			0
$11$		−	68.7640i		−	1.88483i	−0.334446	−	0.942415i	$-0.608549\pi$
$11$		−	68.7640i		−	1.88483i	0.334446	−	0.942415i	$-0.391451\pi$
$12$		0			0
$13$	−34.1431	+	19.7125i	−0.728429	+	0.420559i	−0.817847	−	0.575435i	$-0.804833\pi$
$13$	−34.1431	+	19.7125i	−0.728429	+	0.420559i	0.0894180	+	0.995994i	$0.471499\pi$
$14$		0			0
$15$	49.4923	+	42.7260i	0.851924	+	0.735453i
$16$		0			0
$17$	38.3848	+	66.4844i	0.547628	+	0.948520i	0.998436	+	0.0558991i	$0.0178025\pi$
$17$	38.3848	+	66.4844i	0.547628	+	0.948520i	−0.450808	+	0.892621i	$0.648864\pi$
$18$		0			0
$19$	−69.3139	−	40.0184i	−0.836932	−	0.483203i	0.0192883	−	0.999814i	$-0.493860\pi$
$19$	−69.3139	−	40.0184i	−0.836932	−	0.483203i	−0.856220	+	0.516611i	$0.827193\pi$
$20$		0			0
$21$	−32.5053	+	90.5782i	−0.337773	+	0.941228i
$22$		0			0
$23$			155.420i			1.40902i	0.709696	+	0.704508i	$0.248832\pi$
$23$			155.420i			1.40902i	−0.709696	+	0.704508i	$0.751168\pi$
$24$		0			0
$25$	33.3333			0.266667
$26$		0			0
$27$	75.1964	−	118.442i	0.535984	−	0.844228i
$28$		0			0
$29$	197.862	+	114.236i	1.26697	+	0.731484i	0.974413	−	0.224764i	$-0.0721613\pi$
$29$	197.862	+	114.236i	1.26697	+	0.731484i	0.292555	+	0.956249i	$0.405495\pi$
$30$		0			0
$31$	126.001	+	72.7467i	0.730014	+	0.421474i	0.818427	−	0.574610i	$-0.194846\pi$
$31$	126.001	+	72.7467i	0.730014	+	0.421474i	−0.0884132	+	0.996084i	$0.528180\pi$
$32$		0			0
$33$	−233.489	+	270.466i	−1.23168	+	1.42673i
$34$		0			0
$35$	83.7511	+	217.472i	0.404472	+	1.05027i
$36$		0			0
$37$	74.1910	−	128.503i	0.329647	−	0.570965i	−0.652795	−	0.757534i	$-0.726404\pi$
$37$	74.1910	−	128.503i	0.329647	−	0.570965i	0.982442	+	0.186570i	$0.0597371\pi$
$38$		0			0
$39$	201.227	+	38.3991i	0.826209	+	0.157661i
$40$		0			0
$41$	−27.9434	−	48.3994i	−0.106440	−	0.184359i	0.807886	−	0.589339i	$-0.200612\pi$
$41$	−27.9434	−	48.3994i	−0.106440	−	0.184359i	−0.914325	+	0.404980i	$0.867278\pi$
$42$		0			0
$43$	−109.056	+	188.891i	−0.386766	+	0.669898i	−0.992012	−	0.126140i	$-0.959741\pi$
$43$	−109.056	+	188.891i	−0.386766	+	0.669898i	0.605246	+	0.796038i	$0.293075\pi$
$44$		0			0
$45$	−49.5890	−	336.104i	−0.164273	−	1.11341i
$46$		0			0
$47$	54.9765	+	95.2222i	0.170620	+	0.295523i	0.938637	−	0.344907i	$-0.112090\pi$
$47$	54.9765	+	95.2222i	0.170620	+	0.295523i	−0.768017	+	0.640430i	$0.778756\pi$
$48$		0			0
$49$	−254.399	+	230.066i	−0.741688	+	0.670745i
$50$		0			0
$51$	74.7719	−	391.836i	0.205297	−	1.07584i
$52$		0			0
$53$	257.488	−	148.661i	0.667335	−	0.385286i	−0.127731	−	0.991809i	$-0.540769\pi$
$53$	257.488	−	148.661i	0.667335	−	0.385286i	0.795066	+	0.606523i	$0.207436\pi$
$54$		0			0
$55$			865.262i			2.12131i
$56$		0			0
$57$	136.746	+	392.759i	0.317762	+	0.912670i
$58$		0			0
$59$	−89.5529	+	155.110i	−0.197607	+	0.342265i	−0.947752	−	0.319008i	$-0.896650\pi$
$59$	−89.5529	+	155.110i	−0.197607	+	0.342265i	0.750145	+	0.661273i	$0.229984\pi$
$60$		0			0
$61$	−275.950	+	159.320i	−0.579209	+	0.334406i	−0.760819	−	0.648964i	$-0.775202\pi$
$61$	−275.950	+	159.320i	−0.579209	+	0.334406i	0.181610	+	0.983371i	$0.441869\pi$
$62$		0			0
$63$	435.411	−	245.895i	0.870740	−	0.491743i
$64$		0			0
$65$	429.624	−	248.044i	0.819820	−	0.473323i
$66$		0			0
$67$	326.911	−	566.226i	0.596097	−	1.03247i	−0.397294	−	0.917691i	$-0.630051\pi$
$67$	326.911	−	566.226i	0.596097	−	1.03247i	0.993391	−	0.114779i	$-0.0366160\pi$
$68$		0			0
$69$	527.732	−	611.307i	0.920746	−	1.06656i
$70$		0			0
$71$			157.634i			0.263490i	0.991284	+	0.131745i	$0.0420579\pi$
$71$			157.634i			0.263490i	−0.991284	+	0.131745i	$0.957942\pi$
$72$		0			0
$73$	−1055.68	+	609.495i	−1.69257	+	0.977205i	−0.740134	+	0.672459i	$0.765238\pi$
$73$	−1055.68	+	609.495i	−1.69257	+	0.977205i	−0.952434	+	0.304746i	$0.901429\pi$
$74$		0			0
$75$	−131.108	−	113.184i	−0.201855	−	0.174258i
$76$		0			0
$77$	−1188.44	+	457.684i	−1.75890	+	0.677376i
$78$		0			0
$79$	−409.401	−	709.103i	−0.583053	−	1.00988i	−0.995115	−	0.0987218i	$-0.968525\pi$
$79$	−409.401	−	709.103i	−0.583053	−	1.00988i	0.412062	−	0.911156i	$-0.364809\pi$
$80$		0			0
$81$	−697.938	+	210.531i	−0.957391	+	0.288795i
$82$		0			0
$83$	−404.460	+	700.546i	−0.534883	+	0.926444i	0.464286	+	0.885685i	$0.346311\pi$
$83$	−404.460	+	700.546i	−0.534883	+	0.926444i	−0.999169	+	0.0407592i	$0.987022\pi$
$84$		0			0
$85$	−482.998	−	836.577i	−0.616335	−	1.06752i
$86$		0			0
$87$	−390.352	−	1121.16i	−0.481036	−	1.38162i
$88$		0			0
$89$	−20.9797	+	36.3379i	−0.0249870	+	0.0432788i	−0.878249	−	0.478204i	$-0.841288\pi$
$89$	−20.9797	+	36.3379i	−0.0249870	+	0.0432788i	0.853261	+	0.521483i	$0.174621\pi$
$90$		0			0
$91$	567.941	+	458.888i	0.654246	+	0.528621i
$92$		0			0
$93$	−248.581	−	713.969i	−0.277168	−	0.796077i
$94$		0			0
$95$	872.181	+	503.554i	0.941936	+	0.543827i
$96$		0			0
$97$	161.296	+	93.1244i	0.168837	+	0.0974778i	0.582037	−	0.813162i	$-0.302256\pi$
$97$	161.296	+	93.1244i	0.168837	+	0.0974778i	−0.413201	+	0.910640i	$0.635589\pi$
$98$		0			0
$99$	1836.74	−	270.994i	1.86464	−	0.275111i
$100$		0			0
$101$	−877.206			−0.864210			−0.432105	−	0.901823i	$-0.642229\pi$
$101$	−877.206			−0.864210			−0.432105	+	0.901823i	$0.642229\pi$
$102$		0			0
$103$		−	1508.20i		−	1.44279i	−0.692524	−	0.721395i	$-0.743501\pi$
$103$		−	1508.20i		−	1.44279i	0.692524	−	0.721395i	$-0.256499\pi$
$104$		0			0
$105$	409.016	−	1139.75i	0.380151	−	1.05932i
$106$		0			0
$107$	1401.91	+	809.390i	1.26661	+	0.731278i	0.974345	−	0.225060i	$-0.0722577\pi$
$107$	1401.91	+	809.390i	1.26661	+	0.731278i	0.292265	+	0.956337i	$0.405591\pi$
$108$		0			0
$109$	232.205	+	402.191i	0.204048	+	0.353421i	0.949829	−	0.312770i	$-0.101257\pi$
$109$	232.205	+	402.191i	0.204048	+	0.353421i	−0.745781	+	0.666191i	$0.767924\pi$
$110$		0			0
$111$	−728.144	+	253.516i	−0.622634	+	0.216781i
$112$		0			0
$113$	1075.98	−	621.220i	0.895754	−	0.517164i	0.0199334	−	0.999801i	$-0.493655\pi$
$113$	1075.98	−	621.220i	0.895754	−	0.517164i	0.875820	+	0.482638i	$0.160321\pi$
$114$		0			0
$115$		−	1955.66i		−	1.58579i
$116$		0			0
$117$	−661.093	−	834.304i	−0.522377	−	0.659243i
$118$		0			0
$119$	893.561	−	1105.91i	0.688341	−	0.851923i
$120$		0			0
$121$	−3397.49			−2.55258
$122$		0			0
$123$	−54.4325	+	285.249i	−0.0399025	+	0.209106i
$124$		0			0
$125$	1153.45			0.825339
$126$		0			0
$127$	1091.45			0.762604			0.381302	−	0.924450i	$-0.375476\pi$
$127$	1091.45			0.762604			0.381302	+	0.924450i	$0.375476\pi$
$128$		0			0
$129$	1070.33	−	372.654i	0.730521	−	0.254344i
$130$		0			0
$131$	−899.115			−0.599664			−0.299832	−	0.953992i	$-0.596931\pi$
$131$	−899.115			−0.599664			−0.299832	+	0.953992i	$0.596931\pi$
$132$		0			0
$133$	−230.291	+	1464.30i	−0.150141	+	0.954671i
$134$		0			0
$135$	−946.201	+	1490.36i	−0.603230	+	0.950148i
$136$		0			0
$137$			456.220i			0.284507i	0.989830	+	0.142254i	$0.0454349\pi$
$137$			456.220i			0.284507i	−0.989830	+	0.142254i	$0.954565\pi$
$138$		0			0
$139$	−2341.95	+	1352.12i	−1.42907	+	0.825076i	−0.997048	−	0.0767853i	$-0.975534\pi$
$139$	−2341.95	+	1352.12i	−1.42907	+	0.825076i	−0.432026	+	0.901861i	$0.642201\pi$
$140$		0			0
$141$	107.092	−	561.207i	0.0639629	−	0.335192i
$142$		0			0
$143$	1355.51	+	2347.81i	0.792682	+	1.37297i
$144$		0			0
$145$	−2489.71	−	1437.43i	−1.42593	−	0.823258i
$146$		0			0
$147$	1781.81	−	41.0904i	0.999734	−	0.0230550i
$148$		0			0
$149$		−	2589.63i		−	1.42383i	−0.702265	−	0.711916i	$-0.747828\pi$
$149$		−	2589.63i		−	1.42383i	0.702265	−	0.711916i	$-0.252172\pi$
$150$		0			0
$151$	−953.663			−0.513960			−0.256980	−	0.966417i	$-0.582727\pi$
$151$	−953.663			−0.513960			−0.256980	+	0.966417i	$0.582727\pi$
$152$		0			0
$153$	−1624.58	+	1287.30i	−0.858430	+	0.680210i
$154$		0			0
$155$	−1585.48	−	915.376i	−0.821604	−	0.474353i
$156$		0			0
$157$	2273.59	+	1312.66i	1.15575	+	0.667270i	0.950281	−	0.311395i	$-0.100796\pi$
$157$	2273.59	+	1312.66i	1.15575	+	0.667270i	0.205465	+	0.978665i	$0.434129\pi$
$158$		0			0
$159$	−1517.55	−	289.585i	−0.756914	−	0.144438i
$160$		0			0
$161$	2686.12	−	1034.46i	1.31488	−	0.506376i
$162$		0			0
$163$	−986.513	+	1708.69i	−0.474047	+	0.821073i	−0.999558	−	0.0297132i	$-0.990541\pi$
$163$	−986.513	+	1708.69i	−0.474047	+	0.821073i	0.525512	+	0.850786i	$0.323874\pi$
$164$		0			0
$165$	2938.01	−	3403.29i	1.38620	−	1.60573i
$166$		0			0
$167$	784.607	+	1358.98i	0.363561	+	0.629706i	0.988544	−	0.150932i	$-0.0482274\pi$
$167$	784.607	+	1358.98i	0.363561	+	0.629706i	−0.624983	+	0.780638i	$0.714894\pi$
$168$		0			0
$169$	−321.334	+	556.568i	−0.146261	+	0.253331i
$170$		0			0
$171$	795.764	−	2009.14i	0.355869	−	0.898497i
$172$		0			0
$173$	871.662	+	1509.76i	0.383071	+	0.663498i	0.991500	−	0.130110i	$-0.0415332\pi$
$173$	871.662	+	1509.76i	0.383071	+	0.663498i	−0.608429	+	0.793609i	$0.708200\pi$
$174$		0			0
$175$	−221.862	−	576.098i	−0.0958355	−	0.248851i
$176$		0			0
$177$	878.914	−	306.009i	0.373238	−	0.129949i
$178$		0			0
$179$	−1022.73	+	590.472i	−0.427051	+	0.246558i	−0.698090	−	0.716010i	$-0.745966\pi$
$179$	−1022.73	+	590.472i	−0.427051	+	0.246558i	0.271038	+	0.962569i	$0.412633\pi$
$180$		0			0
$181$		−	2832.54i		−	1.16321i	−0.813471	−	0.581605i	$-0.802425\pi$
$181$		−	2832.54i		−	1.16321i	0.813471	−	0.581605i	$-0.197575\pi$
$182$		0			0
$183$	1626.35	+	310.348i	0.656958	+	0.125364i
$184$		0			0
$185$	−933.549	+	1616.95i	−0.371005	+	0.642599i
$186$		0			0
$187$	4571.73	−	2639.49i	1.78780	−	1.03219i
$188$		0			0
$189$	−2547.52	−	511.280i	−0.980449	−	0.196773i
$190$		0			0
$191$	−1436.89	+	829.589i	−0.544344	+	0.314277i	−0.746838	−	0.665006i	$-0.768429\pi$
$191$	−1436.89	+	829.589i	−0.544344	+	0.314277i	0.202493	+	0.979284i	$0.435096\pi$
$192$		0			0
$193$	−440.410	+	762.812i	−0.164256	+	0.284499i	−0.936391	−	0.350959i	$-0.885856\pi$
$193$	−440.410	+	762.812i	−0.164256	+	0.284499i	0.772135	+	0.635459i	$0.219189\pi$
$194$		0			0
$195$	−2532.06	−	483.178i	−0.929868	−	0.177441i
$196$		0			0
$197$			4941.78i			1.78724i	0.448821	+	0.893622i	$0.351844\pi$
$197$			4941.78i			1.78724i	−0.448821	+	0.893622i	$0.648156\pi$
$198$		0			0
$199$	−4332.54	+	2501.39i	−1.54334	+	0.891050i	−0.544720	+	0.838618i	$0.683364\pi$
$199$	−4332.54	+	2501.39i	−1.54334	+	0.891050i	−0.998624	+	0.0524320i	$0.983303\pi$
$200$		0			0
$201$	−3208.45	+	1117.08i	−1.12590	+	0.392003i
$202$		0			0
$203$	657.384	−	4179.97i	0.227287	−	1.44521i
$204$		0			0
$205$	351.613	+	609.012i	0.119794	+	0.207489i
$206$		0			0
$207$	−4151.40	+	612.501i	−1.39393	+	0.205661i
$208$		0			0
$209$	−2751.83	+	4766.30i	−0.910755	+	1.57747i
$210$		0			0
$211$	2278.03	+	3945.66i	0.743251	+	1.28735i	0.951007	+	0.309168i	$0.100051\pi$
$211$	2278.03	+	3945.66i	0.743251	+	1.28735i	−0.207756	+	0.978181i	$0.566616\pi$
$212$		0			0
$213$	535.250	−	620.016i	0.172182	−	0.199450i
$214$		0			0
$215$	1372.26	−	2376.83i	0.435291	−	0.753946i
$216$		0			0
$217$	418.630	−	2661.86i	0.130961	−	0.832713i
$218$		0			0
$219$	6221.79	+	1187.27i	1.91977	+	0.366339i
$220$		0			0
$221$	−2621.15	−	1513.32i	−0.797817	−	0.460620i
$222$		0			0
$223$	5426.77	+	3133.14i	1.62961	+	0.940856i	0.984209	+	0.177013i	$0.0566434\pi$
$223$	5426.77	+	3133.14i	1.62961	+	0.940856i	0.645402	+	0.763843i	$0.276690\pi$
$224$		0			0
$225$	131.365	+	890.362i	0.0389228	+	0.263811i
$226$		0			0
$227$	−1290.13			−0.377221			−0.188611	−	0.982052i	$-0.560398\pi$
$227$	−1290.13			−0.377221			−0.188611	+	0.982052i	$0.560398\pi$
$228$		0			0
$229$		−	561.128i		−	0.161923i	−0.996717	−	0.0809616i	$-0.974201\pi$
$229$		−	561.128i		−	0.161923i	0.996717	−	0.0809616i	$-0.0257991\pi$
$230$		0			0
$231$	6228.52	+	2235.19i	1.77405	+	0.636644i
$232$		0			0
$233$	26.6649	+	15.3950i	0.00749731	+	0.00432857i	0.503744	−	0.863853i	$-0.331956\pi$
$233$	26.6649	+	15.3950i	0.00749731	+	0.00432857i	−0.496247	+	0.868182i	$0.665289\pi$
$234$		0			0
$235$	−691.773	−	1198.19i	−0.192027	−	0.332600i
$236$		0			0
$237$	−797.495	+	4179.21i	−0.218577	+	1.14544i
$238$		0			0
$239$	−3204.80	+	1850.29i	−0.867369	+	0.500775i	−0.866473	−	0.499224i	$-0.833618\pi$
$239$	−3204.80	+	1850.29i	−0.867369	+	0.500775i	−0.000895650		1.00000i	$0.500285\pi$
$240$		0			0
$241$			4498.80i			1.20246i	0.799075	+	0.601231i	$0.205323\pi$
$241$			4498.80i			1.20246i	−0.799075	+	0.601231i	$0.794677\pi$
$242$		0			0
$243$	3460.03	+	1541.79i	0.913420	+	0.407019i
$244$		0			0
$245$	3201.12	−	2894.93i	0.834742	−	0.754899i
$246$		0			0
$247$	3155.45			0.812861
$248$		0			0
$249$	3969.56	−	1382.07i	1.01028	−	0.351748i
$250$		0			0
$251$	751.424			0.188962			0.0944810	−	0.995527i	$-0.469881\pi$
$251$	751.424			0.188962			0.0944810	+	0.995527i	$0.469881\pi$
$252$		0			0
$253$	10687.3			2.65575
$254$		0			0
$255$	−940.859	+	4930.50i	−0.231054	+	1.21082i
$256$		0			0
$257$	−98.4471			−0.0238948			−0.0119474	−	0.999929i	$-0.503803\pi$
$257$	−98.4471			−0.0238948			−0.0119474	+	0.999929i	$0.503803\pi$
$258$		0			0
$259$	−2714.70	−	426.941i	−0.651288	−	0.102428i
$260$		0			0
$261$	−2271.57	+	5735.26i	−0.538723	+	1.36017i
$262$		0			0
$263$			3757.11i			0.880887i	0.897780	+	0.440443i	$0.145179\pi$
$263$			3757.11i			0.880887i	−0.897780	+	0.440443i	$0.854821\pi$
$264$		0			0
$265$	−3239.99	+	1870.61i	−0.751061	+	0.433625i
$266$		0			0
$267$	205.905	−	71.6893i	0.0471953	−	0.0164319i
$268$		0			0
$269$	−2234.67	−	3870.56i	−0.506506	−	0.877295i	−0.999972	−	0.00752932i	$-0.997603\pi$
$269$	−2234.67	−	3870.56i	−0.506506	−	0.877295i	0.493465	−	0.869766i	$-0.335730\pi$
$270$		0			0
$271$	1482.64	+	856.005i	0.332340	+	0.191877i	0.656880	−	0.753995i	$-0.271876\pi$
$271$	1482.64	+	856.005i	0.332340	+	0.191877i	−0.324539	+	0.945872i	$0.605209\pi$
$272$		0			0
$273$	−675.694	−	3733.38i	−0.149798	−	0.827671i
$274$		0			0
$275$		−	2292.13i		−	0.502621i
$276$		0			0
$277$	−7928.11			−1.71969			−0.859845	−	0.510555i	$-0.829440\pi$
$277$	−7928.11			−1.71969			−0.859845	+	0.510555i	$0.829440\pi$
$278$		0			0
$279$	−1446.56	+	3652.28i	−0.310407	+	0.783715i
$280$		0			0
$281$	4663.84	+	2692.67i	0.990112	+	0.571642i	0.905308	−	0.424756i	$-0.139640\pi$
$281$	4663.84	+	2692.67i	0.990112	+	0.571642i	0.0848043	+	0.996398i	$0.472973\pi$
$282$		0			0
$283$	−1826.90	−	1054.76i	−0.383739	−	0.221552i	0.295705	−	0.955279i	$-0.404445\pi$
$283$	−1826.90	−	1054.76i	−0.383739	−	0.221552i	−0.679444	+	0.733728i	$0.737779\pi$
$284$		0			0
$285$	−1720.68	−	4942.11i	−0.357629	−	1.02718i
$286$		0			0
$287$	−650.495	+	805.083i	−0.133789	+	0.165584i
$288$		0			0
$289$	−490.285	+	849.198i	−0.0997934	+	0.172847i
$290$		0			0
$291$	−318.213	−	913.966i	−0.0641030	−	0.184116i
$292$		0			0
$293$	−1440.95	−	2495.80i	−0.287308	−	0.497633i	0.685858	−	0.727735i	$-0.259427\pi$
$293$	−1440.95	−	2495.80i	−0.287308	−	0.497633i	−0.973166	+	0.230103i	$0.926094\pi$
$294$		0			0
$295$	1126.85	−	1951.76i	0.222399	−	0.385207i
$296$		0			0
$297$	−8144.54	−	5170.81i	−1.59123	−	1.01024i
$298$		0			0
$299$	−3063.72	−	5306.52i	−0.592574	−	1.02637i
$300$		0			0
$301$	3990.46	+	627.578i	0.764140	+	0.120176i
$302$		0			0
$303$	3450.27	+	2978.57i	0.654168	+	0.564733i
$304$		0			0
$305$	3472.29	−	2004.73i	0.651878	−	0.376362i
$306$		0			0
$307$		−	8035.89i		−	1.49392i	−0.664871	−	0.746959i	$-0.731513\pi$
$307$		−	8035.89i		−	1.49392i	0.664871	−	0.746959i	$-0.268487\pi$
$308$		0			0
$309$	−5121.12	+	5932.13i	−0.942816	+	1.09213i
$310$		0			0
$311$	4787.47	−	8292.13i	0.872901	−	1.51191i	0.0139192	−	0.999903i	$-0.495569\pi$
$311$	4787.47	−	8292.13i	0.872901	−	1.51191i	0.858982	−	0.512006i	$-0.171097\pi$
$312$		0			0
$313$	−4500.52	+	2598.38i	−0.812730	+	0.469230i	−0.847903	−	0.530151i	$-0.822135\pi$
$313$	−4500.52	+	2598.38i	−0.812730	+	0.469230i	0.0351731	+	0.999381i	$0.488802\pi$
$314$		0			0
$315$	−5478.80	+	3094.11i	−0.979986	+	0.553439i
$316$		0			0
$317$	−7159.14	+	4133.33i	−1.26845	+	0.732337i	−0.974694	−	0.223544i	$-0.928237\pi$
$317$	−7159.14	+	4133.33i	−1.26845	+	0.732337i	−0.293752	+	0.955882i	$0.594904\pi$
$318$		0			0
$319$	7855.31	−	13605.8i	1.37872	−	2.38802i
$320$		0			0
$321$	−2765.75	−	7943.73i	−0.480900	−	1.38123i
$322$		0			0
$323$		−	6144.39i		−	1.05846i
$324$		0			0
$325$	−1138.10	+	657.084i	−0.194248	+	0.112149i
$326$		0			0
$327$	452.325	−	2370.37i	0.0764942	−	0.400862i
$328$		0			0
$329$	1279.80	−	1583.94i	0.214461	−	0.265427i
$330$		0			0
$331$	−2390.37	−	4140.23i	−0.396938	−	0.687516i	0.596409	−	0.802681i	$-0.296594\pi$
$331$	−2390.37	−	4140.23i	−0.396938	−	0.687516i	−0.993346	+	0.115165i	$0.963260\pi$
$332$		0			0
$333$	3724.79	+	1475.28i	0.612965	+	0.242778i
$334$		0			0
$335$	−4113.54	+	7124.86i	−0.670885	+	1.16201i
$336$		0			0
$337$	2466.28	+	4271.73i	0.398656	+	0.690492i	0.993560	−	0.113305i	$-0.0361436\pi$
$337$	2466.28	+	4271.73i	0.398656	+	0.690492i	−0.594905	+	0.803796i	$0.702810\pi$
$338$		0			0
$339$	−6341.48	−	1210.11i	−1.01599	−	0.193876i
$340$		0			0
$341$	5002.35	−	8664.33i	0.794407	−	1.37595i
$342$		0			0
$343$	5669.45	+	2865.47i	0.892483	+	0.451081i
$344$		0			0
$345$	−6640.48	+	7692.11i	−1.03627	+	1.20037i
$346$		0			0
$347$	−5937.40	−	3427.96i	−0.918549	−	0.530324i	−0.0353771	−	0.999374i	$-0.511263\pi$
$347$	−5937.40	−	3427.96i	−0.918549	−	0.530324i	−0.883172	+	0.469050i	$0.844597\pi$
$348$		0			0
$349$	240.494	+	138.849i	0.0368864	+	0.0212964i	0.518330	−	0.855181i	$-0.326554\pi$
$349$	240.494	+	138.849i	0.0368864	+	0.0212964i	−0.481443	+	0.876477i	$0.659887\pi$
$350$		0			0
$351$	−232.648	+	5526.28i	−0.0353784	+	0.840373i
$352$		0			0
$353$	−2824.97			−0.425943			−0.212971	−	0.977058i	$-0.568314\pi$
$353$	−2824.97			−0.425943			−0.212971	+	0.977058i	$0.568314\pi$
$354$		0			0
$355$		−	1983.52i		−	0.296548i
$356$		0			0
$357$	−7269.75	+	1315.73i	−1.07775	+	0.195059i
$358$		0			0
$359$	−200.509	−	115.764i	−0.0294776	−	0.0170189i	0.485189	−	0.874409i	$-0.338751\pi$
$359$	−200.509	−	115.764i	−0.0294776	−	0.0170189i	−0.514666	+	0.857391i	$0.672084\pi$
$360$		0			0
$361$	−226.553	−	392.401i	−0.0330300	−	0.0572096i
$362$		0			0
$363$	13363.2	+	11536.2i	1.93219	+	1.66803i
$364$		0			0
$365$	13283.6	−	7669.30i	1.90492	−	1.09981i
$366$		0			0
$367$		−	4522.25i		−	0.643214i	−0.946873	−	0.321607i	$-0.895777\pi$
$367$		−	4522.25i		−	0.643214i	0.946873	−	0.321607i	$-0.104223\pi$
$368$		0			0
$369$	1182.66	−	937.130i	0.166848	−	0.132209i
$370$		0			0
$371$	−4283.10	−	3460.68i	−0.599374	−	0.484285i
$372$		0			0
$373$	9141.53			1.26898			0.634492	−	0.772930i	$-0.281210\pi$
$373$	9141.53			1.26898			0.634492	+	0.772930i	$0.281210\pi$
$374$		0			0
$375$	−4536.80	−	3916.55i	−0.624744	−	0.539332i
$376$		0			0
$377$	−9007.49			−1.23053
$378$		0			0
$379$	−1499.84			−0.203276			−0.101638	−	0.994821i	$-0.532408\pi$
$379$	−1499.84			−0.203276			−0.101638	+	0.994821i	$0.532408\pi$
$380$		0			0
$381$	−4292.96	−	3706.04i	−0.577257	−	0.498337i
$382$		0			0
$383$	−8130.00			−1.08466			−0.542328	−	0.840167i	$-0.682457\pi$
$383$	−8130.00			−1.08466			−0.542328	+	0.840167i	$0.682457\pi$
$384$		0			0
$385$	14954.2	−	5759.06i	1.97958	−	0.762361i
$386$		0			0
$387$	−5475.23	−	2168.58i	−0.719177	−	0.284845i
$388$		0			0
$389$			4783.36i			0.623460i	0.950171	+	0.311730i	$0.100908\pi$
$389$			4783.36i			0.623460i	−0.950171	+	0.311730i	$0.899092\pi$
$390$		0			0
$391$	−10333.0	+	5965.77i	−1.33648	+	0.771617i
$392$		0			0
$393$	3536.44	+	3052.96i	0.453919	+	0.391861i
$394$		0			0
$395$	5151.51	+	8922.68i	0.656205	+	1.13658i
$396$		0			0
$397$	1258.45	+	726.567i	0.159093	+	0.0918522i	0.577433	−	0.816438i	$-0.304055\pi$
$397$	1258.45	+	726.567i	0.159093	+	0.0918522i	−0.418340	+	0.908291i	$0.637388\pi$
$398$		0			0
$399$	5877.86	−	4977.52i	0.737497	−	0.624531i
$400$		0			0
$401$		−	320.312i		−	0.0398893i	−0.999801	−	0.0199447i	$-0.993651\pi$
$401$		−	320.312i		−	0.0398893i	0.999801	−	0.0199447i	$-0.00634900\pi$
$402$		0			0
$403$	−5736.08			−0.709018
$404$		0			0
$405$	8782.20	−	2649.13i	1.07751	−	0.325028i
$406$		0			0
$407$	−8836.35	−	5101.67i	−1.07617	−	0.621328i
$408$		0			0
$409$	5538.97	+	3197.93i	0.669644	+	0.386619i	0.795942	−	0.605373i	$-0.206976\pi$
$409$	5538.97	+	3197.93i	0.669644	+	0.386619i	−0.126298	+	0.991992i	$0.540309\pi$
$410$		0			0
$411$	1549.10	−	1794.43i	0.185916	−	0.215359i
$412$		0			0
$413$	3276.81	+	515.344i	0.390415	+	0.0614005i
$414$		0			0
$415$	5089.35	−	8815.01i	0.601991	−	1.04268i
$416$		0			0
$417$	13802.6	+	2633.88i	1.62090	+	0.309308i
$418$		0			0
$419$	−4472.71	−	7746.96i	−0.521495	−	0.903255i	−0.999687	−	0.0250003i	$-0.992041\pi$
$419$	−4472.71	−	7746.96i	−0.521495	−	0.903255i	0.478193	−	0.878255i	$-0.341292\pi$
$420$		0			0
$421$	−29.3000	+	50.7491i	−0.00339191	+	0.00587496i	−0.867716	−	0.497060i	$-0.834413\pi$
$421$	−29.3000	+	50.7491i	−0.00339191	+	0.00587496i	0.864324	+	0.502935i	$0.167746\pi$
$422$		0			0
$423$	−2326.81	+	1843.73i	−0.267454	+	0.211928i
$424$		0			0
$425$	1279.49	+	2216.15i	0.146034	+	0.252939i
$426$		0			0
$427$	4590.19	+	3708.81i	0.520223	+	0.420332i
$428$		0			0
$429$	2640.48	−	13837.2i	0.297164	−	1.55726i
$430$		0			0
$431$	−7923.61	+	4574.70i	−0.885538	+	0.511266i	−0.872480	−	0.488649i	$-0.837490\pi$
$431$	−7923.61	+	4574.70i	−0.885538	+	0.511266i	−0.0130578	+	0.999915i	$0.504157\pi$
$432$		0			0
$433$			13367.0i			1.48355i	0.670651	+	0.741773i	$0.266015\pi$
$433$			13367.0i			1.48355i	−0.670651	+	0.741773i	$0.733985\pi$
$434$		0			0
$435$	4911.82	+	14107.6i	0.541388	+	1.55497i
$436$		0			0
$437$	6219.67	−	10772.8i	0.680840	−	1.17925i
$438$		0			0
$439$	−287.164	+	165.794i	−0.0312200	+	0.0180249i	−0.515529	−	0.856872i	$-0.672404\pi$
$439$	−287.164	+	165.794i	−0.0312200	+	0.0180249i	0.484309	+	0.874897i	$0.339071\pi$
$440$		0			0
$441$	−7147.82	−	5888.53i	−0.771819	−	0.635842i
$442$		0			0
$443$	−12011.2	+	6934.67i	−1.28819	+	0.743738i	−0.978332	−	0.207043i	$-0.933616\pi$
$443$	−12011.2	+	6934.67i	−1.28819	+	0.743738i	−0.309861	+	0.950782i	$0.600283\pi$
$444$		0			0
$445$	263.989	−	457.242i	0.0281220	−	0.0487087i
$446$		0			0
$447$	−8793.14	+	10185.7i	−0.930428	+	1.07778i
$448$		0			0
$449$		−	14773.0i		−	1.55275i	−0.630274	−	0.776373i	$-0.717057\pi$
$449$		−	14773.0i		−	1.55275i	0.630274	−	0.776373i	$-0.282943\pi$
$450$		0			0
$451$	−3328.14	+	1921.50i	−0.347485	+	0.200621i
$452$		0			0
$453$	3751.00	+	3238.18i	0.389045	+	0.335856i
$454$		0			0
$455$	−7146.44	−	5774.22i	−0.736330	−	0.594944i
$456$		0			0
$457$	−641.791	−	1111.61i	−0.0656930	−	0.113784i	0.831308	−	0.555812i	$-0.187592\pi$
$457$	−641.791	−	1111.61i	−0.0656930	−	0.113784i	−0.897001	+	0.442028i	$0.854259\pi$
$458$		0			0
$459$	10760.9	+	453.019i	1.09429	+	0.0460678i
$460$		0			0
$461$	−980.109	+	1697.60i	−0.0990200	+	0.171508i	−0.911279	−	0.411789i	$-0.864904\pi$
$461$	−980.109	+	1697.60i	−0.0990200	+	0.171508i	0.812259	+	0.583297i	$0.198237\pi$
$462$		0			0
$463$	−5890.28	−	10202.3i	−0.591241	−	1.02406i	−0.994066	−	0.108783i	$-0.965305\pi$
$463$	−5890.28	−	10202.3i	−0.591241	−	1.02406i	0.402824	−	0.915277i	$-0.368029\pi$
$464$		0			0
$465$	3127.91	+	8983.92i	0.311942	+	0.895955i
$466$		0			0
$467$	−3117.96	+	5400.47i	−0.308955	+	0.535126i	−0.978134	−	0.207975i	$-0.933313\pi$
$467$	−3117.96	+	5400.47i	−0.308955	+	0.535126i	0.669179	+	0.743101i	$0.266646\pi$
$468$		0			0
$469$	−11961.9	−	1881.25i	−1.17772	−	0.185220i
$470$		0			0
$471$	−4485.44	−	12883.0i	−0.438808	−	1.26033i
$472$		0			0
$473$	12988.9	+	7499.15i	1.26264	+	0.728988i
$474$		0			0
$475$	−2310.47	−	1333.95i	−0.223182	−	0.128854i
$476$		0			0
$477$	4985.60	+	6291.87i	0.478564	+	0.603951i
$478$		0			0
$479$	8868.62			0.845965			0.422983	−	0.906138i	$-0.360983\pi$
$479$	8868.62			0.845965			0.422983	+	0.906138i	$0.360983\pi$
$480$		0			0
$481$			5849.96i			0.554543i
$482$		0			0
$483$	−14077.7	−	5051.97i	−1.32620	−	0.475927i
$484$		0			0
$485$	−2029.60	−	1171.79i	−0.190019	−	0.109708i
$486$		0			0
$487$	−2778.74	−	4812.92i	−0.258556	−	0.447832i	0.707299	−	0.706914i	$-0.249913\pi$
$487$	−2778.74	−	4812.92i	−0.258556	−	0.447832i	−0.965855	+	0.259082i	$0.916580\pi$
$488$		0			0
$489$	9682.09	−	3370.99i	0.895377	−	0.311741i
$490$		0			0
$491$	−10412.2	+	6011.50i	−0.957020	+	0.552536i	−0.895255	−	0.445555i	$-0.853006\pi$
$491$	−10412.2	+	6011.50i	−0.957020	+	0.552536i	−0.0617653	+	0.998091i	$0.519673\pi$
$492$		0			0
$493$			17539.7i			1.60233i
$494$		0			0
$495$	−23111.9	+	3409.94i	−2.09859	+	0.309627i
$496$		0			0
$497$	2724.38	−	1049.19i	0.245886	−	0.0946937i
$498$		0			0
$499$	19168.6			1.71965			0.859824	−	0.510591i	$-0.170573\pi$
$499$	19168.6			1.71965			0.859824	+	0.510591i	$0.170573\pi$
$500$		0			0
$501$	1528.38	−	8009.35i	0.136293	−	0.714235i
$502$		0			0
$503$	13168.5			1.16731			0.583654	−	0.812002i	$-0.301622\pi$
$503$	13168.5			1.16731			0.583654	+	0.812002i	$0.301622\pi$
$504$		0			0
$505$	11037.9			0.972637
$506$		0			0
$507$	3153.72	−	1098.02i	0.276256	−	0.0961833i
$508$		0			0
$509$	−3555.93			−0.309654			−0.154827	−	0.987942i	$-0.549482\pi$
$509$	−3555.93			−0.309654			−0.154827	+	0.987942i	$0.549482\pi$
$510$		0			0
$511$	17560.3	+	14188.4i	1.52020	+	1.22830i
$512$		0			0
$513$	−9952.02	+	5200.44i	−0.856515	+	0.447573i
$514$		0			0
$515$			18977.8i			1.62381i
$516$		0			0
$517$	6547.86	−	3780.41i	0.557011	−	0.321590i
$518$		0			0
$519$	1697.96	−	8898.02i	0.143607	−	0.752562i
$520$		0			0
$521$	11705.2	+	20273.9i	0.984285	+	1.70483i	0.645072	+	0.764122i	$0.276827\pi$
$521$	11705.2	+	20273.9i	0.984285	+	1.70483i	0.339213	+	0.940710i	$0.389839\pi$
$522$		0			0
$523$	6433.74	+	3714.52i	0.537911	+	0.310563i	0.744232	−	0.667921i	$-0.232816\pi$
$523$	6433.74	+	3714.52i	0.537911	+	0.310563i	−0.206321	+	0.978484i	$0.566149\pi$
$524$		0			0
$525$	−1083.51	+	3019.27i	−0.0900728	+	0.250994i
$526$		0			0
$527$			11169.5i			0.923244i
$528$		0			0
$529$	−11988.4			−0.985324
$530$		0			0
$531$	−4496.05	−	1780.76i	−0.367442	−	0.145533i
$532$		0			0
$533$	1908.15	+	1101.67i	0.155067	+	0.0895283i
$534$		0			0
$535$	−17640.3	−	10184.6i	−1.42552	−	0.823026i
$536$		0			0
$537$	6027.60	+	1150.21i	0.484376	+	0.0924308i
$538$		0			0
$539$	15820.2	+	17493.5i	1.26424	+	1.39796i
$540$		0			0
$541$	2767.89	−	4794.13i	0.219965	−	0.380990i	−0.734832	−	0.678249i	$-0.762739\pi$
$541$	2767.89	−	4794.13i	0.219965	−	0.380990i	0.954797	+	0.297259i	$0.0960724\pi$
$542$		0			0
$543$	−9617.94	+	11141.1i	−0.760120	+	0.880498i
$544$		0			0
$545$	−2921.85	−	5060.79i	−0.229648	−	0.397762i
$546$		0			0
$547$	728.680	−	1262.11i	0.0569581	−	0.0986544i	−0.836140	−	0.548515i	$-0.815193\pi$
$547$	728.680	−	1262.11i	0.0569581	−	0.0986544i	0.893099	+	0.449861i	$0.148527\pi$
$548$		0			0
$549$	−5343.06	−	6742.98i	−0.415367	−	0.524196i
$550$		0			0
$551$	−9143.07	−	15836.3i	−0.706911	−	1.22441i
$552$		0			0
$553$	−9530.46	+	11795.3i	−0.732868	+	0.907032i
$554$		0			0
$555$	9162.28	−	3190.01i	0.700752	−	0.243979i
$556$		0			0
$557$	10451.5	−	6034.16i	0.795051	−	0.459023i	−0.0466868	−	0.998910i	$-0.514866\pi$
$557$	10451.5	−	6034.16i	0.795051	−	0.459023i	0.841738	+	0.539887i	$0.181533\pi$
$558$		0			0
$559$		−	8599.10i		−	0.650631i
$560$		0			0
$561$	−26944.2	−	5141.61i	−2.02778	−	0.386950i
$562$		0			0
$563$	1119.12	−	1938.38i	0.0837751	−	0.145103i	−0.821094	−	0.570794i	$-0.806636\pi$
$563$	1119.12	−	1938.38i	0.0837751	−	0.145103i	0.904869	+	0.425691i	$0.139969\pi$
$564$		0			0
$565$	−13539.2	+	7816.85i	−1.00814	+	0.582048i
$566$		0			0
$567$	8283.98	+	10661.1i	0.613570	+	0.789640i
$568$		0			0
$569$	−309.066	+	178.439i	−0.0227710	+	0.0131469i	−0.511342	−	0.859377i	$-0.670852\pi$
$569$	−309.066	+	178.439i	−0.0227710	+	0.0131469i	0.488571	+	0.872524i	$0.337518\pi$
$570$		0			0
$571$	−13132.8	+	22746.6i	−0.962503	+	1.66710i	−0.246325	+	0.969187i	$0.579223\pi$
$571$	−13132.8	+	22746.6i	−0.962503	+	1.66710i	−0.716179	+	0.697917i	$0.754110\pi$
$572$		0			0
$573$	8468.54	+	1616.00i	0.617414	+	0.117818i
$574$		0			0
$575$			5180.67i			0.375738i
$576$		0			0
$577$	−15580.8	+	8995.60i	−1.12416	+	0.649032i	−0.942459	−	0.334322i	$-0.891493\pi$
$577$	−15580.8	+	8995.60i	−1.12416	+	0.649032i	−0.181698	+	0.983354i	$0.558159\pi$
$578$		0			0
$579$	4322.38	−	1504.91i	0.310245	−	0.108017i
$580$		0			0
$581$	14799.5	+	2327.52i	1.05678	+	0.166199i
$582$		0			0
$583$	−10222.5	−	17705.9i	−0.726198	−	1.25781i
$584$		0			0
$585$	8318.57	+	10498.1i	0.587916	+	0.741954i
$586$		0			0
$587$	8123.48	−	14070.3i	0.571196	−	0.989340i	−0.425248	−	0.905077i	$-0.639813\pi$
$587$	8123.48	−	14070.3i	0.571196	−	0.989340i	0.996444	−	0.0842634i	$-0.0268537\pi$
$588$		0			0
$589$	−5822.41	−	10084.7i	−0.407315	−	0.705490i
$590$		0			0
$591$	16779.9	−	19437.2i	1.16791	−	1.35286i
$592$		0			0
$593$	−2220.81	+	3846.55i	−0.153790	+	0.266373i	−0.932618	−	0.360865i	$-0.882481\pi$
$593$	−2220.81	+	3846.55i	−0.153790	+	0.266373i	0.778828	+	0.627238i	$0.215815\pi$
$594$		0			0
$595$	−11243.7	+	13915.8i	−0.774702	+	0.958808i
$596$		0			0
$597$	25534.5	+	4872.60i	1.75051	+	0.334041i
$598$		0			0
$599$	−8923.26	−	5151.85i	−0.608672	−	0.351417i	0.163774	−	0.986498i	$-0.447633\pi$
$599$	−8923.26	−	5151.85i	−0.608672	−	0.351417i	−0.772445	+	0.635081i	$0.780967\pi$
$600$		0			0
$601$	−6090.03	−	3516.08i	−0.413340	−	0.238642i	0.278884	−	0.960325i	$-0.410036\pi$
$601$	−6090.03	−	3516.08i	−0.413340	−	0.238642i	−0.692224	+	0.721683i	$0.743369\pi$
$602$		0			0
$603$	16412.7	+	6500.60i	1.10842	+	0.439013i
$604$		0			0
$605$	42750.8			2.87284
$606$		0			0
$607$			157.238i			0.0105142i	0.999986	+	0.00525708i	$0.00167339\pi$
$607$			157.238i			0.0105142i	−0.999986	+	0.00525708i	$0.998327\pi$
$608$		0			0
$609$	−16778.8	+	14208.7i	−1.11644	+	0.945430i
$610$		0			0
$611$	−3754.13	−	2167.45i	−0.248570	−	0.143512i
$612$		0			0
$613$	−8959.16	−	15517.7i	−0.590305	−	1.02244i	−0.994191	−	0.107629i	$-0.965674\pi$
$613$	−8959.16	−	15517.7i	−0.590305	−	1.02244i	0.403886	−	0.914809i	$-0.367659\pi$
$614$		0			0
$615$	684.927	−	3589.31i	0.0449088	−	0.235341i
$616$		0			0
$617$	−12365.0	+	7138.91i	−0.806798	+	0.465805i	−0.845843	−	0.533432i	$-0.820902\pi$
$617$	−12365.0	+	7138.91i	−0.806798	+	0.465805i	0.0390445	+	0.999237i	$0.487569\pi$
$618$		0			0
$619$		−	1661.43i		−	0.107881i	−0.998544	−	0.0539407i	$-0.982822\pi$
$619$		−	1661.43i		−	0.107881i	0.998544	−	0.0539407i	$-0.0171782\pi$
$620$		0			0
$621$	18408.3	+	11687.0i	1.18953	+	0.755209i
$622$		0			0
$623$	767.664	+	120.730i	0.0493673	+	0.00776398i
$624$		0			0
$625$	−18680.6			−1.19556
$626$		0			0
$627$	27007.7	−	9403.20i	1.72023	−	0.598928i
$628$		0			0
$629$	11391.2			0.722095
$630$		0			0
$631$	23414.7			1.47722			0.738610	−	0.674133i	$-0.235482\pi$
$631$	23414.7			1.47722			0.738610	+	0.674133i	$0.235482\pi$
$632$		0			0
$633$	4437.50	−	23254.4i	0.278633	−	1.46016i
$634$		0			0
$635$	−13733.8			−0.858283
$636$		0			0
$637$	4150.79	−	12870.0i	0.258179	−	0.800514i
$638$		0			0
$639$	−4210.55	+	621.227i	−0.260668	+	0.0384591i
$640$		0			0
$641$			28359.9i			1.74750i	0.486374	+	0.873751i	$0.338319\pi$
$641$			28359.9i			1.74750i	−0.486374	+	0.873751i	$0.661681\pi$
$642$		0			0
$643$	11821.1	−	6824.94i	0.725008	−	0.418584i	−0.0915851	−	0.995797i	$-0.529193\pi$
$643$	11821.1	−	6824.94i	0.725008	−	0.418584i	0.816593	+	0.577214i	$0.195860\pi$
$644$		0			0
$645$	−13468.0	+	4689.12i	−0.822174	+	0.286254i
$646$		0			0
$647$	2516.28	+	4358.33i	0.152898	+	0.264828i	0.932292	−	0.361707i	$-0.117806\pi$
$647$	2516.28	+	4358.33i	0.152898	+	0.264828i	−0.779393	+	0.626535i	$0.784473\pi$
$648$		0			0
$649$	10666.0	+	6158.02i	0.645111	+	0.372455i
$650$		0			0
$651$	−10685.0	+	9048.29i	−0.643282	+	0.544747i
$652$		0			0
$653$			14280.4i			0.855798i	0.903827	+	0.427899i	$0.140746\pi$
$653$			14280.4i			0.855798i	−0.903827	+	0.427899i	$0.859254\pi$
$654$		0			0
$655$	11313.6			0.674900
$656$		0			0
$657$	−20440.5	−	25796.0i	−1.21379	−	1.53181i
$658$		0			0
$659$	−26681.2	−	15404.4i	−1.57716	−	0.910575i	−0.995253	−	0.0973220i	$-0.968972\pi$
$659$	−26681.2	−	15404.4i	−1.57716	−	0.910575i	−0.581910	−	0.813253i	$-0.697694\pi$
$660$		0			0
$661$	−15656.6	−	9039.34i	−0.921287	−	0.531905i	−0.0372418	−	0.999306i	$-0.511857\pi$
$661$	−15656.6	−	9039.34i	−0.921287	−	0.531905i	−0.884046	+	0.467401i	$0.845190\pi$
$662$		0			0
$663$	5171.13	+	14852.4i	0.302911	+	0.870016i
$664$		0			0
$665$	2897.76	−	18425.4i	0.168978	−	1.07445i
$666$		0			0
$667$	−17754.5	+	30751.8i	−1.03067	+	1.78518i
$668$		0			0
$669$	−10706.2	−	30750.1i	−0.618722	−	1.77708i
$670$		0			0
$671$	10955.5	+	18975.4i	0.630299	+	1.09171i
$672$		0			0
$673$	5751.89	−	9962.57i	0.329449	−	0.570622i	−0.652954	−	0.757398i	$-0.726470\pi$
$673$	5751.89	−	9962.57i	0.329449	−	0.570622i	0.982403	+	0.186776i	$0.0598037\pi$
$674$		0			0
$675$	2506.55	−	3948.07i	0.142929	−	0.225128i
$676$		0			0
$677$	−5850.02	−	10132.5i	−0.332104	−	0.575221i	0.650820	−	0.759232i	$-0.274425\pi$
$677$	−5850.02	−	10132.5i	−0.332104	−	0.575221i	−0.982924	+	0.184011i	$0.941092\pi$
$678$		0			0
$679$	535.896	−	3407.49i	0.0302884	−	0.192589i
$680$		0			0
$681$	5074.42	+	4380.67i	0.285539	+	0.246502i
$682$		0			0
$683$	−13060.7	+	7540.58i	−0.731702	+	0.422448i	−0.819044	−	0.573730i	$-0.805496\pi$
$683$	−13060.7	+	7540.58i	−0.731702	+	0.422448i	0.0873425	+	0.996178i	$0.472163\pi$
$684$		0			0
$685$		−	5740.64i		−	0.320202i
$686$		0			0
$687$	−1905.32	+	2207.06i	−0.105812	+	0.122568i
$688$		0			0
$689$	−5860.96	+	10151.5i	−0.324071	+	0.561307i
$690$		0			0
$691$	20562.9	−	11872.0i	1.13206	−	0.653593i	0.187604	−	0.982245i	$-0.439928\pi$
$691$	20562.9	−	11872.0i	1.13206	−	0.653593i	0.944451	+	0.328652i	$0.106594\pi$
$692$		0			0
$693$	−16908.7	−	29940.6i	−0.926852	−	1.64120i
$694$		0			0
$695$	29468.8	−	17013.8i	1.60837	−	0.928592i
$696$		0			0
$697$	2145.20	−	3715.60i	0.116579	−	0.201920i
$698$		0			0
$699$	−52.6057	−	151.093i	−0.00284654	−	0.00817578i
$700$		0			0
$701$			25267.5i			1.36140i	0.732563	+	0.680699i	$0.238324\pi$
$701$			25267.5i			1.36140i	−0.732563	+	0.680699i	$0.761676\pi$
$702$		0			0
$703$	−10284.9	+	5938.01i	−0.551783	+	0.318572i
$704$		0			0
$705$	−1347.54	+	7061.69i	−0.0719878	+	0.377247i
$706$		0			0
$707$	5838.56	+	15160.7i	0.310582	+	0.806473i
$708$		0			0
$709$	2968.94	+	5142.36i	0.157265	+	0.272391i	0.933881	−	0.357583i	$-0.116399\pi$
$709$	2968.94	+	5142.36i	0.157265	+	0.272391i	−0.776616	+	0.629974i	$0.783066\pi$
$710$		0			0
$711$	17327.3	−	13730.0i	0.913959	−	0.724211i
$712$		0			0
$713$	−11306.3	+	19583.1i	−0.593863	+	1.02860i
$714$		0			0
$715$	−17056.5	−	29542.7i	−0.892134	−	1.54522i
$716$		0			0
$717$	18888.0	+	3604.28i	0.983799	+	0.187733i
$718$		0			0
$719$	4987.87	−	8639.24i	0.258715	−	0.448107i	−0.707183	−	0.707031i	$-0.750034\pi$
$719$	4987.87	−	8639.24i	0.258715	−	0.448107i	0.965898	+	0.258923i	$0.0833677\pi$
$720$		0			0
$721$	−26066.1	+	10038.4i	−1.34640	+	0.518514i
$722$		0			0
$723$	15275.8	−	17694.9i	0.785769	−	0.910209i
$724$		0			0
$725$	6595.41	+	3807.86i	0.337858	+	0.195063i
$726$		0			0
$727$	5220.07	+	3013.81i	0.266302	+	0.153750i	0.627206	−	0.778853i	$-0.284198\pi$
$727$	5220.07	+	3013.81i	0.266302	+	0.153750i	−0.360904	+	0.932603i	$0.617532\pi$
$728$		0			0
$729$	−8374.00	−	17812.8i	−0.425443	−	0.904985i
$730$		0			0
$731$	−16744.4			−0.847216
$732$		0			0
$733$			18128.1i			0.913477i	0.889601	+	0.456738i	$0.150982\pi$
$733$			18128.1i			0.913477i	−0.889601	+	0.456738i	$0.849018\pi$
$734$		0			0
$735$	−22420.6	+	517.043i	−1.12516	+	0.0259475i
$736$		0			0
$737$	−38936.0	−	22479.7i	−1.94603	−	1.12354i
$738$		0			0
$739$	−14881.9	−	25776.2i	−0.740784	−	1.28308i	−0.952139	−	0.305667i	$-0.901121\pi$
$739$	−14881.9	−	25776.2i	−0.740784	−	1.28308i	0.211354	−	0.977410i	$-0.432213\pi$
$740$		0			0
$741$	−12411.2	−	10714.4i	−0.615299	−	0.531178i
$742$		0			0
$743$	1928.67	−	1113.52i	0.0952301	−	0.0549811i	−0.451629	−	0.892206i	$-0.649157\pi$
$743$	1928.67	−	1113.52i	0.0952301	−	0.0549811i	0.546859	+	0.837225i	$0.315823\pi$
$744$		0			0
$745$			32585.5i			1.60247i
$746$		0			0
$747$	−20306.1	−	8042.67i	−0.994594	−	0.393930i
$748$		0			0
$749$	4657.74	−	29616.2i	0.227223	−	1.44480i
$750$		0			0
$751$	−14282.2			−0.693962			−0.346981	−	0.937872i	$-0.612793\pi$
$751$	−14282.2			−0.693962			−0.346981	+	0.937872i	$0.612793\pi$
$752$		0			0
$753$	−2955.54	−	2551.47i	−0.143036	−	0.123481i
$754$		0			0
$755$	12000.0			0.578443
$756$		0			0
$757$	7484.80			0.359365			0.179683	−	0.983725i	$-0.442493\pi$
$757$	7484.80			0.359365			0.179683	+	0.983725i	$0.442493\pi$
$758$		0			0
$759$	−42035.9	−	36289.0i	−2.01029	−	1.73545i
$760$		0			0
$761$	19269.9			0.917914			0.458957	−	0.888458i	$-0.348223\pi$
$761$	19269.9			0.917914			0.458957	+	0.888458i	$0.348223\pi$
$762$		0			0
$763$	5405.51	−	6690.11i	0.256478	−	0.317429i
$764$		0			0
$765$	20442.2	−	16198.2i	0.966131	−	0.765551i
$766$		0			0
$767$		−	7061.25i		−	0.332421i
$768$		0			0
$769$	−3478.65	+	2008.40i	−0.163125	+	0.0941805i	−0.579340	−	0.815086i	$-0.696690\pi$
$769$	−3478.65	+	2008.40i	−0.163125	+	0.0941805i	0.416215	+	0.909266i	$0.363356\pi$
$770$		0			0
$771$	387.217	+	334.279i	0.0180873	+	0.0156145i
$772$		0			0
$773$	432.297	+	748.761i	0.0201147	+	0.0348397i	0.875908	−	0.482479i	$-0.160264\pi$
$773$	432.297	+	748.761i	0.0201147	+	0.0348397i	−0.855793	+	0.517319i	$0.826930\pi$
$774$		0			0
$775$	4200.03	+	2424.89i	0.194671	+	0.112393i
$776$		0			0
$777$	9227.93	+	10897.1i	0.426062	+	0.503129i
$778$		0			0
$779$			4473.00i			0.205728i
$780$		0			0
$781$	10839.6			0.496633
$782$		0			0
$783$	28408.8	−	14845.1i	1.29661	−	0.677547i
$784$		0			0
$785$	−28608.7	−	16517.2i	−1.30075	−	0.750987i
$786$		0			0
$787$	−5902.96	−	3408.08i	−0.267367	−	0.154364i	0.360323	−	0.932827i	$-0.382666\pi$
$787$	−5902.96	−	3408.08i	−0.267367	−	0.154364i	−0.627691	+	0.778463i	$0.716000\pi$
$788$		0			0
$789$	12757.3	−	14777.7i	0.575631	−	0.666791i
$790$		0			0
$791$	−17898.1	−	14461.4i	−0.804530	−	0.650049i
$792$		0			0
$793$	6281.18	−	10879.3i	0.281275	−	0.487183i
$794$		0			0
$795$	19095.4	+	3643.86i	0.851879	+	0.162559i
$796$		0			0
$797$	−5482.05	−	9495.19i	−0.243644	−	0.422004i	0.718105	−	0.695934i	$-0.245010\pi$
$797$	−5482.05	−	9495.19i	−0.243644	−	0.422004i	−0.961750	+	0.273930i	$0.911676\pi$
$798$		0			0
$799$	−4220.53	+	7310.17i	−0.186873	+	0.323673i
$800$		0			0
$801$	−1053.30	−	417.180i	−0.0464624	−	0.0184024i
$802$		0			0
$803$	41911.3	+	72592.5i	1.84186	+	3.19020i
$804$		0			0
$805$	−33799.5	+	13016.6i	−1.47985	+	0.569908i
$806$		0			0
$807$	−4353.04	+	22811.8i	−0.189881	+	0.995058i
$808$		0			0
$809$	−17637.3	+	10182.9i	−0.766497	+	0.442537i	−0.831624	−	0.555340i	$-0.812588\pi$
$809$	−17637.3	+	10182.9i	−0.766497	+	0.442537i	0.0651265	+	0.997877i	$0.479255\pi$
$810$		0			0
$811$		−	42250.7i		−	1.82937i	−0.404163	−	0.914687i	$-0.632437\pi$
$811$		−	42250.7i		−	1.82937i	0.404163	−	0.914687i	$-0.367563\pi$
$812$		0			0
$813$	−2925.03	−	8401.22i	−0.126181	−	0.362415i
$814$		0			0
$815$	12413.3	−	21500.5i	0.533522	−	0.924087i
$816$		0			0
$817$	15118.2	−	8728.53i	0.647394	−	0.373773i
$818$		0			0
$819$	−10019.1	+	16978.6i	−0.427466	+	0.724398i
$820$		0			0
$821$	13702.6	−	7911.20i	0.582490	−	0.336301i	−0.179632	−	0.983734i	$-0.557491\pi$
$821$	13702.6	−	7911.20i	0.582490	−	0.336301i	0.762122	+	0.647433i	$0.224157\pi$
$822$		0			0
$823$	−12124.0	+	20999.3i	−0.513505	+	0.889417i	0.486372	+	0.873752i	$0.338320\pi$
$823$	−12124.0	+	20999.3i	−0.513505	+	0.889417i	−0.999877	+	0.0156655i	$0.995013\pi$
$824$		0			0
$825$	−7782.98	+	9015.54i	−0.328447	+	0.380462i
$826$		0			0
$827$		−	37190.0i		−	1.56375i	−0.623434	−	0.781876i	$-0.714263\pi$
$827$		−	37190.0i		−	1.56375i	0.623434	−	0.781876i	$-0.285737\pi$
$828$		0			0
$829$	−15763.2	+	9100.86i	−0.660406	+	0.381286i	−0.792432	−	0.609961i	$-0.791185\pi$
$829$	−15763.2	+	9100.86i	−0.660406	+	0.381286i	0.132025	+	0.991246i	$0.457852\pi$
$830$		0			0
$831$	31183.3	+	26920.0i	1.30173	+	1.12376i
$832$		0			0
$833$	−25060.8	−	8082.54i	−1.04238	−	0.336187i
$834$		0			0
$835$	−9872.76	−	17100.1i	−0.409175	−	0.708711i
$836$		0			0
$837$	18091.1	−	9453.51i	0.747096	−	0.390396i
$838$		0			0
$839$	14170.6	−	24544.3i	0.583105	−	1.00997i	−0.412004	−	0.911182i	$-0.635171\pi$
$839$	14170.6	−	24544.3i	0.583105	−	1.00997i	0.995109	−	0.0987850i	$-0.0314956\pi$
$840$		0			0
$841$	13905.1	+	24084.4i	0.570139	+	0.987509i
$842$		0			0
$843$	−9201.06	−	26427.1i	−0.375921	−	1.07971i
$844$		0			0
$845$	4043.37	−	7003.32i	0.164611	−	0.285114i
$846$		0			0
$847$	22613.2	+	58718.5i	0.917355	+	2.38205i
$848$		0			0
$849$	3604.20	+	10351.9i	0.145696	+	0.418465i
$850$		0			0
$851$	19971.9	+	11530.8i	0.804498	+	0.464477i
$852$		0			0
$853$	−19445.5	−	11226.8i	−0.780540	−	0.450645i	0.0560819	−	0.998426i	$-0.482139\pi$
$853$	−19445.5	−	11226.8i	−0.780540	−	0.450645i	−0.836622	+	0.547781i	$0.815473\pi$
$854$		0			0
$855$	−10013.1	+	25281.2i	−0.400517	+	1.01123i
$856$		0			0
$857$	41605.8			1.65837			0.829187	−	0.558972i	$-0.188804\pi$
$857$	41605.8			1.65837			0.829187	+	0.558972i	$0.188804\pi$
$858$		0			0
$859$		−	11758.5i		−	0.467050i	−0.972351	−	0.233525i	$-0.924974\pi$
$859$		−	11758.5i		−	0.467050i	0.972351	−	0.233525i	$-0.0750260\pi$
$860$		0			0
$861$	5292.24	−	957.828i	0.209476	−	0.0379125i
$862$		0			0
$863$	40160.8	+	23186.8i	1.58411	+	0.914587i	0.994250	+	0.107083i	$0.0341509\pi$
$863$	40160.8	+	23186.8i	1.58411	+	0.914587i	0.589861	+	0.807505i	$0.299182\pi$
$864$		0			0
$865$	−10968.2	−	18997.4i	−0.431132	−	0.746743i
$866$		0			0
$867$	4811.88	−	1675.34i	0.188489	−	0.0656257i
$868$		0			0
$869$	−48760.8	+	28152.0i	−1.90345	+	1.09896i
$870$		0			0
$871$			25776.9i			1.00278i
$872$		0			0
$873$	−1851.77	+	4675.35i	−0.0717904	+	0.181256i
$874$		0			0
$875$	−7677.19	−	19934.9i	−0.296613	−	0.770199i
$876$		0			0
$877$	34916.5			1.34441			0.672204	−	0.740366i	$-0.265348\pi$
$877$	34916.5			1.34441			0.672204	+	0.740366i	$0.265348\pi$
$878$		0			0
$879$	−2806.91	+	14709.4i	−0.107707	+	0.564432i
$880$		0			0
$881$	−7604.81			−0.290820			−0.145410	−	0.989371i	$-0.546450\pi$
$881$	−7604.81			−0.290820			−0.145410	+	0.989371i	$0.546450\pi$
$882$		0			0
$883$	−218.735			−0.00833636			−0.00416818	−	0.999991i	$-0.501327\pi$
$883$	−218.735			−0.00833636			−0.00416818	+	0.999991i	$0.501327\pi$
$884$		0			0
$885$	−11059.4	+	3850.53i	−0.420066	+	0.146253i
$886$		0			0
$887$	33294.4			1.26033			0.630167	−	0.776459i	$-0.282986\pi$
$887$	33294.4			1.26033			0.630167	+	0.776459i	$0.282986\pi$
$888$		0			0
$889$	−7264.56	−	18863.5i	−0.274067	−	0.711655i
$890$		0			0
$891$	14477.0	+	47993.0i	0.544329	+	1.80452i
$892$		0			0
$893$		−	8800.30i		−	0.329777i
$894$		0			0
$895$	12869.0	−	7429.94i	0.480630	−	0.277492i
$896$		0			0
$897$	−5967.99	+	31274.8i	−0.222147	+	1.16414i
$898$		0			0
$899$	16620.5	+	28787.6i	0.616603	+	1.06799i
$900$		0			0
$901$	19767.3	+	11412.6i	0.730903	+	0.421987i
$902$		0			0
$903$	−13564.5	−	16018.1i	−0.499888	−	0.590308i
$904$		0			0
$905$			35642.0i			1.30915i
$906$		0			0
$907$	−44538.9			−1.63053			−0.815265	−	0.579088i	$-0.803409\pi$
$907$	−44538.9			−1.63053			−0.815265	+	0.579088i	$0.803409\pi$
$908$		0			0
$909$	−3457.01	−	23430.9i	−0.126141	−	0.854955i
$910$		0			0
$911$	−31804.3	−	18362.2i	−1.15667	−	0.667802i	−0.206165	−	0.978517i	$-0.566098\pi$
$911$	−31804.3	−	18362.2i	−1.15667	−	0.667802i	−0.950503	+	0.310715i	$0.899432\pi$
$912$		0			0
$913$	48172.3	+	27812.3i	1.74619	+	1.00816i
$914$		0			0
$915$	−20464.5	−	3905.12i	−0.739382	−	0.141092i
$916$		0			0
$917$	5984.39	+	15539.3i	0.215509	+	0.559601i
$918$		0			0
$919$	2484.42	−	4303.15i	0.0891769	−	0.154459i	−0.817987	−	0.575237i	$-0.804910\pi$
$919$	2484.42	−	4303.15i	0.0891769	−	0.154459i	0.907163	+	0.420778i	$0.138243\pi$
$920$		0			0
$921$	−27286.0	+	31607.2i	−0.976226	+	1.13083i
$922$		0			0
$923$	−3107.37	−	5382.12i	−0.110813	−	0.191933i
$924$		0			0
$925$	2473.03	−	4283.42i	0.0879058	−	0.152257i
$926$		0			0
$927$	40285.3	−	5943.72i	1.42734	−	0.210590i
$928$		0			0
$929$	3304.22	+	5723.08i	0.116693	+	0.202118i	0.918455	−	0.395525i	$-0.129437\pi$
$929$	3304.22	+	5723.08i	0.116693	+	0.202118i	−0.801762	+	0.597643i	$0.796104\pi$
$930$		0			0
$931$	26840.2	−	5766.11i	0.944848	−	0.202983i
$932$		0			0
$933$	−46986.4	+	16359.1i	−1.64873	+	0.574034i
$934$		0			0
$935$	−57526.4	+	33212.9i	−2.01210	+	1.16169i
$936$		0			0
$937$		−	3091.16i		−	0.107773i	−0.998547	−	0.0538867i	$-0.982839\pi$
$937$		−	3091.16i		−	0.107773i	0.998547	−	0.0538867i	$-0.0171610\pi$
$938$		0			0
$939$	26524.5	+	5061.52i	0.921826	+	0.175907i
$940$		0			0
$941$	−3476.72	+	6021.86i	−0.120444	+	0.208615i	−0.919943	−	0.392052i	$-0.871765\pi$
$941$	−3476.72	+	6021.86i	−0.120444	+	0.208615i	0.799499	+	0.600668i	$0.205099\pi$
$942$		0			0
$943$	7522.24	−	4342.97i	0.259764	−	0.149975i
$944$		0			0
$945$	32055.6	+	6433.47i	1.10346	+	0.221461i
$946$		0			0
$947$	−21308.2	+	12302.3i	−0.731175	+	0.422144i	−0.818852	−	0.574005i	$-0.805389\pi$
$947$	−21308.2	+	12302.3i	−0.731175	+	0.422144i	0.0876766	+	0.996149i	$0.472056\pi$
$948$		0			0
$949$	24029.3	−	41620.0i	0.821944	−	1.42365i
$950$		0			0
$951$	42193.5	+	8051.54i	1.43871	+	0.274542i
$952$		0			0
$953$		−	31429.2i		−	1.06830i	−0.845389	−	0.534151i	$-0.820631\pi$
$953$		−	31429.2i		−	1.06830i	0.845389	−	0.534151i	$-0.179369\pi$
$954$		0			0
$955$	18080.5	−	10438.8i	0.612639	−	0.353707i
$956$		0			0
$957$	−77095.6	+	26842.2i	−2.60412	+	0.906671i
$958$		0			0
$959$	7884.82	−	3036.54i	0.265499	−	0.102247i
$960$		0			0
$961$	−4311.34	−	7467.46i	−0.144720	−	0.250662i
$962$		0			0
$963$	−16094.7	+	40635.8i	−0.538571	+	1.35978i
$964$		0			0
$965$	5541.70	−	9598.50i	0.184864	−	0.320194i
$966$		0			0
$967$	−1990.71	−	3448.01i	−0.0662016	−	0.114664i	0.831025	−	0.556235i	$-0.187755\pi$
$967$	−1990.71	−	3448.01i	−0.0662016	−	0.114664i	−0.897226	+	0.441571i	$0.854421\pi$
$968$		0			0
$969$	−20863.4	+	24167.4i	−0.691671	+	0.801208i
$970$		0			0
$971$	3738.21	−	6474.76i	0.123548	−	0.213991i	−0.797617	−	0.603165i	$-0.793906\pi$
$971$	3738.21	−	6474.76i	0.123548	−	0.213991i	0.921164	+	0.389174i	$0.127239\pi$
$972$		0			0
$973$	38956.3	+	31476.1i	1.28354	+	1.03708i
$974$		0			0
$975$	6707.58	+	1279.97i	0.220323	+	0.0420429i
$976$		0			0
$977$	17993.6	+	10388.6i	0.589219	+	0.340186i	0.764789	−	0.644281i	$-0.222843\pi$
$977$	17993.6	+	10388.6i	0.589219	+	0.340186i	−0.175570	+	0.984467i	$0.556177\pi$
$978$		0			0
$979$	2498.74	+	1442.65i	0.0815732	+	0.0470963i
$980$		0			0
$981$	−9827.75	+	7787.39i	−0.319853	+	0.253448i
$982$		0			0
$983$	3094.31			0.100400			0.0502000	−	0.998739i	$-0.484014\pi$
$983$	3094.31			0.100400			0.0502000	+	0.998739i	$0.484014\pi$
$984$		0			0
$985$		−	62182.7i		−	2.01148i
$986$		0			0
$987$	−10412.1	+	1884.45i	−0.335785	+	0.0607729i
$988$		0			0
$989$	−29357.5	−	16949.6i	−0.943897	−	0.544959i
$990$		0			0
$991$	−7775.65	−	13467.8i	−0.249245	−	0.431705i	0.714072	−	0.700073i	$-0.246849\pi$
$991$	−7775.65	−	13467.8i	−0.249245	−	0.431705i	−0.963317	+	0.268368i	$0.913516\pi$
$992$		0			0
$993$	−4656.33	+	24401.1i	−0.148806	+	0.779804i
$994$		0			0
$995$	54516.6	−	31475.2i	1.73698	−	1.00284i
$996$		0			0
$997$		−	5169.83i		−	0.164223i	−0.996623	−	0.0821114i	$-0.973834\pi$
$997$		−	5169.83i		−	0.164223i	0.996623	−	0.0821114i	$-0.0261663\pi$
$998$		0			0
$999$	−9641.20	−	18450.3i	−0.305339	−	0.584325i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.bm.a.173.6	yes	48
3.2	odd	2		756.4.bm.a.89.20		48
7.3	odd	6		252.4.w.a.101.14	yes	48
9.4	even	3		756.4.w.a.341.20		48
9.5	odd	6		252.4.w.a.5.14	✓	48
21.17	even	6		756.4.w.a.521.20		48
63.31	odd	6		756.4.bm.a.17.20		48
63.59	even	6	inner	252.4.bm.a.185.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.w.a.5.14	✓	48	9.5	odd	6
252.4.w.a.101.14	yes	48	7.3	odd	6
252.4.bm.a.173.6	yes	48	1.1	even	1	trivial
252.4.bm.a.185.6	yes	48	63.59	even	6	inner
756.4.w.a.341.20		48	9.4	even	3
756.4.w.a.521.20		48	21.17	even	6
756.4.bm.a.17.20		48	63.31	odd	6
756.4.bm.a.89.20		48	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.93325 - 3.39552i) q^{3} -12.5831 q^{5} +(-6.65587 - 17.2829i) q^{7} +(3.94093 + 26.7108i) q^{9} +O(q^{10})\)	\(q+(-3.93325 - 3.39552i) q^{3} -12.5831 q^{5} +(-6.65587 - 17.2829i) q^{7} +(3.94093 + 26.7108i) q^{9} -68.7640i q^{11} +(-34.1431 + 19.7125i) q^{13} +(49.4923 + 42.7260i) q^{15} +(38.3848 + 66.4844i) q^{17} +(-69.3139 - 40.0184i) q^{19} +(-32.5053 + 90.5782i) q^{21} +155.420i q^{23} +33.3333 q^{25} +(75.1964 - 118.442i) q^{27} +(197.862 + 114.236i) q^{29} +(126.001 + 72.7467i) q^{31} +(-233.489 + 270.466i) q^{33} +(83.7511 + 217.472i) q^{35} +(74.1910 - 128.503i) q^{37} +(201.227 + 38.3991i) q^{39} +(-27.9434 - 48.3994i) q^{41} +(-109.056 + 188.891i) q^{43} +(-49.5890 - 336.104i) q^{45} +(54.9765 + 95.2222i) q^{47} +(-254.399 + 230.066i) q^{49} +(74.7719 - 391.836i) q^{51} +(257.488 - 148.661i) q^{53} +865.262i q^{55} +(136.746 + 392.759i) q^{57} +(-89.5529 + 155.110i) q^{59} +(-275.950 + 159.320i) q^{61} +(435.411 - 245.895i) q^{63} +(429.624 - 248.044i) q^{65} +(326.911 - 566.226i) q^{67} +(527.732 - 611.307i) q^{69} +157.634i q^{71} +(-1055.68 + 609.495i) q^{73} +(-131.108 - 113.184i) q^{75} +(-1188.44 + 457.684i) q^{77} +(-409.401 - 709.103i) q^{79} +(-697.938 + 210.531i) q^{81} +(-404.460 + 700.546i) q^{83} +(-482.998 - 836.577i) q^{85} +(-390.352 - 1121.16i) q^{87} +(-20.9797 + 36.3379i) q^{89} +(567.941 + 458.888i) q^{91} +(-248.581 - 713.969i) q^{93} +(872.181 + 503.554i) q^{95} +(161.296 + 93.1244i) q^{97} +(1836.74 - 270.994i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{7} - 30 q^{9}+O(q^{10}) \) 48 * q + 6 * q^7 - 30 * q^9	\( 48 q + 6 q^{7} - 30 q^{9} + 36 q^{13} + 66 q^{15} + 72 q^{17} + 126 q^{21} + 1200 q^{25} + 396 q^{27} + 42 q^{29} - 90 q^{31} + 108 q^{33} - 390 q^{35} + 84 q^{37} + 1014 q^{39} + 618 q^{41} - 42 q^{43} - 1014 q^{45} + 198 q^{47} - 276 q^{49} + 408 q^{51} + 1620 q^{53} + 492 q^{57} + 750 q^{59} - 1314 q^{61} + 1542 q^{63} + 564 q^{65} + 294 q^{67} + 924 q^{69} - 1410 q^{75} - 2448 q^{77} - 804 q^{79} - 666 q^{81} - 360 q^{85} + 1788 q^{87} - 1722 q^{89} + 540 q^{91} + 1128 q^{93} - 2946 q^{95} + 792 q^{97} - 54 q^{99}+O(q^{100}) \) 48 * q + 6 * q^7 - 30 * q^9 + 36 * q^13 + 66 * q^15 + 72 * q^17 + 126 * q^21 + 1200 * q^25 + 396 * q^27 + 42 * q^29 - 90 * q^31 + 108 * q^33 - 390 * q^35 + 84 * q^37 + 1014 * q^39 + 618 * q^41 - 42 * q^43 - 1014 * q^45 + 198 * q^47 - 276 * q^49 + 408 * q^51 + 1620 * q^53 + 492 * q^57 + 750 * q^59 - 1314 * q^61 + 1542 * q^63 + 564 * q^65 + 294 * q^67 + 924 * q^69 - 1410 * q^75 - 2448 * q^77 - 804 * q^79 - 666 * q^81 - 360 * q^85 + 1788 * q^87 - 1722 * q^89 + 540 * q^91 + 1128 * q^93 - 2946 * q^95 + 792 * q^97 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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