LMFDB - Embedded newform 882.4.k.c.521.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,4,Mod(215,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("882.215");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	882.k (of order $6$, degree $2$, not 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:	$52.0396846251$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.721389578983833600000000.8
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 625x^{8} + 390625 $ x^16 - 625*x^8 + 390625
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2^{22}\cdot 3^{12} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.5
Root			$-2.21694 + 0.291865i$ of defining polynomial
Character	$\chi$	$=$	882.521
Dual form			882.4.k.c.215.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73205 - 1.00000i) q^{2} +(2.00000 - 3.46410i) q^{4} +(-7.15634 - 12.3951i) q^{5} -8.00000i q^{8} +O(q^{10})$	\(q+(1.73205 - 1.00000i) q^{2} +(2.00000 - 3.46410i) q^{4} +(-7.15634 - 12.3951i) q^{5} -8.00000i q^{8} +(-24.7903 - 14.3127i) q^{10} +(51.7004 + 29.8492i) q^{11} +53.7779i q^{13} +(-8.00000 - 13.8564i) q^{16} +(-67.8799 + 117.571i) q^{17} +(71.3633 - 41.2016i) q^{19} -57.2507 q^{20} +119.397 q^{22} +(18.0019 - 10.3934i) q^{23} +(-39.9264 + 69.1546i) q^{25} +(53.7779 + 93.1460i) q^{26} +63.0366i q^{29} +(105.176 + 60.7236i) q^{31} +(-27.7128 - 16.0000i) q^{32} +271.520i q^{34} +(162.735 + 281.865i) q^{37} +(82.4032 - 142.727i) q^{38} +(-99.1612 + 57.2507i) q^{40} -206.902 q^{41} +274.250 q^{43} +(206.802 - 119.397i) q^{44} +(20.7868 - 36.0038i) q^{46} +(-147.021 - 254.648i) q^{47} +159.706i q^{50} +(186.292 + 107.556i) q^{52} +(154.948 + 89.4594i) q^{53} -854.445i q^{55} +(63.0366 + 109.183i) q^{58} +(85.0334 - 147.282i) q^{59} +(-63.0704 + 36.4137i) q^{61} +242.894 q^{62} -64.0000 q^{64} +(666.585 - 384.853i) q^{65} +(526.985 - 912.765i) q^{67} +(271.520 + 470.286i) q^{68} +28.8154i q^{71} +(-417.698 - 241.158i) q^{73} +(563.731 + 325.470i) q^{74} -329.613i q^{76} +(353.838 + 612.865i) q^{79} +(-114.501 + 198.322i) q^{80} +(-358.365 + 206.902i) q^{82} +778.145 q^{83} +1943.09 q^{85} +(475.015 - 274.250i) q^{86} +(238.794 - 413.603i) q^{88} +(4.94748 + 8.56929i) q^{89} -83.1472i q^{92} +(-509.296 - 294.042i) q^{94} +(-1021.40 - 589.706i) q^{95} +1561.45i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32 q^{4}+O(q^{10}) $ 16 * q + 32 * q^4	$ 16 q + 32 q^{4} - 128 q^{16} + 960 q^{22} + 40 q^{25} + 160 q^{37} + 2080 q^{43} + 672 q^{46} - 960 q^{58} - 1024 q^{64} + 3680 q^{67} - 448 q^{79} + 13440 q^{85} + 1920 q^{88}+O(q^{100}) $ 16 * q + 32 * q^4 - 128 * q^16 + 960 * q^22 + 40 * q^25 + 160 * q^37 + 2080 * q^43 + 672 * q^46 - 960 * q^58 - 1024 * q^64 + 3680 * q^67 - 448 * q^79 + 13440 * q^85 + 1920 * q^88

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	2.00000	−	3.46410i	0.250000	−	0.433013i
$5$	−7.15634	−	12.3951i	−0.640083	−	1.10866i	−0.985414	−	0.170175i	$-0.945567\pi$
$5$	−7.15634	−	12.3951i	−0.640083	−	1.10866i	0.345331	−	0.938481i	$-0.387767\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	8.00000i		−	0.353553i
$9$		0			0
$10$	−24.7903	−	14.3127i	−0.783938	−	0.452607i
$11$	51.7004	+	29.8492i	1.41711	+	0.818171i	0.996044	−	0.0888568i	$-0.0283213\pi$
$11$	51.7004	+	29.8492i	1.41711	+	0.818171i	0.421070	+	0.907028i	$0.361655\pi$
$12$		0			0
$13$			53.7779i			1.14733i	0.819090	+	0.573665i	$0.194479\pi$
$13$			53.7779i			1.14733i	−0.819090	+	0.573665i	$0.805521\pi$
$14$		0			0
$15$		0			0
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−67.8799	+	117.571i	−0.968429	+	1.67737i	−0.268324	+	0.963329i	$0.586470\pi$
$17$	−67.8799	+	117.571i	−0.968429	+	1.67737i	−0.700105	+	0.714039i	$0.746864\pi$
$18$		0			0
$19$	71.3633	−	41.2016i	0.861677	−	0.497489i	−0.00289647	−	0.999996i	$-0.500922\pi$
$19$	71.3633	−	41.2016i	0.861677	−	0.497489i	0.864574	+	0.502506i	$0.167589\pi$
$20$	−57.2507			−0.640083
$21$		0			0
$22$	119.397			1.15707
$23$	18.0019	−	10.3934i	0.163202	−	0.0942249i	−0.416174	−	0.909285i	$-0.636629\pi$
$23$	18.0019	−	10.3934i	0.163202	−	0.0942249i	0.579377	+	0.815060i	$0.303296\pi$
$24$		0			0
$25$	−39.9264	+	69.1546i	−0.319411	+	0.553237i
$26$	53.7779	+	93.1460i	0.405643	+	0.702594i
$27$		0			0
$28$		0			0
$29$			63.0366i			0.403641i	0.979422	+	0.201821i	$0.0646858\pi$
$29$			63.0366i			0.403641i	−0.979422	+	0.201821i	$0.935314\pi$
$30$		0			0
$31$	105.176	+	60.7236i	0.609362	+	0.351815i	0.772716	−	0.634752i	$-0.218898\pi$
$31$	105.176	+	60.7236i	0.609362	+	0.351815i	−0.163354	+	0.986568i	$0.552231\pi$
$32$	−27.7128	−	16.0000i	−0.153093	−	0.0883883i
$33$		0			0
$34$			271.520i			1.36957i
$35$		0			0
$36$		0			0
$37$	162.735	+	281.865i	0.723067	+	1.25239i	0.959765	+	0.280805i	$0.0906016\pi$
$37$	162.735	+	281.865i	0.723067	+	1.25239i	−0.236698	+	0.971583i	$0.576065\pi$
$38$	82.4032	−	142.727i	0.351778	−	0.609298i
$39$		0			0
$40$	−99.1612	+	57.2507i	−0.391969	+	0.226303i
$41$	−206.902			−0.788113			−0.394057	−	0.919086i	$-0.628929\pi$
$41$	−206.902			−0.788113			−0.394057	+	0.919086i	$0.628929\pi$
$42$		0			0
$43$	274.250			0.972621			0.486310	−	0.873786i	$-0.338342\pi$
$43$	274.250			0.972621			0.486310	+	0.873786i	$0.338342\pi$
$44$	206.802	−	119.397i	0.708557	−	0.409086i
$45$		0			0
$46$	20.7868	−	36.0038i	0.0666271	−	0.115401i
$47$	−147.021	−	254.648i	−0.456281	−	0.790302i	0.542480	−	0.840069i	$-0.317486\pi$
$47$	−147.021	−	254.648i	−0.456281	−	0.790302i	−0.998761	+	0.0497668i	$0.984152\pi$
$48$		0			0
$49$		0			0
$50$			159.706i			0.451716i
$51$		0			0
$52$	186.292	+	107.556i	0.496809	+	0.286833i
$53$	154.948	+	89.4594i	0.401581	+	0.231853i	0.687166	−	0.726501i	$-0.258855\pi$
$53$	154.948	+	89.4594i	0.401581	+	0.231853i	−0.285585	+	0.958353i	$0.592188\pi$
$54$		0			0
$55$		−	854.445i		−	2.09479i
$56$		0			0
$57$		0			0
$58$	63.0366	+	109.183i	0.142709	+	0.247179i
$59$	85.0334	−	147.282i	0.187634	−	0.324992i	−0.756827	−	0.653615i	$-0.773251\pi$
$59$	85.0334	−	147.282i	0.187634	−	0.324992i	0.944461	+	0.328624i	$0.106585\pi$
$60$		0			0
$61$	−63.0704	+	36.4137i	−0.132382	+	0.0764311i	−0.564729	−	0.825277i	$-0.691019\pi$
$61$	−63.0704	+	36.4137i	−0.132382	+	0.0764311i	0.432346	+	0.901708i	$0.357686\pi$
$62$	242.894			0.497542
$63$		0			0
$64$	−64.0000			−0.125000
$65$	666.585	−	384.853i	1.27199	−	0.734386i
$66$		0			0
$67$	526.985	−	912.765i	0.960917	−	1.66436i	0.240711	−	0.970597i	$-0.422619\pi$
$67$	526.985	−	912.765i	0.960917	−	1.66436i	0.720206	−	0.693760i	$-0.244047\pi$
$68$	271.520	+	470.286i	0.484215	+	0.838684i
$69$		0			0
$70$		0			0
$71$			28.8154i			0.0481656i	0.999710	+	0.0240828i	$0.00766653\pi$
$71$			28.8154i			0.0481656i	−0.999710	+	0.0240828i	$0.992333\pi$
$72$		0			0
$73$	−417.698	−	241.158i	−0.669696	−	0.386649i	0.126265	−	0.991996i	$-0.459701\pi$
$73$	−417.698	−	241.158i	−0.669696	−	0.386649i	−0.795961	+	0.605347i	$0.793034\pi$
$74$	563.731	+	325.470i	0.885573	+	0.511286i
$75$		0			0
$76$		−	329.613i		−	0.497489i
$77$		0			0
$78$		0			0
$79$	353.838	+	612.865i	0.503922	+	0.872819i	0.999990	+	0.00453481i	$0.00144348\pi$
$79$	353.838	+	612.865i	0.503922	+	0.872819i	−0.496068	+	0.868284i	$0.665223\pi$
$80$	−114.501	+	198.322i	−0.160021	+	0.277164i
$81$		0			0
$82$	−358.365	+	206.902i	−0.482619	+	0.278640i
$83$	778.145			1.02907			0.514533	−	0.857470i	$-0.327965\pi$
$83$	778.145			1.02907			0.514533	+	0.857470i	$0.327965\pi$
$84$		0			0
$85$	1943.09			2.47950
$86$	475.015	−	274.250i	0.595606	−	0.343873i
$87$		0			0
$88$	238.794	−	413.603i	0.289267	−	0.501026i
$89$	4.94748	+	8.56929i	0.00589249	+	0.0102061i	0.868957	−	0.494888i	$-0.164791\pi$
$89$	4.94748	+	8.56929i	0.00589249	+	0.0102061i	−0.863064	+	0.505094i	$0.831458\pi$
$90$		0			0
$91$		0			0
$92$		−	83.1472i		−	0.0942249i
$93$		0			0
$94$	−509.296	−	294.042i	−0.558828	−	0.322639i
$95$	−1021.40	−	589.706i	−1.10309	−	0.636869i
$96$		0			0
$97$			1561.45i			1.63444i	0.576323	+	0.817222i	$0.304487\pi$
$97$			1561.45i			1.63444i	−0.576323	+	0.817222i	$0.695513\pi$
$98$		0			0
$99$		0			0
$100$	159.706	+	276.618i	0.159706	+	0.276618i
$101$	502.418	−	870.214i	0.494975	−	0.857322i	−0.505008	−	0.863115i	$-0.668510\pi$
$101$	502.418	−	870.214i	0.494975	−	0.857322i	0.999983	+	0.00579235i	$0.00184377\pi$
$102$		0			0
$103$	485.235	−	280.151i	0.464191	−	0.268001i	−0.249614	−	0.968345i	$-0.580304\pi$
$103$	485.235	−	280.151i	0.464191	−	0.268001i	0.713805	+	0.700345i	$0.246970\pi$
$104$	430.223			0.405643
$105$		0			0
$106$	357.838			0.327889
$107$	−286.672	+	165.510i	−0.259006	+	0.149537i	−0.623881	−	0.781519i	$-0.714445\pi$
$107$	−286.672	+	165.510i	−0.259006	+	0.149537i	0.364875	+	0.931057i	$0.381112\pi$
$108$		0			0
$109$	−607.574	+	1052.35i	−0.533899	+	0.924740i	0.465317	+	0.885144i	$0.345940\pi$
$109$	−607.574	+	1052.35i	−0.533899	+	0.924740i	−0.999216	+	0.0395960i	$0.987393\pi$
$110$	−854.445	−	1479.94i	−0.740620	−	1.28279i
$111$		0			0
$112$		0			0
$113$		−	99.2435i		−	0.0826199i	−0.999146	−	0.0413099i	$-0.986847\pi$
$113$		−	99.2435i		−	0.0826199i	0.999146	−	0.0413099i	$-0.0131531\pi$
$114$		0			0
$115$	−257.655	−	148.757i	−0.208926	−	0.120623i
$116$	218.365	+	126.073i	0.174782	+	0.100910i
$117$		0			0
$118$		−	340.134i		−	0.265355i
$119$		0			0
$120$		0			0
$121$	1116.45	+	1933.76i	0.838809	+	1.45286i
$122$	−72.8274	+	126.141i	−0.0540449	+	0.0936086i
$123$		0			0
$124$	420.705	−	242.894i	0.304681	−	0.175908i
$125$	−646.177			−0.462367
$126$		0			0
$127$	703.087			0.491251			0.245625	−	0.969365i	$-0.421007\pi$
$127$	703.087			0.491251			0.245625	+	0.969365i	$0.421007\pi$
$128$	−110.851	+	64.0000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	769.706	−	1333.17i	0.519290	−	0.899436i
$131$	559.982	+	969.917i	0.373480	+	0.646886i	0.990098	−	0.140376i	$-0.0448312\pi$
$131$	559.982	+	969.917i	0.373480	+	0.646886i	−0.616618	+	0.787262i	$0.711498\pi$
$132$		0			0
$133$		0			0
$134$		−	2107.94i		−	1.35894i
$135$		0			0
$136$	940.571	+	543.039i	0.593039	+	0.342391i
$137$	−1465.80	−	846.282i	−0.914102	−	0.527757i	−0.0323536	−	0.999476i	$-0.510300\pi$
$137$	−1465.80	−	846.282i	−0.914102	−	0.527757i	−0.881749	+	0.471719i	$0.843634\pi$
$138$		0			0
$139$		−	733.943i		−	0.447858i	−0.974605	−	0.223929i	$-0.928112\pi$
$139$		−	733.943i		−	0.447858i	0.974605	−	0.223929i	$-0.0718883\pi$
$140$		0			0
$141$		0			0
$142$	28.8154	+	49.9097i	0.0170291	+	0.0294953i
$143$	−1605.23	+	2780.34i	−0.938713	+	1.62590i
$144$		0			0
$145$	781.348	−	451.111i	0.447499	−	0.258364i
$146$	−964.631			−0.546804
$147$		0			0
$148$	1301.88			0.723067
$149$	2531.96	−	1461.83i	1.39212	−	0.803742i	0.398572	−	0.917137i	$-0.369506\pi$
$149$	2531.96	−	1461.83i	1.39212	−	0.803742i	0.993550	+	0.113395i	$0.0361727\pi$
$150$		0			0
$151$	−166.802	+	288.909i	−0.0898950	+	0.155703i	−0.907467	−	0.420124i	$-0.861986\pi$
$151$	−166.802	+	288.909i	−0.0898950	+	0.155703i	0.817572	+	0.575827i	$0.195320\pi$
$152$	−329.613	−	570.906i	−0.175889	−	0.304649i
$153$		0			0
$154$		0			0
$155$		−	1738.23i		−	0.900763i
$156$		0			0
$157$	1853.99	+	1070.40i	0.942447	+	0.544122i	0.890727	−	0.454539i	$-0.150196\pi$
$157$	1853.99	+	1070.40i	0.942447	+	0.544122i	0.0517206	+	0.998662i	$0.483529\pi$
$158$	1225.73	+	707.675i	0.617176	+	0.356327i
$159$		0			0
$160$			458.006i			0.226303i
$161$		0			0
$162$		0			0
$163$	1930.07	+	3342.98i	0.927453	+	1.60640i	0.787568	+	0.616228i	$0.211340\pi$
$163$	1930.07	+	3342.98i	0.927453	+	1.60640i	0.139886	+	0.990168i	$0.455327\pi$
$164$	−413.804	+	716.729i	−0.197028	+	0.341263i
$165$		0			0
$166$	1347.79	−	778.145i	0.630172	−	0.363830i
$167$	−3030.28			−1.40413			−0.702066	−	0.712112i	$-0.747739\pi$
$167$	−3030.28			−1.40413			−0.702066	+	0.712112i	$0.747739\pi$
$168$		0			0
$169$	−695.061			−0.316368
$170$	3365.52	−	1943.09i	1.51838	−	0.876635i
$171$		0			0
$172$	548.500	−	950.029i	0.243155	−	0.421157i
$173$	1145.23	+	1983.59i	0.503294	+	0.871731i	0.999993	+	0.00380769i	$0.00121203\pi$
$173$	1145.23	+	1983.59i	0.503294	+	0.871731i	−0.496699	+	0.867923i	$0.665455\pi$
$174$		0			0
$175$		0			0
$176$		−	955.176i		−	0.409086i
$177$		0			0
$178$	17.1386	+	9.89496i	0.00721680	+	0.00416662i
$179$	−936.724	−	540.818i	−0.391140	−	0.225825i	0.291514	−	0.956567i	$-0.405841\pi$
$179$	−936.724	−	540.818i	−0.391140	−	0.225825i	−0.682654	+	0.730742i	$0.739174\pi$
$180$		0			0
$181$			3076.27i			1.26330i	0.775254	+	0.631650i	$0.217622\pi$
$181$			3076.27i			1.26330i	−0.775254	+	0.631650i	$0.782378\pi$
$182$		0			0
$183$		0			0
$184$	−83.1472	−	144.015i	−0.0333135	−	0.0577007i
$185$	2329.17	−	4034.25i	0.925645	−	1.60326i
$186$		0			0
$187$	−7018.84	+	4052.33i	−2.74475	+	1.58468i
$188$	−1176.17			−0.456281
$189$		0			0
$190$	−2358.82			−0.900668
$191$	−1104.17	+	637.494i	−0.418299	+	0.241505i	−0.694349	−	0.719638i	$-0.744308\pi$
$191$	−1104.17	+	637.494i	−0.418299	+	0.241505i	0.276050	+	0.961143i	$0.410974\pi$
$192$		0			0
$193$	−876.368	+	1517.91i	−0.326851	+	0.566123i	−0.981885	−	0.189476i	$-0.939321\pi$
$193$	−876.368	+	1517.91i	−0.326851	+	0.566123i	0.655034	+	0.755599i	$0.272654\pi$
$194$	1561.45	+	2704.51i	0.577863	+	1.00089i
$195$		0			0
$196$		0			0
$197$		−	2996.70i		−	1.08379i	−0.840448	−	0.541893i	$-0.817708\pi$
$197$		−	2996.70i		−	1.08379i	0.840448	−	0.541893i	$-0.182292\pi$
$198$		0			0
$199$	−1031.44	−	595.502i	−0.367421	−	0.212131i	0.304910	−	0.952381i	$-0.401374\pi$
$199$	−1031.44	−	595.502i	−0.367421	−	0.212131i	−0.672331	+	0.740250i	$0.734707\pi$
$200$	553.237	+	319.411i	0.195599	+	0.112929i
$201$		0			0
$202$		−	2009.67i		−	0.700001i
$203$		0			0
$204$		0			0
$205$	1480.66	+	2564.58i	0.504458	+	0.873746i
$206$	560.301	−	970.470i	0.189505	−	0.328232i
$207$		0			0
$208$	745.168	−	430.223i	0.248404	−	0.143416i
$209$	4919.35			1.62813
$210$		0			0
$211$	1525.81			0.497824			0.248912	−	0.968526i	$-0.419927\pi$
$211$	1525.81			0.497824			0.248912	+	0.968526i	$0.419927\pi$
$212$	619.793	−	357.838i	0.200790	−	0.115926i
$213$		0			0
$214$	−331.021	+	573.344i	−0.105739	+	0.183145i
$215$	−1962.62	−	3399.37i	−0.622558	−	1.07830i
$216$		0			0
$217$		0			0
$218$			2430.29i			0.755047i
$219$		0			0
$220$	−2959.89	−	1708.89i	−0.907070	−	0.523697i
$221$	−6322.74	−	3650.44i	−1.92450	−	1.11111i
$222$		0			0
$223$		−	3687.92i		−	1.10745i	−0.832699	−	0.553725i	$-0.813206\pi$
$223$		−	3687.92i		−	1.10745i	0.832699	−	0.553725i	$-0.186794\pi$
$224$		0			0
$225$		0			0
$226$	−99.2435	−	171.895i	−0.0292105	−	0.0505941i
$227$	−1720.05	+	2979.21i	−0.502924	+	0.871090i	0.497071	+	0.867710i	$0.334409\pi$
$227$	−1720.05	+	2979.21i	−0.502924	+	0.871090i	−0.999994	+	0.00337940i	$0.998924\pi$
$228$		0			0
$229$	4496.79	−	2596.23i	1.29763	−	0.749185i	0.317633	−	0.948214i	$-0.397112\pi$
$229$	4496.79	−	2596.23i	1.29763	−	0.749185i	0.979994	+	0.199028i	$0.0637786\pi$
$230$	−595.030			−0.170587
$231$		0			0
$232$	504.293			0.142709
$233$	−4915.94	+	2838.22i	−1.38221	+	0.798017i	−0.992421	−	0.122888i	$-0.960784\pi$
$233$	−4915.94	+	2838.22i	−1.38221	+	0.798017i	−0.389786	+	0.920905i	$0.627451\pi$
$234$		0			0
$235$	−2104.26	+	3644.69i	−0.584115	+	1.01172i
$236$	−340.134	−	589.129i	−0.0938170	−	0.162496i
$237$		0			0
$238$		0			0
$239$		−	2649.43i		−	0.717061i	−0.933518	−	0.358530i	$-0.883278\pi$
$239$		−	2649.43i		−	0.717061i	0.933518	−	0.358530i	$-0.116722\pi$
$240$		0			0
$241$	2025.59	+	1169.48i	0.541411	+	0.312584i	0.745651	−	0.666337i	$-0.232139\pi$
$241$	2025.59	+	1169.48i	0.541411	+	0.312584i	−0.204240	+	0.978921i	$0.565472\pi$
$242$	3867.51	+	2232.91i	1.02733	+	0.593127i
$243$		0			0
$244$			291.310i			0.0764311i
$245$		0			0
$246$		0			0
$247$	2215.74	+	3837.77i	0.570785	+	0.988629i
$248$	485.788	−	841.410i	0.124385	−	0.215442i
$249$		0			0
$250$	−1119.21	+	646.177i	−0.283141	+	0.163471i
$251$	4862.30			1.22273			0.611366	−	0.791348i	$-0.290620\pi$
$251$	4862.30			1.22273			0.611366	+	0.791348i	$0.290620\pi$
$252$		0			0
$253$	1240.94			0.308369
$254$	1217.78	−	703.087i	0.300828	−	0.173683i
$255$		0			0
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−1889.38	−	3272.51i	−0.458585	−	0.794293i	0.540301	−	0.841472i	$-0.318310\pi$
$257$	−1889.38	−	3272.51i	−0.458585	−	0.794293i	−0.998886	+	0.0471787i	$0.984977\pi$
$258$		0			0
$259$		0			0
$260$		−	3078.82i		−	0.734386i
$261$		0			0
$262$	1939.83	+	1119.96i	0.457418	+	0.264090i
$263$	22.8813	+	13.2105i	0.00536471	+	0.00309732i	0.502680	−	0.864473i	$-0.332347\pi$
$263$	22.8813	+	13.2105i	0.00536471	+	0.00309732i	−0.497315	+	0.867570i	$0.665681\pi$
$264$		0			0
$265$		−	2560.81i		−	0.593620i
$266$		0			0
$267$		0			0
$268$	−2107.94	−	3651.06i	−0.480459	−	0.832179i
$269$	−174.274	+	301.851i	−0.0395006	+	0.0684171i	−0.885100	−	0.465401i	$-0.845910\pi$
$269$	−174.274	+	301.851i	−0.0395006	+	0.0684171i	0.845599	+	0.533818i	$0.179243\pi$
$270$		0			0
$271$	6580.90	−	3799.49i	1.47513	−	0.851669i	0.475528	−	0.879701i	$-0.342257\pi$
$271$	6580.90	−	3799.49i	1.47513	−	0.851669i	0.999607	+	0.0280315i	$0.00892388\pi$
$272$	2172.16			0.484215
$273$		0			0
$274$	−3385.13			−0.746361
$275$	−4128.42	+	2383.55i	−0.905285	+	0.522666i
$276$		0			0
$277$	500.807	−	867.424i	0.108630	−	0.188153i	−0.806585	−	0.591118i	$-0.798687\pi$
$277$	500.807	−	867.424i	0.108630	−	0.188153i	0.915216	+	0.402964i	$0.132020\pi$
$278$	−733.943	−	1271.23i	−0.158342	−	0.274256i
$279$		0			0
$280$		0			0
$281$			3753.32i			0.796812i	0.917209	+	0.398406i	$0.130436\pi$
$281$			3753.32i			0.796812i	−0.917209	+	0.398406i	$0.869564\pi$
$282$		0			0
$283$	−5074.62	−	2929.84i	−1.06592	−	0.615409i	−0.138855	−	0.990313i	$-0.544342\pi$
$283$	−5074.62	−	2929.84i	−1.06592	−	0.615409i	−0.927064	+	0.374904i	$0.877676\pi$
$284$	99.8194	+	57.6307i	0.0208563	+	0.0120414i
$285$		0			0
$286$			6420.92i			1.32754i
$287$		0			0
$288$		0			0
$289$	−6758.86	−	11706.7i	−1.37571	−	2.38280i
$290$	902.222	−	1562.70i	0.182691	−	0.316430i
$291$		0			0
$292$	−1670.79	+	964.631i	−0.334848	+	0.193325i
$293$	−1165.23			−0.232332			−0.116166	−	0.993230i	$-0.537060\pi$
$293$	−1165.23			−0.232332			−0.116166	+	0.993230i	$0.537060\pi$
$294$		0			0
$295$	−2434.11			−0.480405
$296$	2254.92	−	1301.88i	0.442786	−	0.255643i
$297$		0			0
$298$	2923.65	−	5063.92i	0.568331	−	0.984379i
$299$	558.935	+	968.104i	0.108107	+	0.187247i
$300$		0			0
$301$		0			0
$302$			667.208i			0.127131i
$303$		0			0
$304$	−1141.81	−	659.226i	−0.215419	−	0.124372i
$305$	902.706	+	521.177i	0.169471	+	0.0978444i
$306$		0			0
$307$		−	2460.63i		−	0.457445i	−0.973492	−	0.228723i	$-0.926545\pi$
$307$		−	2460.63i		−	0.457445i	0.973492	−	0.228723i	$-0.0734549\pi$
$308$		0			0
$309$		0			0
$310$	−1738.23	−	3010.71i	−0.318468	−	0.551603i
$311$	1679.22	−	2908.49i	0.306173	−	0.530307i	−0.671349	−	0.741141i	$-0.734285\pi$
$311$	1679.22	−	2908.49i	0.306173	−	0.530307i	0.977522	+	0.210835i	$0.0676181\pi$
$312$		0			0
$313$	−3948.58	+	2279.71i	−0.713057	+	0.411684i	−0.812192	−	0.583390i	$-0.801726\pi$
$313$	−3948.58	+	2279.71i	−0.713057	+	0.411684i	0.0991349	+	0.995074i	$0.468392\pi$
$314$	4281.60			0.769505
$315$		0			0
$316$	2830.70			0.503922
$317$	121.741	−	70.2873i	0.0215699	−	0.0124534i	−0.489176	−	0.872185i	$-0.662703\pi$
$317$	121.741	−	70.2873i	0.0215699	−	0.0124534i	0.510746	+	0.859732i	$0.329369\pi$
$318$		0			0
$319$	−1881.59	+	3259.02i	−0.330248	+	0.572006i
$320$	458.006	+	793.289i	0.0800103	+	0.138582i
$321$		0			0
$322$		0			0
$323$			11187.0i			1.92713i
$324$		0			0
$325$	−3718.99	−	2147.16i	−0.634745	−	0.366470i
$326$	6685.96	+	3860.14i	1.13589	+	0.655808i
$327$		0			0
$328$			1655.21i			0.278640i
$329$		0			0
$330$		0			0
$331$	−1601.50	−	2773.88i	−0.265941	−	0.460624i	0.701868	−	0.712307i	$-0.252349\pi$
$331$	−1601.50	−	2773.88i	−0.265941	−	0.460624i	−0.967810	+	0.251683i	$0.919016\pi$
$332$	1556.29	−	2695.57i	0.257267	−	0.445599i
$333$		0			0
$334$	−5248.60	+	3030.28i	−0.859852	+	0.496436i
$335$	−15085.1			−2.46026
$336$		0			0
$337$	−9458.69			−1.52892			−0.764462	−	0.644668i	$-0.776996\pi$
$337$	−9458.69			−1.52892			−0.764462	+	0.644668i	$0.776996\pi$
$338$	−1203.88	+	695.061i	−0.193735	+	0.111853i
$339$		0			0
$340$	3886.17	−	6731.05i	0.619875	−	1.07365i
$341$	3625.10	+	6278.87i	0.575690	+	0.997125i
$342$		0			0
$343$		0			0
$344$		−	2194.00i		−	0.343873i
$345$		0			0
$346$	3967.18	+	2290.45i	0.616407	+	0.355883i
$347$	−2290.96	−	1322.69i	−0.354425	−	0.204627i	0.312208	−	0.950014i	$-0.398932\pi$
$347$	−2290.96	−	1322.69i	−0.354425	−	0.204627i	−0.666632	+	0.745387i	$0.732265\pi$
$348$		0			0
$349$			6172.76i			0.946763i	0.880857	+	0.473382i	$0.156967\pi$
$349$			6172.76i			0.946763i	−0.880857	+	0.473382i	$0.843033\pi$
$350$		0			0
$351$		0			0
$352$	−955.176	−	1654.41i	−0.144634	−	0.250513i
$353$	−4263.60	+	7384.77i	−0.642857	+	1.11346i	0.341935	+	0.939724i	$0.388918\pi$
$353$	−4263.60	+	7384.77i	−0.642857	+	1.11346i	−0.984792	+	0.173738i	$0.944415\pi$
$354$		0			0
$355$	357.171	−	206.213i	0.0533990	−	0.0308299i
$356$	39.5798			0.00589249
$357$		0			0
$358$	−2163.27			−0.319365
$359$	−2993.66	+	1728.39i	−0.440110	+	0.254098i	−0.703644	−	0.710552i	$-0.748445\pi$
$359$	−2993.66	+	1728.39i	−0.440110	+	0.254098i	0.263534	+	0.964650i	$0.415112\pi$
$360$		0			0
$361$	−34.3528	+	59.5008i	−0.00500843	+	0.00867485i
$362$	3076.27	+	5328.25i	0.446644	+	0.773610i
$363$		0			0
$364$		0			0
$365$			6903.23i			0.989949i
$366$		0			0
$367$	10426.1	+	6019.48i	1.48293	+	0.856170i	0.999812	−	0.0193847i	$-0.00617071\pi$
$367$	10426.1	+	6019.48i	1.48293	+	0.856170i	0.483118	+	0.875555i	$0.339504\pi$
$368$	−288.030	−	166.294i	−0.0408006	−	0.0235562i
$369$		0			0
$370$		−	9316.70i		−	1.30906i
$371$		0			0
$372$		0			0
$373$	1163.97	+	2016.06i	0.161577	+	0.279860i	0.935434	−	0.353500i	$-0.115009\pi$
$373$	1163.97	+	2016.06i	0.161577	+	0.279860i	−0.773857	+	0.633360i	$0.781675\pi$
$374$	−8104.65	+	14037.7i	−1.12054	+	1.94083i
$375$		0			0
$376$	−2037.18	+	1176.17i	−0.279414	+	0.161320i
$377$	−3389.97			−0.463110
$378$		0			0
$379$	1313.46			0.178016			0.0890079	−	0.996031i	$-0.471630\pi$
$379$	1313.46			0.178016			0.0890079	+	0.996031i	$0.471630\pi$
$380$	−4085.60	+	2358.82i	−0.551544	+	0.318434i
$381$		0			0
$382$	−1274.99	+	2208.34i	−0.170770	+	0.295782i
$383$	−294.565	−	510.202i	−0.0392992	−	0.0680682i	0.845707	−	0.533648i	$-0.179179\pi$
$383$	−294.565	−	510.202i	−0.0392992	−	0.0680682i	−0.885006	+	0.465580i	$0.845846\pi$
$384$		0			0
$385$		0			0
$386$			3505.47i			0.462238i
$387$		0			0
$388$	5409.02	+	3122.90i	0.707735	+	0.408611i
$389$	−4816.29	−	2780.69i	−0.627752	−	0.362433i	0.152129	−	0.988361i	$-0.451387\pi$
$389$	−4816.29	−	2780.69i	−0.627752	−	0.362433i	−0.779881	+	0.625928i	$0.784720\pi$
$390$		0			0
$391$			2822.01i			0.365001i
$392$		0			0
$393$		0			0
$394$	−2996.70	−	5190.43i	−0.383176	−	0.663680i
$395$	5064.37	−	8771.74i	0.645103	−	1.11735i
$396$		0			0
$397$	−68.5543	+	39.5798i	−0.00866660	+	0.00500366i	−0.504327	−	0.863513i	$-0.668259\pi$
$397$	−68.5543	+	39.5798i	−0.00866660	+	0.00500366i	0.495660	+	0.868516i	$0.334926\pi$
$398$	−2382.01			−0.299998
$399$		0			0
$400$	1277.65			0.159706
$401$	−9784.04	+	5648.82i	−1.21843	+	0.703463i	−0.964583	−	0.263781i	$-0.915030\pi$
$401$	−9784.04	+	5648.82i	−1.21843	+	0.703463i	−0.253851	+	0.967243i	$0.581697\pi$
$402$		0			0
$403$	−3265.58	+	5656.16i	−0.403649	+	0.699140i
$404$	−2009.67	−	3480.86i	−0.247488	−	0.428661i
$405$		0			0
$406$		0			0
$407$			19430.1i			2.36637i
$408$		0			0
$409$	4222.44	+	2437.83i	0.510480	+	0.294726i	0.733031	−	0.680195i	$-0.238105\pi$
$409$	4222.44	+	2437.83i	0.510480	+	0.294726i	−0.222551	+	0.974921i	$0.571438\pi$
$410$	5129.16	+	2961.32i	0.617832	+	0.356705i
$411$		0			0
$412$		−	2241.20i		−	0.268001i
$413$		0			0
$414$		0			0
$415$	−5568.67	−	9645.22i	−0.658687	−	1.14088i
$416$	860.446	−	1490.34i	0.101411	−	0.175648i
$417$		0			0
$418$	8520.56	−	4919.35i	0.997020	−	0.575630i
$419$	3758.73			0.438248			0.219124	−	0.975697i	$-0.429680\pi$
$419$	3758.73			0.438248			0.219124	+	0.975697i	$0.429680\pi$
$420$		0			0
$421$	−1365.09			−0.158029			−0.0790145	−	0.996873i	$-0.525177\pi$
$421$	−1365.09			−0.158029			−0.0790145	+	0.996873i	$0.525177\pi$
$422$	2642.78	−	1525.81i	0.304854	−	0.176007i
$423$		0			0
$424$	715.675	−	1239.59i	0.0819723	−	0.141980i
$425$	−5420.40	−	9388.41i	−0.618654	−	1.07154i
$426$		0			0
$427$		0			0
$428$			1324.08i			0.149537i
$429$		0			0
$430$	−6798.73	−	3925.25i	−0.762474	−	0.440215i
$431$	6990.93	+	4036.22i	0.781302	+	0.451085i	0.836892	−	0.547369i	$-0.184370\pi$
$431$	6990.93	+	4036.22i	0.781302	+	0.451085i	−0.0555892	+	0.998454i	$0.517704\pi$
$432$		0			0
$433$		−	687.622i		−	0.0763164i	−0.999272	−	0.0381582i	$-0.987851\pi$
$433$		−	687.622i		−	0.0763164i	0.999272	−	0.0381582i	$-0.0121491\pi$
$434$		0			0
$435$		0			0
$436$	2430.29	+	4209.39i	0.266950	+	0.462370i
$437$	856.450	−	1483.41i	0.0937518	−	0.162383i
$438$		0			0
$439$	9581.72	−	5532.01i	1.04171	−	0.601432i	0.121393	−	0.992605i	$-0.461264\pi$
$439$	9581.72	−	5532.01i	1.04171	−	0.601432i	0.920317	+	0.391173i	$0.127931\pi$
$440$	−6835.56			−0.740620
$441$		0			0
$442$	−14601.7			−1.57134
$443$	−11117.1	+	6418.44i	−1.19230	+	0.688373i	−0.958827	−	0.283991i	$-0.908341\pi$
$443$	−11117.1	+	6418.44i	−1.19230	+	0.688373i	−0.233470	+	0.972364i	$0.575008\pi$
$444$		0			0
$445$	70.8117	−	122.649i	0.00754336	−	0.0130655i
$446$	−3687.92	−	6387.67i	−0.391543	−	0.678172i
$447$		0			0
$448$		0			0
$449$		−	10439.7i		−	1.09728i	−0.836059	−	0.548640i	$-0.815146\pi$
$449$		−	10439.7i		−	1.09728i	0.836059	−	0.548640i	$-0.184854\pi$
$450$		0			0
$451$	−10696.9	−	6175.86i	−1.11685	−	0.644812i
$452$	−343.790	−	198.487i	−0.0357754	−	0.0206550i
$453$		0			0
$454$			6880.20i			0.711242i
$455$		0			0
$456$		0			0
$457$	−6887.44	−	11929.4i	−0.704991	−	1.22108i	−0.966695	−	0.255931i	$-0.917618\pi$
$457$	−6887.44	−	11929.4i	−0.704991	−	1.22108i	0.261704	−	0.965148i	$-0.415715\pi$
$458$	5192.45	−	8993.59i	0.529754	−	0.917561i
$459$		0			0
$460$	−1030.62	+	595.030i	−0.104463	+	0.0603117i
$461$	6904.60			0.697569			0.348784	−	0.937203i	$-0.386595\pi$
$461$	6904.60			0.697569			0.348784	+	0.937203i	$0.386595\pi$
$462$		0			0
$463$	14767.2			1.48227			0.741134	−	0.671357i	$-0.234288\pi$
$463$	14767.2			1.48227			0.741134	+	0.671357i	$0.234288\pi$
$464$	873.460	−	504.293i	0.0873909	−	0.0504552i
$465$		0			0
$466$	−5676.44	+	9831.89i	−0.564284	+	0.977368i
$467$	8606.44	+	14906.8i	0.852802	+	1.47710i	0.878669	+	0.477431i	$0.158432\pi$
$467$	8606.44	+	14906.8i	0.852802	+	1.47710i	−0.0258670	+	0.999665i	$0.508235\pi$
$468$		0			0
$469$		0			0
$470$			8417.06i			0.826064i
$471$		0			0
$472$	−1178.26	−	680.267i	−0.114902	−	0.0663387i
$473$	14178.8	+	8186.15i	1.37832	+	0.795771i
$474$		0			0
$475$			6580.13i			0.635615i
$476$		0			0
$477$		0			0
$478$	−2649.43	−	4588.95i	−0.253519	−	0.439108i
$479$	2431.06	−	4210.72i	0.231896	−	0.401655i	−0.726470	−	0.687198i	$-0.758841\pi$
$479$	2431.06	−	4210.72i	0.231896	−	0.401655i	0.958366	+	0.285543i	$0.0921739\pi$
$480$		0			0
$481$	−15158.1	+	8751.55i	−1.43690	+	0.829597i
$482$	4677.91			0.442060
$483$		0			0
$484$	8931.64			0.838809
$485$	19354.4	−	11174.3i	1.81204	−	1.04618i
$486$		0			0
$487$	2684.36	−	4649.45i	0.249774	−	0.432622i	−0.713689	−	0.700463i	$-0.752977\pi$
$487$	2684.36	−	4649.45i	0.249774	−	0.432622i	0.963463	+	0.267841i	$0.0863103\pi$
$488$	291.310	+	504.563i	0.0270225	+	0.0468043i
$489$		0			0
$490$		0			0
$491$		−	5093.75i		−	0.468183i	−0.972215	−	0.234092i	$-0.924788\pi$
$491$		−	5093.75i		−	0.468183i	0.972215	−	0.234092i	$-0.0752115\pi$
$492$		0			0
$493$	−7411.30	−	4278.92i	−0.677055	−	0.390898i
$494$	7675.53	+	4431.47i	0.699066	+	0.403606i
$495$		0			0
$496$		−	1943.15i		−	0.175908i
$497$		0			0
$498$		0			0
$499$	1023.57	+	1772.88i	0.0918265	+	0.159048i	0.908280	−	0.418363i	$-0.137396\pi$
$499$	1023.57	+	1772.88i	0.0918265	+	0.159048i	−0.816453	+	0.577412i	$0.804063\pi$
$500$	−1292.35	+	2238.42i	−0.115592	+	0.200211i
$501$		0			0
$502$	8421.75	−	4862.30i	0.748768	−	0.432301i
$503$	16598.7			1.47137			0.735685	−	0.677323i	$-0.236860\pi$
$503$	16598.7			1.47137			0.735685	+	0.677323i	$0.236860\pi$
$504$		0			0
$505$	−14381.9			−1.26730
$506$	2149.37	−	1240.94i	0.188836	−	0.109025i
$507$		0			0
$508$	1406.17	−	2435.56i	0.122813	−	0.212718i
$509$	−5718.95	−	9905.51i	−0.498012	−	0.862582i	0.501986	−	0.864876i	$-0.332603\pi$
$509$	−5718.95	−	9905.51i	−0.498012	−	0.862582i	−0.999997	+	0.00229422i	$0.999270\pi$
$510$		0			0
$511$		0			0
$512$			512.000i			0.0441942i
$513$		0			0
$514$	−6545.01	−	3778.76i	−0.561650	−	0.324269i
$515$	−6945.01	−	4009.71i	−0.594241	−	0.343085i
$516$		0			0
$517$		−	17553.9i		−	1.49326i
$518$		0			0
$519$		0			0
$520$	−3078.82	−	5332.68i	−0.259645	−	0.449718i
$521$	−11709.8	+	20281.9i	−0.984674	+	1.70550i	−0.341295	+	0.939956i	$0.610866\pi$
$521$	−11709.8	+	20281.9i	−0.984674	+	1.70550i	−0.643378	+	0.765548i	$0.722468\pi$
$522$		0			0
$523$	−7747.31	+	4472.91i	−0.647736	+	0.373971i	−0.787588	−	0.616202i	$-0.788671\pi$
$523$	−7747.31	+	4472.91i	−0.647736	+	0.373971i	0.139852	+	0.990172i	$0.455337\pi$
$524$	4479.86			0.373480
$525$		0			0
$526$	52.8420			0.00438027
$527$	−14278.7	+	8243.82i	−1.18025	+	0.681416i
$528$		0			0
$529$	−5867.45	+	10162.7i	−0.482243	+	0.835270i
$530$	−2560.81	−	4435.45i	−0.209876	−	0.363516i
$531$		0			0
$532$		0			0
$533$		−	11126.7i		−	0.904227i
$534$		0			0
$535$	4103.05	+	2368.90i	0.331571	+	0.191432i
$536$	−7302.12	−	4215.88i	−0.588439	−	0.339736i
$537$		0			0
$538$			697.096i			0.0558623i
$539$		0			0
$540$		0			0
$541$	−1249.67	−	2164.49i	−0.0993114	−	0.172012i	0.812088	−	0.583534i	$-0.198331\pi$
$541$	−1249.67	−	2164.49i	−0.0993114	−	0.172012i	−0.911400	+	0.411522i	$0.864997\pi$
$542$	7598.97	−	13161.8i	0.602221	−	1.04308i
$543$		0			0
$544$	3762.29	−	2172.16i	0.296520	−	0.171196i
$545$	17392.0			1.36696
$546$		0			0
$547$	−19005.7			−1.48561			−0.742803	−	0.669510i	$-0.766504\pi$
$547$	−19005.7			−1.48561			−0.742803	+	0.669510i	$0.766504\pi$
$548$	−5863.21	+	3385.13i	−0.457051	+	0.263879i
$549$		0			0
$550$	−4767.09	+	8256.85i	−0.369581	+	0.640133i
$551$	2597.21	+	4498.50i	0.200807	+	0.347808i
$552$		0			0
$553$		0			0
$554$		−	2003.23i		−	0.153626i
$555$		0			0
$556$	−2542.45	−	1467.89i	−0.193928	−	0.111964i
$557$	7082.63	+	4089.16i	0.538781	+	0.311065i	0.744585	−	0.667528i	$-0.232648\pi$
$557$	7082.63	+	4089.16i	0.538781	+	0.311065i	−0.205804	+	0.978593i	$0.565981\pi$
$558$		0			0
$559$			14748.6i			1.11592i
$560$		0			0
$561$		0			0
$562$	3753.32	+	6500.94i	0.281715	+	0.487946i
$563$	−3809.59	+	6598.40i	−0.285177	+	0.493942i	−0.972652	−	0.232266i	$-0.925386\pi$
$563$	−3809.59	+	6598.40i	−0.285177	+	0.493942i	0.687475	+	0.726208i	$0.258719\pi$
$564$		0			0
$565$	−1230.14	+	710.220i	−0.0915970	+	0.0528835i
$566$	−11719.3			−0.870319
$567$		0			0
$568$	230.523			0.0170291
$569$	−5894.54	+	3403.21i	−0.434292	+	0.250738i	−0.701173	−	0.712991i	$-0.747340\pi$
$569$	−5894.54	+	3403.21i	−0.434292	+	0.250738i	0.266882	+	0.963729i	$0.414007\pi$
$570$		0			0
$571$	9129.89	−	15813.4i	0.669131	−	1.15897i	−0.309016	−	0.951057i	$-0.600000\pi$
$571$	9129.89	−	15813.4i	0.669131	−	1.15897i	0.978147	−	0.207913i	$-0.0666670\pi$
$572$	6420.92	+	11121.4i	0.469357	+	0.812950i
$573$		0			0
$574$		0			0
$575$			1659.88i			0.120386i
$576$		0			0
$577$	16661.8	+	9619.70i	1.20215	+	0.694062i	0.961033	−	0.276434i	$-0.0891529\pi$
$577$	16661.8	+	9619.70i	1.20215	+	0.694062i	0.241117	+	0.970496i	$0.422486\pi$
$578$	−23413.4	−	13517.7i	−1.68489	−	0.972774i
$579$		0			0
$580$		−	3608.89i		−	0.258364i
$581$		0			0
$582$		0			0
$583$	5340.59	+	9250.18i	0.379391	+	0.657124i
$584$	−1929.26	+	3341.58i	−0.136701	+	0.236773i
$585$		0			0
$586$	−2018.23	+	1165.23i	−0.142274	+	0.0821417i
$587$	−3612.03			−0.253977			−0.126988	−	0.991904i	$-0.540531\pi$
$587$	−3612.03			−0.253977			−0.126988	+	0.991904i	$0.540531\pi$
$588$		0			0
$589$	10007.6			0.700098
$590$	−4216.01	+	2434.11i	−0.294187	+	0.169849i
$591$		0			0
$592$	2603.76	−	4509.85i	0.180767	−	0.313097i
$593$	−2169.12	−	3757.03i	−0.150211	−	0.260173i	0.781094	−	0.624414i	$-0.214662\pi$
$593$	−2169.12	−	3757.03i	−0.150211	−	0.260173i	−0.931305	+	0.364240i	$0.881329\pi$
$594$		0			0
$595$		0			0
$596$		−	11694.6i		−	0.803742i
$597$		0			0
$598$	1936.21	+	1117.87i	0.132404	+	0.0764433i
$599$	−15236.1	−	8796.59i	−1.03929	−	0.600032i	−0.119654	−	0.992816i	$-0.538179\pi$
$599$	−15236.1	−	8796.59i	−1.03929	−	0.600032i	−0.919631	+	0.392784i	$0.871512\pi$
$600$		0			0
$601$		−	28189.4i		−	1.91326i	−0.291303	−	0.956631i	$-0.594089\pi$
$601$		−	28189.4i		−	1.91326i	0.291303	−	0.956631i	$-0.405911\pi$
$602$		0			0
$603$		0			0
$604$	667.208	+	1155.64i	0.0449475	+	0.0778514i
$605$	15979.5	−	27677.2i	1.07381	−	1.85990i
$606$		0			0
$607$	−5753.67	+	3321.88i	−0.384735	+	0.222127i	−0.679876	−	0.733327i	$-0.737967\pi$
$607$	−5753.67	+	3321.88i	−0.384735	+	0.222127i	0.295141	+	0.955454i	$0.404633\pi$
$608$	−2636.90			−0.175889
$609$		0			0
$610$	2084.71			0.138373
$611$	13694.4	−	7906.48i	0.906738	−	0.523505i
$612$		0			0
$613$	−8205.44	+	14212.2i	−0.540644	+	0.936422i	0.458224	+	0.888837i	$0.348486\pi$
$613$	−8205.44	+	14212.2i	−0.540644	+	0.936422i	−0.998867	+	0.0475851i	$0.984847\pi$
$614$	−2460.63	−	4261.94i	−0.161731	−	0.280127i
$615$		0			0
$616$		0			0
$617$		−	8724.75i		−	0.569279i	−0.958635	−	0.284640i	$-0.908126\pi$
$617$		−	8724.75i		−	0.569279i	0.958635	−	0.284640i	$-0.0918739\pi$
$618$		0			0
$619$	−3034.06	−	1751.71i	−0.197010	−	0.113744i	0.398250	−	0.917277i	$-0.369618\pi$
$619$	−3034.06	−	1751.71i	−0.197010	−	0.113744i	−0.595260	+	0.803533i	$0.702951\pi$
$620$	−6021.42	−	3476.47i	−0.390042	−	0.225191i
$621$		0			0
$622$		−	6716.87i		−	0.432994i
$623$		0			0
$624$		0			0
$625$	9615.06	+	16653.8i	0.615364	+	1.06584i
$626$	−4559.43	+	7897.16i	−0.291104	+	0.504207i
$627$		0			0
$628$	7415.95	−	4281.60i	0.471224	−	0.272061i
$629$	−44185.8			−2.80096
$630$		0			0
$631$	−9975.21			−0.629329			−0.314665	−	0.949203i	$-0.601892\pi$
$631$	−9975.21			−0.629329			−0.314665	+	0.949203i	$0.601892\pi$
$632$	4902.92	−	2830.70i	0.308588	−	0.178163i
$633$		0			0
$634$	140.575	−	243.482i	0.00880589	−	0.0152522i
$635$	−5031.53	−	8714.86i	−0.314441	−	0.544628i
$636$		0			0
$637$		0			0
$638$			7526.38i			0.467041i
$639$		0			0
$640$	1586.58	+	916.012i	0.0979922	+	0.0565758i
$641$	−12621.3	−	7286.91i	−0.777709	−	0.449010i	0.0579089	−	0.998322i	$-0.481557\pi$
$641$	−12621.3	−	7286.91i	−0.777709	−	0.449010i	−0.835618	+	0.549312i	$0.814890\pi$
$642$		0			0
$643$			21396.3i			1.31227i	0.754646	+	0.656133i	$0.227809\pi$
$643$			21396.3i			1.31227i	−0.754646	+	0.656133i	$0.772191\pi$
$644$		0			0
$645$		0			0
$646$	11187.0	+	19376.5i	0.681344	+	1.18012i
$647$	6080.99	−	10532.6i	0.369503	−	0.639997i	−0.619985	−	0.784614i	$-0.712861\pi$
$647$	6080.99	−	10532.6i	0.369503	−	0.639997i	0.989488	+	0.144616i	$0.0461947\pi$
$648$		0			0
$649$	8792.53	−	5076.37i	0.531798	−	0.307034i
$650$	−8588.63			−0.518267
$651$		0			0
$652$	15440.6			0.927453
$653$	24914.5	−	14384.4i	1.49308	−	0.862028i	0.493108	−	0.869968i	$-0.335861\pi$
$653$	24914.5	−	14384.4i	1.49308	−	0.862028i	0.999968	+	0.00793951i	$0.00252725\pi$
$654$		0			0
$655$	8014.84	−	13882.1i	0.478116	−	0.828121i
$656$	1655.21	+	2866.92i	0.0985142	+	0.170632i
$657$		0			0
$658$		0			0
$659$			2881.81i			0.170348i	0.996366	+	0.0851740i	$0.0271446\pi$
$659$			2881.81i			0.170348i	−0.996366	+	0.0851740i	$0.972855\pi$
$660$		0			0
$661$	−2470.80	−	1426.52i	−0.145390	−	0.0839412i	0.425540	−	0.904940i	$-0.360084\pi$
$661$	−2470.80	−	1426.52i	−0.145390	−	0.0839412i	−0.570931	+	0.820998i	$0.693417\pi$
$662$	−5547.77	−	3203.01i	−0.325710	−	0.188049i
$663$		0			0
$664$		−	6225.16i		−	0.363830i
$665$		0			0
$666$		0			0
$667$	655.164	+	1134.78i	0.0380331	+	0.0658752i
$668$	−6060.56	+	10497.2i	−0.351033	+	0.608007i
$669$		0			0
$670$	−26128.2	+	15085.1i	−1.50660	+	0.869835i
$671$	−4347.68			−0.250135
$672$		0			0
$673$	−20107.9			−1.15171			−0.575855	−	0.817552i	$-0.695331\pi$
$673$	−20107.9			−1.15171			−0.575855	+	0.817552i	$0.695331\pi$
$674$	−16382.9	+	9458.69i	−0.936272	+	0.540557i
$675$		0			0
$676$	−1390.12	+	2407.76i	−0.0790920	+	0.136991i
$677$	14302.8	+	24773.2i	0.811966	+	1.40637i	0.911486	+	0.411331i	$0.134936\pi$
$677$	14302.8	+	24773.2i	0.811966	+	1.40637i	−0.0995203	+	0.995036i	$0.531731\pi$
$678$		0			0
$679$		0			0
$680$		−	15544.7i		−	0.876635i
$681$		0			0
$682$	12557.7	+	7250.21i	0.705074	+	0.407075i
$683$	29155.4	+	16832.9i	1.63338	+	0.943034i	0.983040	+	0.183392i	$0.0587078\pi$
$683$	29155.4	+	16832.9i	1.63338	+	0.943034i	0.650342	+	0.759641i	$0.274625\pi$
$684$		0			0
$685$			24225.1i			1.35123i
$686$		0			0
$687$		0			0
$688$	−2194.00	−	3800.12i	−0.121578	−	0.210579i
$689$	−4810.94	+	8332.79i	−0.266012	+	0.460746i
$690$		0			0
$691$	17916.3	−	10344.0i	0.986349	−	0.569469i	0.0821683	−	0.996618i	$-0.473815\pi$
$691$	17916.3	−	10344.0i	0.986349	−	0.569469i	0.904181	+	0.427149i	$0.140482\pi$
$692$	9161.80			0.503294
$693$		0			0
$694$	−5290.75			−0.289386
$695$	−9097.33	+	5252.35i	−0.496520	+	0.286666i
$696$		0			0
$697$	14044.5	−	24325.8i	0.763232	−	1.32196i
$698$	6172.76	+	10691.5i	0.334731	+	0.579772i
$699$		0			0
$700$		0			0
$701$		−	33866.4i		−	1.82470i	−0.409410	−	0.912351i	$-0.634265\pi$
$701$		−	33866.4i		−	1.82470i	0.409410	−	0.912351i	$-0.365735\pi$
$702$		0			0
$703$	23226.6	+	13409.9i	1.24610	+	0.719436i
$704$	−3308.83	−	1910.35i	−0.177139	−	0.102271i
$705$		0			0
$706$			17054.4i			0.909138i
$707$		0			0
$708$		0			0
$709$	−8371.69	−	14500.2i	−0.443449	−	0.768077i	0.554493	−	0.832188i	$-0.312912\pi$
$709$	−8371.69	−	14500.2i	−0.443449	−	0.768077i	−0.997943	+	0.0641113i	$0.979579\pi$
$710$	412.425	−	714.341i	0.0218001	−	0.0377588i
$711$		0			0
$712$	68.5543	−	39.5798i	0.00360840	−	0.00208331i
$713$	2524.50			0.132599
$714$		0			0
$715$	45950.3			2.40342
$716$	−3746.90	+	2163.27i	−0.195570	+	0.112912i
$717$		0			0
$718$	−3456.78	+	5987.32i	−0.179674	+	0.311205i
$719$	−5222.64	−	9045.87i	−0.270892	−	0.469199i	0.698198	−	0.715904i	$-0.253985\pi$
$719$	−5222.64	−	9045.87i	−0.270892	−	0.469199i	−0.969091	+	0.246705i	$0.920652\pi$
$720$		0			0
$721$		0			0
$722$			137.411i			0.00708299i
$723$		0			0
$724$	10656.5	+	6152.54i	0.547025	+	0.315825i
$725$	−4359.27	−	2516.82i	−0.223309	−	0.128928i
$726$		0			0
$727$		−	8798.07i		−	0.448834i	−0.974493	−	0.224417i	$-0.927952\pi$
$727$		−	8798.07i		−	0.448834i	0.974493	−	0.224417i	$-0.0720478\pi$
$728$		0			0
$729$		0			0
$730$	6903.23	+	11956.7i	0.350000	+	0.606218i
$731$	−18616.0	+	32243.9i	−0.941914	+	1.63144i
$732$		0			0
$733$	15443.9	−	8916.53i	0.778217	−	0.449304i	−0.0575811	−	0.998341i	$-0.518339\pi$
$733$	15443.9	−	8916.53i	0.778217	−	0.449304i	0.835798	+	0.549037i	$0.185005\pi$
$734$	24077.9			1.21081
$735$		0			0
$736$	−665.177			−0.0333135
$737$	54490.7	−	31460.2i	2.72346	−	1.57239i
$738$		0			0
$739$	1971.19	−	3414.20i	0.0981209	−	0.169950i	−0.812786	−	0.582562i	$-0.802050\pi$
$739$	1971.19	−	3414.20i	0.0981209	−	0.169950i	0.910907	+	0.412612i	$0.135383\pi$
$740$	−9316.70	−	16137.0i	−0.462823	−	0.801632i
$741$		0			0
$742$		0			0
$743$		−	4260.50i		−	0.210367i	−0.994453	−	0.105183i	$-0.966457\pi$
$743$		−	4260.50i		−	0.210367i	0.994453	−	0.105183i	$-0.0335430\pi$
$744$		0			0
$745$	−36239.1	−	20922.7i	−1.78215	−	1.02892i
$746$	4032.12	+	2327.95i	0.197891	+	0.114252i
$747$		0			0
$748$			32418.6i			1.58468i
$749$		0			0
$750$		0			0
$751$	15446.8	+	26754.6i	0.750548	+	1.29999i	0.947558	+	0.319585i	$0.103543\pi$
$751$	15446.8	+	26754.6i	0.750548	+	1.29999i	−0.197010	+	0.980401i	$0.563123\pi$
$752$	−2352.34	+	4074.36i	−0.114070	+	0.197576i
$753$		0			0
$754$	−5871.61	+	3389.97i	−0.283596	+	0.163734i
$755$	4774.77			0.230161
$756$		0			0
$757$	12559.1			0.602995			0.301497	−	0.953467i	$-0.402514\pi$
$757$	12559.1			0.602995			0.301497	+	0.953467i	$0.402514\pi$
$758$	2274.98	−	1313.46i	0.109012	−	0.0629381i
$759$		0			0
$760$	−4717.65	+	8171.20i	−0.225167	+	0.390001i
$761$	−654.086	−	1132.91i	−0.0311572	−	0.0539658i	0.850026	−	0.526740i	$-0.176586\pi$
$761$	−654.086	−	1132.91i	−0.0311572	−	0.0539658i	−0.881184	+	0.472774i	$0.843253\pi$
$762$		0			0
$763$		0			0
$764$			5099.95i			0.241505i
$765$		0			0
$766$	−1020.40	−	589.131i	−0.0481315	−	0.0277887i
$767$	7920.53	+	4572.92i	0.372873	+	0.215278i
$768$		0			0
$769$		−	3616.24i		−	0.169578i	−0.996399	−	0.0847888i	$-0.972978\pi$
$769$		−	3616.24i		−	0.169578i	0.996399	−	0.0847888i	$-0.0270215\pi$
$770$		0			0
$771$		0			0
$772$	3505.47	+	6071.65i	0.163426	+	0.283062i
$773$	−8703.97	+	15075.7i	−0.404994	+	0.701469i	−0.994321	−	0.106425i	$-0.966060\pi$
$773$	−8703.97	+	15075.7i	−0.404994	+	0.701469i	0.589327	+	0.807894i	$0.299393\pi$
$774$		0			0
$775$	−8398.62	+	4848.95i	−0.389274	+	0.224748i
$776$	12491.6			0.577863
$777$		0			0
$778$	−11122.7			−0.512557
$779$	−14765.2	+	8524.69i	−0.679099	+	0.392078i
$780$		0			0
$781$	−860.117	+	1489.77i	−0.0394077	+	0.0682561i
$782$	2822.01	+	4887.87i	0.129047	+	0.223516i
$783$		0			0
$784$		0			0
$785$		−	30640.6i		−	1.39313i
$786$		0			0
$787$	−23460.7	−	13545.0i	−1.06262	−	0.613505i	−0.136465	−	0.990645i	$-0.543574\pi$
$787$	−23460.7	−	13545.0i	−1.06262	−	0.613505i	−0.926156	+	0.377140i	$0.876908\pi$
$788$	−10380.9	−	5993.39i	−0.469293	−	0.270946i
$789$		0			0
$790$		−	20257.5i		−	0.912314i
$791$		0			0
$792$		0			0
$793$	−1958.25	−	3391.79i	−0.0876917	−	0.151887i
$794$	−79.1597	+	137.109i	−0.00353813	+	0.00612821i
$795$		0			0
$796$	−4125.76	+	2382.01i	−0.183711	+	0.106065i
$797$	−25584.0			−1.13705			−0.568526	−	0.822665i	$-0.692486\pi$
$797$	−25584.0			−1.13705			−0.568526	+	0.822665i	$0.692486\pi$
$798$		0			0
$799$	39919.1			1.76750
$800$	2212.95	−	1277.65i	0.0977993	−	0.0564645i
$801$		0			0
$802$	−11297.6	+	19568.1i	−0.497423	+	0.861562i
$803$	−14396.8	−	24935.9i	−0.632691	−	1.09585i
$804$		0			0
$805$		0			0
$806$			13062.3i			0.570845i
$807$		0			0
$808$	−6961.71	−	4019.35i	−0.303109	−	0.175000i
$809$	9124.25	+	5267.89i	0.396528	+	0.228936i	0.684985	−	0.728557i	$-0.259809\pi$
$809$	9124.25	+	5267.89i	0.396528	+	0.228936i	−0.288457	+	0.957493i	$0.593142\pi$
$810$		0			0
$811$		−	30858.9i		−	1.33613i	−0.744102	−	0.668066i	$-0.767122\pi$
$811$		−	30858.9i		−	1.33613i	0.744102	−	0.668066i	$-0.232878\pi$
$812$		0			0
$813$		0			0
$814$	19430.1	+	33653.9i	0.836638	+	1.44910i
$815$	27624.5	−	47847.0i	1.18729	−	2.05645i
$816$		0			0
$817$	19571.4	−	11299.5i	0.838085	−	0.483869i
$818$	9751.32			0.416805
$819$		0			0
$820$	11845.3			0.504458
$821$	18260.0	−	10542.4i	0.776222	−	0.448152i	−0.0588677	−	0.998266i	$-0.518749\pi$
$821$	18260.0	−	10542.4i	0.776222	−	0.448152i	0.835090	+	0.550114i	$0.185416\pi$
$822$		0			0
$823$	−4258.73	+	7376.34i	−0.180377	+	0.312422i	−0.942009	−	0.335588i	$-0.891065\pi$
$823$	−4258.73	+	7376.34i	−0.180377	+	0.312422i	0.761632	+	0.648010i	$0.224398\pi$
$824$	−2241.20	−	3881.88i	−0.0947525	−	0.164116i
$825$		0			0
$826$		0			0
$827$		−	11824.9i		−	0.497210i	−0.968605	−	0.248605i	$-0.920028\pi$
$827$		−	11824.9i		−	0.497210i	0.968605	−	0.248605i	$-0.0799721\pi$
$828$		0			0
$829$	−27966.8	−	16146.6i	−1.17168	−	0.676472i	−0.217608	−	0.976036i	$-0.569825\pi$
$829$	−27966.8	−	16146.6i	−1.17168	−	0.676472i	−0.954076	+	0.299564i	$0.903159\pi$
$830$	−19290.4	−	11137.3i	−0.806724	−	0.465762i
$831$		0			0
$832$		−	3441.78i		−	0.143416i
$833$		0			0
$834$		0			0
$835$	21685.7	+	37560.8i	0.898760	+	1.55670i
$836$	9838.70	−	17041.1i	0.407032	−	0.705000i
$837$		0			0
$838$	6510.32	−	3758.73i	0.268371	−	0.154944i
$839$	31256.5			1.28617			0.643084	−	0.765796i	$-0.277655\pi$
$839$	31256.5			1.28617			0.643084	+	0.765796i	$0.277655\pi$
$840$		0			0
$841$	20415.4			0.837074
$842$	−2364.40	+	1365.09i	−0.0967727	+	0.0558717i
$843$		0			0
$844$	3051.61	−	5285.55i	0.124456	−	0.215564i
$845$	4974.09	+	8615.38i	0.202502	+	0.350743i
$846$		0			0
$847$		0			0
$848$		−	2862.70i		−	0.115926i
$849$		0			0
$850$	−18776.8	−	10840.8i	−0.757694	−	0.437455i
$851$	5859.08	+	3382.74i	0.236012	+	0.136262i
$852$		0			0
$853$		−	6514.43i		−	0.261488i	−0.991416	−	0.130744i	$-0.958263\pi$
$853$		−	6514.43i		−	0.261488i	0.991416	−	0.130744i	$-0.0417367\pi$
$854$		0			0
$855$		0			0
$856$	1324.08	+	2293.38i	0.0528694	+	0.0915725i
$857$	−1481.26	+	2565.62i	−0.0590419	+	0.102264i	−0.894036	−	0.447996i	$-0.852138\pi$
$857$	−1481.26	+	2565.62i	−0.0590419	+	0.102264i	0.834994	+	0.550260i	$0.185471\pi$
$858$		0			0
$859$	−8076.08	+	4662.73i	−0.320783	+	0.185204i	−0.651741	−	0.758441i	$-0.725961\pi$
$859$	−8076.08	+	4662.73i	−0.320783	+	0.185204i	0.330959	+	0.943645i	$0.392628\pi$
$860$	−15701.0			−0.622558
$861$		0			0
$862$	16144.9			0.637931
$863$	25769.8	−	14878.2i	1.01647	−	0.586859i	0.103390	−	0.994641i	$-0.467031\pi$
$863$	25769.8	−	14878.2i	1.01647	−	0.586859i	0.913079	+	0.407782i	$0.133698\pi$
$864$		0			0
$865$	16391.2	−	28390.5i	0.644299	−	1.11596i
$866$	−687.622	−	1191.00i	−0.0269819	−	0.0467341i
$867$		0			0
$868$		0			0
$869$			42247.1i			1.64918i
$870$		0			0
$871$	49086.5	+	28340.1i	1.90957	+	1.10249i
$872$	8418.79	+	4860.59i	0.326945	+	0.188762i
$873$		0			0
$874$		−	3425.80i		−	0.132585i
$875$		0			0
$876$		0			0
$877$	−16463.2	−	28515.2i	−0.633893	−	1.09793i	−0.986749	−	0.162257i	$-0.948123\pi$
$877$	−16463.2	−	28515.2i	−0.633893	−	1.09793i	0.352856	−	0.935678i	$-0.385211\pi$
$878$	11064.0	−	19163.4i	0.425276	−	0.736600i
$879$		0			0
$880$	−11839.5	+	6835.56i	−0.453535	+	0.261849i
$881$	26780.0			1.02411			0.512056	−	0.858952i	$-0.328884\pi$
$881$	26780.0			1.02411			0.512056	+	0.858952i	$0.328884\pi$
$882$		0			0
$883$	−8561.73			−0.326302			−0.163151	−	0.986601i	$-0.552166\pi$
$883$	−8561.73			−0.326302			−0.163151	+	0.986601i	$0.552166\pi$
$884$	−25291.0	+	14601.7i	−0.962248	+	0.555554i
$885$		0			0
$886$	−12836.9	+	22234.1i	−0.486753	+	0.843081i
$887$	−7222.77	−	12510.2i	−0.273412	−	0.473564i	0.696321	−	0.717731i	$-0.254819\pi$
$887$	−7222.77	−	12510.2i	−0.273412	−	0.473564i	−0.969733	+	0.244166i	$0.921486\pi$
$888$		0			0
$889$		0			0
$890$		−	283.247i		−	0.0106679i
$891$		0			0
$892$	−12775.3	−	7375.84i	−0.479540	−	0.276863i
$893$	−20983.8	−	12115.0i	−0.786334	−	0.453990i
$894$		0			0
$895$			15481.1i			0.578186i
$896$		0			0
$897$		0			0
$898$	−10439.7	−	18082.0i	−0.387947	−	0.671944i
$899$	−3827.81	+	6629.95i	−0.142007	+	0.245964i
$900$		0			0
$901$	−21035.7	+	12145.0i	−0.777805	+	0.449066i
$902$	−24703.5			−0.911901
$903$		0			0
$904$	−793.948			−0.0292105
$905$	38130.8	−	22014.8i	1.40056	−	0.808616i
$906$		0			0
$907$	5402.09	−	9356.69i	0.197766	−	0.342540i	−0.750038	−	0.661395i	$-0.769965\pi$
$907$	5402.09	−	9356.69i	0.197766	−	0.342540i	0.947804	+	0.318855i	$0.103298\pi$
$908$	6880.20	+	11916.9i	0.251462	+	0.435545i
$909$		0			0
$910$		0			0
$911$			21876.6i			0.795612i	0.917470	+	0.397806i	$0.130228\pi$
$911$			21876.6i			0.795612i	−0.917470	+	0.397806i	$0.869772\pi$
$912$		0			0
$913$	40230.4	+	23227.0i	1.45830	+	0.841953i
$914$	−23858.8	−	13774.9i	−0.863434	−	0.498504i
$915$		0			0
$916$		−	20769.8i		−	0.749185i
$917$		0			0
$918$		0			0
$919$	20944.0	+	36276.1i	0.751772	+	1.30211i	0.946963	+	0.321343i	$0.104134\pi$
$919$	20944.0	+	36276.1i	0.751772	+	1.30211i	−0.195191	+	0.980765i	$0.562533\pi$
$920$	−1190.06	+	2061.24i	−0.0426468	+	0.0738665i
$921$		0			0
$922$	11959.1	−	6904.60i	0.427172	−	0.246628i
$923$	−1549.63			−0.0552618
$924$		0			0
$925$	−25989.7			−0.923823
$926$	25577.6	−	14767.2i	0.907700	−	0.524061i
$927$		0			0
$928$	1008.59	−	1746.92i	0.0356772	−	0.0617947i
$929$	21281.8	+	36861.1i	0.751596	+	1.30180i	0.947049	+	0.321090i	$0.104049\pi$
$929$	21281.8	+	36861.1i	0.751596	+	1.30180i	−0.195453	+	0.980713i	$0.562618\pi$
$930$		0			0
$931$		0			0
$932$			22705.8i			0.798017i
$933$		0			0
$934$	29813.6	+	17212.9i	1.04446	+	0.603022i
$935$	100458.	+	57999.7i	3.51373	+	2.02865i
$936$		0			0
$937$		−	14367.8i		−	0.500936i	−0.968125	−	0.250468i	$-0.919416\pi$
$937$		−	14367.8i		−	0.500936i	0.968125	−	0.250468i	$-0.0805844\pi$
$938$		0			0
$939$		0			0
$940$	8417.06	+	14578.8i	0.292058	+	0.505859i
$941$	15587.5	−	26998.4i	0.539999	−	0.935305i	−0.458905	−	0.888486i	$-0.651758\pi$
$941$	15587.5	−	26998.4i	0.539999	−	0.935305i	0.998903	−	0.0468197i	$-0.0149086\pi$
$942$		0			0
$943$	−3724.63	+	2150.41i	−0.128622	+	0.0742599i
$944$	−2721.07			−0.0938170
$945$		0			0
$946$	32744.6			1.12539
$947$	−20439.7	+	11800.9i	−0.701373	+	0.404938i	−0.807859	−	0.589376i	$-0.799373\pi$
$947$	−20439.7	+	11800.9i	−0.701373	+	0.404938i	0.106486	+	0.994314i	$0.466040\pi$
$948$		0			0
$949$	12969.0	−	22462.9i	0.443614	−	0.768363i
$950$	6580.13	+	11397.1i	0.224724	+	0.389233i
$951$		0			0
$952$		0			0
$953$		−	16096.1i		−	0.547117i	−0.961855	−	0.273559i	$-0.911799\pi$
$953$		−	16096.1i		−	0.547117i	0.961855	−	0.273559i	$-0.0882008\pi$
$954$		0			0
$955$	15803.7	+	9124.25i	0.535492	+	0.309166i
$956$	−9177.90	−	5298.87i	−0.310496	−	0.179265i
$957$		0			0
$958$		−	9724.25i		−	0.327950i
$959$		0			0
$960$		0			0
$961$	−7520.80	−	13026.4i	−0.252452	−	0.437260i
$962$	−17503.1	+	30316.2i	−0.586614	+	1.01604i
$963$		0			0
$964$	8102.38	−	4677.91i	0.270705	−	0.156292i
$965$	25086.3			0.836847
$966$		0			0
$967$	−11261.0			−0.374487			−0.187243	−	0.982314i	$-0.559955\pi$
$967$	−11261.0			−0.374487			−0.187243	+	0.982314i	$0.559955\pi$
$968$	15470.0	−	8931.64i	0.513663	−	0.296564i
$969$		0			0
$970$	22348.5	−	38708.8i	0.739760	−	1.28130i
$971$	−3262.04	−	5650.02i	−0.107810	−	0.186733i	0.807073	−	0.590452i	$-0.201051\pi$
$971$	−3262.04	−	5650.02i	−0.107810	−	0.186733i	−0.914883	+	0.403719i	$0.867717\pi$
$972$		0			0
$973$		0			0
$974$		−	10737.4i		−	0.353234i
$975$		0			0
$976$	1009.13	+	582.619i	0.0330956	+	0.0191078i
$977$	19659.9	+	11350.7i	0.643784	+	0.371689i	0.786071	−	0.618137i	$-0.212112\pi$
$977$	19659.9	+	11350.7i	0.643784	+	0.371689i	−0.142287	+	0.989826i	$0.545445\pi$
$978$		0			0
$979$			590.714i			0.0192843i
$980$		0			0
$981$		0			0
$982$	−5093.75	−	8822.64i	−0.165528	−	0.286702i
$983$	−6920.53	+	11986.7i	−0.224548	+	0.388928i	−0.956184	−	0.292767i	$-0.905424\pi$
$983$	−6920.53	+	11986.7i	−0.224548	+	0.388928i	0.731636	+	0.681696i	$0.238757\pi$
$984$		0			0
$985$	−37144.5	+	21445.4i	−1.20154	+	0.693712i
$986$	−17115.7			−0.552813
$987$		0			0
$988$	17725.9			0.570785
$989$	4937.02	−	2850.39i	0.158734	−	0.0916451i
$990$		0			0
$991$	18151.7	−	31439.7i	0.581845	−	1.00778i	−0.413416	−	0.910542i	$-0.635664\pi$
$991$	18151.7	−	31439.7i	0.581845	−	1.00778i	0.995261	−	0.0972426i	$-0.0310023\pi$
$992$	−1943.15	−	3365.64i	−0.0621927	−	0.107721i
$993$		0			0
$994$		0			0
$995$			17046.5i			0.543125i
$996$		0			0
$997$	−19754.6	−	11405.3i	−0.627516	−	0.362296i	0.152273	−	0.988338i	$-0.451341\pi$
$997$	−19754.6	−	11405.3i	−0.627516	−	0.362296i	−0.779789	+	0.626042i	$0.784674\pi$
$998$	3545.76	+	2047.15i	0.112464	+	0.0649311i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.4.k.c.521.5		16
3.2	odd	2	inner	882.4.k.c.521.4		16
7.2	even	3	inner	882.4.k.c.215.1		16
7.3	odd	6		126.4.d.a.125.5	yes	8
7.4	even	3		126.4.d.a.125.8	yes	8
7.5	odd	6	inner	882.4.k.c.215.4		16
7.6	odd	2	inner	882.4.k.c.521.8		16
21.2	odd	6	inner	882.4.k.c.215.8		16
21.5	even	6	inner	882.4.k.c.215.5		16
21.11	odd	6		126.4.d.a.125.1	✓	8
21.17	even	6		126.4.d.a.125.4	yes	8
21.20	even	2	inner	882.4.k.c.521.1		16
28.3	even	6		1008.4.k.c.881.1		8
28.11	odd	6		1008.4.k.c.881.8		8
84.11	even	6		1008.4.k.c.881.2		8
84.59	odd	6		1008.4.k.c.881.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.4.d.a.125.1	✓	8	21.11	odd	6
126.4.d.a.125.4	yes	8	21.17	even	6
126.4.d.a.125.5	yes	8	7.3	odd	6
126.4.d.a.125.8	yes	8	7.4	even	3
882.4.k.c.215.1		16	7.2	even	3	inner
882.4.k.c.215.4		16	7.5	odd	6	inner
882.4.k.c.215.5		16	21.5	even	6	inner
882.4.k.c.215.8		16	21.2	odd	6	inner
882.4.k.c.521.1		16	21.20	even	2	inner
882.4.k.c.521.4		16	3.2	odd	2	inner
882.4.k.c.521.5		16	1.1	even	1	trivial
882.4.k.c.521.8		16	7.6	odd	2	inner
1008.4.k.c.881.1		8	28.3	even	6
1008.4.k.c.881.2		8	84.11	even	6
1008.4.k.c.881.7		8	84.59	odd	6
1008.4.k.c.881.8		8	28.11	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	882.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.73205 - 1.00000i) q^{2} +(2.00000 - 3.46410i) q^{4} +(-7.15634 - 12.3951i) q^{5} -8.00000i q^{8} +O(q^{10})\)	\(q+(1.73205 - 1.00000i) q^{2} +(2.00000 - 3.46410i) q^{4} +(-7.15634 - 12.3951i) q^{5} -8.00000i q^{8} +(-24.7903 - 14.3127i) q^{10} +(51.7004 + 29.8492i) q^{11} +53.7779i q^{13} +(-8.00000 - 13.8564i) q^{16} +(-67.8799 + 117.571i) q^{17} +(71.3633 - 41.2016i) q^{19} -57.2507 q^{20} +119.397 q^{22} +(18.0019 - 10.3934i) q^{23} +(-39.9264 + 69.1546i) q^{25} +(53.7779 + 93.1460i) q^{26} +63.0366i q^{29} +(105.176 + 60.7236i) q^{31} +(-27.7128 - 16.0000i) q^{32} +271.520i q^{34} +(162.735 + 281.865i) q^{37} +(82.4032 - 142.727i) q^{38} +(-99.1612 + 57.2507i) q^{40} -206.902 q^{41} +274.250 q^{43} +(206.802 - 119.397i) q^{44} +(20.7868 - 36.0038i) q^{46} +(-147.021 - 254.648i) q^{47} +159.706i q^{50} +(186.292 + 107.556i) q^{52} +(154.948 + 89.4594i) q^{53} -854.445i q^{55} +(63.0366 + 109.183i) q^{58} +(85.0334 - 147.282i) q^{59} +(-63.0704 + 36.4137i) q^{61} +242.894 q^{62} -64.0000 q^{64} +(666.585 - 384.853i) q^{65} +(526.985 - 912.765i) q^{67} +(271.520 + 470.286i) q^{68} +28.8154i q^{71} +(-417.698 - 241.158i) q^{73} +(563.731 + 325.470i) q^{74} -329.613i q^{76} +(353.838 + 612.865i) q^{79} +(-114.501 + 198.322i) q^{80} +(-358.365 + 206.902i) q^{82} +778.145 q^{83} +1943.09 q^{85} +(475.015 - 274.250i) q^{86} +(238.794 - 413.603i) q^{88} +(4.94748 + 8.56929i) q^{89} -83.1472i q^{92} +(-509.296 - 294.042i) q^{94} +(-1021.40 - 589.706i) q^{95} +1561.45i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{4}+O(q^{10}) \) 16 * q + 32 * q^4	\( 16 q + 32 q^{4} - 128 q^{16} + 960 q^{22} + 40 q^{25} + 160 q^{37} + 2080 q^{43} + 672 q^{46} - 960 q^{58} - 1024 q^{64} + 3680 q^{67} - 448 q^{79} + 13440 q^{85} + 1920 q^{88}+O(q^{100}) \) 16 * q + 32 * q^4 - 128 * q^16 + 960 * q^22 + 40 * q^25 + 160 * q^37 + 2080 * q^43 + 672 * q^46 - 960 * q^58 - 1024 * q^64 + 3680 * q^67 - 448 * q^79 + 13440 * q^85 + 1920 * q^88

Introduction

L-functions

Modular forms

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Database

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