LMFDB - Embedded newform 252.4.e.a.71.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(71,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("252.71");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.e (of order $2$, degree $1$, 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:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.4
Character	$\chi$	$=$	252.71
Dual form			252.4.e.a.71.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.45159 + 1.41057i) q^{2} +(4.02056 - 6.91629i) q^{4} -16.9233i q^{5} +7.00000i q^{7} +(-0.100815 + 22.6272i) q^{8} +O(q^{10})$	\(q+(-2.45159 + 1.41057i) q^{2} +(4.02056 - 6.91629i) q^{4} -16.9233i q^{5} +7.00000i q^{7} +(-0.100815 + 22.6272i) q^{8} +(23.8716 + 41.4889i) q^{10} +13.3747 q^{11} +76.5768 q^{13} +(-9.87402 - 17.1611i) q^{14} +(-31.6702 - 55.6147i) q^{16} -99.7168i q^{17} +121.074i q^{19} +(-117.046 - 68.0411i) q^{20} +(-32.7893 + 18.8660i) q^{22} -151.268 q^{23} -161.398 q^{25} +(-187.735 + 108.017i) q^{26} +(48.4140 + 28.1439i) q^{28} -197.277i q^{29} -268.595i q^{31} +(156.091 + 91.6713i) q^{32} +(140.658 + 244.464i) q^{34} +118.463 q^{35} +19.2350 q^{37} +(-170.784 - 296.823i) q^{38} +(382.926 + 1.70613i) q^{40} +129.537i q^{41} -490.774i q^{43} +(53.7739 - 92.5035i) q^{44} +(370.846 - 213.375i) q^{46} -160.864 q^{47} -49.0000 q^{49} +(395.680 - 227.663i) q^{50} +(307.882 - 529.627i) q^{52} -126.884i q^{53} -226.344i q^{55} +(-158.390 - 0.705707i) q^{56} +(278.274 + 483.643i) q^{58} +285.808 q^{59} -467.355 q^{61} +(378.873 + 658.484i) q^{62} +(-511.980 - 4.56233i) q^{64} -1295.93i q^{65} +323.876i q^{67} +(-689.670 - 400.917i) q^{68} +(-290.422 + 167.101i) q^{70} +673.944 q^{71} -338.197 q^{73} +(-47.1563 + 27.1324i) q^{74} +(837.383 + 486.785i) q^{76} +93.6231i q^{77} -869.368i q^{79} +(-941.184 + 535.963i) q^{80} +(-182.721 - 317.570i) q^{82} -532.510 q^{83} -1687.54 q^{85} +(692.274 + 1203.18i) q^{86} +(-1.34838 + 302.633i) q^{88} +140.339i q^{89} +536.037i q^{91} +(-608.182 + 1046.21i) q^{92} +(394.373 - 226.911i) q^{94} +2048.97 q^{95} +652.093 q^{97} +(120.128 - 69.1181i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 24 q^{4}+O(q^{10}) $ 36 * q - 24 * q^4	$ 36 q - 24 q^{4} + 264 q^{10} - 468 q^{16} + 444 q^{22} - 900 q^{25} - 84 q^{28} - 432 q^{34} - 264 q^{37} + 1416 q^{40} + 180 q^{46} - 1764 q^{49} + 2736 q^{52} + 636 q^{58} - 3960 q^{61} + 1392 q^{64} - 504 q^{70} - 2520 q^{76} + 1032 q^{82} - 3144 q^{85} + 2748 q^{88} + 5496 q^{94}+O(q^{100}) $ 36 * q - 24 * q^4 + 264 * q^10 - 468 * q^16 + 444 * q^22 - 900 * q^25 - 84 * q^28 - 432 * q^34 - 264 * q^37 + 1416 * q^40 + 180 * q^46 - 1764 * q^49 + 2736 * q^52 + 636 * q^58 - 3960 * q^61 + 1392 * q^64 - 504 * q^70 - 2520 * q^76 + 1032 * q^82 - 3144 * q^85 + 2748 * q^88 + 5496 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$73$	$127$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−2.45159	+	1.41057i	−0.866767	+	0.498713i
$2$	−2.45159	+	1.41057i	−0.866767	+	0.498713i
$3$		0			0
$3$		0			0
$4$	4.02056	−	6.91629i	0.502570	−	0.864536i
$5$		−	16.9233i		−	1.51366i	−0.653609	−	0.756832i	$-0.726746\pi$
$5$		−	16.9233i		−	1.51366i	0.653609	−	0.756832i	$-0.273254\pi$
$6$		0			0
$7$			7.00000i			0.377964i
$7$			7.00000i			0.377964i
$8$	−0.100815	+	22.6272i	−0.00445545	+	0.999990i
$9$		0			0
$10$	23.8716	+	41.4889i	0.754885	+	1.31199i
$11$	13.3747			0.366603			0.183301	−	0.983057i	$-0.441322\pi$
$11$	13.3747			0.366603			0.183301	+	0.983057i	$0.441322\pi$
$12$		0			0
$13$	76.5768			1.63374			0.816868	−	0.576824i	$-0.195708\pi$
$13$	76.5768			1.63374			0.816868	+	0.576824i	$0.195708\pi$
$14$	−9.87402	−	17.1611i	−0.188496	−	0.327607i
$15$		0			0
$16$	−31.6702	−	55.6147i	−0.494846	−	0.868980i
$17$		−	99.7168i		−	1.42264i	−0.702868	−	0.711320i	$-0.748098\pi$
$17$		−	99.7168i		−	1.42264i	0.702868	−	0.711320i	$-0.251902\pi$
$18$		0			0
$19$			121.074i			1.46191i	0.682426	+	0.730955i	$0.260925\pi$
$19$			121.074i			1.46191i	−0.682426	+	0.730955i	$0.739075\pi$
$20$	−117.046	−	68.0411i	−1.30862	−	0.760723i
$21$		0			0
$22$	−32.7893	+	18.8660i	−0.317759	+	0.182830i
$23$	−151.268			−1.37137			−0.685685	−	0.727898i	$-0.740497\pi$
$23$	−151.268			−1.37137			−0.685685	+	0.727898i	$0.740497\pi$
$24$		0			0
$25$	−161.398			−1.29118
$26$	−187.735	+	108.017i	−1.41607	+	0.814766i
$27$		0			0
$28$	48.4140	+	28.1439i	0.326764	+	0.189954i
$29$		−	197.277i		−	1.26322i	−0.775285	−	0.631612i	$-0.782394\pi$
$29$		−	197.277i		−	1.26322i	0.775285	−	0.631612i	$-0.217606\pi$
$30$		0			0
$31$		−	268.595i		−	1.55616i	−0.628163	−	0.778082i	$-0.716193\pi$
$31$		−	268.595i		−	1.55616i	0.628163	−	0.778082i	$-0.283807\pi$
$32$	156.091	+	91.6713i	0.862289	+	0.506417i
$33$		0			0
$34$	140.658	+	244.464i	0.709489	+	1.23310i
$35$	118.463			0.572112
$36$		0			0
$37$	19.2350			0.0854652			0.0427326	−	0.999087i	$-0.486394\pi$
$37$	19.2350			0.0854652			0.0427326	+	0.999087i	$0.486394\pi$
$38$	−170.784	−	296.823i	−0.729074	−	1.26713i
$39$		0			0
$40$	382.926	+	1.70613i	1.51365	+	0.00674406i
$41$			129.537i			0.493420i	0.969089	+	0.246710i	$0.0793495\pi$
$41$			129.537i			0.493420i	−0.969089	+	0.246710i	$0.920651\pi$
$42$		0			0
$43$		−	490.774i		−	1.74052i	−0.492592	−	0.870261i	$-0.663950\pi$
$43$		−	490.774i		−	1.74052i	0.492592	−	0.870261i	$-0.336050\pi$
$44$	53.7739	−	92.5035i	0.184244	−	0.316942i
$45$		0			0
$46$	370.846	−	213.375i	1.18866	−	0.683921i
$47$	−160.864			−0.499245			−0.249622	−	0.968343i	$-0.580306\pi$
$47$	−160.864			−0.499245			−0.249622	+	0.968343i	$0.580306\pi$
$48$		0			0
$49$	−49.0000			−0.142857
$50$	395.680	−	227.663i	1.11915	−	0.643929i
$51$		0			0
$52$	307.882	−	529.627i	0.821067	−	1.41242i
$53$		−	126.884i		−	0.328846i	−0.986390	−	0.164423i	$-0.947424\pi$
$53$		−	126.884i		−	0.328846i	0.986390	−	0.164423i	$-0.0525763\pi$
$54$		0			0
$55$		−	226.344i		−	0.554914i
$56$	−158.390	−	0.705707i	−0.377961	−	0.00168400i
$57$		0			0
$58$	278.274	+	483.643i	0.629986	+	1.09492i
$59$	285.808			0.630662			0.315331	−	0.948982i	$-0.397885\pi$
$59$	285.808			0.630662			0.315331	+	0.948982i	$0.397885\pi$
$60$		0			0
$61$	−467.355			−0.980963			−0.490481	−	0.871452i	$-0.663179\pi$
$61$	−467.355			−0.980963			−0.490481	+	0.871452i	$0.663179\pi$
$62$	378.873	+	658.484i	0.776079	+	1.34883i
$63$		0			0
$64$	−511.980	−	4.56233i	−0.999960	−	0.00891081i
$65$		−	1295.93i		−	2.47293i
$66$		0			0
$67$			323.876i			0.590563i	0.955410	+	0.295282i	$0.0954135\pi$
$67$			323.876i			0.590563i	−0.955410	+	0.295282i	$0.904587\pi$
$68$	−689.670	−	400.917i	−1.22992	−	0.714976i
$69$		0			0
$70$	−290.422	+	167.101i	−0.495887	+	0.285320i
$71$	673.944			1.12651			0.563257	−	0.826282i	$-0.309548\pi$
$71$	673.944			1.12651			0.563257	+	0.826282i	$0.309548\pi$
$72$		0			0
$73$	−338.197			−0.542232			−0.271116	−	0.962547i	$-0.587393\pi$
$73$	−338.197			−0.542232			−0.271116	+	0.962547i	$0.587393\pi$
$74$	−47.1563	+	27.1324i	−0.0740784	+	0.0426226i
$75$		0			0
$76$	837.383	+	486.785i	1.26387	+	0.734712i
$77$			93.6231i			0.138563i
$78$		0			0
$79$		−	869.368i		−	1.23812i	−0.785343	−	0.619060i	$-0.787514\pi$
$79$		−	869.368i		−	1.23812i	0.785343	−	0.619060i	$-0.212486\pi$
$80$	−941.184	+	535.963i	−1.31535	+	0.749032i
$81$		0			0
$82$	−182.721	−	317.570i	−0.246075	−	0.427680i
$83$	−532.510			−0.704223			−0.352112	−	0.935958i	$-0.614536\pi$
$83$	−532.510			−0.704223			−0.352112	+	0.935958i	$0.614536\pi$
$84$		0			0
$85$	−1687.54			−2.15340
$86$	692.274	+	1203.18i	0.868021	+	1.50863i
$87$		0			0
$88$	−1.34838	+	302.633i	−0.00163338	+	0.366599i
$89$			140.339i			0.167145i	0.996502	+	0.0835725i	$0.0266330\pi$
$89$			140.339i			0.167145i	−0.996502	+	0.0835725i	$0.973367\pi$
$90$		0			0
$91$			536.037i			0.617494i
$92$	−608.182	+	1046.21i	−0.689210	+	1.18560i
$93$		0			0
$94$	394.373	−	226.911i	0.432729	−	0.248980i
$95$	2048.97			2.21284
$96$		0			0
$97$	652.093			0.682578			0.341289	−	0.939959i	$-0.389137\pi$
$97$	652.093			0.682578			0.341289	+	0.939959i	$0.389137\pi$
$98$	120.128	−	69.1181i	0.123824	−	0.0712448i
$99$		0			0
$100$	−648.909	+	1116.27i	−0.648909	+	1.11627i
$101$			278.977i			0.274844i	0.990513	+	0.137422i	$0.0438817\pi$
$101$			278.977i			0.274844i	−0.990513	+	0.137422i	$0.956118\pi$
$102$		0			0
$103$		−	724.272i		−	0.692860i	−0.938076	−	0.346430i	$-0.887394\pi$
$103$		−	724.272i		−	0.692860i	0.938076	−	0.346430i	$-0.112606\pi$
$104$	−7.72011	+	1732.72i	−0.00727903	+	1.63372i
$105$		0			0
$106$	178.979	+	311.067i	0.164000	+	0.285033i
$107$	−1795.17			−1.62193			−0.810963	−	0.585097i	$-0.801056\pi$
$107$	−1795.17			−1.62193			−0.810963	+	0.585097i	$0.801056\pi$
$108$		0			0
$109$	875.769			0.769573			0.384786	−	0.923006i	$-0.374275\pi$
$109$	875.769			0.769573			0.384786	+	0.923006i	$0.374275\pi$
$110$	319.275	+	554.903i	0.276743	+	0.480981i
$111$		0			0
$112$	389.303	−	221.691i	0.328444	−	0.187034i
$113$		−	124.673i		−	0.103790i	−0.998653	−	0.0518948i	$-0.983474\pi$
$113$		−	124.673i		−	0.103790i	0.998653	−	0.0518948i	$-0.0165261\pi$
$114$		0			0
$115$			2559.95i			2.07580i
$116$	−1364.43	−	793.166i	−1.09210	−	0.634859i
$117$		0			0
$118$	−700.683	+	403.153i	−0.546637	+	0.314519i
$119$	698.018			0.537707
$120$		0			0
$121$	−1152.12			−0.865602
$122$	1145.76	−	659.240i	0.850266	−	0.489219i
$123$		0			0
$124$	−1857.68	−	1079.90i	−1.34536	−	0.782081i
$125$			615.968i			0.440751i
$126$		0			0
$127$			307.355i			0.214751i	0.994219	+	0.107375i	$0.0342446\pi$
$127$			307.355i			0.214751i	−0.994219	+	0.107375i	$0.965755\pi$
$128$	1261.60	−	711.000i	0.871177	−	0.490970i
$129$		0			0
$130$	1828.01	+	3177.09i	1.23328	+	2.14345i
$131$	937.529			0.625285			0.312642	−	0.949871i	$-0.398786\pi$
$131$	937.529			0.625285			0.312642	+	0.949871i	$0.398786\pi$
$132$		0			0
$133$	−847.518			−0.552550
$134$	−456.851	−	794.010i	−0.294522	−	0.511881i
$135$		0			0
$136$	2256.31	+	10.0530i	1.42263	+	0.00633850i
$137$			2608.36i			1.62662i	0.581829	+	0.813311i	$0.302337\pi$
$137$			2608.36i			1.62662i	−0.581829	+	0.813311i	$0.697663\pi$
$138$		0			0
$139$		−	1562.32i		−	0.953338i	−0.879083	−	0.476669i	$-0.841844\pi$
$139$		−	1562.32i		−	0.953338i	0.879083	−	0.476669i	$-0.158156\pi$
$140$	476.288	−	819.325i	0.287526	−	0.494611i
$141$		0			0
$142$	−1652.23	+	950.648i	−0.976425	+	0.561807i
$143$	1024.19			0.598933
$144$		0			0
$145$	−3338.58			−1.91210
$146$	829.119	−	477.052i	0.469989	−	0.270418i
$147$		0			0
$148$	77.3354	−	133.035i	0.0429523	−	0.0738878i
$149$		−	973.569i		−	0.535288i	−0.963518	−	0.267644i	$-0.913755\pi$
$149$		−	973.569i		−	0.535288i	0.963518	−	0.267644i	$-0.0862450\pi$
$150$		0			0
$151$		−	523.787i		−	0.282286i	−0.989989	−	0.141143i	$-0.954922\pi$
$151$		−	523.787i		−	0.282286i	0.989989	−	0.141143i	$-0.0450777\pi$
$152$	−2739.56	−	12.2061i	−1.46189	−	0.00651346i
$153$		0			0
$154$	−132.062	−	229.525i	−0.0691031	−	0.120102i
$155$	−4545.51			−2.35551
$156$		0			0
$157$	−750.516			−0.381514			−0.190757	−	0.981637i	$-0.561094\pi$
$157$	−750.516			−0.381514			−0.190757	+	0.981637i	$0.561094\pi$
$158$	1226.31	+	2131.33i	0.617467	+	1.07316i
$159$		0			0
$160$	1551.38	−	2641.57i	0.766546	−	1.30522i
$161$		−	1058.87i		−	0.518329i
$162$		0			0
$163$			854.952i			0.410828i	0.978675	+	0.205414i	$0.0658542\pi$
$163$			854.952i			0.410828i	−0.978675	+	0.205414i	$0.934146\pi$
$164$	895.912	+	520.810i	0.426579	+	0.247978i
$165$		0			0
$166$	1305.49	−	751.145i	0.610398	−	0.351206i
$167$	−175.567			−0.0813520			−0.0406760	−	0.999172i	$-0.512951\pi$
$167$	−175.567			−0.0813520			−0.0406760	+	0.999172i	$0.512951\pi$
$168$		0			0
$169$	3667.00			1.66909
$170$	4137.14	−	2380.39i	1.86650	−	1.07393i
$171$		0			0
$172$	−3394.34	−	1973.19i	−1.50474	−	0.874734i
$173$			2213.84i			0.972922i	0.873702	+	0.486461i	$0.161712\pi$
$173$			2213.84i			0.972922i	−0.873702	+	0.486461i	$0.838288\pi$
$174$		0			0
$175$		−	1129.78i		−	0.488021i
$176$	−423.580	−	743.832i	−0.181412	−	0.318571i
$177$		0			0
$178$	−197.959	−	344.053i	−0.0833575	−	0.144876i
$179$	375.089			0.156623			0.0783113	−	0.996929i	$-0.475047\pi$
$179$	375.089			0.156623			0.0783113	+	0.996929i	$0.475047\pi$
$180$		0			0
$181$	4181.94			1.71735			0.858677	−	0.512518i	$-0.171287\pi$
$181$	4181.94			1.71735			0.858677	+	0.512518i	$0.171287\pi$
$182$	−756.120	−	1314.14i	−0.307953	−	0.535224i
$183$		0			0
$184$	15.2501	−	3422.77i	0.00611007	−	1.37136i
$185$		−	325.519i		−	0.129366i
$186$		0			0
$187$		−	1333.69i		−	0.521544i
$188$	−646.766	+	1112.59i	−0.250905	+	0.431615i
$189$		0			0
$190$	−5023.23	+	2890.22i	−1.91802	+	1.10357i
$191$	4838.11			1.83284			0.916422	−	0.400213i	$-0.131064\pi$
$191$	4838.11			1.83284			0.916422	+	0.400213i	$0.131064\pi$
$192$		0			0
$193$	3237.52			1.20747			0.603736	−	0.797185i	$-0.293678\pi$
$193$	3237.52			1.20747			0.603736	+	0.797185i	$0.293678\pi$
$194$	−1598.66	+	919.826i	−0.591636	+	0.340410i
$195$		0			0
$196$	−197.008	+	338.898i	−0.0717957	+	0.123505i
$197$			1230.62i			0.445065i	0.974925	+	0.222533i	$0.0714324\pi$
$197$			1230.62i			0.445065i	−0.974925	+	0.222533i	$0.928568\pi$
$198$		0			0
$199$			3859.75i			1.37493i	0.726219	+	0.687463i	$0.241276\pi$
$199$			3859.75i			1.37493i	−0.726219	+	0.687463i	$0.758724\pi$
$200$	16.2713	−	3651.98i	0.00575279	−	1.29117i
$201$		0			0
$202$	−393.518	−	683.937i	−0.137068	−	0.238226i
$203$	1380.94			0.477454
$204$		0			0
$205$	2192.18			0.746872
$206$	1021.64	+	1775.62i	0.345539	+	0.600548i
$207$		0			0
$208$	−2425.20	−	4258.80i	−0.808449	−	1.41968i
$209$			1619.33i			0.535940i
$210$		0			0
$211$		−	4289.47i		−	1.39952i	−0.714377	−	0.699762i	$-0.753290\pi$
$211$		−	4289.47i		−	1.39952i	0.714377	−	0.699762i	$-0.246710\pi$
$212$	−877.567	−	510.145i	−0.284300	−	0.165268i
$213$		0			0
$214$	4401.03	−	2532.23i	1.40583	−	0.808876i
$215$	−8305.52			−2.63457
$216$		0			0
$217$	1880.16			0.588175
$218$	−2147.02	+	1235.34i	−0.667040	+	0.383796i
$219$		0			0
$220$	−1565.46	−	910.031i	−0.479743	−	0.278883i
$221$		−	7635.99i		−	2.32422i
$222$		0			0
$223$		−	300.813i		−	0.0903315i	−0.998980	−	0.0451657i	$-0.985618\pi$
$223$		−	300.813i		−	0.0903315i	0.998980	−	0.0451657i	$-0.0143816\pi$
$224$	−641.699	+	1092.64i	−0.191408	+	0.325914i
$225$		0			0
$226$	175.860	+	305.646i	0.0517613	+	0.0899615i
$227$	−1494.92			−0.437099			−0.218550	−	0.975826i	$-0.570133\pi$
$227$	−1494.92			−0.437099			−0.218550	+	0.975826i	$0.570133\pi$
$228$		0			0
$229$	2307.12			0.665760			0.332880	−	0.942969i	$-0.391980\pi$
$229$	2307.12			0.665760			0.332880	+	0.942969i	$0.391980\pi$
$230$	−3611.00	−	6275.94i	−1.03523	−	1.79923i
$231$		0			0
$232$	4463.83	+	19.8886i	1.26321	+	0.00562823i
$233$		−	2528.85i		−	0.711033i	−0.934670	−	0.355517i	$-0.884305\pi$
$233$		−	2528.85i		−	0.711033i	0.934670	−	0.355517i	$-0.115695\pi$
$234$		0			0
$235$			2722.36i			0.755689i
$236$	1149.11	−	1976.73i	0.316952	−	0.545230i
$237$		0			0
$238$	−1711.25	+	984.606i	−0.466067	+	0.268162i
$239$	1297.89			0.351270			0.175635	−	0.984455i	$-0.443802\pi$
$239$	1297.89			0.351270			0.175635	+	0.984455i	$0.443802\pi$
$240$		0			0
$241$	4570.84			1.22172			0.610858	−	0.791740i	$-0.290825\pi$
$241$	4570.84			1.22172			0.610858	+	0.791740i	$0.290825\pi$
$242$	2824.51	−	1625.15i	0.750276	−	0.431687i
$243$		0			0
$244$	−1879.03	+	3232.37i	−0.493003	+	0.848078i
$245$			829.241i			0.216238i
$246$		0			0
$247$			9271.45i			2.38837i
$248$	6077.55	+	27.0785i	1.55615	+	0.00693341i
$249$		0			0
$250$	−868.868	−	1510.10i	−0.219808	−	0.382028i
$251$	−1024.67			−0.257676			−0.128838	−	0.991666i	$-0.541125\pi$
$251$	−1024.67			−0.257676			−0.128838	+	0.991666i	$0.541125\pi$
$252$		0			0
$253$	−2023.17			−0.502749
$254$	−433.547	−	753.507i	−0.107099	−	0.186139i
$255$		0			0
$256$	−2090.00	+	3522.66i	−0.510254	+	0.860024i
$257$			1741.37i			0.422660i	0.977415	+	0.211330i	$0.0677794\pi$
$257$			1741.37i			0.422660i	−0.977415	+	0.211330i	$0.932221\pi$
$258$		0			0
$259$			134.645i			0.0323028i
$260$	−8963.03	−	5210.37i	−2.13794	−	1.24282i
$261$		0			0
$262$	−2298.43	+	1322.45i	−0.541976	+	0.311838i
$263$	−301.560			−0.0707033			−0.0353516	−	0.999375i	$-0.511255\pi$
$263$	−301.560			−0.0707033			−0.0353516	+	0.999375i	$0.511255\pi$
$264$		0			0
$265$	−2147.29			−0.497763
$266$	2077.76	−	1195.49i	0.478932	−	0.275564i
$267$		0			0
$268$	2240.02	+	1302.16i	0.510563	+	0.296799i
$269$		−	1908.34i		−	0.432540i	−0.976334	−	0.216270i	$-0.930611\pi$
$269$		−	1908.34i		−	0.432540i	0.976334	−	0.216270i	$-0.0693892\pi$
$270$		0			0
$271$			1389.99i			0.311572i	0.987791	+	0.155786i	$0.0497910\pi$
$271$			1389.99i			0.311572i	−0.987791	+	0.155786i	$0.950209\pi$
$272$	−5545.72	+	3158.05i	−1.23625	+	0.703988i
$273$		0			0
$274$	−3679.29	−	6394.62i	−0.811218	−	1.40990i
$275$	−2158.65			−0.473351
$276$		0			0
$277$	5153.77			1.11791			0.558953	−	0.829199i	$-0.311203\pi$
$277$	5153.77			1.11791			0.558953	+	0.829199i	$0.311203\pi$
$278$	2203.76	+	3830.16i	0.475442	+	0.826322i
$279$		0			0
$280$	−11.9429	+	2680.49i	−0.00254901	+	0.572106i
$281$			4591.56i			0.974767i	0.873188	+	0.487384i	$0.162049\pi$
$281$			4591.56i			0.974767i	−0.873188	+	0.487384i	$0.837951\pi$
$282$		0			0
$283$			2376.27i			0.499134i	0.968358	+	0.249567i	$0.0802882\pi$
$283$			2376.27i			0.499134i	−0.968358	+	0.249567i	$0.919712\pi$
$284$	2709.63	−	4661.19i	0.566152	−	0.973912i
$285$		0			0
$286$	−2510.90	+	1444.70i	−0.519135	+	0.298696i
$287$	−906.756			−0.186495
$288$		0			0
$289$	−5030.44			−1.02390
$290$	8184.82	−	4709.32i	1.65734	−	0.953588i
$291$		0			0
$292$	−1359.74	+	2339.07i	−0.272510	+	0.468779i
$293$			7879.34i			1.57104i	0.618834	+	0.785522i	$0.287605\pi$
$293$			7879.34i			1.57104i	−0.618834	+	0.785522i	$0.712395\pi$
$294$		0			0
$295$		−	4836.81i		−	0.954610i
$296$	−1.93918	+	435.234i	−0.000380786	+	0.0854644i
$297$		0			0
$298$	1373.29	+	2386.79i	0.266955	+	0.463970i
$299$	−11583.6			−2.24046
$300$		0			0
$301$	3435.42			0.657855
$302$	738.840	+	1284.11i	0.140780	+	0.244676i
$303$		0			0
$304$	6733.50	−	3834.43i	1.27037	−	0.723421i
$305$			7909.19i			1.48485i
$306$		0			0
$307$		−	5548.95i		−	1.03158i	−0.856715	−	0.515790i	$-0.827498\pi$
$307$		−	5548.95i		−	1.03158i	0.856715	−	0.515790i	$-0.172502\pi$
$308$	647.525	+	376.417i	0.119793	+	0.0696376i
$309$		0			0
$310$	11143.7	−	6411.78i	2.04168	−	1.17472i
$311$	−5674.92			−1.03471			−0.517356	−	0.855771i	$-0.673084\pi$
$311$	−5674.92			−1.03471			−0.517356	+	0.855771i	$0.673084\pi$
$312$		0			0
$313$	1268.28			0.229033			0.114516	−	0.993421i	$-0.463468\pi$
$313$	1268.28			0.229033			0.114516	+	0.993421i	$0.463468\pi$
$314$	1839.96	−	1058.66i	0.330684	−	0.190266i
$315$		0			0
$316$	−6012.80	−	3495.35i	−1.07040	−	0.622243i
$317$			7346.90i			1.30171i	0.759201	+	0.650857i	$0.225590\pi$
$317$			7346.90i			1.30171i	−0.759201	+	0.650857i	$0.774410\pi$
$318$		0			0
$319$		−	2638.53i		−	0.463102i
$320$	−77.2097	+	8664.38i	−0.0134880	+	1.51360i
$321$		0			0
$322$	1493.62	+	2595.92i	0.258498	+	0.449271i
$323$	12073.1			2.07977
$324$		0			0
$325$	−12359.3			−2.10945
$326$	−1205.97	−	2095.99i	−0.204886	−	0.356093i
$327$		0			0
$328$	−2931.05	−	13.0593i	−0.493415	−	0.00219841i
$329$		−	1126.05i		−	0.188697i
$330$		0			0
$331$			7290.12i			1.21058i	0.796006	+	0.605289i	$0.206942\pi$
$331$			7290.12i			1.21058i	−0.796006	+	0.605289i	$0.793058\pi$
$332$	−2140.99	+	3682.99i	−0.353922	+	0.608827i
$333$		0			0
$334$	430.418	−	247.650i	0.0705132	−	0.0405713i
$335$	5481.05			0.893915
$336$		0			0
$337$	1542.25			0.249292			0.124646	−	0.992201i	$-0.460220\pi$
$337$	1542.25			0.249292			0.124646	+	0.992201i	$0.460220\pi$
$338$	−8989.97	+	5172.58i	−1.44672	+	0.832400i
$339$		0			0
$340$	−6784.84	+	11671.5i	−1.08223	+	1.86169i
$341$		−	3592.38i		−	0.570494i
$342$		0			0
$343$		−	343.000i		−	0.0539949i
$344$	11104.8	+	49.4776i	1.74050	+	0.00775480i
$345$		0			0
$346$	−3122.79	−	5427.43i	−0.485209	−	0.843296i
$347$	11622.0			1.79798			0.898991	−	0.437967i	$-0.144301\pi$
$347$	11622.0			1.79798			0.898991	+	0.437967i	$0.144301\pi$
$348$		0			0
$349$	−6684.51			−1.02525			−0.512627	−	0.858612i	$-0.671328\pi$
$349$	−6684.51			−1.02525			−0.512627	+	0.858612i	$0.671328\pi$
$350$	1593.64	+	2769.76i	0.243382	+	0.423000i
$351$		0			0
$352$	2087.67	+	1226.08i	0.316118	+	0.185654i
$353$		−	12023.6i		−	1.81290i	−0.422318	−	0.906448i	$-0.638783\pi$
$353$		−	12023.6i		−	1.81290i	0.422318	−	0.906448i	$-0.361217\pi$
$354$		0			0
$355$		−	11405.3i		−	1.70516i
$356$	970.626	+	564.242i	0.144503	+	0.0840021i
$357$		0			0
$358$	−919.563	+	529.091i	−0.135755	+	0.0781098i
$359$	12797.3			1.88139			0.940693	−	0.339259i	$-0.110176\pi$
$359$	12797.3			1.88139			0.940693	+	0.339259i	$0.110176\pi$
$360$		0			0
$361$	−7799.91			−1.13718
$362$	−10252.4	+	5898.93i	−1.48855	+	0.856467i
$363$		0			0
$364$	3707.39	+	2155.17i	0.533846	+	0.310334i
$365$			5723.40i			0.820757i
$366$		0			0
$367$			8198.88i			1.16615i	0.812417	+	0.583077i	$0.198151\pi$
$367$			8198.88i			1.16615i	−0.812417	+	0.583077i	$0.801849\pi$
$368$	4790.68	+	8412.72i	0.678618	+	1.19169i
$369$		0			0
$370$	459.169	+	798.039i	0.0645164	+	0.112130i
$371$	888.188			0.124292
$372$		0			0
$373$	9525.95			1.32235			0.661173	−	0.750233i	$-0.270059\pi$
$373$	9525.95			1.32235			0.661173	+	0.750233i	$0.270059\pi$
$374$	1881.26	+	3269.65i	0.260101	+	0.452057i
$375$		0			0
$376$	16.2176	−	3639.91i	0.00222436	−	0.499240i
$377$		−	15106.9i		−	2.06377i
$378$		0			0
$379$		−	6367.72i		−	0.863029i	−0.902106	−	0.431514i	$-0.857979\pi$
$379$		−	6367.72i		−	0.863029i	0.902106	−	0.431514i	$-0.142021\pi$
$380$	8238.01	−	14171.3i	1.11211	−	1.91308i
$381$		0			0
$382$	−11861.0	+	6824.51i	−1.58865	+	0.914064i
$383$	3297.28			0.439904			0.219952	−	0.975511i	$-0.429410\pi$
$383$	3297.28			0.439904			0.219952	+	0.975511i	$0.429410\pi$
$384$		0			0
$385$	1584.41			0.209738
$386$	−7937.07	+	4566.76i	−1.04660	+	0.602182i
$387$		0			0
$388$	2621.78	−	4510.07i	0.343043	−	0.590113i
$389$		−	5144.42i		−	0.670521i	−0.942126	−	0.335260i	$-0.891176\pi$
$389$		−	5144.42i		−	0.670521i	0.942126	−	0.335260i	$-0.108824\pi$
$390$		0			0
$391$			15083.9i			1.95097i
$392$	4.93995	−	1108.73i	0.000636493	−	0.142856i
$393$		0			0
$394$	−1735.88	−	3016.96i	−0.221960	−	0.385768i
$395$	−14712.6			−1.87410
$396$		0			0
$397$	−8910.58			−1.12647			−0.563236	−	0.826296i	$-0.690444\pi$
$397$	−8910.58			−1.12647			−0.563236	+	0.826296i	$0.690444\pi$
$398$	−5444.46	−	9462.51i	−0.685694	−	1.19174i
$399$		0			0
$400$	5111.49	+	8976.09i	0.638936	+	1.12201i
$401$			604.478i			0.0752772i	0.999291	+	0.0376386i	$0.0119836\pi$
$401$			604.478i			0.0752772i	−0.999291	+	0.0376386i	$0.988016\pi$
$402$		0			0
$403$		−	20568.1i		−	2.54236i
$404$	1929.49	+	1121.65i	0.237613	+	0.138129i
$405$		0			0
$406$	−3385.50	+	1947.92i	−0.413841	+	0.238113i
$407$	257.263			0.0313318
$408$		0			0
$409$	−907.703			−0.109738			−0.0548692	−	0.998494i	$-0.517474\pi$
$409$	−907.703			−0.109738			−0.0548692	+	0.998494i	$0.517474\pi$
$410$	−5374.33	+	3092.24i	−0.647364	+	0.372475i
$411$		0			0
$412$	−5009.27	−	2911.98i	−0.599003	−	0.348211i
$413$			2000.66i			0.238368i
$414$		0			0
$415$			9011.82i			1.06596i
$416$	11952.9	+	7019.89i	1.40875	+	0.827352i
$417$		0			0
$418$	−2284.19	−	3969.93i	−0.267280	−	0.464535i
$419$	3033.81			0.353726			0.176863	−	0.984235i	$-0.443405\pi$
$419$	3033.81			0.353726			0.176863	+	0.984235i	$0.443405\pi$
$420$		0			0
$421$	4435.93			0.513525			0.256762	−	0.966475i	$-0.417344\pi$
$421$	4435.93			0.513525			0.256762	+	0.966475i	$0.417344\pi$
$422$	6050.62	+	10516.0i	0.697961	+	1.21306i
$423$		0			0
$424$	2871.03	+	12.7918i	0.328843	+	0.00146516i
$425$			16094.1i			1.83689i
$426$		0			0
$427$		−	3271.49i		−	0.370769i
$428$	−7217.61	+	12416.0i	−0.815132	+	1.40221i
$429$		0			0
$430$	20361.7	−	11715.5i	2.28355	−	1.31389i
$431$	13504.0			1.50919			0.754597	−	0.656189i	$-0.227832\pi$
$431$	13504.0			1.50919			0.754597	+	0.656189i	$0.227832\pi$
$432$		0			0
$433$	−10790.3			−1.19757			−0.598785	−	0.800909i	$-0.704350\pi$
$433$	−10790.3			−1.19757			−0.598785	+	0.800909i	$0.704350\pi$
$434$	−4609.39	+	2652.11i	−0.509810	+	0.293330i
$435$		0			0
$436$	3521.08	−	6057.07i	0.386764	−	0.665324i
$437$		−	18314.6i		−	2.00482i
$438$		0			0
$439$			106.231i			0.0115493i	0.999983	+	0.00577465i	$0.00183814\pi$
$439$			106.231i			0.0115493i	−0.999983	+	0.00577465i	$0.998162\pi$
$440$	5121.54	+	22.8190i	0.554908	+	0.00247239i
$441$		0			0
$442$	10771.1	+	18720.3i	1.15912	+	2.01456i
$443$	−3711.65			−0.398072			−0.199036	−	0.979992i	$-0.563781\pi$
$443$	−3711.65			−0.398072			−0.199036	+	0.979992i	$0.563781\pi$
$444$		0			0
$445$	2375.00			0.253002
$446$	424.319	+	737.469i	0.0450495	+	0.0782963i
$447$		0			0
$448$	31.9363	−	3583.86i	0.00336797	−	0.377949i
$449$			1890.30i			0.198683i	0.995053	+	0.0993416i	$0.0316737\pi$
$449$			1890.30i			0.198683i	−0.995053	+	0.0993416i	$0.968326\pi$
$450$		0			0
$451$			1732.52i			0.180889i
$452$	−862.273	−	501.255i	−0.0897299	−	0.0521616i
$453$		0			0
$454$	3664.93	−	2108.70i	0.378863	−	0.217987i
$455$	9071.51			0.934679
$456$		0			0
$457$	−13254.0			−1.35667			−0.678335	−	0.734753i	$-0.737298\pi$
$457$	−13254.0			−1.35667			−0.678335	+	0.734753i	$0.737298\pi$
$458$	−5656.12	+	3254.37i	−0.577059	+	0.332023i
$459$		0			0
$460$	17705.4	+	10292.4i	1.79460	+	1.04323i
$461$			8351.60i			0.843758i	0.906652	+	0.421879i	$0.138629\pi$
$461$			8351.60i			0.843758i	−0.906652	+	0.421879i	$0.861371\pi$
$462$		0			0
$463$		−	3464.82i		−	0.347783i	−0.984765	−	0.173892i	$-0.944366\pi$
$463$		−	3464.82i		−	0.347783i	0.984765	−	0.173892i	$-0.0556343\pi$
$464$	−10971.5	+	6247.81i	−1.09772	+	0.625102i
$465$		0			0
$466$	3567.14	+	6199.71i	0.354602	+	0.616300i
$467$	−11041.6			−1.09410			−0.547050	−	0.837100i	$-0.684249\pi$
$467$	−11041.6			−1.09410			−0.547050	+	0.837100i	$0.684249\pi$
$468$		0			0
$469$	−2267.13			−0.223212
$470$	−3840.08	−	6674.09i	−0.376872	−	0.655006i
$471$		0			0
$472$	−28.8138	+	6467.03i	−0.00280988	+	0.630655i
$473$		−	6563.97i		−	0.638080i
$474$		0			0
$475$		−	19541.1i		−	1.88759i
$476$	2806.42	−	4827.69i	0.270236	−	0.464868i
$477$		0			0
$478$	−3181.89	+	1830.77i	−0.304469	+	0.175183i
$479$	−9513.02			−0.907434			−0.453717	−	0.891146i	$-0.649902\pi$
$479$	−9513.02			−0.907434			−0.453717	+	0.891146i	$0.649902\pi$
$480$		0			0
$481$	1472.95			0.139628
$482$	−11205.8	+	6447.50i	−1.05894	+	0.609286i
$483$		0			0
$484$	−4632.16	+	7968.37i	−0.435026	+	0.748345i
$485$		−	11035.6i		−	1.03319i
$486$		0			0
$487$			13942.4i			1.29731i	0.761083	+	0.648654i	$0.224668\pi$
$487$			13942.4i			1.29731i	−0.761083	+	0.648654i	$0.775332\pi$
$488$	47.1166	−	10574.9i	0.00437063	−	0.980953i
$489$		0			0
$490$	−1169.71	−	2032.96i	−0.107841	−	0.187428i
$491$	−14369.5			−1.32075			−0.660374	−	0.750937i	$-0.729602\pi$
$491$	−14369.5			−1.32075			−0.660374	+	0.750937i	$0.729602\pi$
$492$		0			0
$493$	−19671.9			−1.79711
$494$	−13078.1	−	22729.8i	−1.19111	−	2.07016i
$495$		0			0
$496$	−14937.8	+	8506.45i	−1.35228	+	0.770062i
$497$			4717.61i			0.425782i
$498$		0			0
$499$		−	19456.7i		−	1.74550i	−0.488170	−	0.872748i	$-0.662336\pi$
$499$		−	19456.7i		−	1.74550i	0.488170	−	0.872748i	$-0.337664\pi$
$500$	4260.21	+	2476.54i	0.381045	+	0.221508i
$501$		0			0
$502$	2512.07	−	1445.37i	0.223345	−	0.128506i
$503$	10617.9			0.941212			0.470606	−	0.882344i	$-0.344035\pi$
$503$	10617.9			0.941212			0.470606	+	0.882344i	$0.344035\pi$
$504$		0			0
$505$	4721.21			0.416022
$506$	4959.97	−	2853.83i	0.435766	−	0.250727i
$507$		0			0
$508$	2125.75	+	1235.74i	0.185660	+	0.107927i
$509$		−	21010.6i		−	1.82963i	−0.403878	−	0.914813i	$-0.632338\pi$
$509$		−	21010.6i		−	1.82963i	0.403878	−	0.914813i	$-0.367662\pi$
$510$		0			0
$511$		−	2367.38i		−	0.204944i
$512$	154.848	−	11584.2i	0.0133660	−	0.999911i
$513$		0			0
$514$	−2456.33	−	4269.12i	−0.210786	−	0.366348i
$515$	−12257.1			−1.04876
$516$		0			0
$517$	−2151.52			−0.183025
$518$	−189.927	−	330.094i	−0.0161098	−	0.0279990i
$519$		0			0
$520$	29323.3	+	130.650i	2.47290	+	0.0110180i
$521$			12216.7i			1.02730i	0.857999	+	0.513652i	$0.171708\pi$
$521$			12216.7i			1.02730i	−0.857999	+	0.513652i	$0.828292\pi$
$522$		0			0
$523$			18459.0i			1.54332i	0.636035	+	0.771660i	$0.280573\pi$
$523$			18459.0i			1.54332i	−0.636035	+	0.771660i	$0.719427\pi$
$524$	3769.39	−	6484.22i	0.314249	−	0.540581i
$525$		0			0
$526$	739.300	−	425.372i	0.0612833	−	0.0352607i
$527$	−26783.4			−2.21386
$528$		0			0
$529$	10715.0			0.880658
$530$	5264.28	−	3028.92i	0.431445	−	0.248241i
$531$		0			0
$532$	−3407.50	+	5861.68i	−0.277695	+	0.477699i
$533$			9919.49i			0.806118i
$534$		0			0
$535$			30380.3i			2.45505i
$536$	−7328.40	−	32.6516i	−0.590557	−	0.00263122i
$537$		0			0
$538$	2691.85	+	4678.46i	0.215714	+	0.374912i
$539$	−655.362			−0.0523718
$540$		0			0
$541$	−741.269			−0.0589088			−0.0294544	−	0.999566i	$-0.509377\pi$
$541$	−741.269			−0.0589088			−0.0294544	+	0.999566i	$0.509377\pi$
$542$	−1960.69	−	3407.68i	−0.155385	−	0.270060i
$543$		0			0
$544$	9141.17	−	15564.9i	0.720449	−	1.22673i
$545$		−	14820.9i		−	1.16487i
$546$		0			0
$547$		−	1919.59i		−	0.150047i	−0.997182	−	0.0750236i	$-0.976097\pi$
$547$		−	1919.59i		−	0.150047i	0.997182	−	0.0750236i	$-0.0239032\pi$
$548$	18040.2	+	10487.1i	1.40627	+	0.817492i
$549$		0			0
$550$	5292.12	−	3044.94i	0.410285	−	0.236066i
$551$	23885.2			1.84672
$552$		0			0
$553$	6085.58			0.467966
$554$	−12634.9	+	7269.78i	−0.968964	+	0.557515i
$555$		0			0
$556$	−10805.4	−	6281.39i	−0.824195	−	0.479119i
$557$			2495.97i			0.189870i	0.995483	+	0.0949351i	$0.0302644\pi$
$557$			2495.97i			0.189870i	−0.995483	+	0.0949351i	$0.969736\pi$
$558$		0			0
$559$		−	37581.9i		−	2.84355i
$560$	−3751.74	−	6588.29i	−0.283107	−	0.497154i
$561$		0			0
$562$	−6476.74	−	11256.6i	−0.486129	−	0.844896i
$563$	8882.93			0.664957			0.332478	−	0.943111i	$-0.392115\pi$
$563$	8882.93			0.664957			0.332478	+	0.943111i	$0.392115\pi$
$564$		0			0
$565$	−2109.87			−0.157103
$566$	−3351.91	−	5825.64i	−0.248925	−	0.432633i
$567$		0			0
$568$	−67.9439	+	15249.5i	−0.00501912	+	1.12650i
$569$		−	21303.1i		−	1.56955i	−0.619782	−	0.784774i	$-0.712779\pi$
$569$		−	21303.1i		−	1.56955i	0.619782	−	0.784774i	$-0.287221\pi$
$570$		0			0
$571$		−	8887.19i		−	0.651344i	−0.945483	−	0.325672i	$-0.894410\pi$
$571$		−	8887.19i		−	0.651344i	0.945483	−	0.325672i	$-0.105590\pi$
$572$	4117.83	−	7083.62i	0.301006	−	0.517799i
$573$		0			0
$574$	2222.99	−	1279.05i	0.161648	−	0.0930076i
$575$	24414.3			1.77069
$576$		0			0
$577$	11307.3			0.815821			0.407911	−	0.913022i	$-0.366258\pi$
$577$	11307.3			0.815821			0.407911	+	0.913022i	$0.366258\pi$
$578$	12332.6	−	7095.81i	0.887486	−	0.510634i
$579$		0			0
$580$	−13423.0	+	23090.6i	−0.960963	+	1.65308i
$581$		−	3727.57i		−	0.266171i
$582$		0			0
$583$		−	1697.04i		−	0.120556i
$584$	34.0954	−	7652.44i	0.00241589	−	0.542227i
$585$		0			0
$586$	−11114.4	−	19316.9i	−0.783500	−	1.36173i
$587$	−9103.44			−0.640101			−0.320051	−	0.947400i	$-0.603700\pi$
$587$	−9103.44			−0.640101			−0.320051	+	0.947400i	$0.603700\pi$
$588$		0			0
$589$	32519.9			2.27497
$590$	6822.68	+	11857.9i	0.476077	+	0.827425i
$591$		0			0
$592$	−609.175	−	1069.75i	−0.0422922	−	0.0742676i
$593$		−	15942.3i		−	1.10400i	−0.833843	−	0.552001i	$-0.813864\pi$
$593$		−	15942.3i		−	1.10400i	0.833843	−	0.552001i	$-0.186136\pi$
$594$		0			0
$595$		−	11812.8i		−	0.813909i
$596$	−6733.48	−	3914.29i	−0.462776	−	0.269020i
$597$		0			0
$598$	28398.2	−	16339.5i	1.94196	−	1.11735i
$599$	3596.97			0.245356			0.122678	−	0.992447i	$-0.460852\pi$
$599$	3596.97			0.245356			0.122678	+	0.992447i	$0.460852\pi$
$600$		0			0
$601$	26215.0			1.77926			0.889628	−	0.456685i	$-0.150963\pi$
$601$	26215.0			1.77926			0.889628	+	0.456685i	$0.150963\pi$
$602$	−8422.24	+	4845.92i	−0.570207	+	0.328081i
$603$		0			0
$604$	−3622.66	−	2105.92i	−0.244046	−	0.141868i
$605$			19497.6i			1.31023i
$606$		0			0
$607$			6327.71i			0.423120i	0.977365	+	0.211560i	$0.0678543\pi$
$607$			6327.71i			0.423120i	−0.977365	+	0.211560i	$0.932146\pi$
$608$	−11099.0	+	18898.5i	−0.740336	+	1.26059i
$609$		0			0
$610$	−11156.5	−	19390.1i	−0.740514	−	1.28702i
$611$	−12318.5			−0.815634
$612$		0			0
$613$	−10716.6			−0.706097			−0.353049	−	0.935605i	$-0.614855\pi$
$613$	−10716.6			−0.706097			−0.353049	+	0.935605i	$0.614855\pi$
$614$	7827.20	+	13603.7i	0.514463	+	0.894140i
$615$		0			0
$616$	−2118.43	−	9.43864i	−0.138562	−	0.000617360i
$617$		−	16029.5i		−	1.04591i	−0.852362	−	0.522953i	$-0.824830\pi$
$617$		−	16029.5i		−	1.04591i	0.852362	−	0.522953i	$-0.175170\pi$
$618$		0			0
$619$			25672.9i			1.66701i	0.552508	+	0.833507i	$0.313671\pi$
$619$			25672.9i			1.66701i	−0.552508	+	0.833507i	$0.686329\pi$
$620$	−18275.5	+	31438.1i	−1.18381	+	2.03642i
$621$		0			0
$622$	13912.6	−	8004.89i	0.896854	−	0.516024i
$623$	−982.373			−0.0631749
$624$		0			0
$625$	−9750.51			−0.624033
$626$	−3109.29	+	1789.00i	−0.198518	+	0.114222i
$627$		0			0
$628$	−3017.50	+	5190.79i	−0.191738	+	0.329833i
$629$		−	1918.05i		−	0.121586i
$630$		0			0
$631$		−	18266.6i		−	1.15243i	−0.817299	−	0.576214i	$-0.804529\pi$
$631$		−	18266.6i		−	1.15243i	0.817299	−	0.576214i	$-0.195471\pi$
$632$	19671.4	+	87.6456i	1.23811	+	0.00551638i
$633$		0			0
$634$	−10363.4	−	18011.6i	−0.649182	−	1.12828i
$635$	5201.45			0.325060
$636$		0			0
$637$	−3752.26			−0.233391
$638$	3721.84	+	6468.59i	0.230955	+	0.401401i
$639$		0			0
$640$	−12032.5	−	21350.4i	−0.743164	−	1.31867i
$641$			27067.8i			1.66788i	0.551853	+	0.833941i	$0.313921\pi$
$641$			27067.8i			1.66788i	−0.551853	+	0.833941i	$0.686079\pi$
$642$		0			0
$643$			15727.5i			0.964589i	0.876009	+	0.482294i	$0.160196\pi$
$643$			15727.5i			0.964589i	−0.876009	+	0.482294i	$0.839804\pi$
$644$	−7323.49	−	4257.27i	−0.448115	−	0.260497i
$645$		0			0
$646$	−29598.3	+	17030.0i	−1.80268	+	1.03721i
$647$	14394.0			0.874631			0.437315	−	0.899308i	$-0.355929\pi$
$647$	14394.0			0.874631			0.437315	+	0.899308i	$0.355929\pi$
$648$		0			0
$649$	3822.60			0.231202
$650$	30299.9	−	17433.7i	1.82840	−	1.05201i
$651$		0			0
$652$	5913.10	+	3437.39i	0.355176	+	0.206470i
$653$			14934.3i			0.894984i	0.894288	+	0.447492i	$0.147683\pi$
$653$			14934.3i			0.894984i	−0.894288	+	0.447492i	$0.852317\pi$
$654$		0			0
$655$		−	15866.1i		−	0.946471i
$656$	7204.14	−	4102.45i	0.428772	−	0.244167i
$657$		0			0
$658$	1588.38	+	2760.61i	0.0941056	+	0.163556i
$659$	5165.25			0.305325			0.152663	−	0.988278i	$-0.451215\pi$
$659$	5165.25			0.305325			0.152663	+	0.988278i	$0.451215\pi$
$660$		0			0
$661$	−30379.4			−1.78763			−0.893814	−	0.448438i	$-0.851981\pi$
$661$	−30379.4			−1.78763			−0.893814	+	0.448438i	$0.851981\pi$
$662$	−10283.3	−	17872.4i	−0.603731	−	1.04929i
$663$		0			0
$664$	53.6851	−	12049.2i	0.00313763	−	0.704216i
$665$			14342.8i			0.836375i
$666$		0			0
$667$			29841.7i			1.73235i
$668$	−705.878	+	1214.27i	−0.0408851	+	0.0703317i
$669$		0			0
$670$	−13437.3	+	7731.42i	−0.774816	+	0.445807i
$671$	−6250.75			−0.359624
$672$		0			0
$673$	−27648.0			−1.58358			−0.791791	−	0.610792i	$-0.790851\pi$
$673$	−27648.0			−1.58358			−0.791791	+	0.610792i	$0.790851\pi$
$674$	−3780.95	+	2175.45i	−0.216078	+	0.124325i
$675$		0			0
$676$	14743.4	−	25362.0i	0.838837	−	1.44299i
$677$			23696.2i			1.34523i	0.739994	+	0.672614i	$0.234828\pi$
$677$			23696.2i			1.34523i	−0.739994	+	0.672614i	$0.765172\pi$
$678$		0			0
$679$			4564.65i			0.257990i
$680$	170.129	−	38184.2i	0.00959436	−	2.15338i
$681$		0			0
$682$	5067.32	+	8807.04i	0.284513	+	0.494485i
$683$	−13246.1			−0.742092			−0.371046	−	0.928615i	$-0.621001\pi$
$683$	−13246.1			−0.742092			−0.371046	+	0.928615i	$0.621001\pi$
$684$		0			0
$685$	44142.0			2.46216
$686$	483.827	+	840.894i	0.0269280	+	0.0468010i
$687$		0			0
$688$	−27294.3	+	15542.9i	−1.51248	+	0.861291i
$689$		−	9716.37i		−	0.537248i
$690$		0			0
$691$			19929.8i			1.09720i	0.836084	+	0.548601i	$0.184839\pi$
$691$			19929.8i			1.09720i	−0.836084	+	0.548601i	$0.815161\pi$
$692$	15311.6	+	8900.90i	0.841126	+	0.488961i
$693$		0			0
$694$	−28492.3	+	16393.6i	−1.55843	+	0.896678i
$695$	−26439.5			−1.44303
$696$		0			0
$697$	12917.0			0.701959
$698$	16387.7	−	9428.99i	0.888656	−	0.511308i
$699$		0			0
$700$	−7813.91	−	4542.36i	−0.421912	−	0.245265i
$701$		−	11158.7i		−	0.601226i	−0.953746	−	0.300613i	$-0.902809\pi$
$701$		−	11158.7i		−	0.601226i	0.953746	−	0.300613i	$-0.0971913\pi$
$702$		0			0
$703$			2328.86i			0.124942i
$704$	−6847.59	−	61.0200i	−0.366588	−	0.00326673i
$705$		0			0
$706$	16960.2	+	29476.9i	0.904115	+	1.57136i
$707$	−1952.84			−0.103881
$708$		0			0
$709$	31413.7			1.66399			0.831994	−	0.554784i	$-0.187199\pi$
$709$	31413.7			1.66399			0.831994	+	0.554784i	$0.187199\pi$
$710$	16088.1	+	27961.2i	0.850388	+	1.47798i
$711$		0			0
$712$	−3175.48	−	14.1483i	−0.167143	−	0.000744706i
$713$			40629.8i			2.13408i
$714$		0			0
$715$		−	17332.7i		−	0.906583i
$716$	1508.07	−	2594.22i	0.0787139	−	0.135406i
$717$		0			0
$718$	−31373.8	+	18051.6i	−1.63072	+	0.938272i
$719$	26970.8			1.39894			0.699472	−	0.714660i	$-0.253419\pi$
$719$	26970.8			1.39894			0.699472	+	0.714660i	$0.253419\pi$
$720$		0			0
$721$	5069.90			0.261877
$722$	19122.2	−	11002.4i	0.985669	−	0.567126i
$723$		0			0
$724$	16813.7	−	28923.5i	0.863090	−	1.48471i
$725$			31840.1i			1.63105i
$726$		0			0
$727$			30262.1i			1.54382i	0.635732	+	0.771910i	$0.280699\pi$
$727$			30262.1i			1.54382i	−0.635732	+	0.771910i	$0.719301\pi$
$728$	−12129.0	−	54.0408i	−0.617488	−	0.00275121i
$729$		0			0
$730$	−8073.28	−	14031.4i	−0.409323	−	0.711405i
$731$	−48938.5			−2.47613
$732$		0			0
$733$	−24635.9			−1.24140			−0.620702	−	0.784047i	$-0.713152\pi$
$733$	−24635.9			−1.24140			−0.620702	+	0.784047i	$0.713152\pi$
$734$	−11565.1	−	20100.3i	−0.581576	−	1.01078i
$735$		0			0
$736$	−23611.5	−	13866.9i	−1.18252	−	0.694486i
$737$			4331.75i			0.216502i
$738$		0			0
$739$		−	3397.12i		−	0.169100i	−0.996419	−	0.0845501i	$-0.973055\pi$
$739$		−	3397.12i		−	0.169100i	0.996419	−	0.0845501i	$-0.0269453\pi$
$740$	−2251.39	−	1308.77i	−0.111841	−	0.0650153i
$741$		0			0
$742$	−2177.47	+	1252.86i	−0.107732	+	0.0619862i
$743$	23215.4			1.14629			0.573143	−	0.819455i	$-0.305724\pi$
$743$	23215.4			1.14629			0.573143	+	0.819455i	$0.305724\pi$
$744$		0			0
$745$	−16476.0			−0.810246
$746$	−23353.7	+	13437.1i	−1.14617	+	0.659472i
$747$		0			0
$748$	−9224.15	−	5362.16i	−0.450894	−	0.262112i
$749$		−	12566.2i		−	0.613030i
$750$		0			0
$751$		−	18025.4i		−	0.875840i	−0.899014	−	0.437920i	$-0.855715\pi$
$751$		−	18025.4i		−	0.875840i	0.899014	−	0.437920i	$-0.144285\pi$
$752$	5094.61	+	8946.44i	0.247049	+	0.433834i
$753$		0			0
$754$	21309.4	+	37035.8i	1.02923	+	1.78881i
$755$	−8864.19			−0.427286
$756$		0			0
$757$	14686.1			0.705121			0.352561	−	0.935789i	$-0.385311\pi$
$757$	14686.1			0.705121			0.352561	+	0.935789i	$0.385311\pi$
$758$	8982.15	+	15611.0i	0.430404	+	0.748045i
$759$		0			0
$760$	−206.567	+	46362.4i	−0.00985920	+	2.21282i
$761$			16534.6i			0.787618i	0.919192	+	0.393809i	$0.128843\pi$
$761$			16534.6i			0.787618i	−0.919192	+	0.393809i	$0.871157\pi$
$762$		0			0
$763$			6130.38i			0.290871i
$764$	19451.9	−	33461.8i	0.921133	−	1.58456i
$765$		0			0
$766$	−8083.58	+	4651.06i	−0.381294	+	0.219386i
$767$	21886.3			1.03033
$768$		0			0
$769$	−12385.9			−0.580816			−0.290408	−	0.956903i	$-0.593791\pi$
$769$	−12385.9			−0.580816			−0.290408	+	0.956903i	$0.593791\pi$
$770$	−3884.32	+	2234.93i	−0.181794	+	0.104599i
$771$		0			0
$772$	13016.7	−	22391.6i	0.606839	−	1.04390i
$773$		−	5344.00i		−	0.248655i	−0.992241	−	0.124328i	$-0.960323\pi$
$773$		−	5344.00i		−	0.248655i	0.992241	−	0.124328i	$-0.0396774\pi$
$774$		0			0
$775$			43350.6i			2.00929i
$776$	−65.7409	+	14755.0i	−0.00304119	+	0.682571i
$777$		0			0
$778$	7256.59	+	12612.0i	0.334397	+	0.581185i
$779$	−15683.5			−0.721335
$780$		0			0
$781$	9013.82			0.412983
$782$	−21277.0	−	36979.6i	−0.972973	−	1.69103i
$783$		0			0
$784$	1551.84	+	2725.12i	0.0706924	+	0.124140i
$785$			12701.2i			0.577485i
$786$		0			0
$787$		−	1893.32i		−	0.0857554i	−0.999080	−	0.0428777i	$-0.986347\pi$
$787$		−	1893.32i		−	0.0857554i	0.999080	−	0.0428777i	$-0.0136526\pi$
$788$	8511.30	+	4947.77i	0.384775	+	0.223676i
$789$		0			0
$790$	36069.1	−	20753.2i	1.62441	−	0.934638i
$791$	872.710			0.0392288
$792$		0			0
$793$	−35788.6			−1.60263
$794$	21845.1	−	12569.0i	0.976389	−	0.561786i
$795$		0			0
$796$	26695.1	+	15518.4i	1.18867	+	0.690997i
$797$			11076.9i			0.492301i	0.969232	+	0.246151i	$0.0791658\pi$
$797$			11076.9i			0.492301i	−0.969232	+	0.246151i	$0.920834\pi$
$798$		0			0
$799$			16040.9i			0.710245i
$800$	−25192.7	−	14795.5i	−1.11337	−	0.653876i
$801$		0			0
$802$	−852.660	−	1481.93i	−0.0375418	−	0.0652478i
$803$	−4523.29			−0.198784
$804$		0			0
$805$	−17919.6			−0.784577
$806$	29012.9	+	50424.6i	1.26791	+	2.20363i
$807$		0			0
$808$	−6312.47	−	28.1252i	−0.274842	−	0.00122455i
$809$			2577.82i			0.112029i	0.998430	+	0.0560144i	$0.0178393\pi$
$809$			2577.82i			0.112029i	−0.998430	+	0.0560144i	$0.982161\pi$
$810$		0			0
$811$			1314.23i			0.0569038i	0.999595	+	0.0284519i	$0.00905774\pi$
$811$			1314.23i			0.0569038i	−0.999595	+	0.0284519i	$0.990942\pi$
$812$	5552.16	−	9551.00i	0.239954	−	0.412776i
$813$		0			0
$814$	−630.702	+	362.888i	−0.0271574	+	0.0156256i
$815$	14468.6			0.621857
$816$		0			0
$817$	59420.0			2.54448
$818$	2225.31	−	1280.38i	0.0951177	−	0.0547280i
$819$		0			0
$820$	8813.81	−	15161.8i	0.375356	−	0.645698i
$821$			23769.1i			1.01041i	0.862999	+	0.505206i	$0.168584\pi$
$821$			23769.1i			1.01041i	−0.862999	+	0.505206i	$0.831416\pi$
$822$		0			0
$823$		−	26175.8i		−	1.10866i	−0.832296	−	0.554332i	$-0.812974\pi$
$823$		−	26175.8i		−	1.10866i	0.832296	−	0.554332i	$-0.187026\pi$
$824$	16388.2	+	73.0177i	0.692853	+	0.00308700i
$825$		0			0
$826$	−2822.07	−	4904.78i	−0.118877	−	0.206609i
$827$	−23138.9			−0.972935			−0.486468	−	0.873699i	$-0.661715\pi$
$827$	−23138.9			−0.972935			−0.486468	+	0.873699i	$0.661715\pi$
$828$		0			0
$829$	35835.2			1.50133			0.750667	−	0.660680i	$-0.229732\pi$
$829$	35835.2			1.50133			0.750667	+	0.660680i	$0.229732\pi$
$830$	−12711.8	−	22093.3i	−0.531608	−	0.923937i
$831$		0			0
$832$	−39205.7	−	349.369i	−1.63367	−	0.0145579i
$833$			4886.12i			0.203234i
$834$		0			0
$835$			2971.17i			0.123140i
$836$	11199.8	+	6510.62i	0.463340	+	0.269348i
$837$		0			0
$838$	−7437.64	+	4279.41i	−0.306598	+	0.176408i
$839$	14944.9			0.614964			0.307482	−	0.951554i	$-0.400514\pi$
$839$	14944.9			0.614964			0.307482	+	0.951554i	$0.400514\pi$
$840$		0			0
$841$	−14529.4			−0.595734
$842$	−10875.1	+	6257.21i	−0.445106	+	0.256102i
$843$		0			0
$844$	−29667.2	−	17246.1i	−1.20994	−	0.703358i
$845$		−	62057.7i		−	2.52645i
$846$		0			0
$847$		−	8064.82i		−	0.327167i
$848$	−7056.62	+	4018.44i	−0.285761	+	0.162729i
$849$		0			0
$850$	−22701.9	−	39456.0i	−0.916079	−	1.59215i
$851$	−2909.64			−0.117204
$852$		0			0
$853$	9080.88			0.364506			0.182253	−	0.983252i	$-0.441661\pi$
$853$	9080.88			0.364506			0.182253	+	0.983252i	$0.441661\pi$
$854$	4614.68	+	8020.34i	0.184907	+	0.321370i
$855$		0			0
$856$	180.981	−	40619.8i	0.00722641	−	1.62191i
$857$			22288.3i			0.888393i	0.895929	+	0.444197i	$0.146511\pi$
$857$			22288.3i			0.888393i	−0.895929	+	0.444197i	$0.853489\pi$
$858$		0			0
$859$			4362.16i			0.173266i	0.996240	+	0.0866328i	$0.0276107\pi$
$859$			4362.16i			0.173266i	−0.996240	+	0.0866328i	$0.972389\pi$
$860$	−33392.8	+	57443.4i	−1.32405	+	2.27768i
$861$		0			0
$862$	−33106.1	+	19048.3i	−1.30812	+	0.752655i
$863$	15689.4			0.618858			0.309429	−	0.950923i	$-0.399862\pi$
$863$	15689.4			0.618858			0.309429	+	0.950923i	$0.399862\pi$
$864$		0			0
$865$	37465.5			1.47268
$866$	26453.3	−	15220.5i	1.03802	−	0.597245i
$867$		0			0
$868$	7559.32	−	13003.8i	0.295599	−	0.508498i
$869$		−	11627.6i		−	0.453899i
$870$		0			0
$871$			24801.4i			0.964825i
$872$	−88.2909	+	19816.2i	−0.00342879	+	0.769565i
$873$		0			0
$874$	25834.1	+	44899.8i	0.999830	+	1.73771i
$875$	−4311.77			−0.166588
$876$		0			0
$877$	−27444.7			−1.05672			−0.528358	−	0.849021i	$-0.677192\pi$
$877$	−27444.7			−1.05672			−0.528358	+	0.849021i	$0.677192\pi$
$878$	−149.847	−	260.435i	−0.00575979	−	0.0100106i
$879$		0			0
$880$	−12588.1	+	7168.37i	−0.482209	+	0.274597i
$881$			16731.3i			0.639832i	0.947446	+	0.319916i	$0.103655\pi$
$881$			16731.3i			0.639832i	−0.947446	+	0.319916i	$0.896345\pi$
$882$		0			0
$883$			8681.97i			0.330885i	0.986219	+	0.165443i	$0.0529053\pi$
$883$			8681.97i			0.330885i	−0.986219	+	0.165443i	$0.947095\pi$
$884$	−52812.7	−	30701.0i	−2.00937	−	1.16808i
$885$		0			0
$886$	9099.44	−	5235.56i	0.345036	−	0.198524i
$887$	7585.42			0.287140			0.143570	−	0.989640i	$-0.454142\pi$
$887$	7585.42			0.287140			0.143570	+	0.989640i	$0.454142\pi$
$888$		0			0
$889$	−2151.48			−0.0811681
$890$	−5822.52	+	3350.11i	−0.219293	+	0.126175i
$891$		0			0
$892$	−2080.51	−	1209.44i	−0.0780948	−	0.0453979i
$893$		−	19476.5i		−	0.729850i
$894$		0			0
$895$		−	6347.74i		−	0.237074i
$896$	4977.00	+	8831.19i	0.185569	+	0.329274i
$897$		0			0
$898$	−2666.41	−	4634.24i	−0.0990860	−	0.172212i
$899$	−52987.7			−1.96578
$900$		0			0
$901$	−12652.5			−0.467830
$902$	−2443.84	−	4247.41i	−0.0902118	−	0.156789i
$903$		0			0
$904$	2821.00	+	12.5689i	0.103789	+	0.000462429i
$905$		−	70772.1i		−	2.59950i
$906$		0			0
$907$		−	50795.8i		−	1.85959i	−0.368080	−	0.929794i	$-0.619985\pi$
$907$		−	50795.8i		−	1.85959i	0.368080	−	0.929794i	$-0.380015\pi$
$908$	−6010.43	+	10339.3i	−0.219673	+	0.377888i
$909$		0			0
$910$	−22239.6	+	12796.0i	−0.810149	+	0.466137i
$911$	23040.6			0.837947			0.418973	−	0.907999i	$-0.362390\pi$
$911$	23040.6			0.837947			0.418973	+	0.907999i	$0.362390\pi$
$912$		0			0
$913$	−7122.17			−0.258170
$914$	32493.4	−	18695.8i	1.17592	−	0.676589i
$915$		0			0
$916$	9275.93	−	15956.7i	0.334591	−	0.575574i
$917$			6562.70i			0.236335i
$918$		0			0
$919$		−	3161.63i		−	0.113485i	−0.998389	−	0.0567424i	$-0.981929\pi$
$919$		−	3161.63i		−	0.113485i	0.998389	−	0.0567424i	$-0.0180714\pi$
$920$	−57924.5	−	258.082i	−2.07578	−	0.00924860i
$921$		0			0
$922$	−11780.5	−	20474.7i	−0.420794	−	0.731342i
$923$	51608.5			1.84043
$924$		0			0
$925$	−3104.48			−0.110351
$926$	4887.38	+	8494.30i	0.173444	+	0.301447i
$927$		0			0
$928$	18084.7	−	30793.2i	0.639718	−	1.08926i
$929$		−	22607.2i		−	0.798403i	−0.916863	−	0.399202i	$-0.869287\pi$
$929$		−	22607.2i		−	0.798403i	0.916863	−	0.399202i	$-0.130713\pi$
$930$		0			0
$931$		−	5932.63i		−	0.208844i
$932$	−17490.3	−	10167.4i	−0.614714	−	0.357344i
$933$		0			0
$934$	27069.5	−	15575.0i	0.948330	−	0.545642i
$935$	−22570.3			−0.789443
$936$		0			0
$937$	10752.2			0.374878			0.187439	−	0.982276i	$-0.439981\pi$
$937$	10752.2			0.374878			0.187439	+	0.982276i	$0.439981\pi$
$938$	5558.07	−	3197.96i	0.193473	−	0.111319i
$939$		0			0
$940$	18828.6	+	10945.4i	0.653321	+	0.379787i
$941$		−	33974.1i		−	1.17697i	−0.808510	−	0.588483i	$-0.799725\pi$
$941$		−	33974.1i		−	1.17697i	0.808510	−	0.588483i	$-0.200275\pi$
$942$		0			0
$943$		−	19594.7i		−	0.676661i
$944$	−9051.59	−	15895.1i	−0.312081	−	0.548033i
$945$		0			0
$946$	9258.97	+	16092.2i	0.318219	+	0.553067i
$947$	6432.76			0.220736			0.110368	−	0.993891i	$-0.464797\pi$
$947$	6432.76			0.220736			0.110368	+	0.993891i	$0.464797\pi$
$948$		0			0
$949$	−25898.0			−0.885864
$950$	27564.1	+	47906.6i	0.941366	+	1.63610i
$951$		0			0
$952$	−70.3708	+	15794.2i	−0.00239573	+	0.537702i
$953$		−	25913.1i		−	0.880805i	−0.897801	−	0.440402i	$-0.854836\pi$
$953$		−	25913.1i		−	0.880805i	0.897801	−	0.440402i	$-0.145164\pi$
$954$		0			0
$955$		−	81876.7i		−	2.77431i
$956$	5218.24	−	8976.58i	0.176538	−	0.303686i
$957$		0			0
$958$	23322.0	−	13418.8i	0.786534	−	0.452549i
$959$	−18258.5			−0.614806
$960$		0			0
$961$	−42352.2			−1.42165
$962$	−3611.07	+	2077.71i	−0.121025	+	0.0696341i
$963$		0			0
$964$	18377.3	−	31613.2i	0.613998	−	1.05622i
$965$		−	54789.5i		−	1.82771i
$966$		0			0
$967$			37738.1i			1.25499i	0.778621	+	0.627494i	$0.215919\pi$
$967$			37738.1i			1.25499i	−0.778621	+	0.627494i	$0.784081\pi$
$968$	116.151	−	26069.2i	0.00385665	−	0.865594i
$969$		0			0
$970$	15566.5	+	27054.6i	0.515267	+	0.895538i
$971$	21658.2			0.715801			0.357901	−	0.933760i	$-0.383493\pi$
$971$	21658.2			0.715801			0.357901	+	0.933760i	$0.383493\pi$
$972$		0			0
$973$	10936.2			0.360328
$974$	−19666.7	−	34180.9i	−0.646985	−	1.12446i
$975$		0			0
$976$	14801.2	+	25991.9i	0.485426	+	0.852438i
$977$		−	7552.74i		−	0.247322i	−0.992325	−	0.123661i	$-0.960536\pi$
$977$		−	7552.74i		−	0.247322i	0.992325	−	0.123661i	$-0.0394635\pi$
$978$		0			0
$979$			1877.00i			0.0612759i
$980$	5735.27	+	3334.01i	0.186945	+	0.108675i
$981$		0			0
$982$	35228.1	−	20269.3i	1.14478	−	0.658674i
$983$	−31253.8			−1.01408			−0.507041	−	0.861922i	$-0.669261\pi$
$983$	−31253.8			−1.01408			−0.507041	+	0.861922i	$0.669261\pi$
$984$		0			0
$985$	20826.1			0.673679
$986$	48227.3	−	27748.6i	1.55768	−	0.896244i
$987$		0			0
$988$	64124.1	+	37276.4i	2.06484	+	1.20033i
$989$			74238.4i			2.38690i
$990$		0			0
$991$			50695.5i			1.62502i	0.582946	+	0.812511i	$0.301900\pi$
$991$			50695.5i			1.62502i	−0.582946	+	0.812511i	$0.698100\pi$
$992$	24622.4	−	41925.2i	0.788068	−	1.34186i
$993$		0			0
$994$	−6654.54	−	11565.6i	−0.212343	−	0.369054i
$995$	65319.6			2.08118
$996$		0			0
$997$	7967.10			0.253080			0.126540	−	0.991962i	$-0.459613\pi$
$997$	7967.10			0.253080			0.126540	+	0.991962i	$0.459613\pi$
$998$	27445.2	+	47699.9i	0.870502	+	1.51294i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.e.a.71.4	yes	36
3.2	odd	2	inner	252.4.e.a.71.33	yes	36
4.3	odd	2	inner	252.4.e.a.71.34	yes	36
12.11	even	2	inner	252.4.e.a.71.3	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.e.a.71.3	✓	36	12.11	even	2	inner
252.4.e.a.71.4	yes	36	1.1	even	1	trivial
252.4.e.a.71.33	yes	36	3.2	odd	2	inner
252.4.e.a.71.34	yes	36	4.3	odd	2	inner

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.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.45159 + 1.41057i) q^{2} +(4.02056 - 6.91629i) q^{4} -16.9233i q^{5} +7.00000i q^{7} +(-0.100815 + 22.6272i) q^{8} +O(q^{10})\)	\(q+(-2.45159 + 1.41057i) q^{2} +(4.02056 - 6.91629i) q^{4} -16.9233i q^{5} +7.00000i q^{7} +(-0.100815 + 22.6272i) q^{8} +(23.8716 + 41.4889i) q^{10} +13.3747 q^{11} +76.5768 q^{13} +(-9.87402 - 17.1611i) q^{14} +(-31.6702 - 55.6147i) q^{16} -99.7168i q^{17} +121.074i q^{19} +(-117.046 - 68.0411i) q^{20} +(-32.7893 + 18.8660i) q^{22} -151.268 q^{23} -161.398 q^{25} +(-187.735 + 108.017i) q^{26} +(48.4140 + 28.1439i) q^{28} -197.277i q^{29} -268.595i q^{31} +(156.091 + 91.6713i) q^{32} +(140.658 + 244.464i) q^{34} +118.463 q^{35} +19.2350 q^{37} +(-170.784 - 296.823i) q^{38} +(382.926 + 1.70613i) q^{40} +129.537i q^{41} -490.774i q^{43} +(53.7739 - 92.5035i) q^{44} +(370.846 - 213.375i) q^{46} -160.864 q^{47} -49.0000 q^{49} +(395.680 - 227.663i) q^{50} +(307.882 - 529.627i) q^{52} -126.884i q^{53} -226.344i q^{55} +(-158.390 - 0.705707i) q^{56} +(278.274 + 483.643i) q^{58} +285.808 q^{59} -467.355 q^{61} +(378.873 + 658.484i) q^{62} +(-511.980 - 4.56233i) q^{64} -1295.93i q^{65} +323.876i q^{67} +(-689.670 - 400.917i) q^{68} +(-290.422 + 167.101i) q^{70} +673.944 q^{71} -338.197 q^{73} +(-47.1563 + 27.1324i) q^{74} +(837.383 + 486.785i) q^{76} +93.6231i q^{77} -869.368i q^{79} +(-941.184 + 535.963i) q^{80} +(-182.721 - 317.570i) q^{82} -532.510 q^{83} -1687.54 q^{85} +(692.274 + 1203.18i) q^{86} +(-1.34838 + 302.633i) q^{88} +140.339i q^{89} +536.037i q^{91} +(-608.182 + 1046.21i) q^{92} +(394.373 - 226.911i) q^{94} +2048.97 q^{95} +652.093 q^{97} +(120.128 - 69.1181i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 24 q^{4}+O(q^{10}) \) 36 * q - 24 * q^4	\( 36 q - 24 q^{4} + 264 q^{10} - 468 q^{16} + 444 q^{22} - 900 q^{25} - 84 q^{28} - 432 q^{34} - 264 q^{37} + 1416 q^{40} + 180 q^{46} - 1764 q^{49} + 2736 q^{52} + 636 q^{58} - 3960 q^{61} + 1392 q^{64} - 504 q^{70} - 2520 q^{76} + 1032 q^{82} - 3144 q^{85} + 2748 q^{88} + 5496 q^{94}+O(q^{100}) \) 36 * q - 24 * q^4 + 264 * q^10 - 468 * q^16 + 444 * q^22 - 900 * q^25 - 84 * q^28 - 432 * q^34 - 264 * q^37 + 1416 * q^40 + 180 * q^46 - 1764 * q^49 + 2736 * q^52 + 636 * q^58 - 3960 * q^61 + 1392 * q^64 - 504 * q^70 - 2520 * q^76 + 1032 * q^82 - 3144 * q^85 + 2748 * q^88 + 5496 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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