LMFDB - Embedded newform 252.4.x.a.209.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(41,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 5, 3]))

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

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

chi := DirichletCharacter("252.41");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			209.12
Character	$\chi$	$=$	252.209
Dual form			252.4.x.a.41.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0939923 + 5.19530i) q^{3} +(-7.82452 - 13.5525i) q^{5} +(17.6225 + 5.69627i) q^{7} +(-26.9823 - 0.976636i) q^{9} +O(q^{10})$	\(q+(-0.0939923 + 5.19530i) q^{3} +(-7.82452 - 13.5525i) q^{5} +(17.6225 + 5.69627i) q^{7} +(-26.9823 - 0.976636i) q^{9} +(34.2206 + 19.7573i) q^{11} +(-55.5318 + 32.0613i) q^{13} +(71.1446 - 39.3769i) q^{15} -56.6997 q^{17} +117.055i q^{19} +(-31.2502 + 91.0188i) q^{21} +(-6.59593 + 3.80816i) q^{23} +(-59.9462 + 103.830i) q^{25} +(7.61005 - 140.090i) q^{27} +(39.8226 + 22.9916i) q^{29} +(-251.963 + 145.471i) q^{31} +(-105.861 + 175.929i) q^{33} +(-60.6891 - 283.399i) q^{35} -335.540 q^{37} +(-161.349 - 291.518i) q^{39} +(-97.3000 - 168.529i) q^{41} +(152.264 - 263.729i) q^{43} +(197.888 + 373.319i) q^{45} +(-318.029 + 550.842i) q^{47} +(278.105 + 200.765i) q^{49} +(5.32933 - 294.572i) q^{51} -274.953i q^{53} -618.365i q^{55} +(-608.134 - 11.0022i) q^{57} +(258.871 + 448.377i) q^{59} +(-142.340 - 82.1801i) q^{61} +(-469.933 - 170.909i) q^{63} +(869.019 + 501.728i) q^{65} +(368.103 + 637.573i) q^{67} +(-19.1646 - 34.6258i) q^{69} +599.619i q^{71} +214.435i q^{73} +(-533.793 - 321.198i) q^{75} +(490.510 + 543.102i) q^{77} +(-454.345 + 786.949i) q^{79} +(727.092 + 52.7039i) q^{81} +(389.923 - 675.366i) q^{83} +(443.648 + 768.420i) q^{85} +(-123.191 + 204.729i) q^{87} +443.089 q^{89} +(-1161.24 + 248.676i) q^{91} +(-732.084 - 1322.70i) q^{93} +(1586.38 - 915.896i) q^{95} +(-337.707 - 194.975i) q^{97} +(-904.056 - 566.518i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{7} + 60 q^{9}+O(q^{10}) $ 48 * q + 6 * q^7 + 60 * q^9	$ 48 q + 6 q^{7} + 60 q^{9} - 12 q^{11} + 192 q^{15} - 72 q^{21} - 408 q^{23} - 600 q^{25} - 84 q^{29} + 336 q^{37} + 36 q^{39} + 84 q^{43} + 318 q^{49} - 1812 q^{51} - 852 q^{57} - 564 q^{63} + 2964 q^{65} - 588 q^{67} + 2400 q^{77} + 204 q^{79} + 1980 q^{81} - 360 q^{85} - 1080 q^{91} + 2496 q^{93} + 300 q^{95} - 4968 q^{99}+O(q^{100}) $ 48 * q + 6 * q^7 + 60 * q^9 - 12 * q^11 + 192 * q^15 - 72 * q^21 - 408 * q^23 - 600 * q^25 - 84 * q^29 + 336 * q^37 + 36 * q^39 + 84 * q^43 + 318 * q^49 - 1812 * q^51 - 852 * q^57 - 564 * q^63 + 2964 * q^65 - 588 * q^67 + 2400 * q^77 + 204 * q^79 + 1980 * q^81 - 360 * q^85 - 1080 * q^91 + 2496 * q^93 + 300 * q^95 - 4968 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.0939923	+	5.19530i	−0.0180888	+	0.999836i
$3$	−0.0939923	+	5.19530i	−0.0180888	+	0.999836i
$4$		0			0
$5$	−7.82452	−	13.5525i	−0.699846	−	1.21217i	−0.968519	−	0.248938i	$-0.919919\pi$
$5$	−7.82452	−	13.5525i	−0.699846	−	1.21217i	0.268673	−	0.963231i	$-0.413415\pi$
$6$		0			0
$7$	17.6225	+	5.69627i	0.951526	+	0.307570i
$7$	17.6225	+	5.69627i	0.951526	+	0.307570i
$8$		0			0
$9$	−26.9823	−	0.976636i	−0.999346	−	0.0361717i
$10$		0			0
$11$	34.2206	+	19.7573i	0.937991	+	0.541549i	0.889330	−	0.457266i	$-0.151171\pi$
$11$	34.2206	+	19.7573i	0.937991	+	0.541549i	0.0486610	+	0.998815i	$0.484505\pi$
$12$		0			0
$13$	−55.5318	+	32.0613i	−1.18475	+	0.684015i	−0.957109	−	0.289730i	$-0.906435\pi$
$13$	−55.5318	+	32.0613i	−1.18475	+	0.684015i	−0.227641	+	0.973745i	$0.573101\pi$
$14$		0			0
$15$	71.1446	−	39.3769i	1.22463	−	0.677805i
$16$		0			0
$17$	−56.6997			−0.808923			−0.404462	−	0.914555i	$-0.632541\pi$
$17$	−56.6997			−0.808923			−0.404462	+	0.914555i	$0.632541\pi$
$18$		0			0
$19$			117.055i			1.41338i	0.707525	+	0.706689i	$0.249812\pi$
$19$			117.055i			1.41338i	−0.707525	+	0.706689i	$0.750188\pi$
$20$		0			0
$21$	−31.2502	+	91.0188i	−0.324731	+	0.945806i
$22$		0			0
$23$	−6.59593	+	3.80816i	−0.0597976	+	0.0345242i	−0.529601	−	0.848247i	$-0.677658\pi$
$23$	−6.59593	+	3.80816i	−0.0597976	+	0.0345242i	0.469803	+	0.882771i	$0.344325\pi$
$24$		0			0
$25$	−59.9462	+	103.830i	−0.479569	+	0.830638i
$26$		0			0
$27$	7.61005	−	140.090i	0.0542428	−	0.998528i
$28$		0			0
$29$	39.8226	+	22.9916i	0.254995	+	0.147222i	0.622049	−	0.782978i	$-0.286300\pi$
$29$	39.8226	+	22.9916i	0.254995	+	0.147222i	−0.367054	+	0.930200i	$0.619634\pi$
$30$		0			0
$31$	−251.963	+	145.471i	−1.45980	+	0.842819i	−0.999001	−	0.0446836i	$-0.985772\pi$
$31$	−251.963	+	145.471i	−1.45980	+	0.842819i	−0.460803	+	0.887502i	$0.652439\pi$
$32$		0			0
$33$	−105.861	+	175.929i	−0.558428	+	0.928042i
$34$		0			0
$35$	−60.6891	−	283.399i	−0.293095	−	1.36866i
$36$		0			0
$37$	−335.540			−1.49088			−0.745438	−	0.666575i	$-0.767759\pi$
$37$	−335.540			−1.49088			−0.745438	+	0.666575i	$0.767759\pi$
$38$		0			0
$39$	−161.349	−	291.518i	−0.662473	−	1.19693i
$40$		0			0
$41$	−97.3000	−	168.529i	−0.370627	−	0.641945i	0.619035	−	0.785363i	$-0.287524\pi$
$41$	−97.3000	−	168.529i	−0.370627	−	0.641945i	−0.989662	+	0.143419i	$0.954190\pi$
$42$		0			0
$43$	152.264	−	263.729i	0.540000	−	0.935308i	−0.458903	−	0.888486i	$-0.651757\pi$
$43$	152.264	−	263.729i	0.540000	−	0.935308i	0.998903	−	0.0468214i	$-0.0149092\pi$
$44$		0			0
$45$	197.888	+	373.319i	0.655542	+	1.23669i
$46$		0			0
$47$	−318.029	+	550.842i	−0.987006	+	1.70954i	−0.354347	+	0.935114i	$0.615297\pi$
$47$	−318.029	+	550.842i	−0.987006	+	1.70954i	−0.632659	+	0.774431i	$0.718036\pi$
$48$		0			0
$49$	278.105	+	200.765i	0.810802	+	0.585321i
$50$		0			0
$51$	5.32933	−	294.572i	0.0146325	−	0.808791i
$52$		0			0
$53$		−	274.953i		−	0.712597i	−0.934372	−	0.356299i	$-0.884039\pi$
$53$		−	274.953i		−	0.712597i	0.934372	−	0.356299i	$-0.115961\pi$
$54$		0			0
$55$		−	618.365i		−	1.51600i
$56$		0			0
$57$	−608.134	−	11.0022i	−1.41315	−	0.0255663i
$58$		0			0
$59$	258.871	+	448.377i	0.571222	+	0.989385i	0.996441	+	0.0842947i	$0.0268637\pi$
$59$	258.871	+	448.377i	0.571222	+	0.989385i	−0.425219	+	0.905090i	$0.639803\pi$
$60$		0			0
$61$	−142.340	−	82.1801i	−0.298767	−	0.172493i	0.343122	−	0.939291i	$-0.388516\pi$
$61$	−142.340	−	82.1801i	−0.298767	−	0.172493i	−0.641889	+	0.766798i	$0.721849\pi$
$62$		0			0
$63$	−469.933	−	170.909i	−0.939778	−	0.341787i
$64$		0			0
$65$	869.019	+	501.728i	1.65828	+	0.957411i
$66$		0			0
$67$	368.103	+	637.573i	0.671208	+	1.16257i	0.977562	+	0.210649i	$0.0675578\pi$
$67$	368.103	+	637.573i	0.671208	+	1.16257i	−0.306353	+	0.951918i	$0.599109\pi$
$68$		0			0
$69$	−19.1646	−	34.6258i	−0.0334369	−	0.0604123i
$70$		0			0
$71$			599.619i			1.00228i	0.865367	+	0.501139i	$0.167085\pi$
$71$			599.619i			1.00228i	−0.865367	+	0.501139i	$0.832915\pi$
$72$		0			0
$73$			214.435i			0.343804i	0.985114	+	0.171902i	$0.0549913\pi$
$73$			214.435i			0.343804i	−0.985114	+	0.171902i	$0.945009\pi$
$74$		0			0
$75$	−533.793	−	321.198i	−0.821827	−	0.494516i
$76$		0			0
$77$	490.510	+	543.102i	0.725958	+	0.803796i
$78$		0			0
$79$	−454.345	+	786.949i	−0.647061	+	1.12074i	0.336761	+	0.941590i	$0.390669\pi$
$79$	−454.345	+	786.949i	−0.647061	+	1.12074i	−0.983821	+	0.179152i	$0.942665\pi$
$80$		0			0
$81$	727.092	+	52.7039i	0.997383	+	0.0722961i
$82$		0			0
$83$	389.923	−	675.366i	0.515658	−	0.893146i	−0.484177	−	0.874970i	$-0.660881\pi$
$83$	389.923	−	675.366i	0.515658	−	0.893146i	0.999835	−	0.0181755i	$-0.00578575\pi$
$84$		0			0
$85$	443.648	+	768.420i	0.566122	+	0.980552i
$86$		0			0
$87$	−123.191	+	204.729i	−0.151810	+	0.252290i
$88$		0			0
$89$	443.089			0.527723			0.263862	−	0.964561i	$-0.415004\pi$
$89$	443.089			0.527723			0.263862	+	0.964561i	$0.415004\pi$
$90$		0			0
$91$	−1161.24	+	248.676i	−1.33770	+	0.286465i
$92$		0			0
$93$	−732.084	−	1322.70i	−0.816275	−	1.47481i
$94$		0			0
$95$	1586.38	−	915.896i	1.71325	−	0.989146i
$96$		0			0
$97$	−337.707	−	194.975i	−0.353495	−	0.204090i	0.312729	−	0.949842i	$-0.398757\pi$
$97$	−337.707	−	194.975i	−0.353495	−	0.204090i	−0.666223	+	0.745752i	$0.732090\pi$
$98$		0			0
$99$	−904.056	−	566.518i	−0.917788	−	0.575124i
$100$		0			0
$101$	701.270	−	1214.63i	0.690881	−	1.19664i	−0.280669	−	0.959805i	$-0.590556\pi$
$101$	701.270	−	1214.63i	0.690881	−	1.19664i	0.971550	−	0.236836i	$-0.0761103\pi$
$102$		0			0
$103$	919.911	−	531.111i	0.880015	−	0.508077i	0.00935152	−	0.999956i	$-0.497023\pi$
$103$	919.911	−	531.111i	0.880015	−	0.508077i	0.870663	+	0.491879i	$0.163690\pi$
$104$		0			0
$105$	1478.05	−	288.661i	1.37374	−	0.268290i
$106$		0			0
$107$		−	216.811i		−	0.195887i	−0.995192	−	0.0979433i	$-0.968774\pi$
$107$		−	216.811i		−	0.195887i	0.995192	−	0.0979433i	$-0.0312264\pi$
$108$		0			0
$109$	−947.744			−0.832820			−0.416410	−	0.909177i	$-0.636712\pi$
$109$	−947.744			−0.832820			−0.416410	+	0.909177i	$0.636712\pi$
$110$		0			0
$111$	31.5381	−	1743.23i	0.0269682	−	1.49063i
$112$		0			0
$113$	1219.08	−	703.838i	1.01488	−	0.585942i	0.102265	−	0.994757i	$-0.467391\pi$
$113$	1219.08	−	703.838i	1.01488	−	0.585942i	0.912617	+	0.408815i	$0.134058\pi$
$114$		0			0
$115$	103.220	+	59.5940i	0.0836983	+	0.0483232i
$116$		0			0
$117$	1529.69	−	810.854i	1.20872	−	0.640713i
$118$		0			0
$119$	−999.190	−	322.977i	−0.769711	−	0.248800i
$120$		0			0
$121$	115.200	+	199.532i	0.0865514	+	0.149911i
$122$		0			0
$123$	884.702	−	489.662i	0.648544	−	0.358954i
$124$		0			0
$125$	−79.9306			−0.0571937
$126$		0			0
$127$	1271.11			0.888131			0.444066	−	0.895994i	$-0.353536\pi$
$127$	1271.11			0.888131			0.444066	+	0.895994i	$0.353536\pi$
$128$		0			0
$129$	1355.84	+	815.845i	0.925387	+	0.556830i
$130$		0			0
$131$	−537.201	−	930.459i	−0.358286	−	0.620569i	0.629389	−	0.777091i	$-0.283305\pi$
$131$	−537.201	−	930.459i	−0.358286	−	0.620569i	−0.987675	+	0.156521i	$0.949972\pi$
$132$		0			0
$133$	−666.774	+	2062.79i	−0.434712	+	1.34486i
$134$		0			0
$135$	−1958.10	+	992.998i	−1.24835	+	0.633064i
$136$		0			0
$137$	1303.13	+	752.364i	0.812658	+	0.469188i	0.847878	−	0.530191i	$-0.177880\pi$
$137$	1303.13	+	752.364i	0.812658	+	0.469188i	−0.0352200	+	0.999380i	$0.511213\pi$
$138$		0			0
$139$	−738.300	+	426.257i	−0.450516	+	0.260106i	−0.708048	−	0.706164i	$-0.750424\pi$
$139$	−738.300	+	426.257i	−0.450516	+	0.260106i	0.257532	+	0.966270i	$0.417091\pi$
$140$		0			0
$141$	−2831.90	−	1704.03i	−1.69141	−	1.01777i
$142$		0			0
$143$	−2533.77			−1.48171
$144$		0			0
$145$		−	719.592i		−	0.412130i
$146$		0			0
$147$	−1069.17	+	1425.97i	−0.599891	+	0.800081i
$148$		0			0
$149$	−669.901	+	386.768i	−0.368325	+	0.212653i	−0.672727	−	0.739891i	$-0.734877\pi$
$149$	−669.901	+	386.768i	−0.368325	+	0.212653i	0.304401	+	0.952544i	$0.401544\pi$
$150$		0			0
$151$	−1258.88	+	2180.44i	−0.678451	+	1.17511i	0.296997	+	0.954878i	$0.404015\pi$
$151$	−1258.88	+	2180.44i	−0.678451	+	1.17511i	−0.975447	+	0.220232i	$0.929318\pi$
$152$		0			0
$153$	1529.89	+	55.3750i	0.808394	+	0.0292601i
$154$		0			0
$155$	3942.98	+	2276.48i	2.04328	+	1.17969i
$156$		0			0
$157$	63.2586	−	36.5224i	0.0321566	−	0.0185656i	−0.483836	−	0.875159i	$-0.660757\pi$
$157$	63.2586	−	36.5224i	0.0321566	−	0.0185656i	0.515992	+	0.856593i	$0.327423\pi$
$158$		0			0
$159$	1428.46	+	25.8434i	0.712480	+	0.0128900i
$160$		0			0
$161$	−137.929	+	29.5371i	−0.0675176	+	0.0144587i
$162$		0			0
$163$	1604.80			0.771151			0.385576	−	0.922676i	$-0.374003\pi$
$163$	1604.80			0.771151			0.385576	+	0.922676i	$0.374003\pi$
$164$		0			0
$165$	3212.59	+	58.1215i	1.51576	+	0.0274227i
$166$		0			0
$167$	666.547	+	1154.49i	0.308856	+	0.534954i	0.978112	−	0.208077i	$-0.0667206\pi$
$167$	666.547	+	1154.49i	0.308856	+	0.534954i	−0.669257	+	0.743031i	$0.733387\pi$
$168$		0			0
$169$	957.352	−	1658.18i	0.435754	−	0.754749i
$170$		0			0
$171$	114.320	−	3158.41i	0.0511243	−	1.41245i
$172$		0			0
$173$	1234.93	−	2138.96i	0.542717	−	0.940014i	−0.456029	−	0.889965i	$-0.650729\pi$
$173$	1234.93	−	2138.96i	0.542717	−	0.940014i	0.998747	−	0.0500494i	$-0.0159379\pi$
$174$		0			0
$175$	−1647.84	+	1488.27i	−0.711801	+	0.642873i
$176$		0			0
$177$	−2353.79	+	1302.77i	−0.999556	+	0.553232i
$178$		0			0
$179$		−	4348.42i		−	1.81573i	−0.419261	−	0.907866i	$-0.637711\pi$
$179$		−	4348.42i		−	1.81573i	0.419261	−	0.907866i	$-0.362289\pi$
$180$		0			0
$181$			1523.82i			0.625770i	0.949791	+	0.312885i	$0.101295\pi$
$181$			1523.82i			0.625770i	−0.949791	+	0.312885i	$0.898705\pi$
$182$		0			0
$183$	440.329	−	731.776i	0.177869	−	0.295598i
$184$		0			0
$185$	2625.44	+	4547.39i	1.04338	+	1.80719i
$186$		0			0
$187$	−1940.30	−	1120.23i	−0.758763	−	0.438072i
$188$		0			0
$189$	932.096	−	2425.38i	0.358730	−	0.933441i
$190$		0			0
$191$	−3370.81	−	1946.14i	−1.27698	−	0.737266i	−0.300690	−	0.953722i	$-0.597217\pi$
$191$	−3370.81	−	1946.14i	−1.27698	−	0.737266i	−0.976292	+	0.216456i	$0.930550\pi$
$192$		0			0
$193$	−189.809	−	328.758i	−0.0707914	−	0.122614i	0.828457	−	0.560053i	$-0.189219\pi$
$193$	−189.809	−	328.758i	−0.0707914	−	0.122614i	−0.899248	+	0.437438i	$0.855886\pi$
$194$		0			0
$195$	−2688.31	+	4467.66i	−0.987251	+	1.64070i
$196$		0			0
$197$			2916.71i			1.05486i	0.849599	+	0.527429i	$0.176844\pi$
$197$			2916.71i			1.05486i	−0.849599	+	0.527429i	$0.823156\pi$
$198$		0			0
$199$		−	2913.59i		−	1.03789i	−0.854809	−	0.518943i	$-0.826326\pi$
$199$		−	2913.59i		−	1.03789i	0.854809	−	0.518943i	$-0.173674\pi$
$200$		0			0
$201$	−3346.99	+	1852.48i	−1.17452	+	0.650069i
$202$		0			0
$203$	570.807	+	632.009i	0.197354	+	0.218514i
$204$		0			0
$205$	−1522.65	+	2637.31i	−0.518764	+	0.898525i
$206$		0			0
$207$	181.693	−	96.3112i	0.0610073	−	0.0323386i
$208$		0			0
$209$	−2312.68	+	4005.68i	−0.765413	+	1.32573i
$210$		0			0
$211$	−587.128	−	1016.93i	−0.191562	−	0.331795i	0.754206	−	0.656638i	$-0.228022\pi$
$211$	−587.128	−	1016.93i	−0.191562	−	0.331795i	−0.945768	+	0.324843i	$0.894689\pi$
$212$		0			0
$213$	−3115.20	−	56.3596i	−1.00211	−	0.0181300i
$214$		0			0
$215$	−4765.56			−1.51167
$216$		0			0
$217$	−5268.87	+	1128.31i	−1.64827	+	0.352972i
$218$		0			0
$219$	−1114.05	−	20.1552i	−0.343748	−	0.00621901i
$220$		0			0
$221$	3148.63	−	1817.86i	0.958371	−	0.553316i
$222$		0			0
$223$	1611.22	+	930.237i	0.483834	+	0.279342i	0.722013	−	0.691879i	$-0.243217\pi$
$223$	1611.22	+	930.237i	0.483834	+	0.279342i	−0.238179	+	0.971221i	$0.576550\pi$
$224$		0			0
$225$	1718.89	−	2743.02i	0.509301	−	0.812748i
$226$		0			0
$227$	1240.21	−	2148.11i	0.362624	−	0.628083i	−0.625768	−	0.780009i	$-0.715214\pi$
$227$	1240.21	−	2148.11i	0.362624	−	0.628083i	0.988392	+	0.151926i	$0.0485477\pi$
$228$		0			0
$229$	2878.54	−	1661.92i	0.830651	−	0.479577i	−0.0234243	−	0.999726i	$-0.507457\pi$
$229$	2878.54	−	1661.92i	0.830651	−	0.479577i	0.854076	+	0.520149i	$0.174124\pi$
$230$		0			0
$231$	−2867.69	+	2497.30i	−0.816796	+	0.711300i
$232$		0			0
$233$			2378.25i			0.668689i	0.942451	+	0.334344i	$0.108515\pi$
$233$			2378.25i			0.668689i	−0.942451	+	0.334344i	$0.891485\pi$
$234$		0			0
$235$	9953.69			2.76301
$236$		0			0
$237$	−4045.73	−	2434.43i	−1.10885	−	0.667228i
$238$		0			0
$239$	−5257.58	+	3035.47i	−1.42295	+	0.821539i	−0.996550	−	0.0829961i	$-0.973551\pi$
$239$	−5257.58	+	3035.47i	−1.42295	+	0.821539i	−0.426398	+	0.904536i	$0.640218\pi$
$240$		0			0
$241$	3105.01	+	1792.68i	0.829923	+	0.479156i	0.853826	−	0.520558i	$-0.174276\pi$
$241$	3105.01	+	1792.68i	0.829923	+	0.479156i	−0.0239031	+	0.999714i	$0.507609\pi$
$242$		0			0
$243$	−342.154	+	3772.51i	−0.0903258	+	0.995912i
$244$		0			0
$245$	544.823	−	5339.90i	0.142071	−	1.39246i
$246$		0			0
$247$	−3752.92	−	6500.25i	−0.966772	−	1.67450i
$248$		0			0
$249$	3472.08	+	2089.25i	0.883672	+	0.531729i
$250$		0			0
$251$	4359.22			1.09622			0.548111	−	0.836406i	$-0.315347\pi$
$251$	4359.22			1.09622			0.548111	+	0.836406i	$0.315347\pi$
$252$		0			0
$253$	−300.955			−0.0747862
$254$		0			0
$255$	−4033.88	+	2232.66i	−0.990632	+	0.548292i
$256$		0			0
$257$	1621.40	+	2808.35i	0.393541	+	0.681634i	0.992914	−	0.118837i	$-0.0379165\pi$
$257$	1621.40	+	2808.35i	0.393541	+	0.681634i	−0.599372	+	0.800470i	$0.704583\pi$
$258$		0			0
$259$	−5913.05	−	1911.32i	−1.41861	−	0.458548i
$260$		0			0
$261$	−1052.05	−	659.258i	−0.249503	−	0.156349i
$262$		0			0
$263$	−302.312	−	174.540i	−0.0708796	−	0.0409223i	0.464141	−	0.885761i	$-0.346363\pi$
$263$	−302.312	−	174.540i	−0.0708796	−	0.0409223i	−0.535021	+	0.844839i	$0.679696\pi$
$264$		0			0
$265$	−3726.28	+	2151.37i	−0.863788	+	0.498708i
$266$		0			0
$267$	−41.6470	+	2301.98i	−0.00954589	+	0.527637i
$268$		0			0
$269$	−7924.66			−1.79619			−0.898095	−	0.439802i	$-0.855048\pi$
$269$	−7924.66			−1.79619			−0.898095	+	0.439802i	$0.855048\pi$
$270$		0			0
$271$			6601.56i			1.47976i	0.672737	+	0.739882i	$0.265119\pi$
$271$			6601.56i			1.47976i	−0.672737	+	0.739882i	$0.734881\pi$
$272$		0			0
$273$	−1182.80	−	6056.36i	−0.262221	−	1.34266i
$274$		0			0
$275$	−4102.79	+	2368.75i	−0.899663	+	0.519421i
$276$		0			0
$277$	2868.51	−	4968.41i	0.622210	−	1.07770i	−0.366863	−	0.930275i	$-0.619568\pi$
$277$	2868.51	−	4968.41i	0.622210	−	1.07770i	0.989073	−	0.147424i	$-0.0470983\pi$
$278$		0			0
$279$	6940.63	−	3679.07i	1.48934	−	0.789463i
$280$		0			0
$281$	−640.561	−	369.828i	−0.135988	−	0.0785128i	0.430462	−	0.902608i	$-0.358350\pi$
$281$	−640.561	−	369.828i	−0.135988	−	0.0785128i	−0.566451	+	0.824096i	$0.691684\pi$
$282$		0			0
$283$	−1367.20	+	789.355i	−0.287179	+	0.165803i	−0.636669	−	0.771137i	$-0.719688\pi$
$283$	−1367.20	+	789.355i	−0.287179	+	0.165803i	0.349490	+	0.936940i	$0.386355\pi$
$284$		0			0
$285$	4609.25	+	8327.80i	0.957994	+	1.73086i
$286$		0			0
$287$	−754.685	−	3524.14i	−0.155218	−	0.724820i
$288$		0			0
$289$	−1698.15			−0.345643
$290$		0			0
$291$	1044.70	−	1736.17i	0.210451	−	0.349745i
$292$		0			0
$293$	997.708	+	1728.08i	0.198931	+	0.344558i	0.948182	−	0.317728i	$-0.102920\pi$
$293$	997.708	+	1728.08i	0.198931	+	0.344558i	−0.749251	+	0.662286i	$0.769586\pi$
$294$		0			0
$295$	4051.08	−	7016.67i	0.799535	−	1.38483i
$296$		0			0
$297$	3028.21	−	4643.60i	0.591631	−	0.907235i
$298$		0			0
$299$	244.189	−	422.948i	0.0472301	−	0.0818050i
$300$		0			0
$301$	4185.54	−	3780.22i	0.801496	−	0.723882i
$302$		0			0
$303$	6244.48	+	3757.47i	1.18395	+	0.712413i
$304$		0			0
$305$			2572.08i			0.482875i
$306$		0			0
$307$			1713.47i			0.318543i	0.987235	+	0.159272i	$0.0509146\pi$
$307$			1713.47i			0.318543i	−0.987235	+	0.159272i	$0.949085\pi$
$308$		0			0
$309$	2672.82	+	4829.14i	0.492075	+	0.889061i
$310$		0			0
$311$	−3264.75	−	5654.71i	−0.595263	−	1.03103i	−0.993510	−	0.113748i	$-0.963714\pi$
$311$	−3264.75	−	5654.71i	−0.595263	−	1.03103i	0.398246	−	0.917278i	$-0.369619\pi$
$312$		0			0
$313$	−377.873	−	218.165i	−0.0682384	−	0.0393975i	0.465493	−	0.885052i	$-0.345877\pi$
$313$	−377.873	−	218.165i	−0.0682384	−	0.0393975i	−0.533731	+	0.845654i	$0.679211\pi$
$314$		0			0
$315$	1360.76	+	7706.03i	0.243396	+	1.37837i
$316$		0			0
$317$	1201.15	+	693.486i	0.212818	+	0.122871i	0.602621	−	0.798028i	$-0.294123\pi$
$317$	1201.15	+	693.486i	0.212818	+	0.122871i	−0.389802	+	0.920899i	$0.627457\pi$
$318$		0			0
$319$	908.501	+	1573.57i	0.159456	+	0.276185i
$320$		0			0
$321$	1126.40	+	20.3785i	0.195855	+	0.00354336i
$322$		0			0
$323$		−	6636.96i		−	1.14331i
$324$		0			0
$325$		−	7687.80i		−	1.31213i
$326$		0			0
$327$	89.0806	−	4923.82i	0.0150647	−	0.832684i
$328$		0			0
$329$	−8742.21	+	7895.64i	−1.46497	+	1.32310i
$330$		0			0
$331$	233.117	−	403.771i	0.0387108	−	0.0670491i	−0.846021	−	0.533150i	$-0.821008\pi$
$331$	233.117	−	403.771i	0.0387108	−	0.0670491i	0.884732	+	0.466101i	$0.154342\pi$
$332$		0			0
$333$	9053.64	+	327.700i	1.48990	+	0.0539275i
$334$		0			0
$335$	5760.46	−	9977.41i	0.939485	−	1.62724i
$336$		0			0
$337$	784.235	+	1358.34i	0.126766	+	0.219565i	0.922422	−	0.386184i	$-0.126207\pi$
$337$	784.235	+	1358.34i	0.126766	+	0.219565i	−0.795656	+	0.605749i	$0.792874\pi$
$338$		0			0
$339$	3542.07	+	6399.66i	0.567489	+	1.02532i
$340$		0			0
$341$	−11496.4			−1.82571
$342$		0			0
$343$	3757.29	+	5122.14i	0.591472	+	0.806326i
$344$		0			0
$345$	−319.311	+	530.657i	−0.0498293	+	0.0828105i
$346$		0			0
$347$	−4674.58	+	2698.87i	−0.723184	+	0.417530i	−0.815923	−	0.578160i	$-0.803771\pi$
$347$	−4674.58	+	2698.87i	−0.723184	+	0.417530i	0.0927396	+	0.995690i	$0.470438\pi$
$348$		0			0
$349$	2247.57	+	1297.64i	0.344727	+	0.199029i	0.662361	−	0.749185i	$-0.269555\pi$
$349$	2247.57	+	1297.64i	0.344727	+	0.199029i	−0.317633	+	0.948214i	$0.602888\pi$
$350$		0			0
$351$	4068.85	+	8023.41i	0.618744	+	1.22011i
$352$		0			0
$353$	2303.43	−	3989.65i	0.347306	−	0.601551i	−0.638464	−	0.769652i	$-0.720430\pi$
$353$	2303.43	−	3989.65i	0.347306	−	0.601551i	0.985770	+	0.168100i	$0.0537632\pi$
$354$		0			0
$355$	8126.32	−	4691.73i	1.21493	−	0.701440i
$356$		0			0
$357$	1771.88	−	5160.74i	0.262683	−	0.765085i
$358$		0			0
$359$		−	2973.15i		−	0.437095i	−0.975826	−	0.218547i	$-0.929868\pi$
$359$		−	2973.15i		−	0.437095i	0.975826	−	0.218547i	$-0.0701319\pi$
$360$		0			0
$361$	−6842.78			−0.997635
$362$		0			0
$363$	−1047.46	+	579.744i	−0.151452	+	0.0838255i
$364$		0			0
$365$	2906.12	−	1677.85i	0.416749	−	0.240610i
$366$		0			0
$367$	8243.22	+	4759.22i	1.17246	+	0.676919i	0.954258	−	0.298984i	$-0.0966479\pi$
$367$	8243.22	+	4759.22i	1.17246	+	0.676919i	0.218201	+	0.975904i	$0.429981\pi$
$368$		0			0
$369$	2460.79	+	4642.32i	0.347164	+	0.654931i
$370$		0			0
$371$	1566.20	−	4845.35i	0.219173	−	0.678054i
$372$		0			0
$373$	972.449	+	1684.33i	0.134991	+	0.233811i	0.925594	−	0.378518i	$-0.123566\pi$
$373$	972.449	+	1684.33i	0.134991	+	0.233811i	−0.790603	+	0.612329i	$0.790233\pi$
$374$		0			0
$375$	7.51285	−	415.263i	0.00103457	−	0.0571843i
$376$		0			0
$377$	−2948.56			−0.402807
$378$		0			0
$379$	4140.33			0.561147			0.280573	−	0.959833i	$-0.409475\pi$
$379$	4140.33			0.561147			0.280573	+	0.959833i	$0.409475\pi$
$380$		0			0
$381$	−119.474	+	6603.80i	−0.0160652	+	0.887986i
$382$		0			0
$383$	−549.242	−	951.316i	−0.0732767	−	0.126919i	0.827059	−	0.562115i	$-0.190012\pi$
$383$	−549.242	−	951.316i	−0.0732767	−	0.126919i	−0.900336	+	0.435196i	$0.856679\pi$
$384$		0			0
$385$	3522.37	−	10897.1i	0.466277	−	1.44252i
$386$		0			0
$387$	−4366.00	+	6967.31i	−0.573479	+	0.915163i
$388$		0			0
$389$	7971.13	+	4602.13i	1.03895	+	0.599839i	0.919536	−	0.393005i	$-0.128564\pi$
$389$	7971.13	+	4602.13i	1.03895	+	0.599839i	0.119416	+	0.992844i	$0.461898\pi$
$390$		0			0
$391$	373.987	−	215.921i	0.0483717	−	0.0279274i
$392$		0			0
$393$	4884.51	−	2703.46i	0.626949	−	0.347002i
$394$		0			0
$395$	14220.1			1.81137
$396$		0			0
$397$		−	13251.6i		−	1.67526i	−0.546237	−	0.837630i	$-0.683940\pi$
$397$		−	13251.6i		−	1.67526i	0.546237	−	0.837630i	$-0.316060\pi$
$398$		0			0
$399$	−10654.2	−	3657.98i	−1.33678	−	0.458968i
$400$		0			0
$401$	−10109.5	+	5836.72i	−1.25896	+	0.726862i	−0.972873	−	0.231340i	$-0.925689\pi$
$401$	−10109.5	+	5836.72i	−1.25896	+	0.726862i	−0.286090	+	0.958203i	$0.592356\pi$
$402$		0			0
$403$	9327.98	−	16156.5i	1.15300	−	1.99706i
$404$		0			0
$405$	−4974.88	−	10266.3i	−0.610380	−	1.25959i
$406$		0			0
$407$	−11482.4	−	6629.35i	−1.39843	−	0.807382i
$408$		0			0
$409$	−9968.20	+	5755.14i	−1.20512	+	0.695779i	−0.961690	−	0.274139i	$-0.911607\pi$
$409$	−9968.20	+	5755.14i	−1.20512	+	0.695779i	−0.243434	+	0.969917i	$0.578274\pi$
$410$		0			0
$411$	−4031.24	+	6699.45i	−0.483812	+	0.804038i
$412$		0			0
$413$	2007.87	+	9376.12i	0.239227	+	1.11712i
$414$		0			0
$415$	−12203.8			−1.44352
$416$		0			0
$417$	−2145.14	−	3875.75i	−0.251914	−	0.455148i
$418$		0			0
$419$	7814.88	+	13535.8i	0.911174	+	1.57820i	0.812408	+	0.583090i	$0.198156\pi$
$419$	7814.88	+	13535.8i	0.911174	+	1.57820i	0.0987667	+	0.995111i	$0.468510\pi$
$420$		0			0
$421$	−3771.44	+	6532.33i	−0.436600	+	0.756214i	−0.997425	−	0.0717208i	$-0.977151\pi$
$421$	−3771.44	+	6532.33i	−0.436600	+	0.756214i	0.560824	+	0.827935i	$0.310484\pi$
$422$		0			0
$423$	9119.13	−	14552.4i	1.04820	−	1.67272i
$424$		0			0
$425$	3398.93	−	5887.12i	0.387935	−	0.671922i
$426$		0			0
$427$	−2040.27	−	2259.03i	−0.231231	−	0.256023i
$428$		0			0
$429$	238.155	−	13163.7i	0.0268024	−	1.48147i
$430$		0			0
$431$			13115.9i			1.46582i	0.680324	+	0.732911i	$0.261839\pi$
$431$			13115.9i			1.46582i	−0.680324	+	0.732911i	$0.738161\pi$
$432$		0			0
$433$		−	1126.39i		−	0.125013i	−0.998045	−	0.0625065i	$-0.980091\pi$
$433$		−	1126.39i		−	0.125013i	0.998045	−	0.0625065i	$-0.0199094\pi$
$434$		0			0
$435$	3738.50	+	67.6360i	0.412062	+	0.00745494i
$436$		0			0
$437$	−445.763	−	772.083i	−0.0487957	−	0.0845166i
$438$		0			0
$439$	11682.3	+	6744.81i	1.27009	+	0.733285i	0.975004	−	0.222187i	$-0.0713195\pi$
$439$	11682.3	+	6744.81i	1.27009	+	0.733285i	0.295083	+	0.955472i	$0.404653\pi$
$440$		0			0
$441$	−7307.85	−	5688.72i	−0.789099	−	0.614266i
$442$		0			0
$443$	−7184.54	−	4147.99i	−0.770536	−	0.444869i	0.0625295	−	0.998043i	$-0.480083\pi$
$443$	−7184.54	−	4147.99i	−0.770536	−	0.444869i	−0.833066	+	0.553174i	$0.813417\pi$
$444$		0			0
$445$	−3466.96	−	6004.95i	−0.369325	−	0.639690i
$446$		0			0
$447$	−1946.41	−	3516.69i	−0.205955	−	0.372112i
$448$		0			0
$449$		−	14603.8i		−	1.53496i	−0.641075	−	0.767478i	$-0.721511\pi$
$449$		−	14603.8i		−	1.53496i	0.641075	−	0.767478i	$-0.278489\pi$
$450$		0			0
$451$		−	7689.53i		−	0.802851i
$452$		0			0
$453$	−11209.7	−	6745.20i	−1.16265	−	0.699596i
$454$		0			0
$455$	12456.3	+	13791.9i	1.28343	+	1.42104i
$456$		0			0
$457$	327.533	−	567.304i	0.0335259	−	0.0580686i	−0.848776	−	0.528753i	$-0.822660\pi$
$457$	327.533	−	567.304i	0.0335259	−	0.0580686i	0.882302	+	0.470685i	$0.155993\pi$
$458$		0			0
$459$	−431.488	+	7943.03i	−0.0438782	+	0.807732i
$460$		0			0
$461$	6136.84	−	10629.3i	0.620002	−	1.07387i	−0.369483	−	0.929238i	$-0.620465\pi$
$461$	6136.84	−	10629.3i	0.620002	−	1.07387i	0.989485	−	0.144637i	$-0.0462015\pi$
$462$		0			0
$463$	4612.44	+	7988.98i	0.462977	+	0.801900i	0.999108	−	0.0422354i	$-0.0134479\pi$
$463$	4612.44	+	7988.98i	0.462977	+	0.801900i	−0.536131	+	0.844135i	$0.680115\pi$
$464$		0			0
$465$	−12197.6	+	20271.0i	−1.21645	+	2.02160i
$466$		0			0
$467$	−14189.7			−1.40605			−0.703023	−	0.711167i	$-0.748167\pi$
$467$	−14189.7			−1.40605			−0.703023	+	0.711167i	$0.748167\pi$
$468$		0			0
$469$	2855.11	+	13332.5i	0.281102	+	1.31266i
$470$		0			0
$471$	183.799	+	332.080i	0.0179809	+	0.0324872i
$472$		0			0
$473$	10421.1	−	6016.63i	1.01303	−	0.584873i
$474$		0			0
$475$	−12153.8	−	7016.97i	−1.17401	−	0.677812i
$476$		0			0
$477$	−268.529	+	7418.86i	−0.0257759	+	0.712131i
$478$		0			0
$479$	−5260.23	+	9110.99i	−0.501766	+	0.869085i	0.498232	+	0.867044i	$0.333983\pi$
$479$	−5260.23	+	9110.99i	−0.501766	+	0.869085i	−0.999998	+	0.00204079i	$0.999350\pi$
$480$		0			0
$481$	18633.1	−	10757.8i	1.76631	−	1.01978i
$482$		0			0
$483$	−140.490	−	719.359i	−0.0132350	−	0.0677681i
$484$		0			0
$485$			6102.35i			0.571327i
$486$		0			0
$487$	19692.0			1.83230			0.916149	−	0.400838i	$-0.131281\pi$
$487$	19692.0			1.83230			0.916149	+	0.400838i	$0.131281\pi$
$488$		0			0
$489$	−150.839	+	8337.42i	−0.0139492	+	0.771025i
$490$		0			0
$491$	−585.724	+	338.168i	−0.0538358	+	0.0310821i	−0.526676	−	0.850066i	$-0.676562\pi$
$491$	−585.724	+	338.168i	−0.0538358	+	0.0310821i	0.472841	+	0.881148i	$0.343229\pi$
$492$		0			0
$493$	−2257.93	−	1303.61i	−0.206272	−	0.119091i
$494$		0			0
$495$	−603.917	+	16684.9i	−0.0548365	+	1.51501i
$496$		0			0
$497$	−3415.59	+	10566.8i	−0.308270	+	0.953693i
$498$		0			0
$499$	3095.81	+	5362.10i	0.277730	+	0.481043i	0.970820	−	0.239808i	$-0.0770845\pi$
$499$	3095.81	+	5362.10i	0.277730	+	0.481043i	−0.693090	+	0.720851i	$0.743751\pi$
$500$		0			0
$501$	−6060.59	+	3354.40i	−0.540453	+	0.299129i
$502$		0			0
$503$	−9490.52			−0.841275			−0.420638	−	0.907229i	$-0.638194\pi$
$503$	−9490.52			−0.841275			−0.420638	+	0.907229i	$0.638194\pi$
$504$		0			0
$505$	−21948.4			−1.93404
$506$		0			0
$507$	8524.78	+	5129.59i	0.746743	+	0.449336i
$508$		0			0
$509$	−6484.87	−	11232.1i	−0.564709	−	0.978104i	−0.997077	−	0.0764070i	$-0.975655\pi$
$509$	−6484.87	−	11232.1i	−0.564709	−	0.978104i	0.432368	−	0.901697i	$-0.357678\pi$
$510$		0			0
$511$	−1221.48	+	3778.88i	−0.105744	+	0.327138i
$512$		0			0
$513$	16398.1	+	890.792i	1.41130	+	0.0766655i
$514$		0			0
$515$	−14395.7	−	8311.37i	−1.23175	−	0.711151i
$516$		0			0
$517$	−21766.3	+	12566.8i	−1.85161	+	1.06902i
$518$		0			0
$519$	10996.5	+	6616.89i	0.930043	+	0.559632i
$520$		0			0
$521$	−20707.4			−1.74128			−0.870642	−	0.491917i	$-0.836296\pi$
$521$	−20707.4			−1.74128			−0.870642	+	0.491917i	$0.836296\pi$
$522$		0			0
$523$		−	10537.8i		−	0.881043i	−0.897742	−	0.440522i	$-0.854794\pi$
$523$		−	10537.8i		−	0.881043i	0.897742	−	0.440522i	$-0.145206\pi$
$524$		0			0
$525$	−7577.13	−	8700.93i	−0.629892	−	0.723314i
$526$		0			0
$527$	14286.2	−	8248.16i	1.18087	−	0.681775i
$528$		0			0
$529$	−6054.50	+	10486.7i	−0.497616	+	0.861896i
$530$		0			0
$531$	−6547.03	−	12351.1i	−0.535060	−	1.00940i
$532$		0			0
$533$	10806.5	+	6239.13i	0.878200	+	0.507029i
$534$		0			0
$535$	−2938.32	+	1696.44i	−0.237448	+	0.137090i
$536$		0			0
$537$	22591.3	+	408.718i	1.81543	+	0.0328444i
$538$		0			0
$539$	5550.35	+	12364.9i	0.443545	+	0.988115i
$540$		0			0
$541$	11394.7			0.905542			0.452771	−	0.891627i	$-0.350436\pi$
$541$	11394.7			0.905542			0.452771	+	0.891627i	$0.350436\pi$
$542$		0			0
$543$	−7916.68	−	143.227i	−0.625667	−	0.0113194i
$544$		0			0
$545$	7415.64	+	12844.3i	0.582846	+	1.00952i
$546$		0			0
$547$	−11353.1	+	19664.1i	−0.887426	+	1.53707i	−0.0445177	+	0.999009i	$0.514175\pi$
$547$	−11353.1	+	19664.1i	−0.887426	+	1.53707i	−0.842908	+	0.538058i	$0.819158\pi$
$548$		0			0
$549$	3760.41	+	2356.43i	0.292332	+	0.183187i
$550$		0			0
$551$	−2691.27	+	4661.41i	−0.208080	+	0.360404i
$552$		0			0
$553$	−12489.4	+	11279.9i	−0.960401	+	0.867399i
$554$		0			0
$555$	−23871.8	+	13212.5i	−1.82577	+	1.01052i
$556$		0			0
$557$		−	6229.16i		−	0.473857i	−0.971527	−	0.236928i	$-0.923859\pi$
$557$		−	6229.16i		−	0.473857i	0.971527	−	0.236928i	$-0.0761407\pi$
$558$		0			0
$559$			19527.1i			1.47747i
$560$		0			0
$561$	6002.31	−	9975.14i	0.451725	−	0.750714i
$562$		0			0
$563$	−1558.81	−	2699.94i	−0.116689	−	0.202112i	0.801764	−	0.597640i	$-0.203895\pi$
$563$	−1558.81	−	2699.94i	−0.116689	−	0.202112i	−0.918454	+	0.395528i	$0.870562\pi$
$564$		0			0
$565$	−19077.5	−	11014.4i	−1.42052	−	0.820139i
$566$		0			0
$567$	12513.0	+	5070.49i	0.926800	+	0.375556i
$568$		0			0
$569$	10879.4	+	6281.22i	0.801561	+	0.462781i	0.844017	−	0.536317i	$-0.180185\pi$
$569$	10879.4	+	6281.22i	0.801561	+	0.462781i	−0.0424558	+	0.999098i	$0.513518\pi$
$570$		0			0
$571$	3644.80	+	6312.98i	0.267128	+	0.462679i	0.968119	−	0.250491i	$-0.0805920\pi$
$571$	3644.80	+	6312.98i	0.267128	+	0.462679i	−0.700991	+	0.713170i	$0.747259\pi$
$572$		0			0
$573$	10427.6	−	17329.5i	0.760244	−	1.26344i
$574$		0			0
$575$		−	913.138i		−	0.0662269i
$576$		0			0
$577$			5616.75i			0.405248i	0.979257	+	0.202624i	$0.0649470\pi$
$577$			5616.75i			0.405248i	−0.979257	+	0.202624i	$0.935053\pi$
$578$		0			0
$579$	1725.84	−	955.213i	0.123875	−	0.0685618i
$580$		0			0
$581$	10718.5	−	9680.54i	0.765366	−	0.691250i
$582$		0			0
$583$	5432.31	−	9409.04i	0.385906	−	0.668410i
$584$		0			0
$585$	−22958.1	−	14386.5i	−1.62257	−	1.01677i
$586$		0			0
$587$	897.050	−	1553.74i	0.0630753	−	0.109250i	−0.832763	−	0.553629i	$-0.813242\pi$
$587$	897.050	−	1553.74i	0.0630753	−	0.109250i	0.895839	+	0.444380i	$0.146576\pi$
$588$		0			0
$589$	−17028.1	−	29493.5i	−1.19122	−	2.06325i
$590$		0			0
$591$	−15153.2	−	274.148i	−1.05469	−	0.0190811i
$592$		0			0
$593$	−16863.9			−1.16782			−0.583912	−	0.811817i	$-0.698479\pi$
$593$	−16863.9			−1.16782			−0.583912	+	0.811817i	$0.698479\pi$
$594$		0			0
$595$	3441.05	+	16068.6i	0.237091	+	1.10714i
$596$		0			0
$597$	15137.0	+	273.855i	1.03772	+	0.0187741i
$598$		0			0
$599$	−12704.3	+	7334.84i	−0.866585	+	0.500323i	−0.866212	−	0.499677i	$-0.833452\pi$
$599$	−12704.3	+	7334.84i	−0.866585	+	0.500323i	−0.000372774		1.00000i	$0.500119\pi$
$600$		0			0
$601$	854.824	+	493.533i	0.0580183	+	0.0334969i	0.528729	−	0.848791i	$-0.322669\pi$
$601$	854.824	+	493.533i	0.0580183	+	0.0334969i	−0.470710	+	0.882288i	$0.656002\pi$
$602$		0			0
$603$	−9309.60	−	17562.7i	−0.628717	−	1.18608i
$604$		0			0
$605$	1802.77	−	3122.48i	0.121145	−	0.209830i
$606$		0			0
$607$	12623.0	−	7287.87i	0.844069	−	0.487323i	−0.0145763	−	0.999894i	$-0.504640\pi$
$607$	12623.0	−	7287.87i	0.844069	−	0.487323i	0.858645	+	0.512570i	$0.171307\pi$
$608$		0			0
$609$	−3337.13	+	2906.11i	−0.222048	+	0.193369i
$610$		0			0
$611$		−	40785.7i		−	2.70051i
$612$		0			0
$613$	−20361.1			−1.34156			−0.670780	−	0.741656i	$-0.734041\pi$
$613$	−20361.1			−1.34156			−0.670780	+	0.741656i	$0.734041\pi$
$614$		0			0
$615$	−13558.5	−	8158.52i	−0.888994	−	0.534932i
$616$		0			0
$617$	−3623.21	+	2091.86i	−0.236410	+	0.136491i	−0.613526	−	0.789675i	$-0.710249\pi$
$617$	−3623.21	+	2091.86i	−0.236410	+	0.136491i	0.377116	+	0.926166i	$0.376916\pi$
$618$		0			0
$619$	24006.3	+	13860.0i	1.55879	+	0.899970i	0.997373	+	0.0724400i	$0.0230786\pi$
$619$	24006.3	+	13860.0i	1.55879	+	0.899970i	0.561421	+	0.827530i	$0.310255\pi$
$620$		0			0
$621$	483.288	+	953.001i	0.0312298	+	0.0615823i
$622$		0			0
$623$	7808.34	+	2523.96i	0.502142	+	0.162312i
$624$		0			0
$625$	8118.69	+	14062.0i	0.519596	+	0.899967i
$626$		0			0
$627$	−20593.3	−	12391.6i	−1.31167	−	0.789269i
$628$		0			0
$629$	19025.0			1.20600
$630$		0			0
$631$	6437.94			0.406165			0.203083	−	0.979162i	$-0.434904\pi$
$631$	6437.94			0.406165			0.203083	+	0.979162i	$0.434904\pi$
$632$		0			0
$633$	5338.47	−	2954.72i	0.335206	−	0.185529i
$634$		0			0
$635$	−9945.81	−	17226.7i	−0.621555	−	1.07657i
$636$		0			0
$637$	−21880.5	−	2232.43i	−1.36097	−	0.138858i
$638$		0			0
$639$	585.610	−	16179.1i	0.0362541	−	1.00162i
$640$		0			0
$641$	25430.0	+	14682.0i	1.56696	+	0.904687i	0.996520	+	0.0833510i	$0.0265622\pi$
$641$	25430.0	+	14682.0i	1.56696	+	0.904687i	0.570444	+	0.821336i	$0.306771\pi$
$642$		0			0
$643$	−951.096	+	549.116i	−0.0583321	+	0.0336781i	−0.528882	−	0.848695i	$-0.677389\pi$
$643$	−951.096	+	549.116i	−0.0583321	+	0.0336781i	0.470550	+	0.882373i	$0.344055\pi$
$644$		0			0
$645$	447.926	−	24758.5i	0.0273443	−	1.51142i
$646$		0			0
$647$	8485.25			0.515595			0.257797	−	0.966199i	$-0.417003\pi$
$647$	8485.25			0.515595			0.257797	+	0.966199i	$0.417003\pi$
$648$		0			0
$649$			20458.3i			1.23738i
$650$		0			0
$651$	−5366.70	−	27479.4i	−0.323099	−	1.65438i
$652$		0			0
$653$	2743.06	−	1583.71i	0.164386	−	0.0949085i	−0.415550	−	0.909570i	$-0.636411\pi$
$653$	2743.06	−	1583.71i	0.164386	−	0.0949085i	0.579936	+	0.814662i	$0.303077\pi$
$654$		0			0
$655$	−8406.67	+	14560.8i	−0.501490	+	0.868606i
$656$		0			0
$657$	209.425	−	5785.95i	0.0124360	−	0.343579i
$658$		0			0
$659$	13457.9	+	7769.91i	0.795516	+	0.459291i	0.841901	−	0.539632i	$-0.181437\pi$
$659$	13457.9	+	7769.91i	0.795516	+	0.459291i	−0.0463851	+	0.998924i	$0.514770\pi$
$660$		0			0
$661$	9109.85	−	5259.57i	0.536054	−	0.309491i	−0.207424	−	0.978251i	$-0.566508\pi$
$661$	9109.85	−	5259.57i	0.536054	−	0.309491i	0.743478	+	0.668760i	$0.233175\pi$
$662$		0			0
$663$	9148.41	+	16529.0i	0.535890	+	0.968223i
$664$		0			0
$665$	33173.1	−	7103.94i	1.93443	−	0.414254i
$666$		0			0
$667$	−350.222			−0.0203308
$668$		0			0
$669$	−4984.30	+	8283.32i	−0.288048	+	0.478702i
$670$		0			0
$671$	−3247.31	−	5624.51i	−0.186827	−	0.323594i
$672$		0			0
$673$	−14642.5	+	25361.6i	−0.838674	+	1.45263i	0.0523297	+	0.998630i	$0.483335\pi$
$673$	−14642.5	+	25361.6i	−0.838674	+	1.45263i	−0.891004	+	0.453996i	$0.849998\pi$
$674$		0			0
$675$	14089.3	+	9187.98i	0.803402	+	0.523919i
$676$		0			0
$677$	−2923.06	+	5062.89i	−0.165941	+	0.287419i	−0.936989	−	0.349358i	$-0.886400\pi$
$677$	−2923.06	+	5062.89i	−0.165941	+	0.287419i	0.771048	+	0.636777i	$0.219733\pi$
$678$		0			0
$679$	−4840.61	−	5359.63i	−0.273587	−	0.302921i
$680$		0			0
$681$	11043.5	+	6645.17i	0.621421	+	0.373926i
$682$		0			0
$683$			7438.18i			0.416712i	0.978053	+	0.208356i	$0.0668112\pi$
$683$			7438.18i			0.416712i	−0.978053	+	0.208356i	$0.933189\pi$
$684$		0			0
$685$		−	23547.5i		−	1.31344i
$686$		0			0
$687$	8363.64	+	15111.1i	0.464473	+	0.839190i
$688$		0			0
$689$	8815.33	+	15268.6i	0.487427	+	0.844249i
$690$		0			0
$691$	−7016.10	−	4050.75i	−0.386259	−	0.223007i	0.294279	−	0.955720i	$-0.404921\pi$
$691$	−7016.10	−	4050.75i	−0.386259	−	0.223007i	−0.680538	+	0.732713i	$0.738254\pi$
$692$		0			0
$693$	−12704.7	−	15133.2i	−0.696409	−	0.829529i
$694$		0			0
$695$	11553.7	+	6670.52i	0.630584	+	0.364068i
$696$		0			0
$697$	5516.88	+	9555.51i	0.299809	+	0.519284i
$698$		0			0
$699$	−12355.7	−	223.537i	−0.668579	−	0.0120958i
$700$		0			0
$701$		−	80.5954i		−	0.00434243i	−0.999998	−	0.00217122i	$-0.999309\pi$
$701$		−	80.5954i		−	0.00434243i	0.999998	−	0.00217122i	$-0.000691120\pi$
$702$		0			0
$703$		−	39276.5i		−	2.10717i
$704$		0			0
$705$	−935.570	+	51712.4i	−0.0499796	+	2.76256i
$706$		0			0
$707$	19277.0	−	17410.3i	1.02544	−	0.926140i
$708$		0			0
$709$	−10309.1	+	17855.8i	−0.546071	+	0.945823i	0.452467	+	0.891781i	$0.350544\pi$
$709$	−10309.1	+	17855.8i	−0.546071	+	0.945823i	−0.998539	+	0.0540423i	$0.982789\pi$
$710$		0			0
$711$	13027.8	−	20790.0i	0.687177	−	1.09660i
$712$		0			0
$713$	1107.95	−	1919.03i	0.0581952	−	0.100797i
$714$		0			0
$715$	19825.6	+	34338.9i	1.03697	+	1.79609i
$716$		0			0
$717$	−15276.0	−	27600.0i	−0.795666	−	1.43758i
$718$		0			0
$719$	−7395.39			−0.383591			−0.191795	−	0.981435i	$-0.561431\pi$
$719$	−7395.39			−0.383591			−0.191795	+	0.981435i	$0.561431\pi$
$720$		0			0
$721$	19236.5	−	4119.44i	0.993626	−	0.212782i
$722$		0			0
$723$	−9605.36	+	15963.0i	−0.494090	+	0.821120i
$724$		0			0
$725$	−4774.42	+	2756.51i	−0.244576	+	0.141206i
$726$		0			0
$727$	2335.91	+	1348.64i	0.119167	+	0.0688008i	0.558398	−	0.829573i	$-0.311416\pi$
$727$	2335.91	+	1348.64i	0.119167	+	0.0688008i	−0.439232	+	0.898374i	$0.644749\pi$
$728$		0			0
$729$	−19567.2	−	2132.18i	−0.994115	−	0.108326i
$730$		0			0
$731$	−8633.31	+	14953.3i	−0.436819	+	0.756592i
$732$		0			0
$733$	34067.8	−	19669.0i	1.71667	−	0.991122i	0.791861	−	0.610701i	$-0.209112\pi$
$733$	34067.8	−	19669.0i	1.71667	−	0.991122i	0.924813	−	0.380421i	$-0.124221\pi$
$734$		0			0
$735$	27691.2	+	3332.43i	1.38967	+	0.167236i
$736$		0			0
$737$			29090.9i			1.45397i
$738$		0			0
$739$	−16780.5			−0.835293			−0.417646	−	0.908610i	$-0.637145\pi$
$739$	−16780.5			−0.835293			−0.417646	+	0.908610i	$0.637145\pi$
$740$		0			0
$741$	34123.5	−	18886.6i	1.69171	−	0.936324i
$742$		0			0
$743$	10852.9	−	6265.91i	0.535873	−	0.309386i	−0.207532	−	0.978228i	$-0.566543\pi$
$743$	10852.9	−	6265.91i	0.535873	−	0.309386i	0.743405	+	0.668842i	$0.233210\pi$
$744$		0			0
$745$	10483.3	+	6052.54i	0.515542	+	0.297648i
$746$		0			0
$747$	−11180.6	+	17842.1i	−0.547627	+	0.873909i
$748$		0			0
$749$	1235.01	−	3820.74i	0.0602488	−	0.186391i
$750$		0			0
$751$	−5313.64	−	9203.49i	−0.258186	−	0.447190i	0.707570	−	0.706643i	$-0.249791\pi$
$751$	−5313.64	−	9203.49i	−0.258186	−	0.447190i	−0.965756	+	0.259452i	$0.916458\pi$
$752$		0			0
$753$	−409.733	+	22647.5i	−0.0198293	+	1.09604i
$754$		0			0
$755$	39400.5			1.89924
$756$		0			0
$757$	19420.8			0.932443			0.466221	−	0.884668i	$-0.345615\pi$
$757$	19420.8			0.932443			0.466221	+	0.884668i	$0.345615\pi$
$758$		0			0
$759$	28.2875	−	1563.55i	0.00135279	−	0.0747739i
$760$		0			0
$761$	−1129.12	−	1955.70i	−0.0537854	−	0.0931591i	0.837879	−	0.545856i	$-0.183795\pi$
$761$	−1129.12	−	1955.70i	−0.0537854	−	0.0931591i	−0.891665	+	0.452697i	$0.850462\pi$
$762$		0			0
$763$	−16701.6	−	5398.61i	−0.792450	−	0.256150i
$764$		0			0
$765$	−11220.2	−	21167.1i	−0.530283	−	1.00039i
$766$		0			0
$767$	−28751.1	−	16599.5i	−1.35351	−	0.781449i
$768$		0			0
$769$	−6652.81	+	3841.00i	−0.311972	+	0.180117i	−0.647809	−	0.761803i	$-0.724314\pi$
$769$	−6652.81	+	3841.00i	−0.311972	+	0.180117i	0.335837	+	0.941920i	$0.390981\pi$
$770$		0			0
$771$	−14742.6	+	8159.70i	−0.688641	+	0.381147i
$772$		0			0
$773$	−13041.2			−0.606804			−0.303402	−	0.952863i	$-0.598122\pi$
$773$	−13041.2			−0.606804			−0.303402	+	0.952863i	$0.598122\pi$
$774$		0			0
$775$		−	34881.7i		−	1.61676i
$776$		0			0
$777$	10485.7	−	30540.4i	0.484134	−	1.41008i
$778$		0			0
$779$	19727.0	−	11389.4i	0.907310	−	0.523836i
$780$		0			0
$781$	−11846.8	+	20519.3i	−0.542783	+	0.940127i
$782$		0			0
$783$	3523.93	−	5403.76i	0.160836	−	0.246634i
$784$		0			0
$785$	−989.936	−	571.540i	−0.0450093	−	0.0259861i
$786$		0			0
$787$	−7894.38	+	4557.83i	−0.357566	+	0.206441i	−0.668013	−	0.744150i	$-0.732855\pi$
$787$	−7894.38	+	4557.83i	−0.357566	+	0.206441i	0.310447	+	0.950591i	$0.399521\pi$
$788$		0			0
$789$	935.201	−	1554.19i	0.0421978	−	0.0701277i
$790$		0			0
$791$	25492.5	−	5459.16i	1.14590	−	0.245392i
$792$		0			0
$793$	10539.2			0.471952
$794$		0			0
$795$	−10826.8	−	19561.4i	−0.483002	−	0.872668i
$796$		0			0
$797$	22246.7	+	38532.4i	0.988729	+	1.71253i	0.624021	+	0.781408i	$0.285498\pi$
$797$	22246.7	+	38532.4i	0.988729	+	1.71253i	0.364709	+	0.931122i	$0.381169\pi$
$798$		0			0
$799$	18032.1	−	31232.6i	0.798412	−	1.38289i
$800$		0			0
$801$	−11955.6	−	432.737i	−0.527378	−	0.0190887i
$802$		0			0
$803$	−4236.65	+	7338.09i	−0.186187	+	0.322485i
$804$		0			0
$805$	1479.53	+	1638.16i	0.0647783	+	0.0717238i
$806$		0			0
$807$	744.857	−	41171.0i	0.0324909	−	1.79590i
$808$		0			0
$809$		−	8457.35i		−	0.367546i	−0.982969	−	0.183773i	$-0.941169\pi$
$809$		−	8457.35i		−	0.367546i	0.982969	−	0.183773i	$-0.0588311\pi$
$810$		0			0
$811$			26796.4i			1.16023i	0.814533	+	0.580117i	$0.196993\pi$
$811$			26796.4i			1.16023i	−0.814533	+	0.580117i	$0.803007\pi$
$812$		0			0
$813$	−34297.1	−	620.495i	−1.47952	−	0.0267672i
$814$		0			0
$815$	−12556.8	−	21749.0i	−0.539687	−	0.934766i
$816$		0			0
$817$	30870.6	+	17823.2i	1.32194	+	0.763224i
$818$		0			0
$819$	31575.8	−	5575.75i	1.34719	−	0.237891i
$820$		0			0
$821$	24830.3	+	14335.8i	1.05552	+	0.609405i	0.924190	−	0.381933i	$-0.124742\pi$
$821$	24830.3	+	14335.8i	1.05552	+	0.609405i	0.131331	+	0.991339i	$0.458075\pi$
$822$		0			0
$823$	−11603.6	−	20098.0i	−0.491464	−	0.851241i	0.508488	−	0.861069i	$-0.330205\pi$
$823$	−11603.6	−	20098.0i	−0.491464	−	0.851241i	−0.999952	+	0.00982871i	$0.996871\pi$
$824$		0			0
$825$	−11920.7	−	21537.9i	−0.503062	−	0.908912i
$826$		0			0
$827$		−	1777.49i		−	0.0747393i	−0.999302	−	0.0373696i	$-0.988102\pi$
$827$		−	1777.49i		−	0.0747393i	0.999302	−	0.0373696i	$-0.0118979\pi$
$828$		0			0
$829$		−	13834.0i		−	0.579585i	−0.957090	−	0.289792i	$-0.906414\pi$
$829$		−	13834.0i		−	0.579585i	0.957090	−	0.289792i	$-0.0935862\pi$
$830$		0			0
$831$	25542.8	+	15369.8i	1.06627	+	0.641602i
$832$		0			0
$833$	−15768.5	−	11383.3i	−0.655876	−	0.473479i
$834$		0			0
$835$	10430.8	−	18066.7i	0.432303	−	0.748771i
$836$		0			0
$837$	18461.5	+	36404.5i	0.762394	+	1.50337i
$838$		0			0
$839$	−12455.4	+	21573.4i	−0.512526	+	0.887721i	0.487369	+	0.873196i	$0.337957\pi$
$839$	−12455.4	+	21573.4i	−0.512526	+	0.887721i	−0.999895	+	0.0145243i	$0.995377\pi$
$840$		0			0
$841$	−11137.3	−	19290.3i	−0.456652	−	0.790944i
$842$		0			0
$843$	1981.58	−	3293.15i	0.0809598	−	0.134546i
$844$		0			0
$845$	−29963.3			−1.21984
$846$		0			0
$847$	893.522	+	4172.46i	0.0362477	+	0.169265i
$848$		0			0
$849$	−3972.43	−	7177.22i	−0.160581	−	0.290132i
$850$		0			0
$851$	2213.19	−	1277.79i	0.0891508	−	0.0514712i
$852$		0			0
$853$	3041.79	+	1756.18i	0.122097	+	0.0704928i	0.559805	−	0.828625i	$-0.310876\pi$
$853$	3041.79	+	1756.18i	0.122097	+	0.0704928i	−0.437708	+	0.899117i	$0.644209\pi$
$854$		0			0
$855$	−43698.7	+	23163.7i	−1.74791	+	0.926528i
$856$		0			0
$857$	8211.64	−	14223.0i	0.327310	−	0.566917i	−0.654667	−	0.755917i	$-0.727191\pi$
$857$	8211.64	−	14223.0i	0.327310	−	0.566917i	0.981977	+	0.189000i	$0.0605246\pi$
$858$		0			0
$859$	−1430.46	+	825.876i	−0.0568180	+	0.0328039i	−0.528140	−	0.849157i	$-0.677110\pi$
$859$	−1430.46	+	825.876i	−0.0568180	+	0.0328039i	0.471322	+	0.881961i	$0.343777\pi$
$860$		0			0
$861$	18379.9	−	3589.58i	0.727510	−	0.142082i
$862$		0			0
$863$			20778.9i			0.819610i	0.912173	+	0.409805i	$0.134403\pi$
$863$			20778.9i			0.819610i	−0.912173	+	0.409805i	$0.865597\pi$
$864$		0			0
$865$	−38651.0			−1.51927
$866$		0			0
$867$	159.613	−	8822.38i	0.00625228	−	0.345587i
$868$		0			0
$869$	−31095.9	+	17953.2i	−1.21387	+	0.700831i
$870$		0			0
$871$	−40882.8	−	23603.7i	−1.59043	−	0.918234i
$872$		0			0
$873$	8921.71	+	5590.71i	0.345881	+	0.216743i
$874$		0			0
$875$	−1408.58	−	455.306i	−0.0544212	−	0.0175910i
$876$		0			0
$877$	19789.9	+	34277.1i	0.761981	+	1.31979i	0.941828	+	0.336096i	$0.109107\pi$
$877$	19789.9	+	34277.1i	0.761981	+	1.31979i	−0.179846	+	0.983695i	$0.557560\pi$
$878$		0			0
$879$	−9071.68	+	5020.97i	−0.348100	+	0.192666i
$880$		0			0
$881$	15881.0			0.607314			0.303657	−	0.952781i	$-0.401792\pi$
$881$	15881.0			0.607314			0.303657	+	0.952781i	$0.401792\pi$
$882$		0			0
$883$	10903.6			0.415555			0.207778	−	0.978176i	$-0.433377\pi$
$883$	10903.6			0.415555			0.207778	+	0.978176i	$0.433377\pi$
$884$		0			0
$885$	36072.9	+	21706.1i	1.37015	+	0.824454i
$886$		0			0
$887$	−23758.1	−	41150.3i	−0.899346	−	1.55771i	−0.828331	−	0.560238i	$-0.810710\pi$
$887$	−23758.1	−	41150.3i	−0.899346	−	1.55771i	−0.0710149	−	0.997475i	$-0.522624\pi$
$888$		0			0
$889$	22400.1	+	7240.58i	0.845080	+	0.273162i
$890$		0			0
$891$	23840.3	+	16168.9i	0.896385	+	0.607945i
$892$		0			0
$893$	−64478.6	−	37226.7i	−2.41623	−	1.39501i
$894$		0			0
$895$	−58931.7	+	34024.3i	−2.20097	+	1.27073i
$896$		0			0
$897$	2174.39	+	1308.39i	0.0809373	+	0.0487022i
$898$		0			0
$899$	−13378.4			−0.496324
$900$		0			0
$901$			15589.7i			0.576436i
$902$		0			0
$903$	19246.0	+	22100.4i	0.709265	+	0.814459i
$904$		0			0
$905$	20651.5	−	11923.1i	0.758539	−	0.437942i
$906$		0			0
$907$	−10606.5	+	18371.0i	−0.388294	+	0.672545i	−0.992220	−	0.124495i	$-0.960269\pi$
$907$	−10606.5	+	18371.0i	−0.388294	+	0.672545i	0.603926	+	0.797040i	$0.293602\pi$
$908$		0			0
$909$	−20108.1	+	32088.8i	−0.733713	+	1.17087i
$910$		0			0
$911$	14559.0	+	8405.62i	0.529484	+	0.305698i	0.740806	−	0.671719i	$-0.234444\pi$
$911$	14559.0	+	8405.62i	0.529484	+	0.305698i	−0.211322	+	0.977416i	$0.567777\pi$
$912$		0			0
$913$	26686.8	−	15407.6i	0.967365	−	0.558508i
$914$		0			0
$915$	−13362.7	−	241.756i	−0.482796	−	0.00873464i
$916$		0			0
$917$	−4166.68	−	19457.1i	−0.150050	−	0.700685i
$918$		0			0
$919$	−34695.2			−1.24536			−0.622682	−	0.782475i	$-0.713957\pi$
$919$	−34695.2			−1.24536			−0.622682	+	0.782475i	$0.713957\pi$
$920$		0			0
$921$	−8901.98	−	161.053i	−0.318491	−	0.00576207i
$922$		0			0
$923$	−19224.6	−	33297.9i	−0.685573	−	1.18745i
$924$		0			0
$925$	20114.3	−	34839.0i	0.714978	−	1.23838i
$926$		0			0
$927$	−25340.0	+	13432.2i	−0.897817	+	0.475913i
$928$		0			0
$929$	−22217.1	+	38481.2i	−0.784628	+	1.35902i	0.144592	+	0.989491i	$0.453813\pi$
$929$	−22217.1	+	38481.2i	−0.784628	+	1.35902i	−0.929221	+	0.369525i	$0.879520\pi$
$930$		0			0
$931$	−23500.5	+	32553.5i	−0.827279	+	1.14597i
$932$		0			0
$933$	29684.8	−	16429.9i	1.04162	−	0.576516i
$934$		0			0
$935$			35061.1i			1.22633i
$936$		0			0
$937$			39975.1i			1.39374i	0.717199	+	0.696868i	$0.245424\pi$
$937$			39975.1i			1.39374i	−0.717199	+	0.696868i	$0.754576\pi$
$938$		0			0
$939$	1168.95	−	1942.66i	0.0406254	−	0.0675146i
$940$		0			0
$941$	−15218.5	−	26359.2i	−0.527214	−	0.913161i	−0.999497	−	0.0317144i	$-0.989903\pi$
$941$	−15218.5	−	26359.2i	−0.527214	−	0.913161i	0.472283	−	0.881447i	$-0.343430\pi$
$942$		0			0
$943$	1283.57	+	741.068i	0.0443252	+	0.0255912i
$944$		0			0
$945$	−40163.1	+	6345.23i	−1.38254	+	0.218424i
$946$		0			0
$947$	−13622.3	−	7864.86i	−0.467441	−	0.269877i	0.247727	−	0.968830i	$-0.420316\pi$
$947$	−13622.3	−	7864.86i	−0.467441	−	0.269877i	−0.715168	+	0.698953i	$0.753650\pi$
$948$		0			0
$949$	−6875.06	−	11908.0i	−0.235167	−	0.407322i
$950$		0			0
$951$	−3715.77	+	6175.17i	−0.126700	+	0.210561i
$952$		0			0
$953$			1741.59i			0.0591979i	0.999562	+	0.0295990i	$0.00942302\pi$
$953$			1741.59i			0.0591979i	−0.999562	+	0.0295990i	$0.990577\pi$
$954$		0			0
$955$			60910.4i			2.06389i
$956$		0			0
$957$	−8260.57	+	4572.04i	−0.279024	+	0.154434i
$958$		0			0
$959$	18678.8	+	20681.5i	0.628957	+	0.696394i
$960$		0			0
$961$	27428.2	−	47507.0i	0.920686	−	1.59468i
$962$		0			0
$963$	−211.745	+	5850.05i	−0.00708556	+	0.195758i
$964$		0			0
$965$	−2970.32	+	5144.75i	−0.0990861	+	0.171622i
$966$		0			0
$967$	4096.53	+	7095.40i	0.136231	+	0.235959i	0.926067	−	0.377359i	$-0.123168\pi$
$967$	4096.53	+	7095.40i	0.136231	+	0.235959i	−0.789836	+	0.613318i	$0.789834\pi$
$968$		0			0
$969$	34481.0	+	623.823i	1.14313	+	0.0206812i
$970$		0			0
$971$	7844.92			0.259275			0.129637	−	0.991561i	$-0.458619\pi$
$971$	7844.92			0.259275			0.129637	+	0.991561i	$0.458619\pi$
$972$		0			0
$973$	−15438.8	+	3306.17i	−0.508678	+	0.108932i
$974$		0			0
$975$	39940.5	+	722.594i	1.31192	+	0.0237349i
$976$		0			0
$977$	43445.7	−	25083.4i	1.42267	−	0.821380i	0.426146	−	0.904655i	$-0.359871\pi$
$977$	43445.7	−	25083.4i	1.42267	−	0.821380i	0.996527	+	0.0832744i	$0.0265378\pi$
$978$		0			0
$979$	15162.8	+	8754.23i	0.494999	+	0.285788i
$980$		0			0
$981$	25572.3	+	925.601i	0.832275	+	0.0301245i
$982$		0			0
$983$	−653.927	+	1132.63i	−0.0212177	+	0.0367502i	−0.876439	−	0.481512i	$-0.840088\pi$
$983$	−653.927	+	1132.63i	−0.0212177	+	0.0367502i	0.855222	+	0.518263i	$0.173421\pi$
$984$		0			0
$985$	39528.6	−	22821.9i	1.27867	−	0.738238i
$986$		0			0
$987$	−40198.5	−	46160.6i	−1.29639	−	1.48866i
$988$		0			0
$989$			2319.38i			0.0745722i
$990$		0			0
$991$	−43094.8			−1.38138			−0.690691	−	0.723150i	$-0.742694\pi$
$991$	−43094.8			−1.38138			−0.690691	+	0.723150i	$0.742694\pi$
$992$		0			0
$993$	2075.80	+	1249.07i	0.0663379	+	0.0399173i
$994$		0			0
$995$	−39486.4	+	22797.5i	−1.25809	+	0.726360i
$996$		0			0
$997$	7444.26	+	4297.95i	0.236471	+	0.136527i	0.613554	−	0.789653i	$-0.289739\pi$
$997$	7444.26	+	4297.95i	0.236471	+	0.136527i	−0.377082	+	0.926180i	$0.623073\pi$
$998$		0			0
$999$	−2553.47	+	47005.6i	−0.0808692	+	1.48868i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.x.a.209.12	yes	48
3.2	odd	2		756.4.x.a.629.21		48
7.6	odd	2	inner	252.4.x.a.209.13	yes	48
9.2	odd	6		2268.4.f.a.1133.7		48
9.4	even	3		756.4.x.a.125.4		48
9.5	odd	6	inner	252.4.x.a.41.13	yes	48
9.7	even	3		2268.4.f.a.1133.42		48
21.20	even	2		756.4.x.a.629.4		48
63.13	odd	6		756.4.x.a.125.21		48
63.20	even	6		2268.4.f.a.1133.41		48
63.34	odd	6		2268.4.f.a.1133.8		48
63.41	even	6	inner	252.4.x.a.41.12	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.x.a.41.12	✓	48	63.41	even	6	inner
252.4.x.a.41.13	yes	48	9.5	odd	6	inner
252.4.x.a.209.12	yes	48	1.1	even	1	trivial
252.4.x.a.209.13	yes	48	7.6	odd	2	inner
756.4.x.a.125.4		48	9.4	even	3
756.4.x.a.125.21		48	63.13	odd	6
756.4.x.a.629.4		48	21.20	even	2
756.4.x.a.629.21		48	3.2	odd	2
2268.4.f.a.1133.7		48	9.2	odd	6
2268.4.f.a.1133.8		48	63.34	odd	6
2268.4.f.a.1133.41		48	63.20	even	6
2268.4.f.a.1133.42		48	9.7	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.0939923 + 5.19530i) q^{3} +(-7.82452 - 13.5525i) q^{5} +(17.6225 + 5.69627i) q^{7} +(-26.9823 - 0.976636i) q^{9} +O(q^{10})\)	\(q+(-0.0939923 + 5.19530i) q^{3} +(-7.82452 - 13.5525i) q^{5} +(17.6225 + 5.69627i) q^{7} +(-26.9823 - 0.976636i) q^{9} +(34.2206 + 19.7573i) q^{11} +(-55.5318 + 32.0613i) q^{13} +(71.1446 - 39.3769i) q^{15} -56.6997 q^{17} +117.055i q^{19} +(-31.2502 + 91.0188i) q^{21} +(-6.59593 + 3.80816i) q^{23} +(-59.9462 + 103.830i) q^{25} +(7.61005 - 140.090i) q^{27} +(39.8226 + 22.9916i) q^{29} +(-251.963 + 145.471i) q^{31} +(-105.861 + 175.929i) q^{33} +(-60.6891 - 283.399i) q^{35} -335.540 q^{37} +(-161.349 - 291.518i) q^{39} +(-97.3000 - 168.529i) q^{41} +(152.264 - 263.729i) q^{43} +(197.888 + 373.319i) q^{45} +(-318.029 + 550.842i) q^{47} +(278.105 + 200.765i) q^{49} +(5.32933 - 294.572i) q^{51} -274.953i q^{53} -618.365i q^{55} +(-608.134 - 11.0022i) q^{57} +(258.871 + 448.377i) q^{59} +(-142.340 - 82.1801i) q^{61} +(-469.933 - 170.909i) q^{63} +(869.019 + 501.728i) q^{65} +(368.103 + 637.573i) q^{67} +(-19.1646 - 34.6258i) q^{69} +599.619i q^{71} +214.435i q^{73} +(-533.793 - 321.198i) q^{75} +(490.510 + 543.102i) q^{77} +(-454.345 + 786.949i) q^{79} +(727.092 + 52.7039i) q^{81} +(389.923 - 675.366i) q^{83} +(443.648 + 768.420i) q^{85} +(-123.191 + 204.729i) q^{87} +443.089 q^{89} +(-1161.24 + 248.676i) q^{91} +(-732.084 - 1322.70i) q^{93} +(1586.38 - 915.896i) q^{95} +(-337.707 - 194.975i) q^{97} +(-904.056 - 566.518i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{7} + 60 q^{9}+O(q^{10}) \) 48 * q + 6 * q^7 + 60 * q^9	\( 48 q + 6 q^{7} + 60 q^{9} - 12 q^{11} + 192 q^{15} - 72 q^{21} - 408 q^{23} - 600 q^{25} - 84 q^{29} + 336 q^{37} + 36 q^{39} + 84 q^{43} + 318 q^{49} - 1812 q^{51} - 852 q^{57} - 564 q^{63} + 2964 q^{65} - 588 q^{67} + 2400 q^{77} + 204 q^{79} + 1980 q^{81} - 360 q^{85} - 1080 q^{91} + 2496 q^{93} + 300 q^{95} - 4968 q^{99}+O(q^{100}) \) 48 * q + 6 * q^7 + 60 * q^9 - 12 * q^11 + 192 * q^15 - 72 * q^21 - 408 * q^23 - 600 * q^25 - 84 * q^29 + 336 * q^37 + 36 * q^39 + 84 * q^43 + 318 * q^49 - 1812 * q^51 - 852 * q^57 - 564 * q^63 + 2964 * q^65 - 588 * q^67 + 2400 * q^77 + 204 * q^79 + 1980 * q^81 - 360 * q^85 - 1080 * q^91 + 2496 * q^93 + 300 * q^95 - 4968 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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