LMFDB - Embedded newform 252.4.x.a.41.12

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			41.12
Character	$\chi$	$=$	252.41
Dual form			252.4.x.a.209.12

$q$-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 $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

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

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	0.268673	+	0.963231i	$0.413415\pi$
$5$	−7.82452	+	13.5525i	−0.699846	+	1.21217i	−0.968519	+	0.248938i	$0.919919\pi$
$6$		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	0.0486610	−	0.998815i	$-0.484505\pi$
$11$	34.2206	−	19.7573i	0.937991	−	0.541549i	0.889330	+	0.457266i	$0.151171\pi$
$12$		0			0
$13$	−55.5318	−	32.0613i	−1.18475	−	0.684015i	−0.227641	−	0.973745i	$-0.573101\pi$
$13$	−55.5318	−	32.0613i	−1.18475	−	0.684015i	−0.957109	+	0.289730i	$0.906435\pi$
$14$		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	$-0.750188\pi$
$19$		−	117.055i		−	1.41338i	0.707525	−	0.706689i	$-0.249812\pi$
$20$		0			0
$21$	−31.2502	−	91.0188i	−0.324731	−	0.945806i
$22$		0			0
$23$	−6.59593	−	3.80816i	−0.0597976	−	0.0345242i	0.469803	−	0.882771i	$-0.344325\pi$
$23$	−6.59593	−	3.80816i	−0.0597976	−	0.0345242i	−0.529601	+	0.848247i	$0.677658\pi$
$24$		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	−0.367054	−	0.930200i	$-0.619634\pi$
$29$	39.8226	−	22.9916i	0.254995	−	0.147222i	0.622049	+	0.782978i	$0.286300\pi$
$30$		0			0
$31$	−251.963	−	145.471i	−1.45980	−	0.842819i	−0.460803	−	0.887502i	$-0.652439\pi$
$31$	−251.963	−	145.471i	−1.45980	−	0.842819i	−0.999001	+	0.0446836i	$0.985772\pi$
$32$		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	−0.989662	−	0.143419i	$-0.954190\pi$
$41$	−97.3000	+	168.529i	−0.370627	+	0.641945i	0.619035	+	0.785363i	$0.287524\pi$
$42$		0			0
$43$	152.264	+	263.729i	0.540000	+	0.935308i	0.998903	+	0.0468214i	$0.0149092\pi$
$43$	152.264	+	263.729i	0.540000	+	0.935308i	−0.458903	+	0.888486i	$0.651757\pi$
$44$		0			0
$45$	197.888	−	373.319i	0.655542	−	1.23669i
$46$		0			0
$47$	−318.029	−	550.842i	−0.987006	−	1.70954i	−0.632659	−	0.774431i	$-0.718036\pi$
$47$	−318.029	−	550.842i	−0.987006	−	1.70954i	−0.354347	−	0.935114i	$-0.615297\pi$
$48$		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	$0.115961\pi$
$53$			274.953i			0.712597i	−0.934372	+	0.356299i	$0.884039\pi$
$54$		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	−0.425219	−	0.905090i	$-0.639803\pi$
$59$	258.871	−	448.377i	0.571222	−	0.989385i	0.996441	−	0.0842947i	$-0.0268637\pi$
$60$		0			0
$61$	−142.340	+	82.1801i	−0.298767	+	0.172493i	−0.641889	−	0.766798i	$-0.721849\pi$
$61$	−142.340	+	82.1801i	−0.298767	+	0.172493i	0.343122	+	0.939291i	$0.388516\pi$
$62$		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	−0.306353	−	0.951918i	$-0.599109\pi$
$67$	368.103	−	637.573i	0.671208	−	1.16257i	0.977562	−	0.210649i	$-0.0675578\pi$
$68$		0			0
$69$	−19.1646	+	34.6258i	−0.0334369	+	0.0604123i
$70$		0			0
$71$		−	599.619i		−	1.00228i	−0.865367	−	0.501139i	$-0.832915\pi$
$71$		−	599.619i		−	1.00228i	0.865367	−	0.501139i	$-0.167085\pi$
$72$		0			0
$73$		−	214.435i		−	0.343804i	−0.985114	−	0.171902i	$-0.945009\pi$
$73$		−	214.435i		−	0.343804i	0.985114	−	0.171902i	$-0.0549913\pi$
$74$		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	−0.983821	−	0.179152i	$-0.942665\pi$
$79$	−454.345	−	786.949i	−0.647061	−	1.12074i	0.336761	−	0.941590i	$-0.390669\pi$
$80$		0			0
$81$	727.092	−	52.7039i	0.997383	−	0.0722961i
$82$		0			0
$83$	389.923	+	675.366i	0.515658	+	0.893146i	0.999835	+	0.0181755i	$0.00578575\pi$
$83$	389.923	+	675.366i	0.515658	+	0.893146i	−0.484177	+	0.874970i	$0.660881\pi$
$84$		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	−0.666223	−	0.745752i	$-0.732090\pi$
$97$	−337.707	+	194.975i	−0.353495	+	0.204090i	0.312729	+	0.949842i	$0.398757\pi$
$98$		0			0
$99$	−904.056	+	566.518i	−0.917788	+	0.575124i
$100$		0			0
$101$	701.270	+	1214.63i	0.690881	+	1.19664i	0.971550	+	0.236836i	$0.0761103\pi$
$101$	701.270	+	1214.63i	0.690881	+	1.19664i	−0.280669	+	0.959805i	$0.590556\pi$
$102$		0			0
$103$	919.911	+	531.111i	0.880015	+	0.508077i	0.870663	−	0.491879i	$-0.163690\pi$
$103$	919.911	+	531.111i	0.880015	+	0.508077i	0.00935152	+	0.999956i	$0.497023\pi$
$104$		0			0
$105$	1478.05	+	288.661i	1.37374	+	0.268290i
$106$		0			0
$107$			216.811i			0.195887i	0.995192	+	0.0979433i	$0.0312264\pi$
$107$			216.811i			0.195887i	−0.995192	+	0.0979433i	$0.968774\pi$
$108$		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	0.912617	−	0.408815i	$-0.134058\pi$
$113$	1219.08	+	703.838i	1.01488	+	0.585942i	0.102265	+	0.994757i	$0.467391\pi$
$114$		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	−0.987675	−	0.156521i	$-0.949972\pi$
$131$	−537.201	+	930.459i	−0.358286	+	0.620569i	0.629389	+	0.777091i	$0.283305\pi$
$132$		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	−0.0352200	−	0.999380i	$-0.511213\pi$
$137$	1303.13	−	752.364i	0.812658	−	0.469188i	0.847878	+	0.530191i	$0.177880\pi$
$138$		0			0
$139$	−738.300	−	426.257i	−0.450516	−	0.260106i	0.257532	−	0.966270i	$-0.417091\pi$
$139$	−738.300	−	426.257i	−0.450516	−	0.260106i	−0.708048	+	0.706164i	$0.750424\pi$
$140$		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	0.304401	−	0.952544i	$-0.401544\pi$
$149$	−669.901	−	386.768i	−0.368325	−	0.212653i	−0.672727	+	0.739891i	$0.734877\pi$
$150$		0			0
$151$	−1258.88	−	2180.44i	−0.678451	−	1.17511i	−0.975447	−	0.220232i	$-0.929318\pi$
$151$	−1258.88	−	2180.44i	−0.678451	−	1.17511i	0.296997	−	0.954878i	$-0.404015\pi$
$152$		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	0.515992	−	0.856593i	$-0.327423\pi$
$157$	63.2586	+	36.5224i	0.0321566	+	0.0185656i	−0.483836	+	0.875159i	$0.660757\pi$
$158$		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	−0.669257	−	0.743031i	$-0.733387\pi$
$167$	666.547	−	1154.49i	0.308856	−	0.534954i	0.978112	+	0.208077i	$0.0667206\pi$
$168$		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	0.998747	+	0.0500494i	$0.0159379\pi$
$173$	1234.93	+	2138.96i	0.542717	+	0.940014i	−0.456029	+	0.889965i	$0.650729\pi$
$174$		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	$0.362289\pi$
$179$			4348.42i			1.81573i	−0.419261	+	0.907866i	$0.637711\pi$
$180$		0			0
$181$		−	1523.82i		−	0.625770i	−0.949791	−	0.312885i	$-0.898705\pi$
$181$		−	1523.82i		−	0.625770i	0.949791	−	0.312885i	$-0.101295\pi$
$182$		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	−0.976292	−	0.216456i	$-0.930550\pi$
$191$	−3370.81	+	1946.14i	−1.27698	+	0.737266i	−0.300690	+	0.953722i	$0.597217\pi$
$192$		0			0
$193$	−189.809	+	328.758i	−0.0707914	+	0.122614i	−0.899248	−	0.437438i	$-0.855886\pi$
$193$	−189.809	+	328.758i	−0.0707914	+	0.122614i	0.828457	+	0.560053i	$0.189219\pi$
$194$		0			0
$195$	−2688.31	−	4467.66i	−0.987251	−	1.64070i
$196$		0			0
$197$		−	2916.71i		−	1.05486i	−0.849599	−	0.527429i	$-0.823156\pi$
$197$		−	2916.71i		−	1.05486i	0.849599	−	0.527429i	$-0.176844\pi$
$198$		0			0
$199$			2913.59i			1.03789i	0.854809	+	0.518943i	$0.173674\pi$
$199$			2913.59i			1.03789i	−0.854809	+	0.518943i	$0.826326\pi$
$200$		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	−0.945768	−	0.324843i	$-0.894689\pi$
$211$	−587.128	+	1016.93i	−0.191562	+	0.331795i	0.754206	+	0.656638i	$0.228022\pi$
$212$		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	−0.238179	−	0.971221i	$-0.576550\pi$
$223$	1611.22	−	930.237i	0.483834	−	0.279342i	0.722013	+	0.691879i	$0.243217\pi$
$224$		0			0
$225$	1718.89	+	2743.02i	0.509301	+	0.812748i
$226$		0			0
$227$	1240.21	+	2148.11i	0.362624	+	0.628083i	0.988392	−	0.151926i	$-0.0485477\pi$
$227$	1240.21	+	2148.11i	0.362624	+	0.628083i	−0.625768	+	0.780009i	$0.715214\pi$
$228$		0			0
$229$	2878.54	+	1661.92i	0.830651	+	0.479577i	0.854076	−	0.520149i	$-0.174124\pi$
$229$	2878.54	+	1661.92i	0.830651	+	0.479577i	−0.0234243	+	0.999726i	$0.507457\pi$
$230$		0			0
$231$	−2867.69	−	2497.30i	−0.816796	−	0.711300i
$232$		0			0
$233$		−	2378.25i		−	0.668689i	−0.942451	−	0.334344i	$-0.891485\pi$
$233$		−	2378.25i		−	0.668689i	0.942451	−	0.334344i	$-0.108515\pi$
$234$		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	−0.426398	−	0.904536i	$-0.640218\pi$
$239$	−5257.58	−	3035.47i	−1.42295	−	0.821539i	−0.996550	+	0.0829961i	$0.973551\pi$
$240$		0			0
$241$	3105.01	−	1792.68i	0.829923	−	0.479156i	−0.0239031	−	0.999714i	$-0.507609\pi$
$241$	3105.01	−	1792.68i	0.829923	−	0.479156i	0.853826	+	0.520558i	$0.174276\pi$
$242$		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	−0.599372	−	0.800470i	$-0.704583\pi$
$257$	1621.40	−	2808.35i	0.393541	−	0.681634i	0.992914	+	0.118837i	$0.0379165\pi$
$258$		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	−0.535021	−	0.844839i	$-0.679696\pi$
$263$	−302.312	+	174.540i	−0.0708796	+	0.0409223i	0.464141	+	0.885761i	$0.346363\pi$
$264$		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	$-0.734881\pi$
$271$		−	6601.56i		−	1.47976i	0.672737	−	0.739882i	$-0.265119\pi$
$272$		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	0.989073	+	0.147424i	$0.0470983\pi$
$277$	2868.51	+	4968.41i	0.622210	+	1.07770i	−0.366863	+	0.930275i	$0.619568\pi$
$278$		0			0
$279$	6940.63	+	3679.07i	1.48934	+	0.789463i
$280$		0			0
$281$	−640.561	+	369.828i	−0.135988	+	0.0785128i	−0.566451	−	0.824096i	$-0.691684\pi$
$281$	−640.561	+	369.828i	−0.135988	+	0.0785128i	0.430462	+	0.902608i	$0.358350\pi$
$282$		0			0
$283$	−1367.20	−	789.355i	−0.287179	−	0.165803i	0.349490	−	0.936940i	$-0.386355\pi$
$283$	−1367.20	−	789.355i	−0.287179	−	0.165803i	−0.636669	+	0.771137i	$0.719688\pi$
$284$		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	−0.749251	−	0.662286i	$-0.769586\pi$
$293$	997.708	−	1728.08i	0.198931	−	0.344558i	0.948182	+	0.317728i	$0.102920\pi$
$294$		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	$-0.949085\pi$
$307$		−	1713.47i		−	0.318543i	0.987235	−	0.159272i	$-0.0509146\pi$
$308$		0			0
$309$	2672.82	−	4829.14i	0.492075	−	0.889061i
$310$		0			0
$311$	−3264.75	+	5654.71i	−0.595263	+	1.03103i	0.398246	+	0.917278i	$0.369619\pi$
$311$	−3264.75	+	5654.71i	−0.595263	+	1.03103i	−0.993510	+	0.113748i	$0.963714\pi$
$312$		0			0
$313$	−377.873	+	218.165i	−0.0682384	+	0.0393975i	−0.533731	−	0.845654i	$-0.679211\pi$
$313$	−377.873	+	218.165i	−0.0682384	+	0.0393975i	0.465493	+	0.885052i	$0.345877\pi$
$314$		0			0
$315$	1360.76	−	7706.03i	0.243396	−	1.37837i
$316$		0			0
$317$	1201.15	−	693.486i	0.212818	−	0.122871i	−0.389802	−	0.920899i	$-0.627457\pi$
$317$	1201.15	−	693.486i	0.212818	−	0.122871i	0.602621	+	0.798028i	$0.294123\pi$
$318$		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	0.884732	−	0.466101i	$-0.154342\pi$
$331$	233.117	+	403.771i	0.0387108	+	0.0670491i	−0.846021	+	0.533150i	$0.821008\pi$
$332$		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	−0.795656	−	0.605749i	$-0.792874\pi$
$337$	784.235	−	1358.34i	0.126766	−	0.219565i	0.922422	+	0.386184i	$0.126207\pi$
$338$		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	0.0927396	−	0.995690i	$-0.470438\pi$
$347$	−4674.58	−	2698.87i	−0.723184	−	0.417530i	−0.815923	+	0.578160i	$0.803771\pi$
$348$		0			0
$349$	2247.57	−	1297.64i	0.344727	−	0.199029i	−0.317633	−	0.948214i	$-0.602888\pi$
$349$	2247.57	−	1297.64i	0.344727	−	0.199029i	0.662361	+	0.749185i	$0.269555\pi$
$350$		0			0
$351$	4068.85	−	8023.41i	0.618744	−	1.22011i
$352$		0			0
$353$	2303.43	+	3989.65i	0.347306	+	0.601551i	0.985770	−	0.168100i	$-0.0537632\pi$
$353$	2303.43	+	3989.65i	0.347306	+	0.601551i	−0.638464	+	0.769652i	$0.720430\pi$
$354$		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	$0.0701319\pi$
$359$			2973.15i			0.437095i	−0.975826	+	0.218547i	$0.929868\pi$
$360$		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	0.218201	−	0.975904i	$-0.429981\pi$
$367$	8243.22	−	4759.22i	1.17246	−	0.676919i	0.954258	+	0.298984i	$0.0966479\pi$
$368$		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	−0.790603	−	0.612329i	$-0.790233\pi$
$373$	972.449	−	1684.33i	0.134991	−	0.233811i	0.925594	+	0.378518i	$0.123566\pi$
$374$		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	−0.900336	−	0.435196i	$-0.856679\pi$
$383$	−549.242	+	951.316i	−0.0732767	+	0.126919i	0.827059	+	0.562115i	$0.190012\pi$
$384$		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	0.119416	−	0.992844i	$-0.461898\pi$
$389$	7971.13	−	4602.13i	1.03895	−	0.599839i	0.919536	+	0.393005i	$0.128564\pi$
$390$		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	$0.316060\pi$
$397$			13251.6i			1.67526i	−0.546237	+	0.837630i	$0.683940\pi$
$398$		0			0
$399$	−10654.2	+	3657.98i	−1.33678	+	0.458968i
$400$		0			0
$401$	−10109.5	−	5836.72i	−1.25896	−	0.726862i	−0.286090	−	0.958203i	$-0.592356\pi$
$401$	−10109.5	−	5836.72i	−1.25896	−	0.726862i	−0.972873	+	0.231340i	$0.925689\pi$
$402$		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	−0.243434	−	0.969917i	$-0.578274\pi$
$409$	−9968.20	−	5755.14i	−1.20512	−	0.695779i	−0.961690	+	0.274139i	$0.911607\pi$
$410$		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	0.0987667	−	0.995111i	$-0.468510\pi$
$419$	7814.88	−	13535.8i	0.911174	−	1.57820i	0.812408	−	0.583090i	$-0.198156\pi$
$420$		0			0
$421$	−3771.44	−	6532.33i	−0.436600	−	0.756214i	0.560824	−	0.827935i	$-0.310484\pi$
$421$	−3771.44	−	6532.33i	−0.436600	−	0.756214i	−0.997425	+	0.0717208i	$0.977151\pi$
$422$		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	$-0.738161\pi$
$431$		−	13115.9i		−	1.46582i	0.680324	−	0.732911i	$-0.261839\pi$
$432$		0			0
$433$			1126.39i			0.125013i	0.998045	+	0.0625065i	$0.0199094\pi$
$433$			1126.39i			0.125013i	−0.998045	+	0.0625065i	$0.980091\pi$
$434$		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	0.295083	−	0.955472i	$-0.404653\pi$
$439$	11682.3	−	6744.81i	1.27009	−	0.733285i	0.975004	+	0.222187i	$0.0713195\pi$
$440$		0			0
$441$	−7307.85	+	5688.72i	−0.789099	+	0.614266i
$442$		0			0
$443$	−7184.54	+	4147.99i	−0.770536	+	0.444869i	−0.833066	−	0.553174i	$-0.813417\pi$
$443$	−7184.54	+	4147.99i	−0.770536	+	0.444869i	0.0625295	+	0.998043i	$0.480083\pi$
$444$		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	$0.278489\pi$
$449$			14603.8i			1.53496i	−0.641075	+	0.767478i	$0.721511\pi$
$450$		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	0.882302	−	0.470685i	$-0.155993\pi$
$457$	327.533	+	567.304i	0.0335259	+	0.0580686i	−0.848776	+	0.528753i	$0.822660\pi$
$458$		0			0
$459$	−431.488	−	7943.03i	−0.0438782	−	0.807732i
$460$		0			0
$461$	6136.84	+	10629.3i	0.620002	+	1.07387i	0.989485	+	0.144637i	$0.0462015\pi$
$461$	6136.84	+	10629.3i	0.620002	+	1.07387i	−0.369483	+	0.929238i	$0.620465\pi$
$462$		0			0
$463$	4612.44	−	7988.98i	0.462977	−	0.801900i	−0.536131	−	0.844135i	$-0.680115\pi$
$463$	4612.44	−	7988.98i	0.462977	−	0.801900i	0.999108	+	0.0422354i	$0.0134479\pi$
$464$		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	−0.999998	−	0.00204079i	$-0.999350\pi$
$479$	−5260.23	−	9110.99i	−0.501766	−	0.869085i	0.498232	−	0.867044i	$-0.333983\pi$
$480$		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	0.472841	−	0.881148i	$-0.343229\pi$
$491$	−585.724	−	338.168i	−0.0538358	−	0.0310821i	−0.526676	+	0.850066i	$0.676562\pi$
$492$		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	−0.693090	−	0.720851i	$-0.743751\pi$
$499$	3095.81	−	5362.10i	0.277730	−	0.481043i	0.970820	+	0.239808i	$0.0770845\pi$
$500$		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	0.432368	+	0.901697i	$0.357678\pi$
$509$	−6484.87	+	11232.1i	−0.564709	+	0.978104i	−0.997077	+	0.0764070i	$0.975655\pi$
$510$		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	$0.145206\pi$
$523$			10537.8i			0.881043i	−0.897742	+	0.440522i	$0.854794\pi$
$524$		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	−0.842908	−	0.538058i	$-0.819158\pi$
$547$	−11353.1	−	19664.1i	−0.887426	−	1.53707i	−0.0445177	−	0.999009i	$-0.514175\pi$
$548$		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	$0.0761407\pi$
$557$			6229.16i			0.473857i	−0.971527	+	0.236928i	$0.923859\pi$
$558$		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	−0.918454	−	0.395528i	$-0.870562\pi$
$563$	−1558.81	+	2699.94i	−0.116689	+	0.202112i	0.801764	+	0.597640i	$0.203895\pi$
$564$		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	−0.0424558	−	0.999098i	$-0.513518\pi$
$569$	10879.4	−	6281.22i	0.801561	−	0.462781i	0.844017	+	0.536317i	$0.180185\pi$
$570$		0			0
$571$	3644.80	−	6312.98i	0.267128	−	0.462679i	−0.700991	−	0.713170i	$-0.747259\pi$
$571$	3644.80	−	6312.98i	0.267128	−	0.462679i	0.968119	+	0.250491i	$0.0805920\pi$
$572$		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	$-0.935053\pi$
$577$		−	5616.75i		−	0.405248i	0.979257	−	0.202624i	$-0.0649470\pi$
$578$		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	0.895839	−	0.444380i	$-0.146576\pi$
$587$	897.050	+	1553.74i	0.0630753	+	0.109250i	−0.832763	+	0.553629i	$0.813242\pi$
$588$		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	−0.000372774	−	1.00000i	$-0.500119\pi$
$599$	−12704.3	−	7334.84i	−0.866585	−	0.500323i	−0.866212	+	0.499677i	$0.833452\pi$
$600$		0			0
$601$	854.824	−	493.533i	0.0580183	−	0.0334969i	−0.470710	−	0.882288i	$-0.656002\pi$
$601$	854.824	−	493.533i	0.0580183	−	0.0334969i	0.528729	+	0.848791i	$0.322669\pi$
$602$		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	0.858645	−	0.512570i	$-0.171307\pi$
$607$	12623.0	+	7287.87i	0.844069	+	0.487323i	−0.0145763	+	0.999894i	$0.504640\pi$
$608$		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	0.377116	−	0.926166i	$-0.376916\pi$
$617$	−3623.21	−	2091.86i	−0.236410	−	0.136491i	−0.613526	+	0.789675i	$0.710249\pi$
$618$		0			0
$619$	24006.3	−	13860.0i	1.55879	−	0.899970i	0.561421	−	0.827530i	$-0.310255\pi$
$619$	24006.3	−	13860.0i	1.55879	−	0.899970i	0.997373	−	0.0724400i	$-0.0230786\pi$
$620$		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	0.570444	−	0.821336i	$-0.306771\pi$
$641$	25430.0	−	14682.0i	1.56696	−	0.904687i	0.996520	−	0.0833510i	$-0.0265622\pi$
$642$		0			0
$643$	−951.096	−	549.116i	−0.0583321	−	0.0336781i	0.470550	−	0.882373i	$-0.344055\pi$
$643$	−951.096	−	549.116i	−0.0583321	−	0.0336781i	−0.528882	+	0.848695i	$0.677389\pi$
$644$		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	0.579936	−	0.814662i	$-0.303077\pi$
$653$	2743.06	+	1583.71i	0.164386	+	0.0949085i	−0.415550	+	0.909570i	$0.636411\pi$
$654$		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	−0.0463851	−	0.998924i	$-0.514770\pi$
$659$	13457.9	−	7769.91i	0.795516	−	0.459291i	0.841901	+	0.539632i	$0.181437\pi$
$660$		0			0
$661$	9109.85	+	5259.57i	0.536054	+	0.309491i	0.743478	−	0.668760i	$-0.233175\pi$
$661$	9109.85	+	5259.57i	0.536054	+	0.309491i	−0.207424	+	0.978251i	$0.566508\pi$
$662$		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	−0.891004	−	0.453996i	$-0.849998\pi$
$673$	−14642.5	−	25361.6i	−0.838674	−	1.45263i	0.0523297	−	0.998630i	$-0.483335\pi$
$674$		0			0
$675$	14089.3	−	9187.98i	0.803402	−	0.523919i
$676$		0			0
$677$	−2923.06	−	5062.89i	−0.165941	−	0.287419i	0.771048	−	0.636777i	$-0.219733\pi$
$677$	−2923.06	−	5062.89i	−0.165941	−	0.287419i	−0.936989	+	0.349358i	$0.886400\pi$
$678$		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	$-0.933189\pi$
$683$		−	7438.18i		−	0.416712i	0.978053	−	0.208356i	$-0.0668112\pi$
$684$		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	−0.680538	−	0.732713i	$-0.738254\pi$
$691$	−7016.10	+	4050.75i	−0.386259	+	0.223007i	0.294279	+	0.955720i	$0.404921\pi$
$692$		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	$0.000691120\pi$
$701$			80.5954i			0.00434243i	−0.999998	+	0.00217122i	$0.999309\pi$
$702$		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	−0.998539	−	0.0540423i	$-0.982789\pi$
$709$	−10309.1	−	17855.8i	−0.546071	−	0.945823i	0.452467	−	0.891781i	$-0.350544\pi$
$710$		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	−0.439232	−	0.898374i	$-0.644749\pi$
$727$	2335.91	−	1348.64i	0.119167	−	0.0688008i	0.558398	+	0.829573i	$0.311416\pi$
$728$		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	0.924813	+	0.380421i	$0.124221\pi$
$733$	34067.8	+	19669.0i	1.71667	+	0.991122i	0.791861	+	0.610701i	$0.209112\pi$
$734$		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	0.743405	−	0.668842i	$-0.233210\pi$
$743$	10852.9	+	6265.91i	0.535873	+	0.309386i	−0.207532	+	0.978228i	$0.566543\pi$
$744$		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	−0.965756	−	0.259452i	$-0.916458\pi$
$751$	−5313.64	+	9203.49i	−0.258186	+	0.447190i	0.707570	+	0.706643i	$0.249791\pi$
$752$		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	−0.891665	−	0.452697i	$-0.850462\pi$
$761$	−1129.12	+	1955.70i	−0.0537854	+	0.0931591i	0.837879	+	0.545856i	$0.183795\pi$
$762$		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	0.335837	−	0.941920i	$-0.390981\pi$
$769$	−6652.81	−	3841.00i	−0.311972	−	0.180117i	−0.647809	+	0.761803i	$0.724314\pi$
$770$		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	0.310447	−	0.950591i	$-0.399521\pi$
$787$	−7894.38	−	4557.83i	−0.357566	−	0.206441i	−0.668013	+	0.744150i	$0.732855\pi$
$788$		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	0.364709	−	0.931122i	$-0.381169\pi$
$797$	22246.7	−	38532.4i	0.988729	−	1.71253i	0.624021	−	0.781408i	$-0.285498\pi$
$798$		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	$0.0588311\pi$
$809$			8457.35i			0.367546i	−0.982969	+	0.183773i	$0.941169\pi$
$810$		0			0
$811$		−	26796.4i		−	1.16023i	−0.814533	−	0.580117i	$-0.803007\pi$
$811$		−	26796.4i		−	1.16023i	0.814533	−	0.580117i	$-0.196993\pi$
$812$		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	0.131331	−	0.991339i	$-0.458075\pi$
$821$	24830.3	−	14335.8i	1.05552	−	0.609405i	0.924190	+	0.381933i	$0.124742\pi$
$822$		0			0
$823$	−11603.6	+	20098.0i	−0.491464	+	0.851241i	−0.999952	−	0.00982871i	$-0.996871\pi$
$823$	−11603.6	+	20098.0i	−0.491464	+	0.851241i	0.508488	+	0.861069i	$0.330205\pi$
$824$		0			0
$825$	−11920.7	+	21537.9i	−0.503062	+	0.908912i
$826$		0			0
$827$			1777.49i			0.0747393i	0.999302	+	0.0373696i	$0.0118979\pi$
$827$			1777.49i			0.0747393i	−0.999302	+	0.0373696i	$0.988102\pi$
$828$		0			0
$829$			13834.0i			0.579585i	0.957090	+	0.289792i	$0.0935862\pi$
$829$			13834.0i			0.579585i	−0.957090	+	0.289792i	$0.906414\pi$
$830$		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	−0.999895	−	0.0145243i	$-0.995377\pi$
$839$	−12455.4	−	21573.4i	−0.512526	−	0.887721i	0.487369	−	0.873196i	$-0.337957\pi$
$840$		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	−0.437708	−	0.899117i	$-0.644209\pi$
$853$	3041.79	−	1756.18i	0.122097	−	0.0704928i	0.559805	+	0.828625i	$0.310876\pi$
$854$		0			0
$855$	−43698.7	−	23163.7i	−1.74791	−	0.926528i
$856$		0			0
$857$	8211.64	+	14223.0i	0.327310	+	0.566917i	0.981977	−	0.189000i	$-0.0605246\pi$
$857$	8211.64	+	14223.0i	0.327310	+	0.566917i	−0.654667	+	0.755917i	$0.727191\pi$
$858$		0			0
$859$	−1430.46	−	825.876i	−0.0568180	−	0.0328039i	0.471322	−	0.881961i	$-0.343777\pi$
$859$	−1430.46	−	825.876i	−0.0568180	−	0.0328039i	−0.528140	+	0.849157i	$0.677110\pi$
$860$		0			0
$861$	18379.9	+	3589.58i	0.727510	+	0.142082i
$862$		0			0
$863$		−	20778.9i		−	0.819610i	−0.912173	−	0.409805i	$-0.865597\pi$
$863$		−	20778.9i		−	0.819610i	0.912173	−	0.409805i	$-0.134403\pi$
$864$		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	−0.179846	−	0.983695i	$-0.557560\pi$
$877$	19789.9	−	34277.1i	0.761981	−	1.31979i	0.941828	−	0.336096i	$-0.109107\pi$
$878$		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	−0.0710149	+	0.997475i	$0.522624\pi$
$887$	−23758.1	+	41150.3i	−0.899346	+	1.55771i	−0.828331	+	0.560238i	$0.810710\pi$
$888$		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	0.603926	−	0.797040i	$-0.293602\pi$
$907$	−10606.5	−	18371.0i	−0.388294	−	0.672545i	−0.992220	+	0.124495i	$0.960269\pi$
$908$		0			0
$909$	−20108.1	−	32088.8i	−0.733713	−	1.17087i
$910$		0			0
$911$	14559.0	−	8405.62i	0.529484	−	0.305698i	−0.211322	−	0.977416i	$-0.567777\pi$
$911$	14559.0	−	8405.62i	0.529484	−	0.305698i	0.740806	+	0.671719i	$0.234444\pi$
$912$		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	−0.929221	−	0.369525i	$-0.879520\pi$
$929$	−22217.1	−	38481.2i	−0.784628	−	1.35902i	0.144592	−	0.989491i	$-0.453813\pi$
$930$		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	$-0.754576\pi$
$937$		−	39975.1i		−	1.39374i	0.717199	−	0.696868i	$-0.245424\pi$
$938$		0			0
$939$	1168.95	+	1942.66i	0.0406254	+	0.0675146i
$940$		0			0
$941$	−15218.5	+	26359.2i	−0.527214	+	0.913161i	0.472283	+	0.881447i	$0.343430\pi$
$941$	−15218.5	+	26359.2i	−0.527214	+	0.913161i	−0.999497	+	0.0317144i	$0.989903\pi$
$942$		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	−0.715168	−	0.698953i	$-0.753650\pi$
$947$	−13622.3	+	7864.86i	−0.467441	+	0.269877i	0.247727	+	0.968830i	$0.420316\pi$
$948$		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	$-0.990577\pi$
$953$		−	1741.59i		−	0.0591979i	0.999562	−	0.0295990i	$-0.00942302\pi$
$954$		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	−0.789836	−	0.613318i	$-0.789834\pi$
$967$	4096.53	−	7095.40i	0.136231	−	0.235959i	0.926067	+	0.377359i	$0.123168\pi$
$968$		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	0.996527	−	0.0832744i	$-0.0265378\pi$
$977$	43445.7	+	25083.4i	1.42267	+	0.821380i	0.426146	+	0.904655i	$0.359871\pi$
$978$		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	0.855222	−	0.518263i	$-0.173421\pi$
$983$	−653.927	−	1132.63i	−0.0212177	−	0.0367502i	−0.876439	+	0.481512i	$0.840088\pi$
$984$		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	−0.377082	−	0.926180i	$-0.623073\pi$
$997$	7444.26	−	4297.95i	0.236471	−	0.136527i	0.613554	+	0.789653i	$0.289739\pi$
$998$		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.41.12	✓	48
3.2	odd	2		756.4.x.a.125.21		48
7.6	odd	2	inner	252.4.x.a.41.13	yes	48
9.2	odd	6	inner	252.4.x.a.209.13	yes	48
9.4	even	3		2268.4.f.a.1133.41		48
9.5	odd	6		2268.4.f.a.1133.8		48
9.7	even	3		756.4.x.a.629.4		48
21.20	even	2		756.4.x.a.125.4		48
63.13	odd	6		2268.4.f.a.1133.7		48
63.20	even	6	inner	252.4.x.a.209.12	yes	48
63.34	odd	6		756.4.x.a.629.21		48
63.41	even	6		2268.4.f.a.1133.42		48

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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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