LMFDB - Embedded newform 735.3.e.a.244.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,3,Mod(244,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("735.244");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	735.e (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$20.0272994305$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			244.2
Character	$\chi$	$=$	735.244
Dual form			735.3.e.a.244.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.77385i q^{2} -1.73205 q^{3} -10.2419 q^{4} +(4.71188 + 1.67279i) q^{5} -6.53650i q^{6} -23.5561i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+3.77385i q^{2} -1.73205 q^{3} -10.2419 q^{4} +(4.71188 + 1.67279i) q^{5} -6.53650i q^{6} -23.5561i q^{8} +3.00000 q^{9} +(-6.31286 + 17.7819i) q^{10} +17.9185 q^{11} +17.7395 q^{12} -1.69555 q^{13} +(-8.16121 - 2.89736i) q^{15} +47.9294 q^{16} -2.97871 q^{17} +11.3215i q^{18} +24.9908i q^{19} +(-48.2587 - 17.1326i) q^{20} +67.6218i q^{22} +9.11956i q^{23} +40.8004i q^{24} +(19.4035 + 15.7640i) q^{25} -6.39876i q^{26} -5.19615 q^{27} +17.4522 q^{29} +(10.9342 - 30.7992i) q^{30} -4.94021i q^{31} +86.6540i q^{32} -31.0358 q^{33} -11.2412i q^{34} -30.7258 q^{36} +54.6231i q^{37} -94.3114 q^{38} +2.93678 q^{39} +(39.4044 - 110.993i) q^{40} +29.2216i q^{41} -18.1962i q^{43} -183.520 q^{44} +(14.1356 + 5.01837i) q^{45} -34.4158 q^{46} -4.56448 q^{47} -83.0162 q^{48} +(-59.4908 + 73.2260i) q^{50} +5.15928 q^{51} +17.3657 q^{52} -25.2048i q^{53} -19.6095i q^{54} +(84.4299 + 29.9740i) q^{55} -43.2853i q^{57} +65.8621i q^{58} -22.7016i q^{59} +(83.5865 + 29.6746i) q^{60} -60.2216i q^{61} +18.6436 q^{62} -135.301 q^{64} +(-7.98923 - 2.83631i) q^{65} -117.124i q^{66} +45.4991i q^{67} +30.5077 q^{68} -15.7955i q^{69} +21.4512 q^{71} -70.6683i q^{72} -92.9495 q^{73} -206.139 q^{74} +(-33.6079 - 27.3040i) q^{75} -255.954i q^{76} +11.0830i q^{78} +71.1416 q^{79} +(225.837 + 80.1759i) q^{80} +9.00000 q^{81} -110.278 q^{82} -10.3791 q^{83} +(-14.0353 - 4.98276i) q^{85} +68.6696 q^{86} -30.2282 q^{87} -422.091i q^{88} -12.5524i q^{89} +(-18.9386 + 53.3457i) q^{90} -93.4019i q^{92} +8.55670i q^{93} -17.2256i q^{94} +(-41.8044 + 117.753i) q^{95} -150.089i q^{96} -127.247 q^{97} +53.7556 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 64 q^{4} + 96 q^{9}+O(q^{10}) $ 32 * q - 64 * q^4 + 96 * q^9	$ 32 q - 64 q^{4} + 96 q^{9} + 56 q^{11} - 24 q^{15} + 80 q^{16} + 68 q^{25} - 88 q^{29} - 192 q^{36} - 72 q^{39} - 640 q^{44} + 120 q^{46} - 24 q^{51} + 396 q^{60} - 400 q^{64} + 92 q^{65} + 344 q^{71} - 1800 q^{74} + 40 q^{79} + 288 q^{81} + 304 q^{85} - 288 q^{86} + 684 q^{95} + 168 q^{99}+O(q^{100}) $ 32 * q - 64 * q^4 + 96 * q^9 + 56 * q^11 - 24 * q^15 + 80 * q^16 + 68 * q^25 - 88 * q^29 - 192 * q^36 - 72 * q^39 - 640 * q^44 + 120 * q^46 - 24 * q^51 + 396 * q^60 - 400 * q^64 + 92 * q^65 + 344 * q^71 - 1800 * q^74 + 40 * q^79 + 288 * q^81 + 304 * q^85 - 288 * q^86 + 684 * q^95 + 168 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$			3.77385i			1.88692i	0.331480	+	0.943462i	$0.392452\pi$
$2$			3.77385i			1.88692i	−0.331480	+	0.943462i	$0.607548\pi$
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$	−10.2419			−2.56048
$5$	4.71188	+	1.67279i	0.942375	+	0.334558i
$5$	4.71188	+	1.67279i	0.942375	+	0.334558i
$6$		−	6.53650i		−	1.08942i
$7$		0			0
$7$		0			0
$8$		−	23.5561i		−	2.94451i
$9$	3.00000			0.333333
$10$	−6.31286	+	17.7819i	−0.631286	+	1.77819i
$11$	17.9185			1.62896			0.814479	−	0.580194i	$-0.197023\pi$
$11$	17.9185			1.62896			0.814479	+	0.580194i	$0.197023\pi$
$12$	17.7395			1.47830
$13$	−1.69555			−0.130427			−0.0652135	−	0.997871i	$-0.520773\pi$
$13$	−1.69555			−0.130427			−0.0652135	+	0.997871i	$0.520773\pi$
$14$		0			0
$15$	−8.16121	−	2.89736i	−0.544080	−	0.193157i
$16$	47.9294			2.99559
$17$	−2.97871			−0.175218			−0.0876091	−	0.996155i	$-0.527923\pi$
$17$	−2.97871			−0.175218			−0.0876091	+	0.996155i	$0.527923\pi$
$18$			11.3215i			0.628975i
$19$			24.9908i			1.31530i	0.753322	+	0.657652i	$0.228450\pi$
$19$			24.9908i			1.31530i	−0.753322	+	0.657652i	$0.771550\pi$
$20$	−48.2587	−	17.1326i	−2.41294	−	0.856631i
$21$		0			0
$22$			67.6218i			3.07372i
$23$			9.11956i			0.396502i	0.980151	+	0.198251i	$0.0635262\pi$
$23$			9.11956i			0.396502i	−0.980151	+	0.198251i	$0.936474\pi$
$24$			40.8004i			1.70002i
$25$	19.4035	+	15.7640i	0.776142	+	0.630559i
$26$		−	6.39876i		−	0.246106i
$27$	−5.19615			−0.192450
$28$		0			0
$29$	17.4522			0.601801			0.300901	−	0.953655i	$-0.402713\pi$
$29$	17.4522			0.601801			0.300901	+	0.953655i	$0.402713\pi$
$30$	10.9342	−	30.7992i	0.364473	−	1.02664i
$31$		−	4.94021i		−	0.159362i	−0.996820	−	0.0796808i	$-0.974610\pi$
$31$		−	4.94021i		−	0.159362i	0.996820	−	0.0796808i	$-0.0253901\pi$
$32$			86.6540i			2.70794i
$33$	−31.0358			−0.940479
$34$		−	11.2412i		−	0.330624i
$35$		0			0
$36$	−30.7258			−0.853494
$37$			54.6231i			1.47630i	0.674637	+	0.738150i	$0.264300\pi$
$37$			54.6231i			1.47630i	−0.674637	+	0.738150i	$0.735700\pi$
$38$	−94.3114			−2.48188
$39$	2.93678			0.0753021
$40$	39.4044	−	110.993i	0.985111	−	2.77484i
$41$			29.2216i			0.712723i	0.934348	+	0.356361i	$0.115983\pi$
$41$			29.2216i			0.712723i	−0.934348	+	0.356361i	$0.884017\pi$
$42$		0			0
$43$		−	18.1962i		−	0.423167i	−0.977360	−	0.211583i	$-0.932138\pi$
$43$		−	18.1962i		−	0.423167i	0.977360	−	0.211583i	$-0.0678620\pi$
$44$	−183.520			−4.17092
$45$	14.1356	+	5.01837i	0.314125	+	0.111519i
$46$	−34.4158			−0.748170
$47$	−4.56448			−0.0971165			−0.0485583	−	0.998820i	$-0.515463\pi$
$47$	−4.56448			−0.0971165			−0.0485583	+	0.998820i	$0.515463\pi$
$48$	−83.0162			−1.72950
$49$		0			0
$50$	−59.4908	+	73.2260i	−1.18982	+	1.46452i
$51$	5.15928			0.101162
$52$	17.3657			0.333956
$53$		−	25.2048i		−	0.475563i	−0.971319	−	0.237782i	$-0.923580\pi$
$53$		−	25.2048i		−	0.475563i	0.971319	−	0.237782i	$-0.0764202\pi$
$54$		−	19.6095i		−	0.363139i
$55$	84.4299	+	29.9740i	1.53509	+	0.544981i
$56$		0			0
$57$		−	43.2853i		−	0.759391i
$58$			65.8621i			1.13555i
$59$		−	22.7016i		−	0.384774i	−0.981319	−	0.192387i	$-0.938377\pi$
$59$		−	22.7016i		−	0.384774i	0.981319	−	0.192387i	$-0.0616228\pi$
$60$	83.5865	+	29.6746i	1.39311	+	0.494576i
$61$		−	60.2216i		−	0.987240i	−0.869678	−	0.493620i	$-0.835673\pi$
$61$		−	60.2216i		−	0.987240i	0.869678	−	0.493620i	$-0.164327\pi$
$62$	18.6436			0.300703
$63$		0			0
$64$	−135.301			−2.11408
$65$	−7.98923	−	2.83631i	−0.122911	−	0.0436355i
$66$		−	117.124i		−	1.77461i
$67$			45.4991i			0.679092i	0.940590	+	0.339546i	$0.110273\pi$
$67$			45.4991i			0.679092i	−0.940590	+	0.339546i	$0.889727\pi$
$68$	30.5077			0.448643
$69$		−	15.7955i		−	0.228921i
$70$		0			0
$71$	21.4512			0.302130			0.151065	−	0.988524i	$-0.451730\pi$
$71$	21.4512			0.302130			0.151065	+	0.988524i	$0.451730\pi$
$72$		−	70.6683i		−	0.981504i
$73$	−92.9495			−1.27328			−0.636640	−	0.771161i	$-0.719676\pi$
$73$	−92.9495			−1.27328			−0.636640	+	0.771161i	$0.719676\pi$
$74$	−206.139			−2.78567
$75$	−33.6079	−	27.3040i	−0.448106	−	0.364053i
$76$		−	255.954i		−	3.36781i
$77$		0			0
$78$			11.0830i			0.142089i
$79$	71.1416			0.900527			0.450263	−	0.892896i	$-0.351330\pi$
$79$	71.1416			0.900527			0.450263	+	0.892896i	$0.351330\pi$
$80$	225.837	+	80.1759i	2.82297	+	1.00220i
$81$	9.00000			0.111111
$82$	−110.278			−1.34485
$83$	−10.3791			−0.125050			−0.0625249	−	0.998043i	$-0.519915\pi$
$83$	−10.3791			−0.125050			−0.0625249	+	0.998043i	$0.519915\pi$
$84$		0			0
$85$	−14.0353	−	4.98276i	−0.165121	−	0.0586207i
$86$	68.6696			0.798483
$87$	−30.2282			−0.347450
$88$		−	422.091i		−	4.79648i
$89$		−	12.5524i		−	0.141038i	−0.997510	−	0.0705192i	$-0.977534\pi$
$89$		−	12.5524i		−	0.141038i	0.997510	−	0.0705192i	$-0.0224656\pi$
$90$	−18.9386	+	53.3457i	−0.210429	+	0.592730i
$91$		0			0
$92$		−	93.4019i		−	1.01524i
$93$			8.55670i			0.0920075i
$94$		−	17.2256i		−	0.183251i
$95$	−41.8044	+	117.753i	−0.440046	+	1.23951i
$96$		−	150.089i		−	1.56343i
$97$	−127.247			−1.31182			−0.655911	−	0.754839i	$-0.727715\pi$
$97$	−127.247			−1.31182			−0.655911	+	0.754839i	$0.727715\pi$
$98$		0			0
$99$	53.7556			0.542986
$100$	−198.730	−	161.453i	−1.98730	−	1.61453i
$101$			128.025i			1.26758i	0.773507	+	0.633788i	$0.218501\pi$
$101$			128.025i			1.26758i	−0.773507	+	0.633788i	$0.781499\pi$
$102$			19.4703i			0.190886i
$103$	−139.270			−1.35213			−0.676067	−	0.736840i	$-0.736317\pi$
$103$	−139.270			−1.35213			−0.676067	+	0.736840i	$0.736317\pi$
$104$			39.9406i			0.384044i
$105$		0			0
$106$	95.1193			0.897351
$107$			91.4199i			0.854392i	0.904159	+	0.427196i	$0.140499\pi$
$107$			91.4199i			0.854392i	−0.904159	+	0.427196i	$0.859501\pi$
$108$	53.2186			0.492765
$109$	166.867			1.53089			0.765446	−	0.643500i	$-0.222518\pi$
$109$	166.867			1.53089			0.765446	+	0.643500i	$0.222518\pi$
$110$	−113.117	+	318.626i	−1.02834	+	2.89660i
$111$		−	94.6099i		−	0.852342i
$112$		0			0
$113$			52.2679i			0.462548i	0.972889	+	0.231274i	$0.0742894\pi$
$113$			52.2679i			0.462548i	−0.972889	+	0.231274i	$0.925711\pi$
$114$	163.352			1.43291
$115$	−15.2551	+	42.9702i	−0.132653	+	0.373654i
$116$	−178.745			−1.54090
$117$	−5.08666			−0.0434757
$118$	85.6726			0.726039
$119$		0			0
$120$	−68.2505	+	192.246i	−0.568754	+	1.60205i
$121$	200.074			1.65350
$122$	227.267			1.86285
$123$		−	50.6133i		−	0.411491i
$124$			50.5973i			0.408043i
$125$	65.0572	+	106.736i	0.520458	+	0.853887i
$126$		0			0
$127$			124.502i			0.980329i	0.871630	+	0.490165i	$0.163063\pi$
$127$			124.502i			0.980329i	−0.871630	+	0.490165i	$0.836937\pi$
$128$		−	163.991i		−	1.28118i
$129$			31.5167i			0.244315i
$130$	10.7038	−	30.1501i	0.0823368	−	0.231924i
$131$			204.711i			1.56268i	0.624107	+	0.781339i	$0.285463\pi$
$131$			204.711i			1.56268i	−0.624107	+	0.781339i	$0.714537\pi$
$132$	317.867			2.40808
$133$		0			0
$134$	−171.707			−1.28139
$135$	−24.4836	−	8.69208i	−0.181360	−	0.0643858i
$136$			70.1668i			0.515932i
$137$		−	235.700i		−	1.72044i	−0.509926	−	0.860218i	$-0.670327\pi$
$137$		−	235.700i		−	1.72044i	0.509926	−	0.860218i	$-0.329673\pi$
$138$	59.6100			0.431956
$139$		−	112.692i		−	0.810730i	−0.914155	−	0.405365i	$-0.867144\pi$
$139$		−	112.692i		−	0.810730i	0.914155	−	0.405365i	$-0.132856\pi$
$140$		0			0
$141$	7.90590			0.0560702
$142$			80.9537i			0.570097i
$143$	−30.3818			−0.212460
$144$	143.788			0.998530
$145$	82.2328	+	29.1940i	0.567123	+	0.201338i
$146$		−	350.777i		−	2.40258i
$147$		0			0
$148$		−	559.446i		−	3.78004i
$149$	−174.053			−1.16814			−0.584069	−	0.811704i	$-0.698540\pi$
$149$	−174.053			−1.16814			−0.584069	+	0.811704i	$0.698540\pi$
$150$	103.041	−	126.831i	0.686941	−	0.845541i
$151$	−105.081			−0.695899			−0.347949	−	0.937513i	$-0.613122\pi$
$151$	−105.081			−0.695899			−0.347949	+	0.937513i	$0.613122\pi$
$152$	588.685			3.87293
$153$	−8.93613			−0.0584061
$154$		0			0
$155$	8.26394	−	23.2777i	0.0533157	−	0.150178i
$156$	−30.0783			−0.192810
$157$	−1.79059			−0.0114050			−0.00570251	−	0.999984i	$-0.501815\pi$
$157$	−1.79059			−0.0114050			−0.00570251	+	0.999984i	$0.501815\pi$
$158$			268.478i			1.69923i
$159$			43.6561i			0.274566i
$160$	−144.954	+	408.303i	−0.905963	+	2.55189i
$161$		0			0
$162$			33.9646i			0.209658i
$163$		−	73.0462i		−	0.448136i	−0.974574	−	0.224068i	$-0.928066\pi$
$163$		−	73.0462i		−	0.448136i	0.974574	−	0.224068i	$-0.0719338\pi$
$164$		−	299.286i		−	1.82491i
$165$	−146.237	−	51.9164i	−0.886284	−	0.314645i
$166$		−	39.1693i		−	0.235959i
$167$	319.441			1.91282			0.956409	−	0.292031i	$-0.0943312\pi$
$167$	319.441			1.91282			0.956409	+	0.292031i	$0.0943312\pi$
$168$		0			0
$169$	−166.125			−0.982989
$170$	18.8042	−	52.9671i	0.110613	−	0.311571i
$171$			74.9723i			0.438435i
$172$			186.364i			1.08351i
$173$	−249.548			−1.44247			−0.721237	−	0.692689i	$-0.756426\pi$
$173$	−249.548			−1.44247			−0.721237	+	0.692689i	$0.756426\pi$
$174$		−	114.077i		−	0.655612i
$175$		0			0
$176$	858.825			4.87969
$177$			39.3204i			0.222149i
$178$	47.3709			0.266129
$179$	326.634			1.82477			0.912386	−	0.409332i	$-0.134238\pi$
$179$	326.634			1.82477			0.912386	+	0.409332i	$0.134238\pi$
$180$	−144.776	−	51.3978i	−0.804312	−	0.285544i
$181$			166.724i			0.921129i	0.887626	+	0.460565i	$0.152353\pi$
$181$			166.724i			0.921129i	−0.887626	+	0.460565i	$0.847647\pi$
$182$		0			0
$183$			104.307i			0.569983i
$184$	214.821			1.16751
$185$	−91.3730	+	257.377i	−0.493908	+	1.39123i
$186$	−32.2917			−0.173611
$187$	−53.3741			−0.285423
$188$	46.7490			0.248665
$189$		0			0
$190$	−444.384	−	157.763i	−2.33886	−	0.830333i
$191$	−50.9298			−0.266648			−0.133324	−	0.991072i	$-0.542565\pi$
$191$	−50.9298			−0.266648			−0.133324	+	0.991072i	$0.542565\pi$
$192$	234.349			1.22057
$193$			47.0221i			0.243638i	0.992552	+	0.121819i	$0.0388728\pi$
$193$			47.0221i			0.243638i	−0.992552	+	0.121819i	$0.961127\pi$
$194$		−	480.210i		−	2.47531i
$195$	13.8378	+	4.91262i	0.0709628	+	0.0251929i
$196$		0			0
$197$		−	66.0845i		−	0.335454i	−0.985833	−	0.167727i	$-0.946357\pi$
$197$		−	66.0845i		−	0.335454i	0.985833	−	0.167727i	$-0.0536427\pi$
$198$			202.865i			1.02457i
$199$			75.5423i			0.379609i	0.981822	+	0.189805i	$0.0607855\pi$
$199$			75.5423i			0.379609i	−0.981822	+	0.189805i	$0.939215\pi$
$200$	371.338	−	457.072i	1.85669	−	2.28536i
$201$		−	78.8068i		−	0.392074i
$202$	−483.148			−2.39182
$203$		0			0
$204$	−52.8410			−0.259024
$205$	−48.8817	+	137.689i	−0.238447	+	0.671652i
$206$		−	525.583i		−	2.55137i
$207$			27.3587i			0.132167i
$208$	−81.2669			−0.390706
$209$			447.798i			2.14257i
$210$		0			0
$211$	307.384			1.45680			0.728398	−	0.685155i	$-0.240265\pi$
$211$	307.384			1.45680			0.728398	+	0.685155i	$0.240265\pi$
$212$			258.146i			1.21767i
$213$	−37.1546			−0.174435
$214$	−345.005			−1.61217
$215$	30.4384	−	85.7381i	0.141574	−	0.398782i
$216$			122.401i			0.566672i
$217$		0			0
$218$			629.732i			2.88868i
$219$	160.993			0.735129
$220$	−864.725	−	306.991i	−3.93057	−	1.39541i
$221$	5.05056			0.0228532
$222$	357.044			1.60830
$223$	−6.02940			−0.0270377			−0.0135188	−	0.999909i	$-0.504303\pi$
$223$	−6.02940			−0.0270377			−0.0135188	+	0.999909i	$0.504303\pi$
$224$		0			0
$225$	58.2106	+	47.2919i	0.258714	+	0.210186i
$226$	−197.251			−0.872793
$227$	−32.0609			−0.141238			−0.0706188	−	0.997503i	$-0.522497\pi$
$227$	−32.0609			−0.141238			−0.0706188	+	0.997503i	$0.522497\pi$
$228$			443.325i			1.94441i
$229$			19.6818i			0.0859469i	0.999076	+	0.0429734i	$0.0136831\pi$
$229$			19.6818i			0.0859469i	−0.999076	+	0.0429734i	$0.986317\pi$
$230$	−162.163	−	57.5705i	−0.705057	−	0.250306i
$231$		0			0
$232$		−	411.107i		−	1.77201i
$233$			148.409i			0.636949i	0.947931	+	0.318474i	$0.103170\pi$
$233$			148.409i			0.636949i	−0.947931	+	0.318474i	$0.896830\pi$
$234$		−	19.1963i		−	0.0820353i
$235$	−21.5072	−	7.63542i	−0.0915202	−	0.0324911i
$236$			232.509i			0.985207i
$237$	−123.221			−0.519919
$238$		0			0
$239$	−208.455			−0.872197			−0.436098	−	0.899899i	$-0.643640\pi$
$239$	−208.455			−0.872197			−0.436098	+	0.899899i	$0.643640\pi$
$240$	−391.162	−	138.869i	−1.62984	−	0.578620i
$241$			43.3781i			0.179992i	0.995942	+	0.0899960i	$0.0286854\pi$
$241$			43.3781i			0.179992i	−0.995942	+	0.0899960i	$0.971315\pi$
$242$			755.048i			3.12003i
$243$	−15.5885			−0.0641500
$244$			616.786i			2.52781i
$245$		0			0
$246$	191.007			0.776451
$247$		−	42.3732i		−	0.171551i
$248$	−116.372			−0.469242
$249$	17.9772			0.0721975
$250$	−402.805	+	245.516i	−1.61122	+	0.982064i
$251$		−	37.7937i		−	0.150573i	−0.997162	−	0.0752863i	$-0.976013\pi$
$251$		−	37.7937i		−	0.150573i	0.997162	−	0.0752863i	$-0.0239871\pi$
$252$		0			0
$253$			163.409i			0.645885i
$254$	−469.851			−1.84981
$255$	24.3099	+	8.63040i	0.0953328	+	0.0338447i
$256$	77.6705			0.303400
$257$	−233.160			−0.907236			−0.453618	−	0.891196i	$-0.649867\pi$
$257$	−233.160			−0.907236			−0.453618	+	0.891196i	$0.649867\pi$
$258$	−118.939			−0.461005
$259$		0			0
$260$	81.8252	+	29.0492i	0.314712	+	0.111728i
$261$	52.3567			0.200600
$262$	−772.547			−2.94865
$263$			247.735i			0.941959i	0.882144	+	0.470980i	$0.156099\pi$
$263$			247.735i			0.941959i	−0.882144	+	0.470980i	$0.843901\pi$
$264$			731.082i			2.76925i
$265$	42.1624	−	118.762i	0.159104	−	0.448159i
$266$		0			0
$267$			21.7414i			0.0814286i
$268$		−	465.999i		−	1.73880i
$269$		−	240.057i		−	0.892404i	−0.894932	−	0.446202i	$-0.852776\pi$
$269$		−	240.057i		−	0.892404i	0.894932	−	0.446202i	$-0.147224\pi$
$270$	32.8026	−	92.3975i	0.121491	−	0.342213i
$271$		−	224.634i		−	0.828908i	−0.910070	−	0.414454i	$-0.863973\pi$
$271$		−	224.634i		−	0.828908i	0.910070	−	0.414454i	$-0.136027\pi$
$272$	−142.768			−0.524882
$273$		0			0
$274$	889.495			3.24633
$275$	347.683	+	282.467i	1.26430	+	1.02715i
$276$			161.777i			0.586148i
$277$			83.6745i			0.302074i	0.988528	+	0.151037i	$0.0482613\pi$
$277$			83.6745i			0.302074i	−0.988528	+	0.151037i	$0.951739\pi$
$278$	425.281			1.52979
$279$		−	14.8206i		−	0.0531205i
$280$		0			0
$281$	−245.753			−0.874567			−0.437283	−	0.899324i	$-0.644059\pi$
$281$	−245.753			−0.874567			−0.437283	+	0.899324i	$0.644059\pi$
$282$			29.8357i			0.105800i
$283$	534.955			1.89030			0.945151	−	0.326634i	$-0.105915\pi$
$283$	534.955			1.89030			0.945151	+	0.326634i	$0.105915\pi$
$284$	−219.702			−0.773599
$285$	72.4073	−	203.955i	0.254061	−	0.715631i
$286$		−	114.656i		−	0.400896i
$287$		0			0
$288$			259.962i			0.902646i
$289$	−280.127			−0.969299
$290$	−110.174	+	310.334i	−0.379909	+	1.07012i
$291$	220.398			0.757380
$292$	951.982			3.26021
$293$	−180.678			−0.616650			−0.308325	−	0.951281i	$-0.599768\pi$
$293$	−180.678			−0.616650			−0.308325	+	0.951281i	$0.599768\pi$
$294$		0			0
$295$	37.9751	−	106.967i	0.128729	−	0.362601i
$296$	1286.71			4.34698
$297$	−93.1074			−0.313493
$298$		−	656.848i		−	2.20419i
$299$		−	15.4627i		−	0.0517147i
$300$	344.210	+	279.646i	1.14737	+	0.932152i
$301$		0			0
$302$		−	396.559i		−	1.31311i
$303$		−	221.746i		−	0.731836i
$304$			1197.79i			3.94011i
$305$	100.738	−	283.757i	0.330289	−	0.930350i
$306$		−	33.7236i		−	0.110208i
$307$	365.638			1.19100			0.595502	−	0.803354i	$-0.296953\pi$
$307$	365.638			1.19100			0.595502	+	0.803354i	$0.296953\pi$
$308$		0			0
$309$	241.222			0.780655
$310$	87.8463	+	31.1869i	0.283375	+	0.100603i
$311$			470.552i			1.51303i	0.653977	+	0.756515i	$0.273099\pi$
$311$			470.552i			1.51303i	−0.653977	+	0.756515i	$0.726901\pi$
$312$		−	69.1791i		−	0.221728i
$313$	193.579			0.618463			0.309232	−	0.950987i	$-0.399928\pi$
$313$	193.579			0.618463			0.309232	+	0.950987i	$0.399928\pi$
$314$		−	6.75740i		−	0.0215204i
$315$		0			0
$316$	−728.628			−2.30578
$317$		−	489.732i		−	1.54490i	−0.635079	−	0.772448i	$-0.719032\pi$
$317$		−	489.732i		−	1.54490i	0.635079	−	0.772448i	$-0.280968\pi$
$318$	−164.751			−0.518086
$319$	312.718			0.980309
$320$	−637.523	−	226.331i	−1.99226	−	0.707284i
$321$		−	158.344i		−	0.493283i
$322$		0			0
$323$		−	74.4403i		−	0.230465i
$324$	−92.1774			−0.284498
$325$	−32.8997	−	26.7286i	−0.101230	−	0.0822419i
$326$	275.665			0.845599
$327$	−289.023			−0.883861
$328$	688.348			2.09862
$329$		0			0
$330$	195.925	−	551.876i	0.593711	−	1.67235i
$331$	374.742			1.13215			0.566076	−	0.824353i	$-0.308461\pi$
$331$	374.742			1.13215			0.566076	+	0.824353i	$0.308461\pi$
$332$	106.302			0.320188
$333$			163.869i			0.492100i
$334$			1205.52i			3.60934i
$335$	−76.1106	+	214.386i	−0.227196	+	0.639959i
$336$		0			0
$337$		−	513.540i		−	1.52386i	−0.647661	−	0.761928i	$-0.724253\pi$
$337$		−	513.540i		−	1.52386i	0.647661	−	0.761928i	$-0.275747\pi$
$338$		−	626.931i		−	1.85483i
$339$		−	90.5307i		−	0.267052i
$340$	143.749	+	51.0331i	0.422790	+	0.150097i
$341$		−	88.5213i		−	0.259593i
$342$	−282.934			−0.827293
$343$		0			0
$344$	−428.631			−1.24602
$345$	26.4226	−	74.4266i	0.0765873	−	0.215729i
$346$		−	941.756i		−	2.72184i
$347$		−	398.856i		−	1.14944i	−0.818350	−	0.574721i	$-0.805111\pi$
$347$		−	398.856i		−	1.14944i	0.818350	−	0.574721i	$-0.194889\pi$
$348$	309.595			0.889640
$349$		−	653.580i		−	1.87272i	−0.351039	−	0.936361i	$-0.614171\pi$
$349$		−	653.580i		−	1.87272i	0.351039	−	0.936361i	$-0.385829\pi$
$350$		0			0
$351$	8.81035			0.0251007
$352$			1552.71i			4.41111i
$353$	106.218			0.300900			0.150450	−	0.988618i	$-0.451928\pi$
$353$	106.218			0.300900			0.150450	+	0.988618i	$0.451928\pi$
$354$	−148.389			−0.419179
$355$	101.076	+	35.8834i	0.284720	+	0.101080i
$356$			128.561i			0.361127i
$357$		0			0
$358$			1232.67i			3.44321i
$359$	−345.051			−0.961146			−0.480573	−	0.876955i	$-0.659571\pi$
$359$	−345.051			−0.961146			−0.480573	+	0.876955i	$0.659571\pi$
$360$	118.213	−	332.980i	0.328370	−	0.924945i
$361$	−263.539			−0.730025
$362$	−629.193			−1.73810
$363$	−346.538			−0.954649
$364$		0			0
$365$	−437.966	−	155.485i	−1.19991	−	0.425987i
$366$	−393.639			−1.07552
$367$	274.448			0.747815			0.373908	−	0.927466i	$-0.378018\pi$
$367$	274.448			0.747815			0.373908	+	0.927466i	$0.378018\pi$
$368$			437.095i			1.18776i
$369$			87.6649i			0.237574i
$370$	−971.302	−	344.828i	−2.62514	−	0.931967i
$371$		0			0
$372$		−	87.6371i		−	0.235584i
$373$			455.232i			1.22046i	0.792223	+	0.610231i	$0.208923\pi$
$373$			455.232i			1.22046i	−0.792223	+	0.610231i	$0.791077\pi$
$374$		−	201.426i		−	0.538572i
$375$	−112.682	−	184.872i	−0.300486	−	0.492992i
$376$			107.521i			0.285961i
$377$	−29.5912			−0.0784912
$378$		0			0
$379$	609.977			1.60944			0.804720	−	0.593655i	$-0.202316\pi$
$379$	609.977			1.60944			0.804720	+	0.593655i	$0.202316\pi$
$380$	428.157	−	1206.02i	1.12673	−	3.17374i
$381$		−	215.643i		−	0.565993i
$382$		−	192.201i		−	0.503145i
$383$	560.301			1.46293			0.731464	−	0.681880i	$-0.238837\pi$
$383$	560.301			1.46293			0.731464	+	0.681880i	$0.238837\pi$
$384$			284.040i			0.739688i
$385$		0			0
$386$	−177.454			−0.459727
$387$		−	54.5885i		−	0.141056i
$388$	1303.25			3.35890
$389$	317.892			0.817202			0.408601	−	0.912713i	$-0.366017\pi$
$389$	317.892			0.817202			0.408601	+	0.912713i	$0.366017\pi$
$390$	−18.5395	+	52.2216i	−0.0475372	+	0.133901i
$391$		−	27.1645i		−	0.0694745i
$392$		0			0
$393$		−	354.569i		−	0.902212i
$394$	249.393			0.632976
$395$	335.210	+	119.005i	0.848634	+	0.301279i
$396$	−550.561			−1.39031
$397$	340.973			0.858873			0.429437	−	0.903097i	$-0.358712\pi$
$397$	340.973			0.858873			0.429437	+	0.903097i	$0.358712\pi$
$398$	−285.085			−0.716294
$399$		0			0
$400$	930.000	+	755.558i	2.32500	+	1.88890i
$401$	−195.539			−0.487629			−0.243815	−	0.969822i	$-0.578399\pi$
$401$	−195.539			−0.487629			−0.243815	+	0.969822i	$0.578399\pi$
$402$	297.405			0.739813
$403$			8.37638i			0.0207851i
$404$		−	1311.23i		−	3.24561i
$405$	42.4069	+	15.0551i	0.104708	+	0.0371731i
$406$		0			0
$407$			978.765i			2.40483i
$408$		−	121.532i		−	0.297874i
$409$		−	532.815i		−	1.30273i	−0.758766	−	0.651363i	$-0.774197\pi$
$409$		−	532.815i		−	1.30273i	0.758766	−	0.651363i	$-0.225803\pi$
$410$	−519.616	−	184.472i	−1.26736	−	0.449932i
$411$			408.244i			0.993294i
$412$	1426.39			3.46212
$413$		0			0
$414$	−103.247			−0.249390
$415$	−48.9052	−	17.3621i	−0.117844	−	0.0418364i
$416$		−	146.926i		−	0.353188i
$417$			195.187i			0.468075i
$418$	−1689.92			−4.04287
$419$			221.451i			0.528523i	0.964451	+	0.264262i	$0.0851282\pi$
$419$			221.451i			0.528523i	−0.964451	+	0.264262i	$0.914872\pi$
$420$		0			0
$421$	73.0821			0.173592			0.0867958	−	0.996226i	$-0.472337\pi$
$421$	73.0821			0.173592			0.0867958	+	0.996226i	$0.472337\pi$
$422$			1160.02i			2.74886i
$423$	−13.6934			−0.0323722
$424$	−593.728			−1.40030
$425$	−57.7975	−	46.9563i	−0.135994	−	0.110485i
$426$		−	140.216i		−	0.329145i
$427$		0			0
$428$		−	936.317i		−	2.18766i
$429$	52.6228			0.122664
$430$	323.562	+	114.870i	0.752471	+	0.267139i
$431$	572.600			1.32854			0.664270	−	0.747493i	$-0.268743\pi$
$431$	572.600			1.32854			0.664270	+	0.747493i	$0.268743\pi$
$432$	−249.049			−0.576501
$433$	217.665			0.502691			0.251345	−	0.967897i	$-0.419127\pi$
$433$	217.665			0.502691			0.251345	+	0.967897i	$0.419127\pi$
$434$		0			0
$435$	−142.431	−	50.5654i	−0.327428	−	0.116242i
$436$	−1709.04			−3.91982
$437$	−227.905			−0.521521
$438$			607.564i			1.38713i
$439$		−	732.313i		−	1.66814i	−0.551659	−	0.834070i	$-0.686005\pi$
$439$		−	732.313i		−	1.66814i	0.551659	−	0.834070i	$-0.313995\pi$
$440$	706.070	−	1988.84i	1.60470	−	4.52009i
$441$		0			0
$442$			19.0600i			0.0431223i
$443$		−	394.927i		−	0.891482i	−0.895162	−	0.445741i	$-0.852940\pi$
$443$		−	394.927i		−	0.891482i	0.895162	−	0.445741i	$-0.147060\pi$
$444$			968.989i			2.18241i
$445$	20.9976	−	59.1455i	0.0471856	−	0.132911i
$446$		−	22.7540i		−	0.0510180i
$447$	301.468			0.674425
$448$		0			0
$449$	474.587			1.05699			0.528493	−	0.848938i	$-0.322757\pi$
$449$	474.587			1.05699			0.528493	+	0.848938i	$0.322757\pi$
$450$	−178.472	+	219.678i	−0.396606	+	0.488173i
$451$			523.608i			1.16099i
$452$		−	535.325i		−	1.18435i
$453$	182.005			0.401777
$454$		−	120.993i		−	0.266505i
$455$		0			0
$456$	−1019.63			−2.23604
$457$		−	411.203i		−	0.899788i	−0.893082	−	0.449894i	$-0.851462\pi$
$457$		−	411.203i		−	0.899788i	0.893082	−	0.449894i	$-0.148538\pi$
$458$	−74.2763			−0.162175
$459$	15.4778			0.0337208
$460$	156.242	−	440.098i	0.339656	−	0.956735i
$461$			750.453i			1.62788i	0.580948	+	0.813941i	$0.302682\pi$
$461$			750.453i			1.62788i	−0.580948	+	0.813941i	$0.697318\pi$
$462$		0			0
$463$		−	430.641i		−	0.930110i	−0.885282	−	0.465055i	$-0.846034\pi$
$463$		−	430.641i		−	0.930110i	0.885282	−	0.465055i	$-0.153966\pi$
$464$	836.476			1.80275
$465$	−14.3136	+	40.3181i	−0.0307819	+	0.0867055i
$466$	−560.073			−1.20187
$467$	599.995			1.28479			0.642393	−	0.766375i	$-0.277942\pi$
$467$	599.995			1.28479			0.642393	+	0.766375i	$0.277942\pi$
$468$	52.0972			0.111319
$469$		0			0
$470$	28.8149	−	81.1651i	0.0613083	−	0.172692i
$471$	3.10139			0.00658469
$472$	−534.762			−1.13297
$473$		−	326.049i		−	0.689320i
$474$		−	465.017i		−	0.981049i
$475$	−393.954	+	484.910i	−0.829377	+	1.02086i
$476$		0			0
$477$		−	75.6145i		−	0.158521i
$478$		−	786.678i		−	1.64577i
$479$		−	668.435i		−	1.39548i	−0.716351	−	0.697740i	$-0.754189\pi$
$479$		−	668.435i		−	1.39548i	0.716351	−	0.697740i	$-0.245811\pi$
$480$	251.068	−	707.201i	0.523058	−	1.47334i
$481$		−	92.6163i		−	0.192549i
$482$	−163.702			−0.339631
$483$		0			0
$484$	−2049.14			−4.23376
$485$	−599.570	−	212.857i	−1.23623	−	0.438881i
$486$		−	58.8285i		−	0.121046i
$487$			120.272i			0.246965i	0.992347	+	0.123483i	$0.0394063\pi$
$487$			120.272i			0.246965i	−0.992347	+	0.123483i	$0.960594\pi$
$488$	−1418.59			−2.90694
$489$			126.520i			0.258731i
$490$		0			0
$491$	−749.043			−1.52555			−0.762773	−	0.646666i	$-0.776163\pi$
$491$	−749.043			−1.52555			−0.762773	+	0.646666i	$0.776163\pi$
$492$			518.378i			1.05361i
$493$	−51.9852			−0.105447
$494$	159.910			0.323704
$495$	253.290	+	89.9219i	0.511696	+	0.181660i
$496$		−	236.781i		−	0.477382i
$497$		0			0
$498$			67.8432i			0.136231i
$499$	426.520			0.854750			0.427375	−	0.904074i	$-0.359438\pi$
$499$	426.520			0.854750			0.427375	+	0.904074i	$0.359438\pi$
$500$	−666.312	−	1093.18i	−1.33262	−	2.18636i
$501$	−553.287			−1.10437
$502$	142.628			0.284119
$503$	−84.6359			−0.168262			−0.0841311	−	0.996455i	$-0.526811\pi$
$503$	−84.6359			−0.168262			−0.0841311	+	0.996455i	$0.526811\pi$
$504$		0			0
$505$	−214.159	+	603.239i	−0.424078	+	1.19453i
$506$	−616.681			−1.21874
$507$	287.737			0.567529
$508$		−	1275.14i		−	2.51012i
$509$		−	660.071i		−	1.29680i	−0.761300	−	0.648399i	$-0.775439\pi$
$509$		−	660.071i		−	1.29680i	0.761300	−	0.648399i	$-0.224561\pi$
$510$	−32.5698	+	91.7418i	−0.0638624	+	0.179886i
$511$		0			0
$512$		−	362.846i		−	0.708683i
$513$		−	129.856i		−	0.253130i
$514$		−	879.910i		−	1.71189i
$515$	−656.222	−	232.969i	−1.27422	−	0.452368i
$516$		−	322.792i		−	0.625565i
$517$	−81.7887			−0.158199
$518$		0			0
$519$	432.230			0.832813
$520$	−66.8123	+	188.195i	−0.128485	+	0.361914i
$521$			144.242i			0.276857i	0.990372	+	0.138428i	$0.0442051\pi$
$521$			144.242i			0.276857i	−0.990372	+	0.138428i	$0.955795\pi$
$522$			197.586i			0.378518i
$523$	539.402			1.03136			0.515680	−	0.856781i	$-0.327539\pi$
$523$	539.402			1.03136			0.515680	+	0.856781i	$0.327539\pi$
$524$		−	2096.63i		−	4.00121i
$525$		0			0
$526$	−934.915			−1.77741
$527$			14.7155i			0.0279231i
$528$	−1487.53			−2.81729
$529$	445.834			0.842786
$530$	448.190	+	159.115i	0.845642	+	0.300216i
$531$		−	68.1049i		−	0.128258i
$532$		0			0
$533$		−	49.5468i		−	0.0929583i
$534$	−82.0489			−0.153650
$535$	−152.926	+	430.759i	−0.285844	+	0.805158i
$536$	1071.78			1.99959
$537$	−565.747			−1.05353
$538$	905.938			1.68390
$539$		0			0
$540$	250.760	+	89.0237i	0.464370	+	0.164859i
$541$	75.8844			0.140267			0.0701335	−	0.997538i	$-0.477657\pi$
$541$	75.8844			0.140267			0.0701335	+	0.997538i	$0.477657\pi$
$542$	847.735			1.56409
$543$		−	288.775i		−	0.531814i
$544$		−	258.117i		−	0.474480i
$545$	786.258	+	279.134i	1.44267	+	0.512173i
$546$		0			0
$547$		−	555.937i		−	1.01634i	−0.861257	−	0.508169i	$-0.830322\pi$
$547$		−	555.937i		−	1.01634i	0.861257	−	0.508169i	$-0.169678\pi$
$548$			2414.02i			4.40515i
$549$		−	180.665i		−	0.329080i
$550$	−1065.99	+	1312.10i	−1.93816	+	2.38564i
$551$			436.145i			0.791552i
$552$	−372.081			−0.674060
$553$		0			0
$554$	−315.775			−0.569991
$555$	158.263	−	445.790i	0.285158	−	0.803226i
$556$			1154.18i			2.07586i
$557$			441.191i			0.792084i	0.918232	+	0.396042i	$0.129617\pi$
$557$			441.191i			0.792084i	−0.918232	+	0.396042i	$0.870383\pi$
$558$	55.9308			0.100234
$559$			30.8526i			0.0551924i
$560$		0			0
$561$	92.4467			0.164789
$562$		−	927.436i		−	1.65024i
$563$	359.801			0.639078			0.319539	−	0.947573i	$-0.396472\pi$
$563$	359.801			0.639078			0.319539	+	0.947573i	$0.396472\pi$
$564$	−80.9717			−0.143567
$565$	−87.4334	+	246.280i	−0.154749	+	0.435894i
$566$			2018.84i			3.56686i
$567$		0			0
$568$		−	505.307i		−	0.889626i
$569$	−310.397			−0.545514			−0.272757	−	0.962083i	$-0.587935\pi$
$569$	−310.397			−0.545514			−0.272757	+	0.962083i	$0.587935\pi$
$570$	769.695	+	273.254i	1.35034	+	0.479393i
$571$	21.9793			0.0384927			0.0192464	−	0.999815i	$-0.493873\pi$
$571$	21.9793			0.0384927			0.0192464	+	0.999815i	$0.493873\pi$
$572$	311.168			0.544001
$573$	88.2130			0.153949
$574$		0			0
$575$	−143.760	+	176.952i	−0.250018	+	0.307742i
$576$	−405.904			−0.704694
$577$	270.220			0.468319			0.234160	−	0.972198i	$-0.424766\pi$
$577$	270.220			0.468319			0.234160	+	0.972198i	$0.424766\pi$
$578$		−	1057.16i		−	1.82899i
$579$		−	81.4447i		−	0.140664i
$580$	−842.222	−	299.003i	−1.45211	−	0.515522i
$581$		0			0
$582$			831.747i			1.42912i
$583$		−	451.634i		−	0.774672i
$584$			2189.53i			3.74919i
$585$	−23.9677	−	8.50892i	−0.0409704	−	0.0145452i
$586$		−	681.853i		−	1.16357i
$587$	−680.487			−1.15926			−0.579632	−	0.814879i	$-0.696804\pi$
$587$	−680.487			−1.15926			−0.579632	+	0.814879i	$0.696804\pi$
$588$		0			0
$589$	123.460			0.209609
$590$	403.679	+	143.312i	0.684201	+	0.242902i
$591$			114.462i			0.193675i
$592$			2618.05i			4.42239i
$593$	−224.995			−0.379419			−0.189709	−	0.981840i	$-0.560755\pi$
$593$	−224.995			−0.379419			−0.189709	+	0.981840i	$0.560755\pi$
$594$		−	351.373i		−	0.591537i
$595$		0			0
$596$	1782.63			2.99100
$597$		−	130.843i		−	0.219168i
$598$	58.3538			0.0975816
$599$	−216.857			−0.362032			−0.181016	−	0.983480i	$-0.557939\pi$
$599$	−216.857			−0.362032			−0.181016	+	0.983480i	$0.557939\pi$
$600$	−643.176	+	791.671i	−1.07196	+	1.31945i
$601$			589.460i			0.980798i	0.871498	+	0.490399i	$0.163149\pi$
$601$			589.460i			0.980798i	−0.871498	+	0.490399i	$0.836851\pi$
$602$		0			0
$603$			136.497i			0.226364i
$604$	1076.23			1.78184
$605$	942.722	+	334.681i	1.55822	+	0.553192i
$606$	836.836			1.38092
$607$	804.190			1.32486			0.662430	−	0.749124i	$-0.269525\pi$
$607$	804.190			1.32486			0.662430	+	0.749124i	$0.269525\pi$
$608$	−2165.55			−3.56176
$609$		0			0
$610$	1070.86	+	380.171i	1.75550	+	0.623231i
$611$	7.73931			0.0126666
$612$	91.5232			0.149548
$613$			216.454i			0.353107i	0.984291	+	0.176553i	$0.0564948\pi$
$613$			216.454i			0.353107i	−0.984291	+	0.176553i	$0.943505\pi$
$614$			1379.86i			2.24733i
$615$	84.6656	−	238.484i	0.137668	−	0.387778i
$616$		0			0
$617$			519.617i			0.842167i	0.907022	+	0.421084i	$0.138350\pi$
$617$			519.617i			0.842167i	−0.907022	+	0.421084i	$0.861650\pi$
$618$			910.337i			1.47304i
$619$			167.842i			0.271150i	0.990767	+	0.135575i	$0.0432882\pi$
$619$			167.842i			0.271150i	−0.990767	+	0.135575i	$0.956712\pi$
$620$	−84.6387	+	238.408i	−0.136514	+	0.384529i
$621$		−	47.3866i		−	0.0763069i
$622$	−1775.79			−2.85497
$623$		0			0
$624$	140.758			0.225574
$625$	127.995	+	611.754i	0.204791	+	0.978806i
$626$			730.538i			1.16699i
$627$		−	775.609i		−	1.23702i
$628$	18.3391			0.0292023
$629$		−	162.706i		−	0.258675i
$630$		0			0
$631$	−17.7243			−0.0280892			−0.0140446	−	0.999901i	$-0.504471\pi$
$631$	−17.7243			−0.0280892			−0.0140446	+	0.999901i	$0.504471\pi$
$632$		−	1675.82i		−	2.65161i
$633$	−532.404			−0.841081
$634$	1848.17			2.91510
$635$	−208.266	+	586.637i	−0.327977	+	0.923838i
$636$		−	447.122i		−	0.703023i
$637$		0			0
$638$			1180.15i			1.84977i
$639$	64.3537			0.100710
$640$	274.322	−	772.703i	0.428628	−	1.20735i
$641$	−615.090			−0.959579			−0.479789	−	0.877384i	$-0.659287\pi$
$641$	−615.090			−0.959579			−0.479789	+	0.877384i	$0.659287\pi$
$642$	597.566			0.930788
$643$	−1083.57			−1.68517			−0.842586	−	0.538562i	$-0.818968\pi$
$643$	−1083.57			−1.68517			−0.842586	+	0.538562i	$0.818968\pi$
$644$		0			0
$645$	−52.7208	+	148.503i	−0.0817377	+	0.230237i
$646$	280.926			0.434871
$647$	−92.5299			−0.143014			−0.0715069	−	0.997440i	$-0.522781\pi$
$647$	−92.5299			−0.143014			−0.0715069	+	0.997440i	$0.522781\pi$
$648$		−	212.005i		−	0.327168i
$649$		−	406.780i		−	0.626780i
$650$	100.870	−	124.159i	0.155184	−	0.191013i
$651$		0			0
$652$			748.134i			1.14744i
$653$		−	512.496i		−	0.784834i	−0.919787	−	0.392417i	$-0.871639\pi$
$653$		−	512.496i		−	0.784834i	0.919787	−	0.392417i	$-0.128361\pi$
$654$		−	1090.73i		−	1.66778i
$655$	−342.438	+	964.572i	−0.522807	+	1.47263i
$656$			1400.58i			2.13502i
$657$	−278.849			−0.424427
$658$		0			0
$659$	52.4627			0.0796095			0.0398048	−	0.999207i	$-0.487326\pi$
$659$	52.4627			0.0796095			0.0398048	+	0.999207i	$0.487326\pi$
$660$	1497.75	+	531.724i	2.26931	+	0.805643i
$661$		−	443.803i		−	0.671411i	−0.941967	−	0.335705i	$-0.891025\pi$
$661$		−	443.803i		−	0.671411i	0.941967	−	0.335705i	$-0.108975\pi$
$662$			1414.22i			2.13628i
$663$	−8.74783			−0.0131943
$664$			244.492i			0.368211i
$665$		0			0
$666$	−618.418			−0.928555
$667$			159.157i			0.238616i
$668$	−3271.69			−4.89774
$669$	10.4432			0.0156102
$670$	−809.061	−	287.230i	−1.20755	−	0.428701i
$671$		−	1079.08i		−	1.60817i
$672$		0			0
$673$		−	1281.06i		−	1.90351i	−0.306863	−	0.951754i	$-0.599279\pi$
$673$		−	1281.06i		−	1.90351i	0.306863	−	0.951754i	$-0.400721\pi$
$674$	1938.02			2.87540
$675$	−100.824	−	81.9120i	−0.149369	−	0.121351i
$676$	1701.44			2.51693
$677$	−302.274			−0.446490			−0.223245	−	0.974762i	$-0.571665\pi$
$677$	−302.274			−0.446490			−0.223245	+	0.974762i	$0.571665\pi$
$678$	341.649			0.503907
$679$		0			0
$680$	−117.374	+	330.617i	−0.172609	+	0.486202i
$681$	55.5312			0.0815436
$682$	334.066			0.489833
$683$			333.021i			0.487586i	0.969827	+	0.243793i	$0.0783918\pi$
$683$			333.021i			0.487586i	−0.969827	+	0.243793i	$0.921608\pi$
$684$		−	767.862i		−	1.12260i
$685$	394.276	−	1110.59i	0.575586	−	1.62130i
$686$		0			0
$687$		−	34.0899i		−	0.0496214i
$688$		−	872.132i		−	1.26763i
$689$			42.7361i			0.0620263i
$690$	280.875	+	99.7150i	0.407065	+	0.144515i
$691$			1034.26i			1.49675i	0.663274	+	0.748377i	$0.269166\pi$
$691$			1034.26i			1.49675i	−0.663274	+	0.748377i	$0.730834\pi$
$692$	2555.85			3.69343
$693$		0			0
$694$	1505.22			2.16891
$695$	188.509	−	530.988i	0.271237	−	0.764012i
$696$			712.058i			1.02307i
$697$		−	87.0428i		−	0.124882i
$698$	2466.51			3.53368
$699$		−	257.052i		−	0.367742i
$700$		0			0
$701$	−1080.76			−1.54174			−0.770871	−	0.636992i	$-0.780178\pi$
$701$	−1080.76			−1.54174			−0.770871	+	0.636992i	$0.780178\pi$
$702$			33.2489i			0.0473631i
$703$	−1365.07			−1.94178
$704$	−2424.40			−3.44375
$705$	37.2516	+	13.2249i	0.0528392	+	0.0187588i
$706$			400.849i			0.567775i
$707$		0			0
$708$		−	402.717i		−	0.568809i
$709$	−739.378			−1.04285			−0.521423	−	0.853298i	$-0.674599\pi$
$709$	−739.378			−1.04285			−0.521423	+	0.853298i	$0.674599\pi$
$710$	−135.419	+	381.444i	−0.190731	+	0.537245i
$711$	213.425			0.300176
$712$	−295.686			−0.415290
$713$	45.0525			0.0631873
$714$		0			0
$715$	−143.155	−	50.8224i	−0.200217	−	0.0710803i
$716$	−3345.36			−4.67230
$717$	361.055			0.503563
$718$		−	1302.17i		−	1.81361i
$719$			964.236i			1.34108i	0.741874	+	0.670540i	$0.233937\pi$
$719$			964.236i			1.34108i	−0.741874	+	0.670540i	$0.766063\pi$
$720$	677.512	+	240.528i	0.940990	+	0.334066i
$721$		0			0
$722$		−	994.556i		−	1.37750i
$723$		−	75.1331i		−	0.103918i
$724$		−	1707.58i		−	2.35854i
$725$	338.635	+	275.117i	0.467083	+	0.379471i
$726$		−	1307.78i		−	1.80135i
$727$	−894.210			−1.23000			−0.615000	−	0.788527i	$-0.710844\pi$
$727$	−894.210			−1.23000			−0.615000	+	0.788527i	$0.710844\pi$
$728$		0			0
$729$	27.0000			0.0370370
$730$	586.777	−	1652.82i	0.803804	−	2.26414i
$731$			54.2011i			0.0741465i
$732$		−	1068.30i		−	1.45943i
$733$	−250.214			−0.341357			−0.170678	−	0.985327i	$-0.554596\pi$
$733$	−250.214			−0.341357			−0.170678	+	0.985327i	$0.554596\pi$
$734$			1035.73i			1.41107i
$735$		0			0
$736$	−790.246			−1.07370
$737$			815.277i			1.10621i
$738$	−330.834			−0.448284
$739$	−341.507			−0.462120			−0.231060	−	0.972939i	$-0.574219\pi$
$739$	−341.507			−0.462120			−0.231060	+	0.972939i	$0.574219\pi$
$740$	935.836	−	2636.04i	1.26464	−	3.56221i
$741$			73.3925i			0.0990452i
$742$		0			0
$743$		−	1076.61i		−	1.44900i	−0.689274	−	0.724501i	$-0.742070\pi$
$743$		−	1076.61i		−	1.44900i	0.689274	−	0.724501i	$-0.257930\pi$
$744$	201.562			0.270917
$745$	−820.114	−	291.154i	−1.10082	−	0.390810i
$746$	−1717.98			−2.30292
$747$	−31.1374			−0.0416833
$748$	546.654			0.730821
$749$		0			0
$750$	697.679	−	425.246i	0.930239	−	0.566995i
$751$	−328.129			−0.436923			−0.218462	−	0.975846i	$-0.570104\pi$
$751$	−328.129			−0.436923			−0.218462	+	0.975846i	$0.570104\pi$
$752$	−218.773			−0.290921
$753$			65.4606i			0.0869331i
$754$		−	111.673i		−	0.148107i
$755$	−495.127	−	175.778i	−0.655798	−	0.232819i
$756$		0			0
$757$			560.744i			0.740745i	0.928883	+	0.370372i	$0.120770\pi$
$757$			560.744i			0.740745i	−0.928883	+	0.370372i	$0.879230\pi$
$758$			2301.96i			3.03689i
$759$		−	283.033i		−	0.372902i
$760$	2773.81	+	984.748i	3.64975	+	1.29572i
$761$		−	831.830i		−	1.09307i	−0.837435	−	0.546537i	$-0.815946\pi$
$761$		−	831.830i		−	1.09307i	0.837435	−	0.546537i	$-0.184054\pi$
$762$	813.806			1.06799
$763$		0			0
$764$	521.620			0.682748
$765$	−42.1059	−	14.9483i	−0.0550404	−	0.0195402i
$766$			2114.49i			2.76043i
$767$			38.4918i			0.0501849i
$768$	−134.529			−0.175168
$769$			715.384i			0.930278i	0.885238	+	0.465139i	$0.153996\pi$
$769$			715.384i			0.930278i	−0.885238	+	0.465139i	$0.846004\pi$
$770$		0			0
$771$	403.845			0.523793
$772$		−	481.598i		−	0.623831i
$773$	−277.159			−0.358550			−0.179275	−	0.983799i	$-0.557375\pi$
$773$	−277.159			−0.358550			−0.179275	+	0.983799i	$0.557375\pi$
$774$	206.009			0.266161
$775$	77.8773	−	95.8576i	0.100487	−	0.123687i
$776$			2997.44i			3.86267i
$777$		0			0
$778$			1199.68i			1.54200i
$779$	−730.271			−0.937447
$780$	−141.725	−	50.3148i	−0.181699	−	0.0645061i
$781$	384.375			0.492157
$782$	102.515			0.131093
$783$	−90.6845			−0.115817
$784$		0			0
$785$	−8.43702	−	2.99528i	−0.0107478	−	0.00381564i
$786$	1338.09			1.70241
$787$	902.319			1.14653			0.573265	−	0.819370i	$-0.305677\pi$
$787$	902.319			1.14653			0.573265	+	0.819370i	$0.305677\pi$
$788$			676.832i			0.858924i
$789$		−	429.090i		−	0.543840i
$790$	−449.107	+	1265.03i	−0.568490	+	1.60131i
$791$		0			0
$792$		−	1266.27i		−	1.59883i
$793$			102.109i			0.128763i
$794$			1286.78i			1.62063i
$795$	−73.0275	+	205.702i	−0.0918585	+	0.258745i
$796$		−	773.699i		−	0.971984i
$797$	159.124			0.199654			0.0998271	−	0.995005i	$-0.468171\pi$
$797$	159.124			0.199654			0.0998271	+	0.995005i	$0.468171\pi$
$798$		0			0
$799$	13.5963			0.0170166
$800$	−1366.01	+	1681.39i	−1.70751	+	2.10174i
$801$		−	37.6573i		−	0.0470128i
$802$		−	737.935i		−	0.920119i
$803$	−1665.52			−2.07412
$804$			807.134i			1.00390i
$805$		0			0
$806$	−31.6112			−0.0392199
$807$			415.791i			0.515230i
$808$	3015.77			3.73239
$809$	393.094			0.485901			0.242951	−	0.970039i	$-0.421885\pi$
$809$	393.094			0.485901			0.242951	+	0.970039i	$0.421885\pi$
$810$	−56.8157	+	160.037i	−0.0701429	+	0.197577i
$811$		−	845.797i		−	1.04291i	−0.853280	−	0.521453i	$-0.825390\pi$
$811$		−	845.797i		−	1.04291i	0.853280	−	0.521453i	$-0.174610\pi$
$812$		0			0
$813$			389.078i			0.478570i
$814$	−3693.71			−4.53773
$815$	122.191	−	344.184i	0.149928	−	0.422312i
$816$	247.281			0.303041
$817$	454.736			0.556593
$818$	2010.76			2.45815
$819$		0			0
$820$	500.643	−	1410.20i	0.610540	−	1.71975i
$821$	−76.0957			−0.0926866			−0.0463433	−	0.998926i	$-0.514757\pi$
$821$	−76.0957			−0.0926866			−0.0463433	+	0.998926i	$0.514757\pi$
$822$	−1540.65			−1.87427
$823$			254.523i			0.309263i	0.987972	+	0.154631i	$0.0494190\pi$
$823$			254.523i			0.309263i	−0.987972	+	0.154631i	$0.950581\pi$
$824$			3280.65i			3.98138i
$825$	−602.204	−	489.247i	−0.729945	−	0.593027i
$826$		0			0
$827$			61.6368i			0.0745306i	0.999305	+	0.0372653i	$0.0118647\pi$
$827$			61.6368i			0.0745306i	−0.999305	+	0.0372653i	$0.988135\pi$
$828$		−	280.206i		−	0.338413i
$829$		−	1419.15i		−	1.71188i	−0.517078	−	0.855938i	$-0.672980\pi$
$829$		−	1419.15i		−	1.71188i	0.517078	−	0.855938i	$-0.327020\pi$
$830$	65.5220	−	184.561i	0.0789422	−	0.222362i
$831$		−	144.929i		−	0.174403i
$832$	229.410			0.275734
$833$		0			0
$834$	−736.608			−0.883223
$835$	1505.16	+	534.357i	1.80259	+	0.639949i
$836$		−	4586.32i		−	5.48602i
$837$			25.6701i			0.0306692i
$838$	−835.723			−0.997283
$839$		−	207.296i		−	0.247075i	−0.992340	−	0.123538i	$-0.960576\pi$
$839$		−	207.296i		−	0.247075i	0.992340	−	0.123538i	$-0.0394239\pi$
$840$		0			0
$841$	−536.419			−0.637835
$842$			275.801i			0.327554i
$843$	425.657			0.504931
$844$	−3148.20			−3.73010
$845$	−782.761	−	277.893i	−0.926344	−	0.328867i
$846$		−	51.6769i		−	0.0610838i
$847$		0			0
$848$		−	1208.05i		−	1.42459i
$849$	−926.570			−1.09137
$850$	177.206	−	218.119i	0.208478	−	0.256611i
$851$	−498.138			−0.585356
$852$	380.535			0.446637
$853$	957.163			1.12211			0.561057	−	0.827777i	$-0.310395\pi$
$853$	957.163			1.12211			0.561057	+	0.827777i	$0.310395\pi$
$854$		0			0
$855$	−125.413	+	353.260i	−0.146682	+	0.413170i
$856$	2153.50			2.51577
$857$	−693.316			−0.809003			−0.404502	−	0.914537i	$-0.632555\pi$
$857$	−693.316			−0.809003			−0.404502	+	0.914537i	$0.632555\pi$
$858$			198.591i			0.231458i
$859$		−	214.903i		−	0.250179i	−0.992145	−	0.125089i	$-0.960078\pi$
$859$		−	214.903i		−	0.250179i	0.992145	−	0.125089i	$-0.0399217\pi$
$860$	−311.748	+	878.123i	−0.362498	+	1.02107i
$861$		0			0
$862$			2160.91i			2.50685i
$863$		−	665.112i		−	0.770698i	−0.922771	−	0.385349i	$-0.874081\pi$
$863$		−	665.112i		−	0.770698i	0.922771	−	0.385349i	$-0.125919\pi$
$864$		−	450.267i		−	0.521143i
$865$	−1175.84	−	417.442i	−1.35935	−	0.482591i
$866$			821.435i			0.948540i
$867$	485.195			0.559625
$868$		0			0
$869$	1274.75			1.46692
$870$	190.826	−	537.514i	0.219340	−	0.617833i
$871$		−	77.1462i		−	0.0885719i
$872$		−	3930.74i		−	4.50773i
$873$	−381.740			−0.437274
$874$		−	860.078i		−	0.984071i
$875$		0			0
$876$	−1648.88			−1.88229
$877$			864.963i			0.986275i	0.869951	+	0.493138i	$0.164150\pi$
$877$			864.963i			0.986275i	−0.869951	+	0.493138i	$0.835850\pi$
$878$	2763.64			3.14765
$879$	312.944			0.356023
$880$	4046.68	+	1436.63i	4.59849	+	1.63254i
$881$			203.509i			0.230998i	0.993308	+	0.115499i	$0.0368466\pi$
$881$			203.509i			0.230998i	−0.993308	+	0.115499i	$0.963153\pi$
$882$		0			0
$883$		−	217.585i		−	0.246416i	−0.992381	−	0.123208i	$-0.960682\pi$
$883$		−	217.585i		−	0.246416i	0.992381	−	0.123208i	$-0.0393182\pi$
$884$	−51.7275			−0.0585152
$885$	−65.7748	+	185.273i	−0.0743219	+	0.209348i
$886$	1490.39			1.68216
$887$	−449.888			−0.507202			−0.253601	−	0.967309i	$-0.581615\pi$
$887$	−449.888			−0.507202			−0.253601	+	0.967309i	$0.581615\pi$
$888$	−2228.64			−2.50973
$889$		0			0
$890$	223.206	+	79.2417i	0.250793	+	0.0890356i
$891$	161.267			0.180995
$892$	61.7527			0.0692295
$893$		−	114.070i		−	0.127738i
$894$			1137.69i			1.27259i
$895$	1539.06	+	546.391i	1.71962	+	0.610492i
$896$		0			0
$897$			26.7822i			0.0298575i
$898$			1791.02i			1.99445i
$899$		−	86.2177i		−	0.0959040i
$900$	−596.189	−	484.360i	−0.662432	−	0.538178i
$901$			75.0779i			0.0833273i
$902$	−1976.02			−2.19071
$903$		0			0
$904$	1231.23			1.36198
$905$	−278.895	+	785.585i	−0.308171	+	0.868049i
$906$			686.860i			0.758124i
$907$		−	248.550i		−	0.274036i	−0.990569	−	0.137018i	$-0.956248\pi$
$907$		−	248.550i		−	0.274036i	0.990569	−	0.137018i	$-0.0437518\pi$
$908$	328.366			0.361636
$909$			384.076i			0.422525i
$910$		0			0
$911$	1261.28			1.38450			0.692248	−	0.721660i	$-0.256621\pi$
$911$	1261.28			1.38450			0.692248	+	0.721660i	$0.256621\pi$
$912$		−	2074.64i		−	2.27482i
$913$	−185.979			−0.203701
$914$	1551.82			1.69783
$915$	−174.484	+	491.481i	−0.190693	+	0.537138i
$916$		−	201.580i		−	0.220065i
$917$		0			0
$918$			58.4110i			0.0636285i
$919$	561.289			0.610761			0.305380	−	0.952230i	$-0.401216\pi$
$919$	561.289			0.610761			0.305380	+	0.952230i	$0.401216\pi$
$920$	1012.21	+	359.351i	1.10023	+	0.390599i
$921$	−633.304			−0.687627
$922$	−2832.10			−3.07169
$923$	−36.3717			−0.0394059
$924$		0			0
$925$	−861.077	+	1059.88i	−0.930894	+	1.14582i
$926$	1625.17			1.75505
$927$	−417.809			−0.450711
$928$			1512.31i			1.62964i
$929$			712.944i			0.767432i	0.923451	+	0.383716i	$0.125356\pi$
$929$			712.944i			0.767432i	−0.923451	+	0.383716i	$0.874644\pi$
$930$	−152.154	−	54.0172i	−0.163607	−	0.0580830i
$931$		0			0
$932$		−	1519.99i		−	1.63090i
$933$		−	815.020i		−	0.873548i
$934$			2264.29i			2.42429i
$935$	−251.492	−	89.2837i	−0.268976	−	0.0954906i
$936$			119.822i			0.128015i
$937$	560.643			0.598339			0.299169	−	0.954200i	$-0.403290\pi$
$937$	560.643			0.598339			0.299169	+	0.954200i	$0.403290\pi$
$938$		0			0
$939$	−335.289			−0.357070
$940$	220.276	+	78.2014i	0.234336	+	0.0831930i
$941$		−	724.744i		−	0.770185i	−0.922878	−	0.385092i	$-0.874170\pi$
$941$		−	724.744i		−	0.770185i	0.922878	−	0.385092i	$-0.125830\pi$
$942$			11.7042i			0.0124248i
$943$	−266.488			−0.282596
$944$		−	1088.08i		−	1.15262i
$945$		0			0
$946$	1230.46			1.30070
$947$			902.478i			0.952987i	0.879178	+	0.476493i	$0.158092\pi$
$947$			902.478i			0.952987i	−0.879178	+	0.476493i	$0.841908\pi$
$948$	1262.02			1.33124
$949$	157.601			0.166070
$950$	−1829.97	−	1486.72i	−1.92629	−	1.56497i
$951$			848.240i			0.891946i
$952$		0			0
$953$		−	182.310i		−	0.191301i	−0.995415	−	0.0956506i	$-0.969507\pi$
$953$		−	182.310i		−	0.191301i	0.995415	−	0.0956506i	$-0.0304931\pi$
$954$	285.358			0.299117
$955$	−239.975	−	85.1950i	−0.251283	−	0.0892094i
$956$	2134.98			2.23325
$957$	−541.644			−0.565981
$958$	2522.57			2.63317
$959$		0			0
$960$	1104.22	+	392.017i	1.15023	+	0.408351i
$961$	936.594			0.974604
$962$	349.520			0.363326
$963$			274.260i			0.284797i
$964$		−	444.275i		−	0.460867i
$965$	−78.6582	+	221.562i	−0.0815111	+	0.229598i
$966$		0			0
$967$		−	513.340i		−	0.530859i	−0.964130	−	0.265429i	$-0.914486\pi$
$967$		−	513.340i		−	0.530859i	0.964130	−	0.265429i	$-0.0855137\pi$
$968$		−	4712.95i		−	4.86875i
$969$			128.934i			0.133059i
$970$	803.290	−	2262.69i	0.828135	−	2.33267i
$971$			548.650i			0.565036i	0.959262	+	0.282518i	$0.0911696\pi$
$971$			548.650i			0.565036i	−0.959262	+	0.282518i	$0.908830\pi$
$972$	159.656			0.164255
$973$		0			0
$974$	−453.889			−0.466005
$975$	56.9840	+	46.2954i	0.0584451	+	0.0474824i
$976$		−	2886.39i		−	2.95737i
$977$		−	309.963i		−	0.317260i	−0.987338	−	0.158630i	$-0.949292\pi$
$977$		−	309.963i		−	0.317260i	0.987338	−	0.158630i	$-0.0507077\pi$
$978$	−477.466			−0.488207
$979$		−	224.921i		−	0.229746i
$980$		0			0
$981$	500.602			0.510297
$982$		−	2826.78i		−	2.87859i
$983$	−1096.18			−1.11514			−0.557569	−	0.830130i	$-0.688266\pi$
$983$	−1096.18			−1.11514			−0.557569	+	0.830130i	$0.688266\pi$
$984$	−1192.25			−1.21164
$985$	110.546	−	311.382i	0.112229	−	0.316124i
$986$		−	196.184i		−	0.198970i
$987$		0			0
$988$			433.983i			0.439254i
$989$	165.941			0.167787
$990$	−339.352	+	955.877i	−0.342779	+	0.965532i
$991$	230.477			0.232570			0.116285	−	0.993216i	$-0.462901\pi$
$991$	230.477			0.232570			0.116285	+	0.993216i	$0.462901\pi$
$992$	428.089			0.431541
$993$	−649.073			−0.653648
$994$		0			0
$995$	−126.366	+	355.946i	−0.127001	+	0.357734i
$996$	−184.121			−0.184860
$997$	769.981			0.772298			0.386149	−	0.922436i	$-0.373805\pi$
$997$	769.981			0.772298			0.386149	+	0.922436i	$0.373805\pi$
$998$			1609.62i			1.61285i
$999$		−	283.830i		−	0.284114i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.3.e.a.244.2		32
5.4	even	2	inner	735.3.e.a.244.19		32
7.4	even	3		105.3.r.a.19.1	✓	32
7.5	odd	6		105.3.r.a.94.16	yes	32
7.6	odd	2	inner	735.3.e.a.244.20		32
21.5	even	6		315.3.bi.e.199.1		32
21.11	odd	6		315.3.bi.e.19.16		32
35.4	even	6		105.3.r.a.19.16	yes	32
35.12	even	12		525.3.o.q.451.8		16
35.18	odd	12		525.3.o.p.376.1		16
35.19	odd	6		105.3.r.a.94.1	yes	32
35.32	odd	12		525.3.o.q.376.8		16
35.33	even	12		525.3.o.p.451.1		16
35.34	odd	2	inner	735.3.e.a.244.1		32
105.74	odd	6		315.3.bi.e.19.1		32
105.89	even	6		315.3.bi.e.199.16		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.r.a.19.1	✓	32	7.4	even	3
105.3.r.a.19.16	yes	32	35.4	even	6
105.3.r.a.94.1	yes	32	35.19	odd	6
105.3.r.a.94.16	yes	32	7.5	odd	6
315.3.bi.e.19.1		32	105.74	odd	6
315.3.bi.e.19.16		32	21.11	odd	6
315.3.bi.e.199.1		32	21.5	even	6
315.3.bi.e.199.16		32	105.89	even	6
525.3.o.p.376.1		16	35.18	odd	12
525.3.o.p.451.1		16	35.33	even	12
525.3.o.q.376.8		16	35.32	odd	12
525.3.o.q.451.8		16	35.12	even	12
735.3.e.a.244.1		32	35.34	odd	2	inner
735.3.e.a.244.2		32	1.1	even	1	trivial
735.3.e.a.244.19		32	5.4	even	2	inner
735.3.e.a.244.20		32	7.6	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	735.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+3.77385i q^{2} -1.73205 q^{3} -10.2419 q^{4} +(4.71188 + 1.67279i) q^{5} -6.53650i q^{6} -23.5561i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+3.77385i q^{2} -1.73205 q^{3} -10.2419 q^{4} +(4.71188 + 1.67279i) q^{5} -6.53650i q^{6} -23.5561i q^{8} +3.00000 q^{9} +(-6.31286 + 17.7819i) q^{10} +17.9185 q^{11} +17.7395 q^{12} -1.69555 q^{13} +(-8.16121 - 2.89736i) q^{15} +47.9294 q^{16} -2.97871 q^{17} +11.3215i q^{18} +24.9908i q^{19} +(-48.2587 - 17.1326i) q^{20} +67.6218i q^{22} +9.11956i q^{23} +40.8004i q^{24} +(19.4035 + 15.7640i) q^{25} -6.39876i q^{26} -5.19615 q^{27} +17.4522 q^{29} +(10.9342 - 30.7992i) q^{30} -4.94021i q^{31} +86.6540i q^{32} -31.0358 q^{33} -11.2412i q^{34} -30.7258 q^{36} +54.6231i q^{37} -94.3114 q^{38} +2.93678 q^{39} +(39.4044 - 110.993i) q^{40} +29.2216i q^{41} -18.1962i q^{43} -183.520 q^{44} +(14.1356 + 5.01837i) q^{45} -34.4158 q^{46} -4.56448 q^{47} -83.0162 q^{48} +(-59.4908 + 73.2260i) q^{50} +5.15928 q^{51} +17.3657 q^{52} -25.2048i q^{53} -19.6095i q^{54} +(84.4299 + 29.9740i) q^{55} -43.2853i q^{57} +65.8621i q^{58} -22.7016i q^{59} +(83.5865 + 29.6746i) q^{60} -60.2216i q^{61} +18.6436 q^{62} -135.301 q^{64} +(-7.98923 - 2.83631i) q^{65} -117.124i q^{66} +45.4991i q^{67} +30.5077 q^{68} -15.7955i q^{69} +21.4512 q^{71} -70.6683i q^{72} -92.9495 q^{73} -206.139 q^{74} +(-33.6079 - 27.3040i) q^{75} -255.954i q^{76} +11.0830i q^{78} +71.1416 q^{79} +(225.837 + 80.1759i) q^{80} +9.00000 q^{81} -110.278 q^{82} -10.3791 q^{83} +(-14.0353 - 4.98276i) q^{85} +68.6696 q^{86} -30.2282 q^{87} -422.091i q^{88} -12.5524i q^{89} +(-18.9386 + 53.3457i) q^{90} -93.4019i q^{92} +8.55670i q^{93} -17.2256i q^{94} +(-41.8044 + 117.753i) q^{95} -150.089i q^{96} -127.247 q^{97} +53.7556 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 64 q^{4} + 96 q^{9}+O(q^{10}) \) 32 * q - 64 * q^4 + 96 * q^9	\( 32 q - 64 q^{4} + 96 q^{9} + 56 q^{11} - 24 q^{15} + 80 q^{16} + 68 q^{25} - 88 q^{29} - 192 q^{36} - 72 q^{39} - 640 q^{44} + 120 q^{46} - 24 q^{51} + 396 q^{60} - 400 q^{64} + 92 q^{65} + 344 q^{71} - 1800 q^{74} + 40 q^{79} + 288 q^{81} + 304 q^{85} - 288 q^{86} + 684 q^{95} + 168 q^{99}+O(q^{100}) \) 32 * q - 64 * q^4 + 96 * q^9 + 56 * q^11 - 24 * q^15 + 80 * q^16 + 68 * q^25 - 88 * q^29 - 192 * q^36 - 72 * q^39 - 640 * q^44 + 120 * q^46 - 24 * q^51 + 396 * q^60 - 400 * q^64 + 92 * q^65 + 344 * q^71 - 1800 * q^74 + 40 * q^79 + 288 * q^81 + 304 * q^85 - 288 * q^86 + 684 * q^95 + 168 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more