LMFDB - Embedded newform 230.5.c.a.229.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,5,Mod(229,230)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("230.229"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	230.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$23.7750915093$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			229.11
Character	$\chi$	$=$	230.229
Dual form			230.5.c.a.229.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.82843i q^{2} +7.41746i q^{3} -8.00000 q^{4} +(23.4452 + 8.67897i) q^{5} +20.9797 q^{6} -42.4567 q^{7} +22.6274i q^{8} +25.9814 q^{9} +(24.5478 - 66.3129i) q^{10} -123.637i q^{11} -59.3396i q^{12} -165.863i q^{13} +120.086i q^{14} +(-64.3758 + 173.903i) q^{15} +64.0000 q^{16} +391.732 q^{17} -73.4864i q^{18} +286.191i q^{19} +(-187.561 - 69.4317i) q^{20} -314.921i q^{21} -349.697 q^{22} +(207.789 + 486.482i) q^{23} -167.838 q^{24} +(474.351 + 406.960i) q^{25} -469.130 q^{26} +793.529i q^{27} +339.654 q^{28} -203.819 q^{29} +(491.873 + 182.082i) q^{30} +289.119 q^{31} -181.019i q^{32} +917.069 q^{33} -1107.99i q^{34} +(-995.405 - 368.481i) q^{35} -207.851 q^{36} +1984.72 q^{37} +809.471 q^{38} +1230.28 q^{39} +(-196.383 + 530.503i) q^{40} -2307.37 q^{41} -890.731 q^{42} +2724.20 q^{43} +989.092i q^{44} +(609.137 + 225.491i) q^{45} +(1375.98 - 587.717i) q^{46} +3842.31i q^{47} +474.717i q^{48} -598.426 q^{49} +(1151.06 - 1341.67i) q^{50} +2905.66i q^{51} +1326.90i q^{52} +3756.98 q^{53} +2244.44 q^{54} +(1073.04 - 2898.68i) q^{55} -960.686i q^{56} -2122.81 q^{57} +576.488i q^{58} +5679.11 q^{59} +(515.007 - 1391.23i) q^{60} -2561.96i q^{61} -817.752i q^{62} -1103.08 q^{63} -512.000 q^{64} +(1439.52 - 3888.67i) q^{65} -2593.86i q^{66} +2839.84 q^{67} -3133.86 q^{68} +(-3608.46 + 1541.27i) q^{69} +(-1042.22 + 2815.43i) q^{70} -3495.85 q^{71} +587.891i q^{72} -9295.95i q^{73} -5613.64i q^{74} +(-3018.60 + 3518.48i) q^{75} -2289.53i q^{76} +5249.20i q^{77} -3479.75i q^{78} -2264.79i q^{79} +(1500.49 + 555.454i) q^{80} -3781.48 q^{81} +6526.23i q^{82} -6389.56 q^{83} +2519.37i q^{84} +(9184.23 + 3399.83i) q^{85} -7705.20i q^{86} -1511.82i q^{87} +2797.58 q^{88} -1511.97i q^{89} +(637.786 - 1722.90i) q^{90} +7041.98i q^{91} +(-1662.31 - 3891.86i) q^{92} +2144.53i q^{93} +10867.7 q^{94} +(-2483.84 + 6709.80i) q^{95} +1342.70 q^{96} +1346.65 q^{97} +1692.60i q^{98} -3212.25i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 384 q^{4} - 64 q^{6} - 1608 q^{9} + 3072 q^{16} + 512 q^{24} + 1488 q^{25} - 384 q^{26} - 2940 q^{29} + 4732 q^{31} + 2556 q^{35} + 12864 q^{36} + 2736 q^{39} + 828 q^{41} - 64 q^{46} + 32572 q^{49}+ \cdots - 4096 q^{96}+O(q^{100}) $ 48 * q - 384 * q^4 - 64 * q^6 - 1608 * q^9 + 3072 * q^16 + 512 * q^24 + 1488 * q^25 - 384 * q^26 - 2940 * q^29 + 4732 * q^31 + 2556 * q^35 + 12864 * q^36 + 2736 * q^39 + 828 * q^41 - 64 * q^46 + 32572 * q^49 - 3264 * q^50 + 10112 * q^54 + 12824 * q^55 + 7092 * q^59 - 24576 * q^64 + 14000 * q^69 - 6592 * q^70 - 12708 * q^71 + 24728 * q^75 - 13040 * q^81 - 15700 * q^85 - 9728 * q^94 - 46608 * q^95 - 4096 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$		−	2.82843i		−	0.707107i
$2$		−	2.82843i		−	0.707107i
$3$			7.41746i			0.824162i	0.911147	+	0.412081i	$0.135198\pi$
$3$			7.41746i			0.824162i	−0.911147	+	0.412081i	$0.864802\pi$
$4$	−8.00000			−0.500000
$5$	23.4452	+	8.67897i	0.937806	+	0.347159i
$5$	23.4452	+	8.67897i	0.937806	+	0.347159i
$6$	20.9797			0.582770
$7$	−42.4567			−0.866464			−0.433232	−	0.901282i	$-0.642627\pi$
$7$	−42.4567			−0.866464			−0.433232	+	0.901282i	$0.642627\pi$
$8$			22.6274i			0.353553i
$9$	25.9814			0.320757
$10$	24.5478	−	66.3129i	0.245478	−	0.663129i
$11$		−	123.637i		−	1.02179i	−0.859643	−	0.510895i	$-0.829314\pi$
$11$		−	123.637i		−	1.02179i	0.859643	−	0.510895i	$-0.170686\pi$
$12$		−	59.3396i		−	0.412081i
$13$		−	165.863i		−	0.981435i	−0.871319	−	0.490717i	$-0.836735\pi$
$13$		−	165.863i		−	0.981435i	0.871319	−	0.490717i	$-0.163265\pi$
$14$			120.086i			0.612683i
$15$	−64.3758	+	173.903i	−0.286115	+	0.772904i
$16$	64.0000			0.250000
$17$	391.732			1.35548			0.677738	−	0.735304i	$-0.262961\pi$
$17$	391.732			1.35548			0.677738	+	0.735304i	$0.262961\pi$
$18$		−	73.4864i		−	0.226810i
$19$			286.191i			0.792773i	0.918084	+	0.396387i	$0.129736\pi$
$19$			286.191i			0.792773i	−0.918084	+	0.396387i	$0.870264\pi$
$20$	−187.561	−	69.4317i	−0.468903	−	0.173579i
$21$		−	314.921i		−	0.714106i
$22$	−349.697			−0.722514
$23$	207.789	+	486.482i	0.392796	+	0.919626i
$23$	207.789	+	486.482i	0.392796	+	0.919626i
$24$	−167.838			−0.291385
$25$	474.351	+	406.960i	0.758962	+	0.651135i
$26$	−469.130			−0.693979
$27$			793.529i			1.08852i
$28$	339.654			0.433232
$29$	−203.819			−0.242353			−0.121177	−	0.992631i	$-0.538667\pi$
$29$	−203.819			−0.242353			−0.121177	+	0.992631i	$0.538667\pi$
$30$	491.873	+	182.082i	0.546526	+	0.202314i
$31$	289.119			0.300852			0.150426	−	0.988621i	$-0.451935\pi$
$31$	289.119			0.300852			0.150426	+	0.988621i	$0.451935\pi$
$32$		−	181.019i		−	0.176777i
$33$	917.069			0.842120
$34$		−	1107.99i		−	0.958466i
$35$	−995.405	−	368.481i	−0.812575	−	0.300800i
$36$	−207.851			−0.160379
$37$	1984.72			1.44976			0.724879	−	0.688876i	$-0.241895\pi$
$37$	1984.72			1.44976			0.724879	+	0.688876i	$0.241895\pi$
$38$	809.471			0.560576
$39$	1230.28			0.808861
$40$	−196.383	+	530.503i	−0.122739	+	0.331565i
$41$	−2307.37			−1.37262			−0.686309	−	0.727310i	$-0.740770\pi$
$41$	−2307.37			−1.37262			−0.686309	+	0.727310i	$0.740770\pi$
$42$	−890.731			−0.504949
$43$	2724.20			1.47334			0.736668	−	0.676254i	$-0.236398\pi$
$43$	2724.20			1.47334			0.736668	+	0.676254i	$0.236398\pi$
$44$			989.092i			0.510895i
$45$	609.137	+	225.491i	0.300808	+	0.111354i
$46$	1375.98	−	587.717i	0.650273	−	0.277749i
$47$			3842.31i			1.73939i	0.493590	+	0.869695i	$0.335684\pi$
$47$			3842.31i			1.73939i	−0.493590	+	0.869695i	$0.664316\pi$
$48$			474.717i			0.206040i
$49$	−598.426			−0.249240
$50$	1151.06	−	1341.67i	0.460422	−	0.536667i
$51$			2905.66i			1.11713i
$52$			1326.90i			0.490717i
$53$	3756.98			1.33748			0.668739	−	0.743497i	$-0.266834\pi$
$53$	3756.98			1.33748			0.668739	+	0.743497i	$0.266834\pi$
$54$	2244.44			0.769698
$55$	1073.04	−	2898.68i	0.354723	−	0.958241i
$56$		−	960.686i		−	0.306341i
$57$	−2122.81			−0.653374
$58$			576.488i			0.171370i
$59$	5679.11			1.63146			0.815729	−	0.578434i	$-0.196336\pi$
$59$	5679.11			1.63146			0.815729	+	0.578434i	$0.196336\pi$
$60$	515.007	−	1391.23i	0.143057	−	0.386452i
$61$		−	2561.96i		−	0.688515i	−0.938875	−	0.344257i	$-0.888131\pi$
$61$		−	2561.96i		−	0.688515i	0.938875	−	0.344257i	$-0.111869\pi$
$62$		−	817.752i		−	0.212735i
$63$	−1103.08			−0.277925
$64$	−512.000			−0.125000
$65$	1439.52	−	3888.67i	0.340714	−	0.920396i
$66$		−	2593.86i		−	0.595469i
$67$	2839.84			0.632622			0.316311	−	0.948656i	$-0.397556\pi$
$67$	2839.84			0.632622			0.316311	+	0.948656i	$0.397556\pi$
$68$	−3133.86			−0.677738
$69$	−3608.46	+	1541.27i	−0.757920	+	0.323728i
$70$	−1042.22	+	2815.43i	−0.212698	+	0.574578i
$71$	−3495.85			−0.693484			−0.346742	−	0.937961i	$-0.612712\pi$
$71$	−3495.85			−0.693484			−0.346742	+	0.937961i	$0.612712\pi$
$72$			587.891i			0.113405i
$73$		−	9295.95i		−	1.74441i	−0.489142	−	0.872204i	$-0.662690\pi$
$73$		−	9295.95i		−	1.74441i	0.489142	−	0.872204i	$-0.337310\pi$
$74$		−	5613.64i		−	1.02513i
$75$	−3018.60	+	3518.48i	−0.536641	+	0.625507i
$76$		−	2289.53i		−	0.396387i
$77$			5249.20i			0.885344i
$78$		−	3479.75i		−	0.571951i
$79$		−	2264.79i		−	0.362888i	−0.983401	−	0.181444i	$-0.941923\pi$
$79$		−	2264.79i		−	0.362888i	0.983401	−	0.181444i	$-0.0580772\pi$
$80$	1500.49	+	555.454i	0.234452	+	0.0867897i
$81$	−3781.48			−0.576357
$82$			6526.23i			0.970588i
$83$	−6389.56			−0.927502			−0.463751	−	0.885966i	$-0.653497\pi$
$83$	−6389.56			−0.927502			−0.463751	+	0.885966i	$0.653497\pi$
$84$			2519.37i			0.357053i
$85$	9184.23	+	3399.83i	1.27117	+	0.470565i
$86$		−	7705.20i		−	1.04181i
$87$		−	1511.82i		−	0.199738i
$88$	2797.58			0.361257
$89$		−	1511.97i		−	0.190881i	−0.995435	−	0.0954404i	$-0.969574\pi$
$89$		−	1511.97i		−	0.190881i	0.995435	−	0.0954404i	$-0.0304259\pi$
$90$	637.786	−	1722.90i	0.0787390	−	0.212704i
$91$			7041.98i			0.850378i
$92$	−1662.31	−	3891.86i	−0.196398	−	0.459813i
$93$			2144.53i			0.247951i
$94$	10867.7			1.22993
$95$	−2483.84	+	6709.80i	−0.275218	+	0.743468i
$96$	1342.70			0.145693
$97$	1346.65			0.143124			0.0715619	−	0.997436i	$-0.477202\pi$
$97$	1346.65			0.143124			0.0715619	+	0.997436i	$0.477202\pi$
$98$			1692.60i			0.176240i
$99$		−	3212.25i		−	0.327747i
$100$	−3794.81	−	3255.68i	−0.379481	−	0.325568i
$101$	−864.548			−0.0847513			−0.0423756	−	0.999102i	$-0.513493\pi$
$101$	−864.548			−0.0847513			−0.0423756	+	0.999102i	$0.513493\pi$
$102$	8218.44			0.789931
$103$	−43.7352			−0.00412246			−0.00206123	−	0.999998i	$-0.500656\pi$
$103$	−43.7352			−0.00412246			−0.00206123	+	0.999998i	$0.500656\pi$
$104$	3753.04			0.346990
$105$	2733.19	−	7383.37i	0.247908	−	0.669694i
$106$		−	10626.3i		−	0.945740i
$107$	−10722.4			−0.936532			−0.468266	−	0.883588i	$-0.655121\pi$
$107$	−10722.4			−0.936532			−0.468266	+	0.883588i	$0.655121\pi$
$108$		−	6348.24i		−	0.544259i
$109$			16740.4i			1.40901i	0.709700	+	0.704504i	$0.248830\pi$
$109$			16740.4i			1.40901i	−0.709700	+	0.704504i	$0.751170\pi$
$110$	−8198.70	−	3035.01i	−0.677579	−	0.250827i
$111$			14721.6i			1.19484i
$112$	−2717.23			−0.216616
$113$	9892.14			0.774700			0.387350	−	0.921933i	$-0.373391\pi$
$113$	9892.14			0.774700			0.387350	+	0.921933i	$0.373391\pi$
$114$			6004.22i			0.462005i
$115$	649.491	+	13209.0i	0.0491109	+	0.998793i
$116$	1630.55			0.121177
$117$		−	4309.33i		−	0.314803i
$118$		−	16062.9i		−	1.15362i
$119$	−16631.7			−1.17447
$120$	−3934.99	−	1456.66i	−0.273263	−	0.101157i
$121$	−644.995			−0.0440541
$122$	−7246.33			−0.486853
$123$		−	17114.8i		−	1.13126i
$124$	−2312.95			−0.150426
$125$	7589.25	+	13658.1i	0.485712	+	0.874119i
$126$			3119.99i			0.196522i
$127$			24262.3i			1.50427i	0.659011	+	0.752133i	$0.270975\pi$
$127$			24262.3i			1.50427i	−0.659011	+	0.752133i	$0.729025\pi$
$128$			1448.15i			0.0883883i
$129$			20206.6i			1.21427i
$130$	−10998.8	−	4071.56i	−0.650818	−	0.240921i
$131$	17881.3			1.04198			0.520988	−	0.853564i	$-0.325564\pi$
$131$	17881.3			1.04198			0.520988	+	0.853564i	$0.325564\pi$
$132$	−7336.55			−0.421060
$133$		−	12150.7i		−	0.686910i
$134$		−	8032.28i		−	0.447331i
$135$	−6887.02	+	18604.4i	−0.377888	+	1.02082i
$136$			8863.89i			0.479233i
$137$	−31830.7			−1.69592			−0.847960	−	0.530061i	$-0.822169\pi$
$137$	−31830.7			−1.69592			−0.847960	+	0.530061i	$0.822169\pi$
$138$	4359.36	+	10206.3i	0.228910	+	0.535930i
$139$	−26043.9			−1.34796			−0.673979	−	0.738751i	$-0.735416\pi$
$139$	−26043.9			−1.34796			−0.673979	+	0.738751i	$0.735416\pi$
$140$	7963.24	+	2947.84i	0.406288	+	0.150400i
$141$	−28500.2			−1.43354
$142$			9887.77i			0.490367i
$143$	−20506.7			−1.00282
$144$	1662.81			0.0801894
$145$	−4778.57	−	1768.94i	−0.227281	−	0.0841351i
$146$	−26292.9			−1.23348
$147$		−	4438.80i		−	0.205414i
$148$	−15877.8			−0.724879
$149$		−	26139.8i		−	1.17742i	−0.808346	−	0.588708i	$-0.799637\pi$
$149$		−	26139.8i		−	1.17742i	0.808346	−	0.588708i	$-0.200363\pi$
$150$	9951.76	+	8537.90i	0.442300	+	0.379462i
$151$	−17858.0			−0.783210			−0.391605	−	0.920133i	$-0.628080\pi$
$151$	−17858.0			−0.783210			−0.391605	+	0.920133i	$0.628080\pi$
$152$	−6475.77			−0.280288
$153$	10177.7			0.434779
$154$	14847.0			0.626033
$155$	6778.44	+	2509.25i	0.282141	+	0.104443i
$156$	−9842.22			−0.404431
$157$	26059.4			1.05722			0.528610	−	0.848865i	$-0.322713\pi$
$157$	26059.4			1.05722			0.528610	+	0.848865i	$0.322713\pi$
$158$	−6405.78			−0.256601
$159$			27867.2i			1.10230i
$160$	1571.06	−	4244.03i	0.0613696	−	0.165782i
$161$	−8822.05	−	20654.4i	−0.340344	−	0.796822i
$162$			10695.6i			0.407546i
$163$		−	39171.1i		−	1.47431i	−0.675721	−	0.737157i	$-0.736168\pi$
$163$		−	39171.1i		−	1.47431i	0.675721	−	0.737157i	$-0.263832\pi$
$164$	18459.0			0.686309
$165$	21500.8	+	7959.21i	0.789745	+	0.292349i
$166$			18072.4i			0.655843i
$167$		−	39316.0i		−	1.40973i	−0.709340	−	0.704866i	$-0.751007\pi$
$167$		−	39316.0i		−	1.40973i	0.709340	−	0.704866i	$-0.248993\pi$
$168$	7125.85			0.252475
$169$	1050.63			0.0367855
$170$	9616.18	−	25976.9i	0.332740	−	0.898855i
$171$			7435.64i			0.254288i
$172$	−21793.6			−0.736668
$173$			43641.3i			1.45816i	0.684428	+	0.729081i	$0.260052\pi$
$173$			43641.3i			1.45816i	−0.684428	+	0.729081i	$0.739948\pi$
$174$	−4276.07			−0.141236
$175$	−20139.4	−	17278.2i	−0.657613	−	0.564185i
$176$		−	7912.74i		−	0.255447i
$177$			42124.5i			1.34459i
$178$	−4276.49			−0.134973
$179$	20532.2			0.640811			0.320405	−	0.947281i	$-0.396181\pi$
$179$	20532.2			0.640811			0.320405	+	0.947281i	$0.396181\pi$
$180$	−4873.10	−	1803.93i	−0.150404	−	0.0556769i
$181$		−	39207.4i		−	1.19677i	−0.801209	−	0.598385i	$-0.795809\pi$
$181$		−	39207.4i		−	1.19677i	0.801209	−	0.598385i	$-0.204191\pi$
$182$	19917.7			0.601308
$183$	19003.2			0.567447
$184$	−11007.8	+	4701.73i	−0.325137	+	0.138874i
$185$	46532.1	+	17225.3i	1.35959	+	0.503296i
$186$	6065.64			0.175328
$187$		−	48432.4i		−	1.38501i
$188$		−	30738.5i		−	0.869695i
$189$		−	33690.7i		−	0.943161i
$190$	18978.2	+	7025.37i	0.525711	+	0.194609i
$191$		−	18585.9i		−	0.509467i	−0.967011	−	0.254734i	$-0.918012\pi$
$191$		−	18585.9i		−	0.509467i	0.967011	−	0.254734i	$-0.0819878\pi$
$192$		−	3797.74i		−	0.103020i
$193$			31611.2i			0.848646i	0.905511	+	0.424323i	$0.139488\pi$
$193$			31611.2i			0.848646i	−0.905511	+	0.424323i	$0.860512\pi$
$194$		−	3808.91i		−	0.101204i
$195$	28844.1	+	10677.5i	0.758555	+	0.280803i
$196$	4787.41			0.124620
$197$		−	47643.6i		−	1.22764i	−0.789445	−	0.613821i	$-0.789631\pi$
$197$		−	47643.6i		−	1.22764i	0.789445	−	0.613821i	$-0.210369\pi$
$198$	−9085.60			−0.231752
$199$		−	47076.3i		−	1.18876i	−0.804183	−	0.594382i	$-0.797397\pi$
$199$		−	47076.3i		−	1.18876i	0.804183	−	0.594382i	$-0.202603\pi$
$200$	−9208.44	+	10733.3i	−0.230211	+	0.268333i
$201$			21064.4i			0.521383i
$202$			2445.31i			0.0599282i
$203$	8653.50			0.209990
$204$		−	23245.3i		−	0.558565i
$205$	−54096.7	−	20025.6i	−1.28725	−	0.476516i
$206$			123.702i			0.00291502i
$207$	5398.65	+	12639.5i	0.125992	+	0.294977i
$208$		−	10615.2i		−	0.245359i
$209$	35383.7			0.810048
$210$	−20883.3	−	7730.62i	−0.473545	−	0.175298i
$211$	−79714.6			−1.79050			−0.895248	−	0.445569i	$-0.853001\pi$
$211$	−79714.6			−1.79050			−0.895248	+	0.445569i	$0.853001\pi$
$212$	−30055.8			−0.668739
$213$		−	25930.3i		−	0.571543i
$214$			30327.4i			0.662228i
$215$	63869.3	+	23643.2i	1.38170	+	0.511482i
$216$	−17955.5			−0.384849
$217$	−12275.0			−0.260677
$218$	47349.1			0.996319
$219$	68952.3			1.43767
$220$	−8584.30	+	23189.4i	−0.177362	+	0.479120i
$221$		−	64973.7i		−	1.33031i
$222$	41638.9			0.844876
$223$			51110.5i			1.02778i	0.857856	+	0.513891i	$0.171796\pi$
$223$			51110.5i			1.02778i	−0.857856	+	0.513891i	$0.828204\pi$
$224$			7685.49i			0.153171i
$225$	12324.3	+	10573.4i	0.243443	+	0.208856i
$226$		−	27979.2i		−	0.547795i
$227$	48873.4			0.948464			0.474232	−	0.880400i	$-0.342726\pi$
$227$	48873.4			0.948464			0.474232	+	0.880400i	$0.342726\pi$
$228$	16982.5			0.326687
$229$			85557.7i			1.63150i	0.578402	+	0.815752i	$0.303677\pi$
$229$			85557.7i			1.63150i	−0.578402	+	0.815752i	$0.696323\pi$
$230$	37360.8	−	1837.04i	0.706254	−	0.0347266i
$231$	−38935.7			−0.729666
$232$		−	4611.90i		−	0.0856849i
$233$			5920.95i			0.109064i	0.998512	+	0.0545318i	$0.0173666\pi$
$233$			5920.95i			0.109064i	−0.998512	+	0.0545318i	$0.982633\pi$
$234$	−12188.6			−0.222599
$235$	−33347.3	+	90083.6i	−0.603844	+	1.63121i
$236$	−45432.9			−0.815729
$237$	16799.0			0.299079
$238$			47041.5i			0.830476i
$239$	−32018.5			−0.560538			−0.280269	−	0.959922i	$-0.590424\pi$
$239$	−32018.5			−0.560538			−0.280269	+	0.959922i	$0.590424\pi$
$240$	−4120.05	+	11129.8i	−0.0715287	+	0.193226i
$241$		−	64479.9i		−	1.11017i	−0.831793	−	0.555086i	$-0.812685\pi$
$241$		−	64479.9i		−	1.11017i	0.831793	−	0.555086i	$-0.187315\pi$
$242$			1824.32i			0.0311509i
$243$			36226.9i			0.613506i
$244$			20495.7i			0.344257i
$245$	−14030.2	−	5193.72i	−0.233739	−	0.0865259i
$246$	−48408.0			−0.799921
$247$	47468.4			0.778056
$248$			6542.01i			0.106367i
$249$		−	47394.3i		−	0.764412i
$250$	38631.0	−	21465.6i	0.618095	−	0.343450i
$251$		−	6461.49i		−	0.102562i	−0.998684	−	0.0512809i	$-0.983670\pi$
$251$		−	6461.49i		−	0.102562i	0.998684	−	0.0512809i	$-0.0163304\pi$
$252$	8824.67			0.138962
$253$	60146.9	−	25690.3i	0.939664	−	0.401355i
$254$	68624.2			1.06368
$255$	−25218.1	+	68123.6i	−0.387822	+	1.04765i
$256$	4096.00			0.0625000
$257$		−	36995.7i		−	0.560125i	−0.959982	−	0.280063i	$-0.909645\pi$
$257$		−	36995.7i		−	0.560125i	0.959982	−	0.280063i	$-0.0903552\pi$
$258$	57153.0			0.858617
$259$	−84264.7			−1.25616
$260$	−11516.1	+	31109.4i	−0.170357	+	0.460198i
$261$	−5295.50			−0.0777367
$262$		−	50576.1i		−	0.736788i
$263$	4994.61			0.0722088			0.0361044	−	0.999348i	$-0.488505\pi$
$263$	4994.61			0.0722088			0.0361044	+	0.999348i	$0.488505\pi$
$264$			20750.9i			0.297734i
$265$	88082.9	+	32606.7i	1.25430	+	0.464317i
$266$	−34367.5			−0.485718
$267$	11214.9			0.157317
$268$	−22718.7			−0.316311
$269$	−769.815			−0.0106385			−0.00531927	−	0.999986i	$-0.501693\pi$
$269$	−769.815			−0.0106385			−0.00531927	+	0.999986i	$0.501693\pi$
$270$	52621.3	+	19479.4i	0.721828	+	0.267207i
$271$	20864.0			0.284093			0.142046	−	0.989860i	$-0.454632\pi$
$271$	20864.0			0.284093			0.142046	+	0.989860i	$0.454632\pi$
$272$	25070.9			0.338869
$273$	−52233.6			−0.700849
$274$			90030.8i			1.19920i
$275$	50315.1	−	58647.1i	0.665323	−	0.775499i
$276$	28867.7	−	12330.1i	0.378960	−	0.161864i
$277$		−	30571.6i		−	0.398436i	−0.979955	−	0.199218i	$-0.936160\pi$
$277$		−	30571.6i		−	0.398436i	0.979955	−	0.199218i	$-0.0638401\pi$
$278$			73663.2i			0.953150i
$279$	7511.70			0.0965006
$280$	8337.76	−	22523.4i	0.106349	−	0.287289i
$281$		−	3347.21i		−	0.0423906i	−0.999775	−	0.0211953i	$-0.993253\pi$
$281$		−	3347.21i		−	0.0423906i	0.999775	−	0.0211953i	$-0.00674718\pi$
$282$			80610.7i			1.01366i
$283$	−157106.			−1.96165			−0.980823	−	0.194899i	$-0.937562\pi$
$283$	−157106.			−1.96165			−0.980823	+	0.194899i	$0.937562\pi$
$284$	27966.8			0.346742
$285$	−49769.6	−	18423.8i	−0.612738	−	0.226824i
$286$			58001.6i			0.709101i
$287$	97963.5			1.18932
$288$		−	4703.13i		−	0.0567024i
$289$	69933.2			0.837313
$290$	−5003.32	+	13515.8i	−0.0594925	+	0.160712i
$291$			9988.74i			0.117957i
$292$			74367.6i			0.872204i
$293$	−19146.7			−0.223028			−0.111514	−	0.993763i	$-0.535570\pi$
$293$	−19146.7			−0.223028			−0.111514	+	0.993763i	$0.535570\pi$
$294$	−12554.8			−0.145250
$295$	133148.	+	49288.8i	1.52999	+	0.566375i
$296$			44909.1i			0.512567i
$297$	98109.2			1.11224
$298$	−73934.6			−0.832559
$299$	80689.1	−	34464.4i	0.902553	−	0.385504i
$300$	24148.8	−	28147.8i	0.268320	−	0.312754i
$301$	−115661.			−1.27659
$302$			50510.0i			0.553813i
$303$		−	6412.74i		−	0.0698487i
$304$			18316.2i			0.198193i
$305$	22235.2	−	60065.6i	0.239024	−	0.645693i
$306$		−	28787.0i		−	0.307435i
$307$		−	110404.i		−	1.17141i	−0.810524	−	0.585705i	$-0.800818\pi$
$307$		−	110404.i		−	1.17141i	0.810524	−	0.585705i	$-0.199182\pi$
$308$		−	41993.6i		−	0.442672i
$309$		−	324.404i		−	0.00339757i
$310$	7097.24	−	19172.3i	0.0738526	−	0.199504i
$311$	−20668.3			−0.213689			−0.106845	−	0.994276i	$-0.534075\pi$
$311$	−20668.3			−0.213689			−0.106845	+	0.994276i	$0.534075\pi$
$312$			27838.0i			0.285976i
$313$	−64680.9			−0.660218			−0.330109	−	0.943943i	$-0.607085\pi$
$313$	−64680.9			−0.660218			−0.330109	+	0.943943i	$0.607085\pi$
$314$		−	73707.2i		−	0.747568i
$315$	−25862.0	−	9573.62i	−0.260640	−	0.0964840i
$316$			18118.3i			0.181444i
$317$		−	61498.2i		−	0.611990i	−0.952033	−	0.305995i	$-0.901011\pi$
$317$		−	61498.2i		−	0.611990i	0.952033	−	0.305995i	$-0.0989891\pi$
$318$	78820.4			0.779443
$319$			25199.5i			0.247634i
$320$	−12003.9	−	4443.63i	−0.117226	−	0.0433948i
$321$		−	79532.6i		−	0.771854i
$322$	−58419.6	+	24952.5i	−0.563438	+	0.240659i
$323$			112110.i			1.07458i
$324$	30251.8			0.288179
$325$	67499.3	−	78677.1i	0.639047	−	0.744872i
$326$	−110792.			−1.04250
$327$	−124171.			−1.16125
$328$		−	52209.9i		−	0.485294i
$329$		−	163132.i		−	1.50712i
$330$	22512.0	−	60813.5i	0.206722	−	0.558434i
$331$	−119420.			−1.08998			−0.544992	−	0.838441i	$-0.683467\pi$
$331$	−119420.			−1.08998			−0.544992	+	0.838441i	$0.683467\pi$
$332$	51116.5			0.463751
$333$	51565.7			0.465021
$334$	−111203.			−0.996832
$335$	66580.5	+	24646.9i	0.593277	+	0.219620i
$336$		−	20154.9i		−	0.178527i
$337$	−175589.			−1.54610			−0.773048	−	0.634347i	$-0.781269\pi$
$337$	−175589.			−1.54610			−0.773048	+	0.634347i	$0.781269\pi$
$338$		−	2971.63i		−	0.0260113i
$339$			73374.5i			0.638478i
$340$	−73473.8	−	27198.7i	−0.635587	−	0.235282i
$341$		−	35745.7i		−	0.307408i
$342$	21031.2			0.179809
$343$	127346.			1.08242
$344$			61641.6i			0.520903i
$345$	−97977.5	+	4817.57i	−0.823167	+	0.0404753i
$346$	123436.			1.03108
$347$			128877.i			1.07032i	0.844750	+	0.535162i	$0.179749\pi$
$347$			128877.i			1.07032i	−0.844750	+	0.535162i	$0.820251\pi$
$348$			12094.6i			0.0998692i
$349$	175178.			1.43823			0.719116	−	0.694890i	$-0.244547\pi$
$349$	175178.			1.43823			0.719116	+	0.694890i	$0.244547\pi$
$350$	−48870.0	+	56962.8i	−0.398939	+	0.465003i
$351$	131617.			1.06831
$352$	−22380.6			−0.180629
$353$			98459.4i			0.790147i	0.918650	+	0.395073i	$0.129281\pi$
$353$			98459.4i			0.790147i	−0.918650	+	0.395073i	$0.870719\pi$
$354$	119146.			0.950766
$355$	−81960.8	−	30340.4i	−0.650354	−	0.240749i
$356$			12095.7i			0.0954404i
$357$		−	123365.i		−	0.967953i
$358$		−	58073.9i		−	0.453122i
$359$			75417.7i			0.585173i	0.956239	+	0.292587i	$0.0945160\pi$
$359$			75417.7i			0.585173i	−0.956239	+	0.292587i	$0.905484\pi$
$360$	−5102.29	+	13783.2i	−0.0393695	+	0.106352i
$361$	48415.6			0.371510
$362$	−110895.			−0.846244
$363$		−	4784.23i		−	0.0363077i
$364$		−	56335.8i		−	0.425189i
$365$	80679.2	−	217945.i	0.605586	−	1.63592i
$366$		−	53749.3i		−	0.401246i
$367$	−150504.			−1.11742			−0.558708	−	0.829365i	$-0.688703\pi$
$367$	−150504.			−1.11742			−0.558708	+	0.829365i	$0.688703\pi$
$368$	13298.5	+	31134.8i	0.0981991	+	0.229906i
$369$	−59948.6			−0.440278
$370$	48720.6	−	131613.i	0.355884	−	0.961378i
$371$	−159509.			−1.15888
$372$		−	17156.2i		−	0.123975i
$373$	−211435.			−1.51970			−0.759852	−	0.650097i	$-0.774728\pi$
$373$	−211435.			−1.51970			−0.759852	+	0.650097i	$0.774728\pi$
$374$	−136988.			−0.979350
$375$	−101308.	+	56292.9i	−0.720415	+	0.400305i
$376$	−86941.6			−0.614967
$377$			33806.0i			0.237854i
$378$	−95291.6			−0.666916
$379$			7774.69i			0.0541259i	0.999634	+	0.0270629i	$0.00861545\pi$
$379$			7774.69i			0.0541259i	−0.999634	+	0.0270629i	$0.991385\pi$
$380$	19870.8	−	53678.4i	0.137609	−	0.371734i
$381$	−179965.			−1.23976
$382$	−52568.8			−0.360248
$383$	182563.			1.24456			0.622278	−	0.782796i	$-0.286207\pi$
$383$	182563.			1.24456			0.622278	+	0.782796i	$0.286207\pi$
$384$	−10741.6			−0.0728463
$385$	−45557.7	+	123068.i	−0.307355	+	0.830281i
$386$	89410.0			0.600083
$387$	70778.4			0.472584
$388$	−10773.2			−0.0715619
$389$			67496.5i			0.446049i	0.974813	+	0.223024i	$0.0715930\pi$
$389$			67496.5i			0.446049i	−0.974813	+	0.223024i	$0.928407\pi$
$390$	30200.6	−	81583.3i	0.198558	−	0.536379i
$391$	81397.8	+	190571.i	0.532426	+	1.24653i
$392$		−	13540.8i		−	0.0881198i
$393$			132634.i			0.858757i
$394$	−134756.			−0.868075
$395$	19656.0	−	53098.3i	0.125980	−	0.340319i
$396$			25698.0i			0.163873i
$397$			12253.9i			0.0777488i	0.999244	+	0.0388744i	$0.0123772\pi$
$397$			12253.9i			0.0777488i	−0.999244	+	0.0388744i	$0.987623\pi$
$398$	−133152.			−0.840583
$399$	90127.6			0.566125
$400$	30358.5	+	26045.4i	0.189740	+	0.162784i
$401$		−	58106.7i		−	0.361358i	−0.983542	−	0.180679i	$-0.942171\pi$
$401$		−	58106.7i		−	0.361358i	0.983542	−	0.180679i	$-0.0578294\pi$
$402$	59579.1			0.368673
$403$		−	47954.0i		−	0.295267i
$404$	6916.38			0.0423756
$405$	−88657.4	−	32819.3i	−0.540511	−	0.200087i
$406$		−	24475.8i		−	0.148486i
$407$		−	245384.i		−	1.48135i
$408$	−65747.5			−0.394965
$409$	−18053.9			−0.107926			−0.0539628	−	0.998543i	$-0.517185\pi$
$409$	−18053.9			−0.107926			−0.0539628	+	0.998543i	$0.517185\pi$
$410$	−56641.0	+	153009.i	−0.336948	+	0.910223i
$411$		−	236103.i		−	1.39771i
$412$	349.882			0.00206123
$413$	−241116.			−1.41360
$414$	35749.8	−	15269.7i	0.208580	−	0.0890900i
$415$	−149804.	−	55454.8i	−0.869817	−	0.321990i
$416$	−30024.3			−0.173495
$417$		−	193179.i		−	1.11094i
$418$		−	100080.i		−	0.572790i
$419$			231986.i			1.32140i	0.750650	+	0.660700i	$0.229740\pi$
$419$			231986.i			1.32140i	−0.750650	+	0.660700i	$0.770260\pi$
$420$	−21865.5	+	59067.0i	−0.123954	+	0.334847i
$421$			183224.i			1.03376i	0.856059	+	0.516878i	$0.172906\pi$
$421$			183224.i			1.03376i	−0.856059	+	0.516878i	$0.827094\pi$
$422$			225467.i			1.26607i
$423$			99828.5i			0.557922i
$424$			85010.7i			0.472870i
$425$	185819.	+	159419.i	1.02875	+	0.882598i
$426$	−73342.1			−0.404142
$427$			108773.i			0.596573i
$428$	85778.8			0.468266
$429$		−	152107.i		−	0.826486i
$430$	66873.2	−	180650.i	0.361672	−	0.977013i
$431$			15993.8i			0.0860988i	0.999073	+	0.0430494i	$0.0137073\pi$
$431$			15993.8i			0.0860988i	−0.999073	+	0.0430494i	$0.986293\pi$
$432$			50785.9i			0.272129i
$433$	59507.0			0.317389			0.158695	−	0.987328i	$-0.449271\pi$
$433$	59507.0			0.317389			0.158695	+	0.987328i	$0.449271\pi$
$434$			34719.1i			0.184327i
$435$	13121.0	−	35444.9i	0.0693409	−	0.187316i
$436$		−	133923.i		−	0.704504i
$437$	−139227.	+	59467.5i	−0.729055	+	0.311398i
$438$		−	195027.i		−	1.01659i
$439$	139873.			0.725778			0.362889	−	0.931832i	$-0.381790\pi$
$439$	139873.			0.725778			0.362889	+	0.931832i	$0.381790\pi$
$440$	65589.6	+	24280.1i	0.338789	+	0.125414i
$441$	−15547.9			−0.0799457
$442$	−183773.			−0.940672
$443$		−	44607.6i		−	0.227301i	−0.993521	−	0.113651i	$-0.963746\pi$
$443$		−	44607.6i		−	0.227301i	0.993521	−	0.113651i	$-0.0362545\pi$
$444$		−	117773.i		−	0.597418i
$445$	13122.3	−	35448.3i	0.0662659	−	0.179009i
$446$	144562.			0.726751
$447$	193891.			0.970381
$448$	21737.8			0.108308
$449$	−101366.			−0.502803			−0.251402	−	0.967883i	$-0.580891\pi$
$449$	−101366.			−0.502803			−0.251402	+	0.967883i	$0.580891\pi$
$450$	29906.0	−	34858.3i	0.147684	−	0.172140i
$451$			285275.i			1.40253i
$452$	−79137.1			−0.387350
$453$		−	132461.i		−	0.645492i
$454$		−	138235.i		−	0.670666i
$455$	−61117.1	+	165100.i	−0.295216	+	0.797490i
$456$		−	48033.7i		−	0.231002i
$457$	−156159.			−0.747714			−0.373857	−	0.927486i	$-0.621965\pi$
$457$	−156159.			−0.747714			−0.373857	+	0.927486i	$0.621965\pi$
$458$	241994.			1.15365
$459$			310851.i			1.47546i
$460$	−5195.93	−	105672.i	−0.0245554	−	0.499397i
$461$	−160464.			−0.755049			−0.377525	−	0.926000i	$-0.623225\pi$
$461$	−160464.			−0.755049			−0.377525	+	0.926000i	$0.623225\pi$
$462$			110127.i			0.515952i
$463$			280944.i			1.31056i	0.755385	+	0.655281i	$0.227450\pi$
$463$			280944.i			1.31056i	−0.755385	+	0.655281i	$0.772550\pi$
$464$	−13044.4			−0.0605883
$465$	−18612.3	+	50278.8i	−0.0860783	+	0.232530i
$466$	16747.0			0.0771196
$467$	168542.			0.772814			0.386407	−	0.922328i	$-0.373716\pi$
$467$	168542.			0.772814			0.386407	+	0.922328i	$0.373716\pi$
$468$			34474.7i			0.157401i
$469$	−120570.			−0.548144
$470$	254795.	+	94320.4i	1.15344	+	0.426982i
$471$			193295.i			0.871321i
$472$			128504.i			0.576808i
$473$		−	336811.i		−	1.50544i
$474$		−	47514.6i		−	0.211481i
$475$	−116468.	+	135755.i	−0.516203	+	0.601685i
$476$	133053.			0.587235
$477$	97611.3			0.429006
$478$			90562.0i			0.396360i
$479$		−	219674.i		−	0.957433i	−0.877969	−	0.478717i	$-0.841102\pi$
$479$		−	219674.i		−	0.957433i	0.877969	−	0.478717i	$-0.158898\pi$
$480$	31479.9	+	11653.3i	0.136631	+	0.0505784i
$481$		−	329191.i		−	1.42284i
$482$	−182377.			−0.785011
$483$	153203.	−	65437.2i	0.656710	−	0.280498i
$484$	5159.96			0.0220270
$485$	31572.5	+	11687.6i	0.134222	+	0.0496867i
$486$	102465.			0.433814
$487$			99853.8i			0.421024i	0.977591	+	0.210512i	$0.0675131\pi$
$487$			99853.8i			0.421024i	−0.977591	+	0.210512i	$0.932487\pi$
$488$	57970.6			0.243427
$489$	290550.			1.21507
$490$	−14690.1	+	39683.4i	−0.0611831	+	0.165279i
$491$	−194757.			−0.807848			−0.403924	−	0.914793i	$-0.632354\pi$
$491$	−194757.			−0.807848			−0.403924	+	0.914793i	$0.632354\pi$
$492$			136919.i			0.565630i
$493$	−79842.6			−0.328504
$494$		−	134261.i		−	0.550168i
$495$	27879.0	−	75311.6i	0.113780	−	0.307363i
$496$	18503.6			0.0752130
$497$	148423.			0.600879
$498$	−134051.			−0.540521
$499$	−124367.			−0.499465			−0.249732	−	0.968315i	$-0.580343\pi$
$499$	−124367.			−0.499465			−0.249732	+	0.968315i	$0.580343\pi$
$500$	−60714.0	−	109265.i	−0.242856	−	0.437059i
$501$	291625.			1.16185
$502$	−18275.9			−0.0725221
$503$	262224.			1.03642			0.518211	−	0.855253i	$-0.326598\pi$
$503$	262224.			1.03642			0.518211	+	0.855253i	$0.326598\pi$
$504$		−	24959.9i		−	0.0982612i
$505$	−20269.5	−	7503.38i	−0.0794803	−	0.0294221i
$506$	−72663.3	−	170121.i	−0.283801	−	0.664443i
$507$			7793.00i			0.0303172i
$508$		−	194099.i		−	0.752133i
$509$	75198.8			0.290252			0.145126	−	0.989413i	$-0.453641\pi$
$509$	75198.8			0.290252			0.145126	+	0.989413i	$0.453641\pi$
$510$	192683.	+	71327.6i	0.740802	+	0.274231i
$511$			394676.i			1.51147i
$512$		−	11585.2i		−	0.0441942i
$513$	−227101.			−0.862948
$514$	−104640.			−0.396068
$515$	−1025.38	−	379.576i	−0.00386607	−	0.00143115i
$516$		−	161653.i		−	0.607134i
$517$	475050.			1.77729
$518$			238337.i			0.888242i
$519$	−323707.			−1.20176
$520$	87990.6	+	32572.5i	0.325409	+	0.120460i
$521$		−	347485.i		−	1.28015i	−0.768312	−	0.640075i	$-0.778903\pi$
$521$		−	347485.i		−	1.28015i	0.768312	−	0.640075i	$-0.221097\pi$
$522$			14977.9i			0.0549681i
$523$	−284639.			−1.04062			−0.520310	−	0.853978i	$-0.674183\pi$
$523$	−284639.			−1.04062			−0.520310	+	0.853978i	$0.674183\pi$
$524$	−143051.			−0.520988
$525$	128160.	−	149383.i	0.464980	−	0.541979i
$526$		−	14126.9i		−	0.0510593i
$527$	113257.			0.407798
$528$	58692.4			0.210530
$529$	−193488.	+	202171.i	−0.691422	+	0.722451i
$530$	92225.6	−	249136.i	0.328322	−	0.886921i
$531$	147551.			0.523303
$532$			97206.0i			0.343455i
$533$			382706.i			1.34714i
$534$		−	31720.7i		−	0.111240i
$535$	−251387.	−	93058.9i	−0.878286	−	0.325125i
$536$			64258.3i			0.223666i
$537$			152297.i			0.528132i
$538$			2177.37i			0.00752258i
$539$			73987.3i			0.254671i
$540$	55096.1	−	148835.i	0.188944	−	0.510409i
$541$	−234856.			−0.802431			−0.401215	−	0.915984i	$-0.631412\pi$
$541$	−234856.			−0.802431			−0.401215	+	0.915984i	$0.631412\pi$
$542$		−	59012.4i		−	0.200884i
$543$	290819.			0.986332
$544$		−	70911.1i		−	0.239616i
$545$	−145290.	+	392482.i	−0.489149	+	1.32138i
$546$			147739.i			0.495575i
$547$		−	166206.i		−	0.555484i	−0.960656	−	0.277742i	$-0.910414\pi$
$547$		−	166206.i		−	0.555484i	0.960656	−	0.277742i	$-0.0895861\pi$
$548$	254646.			0.847960
$549$		−	66563.3i		−	0.220846i
$550$	−165879.	−	142313.i	−0.548361	−	0.470455i
$551$		−	58331.3i		−	0.192131i
$552$	−34874.9	−	81650.1i	−0.114455	−	0.267965i
$553$			96155.4i			0.314430i
$554$	−86469.4			−0.281736
$555$	−127768.	+	345150.i	−0.414798	+	1.12052i
$556$	208351.			0.673979
$557$	−436606.			−1.40727			−0.703637	−	0.710559i	$-0.748442\pi$
$557$	−436606.			−1.40727			−0.703637	+	0.710559i	$0.748442\pi$
$558$		−	21246.3i		−	0.0682362i
$559$		−	451843.i		−	1.44598i
$560$	−63705.9	−	23582.8i	−0.203144	−	0.0752001i
$561$	359245.			1.14147
$562$	−9467.33			−0.0299747
$563$	−141801.			−0.447366			−0.223683	−	0.974662i	$-0.571808\pi$
$563$	−141801.			−0.447366			−0.223683	+	0.974662i	$0.571808\pi$
$564$	228001.			0.716769
$565$	231923.	+	85853.5i	0.726518	+	0.268944i
$566$			444364.i			1.38709i
$567$	160549.			0.499393
$568$		−	79102.1i		−	0.245184i
$569$			470474.i			1.45315i	0.687087	+	0.726575i	$0.258889\pi$
$569$			470474.i			1.45315i	−0.687087	+	0.726575i	$0.741111\pi$
$570$	−52110.4	+	140770.i	−0.160389	+	0.433271i
$571$			233740.i			0.716902i	0.933548	+	0.358451i	$0.116695\pi$
$571$			233740.i			0.716902i	−0.933548	+	0.358451i	$0.883305\pi$
$572$	164053.			0.501410
$573$	137860.			0.419883
$574$		−	277082.i		−	0.840979i
$575$	−99413.4	+	315325.i	−0.300683	+	0.953724i
$576$	−13302.5			−0.0400947
$577$		−	567056.i		−	1.70323i	−0.524165	−	0.851617i	$-0.675622\pi$
$577$		−	567056.i		−	1.70323i	0.524165	−	0.851617i	$-0.324378\pi$
$578$		−	197801.i		−	0.592070i
$579$	−234475.			−0.699421
$580$	38228.6	+	14151.5i	0.113640	+	0.0420675i
$581$	271280.			0.803647
$582$	28252.4			0.0834083
$583$		−	464500.i		−	1.36662i
$584$	210343.			0.616741
$585$	37400.6	−	101033.i	0.109286	−	0.295224i
$586$			54155.2i			0.157705i
$587$		−	287154.i		−	0.833371i	−0.909051	−	0.416686i	$-0.863192\pi$
$587$		−	287154.i		−	0.833371i	0.909051	−	0.416686i	$-0.136808\pi$
$588$			35510.4i			0.102707i
$589$			82743.3i			0.238508i
$590$	139410.	−	376598.i	0.400488	−	1.08187i
$591$	353394.			1.01178
$592$	127022.			0.362440
$593$			217042.i			0.617212i	0.951190	+	0.308606i	$0.0998625\pi$
$593$			217042.i			0.617212i	−0.951190	+	0.308606i	$0.900138\pi$
$594$		−	277495.i		−	0.786470i
$595$	−389932.	−	144346.i	−1.10143	−	0.407728i
$596$			209119.i			0.588708i
$597$	349186.			0.979734
$598$	−97480.2	−	228223.i	−0.272592	−	0.638201i
$599$	−295388.			−0.823265			−0.411632	−	0.911350i	$-0.635041\pi$
$599$	−295388.			−0.823265			−0.411632	+	0.911350i	$0.635041\pi$
$600$	−79614.1	−	68303.2i	−0.221150	−	0.189731i
$601$	495122.			1.37077			0.685383	−	0.728183i	$-0.259635\pi$
$601$	495122.			1.37077			0.685383	+	0.728183i	$0.259635\pi$
$602$			327138.i			0.902688i
$603$	73782.9			0.202918
$604$	142864.			0.391605
$605$	−15122.0	−	5597.89i	−0.0413142	−	0.0152937i
$606$	−18138.0			−0.0493905
$607$			61895.4i			0.167989i	0.996466	+	0.0839945i	$0.0267678\pi$
$607$			61895.4i			0.167989i	−0.996466	+	0.0839945i	$0.973232\pi$
$608$	51806.1			0.140144
$609$			64186.9i			0.173066i
$610$	−169891.	−	62890.6i	−0.456574	−	0.169015i
$611$	637295.			1.70710
$612$	−81421.9			−0.217389
$613$	596815.			1.58825			0.794125	−	0.607754i	$-0.207929\pi$
$613$	596815.			1.58825			0.794125	+	0.607754i	$0.207929\pi$
$614$	−312270.			−0.828312
$615$	148539.	−	401260.i	0.392727	−	1.06090i
$616$	−118776.			−0.313016
$617$	590204.			1.55036			0.775178	−	0.631742i	$-0.217660\pi$
$617$	590204.			1.55036			0.775178	+	0.631742i	$0.217660\pi$
$618$	−917.553			−0.00240245
$619$		−	131809.i		−	0.344004i	−0.985097	−	0.172002i	$-0.944976\pi$
$619$		−	131809.i		−	0.344004i	0.985097	−	0.172002i	$-0.0550236\pi$
$620$	−54227.5	−	20074.0i	−0.141070	−	0.0522217i
$621$	−386038.	+	164887.i	−1.00103	+	0.427566i
$622$			58458.7i			0.151101i
$623$			64193.2i			0.165391i
$624$	78737.8			0.202215
$625$	59392.9	+	386083.i	0.152046	+	0.988373i
$626$			182945.i			0.466844i
$627$			262457.i			0.667610i
$628$	−208475.			−0.528610
$629$	777479.			1.96511
$630$	−27078.3	+	73148.7i	−0.0682245	+	0.184300i
$631$			108955.i			0.273646i	0.990596	+	0.136823i	$0.0436891\pi$
$631$			108955.i			0.273646i	−0.990596	+	0.136823i	$0.956311\pi$
$632$	51246.3			0.128300
$633$		−	591280.i		−	1.47566i
$634$	−173943.			−0.432742
$635$	−210572.	+	568834.i	−0.522219	+	1.41071i
$636$		−	222938.i		−	0.551149i
$637$			99256.4i			0.244613i
$638$	71275.0			0.175104
$639$	−90827.0			−0.222440
$640$	−12568.5	+	33952.2i	−0.0306848	+	0.0828912i
$641$		−	410771.i		−	0.999732i	−0.866103	−	0.499866i	$-0.833383\pi$
$641$		−	410771.i		−	0.999732i	0.866103	−	0.499866i	$-0.166617\pi$
$642$	−224952.			−0.545783
$643$	−382058.			−0.924075			−0.462038	−	0.886860i	$-0.652882\pi$
$643$	−382058.			−0.924075			−0.462038	+	0.886860i	$0.652882\pi$
$644$	70576.4	+	165235.i	0.170172	+	0.398411i
$645$	−175373.	+	473748.i	−0.421544	+	1.13875i
$646$	317096.			0.759846
$647$		−	146229.i		−	0.349321i	−0.984629	−	0.174660i	$-0.944117\pi$
$647$		−	146229.i		−	0.349321i	0.984629	−	0.174660i	$-0.0558828\pi$
$648$		−	85565.1i		−	0.203773i
$649$		−	702145.i		−	1.66701i
$650$	−222532.	−	190917.i	−0.526704	−	0.451874i
$651$		−	91049.6i		−	0.214840i
$652$			313368.i			0.737157i
$653$			106526.i			0.249821i	0.992168	+	0.124911i	$0.0398645\pi$
$653$			106526.i			0.249821i	−0.992168	+	0.124911i	$0.960136\pi$
$654$			351209.i			0.821128i
$655$	419231.	+	155192.i	0.977172	+	0.361731i
$656$	−147672.			−0.343155
$657$		−	241521.i		−	0.559532i
$658$	−461407.			−1.06569
$659$			156031.i			0.359286i	0.983732	+	0.179643i	$0.0574943\pi$
$659$			156031.i			0.359286i	−0.983732	+	0.179643i	$0.942506\pi$
$660$	−172007.	−	63673.7i	−0.394873	−	0.146175i
$661$		−	151946.i		−	0.347766i	−0.984766	−	0.173883i	$-0.944368\pi$
$661$		−	151946.i		−	0.347766i	0.984766	−	0.173883i	$-0.0556315\pi$
$662$			337770.i			0.770736i
$663$	481940.			1.09639
$664$		−	144579.i		−	0.327921i
$665$	105456.	−	284876.i	0.238467	−	0.644188i
$666$		−	145850.i		−	0.328820i
$667$	−42351.4	−	99154.3i	−0.0951955	−	0.222874i
$668$			314528.i			0.704866i
$669$	−379110.			−0.847058
$670$	69711.9	−	188318.i	0.155295	−	0.419510i
$671$	−316752.			−0.703517
$672$	−57006.8			−0.126237
$673$			466442.i			1.02983i	0.857240	+	0.514917i	$0.172177\pi$
$673$			466442.i			1.02983i	−0.857240	+	0.514917i	$0.827823\pi$
$674$			496640.i			1.09326i
$675$	−322934.	+	376412.i	−0.708772	+	0.826143i
$676$	−8405.04			−0.0183927
$677$	220560.			0.481226			0.240613	−	0.970621i	$-0.422652\pi$
$677$	220560.			0.481226			0.240613	+	0.970621i	$0.422652\pi$
$678$	207534.			0.451472
$679$	−57174.5			−0.124012
$680$	−76929.4	+	207815.i	−0.166370	+	0.449428i
$681$			362516.i			0.781688i
$682$	−101104.			−0.217370
$683$		−	651456.i		−	1.39651i	−0.715850	−	0.698254i	$-0.753961\pi$
$683$		−	651456.i		−	1.39651i	0.715850	−	0.698254i	$-0.246039\pi$
$684$		−	59485.1i		−	0.127144i
$685$	−746276.	−	276258.i	−1.59044	−	0.588753i
$686$		−	360188.i		−	0.765388i
$687$	−634621.			−1.34462
$688$	174349.			0.368334
$689$		−	623141.i		−	1.31265i
$690$	13626.2	+	277122.i	0.0286204	+	0.582067i
$691$	744575.			1.55938			0.779691	−	0.626164i	$-0.215376\pi$
$691$	744575.			1.55938			0.779691	+	0.626164i	$0.215376\pi$
$692$		−	349130.i		−	0.729081i
$693$			136381.i			0.283981i
$694$	364518.			0.756833
$695$	−610603.	−	226034.i	−1.26412	−	0.467955i
$696$	34208.6			0.0706182
$697$	−903872.			−1.86055
$698$		−	495478.i		−	1.01698i
$699$	−43918.4			−0.0898860
$700$	161115.	+	138225.i	0.328806	+	0.282093i
$701$			538990.i			1.09684i	0.836202	+	0.548421i	$0.184771\pi$
$701$			538990.i			1.09684i	−0.836202	+	0.548421i	$0.815229\pi$
$702$		−	372268.i		−	0.755409i
$703$			568009.i			1.14933i
$704$			63301.9i			0.127724i
$705$	−668191.	−	247352.i	−1.34438	−	0.497665i
$706$	278485.			0.558718
$707$	36705.9			0.0734339
$708$		−	336996.i		−	0.672293i
$709$		−	350269.i		−	0.696802i	−0.937346	−	0.348401i	$-0.886725\pi$
$709$		−	350269.i		−	0.696802i	0.937346	−	0.348401i	$-0.113275\pi$
$710$	−85815.6	+	231820.i	−0.170235	+	0.459870i
$711$		−	58842.2i		−	0.116399i
$712$	34211.9			0.0674866
$713$	60075.8	+	140651.i	0.118174	+	0.276671i
$714$	−348928.			−0.684446
$715$	−480782.	−	177977.i	−0.940451	−	0.348138i
$716$	−164258.			−0.320405
$717$		−	237496.i		−	0.461974i
$718$	213314.			0.413780
$719$	98854.0			0.191221			0.0956107	−	0.995419i	$-0.469520\pi$
$719$	98854.0			0.191221			0.0956107	+	0.995419i	$0.469520\pi$
$720$	38984.8	+	14431.4i	0.0752021	+	0.0278384i
$721$	1856.85			0.00357196
$722$		−	136940.i		−	0.262697i
$723$	478277.			0.914962
$724$			313659.i			0.598385i
$725$	−96681.9	−	82946.2i	−0.183937	−	0.157805i
$726$	−13531.8			−0.0256734
$727$	−52872.0			−0.100036			−0.0500181	−	0.998748i	$-0.515928\pi$
$727$	−52872.0			−0.100036			−0.0500181	+	0.998748i	$0.515928\pi$
$728$	−159342.			−0.300654
$729$	−575011.			−1.08199
$730$	−616442.	−	228195.i	−1.15677	−	0.428214i
$731$	1.06716e6			1.99707
$732$	−152026.			−0.283724
$733$	−884818.			−1.64682			−0.823410	−	0.567447i	$-0.807931\pi$
$733$	−884818.			−1.64682			−0.823410	+	0.567447i	$0.807931\pi$
$734$			425688.i			0.790132i
$735$	38524.2	−	104068.i	0.0713114	−	0.192639i
$736$	88062.6	−	37613.9i	0.162568	−	0.0694372i
$737$		−	351108.i		−	0.646407i
$738$			169560.i			0.311323i
$739$	−120717.			−0.221044			−0.110522	−	0.993874i	$-0.535252\pi$
$739$	−120717.			−0.221044			−0.110522	+	0.993874i	$0.535252\pi$
$740$	−372257.	−	137803.i	−0.679797	−	0.251648i
$741$			352095.i			0.641244i
$742$			451159.i			0.819449i
$743$	−778913.			−1.41095			−0.705474	−	0.708736i	$-0.749266\pi$
$743$	−778913.			−1.41095			−0.705474	+	0.708736i	$0.749266\pi$
$744$	−48525.1			−0.0876638
$745$	226867.	−	612852.i	0.408750	−	1.10419i
$746$			598028.i			1.07459i
$747$	−166009.			−0.297503
$748$			387459.i			0.692505i
$749$	455236.			0.811471
$750$	159220.	+	286543.i	0.283058	+	0.509411i
$751$		−	420803.i		−	0.746103i	−0.927811	−	0.373052i	$-0.878311\pi$
$751$		−	420803.i		−	0.746103i	0.927811	−	0.373052i	$-0.121689\pi$
$752$			245908.i			0.434847i
$753$	47927.8			0.0845274
$754$	95617.7			0.168188
$755$	−418683.	−	154989.i	−0.734499	−	0.271898i
$756$			269525.i			0.471581i
$757$	−389643.			−0.679946			−0.339973	−	0.940435i	$-0.610418\pi$
$757$	−389643.			−0.679946			−0.339973	+	0.940435i	$0.610418\pi$
$758$	21990.1			0.0382728
$759$	190557.	+	446137.i	0.330782	+	0.774435i
$760$	−151825.	−	56203.0i	−0.262856	−	0.0973043i
$761$	−255816.			−0.441732			−0.220866	−	0.975304i	$-0.570888\pi$
$761$	−255816.			−0.441732			−0.220866	+	0.975304i	$0.570888\pi$
$762$			509017.i			0.876642i
$763$		−	710743.i		−	1.22085i
$764$			148687.i			0.254734i
$765$	238619.	+	88332.2i	0.407738	+	0.150937i
$766$		−	516365.i		−	0.880034i
$767$		−	941951.i		−	1.60117i
$768$			30381.9i			0.0515101i
$769$			821213.i			1.38868i	0.719646	+	0.694341i	$0.244304\pi$
$769$			821213.i			1.38868i	−0.719646	+	0.694341i	$0.755696\pi$
$770$	348090.	+	128857.i	0.587097	+	0.217333i
$771$	274414.			0.461634
$772$		−	252890.i		−	0.424323i
$773$	834132.			1.39597			0.697984	−	0.716113i	$-0.254080\pi$
$773$	834132.			1.39597			0.697984	+	0.716113i	$0.254080\pi$
$774$		−	200192.i		−	0.334167i
$775$	137144.	+	117660.i	0.228335	+	0.195895i
$776$			30471.3i			0.0506019i
$777$		−	625030.i		−	1.03528i
$778$	190909.			0.315404
$779$		−	660350.i		−	1.08818i
$780$	−230752.	−	85420.3i	−0.379278	−	0.140402i
$781$			432215.i			0.708595i
$782$	539015.	−	230228.i	0.881430	−	0.376482i
$783$		−	161737.i		−	0.263806i
$784$	−38299.3			−0.0623101
$785$	610968.	+	226169.i	0.991468	+	0.367023i
$786$	375146.			0.607233
$787$	42783.8			0.0690764			0.0345382	−	0.999403i	$-0.489004\pi$
$787$	42783.8			0.0690764			0.0345382	+	0.999403i	$0.489004\pi$
$788$			381149.i			0.613821i
$789$			37047.3i			0.0595117i
$790$	−150185.	−	55595.6i	−0.240642	−	0.0890812i
$791$	−419988.			−0.671249
$792$	72684.8			0.115876
$793$	−424934.			−0.675732
$794$	34659.3			0.0549767
$795$	−241859.	+	653351.i	−0.382672	+	1.03374i
$796$			376610.i			0.594382i
$797$	785890.			1.23721			0.618607	−	0.785700i	$-0.287697\pi$
$797$	785890.			1.23721			0.618607	+	0.785700i	$0.287697\pi$
$798$		−	254919.i		−	0.400311i
$799$			1.50516e6i			2.35770i
$800$	73667.5	−	85866.7i	0.115106	−	0.134167i
$801$		−	39283.0i		−	0.0612264i
$802$	−164350.			−0.255518
$803$	−1.14932e6			−1.78242
$804$		−	168515.i		−	0.260691i
$805$	−27575.3	−	560813.i	−0.0425528	−	0.865418i
$806$	−135634.			−0.208785
$807$		−	5710.07i		−	0.00876787i
$808$		−	19562.5i		−	0.0299641i
$809$	−502736.			−0.768144			−0.384072	−	0.923303i	$-0.625479\pi$
$809$	−502736.			−0.768144			−0.384072	+	0.923303i	$0.625479\pi$
$810$	−92827.1	+	250761.i	−0.141483	+	0.382199i
$811$	248199.			0.377362			0.188681	−	0.982038i	$-0.439579\pi$
$811$	248199.			0.377362			0.188681	+	0.982038i	$0.439579\pi$
$812$	−69228.0			−0.104995
$813$			154758.i			0.234138i
$814$	−694051.			−1.04747
$815$	339964.	−	918372.i	0.511821	−	1.38262i
$816$			185962.i			0.279283i
$817$			779642.i			1.16802i
$818$			51064.2i			0.0763150i
$819$			182960.i			0.272765i
$820$	432774.	+	160205.i	0.643625	+	0.238258i
$821$	−986524.			−1.46360			−0.731798	−	0.681521i	$-0.761319\pi$
$821$	−986524.			−1.46360			−0.731798	+	0.681521i	$0.761319\pi$
$822$	−667800.			−0.988331
$823$		−	538937.i		−	0.795680i	−0.917455	−	0.397840i	$-0.869760\pi$
$823$		−	538937.i		−	0.795680i	0.917455	−	0.397840i	$-0.130240\pi$
$824$		−	989.614i		−	0.00145751i
$825$	435012.	+	373210.i	0.639137	+	0.548334i
$826$			681980.i			0.999566i
$827$	−307312.			−0.449333			−0.224667	−	0.974436i	$-0.572129\pi$
$827$	−307312.			−0.449333			−0.224667	+	0.974436i	$0.572129\pi$
$828$	−43189.2	−	101116.i	−0.0629962	−	0.147488i
$829$	808415.			1.17632			0.588160	−	0.808745i	$-0.299853\pi$
$829$	808415.			1.17632			0.588160	+	0.808745i	$0.299853\pi$
$830$	−156850.	+	423710.i	−0.227682	+	0.615054i
$831$	226763.			0.328375
$832$			84921.6i			0.122679i
$833$	−234423.			−0.337839
$834$	−546394.			−0.785550
$835$	341223.	−	921771.i	0.489401	−	1.32206i
$836$	−283070.			−0.405024
$837$			229424.i			0.327483i
$838$	656156.			0.934371
$839$		−	881476.i		−	1.25224i	−0.779728	−	0.626119i	$-0.784642\pi$
$839$		−	881476.i		−	1.25224i	0.779728	−	0.626119i	$-0.215358\pi$
$840$	167067.	+	61845.0i	0.236772	+	0.0876488i
$841$	−665739.			−0.941265
$842$	518236.			0.730976
$843$	24827.8			0.0349367
$844$	637717.			0.895248
$845$	24632.2	+	9118.38i	0.0344977	+	0.0127704i
$846$	282358.			0.394511
$847$	27384.4			0.0381713
$848$	240446.			0.334370
$849$		−	1.16533e6i		−	1.61671i
$850$	450906.	−	525575.i	0.624091	−	0.727439i
$851$	412403.	+	965530.i	0.569460	+	1.33324i
$852$			207443.i			0.285772i
$853$			444480.i			0.610878i	0.952212	+	0.305439i	$0.0988032\pi$
$853$			444480.i			0.610878i	−0.952212	+	0.305439i	$0.901197\pi$
$854$	307655.			0.421841
$855$	−64533.6	+	174330.i	−0.0882783	+	0.238473i
$856$		−	242619.i		−	0.331114i
$857$			243880.i			0.332058i	0.986121	+	0.166029i	$0.0530945\pi$
$857$			243880.i			0.332058i	−0.986121	+	0.166029i	$0.946905\pi$
$858$	−430224.			−0.584414
$859$	−1.40563e6			−1.90495			−0.952477	−	0.304612i	$-0.901473\pi$
$859$	−1.40563e6			−1.90495			−0.952477	+	0.304612i	$0.901473\pi$
$860$	−510954.	−	189146.i	−0.690852	−	0.255741i
$861$			726640.i			0.980196i
$862$	45237.3			0.0608810
$863$			776534.i			1.04265i	0.853358	+	0.521325i	$0.174562\pi$
$863$			776534.i			1.04265i	−0.853358	+	0.521325i	$0.825438\pi$
$864$	143644.			0.192425
$865$	−378761.	+	1.02318e6i	−0.506213	+	1.36747i
$866$		−	168311.i		−	0.224428i
$867$			518726.i			0.690081i
$868$	98200.3			0.130339
$869$	−280010.			−0.370796
$870$	−100253.	−	37111.9i	−0.132452	−	0.0490314i
$871$		−	471023.i		−	0.620877i
$872$	−378792.			−0.498159
$873$	34987.9			0.0459081
$874$	168199.	+	393793.i	0.220192	+	0.515520i
$875$	−322215.	−	579879.i	−0.420852	−	0.757393i
$876$	−551618.			−0.718837
$877$		−	800001.i		−	1.04014i	−0.854124	−	0.520070i	$-0.825906\pi$
$877$		−	800001.i		−	1.04014i	0.854124	−	0.520070i	$-0.174094\pi$
$878$		−	395620.i		−	0.513202i
$879$		−	142020.i		−	0.183811i
$880$	68674.4	−	185515.i	0.0886808	−	0.239560i
$881$		−	1.27488e6i		−	1.64255i	−0.570532	−	0.821275i	$-0.693263\pi$
$881$		−	1.27488e6i		−	1.64255i	0.570532	−	0.821275i	$-0.306737\pi$
$882$			43976.2i			0.0565301i
$883$			468231.i			0.600536i	0.953855	+	0.300268i	$0.0970761\pi$
$883$			468231.i			0.600536i	−0.953855	+	0.300268i	$0.902924\pi$
$884$			519790.i			0.665155i
$885$	−365597.	+	987616.i	−0.466785	+	1.26096i
$886$	−126169.			−0.160726
$887$			318838.i			0.405250i	0.979256	+	0.202625i	$0.0649473\pi$
$887$			318838.i			0.405250i	−0.979256	+	0.202625i	$0.935053\pi$
$888$	−333111.			−0.422438
$889$		−	1.03010e6i		−	1.30339i
$890$	−100263.	−	37115.5i	−0.126579	−	0.0468571i
$891$			467529.i			0.588916i
$892$		−	408884.i		−	0.513891i
$893$	−1.09964e6			−1.37894
$894$		−	548406.i		−	0.686163i
$895$	481381.	+	178198.i	0.600957	+	0.222463i
$896$		−	61483.9i		−	0.0765853i
$897$	255638.	+	598508.i	0.317718	+	0.743849i
$898$			286705.i			0.355535i
$899$	−58928.0			−0.0729125
$900$	−98594.3	−	84586.9i	−0.121721	−	0.104428i
$901$	1.47173e6			1.81292
$902$	806881.			0.991737
$903$		−	857907.i		−	1.05212i
$904$			223834.i			0.273898i
$905$	340280.	−	919224.i	0.415469	−	1.12234i
$906$	−374655.			−0.456431
$907$	21201.8			0.0257726			0.0128863	−	0.999917i	$-0.495898\pi$
$907$	21201.8			0.0257726			0.0128863	+	0.999917i	$0.495898\pi$
$908$	−390987.			−0.474232
$909$	−22462.1			−0.0271846
$910$	466974.	+	172865.i	0.563911	+	0.208749i
$911$			416227.i			0.501526i	0.968048	+	0.250763i	$0.0806815\pi$
$911$			416227.i			0.501526i	−0.968048	+	0.250763i	$0.919318\pi$
$912$	−135860.			−0.163343
$913$			789983.i			0.947712i
$914$			441686.i			0.528714i
$915$	445534.	+	164929.i	0.532156	+	0.196994i
$916$		−	684462.i		−	0.815752i
$917$	−759184.			−0.902834
$918$	879220.			1.04331
$919$		−	1.07861e6i		−	1.27713i	−0.769568	−	0.638565i	$-0.779528\pi$
$919$		−	1.07861e6i		−	1.27713i	0.769568	−	0.638565i	$-0.220472\pi$
$920$	−298886.	+	14696.3i	−0.353127	+	0.0173633i
$921$	818918.			0.965431
$922$			453860.i			0.533900i
$923$			579831.i			0.680610i
$924$	311486.			0.364833
$925$	941454.	+	807701.i	1.10031	+	0.943989i
$926$	794629.			0.926707
$927$	−1136.30			−0.00132231
$928$			36895.2i			0.0428424i
$929$	512628.			0.593979			0.296990	−	0.954881i	$-0.404017\pi$
$929$	512628.			0.593979			0.296990	+	0.954881i	$0.404017\pi$
$930$	142210.	+	52643.5i	0.164423	+	0.0608665i
$931$		−	171264.i		−	0.197591i
$932$		−	47367.6i		−	0.0545318i
$933$		−	153306.i		−	0.176115i
$934$		−	476709.i		−	0.546462i
$935$	420343.	−	1.13551e6i	0.480818	−	1.29887i
$936$	97509.1			0.111300
$937$	691119.			0.787179			0.393590	−	0.919286i	$-0.371233\pi$
$937$	691119.			0.787179			0.393590	+	0.919286i	$0.371233\pi$
$938$			341024.i			0.387596i
$939$		−	479767.i		−	0.544126i
$940$	266778.	−	720669.i	0.301922	−	0.815605i
$941$		−	847562.i		−	0.957177i	−0.878039	−	0.478588i	$-0.841149\pi$
$941$		−	847562.i		−	0.957177i	0.878039	−	0.478588i	$-0.158851\pi$
$942$	546720.			0.616117
$943$	−479447.	−	1.12249e6i	−0.539159	−	1.26229i
$944$	363463.			0.407865
$945$	292400.	−	789883.i	0.327427	−	0.884503i
$946$	−952644.			−1.06451
$947$			941183.i			1.04948i	0.851262	+	0.524740i	$0.175837\pi$
$947$			941183.i			1.04948i	−0.851262	+	0.524740i	$0.824163\pi$
$948$	−134392.			−0.149539
$949$	−1.54185e6			−1.71202
$950$	383973.	+	329422.i	0.425455	+	0.365010i
$951$	456160.			0.504379
$952$		−	376332.i		−	0.415238i
$953$	1.27744e6			1.40655			0.703273	−	0.710920i	$-0.251721\pi$
$953$	1.27744e6			1.40655			0.703273	+	0.710920i	$0.251721\pi$
$954$		−	276087.i		−	0.303353i
$955$	161306.	−	435749.i	0.176866	−	0.477782i
$956$	256148.			0.280269
$957$	−186916.			−0.204091
$958$	−621333.			−0.677008
$959$	1.35143e6			1.46945
$960$	32960.4	−	89038.6i	0.0357644	−	0.0966130i
$961$	−839931.			−0.909488
$962$	−931092.			−1.00610
$963$	−278581.			−0.300400
$964$			515839.i			0.555086i
$965$	−274353.	+	741130.i	−0.294615	+	0.795865i
$966$	−185084.	−	433324.i	−0.198342	−	0.464364i
$967$			3919.14i			0.00419119i	0.999998	+	0.00209560i	$0.000667050\pi$
$967$			3919.14i			0.00419119i	−0.999998	+	0.00209560i	$0.999333\pi$
$968$		−	14594.6i		−	0.0155755i
$969$	−831574.			−0.885632
$970$	33057.4	−	89300.5i	0.0351338	−	0.0949096i
$971$		−	1.38885e6i		−	1.47305i	−0.676413	−	0.736523i	$-0.736466\pi$
$971$		−	1.38885e6i		−	1.47305i	0.676413	−	0.736523i	$-0.263534\pi$
$972$		−	289815.i		−	0.306753i
$973$	1.10574e6			1.16796
$974$	282429.			0.297709
$975$	583584.	+	500673.i	0.613895	+	0.526678i
$976$		−	163966.i		−	0.172129i
$977$	93269.9			0.0977130			0.0488565	−	0.998806i	$-0.484442\pi$
$977$	93269.9			0.0977130			0.0488565	+	0.998806i	$0.484442\pi$
$978$		−	821798.i		−	0.859187i
$979$	−186934.			−0.195040
$980$	112242.	+	41549.8i	0.116870	+	0.0432630i
$981$			434939.i			0.451950i
$982$			550855.i			0.571235i
$983$	−213843.			−0.221303			−0.110651	−	0.993859i	$-0.535294\pi$
$983$	−213843.			−0.221303			−0.110651	+	0.993859i	$0.535294\pi$
$984$	387264.			0.399961
$985$	413497.	−	1.11701e6i	0.426187	−	1.15129i
$986$			225829.i			0.232287i
$987$	1.21002e6			1.24211
$988$	−379747.			−0.389028
$989$	566059.	+	1.32527e6i	0.578721	+	1.35492i
$990$	−213013.	−	78853.6i	−0.217338	−	0.0804547i
$991$	1.08062e6			1.10033			0.550167	−	0.835055i	$-0.314564\pi$
$991$	1.08062e6			1.10033			0.550167	+	0.835055i	$0.314564\pi$
$992$		−	52336.1i		−	0.0531836i
$993$		−	885791.i		−	0.898324i
$994$		−	419802.i		−	0.424886i
$995$	408573.	−	1.10371e6i	0.412690	−	1.11483i
$996$			379154.i			0.382206i
$997$			1.60901e6i			1.61871i	0.587321	+	0.809354i	$0.300183\pi$
$997$			1.60901e6i			1.61871i	−0.587321	+	0.809354i	$0.699817\pi$
$998$			351764.i			0.353175i
$999$			1.57493e6i			1.57809i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.5.c.a.229.11	✓	48
5.4	even	2	inner	230.5.c.a.229.38	yes	48
23.22	odd	2	inner	230.5.c.a.229.37	yes	48
115.114	odd	2	inner	230.5.c.a.229.12	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.5.c.a.229.11	✓	48	1.1	even	1	trivial
230.5.c.a.229.12	yes	48	115.114	odd	2	inner
230.5.c.a.229.37	yes	48	23.22	odd	2	inner
230.5.c.a.229.38	yes	48	5.4	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	230.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.82843i q^{2} +7.41746i q^{3} -8.00000 q^{4} +(23.4452 + 8.67897i) q^{5} +20.9797 q^{6} -42.4567 q^{7} +22.6274i q^{8} +25.9814 q^{9} +(24.5478 - 66.3129i) q^{10} -123.637i q^{11} -59.3396i q^{12} -165.863i q^{13} +120.086i q^{14} +(-64.3758 + 173.903i) q^{15} +64.0000 q^{16} +391.732 q^{17} -73.4864i q^{18} +286.191i q^{19} +(-187.561 - 69.4317i) q^{20} -314.921i q^{21} -349.697 q^{22} +(207.789 + 486.482i) q^{23} -167.838 q^{24} +(474.351 + 406.960i) q^{25} -469.130 q^{26} +793.529i q^{27} +339.654 q^{28} -203.819 q^{29} +(491.873 + 182.082i) q^{30} +289.119 q^{31} -181.019i q^{32} +917.069 q^{33} -1107.99i q^{34} +(-995.405 - 368.481i) q^{35} -207.851 q^{36} +1984.72 q^{37} +809.471 q^{38} +1230.28 q^{39} +(-196.383 + 530.503i) q^{40} -2307.37 q^{41} -890.731 q^{42} +2724.20 q^{43} +989.092i q^{44} +(609.137 + 225.491i) q^{45} +(1375.98 - 587.717i) q^{46} +3842.31i q^{47} +474.717i q^{48} -598.426 q^{49} +(1151.06 - 1341.67i) q^{50} +2905.66i q^{51} +1326.90i q^{52} +3756.98 q^{53} +2244.44 q^{54} +(1073.04 - 2898.68i) q^{55} -960.686i q^{56} -2122.81 q^{57} +576.488i q^{58} +5679.11 q^{59} +(515.007 - 1391.23i) q^{60} -2561.96i q^{61} -817.752i q^{62} -1103.08 q^{63} -512.000 q^{64} +(1439.52 - 3888.67i) q^{65} -2593.86i q^{66} +2839.84 q^{67} -3133.86 q^{68} +(-3608.46 + 1541.27i) q^{69} +(-1042.22 + 2815.43i) q^{70} -3495.85 q^{71} +587.891i q^{72} -9295.95i q^{73} -5613.64i q^{74} +(-3018.60 + 3518.48i) q^{75} -2289.53i q^{76} +5249.20i q^{77} -3479.75i q^{78} -2264.79i q^{79} +(1500.49 + 555.454i) q^{80} -3781.48 q^{81} +6526.23i q^{82} -6389.56 q^{83} +2519.37i q^{84} +(9184.23 + 3399.83i) q^{85} -7705.20i q^{86} -1511.82i q^{87} +2797.58 q^{88} -1511.97i q^{89} +(637.786 - 1722.90i) q^{90} +7041.98i q^{91} +(-1662.31 - 3891.86i) q^{92} +2144.53i q^{93} +10867.7 q^{94} +(-2483.84 + 6709.80i) q^{95} +1342.70 q^{96} +1346.65 q^{97} +1692.60i q^{98} -3212.25i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 384 q^{4} - 64 q^{6} - 1608 q^{9} + 3072 q^{16} + 512 q^{24} + 1488 q^{25} - 384 q^{26} - 2940 q^{29} + 4732 q^{31} + 2556 q^{35} + 12864 q^{36} + 2736 q^{39} + 828 q^{41} - 64 q^{46} + 32572 q^{49}+ \cdots - 4096 q^{96}+O(q^{100}) \) 48 * q - 384 * q^4 - 64 * q^6 - 1608 * q^9 + 3072 * q^16 + 512 * q^24 + 1488 * q^25 - 384 * q^26 - 2940 * q^29 + 4732 * q^31 + 2556 * q^35 + 12864 * q^36 + 2736 * q^39 + 828 * q^41 - 64 * q^46 + 32572 * q^49 - 3264 * q^50 + 10112 * q^54 + 12824 * q^55 + 7092 * q^59 - 24576 * q^64 + 14000 * q^69 - 6592 * q^70 - 12708 * q^71 + 24728 * q^75 - 13040 * q^81 - 15700 * q^85 - 9728 * q^94 - 46608 * q^95 - 4096 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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