LMFDB - Embedded newform 230.5.c.a.229.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,5,Mod(229,230)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

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	$-0.864802\pi$
$3$		−	7.41746i		−	0.824162i	0.911147	−	0.412081i	$-0.135198\pi$
$4$	−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	$0.170686\pi$
$11$			123.637i			1.02179i	−0.859643	+	0.510895i	$0.829314\pi$
$12$			59.3396i			0.412081i
$13$			165.863i			0.981435i	0.871319	+	0.490717i	$0.163265\pi$
$13$			165.863i			0.981435i	−0.871319	+	0.490717i	$0.836735\pi$
$14$		−	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	$-0.870264\pi$
$19$		−	286.191i		−	0.792773i	0.918084	−	0.396387i	$-0.129736\pi$
$20$	−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	$-0.664316\pi$
$47$		−	3842.31i		−	1.73939i	0.493590	−	0.869695i	$-0.335684\pi$
$48$		−	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	$0.111869\pi$
$61$			2561.96i			0.688515i	−0.938875	+	0.344257i	$0.888131\pi$
$62$			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	$0.337310\pi$
$73$			9295.95i			1.74441i	−0.489142	+	0.872204i	$0.662690\pi$
$74$			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	$0.0580772\pi$
$79$			2264.79i			0.362888i	−0.983401	+	0.181444i	$0.941923\pi$
$80$	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	$0.0304259\pi$
$89$			1511.97i			0.190881i	−0.995435	+	0.0954404i	$0.969574\pi$
$90$	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	$-0.751170\pi$
$109$		−	16740.4i		−	1.40901i	0.709700	−	0.704504i	$-0.248830\pi$
$110$	−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	$-0.729025\pi$
$127$		−	24262.3i		−	1.50427i	0.659011	−	0.752133i	$-0.270975\pi$
$128$		−	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	$0.200363\pi$
$149$			26139.8i			1.17742i	−0.808346	+	0.588708i	$0.799637\pi$
$150$	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	$0.263832\pi$
$163$			39171.1i			1.47431i	−0.675721	+	0.737157i	$0.736168\pi$
$164$	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	$0.248993\pi$
$167$			39316.0i			1.40973i	−0.709340	+	0.704866i	$0.751007\pi$
$168$	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	$-0.739948\pi$
$173$		−	43641.3i		−	1.45816i	0.684428	−	0.729081i	$-0.260052\pi$
$174$	−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	$0.204191\pi$
$181$			39207.4i			1.19677i	−0.801209	+	0.598385i	$0.795809\pi$
$182$	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	$0.0819878\pi$
$191$			18585.9i			0.509467i	−0.967011	+	0.254734i	$0.918012\pi$
$192$			3797.74i			0.103020i
$193$		−	31611.2i		−	0.848646i	−0.905511	−	0.424323i	$-0.860512\pi$
$193$		−	31611.2i		−	0.848646i	0.905511	−	0.424323i	$-0.139488\pi$
$194$			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	$0.210369\pi$
$197$			47643.6i			1.22764i	−0.789445	+	0.613821i	$0.789631\pi$
$198$	−9085.60			−0.231752
$199$			47076.3i			1.18876i	0.804183	+	0.594382i	$0.202603\pi$
$199$			47076.3i			1.18876i	−0.804183	+	0.594382i	$0.797397\pi$
$200$	−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	$-0.828204\pi$
$223$		−	51110.5i		−	1.02778i	0.857856	−	0.513891i	$-0.171796\pi$
$224$		−	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	$-0.696323\pi$
$229$		−	85557.7i		−	1.63150i	0.578402	−	0.815752i	$-0.303677\pi$
$230$	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	$-0.982633\pi$
$233$		−	5920.95i		−	0.109064i	0.998512	−	0.0545318i	$-0.0173666\pi$
$234$	−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	$0.187315\pi$
$241$			64479.9i			1.11017i	−0.831793	+	0.555086i	$0.812685\pi$
$242$		−	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	$0.0163304\pi$
$251$			6461.49i			0.102562i	−0.998684	+	0.0512809i	$0.983670\pi$
$252$	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	$0.0903552\pi$
$257$			36995.7i			0.560125i	−0.959982	+	0.280063i	$0.909645\pi$
$258$	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	$0.0638401\pi$
$277$			30571.6i			0.398436i	−0.979955	+	0.199218i	$0.936160\pi$
$278$		−	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	$0.00674718\pi$
$281$			3347.21i			0.0423906i	−0.999775	+	0.0211953i	$0.993253\pi$
$282$		−	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	$0.199182\pi$
$307$			110404.i			1.17141i	−0.810524	+	0.585705i	$0.800818\pi$
$308$			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	$0.0989891\pi$
$317$			61498.2i			0.611990i	−0.952033	+	0.305995i	$0.901011\pi$
$318$	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	$-0.820251\pi$
$347$		−	128877.i		−	1.07032i	0.844750	−	0.535162i	$-0.179749\pi$
$348$		−	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	$-0.870719\pi$
$353$		−	98459.4i		−	0.790147i	0.918650	−	0.395073i	$-0.129281\pi$
$354$	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	$-0.905484\pi$
$359$		−	75417.7i		−	0.585173i	0.956239	−	0.292587i	$-0.0945160\pi$
$360$	−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	$-0.991385\pi$
$379$		−	7774.69i		−	0.0541259i	0.999634	−	0.0270629i	$-0.00861545\pi$
$380$	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	$-0.928407\pi$
$389$		−	67496.5i		−	0.446049i	0.974813	−	0.223024i	$-0.0715930\pi$
$390$	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	$-0.987623\pi$
$397$		−	12253.9i		−	0.0777488i	0.999244	−	0.0388744i	$-0.0123772\pi$
$398$	−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	$0.0578294\pi$
$401$			58106.7i			0.361358i	−0.983542	+	0.180679i	$0.942171\pi$
$402$	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	$-0.770260\pi$
$419$		−	231986.i		−	1.32140i	0.750650	−	0.660700i	$-0.229740\pi$
$420$	−21865.5	−	59067.0i	−0.123954	−	0.334847i
$421$		−	183224.i		−	1.03376i	−0.856059	−	0.516878i	$-0.827094\pi$
$421$		−	183224.i		−	1.03376i	0.856059	−	0.516878i	$-0.172906\pi$
$422$		−	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	$-0.986293\pi$
$431$		−	15993.8i		−	0.0860988i	0.999073	−	0.0430494i	$-0.0137073\pi$
$432$		−	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	$0.0362545\pi$
$443$			44607.6i			0.227301i	−0.993521	+	0.113651i	$0.963746\pi$
$444$			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	$-0.772550\pi$
$463$		−	280944.i		−	1.31056i	0.755385	−	0.655281i	$-0.227450\pi$
$464$	−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	$0.158898\pi$
$479$			219674.i			0.957433i	−0.877969	+	0.478717i	$0.841102\pi$
$480$	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	$-0.932487\pi$
$487$		−	99853.8i		−	0.421024i	0.977591	−	0.210512i	$-0.0675131\pi$
$488$	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	$0.221097\pi$
$521$			347485.i			1.28015i	−0.768312	+	0.640075i	$0.778903\pi$
$522$		−	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	$0.0895861\pi$
$547$			166206.i			0.555484i	−0.960656	+	0.277742i	$0.910414\pi$
$548$	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	$-0.741111\pi$
$569$		−	470474.i		−	1.45315i	0.687087	−	0.726575i	$-0.258889\pi$
$570$	−52110.4	−	140770.i	−0.160389	−	0.433271i
$571$		−	233740.i		−	0.716902i	−0.933548	−	0.358451i	$-0.883305\pi$
$571$		−	233740.i		−	0.716902i	0.933548	−	0.358451i	$-0.116695\pi$
$572$	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	$0.324378\pi$
$577$			567056.i			1.70323i	−0.524165	+	0.851617i	$0.675622\pi$
$578$			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	$0.136808\pi$
$587$			287154.i			0.833371i	−0.909051	+	0.416686i	$0.863192\pi$
$588$		−	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	$-0.900138\pi$
$593$		−	217042.i		−	0.617212i	0.951190	−	0.308606i	$-0.0998625\pi$
$594$			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	$-0.973232\pi$
$607$		−	61895.4i		−	0.167989i	0.996466	−	0.0839945i	$-0.0267678\pi$
$608$	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	$0.0550236\pi$
$619$			131809.i			0.344004i	−0.985097	+	0.172002i	$0.944976\pi$
$620$	−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	$-0.956311\pi$
$631$		−	108955.i		−	0.273646i	0.990596	−	0.136823i	$-0.0436891\pi$
$632$	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	$0.166617\pi$
$641$			410771.i			0.999732i	−0.866103	+	0.499866i	$0.833383\pi$
$642$	−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	$0.0558828\pi$
$647$			146229.i			0.349321i	−0.984629	+	0.174660i	$0.944117\pi$
$648$			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	$-0.960136\pi$
$653$		−	106526.i		−	0.249821i	0.992168	−	0.124911i	$-0.0398645\pi$
$654$		−	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	$-0.942506\pi$
$659$		−	156031.i		−	0.359286i	0.983732	−	0.179643i	$-0.0574943\pi$
$660$	−172007.	+	63673.7i	−0.394873	+	0.146175i
$661$			151946.i			0.347766i	0.984766	+	0.173883i	$0.0556315\pi$
$661$			151946.i			0.347766i	−0.984766	+	0.173883i	$0.944368\pi$
$662$		−	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	$-0.827823\pi$
$673$		−	466442.i		−	1.02983i	0.857240	−	0.514917i	$-0.172177\pi$
$674$		−	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	$0.246039\pi$
$683$			651456.i			1.39651i	−0.715850	+	0.698254i	$0.753961\pi$
$684$			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	$-0.815229\pi$
$701$		−	538990.i		−	1.09684i	0.836202	−	0.548421i	$-0.184771\pi$
$702$			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	$0.113275\pi$
$709$			350269.i			0.696802i	−0.937346	+	0.348401i	$0.886725\pi$
$710$	−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	$0.121689\pi$
$751$			420803.i			0.746103i	−0.927811	+	0.373052i	$0.878311\pi$
$752$		−	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	$-0.755696\pi$
$769$		−	821213.i		−	1.38868i	0.719646	−	0.694341i	$-0.244304\pi$
$770$	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	$0.130240\pi$
$823$			538937.i			0.795680i	−0.917455	+	0.397840i	$0.869760\pi$
$824$			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	$0.215358\pi$
$839$			881476.i			1.25224i	−0.779728	+	0.626119i	$0.784642\pi$
$840$	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	$-0.901197\pi$
$853$		−	444480.i		−	0.610878i	0.952212	−	0.305439i	$-0.0988032\pi$
$854$	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	$-0.946905\pi$
$857$		−	243880.i		−	0.332058i	0.986121	−	0.166029i	$-0.0530945\pi$
$858$	−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	$-0.825438\pi$
$863$		−	776534.i		−	1.04265i	0.853358	−	0.521325i	$-0.174562\pi$
$864$	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	$0.174094\pi$
$877$			800001.i			1.04014i	−0.854124	+	0.520070i	$0.825906\pi$
$878$			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	$0.306737\pi$
$881$			1.27488e6i			1.64255i	−0.570532	+	0.821275i	$0.693263\pi$
$882$		−	43976.2i		−	0.0565301i
$883$		−	468231.i		−	0.600536i	−0.953855	−	0.300268i	$-0.902924\pi$
$883$		−	468231.i		−	0.600536i	0.953855	−	0.300268i	$-0.0970761\pi$
$884$		−	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	$-0.935053\pi$
$887$		−	318838.i		−	0.405250i	0.979256	−	0.202625i	$-0.0649473\pi$
$888$	−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	$-0.919318\pi$
$911$		−	416227.i		−	0.501526i	0.968048	−	0.250763i	$-0.0806815\pi$
$912$	−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	$0.220472\pi$
$919$			1.07861e6i			1.27713i	−0.769568	+	0.638565i	$0.779528\pi$
$920$	−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	$0.158851\pi$
$941$			847562.i			0.957177i	−0.878039	+	0.478588i	$0.841149\pi$
$942$	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	$-0.824163\pi$
$947$		−	941183.i		−	1.04948i	0.851262	−	0.524740i	$-0.175837\pi$
$948$	−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	$-0.999333\pi$
$967$		−	3919.14i		−	0.00419119i	0.999998	−	0.00209560i	$-0.000667050\pi$
$968$			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	$0.263534\pi$
$971$			1.38885e6i			1.47305i	−0.676413	+	0.736523i	$0.736466\pi$
$972$			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	$-0.699817\pi$
$997$		−	1.60901e6i		−	1.61871i	0.587321	−	0.809354i	$-0.300183\pi$
$998$		−	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.229.12	yes	48
5.4	even	2	inner	230.5.c.a.229.37	yes	48
23.22	odd	2	inner	230.5.c.a.229.38	yes	48
115.114	odd	2	inner	230.5.c.a.229.11	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.5.c.a.229.11	✓	48	115.114	odd	2	inner
230.5.c.a.229.12	yes	48	1.1	even	1	trivial
230.5.c.a.229.37	yes	48	5.4	even	2	inner
230.5.c.a.229.38	yes	48	23.22	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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	230.c (of order \(2\), degree \(1\), minimal)

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

Related objects

Downloads

Learn more