LMFDB - Embedded newform 289.10.a.i.1.29

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,10,Mod(1,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("289.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	289.a (trivial)

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:	yes
Analytic conductor:	$148.845356651$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.29
Character	$\chi$	$=$	289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+6.86896 q^{2} -207.816 q^{3} -464.817 q^{4} +1878.94 q^{5} -1427.48 q^{6} -3271.20 q^{7} -6709.72 q^{8} +23504.5 q^{9} +O(q^{10})$	\(q+6.86896 q^{2} -207.816 q^{3} -464.817 q^{4} +1878.94 q^{5} -1427.48 q^{6} -3271.20 q^{7} -6709.72 q^{8} +23504.5 q^{9} +12906.4 q^{10} -60624.5 q^{11} +96596.5 q^{12} -74153.5 q^{13} -22469.7 q^{14} -390474. q^{15} +191898. q^{16} +161452. q^{18} -640911. q^{19} -873365. q^{20} +679808. q^{21} -416428. q^{22} +1.59080e6 q^{23} +1.39439e6 q^{24} +1.57730e6 q^{25} -509358. q^{26} -794179. q^{27} +1.52051e6 q^{28} -3.96826e6 q^{29} -2.68215e6 q^{30} +874596. q^{31} +4.75352e6 q^{32} +1.25988e7 q^{33} -6.14639e6 q^{35} -1.09253e7 q^{36} -9.52735e6 q^{37} -4.40239e6 q^{38} +1.54103e7 q^{39} -1.26072e7 q^{40} -3.43402e7 q^{41} +4.66958e6 q^{42} -2.35305e7 q^{43} +2.81793e7 q^{44} +4.41637e7 q^{45} +1.09271e7 q^{46} -3.35038e7 q^{47} -3.98794e7 q^{48} -2.96529e7 q^{49} +1.08344e7 q^{50} +3.44679e7 q^{52} -6.55613e7 q^{53} -5.45519e6 q^{54} -1.13910e8 q^{55} +2.19488e7 q^{56} +1.33192e8 q^{57} -2.72578e7 q^{58} +2.92960e7 q^{59} +1.81499e8 q^{60} -1.12882e8 q^{61} +6.00756e6 q^{62} -7.68881e7 q^{63} -6.55999e7 q^{64} -1.39330e8 q^{65} +8.65404e7 q^{66} +2.57167e8 q^{67} -3.30594e8 q^{69} -4.22193e7 q^{70} -1.13735e8 q^{71} -1.57709e8 q^{72} -8.63018e7 q^{73} -6.54430e7 q^{74} -3.27788e8 q^{75} +2.97906e8 q^{76} +1.98315e8 q^{77} +1.05853e8 q^{78} -6.15498e8 q^{79} +3.60564e8 q^{80} -2.97597e8 q^{81} -2.35881e8 q^{82} +5.29670e8 q^{83} -3.15987e8 q^{84} -1.61630e8 q^{86} +8.24668e8 q^{87} +4.06774e8 q^{88} -2.99276e8 q^{89} +3.03359e8 q^{90} +2.42571e8 q^{91} -7.39431e8 q^{92} -1.81755e8 q^{93} -2.30136e8 q^{94} -1.20423e9 q^{95} -9.87857e8 q^{96} -1.53802e9 q^{97} -2.03684e8 q^{98} -1.42495e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 64 q^{2} + 13312 q^{4} + 49152 q^{8} + 341172 q^{9}+O(q^{10}) $ 52 * q + 64 * q^2 + 13312 * q^4 + 49152 * q^8 + 341172 * q^9	$ 52 q + 64 q^{2} + 13312 q^{4} + 49152 q^{8} + 341172 q^{9} + 156200 q^{13} + 1207872 q^{15} + 3407880 q^{16} + 2193336 q^{18} + 1185568 q^{19} + 5198336 q^{21} + 13827692 q^{25} + 3618944 q^{26} - 9167544 q^{30} + 61884888 q^{32} + 1635208 q^{33} + 46992776 q^{35} + 156027320 q^{36} + 84813952 q^{38} - 4635776 q^{42} + 125448912 q^{43} + 164193176 q^{47} + 270850284 q^{49} - 226223888 q^{50} + 103553016 q^{52} + 426167208 q^{53} + 677761520 q^{55} + 375214512 q^{59} + 336918024 q^{60} + 190014416 q^{64} + 1377178928 q^{66} + 311910088 q^{67} + 533688136 q^{69} + 1477690280 q^{70} + 2757942680 q^{72} + 4047975520 q^{76} + 3440336432 q^{77} + 3266558756 q^{81} + 2072890608 q^{83} + 2630025952 q^{84} + 1538547296 q^{86} - 1010436256 q^{87} + 1873849184 q^{89} - 1998451624 q^{93} - 6880776704 q^{94} - 4667454128 q^{98}+O(q^{100}) $ 52 * q + 64 * q^2 + 13312 * q^4 + 49152 * q^8 + 341172 * q^9 + 156200 * q^13 + 1207872 * q^15 + 3407880 * q^16 + 2193336 * q^18 + 1185568 * q^19 + 5198336 * q^21 + 13827692 * q^25 + 3618944 * q^26 - 9167544 * q^30 + 61884888 * q^32 + 1635208 * q^33 + 46992776 * q^35 + 156027320 * q^36 + 84813952 * q^38 - 4635776 * q^42 + 125448912 * q^43 + 164193176 * q^47 + 270850284 * q^49 - 226223888 * q^50 + 103553016 * q^52 + 426167208 * q^53 + 677761520 * q^55 + 375214512 * q^59 + 336918024 * q^60 + 190014416 * q^64 + 1377178928 * q^66 + 311910088 * q^67 + 533688136 * q^69 + 1477690280 * q^70 + 2757942680 * q^72 + 4047975520 * q^76 + 3440336432 * q^77 + 3266558756 * q^81 + 2072890608 * q^83 + 2630025952 * q^84 + 1538547296 * q^86 - 1010436256 * q^87 + 1873849184 * q^89 - 1998451624 * q^93 - 6880776704 * q^94 - 4667454128 * q^98

Display 100 coefficients 10 coefficients

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 $

$2$	6.86896	0.303568	0.151784	−	0.988414i	$-0.451498\pi$
$2$	6.86896	0.303568	0.151784	+	0.988414i	$0.451498\pi$
$3$	−207.816	−1.48127	−0.740634	−	0.671909i	$-0.765475\pi$
$3$	−207.816	−1.48127	−0.740634	+	0.671909i	$0.765475\pi$
$4$	−464.817	−0.907846
$5$	1878.94	1.34446	0.672231	−	0.740342i	$-0.265336\pi$
$5$	1878.94	1.34446	0.672231	+	0.740342i	$0.265336\pi$
$6$	−1427.48	−0.449666
$7$	−3271.20	−0.514951	−0.257475	−	0.966285i	$-0.582891\pi$
$7$	−3271.20	−0.514951	−0.257475	+	0.966285i	$0.582891\pi$
$8$	−6709.72	−0.579161
$9$	23504.5	1.19415
$10$	12906.4	0.408136
$11$	−60624.5	−1.24848	−0.624240	−	0.781233i	$-0.714591\pi$
$11$	−60624.5	−1.24848	−0.624240	+	0.781233i	$0.714591\pi$
$12$	96596.5	1.34476
$13$	−74153.5	−0.720090	−0.360045	−	0.932935i	$-0.617239\pi$
$13$	−74153.5	−0.720090	−0.360045	+	0.932935i	$0.617239\pi$
$14$	−22469.7	−0.156323
$15$	−390474.	−1.99151
$16$	191898.	0.732031
$17$	0	0
$17$	0	0
$18$	161452.	0.362507
$19$	−640911.	−1.12825	−0.564126	−	0.825689i	$-0.690787\pi$
$19$	−640911.	−1.12825	−0.564126	+	0.825689i	$0.690787\pi$
$20$	−873365.	−1.22056
$21$	679808.	0.762780
$22$	−416428.	−0.378999
$23$	1.59080e6	1.18533	0.592666	−	0.805448i	$-0.298075\pi$
$23$	1.59080e6	1.18533	0.592666	+	0.805448i	$0.298075\pi$
$24$	1.39439e6	0.857893
$25$	1.57730e6	0.807576
$26$	−509358.	−0.218596
$27$	−794179.	−0.287595
$28$	1.52051e6	0.467496
$29$	−3.96826e6	−1.04186	−0.520929	−	0.853600i	$-0.674414\pi$
$29$	−3.96826e6	−1.04186	−0.520929	+	0.853600i	$0.674414\pi$
$30$	−2.68215e6	−0.604558
$31$	874596.	0.170090	0.0850452	−	0.996377i	$-0.472897\pi$
$31$	874596.	0.170090	0.0850452	+	0.996377i	$0.472897\pi$
$32$	4.75352e6	0.801383
$33$	1.25988e7	1.84933
$34$	0	0
$35$	−6.14639e6	−0.692332
$36$	−1.09253e7	−1.08411
$37$	−9.52735e6	−0.835727	−0.417864	−	0.908510i	$-0.637221\pi$
$37$	−9.52735e6	−0.835727	−0.417864	+	0.908510i	$0.637221\pi$
$38$	−4.40239e6	−0.342501
$39$	1.54103e7	1.06665
$40$	−1.26072e7	−0.778660
$41$	−3.43402e7	−1.89791	−0.948954	−	0.315413i	$-0.897857\pi$
$41$	−3.43402e7	−1.89791	−0.948954	+	0.315413i	$0.897857\pi$
$42$	4.66958e6	0.231556
$43$	−2.35305e7	−1.04960	−0.524798	−	0.851227i	$-0.675859\pi$
$43$	−2.35305e7	−1.04960	−0.524798	+	0.851227i	$0.675859\pi$
$44$	2.81793e7	1.13343
$45$	4.41637e7	1.60549
$46$	1.09271e7	0.359829
$47$	−3.35038e7	−1.00151	−0.500753	−	0.865590i	$-0.666944\pi$
$47$	−3.35038e7	−1.00151	−0.500753	+	0.865590i	$0.666944\pi$
$48$	−3.98794e7	−1.08433
$49$	−2.96529e7	−0.734825
$50$	1.08344e7	0.245154
$51$	0	0
$52$	3.44679e7	0.653731
$53$	−6.55613e7	−1.14132	−0.570659	−	0.821187i	$-0.693312\pi$
$53$	−6.55613e7	−1.14132	−0.570659	+	0.821187i	$0.693312\pi$
$54$	−5.45519e6	−0.0873047
$55$	−1.13910e8	−1.67853
$56$	2.19488e7	0.298240
$57$	1.33192e8	1.67124
$58$	−2.72578e7	−0.316275
$59$	2.92960e7	0.314757	0.157378	−	0.987538i	$-0.449696\pi$
$59$	2.92960e7	0.314757	0.157378	+	0.987538i	$0.449696\pi$
$60$	1.81499e8	1.80798
$61$	−1.12882e8	−1.04385	−0.521926	−	0.852991i	$-0.674786\pi$
$61$	−1.12882e8	−1.04385	−0.521926	+	0.852991i	$0.674786\pi$
$62$	6.00756e6	0.0516340
$63$	−7.68881e7	−0.614931
$64$	−6.55999e7	−0.488757
$65$	−1.39330e8	−0.968133
$66$	8.65404e7	0.561398
$67$	2.57167e8	1.55912	0.779558	−	0.626330i	$-0.215444\pi$
$67$	2.57167e8	1.55912	0.779558	+	0.626330i	$0.215444\pi$
$68$	0	0
$69$	−3.30594e8	−1.75580
$70$	−4.22193e7	−0.210170
$71$	−1.13735e8	−0.531167	−0.265583	−	0.964088i	$-0.585565\pi$
$71$	−1.13735e8	−0.531167	−0.265583	+	0.964088i	$0.585565\pi$
$72$	−1.57709e8	−0.691608
$73$	−8.63018e7	−0.355686	−0.177843	−	0.984059i	$-0.556912\pi$
$73$	−8.63018e7	−0.355686	−0.177843	+	0.984059i	$0.556912\pi$
$74$	−6.54430e7	−0.253700
$75$	−3.27788e8	−1.19624
$76$	2.97906e8	1.02428
$77$	1.98315e8	0.642906
$78$	1.05853e8	0.323800
$79$	−6.15498e8	−1.77789	−0.888944	−	0.458016i	$-0.848560\pi$
$79$	−6.15498e8	−1.77789	−0.888944	+	0.458016i	$0.848560\pi$
$80$	3.60564e8	0.984188
$81$	−2.97597e8	−0.768149
$82$	−2.35881e8	−0.576145
$83$	5.29670e8	1.22505	0.612525	−	0.790451i	$-0.290154\pi$
$83$	5.29670e8	1.22505	0.612525	+	0.790451i	$0.290154\pi$
$84$	−3.15987e8	−0.692487
$85$	0	0
$86$	−1.61630e8	−0.318624
$87$	8.24668e8	1.54327
$88$	4.06774e8	0.723071
$89$	−2.99276e8	−0.505611	−0.252806	−	0.967517i	$-0.581353\pi$
$89$	−2.99276e8	−0.505611	−0.252806	+	0.967517i	$0.581353\pi$
$90$	3.03359e8	0.487377
$91$	2.42571e8	0.370811
$92$	−7.39431e8	−1.07610
$93$	−1.81755e8	−0.251949
$94$	−2.30136e8	−0.304026
$95$	−1.20423e9	−1.51689
$96$	−9.87857e8	−1.18706
$97$	−1.53802e9	−1.76396	−0.881978	−	0.471290i	$-0.843788\pi$
$97$	−1.53802e9	−1.76396	−0.881978	+	0.471290i	$0.843788\pi$
$98$	−2.03684e8	−0.223070
$99$	−1.42495e9	−1.49088
$100$	−7.33155e8	−0.733155
$101$	9.90921e8	0.947530	0.473765	−	0.880651i	$-0.342895\pi$
$101$	9.90921e8	0.947530	0.473765	+	0.880651i	$0.342895\pi$
$102$	0	0
$103$	4.45097e8	0.389662	0.194831	−	0.980837i	$-0.437584\pi$
$103$	4.45097e8	0.389662	0.194831	+	0.980837i	$0.437584\pi$
$104$	4.97550e8	0.417048
$105$	1.27732e9	1.02553
$106$	−4.50338e8	−0.346467
$107$	−5.62519e8	−0.414868	−0.207434	−	0.978249i	$-0.566511\pi$
$107$	−5.62519e8	−0.414868	−0.207434	+	0.978249i	$0.566511\pi$
$108$	3.69148e8	0.261092
$109$	−1.64052e8	−0.111317	−0.0556587	−	0.998450i	$-0.517726\pi$
$109$	−1.64052e8	−0.111317	−0.0556587	+	0.998450i	$0.517726\pi$
$110$	−7.82443e8	−0.509549
$111$	1.97994e9	1.23794
$112$	−6.27736e8	−0.376960
$113$	2.18017e9	1.25788	0.628938	−	0.777456i	$-0.283490\pi$
$113$	2.18017e9	1.25788	0.628938	+	0.777456i	$0.283490\pi$
$114$	9.14888e8	0.507336
$115$	2.98902e9	1.59363
$116$	1.84451e9	0.945847
$117$	−1.74295e9	−0.859899
$118$	2.01233e8	0.0955501
$119$	0	0
$120$	2.61997e9	1.15340
$121$	1.31739e9	0.558701
$122$	−7.75379e8	−0.316880
$123$	7.13645e9	2.81131
$124$	−4.06527e8	−0.154416
$125$	−7.06160e8	−0.258707
$126$	−5.28141e8	−0.186673
$127$	4.03084e9	1.37493	0.687463	−	0.726219i	$-0.258724\pi$
$127$	4.03084e9	1.37493	0.687463	+	0.726219i	$0.258724\pi$
$128$	−2.88440e9	−0.949754
$129$	4.89001e9	1.55473
$130$	−9.57054e8	−0.293894
$131$	1.38805e9	0.411798	0.205899	−	0.978573i	$-0.433988\pi$
$131$	1.38805e9	0.411798	0.205899	+	0.978573i	$0.433988\pi$
$132$	−5.85612e9	−1.67891
$133$	2.09655e9	0.580995
$134$	1.76647e9	0.473298
$135$	−1.49222e9	−0.386660
$136$	0	0
$137$	2.01261e8	0.0488108	0.0244054	−	0.999702i	$-0.492231\pi$
$137$	2.01261e8	0.0488108	0.0244054	+	0.999702i	$0.492231\pi$
$138$	−2.27084e9	−0.533004
$139$	1.39628e9	0.317254	0.158627	−	0.987339i	$-0.449293\pi$
$139$	1.39628e9	0.317254	0.158627	+	0.987339i	$0.449293\pi$
$140$	2.85695e9	0.628531
$141$	6.96263e9	1.48350
$142$	−7.81240e8	−0.161245
$143$	4.49552e9	0.899018
$144$	4.51047e9	0.874159
$145$	−7.45612e9	−1.40074
$146$	−5.92804e8	−0.107975
$147$	6.16234e9	1.08847
$148$	4.42848e9	0.758712
$149$	7.16177e9	1.19037	0.595185	−	0.803589i	$-0.297079\pi$
$149$	7.16177e9	1.19037	0.595185	+	0.803589i	$0.297079\pi$
$150$	−2.25156e9	−0.363139
$151$	6.94349e8	0.108688	0.0543440	−	0.998522i	$-0.482693\pi$
$151$	6.94349e8	0.108688	0.0543440	+	0.998522i	$0.482693\pi$
$152$	4.30033e9	0.653440
$153$	0	0
$154$	1.36222e9	0.195166
$155$	1.64331e9	0.228680
$156$	−7.16298e9	−0.968351
$157$	8.01340e9	1.05261	0.526306	−	0.850295i	$-0.323577\pi$
$157$	8.01340e9	1.05261	0.526306	+	0.850295i	$0.323577\pi$
$158$	−4.22783e9	−0.539710
$159$	1.36247e10	1.69060
$160$	8.93158e9	1.07743
$161$	−5.20382e9	−0.610388
$162$	−2.04418e9	−0.233186
$163$	−8.61824e9	−0.956256	−0.478128	−	0.878290i	$-0.658685\pi$
$163$	−8.61824e9	−0.956256	−0.478128	+	0.878290i	$0.658685\pi$
$164$	1.59619e10	1.72301
$165$	2.36723e10	2.48636
$166$	3.63828e9	0.371886
$167$	−2.50384e9	−0.249105	−0.124553	−	0.992213i	$-0.539750\pi$
$167$	−2.50384e9	−0.249105	−0.124553	+	0.992213i	$0.539750\pi$
$168$	−4.56132e9	−0.441773
$169$	−5.10575e9	−0.481470
$170$	0	0
$171$	−1.50643e10	−1.34731
$172$	1.09374e10	0.952872
$173$	6.79245e9	0.576526	0.288263	−	0.957551i	$-0.406922\pi$
$173$	6.79245e9	0.576526	0.288263	+	0.957551i	$0.406922\pi$
$174$	5.66461e9	0.468488
$175$	−5.15965e9	−0.415862
$176$	−1.16337e10	−0.913926
$177$	−6.08819e9	−0.466239
$178$	−2.05572e9	−0.153487
$179$	−1.38497e10	−1.00833	−0.504163	−	0.863609i	$-0.668199\pi$
$179$	−1.38497e10	−1.00833	−0.504163	+	0.863609i	$0.668199\pi$
$180$	−2.05280e10	−1.45754
$181$	−2.49946e10	−1.73098	−0.865492	−	0.500922i	$-0.832994\pi$
$181$	−2.49946e10	−1.73098	−0.865492	+	0.500922i	$0.832994\pi$
$182$	1.66621e9	0.112566
$183$	2.34586e10	1.54622
$184$	−1.06738e10	−0.686499
$185$	−1.79013e10	−1.12360
$186$	−1.24847e9	−0.0764838
$187$	0	0
$188$	1.55732e10	0.909214
$189$	2.59792e9	0.148097
$190$	−8.27183e9	−0.460480
$191$	1.03913e10	0.564961	0.282481	−	0.959273i	$-0.408843\pi$
$191$	1.03913e10	0.564961	0.282481	+	0.959273i	$0.408843\pi$
$192$	1.36327e10	0.723980
$193$	−2.31468e10	−1.20084	−0.600418	−	0.799686i	$-0.704999\pi$
$193$	−2.31468e10	−1.20084	−0.600418	+	0.799686i	$0.704999\pi$
$194$	−1.05646e10	−0.535481
$195$	2.89551e10	1.43406
$196$	1.37832e10	0.667109
$197$	−1.95085e10	−0.922839	−0.461420	−	0.887182i	$-0.652660\pi$
$197$	−1.95085e10	−0.922839	−0.461420	+	0.887182i	$0.652660\pi$
$198$	−9.78794e9	−0.452583
$199$	6.81429e9	0.308022	0.154011	−	0.988069i	$-0.450781\pi$
$199$	6.81429e9	0.308022	0.154011	+	0.988069i	$0.450781\pi$
$200$	−1.05832e10	−0.467717
$201$	−5.34434e10	−2.30947
$202$	6.80660e9	0.287640
$203$	1.29810e10	0.536506
$204$	0	0
$205$	−6.45232e10	−2.55166
$206$	3.05736e9	0.118289
$207$	3.73910e10	1.41547
$208$	−1.42299e10	−0.527129
$209$	3.88549e10	1.40860
$210$	8.77386e9	0.311318
$211$	1.51166e10	0.525029	0.262515	−	0.964928i	$-0.415448\pi$
$211$	1.51166e10	0.525029	0.262515	+	0.964928i	$0.415448\pi$
$212$	3.04740e10	1.03614
$213$	2.36359e10	0.786800
$214$	−3.86392e9	−0.125941
$215$	−4.42124e10	−1.41114
$216$	5.32872e9	0.166564
$217$	−2.86098e9	−0.0875882
$218$	−1.12687e9	−0.0337924
$219$	1.79349e10	0.526866
$220$	5.29473e10	1.52385
$221$	0	0
$222$	1.36001e10	0.375798
$223$	5.78898e10	1.56758	0.783791	−	0.621024i	$-0.213283\pi$
$223$	5.78898e10	1.56758	0.783791	+	0.621024i	$0.213283\pi$
$224$	−1.55497e10	−0.412673
$225$	3.70736e10	0.964370
$226$	1.49755e10	0.381851
$227$	3.02288e10	0.755622	0.377811	−	0.925883i	$-0.376677\pi$
$227$	3.02288e10	0.755622	0.377811	+	0.925883i	$0.376677\pi$
$228$	−6.19097e10	−1.51723
$229$	−5.64089e9	−0.135546	−0.0677732	−	0.997701i	$-0.521589\pi$
$229$	−5.64089e9	−0.135546	−0.0677732	+	0.997701i	$0.521589\pi$
$230$	2.05315e10	0.483776
$231$	−4.12131e10	−0.952316
$232$	2.66259e10	0.603404
$233$	2.68133e10	0.596004	0.298002	−	0.954565i	$-0.403680\pi$
$233$	2.68133e10	0.596004	0.298002	+	0.954565i	$0.403680\pi$
$234$	−1.19722e10	−0.261038
$235$	−6.29517e10	−1.34649
$236$	−1.36173e10	−0.285751
$237$	1.27910e11	2.63353
$238$	0	0
$239$	5.97087e10	1.18371	0.591857	−	0.806043i	$-0.298395\pi$
$239$	5.97087e10	1.18371	0.591857	+	0.806043i	$0.298395\pi$
$240$	−7.49311e10	−1.45785
$241$	7.39643e10	1.41236	0.706180	−	0.708032i	$-0.250417\pi$
$241$	7.39643e10	1.41236	0.706180	+	0.708032i	$0.250417\pi$
$242$	9.04909e9	0.169604
$243$	7.74772e10	1.42543
$244$	5.24693e10	0.947657
$245$	−5.57160e10	−0.987944
$246$	4.90200e10	0.853425
$247$	4.75258e10	0.812443
$248$	−5.86829e9	−0.0985098
$249$	−1.10074e11	−1.81463
$250$	−4.85059e9	−0.0785352
$251$	−2.78124e10	−0.442289	−0.221145	−	0.975241i	$-0.570979\pi$
$251$	−2.78124e10	−0.442289	−0.221145	+	0.975241i	$0.570979\pi$
$252$	3.57389e10	0.558263
$253$	−9.64415e10	−1.47986
$254$	2.76877e10	0.417384
$255$	0	0
$256$	1.37743e10	0.200442
$257$	−3.09457e8	−0.00442487	−0.00221244	−	0.999998i	$-0.500704\pi$
$257$	−3.09457e8	−0.00442487	−0.00221244	+	0.999998i	$0.500704\pi$
$258$	3.35893e10	0.471968
$259$	3.11659e10	0.430359
$260$	6.47631e10	0.878916
$261$	−9.32721e10	−1.24414
$262$	9.53446e9	0.125009
$263$	−4.46182e10	−0.575057	−0.287529	−	0.957772i	$-0.592834\pi$
$263$	−4.46182e10	−0.575057	−0.287529	+	0.957772i	$0.592834\pi$
$264$	−8.45342e10	−1.07106
$265$	−1.23186e11	−1.53446
$266$	1.44011e10	0.176371
$267$	6.21944e10	0.748946
$268$	−1.19536e11	−1.41544
$269$	−1.96820e10	−0.229184	−0.114592	−	0.993413i	$-0.536556\pi$
$269$	−1.96820e10	−0.229184	−0.114592	+	0.993413i	$0.536556\pi$
$270$	−1.02500e10	−0.117378
$271$	−5.91781e10	−0.666499	−0.333249	−	0.942839i	$-0.608145\pi$
$271$	−5.91781e10	−0.666499	−0.333249	+	0.942839i	$0.608145\pi$
$272$	0	0
$273$	−5.04102e10	−0.549271
$274$	1.38245e9	0.0148174
$275$	−9.56229e10	−1.00824
$276$	1.53666e11	1.59399
$277$	6.63639e9	0.0677287	0.0338644	−	0.999426i	$-0.489219\pi$
$277$	6.63639e9	0.0677287	0.0338644	+	0.999426i	$0.489219\pi$
$278$	9.59103e9	0.0963083
$279$	2.05570e10	0.203114
$280$	4.12406e10	0.400972
$281$	−6.25062e10	−0.598059	−0.299030	−	0.954244i	$-0.596663\pi$
$281$	−6.25062e10	−0.598059	−0.299030	+	0.954244i	$0.596663\pi$
$282$	4.78261e10	0.450343
$283$	1.43151e11	1.32665	0.663326	−	0.748331i	$-0.269144\pi$
$283$	1.43151e11	1.32665	0.663326	+	0.748331i	$0.269144\pi$
$284$	5.28659e10	0.482218
$285$	2.50259e11	2.24692
$286$	3.08796e10	0.272913
$287$	1.12334e11	0.977330
$288$	1.11729e11	0.956975
$289$	0	0
$290$	−5.12158e10	−0.425219
$291$	3.19624e11	2.61289
$292$	4.01146e10	0.322908
$293$	2.25368e10	0.178643	0.0893217	−	0.996003i	$-0.471530\pi$
$293$	2.25368e10	0.178643	0.0893217	+	0.996003i	$0.471530\pi$
$294$	4.23289e10	0.330426
$295$	5.50456e10	0.423178
$296$	6.39259e10	0.484021
$297$	4.81467e10	0.359057
$298$	4.91939e10	0.361358
$299$	−1.17963e11	−0.853546
$300$	1.52361e11	1.08600
$301$	7.69728e10	0.540491
$302$	4.76946e9	0.0329942
$303$	−2.05929e11	−1.40355
$304$	−1.22989e11	−0.825916
$305$	−2.12098e11	−1.40342
$306$	0	0
$307$	−9.48694e10	−0.609542	−0.304771	−	0.952426i	$-0.598580\pi$
$307$	−9.48694e10	−0.609542	−0.304771	+	0.952426i	$0.598580\pi$
$308$	−9.21803e10	−0.583660
$309$	−9.24984e10	−0.577193
$310$	1.12879e10	0.0694199
$311$	−2.84094e11	−1.72203	−0.861015	−	0.508580i	$-0.830171\pi$
$311$	−2.84094e11	−1.72203	−0.861015	+	0.508580i	$0.830171\pi$
$312$	−1.03399e11	−0.617760
$313$	1.96386e11	1.15654	0.578271	−	0.815845i	$-0.303728\pi$
$313$	1.96386e11	1.15654	0.578271	+	0.815845i	$0.303728\pi$
$314$	5.50437e10	0.319539
$315$	−1.44468e11	−0.826751
$316$	2.86094e11	1.61405
$317$	−1.78281e11	−0.991602	−0.495801	−	0.868436i	$-0.665125\pi$
$317$	−1.78281e11	−0.991602	−0.495801	+	0.868436i	$0.665125\pi$
$318$	9.35876e10	0.513211
$319$	2.40574e11	1.30074
$320$	−1.23258e11	−0.657115
$321$	1.16901e11	0.614531
$322$	−3.57449e10	−0.185294
$323$	0	0
$324$	1.38328e11	0.697362
$325$	−1.16962e11	−0.581527
$326$	−5.91984e10	−0.290289
$327$	3.40927e10	0.164891
$328$	2.30413e11	1.09920
$329$	1.09598e11	0.515727
$330$	1.62604e11	0.754778
$331$	3.12117e11	1.42919	0.714596	−	0.699537i	$-0.246610\pi$
$331$	3.12117e11	1.42919	0.714596	+	0.699537i	$0.246610\pi$
$332$	−2.46200e11	−1.11216
$333$	−2.23936e11	−0.997988
$334$	−1.71988e10	−0.0756204
$335$	4.83202e11	2.09617
$336$	1.30454e11	0.558379
$337$	3.28991e11	1.38947	0.694736	−	0.719265i	$-0.255521\pi$
$337$	3.28991e11	1.38947	0.694736	+	0.719265i	$0.255521\pi$
$338$	−3.50712e10	−0.146159
$339$	−4.53075e11	−1.86325
$340$	0	0
$341$	−5.30220e10	−0.212354
$342$	−1.03476e11	−0.409000
$343$	2.29005e11	0.893350
$344$	1.57883e11	0.607886
$345$	−6.21167e11	−2.36060
$346$	4.66571e10	0.175015
$347$	−6.75169e10	−0.249994	−0.124997	−	0.992157i	$-0.539892\pi$
$347$	−6.75169e10	−0.249994	−0.124997	+	0.992157i	$0.539892\pi$
$348$	−3.83320e11	−1.40105
$349$	−6.43149e10	−0.232058	−0.116029	−	0.993246i	$-0.537017\pi$
$349$	−6.43149e10	−0.232058	−0.116029	+	0.993246i	$0.537017\pi$
$350$	−3.54415e10	−0.126242
$351$	5.88912e10	0.207094
$352$	−2.88180e11	−1.00051
$353$	−9.34564e10	−0.320349	−0.160174	−	0.987089i	$-0.551206\pi$
$353$	−9.34564e10	−0.320349	−0.160174	+	0.987089i	$0.551206\pi$
$354$	−4.18196e10	−0.141535
$355$	−2.13701e11	−0.714133
$356$	1.39109e11	0.459017
$357$	0	0
$358$	−9.51328e10	−0.306095
$359$	1.09486e11	0.347884	0.173942	−	0.984756i	$-0.444349\pi$
$359$	1.09486e11	0.347884	0.173942	+	0.984756i	$0.444349\pi$
$360$	−2.96326e11	−0.929840
$361$	8.80786e10	0.272953
$362$	−1.71687e11	−0.525472
$363$	−2.73774e11	−0.827586
$364$	−1.12751e11	−0.336639
$365$	−1.62156e11	−0.478206
$366$	1.61136e11	0.469384
$367$	4.01152e10	0.115428	0.0577141	−	0.998333i	$-0.481619\pi$
$367$	4.01152e10	0.115428	0.0577141	+	0.998333i	$0.481619\pi$
$368$	3.05271e11	0.867701
$369$	−8.07151e11	−2.26640
$370$	−1.22964e11	−0.341090
$371$	2.14464e11	0.587722
$372$	8.44829e10	0.228731
$373$	−2.96081e10	−0.0791993	−0.0395997	−	0.999216i	$-0.512608\pi$
$373$	−2.96081e10	−0.0791993	−0.0395997	+	0.999216i	$0.512608\pi$
$374$	0	0
$375$	1.46751e11	0.383214
$376$	2.24801e11	0.580034
$377$	2.94260e11	0.750232
$378$	1.78450e10	0.0449576
$379$	4.93211e11	1.22788	0.613941	−	0.789352i	$-0.289583\pi$
$379$	4.93211e11	1.22788	0.613941	+	0.789352i	$0.289583\pi$
$380$	5.59749e11	1.37710
$381$	−8.37675e11	−2.03663
$382$	7.13772e10	0.171504
$383$	5.06575e11	1.20295	0.601477	−	0.798890i	$-0.294579\pi$
$383$	5.06575e11	1.20295	0.601477	+	0.798890i	$0.294579\pi$
$384$	5.99425e11	1.40684
$385$	3.72622e11	0.864362
$386$	−1.58995e11	−0.364535
$387$	−5.53073e11	−1.25338
$388$	7.14896e11	1.60140
$389$	5.74294e11	1.27163	0.635815	−	0.771841i	$-0.280664\pi$
$389$	5.74294e11	1.27163	0.635815	+	0.771841i	$0.280664\pi$
$390$	1.98891e11	0.435336
$391$	0	0
$392$	1.98962e11	0.425583
$393$	−2.88459e11	−0.609983
$394$	−1.34003e11	−0.280145
$395$	−1.15648e12	−2.39030
$396$	6.62343e11	1.35349
$397$	−3.09586e11	−0.625496	−0.312748	−	0.949836i	$-0.601250\pi$
$397$	−3.09586e11	−0.625496	−0.312748	+	0.949836i	$0.601250\pi$
$398$	4.68071e10	0.0935057
$399$	−4.35696e11	−0.860609
$400$	3.02679e11	0.591171
$401$	−1.29844e10	−0.0250769	−0.0125384	−	0.999921i	$-0.503991\pi$
$401$	−1.29844e10	−0.0250769	−0.0125384	+	0.999921i	$0.503991\pi$
$402$	−3.67101e11	−0.701081
$403$	−6.48544e10	−0.122480
$404$	−4.60597e11	−0.860211
$405$	−5.59167e11	−1.03275
$406$	8.91657e10	0.162866
$407$	5.77592e11	1.04339
$408$	0	0
$409$	7.88344e11	1.39303	0.696516	−	0.717542i	$-0.254733\pi$
$409$	7.88344e11	1.39303	0.696516	+	0.717542i	$0.254733\pi$
$410$	−4.43208e11	−0.774604
$411$	−4.18252e10	−0.0723019
$412$	−2.06889e11	−0.353753
$413$	−9.58332e10	−0.162084
$414$	2.56838e11	0.429692
$415$	9.95219e11	1.64703
$416$	−3.52490e11	−0.577068
$417$	−2.90171e11	−0.469939
$418$	2.66893e11	0.427606
$419$	−1.03820e12	−1.64558	−0.822788	−	0.568348i	$-0.807583\pi$
$419$	−1.03820e12	−1.64558	−0.822788	+	0.568348i	$0.807583\pi$
$420$	−5.93720e11	−0.931022
$421$	−7.75804e11	−1.20360	−0.601801	−	0.798646i	$-0.705550\pi$
$421$	−7.75804e11	−1.20360	−0.601801	+	0.798646i	$0.705550\pi$
$422$	1.03835e11	0.159382
$423$	−7.87492e11	−1.19595
$424$	4.39898e11	0.661007
$425$	0	0
$426$	1.62354e11	0.238848
$427$	3.69258e11	0.537532
$428$	2.61469e11	0.376637
$429$	−9.34243e11	−1.33169
$430$	−3.03693e11	−0.428378
$431$	−4.92789e11	−0.687881	−0.343941	−	0.938991i	$-0.611762\pi$
$431$	−4.92789e11	−0.687881	−0.343941	+	0.938991i	$0.611762\pi$
$432$	−1.52401e11	−0.210529
$433$	4.00328e11	0.547294	0.273647	−	0.961830i	$-0.411770\pi$
$433$	4.00328e11	0.547294	0.273647	+	0.961830i	$0.411770\pi$
$434$	−1.96519e10	−0.0265890
$435$	1.54950e12	2.07487
$436$	7.62544e10	0.101059
$437$	−1.01956e12	−1.33735
$438$	1.23194e11	0.159940
$439$	6.76446e11	0.869247	0.434623	−	0.900612i	$-0.356882\pi$
$439$	6.76446e11	0.869247	0.434623	+	0.900612i	$0.356882\pi$
$440$	7.64304e11	0.972141
$441$	−6.96977e11	−0.877495
$442$	0	0
$443$	−1.98225e10	−0.0244536	−0.0122268	−	0.999925i	$-0.503892\pi$
$443$	−1.98225e10	−0.0244536	−0.0122268	+	0.999925i	$0.503892\pi$
$444$	−9.20310e11	−1.12386
$445$	−5.62322e11	−0.679775
$446$	3.97643e11	0.475868
$447$	−1.48833e12	−1.76326
$448$	2.14590e11	0.251686
$449$	−1.56672e12	−1.81921	−0.909607	−	0.415471i	$-0.863617\pi$
$449$	−1.56672e12	−1.81921	−0.909607	+	0.415471i	$0.863617\pi$
$450$	2.54657e11	0.292752
$451$	2.08186e12	2.36950
$452$	−1.01338e12	−1.14196
$453$	−1.44297e11	−0.160996
$454$	2.07641e11	0.229383
$455$	4.55777e11	0.498541
$456$	−8.93678e11	−0.967920
$457$	4.08250e11	0.437827	0.218914	−	0.975744i	$-0.429749\pi$
$457$	4.08250e11	0.437827	0.218914	+	0.975744i	$0.429749\pi$
$458$	−3.87470e10	−0.0411475
$459$	0	0
$460$	−1.38935e12	−1.44677
$461$	−3.80945e11	−0.392834	−0.196417	−	0.980521i	$-0.562931\pi$
$461$	−3.80945e11	−0.392834	−0.196417	+	0.980521i	$0.562931\pi$
$462$	−2.83091e11	−0.289093
$463$	−1.30769e12	−1.32248	−0.661241	−	0.750174i	$-0.729970\pi$
$463$	−1.30769e12	−1.32248	−0.661241	+	0.750174i	$0.729970\pi$
$464$	−7.61499e11	−0.762673
$465$	−3.41507e11	−0.338736
$466$	1.84180e11	0.180928
$467$	−1.95728e12	−1.90426	−0.952131	−	0.305692i	$-0.901112\pi$
$467$	−1.95728e12	−1.90426	−0.952131	+	0.305692i	$0.901112\pi$
$468$	8.10151e11	0.780656
$469$	−8.41244e11	−0.802868
$470$	−4.32413e11	−0.408751
$471$	−1.66531e12	−1.55920
$472$	−1.96568e11	−0.182295
$473$	1.42652e12	1.31040
$474$	8.78611e11	0.799455
$475$	−1.01091e12	−0.911149
$476$	0	0
$477$	−1.54099e12	−1.36291
$478$	4.10137e11	0.359338
$479$	−3.11631e11	−0.270477	−0.135239	−	0.990813i	$-0.543180\pi$
$479$	−3.11631e11	−0.270477	−0.135239	+	0.990813i	$0.543180\pi$
$480$	−1.85613e12	−1.59596
$481$	7.06487e11	0.601799
$482$	5.08058e11	0.428748
$483$	1.08144e12	0.904149
$484$	−6.12345e11	−0.507215
$485$	−2.88984e12	−2.37157
$486$	5.32188e11	0.432715
$487$	1.12370e12	0.905257	0.452628	−	0.891699i	$-0.350486\pi$
$487$	1.12370e12	0.905257	0.452628	+	0.891699i	$0.350486\pi$
$488$	7.57404e11	0.604558
$489$	1.79101e12	1.41647
$490$	−3.82711e11	−0.299908
$491$	−3.77974e11	−0.293492	−0.146746	−	0.989174i	$-0.546880\pi$
$491$	−3.77974e11	−0.293492	−0.146746	+	0.989174i	$0.546880\pi$
$492$	−3.31714e12	−2.55224
$493$	0	0
$494$	3.26453e11	0.246632
$495$	−2.67740e12	−2.00443
$496$	1.67833e11	0.124512
$497$	3.72049e11	0.273525
$498$	−7.56094e11	−0.550863
$499$	−9.28936e11	−0.670708	−0.335354	−	0.942092i	$-0.608856\pi$
$499$	−9.28936e11	−0.670708	−0.335354	+	0.942092i	$0.608856\pi$
$500$	3.28235e11	0.234866
$501$	5.20339e11	0.368992
$502$	−1.91042e11	−0.134265
$503$	2.40133e11	0.167261	0.0836306	−	0.996497i	$-0.473348\pi$
$503$	2.40133e11	0.167261	0.0836306	+	0.996497i	$0.473348\pi$
$504$	5.15898e11	0.356144
$505$	1.86188e12	1.27392
$506$	−6.62453e11	−0.449239
$507$	1.06106e12	0.713187
$508$	−1.87361e12	−1.24822
$509$	−1.09832e12	−0.725270	−0.362635	−	0.931931i	$-0.618123\pi$
$509$	−1.09832e12	−0.725270	−0.362635	+	0.931931i	$0.618123\pi$
$510$	0	0
$511$	2.82310e11	0.183161
$512$	1.57143e12	1.01060
$513$	5.08998e11	0.324480
$514$	−2.12565e9	−0.00134325
$515$	8.36312e11	0.523885
$516$	−2.27296e12	−1.41146
$517$	2.03115e12	1.25036
$518$	2.14077e11	0.130643
$519$	−1.41158e12	−0.853990
$520$	9.34867e11	0.560705
$521$	9.99480e11	0.594298	0.297149	−	0.954831i	$-0.403964\pi$
$521$	9.99480e11	0.594298	0.297149	+	0.954831i	$0.403964\pi$
$522$	−6.40682e11	−0.377681
$523$	1.15126e12	0.672845	0.336423	−	0.941711i	$-0.390783\pi$
$523$	1.15126e12	0.672845	0.336423	+	0.941711i	$0.390783\pi$
$524$	−6.45190e11	−0.373849
$525$	1.07226e12	0.616003
$526$	−3.06481e11	−0.174569
$527$	0	0
$528$	2.41767e12	1.35377
$529$	7.29492e11	0.405014
$530$	−8.46159e11	−0.465812
$531$	6.88590e11	0.375868
$532$	−9.74511e11	−0.527454
$533$	2.54645e12	1.36667
$534$	4.27211e11	0.227356
$535$	−1.05694e12	−0.557774
$536$	−1.72552e12	−0.902980
$537$	2.87818e12	1.49360
$538$	−1.35195e11	−0.0695728
$539$	1.79769e12	0.917415
$540$	6.93608e11	0.351028
$541$	2.50769e12	1.25860	0.629299	−	0.777163i	$-0.283342\pi$
$541$	2.50769e12	1.25860	0.629299	+	0.777163i	$0.283342\pi$
$542$	−4.06492e11	−0.202328
$543$	5.19429e12	2.56405
$544$	0	0
$545$	−3.08245e11	−0.149662
$546$	−3.46266e11	−0.166741
$547$	−3.84252e9	−0.00183516	−0.000917578	−	1.00000i	$-0.500292\pi$
$547$	−3.84252e9	−0.00183516	−0.000917578		1.00000i	$0.500292\pi$
$548$	−9.35494e10	−0.0443127
$549$	−2.65323e12	−1.24652
$550$	−6.56830e11	−0.306070
$551$	2.54330e12	1.17548
$552$	2.21819e12	1.01689
$553$	2.01342e12	0.915525
$554$	4.55851e10	0.0205603
$555$	3.72019e12	1.66436
$556$	−6.49017e11	−0.288018
$557$	−3.92869e12	−1.72942	−0.864708	−	0.502275i	$-0.832496\pi$
$557$	−3.92869e12	−1.72942	−0.864708	+	0.502275i	$0.832496\pi$
$558$	1.41205e11	0.0616590
$559$	1.74487e12	0.755804
$560$	−1.17948e12	−0.506809
$561$	0	0
$562$	−4.29352e11	−0.181552
$563$	−1.95933e12	−0.821903	−0.410952	−	0.911657i	$-0.634803\pi$
$563$	−1.95933e12	−0.821903	−0.410952	+	0.911657i	$0.634803\pi$
$564$	−3.23635e12	−1.34679
$565$	4.09642e12	1.69117
$566$	9.83302e11	0.402729
$567$	9.73498e11	0.395559
$568$	7.63129e11	0.307631
$569$	−4.17441e12	−1.66951	−0.834756	−	0.550620i	$-0.814391\pi$
$569$	−4.17441e12	−1.66951	−0.834756	+	0.550620i	$0.814391\pi$
$570$	1.71902e12	0.682094
$571$	−7.88354e11	−0.310355	−0.155178	−	0.987887i	$-0.549595\pi$
$571$	−7.88354e11	−0.310355	−0.155178	+	0.987887i	$0.549595\pi$
$572$	−2.08960e12	−0.816170
$573$	−2.15947e12	−0.836859
$574$	7.71615e11	0.296686
$575$	2.50916e12	0.957246
$576$	−1.54190e12	−0.583652
$577$	−8.76975e11	−0.329379	−0.164689	−	0.986345i	$-0.552662\pi$
$577$	−8.76975e11	−0.329379	−0.164689	+	0.986345i	$0.552662\pi$
$578$	0	0
$579$	4.81028e12	1.77876
$580$	3.46573e12	1.27165
$581$	−1.73266e12	−0.630841
$582$	2.19549e12	0.793191
$583$	3.97463e12	1.42491
$584$	5.79061e11	0.206000
$585$	−3.27489e12	−1.15610
$586$	1.54804e11	0.0542305
$587$	−1.42678e12	−0.496004	−0.248002	−	0.968759i	$-0.579774\pi$
$587$	−1.42678e12	−0.496004	−0.248002	+	0.968759i	$0.579774\pi$
$588$	−2.86436e12	−0.988167
$589$	−5.60538e11	−0.191905
$590$	3.78106e11	0.128463
$591$	4.05418e12	1.36697
$592$	−1.82828e12	−0.611779
$593$	1.98075e12	0.657785	0.328892	−	0.944367i	$-0.393325\pi$
$593$	1.98075e12	0.657785	0.328892	+	0.944367i	$0.393325\pi$
$594$	3.30718e11	0.108998
$595$	0	0
$596$	−3.32891e12	−1.08067
$597$	−1.41612e12	−0.456263
$598$	−8.10287e11	−0.259109
$599$	3.54488e12	1.12507	0.562536	−	0.826772i	$-0.309826\pi$
$599$	3.54488e12	1.12507	0.562536	+	0.826772i	$0.309826\pi$
$600$	2.19936e12	0.692814
$601$	−2.37834e12	−0.743600	−0.371800	−	0.928313i	$-0.621259\pi$
$601$	−2.37834e12	−0.743600	−0.371800	+	0.928313i	$0.621259\pi$
$602$	5.28724e11	0.164076
$603$	6.04459e12	1.86183
$604$	−3.22746e11	−0.0986720
$605$	2.47529e12	0.751152
$606$	−1.41452e12	−0.426072
$607$	−2.07961e12	−0.621774	−0.310887	−	0.950447i	$-0.600626\pi$
$607$	−2.07961e12	−0.621774	−0.310887	+	0.950447i	$0.600626\pi$
$608$	−3.04658e12	−0.904162
$609$	−2.69765e12	−0.794709
$610$	−1.45689e12	−0.426033
$611$	2.48443e12	0.721175
$612$	0	0
$613$	3.16507e12	0.905339	0.452670	−	0.891678i	$-0.350472\pi$
$613$	3.16507e12	0.905339	0.452670	+	0.891678i	$0.350472\pi$
$614$	−6.51655e11	−0.185038
$615$	1.34090e13	3.77970
$616$	−1.33064e12	−0.372346
$617$	3.19324e11	0.0887050	0.0443525	−	0.999016i	$-0.485878\pi$
$617$	3.19324e11	0.0887050	0.0443525	+	0.999016i	$0.485878\pi$
$618$	−6.35368e11	−0.175217
$619$	−4.83652e12	−1.32411	−0.662056	−	0.749454i	$-0.730316\pi$
$619$	−4.83652e12	−1.32411	−0.662056	+	0.749454i	$0.730316\pi$
$620$	−7.63841e11	−0.207606
$621$	−1.26338e12	−0.340896
$622$	−1.95143e12	−0.522753
$623$	9.78992e11	0.260365
$624$	2.95720e12	0.780819
$625$	−4.40749e12	−1.15540
$626$	1.34897e12	0.351089
$627$	−8.07468e12	−2.08651
$628$	−3.72477e12	−0.955610
$629$	0	0
$630$	−9.92347e11	−0.250975
$631$	5.79834e12	1.45603	0.728017	−	0.685559i	$-0.240442\pi$
$631$	5.79834e12	1.45603	0.728017	+	0.685559i	$0.240442\pi$
$632$	4.12982e12	1.02968
$633$	−3.14148e12	−0.777709
$634$	−1.22460e12	−0.301019
$635$	7.57372e12	1.84853
$636$	−6.33300e12	−1.53480
$637$	2.19886e12	0.529141
$638$	1.65249e12	0.394863
$639$	−2.67329e12	−0.634295
$640$	−5.41962e12	−1.27691
$641$	5.60801e12	1.31204	0.656021	−	0.754743i	$-0.272238\pi$
$641$	5.60801e12	1.31204	0.656021	+	0.754743i	$0.272238\pi$
$642$	8.02986e11	0.186552
$643$	−4.75759e12	−1.09758	−0.548792	−	0.835959i	$-0.684912\pi$
$643$	−4.75759e12	−1.09758	−0.548792	+	0.835959i	$0.684912\pi$
$644$	2.41883e12	0.554139
$645$	9.18804e12	2.09028
$646$	0	0
$647$	−4.09116e12	−0.917863	−0.458931	−	0.888472i	$-0.651768\pi$
$647$	−4.09116e12	−0.917863	−0.458931	+	0.888472i	$0.651768\pi$
$648$	1.99679e12	0.444882
$649$	−1.77606e12	−0.392967
$650$	−8.03408e11	−0.176533
$651$	5.94557e11	0.129742
$652$	4.00591e12	0.868134
$653$	−4.03105e12	−0.867579	−0.433789	−	0.901014i	$-0.642824\pi$
$653$	−4.03105e12	−0.867579	−0.433789	+	0.901014i	$0.642824\pi$
$654$	2.34182e11	0.0500557
$655$	2.60806e12	0.553646
$656$	−6.58980e12	−1.38933
$657$	−2.02848e12	−0.424744
$658$	7.52822e11	0.156558
$659$	5.19090e12	1.07216	0.536078	−	0.844168i	$-0.319905\pi$
$659$	5.19090e12	1.07216	0.536078	+	0.844168i	$0.319905\pi$
$660$	−1.10033e13	−2.25723
$661$	7.52605e12	1.53342	0.766709	−	0.641995i	$-0.221893\pi$
$661$	7.52605e12	1.53342	0.766709	+	0.641995i	$0.221893\pi$
$662$	2.14392e12	0.433857
$663$	0	0
$664$	−3.55394e12	−0.709502
$665$	3.93929e12	0.781125
$666$	−1.53821e12	−0.302957
$667$	−6.31270e12	−1.23495
$668$	1.16383e12	0.226149
$669$	−1.20304e13	−2.32201
$670$	3.31909e12	0.636331
$671$	6.84339e12	1.30323
$672$	3.23148e12	0.611279
$673$	−4.59518e12	−0.863444	−0.431722	−	0.902007i	$-0.642094\pi$
$673$	−4.59518e12	−0.863444	−0.431722	+	0.902007i	$0.642094\pi$
$674$	2.25983e12	0.421800
$675$	−1.25266e12	−0.232255
$676$	2.37324e12	0.437101
$677$	−1.27161e12	−0.232652	−0.116326	−	0.993211i	$-0.537112\pi$
$677$	−1.27161e12	−0.232652	−0.116326	+	0.993211i	$0.537112\pi$
$678$	−3.11215e12	−0.565624
$679$	5.03116e12	0.908351
$680$	0	0
$681$	−6.28203e12	−1.11928
$682$	−3.64206e11	−0.0644640
$683$	−4.60031e12	−0.808899	−0.404449	−	0.914560i	$-0.632537\pi$
$683$	−4.60031e12	−0.808899	−0.404449	+	0.914560i	$0.632537\pi$
$684$	7.00215e12	1.22315
$685$	3.78157e11	0.0656242
$686$	1.57303e12	0.271193
$687$	1.17227e12	0.200780
$688$	−4.51544e12	−0.768338
$689$	4.86160e12	0.821851
$690$	−4.26677e12	−0.716603
$691$	−8.09857e12	−1.35132	−0.675658	−	0.737215i	$-0.736141\pi$
$691$	−8.09857e12	−1.35132	−0.675658	+	0.737215i	$0.736141\pi$
$692$	−3.15725e12	−0.523397
$693$	4.66130e12	0.767729
$694$	−4.63771e11	−0.0758902
$695$	2.62354e12	0.426536
$696$	−5.53329e12	−0.893803
$697$	0	0
$698$	−4.41776e11	−0.0704455
$699$	−5.57224e12	−0.882841
$700$	2.39830e12	0.377539
$701$	6.79917e12	1.06347	0.531734	−	0.846911i	$-0.321541\pi$
$701$	6.79917e12	1.06347	0.531734	+	0.846911i	$0.321541\pi$
$702$	4.04521e11	0.0628673
$703$	6.10618e12	0.942911
$704$	3.97696e12	0.610203
$705$	1.30824e13	1.99451
$706$	−6.41948e11	−0.0972476
$707$	−3.24150e12	−0.487931
$708$	2.82990e12	0.423273
$709$	9.38297e12	1.39454	0.697272	−	0.716806i	$-0.254397\pi$
$709$	9.38297e12	1.39454	0.697272	+	0.716806i	$0.254397\pi$
$710$	−1.46791e12	−0.216788
$711$	−1.44670e13	−2.12307
$712$	2.00806e12	0.292831
$713$	1.39131e12	0.201614
$714$	0	0
$715$	8.44683e12	1.20869
$716$	6.43757e12	0.915404
$717$	−1.24084e13	−1.75340
$718$	7.52058e11	0.105607
$719$	1.04946e12	0.146449	0.0732243	−	0.997315i	$-0.476671\pi$
$719$	1.04946e12	0.146449	0.0732243	+	0.997315i	$0.476671\pi$
$720$	8.47490e12	1.17527
$721$	−1.45600e12	−0.200657
$722$	6.05009e11	0.0828599
$723$	−1.53710e13	−2.09208
$724$	1.16179e13	1.57147
$725$	−6.25912e12	−0.841379
$726$	−1.88055e12	−0.251229
$727$	−1.15803e13	−1.53750	−0.768751	−	0.639548i	$-0.779122\pi$
$727$	−1.15803e13	−1.53750	−0.768751	+	0.639548i	$0.779122\pi$
$728$	−1.62758e12	−0.214759
$729$	−1.02434e13	−1.34329
$730$	−1.11384e12	−0.145168
$731$	0	0
$732$	−1.09040e13	−1.40373
$733$	−2.54040e11	−0.0325038	−0.0162519	−	0.999868i	$-0.505173\pi$
$733$	−2.54040e11	−0.0325038	−0.0162519	+	0.999868i	$0.505173\pi$
$734$	2.75550e11	0.0350403
$735$	1.15787e13	1.46341
$736$	7.56189e12	0.949905
$737$	−1.55906e13	−1.94652
$738$	−5.54429e12	−0.688006
$739$	−6.62768e12	−0.817450	−0.408725	−	0.912658i	$-0.634027\pi$
$739$	−6.62768e12	−0.817450	−0.408725	+	0.912658i	$0.634027\pi$
$740$	8.32085e12	1.02006
$741$	−9.87662e12	−1.20345
$742$	1.47315e12	0.178414
$743$	1.59113e13	1.91539	0.957693	−	0.287791i	$-0.0929207\pi$
$743$	1.59113e13	1.91539	0.957693	+	0.287791i	$0.0929207\pi$
$744$	1.21953e12	0.145919
$745$	1.34565e13	1.60041
$746$	−2.03377e11	−0.0240424
$747$	1.24497e13	1.46290
$748$	0	0
$749$	1.84011e12	0.213637
$750$	1.00803e12	0.116332
$751$	7.98499e12	0.915998	0.457999	−	0.888953i	$-0.348566\pi$
$751$	7.98499e12	0.915998	0.457999	+	0.888953i	$0.348566\pi$
$752$	−6.42930e12	−0.733135
$753$	5.77986e12	0.655149
$754$	2.02126e12	0.227746
$755$	1.30464e12	0.146127
$756$	−1.20756e12	−0.134450
$757$	−1.01537e13	−1.12381	−0.561907	−	0.827201i	$-0.689932\pi$
$757$	−1.01537e13	−1.12381	−0.561907	+	0.827201i	$0.689932\pi$
$758$	3.38785e12	0.372746
$759$	2.00421e13	2.19207
$760$	8.08007e12	0.878525
$761$	−1.44290e12	−0.155957	−0.0779785	−	0.996955i	$-0.524847\pi$
$761$	−1.44290e12	−0.155957	−0.0779785	+	0.996955i	$0.524847\pi$
$762$	−5.75395e12	−0.618257
$763$	5.36648e11	0.0573230
$764$	−4.83004e12	−0.512898
$765$	0	0
$766$	3.47964e12	0.365178
$767$	−2.17241e12	−0.226653
$768$	−2.86252e12	−0.296909
$769$	−9.41854e11	−0.0971214	−0.0485607	−	0.998820i	$-0.515463\pi$
$769$	−9.41854e11	−0.0971214	−0.0485607	+	0.998820i	$0.515463\pi$
$770$	2.55953e12	0.262393
$771$	6.43101e10	0.00655442
$772$	1.07590e13	1.09017
$773$	1.91901e12	0.193317	0.0966584	−	0.995318i	$-0.469185\pi$
$773$	1.91901e12	0.193317	0.0966584	+	0.995318i	$0.469185\pi$
$774$	−3.79904e12	−0.380486
$775$	1.37950e12	0.137361
$776$	1.03197e13	1.02162
$777$	−6.47677e12	−0.637476
$778$	3.94480e12	0.386026
$779$	2.20090e13	2.14132
$780$	−1.34588e13	−1.30191
$781$	6.89512e12	0.663151
$782$	0	0
$783$	3.15151e12	0.299633
$784$	−5.69031e12	−0.537915
$785$	1.50567e13	1.41520
$786$	−1.98142e12	−0.185171
$787$	−1.54674e13	−1.43724	−0.718622	−	0.695401i	$-0.755227\pi$
$787$	−1.54674e13	−1.43724	−0.718622	+	0.695401i	$0.755227\pi$
$788$	9.06789e12	0.837796
$789$	9.27238e12	0.851814
$790$	−7.94384e12	−0.725619
$791$	−7.13178e12	−0.647744
$792$	9.56103e12	0.863459
$793$	8.37057e12	0.751667
$794$	−2.12654e12	−0.189881
$795$	2.56000e13	2.27294
$796$	−3.16740e12	−0.279637
$797$	1.04334e13	0.915932	0.457966	−	0.888970i	$-0.348578\pi$
$797$	1.04334e13	0.915932	0.457966	+	0.888970i	$0.348578\pi$
$798$	−2.99278e12	−0.261253
$799$	0	0
$800$	7.49770e12	0.647177
$801$	−7.03435e12	−0.603778
$802$	−8.91896e10	−0.00761254
$803$	5.23201e12	0.444067
$804$	2.48414e13	2.09664
$805$	−9.77768e12	−0.820643
$806$	−4.45482e11	−0.0371811
$807$	4.09023e12	0.339482
$808$	−6.64880e12	−0.548772
$809$	−1.75963e13	−1.44429	−0.722143	−	0.691744i	$-0.756843\pi$
$809$	−1.75963e13	−1.44429	−0.722143	+	0.691744i	$0.756843\pi$
$810$	−3.84090e12	−0.313509
$811$	8.79860e12	0.714199	0.357100	−	0.934066i	$-0.383766\pi$
$811$	8.79860e12	0.714199	0.357100	+	0.934066i	$0.383766\pi$
$812$	−6.03377e12	−0.487065
$813$	1.22982e13	0.987263
$814$	3.96745e12	0.316739
$815$	−1.61932e13	−1.28565
$816$	0	0
$817$	1.50809e13	1.18421
$818$	5.41511e12	0.422880
$819$	5.70152e12	0.442806
$820$	2.99915e13	2.31652
$821$	−3.84660e12	−0.295483	−0.147742	−	0.989026i	$-0.547200\pi$
$821$	−3.84660e12	−0.295483	−0.147742	+	0.989026i	$0.547200\pi$
$822$	−2.87296e11	−0.0219485
$823$	2.10484e12	0.159926	0.0799632	−	0.996798i	$-0.474520\pi$
$823$	2.10484e12	0.159926	0.0799632	+	0.996798i	$0.474520\pi$
$824$	−2.98648e12	−0.225677
$825$	1.98720e13	1.49348
$826$	−6.58275e11	−0.0492036
$827$	−1.58581e13	−1.17890	−0.589450	−	0.807805i	$-0.700656\pi$
$827$	−1.58581e13	−1.17890	−0.589450	+	0.807805i	$0.700656\pi$
$828$	−1.73800e13	−1.28503
$829$	−2.28549e12	−0.168067	−0.0840337	−	0.996463i	$-0.526780\pi$
$829$	−2.28549e12	−0.168067	−0.0840337	+	0.996463i	$0.526780\pi$
$830$	6.83612e12	0.499986
$831$	−1.37915e12	−0.100324
$832$	4.86446e12	0.351949
$833$	0	0
$834$	−1.99317e12	−0.142658
$835$	−4.70457e12	−0.334912
$836$	−1.80604e13	−1.27879
$837$	−6.94586e11	−0.0489172
$838$	−7.13136e12	−0.499545
$839$	5.32152e11	0.0370772	0.0185386	−	0.999828i	$-0.494099\pi$
$839$	5.32152e11	0.0370772	0.0185386	+	0.999828i	$0.494099\pi$
$840$	−8.57046e12	−0.593946
$841$	1.23991e12	0.0854687
$842$	−5.32897e12	−0.365375
$843$	1.29898e13	0.885886
$844$	−7.02646e12	−0.476646
$845$	−9.59341e12	−0.647318
$846$	−5.40925e12	−0.363054
$847$	−4.30944e12	−0.287704
$848$	−1.25811e13	−0.835480
$849$	−2.97492e13	−1.96513
$850$	0	0
$851$	−1.51561e13	−0.990615
$852$	−1.09864e13	−0.714294
$853$	−8.92259e12	−0.577059	−0.288529	−	0.957471i	$-0.593166\pi$
$853$	−8.92259e12	−0.577059	−0.288529	+	0.957471i	$0.593166\pi$
$854$	2.53642e12	0.163178
$855$	−2.83050e13	−1.81140
$856$	3.77435e12	0.240276
$857$	1.77385e13	1.12332	0.561659	−	0.827369i	$-0.310163\pi$
$857$	1.77385e13	1.12332	0.561659	+	0.827369i	$0.310163\pi$
$858$	−6.41728e12	−0.404257
$859$	6.97971e12	0.437389	0.218695	−	0.975793i	$-0.429820\pi$
$859$	6.97971e12	0.437389	0.218695	+	0.975793i	$0.429820\pi$
$860$	2.05507e13	1.28110
$861$	−2.33447e13	−1.44769
$862$	−3.38495e12	−0.208819
$863$	2.82314e12	0.173255	0.0866273	−	0.996241i	$-0.472391\pi$
$863$	2.82314e12	0.173255	0.0866273	+	0.996241i	$0.472391\pi$
$864$	−3.77514e12	−0.230474
$865$	1.27626e13	0.775117
$866$	2.74984e12	0.166141
$867$	0	0
$868$	1.32983e12	0.0795166
$869$	3.73143e13	2.21966
$870$	1.06435e13	0.629864
$871$	−1.90698e13	−1.12270
$872$	1.10075e12	0.0644708
$873$	−3.61504e13	−2.10644
$874$	−7.00332e12	−0.405978
$875$	2.30999e12	0.133221
$876$	−8.33645e12	−0.478314
$877$	9.36689e12	0.534684	0.267342	−	0.963602i	$-0.413855\pi$
$877$	9.36689e12	0.534684	0.267342	+	0.963602i	$0.413855\pi$
$878$	4.64648e12	0.263876
$879$	−4.68350e12	−0.264619
$880$	−2.18591e13	−1.22874
$881$	−1.62199e13	−0.907102	−0.453551	−	0.891230i	$-0.649843\pi$
$881$	−1.62199e13	−0.907102	−0.453551	+	0.891230i	$0.649843\pi$
$882$	−4.78751e12	−0.266380
$883$	2.38287e13	1.31910	0.659549	−	0.751661i	$-0.270747\pi$
$883$	2.38287e13	1.31910	0.659549	+	0.751661i	$0.270747\pi$
$884$	0	0
$885$	−1.14394e13	−0.626840
$886$	−1.36160e11	−0.00742333
$887$	1.37741e12	0.0747148	0.0373574	−	0.999302i	$-0.488106\pi$
$887$	1.37741e12	0.0747148	0.0373574	+	0.999302i	$0.488106\pi$
$888$	−1.32848e13	−0.716965
$889$	−1.31857e13	−0.708019
$890$	−3.86257e12	−0.206358
$891$	1.80417e13	0.959019
$892$	−2.69082e13	−1.42312
$893$	2.14729e13	1.12995
$894$	−1.02233e13	−0.535269
$895$	−2.60227e13	−1.35565
$896$	9.43546e12	0.489077
$897$	2.45147e13	1.26433
$898$	−1.07618e13	−0.552255
$899$	−3.47062e12	−0.177210
$900$	−1.72325e13	−0.875500
$901$	0	0
$902$	1.43002e13	0.719305
$903$	−1.59962e13	−0.800612
$904$	−1.46283e13	−0.728513
$905$	−4.69635e13	−2.32724
$906$	−9.91170e11	−0.0488733
$907$	1.83535e13	0.900507	0.450253	−	0.892901i	$-0.351334\pi$
$907$	1.83535e13	0.900507	0.450253	+	0.892901i	$0.351334\pi$
$908$	−1.40509e13	−0.685989
$909$	2.32911e13	1.13150
$910$	3.13071e12	0.151341
$911$	−4.02725e12	−0.193721	−0.0968604	−	0.995298i	$-0.530880\pi$
$911$	−4.02725e12	−0.193721	−0.0968604	+	0.995298i	$0.530880\pi$
$912$	2.55591e13	1.22340
$913$	−3.21110e13	−1.52945
$914$	2.80425e12	0.132910
$915$	4.40774e13	2.07884
$916$	2.62198e12	0.123055
$917$	−4.54059e12	−0.212056
$918$	0	0
$919$	−1.35185e13	−0.625184	−0.312592	−	0.949887i	$-0.601197\pi$
$919$	−1.35185e13	−0.625184	−0.312592	+	0.949887i	$0.601197\pi$
$920$	−2.00555e13	−0.922971
$921$	1.97154e13	0.902895
$922$	−2.61670e12	−0.119252
$923$	8.43384e12	0.382488
$924$	1.91565e13	0.864556
$925$	−1.50275e13	−0.674913
$926$	−8.98246e12	−0.401463
$927$	1.04618e13	0.465316
$928$	−1.88632e13	−0.834927
$929$	2.79739e13	1.23220	0.616101	−	0.787667i	$-0.288711\pi$
$929$	2.79739e13	1.23220	0.616101	+	0.787667i	$0.288711\pi$
$930$	−2.34580e12	−0.102830
$931$	1.90048e13	0.829069
$932$	−1.24633e13	−0.541080
$933$	5.90394e13	2.55079
$934$	−1.34445e13	−0.578073
$935$	0	0
$936$	1.16947e13	0.498020
$937$	2.31258e13	0.980095	0.490048	−	0.871696i	$-0.336979\pi$
$937$	2.31258e13	0.980095	0.490048	+	0.871696i	$0.336979\pi$
$938$	−5.77847e12	−0.243725
$939$	−4.08122e13	−1.71315
$940$	2.92610e13	1.22240
$941$	7.74466e12	0.321995	0.160997	−	0.986955i	$-0.448529\pi$
$941$	7.74466e12	0.321995	0.160997	+	0.986955i	$0.448529\pi$
$942$	−1.14390e13	−0.473323
$943$	−5.46284e13	−2.24965
$944$	5.62184e12	0.230412
$945$	4.88134e12	0.199111
$946$	9.79874e12	0.397796
$947$	1.53444e12	0.0619976	0.0309988	−	0.999519i	$-0.490131\pi$
$947$	1.53444e12	0.0619976	0.0309988	+	0.999519i	$0.490131\pi$
$948$	−5.94549e13	−2.39084
$949$	6.39958e12	0.256126
$950$	−6.94387e12	−0.276596
$951$	3.70496e13	1.46883
$952$	0	0
$953$	5.11437e12	0.200851	0.100426	−	0.994945i	$-0.467980\pi$
$953$	5.11437e12	0.200851	0.100426	+	0.994945i	$0.467980\pi$
$954$	−1.05850e13	−0.413736
$955$	1.95246e13	0.759568
$956$	−2.77536e13	−1.07463
$957$	−4.99951e13	−1.92674
$958$	−2.14058e12	−0.0821083
$959$	−6.58363e11	−0.0251352
$960$	2.56151e13	0.973364
$961$	−2.56747e13	−0.971069
$962$	4.85283e12	0.182687
$963$	−1.32218e13	−0.495417
$964$	−3.43799e13	−1.28221
$965$	−4.34915e13	−1.61448
$966$	7.42836e12	0.274471
$967$	1.96394e13	0.722286	0.361143	−	0.932510i	$-0.382387\pi$
$967$	1.96394e13	0.722286	0.361143	+	0.932510i	$0.382387\pi$
$968$	−8.83931e12	−0.323578
$969$	0	0
$970$	−1.98502e13	−0.719933
$971$	−1.59651e12	−0.0576349	−0.0288175	−	0.999585i	$-0.509174\pi$
$971$	−1.59651e12	−0.0576349	−0.0288175	+	0.999585i	$0.509174\pi$
$972$	−3.60128e13	−1.29407
$973$	−4.56753e12	−0.163370
$974$	7.71868e12	0.274807
$975$	2.43066e13	0.861398
$976$	−2.16617e13	−0.764132
$977$	3.35443e13	1.17786	0.588929	−	0.808184i	$-0.299550\pi$
$977$	3.35443e13	1.17786	0.588929	+	0.808184i	$0.299550\pi$
$978$	1.23024e13	0.429996
$979$	1.81435e13	0.631245
$980$	2.58978e13	0.896902
$981$	−3.85598e12	−0.132930
$982$	−2.59629e12	−0.0890947
$983$	−3.20061e13	−1.09331	−0.546653	−	0.837360i	$-0.684098\pi$
$983$	−3.20061e13	−1.09331	−0.546653	+	0.837360i	$0.684098\pi$
$984$	−4.78836e13	−1.62820
$985$	−3.66553e13	−1.24072
$986$	0	0
$987$	−2.27762e13	−0.763930
$988$	−2.20908e13	−0.737574
$989$	−3.74323e13	−1.24412
$990$	−1.83910e13	−0.608480
$991$	7.74502e12	0.255089	0.127544	−	0.991833i	$-0.459290\pi$
$991$	7.74502e12	0.255089	0.127544	+	0.991833i	$0.459290\pi$
$992$	4.15740e12	0.136307
$993$	−6.48629e13	−2.11702
$994$	2.55559e12	0.0830334
$995$	1.28037e13	0.414124
$996$	5.11643e13	1.64740
$997$	−3.48551e13	−1.11722	−0.558609	−	0.829431i	$-0.688665\pi$
$997$	−3.48551e13	−1.11722	−0.558609	+	0.829431i	$0.688665\pi$
$998$	−6.38083e12	−0.203606
$999$	7.56643e12	0.240351

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.i.1.29		52
17.10	odd	16		17.10.d.a.15.6	yes	52
17.12	odd	16		17.10.d.a.8.6	✓	52
17.16	even	2	inner	289.10.a.i.1.30		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.d.a.8.6	✓	52	17.12	odd	16
17.10.d.a.15.6	yes	52	17.10	odd	16
289.10.a.i.1.29		52	1.1	even	1	trivial
289.10.a.i.1.30		52	17.16	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q+6.86896 q^{2} -207.816 q^{3} -464.817 q^{4} +1878.94 q^{5} -1427.48 q^{6} -3271.20 q^{7} -6709.72 q^{8} +23504.5 q^{9} +O(q^{10})\)	\(q+6.86896 q^{2} -207.816 q^{3} -464.817 q^{4} +1878.94 q^{5} -1427.48 q^{6} -3271.20 q^{7} -6709.72 q^{8} +23504.5 q^{9} +12906.4 q^{10} -60624.5 q^{11} +96596.5 q^{12} -74153.5 q^{13} -22469.7 q^{14} -390474. q^{15} +191898. q^{16} +161452. q^{18} -640911. q^{19} -873365. q^{20} +679808. q^{21} -416428. q^{22} +1.59080e6 q^{23} +1.39439e6 q^{24} +1.57730e6 q^{25} -509358. q^{26} -794179. q^{27} +1.52051e6 q^{28} -3.96826e6 q^{29} -2.68215e6 q^{30} +874596. q^{31} +4.75352e6 q^{32} +1.25988e7 q^{33} -6.14639e6 q^{35} -1.09253e7 q^{36} -9.52735e6 q^{37} -4.40239e6 q^{38} +1.54103e7 q^{39} -1.26072e7 q^{40} -3.43402e7 q^{41} +4.66958e6 q^{42} -2.35305e7 q^{43} +2.81793e7 q^{44} +4.41637e7 q^{45} +1.09271e7 q^{46} -3.35038e7 q^{47} -3.98794e7 q^{48} -2.96529e7 q^{49} +1.08344e7 q^{50} +3.44679e7 q^{52} -6.55613e7 q^{53} -5.45519e6 q^{54} -1.13910e8 q^{55} +2.19488e7 q^{56} +1.33192e8 q^{57} -2.72578e7 q^{58} +2.92960e7 q^{59} +1.81499e8 q^{60} -1.12882e8 q^{61} +6.00756e6 q^{62} -7.68881e7 q^{63} -6.55999e7 q^{64} -1.39330e8 q^{65} +8.65404e7 q^{66} +2.57167e8 q^{67} -3.30594e8 q^{69} -4.22193e7 q^{70} -1.13735e8 q^{71} -1.57709e8 q^{72} -8.63018e7 q^{73} -6.54430e7 q^{74} -3.27788e8 q^{75} +2.97906e8 q^{76} +1.98315e8 q^{77} +1.05853e8 q^{78} -6.15498e8 q^{79} +3.60564e8 q^{80} -2.97597e8 q^{81} -2.35881e8 q^{82} +5.29670e8 q^{83} -3.15987e8 q^{84} -1.61630e8 q^{86} +8.24668e8 q^{87} +4.06774e8 q^{88} -2.99276e8 q^{89} +3.03359e8 q^{90} +2.42571e8 q^{91} -7.39431e8 q^{92} -1.81755e8 q^{93} -2.30136e8 q^{94} -1.20423e9 q^{95} -9.87857e8 q^{96} -1.53802e9 q^{97} -2.03684e8 q^{98} -1.42495e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 64 q^{2} + 13312 q^{4} + 49152 q^{8} + 341172 q^{9}+O(q^{10}) \) 52 * q + 64 * q^2 + 13312 * q^4 + 49152 * q^8 + 341172 * q^9	\( 52 q + 64 q^{2} + 13312 q^{4} + 49152 q^{8} + 341172 q^{9} + 156200 q^{13} + 1207872 q^{15} + 3407880 q^{16} + 2193336 q^{18} + 1185568 q^{19} + 5198336 q^{21} + 13827692 q^{25} + 3618944 q^{26} - 9167544 q^{30} + 61884888 q^{32} + 1635208 q^{33} + 46992776 q^{35} + 156027320 q^{36} + 84813952 q^{38} - 4635776 q^{42} + 125448912 q^{43} + 164193176 q^{47} + 270850284 q^{49} - 226223888 q^{50} + 103553016 q^{52} + 426167208 q^{53} + 677761520 q^{55} + 375214512 q^{59} + 336918024 q^{60} + 190014416 q^{64} + 1377178928 q^{66} + 311910088 q^{67} + 533688136 q^{69} + 1477690280 q^{70} + 2757942680 q^{72} + 4047975520 q^{76} + 3440336432 q^{77} + 3266558756 q^{81} + 2072890608 q^{83} + 2630025952 q^{84} + 1538547296 q^{86} - 1010436256 q^{87} + 1873849184 q^{89} - 1998451624 q^{93} - 6880776704 q^{94} - 4667454128 q^{98}+O(q^{100}) \) 52 * q + 64 * q^2 + 13312 * q^4 + 49152 * q^8 + 341172 * q^9 + 156200 * q^13 + 1207872 * q^15 + 3407880 * q^16 + 2193336 * q^18 + 1185568 * q^19 + 5198336 * q^21 + 13827692 * q^25 + 3618944 * q^26 - 9167544 * q^30 + 61884888 * q^32 + 1635208 * q^33 + 46992776 * q^35 + 156027320 * q^36 + 84813952 * q^38 - 4635776 * q^42 + 125448912 * q^43 + 164193176 * q^47 + 270850284 * q^49 - 226223888 * q^50 + 103553016 * q^52 + 426167208 * q^53 + 677761520 * q^55 + 375214512 * q^59 + 336918024 * q^60 + 190014416 * q^64 + 1377178928 * q^66 + 311910088 * q^67 + 533688136 * q^69 + 1477690280 * q^70 + 2757942680 * q^72 + 4047975520 * q^76 + 3440336432 * q^77 + 3266558756 * q^81 + 2072890608 * q^83 + 2630025952 * q^84 + 1538547296 * q^86 - 1010436256 * q^87 + 1873849184 * q^89 - 1998451624 * q^93 - 6880776704 * q^94 - 4667454128 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more