LMFDB - Embedded newform 289.10.a.f.1.19

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:	$1$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
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)

$f(q)$	$=$	$q+28.8329 q^{2} -253.694 q^{3} +319.336 q^{4} +1602.54 q^{5} -7314.73 q^{6} -6961.05 q^{7} -5555.06 q^{8} +44677.5 q^{9} +O(q^{10})$	\(q+28.8329 q^{2} -253.694 q^{3} +319.336 q^{4} +1602.54 q^{5} -7314.73 q^{6} -6961.05 q^{7} -5555.06 q^{8} +44677.5 q^{9} +46205.9 q^{10} +63360.1 q^{11} -81013.6 q^{12} -114552. q^{13} -200707. q^{14} -406554. q^{15} -323669. q^{16} +1.28818e6 q^{18} +50488.5 q^{19} +511749. q^{20} +1.76597e6 q^{21} +1.82685e6 q^{22} +1.13882e6 q^{23} +1.40928e6 q^{24} +615007. q^{25} -3.30287e6 q^{26} -6.34095e6 q^{27} -2.22291e6 q^{28} +2.03871e6 q^{29} -1.17221e7 q^{30} +1.03910e6 q^{31} -6.48811e6 q^{32} -1.60741e7 q^{33} -1.11554e7 q^{35} +1.42671e7 q^{36} +1.84413e7 q^{37} +1.45573e6 q^{38} +2.90612e7 q^{39} -8.90220e6 q^{40} -7.96470e6 q^{41} +5.09182e7 q^{42} +2.09816e7 q^{43} +2.02332e7 q^{44} +7.15974e7 q^{45} +3.28355e7 q^{46} -6.43503e6 q^{47} +8.21127e7 q^{48} +8.10258e6 q^{49} +1.77324e7 q^{50} -3.65807e7 q^{52} +1.61556e7 q^{53} -1.82828e8 q^{54} +1.01537e8 q^{55} +3.86690e7 q^{56} -1.28086e7 q^{57} +5.87819e7 q^{58} -1.17489e8 q^{59} -1.29827e8 q^{60} -3.52242e7 q^{61} +2.99602e7 q^{62} -3.11002e8 q^{63} -2.13528e7 q^{64} -1.83574e8 q^{65} -4.63462e8 q^{66} +2.32033e8 q^{67} -2.88912e8 q^{69} -3.21641e8 q^{70} -7.20809e6 q^{71} -2.48186e8 q^{72} +3.16063e8 q^{73} +5.31716e8 q^{74} -1.56023e8 q^{75} +1.61228e7 q^{76} -4.41053e8 q^{77} +8.37918e8 q^{78} -5.83535e8 q^{79} -5.18692e8 q^{80} +7.29271e8 q^{81} -2.29645e8 q^{82} -2.61757e8 q^{83} +5.63939e8 q^{84} +6.04960e8 q^{86} -5.17208e8 q^{87} -3.51969e8 q^{88} -8.28097e7 q^{89} +2.06436e9 q^{90} +7.97403e8 q^{91} +3.63667e8 q^{92} -2.63613e8 q^{93} -1.85541e8 q^{94} +8.09098e7 q^{95} +1.64599e9 q^{96} +1.66783e8 q^{97} +2.33621e8 q^{98} +2.83077e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 5124 q^{4} + 108368 q^{9}+O(q^{10}) $ 24 * q + 5124 * q^4 + 108368 * q^9	$ 24 q + 5124 q^{4} + 108368 q^{9} - 244832 q^{13} - 127332 q^{15} - 279932 q^{16} + 888764 q^{18} - 2280212 q^{19} + 775748 q^{21} - 2762628 q^{25} - 3334452 q^{26} - 39084792 q^{30} + 2010240 q^{32} - 30349992 q^{33} - 25532364 q^{35} + 31177320 q^{36} - 13171392 q^{38} - 86527192 q^{42} + 61046960 q^{43} - 153365328 q^{47} + 169445876 q^{49} - 236105676 q^{50} - 209898380 q^{52} + 85777812 q^{53} - 255767540 q^{55} - 767709024 q^{59} + 429639656 q^{60} - 1006108924 q^{64} + 346830788 q^{66} - 26076868 q^{67} - 751973532 q^{69} - 319504544 q^{70} - 1171736028 q^{72} - 1640047616 q^{76} - 174401076 q^{77} - 347156560 q^{81} - 1649346672 q^{83} - 935672904 q^{84} + 690159588 q^{86} - 257027500 q^{87} + 191594460 q^{89} + 1842509012 q^{93} + 2877218432 q^{94} + 4413444720 q^{98}+O(q^{100}) $ 24 * q + 5124 * q^4 + 108368 * q^9 - 244832 * q^13 - 127332 * q^15 - 279932 * q^16 + 888764 * q^18 - 2280212 * q^19 + 775748 * q^21 - 2762628 * q^25 - 3334452 * q^26 - 39084792 * q^30 + 2010240 * q^32 - 30349992 * q^33 - 25532364 * q^35 + 31177320 * q^36 - 13171392 * q^38 - 86527192 * q^42 + 61046960 * q^43 - 153365328 * q^47 + 169445876 * q^49 - 236105676 * q^50 - 209898380 * q^52 + 85777812 * q^53 - 255767540 * q^55 - 767709024 * q^59 + 429639656 * q^60 - 1006108924 * q^64 + 346830788 * q^66 - 26076868 * q^67 - 751973532 * q^69 - 319504544 * q^70 - 1171736028 * q^72 - 1640047616 * q^76 - 174401076 * q^77 - 347156560 * q^81 - 1649346672 * q^83 - 935672904 * q^84 + 690159588 * q^86 - 257027500 * q^87 + 191594460 * q^89 + 1842509012 * q^93 + 2877218432 * q^94 + 4413444720 * 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 $

$2$	28.8329	1.27425	0.637123	−	0.770762i	$-0.280124\pi$
$2$	28.8329	1.27425	0.637123	+	0.770762i	$0.280124\pi$
$3$	−253.694	−1.80827	−0.904137	−	0.427243i	$-0.859485\pi$
$3$	−253.694	−1.80827	−0.904137	+	0.427243i	$0.859485\pi$
$4$	319.336	0.623703
$5$	1602.54	1.14668	0.573342	−	0.819316i	$-0.305647\pi$
$5$	1602.54	1.14668	0.573342	+	0.819316i	$0.305647\pi$
$6$	−7314.73	−2.30419
$7$	−6961.05	−1.09581	−0.547903	−	0.836542i	$-0.684574\pi$
$7$	−6961.05	−1.09581	−0.547903	+	0.836542i	$0.684574\pi$
$8$	−5555.06	−0.479494
$9$	44677.5	2.26985
$10$	46205.9	1.46116
$11$	63360.1	1.30481	0.652407	−	0.757869i	$-0.273759\pi$
$11$	63360.1	1.30481	0.652407	+	0.757869i	$0.273759\pi$
$12$	−81013.6	−1.12783
$13$	−114552.	−1.11239	−0.556197	−	0.831051i	$-0.687740\pi$
$13$	−114552.	−1.11239	−0.556197	+	0.831051i	$0.687740\pi$
$14$	−200707.	−1.39633
$15$	−406554.	−2.07352
$16$	−323669.	−1.23470
$17$	0	0
$17$	0	0
$18$	1.28818e6	2.89235
$19$	50488.5	0.0888794	0.0444397	−	0.999012i	$-0.485850\pi$
$19$	50488.5	0.0888794	0.0444397	+	0.999012i	$0.485850\pi$
$20$	511749.	0.715191
$21$	1.76597e6	1.98152
$22$	1.82685e6	1.66265
$23$	1.13882e6	0.848555	0.424278	−	0.905532i	$-0.360528\pi$
$23$	1.13882e6	0.848555	0.424278	+	0.905532i	$0.360528\pi$
$24$	1.40928e6	0.867057
$25$	615007.	0.314884
$26$	−3.30287e6	−1.41746
$27$	−6.34095e6	−2.29624
$28$	−2.22291e6	−0.683458
$29$	2.03871e6	0.535259	0.267630	−	0.963522i	$-0.413760\pi$
$29$	2.03871e6	0.535259	0.267630	+	0.963522i	$0.413760\pi$
$30$	−1.17221e7	−2.64217
$31$	1.03910e6	0.202083	0.101041	−	0.994882i	$-0.467783\pi$
$31$	1.03910e6	0.202083	0.101041	+	0.994882i	$0.467783\pi$
$32$	−6.48811e6	−1.09381
$33$	−1.60741e7	−2.35946
$34$	0	0
$35$	−1.11554e7	−1.25654
$36$	1.42671e7	1.41571
$37$	1.84413e7	1.61765	0.808823	−	0.588052i	$-0.200105\pi$
$37$	1.84413e7	1.61765	0.808823	+	0.588052i	$0.200105\pi$
$38$	1.45573e6	0.113254
$39$	2.90612e7	2.01151
$40$	−8.90220e6	−0.549829
$41$	−7.96470e6	−0.440192	−0.220096	−	0.975478i	$-0.570637\pi$
$41$	−7.96470e6	−0.440192	−0.220096	+	0.975478i	$0.570637\pi$
$42$	5.09182e7	2.52494
$43$	2.09816e7	0.935902	0.467951	−	0.883755i	$-0.344992\pi$
$43$	2.09816e7	0.935902	0.467951	+	0.883755i	$0.344992\pi$
$44$	2.02332e7	0.813817
$45$	7.15974e7	2.60280
$46$	3.28355e7	1.08127
$47$	−6.43503e6	−0.192358	−0.0961790	−	0.995364i	$-0.530662\pi$
$47$	−6.43503e6	−0.192358	−0.0961790	+	0.995364i	$0.530662\pi$
$48$	8.21127e7	2.23267
$49$	8.10258e6	0.200789
$50$	1.77324e7	0.401239
$51$	0	0
$52$	−3.65807e7	−0.693803
$53$	1.61556e7	0.281242	0.140621	−	0.990063i	$-0.455090\pi$
$53$	1.61556e7	0.281242	0.140621	+	0.990063i	$0.455090\pi$
$54$	−1.82828e8	−2.92597
$55$	1.01537e8	1.49621
$56$	3.86690e7	0.525433
$57$	−1.28086e7	−0.160718
$58$	5.87819e7	0.682052
$59$	−1.17489e8	−1.26230	−0.631152	−	0.775659i	$-0.717417\pi$
$59$	−1.17489e8	−1.26230	−0.631152	+	0.775659i	$0.717417\pi$
$60$	−1.29827e8	−1.29326
$61$	−3.52242e7	−0.325729	−0.162865	−	0.986648i	$-0.552073\pi$
$61$	−3.52242e7	−0.325729	−0.162865	+	0.986648i	$0.552073\pi$
$62$	2.99602e7	0.257503
$63$	−3.11002e8	−2.48732
$64$	−2.13528e7	−0.159091
$65$	−1.83574e8	−1.27556
$66$	−4.63462e8	−3.00653
$67$	2.32033e8	1.40674	0.703368	−	0.710826i	$-0.251679\pi$
$67$	2.32033e8	1.40674	0.703368	+	0.710826i	$0.251679\pi$
$68$	0	0
$69$	−2.88912e8	−1.53442
$70$	−3.21641e8	−1.60114
$71$	−7.20809e6	−0.0336634	−0.0168317	−	0.999858i	$-0.505358\pi$
$71$	−7.20809e6	−0.0336634	−0.0168317	+	0.999858i	$0.505358\pi$
$72$	−2.48186e8	−1.08838
$73$	3.16063e8	1.30263	0.651314	−	0.758808i	$-0.274218\pi$
$73$	3.16063e8	1.30263	0.651314	+	0.758808i	$0.274218\pi$
$74$	5.31716e8	2.06128
$75$	−1.56023e8	−0.569396
$76$	1.61228e7	0.0554344
$77$	−4.41053e8	−1.42982
$78$	8.37918e8	2.56316
$79$	−5.83535e8	−1.68556	−0.842782	−	0.538255i	$-0.819084\pi$
$79$	−5.83535e8	−1.68556	−0.842782	+	0.538255i	$0.819084\pi$
$80$	−5.18692e8	−1.41581
$81$	7.29271e8	1.88238
$82$	−2.29645e8	−0.560913
$83$	−2.61757e8	−0.605407	−0.302704	−	0.953085i	$-0.597889\pi$
$83$	−2.61757e8	−0.605407	−0.302704	+	0.953085i	$0.597889\pi$
$84$	5.63939e8	1.23588
$85$	0	0
$86$	6.04960e8	1.19257
$87$	−5.17208e8	−0.967895
$88$	−3.51969e8	−0.625651
$89$	−8.28097e7	−0.139903	−0.0699513	−	0.997550i	$-0.522284\pi$
$89$	−8.28097e7	−0.139903	−0.0699513	+	0.997550i	$0.522284\pi$
$90$	2.06436e9	3.31661
$91$	7.97403e8	1.21897
$92$	3.63667e8	0.529247
$93$	−2.63613e8	−0.365421
$94$	−1.85541e8	−0.245111
$95$	8.09098e7	0.101917
$96$	1.64599e9	1.97791
$97$	1.66783e8	0.191284	0.0956422	−	0.995416i	$-0.469510\pi$
$97$	1.66783e8	0.191284	0.0956422	+	0.995416i	$0.469510\pi$
$98$	2.33621e8	0.255855
$99$	2.83077e9	2.96173
$100$	1.96394e8	0.196394
$101$	−1.93499e9	−1.85026	−0.925130	−	0.379651i	$-0.876044\pi$
$101$	−1.93499e9	−1.85026	−0.925130	+	0.379651i	$0.876044\pi$
$102$	0	0
$103$	−1.87339e9	−1.64006	−0.820031	−	0.572319i	$-0.806044\pi$
$103$	−1.87339e9	−1.64006	−0.820031	+	0.572319i	$0.806044\pi$
$104$	6.36344e8	0.533386
$105$	2.83004e9	2.27217
$106$	4.65812e8	0.358372
$107$	−2.10383e9	−1.55161	−0.775805	−	0.630972i	$-0.782656\pi$
$107$	−2.10383e9	−1.55161	−0.775805	+	0.630972i	$0.782656\pi$
$108$	−2.02489e9	−1.43217
$109$	−1.00138e9	−0.679486	−0.339743	−	0.940518i	$-0.610340\pi$
$109$	−1.00138e9	−0.679486	−0.339743	+	0.940518i	$0.610340\pi$
$110$	2.92761e9	1.90654
$111$	−4.67844e9	−2.92515
$112$	2.25307e9	1.35299
$113$	2.22131e9	1.28161	0.640806	−	0.767703i	$-0.278600\pi$
$113$	2.22131e9	1.28161	0.640806	+	0.767703i	$0.278600\pi$
$114$	−3.69310e8	−0.204795
$115$	1.82500e9	0.973024
$116$	6.51034e8	0.333843
$117$	−5.11790e9	−2.52497
$118$	−3.38755e9	−1.60849
$119$	0	0
$120$	2.25843e9	0.994240
$121$	1.65655e9	0.702540
$122$	−1.01562e9	−0.415060
$123$	2.02059e9	0.795987
$124$	3.31822e8	0.126040
$125$	−2.14439e9	−0.785612
$126$	−8.96710e9	−3.16945
$127$	−1.88159e9	−0.641814	−0.320907	−	0.947111i	$-0.603988\pi$
$127$	−1.88159e9	−0.641814	−0.320907	+	0.947111i	$0.603988\pi$
$128$	2.70625e9	0.891093
$129$	−5.32290e9	−1.69237
$130$	−5.29298e9	−1.62538
$131$	−3.11456e9	−0.924009	−0.462005	−	0.886878i	$-0.652870\pi$
$131$	−3.11456e9	−0.924009	−0.462005	+	0.886878i	$0.652870\pi$
$132$	−5.13303e9	−1.47160
$133$	−3.51453e8	−0.0973946
$134$	6.69017e9	1.79253
$135$	−1.01616e10	−2.63306
$136$	0	0
$137$	4.16041e9	1.00901	0.504503	−	0.863410i	$-0.331676\pi$
$137$	4.16041e9	1.00901	0.504503	+	0.863410i	$0.331676\pi$
$138$	−8.33016e9	−1.95523
$139$	−8.10754e8	−0.184214	−0.0921070	−	0.995749i	$-0.529360\pi$
$139$	−8.10754e8	−0.184214	−0.0921070	+	0.995749i	$0.529360\pi$
$140$	−3.56231e9	−0.783710
$141$	1.63253e9	0.347836
$142$	−2.07830e8	−0.0428954
$143$	−7.25803e9	−1.45147
$144$	−1.44607e10	−2.80258
$145$	3.26711e9	0.613773
$146$	9.11301e9	1.65987
$147$	−2.05557e9	−0.363082
$148$	5.88897e9	1.00893
$149$	1.33926e9	0.222601	0.111301	−	0.993787i	$-0.464498\pi$
$149$	1.33926e9	0.222601	0.111301	+	0.993787i	$0.464498\pi$
$150$	−4.49861e9	−0.725550
$151$	−3.62654e9	−0.567671	−0.283835	−	0.958873i	$-0.591607\pi$
$151$	−3.62654e9	−0.567671	−0.283835	+	0.958873i	$0.591607\pi$
$152$	−2.80467e8	−0.0426172
$153$	0	0
$154$	−1.27168e10	−1.82195
$155$	1.66520e9	0.231725
$156$	9.28028e9	1.25459
$157$	−4.56689e9	−0.599891	−0.299945	−	0.953956i	$-0.596968\pi$
$157$	−4.56689e9	−0.599891	−0.299945	+	0.953956i	$0.596968\pi$
$158$	−1.68250e10	−2.14782
$159$	−4.09856e9	−0.508563
$160$	−1.03975e10	−1.25426
$161$	−7.92738e9	−0.929851
$162$	2.10270e10	2.39861
$163$	−1.59091e9	−0.176523	−0.0882616	−	0.996097i	$-0.528131\pi$
$163$	−1.59091e9	−0.176523	−0.0882616	+	0.996097i	$0.528131\pi$
$164$	−2.54342e9	−0.274549
$165$	−2.57593e10	−2.70555
$166$	−7.54723e9	−0.771438
$167$	−4.47570e9	−0.445284	−0.222642	−	0.974900i	$-0.571468\pi$
$167$	−4.47570e9	−0.445284	−0.222642	+	0.974900i	$0.571468\pi$
$168$	−9.81009e9	−0.950126
$169$	2.51770e9	0.237418
$170$	0	0
$171$	2.25570e9	0.201743
$172$	6.70018e9	0.583725
$173$	−4.80503e9	−0.407839	−0.203920	−	0.978988i	$-0.565368\pi$
$173$	−4.80503e9	−0.407839	−0.203920	+	0.978988i	$0.565368\pi$
$174$	−1.49126e10	−1.23334
$175$	−4.28110e9	−0.345051
$176$	−2.05077e10	−1.61105
$177$	2.98063e10	2.28259
$178$	−2.38764e9	−0.178270
$179$	−1.33451e10	−0.971592	−0.485796	−	0.874072i	$-0.661470\pi$
$179$	−1.33451e10	−0.971592	−0.485796	+	0.874072i	$0.661470\pi$
$180$	2.28637e10	1.62338
$181$	7.08745e9	0.490836	0.245418	−	0.969417i	$-0.421075\pi$
$181$	7.08745e9	0.490836	0.245418	+	0.969417i	$0.421075\pi$
$182$	2.29914e10	1.55326
$183$	8.93616e9	0.589008
$184$	−6.32621e9	−0.406877
$185$	2.95529e10	1.85493
$186$	−7.60072e9	−0.465636
$187$	0	0
$188$	−2.05494e9	−0.119974
$189$	4.41396e10	2.51623
$190$	2.33286e9	0.129867
$191$	−3.04732e10	−1.65679	−0.828396	−	0.560143i	$-0.810746\pi$
$191$	−3.04732e10	−1.65679	−0.828396	+	0.560143i	$0.810746\pi$
$192$	5.41708e9	0.287680
$193$	1.05728e10	0.548508	0.274254	−	0.961657i	$-0.411569\pi$
$193$	1.05728e10	0.548508	0.274254	+	0.961657i	$0.411569\pi$
$194$	4.80884e9	0.243743
$195$	4.65717e10	2.30657
$196$	2.58745e9	0.125233
$197$	−1.29392e10	−0.612080	−0.306040	−	0.952019i	$-0.599004\pi$
$197$	−1.29392e10	−0.612080	−0.306040	+	0.952019i	$0.599004\pi$
$198$	8.16193e10	3.77398
$199$	−1.78277e10	−0.805854	−0.402927	−	0.915232i	$-0.632007\pi$
$199$	−1.78277e10	−0.805854	−0.402927	+	0.915232i	$0.632007\pi$
$200$	−3.41640e9	−0.150985
$201$	−5.88652e10	−2.54376
$202$	−5.57914e10	−2.35769
$203$	−1.41916e10	−0.586540
$204$	0	0
$205$	−1.27637e10	−0.504761
$206$	−5.40152e10	−2.08984
$207$	5.08797e10	1.92609
$208$	3.70769e10	1.37347
$209$	3.19896e9	0.115971
$210$	8.15983e10	2.89531
$211$	−1.68952e10	−0.586801	−0.293401	−	0.955990i	$-0.594787\pi$
$211$	−1.68952e10	−0.586801	−0.293401	+	0.955990i	$0.594787\pi$
$212$	5.15905e9	0.175412
$213$	1.82865e9	0.0608725
$214$	−6.06594e10	−1.97713
$215$	3.36238e10	1.07318
$216$	3.52243e10	1.10103
$217$	−7.23322e9	−0.221443
$218$	−2.88728e10	−0.865833
$219$	−8.01831e10	−2.35551
$220$	3.24244e10	0.933191
$221$	0	0
$222$	−1.34893e11	−3.72736
$223$	−1.23092e10	−0.333319	−0.166659	−	0.986015i	$-0.553298\pi$
$223$	−1.23092e10	−0.333319	−0.166659	+	0.986015i	$0.553298\pi$
$224$	4.51641e10	1.19861
$225$	2.74770e10	0.714739
$226$	6.40469e10	1.63309
$227$	1.11999e10	0.279962	0.139981	−	0.990154i	$-0.455296\pi$
$227$	1.11999e10	0.279962	0.139981	+	0.990154i	$0.455296\pi$
$228$	−4.09025e9	−0.100241
$229$	5.37234e10	1.29093	0.645467	−	0.763788i	$-0.276663\pi$
$229$	5.37234e10	1.29093	0.645467	+	0.763788i	$0.276663\pi$
$230$	5.26202e10	1.23987
$231$	1.11892e11	2.58551
$232$	−1.13251e10	−0.256654
$233$	3.19551e10	0.710295	0.355147	−	0.934810i	$-0.384431\pi$
$233$	3.19551e10	0.710295	0.355147	+	0.934810i	$0.384431\pi$
$234$	−1.47564e11	−3.21743
$235$	−1.03124e10	−0.220574
$236$	−3.75185e10	−0.787303
$237$	1.48039e11	3.04796
$238$	0	0
$239$	−2.64220e10	−0.523813	−0.261906	−	0.965093i	$-0.584351\pi$
$239$	−2.64220e10	−0.523813	−0.261906	+	0.965093i	$0.584351\pi$
$240$	1.31589e11	2.56017
$241$	−6.13523e10	−1.17153	−0.585766	−	0.810480i	$-0.699206\pi$
$241$	−6.13523e10	−1.17153	−0.585766	+	0.810480i	$0.699206\pi$
$242$	4.77632e10	0.895209
$243$	−6.02026e10	−1.10761
$244$	−1.12484e10	−0.203159
$245$	1.29847e10	0.230242
$246$	5.82596e10	1.01428
$247$	−5.78357e9	−0.0988689
$248$	−5.77225e9	−0.0968976
$249$	6.64062e10	1.09474
$250$	−6.18289e10	−1.00106
$251$	1.01008e11	1.60629	0.803145	−	0.595783i	$-0.203158\pi$
$251$	1.01008e11	1.60629	0.803145	+	0.595783i	$0.203158\pi$
$252$	−9.93142e10	−1.55135
$253$	7.21558e10	1.10721
$254$	−5.42518e10	−0.817829
$255$	0	0
$256$	8.89617e10	1.29456
$257$	−6.24220e10	−0.892563	−0.446282	−	0.894893i	$-0.647252\pi$
$257$	−6.24220e10	−0.892563	−0.446282	+	0.894893i	$0.647252\pi$
$258$	−1.53475e11	−2.15649
$259$	−1.28371e11	−1.77262
$260$	−5.86219e10	−0.795573
$261$	9.10844e10	1.21496
$262$	−8.98019e10	−1.17742
$263$	−4.12563e10	−0.531728	−0.265864	−	0.964010i	$-0.585657\pi$
$263$	−4.12563e10	−0.531728	−0.265864	+	0.964010i	$0.585657\pi$
$264$	8.92923e10	1.13135
$265$	2.58899e10	0.322496
$266$	−1.01334e10	−0.124105
$267$	2.10083e10	0.252982
$268$	7.40964e10	0.877386
$269$	−7.37696e10	−0.858998	−0.429499	−	0.903067i	$-0.641310\pi$
$269$	−7.37696e10	−0.858998	−0.429499	+	0.903067i	$0.641310\pi$
$270$	−2.92989e11	−3.35517
$271$	6.04771e10	0.681128	0.340564	−	0.940221i	$-0.389382\pi$
$271$	6.04771e10	0.681128	0.340564	+	0.940221i	$0.389382\pi$
$272$	0	0
$273$	−2.02296e11	−2.20422
$274$	1.19957e11	1.28572
$275$	3.89669e10	0.410865
$276$	−9.22599e10	−0.957023
$277$	−6.65923e10	−0.679618	−0.339809	−	0.940494i	$-0.610362\pi$
$277$	−6.65923e10	−0.679618	−0.339809	+	0.940494i	$0.610362\pi$
$278$	−2.33764e10	−0.234734
$279$	4.64243e10	0.458698
$280$	6.19686e10	0.602505
$281$	1.81317e11	1.73484	0.867419	−	0.497578i	$-0.165777\pi$
$281$	1.81317e11	1.73484	0.867419	+	0.497578i	$0.165777\pi$
$282$	4.70705e10	0.443228
$283$	3.12027e10	0.289170	0.144585	−	0.989492i	$-0.453815\pi$
$283$	3.12027e10	0.289170	0.144585	+	0.989492i	$0.453815\pi$
$284$	−2.30180e9	−0.0209960
$285$	−2.05263e10	−0.184293
$286$	−2.09270e11	−1.84953
$287$	5.54427e10	0.482365
$288$	−2.89873e11	−2.48280
$289$	0	0
$290$	9.42003e10	0.782098
$291$	−4.23118e10	−0.345894
$292$	1.00930e11	0.812454
$293$	−1.41584e11	−1.12230	−0.561151	−	0.827713i	$-0.689641\pi$
$293$	−1.41584e11	−1.12230	−0.561151	+	0.827713i	$0.689641\pi$
$294$	−5.92682e10	−0.462656
$295$	−1.88281e11	−1.44746
$296$	−1.02442e11	−0.775652
$297$	−4.01763e11	−2.99617
$298$	3.86149e10	0.283649
$299$	−1.30454e11	−0.943927
$300$	−4.98239e10	−0.355134
$301$	−1.46054e11	−1.02557
$302$	−1.04564e11	−0.723352
$303$	4.90895e11	3.34578
$304$	−1.63415e10	−0.109739
$305$	−5.64482e10	−0.373509
$306$	0	0
$307$	1.60774e10	0.103299	0.0516493	−	0.998665i	$-0.483552\pi$
$307$	1.60774e10	0.103299	0.0516493	+	0.998665i	$0.483552\pi$
$308$	−1.40844e11	−0.891785
$309$	4.75267e11	2.96568
$310$	4.80125e10	0.295275
$311$	2.50094e11	1.51594	0.757969	−	0.652291i	$-0.226192\pi$
$311$	2.50094e11	1.51594	0.757969	+	0.652291i	$0.226192\pi$
$312$	−1.61436e11	−0.964508
$313$	1.83769e11	1.08224	0.541119	−	0.840946i	$-0.318001\pi$
$313$	1.83769e11	1.08224	0.541119	+	0.840946i	$0.318001\pi$
$314$	−1.31677e11	−0.764408
$315$	−4.98393e11	−2.85217
$316$	−1.86344e11	−1.05129
$317$	−4.13738e8	−0.00230122	−0.00115061	−	0.999999i	$-0.500366\pi$
$317$	−4.13738e8	−0.00230122	−0.00115061	+	0.999999i	$0.500366\pi$
$318$	−1.18173e11	−0.648034
$319$	1.29173e11	0.698414
$320$	−3.42188e10	−0.182427
$321$	5.33727e11	2.80574
$322$	−2.28569e11	−1.18486
$323$	0	0
$324$	2.32883e11	1.17404
$325$	−7.04504e10	−0.350274
$326$	−4.58706e10	−0.224934
$327$	2.54044e11	1.22870
$328$	4.42444e10	0.211070
$329$	4.47945e10	0.210787
$330$	−7.42715e11	−3.44754
$331$	2.02135e11	0.925586	0.462793	−	0.886466i	$-0.346847\pi$
$331$	2.02135e11	0.925586	0.462793	+	0.886466i	$0.346847\pi$
$332$	−8.35886e10	−0.377595
$333$	8.23910e11	3.67182
$334$	−1.29048e11	−0.567402
$335$	3.71841e11	1.61308
$336$	−5.71590e11	−2.44657
$337$	−3.22290e11	−1.36117	−0.680585	−	0.732669i	$-0.738274\pi$
$337$	−3.22290e11	−1.36117	−0.680585	+	0.732669i	$0.738274\pi$
$338$	7.25926e10	0.302529
$339$	−5.63533e11	−2.31750
$340$	0	0
$341$	6.58374e10	0.263680
$342$	6.50384e10	0.257070
$343$	2.24501e11	0.875779
$344$	−1.16554e11	−0.448760
$345$	−4.62992e11	−1.75949
$346$	−1.38543e11	−0.519688
$347$	−5.55411e10	−0.205651	−0.102826	−	0.994699i	$-0.532788\pi$
$347$	−5.55411e10	−0.205651	−0.102826	+	0.994699i	$0.532788\pi$
$348$	−1.65163e11	−0.603680
$349$	−1.80693e11	−0.651968	−0.325984	−	0.945375i	$-0.605696\pi$
$349$	−1.80693e11	−0.651968	−0.325984	+	0.945375i	$0.605696\pi$
$350$	−1.23436e11	−0.439680
$351$	7.26369e11	2.55432
$352$	−4.11087e11	−1.42722
$353$	1.18291e11	0.405475	0.202738	−	0.979233i	$-0.435016\pi$
$353$	1.18291e11	0.405475	0.202738	+	0.979233i	$0.435016\pi$
$354$	8.59401e11	2.90858
$355$	−1.15512e10	−0.0386012
$356$	−2.64441e10	−0.0872578
$357$	0	0
$358$	−3.84779e11	−1.23805
$359$	−4.33360e11	−1.37697	−0.688484	−	0.725251i	$-0.741724\pi$
$359$	−4.33360e11	−1.37697	−0.688484	+	0.725251i	$0.741724\pi$
$360$	−3.97728e11	−1.24803
$361$	−3.20139e11	−0.992100
$362$	2.04352e11	0.625446
$363$	−4.20257e11	−1.27038
$364$	2.54640e11	0.760273
$365$	5.06503e11	1.49370
$366$	2.57655e11	0.750541
$367$	−4.17148e11	−1.20031	−0.600155	−	0.799884i	$-0.704894\pi$
$367$	−4.17148e11	−1.20031	−0.600155	+	0.799884i	$0.704894\pi$
$368$	−3.68600e11	−1.04771
$369$	−3.55843e11	−0.999170
$370$	8.52095e11	2.36364
$371$	−1.12460e11	−0.308187
$372$	−8.41811e10	−0.227914
$373$	−3.22658e11	−0.863083	−0.431542	−	0.902093i	$-0.642030\pi$
$373$	−3.22658e11	−0.863083	−0.431542	+	0.902093i	$0.642030\pi$
$374$	0	0
$375$	5.44017e11	1.42060
$376$	3.57469e10	0.0922346
$377$	−2.33539e11	−0.595419
$378$	1.27267e12	3.20630
$379$	−4.31063e11	−1.07316	−0.536580	−	0.843849i	$-0.680284\pi$
$379$	−4.31063e11	−1.07316	−0.536580	+	0.843849i	$0.680284\pi$
$380$	2.58374e10	0.0635657
$381$	4.77349e11	1.16058
$382$	−8.78631e11	−2.11116
$383$	−7.20550e10	−0.171108	−0.0855539	−	0.996334i	$-0.527266\pi$
$383$	−7.20550e10	−0.171108	−0.0855539	+	0.996334i	$0.527266\pi$
$384$	−6.86559e11	−1.61134
$385$	−7.06804e11	−1.63955
$386$	3.04845e11	0.698934
$387$	9.37405e11	2.12436
$388$	5.32599e10	0.119305
$389$	−2.81453e11	−0.623206	−0.311603	−	0.950212i	$-0.600866\pi$
$389$	−2.81453e11	−0.623206	−0.311603	+	0.950212i	$0.600866\pi$
$390$	1.34280e12	2.93913
$391$	0	0
$392$	−4.50103e10	−0.0962775
$393$	7.90145e11	1.67086
$394$	−3.73074e11	−0.779940
$395$	−9.35139e11	−1.93281
$396$	9.03967e11	1.84724
$397$	6.13368e11	1.23926	0.619632	−	0.784893i	$-0.287282\pi$
$397$	6.13368e11	1.23926	0.619632	+	0.784893i	$0.287282\pi$
$398$	−5.14024e11	−1.02686
$399$	8.91614e10	0.176116
$400$	−1.99059e11	−0.388786
$401$	9.06061e11	1.74988	0.874939	−	0.484233i	$-0.160901\pi$
$401$	9.06061e11	1.74988	0.874939	+	0.484233i	$0.160901\pi$
$402$	−1.69725e12	−3.24138
$403$	−1.19031e11	−0.224795
$404$	−6.17913e11	−1.15401
$405$	1.16869e12	2.15849
$406$	−4.09184e11	−0.747396
$407$	1.16844e12	2.11073
$408$	0	0
$409$	5.05301e11	0.892884	0.446442	−	0.894813i	$-0.352691\pi$
$409$	5.05301e11	0.892884	0.446442	+	0.894813i	$0.352691\pi$
$410$	−3.68016e11	−0.643190
$411$	−1.05547e12	−1.82456
$412$	−5.98241e11	−1.02291
$413$	8.17848e11	1.38324
$414$	1.46701e12	2.45432
$415$	−4.19477e11	−0.694211
$416$	7.43227e11	1.21675
$417$	2.05683e11	0.333109
$418$	9.22352e10	0.147776
$419$	8.55218e11	1.35554	0.677772	−	0.735272i	$-0.262946\pi$
$419$	8.55218e11	1.35554	0.677772	+	0.735272i	$0.262946\pi$
$420$	9.03735e11	1.41716
$421$	1.94096e11	0.301125	0.150563	−	0.988600i	$-0.451891\pi$
$421$	1.94096e11	0.301125	0.150563	+	0.988600i	$0.451891\pi$
$422$	−4.87136e11	−0.747730
$423$	−2.87501e11	−0.436624
$424$	−8.97451e10	−0.134854
$425$	0	0
$426$	5.27252e10	0.0775666
$427$	2.45197e11	0.356936
$428$	−6.71828e11	−0.967745
$429$	1.84132e12	2.62465
$430$	9.69472e11	1.36750
$431$	−1.88698e11	−0.263402	−0.131701	−	0.991289i	$-0.542044\pi$
$431$	−1.88698e11	−0.263402	−0.131701	+	0.991289i	$0.542044\pi$
$432$	2.05236e12	2.83516
$433$	2.24845e11	0.307389	0.153694	−	0.988118i	$-0.450883\pi$
$433$	2.24845e11	0.307389	0.153694	+	0.988118i	$0.450883\pi$
$434$	−2.08555e11	−0.282173
$435$	−8.28846e11	−1.10987
$436$	−3.19778e11	−0.423798
$437$	5.74973e10	0.0754191
$438$	−2.31191e12	−3.00150
$439$	−9.16644e11	−1.17791	−0.588953	−	0.808168i	$-0.700460\pi$
$439$	−9.16644e11	−1.17791	−0.588953	+	0.808168i	$0.700460\pi$
$440$	−5.64044e11	−0.717424
$441$	3.62003e11	0.455762
$442$	0	0
$443$	−4.92953e11	−0.608119	−0.304060	−	0.952653i	$-0.598342\pi$
$443$	−4.92953e11	−0.608119	−0.304060	+	0.952653i	$0.598342\pi$
$444$	−1.49399e12	−1.82442
$445$	−1.32706e11	−0.160424
$446$	−3.54911e11	−0.424730
$447$	−3.39763e11	−0.402524
$448$	1.48638e11	0.174333
$449$	9.28323e11	1.07793	0.538965	−	0.842328i	$-0.318815\pi$
$449$	9.28323e11	1.07793	0.538965	+	0.842328i	$0.318815\pi$
$450$	7.92241e11	0.910754
$451$	−5.04644e11	−0.574369
$452$	7.09345e11	0.799346
$453$	9.20031e11	1.02650
$454$	3.22926e11	0.356740
$455$	1.27787e12	1.39777
$456$	7.11526e10	0.0770635
$457$	1.66023e12	1.78052	0.890258	−	0.455456i	$-0.150524\pi$
$457$	1.66023e12	1.78052	0.890258	+	0.455456i	$0.150524\pi$
$458$	1.54900e12	1.64497
$459$	0	0
$460$	5.82790e11	0.606879
$461$	−1.62302e11	−0.167367	−0.0836837	−	0.996492i	$-0.526669\pi$
$461$	−1.62302e11	−0.167367	−0.0836837	+	0.996492i	$0.526669\pi$
$462$	3.22618e12	3.29458
$463$	7.72644e10	0.0781385	0.0390692	−	0.999237i	$-0.487561\pi$
$463$	7.72644e10	0.0781385	0.0390692	+	0.999237i	$0.487561\pi$
$464$	−6.59866e11	−0.660883
$465$	−4.22450e11	−0.419022
$466$	9.21358e11	0.905090
$467$	6.91956e11	0.673213	0.336607	−	0.941645i	$-0.390721\pi$
$467$	6.91956e11	0.673213	0.336607	+	0.941645i	$0.390721\pi$
$468$	−1.63433e12	−1.57483
$469$	−1.61519e12	−1.54151
$470$	−2.97336e11	−0.281065
$471$	1.15859e12	1.08477
$472$	6.52659e11	0.605268
$473$	1.32939e12	1.22118
$474$	4.26840e12	3.88385
$475$	3.10508e10	0.0279867
$476$	0	0
$477$	7.21790e11	0.638378
$478$	−7.61824e11	−0.667466
$479$	−1.79976e12	−1.56208	−0.781042	−	0.624478i	$-0.785312\pi$
$479$	−1.79976e12	−1.56208	−0.781042	+	0.624478i	$0.785312\pi$
$480$	2.63777e12	2.26804
$481$	−2.11249e12	−1.79946
$482$	−1.76897e12	−1.49282
$483$	2.01113e12	1.68143
$484$	5.28997e11	0.438176
$485$	2.67277e11	0.219343
$486$	−1.73582e12	−1.41137
$487$	8.60582e11	0.693285	0.346643	−	0.937997i	$-0.387322\pi$
$487$	8.60582e11	0.693285	0.346643	+	0.937997i	$0.387322\pi$
$488$	1.95673e11	0.156185
$489$	4.03604e11	0.319202
$490$	3.74387e11	0.293385
$491$	5.49516e11	0.426692	0.213346	−	0.976977i	$-0.431564\pi$
$491$	5.49516e11	0.426692	0.213346	+	0.976977i	$0.431564\pi$
$492$	6.45249e11	0.496460
$493$	0	0
$494$	−1.66757e11	−0.125983
$495$	4.53642e12	3.39617
$496$	−3.36324e11	−0.249511
$497$	5.01758e10	0.0368885
$498$	1.91468e12	1.39497
$499$	1.30212e12	0.940150	0.470075	−	0.882626i	$-0.344227\pi$
$499$	1.30212e12	0.940150	0.470075	+	0.882626i	$0.344227\pi$
$500$	−6.84780e11	−0.489989
$501$	1.13546e12	0.805196
$502$	2.91235e12	2.04681
$503$	−1.54975e12	−1.07946	−0.539730	−	0.841838i	$-0.681474\pi$
$503$	−1.54975e12	−1.07946	−0.539730	+	0.841838i	$0.681474\pi$
$504$	1.72764e12	1.19265
$505$	−3.10090e12	−2.12166
$506$	2.08046e12	1.41085
$507$	−6.38725e11	−0.429317
$508$	−6.00861e11	−0.400302
$509$	−1.50541e12	−0.994091	−0.497045	−	0.867725i	$-0.665582\pi$
$509$	−1.50541e12	−0.994091	−0.497045	+	0.867725i	$0.665582\pi$
$510$	0	0
$511$	−2.20013e12	−1.42743
$512$	1.17942e12	0.758499
$513$	−3.20145e11	−0.204088
$514$	−1.79981e12	−1.13735
$515$	−3.00218e12	−1.88063
$516$	−1.69979e12	−1.05553
$517$	−4.07724e11	−0.250991
$518$	−3.70130e12	−2.25876
$519$	1.21901e12	0.737485
$520$	1.01977e12	0.611625
$521$	−2.16632e12	−1.28811	−0.644056	−	0.764978i	$-0.722750\pi$
$521$	−2.16632e12	−1.28811	−0.644056	+	0.764978i	$0.722750\pi$
$522$	2.62623e12	1.54816
$523$	−2.82309e12	−1.64994	−0.824969	−	0.565178i	$-0.808808\pi$
$523$	−2.82309e12	−1.64994	−0.824969	+	0.565178i	$0.808808\pi$
$524$	−9.94593e11	−0.576308
$525$	1.08609e12	0.623947
$526$	−1.18954e12	−0.677553
$527$	0	0
$528$	5.20267e12	2.91322
$529$	−5.04240e11	−0.279954
$530$	7.46481e11	0.410939
$531$	−5.24912e12	−2.86524
$532$	−1.12232e11	−0.0607453
$533$	9.12374e11	0.489666
$534$	6.05730e11	0.322362
$535$	−3.37146e12	−1.77921
$536$	−1.28895e12	−0.674522
$537$	3.38557e12	1.75690
$538$	−2.12699e12	−1.09457
$539$	5.13380e11	0.261993
$540$	−3.24497e12	−1.64225
$541$	−2.38210e11	−0.119556	−0.0597782	−	0.998212i	$-0.519039\pi$
$541$	−2.38210e11	−0.119556	−0.0597782	+	0.998212i	$0.519039\pi$
$542$	1.74373e12	0.867925
$543$	−1.79804e12	−0.887566
$544$	0	0
$545$	−1.60475e12	−0.779156
$546$	−5.83279e12	−2.80872
$547$	−1.95687e12	−0.934585	−0.467293	−	0.884103i	$-0.654771\pi$
$547$	−1.95687e12	−0.934585	−0.467293	+	0.884103i	$0.654771\pi$
$548$	1.32857e12	0.629320
$549$	−1.57373e12	−0.739358
$550$	1.12353e12	0.523543
$551$	1.02931e11	0.0475735
$552$	1.60492e12	0.735746
$553$	4.06202e12	1.84705
$554$	−1.92005e12	−0.866001
$555$	−7.49738e12	−3.35422
$556$	−2.58903e11	−0.114895
$557$	−5.54013e11	−0.243877	−0.121939	−	0.992538i	$-0.538911\pi$
$557$	−5.54013e11	−0.243877	−0.121939	+	0.992538i	$0.538911\pi$
$558$	1.33855e12	0.584494
$559$	−2.40349e12	−1.04109
$560$	3.61064e12	1.55145
$561$	0	0
$562$	5.22788e12	2.21061
$563$	−6.79128e11	−0.284881	−0.142441	−	0.989803i	$-0.545495\pi$
$563$	−6.79128e11	−0.284881	−0.142441	+	0.989803i	$0.545495\pi$
$564$	5.21325e11	0.216946
$565$	3.55974e12	1.46960
$566$	8.99665e11	0.368474
$567$	−5.07649e12	−2.06272
$568$	4.00413e10	0.0161414
$569$	−2.62380e12	−1.04936	−0.524681	−	0.851299i	$-0.675815\pi$
$569$	−2.62380e12	−1.04936	−0.524681	+	0.851299i	$0.675815\pi$
$570$	−5.91833e11	−0.234835
$571$	−2.30932e12	−0.909123	−0.454561	−	0.890715i	$-0.650204\pi$
$571$	−2.30932e12	−0.909123	−0.454561	+	0.890715i	$0.650204\pi$
$572$	−2.31775e12	−0.905284
$573$	7.73086e12	2.99593
$574$	1.59857e12	0.614651
$575$	7.00383e11	0.267196
$576$	−9.53991e11	−0.361113
$577$	4.55996e12	1.71266	0.856328	−	0.516432i	$-0.172740\pi$
$577$	4.55996e12	1.71266	0.856328	+	0.516432i	$0.172740\pi$
$578$	0	0
$579$	−2.68226e12	−0.991852
$580$	1.04331e12	0.382812
$581$	1.82211e12	0.663408
$582$	−1.21997e12	−0.440755
$583$	1.02362e12	0.366969
$584$	−1.75575e12	−0.624603
$585$	−8.20164e12	−2.89534
$586$	−4.08228e12	−1.43009
$587$	−6.94817e11	−0.241546	−0.120773	−	0.992680i	$-0.538537\pi$
$587$	−6.94817e11	−0.241546	−0.120773	+	0.992680i	$0.538537\pi$
$588$	−6.56419e11	−0.226456
$589$	5.24626e10	0.0179610
$590$	−5.42869e12	−1.84442
$591$	3.28258e12	1.10681
$592$	−5.96886e12	−1.99730
$593$	−3.17510e12	−1.05441	−0.527207	−	0.849737i	$-0.676761\pi$
$593$	−3.17510e12	−1.05441	−0.527207	+	0.849737i	$0.676761\pi$
$594$	−1.15840e13	−3.81785
$595$	0	0
$596$	4.27675e11	0.138837
$597$	4.52277e12	1.45720
$598$	−3.76138e12	−1.20280
$599$	−2.43909e12	−0.774119	−0.387060	−	0.922055i	$-0.626509\pi$
$599$	−2.43909e12	−0.774119	−0.387060	+	0.922055i	$0.626509\pi$
$600$	8.66719e11	0.273022
$601$	−2.36635e12	−0.739851	−0.369925	−	0.929061i	$-0.620617\pi$
$601$	−2.36635e12	−0.739851	−0.369925	+	0.929061i	$0.620617\pi$
$602$	−4.21115e12	−1.30682
$603$	1.03666e13	3.19308
$604$	−1.15809e12	−0.354058
$605$	2.65469e12	0.805591
$606$	1.41539e13	4.26334
$607$	−6.01062e12	−1.79709	−0.898545	−	0.438881i	$-0.855375\pi$
$607$	−6.01062e12	−1.79709	−0.898545	+	0.438881i	$0.855375\pi$
$608$	−3.27575e11	−0.0972176
$609$	3.60031e12	1.06062
$610$	−1.62757e12	−0.475942
$611$	7.37146e11	0.213978
$612$	0	0
$613$	−3.01272e12	−0.861761	−0.430880	−	0.902409i	$-0.641797\pi$
$613$	−3.01272e12	−0.861761	−0.430880	+	0.902409i	$0.641797\pi$
$614$	4.63559e11	0.131628
$615$	3.23808e12	0.912746
$616$	2.45007e12	0.685592
$617$	1.01050e12	0.280707	0.140354	−	0.990101i	$-0.455176\pi$
$617$	1.01050e12	0.280707	0.140354	+	0.990101i	$0.455176\pi$
$618$	1.37033e13	3.77901
$619$	1.82736e11	0.0500284	0.0250142	−	0.999687i	$-0.492037\pi$
$619$	1.82736e11	0.0500284	0.0250142	+	0.999687i	$0.492037\pi$
$620$	5.31758e11	0.144528
$621$	−7.22120e12	−1.94849
$622$	7.21093e12	1.93168
$623$	5.76442e11	0.153306
$624$	−9.40618e12	−2.48361
$625$	−4.63765e12	−1.21573
$626$	5.29860e12	1.37904
$627$	−8.11555e11	−0.209708
$628$	−1.45837e12	−0.374154
$629$	0	0
$630$	−1.43701e13	−3.63436
$631$	−6.42710e11	−0.161392	−0.0806962	−	0.996739i	$-0.525714\pi$
$631$	−6.42710e11	−0.161392	−0.0806962	+	0.996739i	$0.525714\pi$
$632$	3.24157e12	0.808219
$633$	4.28620e12	1.06110
$634$	−1.19293e10	−0.00293233
$635$	−3.01533e12	−0.735958
$636$	−1.30882e12	−0.317192
$637$	−9.28168e11	−0.223357
$638$	3.72443e12	0.889951
$639$	−3.22039e11	−0.0764108
$640$	4.33687e12	1.02180
$641$	6.42109e12	1.50227	0.751134	−	0.660150i	$-0.229507\pi$
$641$	6.42109e12	1.50227	0.751134	+	0.660150i	$0.229507\pi$
$642$	1.53889e13	3.57520
$643$	7.03016e12	1.62187	0.810935	−	0.585137i	$-0.198959\pi$
$643$	7.03016e12	1.62187	0.810935	+	0.585137i	$0.198959\pi$
$644$	−2.53150e12	−0.579951
$645$	−8.53015e12	−1.94061
$646$	0	0
$647$	6.41347e12	1.43888	0.719439	−	0.694556i	$-0.244399\pi$
$647$	6.41347e12	1.43888	0.719439	+	0.694556i	$0.244399\pi$
$648$	−4.05114e12	−0.902589
$649$	−7.44412e12	−1.64707
$650$	−2.03129e12	−0.446336
$651$	1.83502e12	0.400430
$652$	−5.08036e11	−0.110098
$653$	4.35666e11	0.0937659	0.0468829	−	0.998900i	$-0.485071\pi$
$653$	4.35666e11	0.0937659	0.0468829	+	0.998900i	$0.485071\pi$
$654$	7.32484e12	1.56566
$655$	−4.99121e12	−1.05955
$656$	2.57792e12	0.543504
$657$	1.41209e13	2.95677
$658$	1.29156e12	0.268594
$659$	−1.79536e12	−0.370823	−0.185412	−	0.982661i	$-0.559362\pi$
$659$	−1.79536e12	−0.370823	−0.185412	+	0.982661i	$0.559362\pi$
$660$	−8.22588e12	−1.68746
$661$	−1.53076e12	−0.311889	−0.155945	−	0.987766i	$-0.549842\pi$
$661$	−1.53076e12	−0.311889	−0.155945	+	0.987766i	$0.549842\pi$
$662$	5.82815e12	1.17942
$663$	0	0
$664$	1.45408e12	0.290289
$665$	−5.63217e11	−0.111681
$666$	2.37557e13	4.67880
$667$	2.32172e12	0.454197
$668$	−1.42925e12	−0.277725
$669$	3.12278e12	0.602731
$670$	1.07213e13	2.05546
$671$	−2.23181e12	−0.425016
$672$	−1.14578e13	−2.16741
$673$	1.00261e13	1.88393	0.941965	−	0.335710i	$-0.108976\pi$
$673$	1.00261e13	1.88393	0.941965	+	0.335710i	$0.108976\pi$
$674$	−9.29256e12	−1.73447
$675$	−3.89973e12	−0.723048
$676$	8.03993e11	0.148079
$677$	1.68851e12	0.308926	0.154463	−	0.987999i	$-0.450635\pi$
$677$	1.68851e12	0.308926	0.154463	+	0.987999i	$0.450635\pi$
$678$	−1.62483e13	−2.95307
$679$	−1.16099e12	−0.209610
$680$	0	0
$681$	−2.84135e12	−0.506247
$682$	1.89828e12	0.335994
$683$	−9.76584e12	−1.71718	−0.858592	−	0.512660i	$-0.828660\pi$
$683$	−9.76584e12	−1.71718	−0.858592	+	0.512660i	$0.828660\pi$
$684$	7.20327e11	0.125828
$685$	6.66722e12	1.15701
$686$	6.47301e12	1.11596
$687$	−1.36293e13	−2.33436
$688$	−6.79108e12	−1.15556
$689$	−1.85065e12	−0.312852
$690$	−1.33494e13	−2.24203
$691$	−2.34843e12	−0.391856	−0.195928	−	0.980618i	$-0.562772\pi$
$691$	−2.34843e12	−0.391856	−0.195928	+	0.980618i	$0.562772\pi$
$692$	−1.53442e12	−0.254371
$693$	−1.97051e13	−3.24549
$694$	−1.60141e12	−0.262051
$695$	−1.29927e12	−0.211235
$696$	2.87312e12	0.464100
$697$	0	0
$698$	−5.20989e12	−0.830767
$699$	−8.10681e12	−1.28441
$700$	−1.36711e12	−0.215210
$701$	−9.78498e12	−1.53048	−0.765242	−	0.643742i	$-0.777381\pi$
$701$	−9.78498e12	−1.53048	−0.765242	+	0.643742i	$0.777381\pi$
$702$	2.09433e13	3.25483
$703$	9.31073e11	0.143775
$704$	−1.35292e12	−0.207584
$705$	2.61619e12	0.398857
$706$	3.41066e12	0.516675
$707$	1.34696e13	2.02752
$708$	9.51822e12	1.42366
$709$	5.41326e12	0.804545	0.402273	−	0.915520i	$-0.368220\pi$
$709$	5.41326e12	0.804545	0.402273	+	0.915520i	$0.368220\pi$
$710$	−3.33056e11	−0.0491875
$711$	−2.60709e13	−3.82598
$712$	4.60012e11	0.0670826
$713$	1.18335e12	0.171478
$714$	0	0
$715$	−1.16313e13	−1.66437
$716$	−4.26158e12	−0.605985
$717$	6.70311e12	0.947196
$718$	−1.24950e13	−1.75460
$719$	4.91756e11	0.0686229	0.0343115	−	0.999411i	$-0.489076\pi$
$719$	4.91756e11	0.0686229	0.0343115	+	0.999411i	$0.489076\pi$
$720$	−2.31738e13	−3.21367
$721$	1.30407e13	1.79719
$722$	−9.23052e12	−1.26418
$723$	1.55647e13	2.11845
$724$	2.26328e12	0.306136
$725$	1.25382e12	0.168544
$726$	−1.21172e13	−1.61878
$727$	4.85245e11	0.0644253	0.0322127	−	0.999481i	$-0.489745\pi$
$727$	4.85245e11	0.0644253	0.0322127	+	0.999481i	$0.489745\pi$
$728$	−4.42962e12	−0.584488
$729$	9.18785e11	0.120487
$730$	1.46040e13	1.90334
$731$	0	0
$732$	2.85364e12	0.367366
$733$	4.53070e12	0.579693	0.289846	−	0.957073i	$-0.406396\pi$
$733$	4.53070e12	0.579693	0.289846	+	0.957073i	$0.406396\pi$
$734$	−1.20276e13	−1.52949
$735$	−3.29414e12	−0.416341
$736$	−7.38880e12	−0.928162
$737$	1.47016e13	1.83553
$738$	−1.02600e13	−1.27319
$739$	−3.39131e12	−0.418281	−0.209140	−	0.977886i	$-0.567067\pi$
$739$	−3.39131e12	−0.418281	−0.209140	+	0.977886i	$0.567067\pi$
$740$	9.43730e12	1.15692
$741$	1.46725e12	0.178782
$742$	−3.24254e12	−0.392706
$743$	−1.09348e13	−1.31632	−0.658161	−	0.752877i	$-0.728665\pi$
$743$	−1.09348e13	−1.31632	−0.658161	+	0.752877i	$0.728665\pi$
$744$	1.46438e12	0.175217
$745$	2.14622e12	0.255253
$746$	−9.30316e12	−1.09978
$747$	−1.16947e13	−1.37418
$748$	0	0
$749$	1.46448e13	1.70026
$750$	1.56856e13	1.81019
$751$	5.13831e12	0.589441	0.294721	−	0.955583i	$-0.404773\pi$
$751$	5.13831e12	0.589441	0.294721	+	0.955583i	$0.404773\pi$
$752$	2.08282e12	0.237504
$753$	−2.56251e13	−2.90461
$754$	−6.73359e12	−0.758710
$755$	−5.81167e12	−0.650939
$756$	1.40954e13	1.56938
$757$	8.25749e12	0.913938	0.456969	−	0.889483i	$-0.348935\pi$
$757$	8.25749e12	0.913938	0.456969	+	0.889483i	$0.348935\pi$
$758$	−1.24288e13	−1.36747
$759$	−1.83055e13	−2.00213
$760$	−4.49459e11	−0.0488685
$761$	1.37466e13	1.48581	0.742906	−	0.669396i	$-0.233447\pi$
$761$	1.37466e13	1.48581	0.742906	+	0.669396i	$0.233447\pi$
$762$	1.37633e13	1.47886
$763$	6.97067e12	0.744585
$764$	−9.73119e12	−1.03335
$765$	0	0
$766$	−2.07756e12	−0.218033
$767$	1.34586e13	1.40418
$768$	−2.25690e13	−2.34092
$769$	−1.41070e13	−1.45468	−0.727338	−	0.686280i	$-0.759243\pi$
$769$	−1.41070e13	−1.45468	−0.727338	+	0.686280i	$0.759243\pi$
$770$	−2.03792e13	−2.08920
$771$	1.58361e13	1.61400
$772$	3.37628e12	0.342106
$773$	−3.76516e12	−0.379294	−0.189647	−	0.981852i	$-0.560734\pi$
$773$	−3.76516e12	−0.379294	−0.189647	+	0.981852i	$0.560734\pi$
$774$	2.70281e13	2.70696
$775$	6.39053e11	0.0636326
$776$	−9.26490e11	−0.0917198
$777$	3.25668e13	3.20539
$778$	−8.11509e12	−0.794118
$779$	−4.02126e11	−0.0391240
$780$	1.48720e13	1.43861
$781$	−4.56705e11	−0.0439244
$782$	0	0
$783$	−1.29273e13	−1.22908
$784$	−2.62255e12	−0.247914
$785$	−7.31862e12	−0.687885
$786$	2.27822e13	2.12909
$787$	−5.93405e12	−0.551397	−0.275699	−	0.961244i	$-0.588909\pi$
$787$	−5.93405e12	−0.551397	−0.275699	+	0.961244i	$0.588909\pi$
$788$	−4.13194e12	−0.381756
$789$	1.04665e13	0.961510
$790$	−2.69628e13	−2.46287
$791$	−1.54627e13	−1.40440
$792$	−1.57251e13	−1.42014
$793$	4.03501e12	0.362339
$794$	1.76852e13	1.57913
$795$	−6.56811e12	−0.583161
$796$	−5.69303e12	−0.502614
$797$	−1.41517e13	−1.24235	−0.621177	−	0.783670i	$-0.713345\pi$
$797$	−1.41517e13	−1.24235	−0.621177	+	0.783670i	$0.713345\pi$
$798$	2.57078e12	0.224415
$799$	0	0
$800$	−3.99024e12	−0.344424
$801$	−3.69973e12	−0.317558
$802$	2.61244e13	2.22978
$803$	2.00258e13	1.69969
$804$	−1.87978e13	−1.58655
$805$	−1.27039e13	−1.06625
$806$	−3.43201e12	−0.286445
$807$	1.87149e13	1.55330
$808$	1.07490e13	0.887189
$809$	−5.98845e12	−0.491525	−0.245763	−	0.969330i	$-0.579038\pi$
$809$	−5.98845e12	−0.491525	−0.245763	+	0.969330i	$0.579038\pi$
$810$	3.36966e13	2.75045
$811$	−1.95715e13	−1.58865	−0.794327	−	0.607490i	$-0.792176\pi$
$811$	−1.95715e13	−1.58865	−0.794327	+	0.607490i	$0.792176\pi$
$812$	−4.53188e12	−0.365827
$813$	−1.53427e13	−1.23167
$814$	3.36895e13	2.68959
$815$	−2.54950e12	−0.202416
$816$	0	0
$817$	1.05933e12	0.0831824
$818$	1.45693e13	1.13775
$819$	3.56260e13	2.76687
$820$	−4.07593e12	−0.314821
$821$	−3.53238e12	−0.271346	−0.135673	−	0.990754i	$-0.543320\pi$
$821$	−3.53238e12	−0.271346	−0.135673	+	0.990754i	$0.543320\pi$
$822$	−3.04323e13	−2.32494
$823$	−1.42829e13	−1.08522	−0.542609	−	0.839986i	$-0.682563\pi$
$823$	−1.42829e13	−1.08522	−0.542609	+	0.839986i	$0.682563\pi$
$824$	1.04068e13	0.786401
$825$	−9.88566e12	−0.742956
$826$	2.35809e13	1.76259
$827$	−1.97804e12	−0.147048	−0.0735242	−	0.997293i	$-0.523425\pi$
$827$	−1.97804e12	−0.147048	−0.0735242	+	0.997293i	$0.523425\pi$
$828$	1.62477e13	1.20131
$829$	−1.38516e13	−1.01860	−0.509301	−	0.860588i	$-0.670096\pi$
$829$	−1.38516e13	−1.01860	−0.509301	+	0.860588i	$0.670096\pi$
$830$	−1.20947e13	−0.884595
$831$	1.68940e13	1.22893
$832$	2.44601e12	0.176972
$833$	0	0
$834$	5.93044e12	0.424463
$835$	−7.17249e12	−0.510600
$836$	1.02154e12	0.0723316
$837$	−6.58887e12	−0.464030
$838$	2.46584e13	1.72730
$839$	1.47221e13	1.02575	0.512876	−	0.858463i	$-0.328580\pi$
$839$	1.47221e13	1.02575	0.512876	+	0.858463i	$0.328580\pi$
$840$	−1.57211e13	−1.08949
$841$	−1.03508e13	−0.713497
$842$	5.59635e12	0.383708
$843$	−4.59989e13	−3.13706
$844$	−5.39523e12	−0.365990
$845$	4.03472e12	0.272244
$846$	−8.28949e12	−0.556366
$847$	−1.15313e13	−0.769847
$848$	−5.22905e12	−0.347249
$849$	−7.91594e12	−0.522899
$850$	0	0
$851$	2.10013e13	1.37266
$852$	5.83953e11	0.0379664
$853$	−1.19185e13	−0.770817	−0.385408	−	0.922746i	$-0.625939\pi$
$853$	−1.19185e13	−0.770817	−0.385408	+	0.922746i	$0.625939\pi$
$854$	7.06975e12	0.454825
$855$	3.61485e12	0.231336
$856$	1.16869e13	0.743989
$857$	2.67712e13	1.69533	0.847666	−	0.530530i	$-0.178007\pi$
$857$	2.67712e13	1.69533	0.847666	+	0.530530i	$0.178007\pi$
$858$	5.30905e13	3.34445
$859$	−1.36188e13	−0.853431	−0.426716	−	0.904386i	$-0.640329\pi$
$859$	−1.36188e13	−0.853431	−0.426716	+	0.904386i	$0.640329\pi$
$860$	1.07373e13	0.669348
$861$	−1.40655e13	−0.872247
$862$	−5.44071e12	−0.335639
$863$	1.57643e13	0.967446	0.483723	−	0.875221i	$-0.339284\pi$
$863$	1.57643e13	0.967446	0.483723	+	0.875221i	$0.339284\pi$
$864$	4.11408e13	2.51166
$865$	−7.70026e12	−0.467663
$866$	6.48293e12	0.391689
$867$	0	0
$868$	−2.30983e12	−0.138115
$869$	−3.69729e13	−2.19935
$870$	−2.38980e13	−1.41425
$871$	−2.65798e13	−1.56484
$872$	5.56274e12	0.325810
$873$	7.45146e12	0.434187
$874$	1.65782e12	0.0961025
$875$	1.49272e13	0.860878
$876$	−2.56054e13	−1.46914
$877$	2.58985e11	0.0147835	0.00739174	−	0.999973i	$-0.497647\pi$
$877$	2.58985e11	0.0147835	0.00739174	+	0.999973i	$0.497647\pi$
$878$	−2.64295e13	−1.50094
$879$	3.59190e13	2.02943
$880$	−3.28643e13	−1.84737
$881$	−7.41674e12	−0.414784	−0.207392	−	0.978258i	$-0.566497\pi$
$881$	−7.41674e12	−0.414784	−0.207392	+	0.978258i	$0.566497\pi$
$882$	1.04376e13	0.580754
$883$	1.94425e13	1.07629	0.538146	−	0.842852i	$-0.319125\pi$
$883$	1.94425e13	1.07629	0.538146	+	0.842852i	$0.319125\pi$
$884$	0	0
$885$	4.77657e13	2.61741
$886$	−1.42133e13	−0.774893
$887$	2.94376e13	1.59678	0.798391	−	0.602139i	$-0.205685\pi$
$887$	2.94376e13	1.59678	0.798391	+	0.602139i	$0.205685\pi$
$888$	2.59890e13	1.40259
$889$	1.30979e13	0.703303
$890$	−3.82629e12	−0.204420
$891$	4.62067e13	2.45615
$892$	−3.93079e12	−0.207892
$893$	−3.24895e11	−0.0170967
$894$	−9.79635e12	−0.512915
$895$	−2.13861e13	−1.11411
$896$	−1.88383e13	−0.976464
$897$	3.30955e13	1.70688
$898$	2.67663e13	1.37355
$899$	2.11842e12	0.108167
$900$	8.77440e12	0.445785
$901$	0	0
$902$	−1.45504e13	−0.731887
$903$	3.70529e13	1.85450
$904$	−1.23395e13	−0.614526
$905$	1.13579e13	0.562834
$906$	2.65272e13	1.30802
$907$	−3.10008e12	−0.152104	−0.0760520	−	0.997104i	$-0.524231\pi$
$907$	−3.10008e12	−0.152104	−0.0760520	+	0.997104i	$0.524231\pi$
$908$	3.57654e12	0.174613
$909$	−8.64505e13	−4.19982
$910$	3.68447e13	1.78110
$911$	3.17488e13	1.52719	0.763597	−	0.645693i	$-0.223431\pi$
$911$	3.17488e13	1.52719	0.763597	+	0.645693i	$0.223431\pi$
$912$	4.14575e12	0.198438
$913$	−1.65850e13	−0.789944
$914$	4.78693e13	2.26882
$915$	1.43206e13	0.675406
$916$	1.71558e13	0.805160
$917$	2.16806e13	1.01253
$918$	0	0
$919$	−3.86061e13	−1.78540	−0.892702	−	0.450648i	$-0.851193\pi$
$919$	−3.86061e13	−1.78540	−0.892702	+	0.450648i	$0.851193\pi$
$920$	−1.01380e13	−0.466560
$921$	−4.07875e12	−0.186792
$922$	−4.67965e12	−0.213267
$923$	8.25702e11	0.0374469
$924$	3.57312e13	1.61259
$925$	1.13415e13	0.509370
$926$	2.22776e12	0.0995677
$927$	−8.36983e13	−3.72270
$928$	−1.32274e13	−0.585474
$929$	2.55970e13	1.12750	0.563751	−	0.825944i	$-0.309358\pi$
$929$	2.55970e13	1.12750	0.563751	+	0.825944i	$0.309358\pi$
$930$	−1.21805e13	−0.533937
$931$	4.09087e11	0.0178461
$932$	1.02044e13	0.443013
$933$	−6.34472e13	−2.74123
$934$	1.99511e13	0.857840
$935$	0	0
$936$	2.84303e13	1.21071
$937$	2.65934e12	0.112706	0.0563529	−	0.998411i	$-0.482053\pi$
$937$	2.65934e12	0.112706	0.0563529	+	0.998411i	$0.482053\pi$
$938$	−4.65706e13	−1.96426
$939$	−4.66211e13	−1.95698
$940$	−3.29312e12	−0.137573
$941$	4.13336e13	1.71850	0.859251	−	0.511554i	$-0.170930\pi$
$941$	4.13336e13	1.71850	0.859251	+	0.511554i	$0.170930\pi$
$942$	3.34055e13	1.38226
$943$	−9.07036e12	−0.373527
$944$	3.80275e13	1.55856
$945$	7.07355e13	2.88532
$946$	3.83303e13	1.55608
$947$	−2.07199e13	−0.837166	−0.418583	−	0.908178i	$-0.637473\pi$
$947$	−2.07199e13	−0.837166	−0.418583	+	0.908178i	$0.637473\pi$
$948$	4.72743e13	1.90102
$949$	−3.62057e13	−1.44903
$950$	8.95285e11	0.0356619
$951$	1.04963e11	0.00416124
$952$	0	0
$953$	−2.21831e13	−0.871174	−0.435587	−	0.900147i	$-0.643459\pi$
$953$	−2.21831e13	−0.871174	−0.435587	+	0.900147i	$0.643459\pi$
$954$	2.08113e13	0.813451
$955$	−4.88345e13	−1.89982
$956$	−8.43751e12	−0.326704
$957$	−3.27703e13	−1.26292
$958$	−5.18923e13	−1.99048
$959$	−2.89608e13	−1.10567
$960$	8.68108e12	0.329878
$961$	−2.53599e13	−0.959163
$962$	−6.09092e13	−2.29295
$963$	−9.39937e13	−3.52193
$964$	−1.95920e13	−0.730689
$965$	1.69434e13	0.628965
$966$	5.79866e13	2.14255
$967$	2.63617e13	0.969514	0.484757	−	0.874649i	$-0.338908\pi$
$967$	2.63617e13	0.969514	0.484757	+	0.874649i	$0.338908\pi$
$968$	−9.20224e12	−0.336864
$969$	0	0
$970$	7.70636e12	0.279497
$971$	−3.49050e12	−0.126009	−0.0630045	−	0.998013i	$-0.520068\pi$
$971$	−3.49050e12	−0.126009	−0.0630045	+	0.998013i	$0.520068\pi$
$972$	−1.92249e13	−0.690821
$973$	5.64370e12	0.201863
$974$	2.48131e13	0.883416
$975$	1.78728e13	0.633392
$976$	1.14010e13	0.402177
$977$	1.46631e13	0.514875	0.257437	−	0.966295i	$-0.417122\pi$
$977$	1.46631e13	0.514875	0.257437	+	0.966295i	$0.417122\pi$
$978$	1.16371e13	0.406742
$979$	−5.24683e12	−0.182547
$980$	4.14649e12	0.143603
$981$	−4.47392e13	−1.54233
$982$	1.58442e13	0.543710
$983$	9.90226e12	0.338254	0.169127	−	0.985594i	$-0.445905\pi$
$983$	9.90226e12	0.338254	0.169127	+	0.985594i	$0.445905\pi$
$984$	−1.12245e13	−0.381671
$985$	−2.07355e13	−0.701862
$986$	0	0
$987$	−1.13641e13	−0.381160
$988$	−1.84690e12	−0.0616649
$989$	2.38943e13	0.794164
$990$	1.30798e14	4.32756
$991$	5.12906e13	1.68930	0.844649	−	0.535321i	$-0.179809\pi$
$991$	5.12906e13	1.68930	0.844649	+	0.535321i	$0.179809\pi$
$992$	−6.74179e12	−0.221041
$993$	−5.12805e13	−1.67371
$994$	1.44671e12	0.0470050
$995$	−2.85696e13	−0.924060
$996$	2.12059e13	0.682794
$997$	−7.06003e12	−0.226297	−0.113148	−	0.993578i	$-0.536094\pi$
$997$	−7.06003e12	−0.226297	−0.113148	+	0.993578i	$0.536094\pi$
$998$	3.75438e13	1.19798
$999$	−1.16935e14	−3.71450

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.f.1.19		24
17.2	even	8		17.10.c.a.4.10	✓	24
17.9	even	8		17.10.c.a.13.3	yes	24
17.16	even	2	inner	289.10.a.f.1.20		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.c.a.4.10	✓	24	17.2	even	8
17.10.c.a.13.3	yes	24	17.9	even	8
289.10.a.f.1.19		24	1.1	even	1	trivial
289.10.a.f.1.20		24	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)

\(f(q)\)	\(=\)	\(q+28.8329 q^{2} -253.694 q^{3} +319.336 q^{4} +1602.54 q^{5} -7314.73 q^{6} -6961.05 q^{7} -5555.06 q^{8} +44677.5 q^{9} +O(q^{10})\)	\(q+28.8329 q^{2} -253.694 q^{3} +319.336 q^{4} +1602.54 q^{5} -7314.73 q^{6} -6961.05 q^{7} -5555.06 q^{8} +44677.5 q^{9} +46205.9 q^{10} +63360.1 q^{11} -81013.6 q^{12} -114552. q^{13} -200707. q^{14} -406554. q^{15} -323669. q^{16} +1.28818e6 q^{18} +50488.5 q^{19} +511749. q^{20} +1.76597e6 q^{21} +1.82685e6 q^{22} +1.13882e6 q^{23} +1.40928e6 q^{24} +615007. q^{25} -3.30287e6 q^{26} -6.34095e6 q^{27} -2.22291e6 q^{28} +2.03871e6 q^{29} -1.17221e7 q^{30} +1.03910e6 q^{31} -6.48811e6 q^{32} -1.60741e7 q^{33} -1.11554e7 q^{35} +1.42671e7 q^{36} +1.84413e7 q^{37} +1.45573e6 q^{38} +2.90612e7 q^{39} -8.90220e6 q^{40} -7.96470e6 q^{41} +5.09182e7 q^{42} +2.09816e7 q^{43} +2.02332e7 q^{44} +7.15974e7 q^{45} +3.28355e7 q^{46} -6.43503e6 q^{47} +8.21127e7 q^{48} +8.10258e6 q^{49} +1.77324e7 q^{50} -3.65807e7 q^{52} +1.61556e7 q^{53} -1.82828e8 q^{54} +1.01537e8 q^{55} +3.86690e7 q^{56} -1.28086e7 q^{57} +5.87819e7 q^{58} -1.17489e8 q^{59} -1.29827e8 q^{60} -3.52242e7 q^{61} +2.99602e7 q^{62} -3.11002e8 q^{63} -2.13528e7 q^{64} -1.83574e8 q^{65} -4.63462e8 q^{66} +2.32033e8 q^{67} -2.88912e8 q^{69} -3.21641e8 q^{70} -7.20809e6 q^{71} -2.48186e8 q^{72} +3.16063e8 q^{73} +5.31716e8 q^{74} -1.56023e8 q^{75} +1.61228e7 q^{76} -4.41053e8 q^{77} +8.37918e8 q^{78} -5.83535e8 q^{79} -5.18692e8 q^{80} +7.29271e8 q^{81} -2.29645e8 q^{82} -2.61757e8 q^{83} +5.63939e8 q^{84} +6.04960e8 q^{86} -5.17208e8 q^{87} -3.51969e8 q^{88} -8.28097e7 q^{89} +2.06436e9 q^{90} +7.97403e8 q^{91} +3.63667e8 q^{92} -2.63613e8 q^{93} -1.85541e8 q^{94} +8.09098e7 q^{95} +1.64599e9 q^{96} +1.66783e8 q^{97} +2.33621e8 q^{98} +2.83077e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 5124 q^{4} + 108368 q^{9}+O(q^{10}) \) 24 * q + 5124 * q^4 + 108368 * q^9	\( 24 q + 5124 q^{4} + 108368 q^{9} - 244832 q^{13} - 127332 q^{15} - 279932 q^{16} + 888764 q^{18} - 2280212 q^{19} + 775748 q^{21} - 2762628 q^{25} - 3334452 q^{26} - 39084792 q^{30} + 2010240 q^{32} - 30349992 q^{33} - 25532364 q^{35} + 31177320 q^{36} - 13171392 q^{38} - 86527192 q^{42} + 61046960 q^{43} - 153365328 q^{47} + 169445876 q^{49} - 236105676 q^{50} - 209898380 q^{52} + 85777812 q^{53} - 255767540 q^{55} - 767709024 q^{59} + 429639656 q^{60} - 1006108924 q^{64} + 346830788 q^{66} - 26076868 q^{67} - 751973532 q^{69} - 319504544 q^{70} - 1171736028 q^{72} - 1640047616 q^{76} - 174401076 q^{77} - 347156560 q^{81} - 1649346672 q^{83} - 935672904 q^{84} + 690159588 q^{86} - 257027500 q^{87} + 191594460 q^{89} + 1842509012 q^{93} + 2877218432 q^{94} + 4413444720 q^{98}+O(q^{100}) \) 24 * q + 5124 * q^4 + 108368 * q^9 - 244832 * q^13 - 127332 * q^15 - 279932 * q^16 + 888764 * q^18 - 2280212 * q^19 + 775748 * q^21 - 2762628 * q^25 - 3334452 * q^26 - 39084792 * q^30 + 2010240 * q^32 - 30349992 * q^33 - 25532364 * q^35 + 31177320 * q^36 - 13171392 * q^38 - 86527192 * q^42 + 61046960 * q^43 - 153365328 * q^47 + 169445876 * q^49 - 236105676 * q^50 - 209898380 * q^52 + 85777812 * q^53 - 255767540 * q^55 - 767709024 * q^59 + 429639656 * q^60 - 1006108924 * q^64 + 346830788 * q^66 - 26076868 * q^67 - 751973532 * q^69 - 319504544 * q^70 - 1171736028 * q^72 - 1640047616 * q^76 - 174401076 * q^77 - 347156560 * q^81 - 1649346672 * q^83 - 935672904 * q^84 + 690159588 * q^86 - 257027500 * q^87 + 191594460 * q^89 + 1842509012 * q^93 + 2877218432 * q^94 + 4413444720 * q^98

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