LMFDB - Embedded newform 289.10.a.f.1.3

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			1.3
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)

$f(q)$	$=$	$q-36.7615 q^{2} -213.730 q^{3} +839.411 q^{4} -2187.52 q^{5} +7857.06 q^{6} -1444.09 q^{7} -12036.1 q^{8} +25997.7 q^{9} +O(q^{10})$	\(q-36.7615 q^{2} -213.730 q^{3} +839.411 q^{4} -2187.52 q^{5} +7857.06 q^{6} -1444.09 q^{7} -12036.1 q^{8} +25997.7 q^{9} +80416.5 q^{10} +76068.6 q^{11} -179408. q^{12} -61852.4 q^{13} +53087.0 q^{14} +467539. q^{15} +12688.8 q^{16} -955716. q^{18} -1.04250e6 q^{19} -1.83623e6 q^{20} +308646. q^{21} -2.79640e6 q^{22} -268917. q^{23} +2.57249e6 q^{24} +2.83211e6 q^{25} +2.27379e6 q^{26} -1.34965e6 q^{27} -1.21219e6 q^{28} -1.72711e6 q^{29} -1.71875e7 q^{30} -3.62660e6 q^{31} +5.69605e6 q^{32} -1.62582e7 q^{33} +3.15897e6 q^{35} +2.18228e7 q^{36} +3.60322e6 q^{37} +3.83239e7 q^{38} +1.32197e7 q^{39} +2.63293e7 q^{40} -2.03275e7 q^{41} -1.13463e7 q^{42} -7.95939e6 q^{43} +6.38528e7 q^{44} -5.68704e7 q^{45} +9.88580e6 q^{46} -4.08106e7 q^{47} -2.71199e6 q^{48} -3.82682e7 q^{49} -1.04113e8 q^{50} -5.19196e7 q^{52} +3.85473e7 q^{53} +4.96151e7 q^{54} -1.66401e8 q^{55} +1.73813e7 q^{56} +2.22814e8 q^{57} +6.34913e7 q^{58} -1.05644e8 q^{59} +3.92458e8 q^{60} +2.55609e7 q^{61} +1.33319e8 q^{62} -3.75430e7 q^{63} -2.15892e8 q^{64} +1.35303e8 q^{65} +5.97676e8 q^{66} +2.50869e8 q^{67} +5.74757e7 q^{69} -1.16129e8 q^{70} +8.45350e7 q^{71} -3.12912e8 q^{72} +1.68335e8 q^{73} -1.32460e8 q^{74} -6.05307e8 q^{75} -8.75087e8 q^{76} -1.09850e8 q^{77} -4.85978e8 q^{78} +5.45797e8 q^{79} -2.77570e7 q^{80} -2.23252e8 q^{81} +7.47272e8 q^{82} -4.07060e8 q^{83} +2.59081e8 q^{84} +2.92599e8 q^{86} +3.69136e8 q^{87} -9.15573e8 q^{88} +4.72366e8 q^{89} +2.09065e9 q^{90} +8.93203e7 q^{91} -2.25732e8 q^{92} +7.75114e8 q^{93} +1.50026e9 q^{94} +2.28049e9 q^{95} -1.21742e9 q^{96} +4.11050e8 q^{97} +1.40680e9 q^{98} +1.97761e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−36.7615	−1.62465	−0.812323	−	0.583208i	$-0.801797\pi$
$2$	−36.7615	−1.62465	−0.812323	+	0.583208i	$0.801797\pi$
$3$	−213.730	−1.52342	−0.761712	−	0.647916i	$-0.775641\pi$
$3$	−213.730	−1.52342	−0.761712	+	0.647916i	$0.775641\pi$
$4$	839.411	1.63948
$5$	−2187.52	−1.56526	−0.782630	−	0.622487i	$-0.786122\pi$
$5$	−2187.52	−1.56526	−0.782630	+	0.622487i	$0.786122\pi$
$6$	7857.06	2.47503
$7$	−1444.09	−0.227328	−0.113664	−	0.993519i	$-0.536259\pi$
$7$	−1444.09	−0.227328	−0.113664	+	0.993519i	$0.536259\pi$
$8$	−12036.1	−1.03892
$9$	25997.7	1.32082
$10$	80416.5	2.54299
$11$	76068.6	1.56653	0.783264	−	0.621689i	$-0.213553\pi$
$11$	76068.6	1.56653	0.783264	+	0.621689i	$0.213553\pi$
$12$	−179408.	−2.49762
$13$	−61852.4	−0.600636	−0.300318	−	0.953839i	$-0.597093\pi$
$13$	−61852.4	−0.600636	−0.300318	+	0.953839i	$0.597093\pi$
$14$	53087.0	0.369328
$15$	467539.	2.38455
$16$	12688.8	0.0484040
$17$	0	0
$17$	0	0
$18$	−955716.	−2.14587
$19$	−1.04250e6	−1.83521	−0.917604	−	0.397497i	$-0.869879\pi$
$19$	−1.04250e6	−1.83521	−0.917604	+	0.397497i	$0.869879\pi$
$20$	−1.83623e6	−2.56620
$21$	308646.	0.346317
$22$	−2.79640e6	−2.54505
$23$	−268917.	−0.200375	−0.100187	−	0.994969i	$-0.531944\pi$
$23$	−268917.	−0.200375	−0.100187	+	0.994969i	$0.531944\pi$
$24$	2.57249e6	1.58272
$25$	2.83211e6	1.45004
$26$	2.27379e6	0.975821
$27$	−1.34965e6	−0.488746
$28$	−1.21219e6	−0.372699
$29$	−1.72711e6	−0.453450	−0.226725	−	0.973959i	$-0.572802\pi$
$29$	−1.72711e6	−0.453450	−0.226725	+	0.973959i	$0.572802\pi$
$30$	−1.71875e7	−3.87406
$31$	−3.62660e6	−0.705297	−0.352648	−	0.935756i	$-0.614719\pi$
$31$	−3.62660e6	−0.705297	−0.352648	+	0.935756i	$0.614719\pi$
$32$	5.69605e6	0.960282
$33$	−1.62582e7	−2.38649
$34$	0	0
$35$	3.15897e6	0.355827
$36$	2.18228e7	2.16545
$37$	3.60322e6	0.316070	0.158035	−	0.987434i	$-0.449484\pi$
$37$	3.60322e6	0.316070	0.158035	+	0.987434i	$0.449484\pi$
$38$	3.83239e7	2.98156
$39$	1.32197e7	0.915023
$40$	2.63293e7	1.62618
$41$	−2.03275e7	−1.12346	−0.561730	−	0.827321i	$-0.689864\pi$
$41$	−2.03275e7	−1.12346	−0.561730	+	0.827321i	$0.689864\pi$
$42$	−1.13463e7	−0.562642
$43$	−7.95939e6	−0.355035	−0.177518	−	0.984118i	$-0.556807\pi$
$43$	−7.95939e6	−0.355035	−0.177518	+	0.984118i	$0.556807\pi$
$44$	6.38528e7	2.56828
$45$	−5.68704e7	−2.06743
$46$	9.88580e6	0.325538
$47$	−4.08106e7	−1.21992	−0.609962	−	0.792431i	$-0.708815\pi$
$47$	−4.08106e7	−1.21992	−0.609962	+	0.792431i	$0.708815\pi$
$48$	−2.71199e6	−0.0737398
$49$	−3.82682e7	−0.948322
$50$	−1.04113e8	−2.35580
$51$	0	0
$52$	−5.19196e7	−0.984728
$53$	3.85473e7	0.671047	0.335523	−	0.942032i	$-0.391087\pi$
$53$	3.85473e7	0.671047	0.335523	+	0.942032i	$0.391087\pi$
$54$	4.96151e7	0.794039
$55$	−1.66401e8	−2.45202
$56$	1.73813e7	0.236176
$57$	2.22814e8	2.79580
$58$	6.34913e7	0.736696
$59$	−1.05644e8	−1.13504	−0.567520	−	0.823360i	$-0.692097\pi$
$59$	−1.05644e8	−1.13504	−0.567520	+	0.823360i	$0.692097\pi$
$60$	3.92458e8	3.90942
$61$	2.55609e7	0.236370	0.118185	−	0.992992i	$-0.462292\pi$
$61$	2.55609e7	0.236370	0.118185	+	0.992992i	$0.462292\pi$
$62$	1.33319e8	1.14586
$63$	−3.75430e7	−0.300260
$64$	−2.15892e8	−1.60852
$65$	1.35303e8	0.940151
$66$	5.97676e8	3.87720
$67$	2.50869e8	1.52094	0.760468	−	0.649376i	$-0.224970\pi$
$67$	2.50869e8	1.52094	0.760468	+	0.649376i	$0.224970\pi$
$68$	0	0
$69$	5.74757e7	0.305256
$70$	−1.16129e8	−0.578094
$71$	8.45350e7	0.394797	0.197398	−	0.980323i	$-0.436751\pi$
$71$	8.45350e7	0.394797	0.197398	+	0.980323i	$0.436751\pi$
$72$	−3.12912e8	−1.37223
$73$	1.68335e8	0.693781	0.346890	−	0.937906i	$-0.387238\pi$
$73$	1.68335e8	0.693781	0.346890	+	0.937906i	$0.387238\pi$
$74$	−1.32460e8	−0.513502
$75$	−6.05307e8	−2.20902
$76$	−8.75087e8	−3.00878
$77$	−1.09850e8	−0.356116
$78$	−4.85978e8	−1.48659
$79$	5.45797e8	1.57656	0.788278	−	0.615319i	$-0.210973\pi$
$79$	5.45797e8	1.57656	0.788278	+	0.615319i	$0.210973\pi$
$80$	−2.77570e7	−0.0757648
$81$	−2.23252e8	−0.576253
$82$	7.47272e8	1.82522
$83$	−4.07060e8	−0.941471	−0.470736	−	0.882274i	$-0.656011\pi$
$83$	−4.07060e8	−0.941471	−0.470736	+	0.882274i	$0.656011\pi$
$84$	2.59081e8	0.567778
$85$	0	0
$86$	2.92599e8	0.576807
$87$	3.69136e8	0.690797
$88$	−9.15573e8	−1.62750
$89$	4.72366e8	0.798039	0.399019	−	0.916943i	$-0.369351\pi$
$89$	4.72366e8	0.798039	0.399019	+	0.916943i	$0.369351\pi$
$90$	2.09065e9	3.35884
$91$	8.93203e7	0.136541
$92$	−2.25732e8	−0.328509
$93$	7.75114e8	1.07447
$94$	1.50026e9	1.98194
$95$	2.28049e9	2.87258
$96$	−1.21742e9	−1.46292
$97$	4.11050e8	0.471435	0.235717	−	0.971822i	$-0.424256\pi$
$97$	4.11050e8	0.471435	0.235717	+	0.971822i	$0.424256\pi$
$98$	1.40680e9	1.54069
$99$	1.97761e9	2.06910
$100$	2.37730e9	2.37730
$101$	−3.41004e8	−0.326072	−0.163036	−	0.986620i	$-0.552129\pi$
$101$	−3.41004e8	−0.326072	−0.163036	+	0.986620i	$0.552129\pi$
$102$	0	0
$103$	1.07921e9	0.944793	0.472396	−	0.881386i	$-0.343389\pi$
$103$	1.07921e9	0.944793	0.472396	+	0.881386i	$0.343389\pi$
$104$	7.44464e8	0.624013
$105$	−6.75168e8	−0.542076
$106$	−1.41706e9	−1.09021
$107$	7.60659e8	0.561000	0.280500	−	0.959854i	$-0.409500\pi$
$107$	7.60659e8	0.561000	0.280500	+	0.959854i	$0.409500\pi$
$108$	−1.13291e9	−0.801287
$109$	−3.33332e8	−0.226182	−0.113091	−	0.993585i	$-0.536075\pi$
$109$	−3.33332e8	−0.226182	−0.113091	+	0.993585i	$0.536075\pi$
$110$	6.11717e9	3.98367
$111$	−7.70118e8	−0.481508
$112$	−1.83238e7	−0.0110036
$113$	−1.15105e9	−0.664114	−0.332057	−	0.943259i	$-0.607743\pi$
$113$	−1.15105e9	−0.664114	−0.332057	+	0.943259i	$0.607743\pi$
$114$	−8.19099e9	−4.54218
$115$	5.88260e8	0.313638
$116$	−1.44976e9	−0.743420
$117$	−1.60802e9	−0.793332
$118$	3.88364e9	1.84404
$119$	0	0
$120$	−5.62737e9	−2.47736
$121$	3.42848e9	1.45401
$122$	−9.39660e8	−0.384018
$123$	4.34461e9	1.71150
$124$	−3.04421e9	−1.15632
$125$	−1.92278e9	−0.704426
$126$	1.38014e9	0.487815
$127$	4.73219e8	0.161416	0.0807078	−	0.996738i	$-0.474282\pi$
$127$	4.73219e8	0.161416	0.0807078	+	0.996738i	$0.474282\pi$
$128$	5.02015e9	1.65300
$129$	1.70116e9	0.540869
$130$	−4.97395e9	−1.52741
$131$	−1.66746e9	−0.494692	−0.247346	−	0.968927i	$-0.579558\pi$
$131$	−1.66746e9	−0.494692	−0.247346	+	0.968927i	$0.579558\pi$
$132$	−1.36473e10	−3.91259
$133$	1.50546e9	0.417194
$134$	−9.22234e9	−2.47098
$135$	2.95238e9	0.765014
$136$	0	0
$137$	−2.29550e9	−0.556718	−0.278359	−	0.960477i	$-0.589790\pi$
$137$	−2.29550e9	−0.556718	−0.278359	+	0.960477i	$0.589790\pi$
$138$	−2.11290e9	−0.495932
$139$	2.75010e9	0.624858	0.312429	−	0.949941i	$-0.398857\pi$
$139$	2.75010e9	0.624858	0.312429	+	0.949941i	$0.398857\pi$
$140$	2.65168e9	0.583370
$141$	8.72247e9	1.85846
$142$	−3.10764e9	−0.641405
$143$	−4.70502e9	−0.940913
$144$	3.29880e8	0.0639330
$145$	3.77809e9	0.709767
$146$	−6.18826e9	−1.12715
$147$	8.17908e9	1.44470
$148$	3.02458e9	0.518189
$149$	3.61630e9	0.601072	0.300536	−	0.953771i	$-0.402835\pi$
$149$	3.61630e9	0.601072	0.300536	+	0.953771i	$0.402835\pi$
$150$	2.22520e10	3.58888
$151$	−5.46695e9	−0.855754	−0.427877	−	0.903837i	$-0.640738\pi$
$151$	−5.46695e9	−0.855754	−0.427877	+	0.903837i	$0.640738\pi$
$152$	1.25477e10	1.90664
$153$	0	0
$154$	4.03825e9	0.578562
$155$	7.93324e9	1.10397
$156$	1.10968e10	1.50016
$157$	−1.17900e10	−1.54869	−0.774343	−	0.632766i	$-0.781920\pi$
$157$	−1.17900e10	−1.54869	−0.774343	+	0.632766i	$0.781920\pi$
$158$	−2.00643e10	−2.56135
$159$	−8.23874e9	−1.02229
$160$	−1.24602e10	−1.50309
$161$	3.88340e8	0.0455508
$162$	8.20710e9	0.936208
$163$	1.51657e10	1.68274	0.841372	−	0.540457i	$-0.181749\pi$
$163$	1.51657e10	1.68274	0.841372	+	0.540457i	$0.181749\pi$
$164$	−1.70632e10	−1.84188
$165$	3.55650e10	3.73547
$166$	1.49642e10	1.52956
$167$	4.44343e9	0.442074	0.221037	−	0.975265i	$-0.429056\pi$
$167$	4.44343e9	0.442074	0.221037	+	0.975265i	$0.429056\pi$
$168$	−3.71491e9	−0.359796
$169$	−6.77878e9	−0.639237
$170$	0	0
$171$	−2.71026e10	−2.42398
$172$	−6.68120e9	−0.582072
$173$	1.63618e10	1.38875	0.694375	−	0.719614i	$-0.255681\pi$
$173$	1.63618e10	1.38875	0.694375	+	0.719614i	$0.255681\pi$
$174$	−1.35700e10	−1.12230
$175$	−4.08981e9	−0.329634
$176$	9.65220e8	0.0758262
$177$	2.25793e10	1.72915
$178$	−1.73649e10	−1.29653
$179$	−2.95047e9	−0.214809	−0.107405	−	0.994215i	$-0.534254\pi$
$179$	−2.95047e9	−0.214809	−0.107405	+	0.994215i	$0.534254\pi$
$180$	−4.77377e10	−3.38950
$181$	−1.44907e9	−0.100354	−0.0501772	−	0.998740i	$-0.515979\pi$
$181$	−1.44907e9	−0.100354	−0.0501772	+	0.998740i	$0.515979\pi$
$182$	−3.28355e9	−0.221831
$183$	−5.46315e9	−0.360092
$184$	3.23672e9	0.208174
$185$	−7.88210e9	−0.494731
$186$	−2.84944e10	−1.74563
$187$	0	0
$188$	−3.42569e10	−2.00003
$189$	1.94901e9	0.111106
$190$	−8.38343e10	−4.66692
$191$	−1.50851e10	−0.820161	−0.410081	−	0.912049i	$-0.634499\pi$
$191$	−1.50851e10	−0.820161	−0.410081	+	0.912049i	$0.634499\pi$
$192$	4.61427e10	2.45046
$193$	2.45613e10	1.27422	0.637109	−	0.770774i	$-0.280130\pi$
$193$	2.45613e10	1.27422	0.637109	+	0.770774i	$0.280130\pi$
$194$	−1.51108e10	−0.765914
$195$	−2.89184e10	−1.43225
$196$	−3.21228e10	−1.55475
$197$	−4.88429e9	−0.231049	−0.115524	−	0.993305i	$-0.536855\pi$
$197$	−4.88429e9	−0.231049	−0.115524	+	0.993305i	$0.536855\pi$
$198$	−7.27000e10	−3.36156
$199$	−1.63908e10	−0.740903	−0.370451	−	0.928852i	$-0.620797\pi$
$199$	−1.63908e10	−0.740903	−0.370451	+	0.928852i	$0.620797\pi$
$200$	−3.40876e10	−1.50647
$201$	−5.36184e10	−2.31703
$202$	1.25358e10	0.529751
$203$	2.49410e9	0.103082
$204$	0	0
$205$	4.44668e10	1.75851
$206$	−3.96733e10	−1.53495
$207$	−6.99123e9	−0.264659
$208$	−7.84833e8	−0.0290732
$209$	−7.93016e10	−2.87490
$210$	2.48202e10	0.880682
$211$	4.02197e10	1.39691	0.698454	−	0.715655i	$-0.253872\pi$
$211$	4.02197e10	1.39691	0.698454	+	0.715655i	$0.253872\pi$
$212$	3.23571e10	1.10016
$213$	−1.80677e10	−0.601443
$214$	−2.79630e10	−0.911426
$215$	1.74113e10	0.555722
$216$	1.62445e10	0.507769
$217$	5.23713e9	0.160334
$218$	1.22538e10	0.367465
$219$	−3.59784e10	−1.05692
$220$	−1.39679e11	−4.02003
$221$	0	0
$222$	2.83107e10	0.782281
$223$	3.40332e10	0.921575	0.460788	−	0.887510i	$-0.347567\pi$
$223$	3.40332e10	0.921575	0.460788	+	0.887510i	$0.347567\pi$
$224$	−8.22560e9	−0.218299
$225$	7.36283e10	1.91524
$226$	4.23145e10	1.07895
$227$	−5.23971e9	−0.130976	−0.0654879	−	0.997853i	$-0.520860\pi$
$227$	−5.23971e9	−0.130976	−0.0654879	+	0.997853i	$0.520860\pi$
$228$	1.87033e11	4.58364
$229$	6.10304e10	1.46652	0.733258	−	0.679950i	$-0.237999\pi$
$229$	6.10304e10	1.46652	0.733258	+	0.679950i	$0.237999\pi$
$230$	−2.16254e10	−0.509551
$231$	2.34783e10	0.542515
$232$	2.07878e10	0.471099
$233$	2.08286e10	0.462976	0.231488	−	0.972838i	$-0.425641\pi$
$233$	2.08286e10	0.462976	0.231488	+	0.972838i	$0.425641\pi$
$234$	5.91133e10	1.28888
$235$	8.92739e10	1.90950
$236$	−8.86788e10	−1.86087
$237$	−1.16653e11	−2.40176
$238$	0	0
$239$	−2.41341e10	−0.478454	−0.239227	−	0.970964i	$-0.576894\pi$
$239$	−2.41341e10	−0.478454	−0.239227	+	0.970964i	$0.576894\pi$
$240$	5.93252e9	0.115422
$241$	−5.01148e10	−0.956950	−0.478475	−	0.878101i	$-0.658810\pi$
$241$	−5.01148e10	−0.956950	−0.478475	+	0.878101i	$0.658810\pi$
$242$	−1.26036e11	−2.36225
$243$	7.42809e10	1.36662
$244$	2.14561e10	0.387523
$245$	8.37124e10	1.48437
$246$	−1.59715e11	−2.78059
$247$	6.44811e10	1.10229
$248$	4.36503e10	0.732748
$249$	8.70011e10	1.43426
$250$	7.06845e10	1.14444
$251$	−2.66112e10	−0.423187	−0.211594	−	0.977358i	$-0.567865\pi$
$251$	−2.66112e10	−0.423187	−0.211594	+	0.977358i	$0.567865\pi$
$252$	−3.15140e10	−0.492268
$253$	−2.04561e10	−0.313893
$254$	−1.73963e10	−0.262243
$255$	0	0
$256$	−7.40119e10	−1.07701
$257$	−1.12286e9	−0.0160555	−0.00802777	−	0.999968i	$-0.502555\pi$
$257$	−1.12286e9	−0.0160555	−0.00802777	+	0.999968i	$0.502555\pi$
$258$	−6.25374e10	−0.878721
$259$	−5.20337e9	−0.0718515
$260$	1.13575e11	1.54135
$261$	−4.49010e10	−0.598926
$262$	6.12984e10	0.803699
$263$	3.28551e10	0.423450	0.211725	−	0.977329i	$-0.432092\pi$
$263$	3.28551e10	0.423450	0.211725	+	0.977329i	$0.432092\pi$
$264$	1.95686e11	2.47937
$265$	−8.43229e10	−1.05036
$266$	−5.53432e10	−0.677793
$267$	−1.00959e11	−1.21575
$268$	2.10582e11	2.49354
$269$	−1.05339e11	−1.22660	−0.613302	−	0.789849i	$-0.710159\pi$
$269$	−1.05339e11	−1.22660	−0.613302	+	0.789849i	$0.710159\pi$
$270$	−1.08534e11	−1.24288
$271$	1.63792e11	1.84473	0.922363	−	0.386324i	$-0.126255\pi$
$271$	1.63792e11	1.84473	0.922363	+	0.386324i	$0.126255\pi$
$272$	0	0
$273$	−1.90905e10	−0.208010
$274$	8.43862e10	0.904470
$275$	2.15434e11	2.27153
$276$	4.82458e10	0.500459
$277$	−1.17006e10	−0.119412	−0.0597062	−	0.998216i	$-0.519016\pi$
$277$	−1.17006e10	−0.119412	−0.0597062	+	0.998216i	$0.519016\pi$
$278$	−1.01098e11	−1.01517
$279$	−9.42833e10	−0.931570
$280$	−3.80218e10	−0.369677
$281$	−6.90962e10	−0.661113	−0.330556	−	0.943786i	$-0.607236\pi$
$281$	−6.90962e10	−0.661113	−0.330556	+	0.943786i	$0.607236\pi$
$282$	−3.20652e11	−3.01934
$283$	7.96561e10	0.738210	0.369105	−	0.929388i	$-0.379664\pi$
$283$	7.96561e10	0.738210	0.369105	+	0.929388i	$0.379664\pi$
$284$	7.09596e10	0.647260
$285$	−4.87410e11	−4.37615
$286$	1.72964e11	1.52865
$287$	2.93548e10	0.255394
$288$	1.48084e11	1.26836
$289$	0	0
$290$	−1.38888e11	−1.15312
$291$	−8.78538e10	−0.718195
$292$	1.41302e11	1.13744
$293$	−2.06133e10	−0.163396	−0.0816982	−	0.996657i	$-0.526034\pi$
$293$	−2.06133e10	−0.163396	−0.0816982	+	0.996657i	$0.526034\pi$
$294$	−3.00676e11	−2.34712
$295$	2.31098e11	1.77663
$296$	−4.33689e10	−0.328372
$297$	−1.02666e11	−0.765635
$298$	−1.32941e11	−0.976529
$299$	1.66331e10	0.120352
$300$	−5.08102e11	−3.62164
$301$	1.14941e10	0.0807095
$302$	2.00974e11	1.39030
$303$	7.28829e10	0.496745
$304$	−1.32281e10	−0.0888313
$305$	−5.59150e10	−0.369981
$306$	0	0
$307$	1.72164e10	0.110616	0.0553082	−	0.998469i	$-0.482386\pi$
$307$	1.72164e10	0.110616	0.0553082	+	0.998469i	$0.482386\pi$
$308$	−9.22092e10	−0.583843
$309$	−2.30659e11	−1.43932
$310$	−2.91638e11	−1.79356
$311$	−1.66456e11	−1.00897	−0.504484	−	0.863421i	$-0.668317\pi$
$311$	−1.66456e11	−1.00897	−0.504484	+	0.863421i	$0.668317\pi$
$312$	−1.59115e11	−0.950637
$313$	7.12162e9	0.0419401	0.0209700	−	0.999780i	$-0.493325\pi$
$313$	7.12162e9	0.0419401	0.0209700	+	0.999780i	$0.493325\pi$
$314$	4.33417e11	2.51607
$315$	8.21260e10	0.469984
$316$	4.58148e11	2.58472
$317$	−1.45481e11	−0.809168	−0.404584	−	0.914501i	$-0.632584\pi$
$317$	−1.45481e11	−0.809168	−0.404584	+	0.914501i	$0.632584\pi$
$318$	3.02869e11	1.66086
$319$	−1.31379e11	−0.710342
$320$	4.72268e11	2.51775
$321$	−1.62576e11	−0.854641
$322$	−1.42760e10	−0.0740039
$323$	0	0
$324$	−1.87401e11	−0.944753
$325$	−1.75172e11	−0.870945
$326$	−5.57514e11	−2.73386
$327$	7.12432e10	0.344571
$328$	2.44665e11	1.16719
$329$	5.89342e10	0.277323
$330$	−1.30743e12	−6.06882
$331$	9.98473e9	0.0457204	0.0228602	−	0.999739i	$-0.492723\pi$
$331$	9.98473e9	0.0457204	0.0228602	+	0.999739i	$0.492723\pi$
$332$	−3.41691e11	−1.54352
$333$	9.36755e10	0.417472
$334$	−1.63348e11	−0.718213
$335$	−5.48781e11	−2.38066
$336$	3.91635e9	0.0167631
$337$	3.39255e11	1.43282	0.716410	−	0.697680i	$-0.245784\pi$
$337$	3.39255e11	1.43282	0.716410	+	0.697680i	$0.245784\pi$
$338$	2.49199e11	1.03853
$339$	2.46015e11	1.01173
$340$	0	0
$341$	−2.75870e11	−1.10487
$342$	9.96335e11	3.93811
$343$	1.13537e11	0.442908
$344$	9.58004e10	0.368854
$345$	−1.25729e11	−0.477804
$346$	−6.01485e11	−2.25623
$347$	3.40416e11	1.26046	0.630228	−	0.776410i	$-0.282961\pi$
$347$	3.40416e11	1.26046	0.630228	+	0.776410i	$0.282961\pi$
$348$	3.09857e11	1.13254
$349$	3.97277e11	1.43344	0.716719	−	0.697363i	$-0.245643\pi$
$349$	3.97277e11	1.43344	0.716719	+	0.697363i	$0.245643\pi$
$350$	1.50348e11	0.535539
$351$	8.34788e10	0.293558
$352$	4.33290e11	1.50431
$353$	−1.64439e11	−0.563661	−0.281831	−	0.959464i	$-0.590942\pi$
$353$	−1.64439e11	−0.563661	−0.281831	+	0.959464i	$0.590942\pi$
$354$	−8.30052e11	−2.80925
$355$	−1.84922e11	−0.617960
$356$	3.96510e11	1.30836
$357$	0	0
$358$	1.08464e11	0.348989
$359$	−5.88255e11	−1.86914	−0.934568	−	0.355785i	$-0.884214\pi$
$359$	−5.88255e11	−1.86914	−0.934568	+	0.355785i	$0.884214\pi$
$360$	6.84501e11	2.14789
$361$	7.64120e11	2.36799
$362$	5.32701e10	0.163040
$363$	−7.32771e11	−2.21508
$364$	7.49765e10	0.223856
$365$	−3.68236e11	−1.08595
$366$	2.00834e11	0.585022
$367$	2.24905e10	0.0647146	0.0323573	−	0.999476i	$-0.489699\pi$
$367$	2.24905e10	0.0647146	0.0323573	+	0.999476i	$0.489699\pi$
$368$	−3.41224e9	−0.00969893
$369$	−5.28469e11	−1.48389
$370$	2.89758e11	0.803763
$371$	−5.56658e10	−0.152548
$372$	6.50640e11	1.76156
$373$	−2.68589e11	−0.718452	−0.359226	−	0.933251i	$-0.616959\pi$
$373$	−2.68589e11	−0.718452	−0.359226	+	0.933251i	$0.616959\pi$
$374$	0	0
$375$	4.10957e11	1.07314
$376$	4.91203e11	1.26740
$377$	1.06826e11	0.272358
$378$	−7.16487e10	−0.180507
$379$	−1.22563e11	−0.305129	−0.152564	−	0.988294i	$-0.548753\pi$
$379$	−1.22563e11	−0.305129	−0.152564	+	0.988294i	$0.548753\pi$
$380$	1.91427e12	4.70952
$381$	−1.01141e11	−0.245904
$382$	5.54553e11	1.33247
$383$	8.38894e11	1.99211	0.996054	−	0.0887531i	$-0.0282882\pi$
$383$	8.38894e11	1.99211	0.996054	+	0.0887531i	$0.0282882\pi$
$384$	−1.07296e12	−2.51822
$385$	2.40298e11	0.557414
$386$	−9.02911e11	−2.07015
$387$	−2.06926e11	−0.468938
$388$	3.45040e11	0.772905
$389$	4.49034e11	0.994274	0.497137	−	0.867672i	$-0.334385\pi$
$389$	4.49034e11	0.994274	0.497137	+	0.867672i	$0.334385\pi$
$390$	1.06308e12	2.32690
$391$	0	0
$392$	4.60602e11	0.985232
$393$	3.56387e11	0.753625
$394$	1.79554e11	0.375372
$395$	−1.19394e12	−2.46772
$396$	1.66003e12	3.39224
$397$	−8.36506e11	−1.69010	−0.845049	−	0.534690i	$-0.820429\pi$
$397$	−8.36506e11	−1.69010	−0.845049	+	0.534690i	$0.820429\pi$
$398$	6.02551e11	1.20371
$399$	−3.21764e11	−0.635563
$400$	3.59361e10	0.0701876
$401$	5.39834e11	1.04258	0.521292	−	0.853378i	$-0.325450\pi$
$401$	5.39834e11	1.04258	0.521292	+	0.853378i	$0.325450\pi$
$402$	1.97109e12	3.76435
$403$	2.24314e11	0.423626
$404$	−2.86242e11	−0.534586
$405$	4.88368e11	0.901986
$406$	−9.16871e10	−0.167472
$407$	2.74092e11	0.495132
$408$	0	0
$409$	2.38000e11	0.420554	0.210277	−	0.977642i	$-0.432563\pi$
$409$	2.38000e11	0.420554	0.210277	+	0.977642i	$0.432563\pi$
$410$	−1.63467e12	−2.85695
$411$	4.90619e11	0.848117
$412$	9.05897e11	1.54896
$413$	1.52559e11	0.258026
$414$	2.57008e11	0.429977
$415$	8.90451e11	1.47365
$416$	−3.52314e11	−0.576780
$417$	−5.87780e11	−0.951924
$418$	2.91525e12	4.67070
$419$	1.23101e12	1.95119	0.975595	−	0.219577i	$-0.0704678\pi$
$419$	1.23101e12	1.95119	0.975595	+	0.219577i	$0.0704678\pi$
$420$	−5.66744e11	−0.888720
$421$	6.84349e11	1.06172	0.530858	−	0.847461i	$-0.321870\pi$
$421$	6.84349e11	1.06172	0.530858	+	0.847461i	$0.321870\pi$
$422$	−1.47854e12	−2.26948
$423$	−1.06098e12	−1.61130
$424$	−4.63961e11	−0.697165
$425$	0	0
$426$	6.64196e11	0.977132
$427$	−3.69123e10	−0.0537335
$428$	6.38506e11	0.919746
$429$	1.00561e12	1.43341
$430$	−6.40066e11	−0.902852
$431$	7.29846e11	1.01879	0.509394	−	0.860534i	$-0.329870\pi$
$431$	7.29846e11	1.01879	0.509394	+	0.860534i	$0.329870\pi$
$432$	−1.71254e10	−0.0236573
$433$	5.77752e11	0.789852	0.394926	−	0.918713i	$-0.370770\pi$
$433$	5.77752e11	0.789852	0.394926	+	0.918713i	$0.370770\pi$
$434$	−1.92525e11	−0.260485
$435$	−8.07492e11	−1.08128
$436$	−2.79802e11	−0.370819
$437$	2.80346e11	0.367729
$438$	1.32262e12	1.71712
$439$	2.38170e11	0.306053	0.153026	−	0.988222i	$-0.451098\pi$
$439$	2.38170e11	0.306053	0.153026	+	0.988222i	$0.451098\pi$
$440$	2.00283e12	2.54746
$441$	−9.94886e11	−1.25256
$442$	0	0
$443$	1.23250e12	1.52044	0.760220	−	0.649665i	$-0.225091\pi$
$443$	1.23250e12	1.52044	0.760220	+	0.649665i	$0.225091\pi$
$444$	−6.46446e11	−0.789421
$445$	−1.03331e12	−1.24914
$446$	−1.25111e12	−1.49723
$447$	−7.72913e11	−0.915687
$448$	3.11768e11	0.365662
$449$	−3.36220e11	−0.390405	−0.195203	−	0.980763i	$-0.562536\pi$
$449$	−3.36220e11	−0.390405	−0.195203	+	0.980763i	$0.562536\pi$
$450$	−2.70669e12	−3.11159
$451$	−1.54629e12	−1.75993
$452$	−9.66208e11	−1.08880
$453$	1.16845e12	1.30368
$454$	1.92620e11	0.212789
$455$	−1.95390e11	−0.213723
$456$	−2.68182e12	−2.90461
$457$	−5.70226e11	−0.611539	−0.305769	−	0.952106i	$-0.598914\pi$
$457$	−5.70226e11	−0.611539	−0.305769	+	0.952106i	$0.598914\pi$
$458$	−2.24357e12	−2.38257
$459$	0	0
$460$	4.93792e11	0.514202
$461$	1.88591e12	1.94476	0.972380	−	0.233403i	$-0.0749860\pi$
$461$	1.88591e12	1.94476	0.972380	+	0.233403i	$0.0749860\pi$
$462$	−8.63097e11	−0.881396
$463$	−2.34282e11	−0.236932	−0.118466	−	0.992958i	$-0.537798\pi$
$463$	−2.34282e11	−0.236932	−0.118466	+	0.992958i	$0.537798\pi$
$464$	−2.19150e10	−0.0219488
$465$	−1.69558e12	−1.68182
$466$	−7.65692e11	−0.752172
$467$	−4.47116e11	−0.435005	−0.217503	−	0.976060i	$-0.569791\pi$
$467$	−4.47116e11	−0.435005	−0.217503	+	0.976060i	$0.569791\pi$
$468$	−1.34979e12	−1.30065
$469$	−3.62278e11	−0.345751
$470$	−3.28185e12	−3.10226
$471$	2.51987e12	2.35931
$472$	1.27155e12	1.17922
$473$	−6.05459e11	−0.556173
$474$	4.28836e12	3.90201
$475$	−2.95247e12	−2.66112
$476$	0	0
$477$	1.00214e12	0.886332
$478$	8.87207e11	0.777319
$479$	−9.74596e11	−0.845892	−0.422946	−	0.906155i	$-0.639004\pi$
$479$	−9.74596e11	−0.845892	−0.422946	+	0.906155i	$0.639004\pi$
$480$	2.66312e12	2.28984
$481$	−2.22868e11	−0.189843
$482$	1.84230e12	1.55471
$483$	−8.30001e10	−0.0693931
$484$	2.87791e12	2.38382
$485$	−8.99178e11	−0.737918
$486$	−2.73068e12	−2.22028
$487$	−3.54345e11	−0.285460	−0.142730	−	0.989762i	$-0.545588\pi$
$487$	−3.54345e11	−0.285460	−0.142730	+	0.989762i	$0.545588\pi$
$488$	−3.07655e11	−0.245570
$489$	−3.24137e12	−2.56353
$490$	−3.07740e12	−2.41158
$491$	−1.43848e12	−1.11696	−0.558480	−	0.829518i	$-0.688615\pi$
$491$	−1.43848e12	−1.11696	−0.558480	+	0.829518i	$0.688615\pi$
$492$	3.64692e12	2.80597
$493$	0	0
$494$	−2.37043e12	−1.79083
$495$	−4.32605e12	−3.23868
$496$	−4.60172e10	−0.0341392
$497$	−1.22076e11	−0.0897484
$498$	−3.19830e12	−2.33016
$499$	8.68070e11	0.626761	0.313381	−	0.949628i	$-0.398538\pi$
$499$	8.68070e11	0.626761	0.313381	+	0.949628i	$0.398538\pi$
$500$	−1.61401e12	−1.15489
$501$	−9.49697e11	−0.673466
$502$	9.78268e11	0.687529
$503$	2.73042e12	1.90184	0.950919	−	0.309441i	$-0.100142\pi$
$503$	2.73042e12	1.90184	0.950919	+	0.309441i	$0.100142\pi$
$504$	4.51873e11	0.311946
$505$	7.45952e11	0.510387
$506$	7.51999e11	0.509965
$507$	1.44883e12	0.973828
$508$	3.97226e11	0.264637
$509$	2.31278e12	1.52723	0.763615	−	0.645672i	$-0.223423\pi$
$509$	2.31278e12	1.52723	0.763615	+	0.645672i	$0.223423\pi$
$510$	0	0
$511$	−2.43091e11	−0.157716
$512$	1.50471e11	0.0967694
$513$	1.40701e12	0.896950
$514$	4.12779e10	0.0260846
$515$	−2.36078e12	−1.47885
$516$	1.42798e12	0.886742
$517$	−3.10441e12	−1.91105
$518$	1.91284e11	0.116733
$519$	−3.49702e12	−2.11565
$520$	−1.62853e12	−0.976743
$521$	−3.58544e9	−0.00213193	−0.00106597	−	0.999999i	$-0.500339\pi$
$521$	−3.58544e9	−0.00213193	−0.00106597	+	0.999999i	$0.500339\pi$
$522$	1.65063e12	0.973043
$523$	7.11572e11	0.415873	0.207937	−	0.978142i	$-0.433325\pi$
$523$	7.11572e11	0.415873	0.207937	+	0.978142i	$0.433325\pi$
$524$	−1.39969e12	−0.811035
$525$	8.74118e11	0.502173
$526$	−1.20781e12	−0.687957
$527$	0	0
$528$	−2.06297e11	−0.115515
$529$	−1.72884e12	−0.959850
$530$	3.09984e12	1.70647
$531$	−2.74650e12	−1.49918
$532$	1.26370e12	0.683979
$533$	1.25731e12	0.674790
$534$	3.71141e12	1.97517
$535$	−1.66395e12	−0.878111
$536$	−3.01950e12	−1.58013
$537$	6.30605e11	0.327245
$538$	3.87243e12	1.99280
$539$	−2.91101e12	−1.48557
$540$	2.47826e12	1.25422
$541$	2.33946e12	1.17416	0.587081	−	0.809528i	$-0.300277\pi$
$541$	2.33946e12	1.17416	0.587081	+	0.809528i	$0.300277\pi$
$542$	−6.02126e12	−2.99703
$543$	3.09711e11	0.152882
$544$	0	0
$545$	7.29169e11	0.354033
$546$	7.01796e11	0.337943
$547$	−1.42156e12	−0.678928	−0.339464	−	0.940619i	$-0.610246\pi$
$547$	−1.42156e12	−0.678928	−0.339464	+	0.940619i	$0.610246\pi$
$548$	−1.92687e12	−0.912725
$549$	6.64526e11	0.312203
$550$	−7.91970e12	−3.69043
$551$	1.80051e12	0.832175
$552$	−6.91787e11	−0.317137
$553$	−7.88180e11	−0.358395
$554$	4.30132e11	0.194003
$555$	1.68465e12	0.753685
$556$	2.30846e12	1.02444
$557$	4.32681e11	0.190467	0.0952334	−	0.995455i	$-0.469640\pi$
$557$	4.32681e11	0.190467	0.0952334	+	0.995455i	$0.469640\pi$
$558$	3.46600e12	1.51347
$559$	4.92307e11	0.213247
$560$	4.00836e10	0.0172235
$561$	0	0
$562$	2.54008e12	1.07407
$563$	9.29044e11	0.389716	0.194858	−	0.980831i	$-0.437575\pi$
$563$	9.29044e11	0.389716	0.194858	+	0.980831i	$0.437575\pi$
$564$	7.32174e12	3.04690
$565$	2.51795e12	1.03951
$566$	−2.92828e12	−1.19933
$567$	3.22396e11	0.130999
$568$	−1.01748e12	−0.410163
$569$	−7.31058e11	−0.292379	−0.146190	−	0.989257i	$-0.546701\pi$
$569$	−7.31058e11	−0.292379	−0.146190	+	0.989257i	$0.546701\pi$
$570$	1.79179e13	7.10970
$571$	−1.97247e12	−0.776510	−0.388255	−	0.921552i	$-0.626922\pi$
$571$	−1.97247e12	−0.776510	−0.388255	+	0.921552i	$0.626922\pi$
$572$	−3.94945e12	−1.54260
$573$	3.22415e12	1.24945
$574$	−1.07913e12	−0.414924
$575$	−7.61601e11	−0.290551
$576$	−5.61270e12	−2.12457
$577$	4.96540e12	1.86493	0.932467	−	0.361256i	$-0.117652\pi$
$577$	4.96540e12	1.86493	0.932467	+	0.361256i	$0.117652\pi$
$578$	0	0
$579$	−5.24950e12	−1.94117
$580$	3.17137e12	1.16365
$581$	5.87831e11	0.214023
$582$	3.22964e12	1.16681
$583$	2.93224e12	1.05121
$584$	−2.02611e12	−0.720783
$585$	3.51757e12	1.24177
$586$	7.57776e11	0.265461
$587$	−3.66373e12	−1.27366	−0.636829	−	0.771005i	$-0.719754\pi$
$587$	−3.66373e12	−1.27366	−0.636829	+	0.771005i	$0.719754\pi$
$588$	6.86562e12	2.36854
$589$	3.78073e12	1.29437
$590$	−8.49552e12	−2.88640
$591$	1.04392e12	0.351985
$592$	4.57206e10	0.0152990
$593$	−4.77019e12	−1.58413	−0.792063	−	0.610439i	$-0.790993\pi$
$593$	−4.77019e12	−1.58413	−0.792063	+	0.610439i	$0.790993\pi$
$594$	3.77415e12	1.24389
$595$	0	0
$596$	3.03556e12	0.985442
$597$	3.50321e12	1.12871
$598$	−6.11460e11	−0.195530
$599$	1.72396e12	0.547150	0.273575	−	0.961851i	$-0.411794\pi$
$599$	1.72396e12	0.547150	0.273575	+	0.961851i	$0.411794\pi$
$600$	7.28557e12	2.29500
$601$	−5.24790e12	−1.64078	−0.820391	−	0.571803i	$-0.806244\pi$
$601$	−5.24790e12	−1.64078	−0.820391	+	0.571803i	$0.806244\pi$
$602$	−4.22540e11	−0.131124
$603$	6.52202e12	2.00888
$604$	−4.58902e12	−1.40299
$605$	−7.49987e12	−2.27591
$606$	−2.67929e12	−0.807036
$607$	−5.70610e12	−1.70604	−0.853021	−	0.521876i	$-0.825232\pi$
$607$	−5.70610e12	−1.70604	−0.853021	+	0.521876i	$0.825232\pi$
$608$	−5.93813e12	−1.76232
$609$	−5.33066e11	−0.157037
$610$	2.05552e12	0.601088
$611$	2.52423e12	0.732730
$612$	0	0
$613$	−1.99333e12	−0.570173	−0.285086	−	0.958502i	$-0.592022\pi$
$613$	−1.99333e12	−0.570173	−0.285086	+	0.958502i	$0.592022\pi$
$614$	−6.32901e11	−0.179712
$615$	−9.50391e12	−2.67895
$616$	1.32217e12	0.369976
$617$	−3.13683e11	−0.0871381	−0.0435690	−	0.999050i	$-0.513873\pi$
$617$	−3.13683e11	−0.0871381	−0.0435690	+	0.999050i	$0.513873\pi$
$618$	8.47938e12	2.33839
$619$	−2.30202e12	−0.630232	−0.315116	−	0.949053i	$-0.602043\pi$
$619$	−2.30202e12	−0.630232	−0.315116	+	0.949053i	$0.602043\pi$
$620$	6.65926e12	1.80994
$621$	3.62943e11	0.0979323
$622$	6.11918e12	1.63922
$623$	−6.82139e11	−0.181417
$624$	1.67743e11	0.0442908
$625$	−1.32533e12	−0.347428
$626$	−2.61802e11	−0.0681378
$627$	1.69492e13	4.37970
$628$	−9.89662e12	−2.53903
$629$	0	0
$630$	−3.01908e12	−0.763558
$631$	−4.58901e11	−0.115236	−0.0576178	−	0.998339i	$-0.518350\pi$
$631$	−4.58901e11	−0.115236	−0.0576178	+	0.998339i	$0.518350\pi$
$632$	−6.56929e12	−1.63792
$633$	−8.59618e12	−2.12808
$634$	5.34810e12	1.31461
$635$	−1.03517e12	−0.252657
$636$	−6.91569e12	−1.67602
$637$	2.36698e12	0.569596
$638$	4.82969e12	1.15406
$639$	2.19772e12	0.521456
$640$	−1.09817e13	−2.58737
$641$	−1.02918e12	−0.240785	−0.120392	−	0.992726i	$-0.538415\pi$
$641$	−1.02918e12	−0.240785	−0.120392	+	0.992726i	$0.538415\pi$
$642$	5.97654e12	1.38849
$643$	4.16068e12	0.959875	0.479937	−	0.877303i	$-0.340659\pi$
$643$	4.16068e12	0.959875	0.479937	+	0.877303i	$0.340659\pi$
$644$	3.25977e11	0.0746794
$645$	−3.72132e12	−0.846601
$646$	0	0
$647$	−3.69231e12	−0.828378	−0.414189	−	0.910191i	$-0.635935\pi$
$647$	−3.69231e12	−0.828378	−0.414189	+	0.910191i	$0.635935\pi$
$648$	2.68710e12	0.598682
$649$	−8.03619e12	−1.77807
$650$	6.43961e12	1.41498
$651$	−1.11933e12	−0.244256
$652$	1.27303e13	2.75882
$653$	3.79017e11	0.0815735	0.0407868	−	0.999168i	$-0.487014\pi$
$653$	3.79017e11	0.0815735	0.0407868	+	0.999168i	$0.487014\pi$
$654$	−2.61901e12	−0.559805
$655$	3.64760e12	0.774321
$656$	−2.57932e11	−0.0543799
$657$	4.37633e12	0.916360
$658$	−2.16651e12	−0.450551
$659$	−7.58856e12	−1.56738	−0.783691	−	0.621150i	$-0.786666\pi$
$659$	−7.58856e12	−1.56738	−0.783691	+	0.621150i	$0.786666\pi$
$660$	2.98537e13	6.12421
$661$	4.30690e12	0.877522	0.438761	−	0.898604i	$-0.355418\pi$
$661$	4.30690e12	0.877522	0.438761	+	0.898604i	$0.355418\pi$
$662$	−3.67054e11	−0.0742795
$663$	0	0
$664$	4.89943e12	0.978114
$665$	−3.29323e12	−0.653017
$666$	−3.44366e12	−0.678244
$667$	4.64450e11	0.0908599
$668$	3.72987e12	0.724769
$669$	−7.27393e12	−1.40395
$670$	2.01740e13	3.86773
$671$	1.94438e12	0.370280
$672$	1.75806e12	0.332562
$673$	−7.34668e12	−1.38046	−0.690229	−	0.723591i	$-0.742490\pi$
$673$	−7.34668e12	−1.38046	−0.690229	+	0.723591i	$0.742490\pi$
$674$	−1.24715e13	−2.32783
$675$	−3.82234e12	−0.708700
$676$	−5.69019e12	−1.04801
$677$	−9.74181e12	−1.78234	−0.891170	−	0.453669i	$-0.850115\pi$
$677$	−9.74181e12	−1.78234	−0.891170	+	0.453669i	$0.850115\pi$
$678$	−9.04391e12	−1.64370
$679$	−5.93592e11	−0.107170
$680$	0	0
$681$	1.11989e12	0.199532
$682$	1.01414e13	1.79502
$683$	1.01934e13	1.79236	0.896180	−	0.443691i	$-0.146331\pi$
$683$	1.01934e13	1.79236	0.896180	+	0.443691i	$0.146331\pi$
$684$	−2.27503e13	−3.97405
$685$	5.02145e12	0.871408
$686$	−4.17379e12	−0.719569
$687$	−1.30441e13	−2.23413
$688$	−1.00995e11	−0.0171851
$689$	−2.38424e12	−0.403055
$690$	4.62200e12	0.776263
$691$	−9.70215e12	−1.61889	−0.809444	−	0.587197i	$-0.800231\pi$
$691$	−9.70215e12	−1.61889	−0.809444	+	0.587197i	$0.800231\pi$
$692$	1.37343e13	2.27682
$693$	−2.85585e12	−0.470365
$694$	−1.25142e13	−2.04779
$695$	−6.01589e12	−0.978066
$696$	−4.44298e12	−0.717683
$697$	0	0
$698$	−1.46045e13	−2.32883
$699$	−4.45171e12	−0.705309
$700$	−3.43304e12	−0.540427
$701$	−5.20929e12	−0.814794	−0.407397	−	0.913251i	$-0.633563\pi$
$701$	−5.20929e12	−0.814794	−0.407397	+	0.913251i	$0.633563\pi$
$702$	−3.06881e12	−0.476928
$703$	−3.75636e12	−0.580054
$704$	−1.64226e13	−2.51980
$705$	−1.90806e13	−2.90897
$706$	6.04503e12	0.915750
$707$	4.92440e11	0.0741252
$708$	1.89534e13	2.83489
$709$	7.75616e10	0.0115276	0.00576380	−	0.999983i	$-0.498165\pi$
$709$	7.75616e10	0.0115276	0.00576380	+	0.999983i	$0.498165\pi$
$710$	6.79801e12	1.00397
$711$	1.41895e13	2.08235
$712$	−5.68547e12	−0.829099
$713$	9.75254e11	0.141324
$714$	0	0
$715$	1.02923e13	1.47277
$716$	−2.47666e12	−0.352174
$717$	5.15819e12	0.728889
$718$	2.16252e13	3.03668
$719$	−5.73539e12	−0.800356	−0.400178	−	0.916437i	$-0.631052\pi$
$719$	−5.73539e12	−0.800356	−0.400178	+	0.916437i	$0.631052\pi$
$720$	−7.21618e11	−0.100072
$721$	−1.55847e12	−0.214778
$722$	−2.80902e13	−3.84714
$723$	1.07111e13	1.45784
$724$	−1.21637e12	−0.164529
$725$	−4.89136e12	−0.657520
$726$	2.69378e13	3.59872
$727$	7.17424e12	0.952513	0.476256	−	0.879306i	$-0.341993\pi$
$727$	7.17424e12	0.952513	0.476256	+	0.879306i	$0.341993\pi$
$728$	−1.07507e12	−0.141856
$729$	−1.14818e13	−1.50569
$730$	1.35369e13	1.76428
$731$	0	0
$732$	−4.58583e12	−0.590362
$733$	2.59216e12	0.331661	0.165830	−	0.986154i	$-0.446970\pi$
$733$	2.59216e12	0.331661	0.165830	+	0.986154i	$0.446970\pi$
$734$	−8.26786e11	−0.105138
$735$	−1.78919e13	−2.26133
$736$	−1.53176e12	−0.192416
$737$	1.90833e13	2.38259
$738$	1.94274e13	2.41079
$739$	6.31144e12	0.778446	0.389223	−	0.921143i	$-0.372743\pi$
$739$	6.31144e12	0.778446	0.389223	+	0.921143i	$0.372743\pi$
$740$	−6.61633e12	−0.811100
$741$	−1.37816e13	−1.67926
$742$	2.04636e12	0.247836
$743$	−1.14750e11	−0.0138135	−0.00690676	−	0.999976i	$-0.502199\pi$
$743$	−1.14750e11	−0.0138135	−0.00690676	+	0.999976i	$0.502199\pi$
$744$	−9.32939e12	−1.11629
$745$	−7.91072e12	−0.940833
$746$	9.87374e12	1.16723
$747$	−1.05826e13	−1.24351
$748$	0	0
$749$	−1.09846e12	−0.127531
$750$	−1.51074e13	−1.74347
$751$	−4.25171e12	−0.487735	−0.243867	−	0.969809i	$-0.578416\pi$
$751$	−4.25171e12	−0.487735	−0.243867	+	0.969809i	$0.578416\pi$
$752$	−5.17838e11	−0.0590492
$753$	5.68762e12	0.644693
$754$	−3.92709e12	−0.442486
$755$	1.19590e13	1.33948
$756$	1.63602e12	0.182155
$757$	−1.23621e13	−1.36824	−0.684118	−	0.729371i	$-0.739813\pi$
$757$	−1.23621e13	−1.36824	−0.684118	+	0.729371i	$0.739813\pi$
$758$	4.50561e12	0.495726
$759$	4.37210e12	0.478192
$760$	−2.74483e13	−2.98438
$761$	−1.78926e12	−0.193393	−0.0966966	−	0.995314i	$-0.530828\pi$
$761$	−1.78926e12	−0.193393	−0.0966966	+	0.995314i	$0.530828\pi$
$762$	3.71811e12	0.399508
$763$	4.81361e11	0.0514174
$764$	−1.26626e13	−1.34463
$765$	0	0
$766$	−3.08391e13	−3.23647
$767$	6.53433e12	0.681745
$768$	1.58186e13	1.64075
$769$	7.61998e12	0.785752	0.392876	−	0.919591i	$-0.371480\pi$
$769$	7.61998e12	0.785752	0.392876	+	0.919591i	$0.371480\pi$
$770$	−8.83374e12	−0.905600
$771$	2.39989e11	0.0244594
$772$	2.06170e13	2.08905
$773$	5.46599e12	0.550632	0.275316	−	0.961354i	$-0.411218\pi$
$773$	5.46599e12	0.550632	0.275316	+	0.961354i	$0.411218\pi$
$774$	7.60691e12	0.761858
$775$	−1.02709e13	−1.02271
$776$	−4.94745e12	−0.489783
$777$	1.11212e12	0.109460
$778$	−1.65072e13	−1.61534
$779$	2.11915e13	2.06178
$780$	−2.42744e13	−2.34814
$781$	6.43046e12	0.618461
$782$	0	0
$783$	2.33099e12	0.221622
$784$	−4.85578e11	−0.0459026
$785$	2.57907e13	2.42410
$786$	−1.31013e13	−1.22437
$787$	1.27287e12	0.118277	0.0591383	−	0.998250i	$-0.481165\pi$
$787$	1.27287e12	0.118277	0.0591383	+	0.998250i	$0.481165\pi$
$788$	−4.09993e12	−0.378799
$789$	−7.02214e12	−0.645094
$790$	4.38911e13	4.00917
$791$	1.66223e12	0.150972
$792$	−2.38028e13	−2.14964
$793$	−1.58100e12	−0.141972
$794$	3.07512e13	2.74581
$795$	1.80224e13	1.60015
$796$	−1.37586e13	−1.21469
$797$	1.54063e12	0.135250	0.0676248	−	0.997711i	$-0.478458\pi$
$797$	1.54063e12	0.135250	0.0676248	+	0.997711i	$0.478458\pi$
$798$	1.18285e13	1.03257
$799$	0	0
$800$	1.61318e13	1.39244
$801$	1.22804e13	1.05407
$802$	−1.98451e13	−1.69383
$803$	1.28050e13	1.08683
$804$	−4.50079e13	−3.79871
$805$	−8.49501e11	−0.0712988
$806$	−8.24612e12	−0.688243
$807$	2.25142e13	1.86864
$808$	4.10437e12	0.338763
$809$	1.64916e13	1.35362	0.676808	−	0.736159i	$-0.263363\pi$
$809$	1.64916e13	1.35362	0.676808	+	0.736159i	$0.263363\pi$
$810$	−1.79532e13	−1.46541
$811$	−1.27047e13	−1.03126	−0.515632	−	0.856810i	$-0.672443\pi$
$811$	−1.27047e13	−1.03126	−0.515632	+	0.856810i	$0.672443\pi$
$812$	2.09358e12	0.169000
$813$	−3.50074e13	−2.81030
$814$	−1.00760e13	−0.804415
$815$	−3.31752e13	−2.63393
$816$	0	0
$817$	8.29767e12	0.651563
$818$	−8.74924e12	−0.683251
$819$	2.32212e12	0.180347
$820$	3.73260e13	2.88303
$821$	2.24085e13	1.72135	0.860675	−	0.509155i	$-0.170042\pi$
$821$	2.24085e13	1.72135	0.860675	+	0.509155i	$0.170042\pi$
$822$	−1.80359e13	−1.37789
$823$	1.93704e13	1.47177	0.735885	−	0.677106i	$-0.236766\pi$
$823$	1.93704e13	1.47177	0.735885	+	0.677106i	$0.236766\pi$
$824$	−1.29895e13	−0.981565
$825$	−4.60449e13	−3.46050
$826$	−5.60832e12	−0.419201
$827$	−3.38768e12	−0.251841	−0.125921	−	0.992040i	$-0.540188\pi$
$827$	−3.38768e12	−0.251841	−0.125921	+	0.992040i	$0.540188\pi$
$828$	−5.86851e12	−0.433902
$829$	1.60725e13	1.18192	0.590960	−	0.806701i	$-0.298749\pi$
$829$	1.60725e13	1.18192	0.590960	+	0.806701i	$0.298749\pi$
$830$	−3.27343e13	−2.39415
$831$	2.50078e12	0.181916
$832$	1.33534e13	0.966136
$833$	0	0
$834$	2.16077e13	1.54654
$835$	−9.72009e12	−0.691960
$836$	−6.65666e13	−4.71333
$837$	4.89463e12	0.344711
$838$	−4.52539e13	−3.16999
$839$	−1.90826e13	−1.32957	−0.664783	−	0.747037i	$-0.731476\pi$
$839$	−1.90826e13	−1.32957	−0.664783	+	0.747037i	$0.731476\pi$
$840$	8.12642e12	0.563174
$841$	−1.15242e13	−0.794383
$842$	−2.51577e13	−1.72491
$843$	1.47680e13	1.00716
$844$	3.37609e13	2.29020
$845$	1.48287e13	1.00057
$846$	3.90034e13	2.61779
$847$	−4.95104e12	−0.330538
$848$	4.89120e11	0.0324813
$849$	−1.70249e13	−1.12461
$850$	0	0
$851$	−9.68967e11	−0.0633324
$852$	−1.51662e13	−0.986051
$853$	1.22475e13	0.792097	0.396049	−	0.918230i	$-0.370381\pi$
$853$	1.22475e13	0.792097	0.396049	+	0.918230i	$0.370381\pi$
$854$	1.35695e12	0.0872980
$855$	5.92875e13	3.79416
$856$	−9.15540e12	−0.582835
$857$	−2.83324e12	−0.179419	−0.0897096	−	0.995968i	$-0.528594\pi$
$857$	−2.83324e12	−0.179419	−0.0897096	+	0.995968i	$0.528594\pi$
$858$	−3.69677e13	−2.32878
$859$	−5.31654e12	−0.333166	−0.166583	−	0.986027i	$-0.553273\pi$
$859$	−5.31654e12	−0.333166	−0.166583	+	0.986027i	$0.553273\pi$
$860$	1.46152e13	0.911093
$861$	−6.27401e12	−0.389073
$862$	−2.68303e13	−1.65517
$863$	−1.93500e13	−1.18750	−0.593749	−	0.804650i	$-0.702353\pi$
$863$	−1.93500e13	−1.18750	−0.593749	+	0.804650i	$0.702353\pi$
$864$	−7.68765e12	−0.469334
$865$	−3.57917e13	−2.17375
$866$	−2.12391e13	−1.28323
$867$	0	0
$868$	4.39611e12	0.262863
$869$	4.15180e13	2.46972
$870$	2.96847e13	1.75669
$871$	−1.55168e13	−0.913528
$872$	4.01203e12	0.234985
$873$	1.06864e13	0.622681
$874$	−1.03060e13	−0.597430
$875$	2.77667e12	0.160136
$876$	−3.02006e13	−1.73280
$877$	−8.38689e12	−0.478743	−0.239372	−	0.970928i	$-0.576941\pi$
$877$	−8.38689e12	−0.478743	−0.239372	+	0.970928i	$0.576941\pi$
$878$	−8.75549e12	−0.497228
$879$	4.40569e12	0.248922
$880$	−2.11144e12	−0.118688
$881$	2.03445e13	1.13777	0.568886	−	0.822416i	$-0.307374\pi$
$881$	2.03445e13	1.13777	0.568886	+	0.822416i	$0.307374\pi$
$882$	3.65736e13	2.03497
$883$	5.99288e12	0.331751	0.165876	−	0.986147i	$-0.446955\pi$
$883$	5.99288e12	0.331751	0.165876	+	0.986147i	$0.446955\pi$
$884$	0	0
$885$	−4.93927e13	−2.70656
$886$	−4.53085e13	−2.47018
$887$	−9.14663e12	−0.496141	−0.248070	−	0.968742i	$-0.579796\pi$
$887$	−9.14663e12	−0.496141	−0.248070	+	0.968742i	$0.579796\pi$
$888$	9.26925e12	0.500249
$889$	−6.83371e11	−0.0366943
$890$	3.79860e13	2.02941
$891$	−1.69825e13	−0.902717
$892$	2.85678e13	1.51090
$893$	4.25451e13	2.23881
$894$	2.84135e13	1.48767
$895$	6.45420e12	0.336232
$896$	−7.24955e12	−0.375773
$897$	−3.55501e12	−0.183347
$898$	1.23600e13	0.634270
$899$	6.26354e12	0.319817
$900$	6.18044e13	3.13999
$901$	0	0
$902$	5.68439e13	2.85927
$903$	−2.45663e12	−0.122955
$904$	1.38543e13	0.689962
$905$	3.16987e12	0.157081
$906$	−4.29542e13	−2.11801
$907$	−1.24855e13	−0.612593	−0.306296	−	0.951936i	$-0.599090\pi$
$907$	−1.24855e13	−0.612593	−0.306296	+	0.951936i	$0.599090\pi$
$908$	−4.39827e12	−0.214731
$909$	−8.86532e12	−0.430682
$910$	7.18283e12	0.347224
$911$	−3.03245e13	−1.45869	−0.729343	−	0.684149i	$-0.760174\pi$
$911$	−3.03245e13	−1.45869	−0.729343	+	0.684149i	$0.760174\pi$
$912$	2.82725e12	0.135328
$913$	−3.09645e13	−1.47484
$914$	2.09624e13	0.993534
$915$	1.19507e13	0.563637
$916$	5.12296e13	2.40432
$917$	2.40796e12	0.112457
$918$	0	0
$919$	3.21656e13	1.48755	0.743776	−	0.668429i	$-0.233033\pi$
$919$	3.21656e13	1.48755	0.743776	+	0.668429i	$0.233033\pi$
$920$	−7.08039e12	−0.325846
$921$	−3.67967e12	−0.168516
$922$	−6.93289e13	−3.15955
$923$	−5.22869e12	−0.237129
$924$	1.97079e13	0.889441
$925$	1.02047e13	0.458313
$926$	8.61256e12	0.384931
$927$	2.80569e13	1.24790
$928$	−9.83771e12	−0.435440
$929$	3.82698e13	1.68572	0.842861	−	0.538132i	$-0.180870\pi$
$929$	3.82698e13	1.68572	0.842861	+	0.538132i	$0.180870\pi$
$930$	6.23320e13	2.73236
$931$	3.98946e13	1.74037
$932$	1.74838e13	0.759038
$933$	3.55767e13	1.53709
$934$	1.64367e13	0.706729
$935$	0	0
$936$	1.93544e13	0.824210
$937$	1.50633e13	0.638399	0.319199	−	0.947688i	$-0.396586\pi$
$937$	1.50633e13	0.638399	0.319199	+	0.947688i	$0.396586\pi$
$938$	1.33179e13	0.561723
$939$	−1.52211e12	−0.0638925
$940$	7.49375e13	3.13057
$941$	3.26362e12	0.135689	0.0678447	−	0.997696i	$-0.478388\pi$
$941$	3.26362e12	0.135689	0.0678447	+	0.997696i	$0.478388\pi$
$942$	−9.26344e13	−3.83304
$943$	5.46642e12	0.225113
$944$	−1.34050e12	−0.0549404
$945$	−4.26349e12	−0.173909
$946$	2.22576e13	0.903584
$947$	1.26818e13	0.512396	0.256198	−	0.966624i	$-0.417530\pi$
$947$	1.26818e13	0.512396	0.256198	+	0.966624i	$0.417530\pi$
$948$	−9.79203e13	−3.93763
$949$	−1.04119e13	−0.416709
$950$	1.08537e14	4.32338
$951$	3.10937e13	1.23271
$952$	0	0
$953$	−4.11789e13	−1.61717	−0.808587	−	0.588377i	$-0.799767\pi$
$953$	−4.11789e13	−1.61717	−0.808587	+	0.588377i	$0.799767\pi$
$954$	−3.68403e13	−1.43998
$955$	3.29990e13	1.28377
$956$	−2.02584e13	−0.784414
$957$	2.80797e13	1.08215
$958$	3.58277e13	1.37428
$959$	3.31491e12	0.126558
$960$	−1.00938e14	−3.83561
$961$	−1.32874e13	−0.502557
$962$	8.19296e12	0.308427
$963$	1.97754e13	0.740980
$964$	−4.20669e13	−1.56890
$965$	−5.37283e13	−1.99448
$966$	3.05121e12	0.112739
$967$	6.11328e12	0.224831	0.112415	−	0.993661i	$-0.464141\pi$
$967$	6.11328e12	0.224831	0.112415	+	0.993661i	$0.464141\pi$
$968$	−4.12657e13	−1.51060
$969$	0	0
$970$	3.30552e13	1.19885
$971$	1.20763e13	0.435960	0.217980	−	0.975953i	$-0.430053\pi$
$971$	1.20763e13	0.435960	0.217980	+	0.975953i	$0.430053\pi$
$972$	6.23523e13	2.24055
$973$	−3.97139e12	−0.142048
$974$	1.30263e13	0.463772
$975$	3.74397e13	1.32682
$976$	3.24338e11	0.0114413
$977$	2.07066e13	0.727082	0.363541	−	0.931578i	$-0.381568\pi$
$977$	2.07066e13	0.727082	0.363541	+	0.931578i	$0.381568\pi$
$978$	1.19158e14	4.16483
$979$	3.59322e13	1.25015
$980$	7.02691e13	2.43359
$981$	−8.66586e12	−0.298745
$982$	5.28808e13	1.81466
$983$	−5.15470e13	−1.76081	−0.880406	−	0.474221i	$-0.842730\pi$
$983$	−5.15470e13	−1.76081	−0.880406	+	0.474221i	$0.842730\pi$
$984$	−5.22924e13	−1.77812
$985$	1.06845e13	0.361651
$986$	0	0
$987$	−1.25960e13	−0.422480
$988$	5.41262e13	1.80718
$989$	2.14041e12	0.0711401
$990$	1.59032e14	5.26172
$991$	−5.09054e12	−0.167661	−0.0838305	−	0.996480i	$-0.526715\pi$
$991$	−5.09054e12	−0.167661	−0.0838305	+	0.996480i	$0.526715\pi$
$992$	−2.06573e13	−0.677283
$993$	−2.13404e12	−0.0696516
$994$	4.48770e12	0.145809
$995$	3.58552e13	1.15971
$996$	7.30297e13	2.35143
$997$	−5.08971e13	−1.63142	−0.815708	−	0.578463i	$-0.803653\pi$
$997$	−5.08971e13	−1.63142	−0.815708	+	0.578463i	$0.803653\pi$
$998$	−3.19116e13	−1.01827
$999$	−4.86307e12	−0.154478

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.f.1.3		24
17.8	even	8		17.10.c.a.13.11	yes	24
17.15	even	8		17.10.c.a.4.2	✓	24
17.16	even	2	inner	289.10.a.f.1.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.c.a.4.2	✓	24	17.15	even	8
17.10.c.a.13.11	yes	24	17.8	even	8
289.10.a.f.1.3		24	1.1	even	1	trivial
289.10.a.f.1.4		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)

\(f(q)\)	\(=\)	\(q-36.7615 q^{2} -213.730 q^{3} +839.411 q^{4} -2187.52 q^{5} +7857.06 q^{6} -1444.09 q^{7} -12036.1 q^{8} +25997.7 q^{9} +O(q^{10})\)	\(q-36.7615 q^{2} -213.730 q^{3} +839.411 q^{4} -2187.52 q^{5} +7857.06 q^{6} -1444.09 q^{7} -12036.1 q^{8} +25997.7 q^{9} +80416.5 q^{10} +76068.6 q^{11} -179408. q^{12} -61852.4 q^{13} +53087.0 q^{14} +467539. q^{15} +12688.8 q^{16} -955716. q^{18} -1.04250e6 q^{19} -1.83623e6 q^{20} +308646. q^{21} -2.79640e6 q^{22} -268917. q^{23} +2.57249e6 q^{24} +2.83211e6 q^{25} +2.27379e6 q^{26} -1.34965e6 q^{27} -1.21219e6 q^{28} -1.72711e6 q^{29} -1.71875e7 q^{30} -3.62660e6 q^{31} +5.69605e6 q^{32} -1.62582e7 q^{33} +3.15897e6 q^{35} +2.18228e7 q^{36} +3.60322e6 q^{37} +3.83239e7 q^{38} +1.32197e7 q^{39} +2.63293e7 q^{40} -2.03275e7 q^{41} -1.13463e7 q^{42} -7.95939e6 q^{43} +6.38528e7 q^{44} -5.68704e7 q^{45} +9.88580e6 q^{46} -4.08106e7 q^{47} -2.71199e6 q^{48} -3.82682e7 q^{49} -1.04113e8 q^{50} -5.19196e7 q^{52} +3.85473e7 q^{53} +4.96151e7 q^{54} -1.66401e8 q^{55} +1.73813e7 q^{56} +2.22814e8 q^{57} +6.34913e7 q^{58} -1.05644e8 q^{59} +3.92458e8 q^{60} +2.55609e7 q^{61} +1.33319e8 q^{62} -3.75430e7 q^{63} -2.15892e8 q^{64} +1.35303e8 q^{65} +5.97676e8 q^{66} +2.50869e8 q^{67} +5.74757e7 q^{69} -1.16129e8 q^{70} +8.45350e7 q^{71} -3.12912e8 q^{72} +1.68335e8 q^{73} -1.32460e8 q^{74} -6.05307e8 q^{75} -8.75087e8 q^{76} -1.09850e8 q^{77} -4.85978e8 q^{78} +5.45797e8 q^{79} -2.77570e7 q^{80} -2.23252e8 q^{81} +7.47272e8 q^{82} -4.07060e8 q^{83} +2.59081e8 q^{84} +2.92599e8 q^{86} +3.69136e8 q^{87} -9.15573e8 q^{88} +4.72366e8 q^{89} +2.09065e9 q^{90} +8.93203e7 q^{91} -2.25732e8 q^{92} +7.75114e8 q^{93} +1.50026e9 q^{94} +2.28049e9 q^{95} -1.21742e9 q^{96} +4.11050e8 q^{97} +1.40680e9 q^{98} +1.97761e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 5124 q^{4} + 108368 q^{9}+O(q^{10}) \) 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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