LMFDB - Embedded newform 25.34.a.e.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,34,Mod(1,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 34, names="a")

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

chi := DirichletCharacter("25.1");

S:= CuspForms(chi, 34);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 34 $
Character orbit:	$[\chi]$	$=$	25.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:	$172.457072203$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - x^{10} - 71909733210 x^{9} - 392361971317440 x^{8} + \cdots + 13\!\cdots\!48 $ x^11 - x^10 - 71909733210x^9 - 392361971317440x^8 + 1789020862523351140800x^7 + 15057968169589785919302432x^6 - 18240376108577281349602470726592x^5 - 118793082389247521352101537474727680x^4 + 70339384981314044531499864093672157167360x^3 - 93184212295829066424280494839341830566058240x^2 - 66043164692761651440492767327962940420438352419328*x + 13944892725752680722269718925910686764312949634715648
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{47}\cdot 3^{12}\cdot 5^{30}\cdot 7^{2}\cdot 11^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$211.095$ of defining polynomial
Character	$\chi$	$=$	25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+642.905 q^{2} +5.85306e7 q^{3} -8.58952e9 q^{4} +3.76296e10 q^{6} -1.03914e14 q^{7} -1.10448e13 q^{8} -2.13323e15 q^{9} +O(q^{10})$	\(q+642.905 q^{2} +5.85306e7 q^{3} -8.58952e9 q^{4} +3.76296e10 q^{6} -1.03914e14 q^{7} -1.10448e13 q^{8} -2.13323e15 q^{9} -4.04723e16 q^{11} -5.02750e17 q^{12} +3.61885e18 q^{13} -6.68070e16 q^{14} +7.37763e19 q^{16} -2.12343e20 q^{17} -1.37147e18 q^{18} -6.69296e20 q^{19} -6.08216e21 q^{21} -2.60199e19 q^{22} -4.58890e21 q^{23} -6.46456e20 q^{24} +2.32658e21 q^{26} -4.50234e23 q^{27} +8.92574e23 q^{28} -2.08845e24 q^{29} -2.71951e24 q^{31} +1.42305e23 q^{32} -2.36887e24 q^{33} -1.36516e23 q^{34} +1.83234e25 q^{36} -2.98538e25 q^{37} -4.30294e23 q^{38} +2.11813e26 q^{39} -2.01426e26 q^{41} -3.91025e24 q^{42} -9.42876e26 q^{43} +3.47638e26 q^{44} -2.95023e24 q^{46} -4.81286e27 q^{47} +4.31817e27 q^{48} +3.06719e27 q^{49} -1.24286e28 q^{51} -3.10842e28 q^{52} -1.34565e28 q^{53} -2.89458e26 q^{54} +1.14771e27 q^{56} -3.91743e28 q^{57} -1.34267e27 q^{58} +3.17580e29 q^{59} +4.25546e29 q^{61} -1.74839e27 q^{62} +2.21673e29 q^{63} -6.33642e29 q^{64} -1.52296e27 q^{66} -3.16821e29 q^{67} +1.82392e30 q^{68} -2.68591e29 q^{69} +5.91891e30 q^{71} +2.35610e28 q^{72} +2.98266e30 q^{73} -1.91932e28 q^{74} +5.74893e30 q^{76} +4.20565e30 q^{77} +1.36176e29 q^{78} +4.21980e30 q^{79} -1.44937e31 q^{81} -1.29498e29 q^{82} -2.51439e31 q^{83} +5.22429e31 q^{84} -6.06179e29 q^{86} -1.22238e32 q^{87} +4.47007e29 q^{88} -1.35942e32 q^{89} -3.76050e32 q^{91} +3.94165e31 q^{92} -1.59175e32 q^{93} -3.09421e30 q^{94} +8.32918e30 q^{96} +7.72579e32 q^{97} +1.97191e30 q^{98} +8.63369e31 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 9393 q^{2} + 80330849 q^{3} + 49338206677 q^{4} - 17783977676723 q^{6} + 21344025107658 q^{7} - 970199832420105 q^{8} + 24\!\cdots\!58 q^{9}+O(q^{10}) $ 11 * q + 9393 * q^2 + 80330849 * q^3 + 49338206677 * q^4 - 17783977676723 * q^6 + 21344025107658 * q^7 - 970199832420105 * q^8 + 24299637974625658 * q^9	$ 11 q + 9393 q^{2} + 80330849 q^{3} + 49338206677 q^{4} - 17783977676723 q^{6} + 21344025107658 q^{7} - 970199832420105 q^{8} + 24\!\cdots\!58 q^{9}+ \cdots + 13\!\cdots\!06 q^{99}+O(q^{100}) $ 11 * q + 9393 * q^2 + 80330849 * q^3 + 49338206677 * q^4 - 17783977676723 * q^6 + 21344025107658 * q^7 - 970199832420105 * q^8 + 24299637974625658 * q^9 - 194487534567113523 * q^11 + 1128411534853252093 * q^12 + 5151173641795199804 * q^13 + 9695004297667451034 * q^14 + 287795879559665379601 * q^16 + 217450883530375665663 * q^17 - 883205358438912773746 * q^18 - 2304421397121542404315 * q^19 + 3951679538424255448062 * q^21 + 65697936516541243081001 * q^22 + 39745489889804460665334 * q^23 - 202096278074290714435545 * q^24 + 232341332678498439460092 * q^26 + 215757396930304201071995 * q^27 - 1844234528929870945073094 * q^28 + 1675632286595729558796840 * q^29 - 1879684496680578139929438 * q^31 - 22333622446463598116694177 * q^32 - 36653442436454147951147057 * q^33 - 44873360881289881717450051 * q^34 + 193677686753165783059502006 * q^36 + 180277972113296426057413198 * q^37 + 216179528860395412757129505 * q^38 - 359172746626046600427282844 * q^39 + 549519804753897528529573167 * q^41 + 2593357144102832185922898306 * q^42 + 50270064758017307324647244 * q^43 - 2976543624086726877274410711 * q^44 + 1688362231334867471013357582 * q^46 + 10903258570108047175558188228 * q^47 + 28193416941275907016447196209 * q^48 - 2501658924474402528580483073 * q^49 + 66317965316246498072666600557 * q^51 + 155672232460399094184759234028 * q^52 + 33298643916770080171872677874 * q^53 - 213393152239696124781888030065 * q^54 + 339537122636968128125815064910 * q^56 + 159006470550216362740785378215 * q^57 + 62377017575001287720537209120 * q^58 - 67706990548480155796584121920 * q^59 - 344769258471797286249471450898 * q^61 - 1319517422843123577963573948294 * q^62 - 699283498025109144495841661076 * q^63 + 1420026267960910564014627900737 * q^64 - 160016657586606697551149537011 * q^66 - 1671796054942808947714198855437 * q^67 + 3088683653934580261727419953441 * q^68 + 7218504661993692063958711761426 * q^69 - 5525905608449961693610592189868 * q^71 - 21423093069732612399854192774190 * q^72 + 1280933432508086429255473349609 * q^73 + 8483102027446485651051216797154 * q^74 - 3794387798301159395171650466255 * q^76 - 25187595245022035764699127942394 * q^77 - 56671274702179561872150030862772 * q^78 + 28416813573575354189758739594190 * q^79 - 4511447703484319172258978381029 * q^81 + 94213252968905060003342215055821 * q^82 + 127792566726367853829683612248839 * q^83 - 299946577157245367261151073271766 * q^84 + 455910432123816097591159189088412 * q^86 + 485010641407021414487926087945160 * q^87 + 5212296644003692182363473725515 * q^88 - 24030870261451879999370600550555 * q^89 - 346687858887153608395037323300248 * q^91 + 535778496942575427226503821168238 * q^92 + 789528086332099641022541300872758 * q^93 + 232538212076560959503267655560444 * q^94 - 1842110282591420302371913525952353 * q^96 - 674692794164529660649398963528122 * q^97 - 2571899453674006542996540156918099 * q^98 + 1300949547786735016969037553636806 * q^99

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 $

$2$	642.905	0.00693668	0.00346834	−	0.999994i	$-0.498896\pi$
$2$	642.905	0.00693668	0.00346834	+	0.999994i	$0.498896\pi$
$3$	5.85306e7	0.785022	0.392511	−	0.919747i	$-0.371606\pi$
$3$	5.85306e7	0.785022	0.392511	+	0.919747i	$0.371606\pi$
$4$	−8.58952e9	−0.999952
$5$	0	0
$5$	0	0
$6$	3.76296e10	0.00544545
$7$	−1.03914e14	−1.18184	−0.590919	−	0.806731i	$-0.701235\pi$
$7$	−1.03914e14	−1.18184	−0.590919	+	0.806731i	$0.701235\pi$
$8$	−1.10448e13	−0.0138730
$9$	−2.13323e15	−0.383740
$10$	0	0
$11$	−4.04723e16	−0.265570	−0.132785	−	0.991145i	$-0.542392\pi$
$11$	−4.04723e16	−0.265570	−0.132785	+	0.991145i	$0.542392\pi$
$12$	−5.02750e17	−0.784985
$13$	3.61885e18	1.50836	0.754181	−	0.656667i	$-0.228034\pi$
$13$	3.61885e18	1.50836	0.754181	+	0.656667i	$0.228034\pi$
$14$	−6.68070e16	−0.00819803
$15$	0	0
$16$	7.37763e19	0.999856
$17$	−2.12343e20	−1.05835	−0.529176	−	0.848512i	$-0.677499\pi$
$17$	−2.12343e20	−1.05835	−0.529176	+	0.848512i	$0.677499\pi$
$18$	−1.37147e18	−0.00266188
$19$	−6.69296e20	−0.532334	−0.266167	−	0.963927i	$-0.585757\pi$
$19$	−6.69296e20	−0.532334	−0.266167	+	0.963927i	$0.585757\pi$
$20$	0	0
$21$	−6.08216e21	−0.927769
$22$	−2.60199e19	−0.00184217
$23$	−4.58890e21	−0.156027	−0.0780134	−	0.996952i	$-0.524858\pi$
$23$	−4.58890e21	−0.156027	−0.0780134	+	0.996952i	$0.524858\pi$
$24$	−6.46456e20	−0.0108906
$25$	0	0
$26$	2.32658e21	0.0104630
$27$	−4.50234e23	−1.08627
$28$	8.92574e23	1.18178
$29$	−2.08845e24	−1.54973	−0.774866	−	0.632125i	$-0.782183\pi$
$29$	−2.08845e24	−1.54973	−0.774866	+	0.632125i	$0.782183\pi$
$30$	0	0
$31$	−2.71951e24	−0.671465	−0.335732	−	0.941957i	$-0.608984\pi$
$31$	−2.71951e24	−0.671465	−0.335732	+	0.941957i	$0.608984\pi$
$32$	1.42305e23	0.0208087
$33$	−2.36887e24	−0.208478
$34$	−1.36516e23	−0.00734146
$35$	0	0
$36$	1.83234e25	0.383721
$37$	−2.98538e25	−0.397806	−0.198903	−	0.980019i	$-0.563738\pi$
$37$	−2.98538e25	−0.397806	−0.198903	+	0.980019i	$0.563738\pi$
$38$	−4.30294e23	−0.00369263
$39$	2.11813e26	1.18410
$40$	0	0
$41$	−2.01426e26	−0.493380	−0.246690	−	0.969094i	$-0.579343\pi$
$41$	−2.01426e26	−0.493380	−0.246690	+	0.969094i	$0.579343\pi$
$42$	−3.91025e24	−0.00643563
$43$	−9.42876e26	−1.05251	−0.526254	−	0.850328i	$-0.676404\pi$
$43$	−9.42876e26	−1.05251	−0.526254	+	0.850328i	$0.676404\pi$
$44$	3.47638e26	0.265557
$45$	0	0
$46$	−2.95023e24	−0.00108231
$47$	−4.81286e27	−1.23819	−0.619097	−	0.785315i	$-0.712501\pi$
$47$	−4.81286e27	−1.23819	−0.619097	+	0.785315i	$0.712501\pi$
$48$	4.31817e27	0.784909
$49$	3.06719e27	0.396739
$50$	0	0
$51$	−1.24286e28	−0.830831
$52$	−3.10842e28	−1.50829
$53$	−1.34565e28	−0.476850	−0.238425	−	0.971161i	$-0.576631\pi$
$53$	−1.34565e28	−0.476850	−0.238425	+	0.971161i	$0.576631\pi$
$54$	−2.89458e26	−0.00753509
$55$	0	0
$56$	1.14771e27	0.0163957
$57$	−3.91743e28	−0.417894
$58$	−1.34267e27	−0.0107500
$59$	3.17580e29	1.91776	0.958880	−	0.283812i	$-0.0915990\pi$
$59$	3.17580e29	1.91776	0.958880	+	0.283812i	$0.0915990\pi$
$60$	0	0
$61$	4.25546e29	1.48253	0.741266	−	0.671211i	$-0.234225\pi$
$61$	4.25546e29	1.48253	0.741266	+	0.671211i	$0.234225\pi$
$62$	−1.74839e27	−0.00465774
$63$	2.21673e29	0.453518
$64$	−6.33642e29	−0.999711
$65$	0	0
$66$	−1.52296e27	−0.00144615
$67$	−3.16821e29	−0.234736	−0.117368	−	0.993088i	$-0.537446\pi$
$67$	−3.16821e29	−0.234736	−0.117368	+	0.993088i	$0.537446\pi$
$68$	1.82392e30	1.05830
$69$	−2.68591e29	−0.122485
$70$	0	0
$71$	5.91891e30	1.68453	0.842266	−	0.539062i	$-0.181221\pi$
$71$	5.91891e30	1.68453	0.842266	+	0.539062i	$0.181221\pi$
$72$	2.35610e28	0.00532363
$73$	2.98266e30	0.536756	0.268378	−	0.963314i	$-0.413512\pi$
$73$	2.98266e30	0.536756	0.268378	+	0.963314i	$0.413512\pi$
$74$	−1.91932e28	−0.00275945
$75$	0	0
$76$	5.74893e30	0.532308
$77$	4.20565e30	0.313860
$78$	1.36176e29	0.00821371
$79$	4.21980e30	0.206274	0.103137	−	0.994667i	$-0.467112\pi$
$79$	4.21980e30	0.206274	0.103137	+	0.994667i	$0.467112\pi$
$80$	0	0
$81$	−1.44937e31	−0.469004
$82$	−1.29498e29	−0.00342242
$83$	−2.51439e31	−0.544057	−0.272029	−	0.962289i	$-0.587695\pi$
$83$	−2.51439e31	−0.544057	−0.272029	+	0.962289i	$0.587695\pi$
$84$	5.22429e31	0.927724
$85$	0	0
$86$	−6.06179e29	−0.00730090
$87$	−1.22238e32	−1.21657
$88$	4.47007e29	0.00368426
$89$	−1.35942e32	−0.929859	−0.464930	−	0.885348i	$-0.653920\pi$
$89$	−1.35942e32	−0.929859	−0.464930	+	0.885348i	$0.653920\pi$
$90$	0	0
$91$	−3.76050e32	−1.78264
$92$	3.94165e31	0.156019
$93$	−1.59175e32	−0.527115
$94$	−3.09421e30	−0.00858895
$95$	0	0
$96$	8.32918e30	0.0163353
$97$	7.72579e32	1.27705	0.638527	−	0.769599i	$-0.279544\pi$
$97$	7.72579e32	1.27705	0.638527	+	0.769599i	$0.279544\pi$
$98$	1.97191e30	0.00275205
$99$	8.63369e31	0.101910
$100$	0	0
$101$	8.12814e32	0.689745	0.344873	−	0.938650i	$-0.387922\pi$
$101$	8.12814e32	0.689745	0.344873	+	0.938650i	$0.387922\pi$
$102$	−7.99037e30	−0.00576321
$103$	−9.66587e32	−0.593508	−0.296754	−	0.954954i	$-0.595904\pi$
$103$	−9.66587e32	−0.593508	−0.296754	+	0.954954i	$0.595904\pi$
$104$	−3.99693e31	−0.0209255
$105$	0	0
$106$	−8.65128e30	−0.00330776
$107$	2.85497e33	0.934910	0.467455	−	0.884017i	$-0.345171\pi$
$107$	2.85497e33	0.934910	0.467455	+	0.884017i	$0.345171\pi$
$108$	3.86730e33	1.08621
$109$	−2.85246e33	−0.688149	−0.344074	−	0.938942i	$-0.611807\pi$
$109$	−2.85246e33	−0.688149	−0.344074	+	0.938942i	$0.611807\pi$
$110$	0	0
$111$	−1.74736e33	−0.312287
$112$	−7.66641e33	−1.18167
$113$	1.89710e33	0.252520	0.126260	−	0.991997i	$-0.459703\pi$
$113$	1.89710e33	0.252520	0.126260	+	0.991997i	$0.459703\pi$
$114$	−2.51853e31	−0.00289880
$115$	0	0
$116$	1.79388e34	1.54966
$117$	−7.71985e33	−0.578818
$118$	2.04173e32	0.0133029
$119$	2.20655e34	1.25080
$120$	0	0
$121$	−2.15871e34	−0.929473
$122$	2.73586e32	0.0102839
$123$	−1.17896e34	−0.387314
$124$	2.33593e34	0.671432
$125$	0	0
$126$	1.42515e32	0.00314591
$127$	−2.09944e34	−0.406764	−0.203382	−	0.979099i	$-0.565193\pi$
$127$	−2.09944e34	−0.406764	−0.203382	+	0.979099i	$0.565193\pi$
$128$	−1.62976e33	−0.0277434
$129$	−5.51871e34	−0.826242
$130$	0	0
$131$	−9.99620e33	−0.116107	−0.0580535	−	0.998313i	$-0.518489\pi$
$131$	−9.99620e33	−0.116107	−0.0580535	+	0.998313i	$0.518489\pi$
$132$	2.03475e34	0.208468
$133$	6.95494e34	0.629132
$134$	−2.03686e32	−0.00162829
$135$	0	0
$136$	2.34527e33	0.0146826
$137$	2.62787e35	1.45786	0.728929	−	0.684589i	$-0.240018\pi$
$137$	2.62787e35	1.45786	0.728929	+	0.684589i	$0.240018\pi$
$138$	−1.72678e32	−0.000849636 0
$139$	−1.85064e35	−0.808310	−0.404155	−	0.914691i	$-0.632434\pi$
$139$	−1.85064e35	−0.808310	−0.404155	+	0.914691i	$0.632434\pi$
$140$	0	0
$141$	−2.81699e35	−0.972010
$142$	3.80530e33	0.0116851
$143$	−1.46463e35	−0.400576
$144$	−1.57382e35	−0.383684
$145$	0	0
$146$	1.91757e33	0.00372331
$147$	1.79524e35	0.311449
$148$	2.56430e35	0.397787
$149$	1.40401e36	1.94893	0.974466	−	0.224533i	$-0.0720857\pi$
$149$	1.40401e36	1.94893	0.974466	+	0.224533i	$0.0720857\pi$
$150$	0	0
$151$	5.76801e35	0.642549	0.321274	−	0.946986i	$-0.395889\pi$
$151$	5.76801e35	0.642549	0.321274	+	0.946986i	$0.395889\pi$
$152$	7.39221e33	0.00738508
$153$	4.52977e35	0.406132
$154$	2.70383e33	0.00217715
$155$	0	0
$156$	−1.81938e36	−1.18404
$157$	−2.11922e36	−1.24117	−0.620586	−	0.784138i	$-0.713105\pi$
$157$	−2.11922e36	−1.24117	−0.620586	+	0.784138i	$0.713105\pi$
$158$	2.71293e33	0.00143086
$159$	−7.87620e35	−0.374338
$160$	0	0
$161$	4.76852e35	0.184398
$162$	−9.31807e33	−0.00325333
$163$	5.64371e36	1.78020	0.890101	−	0.455764i	$-0.150634\pi$
$163$	5.64371e36	1.78020	0.890101	+	0.455764i	$0.150634\pi$
$164$	1.73015e36	0.493356
$165$	0	0
$166$	−1.61651e34	−0.00377395
$167$	−3.22707e35	−0.0682317	−0.0341159	−	0.999418i	$-0.510862\pi$
$167$	−3.22707e35	−0.0682317	−0.0341159	+	0.999418i	$0.510862\pi$
$168$	6.71760e34	0.0128710
$169$	7.33996e36	1.27515
$170$	0	0
$171$	1.42776e36	0.204278
$172$	8.09885e36	1.05246
$173$	7.28030e36	0.859782	0.429891	−	0.902881i	$-0.358552\pi$
$173$	7.28030e36	0.859782	0.429891	+	0.902881i	$0.358552\pi$
$174$	−7.85874e34	−0.00843899
$175$	0	0
$176$	−2.98590e36	−0.265532
$177$	1.85881e37	1.50548
$178$	−8.73975e34	−0.00645013
$179$	−3.91390e36	−0.263351	−0.131675	−	0.991293i	$-0.542036\pi$
$179$	−3.91390e36	−0.263351	−0.131675	+	0.991293i	$0.542036\pi$
$180$	0	0
$181$	−2.82964e37	−1.58502	−0.792509	−	0.609860i	$-0.791226\pi$
$181$	−2.82964e37	−1.58502	−0.792509	+	0.609860i	$0.791226\pi$
$182$	−2.41765e35	−0.0123656
$183$	2.49075e37	1.16382
$184$	5.06833e34	0.00216456
$185$	0	0
$186$	−1.02334e35	−0.00365643
$187$	8.59401e36	0.281067
$188$	4.13402e37	1.23813
$189$	4.67858e37	1.28379
$190$	0	0
$191$	−8.41989e37	−1.94203	−0.971015	−	0.239017i	$-0.923175\pi$
$191$	−8.41989e37	−1.94203	−0.971015	+	0.239017i	$0.923175\pi$
$192$	−3.70874e37	−0.784796
$193$	1.21898e37	0.236755	0.118378	−	0.992969i	$-0.462231\pi$
$193$	1.21898e37	0.236755	0.118378	+	0.992969i	$0.462231\pi$
$194$	4.96695e35	0.00885852
$195$	0	0
$196$	−2.63457e37	−0.396720
$197$	7.93299e37	1.09836	0.549180	−	0.835704i	$-0.314940\pi$
$197$	7.93299e37	1.09836	0.549180	+	0.835704i	$0.314940\pi$
$198$	5.55064e34	0.000706915 0
$199$	1.43151e38	1.67772	0.838860	−	0.544348i	$-0.183223\pi$
$199$	1.43151e38	1.67772	0.838860	+	0.544348i	$0.183223\pi$
$200$	0	0
$201$	−1.85437e37	−0.184273
$202$	5.22562e35	0.00478454
$203$	2.17020e38	1.83153
$204$	1.06755e38	0.830791
$205$	0	0
$206$	−6.21423e35	−0.00411698
$207$	9.78919e36	0.0598737
$208$	2.66986e38	1.50814
$209$	2.70880e37	0.141372
$210$	0	0
$211$	6.95232e35	0.00310077	0.00155038	−	0.999999i	$-0.499506\pi$
$211$	6.95232e35	0.00310077	0.00155038	+	0.999999i	$0.499506\pi$
$212$	1.15585e38	0.476827
$213$	3.46437e38	1.32240
$214$	1.83548e36	0.00648517
$215$	0	0
$216$	4.97273e36	0.0150698
$217$	2.82596e38	0.793562
$218$	−1.83386e36	−0.00477347
$219$	1.74577e38	0.421366
$220$	0	0
$221$	−7.68437e38	−1.59638
$222$	−1.12339e36	−0.00216623
$223$	8.42136e38	1.50783	0.753914	−	0.656973i	$-0.228163\pi$
$223$	8.42136e38	1.50783	0.753914	+	0.656973i	$0.228163\pi$
$224$	−1.47875e37	−0.0245925
$225$	0	0
$226$	1.21965e36	0.00175165
$227$	4.33859e38	0.579324	0.289662	−	0.957129i	$-0.406457\pi$
$227$	4.33859e38	0.579324	0.289662	+	0.957129i	$0.406457\pi$
$228$	3.36488e38	0.417874
$229$	1.01177e39	1.16896	0.584478	−	0.811410i	$-0.301299\pi$
$229$	1.01177e39	1.16896	0.584478	+	0.811410i	$0.301299\pi$
$230$	0	0
$231$	2.46159e38	0.246388
$232$	2.30664e37	0.0214995
$233$	−1.30327e39	−1.13151	−0.565757	−	0.824572i	$-0.691416\pi$
$233$	−1.30327e39	−1.13151	−0.565757	+	0.824572i	$0.691416\pi$
$234$	−4.96313e36	−0.00401508
$235$	0	0
$236$	−2.72786e39	−1.91767
$237$	2.46988e38	0.161930
$238$	1.41860e37	0.00867640
$239$	2.27541e39	1.29865	0.649327	−	0.760509i	$-0.275051\pi$
$239$	2.27541e39	1.29865	0.649327	+	0.760509i	$0.275051\pi$
$240$	0	0
$241$	−7.73852e38	−0.384926	−0.192463	−	0.981304i	$-0.561647\pi$
$241$	−7.73852e38	−0.384926	−0.192463	+	0.981304i	$0.561647\pi$
$242$	−1.38785e37	−0.00644745
$243$	1.65455e39	0.718088
$244$	−3.65524e39	−1.48246
$245$	0	0
$246$	−7.57957e36	−0.00268668
$247$	−2.42208e39	−0.802952
$248$	3.00363e37	0.00931525
$249$	−1.47169e39	−0.427097
$250$	0	0
$251$	4.56085e39	1.15992	0.579962	−	0.814644i	$-0.303067\pi$
$251$	4.56085e39	1.15992	0.579962	+	0.814644i	$0.303067\pi$
$252$	−1.90407e39	−0.453496
$253$	1.85724e38	0.0414360
$254$	−1.34974e37	−0.00282160
$255$	0	0
$256$	5.44190e39	0.999519
$257$	8.75106e39	1.50718	0.753588	−	0.657347i	$-0.228321\pi$
$257$	8.75106e39	1.50718	0.753588	+	0.657347i	$0.228321\pi$
$258$	−3.54800e37	−0.00573137
$259$	3.10224e39	0.470142
$260$	0	0
$261$	4.45515e39	0.594694
$262$	−6.42660e36	−0.000805397 0
$263$	−1.10339e40	−1.29855	−0.649273	−	0.760555i	$-0.724927\pi$
$263$	−1.10339e40	−1.29855	−0.649273	+	0.760555i	$0.724927\pi$
$264$	2.61636e37	0.00289223
$265$	0	0
$266$	4.47137e37	0.00436409
$267$	−7.95674e39	−0.729960
$268$	2.72134e39	0.234725
$269$	−1.84619e40	−1.49749	−0.748745	−	0.662858i	$-0.769343\pi$
$269$	−1.84619e40	−1.49749	−0.748745	+	0.662858i	$0.769343\pi$
$270$	0	0
$271$	1.48576e40	1.06649	0.533244	−	0.845962i	$-0.320973\pi$
$271$	1.48576e40	1.06649	0.533244	+	0.845962i	$0.320973\pi$
$272$	−1.56659e40	−1.05820
$273$	−2.20104e40	−1.39941
$274$	1.68947e38	0.0101127
$275$	0	0
$276$	2.30707e39	0.122479
$277$	−1.63998e40	−0.820204	−0.410102	−	0.912040i	$-0.634507\pi$
$277$	−1.63998e40	−0.820204	−0.410102	+	0.912040i	$0.634507\pi$
$278$	−1.18979e38	−0.00560699
$279$	5.80135e39	0.257668
$280$	0	0
$281$	−2.80874e40	−1.10881	−0.554406	−	0.832246i	$-0.687055\pi$
$281$	−2.80874e40	−1.10881	−0.554406	+	0.832246i	$0.687055\pi$
$282$	−1.81106e38	−0.00674252
$283$	−5.30091e40	−1.86155	−0.930774	−	0.365595i	$-0.880865\pi$
$283$	−5.30091e40	−1.86155	−0.930774	+	0.365595i	$0.880865\pi$
$284$	−5.08406e40	−1.68445
$285$	0	0
$286$	−9.41620e37	−0.00277866
$287$	2.09310e40	0.583095
$288$	−3.03569e38	−0.00798513
$289$	4.83501e39	0.120111
$290$	0	0
$291$	4.52195e40	1.00252
$292$	−2.56196e40	−0.536730
$293$	−9.02974e40	−1.78797	−0.893984	−	0.448100i	$-0.852101\pi$
$293$	−9.02974e40	−1.78797	−0.893984	+	0.448100i	$0.852101\pi$
$294$	1.15417e38	0.00216042
$295$	0	0
$296$	3.29728e38	0.00551878
$297$	1.82220e40	0.288480
$298$	9.02645e38	0.0135191
$299$	−1.66065e40	−0.235345
$300$	0	0
$301$	9.79783e40	1.24389
$302$	3.70828e38	0.00445716
$303$	4.75745e40	0.541465
$304$	−4.93782e40	−0.532257
$305$	0	0
$306$	2.91221e38	0.00281721
$307$	2.72894e40	0.250156	0.125078	−	0.992147i	$-0.460082\pi$
$307$	2.72894e40	0.250156	0.125078	+	0.992147i	$0.460082\pi$
$308$	−3.61246e40	−0.313845
$309$	−5.65749e40	−0.465917
$310$	0	0
$311$	9.31751e39	0.0689848	0.0344924	−	0.999405i	$-0.489019\pi$
$311$	9.31751e39	0.0689848	0.0344924	+	0.999405i	$0.489019\pi$
$312$	−2.33943e39	−0.0164270
$313$	1.02687e41	0.683963	0.341982	−	0.939707i	$-0.388902\pi$
$313$	1.02687e41	0.683963	0.341982	+	0.939707i	$0.388902\pi$
$314$	−1.36246e39	−0.00860962
$315$	0	0
$316$	−3.62461e40	−0.206264
$317$	−1.75249e41	−0.946623	−0.473311	−	0.880895i	$-0.656941\pi$
$317$	−1.75249e41	−0.946623	−0.473311	+	0.880895i	$0.656941\pi$
$318$	−5.06364e38	−0.00259666
$319$	8.45244e40	0.411562
$320$	0	0
$321$	1.67103e41	0.733925
$322$	3.06571e38	0.00127911
$323$	1.42120e41	0.563397
$324$	1.24494e41	0.468982
$325$	0	0
$326$	3.62837e39	0.0123487
$327$	−1.66956e41	−0.540212
$328$	2.22470e39	0.00684467
$329$	5.00125e41	1.46334
$330$	0	0
$331$	−6.69187e41	−1.77168	−0.885841	−	0.463989i	$-0.846418\pi$
$331$	−6.69187e41	−1.77168	−0.885841	+	0.463989i	$0.846418\pi$
$332$	2.15974e41	0.544031
$333$	6.36852e40	0.152654
$334$	−2.07470e38	−0.000473302 0
$335$	0	0
$336$	−4.48720e41	−0.927635
$337$	5.57473e41	1.09731	0.548656	−	0.836048i	$-0.315140\pi$
$337$	5.57473e41	1.09731	0.548656	+	0.836048i	$0.315140\pi$
$338$	4.71889e39	0.00884534
$339$	1.11038e41	0.198234
$340$	0	0
$341$	1.10065e41	0.178321
$342$	9.17916e38	0.00141701
$343$	4.84636e41	0.712956
$344$	1.04138e40	0.0146015
$345$	0	0
$346$	4.68054e39	0.00596403
$347$	5.73680e41	0.697001	0.348500	−	0.937309i	$-0.386691\pi$
$347$	5.73680e41	0.697001	0.348500	+	0.937309i	$0.386691\pi$
$348$	1.04997e42	1.21652
$349$	−6.96962e41	−0.770176	−0.385088	−	0.922880i	$-0.625829\pi$
$349$	−6.96962e41	−0.770176	−0.385088	+	0.922880i	$0.625829\pi$
$350$	0	0
$351$	−1.62933e42	−1.63848
$352$	−5.75941e39	−0.00552617
$353$	1.71218e42	1.56772	0.783858	−	0.620941i	$-0.213249\pi$
$353$	1.71218e42	1.56772	0.783858	+	0.620941i	$0.213249\pi$
$354$	1.19504e40	0.0104431
$355$	0	0
$356$	1.16767e42	0.929814
$357$	1.29150e42	0.981907
$358$	−2.51627e39	−0.00182678
$359$	6.40235e41	0.443896	0.221948	−	0.975059i	$-0.428759\pi$
$359$	6.40235e41	0.443896	0.221948	+	0.975059i	$0.428759\pi$
$360$	0	0
$361$	−1.13281e42	−0.716621
$362$	−1.81919e40	−0.0109948
$363$	−1.26351e42	−0.729657
$364$	3.23009e42	1.78255
$365$	0	0
$366$	1.60131e40	0.00807306
$367$	−2.44832e41	−0.117999	−0.0589994	−	0.998258i	$-0.518791\pi$
$367$	−2.44832e41	−0.117999	−0.0589994	+	0.998258i	$0.518791\pi$
$368$	−3.38552e41	−0.156004
$369$	4.29688e41	0.189329
$370$	0	0
$371$	1.39833e42	0.563559
$372$	1.36723e42	0.527090
$373$	5.34187e42	1.97014	0.985071	−	0.172147i	$-0.0550703\pi$
$373$	5.34187e42	1.97014	0.985071	+	0.172147i	$0.0550703\pi$
$374$	5.52513e39	0.00194967
$375$	0	0
$376$	5.31568e40	0.0171775
$377$	−7.55778e42	−2.33756
$378$	3.00788e40	0.00890524
$379$	3.34915e41	0.0949265	0.0474632	−	0.998873i	$-0.484886\pi$
$379$	3.34915e41	0.0949265	0.0474632	+	0.998873i	$0.484886\pi$
$380$	0	0
$381$	−1.22882e42	−0.319319
$382$	−5.41319e40	−0.0134712
$383$	−1.22154e42	−0.291157	−0.145579	−	0.989347i	$-0.546504\pi$
$383$	−1.22154e42	−0.291157	−0.145579	+	0.989347i	$0.546504\pi$
$384$	−9.53908e40	−0.0217792
$385$	0	0
$386$	7.83685e39	0.00164229
$387$	2.01137e42	0.403889
$388$	−6.63609e42	−1.27699
$389$	−7.03138e42	−1.29680	−0.648399	−	0.761301i	$-0.724561\pi$
$389$	−7.03138e42	−1.29680	−0.648399	+	0.761301i	$0.724561\pi$
$390$	0	0
$391$	9.74420e41	0.165131
$392$	−3.38763e40	−0.00550397
$393$	−5.85083e41	−0.0911466
$394$	5.10016e40	0.00761897
$395$	0	0
$396$	−7.41593e41	−0.101905
$397$	4.57583e42	0.603152	0.301576	−	0.953442i	$-0.402487\pi$
$397$	4.57583e42	0.603152	0.301576	+	0.953442i	$0.402487\pi$
$398$	9.20326e40	0.0116378
$399$	4.07077e42	0.493883
$400$	0	0
$401$	6.37629e42	0.712338	0.356169	−	0.934422i	$-0.384083\pi$
$401$	6.37629e42	0.712338	0.356169	+	0.934422i	$0.384083\pi$
$402$	−1.19219e40	−0.00127824
$403$	−9.84151e42	−1.01281
$404$	−6.98168e42	−0.689712
$405$	0	0
$406$	1.39523e41	0.0127047
$407$	1.20825e42	0.105645
$408$	1.37270e41	0.0115261
$409$	−1.70899e43	−1.37818	−0.689088	−	0.724678i	$-0.741989\pi$
$409$	−1.70899e43	−1.37818	−0.689088	+	0.724678i	$0.741989\pi$
$410$	0	0
$411$	1.53811e43	1.14445
$412$	8.30252e42	0.593479
$413$	−3.30010e43	−2.26648
$414$	6.29352e39	0.000415325 0
$415$	0	0
$416$	5.14980e41	0.0313871
$417$	−1.08319e43	−0.634542
$418$	1.74150e40	0.000980651 0
$419$	−6.84932e42	−0.370780	−0.185390	−	0.982665i	$-0.559355\pi$
$419$	−6.84932e42	−0.370780	−0.185390	+	0.982665i	$0.559355\pi$
$420$	0	0
$421$	−1.32258e43	−0.661861	−0.330930	−	0.943655i	$-0.607363\pi$
$421$	−1.32258e43	−0.661861	−0.330930	+	0.943655i	$0.607363\pi$
$422$	4.46968e38	2.15090e−5 0
$423$	1.02669e43	0.475144
$424$	1.48624e41	0.00661535
$425$	0	0
$426$	2.22726e41	0.00917304
$427$	−4.42203e43	−1.75211
$428$	−2.45229e43	−0.934865
$429$	−8.57259e42	−0.314461
$430$	0	0
$431$	3.28785e43	1.11696	0.558478	−	0.829519i	$-0.311385\pi$
$431$	3.28785e43	1.11696	0.558478	+	0.829519i	$0.311385\pi$
$432$	−3.32166e43	−1.08611
$433$	1.68338e43	0.529824	0.264912	−	0.964273i	$-0.414657\pi$
$433$	1.68338e43	0.529824	0.264912	+	0.964273i	$0.414657\pi$
$434$	1.81682e41	0.00550468
$435$	0	0
$436$	2.45013e43	0.688116
$437$	3.07133e42	0.0830583
$438$	1.12236e41	0.00292288
$439$	3.05836e43	0.767050	0.383525	−	0.923531i	$-0.374710\pi$
$439$	3.05836e43	0.767050	0.383525	+	0.923531i	$0.374710\pi$
$440$	0	0
$441$	−6.54302e42	−0.152244
$442$	−4.94032e41	−0.0110736
$443$	−8.21070e43	−1.77304	−0.886520	−	0.462690i	$-0.846884\pi$
$443$	−8.21070e43	−1.77304	−0.886520	+	0.462690i	$0.846884\pi$
$444$	1.50090e43	0.312272
$445$	0	0
$446$	5.41413e41	0.0104593
$447$	8.21775e43	1.52996
$448$	6.58445e43	1.18150
$449$	−4.67364e43	−0.808334	−0.404167	−	0.914685i	$-0.632439\pi$
$449$	−4.67364e43	−0.808334	−0.404167	+	0.914685i	$0.632439\pi$
$450$	0	0
$451$	8.15217e42	0.131027
$452$	−1.62951e43	−0.252507
$453$	3.37605e43	0.504415
$454$	2.78930e41	0.00401859
$455$	0	0
$456$	4.32670e41	0.00579745
$457$	4.35799e43	0.563208	0.281604	−	0.959531i	$-0.409134\pi$
$457$	4.35799e43	0.563208	0.281604	+	0.959531i	$0.409134\pi$
$458$	6.50474e41	0.00810867
$459$	9.56041e43	1.14965
$460$	0	0
$461$	−5.51173e43	−0.616911	−0.308456	−	0.951239i	$-0.599812\pi$
$461$	−5.51173e43	−0.616911	−0.308456	+	0.951239i	$0.599812\pi$
$462$	1.58257e41	0.00170911
$463$	7.61652e43	0.793726	0.396863	−	0.917878i	$-0.370099\pi$
$463$	7.61652e43	0.793726	0.396863	+	0.917878i	$0.370099\pi$
$464$	−1.54078e44	−1.54951
$465$	0	0
$466$	−8.37875e41	−0.00784895
$467$	5.66070e43	0.511848	0.255924	−	0.966697i	$-0.417620\pi$
$467$	5.66070e43	0.511848	0.255924	+	0.966697i	$0.417620\pi$
$468$	6.63098e43	0.578790
$469$	3.29223e43	0.277420
$470$	0	0
$471$	−1.24039e44	−0.974348
$472$	−3.50759e42	−0.0266051
$473$	3.81604e43	0.279514
$474$	1.58789e41	0.00112326
$475$	0	0
$476$	−1.89532e44	−1.25074
$477$	2.87059e43	0.182986
$478$	1.46287e42	0.00900835
$479$	1.53369e44	0.912436	0.456218	−	0.889868i	$-0.349204\pi$
$479$	1.53369e44	0.912436	0.456218	+	0.889868i	$0.349204\pi$
$480$	0	0
$481$	−1.08037e44	−0.600036
$482$	−4.97513e41	−0.00267011
$483$	2.79104e43	0.144757
$484$	1.85423e44	0.929428
$485$	0	0
$486$	1.06372e42	0.00498115
$487$	1.56849e44	0.709993	0.354996	−	0.934868i	$-0.384482\pi$
$487$	1.56849e44	0.709993	0.354996	+	0.934868i	$0.384482\pi$
$488$	−4.70005e42	−0.0205672
$489$	3.30330e44	1.39750
$490$	0	0
$491$	2.66401e44	1.05364	0.526818	−	0.849978i	$-0.323385\pi$
$491$	2.66401e44	1.05364	0.526818	+	0.849978i	$0.323385\pi$
$492$	1.01267e44	0.387296
$493$	4.43467e44	1.64016
$494$	−1.55717e42	−0.00556982
$495$	0	0
$496$	−2.00636e44	−0.671368
$497$	−6.15060e44	−1.99084
$498$	−9.46155e41	−0.00296264
$499$	3.44761e43	0.104438	0.0522190	−	0.998636i	$-0.483371\pi$
$499$	3.44761e43	0.104438	0.0522190	+	0.998636i	$0.483371\pi$
$500$	0	0
$501$	−1.88882e43	−0.0535634
$502$	2.93219e42	0.00804602
$503$	1.97299e44	0.523905	0.261952	−	0.965081i	$-0.415634\pi$
$503$	1.97299e44	0.523905	0.261952	+	0.965081i	$0.415634\pi$
$504$	−2.44833e42	−0.00629166
$505$	0	0
$506$	1.19403e41	0.000287429 0
$507$	4.29612e44	1.00102
$508$	1.80332e44	0.406745
$509$	−5.99115e44	−1.30818	−0.654089	−	0.756417i	$-0.726948\pi$
$509$	−5.99115e44	−1.30818	−0.654089	+	0.756417i	$0.726948\pi$
$510$	0	0
$511$	−3.09941e44	−0.634358
$512$	1.74982e43	0.0346767
$513$	3.01340e44	0.578256
$514$	5.62610e42	0.0104548
$515$	0	0
$516$	4.74030e44	0.826202
$517$	1.94788e44	0.328827
$518$	1.99444e42	0.00326123
$519$	4.26120e44	0.674948
$520$	0	0
$521$	9.20734e44	1.36871	0.684356	−	0.729148i	$-0.260084\pi$
$521$	9.20734e44	1.36871	0.684356	+	0.729148i	$0.260084\pi$
$522$	2.86423e42	0.00412520
$523$	−8.50723e44	−1.18716	−0.593581	−	0.804774i	$-0.702286\pi$
$523$	−8.50723e44	−1.18716	−0.593581	+	0.804774i	$0.702286\pi$
$524$	8.58625e43	0.116101
$525$	0	0
$526$	−7.09372e42	−0.00900760
$527$	5.77469e44	0.710647
$528$	−1.74766e44	−0.208448
$529$	−8.43947e44	−0.975656
$530$	0	0
$531$	−6.77471e44	−0.735921
$532$	−5.97396e44	−0.629101
$533$	−7.28930e44	−0.744195
$534$	−5.11542e42	−0.00506350
$535$	0	0
$536$	3.49921e42	0.00325650
$537$	−2.29083e44	−0.206736
$538$	−1.18693e43	−0.0103876
$539$	−1.24136e44	−0.105362
$540$	0	0
$541$	−1.15298e45	−0.920593	−0.460296	−	0.887765i	$-0.652257\pi$
$541$	−1.15298e45	−0.920593	−0.460296	+	0.887765i	$0.652257\pi$
$542$	9.55203e42	0.00739788
$543$	−1.65620e45	−1.24427
$544$	−3.02174e43	−0.0220230
$545$	0	0
$546$	−1.41506e43	−0.00970726
$547$	−1.27201e45	−0.846638	−0.423319	−	0.905981i	$-0.639135\pi$
$547$	−1.27201e45	−0.846638	−0.423319	+	0.905981i	$0.639135\pi$
$548$	−2.25722e45	−1.45779
$549$	−9.07789e44	−0.568907
$550$	0	0
$551$	1.39779e45	0.824975
$552$	2.96652e42	0.00169923
$553$	−4.38498e44	−0.243783
$554$	−1.05435e43	−0.00568949
$555$	0	0
$556$	1.58961e45	0.808271
$557$	−3.03968e45	−1.50044	−0.750218	−	0.661191i	$-0.770051\pi$
$557$	−3.03968e45	−1.50044	−0.750218	+	0.661191i	$0.770051\pi$
$558$	3.72972e42	0.00178736
$559$	−3.41213e45	−1.58756
$560$	0	0
$561$	5.03013e44	0.220644
$562$	−1.80576e43	−0.00769148
$563$	2.40727e45	0.995716	0.497858	−	0.867259i	$-0.334120\pi$
$563$	2.40727e45	0.995716	0.497858	+	0.867259i	$0.334120\pi$
$564$	2.41966e45	0.971963
$565$	0	0
$566$	−3.40798e43	−0.0129130
$567$	1.50610e45	0.554286
$568$	−6.53729e43	−0.0233696
$569$	−1.67468e45	−0.581539	−0.290769	−	0.956793i	$-0.593911\pi$
$569$	−1.67468e45	−0.581539	−0.290769	+	0.956793i	$0.593911\pi$
$570$	0	0
$571$	3.07822e45	1.00880	0.504399	−	0.863471i	$-0.331714\pi$
$571$	3.07822e45	1.00880	0.504399	+	0.863471i	$0.331714\pi$
$572$	1.25805e45	0.400556
$573$	−4.92821e45	−1.52454
$574$	1.34567e43	0.00404474
$575$	0	0
$576$	1.35171e45	0.383629
$577$	2.65106e45	0.731169	0.365585	−	0.930778i	$-0.380869\pi$
$577$	2.65106e45	0.731169	0.365585	+	0.930778i	$0.380869\pi$
$578$	3.10845e42	0.000833172 0
$579$	7.13473e44	0.185858
$580$	0	0
$581$	2.61281e45	0.642987
$582$	2.90718e43	0.00695414
$583$	5.44618e44	0.126637
$584$	−3.29428e43	−0.00744643
$585$	0	0
$586$	−5.80526e43	−0.0124026
$587$	−5.61606e45	−1.16655	−0.583274	−	0.812275i	$-0.698229\pi$
$587$	−5.61606e45	−1.16655	−0.583274	+	0.812275i	$0.698229\pi$
$588$	−1.54203e45	−0.311434
$589$	1.82016e45	0.357443
$590$	0	0
$591$	4.64323e45	0.862237
$592$	−2.20251e45	−0.397749
$593$	1.02970e46	1.80845	0.904225	−	0.427056i	$-0.140449\pi$
$593$	1.02970e46	1.80845	0.904225	+	0.427056i	$0.140449\pi$
$594$	1.17150e43	0.00200109
$595$	0	0
$596$	−1.20598e46	−1.94884
$597$	8.37872e45	1.31705
$598$	−1.06764e43	−0.00163251
$599$	−2.88158e45	−0.428636	−0.214318	−	0.976764i	$-0.568753\pi$
$599$	−2.88158e45	−0.428636	−0.214318	+	0.976764i	$0.568753\pi$
$600$	0	0
$601$	−5.17029e45	−0.727924	−0.363962	−	0.931414i	$-0.618576\pi$
$601$	−5.17029e45	−0.727924	−0.363962	+	0.931414i	$0.618576\pi$
$602$	6.29907e43	0.00862848
$603$	6.75853e44	0.0900776
$604$	−4.95444e45	−0.642518
$605$	0	0
$606$	3.05859e43	0.00375597
$607$	−6.70496e45	−0.801277	−0.400639	−	0.916236i	$-0.631212\pi$
$607$	−6.70496e45	−0.801277	−0.400639	+	0.916236i	$0.631212\pi$
$608$	−9.52441e43	−0.0110772
$609$	1.27023e46	1.43779
$610$	0	0
$611$	−1.74170e46	−1.86764
$612$	−3.89085e45	−0.406113
$613$	−5.31969e45	−0.540491	−0.270246	−	0.962791i	$-0.587105\pi$
$613$	−5.31969e45	−0.540491	−0.270246	+	0.962791i	$0.587105\pi$
$614$	1.75445e43	0.00173525
$615$	0	0
$616$	−4.64504e43	−0.00435419
$617$	1.86107e46	1.69847	0.849237	−	0.528013i	$-0.177063\pi$
$617$	1.86107e46	1.69847	0.849237	+	0.528013i	$0.177063\pi$
$618$	−3.63723e43	−0.00323192
$619$	5.57296e45	0.482159	0.241080	−	0.970505i	$-0.422499\pi$
$619$	5.57296e45	0.482159	0.241080	+	0.970505i	$0.422499\pi$
$620$	0	0
$621$	2.06608e45	0.169487
$622$	5.99027e42	0.000478526 0
$623$	1.41263e46	1.09894
$624$	1.56268e46	1.18393
$625$	0	0
$626$	6.60178e43	0.00474443
$627$	1.58548e45	0.110980
$628$	1.82031e46	1.24111
$629$	6.33925e45	0.421019
$630$	0	0
$631$	−3.09333e45	−0.194958	−0.0974792	−	0.995238i	$-0.531078\pi$
$631$	−3.09333e45	−0.194958	−0.0974792	+	0.995238i	$0.531078\pi$
$632$	−4.66067e43	−0.00286165
$633$	4.06923e43	0.00243417
$634$	−1.12668e44	−0.00656642
$635$	0	0
$636$	6.76527e45	0.374320
$637$	1.10997e46	0.598426
$638$	5.43411e43	0.00285488
$639$	−1.26264e46	−0.646422
$640$	0	0
$641$	−9.35057e45	−0.454654	−0.227327	−	0.973819i	$-0.572999\pi$
$641$	−9.35057e45	−0.454654	−0.227327	+	0.973819i	$0.572999\pi$
$642$	1.07431e44	0.00509101
$643$	2.94884e46	1.36198	0.680989	−	0.732294i	$-0.261550\pi$
$643$	2.94884e46	1.36198	0.680989	+	0.732294i	$0.261550\pi$
$644$	−4.09593e45	−0.184389
$645$	0	0
$646$	9.13698e43	0.00390810
$647$	3.28551e46	1.36988	0.684940	−	0.728600i	$-0.259829\pi$
$647$	3.28551e46	1.36988	0.684940	+	0.728600i	$0.259829\pi$
$648$	1.60079e44	0.00650651
$649$	−1.28532e46	−0.509300
$650$	0	0
$651$	1.65405e46	0.622964
$652$	−4.84768e46	−1.78012
$653$	3.34222e46	1.19665	0.598325	−	0.801253i	$-0.295833\pi$
$653$	3.34222e46	1.19665	0.598325	+	0.801253i	$0.295833\pi$
$654$	−1.07337e44	−0.00374728
$655$	0	0
$656$	−1.48605e46	−0.493309
$657$	−6.36271e45	−0.205975
$658$	3.21533e44	0.0101507
$659$	3.13180e46	0.964238	0.482119	−	0.876106i	$-0.339867\pi$
$659$	3.13180e46	0.964238	0.482119	+	0.876106i	$0.339867\pi$
$660$	0	0
$661$	4.24878e46	1.24434	0.622172	−	0.782881i	$-0.286251\pi$
$661$	4.24878e46	1.24434	0.622172	+	0.782881i	$0.286251\pi$
$662$	−4.30224e44	−0.0122896
$663$	−4.49771e46	−1.25319
$664$	2.77708e44	0.00754772
$665$	0	0
$666$	4.09435e43	0.00105891
$667$	9.58368e45	0.241800
$668$	2.77190e45	0.0682284
$669$	4.92907e46	1.18368
$670$	0	0
$671$	−1.72228e46	−0.393716
$672$	−8.65521e44	−0.0193057
$673$	−7.35045e46	−1.59980	−0.799900	−	0.600134i	$-0.795114\pi$
$673$	−7.35045e46	−1.59980	−0.799900	+	0.600134i	$0.795114\pi$
$674$	3.58402e44	0.00761170
$675$	0	0
$676$	−6.30467e46	−1.27509
$677$	−5.34649e46	−1.05525	−0.527625	−	0.849477i	$-0.676917\pi$
$677$	−5.34649e46	−1.05525	−0.527625	+	0.849477i	$0.676917\pi$
$678$	7.13869e43	0.00137508
$679$	−8.02820e46	−1.50927
$680$	0	0
$681$	2.53940e46	0.454782
$682$	7.07613e43	0.00123695
$683$	−2.23782e46	−0.381841	−0.190921	−	0.981605i	$-0.561147\pi$
$683$	−2.23782e46	−0.381841	−0.190921	+	0.981605i	$0.561147\pi$
$684$	−1.22638e46	−0.204268
$685$	0	0
$686$	3.11575e44	0.00494555
$687$	5.92197e46	0.917656
$688$	−6.95619e46	−1.05236
$689$	−4.86973e46	−0.719262
$690$	0	0
$691$	1.74443e46	0.245622	0.122811	−	0.992430i	$-0.460809\pi$
$691$	1.74443e46	0.245622	0.122811	+	0.992430i	$0.460809\pi$
$692$	−6.25343e46	−0.859741
$693$	−8.97164e45	−0.120441
$694$	3.68821e44	0.00483487
$695$	0	0
$696$	1.35009e45	0.0168776
$697$	4.27713e46	0.522170
$698$	−4.48080e44	−0.00534246
$699$	−7.62809e46	−0.888264
$700$	0	0
$701$	1.34856e47	1.49804	0.749019	−	0.662549i	$-0.230525\pi$
$701$	1.34856e47	1.49804	0.749019	+	0.662549i	$0.230525\pi$
$702$	−1.04750e45	−0.0113656
$703$	1.99811e46	0.211766
$704$	2.56450e46	0.265493
$705$	0	0
$706$	1.10077e45	0.0108747
$707$	−8.44630e46	−0.815166
$708$	−1.59663e47	−1.50541
$709$	−1.33803e47	−1.23254	−0.616271	−	0.787535i	$-0.711357\pi$
$709$	−1.33803e47	−1.23254	−0.616271	+	0.787535i	$0.711357\pi$
$710$	0	0
$711$	−9.00182e45	−0.0791557
$712$	1.50144e45	0.0129000
$713$	1.24796e46	0.104767
$714$	8.30314e44	0.00681117
$715$	0	0
$716$	3.36185e46	0.263338
$717$	1.33181e47	1.01947
$718$	4.11610e44	0.00307916
$719$	−1.63878e47	−1.19811	−0.599053	−	0.800710i	$-0.704456\pi$
$719$	−1.63878e47	−1.19811	−0.599053	+	0.800710i	$0.704456\pi$
$720$	0	0
$721$	1.00442e47	0.701430
$722$	−7.28291e44	−0.00497097
$723$	−4.52940e46	−0.302175
$724$	2.43052e47	1.58494
$725$	0	0
$726$	−8.12315e44	−0.00506140
$727$	−7.90263e46	−0.481342	−0.240671	−	0.970607i	$-0.577368\pi$
$727$	−7.90263e46	−0.481342	−0.240671	+	0.970607i	$0.577368\pi$
$728$	4.15338e45	0.0247306
$729$	1.77413e47	1.03272
$730$	0	0
$731$	2.00213e47	1.11392
$732$	−2.13943e47	−1.16377
$733$	5.70441e46	0.303386	0.151693	−	0.988428i	$-0.451528\pi$
$733$	5.70441e46	0.303386	0.151693	+	0.988428i	$0.451528\pi$
$734$	−1.57403e44	−0.000818520 0
$735$	0	0
$736$	−6.53023e44	−0.00324672
$737$	1.28225e46	0.0623389
$738$	2.76248e44	0.00131332
$739$	3.20833e46	0.149158	0.0745789	−	0.997215i	$-0.476239\pi$
$739$	3.20833e46	0.149158	0.0745789	+	0.997215i	$0.476239\pi$
$740$	0	0
$741$	−1.41766e47	−0.630335
$742$	8.98991e44	0.00390923
$743$	3.44334e46	0.146442	0.0732208	−	0.997316i	$-0.476672\pi$
$743$	3.44334e46	0.146442	0.0732208	+	0.997316i	$0.476672\pi$
$744$	1.75804e45	0.00731268
$745$	0	0
$746$	3.43431e45	0.0136662
$747$	5.36378e46	0.208776
$748$	−7.38185e46	−0.281053
$749$	−2.96673e47	−1.10491
$750$	0	0
$751$	−2.36045e47	−0.841271	−0.420635	−	0.907230i	$-0.638193\pi$
$751$	−2.36045e47	−0.841271	−0.420635	+	0.907230i	$0.638193\pi$
$752$	−3.55075e47	−1.23801
$753$	2.66949e47	0.910566
$754$	−4.85893e45	−0.0162149
$755$	0	0
$756$	−4.01867e47	−1.28373
$757$	1.08268e47	0.338390	0.169195	−	0.985583i	$-0.445883\pi$
$757$	1.08268e47	0.338390	0.169195	+	0.985583i	$0.445883\pi$
$758$	2.15318e44	0.000658475 0
$759$	1.08705e46	0.0325282
$760$	0	0
$761$	−3.72392e47	−1.06697	−0.533486	−	0.845809i	$-0.679118\pi$
$761$	−3.72392e47	−1.06697	−0.533486	+	0.845809i	$0.679118\pi$
$762$	−7.90012e44	−0.00221502
$763$	2.96411e47	0.813280
$764$	7.23229e47	1.94194
$765$	0	0
$766$	−7.85333e44	−0.00201966
$767$	1.14927e48	2.89268
$768$	3.18517e47	0.784645
$769$	−9.78850e46	−0.236011	−0.118005	−	0.993013i	$-0.537650\pi$
$769$	−9.78850e46	−0.236011	−0.118005	+	0.993013i	$0.537650\pi$
$770$	0	0
$771$	5.12204e47	1.18317
$772$	−1.04704e47	−0.236744
$773$	−3.96450e47	−0.877458	−0.438729	−	0.898619i	$-0.644571\pi$
$773$	−3.96450e47	−0.877458	−0.438729	+	0.898619i	$0.644571\pi$
$774$	1.29312e45	0.00280165
$775$	0	0
$776$	−8.53295e45	−0.0177166
$777$	1.81576e47	0.369072
$778$	−4.52051e45	−0.00899547
$779$	1.34814e47	0.262643
$780$	0	0
$781$	−2.39552e47	−0.447361
$782$	6.26459e44	0.00114546
$783$	9.40291e47	1.68342
$784$	2.26286e47	0.396682
$785$	0	0
$786$	−3.76153e44	−0.000632255 0
$787$	5.95539e47	0.980228	0.490114	−	0.871658i	$-0.336955\pi$
$787$	5.95539e47	0.980228	0.490114	+	0.871658i	$0.336955\pi$
$788$	−6.81406e47	−1.09831
$789$	−6.45818e47	−1.01939
$790$	0	0
$791$	−1.97135e47	−0.298437
$792$	−9.53570e44	−0.00141380
$793$	1.53999e48	2.23620
$794$	2.94182e45	0.00418387
$795$	0	0
$796$	−1.22960e48	−1.67764
$797$	−2.43995e47	−0.326076	−0.163038	−	0.986620i	$-0.552129\pi$
$797$	−2.43995e47	−0.326076	−0.163038	+	0.986620i	$0.552129\pi$
$798$	2.61712e45	0.00342591
$799$	1.02198e48	1.31045
$800$	0	0
$801$	2.89995e47	0.356824
$802$	4.09935e45	0.00494126
$803$	−1.20715e47	−0.142546
$804$	1.59282e47	0.184264
$805$	0	0
$806$	−6.32716e45	−0.00702555
$807$	−1.08059e48	−1.17556
$808$	−8.97733e45	−0.00956885
$809$	−4.06571e47	−0.424606	−0.212303	−	0.977204i	$-0.568096\pi$
$809$	−4.06571e47	−0.424606	−0.212303	+	0.977204i	$0.568096\pi$
$810$	0	0
$811$	1.74453e48	1.74918	0.874591	−	0.484862i	$-0.161130\pi$
$811$	1.74453e48	1.74918	0.874591	+	0.484862i	$0.161130\pi$
$812$	−1.86409e48	−1.83144
$813$	8.69625e47	0.837216
$814$	7.76792e44	0.000732828 0
$815$	0	0
$816$	−9.16933e47	−0.830711
$817$	6.31063e47	0.560285
$818$	−1.09872e46	−0.00955997
$819$	8.02203e47	0.684069
$820$	0	0
$821$	8.84220e47	0.724267	0.362133	−	0.932126i	$-0.382049\pi$
$821$	8.84220e47	0.724267	0.362133	+	0.932126i	$0.382049\pi$
$822$	9.88858e45	0.00793869
$823$	−1.96507e48	−1.54625	−0.773127	−	0.634251i	$-0.781309\pi$
$823$	−1.96507e48	−1.54625	−0.773127	+	0.634251i	$0.781309\pi$
$824$	1.06757e46	0.00823375
$825$	0	0
$826$	−2.12165e46	−0.0157218
$827$	2.21957e48	1.61223	0.806117	−	0.591757i	$-0.201565\pi$
$827$	2.21957e48	1.61223	0.806117	+	0.591757i	$0.201565\pi$
$828$	−8.40845e46	−0.0598708
$829$	7.98020e47	0.557012	0.278506	−	0.960435i	$-0.410161\pi$
$829$	7.98020e47	0.557012	0.278506	+	0.960435i	$0.410161\pi$
$830$	0	0
$831$	−9.59889e47	−0.643879
$832$	−2.29306e48	−1.50793
$833$	−6.51295e47	−0.419890
$834$	−6.96388e45	−0.00440161
$835$	0	0
$836$	−2.32673e47	−0.141365
$837$	1.22442e48	0.729390
$838$	−4.40346e45	−0.00257198
$839$	−2.69129e48	−1.54131	−0.770653	−	0.637255i	$-0.780070\pi$
$839$	−2.69129e48	−1.54131	−0.770653	+	0.637255i	$0.780070\pi$
$840$	0	0
$841$	2.54554e48	1.40167
$842$	−8.50292e45	−0.00459112
$843$	−1.64397e48	−0.870442
$844$	−5.97171e45	−0.00310062
$845$	0	0
$846$	6.60067e45	0.00329592
$847$	2.24321e48	1.09849
$848$	−9.92775e47	−0.476781
$849$	−3.10265e48	−1.46136
$850$	0	0
$851$	1.36996e47	0.0620685
$852$	−2.97573e48	−1.32233
$853$	−2.54820e46	−0.0111064	−0.00555321	−	0.999985i	$-0.501768\pi$
$853$	−2.54820e46	−0.0111064	−0.00555321	+	0.999985i	$0.501768\pi$
$854$	−2.84295e46	−0.0121538
$855$	0	0
$856$	−3.15325e46	−0.0129700
$857$	1.60067e47	0.0645831	0.0322915	−	0.999478i	$-0.489719\pi$
$857$	1.60067e47	0.0645831	0.0322915	+	0.999478i	$0.489719\pi$
$858$	−5.51136e45	−0.00218131
$859$	−2.01059e48	−0.780612	−0.390306	−	0.920685i	$-0.627631\pi$
$859$	−2.01059e48	−0.780612	−0.390306	+	0.920685i	$0.627631\pi$
$860$	0	0
$861$	1.22510e48	0.457742
$862$	2.11377e46	0.00774797
$863$	−1.75008e48	−0.629332	−0.314666	−	0.949202i	$-0.601893\pi$
$863$	−1.75008e48	−0.629332	−0.314666	+	0.949202i	$0.601893\pi$
$864$	−6.40705e46	−0.0226038
$865$	0	0
$866$	1.08225e46	0.00367522
$867$	2.82996e47	0.0942898
$868$	−2.42737e48	−0.793524
$869$	−1.70785e47	−0.0547803
$870$	0	0
$871$	−1.14653e48	−0.354067
$872$	3.15047e46	0.00954671
$873$	−1.64809e48	−0.490057
$874$	1.97457e45	0.000576149 0
$875$	0	0
$876$	−1.49953e48	−0.421345
$877$	6.70977e47	0.185018	0.0925091	−	0.995712i	$-0.470511\pi$
$877$	6.70977e47	0.185018	0.0925091	+	0.995712i	$0.470511\pi$
$878$	1.96623e46	0.00532078
$879$	−5.28516e48	−1.40359
$880$	0	0
$881$	5.25499e48	1.34422	0.672109	−	0.740452i	$-0.265389\pi$
$881$	5.25499e48	1.34422	0.672109	+	0.740452i	$0.265389\pi$
$882$	−4.20654e45	−0.00105607
$883$	−3.43775e48	−0.847076	−0.423538	−	0.905878i	$-0.639212\pi$
$883$	−3.43775e48	−0.847076	−0.423538	+	0.905878i	$0.639212\pi$
$884$	6.60051e48	1.59630
$885$	0	0
$886$	−5.27870e46	−0.0122990
$887$	−3.38480e48	−0.774092	−0.387046	−	0.922060i	$-0.626505\pi$
$887$	−3.38480e48	−0.774092	−0.387046	+	0.922060i	$0.626505\pi$
$888$	1.92992e46	0.00433236
$889$	2.18162e48	0.480729
$890$	0	0
$891$	5.86594e47	0.124553
$892$	−7.23355e48	−1.50776
$893$	3.22123e48	0.659132
$894$	5.28323e46	0.0106128
$895$	0	0
$896$	1.69355e47	0.0327882
$897$	−9.71991e47	−0.184751
$898$	−3.00471e46	−0.00560715
$899$	5.67956e48	1.04059
$900$	0	0
$901$	2.85740e48	0.504676
$902$	5.24107e45	0.000908892 0
$903$	5.73472e48	0.976483
$904$	−2.09530e46	−0.00350321
$905$	0	0
$906$	2.17048e46	0.00349897
$907$	8.28291e48	1.31118	0.655590	−	0.755117i	$-0.272420\pi$
$907$	8.28291e48	1.31118	0.655590	+	0.755117i	$0.272420\pi$
$908$	−3.72664e48	−0.579296
$909$	−1.73392e48	−0.264683
$910$	0	0
$911$	−2.04653e48	−0.301277	−0.150638	−	0.988589i	$-0.548133\pi$
$911$	−2.04653e48	−0.301277	−0.150638	+	0.988589i	$0.548133\pi$
$912$	−2.89014e48	−0.417834
$913$	1.01763e48	0.144485
$914$	2.80177e46	0.00390680
$915$	0	0
$916$	−8.69065e48	−1.16890
$917$	1.03875e48	0.137220
$918$	6.14643e46	0.00797478
$919$	−8.18528e48	−1.04310	−0.521552	−	0.853219i	$-0.674647\pi$
$919$	−8.18528e48	−1.04310	−0.521552	+	0.853219i	$0.674647\pi$
$920$	0	0
$921$	1.59726e48	0.196378
$922$	−3.54352e46	−0.00427932
$923$	2.14197e49	2.54088
$924$	−2.11439e48	−0.246376
$925$	0	0
$926$	4.89670e46	0.00550582
$927$	2.06195e48	0.227753
$928$	−2.97196e47	−0.0322479
$929$	1.84054e48	0.196194	0.0980971	−	0.995177i	$-0.468724\pi$
$929$	1.84054e48	0.196194	0.0980971	+	0.995177i	$0.468724\pi$
$930$	0	0
$931$	−2.05286e48	−0.211197
$932$	1.11944e49	1.13146
$933$	5.45359e47	0.0541546
$934$	3.63929e46	0.00355053
$935$	0	0
$936$	8.52638e46	0.00802996
$937$	1.09333e49	1.01169	0.505844	−	0.862625i	$-0.331181\pi$
$937$	1.09333e49	1.01169	0.505844	+	0.862625i	$0.331181\pi$
$938$	2.11659e46	0.00192437
$939$	6.01031e48	0.536927
$940$	0	0
$941$	−4.25945e48	−0.367388	−0.183694	−	0.982984i	$-0.558805\pi$
$941$	−4.25945e48	−0.367388	−0.183694	+	0.982984i	$0.558805\pi$
$942$	−7.97454e46	−0.00675874
$943$	9.24323e47	0.0769805
$944$	2.34298e49	1.91748
$945$	0	0
$946$	2.45335e46	0.00193890
$947$	6.13570e48	0.476529	0.238265	−	0.971200i	$-0.423421\pi$
$947$	6.13570e48	0.476529	0.238265	+	0.971200i	$0.423421\pi$
$948$	−2.12151e48	−0.161922
$949$	1.07938e49	0.809622
$950$	0	0
$951$	−1.02574e49	−0.743120
$952$	−2.43708e47	−0.0173524
$953$	1.00078e49	0.700334	0.350167	−	0.936687i	$-0.386125\pi$
$953$	1.00078e49	0.700334	0.350167	+	0.936687i	$0.386125\pi$
$954$	1.84552e46	0.00126932
$955$	0	0
$956$	−1.95447e49	−1.29859
$957$	4.94726e48	0.323086
$958$	9.86018e46	0.00632928
$959$	−2.73074e49	−1.72295
$960$	0	0
$961$	−9.00773e48	−0.549135
$962$	−6.94572e46	−0.00416226
$963$	−6.09032e48	−0.358762
$964$	6.64702e48	0.384907
$965$	0	0
$966$	1.79438e46	0.00100413
$967$	−2.67343e49	−1.47072	−0.735362	−	0.677674i	$-0.762988\pi$
$967$	−2.67343e49	−1.47072	−0.735362	+	0.677674i	$0.762988\pi$
$968$	2.38425e47	0.0128946
$969$	8.31838e48	0.442279
$970$	0	0
$971$	−1.33820e49	−0.687708	−0.343854	−	0.939023i	$-0.611732\pi$
$971$	−1.33820e49	−0.687708	−0.343854	+	0.939023i	$0.611732\pi$
$972$	−1.42118e49	−0.718053
$973$	1.92308e49	0.955291
$974$	1.00839e47	0.00492499
$975$	0	0
$976$	3.13952e49	1.48232
$977$	−9.15286e48	−0.424909	−0.212455	−	0.977171i	$-0.568146\pi$
$977$	−9.15286e48	−0.424909	−0.212455	+	0.977171i	$0.568146\pi$
$978$	2.12370e47	0.00969400
$979$	5.50187e48	0.246943
$980$	0	0
$981$	6.08496e48	0.264070
$982$	1.71270e47	0.00730873
$983$	1.92101e49	0.806114	0.403057	−	0.915175i	$-0.367948\pi$
$983$	1.92101e49	0.806114	0.403057	+	0.915175i	$0.367948\pi$
$984$	1.30213e47	0.00537322
$985$	0	0
$986$	2.85107e47	0.0113773
$987$	2.92726e49	1.14876
$988$	2.08045e49	0.802913
$989$	4.32676e48	0.164219
$990$	0	0
$991$	1.15219e49	0.422968	0.211484	−	0.977381i	$-0.432170\pi$
$991$	1.15219e49	0.422968	0.211484	+	0.977381i	$0.432170\pi$
$992$	−3.87000e47	−0.0139723
$993$	−3.91679e49	−1.39081
$994$	−3.95425e47	−0.0138098
$995$	0	0
$996$	1.26411e49	0.427076
$997$	−8.77081e48	−0.291454	−0.145727	−	0.989325i	$-0.546552\pi$
$997$	−8.77081e48	−0.291454	−0.145727	+	0.989325i	$0.546552\pi$
$998$	2.21648e46	0.000724453 0
$999$	1.34412e49	0.432124

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.34.a.e.1.6	yes	11
5.2	odd	4		25.34.b.d.24.12		22
5.3	odd	4		25.34.b.d.24.11		22
5.4	even	2		25.34.a.d.1.6	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.34.a.d.1.6	✓	11	5.4	even	2
25.34.a.e.1.6	yes	11	1.1	even	1	trivial
25.34.b.d.24.11		22	5.3	odd	4
25.34.b.d.24.12		22	5.2	odd	4

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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 34 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)

\(f(q)\)	\(=\)	\(q+642.905 q^{2} +5.85306e7 q^{3} -8.58952e9 q^{4} +3.76296e10 q^{6} -1.03914e14 q^{7} -1.10448e13 q^{8} -2.13323e15 q^{9} +O(q^{10})\)	\(q+642.905 q^{2} +5.85306e7 q^{3} -8.58952e9 q^{4} +3.76296e10 q^{6} -1.03914e14 q^{7} -1.10448e13 q^{8} -2.13323e15 q^{9} -4.04723e16 q^{11} -5.02750e17 q^{12} +3.61885e18 q^{13} -6.68070e16 q^{14} +7.37763e19 q^{16} -2.12343e20 q^{17} -1.37147e18 q^{18} -6.69296e20 q^{19} -6.08216e21 q^{21} -2.60199e19 q^{22} -4.58890e21 q^{23} -6.46456e20 q^{24} +2.32658e21 q^{26} -4.50234e23 q^{27} +8.92574e23 q^{28} -2.08845e24 q^{29} -2.71951e24 q^{31} +1.42305e23 q^{32} -2.36887e24 q^{33} -1.36516e23 q^{34} +1.83234e25 q^{36} -2.98538e25 q^{37} -4.30294e23 q^{38} +2.11813e26 q^{39} -2.01426e26 q^{41} -3.91025e24 q^{42} -9.42876e26 q^{43} +3.47638e26 q^{44} -2.95023e24 q^{46} -4.81286e27 q^{47} +4.31817e27 q^{48} +3.06719e27 q^{49} -1.24286e28 q^{51} -3.10842e28 q^{52} -1.34565e28 q^{53} -2.89458e26 q^{54} +1.14771e27 q^{56} -3.91743e28 q^{57} -1.34267e27 q^{58} +3.17580e29 q^{59} +4.25546e29 q^{61} -1.74839e27 q^{62} +2.21673e29 q^{63} -6.33642e29 q^{64} -1.52296e27 q^{66} -3.16821e29 q^{67} +1.82392e30 q^{68} -2.68591e29 q^{69} +5.91891e30 q^{71} +2.35610e28 q^{72} +2.98266e30 q^{73} -1.91932e28 q^{74} +5.74893e30 q^{76} +4.20565e30 q^{77} +1.36176e29 q^{78} +4.21980e30 q^{79} -1.44937e31 q^{81} -1.29498e29 q^{82} -2.51439e31 q^{83} +5.22429e31 q^{84} -6.06179e29 q^{86} -1.22238e32 q^{87} +4.47007e29 q^{88} -1.35942e32 q^{89} -3.76050e32 q^{91} +3.94165e31 q^{92} -1.59175e32 q^{93} -3.09421e30 q^{94} +8.32918e30 q^{96} +7.72579e32 q^{97} +1.97191e30 q^{98} +8.63369e31 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 9393 q^{2} + 80330849 q^{3} + 49338206677 q^{4} - 17783977676723 q^{6} + 21344025107658 q^{7} - 970199832420105 q^{8} + 24\!\cdots\!58 q^{9}+O(q^{10}) \) 11 * q + 9393 * q^2 + 80330849 * q^3 + 49338206677 * q^4 - 17783977676723 * q^6 + 21344025107658 * q^7 - 970199832420105 * q^8 + 24299637974625658 * q^9	\( 11 q + 9393 q^{2} + 80330849 q^{3} + 49338206677 q^{4} - 17783977676723 q^{6} + 21344025107658 q^{7} - 970199832420105 q^{8} + 24\!\cdots\!58 q^{9}+ \cdots + 13\!\cdots\!06 q^{99}+O(q^{100}) \) 11 * q + 9393 * q^2 + 80330849 * q^3 + 49338206677 * q^4 - 17783977676723 * q^6 + 21344025107658 * q^7 - 970199832420105 * q^8 + 24299637974625658 * q^9 - 194487534567113523 * q^11 + 1128411534853252093 * q^12 + 5151173641795199804 * q^13 + 9695004297667451034 * q^14 + 287795879559665379601 * q^16 + 217450883530375665663 * q^17 - 883205358438912773746 * q^18 - 2304421397121542404315 * q^19 + 3951679538424255448062 * q^21 + 65697936516541243081001 * q^22 + 39745489889804460665334 * q^23 - 202096278074290714435545 * q^24 + 232341332678498439460092 * q^26 + 215757396930304201071995 * q^27 - 1844234528929870945073094 * q^28 + 1675632286595729558796840 * q^29 - 1879684496680578139929438 * q^31 - 22333622446463598116694177 * q^32 - 36653442436454147951147057 * q^33 - 44873360881289881717450051 * q^34 + 193677686753165783059502006 * q^36 + 180277972113296426057413198 * q^37 + 216179528860395412757129505 * q^38 - 359172746626046600427282844 * q^39 + 549519804753897528529573167 * q^41 + 2593357144102832185922898306 * q^42 + 50270064758017307324647244 * q^43 - 2976543624086726877274410711 * q^44 + 1688362231334867471013357582 * q^46 + 10903258570108047175558188228 * q^47 + 28193416941275907016447196209 * q^48 - 2501658924474402528580483073 * q^49 + 66317965316246498072666600557 * q^51 + 155672232460399094184759234028 * q^52 + 33298643916770080171872677874 * q^53 - 213393152239696124781888030065 * q^54 + 339537122636968128125815064910 * q^56 + 159006470550216362740785378215 * q^57 + 62377017575001287720537209120 * q^58 - 67706990548480155796584121920 * q^59 - 344769258471797286249471450898 * q^61 - 1319517422843123577963573948294 * q^62 - 699283498025109144495841661076 * q^63 + 1420026267960910564014627900737 * q^64 - 160016657586606697551149537011 * q^66 - 1671796054942808947714198855437 * q^67 + 3088683653934580261727419953441 * q^68 + 7218504661993692063958711761426 * q^69 - 5525905608449961693610592189868 * q^71 - 21423093069732612399854192774190 * q^72 + 1280933432508086429255473349609 * q^73 + 8483102027446485651051216797154 * q^74 - 3794387798301159395171650466255 * q^76 - 25187595245022035764699127942394 * q^77 - 56671274702179561872150030862772 * q^78 + 28416813573575354189758739594190 * q^79 - 4511447703484319172258978381029 * q^81 + 94213252968905060003342215055821 * q^82 + 127792566726367853829683612248839 * q^83 - 299946577157245367261151073271766 * q^84 + 455910432123816097591159189088412 * q^86 + 485010641407021414487926087945160 * q^87 + 5212296644003692182363473725515 * q^88 - 24030870261451879999370600550555 * q^89 - 346687858887153608395037323300248 * q^91 + 535778496942575427226503821168238 * q^92 + 789528086332099641022541300872758 * q^93 + 232538212076560959503267655560444 * q^94 - 1842110282591420302371913525952353 * q^96 - 674692794164529660649398963528122 * q^97 - 2571899453674006542996540156918099 * q^98 + 1300949547786735016969037553636806 * q^99

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