LMFDB - Embedded newform 25.34.a.d.1.5

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:	$1$
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			1.5
Root			$-33894.6$ 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)

$f(q)$	$=$	$q-34748.6 q^{2} +4.98225e7 q^{3} -7.38247e9 q^{4} -1.73126e12 q^{6} -1.47813e14 q^{7} +5.55018e14 q^{8} -3.07678e15 q^{9} +O(q^{10})$	\(q-34748.6 q^{2} +4.98225e7 q^{3} -7.38247e9 q^{4} -1.73126e12 q^{6} -1.47813e14 q^{7} +5.55018e14 q^{8} -3.07678e15 q^{9} +5.98091e16 q^{11} -3.67813e17 q^{12} -1.87169e18 q^{13} +5.13629e18 q^{14} +4.41289e19 q^{16} -1.50089e19 q^{17} +1.06914e20 q^{18} +9.64673e20 q^{19} -7.36441e21 q^{21} -2.07828e21 q^{22} +2.94875e22 q^{23} +2.76524e22 q^{24} +6.50384e22 q^{26} -4.30259e23 q^{27} +1.09122e24 q^{28} +2.20516e24 q^{29} +2.16118e24 q^{31} -6.30098e24 q^{32} +2.97984e24 q^{33} +5.21536e23 q^{34} +2.27142e25 q^{36} +1.14738e26 q^{37} -3.35210e25 q^{38} -9.32521e25 q^{39} -5.38743e26 q^{41} +2.55903e26 q^{42} +5.52603e25 q^{43} -4.41539e26 q^{44} -1.02465e27 q^{46} +2.40153e26 q^{47} +2.19861e27 q^{48} +1.41177e28 q^{49} -7.47779e26 q^{51} +1.38177e28 q^{52} +3.29442e28 q^{53} +1.49509e28 q^{54} -8.20389e28 q^{56} +4.80624e28 q^{57} -7.66261e28 q^{58} -2.15515e29 q^{59} -2.06092e29 q^{61} -7.50979e28 q^{62} +4.54788e29 q^{63} -1.60114e29 q^{64} -1.03545e29 q^{66} -2.34745e30 q^{67} +1.10802e29 q^{68} +1.46914e30 q^{69} +5.77599e29 q^{71} -1.70767e30 q^{72} +1.07901e30 q^{73} -3.98697e30 q^{74} -7.12167e30 q^{76} -8.84056e30 q^{77} +3.24038e30 q^{78} -2.26255e31 q^{79} -4.33260e30 q^{81} +1.87205e31 q^{82} +2.41922e30 q^{83} +5.43676e31 q^{84} -1.92022e30 q^{86} +1.09867e32 q^{87} +3.31951e31 q^{88} +2.76225e32 q^{89} +2.76659e32 q^{91} -2.17690e32 q^{92} +1.07675e32 q^{93} -8.34497e30 q^{94} -3.13931e32 q^{96} +1.55540e32 q^{97} -4.90569e32 q^{98} -1.84019e32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−34748.6	−0.374923	−0.187461	−	0.982272i	$-0.560026\pi$
$2$	−34748.6	−0.374923	−0.187461	+	0.982272i	$0.560026\pi$
$3$	4.98225e7	0.668228	0.334114	−	0.942533i	$-0.391563\pi$
$3$	4.98225e7	0.668228	0.334114	+	0.942533i	$0.391563\pi$
$4$	−7.38247e9	−0.859433
$5$	0	0
$5$	0	0
$6$	−1.73126e12	−0.250534
$7$	−1.47813e14	−1.68110	−0.840552	−	0.541730i	$-0.817769\pi$
$7$	−1.47813e14	−1.68110	−0.840552	+	0.541730i	$0.817769\pi$
$8$	5.55018e14	0.697144
$9$	−3.07678e15	−0.553471
$10$	0	0
$11$	5.98091e16	0.392453	0.196227	−	0.980559i	$-0.437131\pi$
$11$	5.98091e16	0.392453	0.196227	+	0.980559i	$0.437131\pi$
$12$	−3.67813e17	−0.574297
$13$	−1.87169e18	−0.780131	−0.390066	−	0.920787i	$-0.627548\pi$
$13$	−1.87169e18	−0.780131	−0.390066	+	0.920787i	$0.627548\pi$
$14$	5.13629e18	0.630285
$15$	0	0
$16$	4.41289e19	0.598058
$17$	−1.50089e19	−0.0748067	−0.0374033	−	0.999300i	$-0.511909\pi$
$17$	−1.50089e19	−0.0748067	−0.0374033	+	0.999300i	$0.511909\pi$
$18$	1.06914e20	0.207509
$19$	9.64673e20	0.767266	0.383633	−	0.923486i	$-0.374673\pi$
$19$	9.64673e20	0.767266	0.383633	+	0.923486i	$0.374673\pi$
$20$	0	0
$21$	−7.36441e21	−1.12336
$22$	−2.07828e21	−0.147140
$23$	2.94875e22	1.00260	0.501301	−	0.865273i	$-0.332855\pi$
$23$	2.94875e22	1.00260	0.501301	+	0.865273i	$0.332855\pi$
$24$	2.76524e22	0.465851
$25$	0	0
$26$	6.50384e22	0.292489
$27$	−4.30259e23	−1.03807
$28$	1.09122e24	1.44480
$29$	2.20516e24	1.63634	0.818169	−	0.574978i	$-0.194990\pi$
$29$	2.20516e24	1.63634	0.818169	+	0.574978i	$0.194990\pi$
$30$	0	0
$31$	2.16118e24	0.533609	0.266804	−	0.963751i	$-0.414032\pi$
$31$	2.16118e24	0.533609	0.266804	+	0.963751i	$0.414032\pi$
$32$	−6.30098e24	−0.921369
$33$	2.97984e24	0.262249
$34$	5.21536e23	0.0280467
$35$	0	0
$36$	2.27142e25	0.475671
$37$	1.14738e26	1.52890	0.764448	−	0.644685i	$-0.223012\pi$
$37$	1.14738e26	1.52890	0.764448	+	0.644685i	$0.223012\pi$
$38$	−3.35210e25	−0.287665
$39$	−9.32521e25	−0.521306
$40$	0	0
$41$	−5.38743e26	−1.31962	−0.659809	−	0.751434i	$-0.729363\pi$
$41$	−5.38743e26	−1.31962	−0.659809	+	0.751434i	$0.729363\pi$
$42$	2.55903e26	0.421174
$43$	5.52603e25	0.0616856	0.0308428	−	0.999524i	$-0.490181\pi$
$43$	5.52603e25	0.0616856	0.0308428	+	0.999524i	$0.490181\pi$
$44$	−4.41539e26	−0.337287
$45$	0	0
$46$	−1.02465e27	−0.375898
$47$	2.40153e26	0.0617836	0.0308918	−	0.999523i	$-0.490165\pi$
$47$	2.40153e26	0.0617836	0.0308918	+	0.999523i	$0.490165\pi$
$48$	2.19861e27	0.399639
$49$	1.41177e28	1.82611
$50$	0	0
$51$	−7.47779e26	−0.0499879
$52$	1.38177e28	0.670470
$53$	3.29442e28	1.16742	0.583710	−	0.811962i	$-0.301601\pi$
$53$	3.29442e28	1.16742	0.583710	+	0.811962i	$0.301601\pi$
$54$	1.49509e28	0.389197
$55$	0	0
$56$	−8.20389e28	−1.17197
$57$	4.80624e28	0.512709
$58$	−7.66261e28	−0.613500
$59$	−2.15515e29	−1.30143	−0.650714	−	0.759323i	$-0.725530\pi$
$59$	−2.15515e29	−1.30143	−0.650714	+	0.759323i	$0.725530\pi$
$60$	0	0
$61$	−2.06092e29	−0.717989	−0.358995	−	0.933340i	$-0.616880\pi$
$61$	−2.06092e29	−0.717989	−0.358995	+	0.933340i	$0.616880\pi$
$62$	−7.50979e28	−0.200062
$63$	4.54788e29	0.930442
$64$	−1.60114e29	−0.252615
$65$	0	0
$66$	−1.03545e29	−0.0983229
$67$	−2.34745e30	−1.73925	−0.869626	−	0.493710i	$-0.835640\pi$
$67$	−2.34745e30	−1.73925	−0.869626	+	0.493710i	$0.835640\pi$
$68$	1.10802e29	0.0642913
$69$	1.46914e30	0.669967
$70$	0	0
$71$	5.77599e29	0.164385	0.0821927	−	0.996616i	$-0.473808\pi$
$71$	5.77599e29	0.164385	0.0821927	+	0.996616i	$0.473808\pi$
$72$	−1.70767e30	−0.385849
$73$	1.07901e30	0.194177	0.0970887	−	0.995276i	$-0.469047\pi$
$73$	1.07901e30	0.194177	0.0970887	+	0.995276i	$0.469047\pi$
$74$	−3.98697e30	−0.573218
$75$	0	0
$76$	−7.12167e30	−0.659413
$77$	−8.84056e30	−0.659755
$78$	3.24038e30	0.195449
$79$	−2.26255e31	−1.10599	−0.552994	−	0.833185i	$-0.686515\pi$
$79$	−2.26255e31	−1.10599	−0.552994	+	0.833185i	$0.686515\pi$
$80$	0	0
$81$	−4.33260e30	−0.140199
$82$	1.87205e31	0.494755
$83$	2.41922e30	0.0523464	0.0261732	−	0.999657i	$-0.491668\pi$
$83$	2.41922e30	0.0523464	0.0261732	+	0.999657i	$0.491668\pi$
$84$	5.43676e31	0.965454
$85$	0	0
$86$	−1.92022e30	−0.0231273
$87$	1.09867e32	1.09345
$88$	3.31951e31	0.273596
$89$	2.76225e32	1.88942	0.944709	−	0.327910i	$-0.106344\pi$
$89$	2.76225e32	1.88942	0.944709	+	0.327910i	$0.106344\pi$
$90$	0	0
$91$	2.76659e32	1.31148
$92$	−2.17690e32	−0.861669
$93$	1.07675e32	0.356573
$94$	−8.34497e30	−0.0231641
$95$	0	0
$96$	−3.13931e32	−0.615685
$97$	1.55540e32	0.257104	0.128552	−	0.991703i	$-0.458967\pi$
$97$	1.55540e32	0.257104	0.128552	+	0.991703i	$0.458967\pi$
$98$	−4.90569e32	−0.684652
$99$	−1.84019e32	−0.217212
$100$	0	0
$101$	1.52582e33	1.29479	0.647396	−	0.762154i	$-0.275858\pi$
$101$	1.52582e33	1.29479	0.647396	+	0.762154i	$0.275858\pi$
$102$	2.59842e31	0.0187416
$103$	−4.59708e32	−0.282272	−0.141136	−	0.989990i	$-0.545075\pi$
$103$	−4.59708e32	−0.282272	−0.141136	+	0.989990i	$0.545075\pi$
$104$	−1.03882e33	−0.543864
$105$	0	0
$106$	−1.14476e33	−0.437692
$107$	−2.72069e33	−0.890937	−0.445468	−	0.895298i	$-0.646963\pi$
$107$	−2.72069e33	−0.890937	−0.445468	+	0.895298i	$0.646963\pi$
$108$	3.17638e33	0.892154
$109$	6.43214e33	1.55174	0.775868	−	0.630895i	$-0.217312\pi$
$109$	6.43214e33	1.55174	0.775868	+	0.630895i	$0.217312\pi$
$110$	0	0
$111$	5.71652e33	1.02165
$112$	−6.52282e33	−1.00540
$113$	2.91698e33	0.388275	0.194138	−	0.980974i	$-0.437809\pi$
$113$	2.91698e33	0.388275	0.194138	+	0.980974i	$0.437809\pi$
$114$	−1.67010e33	−0.192226
$115$	0	0
$116$	−1.62795e34	−1.40632
$117$	5.75876e33	0.431780
$118$	7.48885e33	0.487935
$119$	2.21850e33	0.125758
$120$	0	0
$121$	−1.96480e34	−0.845980
$122$	7.16138e33	0.269190
$123$	−2.68415e34	−0.881806
$124$	−1.59549e34	−0.458601
$125$	0	0
$126$	−1.58032e34	−0.348844
$127$	3.87947e34	0.751642	0.375821	−	0.926692i	$-0.377361\pi$
$127$	3.87947e34	0.751642	0.375821	+	0.926692i	$0.377361\pi$
$128$	5.96888e34	1.01608
$129$	2.75321e33	0.0412201
$130$	0	0
$131$	1.21068e35	1.40622	0.703112	−	0.711079i	$-0.251793\pi$
$131$	1.21068e35	1.40622	0.703112	+	0.711079i	$0.251793\pi$
$132$	−2.19986e34	−0.225385
$133$	−1.42591e35	−1.28985
$134$	8.15706e34	0.652086
$135$	0	0
$136$	−8.33018e33	−0.0521510
$137$	−1.56794e35	−0.869839	−0.434920	−	0.900469i	$-0.643223\pi$
$137$	−1.56794e35	−0.869839	−0.434920	+	0.900469i	$0.643223\pi$
$138$	−5.10505e34	−0.251186
$139$	−1.50046e35	−0.655359	−0.327680	−	0.944789i	$-0.606267\pi$
$139$	−1.50046e35	−0.655359	−0.327680	+	0.944789i	$0.606267\pi$
$140$	0	0
$141$	1.19650e34	0.0412855
$142$	−2.00707e34	−0.0616319
$143$	−1.11944e35	−0.306165
$144$	−1.35775e35	−0.331008
$145$	0	0
$146$	−3.74941e34	−0.0728015
$147$	7.03378e35	1.22026
$148$	−8.47048e35	−1.31398
$149$	−9.65504e34	−0.134023	−0.0670117	−	0.997752i	$-0.521346\pi$
$149$	−9.65504e34	−0.134023	−0.0670117	+	0.997752i	$0.521346\pi$
$150$	0	0
$151$	−8.83975e35	−0.984737	−0.492369	−	0.870387i	$-0.663869\pi$
$151$	−8.83975e35	−0.984737	−0.492369	+	0.870387i	$0.663869\pi$
$152$	5.35411e35	0.534894
$153$	4.61789e34	0.0414033
$154$	3.07197e35	0.247357
$155$	0	0
$156$	6.88431e35	0.448027
$157$	−2.48782e36	−1.45705	−0.728524	−	0.685020i	$-0.759793\pi$
$157$	−2.48782e36	−1.45705	−0.728524	+	0.685020i	$0.759793\pi$
$158$	7.86203e35	0.414660
$159$	1.64136e36	0.780103
$160$	0	0
$161$	−4.35863e36	−1.68548
$162$	1.50552e35	0.0525639
$163$	1.85238e36	0.584297	0.292148	−	0.956373i	$-0.405630\pi$
$163$	1.85238e36	0.584297	0.292148	+	0.956373i	$0.405630\pi$
$164$	3.97726e36	1.13412
$165$	0	0
$166$	−8.40645e34	−0.0196259
$167$	−2.76869e36	−0.585399	−0.292700	−	0.956204i	$-0.594554\pi$
$167$	−2.76869e36	−0.585399	−0.292700	+	0.956204i	$0.594554\pi$
$168$	−4.08738e36	−0.783145
$169$	−2.25292e36	−0.391395
$170$	0	0
$171$	−2.96808e36	−0.424659
$172$	−4.07958e35	−0.0530146
$173$	−1.52101e37	−1.79627	−0.898137	−	0.439716i	$-0.855079\pi$
$173$	−1.52101e37	−1.79627	−0.898137	+	0.439716i	$0.855079\pi$
$174$	−3.81770e36	−0.409958
$175$	0	0
$176$	2.63931e36	0.234710
$177$	−1.07375e37	−0.869651
$178$	−9.59842e36	−0.708386
$179$	2.02009e37	1.35924	0.679619	−	0.733565i	$-0.262145\pi$
$179$	2.02009e37	1.35924	0.679619	+	0.733565i	$0.262145\pi$
$180$	0	0
$181$	1.64324e36	0.0920459	0.0460230	−	0.998940i	$-0.485345\pi$
$181$	1.64324e36	0.0920459	0.0460230	+	0.998940i	$0.485345\pi$
$182$	−9.61351e36	−0.491705
$183$	−1.02680e37	−0.479781
$184$	1.63661e37	0.698957
$185$	0	0
$186$	−3.74157e36	−0.133687
$187$	−8.97666e35	−0.0293581
$188$	−1.77292e36	−0.0530988
$189$	6.35979e37	1.74511
$190$	0	0
$191$	−1.89197e37	−0.436379	−0.218190	−	0.975906i	$-0.570015\pi$
$191$	−1.89197e37	−0.436379	−0.218190	+	0.975906i	$0.570015\pi$
$192$	−7.97729e36	−0.168805
$193$	−9.41864e37	−1.82933	−0.914666	−	0.404211i	$-0.867546\pi$
$193$	−9.41864e37	−1.82933	−0.914666	+	0.404211i	$0.867546\pi$
$194$	−5.40479e36	−0.0963940
$195$	0	0
$196$	−1.04223e38	−1.56942
$197$	5.25145e37	0.727087	0.363543	−	0.931577i	$-0.381567\pi$
$197$	5.25145e37	0.727087	0.363543	+	0.931577i	$0.381567\pi$
$198$	6.39441e36	0.0814375
$199$	2.03516e37	0.238518	0.119259	−	0.992863i	$-0.461948\pi$
$199$	2.03516e37	0.238518	0.119259	+	0.992863i	$0.461948\pi$
$200$	0	0
$201$	−1.16956e38	−1.16222
$202$	−5.30200e37	−0.485447
$203$	−3.25951e38	−2.75085
$204$	5.52046e36	0.0429613
$205$	0	0
$206$	1.59742e37	0.105830
$207$	−9.07264e37	−0.554911
$208$	−8.25954e37	−0.466564
$209$	5.76962e37	0.301116
$210$	0	0
$211$	−2.62126e38	−1.16910	−0.584548	−	0.811359i	$-0.698728\pi$
$211$	−2.62126e38	−1.16910	−0.584548	+	0.811359i	$0.698728\pi$
$212$	−2.43210e38	−1.00332
$213$	2.87774e37	0.109847
$214$	9.45401e37	0.334033
$215$	0	0
$216$	−2.38802e38	−0.723686
$217$	−3.19450e38	−0.897053
$218$	−2.23507e38	−0.581782
$219$	5.37590e37	0.129755
$220$	0	0
$221$	2.80919e37	0.0583590
$222$	−1.98641e38	−0.383040
$223$	−8.87264e38	−1.58863	−0.794315	−	0.607507i	$-0.792170\pi$
$223$	−8.87264e38	−1.58863	−0.794315	+	0.607507i	$0.792170\pi$
$224$	9.31367e38	1.54892
$225$	0	0
$226$	−1.01361e38	−0.145573
$227$	3.70583e38	0.494833	0.247417	−	0.968909i	$-0.420418\pi$
$227$	3.70583e38	0.494833	0.247417	+	0.968909i	$0.420418\pi$
$228$	−3.54820e38	−0.440639
$229$	−4.99095e38	−0.576631	−0.288315	−	0.957536i	$-0.593095\pi$
$229$	−4.99095e38	−0.576631	−0.288315	+	0.957536i	$0.593095\pi$
$230$	0	0
$231$	−4.40459e38	−0.440867
$232$	1.22390e39	1.14076
$233$	−1.15626e39	−1.00389	−0.501943	−	0.864901i	$-0.667381\pi$
$233$	−1.15626e39	−1.00389	−0.501943	+	0.864901i	$0.667381\pi$
$234$	−2.00109e38	−0.161884
$235$	0	0
$236$	1.59104e39	1.11849
$237$	−1.12726e39	−0.739053
$238$	−7.70898e37	−0.0471495
$239$	2.99187e39	1.70756	0.853782	−	0.520630i	$-0.174303\pi$
$239$	2.99187e39	1.70756	0.853782	+	0.520630i	$0.174303\pi$
$240$	0	0
$241$	−3.75743e39	−1.86900	−0.934500	−	0.355962i	$-0.884153\pi$
$241$	−3.75743e39	−1.86900	−0.934500	+	0.355962i	$0.884153\pi$
$242$	6.82740e38	0.317177
$243$	2.17598e39	0.944388
$244$	1.52146e39	0.617063
$245$	0	0
$246$	9.32704e38	0.330609
$247$	−1.80556e39	−0.598568
$248$	1.19949e39	0.372002
$249$	1.20532e38	0.0349794
$250$	0	0
$251$	6.73222e39	1.71215	0.856075	−	0.516852i	$-0.172896\pi$
$251$	6.73222e39	1.71215	0.856075	+	0.516852i	$0.172896\pi$
$252$	−3.35746e39	−0.799653
$253$	1.76362e39	0.393474
$254$	−1.34806e39	−0.281808
$255$	0	0
$256$	−6.98729e38	−0.128336
$257$	2.99334e39	0.515537	0.257769	−	0.966207i	$-0.417013\pi$
$257$	2.99334e39	0.515537	0.257769	+	0.966207i	$0.417013\pi$
$258$	−9.56700e37	−0.0154543
$259$	−1.69597e40	−2.57023
$260$	0	0
$261$	−6.78478e39	−0.905665
$262$	−4.20695e39	−0.527226
$263$	−2.92876e39	−0.344678	−0.172339	−	0.985038i	$-0.555132\pi$
$263$	−2.92876e39	−0.344678	−0.172339	+	0.985038i	$0.555132\pi$
$264$	1.65387e39	0.182825
$265$	0	0
$266$	4.95484e39	0.483596
$267$	1.37622e40	1.26256
$268$	1.73300e40	1.49477
$269$	−6.92919e39	−0.562044	−0.281022	−	0.959701i	$-0.590673\pi$
$269$	−6.92919e39	−0.562044	−0.281022	+	0.959701i	$0.590673\pi$
$270$	0	0
$271$	6.74538e39	0.484187	0.242093	−	0.970253i	$-0.422166\pi$
$271$	6.74538e39	0.484187	0.242093	+	0.970253i	$0.422166\pi$
$272$	−6.62324e38	−0.0447387
$273$	1.37839e40	0.876370
$274$	5.44835e39	0.326123
$275$	0	0
$276$	−1.08459e40	−0.575791
$277$	9.43527e39	0.471887	0.235943	−	0.971767i	$-0.424182\pi$
$277$	9.43527e39	0.471887	0.235943	+	0.971767i	$0.424182\pi$
$278$	5.21387e39	0.245709
$279$	−6.64947e39	−0.295337
$280$	0	0
$281$	5.04578e40	1.99193	0.995964	−	0.0897488i	$-0.0286064\pi$
$281$	5.04578e40	1.99193	0.995964	+	0.0897488i	$0.0286064\pi$
$282$	−4.15767e38	−0.0154789
$283$	3.16955e40	1.11307	0.556534	−	0.830825i	$-0.312131\pi$
$283$	3.16955e40	1.11307	0.556534	+	0.830825i	$0.312131\pi$
$284$	−4.26411e39	−0.141278
$285$	0	0
$286$	3.88989e39	0.114788
$287$	7.96332e40	2.21841
$288$	1.93867e40	0.509951
$289$	−4.00292e40	−0.994404
$290$	0	0
$291$	7.74939e39	0.171804
$292$	−7.96577e39	−0.166882
$293$	−2.29636e40	−0.454700	−0.227350	−	0.973813i	$-0.573006\pi$
$293$	−2.29636e40	−0.454700	−0.227350	+	0.973813i	$0.573006\pi$
$294$	−2.44414e40	−0.457504
$295$	0	0
$296$	6.36815e40	1.06586
$297$	−2.57334e40	−0.407395
$298$	3.35499e39	0.0502484
$299$	−5.51913e40	−0.782161
$300$	0	0
$301$	−8.16819e39	−0.103700
$302$	3.07169e40	0.369200
$303$	7.60201e40	0.865217
$304$	4.25699e40	0.458869
$305$	0	0
$306$	−1.60465e39	−0.0155230
$307$	−1.43500e41	−1.31543	−0.657717	−	0.753265i	$-0.728478\pi$
$307$	−1.43500e41	−1.31543	−0.657717	+	0.753265i	$0.728478\pi$
$308$	6.52652e40	0.567015
$309$	−2.29038e40	−0.188622
$310$	0	0
$311$	−8.91385e40	−0.659962	−0.329981	−	0.943988i	$-0.607042\pi$
$311$	−8.91385e40	−0.659962	−0.329981	+	0.943988i	$0.607042\pi$
$312$	−5.17566e40	−0.363425
$313$	1.04450e41	0.695707	0.347853	−	0.937549i	$-0.386911\pi$
$313$	1.04450e41	0.695707	0.347853	+	0.937549i	$0.386911\pi$
$314$	8.64480e40	0.546281
$315$	0	0
$316$	1.67032e41	0.950523
$317$	−1.29790e41	−0.701071	−0.350536	−	0.936549i	$-0.614000\pi$
$317$	−1.29790e41	−0.701071	−0.350536	+	0.936549i	$0.614000\pi$
$318$	−5.70350e40	−0.292478
$319$	1.31889e41	0.642186
$320$	0	0
$321$	−1.35552e41	−0.595349
$322$	1.51456e41	0.631924
$323$	−1.44786e40	−0.0573966
$324$	3.19853e40	0.120492
$325$	0	0
$326$	−6.43674e40	−0.219066
$327$	3.20465e41	1.03691
$328$	−2.99012e41	−0.919963
$329$	−3.54977e40	−0.103865
$330$	0	0
$331$	−4.67334e41	−1.23727	−0.618636	−	0.785678i	$-0.712315\pi$
$331$	−4.67334e41	−1.23727	−0.618636	+	0.785678i	$0.712315\pi$
$332$	−1.78598e40	−0.0449883
$333$	−3.53023e41	−0.846199
$334$	9.62079e40	0.219480
$335$	0	0
$336$	−3.24983e41	−0.671835
$337$	−1.86982e41	−0.368049	−0.184025	−	0.982922i	$-0.558913\pi$
$337$	−1.86982e41	−0.368049	−0.184025	+	0.982922i	$0.558913\pi$
$338$	7.82858e40	0.146743
$339$	1.45331e41	0.259457
$340$	0	0
$341$	1.29258e41	0.209417
$342$	1.03137e41	0.159214
$343$	−9.44034e41	−1.38878
$344$	3.06705e40	0.0430037
$345$	0	0
$346$	5.28530e41	0.673464
$347$	−1.15583e42	−1.40430	−0.702148	−	0.712031i	$-0.747776\pi$
$347$	−1.15583e42	−1.40430	−0.702148	+	0.712031i	$0.747776\pi$
$348$	−8.11087e41	−0.939744
$349$	1.47840e42	1.63370	0.816849	−	0.576852i	$-0.195719\pi$
$349$	1.47840e42	1.63370	0.816849	+	0.576852i	$0.195719\pi$
$350$	0	0
$351$	8.05310e41	0.809833
$352$	−3.76856e41	−0.361595
$353$	−1.01010e42	−0.924874	−0.462437	−	0.886652i	$-0.653025\pi$
$353$	−1.01010e42	−0.924874	−0.462437	+	0.886652i	$0.653025\pi$
$354$	3.73113e41	0.326052
$355$	0	0
$356$	−2.03922e42	−1.62383
$357$	1.10531e41	0.0840349
$358$	−7.01952e41	−0.509610
$359$	−1.06005e42	−0.734968	−0.367484	−	0.930030i	$-0.619781\pi$
$359$	−1.06005e42	−0.734968	−0.367484	+	0.930030i	$0.619781\pi$
$360$	0	0
$361$	−6.50176e41	−0.411303
$362$	−5.71002e40	−0.0345101
$363$	−9.78914e41	−0.565308
$364$	−2.04243e42	−1.12713
$365$	0	0
$366$	3.56798e41	0.179881
$367$	2.19794e42	1.05932	0.529658	−	0.848211i	$-0.322320\pi$
$367$	2.19794e42	1.05932	0.529658	+	0.848211i	$0.322320\pi$
$368$	1.30125e42	0.599614
$369$	1.65759e42	0.730370
$370$	0	0
$371$	−4.86958e42	−1.96255
$372$	−7.94911e41	−0.306450
$373$	−1.14120e41	−0.0420888	−0.0210444	−	0.999779i	$-0.506699\pi$
$373$	−1.14120e41	−0.0420888	−0.0210444	+	0.999779i	$0.506699\pi$
$374$	3.11926e40	0.0110070
$375$	0	0
$376$	1.33289e41	0.0430720
$377$	−4.12736e42	−1.27656
$378$	−2.20993e42	−0.654282
$379$	2.65954e42	0.753807	0.376904	−	0.926253i	$-0.376989\pi$
$379$	2.65954e42	0.753807	0.376904	+	0.926253i	$0.376989\pi$
$380$	0	0
$381$	1.93285e42	0.502268
$382$	6.57433e41	0.163609
$383$	7.20492e42	1.71731	0.858656	−	0.512553i	$-0.171300\pi$
$383$	7.20492e42	1.71731	0.858656	+	0.512553i	$0.171300\pi$
$384$	2.97384e42	0.678974
$385$	0	0
$386$	3.27284e42	0.685858
$387$	−1.70024e41	−0.0341412
$388$	−1.14827e42	−0.220963
$389$	1.91127e42	0.352495	0.176247	−	0.984346i	$-0.443604\pi$
$389$	1.91127e42	0.352495	0.176247	+	0.984346i	$0.443604\pi$
$390$	0	0
$391$	−4.42573e41	−0.0750012
$392$	7.83556e42	1.27306
$393$	6.03194e42	0.939679
$394$	−1.82480e42	−0.272601
$395$	0	0
$396$	1.35852e42	0.186679
$397$	−8.29118e42	−1.09288	−0.546440	−	0.837498i	$-0.684017\pi$
$397$	−8.29118e42	−1.09288	−0.546440	+	0.837498i	$0.684017\pi$
$398$	−7.07187e41	−0.0894260
$399$	−7.10425e42	−0.861917
$400$	0	0
$401$	1.28162e43	1.43178	0.715892	−	0.698211i	$-0.246020\pi$
$401$	1.28162e43	1.43178	0.715892	+	0.698211i	$0.246020\pi$
$402$	4.06405e42	0.435742
$403$	−4.04505e42	−0.416285
$404$	−1.12643e43	−1.11279
$405$	0	0
$406$	1.13263e43	1.03136
$407$	6.86236e42	0.600020
$408$	−4.15031e41	−0.0348488
$409$	−8.25702e42	−0.665869	−0.332935	−	0.942950i	$-0.608039\pi$
$409$	−8.25702e42	−0.665869	−0.332935	+	0.942950i	$0.608039\pi$
$410$	0	0
$411$	−7.81185e42	−0.581251
$412$	3.39378e42	0.242594
$413$	3.18560e43	2.18784
$414$	3.15261e42	0.208049
$415$	0	0
$416$	1.17935e43	0.718789
$417$	−7.47566e42	−0.437930
$418$	−2.00486e42	−0.112895
$419$	−1.60647e43	−0.869644	−0.434822	−	0.900516i	$-0.643189\pi$
$419$	−1.60647e43	−0.869644	−0.434822	+	0.900516i	$0.643189\pi$
$420$	0	0
$421$	−1.30743e42	−0.0654279	−0.0327139	−	0.999465i	$-0.510415\pi$
$421$	−1.30743e42	−0.0654279	−0.0327139	+	0.999465i	$0.510415\pi$
$422$	9.10852e42	0.438321
$423$	−7.38897e41	−0.0341954
$424$	1.82846e43	0.813859
$425$	0	0
$426$	−9.99974e41	−0.0411842
$427$	3.04630e43	1.20701
$428$	2.00854e43	0.765700
$429$	−5.57733e42	−0.204588
$430$	0	0
$431$	3.20058e43	1.08731	0.543656	−	0.839308i	$-0.317040\pi$
$431$	3.20058e43	1.08731	0.543656	+	0.839308i	$0.317040\pi$
$432$	−1.89869e43	−0.620828
$433$	4.41459e43	1.38944	0.694720	−	0.719280i	$-0.255528\pi$
$433$	4.41459e43	1.38944	0.694720	+	0.719280i	$0.255528\pi$
$434$	1.11004e43	0.336325
$435$	0	0
$436$	−4.74851e43	−1.33361
$437$	2.84458e43	0.769262
$438$	−1.86805e42	−0.0486480
$439$	−5.37132e43	−1.34715	−0.673575	−	0.739118i	$-0.735242\pi$
$439$	−5.37132e43	−1.34715	−0.673575	+	0.739118i	$0.735242\pi$
$440$	0	0
$441$	−4.34369e43	−1.01070
$442$	−9.76151e41	−0.0218801
$443$	−4.72272e43	−1.01984	−0.509918	−	0.860223i	$-0.670324\pi$
$443$	−4.72272e43	−1.01984	−0.509918	+	0.860223i	$0.670324\pi$
$444$	−4.22021e43	−0.878041
$445$	0	0
$446$	3.08311e43	0.595613
$447$	−4.81038e42	−0.0895582
$448$	2.36669e43	0.424673
$449$	1.39516e43	0.241302	0.120651	−	0.992695i	$-0.461502\pi$
$449$	1.39516e43	0.241302	0.120651	+	0.992695i	$0.461502\pi$
$450$	0	0
$451$	−3.22217e43	−0.517888
$452$	−2.15346e43	−0.333697
$453$	−4.40419e43	−0.658029
$454$	−1.28772e43	−0.185524
$455$	0	0
$456$	2.66755e43	0.357432
$457$	−9.95409e43	−1.28642	−0.643212	−	0.765688i	$-0.722399\pi$
$457$	−9.95409e43	−1.28642	−0.643212	+	0.765688i	$0.722399\pi$
$458$	1.73428e43	0.216192
$459$	6.45770e42	0.0776548
$460$	0	0
$461$	1.24434e44	1.39276	0.696378	−	0.717675i	$-0.254794\pi$
$461$	1.24434e44	1.39276	0.696378	+	0.717675i	$0.254794\pi$
$462$	1.53053e43	0.165291
$463$	−9.53882e43	−0.994051	−0.497025	−	0.867736i	$-0.665574\pi$
$463$	−9.53882e43	−0.994051	−0.497025	+	0.867736i	$0.665574\pi$
$464$	9.73112e43	0.978624
$465$	0	0
$466$	4.01785e43	0.376380
$467$	7.43521e43	0.672303	0.336151	−	0.941808i	$-0.390875\pi$
$467$	7.43521e43	0.672303	0.336151	+	0.941808i	$0.390875\pi$
$468$	−4.25139e43	−0.371086
$469$	3.46984e44	2.92387
$470$	0	0
$471$	−1.23949e44	−0.973641
$472$	−1.19615e44	−0.907283
$473$	3.30507e42	0.0242087
$474$	3.91706e43	0.277088
$475$	0	0
$476$	−1.63780e43	−0.108080
$477$	−1.01362e44	−0.646133
$478$	−1.03963e44	−0.640205
$479$	−2.98587e44	−1.77638	−0.888189	−	0.459478i	$-0.848036\pi$
$479$	−2.98587e44	−1.77638	−0.888189	+	0.459478i	$0.848036\pi$
$480$	0	0
$481$	−2.14753e44	−1.19274
$482$	1.30565e44	0.700731
$483$	−2.17158e44	−1.12628
$484$	1.45051e44	0.727063
$485$	0	0
$486$	−7.56120e43	−0.354073
$487$	−4.43630e43	−0.200813	−0.100407	−	0.994946i	$-0.532014\pi$
$487$	−4.43630e43	−0.200813	−0.100407	+	0.994946i	$0.532014\pi$
$488$	−1.14385e44	−0.500542
$489$	9.22900e43	0.390444
$490$	0	0
$491$	−2.24506e44	−0.887939	−0.443970	−	0.896042i	$-0.646430\pi$
$491$	−2.24506e44	−0.887939	−0.443970	+	0.896042i	$0.646430\pi$
$492$	1.98157e44	0.757853
$493$	−3.30969e43	−0.122409
$494$	6.27408e43	0.224417
$495$	0	0
$496$	9.53705e43	0.319129
$497$	−8.53765e43	−0.276349
$498$	−4.18830e42	−0.0131146
$499$	−1.25154e44	−0.379128	−0.189564	−	0.981868i	$-0.560708\pi$
$499$	−1.25154e44	−0.379128	−0.189564	+	0.981868i	$0.560708\pi$
$500$	0	0
$501$	−1.37943e44	−0.391180
$502$	−2.33935e44	−0.641924
$503$	2.88371e44	0.765736	0.382868	−	0.923803i	$-0.374936\pi$
$503$	2.88371e44	0.765736	0.382868	+	0.923803i	$0.374936\pi$
$504$	2.52415e44	0.648652
$505$	0	0
$506$	−6.12832e43	−0.147522
$507$	−1.12246e44	−0.261541
$508$	−2.86401e44	−0.645986
$509$	3.22743e44	0.704715	0.352358	−	0.935865i	$-0.385380\pi$
$509$	3.22743e44	0.704715	0.352358	+	0.935865i	$0.385380\pi$
$510$	0	0
$511$	−1.59492e44	−0.326433
$512$	−4.88443e44	−0.967964
$513$	−4.15059e44	−0.796478
$514$	−1.04014e44	−0.193287
$515$	0	0
$516$	−2.03255e43	−0.0354259
$517$	1.43633e43	0.0242472
$518$	5.89326e44	0.963639
$519$	−7.57807e44	−1.20032
$520$	0	0
$521$	5.13992e44	0.764072	0.382036	−	0.924148i	$-0.375223\pi$
$521$	5.13992e44	0.764072	0.382036	+	0.924148i	$0.375223\pi$
$522$	2.35761e44	0.339554
$523$	−7.81512e44	−1.09058	−0.545290	−	0.838247i	$-0.683581\pi$
$523$	−7.81512e44	−1.09058	−0.545290	+	0.838247i	$0.683581\pi$
$524$	−8.93785e44	−1.20856
$525$	0	0
$526$	1.01770e44	0.129228
$527$	−3.24368e43	−0.0399175
$528$	1.31497e44	0.156840
$529$	4.50617e42	0.00520942
$530$	0	0
$531$	6.63093e44	0.720303
$532$	1.05268e45	1.10854
$533$	1.00836e45	1.02947
$534$	−4.78218e44	−0.473364
$535$	0	0
$536$	−1.30288e45	−1.21251
$537$	1.00646e45	0.908282
$538$	2.40780e44	0.210723
$539$	8.44365e44	0.716664
$540$	0	0
$541$	2.18342e45	1.74334	0.871672	−	0.490090i	$-0.163036\pi$
$541$	2.18342e45	1.74334	0.871672	+	0.490090i	$0.163036\pi$
$542$	−2.34392e44	−0.181533
$543$	8.18704e43	0.0615077
$544$	9.45705e43	0.0689246
$545$	0	0
$546$	−4.78969e44	−0.328571
$547$	1.36194e45	0.906499	0.453249	−	0.891384i	$-0.350265\pi$
$547$	1.36194e45	0.906499	0.453249	+	0.891384i	$0.350265\pi$
$548$	1.15752e45	0.747568
$549$	6.34098e44	0.397386
$550$	0	0
$551$	2.12726e45	1.25551
$552$	8.15399e44	0.467063
$553$	3.34434e45	1.85928
$554$	−3.27862e44	−0.176921
$555$	0	0
$556$	1.10771e45	0.563237
$557$	−1.85262e45	−0.914482	−0.457241	−	0.889343i	$-0.651162\pi$
$557$	−1.85262e45	−0.914482	−0.457241	+	0.889343i	$0.651162\pi$
$558$	2.31060e44	0.110729
$559$	−1.03430e44	−0.0481229
$560$	0	0
$561$	−4.47240e43	−0.0196179
$562$	−1.75333e45	−0.746820
$563$	1.83880e45	0.760581	0.380291	−	0.924867i	$-0.375824\pi$
$563$	1.83880e45	0.760581	0.380291	+	0.924867i	$0.375824\pi$
$564$	−8.83314e43	−0.0354822
$565$	0	0
$566$	−1.10137e45	−0.417315
$567$	6.40414e44	0.235690
$568$	3.20578e44	0.114600
$569$	−1.77967e45	−0.618000	−0.309000	−	0.951062i	$-0.599994\pi$
$569$	−1.77967e45	−0.618000	−0.309000	+	0.951062i	$0.599994\pi$
$570$	0	0
$571$	−1.22115e45	−0.400196	−0.200098	−	0.979776i	$-0.564126\pi$
$571$	−1.22115e45	−0.400196	−0.200098	+	0.979776i	$0.564126\pi$
$572$	8.26423e44	0.263128
$573$	−9.42628e44	−0.291601
$574$	−2.76714e45	−0.831734
$575$	0	0
$576$	4.92635e44	0.139815
$577$	−1.86986e45	−0.515713	−0.257856	−	0.966183i	$-0.583016\pi$
$577$	−1.86986e45	−0.515713	−0.257856	+	0.966183i	$0.583016\pi$
$578$	1.39096e45	0.372825
$579$	−4.69260e45	−1.22241
$580$	0	0
$581$	−3.57592e44	−0.0879999
$582$	−2.69280e44	−0.0644132
$583$	1.97036e45	0.458158
$584$	5.98871e44	0.135370
$585$	0	0
$586$	7.97953e44	0.170477
$587$	−1.39944e45	−0.290687	−0.145344	−	0.989381i	$-0.546429\pi$
$587$	−1.39944e45	−0.290687	−0.145344	+	0.989381i	$0.546429\pi$
$588$	−5.19267e45	−1.04873
$589$	2.08483e45	0.409420
$590$	0	0
$591$	2.61640e45	0.485860
$592$	5.06325e45	0.914368
$593$	−3.92359e45	−0.689099	−0.344549	−	0.938768i	$-0.611968\pi$
$593$	−3.92359e45	−0.689099	−0.344549	+	0.938768i	$0.611968\pi$
$594$	8.94199e44	0.152742
$595$	0	0
$596$	7.12781e44	0.115184
$597$	1.01397e45	0.159385
$598$	1.91782e45	0.293250
$599$	1.16463e46	1.73239	0.866194	−	0.499707i	$-0.166559\pi$
$599$	1.16463e46	1.73239	0.866194	+	0.499707i	$0.166559\pi$
$600$	0	0
$601$	−4.32095e45	−0.608346	−0.304173	−	0.952617i	$-0.598380\pi$
$601$	−4.32095e45	−0.608346	−0.304173	+	0.952617i	$0.598380\pi$
$602$	2.83833e44	0.0388795
$603$	7.22259e45	0.962626
$604$	6.52592e45	0.846316
$605$	0	0
$606$	−2.64159e45	−0.324389
$607$	−9.90727e45	−1.18397	−0.591985	−	0.805949i	$-0.701655\pi$
$607$	−9.90727e45	−1.18397	−0.591985	+	0.805949i	$0.701655\pi$
$608$	−6.07839e45	−0.706935
$609$	−1.62397e46	−1.83820
$610$	0	0
$611$	−4.49491e44	−0.0481993
$612$	−3.40914e44	−0.0355834
$613$	−1.56875e46	−1.59388	−0.796941	−	0.604057i	$-0.793550\pi$
$613$	−1.56875e46	−1.59388	−0.796941	+	0.604057i	$0.793550\pi$
$614$	4.98642e45	0.493186
$615$	0	0
$616$	−4.90667e45	−0.459944
$617$	1.69800e46	1.54965	0.774823	−	0.632179i	$-0.217839\pi$
$617$	1.69800e46	1.54965	0.774823	+	0.632179i	$0.217839\pi$
$618$	7.95874e44	0.0707187
$619$	1.32248e46	1.14418	0.572090	−	0.820191i	$-0.306133\pi$
$619$	1.32248e46	1.14418	0.572090	+	0.820191i	$0.306133\pi$
$620$	0	0
$621$	−1.26873e46	−1.04077
$622$	3.09743e45	0.247435
$623$	−4.08296e46	−3.17631
$624$	−4.11511e45	−0.311771
$625$	0	0
$626$	−3.62948e45	−0.260836
$627$	2.87457e45	0.201214
$628$	1.83662e46	1.25224
$629$	−1.72208e45	−0.114372
$630$	0	0
$631$	7.36088e45	0.463923	0.231961	−	0.972725i	$-0.425486\pi$
$631$	7.36088e45	0.463923	0.231961	+	0.972725i	$0.425486\pi$
$632$	−1.25576e46	−0.771033
$633$	−1.30598e46	−0.781223
$634$	4.51000e45	0.262848
$635$	0	0
$636$	−1.21173e46	−0.670446
$637$	−2.64238e46	−1.42461
$638$	−4.58294e45	−0.240770
$639$	−1.77714e45	−0.0909826
$640$	0	0
$641$	1.87269e46	0.910559	0.455280	−	0.890349i	$-0.349539\pi$
$641$	1.87269e46	0.910559	0.455280	+	0.890349i	$0.349539\pi$
$642$	4.71023e45	0.223210
$643$	2.12986e46	0.983719	0.491859	−	0.870675i	$-0.336317\pi$
$643$	2.12986e46	0.983719	0.491859	+	0.870675i	$0.336317\pi$
$644$	3.21775e46	1.44856
$645$	0	0
$646$	5.03112e44	0.0215193
$647$	−4.36741e46	−1.82097	−0.910486	−	0.413539i	$-0.864292\pi$
$647$	−4.36741e46	−1.82097	−0.910486	+	0.413539i	$0.864292\pi$
$648$	−2.40467e45	−0.0977390
$649$	−1.28898e46	−0.510750
$650$	0	0
$651$	−1.59158e46	−0.599436
$652$	−1.36751e46	−0.502164
$653$	5.30148e45	0.189815	0.0949074	−	0.995486i	$-0.469745\pi$
$653$	5.30148e45	0.189815	0.0949074	+	0.995486i	$0.469745\pi$
$654$	−1.11357e46	−0.388763
$655$	0	0
$656$	−2.37741e46	−0.789207
$657$	−3.31988e45	−0.107472
$658$	1.23349e45	0.0389412
$659$	3.74458e46	1.15290	0.576452	−	0.817131i	$-0.304437\pi$
$659$	3.74458e46	1.15290	0.576452	+	0.817131i	$0.304437\pi$
$660$	0	0
$661$	−3.96439e44	−0.0116105	−0.00580527	−	0.999983i	$-0.501848\pi$
$661$	−3.96439e44	−0.0116105	−0.00580527	+	0.999983i	$0.501848\pi$
$662$	1.62392e46	0.463882
$663$	1.39961e45	0.0389971
$664$	1.34271e45	0.0364930
$665$	0	0
$666$	1.22670e46	0.317259
$667$	6.50245e46	1.64059
$668$	2.04398e46	0.503111
$669$	−4.42057e46	−1.06157
$670$	0	0
$671$	−1.23262e46	−0.281777
$672$	4.64030e46	1.03503
$673$	−3.16567e46	−0.688996	−0.344498	−	0.938787i	$-0.611951\pi$
$673$	−3.16567e46	−0.688996	−0.344498	+	0.938787i	$0.611951\pi$
$674$	6.49735e45	0.137990
$675$	0	0
$676$	1.66321e46	0.336378
$677$	−1.24991e46	−0.246697	−0.123349	−	0.992363i	$-0.539363\pi$
$677$	−1.24991e46	−0.246697	−0.123349	+	0.992363i	$0.539363\pi$
$678$	−5.05006e45	−0.0972762
$679$	−2.29908e46	−0.432218
$680$	0	0
$681$	1.84634e46	0.330662
$682$	−4.49154e45	−0.0785151
$683$	9.37524e46	1.59971	0.799854	−	0.600194i	$-0.204910\pi$
$683$	9.37524e46	1.59971	0.799854	+	0.600194i	$0.204910\pi$
$684$	2.19118e46	0.364966
$685$	0	0
$686$	3.28038e46	0.520686
$687$	−2.48662e46	−0.385321
$688$	2.43858e45	0.0368916
$689$	−6.16612e46	−0.910741
$690$	0	0
$691$	8.61308e46	1.21275	0.606374	−	0.795180i	$-0.292623\pi$
$691$	8.61308e46	1.21275	0.606374	+	0.795180i	$0.292623\pi$
$692$	1.12288e47	1.54378
$693$	2.72004e46	0.365155
$694$	4.01635e46	0.526503
$695$	0	0
$696$	6.09779e46	0.762290
$697$	8.08591e45	0.0987161
$698$	−5.13722e46	−0.612511
$699$	−5.76080e46	−0.670825
$700$	0	0
$701$	−3.60374e46	−0.400319	−0.200159	−	0.979763i	$-0.564146\pi$
$701$	−3.60374e46	−0.400319	−0.200159	+	0.979763i	$0.564146\pi$
$702$	−2.79834e46	−0.303625
$703$	1.10684e47	1.17307
$704$	−9.57628e45	−0.0991398
$705$	0	0
$706$	3.50996e46	0.346756
$707$	−2.25536e47	−2.17668
$708$	7.92695e46	0.747407
$709$	−9.39378e46	−0.865321	−0.432661	−	0.901557i	$-0.642425\pi$
$709$	−9.39378e46	−0.865321	−0.432661	+	0.901557i	$0.642425\pi$
$710$	0	0
$711$	6.96136e46	0.612133
$712$	1.53310e47	1.31720
$713$	6.37278e46	0.534997
$714$	−3.84081e45	−0.0315066
$715$	0	0
$716$	−1.49133e47	−1.16817
$717$	1.49062e47	1.14104
$718$	3.68352e46	0.275556
$719$	−2.60794e47	−1.90665	−0.953324	−	0.301948i	$-0.902363\pi$
$719$	−2.60794e47	−1.90665	−0.953324	+	0.301948i	$0.902363\pi$
$720$	0	0
$721$	6.79508e46	0.474529
$722$	2.25927e46	0.154207
$723$	−1.87205e47	−1.24892
$724$	−1.21312e46	−0.0791073
$725$	0	0
$726$	3.40158e46	0.211947
$727$	−1.22346e47	−0.745200	−0.372600	−	0.927992i	$-0.621534\pi$
$727$	−1.22346e47	−0.745200	−0.372600	+	0.927992i	$0.621534\pi$
$728$	1.53551e47	0.914292
$729$	1.32498e47	0.771266
$730$	0	0
$731$	−8.29394e44	−0.00461449
$732$	7.58032e46	0.412339
$733$	−1.26865e47	−0.674722	−0.337361	−	0.941375i	$-0.609534\pi$
$733$	−1.26865e47	−0.674722	−0.337361	+	0.941375i	$0.609534\pi$
$734$	−7.63752e46	−0.397162
$735$	0	0
$736$	−1.85800e47	−0.923766
$737$	−1.40399e47	−0.682576
$738$	−5.75989e46	−0.273832
$739$	1.56062e47	0.725544	0.362772	−	0.931878i	$-0.381830\pi$
$739$	1.56062e47	0.725544	0.362772	+	0.931878i	$0.381830\pi$
$740$	0	0
$741$	−8.99578e46	−0.399980
$742$	1.69211e47	0.735807
$743$	2.85856e47	1.21572	0.607858	−	0.794046i	$-0.292029\pi$
$743$	2.85856e47	1.21572	0.607858	+	0.794046i	$0.292029\pi$
$744$	5.97618e46	0.248582
$745$	0	0
$746$	3.96551e45	0.0157800
$747$	−7.44341e45	−0.0289722
$748$	6.62700e45	0.0252313
$749$	4.02153e47	1.49776
$750$	0	0
$751$	2.65937e47	0.947805	0.473903	−	0.880577i	$-0.342845\pi$
$751$	2.65937e47	0.947805	0.473903	+	0.880577i	$0.342845\pi$
$752$	1.05977e46	0.0369502
$753$	3.35416e47	1.14411
$754$	1.43420e47	0.478611
$755$	0	0
$756$	−4.69510e47	−1.49980
$757$	−6.24348e47	−1.95139	−0.975697	−	0.219125i	$-0.929680\pi$
$757$	−6.24348e47	−1.95139	−0.975697	+	0.219125i	$0.929680\pi$
$758$	−9.24153e46	−0.282619
$759$	8.78680e46	0.262931
$760$	0	0
$761$	3.71910e47	1.06559	0.532796	−	0.846244i	$-0.321141\pi$
$761$	3.71910e47	1.06559	0.532796	+	0.846244i	$0.321141\pi$
$762$	−6.71637e46	−0.188312
$763$	−9.50753e47	−2.60863
$764$	1.39674e47	0.375039
$765$	0	0
$766$	−2.50360e47	−0.643859
$767$	4.03377e47	1.01528
$768$	−3.48124e46	−0.0857580
$769$	−1.23681e47	−0.298208	−0.149104	−	0.988821i	$-0.547639\pi$
$769$	−1.23681e47	−0.298208	−0.149104	+	0.988821i	$0.547639\pi$
$770$	0	0
$771$	1.49136e47	0.344497
$772$	6.95328e47	1.57219
$773$	−5.41736e47	−1.19902	−0.599509	−	0.800368i	$-0.704638\pi$
$773$	−5.41736e47	−1.19902	−0.599509	+	0.800368i	$0.704638\pi$
$774$	5.90808e45	0.0128003
$775$	0	0
$776$	8.63275e46	0.179238
$777$	−8.44976e47	−1.71750
$778$	−6.64138e46	−0.132158
$779$	−5.19711e47	−1.01250
$780$	0	0
$781$	3.45457e46	0.0645136
$782$	1.53788e46	0.0281197
$783$	−9.48789e47	−1.69864
$784$	6.22997e47	1.09212
$785$	0	0
$786$	−2.09601e47	−0.352307
$787$	−4.40426e47	−0.724920	−0.362460	−	0.931999i	$-0.618063\pi$
$787$	−4.40426e47	−0.724920	−0.362460	+	0.931999i	$0.618063\pi$
$788$	−3.87687e47	−0.624882
$789$	−1.45918e47	−0.230323
$790$	0	0
$791$	−4.31168e47	−0.652731
$792$	−1.02134e47	−0.151428
$793$	3.85739e47	0.560126
$794$	2.88106e47	0.409746
$795$	0	0
$796$	−1.50245e47	−0.204991
$797$	−3.20079e47	−0.427755	−0.213877	−	0.976860i	$-0.568609\pi$
$797$	−3.20079e47	−0.427755	−0.213877	+	0.976860i	$0.568609\pi$
$798$	2.46862e47	0.323152
$799$	−3.60442e45	−0.00462182
$800$	0	0
$801$	−8.49883e47	−1.04574
$802$	−4.45345e47	−0.536809
$803$	6.45347e46	0.0762056
$804$	8.63425e47	0.998849
$805$	0	0
$806$	1.40560e47	0.156075
$807$	−3.45230e47	−0.375574
$808$	8.46856e47	0.902656
$809$	8.78251e46	0.0917209	0.0458604	−	0.998948i	$-0.485397\pi$
$809$	8.78251e46	0.0917209	0.0458604	+	0.998948i	$0.485397\pi$
$810$	0	0
$811$	−6.75926e47	−0.677727	−0.338864	−	0.940836i	$-0.610043\pi$
$811$	−6.75926e47	−0.677727	−0.338864	+	0.940836i	$0.610043\pi$
$812$	2.40632e48	2.36417
$813$	3.36072e47	0.323547
$814$	−2.38457e47	−0.224961
$815$	0	0
$816$	−3.29986e46	−0.0298957
$817$	5.33081e46	0.0473292
$818$	2.86920e47	0.249650
$819$	−8.51219e47	−0.725867
$820$	0	0
$821$	9.00463e47	0.737571	0.368785	−	0.929515i	$-0.379774\pi$
$821$	9.00463e47	0.737571	0.368785	+	0.929515i	$0.379774\pi$
$822$	2.71451e47	0.217924
$823$	−2.11922e48	−1.66755	−0.833774	−	0.552106i	$-0.813824\pi$
$823$	−2.11922e48	−1.66755	−0.833774	+	0.552106i	$0.813824\pi$
$824$	−2.55146e47	−0.196784
$825$	0	0
$826$	−1.10695e48	−0.820270
$827$	−6.52978e47	−0.474305	−0.237152	−	0.971472i	$-0.576214\pi$
$827$	−6.52978e47	−0.474305	−0.237152	+	0.971472i	$0.576214\pi$
$828$	6.69785e47	0.476908
$829$	−1.27715e48	−0.891438	−0.445719	−	0.895173i	$-0.647052\pi$
$829$	−1.27715e48	−0.891438	−0.445719	+	0.895173i	$0.647052\pi$
$830$	0	0
$831$	4.70089e47	0.315328
$832$	2.99683e47	0.197073
$833$	−2.11890e47	−0.136605
$834$	2.59768e47	0.164190
$835$	0	0
$836$	−4.25941e47	−0.258789
$837$	−9.29868e47	−0.553925
$838$	5.58225e47	0.326049
$839$	−2.62590e48	−1.50386	−0.751928	−	0.659245i	$-0.770876\pi$
$839$	−2.62590e48	−1.50386	−0.751928	+	0.659245i	$0.770876\pi$
$840$	0	0
$841$	3.04665e48	1.67760
$842$	4.54312e46	0.0245304
$843$	2.51393e48	1.33106
$844$	1.93514e48	1.00476
$845$	0	0
$846$	2.56756e46	0.0128206
$847$	2.90423e48	1.42218
$848$	1.45379e48	0.698184
$849$	1.57915e48	0.743784
$850$	0	0
$851$	3.38333e48	1.53287
$852$	−2.12448e47	−0.0944061
$853$	−1.44658e47	−0.0630497	−0.0315248	−	0.999503i	$-0.510036\pi$
$853$	−1.44658e47	−0.0630497	−0.0315248	+	0.999503i	$0.510036\pi$
$854$	−1.05854e48	−0.452537
$855$	0	0
$856$	−1.51003e48	−0.621111
$857$	−2.48913e48	−1.00430	−0.502150	−	0.864781i	$-0.667457\pi$
$857$	−2.48913e48	−1.00430	−0.502150	+	0.864781i	$0.667457\pi$
$858$	1.93804e47	0.0767048
$859$	−1.48194e48	−0.575364	−0.287682	−	0.957726i	$-0.592885\pi$
$859$	−1.48194e48	−0.575364	−0.287682	+	0.957726i	$0.592885\pi$
$860$	0	0
$861$	3.96753e48	1.48241
$862$	−1.11216e48	−0.407658
$863$	2.44226e48	0.878240	0.439120	−	0.898428i	$-0.355290\pi$
$863$	2.44226e48	0.878240	0.439120	+	0.898428i	$0.355290\pi$
$864$	2.71106e48	0.956449
$865$	0	0
$866$	−1.53401e48	−0.520933
$867$	−1.99436e48	−0.664489
$868$	2.35833e48	0.770957
$869$	−1.35321e48	−0.434049
$870$	0	0
$871$	4.39370e48	1.35685
$872$	3.56995e48	1.08178
$873$	−4.78562e47	−0.142299
$874$	−9.88450e47	−0.288414
$875$	0	0
$876$	−3.96875e47	−0.111516
$877$	3.67485e48	1.01332	0.506659	−	0.862146i	$-0.330880\pi$
$877$	3.67485e48	1.01332	0.506659	+	0.862146i	$0.330880\pi$
$878$	1.86646e48	0.505078
$879$	−1.14411e48	−0.303843
$880$	0	0
$881$	−3.46572e48	−0.886525	−0.443263	−	0.896392i	$-0.646179\pi$
$881$	−3.46572e48	−0.886525	−0.443263	+	0.896392i	$0.646179\pi$
$882$	1.50937e48	0.378935
$883$	−2.00067e48	−0.492974	−0.246487	−	0.969146i	$-0.579276\pi$
$883$	−2.00067e48	−0.492974	−0.246487	+	0.969146i	$0.579276\pi$
$884$	−2.07387e47	−0.0501556
$885$	0	0
$886$	1.64108e48	0.382360
$887$	−2.66648e48	−0.609815	−0.304908	−	0.952382i	$-0.598626\pi$
$887$	−2.66648e48	−0.609815	−0.304908	+	0.952382i	$0.598626\pi$
$888$	3.17277e48	0.712238
$889$	−5.73436e48	−1.26359
$890$	0	0
$891$	−2.59129e47	−0.0550217
$892$	6.55020e48	1.36532
$893$	2.31669e47	0.0474044
$894$	1.67154e47	0.0335774
$895$	0	0
$896$	−8.82277e48	−1.70814
$897$	−2.74977e48	−0.522662
$898$	−4.84799e47	−0.0904694
$899$	4.76575e48	0.873164
$900$	0	0
$901$	−4.94454e47	−0.0873308
$902$	1.11966e48	0.194168
$903$	−4.06960e47	−0.0692953
$904$	1.61898e48	0.270684
$905$	0	0
$906$	1.53039e48	0.246710
$907$	−2.45576e48	−0.388745	−0.194373	−	0.980928i	$-0.562267\pi$
$907$	−2.45576e48	−0.388745	−0.194373	+	0.980928i	$0.562267\pi$
$908$	−2.73582e48	−0.425276
$909$	−4.69460e48	−0.716629
$910$	0	0
$911$	−6.52212e48	−0.960142	−0.480071	−	0.877230i	$-0.659389\pi$
$911$	−6.52212e48	−0.960142	−0.480071	+	0.877230i	$0.659389\pi$
$912$	2.12094e48	0.306629
$913$	1.44692e47	0.0205435
$914$	3.45890e48	0.482310
$915$	0	0
$916$	3.68455e48	0.495575
$917$	−1.78955e49	−2.36401
$918$	−2.24396e47	−0.0291145
$919$	5.09072e48	0.648743	0.324372	−	0.945930i	$-0.394847\pi$
$919$	5.09072e48	0.648743	0.324372	+	0.945930i	$0.394847\pi$
$920$	0	0
$921$	−7.14953e48	−0.879010
$922$	−4.32392e48	−0.522176
$923$	−1.08108e48	−0.128242
$924$	3.25168e48	0.378896
$925$	0	0
$926$	3.31460e48	0.372692
$927$	1.41442e48	0.156229
$928$	−1.38947e49	−1.50767
$929$	−1.85412e48	−0.197642	−0.0988210	−	0.995105i	$-0.531507\pi$
$929$	−1.85412e48	−0.197642	−0.0988210	+	0.995105i	$0.531507\pi$
$930$	0	0
$931$	1.36189e49	1.40111
$932$	8.53609e48	0.862772
$933$	−4.44110e48	−0.441005
$934$	−2.58363e48	−0.252062
$935$	0	0
$936$	3.19622e48	0.301013
$937$	5.95689e48	0.551209	0.275605	−	0.961271i	$-0.411122\pi$
$937$	5.95689e48	0.551209	0.275605	+	0.961271i	$0.411122\pi$
$938$	−1.20572e49	−1.09622
$939$	5.20395e48	0.464891
$940$	0	0
$941$	−9.68431e48	−0.835295	−0.417647	−	0.908609i	$-0.637145\pi$
$941$	−9.68431e48	−0.835295	−0.417647	+	0.908609i	$0.637145\pi$
$942$	4.30706e48	0.365040
$943$	−1.58862e49	−1.32305
$944$	−9.51046e48	−0.778329
$945$	0	0
$946$	−1.14846e47	−0.00907640
$947$	−1.31218e49	−1.01911	−0.509554	−	0.860439i	$-0.670190\pi$
$947$	−1.31218e49	−1.01911	−0.509554	+	0.860439i	$0.670190\pi$
$948$	8.32195e48	0.635167
$949$	−2.01957e48	−0.151484
$950$	0	0
$951$	−6.46644e48	−0.468476
$952$	1.23131e48	0.0876713
$953$	−1.89854e49	−1.32857	−0.664287	−	0.747477i	$-0.731265\pi$
$953$	−1.89854e49	−1.32857	−0.664287	+	0.747477i	$0.731265\pi$
$954$	3.52218e48	0.242250
$955$	0	0
$956$	−2.20874e49	−1.46754
$957$	6.57102e48	0.429127
$958$	1.03755e49	0.666005
$959$	2.31761e49	1.46229
$960$	0	0
$961$	−1.17328e49	−0.715261
$962$	7.46236e48	0.447185
$963$	8.37096e48	0.493108
$964$	2.77391e49	1.60628
$965$	0	0
$966$	7.54592e48	0.422270
$967$	−1.81718e49	−0.999681	−0.499841	−	0.866117i	$-0.666608\pi$
$967$	−1.81718e49	−0.999681	−0.499841	+	0.866117i	$0.666608\pi$
$968$	−1.09050e49	−0.589770
$969$	−7.21362e47	−0.0383540
$970$	0	0
$971$	2.89478e49	1.48764	0.743822	−	0.668378i	$-0.233011\pi$
$971$	2.89478e49	1.48764	0.743822	+	0.668378i	$0.233011\pi$
$972$	−1.60641e49	−0.811638
$973$	2.21787e49	1.10173
$974$	1.54155e48	0.0752896
$975$	0	0
$976$	−9.09459e48	−0.429399
$977$	4.90142e48	0.227542	0.113771	−	0.993507i	$-0.463707\pi$
$977$	4.90142e48	0.227542	0.113771	+	0.993507i	$0.463707\pi$
$978$	−3.20694e48	−0.146386
$979$	1.65208e49	0.741508
$980$	0	0
$981$	−1.97903e49	−0.858841
$982$	7.80126e48	0.332909
$983$	9.75776e48	0.409465	0.204733	−	0.978818i	$-0.434368\pi$
$983$	9.75776e48	0.409465	0.204733	+	0.978818i	$0.434368\pi$
$984$	−1.48975e49	−0.614745
$985$	0	0
$986$	1.15007e48	0.0458939
$987$	−1.76858e48	−0.0694053
$988$	1.33295e49	0.514429
$989$	1.62949e48	0.0618461
$990$	0	0
$991$	1.34587e49	0.494068	0.247034	−	0.969007i	$-0.420544\pi$
$991$	1.34587e49	0.494068	0.247034	+	0.969007i	$0.420544\pi$
$992$	−1.36176e49	−0.491651
$993$	−2.32837e49	−0.826781
$994$	2.96671e48	0.103610
$995$	0	0
$996$	−8.89822e47	−0.0300624
$997$	−1.26772e48	−0.0421262	−0.0210631	−	0.999778i	$-0.506705\pi$
$997$	−1.26772e48	−0.0421262	−0.0210631	+	0.999778i	$0.506705\pi$
$998$	4.34893e48	0.142144
$999$	−4.93670e49	−1.58711

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.34.a.d.1.5	✓	11
5.2	odd	4		25.34.b.d.24.10		22
5.3	odd	4		25.34.b.d.24.13		22
5.4	even	2		25.34.a.e.1.7	yes	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.34.a.d.1.5	✓	11	1.1	even	1	trivial
25.34.a.e.1.7	yes	11	5.4	even	2
25.34.b.d.24.10		22	5.2	odd	4
25.34.b.d.24.13		22	5.3	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)

\(f(q)\)	\(=\)	\(q-34748.6 q^{2} +4.98225e7 q^{3} -7.38247e9 q^{4} -1.73126e12 q^{6} -1.47813e14 q^{7} +5.55018e14 q^{8} -3.07678e15 q^{9} +O(q^{10})\)	\(q-34748.6 q^{2} +4.98225e7 q^{3} -7.38247e9 q^{4} -1.73126e12 q^{6} -1.47813e14 q^{7} +5.55018e14 q^{8} -3.07678e15 q^{9} +5.98091e16 q^{11} -3.67813e17 q^{12} -1.87169e18 q^{13} +5.13629e18 q^{14} +4.41289e19 q^{16} -1.50089e19 q^{17} +1.06914e20 q^{18} +9.64673e20 q^{19} -7.36441e21 q^{21} -2.07828e21 q^{22} +2.94875e22 q^{23} +2.76524e22 q^{24} +6.50384e22 q^{26} -4.30259e23 q^{27} +1.09122e24 q^{28} +2.20516e24 q^{29} +2.16118e24 q^{31} -6.30098e24 q^{32} +2.97984e24 q^{33} +5.21536e23 q^{34} +2.27142e25 q^{36} +1.14738e26 q^{37} -3.35210e25 q^{38} -9.32521e25 q^{39} -5.38743e26 q^{41} +2.55903e26 q^{42} +5.52603e25 q^{43} -4.41539e26 q^{44} -1.02465e27 q^{46} +2.40153e26 q^{47} +2.19861e27 q^{48} +1.41177e28 q^{49} -7.47779e26 q^{51} +1.38177e28 q^{52} +3.29442e28 q^{53} +1.49509e28 q^{54} -8.20389e28 q^{56} +4.80624e28 q^{57} -7.66261e28 q^{58} -2.15515e29 q^{59} -2.06092e29 q^{61} -7.50979e28 q^{62} +4.54788e29 q^{63} -1.60114e29 q^{64} -1.03545e29 q^{66} -2.34745e30 q^{67} +1.10802e29 q^{68} +1.46914e30 q^{69} +5.77599e29 q^{71} -1.70767e30 q^{72} +1.07901e30 q^{73} -3.98697e30 q^{74} -7.12167e30 q^{76} -8.84056e30 q^{77} +3.24038e30 q^{78} -2.26255e31 q^{79} -4.33260e30 q^{81} +1.87205e31 q^{82} +2.41922e30 q^{83} +5.43676e31 q^{84} -1.92022e30 q^{86} +1.09867e32 q^{87} +3.31951e31 q^{88} +2.76225e32 q^{89} +2.76659e32 q^{91} -2.17690e32 q^{92} +1.07675e32 q^{93} -8.34497e30 q^{94} -3.13931e32 q^{96} +1.55540e32 q^{97} -4.90569e32 q^{98} -1.84019e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 9393 q^{2} - 80330849 q^{3} + 49338206677 q^{4} - 17783977676723 q^{6} - 21344025107658 q^{7} + 970199832420105 q^{8} + 24\!\cdots\!58 q^{9}+O(q^{10}) \) 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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