LMFDB - Embedded newform 25.34.a.b.1.1

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:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 1372039866x^{3} - 648067657640x^{2} + 285631173782445856x - 33409741805340964224 $ x^5 - 2x^4 - 1372039866x^3 - 648067657640x^2 + 285631173782445856x - 33409741805340964224
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{21}\cdot 3^{5}\cdot 5^{4}\cdot 11 $
Twist minimal:	no (minimal twist has level 5)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-33002.4$ 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)

$f(q)$	$=$	$q-138106. q^{2} +1.45282e7 q^{3} +1.04832e10 q^{4} -2.00642e12 q^{6} -3.75584e13 q^{7} -2.61472e14 q^{8} -5.34799e15 q^{9} +O(q^{10})$	\(q-138106. q^{2} +1.45282e7 q^{3} +1.04832e10 q^{4} -2.00642e12 q^{6} -3.75584e13 q^{7} -2.61472e14 q^{8} -5.34799e15 q^{9} -7.18987e16 q^{11} +1.52302e17 q^{12} -1.13201e18 q^{13} +5.18702e18 q^{14} -5.39393e19 q^{16} +1.70846e20 q^{17} +7.38588e20 q^{18} -8.48651e20 q^{19} -5.45655e20 q^{21} +9.92962e21 q^{22} +3.95696e22 q^{23} -3.79872e21 q^{24} +1.56337e23 q^{26} -1.58460e23 q^{27} -3.93732e23 q^{28} +9.30999e23 q^{29} -8.60649e23 q^{31} +9.69535e24 q^{32} -1.04456e24 q^{33} -2.35948e25 q^{34} -5.60641e25 q^{36} +5.07725e25 q^{37} +1.17203e26 q^{38} -1.64461e25 q^{39} -1.78283e26 q^{41} +7.53580e25 q^{42} -8.10579e26 q^{43} -7.53730e26 q^{44} -5.46479e27 q^{46} +5.64217e27 q^{47} -7.83641e26 q^{48} -6.32036e27 q^{49} +2.48208e27 q^{51} -1.18671e28 q^{52} -5.15002e28 q^{53} +2.18842e28 q^{54} +9.82047e27 q^{56} -1.23294e28 q^{57} -1.28576e29 q^{58} +1.40126e29 q^{59} -8.28448e28 q^{61} +1.18860e29 q^{62} +2.00862e29 q^{63} -8.75647e29 q^{64} +1.44259e29 q^{66} -2.02520e29 q^{67} +1.79102e30 q^{68} +5.74875e29 q^{69} +6.89895e30 q^{71} +1.39835e30 q^{72} +3.84757e30 q^{73} -7.01196e30 q^{74} -8.89659e30 q^{76} +2.70040e30 q^{77} +2.27129e30 q^{78} +9.36491e30 q^{79} +2.74277e31 q^{81} +2.46218e31 q^{82} -7.23102e31 q^{83} -5.72021e30 q^{84} +1.11945e32 q^{86} +1.35257e31 q^{87} +1.87995e31 q^{88} +4.37547e31 q^{89} +4.25165e31 q^{91} +4.14817e32 q^{92} -1.25037e31 q^{93} -7.79216e32 q^{94} +1.40856e32 q^{96} +1.02091e33 q^{97} +8.72877e32 q^{98} +3.84514e32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 30472 q^{2} + 14988714 q^{3} + 1141311360 q^{4} + 12925063115760 q^{6} + 65452561787158 q^{7} - 155610638035200 q^{8} + 14\!\cdots\!65 q^{9}+O(q^{10}) $ 5 * q - 30472 * q^2 + 14988714 * q^3 + 1141311360 * q^4 + 12925063115760 * q^6 + 65452561787158 * q^7 - 155610638035200 * q^8 + 14541250990408965 * q^9	$ 5 q - 30472 q^{2} + 14988714 q^{3} + 1141311360 q^{4} + 12925063115760 q^{6} + 65452561787158 q^{7} - 155610638035200 q^{8} + 14\!\cdots\!65 q^{9}+ \cdots - 17\!\cdots\!20 q^{99}+O(q^{100}) $ 5 * q - 30472 * q^2 + 14988714 * q^3 + 1141311360 * q^4 + 12925063115760 * q^6 + 65452561787158 * q^7 - 155610638035200 * q^8 + 14541250990408965 * q^9 - 287801801877976640 * q^11 + 405379955363513088 * q^12 - 2397201150889907466 * q^13 + 11676449916272482320 * q^14 - 89180089543245957120 * q^16 + 308725634324001653918 * q^17 - 537830699104521134856 * q^18 + 918364712195153947500 * q^19 - 10535115771712805413140 * q^21 + 13757888128329419319296 * q^22 - 55453893359806770035646 * q^23 - 71953200752757895180800 * q^24 - 424902360762721464761840 * q^26 - 679342131249712739644500 * q^27 + 1365491680784291850286336 * q^28 - 926877224993589271166050 * q^29 - 1336046479411821372201940 * q^31 + 813043271605502937899008 * q^32 + 33213386789605758547506048 * q^33 - 68630658492513538369567280 * q^34 - 180374200000978588488558720 * q^36 + 142836045294254023962738038 * q^37 + 330380182336023289264570400 * q^38 - 785791651509490753882465620 * q^39 - 1325620030754525933329256290 * q^41 + 2645870671030939362357320736 * q^42 + 2343083972337632823995338194 * q^43 - 1855939386652616358153902080 * q^44 - 2874649720834424257835685840 * q^46 + 7724956189479550762134222398 * q^47 + 7356143571895968866126229504 * q^48 + 4143234303500031791722947185 * q^49 + 7346719218915268753088875260 * q^51 - 48963787841701555176191049472 * q^52 - 109528513717338677312301826786 * q^53 + 64134717586148777280751188000 * q^54 + 144880509244845944794630156800 * q^56 - 208512654554635835530896805800 * q^57 - 211870362017554277516078730800 * q^58 + 257176212490429778182108906300 * q^59 + 742889693167672203496619446410 * q^61 - 532537079706659761431026425824 * q^62 + 1004528834780444187135312826134 * q^63 - 1039367551847251405574221987840 * q^64 - 3327517517031282146197646561280 * q^66 + 3757683664783078488809531637718 * q^67 - 1174937222155965542229368447744 * q^68 - 2767417175780175137072429257020 * q^69 - 5502085339682331744817794354940 * q^71 + 15971664273931445780329968326400 * q^72 + 13667431819995552941083819387254 * q^73 - 3638621909178354336866018756080 * q^74 + 7186339982587317558706196185600 * q^76 - 47237885671577674597763242652544 * q^77 - 12077118142241690266249318498272 * q^78 - 10258197004592737759121926298200 * q^79 + 78583804836302041006582647314505 * q^81 - 27306575776891610455800103348784 * q^82 - 92562254147118615583166775350526 * q^83 + 174445330599959716374040873566720 * q^84 + 65486114707827974097903540464560 * q^86 - 137286065258860195168416991536900 * q^87 - 194246091941469769694864674406400 * q^88 - 60853500388863684631316333445150 * q^89 - 268937084803738847432203207735340 * q^91 + 697440932909638690403668496563968 * q^92 + 696145220941341231280490115670488 * q^93 - 363437055538131894048725908447280 * q^94 - 344518603172836645970889894051840 * q^96 + 867959773515074594808067717684598 * q^97 + 1991101889094264762194115874723096 * q^98 - 1790665589323481921279813177939520 * 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 $

$2$	−138106.	−1.49010	−0.745051	−	0.667007i	$-0.767575\pi$
$2$	−138106.	−1.49010	−0.745051	+	0.667007i	$0.767575\pi$
$3$	1.45282e7	0.194855	0.0974273	−	0.995243i	$-0.468939\pi$
$3$	1.45282e7	0.194855	0.0974273	+	0.995243i	$0.468939\pi$
$4$	1.04832e10	1.22041
$5$	0	0
$5$	0	0
$6$	−2.00642e12	−0.290353
$7$	−3.75584e13	−0.427158	−0.213579	−	0.976926i	$-0.568512\pi$
$7$	−3.75584e13	−0.427158	−0.213579	+	0.976926i	$0.568512\pi$
$8$	−2.61472e14	−0.328428
$9$	−5.34799e15	−0.962032
$10$	0	0
$11$	−7.18987e16	−0.471783	−0.235891	−	0.971779i	$-0.575801\pi$
$11$	−7.18987e16	−0.471783	−0.235891	+	0.971779i	$0.575801\pi$
$12$	1.52302e17	0.237802
$13$	−1.13201e18	−0.471830	−0.235915	−	0.971774i	$-0.575809\pi$
$13$	−1.13201e18	−0.471830	−0.235915	+	0.971774i	$0.575809\pi$
$14$	5.18702e18	0.636510
$15$	0	0
$16$	−5.39393e19	−0.731014
$17$	1.70846e20	0.851526	0.425763	−	0.904835i	$-0.360006\pi$
$17$	1.70846e20	0.851526	0.425763	+	0.904835i	$0.360006\pi$
$18$	7.38588e20	1.43353
$19$	−8.48651e20	−0.674986	−0.337493	−	0.941328i	$-0.609579\pi$
$19$	−8.48651e20	−0.674986	−0.337493	+	0.941328i	$0.609579\pi$
$20$	0	0
$21$	−5.45655e20	−0.0832338
$22$	9.92962e21	0.703005
$23$	3.95696e22	1.34540	0.672702	−	0.739914i	$-0.265134\pi$
$23$	3.95696e22	1.34540	0.672702	+	0.739914i	$0.265134\pi$
$24$	−3.79872e21	−0.0639958
$25$	0	0
$26$	1.56337e23	0.703075
$27$	−1.58460e23	−0.382311
$28$	−3.93732e23	−0.521307
$29$	9.30999e23	0.690848	0.345424	−	0.938447i	$-0.387735\pi$
$29$	9.30999e23	0.690848	0.345424	+	0.938447i	$0.387735\pi$
$30$	0	0
$31$	−8.60649e23	−0.212500	−0.106250	−	0.994339i	$-0.533884\pi$
$31$	−8.60649e23	−0.212500	−0.106250	+	0.994339i	$0.533884\pi$
$32$	9.69535e24	1.41772
$33$	−1.04456e24	−0.0919290
$34$	−2.35948e25	−1.26886
$35$	0	0
$36$	−5.60641e25	−1.17407
$37$	5.07725e25	0.676550	0.338275	−	0.941047i	$-0.390157\pi$
$37$	5.07725e25	0.676550	0.338275	+	0.941047i	$0.390157\pi$
$38$	1.17203e26	1.00580
$39$	−1.64461e25	−0.0919383
$40$	0	0
$41$	−1.78283e26	−0.436692	−0.218346	−	0.975871i	$-0.570066\pi$
$41$	−1.78283e26	−0.436692	−0.218346	+	0.975871i	$0.570066\pi$
$42$	7.53580e25	0.124027
$43$	−8.10579e26	−0.904827	−0.452414	−	0.891808i	$-0.649437\pi$
$43$	−8.10579e26	−0.904827	−0.452414	+	0.891808i	$0.649437\pi$
$44$	−7.53730e26	−0.575767
$45$	0	0
$46$	−5.46479e27	−2.00479
$47$	5.64217e27	1.45155	0.725775	−	0.687933i	$-0.241482\pi$
$47$	5.64217e27	1.45155	0.725775	+	0.687933i	$0.241482\pi$
$48$	−7.83641e26	−0.142441
$49$	−6.32036e27	−0.817536
$50$	0	0
$51$	2.48208e27	0.165924
$52$	−1.18671e28	−0.575825
$53$	−5.15002e28	−1.82497	−0.912487	−	0.409105i	$-0.865841\pi$
$53$	−5.15002e28	−1.82497	−0.912487	+	0.409105i	$0.865841\pi$
$54$	2.18842e28	0.569682
$55$	0	0
$56$	9.82047e27	0.140291
$57$	−1.23294e28	−0.131524
$58$	−1.28576e29	−1.02943
$59$	1.40126e29	0.846175	0.423088	−	0.906089i	$-0.360946\pi$
$59$	1.40126e29	0.846175	0.423088	+	0.906089i	$0.360946\pi$
$60$	0	0
$61$	−8.28448e28	−0.288618	−0.144309	−	0.989533i	$-0.546096\pi$
$61$	−8.28448e28	−0.288618	−0.144309	+	0.989533i	$0.546096\pi$
$62$	1.18860e29	0.316646
$63$	2.00862e29	0.410940
$64$	−8.75647e29	−1.38153
$65$	0	0
$66$	1.44259e29	0.136984
$67$	−2.02520e29	−0.150049	−0.0750246	−	0.997182i	$-0.523904\pi$
$67$	−2.02520e29	−0.150049	−0.0750246	+	0.997182i	$0.523904\pi$
$68$	1.79102e30	1.03921
$69$	5.74875e29	0.262158
$70$	0	0
$71$	6.89895e30	1.96345	0.981726	−	0.190302i	$-0.0609466\pi$
$71$	6.89895e30	1.96345	0.981726	+	0.190302i	$0.0609466\pi$
$72$	1.39835e30	0.315959
$73$	3.84757e30	0.692404	0.346202	−	0.938160i	$-0.387471\pi$
$73$	3.84757e30	0.692404	0.346202	+	0.938160i	$0.387471\pi$
$74$	−7.01196e30	−1.00813
$75$	0	0
$76$	−8.89659e30	−0.823757
$77$	2.70040e30	0.201526
$78$	2.27129e30	0.136997
$79$	9.36491e30	0.457780	0.228890	−	0.973452i	$-0.426490\pi$
$79$	9.36491e30	0.457780	0.228890	+	0.973452i	$0.426490\pi$
$80$	0	0
$81$	2.74277e31	0.887537
$82$	2.46218e31	0.650716
$83$	−7.23102e31	−1.56463	−0.782314	−	0.622884i	$-0.785961\pi$
$83$	−7.23102e31	−1.56463	−0.782314	+	0.622884i	$0.785961\pi$
$84$	−5.72021e30	−0.101579
$85$	0	0
$86$	1.11945e32	1.34829
$87$	1.35257e31	0.134615
$88$	1.87995e31	0.154947
$89$	4.37547e31	0.299288	0.149644	−	0.988740i	$-0.452187\pi$
$89$	4.37547e31	0.299288	0.149644	+	0.988740i	$0.452187\pi$
$90$	0	0
$91$	4.25165e31	0.201546
$92$	4.14817e32	1.64194
$93$	−1.25037e31	−0.0414065
$94$	−7.79216e32	−2.16296
$95$	0	0
$96$	1.40856e32	0.276248
$97$	1.02091e33	1.68754	0.843771	−	0.536703i	$-0.180331\pi$
$97$	1.02091e33	1.68754	0.843771	+	0.536703i	$0.180331\pi$
$98$	8.72877e32	1.21821
$99$	3.84514e32	0.453870
$100$	0	0
$101$	2.20022e33	1.86709	0.933543	−	0.358466i	$-0.116700\pi$
$101$	2.20022e33	1.86709	0.933543	+	0.358466i	$0.116700\pi$
$102$	−3.42790e32	−0.247244
$103$	1.21369e33	0.745234	0.372617	−	0.927985i	$-0.378461\pi$
$103$	1.21369e33	0.745234	0.372617	+	0.927985i	$0.378461\pi$
$104$	2.95990e32	0.154962
$105$	0	0
$106$	7.11246e33	2.71940
$107$	3.78167e33	1.23837	0.619187	−	0.785244i	$-0.287462\pi$
$107$	3.78167e33	1.23837	0.619187	+	0.785244i	$0.287462\pi$
$108$	−1.66117e33	−0.466575
$109$	−4.93974e33	−1.19170	−0.595849	−	0.803096i	$-0.703184\pi$
$109$	−4.93974e33	−1.19170	−0.595849	+	0.803096i	$0.703184\pi$
$110$	0	0
$111$	7.37632e32	0.131829
$112$	2.02587e33	0.312259
$113$	3.63884e33	0.484360	0.242180	−	0.970231i	$-0.422138\pi$
$113$	3.63884e33	0.484360	0.242180	+	0.970231i	$0.422138\pi$
$114$	1.70275e33	0.195984
$115$	0	0
$116$	9.75986e33	0.843115
$117$	6.05399e33	0.453916
$118$	−1.93522e34	−1.26089
$119$	−6.41670e33	−0.363737
$120$	0	0
$121$	−1.80557e34	−0.777421
$122$	1.14413e34	0.430070
$123$	−2.59012e33	−0.0850915
$124$	−9.02236e33	−0.259336
$125$	0	0
$126$	−2.77401e34	−0.612343
$127$	−3.03012e34	−0.587082	−0.293541	−	0.955947i	$-0.594834\pi$
$127$	−3.03012e34	−0.587082	−0.293541	+	0.955947i	$0.594834\pi$
$128$	3.76492e34	0.640902
$129$	−1.17762e34	−0.176310
$130$	0	0
$131$	−7.83378e34	−0.909903	−0.454951	−	0.890516i	$-0.650343\pi$
$131$	−7.83378e34	−0.909903	−0.454951	+	0.890516i	$0.650343\pi$
$132$	−1.09503e34	−0.112191
$133$	3.18739e34	0.288326
$134$	2.79691e34	0.223589
$135$	0	0
$136$	−4.46715e34	−0.279665
$137$	−1.43675e35	−0.797060	−0.398530	−	0.917155i	$-0.630480\pi$
$137$	−1.43675e35	−0.797060	−0.398530	+	0.917155i	$0.630480\pi$
$138$	−7.93934e34	−0.390642
$139$	3.03428e35	1.32529	0.662647	−	0.748932i	$-0.269433\pi$
$139$	3.03428e35	1.32529	0.662647	+	0.748932i	$0.269433\pi$
$140$	0	0
$141$	8.19705e34	0.282841
$142$	−9.52783e35	−2.92574
$143$	8.13902e34	0.222601
$144$	2.88467e35	0.703259
$145$	0	0
$146$	−5.31371e35	−1.03175
$147$	−9.18234e34	−0.159301
$148$	5.32259e35	0.825666
$149$	−8.47533e35	−1.17648	−0.588238	−	0.808688i	$-0.700178\pi$
$149$	−8.47533e35	−1.17648	−0.588238	+	0.808688i	$0.700178\pi$
$150$	0	0
$151$	−1.42730e36	−1.59000	−0.794999	−	0.606610i	$-0.792529\pi$
$151$	−1.42730e36	−1.59000	−0.794999	+	0.606610i	$0.792529\pi$
$152$	2.21899e35	0.221685
$153$	−9.13684e35	−0.819195
$154$	−3.72940e35	−0.300294
$155$	0	0
$156$	−1.72408e35	−0.112202
$157$	1.47748e36	0.865320	0.432660	−	0.901557i	$-0.357575\pi$
$157$	1.47748e36	0.865320	0.432660	+	0.901557i	$0.357575\pi$
$158$	−1.29335e36	−0.682139
$159$	−7.48204e35	−0.355605
$160$	0	0
$161$	−1.48617e36	−0.574701
$162$	−3.78792e36	−1.32252
$163$	1.91804e36	0.605011	0.302505	−	0.953148i	$-0.402177\pi$
$163$	1.91804e36	0.605011	0.302505	+	0.953148i	$0.402177\pi$
$164$	−1.86897e36	−0.532942
$165$	0	0
$166$	9.98644e36	2.33146
$167$	3.91696e36	0.828185	0.414093	−	0.910235i	$-0.364099\pi$
$167$	3.91696e36	0.828185	0.414093	+	0.910235i	$0.364099\pi$
$168$	1.42674e35	0.0273363
$169$	−4.47468e36	−0.777376
$170$	0	0
$171$	4.53858e36	0.649358
$172$	−8.49747e36	−1.10426
$173$	1.42658e37	1.68475	0.842375	−	0.538892i	$-0.181157\pi$
$173$	1.42658e37	1.68475	0.842375	+	0.538892i	$0.181157\pi$
$174$	−1.86798e36	−0.200590
$175$	0	0
$176$	3.87817e36	0.344880
$177$	2.03577e36	0.164881
$178$	−6.04277e36	−0.445970
$179$	−1.89294e37	−1.27368	−0.636842	−	0.770994i	$-0.719760\pi$
$179$	−1.89294e37	−1.27368	−0.636842	+	0.770994i	$0.719760\pi$
$180$	0	0
$181$	2.60338e37	1.45828	0.729140	−	0.684365i	$-0.239920\pi$
$181$	2.60338e37	1.45828	0.729140	+	0.684365i	$0.239920\pi$
$182$	−5.87177e36	−0.300325
$183$	−1.20358e36	−0.0562385
$184$	−1.03464e37	−0.441869
$185$	0	0
$186$	1.72683e36	0.0616999
$187$	−1.22836e37	−0.401735
$188$	5.91481e37	1.77148
$189$	5.95148e36	0.163307
$190$	0	0
$191$	−7.37079e37	−1.70006	−0.850029	−	0.526736i	$-0.823415\pi$
$191$	−7.37079e37	−1.70006	−0.850029	+	0.526736i	$0.823415\pi$
$192$	−1.27216e37	−0.269197
$193$	−9.51744e36	−0.184852	−0.0924261	−	0.995720i	$-0.529462\pi$
$193$	−9.51744e36	−0.184852	−0.0924261	+	0.995720i	$0.529462\pi$
$194$	−1.40994e38	−2.51461
$195$	0	0
$196$	−6.62577e37	−0.997726
$197$	−5.57117e37	−0.771353	−0.385677	−	0.922634i	$-0.626032\pi$
$197$	−5.57117e37	−0.771353	−0.385677	+	0.922634i	$0.626032\pi$
$198$	−5.31035e37	−0.676313
$199$	1.97421e37	0.231375	0.115688	−	0.993286i	$-0.463093\pi$
$199$	1.97421e37	0.231375	0.115688	+	0.993286i	$0.463093\pi$
$200$	0	0
$201$	−2.94225e36	−0.0292378
$202$	−3.03863e38	−2.78215
$203$	−3.49668e37	−0.295101
$204$	2.60202e37	0.202494
$205$	0	0
$206$	−1.67617e38	−1.11048
$207$	−2.11618e38	−1.29432
$208$	6.10600e37	0.344915
$209$	6.10169e37	0.318447
$210$	0	0
$211$	1.86677e37	0.0832589	0.0416294	−	0.999133i	$-0.486745\pi$
$211$	1.86677e37	0.0832589	0.0416294	+	0.999133i	$0.486745\pi$
$212$	−5.39887e38	−2.22721
$213$	1.00229e38	0.382587
$214$	−5.22270e38	−1.84530
$215$	0	0
$216$	4.14328e37	0.125562
$217$	3.23246e37	0.0907710
$218$	6.82205e38	1.77575
$219$	5.58983e37	0.134918
$220$	0	0
$221$	−1.93400e38	−0.401776
$222$	−1.01871e38	−0.196439
$223$	2.13813e38	0.382828	0.191414	−	0.981509i	$-0.438693\pi$
$223$	2.13813e38	0.382828	0.191414	+	0.981509i	$0.438693\pi$
$224$	−3.64142e38	−0.605589
$225$	0	0
$226$	−5.02544e38	−0.721746
$227$	−2.97111e38	−0.396727	−0.198364	−	0.980128i	$-0.563563\pi$
$227$	−2.97111e38	−0.396727	−0.198364	+	0.980128i	$0.563563\pi$
$228$	−1.29251e38	−0.160513
$229$	−6.71382e38	−0.775683	−0.387841	−	0.921726i	$-0.626779\pi$
$229$	−6.71382e38	−0.775683	−0.387841	+	0.921726i	$0.626779\pi$
$230$	0	0
$231$	3.92319e37	0.0392683
$232$	−2.43430e38	−0.226894
$233$	−1.66756e39	−1.44780	−0.723899	−	0.689906i	$-0.757652\pi$
$233$	−1.66756e39	−1.44780	−0.723899	+	0.689906i	$0.757652\pi$
$234$	−8.36090e38	−0.676381
$235$	0	0
$236$	1.46897e39	1.03268
$237$	1.36055e38	0.0892005
$238$	8.86182e38	0.542005
$239$	6.59391e38	0.376338	0.188169	−	0.982137i	$-0.439745\pi$
$239$	6.59391e38	0.376338	0.188169	+	0.982137i	$0.439745\pi$
$240$	0	0
$241$	1.79835e39	0.894524	0.447262	−	0.894403i	$-0.352399\pi$
$241$	1.79835e39	0.894524	0.447262	+	0.894403i	$0.352399\pi$
$242$	2.49360e39	1.15844
$243$	1.27936e39	0.555251
$244$	−8.68479e38	−0.352231
$245$	0	0
$246$	3.57710e38	0.126795
$247$	9.60683e38	0.318479
$248$	2.25036e38	0.0697909
$249$	−1.05054e39	−0.304875
$250$	0	0
$251$	4.62035e39	1.17506	0.587528	−	0.809204i	$-0.300101\pi$
$251$	4.62035e39	1.17506	0.587528	+	0.809204i	$0.300101\pi$
$252$	2.10568e39	0.501514
$253$	−2.84501e39	−0.634738
$254$	4.18477e39	0.874812
$255$	0	0
$256$	2.32218e39	0.426517
$257$	−4.29716e39	−0.740090	−0.370045	−	0.929014i	$-0.620658\pi$
$257$	−4.29716e39	−0.740090	−0.370045	+	0.929014i	$0.620658\pi$
$258$	1.62636e39	0.262720
$259$	−1.90693e39	−0.288994
$260$	0	0
$261$	−4.97898e39	−0.664618
$262$	1.08189e40	1.35585
$263$	5.41479e39	0.637253	0.318627	−	0.947880i	$-0.396778\pi$
$263$	5.41479e39	0.637253	0.318627	+	0.947880i	$0.396778\pi$
$264$	2.73123e38	0.0301921
$265$	0	0
$266$	−4.40197e39	−0.429635
$267$	6.35677e38	0.0583177
$268$	−2.12306e39	−0.183121
$269$	9.46661e39	0.767860	0.383930	−	0.923362i	$-0.374570\pi$
$269$	9.46661e39	0.767860	0.383930	+	0.923362i	$0.374570\pi$
$270$	0	0
$271$	−2.02716e40	−1.45511	−0.727555	−	0.686050i	$-0.759343\pi$
$271$	−2.02716e40	−1.45511	−0.727555	+	0.686050i	$0.759343\pi$
$272$	−9.21533e39	−0.622478
$273$	6.17688e38	0.0392722
$274$	1.98423e40	1.18770
$275$	0	0
$276$	6.02653e39	0.319939
$277$	2.14513e40	1.07285	0.536423	−	0.843949i	$-0.319775\pi$
$277$	2.14513e40	1.07285	0.536423	+	0.843949i	$0.319775\pi$
$278$	−4.19052e40	−1.97482
$279$	4.60274e39	0.204431
$280$	0	0
$281$	−2.22768e40	−0.879425	−0.439712	−	0.898139i	$-0.644920\pi$
$281$	−2.22768e40	−0.879425	−0.439712	+	0.898139i	$0.644920\pi$
$282$	−1.13206e40	−0.421462
$283$	−1.45996e40	−0.512702	−0.256351	−	0.966584i	$-0.582520\pi$
$283$	−1.45996e40	−0.512702	−0.256351	+	0.966584i	$0.582520\pi$
$284$	7.23231e40	2.39621
$285$	0	0
$286$	−1.12404e40	−0.331699
$287$	6.69600e39	0.186537
$288$	−5.18507e40	−1.36389
$289$	−1.10661e40	−0.274903
$290$	0	0
$291$	1.48320e40	0.328825
$292$	4.03349e40	0.845015
$293$	3.33509e40	0.660377	0.330188	−	0.943915i	$-0.392888\pi$
$293$	3.33509e40	0.660377	0.330188	+	0.943915i	$0.392888\pi$
$294$	1.26813e40	0.237374
$295$	0	0
$296$	−1.32756e40	−0.222198
$297$	1.13931e40	0.180368
$298$	1.17049e41	1.75307
$299$	−4.47933e40	−0.634802
$300$	0	0
$301$	3.04440e40	0.386504
$302$	1.97119e41	2.36926
$303$	3.19653e40	0.363810
$304$	4.57757e40	0.493424
$305$	0	0
$306$	1.26185e41	1.22069
$307$	−8.68250e40	−0.795906	−0.397953	−	0.917406i	$-0.630279\pi$
$307$	−8.68250e40	−0.795906	−0.397953	+	0.917406i	$0.630279\pi$
$308$	2.83089e40	0.245944
$309$	1.76327e40	0.145212
$310$	0	0
$311$	1.66474e41	1.23254	0.616270	−	0.787535i	$-0.288643\pi$
$311$	1.66474e41	1.23254	0.616270	+	0.787535i	$0.288643\pi$
$312$	4.30019e39	0.0301951
$313$	−2.38300e41	−1.58724	−0.793618	−	0.608416i	$-0.791805\pi$
$313$	−2.38300e41	−1.58724	−0.793618	+	0.608416i	$0.791805\pi$
$314$	−2.04048e41	−1.28942
$315$	0	0
$316$	9.81743e40	0.558677
$317$	1.03851e41	0.560964	0.280482	−	0.959859i	$-0.409506\pi$
$317$	1.03851e41	0.560964	0.280482	+	0.959859i	$0.409506\pi$
$318$	1.03331e41	0.529888
$319$	−6.69377e40	−0.325930
$320$	0	0
$321$	5.49408e40	0.241303
$322$	2.05248e41	0.856363
$323$	−1.44989e41	−0.574768
$324$	2.87530e41	1.08316
$325$	0	0
$326$	−2.64893e41	−0.901528
$327$	−7.17654e40	−0.232208
$328$	4.66160e40	0.143422
$329$	−2.11911e41	−0.620041
$330$	0	0
$331$	−1.38040e41	−0.365463	−0.182732	−	0.983163i	$-0.558494\pi$
$331$	−1.38040e41	−0.365463	−0.182732	+	0.983163i	$0.558494\pi$
$332$	−7.58043e41	−1.90948
$333$	−2.71531e41	−0.650863
$334$	−5.40954e41	−1.23408
$335$	0	0
$336$	2.94323e40	0.0608451
$337$	−1.52333e40	−0.0299847	−0.0149923	−	0.999888i	$-0.504772\pi$
$337$	−1.52333e40	−0.0299847	−0.0149923	+	0.999888i	$0.504772\pi$
$338$	6.17978e41	1.15837
$339$	5.28657e40	0.0943798
$340$	0	0
$341$	6.18796e40	0.100254
$342$	−6.26803e41	−0.967610
$343$	5.27746e41	0.776376
$344$	2.11944e41	0.297171
$345$	0	0
$346$	−1.97019e42	−2.51045
$347$	−1.11878e42	−1.35928	−0.679639	−	0.733547i	$-0.737864\pi$
$347$	−1.11878e42	−1.35928	−0.679639	+	0.733547i	$0.737864\pi$
$348$	1.41793e41	0.164285
$349$	−6.63572e41	−0.733278	−0.366639	−	0.930363i	$-0.619492\pi$
$349$	−6.63572e41	−0.733278	−0.366639	+	0.930363i	$0.619492\pi$
$350$	0	0
$351$	1.79378e41	0.180386
$352$	−6.97084e41	−0.668853
$353$	−4.28180e41	−0.392052	−0.196026	−	0.980599i	$-0.562804\pi$
$353$	−4.28180e41	−0.392052	−0.196026	+	0.980599i	$0.562804\pi$
$354$	−2.81152e41	−0.245690
$355$	0	0
$356$	4.58690e41	0.365253
$357$	−9.32230e40	−0.0708757
$358$	2.61426e42	1.89792
$359$	−9.04901e41	−0.627397	−0.313698	−	0.949523i	$-0.601568\pi$
$359$	−9.04901e41	−0.627397	−0.313698	+	0.949523i	$0.601568\pi$
$360$	0	0
$361$	−8.60562e41	−0.544394
$362$	−3.59541e42	−2.17299
$363$	−2.62317e41	−0.151484
$364$	4.45710e41	0.245968
$365$	0	0
$366$	1.66222e41	0.0838011
$367$	2.16128e41	0.104165	0.0520823	−	0.998643i	$-0.483414\pi$
$367$	2.16128e41	0.104165	0.0520823	+	0.998643i	$0.483414\pi$
$368$	−2.13436e42	−0.983510
$369$	9.53454e41	0.420112
$370$	0	0
$371$	1.93426e42	0.779553
$372$	−1.31079e41	−0.0505328
$373$	−3.17253e42	−1.17007	−0.585033	−	0.811009i	$-0.698919\pi$
$373$	−3.17253e42	−1.17007	−0.585033	+	0.811009i	$0.698919\pi$
$374$	1.69644e42	0.598627
$375$	0	0
$376$	−1.47527e42	−0.476730
$377$	−1.05390e42	−0.325963
$378$	−8.21933e41	−0.243345
$379$	−5.62885e42	−1.59541	−0.797705	−	0.603048i	$-0.793953\pi$
$379$	−5.62885e42	−1.59541	−0.797705	+	0.603048i	$0.793953\pi$
$380$	0	0
$381$	−4.40221e41	−0.114396
$382$	1.01795e43	2.53326
$383$	−1.01197e42	−0.241205	−0.120603	−	0.992701i	$-0.538483\pi$
$383$	−1.01197e42	−0.241205	−0.120603	+	0.992701i	$0.538483\pi$
$384$	5.46975e41	0.124883
$385$	0	0
$386$	1.31441e42	0.275449
$387$	4.33497e42	0.870472
$388$	1.07024e43	2.05949
$389$	−9.74782e42	−1.79779	−0.898896	−	0.438163i	$-0.855629\pi$
$389$	−9.74782e42	−1.79779	−0.898896	+	0.438163i	$0.855629\pi$
$390$	0	0
$391$	6.76032e42	1.14565
$392$	1.65260e42	0.268502
$393$	−1.13811e42	−0.177299
$394$	7.69409e42	1.14940
$395$	0	0
$396$	4.03094e42	0.553906
$397$	5.84553e42	0.770514	0.385257	−	0.922809i	$-0.374113\pi$
$397$	5.84553e42	0.770514	0.385257	+	0.922809i	$0.374113\pi$
$398$	−2.72649e42	−0.344773
$399$	4.63070e41	0.0561816
$400$	0	0
$401$	6.82021e42	0.761931	0.380966	−	0.924589i	$-0.375592\pi$
$401$	6.82021e42	0.761931	0.380966	+	0.924589i	$0.375592\pi$
$402$	4.06341e41	0.0435673
$403$	9.74265e41	0.100264
$404$	2.30654e43	2.27860
$405$	0	0
$406$	4.82911e42	0.439732
$407$	−3.65048e42	−0.319185
$408$	−6.48996e41	−0.0544941
$409$	−7.09650e42	−0.572281	−0.286141	−	0.958188i	$-0.592372\pi$
$409$	−7.09650e42	−0.572281	−0.286141	+	0.958188i	$0.592372\pi$
$410$	0	0
$411$	−2.08733e42	−0.155311
$412$	1.27233e43	0.909488
$413$	−5.26290e42	−0.361451
$414$	2.92256e43	1.92867
$415$	0	0
$416$	−1.09753e43	−0.668921
$417$	4.40826e42	0.258239
$418$	−8.42678e42	−0.474518
$419$	−1.41115e43	−0.763912	−0.381956	−	0.924181i	$-0.624749\pi$
$419$	−1.41115e43	−0.763912	−0.381956	+	0.924181i	$0.624749\pi$
$420$	0	0
$421$	−9.28037e42	−0.464420	−0.232210	−	0.972666i	$-0.574596\pi$
$421$	−9.28037e42	−0.464420	−0.232210	+	0.972666i	$0.574596\pi$
$422$	−2.57811e42	−0.124064
$423$	−3.01743e43	−1.39644
$424$	1.34659e43	0.599374
$425$	0	0
$426$	−1.38422e43	−0.570095
$427$	3.11151e42	0.123285
$428$	3.96441e43	1.51132
$429$	1.18245e42	0.0433749
$430$	0	0
$431$	−2.40707e43	−0.817738	−0.408869	−	0.912593i	$-0.634077\pi$
$431$	−2.40707e43	−0.817738	−0.408869	+	0.912593i	$0.634077\pi$
$432$	8.54721e42	0.279475
$433$	−4.96426e43	−1.56244	−0.781222	−	0.624253i	$-0.785403\pi$
$433$	−4.96426e43	−1.56244	−0.781222	+	0.624253i	$0.785403\pi$
$434$	−4.46420e42	−0.135258
$435$	0	0
$436$	−5.17843e43	−1.45436
$437$	−3.35808e43	−0.908128
$438$	−7.71986e42	−0.201042
$439$	4.80839e43	1.20597	0.602984	−	0.797754i	$-0.293978\pi$
$439$	4.80839e43	1.20597	0.602984	+	0.797754i	$0.293978\pi$
$440$	0	0
$441$	3.38013e43	0.786495
$442$	2.67096e43	0.598687
$443$	8.49113e42	0.183360	0.0916799	−	0.995789i	$-0.470776\pi$
$443$	8.49113e42	0.183360	0.0916799	+	0.995789i	$0.470776\pi$
$444$	7.73275e42	0.160885
$445$	0	0
$446$	−2.95287e43	−0.570453
$447$	−1.23131e43	−0.229242
$448$	3.28879e43	0.590131
$449$	−8.15651e43	−1.41072	−0.705359	−	0.708851i	$-0.749214\pi$
$449$	−8.15651e43	−1.41072	−0.705359	+	0.708851i	$0.749214\pi$
$450$	0	0
$451$	1.28183e43	0.206024
$452$	3.81467e43	0.591116
$453$	−2.07361e43	−0.309819
$454$	4.10327e43	0.591165
$455$	0	0
$456$	3.22378e42	0.0431962
$457$	−3.82156e43	−0.493882	−0.246941	−	0.969030i	$-0.579425\pi$
$457$	−3.82156e43	−0.493882	−0.246941	+	0.969030i	$0.579425\pi$
$458$	9.27216e43	1.15585
$459$	−2.70722e43	−0.325548
$460$	0	0
$461$	1.42045e44	1.58987	0.794933	−	0.606698i	$-0.207506\pi$
$461$	1.42045e44	1.58987	0.794933	+	0.606698i	$0.207506\pi$
$462$	−5.41814e42	−0.0585137
$463$	−1.76412e43	−0.183841	−0.0919203	−	0.995766i	$-0.529300\pi$
$463$	−1.76412e43	−0.183841	−0.0919203	+	0.995766i	$0.529300\pi$
$464$	−5.02175e43	−0.505020
$465$	0	0
$466$	2.30299e44	2.15737
$467$	−1.44747e44	−1.30882	−0.654410	−	0.756140i	$-0.727083\pi$
$467$	−1.44747e44	−1.30882	−0.654410	+	0.756140i	$0.727083\pi$
$468$	6.34653e43	0.553962
$469$	7.60631e42	0.0640947
$470$	0	0
$471$	2.14651e43	0.168612
$472$	−3.66390e43	−0.277908
$473$	5.82796e43	0.426882
$474$	−1.87900e43	−0.132918
$475$	0	0
$476$	−6.72677e43	−0.443907
$477$	2.75423e44	1.75568
$478$	−9.10656e43	−0.560782
$479$	−2.82253e44	−1.67920	−0.839602	−	0.543203i	$-0.817212\pi$
$479$	−2.82253e44	−1.67920	−0.839602	+	0.543203i	$0.817212\pi$
$480$	0	0
$481$	−5.74751e43	−0.319217
$482$	−2.48362e44	−1.33293
$483$	−2.15914e43	−0.111983
$484$	−1.89282e44	−0.948770
$485$	0	0
$486$	−1.76687e44	−0.827382
$487$	2.41873e44	1.09486	0.547432	−	0.836850i	$-0.315605\pi$
$487$	2.41873e44	1.09486	0.547432	+	0.836850i	$0.315605\pi$
$488$	2.16616e43	0.0947902
$489$	2.78657e43	0.117889
$490$	0	0
$491$	−3.36324e44	−1.33019	−0.665095	−	0.746759i	$-0.731609\pi$
$491$	−3.36324e44	−1.33019	−0.665095	+	0.746759i	$0.731609\pi$
$492$	−2.71528e43	−0.103846
$493$	1.59058e44	0.588275
$494$	−1.32676e44	−0.474566
$495$	0	0
$496$	4.64228e43	0.155340
$497$	−2.59113e44	−0.838705
$498$	1.45085e44	0.454295
$499$	−8.01313e43	−0.242741	−0.121371	−	0.992607i	$-0.538729\pi$
$499$	−8.01313e43	−0.242741	−0.121371	+	0.992607i	$0.538729\pi$
$500$	0	0
$501$	5.69063e43	0.161376
$502$	−6.38096e44	−1.75095
$503$	−2.08304e44	−0.553129	−0.276565	−	0.960995i	$-0.589196\pi$
$503$	−2.08304e44	−0.553129	−0.276565	+	0.960995i	$0.589196\pi$
$504$	−5.25198e43	−0.134964
$505$	0	0
$506$	3.92911e44	0.945825
$507$	−6.50090e43	−0.151475
$508$	−3.17654e44	−0.716478
$509$	3.65736e44	0.798591	0.399296	−	0.916822i	$-0.369255\pi$
$509$	3.65736e44	0.798591	0.399296	+	0.916822i	$0.369255\pi$
$510$	0	0
$511$	−1.44509e44	−0.295766
$512$	−6.44110e44	−1.27646
$513$	1.34477e44	0.258054
$514$	5.93461e44	1.10281
$515$	0	0
$516$	−1.23453e44	−0.215169
$517$	−4.05665e44	−0.684816
$518$	2.63358e44	0.430631
$519$	2.07256e44	0.328281
$520$	0	0
$521$	−3.73678e44	−0.555488	−0.277744	−	0.960655i	$-0.589587\pi$
$521$	−3.73678e44	−0.555488	−0.277744	+	0.960655i	$0.589587\pi$
$522$	6.87625e44	0.990349
$523$	2.43582e44	0.339913	0.169957	−	0.985452i	$-0.445637\pi$
$523$	2.43582e44	0.339913	0.169957	+	0.985452i	$0.445637\pi$
$524$	−8.21232e44	−1.11045
$525$	0	0
$526$	−7.47813e44	−0.949573
$527$	−1.47039e44	−0.180949
$528$	5.63428e43	0.0672014
$529$	7.00750e44	0.810111
$530$	0	0
$531$	−7.49392e44	−0.814047
$532$	3.34141e44	0.351875
$533$	2.01818e44	0.206045
$534$	−8.77905e43	−0.0868994
$535$	0	0
$536$	5.29533e43	0.0492804
$537$	−2.75010e44	−0.248183
$538$	−1.30739e45	−1.14419
$539$	4.54426e44	0.385699
$540$	0	0
$541$	1.83384e45	1.46422	0.732112	−	0.681184i	$-0.238535\pi$
$541$	1.83384e45	1.46422	0.732112	+	0.681184i	$0.238535\pi$
$542$	2.79963e45	2.16826
$543$	3.78224e44	0.284153
$544$	1.65641e45	1.20722
$545$	0	0
$546$	−8.53061e43	−0.0585196
$547$	2.32228e45	1.54570	0.772848	−	0.634592i	$-0.218832\pi$
$547$	2.32228e45	1.54570	0.772848	+	0.634592i	$0.218832\pi$
$548$	−1.50617e45	−0.972738
$549$	4.43053e44	0.277659
$550$	0	0
$551$	−7.90093e44	−0.466312
$552$	−1.50314e44	−0.0861002
$553$	−3.51731e44	−0.195544
$554$	−2.96255e45	−1.59865
$555$	0	0
$556$	3.18090e45	1.61740
$557$	2.15312e45	1.06281	0.531406	−	0.847117i	$-0.321664\pi$
$557$	2.15312e45	1.06281	0.531406	+	0.847117i	$0.321664\pi$
$558$	−6.35664e44	−0.304624
$559$	9.17585e44	0.426925
$560$	0	0
$561$	−1.78459e44	−0.0782800
$562$	3.07655e45	1.31043
$563$	2.18829e45	0.905142	0.452571	−	0.891728i	$-0.350507\pi$
$563$	2.18829e45	0.905142	0.452571	+	0.891728i	$0.350507\pi$
$564$	8.59314e44	0.345181
$565$	0	0
$566$	2.01629e45	0.763979
$567$	−1.03014e45	−0.379119
$568$	−1.80388e45	−0.644853
$569$	3.69991e45	1.28481	0.642404	−	0.766366i	$-0.277937\pi$
$569$	3.69991e45	1.28481	0.642404	+	0.766366i	$0.277937\pi$
$570$	0	0
$571$	4.09741e44	0.134281	0.0671403	−	0.997744i	$-0.478612\pi$
$571$	4.09741e44	0.134281	0.0671403	+	0.997744i	$0.478612\pi$
$572$	8.53231e44	0.271664
$573$	−1.07084e45	−0.331264
$574$	−9.24755e44	−0.277959
$575$	0	0
$576$	4.68295e45	1.32907
$577$	−2.41392e45	−0.665767	−0.332884	−	0.942968i	$-0.608022\pi$
$577$	−2.41392e45	−0.665767	−0.332884	+	0.942968i	$0.608022\pi$
$578$	1.52829e45	0.409634
$579$	−1.38271e44	−0.0360193
$580$	0	0
$581$	2.71585e45	0.668344
$582$	−2.04838e45	−0.489983
$583$	3.70280e45	0.860992
$584$	−1.00603e45	−0.227405
$585$	0	0
$586$	−4.60594e45	−0.984029
$587$	3.30502e45	0.686507	0.343253	−	0.939243i	$-0.388471\pi$
$587$	3.30502e45	0.686507	0.343253	+	0.939243i	$0.388471\pi$
$588$	−9.62604e44	−0.194411
$589$	7.30390e44	0.143434
$590$	0	0
$591$	−8.09389e44	−0.150302
$592$	−2.73863e45	−0.494568
$593$	−3.04911e45	−0.535514	−0.267757	−	0.963486i	$-0.586282\pi$
$593$	−3.04911e45	−0.535514	−0.267757	+	0.963486i	$0.586282\pi$
$594$	−1.57344e45	−0.268766
$595$	0	0
$596$	−8.88487e45	−1.43578
$597$	2.86816e44	0.0450845
$598$	6.18620e45	0.945920
$599$	4.77681e45	0.710551	0.355276	−	0.934762i	$-0.384387\pi$
$599$	4.77681e45	0.710551	0.355276	+	0.934762i	$0.384387\pi$
$600$	0	0
$601$	−1.11023e46	−1.56310	−0.781549	−	0.623844i	$-0.785570\pi$
$601$	−1.11023e46	−1.56310	−0.781549	+	0.623844i	$0.785570\pi$
$602$	−4.20449e45	−0.575931
$603$	1.08307e45	0.144352
$604$	−1.49627e46	−1.94045
$605$	0	0
$606$	−4.41458e45	−0.542115
$607$	−9.37646e44	−0.112054	−0.0560268	−	0.998429i	$-0.517843\pi$
$607$	−9.37646e44	−0.112054	−0.0560268	+	0.998429i	$0.517843\pi$
$608$	−8.22797e45	−0.956937
$609$	−5.08004e44	−0.0575019
$610$	0	0
$611$	−6.38701e45	−0.684885
$612$	−9.57834e45	−0.999751
$613$	−3.40725e45	−0.346183	−0.173092	−	0.984906i	$-0.555376\pi$
$613$	−3.40725e45	−0.346183	−0.173092	+	0.984906i	$0.555376\pi$
$614$	1.19910e46	1.18598
$615$	0	0
$616$	−7.06079e44	−0.0661869
$617$	−1.51984e46	−1.38705	−0.693525	−	0.720432i	$-0.743943\pi$
$617$	−1.51984e46	−1.38705	−0.693525	+	0.720432i	$0.743943\pi$
$618$	−2.43517e45	−0.216381
$619$	−3.99242e45	−0.345415	−0.172707	−	0.984973i	$-0.555251\pi$
$619$	−3.99242e45	−0.345415	−0.172707	+	0.984973i	$0.555251\pi$
$620$	0	0
$621$	−6.27019e45	−0.514362
$622$	−2.29910e46	−1.83661
$623$	−1.64336e45	−0.127844
$624$	8.87091e44	0.0672082
$625$	0	0
$626$	3.29105e46	2.36515
$627$	8.86465e44	0.0620508
$628$	1.54887e46	1.05604
$629$	8.67429e45	0.576100
$630$	0	0
$631$	−8.68878e45	−0.547614	−0.273807	−	0.961785i	$-0.588283\pi$
$631$	−8.68878e45	−0.547614	−0.273807	+	0.961785i	$0.588283\pi$
$632$	−2.44866e45	−0.150348
$633$	2.71208e44	0.0162234
$634$	−1.43425e46	−0.835894
$635$	0	0
$636$	−7.84358e45	−0.433982
$637$	7.15473e45	0.385738
$638$	9.24447e45	0.485669
$639$	−3.68955e46	−1.88890
$640$	0	0
$641$	1.75762e46	0.854609	0.427305	−	0.904108i	$-0.359463\pi$
$641$	1.75762e46	0.854609	0.427305	+	0.904108i	$0.359463\pi$
$642$	−7.58763e45	−0.359566
$643$	3.90754e46	1.80477	0.902386	−	0.430928i	$-0.141814\pi$
$643$	3.90754e46	1.80477	0.902386	+	0.430928i	$0.141814\pi$
$644$	−1.55798e46	−0.701368
$645$	0	0
$646$	2.00238e46	0.856464
$647$	3.44345e46	1.43573	0.717865	−	0.696182i	$-0.245119\pi$
$647$	3.44345e46	1.43573	0.717865	+	0.696182i	$0.245119\pi$
$648$	−7.17158e45	−0.291492
$649$	−1.00749e46	−0.399211
$650$	0	0
$651$	4.69617e44	0.0176871
$652$	2.01073e46	0.738359
$653$	−4.09793e46	−1.46723	−0.733613	−	0.679567i	$-0.762168\pi$
$653$	−4.09793e46	−1.46723	−0.733613	+	0.679567i	$0.762168\pi$
$654$	9.91120e45	0.346014
$655$	0	0
$656$	9.61645e45	0.319228
$657$	−2.05768e46	−0.666115
$658$	2.92661e46	0.923926
$659$	7.05687e44	0.0217271	0.0108636	−	0.999941i	$-0.496542\pi$
$659$	7.05687e44	0.0217271	0.0108636	+	0.999941i	$0.496542\pi$
$660$	0	0
$661$	5.13888e45	0.150503	0.0752514	−	0.997165i	$-0.476024\pi$
$661$	5.13888e45	0.150503	0.0752514	+	0.997165i	$0.476024\pi$
$662$	1.90641e46	0.544578
$663$	−2.80975e45	−0.0782878
$664$	1.89071e46	0.513868
$665$	0	0
$666$	3.74999e46	0.969852
$667$	3.68393e46	0.929469
$668$	4.10623e46	1.01072
$669$	3.10631e45	0.0745958
$670$	0	0
$671$	5.95644e45	0.136165
$672$	−5.29031e45	−0.118002
$673$	−8.48563e46	−1.84687	−0.923434	−	0.383758i	$-0.874630\pi$
$673$	−8.48563e46	−1.84687	−0.923434	+	0.383758i	$0.874630\pi$
$674$	2.10380e45	0.0446803
$675$	0	0
$676$	−4.69090e46	−0.948715
$677$	−1.97690e46	−0.390185	−0.195093	−	0.980785i	$-0.562501\pi$
$677$	−1.97690e46	−0.390185	−0.195093	+	0.980785i	$0.562501\pi$
$678$	−7.30105e45	−0.140636
$679$	−3.83438e46	−0.720848
$680$	0	0
$681$	−4.31648e45	−0.0773042
$682$	−8.54591e45	−0.149388
$683$	−1.05640e47	−1.80254	−0.901272	−	0.433254i	$-0.857365\pi$
$683$	−1.05640e47	−1.80254	−0.901272	+	0.433254i	$0.857365\pi$
$684$	4.75789e46	0.792480
$685$	0	0
$686$	−7.28847e46	−1.15688
$687$	−9.75396e45	−0.151145
$688$	4.37221e46	0.661442
$689$	5.82988e46	0.861078
$690$	0	0
$691$	−2.86100e46	−0.402838	−0.201419	−	0.979505i	$-0.564555\pi$
$691$	−2.86100e46	−0.402838	−0.201419	+	0.979505i	$0.564555\pi$
$692$	1.49551e47	2.05608
$693$	−1.44417e46	−0.193874
$694$	1.54510e47	2.02546
$695$	0	0
$696$	−3.53660e45	−0.0442113
$697$	−3.04589e46	−0.371855
$698$	9.16430e46	1.09266
$699$	−2.42266e46	−0.282110
$700$	0	0
$701$	5.94385e46	0.660269	0.330134	−	0.943934i	$-0.392906\pi$
$701$	5.94385e46	0.660269	0.330134	+	0.943934i	$0.392906\pi$
$702$	−2.47731e46	−0.268793
$703$	−4.30881e46	−0.456662
$704$	6.29579e46	0.651781
$705$	0	0
$706$	5.91340e46	0.584197
$707$	−8.26368e46	−0.797541
$708$	2.13415e46	0.201222
$709$	6.13936e46	0.565536	0.282768	−	0.959188i	$-0.408747\pi$
$709$	6.13936e46	0.565536	0.282768	+	0.959188i	$0.408747\pi$
$710$	0	0
$711$	−5.00835e46	−0.440399
$712$	−1.14406e46	−0.0982948
$713$	−3.40555e46	−0.285898
$714$	1.28746e46	0.105612
$715$	0	0
$716$	−1.98441e47	−1.55441
$717$	9.57976e45	0.0733311
$718$	1.24972e47	0.934886
$719$	−2.54160e47	−1.85815	−0.929075	−	0.369891i	$-0.879395\pi$
$719$	−2.54160e47	−1.85815	−0.929075	+	0.369891i	$0.879395\pi$
$720$	0	0
$721$	−4.55841e46	−0.318333
$722$	1.18848e47	0.811203
$723$	2.61267e46	0.174302
$724$	2.72918e47	1.77969
$725$	0	0
$726$	3.62274e46	0.225727
$727$	1.41220e47	0.860157	0.430079	−	0.902791i	$-0.358486\pi$
$727$	1.41220e47	0.860157	0.430079	+	0.902791i	$0.358486\pi$
$728$	−1.11169e46	−0.0661935
$729$	−1.33885e47	−0.779343
$730$	0	0
$731$	−1.38484e47	−0.770484
$732$	−1.26174e46	−0.0686338
$733$	−1.82342e47	−0.969778	−0.484889	−	0.874576i	$-0.661140\pi$
$733$	−1.82342e47	−0.969778	−0.484889	+	0.874576i	$0.661140\pi$
$734$	−2.98484e46	−0.155216
$735$	0	0
$736$	3.83641e47	1.90740
$737$	1.45609e46	0.0707906
$738$	−1.31677e47	−0.626010
$739$	5.23297e46	0.243285	0.121642	−	0.992574i	$-0.461184\pi$
$739$	5.23297e46	0.243285	0.121642	+	0.992574i	$0.461184\pi$
$740$	0	0
$741$	1.39570e46	0.0620570
$742$	−2.67132e47	−1.16161
$743$	−2.92156e47	−1.24251	−0.621255	−	0.783609i	$-0.713377\pi$
$743$	−2.92156e47	−1.24251	−0.621255	+	0.783609i	$0.713377\pi$
$744$	3.26936e45	0.0135991
$745$	0	0
$746$	4.38145e47	1.74352
$747$	3.86715e47	1.50522
$748$	−1.28772e47	−0.490281
$749$	−1.42033e47	−0.528982
$750$	0	0
$751$	−3.59878e47	−1.28261	−0.641307	−	0.767284i	$-0.721608\pi$
$751$	−3.59878e47	−1.28261	−0.641307	+	0.767284i	$0.721608\pi$
$752$	−3.04335e47	−1.06110
$753$	6.71252e46	0.228965
$754$	1.45550e47	0.485718
$755$	0	0
$756$	6.23907e46	0.199301
$757$	3.31803e47	1.03705	0.518524	−	0.855063i	$-0.326482\pi$
$757$	3.31803e47	1.03705	0.518524	+	0.855063i	$0.326482\pi$
$758$	7.77375e47	2.37733
$759$	−4.13328e46	−0.123682
$760$	0	0
$761$	4.31914e47	1.23752	0.618758	−	0.785582i	$-0.287636\pi$
$761$	4.31914e47	1.23752	0.618758	+	0.785582i	$0.287636\pi$
$762$	6.07970e46	0.170461
$763$	1.85528e47	0.509044
$764$	−7.72696e47	−2.07476
$765$	0	0
$766$	1.39758e47	0.359420
$767$	−1.58624e47	−0.399251
$768$	3.37370e46	0.0831087
$769$	−7.36766e46	−0.177642	−0.0888209	−	0.996048i	$-0.528310\pi$
$769$	−7.36766e46	−0.177642	−0.0888209	+	0.996048i	$0.528310\pi$
$770$	0	0
$771$	−6.24299e46	−0.144210
$772$	−9.97733e46	−0.225595
$773$	−3.43337e47	−0.759904	−0.379952	−	0.925006i	$-0.624059\pi$
$773$	−3.43337e47	−0.759904	−0.379952	+	0.925006i	$0.624059\pi$
$774$	−5.98683e47	−1.29709
$775$	0	0
$776$	−2.66940e47	−0.554237
$777$	−2.77042e46	−0.0563118
$778$	1.34623e48	2.67889
$779$	1.51300e47	0.294761
$780$	0	0
$781$	−4.96026e47	−0.926322
$782$	−9.33638e47	−1.70713
$783$	−1.47526e47	−0.264119
$784$	3.40916e47	0.597630
$785$	0	0
$786$	1.57179e47	0.264193
$787$	−2.31817e47	−0.381560	−0.190780	−	0.981633i	$-0.561102\pi$
$787$	−2.31817e47	−0.381560	−0.190780	+	0.981633i	$0.561102\pi$
$788$	−5.84037e47	−0.941365
$789$	7.86671e46	0.124172
$790$	0	0
$791$	−1.36669e47	−0.206898
$792$	−1.00540e47	−0.149064
$793$	9.37813e46	0.136179
$794$	−8.07300e47	−1.14815
$795$	0	0
$796$	2.06960e47	0.282372
$797$	−9.59340e47	−1.28206	−0.641032	−	0.767514i	$-0.721494\pi$
$797$	−9.59340e47	−1.28206	−0.641032	+	0.767514i	$0.721494\pi$
$798$	−6.39526e46	−0.0837164
$799$	9.63944e47	1.23603
$800$	0	0
$801$	−2.34000e47	−0.287925
$802$	−9.41909e47	−1.13536
$803$	−2.76636e47	−0.326664
$804$	−3.08442e46	−0.0356819
$805$	0	0
$806$	−1.34551e47	−0.149403
$807$	1.37533e47	0.149621
$808$	−5.75297e47	−0.613204
$809$	−2.85029e47	−0.297672	−0.148836	−	0.988862i	$-0.547553\pi$
$809$	−2.85029e47	−0.297672	−0.148836	+	0.988862i	$0.547553\pi$
$810$	0	0
$811$	−1.46166e48	−1.46555	−0.732777	−	0.680469i	$-0.761776\pi$
$811$	−1.46166e48	−1.46555	−0.732777	+	0.680469i	$0.761776\pi$
$812$	−3.66565e47	−0.360144
$813$	−2.94510e47	−0.283535
$814$	5.04151e47	0.475618
$815$	0	0
$816$	−1.33882e47	−0.121293
$817$	6.87898e47	0.610745
$818$	9.80066e47	0.852758
$819$	−2.27378e47	−0.193894
$820$	0	0
$821$	−1.92594e48	−1.57754	−0.788771	−	0.614687i	$-0.789282\pi$
$821$	−1.92594e48	−1.57754	−0.788771	+	0.614687i	$0.789282\pi$
$822$	2.88272e47	0.231429
$823$	−4.92693e47	−0.387685	−0.193842	−	0.981033i	$-0.562095\pi$
$823$	−4.92693e47	−0.387685	−0.193842	+	0.981033i	$0.562095\pi$
$824$	−3.17345e47	−0.244756
$825$	0	0
$826$	7.26836e47	0.538599
$827$	4.17990e46	0.0303616	0.0151808	−	0.999885i	$-0.495168\pi$
$827$	4.17990e46	0.0303616	0.0151808	+	0.999885i	$0.495168\pi$
$828$	−2.21844e48	−1.57960
$829$	1.71716e48	1.19857	0.599283	−	0.800538i	$-0.295453\pi$
$829$	1.71716e48	1.19857	0.599283	+	0.800538i	$0.295453\pi$
$830$	0	0
$831$	3.11649e47	0.209049
$832$	9.91243e47	0.651846
$833$	−1.07981e48	−0.696153
$834$	−6.08806e47	−0.384803
$835$	0	0
$836$	6.39653e47	0.388634
$837$	1.36378e47	0.0812409
$838$	1.94888e48	1.13831
$839$	4.33094e46	0.0248033	0.0124016	−	0.999923i	$-0.496052\pi$
$839$	4.33094e46	0.0248033	0.0124016	+	0.999923i	$0.496052\pi$
$840$	0	0
$841$	−9.49316e47	−0.522729
$842$	1.28167e48	0.692033
$843$	−3.23641e47	−0.171360
$844$	1.95698e47	0.101610
$845$	0	0
$846$	4.16724e48	2.08083
$847$	6.78143e47	0.332082
$848$	2.77789e48	1.33408
$849$	−2.12106e47	−0.0999024
$850$	0	0
$851$	2.00905e48	0.910233
$852$	1.05072e48	0.466912
$853$	3.98289e48	1.73596	0.867979	−	0.496601i	$-0.165419\pi$
$853$	3.98289e48	1.73596	0.867979	+	0.496601i	$0.165419\pi$
$854$	−4.29717e47	−0.183708
$855$	0	0
$856$	−9.88802e47	−0.406717
$857$	3.66149e48	1.47732	0.738660	−	0.674078i	$-0.235459\pi$
$857$	3.66149e48	1.47732	0.738660	+	0.674078i	$0.235459\pi$
$858$	−1.63303e47	−0.0646330
$859$	4.14441e48	1.60907	0.804536	−	0.593904i	$-0.202414\pi$
$859$	4.14441e48	1.60907	0.804536	+	0.593904i	$0.202414\pi$
$860$	0	0
$861$	9.72808e46	0.0363475
$862$	3.32430e48	1.21851
$863$	−2.44535e48	−0.879353	−0.439676	−	0.898156i	$-0.644907\pi$
$863$	−2.44535e48	−0.879353	−0.439676	+	0.898156i	$0.644907\pi$
$864$	−1.53632e48	−0.542008
$865$	0	0
$866$	6.85593e48	2.32820
$867$	−1.60770e47	−0.0535661
$868$	3.38865e47	0.110777
$869$	−6.73325e47	−0.215973
$870$	0	0
$871$	2.29255e47	0.0707977
$872$	1.29160e48	0.391388
$873$	−5.45983e48	−1.62347
$874$	4.63769e48	1.35320
$875$	0	0
$876$	5.85993e47	0.164655
$877$	5.05120e48	1.39284	0.696420	−	0.717635i	$-0.254775\pi$
$877$	5.05120e48	1.39284	0.696420	+	0.717635i	$0.254775\pi$
$878$	−6.64066e48	−1.79702
$879$	4.84528e47	0.128677
$880$	0	0
$881$	−3.16644e48	−0.809971	−0.404985	−	0.914323i	$-0.632723\pi$
$881$	−3.16644e48	−0.809971	−0.404985	+	0.914323i	$0.632723\pi$
$882$	−4.66814e48	−1.17196
$883$	1.69432e48	0.417489	0.208744	−	0.977970i	$-0.433062\pi$
$883$	1.69432e48	0.417489	0.208744	+	0.977970i	$0.433062\pi$
$884$	−2.02745e48	−0.490330
$885$	0	0
$886$	−1.17267e48	−0.273225
$887$	−3.16518e48	−0.723868	−0.361934	−	0.932204i	$-0.617883\pi$
$887$	−3.16518e48	−0.723868	−0.361934	+	0.932204i	$0.617883\pi$
$888$	−1.92870e47	−0.0432964
$889$	1.13806e48	0.250777
$890$	0	0
$891$	−1.97202e48	−0.418724
$892$	2.24145e48	0.467206
$893$	−4.78823e48	−0.979775
$894$	1.70051e48	0.341594
$895$	0	0
$896$	−1.41404e48	−0.273767
$897$	−6.50765e47	−0.123694
$898$	1.12646e49	2.10211
$899$	−8.01263e47	−0.146805
$900$	0	0
$901$	−8.79861e48	−1.55401
$902$	−1.77028e48	−0.306997
$903$	4.42296e47	0.0753122
$904$	−9.51455e47	−0.159078
$905$	0	0
$906$	2.86378e48	0.461661
$907$	−1.08873e48	−0.172346	−0.0861731	−	0.996280i	$-0.527464\pi$
$907$	−1.08873e48	−0.172346	−0.0861731	+	0.996280i	$0.527464\pi$
$908$	−3.11468e48	−0.484169
$909$	−1.17668e49	−1.79620
$910$	0	0
$911$	−4.59000e48	−0.675708	−0.337854	−	0.941199i	$-0.609701\pi$
$911$	−4.59000e48	−0.675708	−0.337854	+	0.941199i	$0.609701\pi$
$912$	6.65037e47	0.0961460
$913$	5.19901e48	0.738165
$914$	5.27779e48	0.735935
$915$	0	0
$916$	−7.03824e48	−0.946648
$917$	2.94224e48	0.388673
$918$	3.73883e48	0.485100
$919$	−2.32948e48	−0.296861	−0.148431	−	0.988923i	$-0.547422\pi$
$919$	−2.32948e48	−0.296861	−0.148431	+	0.988923i	$0.547422\pi$
$920$	0	0
$921$	−1.26141e48	−0.155086
$922$	−1.96172e49	−2.36906
$923$	−7.80969e48	−0.926416
$924$	4.11276e47	0.0479232
$925$	0	0
$926$	2.43634e48	0.273941
$927$	−6.49079e48	−0.716939
$928$	9.02637e48	0.979425
$929$	−3.31257e48	−0.353107	−0.176553	−	0.984291i	$-0.556495\pi$
$929$	−3.31257e48	−0.353107	−0.176553	+	0.984291i	$0.556495\pi$
$930$	0	0
$931$	5.36378e48	0.551825
$932$	−1.74814e49	−1.76690
$933$	2.41857e48	0.240166
$934$	1.99903e49	1.95028
$935$	0	0
$936$	−1.58295e48	−0.149079
$937$	−8.43738e48	−0.780737	−0.390368	−	0.920659i	$-0.627652\pi$
$937$	−8.43738e48	−0.780737	−0.390368	+	0.920659i	$0.627652\pi$
$938$	−1.05047e48	−0.0955078
$939$	−3.46206e48	−0.309280
$940$	0	0
$941$	1.19866e49	1.03387	0.516937	−	0.856023i	$-0.327072\pi$
$941$	1.19866e49	1.03387	0.516937	+	0.856023i	$0.327072\pi$
$942$	−2.96445e48	−0.251249
$943$	−7.05458e48	−0.587527
$944$	−7.55830e48	−0.618566
$945$	0	0
$946$	−8.04873e48	−0.636098
$947$	1.53140e49	1.18936	0.594681	−	0.803961i	$-0.297278\pi$
$947$	1.53140e49	1.18936	0.594681	+	0.803961i	$0.297278\pi$
$948$	1.42629e48	0.108861
$949$	−4.35550e48	−0.326697
$950$	0	0
$951$	1.50877e48	0.109306
$952$	1.67779e48	0.119461
$953$	−4.05106e48	−0.283488	−0.141744	−	0.989903i	$-0.545271\pi$
$953$	−4.05106e48	−0.283488	−0.141744	+	0.989903i	$0.545271\pi$
$954$	−3.80374e49	−2.61615
$955$	0	0
$956$	6.91254e48	0.459285
$957$	−9.72483e47	−0.0635090
$958$	3.89808e49	2.50219
$959$	5.39619e48	0.340471
$960$	0	0
$961$	−1.56628e49	−0.954844
$962$	7.93763e48	0.475666
$963$	−2.02244e49	−1.19135
$964$	1.88525e49	1.09168
$965$	0	0
$966$	2.98189e48	0.166866
$967$	−1.43741e49	−0.790757	−0.395378	−	0.918518i	$-0.629387\pi$
$967$	−1.43741e49	−0.790757	−0.395378	+	0.918518i	$0.629387\pi$
$968$	4.72107e48	0.255327
$969$	−2.10642e48	−0.111996
$970$	0	0
$971$	1.56174e49	0.802585	0.401293	−	0.915950i	$-0.368561\pi$
$971$	1.56174e49	0.802585	0.401293	+	0.915950i	$0.368561\pi$
$972$	1.34118e49	0.677632
$973$	−1.13963e49	−0.566110
$974$	−3.34041e49	−1.63146
$975$	0	0
$976$	4.46859e48	0.210984
$977$	1.09477e49	0.508235	0.254117	−	0.967173i	$-0.418215\pi$
$977$	1.09477e49	0.508235	0.254117	+	0.967173i	$0.418215\pi$
$978$	−3.84841e48	−0.175667
$979$	−3.14591e48	−0.141199
$980$	0	0
$981$	2.64177e49	1.14645
$982$	4.64482e49	1.98212
$983$	−1.92109e49	−0.806150	−0.403075	−	0.915167i	$-0.632059\pi$
$983$	−1.92109e49	−0.806150	−0.403075	+	0.915167i	$0.632059\pi$
$984$	6.77245e47	0.0279465
$985$	0	0
$986$	−2.19668e49	−0.876591
$987$	−3.07868e48	−0.120818
$988$	1.00710e49	0.388673
$989$	−3.20743e49	−1.21736
$990$	0	0
$991$	2.18652e49	0.802672	0.401336	−	0.915931i	$-0.368546\pi$
$991$	2.18652e49	0.802672	0.401336	+	0.915931i	$0.368546\pi$
$992$	−8.34429e48	−0.301264
$993$	−2.00547e48	−0.0712122
$994$	3.57850e49	1.24976
$995$	0	0
$996$	−1.10130e49	−0.372071
$997$	−1.75251e49	−0.582357	−0.291179	−	0.956669i	$-0.594047\pi$
$997$	−1.75251e49	−0.582357	−0.291179	+	0.956669i	$0.594047\pi$
$998$	1.10666e49	0.361709
$999$	−8.04539e48	−0.258652

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.34.a.b.1.1		5
5.2	odd	4		25.34.b.b.24.1		10
5.3	odd	4		25.34.b.b.24.10		10
5.4	even	2		5.34.a.a.1.5	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.34.a.a.1.5	✓	5	5.4	even	2
25.34.a.b.1.1		5	1.1	even	1	trivial
25.34.b.b.24.1		10	5.2	odd	4
25.34.b.b.24.10		10	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)

\(f(q)\)	\(=\)	\(q-138106. q^{2} +1.45282e7 q^{3} +1.04832e10 q^{4} -2.00642e12 q^{6} -3.75584e13 q^{7} -2.61472e14 q^{8} -5.34799e15 q^{9} +O(q^{10})\)	\(q-138106. q^{2} +1.45282e7 q^{3} +1.04832e10 q^{4} -2.00642e12 q^{6} -3.75584e13 q^{7} -2.61472e14 q^{8} -5.34799e15 q^{9} -7.18987e16 q^{11} +1.52302e17 q^{12} -1.13201e18 q^{13} +5.18702e18 q^{14} -5.39393e19 q^{16} +1.70846e20 q^{17} +7.38588e20 q^{18} -8.48651e20 q^{19} -5.45655e20 q^{21} +9.92962e21 q^{22} +3.95696e22 q^{23} -3.79872e21 q^{24} +1.56337e23 q^{26} -1.58460e23 q^{27} -3.93732e23 q^{28} +9.30999e23 q^{29} -8.60649e23 q^{31} +9.69535e24 q^{32} -1.04456e24 q^{33} -2.35948e25 q^{34} -5.60641e25 q^{36} +5.07725e25 q^{37} +1.17203e26 q^{38} -1.64461e25 q^{39} -1.78283e26 q^{41} +7.53580e25 q^{42} -8.10579e26 q^{43} -7.53730e26 q^{44} -5.46479e27 q^{46} +5.64217e27 q^{47} -7.83641e26 q^{48} -6.32036e27 q^{49} +2.48208e27 q^{51} -1.18671e28 q^{52} -5.15002e28 q^{53} +2.18842e28 q^{54} +9.82047e27 q^{56} -1.23294e28 q^{57} -1.28576e29 q^{58} +1.40126e29 q^{59} -8.28448e28 q^{61} +1.18860e29 q^{62} +2.00862e29 q^{63} -8.75647e29 q^{64} +1.44259e29 q^{66} -2.02520e29 q^{67} +1.79102e30 q^{68} +5.74875e29 q^{69} +6.89895e30 q^{71} +1.39835e30 q^{72} +3.84757e30 q^{73} -7.01196e30 q^{74} -8.89659e30 q^{76} +2.70040e30 q^{77} +2.27129e30 q^{78} +9.36491e30 q^{79} +2.74277e31 q^{81} +2.46218e31 q^{82} -7.23102e31 q^{83} -5.72021e30 q^{84} +1.11945e32 q^{86} +1.35257e31 q^{87} +1.87995e31 q^{88} +4.37547e31 q^{89} +4.25165e31 q^{91} +4.14817e32 q^{92} -1.25037e31 q^{93} -7.79216e32 q^{94} +1.40856e32 q^{96} +1.02091e33 q^{97} +8.72877e32 q^{98} +3.84514e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 30472 q^{2} + 14988714 q^{3} + 1141311360 q^{4} + 12925063115760 q^{6} + 65452561787158 q^{7} - 155610638035200 q^{8} + 14\!\cdots\!65 q^{9}+O(q^{10}) \) 5 * q - 30472 * q^2 + 14988714 * q^3 + 1141311360 * q^4 + 12925063115760 * q^6 + 65452561787158 * q^7 - 155610638035200 * q^8 + 14541250990408965 * q^9	\( 5 q - 30472 q^{2} + 14988714 q^{3} + 1141311360 q^{4} + 12925063115760 q^{6} + 65452561787158 q^{7} - 155610638035200 q^{8} + 14\!\cdots\!65 q^{9}+ \cdots - 17\!\cdots\!20 q^{99}+O(q^{100}) \) 5 * q - 30472 * q^2 + 14988714 * q^3 + 1141311360 * q^4 + 12925063115760 * q^6 + 65452561787158 * q^7 - 155610638035200 * q^8 + 14541250990408965 * q^9 - 287801801877976640 * q^11 + 405379955363513088 * q^12 - 2397201150889907466 * q^13 + 11676449916272482320 * q^14 - 89180089543245957120 * q^16 + 308725634324001653918 * q^17 - 537830699104521134856 * q^18 + 918364712195153947500 * q^19 - 10535115771712805413140 * q^21 + 13757888128329419319296 * q^22 - 55453893359806770035646 * q^23 - 71953200752757895180800 * q^24 - 424902360762721464761840 * q^26 - 679342131249712739644500 * q^27 + 1365491680784291850286336 * q^28 - 926877224993589271166050 * q^29 - 1336046479411821372201940 * q^31 + 813043271605502937899008 * q^32 + 33213386789605758547506048 * q^33 - 68630658492513538369567280 * q^34 - 180374200000978588488558720 * q^36 + 142836045294254023962738038 * q^37 + 330380182336023289264570400 * q^38 - 785791651509490753882465620 * q^39 - 1325620030754525933329256290 * q^41 + 2645870671030939362357320736 * q^42 + 2343083972337632823995338194 * q^43 - 1855939386652616358153902080 * q^44 - 2874649720834424257835685840 * q^46 + 7724956189479550762134222398 * q^47 + 7356143571895968866126229504 * q^48 + 4143234303500031791722947185 * q^49 + 7346719218915268753088875260 * q^51 - 48963787841701555176191049472 * q^52 - 109528513717338677312301826786 * q^53 + 64134717586148777280751188000 * q^54 + 144880509244845944794630156800 * q^56 - 208512654554635835530896805800 * q^57 - 211870362017554277516078730800 * q^58 + 257176212490429778182108906300 * q^59 + 742889693167672203496619446410 * q^61 - 532537079706659761431026425824 * q^62 + 1004528834780444187135312826134 * q^63 - 1039367551847251405574221987840 * q^64 - 3327517517031282146197646561280 * q^66 + 3757683664783078488809531637718 * q^67 - 1174937222155965542229368447744 * q^68 - 2767417175780175137072429257020 * q^69 - 5502085339682331744817794354940 * q^71 + 15971664273931445780329968326400 * q^72 + 13667431819995552941083819387254 * q^73 - 3638621909178354336866018756080 * q^74 + 7186339982587317558706196185600 * q^76 - 47237885671577674597763242652544 * q^77 - 12077118142241690266249318498272 * q^78 - 10258197004592737759121926298200 * q^79 + 78583804836302041006582647314505 * q^81 - 27306575776891610455800103348784 * q^82 - 92562254147118615583166775350526 * q^83 + 174445330599959716374040873566720 * q^84 + 65486114707827974097903540464560 * q^86 - 137286065258860195168416991536900 * q^87 - 194246091941469769694864674406400 * q^88 - 60853500388863684631316333445150 * q^89 - 268937084803738847432203207735340 * q^91 + 697440932909638690403668496563968 * q^92 + 696145220941341231280490115670488 * q^93 - 363437055538131894048725908447280 * q^94 - 344518603172836645970889894051840 * q^96 + 867959773515074594808067717684598 * q^97 + 1991101889094264762194115874723096 * q^98 - 1790665589323481921279813177939520 * q^99

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