LMFDB - Embedded newform 25.34.a.f.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("25.1");

S:= CuspForms(chi, 34);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$172.457072203$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 26286285043 x^{14} + \cdots + 16\!\cdots\!36 $ x^16 - 26286285043x^14 + 277176279803774573548x^12 - 1496006322727341104924267746816x^10 + 4376228902975645752284567792282218577920x^8 - 6785210496827316795155770011788917433647451078656x^6 + 5093319366938751307797338793282286802764384084972313509888x^4 - 1608229292592013531797229664939538769264311330074914543142623510528*x^2 + 163532475457876517394407745867705361011086521692855999713211555842344615936
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	multiple of $ 2^{85}\cdot 3^{26}\cdot 5^{66}\cdot 7^{4}\cdot 11^{8} $
Twist minimal:	no (minimal twist has level 5)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$13863.7$ 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)

$f(q)$	$=$	$q+27727.3 q^{2} +6.45007e7 q^{3} -7.82113e9 q^{4} +1.78843e12 q^{6} +3.09117e13 q^{7} -4.55035e14 q^{8} -1.39871e15 q^{9} +O(q^{10})$	\(q+27727.3 q^{2} +6.45007e7 q^{3} -7.82113e9 q^{4} +1.78843e12 q^{6} +3.09117e13 q^{7} -4.55035e14 q^{8} -1.39871e15 q^{9} +1.96079e17 q^{11} -5.04469e17 q^{12} -4.53343e18 q^{13} +8.57100e17 q^{14} +5.45661e19 q^{16} -2.94288e20 q^{17} -3.87826e19 q^{18} +6.15724e20 q^{19} +1.99383e21 q^{21} +5.43675e21 q^{22} +1.65655e22 q^{23} -2.93501e22 q^{24} -1.25700e23 q^{26} -4.48782e23 q^{27} -2.41765e23 q^{28} -9.17408e22 q^{29} +5.75654e24 q^{31} +5.42169e24 q^{32} +1.26472e25 q^{33} -8.15982e24 q^{34} +1.09395e25 q^{36} -9.32591e25 q^{37} +1.70724e25 q^{38} -2.92410e26 q^{39} +4.59334e26 q^{41} +5.52836e25 q^{42} +2.98860e26 q^{43} -1.53356e27 q^{44} +4.59317e26 q^{46} -3.83658e27 q^{47} +3.51955e27 q^{48} -6.77546e27 q^{49} -1.89818e28 q^{51} +3.54566e28 q^{52} -1.34770e28 q^{53} -1.24435e28 q^{54} -1.40659e28 q^{56} +3.97147e28 q^{57} -2.54373e27 q^{58} +1.39545e29 q^{59} -1.27289e29 q^{61} +1.59614e29 q^{62} -4.32367e28 q^{63} -3.18390e29 q^{64} +3.50674e29 q^{66} +1.55253e30 q^{67} +2.30166e30 q^{68} +1.06849e30 q^{69} +4.80212e30 q^{71} +6.36464e29 q^{72} +2.54238e30 q^{73} -2.58583e30 q^{74} -4.81566e30 q^{76} +6.06114e30 q^{77} -8.10774e30 q^{78} +1.90983e31 q^{79} -2.11712e31 q^{81} +1.27361e31 q^{82} +1.69264e31 q^{83} -1.55940e31 q^{84} +8.28660e30 q^{86} -5.91735e30 q^{87} -8.92228e31 q^{88} -8.93087e31 q^{89} -1.40136e32 q^{91} -1.29561e32 q^{92} +3.71301e32 q^{93} -1.06378e32 q^{94} +3.49703e32 q^{96} -6.99431e32 q^{97} -1.87865e32 q^{98} -2.74259e32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 72851326872 q^{4} + 11001777346872 q^{6} + 27\!\cdots\!68 q^{9}+O(q^{10}) $ 16 * q + 72851326872 * q^4 + 11001777346872 * q^6 + 27535156574590368 * q^9	$ 16 q + 72851326872 q^{4} + 11001777346872 q^{6} + 27\!\cdots\!68 q^{9}+ \cdots - 34\!\cdots\!24 q^{99}+O(q^{100}) $ 16 * q + 72851326872 * q^4 + 11001777346872 * q^6 + 27535156574590368 * q^9 + 219974590742466912 * q^11 + 10416043581549356184 * q^14 + 133171456389985196576 * q^16 + 2949217257058889591200 * q^19 + 20126160533851210892592 * q^21 + 236696360036140740492000 * q^24 + 23043234216449373353232 * q^26 - 2210824656972934579370400 * q^29 + 4805180075928582021889472 * q^31 + 106706080442140703440064 * q^34 + 150609707516636111776170456 * q^36 + 950668737676648885834065216 * q^39 + 960625982433026021733974352 * q^41 + 4300041994750366563328828704 * q^44 + 4030532465737707969346868392 * q^46 + 48902999941413820155855454112 * q^49 + 37677263492556888574173469632 * q^51 + 416785644990759180210455480400 * q^54 + 209868986171565551575474447200 * q^56 + 204679212804521237512362904800 * q^59 - 62902839261738400132019069488 * q^61 - 3273202940251902417009873735808 * q^64 - 2991219624550267460630717491296 * q^66 - 6899695112224183044828868241904 * q^69 - 87525095316001019795902439808 * q^71 - 43140282179597200538055251968176 * q^74 - 38605994956626944020944749752800 * q^76 + 10590745643822309766800662264000 * q^79 + 126385893984816788804508532470336 * q^81 + 401968339664232685914350670917664 * q^84 - 18805496634715830052189508032488 * q^86 + 816457769414638729740610145056800 * q^89 + 572310345418666359618454810906752 * q^91 - 1084618018208246129370832376900296 * q^94 - 1376269400022374885061468958478208 * q^96 - 3432482025669259323040953857901024 * 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 $

$2$	27727.3	0.299167	0.149583	−	0.988749i	$-0.452207\pi$
$2$	27727.3	0.299167	0.149583	+	0.988749i	$0.452207\pi$
$3$	6.45007e7	0.865095	0.432548	−	0.901611i	$-0.357615\pi$
$3$	6.45007e7	0.865095	0.432548	+	0.901611i	$0.357615\pi$
$4$	−7.82113e9	−0.910499
$5$	0	0
$5$	0	0
$6$	1.78843e12	0.258808
$7$	3.09117e13	0.351565	0.175782	−	0.984429i	$-0.443754\pi$
$7$	3.09117e13	0.351565	0.175782	+	0.984429i	$0.443754\pi$
$8$	−4.55035e14	−0.571558
$9$	−1.39871e15	−0.251610
$10$	0	0
$11$	1.96079e17	1.28662	0.643312	−	0.765604i	$-0.277560\pi$
$11$	1.96079e17	1.28662	0.643312	+	0.765604i	$0.277560\pi$
$12$	−5.04469e17	−0.787669
$13$	−4.53343e18	−1.88956	−0.944782	−	0.327699i	$-0.893727\pi$
$13$	−4.53343e18	−1.88956	−0.944782	+	0.327699i	$0.893727\pi$
$14$	8.57100e17	0.105177
$15$	0	0
$16$	5.45661e19	0.739508
$17$	−2.94288e20	−1.46678	−0.733390	−	0.679808i	$-0.762063\pi$
$17$	−2.94288e20	−1.46678	−0.733390	+	0.679808i	$0.762063\pi$
$18$	−3.87826e19	−0.0752733
$19$	6.15724e20	0.489725	0.244862	−	0.969558i	$-0.421257\pi$
$19$	6.15724e20	0.489725	0.244862	+	0.969558i	$0.421257\pi$
$20$	0	0
$21$	1.99383e21	0.304137
$22$	5.43675e21	0.384915
$23$	1.65655e22	0.563242	0.281621	−	0.959526i	$-0.409128\pi$
$23$	1.65655e22	0.563242	0.281621	+	0.959526i	$0.409128\pi$
$24$	−2.93501e22	−0.494452
$25$	0	0
$26$	−1.25700e23	−0.565295
$27$	−4.48782e23	−1.08276
$28$	−2.41765e23	−0.320100
$29$	−9.17408e22	−0.0680762	−0.0340381	−	0.999421i	$-0.510837\pi$
$29$	−9.17408e22	−0.0680762	−0.0340381	+	0.999421i	$0.510837\pi$
$30$	0	0
$31$	5.75654e24	1.42133	0.710663	−	0.703533i	$-0.248395\pi$
$31$	5.75654e24	1.42133	0.710663	+	0.703533i	$0.248395\pi$
$32$	5.42169e24	0.792794
$33$	1.26472e25	1.11305
$34$	−8.15982e24	−0.438812
$35$	0	0
$36$	1.09395e25	0.229091
$37$	−9.32591e25	−1.24269	−0.621345	−	0.783537i	$-0.713413\pi$
$37$	−9.32591e25	−1.24269	−0.621345	+	0.783537i	$0.713413\pi$
$38$	1.70724e25	0.146509
$39$	−2.92410e26	−1.63465
$40$	0	0
$41$	4.59334e26	1.12511	0.562555	−	0.826760i	$-0.309818\pi$
$41$	4.59334e26	1.12511	0.562555	+	0.826760i	$0.309818\pi$
$42$	5.52836e25	0.0909877
$43$	2.98860e26	0.333610	0.166805	−	0.985990i	$-0.446655\pi$
$43$	2.98860e26	0.333610	0.166805	+	0.985990i	$0.446655\pi$
$44$	−1.53356e27	−1.17147
$45$	0	0
$46$	4.59317e26	0.168503
$47$	−3.83658e27	−0.987029	−0.493514	−	0.869738i	$-0.664288\pi$
$47$	−3.83658e27	−0.987029	−0.493514	+	0.869738i	$0.664288\pi$
$48$	3.51955e27	0.639745
$49$	−6.77546e27	−0.876402
$50$	0	0
$51$	−1.89818e28	−1.26891
$52$	3.54566e28	1.72045
$53$	−1.34770e28	−0.477575	−0.238788	−	0.971072i	$-0.576750\pi$
$53$	−1.34770e28	−0.477575	−0.238788	+	0.971072i	$0.576750\pi$
$54$	−1.24435e28	−0.323926
$55$	0	0
$56$	−1.40659e28	−0.200940
$57$	3.97147e28	0.423658
$58$	−2.54373e27	−0.0203661
$59$	1.39545e29	0.842667	0.421333	−	0.906906i	$-0.361562\pi$
$59$	1.39545e29	0.842667	0.421333	+	0.906906i	$0.361562\pi$
$60$	0	0
$61$	−1.27289e29	−0.443454	−0.221727	−	0.975109i	$-0.571169\pi$
$61$	−1.27289e29	−0.443454	−0.221727	+	0.975109i	$0.571169\pi$
$62$	1.59614e29	0.425213
$63$	−4.32367e28	−0.0884572
$64$	−3.18390e29	−0.502331
$65$	0	0
$66$	3.50674e29	0.332988
$67$	1.55253e30	1.15029	0.575144	−	0.818052i	$-0.304946\pi$
$67$	1.55253e30	1.15029	0.575144	+	0.818052i	$0.304946\pi$
$68$	2.30166e30	1.33550
$69$	1.06849e30	0.487258
$70$	0	0
$71$	4.80212e30	1.36669	0.683346	−	0.730095i	$-0.260524\pi$
$71$	4.80212e30	1.36669	0.683346	+	0.730095i	$0.260524\pi$
$72$	6.36464e29	0.143810
$73$	2.54238e30	0.457523	0.228761	−	0.973483i	$-0.426532\pi$
$73$	2.54238e30	0.457523	0.228761	+	0.973483i	$0.426532\pi$
$74$	−2.58583e30	−0.371771
$75$	0	0
$76$	−4.81566e30	−0.445894
$77$	6.06114e30	0.452332
$78$	−8.10774e30	−0.489034
$79$	1.90983e31	0.933573	0.466787	−	0.884370i	$-0.345412\pi$
$79$	1.90983e31	0.933573	0.466787	+	0.884370i	$0.345412\pi$
$80$	0	0
$81$	−2.11712e31	−0.685082
$82$	1.27361e31	0.336595
$83$	1.69264e31	0.366249	0.183125	−	0.983090i	$-0.441379\pi$
$83$	1.69264e31	0.366249	0.183125	+	0.983090i	$0.441379\pi$
$84$	−1.55940e31	−0.276917
$85$	0	0
$86$	8.28660e30	0.0998049
$87$	−5.91735e30	−0.0588924
$88$	−8.92228e31	−0.735380
$89$	−8.93087e31	−0.610884	−0.305442	−	0.952211i	$-0.598804\pi$
$89$	−8.93087e31	−0.610884	−0.305442	+	0.952211i	$0.598804\pi$
$90$	0	0
$91$	−1.40136e32	−0.664305
$92$	−1.29561e32	−0.512831
$93$	3.71301e32	1.22958
$94$	−1.06378e32	−0.295286
$95$	0	0
$96$	3.49703e32	0.685842
$97$	−6.99431e32	−1.15614	−0.578071	−	0.815987i	$-0.696194\pi$
$97$	−6.99431e32	−1.15614	−0.578071	+	0.815987i	$0.696194\pi$
$98$	−1.87865e32	−0.262190
$99$	−2.74259e32	−0.323728
$100$	0	0
$101$	9.76429e32	0.828587	0.414293	−	0.910143i	$-0.364029\pi$
$101$	9.76429e32	0.828587	0.414293	+	0.910143i	$0.364029\pi$
$102$	−5.26314e32	−0.379614
$103$	−1.55055e32	−0.0952076	−0.0476038	−	0.998866i	$-0.515158\pi$
$103$	−1.55055e32	−0.0952076	−0.0476038	+	0.998866i	$0.515158\pi$
$104$	2.06287e33	1.08000
$105$	0	0
$106$	−3.73682e32	−0.142875
$107$	4.85223e33	1.58895	0.794473	−	0.607299i	$-0.207747\pi$
$107$	4.85223e33	1.58895	0.794473	+	0.607299i	$0.207747\pi$
$108$	3.50998e33	0.985854
$109$	1.75363e33	0.423059	0.211530	−	0.977372i	$-0.432155\pi$
$109$	1.75363e33	0.423059	0.211530	+	0.977372i	$0.432155\pi$
$110$	0	0
$111$	−6.01528e33	−1.07505
$112$	1.68673e33	0.259985
$113$	−3.25949e33	−0.433866	−0.216933	−	0.976187i	$-0.569605\pi$
$113$	−3.25949e33	−0.433866	−0.216933	+	0.976187i	$0.569605\pi$
$114$	1.10118e33	0.126744
$115$	0	0
$116$	7.17517e32	0.0619834
$117$	6.34098e33	0.475433
$118$	3.86921e33	0.252098
$119$	−9.09695e33	−0.515669
$120$	0	0
$121$	1.52218e34	0.655402
$122$	−3.52938e33	−0.132667
$123$	2.96274e34	0.973328
$124$	−4.50227e34	−1.29412
$125$	0	0
$126$	−1.19884e33	−0.0264635
$127$	1.49443e34	0.289543	0.144771	−	0.989465i	$-0.453755\pi$
$127$	1.49443e34	0.289543	0.144771	+	0.989465i	$0.453755\pi$
$128$	−5.54001e34	−0.943075
$129$	1.92767e34	0.288604
$130$	0	0
$131$	4.63758e33	0.0538660	0.0269330	−	0.999637i	$-0.491426\pi$
$131$	4.63758e33	0.0538660	0.0269330	+	0.999637i	$0.491426\pi$
$132$	−9.89157e34	−1.01343
$133$	1.90331e34	0.172170
$134$	4.30476e34	0.344128
$135$	0	0
$136$	1.33911e35	0.838350
$137$	−5.85558e34	−0.324848	−0.162424	−	0.986721i	$-0.551931\pi$
$137$	−5.85558e34	−0.324848	−0.162424	+	0.986721i	$0.551931\pi$
$138$	2.96263e34	0.145771
$139$	3.91943e35	1.71190	0.855950	−	0.517059i	$-0.172973\pi$
$139$	3.91943e35	1.71190	0.855950	+	0.517059i	$0.172973\pi$
$140$	0	0
$141$	−2.47462e35	−0.853874
$142$	1.33150e35	0.408869
$143$	−8.88911e35	−2.43116
$144$	−7.63224e34	−0.186068
$145$	0	0
$146$	7.04933e34	0.136876
$147$	−4.37022e35	−0.758171
$148$	7.29391e35	1.13147
$149$	−5.37014e35	−0.745440	−0.372720	−	0.927944i	$-0.621575\pi$
$149$	−5.37014e35	−0.745440	−0.372720	+	0.927944i	$0.621575\pi$
$150$	0	0
$151$	2.49511e35	0.277953	0.138976	−	0.990296i	$-0.455619\pi$
$151$	2.49511e35	0.277953	0.138976	+	0.990296i	$0.455619\pi$
$152$	−2.80176e35	−0.279906
$153$	4.11625e35	0.369057
$154$	1.68059e35	0.135323
$155$	0	0
$156$	2.28697e36	1.48835
$157$	2.08550e36	1.22142	0.610712	−	0.791853i	$-0.290883\pi$
$157$	2.08550e36	1.22142	0.610712	+	0.791853i	$0.290883\pi$
$158$	5.29546e35	0.279294
$159$	−8.69278e35	−0.413148
$160$	0	0
$161$	5.12068e35	0.198016
$162$	−5.87021e35	−0.204954
$163$	4.35976e35	0.137520	0.0687601	−	0.997633i	$-0.478096\pi$
$163$	4.35976e35	0.137520	0.0687601	+	0.997633i	$0.478096\pi$
$164$	−3.59251e36	−1.02441
$165$	0	0
$166$	4.69325e35	0.109570
$167$	2.81153e36	0.594459	0.297229	−	0.954806i	$-0.403937\pi$
$167$	2.81153e36	0.594459	0.297229	+	0.954806i	$0.403937\pi$
$168$	−9.07262e35	−0.173832
$169$	1.47959e37	2.57045
$170$	0	0
$171$	−8.61223e35	−0.123220
$172$	−2.33743e36	−0.303751
$173$	2.92048e36	0.344900	0.172450	−	0.985018i	$-0.444832\pi$
$173$	2.92048e36	0.344900	0.172450	+	0.985018i	$0.444832\pi$
$174$	−1.64072e35	−0.0176187
$175$	0	0
$176$	1.06993e37	0.951469
$177$	9.00075e36	0.728987
$178$	−2.47629e36	−0.182756
$179$	1.58216e37	1.06457	0.532286	−	0.846565i	$-0.321333\pi$
$179$	1.58216e37	1.06457	0.532286	+	0.846565i	$0.321333\pi$
$180$	0	0
$181$	3.01773e37	1.69038	0.845190	−	0.534466i	$-0.179487\pi$
$181$	3.01773e37	1.69038	0.845190	+	0.534466i	$0.179487\pi$
$182$	−3.88560e36	−0.198738
$183$	−8.21023e36	−0.383630
$184$	−7.53787e36	−0.321925
$185$	0	0
$186$	1.02952e37	0.367850
$187$	−5.77037e37	−1.88720
$188$	3.00064e37	0.898689
$189$	−1.38726e37	−0.380661
$190$	0	0
$191$	5.41896e37	1.24987	0.624936	−	0.780676i	$-0.285125\pi$
$191$	5.41896e37	1.24987	0.624936	+	0.780676i	$0.285125\pi$
$192$	−2.05364e37	−0.434564
$193$	−1.59025e37	−0.308865	−0.154433	−	0.988003i	$-0.549355\pi$
$193$	−1.59025e37	−0.308865	−0.154433	+	0.988003i	$0.549355\pi$
$194$	−1.93933e37	−0.345879
$195$	0	0
$196$	5.29917e37	0.797964
$197$	1.05989e38	1.46747	0.733734	−	0.679436i	$-0.237776\pi$
$197$	1.05989e38	1.46747	0.733734	+	0.679436i	$0.237776\pi$
$198$	−7.60446e36	−0.0968485
$199$	4.20262e37	0.492543	0.246271	−	0.969201i	$-0.420795\pi$
$199$	4.20262e37	0.492543	0.246271	+	0.969201i	$0.420795\pi$
$200$	0	0
$201$	1.00140e38	0.995109
$202$	2.70738e37	0.247886
$203$	−2.83587e36	−0.0239332
$204$	1.48459e38	1.15534
$205$	0	0
$206$	−4.29926e36	−0.0284829
$207$	−2.31704e37	−0.141717
$208$	−2.47372e38	−1.39735
$209$	1.20731e38	0.630092
$210$	0	0
$211$	2.20364e38	0.982832	0.491416	−	0.870925i	$-0.336479\pi$
$211$	2.20364e38	0.982832	0.491416	+	0.870925i	$0.336479\pi$
$212$	1.05406e38	0.434832
$213$	3.09740e38	1.18232
$214$	1.34539e38	0.475360
$215$	0	0
$216$	2.04211e38	0.618861
$217$	1.77945e38	0.499688
$218$	4.86236e37	0.126565
$219$	1.63985e38	0.395801
$220$	0	0
$221$	1.33413e39	2.77158
$222$	−1.66788e38	−0.321618
$223$	6.67659e35	0.00119543	0.000597716	−	1.00000i	$-0.499810\pi$
$223$	6.67659e35	0.00119543	0.000597716		1.00000i	$0.499810\pi$
$224$	1.67594e38	0.278719
$225$	0	0
$226$	−9.03770e37	−0.129798
$227$	−1.16773e39	−1.55925	−0.779626	−	0.626246i	$-0.784591\pi$
$227$	−1.16773e39	−1.55925	−0.779626	+	0.626246i	$0.784591\pi$
$228$	−3.10614e38	−0.385741
$229$	−8.43095e38	−0.974072	−0.487036	−	0.873382i	$-0.661922\pi$
$229$	−8.43095e38	−0.974072	−0.487036	+	0.873382i	$0.661922\pi$
$230$	0	0
$231$	3.90948e38	0.391310
$232$	4.17453e37	0.0389095
$233$	1.88168e38	0.163371	0.0816853	−	0.996658i	$-0.473970\pi$
$233$	1.88168e38	0.163371	0.0816853	+	0.996658i	$0.473970\pi$
$234$	1.75818e38	0.142234
$235$	0	0
$236$	−1.09140e39	−0.767247
$237$	1.23186e39	0.807630
$238$	−2.52234e38	−0.154271
$239$	2.56527e38	0.146409	0.0732046	−	0.997317i	$-0.476677\pi$
$239$	2.56527e38	0.146409	0.0732046	+	0.997317i	$0.476677\pi$
$240$	0	0
$241$	2.87265e38	0.142890	0.0714450	−	0.997445i	$-0.477239\pi$
$241$	2.87265e38	0.142890	0.0714450	+	0.997445i	$0.477239\pi$
$242$	4.22061e38	0.196075
$243$	1.12925e39	0.490100
$244$	9.95543e38	0.403764
$245$	0	0
$246$	8.21489e38	0.291187
$247$	−2.79134e39	−0.925366
$248$	−2.61943e39	−0.812370
$249$	1.09177e39	0.316841
$250$	0	0
$251$	−2.84747e39	−0.724173	−0.362087	−	0.932144i	$-0.617936\pi$
$251$	−2.84747e39	−0.724173	−0.362087	+	0.932144i	$0.617936\pi$
$252$	3.38160e38	0.0805403
$253$	3.24814e39	0.724680
$254$	4.14364e38	0.0866216
$255$	0	0
$256$	1.19885e39	0.220194
$257$	9.94184e39	1.71226	0.856131	−	0.516759i	$-0.172862\pi$
$257$	9.94184e39	1.71226	0.856131	+	0.516759i	$0.172862\pi$
$258$	5.34492e38	0.0863408
$259$	−2.88280e39	−0.436886
$260$	0	0
$261$	1.28319e38	0.0171287
$262$	1.28588e38	0.0161149
$263$	1.00062e40	1.17761	0.588803	−	0.808277i	$-0.299599\pi$
$263$	1.00062e40	1.17761	0.588803	+	0.808277i	$0.299599\pi$
$264$	−5.75494e39	−0.636174
$265$	0	0
$266$	5.27737e38	0.0515075
$267$	−5.76048e39	−0.528473
$268$	−1.21426e40	−1.04734
$269$	−1.26431e39	−0.102551	−0.0512756	−	0.998685i	$-0.516329\pi$
$269$	−1.26431e39	−0.102551	−0.0512756	+	0.998685i	$0.516329\pi$
$270$	0	0
$271$	−2.61010e40	−1.87355	−0.936773	−	0.349937i	$-0.886203\pi$
$271$	−2.61010e40	−1.87355	−0.936773	+	0.349937i	$0.886203\pi$
$272$	−1.60581e40	−1.08470
$273$	−9.03889e39	−0.574687
$274$	−1.62359e39	−0.0971837
$275$	0	0
$276$	−8.35677e39	−0.443648
$277$	1.68059e40	0.840516	0.420258	−	0.907405i	$-0.361940\pi$
$277$	1.68059e40	0.840516	0.420258	+	0.907405i	$0.361940\pi$
$278$	1.08675e40	0.512143
$279$	−8.05176e39	−0.357620
$280$	0	0
$281$	−3.61653e40	−1.42770	−0.713851	−	0.700298i	$-0.753051\pi$
$281$	−3.61653e40	−1.42770	−0.713851	+	0.700298i	$0.753051\pi$
$282$	−6.86147e39	−0.255451
$283$	−2.73592e40	−0.960787	−0.480394	−	0.877053i	$-0.659506\pi$
$283$	−2.73592e40	−0.960787	−0.480394	+	0.877053i	$0.659506\pi$
$284$	−3.75580e40	−1.24437
$285$	0	0
$286$	−2.46471e40	−0.727322
$287$	1.41988e40	0.395549
$288$	−7.58340e39	−0.199475
$289$	4.63509e40	1.15145
$290$	0	0
$291$	−4.51138e40	−1.00017
$292$	−1.98843e40	−0.416574
$293$	1.89832e40	0.375883	0.187942	−	0.982180i	$-0.439818\pi$
$293$	1.89832e40	0.375883	0.187942	+	0.982180i	$0.439818\pi$
$294$	−1.21175e40	−0.226820
$295$	0	0
$296$	4.24362e40	0.710269
$297$	−8.79967e40	−1.39311
$298$	−1.48900e40	−0.223011
$299$	−7.50985e40	−1.06428
$300$	0	0
$301$	9.23829e39	0.117285
$302$	6.91829e39	0.0831542
$303$	6.29804e40	0.716807
$304$	3.35977e40	0.362155
$305$	0	0
$306$	1.14133e40	0.110409
$307$	1.00795e41	0.923964	0.461982	−	0.886889i	$-0.347138\pi$
$307$	1.00795e41	0.923964	0.461982	+	0.886889i	$0.347138\pi$
$308$	−4.74050e40	−0.411848
$309$	−1.00012e40	−0.0823636
$310$	0	0
$311$	−9.05837e40	−0.670662	−0.335331	−	0.942100i	$-0.608848\pi$
$311$	−9.05837e40	−0.670662	−0.335331	+	0.942100i	$0.608848\pi$
$312$	1.33057e41	0.934299
$313$	2.27354e41	1.51433	0.757165	−	0.653224i	$-0.226584\pi$
$313$	2.27354e41	1.51433	0.757165	+	0.653224i	$0.226584\pi$
$314$	5.78255e40	0.365410
$315$	0	0
$316$	−1.49371e41	−0.850018
$317$	2.78295e40	0.150324	0.0751620	−	0.997171i	$-0.476053\pi$
$317$	2.78295e40	0.150324	0.0751620	+	0.997171i	$0.476053\pi$
$318$	−2.41028e40	−0.123600
$319$	−1.79884e40	−0.0875885
$320$	0	0
$321$	3.12973e41	1.37459
$322$	1.41983e40	0.0592398
$323$	−1.81200e41	−0.718319
$324$	1.65583e41	0.623767
$325$	0	0
$326$	1.20884e40	0.0411415
$327$	1.13111e41	0.365987
$328$	−2.09013e41	−0.643065
$329$	−1.18595e41	−0.347005
$330$	0	0
$331$	−6.40534e40	−0.169582	−0.0847911	−	0.996399i	$-0.527022\pi$
$331$	−6.40534e40	−0.169582	−0.0847911	+	0.996399i	$0.527022\pi$
$332$	−1.32384e41	−0.333470
$333$	1.30443e41	0.312673
$334$	7.79564e40	0.177842
$335$	0	0
$336$	1.08795e41	0.224912
$337$	−3.19783e41	−0.629452	−0.314726	−	0.949183i	$-0.601913\pi$
$337$	−3.19783e41	−0.629452	−0.314726	+	0.949183i	$0.601913\pi$
$338$	4.10250e41	0.768994
$339$	−2.10240e41	−0.375335
$340$	0	0
$341$	1.12874e42	1.82871
$342$	−2.38794e40	−0.0368632
$343$	−4.48419e41	−0.659677
$344$	−1.35992e41	−0.190677
$345$	0	0
$346$	8.09771e40	0.103183
$347$	−1.48796e42	−1.80782	−0.903911	−	0.427721i	$-0.859317\pi$
$347$	−1.48796e42	−1.80782	−0.903911	+	0.427721i	$0.859317\pi$
$348$	4.62804e40	0.0536215
$349$	1.19302e42	1.31834	0.659172	−	0.751992i	$-0.270907\pi$
$349$	1.19302e42	1.31834	0.659172	+	0.751992i	$0.270907\pi$
$350$	0	0
$351$	2.03452e42	2.04595
$352$	1.06308e42	1.02003
$353$	−1.00990e42	−0.924689	−0.462344	−	0.886701i	$-0.652992\pi$
$353$	−1.00990e42	−0.924689	−0.462344	+	0.886701i	$0.652992\pi$
$354$	2.49567e41	0.218089
$355$	0	0
$356$	6.98495e41	0.556209
$357$	−5.86760e41	−0.446103
$358$	4.38690e41	0.318484
$359$	7.30004e41	0.506136	0.253068	−	0.967449i	$-0.418560\pi$
$359$	7.30004e41	0.506136	0.253068	+	0.967449i	$0.418560\pi$
$360$	0	0
$361$	−1.20165e42	−0.760170
$362$	8.36737e41	0.505705
$363$	9.81819e41	0.566986
$364$	1.09602e42	0.604849
$365$	0	0
$366$	−2.27648e41	−0.114769
$367$	3.74858e42	1.80666	0.903330	−	0.428947i	$-0.141115\pi$
$367$	3.74858e42	1.80666	0.903330	+	0.428947i	$0.141115\pi$
$368$	9.03913e41	0.416522
$369$	−6.42477e41	−0.283089
$370$	0	0
$371$	−4.16598e41	−0.167899
$372$	−2.90399e42	−1.11953
$373$	−4.86523e42	−1.79435	−0.897176	−	0.441673i	$-0.854385\pi$
$373$	−4.86523e42	−1.79435	−0.897176	+	0.441673i	$0.854385\pi$
$374$	−1.59997e42	−0.564586
$375$	0	0
$376$	1.74578e42	0.564144
$377$	4.15901e41	0.128634
$378$	−3.84651e41	−0.113881
$379$	1.92428e42	0.545409	0.272704	−	0.962098i	$-0.412082\pi$
$379$	1.92428e42	0.545409	0.272704	+	0.962098i	$0.412082\pi$
$380$	0	0
$381$	9.63916e41	0.250482
$382$	1.50253e42	0.373920
$383$	7.09477e42	1.69106	0.845529	−	0.533929i	$-0.179285\pi$
$383$	7.09477e42	1.69106	0.845529	+	0.533929i	$0.179285\pi$
$384$	−3.57335e42	−0.815849
$385$	0	0
$386$	−4.40933e41	−0.0924021
$387$	−4.18020e41	−0.0839395
$388$	5.47034e42	1.05267
$389$	−5.42411e42	−1.00037	−0.500184	−	0.865919i	$-0.666734\pi$
$389$	−5.42411e42	−1.00037	−0.500184	+	0.865919i	$0.666734\pi$
$390$	0	0
$391$	−4.87502e42	−0.826152
$392$	3.08307e42	0.500914
$393$	2.99127e41	0.0465993
$394$	2.93880e42	0.439018
$395$	0	0
$396$	2.14501e42	0.294754
$397$	−8.06392e42	−1.06293	−0.531463	−	0.847082i	$-0.678357\pi$
$397$	−8.06392e42	−1.06293	−0.531463	+	0.847082i	$0.678357\pi$
$398$	1.16527e42	0.147352
$399$	1.22765e42	0.148943
$400$	0	0
$401$	−9.36366e42	−1.04608	−0.523038	−	0.852309i	$-0.675202\pi$
$401$	−9.36366e42	−1.04608	−0.523038	+	0.852309i	$0.675202\pi$
$402$	2.77660e42	0.297703
$403$	−2.60969e43	−2.68569
$404$	−7.63678e42	−0.754428
$405$	0	0
$406$	−7.86310e40	−0.00716002
$407$	−1.82861e43	−1.59887
$408$	8.63738e42	0.725253
$409$	2.18606e43	1.76290	0.881448	−	0.472281i	$-0.156569\pi$
$409$	2.18606e43	1.76290	0.881448	+	0.472281i	$0.156569\pi$
$410$	0	0
$411$	−3.77689e42	−0.281025
$412$	1.21270e42	0.0866864
$413$	4.31357e42	0.296252
$414$	−6.42453e41	−0.0423971
$415$	0	0
$416$	−2.45789e43	−1.49804
$417$	2.52806e43	1.48096
$418$	3.34754e42	0.188502
$419$	−1.61908e43	−0.876469	−0.438235	−	0.898861i	$-0.644396\pi$
$419$	−1.61908e43	−0.876469	−0.438235	+	0.898861i	$0.644396\pi$
$420$	0	0
$421$	−2.91687e43	−1.45970	−0.729849	−	0.683608i	$-0.760410\pi$
$421$	−2.91687e43	−1.45970	−0.729849	+	0.683608i	$0.760410\pi$
$422$	6.11009e42	0.294031
$423$	5.36629e42	0.248346
$424$	6.13252e42	0.272962
$425$	0	0
$426$	8.58828e42	0.353710
$427$	−3.93472e42	−0.155903
$428$	−3.79499e43	−1.44673
$429$	−5.73354e43	−2.10319
$430$	0	0
$431$	−1.93794e42	−0.0658362	−0.0329181	−	0.999458i	$-0.510480\pi$
$431$	−1.93794e42	−0.0658362	−0.0329181	+	0.999458i	$0.510480\pi$
$432$	−2.44883e43	−0.800711
$433$	4.34077e43	1.36621	0.683103	−	0.730322i	$-0.260630\pi$
$433$	4.34077e43	1.36621	0.683103	+	0.730322i	$0.260630\pi$
$434$	4.93393e42	0.149490
$435$	0	0
$436$	−1.37154e43	−0.385195
$437$	1.01998e43	0.275833
$438$	4.54687e42	0.118410
$439$	−4.67712e43	−1.17304	−0.586522	−	0.809934i	$-0.699503\pi$
$439$	−4.67712e43	−1.17304	−0.586522	+	0.809934i	$0.699503\pi$
$440$	0	0
$441$	9.47694e42	0.220511
$442$	3.69920e43	0.829163
$443$	−1.13003e43	−0.244022	−0.122011	−	0.992529i	$-0.538934\pi$
$443$	−1.13003e43	−0.244022	−0.122011	+	0.992529i	$0.538934\pi$
$444$	4.70463e43	0.978828
$445$	0	0
$446$	1.85124e40	0.000357633 0
$447$	−3.46378e43	−0.644876
$448$	−9.84198e42	−0.176602
$449$	4.90070e43	0.847605	0.423802	−	0.905755i	$-0.360695\pi$
$449$	4.90070e43	0.847605	0.423802	+	0.905755i	$0.360695\pi$
$450$	0	0
$451$	9.00658e43	1.44759
$452$	2.54929e43	0.395034
$453$	1.60937e43	0.240456
$454$	−3.23781e43	−0.466476
$455$	0	0
$456$	−1.80716e43	−0.242145
$457$	−1.56154e43	−0.201807	−0.100904	−	0.994896i	$-0.532173\pi$
$457$	−1.56154e43	−0.201807	−0.100904	+	0.994896i	$0.532173\pi$
$458$	−2.33768e43	−0.291410
$459$	1.32071e44	1.58817
$460$	0	0
$461$	−8.98487e43	−1.00565	−0.502824	−	0.864389i	$-0.667706\pi$
$461$	−8.98487e43	−1.00565	−0.502824	+	0.864389i	$0.667706\pi$
$462$	1.08399e43	0.117067
$463$	3.43299e42	0.0357755	0.0178878	−	0.999840i	$-0.494306\pi$
$463$	3.43299e42	0.0357755	0.0178878	+	0.999840i	$0.494306\pi$
$464$	−5.00594e42	−0.0503429
$465$	0	0
$466$	5.21741e42	0.0488750
$467$	−1.84417e43	−0.166752	−0.0833760	−	0.996518i	$-0.526570\pi$
$467$	−1.84417e43	−0.166752	−0.0833760	+	0.996518i	$0.526570\pi$
$468$	−4.95936e43	−0.432882
$469$	4.79915e43	0.404401
$470$	0	0
$471$	1.34517e44	1.05665
$472$	−6.34978e43	−0.481633
$473$	5.86002e43	0.429230
$474$	3.41561e43	0.241616
$475$	0	0
$476$	7.11484e43	0.469516
$477$	1.88505e43	0.120163
$478$	7.11282e42	0.0438007
$479$	−9.81532e43	−0.583941	−0.291970	−	0.956427i	$-0.594311\pi$
$479$	−9.81532e43	−0.583941	−0.291970	+	0.956427i	$0.594311\pi$
$480$	0	0
$481$	4.22784e44	2.34814
$482$	7.96510e42	0.0427479
$483$	3.30287e43	0.171303
$484$	−1.19052e44	−0.596743
$485$	0	0
$486$	3.13110e43	0.146622
$487$	−1.63587e43	−0.0740494	−0.0370247	−	0.999314i	$-0.511788\pi$
$487$	−1.63587e43	−0.0740494	−0.0370247	+	0.999314i	$0.511788\pi$
$488$	5.79209e43	0.253459
$489$	2.81208e43	0.118968
$490$	0	0
$491$	−2.99512e44	−1.18459	−0.592297	−	0.805719i	$-0.701779\pi$
$491$	−2.99512e44	−1.18459	−0.592297	+	0.805719i	$0.701779\pi$
$492$	−2.31720e44	−0.886214
$493$	2.69982e43	0.0998529
$494$	−7.73965e43	−0.276839
$495$	0	0
$496$	3.14112e44	1.05108
$497$	1.48442e44	0.480481
$498$	3.02718e43	0.0947882
$499$	8.53560e43	0.258568	0.129284	−	0.991608i	$-0.458732\pi$
$499$	8.53560e43	0.258568	0.129284	+	0.991608i	$0.458732\pi$
$500$	0	0
$501$	1.81346e44	0.514263
$502$	−7.89527e43	−0.216648
$503$	−1.06922e43	−0.0283918	−0.0141959	−	0.999899i	$-0.504519\pi$
$503$	−1.06922e43	−0.0283918	−0.0141959	+	0.999899i	$0.504519\pi$
$504$	1.96742e43	0.0505584
$505$	0	0
$506$	9.00623e43	0.216800
$507$	9.54345e44	2.22369
$508$	−1.16881e44	−0.263629
$509$	5.61788e44	1.22667	0.613336	−	0.789822i	$-0.289827\pi$
$509$	5.61788e44	1.22667	0.613336	+	0.789822i	$0.289827\pi$
$510$	0	0
$511$	7.85892e43	0.160849
$512$	5.09124e44	1.00895
$513$	−2.76326e44	−0.530255
$514$	2.75661e44	0.512252
$515$	0	0
$516$	−1.50766e44	−0.262774
$517$	−7.52273e44	−1.26994
$518$	−7.99323e43	−0.130702
$519$	1.88373e44	0.298371
$520$	0	0
$521$	−9.13138e44	−1.35742	−0.678709	−	0.734407i	$-0.737460\pi$
$521$	−9.13138e44	−1.35742	−0.678709	+	0.734407i	$0.737460\pi$
$522$	3.55795e42	0.00512432
$523$	2.09069e44	0.291751	0.145876	−	0.989303i	$-0.453400\pi$
$523$	2.09069e44	0.291751	0.145876	+	0.989303i	$0.453400\pi$
$524$	−3.62711e43	−0.0490450
$525$	0	0
$526$	2.77446e44	0.352300
$527$	−1.69408e45	−2.08477
$528$	6.90110e44	0.823112
$529$	−5.90590e44	−0.682759
$530$	0	0
$531$	−1.95184e44	−0.212023
$532$	−1.48860e44	−0.156761
$533$	−2.08236e45	−2.12597
$534$	−1.59723e44	−0.158101
$535$	0	0
$536$	−7.06457e44	−0.657456
$537$	1.02050e45	0.920956
$538$	−3.50559e43	−0.0306799
$539$	−1.32853e45	−1.12760
$540$	0	0
$541$	4.44639e44	0.355020	0.177510	−	0.984119i	$-0.443196\pi$
$541$	4.44639e44	0.355020	0.177510	+	0.984119i	$0.443196\pi$
$542$	−7.23712e44	−0.560503
$543$	1.94646e45	1.46234
$544$	−1.59554e45	−1.16285
$545$	0	0
$546$	−2.50624e44	−0.171927
$547$	8.21042e44	0.546480	0.273240	−	0.961946i	$-0.411905\pi$
$547$	8.21042e44	0.546480	0.273240	+	0.961946i	$0.411905\pi$
$548$	4.57972e44	0.295774
$549$	1.78041e44	0.111577
$550$	0	0
$551$	−5.64870e43	−0.0333386
$552$	−4.86198e44	−0.278496
$553$	5.90362e44	0.328212
$554$	4.65983e44	0.251454
$555$	0	0
$556$	−3.06543e45	−1.55868
$557$	1.43178e44	0.0706749	0.0353374	−	0.999375i	$-0.488749\pi$
$557$	1.43178e44	0.0706749	0.0353374	+	0.999375i	$0.488749\pi$
$558$	−2.23254e44	−0.106988
$559$	−1.35486e45	−0.630377
$560$	0	0
$561$	−3.72193e45	−1.63260
$562$	−1.00277e45	−0.427121
$563$	−1.43126e45	−0.592010	−0.296005	−	0.955186i	$-0.595654\pi$
$563$	−1.43126e45	−0.592010	−0.296005	+	0.955186i	$0.595654\pi$
$564$	1.93544e45	0.777452
$565$	0	0
$566$	−7.58598e44	−0.287436
$567$	−6.54439e44	−0.240851
$568$	−2.18513e45	−0.781143
$569$	1.75762e45	0.610342	0.305171	−	0.952298i	$-0.401286\pi$
$569$	1.75762e45	0.610342	0.305171	+	0.952298i	$0.401286\pi$
$570$	0	0
$571$	2.78038e43	0.00911189	0.00455595	−	0.999990i	$-0.498550\pi$
$571$	2.78038e43	0.00911189	0.00455595	+	0.999990i	$0.498550\pi$
$572$	6.95229e45	2.21357
$573$	3.49527e45	1.08126
$574$	3.93695e44	0.118335
$575$	0	0
$576$	4.45337e44	0.126391
$577$	3.59566e45	0.991694	0.495847	−	0.868410i	$-0.334858\pi$
$577$	3.59566e45	0.991694	0.495847	+	0.868410i	$0.334858\pi$
$578$	1.28519e45	0.344474
$579$	−1.02572e45	−0.267198
$580$	0	0
$581$	5.23225e44	0.128760
$582$	−1.25089e45	−0.299218
$583$	−2.64256e45	−0.614460
$584$	−1.15687e45	−0.261501
$585$	0	0
$586$	5.26352e44	0.112452
$587$	−6.08351e45	−1.26365	−0.631823	−	0.775113i	$-0.717693\pi$
$587$	−6.08351e45	−1.26365	−0.631823	+	0.775113i	$0.717693\pi$
$588$	3.41801e45	0.690315
$589$	3.54444e45	0.696058
$590$	0	0
$591$	6.83638e45	1.26950
$592$	−5.08878e45	−0.918979
$593$	2.13640e44	0.0375215	0.0187607	−	0.999824i	$-0.494028\pi$
$593$	2.13640e44	0.0375215	0.0187607	+	0.999824i	$0.494028\pi$
$594$	−2.43991e45	−0.416771
$595$	0	0
$596$	4.20006e45	0.678722
$597$	2.71072e45	0.426096
$598$	−2.08228e45	−0.318398
$599$	−5.45715e45	−0.811751	−0.405876	−	0.913928i	$-0.633033\pi$
$599$	−5.45715e45	−0.811751	−0.405876	+	0.913928i	$0.633033\pi$
$600$	0	0
$601$	−8.95801e45	−1.26120	−0.630598	−	0.776110i	$-0.717190\pi$
$601$	−8.95801e45	−1.26120	−0.630598	+	0.776110i	$0.717190\pi$
$602$	2.56153e44	0.0350879
$603$	−2.17155e45	−0.289424
$604$	−1.95146e45	−0.253076
$605$	0	0
$606$	1.74628e45	0.214445
$607$	−1.83041e45	−0.218744	−0.109372	−	0.994001i	$-0.534884\pi$
$607$	−1.83041e45	−0.218744	−0.109372	+	0.994001i	$0.534884\pi$
$608$	3.33827e45	0.388251
$609$	−1.82915e44	−0.0207045
$610$	0	0
$611$	1.73929e46	1.86505
$612$	−3.21937e45	−0.336026
$613$	−9.17673e45	−0.932374	−0.466187	−	0.884686i	$-0.654373\pi$
$613$	−9.17673e45	−0.932374	−0.466187	+	0.884686i	$0.654373\pi$
$614$	2.79477e45	0.276419
$615$	0	0
$616$	−2.75803e45	−0.258534
$617$	−4.72501e45	−0.431218	−0.215609	−	0.976480i	$-0.569174\pi$
$617$	−4.72501e45	−0.431218	−0.215609	+	0.976480i	$0.569174\pi$
$618$	−2.77306e44	−0.0246405
$619$	1.89434e46	1.63894	0.819469	−	0.573124i	$-0.194269\pi$
$619$	1.89434e46	1.63894	0.819469	+	0.573124i	$0.194269\pi$
$620$	0	0
$621$	−7.43428e45	−0.609857
$622$	−2.51164e45	−0.200640
$623$	−2.76069e45	−0.214765
$624$	−1.59557e46	−1.20884
$625$	0	0
$626$	6.30391e45	0.453037
$627$	7.78721e45	0.545089
$628$	−1.63110e46	−1.11211
$629$	2.74450e46	1.82275
$630$	0	0
$631$	1.47344e46	0.928639	0.464319	−	0.885668i	$-0.346299\pi$
$631$	1.47344e46	0.928639	0.464319	+	0.885668i	$0.346299\pi$
$632$	−8.69041e45	−0.533591
$633$	1.42136e46	0.850244
$634$	7.71639e44	0.0449719
$635$	0	0
$636$	6.79873e45	0.376171
$637$	3.07161e46	1.65602
$638$	−4.98772e44	−0.0262036
$639$	−6.71680e45	−0.343873
$640$	0	0
$641$	1.80612e46	0.878189	0.439095	−	0.898441i	$-0.355299\pi$
$641$	1.80612e46	0.878189	0.439095	+	0.898441i	$0.355299\pi$
$642$	8.67790e45	0.411232
$643$	3.87997e46	1.79204	0.896020	−	0.444013i	$-0.146446\pi$
$643$	3.87997e46	1.79204	0.896020	+	0.444013i	$0.146446\pi$
$644$	−4.00495e45	−0.180293
$645$	0	0
$646$	−5.02420e45	−0.214897
$647$	−1.26941e46	−0.529277	−0.264638	−	0.964348i	$-0.585253\pi$
$647$	−1.26941e46	−0.529277	−0.264638	+	0.964348i	$0.585253\pi$
$648$	9.63364e45	0.391564
$649$	2.73618e46	1.08420
$650$	0	0
$651$	1.14776e46	0.432278
$652$	−3.40982e45	−0.125212
$653$	−3.71297e46	−1.32940	−0.664698	−	0.747112i	$-0.731440\pi$
$653$	−3.71297e46	−1.32940	−0.664698	+	0.747112i	$0.731440\pi$
$654$	3.13626e45	0.109491
$655$	0	0
$656$	2.50641e46	0.832028
$657$	−3.55606e45	−0.115117
$658$	−3.28833e45	−0.103812
$659$	−4.60623e46	−1.41820	−0.709098	−	0.705110i	$-0.750898\pi$
$659$	−4.60623e46	−1.41820	−0.709098	+	0.705110i	$0.750898\pi$
$660$	0	0
$661$	3.33859e45	0.0977775	0.0488888	−	0.998804i	$-0.484432\pi$
$661$	3.33859e45	0.0977775	0.0488888	+	0.998804i	$0.484432\pi$
$662$	−1.77603e45	−0.0507333
$663$	8.60526e46	2.39768
$664$	−7.70212e45	−0.209333
$665$	0	0
$666$	3.61683e45	0.0935414
$667$	−1.51973e45	−0.0383434
$668$	−2.19894e46	−0.541254
$669$	4.30645e43	0.00103416
$670$	0	0
$671$	−2.49587e46	−0.570558
$672$	1.08099e46	0.241118
$673$	−8.45139e46	−1.83941	−0.919707	−	0.392606i	$-0.871574\pi$
$673$	−8.45139e46	−1.83941	−0.919707	+	0.392606i	$0.871574\pi$
$674$	−8.86674e45	−0.188311
$675$	0	0
$676$	−1.15720e47	−2.34040
$677$	1.49073e46	0.294230	0.147115	−	0.989119i	$-0.453001\pi$
$677$	1.49073e46	0.294230	0.147115	+	0.989119i	$0.453001\pi$
$678$	−5.82938e45	−0.112288
$679$	−2.16206e46	−0.406459
$680$	0	0
$681$	−7.53195e46	−1.34890
$682$	3.12969e46	0.547090
$683$	−2.90497e45	−0.0495678	−0.0247839	−	0.999693i	$-0.507890\pi$
$683$	−2.90497e45	−0.0495678	−0.0247839	+	0.999693i	$0.507890\pi$
$684$	6.73574e45	0.112191
$685$	0	0
$686$	−1.24335e46	−0.197353
$687$	−5.43803e46	−0.842665
$688$	1.63076e46	0.246707
$689$	6.10971e46	0.902410
$690$	0	0
$691$	3.48577e46	0.490807	0.245403	−	0.969421i	$-0.421080\pi$
$691$	3.48577e46	0.490807	0.245403	+	0.969421i	$0.421080\pi$
$692$	−2.28414e46	−0.314031
$693$	−8.47781e45	−0.113811
$694$	−4.12572e46	−0.540840
$695$	0	0
$696$	2.69260e45	0.0336604
$697$	−1.35176e47	−1.65029
$698$	3.30793e46	0.394404
$699$	1.21370e46	0.141331
$700$	0	0
$701$	1.80849e46	0.200895	0.100447	−	0.994942i	$-0.467973\pi$
$701$	1.80849e46	0.200895	0.100447	+	0.994942i	$0.467973\pi$
$702$	5.64118e46	0.612080
$703$	−5.74219e46	−0.608576
$704$	−6.24296e46	−0.646311
$705$	0	0
$706$	−2.80018e46	−0.276636
$707$	3.01831e46	0.291302
$708$	−7.03960e46	−0.663742
$709$	−1.69160e46	−0.155824	−0.0779121	−	0.996960i	$-0.524825\pi$
$709$	−1.69160e46	−0.155824	−0.0779121	+	0.996960i	$0.524825\pi$
$710$	0	0
$711$	−2.67131e46	−0.234896
$712$	4.06386e46	0.349155
$713$	9.53599e46	0.800550
$714$	−1.62693e46	−0.133459
$715$	0	0
$716$	−1.23743e47	−0.969292
$717$	1.65462e46	0.126658
$718$	2.02411e46	0.151419
$719$	3.49896e46	0.255807	0.127904	−	0.991787i	$-0.459175\pi$
$719$	3.49896e46	0.255807	0.127904	+	0.991787i	$0.459175\pi$
$720$	0	0
$721$	−4.79302e45	−0.0334716
$722$	−3.33187e46	−0.227417
$723$	1.85288e46	0.123613
$724$	−2.36021e47	−1.53909
$725$	0	0
$726$	2.72232e46	0.169623
$727$	−1.04633e46	−0.0637311	−0.0318655	−	0.999492i	$-0.510145\pi$
$727$	−1.04633e46	−0.0637311	−0.0318655	+	0.999492i	$0.510145\pi$
$728$	6.37669e46	0.379688
$729$	1.90529e47	1.10907
$730$	0	0
$731$	−8.79510e46	−0.489332
$732$	6.42132e46	0.349295
$733$	3.33329e46	0.177279	0.0886395	−	0.996064i	$-0.471748\pi$
$733$	3.33329e46	0.177279	0.0886395	+	0.996064i	$0.471748\pi$
$734$	1.03938e47	0.540492
$735$	0	0
$736$	8.98130e46	0.446535
$737$	3.04419e47	1.47999
$738$	−1.78142e46	−0.0846908
$739$	−4.78197e46	−0.222317	−0.111159	−	0.993803i	$-0.535456\pi$
$739$	−4.78197e46	−0.222317	−0.111159	+	0.993803i	$0.535456\pi$
$740$	0	0
$741$	−1.80044e47	−0.800530
$742$	−1.15511e46	−0.0502297
$743$	−3.94781e47	−1.67896	−0.839482	−	0.543388i	$-0.817141\pi$
$743$	−3.94781e47	−1.67896	−0.839482	+	0.543388i	$0.817141\pi$
$744$	−1.68955e47	−0.702777
$745$	0	0
$746$	−1.34900e47	−0.536810
$747$	−2.36753e46	−0.0921520
$748$	4.51308e47	1.71829
$749$	1.49991e47	0.558618
$750$	0	0
$751$	4.15026e47	1.47916	0.739582	−	0.673067i	$-0.235023\pi$
$751$	4.15026e47	1.47916	0.739582	+	0.673067i	$0.235023\pi$
$752$	−2.09347e47	−0.729916
$753$	−1.83664e47	−0.626479
$754$	1.15318e46	0.0384831
$755$	0	0
$756$	1.08500e47	0.346592
$757$	1.09180e47	0.341240	0.170620	−	0.985337i	$-0.445423\pi$
$757$	1.09180e47	0.341240	0.170620	+	0.985337i	$0.445423\pi$
$758$	5.33553e46	0.163168
$759$	2.09508e47	0.626918
$760$	0	0
$761$	−1.59076e47	−0.455784	−0.227892	−	0.973686i	$-0.573183\pi$
$761$	−1.59076e47	−0.455784	−0.227892	+	0.973686i	$0.573183\pi$
$762$	2.67268e46	0.0749359
$763$	5.42078e46	0.148733
$764$	−4.23824e47	−1.13801
$765$	0	0
$766$	1.96719e47	0.505908
$767$	−6.32617e47	−1.59227
$768$	7.73268e46	0.190489
$769$	4.86716e47	1.17352	0.586761	−	0.809760i	$-0.300403\pi$
$769$	4.86716e47	1.17352	0.586761	+	0.809760i	$0.300403\pi$
$770$	0	0
$771$	6.41256e47	1.48127
$772$	1.24375e47	0.281221
$773$	1.81874e47	0.402540	0.201270	−	0.979536i	$-0.435493\pi$
$773$	1.81874e47	0.402540	0.201270	+	0.979536i	$0.435493\pi$
$774$	−1.15906e46	−0.0251119
$775$	0	0
$776$	3.18265e47	0.660802
$777$	−1.85943e47	−0.377948
$778$	−1.50396e47	−0.299277
$779$	2.82823e47	0.550994
$780$	0	0
$781$	9.41595e47	1.75842
$782$	−1.35171e47	−0.247157
$783$	4.11716e46	0.0737104
$784$	−3.69710e47	−0.648107
$785$	0	0
$786$	8.29400e45	0.0139409
$787$	−7.92430e46	−0.130430	−0.0652150	−	0.997871i	$-0.520773\pi$
$787$	−7.92430e46	−0.130430	−0.0652150	+	0.997871i	$0.520773\pi$
$788$	−8.28955e47	−1.33613
$789$	6.45408e47	1.01874
$790$	0	0
$791$	−1.00756e47	−0.152532
$792$	1.24797e47	0.185029
$793$	5.77055e47	0.837934
$794$	−2.23591e47	−0.317992
$795$	0	0
$796$	−3.28692e47	−0.448460
$797$	1.23720e48	1.65340	0.826701	−	0.562641i	$-0.190215\pi$
$797$	1.23720e48	1.65340	0.826701	+	0.562641i	$0.190215\pi$
$798$	3.40394e46	0.0445589
$799$	1.12906e48	1.44776
$800$	0	0
$801$	1.24917e47	0.153704
$802$	−2.59629e47	−0.312951
$803$	4.98507e47	0.588660
$804$	−7.83204e47	−0.906046
$805$	0	0
$806$	−7.23597e47	−0.803468
$807$	−8.15488e46	−0.0887165
$808$	−4.44309e47	−0.473585
$809$	−1.21597e47	−0.126991	−0.0634956	−	0.997982i	$-0.520225\pi$
$809$	−1.21597e47	−0.126991	−0.0634956	+	0.997982i	$0.520225\pi$
$810$	0	0
$811$	2.95931e47	0.296720	0.148360	−	0.988933i	$-0.452601\pi$
$811$	2.95931e47	0.296720	0.148360	+	0.988933i	$0.452601\pi$
$812$	2.21797e46	0.0217912
$813$	−1.68354e48	−1.62080
$814$	−5.07026e47	−0.478330
$815$	0	0
$816$	−1.03576e48	−0.938366
$817$	1.84016e47	0.163377
$818$	6.06135e47	0.527400
$819$	1.96011e47	0.167146
$820$	0	0
$821$	7.27375e47	0.595794	0.297897	−	0.954598i	$-0.403715\pi$
$821$	7.27375e47	0.595794	0.297897	+	0.954598i	$0.403715\pi$
$822$	−1.04723e47	−0.0840732
$823$	6.72010e47	0.528784	0.264392	−	0.964415i	$-0.414829\pi$
$823$	6.72010e47	0.528784	0.264392	+	0.964415i	$0.414829\pi$
$824$	7.05554e46	0.0544166
$825$	0	0
$826$	1.19604e47	0.0886287
$827$	8.31356e47	0.603874	0.301937	−	0.953328i	$-0.402367\pi$
$827$	8.31356e47	0.603874	0.301937	+	0.953328i	$0.402367\pi$
$828$	1.81219e47	0.129033
$829$	−1.01391e48	−0.707702	−0.353851	−	0.935302i	$-0.615128\pi$
$829$	−1.01391e48	−0.707702	−0.353851	+	0.935302i	$0.615128\pi$
$830$	0	0
$831$	1.08399e48	0.727127
$832$	1.44340e48	0.949186
$833$	1.99394e48	1.28549
$834$	7.00963e47	0.443053
$835$	0	0
$836$	−9.44250e47	−0.573698
$837$	−2.58343e48	−1.53896
$838$	−4.48928e47	−0.262210
$839$	−1.56484e47	−0.0896186	−0.0448093	−	0.998996i	$-0.514268\pi$
$839$	−1.56484e47	−0.0896186	−0.0448093	+	0.998996i	$0.514268\pi$
$840$	0	0
$841$	−1.80766e48	−0.995366
$842$	−8.08771e47	−0.436693
$843$	−2.33269e48	−1.23510
$844$	−1.72349e48	−0.894868
$845$	0	0
$846$	1.48793e47	0.0742969
$847$	4.70533e47	0.230416
$848$	−7.35388e47	−0.353171
$849$	−1.76469e48	−0.831173
$850$	0	0
$851$	−1.54488e48	−0.699934
$852$	−2.42252e48	−1.07650
$853$	2.34435e48	1.02179	0.510896	−	0.859642i	$-0.329314\pi$
$853$	2.34435e48	1.02179	0.510896	+	0.859642i	$0.329314\pi$
$854$	−1.09099e47	−0.0466409
$855$	0	0
$856$	−2.20794e48	−0.908175
$857$	−1.46847e48	−0.592489	−0.296245	−	0.955112i	$-0.595734\pi$
$857$	−1.46847e48	−0.592489	−0.296245	+	0.955112i	$0.595734\pi$
$858$	−1.58976e48	−0.629203
$859$	4.47736e48	1.73834	0.869170	−	0.494513i	$-0.164654\pi$
$859$	4.47736e48	1.73834	0.869170	+	0.494513i	$0.164654\pi$
$860$	0	0
$861$	9.15834e47	0.342188
$862$	−5.37338e46	−0.0196960
$863$	3.32539e48	1.19581	0.597907	−	0.801565i	$-0.295999\pi$
$863$	3.32539e48	1.19581	0.597907	+	0.801565i	$0.295999\pi$
$864$	−2.43316e48	−0.858407
$865$	0	0
$866$	1.20358e48	0.408724
$867$	2.98967e48	0.996111
$868$	−1.39173e48	−0.454966
$869$	3.74478e48	1.20116
$870$	0	0
$871$	−7.03830e48	−2.17354
$872$	−7.97964e47	−0.241803
$873$	9.78304e47	0.290897
$874$	2.82812e47	0.0825201
$875$	0	0
$876$	−1.28255e48	−0.360376
$877$	6.37678e48	1.75836	0.879181	−	0.476487i	$-0.158090\pi$
$877$	6.37678e48	1.75836	0.879181	+	0.476487i	$0.158090\pi$
$878$	−1.29684e48	−0.350935
$879$	1.22443e48	0.325175
$880$	0	0
$881$	2.27415e48	0.581724	0.290862	−	0.956765i	$-0.406058\pi$
$881$	2.27415e48	0.581724	0.290862	+	0.956765i	$0.406058\pi$
$882$	2.62770e47	0.0659697
$883$	−4.10071e48	−1.01043	−0.505216	−	0.862993i	$-0.668587\pi$
$883$	−4.10071e48	−1.01043	−0.505216	+	0.862993i	$0.668587\pi$
$884$	−1.04344e49	−2.52352
$885$	0	0
$886$	−3.13327e47	−0.0730032
$887$	−2.02235e48	−0.462504	−0.231252	−	0.972894i	$-0.574282\pi$
$887$	−2.02235e48	−0.462504	−0.231252	+	0.972894i	$0.574282\pi$
$888$	2.73716e48	0.614450
$889$	4.61953e47	0.101793
$890$	0	0
$891$	−4.15123e48	−0.881444
$892$	−5.22185e45	−0.00108844
$893$	−2.36228e48	−0.483372
$894$	−9.60415e47	−0.192926
$895$	0	0
$896$	−1.71251e48	−0.331552
$897$	−4.84391e48	−0.920705
$898$	1.35883e48	0.253575
$899$	−5.28110e47	−0.0967585
$900$	0	0
$901$	3.96612e48	0.700499
$902$	2.49728e48	0.433072
$903$	5.95876e47	0.101463
$904$	1.48318e48	0.247979
$905$	0	0
$906$	4.46235e47	0.0719363
$907$	7.98241e47	0.126361	0.0631806	−	0.998002i	$-0.479876\pi$
$907$	7.98241e47	0.126361	0.0631806	+	0.998002i	$0.479876\pi$
$908$	9.13298e48	1.41970
$909$	−1.36575e48	−0.208481
$910$	0	0
$911$	8.71761e48	1.28335	0.641674	−	0.766978i	$-0.278240\pi$
$911$	8.71761e48	1.28335	0.641674	+	0.766978i	$0.278240\pi$
$912$	2.16707e48	0.313299
$913$	3.31892e48	0.471226
$914$	−4.32974e47	−0.0603740
$915$	0	0
$916$	6.59396e48	0.886892
$917$	1.43356e47	0.0189374
$918$	3.66198e48	0.475129
$919$	5.61506e48	0.715563	0.357782	−	0.933805i	$-0.383533\pi$
$919$	5.61506e48	0.715563	0.357782	+	0.933805i	$0.383533\pi$
$920$	0	0
$921$	6.50134e48	0.799317
$922$	−2.49126e48	−0.300857
$923$	−2.17701e49	−2.58245
$924$	−3.05765e48	−0.356288
$925$	0	0
$926$	9.51876e46	0.0107028
$927$	2.16878e47	0.0239552
$928$	−4.97390e47	−0.0539704
$929$	1.39756e49	1.48974	0.744871	−	0.667209i	$-0.232511\pi$
$929$	1.39756e49	1.48974	0.744871	+	0.667209i	$0.232511\pi$
$930$	0	0
$931$	−4.17182e48	−0.429196
$932$	−1.47169e48	−0.148749
$933$	−5.84271e48	−0.580186
$934$	−5.11338e47	−0.0498867
$935$	0	0
$936$	−2.88537e48	−0.271738
$937$	1.20423e48	0.111431	0.0557156	−	0.998447i	$-0.482256\pi$
$937$	1.20423e48	0.111431	0.0557156	+	0.998447i	$0.482256\pi$
$938$	1.33068e48	0.120983
$939$	1.46645e49	1.31004
$940$	0	0
$941$	1.31236e49	1.13194	0.565971	−	0.824425i	$-0.308502\pi$
$941$	1.31236e49	1.13194	0.565971	+	0.824425i	$0.308502\pi$
$942$	3.72979e48	0.316114
$943$	7.60909e48	0.633709
$944$	7.61442e48	0.623159
$945$	0	0
$946$	1.62483e48	0.128411
$947$	−2.09928e49	−1.63041	−0.815203	−	0.579175i	$-0.803375\pi$
$947$	−2.09928e49	−1.63041	−0.815203	+	0.579175i	$0.803375\pi$
$948$	−9.63451e48	−0.735347
$949$	−1.15257e49	−0.864519
$950$	0	0
$951$	1.79503e48	0.130045
$952$	4.13943e48	0.294734
$953$	1.57940e49	1.10524	0.552622	−	0.833432i	$-0.313627\pi$
$953$	1.57940e49	1.10524	0.552622	+	0.833432i	$0.313627\pi$
$954$	5.22674e47	0.0359487
$955$	0	0
$956$	−2.00633e48	−0.133305
$957$	−1.16027e48	−0.0757724
$958$	−2.72153e48	−0.174696
$959$	−1.81006e48	−0.114205
$960$	0	0
$961$	1.67343e49	1.02017
$962$	1.17227e49	0.702486
$963$	−6.78689e48	−0.399795
$964$	−2.24674e48	−0.130101
$965$	0	0
$966$	9.15799e47	0.0512481
$967$	3.32626e48	0.182987	0.0914933	−	0.995806i	$-0.470836\pi$
$967$	3.32626e48	0.182987	0.0914933	+	0.995806i	$0.470836\pi$
$968$	−6.92646e48	−0.374600
$969$	−1.16875e49	−0.621414
$970$	0	0
$971$	1.28962e49	0.662743	0.331371	−	0.943500i	$-0.392489\pi$
$971$	1.28962e49	0.662743	0.331371	+	0.943500i	$0.392489\pi$
$972$	−8.83198e48	−0.446236
$973$	1.21156e49	0.601844
$974$	−4.53584e47	−0.0221531
$975$	0	0
$976$	−6.94566e48	−0.327938
$977$	2.39192e48	0.111042	0.0555208	−	0.998458i	$-0.482318\pi$
$977$	2.39192e48	0.111042	0.0555208	+	0.998458i	$0.482318\pi$
$978$	7.79714e47	0.0355913
$979$	−1.75116e49	−0.785978
$980$	0	0
$981$	−2.45283e48	−0.106446
$982$	−8.30467e48	−0.354391
$983$	2.85699e49	1.19888	0.599440	−	0.800420i	$-0.295390\pi$
$983$	2.85699e49	1.19888	0.599440	+	0.800420i	$0.295390\pi$
$984$	−1.34815e49	−0.556313
$985$	0	0
$986$	7.48588e47	0.0298727
$987$	−7.64949e48	−0.300192
$988$	2.18315e49	0.842545
$989$	4.95076e48	0.187903
$990$	0	0
$991$	2.21432e48	0.0812876	0.0406438	−	0.999174i	$-0.487059\pi$
$991$	2.21432e48	0.0812876	0.0406438	+	0.999174i	$0.487059\pi$
$992$	3.12102e49	1.12682
$993$	−4.13149e48	−0.146705
$994$	4.11590e48	0.143744
$995$	0	0
$996$	−8.53886e48	−0.288483
$997$	4.21638e49	1.40110	0.700551	−	0.713603i	$-0.252938\pi$
$997$	4.21638e49	1.40110	0.700551	+	0.713603i	$0.252938\pi$
$998$	2.36669e48	0.0773550
$999$	4.18530e49	1.34554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.34.a.f.1.9		16
5.2	odd	4		5.34.b.a.4.9	yes	16
5.3	odd	4		5.34.b.a.4.8	✓	16
5.4	even	2	inner	25.34.a.f.1.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.34.b.a.4.8	✓	16	5.3	odd	4
5.34.b.a.4.9	yes	16	5.2	odd	4
25.34.a.f.1.8		16	5.4	even	2	inner
25.34.a.f.1.9		16	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+27727.3 q^{2} +6.45007e7 q^{3} -7.82113e9 q^{4} +1.78843e12 q^{6} +3.09117e13 q^{7} -4.55035e14 q^{8} -1.39871e15 q^{9} +O(q^{10})\)	\(q+27727.3 q^{2} +6.45007e7 q^{3} -7.82113e9 q^{4} +1.78843e12 q^{6} +3.09117e13 q^{7} -4.55035e14 q^{8} -1.39871e15 q^{9} +1.96079e17 q^{11} -5.04469e17 q^{12} -4.53343e18 q^{13} +8.57100e17 q^{14} +5.45661e19 q^{16} -2.94288e20 q^{17} -3.87826e19 q^{18} +6.15724e20 q^{19} +1.99383e21 q^{21} +5.43675e21 q^{22} +1.65655e22 q^{23} -2.93501e22 q^{24} -1.25700e23 q^{26} -4.48782e23 q^{27} -2.41765e23 q^{28} -9.17408e22 q^{29} +5.75654e24 q^{31} +5.42169e24 q^{32} +1.26472e25 q^{33} -8.15982e24 q^{34} +1.09395e25 q^{36} -9.32591e25 q^{37} +1.70724e25 q^{38} -2.92410e26 q^{39} +4.59334e26 q^{41} +5.52836e25 q^{42} +2.98860e26 q^{43} -1.53356e27 q^{44} +4.59317e26 q^{46} -3.83658e27 q^{47} +3.51955e27 q^{48} -6.77546e27 q^{49} -1.89818e28 q^{51} +3.54566e28 q^{52} -1.34770e28 q^{53} -1.24435e28 q^{54} -1.40659e28 q^{56} +3.97147e28 q^{57} -2.54373e27 q^{58} +1.39545e29 q^{59} -1.27289e29 q^{61} +1.59614e29 q^{62} -4.32367e28 q^{63} -3.18390e29 q^{64} +3.50674e29 q^{66} +1.55253e30 q^{67} +2.30166e30 q^{68} +1.06849e30 q^{69} +4.80212e30 q^{71} +6.36464e29 q^{72} +2.54238e30 q^{73} -2.58583e30 q^{74} -4.81566e30 q^{76} +6.06114e30 q^{77} -8.10774e30 q^{78} +1.90983e31 q^{79} -2.11712e31 q^{81} +1.27361e31 q^{82} +1.69264e31 q^{83} -1.55940e31 q^{84} +8.28660e30 q^{86} -5.91735e30 q^{87} -8.92228e31 q^{88} -8.93087e31 q^{89} -1.40136e32 q^{91} -1.29561e32 q^{92} +3.71301e32 q^{93} -1.06378e32 q^{94} +3.49703e32 q^{96} -6.99431e32 q^{97} -1.87865e32 q^{98} -2.74259e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 72851326872 q^{4} + 11001777346872 q^{6} + 27\!\cdots\!68 q^{9}+O(q^{10}) \) 16 * q + 72851326872 * q^4 + 11001777346872 * q^6 + 27535156574590368 * q^9	\( 16 q + 72851326872 q^{4} + 11001777346872 q^{6} + 27\!\cdots\!68 q^{9}+ \cdots - 34\!\cdots\!24 q^{99}+O(q^{100}) \) 16 * q + 72851326872 * q^4 + 11001777346872 * q^6 + 27535156574590368 * q^9 + 219974590742466912 * q^11 + 10416043581549356184 * q^14 + 133171456389985196576 * q^16 + 2949217257058889591200 * q^19 + 20126160533851210892592 * q^21 + 236696360036140740492000 * q^24 + 23043234216449373353232 * q^26 - 2210824656972934579370400 * q^29 + 4805180075928582021889472 * q^31 + 106706080442140703440064 * q^34 + 150609707516636111776170456 * q^36 + 950668737676648885834065216 * q^39 + 960625982433026021733974352 * q^41 + 4300041994750366563328828704 * q^44 + 4030532465737707969346868392 * q^46 + 48902999941413820155855454112 * q^49 + 37677263492556888574173469632 * q^51 + 416785644990759180210455480400 * q^54 + 209868986171565551575474447200 * q^56 + 204679212804521237512362904800 * q^59 - 62902839261738400132019069488 * q^61 - 3273202940251902417009873735808 * q^64 - 2991219624550267460630717491296 * q^66 - 6899695112224183044828868241904 * q^69 - 87525095316001019795902439808 * q^71 - 43140282179597200538055251968176 * q^74 - 38605994956626944020944749752800 * q^76 + 10590745643822309766800662264000 * q^79 + 126385893984816788804508532470336 * q^81 + 401968339664232685914350670917664 * q^84 - 18805496634715830052189508032488 * q^86 + 816457769414638729740610145056800 * q^89 + 572310345418666359618454810906752 * q^91 - 1084618018208246129370832376900296 * q^94 - 1376269400022374885061468958478208 * q^96 - 3432482025669259323040953857901024 * q^99

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