LMFDB - Embedded newform 25.34.a.f.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("25.1");

S:= CuspForms(chi, 34);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$172.457072203$
Analytic rank:	$0$
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			1.5
Root			$-51228.2$ 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)

$f(q)$	$=$	$q-102456. q^{2} +8.77372e7 q^{3} +1.90737e9 q^{4} -8.98924e12 q^{6} -1.11815e14 q^{7} +6.84671e14 q^{8} +2.13876e15 q^{9} +O(q^{10})$	\(q-102456. q^{2} +8.77372e7 q^{3} +1.90737e9 q^{4} -8.98924e12 q^{6} -1.11815e14 q^{7} +6.84671e14 q^{8} +2.13876e15 q^{9} -2.24867e17 q^{11} +1.67348e17 q^{12} -2.46334e18 q^{13} +1.14562e19 q^{14} -8.65331e19 q^{16} +3.31898e19 q^{17} -2.19130e20 q^{18} -7.93484e19 q^{19} -9.81036e21 q^{21} +2.30391e22 q^{22} -2.88111e22 q^{23} +6.00711e22 q^{24} +2.52385e23 q^{26} -3.00088e23 q^{27} -2.13273e23 q^{28} -2.32679e24 q^{29} -7.38565e24 q^{31} +2.98459e24 q^{32} -1.97292e25 q^{33} -3.40050e24 q^{34} +4.07941e24 q^{36} +1.63972e25 q^{37} +8.12975e24 q^{38} -2.16126e26 q^{39} +4.37241e26 q^{41} +1.00513e27 q^{42} +2.93769e26 q^{43} -4.28906e26 q^{44} +2.95188e27 q^{46} +6.15905e26 q^{47} -7.59218e27 q^{48} +4.77164e27 q^{49} +2.91198e27 q^{51} -4.69850e27 q^{52} +1.66687e28 q^{53} +3.07459e28 q^{54} -7.65566e28 q^{56} -6.96181e27 q^{57} +2.38395e29 q^{58} -6.84322e28 q^{59} -3.85377e29 q^{61} +7.56707e29 q^{62} -2.39146e29 q^{63} +4.37524e29 q^{64} +2.02139e30 q^{66} +1.10044e30 q^{67} +6.33053e28 q^{68} -2.52780e30 q^{69} +7.46328e29 q^{71} +1.46435e30 q^{72} -6.29592e30 q^{73} -1.68000e30 q^{74} -1.51347e29 q^{76} +2.51436e31 q^{77} +2.21435e31 q^{78} +1.61054e31 q^{79} -3.82184e31 q^{81} -4.47982e31 q^{82} -2.30501e31 q^{83} -1.87120e31 q^{84} -3.00985e31 q^{86} -2.04146e32 q^{87} -1.53960e32 q^{88} +1.08152e32 q^{89} +2.75439e32 q^{91} -5.49534e31 q^{92} -6.47996e32 q^{93} -6.31033e31 q^{94} +2.61860e32 q^{96} -2.96871e32 q^{97} -4.88885e32 q^{98} -4.80938e32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−102456.	−1.10546	−0.552731	−	0.833360i	$-0.686414\pi$
$2$	−102456.	−1.10546	−0.552731	+	0.833360i	$0.686414\pi$
$3$	8.77372e7	1.17675	0.588374	−	0.808589i	$-0.299768\pi$
$3$	8.77372e7	1.17675	0.588374	+	0.808589i	$0.299768\pi$
$4$	1.90737e9	0.222047
$5$	0	0
$5$	0	0
$6$	−8.98924e12	−1.30085
$7$	−1.11815e14	−1.27170	−0.635848	−	0.771815i	$-0.719349\pi$
$7$	−1.11815e14	−1.27170	−0.635848	+	0.771815i	$0.719349\pi$
$8$	6.84671e14	0.859997
$9$	2.13876e15	0.384734
$10$	0	0
$11$	−2.24867e17	−1.47553	−0.737763	−	0.675060i	$-0.764118\pi$
$11$	−2.24867e17	−1.47553	−0.737763	+	0.675060i	$0.764118\pi$
$12$	1.67348e17	0.261294
$13$	−2.46334e18	−1.02674	−0.513368	−	0.858169i	$-0.671602\pi$
$13$	−2.46334e18	−1.02674	−0.513368	+	0.858169i	$0.671602\pi$
$14$	1.14562e19	1.40581
$15$	0	0
$16$	−8.65331e19	−1.17274
$17$	3.31898e19	0.165424	0.0827118	−	0.996574i	$-0.473642\pi$
$17$	3.31898e19	0.165424	0.0827118	+	0.996574i	$0.473642\pi$
$18$	−2.19130e20	−0.425309
$19$	−7.93484e19	−0.0631108	−0.0315554	−	0.999502i	$-0.510046\pi$
$19$	−7.93484e19	−0.0631108	−0.0315554	+	0.999502i	$0.510046\pi$
$20$	0	0
$21$	−9.81036e21	−1.49646
$22$	2.30391e22	1.63114
$23$	−2.88111e22	−0.979602	−0.489801	−	0.871834i	$-0.662931\pi$
$23$	−2.88111e22	−0.979602	−0.489801	+	0.871834i	$0.662931\pi$
$24$	6.00711e22	1.01200
$25$	0	0
$26$	2.52385e23	1.13502
$27$	−3.00088e23	−0.724012
$28$	−2.13273e23	−0.282377
$29$	−2.32679e24	−1.72659	−0.863297	−	0.504695i	$-0.831605\pi$
$29$	−2.32679e24	−1.72659	−0.863297	+	0.504695i	$0.831605\pi$
$30$	0	0
$31$	−7.38565e24	−1.82356	−0.911781	−	0.410676i	$-0.865293\pi$
$31$	−7.38565e24	−1.82356	−0.911781	+	0.410676i	$0.865293\pi$
$32$	2.98459e24	0.436425
$33$	−1.97292e25	−1.73632
$34$	−3.40050e24	−0.182869
$35$	0	0
$36$	4.07941e24	0.0854292
$37$	1.63972e25	0.218495	0.109247	−	0.994015i	$-0.465156\pi$
$37$	1.63972e25	0.218495	0.109247	+	0.994015i	$0.465156\pi$
$38$	8.12975e24	0.0697666
$39$	−2.16126e26	−1.20821
$40$	0	0
$41$	4.37241e26	1.07100	0.535498	−	0.844537i	$-0.320124\pi$
$41$	4.37241e26	1.07100	0.535498	+	0.844537i	$0.320124\pi$
$42$	1.00513e27	1.65429
$43$	2.93769e26	0.327927	0.163963	−	0.986466i	$-0.447572\pi$
$43$	2.93769e26	0.327927	0.163963	+	0.986466i	$0.447572\pi$
$44$	−4.28906e26	−0.327637
$45$	0	0
$46$	2.95188e27	1.08291
$47$	6.15905e26	0.158452	0.0792262	−	0.996857i	$-0.474755\pi$
$47$	6.15905e26	0.158452	0.0792262	+	0.996857i	$0.474755\pi$
$48$	−7.59218e27	−1.38002
$49$	4.77164e27	0.617209
$50$	0	0
$51$	2.91198e27	0.194662
$52$	−4.69850e27	−0.227984
$53$	1.66687e28	0.590678	0.295339	−	0.955393i	$-0.404567\pi$
$53$	1.66687e28	0.590678	0.295339	+	0.955393i	$0.404567\pi$
$54$	3.07459e28	0.800368
$55$	0	0
$56$	−7.65566e28	−1.09365
$57$	−6.96181e27	−0.0742655
$58$	2.38395e29	1.90869
$59$	−6.84322e28	−0.413240	−0.206620	−	0.978421i	$-0.566246\pi$
$59$	−6.84322e28	−0.413240	−0.206620	+	0.978421i	$0.566246\pi$
$60$	0	0
$61$	−3.85377e29	−1.34259	−0.671295	−	0.741191i	$-0.734261\pi$
$61$	−3.85377e29	−1.34259	−0.671295	+	0.741191i	$0.734261\pi$
$62$	7.56707e29	2.01588
$63$	−2.39146e29	−0.489265
$64$	4.37524e29	0.690291
$65$	0	0
$66$	2.02139e30	1.91944
$67$	1.10044e30	0.815327	0.407664	−	0.913132i	$-0.366344\pi$
$67$	1.10044e30	0.815327	0.407664	+	0.913132i	$0.366344\pi$
$68$	6.33053e28	0.0367318
$69$	−2.52780e30	−1.15274
$70$	0	0
$71$	7.46328e29	0.212406	0.106203	−	0.994344i	$-0.466131\pi$
$71$	7.46328e29	0.212406	0.106203	+	0.994344i	$0.466131\pi$
$72$	1.46435e30	0.330871
$73$	−6.29592e30	−1.13301	−0.566503	−	0.824060i	$-0.691704\pi$
$73$	−6.29592e30	−1.13301	−0.566503	+	0.824060i	$0.691704\pi$
$74$	−1.68000e30	−0.241538
$75$	0	0
$76$	−1.51347e29	−0.0140136
$77$	2.51436e31	1.87642
$78$	2.21435e31	1.33563
$79$	1.61054e31	0.787273	0.393636	−	0.919266i	$-0.371217\pi$
$79$	1.61054e31	0.787273	0.393636	+	0.919266i	$0.371217\pi$
$80$	0	0
$81$	−3.82184e31	−1.23671
$82$	−4.47982e31	−1.18394
$83$	−2.30501e31	−0.498753	−0.249376	−	0.968407i	$-0.580226\pi$
$83$	−2.30501e31	−0.498753	−0.249376	+	0.968407i	$0.580226\pi$
$84$	−1.87120e31	−0.332286
$85$	0	0
$86$	−3.00985e31	−0.362510
$87$	−2.04146e32	−2.03177
$88$	−1.53960e32	−1.26895
$89$	1.08152e32	0.739773	0.369886	−	0.929077i	$-0.379397\pi$
$89$	1.08152e32	0.739773	0.369886	+	0.929077i	$0.379397\pi$
$90$	0	0
$91$	2.75439e32	1.30569
$92$	−5.49534e31	−0.217518
$93$	−6.47996e32	−2.14587
$94$	−6.31033e31	−0.175163
$95$	0	0
$96$	2.61860e32	0.513562
$97$	−2.96871e32	−0.490721	−0.245361	−	0.969432i	$-0.578906\pi$
$97$	−2.96871e32	−0.490721	−0.245361	+	0.969432i	$0.578906\pi$
$98$	−4.88885e32	−0.682302
$99$	−4.80938e32	−0.567686
$100$	0	0
$101$	−7.27121e32	−0.617027	−0.308513	−	0.951220i	$-0.599831\pi$
$101$	−7.27121e32	−0.617027	−0.308513	+	0.951220i	$0.599831\pi$
$102$	−2.98351e32	−0.215191
$103$	−1.81397e33	−1.11382	−0.556912	−	0.830572i	$-0.688014\pi$
$103$	−1.81397e33	−1.11382	−0.556912	+	0.830572i	$0.688014\pi$
$104$	−1.68658e33	−0.882990
$105$	0	0
$106$	−1.70782e33	−0.652972
$107$	−5.42390e33	−1.77615	−0.888074	−	0.459701i	$-0.847957\pi$
$107$	−5.42390e33	−1.77615	−0.888074	+	0.459701i	$0.847957\pi$
$108$	−5.72379e32	−0.160765
$109$	6.01657e33	1.45148	0.725741	−	0.687968i	$-0.241497\pi$
$109$	6.01657e33	1.45148	0.725741	+	0.687968i	$0.241497\pi$
$110$	0	0
$111$	1.43864e33	0.257113
$112$	9.67572e33	1.49137
$113$	−1.07074e34	−1.42524	−0.712620	−	0.701550i	$-0.752492\pi$
$113$	−1.07074e34	−1.42524	−0.712620	+	0.701550i	$0.752492\pi$
$114$	7.13282e32	0.0820977
$115$	0	0
$116$	−4.43806e33	−0.383386
$117$	−5.26849e33	−0.395020
$118$	7.01131e33	0.456821
$119$	−3.71112e33	−0.210368
$120$	0	0
$121$	2.73402e34	1.17718
$122$	3.94843e34	1.48418
$123$	3.83623e34	1.26029
$124$	−1.40872e34	−0.404917
$125$	0	0
$126$	2.45020e34	0.540864
$127$	2.11841e33	0.0410440	0.0205220	−	0.999789i	$-0.493467\pi$
$127$	2.11841e33	0.0410440	0.0205220	+	0.999789i	$0.493467\pi$
$128$	−7.04645e34	−1.19952
$129$	2.57745e34	0.385887
$130$	0	0
$131$	−1.12103e35	−1.30209	−0.651044	−	0.759040i	$-0.725669\pi$
$131$	−1.12103e35	−1.30209	−0.651044	+	0.759040i	$0.725669\pi$
$132$	−3.76310e34	−0.385546
$133$	8.87236e33	0.0802577
$134$	−1.12747e35	−0.901314
$135$	0	0
$136$	2.27241e34	0.142264
$137$	−1.87942e35	−1.04264	−0.521320	−	0.853361i	$-0.674560\pi$
$137$	−1.87942e35	−1.04264	−0.521320	+	0.853361i	$0.674560\pi$
$138$	2.58989e35	1.27432
$139$	2.77030e35	1.20999	0.604997	−	0.796228i	$-0.293174\pi$
$139$	2.77030e35	1.20999	0.604997	+	0.796228i	$0.293174\pi$
$140$	0	0
$141$	5.40378e34	0.186458
$142$	−7.64661e34	−0.234807
$143$	5.53924e35	1.51498
$144$	−1.85074e35	−0.451194
$145$	0	0
$146$	6.45057e35	1.25250
$147$	4.18651e35	0.726300
$148$	3.12755e34	0.0485162
$149$	1.17332e36	1.62871	0.814354	−	0.580369i	$-0.197092\pi$
$149$	1.17332e36	1.62871	0.814354	+	0.580369i	$0.197092\pi$
$150$	0	0
$151$	−2.03363e35	−0.226544	−0.113272	−	0.993564i	$-0.536133\pi$
$151$	−2.03363e35	−0.226544	−0.113272	+	0.993564i	$0.536133\pi$
$152$	−5.43276e34	−0.0542751
$153$	7.09850e34	0.0636441
$154$	−2.57612e36	−2.07431
$155$	0	0
$156$	−4.12233e35	−0.268279
$157$	1.48553e36	0.870036	0.435018	−	0.900422i	$-0.356742\pi$
$157$	1.48553e36	0.870036	0.435018	+	0.900422i	$0.356742\pi$
$158$	−1.65010e36	−0.870300
$159$	1.46247e36	0.695079
$160$	0	0
$161$	3.22151e36	1.24576
$162$	3.91571e36	1.36714
$163$	2.41405e36	0.761466	0.380733	−	0.924685i	$-0.375672\pi$
$163$	2.41405e36	0.761466	0.380733	+	0.924685i	$0.375672\pi$
$164$	8.33982e35	0.237812
$165$	0	0
$166$	2.36163e36	0.551352
$167$	−6.50430e36	−1.37524	−0.687620	−	0.726071i	$-0.741345\pi$
$167$	−6.50430e36	−1.37524	−0.687620	+	0.726071i	$0.741345\pi$
$168$	−6.71687e36	−1.28696
$169$	3.11899e35	0.0541856
$170$	0	0
$171$	−1.69707e35	−0.0242809
$172$	5.60327e35	0.0728152
$173$	5.44353e36	0.642865	0.321432	−	0.946933i	$-0.395836\pi$
$173$	5.44353e36	0.642865	0.321432	+	0.946933i	$0.395836\pi$
$174$	2.09161e37	2.24604
$175$	0	0
$176$	1.94585e37	1.73041
$177$	−6.00405e36	−0.486279
$178$	−1.10808e37	−0.817791
$179$	−1.55767e37	−1.04809	−0.524047	−	0.851690i	$-0.675578\pi$
$179$	−1.55767e37	−1.04809	−0.524047	+	0.851690i	$0.675578\pi$
$180$	0	0
$181$	−2.16095e37	−1.21045	−0.605227	−	0.796053i	$-0.706917\pi$
$181$	−2.16095e37	−1.21045	−0.605227	+	0.796053i	$0.706917\pi$
$182$	−2.82204e37	−1.44340
$183$	−3.38119e37	−1.57989
$184$	−1.97261e37	−0.842456
$185$	0	0
$186$	6.63914e37	2.37218
$187$	−7.46330e36	−0.244087
$188$	1.17476e36	0.0351839
$189$	3.35543e37	0.920723
$190$	0	0
$191$	5.39109e37	1.24344	0.621722	−	0.783238i	$-0.286433\pi$
$191$	5.39109e37	1.24344	0.621722	+	0.783238i	$0.286433\pi$
$192$	3.83871e37	0.812298
$193$	−2.82434e37	−0.548557	−0.274278	−	0.961650i	$-0.588439\pi$
$193$	−2.82434e37	−0.548557	−0.274278	+	0.961650i	$0.588439\pi$
$194$	3.04164e37	0.542474
$195$	0	0
$196$	9.10130e36	0.137050
$197$	1.24116e37	0.171844	0.0859220	−	0.996302i	$-0.472616\pi$
$197$	1.24116e37	0.171844	0.0859220	+	0.996302i	$0.472616\pi$
$198$	4.92751e37	0.627555
$199$	7.16373e37	0.839582	0.419791	−	0.907621i	$-0.362103\pi$
$199$	7.16373e37	0.839582	0.419791	+	0.907621i	$0.362103\pi$
$200$	0	0
$201$	9.65495e37	0.959434
$202$	7.44982e37	0.682100
$203$	2.60171e38	2.19570
$204$	5.55423e36	0.0432241
$205$	0	0
$206$	1.85853e38	1.23129
$207$	−6.16200e37	−0.376887
$208$	2.13160e38	1.20410
$209$	1.78429e37	0.0931217
$210$	0	0
$211$	3.78989e38	1.69031	0.845154	−	0.534523i	$-0.179509\pi$
$211$	3.78989e38	1.69031	0.845154	+	0.534523i	$0.179509\pi$
$212$	3.17935e37	0.131158
$213$	6.54808e37	0.249948
$214$	5.55713e38	1.96346
$215$	0	0
$216$	−2.05461e38	−0.622649
$217$	8.25828e38	2.31902
$218$	−6.16436e38	−1.60456
$219$	−5.52387e38	−1.33326
$220$	0	0
$221$	−8.17576e37	−0.169846
$222$	−1.47398e38	−0.284229
$223$	4.51907e38	0.809131	0.404565	−	0.914509i	$-0.367423\pi$
$223$	4.51907e38	0.809131	0.404565	+	0.914509i	$0.367423\pi$
$224$	−3.33722e38	−0.555000
$225$	0	0
$226$	1.09704e39	1.57555
$227$	−9.98415e38	−1.33317	−0.666583	−	0.745431i	$-0.732244\pi$
$227$	−9.98415e38	−1.33317	−0.666583	+	0.745431i	$0.732244\pi$
$228$	−1.32788e37	−0.0164905
$229$	5.32577e38	0.615314	0.307657	−	0.951497i	$-0.400455\pi$
$229$	5.32577e38	0.615314	0.307657	+	0.951497i	$0.400455\pi$
$230$	0	0
$231$	2.20603e39	2.20807
$232$	−1.59309e39	−1.48487
$233$	−1.58065e39	−1.37234	−0.686171	−	0.727440i	$-0.740710\pi$
$233$	−1.58065e39	−1.37234	−0.686171	+	0.727440i	$0.740710\pi$
$234$	5.39790e38	0.436680
$235$	0	0
$236$	−1.30526e38	−0.0917588
$237$	1.41305e39	0.926421
$238$	3.80228e38	0.232554
$239$	2.18770e39	1.24860	0.624300	−	0.781185i	$-0.285384\pi$
$239$	2.18770e39	1.24860	0.624300	+	0.781185i	$0.285384\pi$
$240$	0	0
$241$	−1.34545e39	−0.669248	−0.334624	−	0.942352i	$-0.608609\pi$
$241$	−1.34545e39	−0.669248	−0.334624	+	0.942352i	$0.608609\pi$
$242$	−2.80117e39	−1.30133
$243$	−1.68497e39	−0.731288
$244$	−7.35057e38	−0.298118
$245$	0	0
$246$	−3.93047e39	−1.39320
$247$	1.95462e38	0.0647981
$248$	−5.05674e39	−1.56826
$249$	−2.02236e39	−0.586906
$250$	0	0
$251$	1.33521e38	0.0339574	0.0169787	−	0.999856i	$-0.494595\pi$
$251$	1.33521e38	0.0339574	0.0169787	+	0.999856i	$0.494595\pi$
$252$	−4.56141e38	−0.108640
$253$	6.47866e39	1.44543
$254$	−2.17045e38	−0.0453726
$255$	0	0
$256$	3.46124e39	0.635729
$257$	3.02015e39	0.520154	0.260077	−	0.965588i	$-0.416252\pi$
$257$	3.02015e39	0.520154	0.260077	+	0.965588i	$0.416252\pi$
$258$	−2.64076e39	−0.426583
$259$	−1.83346e39	−0.277859
$260$	0	0
$261$	−4.97645e39	−0.664280
$262$	1.14857e40	1.43941
$263$	5.25973e39	0.619004	0.309502	−	0.950899i	$-0.399838\pi$
$263$	5.25973e39	0.619004	0.309502	+	0.950899i	$0.399838\pi$
$264$	−1.35080e40	−1.49323
$265$	0	0
$266$	−9.09029e38	−0.0887219
$267$	9.48893e39	0.870526
$268$	2.09895e39	0.181041
$269$	4.00271e39	0.324670	0.162335	−	0.986736i	$-0.448098\pi$
$269$	4.00271e39	0.324670	0.162335	+	0.986736i	$0.448098\pi$
$270$	0	0
$271$	−1.43945e40	−1.03325	−0.516624	−	0.856212i	$-0.672812\pi$
$271$	−1.43945e40	−1.03325	−0.516624	+	0.856212i	$0.672812\pi$
$272$	−2.87202e39	−0.193999
$273$	2.41662e40	1.53647
$274$	1.92559e40	1.15260
$275$	0	0
$276$	−4.82146e39	−0.255964
$277$	−1.51033e40	−0.755364	−0.377682	−	0.925935i	$-0.623279\pi$
$277$	−1.51033e40	−0.755364	−0.377682	+	0.925935i	$0.623279\pi$
$278$	−2.83835e40	−1.33760
$279$	−1.57961e40	−0.701587
$280$	0	0
$281$	−2.79172e40	−1.10209	−0.551045	−	0.834476i	$-0.685771\pi$
$281$	−2.79172e40	−1.10209	−0.551045	+	0.834476i	$0.685771\pi$
$282$	−5.53651e39	−0.206123
$283$	3.85510e40	1.35381	0.676907	−	0.736069i	$-0.263320\pi$
$283$	3.85510e40	1.35381	0.676907	+	0.736069i	$0.263320\pi$
$284$	1.42353e39	0.0471642
$285$	0	0
$286$	−5.67530e40	−1.67475
$287$	−4.88902e40	−1.36198
$288$	6.38332e39	0.167908
$289$	−3.91529e40	−0.972635
$290$	0	0
$291$	−2.60467e40	−0.577455
$292$	−1.20087e40	−0.251581
$293$	3.74622e40	0.741784	0.370892	−	0.928676i	$-0.379052\pi$
$293$	3.74622e40	0.741784	0.370892	+	0.928676i	$0.379052\pi$
$294$	−4.28934e40	−0.802897
$295$	0	0
$296$	1.12267e40	0.187905
$297$	6.74799e40	1.06830
$298$	−1.20214e41	−1.80048
$299$	7.09713e40	1.00579
$300$	0	0
$301$	−3.28478e40	−0.417023
$302$	2.08358e40	0.250436
$303$	−6.37956e40	−0.726085
$304$	6.86626e39	0.0740127
$305$	0	0
$306$	−7.27287e39	−0.0703562
$307$	1.07461e41	0.985068	0.492534	−	0.870293i	$-0.336071\pi$
$307$	1.07461e41	0.985068	0.492534	+	0.870293i	$0.336071\pi$
$308$	4.79582e40	0.416654
$309$	−1.59153e41	−1.31069
$310$	0	0
$311$	2.27431e41	1.68385	0.841924	−	0.539597i	$-0.181423\pi$
$311$	2.27431e41	1.68385	0.841924	+	0.539597i	$0.181423\pi$
$312$	−1.47975e41	−1.03906
$313$	−6.49777e40	−0.432796	−0.216398	−	0.976305i	$-0.569431\pi$
$313$	−6.49777e40	−0.432796	−0.216398	+	0.976305i	$0.569431\pi$
$314$	−1.52202e41	−0.961792
$315$	0	0
$316$	3.07190e40	0.174812
$317$	5.13146e40	0.277181	0.138590	−	0.990350i	$-0.455743\pi$
$317$	5.13146e40	0.277181	0.138590	+	0.990350i	$0.455743\pi$
$318$	−1.49839e41	−0.768383
$319$	5.23219e41	2.54764
$320$	0	0
$321$	−4.75878e41	−2.09008
$322$	−3.30065e41	−1.37714
$323$	−2.63356e39	−0.0104400
$324$	−7.28966e40	−0.274609
$325$	0	0
$326$	−2.47335e41	−0.841772
$327$	5.27877e41	1.70803
$328$	2.99366e41	0.921053
$329$	−6.88675e40	−0.201503
$330$	0	0
$331$	3.99589e41	1.05792	0.528958	−	0.848648i	$-0.322583\pi$
$331$	3.99589e41	1.05792	0.528958	+	0.848648i	$0.322583\pi$
$332$	−4.39652e40	−0.110747
$333$	3.50697e40	0.0840624
$334$	6.66407e41	1.52028
$335$	0	0
$336$	8.48921e41	1.75497
$337$	−5.12879e41	−1.00954	−0.504768	−	0.863255i	$-0.668422\pi$
$337$	−5.12879e41	−1.00954	−0.504768	+	0.863255i	$0.668422\pi$
$338$	−3.19560e40	−0.0599001
$339$	−9.39434e41	−1.67715
$340$	0	0
$341$	1.66079e42	2.69072
$342$	1.73876e40	0.0268416
$343$	3.30900e41	0.486793
$344$	2.01135e41	0.282016
$345$	0	0
$346$	−5.57724e41	−0.710663
$347$	4.02876e41	0.489480	0.244740	−	0.969589i	$-0.421297\pi$
$347$	4.02876e41	0.489480	0.244740	+	0.969589i	$0.421297\pi$
$348$	−3.89383e41	−0.451148
$349$	4.84486e41	0.535380	0.267690	−	0.963505i	$-0.413740\pi$
$349$	4.84486e41	0.535380	0.267690	+	0.963505i	$0.413740\pi$
$350$	0	0
$351$	7.39217e41	0.743369
$352$	−6.71136e41	−0.643957
$353$	−1.01645e42	−0.930687	−0.465344	−	0.885130i	$-0.654069\pi$
$353$	−1.01645e42	−0.930687	−0.465344	+	0.885130i	$0.654069\pi$
$354$	6.15153e41	0.537563
$355$	0	0
$356$	2.06286e41	0.164265
$357$	−3.25604e41	−0.247550
$358$	1.59593e42	1.15863
$359$	−3.81937e41	−0.264809	−0.132405	−	0.991196i	$-0.542270\pi$
$359$	−3.81937e41	−0.264809	−0.132405	+	0.991196i	$0.542270\pi$
$360$	0	0
$361$	−1.57447e42	−0.996017
$362$	2.21403e42	1.33811
$363$	2.39875e42	1.38524
$364$	5.25364e41	0.289926
$365$	0	0
$366$	3.46424e42	1.74651
$367$	−1.28100e41	−0.0617391	−0.0308695	−	0.999523i	$-0.509828\pi$
$367$	−1.28100e41	−0.0617391	−0.0308695	+	0.999523i	$0.509828\pi$
$368$	2.49311e42	1.14882
$369$	9.35155e41	0.412049
$370$	0	0
$371$	−1.86382e42	−0.751162
$372$	−1.23597e42	−0.476485
$373$	−4.95556e41	−0.182767	−0.0913834	−	0.995816i	$-0.529129\pi$
$373$	−4.95556e41	−0.182767	−0.0913834	+	0.995816i	$0.529129\pi$
$374$	7.64662e41	0.269829
$375$	0	0
$376$	4.21692e41	0.136269
$377$	5.73167e42	1.77276
$378$	−3.43786e42	−1.01782
$379$	2.01391e42	0.570813	0.285406	−	0.958407i	$-0.407871\pi$
$379$	2.01391e42	0.570813	0.285406	+	0.958407i	$0.407871\pi$
$380$	0	0
$381$	1.85864e41	0.0482984
$382$	−5.52352e42	−1.37458
$383$	−6.11625e42	−1.45782	−0.728912	−	0.684607i	$-0.759974\pi$
$383$	−6.11625e42	−1.45782	−0.728912	+	0.684607i	$0.759974\pi$
$384$	−6.18236e42	−1.41153
$385$	0	0
$386$	2.89372e42	0.606409
$387$	6.28302e41	0.126165
$388$	−5.66244e41	−0.108963
$389$	8.01591e41	0.147837	0.0739187	−	0.997264i	$-0.476449\pi$
$389$	8.01591e41	0.147837	0.0739187	+	0.997264i	$0.476449\pi$
$390$	0	0
$391$	−9.56233e41	−0.162049
$392$	3.26701e42	0.530799
$393$	−9.83560e42	−1.53223
$394$	−1.27165e42	−0.189967
$395$	0	0
$396$	−9.17327e41	−0.126053
$397$	−6.77326e42	−0.892800	−0.446400	−	0.894834i	$-0.647294\pi$
$397$	−6.77326e42	−0.892800	−0.446400	+	0.894834i	$0.647294\pi$
$398$	−7.33969e42	−0.928127
$399$	7.78436e41	0.0944431
$400$	0	0
$401$	−1.14344e42	−0.127741	−0.0638707	−	0.997958i	$-0.520345\pi$
$401$	−1.14344e42	−0.127741	−0.0638707	+	0.997958i	$0.520345\pi$
$402$	−9.89212e42	−1.06062
$403$	1.81933e43	1.87232
$404$	−1.38689e42	−0.137009
$405$	0	0
$406$	−2.66561e43	−2.42727
$407$	−3.68719e42	−0.322395
$408$	1.99375e42	0.167409
$409$	−1.58336e43	−1.27687	−0.638434	−	0.769677i	$-0.720417\pi$
$409$	−1.58336e43	−1.27687	−0.638434	+	0.769677i	$0.720417\pi$
$410$	0	0
$411$	−1.64895e43	−1.22692
$412$	−3.45992e42	−0.247321
$413$	7.65176e42	0.525515
$414$	6.31336e42	0.416634
$415$	0	0
$416$	−7.35205e42	−0.448093
$417$	2.43059e43	1.42386
$418$	−1.82811e42	−0.102943
$419$	−5.87784e42	−0.318190	−0.159095	−	0.987263i	$-0.550858\pi$
$419$	−5.87784e42	−0.318190	−0.159095	+	0.987263i	$0.550858\pi$
$420$	0	0
$421$	−7.76874e41	−0.0388773	−0.0194386	−	0.999811i	$-0.506188\pi$
$421$	−7.76874e41	−0.0388773	−0.0194386	+	0.999811i	$0.506188\pi$
$422$	−3.88298e43	−1.86857
$423$	1.31727e42	0.0609621
$424$	1.14126e43	0.507982
$425$	0	0
$426$	−6.70892e42	−0.276309
$427$	4.30910e43	1.70736
$428$	−1.03454e43	−0.394389
$429$	4.85998e43	1.78274
$430$	0	0
$431$	2.29433e43	0.779438	0.389719	−	0.920934i	$-0.372572\pi$
$431$	2.29433e43	0.779438	0.389719	+	0.920934i	$0.372572\pi$
$432$	2.59675e43	0.849080
$433$	1.80460e43	0.567977	0.283988	−	0.958828i	$-0.408342\pi$
$433$	1.80460e43	0.567977	0.283988	+	0.958828i	$0.408342\pi$
$434$	−8.46113e43	−2.56359
$435$	0	0
$436$	1.14758e43	0.322298
$437$	2.28611e42	0.0618235
$438$	5.65956e43	1.47387
$439$	−1.60697e43	−0.403035	−0.201517	−	0.979485i	$-0.564587\pi$
$439$	−1.60697e43	−0.403035	−0.201517	+	0.979485i	$0.564587\pi$
$440$	0	0
$441$	1.02054e43	0.237462
$442$	8.37659e42	0.187759
$443$	4.88560e43	1.05501	0.527504	−	0.849552i	$-0.323128\pi$
$443$	4.88560e43	1.05501	0.527504	+	0.849552i	$0.323128\pi$
$444$	2.74403e42	0.0570913
$445$	0	0
$446$	−4.63007e43	−0.894464
$447$	1.02944e44	1.91658
$448$	−4.89218e43	−0.877840
$449$	−4.45262e43	−0.770106	−0.385053	−	0.922894i	$-0.625817\pi$
$449$	−4.45262e43	−0.770106	−0.385053	+	0.922894i	$0.625817\pi$
$450$	0	0
$451$	−9.83213e43	−1.58028
$452$	−2.04229e43	−0.316471
$453$	−1.78425e43	−0.266585
$454$	1.02294e44	1.47377
$455$	0	0
$456$	−4.76655e42	−0.0638681
$457$	−5.52879e43	−0.714517	−0.357259	−	0.934006i	$-0.616289\pi$
$457$	−5.52879e43	−0.714517	−0.357259	+	0.934006i	$0.616289\pi$
$458$	−5.45659e43	−0.680207
$459$	−9.95984e42	−0.119769
$460$	0	0
$461$	1.08910e44	1.21900	0.609501	−	0.792785i	$-0.291370\pi$
$461$	1.08910e44	1.21900	0.609501	+	0.792785i	$0.291370\pi$
$462$	−2.26022e44	−2.44094
$463$	−7.34911e43	−0.765858	−0.382929	−	0.923778i	$-0.625085\pi$
$463$	−7.34911e43	−0.765858	−0.382929	+	0.923778i	$0.625085\pi$
$464$	2.01344e44	2.02485
$465$	0	0
$466$	1.61947e44	1.51707
$467$	−1.16367e44	−1.05220	−0.526102	−	0.850421i	$-0.676347\pi$
$467$	−1.16367e44	−1.05220	−0.526102	+	0.850421i	$0.676347\pi$
$468$	−1.00490e43	−0.0877132
$469$	−1.23046e44	−1.03685
$470$	0	0
$471$	1.30336e44	1.02381
$472$	−4.68535e43	−0.355385
$473$	−6.60591e43	−0.483864
$474$	−1.44775e44	−1.02412
$475$	0	0
$476$	−7.07849e42	−0.0467117
$477$	3.56504e43	0.227254
$478$	−2.24144e44	−1.38028
$479$	1.45527e44	0.865783	0.432891	−	0.901446i	$-0.357493\pi$
$479$	1.45527e44	0.865783	0.432891	+	0.901446i	$0.357493\pi$
$480$	0	0
$481$	−4.03918e43	−0.224336
$482$	1.37850e44	0.739828
$483$	2.82647e44	1.46594
$484$	5.21479e43	0.261389
$485$	0	0
$486$	1.72636e44	0.808411
$487$	2.82151e44	1.27718	0.638591	−	0.769546i	$-0.279517\pi$
$487$	2.82151e44	1.27718	0.638591	+	0.769546i	$0.279517\pi$
$488$	−2.63856e44	−1.15462
$489$	2.11802e44	0.896053
$490$	0	0
$491$	2.10330e44	0.831874	0.415937	−	0.909393i	$-0.363454\pi$
$491$	2.10330e44	0.831874	0.415937	+	0.909393i	$0.363454\pi$
$492$	7.31713e43	0.279844
$493$	−7.72257e43	−0.285619
$494$	−2.00263e43	−0.0716319
$495$	0	0
$496$	6.39103e44	2.13857
$497$	−8.34508e43	−0.270116
$498$	2.07203e44	0.648802
$499$	−3.94604e44	−1.19537	−0.597686	−	0.801730i	$-0.703913\pi$
$499$	−3.94604e44	−1.19537	−0.597686	+	0.801730i	$0.703913\pi$
$500$	0	0
$501$	−5.70669e44	−1.61831
$502$	−1.36801e43	−0.0375386
$503$	7.12742e44	1.89261	0.946304	−	0.323279i	$-0.104785\pi$
$503$	7.12742e44	1.89261	0.946304	+	0.323279i	$0.104785\pi$
$504$	−1.63736e44	−0.420767
$505$	0	0
$506$	−6.63780e44	−1.59787
$507$	2.73652e43	0.0637627
$508$	4.04060e42	0.00911370
$509$	9.04650e44	1.97532	0.987659	−	0.156618i	$-0.0500592\pi$
$509$	9.04650e44	1.97532	0.987659	+	0.156618i	$0.0500592\pi$
$510$	0	0
$511$	7.03980e44	1.44084
$512$	2.50660e44	0.496741
$513$	2.38115e43	0.0456930
$514$	−3.09434e44	−0.575011
$515$	0	0
$516$	4.91615e43	0.0856851
$517$	−1.38497e44	−0.233801
$518$	1.87849e44	0.307162
$519$	4.77600e44	0.756490
$520$	0	0
$521$	5.72183e43	0.0850575	0.0425288	−	0.999095i	$-0.486459\pi$
$521$	5.72183e43	0.0850575	0.0425288	+	0.999095i	$0.486459\pi$
$522$	5.09869e44	0.734337
$523$	−6.60401e43	−0.0921573	−0.0460787	−	0.998938i	$-0.514672\pi$
$523$	−6.60401e43	−0.0921573	−0.0460787	+	0.998938i	$0.514672\pi$
$524$	−2.13822e44	−0.289125
$525$	0	0
$526$	−5.38893e44	−0.684286
$527$	−2.45128e44	−0.301660
$528$	1.70723e45	2.03626
$529$	−3.49283e43	−0.0403793
$530$	0	0
$531$	−1.46360e44	−0.158988
$532$	1.69229e43	0.0178210
$533$	−1.07707e45	−1.09963
$534$	−9.72202e44	−0.962334
$535$	0	0
$536$	7.53439e44	0.701180
$537$	−1.36665e45	−1.23334
$538$	−4.10103e44	−0.358910
$539$	−1.07299e45	−0.910709
$540$	0	0
$541$	−1.77379e45	−1.41628	−0.708138	−	0.706074i	$-0.750464\pi$
$541$	−1.77379e45	−1.41628	−0.708138	+	0.706074i	$0.750464\pi$
$542$	1.47481e45	1.14222
$543$	−1.89596e45	−1.42440
$544$	9.90578e43	0.0721950
$545$	0	0
$546$	−2.47598e45	−1.69851
$547$	−1.16728e45	−0.776937	−0.388468	−	0.921462i	$-0.626996\pi$
$547$	−1.16728e45	−0.776937	−0.388468	+	0.921462i	$0.626996\pi$
$548$	−3.58475e44	−0.231515
$549$	−8.24229e44	−0.516540
$550$	0	0
$551$	1.84627e44	0.108967
$552$	−1.73071e45	−0.991357
$553$	−1.80083e45	−1.00117
$554$	1.54743e45	0.835027
$555$	0	0
$556$	5.28400e44	0.268676
$557$	−3.04688e45	−1.50399	−0.751994	−	0.659170i	$-0.770908\pi$
$557$	−3.04688e45	−1.50399	−0.751994	+	0.659170i	$0.770908\pi$
$558$	1.61842e45	0.775579
$559$	−7.23652e44	−0.336694
$560$	0	0
$561$	−6.54809e44	−0.287228
$562$	2.86029e45	1.21832
$563$	−3.49063e45	−1.44383	−0.721914	−	0.691982i	$-0.756738\pi$
$563$	−3.49063e45	−1.44383	−0.721914	+	0.691982i	$0.756738\pi$
$564$	1.03070e44	0.0414026
$565$	0	0
$566$	−3.94979e45	−1.49659
$567$	4.27339e45	1.57272
$568$	5.10989e44	0.182669
$569$	−1.15922e45	−0.402543	−0.201272	−	0.979535i	$-0.564507\pi$
$569$	−1.15922e45	−0.402543	−0.201272	+	0.979535i	$0.564507\pi$
$570$	0	0
$571$	−3.31452e44	−0.108624	−0.0543119	−	0.998524i	$-0.517297\pi$
$571$	−3.31452e44	−0.108624	−0.0543119	+	0.998524i	$0.517297\pi$
$572$	1.05654e45	0.336396
$573$	4.72999e45	1.46322
$574$	5.00911e45	1.50562
$575$	0	0
$576$	9.35759e44	0.265579
$577$	−1.81007e45	−0.499224	−0.249612	−	0.968346i	$-0.580303\pi$
$577$	−1.81007e45	−0.499224	−0.249612	+	0.968346i	$0.580303\pi$
$578$	4.01147e45	1.07521
$579$	−2.47800e45	−0.645513
$580$	0	0
$581$	2.57736e45	0.634262
$582$	2.66865e45	0.638355
$583$	−3.74825e45	−0.871561
$584$	−4.31064e45	−0.974382
$585$	0	0
$586$	−3.83824e45	−0.820014
$587$	−4.38043e45	−0.909887	−0.454944	−	0.890520i	$-0.650341\pi$
$587$	−4.38043e45	−0.909887	−0.454944	+	0.890520i	$0.650341\pi$
$588$	7.98523e44	0.161273
$589$	5.86039e44	0.115087
$590$	0	0
$591$	1.08896e45	0.202217
$592$	−1.41890e45	−0.256238
$593$	−4.28135e44	−0.0751932	−0.0375966	−	0.999293i	$-0.511970\pi$
$593$	−4.28135e44	−0.0751932	−0.0375966	+	0.999293i	$0.511970\pi$
$594$	−6.91374e45	−1.18096
$595$	0	0
$596$	2.23796e45	0.361650
$597$	6.28526e45	0.987976
$598$	−7.27146e45	−1.11187
$599$	3.79121e45	0.563944	0.281972	−	0.959423i	$-0.409012\pi$
$599$	3.79121e45	0.563944	0.281972	+	0.959423i	$0.409012\pi$
$600$	0	0
$601$	9.56105e44	0.134610	0.0673049	−	0.997732i	$-0.478560\pi$
$601$	9.56105e44	0.134610	0.0673049	+	0.997732i	$0.478560\pi$
$602$	3.36547e45	0.461003
$603$	2.35358e45	0.313685
$604$	−3.87889e44	−0.0503035
$605$	0	0
$606$	6.53626e45	0.802659
$607$	−3.04630e45	−0.364049	−0.182025	−	0.983294i	$-0.558265\pi$
$607$	−3.04630e45	−0.364049	−0.182025	+	0.983294i	$0.558265\pi$
$608$	−2.36822e44	−0.0275431
$609$	2.28266e46	2.58379
$610$	0	0
$611$	−1.51718e45	−0.162689
$612$	1.35395e44	0.0141320
$613$	1.50267e46	1.52674	0.763372	−	0.645959i	$-0.223542\pi$
$613$	1.50267e46	1.52674	0.763372	+	0.645959i	$0.223542\pi$
$614$	−1.10100e46	−1.08896
$615$	0	0
$616$	1.72151e46	1.61372
$617$	−3.76624e45	−0.343718	−0.171859	−	0.985122i	$-0.554977\pi$
$617$	−3.76624e45	−0.343718	−0.171859	+	0.985122i	$0.554977\pi$
$618$	1.63062e46	1.44892
$619$	−3.61256e45	−0.312549	−0.156275	−	0.987714i	$-0.549949\pi$
$619$	−3.61256e45	−0.312549	−0.156275	+	0.987714i	$0.549949\pi$
$620$	0	0
$621$	8.64584e45	0.709244
$622$	−2.33017e46	−1.86143
$623$	−1.20930e46	−0.940766
$624$	1.87021e46	1.41692
$625$	0	0
$626$	6.65738e45	0.478440
$627$	1.56548e45	0.109581
$628$	2.83346e45	0.193189
$629$	5.44219e44	0.0361442
$630$	0	0
$631$	−1.19160e46	−0.751008	−0.375504	−	0.926821i	$-0.622530\pi$
$631$	−1.19160e46	−0.751008	−0.375504	+	0.926821i	$0.622530\pi$
$632$	1.10269e46	0.677052
$633$	3.32514e46	1.98907
$634$	−5.25750e45	−0.306413
$635$	0	0
$636$	2.78947e45	0.154340
$637$	−1.17542e46	−0.633711
$638$	−5.36071e46	−2.81632
$639$	1.59622e45	0.0817200
$640$	0	0
$641$	1.22124e45	0.0593806	0.0296903	−	0.999559i	$-0.490548\pi$
$641$	1.22124e45	0.0593806	0.0296903	+	0.999559i	$0.490548\pi$
$642$	4.87567e46	2.31050
$643$	−2.16557e46	−1.00021	−0.500105	−	0.865965i	$-0.666705\pi$
$643$	−2.16557e46	−1.00021	−0.500105	+	0.865965i	$0.666705\pi$
$644$	6.14462e45	0.276617
$645$	0	0
$646$	2.69825e44	0.0115410
$647$	1.30233e45	0.0543002	0.0271501	−	0.999631i	$-0.491357\pi$
$647$	1.30233e45	0.0543002	0.0271501	+	0.999631i	$0.491357\pi$
$648$	−2.61670e46	−1.06357
$649$	1.53882e46	0.609747
$650$	0	0
$651$	7.24559e46	2.72890
$652$	4.60449e45	0.169081
$653$	1.93235e46	0.691861	0.345930	−	0.938260i	$-0.387563\pi$
$653$	1.93235e46	0.691861	0.345930	+	0.938260i	$0.387563\pi$
$654$	−5.40844e46	−1.88816
$655$	0	0
$656$	−3.78358e46	−1.25600
$657$	−1.34655e46	−0.435906
$658$	7.05591e45	0.222754
$659$	−1.11486e46	−0.343249	−0.171625	−	0.985162i	$-0.554902\pi$
$659$	−1.11486e46	−0.343249	−0.171625	+	0.985162i	$0.554902\pi$
$660$	0	0
$661$	−5.28685e46	−1.54836	−0.774182	−	0.632963i	$-0.781839\pi$
$661$	−5.28685e46	−1.54836	−0.774182	+	0.632963i	$0.781839\pi$
$662$	−4.09404e46	−1.16949
$663$	−7.17319e45	−0.199866
$664$	−1.57818e46	−0.428926
$665$	0	0
$666$	−3.59311e45	−0.0929279
$667$	6.70373e46	1.69138
$668$	−1.24061e46	−0.305368
$669$	3.96491e46	0.952143
$670$	0	0
$671$	8.66586e46	1.98103
$672$	−2.92799e46	−0.653095
$673$	−3.85972e46	−0.840054	−0.420027	−	0.907512i	$-0.637979\pi$
$673$	−3.85972e46	−0.840054	−0.420027	+	0.907512i	$0.637979\pi$
$674$	5.25478e46	1.11600
$675$	0	0
$676$	5.94908e44	0.0120318
$677$	2.19045e46	0.432335	0.216167	−	0.976356i	$-0.430644\pi$
$677$	2.19045e46	0.432335	0.216167	+	0.976356i	$0.430644\pi$
$678$	9.62510e46	1.85402
$679$	3.31947e46	0.624048
$680$	0	0
$681$	−8.75981e46	−1.56880
$682$	−1.70159e47	−2.97449
$683$	−8.23915e44	−0.0140586	−0.00702928	−	0.999975i	$-0.502238\pi$
$683$	−8.23915e44	−0.0140586	−0.00702928	+	0.999975i	$0.502238\pi$
$684$	−3.23695e44	−0.00539151
$685$	0	0
$686$	−3.39029e46	−0.538131
$687$	4.67268e46	0.724069
$688$	−2.54208e46	−0.384573
$689$	−4.10607e46	−0.606470
$690$	0	0
$691$	−6.11797e46	−0.861430	−0.430715	−	0.902488i	$-0.641739\pi$
$691$	−6.11797e46	−0.861430	−0.430715	+	0.902488i	$0.641739\pi$
$692$	1.03828e46	0.142746
$693$	5.37761e46	0.721924
$694$	−4.12772e46	−0.541102
$695$	0	0
$696$	−1.39773e47	−1.74731
$697$	1.45119e46	0.177168
$698$	−4.96387e46	−0.591842
$699$	−1.38682e47	−1.61490
$700$	0	0
$701$	−9.95653e46	−1.10601	−0.553007	−	0.833177i	$-0.686520\pi$
$701$	−9.95653e46	−1.10601	−0.553007	+	0.833177i	$0.686520\pi$
$702$	−7.57375e46	−0.821766
$703$	−1.30109e45	−0.0137894
$704$	−9.83848e46	−1.01854
$705$	0	0
$706$	1.04142e47	1.02884
$707$	8.13032e46	0.784670
$708$	−1.14520e46	−0.107977
$709$	1.13327e47	1.04393	0.521964	−	0.852967i	$-0.325199\pi$
$709$	1.13327e47	1.04393	0.521964	+	0.852967i	$0.325199\pi$
$710$	0	0
$711$	3.44457e46	0.302891
$712$	7.40484e46	0.636203
$713$	2.12788e47	1.78637
$714$	3.33602e46	0.273658
$715$	0	0
$716$	−2.97105e46	−0.232726
$717$	1.91943e47	1.46929
$718$	3.91319e46	0.292737
$719$	−5.42492e46	−0.396613	−0.198306	−	0.980140i	$-0.563544\pi$
$719$	−5.42492e46	−0.396613	−0.198306	+	0.980140i	$0.563544\pi$
$720$	0	0
$721$	2.02830e47	1.41644
$722$	1.61315e47	1.10106
$723$	−1.18046e47	−0.787536
$724$	−4.12173e46	−0.268778
$725$	0	0
$726$	−2.45767e47	−1.53133
$727$	−1.08635e47	−0.661687	−0.330843	−	0.943686i	$-0.607333\pi$
$727$	−1.08635e47	−0.661687	−0.330843	+	0.943686i	$0.607333\pi$
$728$	1.88585e47	1.12289
$729$	6.46237e46	0.376173
$730$	0	0
$731$	9.75013e45	0.0542468
$732$	−6.44918e46	−0.350810
$733$	−1.51370e47	−0.805054	−0.402527	−	0.915408i	$-0.631868\pi$
$733$	−1.51370e47	−0.805054	−0.402527	+	0.915408i	$0.631868\pi$
$734$	1.31247e46	0.0682502
$735$	0	0
$736$	−8.59891e46	−0.427523
$737$	−2.47453e47	−1.20304
$738$	−9.58126e46	−0.455504
$739$	2.57207e47	1.19578	0.597888	−	0.801580i	$-0.296007\pi$
$739$	2.57207e47	1.19578	0.597888	+	0.801580i	$0.296007\pi$
$740$	0	0
$741$	1.71493e46	0.0762510
$742$	1.90960e47	0.830382
$743$	−1.84386e46	−0.0784173	−0.0392087	−	0.999231i	$-0.512484\pi$
$743$	−1.84386e46	−0.0784173	−0.0392087	+	0.999231i	$0.512484\pi$
$744$	−4.43664e47	−1.84545
$745$	0	0
$746$	5.07729e46	0.202042
$747$	−4.92988e46	−0.191887
$748$	−1.42353e46	−0.0541988
$749$	6.06474e47	2.25872
$750$	0	0
$751$	−4.41078e46	−0.157201	−0.0786007	−	0.996906i	$-0.525045\pi$
$751$	−4.41078e46	−0.157201	−0.0786007	+	0.996906i	$0.525045\pi$
$752$	−5.32961e46	−0.185824
$753$	1.17148e46	0.0399593
$754$	−5.87246e47	−1.95972
$755$	0	0
$756$	6.40006e46	0.204444
$757$	−4.65678e47	−1.45547	−0.727736	−	0.685857i	$-0.759427\pi$
$757$	−4.65678e47	−1.45547	−0.727736	+	0.685857i	$0.759427\pi$
$758$	−2.06338e47	−0.631012
$759$	5.68420e47	1.70091
$760$	0	0
$761$	1.32920e47	0.380841	0.190420	−	0.981703i	$-0.439015\pi$
$761$	1.32920e47	0.380841	0.190420	+	0.981703i	$0.439015\pi$
$762$	−1.90429e46	−0.0533920
$763$	−6.72744e47	−1.84584
$764$	1.02828e47	0.276103
$765$	0	0
$766$	6.26648e47	1.61157
$767$	1.68572e47	0.424288
$768$	3.03679e47	0.748092
$769$	−2.70521e47	−0.652253	−0.326127	−	0.945326i	$-0.605744\pi$
$769$	−2.70521e47	−0.652253	−0.326127	+	0.945326i	$0.605744\pi$
$770$	0	0
$771$	2.64980e47	0.612090
$772$	−5.38707e46	−0.121806
$773$	−6.16100e47	−1.36361	−0.681804	−	0.731535i	$-0.738804\pi$
$773$	−6.16100e47	−1.36361	−0.681804	+	0.731535i	$0.738804\pi$
$774$	−6.43736e46	−0.139470
$775$	0	0
$776$	−2.03259e47	−0.422019
$777$	−1.60862e47	−0.326970
$778$	−8.21281e46	−0.163429
$779$	−3.46944e46	−0.0675914
$780$	0	0
$781$	−1.67825e47	−0.313411
$782$	9.79721e46	0.179139
$783$	6.98241e47	1.25008
$784$	−4.12905e47	−0.723828
$785$	0	0
$786$	1.00772e48	1.69382
$787$	−9.09975e46	−0.149777	−0.0748887	−	0.997192i	$-0.523860\pi$
$787$	−9.09975e46	−0.149777	−0.0748887	+	0.997192i	$0.523860\pi$
$788$	2.36735e46	0.0381575
$789$	4.61474e47	0.728412
$790$	0	0
$791$	1.19725e48	1.81247
$792$	−3.29284e47	−0.488208
$793$	9.49313e47	1.37848
$794$	6.93963e47	0.986957
$795$	0	0
$796$	1.36639e47	0.186427
$797$	9.51335e47	1.27137	0.635684	−	0.771950i	$-0.280718\pi$
$797$	9.51335e47	1.27137	0.635684	+	0.771950i	$0.280718\pi$
$798$	−7.97557e46	−0.104403
$799$	2.04417e46	0.0262117
$800$	0	0
$801$	2.31311e47	0.284616
$802$	1.17153e47	0.141213
$803$	1.41575e48	1.67178
$804$	1.84156e47	0.213040
$805$	0	0
$806$	−1.86402e48	−2.06978
$807$	3.51187e47	0.382054
$808$	−4.97839e47	−0.530642
$809$	6.61127e46	0.0690453	0.0345227	−	0.999404i	$-0.489009\pi$
$809$	6.61127e46	0.0690453	0.0345227	+	0.999404i	$0.489009\pi$
$810$	0	0
$811$	−1.12294e48	−1.12593	−0.562966	−	0.826480i	$-0.690340\pi$
$811$	−1.12294e48	−1.12593	−0.562966	+	0.826480i	$0.690340\pi$
$812$	4.96242e47	0.487550
$813$	−1.26294e48	−1.21587
$814$	3.77776e47	0.356395
$815$	0	0
$816$	−2.51983e47	−0.228288
$817$	−2.33101e46	−0.0206957
$818$	1.62226e48	1.41153
$819$	5.89097e47	0.502346
$820$	0	0
$821$	1.43390e48	1.17451	0.587257	−	0.809401i	$-0.300208\pi$
$821$	1.43390e48	1.17451	0.587257	+	0.809401i	$0.300208\pi$
$822$	1.68946e48	1.35632
$823$	1.07892e48	0.848970	0.424485	−	0.905435i	$-0.360455\pi$
$823$	1.07892e48	0.848970	0.424485	+	0.905435i	$0.360455\pi$
$824$	−1.24197e48	−0.957885
$825$	0	0
$826$	−7.83971e47	−0.580938
$827$	−1.67232e48	−1.21473	−0.607364	−	0.794424i	$-0.707773\pi$
$827$	−1.67232e48	−1.21473	−0.607364	+	0.794424i	$0.707773\pi$
$828$	−1.17532e47	−0.0836867
$829$	3.48680e47	0.243376	0.121688	−	0.992568i	$-0.461169\pi$
$829$	3.48680e47	0.243376	0.121688	+	0.992568i	$0.461169\pi$
$830$	0	0
$831$	−1.32512e48	−0.888873
$832$	−1.07777e48	−0.708746
$833$	1.58370e47	0.102101
$834$	−2.49029e48	−1.57402
$835$	0	0
$836$	3.40330e46	0.0206774
$837$	2.21634e48	1.32028
$838$	6.02222e47	0.351747
$839$	−1.43688e48	−0.822900	−0.411450	−	0.911432i	$-0.634978\pi$
$839$	−1.43688e48	−0.822900	−0.411450	+	0.911432i	$0.634978\pi$
$840$	0	0
$841$	3.59788e48	1.98113
$842$	7.95957e46	0.0429774
$843$	−2.44937e48	−1.29688
$844$	7.22873e47	0.375328
$845$	0	0
$846$	−1.34963e47	−0.0673913
$847$	−3.05704e48	−1.49701
$848$	−1.44240e48	−0.692713
$849$	3.38235e48	1.59310
$850$	0	0
$851$	−4.72420e47	−0.214038
$852$	1.24896e47	0.0555004
$853$	−3.06470e48	−1.33576	−0.667880	−	0.744269i	$-0.732798\pi$
$853$	−3.06470e48	−1.33576	−0.667880	+	0.744269i	$0.732798\pi$
$854$	−4.41494e48	−1.88743
$855$	0	0
$856$	−3.71358e48	−1.52748
$857$	−3.52656e47	−0.142288	−0.0711439	−	0.997466i	$-0.522665\pi$
$857$	−3.52656e47	−0.142288	−0.0711439	+	0.997466i	$0.522665\pi$
$858$	−4.97935e48	−1.97076
$859$	3.49821e48	1.35819	0.679093	−	0.734052i	$-0.262373\pi$
$859$	3.49821e48	1.35819	0.679093	+	0.734052i	$0.262373\pi$
$860$	0	0
$861$	−4.28949e48	−1.60271
$862$	−2.35069e48	−0.861639
$863$	2.18223e48	0.784733	0.392366	−	0.919809i	$-0.371657\pi$
$863$	2.18223e48	0.784733	0.392366	+	0.919809i	$0.371657\pi$
$864$	−8.95638e47	−0.315977
$865$	0	0
$866$	−1.84893e48	−0.627877
$867$	−3.43517e48	−1.14455
$868$	1.57516e48	0.514932
$869$	−3.62158e48	−1.16164
$870$	0	0
$871$	−2.71075e48	−0.837125
$872$	4.11937e48	1.24827
$873$	−6.34937e47	−0.188797
$874$	−2.34227e47	−0.0683436
$875$	0	0
$876$	−1.05361e48	−0.296047
$877$	−5.47361e48	−1.50932	−0.754659	−	0.656117i	$-0.772198\pi$
$877$	−5.47361e48	−1.50932	−0.754659	+	0.656117i	$0.772198\pi$
$878$	1.64644e48	0.445540
$879$	3.28683e48	0.872892
$880$	0	0
$881$	−1.58161e48	−0.404572	−0.202286	−	0.979326i	$-0.564837\pi$
$881$	−1.58161e48	−0.404572	−0.202286	+	0.979326i	$0.564837\pi$
$882$	−1.04561e48	−0.262505
$883$	2.91205e48	0.717542	0.358771	−	0.933426i	$-0.383196\pi$
$883$	2.91205e48	0.717542	0.358771	+	0.933426i	$0.383196\pi$
$884$	−1.55942e47	−0.0377139
$885$	0	0
$886$	−5.00561e48	−1.16627
$887$	5.31827e48	1.21627	0.608136	−	0.793833i	$-0.291918\pi$
$887$	5.31827e48	1.21627	0.608136	+	0.793833i	$0.291918\pi$
$888$	9.84998e47	0.221117
$889$	−2.36871e47	−0.0521954
$890$	0	0
$891$	8.59406e48	1.82480
$892$	8.61955e47	0.179665
$893$	−4.88710e46	−0.0100001
$894$	−1.05473e49	−2.11870
$895$	0	0
$896$	7.87900e48	1.52542
$897$	6.22683e48	1.18356
$898$	4.56199e48	0.851324
$899$	1.71849e49	3.14855
$900$	0	0
$901$	5.53232e47	0.0977120
$902$	1.00736e49	1.74694
$903$	−2.88198e48	−0.490730
$904$	−7.33102e48	−1.22570
$905$	0	0
$906$	1.82808e48	0.294700
$907$	−3.23851e48	−0.512654	−0.256327	−	0.966590i	$-0.582512\pi$
$907$	−3.23851e48	−0.512654	−0.256327	+	0.966590i	$0.582512\pi$
$908$	−1.90435e48	−0.296026
$909$	−1.55514e48	−0.237391
$910$	0	0
$911$	−5.41124e48	−0.796605	−0.398303	−	0.917254i	$-0.630401\pi$
$911$	−5.41124e48	−0.796605	−0.398303	+	0.917254i	$0.630401\pi$
$912$	6.02427e47	0.0870943
$913$	5.18323e48	0.735923
$914$	5.66460e48	0.789872
$915$	0	0
$916$	1.01582e48	0.136629
$917$	1.25348e49	1.65586
$918$	1.02045e48	0.132400
$919$	−4.23316e48	−0.539459	−0.269730	−	0.962936i	$-0.586934\pi$
$919$	−4.23316e48	−0.539459	−0.269730	+	0.962936i	$0.586934\pi$
$920$	0	0
$921$	9.42830e48	1.15918
$922$	−1.11586e49	−1.34756
$923$	−1.83846e48	−0.218085
$924$	4.20772e48	0.490297
$925$	0	0
$926$	7.52963e48	0.846627
$927$	−3.87965e48	−0.428526
$928$	−6.94451e48	−0.753529
$929$	−1.09693e49	−1.16929	−0.584644	−	0.811290i	$-0.698766\pi$
$929$	−1.09693e49	−1.16929	−0.584644	+	0.811290i	$0.698766\pi$
$930$	0	0
$931$	−3.78622e47	−0.0389526
$932$	−3.01488e48	−0.304725
$933$	1.99541e49	1.98146
$934$	1.19225e49	1.16317
$935$	0	0
$936$	−3.60718e48	−0.339717
$937$	−8.82160e48	−0.816289	−0.408145	−	0.912917i	$-0.633824\pi$
$937$	−8.82160e48	−0.816289	−0.408145	+	0.912917i	$0.633824\pi$
$938$	1.26068e49	1.14620
$939$	−5.70097e48	−0.509291
$940$	0	0
$941$	−7.63482e48	−0.658522	−0.329261	−	0.944239i	$-0.606800\pi$
$941$	−7.63482e48	−0.658522	−0.329261	+	0.944239i	$0.606800\pi$
$942$	−1.33538e49	−1.13179
$943$	−1.25974e49	−1.04915
$944$	5.92165e48	0.484624
$945$	0	0
$946$	6.76817e48	0.534894
$947$	−1.62448e49	−1.26165	−0.630827	−	0.775924i	$-0.717284\pi$
$947$	−1.62448e49	−1.26165	−0.630827	+	0.775924i	$0.717284\pi$
$948$	2.69520e48	0.205709
$949$	1.55090e49	1.16330
$950$	0	0
$951$	4.50220e48	0.326172
$952$	−2.54090e48	−0.180916
$953$	−9.94250e48	−0.695766	−0.347883	−	0.937538i	$-0.613099\pi$
$953$	−9.94250e48	−0.695766	−0.347883	+	0.937538i	$0.613099\pi$
$954$	−3.65262e48	−0.251221
$955$	0	0
$956$	4.17277e48	0.277248
$957$	4.59058e49	2.99792
$958$	−1.49102e49	−0.957090
$959$	2.10148e49	1.32592
$960$	0	0
$961$	3.81443e49	2.32538
$962$	4.13840e48	0.247995
$963$	−1.16004e49	−0.683345
$964$	−2.56628e48	−0.148605
$965$	0	0
$966$	−2.89589e49	−1.62054
$967$	−2.72293e49	−1.49796	−0.748980	−	0.662593i	$-0.769456\pi$
$967$	−2.72293e49	−1.49796	−0.748980	+	0.662593i	$0.769456\pi$
$968$	1.87190e49	1.01237
$969$	−2.31061e47	−0.0122853
$970$	0	0
$971$	3.20196e48	0.164550	0.0822751	−	0.996610i	$-0.473781\pi$
$971$	3.20196e48	0.164550	0.0822751	+	0.996610i	$0.473781\pi$
$972$	−3.21386e48	−0.162380
$973$	−3.09762e49	−1.53874
$974$	−2.89081e49	−1.41188
$975$	0	0
$976$	3.33478e49	1.57451
$977$	2.56729e49	1.19183	0.595915	−	0.803047i	$-0.296789\pi$
$977$	2.56729e49	1.19183	0.595915	+	0.803047i	$0.296789\pi$
$978$	−2.17005e49	−0.990553
$979$	−2.43198e49	−1.09155
$980$	0	0
$981$	1.28680e49	0.558435
$982$	−2.15497e49	−0.919606
$983$	−2.12937e49	−0.893548	−0.446774	−	0.894647i	$-0.647427\pi$
$983$	−2.12937e49	−0.893548	−0.446774	+	0.894647i	$0.647427\pi$
$984$	2.62656e49	1.08385
$985$	0	0
$986$	7.91226e48	0.315742
$987$	−6.04224e48	−0.237118
$988$	3.72818e47	0.0143882
$989$	−8.46380e48	−0.321238
$990$	0	0
$991$	−1.22972e49	−0.451432	−0.225716	−	0.974193i	$-0.572472\pi$
$991$	−1.22972e49	−0.451432	−0.225716	+	0.974193i	$0.572472\pi$
$992$	−2.20431e49	−0.795849
$993$	3.50588e49	1.24490
$994$	8.55007e48	0.298603
$995$	0	0
$996$	−3.85739e48	−0.130321
$997$	4.53447e49	1.50680	0.753401	−	0.657562i	$-0.228412\pi$
$997$	4.53447e49	1.50680	0.753401	+	0.657562i	$0.228412\pi$
$998$	4.04297e49	1.32144
$999$	−4.92059e48	−0.158193

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.34.a.f.1.5		16
5.2	odd	4		5.34.b.a.4.5	✓	16
5.3	odd	4		5.34.b.a.4.12	yes	16
5.4	even	2	inner	25.34.a.f.1.12		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.34.b.a.4.5	✓	16	5.2	odd	4
5.34.b.a.4.12	yes	16	5.3	odd	4
25.34.a.f.1.5		16	1.1	even	1	trivial
25.34.a.f.1.12		16	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-102456. q^{2} +8.77372e7 q^{3} +1.90737e9 q^{4} -8.98924e12 q^{6} -1.11815e14 q^{7} +6.84671e14 q^{8} +2.13876e15 q^{9} +O(q^{10})\)	\(q-102456. q^{2} +8.77372e7 q^{3} +1.90737e9 q^{4} -8.98924e12 q^{6} -1.11815e14 q^{7} +6.84671e14 q^{8} +2.13876e15 q^{9} -2.24867e17 q^{11} +1.67348e17 q^{12} -2.46334e18 q^{13} +1.14562e19 q^{14} -8.65331e19 q^{16} +3.31898e19 q^{17} -2.19130e20 q^{18} -7.93484e19 q^{19} -9.81036e21 q^{21} +2.30391e22 q^{22} -2.88111e22 q^{23} +6.00711e22 q^{24} +2.52385e23 q^{26} -3.00088e23 q^{27} -2.13273e23 q^{28} -2.32679e24 q^{29} -7.38565e24 q^{31} +2.98459e24 q^{32} -1.97292e25 q^{33} -3.40050e24 q^{34} +4.07941e24 q^{36} +1.63972e25 q^{37} +8.12975e24 q^{38} -2.16126e26 q^{39} +4.37241e26 q^{41} +1.00513e27 q^{42} +2.93769e26 q^{43} -4.28906e26 q^{44} +2.95188e27 q^{46} +6.15905e26 q^{47} -7.59218e27 q^{48} +4.77164e27 q^{49} +2.91198e27 q^{51} -4.69850e27 q^{52} +1.66687e28 q^{53} +3.07459e28 q^{54} -7.65566e28 q^{56} -6.96181e27 q^{57} +2.38395e29 q^{58} -6.84322e28 q^{59} -3.85377e29 q^{61} +7.56707e29 q^{62} -2.39146e29 q^{63} +4.37524e29 q^{64} +2.02139e30 q^{66} +1.10044e30 q^{67} +6.33053e28 q^{68} -2.52780e30 q^{69} +7.46328e29 q^{71} +1.46435e30 q^{72} -6.29592e30 q^{73} -1.68000e30 q^{74} -1.51347e29 q^{76} +2.51436e31 q^{77} +2.21435e31 q^{78} +1.61054e31 q^{79} -3.82184e31 q^{81} -4.47982e31 q^{82} -2.30501e31 q^{83} -1.87120e31 q^{84} -3.00985e31 q^{86} -2.04146e32 q^{87} -1.53960e32 q^{88} +1.08152e32 q^{89} +2.75439e32 q^{91} -5.49534e31 q^{92} -6.47996e32 q^{93} -6.31033e31 q^{94} +2.61860e32 q^{96} -2.96871e32 q^{97} -4.88885e32 q^{98} -4.80938e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 72851326872 q^{4} + 11001777346872 q^{6} + 27\!\cdots\!68 q^{9}+O(q^{10}) \) 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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