LMFDB - Embedded newform 25.34.a.f.1.11

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			1.11
Root			$31348.8$ 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)

$f(q)$	$=$	$q+62697.7 q^{2} +3.24591e7 q^{3} -4.65894e9 q^{4} +2.03511e12 q^{6} +2.03055e13 q^{7} -8.30673e14 q^{8} -4.50547e15 q^{9} +O(q^{10})$	\(q+62697.7 q^{2} +3.24591e7 q^{3} -4.65894e9 q^{4} +2.03511e12 q^{6} +2.03055e13 q^{7} -8.30673e14 q^{8} -4.50547e15 q^{9} -1.08204e17 q^{11} -1.51225e17 q^{12} +2.32496e17 q^{13} +1.27311e18 q^{14} -1.20613e19 q^{16} +2.21357e19 q^{17} -2.82482e20 q^{18} -2.01169e21 q^{19} +6.59098e20 q^{21} -6.78414e21 q^{22} -7.09891e21 q^{23} -2.69629e22 q^{24} +1.45770e22 q^{26} -3.26686e23 q^{27} -9.46020e22 q^{28} +1.18108e24 q^{29} -9.41403e23 q^{31} +6.37921e24 q^{32} -3.51220e24 q^{33} +1.38786e24 q^{34} +2.09907e25 q^{36} +1.19059e26 q^{37} -1.26128e26 q^{38} +7.54661e24 q^{39} -5.26633e26 q^{41} +4.13239e25 q^{42} -1.00685e27 q^{43} +5.04115e26 q^{44} -4.45085e26 q^{46} +3.06131e27 q^{47} -3.91500e26 q^{48} -7.31868e27 q^{49} +7.18505e26 q^{51} -1.08318e27 q^{52} +2.92557e28 q^{53} -2.04824e28 q^{54} -1.68672e28 q^{56} -6.52976e28 q^{57} +7.40509e28 q^{58} -9.11668e28 q^{59} +2.27634e29 q^{61} -5.90238e28 q^{62} -9.14857e28 q^{63} +5.03568e29 q^{64} -2.20207e29 q^{66} +2.33634e30 q^{67} -1.03129e29 q^{68} -2.30424e29 q^{69} -3.44979e30 q^{71} +3.74257e30 q^{72} +3.16717e29 q^{73} +7.46471e30 q^{74} +9.37233e30 q^{76} -2.19713e30 q^{77} +4.73155e29 q^{78} -1.55504e31 q^{79} +1.44422e31 q^{81} -3.30187e31 q^{82} +5.93046e31 q^{83} -3.07069e30 q^{84} -6.31272e31 q^{86} +3.83367e31 q^{87} +8.98822e31 q^{88} -1.27051e32 q^{89} +4.72095e30 q^{91} +3.30734e31 q^{92} -3.05571e31 q^{93} +1.91937e32 q^{94} +2.07063e32 q^{96} +1.84352e32 q^{97} -4.58864e32 q^{98} +4.87509e32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	62697.7	0.676482	0.338241	−	0.941059i	$-0.390168\pi$
$2$	62697.7	0.676482	0.338241	+	0.941059i	$0.390168\pi$
$3$	3.24591e7	0.435347	0.217674	−	0.976022i	$-0.430153\pi$
$3$	3.24591e7	0.435347	0.217674	+	0.976022i	$0.430153\pi$
$4$	−4.65894e9	−0.542371
$5$	0	0
$5$	0	0
$6$	2.03511e12	0.294505
$7$	2.03055e13	0.230938	0.115469	−	0.993311i	$-0.463163\pi$
$7$	2.03055e13	0.230938	0.115469	+	0.993311i	$0.463163\pi$
$8$	−8.30673e14	−1.04339
$9$	−4.50547e15	−0.810473
$10$	0	0
$11$	−1.08204e17	−0.710009	−0.355005	−	0.934865i	$-0.615521\pi$
$11$	−1.08204e17	−0.710009	−0.355005	+	0.934865i	$0.615521\pi$
$12$	−1.51225e17	−0.236120
$13$	2.32496e17	0.0969059	0.0484529	−	0.998825i	$-0.484571\pi$
$13$	2.32496e17	0.0969059	0.0484529	+	0.998825i	$0.484571\pi$
$14$	1.27311e18	0.156226
$15$	0	0
$16$	−1.20613e19	−0.163462
$17$	2.21357e19	0.110328	0.0551641	−	0.998477i	$-0.482432\pi$
$17$	2.21357e19	0.110328	0.0551641	+	0.998477i	$0.482432\pi$
$18$	−2.82482e20	−0.548271
$19$	−2.01169e21	−1.60002	−0.800012	−	0.599984i	$-0.795173\pi$
$19$	−2.01169e21	−1.60002	−0.800012	+	0.599984i	$0.795173\pi$
$20$	0	0
$21$	6.59098e20	0.100538
$22$	−6.78414e21	−0.480309
$23$	−7.09891e21	−0.241370	−0.120685	−	0.992691i	$-0.538509\pi$
$23$	−7.09891e21	−0.241370	−0.120685	+	0.992691i	$0.538509\pi$
$24$	−2.69629e22	−0.454236
$25$	0	0
$26$	1.45770e22	0.0655551
$27$	−3.26686e23	−0.788184
$28$	−9.46020e22	−0.125254
$29$	1.18108e24	0.876419	0.438209	−	0.898873i	$-0.355613\pi$
$29$	1.18108e24	0.876419	0.438209	+	0.898873i	$0.355613\pi$
$30$	0	0
$31$	−9.41403e23	−0.232438	−0.116219	−	0.993224i	$-0.537078\pi$
$31$	−9.41403e23	−0.232438	−0.116219	+	0.993224i	$0.537078\pi$
$32$	6.37921e24	0.932808
$33$	−3.51220e24	−0.309100
$34$	1.38786e24	0.0746350
$35$	0	0
$36$	2.09907e25	0.439577
$37$	1.19059e26	1.58647	0.793237	−	0.608913i	$-0.208394\pi$
$37$	1.19059e26	1.58647	0.793237	+	0.608913i	$0.208394\pi$
$38$	−1.26128e26	−1.08239
$39$	7.54661e24	0.0421877
$40$	0	0
$41$	−5.26633e26	−1.28996	−0.644978	−	0.764201i	$-0.723133\pi$
$41$	−5.26633e26	−1.28996	−0.644978	+	0.764201i	$0.723133\pi$
$42$	4.13239e25	0.0680124
$43$	−1.00685e27	−1.12392	−0.561960	−	0.827165i	$-0.689952\pi$
$43$	−1.00685e27	−1.12392	−0.561960	+	0.827165i	$0.689952\pi$
$44$	5.04115e26	0.385089
$45$	0	0
$46$	−4.45085e26	−0.163282
$47$	3.06131e27	0.787577	0.393788	−	0.919201i	$-0.371164\pi$
$47$	3.06131e27	0.787577	0.393788	+	0.919201i	$0.371164\pi$
$48$	−3.91500e26	−0.0711626
$49$	−7.31868e27	−0.946668
$50$	0	0
$51$	7.18505e26	0.0480310
$52$	−1.08318e27	−0.0525590
$53$	2.92557e28	1.03671	0.518356	−	0.855165i	$-0.326544\pi$
$53$	2.92557e28	1.03671	0.518356	+	0.855165i	$0.326544\pi$
$54$	−2.04824e28	−0.533193
$55$	0	0
$56$	−1.68672e28	−0.240958
$57$	−6.52976e28	−0.696566
$58$	7.40509e28	0.592882
$59$	−9.11668e28	−0.550527	−0.275263	−	0.961369i	$-0.588765\pi$
$59$	−9.11668e28	−0.550527	−0.275263	+	0.961369i	$0.588765\pi$
$60$	0	0
$61$	2.27634e29	0.793038	0.396519	−	0.918026i	$-0.370218\pi$
$61$	2.27634e29	0.793038	0.396519	+	0.918026i	$0.370218\pi$
$62$	−5.90238e28	−0.157240
$63$	−9.14857e28	−0.187169
$64$	5.03568e29	0.794490
$65$	0	0
$66$	−2.20207e29	−0.209101
$67$	2.33634e30	1.73102	0.865511	−	0.500889i	$-0.166994\pi$
$67$	2.33634e30	1.73102	0.865511	+	0.500889i	$0.166994\pi$
$68$	−1.03129e29	−0.0598388
$69$	−2.30424e29	−0.105080
$70$	0	0
$71$	−3.44979e30	−0.981814	−0.490907	−	0.871212i	$-0.663335\pi$
$71$	−3.44979e30	−0.981814	−0.490907	+	0.871212i	$0.663335\pi$
$72$	3.74257e30	0.845637
$73$	3.16717e29	0.0569960	0.0284980	−	0.999594i	$-0.490928\pi$
$73$	3.16717e29	0.0569960	0.0284980	+	0.999594i	$0.490928\pi$
$74$	7.46471e30	1.07322
$75$	0	0
$76$	9.37233e30	0.867807
$77$	−2.19713e30	−0.163968
$78$	4.73155e29	0.0285392
$79$	−1.55504e31	−0.760141	−0.380070	−	0.924958i	$-0.624100\pi$
$79$	−1.55504e31	−0.760141	−0.380070	+	0.924958i	$0.624100\pi$
$80$	0	0
$81$	1.44422e31	0.467339
$82$	−3.30187e31	−0.872632
$83$	5.93046e31	1.28322	0.641608	−	0.767033i	$-0.278268\pi$
$83$	5.93046e31	1.28322	0.641608	+	0.767033i	$0.278268\pi$
$84$	−3.07069e30	−0.0545291
$85$	0	0
$86$	−6.31272e31	−0.760312
$87$	3.83367e31	0.381547
$88$	8.98822e31	0.740814
$89$	−1.27051e32	−0.869050	−0.434525	−	0.900660i	$-0.643084\pi$
$89$	−1.27051e32	−0.869050	−0.434525	+	0.900660i	$0.643084\pi$
$90$	0	0
$91$	4.72095e30	0.0223793
$92$	3.30734e31	0.130912
$93$	−3.05571e31	−0.101191
$94$	1.91937e32	0.532782
$95$	0	0
$96$	2.07063e32	0.406095
$97$	1.84352e32	0.304729	0.152365	−	0.988324i	$-0.451311\pi$
$97$	1.84352e32	0.304729	0.152365	+	0.988324i	$0.451311\pi$
$98$	−4.58864e32	−0.640404
$99$	4.87509e32	0.575443
$100$	0	0
$101$	−1.05952e33	−0.899101	−0.449550	−	0.893255i	$-0.648416\pi$
$101$	−1.05952e33	−0.899101	−0.449550	+	0.893255i	$0.648416\pi$
$102$	4.50486e31	0.0324922
$103$	2.58769e33	1.58891	0.794454	−	0.607325i	$-0.207757\pi$
$103$	2.58769e33	1.58891	0.794454	+	0.607325i	$0.207757\pi$
$104$	−1.93128e32	−0.101110
$105$	0	0
$106$	1.83426e33	0.701317
$107$	1.25320e33	0.410383	0.205191	−	0.978722i	$-0.434218\pi$
$107$	1.25320e33	0.410383	0.205191	+	0.978722i	$0.434218\pi$
$108$	1.52201e33	0.427489
$109$	4.85391e32	0.117099	0.0585497	−	0.998284i	$-0.481352\pi$
$109$	4.85391e32	0.117099	0.0585497	+	0.998284i	$0.481352\pi$
$110$	0	0
$111$	3.86454e33	0.690667
$112$	−2.44912e32	−0.0377496
$113$	1.19302e34	1.58801	0.794007	−	0.607908i	$-0.207991\pi$
$113$	1.19302e34	1.58801	0.794007	+	0.607908i	$0.207991\pi$
$114$	−4.09401e33	−0.471215
$115$	0	0
$116$	−5.50257e33	−0.475345
$117$	−1.04750e33	−0.0785396
$118$	−5.71594e33	−0.372422
$119$	4.49476e32	0.0254790
$120$	0	0
$121$	−1.15171e34	−0.495887
$122$	1.42721e34	0.536476
$123$	−1.70940e34	−0.561578
$124$	4.38594e33	0.126068
$125$	0	0
$126$	−5.73594e33	−0.126617
$127$	3.24467e34	0.628650	0.314325	−	0.949315i	$-0.398222\pi$
$127$	3.24467e34	0.628650	0.314325	+	0.949315i	$0.398222\pi$
$128$	−2.32245e34	−0.395350
$129$	−3.26814e34	−0.489295
$130$	0	0
$131$	7.67974e34	0.892010	0.446005	−	0.895030i	$-0.352846\pi$
$131$	7.67974e34	0.892010	0.446005	+	0.895030i	$0.352846\pi$
$132$	1.63631e34	0.167647
$133$	−4.08483e34	−0.369507
$134$	1.46483e35	1.17101
$135$	0	0
$136$	−1.83875e34	−0.115115
$137$	−3.25139e35	−1.80377	−0.901883	−	0.431980i	$-0.857815\pi$
$137$	−3.25139e35	−1.80377	−0.901883	+	0.431980i	$0.857815\pi$
$138$	−1.44471e34	−0.0710845
$139$	−1.06447e35	−0.464933	−0.232466	−	0.972604i	$-0.574680\pi$
$139$	−1.06447e35	−0.464933	−0.232466	+	0.972604i	$0.574680\pi$
$140$	0	0
$141$	9.93674e34	0.342869
$142$	−2.16294e35	−0.664180
$143$	−2.51570e34	−0.0688041
$144$	5.43420e34	0.132481
$145$	0	0
$146$	1.98574e34	0.0385568
$147$	−2.37558e35	−0.412129
$148$	−5.54687e35	−0.860458
$149$	−3.66491e33	−0.00508733	−0.00254366	−	0.999997i	$-0.500810\pi$
$149$	−3.66491e33	−0.00508733	−0.00254366	+	0.999997i	$0.500810\pi$
$150$	0	0
$151$	5.64872e35	0.629261	0.314630	−	0.949214i	$-0.398119\pi$
$151$	5.64872e35	0.629261	0.314630	+	0.949214i	$0.398119\pi$
$152$	1.67106e36	1.66944
$153$	−9.97317e34	−0.0894179
$154$	−1.37755e35	−0.110922
$155$	0	0
$156$	−3.51592e34	−0.0228814
$157$	−1.11445e34	−0.00652702	−0.00326351	−	0.999995i	$-0.501039\pi$
$157$	−1.11445e34	−0.00652702	−0.00326351	+	0.999995i	$0.501039\pi$
$158$	−9.74973e35	−0.514222
$159$	9.49612e35	0.451329
$160$	0	0
$161$	−1.44147e35	−0.0557415
$162$	9.05496e35	0.316147
$163$	2.92217e36	0.921742	0.460871	−	0.887467i	$-0.347537\pi$
$163$	2.92217e36	0.921742	0.460871	+	0.887467i	$0.347537\pi$
$164$	2.45355e36	0.699635
$165$	0	0
$166$	3.71826e36	0.868073
$167$	−3.59336e36	−0.759764	−0.379882	−	0.925035i	$-0.624035\pi$
$167$	−3.59336e36	−0.759764	−0.379882	+	0.925035i	$0.624035\pi$
$168$	−5.47495e35	−0.104900
$169$	−5.70208e36	−0.990609
$170$	0	0
$171$	9.06360e36	1.29678
$172$	4.69085e36	0.609582
$173$	1.66997e37	1.97218	0.986092	−	0.166201i	$-0.0531501\pi$
$173$	1.66997e37	1.97218	0.986092	+	0.166201i	$0.0531501\pi$
$174$	2.40362e36	0.258110
$175$	0	0
$176$	1.30509e36	0.116059
$177$	−2.95919e36	−0.239670
$178$	−7.96583e36	−0.587897
$179$	2.30603e37	1.55164	0.775818	−	0.630957i	$-0.217337\pi$
$179$	2.30603e37	1.55164	0.775818	+	0.630957i	$0.217337\pi$
$180$	0	0
$181$	2.49511e37	1.39763	0.698815	−	0.715302i	$-0.253711\pi$
$181$	2.49511e37	1.39763	0.698815	+	0.715302i	$0.253711\pi$
$182$	2.95992e35	0.0151392
$183$	7.38878e36	0.345247
$184$	5.89688e36	0.251842
$185$	0	0
$186$	−1.91586e36	−0.0684542
$187$	−2.39517e36	−0.0783340
$188$	−1.42625e37	−0.427159
$189$	−6.63351e36	−0.182022
$190$	0	0
$191$	6.59976e37	1.52222	0.761110	−	0.648622i	$-0.224655\pi$
$191$	6.59976e37	1.52222	0.761110	+	0.648622i	$0.224655\pi$
$192$	1.63454e37	0.345879
$193$	−5.32383e37	−1.03402	−0.517010	−	0.855980i	$-0.672955\pi$
$193$	−5.32383e37	−1.03402	−0.517010	+	0.855980i	$0.672955\pi$
$194$	1.15584e37	0.206144
$195$	0	0
$196$	3.40973e37	0.513445
$197$	6.19936e36	0.0858330	0.0429165	−	0.999079i	$-0.486335\pi$
$197$	6.19936e36	0.0858330	0.0429165	+	0.999079i	$0.486335\pi$
$198$	3.05657e37	0.389277
$199$	2.13198e37	0.249866	0.124933	−	0.992165i	$-0.460128\pi$
$199$	2.13198e37	0.249866	0.124933	+	0.992165i	$0.460128\pi$
$200$	0	0
$201$	7.58357e37	0.753596
$202$	−6.64297e37	−0.608226
$203$	2.39824e37	0.202399
$204$	−3.34747e36	−0.0260507
$205$	0	0
$206$	1.62242e38	1.07487
$207$	3.19839e37	0.195624
$208$	−2.80421e36	−0.0158404
$209$	2.17673e38	1.13603
$210$	0	0
$211$	3.45541e38	1.54113	0.770566	−	0.637361i	$-0.219974\pi$
$211$	3.45541e38	1.54113	0.770566	+	0.637361i	$0.219974\pi$
$212$	−1.36300e38	−0.562283
$213$	−1.11977e38	−0.427430
$214$	7.85729e37	0.277617
$215$	0	0
$216$	2.71369e38	0.822381
$217$	−1.91157e37	−0.0536789
$218$	3.04329e37	0.0792157
$219$	1.02804e37	0.0248131
$220$	0	0
$221$	5.14646e36	0.0106914
$222$	2.42298e38	0.467224
$223$	−7.52757e38	−1.34780	−0.673899	−	0.738824i	$-0.735382\pi$
$223$	−7.52757e38	−1.34780	−0.673899	+	0.738824i	$0.735382\pi$
$224$	1.29533e38	0.215421
$225$	0	0
$226$	7.47998e38	1.07426
$227$	8.77387e38	1.17156	0.585780	−	0.810470i	$-0.300788\pi$
$227$	8.77387e38	1.17156	0.585780	+	0.810470i	$0.300788\pi$
$228$	3.04217e38	0.377797
$229$	1.04883e39	1.21177	0.605887	−	0.795551i	$-0.292818\pi$
$229$	1.04883e39	1.21177	0.605887	+	0.795551i	$0.292818\pi$
$230$	0	0
$231$	−7.13170e37	−0.0713831
$232$	−9.81090e38	−0.914444
$233$	9.75026e38	0.846532	0.423266	−	0.906005i	$-0.360884\pi$
$233$	9.75026e38	0.846532	0.423266	+	0.906005i	$0.360884\pi$
$234$	−6.56760e37	−0.0531307
$235$	0	0
$236$	4.24740e38	0.298590
$237$	−5.04751e38	−0.330925
$238$	2.81811e37	0.0172361
$239$	−2.23598e39	−1.27615	−0.638076	−	0.769973i	$-0.720269\pi$
$239$	−2.23598e39	−1.27615	−0.638076	+	0.769973i	$0.720269\pi$
$240$	0	0
$241$	8.11623e38	0.403713	0.201857	−	0.979415i	$-0.435302\pi$
$241$	8.11623e38	0.403713	0.201857	+	0.979415i	$0.435302\pi$
$242$	−7.22093e38	−0.335459
$243$	2.28485e39	0.991639
$244$	−1.06053e39	−0.430121
$245$	0	0
$246$	−1.07176e39	−0.379898
$247$	−4.67710e38	−0.155052
$248$	7.81999e38	0.242523
$249$	1.92497e39	0.558644
$250$	0	0
$251$	3.08797e39	0.785338	0.392669	−	0.919680i	$-0.371552\pi$
$251$	3.08797e39	0.785338	0.392669	+	0.919680i	$0.371552\pi$
$252$	4.26226e38	0.101515
$253$	7.68131e38	0.171375
$254$	2.03433e39	0.425271
$255$	0	0
$256$	−5.78174e39	−1.06194
$257$	7.37117e39	1.26952	0.634761	−	0.772709i	$-0.281099\pi$
$257$	7.37117e39	1.26952	0.634761	+	0.772709i	$0.281099\pi$
$258$	−2.04905e39	−0.331000
$259$	2.41755e39	0.366377
$260$	0	0
$261$	−5.32131e39	−0.710314
$262$	4.81502e39	0.603429
$263$	−2.81811e39	−0.331656	−0.165828	−	0.986155i	$-0.553030\pi$
$263$	−2.81811e39	−0.331656	−0.165828	+	0.986155i	$0.553030\pi$
$264$	2.91749e39	0.322511
$265$	0	0
$266$	−2.56110e39	−0.249965
$267$	−4.12398e39	−0.378338
$268$	−1.08849e40	−0.938857
$269$	−1.58985e40	−1.28956	−0.644781	−	0.764367i	$-0.723052\pi$
$269$	−1.58985e40	−1.28956	−0.644781	+	0.764367i	$0.723052\pi$
$270$	0	0
$271$	−1.95396e40	−1.40256	−0.701281	−	0.712885i	$-0.747388\pi$
$271$	−1.95396e40	−1.40256	−0.701281	+	0.712885i	$0.747388\pi$
$272$	−2.66986e38	−0.0180344
$273$	1.53238e38	0.00974275
$274$	−2.03855e40	−1.22022
$275$	0	0
$276$	1.07353e39	0.0569922
$277$	−3.35857e40	−1.67973	−0.839863	−	0.542799i	$-0.817365\pi$
$277$	−3.35857e40	−1.67973	−0.839863	+	0.542799i	$0.817365\pi$
$278$	−6.67399e39	−0.314519
$279$	4.24146e39	0.188385
$280$	0	0
$281$	−3.53786e40	−1.39665	−0.698323	−	0.715783i	$-0.746070\pi$
$281$	−3.53786e40	−1.39665	−0.698323	+	0.715783i	$0.746070\pi$
$282$	6.23011e39	0.231945
$283$	3.47855e40	1.22158	0.610790	−	0.791793i	$-0.290852\pi$
$283$	3.47855e40	1.22158	0.610790	+	0.791793i	$0.290852\pi$
$284$	1.60723e40	0.532508
$285$	0	0
$286$	−1.57728e39	−0.0465447
$287$	−1.06935e40	−0.297900
$288$	−2.87413e40	−0.756016
$289$	−3.97645e40	−0.987828
$290$	0	0
$291$	5.98389e39	0.132663
$292$	−1.47557e39	−0.0309130
$293$	−1.96947e40	−0.389973	−0.194986	−	0.980806i	$-0.562466\pi$
$293$	−1.96947e40	−0.389973	−0.194986	+	0.980806i	$0.562466\pi$
$294$	−1.48943e40	−0.278798
$295$	0	0
$296$	−9.88989e40	−1.65531
$297$	3.53487e40	0.559618
$298$	−2.29781e38	−0.00344149
$299$	−1.65047e39	−0.0233901
$300$	0	0
$301$	−2.04446e40	−0.259556
$302$	3.54162e40	0.425684
$303$	−3.43912e40	−0.391421
$304$	2.42637e40	0.261543
$305$	0	0
$306$	−6.25295e39	−0.0604897
$307$	1.02313e40	0.0937882	0.0468941	−	0.998900i	$-0.485068\pi$
$307$	1.02313e40	0.0937882	0.0468941	+	0.998900i	$0.485068\pi$
$308$	1.02363e40	0.0889317
$309$	8.39942e40	0.691726
$310$	0	0
$311$	−1.63827e40	−0.121294	−0.0606469	−	0.998159i	$-0.519316\pi$
$311$	−1.63827e40	−0.121294	−0.0606469	+	0.998159i	$0.519316\pi$
$312$	−6.26877e39	−0.0440181
$313$	2.45388e41	1.63445	0.817225	−	0.576319i	$-0.195511\pi$
$313$	2.45388e41	1.63445	0.817225	+	0.576319i	$0.195511\pi$
$314$	−6.98732e38	−0.00441541
$315$	0	0
$316$	7.24482e40	0.412279
$317$	9.53656e40	0.515127	0.257563	−	0.966261i	$-0.417080\pi$
$317$	9.53656e40	0.515127	0.257563	+	0.966261i	$0.417080\pi$
$318$	5.95385e40	0.305316
$319$	−1.27797e41	−0.622265
$320$	0	0
$321$	4.06778e40	0.178659
$322$	−9.03768e39	−0.0377081
$323$	−4.45302e40	−0.176528
$324$	−6.72855e40	−0.253471
$325$	0	0
$326$	1.83213e41	0.623543
$327$	1.57554e40	0.0509789
$328$	4.37460e41	1.34592
$329$	6.21614e40	0.181882
$330$	0	0
$331$	3.20466e41	0.848439	0.424219	−	0.905559i	$-0.360549\pi$
$331$	3.20466e41	0.848439	0.424219	+	0.905559i	$0.360549\pi$
$332$	−2.76296e41	−0.695980
$333$	−5.36415e41	−1.28579
$334$	−2.25295e41	−0.513967
$335$	0	0
$336$	−7.94961e39	−0.0164342
$337$	−3.99673e41	−0.786704	−0.393352	−	0.919388i	$-0.628685\pi$
$337$	−3.99673e41	−0.786704	−0.393352	+	0.919388i	$0.628685\pi$
$338$	−3.57507e41	−0.670130
$339$	3.87245e41	0.691338
$340$	0	0
$341$	1.01864e41	0.165033
$342$	5.68267e41	0.877246
$343$	−3.05591e41	−0.449560
$344$	8.36364e41	1.17268
$345$	0	0
$346$	1.04703e42	1.33415
$347$	2.95633e41	0.359183	0.179592	−	0.983741i	$-0.442522\pi$
$347$	2.95633e41	0.359183	0.179592	+	0.983741i	$0.442522\pi$
$348$	−1.78608e41	−0.206940
$349$	9.02618e41	0.997434	0.498717	−	0.866765i	$-0.333805\pi$
$349$	9.02618e41	0.997434	0.498717	+	0.866765i	$0.333805\pi$
$350$	0	0
$351$	−7.59531e40	−0.0763797
$352$	−6.90256e41	−0.662302
$353$	−1.20764e42	−1.10575	−0.552874	−	0.833265i	$-0.686469\pi$
$353$	−1.20764e42	−1.10575	−0.552874	+	0.833265i	$0.686469\pi$
$354$	−1.85534e41	−0.162133
$355$	0	0
$356$	5.91925e41	0.471348
$357$	1.45896e40	0.0110922
$358$	1.44583e42	1.04965
$359$	−1.37495e42	−0.953299	−0.476649	−	0.879093i	$-0.658149\pi$
$359$	−1.37495e42	−0.953299	−0.476649	+	0.879093i	$0.658149\pi$
$360$	0	0
$361$	2.46612e42	1.56008
$362$	1.56437e42	0.945473
$363$	−3.73833e41	−0.215883
$364$	−2.19946e40	−0.0121379
$365$	0	0
$366$	4.63260e41	0.233554
$367$	−3.82875e42	−1.84530	−0.922651	−	0.385637i	$-0.873982\pi$
$367$	−3.82875e42	−1.84530	−0.922651	+	0.385637i	$0.873982\pi$
$368$	8.56224e40	0.0394547
$369$	2.37273e42	1.04547
$370$	0	0
$371$	5.94050e41	0.239416
$372$	1.42364e41	0.0548833
$373$	2.86200e42	1.05554	0.527770	−	0.849387i	$-0.323028\pi$
$373$	2.86200e42	1.05554	0.527770	+	0.849387i	$0.323028\pi$
$374$	−1.50172e41	−0.0529916
$375$	0	0
$376$	−2.54295e42	−0.821747
$377$	2.74596e41	0.0849302
$378$	−4.15906e41	−0.123135
$379$	−2.49740e42	−0.707849	−0.353925	−	0.935274i	$-0.615153\pi$
$379$	−2.49740e42	−0.707849	−0.353925	+	0.935274i	$0.615153\pi$
$380$	0	0
$381$	1.05319e42	0.273681
$382$	4.13790e42	1.02976
$383$	−4.91079e41	−0.117050	−0.0585250	−	0.998286i	$-0.518640\pi$
$383$	−4.91079e41	−0.117050	−0.0585250	+	0.998286i	$0.518640\pi$
$384$	−7.53845e41	−0.172114
$385$	0	0
$386$	−3.33792e42	−0.699496
$387$	4.53633e42	0.910906
$388$	−8.58883e41	−0.165276
$389$	5.44420e41	0.100407	0.0502037	−	0.998739i	$-0.484013\pi$
$389$	5.44420e41	0.100407	0.0502037	+	0.998739i	$0.484013\pi$
$390$	0	0
$391$	−1.57139e41	−0.0266299
$392$	6.07943e42	0.987741
$393$	2.49277e42	0.388334
$394$	3.88686e41	0.0580645
$395$	0	0
$396$	−2.27128e42	−0.312104
$397$	−1.16147e43	−1.53096	−0.765481	−	0.643459i	$-0.777499\pi$
$397$	−1.16147e43	−1.53096	−0.765481	+	0.643459i	$0.777499\pi$
$398$	1.33670e42	0.169030
$399$	−1.32590e42	−0.160864
$400$	0	0
$401$	−1.02132e43	−1.14098	−0.570492	−	0.821303i	$-0.693247\pi$
$401$	−1.02132e43	−1.14098	−0.570492	+	0.821303i	$0.693247\pi$
$402$	4.75472e42	0.509794
$403$	−2.18873e41	−0.0225246
$404$	4.93626e42	0.487647
$405$	0	0
$406$	1.50364e42	0.136919
$407$	−1.28826e43	−1.12641
$408$	−5.96843e41	−0.0501150
$409$	−8.75689e42	−0.706180	−0.353090	−	0.935589i	$-0.614869\pi$
$409$	−8.75689e42	−0.706180	−0.353090	+	0.935589i	$0.614869\pi$
$410$	0	0
$411$	−1.05537e43	−0.785265
$412$	−1.20559e43	−0.861778
$413$	−1.85119e42	−0.127138
$414$	2.00532e42	0.132336
$415$	0	0
$416$	1.48314e42	0.0903946
$417$	−3.45518e42	−0.202407
$418$	1.36476e43	0.768505
$419$	−8.87775e42	−0.480586	−0.240293	−	0.970700i	$-0.577244\pi$
$419$	−8.87775e42	−0.480586	−0.240293	+	0.970700i	$0.577244\pi$
$420$	0	0
$421$	−9.76948e42	−0.488897	−0.244448	−	0.969662i	$-0.578607\pi$
$421$	−9.76948e42	−0.488897	−0.244448	+	0.969662i	$0.578607\pi$
$422$	2.16646e43	1.04255
$423$	−1.37926e43	−0.638309
$424$	−2.43019e43	−1.08169
$425$	0	0
$426$	−7.02070e42	−0.289149
$427$	4.62221e42	0.183143
$428$	−5.83859e42	−0.222580
$429$	−8.16573e41	−0.0299537
$430$	0	0
$431$	−5.70318e43	−1.93750	−0.968751	−	0.248034i	$-0.920215\pi$
$431$	−5.70318e43	−1.93750	−0.968751	+	0.248034i	$0.920215\pi$
$432$	3.94027e42	0.128838
$433$	−2.71186e43	−0.853528	−0.426764	−	0.904363i	$-0.640346\pi$
$433$	−2.71186e43	−0.853528	−0.426764	+	0.904363i	$0.640346\pi$
$434$	−1.19851e42	−0.0363128
$435$	0	0
$436$	−2.26141e42	−0.0635114
$437$	1.42808e43	0.386197
$438$	6.44555e41	0.0167856
$439$	3.17561e43	0.796457	0.398228	−	0.917286i	$-0.369625\pi$
$439$	3.17561e43	0.796457	0.398228	+	0.917286i	$0.369625\pi$
$440$	0	0
$441$	3.29741e43	0.767248
$442$	3.22671e41	0.00723257
$443$	−4.05139e43	−0.874868	−0.437434	−	0.899250i	$-0.644113\pi$
$443$	−4.05139e43	−0.874868	−0.437434	+	0.899250i	$0.644113\pi$
$444$	−1.80046e43	−0.374598
$445$	0	0
$446$	−4.71961e43	−0.911761
$447$	−1.18960e41	−0.00221475
$448$	1.02252e43	0.183478
$449$	−1.03840e43	−0.179598	−0.0897989	−	0.995960i	$-0.528622\pi$
$449$	−1.03840e43	−0.179598	−0.0897989	+	0.995960i	$0.528622\pi$
$450$	0	0
$451$	5.69838e43	0.915880
$452$	−5.55822e43	−0.861294
$453$	1.83352e43	0.273947
$454$	5.50101e43	0.792540
$455$	0	0
$456$	5.42410e43	0.726788
$457$	2.54691e43	0.329152	0.164576	−	0.986364i	$-0.447374\pi$
$457$	2.54691e43	0.329152	0.164576	+	0.986364i	$0.447374\pi$
$458$	6.57595e43	0.819744
$459$	−7.23142e42	−0.0869589
$460$	0	0
$461$	6.21946e43	0.696126	0.348063	−	0.937471i	$-0.386840\pi$
$461$	6.21946e43	0.696126	0.348063	+	0.937471i	$0.386840\pi$
$462$	−4.47141e42	−0.0482894
$463$	8.30551e43	0.865525	0.432763	−	0.901508i	$-0.357539\pi$
$463$	8.30551e43	0.865525	0.432763	+	0.901508i	$0.357539\pi$
$464$	−1.42454e43	−0.143261
$465$	0	0
$466$	6.11318e43	0.572664
$467$	−4.20816e43	−0.380508	−0.190254	−	0.981735i	$-0.560931\pi$
$467$	−4.20816e43	−0.380508	−0.190254	+	0.981735i	$0.560931\pi$
$468$	4.88025e42	0.0425976
$469$	4.74406e43	0.399759
$470$	0	0
$471$	−3.61739e41	−0.00284152
$472$	7.57298e43	0.574412
$473$	1.08945e44	0.797993
$474$	−3.16467e43	−0.223865
$475$	0	0
$476$	−2.09408e42	−0.0138191
$477$	−1.31810e44	−0.840227
$478$	−1.40191e44	−0.863295
$479$	7.24792e43	0.431199	0.215599	−	0.976482i	$-0.430829\pi$
$479$	7.24792e43	0.431199	0.215599	+	0.976482i	$0.430829\pi$
$480$	0	0
$481$	2.76807e43	0.153739
$482$	5.08869e43	0.273105
$483$	−4.67888e42	−0.0242669
$484$	5.36572e43	0.268955
$485$	0	0
$486$	1.43255e44	0.670826
$487$	1.88889e44	0.855023	0.427512	−	0.904010i	$-0.359390\pi$
$487$	1.88889e44	0.855023	0.427512	+	0.904010i	$0.359390\pi$
$488$	−1.89089e44	−0.827446
$489$	9.48509e43	0.401278
$490$	0	0
$491$	4.17277e44	1.65036	0.825182	−	0.564867i	$-0.191073\pi$
$491$	4.17277e44	1.65036	0.825182	+	0.564867i	$0.191073\pi$
$492$	7.96400e43	0.304584
$493$	2.61440e43	0.0966937
$494$	−2.93243e43	−0.104890
$495$	0	0
$496$	1.13546e43	0.0379948
$497$	−7.00496e43	−0.226738
$498$	1.20691e44	0.377913
$499$	2.81200e43	0.0851838	0.0425919	−	0.999093i	$-0.486438\pi$
$499$	2.81200e43	0.0851838	0.0425919	+	0.999093i	$0.486438\pi$
$500$	0	0
$501$	−1.16637e44	−0.330761
$502$	1.93609e44	0.531267
$503$	−7.45270e43	−0.197898	−0.0989491	−	0.995092i	$-0.531548\pi$
$503$	−7.45270e43	−0.197898	−0.0989491	+	0.995092i	$0.531548\pi$
$504$	7.59948e43	0.195290
$505$	0	0
$506$	4.81600e43	0.115932
$507$	−1.85084e44	−0.431259
$508$	−1.51167e44	−0.340962
$509$	−4.47746e44	−0.977661	−0.488831	−	0.872379i	$-0.662576\pi$
$509$	−4.47746e44	−0.977661	−0.488831	+	0.872379i	$0.662576\pi$
$510$	0	0
$511$	6.43110e42	0.0131626
$512$	−1.63005e44	−0.323032
$513$	6.57190e44	1.26111
$514$	4.62155e44	0.858809
$515$	0	0
$516$	1.52261e44	0.265380
$517$	−3.31246e44	−0.559187
$518$	1.51575e44	0.247848
$519$	5.42056e44	0.858585
$520$	0	0
$521$	6.18290e43	0.0919115	0.0459558	−	0.998943i	$-0.485367\pi$
$521$	6.18290e43	0.0919115	0.0459558	+	0.998943i	$0.485367\pi$
$522$	−3.33634e44	−0.480515
$523$	−1.40874e45	−1.96586	−0.982928	−	0.183989i	$-0.941099\pi$
$523$	−1.40874e45	−1.96586	−0.982928	+	0.183989i	$0.941099\pi$
$524$	−3.57794e44	−0.483801
$525$	0	0
$526$	−1.76689e44	−0.224359
$527$	−2.08386e43	−0.0256445
$528$	4.23619e43	0.0505261
$529$	−8.14610e44	−0.941741
$530$	0	0
$531$	4.10749e44	0.446187
$532$	1.90310e44	0.200410
$533$	−1.22440e44	−0.125004
$534$	−2.58564e44	−0.255939
$535$	0	0
$536$	−1.94074e45	−1.80613
$537$	7.48516e44	0.675500
$538$	−9.96797e44	−0.872367
$539$	7.91910e44	0.672143
$540$	0	0
$541$	−1.33014e45	−1.06205	−0.531023	−	0.847357i	$-0.678192\pi$
$541$	−1.33014e45	−1.06205	−0.531023	+	0.847357i	$0.678192\pi$
$542$	−1.22509e45	−0.948808
$543$	8.09889e44	0.608455
$544$	1.41208e44	0.102915
$545$	0	0
$546$	9.60764e42	0.00659080
$547$	2.40170e45	1.59856	0.799279	−	0.600961i	$-0.205215\pi$
$547$	2.40170e45	1.59856	0.799279	+	0.600961i	$0.205215\pi$
$548$	1.51480e45	0.978312
$549$	−1.02560e45	−0.642736
$550$	0	0
$551$	−2.37596e45	−1.40229
$552$	1.91407e44	0.109639
$553$	−3.15758e44	−0.175546
$554$	−2.10575e45	−1.13631
$555$	0	0
$556$	4.95931e44	0.252166
$557$	−5.78171e44	−0.285394	−0.142697	−	0.989766i	$-0.545578\pi$
$557$	−5.78171e44	−0.285394	−0.142697	+	0.989766i	$0.545578\pi$
$558$	2.65930e44	0.127439
$559$	−2.34089e44	−0.108914
$560$	0	0
$561$	−7.77451e43	−0.0341025
$562$	−2.21816e45	−0.944807
$563$	9.78977e44	0.404934	0.202467	−	0.979289i	$-0.435104\pi$
$563$	9.78977e44	0.404934	0.202467	+	0.979289i	$0.435104\pi$
$564$	−4.62946e44	−0.185963
$565$	0	0
$566$	2.18097e45	0.826378
$567$	2.93257e44	0.107926
$568$	2.86565e45	1.02441
$569$	2.73187e45	0.948654	0.474327	−	0.880349i	$-0.342691\pi$
$569$	2.73187e45	0.948654	0.474327	+	0.880349i	$0.342691\pi$
$570$	0	0
$571$	−3.69219e45	−1.21001	−0.605004	−	0.796222i	$-0.706829\pi$
$571$	−3.69219e45	−1.21001	−0.605004	+	0.796222i	$0.706829\pi$
$572$	1.17205e44	0.0373174
$573$	2.14222e45	0.662695
$574$	−6.70461e44	−0.201524
$575$	0	0
$576$	−2.26881e45	−0.643913
$577$	−6.65464e44	−0.183537	−0.0917685	−	0.995780i	$-0.529252\pi$
$577$	−6.65464e44	−0.183537	−0.0917685	+	0.995780i	$0.529252\pi$
$578$	−2.49314e45	−0.668248
$579$	−1.72807e45	−0.450157
$580$	0	0
$581$	1.20421e45	0.296344
$582$	3.75176e44	0.0897441
$583$	−3.16558e45	−0.736075
$584$	−2.63089e44	−0.0594689
$585$	0	0
$586$	−1.23481e45	−0.263810
$587$	7.63092e45	1.58507	0.792535	−	0.609827i	$-0.208761\pi$
$587$	7.63092e45	1.58507	0.792535	+	0.609827i	$0.208761\pi$
$588$	1.10677e45	0.223527
$589$	1.89381e45	0.371907
$590$	0	0
$591$	2.01226e44	0.0373672
$592$	−1.43601e45	−0.259328
$593$	−1.35734e45	−0.238388	−0.119194	−	0.992871i	$-0.538031\pi$
$593$	−1.35734e45	−0.238388	−0.119194	+	0.992871i	$0.538031\pi$
$594$	2.21628e45	0.378572
$595$	0	0
$596$	1.70746e43	0.00275922
$597$	6.92022e44	0.108779
$598$	−1.03481e44	−0.0158230
$599$	2.59608e45	0.386167	0.193083	−	0.981182i	$-0.438151\pi$
$599$	2.59608e45	0.386167	0.193083	+	0.981182i	$0.438151\pi$
$600$	0	0
$601$	1.37129e46	1.93063	0.965316	−	0.261086i	$-0.0840807\pi$
$601$	1.37129e46	1.93063	0.965316	+	0.261086i	$0.0840807\pi$
$602$	−1.28183e45	−0.175585
$603$	−1.05263e46	−1.40295
$604$	−2.63170e45	−0.341293
$605$	0	0
$606$	−2.15625e45	−0.264789
$607$	−6.01305e45	−0.718590	−0.359295	−	0.933224i	$-0.616983\pi$
$607$	−6.01305e45	−0.718590	−0.359295	+	0.933224i	$0.616983\pi$
$608$	−1.28330e46	−1.49252
$609$	7.78446e44	0.0881137
$610$	0	0
$611$	7.11743e44	0.0763208
$612$	4.64644e44	0.0484977
$613$	1.58173e46	1.60707	0.803533	−	0.595260i	$-0.202951\pi$
$613$	1.58173e46	1.60707	0.803533	+	0.595260i	$0.202951\pi$
$614$	6.41479e44	0.0634460
$615$	0	0
$616$	1.82510e45	0.171082
$617$	−2.03656e46	−1.85863	−0.929313	−	0.369294i	$-0.879600\pi$
$617$	−2.03656e46	−1.85863	−0.929313	+	0.369294i	$0.879600\pi$
$618$	5.26624e45	0.467941
$619$	−3.14597e45	−0.272181	−0.136091	−	0.990696i	$-0.543454\pi$
$619$	−3.14597e45	−0.272181	−0.136091	+	0.990696i	$0.543454\pi$
$620$	0	0
$621$	2.31911e45	0.190244
$622$	−1.02716e45	−0.0820531
$623$	−2.57984e45	−0.200697
$624$	−9.10223e43	−0.00689607
$625$	0	0
$626$	1.53853e46	1.10568
$627$	7.06546e45	0.494568
$628$	5.19213e43	0.00354007
$629$	2.63545e45	0.175033
$630$	0	0
$631$	1.08624e46	0.684607	0.342303	−	0.939589i	$-0.388793\pi$
$631$	1.08624e46	0.684607	0.342303	+	0.939589i	$0.388793\pi$
$632$	1.29173e46	0.793121
$633$	1.12160e46	0.670927
$634$	5.97920e45	0.348474
$635$	0	0
$636$	−4.42418e45	−0.244788
$637$	−1.70156e45	−0.0917377
$638$	−8.01260e45	−0.420952
$639$	1.55429e46	0.795734
$640$	0	0
$641$	3.22979e46	1.57042	0.785211	−	0.619228i	$-0.212554\pi$
$641$	3.22979e46	1.57042	0.785211	+	0.619228i	$0.212554\pi$
$642$	2.55041e45	0.120860
$643$	1.51385e46	0.699201	0.349600	−	0.936899i	$-0.386317\pi$
$643$	1.51385e46	0.699201	0.349600	+	0.936899i	$0.386317\pi$
$644$	6.71571e44	0.0302326
$645$	0	0
$646$	−2.79194e45	−0.119418
$647$	3.60709e46	1.50396	0.751981	−	0.659185i	$-0.229099\pi$
$647$	3.60709e46	1.50396	0.751981	+	0.659185i	$0.229099\pi$
$648$	−1.19968e46	−0.487616
$649$	9.86460e45	0.390879
$650$	0	0
$651$	−6.20477e44	−0.0233690
$652$	−1.36142e46	−0.499927
$653$	9.59570e44	0.0343565	0.0171783	−	0.999852i	$-0.494532\pi$
$653$	9.59570e44	0.0343565	0.0171783	+	0.999852i	$0.494532\pi$
$654$	9.87825e44	0.0344863
$655$	0	0
$656$	6.35191e45	0.210858
$657$	−1.42696e45	−0.0461937
$658$	3.89738e45	0.123040
$659$	3.45120e46	1.06258	0.531289	−	0.847191i	$-0.321708\pi$
$659$	3.45120e46	1.06258	0.531289	+	0.847191i	$0.321708\pi$
$660$	0	0
$661$	−3.13661e46	−0.918622	−0.459311	−	0.888276i	$-0.651904\pi$
$661$	−3.13661e46	−0.918622	−0.459311	+	0.888276i	$0.651904\pi$
$662$	2.00925e46	0.573954
$663$	1.67050e44	0.00465449
$664$	−4.92627e46	−1.33889
$665$	0	0
$666$	−3.36320e46	−0.869817
$667$	−8.38437e45	−0.211541
$668$	1.67412e46	0.412074
$669$	−2.44338e46	−0.586760
$670$	0	0
$671$	−2.46309e46	−0.563064
$672$	4.20453e45	0.0937830
$673$	2.02753e46	0.441284	0.220642	−	0.975355i	$-0.429185\pi$
$673$	2.02753e46	0.441284	0.220642	+	0.975355i	$0.429185\pi$
$674$	−2.50586e46	−0.532191
$675$	0	0
$676$	2.65656e46	0.537278
$677$	−6.36048e46	−1.25539	−0.627693	−	0.778461i	$-0.716001\pi$
$677$	−6.36048e46	−1.25539	−0.627693	+	0.778461i	$0.716001\pi$
$678$	2.42793e46	0.467678
$679$	3.74335e45	0.0703736
$680$	0	0
$681$	2.84792e46	0.510036
$682$	6.38661e45	0.111642
$683$	−5.99654e46	−1.02320	−0.511599	−	0.859225i	$-0.670946\pi$
$683$	−5.99654e46	−1.02320	−0.511599	+	0.859225i	$0.670946\pi$
$684$	−4.22267e46	−0.703334
$685$	0	0
$686$	−1.91598e46	−0.304119
$687$	3.40442e46	0.527542
$688$	1.21440e46	0.183718
$689$	6.80182e45	0.100463
$690$	0	0
$691$	−5.59226e46	−0.787407	−0.393704	−	0.919237i	$-0.628806\pi$
$691$	−5.59226e46	−0.787407	−0.393704	+	0.919237i	$0.628806\pi$
$692$	−7.78027e46	−1.06966
$693$	9.89912e45	0.132892
$694$	1.85355e46	0.242981
$695$	0	0
$696$	−3.18453e46	−0.398101
$697$	−1.16574e46	−0.142318
$698$	5.65920e46	0.674747
$699$	3.16485e46	0.368535
$700$	0	0
$701$	−1.24770e47	−1.38600	−0.692999	−	0.720938i	$-0.743711\pi$
$701$	−1.24770e47	−1.38600	−0.692999	+	0.720938i	$0.743711\pi$
$702$	−4.76208e45	−0.0516695
$703$	−2.39509e47	−2.53840
$704$	−5.44881e46	−0.564095
$705$	0	0
$706$	−7.57165e46	−0.748019
$707$	−2.15142e46	−0.207637
$708$	1.37867e46	0.129990
$709$	2.48163e46	0.228599	0.114300	−	0.993446i	$-0.463538\pi$
$709$	2.48163e46	0.228599	0.114300	+	0.993446i	$0.463538\pi$
$710$	0	0
$711$	7.00617e46	0.616073
$712$	1.05538e47	0.906755
$713$	6.68294e45	0.0561036
$714$	9.14734e44	0.00750368
$715$	0	0
$716$	−1.07436e47	−0.841563
$717$	−7.25779e46	−0.555569
$718$	−8.62063e46	−0.644890
$719$	7.59986e46	0.555621	0.277811	−	0.960636i	$-0.410391\pi$
$719$	7.59986e46	0.555621	0.277811	+	0.960636i	$0.410391\pi$
$720$	0	0
$721$	5.25444e46	0.366939
$722$	1.54620e47	1.05536
$723$	2.63446e46	0.175756
$724$	−1.16245e47	−0.758035
$725$	0	0
$726$	−2.34385e46	−0.146041
$727$	1.84497e47	1.12376	0.561879	−	0.827220i	$-0.310079\pi$
$727$	1.84497e47	1.12376	0.561879	+	0.827220i	$0.310079\pi$
$728$	−3.92156e45	−0.0233502
$729$	−6.12127e45	−0.0356318
$730$	0	0
$731$	−2.22873e46	−0.124000
$732$	−3.44239e46	−0.187252
$733$	1.24110e47	0.660071	0.330035	−	0.943969i	$-0.392939\pi$
$733$	1.24110e47	0.660071	0.330035	+	0.943969i	$0.392939\pi$
$734$	−2.40054e47	−1.24831
$735$	0	0
$736$	−4.52855e46	−0.225152
$737$	−2.52802e47	−1.22904
$738$	1.48765e47	0.707245
$739$	1.88241e47	0.875146	0.437573	−	0.899183i	$-0.355838\pi$
$739$	1.88241e47	0.875146	0.437573	+	0.899183i	$0.355838\pi$
$740$	0	0
$741$	−1.51814e46	−0.0675013
$742$	3.72456e46	0.161961
$743$	2.41383e47	1.02657	0.513287	−	0.858217i	$-0.328428\pi$
$743$	2.41383e47	1.02657	0.513287	+	0.858217i	$0.328428\pi$
$744$	2.53830e46	0.105582
$745$	0	0
$746$	1.79441e47	0.714054
$747$	−2.67195e47	−1.04001
$748$	1.11589e46	0.0424861
$749$	2.54469e46	0.0947730
$750$	0	0
$751$	2.35425e46	0.0839062	0.0419531	−	0.999120i	$-0.486642\pi$
$751$	2.35425e46	0.0839062	0.0419531	+	0.999120i	$0.486642\pi$
$752$	−3.69235e46	−0.128739
$753$	1.00233e47	0.341895
$754$	1.72165e46	0.0574538
$755$	0	0
$756$	3.09051e46	0.0987235
$757$	2.42635e47	0.758354	0.379177	−	0.925324i	$-0.376207\pi$
$757$	2.42635e47	0.758354	0.379177	+	0.925324i	$0.376207\pi$
$758$	−1.56581e47	−0.478847
$759$	2.49328e46	0.0746075
$760$	0	0
$761$	5.89468e47	1.68894	0.844468	−	0.535606i	$-0.179917\pi$
$761$	5.89468e47	1.68894	0.844468	+	0.535606i	$0.179917\pi$
$762$	6.60326e46	0.185140
$763$	9.85611e45	0.0270427
$764$	−3.07479e47	−0.825609
$765$	0	0
$766$	−3.07895e46	−0.0791822
$767$	−2.11959e46	−0.0533493
$768$	−1.87670e47	−0.462311
$769$	2.00353e47	0.483071	0.241536	−	0.970392i	$-0.422349\pi$
$769$	2.00353e47	0.483071	0.241536	+	0.970392i	$0.422349\pi$
$770$	0	0
$771$	2.39262e47	0.552682
$772$	2.48034e47	0.560822
$773$	7.65303e45	0.0169384	0.00846919	−	0.999964i	$-0.497304\pi$
$773$	7.65303e45	0.0169384	0.00846919	+	0.999964i	$0.497304\pi$
$774$	2.84417e47	0.616212
$775$	0	0
$776$	−1.53136e47	−0.317950
$777$	7.84714e46	0.159501
$778$	3.41339e46	0.0679239
$779$	1.05942e48	2.06396
$780$	0	0
$781$	3.73281e47	0.697097
$782$	−9.85228e45	−0.0180146
$783$	−3.85841e47	−0.690780
$784$	8.82731e46	0.154744
$785$	0	0
$786$	1.56291e47	0.262701
$787$	3.82823e47	0.630108	0.315054	−	0.949074i	$-0.397977\pi$
$787$	3.82823e47	0.630108	0.315054	+	0.949074i	$0.397977\pi$
$788$	−2.88824e46	−0.0465534
$789$	−9.14732e46	−0.144385
$790$	0	0
$791$	2.42249e47	0.366733
$792$	−4.04961e47	−0.600410
$793$	5.29239e46	0.0768501
$794$	−7.28214e47	−1.03567
$795$	0	0
$796$	−9.93277e46	−0.135520
$797$	−5.46986e47	−0.730994	−0.365497	−	0.930812i	$-0.619101\pi$
$797$	−5.46986e47	−0.730994	−0.365497	+	0.930812i	$0.619101\pi$
$798$	−8.31308e46	−0.108821
$799$	6.77643e46	0.0868918
$800$	0	0
$801$	5.72426e47	0.704341
$802$	−6.40344e47	−0.771856
$803$	−3.42701e46	−0.0404677
$804$	−3.53313e47	−0.408729
$805$	0	0
$806$	−1.37228e46	−0.0152375
$807$	−5.16050e47	−0.561408
$808$	8.80119e47	0.938110
$809$	6.85674e47	0.716089	0.358045	−	0.933704i	$-0.383444\pi$
$809$	6.85674e47	0.716089	0.358045	+	0.933704i	$0.383444\pi$
$810$	0	0
$811$	1.01450e48	1.01720	0.508602	−	0.861002i	$-0.330162\pi$
$811$	1.01450e48	1.01720	0.508602	+	0.861002i	$0.330162\pi$
$812$	−1.11732e47	−0.109775
$813$	−6.34237e47	−0.610601
$814$	−8.07711e47	−0.761997
$815$	0	0
$816$	−8.66614e45	−0.00785124
$817$	2.02547e48	1.79830
$818$	−5.49037e47	−0.477718
$819$	−2.12701e46	−0.0181378
$820$	0	0
$821$	−1.33191e48	−1.09097	−0.545486	−	0.838120i	$-0.683655\pi$
$821$	−1.33191e48	−1.09097	−0.545486	+	0.838120i	$0.683655\pi$
$822$	−6.61695e47	−0.531218
$823$	4.48712e47	0.353078	0.176539	−	0.984294i	$-0.443510\pi$
$823$	4.48712e47	0.353078	0.176539	+	0.984294i	$0.443510\pi$
$824$	−2.14953e48	−1.65785
$825$	0	0
$826$	−1.16065e47	−0.0860064
$827$	7.36744e47	0.535150	0.267575	−	0.963537i	$-0.413778\pi$
$827$	7.36744e47	0.535150	0.267575	+	0.963537i	$0.413778\pi$
$828$	−1.49011e47	−0.106101
$829$	2.69972e48	1.88438	0.942191	−	0.335077i	$-0.108762\pi$
$829$	2.69972e48	1.88438	0.942191	+	0.335077i	$0.108762\pi$
$830$	0	0
$831$	−1.09016e48	−0.731264
$832$	1.17078e47	0.0769908
$833$	−1.62004e47	−0.104444
$834$	−2.16632e47	−0.136925
$835$	0	0
$836$	−1.01412e48	−0.616151
$837$	3.07543e47	0.183204
$838$	−5.56614e47	−0.325108
$839$	1.22574e48	0.701980	0.350990	−	0.936379i	$-0.385845\pi$
$839$	1.22574e48	0.701980	0.350990	+	0.936379i	$0.385845\pi$
$840$	0	0
$841$	−4.21129e47	−0.231890
$842$	−6.12524e47	−0.330730
$843$	−1.14836e48	−0.608026
$844$	−1.60986e48	−0.835866
$845$	0	0
$846$	−8.64766e47	−0.431805
$847$	−2.33859e47	−0.114519
$848$	−3.52863e47	−0.169463
$849$	1.12911e48	0.531811
$850$	0	0
$851$	−8.45188e47	−0.382927
$852$	5.21693e47	0.231826
$853$	2.46709e48	1.07529	0.537645	−	0.843171i	$-0.319314\pi$
$853$	2.46709e48	1.07529	0.537645	+	0.843171i	$0.319314\pi$
$854$	2.89802e47	0.123893
$855$	0	0
$856$	−1.04100e48	−0.428188
$857$	1.57881e48	0.637008	0.318504	−	0.947921i	$-0.396819\pi$
$857$	1.57881e48	0.637008	0.318504	+	0.947921i	$0.396819\pi$
$858$	−5.11972e46	−0.0202631
$859$	−4.06189e48	−1.57703	−0.788517	−	0.615013i	$-0.789151\pi$
$859$	−4.06189e48	−1.57703	−0.788517	+	0.615013i	$0.789151\pi$
$860$	0	0
$861$	−3.47103e47	−0.129690
$862$	−3.57576e48	−1.31069
$863$	2.97250e48	1.06891	0.534457	−	0.845195i	$-0.320516\pi$
$863$	2.97250e48	1.06891	0.534457	+	0.845195i	$0.320516\pi$
$864$	−2.08400e48	−0.735225
$865$	0	0
$866$	−1.70028e48	−0.577396
$867$	−1.29072e48	−0.430048
$868$	8.90586e46	0.0291139
$869$	1.68261e48	0.539707
$870$	0	0
$871$	5.43191e47	0.167746
$872$	−4.03202e47	−0.122180
$873$	−8.30591e47	−0.246975
$874$	8.95373e47	0.261256
$875$	0	0
$876$	−4.78955e46	−0.0134579
$877$	2.87186e48	0.791900	0.395950	−	0.918272i	$-0.370415\pi$
$877$	2.87186e48	0.791900	0.395950	+	0.918272i	$0.370415\pi$
$878$	1.99103e48	0.538789
$879$	−6.39273e47	−0.169774
$880$	0	0
$881$	−4.74319e47	−0.121330	−0.0606650	−	0.998158i	$-0.519322\pi$
$881$	−4.74319e47	−0.121330	−0.0606650	+	0.998158i	$0.519322\pi$
$882$	2.06740e48	0.519030
$883$	6.06557e48	1.49458	0.747292	−	0.664496i	$-0.231354\pi$
$883$	6.06557e48	1.49458	0.747292	+	0.664496i	$0.231354\pi$
$884$	−2.39770e46	−0.00579873
$885$	0	0
$886$	−2.54013e48	−0.591833
$887$	−4.64999e48	−1.06344	−0.531719	−	0.846921i	$-0.678454\pi$
$887$	−4.64999e48	−1.06344	−0.531719	+	0.846921i	$0.678454\pi$
$888$	−3.21017e48	−0.720633
$889$	6.58846e47	0.145179
$890$	0	0
$891$	−1.56271e48	−0.331815
$892$	3.50705e48	0.731007
$893$	−6.15840e48	−1.26014
$894$	−7.45849e45	−0.00149824
$895$	0	0
$896$	−4.71584e47	−0.0913013
$897$	−5.35727e46	−0.0101828
$898$	−6.51054e47	−0.121495
$899$	−1.11187e48	−0.203713
$900$	0	0
$901$	6.47595e47	0.114378
$902$	3.57275e48	0.619577
$903$	−6.63613e47	−0.112997
$904$	−9.91012e48	−1.65691
$905$	0	0
$906$	1.14958e48	0.185320
$907$	−1.71333e48	−0.271219	−0.135610	−	0.990762i	$-0.543299\pi$
$907$	−1.71333e48	−0.271219	−0.135610	+	0.990762i	$0.543299\pi$
$908$	−4.08769e48	−0.635421
$909$	4.77365e48	0.728697
$910$	0	0
$911$	6.80039e48	1.00111	0.500553	−	0.865706i	$-0.333130\pi$
$911$	6.80039e48	1.00111	0.500553	+	0.865706i	$0.333130\pi$
$912$	7.87577e47	0.113862
$913$	−6.41699e48	−0.911095
$914$	1.59685e48	0.222665
$915$	0	0
$916$	−4.88645e48	−0.657232
$917$	1.55941e48	0.205999
$918$	−4.53393e47	−0.0588262
$919$	1.53654e49	1.95811	0.979056	−	0.203593i	$-0.0652620\pi$
$919$	1.53654e49	1.95811	0.979056	+	0.203593i	$0.0652620\pi$
$920$	0	0
$921$	3.32099e47	0.0408304
$922$	3.89946e48	0.470917
$923$	−8.02062e47	−0.0951436
$924$	3.32261e47	0.0387162
$925$	0	0
$926$	5.20736e48	0.585513
$927$	−1.16588e49	−1.28777
$928$	7.53435e48	0.817531
$929$	−3.67102e47	−0.0391316	−0.0195658	−	0.999809i	$-0.506228\pi$
$929$	−3.67102e47	−0.0391316	−0.0195658	+	0.999809i	$0.506228\pi$
$930$	0	0
$931$	1.47229e49	1.51469
$932$	−4.54258e48	−0.459135
$933$	−5.31767e47	−0.0528049
$934$	−2.63842e48	−0.257407
$935$	0	0
$936$	8.70133e47	0.0819472
$937$	6.55944e48	0.606964	0.303482	−	0.952837i	$-0.401851\pi$
$937$	6.55944e48	0.606964	0.303482	+	0.952837i	$0.401851\pi$
$938$	2.97442e48	0.270430
$939$	7.96507e48	0.711553
$940$	0	0
$941$	1.21575e49	1.04861	0.524306	−	0.851530i	$-0.324325\pi$
$941$	1.21575e49	1.04861	0.524306	+	0.851530i	$0.324325\pi$
$942$	−2.26802e46	−0.00192224
$943$	3.73852e48	0.311356
$944$	1.09959e48	0.0899900
$945$	0	0
$946$	6.83061e48	0.539828
$947$	−1.65747e49	−1.28728	−0.643639	−	0.765329i	$-0.722576\pi$
$947$	−1.65747e49	−1.28728	−0.643639	+	0.765329i	$0.722576\pi$
$948$	2.35160e48	0.179484
$949$	7.36355e46	0.00552325
$950$	0	0
$951$	3.09548e48	0.224259
$952$	−3.73368e47	−0.0265844
$953$	−6.56420e48	−0.459356	−0.229678	−	0.973267i	$-0.573767\pi$
$953$	−6.56420e48	−0.459356	−0.229678	+	0.973267i	$0.573767\pi$
$954$	−8.26421e48	−0.568399
$955$	0	0
$956$	1.04173e49	0.692149
$957$	−4.14819e48	−0.270901
$958$	4.54428e48	0.291698
$959$	−6.60212e48	−0.416559
$960$	0	0
$961$	−1.55172e49	−0.945972
$962$	1.73551e48	0.104001
$963$	−5.64626e48	−0.332604
$964$	−3.78130e48	−0.218963
$965$	0	0
$966$	−2.93355e47	−0.0164161
$967$	2.72573e49	1.49950	0.749751	−	0.661721i	$-0.230173\pi$
$967$	2.72573e49	1.49950	0.749751	+	0.661721i	$0.230173\pi$
$968$	9.56691e48	0.517402
$969$	−1.44541e48	−0.0768508
$970$	0	0
$971$	−2.17486e47	−0.0111767	−0.00558835	−	0.999984i	$-0.501779\pi$
$971$	−2.17486e47	−0.0111767	−0.00558835	+	0.999984i	$0.501779\pi$
$972$	−1.06450e49	−0.537837
$973$	−2.16146e48	−0.107371
$974$	1.18429e49	0.578408
$975$	0	0
$976$	−2.74557e48	−0.129631
$977$	1.03056e49	0.478426	0.239213	−	0.970967i	$-0.423111\pi$
$977$	1.03056e49	0.478426	0.239213	+	0.970967i	$0.423111\pi$
$978$	5.94693e48	0.271457
$979$	1.37475e49	0.617033
$980$	0	0
$981$	−2.18691e48	−0.0949059
$982$	2.61623e49	1.11644
$983$	−6.87428e47	−0.0288466	−0.0144233	−	0.999896i	$-0.504591\pi$
$983$	−6.87428e47	−0.0288466	−0.0144233	+	0.999896i	$0.504591\pi$
$984$	1.41996e49	0.585944
$985$	0	0
$986$	1.63917e48	0.0654116
$987$	2.01770e48	0.0791816
$988$	2.17903e48	0.0840956
$989$	7.14754e48	0.271280
$990$	0	0
$991$	3.45059e48	0.126671	0.0633356	−	0.997992i	$-0.479826\pi$
$991$	3.45059e48	0.126671	0.0633356	+	0.997992i	$0.479826\pi$
$992$	−6.00541e48	−0.216820
$993$	1.04020e49	0.369365
$994$	−4.39195e48	−0.153385
$995$	0	0
$996$	−8.96833e48	−0.302993
$997$	3.48409e49	1.15776	0.578881	−	0.815412i	$-0.303490\pi$
$997$	3.48409e49	1.15776	0.578881	+	0.815412i	$0.303490\pi$
$998$	1.76306e48	0.0576253
$999$	−3.88948e49	−1.25043

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.34.a.f.1.11		16
5.2	odd	4		5.34.b.a.4.11	yes	16
5.3	odd	4		5.34.b.a.4.6	✓	16
5.4	even	2	inner	25.34.a.f.1.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.34.b.a.4.6	✓	16	5.3	odd	4
5.34.b.a.4.11	yes	16	5.2	odd	4
25.34.a.f.1.6		16	5.4	even	2	inner
25.34.a.f.1.11		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)

\(f(q)\)	\(=\)	\(q+62697.7 q^{2} +3.24591e7 q^{3} -4.65894e9 q^{4} +2.03511e12 q^{6} +2.03055e13 q^{7} -8.30673e14 q^{8} -4.50547e15 q^{9} +O(q^{10})\)	\(q+62697.7 q^{2} +3.24591e7 q^{3} -4.65894e9 q^{4} +2.03511e12 q^{6} +2.03055e13 q^{7} -8.30673e14 q^{8} -4.50547e15 q^{9} -1.08204e17 q^{11} -1.51225e17 q^{12} +2.32496e17 q^{13} +1.27311e18 q^{14} -1.20613e19 q^{16} +2.21357e19 q^{17} -2.82482e20 q^{18} -2.01169e21 q^{19} +6.59098e20 q^{21} -6.78414e21 q^{22} -7.09891e21 q^{23} -2.69629e22 q^{24} +1.45770e22 q^{26} -3.26686e23 q^{27} -9.46020e22 q^{28} +1.18108e24 q^{29} -9.41403e23 q^{31} +6.37921e24 q^{32} -3.51220e24 q^{33} +1.38786e24 q^{34} +2.09907e25 q^{36} +1.19059e26 q^{37} -1.26128e26 q^{38} +7.54661e24 q^{39} -5.26633e26 q^{41} +4.13239e25 q^{42} -1.00685e27 q^{43} +5.04115e26 q^{44} -4.45085e26 q^{46} +3.06131e27 q^{47} -3.91500e26 q^{48} -7.31868e27 q^{49} +7.18505e26 q^{51} -1.08318e27 q^{52} +2.92557e28 q^{53} -2.04824e28 q^{54} -1.68672e28 q^{56} -6.52976e28 q^{57} +7.40509e28 q^{58} -9.11668e28 q^{59} +2.27634e29 q^{61} -5.90238e28 q^{62} -9.14857e28 q^{63} +5.03568e29 q^{64} -2.20207e29 q^{66} +2.33634e30 q^{67} -1.03129e29 q^{68} -2.30424e29 q^{69} -3.44979e30 q^{71} +3.74257e30 q^{72} +3.16717e29 q^{73} +7.46471e30 q^{74} +9.37233e30 q^{76} -2.19713e30 q^{77} +4.73155e29 q^{78} -1.55504e31 q^{79} +1.44422e31 q^{81} -3.30187e31 q^{82} +5.93046e31 q^{83} -3.07069e30 q^{84} -6.31272e31 q^{86} +3.83367e31 q^{87} +8.98822e31 q^{88} -1.27051e32 q^{89} +4.72095e30 q^{91} +3.30734e31 q^{92} -3.05571e31 q^{93} +1.91937e32 q^{94} +2.07063e32 q^{96} +1.84352e32 q^{97} -4.58864e32 q^{98} +4.87509e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 72851326872 q^{4} + 11001777346872 q^{6} + 27\!\cdots\!68 q^{9}+O(q^{10}) \) 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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