LMFDB - Embedded newform 25.34.a.f.1.13

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			1.13
Root			$57471.0$ 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)

$f(q)$	$=$	$q+114942. q^{2} +6.13071e7 q^{3} +4.62174e9 q^{4} +7.04677e12 q^{6} -1.47106e14 q^{7} -4.56113e14 q^{8} -1.80050e15 q^{9} +O(q^{10})$	\(q+114942. q^{2} +6.13071e7 q^{3} +4.62174e9 q^{4} +7.04677e12 q^{6} -1.47106e14 q^{7} -4.56113e14 q^{8} -1.80050e15 q^{9} -9.00404e16 q^{11} +2.83345e17 q^{12} +2.24010e18 q^{13} -1.69087e19 q^{14} -9.21269e19 q^{16} +1.71070e20 q^{17} -2.06953e20 q^{18} +2.31714e21 q^{19} -9.01867e21 q^{21} -1.03494e22 q^{22} -4.04833e22 q^{23} -2.79630e22 q^{24} +2.57481e23 q^{26} -4.51193e23 q^{27} -6.79887e23 q^{28} +2.58627e23 q^{29} +3.06684e24 q^{31} -6.67128e24 q^{32} -5.52012e24 q^{33} +1.96631e25 q^{34} -8.32142e24 q^{36} +1.35305e25 q^{37} +2.66337e26 q^{38} +1.37334e26 q^{39} +2.64491e26 q^{41} -1.03662e27 q^{42} +1.37193e27 q^{43} -4.16143e26 q^{44} -4.65323e27 q^{46} +5.93699e26 q^{47} -5.64804e27 q^{48} +1.39093e28 q^{49} +1.04878e28 q^{51} +1.03531e28 q^{52} -1.16830e28 q^{53} -5.18611e28 q^{54} +6.70970e28 q^{56} +1.42057e29 q^{57} +2.97271e28 q^{58} +1.75566e29 q^{59} +7.22481e28 q^{61} +3.52508e29 q^{62} +2.64864e29 q^{63} +2.45537e28 q^{64} -6.34493e29 q^{66} -1.22629e29 q^{67} +7.90639e29 q^{68} -2.48191e30 q^{69} -3.82879e30 q^{71} +8.21229e29 q^{72} +4.64374e30 q^{73} +1.55522e30 q^{74} +1.07092e31 q^{76} +1.32455e31 q^{77} +1.57854e31 q^{78} +1.29395e31 q^{79} -1.76523e31 q^{81} +3.04012e31 q^{82} -7.76932e30 q^{83} -4.16819e31 q^{84} +1.57693e32 q^{86} +1.58557e31 q^{87} +4.10685e31 q^{88} +7.56590e31 q^{89} -3.29533e32 q^{91} -1.87103e32 q^{92} +1.88019e32 q^{93} +6.82410e31 q^{94} -4.08997e32 q^{96} -4.71439e32 q^{97} +1.59876e33 q^{98} +1.62117e32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	114942.	1.24018	0.620089	−	0.784532i	$-0.287097\pi$
$2$	114942.	1.24018	0.620089	+	0.784532i	$0.287097\pi$
$3$	6.13071e7	0.822262	0.411131	−	0.911576i	$-0.365134\pi$
$3$	6.13071e7	0.822262	0.411131	+	0.911576i	$0.365134\pi$
$4$	4.62174e9	0.538041
$5$	0	0
$5$	0	0
$6$	7.04677e12	1.01975
$7$	−1.47106e14	−1.67307	−0.836534	−	0.547915i	$-0.815422\pi$
$7$	−1.47106e14	−1.67307	−0.836534	+	0.547915i	$0.815422\pi$
$8$	−4.56113e14	−0.572911
$9$	−1.80050e15	−0.323885
$10$	0	0
$11$	−9.00404e16	−0.590824	−0.295412	−	0.955370i	$-0.595457\pi$
$11$	−9.00404e16	−0.590824	−0.295412	+	0.955370i	$0.595457\pi$
$12$	2.83345e17	0.442411
$13$	2.24010e18	0.933688	0.466844	−	0.884340i	$-0.345391\pi$
$13$	2.24010e18	0.933688	0.466844	+	0.884340i	$0.345391\pi$
$14$	−1.69087e19	−2.07490
$15$	0	0
$16$	−9.21269e19	−1.24855
$17$	1.71070e20	0.852640	0.426320	−	0.904572i	$-0.359810\pi$
$17$	1.71070e20	0.852640	0.426320	+	0.904572i	$0.359810\pi$
$18$	−2.06953e20	−0.401675
$19$	2.31714e21	1.84297	0.921484	−	0.388417i	$-0.126978\pi$
$19$	2.31714e21	1.84297	0.921484	+	0.388417i	$0.126978\pi$
$20$	0	0
$21$	−9.01867e21	−1.37570
$22$	−1.03494e22	−0.732727
$23$	−4.04833e22	−1.37647	−0.688235	−	0.725488i	$-0.741614\pi$
$23$	−4.04833e22	−1.37647	−0.688235	+	0.725488i	$0.741614\pi$
$24$	−2.79630e22	−0.471083
$25$	0	0
$26$	2.57481e23	1.15794
$27$	−4.51193e23	−1.08858
$28$	−6.79887e23	−0.900179
$29$	2.58627e23	0.191914	0.0959569	−	0.995385i	$-0.469409\pi$
$29$	2.58627e23	0.191914	0.0959569	+	0.995385i	$0.469409\pi$
$30$	0	0
$31$	3.06684e24	0.757221	0.378610	−	0.925556i	$-0.376402\pi$
$31$	3.06684e24	0.757221	0.378610	+	0.925556i	$0.376402\pi$
$32$	−6.67128e24	−0.975516
$33$	−5.52012e24	−0.485812
$34$	1.96631e25	1.05743
$35$	0	0
$36$	−8.32142e24	−0.174263
$37$	1.35305e25	0.180295	0.0901476	−	0.995928i	$-0.471266\pi$
$37$	1.35305e25	0.180295	0.0901476	+	0.995928i	$0.471266\pi$
$38$	2.66337e26	2.28561
$39$	1.37334e26	0.767736
$40$	0	0
$41$	2.64491e26	0.647855	0.323927	−	0.946082i	$-0.394997\pi$
$41$	2.64491e26	0.647855	0.323927	+	0.946082i	$0.394997\pi$
$42$	−1.03662e27	−1.70611
$43$	1.37193e27	1.53145	0.765727	−	0.643166i	$-0.222379\pi$
$43$	1.37193e27	1.53145	0.765727	+	0.643166i	$0.222379\pi$
$44$	−4.16143e26	−0.317887
$45$	0	0
$46$	−4.65323e27	−1.70707
$47$	5.93699e26	0.152740	0.0763698	−	0.997080i	$-0.475667\pi$
$47$	5.93699e26	0.152740	0.0763698	+	0.997080i	$0.475667\pi$
$48$	−5.64804e27	−1.02664
$49$	1.39093e28	1.79916
$50$	0	0
$51$	1.04878e28	0.701094
$52$	1.03531e28	0.502362
$53$	−1.16830e28	−0.414002	−0.207001	−	0.978341i	$-0.566370\pi$
$53$	−1.16830e28	−0.414002	−0.207001	+	0.978341i	$0.566370\pi$
$54$	−5.18611e28	−1.35003
$55$	0	0
$56$	6.70970e28	0.958519
$57$	1.42057e29	1.51540
$58$	2.97271e28	0.238007
$59$	1.75566e29	1.06019	0.530094	−	0.847939i	$-0.322157\pi$
$59$	1.75566e29	1.06019	0.530094	+	0.847939i	$0.322157\pi$
$60$	0	0
$61$	7.22481e28	0.251700	0.125850	−	0.992049i	$-0.459834\pi$
$61$	7.22481e28	0.251700	0.125850	+	0.992049i	$0.459834\pi$
$62$	3.52508e29	0.939088
$63$	2.64864e29	0.541882
$64$	2.45537e28	0.0387389
$65$	0	0
$66$	−6.34493e29	−0.602493
$67$	−1.22629e29	−0.0908570	−0.0454285	−	0.998968i	$-0.514465\pi$
$67$	−1.22629e29	−0.0908570	−0.0454285	+	0.998968i	$0.514465\pi$
$68$	7.90639e29	0.458756
$69$	−2.48191e30	−1.13182
$70$	0	0
$71$	−3.82879e30	−1.08968	−0.544840	−	0.838540i	$-0.683410\pi$
$71$	−3.82879e30	−1.08968	−0.544840	+	0.838540i	$0.683410\pi$
$72$	8.21229e29	0.185557
$73$	4.64374e30	0.835681	0.417841	−	0.908520i	$-0.362787\pi$
$73$	4.64374e30	0.835681	0.417841	+	0.908520i	$0.362787\pi$
$74$	1.55522e30	0.223598
$75$	0	0
$76$	1.07092e31	0.991592
$77$	1.32455e31	0.988488
$78$	1.57854e31	0.952129
$79$	1.29395e31	0.632514	0.316257	−	0.948674i	$-0.397574\pi$
$79$	1.29395e31	0.632514	0.316257	+	0.948674i	$0.397574\pi$
$80$	0	0
$81$	−1.76523e31	−0.571213
$82$	3.04012e31	0.803455
$83$	−7.76932e30	−0.168110	−0.0840551	−	0.996461i	$-0.526787\pi$
$83$	−7.76932e30	−0.168110	−0.0840551	+	0.996461i	$0.526787\pi$
$84$	−4.16819e31	−0.740183
$85$	0	0
$86$	1.57693e32	1.89928
$87$	1.58557e31	0.157803
$88$	4.10685e31	0.338490
$89$	7.56590e31	0.517518	0.258759	−	0.965942i	$-0.416686\pi$
$89$	7.56590e31	0.517518	0.258759	+	0.965942i	$0.416686\pi$
$90$	0	0
$91$	−3.29533e32	−1.56212
$92$	−1.87103e32	−0.740597
$93$	1.88019e32	0.622634
$94$	6.82410e31	0.189424
$95$	0	0
$96$	−4.08997e32	−0.802130
$97$	−4.71439e32	−0.779278	−0.389639	−	0.920968i	$-0.627400\pi$
$97$	−4.71439e32	−0.779278	−0.389639	+	0.920968i	$0.627400\pi$
$98$	1.59876e33	2.23127
$99$	1.62117e32	0.191359
$100$	0	0
$101$	1.75641e33	1.49047	0.745233	−	0.666804i	$-0.232338\pi$
$101$	1.75641e33	1.49047	0.745233	+	0.666804i	$0.232338\pi$
$102$	1.20549e33	0.869481
$103$	3.16211e33	1.94161	0.970806	−	0.239864i	$-0.0771029\pi$
$103$	3.16211e33	1.94161	0.970806	+	0.239864i	$0.0771029\pi$
$104$	−1.02174e33	−0.534920
$105$	0	0
$106$	−1.34287e33	−0.513436
$107$	1.04098e33	0.340887	0.170444	−	0.985367i	$-0.445480\pi$
$107$	1.04098e33	0.340887	0.170444	+	0.985367i	$0.445480\pi$
$108$	−2.08530e33	−0.585701
$109$	−4.02698e33	−0.971498	−0.485749	−	0.874098i	$-0.661453\pi$
$109$	−4.02698e33	−0.971498	−0.485749	+	0.874098i	$0.661453\pi$
$110$	0	0
$111$	8.29514e32	0.148250
$112$	1.35525e34	2.08891
$113$	9.40525e32	0.125192	0.0625959	−	0.998039i	$-0.480062\pi$
$113$	9.40525e32	0.125192	0.0625959	+	0.998039i	$0.480062\pi$
$114$	1.63283e34	1.87937
$115$	0	0
$116$	1.19530e33	0.103258
$117$	−4.03329e33	−0.302408
$118$	2.01800e34	1.31482
$119$	−2.51654e34	−1.42653
$120$	0	0
$121$	−1.51179e34	−0.650927
$122$	8.30434e33	0.312153
$123$	1.62152e34	0.532706
$124$	1.41741e34	0.407416
$125$	0	0
$126$	3.04441e34	0.672030
$127$	−3.78295e34	−0.732941	−0.366471	−	0.930430i	$-0.619434\pi$
$127$	−3.78295e34	−0.732941	−0.366471	+	0.930430i	$0.619434\pi$
$128$	6.01281e34	1.02356
$129$	8.41094e34	1.25926
$130$	0	0
$131$	3.99552e34	0.464085	0.232042	−	0.972706i	$-0.425459\pi$
$131$	3.99552e34	0.464085	0.232042	+	0.972706i	$0.425459\pi$
$132$	−2.55125e34	−0.261387
$133$	−3.40866e35	−3.08341
$134$	−1.40952e34	−0.112679
$135$	0	0
$136$	−7.80270e34	−0.488487
$137$	−1.06322e35	−0.589841	−0.294921	−	0.955522i	$-0.595293\pi$
$137$	−1.06322e35	−0.589841	−0.294921	+	0.955522i	$0.595293\pi$
$138$	−2.85276e35	−1.40366
$139$	−4.09181e35	−1.78719	−0.893596	−	0.448872i	$-0.851826\pi$
$139$	−4.09181e35	−1.78719	−0.893596	+	0.448872i	$0.851826\pi$
$140$	0	0
$141$	3.63980e34	0.125592
$142$	−4.40089e35	−1.35140
$143$	−2.01699e35	−0.551645
$144$	1.65874e35	0.404388
$145$	0	0
$146$	5.33761e35	1.03639
$147$	8.52737e35	1.47938
$148$	6.25343e34	0.0970063
$149$	3.00512e35	0.417147	0.208573	−	0.978007i	$-0.433118\pi$
$149$	3.00512e35	0.417147	0.208573	+	0.978007i	$0.433118\pi$
$150$	0	0
$151$	−8.94534e35	−0.996500	−0.498250	−	0.867033i	$-0.666024\pi$
$151$	−8.94534e35	−0.996500	−0.498250	+	0.867033i	$0.666024\pi$
$152$	−1.05688e36	−1.05586
$153$	−3.08010e35	−0.276157
$154$	1.52247e36	1.22590
$155$	0	0
$156$	6.34722e35	0.413074
$157$	5.63407e35	0.329973	0.164986	−	0.986296i	$-0.447242\pi$
$157$	5.63407e35	0.329973	0.164986	+	0.986296i	$0.447242\pi$
$158$	1.48729e36	0.784430
$159$	−7.16251e35	−0.340418
$160$	0	0
$161$	5.95535e36	2.30293
$162$	−2.02899e36	−0.708406
$163$	−3.33141e35	−0.105083	−0.0525415	−	0.998619i	$-0.516732\pi$
$163$	−3.33141e35	−0.105083	−0.0525415	+	0.998619i	$0.516732\pi$
$164$	1.22241e36	0.348572
$165$	0	0
$166$	−8.93021e35	−0.208487
$167$	8.17649e36	1.72880	0.864401	−	0.502804i	$-0.167698\pi$
$167$	8.17649e36	1.72880	0.864401	+	0.502804i	$0.167698\pi$
$168$	4.11353e36	0.788154
$169$	−7.38091e35	−0.128227
$170$	0	0
$171$	−4.17200e36	−0.596910
$172$	6.34072e36	0.823985
$173$	6.51984e36	0.769974	0.384987	−	0.922922i	$-0.374206\pi$
$173$	6.51984e36	0.769974	0.384987	+	0.922922i	$0.374206\pi$
$174$	1.82248e36	0.195704
$175$	0	0
$176$	8.29514e36	0.737675
$177$	1.07635e37	0.871753
$178$	8.69639e36	0.641814
$179$	−1.01361e37	−0.682019	−0.341010	−	0.940060i	$-0.610769\pi$
$179$	−1.01361e37	−0.682019	−0.341010	+	0.940060i	$0.610769\pi$
$180$	0	0
$181$	3.31312e37	1.85584	0.927921	−	0.372777i	$-0.121594\pi$
$181$	3.31312e37	1.85584	0.927921	+	0.372777i	$0.121594\pi$
$182$	−3.78771e37	−1.93731
$183$	4.42932e36	0.206964
$184$	1.84649e37	0.788595
$185$	0	0
$186$	2.16113e37	0.772177
$187$	−1.54032e37	−0.503760
$188$	2.74392e36	0.0821802
$189$	6.63734e37	1.82127
$190$	0	0
$191$	2.74034e37	0.632054	0.316027	−	0.948750i	$-0.397651\pi$
$191$	2.74034e37	0.632054	0.316027	+	0.948750i	$0.397651\pi$
$192$	1.50532e36	0.0318536
$193$	−3.82204e37	−0.742335	−0.371167	−	0.928566i	$-0.621042\pi$
$193$	−3.82204e37	−0.742335	−0.371167	+	0.928566i	$0.621042\pi$
$194$	−5.41882e37	−0.966443
$195$	0	0
$196$	6.42850e37	0.968020
$197$	−7.09083e37	−0.981758	−0.490879	−	0.871228i	$-0.663324\pi$
$197$	−7.09083e37	−0.981758	−0.490879	+	0.871228i	$0.663324\pi$
$198$	1.86341e37	0.237319
$199$	1.13373e38	1.32872	0.664362	−	0.747411i	$-0.268703\pi$
$199$	1.13373e38	1.32872	0.664362	+	0.747411i	$0.268703\pi$
$200$	0	0
$201$	−7.51802e36	−0.0747083
$202$	2.01885e38	1.84844
$203$	−3.80456e37	−0.321085
$204$	4.84718e37	0.377217
$205$	0	0
$206$	3.63459e38	2.40795
$207$	7.28900e37	0.445818
$208$	−2.06373e38	−1.16576
$209$	−2.08636e38	−1.08887
$210$	0	0
$211$	1.11202e38	0.495966	0.247983	−	0.968764i	$-0.420232\pi$
$211$	1.11202e38	0.495966	0.247983	+	0.968764i	$0.420232\pi$
$212$	−5.39957e37	−0.222750
$213$	−2.34732e38	−0.896003
$214$	1.19653e38	0.422761
$215$	0	0
$216$	2.05795e38	0.623660
$217$	−4.51151e38	−1.26688
$218$	−4.62869e38	−1.20483
$219$	2.84694e38	0.687149
$220$	0	0
$221$	3.83213e38	0.796100
$222$	9.53460e37	0.183856
$223$	8.14790e38	1.45887	0.729433	−	0.684053i	$-0.239784\pi$
$223$	8.14790e38	1.45887	0.729433	+	0.684053i	$0.239784\pi$
$224$	9.81388e38	1.63211
$225$	0	0
$226$	1.08106e38	0.155260
$227$	−1.43394e38	−0.191472	−0.0957359	−	0.995407i	$-0.530520\pi$
$227$	−1.43394e38	−0.191472	−0.0957359	+	0.995407i	$0.530520\pi$
$228$	6.56551e38	0.815349
$229$	−9.59263e38	−1.10829	−0.554144	−	0.832421i	$-0.686954\pi$
$229$	−9.59263e38	−1.10829	−0.554144	+	0.832421i	$0.686954\pi$
$230$	0	0
$231$	8.12044e38	0.812796
$232$	−1.17963e38	−0.109950
$233$	1.97860e39	1.71785	0.858926	−	0.512101i	$-0.171132\pi$
$233$	1.97860e39	1.71785	0.858926	+	0.512101i	$0.171132\pi$
$234$	−4.63594e38	−0.375039
$235$	0	0
$236$	8.11422e38	0.570425
$237$	7.93283e38	0.520092
$238$	−2.89257e39	−1.76915
$239$	1.90840e39	1.08919	0.544595	−	0.838699i	$-0.316683\pi$
$239$	1.90840e39	1.08919	0.544595	+	0.838699i	$0.316683\pi$
$240$	0	0
$241$	−1.40986e39	−0.701288	−0.350644	−	0.936509i	$-0.614037\pi$
$241$	−1.40986e39	−0.701288	−0.350644	+	0.936509i	$0.614037\pi$
$242$	−1.73768e39	−0.807266
$243$	1.42600e39	0.618893
$244$	3.33912e38	0.135425
$245$	0	0
$246$	1.86381e39	0.660651
$247$	5.19062e39	1.72076
$248$	−1.39882e39	−0.433820
$249$	−4.76314e38	−0.138231
$250$	0	0
$251$	−3.94267e39	−1.00271	−0.501353	−	0.865243i	$-0.667164\pi$
$251$	−3.94267e39	−1.00271	−0.501353	+	0.865243i	$0.667164\pi$
$252$	1.22413e39	0.291555
$253$	3.64513e39	0.813251
$254$	−4.34820e39	−0.908977
$255$	0	0
$256$	6.70033e39	1.23066
$257$	−5.83966e39	−1.00575	−0.502876	−	0.864359i	$-0.667725\pi$
$257$	−5.83966e39	−1.00575	−0.502876	+	0.864359i	$0.667725\pi$
$258$	9.66770e39	1.56170
$259$	−1.99042e39	−0.301646
$260$	0	0
$261$	−4.65656e38	−0.0621580
$262$	4.59254e39	0.575548
$263$	−2.07896e39	−0.244667	−0.122334	−	0.992489i	$-0.539038\pi$
$263$	−2.07896e39	−0.244667	−0.122334	+	0.992489i	$0.539038\pi$
$264$	2.51779e39	0.278327
$265$	0	0
$266$	−3.91798e40	−3.82398
$267$	4.63843e39	0.425535
$268$	−5.66759e38	−0.0488848
$269$	2.34730e39	0.190395	0.0951975	−	0.995458i	$-0.469652\pi$
$269$	2.34730e39	0.190395	0.0951975	+	0.995458i	$0.469652\pi$
$270$	0	0
$271$	3.12807e39	0.224534	0.112267	−	0.993678i	$-0.464189\pi$
$271$	3.12807e39	0.224534	0.112267	+	0.993678i	$0.464189\pi$
$272$	−1.57601e40	−1.06457
$273$	−2.02027e40	−1.28447
$274$	−1.22209e40	−0.731508
$275$	0	0
$276$	−1.14708e40	−0.608965
$277$	−3.37275e39	−0.168682	−0.0843409	−	0.996437i	$-0.526878\pi$
$277$	−3.37275e39	−0.168682	−0.0843409	+	0.996437i	$0.526878\pi$
$278$	−4.70321e40	−2.21644
$279$	−5.52183e39	−0.245252
$280$	0	0
$281$	1.89293e40	0.747276	0.373638	−	0.927575i	$-0.378110\pi$
$281$	1.89293e40	0.747276	0.373638	+	0.927575i	$0.378110\pi$
$282$	4.18366e39	0.155756
$283$	−2.24275e40	−0.787597	−0.393799	−	0.919197i	$-0.628839\pi$
$283$	−2.24275e40	−0.787597	−0.393799	+	0.919197i	$0.628839\pi$
$284$	−1.76957e40	−0.586293
$285$	0	0
$286$	−2.31837e40	−0.684138
$287$	−3.89083e40	−1.08391
$288$	1.20116e40	0.315955
$289$	−1.09897e40	−0.273004
$290$	0	0
$291$	−2.89026e40	−0.640770
$292$	2.14621e40	0.449631
$293$	3.48215e40	0.689495	0.344748	−	0.938695i	$-0.387964\pi$
$293$	3.48215e40	0.689495	0.344748	+	0.938695i	$0.387964\pi$
$294$	9.80154e40	1.83469
$295$	0	0
$296$	−6.17142e39	−0.103293
$297$	4.06256e40	0.643159
$298$	3.45415e40	0.517336
$299$	−9.06865e40	−1.28519
$300$	0	0
$301$	−2.01820e41	−2.56223
$302$	−1.02820e41	−1.23584
$303$	1.07680e41	1.22555
$304$	−2.13471e41	−2.30104
$305$	0	0
$306$	−3.54033e40	−0.342484
$307$	9.03462e40	0.828183	0.414092	−	0.910235i	$-0.364099\pi$
$307$	9.03462e40	0.828183	0.414092	+	0.910235i	$0.364099\pi$
$308$	6.12173e40	0.531847
$309$	1.93860e41	1.59651
$310$	0	0
$311$	1.95849e41	1.45002	0.725012	−	0.688737i	$-0.241834\pi$
$311$	1.95849e41	1.45002	0.725012	+	0.688737i	$0.241834\pi$
$312$	−6.26398e40	−0.439845
$313$	−3.62894e40	−0.241712	−0.120856	−	0.992670i	$-0.538564\pi$
$313$	−3.62894e40	−0.241712	−0.120856	+	0.992670i	$0.538564\pi$
$314$	6.47592e40	0.409225
$315$	0	0
$316$	5.98029e40	0.340319
$317$	1.28365e41	0.693377	0.346689	−	0.937980i	$-0.387306\pi$
$317$	1.28365e41	0.693377	0.346689	+	0.937980i	$0.387306\pi$
$318$	−8.23273e40	−0.422179
$319$	−2.32868e40	−0.113387
$320$	0	0
$321$	6.38196e40	0.280299
$322$	6.84520e41	2.85604
$323$	3.96392e41	1.57139
$324$	−8.15843e40	−0.307336
$325$	0	0
$326$	−3.82919e40	−0.130322
$327$	−2.46882e41	−0.798826
$328$	−1.20638e41	−0.371163
$329$	−8.73369e40	−0.255544
$330$	0	0
$331$	2.62324e41	0.694505	0.347253	−	0.937772i	$-0.387115\pi$
$331$	2.62324e41	0.694505	0.347253	+	0.937772i	$0.387115\pi$
$332$	−3.59077e40	−0.0904502
$333$	−2.43616e40	−0.0583949
$334$	9.39822e41	2.14402
$335$	0	0
$336$	8.30862e41	1.71763
$337$	−8.33065e41	−1.63978	−0.819890	−	0.572521i	$-0.805966\pi$
$337$	−8.33065e41	−1.63978	−0.819890	+	0.572521i	$0.805966\pi$
$338$	−8.48377e40	−0.159024
$339$	5.76609e40	0.102941
$340$	0	0
$341$	−2.76139e41	−0.447384
$342$	−4.79538e41	−0.740274
$343$	−9.08863e41	−1.33704
$344$	−6.25757e41	−0.877387
$345$	0	0
$346$	7.49404e41	0.954905
$347$	−8.33744e41	−1.01297	−0.506485	−	0.862249i	$-0.669055\pi$
$347$	−8.33744e41	−1.01297	−0.506485	+	0.862249i	$0.669055\pi$
$348$	7.32807e40	0.0849047
$349$	−9.38117e41	−1.03666	−0.518331	−	0.855180i	$-0.673447\pi$
$349$	−9.38117e41	−1.03666	−0.518331	+	0.855180i	$0.673447\pi$
$350$	0	0
$351$	−1.01072e42	−1.01639
$352$	6.00685e41	0.576358
$353$	−8.17332e41	−0.748369	−0.374184	−	0.927354i	$-0.622077\pi$
$353$	−8.17332e41	−0.748369	−0.374184	+	0.927354i	$0.622077\pi$
$354$	1.23718e42	1.08113
$355$	0	0
$356$	3.49676e41	0.278446
$357$	−1.54282e42	−1.17298
$358$	−1.16507e42	−0.845825
$359$	2.57757e42	1.78711	0.893557	−	0.448950i	$-0.148202\pi$
$359$	2.57757e42	1.78711	0.893557	+	0.448950i	$0.148202\pi$
$360$	0	0
$361$	3.78836e42	2.39653
$362$	3.80817e42	2.30157
$363$	−9.26834e41	−0.535233
$364$	−1.52301e42	−0.840487
$365$	0	0
$366$	5.09115e41	0.256672
$367$	−4.60710e41	−0.222043	−0.111022	−	0.993818i	$-0.535412\pi$
$367$	−4.60710e41	−0.222043	−0.111022	+	0.993818i	$0.535412\pi$
$368$	3.72960e42	1.71859
$369$	−4.76216e41	−0.209830
$370$	0	0
$371$	1.71864e42	0.692653
$372$	8.68974e41	0.335003
$373$	−3.71623e42	−1.37059	−0.685293	−	0.728267i	$-0.740326\pi$
$373$	−3.71623e42	−1.37059	−0.685293	+	0.728267i	$0.740326\pi$
$374$	−1.77047e42	−0.624752
$375$	0	0
$376$	−2.70794e41	−0.0875062
$377$	5.79349e41	0.179188
$378$	7.62909e42	2.25870
$379$	3.26125e41	0.0924351	0.0462175	−	0.998931i	$-0.485283\pi$
$379$	3.26125e41	0.0924351	0.0462175	+	0.998931i	$0.485283\pi$
$380$	0	0
$381$	−2.31922e42	−0.602670
$382$	3.14981e42	0.783859
$383$	−1.15184e41	−0.0274543	−0.0137272	−	0.999906i	$-0.504370\pi$
$383$	−1.15184e41	−0.0274543	−0.0137272	+	0.999906i	$0.504370\pi$
$384$	3.68628e42	0.841634
$385$	0	0
$386$	−4.39313e42	−0.920627
$387$	−2.47016e42	−0.496015
$388$	−2.17887e42	−0.419283
$389$	9.31961e42	1.71882	0.859408	−	0.511291i	$-0.170833\pi$
$389$	9.31961e42	1.71882	0.859408	+	0.511291i	$0.170833\pi$
$390$	0	0
$391$	−6.92546e42	−1.17363
$392$	−6.34419e42	−1.03076
$393$	2.44954e42	0.381599
$394$	−8.15035e42	−1.21755
$395$	0	0
$396$	7.49264e41	0.102959
$397$	3.26152e42	0.429909	0.214954	−	0.976624i	$-0.431040\pi$
$397$	3.26152e42	0.429909	0.214954	+	0.976624i	$0.431040\pi$
$398$	1.30314e43	1.64785
$399$	−2.08975e43	−2.53537
$400$	0	0
$401$	4.46379e42	0.498679	0.249340	−	0.968416i	$-0.419786\pi$
$401$	4.46379e42	0.498679	0.249340	+	0.968416i	$0.419786\pi$
$402$	−8.64137e41	−0.0926516
$403$	6.87001e42	0.707008
$404$	8.11765e42	0.801932
$405$	0	0
$406$	−4.37304e42	−0.398202
$407$	−1.21829e42	−0.106523
$408$	−4.78361e42	−0.401665
$409$	−6.27138e42	−0.505741	−0.252871	−	0.967500i	$-0.581375\pi$
$409$	−6.27138e42	−0.505741	−0.252871	+	0.967500i	$0.581375\pi$
$410$	0	0
$411$	−6.51832e42	−0.485004
$412$	1.46144e43	1.04467
$413$	−2.58269e43	−1.77377
$414$	8.37813e42	0.552893
$415$	0	0
$416$	−1.49443e43	−0.910828
$417$	−2.50857e43	−1.46954
$418$	−2.39811e43	−1.35039
$419$	−5.47353e42	−0.296303	−0.148152	−	0.988965i	$-0.547332\pi$
$419$	−5.47353e42	−0.296303	−0.148152	+	0.988965i	$0.547332\pi$
$420$	0	0
$421$	−1.46420e43	−0.732735	−0.366367	−	0.930470i	$-0.619399\pi$
$421$	−1.46420e43	−0.732735	−0.366367	+	0.930470i	$0.619399\pi$
$422$	1.27818e43	0.615086
$423$	−1.06895e42	−0.0494701
$424$	5.32876e42	0.237186
$425$	0	0
$426$	−2.69806e43	−1.11120
$427$	−1.06281e43	−0.421112
$428$	4.81114e42	0.183411
$429$	−1.23656e43	−0.453597
$430$	0	0
$431$	1.17291e43	0.398464	0.199232	−	0.979952i	$-0.436155\pi$
$431$	1.17291e43	0.398464	0.199232	+	0.979952i	$0.436155\pi$
$432$	4.15671e43	1.35915
$433$	−3.61098e43	−1.13651	−0.568257	−	0.822851i	$-0.692382\pi$
$433$	−3.61098e43	−1.13651	−0.568257	+	0.822851i	$0.692382\pi$
$434$	−5.18562e43	−1.57116
$435$	0	0
$436$	−1.86116e43	−0.522706
$437$	−9.38054e43	−2.53679
$438$	3.27233e43	0.852187
$439$	7.03437e43	1.76425	0.882125	−	0.471015i	$-0.156112\pi$
$439$	7.03437e43	1.76425	0.882125	+	0.471015i	$0.156112\pi$
$440$	0	0
$441$	−2.50436e43	−0.582720
$442$	4.40473e43	0.987306
$443$	6.56917e43	1.41856	0.709282	−	0.704925i	$-0.249019\pi$
$443$	6.56917e43	1.41856	0.709282	+	0.704925i	$0.249019\pi$
$444$	3.83380e42	0.0797646
$445$	0	0
$446$	9.36536e43	1.80925
$447$	1.84235e43	0.343004
$448$	−3.61201e42	−0.0648129
$449$	2.76233e43	0.477761	0.238880	−	0.971049i	$-0.423220\pi$
$449$	2.76233e43	0.477761	0.238880	+	0.971049i	$0.423220\pi$
$450$	0	0
$451$	−2.38149e43	−0.382768
$452$	4.34686e42	0.0673584
$453$	−5.48413e43	−0.819384
$454$	−1.64820e43	−0.237459
$455$	0	0
$456$	−6.47941e43	−0.868191
$457$	−5.02283e42	−0.0649130	−0.0324565	−	0.999473i	$-0.510333\pi$
$457$	−5.02283e42	−0.0649130	−0.0324565	+	0.999473i	$0.510333\pi$
$458$	−1.10260e44	−1.37447
$459$	−7.71855e43	−0.928168
$460$	0	0
$461$	4.36789e43	0.488885	0.244442	−	0.969664i	$-0.421395\pi$
$461$	4.36789e43	0.488885	0.244442	+	0.969664i	$0.421395\pi$
$462$	9.33380e43	1.00801
$463$	1.71715e44	1.78946	0.894730	−	0.446608i	$-0.147368\pi$
$463$	1.71715e44	1.78946	0.894730	+	0.446608i	$0.147368\pi$
$464$	−2.38265e43	−0.239614
$465$	0	0
$466$	2.27424e44	2.13044
$467$	−2.18196e43	−0.197296	−0.0986478	−	0.995122i	$-0.531452\pi$
$467$	−2.18196e43	−0.197296	−0.0986478	+	0.995122i	$0.531452\pi$
$468$	−1.86408e43	−0.162708
$469$	1.80395e43	0.152010
$470$	0	0
$471$	3.45409e43	0.271324
$472$	−8.00780e43	−0.607394
$473$	−1.23529e44	−0.904819
$474$	9.11815e43	0.645007
$475$	0	0
$476$	−1.16308e44	−0.767529
$477$	2.10352e43	0.134089
$478$	2.19355e44	1.35079
$479$	1.45915e44	0.868091	0.434045	−	0.900891i	$-0.357086\pi$
$479$	1.45915e44	0.868091	0.434045	+	0.900891i	$0.357086\pi$
$480$	0	0
$481$	3.03096e43	0.168339
$482$	−1.62053e44	−0.869722
$483$	3.65105e44	1.89361
$484$	−6.98709e43	−0.350226
$485$	0	0
$486$	1.63907e44	0.767538
$487$	4.30582e42	0.0194907	0.00974536	−	0.999953i	$-0.496898\pi$
$487$	4.30582e42	0.0194907	0.00974536	+	0.999953i	$0.496898\pi$
$488$	−3.29533e43	−0.144202
$489$	−2.04239e43	−0.0864058
$490$	0	0
$491$	4.25937e44	1.68461	0.842307	−	0.538998i	$-0.181197\pi$
$491$	4.25937e44	1.68461	0.842307	+	0.538998i	$0.181197\pi$
$492$	7.49424e43	0.286618
$493$	4.42432e43	0.163633
$494$	5.96620e44	2.13404
$495$	0	0
$496$	−2.82538e44	−0.945430
$497$	5.63240e44	1.82311
$498$	−5.47486e43	−0.171431
$499$	7.59554e43	0.230091	0.115046	−	0.993360i	$-0.463299\pi$
$499$	7.59554e43	0.230091	0.115046	+	0.993360i	$0.463299\pi$
$500$	0	0
$501$	5.01277e44	1.42153
$502$	−4.53178e44	−1.24353
$503$	−4.02949e44	−1.06999	−0.534994	−	0.844856i	$-0.679686\pi$
$503$	−4.02949e44	−1.06999	−0.534994	+	0.844856i	$0.679686\pi$
$504$	−1.20808e44	−0.310450
$505$	0	0
$506$	4.18979e44	1.00858
$507$	−4.52502e43	−0.105436
$508$	−1.74838e44	−0.394352
$509$	−7.18310e44	−1.56844	−0.784221	−	0.620482i	$-0.786937\pi$
$509$	−7.18310e44	−1.56844	−0.784221	+	0.620482i	$0.786937\pi$
$510$	0	0
$511$	−6.83123e44	−1.39815
$512$	2.53653e44	0.502674
$513$	−1.04548e45	−2.00622
$514$	−6.71222e44	−1.24731
$515$	0	0
$516$	3.88732e44	0.677532
$517$	−5.34569e43	−0.0902422
$518$	−2.28783e44	−0.374095
$519$	3.99713e44	0.633121
$520$	0	0
$521$	−1.09024e45	−1.62069	−0.810344	−	0.585955i	$-0.800720\pi$
$521$	−1.09024e45	−1.62069	−0.810344	+	0.585955i	$0.800720\pi$
$522$	−5.35235e43	−0.0770870
$523$	−2.49115e44	−0.347633	−0.173817	−	0.984778i	$-0.555610\pi$
$523$	−2.49115e44	−0.347633	−0.173817	+	0.984778i	$0.555610\pi$
$524$	1.84663e44	0.249697
$525$	0	0
$526$	−2.38960e44	−0.303431
$527$	5.24643e44	0.645637
$528$	5.08551e44	0.606562
$529$	7.73892e44	0.894667
$530$	0	0
$531$	−3.16107e44	−0.343379
$532$	−1.57539e45	−1.65900
$533$	5.92486e44	0.604894
$534$	5.33151e44	0.527739
$535$	0	0
$536$	5.59326e43	0.0520530
$537$	−6.21416e44	−0.560799
$538$	2.69803e44	0.236124
$539$	−1.25240e45	−1.06298
$540$	0	0
$541$	8.08608e44	0.645629	0.322814	−	0.946462i	$-0.395371\pi$
$541$	8.08608e44	0.645629	0.322814	+	0.946462i	$0.395371\pi$
$542$	3.59547e44	0.278463
$543$	2.03118e45	1.52599
$544$	−1.14125e45	−0.831765
$545$	0	0
$546$	−2.32214e45	−1.59298
$547$	−1.73824e45	−1.15696	−0.578481	−	0.815696i	$-0.696354\pi$
$547$	−1.73824e45	−1.15696	−0.578481	+	0.815696i	$0.696354\pi$
$548$	−4.91394e44	−0.317359
$549$	−1.30082e44	−0.0815220
$550$	0	0
$551$	5.99274e44	0.353691
$552$	1.13203e45	0.648431
$553$	−1.90348e45	−1.05824
$554$	−3.87671e44	−0.209195
$555$	0	0
$556$	−1.89113e45	−0.961583
$557$	1.55592e45	0.768029	0.384014	−	0.923327i	$-0.374541\pi$
$557$	1.55592e45	0.768029	0.384014	+	0.923327i	$0.374541\pi$
$558$	−6.34690e44	−0.304157
$559$	3.07327e45	1.42990
$560$	0	0
$561$	−9.44325e44	−0.414223
$562$	2.17578e45	0.926755
$563$	3.15388e45	1.30454	0.652270	−	0.757987i	$-0.273817\pi$
$563$	3.15388e45	1.30454	0.652270	+	0.757987i	$0.273817\pi$
$564$	1.68222e44	0.0675737
$565$	0	0
$566$	−2.57786e45	−0.976761
$567$	2.59676e45	0.955679
$568$	1.74636e45	0.624290
$569$	−3.00203e45	−1.04247	−0.521235	−	0.853413i	$-0.674528\pi$
$569$	−3.00203e45	−1.04247	−0.521235	+	0.853413i	$0.674528\pi$
$570$	0	0
$571$	−1.16838e45	−0.382903	−0.191452	−	0.981502i	$-0.561320\pi$
$571$	−1.16838e45	−0.382903	−0.191452	+	0.981502i	$0.561320\pi$
$572$	−9.32201e44	−0.296808
$573$	1.68003e45	0.519714
$574$	−4.47220e45	−1.34424
$575$	0	0
$576$	−4.42089e43	−0.0125470
$577$	3.87047e45	1.06749	0.533744	−	0.845646i	$-0.320784\pi$
$577$	3.87047e45	1.06749	0.533744	+	0.845646i	$0.320784\pi$
$578$	−1.26317e45	−0.338574
$579$	−2.34318e45	−0.610394
$580$	0	0
$581$	1.14292e45	0.281260
$582$	−3.32212e45	−0.794669
$583$	1.05194e45	0.244602
$584$	−2.11807e45	−0.478771
$585$	0	0
$586$	4.00245e45	0.855097
$587$	−1.28795e45	−0.267529	−0.133764	−	0.991013i	$-0.542707\pi$
$587$	−1.28795e45	−0.267529	−0.133764	+	0.991013i	$0.542707\pi$
$588$	3.94113e45	0.795966
$589$	7.10629e45	1.39553
$590$	0	0
$591$	−4.34718e45	−0.807262
$592$	−1.24652e45	−0.225108
$593$	−2.99374e45	−0.525789	−0.262895	−	0.964825i	$-0.584677\pi$
$593$	−2.99374e45	−0.525789	−0.262895	+	0.964825i	$0.584677\pi$
$594$	4.66959e45	0.797632
$595$	0	0
$596$	1.38889e45	0.224442
$597$	6.95059e45	1.09256
$598$	−1.04237e46	−1.59387
$599$	8.06321e45	1.19940	0.599702	−	0.800224i	$-0.295286\pi$
$599$	8.06321e45	1.19940	0.599702	+	0.800224i	$0.295286\pi$
$600$	0	0
$601$	1.61450e45	0.227305	0.113653	−	0.993521i	$-0.463745\pi$
$601$	1.61450e45	0.227305	0.113653	+	0.993521i	$0.463745\pi$
$602$	−2.31976e46	−3.17762
$603$	2.20793e44	0.0294272
$604$	−4.13430e45	−0.536158
$605$	0	0
$606$	1.23770e46	1.51991
$607$	−4.15288e45	−0.496291	−0.248146	−	0.968723i	$-0.579821\pi$
$607$	−4.15288e45	−0.496291	−0.248146	+	0.968723i	$0.579821\pi$
$608$	−1.54583e46	−1.79785
$609$	−2.33247e45	−0.264016
$610$	0	0
$611$	1.32994e45	0.142611
$612$	−1.42354e45	−0.148584
$613$	−1.06882e46	−1.08594	−0.542972	−	0.839751i	$-0.682701\pi$
$613$	−1.06882e46	−1.08594	−0.542972	+	0.839751i	$0.682701\pi$
$614$	1.03846e46	1.02709
$615$	0	0
$616$	−6.04144e45	−0.566316
$617$	5.25494e45	0.479581	0.239791	−	0.970825i	$-0.422921\pi$
$617$	5.25494e45	0.479581	0.239791	+	0.970825i	$0.422921\pi$
$618$	2.22826e46	1.97996
$619$	−8.16631e45	−0.706530	−0.353265	−	0.935523i	$-0.614929\pi$
$619$	−8.16631e45	−0.706530	−0.353265	+	0.935523i	$0.614929\pi$
$620$	0	0
$621$	1.82658e46	1.49840
$622$	2.25113e46	1.79829
$623$	−1.11299e46	−0.865842
$624$	−1.26522e46	−0.958559
$625$	0	0
$626$	−4.17118e45	−0.299766
$627$	−1.27909e46	−0.895336
$628$	2.60392e45	0.177539
$629$	2.31465e45	0.153727
$630$	0	0
$631$	2.01093e46	1.26740	0.633700	−	0.773579i	$-0.281536\pi$
$631$	2.01093e46	1.26740	0.633700	+	0.773579i	$0.281536\pi$
$632$	−5.90186e45	−0.362374
$633$	6.81747e45	0.407814
$634$	1.47546e46	0.859911
$635$	0	0
$636$	−3.31032e45	−0.183159
$637$	3.11581e46	1.67985
$638$	−2.67664e45	−0.140620
$639$	6.89373e45	0.352931
$640$	0	0
$641$	−7.81637e44	−0.0380056	−0.0190028	−	0.999819i	$-0.506049\pi$
$641$	−7.81637e44	−0.0380056	−0.0190028	+	0.999819i	$0.506049\pi$
$642$	7.33555e45	0.347620
$643$	1.16633e46	0.538690	0.269345	−	0.963044i	$-0.413193\pi$
$643$	1.16633e46	0.538690	0.269345	+	0.963044i	$0.413193\pi$
$644$	2.75241e46	1.23907
$645$	0	0
$646$	4.55621e46	1.94880
$647$	−2.67092e46	−1.11363	−0.556814	−	0.830637i	$-0.687976\pi$
$647$	−2.67092e46	−1.11363	−0.556814	+	0.830637i	$0.687976\pi$
$648$	8.05144e45	0.327255
$649$	−1.58081e46	−0.626385
$650$	0	0
$651$	−2.76588e46	−1.04171
$652$	−1.53969e45	−0.0565390
$653$	4.60253e46	1.64789	0.823946	−	0.566668i	$-0.191768\pi$
$653$	4.60253e46	1.64789	0.823946	+	0.566668i	$0.191768\pi$
$654$	−2.83772e46	−0.990686
$655$	0	0
$656$	−2.43668e46	−0.808881
$657$	−8.36103e45	−0.270665
$658$	−1.00387e46	−0.316920
$659$	4.83888e45	0.148983	0.0744913	−	0.997222i	$-0.476267\pi$
$659$	4.83888e45	0.148983	0.0744913	+	0.997222i	$0.476267\pi$
$660$	0	0
$661$	1.42709e46	0.417953	0.208976	−	0.977921i	$-0.432987\pi$
$661$	1.42709e46	0.417953	0.208976	+	0.977921i	$0.432987\pi$
$662$	3.01520e46	0.861310
$663$	2.34937e46	0.654603
$664$	3.54368e45	0.0963122
$665$	0	0
$666$	−2.80017e45	−0.0724201
$667$	−1.04701e46	−0.264163
$668$	3.77896e46	0.930166
$669$	4.99524e46	1.19957
$670$	0	0
$671$	−6.50524e45	−0.148711
$672$	6.01661e46	1.34202
$673$	−1.75051e46	−0.380993	−0.190496	−	0.981688i	$-0.561010\pi$
$673$	−1.75051e46	−0.380993	−0.190496	+	0.981688i	$0.561010\pi$
$674$	−9.57542e46	−2.03362
$675$	0	0
$676$	−3.41126e45	−0.0689914
$677$	−3.69547e45	−0.0729385	−0.0364693	−	0.999335i	$-0.511611\pi$
$677$	−3.69547e45	−0.0729385	−0.0364693	+	0.999335i	$0.511611\pi$
$678$	6.62766e45	0.127665
$679$	6.93517e46	1.30378
$680$	0	0
$681$	−8.79109e45	−0.157440
$682$	−3.17400e46	−0.554836
$683$	−4.71360e46	−0.804287	−0.402143	−	0.915577i	$-0.631735\pi$
$683$	−4.71360e46	−0.804287	−0.402143	+	0.915577i	$0.631735\pi$
$684$	−1.92819e46	−0.321162
$685$	0	0
$686$	−1.04467e47	−1.65817
$687$	−5.88097e46	−0.911302
$688$	−1.26392e47	−1.91210
$689$	−2.61710e46	−0.386548
$690$	0	0
$691$	−6.96899e46	−0.981256	−0.490628	−	0.871369i	$-0.663233\pi$
$691$	−6.96899e46	−0.981256	−0.490628	+	0.871369i	$0.663233\pi$
$692$	3.01330e46	0.414278
$693$	−2.38485e46	−0.320157
$694$	−9.58323e46	−1.25626
$695$	0	0
$696$	−7.23196e45	−0.0904073
$697$	4.52464e46	0.552387
$698$	−1.07829e47	−1.28565
$699$	1.21302e47	1.41252
$700$	0	0
$701$	1.69511e47	1.88300	0.941502	−	0.337007i	$-0.109415\pi$
$701$	1.69511e47	1.88300	0.941502	+	0.337007i	$0.109415\pi$
$702$	−1.16174e47	−1.26051
$703$	3.13520e46	0.332278
$704$	−2.21083e45	−0.0228879
$705$	0	0
$706$	−9.39458e46	−0.928110
$707$	−2.58378e47	−2.49365
$708$	4.97459e46	0.469039
$709$	−9.17561e46	−0.845224	−0.422612	−	0.906311i	$-0.638887\pi$
$709$	−9.17561e46	−0.845224	−0.422612	+	0.906311i	$0.638887\pi$
$710$	0	0
$711$	−2.32975e46	−0.204862
$712$	−3.45090e46	−0.296492
$713$	−1.24156e47	−1.04229
$714$	−1.77335e47	−1.45470
$715$	0	0
$716$	−4.68465e46	−0.366954
$717$	1.16998e47	0.895600
$718$	2.96271e47	2.21634
$719$	−1.82786e46	−0.133634	−0.0668169	−	0.997765i	$-0.521284\pi$
$719$	−1.82786e46	−0.133634	−0.0668169	+	0.997765i	$0.521284\pi$
$720$	0	0
$721$	−4.65166e47	−3.24845
$722$	4.35442e47	2.97212
$723$	−8.64348e46	−0.576642
$724$	1.53124e47	0.998519
$725$	0	0
$726$	−1.06532e47	−0.663784
$727$	−1.06219e47	−0.646968	−0.323484	−	0.946234i	$-0.604854\pi$
$727$	−1.06219e47	−0.646968	−0.323484	+	0.946234i	$0.604854\pi$
$728$	1.50304e47	0.894958
$729$	1.85554e47	1.08011
$730$	0	0
$731$	2.34696e47	1.30578
$732$	2.04712e46	0.111355
$733$	−1.43149e47	−0.761328	−0.380664	−	0.924713i	$-0.624305\pi$
$733$	−1.43149e47	−0.761328	−0.380664	+	0.924713i	$0.624305\pi$
$734$	−5.29550e46	−0.275373
$735$	0	0
$736$	2.70075e47	1.34277
$737$	1.10415e46	0.0536805
$738$	−5.47372e46	−0.260227
$739$	−4.66202e46	−0.216741	−0.108370	−	0.994111i	$-0.534563\pi$
$739$	−4.66202e46	−0.216741	−0.108370	+	0.994111i	$0.534563\pi$
$740$	0	0
$741$	3.18222e47	1.41491
$742$	1.97544e47	0.859013
$743$	2.31079e47	0.982753	0.491376	−	0.870947i	$-0.336494\pi$
$743$	2.31079e47	0.982753	0.491376	+	0.870947i	$0.336494\pi$
$744$	−8.57578e46	−0.356714
$745$	0	0
$746$	−4.27151e47	−1.69977
$747$	1.39886e46	0.0544484
$748$	−7.11895e46	−0.271044
$749$	−1.53135e47	−0.570327
$750$	0	0
$751$	3.21140e47	1.14455	0.572276	−	0.820061i	$-0.306061\pi$
$751$	3.21140e47	1.14455	0.572276	+	0.820061i	$0.306061\pi$
$752$	−5.46957e46	−0.190703
$753$	−2.41714e47	−0.824488
$754$	6.65915e46	0.222224
$755$	0	0
$756$	3.06760e47	0.979918
$757$	−1.82914e47	−0.571697	−0.285848	−	0.958275i	$-0.592275\pi$
$757$	−1.82914e47	−0.571697	−0.285848	+	0.958275i	$0.592275\pi$
$758$	3.74854e46	0.114636
$759$	2.23472e47	0.668705
$760$	0	0
$761$	2.41723e47	0.692583	0.346291	−	0.938127i	$-0.387441\pi$
$761$	2.41723e47	0.692583	0.346291	+	0.938127i	$0.387441\pi$
$762$	−2.66576e47	−0.747418
$763$	5.92394e47	1.62538
$764$	1.26651e47	0.340071
$765$	0	0
$766$	−1.32394e46	−0.0340482
$767$	3.93286e47	0.989885
$768$	4.10778e47	1.01192
$769$	6.03900e47	1.45606	0.728032	−	0.685543i	$-0.240435\pi$
$769$	6.03900e47	1.45606	0.728032	+	0.685543i	$0.240435\pi$
$770$	0	0
$771$	−3.58013e47	−0.826991
$772$	−1.76645e47	−0.399407
$773$	−6.05174e47	−1.33943	−0.669713	−	0.742620i	$-0.733583\pi$
$773$	−6.05174e47	−1.33943	−0.669713	+	0.742620i	$0.733583\pi$
$774$	−2.83926e47	−0.615147
$775$	0	0
$776$	2.15029e47	0.446457
$777$	−1.22027e47	−0.248032
$778$	1.07121e48	2.13164
$779$	6.12863e47	1.19398
$780$	0	0
$781$	3.44746e47	0.643809
$782$	−7.96027e47	−1.45551
$783$	−1.16691e47	−0.208914
$784$	−1.28142e48	−2.24634
$785$	0	0
$786$	2.81555e47	0.473251
$787$	9.28560e47	1.52836	0.764182	−	0.645001i	$-0.223143\pi$
$787$	9.28560e47	1.52836	0.764182	+	0.645001i	$0.223143\pi$
$788$	−3.27720e47	−0.528226
$789$	−1.27455e47	−0.201181
$790$	0	0
$791$	−1.38357e47	−0.209455
$792$	−7.39438e46	−0.109632
$793$	1.61843e47	0.235010
$794$	3.74886e47	0.533163
$795$	0	0
$796$	5.23982e47	0.714908
$797$	−9.79619e47	−1.30917	−0.654583	−	0.755990i	$-0.727156\pi$
$797$	−9.79619e47	−1.30917	−0.654583	+	0.755990i	$0.727156\pi$
$798$	−2.40200e48	−3.14431
$799$	1.01564e47	0.130232
$800$	0	0
$801$	−1.36224e47	−0.167616
$802$	5.13077e47	0.618451
$803$	−4.18124e47	−0.493740
$804$	−3.47463e46	−0.0401961
$805$	0	0
$806$	7.89653e47	0.876816
$807$	1.43906e47	0.156555
$808$	−8.01119e47	−0.853905
$809$	1.24773e48	1.30308	0.651538	−	0.758616i	$-0.274124\pi$
$809$	1.24773e48	1.30308	0.651538	+	0.758616i	$0.274124\pi$
$810$	0	0
$811$	8.60037e47	0.862329	0.431165	−	0.902273i	$-0.358103\pi$
$811$	8.60037e47	0.862329	0.431165	+	0.902273i	$0.358103\pi$
$812$	−1.75837e47	−0.172757
$813$	1.91773e47	0.184626
$814$	−1.40033e47	−0.132107
$815$	0	0
$816$	−9.66208e47	−0.875353
$817$	3.17896e48	2.82242
$818$	−7.20845e47	−0.627209
$819$	5.93322e47	0.505948
$820$	0	0
$821$	1.92448e48	1.57635	0.788174	−	0.615453i	$-0.211027\pi$
$821$	1.92448e48	1.57635	0.788174	+	0.615453i	$0.211027\pi$
$822$	−7.49229e47	−0.601491
$823$	1.38046e48	1.08624	0.543122	−	0.839654i	$-0.317242\pi$
$823$	1.38046e48	1.08624	0.543122	+	0.839654i	$0.317242\pi$
$824$	−1.44228e48	−1.11237
$825$	0	0
$826$	−2.96860e48	−2.19979
$827$	−1.55530e48	−1.12973	−0.564863	−	0.825184i	$-0.691071\pi$
$827$	−1.55530e48	−1.12973	−0.564863	+	0.825184i	$0.691071\pi$
$828$	3.36879e47	0.239868
$829$	2.23465e48	1.55977	0.779883	−	0.625925i	$-0.215278\pi$
$829$	2.23465e48	1.55977	0.779883	+	0.625925i	$0.215278\pi$
$830$	0	0
$831$	−2.06774e47	−0.138701
$832$	5.50027e46	0.0361701
$833$	2.37945e48	1.53403
$834$	−2.88340e48	−1.82249
$835$	0	0
$836$	−9.64261e47	−0.585856
$837$	−1.38374e48	−0.824296
$838$	−6.29139e47	−0.367469
$839$	−8.98826e47	−0.514758	−0.257379	−	0.966311i	$-0.582859\pi$
$839$	−8.98826e47	−0.514758	−0.257379	+	0.966311i	$0.582859\pi$
$840$	0	0
$841$	−1.74919e48	−0.963169
$842$	−1.68298e48	−0.908721
$843$	1.16050e48	0.614456
$844$	5.13946e47	0.266850
$845$	0	0
$846$	−1.22868e47	−0.0613517
$847$	2.22394e48	1.08905
$848$	1.07632e48	0.516903
$849$	−1.37496e48	−0.647612
$850$	0	0
$851$	−5.47758e47	−0.248171
$852$	−1.08487e48	−0.482087
$853$	8.48820e47	0.369962	0.184981	−	0.982742i	$-0.440778\pi$
$853$	8.48820e47	0.369962	0.184981	+	0.982742i	$0.440778\pi$
$854$	−1.22162e48	−0.522254
$855$	0	0
$856$	−4.74805e47	−0.195298
$857$	−1.03658e48	−0.418233	−0.209117	−	0.977891i	$-0.567059\pi$
$857$	−1.03658e48	−0.418233	−0.209117	+	0.977891i	$0.567059\pi$
$858$	−1.42133e48	−0.562541
$859$	2.13979e48	0.830777	0.415389	−	0.909644i	$-0.363646\pi$
$859$	2.13979e48	0.830777	0.415389	+	0.909644i	$0.363646\pi$
$860$	0	0
$861$	−2.38536e48	−0.891254
$862$	1.34816e48	0.494166
$863$	−2.94316e48	−1.05837	−0.529183	−	0.848508i	$-0.677502\pi$
$863$	−2.94316e48	−1.05837	−0.529183	+	0.848508i	$0.677502\pi$
$864$	3.01004e48	1.06193
$865$	0	0
$866$	−4.15053e48	−1.40948
$867$	−6.73744e47	−0.224481
$868$	−2.08510e48	−0.681635
$869$	−1.16508e48	−0.373704
$870$	0	0
$871$	−2.74701e47	−0.0848321
$872$	1.83675e48	0.556582
$873$	8.48825e47	0.252396
$874$	−1.07822e49	−3.14607
$875$	0	0
$876$	1.31578e48	0.369714
$877$	5.36775e48	1.48013	0.740064	−	0.672537i	$-0.234795\pi$
$877$	5.36775e48	1.48013	0.740064	+	0.672537i	$0.234795\pi$
$878$	8.08544e48	2.18798
$879$	2.13480e48	0.566946
$880$	0	0
$881$	2.27380e48	0.581633	0.290817	−	0.956779i	$-0.406073\pi$
$881$	2.27380e48	0.581633	0.290817	+	0.956779i	$0.406073\pi$
$882$	−2.87856e48	−0.722676
$883$	8.98895e47	0.221492	0.110746	−	0.993849i	$-0.464676\pi$
$883$	8.98895e47	0.221492	0.110746	+	0.993849i	$0.464676\pi$
$884$	1.77111e48	0.428335
$885$	0	0
$886$	7.55074e48	1.75927
$887$	2.83277e48	0.647847	0.323923	−	0.946083i	$-0.394998\pi$
$887$	2.83277e48	0.647847	0.323923	+	0.946083i	$0.394998\pi$
$888$	−3.78352e47	−0.0849341
$889$	5.56496e48	1.22626
$890$	0	0
$891$	1.58942e48	0.337486
$892$	3.76574e48	0.784930
$893$	1.37568e48	0.281494
$894$	2.11764e48	0.425386
$895$	0	0
$896$	−8.84523e48	−1.71248
$897$	−5.55973e48	−1.05677
$898$	3.17508e48	0.592508
$899$	7.93165e47	0.145321
$900$	0	0
$901$	−1.99861e48	−0.352995
$902$	−2.73733e48	−0.474700
$903$	−1.23730e49	−2.10682
$904$	−4.28985e47	−0.0717238
$905$	0	0
$906$	−6.30357e48	−1.01618
$907$	6.13917e48	0.971828	0.485914	−	0.874007i	$-0.338487\pi$
$907$	6.13917e48	0.971828	0.485914	+	0.874007i	$0.338487\pi$
$908$	−6.62730e47	−0.103020
$909$	−3.16240e48	−0.482740
$910$	0	0
$911$	−2.28503e48	−0.336387	−0.168193	−	0.985754i	$-0.553793\pi$
$911$	−2.28503e48	−0.336387	−0.168193	+	0.985754i	$0.553793\pi$
$912$	−1.30873e49	−1.89206
$913$	6.99552e47	0.0993235
$914$	−5.77335e47	−0.0805036
$915$	0	0
$916$	−4.43346e48	−0.596304
$917$	−5.87767e48	−0.776445
$918$	−8.87186e48	−1.15109
$919$	−5.63252e48	−0.717788	−0.358894	−	0.933378i	$-0.616846\pi$
$919$	−5.63252e48	−0.717788	−0.358894	+	0.933378i	$0.616846\pi$
$920$	0	0
$921$	5.53886e48	0.680984
$922$	5.02054e48	0.606304
$923$	−8.57687e48	−1.01742
$924$	3.75305e48	0.437318
$925$	0	0
$926$	1.97373e49	2.21925
$927$	−5.69337e48	−0.628859
$928$	−1.72537e48	−0.187215
$929$	1.44930e49	1.54489	0.772446	−	0.635080i	$-0.219033\pi$
$929$	1.44930e49	1.54489	0.772446	+	0.635080i	$0.219033\pi$
$930$	0	0
$931$	3.22297e49	3.31579
$932$	9.14458e48	0.924275
$933$	1.20069e49	1.19230
$934$	−2.50798e48	−0.244682
$935$	0	0
$936$	1.83963e48	0.173253
$937$	5.08727e48	0.470741	0.235370	−	0.971906i	$-0.424370\pi$
$937$	5.08727e48	0.470741	0.235370	+	0.971906i	$0.424370\pi$
$938$	2.07349e48	0.188519
$939$	−2.22480e48	−0.198751
$940$	0	0
$941$	−1.08712e49	−0.937669	−0.468835	−	0.883286i	$-0.655326\pi$
$941$	−1.08712e49	−0.937669	−0.468835	+	0.883286i	$0.655326\pi$
$942$	3.97020e48	0.336490
$943$	−1.07075e49	−0.891752
$944$	−1.61744e49	−1.32370
$945$	0	0
$946$	−1.41987e49	−1.12214
$947$	−1.44245e49	−1.12028	−0.560139	−	0.828399i	$-0.689252\pi$
$947$	−1.44245e49	−1.12028	−0.560139	+	0.828399i	$0.689252\pi$
$948$	3.66635e48	0.279831
$949$	1.04024e49	0.780265
$950$	0	0
$951$	7.86970e48	0.570138
$952$	1.14783e49	0.817272
$953$	−1.16910e49	−0.818126	−0.409063	−	0.912506i	$-0.634144\pi$
$953$	−1.16910e49	−0.818126	−0.409063	+	0.912506i	$0.634144\pi$
$954$	2.41783e48	0.166294
$955$	0	0
$956$	8.82012e48	0.586029
$957$	−1.42765e48	−0.0932340
$958$	1.67718e49	1.07659
$959$	1.56407e49	0.986845
$960$	0	0
$961$	−6.99800e48	−0.426617
$962$	3.48384e48	0.208771
$963$	−1.87428e48	−0.110408
$964$	−6.51603e48	−0.377322
$965$	0	0
$966$	4.19659e49	2.34841
$967$	−2.42971e49	−1.33665	−0.668325	−	0.743869i	$-0.732988\pi$
$967$	−2.42971e49	−1.33665	−0.668325	+	0.743869i	$0.732988\pi$
$968$	6.89546e48	0.372924
$969$	2.43017e49	1.29209
$970$	0	0
$971$	−3.35304e49	−1.72314	−0.861571	−	0.507637i	$-0.830519\pi$
$971$	−3.35304e49	−1.72314	−0.861571	+	0.507637i	$0.830519\pi$
$972$	6.59060e48	0.332990
$973$	6.01931e49	2.99009
$974$	4.94920e47	0.0241720
$975$	0	0
$976$	−6.65599e48	−0.314261
$977$	−1.40753e49	−0.653426	−0.326713	−	0.945124i	$-0.605941\pi$
$977$	−1.40753e49	−0.653426	−0.326713	+	0.945124i	$0.605941\pi$
$978$	−2.34757e48	−0.107159
$979$	−6.81236e48	−0.305762
$980$	0	0
$981$	7.25056e48	0.314654
$982$	4.89580e49	2.08922
$983$	−4.27099e49	−1.79224	−0.896118	−	0.443816i	$-0.853624\pi$
$983$	−4.27099e49	−1.79224	−0.896118	+	0.443816i	$0.853624\pi$
$984$	−7.39596e48	−0.305193
$985$	0	0
$986$	5.08540e48	0.202935
$987$	−5.35437e48	−0.210124
$988$	2.39897e49	0.925838
$989$	−5.55404e49	−2.10800
$990$	0	0
$991$	−1.10871e49	−0.407008	−0.203504	−	0.979074i	$-0.565233\pi$
$991$	−1.10871e49	−0.407008	−0.203504	+	0.979074i	$0.565233\pi$
$992$	−2.04597e49	−0.738681
$993$	1.60823e49	0.571065
$994$	6.47399e49	2.26098
$995$	0	0
$996$	−2.20140e48	−0.0743738
$997$	2.30126e49	0.764709	0.382354	−	0.924016i	$-0.375113\pi$
$997$	2.30126e49	0.764709	0.382354	+	0.924016i	$0.375113\pi$
$998$	8.73047e48	0.285354
$999$	−6.10486e48	−0.196266

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.34.a.f.1.13		16
5.2	odd	4		5.34.b.a.4.13	yes	16
5.3	odd	4		5.34.b.a.4.4	✓	16
5.4	even	2	inner	25.34.a.f.1.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.34.b.a.4.4	✓	16	5.3	odd	4
5.34.b.a.4.13	yes	16	5.2	odd	4
25.34.a.f.1.4		16	5.4	even	2	inner
25.34.a.f.1.13		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)

\(f(q)\)	\(=\)	\(q+114942. q^{2} +6.13071e7 q^{3} +4.62174e9 q^{4} +7.04677e12 q^{6} -1.47106e14 q^{7} -4.56113e14 q^{8} -1.80050e15 q^{9} +O(q^{10})\)	\(q+114942. q^{2} +6.13071e7 q^{3} +4.62174e9 q^{4} +7.04677e12 q^{6} -1.47106e14 q^{7} -4.56113e14 q^{8} -1.80050e15 q^{9} -9.00404e16 q^{11} +2.83345e17 q^{12} +2.24010e18 q^{13} -1.69087e19 q^{14} -9.21269e19 q^{16} +1.71070e20 q^{17} -2.06953e20 q^{18} +2.31714e21 q^{19} -9.01867e21 q^{21} -1.03494e22 q^{22} -4.04833e22 q^{23} -2.79630e22 q^{24} +2.57481e23 q^{26} -4.51193e23 q^{27} -6.79887e23 q^{28} +2.58627e23 q^{29} +3.06684e24 q^{31} -6.67128e24 q^{32} -5.52012e24 q^{33} +1.96631e25 q^{34} -8.32142e24 q^{36} +1.35305e25 q^{37} +2.66337e26 q^{38} +1.37334e26 q^{39} +2.64491e26 q^{41} -1.03662e27 q^{42} +1.37193e27 q^{43} -4.16143e26 q^{44} -4.65323e27 q^{46} +5.93699e26 q^{47} -5.64804e27 q^{48} +1.39093e28 q^{49} +1.04878e28 q^{51} +1.03531e28 q^{52} -1.16830e28 q^{53} -5.18611e28 q^{54} +6.70970e28 q^{56} +1.42057e29 q^{57} +2.97271e28 q^{58} +1.75566e29 q^{59} +7.22481e28 q^{61} +3.52508e29 q^{62} +2.64864e29 q^{63} +2.45537e28 q^{64} -6.34493e29 q^{66} -1.22629e29 q^{67} +7.90639e29 q^{68} -2.48191e30 q^{69} -3.82879e30 q^{71} +8.21229e29 q^{72} +4.64374e30 q^{73} +1.55522e30 q^{74} +1.07092e31 q^{76} +1.32455e31 q^{77} +1.57854e31 q^{78} +1.29395e31 q^{79} -1.76523e31 q^{81} +3.04012e31 q^{82} -7.76932e30 q^{83} -4.16819e31 q^{84} +1.57693e32 q^{86} +1.58557e31 q^{87} +4.10685e31 q^{88} +7.56590e31 q^{89} -3.29533e32 q^{91} -1.87103e32 q^{92} +1.88019e32 q^{93} +6.82410e31 q^{94} -4.08997e32 q^{96} -4.71439e32 q^{97} +1.59876e33 q^{98} +1.62117e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 72851326872 q^{4} + 11001777346872 q^{6} + 27\!\cdots\!68 q^{9}+O(q^{10}) \) 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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