LMFDB - Embedded newform 25.34.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("25.1");

S:= CuspForms(chi, 34);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$172.457072203$
Analytic rank:	$0$
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			1.1
Root			$-81004.3$ 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)

$f(q)$	$=$	$q-162009. q^{2} +1.50582e7 q^{3} +1.76568e10 q^{4} -2.43956e12 q^{6} -1.33679e14 q^{7} -1.46891e15 q^{8} -5.33231e15 q^{9} +O(q^{10})$	\(q-162009. q^{2} +1.50582e7 q^{3} +1.76568e10 q^{4} -2.43956e12 q^{6} -1.33679e14 q^{7} -1.46891e15 q^{8} -5.33231e15 q^{9} +2.82007e17 q^{11} +2.65881e17 q^{12} +1.43267e18 q^{13} +2.16571e19 q^{14} +8.63057e19 q^{16} -2.38442e20 q^{17} +8.63880e20 q^{18} -5.86844e20 q^{19} -2.01297e21 q^{21} -4.56875e22 q^{22} -1.73446e22 q^{23} -2.21193e22 q^{24} -2.32104e23 q^{26} -1.64005e23 q^{27} -2.36034e24 q^{28} -1.13413e23 q^{29} +2.12133e24 q^{31} -1.36438e24 q^{32} +4.24652e24 q^{33} +3.86296e25 q^{34} -9.41517e25 q^{36} +8.11541e25 q^{37} +9.50738e25 q^{38} +2.15734e25 q^{39} -1.96159e26 q^{41} +3.26118e26 q^{42} -8.68674e26 q^{43} +4.97935e27 q^{44} +2.80997e27 q^{46} -5.03480e27 q^{47} +1.29961e27 q^{48} +1.01390e28 q^{49} -3.59051e27 q^{51} +2.52963e28 q^{52} -7.43106e27 q^{53} +2.65702e28 q^{54} +1.96363e29 q^{56} -8.83684e27 q^{57} +1.83740e28 q^{58} +5.72962e28 q^{59} -2.92431e29 q^{61} -3.43673e29 q^{62} +7.12817e29 q^{63} -5.20320e29 q^{64} -6.87973e29 q^{66} +8.52723e29 q^{67} -4.21013e30 q^{68} -2.61178e29 q^{69} -1.52022e30 q^{71} +7.83271e30 q^{72} +1.66290e30 q^{73} -1.31477e31 q^{74} -1.03618e31 q^{76} -3.76983e31 q^{77} -3.49508e30 q^{78} +2.86123e31 q^{79} +2.71730e31 q^{81} +3.17794e31 q^{82} +1.27605e30 q^{83} -3.55426e31 q^{84} +1.40733e32 q^{86} -1.70781e30 q^{87} -4.14244e32 q^{88} +1.21015e32 q^{89} -1.91517e32 q^{91} -3.06250e32 q^{92} +3.19435e31 q^{93} +8.15681e32 q^{94} -2.05451e31 q^{96} -9.03160e32 q^{97} -1.64261e33 q^{98} -1.50375e33 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−162009.	−1.74801	−0.874003	−	0.485920i	$-0.838485\pi$
$2$	−162009.	−1.74801	−0.874003	+	0.485920i	$0.838485\pi$
$3$	1.50582e7	0.201964	0.100982	−	0.994888i	$-0.467802\pi$
$3$	1.50582e7	0.201964	0.100982	+	0.994888i	$0.467802\pi$
$4$	1.76568e10	2.05553
$5$	0	0
$5$	0	0
$6$	−2.43956e12	−0.353034
$7$	−1.33679e14	−1.52035	−0.760177	−	0.649716i	$-0.774888\pi$
$7$	−1.33679e14	−1.52035	−0.760177	+	0.649716i	$0.774888\pi$
$8$	−1.46891e15	−1.84507
$9$	−5.33231e15	−0.959211
$10$	0	0
$11$	2.82007e17	1.85046	0.925231	−	0.379403i	$-0.123871\pi$
$11$	2.82007e17	1.85046	0.925231	+	0.379403i	$0.123871\pi$
$12$	2.65881e17	0.415141
$13$	1.43267e18	0.597145	0.298572	−	0.954387i	$-0.403490\pi$
$13$	1.43267e18	0.597145	0.298572	+	0.954387i	$0.403490\pi$
$14$	2.16571e19	2.65759
$15$	0	0
$16$	8.63057e19	1.16966
$17$	−2.38442e20	−1.18843	−0.594217	−	0.804304i	$-0.702538\pi$
$17$	−2.38442e20	−1.18843	−0.594217	+	0.804304i	$0.702538\pi$
$18$	8.63880e20	1.67671
$19$	−5.86844e20	−0.466754	−0.233377	−	0.972386i	$-0.574978\pi$
$19$	−5.86844e20	−0.466754	−0.233377	+	0.972386i	$0.574978\pi$
$20$	0	0
$21$	−2.01297e21	−0.307056
$22$	−4.56875e22	−3.23462
$23$	−1.73446e22	−0.589731	−0.294866	−	0.955539i	$-0.595275\pi$
$23$	−1.73446e22	−0.589731	−0.294866	+	0.955539i	$0.595275\pi$
$24$	−2.21193e22	−0.372636
$25$	0	0
$26$	−2.32104e23	−1.04381
$27$	−1.64005e23	−0.395689
$28$	−2.36034e24	−3.12513
$29$	−1.13413e23	−0.0841585	−0.0420792	−	0.999114i	$-0.513398\pi$
$29$	−1.13413e23	−0.0841585	−0.0420792	+	0.999114i	$0.513398\pi$
$30$	0	0
$31$	2.12133e24	0.523769	0.261885	−	0.965099i	$-0.415656\pi$
$31$	2.12133e24	0.523769	0.261885	+	0.965099i	$0.415656\pi$
$32$	−1.36438e24	−0.199507
$33$	4.24652e24	0.373726
$34$	3.86296e25	2.07739
$35$	0	0
$36$	−9.41517e25	−1.97168
$37$	8.11541e25	1.08139	0.540695	−	0.841219i	$-0.318161\pi$
$37$	8.11541e25	1.08139	0.540695	+	0.841219i	$0.318161\pi$
$38$	9.50738e25	0.815890
$39$	2.15734e25	0.120602
$40$	0	0
$41$	−1.96159e26	−0.480478	−0.240239	−	0.970714i	$-0.577226\pi$
$41$	−1.96159e26	−0.480478	−0.240239	+	0.970714i	$0.577226\pi$
$42$	3.26118e26	0.536736
$43$	−8.68674e26	−0.969677	−0.484838	−	0.874604i	$-0.661122\pi$
$43$	−8.68674e26	−0.969677	−0.484838	+	0.874604i	$0.661122\pi$
$44$	4.97935e27	3.80367
$45$	0	0
$46$	2.80997e27	1.03085
$47$	−5.03480e27	−1.29529	−0.647646	−	0.761941i	$-0.724246\pi$
$47$	−5.03480e27	−1.29529	−0.647646	+	0.761941i	$0.724246\pi$
$48$	1.29961e27	0.236229
$49$	1.01390e28	1.31148
$50$	0	0
$51$	−3.59051e27	−0.240021
$52$	2.52963e28	1.22745
$53$	−7.43106e27	−0.263329	−0.131665	−	0.991294i	$-0.542032\pi$
$53$	−7.43106e27	−0.263329	−0.131665	+	0.991294i	$0.542032\pi$
$54$	2.65702e28	0.691667
$55$	0	0
$56$	1.96363e29	2.80515
$57$	−8.83684e27	−0.0942674
$58$	1.83740e28	0.147110
$59$	5.72962e28	0.345993	0.172997	−	0.984922i	$-0.444655\pi$
$59$	5.72962e28	0.345993	0.172997	+	0.984922i	$0.444655\pi$
$60$	0	0
$61$	−2.92431e29	−1.01878	−0.509392	−	0.860535i	$-0.670129\pi$
$61$	−2.92431e29	−1.01878	−0.509392	+	0.860535i	$0.670129\pi$
$62$	−3.43673e29	−0.915552
$63$	7.12817e29	1.45834
$64$	−5.20320e29	−0.820920
$65$	0	0
$66$	−6.87973e29	−0.653276
$67$	8.52723e29	0.631791	0.315896	−	0.948794i	$-0.397695\pi$
$67$	8.52723e29	0.631791	0.315896	+	0.948794i	$0.397695\pi$
$68$	−4.21013e30	−2.44286
$69$	−2.61178e29	−0.119104
$70$	0	0
$71$	−1.52022e30	−0.432656	−0.216328	−	0.976321i	$-0.569408\pi$
$71$	−1.52022e30	−0.432656	−0.216328	+	0.976321i	$0.569408\pi$
$72$	7.83271e30	1.76981
$73$	1.66290e30	0.299253	0.149627	−	0.988743i	$-0.452193\pi$
$73$	1.66290e30	0.299253	0.149627	+	0.988743i	$0.452193\pi$
$74$	−1.31477e31	−1.89028
$75$	0	0
$76$	−1.03618e31	−0.959426
$77$	−3.76983e31	−2.81336
$78$	−3.49508e30	−0.210812
$79$	2.86123e31	1.39864	0.699319	−	0.714810i	$-0.253487\pi$
$79$	2.86123e31	1.39864	0.699319	+	0.714810i	$0.253487\pi$
$80$	0	0
$81$	2.71730e31	0.879296
$82$	3.17794e31	0.839879
$83$	1.27605e30	0.0276109	0.0138054	−	0.999905i	$-0.495605\pi$
$83$	1.27605e30	0.0276109	0.0138054	+	0.999905i	$0.495605\pi$
$84$	−3.55426e31	−0.631162
$85$	0	0
$86$	1.40733e32	1.69500
$87$	−1.70781e30	−0.0169969
$88$	−4.14244e32	−3.41422
$89$	1.21015e32	0.827762	0.413881	−	0.910331i	$-0.364173\pi$
$89$	1.21015e32	0.827762	0.413881	+	0.910331i	$0.364173\pi$
$90$	0	0
$91$	−1.91517e32	−0.907872
$92$	−3.06250e32	−1.21221
$93$	3.19435e31	0.105782
$94$	8.15681e32	2.26418
$95$	0	0
$96$	−2.05451e31	−0.0402933
$97$	−9.03160e32	−1.49290	−0.746451	−	0.665441i	$-0.768244\pi$
$97$	−9.03160e32	−1.49290	−0.746451	+	0.665441i	$0.768244\pi$
$98$	−1.64261e33	−2.29247
$99$	−1.50375e33	−1.77498
$100$	0	0
$101$	−1.32921e33	−1.12795	−0.563976	−	0.825791i	$-0.690729\pi$
$101$	−1.32921e33	−1.12795	−0.563976	+	0.825791i	$0.690729\pi$
$102$	5.81694e32	0.419558
$103$	−2.85224e33	−1.75135	−0.875673	−	0.482905i	$-0.839582\pi$
$103$	−2.85224e33	−1.75135	−0.875673	+	0.482905i	$0.839582\pi$
$104$	−2.10446e33	−1.10177
$105$	0	0
$106$	1.20389e33	0.460301
$107$	3.50122e32	0.114654	0.0573268	−	0.998355i	$-0.481742\pi$
$107$	3.50122e32	0.114654	0.0573268	+	0.998355i	$0.481742\pi$
$108$	−2.89580e33	−0.813350
$109$	−3.72764e33	−0.899285	−0.449642	−	0.893209i	$-0.648449\pi$
$109$	−3.72764e33	−0.899285	−0.449642	+	0.893209i	$0.648449\pi$
$110$	0	0
$111$	1.22204e33	0.218401
$112$	−1.15372e34	−1.77830
$113$	−9.88914e33	−1.31633	−0.658164	−	0.752875i	$-0.728667\pi$
$113$	−9.88914e33	−1.31633	−0.658164	+	0.752875i	$0.728667\pi$
$114$	1.43164e33	0.164780
$115$	0	0
$116$	−2.00252e33	−0.172990
$117$	−7.63942e33	−0.572788
$118$	−9.28248e33	−0.604799
$119$	3.18746e34	1.80684
$120$	0	0
$121$	5.63027e34	2.42421
$122$	4.73764e34	1.78084
$123$	−2.95380e33	−0.0970391
$124$	3.74560e34	1.07662
$125$	0	0
$126$	−1.15482e35	−2.54919
$127$	−2.44742e34	−0.474185	−0.237092	−	0.971487i	$-0.576194\pi$
$127$	−2.44742e34	−0.474185	−0.237092	+	0.971487i	$0.576194\pi$
$128$	9.60161e34	1.63448
$129$	−1.30807e34	−0.195839
$130$	0	0
$131$	−5.29429e34	−0.614939	−0.307469	−	0.951558i	$-0.599482\pi$
$131$	−5.29429e34	−0.614939	−0.307469	+	0.951558i	$0.599482\pi$
$132$	7.49801e34	0.768204
$133$	7.84486e34	0.709632
$134$	−1.38148e35	−1.10438
$135$	0	0
$136$	3.50251e35	2.19274
$137$	−1.36353e35	−0.756443	−0.378221	−	0.925715i	$-0.623464\pi$
$137$	−1.36353e35	−0.756443	−0.378221	+	0.925715i	$0.623464\pi$
$138$	4.23131e34	0.208195
$139$	−1.17476e35	−0.513103	−0.256551	−	0.966531i	$-0.582586\pi$
$139$	−1.17476e35	−0.513103	−0.256551	+	0.966531i	$0.582586\pi$
$140$	0	0
$141$	−7.58152e34	−0.261602
$142$	2.46288e35	0.756286
$143$	4.04022e35	1.10499
$144$	−4.60209e35	−1.12195
$145$	0	0
$146$	−2.69404e35	−0.523096
$147$	1.52676e35	0.264871
$148$	1.43292e36	2.22282
$149$	−6.69109e35	−0.928802	−0.464401	−	0.885625i	$-0.653730\pi$
$149$	−6.69109e35	−0.928802	−0.464401	+	0.885625i	$0.653730\pi$
$150$	0	0
$151$	6.65432e35	0.741283	0.370641	−	0.928776i	$-0.379138\pi$
$151$	6.65432e35	0.741283	0.370641	+	0.928776i	$0.379138\pi$
$152$	8.62024e35	0.861192
$153$	1.27145e36	1.13996
$154$	6.10745e36	4.91777
$155$	0	0
$156$	3.80918e35	0.247900
$157$	4.40049e35	0.257725	0.128862	−	0.991662i	$-0.458867\pi$
$157$	4.40049e35	0.257725	0.128862	+	0.991662i	$0.458867\pi$
$158$	−4.63543e36	−2.44483
$159$	−1.11899e35	−0.0531829
$160$	0	0
$161$	2.31860e36	0.896600
$162$	−4.40226e36	−1.53701
$163$	−4.21573e36	−1.32977	−0.664886	−	0.746945i	$-0.731520\pi$
$163$	−4.21573e36	−1.32977	−0.664886	+	0.746945i	$0.731520\pi$
$164$	−3.46354e36	−0.987635
$165$	0	0
$166$	−2.06732e35	−0.0482640
$167$	5.63316e36	1.19105	0.595525	−	0.803337i	$-0.296944\pi$
$167$	5.63316e36	1.19105	0.595525	+	0.803337i	$0.296944\pi$
$168$	2.95687e36	0.566539
$169$	−3.70360e36	−0.643418
$170$	0	0
$171$	3.12924e36	0.447716
$172$	−1.53380e37	−1.99320
$173$	−2.83870e36	−0.335243	−0.167621	−	0.985851i	$-0.553609\pi$
$173$	−2.83870e36	−0.335243	−0.167621	+	0.985851i	$0.553609\pi$
$174$	2.76679e35	0.0297108
$175$	0	0
$176$	2.43388e37	2.16441
$177$	8.62780e35	0.0698781
$178$	−1.96055e37	−1.44693
$179$	−1.55048e37	−1.04326	−0.521630	−	0.853172i	$-0.674676\pi$
$179$	−1.55048e37	−1.04326	−0.521630	+	0.853172i	$0.674676\pi$
$180$	0	0
$181$	−1.55561e36	−0.0871373	−0.0435686	−	0.999050i	$-0.513873\pi$
$181$	−1.55561e36	−0.0871373	−0.0435686	+	0.999050i	$0.513873\pi$
$182$	3.10274e37	1.58697
$183$	−4.40350e36	−0.205757
$184$	2.54777e37	1.08809
$185$	0	0
$186$	−5.17511e36	−0.184908
$187$	−6.72423e37	−2.19915
$188$	−8.88986e37	−2.66251
$189$	2.19240e37	0.601588
$190$	0	0
$191$	2.05424e37	0.473806	0.236903	−	0.971533i	$-0.423868\pi$
$191$	2.05424e37	0.473806	0.236903	+	0.971533i	$0.423868\pi$
$192$	−7.83509e36	−0.165796
$193$	6.16112e37	1.19664	0.598321	−	0.801257i	$-0.295835\pi$
$193$	6.16112e37	1.19664	0.598321	+	0.801257i	$0.295835\pi$
$194$	1.46320e38	2.60960
$195$	0	0
$196$	1.79023e38	2.69578
$197$	2.45666e37	0.340136	0.170068	−	0.985432i	$-0.445601\pi$
$197$	2.45666e37	0.340136	0.170068	+	0.985432i	$0.445601\pi$
$198$	2.43620e38	3.10268
$199$	3.10206e37	0.363558	0.181779	−	0.983339i	$-0.441814\pi$
$199$	3.10206e37	0.363558	0.181779	+	0.983339i	$0.441814\pi$
$200$	0	0
$201$	1.28405e37	0.127599
$202$	2.15343e38	1.97167
$203$	1.51610e37	0.127951
$204$	−6.33971e37	−0.493369
$205$	0	0
$206$	4.62087e38	3.06136
$207$	9.24866e37	0.565676
$208$	1.23647e38	0.698456
$209$	−1.65494e38	−0.863712
$210$	0	0
$211$	−2.11768e38	−0.944494	−0.472247	−	0.881466i	$-0.656557\pi$
$211$	−2.11768e38	−0.944494	−0.472247	+	0.881466i	$0.656557\pi$
$212$	−1.31209e38	−0.541280
$213$	−2.28918e37	−0.0873808
$214$	−5.67228e37	−0.200415
$215$	0	0
$216$	2.40909e38	0.730073
$217$	−2.83577e38	−0.796315
$218$	6.03910e38	1.57196
$219$	2.50403e37	0.0604382
$220$	0	0
$221$	−3.41608e38	−0.709668
$222$	−1.97981e38	−0.381767
$223$	−6.71903e38	−1.20303	−0.601515	−	0.798861i	$-0.705436\pi$
$223$	−6.71903e38	−1.20303	−0.601515	+	0.798861i	$0.705436\pi$
$224$	1.82388e38	0.303322
$225$	0	0
$226$	1.60212e39	2.30095
$227$	1.29399e39	1.72784	0.863919	−	0.503631i	$-0.168003\pi$
$227$	1.29399e39	1.72784	0.863919	+	0.503631i	$0.168003\pi$
$228$	−1.56031e38	−0.193769
$229$	1.37545e39	1.58913	0.794565	−	0.607179i	$-0.207699\pi$
$229$	1.37545e39	1.58913	0.794565	+	0.607179i	$0.207699\pi$
$230$	0	0
$231$	−5.67670e38	−0.568196
$232$	1.66595e38	0.155278
$233$	7.86418e38	0.682780	0.341390	−	0.939922i	$-0.389102\pi$
$233$	7.86418e38	0.682780	0.341390	+	0.939922i	$0.389102\pi$
$234$	1.23765e39	1.00124
$235$	0	0
$236$	1.01167e39	0.711198
$237$	4.30850e38	0.282474
$238$	−5.16396e39	−3.15837
$239$	1.12913e39	0.644437	0.322218	−	0.946665i	$-0.395571\pi$
$239$	1.12913e39	0.644437	0.322218	+	0.946665i	$0.395571\pi$
$240$	0	0
$241$	2.98000e39	1.48230	0.741149	−	0.671341i	$-0.234281\pi$
$241$	2.98000e39	1.48230	0.741149	+	0.671341i	$0.234281\pi$
$242$	−9.12152e39	−4.23754
$243$	1.32089e39	0.573275
$244$	−5.16341e39	−2.09413
$245$	0	0
$246$	4.78541e38	0.169625
$247$	−8.40752e38	−0.278720
$248$	−3.11605e39	−0.966389
$249$	1.92151e37	0.00557640
$250$	0	0
$251$	−3.13439e39	−0.797144	−0.398572	−	0.917137i	$-0.630494\pi$
$251$	−3.13439e39	−0.797144	−0.398572	+	0.917137i	$0.630494\pi$
$252$	1.25861e40	2.99766
$253$	−4.89129e39	−1.09128
$254$	3.96503e39	0.828878
$255$	0	0
$256$	−1.10859e40	−2.03616
$257$	−4.76577e39	−0.820798	−0.410399	−	0.911906i	$-0.634611\pi$
$257$	−4.76577e39	−0.820798	−0.410399	+	0.911906i	$0.634611\pi$
$258$	2.11918e39	0.342329
$259$	−1.08486e40	−1.64410
$260$	0	0
$261$	6.04756e38	0.0807257
$262$	8.57721e39	1.07492
$263$	1.23745e40	1.45632	0.728160	−	0.685407i	$-0.240376\pi$
$263$	1.23745e40	1.45632	0.728160	+	0.685407i	$0.240376\pi$
$264$	−6.23778e39	−0.689549
$265$	0	0
$266$	−1.27093e40	−1.24044
$267$	1.82228e39	0.167178
$268$	1.50564e40	1.29866
$269$	4.11483e39	0.333763	0.166882	−	0.985977i	$-0.446630\pi$
$269$	4.11483e39	0.333763	0.166882	+	0.985977i	$0.446630\pi$
$270$	0	0
$271$	−5.73521e39	−0.411676	−0.205838	−	0.978586i	$-0.565992\pi$
$271$	−5.73521e39	−0.411676	−0.205838	+	0.978586i	$0.565992\pi$
$272$	−2.05789e40	−1.39006
$273$	−2.88391e39	−0.183357
$274$	2.20904e40	1.32227
$275$	0	0
$276$	−4.61158e39	−0.244822
$277$	9.95302e39	0.497782	0.248891	−	0.968532i	$-0.419934\pi$
$277$	9.95302e39	0.497782	0.248891	+	0.968532i	$0.419934\pi$
$278$	1.90321e40	0.896907
$279$	−1.13116e40	−0.502405
$280$	0	0
$281$	3.27698e40	1.29366	0.646829	−	0.762635i	$-0.276095\pi$
$281$	3.27698e40	1.29366	0.646829	+	0.762635i	$0.276095\pi$
$282$	1.22827e40	0.457282
$283$	2.13448e39	0.0749576	0.0374788	−	0.999297i	$-0.488067\pi$
$283$	2.13448e39	0.0749576	0.0374788	+	0.999297i	$0.488067\pi$
$284$	−2.68422e40	−0.889336
$285$	0	0
$286$	−6.54550e40	−1.93154
$287$	2.62222e40	0.730497
$288$	7.27527e39	0.191370
$289$	1.66001e40	0.412378
$290$	0	0
$291$	−1.36000e40	−0.301512
$292$	2.93615e40	0.615122
$293$	9.84017e39	0.194844	0.0974219	−	0.995243i	$-0.468940\pi$
$293$	9.84017e39	0.194844	0.0974219	+	0.995243i	$0.468940\pi$
$294$	−2.47348e40	−0.462996
$295$	0	0
$296$	−1.19208e41	−1.99523
$297$	−4.62505e40	−0.732208
$298$	1.08401e41	1.62355
$299$	−2.48490e40	−0.352155
$300$	0	0
$301$	1.16123e41	1.47425
$302$	−1.07806e41	−1.29577
$303$	−2.00155e40	−0.227805
$304$	−5.06480e40	−0.545944
$305$	0	0
$306$	−2.05985e41	−1.99266
$307$	−2.89468e39	−0.0265349	−0.0132675	−	0.999912i	$-0.504223\pi$
$307$	−2.89468e39	−0.0265349	−0.0132675	+	0.999912i	$0.504223\pi$
$308$	−6.65633e41	−5.78293
$309$	−4.29497e40	−0.353708
$310$	0	0
$311$	−2.35932e41	−1.74679	−0.873395	−	0.487013i	$-0.838087\pi$
$311$	−2.35932e41	−1.74679	−0.873395	+	0.487013i	$0.838087\pi$
$312$	−3.16895e40	−0.222518
$313$	1.20774e41	0.804437	0.402219	−	0.915544i	$-0.368239\pi$
$313$	1.20774e41	0.804437	0.402219	+	0.915544i	$0.368239\pi$
$314$	−7.12916e40	−0.450505
$315$	0	0
$316$	5.05202e41	2.87494
$317$	2.94161e41	1.58894	0.794470	−	0.607304i	$-0.207749\pi$
$317$	2.94161e41	1.58894	0.794470	+	0.607304i	$0.207749\pi$
$318$	1.81285e40	0.0929640
$319$	−3.19834e40	−0.155732
$320$	0	0
$321$	5.27222e39	0.0231558
$322$	−3.75633e41	−1.56726
$323$	1.39928e41	0.554707
$324$	4.79789e41	1.80742
$325$	0	0
$326$	6.82984e41	2.32445
$327$	−5.61317e40	−0.181623
$328$	2.88140e41	0.886513
$329$	6.73046e41	1.96930
$330$	0	0
$331$	−2.83548e41	−0.750698	−0.375349	−	0.926884i	$-0.622477\pi$
$331$	−2.83548e41	−0.750698	−0.375349	+	0.926884i	$0.622477\pi$
$332$	2.25311e40	0.0567549
$333$	−4.32739e41	−1.03728
$334$	−9.12619e41	−2.08196
$335$	0	0
$336$	−1.73730e41	−0.359151
$337$	3.05502e41	0.601341	0.300671	−	0.953728i	$-0.402790\pi$
$337$	3.05502e41	0.601341	0.300671	+	0.953728i	$0.402790\pi$
$338$	6.00015e41	1.12470
$339$	−1.48913e41	−0.265850
$340$	0	0
$341$	5.98229e41	0.969216
$342$	−5.06963e41	−0.782610
$343$	−3.21903e41	−0.473557
$344$	1.27601e42	1.78912
$345$	0	0
$346$	4.59894e41	0.586006
$347$	1.39593e42	1.69601	0.848005	−	0.529989i	$-0.177804\pi$
$347$	1.39593e42	1.69601	0.848005	+	0.529989i	$0.177804\pi$
$348$	−3.01544e40	−0.0349377
$349$	2.89779e41	0.320219	0.160109	−	0.987099i	$-0.448815\pi$
$349$	2.89779e41	0.320219	0.160109	+	0.987099i	$0.448815\pi$
$350$	0	0
$351$	−2.34964e41	−0.236284
$352$	−3.84763e41	−0.369181
$353$	1.76391e42	1.61508	0.807539	−	0.589815i	$-0.200799\pi$
$353$	1.76391e42	1.61508	0.807539	+	0.589815i	$0.200799\pi$
$354$	−1.39778e41	−0.122147
$355$	0	0
$356$	2.13675e42	1.70149
$357$	4.79975e41	0.364916
$358$	2.51192e42	1.82362
$359$	−1.86130e42	−1.29050	−0.645250	−	0.763971i	$-0.723247\pi$
$359$	−1.86130e42	−1.29050	−0.645250	+	0.763971i	$0.723247\pi$
$360$	0	0
$361$	−1.23638e42	−0.782140
$362$	2.52022e41	0.152317
$363$	8.47819e41	0.489603
$364$	−3.38158e42	−1.86615
$365$	0	0
$366$	7.13404e41	0.359665
$367$	−8.65748e41	−0.417255	−0.208628	−	0.977995i	$-0.566900\pi$
$367$	−8.65748e41	−0.417255	−0.208628	+	0.977995i	$0.566900\pi$
$368$	−1.49693e42	−0.689785
$369$	1.04598e42	0.460880
$370$	0	0
$371$	9.93375e41	0.400354
$372$	5.64020e41	0.217438
$373$	−3.49461e42	−1.28885	−0.644426	−	0.764667i	$-0.722904\pi$
$373$	−3.49461e42	−1.28885	−0.644426	+	0.764667i	$0.722904\pi$
$374$	1.08938e43	3.84414
$375$	0	0
$376$	7.39569e42	2.38990
$377$	−1.62484e41	−0.0502548
$378$	−3.55187e42	−1.05158
$379$	−1.11686e42	−0.316557	−0.158279	−	0.987394i	$-0.550594\pi$
$379$	−1.11686e42	−0.316557	−0.158279	+	0.987394i	$0.550594\pi$
$380$	0	0
$381$	−3.68538e41	−0.0957680
$382$	−3.32804e42	−0.828215
$383$	6.73691e42	1.60576	0.802880	−	0.596140i	$-0.203300\pi$
$383$	6.73691e42	1.60576	0.802880	+	0.596140i	$0.203300\pi$
$384$	1.44583e42	0.330106
$385$	0	0
$386$	−9.98154e42	−2.09174
$387$	4.63204e42	0.930125
$388$	−1.59469e43	−3.06870
$389$	−2.38206e42	−0.439324	−0.219662	−	0.975576i	$-0.570495\pi$
$389$	−2.38206e42	−0.439324	−0.219662	+	0.975576i	$0.570495\pi$
$390$	0	0
$391$	4.13567e42	0.700857
$392$	−1.48934e43	−2.41976
$393$	−7.97227e41	−0.124195
$394$	−3.98000e42	−0.594560
$395$	0	0
$396$	−2.65514e43	−3.64852
$397$	1.10200e43	1.45257	0.726286	−	0.687393i	$-0.241245\pi$
$397$	1.10200e43	1.45257	0.726286	+	0.687393i	$0.241245\pi$
$398$	−5.02560e42	−0.635502
$399$	1.18130e42	0.143320
$400$	0	0
$401$	1.04368e43	1.16596	0.582980	−	0.812487i	$-0.301887\pi$
$401$	1.04368e43	1.16596	0.582980	+	0.812487i	$0.301887\pi$
$402$	−2.08027e42	−0.223044
$403$	3.03916e42	0.312766
$404$	−2.34696e43	−2.31853
$405$	0	0
$406$	−2.45621e42	−0.223659
$407$	2.28860e43	2.00107
$408$	5.27416e42	0.442854
$409$	−6.52594e42	−0.526270	−0.263135	−	0.964759i	$-0.584756\pi$
$409$	−6.52594e42	−0.526270	−0.263135	+	0.964759i	$0.584756\pi$
$410$	0	0
$411$	−2.05324e42	−0.152774
$412$	−5.03615e43	−3.59994
$413$	−7.65929e42	−0.526033
$414$	−1.49836e43	−0.988806
$415$	0	0
$416$	−1.95469e42	−0.119135
$417$	−1.76898e42	−0.103628
$418$	2.68115e43	1.50977
$419$	1.95597e43	1.05884	0.529421	−	0.848359i	$-0.322409\pi$
$419$	1.95597e43	1.05884	0.529421	+	0.848359i	$0.322409\pi$
$420$	0	0
$421$	−3.38938e43	−1.69616	−0.848079	−	0.529871i	$-0.822241\pi$
$421$	−3.38938e43	−1.69616	−0.848079	+	0.529871i	$0.822241\pi$
$422$	3.43082e43	1.65098
$423$	2.68471e43	1.24246
$424$	1.09156e43	0.485859
$425$	0	0
$426$	3.70866e42	0.152742
$427$	3.90919e43	1.54891
$428$	6.18205e42	0.235673
$429$	6.08385e42	0.223169
$430$	0	0
$431$	3.61239e43	1.22721	0.613607	−	0.789612i	$-0.289718\pi$
$431$	3.61239e43	1.22721	0.613607	+	0.789612i	$0.289718\pi$
$432$	−1.41545e43	−0.462822
$433$	−3.19821e42	−0.100660	−0.0503299	−	0.998733i	$-0.516027\pi$
$433$	−3.19821e42	−0.100660	−0.0503299	+	0.998733i	$0.516027\pi$
$434$	4.59419e43	1.39196
$435$	0	0
$436$	−6.58184e43	−1.84850
$437$	1.01786e43	0.275260
$438$	−4.05674e42	−0.105646
$439$	−2.67557e43	−0.671046	−0.335523	−	0.942032i	$-0.608913\pi$
$439$	−2.67557e43	−0.671046	−0.335523	+	0.942032i	$0.608913\pi$
$440$	0	0
$441$	−5.40644e43	−1.25798
$442$	5.53434e43	1.24050
$443$	3.50289e43	0.756424	0.378212	−	0.925719i	$-0.376539\pi$
$443$	3.50289e43	0.756424	0.378212	+	0.925719i	$0.376539\pi$
$444$	2.15773e43	0.448930
$445$	0	0
$446$	1.08854e44	2.10290
$447$	−1.00756e43	−0.187584
$448$	6.95557e43	1.24809
$449$	4.00499e43	0.692686	0.346343	−	0.938108i	$-0.387423\pi$
$449$	4.00499e43	0.692686	0.346343	+	0.938108i	$0.387423\pi$
$450$	0	0
$451$	−5.53180e43	−0.889107
$452$	−1.74611e44	−2.70575
$453$	1.00202e43	0.149712
$454$	−2.09637e44	−3.02027
$455$	0	0
$456$	1.29806e43	0.173930
$457$	5.79727e42	0.0749215	0.0374607	−	0.999298i	$-0.488073\pi$
$457$	5.79727e42	0.0749215	0.0374607	+	0.999298i	$0.488073\pi$
$458$	−2.22835e44	−2.77781
$459$	3.91056e43	0.470251
$460$	0	0
$461$	1.20731e44	1.35131	0.675653	−	0.737220i	$-0.263862\pi$
$461$	1.20731e44	1.35131	0.675653	+	0.737220i	$0.263862\pi$
$462$	9.19674e43	0.993211
$463$	9.13506e43	0.951974	0.475987	−	0.879452i	$-0.342091\pi$
$463$	9.13506e43	0.951974	0.475987	+	0.879452i	$0.342091\pi$
$464$	−9.78823e42	−0.0984368
$465$	0	0
$466$	−1.27406e44	−1.19350
$467$	5.31862e43	0.480918	0.240459	−	0.970659i	$-0.422702\pi$
$467$	5.31862e43	0.480918	0.240459	+	0.970659i	$0.422702\pi$
$468$	−1.34888e44	−1.17738
$469$	−1.13991e44	−0.960547
$470$	0	0
$471$	6.62635e42	0.0520511
$472$	−8.41632e43	−0.638380
$473$	−2.44972e44	−1.79435
$474$	−6.98014e43	−0.493766
$475$	0	0
$476$	5.62805e44	3.71401
$477$	3.96247e43	0.252588
$478$	−1.82929e44	−1.12648
$479$	1.68051e44	0.999784	0.499892	−	0.866088i	$-0.333373\pi$
$479$	1.68051e44	0.999784	0.499892	+	0.866088i	$0.333373\pi$
$480$	0	0
$481$	1.16267e44	0.645746
$482$	−4.82786e44	−2.59107
$483$	3.49140e43	0.181081
$484$	9.94127e44	4.98303
$485$	0	0
$486$	−2.13995e44	−1.00209
$487$	2.21035e44	1.00054	0.500269	−	0.865870i	$-0.333234\pi$
$487$	2.21035e44	1.00054	0.500269	+	0.865870i	$0.333234\pi$
$488$	4.29557e44	1.87972
$489$	−6.34814e43	−0.268566
$490$	0	0
$491$	−2.22461e44	−0.879853	−0.439926	−	0.898034i	$-0.644995\pi$
$491$	−2.22461e44	−0.879853	−0.439926	+	0.898034i	$0.644995\pi$
$492$	−5.21547e43	−0.199466
$493$	2.70425e43	0.100017
$494$	1.36209e44	0.487204
$495$	0	0
$496$	1.83083e44	0.612632
$497$	2.03221e44	0.657791
$498$	−3.11301e42	−0.00974758
$499$	−2.12116e44	−0.642561	−0.321281	−	0.946984i	$-0.604113\pi$
$499$	−2.12116e44	−0.642561	−0.321281	+	0.946984i	$0.604113\pi$
$500$	0	0
$501$	8.48254e43	0.240549
$502$	5.07798e44	1.39341
$503$	2.56784e44	0.681861	0.340930	−	0.940089i	$-0.389258\pi$
$503$	2.56784e44	0.681861	0.340930	+	0.940089i	$0.389258\pi$
$504$	−1.04707e45	−2.69073
$505$	0	0
$506$	7.92430e44	1.90756
$507$	−5.57696e43	−0.129947
$508$	−4.32137e44	−0.974698
$509$	−3.35063e44	−0.731617	−0.365808	−	0.930690i	$-0.619207\pi$
$509$	−3.35063e44	−0.731617	−0.365808	+	0.930690i	$0.619207\pi$
$510$	0	0
$511$	−2.22294e44	−0.454971
$512$	9.71241e44	1.92474
$513$	9.62452e43	0.184690
$514$	7.72095e44	1.43476
$515$	0	0
$516$	−2.30963e44	−0.402553
$517$	−1.41985e45	−2.39689
$518$	1.75756e45	2.87389
$519$	−4.27458e43	−0.0677068
$520$	0	0
$521$	9.60997e44	1.42856	0.714282	−	0.699858i	$-0.246753\pi$
$521$	9.60997e44	1.42856	0.714282	+	0.699858i	$0.246753\pi$
$522$	−9.79756e43	−0.141109
$523$	2.83456e44	0.395555	0.197778	−	0.980247i	$-0.436628\pi$
$523$	2.83456e44	0.395555	0.197778	+	0.980247i	$0.436628\pi$
$524$	−9.34805e44	−1.26402
$525$	0	0
$526$	−2.00477e45	−2.54566
$527$	−5.05814e44	−0.622466
$528$	3.66499e44	0.437133
$529$	−5.64171e44	−0.652217
$530$	0	0
$531$	−3.05521e44	−0.331881
$532$	1.38515e45	1.45867
$533$	−2.81030e44	−0.286915
$534$	−2.95224e44	−0.292228
$535$	0	0
$536$	−1.25258e45	−1.16570
$537$	−2.33476e44	−0.210701
$538$	−6.66637e44	−0.583421
$539$	2.85928e45	2.42684
$540$	0	0
$541$	2.87443e43	0.0229508	0.0114754	−	0.999934i	$-0.496347\pi$
$541$	2.87443e43	0.0229508	0.0114754	+	0.999934i	$0.496347\pi$
$542$	9.29153e44	0.719613
$543$	−2.34247e43	−0.0175986
$544$	3.25324e44	0.237102
$545$	0	0
$546$	4.67218e44	0.320509
$547$	−4.18837e44	−0.278775	−0.139387	−	0.990238i	$-0.544513\pi$
$547$	−4.18837e44	−0.278775	−0.139387	+	0.990238i	$0.544513\pi$
$548$	−2.40757e45	−1.55489
$549$	1.55933e45	0.977228
$550$	0	0
$551$	6.65561e43	0.0392813
$552$	3.83649e44	0.219755
$553$	−3.82485e45	−2.12643
$554$	−1.61247e45	−0.870125
$555$	0	0
$556$	−2.07425e45	−1.05470
$557$	−9.66111e44	−0.476888	−0.238444	−	0.971156i	$-0.576637\pi$
$557$	−9.66111e44	−0.476888	−0.238444	+	0.971156i	$0.576637\pi$
$558$	1.83257e45	0.878207
$559$	−1.24452e45	−0.579038
$560$	0	0
$561$	−1.01255e45	−0.444149
$562$	−5.30899e45	−2.26132
$563$	−2.31505e45	−0.957572	−0.478786	−	0.877932i	$-0.658923\pi$
$563$	−2.31505e45	−0.957572	−0.478786	+	0.877932i	$0.658923\pi$
$564$	−1.33866e45	−0.537729
$565$	0	0
$566$	−3.45804e44	−0.131026
$567$	−3.63246e45	−1.33684
$568$	2.23307e45	0.798279
$569$	−2.87517e45	−0.998416	−0.499208	−	0.866482i	$-0.666376\pi$
$569$	−2.87517e45	−0.998416	−0.499208	+	0.866482i	$0.666376\pi$
$570$	0	0
$571$	−2.65488e45	−0.870060	−0.435030	−	0.900416i	$-0.643262\pi$
$571$	−2.65488e45	−0.870060	−0.435030	+	0.900416i	$0.643262\pi$
$572$	7.13374e45	2.27134
$573$	3.09332e44	0.0956915
$574$	−4.24823e45	−1.27691
$575$	0	0
$576$	2.77451e45	0.787435
$577$	−2.47694e45	−0.683148	−0.341574	−	0.939855i	$-0.610960\pi$
$577$	−2.47694e45	−0.683148	−0.341574	+	0.939855i	$0.610960\pi$
$578$	−2.68935e45	−0.720839
$579$	9.27756e44	0.241678
$580$	0	0
$581$	−1.70581e44	−0.0419784
$582$	2.20331e45	0.527045
$583$	−2.09561e45	−0.487281
$584$	−2.44266e45	−0.552141
$585$	0	0
$586$	−1.59419e45	−0.340588
$587$	6.47352e45	1.34466	0.672328	−	0.740253i	$-0.265294\pi$
$587$	6.47352e45	1.34466	0.672328	+	0.740253i	$0.265294\pi$
$588$	2.69577e45	0.544449
$589$	−1.24489e45	−0.244472
$590$	0	0
$591$	3.69930e44	0.0686951
$592$	7.00406e45	1.26486
$593$	9.12580e45	1.60276	0.801380	−	0.598156i	$-0.204100\pi$
$593$	9.12580e45	1.60276	0.801380	+	0.598156i	$0.204100\pi$
$594$	7.49297e45	1.27990
$595$	0	0
$596$	−1.18143e46	−1.90918
$597$	4.67115e44	0.0734256
$598$	4.02574e45	0.615569
$599$	5.76161e45	0.857040	0.428520	−	0.903532i	$-0.359035\pi$
$599$	5.76161e45	0.857040	0.428520	+	0.903532i	$0.359035\pi$
$600$	0	0
$601$	1.06122e46	1.49409	0.747045	−	0.664773i	$-0.231472\pi$
$601$	1.06122e46	1.49409	0.747045	+	0.664773i	$0.231472\pi$
$602$	−1.88130e46	−2.57700
$603$	−4.54698e45	−0.606021
$604$	1.17494e46	1.52373
$605$	0	0
$606$	3.24269e45	0.398205
$607$	−1.19114e46	−1.42347	−0.711734	−	0.702449i	$-0.752090\pi$
$607$	−1.19114e46	−1.42347	−0.711734	+	0.702449i	$0.752090\pi$
$608$	8.00676e44	0.0931210
$609$	2.28298e44	0.0258414
$610$	0	0
$611$	−7.21319e45	−0.773477
$612$	2.24497e46	2.34322
$613$	1.87761e46	1.90769	0.953843	−	0.300304i	$-0.0970883\pi$
$613$	1.87761e46	1.90769	0.953843	+	0.300304i	$0.0970883\pi$
$614$	4.68964e44	0.0463832
$615$	0	0
$616$	5.53756e46	5.19083
$617$	−9.77185e45	−0.891808	−0.445904	−	0.895081i	$-0.647118\pi$
$617$	−9.77185e45	−0.891808	−0.445904	+	0.895081i	$0.647118\pi$
$618$	6.95822e45	0.618284
$619$	1.04212e46	0.901615	0.450808	−	0.892621i	$-0.351136\pi$
$619$	1.04212e46	0.901615	0.450808	+	0.892621i	$0.351136\pi$
$620$	0	0
$621$	2.84459e45	0.233350
$622$	3.82230e46	3.05340
$623$	−1.61772e46	−1.25849
$624$	1.86191e45	0.141063
$625$	0	0
$626$	−1.95664e46	−1.40616
$627$	−2.49205e45	−0.174438
$628$	7.76986e45	0.529760
$629$	−1.93506e46	−1.28516
$630$	0	0
$631$	1.47410e46	0.929056	0.464528	−	0.885558i	$-0.346224\pi$
$631$	1.47410e46	0.929056	0.464528	+	0.885558i	$0.346224\pi$
$632$	−4.20290e46	−2.58058
$633$	−3.18884e45	−0.190753
$634$	−4.76566e46	−2.77748
$635$	0	0
$636$	−1.97577e45	−0.109319
$637$	1.45258e46	0.783142
$638$	5.18158e45	0.272221
$639$	8.10627e45	0.415008
$640$	0	0
$641$	−2.92413e45	−0.142180	−0.0710902	−	0.997470i	$-0.522648\pi$
$641$	−2.92413e45	−0.142180	−0.0710902	+	0.997470i	$0.522648\pi$
$642$	−8.54145e44	−0.0404766
$643$	6.54844e45	0.302452	0.151226	−	0.988499i	$-0.451678\pi$
$643$	6.54844e45	0.302452	0.151226	+	0.988499i	$0.451678\pi$
$644$	4.09391e46	1.84299
$645$	0	0
$646$	−2.26696e46	−0.969632
$647$	2.24177e46	0.934696	0.467348	−	0.884074i	$-0.345210\pi$
$647$	2.24177e46	0.934696	0.467348	+	0.884074i	$0.345210\pi$
$648$	−3.99148e46	−1.62236
$649$	1.61579e46	0.640248
$650$	0	0
$651$	−4.27016e45	−0.160827
$652$	−7.44364e46	−2.73338
$653$	−4.25379e46	−1.52303	−0.761515	−	0.648148i	$-0.775544\pi$
$653$	−4.25379e46	−1.52303	−0.761515	+	0.648148i	$0.775544\pi$
$654$	9.09382e45	0.317478
$655$	0	0
$656$	−1.69296e46	−0.561996
$657$	−8.86709e45	−0.287047
$658$	−1.09039e47	−3.44235
$659$	−1.43240e46	−0.441017	−0.220509	−	0.975385i	$-0.570772\pi$
$659$	−1.43240e46	−0.441017	−0.220509	+	0.975385i	$0.570772\pi$
$660$	0	0
$661$	5.54323e46	1.62345	0.811725	−	0.584040i	$-0.198529\pi$
$661$	5.54323e46	1.62345	0.811725	+	0.584040i	$0.198529\pi$
$662$	4.59372e46	1.31222
$663$	−5.14401e45	−0.143327
$664$	−1.87441e45	−0.0509439
$665$	0	0
$666$	7.01074e46	1.81317
$667$	1.96711e45	0.0496309
$668$	9.94637e46	2.44823
$669$	−1.01177e46	−0.242968
$670$	0	0
$671$	−8.24677e46	−1.88522
$672$	2.74644e45	0.0612600
$673$	7.20788e46	1.56877	0.784385	−	0.620275i	$-0.212979\pi$
$673$	7.20788e46	1.56877	0.784385	+	0.620275i	$0.212979\pi$
$674$	−4.94940e46	−1.05115
$675$	0	0
$676$	−6.53938e46	−1.32256
$677$	6.09779e46	1.20354	0.601769	−	0.798670i	$-0.294463\pi$
$677$	6.09779e46	1.20354	0.601769	+	0.798670i	$0.294463\pi$
$678$	2.41252e46	0.464708
$679$	1.20733e47	2.26974
$680$	0	0
$681$	1.94851e46	0.348960
$682$	−9.69183e46	−1.69420
$683$	−2.92500e46	−0.499095	−0.249548	−	0.968363i	$-0.580282\pi$
$683$	−2.92500e46	−0.499095	−0.249548	+	0.968363i	$0.580282\pi$
$684$	5.52524e46	0.920291
$685$	0	0
$686$	5.21510e46	0.827780
$687$	2.07119e46	0.320947
$688$	−7.49715e46	−1.13419
$689$	−1.06462e46	−0.157246
$690$	0	0
$691$	−5.05530e46	−0.711803	−0.355901	−	0.934524i	$-0.615826\pi$
$691$	−5.05530e46	−0.711803	−0.355901	+	0.934524i	$0.615826\pi$
$692$	−5.01225e46	−0.689100
$693$	2.01019e47	2.69860
$694$	−2.26153e47	−2.96464
$695$	0	0
$696$	2.50862e45	0.0313605
$697$	4.67724e46	0.571017
$698$	−4.69466e46	−0.559744
$699$	1.18421e46	0.137897
$700$	0	0
$701$	7.87167e45	0.0874419	0.0437209	−	0.999044i	$-0.486079\pi$
$701$	7.87167e45	0.0874419	0.0437209	+	0.999044i	$0.486079\pi$
$702$	3.80662e46	0.413026
$703$	−4.76248e46	−0.504743
$704$	−1.46734e47	−1.51908
$705$	0	0
$706$	−2.85768e47	−2.82317
$707$	1.77687e47	1.71489
$708$	1.52340e46	0.143636
$709$	6.37039e46	0.586818	0.293409	−	0.955987i	$-0.405210\pi$
$709$	6.37039e46	0.586818	0.293409	+	0.955987i	$0.405210\pi$
$710$	0	0
$711$	−1.52570e47	−1.34159
$712$	−1.77761e47	−1.52727
$713$	−3.67935e46	−0.308883
$714$	−7.77601e46	−0.637876
$715$	0	0
$716$	−2.73766e47	−2.14445
$717$	1.70028e46	0.130153
$718$	3.01547e47	2.25580
$719$	1.38244e47	1.01070	0.505349	−	0.862915i	$-0.331364\pi$
$719$	1.38244e47	1.01070	0.505349	+	0.862915i	$0.331364\pi$
$720$	0	0
$721$	3.81284e47	2.66267
$722$	2.00305e47	1.36719
$723$	4.48736e46	0.299370
$724$	−2.74671e46	−0.179113
$725$	0	0
$726$	−1.37354e47	−0.855829
$727$	−9.54196e46	−0.581192	−0.290596	−	0.956846i	$-0.593854\pi$
$727$	−9.54196e46	−0.581192	−0.290596	+	0.956846i	$0.593854\pi$
$728$	2.81322e47	1.67508
$729$	−1.31166e47	−0.763515
$730$	0	0
$731$	2.07128e47	1.15240
$732$	−7.77518e46	−0.422939
$733$	−1.90546e47	−1.01341	−0.506704	−	0.862120i	$-0.669136\pi$
$733$	−1.90546e47	−1.01341	−0.506704	+	0.862120i	$0.669136\pi$
$734$	1.40259e47	0.729364
$735$	0	0
$736$	2.36645e46	0.117656
$737$	2.40474e47	1.16911
$738$	−1.69457e47	−0.805620
$739$	3.12949e47	1.45492	0.727462	−	0.686148i	$-0.240700\pi$
$739$	3.12949e47	1.45492	0.727462	+	0.686148i	$0.240700\pi$
$740$	0	0
$741$	−1.26602e46	−0.0562913
$742$	−1.60935e47	−0.699821
$743$	−1.30046e47	−0.553074	−0.276537	−	0.961003i	$-0.589187\pi$
$743$	−1.30046e47	−0.553074	−0.276537	+	0.961003i	$0.589187\pi$
$744$	−4.69222e46	−0.195175
$745$	0	0
$746$	5.66157e47	2.25292
$747$	−6.80432e45	−0.0264847
$748$	−1.18729e48	−4.52042
$749$	−4.68039e46	−0.174314
$750$	0	0
$751$	−1.13850e47	−0.405766	−0.202883	−	0.979203i	$-0.565031\pi$
$751$	−1.13850e47	−0.405766	−0.202883	+	0.979203i	$0.565031\pi$
$752$	−4.34532e47	−1.51505
$753$	−4.71984e46	−0.160994
$754$	2.63237e46	0.0878457
$755$	0	0
$756$	3.87108e47	1.23658
$757$	−5.43917e47	−1.70001	−0.850003	−	0.526778i	$-0.823400\pi$
$757$	−5.43917e47	−1.70001	−0.850003	+	0.526778i	$0.823400\pi$
$758$	1.80941e47	0.553344
$759$	−7.36541e46	−0.220398
$760$	0	0
$761$	3.05470e46	0.0875230	0.0437615	−	0.999042i	$-0.486066\pi$
$761$	3.05470e46	0.0875230	0.0437615	+	0.999042i	$0.486066\pi$
$762$	5.97064e46	0.167403
$763$	4.98307e47	1.36723
$764$	3.62713e47	0.973920
$765$	0	0
$766$	−1.09144e48	−2.80688
$767$	8.20863e46	0.206608
$768$	−1.66934e47	−0.411231
$769$	1.42016e46	0.0342415	0.0171208	−	0.999853i	$-0.494550\pi$
$769$	1.42016e46	0.0342415	0.0171208	+	0.999853i	$0.494550\pi$
$770$	0	0
$771$	−7.17640e46	−0.165771
$772$	1.08786e48	2.45973
$773$	−1.83451e47	−0.406029	−0.203015	−	0.979176i	$-0.565074\pi$
$773$	−1.83451e47	−0.406029	−0.203015	+	0.979176i	$0.565074\pi$
$774$	−7.50430e47	−1.62586
$775$	0	0
$776$	1.32667e48	2.75450
$777$	−1.63361e47	−0.332048
$778$	3.85915e47	0.767941
$779$	1.15115e47	0.224265
$780$	0	0
$781$	−4.28712e47	−0.800614
$782$	−6.70014e47	−1.22510
$783$	1.86004e46	0.0333006
$784$	8.75055e47	1.53398
$785$	0	0
$786$	1.29158e47	0.217094
$787$	−1.26346e47	−0.207959	−0.103980	−	0.994579i	$-0.533158\pi$
$787$	−1.26346e47	−0.207959	−0.103980	+	0.994579i	$0.533158\pi$
$788$	4.33768e47	0.699158
$789$	1.86338e47	0.294124
$790$	0	0
$791$	1.32197e48	2.00128
$792$	2.20888e48	3.27496
$793$	−4.18957e47	−0.608361
$794$	−1.78533e48	−2.53910
$795$	0	0
$796$	5.47725e47	0.747303
$797$	−6.98979e47	−0.934118	−0.467059	−	0.884226i	$-0.654686\pi$
$797$	−6.98979e47	−0.934118	−0.467059	+	0.884226i	$0.654686\pi$
$798$	−1.91380e47	−0.250524
$799$	1.20051e48	1.53937
$800$	0	0
$801$	−6.45291e47	−0.793998
$802$	−1.69084e48	−2.03810
$803$	4.68949e47	0.553757
$804$	2.26722e47	0.262283
$805$	0	0
$806$	−4.92369e47	−0.546717
$807$	6.19620e46	0.0674081
$808$	1.95249e48	2.08114
$809$	1.36317e48	1.42364	0.711818	−	0.702364i	$-0.247872\pi$
$809$	1.36317e48	1.42364	0.711818	+	0.702364i	$0.247872\pi$
$810$	0	0
$811$	6.10621e47	0.612248	0.306124	−	0.951992i	$-0.400968\pi$
$811$	6.10621e47	0.612248	0.306124	+	0.951992i	$0.400968\pi$
$812$	2.67695e47	0.263006
$813$	−8.63621e46	−0.0831437
$814$	−3.70773e48	−3.49789
$815$	0	0
$816$	−3.09882e47	−0.280743
$817$	5.09776e47	0.452601
$818$	1.05726e48	0.919922
$819$	1.02123e48	0.870840
$820$	0	0
$821$	8.40767e47	0.688674	0.344337	−	0.938846i	$-0.388104\pi$
$821$	8.40767e47	0.688674	0.344337	+	0.938846i	$0.388104\pi$
$822$	3.32642e47	0.267050
$823$	8.92715e47	0.702450	0.351225	−	0.936291i	$-0.385765\pi$
$823$	8.92715e47	0.702450	0.351225	+	0.936291i	$0.385765\pi$
$824$	4.18970e48	3.23135
$825$	0	0
$826$	1.24087e48	0.919508
$827$	2.30578e48	1.67485	0.837426	−	0.546550i	$-0.184059\pi$
$827$	2.30578e48	1.67485	0.837426	+	0.546550i	$0.184059\pi$
$828$	1.63302e48	1.16276
$829$	6.85395e47	0.478400	0.239200	−	0.970970i	$-0.423115\pi$
$829$	6.85395e47	0.478400	0.239200	+	0.970970i	$0.423115\pi$
$830$	0	0
$831$	1.49875e47	0.100534
$832$	−7.45444e47	−0.490208
$833$	−2.41757e48	−1.55861
$834$	2.86590e47	0.181143
$835$	0	0
$836$	−2.92210e48	−1.77538
$837$	−3.47908e47	−0.207250
$838$	−3.16884e48	−1.85086
$839$	−1.53456e48	−0.878841	−0.439420	−	0.898282i	$-0.644816\pi$
$839$	−1.53456e48	−0.878841	−0.439420	+	0.898282i	$0.644816\pi$
$840$	0	0
$841$	−1.80321e48	−0.992917
$842$	5.49109e48	2.96489
$843$	4.93455e47	0.261272
$844$	−3.73914e48	−1.94143
$845$	0	0
$846$	−4.34946e48	−2.17182
$847$	−7.52648e48	−3.68566
$848$	−6.41342e47	−0.308005
$849$	3.21415e46	0.0151387
$850$	0	0
$851$	−1.40758e48	−0.637729
$852$	−4.04196e47	−0.179614
$853$	−1.76958e48	−0.771278	−0.385639	−	0.922650i	$-0.626019\pi$
$853$	−1.76958e48	−0.771278	−0.385639	+	0.922650i	$0.626019\pi$
$854$	−6.33322e48	−2.70751
$855$	0	0
$856$	−5.14300e47	−0.211543
$857$	−3.25318e48	−1.31258	−0.656288	−	0.754510i	$-0.727875\pi$
$857$	−3.25318e48	−1.31258	−0.656288	+	0.754510i	$0.727875\pi$
$858$	−9.85636e47	−0.390100
$859$	−1.29796e48	−0.503934	−0.251967	−	0.967736i	$-0.581078\pi$
$859$	−1.29796e48	−0.503934	−0.251967	+	0.967736i	$0.581078\pi$
$860$	0	0
$861$	3.94860e47	0.147534
$862$	−5.85239e48	−2.14518
$863$	−4.45924e48	−1.60355	−0.801775	−	0.597626i	$-0.796111\pi$
$863$	−4.45924e48	−1.60355	−0.801775	+	0.597626i	$0.796111\pi$
$864$	2.23764e47	0.0789430
$865$	0	0
$866$	5.18137e47	0.175954
$867$	2.49967e47	0.0832853
$868$	−5.00707e48	−1.63685
$869$	8.06886e48	2.58813
$870$	0	0
$871$	1.22167e48	0.377271
$872$	5.47559e48	1.65924
$873$	4.81593e48	1.43201
$874$	−1.64901e48	−0.481156
$875$	0	0
$876$	4.42132e47	0.124232
$877$	3.25524e48	0.897615	0.448808	−	0.893628i	$-0.351849\pi$
$877$	3.25524e48	0.897615	0.448808	+	0.893628i	$0.351849\pi$
$878$	4.33466e48	1.17299
$879$	1.48175e47	0.0393514
$880$	0	0
$881$	2.55040e48	0.652387	0.326193	−	0.945303i	$-0.394234\pi$
$881$	2.55040e48	0.652387	0.326193	+	0.945303i	$0.394234\pi$
$882$	8.75890e48	2.19896
$883$	7.29440e47	0.179737	0.0898686	−	0.995954i	$-0.471355\pi$
$883$	7.29440e47	0.179737	0.0898686	+	0.995954i	$0.471355\pi$
$884$	−6.03171e48	−1.45874
$885$	0	0
$886$	−5.67498e48	−1.32223
$887$	−7.19151e47	−0.164468	−0.0822338	−	0.996613i	$-0.526205\pi$
$887$	−7.19151e47	−0.164468	−0.0822338	+	0.996613i	$0.526205\pi$
$888$	−1.79507e48	−0.402965
$889$	3.27168e48	0.720929
$890$	0	0
$891$	7.66298e48	1.62710
$892$	−1.18637e49	−2.47286
$893$	2.95464e48	0.604583
$894$	1.63233e48	0.327898
$895$	0	0
$896$	−1.28353e49	−2.48499
$897$	−3.74181e47	−0.0711225
$898$	−6.48842e48	−1.21082
$899$	−2.40587e47	−0.0440796
$900$	0	0
$901$	1.77188e48	0.312950
$902$	8.96200e48	1.55416
$903$	1.74861e48	0.297745
$904$	1.45263e49	2.42871
$905$	0	0
$906$	−1.62336e48	−0.261698
$907$	−3.79462e48	−0.600686	−0.300343	−	0.953831i	$-0.597101\pi$
$907$	−3.79462e48	−0.600686	−0.300343	+	0.953831i	$0.597101\pi$
$908$	2.28477e49	3.55161
$909$	7.08775e48	1.08194
$910$	0	0
$911$	5.16241e47	0.0759974	0.0379987	−	0.999278i	$-0.487902\pi$
$911$	5.16241e47	0.0759974	0.0379987	+	0.999278i	$0.487902\pi$
$912$	−7.62669e47	−0.110261
$913$	3.59856e47	0.0510929
$914$	−9.39208e47	−0.130963
$915$	0	0
$916$	2.42861e49	3.26650
$917$	7.07735e48	0.934925
$918$	−6.33544e48	−0.822002
$919$	−1.41530e49	−1.80361	−0.901806	−	0.432141i	$-0.857758\pi$
$919$	−1.41530e49	−1.80361	−0.901806	+	0.432141i	$0.857758\pi$
$920$	0	0
$921$	−4.35888e46	−0.00535909
$922$	−1.95595e49	−2.36209
$923$	−2.17796e48	−0.258358
$924$	−1.00233e49	−1.16794
$925$	0	0
$926$	−1.47996e49	−1.66406
$927$	1.52090e49	1.67991
$928$	1.54739e47	0.0167902
$929$	−3.30086e48	−0.351859	−0.175929	−	0.984403i	$-0.556293\pi$
$929$	−3.30086e48	−0.351859	−0.175929	+	0.984403i	$0.556293\pi$
$930$	0	0
$931$	−5.95003e48	−0.612138
$932$	1.38856e49	1.40347
$933$	−3.55272e48	−0.352788
$934$	−8.61663e48	−0.840647
$935$	0	0
$936$	1.12217e49	1.05683
$937$	1.77391e49	1.64146	0.820729	−	0.571318i	$-0.193568\pi$
$937$	1.77391e49	1.64146	0.820729	+	0.571318i	$0.193568\pi$
$938$	1.84675e49	1.67904
$939$	1.81864e48	0.162467
$940$	0	0
$941$	−7.81290e48	−0.673882	−0.336941	−	0.941526i	$-0.609392\pi$
$941$	−7.81290e48	−0.673882	−0.336941	+	0.941526i	$0.609392\pi$
$942$	−1.07353e48	−0.0909856
$943$	3.40228e48	0.283353
$944$	4.94499e48	0.404695
$945$	0	0
$946$	3.96875e49	3.13654
$947$	−4.67824e48	−0.363336	−0.181668	−	0.983360i	$-0.558150\pi$
$947$	−4.67824e48	−0.363336	−0.181668	+	0.983360i	$0.558150\pi$
$948$	7.60745e48	0.580633
$949$	2.38238e48	0.178697
$950$	0	0
$951$	4.42954e48	0.320908
$952$	−4.68211e49	−3.33374
$953$	5.74579e48	0.402084	0.201042	−	0.979583i	$-0.435567\pi$
$953$	5.74579e48	0.402084	0.201042	+	0.979583i	$0.435567\pi$
$954$	−6.41954e48	−0.441526
$955$	0	0
$956$	1.99369e49	1.32466
$957$	−4.81613e47	−0.0314522
$958$	−2.72258e49	−1.74763
$959$	1.82275e49	1.15006
$960$	0	0
$961$	−1.19034e49	−0.725666
$962$	−1.88362e49	−1.12877
$963$	−1.86696e48	−0.109977
$964$	5.26174e49	3.04690
$965$	0	0
$966$	−5.65637e48	−0.316530
$967$	−7.95661e48	−0.437715	−0.218857	−	0.975757i	$-0.570233\pi$
$967$	−7.95661e48	−0.437715	−0.218857	+	0.975757i	$0.570233\pi$
$968$	−8.27039e49	−4.47283
$969$	2.10707e48	0.112031
$970$	0	0
$971$	8.39693e48	0.431522	0.215761	−	0.976446i	$-0.430777\pi$
$971$	8.39693e48	0.431522	0.215761	+	0.976446i	$0.430777\pi$
$972$	2.33227e49	1.17838
$973$	1.57040e49	0.780098
$974$	−3.58096e49	−1.74895
$975$	0	0
$976$	−2.52385e49	−1.19163
$977$	3.91342e48	0.181675	0.0908377	−	0.995866i	$-0.471046\pi$
$977$	3.91342e48	0.181675	0.0908377	+	0.995866i	$0.471046\pi$
$978$	1.02845e49	0.469454
$979$	3.41272e49	1.53174
$980$	0	0
$981$	1.98770e49	0.862604
$982$	3.60406e49	1.53799
$983$	−1.84117e49	−0.772612	−0.386306	−	0.922371i	$-0.626249\pi$
$983$	−1.84117e49	−0.772612	−0.386306	+	0.922371i	$0.626249\pi$
$984$	4.33888e48	0.179043
$985$	0	0
$986$	−4.38112e48	−0.174830
$987$	1.01349e49	0.397728
$988$	−1.48450e49	−0.572916
$989$	1.50668e49	0.571849
$990$	0	0
$991$	4.75733e47	0.0174642	0.00873208	−	0.999962i	$-0.497220\pi$
$991$	4.75733e47	0.0174642	0.00873208	+	0.999962i	$0.497220\pi$
$992$	−2.89429e48	−0.104496
$993$	−4.26973e48	−0.151614
$994$	−3.29235e49	−1.14982
$995$	0	0
$996$	3.39278e47	0.0114624
$997$	−2.41124e49	−0.801254	−0.400627	−	0.916241i	$-0.631208\pi$
$997$	−2.41124e49	−0.801254	−0.400627	+	0.916241i	$0.631208\pi$
$998$	3.43646e49	1.12320
$999$	−1.33097e49	−0.427894

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.34.a.f.1.1		16
5.2	odd	4		5.34.b.a.4.1	✓	16
5.3	odd	4		5.34.b.a.4.16	yes	16
5.4	even	2	inner	25.34.a.f.1.16		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.34.b.a.4.1	✓	16	5.2	odd	4
5.34.b.a.4.16	yes	16	5.3	odd	4
25.34.a.f.1.1		16	1.1	even	1	trivial
25.34.a.f.1.16		16	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-162009. q^{2} +1.50582e7 q^{3} +1.76568e10 q^{4} -2.43956e12 q^{6} -1.33679e14 q^{7} -1.46891e15 q^{8} -5.33231e15 q^{9} +O(q^{10})\)	\(q-162009. q^{2} +1.50582e7 q^{3} +1.76568e10 q^{4} -2.43956e12 q^{6} -1.33679e14 q^{7} -1.46891e15 q^{8} -5.33231e15 q^{9} +2.82007e17 q^{11} +2.65881e17 q^{12} +1.43267e18 q^{13} +2.16571e19 q^{14} +8.63057e19 q^{16} -2.38442e20 q^{17} +8.63880e20 q^{18} -5.86844e20 q^{19} -2.01297e21 q^{21} -4.56875e22 q^{22} -1.73446e22 q^{23} -2.21193e22 q^{24} -2.32104e23 q^{26} -1.64005e23 q^{27} -2.36034e24 q^{28} -1.13413e23 q^{29} +2.12133e24 q^{31} -1.36438e24 q^{32} +4.24652e24 q^{33} +3.86296e25 q^{34} -9.41517e25 q^{36} +8.11541e25 q^{37} +9.50738e25 q^{38} +2.15734e25 q^{39} -1.96159e26 q^{41} +3.26118e26 q^{42} -8.68674e26 q^{43} +4.97935e27 q^{44} +2.80997e27 q^{46} -5.03480e27 q^{47} +1.29961e27 q^{48} +1.01390e28 q^{49} -3.59051e27 q^{51} +2.52963e28 q^{52} -7.43106e27 q^{53} +2.65702e28 q^{54} +1.96363e29 q^{56} -8.83684e27 q^{57} +1.83740e28 q^{58} +5.72962e28 q^{59} -2.92431e29 q^{61} -3.43673e29 q^{62} +7.12817e29 q^{63} -5.20320e29 q^{64} -6.87973e29 q^{66} +8.52723e29 q^{67} -4.21013e30 q^{68} -2.61178e29 q^{69} -1.52022e30 q^{71} +7.83271e30 q^{72} +1.66290e30 q^{73} -1.31477e31 q^{74} -1.03618e31 q^{76} -3.76983e31 q^{77} -3.49508e30 q^{78} +2.86123e31 q^{79} +2.71730e31 q^{81} +3.17794e31 q^{82} +1.27605e30 q^{83} -3.55426e31 q^{84} +1.40733e32 q^{86} -1.70781e30 q^{87} -4.14244e32 q^{88} +1.21015e32 q^{89} -1.91517e32 q^{91} -3.06250e32 q^{92} +3.19435e31 q^{93} +8.15681e32 q^{94} -2.05451e31 q^{96} -9.03160e32 q^{97} -1.64261e33 q^{98} -1.50375e33 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 72851326872 q^{4} + 11001777346872 q^{6} + 27\!\cdots\!68 q^{9}+O(q^{10}) \) 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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