LMFDB - Embedded newform 245.10.a.e.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [245,10,Mod(1,245)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("245.1"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(245, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 10, names="a")

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	245.a (trivial)

Newform invariants

comment:select newform

sage:traces = [4,-19,18] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$126.183779860$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 648x^{2} + 6926x - 8308 $ x^4 - x^3 - 648x^2 + 6926x - 8308
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2\cdot 3^{2}\cdot 5 $
Twist minimal:	no (minimal twist has level 35)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$16.7769$ of defining polynomial
Character	$\chi$	$=$	245.1

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+33.3659 q^{2} +72.5961 q^{3} +601.285 q^{4} +625.000 q^{5} +2422.24 q^{6} +2979.08 q^{8} -14412.8 q^{9} +20853.7 q^{10} -31567.7 q^{11} +43651.0 q^{12} -67041.9 q^{13} +45372.6 q^{15} -208458. q^{16} +221458. q^{17} -480897. q^{18} +631713. q^{19} +375803. q^{20} -1.05329e6 q^{22} +290099. q^{23} +216270. q^{24} +390625. q^{25} -2.23692e6 q^{26} -2.47522e6 q^{27} -2.34008e6 q^{29} +1.51390e6 q^{30} -6.68779e6 q^{31} -8.48069e6 q^{32} -2.29170e6 q^{33} +7.38915e6 q^{34} -8.66620e6 q^{36} -4.33836e6 q^{37} +2.10777e7 q^{38} -4.86698e6 q^{39} +1.86193e6 q^{40} -1.29663e7 q^{41} -3.85567e7 q^{43} -1.89812e7 q^{44} -9.00800e6 q^{45} +9.67941e6 q^{46} -5.63758e7 q^{47} -1.51333e7 q^{48} +1.30336e7 q^{50} +1.60770e7 q^{51} -4.03113e7 q^{52} +4.95291e7 q^{53} -8.25881e7 q^{54} -1.97298e7 q^{55} +4.58599e7 q^{57} -7.80789e7 q^{58} +1.21109e7 q^{59} +2.72819e7 q^{60} +6.35756e7 q^{61} -2.23144e8 q^{62} -1.76236e8 q^{64} -4.19012e7 q^{65} -7.64645e7 q^{66} +1.35134e8 q^{67} +1.33159e8 q^{68} +2.10600e7 q^{69} -8.05749e7 q^{71} -4.29369e7 q^{72} -2.43855e6 q^{73} -1.44754e8 q^{74} +2.83579e7 q^{75} +3.79840e8 q^{76} -1.62391e8 q^{78} -5.06746e8 q^{79} -1.30286e8 q^{80} +1.03996e8 q^{81} -4.32634e8 q^{82} +5.73793e8 q^{83} +1.38411e8 q^{85} -1.28648e9 q^{86} -1.69881e8 q^{87} -9.40429e7 q^{88} +5.34274e8 q^{89} -3.00560e8 q^{90} +1.74432e8 q^{92} -4.85508e8 q^{93} -1.88103e9 q^{94} +3.94821e8 q^{95} -6.15665e8 q^{96} +1.27379e9 q^{97} +4.54980e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 19 q^{2} + 18 q^{3} + 1729 q^{4} + 2500 q^{5} + 144 q^{6} - 30495 q^{8} + 5382 q^{9} - 11875 q^{10} + 82438 q^{11} - 41328 q^{12} + 72962 q^{13} + 11250 q^{15} + 64257 q^{16} + 357542 q^{17} - 965367 q^{18}+ \cdots + 1222369524 q^{99}+O(q^{100}) $ 4 * q - 19 * q^2 + 18 * q^3 + 1729 * q^4 + 2500 * q^5 + 144 * q^6 - 30495 * q^8 + 5382 * q^9 - 11875 * q^10 + 82438 * q^11 - 41328 * q^12 + 72962 * q^13 + 11250 * q^15 + 64257 * q^16 + 357542 * q^17 - 965367 * q^18 - 300732 * q^19 + 1080625 * q^20 - 5595068 * q^22 - 2340836 * q^23 + 7636320 * q^24 + 1562500 * q^25 - 1305666 * q^26 + 4240350 * q^27 - 1372022 * q^29 + 90000 * q^30 + 4590888 * q^31 - 10529439 * q^32 - 2000034 * q^33 + 7199478 * q^34 - 9144243 * q^36 - 38868456 * q^37 + 15477280 * q^38 - 46666242 * q^39 - 19059375 * q^40 - 57287084 * q^41 - 43403452 * q^43 + 87639348 * q^44 + 3363750 * q^45 + 28892416 * q^46 - 91822222 * q^47 - 156168864 * q^48 - 7421875 * q^50 + 86342634 * q^51 - 1953386 * q^52 - 61086884 * q^53 - 187589520 * q^54 + 51523750 * q^55 - 79928892 * q^57 + 29615390 * q^58 - 72569680 * q^59 - 25830000 * q^60 + 225681036 * q^61 - 190286472 * q^62 + 141443393 * q^64 + 45601250 * q^65 + 119673648 * q^66 - 4429720 * q^67 - 15339698 * q^68 - 348300612 * q^69 - 470468984 * q^71 + 298610685 * q^72 + 168326464 * q^73 + 927809502 * q^74 + 7031250 * q^75 + 892265344 * q^76 + 281290896 * q^78 - 598805646 * q^79 + 40160625 * q^80 - 847155996 * q^81 + 1821993318 * q^82 + 1159074304 * q^83 + 223463750 * q^85 + 706791156 * q^86 + 421480998 * q^87 - 1992103900 * q^88 + 1380153012 * q^89 - 603354375 * q^90 + 710319264 * q^92 - 1601969400 * q^93 - 2466744152 * q^94 - 187957500 * q^95 + 799321824 * q^96 - 754874082 * q^97 + 1222369524 * q^99

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 $

$2$	33.3659	1.47458	0.737290	−	0.675577i	$-0.236105\pi$
$2$	33.3659	1.47458	0.737290	+	0.675577i	$0.236105\pi$
$3$	72.5961	0.517449	0.258725	−	0.965951i	$-0.416698\pi$
$3$	72.5961	0.517449	0.258725	+	0.965951i	$0.416698\pi$
$4$	601.285	1.17439
$5$	625.000	0.447214
$5$	625.000	0.447214
$6$	2422.24	0.763020
$7$	0	0
$7$	0	0
$8$	2979.08	0.257145
$9$	−14412.8	−0.732246
$10$	20853.7	0.659452
$11$	−31567.7	−0.650094	−0.325047	−	0.945698i	$-0.605380\pi$
$11$	−31567.7	−0.650094	−0.325047	+	0.945698i	$0.605380\pi$
$12$	43651.0	0.607685
$13$	−67041.9	−0.651031	−0.325515	−	0.945537i	$-0.605538\pi$
$13$	−67041.9	−0.651031	−0.325515	+	0.945537i	$0.605538\pi$
$14$	0	0
$15$	45372.6	0.231410
$16$	−208458.	−0.795205
$17$	221458.	0.643089	0.321545	−	0.946894i	$-0.395798\pi$
$17$	221458.	0.643089	0.321545	+	0.946894i	$0.395798\pi$
$18$	−480897.	−1.07976
$19$	631713.	1.11206	0.556031	−	0.831162i	$-0.312324\pi$
$19$	631713.	1.11206	0.556031	+	0.831162i	$0.312324\pi$
$20$	375803.	0.525201
$21$	0	0
$22$	−1.05329e6	−0.958616
$23$	290099.	0.216157	0.108079	−	0.994142i	$-0.465530\pi$
$23$	290099.	0.216157	0.108079	+	0.994142i	$0.465530\pi$
$24$	216270.	0.133059
$25$	390625.	0.200000
$26$	−2.23692e6	−0.959996
$27$	−2.47522e6	−0.896350
$28$	0	0
$29$	−2.34008e6	−0.614383	−0.307192	−	0.951648i	$-0.599389\pi$
$29$	−2.34008e6	−0.614383	−0.307192	+	0.951648i	$0.599389\pi$
$30$	1.51390e6	0.341233
$31$	−6.68779e6	−1.30063	−0.650317	−	0.759663i	$-0.725364\pi$
$31$	−6.68779e6	−1.30063	−0.650317	+	0.759663i	$0.725364\pi$
$32$	−8.48069e6	−1.42974
$33$	−2.29170e6	−0.336391
$34$	7.38915e6	0.948286
$35$	0	0
$36$	−8.66620e6	−0.859939
$37$	−4.33836e6	−0.380556	−0.190278	−	0.981730i	$-0.560939\pi$
$37$	−4.33836e6	−0.380556	−0.190278	+	0.981730i	$0.560939\pi$
$38$	2.10777e7	1.63982
$39$	−4.86698e6	−0.336875
$40$	1.86193e6	0.114999
$41$	−1.29663e7	−0.716621	−0.358311	−	0.933602i	$-0.616647\pi$
$41$	−1.29663e7	−0.716621	−0.358311	+	0.933602i	$0.616647\pi$
$42$	0	0
$43$	−3.85567e7	−1.71985	−0.859927	−	0.510416i	$-0.829491\pi$
$43$	−3.85567e7	−1.71985	−0.859927	+	0.510416i	$0.829491\pi$
$44$	−1.89812e7	−0.763461
$45$	−9.00800e6	−0.327470
$46$	9.67941e6	0.318741
$47$	−5.63758e7	−1.68520	−0.842602	−	0.538536i	$-0.818978\pi$
$47$	−5.63758e7	−1.68520	−0.842602	+	0.538536i	$0.818978\pi$
$48$	−1.51333e7	−0.411478
$49$	0	0
$50$	1.30336e7	0.294916
$51$	1.60770e7	0.332766
$52$	−4.03113e7	−0.764561
$53$	4.95291e7	0.862222	0.431111	−	0.902299i	$-0.358122\pi$
$53$	4.95291e7	0.862222	0.431111	+	0.902299i	$0.358122\pi$
$54$	−8.25881e7	−1.32174
$55$	−1.97298e7	−0.290731
$56$	0	0
$57$	4.58599e7	0.575435
$58$	−7.80789e7	−0.905957
$59$	1.21109e7	0.130119	0.0650597	−	0.997881i	$-0.479276\pi$
$59$	1.21109e7	0.130119	0.0650597	+	0.997881i	$0.479276\pi$
$60$	2.72819e7	0.271765
$61$	6.35756e7	0.587904	0.293952	−	0.955820i	$-0.405029\pi$
$61$	6.35756e7	0.587904	0.293952	+	0.955820i	$0.405029\pi$
$62$	−2.23144e8	−1.91789
$63$	0	0
$64$	−1.76236e8	−1.31306
$65$	−4.19012e7	−0.291150
$66$	−7.64645e7	−0.496035
$67$	1.35134e8	0.819270	0.409635	−	0.912249i	$-0.365656\pi$
$67$	1.35134e8	0.819270	0.409635	+	0.912249i	$0.365656\pi$
$68$	1.33159e8	0.755234
$69$	2.10600e7	0.111851
$70$	0	0
$71$	−8.05749e7	−0.376302	−0.188151	−	0.982140i	$-0.560249\pi$
$71$	−8.05749e7	−0.376302	−0.188151	+	0.982140i	$0.560249\pi$
$72$	−4.29369e7	−0.188293
$73$	−2.43855e6	−0.0100503	−0.00502516	−	0.999987i	$-0.501600\pi$
$73$	−2.43855e6	−0.0100503	−0.00502516	+	0.999987i	$0.501600\pi$
$74$	−1.44754e8	−0.561160
$75$	2.83579e7	0.103490
$76$	3.79840e8	1.30599
$77$	0	0
$78$	−1.62391e8	−0.496749
$79$	−5.06746e8	−1.46376	−0.731878	−	0.681436i	$-0.761356\pi$
$79$	−5.06746e8	−1.46376	−0.731878	+	0.681436i	$0.761356\pi$
$80$	−1.30286e8	−0.355626
$81$	1.03996e8	0.268431
$82$	−4.32634e8	−1.05672
$83$	5.73793e8	1.32710	0.663550	−	0.748132i	$-0.269049\pi$
$83$	5.73793e8	1.32710	0.663550	+	0.748132i	$0.269049\pi$
$84$	0	0
$85$	1.38411e8	0.287598
$86$	−1.28648e9	−2.53606
$87$	−1.69881e8	−0.317912
$88$	−9.40429e7	−0.167168
$89$	5.34274e8	0.902628	0.451314	−	0.892365i	$-0.350955\pi$
$89$	5.34274e8	0.902628	0.451314	+	0.892365i	$0.350955\pi$
$90$	−3.00560e8	−0.482881
$91$	0	0
$92$	1.74432e8	0.253852
$93$	−4.85508e8	−0.673012
$94$	−1.88103e9	−2.48497
$95$	3.94821e8	0.497329
$96$	−6.15665e8	−0.739817
$97$	1.27379e9	1.46091	0.730456	−	0.682960i	$-0.239308\pi$
$97$	1.27379e9	1.46091	0.730456	+	0.682960i	$0.239308\pi$
$98$	0	0
$99$	4.54980e8	0.476029
$100$	2.34877e8	0.234877
$101$	−8.98270e8	−0.858936	−0.429468	−	0.903082i	$-0.641299\pi$
$101$	−8.98270e8	−0.858936	−0.429468	+	0.903082i	$0.641299\pi$
$102$	5.36424e8	0.490690
$103$	−2.71408e8	−0.237605	−0.118802	−	0.992918i	$-0.537905\pi$
$103$	−2.71408e8	−0.237605	−0.118802	+	0.992918i	$0.537905\pi$
$104$	−1.99724e8	−0.167409
$105$	0	0
$106$	1.65258e9	1.27141
$107$	−2.35700e9	−1.73833	−0.869167	−	0.494519i	$-0.835344\pi$
$107$	−2.35700e9	−1.73833	−0.869167	+	0.494519i	$0.835344\pi$
$108$	−1.48832e9	−1.05266
$109$	8.33176e7	0.0565350	0.0282675	−	0.999600i	$-0.491001\pi$
$109$	8.33176e7	0.0565350	0.0282675	+	0.999600i	$0.491001\pi$
$110$	−6.58304e8	−0.428706
$111$	−3.14948e8	−0.196918
$112$	0	0
$113$	−2.81122e9	−1.62197	−0.810984	−	0.585068i	$-0.801068\pi$
$113$	−2.81122e9	−1.62197	−0.810984	+	0.585068i	$0.801068\pi$
$114$	1.53016e9	0.848525
$115$	1.81312e8	0.0966686
$116$	−1.40705e9	−0.721523
$117$	9.66262e8	0.476715
$118$	4.04091e8	0.191871
$119$	0	0
$120$	1.35169e8	0.0595060
$121$	−1.36143e9	−0.577377
$122$	2.12126e9	0.866911
$123$	−9.41305e8	−0.370815
$124$	−4.02127e9	−1.52745
$125$	2.44141e8	0.0894427
$126$	0	0
$127$	2.64718e9	0.902956	0.451478	−	0.892282i	$-0.350897\pi$
$127$	2.64718e9	0.902956	0.451478	+	0.892282i	$0.350897\pi$
$128$	−1.53815e9	−0.506470
$129$	−2.79907e9	−0.889938
$130$	−1.39807e9	−0.429323
$131$	1.19960e9	0.355889	0.177944	−	0.984041i	$-0.443055\pi$
$131$	1.19960e9	0.355889	0.177944	+	0.984041i	$0.443055\pi$
$132$	−1.37796e9	−0.395052
$133$	0	0
$134$	4.50886e9	1.20808
$135$	−1.54701e9	−0.400860
$136$	6.59742e8	0.165367
$137$	−5.99431e9	−1.45377	−0.726886	−	0.686758i	$-0.759033\pi$
$137$	−5.99431e9	−1.45377	−0.726886	+	0.686758i	$0.759033\pi$
$138$	7.02687e8	0.164933
$139$	−2.37734e9	−0.540162	−0.270081	−	0.962838i	$-0.587051\pi$
$139$	−2.37734e9	−0.540162	−0.270081	+	0.962838i	$0.587051\pi$
$140$	0	0
$141$	−4.09267e9	−0.872008
$142$	−2.68845e9	−0.554888
$143$	2.11636e9	0.423231
$144$	3.00447e9	0.582286
$145$	−1.46255e9	−0.274761
$146$	−8.13646e7	−0.0148200
$147$	0	0
$148$	−2.60859e9	−0.446919
$149$	9.90778e9	1.64679	0.823395	−	0.567469i	$-0.192077\pi$
$149$	9.90778e9	1.64679	0.823395	+	0.567469i	$0.192077\pi$
$150$	9.46186e8	0.152604
$151$	1.26968e8	0.0198746	0.00993731	−	0.999951i	$-0.496837\pi$
$151$	1.26968e8	0.0198746	0.00993731	+	0.999951i	$0.496837\pi$
$152$	1.88193e9	0.285961
$153$	−3.19183e9	−0.470900
$154$	0	0
$155$	−4.17987e9	−0.581661
$156$	−2.92645e9	−0.395621
$157$	6.13719e8	0.0806160	0.0403080	−	0.999187i	$-0.487166\pi$
$157$	6.13719e8	0.0806160	0.0403080	+	0.999187i	$0.487166\pi$
$158$	−1.69081e10	−2.15842
$159$	3.59562e9	0.446156
$160$	−5.30043e9	−0.639398
$161$	0	0
$162$	3.46991e9	0.395823
$163$	2.44352e9	0.271126	0.135563	−	0.990769i	$-0.456716\pi$
$163$	2.44352e9	0.271126	0.135563	+	0.990769i	$0.456716\pi$
$164$	−7.79646e9	−0.841589
$165$	−1.43231e9	−0.150439
$166$	1.91451e10	1.95692
$167$	−4.06048e9	−0.403974	−0.201987	−	0.979388i	$-0.564740\pi$
$167$	−4.06048e9	−0.403974	−0.201987	+	0.979388i	$0.564740\pi$
$168$	0	0
$169$	−6.10988e9	−0.576159
$170$	4.61822e9	0.424086
$171$	−9.10476e9	−0.814303
$172$	−2.31836e10	−2.01977
$173$	1.21147e10	1.02827	0.514135	−	0.857710i	$-0.328113\pi$
$173$	1.21147e10	1.02827	0.514135	+	0.857710i	$0.328113\pi$
$174$	−5.66823e9	−0.468787
$175$	0	0
$176$	6.58055e9	0.516958
$177$	8.79204e8	0.0673302
$178$	1.78265e10	1.33100
$179$	9.79296e9	0.712977	0.356488	−	0.934300i	$-0.383974\pi$
$179$	9.79296e9	0.712977	0.356488	+	0.934300i	$0.383974\pi$
$180$	−5.41638e9	−0.384576
$181$	−2.76258e9	−0.191320	−0.0956602	−	0.995414i	$-0.530496\pi$
$181$	−2.76258e9	−0.191320	−0.0956602	+	0.995414i	$0.530496\pi$
$182$	0	0
$183$	4.61534e9	0.304210
$184$	8.64228e8	0.0555838
$185$	−2.71148e9	−0.170190
$186$	−1.61994e10	−0.992410
$187$	−6.99093e9	−0.418069
$188$	−3.38980e10	−1.97908
$189$	0	0
$190$	1.31736e10	0.733351
$191$	2.56580e10	1.39500	0.697498	−	0.716587i	$-0.254297\pi$
$191$	2.56580e10	1.39500	0.697498	+	0.716587i	$0.254297\pi$
$192$	−1.27940e10	−0.679440
$193$	−5.05038e9	−0.262009	−0.131004	−	0.991382i	$-0.541820\pi$
$193$	−5.05038e9	−0.262009	−0.131004	+	0.991382i	$0.541820\pi$
$194$	4.25011e10	2.15423
$195$	−3.04186e9	−0.150655
$196$	0	0
$197$	3.28142e10	1.55226	0.776130	−	0.630573i	$-0.217180\pi$
$197$	3.28142e10	1.55226	0.776130	+	0.630573i	$0.217180\pi$
$198$	1.51808e10	0.701943
$199$	−8.62788e9	−0.390000	−0.195000	−	0.980803i	$-0.562471\pi$
$199$	−8.62788e9	−0.390000	−0.195000	+	0.980803i	$0.562471\pi$
$200$	1.16370e9	0.0514290
$201$	9.81019e9	0.423931
$202$	−2.99716e10	−1.26657
$203$	0	0
$204$	9.66686e9	0.390795
$205$	−8.10396e9	−0.320483
$206$	−9.05578e9	−0.350367
$207$	−4.18113e9	−0.158281
$208$	1.39754e10	0.517703
$209$	−1.99418e10	−0.722945
$210$	0	0
$211$	4.74503e10	1.64804	0.824021	−	0.566560i	$-0.191726\pi$
$211$	4.74503e10	1.64804	0.824021	+	0.566560i	$0.191726\pi$
$212$	2.97811e10	1.01258
$213$	−5.84942e9	−0.194717
$214$	−7.86436e10	−2.56331
$215$	−2.40979e10	−0.769142
$216$	−7.37390e9	−0.230492
$217$	0	0
$218$	2.77997e9	0.0833654
$219$	−1.77030e8	−0.00520053
$220$	−1.18633e10	−0.341430
$221$	−1.48470e10	−0.418671
$222$	−1.05085e10	−0.290372
$223$	3.36546e10	0.911323	0.455662	−	0.890153i	$-0.349403\pi$
$223$	3.36546e10	0.911323	0.455662	+	0.890153i	$0.349403\pi$
$224$	0	0
$225$	−5.63000e9	−0.146449
$226$	−9.37991e10	−2.39172
$227$	1.07110e10	0.267739	0.133870	−	0.990999i	$-0.457260\pi$
$227$	1.07110e10	0.267739	0.133870	+	0.990999i	$0.457260\pi$
$228$	2.75749e10	0.675783
$229$	7.75472e10	1.86340	0.931701	−	0.363227i	$-0.118325\pi$
$229$	7.75472e10	1.86340	0.931701	+	0.363227i	$0.118325\pi$
$230$	6.04963e9	0.142546
$231$	0	0
$232$	−6.97129e9	−0.157986
$233$	−3.86201e10	−0.858443	−0.429221	−	0.903199i	$-0.641212\pi$
$233$	−3.86201e10	−0.858443	−0.429221	+	0.903199i	$0.641212\pi$
$234$	3.22402e10	0.702954
$235$	−3.52349e10	−0.753647
$236$	7.28210e9	0.152810
$237$	−3.67878e10	−0.757419
$238$	0	0
$239$	−2.14449e10	−0.425141	−0.212570	−	0.977146i	$-0.568183\pi$
$239$	−2.14449e10	−0.425141	−0.212570	+	0.977146i	$0.568183\pi$
$240$	−9.45828e9	−0.184019
$241$	4.13579e9	0.0789735	0.0394867	−	0.999220i	$-0.487428\pi$
$241$	4.13579e9	0.0789735	0.0394867	+	0.999220i	$0.487428\pi$
$242$	−4.54252e10	−0.851389
$243$	5.62695e10	1.03525
$244$	3.82271e10	0.690425
$245$	0	0
$246$	−3.14075e10	−0.546797
$247$	−4.23513e10	−0.723986
$248$	−1.99235e10	−0.334451
$249$	4.16552e10	0.686707
$250$	8.14598e9	0.131890
$251$	3.40309e9	0.0541179	0.0270590	−	0.999634i	$-0.491386\pi$
$251$	3.40309e9	0.0541179	0.0270590	+	0.999634i	$0.491386\pi$
$252$	0	0
$253$	−9.15776e9	−0.140523
$254$	8.83256e10	1.33148
$255$	1.00481e10	0.148817
$256$	3.89108e10	0.566227
$257$	−1.21780e11	−1.74131	−0.870656	−	0.491892i	$-0.836305\pi$
$257$	−1.21780e11	−1.74131	−0.870656	+	0.491892i	$0.836305\pi$
$258$	−9.33935e10	−1.31228
$259$	0	0
$260$	−2.51946e10	−0.341922
$261$	3.37271e10	0.449880
$262$	4.00256e10	0.524786
$263$	−3.31945e9	−0.0427824	−0.0213912	−	0.999771i	$-0.506810\pi$
$263$	−3.31945e9	−0.0427824	−0.0213912	+	0.999771i	$0.506810\pi$
$264$	−6.82715e9	−0.0865012
$265$	3.09557e10	0.385597
$266$	0	0
$267$	3.87862e10	0.467064
$268$	8.12539e10	0.962139
$269$	−1.58296e11	−1.84326	−0.921628	−	0.388074i	$-0.873141\pi$
$269$	−1.58296e11	−1.84326	−0.921628	+	0.388074i	$0.873141\pi$
$270$	−5.16176e10	−0.591100
$271$	−1.48795e11	−1.67581	−0.837907	−	0.545813i	$-0.816221\pi$
$271$	−1.48795e11	−1.67581	−0.837907	+	0.545813i	$0.816221\pi$
$272$	−4.61647e10	−0.511387
$273$	0	0
$274$	−2.00006e11	−2.14370
$275$	−1.23311e10	−0.130019
$276$	1.26631e10	0.131356
$277$	−1.35981e11	−1.38777	−0.693886	−	0.720085i	$-0.744103\pi$
$277$	−1.35981e11	−1.38777	−0.693886	+	0.720085i	$0.744103\pi$
$278$	−7.93221e10	−0.796512
$279$	9.63899e10	0.952385
$280$	0	0
$281$	4.38976e10	0.420012	0.210006	−	0.977700i	$-0.432652\pi$
$281$	4.38976e10	0.420012	0.210006	+	0.977700i	$0.432652\pi$
$282$	−1.36556e11	−1.28585
$283$	−9.75168e10	−0.903734	−0.451867	−	0.892085i	$-0.649242\pi$
$283$	−9.75168e10	−0.903734	−0.451867	+	0.892085i	$0.649242\pi$
$284$	−4.84485e10	−0.441924
$285$	2.86625e10	0.257342
$286$	7.06144e10	0.624088
$287$	0	0
$288$	1.22231e11	1.04692
$289$	−6.95442e10	−0.586436
$290$	−4.87993e10	−0.405156
$291$	9.24720e10	0.755948
$292$	−1.46627e9	−0.0118029
$293$	1.09292e11	0.866334	0.433167	−	0.901314i	$-0.357396\pi$
$293$	1.09292e11	0.866334	0.433167	+	0.901314i	$0.357396\pi$
$294$	0	0
$295$	7.56931e9	0.0581912
$296$	−1.29244e10	−0.0978579
$297$	7.81372e10	0.582712
$298$	3.30582e11	2.42832
$299$	−1.94488e10	−0.140725
$300$	1.70512e10	0.121537
$301$	0	0
$302$	4.23641e9	0.0293067
$303$	−6.52110e10	−0.444456
$304$	−1.31686e11	−0.884316
$305$	3.97347e10	0.262918
$306$	−1.06498e11	−0.694379
$307$	2.13340e11	1.37072	0.685361	−	0.728204i	$-0.259644\pi$
$307$	2.13340e11	1.37072	0.685361	+	0.728204i	$0.259644\pi$
$308$	0	0
$309$	−1.97032e10	−0.122948
$310$	−1.39465e11	−0.857706
$311$	−1.99732e11	−1.21067	−0.605334	−	0.795972i	$-0.706960\pi$
$311$	−1.99732e11	−1.21067	−0.605334	+	0.795972i	$0.706960\pi$
$312$	−1.44992e10	−0.0866257
$313$	1.43229e11	0.843493	0.421747	−	0.906714i	$-0.361417\pi$
$313$	1.43229e11	0.843493	0.421747	+	0.906714i	$0.361417\pi$
$314$	2.04773e10	0.118875
$315$	0	0
$316$	−3.04699e11	−1.71901
$317$	−5.09593e10	−0.283437	−0.141719	−	0.989907i	$-0.545263\pi$
$317$	−5.09593e10	−0.283437	−0.141719	+	0.989907i	$0.545263\pi$
$318$	1.19971e11	0.657892
$319$	7.38710e10	0.399407
$320$	−1.10147e11	−0.587217
$321$	−1.71109e11	−0.899499
$322$	0	0
$323$	1.39898e11	0.715155
$324$	6.25310e10	0.315241
$325$	−2.61883e10	−0.130206
$326$	8.15304e10	0.399798
$327$	6.04854e9	0.0292540
$328$	−3.86278e10	−0.184275
$329$	0	0
$330$	−4.77903e10	−0.221834
$331$	−2.98793e11	−1.36819	−0.684093	−	0.729395i	$-0.739802\pi$
$331$	−2.98793e11	−1.36819	−0.684093	+	0.729395i	$0.739802\pi$
$332$	3.45013e11	1.55853
$333$	6.25280e10	0.278660
$334$	−1.35482e11	−0.595692
$335$	8.44586e10	0.366389
$336$	0	0
$337$	2.23348e11	0.943293	0.471647	−	0.881788i	$-0.343660\pi$
$337$	2.23348e11	0.943293	0.471647	+	0.881788i	$0.343660\pi$
$338$	−2.03862e11	−0.849593
$339$	−2.04084e11	−0.839286
$340$	8.32246e10	0.337751
$341$	2.11119e11	0.845535
$342$	−3.03789e11	−1.20075
$343$	0	0
$344$	−1.14864e11	−0.442252
$345$	1.31625e10	0.0500211
$346$	4.04220e11	1.51626
$347$	2.51012e11	0.929420	0.464710	−	0.885463i	$-0.346159\pi$
$347$	2.51012e11	0.929420	0.464710	+	0.885463i	$0.346159\pi$
$348$	−1.02147e11	−0.373351
$349$	4.70348e11	1.69709	0.848546	−	0.529122i	$-0.177479\pi$
$349$	4.70348e11	1.69709	0.848546	+	0.529122i	$0.177479\pi$
$350$	0	0
$351$	1.65944e11	0.583551
$352$	2.67716e11	0.929464
$353$	4.00610e11	1.37321	0.686603	−	0.727033i	$-0.259101\pi$
$353$	4.00610e11	1.37321	0.686603	+	0.727033i	$0.259101\pi$
$354$	2.93355e10	0.0992837
$355$	−5.03593e10	−0.168288
$356$	3.21251e11	1.06003
$357$	0	0
$358$	3.26751e11	1.05134
$359$	3.52353e11	1.11957	0.559787	−	0.828636i	$-0.310883\pi$
$359$	3.52353e11	1.11957	0.559787	+	0.828636i	$0.310883\pi$
$360$	−2.68356e10	−0.0842073
$361$	7.63738e10	0.236680
$362$	−9.21761e10	−0.282117
$363$	−9.88342e10	−0.298763
$364$	0	0
$365$	−1.52410e9	−0.00449464
$366$	1.53995e11	0.448582
$367$	−1.75971e11	−0.506341	−0.253170	−	0.967422i	$-0.581473\pi$
$367$	−1.75971e11	−0.506341	−0.253170	+	0.967422i	$0.581473\pi$
$368$	−6.04734e10	−0.171889
$369$	1.86881e11	0.524743
$370$	−9.04710e10	−0.250958
$371$	0	0
$372$	−2.91929e11	−0.790376
$373$	−3.80474e11	−1.01774	−0.508868	−	0.860844i	$-0.669936\pi$
$373$	−3.80474e11	−1.01774	−0.508868	+	0.860844i	$0.669936\pi$
$374$	−2.33259e11	−0.616475
$375$	1.77237e10	0.0462821
$376$	−1.67948e11	−0.433342
$377$	1.56883e11	0.399982
$378$	0	0
$379$	−5.66093e11	−1.40933	−0.704663	−	0.709542i	$-0.748902\pi$
$379$	−5.66093e11	−1.40933	−0.704663	+	0.709542i	$0.748902\pi$
$380$	2.37400e11	0.584056
$381$	1.92175e11	0.467234
$382$	8.56103e11	2.05703
$383$	7.72152e11	1.83362	0.916808	−	0.399328i	$-0.130757\pi$
$383$	7.72152e11	1.83362	0.916808	+	0.399328i	$0.130757\pi$
$384$	−1.11664e11	−0.262072
$385$	0	0
$386$	−1.68511e11	−0.386353
$387$	5.55710e11	1.25936
$388$	7.65909e11	1.71567
$389$	−7.13084e11	−1.57895	−0.789473	−	0.613785i	$-0.789646\pi$
$389$	−7.13084e11	−1.57895	−0.789473	+	0.613785i	$0.789646\pi$
$390$	−1.01495e11	−0.222153
$391$	6.42446e10	0.139009
$392$	0	0
$393$	8.70860e10	0.184154
$394$	1.09488e12	2.28893
$395$	−3.16716e11	−0.654611
$396$	2.73572e11	0.559042
$397$	2.69598e11	0.544703	0.272351	−	0.962198i	$-0.412199\pi$
$397$	2.69598e11	0.544703	0.272351	+	0.962198i	$0.412199\pi$
$398$	−2.87877e11	−0.575087
$399$	0	0
$400$	−8.14290e10	−0.159041
$401$	−2.29145e11	−0.442549	−0.221275	−	0.975212i	$-0.571022\pi$
$401$	−2.29145e11	−0.442549	−0.221275	+	0.975212i	$0.571022\pi$
$402$	3.27326e11	0.625120
$403$	4.48363e11	0.846753
$404$	−5.40117e11	−1.00872
$405$	6.49972e10	0.120046
$406$	0	0
$407$	1.36952e11	0.247397
$408$	4.78947e10	0.0855691
$409$	−1.84171e11	−0.325437	−0.162719	−	0.986673i	$-0.552026\pi$
$409$	−1.84171e11	−0.325437	−0.162719	+	0.986673i	$0.552026\pi$
$410$	−2.70396e11	−0.472577
$411$	−4.35163e11	−0.752253
$412$	−1.63194e11	−0.279039
$413$	0	0
$414$	−1.39507e11	−0.233397
$415$	3.58621e11	0.593498
$416$	5.68562e11	0.930803
$417$	−1.72586e11	−0.279507
$418$	−6.65375e11	−1.06604
$419$	−3.95084e11	−0.626219	−0.313109	−	0.949717i	$-0.601371\pi$
$419$	−3.95084e11	−0.626219	−0.313109	+	0.949717i	$0.601371\pi$
$420$	0	0
$421$	6.68894e11	1.03774	0.518870	−	0.854853i	$-0.326353\pi$
$421$	6.68894e11	1.03774	0.518870	+	0.854853i	$0.326353\pi$
$422$	1.58322e12	2.43017
$423$	8.12534e11	1.23398
$424$	1.47551e11	0.221716
$425$	8.65070e10	0.128618
$426$	−1.95171e11	−0.287126
$427$	0	0
$428$	−1.41723e12	−2.04147
$429$	1.53640e11	0.219001
$430$	−8.04050e11	−1.13416
$431$	1.14002e12	1.59134	0.795672	−	0.605728i	$-0.207118\pi$
$431$	1.14002e12	1.59134	0.795672	+	0.605728i	$0.207118\pi$
$432$	5.15980e11	0.712781
$433$	−2.51421e11	−0.343721	−0.171860	−	0.985121i	$-0.554978\pi$
$433$	−2.51421e11	−0.343721	−0.171860	+	0.985121i	$0.554978\pi$
$434$	0	0
$435$	−1.06175e11	−0.142175
$436$	5.00977e10	0.0663939
$437$	1.83259e11	0.240380
$438$	−5.90676e9	−0.00766859
$439$	−1.30274e12	−1.67405	−0.837026	−	0.547163i	$-0.815708\pi$
$439$	−1.30274e12	−1.67405	−0.837026	+	0.547163i	$0.815708\pi$
$440$	−5.87768e10	−0.0747600
$441$	0	0
$442$	−4.95383e11	−0.617363
$443$	−5.90185e10	−0.0728067	−0.0364033	−	0.999337i	$-0.511590\pi$
$443$	−5.90185e10	−0.0728067	−0.0364033	+	0.999337i	$0.511590\pi$
$444$	−1.89374e11	−0.231258
$445$	3.33921e11	0.403668
$446$	1.12292e12	1.34382
$447$	7.19267e11	0.852130
$448$	0	0
$449$	7.84371e11	0.910779	0.455389	−	0.890292i	$-0.349500\pi$
$449$	7.84371e11	0.910779	0.455389	+	0.890292i	$0.349500\pi$
$450$	−1.87850e11	−0.215951
$451$	4.09318e11	0.465871
$452$	−1.69035e12	−1.90482
$453$	9.21740e9	0.0102841
$454$	3.57381e11	0.394803
$455$	0	0
$456$	1.36621e11	0.147970
$457$	−1.36032e12	−1.45887	−0.729437	−	0.684048i	$-0.760218\pi$
$457$	−1.36032e12	−1.45887	−0.729437	+	0.684048i	$0.760218\pi$
$458$	2.58743e12	2.74773
$459$	−5.48158e11	−0.576433
$460$	1.09020e11	0.113526
$461$	5.75808e11	0.593777	0.296888	−	0.954912i	$-0.404051\pi$
$461$	5.75808e11	0.593777	0.296888	+	0.954912i	$0.404051\pi$
$462$	0	0
$463$	1.45879e12	1.47530	0.737648	−	0.675185i	$-0.235936\pi$
$463$	1.45879e12	1.47530	0.737648	+	0.675185i	$0.235936\pi$
$464$	4.87808e11	0.488561
$465$	−3.03442e11	−0.300980
$466$	−1.28859e12	−1.26584
$467$	1.19325e12	1.16093	0.580466	−	0.814284i	$-0.302870\pi$
$467$	1.19325e12	1.16093	0.580466	+	0.814284i	$0.302870\pi$
$468$	5.80999e11	0.559847
$469$	0	0
$470$	−1.17565e12	−1.11131
$471$	4.45536e10	0.0417147
$472$	3.60794e10	0.0334595
$473$	1.21715e12	1.11807
$474$	−1.22746e12	−1.11688
$475$	2.46763e11	0.222412
$476$	0	0
$477$	−7.13853e11	−0.631358
$478$	−7.15528e11	−0.626904
$479$	−2.14005e12	−1.85743	−0.928717	−	0.370789i	$-0.879087\pi$
$479$	−2.14005e12	−1.85743	−0.928717	+	0.370789i	$0.879087\pi$
$480$	−3.84791e11	−0.330856
$481$	2.90852e11	0.247753
$482$	1.37994e11	0.116453
$483$	0	0
$484$	−8.18605e11	−0.678063
$485$	7.96117e11	0.653339
$486$	1.87748e12	1.52656
$487$	1.92789e12	1.55311	0.776554	−	0.630050i	$-0.216966\pi$
$487$	1.92789e12	1.55311	0.776554	+	0.630050i	$0.216966\pi$
$488$	1.89397e11	0.151176
$489$	1.77390e11	0.140294
$490$	0	0
$491$	2.41513e12	1.87531	0.937655	−	0.347567i	$-0.112992\pi$
$491$	2.41513e12	1.87531	0.937655	+	0.347567i	$0.112992\pi$
$492$	−5.65993e11	−0.435480
$493$	−5.18229e11	−0.395103
$494$	−1.41309e12	−1.06757
$495$	2.84362e11	0.212887
$496$	1.39413e12	1.03427
$497$	0	0
$498$	1.38986e12	1.01260
$499$	−1.81213e12	−1.30839	−0.654194	−	0.756327i	$-0.726992\pi$
$499$	−1.81213e12	−1.30839	−0.654194	+	0.756327i	$0.726992\pi$
$500$	1.46798e11	0.105040
$501$	−2.94775e11	−0.209036
$502$	1.13547e11	0.0798012
$503$	−2.71747e12	−1.89282	−0.946408	−	0.322973i	$-0.895318\pi$
$503$	−2.71747e12	−1.89282	−0.946408	+	0.322973i	$0.895318\pi$
$504$	0	0
$505$	−5.61419e11	−0.384128
$506$	−3.05557e11	−0.207212
$507$	−4.43554e11	−0.298133
$508$	1.59171e12	1.06042
$509$	1.70246e11	0.112421	0.0562104	−	0.998419i	$-0.482098\pi$
$509$	1.70246e11	0.112421	0.0562104	+	0.998419i	$0.482098\pi$
$510$	3.35265e11	0.219443
$511$	0	0
$512$	2.08583e12	1.34142
$513$	−1.56363e12	−0.996796
$514$	−4.06330e12	−2.56770
$515$	−1.69630e11	−0.106260
$516$	−1.68304e12	−1.04513
$517$	1.77966e12	1.09554
$518$	0	0
$519$	8.79483e11	0.532077
$520$	−1.24827e11	−0.0748676
$521$	−1.97927e12	−1.17689	−0.588446	−	0.808537i	$-0.700260\pi$
$521$	−1.97927e12	−1.17689	−0.588446	+	0.808537i	$0.700260\pi$
$522$	1.12534e12	0.663384
$523$	−5.37017e11	−0.313856	−0.156928	−	0.987610i	$-0.550159\pi$
$523$	−5.37017e11	−0.313856	−0.156928	+	0.987610i	$0.550159\pi$
$524$	7.21299e11	0.417950
$525$	0	0
$526$	−1.10756e11	−0.0630860
$527$	−1.48107e12	−0.836424
$528$	4.77723e11	0.267500
$529$	−1.71700e12	−0.953276
$530$	1.03286e12	0.568594
$531$	−1.74552e11	−0.0952795
$532$	0	0
$533$	8.69288e11	0.466542
$534$	1.29414e12	0.688724
$535$	−1.47313e12	−0.777406
$536$	4.02575e11	0.210671
$537$	7.10931e11	0.368929
$538$	−5.28171e12	−2.71803
$539$	0	0
$540$	−9.30197e11	−0.470764
$541$	−2.85545e12	−1.43313	−0.716567	−	0.697518i	$-0.754288\pi$
$541$	−2.85545e12	−1.43313	−0.716567	+	0.697518i	$0.754288\pi$
$542$	−4.96468e12	−2.47112
$543$	−2.00553e11	−0.0989986
$544$	−1.87812e12	−0.919449
$545$	5.20735e10	0.0252832
$546$	0	0
$547$	−2.23707e12	−1.06841	−0.534203	−	0.845356i	$-0.679388\pi$
$547$	−2.23707e12	−1.06841	−0.534203	+	0.845356i	$0.679388\pi$
$548$	−3.60429e12	−1.70729
$549$	−9.16302e11	−0.430490
$550$	−4.11440e11	−0.191723
$551$	−1.47826e12	−0.683232
$552$	6.27396e10	0.0287618
$553$	0	0
$554$	−4.53712e12	−2.04638
$555$	−1.96843e11	−0.0880645
$556$	−1.42946e12	−0.634359
$557$	−1.45892e11	−0.0642220	−0.0321110	−	0.999484i	$-0.510223\pi$
$557$	−1.45892e11	−0.0642220	−0.0321110	+	0.999484i	$0.510223\pi$
$558$	3.21614e12	1.40437
$559$	2.58492e12	1.11968
$560$	0	0
$561$	−5.07514e11	−0.216329
$562$	1.46468e12	0.619341
$563$	−6.26127e11	−0.262648	−0.131324	−	0.991339i	$-0.541923\pi$
$563$	−6.26127e11	−0.262648	−0.131324	+	0.991339i	$0.541923\pi$
$564$	−2.46086e12	−1.02407
$565$	−1.75701e12	−0.725366
$566$	−3.25374e12	−1.33263
$567$	0	0
$568$	−2.40039e11	−0.0967642
$569$	−1.79174e12	−0.716590	−0.358295	−	0.933608i	$-0.616642\pi$
$569$	−1.79174e12	−0.716590	−0.358295	+	0.933608i	$0.616642\pi$
$570$	9.56349e11	0.379472
$571$	−8.46019e11	−0.333056	−0.166528	−	0.986037i	$-0.553256\pi$
$571$	−8.46019e11	−0.333056	−0.166528	+	0.986037i	$0.553256\pi$
$572$	1.27254e12	0.497037
$573$	1.86267e12	0.721839
$574$	0	0
$575$	1.13320e11	0.0432315
$576$	2.54005e12	0.961481
$577$	4.84713e12	1.82051	0.910256	−	0.414045i	$-0.135885\pi$
$577$	4.84713e12	1.82051	0.910256	+	0.414045i	$0.135885\pi$
$578$	−2.32041e12	−0.864747
$579$	−3.66638e11	−0.135576
$580$	−8.79409e11	−0.322675
$581$	0	0
$582$	3.08541e12	1.11470
$583$	−1.56352e12	−0.560525
$584$	−7.26466e9	−0.00258439
$585$	6.03914e11	0.213193
$586$	3.64664e12	1.27748
$587$	−6.75571e11	−0.234855	−0.117427	−	0.993081i	$-0.537465\pi$
$587$	−6.75571e11	−0.234855	−0.117427	+	0.993081i	$0.537465\pi$
$588$	0	0
$589$	−4.22477e12	−1.44639
$590$	2.52557e11	0.0858075
$591$	2.38219e12	0.803216
$592$	9.04367e11	0.302620
$593$	−1.54901e12	−0.514407	−0.257204	−	0.966357i	$-0.582801\pi$
$593$	−1.54901e12	−0.514407	−0.257204	+	0.966357i	$0.582801\pi$
$594$	2.60712e12	0.859255
$595$	0	0
$596$	5.95740e12	1.93397
$597$	−6.26350e11	−0.201805
$598$	−6.48926e11	−0.207510
$599$	−5.20525e12	−1.65204	−0.826021	−	0.563639i	$-0.809401\pi$
$599$	−5.20525e12	−1.65204	−0.826021	+	0.563639i	$0.809401\pi$
$600$	8.44804e10	0.0266119
$601$	−2.91496e11	−0.0911377	−0.0455689	−	0.998961i	$-0.514510\pi$
$601$	−2.91496e11	−0.0911377	−0.0455689	+	0.998961i	$0.514510\pi$
$602$	0	0
$603$	−1.94766e12	−0.599908
$604$	7.63441e10	0.0233405
$605$	−8.50891e11	−0.258211
$606$	−2.17582e12	−0.655386
$607$	−1.54113e12	−0.460776	−0.230388	−	0.973099i	$-0.574000\pi$
$607$	−1.54113e12	−0.460776	−0.230388	+	0.973099i	$0.574000\pi$
$608$	−5.35736e12	−1.58996
$609$	0	0
$610$	1.32579e12	0.387694
$611$	3.77955e12	1.09712
$612$	−1.91920e12	−0.553017
$613$	5.24345e12	1.49984	0.749920	−	0.661529i	$-0.230092\pi$
$613$	5.24345e12	1.49984	0.749920	+	0.661529i	$0.230092\pi$
$614$	7.11828e12	2.02124
$615$	−5.88316e11	−0.165834
$616$	0	0
$617$	2.49183e11	0.0692205	0.0346102	−	0.999401i	$-0.488981\pi$
$617$	2.49183e11	0.0692205	0.0346102	+	0.999401i	$0.488981\pi$
$618$	−6.57414e11	−0.181297
$619$	−3.16237e12	−0.865774	−0.432887	−	0.901448i	$-0.642505\pi$
$619$	−3.16237e12	−0.865774	−0.432887	+	0.901448i	$0.642505\pi$
$620$	−2.51329e12	−0.683095
$621$	−7.18059e11	−0.193753
$622$	−6.66423e12	−1.78523
$623$	0	0
$624$	1.01456e12	0.267885
$625$	1.52588e11	0.0400000
$626$	4.77897e12	1.24380
$627$	−1.44769e12	−0.374087
$628$	3.69020e11	0.0946742
$629$	−9.60765e11	−0.244731
$630$	0	0
$631$	−2.39534e12	−0.601499	−0.300749	−	0.953703i	$-0.597237\pi$
$631$	−2.39534e12	−0.601499	−0.300749	+	0.953703i	$0.597237\pi$
$632$	−1.50964e12	−0.376397
$633$	3.44471e12	0.852778
$634$	−1.70031e12	−0.417951
$635$	1.65449e12	0.403814
$636$	2.16199e12	0.523959
$637$	0	0
$638$	2.46477e12	0.588958
$639$	1.16131e12	0.275546
$640$	−9.61343e11	−0.226500
$641$	−1.65554e12	−0.387329	−0.193664	−	0.981068i	$-0.562037\pi$
$641$	−1.65554e12	−0.387329	−0.193664	+	0.981068i	$0.562037\pi$
$642$	−5.70922e12	−1.32638
$643$	1.41071e12	0.325454	0.162727	−	0.986671i	$-0.447971\pi$
$643$	1.41071e12	0.325454	0.162727	+	0.986671i	$0.447971\pi$
$644$	0	0
$645$	−1.74942e12	−0.397992
$646$	4.66782e12	1.05455
$647$	2.43561e11	0.0546435	0.0273217	−	0.999627i	$-0.491302\pi$
$647$	2.43561e11	0.0546435	0.0273217	+	0.999627i	$0.491302\pi$
$648$	3.09812e11	0.0690256
$649$	−3.82314e11	−0.0845899
$650$	−8.73795e11	−0.191999
$651$	0	0
$652$	1.46925e12	0.318407
$653$	−3.12403e12	−0.672365	−0.336183	−	0.941797i	$-0.609136\pi$
$653$	−3.12403e12	−0.672365	−0.336183	+	0.941797i	$0.609136\pi$
$654$	2.01815e11	0.0431374
$655$	7.49747e11	0.159158
$656$	2.70294e12	0.569861
$657$	3.51464e10	0.00735931
$658$	0	0
$659$	−5.83093e12	−1.20435	−0.602176	−	0.798364i	$-0.705699\pi$
$659$	−5.83093e12	−1.20435	−0.602176	+	0.798364i	$0.705699\pi$
$660$	−8.61227e11	−0.176673
$661$	4.44177e12	0.905002	0.452501	−	0.891764i	$-0.350532\pi$
$661$	4.44177e12	0.905002	0.452501	+	0.891764i	$0.350532\pi$
$662$	−9.96952e12	−2.01750
$663$	−1.07783e12	−0.216641
$664$	1.70938e12	0.341257
$665$	0	0
$666$	2.08630e12	0.410907
$667$	−6.78853e11	−0.132804
$668$	−2.44151e12	−0.474421
$669$	2.44319e12	0.471564
$670$	2.81804e12	0.540270
$671$	−2.00694e12	−0.382193
$672$	0	0
$673$	6.48698e12	1.21892	0.609460	−	0.792817i	$-0.291386\pi$
$673$	6.48698e12	1.21892	0.609460	+	0.792817i	$0.291386\pi$
$674$	7.45220e12	1.39096
$675$	−9.66884e11	−0.179270
$676$	−3.67378e12	−0.676633
$677$	−4.52781e12	−0.828399	−0.414199	−	0.910186i	$-0.635938\pi$
$677$	−4.52781e12	−0.828399	−0.414199	+	0.910186i	$0.635938\pi$
$678$	−6.80945e12	−1.23759
$679$	0	0
$680$	4.12339e11	0.0739544
$681$	7.77574e11	0.138541
$682$	7.04417e12	1.24681
$683$	−2.60741e12	−0.458476	−0.229238	−	0.973370i	$-0.573623\pi$
$683$	−2.60741e12	−0.458476	−0.229238	+	0.973370i	$0.573623\pi$
$684$	−5.47456e12	−0.956305
$685$	−3.74644e12	−0.650147
$686$	0	0
$687$	5.62963e12	0.964216
$688$	8.03746e12	1.36764
$689$	−3.32052e12	−0.561333
$690$	4.39180e11	0.0737601
$691$	5.31067e12	0.886131	0.443066	−	0.896489i	$-0.353891\pi$
$691$	5.31067e12	0.886131	0.443066	+	0.896489i	$0.353891\pi$
$692$	7.28442e12	1.20758
$693$	0	0
$694$	8.37525e12	1.37050
$695$	−1.48584e12	−0.241568
$696$	−5.06089e11	−0.0817495
$697$	−2.87150e12	−0.460851
$698$	1.56936e13	2.50250
$699$	−2.80367e12	−0.444201
$700$	0	0
$701$	3.37189e12	0.527403	0.263702	−	0.964604i	$-0.415057\pi$
$701$	3.37189e12	0.527403	0.263702	+	0.964604i	$0.415057\pi$
$702$	5.53687e12	0.860492
$703$	−2.74060e12	−0.423201
$704$	5.56336e12	0.853611
$705$	−2.55792e12	−0.389974
$706$	1.33667e13	2.02490
$707$	0	0
$708$	5.28652e11	0.0790716
$709$	7.95694e12	1.18260	0.591300	−	0.806451i	$-0.298615\pi$
$709$	7.95694e12	1.18260	0.591300	+	0.806451i	$0.298615\pi$
$710$	−1.68028e12	−0.248153
$711$	7.30363e12	1.07183
$712$	1.59165e12	0.232106
$713$	−1.94012e12	−0.281142
$714$	0	0
$715$	1.32273e12	0.189275
$716$	5.88836e12	0.837309
$717$	−1.55681e12	−0.219989
$718$	1.17566e13	1.65090
$719$	4.47402e12	0.624335	0.312167	−	0.950027i	$-0.398945\pi$
$719$	4.47402e12	0.624335	0.312167	+	0.950027i	$0.398945\pi$
$720$	1.87779e12	0.260406
$721$	0	0
$722$	2.54828e12	0.349004
$723$	3.00242e11	0.0408648
$724$	−1.66110e12	−0.224684
$725$	−9.14093e11	−0.122877
$726$	−3.29770e12	−0.440551
$727$	1.21244e13	1.60974	0.804870	−	0.593452i	$-0.202235\pi$
$727$	1.21244e13	1.60974	0.804870	+	0.593452i	$0.202235\pi$
$728$	0	0
$729$	2.03800e12	0.267258
$730$	−5.08529e10	−0.00662770
$731$	−8.53869e12	−1.10602
$732$	2.77514e12	0.357260
$733$	7.66177e12	0.980305	0.490153	−	0.871637i	$-0.336941\pi$
$733$	7.66177e12	0.980305	0.490153	+	0.871637i	$0.336941\pi$
$734$	−5.87142e12	−0.746640
$735$	0	0
$736$	−2.46024e12	−0.309048
$737$	−4.26587e12	−0.532603
$738$	6.23546e12	0.773776
$739$	9.14837e10	0.0112835	0.00564175	−	0.999984i	$-0.498204\pi$
$739$	9.14837e10	0.0112835	0.00564175	+	0.999984i	$0.498204\pi$
$740$	−1.63037e12	−0.199868
$741$	−3.07454e12	−0.374626
$742$	0	0
$743$	−1.22270e13	−1.47188	−0.735938	−	0.677049i	$-0.763259\pi$
$743$	−1.22270e13	−1.47188	−0.735938	+	0.677049i	$0.763259\pi$
$744$	−1.44637e12	−0.173062
$745$	6.19236e12	0.736467
$746$	−1.26949e13	−1.50073
$747$	−8.26997e12	−0.971765
$748$	−4.20354e12	−0.490974
$749$	0	0
$750$	5.91366e11	0.0682466
$751$	1.22305e13	1.40302	0.701512	−	0.712658i	$-0.252509\pi$
$751$	1.22305e13	1.40302	0.701512	+	0.712658i	$0.252509\pi$
$752$	1.17520e13	1.34008
$753$	2.47051e11	0.0280033
$754$	5.23456e12	0.589806
$755$	7.93551e10	0.00888820
$756$	0	0
$757$	−1.56839e13	−1.73590	−0.867948	−	0.496655i	$-0.834561\pi$
$757$	−1.56839e13	−1.73590	−0.867948	+	0.496655i	$0.834561\pi$
$758$	−1.88882e13	−2.07816
$759$	−6.64818e11	−0.0727134
$760$	1.17620e12	0.127886
$761$	−1.62151e13	−1.75262	−0.876312	−	0.481745i	$-0.840003\pi$
$761$	−1.62151e13	−1.75262	−0.876312	+	0.481745i	$0.840003\pi$
$762$	6.41210e12	0.688974
$763$	0	0
$764$	1.54278e13	1.63826
$765$	−1.99489e12	−0.210593
$766$	2.57636e13	2.70381
$767$	−8.11938e11	−0.0847117
$768$	2.82477e12	0.292994
$769$	5.71613e12	0.589432	0.294716	−	0.955585i	$-0.404775\pi$
$769$	5.71613e12	0.589432	0.294716	+	0.955585i	$0.404775\pi$
$770$	0	0
$771$	−8.84075e12	−0.901041
$772$	−3.03672e12	−0.307699
$773$	−1.06739e13	−1.07527	−0.537634	−	0.843178i	$-0.680682\pi$
$773$	−1.06739e13	−1.07527	−0.537634	+	0.843178i	$0.680682\pi$
$774$	1.85418e13	1.85702
$775$	−2.61242e12	−0.260127
$776$	3.79472e12	0.375666
$777$	0	0
$778$	−2.37927e13	−2.32828
$779$	−8.19100e12	−0.796927
$780$	−1.82903e12	−0.176927
$781$	2.54357e12	0.244632
$782$	2.14358e12	0.204979
$783$	5.79222e12	0.550702
$784$	0	0
$785$	3.83574e11	0.0360526
$786$	2.90570e12	0.271550
$787$	−4.23924e12	−0.393914	−0.196957	−	0.980412i	$-0.563106\pi$
$787$	−4.23924e12	−0.393914	−0.196957	+	0.980412i	$0.563106\pi$
$788$	1.97307e13	1.82295
$789$	−2.40979e11	−0.0221377
$790$	−1.05675e13	−0.965277
$791$	0	0
$792$	1.35542e12	0.122408
$793$	−4.26223e12	−0.382743
$794$	8.99539e12	0.803207
$795$	2.24726e12	0.199527
$796$	−5.18782e12	−0.458011
$797$	−1.03352e13	−0.907308	−0.453654	−	0.891178i	$-0.649880\pi$
$797$	−1.03352e13	−0.907308	−0.453654	+	0.891178i	$0.649880\pi$
$798$	0	0
$799$	−1.24849e13	−1.08374
$800$	−3.31277e12	−0.285947
$801$	−7.70039e12	−0.660946
$802$	−7.64565e12	−0.652574
$803$	7.69797e10	0.00653365
$804$	5.89872e12	0.497858
$805$	0	0
$806$	1.49600e13	1.24860
$807$	−1.14917e13	−0.953792
$808$	−2.67602e12	−0.220871
$809$	1.00952e13	0.828601	0.414300	−	0.910140i	$-0.364026\pi$
$809$	1.00952e13	0.828601	0.414300	+	0.910140i	$0.364026\pi$
$810$	2.16869e12	0.177017
$811$	1.46569e13	1.18973	0.594865	−	0.803825i	$-0.297205\pi$
$811$	1.46569e13	1.18973	0.594865	+	0.803825i	$0.297205\pi$
$812$	0	0
$813$	−1.08019e13	−0.867149
$814$	4.56954e12	0.364807
$815$	1.52720e12	0.121251
$816$	−3.35138e12	−0.264617
$817$	−2.43568e13	−1.91258
$818$	−6.14505e12	−0.479883
$819$	0	0
$820$	−4.87279e12	−0.376370
$821$	−1.37332e13	−1.05494	−0.527471	−	0.849573i	$-0.676860\pi$
$821$	−1.37332e13	−1.05494	−0.527471	+	0.849573i	$0.676860\pi$
$822$	−1.45196e13	−1.10926
$823$	−6.38239e12	−0.484936	−0.242468	−	0.970159i	$-0.577957\pi$
$823$	−6.38239e12	−0.484936	−0.242468	+	0.970159i	$0.577957\pi$
$824$	−8.08547e11	−0.0610988
$825$	−8.95194e11	−0.0672782
$826$	0	0
$827$	−1.00483e12	−0.0746993	−0.0373496	−	0.999302i	$-0.511892\pi$
$827$	−1.00483e12	−0.0746993	−0.0373496	+	0.999302i	$0.511892\pi$
$828$	−2.51405e12	−0.185882
$829$	1.62815e13	1.19729	0.598645	−	0.801014i	$-0.295706\pi$
$829$	1.62815e13	1.19729	0.598645	+	0.801014i	$0.295706\pi$
$830$	1.19657e13	0.875159
$831$	−9.87166e12	−0.718101
$832$	1.18152e13	0.854840
$833$	0	0
$834$	−5.75848e12	−0.412155
$835$	−2.53780e12	−0.180663
$836$	−1.19907e13	−0.849016
$837$	1.65538e13	1.16582
$838$	−1.31823e13	−0.923410
$839$	−1.00724e13	−0.701786	−0.350893	−	0.936416i	$-0.614122\pi$
$839$	−1.00724e13	−0.701786	−0.350893	+	0.936416i	$0.614122\pi$
$840$	0	0
$841$	−9.03118e12	−0.622533
$842$	2.23183e13	1.53023
$843$	3.18679e12	0.217335
$844$	2.85312e13	1.93544
$845$	−3.81868e12	−0.257666
$846$	2.71110e13	1.81961
$847$	0	0
$848$	−1.03247e13	−0.685643
$849$	−7.07934e12	−0.467637
$850$	2.88639e12	0.189657
$851$	−1.25855e12	−0.0822600
$852$	−3.51717e12	−0.228673
$853$	−1.88184e13	−1.21706	−0.608530	−	0.793531i	$-0.708240\pi$
$853$	−1.88184e13	−1.21706	−0.608530	+	0.793531i	$0.708240\pi$
$854$	0	0
$855$	−5.69047e12	−0.364167
$856$	−7.02171e12	−0.447003
$857$	−1.09505e13	−0.693461	−0.346730	−	0.937965i	$-0.612708\pi$
$857$	−1.09505e13	−0.693461	−0.346730	+	0.937965i	$0.612708\pi$
$858$	5.12633e12	0.322934
$859$	−1.73683e13	−1.08840	−0.544198	−	0.838957i	$-0.683166\pi$
$859$	−1.73683e13	−1.08840	−0.544198	+	0.838957i	$0.683166\pi$
$860$	−1.44897e13	−0.903269
$861$	0	0
$862$	3.80378e13	2.34656
$863$	−1.20253e13	−0.737988	−0.368994	−	0.929432i	$-0.620298\pi$
$863$	−1.20253e13	−0.737988	−0.368994	+	0.929432i	$0.620298\pi$
$864$	2.09916e13	1.28154
$865$	7.57172e12	0.459856
$866$	−8.38889e12	−0.506844
$867$	−5.04864e12	−0.303451
$868$	0	0
$869$	1.59968e13	0.951579
$870$	−3.54264e12	−0.209648
$871$	−9.05963e12	−0.533370
$872$	2.48210e11	0.0145377
$873$	−1.83588e13	−1.06975
$874$	6.11461e12	0.354460
$875$	0	0
$876$	−1.06445e11	−0.00610742
$877$	1.17519e13	0.670826	0.335413	−	0.942071i	$-0.391124\pi$
$877$	1.17519e13	0.670826	0.335413	+	0.942071i	$0.391124\pi$
$878$	−4.34673e13	−2.46852
$879$	7.93420e12	0.448284
$880$	4.11284e12	0.231191
$881$	2.81040e13	1.57172	0.785862	−	0.618402i	$-0.212219\pi$
$881$	2.81040e13	1.57172	0.785862	+	0.618402i	$0.212219\pi$
$882$	0	0
$883$	−3.35502e13	−1.85726	−0.928629	−	0.371010i	$-0.879011\pi$
$883$	−3.35502e13	−1.85726	−0.928629	+	0.371010i	$0.879011\pi$
$884$	−8.92726e12	−0.491681
$885$	5.49502e11	0.0301110
$886$	−1.96921e12	−0.107359
$887$	3.39815e12	0.184326	0.0921628	−	0.995744i	$-0.470622\pi$
$887$	3.39815e12	0.184326	0.0921628	+	0.995744i	$0.470622\pi$
$888$	−9.38258e11	−0.0506365
$889$	0	0
$890$	1.11416e13	0.595240
$891$	−3.28291e12	−0.174505
$892$	2.02360e13	1.07024
$893$	−3.56134e13	−1.87405
$894$	2.39990e13	1.25653
$895$	6.12060e12	0.318853
$896$	0	0
$897$	−1.41190e12	−0.0728181
$898$	2.61713e13	1.34302
$899$	1.56500e13	0.799088
$900$	−3.38524e12	−0.171988
$901$	1.09686e13	0.554485
$902$	1.36573e13	0.686965
$903$	0	0
$904$	−8.37487e12	−0.417081
$905$	−1.72661e12	−0.0855611
$906$	3.07547e11	0.0151647
$907$	9.35897e12	0.459193	0.229596	−	0.973286i	$-0.426259\pi$
$907$	9.35897e12	0.459193	0.229596	+	0.973286i	$0.426259\pi$
$908$	6.44034e12	0.314429
$909$	1.29466e13	0.628953
$910$	0	0
$911$	1.34819e13	0.648512	0.324256	−	0.945969i	$-0.394886\pi$
$911$	1.34819e13	0.648512	0.324256	+	0.945969i	$0.394886\pi$
$912$	−9.55987e12	−0.457589
$913$	−1.81134e13	−0.862741
$914$	−4.53883e13	−2.15123
$915$	2.88459e12	0.136047
$916$	4.66280e13	2.18835
$917$	0	0
$918$	−1.82898e13	−0.849996
$919$	−2.27543e13	−1.05231	−0.526155	−	0.850389i	$-0.676367\pi$
$919$	−2.27543e13	−1.05231	−0.526155	+	0.850389i	$0.676367\pi$
$920$	5.40142e11	0.0248578
$921$	1.54876e13	0.709279
$922$	1.92124e13	0.875571
$923$	5.40189e12	0.244984
$924$	0	0
$925$	−1.69467e12	−0.0761111
$926$	4.86740e13	2.17544
$927$	3.91175e12	0.173985
$928$	1.98455e13	0.878407
$929$	−1.07501e13	−0.473523	−0.236761	−	0.971568i	$-0.576086\pi$
$929$	−1.07501e13	−0.473523	−0.236761	+	0.971568i	$0.576086\pi$
$930$	−1.01246e13	−0.443819
$931$	0	0
$932$	−2.32217e13	−1.00814
$933$	−1.44997e13	−0.626459
$934$	3.98140e13	1.71189
$935$	−4.36933e12	−0.186966
$936$	2.87858e12	0.122585
$937$	−1.23702e11	−0.00524264	−0.00262132	−	0.999997i	$-0.500834\pi$
$937$	−1.23702e11	−0.00524264	−0.00262132	+	0.999997i	$0.500834\pi$
$938$	0	0
$939$	1.03979e13	0.436465
$940$	−2.11862e13	−0.885071
$941$	−2.86225e13	−1.19002	−0.595011	−	0.803718i	$-0.702852\pi$
$941$	−2.86225e13	−1.19002	−0.595011	+	0.803718i	$0.702852\pi$
$942$	1.48657e12	0.0615116
$943$	−3.76151e12	−0.154903
$944$	−2.52461e12	−0.103472
$945$	0	0
$946$	4.06113e13	1.64868
$947$	−8.05243e12	−0.325351	−0.162676	−	0.986680i	$-0.552012\pi$
$947$	−8.05243e12	−0.325351	−0.162676	+	0.986680i	$0.552012\pi$
$948$	−2.21200e13	−0.889502
$949$	1.63485e11	0.00654306
$950$	8.23347e12	0.327965
$951$	−3.69945e12	−0.146664
$952$	0	0
$953$	1.69087e13	0.664039	0.332019	−	0.943273i	$-0.392270\pi$
$953$	1.69087e13	0.664039	0.332019	+	0.943273i	$0.392270\pi$
$954$	−2.38184e13	−0.930988
$955$	1.60363e13	0.623861
$956$	−1.28945e13	−0.499279
$957$	5.36275e12	0.206673
$958$	−7.14047e13	−2.73893
$959$	0	0
$960$	−7.99626e12	−0.303855
$961$	1.82870e13	0.691650
$962$	9.70456e12	0.365332
$963$	3.39710e13	1.27289
$964$	2.48679e12	0.0927453
$965$	−3.15649e12	−0.117174
$966$	0	0
$967$	9.86586e12	0.362840	0.181420	−	0.983406i	$-0.441931\pi$
$967$	9.86586e12	0.362840	0.181420	+	0.983406i	$0.441931\pi$
$968$	−4.05580e12	−0.148470
$969$	1.01560e13	0.370056
$970$	2.65632e13	0.963401
$971$	2.67844e13	0.966932	0.483466	−	0.875363i	$-0.339378\pi$
$971$	2.67844e13	0.966932	0.483466	+	0.875363i	$0.339378\pi$
$972$	3.38340e13	1.21578
$973$	0	0
$974$	6.43258e13	2.29018
$975$	−1.90117e12	−0.0673751
$976$	−1.32528e13	−0.467504
$977$	−3.66357e13	−1.28641	−0.643205	−	0.765694i	$-0.722396\pi$
$977$	−3.66357e13	−1.28641	−0.643205	+	0.765694i	$0.722396\pi$
$978$	5.91879e12	0.206875
$979$	−1.68658e13	−0.586794
$980$	0	0
$981$	−1.20084e12	−0.0413976
$982$	8.05829e13	2.76529
$983$	−2.13833e13	−0.730438	−0.365219	−	0.930922i	$-0.619006\pi$
$983$	−2.13833e13	−0.730438	−0.365219	+	0.930922i	$0.619006\pi$
$984$	−2.80423e12	−0.0953532
$985$	2.05089e13	0.694192
$986$	−1.72912e13	−0.582611
$987$	0	0
$988$	−2.54652e13	−0.850238
$989$	−1.11852e13	−0.371759
$990$	9.48801e12	0.313918
$991$	−2.42716e13	−0.799405	−0.399702	−	0.916645i	$-0.630887\pi$
$991$	−2.42716e13	−0.799405	−0.399702	+	0.916645i	$0.630887\pi$
$992$	5.67171e13	1.85957
$993$	−2.16912e13	−0.707967
$994$	0	0
$995$	−5.39242e12	−0.174414
$996$	2.50466e13	0.806459
$997$	2.60119e13	0.833765	0.416882	−	0.908960i	$-0.363123\pi$
$997$	2.60119e13	0.833765	0.416882	+	0.908960i	$0.363123\pi$
$998$	−6.04633e13	−1.92932
$999$	1.07384e13	0.341111

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.10.a.e.1.4		4
7.6	odd	2		35.10.a.c.1.4	✓	4
21.20	even	2		315.10.a.g.1.1		4
35.13	even	4		175.10.b.e.99.2		8
35.27	even	4		175.10.b.e.99.7		8
35.34	odd	2		175.10.a.e.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.10.a.c.1.4	✓	4	7.6	odd	2
175.10.a.e.1.1		4	35.34	odd	2
175.10.b.e.99.2		8	35.13	even	4
175.10.b.e.99.7		8	35.27	even	4
245.10.a.e.1.4		4	1.1	even	1	trivial
315.10.a.g.1.1		4	21.20	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	245.a (trivial)

\(f(q)\)	\(=\)	\(q+33.3659 q^{2} +72.5961 q^{3} +601.285 q^{4} +625.000 q^{5} +2422.24 q^{6} +2979.08 q^{8} -14412.8 q^{9} +20853.7 q^{10} -31567.7 q^{11} +43651.0 q^{12} -67041.9 q^{13} +45372.6 q^{15} -208458. q^{16} +221458. q^{17} -480897. q^{18} +631713. q^{19} +375803. q^{20} -1.05329e6 q^{22} +290099. q^{23} +216270. q^{24} +390625. q^{25} -2.23692e6 q^{26} -2.47522e6 q^{27} -2.34008e6 q^{29} +1.51390e6 q^{30} -6.68779e6 q^{31} -8.48069e6 q^{32} -2.29170e6 q^{33} +7.38915e6 q^{34} -8.66620e6 q^{36} -4.33836e6 q^{37} +2.10777e7 q^{38} -4.86698e6 q^{39} +1.86193e6 q^{40} -1.29663e7 q^{41} -3.85567e7 q^{43} -1.89812e7 q^{44} -9.00800e6 q^{45} +9.67941e6 q^{46} -5.63758e7 q^{47} -1.51333e7 q^{48} +1.30336e7 q^{50} +1.60770e7 q^{51} -4.03113e7 q^{52} +4.95291e7 q^{53} -8.25881e7 q^{54} -1.97298e7 q^{55} +4.58599e7 q^{57} -7.80789e7 q^{58} +1.21109e7 q^{59} +2.72819e7 q^{60} +6.35756e7 q^{61} -2.23144e8 q^{62} -1.76236e8 q^{64} -4.19012e7 q^{65} -7.64645e7 q^{66} +1.35134e8 q^{67} +1.33159e8 q^{68} +2.10600e7 q^{69} -8.05749e7 q^{71} -4.29369e7 q^{72} -2.43855e6 q^{73} -1.44754e8 q^{74} +2.83579e7 q^{75} +3.79840e8 q^{76} -1.62391e8 q^{78} -5.06746e8 q^{79} -1.30286e8 q^{80} +1.03996e8 q^{81} -4.32634e8 q^{82} +5.73793e8 q^{83} +1.38411e8 q^{85} -1.28648e9 q^{86} -1.69881e8 q^{87} -9.40429e7 q^{88} +5.34274e8 q^{89} -3.00560e8 q^{90} +1.74432e8 q^{92} -4.85508e8 q^{93} -1.88103e9 q^{94} +3.94821e8 q^{95} -6.15665e8 q^{96} +1.27379e9 q^{97} +4.54980e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 19 q^{2} + 18 q^{3} + 1729 q^{4} + 2500 q^{5} + 144 q^{6} - 30495 q^{8} + 5382 q^{9} - 11875 q^{10} + 82438 q^{11} - 41328 q^{12} + 72962 q^{13} + 11250 q^{15} + 64257 q^{16} + 357542 q^{17} - 965367 q^{18}+ \cdots + 1222369524 q^{99}+O(q^{100}) \) 4 * q - 19 * q^2 + 18 * q^3 + 1729 * q^4 + 2500 * q^5 + 144 * q^6 - 30495 * q^8 + 5382 * q^9 - 11875 * q^10 + 82438 * q^11 - 41328 * q^12 + 72962 * q^13 + 11250 * q^15 + 64257 * q^16 + 357542 * q^17 - 965367 * q^18 - 300732 * q^19 + 1080625 * q^20 - 5595068 * q^22 - 2340836 * q^23 + 7636320 * q^24 + 1562500 * q^25 - 1305666 * q^26 + 4240350 * q^27 - 1372022 * q^29 + 90000 * q^30 + 4590888 * q^31 - 10529439 * q^32 - 2000034 * q^33 + 7199478 * q^34 - 9144243 * q^36 - 38868456 * q^37 + 15477280 * q^38 - 46666242 * q^39 - 19059375 * q^40 - 57287084 * q^41 - 43403452 * q^43 + 87639348 * q^44 + 3363750 * q^45 + 28892416 * q^46 - 91822222 * q^47 - 156168864 * q^48 - 7421875 * q^50 + 86342634 * q^51 - 1953386 * q^52 - 61086884 * q^53 - 187589520 * q^54 + 51523750 * q^55 - 79928892 * q^57 + 29615390 * q^58 - 72569680 * q^59 - 25830000 * q^60 + 225681036 * q^61 - 190286472 * q^62 + 141443393 * q^64 + 45601250 * q^65 + 119673648 * q^66 - 4429720 * q^67 - 15339698 * q^68 - 348300612 * q^69 - 470468984 * q^71 + 298610685 * q^72 + 168326464 * q^73 + 927809502 * q^74 + 7031250 * q^75 + 892265344 * q^76 + 281290896 * q^78 - 598805646 * q^79 + 40160625 * q^80 - 847155996 * q^81 + 1821993318 * q^82 + 1159074304 * q^83 + 223463750 * q^85 + 706791156 * q^86 + 421480998 * q^87 - 1992103900 * q^88 + 1380153012 * q^89 - 603354375 * q^90 + 710319264 * q^92 - 1601969400 * q^93 - 2466744152 * q^94 - 187957500 * q^95 + 799321824 * q^96 - 754874082 * q^97 + 1222369524 * q^99

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