LMFDB - Embedded newform 245.10.a.g.1.2

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 = [6,15,124] 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:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 3018x^{4} + 3368x^{3} + 2066979x^{2} - 6329061x - 14714266 $ x^6 - 3x^5 - 3018x^4 + 3368x^3 + 2066979x^2 - 6329061*x - 14714266
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3}\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			1.2
Root			$29.3435$ 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)

$f(q)$	$=$	\(q-26.3435 q^{2} +1.97103 q^{3} +181.982 q^{4} -625.000 q^{5} -51.9238 q^{6} +8693.85 q^{8} -19679.1 q^{9} +16464.7 q^{10} -2245.43 q^{11} +358.691 q^{12} +123379. q^{13} -1231.89 q^{15} -322201. q^{16} +18794.1 q^{17} +518417. q^{18} -404776. q^{19} -113739. q^{20} +59152.4 q^{22} +1.75527e6 q^{23} +17135.8 q^{24} +390625. q^{25} -3.25024e6 q^{26} -77583.8 q^{27} +3.94483e6 q^{29} +32452.4 q^{30} -8.99428e6 q^{31} +4.03667e6 q^{32} -4425.79 q^{33} -495103. q^{34} -3.58124e6 q^{36} -1.04609e7 q^{37} +1.06632e7 q^{38} +243184. q^{39} -5.43366e6 q^{40} -3.02704e6 q^{41} +1.60767e7 q^{43} -408626. q^{44} +1.22994e7 q^{45} -4.62401e7 q^{46} +3.97557e7 q^{47} -635067. q^{48} -1.02904e7 q^{50} +37043.7 q^{51} +2.24528e7 q^{52} +4.08073e7 q^{53} +2.04383e6 q^{54} +1.40339e6 q^{55} -797825. q^{57} -1.03921e8 q^{58} -1.60585e8 q^{59} -224182. q^{60} -1.49289e8 q^{61} +2.36941e8 q^{62} +5.86269e7 q^{64} -7.71120e7 q^{65} +116591. q^{66} +5.12683e7 q^{67} +3.42018e6 q^{68} +3.45969e6 q^{69} -3.35362e8 q^{71} -1.71087e8 q^{72} -1.35293e8 q^{73} +2.75578e8 q^{74} +769932. q^{75} -7.36618e7 q^{76} -6.40632e6 q^{78} +1.65365e8 q^{79} +2.01376e8 q^{80} +3.87191e8 q^{81} +7.97429e7 q^{82} +1.61436e8 q^{83} -1.17463e7 q^{85} -4.23516e8 q^{86} +7.77536e6 q^{87} -1.95214e7 q^{88} -1.00313e9 q^{89} -3.24011e8 q^{90} +3.19428e8 q^{92} -1.77280e7 q^{93} -1.04731e9 q^{94} +2.52985e8 q^{95} +7.95639e6 q^{96} +2.89165e8 q^{97} +4.41880e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 15 q^{2} + 124 q^{3} + 3009 q^{4} - 3750 q^{5} - 4888 q^{6} + 22041 q^{8} + 111090 q^{9} - 9375 q^{10} - 47796 q^{11} + 541656 q^{12} - 102168 q^{13} - 77500 q^{15} + 2371065 q^{16} + 38472 q^{17}+ \cdots + 3571968784 q^{99}+O(q^{100}) $ 6 * q + 15 * q^2 + 124 * q^3 + 3009 * q^4 - 3750 * q^5 - 4888 * q^6 + 22041 * q^8 + 111090 * q^9 - 9375 * q^10 - 47796 * q^11 + 541656 * q^12 - 102168 * q^13 - 77500 * q^15 + 2371065 * q^16 + 38472 * q^17 + 1837015 * q^18 - 361056 * q^19 - 1880625 * q^20 + 2068680 * q^22 + 697032 * q^23 - 4828076 * q^24 + 2343750 * q^25 - 10847622 * q^26 - 1653188 * q^27 + 16028184 * q^29 + 3055000 * q^30 - 1362912 * q^31 - 1148823 * q^32 - 14059020 * q^33 + 9216294 * q^34 + 92319641 * q^36 - 3912924 * q^37 - 39877140 * q^38 - 20341868 * q^39 - 13775625 * q^40 - 22452756 * q^41 - 29998992 * q^43 - 94378728 * q^44 - 69431250 * q^45 + 49589520 * q^46 + 121271508 * q^47 + 327116052 * q^48 + 5859375 * q^50 - 281338180 * q^51 + 44528550 * q^52 - 20308596 * q^53 + 290104308 * q^54 + 29872500 * q^55 + 186940744 * q^57 + 256759494 * q^58 - 120280392 * q^59 - 338535000 * q^60 + 87693540 * q^61 + 344802528 * q^62 + 640647105 * q^64 + 63855000 * q^65 + 1393970692 * q^66 + 495050664 * q^67 + 141443706 * q^68 - 1031633640 * q^69 + 253762512 * q^71 + 856452205 * q^72 - 187195308 * q^73 - 418806054 * q^74 + 48437500 * q^75 + 584719476 * q^76 - 1728062324 * q^78 + 831079500 * q^79 - 1481915625 * q^80 + 1869314710 * q^81 - 2286848814 * q^82 + 767650536 * q^83 - 24045000 * q^85 + 566199948 * q^86 - 1303216852 * q^87 + 2952495444 * q^88 - 582579684 * q^89 - 1148134375 * q^90 - 4259382384 * q^92 + 15388800 * q^93 + 1115946660 * q^94 + 225660000 * q^95 - 989345252 * q^96 + 1184506872 * q^97 + 3571968784 * 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 $

$2$	−26.3435	−1.16423	−0.582115	−	0.813106i	$-0.697775\pi$
$2$	−26.3435	−1.16423	−0.582115	+	0.813106i	$0.697775\pi$
$3$	1.97103	0.0140490	0.00702452	−	0.999975i	$-0.497764\pi$
$3$	1.97103	0.0140490	0.00702452	+	0.999975i	$0.497764\pi$
$4$	181.982	0.355433
$5$	−625.000	−0.447214
$5$	−625.000	−0.447214
$6$	−51.9238	−0.0163563
$7$	0	0
$7$	0	0
$8$	8693.85	0.750425
$9$	−19679.1	−0.999803
$10$	16464.7	0.520660
$11$	−2245.43	−0.0462415	−0.0231207	−	0.999733i	$-0.507360\pi$
$11$	−2245.43	−0.0462415	−0.0231207	+	0.999733i	$0.507360\pi$
$12$	358.691	0.00499350
$13$	123379.	1.19811	0.599055	−	0.800708i	$-0.295543\pi$
$13$	123379.	1.19811	0.599055	+	0.800708i	$0.295543\pi$
$14$	0	0
$15$	−1231.89	−0.00628293
$16$	−322201.	−1.22910
$17$	18794.1	0.0545760	0.0272880	−	0.999628i	$-0.491313\pi$
$17$	18794.1	0.0545760	0.0272880	+	0.999628i	$0.491313\pi$
$18$	518417.	1.16400
$19$	−404776.	−0.712564	−0.356282	−	0.934379i	$-0.615956\pi$
$19$	−404776.	−0.712564	−0.356282	+	0.934379i	$0.615956\pi$
$20$	−113739.	−0.158954
$21$	0	0
$22$	59152.4	0.0538357
$23$	1.75527e6	1.30789	0.653943	−	0.756544i	$-0.273114\pi$
$23$	1.75527e6	1.30789	0.653943	+	0.756544i	$0.273114\pi$
$24$	17135.8	0.0105428
$25$	390625.	0.200000
$26$	−3.25024e6	−1.39488
$27$	−77583.8	−0.0280953
$28$	0	0
$29$	3.94483e6	1.03571	0.517854	−	0.855469i	$-0.326731\pi$
$29$	3.94483e6	1.03571	0.517854	+	0.855469i	$0.326731\pi$
$30$	32452.4	0.00731477
$31$	−8.99428e6	−1.74920	−0.874599	−	0.484847i	$-0.838875\pi$
$31$	−8.99428e6	−1.74920	−0.874599	+	0.484847i	$0.838875\pi$
$32$	4.03667e6	0.680532
$33$	−4425.79	−0.000649648 0
$34$	−495103.	−0.0635390
$35$	0	0
$36$	−3.58124e6	−0.355363
$37$	−1.04609e7	−0.917618	−0.458809	−	0.888535i	$-0.651724\pi$
$37$	−1.04609e7	−0.917618	−0.458809	+	0.888535i	$0.651724\pi$
$38$	1.06632e7	0.829589
$39$	243184.	0.0168323
$40$	−5.43366e6	−0.335600
$41$	−3.02704e6	−0.167298	−0.0836489	−	0.996495i	$-0.526657\pi$
$41$	−3.02704e6	−0.167298	−0.0836489	+	0.996495i	$0.526657\pi$
$42$	0	0
$43$	1.60767e7	0.717114	0.358557	−	0.933508i	$-0.383269\pi$
$43$	1.60767e7	0.717114	0.358557	+	0.933508i	$0.383269\pi$
$44$	−408626.	−0.0164357
$45$	1.22994e7	0.447125
$46$	−4.62401e7	−1.52268
$47$	3.97557e7	1.18839	0.594196	−	0.804321i	$-0.297471\pi$
$47$	3.97557e7	1.18839	0.594196	+	0.804321i	$0.297471\pi$
$48$	−635067.	−0.0172677
$49$	0	0
$50$	−1.02904e7	−0.232846
$51$	37043.7	0.000766740 0
$52$	2.24528e7	0.425848
$53$	4.08073e7	0.710389	0.355195	−	0.934792i	$-0.384415\pi$
$53$	4.08073e7	0.710389	0.355195	+	0.934792i	$0.384415\pi$
$54$	2.04383e6	0.0327094
$55$	1.40339e6	0.0206798
$56$	0	0
$57$	−797825.	−0.0100108
$58$	−1.03921e8	−1.20580
$59$	−1.60585e8	−1.72532	−0.862660	−	0.505784i	$-0.831203\pi$
$59$	−1.60585e8	−1.72532	−0.862660	+	0.505784i	$0.831203\pi$
$60$	−224182.	−0.00223316
$61$	−1.49289e8	−1.38052	−0.690260	−	0.723561i	$-0.742504\pi$
$61$	−1.49289e8	−1.38052	−0.690260	+	0.723561i	$0.742504\pi$
$62$	2.36941e8	2.03647
$63$	0	0
$64$	5.86269e7	0.436805
$65$	−7.71120e7	−0.535811
$66$	116591.	0.000756341 0
$67$	5.12683e7	0.310822	0.155411	−	0.987850i	$-0.450330\pi$
$67$	5.12683e7	0.310822	0.155411	+	0.987850i	$0.450330\pi$
$68$	3.42018e6	0.0193981
$69$	3.45969e6	0.0183745
$70$	0	0
$71$	−3.35362e8	−1.56622	−0.783108	−	0.621886i	$-0.786367\pi$
$71$	−3.35362e8	−1.56622	−0.783108	+	0.621886i	$0.786367\pi$
$72$	−1.71087e8	−0.750277
$73$	−1.35293e8	−0.557601	−0.278801	−	0.960349i	$-0.589937\pi$
$73$	−1.35293e8	−0.557601	−0.278801	+	0.960349i	$0.589937\pi$
$74$	2.75578e8	1.06832
$75$	769932.	0.00280981
$76$	−7.36618e7	−0.253269
$77$	0	0
$78$	−6.40632e6	−0.0195967
$79$	1.65365e8	0.477665	0.238832	−	0.971061i	$-0.423235\pi$
$79$	1.65365e8	0.477665	0.238832	+	0.971061i	$0.423235\pi$
$80$	2.01376e8	0.549670
$81$	3.87191e8	0.999408
$82$	7.97429e7	0.194773
$83$	1.61436e8	0.373379	0.186690	−	0.982419i	$-0.440224\pi$
$83$	1.61436e8	0.373379	0.186690	+	0.982419i	$0.440224\pi$
$84$	0	0
$85$	−1.17463e7	−0.0244071
$86$	−4.23516e8	−0.834886
$87$	7.77536e6	0.0145507
$88$	−1.95214e7	−0.0347007
$89$	−1.00313e9	−1.69473	−0.847366	−	0.531009i	$-0.821813\pi$
$89$	−1.00313e9	−1.69473	−0.847366	+	0.531009i	$0.821813\pi$
$90$	−3.24011e8	−0.520557
$91$	0	0
$92$	3.19428e8	0.464866
$93$	−1.77280e7	−0.0245746
$94$	−1.04731e9	−1.38356
$95$	2.52985e8	0.318668
$96$	7.95639e6	0.00956082
$97$	2.89165e8	0.331644	0.165822	−	0.986156i	$-0.446972\pi$
$97$	2.89165e8	0.331644	0.165822	+	0.986156i	$0.446972\pi$
$98$	0	0
$99$	4.41880e7	0.0462323
$100$	7.10866e7	0.0710866
$101$	−1.57210e8	−0.150326	−0.0751629	−	0.997171i	$-0.523948\pi$
$101$	−1.57210e8	−0.150326	−0.0751629	+	0.997171i	$0.523948\pi$
$102$	−975861.	−0.000892663 0
$103$	−5.15072e8	−0.450921	−0.225461	−	0.974252i	$-0.572389\pi$
$103$	−5.15072e8	−0.450921	−0.225461	+	0.974252i	$0.572389\pi$
$104$	1.07264e9	0.899092
$105$	0	0
$106$	−1.07501e9	−0.827057
$107$	−2.36823e9	−1.74662	−0.873308	−	0.487168i	$-0.838030\pi$
$107$	−2.36823e9	−1.74662	−0.873308	+	0.487168i	$0.838030\pi$
$108$	−1.41188e7	−0.00998601
$109$	2.25821e8	0.153231	0.0766154	−	0.997061i	$-0.475589\pi$
$109$	2.25821e8	0.153231	0.0766154	+	0.997061i	$0.475589\pi$
$110$	−3.69703e7	−0.0240761
$111$	−2.06188e7	−0.0128917
$112$	0	0
$113$	−2.93829e9	−1.69528	−0.847640	−	0.530572i	$-0.821977\pi$
$113$	−2.93829e9	−1.69528	−0.847640	+	0.530572i	$0.821977\pi$
$114$	2.10175e7	0.0116549
$115$	−1.09705e9	−0.584904
$116$	7.17886e8	0.368125
$117$	−2.42799e9	−1.19787
$118$	4.23036e9	2.00867
$119$	0	0
$120$	−1.07099e7	−0.00471486
$121$	−2.35291e9	−0.997862
$122$	3.93279e9	1.60724
$123$	−5.96637e6	−0.00235038
$124$	−1.63679e9	−0.621723
$125$	−2.44141e8	−0.0894427
$126$	0	0
$127$	3.08644e9	1.05279	0.526393	−	0.850241i	$-0.323544\pi$
$127$	3.08644e9	1.05279	0.526393	+	0.850241i	$0.323544\pi$
$128$	−3.61122e9	−1.18907
$129$	3.16876e7	0.0100748
$130$	2.03140e9	0.623808
$131$	2.40858e9	0.714561	0.357281	−	0.933997i	$-0.383704\pi$
$131$	2.40858e9	0.714561	0.357281	+	0.933997i	$0.383704\pi$
$132$	−805413.	−0.000230906 0
$133$	0	0
$134$	−1.35059e9	−0.361869
$135$	4.84899e7	0.0125646
$136$	1.63393e8	0.0409551
$137$	5.47458e9	1.32772	0.663862	−	0.747855i	$-0.268916\pi$
$137$	5.47458e9	1.32772	0.663862	+	0.747855i	$0.268916\pi$
$138$	−9.11405e7	−0.0213922
$139$	−9.08897e8	−0.206513	−0.103257	−	0.994655i	$-0.532926\pi$
$139$	−9.08897e8	−0.206513	−0.103257	+	0.994655i	$0.532926\pi$
$140$	0	0
$141$	7.83596e7	0.0166958
$142$	8.83462e9	1.82344
$143$	−2.77039e8	−0.0554024
$144$	6.34064e9	1.22886
$145$	−2.46552e9	−0.463182
$146$	3.56411e9	0.649176
$147$	0	0
$148$	−1.90370e9	−0.326152
$149$	6.00080e9	0.997403	0.498702	−	0.866774i	$-0.333810\pi$
$149$	6.00080e9	0.997403	0.498702	+	0.866774i	$0.333810\pi$
$150$	−2.02827e7	−0.00327127
$151$	5.35390e9	0.838058	0.419029	−	0.907973i	$-0.362371\pi$
$151$	5.35390e9	0.838058	0.419029	+	0.907973i	$0.362371\pi$
$152$	−3.51906e9	−0.534725
$153$	−3.69851e8	−0.0545652
$154$	0	0
$155$	5.62143e9	0.782265
$156$	4.42550e7	0.00598276
$157$	3.05256e8	0.0400973	0.0200487	−	0.999799i	$-0.493618\pi$
$157$	3.05256e8	0.0400973	0.0200487	+	0.999799i	$0.493618\pi$
$158$	−4.35631e9	−0.556112
$159$	8.04323e7	0.00998030
$160$	−2.52292e9	−0.304343
$161$	0	0
$162$	−1.02000e10	−1.16354
$163$	9.53729e9	1.05823	0.529116	−	0.848550i	$-0.322524\pi$
$163$	9.53729e9	1.05823	0.529116	+	0.848550i	$0.322524\pi$
$164$	−5.50865e8	−0.0594632
$165$	2.76612e6	0.000290532 0
$166$	−4.25281e9	−0.434700
$167$	7.59729e9	0.755848	0.377924	−	0.925837i	$-0.376638\pi$
$167$	7.59729e9	0.755848	0.377924	+	0.925837i	$0.376638\pi$
$168$	0	0
$169$	4.61792e9	0.435468
$170$	3.09439e8	0.0284155
$171$	7.96564e9	0.712423
$172$	2.92566e9	0.254886
$173$	1.61106e10	1.36742	0.683712	−	0.729751i	$-0.260364\pi$
$173$	1.61106e10	1.36742	0.683712	+	0.729751i	$0.260364\pi$
$174$	−2.04831e8	−0.0169404
$175$	0	0
$176$	7.23479e8	0.0568354
$177$	−3.16516e8	−0.0242391
$178$	2.64259e10	1.97306
$179$	5.90583e9	0.429974	0.214987	−	0.976617i	$-0.431029\pi$
$179$	5.90583e9	0.429974	0.214987	+	0.976617i	$0.431029\pi$
$180$	2.23827e9	0.158923
$181$	4.57036e9	0.316517	0.158258	−	0.987398i	$-0.449412\pi$
$181$	4.57036e9	0.316517	0.158258	+	0.987398i	$0.449412\pi$
$182$	0	0
$183$	−2.94252e8	−0.0193950
$184$	1.52601e10	0.981469
$185$	6.53807e9	0.410371
$186$	4.67018e8	0.0286105
$187$	−4.22007e7	−0.00252367
$188$	7.23481e9	0.422393
$189$	0	0
$190$	−6.66452e9	−0.371003
$191$	1.08620e10	0.590555	0.295277	−	0.955412i	$-0.404588\pi$
$191$	1.08620e10	0.590555	0.295277	+	0.955412i	$0.404588\pi$
$192$	1.15555e8	0.00613669
$193$	3.53101e10	1.83185	0.915926	−	0.401346i	$-0.131458\pi$
$193$	3.53101e10	1.83185	0.915926	+	0.401346i	$0.131458\pi$
$194$	−7.61762e9	−0.386110
$195$	−1.51990e8	−0.00752764
$196$	0	0
$197$	−1.34688e10	−0.637136	−0.318568	−	0.947900i	$-0.603202\pi$
$197$	−1.34688e10	−0.637136	−0.318568	+	0.947900i	$0.603202\pi$
$198$	−1.16407e9	−0.0538251
$199$	2.38956e10	1.08014	0.540068	−	0.841621i	$-0.318399\pi$
$199$	2.38956e10	1.08014	0.540068	+	0.841621i	$0.318399\pi$
$200$	3.39603e9	0.150085
$201$	1.01051e8	0.00436676
$202$	4.14146e9	0.175014
$203$	0	0
$204$	6.74127e6	0.000272525 0
$205$	1.89190e9	0.0748179
$206$	1.35688e10	0.524976
$207$	−3.45422e10	−1.30763
$208$	−3.97529e10	−1.47260
$209$	9.08895e8	0.0329500
$210$	0	0
$211$	−2.71767e10	−0.943898	−0.471949	−	0.881626i	$-0.656449\pi$
$211$	−2.71767e10	−0.943898	−0.471949	+	0.881626i	$0.656449\pi$
$212$	7.42618e9	0.252496
$213$	−6.61008e8	−0.0220038
$214$	6.23876e10	2.03346
$215$	−1.00479e10	−0.320703
$216$	−6.74502e8	−0.0210834
$217$	0	0
$218$	−5.94893e9	−0.178396
$219$	−2.66667e8	−0.00783377
$220$	2.55391e8	0.00735029
$221$	2.31880e9	0.0653880
$222$	5.43171e8	0.0150089
$223$	2.65338e8	0.00718502	0.00359251	−	0.999994i	$-0.498856\pi$
$223$	2.65338e8	0.00718502	0.00359251	+	0.999994i	$0.498856\pi$
$224$	0	0
$225$	−7.68715e9	−0.199961
$226$	7.74049e10	1.97370
$227$	2.92609e10	0.731428	0.365714	−	0.930727i	$-0.380825\pi$
$227$	2.92609e10	0.731428	0.365714	+	0.930727i	$0.380825\pi$
$228$	−1.45189e8	−0.00355818
$229$	3.93335e10	0.945156	0.472578	−	0.881289i	$-0.343324\pi$
$229$	3.93335e10	0.945156	0.472578	+	0.881289i	$0.343324\pi$
$230$	2.89001e10	0.680963
$231$	0	0
$232$	3.42957e10	0.777220
$233$	4.02983e10	0.895746	0.447873	−	0.894097i	$-0.352182\pi$
$233$	4.02983e10	0.895746	0.447873	+	0.894097i	$0.352182\pi$
$234$	6.39619e10	1.39460
$235$	−2.48473e10	−0.531465
$236$	−2.92234e10	−0.613236
$237$	3.25940e8	0.00671073
$238$	0	0
$239$	3.54020e10	0.701839	0.350919	−	0.936406i	$-0.385869\pi$
$239$	3.54020e10	0.701839	0.350919	+	0.936406i	$0.385869\pi$
$240$	3.96917e8	0.00772235
$241$	−3.42729e9	−0.0654446	−0.0327223	−	0.999464i	$-0.510418\pi$
$241$	−3.42729e9	−0.0654446	−0.0327223	+	0.999464i	$0.510418\pi$
$242$	6.19838e10	1.16174
$243$	2.29025e9	0.0421361
$244$	−2.71678e10	−0.490683
$245$	0	0
$246$	1.57175e8	0.00273638
$247$	−4.99410e10	−0.853730
$248$	−7.81949e10	−1.31264
$249$	3.18196e8	0.00524563
$250$	6.43153e9	0.104132
$251$	6.49927e10	1.03355	0.516776	−	0.856120i	$-0.327132\pi$
$251$	6.49927e10	1.03355	0.516776	+	0.856120i	$0.327132\pi$
$252$	0	0
$253$	−3.94134e9	−0.0604785
$254$	−8.13076e10	−1.22569
$255$	−2.31523e7	−0.000342897 0
$256$	6.51152e10	0.947551
$257$	−7.71755e10	−1.10352	−0.551760	−	0.834003i	$-0.686044\pi$
$257$	−7.71755e10	−1.10352	−0.551760	+	0.834003i	$0.686044\pi$
$258$	−8.34762e8	−0.0117294
$259$	0	0
$260$	−1.40330e10	−0.190445
$261$	−7.76307e10	−1.03550
$262$	−6.34504e10	−0.831914
$263$	5.32154e10	0.685862	0.342931	−	0.939361i	$-0.388580\pi$
$263$	5.32154e10	0.685862	0.342931	+	0.939361i	$0.388580\pi$
$264$	−3.84772e7	−0.000487512 0
$265$	−2.55046e10	−0.317696
$266$	0	0
$267$	−1.97719e9	−0.0238094
$268$	9.32989e9	0.110476
$269$	−2.15319e10	−0.250725	−0.125362	−	0.992111i	$-0.540009\pi$
$269$	−2.15319e10	−0.250725	−0.125362	+	0.992111i	$0.540009\pi$
$270$	−1.27739e9	−0.0146281
$271$	−4.81053e10	−0.541790	−0.270895	−	0.962609i	$-0.587320\pi$
$271$	−4.81053e10	−0.541790	−0.270895	+	0.962609i	$0.587320\pi$
$272$	−6.05548e9	−0.0670793
$273$	0	0
$274$	−1.44220e11	−1.54578
$275$	−8.77119e8	−0.00924829
$276$	6.29601e8	0.00653092
$277$	6.60074e10	0.673649	0.336824	−	0.941568i	$-0.390647\pi$
$277$	6.60074e10	0.673649	0.336824	+	0.941568i	$0.390647\pi$
$278$	2.39436e10	0.240429
$279$	1.77000e11	1.74885
$280$	0	0
$281$	7.31129e10	0.699545	0.349772	−	0.936835i	$-0.386259\pi$
$281$	7.31129e10	0.699545	0.349772	+	0.936835i	$0.386259\pi$
$282$	−2.06427e9	−0.0194377
$283$	−1.32293e11	−1.22602	−0.613012	−	0.790073i	$-0.710042\pi$
$283$	−1.32293e11	−1.22602	−0.613012	+	0.790073i	$0.710042\pi$
$284$	−6.10298e10	−0.556685
$285$	4.98640e8	0.00447699
$286$	7.29818e9	0.0645011
$287$	0	0
$288$	−7.94381e10	−0.680397
$289$	−1.18235e11	−0.997021
$290$	6.49504e10	0.539251
$291$	5.69951e8	0.00465929
$292$	−2.46209e10	−0.198190
$293$	4.00575e10	0.317526	0.158763	−	0.987317i	$-0.449249\pi$
$293$	4.00575e10	0.317526	0.158763	+	0.987317i	$0.449249\pi$
$294$	0	0
$295$	1.00365e11	0.771586
$296$	−9.09456e10	−0.688603
$297$	1.74209e8	0.00129917
$298$	−1.58082e11	−1.16121
$299$	2.16564e11	1.56699
$300$	1.40114e8	0.000998699 0
$301$	0	0
$302$	−1.41041e11	−0.975693
$303$	−3.09865e8	−0.00211193
$304$	1.30419e11	0.875812
$305$	9.33055e10	0.617388
$306$	9.74319e9	0.0635265
$307$	−3.61839e10	−0.232484	−0.116242	−	0.993221i	$-0.537085\pi$
$307$	−3.61839e10	−0.232484	−0.116242	+	0.993221i	$0.537085\pi$
$308$	0	0
$309$	−1.01522e9	−0.00633501
$310$	−1.48088e11	−0.910737
$311$	−1.58042e11	−0.957968	−0.478984	−	0.877824i	$-0.658995\pi$
$311$	−1.58042e11	−0.957968	−0.478984	+	0.877824i	$0.658995\pi$
$312$	2.11420e9	0.0126314
$313$	−1.78114e11	−1.04894	−0.524468	−	0.851430i	$-0.675736\pi$
$313$	−1.78114e11	−1.04894	−0.524468	+	0.851430i	$0.675736\pi$
$314$	−8.04151e9	−0.0466825
$315$	0	0
$316$	3.00935e10	0.169778
$317$	3.74923e10	0.208533	0.104267	−	0.994549i	$-0.466751\pi$
$317$	3.74923e10	0.208533	0.104267	+	0.994549i	$0.466751\pi$
$318$	−2.11887e9	−0.0116194
$319$	−8.85782e9	−0.0478926
$320$	−3.66418e10	−0.195345
$321$	−4.66785e9	−0.0245383
$322$	0	0
$323$	−7.60740e9	−0.0388888
$324$	7.04617e10	0.355223
$325$	4.81950e10	0.239622
$326$	−2.51246e11	−1.23203
$327$	4.45100e8	0.00215275
$328$	−2.63166e10	−0.125544
$329$	0	0
$330$	−7.28694e7	−0.000338246 0
$331$	1.08393e11	0.496335	0.248167	−	0.968717i	$-0.420172\pi$
$331$	1.08393e11	0.496335	0.248167	+	0.968717i	$0.420172\pi$
$332$	2.93785e10	0.132711
$333$	2.05862e11	0.917437
$334$	−2.00139e11	−0.879981
$335$	−3.20427e10	−0.139004
$336$	0	0
$337$	3.53012e11	1.49092	0.745462	−	0.666548i	$-0.232229\pi$
$337$	3.53012e11	1.49092	0.745462	+	0.666548i	$0.232229\pi$
$338$	−1.21652e11	−0.506986
$339$	−5.79145e9	−0.0238171
$340$	−2.13761e9	−0.00867509
$341$	2.01960e10	0.0808855
$342$	−2.09843e11	−0.829425
$343$	0	0
$344$	1.39768e11	0.538140
$345$	−2.16231e9	−0.00821735
$346$	−4.24409e11	−1.59200
$347$	−4.58221e11	−1.69665	−0.848324	−	0.529477i	$-0.822388\pi$
$347$	−4.58221e11	−1.69665	−0.848324	+	0.529477i	$0.822388\pi$
$348$	1.41497e9	0.00517180
$349$	−4.77589e11	−1.72322	−0.861608	−	0.507575i	$-0.830542\pi$
$349$	−4.77589e11	−1.72322	−0.861608	+	0.507575i	$0.830542\pi$
$350$	0	0
$351$	−9.57223e9	−0.0336613
$352$	−9.06404e9	−0.0314688
$353$	−4.13087e11	−1.41597	−0.707986	−	0.706226i	$-0.750396\pi$
$353$	−4.13087e11	−1.41597	−0.707986	+	0.706226i	$0.750396\pi$
$354$	8.33816e9	0.0282199
$355$	2.09601e11	0.700433
$356$	−1.82551e11	−0.602364
$357$	0	0
$358$	−1.55581e11	−0.500589
$359$	−1.83554e11	−0.583230	−0.291615	−	0.956536i	$-0.594193\pi$
$359$	−1.83554e11	−0.583230	−0.291615	+	0.956536i	$0.594193\pi$
$360$	1.06930e11	0.335534
$361$	−1.58844e11	−0.492253
$362$	−1.20399e11	−0.368498
$363$	−4.63764e9	−0.0140190
$364$	0	0
$365$	8.45584e10	0.249367
$366$	7.75164e9	0.0225803
$367$	1.52885e11	0.439915	0.219957	−	0.975509i	$-0.429408\pi$
$367$	1.52885e11	0.439915	0.219957	+	0.975509i	$0.429408\pi$
$368$	−5.65552e11	−1.60752
$369$	5.95694e10	0.167265
$370$	−1.72236e11	−0.477767
$371$	0	0
$372$	−3.22617e9	−0.00873461
$373$	3.94586e11	1.05548	0.527742	−	0.849405i	$-0.323039\pi$
$373$	3.94586e11	1.05548	0.527742	+	0.849405i	$0.323039\pi$
$374$	1.11172e9	0.00293814
$375$	−4.81208e8	−0.00125659
$376$	3.45630e11	0.891798
$377$	4.86710e11	1.24089
$378$	0	0
$379$	7.26412e11	1.80845	0.904225	−	0.427057i	$-0.140450\pi$
$379$	7.26412e11	1.80845	0.904225	+	0.427057i	$0.140450\pi$
$380$	4.60387e10	0.113265
$381$	6.08345e9	0.0147907
$382$	−2.86144e11	−0.687542
$383$	5.73936e11	1.36292	0.681458	−	0.731857i	$-0.261346\pi$
$383$	5.73936e11	1.36292	0.681458	+	0.731857i	$0.261346\pi$
$384$	−7.11780e9	−0.0167053
$385$	0	0
$386$	−9.30192e11	−2.13270
$387$	−3.16375e11	−0.716972
$388$	5.26227e10	0.117877
$389$	2.27345e11	0.503400	0.251700	−	0.967805i	$-0.419010\pi$
$389$	2.27345e11	0.503400	0.251700	+	0.967805i	$0.419010\pi$
$390$	4.00395e9	0.00876391
$391$	3.29888e10	0.0713791
$392$	0	0
$393$	4.74737e9	0.0100389
$394$	3.54817e11	0.741773
$395$	−1.03353e11	−0.213618
$396$	8.04140e9	0.0164325
$397$	9.03630e11	1.82572	0.912858	−	0.408277i	$-0.133870\pi$
$397$	9.03630e11	1.82572	0.912858	+	0.408277i	$0.133870\pi$
$398$	−6.29493e11	−1.25753
$399$	0	0
$400$	−1.25860e11	−0.245820
$401$	3.47203e11	0.670555	0.335277	−	0.942119i	$-0.391170\pi$
$401$	3.47203e11	0.670555	0.335277	+	0.942119i	$0.391170\pi$
$402$	−2.66204e9	−0.00508391
$403$	−1.10971e12	−2.09573
$404$	−2.86093e10	−0.0534307
$405$	−2.41994e11	−0.446949
$406$	0	0
$407$	2.34892e10	0.0424320
$408$	3.22052e8	0.000575381 0
$409$	1.06690e12	1.88524	0.942621	−	0.333866i	$-0.108353\pi$
$409$	1.06690e12	1.88524	0.942621	+	0.333866i	$0.108353\pi$
$410$	−4.98393e10	−0.0871053
$411$	1.07905e10	0.0186533
$412$	−9.37337e10	−0.160272
$413$	0	0
$414$	9.09965e11	1.52238
$415$	−1.00898e11	−0.166980
$416$	4.98041e11	0.815352
$417$	−1.79146e9	−0.00290132
$418$	−2.39435e10	−0.0383614
$419$	−8.89018e11	−1.40912	−0.704559	−	0.709645i	$-0.748855\pi$
$419$	−8.89018e11	−1.40912	−0.704559	+	0.709645i	$0.748855\pi$
$420$	0	0
$421$	9.18431e11	1.42488	0.712438	−	0.701735i	$-0.247591\pi$
$421$	9.18431e11	1.42488	0.712438	+	0.701735i	$0.247591\pi$
$422$	7.15929e11	1.09891
$423$	−7.82358e11	−1.18816
$424$	3.54773e11	0.533094
$425$	7.34144e9	0.0109152
$426$	1.74133e10	0.0256175
$427$	0	0
$428$	−4.30975e11	−0.620805
$429$	−5.46051e8	−0.000778351 0
$430$	2.64698e11	0.373372
$431$	−7.15695e11	−0.999034	−0.499517	−	0.866304i	$-0.666489\pi$
$431$	−7.15695e11	−0.999034	−0.499517	+	0.866304i	$0.666489\pi$
$432$	2.49976e10	0.0345320
$433$	1.30709e12	1.78694	0.893472	−	0.449119i	$-0.148262\pi$
$433$	1.30709e12	1.78694	0.893472	+	0.449119i	$0.148262\pi$
$434$	0	0
$435$	−4.85960e9	−0.00650727
$436$	4.10954e10	0.0544633
$437$	−7.10493e11	−0.931952
$438$	7.02495e9	0.00912031
$439$	8.08851e11	1.03939	0.519695	−	0.854352i	$-0.326046\pi$
$439$	8.08851e11	1.03939	0.519695	+	0.854352i	$0.326046\pi$
$440$	1.22009e10	0.0155186
$441$	0	0
$442$	−6.10854e10	−0.0761267
$443$	2.49522e11	0.307816	0.153908	−	0.988085i	$-0.450814\pi$
$443$	2.49522e11	0.307816	0.153908	+	0.988085i	$0.450814\pi$
$444$	−3.75223e9	−0.00458212
$445$	6.26955e11	0.757907
$446$	−6.98995e9	−0.00836503
$447$	1.18277e10	0.0140126
$448$	0	0
$449$	1.12524e12	1.30658	0.653291	−	0.757107i	$-0.273388\pi$
$449$	1.12524e12	1.30658	0.653291	+	0.757107i	$0.273388\pi$
$450$	2.02507e11	0.232800
$451$	6.79699e9	0.00773610
$452$	−5.34715e11	−0.602558
$453$	1.05527e10	0.0117739
$454$	−7.70835e11	−0.851550
$455$	0	0
$456$	−6.93617e9	−0.00751238
$457$	7.92565e11	0.849987	0.424993	−	0.905196i	$-0.360276\pi$
$457$	7.92565e11	0.849987	0.424993	+	0.905196i	$0.360276\pi$
$458$	−1.03618e12	−1.10038
$459$	−1.45812e9	−0.00153333
$460$	−1.99642e11	−0.207894
$461$	−8.54573e11	−0.881241	−0.440621	−	0.897693i	$-0.645242\pi$
$461$	−8.54573e11	−0.881241	−0.440621	+	0.897693i	$0.645242\pi$
$462$	0	0
$463$	−1.55057e12	−1.56811	−0.784056	−	0.620690i	$-0.786852\pi$
$463$	−1.55057e12	−1.56811	−0.784056	+	0.620690i	$0.786852\pi$
$464$	−1.27103e12	−1.27299
$465$	1.10800e10	0.0109901
$466$	−1.06160e12	−1.04285
$467$	1.54154e11	0.149979	0.0749893	−	0.997184i	$-0.476108\pi$
$467$	1.54154e11	0.149979	0.0749893	+	0.997184i	$0.476108\pi$
$468$	−4.41850e11	−0.425764
$469$	0	0
$470$	6.54566e11	0.618747
$471$	6.01667e8	0.000563329 0
$472$	−1.39610e12	−1.29472
$473$	−3.60990e10	−0.0331604
$474$	−8.58641e9	−0.00781284
$475$	−1.58116e11	−0.142513
$476$	0	0
$477$	−8.03052e11	−0.710249
$478$	−9.32614e11	−0.817102
$479$	1.96197e12	1.70287	0.851437	−	0.524457i	$-0.175732\pi$
$479$	1.96197e12	1.70287	0.851437	+	0.524457i	$0.175732\pi$
$480$	−4.97274e9	−0.00427573
$481$	−1.29066e12	−1.09941
$482$	9.02868e10	0.0761926
$483$	0	0
$484$	−4.28186e11	−0.354673
$485$	−1.80728e11	−0.148316
$486$	−6.03332e10	−0.0490561
$487$	8.97598e11	0.723106	0.361553	−	0.932352i	$-0.382247\pi$
$487$	8.97598e11	0.723106	0.361553	+	0.932352i	$0.382247\pi$
$488$	−1.29789e12	−1.03598
$489$	1.87983e10	0.0148671
$490$	0	0
$491$	4.80068e11	0.372766	0.186383	−	0.982477i	$-0.440324\pi$
$491$	4.80068e11	0.372766	0.186383	+	0.982477i	$0.440324\pi$
$492$	−1.08577e9	−0.000835401 0
$493$	7.41395e10	0.0565247
$494$	1.31562e12	0.993939
$495$	−2.76175e10	−0.0206757
$496$	2.89797e12	2.14994
$497$	0	0
$498$	−8.38240e9	−0.00610712
$499$	−1.81750e12	−1.31227	−0.656133	−	0.754646i	$-0.727809\pi$
$499$	−1.81750e12	−1.31227	−0.656133	+	0.754646i	$0.727809\pi$
$500$	−4.44291e10	−0.0317909
$501$	1.49745e10	0.0106189
$502$	−1.71214e12	−1.20329
$503$	−9.78467e11	−0.681538	−0.340769	−	0.940147i	$-0.610687\pi$
$503$	−9.78467e11	−0.681538	−0.340769	+	0.940147i	$0.610687\pi$
$504$	0	0
$505$	9.82561e10	0.0672277
$506$	1.03829e11	0.0704109
$507$	9.10205e9	0.00611792
$508$	5.61675e11	0.374195
$509$	−9.49400e11	−0.626930	−0.313465	−	0.949600i	$-0.601490\pi$
$509$	−9.49400e11	−0.626930	−0.313465	+	0.949600i	$0.601490\pi$
$510$	6.09913e8	0.000399211 0
$511$	0	0
$512$	1.33578e11	0.0859056
$513$	3.14041e10	0.0200197
$514$	2.03308e12	1.28475
$515$	3.21920e11	0.201658
$516$	5.76655e9	0.00358090
$517$	−8.92685e10	−0.0549529
$518$	0	0
$519$	3.17544e10	0.0192110
$520$	−6.70400e11	−0.402086
$521$	−3.20965e12	−1.90848	−0.954240	−	0.299042i	$-0.903333\pi$
$521$	−3.20965e12	−1.90848	−0.954240	+	0.299042i	$0.903333\pi$
$522$	2.04507e12	1.20556
$523$	2.27961e12	1.33230	0.666152	−	0.745816i	$-0.267940\pi$
$523$	2.27961e12	1.33230	0.666152	+	0.745816i	$0.267940\pi$
$524$	4.38317e11	0.253979
$525$	0	0
$526$	−1.40188e12	−0.798501
$527$	−1.69039e11	−0.0954642
$528$	1.42600e9	0.000798483 0
$529$	1.27983e12	0.710564
$530$	6.71880e11	0.369871
$531$	3.16016e12	1.72498
$532$	0	0
$533$	−3.73473e11	−0.200441
$534$	5.20862e10	0.0277196
$535$	1.48015e12	0.781111
$536$	4.45719e11	0.233249
$537$	1.16406e10	0.00604073
$538$	5.67226e11	0.291901
$539$	0	0
$540$	8.82427e9	0.00446588
$541$	2.51926e12	1.26440	0.632201	−	0.774804i	$-0.282152\pi$
$541$	2.51926e12	1.26440	0.632201	+	0.774804i	$0.282152\pi$
$542$	1.26726e12	0.630769
$543$	9.00830e9	0.00444676
$544$	7.58656e10	0.0371407
$545$	−1.41138e11	−0.0685269
$546$	0	0
$547$	−2.15157e12	−1.02757	−0.513787	−	0.857918i	$-0.671758\pi$
$547$	−2.15157e12	−1.02757	−0.513787	+	0.857918i	$0.671758\pi$
$548$	9.96272e11	0.471917
$549$	2.93787e12	1.38025
$550$	2.31064e10	0.0107671
$551$	−1.59677e12	−0.738008
$552$	3.00780e10	0.0137887
$553$	0	0
$554$	−1.73887e12	−0.784282
$555$	1.28867e10	0.00576533
$556$	−1.65403e11	−0.0734016
$557$	−2.27895e12	−1.00320	−0.501600	−	0.865100i	$-0.667255\pi$
$557$	−2.27895e12	−1.00320	−0.501600	+	0.865100i	$0.667255\pi$
$558$	−4.66279e12	−2.03607
$559$	1.98353e12	0.859181
$560$	0	0
$561$	−8.31788e7	−3.54552e−5 0
$562$	−1.92605e12	−0.814431
$563$	−3.82145e12	−1.60303	−0.801513	−	0.597978i	$-0.795971\pi$
$563$	−3.82145e12	−1.60303	−0.801513	+	0.597978i	$0.795971\pi$
$564$	1.42600e10	0.00593423
$565$	1.83643e12	0.758152
$566$	3.48508e12	1.42738
$567$	0	0
$568$	−2.91559e12	−1.17533
$569$	−2.94845e12	−1.17920	−0.589601	−	0.807695i	$-0.700715\pi$
$569$	−2.94845e12	−1.17920	−0.589601	+	0.807695i	$0.700715\pi$
$570$	−1.31360e10	−0.00521224
$571$	2.99642e12	1.17962	0.589808	−	0.807544i	$-0.299203\pi$
$571$	2.99642e12	1.17962	0.589808	+	0.807544i	$0.299203\pi$
$572$	−5.04160e10	−0.0196918
$573$	2.14093e10	0.00829673
$574$	0	0
$575$	6.85654e11	0.261577
$576$	−1.15373e12	−0.436718
$577$	1.87283e12	0.703407	0.351703	−	0.936111i	$-0.385603\pi$
$577$	1.87283e12	0.703407	0.351703	+	0.936111i	$0.385603\pi$
$578$	3.11472e12	1.16076
$579$	6.95971e10	0.0257358
$580$	−4.48679e11	−0.164630
$581$	0	0
$582$	−1.50145e10	−0.00542448
$583$	−9.16297e10	−0.0328494
$584$	−1.17622e12	−0.418438
$585$	1.51750e12	0.535705
$586$	−1.05525e12	−0.369673
$587$	1.94572e12	0.676410	0.338205	−	0.941073i	$-0.390180\pi$
$587$	1.94572e12	0.676410	0.338205	+	0.941073i	$0.390180\pi$
$588$	0	0
$589$	3.64067e12	1.24642
$590$	−2.64398e12	−0.898305
$591$	−2.65474e10	−0.00895116
$592$	3.37052e12	1.12784
$593$	−8.61235e11	−0.286006	−0.143003	−	0.989722i	$-0.545676\pi$
$593$	−8.61235e11	−0.286006	−0.143003	+	0.989722i	$0.545676\pi$
$594$	−4.58927e9	−0.00151253
$595$	0	0
$596$	1.09204e12	0.354510
$597$	4.70988e10	0.0151749
$598$	−5.70507e12	−1.82434
$599$	2.81546e12	0.893570	0.446785	−	0.894641i	$-0.352569\pi$
$599$	2.81546e12	0.893570	0.446785	+	0.894641i	$0.352569\pi$
$600$	6.69368e9	0.00210855
$601$	−4.79484e12	−1.49913	−0.749565	−	0.661931i	$-0.769737\pi$
$601$	−4.79484e12	−1.49913	−0.749565	+	0.661931i	$0.769737\pi$
$602$	0	0
$603$	−1.00891e12	−0.310761
$604$	9.74312e11	0.297873
$605$	1.47057e12	0.446257
$606$	8.16293e9	0.00245878
$607$	−7.43279e11	−0.222230	−0.111115	−	0.993808i	$-0.535442\pi$
$607$	−7.43279e11	−0.222230	−0.111115	+	0.993808i	$0.535442\pi$
$608$	−1.63395e12	−0.484922
$609$	0	0
$610$	−2.45800e12	−0.718782
$611$	4.90503e12	1.42382
$612$	−6.73061e10	−0.0193943
$613$	6.45388e11	0.184607	0.0923036	−	0.995731i	$-0.470577\pi$
$613$	6.45388e11	0.184607	0.0923036	+	0.995731i	$0.470577\pi$
$614$	9.53213e11	0.270665
$615$	3.72898e9	0.00105112
$616$	0	0
$617$	4.66543e12	1.29601	0.648005	−	0.761636i	$-0.275604\pi$
$617$	4.66543e12	1.29601	0.648005	+	0.761636i	$0.275604\pi$
$618$	2.67445e10	0.00737542
$619$	2.49665e12	0.683519	0.341759	−	0.939787i	$-0.388977\pi$
$619$	2.49665e12	0.683519	0.341759	+	0.939787i	$0.388977\pi$
$620$	1.02300e12	0.278043
$621$	−1.36181e11	−0.0367455
$622$	4.16338e12	1.11530
$623$	0	0
$624$	−7.83541e10	−0.0206886
$625$	1.52588e11	0.0400000
$626$	4.69215e12	1.22120
$627$	1.79146e9	0.000462916 0
$628$	5.55509e10	0.0142519
$629$	−1.96604e11	−0.0500799
$630$	0	0
$631$	2.92442e12	0.734357	0.367179	−	0.930150i	$-0.380324\pi$
$631$	2.92442e12	0.734357	0.367179	+	0.930150i	$0.380324\pi$
$632$	1.43766e12	0.358451
$633$	−5.35659e10	−0.0132609
$634$	−9.87678e11	−0.242781
$635$	−1.92902e12	−0.470821
$636$	1.46372e10	0.00354733
$637$	0	0
$638$	2.33346e11	0.0557581
$639$	6.59963e12	1.56591
$640$	2.25701e12	0.531770
$641$	−4.23039e12	−0.989736	−0.494868	−	0.868968i	$-0.664784\pi$
$641$	−4.23039e12	−0.989736	−0.494868	+	0.868968i	$0.664784\pi$
$642$	1.22968e11	0.0285682
$643$	−1.95718e12	−0.451524	−0.225762	−	0.974183i	$-0.572487\pi$
$643$	−1.95718e12	−0.451524	−0.225762	+	0.974183i	$0.572487\pi$
$644$	0	0
$645$	−1.98047e10	−0.00450557
$646$	2.00406e11	0.0452756
$647$	4.71751e12	1.05838	0.529192	−	0.848502i	$-0.322495\pi$
$647$	4.71751e12	1.05838	0.529192	+	0.848502i	$0.322495\pi$
$648$	3.36618e12	0.749980
$649$	3.60580e11	0.0797813
$650$	−1.26963e12	−0.278975
$651$	0	0
$652$	1.73561e12	0.376130
$653$	5.50754e12	1.18536	0.592678	−	0.805440i	$-0.298071\pi$
$653$	5.50754e12	1.18536	0.592678	+	0.805440i	$0.298071\pi$
$654$	−1.17255e10	−0.00250629
$655$	−1.50536e12	−0.319562
$656$	9.75315e11	0.205626
$657$	2.66245e12	0.557491
$658$	0	0
$659$	−4.05044e12	−0.836599	−0.418300	−	0.908309i	$-0.637374\pi$
$659$	−4.05044e12	−0.836599	−0.418300	+	0.908309i	$0.637374\pi$
$660$	5.03383e8	0.000103265 0
$661$	2.16897e12	0.441923	0.220962	−	0.975283i	$-0.429080\pi$
$661$	2.16897e12	0.441923	0.220962	+	0.975283i	$0.429080\pi$
$662$	−2.85545e12	−0.577848
$663$	4.57042e9	0.000918640 0
$664$	1.40350e12	0.280193
$665$	0	0
$666$	−5.42312e12	−1.06811
$667$	6.92425e12	1.35459
$668$	1.38257e12	0.268653
$669$	5.22989e8	0.000100943 0
$670$	8.44117e11	0.161833
$671$	3.35217e11	0.0638373
$672$	0	0
$673$	−7.79666e12	−1.46501	−0.732505	−	0.680761i	$-0.761649\pi$
$673$	−7.79666e12	−1.46501	−0.732505	+	0.680761i	$0.761649\pi$
$674$	−9.29959e12	−1.73578
$675$	−3.03062e10	−0.00561907
$676$	8.40378e11	0.154780
$677$	3.98612e12	0.729293	0.364646	−	0.931146i	$-0.381190\pi$
$677$	3.98612e12	0.729293	0.364646	+	0.931146i	$0.381190\pi$
$678$	1.52567e11	0.0277286
$679$	0	0
$680$	−1.02121e11	−0.0183157
$681$	5.76740e10	0.0102759
$682$	−5.32034e11	−0.0941693
$683$	−7.20461e12	−1.26683	−0.633413	−	0.773814i	$-0.718347\pi$
$683$	−7.20461e12	−1.26683	−0.633413	+	0.773814i	$0.718347\pi$
$684$	1.44960e12	0.253219
$685$	−3.42161e12	−0.593776
$686$	0	0
$687$	7.75275e10	0.0132785
$688$	−5.17992e12	−0.881405
$689$	5.03477e12	0.851125
$690$	5.69628e10	0.00956689
$691$	−7.66976e12	−1.27977	−0.639883	−	0.768472i	$-0.721017\pi$
$691$	−7.66976e12	−1.27977	−0.639883	+	0.768472i	$0.721017\pi$
$692$	2.93183e12	0.486028
$693$	0	0
$694$	1.20711e13	1.97529
$695$	5.68061e11	0.0923555
$696$	6.75978e10	0.0109192
$697$	−5.68904e10	−0.00913044
$698$	1.25814e13	2.00622
$699$	7.94290e10	0.0125844
$700$	0	0
$701$	−6.76464e11	−0.105807	−0.0529034	−	0.998600i	$-0.516848\pi$
$701$	−6.76464e11	−0.105807	−0.0529034	+	0.998600i	$0.516848\pi$
$702$	2.52166e11	0.0391895
$703$	4.23433e12	0.653861
$704$	−1.31642e11	−0.0201985
$705$	−4.89748e10	−0.00746657
$706$	1.08822e13	1.64852
$707$	0	0
$708$	−5.76002e10	−0.00861538
$709$	1.19764e13	1.77999	0.889995	−	0.455970i	$-0.150708\pi$
$709$	1.19764e13	1.77999	0.889995	+	0.455970i	$0.150708\pi$
$710$	−5.52164e12	−0.815465
$711$	−3.25425e12	−0.477570
$712$	−8.72104e12	−1.27177
$713$	−1.57874e13	−2.28775
$714$	0	0
$715$	1.73149e11	0.0247767
$716$	1.07475e12	0.152827
$717$	6.97783e10	0.00986016
$718$	4.83547e12	0.679014
$719$	9.56848e12	1.33525	0.667626	−	0.744497i	$-0.267311\pi$
$719$	9.56848e12	1.33525	0.667626	+	0.744497i	$0.267311\pi$
$720$	−3.96290e12	−0.549562
$721$	0	0
$722$	4.18451e12	0.573096
$723$	−6.75527e9	−0.000919434 0
$724$	8.31721e11	0.112500
$725$	1.54095e12	0.207141
$726$	1.22172e11	0.0163214
$727$	−1.05787e13	−1.40451	−0.702257	−	0.711924i	$-0.747824\pi$
$727$	−1.05787e13	−1.40451	−0.702257	+	0.711924i	$0.747824\pi$
$728$	0	0
$729$	−7.61657e12	−0.998816
$730$	−2.22757e12	−0.290320
$731$	3.02147e11	0.0391372
$732$	−5.35485e10	−0.00689362
$733$	5.59263e12	0.715563	0.357782	−	0.933805i	$-0.383533\pi$
$733$	5.59263e12	0.715563	0.357782	+	0.933805i	$0.383533\pi$
$734$	−4.02754e12	−0.512162
$735$	0	0
$736$	7.08546e12	0.890057
$737$	−1.15119e11	−0.0143729
$738$	−1.56927e12	−0.194735
$739$	−7.75052e11	−0.0955941	−0.0477970	−	0.998857i	$-0.515220\pi$
$739$	−7.75052e11	−0.0955941	−0.0477970	+	0.998857i	$0.515220\pi$
$740$	1.18981e12	0.145859
$741$	−9.84350e10	−0.0119941
$742$	0	0
$743$	2.61033e12	0.314228	0.157114	−	0.987580i	$-0.449781\pi$
$743$	2.61033e12	0.314228	0.157114	+	0.987580i	$0.449781\pi$
$744$	−1.54124e11	−0.0184414
$745$	−3.75050e12	−0.446052
$746$	−1.03948e13	−1.22883
$747$	−3.17693e12	−0.373306
$748$	−7.67976e9	−0.000896996 0
$749$	0	0
$750$	1.26767e10	0.00146295
$751$	1.00388e13	1.15160	0.575801	−	0.817590i	$-0.304690\pi$
$751$	1.00388e13	1.15160	0.575801	+	0.817590i	$0.304690\pi$
$752$	−1.28093e13	−1.46065
$753$	1.28102e11	0.0145204
$754$	−1.28217e13	−1.44468
$755$	−3.34619e12	−0.374791
$756$	0	0
$757$	−1.40463e12	−0.155464	−0.0777320	−	0.996974i	$-0.524768\pi$
$757$	−1.40463e12	−0.155464	−0.0777320	+	0.996974i	$0.524768\pi$
$758$	−1.91363e13	−2.10545
$759$	−7.76848e9	−0.000849666 0
$760$	2.19941e12	0.239136
$761$	1.42436e13	1.53954	0.769769	−	0.638323i	$-0.220372\pi$
$761$	1.42436e13	1.53954	0.769769	+	0.638323i	$0.220372\pi$
$762$	−1.60260e11	−0.0172197
$763$	0	0
$764$	1.97669e12	0.209903
$765$	2.31157e11	0.0244023
$766$	−1.51195e13	−1.58675
$767$	−1.98128e13	−2.06712
$768$	1.28344e11	0.0133122
$769$	1.29105e12	0.133129	0.0665647	−	0.997782i	$-0.478796\pi$
$769$	1.29105e12	0.133129	0.0665647	+	0.997782i	$0.478796\pi$
$770$	0	0
$771$	−1.52115e11	−0.0155034
$772$	6.42578e12	0.651101
$773$	8.58124e12	0.864455	0.432227	−	0.901765i	$-0.357728\pi$
$773$	8.58124e12	0.864455	0.432227	+	0.901765i	$0.357728\pi$
$774$	8.33443e12	0.834721
$775$	−3.51339e12	−0.349840
$776$	2.51395e12	0.248874
$777$	0	0
$778$	−5.98908e12	−0.586073
$779$	1.22527e12	0.119210
$780$	−2.76594e10	−0.00267557
$781$	7.53031e11	0.0724241
$782$	−8.69041e11	−0.0831017
$783$	−3.06055e11	−0.0290985
$784$	0	0
$785$	−1.90785e11	−0.0179321
$786$	−1.25062e11	−0.0116876
$787$	3.12167e11	0.0290068	0.0145034	−	0.999895i	$-0.495383\pi$
$787$	3.12167e11	0.0290068	0.0145034	+	0.999895i	$0.495383\pi$
$788$	−2.45108e12	−0.226459
$789$	1.04889e11	0.00963570
$790$	2.72269e12	0.248701
$791$	0	0
$792$	3.84164e11	0.0346939
$793$	−1.84191e13	−1.65402
$794$	−2.38048e13	−2.12555
$795$	−5.02702e10	−0.00446332
$796$	4.34855e12	0.383916
$797$	8.61341e12	0.756159	0.378079	−	0.925773i	$-0.376585\pi$
$797$	8.61341e12	0.756159	0.378079	+	0.925773i	$0.376585\pi$
$798$	0	0
$799$	7.47173e11	0.0648576
$800$	1.57682e12	0.136106
$801$	1.97407e13	1.69440
$802$	−9.14656e12	−0.780680
$803$	3.03791e11	0.0257843
$804$	1.83895e10	0.00155209
$805$	0	0
$806$	2.92336e13	2.43992
$807$	−4.24400e10	−0.00352244
$808$	−1.36676e12	−0.112808
$809$	−2.01016e13	−1.64992	−0.824958	−	0.565193i	$-0.808802\pi$
$809$	−2.01016e13	−1.64992	−0.824958	+	0.565193i	$0.808802\pi$
$810$	6.37499e12	0.520351
$811$	1.62455e13	1.31868	0.659340	−	0.751845i	$-0.270836\pi$
$811$	1.62455e13	1.31868	0.659340	+	0.751845i	$0.270836\pi$
$812$	0	0
$813$	−9.48169e10	−0.00761164
$814$	−6.18789e11	−0.0494006
$815$	−5.96081e12	−0.473256
$816$	−1.19355e10	−0.000942401 0
$817$	−6.50745e12	−0.510989
$818$	−2.81058e13	−2.19486
$819$	0	0
$820$	3.44291e11	0.0265927
$821$	−8.24254e11	−0.0633165	−0.0316583	−	0.999499i	$-0.510079\pi$
$821$	−8.24254e11	−0.0633165	−0.0316583	+	0.999499i	$0.510079\pi$
$822$	−2.84261e11	−0.0217167
$823$	2.59567e13	1.97220	0.986099	−	0.166159i	$-0.0531364\pi$
$823$	2.59567e13	1.97220	0.986099	+	0.166159i	$0.0531364\pi$
$824$	−4.47796e12	−0.338382
$825$	−1.72883e9	−0.000129930 0
$826$	0	0
$827$	−1.31498e13	−0.977560	−0.488780	−	0.872407i	$-0.662558\pi$
$827$	−1.31498e13	−0.977560	−0.488780	+	0.872407i	$0.662558\pi$
$828$	−6.28605e12	−0.464774
$829$	−1.78218e13	−1.31056	−0.655279	−	0.755387i	$-0.727449\pi$
$829$	−1.78218e13	−1.31056	−0.655279	+	0.755387i	$0.727449\pi$
$830$	2.65800e12	0.194404
$831$	1.30102e11	0.00946412
$832$	7.23334e12	0.523340
$833$	0	0
$834$	4.71934e10	0.00337780
$835$	−4.74830e12	−0.338025
$836$	1.65402e11	0.0117115
$837$	6.97811e11	0.0491443
$838$	2.34199e13	1.64054
$839$	−1.79273e13	−1.24906	−0.624532	−	0.780999i	$-0.714710\pi$
$839$	−1.79273e13	−1.24906	−0.624532	+	0.780999i	$0.714710\pi$
$840$	0	0
$841$	1.05452e12	0.0726898
$842$	−2.41947e13	−1.65888
$843$	1.44107e11	0.00982794
$844$	−4.94565e12	−0.335492
$845$	−2.88620e12	−0.194747
$846$	2.06101e13	1.38329
$847$	0	0
$848$	−1.31482e13	−0.873140
$849$	−2.60754e11	−0.0172245
$850$	−1.93400e11	−0.0127078
$851$	−1.83618e13	−1.20014
$852$	−1.20291e11	−0.00782089
$853$	−1.65652e13	−1.07134	−0.535668	−	0.844429i	$-0.679940\pi$
$853$	−1.65652e13	−1.07134	−0.535668	+	0.844429i	$0.679940\pi$
$854$	0	0
$855$	−4.97852e12	−0.318605
$856$	−2.05891e13	−1.31070
$857$	1.00056e13	0.633619	0.316810	−	0.948489i	$-0.397388\pi$
$857$	1.00056e13	0.633619	0.316810	+	0.948489i	$0.397388\pi$
$858$	1.43849e10	0.000906180 0
$859$	−4.82691e12	−0.302482	−0.151241	−	0.988497i	$-0.548327\pi$
$859$	−4.82691e12	−0.302482	−0.151241	+	0.988497i	$0.548327\pi$
$860$	−1.82854e12	−0.113988
$861$	0	0
$862$	1.88539e13	1.16311
$863$	2.92326e12	0.179398	0.0896992	−	0.995969i	$-0.471409\pi$
$863$	2.92326e12	0.179398	0.0896992	+	0.995969i	$0.471409\pi$
$864$	−3.13180e11	−0.0191198
$865$	−1.00691e13	−0.611531
$866$	−3.44334e13	−2.08042
$867$	−2.33044e11	−0.0140072
$868$	0	0
$869$	−3.71316e11	−0.0220879
$870$	1.28019e11	0.00757597
$871$	6.32544e12	0.372399
$872$	1.96326e12	0.114988
$873$	−5.69050e12	−0.331579
$874$	1.87169e13	1.08501
$875$	0	0
$876$	−4.85285e10	−0.00278438
$877$	−9.67239e12	−0.552123	−0.276061	−	0.961140i	$-0.589029\pi$
$877$	−9.67239e12	−0.552123	−0.276061	+	0.961140i	$0.589029\pi$
$878$	−2.13080e13	−1.21009
$879$	7.89543e10	0.00446094
$880$	−4.52174e11	−0.0254176
$881$	−1.87103e12	−0.104638	−0.0523191	−	0.998630i	$-0.516661\pi$
$881$	−1.87103e12	−0.104638	−0.0523191	+	0.998630i	$0.516661\pi$
$882$	0	0
$883$	8.57451e12	0.474664	0.237332	−	0.971429i	$-0.423727\pi$
$883$	8.57451e12	0.474664	0.237332	+	0.971429i	$0.423727\pi$
$884$	4.21979e11	0.0232411
$885$	1.97823e11	0.0108401
$886$	−6.57328e12	−0.358369
$887$	1.80022e13	0.976494	0.488247	−	0.872705i	$-0.337636\pi$
$887$	1.80022e13	0.976494	0.488247	+	0.872705i	$0.337636\pi$
$888$	−1.79256e11	−0.00967422
$889$	0	0
$890$	−1.65162e13	−0.882379
$891$	−8.69409e11	−0.0462141
$892$	4.82867e10	0.00255379
$893$	−1.60922e13	−0.846804
$894$	−3.11584e11	−0.0163139
$895$	−3.69115e12	−0.192290
$896$	0	0
$897$	4.26854e11	0.0220147
$898$	−2.96428e13	−1.52116
$899$	−3.54809e13	−1.81166
$900$	−1.39892e12	−0.0710726
$901$	7.66937e11	0.0387702
$902$	−1.79057e11	−0.00900660
$903$	0	0
$904$	−2.55450e13	−1.27218
$905$	−2.85647e12	−0.141551
$906$	−2.77995e11	−0.0137076
$907$	2.53756e13	1.24504	0.622520	−	0.782604i	$-0.286109\pi$
$907$	2.53756e13	1.24504	0.622520	+	0.782604i	$0.286109\pi$
$908$	5.32495e12	0.259973
$909$	3.09375e12	0.150296
$910$	0	0
$911$	1.84038e13	0.885268	0.442634	−	0.896702i	$-0.354044\pi$
$911$	1.84038e13	0.885268	0.442634	+	0.896702i	$0.354044\pi$
$912$	2.57060e11	0.0123043
$913$	−3.62494e11	−0.0172656
$914$	−2.08790e13	−0.989581
$915$	1.83908e11	0.00867371
$916$	7.15798e12	0.335939
$917$	0	0
$918$	3.84120e10	0.00178515
$919$	7.61943e12	0.352373	0.176186	−	0.984357i	$-0.443624\pi$
$919$	7.61943e12	0.352373	0.176186	+	0.984357i	$0.443624\pi$
$920$	−9.53755e12	−0.438926
$921$	−7.13195e10	−0.00326618
$922$	2.25125e13	1.02597
$923$	−4.13767e13	−1.87650
$924$	0	0
$925$	−4.08630e12	−0.183524
$926$	4.08475e13	1.82564
$927$	1.01362e13	0.450832
$928$	1.59240e13	0.704832
$929$	3.02391e12	0.133198	0.0665991	−	0.997780i	$-0.478785\pi$
$929$	3.02391e12	0.133198	0.0665991	+	0.997780i	$0.478785\pi$
$930$	−2.91886e11	−0.0127950
$931$	0	0
$932$	7.33355e12	0.318378
$933$	−3.11505e11	−0.0134585
$934$	−4.06097e12	−0.174610
$935$	2.63755e10	0.00112862
$936$	−2.11086e13	−0.898914
$937$	1.00516e13	0.425999	0.212999	−	0.977052i	$-0.431677\pi$
$937$	1.00516e13	0.425999	0.212999	+	0.977052i	$0.431677\pi$
$938$	0	0
$939$	−3.51068e11	−0.0147365
$940$	−4.52176e12	−0.188900
$941$	1.52744e13	0.635053	0.317526	−	0.948249i	$-0.397148\pi$
$941$	1.52744e13	0.635053	0.317526	+	0.948249i	$0.397148\pi$
$942$	−1.58500e10	−0.000655845 0
$943$	−5.31328e12	−0.218806
$944$	5.17405e13	2.12059
$945$	0	0
$946$	9.50974e11	0.0386063
$947$	4.29774e13	1.73646	0.868230	−	0.496162i	$-0.165258\pi$
$947$	4.29774e13	1.73646	0.868230	+	0.496162i	$0.165258\pi$
$948$	5.93151e10	0.00238522
$949$	−1.66924e13	−0.668068
$950$	4.16533e12	0.165918
$951$	7.38982e10	0.00292969
$952$	0	0
$953$	1.01121e13	0.397120	0.198560	−	0.980089i	$-0.436373\pi$
$953$	1.01121e13	0.397120	0.198560	+	0.980089i	$0.436373\pi$
$954$	2.11552e13	0.826894
$955$	−6.78876e12	−0.264104
$956$	6.44251e12	0.249457
$957$	−1.74590e10	−0.000672846 0
$958$	−5.16852e13	−1.98254
$959$	0	0
$960$	−7.22220e10	−0.00274441
$961$	5.44575e13	2.05969
$962$	3.40005e13	1.27996
$963$	4.66047e13	1.74627
$964$	−6.23703e11	−0.0232612
$965$	−2.20688e13	−0.819229
$966$	0	0
$967$	4.14688e13	1.52511	0.762556	−	0.646922i	$-0.223944\pi$
$967$	4.14688e13	1.52511	0.762556	+	0.646922i	$0.223944\pi$
$968$	−2.04558e13	−0.748820
$969$	−1.49944e10	−0.000546351 0
$970$	4.76101e12	0.172674
$971$	−3.67205e12	−0.132563	−0.0662814	−	0.997801i	$-0.521114\pi$
$971$	−3.67205e12	−0.132563	−0.0662814	+	0.997801i	$0.521114\pi$
$972$	4.16783e11	0.0149765
$973$	0	0
$974$	−2.36459e13	−0.841862
$975$	9.49936e10	0.00336646
$976$	4.81010e13	1.69680
$977$	8.95608e10	0.00314480	0.00157240	−	0.999999i	$-0.499499\pi$
$977$	8.95608e10	0.00314480	0.00157240	+	0.999999i	$0.499499\pi$
$978$	−4.95212e11	−0.0173088
$979$	2.25245e12	0.0783669
$980$	0	0
$981$	−4.44397e12	−0.153200
$982$	−1.26467e13	−0.433985
$983$	4.67974e13	1.59857	0.799284	−	0.600953i	$-0.205212\pi$
$983$	4.67974e13	1.59857	0.799284	+	0.600953i	$0.205212\pi$
$984$	−5.18707e10	−0.00176378
$985$	8.41802e12	0.284936
$986$	−1.95310e12	−0.0658078
$987$	0	0
$988$	−9.08834e12	−0.303444
$989$	2.82190e13	0.937902
$990$	7.27542e11	0.0240713
$991$	−1.94121e12	−0.0639353	−0.0319677	−	0.999489i	$-0.510177\pi$
$991$	−1.94121e12	−0.0639353	−0.0319677	+	0.999489i	$0.510177\pi$
$992$	−3.63070e13	−1.19038
$993$	2.13645e11	0.00697303
$994$	0	0
$995$	−1.49347e13	−0.483051
$996$	5.79058e10	0.00186447
$997$	−2.62275e13	−0.840677	−0.420338	−	0.907367i	$-0.638089\pi$
$997$	−2.62275e13	−0.840677	−0.420338	+	0.907367i	$0.638089\pi$
$998$	4.78793e13	1.52778
$999$	8.11598e11	0.0257808

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.10.a.g.1.2		6
7.6	odd	2		35.10.a.e.1.2	✓	6
21.20	even	2		315.10.a.l.1.5		6
35.13	even	4		175.10.b.g.99.9		12
35.27	even	4		175.10.b.g.99.4		12
35.34	odd	2		175.10.a.g.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.10.a.e.1.2	✓	6	7.6	odd	2
175.10.a.g.1.5		6	35.34	odd	2
175.10.b.g.99.4		12	35.27	even	4
175.10.b.g.99.9		12	35.13	even	4
245.10.a.g.1.2		6	1.1	even	1	trivial
315.10.a.l.1.5		6	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)

\(f(q)\)	\(=\)	\(q-26.3435 q^{2} +1.97103 q^{3} +181.982 q^{4} -625.000 q^{5} -51.9238 q^{6} +8693.85 q^{8} -19679.1 q^{9} +16464.7 q^{10} -2245.43 q^{11} +358.691 q^{12} +123379. q^{13} -1231.89 q^{15} -322201. q^{16} +18794.1 q^{17} +518417. q^{18} -404776. q^{19} -113739. q^{20} +59152.4 q^{22} +1.75527e6 q^{23} +17135.8 q^{24} +390625. q^{25} -3.25024e6 q^{26} -77583.8 q^{27} +3.94483e6 q^{29} +32452.4 q^{30} -8.99428e6 q^{31} +4.03667e6 q^{32} -4425.79 q^{33} -495103. q^{34} -3.58124e6 q^{36} -1.04609e7 q^{37} +1.06632e7 q^{38} +243184. q^{39} -5.43366e6 q^{40} -3.02704e6 q^{41} +1.60767e7 q^{43} -408626. q^{44} +1.22994e7 q^{45} -4.62401e7 q^{46} +3.97557e7 q^{47} -635067. q^{48} -1.02904e7 q^{50} +37043.7 q^{51} +2.24528e7 q^{52} +4.08073e7 q^{53} +2.04383e6 q^{54} +1.40339e6 q^{55} -797825. q^{57} -1.03921e8 q^{58} -1.60585e8 q^{59} -224182. q^{60} -1.49289e8 q^{61} +2.36941e8 q^{62} +5.86269e7 q^{64} -7.71120e7 q^{65} +116591. q^{66} +5.12683e7 q^{67} +3.42018e6 q^{68} +3.45969e6 q^{69} -3.35362e8 q^{71} -1.71087e8 q^{72} -1.35293e8 q^{73} +2.75578e8 q^{74} +769932. q^{75} -7.36618e7 q^{76} -6.40632e6 q^{78} +1.65365e8 q^{79} +2.01376e8 q^{80} +3.87191e8 q^{81} +7.97429e7 q^{82} +1.61436e8 q^{83} -1.17463e7 q^{85} -4.23516e8 q^{86} +7.77536e6 q^{87} -1.95214e7 q^{88} -1.00313e9 q^{89} -3.24011e8 q^{90} +3.19428e8 q^{92} -1.77280e7 q^{93} -1.04731e9 q^{94} +2.52985e8 q^{95} +7.95639e6 q^{96} +2.89165e8 q^{97} +4.41880e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 15 q^{2} + 124 q^{3} + 3009 q^{4} - 3750 q^{5} - 4888 q^{6} + 22041 q^{8} + 111090 q^{9} - 9375 q^{10} - 47796 q^{11} + 541656 q^{12} - 102168 q^{13} - 77500 q^{15} + 2371065 q^{16} + 38472 q^{17}+ \cdots + 3571968784 q^{99}+O(q^{100}) \) 6 * q + 15 * q^2 + 124 * q^3 + 3009 * q^4 - 3750 * q^5 - 4888 * q^6 + 22041 * q^8 + 111090 * q^9 - 9375 * q^10 - 47796 * q^11 + 541656 * q^12 - 102168 * q^13 - 77500 * q^15 + 2371065 * q^16 + 38472 * q^17 + 1837015 * q^18 - 361056 * q^19 - 1880625 * q^20 + 2068680 * q^22 + 697032 * q^23 - 4828076 * q^24 + 2343750 * q^25 - 10847622 * q^26 - 1653188 * q^27 + 16028184 * q^29 + 3055000 * q^30 - 1362912 * q^31 - 1148823 * q^32 - 14059020 * q^33 + 9216294 * q^34 + 92319641 * q^36 - 3912924 * q^37 - 39877140 * q^38 - 20341868 * q^39 - 13775625 * q^40 - 22452756 * q^41 - 29998992 * q^43 - 94378728 * q^44 - 69431250 * q^45 + 49589520 * q^46 + 121271508 * q^47 + 327116052 * q^48 + 5859375 * q^50 - 281338180 * q^51 + 44528550 * q^52 - 20308596 * q^53 + 290104308 * q^54 + 29872500 * q^55 + 186940744 * q^57 + 256759494 * q^58 - 120280392 * q^59 - 338535000 * q^60 + 87693540 * q^61 + 344802528 * q^62 + 640647105 * q^64 + 63855000 * q^65 + 1393970692 * q^66 + 495050664 * q^67 + 141443706 * q^68 - 1031633640 * q^69 + 253762512 * q^71 + 856452205 * q^72 - 187195308 * q^73 - 418806054 * q^74 + 48437500 * q^75 + 584719476 * q^76 - 1728062324 * q^78 + 831079500 * q^79 - 1481915625 * q^80 + 1869314710 * q^81 - 2286848814 * q^82 + 767650536 * q^83 - 24045000 * q^85 + 566199948 * q^86 - 1303216852 * q^87 + 2952495444 * q^88 - 582579684 * q^89 - 1148134375 * q^90 - 4259382384 * q^92 + 15388800 * q^93 + 1115946660 * q^94 + 225660000 * q^95 - 989345252 * q^96 + 1184506872 * q^97 + 3571968784 * q^99

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