LMFDB - Embedded newform 49.26.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,26,Mod(1,49)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 26, names="a")

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

chi := DirichletCharacter("49.1");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	49.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$194.038422177$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} - 1893235651143 x^{10} + \cdots + 18\!\cdots\!00 $ x^12 - 6x^11 - 1893235651143x^10 - 2806413319284680x^9 + 1366207034897721655024398x^8 + 3312795166707293294503326972x^7 - 472740950482561735952171872520774042x^6 - 1306463460138017667257494385745612412176x^5 + 81582696677278884463837972328572242548650191945x^4 + 210395555452534295320647430642617820851383278332906x^3 - 6559737221151479218960148352096969186826132314084199521375x^2 - 10145823620894406299505180212681539035695843286608488793425800*x + 186490559268947851964754942137649552284372963082878767942887530577000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	multiple of $ 2^{48}\cdot 3^{20}\cdot 5^{5}\cdot 7^{15} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$365993.$ of defining polynomial
Character	$\chi$	$=$	49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-10092.2 q^{2} -741372. q^{3} +6.82987e7 q^{4} -7.48736e8 q^{5} +7.48209e9 q^{6} -3.50647e11 q^{8} -2.97656e11 q^{9} +O(q^{10})$	\(q-10092.2 q^{2} -741372. q^{3} +6.82987e7 q^{4} -7.48736e8 q^{5} +7.48209e9 q^{6} -3.50647e11 q^{8} -2.97656e11 q^{9} +7.55642e12 q^{10} +1.30493e13 q^{11} -5.06347e13 q^{12} -1.14290e14 q^{13} +5.55092e14 q^{15} +1.24708e15 q^{16} -8.99825e14 q^{17} +3.00402e15 q^{18} +1.76144e16 q^{19} -5.11377e16 q^{20} -1.31697e17 q^{22} +1.17194e16 q^{23} +2.59960e17 q^{24} +2.62582e17 q^{25} +1.15344e18 q^{26} +8.48830e17 q^{27} -2.64229e18 q^{29} -5.60211e18 q^{30} -2.61641e18 q^{31} -8.20107e17 q^{32} -9.67441e18 q^{33} +9.08124e18 q^{34} -2.03295e19 q^{36} +1.53171e19 q^{37} -1.77769e20 q^{38} +8.47313e19 q^{39} +2.62542e20 q^{40} +7.08765e19 q^{41} +3.68190e20 q^{43} +8.91252e20 q^{44} +2.22866e20 q^{45} -1.18275e20 q^{46} +1.15603e21 q^{47} -9.24553e20 q^{48} -2.65004e21 q^{50} +6.67105e20 q^{51} -7.80585e21 q^{52} +7.12832e21 q^{53} -8.56659e21 q^{54} -9.77051e21 q^{55} -1.30588e22 q^{57} +2.66666e22 q^{58} +5.10532e21 q^{59} +3.79120e22 q^{60} -6.66187e21 q^{61} +2.64055e22 q^{62} -3.35685e22 q^{64} +8.55730e22 q^{65} +9.76363e22 q^{66} +9.02779e21 q^{67} -6.14569e22 q^{68} -8.68843e21 q^{69} +1.81077e23 q^{71} +1.04372e23 q^{72} -3.01084e23 q^{73} -1.54584e23 q^{74} -1.94671e23 q^{75} +1.20304e24 q^{76} -8.55128e23 q^{78} -3.98771e23 q^{79} -9.33737e23 q^{80} -3.77098e23 q^{81} -7.15302e23 q^{82} -1.81597e24 q^{83} +6.73732e23 q^{85} -3.71586e24 q^{86} +1.95892e24 q^{87} -4.57571e24 q^{88} -2.96441e23 q^{89} -2.24922e24 q^{90} +8.00419e23 q^{92} +1.93974e24 q^{93} -1.16669e25 q^{94} -1.31886e25 q^{95} +6.08004e23 q^{96} -6.37858e24 q^{97} -3.88422e24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 8460 q^{2} + 161848296 q^{4} - 61395028560 q^{8} + 4977863358780 q^{9}+O(q^{10}) $ 12 * q - 8460 * q^2 + 161848296 * q^4 - 61395028560 * q^8 + 4977863358780 * q^9	$ 12 q - 8460 q^{2} + 161848296 q^{4} - 61395028560 q^{8} + 4977863358780 q^{9} + 39593455677648 q^{11} + 357546272706144 q^{15} + 18\!\cdots\!56 q^{16}+ \cdots - 14\!\cdots\!88 q^{99}+O(q^{100}) $ 12 * q - 8460 * q^2 + 161848296 * q^4 - 61395028560 * q^8 + 4977863358780 * q^9 + 39593455677648 * q^11 + 357546272706144 * q^15 + 1897434424858656 * q^16 + 19017456854067300 * q^18 + 85409383356235920 * q^22 + 77196982648366080 * q^23 + 2296738995597808932 * q^25 + 8694499082723336088 * q^29 - 12169958791851770688 * q^30 - 6483391660121958720 * q^32 - 109652263099391094456 * q^36 + 151853425001596848120 * q^37 - 122709680243235084384 * q^39 - 380869142455132177200 * q^43 + 991389584873062609056 * q^44 + 2303857023830118404064 * q^46 + 3165366920999170599036 * q^50 + 1280977431762493664064 * q^51 + 17755418685871290573000 * q^53 - 40456075816140877421280 * q^57 + 90683689500928436394600 * q^58 + 27395532648965383354368 * q^60 - 153351020298413953854336 * q^64 + 200499279532648292123424 * q^65 + 148336212990069406108560 * q^67 + 562419591698095656528384 * q^71 - 554920453414323154337040 * q^72 + 509427689055313155358536 * q^74 - 812506544978626047049920 * q^78 + 1488381592136271978244704 * q^79 - 2624302005301676288302452 * q^81 - 333667887446182173142464 * q^85 - 10612071587035448449112880 * q^86 - 14889193934757325628907840 * q^88 + 8074123164162948551757120 * q^92 + 1647472274074578272984640 * q^93 + 10792312351147270637620128 * q^95 - 148376588023327766946288 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−10092.2	−1.74226	−0.871128	−	0.491055i	$-0.836611\pi$
$2$	−10092.2	−1.74226	−0.871128	+	0.491055i	$0.836611\pi$
$3$	−741372.	−0.805416	−0.402708	−	0.915328i	$-0.631931\pi$
$3$	−741372.	−0.805416	−0.402708	+	0.915328i	$0.631931\pi$
$4$	6.82987e7	2.03546
$5$	−7.48736e8	−1.37152	−0.685762	−	0.727825i	$-0.740531\pi$
$5$	−7.48736e8	−1.37152	−0.685762	+	0.727825i	$0.740531\pi$
$6$	7.48209e9	1.40324
$7$	0	0
$7$	0	0
$8$	−3.50647e11	−1.80403
$9$	−2.97656e11	−0.351305
$10$	7.55642e12	2.38955
$11$	1.30493e13	1.25366	0.626830	−	0.779156i	$-0.284352\pi$
$11$	1.30493e13	1.25366	0.626830	+	0.779156i	$0.284352\pi$
$12$	−5.06347e13	−1.63939
$13$	−1.14290e14	−1.36055	−0.680277	−	0.732955i	$-0.738141\pi$
$13$	−1.14290e14	−1.36055	−0.680277	+	0.732955i	$0.738141\pi$
$14$	0	0
$15$	5.55092e14	1.10465
$16$	1.24708e15	1.10763
$17$	−8.99825e14	−0.374582	−0.187291	−	0.982304i	$-0.559971\pi$
$17$	−8.99825e14	−0.374582	−0.187291	+	0.982304i	$0.559971\pi$
$18$	3.00402e15	0.612063
$19$	1.76144e16	1.82578	0.912891	−	0.408204i	$-0.133845\pi$
$19$	1.76144e16	1.82578	0.912891	+	0.408204i	$0.133845\pi$
$20$	−5.11377e16	−2.79168
$21$	0	0
$22$	−1.31697e17	−2.18420
$23$	1.17194e16	0.111508	0.0557542	−	0.998445i	$-0.482244\pi$
$23$	1.17194e16	0.111508	0.0557542	+	0.998445i	$0.482244\pi$
$24$	2.59960e17	1.45300
$25$	2.62582e17	0.881080
$26$	1.15344e18	2.37044
$27$	8.48830e17	1.08836
$28$	0	0
$29$	−2.64229e18	−1.38677	−0.693387	−	0.720565i	$-0.743882\pi$
$29$	−2.64229e18	−1.38677	−0.693387	+	0.720565i	$0.743882\pi$
$30$	−5.60211e18	−1.92458
$31$	−2.61641e18	−0.596603	−0.298302	−	0.954472i	$-0.596420\pi$
$31$	−2.61641e18	−0.596603	−0.298302	+	0.954472i	$0.596420\pi$
$32$	−8.20107e17	−0.125746
$33$	−9.67441e18	−1.00972
$34$	9.08124e18	0.652618
$35$	0	0
$36$	−2.03295e19	−0.715066
$37$	1.53171e19	0.382522	0.191261	−	0.981539i	$-0.438742\pi$
$37$	1.53171e19	0.382522	0.191261	+	0.981539i	$0.438742\pi$
$38$	−1.77769e20	−3.18098
$39$	8.47313e19	1.09581
$40$	2.62542e20	2.47428
$41$	7.08765e19	0.490573	0.245287	−	0.969451i	$-0.421118\pi$
$41$	7.08765e19	0.490573	0.245287	+	0.969451i	$0.421118\pi$
$42$	0	0
$43$	3.68190e20	1.40513	0.702565	−	0.711619i	$-0.252038\pi$
$43$	3.68190e20	1.40513	0.702565	+	0.711619i	$0.252038\pi$
$44$	8.91252e20	2.55177
$45$	2.22866e20	0.481823
$46$	−1.18275e20	−0.194276
$47$	1.15603e21	1.45126	0.725629	−	0.688086i	$-0.241549\pi$
$47$	1.15603e21	1.45126	0.725629	+	0.688086i	$0.241549\pi$
$48$	−9.24553e20	−0.892106
$49$	0	0
$50$	−2.65004e21	−1.53507
$51$	6.67105e20	0.301694
$52$	−7.80585e21	−2.76935
$53$	7.12832e21	1.99314	0.996572	−	0.0827325i	$-0.0263647\pi$
$53$	7.12832e21	1.99314	0.996572	+	0.0827325i	$0.0263647\pi$
$54$	−8.56659e21	−1.89621
$55$	−9.77051e21	−1.71943
$56$	0	0
$57$	−1.30588e22	−1.47051
$58$	2.66666e22	2.41612
$59$	5.10532e21	0.373571	0.186785	−	0.982401i	$-0.440193\pi$
$59$	5.10532e21	0.373571	0.186785	+	0.982401i	$0.440193\pi$
$60$	3.79120e22	2.24847
$61$	−6.66187e21	−0.321346	−0.160673	−	0.987008i	$-0.551366\pi$
$61$	−6.66187e21	−0.321346	−0.160673	+	0.987008i	$0.551366\pi$
$62$	2.64055e22	1.03944
$63$	0	0
$64$	−3.35685e22	−0.888550
$65$	8.55730e22	1.86603
$66$	9.76363e22	1.75919
$67$	9.02779e21	0.134787	0.0673933	−	0.997726i	$-0.478532\pi$
$67$	9.02779e21	0.134787	0.0673933	+	0.997726i	$0.478532\pi$
$68$	−6.14569e22	−0.762446
$69$	−8.68843e21	−0.0898106
$70$	0	0
$71$	1.81077e23	1.30958	0.654792	−	0.755809i	$-0.272756\pi$
$71$	1.81077e23	1.30958	0.654792	+	0.755809i	$0.272756\pi$
$72$	1.04372e23	0.633766
$73$	−3.01084e23	−1.53870	−0.769348	−	0.638830i	$-0.779419\pi$
$73$	−3.01084e23	−1.53870	−0.769348	+	0.638830i	$0.779419\pi$
$74$	−1.54584e23	−0.666451
$75$	−1.94671e23	−0.709637
$76$	1.20304e24	3.71630
$77$	0	0
$78$	−8.55128e23	−1.90919
$79$	−3.98771e23	−0.759250	−0.379625	−	0.925141i	$-0.623947\pi$
$79$	−3.98771e23	−0.759250	−0.379625	+	0.925141i	$0.623947\pi$
$80$	−9.33737e23	−1.51915
$81$	−3.77098e23	−0.525280
$82$	−7.15302e23	−0.854704
$83$	−1.81597e24	−1.86480	−0.932398	−	0.361433i	$-0.882288\pi$
$83$	−1.81597e24	−1.86480	−0.932398	+	0.361433i	$0.882288\pi$
$84$	0	0
$85$	6.73732e23	0.513748
$86$	−3.71586e24	−2.44810
$87$	1.95892e24	1.11693
$88$	−4.57571e24	−2.26165
$89$	−2.96441e23	−0.127222	−0.0636112	−	0.997975i	$-0.520262\pi$
$89$	−2.96441e23	−0.127222	−0.0636112	+	0.997975i	$0.520262\pi$
$90$	−2.24922e24	−0.839459
$91$	0	0
$92$	8.00419e23	0.226971
$93$	1.93974e24	0.480514
$94$	−1.16669e25	−2.52846
$95$	−1.31886e25	−2.50410
$96$	6.08004e23	0.101278
$97$	−6.37858e24	−0.933420	−0.466710	−	0.884410i	$-0.654561\pi$
$97$	−6.37858e24	−0.933420	−0.466710	+	0.884410i	$0.654561\pi$
$98$	0	0
$99$	−3.88422e24	−0.440417
$100$	1.79340e25	1.79340
$101$	6.04290e24	0.533615	0.266808	−	0.963750i	$-0.414031\pi$
$101$	6.04290e24	0.533615	0.266808	+	0.963750i	$0.414031\pi$
$102$	−6.73258e24	−0.525629
$103$	−2.51532e25	−1.73832	−0.869158	−	0.494534i	$-0.835339\pi$
$103$	−2.51532e25	−1.73832	−0.869158	+	0.494534i	$0.835339\pi$
$104$	4.00754e25	2.45449
$105$	0	0
$106$	−7.19406e25	−3.47257
$107$	1.24078e25	0.532597	0.266299	−	0.963891i	$-0.414199\pi$
$107$	1.24078e25	0.532597	0.266299	+	0.963891i	$0.414199\pi$
$108$	5.79739e25	2.21532
$109$	1.71217e25	0.583063	0.291532	−	0.956561i	$-0.405835\pi$
$109$	1.71217e25	0.583063	0.291532	+	0.956561i	$0.405835\pi$
$110$	9.86062e25	2.99568
$111$	−1.13557e25	−0.308089
$112$	0	0
$113$	−5.29255e25	−1.14864	−0.574321	−	0.818630i	$-0.694734\pi$
$113$	−5.29255e25	−1.14864	−0.574321	+	0.818630i	$0.694734\pi$
$114$	1.31793e26	2.56201
$115$	−8.77473e24	−0.152936
$116$	−1.80465e26	−2.82272
$117$	3.40191e25	0.477969
$118$	−5.15241e25	−0.650856
$119$	0	0
$120$	−1.94641e26	−1.99282
$121$	6.19380e25	0.571663
$122$	6.72331e25	0.559867
$123$	−5.25458e25	−0.395116
$124$	−1.78698e26	−1.21436
$125$	2.65358e25	0.163101
$126$	0	0
$127$	−2.50368e25	−0.126192	−0.0630962	−	0.998007i	$-0.520097\pi$
$127$	−2.50368e25	−0.126192	−0.0630962	+	0.998007i	$0.520097\pi$
$128$	3.66299e26	1.67383
$129$	−2.72966e26	−1.13171
$130$	−8.63622e26	−3.25111
$131$	2.37382e25	0.0812001	0.0406001	−	0.999175i	$-0.487073\pi$
$131$	2.37382e25	0.0812001	0.0406001	+	0.999175i	$0.487073\pi$
$132$	−6.60749e26	−2.05524
$133$	0	0
$134$	−9.11106e25	−0.234833
$135$	−6.35550e26	−1.49272
$136$	3.15521e26	0.675759
$137$	−8.51969e26	−1.66501	−0.832505	−	0.554018i	$-0.813094\pi$
$137$	−8.51969e26	−1.66501	−0.832505	+	0.554018i	$0.813094\pi$
$138$	8.76856e25	0.156473
$139$	4.02692e25	0.0656581	0.0328290	−	0.999461i	$-0.489548\pi$
$139$	4.02692e25	0.0656581	0.0328290	+	0.999461i	$0.489548\pi$
$140$	0	0
$141$	−8.57045e26	−1.16887
$142$	−1.82747e27	−2.28163
$143$	−1.49141e27	−1.70567
$144$	−3.71203e26	−0.389117
$145$	1.97838e27	1.90200
$146$	3.03861e27	2.68080
$147$	0	0
$148$	1.04614e27	0.778607
$149$	1.76662e27	1.20869	0.604345	−	0.796723i	$-0.293435\pi$
$149$	1.76662e27	1.20869	0.604345	+	0.796723i	$0.293435\pi$
$150$	1.96467e27	1.23637
$151$	9.37557e26	0.542982	0.271491	−	0.962441i	$-0.412483\pi$
$151$	9.37557e26	0.542982	0.271491	+	0.962441i	$0.412483\pi$
$152$	−6.17644e27	−3.29377
$153$	2.67839e26	0.131592
$154$	0	0
$155$	1.95900e27	0.818256
$156$	5.78704e27	2.23048
$157$	−2.29998e27	−0.818425	−0.409212	−	0.912439i	$-0.634196\pi$
$157$	−2.29998e27	−0.818425	−0.409212	+	0.912439i	$0.634196\pi$
$158$	4.02449e27	1.32281
$159$	−5.28473e27	−1.60531
$160$	6.14044e26	0.172464
$161$	0	0
$162$	3.80576e27	0.915173
$163$	1.35760e27	0.302292	0.151146	−	0.988511i	$-0.451704\pi$
$163$	1.35760e27	0.302292	0.151146	+	0.988511i	$0.451704\pi$
$164$	4.84077e27	0.998541
$165$	7.24358e27	1.38485
$166$	1.83271e28	3.24895
$167$	−5.75627e27	−0.946641	−0.473320	−	0.880890i	$-0.656945\pi$
$167$	−5.75627e27	−0.946641	−0.473320	+	0.880890i	$0.656945\pi$
$168$	0	0
$169$	6.00577e27	0.851109
$170$	−6.79945e27	−0.895082
$171$	−5.24305e27	−0.641405
$172$	2.51469e28	2.86008
$173$	−9.86630e27	−1.04371	−0.521853	−	0.853036i	$-0.674759\pi$
$173$	−9.86630e27	−1.04371	−0.521853	+	0.853036i	$0.674759\pi$
$174$	−1.97699e28	−1.94598
$175$	0	0
$176$	1.62736e28	1.38860
$177$	−3.78494e27	−0.300880
$178$	2.99175e27	0.221654
$179$	2.99708e27	0.207031	0.103516	−	0.994628i	$-0.466991\pi$
$179$	2.99708e27	0.207031	0.103516	+	0.994628i	$0.466991\pi$
$180$	1.52215e28	0.980731
$181$	1.80286e27	0.108388	0.0541938	−	0.998530i	$-0.482741\pi$
$181$	1.80286e27	0.108388	0.0541938	+	0.998530i	$0.482741\pi$
$182$	0	0
$183$	4.93892e27	0.258817
$184$	−4.10937e27	−0.201165
$185$	−1.14685e28	−0.524638
$186$	−1.95763e28	−0.837178
$187$	−1.17421e28	−0.469598
$188$	7.89550e28	2.95397
$189$	0	0
$190$	1.33102e29	4.36279
$191$	−2.74701e28	−0.843225	−0.421613	−	0.906776i	$-0.638536\pi$
$191$	−2.74701e28	−0.843225	−0.421613	+	0.906776i	$0.638536\pi$
$192$	2.48867e28	0.715653
$193$	−2.09176e28	−0.563697	−0.281849	−	0.959459i	$-0.590948\pi$
$193$	−2.09176e28	−0.563697	−0.281849	+	0.959459i	$0.590948\pi$
$194$	6.43741e28	1.62626
$195$	−6.34414e28	−1.50293
$196$	0	0
$197$	−8.82410e27	−0.184011	−0.0920053	−	0.995759i	$-0.529328\pi$
$197$	−8.82410e27	−0.184011	−0.0920053	+	0.995759i	$0.529328\pi$
$198$	3.92004e28	0.767319
$199$	−2.94130e28	−0.540600	−0.270300	−	0.962776i	$-0.587123\pi$
$199$	−2.94130e28	−0.540600	−0.270300	+	0.962776i	$0.587123\pi$
$200$	−9.20737e28	−1.58950
$201$	−6.69295e27	−0.108559
$202$	−6.09864e28	−0.929695
$203$	0	0
$204$	4.55624e28	0.614086
$205$	−5.30678e28	−0.672833
$206$	2.53852e29	3.02859
$207$	−3.48835e27	−0.0391734
$208$	−1.42529e29	−1.50700
$209$	2.29857e29	2.28891
$210$	0	0
$211$	−9.95388e28	−0.879957	−0.439979	−	0.898008i	$-0.645014\pi$
$211$	−9.95388e28	−0.879957	−0.439979	+	0.898008i	$0.645014\pi$
$212$	4.86854e29	4.05696
$213$	−1.34245e29	−1.05476
$214$	−1.25223e29	−0.927921
$215$	−2.75677e29	−1.92717
$216$	−2.97639e29	−1.96344
$217$	0	0
$218$	−1.72796e29	−1.01585
$219$	2.23216e29	1.23929
$220$	−6.67312e29	−3.49982
$221$	1.02841e29	0.509639
$222$	1.14604e29	0.536771
$223$	7.92559e28	0.350930	0.175465	−	0.984486i	$-0.443857\pi$
$223$	7.92559e28	0.350930	0.175465	+	0.984486i	$0.443857\pi$
$224$	0	0
$225$	−7.81594e28	−0.309528
$226$	5.34137e29	2.00123
$227$	2.35051e29	0.833372	0.416686	−	0.909051i	$-0.363192\pi$
$227$	2.35051e29	0.833372	0.416686	+	0.909051i	$0.363192\pi$
$228$	−8.91902e29	−2.99317
$229$	4.85254e29	1.54179	0.770895	−	0.636962i	$-0.219809\pi$
$229$	4.85254e29	1.54179	0.770895	+	0.636962i	$0.219809\pi$
$230$	8.85566e28	0.266455
$231$	0	0
$232$	9.26511e29	2.50179
$233$	6.64793e29	1.70113	0.850565	−	0.525870i	$-0.176260\pi$
$233$	6.64793e29	1.70113	0.850565	+	0.525870i	$0.176260\pi$
$234$	−3.43329e29	−0.832745
$235$	−8.65559e29	−1.99044
$236$	3.48687e29	0.760388
$237$	2.95637e29	0.611512
$238$	0	0
$239$	2.54933e29	0.474737	0.237368	−	0.971420i	$-0.423715\pi$
$239$	2.54933e29	0.474737	0.237368	+	0.971420i	$0.423715\pi$
$240$	6.92246e29	1.22355
$241$	1.04121e30	1.74713	0.873567	−	0.486704i	$-0.161801\pi$
$241$	1.04121e30	1.74713	0.873567	+	0.486704i	$0.161801\pi$
$242$	−6.25093e29	−0.995984
$243$	−4.39634e29	−0.665293
$244$	−4.54996e29	−0.654087
$245$	0	0
$246$	5.30304e29	0.688393
$247$	−2.01315e30	−2.48408
$248$	9.17437e29	1.07629
$249$	1.34631e30	1.50194
$250$	−2.67805e29	−0.284164
$251$	−2.10916e29	−0.212906	−0.106453	−	0.994318i	$-0.533949\pi$
$251$	−2.10916e29	−0.212906	−0.106453	+	0.994318i	$0.533949\pi$
$252$	0	0
$253$	1.52930e29	0.139794
$254$	2.52678e29	0.219859
$255$	−4.99486e29	−0.413781
$256$	−2.57040e30	−2.02769
$257$	−1.63964e30	−1.23193	−0.615964	−	0.787774i	$-0.711233\pi$
$257$	−1.63964e30	−1.23193	−0.615964	+	0.787774i	$0.711233\pi$
$258$	2.75483e30	1.97174
$259$	0	0
$260$	5.84452e30	3.79824
$261$	7.86495e29	0.487180
$262$	−2.39571e29	−0.141471
$263$	−4.92273e29	−0.277178	−0.138589	−	0.990350i	$-0.544257\pi$
$263$	−4.92273e29	−0.277178	−0.138589	+	0.990350i	$0.544257\pi$
$264$	3.39230e30	1.82157
$265$	−5.33723e30	−2.73365
$266$	0	0
$267$	2.19773e29	0.102467
$268$	6.16586e29	0.274352
$269$	2.86089e30	1.21506	0.607529	−	0.794297i	$-0.292161\pi$
$269$	2.86089e30	1.21506	0.607529	+	0.794297i	$0.292161\pi$
$270$	6.41411e30	2.60070
$271$	−9.82687e28	−0.0380451	−0.0190226	−	0.999819i	$-0.506055\pi$
$271$	−9.82687e28	−0.0380451	−0.0190226	+	0.999819i	$0.506055\pi$
$272$	−1.12216e30	−0.414899
$273$	0	0
$274$	8.59826e30	2.90087
$275$	3.42653e30	1.10458
$276$	−5.93408e29	−0.182806
$277$	2.02544e30	0.596378	0.298189	−	0.954507i	$-0.403617\pi$
$277$	2.02544e30	0.596378	0.298189	+	0.954507i	$0.403617\pi$
$278$	−4.06406e29	−0.114393
$279$	7.78793e29	0.209589
$280$	0	0
$281$	−1.14549e30	−0.281943	−0.140972	−	0.990014i	$-0.545023\pi$
$281$	−1.14549e30	−0.281943	−0.140972	+	0.990014i	$0.545023\pi$
$282$	8.64950e30	2.03647
$283$	−5.15996e30	−1.16229	−0.581147	−	0.813798i	$-0.697396\pi$
$283$	−5.15996e30	−1.16229	−0.581147	+	0.813798i	$0.697396\pi$
$284$	1.23673e31	2.66560
$285$	9.77763e30	2.01685
$286$	1.50516e31	2.97172
$287$	0	0
$288$	2.44110e29	0.0441753
$289$	−4.96094e30	−0.859688
$290$	−1.99663e31	−3.31376
$291$	4.72890e30	0.751792
$292$	−2.05637e31	−3.13195
$293$	−6.73012e30	−0.982149	−0.491075	−	0.871117i	$-0.663396\pi$
$293$	−6.73012e30	−0.982149	−0.491075	+	0.871117i	$0.663396\pi$
$294$	0	0
$295$	−3.82254e30	−0.512362
$296$	−5.37090e30	−0.690083
$297$	1.10767e31	1.36444
$298$	−1.78291e31	−2.10585
$299$	−1.33941e30	−0.151713
$300$	−1.32958e31	−1.44444
$301$	0	0
$302$	−9.46204e30	−0.946015
$303$	−4.48004e30	−0.429783
$304$	2.19667e31	2.02230
$305$	4.98798e30	0.440734
$306$	−2.70309e30	−0.229268
$307$	3.14102e30	0.255765	0.127882	−	0.991789i	$-0.459182\pi$
$307$	3.14102e30	0.255765	0.127882	+	0.991789i	$0.459182\pi$
$308$	0	0
$309$	1.86479e31	1.40007
$310$	−1.97707e31	−1.42561
$311$	−6.00370e30	−0.415828	−0.207914	−	0.978147i	$-0.566667\pi$
$311$	−6.00370e30	−0.415828	−0.207914	+	0.978147i	$0.566667\pi$
$312$	−2.97108e31	−1.97688
$313$	−4.62328e30	−0.295560	−0.147780	−	0.989020i	$-0.547213\pi$
$313$	−4.62328e30	−0.295560	−0.147780	+	0.989020i	$0.547213\pi$
$314$	2.32119e31	1.42591
$315$	0	0
$316$	−2.72355e31	−1.54542
$317$	1.62145e31	0.884427	0.442214	−	0.896910i	$-0.354193\pi$
$317$	1.62145e31	0.884427	0.442214	+	0.896910i	$0.354193\pi$
$318$	5.33347e31	2.79686
$319$	−3.44801e31	−1.73854
$320$	2.51339e31	1.21867
$321$	−9.19882e30	−0.428963
$322$	0	0
$323$	−1.58499e31	−0.683905
$324$	−2.57553e31	−1.06919
$325$	−3.00105e31	−1.19876
$326$	−1.37012e31	−0.526671
$327$	−1.26935e31	−0.469608
$328$	−2.48526e31	−0.885011
$329$	0	0
$330$	−7.31038e31	−2.41277
$331$	3.13620e31	0.996675	0.498338	−	0.866983i	$-0.333944\pi$
$331$	3.13620e31	0.996675	0.498338	+	0.866983i	$0.333944\pi$
$332$	−1.24028e32	−3.79572
$333$	−4.55925e30	−0.134382
$334$	5.80936e31	1.64929
$335$	−6.75943e30	−0.184863
$336$	0	0
$337$	−3.52218e31	−0.894206	−0.447103	−	0.894483i	$-0.647544\pi$
$337$	−3.52218e31	−0.894206	−0.447103	+	0.894483i	$0.647544\pi$
$338$	−6.06116e31	−1.48285
$339$	3.92375e31	0.925135
$340$	4.60150e31	1.04571
$341$	−3.41425e31	−0.747937
$342$	5.29141e31	1.11749
$343$	0	0
$344$	−1.29105e32	−2.53490
$345$	6.50534e30	0.123177
$346$	9.95730e31	1.81840
$347$	2.52525e31	0.444822	0.222411	−	0.974953i	$-0.428607\pi$
$347$	2.52525e31	0.444822	0.222411	+	0.974953i	$0.428607\pi$
$348$	1.33792e32	2.27347
$349$	−6.74588e31	−1.10591	−0.552956	−	0.833210i	$-0.686500\pi$
$349$	−6.74588e31	−1.10591	−0.552956	+	0.833210i	$0.686500\pi$
$350$	0	0
$351$	−9.70127e31	−1.48078
$352$	−1.07018e31	−0.157643
$353$	5.98802e31	0.851333	0.425666	−	0.904880i	$-0.360040\pi$
$353$	5.98802e31	0.851333	0.425666	+	0.904880i	$0.360040\pi$
$354$	3.81985e31	0.524210
$355$	−1.35579e32	−1.79613
$356$	−2.02465e31	−0.258956
$357$	0	0
$358$	−3.02472e31	−0.360702
$359$	1.29011e32	1.48575	0.742876	−	0.669429i	$-0.233461\pi$
$359$	1.29011e32	1.48575	0.742876	+	0.669429i	$0.233461\pi$
$360$	−7.81473e31	−0.869225
$361$	2.17192e32	2.33348
$362$	−1.81949e31	−0.188839
$363$	−4.59191e31	−0.460427
$364$	0	0
$365$	2.25433e32	2.11036
$366$	−4.98447e31	−0.450926
$367$	−7.53135e31	−0.658487	−0.329243	−	0.944245i	$-0.606794\pi$
$367$	−7.53135e31	−0.658487	−0.329243	+	0.944245i	$0.606794\pi$
$368$	1.46151e31	0.123510
$369$	−2.10968e31	−0.172341
$370$	1.15743e32	0.914054
$371$	0	0
$372$	1.32481e32	0.978066
$373$	−1.43707e32	−1.02593	−0.512964	−	0.858410i	$-0.671453\pi$
$373$	−1.43707e32	−1.02593	−0.512964	+	0.858410i	$0.671453\pi$
$374$	1.18504e32	0.818161
$375$	−1.96729e31	−0.131364
$376$	−4.05357e32	−2.61812
$377$	3.01987e32	1.88678
$378$	0	0
$379$	−1.66941e32	−0.976280	−0.488140	−	0.872765i	$-0.662324\pi$
$379$	−1.66941e32	−0.976280	−0.488140	+	0.872765i	$0.662324\pi$
$380$	−9.00761e32	−5.09700
$381$	1.85616e31	0.101637
$382$	2.77235e32	1.46911
$383$	−1.44965e32	−0.743496	−0.371748	−	0.928334i	$-0.621241\pi$
$383$	−1.44965e32	−0.743496	−0.371748	+	0.928334i	$0.621241\pi$
$384$	−2.71564e32	−1.34813
$385$	0	0
$386$	2.11105e32	0.982105
$387$	−1.09594e32	−0.493629
$388$	−4.35648e32	−1.89994
$389$	2.50197e31	0.105660	0.0528301	−	0.998604i	$-0.483176\pi$
$389$	2.50197e31	0.105660	0.0528301	+	0.998604i	$0.483176\pi$
$390$	6.40265e32	2.61850
$391$	−1.05454e31	−0.0417690
$392$	0	0
$393$	−1.75988e31	−0.0653999
$394$	8.90549e31	0.320594
$395$	2.98574e32	1.04133
$396$	−2.65287e32	−0.896450
$397$	2.06232e32	0.675266	0.337633	−	0.941278i	$-0.390374\pi$
$397$	2.06232e32	0.675266	0.337633	+	0.941278i	$0.390374\pi$
$398$	2.96843e32	0.941863
$399$	0	0
$400$	3.27462e32	0.975914
$401$	3.59441e32	1.03830	0.519150	−	0.854683i	$-0.326249\pi$
$401$	3.59441e32	1.03830	0.519150	+	0.854683i	$0.326249\pi$
$402$	6.75468e31	0.189138
$403$	2.99030e32	0.811711
$404$	4.12722e32	1.08615
$405$	2.82347e32	0.720435
$406$	0	0
$407$	1.99878e32	0.479552
$408$	−2.33918e32	−0.544267
$409$	−5.10053e32	−1.15100	−0.575498	−	0.817803i	$-0.695192\pi$
$409$	−5.10053e32	−1.15100	−0.575498	+	0.817803i	$0.695192\pi$
$410$	5.35572e32	1.17225
$411$	6.31626e32	1.34103
$412$	−1.71793e33	−3.53827
$413$	0	0
$414$	3.52053e31	0.0682501
$415$	1.35968e33	2.55761
$416$	9.37299e31	0.171085
$417$	−2.98545e31	−0.0528821
$418$	−2.31977e33	−3.98787
$419$	−2.90769e32	−0.485147	−0.242573	−	0.970133i	$-0.577992\pi$
$419$	−2.90769e32	−0.485147	−0.242573	+	0.970133i	$0.577992\pi$
$420$	0	0
$421$	−4.82461e32	−0.758466	−0.379233	−	0.925301i	$-0.623812\pi$
$421$	−4.82461e32	−0.758466	−0.379233	+	0.925301i	$0.623812\pi$
$422$	1.00457e33	1.53311
$423$	−3.44099e32	−0.509834
$424$	−2.49952e33	−3.59570
$425$	−2.36278e32	−0.330037
$426$	1.35483e33	1.83766
$427$	0	0
$428$	8.47439e32	1.08408
$429$	1.10569e33	1.37378
$430$	2.78220e33	3.35763
$431$	1.42605e33	1.67174	0.835870	−	0.548928i	$-0.184964\pi$
$431$	1.42605e33	1.67174	0.835870	+	0.548928i	$0.184964\pi$
$432$	1.05856e33	1.20551
$433$	−9.25499e32	−1.02395	−0.511973	−	0.859001i	$-0.671085\pi$
$433$	−9.25499e32	−1.02395	−0.511973	+	0.859001i	$0.671085\pi$
$434$	0	0
$435$	−1.46671e33	−1.53190
$436$	1.16939e33	1.18680
$437$	2.06431e32	0.203590
$438$	−2.25274e33	−2.15916
$439$	2.04358e33	1.90364	0.951821	−	0.306655i	$-0.0992098\pi$
$439$	2.04358e33	1.90364	0.951821	+	0.306655i	$0.0992098\pi$
$440$	3.42600e33	3.10190
$441$	0	0
$442$	−1.03789e33	−0.887922
$443$	−8.90453e32	−0.740567	−0.370284	−	0.928919i	$-0.620740\pi$
$443$	−8.90453e32	−0.740567	−0.370284	+	0.928919i	$0.620740\pi$
$444$	−7.75579e32	−0.627103
$445$	2.21956e32	0.174489
$446$	−7.99869e32	−0.611411
$447$	−1.30972e33	−0.973498
$448$	0	0
$449$	−2.15317e32	−0.151356	−0.0756778	−	0.997132i	$-0.524112\pi$
$449$	−2.15317e32	−0.151356	−0.0756778	+	0.997132i	$0.524112\pi$
$450$	7.88802e32	0.539277
$451$	9.24891e32	0.615012
$452$	−3.61474e33	−2.33801
$453$	−6.95078e32	−0.437327
$454$	−2.37219e33	−1.45195
$455$	0	0
$456$	4.57904e33	2.65286
$457$	1.96236e33	1.10618	0.553090	−	0.833121i	$-0.313448\pi$
$457$	1.96236e33	1.10618	0.553090	+	0.833121i	$0.313448\pi$
$458$	−4.89729e33	−2.68619
$459$	−7.63799e32	−0.407681
$460$	−5.99303e32	−0.311296
$461$	7.93937e32	0.401351	0.200676	−	0.979658i	$-0.435686\pi$
$461$	7.93937e32	0.401351	0.200676	+	0.979658i	$0.435686\pi$
$462$	0	0
$463$	−1.06011e33	−0.507678	−0.253839	−	0.967246i	$-0.581693\pi$
$463$	−1.06011e33	−0.507678	−0.253839	+	0.967246i	$0.581693\pi$
$464$	−3.29516e33	−1.53604
$465$	−1.45235e33	−0.659037
$466$	−6.70925e33	−2.96381
$467$	4.50354e30	0.00193684	0.000968418	−	1.00000i	$-0.499692\pi$
$467$	4.50354e30	0.00193684	0.000968418		1.00000i	$0.499692\pi$
$468$	2.32346e33	0.972886
$469$	0	0
$470$	8.73542e33	3.46785
$471$	1.70514e33	0.659173
$472$	−1.79016e33	−0.673935
$473$	4.80464e33	1.76156
$474$	−2.98364e33	−1.06541
$475$	4.62524e33	1.60866
$476$	0	0
$477$	−2.12179e33	−0.700201
$478$	−2.57285e33	−0.827113
$479$	9.76573e32	0.305852	0.152926	−	0.988238i	$-0.451130\pi$
$479$	9.76573e32	0.305852	0.152926	+	0.988238i	$0.451130\pi$
$480$	−4.55235e32	−0.138906
$481$	−1.75059e33	−0.520442
$482$	−1.05082e34	−3.04396
$483$	0	0
$484$	4.23028e33	1.16360
$485$	4.77587e33	1.28021
$486$	4.43689e33	1.15911
$487$	2.59935e33	0.661840	0.330920	−	0.943659i	$-0.392641\pi$
$487$	2.59935e33	0.661840	0.330920	+	0.943659i	$0.392641\pi$
$488$	2.33596e33	0.579719
$489$	−1.00649e33	−0.243471
$490$	0	0
$491$	3.39444e33	0.780278	0.390139	−	0.920756i	$-0.372427\pi$
$491$	3.39444e33	0.780278	0.390139	+	0.920756i	$0.372427\pi$
$492$	−3.58881e33	−0.804242
$493$	2.37760e33	0.519461
$494$	2.03172e34	4.32790
$495$	2.90825e33	0.604042
$496$	−3.26289e33	−0.660817
$497$	0	0
$498$	−1.35872e34	−2.61676
$499$	1.19472e33	0.224393	0.112196	−	0.993686i	$-0.464211\pi$
$499$	1.19472e33	0.224393	0.112196	+	0.993686i	$0.464211\pi$
$500$	1.81236e33	0.331985
$501$	4.26754e33	0.762440
$502$	2.12861e33	0.370937
$503$	4.20293e33	0.714417	0.357209	−	0.934025i	$-0.383729\pi$
$503$	4.20293e33	0.714417	0.357209	+	0.934025i	$0.383729\pi$
$504$	0	0
$505$	−4.52454e33	−0.731867
$506$	−1.54341e33	−0.243556
$507$	−4.45251e33	−0.685497
$508$	−1.70998e33	−0.256859
$509$	9.54036e33	1.39827	0.699137	−	0.714988i	$-0.253568\pi$
$509$	9.54036e33	1.39827	0.699137	+	0.714988i	$0.253568\pi$
$510$	5.04092e33	0.720913
$511$	0	0
$512$	1.36501e34	1.85893
$513$	1.49517e34	1.98711
$514$	1.65476e34	2.14633
$515$	1.88331e34	2.38414
$516$	−1.86432e34	−2.30356
$517$	1.50854e34	1.81938
$518$	0	0
$519$	7.31460e33	0.840617
$520$	−3.00059e34	−3.36639
$521$	−2.33533e33	−0.255786	−0.127893	−	0.991788i	$-0.540821\pi$
$521$	−2.33533e33	−0.255786	−0.127893	+	0.991788i	$0.540821\pi$
$522$	−7.93749e33	−0.848793
$523$	−1.63558e34	−1.70765	−0.853826	−	0.520558i	$-0.825724\pi$
$523$	−1.63558e34	−1.70765	−0.853826	+	0.520558i	$0.825724\pi$
$524$	1.62129e33	0.165279
$525$	0	0
$526$	4.96813e33	0.482915
$527$	2.35432e33	0.223477
$528$	−1.20648e34	−1.11840
$529$	−1.09084e34	−0.987566
$530$	5.38645e34	4.76271
$531$	−1.51963e33	−0.131237
$532$	0	0
$533$	−8.10046e33	−0.667452
$534$	−2.21800e33	−0.178524
$535$	−9.29020e33	−0.730470
$536$	−3.16557e33	−0.243160
$537$	−2.22195e33	−0.166746
$538$	−2.88727e34	−2.11694
$539$	0	0
$540$	−4.34072e34	−3.03836
$541$	−2.62581e33	−0.179596	−0.0897982	−	0.995960i	$-0.528622\pi$
$541$	−2.62581e33	−0.179596	−0.0897982	+	0.995960i	$0.528622\pi$
$542$	9.91750e32	0.0662844
$543$	−1.33659e33	−0.0872972
$544$	7.37953e32	0.0471023
$545$	−1.28196e34	−0.799685
$546$	0	0
$547$	−2.22146e34	−1.32372	−0.661862	−	0.749626i	$-0.730234\pi$
$547$	−2.22146e34	−1.32372	−0.661862	+	0.749626i	$0.730234\pi$
$548$	−5.81883e34	−3.38906
$549$	1.98295e33	0.112890
$550$	−3.45813e34	−1.92445
$551$	−4.65425e34	−2.53195
$552$	3.04657e33	0.162021
$553$	0	0
$554$	−2.04412e34	−1.03904
$555$	8.50242e33	0.422552
$556$	2.75033e33	0.133644
$557$	8.92028e33	0.423827	0.211913	−	0.977288i	$-0.432031\pi$
$557$	8.92028e33	0.423827	0.211913	+	0.977288i	$0.432031\pi$
$558$	−7.85975e33	−0.365159
$559$	−4.20804e34	−1.91176
$560$	0	0
$561$	8.70528e33	0.378222
$562$	1.15605e34	0.491218
$563$	2.86921e34	1.19236	0.596180	−	0.802851i	$-0.296684\pi$
$563$	2.86921e34	1.19236	0.596180	+	0.802851i	$0.296684\pi$
$564$	−5.85350e34	−2.37918
$565$	3.96273e34	1.57539
$566$	5.20755e34	2.02502
$567$	0	0
$568$	−6.34939e34	−2.36253
$569$	−2.28890e34	−0.833152	−0.416576	−	0.909101i	$-0.636770\pi$
$569$	−2.28890e34	−0.833152	−0.416576	+	0.909101i	$0.636770\pi$
$570$	−9.86781e34	−3.51386
$571$	1.66727e34	0.580838	0.290419	−	0.956900i	$-0.406205\pi$
$571$	1.66727e34	0.580838	0.290419	+	0.956900i	$0.406205\pi$
$572$	−1.01861e35	−3.47183
$573$	2.03656e34	0.679147
$574$	0	0
$575$	3.07731e33	0.0982478
$576$	9.99188e33	0.312152
$577$	5.81230e32	0.0177685	0.00888425	−	0.999961i	$-0.497172\pi$
$577$	5.81230e32	0.0177685	0.00888425	+	0.999961i	$0.497172\pi$
$578$	5.00670e34	1.49780
$579$	1.55077e34	0.454011
$580$	1.35121e35	3.87143
$581$	0	0
$582$	−4.77251e34	−1.30981
$583$	9.30198e34	2.49872
$584$	1.05574e35	2.77586
$585$	−2.54713e34	−0.655547
$586$	6.79219e34	1.71116
$587$	−4.04029e34	−0.996407	−0.498203	−	0.867060i	$-0.666007\pi$
$587$	−4.04029e34	−0.996407	−0.498203	+	0.867060i	$0.666007\pi$
$588$	0	0
$589$	−4.60867e34	−1.08927
$590$	3.85779e34	0.892665
$591$	6.54194e33	0.148205
$592$	1.91018e34	0.423694
$593$	−7.53916e33	−0.163734	−0.0818670	−	0.996643i	$-0.526088\pi$
$593$	−7.53916e33	−0.163734	−0.0818670	+	0.996643i	$0.526088\pi$
$594$	−1.11788e35	−2.37720
$595$	0	0
$596$	1.20658e35	2.46024
$597$	2.18060e34	0.435408
$598$	1.35176e34	0.264323
$599$	3.24679e34	0.621754	0.310877	−	0.950450i	$-0.399377\pi$
$599$	3.24679e34	0.621754	0.310877	+	0.950450i	$0.399377\pi$
$600$	6.82608e34	1.28021
$601$	−2.59982e34	−0.477542	−0.238771	−	0.971076i	$-0.576745\pi$
$601$	−2.59982e34	−0.477542	−0.238771	+	0.971076i	$0.576745\pi$
$602$	0	0
$603$	−2.68718e33	−0.0473511
$604$	6.40339e34	1.10522
$605$	−4.63752e34	−0.784050
$606$	4.52136e34	0.748792
$607$	3.93245e34	0.637976	0.318988	−	0.947759i	$-0.396657\pi$
$607$	3.93245e34	0.637976	0.318988	+	0.947759i	$0.396657\pi$
$608$	−1.44457e34	−0.229585
$609$	0	0
$610$	−5.03398e34	−0.767872
$611$	−1.32122e35	−1.97452
$612$	1.82930e34	0.267851
$613$	3.61121e34	0.518080	0.259040	−	0.965867i	$-0.416594\pi$
$613$	3.61121e34	0.518080	0.259040	+	0.965867i	$0.416594\pi$
$614$	−3.16999e34	−0.445608
$615$	3.93429e34	0.541911
$616$	0	0
$617$	1.01849e35	1.34708	0.673538	−	0.739153i	$-0.264774\pi$
$617$	1.01849e35	1.34708	0.673538	+	0.739153i	$0.264774\pi$
$618$	−1.88199e35	−2.43928
$619$	−5.04269e34	−0.640515	−0.320258	−	0.947330i	$-0.603769\pi$
$619$	−5.04269e34	−0.640515	−0.320258	+	0.947330i	$0.603769\pi$
$620$	1.33797e35	1.66553
$621$	9.94778e33	0.121362
$622$	6.05907e34	0.724480
$623$	0	0
$624$	1.05667e35	1.21376
$625$	−9.81240e34	−1.10478
$626$	4.66592e34	0.514942
$627$	−1.70409e35	−1.84352
$628$	−1.57086e35	−1.66587
$629$	−1.37828e34	−0.143286
$630$	0	0
$631$	1.29495e35	1.29386	0.646930	−	0.762549i	$-0.276053\pi$
$631$	1.29495e35	1.29386	0.646930	+	0.762549i	$0.276053\pi$
$632$	1.39828e35	1.36971
$633$	7.37953e34	0.708732
$634$	−1.63640e35	−1.54090
$635$	1.87460e34	0.173076
$636$	−3.60940e35	−3.26754
$637$	0	0
$638$	3.47982e35	3.02899
$639$	−5.38986e34	−0.460063
$640$	−2.74261e35	−2.29570
$641$	1.62419e35	1.33325	0.666623	−	0.745395i	$-0.267739\pi$
$641$	1.62419e35	1.33325	0.666623	+	0.745395i	$0.267739\pi$
$642$	9.28366e34	0.747363
$643$	−8.18831e34	−0.646483	−0.323241	−	0.946317i	$-0.604773\pi$
$643$	−8.18831e34	−0.646483	−0.323241	+	0.946317i	$0.604773\pi$
$644$	0	0
$645$	2.04379e35	1.55218
$646$	1.59961e35	1.19154
$647$	1.18589e35	0.866446	0.433223	−	0.901287i	$-0.357376\pi$
$647$	1.18589e35	0.866446	0.433223	+	0.901287i	$0.357376\pi$
$648$	1.32228e35	0.947624
$649$	6.66210e34	0.468331
$650$	3.02873e35	2.08854
$651$	0	0
$652$	9.27223e34	0.615304
$653$	−1.31973e35	−0.859155	−0.429577	−	0.903030i	$-0.641337\pi$
$653$	−1.31973e35	−0.859155	−0.429577	+	0.903030i	$0.641337\pi$
$654$	1.28106e35	0.818178
$655$	−1.77737e34	−0.111368
$656$	8.83889e34	0.543375
$657$	8.96197e34	0.540551
$658$	0	0
$659$	−6.79113e34	−0.394343	−0.197172	−	0.980369i	$-0.563176\pi$
$659$	−6.79113e34	−0.394343	−0.197172	+	0.980369i	$0.563176\pi$
$660$	4.94727e35	2.81881
$661$	1.99504e35	1.11541	0.557703	−	0.830040i	$-0.311683\pi$
$661$	1.99504e35	1.11541	0.557703	+	0.830040i	$0.311683\pi$
$662$	−3.16512e35	−1.73646
$663$	−7.62434e34	−0.410472
$664$	6.36762e35	3.36416
$665$	0	0
$666$	4.60130e34	0.234127
$667$	−3.09661e34	−0.154637
$668$	−3.93146e35	−1.92685
$669$	−5.87581e34	−0.282645
$670$	6.82178e34	0.322079
$671$	−8.69329e34	−0.402859
$672$	0	0
$673$	−2.56124e35	−1.14357	−0.571785	−	0.820404i	$-0.693749\pi$
$673$	−2.56124e35	−1.14357	−0.571785	+	0.820404i	$0.693749\pi$
$674$	3.55466e35	1.55794
$675$	2.22888e35	0.958935
$676$	4.10186e35	1.73240
$677$	−4.35721e35	−1.80655	−0.903275	−	0.429061i	$-0.858844\pi$
$677$	−4.35721e35	−1.80655	−0.903275	+	0.429061i	$0.858844\pi$
$678$	−3.95994e35	−1.61182
$679$	0	0
$680$	−2.36242e35	−0.926820
$681$	−1.74260e35	−0.671211
$682$	3.44574e35	1.30310
$683$	−4.33409e35	−1.60931	−0.804655	−	0.593743i	$-0.797650\pi$
$683$	−4.33409e35	−1.60931	−0.804655	+	0.593743i	$0.797650\pi$
$684$	−3.58093e35	−1.30555
$685$	6.37900e35	2.28360
$686$	0	0
$687$	−3.59753e35	−1.24178
$688$	4.59164e35	1.55637
$689$	−8.14695e35	−2.71178
$690$	−6.56534e34	−0.214607
$691$	−3.66784e35	−1.17743	−0.588714	−	0.808341i	$-0.700366\pi$
$691$	−3.66784e35	−1.17743	−0.588714	+	0.808341i	$0.700366\pi$
$692$	−6.73855e35	−2.12442
$693$	0	0
$694$	−2.54854e35	−0.774994
$695$	−3.01510e34	−0.0900517
$696$	−6.86889e35	−2.01498
$697$	−6.37764e34	−0.183760
$698$	6.80810e35	1.92678
$699$	−4.92859e35	−1.37012
$700$	0	0
$701$	3.43255e35	0.920750	0.460375	−	0.887725i	$-0.347715\pi$
$701$	3.43255e35	0.920750	0.460375	+	0.887725i	$0.347715\pi$
$702$	9.79074e35	2.57989
$703$	2.69803e35	0.698401
$704$	−4.38046e35	−1.11394
$705$	6.41701e35	1.60313
$706$	−6.04325e35	−1.48324
$707$	0	0
$708$	−2.58506e35	−0.612429
$709$	−3.65410e35	−0.850554	−0.425277	−	0.905063i	$-0.639823\pi$
$709$	−3.65410e35	−0.850554	−0.425277	+	0.905063i	$0.639823\pi$
$710$	1.36829e36	3.12931
$711$	1.18697e35	0.266728
$712$	1.03946e35	0.229514
$713$	−3.06628e34	−0.0665262
$714$	0	0
$715$	1.11667e36	2.33937
$716$	2.04697e35	0.421403
$717$	−1.89000e35	−0.382361
$718$	−1.30201e36	−2.58856
$719$	−4.60590e35	−0.899918	−0.449959	−	0.893049i	$-0.648561\pi$
$719$	−4.60590e35	−0.899918	−0.449959	+	0.893049i	$0.648561\pi$
$720$	2.77933e35	0.533683
$721$	0	0
$722$	−2.19195e36	−4.06552
$723$	−7.71925e35	−1.40717
$724$	1.23133e35	0.220619
$725$	−6.93820e35	−1.22186
$726$	4.63426e35	0.802182
$727$	2.32128e35	0.394955	0.197478	−	0.980307i	$-0.436725\pi$
$727$	2.32128e35	0.394955	0.197478	+	0.980307i	$0.436725\pi$
$728$	0	0
$729$	6.45443e35	1.06112
$730$	−2.27512e36	−3.67679
$731$	−3.31307e35	−0.526336
$732$	3.37322e35	0.526812
$733$	1.11346e36	1.70953	0.854764	−	0.519017i	$-0.173702\pi$
$733$	1.11346e36	1.70953	0.854764	+	0.519017i	$0.173702\pi$
$734$	7.60081e35	1.14725
$735$	0	0
$736$	−9.61116e33	−0.0140218
$737$	1.17807e35	0.168977
$738$	2.12914e35	0.300262
$739$	2.58573e35	0.358532	0.179266	−	0.983801i	$-0.442628\pi$
$739$	2.58573e35	0.358532	0.179266	+	0.983801i	$0.442628\pi$
$740$	−7.83283e35	−1.06788
$741$	1.49249e36	2.00071
$742$	0	0
$743$	2.32664e35	0.301557	0.150779	−	0.988568i	$-0.451822\pi$
$743$	2.32664e35	0.301557	0.150779	+	0.988568i	$0.451822\pi$
$744$	−6.80162e35	−0.866864
$745$	−1.32273e36	−1.65775
$746$	1.45032e36	1.78743
$747$	5.40534e35	0.655112
$748$	−8.01971e35	−0.955848
$749$	0	0
$750$	1.98543e35	0.228870
$751$	−1.62061e36	−1.83730	−0.918648	−	0.395077i	$-0.870718\pi$
$751$	−1.62061e36	−1.83730	−0.918648	+	0.395077i	$0.870718\pi$
$752$	1.44166e36	1.60746
$753$	1.56367e35	0.171478
$754$	−3.04773e36	−3.28726
$755$	−7.01983e35	−0.744714
$756$	0	0
$757$	−9.97731e35	−1.02404	−0.512018	−	0.858975i	$-0.671102\pi$
$757$	−9.97731e35	−1.02404	−0.512018	+	0.858975i	$0.671102\pi$
$758$	1.68481e36	1.70093
$759$	−1.13378e35	−0.112592
$760$	4.62453e36	4.51749
$761$	6.68153e35	0.642048	0.321024	−	0.947071i	$-0.395973\pi$
$761$	6.68153e35	0.642048	0.321024	+	0.947071i	$0.395973\pi$
$762$	−1.87328e35	−0.177078
$763$	0	0
$764$	−1.87617e36	−1.71635
$765$	−2.00541e35	−0.180482
$766$	1.46302e36	1.29536
$767$	−5.83487e35	−0.508263
$768$	1.90562e36	1.63313
$769$	−3.13381e35	−0.264237	−0.132118	−	0.991234i	$-0.542178\pi$
$769$	−3.13381e35	−0.264237	−0.132118	+	0.991234i	$0.542178\pi$
$770$	0	0
$771$	1.21558e36	0.992215
$772$	−1.42865e36	−1.14738
$773$	8.09130e35	0.639403	0.319701	−	0.947518i	$-0.396417\pi$
$773$	8.09130e35	0.639403	0.319701	+	0.947518i	$0.396417\pi$
$774$	1.10605e36	0.860028
$775$	−6.87025e35	−0.525655
$776$	2.23663e36	1.68392
$777$	0	0
$778$	−2.52504e35	−0.184087
$779$	1.24845e36	0.895679
$780$	−4.33296e36	−3.05916
$781$	2.36293e36	1.64177
$782$	1.06427e35	0.0727723
$783$	−2.24286e36	−1.50931
$784$	0	0
$785$	1.72208e36	1.12249
$786$	1.77611e35	0.113943
$787$	2.18988e36	1.38273	0.691364	−	0.722506i	$-0.257010\pi$
$787$	2.18988e36	1.38273	0.691364	+	0.722506i	$0.257010\pi$
$788$	−6.02674e35	−0.374546
$789$	3.64957e35	0.223244
$790$	−3.01328e36	−1.81426
$791$	0	0
$792$	1.36199e36	0.794527
$793$	7.61384e35	0.437209
$794$	−2.08134e36	−1.17649
$795$	3.95687e36	2.20172
$796$	−2.00887e36	−1.10037
$797$	2.70967e36	1.46112	0.730561	−	0.682847i	$-0.239258\pi$
$797$	2.70967e36	1.46112	0.730561	+	0.682847i	$0.239258\pi$
$798$	0	0
$799$	−1.04022e36	−0.543615
$800$	−2.15346e35	−0.110793
$801$	8.82377e34	0.0446938
$802$	−3.62756e36	−1.80898
$803$	−3.92895e36	−1.92900
$804$	−4.57120e35	−0.220968
$805$	0	0
$806$	−3.01788e36	−1.41421
$807$	−2.12098e36	−0.978628
$808$	−2.11892e36	−0.962661
$809$	−2.71989e36	−1.21673	−0.608367	−	0.793656i	$-0.708175\pi$
$809$	−2.71989e36	−1.21673	−0.608367	+	0.793656i	$0.708175\pi$
$810$	−2.84951e36	−1.25518
$811$	−1.88698e36	−0.818478	−0.409239	−	0.912427i	$-0.634206\pi$
$811$	−1.88698e36	−0.818478	−0.409239	+	0.912427i	$0.634206\pi$
$812$	0	0
$813$	7.28536e34	0.0306422
$814$	−2.01722e36	−0.835503
$815$	−1.01649e36	−0.414602
$816$	8.31936e35	0.334167
$817$	6.48546e36	2.56546
$818$	5.14757e36	2.00533
$819$	0	0
$820$	−3.62446e36	−1.36952
$821$	−4.05910e36	−1.51057	−0.755284	−	0.655398i	$-0.772501\pi$
$821$	−4.05910e36	−1.51057	−0.755284	+	0.655398i	$0.772501\pi$
$822$	−6.37451e36	−2.33641
$823$	4.03937e36	1.45820	0.729099	−	0.684409i	$-0.239940\pi$
$823$	4.03937e36	1.45820	0.729099	+	0.684409i	$0.239940\pi$
$824$	8.81990e36	3.13598
$825$	−2.54033e36	−0.889643
$826$	0	0
$827$	−7.90001e35	−0.268416	−0.134208	−	0.990953i	$-0.542849\pi$
$827$	−7.90001e35	−0.268416	−0.134208	+	0.990953i	$0.542849\pi$
$828$	−2.38250e35	−0.0797358
$829$	5.58299e36	1.84050	0.920248	−	0.391335i	$-0.127987\pi$
$829$	5.58299e36	1.84050	0.920248	+	0.391335i	$0.127987\pi$
$830$	−1.37222e37	−4.45602
$831$	−1.50160e36	−0.480332
$832$	3.83654e36	1.20892
$833$	0	0
$834$	3.01298e35	0.0921341
$835$	4.30993e36	1.29834
$836$	1.56989e37	4.65898
$837$	−2.22089e36	−0.649320
$838$	2.93451e36	0.845250
$839$	1.99089e36	0.564965	0.282483	−	0.959272i	$-0.408842\pi$
$839$	1.99089e36	0.564965	0.282483	+	0.959272i	$0.408842\pi$
$840$	0	0
$841$	3.35135e36	0.923144
$842$	4.86911e36	1.32144
$843$	8.49233e35	0.227082
$844$	−6.79837e36	−1.79112
$845$	−4.49674e36	−1.16732
$846$	3.47272e36	0.888261
$847$	0	0
$848$	8.88961e36	2.20767
$849$	3.82545e36	0.936131
$850$	2.38458e36	0.575009
$851$	1.79508e35	0.0426544
$852$	−9.16876e36	−2.14692
$853$	−3.48694e36	−0.804602	−0.402301	−	0.915507i	$-0.631789\pi$
$853$	−3.48694e36	−0.804602	−0.402301	+	0.915507i	$0.631789\pi$
$854$	0	0
$855$	3.92566e36	0.879703
$856$	−4.35077e36	−0.960824
$857$	−5.94582e36	−1.29405	−0.647026	−	0.762468i	$-0.723988\pi$
$857$	−5.94582e36	−1.29405	−0.647026	+	0.762468i	$0.723988\pi$
$858$	−1.11588e37	−2.39347
$859$	−5.92659e35	−0.125283	−0.0626413	−	0.998036i	$-0.519952\pi$
$859$	−5.92659e35	−0.125283	−0.0626413	+	0.998036i	$0.519952\pi$
$860$	−1.88284e37	−3.92268
$861$	0	0
$862$	−1.43920e37	−2.91260
$863$	5.84392e36	1.16565	0.582827	−	0.812596i	$-0.301947\pi$
$863$	5.84392e36	1.16565	0.582827	+	0.812596i	$0.301947\pi$
$864$	−6.96131e35	−0.136858
$865$	7.38725e36	1.43147
$866$	9.34035e36	1.78398
$867$	3.67790e36	0.692407
$868$	0	0
$869$	−5.20369e36	−0.951841
$870$	1.48024e37	2.66896
$871$	−1.03179e36	−0.183384
$872$	−6.00366e36	−1.05187
$873$	1.89862e36	0.327915
$874$	−2.08334e36	−0.354706
$875$	0	0
$876$	1.52453e37	2.52252
$877$	6.95724e36	1.13486	0.567429	−	0.823422i	$-0.307938\pi$
$877$	6.95724e36	1.13486	0.567429	+	0.823422i	$0.307938\pi$
$878$	−2.06243e37	−3.31663
$879$	4.98952e36	0.791039
$880$	−1.21846e37	−1.90449
$881$	1.13485e37	1.74880	0.874400	−	0.485205i	$-0.161255\pi$
$881$	1.13485e37	1.74880	0.874400	+	0.485205i	$0.161255\pi$
$882$	0	0
$883$	−4.40757e36	−0.660223	−0.330112	−	0.943942i	$-0.607086\pi$
$883$	−4.40757e36	−0.660223	−0.330112	+	0.943942i	$0.607086\pi$
$884$	7.02390e36	1.03735
$885$	2.83392e36	0.412664
$886$	8.98666e36	1.29026
$887$	−1.34737e36	−0.190740	−0.0953701	−	0.995442i	$-0.530403\pi$
$887$	−1.34737e36	−0.190740	−0.0953701	+	0.995442i	$0.530403\pi$
$888$	3.98184e36	0.555804
$889$	0	0
$890$	−2.24003e36	−0.304004
$891$	−4.92087e36	−0.658523
$892$	5.41307e36	0.714304
$893$	2.03628e37	2.64968
$894$	1.32180e37	1.69608
$895$	−2.24402e36	−0.283948
$896$	0	0
$897$	9.93000e35	0.122192
$898$	2.17303e36	0.263700
$899$	6.91333e36	0.827354
$900$	−5.33818e36	−0.630031
$901$	−6.41424e36	−0.746595
$902$	−9.33421e36	−1.07151
$903$	0	0
$904$	1.85582e37	2.07219
$905$	−1.34987e36	−0.148656
$906$	7.01489e36	0.761936
$907$	1.17171e37	1.25524	0.627622	−	0.778518i	$-0.284028\pi$
$907$	1.17171e37	1.25524	0.627622	+	0.778518i	$0.284028\pi$
$908$	1.60537e37	1.69629
$909$	−1.79871e36	−0.187462
$910$	0	0
$911$	1.28205e37	1.29994	0.649972	−	0.759958i	$-0.274781\pi$
$911$	1.28205e37	1.29994	0.649972	+	0.759958i	$0.274781\pi$
$912$	−1.62855e37	−1.62879
$913$	−2.36971e37	−2.33782
$914$	−1.98046e37	−1.92725
$915$	−3.69795e36	−0.354974
$916$	3.31422e37	3.13825
$917$	0	0
$918$	7.70843e36	0.710285
$919$	−6.02493e36	−0.547656	−0.273828	−	0.961779i	$-0.588290\pi$
$919$	−6.02493e36	−0.547656	−0.273828	+	0.961779i	$0.588290\pi$
$920$	3.07683e36	0.275903
$921$	−2.32866e36	−0.205997
$922$	−8.01260e36	−0.699257
$923$	−2.06952e37	−1.78176
$924$	0	0
$925$	4.02201e36	0.337032
$926$	1.06989e37	0.884505
$927$	7.48703e36	0.610678
$928$	2.16696e36	0.174382
$929$	−1.09526e37	−0.869599	−0.434799	−	0.900527i	$-0.643181\pi$
$929$	−1.09526e37	−0.869599	−0.434799	+	0.900527i	$0.643181\pi$
$930$	1.46575e37	1.14821
$931$	0	0
$932$	4.54045e37	3.46258
$933$	4.45097e36	0.334915
$934$	−4.54507e34	−0.00337446
$935$	8.79175e36	0.644066
$936$	−1.19287e37	−0.862273
$937$	−6.79461e36	−0.484640	−0.242320	−	0.970196i	$-0.577908\pi$
$937$	−6.79461e36	−0.484640	−0.242320	+	0.970196i	$0.577908\pi$
$938$	0	0
$939$	3.42757e36	0.238049
$940$	−5.91165e37	−4.05145
$941$	−1.49778e37	−1.01292	−0.506462	−	0.862262i	$-0.669047\pi$
$941$	−1.49778e37	−1.01292	−0.506462	+	0.862262i	$0.669047\pi$
$942$	−1.72087e37	−1.14845
$943$	8.30629e35	0.0547030
$944$	6.36676e36	0.413779
$945$	0	0
$946$	−4.84895e37	−3.06908
$947$	9.50271e35	0.0593571	0.0296786	−	0.999559i	$-0.490552\pi$
$947$	9.50271e35	0.0593571	0.0296786	+	0.999559i	$0.490552\pi$
$948$	2.01916e37	1.24471
$949$	3.44109e37	2.09348
$950$	−4.66790e37	−2.80270
$951$	−1.20210e37	−0.712332
$952$	0	0
$953$	2.44003e37	1.40843	0.704214	−	0.709988i	$-0.251300\pi$
$953$	2.44003e37	1.40843	0.704214	+	0.709988i	$0.251300\pi$
$954$	2.14136e37	1.21993
$955$	2.05679e37	1.15650
$956$	1.74116e37	0.966307
$957$	2.55626e37	1.40025
$958$	−9.85580e36	−0.532872
$959$	0	0
$960$	−1.86336e37	−0.981536
$961$	−1.23872e37	−0.644065
$962$	1.76674e37	0.906743
$963$	−3.69327e36	−0.187104
$964$	7.11134e37	3.55622
$965$	1.56618e37	0.773125
$966$	0	0
$967$	−1.72034e37	−0.827530	−0.413765	−	0.910384i	$-0.635786\pi$
$967$	−1.72034e37	−0.827530	−0.413765	+	0.910384i	$0.635786\pi$
$968$	−2.17184e37	−1.03130
$969$	1.17507e37	0.550828
$970$	−4.81992e37	−2.23045
$971$	−3.88720e36	−0.177581	−0.0887905	−	0.996050i	$-0.528300\pi$
$971$	−3.88720e36	−0.177581	−0.0887905	+	0.996050i	$0.528300\pi$
$972$	−3.00264e37	−1.35418
$973$	0	0
$974$	−2.62333e37	−1.15310
$975$	2.22490e37	0.965499
$976$	−8.30791e36	−0.355933
$977$	4.31167e37	1.82374	0.911870	−	0.410479i	$-0.134638\pi$
$977$	4.31167e37	1.82374	0.911870	+	0.410479i	$0.134638\pi$
$978$	1.01577e37	0.424189
$979$	−3.86836e36	−0.159494
$980$	0	0
$981$	−5.09638e36	−0.204833
$982$	−3.42575e37	−1.35945
$983$	−3.36076e37	−1.31679	−0.658397	−	0.752671i	$-0.728765\pi$
$983$	−3.36076e37	−1.31679	−0.658397	+	0.752671i	$0.728765\pi$
$984$	1.84250e37	0.712802
$985$	6.60692e36	0.252375
$986$	−2.39953e37	−0.905034
$987$	0	0
$988$	−1.37496e38	−5.05623
$989$	4.31497e36	0.156684
$990$	−2.93508e37	−1.05240
$991$	−3.62187e37	−1.28237	−0.641183	−	0.767388i	$-0.721556\pi$
$991$	−3.62187e37	−1.28237	−0.641183	+	0.767388i	$0.721556\pi$
$992$	2.14574e36	0.0750207
$993$	−2.32509e37	−0.802739
$994$	0	0
$995$	2.20226e37	0.741446
$996$	9.19509e37	3.05713
$997$	−6.23888e35	−0.0204841	−0.0102421	−	0.999948i	$-0.503260\pi$
$997$	−6.23888e35	−0.0204841	−0.0102421	+	0.999948i	$0.503260\pi$
$998$	−1.20574e37	−0.390950
$999$	1.30016e37	0.416322

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.26.a.e.1.1	✓	12
7.6	odd	2	inner	49.26.a.e.1.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.26.a.e.1.1	✓	12	1.1	even	1	trivial
49.26.a.e.1.2	yes	12	7.6	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	49.a (trivial)

\(f(q)\)	\(=\)	\(q-10092.2 q^{2} -741372. q^{3} +6.82987e7 q^{4} -7.48736e8 q^{5} +7.48209e9 q^{6} -3.50647e11 q^{8} -2.97656e11 q^{9} +O(q^{10})\)	\(q-10092.2 q^{2} -741372. q^{3} +6.82987e7 q^{4} -7.48736e8 q^{5} +7.48209e9 q^{6} -3.50647e11 q^{8} -2.97656e11 q^{9} +7.55642e12 q^{10} +1.30493e13 q^{11} -5.06347e13 q^{12} -1.14290e14 q^{13} +5.55092e14 q^{15} +1.24708e15 q^{16} -8.99825e14 q^{17} +3.00402e15 q^{18} +1.76144e16 q^{19} -5.11377e16 q^{20} -1.31697e17 q^{22} +1.17194e16 q^{23} +2.59960e17 q^{24} +2.62582e17 q^{25} +1.15344e18 q^{26} +8.48830e17 q^{27} -2.64229e18 q^{29} -5.60211e18 q^{30} -2.61641e18 q^{31} -8.20107e17 q^{32} -9.67441e18 q^{33} +9.08124e18 q^{34} -2.03295e19 q^{36} +1.53171e19 q^{37} -1.77769e20 q^{38} +8.47313e19 q^{39} +2.62542e20 q^{40} +7.08765e19 q^{41} +3.68190e20 q^{43} +8.91252e20 q^{44} +2.22866e20 q^{45} -1.18275e20 q^{46} +1.15603e21 q^{47} -9.24553e20 q^{48} -2.65004e21 q^{50} +6.67105e20 q^{51} -7.80585e21 q^{52} +7.12832e21 q^{53} -8.56659e21 q^{54} -9.77051e21 q^{55} -1.30588e22 q^{57} +2.66666e22 q^{58} +5.10532e21 q^{59} +3.79120e22 q^{60} -6.66187e21 q^{61} +2.64055e22 q^{62} -3.35685e22 q^{64} +8.55730e22 q^{65} +9.76363e22 q^{66} +9.02779e21 q^{67} -6.14569e22 q^{68} -8.68843e21 q^{69} +1.81077e23 q^{71} +1.04372e23 q^{72} -3.01084e23 q^{73} -1.54584e23 q^{74} -1.94671e23 q^{75} +1.20304e24 q^{76} -8.55128e23 q^{78} -3.98771e23 q^{79} -9.33737e23 q^{80} -3.77098e23 q^{81} -7.15302e23 q^{82} -1.81597e24 q^{83} +6.73732e23 q^{85} -3.71586e24 q^{86} +1.95892e24 q^{87} -4.57571e24 q^{88} -2.96441e23 q^{89} -2.24922e24 q^{90} +8.00419e23 q^{92} +1.93974e24 q^{93} -1.16669e25 q^{94} -1.31886e25 q^{95} +6.08004e23 q^{96} -6.37858e24 q^{97} -3.88422e24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8460 q^{2} + 161848296 q^{4} - 61395028560 q^{8} + 4977863358780 q^{9}+O(q^{10}) \) 12 * q - 8460 * q^2 + 161848296 * q^4 - 61395028560 * q^8 + 4977863358780 * q^9	\( 12 q - 8460 q^{2} + 161848296 q^{4} - 61395028560 q^{8} + 4977863358780 q^{9} + 39593455677648 q^{11} + 357546272706144 q^{15} + 18\!\cdots\!56 q^{16}+ \cdots - 14\!\cdots\!88 q^{99}+O(q^{100}) \) 12 * q - 8460 * q^2 + 161848296 * q^4 - 61395028560 * q^8 + 4977863358780 * q^9 + 39593455677648 * q^11 + 357546272706144 * q^15 + 1897434424858656 * q^16 + 19017456854067300 * q^18 + 85409383356235920 * q^22 + 77196982648366080 * q^23 + 2296738995597808932 * q^25 + 8694499082723336088 * q^29 - 12169958791851770688 * q^30 - 6483391660121958720 * q^32 - 109652263099391094456 * q^36 + 151853425001596848120 * q^37 - 122709680243235084384 * q^39 - 380869142455132177200 * q^43 + 991389584873062609056 * q^44 + 2303857023830118404064 * q^46 + 3165366920999170599036 * q^50 + 1280977431762493664064 * q^51 + 17755418685871290573000 * q^53 - 40456075816140877421280 * q^57 + 90683689500928436394600 * q^58 + 27395532648965383354368 * q^60 - 153351020298413953854336 * q^64 + 200499279532648292123424 * q^65 + 148336212990069406108560 * q^67 + 562419591698095656528384 * q^71 - 554920453414323154337040 * q^72 + 509427689055313155358536 * q^74 - 812506544978626047049920 * q^78 + 1488381592136271978244704 * q^79 - 2624302005301676288302452 * q^81 - 333667887446182173142464 * q^85 - 10612071587035448449112880 * q^86 - 14889193934757325628907840 * q^88 + 8074123164162948551757120 * q^92 + 1647472274074578272984640 * q^93 + 10792312351147270637620128 * q^95 - 148376588023327766946288 * q^99

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