LMFDB - Embedded newform 49.24.a.h.1.22

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [49,24,Mod(1,49)] 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("49.1"); S:= CuspForms(chi, 24); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(49, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 24, names="a")

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 24 $
Character orbit:	$[\chi]$	$=$	49.a (trivial)

Newform invariants

comment:select newform

sage:traces = [24,6030,0] 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:	$164.249978299$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.22
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)

$f(q)$	$=$	\(q+4682.86 q^{2} +533419. q^{3} +1.35406e7 q^{4} -4.63050e7 q^{5} +2.49793e9 q^{6} +2.41261e10 q^{8} +1.90393e11 q^{9} -2.16840e11 q^{10} +1.60986e12 q^{11} +7.22281e12 q^{12} -9.50878e12 q^{13} -2.47000e13 q^{15} -6.07746e11 q^{16} +1.24885e14 q^{17} +8.91583e14 q^{18} +3.62029e14 q^{19} -6.26998e14 q^{20} +7.53875e15 q^{22} +6.10783e15 q^{23} +1.28693e16 q^{24} -9.77677e15 q^{25} -4.45283e16 q^{26} +5.13413e16 q^{27} +8.30094e16 q^{29} -1.15667e17 q^{30} +1.39797e17 q^{31} -2.05230e17 q^{32} +8.58730e17 q^{33} +5.84819e17 q^{34} +2.57803e18 q^{36} -1.00014e18 q^{37} +1.69533e18 q^{38} -5.07216e18 q^{39} -1.11716e18 q^{40} -4.51785e18 q^{41} +3.67753e18 q^{43} +2.17985e19 q^{44} -8.81614e18 q^{45} +2.86021e19 q^{46} +1.92884e19 q^{47} -3.24184e17 q^{48} -4.57833e19 q^{50} +6.66160e19 q^{51} -1.28755e20 q^{52} +2.65567e18 q^{53} +2.40424e20 q^{54} -7.45446e19 q^{55} +1.93113e20 q^{57} +3.88721e20 q^{58} -4.66189e19 q^{59} -3.34452e20 q^{60} +2.44943e19 q^{61} +6.54649e20 q^{62} -9.55966e20 q^{64} +4.40304e20 q^{65} +4.02131e21 q^{66} +7.22237e19 q^{67} +1.69102e21 q^{68} +3.25803e21 q^{69} +3.05802e21 q^{71} +4.59342e21 q^{72} -3.22856e21 q^{73} -4.68353e21 q^{74} -5.21512e21 q^{75} +4.90209e21 q^{76} -2.37522e22 q^{78} +6.23431e21 q^{79} +2.81417e19 q^{80} +9.46225e21 q^{81} -2.11565e22 q^{82} -1.46030e22 q^{83} -5.78280e21 q^{85} +1.72214e22 q^{86} +4.42788e22 q^{87} +3.88396e22 q^{88} +2.77977e22 q^{89} -4.12848e22 q^{90} +8.27037e22 q^{92} +7.45702e22 q^{93} +9.03251e22 q^{94} -1.67638e22 q^{95} -1.09474e23 q^{96} -6.21716e22 q^{97} +3.06505e23 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6030 q^{2} + 99000906 q^{4} + 31751706690 q^{8} + 975236583640 q^{9} + 3514223137536 q^{11} + 96662500006976 q^{15} + 850136746459362 q^{16} - 774764811988990 q^{18} + 81\!\cdots\!60 q^{22} + 34\!\cdots\!60 q^{23}+ \cdots + 70\!\cdots\!64 q^{99}+O(q^{100}) $ 24 * q + 6030 * q^2 + 99000906 * q^4 + 31751706690 * q^8 + 975236583640 * q^9 + 3514223137536 * q^11 + 96662500006976 * q^15 + 850136746459362 * q^16 - 774764811988990 * q^18 + 8148420455553060 * q^22 + 34774948016084160 * q^23 + 94149150991117272 * q^25 + 190645622093096064 * q^29 - 634449556982285592 * q^30 - 1493697165631220430 * q^32 + 6671026323612877990 * q^36 + 878462893450581120 * q^37 + 6115839814038109120 * q^39 + 20811373010373199680 * q^43 + 54730049479951369500 * q^44 + 73203364608168908808 * q^46 + 387333163519636443066 * q^50 + 270153244272168521696 * q^51 + 34330885176487486320 * q^53 + 496656755807681949600 * q^57 - 397574761992930674580 * q^58 + 292003879381856022136 * q^60 + 2439494576203335787554 * q^64 + 4869166958052334391664 * q^65 - 1121753136531158010720 * q^67 - 1755055962268130457216 * q^71 - 32377694763810926605650 * q^72 + 1005354247436267388732 * q^74 - 79646865826469682676320 * q^78 + 5008005983294871013824 * q^79 + 21826965675021517050808 * q^81 + 20177850245757616713456 * q^85 + 38898565641929075253660 * q^86 - 21751191568485361565940 * q^88 + 247141757180010545124120 * q^92 + 241670386431567345282560 * q^93 + 278606632818920869216512 * q^95 + 708951281314482353318464 * 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 $

$2$	4682.86	1.61684	0.808419	−	0.588607i	$-0.200324\pi$
$2$	4682.86	1.61684	0.808419	+	0.588607i	$0.200324\pi$
$3$	533419.	1.73850	0.869249	−	0.494375i	$-0.164603\pi$
$3$	533419.	1.73850	0.869249	+	0.494375i	$0.164603\pi$
$4$	1.35406e7	1.61416
$5$	−4.63050e7	−0.424105	−0.212052	−	0.977258i	$-0.568015\pi$
$5$	−4.63050e7	−0.424105	−0.212052	+	0.977258i	$0.568015\pi$
$6$	2.49793e9	2.81087
$7$	0	0
$7$	0	0
$8$	2.41261e10	0.993005
$9$	1.90393e11	2.02237
$10$	−2.16840e11	−0.685709
$11$	1.60986e12	1.70127	0.850633	−	0.525760i	$-0.176219\pi$
$11$	1.60986e12	1.70127	0.850633	+	0.525760i	$0.176219\pi$
$12$	7.22281e12	2.80622
$13$	−9.50878e12	−1.47155	−0.735777	−	0.677224i	$-0.763183\pi$
$13$	−9.50878e12	−1.47155	−0.735777	+	0.677224i	$0.763183\pi$
$14$	0	0
$15$	−2.47000e13	−0.737305
$16$	−6.07746e11	−0.00863660
$17$	1.24885e14	0.883787	0.441894	−	0.897067i	$-0.354307\pi$
$17$	1.24885e14	0.883787	0.441894	+	0.897067i	$0.354307\pi$
$18$	8.91583e14	3.26985
$19$	3.62029e14	0.712980	0.356490	−	0.934299i	$-0.383973\pi$
$19$	3.62029e14	0.712980	0.356490	+	0.934299i	$0.383973\pi$
$20$	−6.26998e14	−0.684575
$21$	0	0
$22$	7.53875e15	2.75067
$23$	6.10783e15	1.33665	0.668324	−	0.743870i	$-0.267012\pi$
$23$	6.10783e15	1.33665	0.668324	+	0.743870i	$0.267012\pi$
$24$	1.28693e16	1.72634
$25$	−9.77677e15	−0.820135
$26$	−4.45283e16	−2.37926
$27$	5.13413e16	1.77739
$28$	0	0
$29$	8.30094e16	1.26343	0.631713	−	0.775202i	$-0.282352\pi$
$29$	8.30094e16	1.26343	0.631713	+	0.775202i	$0.282352\pi$
$30$	−1.15667e17	−1.19210
$31$	1.39797e17	0.988183	0.494091	−	0.869410i	$-0.335501\pi$
$31$	1.39797e17	0.988183	0.494091	+	0.869410i	$0.335501\pi$
$32$	−2.05230e17	−1.00697
$33$	8.58730e17	2.95765
$34$	5.84819e17	1.42894
$35$	0	0
$36$	2.57803e18	3.26444
$37$	−1.00014e18	−0.924149	−0.462075	−	0.886841i	$-0.652895\pi$
$37$	−1.00014e18	−0.924149	−0.462075	+	0.886841i	$0.652895\pi$
$38$	1.69533e18	1.15277
$39$	−5.07216e18	−2.55829
$40$	−1.11716e18	−0.421138
$41$	−4.51785e18	−1.28209	−0.641044	−	0.767504i	$-0.721498\pi$
$41$	−4.51785e18	−1.28209	−0.641044	+	0.767504i	$0.721498\pi$
$42$	0	0
$43$	3.67753e18	0.603489	0.301745	−	0.953389i	$-0.402431\pi$
$43$	3.67753e18	0.603489	0.301745	+	0.953389i	$0.402431\pi$
$44$	2.17985e19	2.74612
$45$	−8.81614e18	−0.857698
$46$	2.86021e19	2.16114
$47$	1.92884e19	1.13808	0.569038	−	0.822311i	$-0.307316\pi$
$47$	1.92884e19	1.13808	0.569038	+	0.822311i	$0.307316\pi$
$48$	−3.24184e17	−0.0150147
$49$	0	0
$50$	−4.57833e19	−1.32603
$51$	6.66160e19	1.53646
$52$	−1.28755e20	−2.37533
$53$	2.65567e18	0.0393552	0.0196776	−	0.999806i	$-0.493736\pi$
$53$	2.65567e18	0.0393552	0.0196776	+	0.999806i	$0.493736\pi$
$54$	2.40424e20	2.87376
$55$	−7.45446e19	−0.721515
$56$	0	0
$57$	1.93113e20	1.23951
$58$	3.88721e20	2.04276
$59$	−4.66189e19	−0.201263	−0.100631	−	0.994924i	$-0.532086\pi$
$59$	−4.66189e19	−0.201263	−0.100631	+	0.994924i	$0.532086\pi$
$60$	−3.34452e20	−1.19013
$61$	2.44943e19	0.0720730	0.0360365	−	0.999350i	$-0.488527\pi$
$61$	2.44943e19	0.0720730	0.0360365	+	0.999350i	$0.488527\pi$
$62$	6.54649e20	1.59773
$63$	0	0
$64$	−9.55966e20	−1.61947
$65$	4.40304e20	0.624093
$66$	4.02131e21	4.78203
$67$	7.22237e19	0.0722469	0.0361235	−	0.999347i	$-0.488499\pi$
$67$	7.22237e19	0.0722469	0.0361235	+	0.999347i	$0.488499\pi$
$68$	1.69102e21	1.42658
$69$	3.25803e21	2.32376
$70$	0	0
$71$	3.05802e21	1.57025	0.785125	−	0.619337i	$-0.212599\pi$
$71$	3.05802e21	1.57025	0.785125	+	0.619337i	$0.212599\pi$
$72$	4.59342e21	2.00823
$73$	−3.22856e21	−1.20447	−0.602235	−	0.798319i	$-0.705723\pi$
$73$	−3.22856e21	−1.20447	−0.602235	+	0.798319i	$0.705723\pi$
$74$	−4.68353e21	−1.49420
$75$	−5.21512e21	−1.42580
$76$	4.90209e21	1.15087
$77$	0	0
$78$	−2.37522e22	−4.13635
$79$	6.23431e21	0.937728	0.468864	−	0.883270i	$-0.344663\pi$
$79$	6.23431e21	0.937728	0.468864	+	0.883270i	$0.344663\pi$
$80$	2.81417e19	0.00366282
$81$	9.46225e21	1.06762
$82$	−2.11565e22	−2.07293
$83$	−1.46030e22	−1.24464	−0.622321	−	0.782762i	$-0.713810\pi$
$83$	−1.46030e22	−1.24464	−0.622321	+	0.782762i	$0.713810\pi$
$84$	0	0
$85$	−5.78280e21	−0.374818
$86$	1.72214e22	0.975744
$87$	4.42788e22	2.19646
$88$	3.88396e22	1.68937
$89$	2.77977e22	1.06175	0.530877	−	0.847449i	$-0.321863\pi$
$89$	2.77977e22	1.06175	0.530877	+	0.847449i	$0.321863\pi$
$90$	−4.12848e22	−1.38676
$91$	0	0
$92$	8.27037e22	2.15757
$93$	7.45702e22	1.71795
$94$	9.03251e22	1.84009
$95$	−1.67638e22	−0.302378
$96$	−1.09474e23	−1.75061
$97$	−6.21716e22	−0.882505	−0.441253	−	0.897383i	$-0.645466\pi$
$97$	−6.21716e22	−0.882505	−0.441253	+	0.897383i	$0.645466\pi$
$98$	0	0
$99$	3.06505e23	3.44059
$100$	−1.32383e23	−1.32383
$101$	−4.85268e22	−0.432799	−0.216399	−	0.976305i	$-0.569431\pi$
$101$	−4.85268e22	−0.432799	−0.216399	+	0.976305i	$0.569431\pi$
$102$	3.11954e23	2.48421
$103$	5.65096e22	0.402248	0.201124	−	0.979566i	$-0.435541\pi$
$103$	5.65096e22	0.402248	0.201124	+	0.979566i	$0.435541\pi$
$104$	−2.29409e23	−1.46126
$105$	0	0
$106$	1.24362e22	0.0636310
$107$	7.38533e22	0.339200	0.169600	−	0.985513i	$-0.445752\pi$
$107$	7.38533e22	0.339200	0.169600	+	0.985513i	$0.445752\pi$
$108$	6.95192e23	2.86901
$109$	1.17182e23	0.434968	0.217484	−	0.976064i	$-0.430215\pi$
$109$	1.17182e23	0.434968	0.217484	+	0.976064i	$0.430215\pi$
$110$	−3.49082e23	−1.16657
$111$	−5.33495e23	−1.60663
$112$	0	0
$113$	−4.94797e23	−1.21346	−0.606729	−	0.794909i	$-0.707519\pi$
$113$	−4.94797e23	−1.21346	−0.606729	+	0.794909i	$0.707519\pi$
$114$	9.04323e23	2.00409
$115$	−2.82823e23	−0.566879
$116$	1.12400e24	2.03938
$117$	−1.81040e24	−2.97603
$118$	−2.18310e23	−0.325409
$119$	0	0
$120$	−5.95913e23	−0.732147
$121$	1.69622e24	1.89430
$122$	1.14704e23	0.116530
$123$	−2.40991e24	−2.22891
$124$	1.89293e24	1.59509
$125$	1.00471e24	0.771928
$126$	0	0
$127$	−8.44917e23	−0.540843	−0.270422	−	0.962742i	$-0.587163\pi$
$127$	−8.44917e23	−0.540843	−0.270422	+	0.962742i	$0.587163\pi$
$128$	−2.75506e24	−1.61145
$129$	1.96167e24	1.04916
$130$	2.06188e24	1.00906
$131$	−3.30362e24	−1.48037	−0.740184	−	0.672404i	$-0.765262\pi$
$131$	−3.30362e24	−1.48037	−0.740184	+	0.672404i	$0.765262\pi$
$132$	1.16277e25	4.77413
$133$	0	0
$134$	3.38213e23	0.116812
$135$	−2.37736e24	−0.753801
$136$	3.01298e24	0.877605
$137$	−5.69859e24	−1.52574	−0.762871	−	0.646550i	$-0.776211\pi$
$137$	−5.69859e24	−1.52574	−0.762871	+	0.646550i	$0.776211\pi$
$138$	1.52569e25	3.75714
$139$	−2.51026e24	−0.568916	−0.284458	−	0.958689i	$-0.591814\pi$
$139$	−2.51026e24	−0.568916	−0.284458	+	0.958689i	$0.591814\pi$
$140$	0	0
$141$	1.02888e25	1.97854
$142$	1.43203e25	2.53884
$143$	−1.53078e25	−2.50350
$144$	−1.15710e23	−0.0174664
$145$	−3.84375e24	−0.535825
$146$	−1.51189e25	−1.94743
$147$	0	0
$148$	−1.35425e25	−1.49173
$149$	−1.78941e24	−0.182419	−0.0912093	−	0.995832i	$-0.529073\pi$
$149$	−1.78941e24	−0.182419	−0.0912093	+	0.995832i	$0.529073\pi$
$150$	−2.44217e25	−2.30529
$151$	6.43708e24	0.562929	0.281465	−	0.959572i	$-0.409180\pi$
$151$	6.43708e24	0.562929	0.281465	+	0.959572i	$0.409180\pi$
$152$	8.73434e24	0.707992
$153$	2.37772e25	1.78735
$154$	0	0
$155$	−6.47329e24	−0.419093
$156$	−6.86801e25	−4.12951
$157$	−2.65261e25	−1.48193	−0.740964	−	0.671545i	$-0.765631\pi$
$157$	−2.65261e25	−1.48193	−0.740964	+	0.671545i	$0.765631\pi$
$158$	2.91944e25	1.51615
$159$	1.41659e24	0.0684190
$160$	9.50318e24	0.427060
$161$	0	0
$162$	4.43104e25	1.72617
$163$	−9.86677e24	−0.358111	−0.179055	−	0.983839i	$-0.557304\pi$
$163$	−9.86677e24	−0.358111	−0.179055	+	0.983839i	$0.557304\pi$
$164$	−6.11745e25	−2.06950
$165$	−3.97635e25	−1.25435
$166$	−6.83839e25	−2.01239
$167$	−3.07173e25	−0.843614	−0.421807	−	0.906686i	$-0.638604\pi$
$167$	−3.07173e25	−0.843614	−0.421807	+	0.906686i	$0.638604\pi$
$168$	0	0
$169$	4.86630e25	1.16547
$170$	−2.70801e25	−0.606020
$171$	6.89277e25	1.44191
$172$	4.97960e25	0.974131
$173$	−2.88321e25	−0.527651	−0.263825	−	0.964570i	$-0.584984\pi$
$173$	−2.88321e25	−0.527651	−0.263825	+	0.964570i	$0.584984\pi$
$174$	2.07351e26	3.55133
$175$	0	0
$176$	−9.78387e23	−0.0146931
$177$	−2.48674e25	−0.349895
$178$	1.30173e26	1.71668
$179$	−2.07043e25	−0.256007	−0.128003	−	0.991774i	$-0.540857\pi$
$179$	−2.07043e25	−0.256007	−0.128003	+	0.991774i	$0.540857\pi$
$180$	−1.19376e26	−1.38447
$181$	−1.25168e26	−1.36204	−0.681021	−	0.732264i	$-0.738464\pi$
$181$	−1.25168e26	−1.36204	−0.681021	+	0.732264i	$0.738464\pi$
$182$	0	0
$183$	1.30657e25	0.125299
$184$	1.47358e26	1.32730
$185$	4.63116e25	0.391936
$186$	3.49202e26	2.77765
$187$	2.01047e26	1.50356
$188$	2.61177e26	1.83704
$189$	0	0
$190$	−7.85024e25	−0.488896
$191$	5.36605e25	0.314609	0.157304	−	0.987550i	$-0.449720\pi$
$191$	5.36605e25	0.314609	0.157304	+	0.987550i	$0.449720\pi$
$192$	−5.09930e26	−2.81544
$193$	2.97683e26	1.54827	0.774133	−	0.633024i	$-0.218186\pi$
$193$	2.97683e26	1.54827	0.774133	+	0.633024i	$0.218186\pi$
$194$	−2.91141e26	−1.42687
$195$	2.34867e26	1.08498
$196$	0	0
$197$	−1.24865e26	−0.512953	−0.256477	−	0.966550i	$-0.582562\pi$
$197$	−1.24865e26	−0.512953	−0.256477	+	0.966550i	$0.582562\pi$
$198$	1.43532e27	5.56288
$199$	1.54378e25	0.0564644	0.0282322	−	0.999601i	$-0.491012\pi$
$199$	1.54378e25	0.0564644	0.0282322	+	0.999601i	$0.491012\pi$
$200$	−2.35875e26	−0.814398
$201$	3.85255e25	0.125601
$202$	−2.27244e26	−0.699765
$203$	0	0
$204$	9.02021e26	2.48010
$205$	2.09199e26	0.543740
$206$	2.64627e26	0.650370
$207$	1.16289e27	2.70320
$208$	5.77893e24	0.0127092
$209$	5.82816e26	1.21297
$210$	0	0
$211$	8.50068e26	1.58564	0.792821	−	0.609454i	$-0.208611\pi$
$211$	8.50068e26	1.58564	0.792821	+	0.609454i	$0.208611\pi$
$212$	3.59594e25	0.0635258
$213$	1.63120e27	2.72988
$214$	3.45845e26	0.548432
$215$	−1.70288e26	−0.255943
$216$	1.23866e27	1.76496
$217$	0	0
$218$	5.48748e26	0.703272
$219$	−1.72218e27	−2.09397
$220$	−1.00938e27	−1.16464
$221$	−1.18750e27	−1.30054
$222$	−2.49828e27	−2.59766
$223$	3.94025e26	0.389061	0.194531	−	0.980896i	$-0.437682\pi$
$223$	3.94025e26	0.389061	0.194531	+	0.980896i	$0.437682\pi$
$224$	0	0
$225$	−1.86143e27	−1.65862
$226$	−2.31707e27	−1.96197
$227$	−6.53188e26	−0.525704	−0.262852	−	0.964836i	$-0.584663\pi$
$227$	−6.53188e26	−0.525704	−0.262852	+	0.964836i	$0.584663\pi$
$228$	2.61487e27	2.00078
$229$	9.25953e24	0.00673722	0.00336861	−	0.999994i	$-0.498928\pi$
$229$	9.25953e24	0.00673722	0.00336861	+	0.999994i	$0.498928\pi$
$230$	−1.32442e27	−0.916551
$231$	0	0
$232$	2.00269e27	1.25459
$233$	−3.94406e26	−0.235153	−0.117576	−	0.993064i	$-0.537512\pi$
$233$	−3.94406e26	−0.235153	−0.117576	+	0.993064i	$0.537512\pi$
$234$	−8.47786e27	−4.81176
$235$	−8.93151e26	−0.482664
$236$	−6.31247e26	−0.324871
$237$	3.32550e27	1.63024
$238$	0	0
$239$	1.77841e27	0.791510	0.395755	−	0.918356i	$-0.370483\pi$
$239$	1.77841e27	0.791510	0.395755	+	0.918356i	$0.370483\pi$
$240$	1.50113e25	0.00636781
$241$	9.72071e26	0.393099	0.196549	−	0.980494i	$-0.437026\pi$
$241$	9.72071e26	0.393099	0.196549	+	0.980494i	$0.437026\pi$
$242$	7.94315e27	3.06278
$243$	2.13912e26	0.0786615
$244$	3.31668e26	0.116338
$245$	0	0
$246$	−1.12853e28	−3.60378
$247$	−3.44246e27	−1.04919
$248$	3.37274e27	0.981271
$249$	−7.78953e27	−2.16381
$250$	4.70493e27	1.24808
$251$	−3.00272e27	−0.760793	−0.380397	−	0.924823i	$-0.624213\pi$
$251$	−3.00272e27	−0.760793	−0.380397	+	0.924823i	$0.624213\pi$
$252$	0	0
$253$	9.83275e27	2.27399
$254$	−3.95663e27	−0.874456
$255$	−3.08466e27	−0.651621
$256$	−4.88236e27	−0.985985
$257$	−2.32862e26	−0.0449643	−0.0224821	−	0.999747i	$-0.507157\pi$
$257$	−2.32862e26	−0.0449643	−0.0224821	+	0.999747i	$0.507157\pi$
$258$	9.18621e27	1.69633
$259$	0	0
$260$	5.96198e27	1.00739
$261$	1.58044e28	2.55512
$262$	−1.54704e28	−2.39351
$263$	−1.10968e28	−1.64327	−0.821633	−	0.570016i	$-0.806937\pi$
$263$	−1.10968e28	−1.64327	−0.821633	+	0.570016i	$0.806937\pi$
$264$	2.07178e28	2.93696
$265$	−1.22971e26	−0.0166907
$266$	0	0
$267$	1.48278e28	1.84586
$268$	9.77951e26	0.116618
$269$	8.43909e27	0.964149	0.482075	−	0.876130i	$-0.339883\pi$
$269$	8.43909e27	0.964149	0.482075	+	0.876130i	$0.339883\pi$
$270$	−1.11328e28	−1.21877
$271$	1.67129e27	0.175350	0.0876750	−	0.996149i	$-0.472056\pi$
$271$	1.67129e27	0.175350	0.0876750	+	0.996149i	$0.472056\pi$
$272$	−7.58984e25	−0.00763291
$273$	0	0
$274$	−2.66857e28	−2.46688
$275$	−1.57392e28	−1.39527
$276$	4.41157e28	3.75093
$277$	1.33338e28	1.08752	0.543759	−	0.839241i	$-0.317001\pi$
$277$	1.33338e28	1.08752	0.543759	+	0.839241i	$0.317001\pi$
$278$	−1.17552e28	−0.919844
$279$	2.66163e28	1.99847
$280$	0	0
$281$	−1.98782e28	−1.37485	−0.687423	−	0.726258i	$-0.741258\pi$
$281$	−1.98782e28	−1.37485	−0.687423	+	0.726258i	$0.741258\pi$
$282$	4.81811e28	3.19898
$283$	−5.32061e27	−0.339170	−0.169585	−	0.985516i	$-0.554243\pi$
$283$	−5.32061e27	−0.339170	−0.169585	+	0.985516i	$0.554243\pi$
$284$	4.14074e28	2.53464
$285$	−8.94211e27	−0.525683
$286$	−7.16843e28	−4.04776
$287$	0	0
$288$	−3.90743e28	−2.03647
$289$	−4.37130e27	−0.218920
$290$	−1.79998e28	−0.866343
$291$	−3.31635e28	−1.53423
$292$	−4.37166e28	−1.94421
$293$	−3.59762e28	−1.53829	−0.769143	−	0.639077i	$-0.779317\pi$
$293$	−3.59762e28	−1.53829	−0.769143	+	0.639077i	$0.779317\pi$
$294$	0	0
$295$	2.15869e27	0.0853565
$296$	−2.41295e28	−0.917685
$297$	8.26523e28	3.02382
$298$	−8.37958e27	−0.294941
$299$	−5.80780e28	−1.96695
$300$	−7.06158e28	−2.30148
$301$	0	0
$302$	3.01440e28	0.910165
$303$	−2.58851e28	−0.752419
$304$	−2.20022e26	−0.00615772
$305$	−1.13421e27	−0.0305665
$306$	1.11345e29	2.88985
$307$	6.46598e28	1.61638	0.808190	−	0.588922i	$-0.200448\pi$
$307$	6.46598e28	1.61638	0.808190	+	0.588922i	$0.200448\pi$
$308$	0	0
$309$	3.01433e28	0.699307
$310$	−3.03135e28	−0.677605
$311$	4.18416e28	0.901287	0.450644	−	0.892704i	$-0.351194\pi$
$311$	4.18416e28	0.901287	0.450644	+	0.892704i	$0.351194\pi$
$312$	−1.22371e29	−2.54040
$313$	−1.55289e27	−0.0310728	−0.0155364	−	0.999879i	$-0.504946\pi$
$313$	−1.55289e27	−0.0310728	−0.0155364	+	0.999879i	$0.504946\pi$
$314$	−1.24218e29	−2.39604
$315$	0	0
$316$	8.44163e28	1.51365
$317$	−4.54172e28	−0.785305	−0.392653	−	0.919687i	$-0.628443\pi$
$317$	−4.54172e28	−0.785305	−0.392653	+	0.919687i	$0.628443\pi$
$318$	6.63368e27	0.110622
$319$	1.33633e29	2.14942
$320$	4.42660e28	0.686824
$321$	3.93947e28	0.589699
$322$	0	0
$323$	4.52120e28	0.630122
$324$	1.28125e29	1.72331
$325$	9.29652e28	1.20687
$326$	−4.62047e28	−0.579007
$327$	6.25072e28	0.756190
$328$	−1.08998e29	−1.27312
$329$	0	0
$330$	−1.86207e29	−2.02808
$331$	−8.48775e28	−0.892834	−0.446417	−	0.894825i	$-0.647300\pi$
$331$	−8.48775e28	−0.892834	−0.446417	+	0.894825i	$0.647300\pi$
$332$	−1.97734e29	−2.00906
$333$	−1.90420e29	−1.86898
$334$	−1.43845e29	−1.36399
$335$	−3.34432e27	−0.0306402
$336$	0	0
$337$	−1.88061e29	−1.60899	−0.804497	−	0.593956i	$-0.797565\pi$
$337$	−1.88061e29	−1.60899	−0.804497	+	0.593956i	$0.797565\pi$
$338$	2.27882e29	1.88438
$339$	−2.63934e29	−2.10959
$340$	−7.83026e28	−0.605019
$341$	2.25053e29	1.68116
$342$	3.22779e29	2.33134
$343$	0	0
$344$	8.87244e28	0.599268
$345$	−1.50863e29	−0.985517
$346$	−1.35017e29	−0.853126
$347$	5.05081e28	0.308725	0.154363	−	0.988014i	$-0.450668\pi$
$347$	5.05081e28	0.308725	0.154363	+	0.988014i	$0.450668\pi$
$348$	5.99561e29	3.54546
$349$	−2.43633e29	−1.39394	−0.696968	−	0.717102i	$-0.745468\pi$
$349$	−2.43633e29	−1.39394	−0.696968	+	0.717102i	$0.745468\pi$
$350$	0	0
$351$	−4.88193e29	−2.61553
$352$	−3.30392e29	−1.71312
$353$	2.89269e29	1.45175	0.725877	−	0.687825i	$-0.241434\pi$
$353$	2.89269e29	1.45175	0.725877	+	0.687825i	$0.241434\pi$
$354$	−1.16451e29	−0.565723
$355$	−1.41602e29	−0.665950
$356$	3.76398e29	1.71385
$357$	0	0
$358$	−9.69555e28	−0.413921
$359$	−1.15389e29	−0.477068	−0.238534	−	0.971134i	$-0.576667\pi$
$359$	−1.15389e29	−0.477068	−0.238534	+	0.971134i	$0.576667\pi$
$360$	−2.12699e29	−0.851698
$361$	−1.26765e29	−0.491660
$362$	−5.86146e29	−2.20220
$363$	9.04795e29	3.29324
$364$	0	0
$365$	1.49499e29	0.510822
$366$	6.11851e28	0.202588
$367$	−9.96647e28	−0.319802	−0.159901	−	0.987133i	$-0.551118\pi$
$367$	−9.96647e28	−0.319802	−0.159901	+	0.987133i	$0.551118\pi$
$368$	−3.71201e27	−0.0115441
$369$	−8.60166e29	−2.59286
$370$	2.16871e29	0.633697
$371$	0	0
$372$	1.00972e30	2.77306
$373$	1.22846e29	0.327121	0.163561	−	0.986533i	$-0.447702\pi$
$373$	1.22846e29	0.327121	0.163561	+	0.986533i	$0.447702\pi$
$374$	9.41477e29	2.43101
$375$	5.35933e29	1.34199
$376$	4.65354e29	1.13012
$377$	−7.89318e29	−1.85920
$378$	0	0
$379$	6.24049e29	1.38314	0.691572	−	0.722307i	$-0.256918\pi$
$379$	6.24049e29	1.38314	0.691572	+	0.722307i	$0.256918\pi$
$380$	−2.26991e29	−0.488088
$381$	−4.50695e29	−0.940254
$382$	2.51285e29	0.508671
$383$	−5.02673e29	−0.987416	−0.493708	−	0.869628i	$-0.664359\pi$
$383$	−5.02673e29	−0.987416	−0.493708	+	0.869628i	$0.664359\pi$
$384$	−1.46960e30	−2.80150
$385$	0	0
$386$	1.39401e30	2.50329
$387$	7.00175e29	1.22048
$388$	−8.41841e29	−1.42451
$389$	7.28857e28	0.119735	0.0598676	−	0.998206i	$-0.480932\pi$
$389$	7.28857e28	0.119735	0.0598676	+	0.998206i	$0.480932\pi$
$390$	1.09985e30	1.75424
$391$	7.62777e29	1.18131
$392$	0	0
$393$	−1.76221e30	−2.57362
$394$	−5.84724e29	−0.829363
$395$	−2.88680e29	−0.397695
$396$	4.15027e30	5.55369
$397$	−8.25507e29	−1.07307	−0.536537	−	0.843877i	$-0.680268\pi$
$397$	−8.25507e29	−1.07307	−0.536537	+	0.843877i	$0.680268\pi$
$398$	7.22931e28	0.0912938
$399$	0	0
$400$	5.94180e27	0.00708318
$401$	9.36237e29	1.08449	0.542245	−	0.840220i	$-0.317574\pi$
$401$	9.36237e29	1.08449	0.542245	+	0.840220i	$0.317574\pi$
$402$	1.80409e29	0.203077
$403$	−1.32930e30	−1.45416
$404$	−6.57082e29	−0.698609
$405$	−4.38150e29	−0.452783
$406$	0	0
$407$	−1.61009e30	−1.57222
$408$	1.60718e30	1.52571
$409$	−9.09429e29	−0.839365	−0.419682	−	0.907671i	$-0.637858\pi$
$409$	−9.09429e29	−0.839365	−0.419682	+	0.907671i	$0.637858\pi$
$410$	9.79652e29	0.879139
$411$	−3.03974e30	−2.65250
$412$	7.65173e29	0.649294
$413$	0	0
$414$	5.44564e30	4.37064
$415$	6.76193e29	0.527859
$416$	1.95149e30	1.48181
$417$	−1.33902e30	−0.989058
$418$	2.72925e30	1.96117
$419$	−7.07532e29	−0.494635	−0.247318	−	0.968934i	$-0.579549\pi$
$419$	−7.07532e29	−0.494635	−0.247318	+	0.968934i	$0.579549\pi$
$420$	0	0
$421$	−1.66361e30	−1.10105	−0.550524	−	0.834819i	$-0.685572\pi$
$421$	−1.66361e30	−1.10105	−0.550524	+	0.834819i	$0.685572\pi$
$422$	3.98075e30	2.56373
$423$	3.67238e30	2.30162
$424$	6.40710e28	0.0390799
$425$	−1.22097e30	−0.724825
$426$	7.63870e30	4.41377
$427$	0	0
$428$	1.00002e30	0.547525
$429$	−8.16547e30	−4.35234
$430$	−7.97437e29	−0.413818
$431$	3.77883e30	1.90927	0.954637	−	0.297771i	$-0.0962430\pi$
$431$	3.77883e30	1.90927	0.954637	+	0.297771i	$0.0962430\pi$
$432$	−3.12025e28	−0.0153506
$433$	2.45668e30	1.17690	0.588448	−	0.808535i	$-0.299739\pi$
$433$	2.45668e30	1.17690	0.588448	+	0.808535i	$0.299739\pi$
$434$	0	0
$435$	−2.05033e30	−0.931531
$436$	1.58672e30	0.702109
$437$	2.21121e30	0.953003
$438$	−8.06471e30	−3.38561
$439$	2.11265e30	0.863944	0.431972	−	0.901887i	$-0.357818\pi$
$439$	2.11265e30	0.863944	0.431972	+	0.901887i	$0.357818\pi$
$440$	−1.79847e30	−0.716468
$441$	0	0
$442$	−5.56092e30	−2.10276
$443$	4.94284e30	1.82110	0.910549	−	0.413401i	$-0.135659\pi$
$443$	4.94284e30	1.82110	0.910549	+	0.413401i	$0.135659\pi$
$444$	−7.22384e30	−2.59337
$445$	−1.28717e30	−0.450295
$446$	1.84517e30	0.629049
$447$	−9.54508e29	−0.317134
$448$	0	0
$449$	−3.96638e30	−1.25188	−0.625938	−	0.779873i	$-0.715284\pi$
$449$	−3.96638e30	−1.25188	−0.625938	+	0.779873i	$0.715284\pi$
$450$	−8.71680e30	−2.68172
$451$	−7.27311e30	−2.18117
$452$	−6.69984e30	−1.95872
$453$	3.43366e30	0.978651
$454$	−3.05879e30	−0.849978
$455$	0	0
$456$	4.65906e30	1.23084
$457$	2.22766e30	0.573869	0.286934	−	0.957950i	$-0.407364\pi$
$457$	2.22766e30	0.573869	0.286934	+	0.957950i	$0.407364\pi$
$458$	4.33611e28	0.0108930
$459$	6.41176e30	1.57084
$460$	−3.82960e30	−0.915035
$461$	6.19772e30	1.44435	0.722173	−	0.691713i	$-0.243144\pi$
$461$	6.19772e30	1.44435	0.722173	+	0.691713i	$0.243144\pi$
$462$	0	0
$463$	1.66106e30	0.368301	0.184151	−	0.982898i	$-0.441047\pi$
$463$	1.66106e30	0.368301	0.184151	+	0.982898i	$0.441047\pi$
$464$	−5.04487e28	−0.0109117
$465$	−3.45297e30	−0.728592
$466$	−1.84695e30	−0.380204
$467$	−3.96880e30	−0.797105	−0.398553	−	0.917145i	$-0.630487\pi$
$467$	−3.96880e30	−0.797105	−0.398553	+	0.917145i	$0.630487\pi$
$468$	−2.45139e31	−4.80381
$469$	0	0
$470$	−4.18250e30	−0.780389
$471$	−1.41495e31	−2.57633
$472$	−1.12473e30	−0.199855
$473$	5.92031e30	1.02670
$474$	1.55729e31	2.63583
$475$	−3.53948e30	−0.584740
$476$	0	0
$477$	5.05621e29	0.0795910
$478$	8.32806e30	1.27974
$479$	7.39482e30	1.10935	0.554675	−	0.832067i	$-0.312842\pi$
$479$	7.39482e30	1.10935	0.554675	+	0.832067i	$0.312842\pi$
$480$	5.06918e30	0.742443
$481$	9.51014e30	1.35994
$482$	4.55207e30	0.635577
$483$	0	0
$484$	2.29678e31	3.05772
$485$	2.87886e30	0.374275
$486$	1.00172e30	0.127183
$487$	−1.12456e31	−1.39443	−0.697217	−	0.716860i	$-0.745579\pi$
$487$	−1.12456e31	−1.39443	−0.697217	+	0.716860i	$0.745579\pi$
$488$	5.90952e29	0.0715689
$489$	−5.26312e30	−0.622575
$490$	0	0
$491$	2.95602e30	0.333634	0.166817	−	0.985988i	$-0.446651\pi$
$491$	2.95602e30	0.333634	0.166817	+	0.985988i	$0.446651\pi$
$492$	−3.26316e31	−3.59782
$493$	1.03666e31	1.11660
$494$	−1.61205e31	−1.69637
$495$	−1.41927e31	−1.45917
$496$	−8.49609e28	−0.00853454
$497$	0	0
$498$	−3.64773e31	−3.49853
$499$	−1.00086e31	−0.938030	−0.469015	−	0.883190i	$-0.655391\pi$
$499$	−1.00086e31	−0.938030	−0.469015	+	0.883190i	$0.655391\pi$
$500$	1.36044e31	1.24602
$501$	−1.63852e31	−1.46662
$502$	−1.40613e31	−1.23008
$503$	−3.37564e30	−0.288618	−0.144309	−	0.989533i	$-0.546096\pi$
$503$	−3.37564e30	−0.288618	−0.144309	+	0.989533i	$0.546096\pi$
$504$	0	0
$505$	2.24704e30	0.183552
$506$	4.60454e31	3.67668
$507$	2.59578e31	2.02617
$508$	−1.14407e31	−0.873010
$509$	−2.17425e31	−1.62202	−0.811008	−	0.585036i	$-0.801081\pi$
$509$	−2.17425e31	−1.62202	−0.811008	+	0.585036i	$0.801081\pi$
$510$	−1.44450e31	−1.05357
$511$	0	0
$512$	2.47726e29	0.0172730
$513$	1.85870e31	1.26725
$514$	−1.09046e30	−0.0727000
$515$	−2.61668e30	−0.170595
$516$	2.65621e31	1.69352
$517$	3.10517e31	1.93617
$518$	0	0
$519$	−1.53796e31	−0.917319
$520$	1.06228e31	0.619728
$521$	4.06923e30	0.232209	0.116104	−	0.993237i	$-0.462959\pi$
$521$	4.06923e30	0.232209	0.116104	+	0.993237i	$0.462959\pi$
$522$	7.40097e31	4.13122
$523$	2.50335e30	0.136695	0.0683475	−	0.997662i	$-0.478227\pi$
$523$	2.50335e30	0.136695	0.0683475	+	0.997662i	$0.478227\pi$
$524$	−4.47329e31	−2.38956
$525$	0	0
$526$	−5.19650e31	−2.65690
$527$	1.74585e31	0.873343
$528$	−5.21890e29	−0.0255440
$529$	1.64251e31	0.786627
$530$	−5.75857e29	−0.0269862
$531$	−8.87589e30	−0.407029
$532$	0	0
$533$	4.29593e31	1.88666
$534$	6.94367e31	2.98445
$535$	−3.41978e30	−0.143856
$536$	1.74247e30	0.0717415
$537$	−1.10441e31	−0.445067
$538$	3.95191e31	1.55887
$539$	0	0
$540$	−3.21909e31	−1.21676
$541$	−2.02315e31	−0.748617	−0.374309	−	0.927304i	$-0.622120\pi$
$541$	−2.02315e31	−0.748617	−0.374309	+	0.927304i	$0.622120\pi$
$542$	7.82643e30	0.283512
$543$	−6.67671e31	−2.36791
$544$	−2.56302e31	−0.889946
$545$	−5.42612e30	−0.184472
$546$	0	0
$547$	2.47835e31	0.807808	0.403904	−	0.914801i	$-0.367653\pi$
$547$	2.47835e31	0.807808	0.403904	+	0.914801i	$0.367653\pi$
$548$	−7.71624e31	−2.46280
$549$	4.66354e30	0.145759
$550$	−7.37047e31	−2.25592
$551$	3.00518e31	0.900798
$552$	7.86035e31	2.30750
$553$	0	0
$554$	6.24403e31	1.75834
$555$	2.47035e31	0.681380
$556$	−3.39904e31	−0.918324
$557$	2.25689e31	0.597278	0.298639	−	0.954366i	$-0.403467\pi$
$557$	2.25689e31	0.597278	0.298639	+	0.954366i	$0.403467\pi$
$558$	1.24640e32	3.23121
$559$	−3.49689e31	−0.888067
$560$	0	0
$561$	1.07242e32	2.61393
$562$	−9.30868e31	−2.22290
$563$	−3.09646e31	−0.724467	−0.362233	−	0.932087i	$-0.617986\pi$
$563$	−3.09646e31	−0.724467	−0.362233	+	0.932087i	$0.617986\pi$
$564$	1.39317e32	3.19370
$565$	2.29116e31	0.514633
$566$	−2.49157e31	−0.548383
$567$	0	0
$568$	7.37779e31	1.55927
$569$	5.92689e31	1.22754	0.613770	−	0.789485i	$-0.289652\pi$
$569$	5.92689e31	1.22754	0.613770	+	0.789485i	$0.289652\pi$
$570$	−4.18747e31	−0.849945
$571$	9.46958e30	0.188372	0.0941858	−	0.995555i	$-0.469975\pi$
$571$	9.46958e30	0.188372	0.0941858	+	0.995555i	$0.469975\pi$
$572$	−2.07277e32	−4.04107
$573$	2.86235e31	0.546947
$574$	0	0
$575$	−5.97149e31	−1.09623
$576$	−1.82009e32	−3.27517
$577$	−2.32182e30	−0.0409550	−0.0204775	−	0.999790i	$-0.506519\pi$
$577$	−2.32182e30	−0.0409550	−0.0204775	+	0.999790i	$0.506519\pi$
$578$	−2.04702e31	−0.353958
$579$	1.58790e32	2.69165
$580$	−5.20467e31	−0.864910
$581$	0	0
$582$	−1.55300e32	−2.48061
$583$	4.27526e30	0.0669537
$584$	−7.78925e31	−1.19605
$585$	8.38307e31	1.26215
$586$	−1.68471e32	−2.48716
$587$	−3.19769e31	−0.462912	−0.231456	−	0.972845i	$-0.574349\pi$
$587$	−3.19769e31	−0.462912	−0.231456	+	0.972845i	$0.574349\pi$
$588$	0	0
$589$	5.06105e31	0.704554
$590$	1.01088e31	0.138008
$591$	−6.66052e31	−0.891768
$592$	6.07833e29	0.00798151
$593$	−1.18158e32	−1.52172	−0.760858	−	0.648919i	$-0.775221\pi$
$593$	−1.18158e32	−1.52172	−0.760858	+	0.648919i	$0.775221\pi$
$594$	3.87049e32	4.88902
$595$	0	0
$596$	−2.42297e31	−0.294454
$597$	8.23481e30	0.0981632
$598$	−2.71971e32	−3.18024
$599$	−2.76710e31	−0.317407	−0.158704	−	0.987326i	$-0.550731\pi$
$599$	−2.76710e31	−0.317407	−0.158704	+	0.987326i	$0.550731\pi$
$600$	−1.25820e32	−1.41583
$601$	−4.27973e31	−0.472454	−0.236227	−	0.971698i	$-0.575911\pi$
$601$	−4.27973e31	−0.472454	−0.236227	+	0.971698i	$0.575911\pi$
$602$	0	0
$603$	1.37509e31	0.146110
$604$	8.71619e31	0.908661
$605$	−7.85434e31	−0.803383
$606$	−1.21216e32	−1.21654
$607$	1.90086e31	0.187189	0.0935945	−	0.995610i	$-0.470164\pi$
$607$	1.90086e31	0.187189	0.0935945	+	0.995610i	$0.470164\pi$
$608$	−7.42993e31	−0.717948
$609$	0	0
$610$	−5.31136e30	−0.0494211
$611$	−1.83409e32	−1.67474
$612$	3.21957e32	2.88507
$613$	1.40286e32	1.23373	0.616865	−	0.787069i	$-0.288403\pi$
$613$	1.40286e32	1.23373	0.616865	+	0.787069i	$0.288403\pi$
$614$	3.02793e32	2.61342
$615$	1.11591e32	0.945290
$616$	0	0
$617$	−2.02136e32	−1.64954	−0.824771	−	0.565467i	$-0.808696\pi$
$617$	−2.02136e32	−1.64954	−0.824771	+	0.565467i	$0.808696\pi$
$618$	1.41157e32	1.13067
$619$	9.37113e31	0.736800	0.368400	−	0.929667i	$-0.379906\pi$
$619$	9.37113e31	0.736800	0.368400	+	0.929667i	$0.379906\pi$
$620$	−8.76522e31	−0.676485
$621$	3.13584e32	2.37575
$622$	1.95938e32	1.45724
$623$	0	0
$624$	3.08259e30	0.0220949
$625$	7.00250e31	0.492757
$626$	−7.27197e30	−0.0502397
$627$	3.10885e32	2.10874
$628$	−3.59179e32	−2.39207
$629$	−1.24903e32	−0.816752
$630$	0	0
$631$	2.80429e32	1.76801	0.884006	−	0.467476i	$-0.154837\pi$
$631$	2.80429e32	1.76801	0.884006	+	0.467476i	$0.154837\pi$
$632$	1.50409e32	0.931169
$633$	4.53442e32	2.75664
$634$	−2.12682e32	−1.26971
$635$	3.91239e31	0.229374
$636$	1.91814e31	0.110439
$637$	0	0
$638$	6.25787e32	3.47527
$639$	5.82224e32	3.17563
$640$	1.27573e32	0.683424
$641$	−1.19413e32	−0.628323	−0.314162	−	0.949370i	$-0.601723\pi$
$641$	−1.19413e32	−0.628323	−0.314162	+	0.949370i	$0.601723\pi$
$642$	1.84480e32	0.953447
$643$	−3.13384e32	−1.59093	−0.795463	−	0.606002i	$-0.792772\pi$
$643$	−3.13384e32	−1.59093	−0.795463	+	0.606002i	$0.792772\pi$
$644$	0	0
$645$	−9.08350e31	−0.444955
$646$	2.11722e32	1.01881
$647$	−1.16353e32	−0.550018	−0.275009	−	0.961442i	$-0.588681\pi$
$647$	−1.16353e32	−0.550018	−0.275009	+	0.961442i	$0.588681\pi$
$648$	2.28287e32	1.06015
$649$	−7.50498e31	−0.342402
$650$	4.35343e32	1.95132
$651$	0	0
$652$	−1.33602e32	−0.578050
$653$	2.52698e31	0.107424	0.0537119	−	0.998556i	$-0.482895\pi$
$653$	2.52698e31	0.107424	0.0537119	+	0.998556i	$0.482895\pi$
$654$	2.92713e32	1.22264
$655$	1.52974e32	0.627831
$656$	2.74571e30	0.0110729
$657$	−6.14694e32	−2.43589
$658$	0	0
$659$	−3.85321e32	−1.47448	−0.737242	−	0.675629i	$-0.763872\pi$
$659$	−3.85321e32	−1.47448	−0.737242	+	0.675629i	$0.763872\pi$
$660$	−5.38421e32	−2.02473
$661$	−2.70466e32	−0.999531	−0.499766	−	0.866161i	$-0.666581\pi$
$661$	−2.70466e32	−0.999531	−0.499766	+	0.866161i	$0.666581\pi$
$662$	−3.97470e32	−1.44357
$663$	−6.33437e32	−2.26099
$664$	−3.52313e32	−1.23594
$665$	0	0
$666$	−8.91710e32	−3.02183
$667$	5.07007e32	1.68876
$668$	−4.15931e32	−1.36173
$669$	2.10181e32	0.676382
$670$	−1.56610e31	−0.0495403
$671$	3.94325e31	0.122615
$672$	0	0
$673$	4.60479e32	1.38368	0.691842	−	0.722049i	$-0.256800\pi$
$673$	4.60479e32	1.38368	0.691842	+	0.722049i	$0.256800\pi$
$674$	−8.80663e32	−2.60148
$675$	−5.01952e32	−1.45770
$676$	6.58926e32	1.88126
$677$	2.16211e32	0.606887	0.303443	−	0.952849i	$-0.401864\pi$
$677$	2.16211e32	0.606887	0.303443	+	0.952849i	$0.401864\pi$
$678$	−1.23597e33	−3.41087
$679$	0	0
$680$	−1.39516e32	−0.372197
$681$	−3.48423e32	−0.913934
$682$	1.05389e33	2.71817
$683$	−5.14337e32	−1.30440	−0.652199	−	0.758048i	$-0.726153\pi$
$683$	−5.14337e32	−1.30440	−0.652199	+	0.758048i	$0.726153\pi$
$684$	9.33322e32	2.32748
$685$	2.63874e32	0.647075
$686$	0	0
$687$	4.93921e30	0.0117126
$688$	−2.23501e30	−0.00521209
$689$	−2.52522e31	−0.0579133
$690$	−7.06472e32	−1.59342
$691$	−4.83212e32	−1.07187	−0.535933	−	0.844260i	$-0.680040\pi$
$691$	−4.83212e32	−1.07187	−0.535933	+	0.844260i	$0.680040\pi$
$692$	−3.90404e32	−0.851715
$693$	0	0
$694$	2.36523e32	0.499159
$695$	1.16237e32	0.241280
$696$	1.06827e33	2.18110
$697$	−5.64212e32	−1.13309
$698$	−1.14090e33	−2.25377
$699$	−2.10383e32	−0.408812
$700$	0	0
$701$	7.49198e29	0.00140877	0.000704384	−	1.00000i	$-0.499776\pi$
$701$	7.49198e29	0.00140877	0.000704384		1.00000i	$0.499776\pi$
$702$	−2.28614e33	−4.22889
$703$	−3.62081e32	−0.658900
$704$	−1.53897e33	−2.75515
$705$	−4.76424e32	−0.839110
$706$	1.35461e33	2.34725
$707$	0	0
$708$	−3.36719e32	−0.564788
$709$	6.25812e32	1.03279	0.516395	−	0.856351i	$-0.327274\pi$
$709$	6.25812e32	1.03279	0.516395	+	0.856351i	$0.327274\pi$
$710$	−6.63100e32	−1.07673
$711$	1.18697e33	1.89644
$712$	6.70649e32	1.05433
$713$	8.53854e32	1.32085
$714$	0	0
$715$	7.08828e32	1.06175
$716$	−2.80349e32	−0.413237
$717$	9.48639e32	1.37604
$718$	−5.40353e32	−0.771341
$719$	7.22330e32	1.01474	0.507368	−	0.861729i	$-0.330618\pi$
$719$	7.22330e32	1.01474	0.507368	+	0.861729i	$0.330618\pi$
$720$	5.35798e30	0.00740759
$721$	0	0
$722$	−5.93621e32	−0.794934
$723$	5.18521e32	0.683402
$724$	−1.69485e33	−2.19856
$725$	−8.11564e32	−1.03618
$726$	4.23703e33	5.32464
$727$	−2.49972e32	−0.309205	−0.154602	−	0.987977i	$-0.549410\pi$
$727$	−2.49972e32	−0.309205	−0.154602	+	0.987977i	$0.549410\pi$
$728$	0	0
$729$	−7.76702e32	−0.930867
$730$	7.00082e32	0.825916
$731$	4.59269e32	0.533356
$732$	1.76918e32	0.202253
$733$	1.18563e33	1.33430	0.667150	−	0.744923i	$-0.267514\pi$
$733$	1.18563e33	1.33430	0.667150	+	0.744923i	$0.267514\pi$
$734$	−4.66716e32	−0.517068
$735$	0	0
$736$	−1.25351e33	−1.34596
$737$	1.16270e32	0.122911
$738$	−4.02804e33	−4.19224
$739$	7.64811e32	0.783688	0.391844	−	0.920032i	$-0.371837\pi$
$739$	7.64811e32	0.783688	0.391844	+	0.920032i	$0.371837\pi$
$740$	6.27087e32	0.632650
$741$	−1.83627e33	−1.82401
$742$	0	0
$743$	−6.08157e31	−0.0585658	−0.0292829	−	0.999571i	$-0.509322\pi$
$743$	−6.08157e31	−0.0585658	−0.0292829	+	0.999571i	$0.509322\pi$
$744$	1.79908e33	1.70594
$745$	8.28589e31	0.0773645
$746$	5.75270e32	0.528902
$747$	−2.78031e33	−2.51713
$748$	2.72230e33	2.42699
$749$	0	0
$750$	2.50970e33	2.16979
$751$	−9.65039e32	−0.821647	−0.410824	−	0.911715i	$-0.634759\pi$
$751$	−9.65039e32	−0.821647	−0.410824	+	0.911715i	$0.634759\pi$
$752$	−1.17225e31	−0.00982911
$753$	−1.60171e33	−1.32264
$754$	−3.69627e33	−3.00603
$755$	−2.98069e32	−0.238741
$756$	0	0
$757$	−2.00751e33	−1.55975	−0.779874	−	0.625936i	$-0.784717\pi$
$757$	−2.00751e33	−1.55975	−0.779874	+	0.625936i	$0.784717\pi$
$758$	2.92233e33	2.23632
$759$	5.24498e33	3.95333
$760$	−4.04444e32	−0.300263
$761$	2.00839e33	1.46867	0.734334	−	0.678788i	$-0.237494\pi$
$761$	2.00839e33	1.46867	0.734334	+	0.678788i	$0.237494\pi$
$762$	−2.11054e33	−1.52024
$763$	0	0
$764$	7.26595e32	0.507830
$765$	−1.10100e33	−0.758023
$766$	−2.35395e33	−1.59649
$767$	4.43289e32	0.296169
$768$	−2.60434e33	−1.71413
$769$	2.70345e33	1.75293	0.876467	−	0.481463i	$-0.159894\pi$
$769$	2.70345e33	1.75293	0.876467	+	0.481463i	$0.159894\pi$
$770$	0	0
$771$	−1.24213e32	−0.0781703
$772$	4.03081e33	2.49916
$773$	1.92398e33	1.17527	0.587633	−	0.809128i	$-0.300060\pi$
$773$	1.92398e33	1.17527	0.587633	+	0.809128i	$0.300060\pi$
$774$	3.27883e33	1.97332
$775$	−1.36676e33	−0.810444
$776$	−1.49996e33	−0.876332
$777$	0	0
$778$	3.41314e32	0.193593
$779$	−1.63560e33	−0.914103
$780$	3.18023e33	1.75134
$781$	4.92298e33	2.67141
$782$	3.57198e33	1.90999
$783$	4.26181e33	2.24561
$784$	0	0
$785$	1.22829e33	0.628492
$786$	−8.25219e33	−4.16112
$787$	3.91253e32	0.194423	0.0972116	−	0.995264i	$-0.469008\pi$
$787$	3.91253e32	0.194423	0.0972116	+	0.995264i	$0.469008\pi$
$788$	−1.69074e33	−0.827991
$789$	−5.91926e33	−2.85681
$790$	−1.35185e33	−0.643008
$791$	0	0
$792$	7.39477e33	3.41653
$793$	−2.32911e32	−0.106059
$794$	−3.86574e33	−1.73499
$795$	−6.55951e31	−0.0290168
$796$	2.09037e32	0.0911429
$797$	2.49718e33	1.07320	0.536598	−	0.843838i	$-0.319709\pi$
$797$	2.49718e33	1.07320	0.536598	+	0.843838i	$0.319709\pi$
$798$	0	0
$799$	2.40884e33	1.00582
$800$	2.00649e33	0.825851
$801$	5.29248e33	2.14726
$802$	4.38427e33	1.75345
$803$	−5.19753e33	−2.04912
$804$	5.21658e32	0.202741
$805$	0	0
$806$	−6.22491e33	−2.35115
$807$	4.50157e33	1.67617
$808$	−1.17076e33	−0.429771
$809$	2.05732e33	0.744552	0.372276	−	0.928122i	$-0.378578\pi$
$809$	2.05732e33	0.744552	0.372276	+	0.928122i	$0.378578\pi$
$810$	−2.05179e33	−0.732076
$811$	−1.59034e33	−0.559437	−0.279718	−	0.960082i	$-0.590241\pi$
$811$	−1.59034e33	−0.559437	−0.279718	+	0.960082i	$0.590241\pi$
$812$	0	0
$813$	8.91499e32	0.304845
$814$	−7.53983e33	−2.54203
$815$	4.56881e32	0.151877
$816$	−4.04857e31	−0.0132698
$817$	1.33137e33	0.430275
$818$	−4.25873e33	−1.35712
$819$	0	0
$820$	2.83268e33	0.877685
$821$	2.23471e33	0.682771	0.341385	−	0.939923i	$-0.389104\pi$
$821$	2.23471e33	0.682771	0.341385	+	0.939923i	$0.389104\pi$
$822$	−1.42347e34	−4.28866
$823$	−5.67980e33	−1.68747	−0.843733	−	0.536764i	$-0.819647\pi$
$823$	−5.67980e33	−1.68747	−0.843733	+	0.536764i	$0.819647\pi$
$824$	1.36335e33	0.399434
$825$	−8.39561e33	−2.42567
$826$	0	0
$827$	−3.34983e33	−0.941259	−0.470630	−	0.882331i	$-0.655973\pi$
$827$	−3.34983e33	−0.941259	−0.470630	+	0.882331i	$0.655973\pi$
$828$	1.57462e34	4.36341
$829$	2.54623e33	0.695858	0.347929	−	0.937521i	$-0.386885\pi$
$829$	2.54623e33	0.695858	0.347929	+	0.937521i	$0.386885\pi$
$830$	3.16652e33	0.853462
$831$	7.11250e33	1.89065
$832$	9.09007e33	2.38314
$833$	0	0
$834$	−6.27044e33	−1.59915
$835$	1.42237e33	0.357781
$836$	7.89168e33	1.95793
$837$	7.17734e33	1.75639
$838$	−3.31328e33	−0.799745
$839$	−4.29761e33	−1.02321	−0.511604	−	0.859221i	$-0.670949\pi$
$839$	−4.29761e33	−1.02321	−0.511604	+	0.859221i	$0.670949\pi$
$840$	0	0
$841$	2.57383e33	0.596247
$842$	−7.79044e33	−1.78022
$843$	−1.06034e34	−2.39017
$844$	1.15104e34	2.55949
$845$	−2.25334e33	−0.494282
$846$	1.71972e34	3.72134
$847$	0	0
$848$	−1.61398e30	−0.000339895 0
$849$	−2.83811e33	−0.589646
$850$	−5.71765e33	−1.17192
$851$	−6.10870e33	−1.23526
$852$	2.20875e34	4.40647
$853$	5.85716e33	1.15285	0.576426	−	0.817150i	$-0.304447\pi$
$853$	5.85716e33	1.15285	0.576426	+	0.817150i	$0.304447\pi$
$854$	0	0
$855$	−3.19170e33	−0.611521
$856$	1.78179e33	0.336828
$857$	7.54719e33	1.40769	0.703843	−	0.710355i	$-0.251466\pi$
$857$	7.54719e33	1.40769	0.703843	+	0.710355i	$0.251466\pi$
$858$	−3.82378e34	−7.03702
$859$	−2.46676e33	−0.447926	−0.223963	−	0.974598i	$-0.571899\pi$
$859$	−2.46676e33	−0.447926	−0.223963	+	0.974598i	$0.571899\pi$
$860$	−2.30581e33	−0.413133
$861$	0	0
$862$	1.76957e34	3.08699
$863$	1.06233e33	0.182867	0.0914334	−	0.995811i	$-0.470855\pi$
$863$	1.06233e33	0.182867	0.0914334	+	0.995811i	$0.470855\pi$
$864$	−1.05368e34	−1.78978
$865$	1.33507e33	0.223779
$866$	1.15043e34	1.90285
$867$	−2.33173e33	−0.380592
$868$	0	0
$869$	1.00364e34	1.59532
$870$	−9.60141e33	−1.50613
$871$	−6.86759e32	−0.106315
$872$	2.82714e33	0.431925
$873$	−1.18370e34	−1.78475
$874$	1.03548e34	1.54085
$875$	0	0
$876$	−2.33193e34	−3.38001
$877$	−2.49039e33	−0.356264	−0.178132	−	0.984007i	$-0.557005\pi$
$877$	−2.49039e33	−0.356264	−0.178132	+	0.984007i	$0.557005\pi$
$878$	9.89325e33	1.39686
$879$	−1.91904e34	−2.67431
$880$	4.53042e31	0.00623143
$881$	5.81218e33	0.789071	0.394536	−	0.918881i	$-0.370906\pi$
$881$	5.81218e33	0.789071	0.394536	+	0.918881i	$0.370906\pi$
$882$	0	0
$883$	−7.58884e32	−0.100375	−0.0501877	−	0.998740i	$-0.515982\pi$
$883$	−7.58884e32	−0.100375	−0.0501877	+	0.998740i	$0.515982\pi$
$884$	−1.60795e34	−2.09929
$885$	1.15149e33	0.148392
$886$	2.31466e34	2.94442
$887$	−7.96331e33	−0.999936	−0.499968	−	0.866044i	$-0.666655\pi$
$887$	−7.96331e33	−0.999936	−0.499968	+	0.866044i	$0.666655\pi$
$888$	−1.28711e34	−1.59539
$889$	0	0
$890$	−6.02766e33	−0.728054
$891$	1.52329e34	1.81631
$892$	5.33534e33	0.628009
$893$	6.98297e33	0.811426
$894$	−4.46983e33	−0.512754
$895$	9.58714e32	0.108574
$896$	0	0
$897$	−3.09799e34	−3.41954
$898$	−1.85740e34	−2.02408
$899$	1.16044e34	1.24850
$900$	−2.52048e34	−2.67729
$901$	3.31654e32	0.0347816
$902$	−3.40590e34	−3.52660
$903$	0	0
$904$	−1.19375e34	−1.20497
$905$	5.79592e33	0.577649
$906$	1.60794e34	1.58232
$907$	1.04093e34	1.01143	0.505716	−	0.862700i	$-0.331228\pi$
$907$	1.04093e34	1.01143	0.505716	+	0.862700i	$0.331228\pi$
$908$	−8.84456e33	−0.848572
$909$	−9.23915e33	−0.875281
$910$	0	0
$911$	9.22536e33	0.852162	0.426081	−	0.904685i	$-0.359894\pi$
$911$	9.22536e33	0.852162	0.426081	+	0.904685i	$0.359894\pi$
$912$	−1.17364e32	−0.0107052
$913$	−2.35088e34	−2.11747
$914$	1.04318e34	0.927853
$915$	−6.05010e32	−0.0531398
$916$	1.25380e32	0.0108750
$917$	0	0
$918$	3.00254e34	2.53979
$919$	3.37058e33	0.281564	0.140782	−	0.990041i	$-0.455038\pi$
$919$	3.37058e33	0.281564	0.140782	+	0.990041i	$0.455038\pi$
$920$	−6.82341e33	−0.562913
$921$	3.44908e34	2.81007
$922$	2.90231e34	2.33527
$923$	−2.90780e34	−2.31071
$924$	0	0
$925$	9.77817e33	0.757928
$926$	7.77851e33	0.595484
$927$	1.07590e34	0.813495
$928$	−1.70360e34	−1.27223
$929$	1.35687e34	1.00082	0.500411	−	0.865788i	$-0.333182\pi$
$929$	1.35687e34	1.00082	0.500411	+	0.865788i	$0.333182\pi$
$930$	−1.61698e34	−1.17802
$931$	0	0
$932$	−5.34049e33	−0.379575
$933$	2.23191e34	1.56689
$934$	−1.85854e34	−1.28879
$935$	−9.30950e33	−0.637666
$936$	−4.36779e34	−2.95521
$937$	1.03905e34	0.694437	0.347218	−	0.937784i	$-0.387126\pi$
$937$	1.03905e34	0.694437	0.347218	+	0.937784i	$0.387126\pi$
$938$	0	0
$939$	−8.28341e32	−0.0540200
$940$	−1.20938e34	−0.779099
$941$	1.35623e34	0.863084	0.431542	−	0.902093i	$-0.357970\pi$
$941$	1.35623e34	0.863084	0.431542	+	0.902093i	$0.357970\pi$
$942$	−6.62602e34	−4.16550
$943$	−2.75943e34	−1.71370
$944$	2.83325e31	0.00173823
$945$	0	0
$946$	2.77240e34	1.66000
$947$	−1.14790e34	−0.679018	−0.339509	−	0.940603i	$-0.610261\pi$
$947$	−1.14790e34	−0.679018	−0.339509	+	0.940603i	$0.610261\pi$
$948$	4.50293e34	2.63147
$949$	3.06997e34	1.77244
$950$	−1.65749e34	−0.945429
$951$	−2.42264e34	−1.36525
$952$	0	0
$953$	−1.90549e34	−1.04819	−0.524093	−	0.851661i	$-0.675596\pi$
$953$	−1.90549e34	−1.04819	−0.524093	+	0.851661i	$0.675596\pi$
$954$	2.36775e33	0.128686
$955$	−2.48475e33	−0.133427
$956$	2.40808e34	1.27763
$957$	7.12826e34	3.73677
$958$	3.46289e34	1.79364
$959$	0	0
$960$	2.36123e34	1.19404
$961$	−4.70207e32	−0.0234947
$962$	4.45347e34	2.19880
$963$	1.40611e34	0.685990
$964$	1.31624e34	0.634527
$965$	−1.37842e34	−0.656626
$966$	0	0
$967$	2.28305e34	1.06197	0.530983	−	0.847383i	$-0.321823\pi$
$967$	2.28305e34	1.06197	0.530983	+	0.847383i	$0.321823\pi$
$968$	4.09230e34	1.88105
$969$	2.41170e34	1.09547
$970$	1.34813e34	0.605141
$971$	3.42378e34	1.51874	0.759372	−	0.650657i	$-0.225506\pi$
$971$	3.42378e34	1.51874	0.759372	+	0.650657i	$0.225506\pi$
$972$	2.89649e33	0.126973
$973$	0	0
$974$	−5.26614e34	−2.25457
$975$	4.95894e34	2.09815
$976$	−1.48864e31	−0.000622466 0
$977$	−1.00426e34	−0.415009	−0.207504	−	0.978234i	$-0.566534\pi$
$977$	−1.00426e34	−0.415009	−0.207504	+	0.978234i	$0.566534\pi$
$978$	−2.46465e34	−1.00660
$979$	4.47504e34	1.80633
$980$	0	0
$981$	2.23106e34	0.879667
$982$	1.38427e34	0.539433
$983$	−1.06593e34	−0.410547	−0.205274	−	0.978705i	$-0.565808\pi$
$983$	−1.06593e34	−0.410547	−0.205274	+	0.978705i	$0.565808\pi$
$984$	−5.81416e34	−2.21332
$985$	5.78186e33	0.217546
$986$	4.85455e34	1.80536
$987$	0	0
$988$	−4.66129e34	−1.69356
$989$	2.24618e34	0.806652
$990$	−6.64627e34	−2.35924
$991$	2.52628e34	0.886409	0.443204	−	0.896421i	$-0.353842\pi$
$991$	2.52628e34	0.886409	0.443204	+	0.896421i	$0.353842\pi$
$992$	−2.86905e34	−0.995070
$993$	−4.52753e34	−1.55219
$994$	0	0
$995$	−7.14847e32	−0.0239468
$996$	−1.05475e35	−3.49274
$997$	−7.03487e33	−0.230283	−0.115141	−	0.993349i	$-0.536732\pi$
$997$	−7.03487e33	−0.230283	−0.115141	+	0.993349i	$0.536732\pi$
$998$	−4.68688e34	−1.51664
$999$	−5.13486e34	−1.64258

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.24.a.h.1.22	yes	24
7.6	odd	2	inner	49.24.a.h.1.21	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.24.a.h.1.21	✓	24	7.6	odd	2	inner
49.24.a.h.1.22	yes	24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	49.a (trivial)

\(f(q)\)	\(=\)	\(q+4682.86 q^{2} +533419. q^{3} +1.35406e7 q^{4} -4.63050e7 q^{5} +2.49793e9 q^{6} +2.41261e10 q^{8} +1.90393e11 q^{9} -2.16840e11 q^{10} +1.60986e12 q^{11} +7.22281e12 q^{12} -9.50878e12 q^{13} -2.47000e13 q^{15} -6.07746e11 q^{16} +1.24885e14 q^{17} +8.91583e14 q^{18} +3.62029e14 q^{19} -6.26998e14 q^{20} +7.53875e15 q^{22} +6.10783e15 q^{23} +1.28693e16 q^{24} -9.77677e15 q^{25} -4.45283e16 q^{26} +5.13413e16 q^{27} +8.30094e16 q^{29} -1.15667e17 q^{30} +1.39797e17 q^{31} -2.05230e17 q^{32} +8.58730e17 q^{33} +5.84819e17 q^{34} +2.57803e18 q^{36} -1.00014e18 q^{37} +1.69533e18 q^{38} -5.07216e18 q^{39} -1.11716e18 q^{40} -4.51785e18 q^{41} +3.67753e18 q^{43} +2.17985e19 q^{44} -8.81614e18 q^{45} +2.86021e19 q^{46} +1.92884e19 q^{47} -3.24184e17 q^{48} -4.57833e19 q^{50} +6.66160e19 q^{51} -1.28755e20 q^{52} +2.65567e18 q^{53} +2.40424e20 q^{54} -7.45446e19 q^{55} +1.93113e20 q^{57} +3.88721e20 q^{58} -4.66189e19 q^{59} -3.34452e20 q^{60} +2.44943e19 q^{61} +6.54649e20 q^{62} -9.55966e20 q^{64} +4.40304e20 q^{65} +4.02131e21 q^{66} +7.22237e19 q^{67} +1.69102e21 q^{68} +3.25803e21 q^{69} +3.05802e21 q^{71} +4.59342e21 q^{72} -3.22856e21 q^{73} -4.68353e21 q^{74} -5.21512e21 q^{75} +4.90209e21 q^{76} -2.37522e22 q^{78} +6.23431e21 q^{79} +2.81417e19 q^{80} +9.46225e21 q^{81} -2.11565e22 q^{82} -1.46030e22 q^{83} -5.78280e21 q^{85} +1.72214e22 q^{86} +4.42788e22 q^{87} +3.88396e22 q^{88} +2.77977e22 q^{89} -4.12848e22 q^{90} +8.27037e22 q^{92} +7.45702e22 q^{93} +9.03251e22 q^{94} -1.67638e22 q^{95} -1.09474e23 q^{96} -6.21716e22 q^{97} +3.06505e23 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6030 q^{2} + 99000906 q^{4} + 31751706690 q^{8} + 975236583640 q^{9} + 3514223137536 q^{11} + 96662500006976 q^{15} + 850136746459362 q^{16} - 774764811988990 q^{18} + 81\!\cdots\!60 q^{22} + 34\!\cdots\!60 q^{23}+ \cdots + 70\!\cdots\!64 q^{99}+O(q^{100}) \) 24 * q + 6030 * q^2 + 99000906 * q^4 + 31751706690 * q^8 + 975236583640 * q^9 + 3514223137536 * q^11 + 96662500006976 * q^15 + 850136746459362 * q^16 - 774764811988990 * q^18 + 8148420455553060 * q^22 + 34774948016084160 * q^23 + 94149150991117272 * q^25 + 190645622093096064 * q^29 - 634449556982285592 * q^30 - 1493697165631220430 * q^32 + 6671026323612877990 * q^36 + 878462893450581120 * q^37 + 6115839814038109120 * q^39 + 20811373010373199680 * q^43 + 54730049479951369500 * q^44 + 73203364608168908808 * q^46 + 387333163519636443066 * q^50 + 270153244272168521696 * q^51 + 34330885176487486320 * q^53 + 496656755807681949600 * q^57 - 397574761992930674580 * q^58 + 292003879381856022136 * q^60 + 2439494576203335787554 * q^64 + 4869166958052334391664 * q^65 - 1121753136531158010720 * q^67 - 1755055962268130457216 * q^71 - 32377694763810926605650 * q^72 + 1005354247436267388732 * q^74 - 79646865826469682676320 * q^78 + 5008005983294871013824 * q^79 + 21826965675021517050808 * q^81 + 20177850245757616713456 * q^85 + 38898565641929075253660 * q^86 - 21751191568485361565940 * q^88 + 247141757180010545124120 * q^92 + 241670386431567345282560 * q^93 + 278606632818920869216512 * q^95 + 708951281314482353318464 * q^99

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