LMFDB - Embedded newform 49.24.a.h.1.9

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			1.9
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)

$f(q)$	$=$	\(q-867.700 q^{2} -393094. q^{3} -7.63570e6 q^{4} +1.46240e8 q^{5} +3.41087e8 q^{6} +1.39043e10 q^{8} +6.03794e10 q^{9} -1.26893e11 q^{10} -1.21063e12 q^{11} +3.00155e12 q^{12} +9.16798e12 q^{13} -5.74862e13 q^{15} +5.19882e13 q^{16} +5.25523e13 q^{17} -5.23912e13 q^{18} +8.24698e14 q^{19} -1.11665e15 q^{20} +1.05046e15 q^{22} +2.00869e15 q^{23} -5.46569e15 q^{24} +9.46533e15 q^{25} -7.95505e15 q^{26} +1.32723e16 q^{27} +1.28495e16 q^{29} +4.98808e16 q^{30} +2.57650e17 q^{31} -1.61748e17 q^{32} +4.75890e17 q^{33} -4.55996e16 q^{34} -4.61039e17 q^{36} +5.69048e16 q^{37} -7.15591e17 q^{38} -3.60387e18 q^{39} +2.03337e18 q^{40} +4.76879e17 q^{41} -7.55870e17 q^{43} +9.24399e18 q^{44} +8.82991e18 q^{45} -1.74294e18 q^{46} +2.74664e19 q^{47} -2.04362e19 q^{48} -8.21307e18 q^{50} -2.06580e19 q^{51} -7.00039e19 q^{52} -9.15779e19 q^{53} -1.15164e19 q^{54} -1.77043e20 q^{55} -3.24184e20 q^{57} -1.11495e19 q^{58} -7.57316e19 q^{59} +4.38947e20 q^{60} -5.95345e20 q^{61} -2.23563e20 q^{62} -2.95760e20 q^{64} +1.34073e21 q^{65} -4.12930e20 q^{66} -1.28180e21 q^{67} -4.01274e20 q^{68} -7.89602e20 q^{69} -6.22375e20 q^{71} +8.39534e20 q^{72} +1.49176e21 q^{73} -4.93763e19 q^{74} -3.72076e21 q^{75} -6.29715e21 q^{76} +3.12708e21 q^{78} +1.10354e22 q^{79} +7.60277e21 q^{80} -1.09016e22 q^{81} -4.13788e20 q^{82} +1.30716e22 q^{83} +7.68527e21 q^{85} +6.55868e20 q^{86} -5.05107e21 q^{87} -1.68329e22 q^{88} -2.41898e21 q^{89} -7.66172e21 q^{90} -1.53377e22 q^{92} -1.01281e23 q^{93} -2.38326e22 q^{94} +1.20604e23 q^{95} +6.35820e22 q^{96} -1.34288e22 q^{97} -7.30970e22 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−867.700	−0.299588	−0.149794	−	0.988717i	$-0.547861\pi$
$2$	−867.700	−0.299588	−0.149794	+	0.988717i	$0.547861\pi$
$3$	−393094.	−1.28115	−0.640577	−	0.767894i	$-0.721305\pi$
$3$	−393094.	−1.28115	−0.640577	+	0.767894i	$0.721305\pi$
$4$	−7.63570e6	−0.910247
$5$	1.46240e8	1.33941	0.669703	−	0.742629i	$-0.266421\pi$
$5$	1.46240e8	1.33941	0.669703	+	0.742629i	$0.266421\pi$
$6$	3.41087e8	0.383819
$7$	0	0
$7$	0	0
$8$	1.39043e10	0.572287
$9$	6.03794e10	0.641357
$10$	−1.26893e11	−0.401270
$11$	−1.21063e12	−1.27937	−0.639683	−	0.768639i	$-0.720934\pi$
$11$	−1.21063e12	−1.27937	−0.639683	+	0.768639i	$0.720934\pi$
$12$	3.00155e12	1.16617
$13$	9.16798e12	1.41881	0.709406	−	0.704800i	$-0.248963\pi$
$13$	9.16798e12	1.41881	0.709406	+	0.704800i	$0.248963\pi$
$14$	0	0
$15$	−5.74862e13	−1.71599
$16$	5.19882e13	0.738796
$17$	5.25523e13	0.371902	0.185951	−	0.982559i	$-0.440463\pi$
$17$	5.25523e13	0.371902	0.185951	+	0.982559i	$0.440463\pi$
$18$	−5.23912e13	−0.192143
$19$	8.24698e14	1.62416	0.812080	−	0.583546i	$-0.198335\pi$
$19$	8.24698e14	1.62416	0.812080	+	0.583546i	$0.198335\pi$
$20$	−1.11665e15	−1.21919
$21$	0	0
$22$	1.05046e15	0.383283
$23$	2.00869e15	0.439584	0.219792	−	0.975547i	$-0.429462\pi$
$23$	2.00869e15	0.439584	0.219792	+	0.975547i	$0.429462\pi$
$24$	−5.46569e15	−0.733189
$25$	9.46533e15	0.794009
$26$	−7.95505e15	−0.425059
$27$	1.32723e16	0.459477
$28$	0	0
$29$	1.28495e16	0.195574	0.0977868	−	0.995207i	$-0.468824\pi$
$29$	1.28495e16	0.195574	0.0977868	+	0.995207i	$0.468824\pi$
$30$	4.98808e16	0.514089
$31$	2.57650e17	1.82126	0.910629	−	0.413226i	$-0.135598\pi$
$31$	2.57650e17	1.82126	0.910629	+	0.413226i	$0.135598\pi$
$32$	−1.61748e17	−0.793622
$33$	4.75890e17	1.63907
$34$	−4.55996e16	−0.111418
$35$	0	0
$36$	−4.61039e17	−0.583794
$37$	5.69048e16	0.0525810	0.0262905	−	0.999654i	$-0.491631\pi$
$37$	5.69048e16	0.0525810	0.0262905	+	0.999654i	$0.491631\pi$
$38$	−7.15591e17	−0.486579
$39$	−3.60387e18	−1.81772
$40$	2.03337e18	0.766525
$41$	4.76879e17	0.135330	0.0676649	−	0.997708i	$-0.478445\pi$
$41$	4.76879e17	0.135330	0.0676649	+	0.997708i	$0.478445\pi$
$42$	0	0
$43$	−7.55870e17	−0.124039	−0.0620197	−	0.998075i	$-0.519754\pi$
$43$	−7.55870e17	−0.124039	−0.0620197	+	0.998075i	$0.519754\pi$
$44$	9.24399e18	1.16454
$45$	8.82991e18	0.859038
$46$	−1.74294e18	−0.131694
$47$	2.74664e19	1.62060	0.810301	−	0.586014i	$-0.199304\pi$
$47$	2.74664e19	1.62060	0.810301	+	0.586014i	$0.199304\pi$
$48$	−2.04362e19	−0.946512
$49$	0	0
$50$	−8.21307e18	−0.237876
$51$	−2.06580e19	−0.476465
$52$	−7.00039e19	−1.29147
$53$	−9.15779e19	−1.35712	−0.678560	−	0.734545i	$-0.737396\pi$
$53$	−9.15779e19	−1.35712	−0.678560	+	0.734545i	$0.737396\pi$
$54$	−1.15164e19	−0.137654
$55$	−1.77043e20	−1.71359
$56$	0	0
$57$	−3.24184e20	−2.08080
$58$	−1.11495e19	−0.0585916
$59$	−7.57316e19	−0.326948	−0.163474	−	0.986548i	$-0.552270\pi$
$59$	−7.57316e19	−0.326948	−0.163474	+	0.986548i	$0.552270\pi$
$60$	4.38947e20	1.56197
$61$	−5.95345e20	−1.75177	−0.875883	−	0.482524i	$-0.839720\pi$
$61$	−5.95345e20	−1.75177	−0.875883	+	0.482524i	$0.839720\pi$
$62$	−2.23563e20	−0.545627
$63$	0	0
$64$	−2.95760e20	−0.501037
$65$	1.34073e21	1.90037
$66$	−4.12930e20	−0.491045
$67$	−1.28180e21	−1.28221	−0.641107	−	0.767452i	$-0.721524\pi$
$67$	−1.28180e21	−1.28221	−0.641107	+	0.767452i	$0.721524\pi$
$68$	−4.01274e20	−0.338523
$69$	−7.89602e20	−0.563175
$70$	0	0
$71$	−6.22375e20	−0.319581	−0.159791	−	0.987151i	$-0.551082\pi$
$71$	−6.22375e20	−0.319581	−0.159791	+	0.987151i	$0.551082\pi$
$72$	8.39534e20	0.367041
$73$	1.49176e21	0.556526	0.278263	−	0.960505i	$-0.410241\pi$
$73$	1.49176e21	0.556526	0.278263	+	0.960505i	$0.410241\pi$
$74$	−4.93763e19	−0.0157526
$75$	−3.72076e21	−1.01725
$76$	−6.29715e21	−1.47839
$77$	0	0
$78$	3.12708e21	0.544567
$79$	1.10354e22	1.65989	0.829943	−	0.557848i	$-0.188373\pi$
$79$	1.10354e22	1.65989	0.829943	+	0.557848i	$0.188373\pi$
$80$	7.60277e21	0.989548
$81$	−1.09016e22	−1.23002
$82$	−4.13788e20	−0.0405432
$83$	1.30716e22	1.11411	0.557057	−	0.830474i	$-0.311931\pi$
$83$	1.30716e22	1.11411	0.557057	+	0.830474i	$0.311931\pi$
$84$	0	0
$85$	7.68527e21	0.498128
$86$	6.55868e20	0.0371608
$87$	−5.05107e21	−0.250560
$88$	−1.68329e22	−0.732165
$89$	−2.41898e21	−0.0923948	−0.0461974	−	0.998932i	$-0.514710\pi$
$89$	−2.41898e21	−0.0923948	−0.0461974	+	0.998932i	$0.514710\pi$
$90$	−7.66172e21	−0.257358
$91$	0	0
$92$	−1.53377e22	−0.400130
$93$	−1.01281e23	−2.33331
$94$	−2.38326e22	−0.485513
$95$	1.20604e23	2.17541
$96$	6.35820e22	1.01675
$97$	−1.34288e22	−0.190617	−0.0953083	−	0.995448i	$-0.530384\pi$
$97$	−1.34288e22	−0.190617	−0.0953083	+	0.995448i	$0.530384\pi$
$98$	0	0
$99$	−7.30970e22	−0.820531
$100$	−7.22744e22	−0.722744
$101$	1.37860e23	1.22954	0.614768	−	0.788708i	$-0.289249\pi$
$101$	1.37860e23	1.22954	0.614768	+	0.788708i	$0.289249\pi$
$102$	1.79249e22	0.142743
$103$	−6.85655e22	−0.488065	−0.244032	−	0.969767i	$-0.578470\pi$
$103$	−6.85655e22	−0.488065	−0.244032	+	0.969767i	$0.578470\pi$
$104$	1.27474e23	0.811968
$105$	0	0
$106$	7.94622e22	0.406577
$107$	−3.19316e23	−1.46658	−0.733291	−	0.679914i	$-0.762017\pi$
$107$	−3.19316e23	−1.46658	−0.733291	+	0.679914i	$0.762017\pi$
$108$	−1.01343e23	−0.418237
$109$	−1.90338e23	−0.706512	−0.353256	−	0.935527i	$-0.614926\pi$
$109$	−1.90338e23	−0.706512	−0.353256	+	0.935527i	$0.614926\pi$
$110$	1.53620e23	0.513371
$111$	−2.23689e22	−0.0673644
$112$	0	0
$113$	6.33182e23	1.55284	0.776419	−	0.630217i	$-0.217034\pi$
$113$	6.33182e23	1.55284	0.776419	+	0.630217i	$0.217034\pi$
$114$	2.81294e23	0.623383
$115$	2.93751e23	0.588782
$116$	−9.81152e22	−0.178020
$117$	5.53557e23	0.909966
$118$	6.57123e22	0.0979498
$119$	0	0
$120$	−7.99305e23	−0.982038
$121$	5.70189e23	0.636777
$122$	5.16581e23	0.524808
$123$	−1.87458e23	−0.173378
$124$	−1.96734e24	−1.65779
$125$	−3.59108e23	−0.275905
$126$	0	0
$127$	8.64318e23	0.553262	0.276631	−	0.960976i	$-0.410782\pi$
$127$	8.64318e23	0.553262	0.276631	+	0.960976i	$0.410782\pi$
$128$	1.61347e24	0.943727
$129$	2.97128e23	0.158914
$130$	−1.16335e24	−0.569327
$131$	−1.22003e24	−0.546702	−0.273351	−	0.961914i	$-0.588132\pi$
$131$	−1.22003e24	−0.546702	−0.273351	+	0.961914i	$0.588132\pi$
$132$	−3.63376e24	−1.49195
$133$	0	0
$134$	1.11222e24	0.384136
$135$	1.94095e24	0.615426
$136$	7.30703e23	0.212835
$137$	5.66613e24	1.51705	0.758526	−	0.651643i	$-0.225920\pi$
$137$	5.66613e24	1.51705	0.758526	+	0.651643i	$0.225920\pi$
$138$	6.85138e23	0.168721
$139$	−2.68692e24	−0.608955	−0.304478	−	0.952520i	$-0.598482\pi$
$139$	−2.68692e24	−0.608955	−0.304478	+	0.952520i	$0.598482\pi$
$140$	0	0
$141$	−1.07969e25	−2.07624
$142$	5.40035e23	0.0957427
$143$	−1.10990e25	−1.81518
$144$	3.13902e24	0.473833
$145$	1.87912e24	0.261953
$146$	−1.29440e24	−0.166729
$147$	0	0
$148$	−4.34508e23	−0.0478617
$149$	−1.36100e25	−1.38744	−0.693721	−	0.720244i	$-0.744030\pi$
$149$	−1.36100e25	−1.38744	−0.693721	+	0.720244i	$0.744030\pi$
$150$	3.22850e24	0.304756
$151$	−2.80397e23	−0.0245210	−0.0122605	−	0.999925i	$-0.503903\pi$
$151$	−2.80397e23	−0.0245210	−0.0122605	+	0.999925i	$0.503903\pi$
$152$	1.14669e25	0.929486
$153$	3.17308e24	0.238522
$154$	0	0
$155$	3.76789e25	2.43940
$156$	2.75181e25	1.65457
$157$	2.62673e25	1.46747	0.733736	−	0.679434i	$-0.237775\pi$
$157$	2.62673e25	1.46747	0.733736	+	0.679434i	$0.237775\pi$
$158$	−9.57546e24	−0.497282
$159$	3.59987e25	1.73868
$160$	−2.36541e25	−1.06298
$161$	0	0
$162$	9.45930e24	0.368499
$163$	−3.07548e25	−1.11623	−0.558117	−	0.829762i	$-0.688476\pi$
$163$	−3.07548e25	−1.11623	−0.558117	+	0.829762i	$0.688476\pi$
$164$	−3.64130e24	−0.123184
$165$	6.95943e25	2.19537
$166$	−1.13422e25	−0.333775
$167$	3.67525e25	1.00936	0.504681	−	0.863306i	$-0.331610\pi$
$167$	3.67525e25	1.00936	0.504681	+	0.863306i	$0.331610\pi$
$168$	0	0
$169$	4.22979e25	1.01303
$170$	−6.66851e24	−0.149233
$171$	4.97948e25	1.04167
$172$	5.77160e24	0.112907
$173$	3.92730e25	0.718728	0.359364	−	0.933198i	$-0.382994\pi$
$173$	3.92730e25	0.718728	0.359364	+	0.933198i	$0.382994\pi$
$174$	4.38281e24	0.0750649
$175$	0	0
$176$	−6.29383e25	−0.945191
$177$	2.97696e25	0.418871
$178$	2.09895e24	0.0276804
$179$	1.23200e26	1.52335	0.761675	−	0.647959i	$-0.224377\pi$
$179$	1.23200e26	1.52335	0.761675	+	0.647959i	$0.224377\pi$
$180$	−6.74226e25	−0.781937
$181$	−1.48781e26	−1.61899	−0.809497	−	0.587124i	$-0.800260\pi$
$181$	−1.48781e26	−1.61899	−0.809497	+	0.587124i	$0.800260\pi$
$182$	0	0
$183$	2.34027e26	2.24428
$184$	2.79294e25	0.251568
$185$	8.32178e24	0.0704273
$186$	8.78813e25	0.699033
$187$	−6.36212e25	−0.475799
$188$	−2.09725e26	−1.47515
$189$	0	0
$190$	−1.04648e26	−0.651727
$191$	4.80899e25	0.281949	0.140975	−	0.990013i	$-0.454976\pi$
$191$	4.80899e25	0.281949	0.140975	+	0.990013i	$0.454976\pi$
$192$	1.16261e26	0.641905
$193$	−2.43566e25	−0.126680	−0.0633399	−	0.997992i	$-0.520175\pi$
$193$	−2.43566e25	−0.126680	−0.0633399	+	0.997992i	$0.520175\pi$
$194$	1.16521e25	0.0571065
$195$	−5.27032e26	−2.43466
$196$	0	0
$197$	−2.46808e26	−1.01390	−0.506952	−	0.861974i	$-0.669228\pi$
$197$	−2.46808e26	−1.01390	−0.506952	+	0.861974i	$0.669228\pi$
$198$	6.34263e25	0.245821
$199$	2.64390e26	0.967018	0.483509	−	0.875339i	$-0.339362\pi$
$199$	2.64390e26	0.967018	0.483509	+	0.875339i	$0.339362\pi$
$200$	1.31609e26	0.454401
$201$	5.03868e26	1.64271
$202$	−1.19621e26	−0.368355
$203$	0	0
$204$	1.57738e26	0.433700
$205$	6.97389e25	0.181262
$206$	5.94943e25	0.146218
$207$	1.21283e26	0.281931
$208$	4.76626e26	1.04821
$209$	−9.98403e26	−2.07789
$210$	0	0
$211$	9.33614e26	1.74148	0.870741	−	0.491741i	$-0.163639\pi$
$211$	9.33614e26	1.74148	0.870741	+	0.491741i	$0.163639\pi$
$212$	6.99262e26	1.23531
$213$	2.44652e26	0.409433
$214$	2.77070e26	0.439371
$215$	−1.10539e26	−0.166139
$216$	1.84542e26	0.262953
$217$	0	0
$218$	1.65156e26	0.211663
$219$	−5.86400e26	−0.712996
$220$	1.35185e27	1.55979
$221$	4.81798e26	0.527660
$222$	1.94095e25	0.0201816
$223$	7.37824e26	0.728529	0.364264	−	0.931296i	$-0.381320\pi$
$223$	7.37824e26	0.728529	0.364264	+	0.931296i	$0.381320\pi$
$224$	0	0
$225$	5.71511e26	0.509244
$226$	−5.49412e26	−0.465212
$227$	1.43157e26	0.115217	0.0576083	−	0.998339i	$-0.481653\pi$
$227$	1.43157e26	0.115217	0.0576083	+	0.998339i	$0.481653\pi$
$228$	2.47537e27	1.89404
$229$	−4.53788e26	−0.330176	−0.165088	−	0.986279i	$-0.552791\pi$
$229$	−4.53788e26	−0.330176	−0.165088	+	0.986279i	$0.552791\pi$
$230$	−2.54888e26	−0.176392
$231$	0	0
$232$	1.78664e26	0.111924
$233$	−7.65394e26	−0.456344	−0.228172	−	0.973621i	$-0.573275\pi$
$233$	−7.65394e26	−0.456344	−0.228172	+	0.973621i	$0.573275\pi$
$234$	−4.80322e26	−0.272615
$235$	4.01670e27	2.17064
$236$	5.78264e26	0.297604
$237$	−4.33796e27	−2.12657
$238$	0	0
$239$	4.15067e27	1.84732	0.923661	−	0.383210i	$-0.125182\pi$
$239$	4.15067e27	1.84732	0.923661	+	0.383210i	$0.125182\pi$
$240$	−2.98860e27	−1.26776
$241$	−1.72088e27	−0.695911	−0.347955	−	0.937511i	$-0.613124\pi$
$241$	−1.72088e27	−0.695911	−0.347955	+	0.937511i	$0.613124\pi$
$242$	−4.94753e26	−0.190771
$243$	3.03584e27	1.11637
$244$	4.54588e27	1.59454
$245$	0	0
$246$	1.62657e26	0.0519421
$247$	7.56081e27	2.30438
$248$	3.58245e27	1.04228
$249$	−5.13835e27	−1.42735
$250$	3.11598e26	0.0826580
$251$	−8.84045e26	−0.223989	−0.111995	−	0.993709i	$-0.535724\pi$
$251$	−8.84045e26	−0.223989	−0.111995	+	0.993709i	$0.535724\pi$
$252$	0	0
$253$	−2.43177e27	−0.562389
$254$	−7.49969e26	−0.165751
$255$	−3.02103e27	−0.638180
$256$	1.08100e27	0.218307
$257$	−1.59535e27	−0.308052	−0.154026	−	0.988067i	$-0.549224\pi$
$257$	−1.59535e27	−0.308052	−0.154026	+	0.988067i	$0.549224\pi$
$258$	−2.57818e26	−0.0476087
$259$	0	0
$260$	−1.02374e28	−1.72980
$261$	7.75847e26	0.125433
$262$	1.05862e27	0.163785
$263$	−4.74872e27	−0.703211	−0.351606	−	0.936148i	$-0.614364\pi$
$263$	−4.74872e27	−0.703211	−0.351606	+	0.936148i	$0.614364\pi$
$264$	6.61692e27	0.938017
$265$	−1.33924e28	−1.81773
$266$	0	0
$267$	9.50887e26	0.118372
$268$	9.78745e27	1.16713
$269$	−5.15524e27	−0.588976	−0.294488	−	0.955655i	$-0.595149\pi$
$269$	−5.15524e27	−0.588976	−0.294488	+	0.955655i	$0.595149\pi$
$270$	−1.68416e27	−0.184374
$271$	−7.03660e27	−0.738271	−0.369135	−	0.929376i	$-0.620346\pi$
$271$	−7.03660e27	−0.738271	−0.369135	+	0.929376i	$0.620346\pi$
$272$	2.73210e27	0.274760
$273$	0	0
$274$	−4.91651e27	−0.454491
$275$	−1.14590e28	−1.01583
$276$	6.02917e27	0.512629
$277$	−1.48551e28	−1.21160	−0.605800	−	0.795617i	$-0.707147\pi$
$277$	−1.48551e28	−1.21160	−0.605800	+	0.795617i	$0.707147\pi$
$278$	2.33144e27	0.182436
$279$	1.55568e28	1.16808
$280$	0	0
$281$	8.52564e27	0.589664	0.294832	−	0.955549i	$-0.404736\pi$
$281$	8.52564e27	0.589664	0.294832	+	0.955549i	$0.404736\pi$
$282$	9.36844e27	0.622017
$283$	−1.77120e28	−1.12908	−0.564538	−	0.825407i	$-0.690946\pi$
$283$	−1.77120e28	−1.12908	−0.564538	+	0.825407i	$0.690946\pi$
$284$	4.75227e27	0.290898
$285$	−4.74088e28	−2.78704
$286$	9.63061e27	0.543806
$287$	0	0
$288$	−9.76624e27	−0.508995
$289$	−1.72058e28	−0.861689
$290$	−1.63051e27	−0.0784779
$291$	5.27876e27	0.244209
$292$	−1.13906e28	−0.506576
$293$	2.69579e28	1.15268	0.576339	−	0.817211i	$-0.304481\pi$
$293$	2.69579e28	1.15268	0.576339	+	0.817211i	$0.304481\pi$
$294$	0	0
$295$	−1.10750e28	−0.437916
$296$	7.91221e26	0.0300914
$297$	−1.60678e28	−0.587839
$298$	1.18094e28	0.415661
$299$	1.84156e28	0.623687
$300$	2.84106e28	0.925947
$301$	0	0
$302$	2.43301e26	0.00734622
$303$	−5.41918e28	−1.57523
$304$	4.28746e28	1.19992
$305$	−8.70636e28	−2.34633
$306$	−2.75328e27	−0.0714585
$307$	6.16268e28	1.54056	0.770280	−	0.637706i	$-0.220117\pi$
$307$	6.16268e28	1.54056	0.770280	+	0.637706i	$0.220117\pi$
$308$	0	0
$309$	2.69526e28	0.625286
$310$	−3.26940e28	−0.730816
$311$	−4.28264e28	−0.922503	−0.461251	−	0.887270i	$-0.652599\pi$
$311$	−4.28264e28	−0.922503	−0.461251	+	0.887270i	$0.652599\pi$
$312$	−5.01093e28	−1.04026
$313$	6.87033e28	1.37473	0.687366	−	0.726311i	$-0.258767\pi$
$313$	6.87033e28	1.37473	0.687366	+	0.726311i	$0.258767\pi$
$314$	−2.27922e28	−0.439638
$315$	0	0
$316$	−8.42634e28	−1.51091
$317$	−3.91432e27	−0.0676823	−0.0338411	−	0.999427i	$-0.510774\pi$
$317$	−3.91432e27	−0.0676823	−0.0338411	+	0.999427i	$0.510774\pi$
$318$	−3.12361e28	−0.520888
$319$	−1.55560e28	−0.250210
$320$	−4.32520e28	−0.671091
$321$	1.25521e29	1.87892
$322$	0	0
$323$	4.33398e28	0.604029
$324$	8.32412e28	1.11962
$325$	8.67779e28	1.12655
$326$	2.66859e28	0.334410
$327$	7.48205e28	0.905152
$328$	6.63066e27	0.0774476
$329$	0	0
$330$	−6.03870e28	−0.657708
$331$	4.74765e28	0.499410	0.249705	−	0.968322i	$-0.419666\pi$
$331$	4.74765e28	0.499410	0.249705	+	0.968322i	$0.419666\pi$
$332$	−9.98106e28	−1.01412
$333$	3.43588e27	0.0337232
$334$	−3.18901e28	−0.302393
$335$	−1.87451e29	−1.71740
$336$	0	0
$337$	−1.40868e29	−1.20523	−0.602613	−	0.798034i	$-0.705874\pi$
$337$	−1.40868e29	−1.20523	−0.602613	+	0.798034i	$0.705874\pi$
$338$	−3.67019e28	−0.303491
$339$	−2.48900e29	−1.98943
$340$	−5.86824e28	−0.453420
$341$	−3.11919e29	−2.33005
$342$	−4.32070e28	−0.312071
$343$	0	0
$344$	−1.05098e28	−0.0709862
$345$	−1.15472e29	−0.754321
$346$	−3.40772e28	−0.215322
$347$	−6.22822e28	−0.380693	−0.190346	−	0.981717i	$-0.560961\pi$
$347$	−6.22822e28	−0.380693	−0.190346	+	0.981717i	$0.560961\pi$
$348$	3.85685e28	0.228072
$349$	1.06957e29	0.611952	0.305976	−	0.952039i	$-0.401017\pi$
$349$	1.06957e29	0.611952	0.305976	+	0.952039i	$0.401017\pi$
$350$	0	0
$351$	1.21680e29	0.651911
$352$	1.95816e29	1.01533
$353$	1.40554e29	0.705399	0.352699	−	0.935737i	$-0.385264\pi$
$353$	1.40554e29	0.705399	0.352699	+	0.935737i	$0.385264\pi$
$354$	−2.58311e28	−0.125489
$355$	−9.10164e28	−0.428049
$356$	1.84706e28	0.0841021
$357$	0	0
$358$	−1.06900e29	−0.456378
$359$	4.59325e29	1.89904	0.949519	−	0.313711i	$-0.101572\pi$
$359$	4.59325e29	1.89904	0.949519	+	0.313711i	$0.101572\pi$
$360$	1.22774e29	0.491617
$361$	4.22298e29	1.63789
$362$	1.29098e29	0.485031
$363$	−2.24138e29	−0.815809
$364$	0	0
$365$	2.18155e29	0.745414
$366$	−2.03065e29	−0.672361
$367$	4.24622e29	1.36252	0.681260	−	0.732041i	$-0.261432\pi$
$367$	4.24622e29	1.36252	0.681260	+	0.732041i	$0.261432\pi$
$368$	1.04428e29	0.324763
$369$	2.87937e28	0.0867948
$370$	−7.22081e27	−0.0210992
$371$	0	0
$372$	7.73350e29	2.12389
$373$	2.57231e29	0.684970	0.342485	−	0.939523i	$-0.388731\pi$
$373$	2.57231e29	0.684970	0.342485	+	0.939523i	$0.388731\pi$
$374$	5.52042e28	0.142544
$375$	1.41163e29	0.353478
$376$	3.81901e29	0.927450
$377$	1.17804e29	0.277482
$378$	0	0
$379$	−4.48606e29	−0.994292	−0.497146	−	0.867667i	$-0.665619\pi$
$379$	−4.48606e29	−0.994292	−0.497146	+	0.867667i	$0.665619\pi$
$380$	−9.20898e29	−1.98016
$381$	−3.39758e29	−0.708814
$382$	−4.17277e28	−0.0844686
$383$	5.93935e29	1.16668	0.583342	−	0.812227i	$-0.301745\pi$
$383$	5.93935e29	1.16668	0.583342	+	0.812227i	$0.301745\pi$
$384$	−6.34245e29	−1.20906
$385$	0	0
$386$	2.11342e28	0.0379518
$387$	−4.56390e28	−0.0795536
$388$	1.02538e29	0.173508
$389$	−3.88484e29	−0.638194	−0.319097	−	0.947722i	$-0.603380\pi$
$389$	−3.88484e29	−0.638194	−0.319097	+	0.947722i	$0.603380\pi$
$390$	4.57306e29	0.729396
$391$	1.05561e29	0.163482
$392$	0	0
$393$	4.79586e29	0.700409
$394$	2.14155e29	0.303754
$395$	1.61383e30	2.22326
$396$	5.58147e29	0.746885
$397$	1.10976e30	1.44257	0.721287	−	0.692637i	$-0.243551\pi$
$397$	1.10976e30	1.44257	0.721287	+	0.692637i	$0.243551\pi$
$398$	−2.29411e29	−0.289707
$399$	0	0
$400$	4.92085e29	0.586611
$401$	−1.44141e30	−1.66966	−0.834828	−	0.550511i	$-0.814433\pi$
$401$	−1.44141e30	−1.66966	−0.834828	+	0.550511i	$0.814433\pi$
$402$	−4.37206e29	−0.492138
$403$	2.36213e30	2.58402
$404$	−1.05266e30	−1.11918
$405$	−1.59425e30	−1.64749
$406$	0	0
$407$	−6.88905e28	−0.0672703
$408$	−2.87235e29	−0.272675
$409$	1.68194e29	0.155236	0.0776178	−	0.996983i	$-0.475269\pi$
$409$	1.68194e29	0.155236	0.0776178	+	0.996983i	$0.475269\pi$
$410$	−6.05125e28	−0.0543038
$411$	−2.22732e30	−1.94358
$412$	5.23546e29	0.444259
$413$	0	0
$414$	−1.05238e29	−0.0844631
$415$	1.91159e30	1.49225
$416$	−1.48290e30	−1.12600
$417$	1.05621e30	0.780166
$418$	8.66314e29	0.622513
$419$	−2.41718e30	−1.68985	−0.844925	−	0.534884i	$-0.820355\pi$
$419$	−2.41718e30	−1.68985	−0.844925	+	0.534884i	$0.820355\pi$
$420$	0	0
$421$	−1.21472e30	−0.803959	−0.401979	−	0.915649i	$-0.631678\pi$
$421$	−1.21472e30	−0.803959	−0.401979	+	0.915649i	$0.631678\pi$
$422$	−8.10097e29	−0.521728
$423$	1.65840e30	1.03938
$424$	−1.27333e30	−0.776663
$425$	4.97425e29	0.295294
$426$	−2.12284e29	−0.122661
$427$	0	0
$428$	2.43820e30	1.33495
$429$	4.36295e30	2.32553
$430$	9.59145e28	0.0497733
$431$	−1.38543e30	−0.699998	−0.349999	−	0.936750i	$-0.613818\pi$
$431$	−1.38543e30	−0.699998	−0.349999	+	0.936750i	$0.613818\pi$
$432$	6.90003e29	0.339460
$433$	4.36873e29	0.209288	0.104644	−	0.994510i	$-0.466630\pi$
$433$	4.36873e29	0.209288	0.104644	+	0.994510i	$0.466630\pi$
$434$	0	0
$435$	−7.38670e29	−0.335602
$436$	1.45336e30	0.643101
$437$	1.65656e30	0.713955
$438$	5.08820e29	0.213605
$439$	−1.09246e30	−0.446749	−0.223374	−	0.974733i	$-0.571707\pi$
$439$	−1.09246e30	−0.446749	−0.223374	+	0.974733i	$0.571707\pi$
$440$	−2.46165e30	−0.980666
$441$	0	0
$442$	−4.18056e29	−0.158081
$443$	−5.42391e29	−0.199834	−0.0999171	−	0.994996i	$-0.531858\pi$
$443$	−5.42391e29	−0.199834	−0.0999171	+	0.994996i	$0.531858\pi$
$444$	1.70802e29	0.0613182
$445$	−3.53753e29	−0.123754
$446$	−6.40210e29	−0.218259
$447$	5.34999e30	1.77753
$448$	0	0
$449$	1.44285e30	0.455395	0.227697	−	0.973732i	$-0.426880\pi$
$449$	1.44285e30	0.455395	0.227697	+	0.973732i	$0.426880\pi$
$450$	−4.95900e29	−0.152563
$451$	−5.77323e29	−0.173136
$452$	−4.83479e30	−1.41347
$453$	1.10222e29	0.0314153
$454$	−1.24217e29	−0.0345175
$455$	0	0
$456$	−4.50755e30	−1.19082
$457$	−1.19186e30	−0.307035	−0.153518	−	0.988146i	$-0.549060\pi$
$457$	−1.19186e30	−0.307035	−0.153518	+	0.988146i	$0.549060\pi$
$458$	3.93752e29	0.0989168
$459$	6.97491e29	0.170880
$460$	−2.24300e30	−0.535937
$461$	4.91770e30	1.14604	0.573022	−	0.819540i	$-0.305771\pi$
$461$	4.91770e30	1.14604	0.573022	+	0.819540i	$0.305771\pi$
$462$	0	0
$463$	5.21961e30	1.15733	0.578664	−	0.815566i	$-0.303574\pi$
$463$	5.21961e30	1.15733	0.578664	+	0.815566i	$0.303574\pi$
$464$	6.68024e29	0.144489
$465$	−1.48113e31	−3.12525
$466$	6.64132e29	0.136715
$467$	5.70190e30	1.14519	0.572593	−	0.819840i	$-0.305938\pi$
$467$	5.70190e30	1.14519	0.572593	+	0.819840i	$0.305938\pi$
$468$	−4.22680e30	−0.828293
$469$	0	0
$470$	−3.48529e30	−0.650299
$471$	−1.03255e31	−1.88006
$472$	−1.05299e30	−0.187108
$473$	9.15077e29	0.158692
$474$	3.76405e30	0.637096
$475$	7.80604e30	1.28960
$476$	0	0
$477$	−5.52942e30	−0.870399
$478$	−3.60154e30	−0.553436
$479$	7.33707e30	1.10069	0.550344	−	0.834938i	$-0.314497\pi$
$479$	7.33707e30	1.10069	0.550344	+	0.834938i	$0.314497\pi$
$480$	9.29826e30	1.36184
$481$	5.21701e29	0.0746025
$482$	1.49320e30	0.208487
$483$	0	0
$484$	−4.35379e30	−0.579624
$485$	−1.96383e30	−0.255313
$486$	−2.63420e30	−0.334450
$487$	−9.68270e30	−1.20064	−0.600321	−	0.799759i	$-0.704960\pi$
$487$	−9.68270e30	−1.20064	−0.600321	+	0.799759i	$0.704960\pi$
$488$	−8.27786e30	−1.00251
$489$	1.20895e31	1.43007
$490$	0	0
$491$	−6.95735e30	−0.785248	−0.392624	−	0.919699i	$-0.628433\pi$
$491$	−6.95735e30	−0.785248	−0.392624	+	0.919699i	$0.628433\pi$
$492$	1.43137e30	0.157817
$493$	6.75272e29	0.0727343
$494$	−6.56052e30	−0.690364
$495$	−1.06897e31	−1.09902
$496$	1.33948e31	1.34554
$497$	0	0
$498$	4.45855e30	0.427618
$499$	−3.82109e30	−0.358122	−0.179061	−	0.983838i	$-0.557306\pi$
$499$	−3.82109e30	−0.358122	−0.179061	+	0.983838i	$0.557306\pi$
$500$	2.74204e30	0.251142
$501$	−1.44472e31	−1.29315
$502$	7.67086e29	0.0671045
$503$	5.35790e30	0.458103	0.229051	−	0.973414i	$-0.426438\pi$
$503$	5.35790e30	0.458103	0.229051	+	0.973414i	$0.426438\pi$
$504$	0	0
$505$	2.01607e31	1.64685
$506$	2.11005e30	0.168485
$507$	−1.66270e31	−1.29785
$508$	−6.59968e30	−0.503605
$509$	−1.49403e31	−1.11456	−0.557282	−	0.830323i	$-0.688156\pi$
$509$	−1.49403e31	−1.11456	−0.557282	+	0.830323i	$0.688156\pi$
$510$	2.62135e30	0.191191
$511$	0	0
$512$	−1.44728e31	−1.00913
$513$	1.09457e31	0.746263
$514$	1.38428e30	0.0922887
$515$	−1.00270e31	−0.653717
$516$	−2.26878e30	−0.144651
$517$	−3.32516e31	−2.07334
$518$	0	0
$519$	−1.54380e31	−0.920801
$520$	1.86419e31	1.08756
$521$	1.97941e31	1.12954	0.564769	−	0.825249i	$-0.308965\pi$
$521$	1.97941e31	1.12954	0.564769	+	0.825249i	$0.308965\pi$
$522$	−6.73203e29	−0.0375781
$523$	2.13891e31	1.16795	0.583974	−	0.811773i	$-0.301497\pi$
$523$	2.13891e31	1.16795	0.583974	+	0.811773i	$0.301497\pi$
$524$	9.31578e30	0.497633
$525$	0	0
$526$	4.12047e30	0.210674
$527$	1.35401e31	0.677330
$528$	2.47407e31	1.21094
$529$	−1.68456e31	−0.806766
$530$	1.16206e31	0.544572
$531$	−4.57263e30	−0.209691
$532$	0	0
$533$	4.37201e30	0.192008
$534$	−8.25085e29	−0.0354629
$535$	−4.66968e31	−1.96435
$536$	−1.78225e31	−0.733795
$537$	−4.84290e31	−1.95165
$538$	4.47320e30	0.176450
$539$	0	0
$540$	−1.48205e31	−0.560190
$541$	−1.09249e31	−0.404250	−0.202125	−	0.979360i	$-0.564785\pi$
$541$	−1.09249e31	−0.404250	−0.202125	+	0.979360i	$0.564785\pi$
$542$	6.10565e30	0.221177
$543$	5.84850e31	2.07418
$544$	−8.50022e30	−0.295150
$545$	−2.78350e31	−0.946307
$546$	0	0
$547$	−1.76051e31	−0.573831	−0.286916	−	0.957956i	$-0.592630\pi$
$547$	−1.76051e31	−0.573831	−0.286916	+	0.957956i	$0.592630\pi$
$548$	−4.32649e31	−1.38089
$549$	−3.59466e31	−1.12351
$550$	9.94296e30	0.304330
$551$	1.05970e31	0.317643
$552$	−1.09789e31	−0.322298
$553$	0	0
$554$	1.28898e31	0.362981
$555$	−3.27124e30	−0.0902283
$556$	2.05166e31	0.554299
$557$	2.04064e31	0.540047	0.270024	−	0.962854i	$-0.412968\pi$
$557$	2.04064e31	0.540047	0.270024	+	0.962854i	$0.412968\pi$
$558$	−1.34986e31	−0.349942
$559$	−6.92980e30	−0.175989
$560$	0	0
$561$	2.50091e31	0.609572
$562$	−7.39770e30	−0.176656
$563$	4.68033e31	1.09504	0.547520	−	0.836792i	$-0.315572\pi$
$563$	4.68033e31	1.09504	0.547520	+	0.836792i	$0.315572\pi$
$564$	8.24417e31	1.88989
$565$	9.25967e31	2.07988
$566$	1.53687e31	0.338258
$567$	0	0
$568$	−8.65369e30	−0.182892
$569$	−6.83899e30	−0.141645	−0.0708224	−	0.997489i	$-0.522562\pi$
$569$	−6.83899e30	−0.141645	−0.0708224	+	0.997489i	$0.522562\pi$
$570$	4.11366e31	0.834963
$571$	−6.64727e31	−1.32229	−0.661147	−	0.750257i	$-0.729930\pi$
$571$	−6.64727e31	−1.32229	−0.661147	+	0.750257i	$0.729930\pi$
$572$	8.47487e31	1.65226
$573$	−1.89039e31	−0.361220
$574$	0	0
$575$	1.90129e31	0.349034
$576$	−1.78578e31	−0.321343
$577$	−6.48872e31	−1.14456	−0.572278	−	0.820060i	$-0.693940\pi$
$577$	−6.48872e31	−1.14456	−0.572278	+	0.820060i	$0.693940\pi$
$578$	1.49295e31	0.258152
$579$	9.57442e30	0.162297
$580$	−1.43484e31	−0.238442
$581$	0	0
$582$	−4.58038e30	−0.0731623
$583$	1.10867e32	1.73625
$584$	2.07418e31	0.318493
$585$	8.09524e31	1.21881
$586$	−2.33914e31	−0.345329
$587$	4.13155e31	0.598101	0.299051	−	0.954237i	$-0.403330\pi$
$587$	4.13155e31	0.598101	0.299051	+	0.954237i	$0.403330\pi$
$588$	0	0
$589$	2.12484e32	2.95801
$590$	9.60979e30	0.131195
$591$	9.70185e31	1.29897
$592$	2.95837e30	0.0388466
$593$	1.74273e31	0.224440	0.112220	−	0.993683i	$-0.464204\pi$
$593$	1.74273e31	0.224440	0.112220	+	0.993683i	$0.464204\pi$
$594$	1.39421e31	0.176110
$595$	0	0
$596$	1.03922e32	1.26291
$597$	−1.03930e32	−1.23890
$598$	−1.59792e31	−0.186849
$599$	8.60056e31	0.986549	0.493274	−	0.869874i	$-0.335800\pi$
$599$	8.60056e31	0.986549	0.493274	+	0.869874i	$0.335800\pi$
$600$	−5.17346e31	−0.582159
$601$	−1.22654e32	−1.35402	−0.677012	−	0.735972i	$-0.736726\pi$
$601$	−1.22654e32	−1.35402	−0.677012	+	0.735972i	$0.736726\pi$
$602$	0	0
$603$	−7.73944e31	−0.822357
$604$	2.14103e30	0.0223202
$605$	8.33847e31	0.852902
$606$	4.70222e31	0.471919
$607$	4.35936e31	0.429292	0.214646	−	0.976692i	$-0.431140\pi$
$607$	4.35936e31	0.429292	0.214646	+	0.976692i	$0.431140\pi$
$608$	−1.33393e32	−1.28897
$609$	0	0
$610$	7.55451e31	0.702931
$611$	2.51811e32	2.29933
$612$	−2.42287e31	−0.217114
$613$	−5.83683e31	−0.513312	−0.256656	−	0.966503i	$-0.582621\pi$
$613$	−5.83683e31	−0.513312	−0.256656	+	0.966503i	$0.582621\pi$
$614$	−5.34736e31	−0.461533
$615$	−2.74139e31	−0.232224
$616$	0	0
$617$	−1.23925e32	−1.01130	−0.505649	−	0.862739i	$-0.668747\pi$
$617$	−1.23925e32	−1.01130	−0.505649	+	0.862739i	$0.668747\pi$
$618$	−2.33868e31	−0.187328
$619$	7.79384e31	0.612786	0.306393	−	0.951905i	$-0.400878\pi$
$619$	7.79384e31	0.612786	0.306393	+	0.951905i	$0.400878\pi$
$620$	−2.87705e32	−2.22046
$621$	2.66599e31	0.201979
$622$	3.71605e31	0.276371
$623$	0	0
$624$	−1.87359e32	−1.34292
$625$	−1.65352e32	−1.16356
$626$	−5.96139e31	−0.411853
$627$	3.92466e32	2.66210
$628$	−2.00570e32	−1.33576
$629$	2.99048e30	0.0195550
$630$	0	0
$631$	−2.43061e32	−1.53242	−0.766211	−	0.642589i	$-0.777860\pi$
$631$	−2.43061e32	−1.53242	−0.766211	+	0.642589i	$0.777860\pi$
$632$	1.53440e32	0.949932
$633$	−3.66998e32	−2.23111
$634$	3.39646e30	0.0202768
$635$	1.26398e32	0.741042
$636$	−2.74875e32	−1.58263
$637$	0	0
$638$	1.34979e31	0.0749600
$639$	−3.75786e31	−0.204966
$640$	2.35955e32	1.26403
$641$	−6.12602e30	−0.0322338	−0.0161169	−	0.999870i	$-0.505130\pi$
$641$	−6.12602e30	−0.0322338	−0.0161169	+	0.999870i	$0.505130\pi$
$642$	−1.08914e32	−0.562902
$643$	5.36539e31	0.272380	0.136190	−	0.990683i	$-0.456514\pi$
$643$	5.36539e31	0.272380	0.136190	+	0.990683i	$0.456514\pi$
$644$	0	0
$645$	4.34521e31	0.212850
$646$	−3.76059e31	−0.180960
$647$	−3.71387e31	−0.175561	−0.0877804	−	0.996140i	$-0.527977\pi$
$647$	−3.71387e31	−0.175561	−0.0877804	+	0.996140i	$0.527977\pi$
$648$	−1.51579e32	−0.703924
$649$	9.16828e31	0.418286
$650$	−7.52972e31	−0.337501
$651$	0	0
$652$	2.34834e32	1.01605
$653$	1.24607e32	0.529711	0.264856	−	0.964288i	$-0.414676\pi$
$653$	1.24607e32	0.529711	0.264856	+	0.964288i	$0.414676\pi$
$654$	−6.49217e31	−0.271173
$655$	−1.78418e32	−0.732255
$656$	2.47921e31	0.0999812
$657$	9.00715e31	0.356932
$658$	0	0
$659$	5.55107e31	0.212420	0.106210	−	0.994344i	$-0.466128\pi$
$659$	5.55107e31	0.212420	0.106210	+	0.994344i	$0.466128\pi$
$660$	−5.31402e32	−1.99833
$661$	3.41863e32	1.26338	0.631692	−	0.775220i	$-0.282361\pi$
$661$	3.41863e32	1.26338	0.631692	+	0.775220i	$0.282361\pi$
$662$	−4.11954e31	−0.149617
$663$	−1.89392e32	−0.676014
$664$	1.81751e32	0.637593
$665$	0	0
$666$	−2.98131e30	−0.0101031
$667$	2.58107e31	0.0859711
$668$	−2.80631e32	−0.918769
$669$	−2.90034e32	−0.933358
$670$	1.62651e32	0.514514
$671$	7.20742e32	2.24115
$672$	0	0
$673$	−4.26257e32	−1.28085	−0.640425	−	0.768021i	$-0.721242\pi$
$673$	−4.26257e32	−1.28085	−0.640425	+	0.768021i	$0.721242\pi$
$674$	1.22231e32	0.361071
$675$	1.25627e32	0.364829
$676$	−3.22974e32	−0.922105
$677$	4.92042e32	1.38112	0.690561	−	0.723274i	$-0.257364\pi$
$677$	4.92042e32	1.38112	0.690561	+	0.723274i	$0.257364\pi$
$678$	2.15970e32	0.596009
$679$	0	0
$680$	1.06858e32	0.285073
$681$	−5.62741e31	−0.147610
$682$	2.70652e32	0.698057
$683$	−2.43788e32	−0.618266	−0.309133	−	0.951019i	$-0.600039\pi$
$683$	−2.43788e32	−0.618266	−0.309133	+	0.951019i	$0.600039\pi$
$684$	−3.80218e32	−0.948174
$685$	8.28618e32	2.03195
$686$	0	0
$687$	1.78381e32	0.423006
$688$	−3.92963e31	−0.0916399
$689$	−8.39584e32	−1.92550
$690$	1.00195e32	0.225986
$691$	−2.35982e31	−0.0523458	−0.0261729	−	0.999657i	$-0.508332\pi$
$691$	−2.35982e31	−0.0523458	−0.0261729	+	0.999657i	$0.508332\pi$
$692$	−2.99877e32	−0.654220
$693$	0	0
$694$	5.40423e31	0.114051
$695$	−3.92937e32	−0.815638
$696$	−7.02316e31	−0.143392
$697$	2.50611e31	0.0503295
$698$	−9.28067e31	−0.183334
$699$	3.00871e32	0.584647
$700$	0	0
$701$	6.25606e32	1.17637	0.588184	−	0.808727i	$-0.299843\pi$
$701$	6.25606e32	1.17637	0.588184	+	0.808727i	$0.299843\pi$
$702$	−1.05582e32	−0.195305
$703$	4.69293e31	0.0853999
$704$	3.58055e32	0.641009
$705$	−1.57894e33	−2.78093
$706$	−1.21959e32	−0.211329
$707$	0	0
$708$	−2.27312e32	−0.381276
$709$	9.07599e32	1.49783	0.748915	−	0.662666i	$-0.230575\pi$
$709$	9.07599e32	1.49783	0.748915	+	0.662666i	$0.230575\pi$
$710$	7.89749e31	0.128238
$711$	6.66314e32	1.06458
$712$	−3.36343e31	−0.0528764
$713$	5.17539e32	0.800596
$714$	0	0
$715$	−1.62312e33	−2.43126
$716$	−9.40716e32	−1.38662
$717$	−1.63160e33	−2.36671
$718$	−3.98556e32	−0.568929
$719$	8.51650e32	1.19641	0.598203	−	0.801344i	$-0.295881\pi$
$719$	8.51650e32	1.19641	0.598203	+	0.801344i	$0.295881\pi$
$720$	4.59051e32	0.634654
$721$	0	0
$722$	−3.66428e32	−0.490694
$723$	6.76465e32	0.891569
$724$	1.13605e33	1.47368
$725$	1.21625e32	0.155287
$726$	1.94484e32	0.244407
$727$	−4.13708e32	−0.511738	−0.255869	−	0.966711i	$-0.582362\pi$
$727$	−4.13708e32	−0.511738	−0.255869	+	0.966711i	$0.582362\pi$
$728$	0	0
$729$	−1.67061e32	−0.200221
$730$	−1.89293e32	−0.223317
$731$	−3.97227e31	−0.0461306
$732$	−1.78696e33	−2.04285
$733$	1.18029e32	0.132829	0.0664143	−	0.997792i	$-0.478844\pi$
$733$	1.18029e32	0.132829	0.0664143	+	0.997792i	$0.478844\pi$
$734$	−3.68445e32	−0.408195
$735$	0	0
$736$	−3.24901e32	−0.348864
$737$	1.55178e33	1.64042
$738$	−2.49843e31	−0.0260027
$739$	−6.13794e32	−0.628944	−0.314472	−	0.949267i	$-0.601827\pi$
$739$	−6.13794e32	−0.628944	−0.314472	+	0.949267i	$0.601827\pi$
$740$	−6.35426e31	−0.0641062
$741$	−2.97211e33	−2.95226
$742$	0	0
$743$	3.90366e32	0.375924	0.187962	−	0.982176i	$-0.439812\pi$
$743$	3.90366e32	0.375924	0.187962	+	0.982176i	$0.439812\pi$
$744$	−1.40824e33	−1.33533
$745$	−1.99033e33	−1.85835
$746$	−2.23199e32	−0.205209
$747$	7.89254e32	0.714545
$748$	4.85793e32	0.433095
$749$	0	0
$750$	−1.22487e32	−0.105898
$751$	9.43338e32	0.803171	0.401586	−	0.915821i	$-0.368459\pi$
$751$	9.43338e32	0.803171	0.401586	+	0.915821i	$0.368459\pi$
$752$	1.42793e33	1.19729
$753$	3.47513e32	0.286965
$754$	−1.02219e32	−0.0831304
$755$	−4.10054e31	−0.0328436
$756$	0	0
$757$	1.33353e33	1.03609	0.518047	−	0.855352i	$-0.326659\pi$
$757$	1.33353e33	1.03609	0.518047	+	0.855352i	$0.326659\pi$
$758$	3.89255e32	0.297878
$759$	9.55914e32	0.720507
$760$	1.67692e33	1.24496
$761$	−9.89262e32	−0.723415	−0.361708	−	0.932292i	$-0.617806\pi$
$761$	−9.89262e32	−0.723415	−0.361708	+	0.932292i	$0.617806\pi$
$762$	2.94808e32	0.212352
$763$	0	0
$764$	−3.67201e32	−0.256643
$765$	4.64032e32	0.319478
$766$	−5.15358e32	−0.349525
$767$	−6.94305e32	−0.463878
$768$	−4.24936e32	−0.279685
$769$	1.31237e33	0.850947	0.425474	−	0.904971i	$-0.360107\pi$
$769$	1.31237e33	0.850947	0.425474	+	0.904971i	$0.360107\pi$
$770$	0	0
$771$	6.27120e32	0.394662
$772$	1.85980e32	0.115310
$773$	2.81718e32	0.172088	0.0860441	−	0.996291i	$-0.472577\pi$
$773$	2.81718e32	0.172088	0.0860441	+	0.996291i	$0.472577\pi$
$774$	3.96010e31	0.0238333
$775$	2.43874e33	1.44609
$776$	−1.86717e32	−0.109088
$777$	0	0
$778$	3.37088e32	0.191195
$779$	3.93281e32	0.219797
$780$	4.02426e33	2.21614
$781$	7.53464e32	0.408861
$782$	−9.15953e31	−0.0489774
$783$	1.70543e32	0.0898615
$784$	0	0
$785$	3.84135e33	1.96554
$786$	−4.16137e32	−0.209834
$787$	1.73439e33	0.861860	0.430930	−	0.902385i	$-0.358186\pi$
$787$	1.73439e33	0.861860	0.430930	+	0.902385i	$0.358186\pi$
$788$	1.88455e33	0.922904
$789$	1.86669e33	0.900922
$790$	−1.40032e33	−0.666063
$791$	0	0
$792$	−1.01636e33	−0.469579
$793$	−5.45811e33	−2.48543
$794$	−9.62938e32	−0.432178
$795$	5.26446e33	2.32880
$796$	−2.01880e33	−0.880225
$797$	−2.25195e33	−0.967807	−0.483904	−	0.875121i	$-0.660782\pi$
$797$	−2.25195e33	−0.967807	−0.483904	+	0.875121i	$0.660782\pi$
$798$	0	0
$799$	1.44342e33	0.602706
$800$	−1.53100e33	−0.630143
$801$	−1.46057e32	−0.0592581
$802$	1.25071e33	0.500209
$803$	−1.80596e33	−0.712000
$804$	−3.84739e33	−1.49528
$805$	0	0
$806$	−2.04962e33	−0.774142
$807$	2.02649e33	0.754569
$808$	1.91684e33	0.703648
$809$	1.35118e33	0.488996	0.244498	−	0.969650i	$-0.421377\pi$
$809$	1.35118e33	0.488996	0.244498	+	0.969650i	$0.421377\pi$
$810$	1.38333e33	0.493570
$811$	2.16124e33	0.760261	0.380130	−	0.924933i	$-0.375879\pi$
$811$	2.16124e33	0.760261	0.380130	+	0.924933i	$0.375879\pi$
$812$	0	0
$813$	2.76604e33	0.945839
$814$	5.97763e31	0.0201534
$815$	−4.49759e33	−1.49509
$816$	−1.07397e33	−0.352010
$817$	−6.23365e32	−0.201460
$818$	−1.45942e32	−0.0465068
$819$	0	0
$820$	−5.32506e32	−0.164993
$821$	−1.19447e32	−0.0364945	−0.0182473	−	0.999834i	$-0.505809\pi$
$821$	−1.19447e32	−0.0364945	−0.0182473	+	0.999834i	$0.505809\pi$
$822$	1.93265e33	0.582273
$823$	−7.15722e32	−0.212641	−0.106320	−	0.994332i	$-0.533907\pi$
$823$	−7.15722e32	−0.212641	−0.106320	+	0.994332i	$0.533907\pi$
$824$	−9.53355e32	−0.279313
$825$	4.50445e33	1.30143
$826$	0	0
$827$	2.70094e33	0.758931	0.379465	−	0.925206i	$-0.376108\pi$
$827$	2.70094e33	0.758931	0.379465	+	0.925206i	$0.376108\pi$
$828$	−9.26084e32	−0.256626
$829$	−3.20363e33	−0.875518	−0.437759	−	0.899092i	$-0.644228\pi$
$829$	−3.20363e33	−0.875518	−0.437759	+	0.899092i	$0.644228\pi$
$830$	−1.65869e33	−0.447061
$831$	5.83946e33	1.55225
$832$	−2.71152e33	−0.710877
$833$	0	0
$834$	−9.16476e32	−0.233728
$835$	5.37470e33	1.35195
$836$	7.62351e33	1.89140
$837$	3.41962e33	0.836825
$838$	2.09739e33	0.506259
$839$	−5.78465e33	−1.37725	−0.688627	−	0.725115i	$-0.741786\pi$
$839$	−5.78465e33	−1.37725	−0.688627	+	0.725115i	$0.741786\pi$
$840$	0	0
$841$	−4.15161e33	−0.961751
$842$	1.05402e33	0.240856
$843$	−3.35138e33	−0.755450
$844$	−7.12880e33	−1.58518
$845$	6.18566e33	1.35686
$846$	−1.43900e33	−0.311387
$847$	0	0
$848$	−4.76097e33	−1.00264
$849$	6.96247e33	1.44652
$850$	−4.31615e32	−0.0884666
$851$	1.14304e32	0.0231138
$852$	−1.86809e33	−0.372685
$853$	−8.31369e33	−1.63636	−0.818182	−	0.574960i	$-0.805018\pi$
$853$	−8.31369e33	−1.63636	−0.818182	+	0.574960i	$0.805018\pi$
$854$	0	0
$855$	7.28201e33	1.39522
$856$	−4.43986e33	−0.839307
$857$	3.59313e33	0.670183	0.335092	−	0.942186i	$-0.391233\pi$
$857$	3.59313e33	0.670183	0.335092	+	0.942186i	$0.391233\pi$
$858$	−3.78573e33	−0.696700
$859$	−4.98478e33	−0.905158	−0.452579	−	0.891724i	$-0.649496\pi$
$859$	−4.98478e33	−0.905158	−0.452579	+	0.891724i	$0.649496\pi$
$860$	8.44041e32	0.151228
$861$	0	0
$862$	1.20214e33	0.209711
$863$	2.60278e33	0.448037	0.224019	−	0.974585i	$-0.428082\pi$
$863$	2.60278e33	0.448037	0.224019	+	0.974585i	$0.428082\pi$
$864$	−2.14677e33	−0.364651
$865$	5.74331e33	0.962669
$866$	−3.79075e32	−0.0627002
$867$	6.76350e33	1.10396
$868$	0	0
$869$	−1.33598e34	−2.12360
$870$	6.40944e32	0.100542
$871$	−1.17515e34	−1.81922
$872$	−2.64651e33	−0.404328
$873$	−8.10820e32	−0.122253
$874$	−1.43740e33	−0.213892
$875$	0	0
$876$	4.47758e33	0.649002
$877$	7.42633e32	0.106238	0.0531188	−	0.998588i	$-0.483084\pi$
$877$	7.42633e32	0.106238	0.0531188	+	0.998588i	$0.483084\pi$
$878$	9.47927e32	0.133841
$879$	−1.05970e34	−1.47676
$880$	−9.20412e33	−1.26599
$881$	1.21269e34	1.64637	0.823185	−	0.567773i	$-0.192195\pi$
$881$	1.21269e34	1.64637	0.823185	+	0.567773i	$0.192195\pi$
$882$	0	0
$883$	−1.73682e32	−0.0229724	−0.0114862	−	0.999934i	$-0.503656\pi$
$883$	−1.73682e32	−0.0229724	−0.0114862	+	0.999934i	$0.503656\pi$
$884$	−3.67887e33	−0.480301
$885$	4.35352e33	0.561039
$886$	4.70633e32	0.0598680
$887$	−9.95561e33	−1.25010	−0.625052	−	0.780583i	$-0.714922\pi$
$887$	−9.95561e33	−1.25010	−0.625052	+	0.780583i	$0.714922\pi$
$888$	−3.11024e32	−0.0385518
$889$	0	0
$890$	3.06952e32	0.0370753
$891$	1.31977e34	1.57364
$892$	−5.63381e33	−0.663141
$893$	2.26515e34	2.63212
$894$	−4.64219e33	−0.532526
$895$	1.80168e34	2.04038
$896$	0	0
$897$	−7.23905e33	−0.799040
$898$	−1.25196e33	−0.136431
$899$	3.31069e33	0.356190
$900$	−4.36389e33	−0.463537
$901$	−4.81263e33	−0.504716
$902$	5.00943e32	0.0518696
$903$	0	0
$904$	8.80395e33	0.888670
$905$	−2.17579e34	−2.16849
$906$	−9.56400e31	−0.00941164
$907$	−1.21330e34	−1.17892	−0.589459	−	0.807799i	$-0.700659\pi$
$907$	−1.21330e34	−1.17892	−0.589459	+	0.807799i	$0.700659\pi$
$908$	−1.09310e33	−0.104876
$909$	8.32389e33	0.788573
$910$	0	0
$911$	1.18968e33	0.109893	0.0549464	−	0.998489i	$-0.482501\pi$
$911$	1.18968e33	0.109893	0.0549464	+	0.998489i	$0.482501\pi$
$912$	−1.68537e34	−1.53729
$913$	−1.58248e34	−1.42536
$914$	1.03418e33	0.0919842
$915$	3.42241e34	3.00601
$916$	3.46499e33	0.300542
$917$	0	0
$918$	−6.05213e32	−0.0511938
$919$	−2.75671e32	−0.0230283	−0.0115142	−	0.999934i	$-0.503665\pi$
$919$	−2.75671e32	−0.0230283	−0.0115142	+	0.999934i	$0.503665\pi$
$920$	4.08440e33	0.336952
$921$	−2.42251e34	−1.97370
$922$	−4.26709e33	−0.343341
$923$	−5.70592e33	−0.453426
$924$	0	0
$925$	5.38622e32	0.0417498
$926$	−4.52905e33	−0.346722
$927$	−4.13994e33	−0.313024
$928$	−2.07838e33	−0.155212
$929$	−1.53078e34	−1.12910	−0.564550	−	0.825399i	$-0.690950\pi$
$929$	−1.53078e34	−1.12910	−0.564550	+	0.825399i	$0.690950\pi$
$930$	1.28518e34	0.936289
$931$	0	0
$932$	5.84432e33	0.415385
$933$	1.68348e34	1.18187
$934$	−4.94754e33	−0.343084
$935$	−9.30400e33	−0.637288
$936$	7.69682e33	0.520762
$937$	1.10128e34	0.736026	0.368013	−	0.929821i	$-0.380038\pi$
$937$	1.10128e34	0.736026	0.368013	+	0.929821i	$0.380038\pi$
$938$	0	0
$939$	−2.70068e34	−1.76124
$940$	−3.06703e34	−1.97582
$941$	1.42300e33	0.0905574	0.0452787	−	0.998974i	$-0.485582\pi$
$941$	1.42300e33	0.0905574	0.0452787	+	0.998974i	$0.485582\pi$
$942$	8.95946e33	0.563244
$943$	9.57900e32	0.0594889
$944$	−3.93715e33	−0.241548
$945$	0	0
$946$	−7.94012e32	−0.0475422
$947$	4.10907e33	0.243063	0.121531	−	0.992588i	$-0.461219\pi$
$947$	4.10907e33	0.243063	0.121531	+	0.992588i	$0.461219\pi$
$948$	3.31234e34	1.93570
$949$	1.36764e34	0.789606
$950$	−6.77330e33	−0.386348
$951$	1.53869e33	0.0867114
$952$	0	0
$953$	−2.27480e34	−1.25134	−0.625668	−	0.780089i	$-0.715174\pi$
$953$	−2.27480e34	−1.25134	−0.625668	+	0.780089i	$0.715174\pi$
$954$	4.79788e33	0.260761
$955$	7.03269e33	0.377644
$956$	−3.16933e34	−1.68152
$957$	6.11496e33	0.320558
$958$	−6.36638e33	−0.329753
$959$	0	0
$960$	1.70021e34	0.859772
$961$	4.63704e34	2.31698
$962$	−4.52680e32	−0.0223500
$963$	−1.92801e34	−0.940604
$964$	1.31401e34	0.633451
$965$	−3.56192e33	−0.169676
$966$	0	0
$967$	1.27203e34	0.591690	0.295845	−	0.955236i	$-0.404399\pi$
$967$	1.27203e34	0.591690	0.295845	+	0.955236i	$0.404399\pi$
$968$	7.92808e33	0.364419
$969$	−1.70366e34	−0.773855
$970$	1.70401e33	0.0764888
$971$	5.54810e33	0.246107	0.123053	−	0.992400i	$-0.460731\pi$
$971$	5.54810e33	0.246107	0.123053	+	0.992400i	$0.460731\pi$
$972$	−2.31808e34	−1.01617
$973$	0	0
$974$	8.40168e33	0.359698
$975$	−3.41118e34	−1.44328
$976$	−3.09509e34	−1.29420
$977$	2.75586e34	1.13886	0.569429	−	0.822041i	$-0.307164\pi$
$977$	2.75586e34	1.13886	0.569429	+	0.822041i	$0.307164\pi$
$978$	−1.04901e34	−0.428432
$979$	2.92849e33	0.118207
$980$	0	0
$981$	−1.14925e34	−0.453127
$982$	6.03689e33	0.235251
$983$	−2.65220e34	−1.02150	−0.510752	−	0.859728i	$-0.670633\pi$
$983$	−2.65220e34	−1.02150	−0.510752	+	0.859728i	$0.670633\pi$
$984$	−2.60647e33	−0.0992223
$985$	−3.60933e34	−1.35803
$986$	−5.85934e32	−0.0217903
$987$	0	0
$988$	−5.77321e34	−2.09755
$989$	−1.51831e33	−0.0545258
$990$	9.27548e33	0.329255
$991$	1.56887e34	0.550479	0.275240	−	0.961376i	$-0.411243\pi$
$991$	1.56887e34	0.550479	0.275240	+	0.961376i	$0.411243\pi$
$992$	−4.16744e34	−1.44539
$993$	−1.86627e34	−0.639821
$994$	0	0
$995$	3.86645e34	1.29523
$996$	3.92349e34	1.29924
$997$	1.65550e34	0.541920	0.270960	−	0.962591i	$-0.412659\pi$
$997$	1.65550e34	0.541920	0.270960	+	0.962591i	$0.412659\pi$
$998$	3.31556e33	0.107289
$999$	7.55258e32	0.0241597

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.24.a.h.1.9	✓	24
7.6	odd	2	inner	49.24.a.h.1.10	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.24.a.h.1.9	✓	24	1.1	even	1	trivial
49.24.a.h.1.10	yes	24	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q-867.700 q^{2} -393094. q^{3} -7.63570e6 q^{4} +1.46240e8 q^{5} +3.41087e8 q^{6} +1.39043e10 q^{8} +6.03794e10 q^{9} -1.26893e11 q^{10} -1.21063e12 q^{11} +3.00155e12 q^{12} +9.16798e12 q^{13} -5.74862e13 q^{15} +5.19882e13 q^{16} +5.25523e13 q^{17} -5.23912e13 q^{18} +8.24698e14 q^{19} -1.11665e15 q^{20} +1.05046e15 q^{22} +2.00869e15 q^{23} -5.46569e15 q^{24} +9.46533e15 q^{25} -7.95505e15 q^{26} +1.32723e16 q^{27} +1.28495e16 q^{29} +4.98808e16 q^{30} +2.57650e17 q^{31} -1.61748e17 q^{32} +4.75890e17 q^{33} -4.55996e16 q^{34} -4.61039e17 q^{36} +5.69048e16 q^{37} -7.15591e17 q^{38} -3.60387e18 q^{39} +2.03337e18 q^{40} +4.76879e17 q^{41} -7.55870e17 q^{43} +9.24399e18 q^{44} +8.82991e18 q^{45} -1.74294e18 q^{46} +2.74664e19 q^{47} -2.04362e19 q^{48} -8.21307e18 q^{50} -2.06580e19 q^{51} -7.00039e19 q^{52} -9.15779e19 q^{53} -1.15164e19 q^{54} -1.77043e20 q^{55} -3.24184e20 q^{57} -1.11495e19 q^{58} -7.57316e19 q^{59} +4.38947e20 q^{60} -5.95345e20 q^{61} -2.23563e20 q^{62} -2.95760e20 q^{64} +1.34073e21 q^{65} -4.12930e20 q^{66} -1.28180e21 q^{67} -4.01274e20 q^{68} -7.89602e20 q^{69} -6.22375e20 q^{71} +8.39534e20 q^{72} +1.49176e21 q^{73} -4.93763e19 q^{74} -3.72076e21 q^{75} -6.29715e21 q^{76} +3.12708e21 q^{78} +1.10354e22 q^{79} +7.60277e21 q^{80} -1.09016e22 q^{81} -4.13788e20 q^{82} +1.30716e22 q^{83} +7.68527e21 q^{85} +6.55868e20 q^{86} -5.05107e21 q^{87} -1.68329e22 q^{88} -2.41898e21 q^{89} -7.66172e21 q^{90} -1.53377e22 q^{92} -1.01281e23 q^{93} -2.38326e22 q^{94} +1.20604e23 q^{95} +6.35820e22 q^{96} -1.34288e22 q^{97} -7.30970e22 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6030 q^{2} + 99000906 q^{4} + 31751706690 q^{8} + 975236583640 q^{9} + 3514223137536 q^{11} + 96662500006976 q^{15} + 850136746459362 q^{16} - 774764811988990 q^{18} + 81\!\cdots\!60 q^{22} + 34\!\cdots\!60 q^{23}+ \cdots + 70\!\cdots\!64 q^{99}+O(q^{100}) \) 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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