LMFDB - Embedded newform 147.6.a.l.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [147,6,Mod(1,147)] 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("147.1"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(147, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	147.a (trivial)

Newform invariants

comment:select newform

sage:traces = [4,3,-36,69] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	yes
Analytic conductor:	$23.5764215125$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 97x^{2} + 7x + 294 $ x^4 - x^3 - 97x^2 + 7x + 294
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 7 $
Twist minimal:	no (minimal twist has level 21)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.79080$ of defining polynomial
Character	$\chi$	$=$	147.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.790805 q^{2} -9.00000 q^{3} -31.3746 q^{4} +104.192 q^{5} +7.11724 q^{6} +50.1170 q^{8} +81.0000 q^{9} -82.3953 q^{10} -497.660 q^{11} +282.372 q^{12} +206.551 q^{13} -937.725 q^{15} +964.355 q^{16} -63.1586 q^{17} -64.0552 q^{18} -1323.95 q^{19} -3268.98 q^{20} +393.552 q^{22} -194.437 q^{23} -451.053 q^{24} +7730.91 q^{25} -163.342 q^{26} -729.000 q^{27} +4323.14 q^{29} +741.558 q^{30} +7525.31 q^{31} -2366.36 q^{32} +4478.94 q^{33} +49.9461 q^{34} -2541.34 q^{36} +10355.6 q^{37} +1046.99 q^{38} -1858.96 q^{39} +5221.77 q^{40} +4180.92 q^{41} +5960.87 q^{43} +15613.9 q^{44} +8439.53 q^{45} +153.762 q^{46} +4389.74 q^{47} -8679.20 q^{48} -6113.64 q^{50} +568.427 q^{51} -6480.47 q^{52} +17784.8 q^{53} +576.497 q^{54} -51852.0 q^{55} +11915.6 q^{57} -3418.76 q^{58} -3500.47 q^{59} +29420.8 q^{60} +10632.5 q^{61} -5951.06 q^{62} -28988.0 q^{64} +21520.9 q^{65} -3541.97 q^{66} -13274.7 q^{67} +1981.58 q^{68} +1749.94 q^{69} +38811.1 q^{71} +4059.47 q^{72} -31375.6 q^{73} -8189.30 q^{74} -69578.2 q^{75} +41538.6 q^{76} +1470.08 q^{78} +39491.5 q^{79} +100478. q^{80} +6561.00 q^{81} -3306.29 q^{82} +102372. q^{83} -6580.60 q^{85} -4713.88 q^{86} -38908.2 q^{87} -24941.2 q^{88} +112821. q^{89} -6674.02 q^{90} +6100.40 q^{92} -67727.8 q^{93} -3471.43 q^{94} -137945. q^{95} +21297.2 q^{96} -30334.3 q^{97} -40310.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} - 36 q^{3} + 69 q^{4} - 27 q^{6} + 123 q^{8} + 324 q^{9} - 283 q^{10} + 402 q^{11} - 621 q^{12} - 462 q^{13} + 3273 q^{16} - 276 q^{17} + 243 q^{18} - 510 q^{19} - 4719 q^{20} + 1375 q^{22}+ \cdots + 32562 q^{99}+O(q^{100}) $ 4 * q + 3 * q^2 - 36 * q^3 + 69 * q^4 - 27 * q^6 + 123 * q^8 + 324 * q^9 - 283 * q^10 + 402 * q^11 - 621 * q^12 - 462 * q^13 + 3273 * q^16 - 276 * q^17 + 243 * q^18 - 510 * q^19 - 4719 * q^20 + 1375 * q^22 + 6900 * q^23 - 1107 * q^24 + 2814 * q^25 + 15138 * q^26 - 2916 * q^27 + 540 * q^29 + 2547 * q^30 + 6410 * q^31 + 15519 * q^32 - 3618 * q^33 - 21144 * q^34 + 5589 * q^36 + 15250 * q^37 + 41250 * q^38 + 4158 * q^39 + 8547 * q^40 - 4308 * q^41 + 29198 * q^43 + 70743 * q^44 + 61800 * q^46 + 15060 * q^47 - 29457 * q^48 - 7302 * q^50 + 2484 * q^51 + 47476 * q^52 + 13692 * q^53 - 2187 * q^54 - 73124 * q^55 + 4590 * q^57 + 52309 * q^58 - 34830 * q^59 + 42471 * q^60 + 5364 * q^61 - 16029 * q^62 - 73487 * q^64 + 66864 * q^65 - 12375 * q^66 - 5994 * q^67 + 58272 * q^68 - 62100 * q^69 + 89268 * q^71 + 9963 * q^72 - 59638 * q^73 - 185442 * q^74 - 25326 * q^75 - 21308 * q^76 - 136242 * q^78 - 44062 * q^79 + 33381 * q^80 + 26244 * q^81 - 57596 * q^82 + 208446 * q^83 + 36324 * q^85 - 136968 * q^86 - 4860 * q^87 + 87597 * q^88 + 77520 * q^89 - 22923 * q^90 + 158256 * q^92 - 57690 * q^93 + 73722 * q^94 - 221376 * q^95 - 139671 * q^96 + 188630 * q^97 + 32562 * 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 $

$2$	−0.790805	−0.139796	−0.0698979	−	0.997554i	$-0.522267\pi$
$2$	−0.790805	−0.139796	−0.0698979	+	0.997554i	$0.522267\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	−31.3746	−0.980457
$5$	104.192	1.86384	0.931919	−	0.362667i	$-0.118134\pi$
$5$	104.192	1.86384	0.931919	+	0.362667i	$0.118134\pi$
$6$	7.11724	0.0807112
$7$	0	0
$7$	0	0
$8$	50.1170	0.276860
$9$	81.0000	0.333333
$10$	−82.3953	−0.260557
$11$	−497.660	−1.24008	−0.620041	−	0.784569i	$-0.712884\pi$
$11$	−497.660	−1.24008	−0.620041	+	0.784569i	$0.712884\pi$
$12$	282.372	0.566067
$13$	206.551	0.338977	0.169488	−	0.985532i	$-0.445789\pi$
$13$	206.551	0.338977	0.169488	+	0.985532i	$0.445789\pi$
$14$	0	0
$15$	−937.725	−1.07609
$16$	964.355	0.941753
$17$	−63.1586	−0.0530042	−0.0265021	−	0.999649i	$-0.508437\pi$
$17$	−63.1586	−0.0530042	−0.0265021	+	0.999649i	$0.508437\pi$
$18$	−64.0552	−0.0465986
$19$	−1323.95	−0.841374	−0.420687	−	0.907206i	$-0.638211\pi$
$19$	−1323.95	−0.841374	−0.420687	+	0.907206i	$0.638211\pi$
$20$	−3268.98	−1.82741
$21$	0	0
$22$	393.552	0.173358
$23$	−194.437	−0.0766408	−0.0383204	−	0.999266i	$-0.512201\pi$
$23$	−194.437	−0.0766408	−0.0383204	+	0.999266i	$0.512201\pi$
$24$	−451.053	−0.159845
$25$	7730.91	2.47389
$26$	−163.342	−0.0473875
$27$	−729.000	−0.192450
$28$	0	0
$29$	4323.14	0.954562	0.477281	−	0.878751i	$-0.341622\pi$
$29$	4323.14	0.954562	0.477281	+	0.878751i	$0.341622\pi$
$30$	741.558	0.150433
$31$	7525.31	1.40644	0.703219	−	0.710974i	$-0.251745\pi$
$31$	7525.31	1.40644	0.703219	+	0.710974i	$0.251745\pi$
$32$	−2366.36	−0.408513
$33$	4478.94	0.715962
$34$	49.9461	0.00740977
$35$	0	0
$36$	−2541.34	−0.326819
$37$	10355.6	1.24358	0.621789	−	0.783185i	$-0.286406\pi$
$37$	10355.6	1.24358	0.621789	+	0.783185i	$0.286406\pi$
$38$	1046.99	0.117621
$39$	−1858.96	−0.195708
$40$	5221.77	0.516022
$41$	4180.92	0.388429	0.194215	−	0.980959i	$-0.437784\pi$
$41$	4180.92	0.388429	0.194215	+	0.980959i	$0.437784\pi$
$42$	0	0
$43$	5960.87	0.491630	0.245815	−	0.969317i	$-0.420944\pi$
$43$	5960.87	0.491630	0.245815	+	0.969317i	$0.420944\pi$
$44$	15613.9	1.21585
$45$	8439.53	0.621279
$46$	153.762	0.0107141
$47$	4389.74	0.289864	0.144932	−	0.989442i	$-0.453704\pi$
$47$	4389.74	0.289864	0.144932	+	0.989442i	$0.453704\pi$
$48$	−8679.20	−0.543721
$49$	0	0
$50$	−6113.64	−0.345840
$51$	568.427	0.0306020
$52$	−6480.47	−0.332352
$53$	17784.8	0.869679	0.434839	−	0.900508i	$-0.356805\pi$
$53$	17784.8	0.869679	0.434839	+	0.900508i	$0.356805\pi$
$54$	576.497	0.0269037
$55$	−51852.0	−2.31131
$56$	0	0
$57$	11915.6	0.485768
$58$	−3418.76	−0.133444
$59$	−3500.47	−0.130917	−0.0654585	−	0.997855i	$-0.520851\pi$
$59$	−3500.47	−0.130917	−0.0654585	+	0.997855i	$0.520851\pi$
$60$	29420.8	1.05506
$61$	10632.5	0.365855	0.182928	−	0.983126i	$-0.441443\pi$
$61$	10632.5	0.365855	0.182928	+	0.983126i	$0.441443\pi$
$62$	−5951.06	−0.196614
$63$	0	0
$64$	−28988.0	−0.884645
$65$	21520.9	0.631797
$66$	−3541.97	−0.100089
$67$	−13274.7	−0.361276	−0.180638	−	0.983550i	$-0.557816\pi$
$67$	−13274.7	−0.361276	−0.180638	+	0.983550i	$0.557816\pi$
$68$	1981.58	0.0519683
$69$	1749.94	0.0442486
$70$	0	0
$71$	38811.1	0.913713	0.456857	−	0.889540i	$-0.348975\pi$
$71$	38811.1	0.913713	0.456857	+	0.889540i	$0.348975\pi$
$72$	4059.47	0.0922866
$73$	−31375.6	−0.689105	−0.344552	−	0.938767i	$-0.611969\pi$
$73$	−31375.6	−0.689105	−0.344552	+	0.938767i	$0.611969\pi$
$74$	−8189.30	−0.173847
$75$	−69578.2	−1.42830
$76$	41538.6	0.824931
$77$	0	0
$78$	1470.08	0.0273592
$79$	39491.5	0.711927	0.355964	−	0.934500i	$-0.384153\pi$
$79$	39491.5	0.711927	0.355964	+	0.934500i	$0.384153\pi$
$80$	100478.	1.75528
$81$	6561.00	0.111111
$82$	−3306.29	−0.0543008
$83$	102372.	1.63112	0.815559	−	0.578675i	$-0.196430\pi$
$83$	102372.	1.63112	0.815559	+	0.578675i	$0.196430\pi$
$84$	0	0
$85$	−6580.60	−0.0987912
$86$	−4713.88	−0.0687279
$87$	−38908.2	−0.551117
$88$	−24941.2	−0.343329
$89$	112821.	1.50978	0.754892	−	0.655849i	$-0.227689\pi$
$89$	112821.	1.50978	0.754892	+	0.655849i	$0.227689\pi$
$90$	−6674.02	−0.0868523
$91$	0	0
$92$	6100.40	0.0751430
$93$	−67727.8	−0.812007
$94$	−3471.43	−0.0405218
$95$	−137945.	−1.56818
$96$	21297.2	0.235855
$97$	−30334.3	−0.327345	−0.163672	−	0.986515i	$-0.552334\pi$
$97$	−30334.3	−0.327345	−0.163672	+	0.986515i	$0.552334\pi$
$98$	0	0
$99$	−40310.4	−0.413361
$100$	−242554.	−2.42554
$101$	−106796.	−1.04172	−0.520862	−	0.853641i	$-0.674390\pi$
$101$	−106796.	−1.04172	−0.520862	+	0.853641i	$0.674390\pi$
$102$	−449.515	−0.00427803
$103$	−157536.	−1.46314	−0.731570	−	0.681767i	$-0.761212\pi$
$103$	−157536.	−1.46314	−0.731570	+	0.681767i	$0.761212\pi$
$104$	10351.7	0.0938490
$105$	0	0
$106$	−14064.3	−0.121578
$107$	−89324.3	−0.754241	−0.377121	−	0.926164i	$-0.623086\pi$
$107$	−89324.3	−0.754241	−0.377121	+	0.926164i	$0.623086\pi$
$108$	22872.1	0.188689
$109$	167605.	1.35120	0.675600	−	0.737268i	$-0.263885\pi$
$109$	167605.	1.35120	0.675600	+	0.737268i	$0.263885\pi$
$110$	41004.8	0.323112
$111$	−93200.8	−0.717980
$112$	0	0
$113$	−115794.	−0.853079	−0.426539	−	0.904469i	$-0.640267\pi$
$113$	−115794.	−0.853079	−0.426539	+	0.904469i	$0.640267\pi$
$114$	−9422.91	−0.0679083
$115$	−20258.8	−0.142846
$116$	−135637.	−0.935907
$117$	16730.7	0.112992
$118$	2768.19	0.0183017
$119$	0	0
$120$	−46995.9	−0.297925
$121$	86614.1	0.537805
$122$	−8408.20	−0.0511451
$123$	−37628.2	−0.224260
$124$	−236104.	−1.37895
$125$	479898.	2.74709
$126$	0	0
$127$	201513.	1.10865	0.554325	−	0.832300i	$-0.312977\pi$
$127$	201513.	1.10865	0.554325	+	0.832300i	$0.312977\pi$
$128$	98647.4	0.532183
$129$	−53647.8	−0.283843
$130$	−17018.9	−0.0883227
$131$	−38469.6	−0.195857	−0.0979285	−	0.995193i	$-0.531222\pi$
$131$	−38469.6	−0.195857	−0.0979285	+	0.995193i	$0.531222\pi$
$132$	−140525.	−0.701970
$133$	0	0
$134$	10497.7	0.0505049
$135$	−75955.7	−0.358696
$136$	−3165.32	−0.0146747
$137$	−241722.	−1.10031	−0.550155	−	0.835063i	$-0.685431\pi$
$137$	−241722.	−1.10031	−0.550155	+	0.835063i	$0.685431\pi$
$138$	−1383.86	−0.00618577
$139$	53112.2	0.233162	0.116581	−	0.993181i	$-0.462807\pi$
$139$	53112.2	0.233162	0.116581	+	0.993181i	$0.462807\pi$
$140$	0	0
$141$	−39507.6	−0.167353
$142$	−30692.0	−0.127733
$143$	−102792.	−0.420359
$144$	78112.8	0.313918
$145$	450435.	1.77915
$146$	24812.0	0.0963340
$147$	0	0
$148$	−324905.	−1.21927
$149$	129062.	0.476248	0.238124	−	0.971235i	$-0.423468\pi$
$149$	129062.	0.476248	0.238124	+	0.971235i	$0.423468\pi$
$150$	55022.8	0.199671
$151$	153206.	0.546808	0.273404	−	0.961899i	$-0.411850\pi$
$151$	153206.	0.546808	0.273404	+	0.961899i	$0.411850\pi$
$152$	−66352.6	−0.232943
$153$	−5115.85	−0.0176681
$154$	0	0
$155$	784075.	2.62137
$156$	58324.2	0.191884
$157$	151188.	0.489517	0.244758	−	0.969584i	$-0.421291\pi$
$157$	151188.	0.489517	0.244758	+	0.969584i	$0.421291\pi$
$158$	−31230.0	−0.0995245
$159$	−160063.	−0.502109
$160$	−246555.	−0.761402
$161$	0	0
$162$	−5188.47	−0.0155329
$163$	−32916.7	−0.0970392	−0.0485196	−	0.998822i	$-0.515450\pi$
$163$	−32916.7	−0.0970392	−0.0485196	+	0.998822i	$0.515450\pi$
$164$	−131175.	−0.380838
$165$	466668.	1.33444
$166$	−80956.1	−0.228023
$167$	−217586.	−0.603725	−0.301862	−	0.953352i	$-0.597608\pi$
$167$	−217586.	−0.603725	−0.301862	+	0.953352i	$0.597608\pi$
$168$	0	0
$169$	−328630.	−0.885095
$170$	5203.97	0.0138106
$171$	−107240.	−0.280458
$172$	−187020.	−0.482022
$173$	421242.	1.07008	0.535041	−	0.844826i	$-0.320296\pi$
$173$	421242.	1.07008	0.535041	+	0.844826i	$0.320296\pi$
$174$	30768.8	0.0770438
$175$	0	0
$176$	−479921.	−1.16785
$177$	31504.2	0.0755849
$178$	−89219.4	−0.211062
$179$	3494.06	0.00815075	0.00407538	−	0.999992i	$-0.498703\pi$
$179$	3494.06	0.00815075	0.00407538	+	0.999992i	$0.498703\pi$
$180$	−264787.	−0.609138
$181$	−594611.	−1.34908	−0.674538	−	0.738240i	$-0.735657\pi$
$181$	−594611.	−1.34908	−0.674538	+	0.738240i	$0.735657\pi$
$182$	0	0
$183$	−95692.2	−0.211227
$184$	−9744.61	−0.0212188
$185$	1.07897e6	2.31783
$186$	53559.5	0.113515
$187$	31431.5	0.0657296
$188$	−137726.	−0.284199
$189$	0	0
$190$	109088.	0.219226
$191$	828644.	1.64356	0.821778	−	0.569807i	$-0.192982\pi$
$191$	828644.	1.64356	0.821778	+	0.569807i	$0.192982\pi$
$192$	260892.	0.510750
$193$	219739.	0.424633	0.212316	−	0.977201i	$-0.431899\pi$
$193$	219739.	0.424633	0.212316	+	0.977201i	$0.431899\pi$
$194$	23988.5	0.0457614
$195$	−193688.	−0.364768
$196$	0	0
$197$	475612.	0.873146	0.436573	−	0.899669i	$-0.356192\pi$
$197$	475612.	0.873146	0.436573	+	0.899669i	$0.356192\pi$
$198$	31877.7	0.0577862
$199$	−627555.	−1.12336	−0.561681	−	0.827354i	$-0.689845\pi$
$199$	−627555.	−1.12336	−0.561681	+	0.827354i	$0.689845\pi$
$200$	387450.	0.684921
$201$	119473.	0.208583
$202$	84455.1	0.145629
$203$	0	0
$204$	−17834.2	−0.0300039
$205$	435617.	0.723969
$206$	124580.	0.204541
$207$	−15749.4	−0.0255469
$208$	199189.	0.319232
$209$	658879.	1.04337
$210$	0	0
$211$	570989.	0.882920	0.441460	−	0.897281i	$-0.354461\pi$
$211$	570989.	0.882920	0.441460	+	0.897281i	$0.354461\pi$
$212$	−557991.	−0.852683
$213$	−349300.	−0.527533
$214$	70638.1	0.105440
$215$	621073.	0.916319
$216$	−36535.3	−0.0532817
$217$	0	0
$218$	−132543.	−0.188892
$219$	282381.	0.397855
$220$	1.62684e6	2.26614
$221$	−13045.5	−0.0179672
$222$	73703.7	0.100371
$223$	−4233.11	−0.00570029	−0.00285015	−	0.999996i	$-0.500907\pi$
$223$	−4233.11	−0.00570029	−0.00285015	+	0.999996i	$0.500907\pi$
$224$	0	0
$225$	626204.	0.824630
$226$	91570.3	0.119257
$227$	−1.12986e6	−1.45533	−0.727664	−	0.685934i	$-0.759394\pi$
$227$	−1.12986e6	−1.45533	−0.727664	+	0.685934i	$0.759394\pi$
$228$	−373847.	−0.476274
$229$	−804643.	−1.01395	−0.506973	−	0.861962i	$-0.669236\pi$
$229$	−804643.	−1.01395	−0.506973	+	0.861962i	$0.669236\pi$
$230$	16020.7	0.0199693
$231$	0	0
$232$	216663.	0.264280
$233$	1.16927e6	1.41100	0.705498	−	0.708712i	$-0.250723\pi$
$233$	1.16927e6	1.41100	0.705498	+	0.708712i	$0.250723\pi$
$234$	−13230.7	−0.0157958
$235$	457374.	0.540259
$236$	109826.	0.128358
$237$	−355423.	−0.411031
$238$	0	0
$239$	−1.70554e6	−1.93138	−0.965689	−	0.259700i	$-0.916376\pi$
$239$	−1.70554e6	−1.93138	−0.965689	+	0.259700i	$0.916376\pi$
$240$	−904300.	−1.01341
$241$	−951196.	−1.05494	−0.527470	−	0.849574i	$-0.676859\pi$
$241$	−951196.	−1.05494	−0.527470	+	0.849574i	$0.676859\pi$
$242$	−68494.9	−0.0751830
$243$	−59049.0	−0.0641500
$244$	−333590.	−0.358705
$245$	0	0
$246$	29756.6	0.0313506
$247$	−273465.	−0.285206
$248$	377146.	0.389386
$249$	−921346.	−0.941726
$250$	−379505.	−0.384032
$251$	−1.14498e6	−1.14713	−0.573566	−	0.819159i	$-0.694440\pi$
$251$	−1.14498e6	−1.14713	−0.573566	+	0.819159i	$0.694440\pi$
$252$	0	0
$253$	96763.6	0.0950409
$254$	−159358.	−0.154985
$255$	59225.4	0.0570371
$256$	849606.	0.810248
$257$	−1.18374e6	−1.11795	−0.558976	−	0.829184i	$-0.688806\pi$
$257$	−1.18374e6	−1.11795	−0.558976	+	0.829184i	$0.688806\pi$
$258$	42425.0	0.0396800
$259$	0	0
$260$	−675211.	−0.619450
$261$	350174.	0.318187
$262$	30421.9	0.0273800
$263$	448316.	0.399664	0.199832	−	0.979830i	$-0.435960\pi$
$263$	448316.	0.399664	0.199832	+	0.979830i	$0.435960\pi$
$264$	224471.	0.198221
$265$	1.85303e6	1.62094
$266$	0	0
$267$	−1.01539e6	−0.871674
$268$	416490.	0.354216
$269$	−747474.	−0.629819	−0.314909	−	0.949122i	$-0.601974\pi$
$269$	−747474.	−0.629819	−0.314909	+	0.949122i	$0.601974\pi$
$270$	60066.2	0.0501442
$271$	232637.	0.192423	0.0962114	−	0.995361i	$-0.469328\pi$
$271$	232637.	0.192423	0.0962114	+	0.995361i	$0.469328\pi$
$272$	−60907.3	−0.0499169
$273$	0	0
$274$	191155.	0.153819
$275$	−3.84736e6	−3.06783
$276$	−54903.6	−0.0433838
$277$	−2.42924e6	−1.90227	−0.951134	−	0.308778i	$-0.900080\pi$
$277$	−2.42924e6	−1.90227	−0.951134	+	0.308778i	$0.900080\pi$
$278$	−42001.4	−0.0325951
$279$	609550.	0.468812
$280$	0	0
$281$	2.51704e6	1.90163	0.950813	−	0.309766i	$-0.100251\pi$
$281$	2.51704e6	1.90163	0.950813	+	0.309766i	$0.100251\pi$
$282$	31242.8	0.0233953
$283$	−260994.	−0.193716	−0.0968579	−	0.995298i	$-0.530879\pi$
$283$	−260994.	−0.193716	−0.0968579	+	0.995298i	$0.530879\pi$
$284$	−1.21768e6	−0.895857
$285$	1.24151e6	0.905392
$286$	81288.6	0.0587645
$287$	0	0
$288$	−191675.	−0.136171
$289$	−1.41587e6	−0.997191
$290$	−356206.	−0.248718
$291$	273009.	0.188993
$292$	984399.	0.675638
$293$	−65011.7	−0.0442408	−0.0221204	−	0.999755i	$-0.507042\pi$
$293$	−65011.7	−0.0442408	−0.0221204	+	0.999755i	$0.507042\pi$
$294$	0	0
$295$	−364720.	−0.244008
$296$	518994.	0.344297
$297$	362794.	0.238654
$298$	−102063.	−0.0665775
$299$	−40161.3	−0.0259794
$300$	2.18299e6	1.40039
$301$	0	0
$302$	−121156.	−0.0764414
$303$	961167.	0.601440
$304$	−1.27676e6	−0.792367
$305$	1.10781e6	0.681895
$306$	4045.64	0.00246992
$307$	2.35599e6	1.42668	0.713342	−	0.700816i	$-0.247181\pi$
$307$	2.35599e6	1.42668	0.713342	+	0.700816i	$0.247181\pi$
$308$	0	0
$309$	1.41782e6	0.844744
$310$	−620051.	−0.366457
$311$	2.11805e6	1.24176	0.620878	−	0.783907i	$-0.286776\pi$
$311$	2.11805e6	1.24176	0.620878	+	0.783907i	$0.286776\pi$
$312$	−93165.6	−0.0541837
$313$	187514.	0.108186	0.0540931	−	0.998536i	$-0.482773\pi$
$313$	187514.	0.108186	0.0540931	+	0.998536i	$0.482773\pi$
$314$	−119560.	−0.0684324
$315$	0	0
$316$	−1.23903e6	−0.698014
$317$	−1.00541e6	−0.561947	−0.280974	−	0.959716i	$-0.590657\pi$
$317$	−1.00541e6	−0.561947	−0.280974	+	0.959716i	$0.590657\pi$
$318$	126579.	0.0701928
$319$	−2.15145e6	−1.18374
$320$	−3.02031e6	−1.64883
$321$	803919.	0.435461
$322$	0	0
$323$	83619.1	0.0445964
$324$	−205849.	−0.108940
$325$	1.59683e6	0.838591
$326$	26030.7	0.0135657
$327$	−1.50844e6	−0.780116
$328$	209535.	0.107540
$329$	0	0
$330$	−369043.	−0.186549
$331$	1.67984e6	0.842748	0.421374	−	0.906887i	$-0.361548\pi$
$331$	1.67984e6	0.842748	0.421374	+	0.906887i	$0.361548\pi$
$332$	−3.21188e6	−1.59924
$333$	838807.	0.414526
$334$	172068.	0.0843982
$335$	−1.38312e6	−0.673360
$336$	0	0
$337$	−995036.	−0.477270	−0.238635	−	0.971109i	$-0.576700\pi$
$337$	−995036.	−0.477270	−0.238635	+	0.971109i	$0.576700\pi$
$338$	259882.	0.123733
$339$	1.04214e6	0.492525
$340$	206464.	0.0968605
$341$	−3.74505e6	−1.74410
$342$	84806.2	0.0392069
$343$	0	0
$344$	298741.	0.136113
$345$	182329.	0.0824722
$346$	−333121.	−0.149593
$347$	4.05665e6	1.80861	0.904304	−	0.426890i	$-0.140391\pi$
$347$	4.05665e6	1.80861	0.904304	+	0.426890i	$0.140391\pi$
$348$	1.22073e6	0.540346
$349$	−2.86202e6	−1.25779	−0.628897	−	0.777488i	$-0.716493\pi$
$349$	−2.86202e6	−1.25779	−0.628897	+	0.777488i	$0.716493\pi$
$350$	0	0
$351$	−150576.	−0.0652361
$352$	1.17764e6	0.506590
$353$	−832685.	−0.355667	−0.177834	−	0.984061i	$-0.556909\pi$
$353$	−832685.	−0.355667	−0.177834	+	0.984061i	$0.556909\pi$
$354$	−24913.7	−0.0105665
$355$	4.04379e6	1.70301
$356$	−3.53972e6	−1.48028
$357$	0	0
$358$	−2763.12	−0.00113944
$359$	−2.69751e6	−1.10465	−0.552327	−	0.833627i	$-0.686260\pi$
$359$	−2.69751e6	−1.10465	−0.552327	+	0.833627i	$0.686260\pi$
$360$	422964.	0.172007
$361$	−723243.	−0.292090
$362$	470221.	0.188595
$363$	−779527.	−0.310502
$364$	0	0
$365$	−3.26908e6	−1.28438
$366$	75673.8	0.0295286
$367$	−1.45482e6	−0.563826	−0.281913	−	0.959440i	$-0.590969\pi$
$367$	−1.45482e6	−0.563826	−0.281913	+	0.959440i	$0.590969\pi$
$368$	−187507.	−0.0721767
$369$	338654.	0.129476
$370$	−853257.	−0.324023
$371$	0	0
$372$	2.12494e6	0.796138
$373$	−2.04689e6	−0.761766	−0.380883	−	0.924623i	$-0.624380\pi$
$373$	−2.04689e6	−0.761766	−0.380883	+	0.924623i	$0.624380\pi$
$374$	−24856.2	−0.00918872
$375$	−4.31908e6	−1.58604
$376$	220000.	0.0802516
$377$	892950.	0.323574
$378$	0	0
$379$	−416898.	−0.149084	−0.0745421	−	0.997218i	$-0.523750\pi$
$379$	−416898.	−0.149084	−0.0745421	+	0.997218i	$0.523750\pi$
$380$	4.32798e6	1.53754
$381$	−1.81362e6	−0.640079
$382$	−655296.	−0.229762
$383$	3.87626e6	1.35025	0.675127	−	0.737701i	$-0.264089\pi$
$383$	3.87626e6	1.35025	0.675127	+	0.737701i	$0.264089\pi$
$384$	−887827.	−0.307256
$385$	0	0
$386$	−173771.	−0.0593619
$387$	482830.	0.163877
$388$	951729.	0.320947
$389$	2.83802e6	0.950915	0.475458	−	0.879739i	$-0.342283\pi$
$389$	2.83802e6	0.950915	0.475458	+	0.879739i	$0.342283\pi$
$390$	153170.	0.0509931
$391$	12280.4	0.00406228
$392$	0	0
$393$	346226.	0.113078
$394$	−376116.	−0.122062
$395$	4.11468e6	1.32692
$396$	1.26472e6	0.405283
$397$	−4.34266e6	−1.38286	−0.691432	−	0.722442i	$-0.743020\pi$
$397$	−4.34266e6	−1.38286	−0.691432	+	0.722442i	$0.743020\pi$
$398$	496274.	0.157041
$399$	0	0
$400$	7.45534e6	2.32979
$401$	3.40304e6	1.05683	0.528417	−	0.848985i	$-0.322786\pi$
$401$	3.40304e6	1.05683	0.528417	+	0.848985i	$0.322786\pi$
$402$	−94479.6	−0.0291590
$403$	1.55436e6	0.476749
$404$	3.35070e6	1.02137
$405$	683602.	0.207093
$406$	0	0
$407$	−5.15359e6	−1.54214
$408$	28487.9	0.00847246
$409$	5.29431e6	1.56495	0.782477	−	0.622680i	$-0.213956\pi$
$409$	5.29431e6	1.56495	0.782477	+	0.622680i	$0.213956\pi$
$410$	−344488.	−0.101208
$411$	2.17550e6	0.635264
$412$	4.94262e6	1.43455
$413$	0	0
$414$	12454.7	0.00357136
$415$	1.06663e7	3.04014
$416$	−488775.	−0.138476
$417$	−478010.	−0.134616
$418$	−521045.	−0.145859
$419$	−2.87267e6	−0.799376	−0.399688	−	0.916651i	$-0.630881\pi$
$419$	−2.87267e6	−0.799376	−0.399688	+	0.916651i	$0.630881\pi$
$420$	0	0
$421$	2.08688e6	0.573843	0.286921	−	0.957954i	$-0.407368\pi$
$421$	2.08688e6	0.573843	0.286921	+	0.957954i	$0.407368\pi$
$422$	−451541.	−0.123429
$423$	355569.	0.0966213
$424$	891319.	0.240779
$425$	−488273.	−0.131127
$426$	276228.	0.0737469
$427$	0	0
$428$	2.80252e6	0.739501
$429$	925130.	0.242694
$430$	−491148.	−0.128098
$431$	−2.42863e6	−0.629751	−0.314876	−	0.949133i	$-0.601963\pi$
$431$	−2.42863e6	−0.629751	−0.314876	+	0.949133i	$0.601963\pi$
$432$	−703015.	−0.181240
$433$	−956219.	−0.245097	−0.122548	−	0.992463i	$-0.539107\pi$
$433$	−956219.	−0.245097	−0.122548	+	0.992463i	$0.539107\pi$
$434$	0	0
$435$	−4.05392e6	−1.02719
$436$	−5.25853e6	−1.32479
$437$	257426.	0.0644836
$438$	−223308.	−0.0556185
$439$	−2.64205e6	−0.654304	−0.327152	−	0.944972i	$-0.606089\pi$
$439$	−2.64205e6	−0.654304	−0.327152	+	0.944972i	$0.606089\pi$
$440$	−2.59867e6	−0.639910
$441$	0	0
$442$	10316.4	0.00251174
$443$	−3.43966e6	−0.832733	−0.416366	−	0.909197i	$-0.636697\pi$
$443$	−3.43966e6	−0.832733	−0.416366	+	0.909197i	$0.636697\pi$
$444$	2.92414e6	0.703949
$445$	1.17550e7	2.81399
$446$	3347.56	0.000796878 0
$447$	−1.16156e6	−0.274962
$448$	0	0
$449$	4.39903e6	1.02977	0.514886	−	0.857259i	$-0.327834\pi$
$449$	4.39903e6	1.02977	0.514886	+	0.857259i	$0.327834\pi$
$450$	−495205.	−0.115280
$451$	−2.08067e6	−0.481684
$452$	3.63299e6	0.836407
$453$	−1.37886e6	−0.315699
$454$	893501.	0.203449
$455$	0	0
$456$	597173.	0.134490
$457$	−2.25110e6	−0.504202	−0.252101	−	0.967701i	$-0.581122\pi$
$457$	−2.25110e6	−0.504202	−0.252101	+	0.967701i	$0.581122\pi$
$458$	636316.	0.141745
$459$	46042.6	0.0102007
$460$	635611.	0.140054
$461$	−1.85307e6	−0.406107	−0.203053	−	0.979168i	$-0.565087\pi$
$461$	−1.85307e6	−0.406107	−0.203053	+	0.979168i	$0.565087\pi$
$462$	0	0
$463$	−3.01089e6	−0.652744	−0.326372	−	0.945241i	$-0.605826\pi$
$463$	−3.01089e6	−0.652744	−0.326372	+	0.945241i	$0.605826\pi$
$464$	4.16904e6	0.898962
$465$	−7.05668e6	−1.51345
$466$	−924667.	−0.197252
$467$	1.06725e6	0.226452	0.113226	−	0.993569i	$-0.463882\pi$
$467$	1.06725e6	0.226452	0.113226	+	0.993569i	$0.463882\pi$
$468$	−524918.	−0.110784
$469$	0	0
$470$	−361694.	−0.0755260
$471$	−1.36069e6	−0.282623
$472$	−175433.	−0.0362456
$473$	−2.96648e6	−0.609662
$474$	281070.	0.0574605
$475$	−1.02354e7	−2.08147
$476$	0	0
$477$	1.44057e6	0.289893
$478$	1.34875e6	0.269999
$479$	5.68788e6	1.13269	0.566346	−	0.824168i	$-0.308357\pi$
$479$	5.68788e6	1.13269	0.566346	+	0.824168i	$0.308357\pi$
$480$	2.21900e6	0.439596
$481$	2.13897e6	0.421544
$482$	752211.	0.147476
$483$	0	0
$484$	−2.71749e6	−0.527295
$485$	−3.16059e6	−0.610117
$486$	46696.2	0.00896791
$487$	−6.84477e6	−1.30779	−0.653893	−	0.756587i	$-0.726865\pi$
$487$	−6.84477e6	−1.30779	−0.653893	+	0.756587i	$0.726865\pi$
$488$	532867.	0.101291
$489$	296250.	0.0560256
$490$	0	0
$491$	5.60132e6	1.04854	0.524272	−	0.851551i	$-0.324338\pi$
$491$	5.60132e6	1.04854	0.524272	+	0.851551i	$0.324338\pi$
$492$	1.18057e6	0.219877
$493$	−273043.	−0.0505958
$494$	216257.	0.0398706
$495$	−4.20001e6	−0.770438
$496$	7.25708e6	1.32452
$497$	0	0
$498$	728605.	0.131649
$499$	−2.33529e6	−0.419845	−0.209923	−	0.977718i	$-0.567321\pi$
$499$	−2.33529e6	−0.419845	−0.209923	+	0.977718i	$0.567321\pi$
$500$	−1.50566e7	−2.69341
$501$	1.95827e6	0.348561
$502$	905455.	0.160364
$503$	1.08278e7	1.90819	0.954093	−	0.299510i	$-0.0968233\pi$
$503$	1.08278e7	1.90819	0.954093	+	0.299510i	$0.0968233\pi$
$504$	0	0
$505$	−1.11273e7	−1.94161
$506$	−76521.1	−0.0132863
$507$	2.95767e6	0.511010
$508$	−6.32240e6	−1.08698
$509$	−3.17847e6	−0.543781	−0.271890	−	0.962328i	$-0.587649\pi$
$509$	−3.17847e6	−0.543781	−0.271890	+	0.962328i	$0.587649\pi$
$510$	−46835.7	−0.00797356
$511$	0	0
$512$	−3.82859e6	−0.645452
$513$	965163.	0.161923
$514$	936107.	0.156285
$515$	−1.64139e7	−2.72705
$516$	1.68318e6	0.278296
$517$	−2.18460e6	−0.359455
$518$	0	0
$519$	−3.79118e6	−0.617812
$520$	1.07856e6	0.174919
$521$	6.35837e6	1.02625	0.513123	−	0.858315i	$-0.328489\pi$
$521$	6.35837e6	1.02625	0.513123	+	0.858315i	$0.328489\pi$
$522$	−276919.	−0.0444813
$523$	7.22187e6	1.15450	0.577252	−	0.816566i	$-0.304125\pi$
$523$	7.22187e6	1.15450	0.577252	+	0.816566i	$0.304125\pi$
$524$	1.20697e6	0.192029
$525$	0	0
$526$	−354531.	−0.0558714
$527$	−475288.	−0.0745471
$528$	4.31929e6	0.674260
$529$	−6.39854e6	−0.994126
$530$	−1.46538e6	−0.226601
$531$	−283538.	−0.0436390
$532$	0	0
$533$	863574.	0.131668
$534$	802974.	0.121856
$535$	−9.30685e6	−1.40578
$536$	−665290.	−0.100023
$537$	−31446.5	−0.00470584
$538$	591106.	0.0880461
$539$	0	0
$540$	2.38308e6	0.351686
$541$	−9.43165e6	−1.38546	−0.692731	−	0.721196i	$-0.743593\pi$
$541$	−9.43165e6	−1.38546	−0.692731	+	0.721196i	$0.743593\pi$
$542$	−183971.	−0.0268999
$543$	5.35150e6	0.778889
$544$	149456.	0.0216529
$545$	1.74630e7	2.51842
$546$	0	0
$547$	9.91568e6	1.41695	0.708474	−	0.705737i	$-0.249384\pi$
$547$	9.91568e6	1.41695	0.708474	+	0.705737i	$0.249384\pi$
$548$	7.58394e6	1.07881
$549$	861230.	0.121952
$550$	3.04251e6	0.428870
$551$	−5.72364e6	−0.803144
$552$	87701.5	0.0122507
$553$	0	0
$554$	1.92106e6	0.265929
$555$	−9.71075e6	−1.33820
$556$	−1.66638e6	−0.228605
$557$	9.64613e6	1.31739	0.658696	−	0.752409i	$-0.271108\pi$
$557$	9.64613e6	1.31739	0.658696	+	0.752409i	$0.271108\pi$
$558$	−482036.	−0.0655381
$559$	1.23123e6	0.166651
$560$	0	0
$561$	−282883.	−0.0379490
$562$	−1.99049e6	−0.265839
$563$	−3.09504e6	−0.411524	−0.205762	−	0.978602i	$-0.565967\pi$
$563$	−3.09504e6	−0.411524	−0.205762	+	0.978602i	$0.565967\pi$
$564$	1.23954e6	0.164082
$565$	−1.20648e7	−1.59000
$566$	206396.	0.0270807
$567$	0	0
$568$	1.94509e6	0.252970
$569$	−1.23185e7	−1.59507	−0.797533	−	0.603275i	$-0.793862\pi$
$569$	−1.23185e7	−1.59507	−0.797533	+	0.603275i	$0.793862\pi$
$570$	−981789.	−0.126570
$571$	−3.23510e6	−0.415238	−0.207619	−	0.978210i	$-0.566571\pi$
$571$	−3.23510e6	−0.415238	−0.207619	+	0.978210i	$0.566571\pi$
$572$	3.22507e6	0.412144
$573$	−7.45780e6	−0.948908
$574$	0	0
$575$	−1.50318e6	−0.189601
$576$	−2.34803e6	−0.294882
$577$	9.05049e6	1.13170	0.565852	−	0.824507i	$-0.308547\pi$
$577$	9.05049e6	1.13170	0.565852	+	0.824507i	$0.308547\pi$
$578$	1.11968e6	0.139403
$579$	−1.97765e6	−0.245162
$580$	−1.41322e7	−1.74438
$581$	0	0
$582$	−215897.	−0.0264204
$583$	−8.85077e6	−1.07847
$584$	−1.57245e6	−0.190785
$585$	1.74320e6	0.210599
$586$	51411.6	0.00618468
$587$	2.13170e6	0.255347	0.127673	−	0.991816i	$-0.459249\pi$
$587$	2.13170e6	0.255347	0.127673	+	0.991816i	$0.459249\pi$
$588$	0	0
$589$	−9.96318e6	−1.18334
$590$	288422.	0.0341113
$591$	−4.28051e6	−0.504111
$592$	9.98652e6	1.17114
$593$	7.26933e6	0.848903	0.424451	−	0.905451i	$-0.360467\pi$
$593$	7.26933e6	0.848903	0.424451	+	0.905451i	$0.360467\pi$
$594$	−286899.	−0.0333629
$595$	0	0
$596$	−4.04927e6	−0.466941
$597$	5.64800e6	0.648573
$598$	31759.8	0.00363182
$599$	−2.20565e6	−0.251171	−0.125585	−	0.992083i	$-0.540081\pi$
$599$	−2.20565e6	−0.251171	−0.125585	+	0.992083i	$0.540081\pi$
$600$	−3.48705e6	−0.395439
$601$	1.00121e7	1.13067	0.565336	−	0.824860i	$-0.308746\pi$
$601$	1.00121e7	1.13067	0.565336	+	0.824860i	$0.308746\pi$
$602$	0	0
$603$	−1.07525e6	−0.120425
$604$	−4.80679e6	−0.536121
$605$	9.02447e6	1.00238
$606$	−760096.	−0.0840789
$607$	−6.32139e6	−0.696371	−0.348185	−	0.937426i	$-0.613202\pi$
$607$	−6.32139e6	−0.696371	−0.348185	+	0.937426i	$0.613202\pi$
$608$	3.13295e6	0.343712
$609$	0	0
$610$	−876065.	−0.0953261
$611$	906706.	0.0982570
$612$	160508.	0.0173228
$613$	1.43078e7	1.53788	0.768941	−	0.639319i	$-0.220784\pi$
$613$	1.43078e7	1.53788	0.768941	+	0.639319i	$0.220784\pi$
$614$	−1.86313e6	−0.199445
$615$	−3.92055e6	−0.417984
$616$	0	0
$617$	1.73991e7	1.83999	0.919993	−	0.391936i	$-0.128194\pi$
$617$	1.73991e7	1.83999	0.919993	+	0.391936i	$0.128194\pi$
$618$	−1.12122e6	−0.118092
$619$	−8.26736e6	−0.867242	−0.433621	−	0.901095i	$-0.642764\pi$
$619$	−8.26736e6	−0.867242	−0.433621	+	0.901095i	$0.642764\pi$
$620$	−2.46001e7	−2.57014
$621$	141745.	0.0147495
$622$	−1.67497e6	−0.173592
$623$	0	0
$624$	−1.79270e6	−0.184309
$625$	2.58422e7	2.64625
$626$	−148287.	−0.0151240
$627$	−5.92991e6	−0.602392
$628$	−4.74346e6	−0.479950
$629$	−654048.	−0.0659148
$630$	0	0
$631$	2.83238e6	0.283190	0.141595	−	0.989925i	$-0.454777\pi$
$631$	2.83238e6	0.283190	0.141595	+	0.989925i	$0.454777\pi$
$632$	1.97919e6	0.197104
$633$	−5.13890e6	−0.509754
$634$	795084.	0.0785579
$635$	2.09960e7	2.06634
$636$	5.02192e6	0.492297
$637$	0	0
$638$	1.70138e6	0.165481
$639$	3.14370e6	0.304571
$640$	1.02782e7	0.991902
$641$	−3.57176e6	−0.343350	−0.171675	−	0.985154i	$-0.554918\pi$
$641$	−3.57176e6	−0.343350	−0.171675	+	0.985154i	$0.554918\pi$
$642$	−635743.	−0.0608757
$643$	5.96911e6	0.569354	0.284677	−	0.958624i	$-0.408114\pi$
$643$	5.96911e6	0.569354	0.284677	+	0.958624i	$0.408114\pi$
$644$	0	0
$645$	−5.58966e6	−0.529037
$646$	−66126.4	−0.00623439
$647$	1.68276e6	0.158038	0.0790189	−	0.996873i	$-0.474821\pi$
$647$	1.68276e6	0.158038	0.0790189	+	0.996873i	$0.474821\pi$
$648$	328817.	0.0307622
$649$	1.74204e6	0.162348
$650$	−1.26278e6	−0.117232
$651$	0	0
$652$	1.03275e6	0.0951427
$653$	1.70305e7	1.56295	0.781475	−	0.623937i	$-0.214468\pi$
$653$	1.70305e7	1.56295	0.781475	+	0.623937i	$0.214468\pi$
$654$	1.19288e6	0.109057
$655$	−4.00821e6	−0.365046
$656$	4.03189e6	0.365804
$657$	−2.54143e6	−0.229702
$658$	0	0
$659$	−1.99303e7	−1.78772	−0.893862	−	0.448342i	$-0.852015\pi$
$659$	−1.99303e7	−1.78772	−0.893862	+	0.448342i	$0.852015\pi$
$660$	−1.46415e7	−1.30836
$661$	−9.55735e6	−0.850812	−0.425406	−	0.905003i	$-0.639869\pi$
$661$	−9.55735e6	−0.850812	−0.425406	+	0.905003i	$0.639869\pi$
$662$	−1.32843e6	−0.117813
$663$	117409.	0.0103734
$664$	5.13056e6	0.451591
$665$	0	0
$666$	−663333.	−0.0579490
$667$	−840579.	−0.0731584
$668$	6.82666e6	0.591926
$669$	38098.0	0.00329107
$670$	1.09378e6	0.0941330
$671$	−5.29135e6	−0.453691
$672$	0	0
$673$	1.80397e7	1.53530	0.767648	−	0.640872i	$-0.221427\pi$
$673$	1.80397e7	1.53530	0.767648	+	0.640872i	$0.221427\pi$
$674$	786879.	0.0667204
$675$	−5.63583e6	−0.476101
$676$	1.03106e7	0.867798
$677$	1.44741e7	1.21372	0.606861	−	0.794808i	$-0.292429\pi$
$677$	1.44741e7	1.21372	0.606861	+	0.794808i	$0.292429\pi$
$678$	−824133.	−0.0688530
$679$	0	0
$680$	−329800.	−0.0273513
$681$	1.01688e7	0.840234
$682$	2.96160e6	0.243818
$683$	2.68785e6	0.220472	0.110236	−	0.993905i	$-0.464839\pi$
$683$	2.68785e6	0.220472	0.110236	+	0.993905i	$0.464839\pi$
$684$	3.36463e6	0.274977
$685$	−2.51854e7	−2.05080
$686$	0	0
$687$	7.24179e6	0.585402
$688$	5.74839e6	0.462994
$689$	3.67347e6	0.294801
$690$	−144187.	−0.0115293
$691$	−4.67627e6	−0.372567	−0.186284	−	0.982496i	$-0.559644\pi$
$691$	−4.67627e6	−0.372567	−0.186284	+	0.982496i	$0.559644\pi$
$692$	−1.32163e7	−1.04917
$693$	0	0
$694$	−3.20802e6	−0.252836
$695$	5.53385e6	0.434576
$696$	−1.94996e6	−0.152582
$697$	−264061.	−0.0205884
$698$	2.26330e6	0.175834
$699$	−1.05235e7	−0.814639
$700$	0	0
$701$	6.34801e6	0.487913	0.243957	−	0.969786i	$-0.421555\pi$
$701$	6.34801e6	0.487913	0.243957	+	0.969786i	$0.421555\pi$
$702$	119076.	0.00911973
$703$	−1.37104e7	−1.04631
$704$	1.44262e7	1.09703
$705$	−4.11637e6	−0.311919
$706$	658492.	0.0497208
$707$	0	0
$708$	−988433.	−0.0741078
$709$	−6.41052e6	−0.478936	−0.239468	−	0.970904i	$-0.576973\pi$
$709$	−6.41052e6	−0.478936	−0.239468	+	0.970904i	$0.576973\pi$
$710$	−3.19785e6	−0.238074
$711$	3.19881e6	0.237309
$712$	5.65425e6	0.417998
$713$	−1.46320e6	−0.107790
$714$	0	0
$715$	−1.07101e7	−0.783481
$716$	−109625.	−0.00799146
$717$	1.53499e7	1.11508
$718$	2.13320e6	0.154426
$719$	−7.34505e6	−0.529874	−0.264937	−	0.964266i	$-0.585351\pi$
$719$	−7.34505e6	−0.529874	−0.264937	+	0.964266i	$0.585351\pi$
$720$	8.13870e6	0.585092
$721$	0	0
$722$	571944.	0.0408329
$723$	8.56077e6	0.609070
$724$	1.86557e7	1.32271
$725$	3.34218e7	2.36148
$726$	616454.	0.0434069
$727$	−1.57839e7	−1.10759	−0.553793	−	0.832655i	$-0.686820\pi$
$727$	−1.57839e7	−1.10759	−0.553793	+	0.832655i	$0.686820\pi$
$728$	0	0
$729$	531441.	0.0370370
$730$	2.58520e6	0.179551
$731$	−376480.	−0.0260584
$732$	3.00231e6	0.207099
$733$	−1.35367e7	−0.930579	−0.465289	−	0.885159i	$-0.654050\pi$
$733$	−1.35367e7	−0.930579	−0.465289	+	0.885159i	$0.654050\pi$
$734$	1.15048e6	0.0788205
$735$	0	0
$736$	460109.	0.0313088
$737$	6.60631e6	0.448012
$738$	−267809.	−0.0181003
$739$	−7.33702e6	−0.494207	−0.247103	−	0.968989i	$-0.579479\pi$
$739$	−7.33702e6	−0.494207	−0.247103	+	0.968989i	$0.579479\pi$
$740$	−3.38524e7	−2.27253
$741$	2.46118e6	0.164664
$742$	0	0
$743$	1.20844e7	0.803068	0.401534	−	0.915844i	$-0.368477\pi$
$743$	1.20844e7	0.803068	0.401534	+	0.915844i	$0.368477\pi$
$744$	−3.39431e6	−0.224812
$745$	1.34472e7	0.887649
$746$	1.61869e6	0.106492
$747$	8.29212e6	0.543706
$748$	−986151.	−0.0644450
$749$	0	0
$750$	3.41555e6	0.221721
$751$	8.78176e6	0.568175	0.284087	−	0.958798i	$-0.408309\pi$
$751$	8.78176e6	0.568175	0.284087	+	0.958798i	$0.408309\pi$
$752$	4.23327e6	0.272980
$753$	1.03048e7	0.662297
$754$	−706149.	−0.0452343
$755$	1.59628e7	1.01916
$756$	0	0
$757$	465874.	0.0295480	0.0147740	−	0.999891i	$-0.495297\pi$
$757$	465874.	0.0295480	0.0147740	+	0.999891i	$0.495297\pi$
$758$	329685.	0.0208414
$759$	−870872.	−0.0548719
$760$	−6.91339e6	−0.434167
$761$	−1.49978e7	−0.938786	−0.469393	−	0.882989i	$-0.655527\pi$
$761$	−1.49978e7	−0.938786	−0.469393	+	0.882989i	$0.655527\pi$
$762$	1.43422e6	0.0894804
$763$	0	0
$764$	−2.59984e7	−1.61144
$765$	−533029.	−0.0329304
$766$	−3.06536e6	−0.188760
$767$	−723026.	−0.0443778
$768$	−7.64646e6	−0.467797
$769$	1.85606e7	1.13181	0.565907	−	0.824469i	$-0.308526\pi$
$769$	1.85606e7	1.13181	0.565907	+	0.824469i	$0.308526\pi$
$770$	0	0
$771$	1.06537e7	0.645450
$772$	−6.89422e6	−0.416334
$773$	−1.22760e7	−0.738941	−0.369470	−	0.929243i	$-0.620461\pi$
$773$	−1.22760e7	−0.738941	−0.369470	+	0.929243i	$0.620461\pi$
$774$	−381825.	−0.0229093
$775$	5.81775e7	3.47937
$776$	−1.52027e6	−0.0906286
$777$	0	0
$778$	−2.24432e6	−0.132934
$779$	−5.53534e6	−0.326814
$780$	6.07690e6	0.357640
$781$	−1.93147e7	−1.13308
$782$	−9711.39	−0.000567890 0
$783$	−3.15157e6	−0.183706
$784$	0	0
$785$	1.57525e7	0.912380
$786$	−273797.	−0.0158079
$787$	−5.26991e6	−0.303296	−0.151648	−	0.988435i	$-0.548458\pi$
$787$	−5.26991e6	−0.303296	−0.151648	+	0.988435i	$0.548458\pi$
$788$	−1.49221e7	−0.856082
$789$	−4.03484e6	−0.230746
$790$	−3.25391e6	−0.185497
$791$	0	0
$792$	−2.02024e6	−0.114443
$793$	2.19615e6	0.124016
$794$	3.43420e6	0.193319
$795$	−1.66772e7	−0.935850
$796$	1.96893e7	1.10141
$797$	−1.11889e7	−0.623940	−0.311970	−	0.950092i	$-0.600989\pi$
$797$	−1.11889e7	−0.623940	−0.311970	+	0.950092i	$0.600989\pi$
$798$	0	0
$799$	−277250.	−0.0153640
$800$	−1.82941e7	−1.01062
$801$	9.13850e6	0.503261
$802$	−2.69114e6	−0.147741
$803$	1.56144e7	0.854547
$804$	−3.74841e6	−0.204507
$805$	0	0
$806$	−1.22920e6	−0.0666476
$807$	6.72727e6	0.363626
$808$	−5.35231e6	−0.288412
$809$	7.05051e6	0.378747	0.189374	−	0.981905i	$-0.439354\pi$
$809$	7.05051e6	0.378747	0.189374	+	0.981905i	$0.439354\pi$
$810$	−540596.	−0.0289508
$811$	2.54873e7	1.36073	0.680364	−	0.732875i	$-0.261822\pi$
$811$	2.54873e7	1.36073	0.680364	+	0.732875i	$0.261822\pi$
$812$	0	0
$813$	−2.09374e6	−0.111095
$814$	4.07548e6	0.215585
$815$	−3.42964e6	−0.180865
$816$	548166.	0.0288195
$817$	−7.89192e6	−0.413645
$818$	−4.18677e6	−0.218774
$819$	0	0
$820$	−1.36673e7	−0.709820
$821$	−2.34879e7	−1.21615	−0.608073	−	0.793881i	$-0.708057\pi$
$821$	−2.34879e7	−1.21615	−0.608073	+	0.793881i	$0.708057\pi$
$822$	−1.72040e6	−0.0888073
$823$	−1.20903e7	−0.622213	−0.311107	−	0.950375i	$-0.600700\pi$
$823$	−1.20903e7	−0.622213	−0.311107	+	0.950375i	$0.600700\pi$
$824$	−7.89521e6	−0.405084
$825$	3.46263e7	1.77121
$826$	0	0
$827$	3.33335e6	0.169480	0.0847398	−	0.996403i	$-0.472994\pi$
$827$	3.33335e6	0.169480	0.0847398	+	0.996403i	$0.472994\pi$
$828$	494132.	0.0250477
$829$	7.70534e6	0.389408	0.194704	−	0.980862i	$-0.437625\pi$
$829$	7.70534e6	0.389408	0.194704	+	0.980862i	$0.437625\pi$
$830$	−8.43496e6	−0.424999
$831$	2.18632e7	1.09828
$832$	−5.98752e6	−0.299874
$833$	0	0
$834$	378013.	0.0188188
$835$	−2.26706e7	−1.12524
$836$	−2.06721e7	−1.02298
$837$	−5.48595e6	−0.270669
$838$	2.27172e6	0.111749
$839$	−2.40843e7	−1.18121	−0.590607	−	0.806959i	$-0.701112\pi$
$839$	−2.40843e7	−1.18121	−0.590607	+	0.806959i	$0.701112\pi$
$840$	0	0
$841$	−1.82163e6	−0.0888116
$842$	−1.65032e6	−0.0802208
$843$	−2.26534e7	−1.09790
$844$	−1.79146e7	−0.865665
$845$	−3.42405e7	−1.64967
$846$	−281186.	−0.0135073
$847$	0	0
$848$	1.71509e7	0.819023
$849$	2.34895e6	0.111842
$850$	386129.	0.0183310
$851$	−2.01352e6	−0.0953088
$852$	1.09592e7	0.517223
$853$	2.82938e7	1.33143	0.665716	−	0.746206i	$-0.268126\pi$
$853$	2.82938e7	1.33143	0.665716	+	0.746206i	$0.268126\pi$
$854$	0	0
$855$	−1.11736e7	−0.522728
$856$	−4.47666e6	−0.208819
$857$	−2.16176e7	−1.00544	−0.502719	−	0.864450i	$-0.667667\pi$
$857$	−2.16176e7	−1.00544	−0.502719	+	0.864450i	$0.667667\pi$
$858$	−731598.	−0.0339277
$859$	−3.25382e7	−1.50456	−0.752282	−	0.658841i	$-0.771047\pi$
$859$	−3.25382e7	−1.50456	−0.752282	+	0.658841i	$0.771047\pi$
$860$	−1.94859e7	−0.898411
$861$	0	0
$862$	1.92058e6	0.0880366
$863$	8.06384e6	0.368566	0.184283	−	0.982873i	$-0.441004\pi$
$863$	8.06384e6	0.368566	0.184283	+	0.982873i	$0.441004\pi$
$864$	1.72508e6	0.0786184
$865$	4.38900e7	1.99446
$866$	756183.	0.0342635
$867$	1.27428e7	0.575728
$868$	0	0
$869$	−1.96533e7	−0.882849
$870$	3.20586e6	0.143597
$871$	−2.74192e6	−0.122464
$872$	8.39983e6	0.374093
$873$	−2.45708e6	−0.109115
$874$	−203574.	−0.00901454
$875$	0	0
$876$	−8.85959e6	−0.390080
$877$	1.70312e7	0.747732	0.373866	−	0.927483i	$-0.378032\pi$
$877$	1.70312e7	0.747732	0.373866	+	0.927483i	$0.378032\pi$
$878$	2.08934e6	0.0914690
$879$	585106.	0.0255424
$880$	−5.00038e7	−2.17669
$881$	−1.24740e7	−0.541459	−0.270729	−	0.962655i	$-0.587265\pi$
$881$	−1.24740e7	−0.541459	−0.270729	+	0.962655i	$0.587265\pi$
$882$	0	0
$883$	7.28955e6	0.314629	0.157315	−	0.987549i	$-0.449716\pi$
$883$	7.28955e6	0.314629	0.157315	+	0.987549i	$0.449716\pi$
$884$	409298.	0.0176160
$885$	3.28248e6	0.140878
$886$	2.72010e6	0.116413
$887$	−1.87675e7	−0.800937	−0.400469	−	0.916310i	$-0.631153\pi$
$887$	−1.87675e7	−0.800937	−0.400469	+	0.916310i	$0.631153\pi$
$888$	−4.67094e6	−0.198780
$889$	0	0
$890$	−9.29592e6	−0.393385
$891$	−3.26514e6	−0.137787
$892$	132812.	0.00558889
$893$	−5.81181e6	−0.243884
$894$	918566.	0.0384385
$895$	364052.	0.0151917
$896$	0	0
$897$	361452.	0.0149992
$898$	−3.47878e6	−0.143958
$899$	3.25330e7	1.34253
$900$	−1.96469e7	−0.808515
$901$	−1.12326e6	−0.0460966
$902$	1.64541e6	0.0673375
$903$	0	0
$904$	−5.80323e6	−0.236183
$905$	−6.19535e7	−2.51446
$906$	1.09041e6	0.0441335
$907$	1.26367e6	0.0510052	0.0255026	−	0.999675i	$-0.491881\pi$
$907$	1.26367e6	0.0510052	0.0255026	+	0.999675i	$0.491881\pi$
$908$	3.54490e7	1.42689
$909$	−8.65051e6	−0.347242
$910$	0	0
$911$	−2.47718e7	−0.988921	−0.494461	−	0.869200i	$-0.664634\pi$
$911$	−2.47718e7	−0.988921	−0.494461	+	0.869200i	$0.664634\pi$
$912$	1.14909e7	0.457473
$913$	−5.09463e7	−2.02272
$914$	1.78018e6	0.0704854
$915$	−9.97033e6	−0.393692
$916$	2.52454e7	0.994130
$917$	0	0
$918$	−36410.7	−0.00142601
$919$	−9.36676e6	−0.365848	−0.182924	−	0.983127i	$-0.558556\pi$
$919$	−9.36676e6	−0.365848	−0.182924	+	0.983127i	$0.558556\pi$
$920$	−1.01531e6	−0.0395483
$921$	−2.12039e7	−0.823696
$922$	1.46542e6	0.0567721
$923$	8.01648e6	0.309727
$924$	0	0
$925$	8.00586e7	3.07648
$926$	2.38103e6	0.0912509
$927$	−1.27604e7	−0.487713
$928$	−1.02301e7	−0.389951
$929$	6.87350e6	0.261300	0.130650	−	0.991429i	$-0.458294\pi$
$929$	6.87350e6	0.261300	0.130650	+	0.991429i	$0.458294\pi$
$930$	5.58046e6	0.211574
$931$	0	0
$932$	−3.66855e7	−1.38342
$933$	−1.90625e7	−0.716928
$934$	−843990.	−0.0316570
$935$	3.27490e6	0.122509
$936$	838490.	0.0312830
$937$	4.26197e7	1.58585	0.792923	−	0.609322i	$-0.208558\pi$
$937$	4.26197e7	1.58585	0.792923	+	0.609322i	$0.208558\pi$
$938$	0	0
$939$	−1.68762e6	−0.0624614
$940$	−1.43499e7	−0.529701
$941$	−4.50226e6	−0.165751	−0.0828755	−	0.996560i	$-0.526410\pi$
$941$	−4.50226e6	−0.165751	−0.0828755	+	0.996560i	$0.526410\pi$
$942$	1.07604e6	0.0395095
$943$	−812926.	−0.0297695
$944$	−3.37569e6	−0.123291
$945$	0	0
$946$	2.34591e6	0.0852282
$947$	3.37725e7	1.22374	0.611870	−	0.790959i	$-0.290418\pi$
$947$	3.37725e7	1.22374	0.611870	+	0.790959i	$0.290418\pi$
$948$	1.11513e7	0.402999
$949$	−6.48068e6	−0.233590
$950$	8.09419e6	0.290981
$951$	9.04870e6	0.324440
$952$	0	0
$953$	4.81813e7	1.71849	0.859244	−	0.511566i	$-0.170934\pi$
$953$	4.81813e7	1.71849	0.859244	+	0.511566i	$0.170934\pi$
$954$	−1.13921e6	−0.0405258
$955$	8.63379e7	3.06332
$956$	5.35107e7	1.89363
$957$	1.93631e7	0.683430
$958$	−4.49800e6	−0.158346
$959$	0	0
$960$	2.71828e7	0.951955
$961$	2.80012e7	0.978066
$962$	−1.69151e6	−0.0589301
$963$	−7.23527e6	−0.251414
$964$	2.98434e7	1.03432
$965$	2.28950e7	0.791446
$966$	0	0
$967$	−3.54640e7	−1.21961	−0.609805	−	0.792551i	$-0.708752\pi$
$967$	−3.54640e7	−1.21961	−0.609805	+	0.792551i	$0.708752\pi$
$968$	4.34084e6	0.148897
$969$	−752572.	−0.0257477
$970$	2.49941e6	0.0852919
$971$	7.84296e6	0.266951	0.133476	−	0.991052i	$-0.457386\pi$
$971$	7.84296e6	0.266951	0.133476	+	0.991052i	$0.457386\pi$
$972$	1.85264e6	0.0628964
$973$	0	0
$974$	5.41288e6	0.182823
$975$	−1.43715e7	−0.484161
$976$	1.02535e7	0.344545
$977$	−2.47534e7	−0.829658	−0.414829	−	0.909899i	$-0.636159\pi$
$977$	−2.47534e7	−0.829658	−0.414829	+	0.909899i	$0.636159\pi$
$978$	−234276.	−0.00783215
$979$	−5.61464e7	−1.87226
$980$	0	0
$981$	1.35760e7	0.450400
$982$	−4.42955e6	−0.146582
$983$	−4.53129e7	−1.49568	−0.747838	−	0.663881i	$-0.768908\pi$
$983$	−4.53129e7	−1.49568	−0.747838	+	0.663881i	$0.768908\pi$
$984$	−1.88581e6	−0.0620885
$985$	4.95548e7	1.62740
$986$	215924.	0.00707308
$987$	0	0
$988$	8.57985e6	0.279632
$989$	−1.15902e6	−0.0376789
$990$	3.32139e6	0.107704
$991$	−3.74143e7	−1.21019	−0.605095	−	0.796154i	$-0.706865\pi$
$991$	−3.74143e7	−1.21019	−0.605095	+	0.796154i	$0.706865\pi$
$992$	−1.78076e7	−0.574548
$993$	−1.51186e7	−0.486561
$994$	0	0
$995$	−6.53861e7	−2.09376
$996$	2.89069e7	0.923322
$997$	−4.65278e7	−1.48243	−0.741216	−	0.671267i	$-0.765751\pi$
$997$	−4.65278e7	−1.48243	−0.741216	+	0.671267i	$0.765751\pi$
$998$	1.84676e6	0.0586926
$999$	−7.54927e6	−0.239327

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.6.a.l.1.2		4
3.2	odd	2		441.6.a.v.1.3		4
7.2	even	3		147.6.e.o.67.3		8
7.3	odd	6		21.6.e.c.16.3	yes	8
7.4	even	3		147.6.e.o.79.3		8
7.5	odd	6		21.6.e.c.4.3	✓	8
7.6	odd	2		147.6.a.m.1.2		4
21.5	even	6		63.6.e.e.46.2		8
21.17	even	6		63.6.e.e.37.2		8
21.20	even	2		441.6.a.w.1.3		4
28.3	even	6		336.6.q.j.289.4		8
28.19	even	6		336.6.q.j.193.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.e.c.4.3	✓	8	7.5	odd	6
21.6.e.c.16.3	yes	8	7.3	odd	6
63.6.e.e.37.2		8	21.17	even	6
63.6.e.e.46.2		8	21.5	even	6
147.6.a.l.1.2		4	1.1	even	1	trivial
147.6.a.m.1.2		4	7.6	odd	2
147.6.e.o.67.3		8	7.2	even	3
147.6.e.o.79.3		8	7.4	even	3
336.6.q.j.193.4		8	28.19	even	6
336.6.q.j.289.4		8	28.3	even	6
441.6.a.v.1.3		4	3.2	odd	2
441.6.a.w.1.3		4	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	147.a (trivial)

\(f(q)\)	\(=\)	\(q-0.790805 q^{2} -9.00000 q^{3} -31.3746 q^{4} +104.192 q^{5} +7.11724 q^{6} +50.1170 q^{8} +81.0000 q^{9} -82.3953 q^{10} -497.660 q^{11} +282.372 q^{12} +206.551 q^{13} -937.725 q^{15} +964.355 q^{16} -63.1586 q^{17} -64.0552 q^{18} -1323.95 q^{19} -3268.98 q^{20} +393.552 q^{22} -194.437 q^{23} -451.053 q^{24} +7730.91 q^{25} -163.342 q^{26} -729.000 q^{27} +4323.14 q^{29} +741.558 q^{30} +7525.31 q^{31} -2366.36 q^{32} +4478.94 q^{33} +49.9461 q^{34} -2541.34 q^{36} +10355.6 q^{37} +1046.99 q^{38} -1858.96 q^{39} +5221.77 q^{40} +4180.92 q^{41} +5960.87 q^{43} +15613.9 q^{44} +8439.53 q^{45} +153.762 q^{46} +4389.74 q^{47} -8679.20 q^{48} -6113.64 q^{50} +568.427 q^{51} -6480.47 q^{52} +17784.8 q^{53} +576.497 q^{54} -51852.0 q^{55} +11915.6 q^{57} -3418.76 q^{58} -3500.47 q^{59} +29420.8 q^{60} +10632.5 q^{61} -5951.06 q^{62} -28988.0 q^{64} +21520.9 q^{65} -3541.97 q^{66} -13274.7 q^{67} +1981.58 q^{68} +1749.94 q^{69} +38811.1 q^{71} +4059.47 q^{72} -31375.6 q^{73} -8189.30 q^{74} -69578.2 q^{75} +41538.6 q^{76} +1470.08 q^{78} +39491.5 q^{79} +100478. q^{80} +6561.00 q^{81} -3306.29 q^{82} +102372. q^{83} -6580.60 q^{85} -4713.88 q^{86} -38908.2 q^{87} -24941.2 q^{88} +112821. q^{89} -6674.02 q^{90} +6100.40 q^{92} -67727.8 q^{93} -3471.43 q^{94} -137945. q^{95} +21297.2 q^{96} -30334.3 q^{97} -40310.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} - 36 q^{3} + 69 q^{4} - 27 q^{6} + 123 q^{8} + 324 q^{9} - 283 q^{10} + 402 q^{11} - 621 q^{12} - 462 q^{13} + 3273 q^{16} - 276 q^{17} + 243 q^{18} - 510 q^{19} - 4719 q^{20} + 1375 q^{22}+ \cdots + 32562 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 - 36 * q^3 + 69 * q^4 - 27 * q^6 + 123 * q^8 + 324 * q^9 - 283 * q^10 + 402 * q^11 - 621 * q^12 - 462 * q^13 + 3273 * q^16 - 276 * q^17 + 243 * q^18 - 510 * q^19 - 4719 * q^20 + 1375 * q^22 + 6900 * q^23 - 1107 * q^24 + 2814 * q^25 + 15138 * q^26 - 2916 * q^27 + 540 * q^29 + 2547 * q^30 + 6410 * q^31 + 15519 * q^32 - 3618 * q^33 - 21144 * q^34 + 5589 * q^36 + 15250 * q^37 + 41250 * q^38 + 4158 * q^39 + 8547 * q^40 - 4308 * q^41 + 29198 * q^43 + 70743 * q^44 + 61800 * q^46 + 15060 * q^47 - 29457 * q^48 - 7302 * q^50 + 2484 * q^51 + 47476 * q^52 + 13692 * q^53 - 2187 * q^54 - 73124 * q^55 + 4590 * q^57 + 52309 * q^58 - 34830 * q^59 + 42471 * q^60 + 5364 * q^61 - 16029 * q^62 - 73487 * q^64 + 66864 * q^65 - 12375 * q^66 - 5994 * q^67 + 58272 * q^68 - 62100 * q^69 + 89268 * q^71 + 9963 * q^72 - 59638 * q^73 - 185442 * q^74 - 25326 * q^75 - 21308 * q^76 - 136242 * q^78 - 44062 * q^79 + 33381 * q^80 + 26244 * q^81 - 57596 * q^82 + 208446 * q^83 + 36324 * q^85 - 136968 * q^86 - 4860 * q^87 + 87597 * q^88 + 77520 * q^89 - 22923 * q^90 + 158256 * q^92 - 57690 * q^93 + 73722 * q^94 - 221376 * q^95 - 139671 * q^96 + 188630 * q^97 + 32562 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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