LMFDB - Embedded newform 294.6.a.r.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [294,6,Mod(1,294)] 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("294.1"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(294, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	294.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,8,-18,32,-53,-72,0,128,162,-212,191] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	yes
Analytic conductor:	$47.1528430250$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{9601}) $
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 2400 $ x^2 - x - 2400
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$49.4923$ of defining polynomial
Character	$\chi$	$=$	294.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -75.4923 q^{5} -36.0000 q^{6} +64.0000 q^{8} +81.0000 q^{9} -301.969 q^{10} -149.462 q^{11} -144.000 q^{12} +349.416 q^{13} +679.431 q^{15} +256.000 q^{16} -1149.85 q^{17} +324.000 q^{18} -2795.20 q^{19} -1207.88 q^{20} -597.847 q^{22} +1813.97 q^{23} -576.000 q^{24} +2574.09 q^{25} +1397.66 q^{26} -729.000 q^{27} -759.033 q^{29} +2717.72 q^{30} +9031.74 q^{31} +1024.00 q^{32} +1345.16 q^{33} -4599.39 q^{34} +1296.00 q^{36} +7794.89 q^{37} -11180.8 q^{38} -3144.74 q^{39} -4831.51 q^{40} +7640.49 q^{41} +12188.8 q^{43} -2391.39 q^{44} -6114.88 q^{45} +7255.88 q^{46} +24598.8 q^{47} -2304.00 q^{48} +10296.4 q^{50} +10348.6 q^{51} +5590.65 q^{52} +13596.2 q^{53} -2916.00 q^{54} +11283.2 q^{55} +25156.8 q^{57} -3036.13 q^{58} -26358.8 q^{59} +10870.9 q^{60} +35321.8 q^{61} +36127.0 q^{62} +4096.00 q^{64} -26378.2 q^{65} +5380.62 q^{66} +54371.9 q^{67} -18397.6 q^{68} -16325.7 q^{69} -70145.7 q^{71} +5184.00 q^{72} -44468.8 q^{73} +31179.6 q^{74} -23166.8 q^{75} -44723.2 q^{76} -12579.0 q^{78} +61612.5 q^{79} -19326.0 q^{80} +6561.00 q^{81} +30562.0 q^{82} -87142.0 q^{83} +86804.6 q^{85} +48755.3 q^{86} +6831.30 q^{87} -9565.55 q^{88} +98569.4 q^{89} -24459.5 q^{90} +29023.5 q^{92} -81285.7 q^{93} +98395.2 q^{94} +211016. q^{95} -9216.00 q^{96} +32342.3 q^{97} -12106.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 8 q^{2} - 18 q^{3} + 32 q^{4} - 53 q^{5} - 72 q^{6} + 128 q^{8} + 162 q^{9} - 212 q^{10} + 191 q^{11} - 288 q^{12} - 379 q^{13} + 477 q^{15} + 512 q^{16} - 340 q^{17} + 648 q^{18} - 1769 q^{19} - 848 q^{20}+ \cdots + 15471 q^{99}+O(q^{100}) $ 2 * q + 8 * q^2 - 18 * q^3 + 32 * q^4 - 53 * q^5 - 72 * q^6 + 128 * q^8 + 162 * q^9 - 212 * q^10 + 191 * q^11 - 288 * q^12 - 379 * q^13 + 477 * q^15 + 512 * q^16 - 340 * q^17 + 648 * q^18 - 1769 * q^19 - 848 * q^20 + 764 * q^22 + 3236 * q^23 - 1152 * q^24 - 45 * q^25 - 1516 * q^26 - 1458 * q^27 + 4459 * q^29 + 1908 * q^30 + 1994 * q^31 + 2048 * q^32 - 1719 * q^33 - 1360 * q^34 + 2592 * q^36 + 20587 * q^37 - 7076 * q^38 + 3411 * q^39 - 3392 * q^40 + 8814 * q^41 + 15853 * q^43 + 3056 * q^44 - 4293 * q^45 + 12944 * q^46 + 33912 * q^47 - 4608 * q^48 - 180 * q^50 + 3060 * q^51 - 6064 * q^52 + 49239 * q^53 - 5832 * q^54 + 18941 * q^55 + 15921 * q^57 + 17836 * q^58 - 56735 * q^59 + 7632 * q^60 + 67508 * q^61 + 7976 * q^62 + 8192 * q^64 - 42762 * q^65 - 6876 * q^66 + 75723 * q^67 - 5440 * q^68 - 29124 * q^69 - 8992 * q^71 + 10368 * q^72 - 3201 * q^73 + 82348 * q^74 + 405 * q^75 - 28304 * q^76 + 13644 * q^78 + 26612 * q^79 - 13568 * q^80 + 13122 * q^81 + 35256 * q^82 - 949 * q^83 + 105020 * q^85 + 63412 * q^86 - 40131 * q^87 + 12224 * q^88 + 176562 * q^89 - 17172 * q^90 + 51776 * q^92 - 17946 * q^93 + 135648 * q^94 + 234098 * q^95 - 18432 * q^96 - 129423 * q^97 + 15471 * 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 $

$2$	4.00000	0.707107
$2$	4.00000	0.707107
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	16.0000	0.500000
$5$	−75.4923	−1.35045	−0.675224	−	0.737613i	$-0.735953\pi$
$5$	−75.4923	−1.35045	−0.675224	+	0.737613i	$0.735953\pi$
$6$	−36.0000	−0.408248
$7$	0	0
$7$	0	0
$8$	64.0000	0.353553
$9$	81.0000	0.333333
$10$	−301.969	−0.954911
$11$	−149.462	−0.372433	−0.186217	−	0.982509i	$-0.559623\pi$
$11$	−149.462	−0.372433	−0.186217	+	0.982509i	$0.559623\pi$
$12$	−144.000	−0.288675
$13$	349.416	0.573435	0.286717	−	0.958015i	$-0.407436\pi$
$13$	349.416	0.573435	0.286717	+	0.958015i	$0.407436\pi$
$14$	0	0
$15$	679.431	0.779682
$16$	256.000	0.250000
$17$	−1149.85	−0.964979	−0.482489	−	0.875902i	$-0.660267\pi$
$17$	−1149.85	−0.964979	−0.482489	+	0.875902i	$0.660267\pi$
$18$	324.000	0.235702
$19$	−2795.20	−1.77635	−0.888176	−	0.459503i	$-0.848028\pi$
$19$	−2795.20	−1.77635	−0.888176	+	0.459503i	$0.848028\pi$
$20$	−1207.88	−0.675224
$21$	0	0
$22$	−597.847	−0.263350
$23$	1813.97	0.715007	0.357504	−	0.933912i	$-0.383628\pi$
$23$	1813.97	0.715007	0.357504	+	0.933912i	$0.383628\pi$
$24$	−576.000	−0.204124
$25$	2574.09	0.823710
$26$	1397.66	0.405480
$27$	−729.000	−0.192450
$28$	0	0
$29$	−759.033	−0.167597	−0.0837984	−	0.996483i	$-0.526705\pi$
$29$	−759.033	−0.167597	−0.0837984	+	0.996483i	$0.526705\pi$
$30$	2717.72	0.551318
$31$	9031.74	1.68798	0.843990	−	0.536359i	$-0.180201\pi$
$31$	9031.74	1.68798	0.843990	+	0.536359i	$0.180201\pi$
$32$	1024.00	0.176777
$33$	1345.16	0.215024
$34$	−4599.39	−0.682343
$35$	0	0
$36$	1296.00	0.166667
$37$	7794.89	0.936064	0.468032	−	0.883711i	$-0.344963\pi$
$37$	7794.89	0.936064	0.468032	+	0.883711i	$0.344963\pi$
$38$	−11180.8	−1.25607
$39$	−3144.74	−0.331073
$40$	−4831.51	−0.477456
$41$	7640.49	0.709842	0.354921	−	0.934896i	$-0.384508\pi$
$41$	7640.49	0.709842	0.354921	+	0.934896i	$0.384508\pi$
$42$	0	0
$43$	12188.8	1.00529	0.502645	−	0.864493i	$-0.332360\pi$
$43$	12188.8	1.00529	0.502645	+	0.864493i	$0.332360\pi$
$44$	−2391.39	−0.186217
$45$	−6114.88	−0.450149
$46$	7255.88	0.505586
$47$	24598.8	1.62431	0.812156	−	0.583441i	$-0.198294\pi$
$47$	24598.8	1.62431	0.812156	+	0.583441i	$0.198294\pi$
$48$	−2304.00	−0.144338
$49$	0	0
$50$	10296.4	0.582451
$51$	10348.6	0.557131
$52$	5590.65	0.286717
$53$	13596.2	0.664858	0.332429	−	0.943128i	$-0.392132\pi$
$53$	13596.2	0.664858	0.332429	+	0.943128i	$0.392132\pi$
$54$	−2916.00	−0.136083
$55$	11283.2	0.502952
$56$	0	0
$57$	25156.8	1.02558
$58$	−3036.13	−0.118509
$59$	−26358.8	−0.985816	−0.492908	−	0.870081i	$-0.664066\pi$
$59$	−26358.8	−0.985816	−0.492908	+	0.870081i	$0.664066\pi$
$60$	10870.9	0.389841
$61$	35321.8	1.21540	0.607698	−	0.794168i	$-0.292093\pi$
$61$	35321.8	1.21540	0.607698	+	0.794168i	$0.292093\pi$
$62$	36127.0	1.19358
$63$	0	0
$64$	4096.00	0.125000
$65$	−26378.2	−0.774394
$66$	5380.62	0.152045
$67$	54371.9	1.47975	0.739874	−	0.672746i	$-0.234885\pi$
$67$	54371.9	1.47975	0.739874	+	0.672746i	$0.234885\pi$
$68$	−18397.6	−0.482489
$69$	−16325.7	−0.412810
$70$	0	0
$71$	−70145.7	−1.65141	−0.825706	−	0.564101i	$-0.809223\pi$
$71$	−70145.7	−1.65141	−0.825706	+	0.564101i	$0.809223\pi$
$72$	5184.00	0.117851
$73$	−44468.8	−0.976671	−0.488335	−	0.872656i	$-0.662396\pi$
$73$	−44468.8	−0.976671	−0.488335	+	0.872656i	$0.662396\pi$
$74$	31179.6	0.661897
$75$	−23166.8	−0.475569
$76$	−44723.2	−0.888176
$77$	0	0
$78$	−12579.0	−0.234104
$79$	61612.5	1.11071	0.555355	−	0.831613i	$-0.312582\pi$
$79$	61612.5	1.11071	0.555355	+	0.831613i	$0.312582\pi$
$80$	−19326.0	−0.337612
$81$	6561.00	0.111111
$82$	30562.0	0.501934
$83$	−87142.0	−1.38846	−0.694228	−	0.719755i	$-0.744254\pi$
$83$	−87142.0	−1.38846	−0.694228	+	0.719755i	$0.744254\pi$
$84$	0	0
$85$	86804.6	1.30315
$86$	48755.3	0.710847
$87$	6831.30	0.0967621
$88$	−9565.55	−0.131675
$89$	98569.4	1.31907	0.659534	−	0.751675i	$-0.270754\pi$
$89$	98569.4	1.31907	0.659534	+	0.751675i	$0.270754\pi$
$90$	−24459.5	−0.318304
$91$	0	0
$92$	29023.5	0.357504
$93$	−81285.7	−0.974556
$94$	98395.2	1.14856
$95$	211016.	2.39887
$96$	−9216.00	−0.102062
$97$	32342.3	0.349013	0.174507	−	0.984656i	$-0.444167\pi$
$97$	32342.3	0.349013	0.174507	+	0.984656i	$0.444167\pi$
$98$	0	0
$99$	−12106.4	−0.124144
$100$	41185.5	0.411855
$101$	31346.4	0.305763	0.152881	−	0.988245i	$-0.451145\pi$
$101$	31346.4	0.305763	0.152881	+	0.988245i	$0.451145\pi$
$102$	41394.5	0.393951
$103$	99332.9	0.922572	0.461286	−	0.887252i	$-0.347388\pi$
$103$	99332.9	0.922572	0.461286	+	0.887252i	$0.347388\pi$
$104$	22362.6	0.202740
$105$	0	0
$106$	54384.9	0.470125
$107$	−145268.	−1.22662	−0.613310	−	0.789842i	$-0.710163\pi$
$107$	−145268.	−1.22662	−0.613310	+	0.789842i	$0.710163\pi$
$108$	−11664.0	−0.0962250
$109$	−180851.	−1.45799	−0.728994	−	0.684520i	$-0.760012\pi$
$109$	−180851.	−1.45799	−0.728994	+	0.684520i	$0.760012\pi$
$110$	45132.9	0.355640
$111$	−70154.0	−0.540437
$112$	0	0
$113$	197832.	1.45748	0.728738	−	0.684793i	$-0.240107\pi$
$113$	197832.	1.45748	0.728738	+	0.684793i	$0.240107\pi$
$114$	100627.	0.725193
$115$	−136941.	−0.965580
$116$	−12144.5	−0.0837984
$117$	28302.7	0.191145
$118$	−105435.	−0.697077
$119$	0	0
$120$	43483.6	0.275659
$121$	−138712.	−0.861294
$122$	141287.	0.859415
$123$	−68764.5	−0.409828
$124$	144508.	0.843990
$125$	41589.2	0.238070
$126$	0	0
$127$	−33517.2	−0.184399	−0.0921996	−	0.995741i	$-0.529390\pi$
$127$	−33517.2	−0.184399	−0.0921996	+	0.995741i	$0.529390\pi$
$128$	16384.0	0.0883883
$129$	−109700.	−0.580404
$130$	−105513.	−0.547579
$131$	−10808.9	−0.0550305	−0.0275153	−	0.999621i	$-0.508759\pi$
$131$	−10808.9	−0.0550305	−0.0275153	+	0.999621i	$0.508759\pi$
$132$	21522.5	0.107512
$133$	0	0
$134$	217488.	1.04634
$135$	55033.9	0.259894
$136$	−73590.2	−0.341171
$137$	−18932.0	−0.0861778	−0.0430889	−	0.999071i	$-0.513720\pi$
$137$	−18932.0	−0.0861778	−0.0430889	+	0.999071i	$0.513720\pi$
$138$	−65302.9	−0.291900
$139$	−168897.	−0.741457	−0.370729	−	0.928741i	$-0.620892\pi$
$139$	−168897.	−0.741457	−0.370729	+	0.928741i	$0.620892\pi$
$140$	0	0
$141$	−221389.	−0.937797
$142$	−280583.	−1.16772
$143$	−52224.3	−0.213566
$144$	20736.0	0.0833333
$145$	57301.2	0.226331
$146$	−177875.	−0.690611
$147$	0	0
$148$	124718.	0.468032
$149$	264002.	0.974186	0.487093	−	0.873350i	$-0.338057\pi$
$149$	264002.	0.974186	0.487093	+	0.873350i	$0.338057\pi$
$150$	−92667.4	−0.336278
$151$	279175.	0.996400	0.498200	−	0.867062i	$-0.333994\pi$
$151$	279175.	0.996400	0.498200	+	0.867062i	$0.333994\pi$
$152$	−178893.	−0.628035
$153$	−93137.6	−0.321660
$154$	0	0
$155$	−681828.	−2.27953
$156$	−50315.9	−0.165536
$157$	188602.	0.610658	0.305329	−	0.952247i	$-0.401234\pi$
$157$	188602.	0.610658	0.305329	+	0.952247i	$0.401234\pi$
$158$	246450.	0.785391
$159$	−122366.	−0.383856
$160$	−77304.2	−0.238728
$161$	0	0
$162$	26244.0	0.0785674
$163$	89717.4	0.264489	0.132244	−	0.991217i	$-0.457782\pi$
$163$	89717.4	0.264489	0.132244	+	0.991217i	$0.457782\pi$
$164$	122248.	0.354921
$165$	−101549.	−0.290379
$166$	−348568.	−0.981787
$167$	529411.	1.46893	0.734467	−	0.678645i	$-0.237432\pi$
$167$	529411.	1.46893	0.734467	+	0.678645i	$0.237432\pi$
$168$	0	0
$169$	−249202.	−0.671172
$170$	347219.	0.921469
$171$	−226411.	−0.592117
$172$	195021.	0.502645
$173$	33838.3	0.0859594	0.0429797	−	0.999076i	$-0.486315\pi$
$173$	33838.3	0.0859594	0.0429797	+	0.999076i	$0.486315\pi$
$174$	27325.2	0.0684211
$175$	0	0
$176$	−38262.2	−0.0931083
$177$	237229.	0.569161
$178$	394278.	0.932722
$179$	−247744.	−0.577923	−0.288962	−	0.957341i	$-0.593310\pi$
$179$	−247744.	−0.577923	−0.288962	+	0.957341i	$0.593310\pi$
$180$	−97838.1	−0.225075
$181$	369470.	0.838268	0.419134	−	0.907924i	$-0.362334\pi$
$181$	369470.	0.838268	0.419134	+	0.907924i	$0.362334\pi$
$182$	0	0
$183$	−317896.	−0.701709
$184$	116094.	0.252793
$185$	−588455.	−1.26411
$186$	−325143.	−0.689115
$187$	171858.	0.359390
$188$	393581.	0.812156
$189$	0	0
$190$	844065.	1.69626
$191$	−485225.	−0.962408	−0.481204	−	0.876609i	$-0.659800\pi$
$191$	−485225.	−0.962408	−0.481204	+	0.876609i	$0.659800\pi$
$192$	−36864.0	−0.0721688
$193$	−330817.	−0.639285	−0.319643	−	0.947538i	$-0.603563\pi$
$193$	−330817.	−0.639285	−0.319643	+	0.947538i	$0.603563\pi$
$194$	129369.	0.246790
$195$	237404.	0.447097
$196$	0	0
$197$	−161963.	−0.297337	−0.148669	−	0.988887i	$-0.547499\pi$
$197$	−161963.	−0.297337	−0.148669	+	0.988887i	$0.547499\pi$
$198$	−48425.6	−0.0877833
$199$	55396.2	0.0991625	0.0495813	−	0.998770i	$-0.484211\pi$
$199$	55396.2	0.0991625	0.0495813	+	0.998770i	$0.484211\pi$
$200$	164742.	0.291226
$201$	−489347.	−0.854333
$202$	125386.	0.216207
$203$	0	0
$204$	165578.	0.278565
$205$	−576799.	−0.958605
$206$	397332.	0.652357
$207$	146932.	0.238336
$208$	89450.4	0.143359
$209$	417776.	0.661572
$210$	0	0
$211$	481748.	0.744926	0.372463	−	0.928047i	$-0.378513\pi$
$211$	481748.	0.744926	0.372463	+	0.928047i	$0.378513\pi$
$212$	217540.	0.332429
$213$	631312.	0.953443
$214$	−581072.	−0.867352
$215$	−920164.	−1.35759
$216$	−46656.0	−0.0680414
$217$	0	0
$218$	−723403.	−1.03095
$219$	400219.	0.563881
$220$	180531.	0.251476
$221$	−401775.	−0.553353
$222$	−280616.	−0.382147
$223$	638779.	0.860178	0.430089	−	0.902787i	$-0.358482\pi$
$223$	638779.	0.860178	0.430089	+	0.902787i	$0.358482\pi$
$224$	0	0
$225$	208502.	0.274570
$226$	791330.	1.03059
$227$	−525682.	−0.677109	−0.338554	−	0.940947i	$-0.609938\pi$
$227$	−525682.	−0.677109	−0.338554	+	0.940947i	$0.609938\pi$
$228$	402509.	0.512789
$229$	932686.	1.17529	0.587647	−	0.809117i	$-0.300054\pi$
$229$	932686.	1.17529	0.587647	+	0.809117i	$0.300054\pi$
$230$	−547763.	−0.682768
$231$	0	0
$232$	−48578.1	−0.0592544
$233$	−707793.	−0.854115	−0.427058	−	0.904224i	$-0.640450\pi$
$233$	−707793.	−0.854115	−0.427058	+	0.904224i	$0.640450\pi$
$234$	113211.	0.135160
$235$	−1.85702e6	−2.19355
$236$	−421741.	−0.492908
$237$	−554512.	−0.641269
$238$	0	0
$239$	−500614.	−0.566902	−0.283451	−	0.958987i	$-0.591479\pi$
$239$	−500614.	−0.566902	−0.283451	+	0.958987i	$0.591479\pi$
$240$	173934.	0.194920
$241$	1.20822e6	1.33999	0.669997	−	0.742364i	$-0.266295\pi$
$241$	1.20822e6	1.33999	0.669997	+	0.742364i	$0.266295\pi$
$242$	−554849.	−0.609027
$243$	−59049.0	−0.0641500
$244$	565148.	0.607698
$245$	0	0
$246$	−275058.	−0.289792
$247$	−976688.	−1.01862
$248$	578032.	0.596791
$249$	784278.	0.801625
$250$	166357.	0.168341
$251$	97826.7	0.0980106	0.0490053	−	0.998799i	$-0.484395\pi$
$251$	97826.7	0.0980106	0.0490053	+	0.998799i	$0.484395\pi$
$252$	0	0
$253$	−271119.	−0.266292
$254$	−134069.	−0.130390
$255$	−781242.	−0.752376
$256$	65536.0	0.0625000
$257$	−1.10791e6	−1.04634	−0.523170	−	0.852228i	$-0.675251\pi$
$257$	−1.10791e6	−1.04634	−0.523170	+	0.852228i	$0.675251\pi$
$258$	−438798.	−0.410408
$259$	0	0
$260$	−422052.	−0.387197
$261$	−61481.7	−0.0558656
$262$	−43235.6	−0.0389125
$263$	1.50685e6	1.34333	0.671663	−	0.740856i	$-0.265580\pi$
$263$	1.50685e6	1.34333	0.671663	+	0.740856i	$0.265580\pi$
$264$	86090.0	0.0760226
$265$	−1.02641e6	−0.897856
$266$	0	0
$267$	−887125.	−0.761564
$268$	869951.	0.739874
$269$	−2.13502e6	−1.79896	−0.899481	−	0.436960i	$-0.856055\pi$
$269$	−2.13502e6	−1.79896	−0.899481	+	0.436960i	$0.856055\pi$
$270$	220136.	0.183773
$271$	1.22860e6	1.01622	0.508108	−	0.861293i	$-0.330345\pi$
$271$	1.22860e6	1.01622	0.508108	+	0.861293i	$0.330345\pi$
$272$	−294361.	−0.241245
$273$	0	0
$274$	−75728.1	−0.0609369
$275$	−384729.	−0.306777
$276$	−261212.	−0.206405
$277$	−1.84682e6	−1.44619	−0.723097	−	0.690747i	$-0.757282\pi$
$277$	−1.84682e6	−1.44619	−0.723097	+	0.690747i	$0.757282\pi$
$278$	−675590.	−0.524289
$279$	731571.	0.562660
$280$	0	0
$281$	−2.28326e6	−1.72500	−0.862500	−	0.506056i	$-0.831103\pi$
$281$	−2.28326e6	−1.72500	−0.862500	+	0.506056i	$0.831103\pi$
$282$	−885557.	−0.663122
$283$	1.33693e6	0.992296	0.496148	−	0.868238i	$-0.334747\pi$
$283$	1.33693e6	0.992296	0.496148	+	0.868238i	$0.334747\pi$
$284$	−1.12233e6	−0.825706
$285$	−1.89915e6	−1.38499
$286$	−208897.	−0.151014
$287$	0	0
$288$	82944.0	0.0589256
$289$	−97709.0	−0.0688161
$290$	229205.	0.160040
$291$	−291081.	−0.201503
$292$	−711501.	−0.488335
$293$	−2.23033e6	−1.51775	−0.758875	−	0.651236i	$-0.774251\pi$
$293$	−2.23033e6	−1.51775	−0.758875	+	0.651236i	$0.774251\pi$
$294$	0	0
$295$	1.98989e6	1.33129
$296$	498873.	0.330949
$297$	108958.	0.0716748
$298$	1.05601e6	0.688853
$299$	633830.	0.410010
$300$	−370670.	−0.237785
$301$	0	0
$302$	1.11670e6	0.704561
$303$	−282118.	−0.176532
$304$	−715572.	−0.444088
$305$	−2.66652e6	−1.64133
$306$	−372550.	−0.227448
$307$	1.77782e6	1.07657	0.538284	−	0.842763i	$-0.319073\pi$
$307$	1.77782e6	1.07657	0.538284	+	0.842763i	$0.319073\pi$
$308$	0	0
$309$	−893996.	−0.532647
$310$	−2.72731e6	−1.61187
$311$	1.40272e6	0.822373	0.411187	−	0.911551i	$-0.365114\pi$
$311$	1.40272e6	0.822373	0.411187	+	0.911551i	$0.365114\pi$
$312$	−201264.	−0.117052
$313$	1.21894e6	0.703271	0.351636	−	0.936137i	$-0.385626\pi$
$313$	1.21894e6	0.703271	0.351636	+	0.936137i	$0.385626\pi$
$314$	754409.	0.431800
$315$	0	0
$316$	985799.	0.555355
$317$	2.68001e6	1.49792	0.748961	−	0.662615i	$-0.230553\pi$
$317$	2.68001e6	1.49792	0.748961	+	0.662615i	$0.230553\pi$
$318$	−489464.	−0.271427
$319$	113446.	0.0624186
$320$	−309217.	−0.168806
$321$	1.30741e6	0.708190
$322$	0	0
$323$	3.21405e6	1.71414
$324$	104976.	0.0555556
$325$	899429.	0.472344
$326$	358869.	0.187022
$327$	1.62766e6	0.841770
$328$	488992.	0.250967
$329$	0	0
$330$	−406196.	−0.205329
$331$	142560.	0.0715202	0.0357601	−	0.999360i	$-0.488615\pi$
$331$	142560.	0.0715202	0.0357601	+	0.999360i	$0.488615\pi$
$332$	−1.39427e6	−0.694228
$333$	631386.	0.312021
$334$	2.11765e6	1.03869
$335$	−4.10466e6	−1.99832
$336$	0	0
$337$	−1.21206e6	−0.581367	−0.290683	−	0.956819i	$-0.593883\pi$
$337$	−1.21206e6	−0.581367	−0.290683	+	0.956819i	$0.593883\pi$
$338$	−996806.	−0.474591
$339$	−1.78049e6	−0.841474
$340$	1.38887e6	0.651577
$341$	−1.34990e6	−0.628660
$342$	−905645.	−0.418690
$343$	0	0
$344$	780085.	0.355423
$345$	1.23247e6	0.557478
$346$	135353.	0.0607825
$347$	3.46853e6	1.54640	0.773199	−	0.634163i	$-0.218655\pi$
$347$	3.46853e6	1.54640	0.773199	+	0.634163i	$0.218655\pi$
$348$	109301.	0.0483810
$349$	1.01692e6	0.446911	0.223456	−	0.974714i	$-0.428266\pi$
$349$	1.01692e6	0.446911	0.223456	+	0.974714i	$0.428266\pi$
$350$	0	0
$351$	−254724.	−0.110358
$352$	−153049.	−0.0658375
$353$	1.56385e6	0.667974	0.333987	−	0.942578i	$-0.391606\pi$
$353$	1.56385e6	0.667974	0.333987	+	0.942578i	$0.391606\pi$
$354$	948917.	0.402458
$355$	5.29547e6	2.23015
$356$	1.57711e6	0.659534
$357$	0	0
$358$	−990975.	−0.408653
$359$	49553.1	0.0202925	0.0101462	−	0.999949i	$-0.496770\pi$
$359$	49553.1	0.0202925	0.0101462	+	0.999949i	$0.496770\pi$
$360$	−391352.	−0.159152
$361$	5.33705e6	2.15543
$362$	1.47788e6	0.592745
$363$	1.24841e6	0.497268
$364$	0	0
$365$	3.35705e6	1.31894
$366$	−1.27158e6	−0.496183
$367$	3.54831e6	1.37517	0.687585	−	0.726104i	$-0.258671\pi$
$367$	3.54831e6	1.37517	0.687585	+	0.726104i	$0.258671\pi$
$368$	464376.	0.178752
$369$	618880.	0.236614
$370$	−2.35382e6	−0.893858
$371$	0	0
$372$	−1.30057e6	−0.487278
$373$	−2.25573e6	−0.839490	−0.419745	−	0.907642i	$-0.637880\pi$
$373$	−2.25573e6	−0.839490	−0.419745	+	0.907642i	$0.637880\pi$
$374$	687432.	0.254127
$375$	−374302.	−0.137450
$376$	1.57432e6	0.574281
$377$	−265218.	−0.0961059
$378$	0	0
$379$	4.39503e6	1.57168	0.785840	−	0.618430i	$-0.212231\pi$
$379$	4.39503e6	1.57168	0.785840	+	0.618430i	$0.212231\pi$
$380$	3.37626e6	1.19944
$381$	301655.	0.106463
$382$	−1.94090e6	−0.680525
$383$	−1.22781e6	−0.427694	−0.213847	−	0.976867i	$-0.568599\pi$
$383$	−1.22781e6	−0.427694	−0.213847	+	0.976867i	$0.568599\pi$
$384$	−147456.	−0.0510310
$385$	0	0
$386$	−1.32327e6	−0.452043
$387$	987296.	0.335096
$388$	517477.	0.174507
$389$	2.05424e6	0.688300	0.344150	−	0.938915i	$-0.388167\pi$
$389$	2.05424e6	0.688300	0.344150	+	0.938915i	$0.388167\pi$
$390$	949616.	0.316145
$391$	−2.08579e6	−0.689967
$392$	0	0
$393$	97280.2	0.0317719
$394$	−647851.	−0.210249
$395$	−4.65127e6	−1.49996
$396$	−193702.	−0.0620722
$397$	−3.80367e6	−1.21123	−0.605615	−	0.795758i	$-0.707073\pi$
$397$	−3.80367e6	−1.21123	−0.605615	+	0.795758i	$0.707073\pi$
$398$	221585.	0.0701185
$399$	0	0
$400$	658968.	0.205928
$401$	1.18524e6	0.368084	0.184042	−	0.982918i	$-0.441082\pi$
$401$	1.18524e6	0.368084	0.184042	+	0.982918i	$0.441082\pi$
$402$	−1.95739e6	−0.604104
$403$	3.15583e6	0.967947
$404$	501543.	0.152881
$405$	−495305.	−0.150050
$406$	0	0
$407$	−1.16504e6	−0.348621
$408$	662312.	0.196975
$409$	−4.30393e6	−1.27220	−0.636102	−	0.771605i	$-0.719454\pi$
$409$	−4.30393e6	−1.27220	−0.636102	+	0.771605i	$0.719454\pi$
$410$	−2.30720e6	−0.677836
$411$	170388.	0.0497548
$412$	1.58933e6	0.461286
$413$	0	0
$414$	587726.	0.168529
$415$	6.57855e6	1.87504
$416$	357802.	0.101370
$417$	1.52008e6	0.428080
$418$	1.67110e6	0.467802
$419$	−113725.	−0.0316461	−0.0158230	−	0.999875i	$-0.505037\pi$
$419$	−113725.	−0.0316461	−0.0158230	+	0.999875i	$0.505037\pi$
$420$	0	0
$421$	443417.	0.121929	0.0609645	−	0.998140i	$-0.480582\pi$
$421$	443417.	0.121929	0.0609645	+	0.998140i	$0.480582\pi$
$422$	1.92699e6	0.526743
$423$	1.99250e6	0.541437
$424$	870158.	0.235063
$425$	−2.95981e6	−0.794863
$426$	2.52525e6	0.674186
$427$	0	0
$428$	−2.32429e6	−0.613310
$429$	470019.	0.123302
$430$	−3.68065e6	−0.959962
$431$	4.63310e6	1.20138	0.600688	−	0.799484i	$-0.294893\pi$
$431$	4.63310e6	1.20138	0.600688	+	0.799484i	$0.294893\pi$
$432$	−186624.	−0.0481125
$433$	6.57955e6	1.68646	0.843231	−	0.537552i	$-0.180651\pi$
$433$	6.57955e6	1.68646	0.843231	+	0.537552i	$0.180651\pi$
$434$	0	0
$435$	−515711.	−0.130672
$436$	−2.89361e6	−0.728994
$437$	−5.07041e6	−1.27010
$438$	1.60088e6	0.398724
$439$	−1.82070e6	−0.450896	−0.225448	−	0.974255i	$-0.572385\pi$
$439$	−1.82070e6	−0.450896	−0.225448	+	0.974255i	$0.572385\pi$
$440$	722126.	0.177820
$441$	0	0
$442$	−1.60710e6	−0.391279
$443$	−2.06990e6	−0.501119	−0.250559	−	0.968101i	$-0.580615\pi$
$443$	−2.06990e6	−0.501119	−0.250559	+	0.968101i	$0.580615\pi$
$444$	−1.12246e6	−0.270218
$445$	−7.44123e6	−1.78133
$446$	2.55511e6	0.608238
$447$	−2.37602e6	−0.562447
$448$	0	0
$449$	5.72581e6	1.34036	0.670180	−	0.742199i	$-0.266217\pi$
$449$	5.72581e6	1.34036	0.670180	+	0.742199i	$0.266217\pi$
$450$	834007.	0.194150
$451$	−1.14196e6	−0.264369
$452$	3.16532e6	0.728738
$453$	−2.51257e6	−0.575272
$454$	−2.10273e6	−0.478788
$455$	0	0
$456$	1.61004e6	0.362596
$457$	318676.	0.0713771	0.0356886	−	0.999363i	$-0.488638\pi$
$457$	318676.	0.0713771	0.0356886	+	0.999363i	$0.488638\pi$
$458$	3.73074e6	0.831059
$459$	838238.	0.185710
$460$	−2.19105e6	−0.482790
$461$	−3.42470e6	−0.750535	−0.375267	−	0.926917i	$-0.622449\pi$
$461$	−3.42470e6	−0.750535	−0.375267	+	0.926917i	$0.622449\pi$
$462$	0	0
$463$	3.82945e6	0.830201	0.415101	−	0.909775i	$-0.363746\pi$
$463$	3.82945e6	0.830201	0.415101	+	0.909775i	$0.363746\pi$
$464$	−194312.	−0.0418992
$465$	6.13645e6	1.31609
$466$	−2.83117e6	−0.603951
$467$	2.84462e6	0.603576	0.301788	−	0.953375i	$-0.402417\pi$
$467$	2.84462e6	0.603576	0.301788	+	0.953375i	$0.402417\pi$
$468$	452843.	0.0955725
$469$	0	0
$470$	−7.42809e6	−1.55107
$471$	−1.69742e6	−0.352563
$472$	−1.68696e6	−0.348539
$473$	−1.82176e6	−0.374403
$474$	−2.21805e6	−0.453446
$475$	−7.19511e6	−1.46320
$476$	0	0
$477$	1.10129e6	0.221619
$478$	−2.00246e6	−0.400860
$479$	1.30365e6	0.259611	0.129806	−	0.991539i	$-0.458565\pi$
$479$	1.30365e6	0.259611	0.129806	+	0.991539i	$0.458565\pi$
$480$	695737.	0.137830
$481$	2.72366e6	0.536772
$482$	4.83287e6	0.947519
$483$	0	0
$484$	−2.21940e6	−0.430647
$485$	−2.44160e6	−0.471324
$486$	−236196.	−0.0453609
$487$	6.23624e6	1.19152	0.595759	−	0.803164i	$-0.296852\pi$
$487$	6.23624e6	1.19152	0.595759	+	0.803164i	$0.296852\pi$
$488$	2.26059e6	0.429707
$489$	−807456.	−0.152703
$490$	0	0
$491$	−3.93928e6	−0.737417	−0.368709	−	0.929545i	$-0.620200\pi$
$491$	−3.93928e6	−0.737417	−0.368709	+	0.929545i	$0.620200\pi$
$492$	−1.10023e6	−0.204914
$493$	872772.	0.161727
$494$	−3.90675e6	−0.720275
$495$	913941.	0.167651
$496$	2.31213e6	0.421995
$497$	0	0
$498$	3.13711e6	0.566835
$499$	7.97571e6	1.43390	0.716948	−	0.697126i	$-0.245538\pi$
$499$	7.97571e6	1.43390	0.716948	+	0.697126i	$0.245538\pi$
$500$	665427.	0.119035
$501$	−4.76470e6	−0.848089
$502$	391307.	0.0693040
$503$	−2.70777e6	−0.477190	−0.238595	−	0.971119i	$-0.576687\pi$
$503$	−2.70777e6	−0.477190	−0.238595	+	0.971119i	$0.576687\pi$
$504$	0	0
$505$	−2.36641e6	−0.412917
$506$	−1.08448e6	−0.188297
$507$	2.24281e6	0.387502
$508$	−536276.	−0.0921996
$509$	3.90049e6	0.667306	0.333653	−	0.942696i	$-0.391719\pi$
$509$	3.90049e6	0.667306	0.333653	+	0.942696i	$0.391719\pi$
$510$	−3.12497e6	−0.532010
$511$	0	0
$512$	262144.	0.0441942
$513$	2.03770e6	0.341859
$514$	−4.43165e6	−0.739874
$515$	−7.49887e6	−1.24589
$516$	−1.75519e6	−0.290202
$517$	−3.67658e6	−0.604947
$518$	0	0
$519$	−304545.	−0.0496287
$520$	−1.68821e6	−0.273790
$521$	7.00063e6	1.12991	0.564954	−	0.825122i	$-0.308894\pi$
$521$	7.00063e6	1.12991	0.564954	+	0.825122i	$0.308894\pi$
$522$	−245927.	−0.0395029
$523$	−2.11208e6	−0.337641	−0.168821	−	0.985647i	$-0.553996\pi$
$523$	−2.11208e6	−0.337641	−0.168821	+	0.985647i	$0.553996\pi$
$524$	−172943.	−0.0275153
$525$	0	0
$526$	6.02741e6	0.949875
$527$	−1.03851e7	−1.62887
$528$	344360.	0.0537561
$529$	−3.14586e6	−0.488765
$530$	−4.10564e6	−0.634880
$531$	−2.13506e6	−0.328605
$532$	0	0
$533$	2.66971e6	0.407048
$534$	−3.54850e6	−0.538507
$535$	1.09666e7	1.65649
$536$	3.47980e6	0.523170
$537$	2.22969e6	0.333664
$538$	−8.54009e6	−1.27206
$539$	0	0
$540$	880543.	0.129947
$541$	5.70567e6	0.838134	0.419067	−	0.907955i	$-0.362357\pi$
$541$	5.70567e6	0.838134	0.419067	+	0.907955i	$0.362357\pi$
$542$	4.91439e6	0.718574
$543$	−3.32523e6	−0.483974
$544$	−1.17744e6	−0.170586
$545$	1.36528e7	1.96894
$546$	0	0
$547$	2.28054e6	0.325888	0.162944	−	0.986635i	$-0.447901\pi$
$547$	2.28054e6	0.325888	0.162944	+	0.986635i	$0.447901\pi$
$548$	−302912.	−0.0430889
$549$	2.86106e6	0.405132
$550$	−1.53891e6	−0.216924
$551$	2.12165e6	0.297711
$552$	−1.04485e6	−0.145950
$553$	0	0
$554$	−7.38730e6	−1.02261
$555$	5.29609e6	0.729832
$556$	−2.70236e6	−0.370729
$557$	−6.73941e6	−0.920415	−0.460208	−	0.887811i	$-0.652225\pi$
$557$	−6.73941e6	−0.920415	−0.460208	+	0.887811i	$0.652225\pi$
$558$	2.92629e6	0.397861
$559$	4.25897e6	0.576468
$560$	0	0
$561$	−1.54672e6	−0.207494
$562$	−9.13304e6	−1.21976
$563$	−9.66820e6	−1.28551	−0.642754	−	0.766073i	$-0.722208\pi$
$563$	−9.66820e6	−1.28551	−0.642754	+	0.766073i	$0.722208\pi$
$564$	−3.54223e6	−0.468898
$565$	−1.49348e7	−1.96825
$566$	5.34770e6	0.701659
$567$	0	0
$568$	−4.48933e6	−0.583862
$569$	−1.39587e7	−1.80744	−0.903719	−	0.428125i	$-0.859174\pi$
$569$	−1.39587e7	−1.80744	−0.903719	+	0.428125i	$0.859174\pi$
$570$	−7.59659e6	−0.979335
$571$	−2.35841e6	−0.302711	−0.151355	−	0.988479i	$-0.548364\pi$
$571$	−2.35841e6	−0.302711	−0.151355	+	0.988479i	$0.548364\pi$
$572$	−835589.	−0.106783
$573$	4.36702e6	0.555647
$574$	0	0
$575$	4.66933e6	0.588959
$576$	331776.	0.0416667
$577$	5.01098e6	0.626589	0.313295	−	0.949656i	$-0.398567\pi$
$577$	5.01098e6	0.626589	0.313295	+	0.949656i	$0.398567\pi$
$578$	−390836.	−0.0486603
$579$	2.97735e6	0.369091
$580$	916819.	0.113165
$581$	0	0
$582$	−1.16432e6	−0.142484
$583$	−2.03211e6	−0.247615
$584$	−2.84600e6	−0.345305
$585$	−2.13664e6	−0.258131
$586$	−8.92132e6	−1.07321
$587$	3.95106e6	0.473280	0.236640	−	0.971597i	$-0.423954\pi$
$587$	3.95106e6	0.473280	0.236640	+	0.971597i	$0.423954\pi$
$588$	0	0
$589$	−2.52455e7	−2.99845
$590$	7.95955e6	0.941367
$591$	1.45766e6	0.171668
$592$	1.99549e6	0.234016
$593$	−2.53680e6	−0.296244	−0.148122	−	0.988969i	$-0.547323\pi$
$593$	−2.53680e6	−0.296244	−0.148122	+	0.988969i	$0.547323\pi$
$594$	435830.	0.0506817
$595$	0	0
$596$	4.22403e6	0.487093
$597$	−498566.	−0.0572515
$598$	2.53532e6	0.289921
$599$	7.17714e6	0.817305	0.408652	−	0.912690i	$-0.365999\pi$
$599$	7.17714e6	0.817305	0.408652	+	0.912690i	$0.365999\pi$
$600$	−1.48268e6	−0.168139
$601$	1.12527e7	1.27078	0.635392	−	0.772190i	$-0.280838\pi$
$601$	1.12527e7	1.27078	0.635392	+	0.772190i	$0.280838\pi$
$602$	0	0
$603$	4.40413e6	0.493249
$604$	4.46680e6	0.498200
$605$	1.04717e7	1.16313
$606$	−1.12847e6	−0.124827
$607$	−1.40370e7	−1.54633	−0.773167	−	0.634202i	$-0.781329\pi$
$607$	−1.40370e7	−1.54633	−0.773167	+	0.634202i	$0.781329\pi$
$608$	−2.86229e6	−0.314018
$609$	0	0
$610$	−1.06661e7	−1.16059
$611$	8.59521e6	0.931437
$612$	−1.49020e6	−0.160830
$613$	−7.62872e6	−0.819975	−0.409988	−	0.912091i	$-0.634467\pi$
$613$	−7.62872e6	−0.819975	−0.409988	+	0.912091i	$0.634467\pi$
$614$	7.11128e6	0.761249
$615$	5.19119e6	0.553451
$616$	0	0
$617$	−4.41080e6	−0.466450	−0.233225	−	0.972423i	$-0.574928\pi$
$617$	−4.41080e6	−0.466450	−0.233225	+	0.972423i	$0.574928\pi$
$618$	−3.57598e6	−0.376638
$619$	−9.04355e6	−0.948664	−0.474332	−	0.880346i	$-0.657310\pi$
$619$	−9.04355e6	−0.948664	−0.474332	+	0.880346i	$0.657310\pi$
$620$	−1.09092e7	−1.13977
$621$	−1.32238e6	−0.137603
$622$	5.61087e6	0.581506
$623$	0	0
$624$	−805054.	−0.0827682
$625$	−1.11837e7	−1.14521
$626$	4.87578e6	0.497288
$627$	−3.75998e6	−0.381959
$628$	3.01764e6	0.305329
$629$	−8.96293e6	−0.903282
$630$	0	0
$631$	−7.33039e6	−0.732916	−0.366458	−	0.930435i	$-0.619430\pi$
$631$	−7.33039e6	−0.732916	−0.366458	+	0.930435i	$0.619430\pi$
$632$	3.94320e6	0.392695
$633$	−4.33573e6	−0.430083
$634$	1.07201e7	1.05919
$635$	2.53030e6	0.249022
$636$	−1.95786e6	−0.191928
$637$	0	0
$638$	453786.	0.0441366
$639$	−5.68181e6	−0.550471
$640$	−1.23687e6	−0.119364
$641$	3.68824e6	0.354547	0.177273	−	0.984162i	$-0.443272\pi$
$641$	3.68824e6	0.354547	0.177273	+	0.984162i	$0.443272\pi$
$642$	5.22965e6	0.500766
$643$	−1.17584e7	−1.12155	−0.560776	−	0.827968i	$-0.689497\pi$
$643$	−1.17584e7	−1.12155	−0.560776	+	0.827968i	$0.689497\pi$
$644$	0	0
$645$	8.28147e6	0.783806
$646$	1.28562e7	1.21208
$647$	−9.94050e6	−0.933572	−0.466786	−	0.884370i	$-0.654588\pi$
$647$	−9.94050e6	−0.933572	−0.466786	+	0.884370i	$0.654588\pi$
$648$	419904.	0.0392837
$649$	3.93963e6	0.367151
$650$	3.59772e6	0.333998
$651$	0	0
$652$	1.43548e6	0.132244
$653$	−1.02620e6	−0.0941778	−0.0470889	−	0.998891i	$-0.514994\pi$
$653$	−1.02620e6	−0.0941778	−0.0470889	+	0.998891i	$0.514994\pi$
$654$	6.51063e6	0.595221
$655$	815990.	0.0743159
$656$	1.95597e6	0.177461
$657$	−3.60197e6	−0.325557
$658$	0	0
$659$	1.00207e7	0.898846	0.449423	−	0.893319i	$-0.351630\pi$
$659$	1.00207e7	0.898846	0.449423	+	0.893319i	$0.351630\pi$
$660$	−1.62478e6	−0.145190
$661$	2.62826e6	0.233972	0.116986	−	0.993134i	$-0.462677\pi$
$661$	2.62826e6	0.233972	0.116986	+	0.993134i	$0.462677\pi$
$662$	570241.	0.0505724
$663$	3.61597e6	0.319478
$664$	−5.57709e6	−0.490893
$665$	0	0
$666$	2.52554e6	0.220632
$667$	−1.37686e6	−0.119833
$668$	8.47058e6	0.734467
$669$	−5.74901e6	−0.496624
$670$	−1.64187e7	−1.41303
$671$	−5.27925e6	−0.452654
$672$	0	0
$673$	−1.50220e7	−1.27847	−0.639233	−	0.769013i	$-0.720748\pi$
$673$	−1.50220e7	−1.27847	−0.639233	+	0.769013i	$0.720748\pi$
$674$	−4.84825e6	−0.411088
$675$	−1.87651e6	−0.158523
$676$	−3.98723e6	−0.335586
$677$	−6.03310e6	−0.505905	−0.252953	−	0.967479i	$-0.581402\pi$
$677$	−6.03310e6	−0.505905	−0.252953	+	0.967479i	$0.581402\pi$
$678$	−7.12197e6	−0.595012
$679$	0	0
$680$	5.55550e6	0.460734
$681$	4.73114e6	0.390929
$682$	−5.39960e6	−0.444530
$683$	1.10720e7	0.908187	0.454093	−	0.890954i	$-0.349963\pi$
$683$	1.10720e7	0.908187	0.454093	+	0.890954i	$0.349963\pi$
$684$	−3.62258e6	−0.296059
$685$	1.42922e6	0.116379
$686$	0	0
$687$	−8.39417e6	−0.678557
$688$	3.12034e6	0.251322
$689$	4.75073e6	0.381253
$690$	4.92987e6	0.394196
$691$	−1.05548e7	−0.840919	−0.420460	−	0.907311i	$-0.638131\pi$
$691$	−1.05548e7	−0.840919	−0.420460	+	0.907311i	$0.638131\pi$
$692$	541413.	0.0429797
$693$	0	0
$694$	1.38741e7	1.09347
$695$	1.27505e7	1.00130
$696$	437203.	0.0342106
$697$	−8.78540e6	−0.684983
$698$	4.06766e6	0.316014
$699$	6.37014e6	0.493124
$700$	0	0
$701$	−7.20675e6	−0.553917	−0.276958	−	0.960882i	$-0.589326\pi$
$701$	−7.20675e6	−0.553917	−0.276958	+	0.960882i	$0.589326\pi$
$702$	−1.01890e6	−0.0780346
$703$	−2.17883e7	−1.66278
$704$	−612195.	−0.0465541
$705$	1.67132e7	1.26645
$706$	6.25542e6	0.472329
$707$	0	0
$708$	3.79567e6	0.284581
$709$	2.69373e6	0.201252	0.100626	−	0.994924i	$-0.467916\pi$
$709$	2.69373e6	0.201252	0.100626	+	0.994924i	$0.467916\pi$
$710$	2.11819e7	1.57695
$711$	4.99061e6	0.370237
$712$	6.30844e6	0.466361
$713$	1.63833e7	1.20692
$714$	0	0
$715$	3.94253e6	0.288410
$716$	−3.96390e6	−0.288962
$717$	4.50552e6	0.327301
$718$	198213.	0.0143489
$719$	6.92550e6	0.499608	0.249804	−	0.968296i	$-0.419634\pi$
$719$	6.92550e6	0.499608	0.249804	+	0.968296i	$0.419634\pi$
$720$	−1.56541e6	−0.112537
$721$	0	0
$722$	2.13482e7	1.52412
$723$	−1.08740e7	−0.773646
$724$	5.91152e6	0.419134
$725$	−1.95382e6	−0.138051
$726$	4.99364e6	0.351622
$727$	4.11366e6	0.288664	0.144332	−	0.989529i	$-0.453897\pi$
$727$	4.11366e6	0.288664	0.144332	+	0.989529i	$0.453897\pi$
$728$	0	0
$729$	531441.	0.0370370
$730$	1.34282e7	0.932634
$731$	−1.40153e7	−0.970083
$732$	−5.08633e6	−0.350855
$733$	7.92038e6	0.544485	0.272243	−	0.962229i	$-0.412235\pi$
$733$	7.92038e6	0.544485	0.272243	+	0.962229i	$0.412235\pi$
$734$	1.41932e7	0.972392
$735$	0	0
$736$	1.85750e6	0.126397
$737$	−8.12652e6	−0.551107
$738$	2.47552e6	0.167311
$739$	1.60410e7	1.08049	0.540245	−	0.841508i	$-0.318332\pi$
$739$	1.60410e7	1.08049	0.540245	+	0.841508i	$0.318332\pi$
$740$	−9.41527e6	−0.632053
$741$	8.79019e6	0.588102
$742$	0	0
$743$	1.53453e7	1.01977	0.509887	−	0.860241i	$-0.329687\pi$
$743$	1.53453e7	1.01977	0.509887	+	0.860241i	$0.329687\pi$
$744$	−5.20229e6	−0.344558
$745$	−1.99301e7	−1.31559
$746$	−9.02293e6	−0.593609
$747$	−7.05850e6	−0.462819
$748$	2.74973e6	0.179695
$749$	0	0
$750$	−1.49721e6	−0.0971918
$751$	2.24976e7	1.45558	0.727790	−	0.685800i	$-0.240547\pi$
$751$	2.24976e7	1.45558	0.727790	+	0.685800i	$0.240547\pi$
$752$	6.29729e6	0.406078
$753$	−880440.	−0.0565864
$754$	−1.06087e6	−0.0679571
$755$	−2.10756e7	−1.34559
$756$	0	0
$757$	2.30349e7	1.46099	0.730494	−	0.682919i	$-0.239290\pi$
$757$	2.30349e7	1.46099	0.730494	+	0.682919i	$0.239290\pi$
$758$	1.75801e7	1.11135
$759$	2.44007e6	0.153744
$760$	1.35050e7	0.848129
$761$	5.40735e6	0.338472	0.169236	−	0.985576i	$-0.445870\pi$
$761$	5.40735e6	0.338472	0.169236	+	0.985576i	$0.445870\pi$
$762$	1.20662e6	0.0752806
$763$	0	0
$764$	−7.76359e6	−0.481204
$765$	7.03118e6	0.434385
$766$	−4.91123e6	−0.302426
$767$	−9.21019e6	−0.565301
$768$	−589824.	−0.0360844
$769$	−7.93100e6	−0.483629	−0.241814	−	0.970323i	$-0.577742\pi$
$769$	−7.93100e6	−0.483629	−0.241814	+	0.970323i	$0.577742\pi$
$770$	0	0
$771$	9.97122e6	0.604105
$772$	−5.29307e6	−0.319643
$773$	269579.	0.0162270	0.00811349	−	0.999967i	$-0.497417\pi$
$773$	269579.	0.0162270	0.00811349	+	0.999967i	$0.497417\pi$
$774$	3.94918e6	0.236949
$775$	2.32486e7	1.39041
$776$	2.06991e6	0.123395
$777$	0	0
$778$	8.21698e6	0.486702
$779$	−2.13567e7	−1.26093
$780$	3.79846e6	0.223548
$781$	1.04841e7	0.615041
$782$	−8.34315e6	−0.487880
$783$	553335.	0.0322540
$784$	0	0
$785$	−1.42380e7	−0.824662
$786$	389121.	0.0224661
$787$	−8.98621e6	−0.517177	−0.258589	−	0.965988i	$-0.583257\pi$
$787$	−8.98621e6	−0.517177	−0.258589	+	0.965988i	$0.583257\pi$
$788$	−2.59140e6	−0.148669
$789$	−1.35617e7	−0.775570
$790$	−1.86051e7	−1.06063
$791$	0	0
$792$	−774810.	−0.0438917
$793$	1.23420e7	0.696950
$794$	−1.52147e7	−0.856469
$795$	9.23770e6	0.518377
$796$	886340.	0.0495813
$797$	−2.65558e7	−1.48086	−0.740429	−	0.672135i	$-0.765378\pi$
$797$	−2.65558e7	−1.48086	−0.740429	+	0.672135i	$0.765378\pi$
$798$	0	0
$799$	−2.82849e7	−1.56743
$800$	2.63587e6	0.145613
$801$	7.98412e6	0.439689
$802$	4.74098e6	0.260275
$803$	6.64638e6	0.363745
$804$	−7.82956e6	−0.427166
$805$	0	0
$806$	1.26233e7	0.684442
$807$	1.92152e7	1.03863
$808$	2.00617e6	0.108103
$809$	2.52557e7	1.35671	0.678356	−	0.734733i	$-0.262693\pi$
$809$	2.52557e7	1.35671	0.678356	+	0.734733i	$0.262693\pi$
$810$	−1.98122e6	−0.106101
$811$	−4.76866e6	−0.254592	−0.127296	−	0.991865i	$-0.540630\pi$
$811$	−4.76866e6	−0.254592	−0.127296	+	0.991865i	$0.540630\pi$
$812$	0	0
$813$	−1.10574e7	−0.586713
$814$	−4.66015e6	−0.246513
$815$	−6.77297e6	−0.357179
$816$	2.64925e6	0.139283
$817$	−3.40702e7	−1.78575
$818$	−1.72157e7	−0.899585
$819$	0	0
$820$	−9.22878e6	−0.479303
$821$	−5.95534e6	−0.308353	−0.154177	−	0.988043i	$-0.549273\pi$
$821$	−5.95534e6	−0.308353	−0.154177	+	0.988043i	$0.549273\pi$
$822$	681553.	0.0351819
$823$	1.06659e7	0.548907	0.274453	−	0.961600i	$-0.411503\pi$
$823$	1.06659e7	0.548907	0.274453	+	0.961600i	$0.411503\pi$
$824$	6.35731e6	0.326178
$825$	3.46256e6	0.177118
$826$	0	0
$827$	−8.52356e6	−0.433369	−0.216684	−	0.976242i	$-0.569524\pi$
$827$	−8.52356e6	−0.433369	−0.216684	+	0.976242i	$0.569524\pi$
$828$	2.35090e6	0.119168
$829$	3.87458e6	0.195811	0.0979057	−	0.995196i	$-0.468786\pi$
$829$	3.87458e6	0.195811	0.0979057	+	0.995196i	$0.468786\pi$
$830$	2.63142e7	1.32585
$831$	1.66214e7	0.834960
$832$	1.43121e6	0.0716794
$833$	0	0
$834$	6.08031e6	0.302699
$835$	−3.99665e7	−1.98372
$836$	6.68441e6	0.330786
$837$	−6.58414e6	−0.324852
$838$	−454899.	−0.0223772
$839$	2.13769e7	1.04843	0.524215	−	0.851586i	$-0.324359\pi$
$839$	2.13769e7	1.04843	0.524215	+	0.851586i	$0.324359\pi$
$840$	0	0
$841$	−1.99350e7	−0.971911
$842$	1.77367e6	0.0862168
$843$	2.05493e7	0.995930
$844$	7.70796e6	0.372463
$845$	1.88128e7	0.906383
$846$	7.97001e6	0.382854
$847$	0	0
$848$	3.48063e6	0.166214
$849$	−1.20323e7	−0.572902
$850$	−1.18393e7	−0.562053
$851$	1.41397e7	0.669293
$852$	1.01010e7	0.476722
$853$	−85930.0	−0.00404364	−0.00202182	−	0.999998i	$-0.500644\pi$
$853$	−85930.0	−0.00404364	−0.00202182	+	0.999998i	$0.500644\pi$
$854$	0	0
$855$	1.70923e7	0.799624
$856$	−9.29715e6	−0.433676
$857$	−1.85664e7	−0.863528	−0.431764	−	0.901987i	$-0.642109\pi$
$857$	−1.85664e7	−0.863528	−0.431764	+	0.901987i	$0.642109\pi$
$858$	1.88007e6	0.0871880
$859$	3.92215e7	1.81360	0.906799	−	0.421564i	$-0.138519\pi$
$859$	3.92215e7	1.81360	0.906799	+	0.421564i	$0.138519\pi$
$860$	−1.47226e7	−0.678795
$861$	0	0
$862$	1.85324e7	0.849501
$863$	1.83642e7	0.839352	0.419676	−	0.907674i	$-0.362144\pi$
$863$	1.83642e7	0.839352	0.419676	+	0.907674i	$0.362144\pi$
$864$	−746496.	−0.0340207
$865$	−2.55453e6	−0.116084
$866$	2.63182e7	1.19251
$867$	879381.	0.0397310
$868$	0	0
$869$	−9.20870e6	−0.413665
$870$	−2.06284e6	−0.0923992
$871$	1.89984e7	0.848539
$872$	−1.15744e7	−0.515477
$873$	2.61973e6	0.116338
$874$	−2.02816e7	−0.898100
$875$	0	0
$876$	6.40351e6	0.281941
$877$	−9.42578e6	−0.413826	−0.206913	−	0.978359i	$-0.566342\pi$
$877$	−9.42578e6	−0.413826	−0.206913	+	0.978359i	$0.566342\pi$
$878$	−7.28278e6	−0.318831
$879$	2.00730e7	0.876273
$880$	2.88850e6	0.125738
$881$	1.32820e7	0.576534	0.288267	−	0.957550i	$-0.406921\pi$
$881$	1.32820e7	0.576534	0.288267	+	0.957550i	$0.406921\pi$
$882$	0	0
$883$	1.88897e7	0.815309	0.407655	−	0.913136i	$-0.366347\pi$
$883$	1.88897e7	0.815309	0.407655	+	0.913136i	$0.366347\pi$
$884$	−6.42840e6	−0.276676
$885$	−1.79090e7	−0.768623
$886$	−8.27961e6	−0.354345
$887$	4.17083e7	1.77997	0.889987	−	0.455985i	$-0.150713\pi$
$887$	4.17083e7	1.77997	0.889987	+	0.455985i	$0.150713\pi$
$888$	−4.48986e6	−0.191073
$889$	0	0
$890$	−2.97649e7	−1.25959
$891$	−980618.	−0.0413815
$892$	1.02205e7	0.430089
$893$	−6.87586e7	−2.88535
$894$	−9.50408e6	−0.397710
$895$	1.87028e7	0.780455
$896$	0	0
$897$	−5.70447e6	−0.236719
$898$	2.29033e7	0.947777
$899$	−6.85539e6	−0.282900
$900$	3.33603e6	0.137285
$901$	−1.56336e7	−0.641573
$902$	−4.56785e6	−0.186937
$903$	0	0
$904$	1.26613e7	0.515295
$905$	−2.78922e7	−1.13204
$906$	−1.00503e7	−0.406779
$907$	4.60801e7	1.85993	0.929963	−	0.367654i	$-0.119839\pi$
$907$	4.60801e7	1.85993	0.929963	+	0.367654i	$0.119839\pi$
$908$	−8.41091e6	−0.338554
$909$	2.53906e6	0.101921
$910$	0	0
$911$	2.25527e7	0.900334	0.450167	−	0.892944i	$-0.351364\pi$
$911$	2.25527e7	0.900334	0.450167	+	0.892944i	$0.351364\pi$
$912$	6.44014e6	0.256394
$913$	1.30244e7	0.517107
$914$	1.27470e6	0.0504712
$915$	2.39987e7	0.947622
$916$	1.49230e7	0.587647
$917$	0	0
$918$	3.35295e6	0.131317
$919$	−3.25898e7	−1.27290	−0.636448	−	0.771319i	$-0.719597\pi$
$919$	−3.25898e7	−1.27290	−0.636448	+	0.771319i	$0.719597\pi$
$920$	−8.76421e6	−0.341384
$921$	−1.60004e7	−0.621557
$922$	−1.36988e7	−0.530708
$923$	−2.45100e7	−0.946977
$924$	0	0
$925$	2.00648e7	0.771046
$926$	1.53178e7	0.587041
$927$	8.04597e6	0.307524
$928$	−777250.	−0.0296272
$929$	−4.56149e7	−1.73407	−0.867036	−	0.498246i	$-0.833978\pi$
$929$	−4.56149e7	−1.73407	−0.867036	+	0.498246i	$0.833978\pi$
$930$	2.45458e7	0.930614
$931$	0	0
$932$	−1.13247e7	−0.427058
$933$	−1.26244e7	−0.474797
$934$	1.13785e7	0.426792
$935$	−1.29740e7	−0.485338
$936$	1.81137e6	0.0675800
$937$	3.60574e6	0.134167	0.0670835	−	0.997747i	$-0.478631\pi$
$937$	3.60574e6	0.134167	0.0670835	+	0.997747i	$0.478631\pi$
$938$	0	0
$939$	−1.09705e7	−0.406034
$940$	−2.97123e7	−1.09677
$941$	−4.40826e6	−0.162290	−0.0811452	−	0.996702i	$-0.525858\pi$
$941$	−4.40826e6	−0.162290	−0.0811452	+	0.996702i	$0.525858\pi$
$942$	−6.78968e6	−0.249300
$943$	1.38596e7	0.507542
$944$	−6.74786e6	−0.246454
$945$	0	0
$946$	−7.28706e6	−0.264743
$947$	7.36278e6	0.266788	0.133394	−	0.991063i	$-0.457412\pi$
$947$	7.36278e6	0.266788	0.133394	+	0.991063i	$0.457412\pi$
$948$	−8.87219e6	−0.320634
$949$	−1.55381e7	−0.560057
$950$	−2.87804e7	−1.03464
$951$	−2.41201e7	−0.864825
$952$	0	0
$953$	3.73903e7	1.33360	0.666802	−	0.745235i	$-0.267663\pi$
$953$	3.73903e7	1.33360	0.666802	+	0.745235i	$0.267663\pi$
$954$	4.40518e6	0.156708
$955$	3.66307e7	1.29968
$956$	−8.00982e6	−0.283451
$957$	−1.02102e6	−0.0360374
$958$	5.21462e6	0.183573
$959$	0	0
$960$	2.78295e6	0.0974602
$961$	5.29433e7	1.84928
$962$	1.08946e7	0.379555
$963$	−1.17667e7	−0.408874
$964$	1.93315e7	0.669997
$965$	2.49742e7	0.863322
$966$	0	0
$967$	1.30730e7	0.449582	0.224791	−	0.974407i	$-0.427830\pi$
$967$	1.30730e7	0.449582	0.224791	+	0.974407i	$0.427830\pi$
$968$	−8.87758e6	−0.304513
$969$	−2.89265e7	−0.989660
$970$	−9.76640e6	−0.333277
$971$	−1.52454e7	−0.518908	−0.259454	−	0.965755i	$-0.583543\pi$
$971$	−1.52454e7	−0.518908	−0.259454	+	0.965755i	$0.583543\pi$
$972$	−944784.	−0.0320750
$973$	0	0
$974$	2.49450e7	0.842530
$975$	−8.09486e6	−0.272708
$976$	9.04237e6	0.303849
$977$	3.08690e6	0.103463	0.0517316	−	0.998661i	$-0.483526\pi$
$977$	3.08690e6	0.103463	0.0517316	+	0.998661i	$0.483526\pi$
$978$	−3.22983e6	−0.107977
$979$	−1.47324e7	−0.491264
$980$	0	0
$981$	−1.46489e7	−0.485996
$982$	−1.57571e7	−0.521433
$983$	1.70201e7	0.561796	0.280898	−	0.959738i	$-0.409368\pi$
$983$	1.70201e7	0.561796	0.280898	+	0.959738i	$0.409368\pi$
$984$	−4.40093e6	−0.144896
$985$	1.22269e7	0.401539
$986$	3.49109e6	0.114359
$987$	0	0
$988$	−1.56270e7	−0.509311
$989$	2.21102e7	0.718789
$990$	3.65576e6	0.118547
$991$	−4.34672e7	−1.40597	−0.702987	−	0.711203i	$-0.748151\pi$
$991$	−4.34672e7	−1.40597	−0.702987	+	0.711203i	$0.748151\pi$
$992$	9.24851e6	0.298396
$993$	−1.28304e6	−0.0412922
$994$	0	0
$995$	−4.18199e6	−0.133914
$996$	1.25484e7	0.400813
$997$	−2.46672e7	−0.785926	−0.392963	−	0.919554i	$-0.628550\pi$
$997$	−2.46672e7	−0.785926	−0.392963	+	0.919554i	$0.628550\pi$
$998$	3.19028e7	1.01392
$999$	−5.68248e6	−0.180146

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.6.a.r.1.1		2
3.2	odd	2		882.6.a.bh.1.2		2
7.2	even	3		42.6.e.c.25.2	✓	4
7.3	odd	6		294.6.e.s.79.1		4
7.4	even	3		42.6.e.c.37.2	yes	4
7.5	odd	6		294.6.e.s.67.1		4
7.6	odd	2		294.6.a.w.1.2		2
21.2	odd	6		126.6.g.h.109.1		4
21.11	odd	6		126.6.g.h.37.1		4
21.20	even	2		882.6.a.bb.1.1		2
28.11	odd	6		336.6.q.f.289.2		4
28.23	odd	6		336.6.q.f.193.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.6.e.c.25.2	✓	4	7.2	even	3
42.6.e.c.37.2	yes	4	7.4	even	3
126.6.g.h.37.1		4	21.11	odd	6
126.6.g.h.109.1		4	21.2	odd	6
294.6.a.r.1.1		2	1.1	even	1	trivial
294.6.a.w.1.2		2	7.6	odd	2
294.6.e.s.67.1		4	7.5	odd	6
294.6.e.s.79.1		4	7.3	odd	6
336.6.q.f.193.2		4	28.23	odd	6
336.6.q.f.289.2		4	28.11	odd	6
882.6.a.bb.1.1		2	21.20	even	2
882.6.a.bh.1.2		2	3.2	odd	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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	294.a (trivial)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -75.4923 q^{5} -36.0000 q^{6} +64.0000 q^{8} +81.0000 q^{9} -301.969 q^{10} -149.462 q^{11} -144.000 q^{12} +349.416 q^{13} +679.431 q^{15} +256.000 q^{16} -1149.85 q^{17} +324.000 q^{18} -2795.20 q^{19} -1207.88 q^{20} -597.847 q^{22} +1813.97 q^{23} -576.000 q^{24} +2574.09 q^{25} +1397.66 q^{26} -729.000 q^{27} -759.033 q^{29} +2717.72 q^{30} +9031.74 q^{31} +1024.00 q^{32} +1345.16 q^{33} -4599.39 q^{34} +1296.00 q^{36} +7794.89 q^{37} -11180.8 q^{38} -3144.74 q^{39} -4831.51 q^{40} +7640.49 q^{41} +12188.8 q^{43} -2391.39 q^{44} -6114.88 q^{45} +7255.88 q^{46} +24598.8 q^{47} -2304.00 q^{48} +10296.4 q^{50} +10348.6 q^{51} +5590.65 q^{52} +13596.2 q^{53} -2916.00 q^{54} +11283.2 q^{55} +25156.8 q^{57} -3036.13 q^{58} -26358.8 q^{59} +10870.9 q^{60} +35321.8 q^{61} +36127.0 q^{62} +4096.00 q^{64} -26378.2 q^{65} +5380.62 q^{66} +54371.9 q^{67} -18397.6 q^{68} -16325.7 q^{69} -70145.7 q^{71} +5184.00 q^{72} -44468.8 q^{73} +31179.6 q^{74} -23166.8 q^{75} -44723.2 q^{76} -12579.0 q^{78} +61612.5 q^{79} -19326.0 q^{80} +6561.00 q^{81} +30562.0 q^{82} -87142.0 q^{83} +86804.6 q^{85} +48755.3 q^{86} +6831.30 q^{87} -9565.55 q^{88} +98569.4 q^{89} -24459.5 q^{90} +29023.5 q^{92} -81285.7 q^{93} +98395.2 q^{94} +211016. q^{95} -9216.00 q^{96} +32342.3 q^{97} -12106.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 8 q^{2} - 18 q^{3} + 32 q^{4} - 53 q^{5} - 72 q^{6} + 128 q^{8} + 162 q^{9} - 212 q^{10} + 191 q^{11} - 288 q^{12} - 379 q^{13} + 477 q^{15} + 512 q^{16} - 340 q^{17} + 648 q^{18} - 1769 q^{19} - 848 q^{20}+ \cdots + 15471 q^{99}+O(q^{100}) \) 2 * q + 8 * q^2 - 18 * q^3 + 32 * q^4 - 53 * q^5 - 72 * q^6 + 128 * q^8 + 162 * q^9 - 212 * q^10 + 191 * q^11 - 288 * q^12 - 379 * q^13 + 477 * q^15 + 512 * q^16 - 340 * q^17 + 648 * q^18 - 1769 * q^19 - 848 * q^20 + 764 * q^22 + 3236 * q^23 - 1152 * q^24 - 45 * q^25 - 1516 * q^26 - 1458 * q^27 + 4459 * q^29 + 1908 * q^30 + 1994 * q^31 + 2048 * q^32 - 1719 * q^33 - 1360 * q^34 + 2592 * q^36 + 20587 * q^37 - 7076 * q^38 + 3411 * q^39 - 3392 * q^40 + 8814 * q^41 + 15853 * q^43 + 3056 * q^44 - 4293 * q^45 + 12944 * q^46 + 33912 * q^47 - 4608 * q^48 - 180 * q^50 + 3060 * q^51 - 6064 * q^52 + 49239 * q^53 - 5832 * q^54 + 18941 * q^55 + 15921 * q^57 + 17836 * q^58 - 56735 * q^59 + 7632 * q^60 + 67508 * q^61 + 7976 * q^62 + 8192 * q^64 - 42762 * q^65 - 6876 * q^66 + 75723 * q^67 - 5440 * q^68 - 29124 * q^69 - 8992 * q^71 + 10368 * q^72 - 3201 * q^73 + 82348 * q^74 + 405 * q^75 - 28304 * q^76 + 13644 * q^78 + 26612 * q^79 - 13568 * q^80 + 13122 * q^81 + 35256 * q^82 - 949 * q^83 + 105020 * q^85 + 63412 * q^86 - 40131 * q^87 + 12224 * q^88 + 176562 * q^89 - 17172 * q^90 + 51776 * q^92 - 17946 * q^93 + 135648 * q^94 + 234098 * q^95 - 18432 * q^96 - 129423 * q^97 + 15471 * q^99

Introduction

L-functions

Modular forms

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Groups

Database

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