LMFDB - Embedded newform 1767.4.a.h.1.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1767,4,Mod(1,1767)] 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("1767.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1767, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 1767 = 3 \cdot 19 \cdot 31 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1767.a (trivial)

Newform invariants

comment:select newform

sage:traces = [40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	yes
Analytic conductor:	$104.256374980$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	1767.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.12215 q^{2} +3.00000 q^{3} -3.49649 q^{4} +15.8207 q^{5} -6.36644 q^{6} +34.4325 q^{7} +24.3972 q^{8} +9.00000 q^{9} -33.5738 q^{10} -18.9697 q^{11} -10.4895 q^{12} +20.8311 q^{13} -73.0709 q^{14} +47.4620 q^{15} -23.8026 q^{16} -75.2706 q^{17} -19.0993 q^{18} -19.0000 q^{19} -55.3168 q^{20} +103.298 q^{21} +40.2566 q^{22} +66.4577 q^{23} +73.1917 q^{24} +125.293 q^{25} -44.2066 q^{26} +27.0000 q^{27} -120.393 q^{28} -27.2789 q^{29} -100.721 q^{30} +31.0000 q^{31} -144.665 q^{32} -56.9092 q^{33} +159.735 q^{34} +544.745 q^{35} -31.4684 q^{36} +268.093 q^{37} +40.3208 q^{38} +62.4932 q^{39} +385.980 q^{40} -215.775 q^{41} -219.213 q^{42} +90.8472 q^{43} +66.3275 q^{44} +142.386 q^{45} -141.033 q^{46} -8.82826 q^{47} -71.4078 q^{48} +842.599 q^{49} -265.890 q^{50} -225.812 q^{51} -72.8356 q^{52} +178.538 q^{53} -57.2980 q^{54} -300.114 q^{55} +840.059 q^{56} -57.0000 q^{57} +57.8897 q^{58} +699.937 q^{59} -165.950 q^{60} -2.53038 q^{61} -65.7866 q^{62} +309.893 q^{63} +497.422 q^{64} +329.561 q^{65} +120.770 q^{66} +531.622 q^{67} +263.183 q^{68} +199.373 q^{69} -1156.03 q^{70} -386.616 q^{71} +219.575 q^{72} +220.587 q^{73} -568.934 q^{74} +375.879 q^{75} +66.4333 q^{76} -653.176 q^{77} -132.620 q^{78} -716.636 q^{79} -376.573 q^{80} +81.0000 q^{81} +457.905 q^{82} +1023.83 q^{83} -361.179 q^{84} -1190.83 q^{85} -192.791 q^{86} -81.8366 q^{87} -462.809 q^{88} +1175.19 q^{89} -302.164 q^{90} +717.266 q^{91} -232.369 q^{92} +93.0000 q^{93} +18.7349 q^{94} -300.592 q^{95} -433.996 q^{96} +768.638 q^{97} -1788.12 q^{98} -170.728 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 7 q^{2} + 120 q^{3} + 195 q^{4} + 5 q^{5} + 21 q^{6} + 23 q^{7} + 90 q^{8} + 360 q^{9} + 98 q^{10} + 50 q^{11} + 585 q^{12} + 222 q^{13} + 89 q^{14} + 15 q^{15} + 1155 q^{16} + 165 q^{17} + 63 q^{18}+ \cdots + 450 q^{99}+O(q^{100}) $ 40 * q + 7 * q^2 + 120 * q^3 + 195 * q^4 + 5 * q^5 + 21 * q^6 + 23 * q^7 + 90 * q^8 + 360 * q^9 + 98 * q^10 + 50 * q^11 + 585 * q^12 + 222 * q^13 + 89 * q^14 + 15 * q^15 + 1155 * q^16 + 165 * q^17 + 63 * q^18 - 760 * q^19 - 236 * q^20 + 69 * q^21 + 384 * q^22 + 159 * q^23 + 270 * q^24 + 2013 * q^25 + 531 * q^26 + 1080 * q^27 + 382 * q^28 + 355 * q^29 + 294 * q^30 + 1240 * q^31 + 1947 * q^32 + 150 * q^33 + 1323 * q^34 - 34 * q^35 + 1755 * q^36 + 870 * q^37 - 133 * q^38 + 666 * q^39 + 1333 * q^40 + 1227 * q^41 + 267 * q^42 + 907 * q^43 + 1889 * q^44 + 45 * q^45 + 817 * q^46 + 128 * q^47 + 3465 * q^48 + 3403 * q^49 + 1368 * q^50 + 495 * q^51 + 3686 * q^52 + 2331 * q^53 + 189 * q^54 + 834 * q^55 + 1516 * q^56 - 2280 * q^57 + 2768 * q^58 + 272 * q^59 - 708 * q^60 + 2243 * q^61 + 217 * q^62 + 207 * q^63 + 8968 * q^64 + 1958 * q^65 + 1152 * q^66 + 2201 * q^67 + 1335 * q^68 + 477 * q^69 + 1406 * q^70 + 1839 * q^71 + 810 * q^72 + 2648 * q^73 + 819 * q^74 + 6039 * q^75 - 3705 * q^76 + 4422 * q^77 + 1593 * q^78 + 2413 * q^79 - 1751 * q^80 + 3240 * q^81 + 2661 * q^82 - 94 * q^83 + 1146 * q^84 + 2620 * q^85 + 96 * q^86 + 1065 * q^87 + 3089 * q^88 + 2578 * q^89 + 882 * q^90 + 1736 * q^91 + 1408 * q^92 + 3720 * q^93 + 3275 * q^94 - 95 * q^95 + 5841 * q^96 + 7780 * q^97 + 4040 * q^98 + 450 * 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 $

$2$	−2.12215	−0.750292	−0.375146	−	0.926966i	$-0.622407\pi$
$2$	−2.12215	−0.750292	−0.375146	+	0.926966i	$0.622407\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−3.49649	−0.437061
$5$	15.8207	1.41504	0.707521	−	0.706692i	$-0.249813\pi$
$5$	15.8207	1.41504	0.707521	+	0.706692i	$0.249813\pi$
$6$	−6.36644	−0.433181
$7$	34.4325	1.85918	0.929591	−	0.368593i	$-0.120160\pi$
$7$	34.4325	1.85918	0.929591	+	0.368593i	$0.120160\pi$
$8$	24.3972	1.07822
$9$	9.00000	0.333333
$10$	−33.5738	−1.06170
$11$	−18.9697	−0.519963	−0.259981	−	0.965614i	$-0.583716\pi$
$11$	−18.9697	−0.519963	−0.259981	+	0.965614i	$0.583716\pi$
$12$	−10.4895	−0.252338
$13$	20.8311	0.444423	0.222211	−	0.974998i	$-0.428672\pi$
$13$	20.8311	0.444423	0.222211	+	0.974998i	$0.428672\pi$
$14$	−73.0709	−1.39493
$15$	47.4620	0.816975
$16$	−23.8026	−0.371916
$17$	−75.2706	−1.07387	−0.536935	−	0.843623i	$-0.680418\pi$
$17$	−75.2706	−1.07387	−0.536935	+	0.843623i	$0.680418\pi$
$18$	−19.0993	−0.250097
$19$	−19.0000	−0.229416
$19$	−19.0000	−0.229416
$20$	−55.3168	−0.618460
$21$	103.298	1.07340
$22$	40.2566	0.390124
$23$	66.4577	0.602495	0.301248	−	0.953546i	$-0.402597\pi$
$23$	66.4577	0.602495	0.301248	+	0.953546i	$0.402597\pi$
$24$	73.1917	0.622508
$25$	125.293	1.00234
$26$	−44.2066	−0.333447
$27$	27.0000	0.192450
$28$	−120.393	−0.812577
$29$	−27.2789	−0.174674	−0.0873372	−	0.996179i	$-0.527836\pi$
$29$	−27.2789	−0.174674	−0.0873372	+	0.996179i	$0.527836\pi$
$30$	−100.721	−0.612970
$31$	31.0000	0.179605
$31$	31.0000	0.179605
$32$	−144.665	−0.799171
$33$	−56.9092	−0.300201
$34$	159.735	0.805717
$35$	544.745	2.63082
$36$	−31.4684	−0.145687
$37$	268.093	1.19120	0.595598	−	0.803282i	$-0.296915\pi$
$37$	268.093	1.19120	0.595598	+	0.803282i	$0.296915\pi$
$38$	40.3208	0.172129
$39$	62.4932	0.256588
$40$	385.980	1.52572
$41$	−215.775	−0.821910	−0.410955	−	0.911656i	$-0.634805\pi$
$41$	−215.775	−0.821910	−0.410955	+	0.911656i	$0.634805\pi$
$42$	−219.213	−0.805363
$43$	90.8472	0.322188	0.161094	−	0.986939i	$-0.448498\pi$
$43$	90.8472	0.322188	0.161094	+	0.986939i	$0.448498\pi$
$44$	66.3275	0.227256
$45$	142.386	0.471681
$46$	−141.033	−0.452048
$47$	−8.82826	−0.0273986	−0.0136993	−	0.999906i	$-0.504361\pi$
$47$	−8.82826	−0.0273986	−0.0136993	+	0.999906i	$0.504361\pi$
$48$	−71.4078	−0.214726
$49$	842.599	2.45656
$50$	−265.890	−0.752051
$51$	−225.812	−0.620000
$52$	−72.8356	−0.194240
$53$	178.538	0.462720	0.231360	−	0.972868i	$-0.425683\pi$
$53$	178.538	0.462720	0.231360	+	0.972868i	$0.425683\pi$
$54$	−57.2980	−0.144394
$55$	−300.114	−0.735769
$56$	840.059	2.00460
$57$	−57.0000	−0.132453
$58$	57.8897	0.131057
$59$	699.937	1.54448	0.772238	−	0.635334i	$-0.219137\pi$
$59$	699.937	1.54448	0.772238	+	0.635334i	$0.219137\pi$
$60$	−165.950	−0.357068
$61$	−2.53038	−0.00531118	−0.00265559	−	0.999996i	$-0.500845\pi$
$61$	−2.53038	−0.00531118	−0.00265559	+	0.999996i	$0.500845\pi$
$62$	−65.7866	−0.134756
$63$	309.893	0.619727
$64$	497.422	0.971527
$65$	329.561	0.628877
$66$	120.770	0.225238
$67$	531.622	0.969372	0.484686	−	0.874688i	$-0.338934\pi$
$67$	531.622	0.969372	0.484686	+	0.874688i	$0.338934\pi$
$68$	263.183	0.469348
$69$	199.373	0.347851
$70$	−1156.03	−1.97388
$71$	−386.616	−0.646237	−0.323119	−	0.946359i	$-0.604731\pi$
$71$	−386.616	−0.646237	−0.323119	+	0.946359i	$0.604731\pi$
$72$	219.575	0.359405
$73$	220.587	0.353667	0.176834	−	0.984241i	$-0.443415\pi$
$73$	220.587	0.353667	0.176834	+	0.984241i	$0.443415\pi$
$74$	−568.934	−0.893746
$75$	375.879	0.578704
$76$	66.4333	0.100269
$77$	−653.176	−0.966705
$78$	−132.620	−0.192516
$79$	−716.636	−1.02061	−0.510303	−	0.859995i	$-0.670467\pi$
$79$	−716.636	−1.02061	−0.510303	+	0.859995i	$0.670467\pi$
$80$	−376.573	−0.526277
$81$	81.0000	0.111111
$82$	457.905	0.616673
$83$	1023.83	1.35398	0.676988	−	0.735994i	$-0.263285\pi$
$83$	1023.83	1.35398	0.676988	+	0.735994i	$0.263285\pi$
$84$	−361.179	−0.469141
$85$	−1190.83	−1.51957
$86$	−192.791	−0.241735
$87$	−81.8366	−0.100848
$88$	−462.809	−0.560632
$89$	1175.19	1.39966	0.699828	−	0.714311i	$-0.253260\pi$
$89$	1175.19	1.39966	0.699828	+	0.714311i	$0.253260\pi$
$90$	−302.164	−0.353898
$91$	717.266	0.826263
$92$	−232.369	−0.263328
$93$	93.0000	0.103695
$94$	18.7349	0.0205570
$95$	−300.592	−0.324633
$96$	−433.996	−0.461401
$97$	768.638	0.804570	0.402285	−	0.915514i	$-0.368216\pi$
$97$	768.638	0.804570	0.402285	+	0.915514i	$0.368216\pi$
$98$	−1788.12	−1.84314
$99$	−170.728	−0.173321
$100$	−438.086	−0.438086
$101$	−1233.30	−1.21503	−0.607516	−	0.794308i	$-0.707834\pi$
$101$	−1233.30	−1.21503	−0.607516	+	0.794308i	$0.707834\pi$
$102$	479.206	0.465181
$103$	−173.466	−0.165943	−0.0829715	−	0.996552i	$-0.526441\pi$
$103$	−173.466	−0.165943	−0.0829715	+	0.996552i	$0.526441\pi$
$104$	508.221	0.479184
$105$	1634.24	1.51890
$106$	−378.885	−0.347175
$107$	78.5465	0.0709661	0.0354831	−	0.999370i	$-0.488703\pi$
$107$	78.5465	0.0709661	0.0354831	+	0.999370i	$0.488703\pi$
$108$	−94.4053	−0.0841125
$109$	−1192.75	−1.04812	−0.524058	−	0.851683i	$-0.675583\pi$
$109$	−1192.75	−1.04812	−0.524058	+	0.851683i	$0.675583\pi$
$110$	636.885	0.552042
$111$	804.280	0.687738
$112$	−819.584	−0.691459
$113$	−500.480	−0.416648	−0.208324	−	0.978060i	$-0.566801\pi$
$113$	−500.480	−0.416648	−0.208324	+	0.978060i	$0.566801\pi$
$114$	120.962	0.0993786
$115$	1051.40	0.852556
$116$	95.3803	0.0763434
$117$	187.480	0.148141
$118$	−1485.37	−1.15881
$119$	−2591.76	−1.99652
$120$	1157.94	0.880876
$121$	−971.149	−0.729639
$122$	5.36984	0.00398494
$123$	−647.324	−0.474530
$124$	−108.391	−0.0784986
$125$	4.63576	0.00331708
$126$	−657.638	−0.464977
$127$	−1246.91	−0.871225	−0.435612	−	0.900134i	$-0.643468\pi$
$127$	−1246.91	−0.871225	−0.435612	+	0.900134i	$0.643468\pi$
$128$	101.720	0.0702411
$129$	272.542	0.186015
$130$	−699.377	−0.471842
$131$	−807.648	−0.538661	−0.269330	−	0.963048i	$-0.586802\pi$
$131$	−807.648	−0.538661	−0.269330	+	0.963048i	$0.586802\pi$
$132$	198.983	0.131206
$133$	−654.218	−0.426526
$134$	−1128.18	−0.727312
$135$	427.158	0.272325
$136$	−1836.40	−1.15786
$137$	2632.09	1.64142	0.820712	−	0.571342i	$-0.193577\pi$
$137$	2632.09	1.64142	0.820712	+	0.571342i	$0.193577\pi$
$138$	−423.099	−0.260990
$139$	813.905	0.496651	0.248326	−	0.968677i	$-0.420120\pi$
$139$	813.905	0.496651	0.248326	+	0.968677i	$0.420120\pi$
$140$	−1904.70	−1.14983
$141$	−26.4848	−0.0158186
$142$	820.455	0.484867
$143$	−395.160	−0.231083
$144$	−214.224	−0.123972
$145$	−431.569	−0.247172
$146$	−468.117	−0.265354
$147$	2527.80	1.41829
$148$	−937.386	−0.520626
$149$	−2252.31	−1.23837	−0.619183	−	0.785247i	$-0.712536\pi$
$149$	−2252.31	−1.23837	−0.619183	+	0.785247i	$0.712536\pi$
$150$	−797.671	−0.434197
$151$	−854.567	−0.460554	−0.230277	−	0.973125i	$-0.573963\pi$
$151$	−854.567	−0.460554	−0.230277	+	0.973125i	$0.573963\pi$
$152$	−463.548	−0.247360
$153$	−677.435	−0.357957
$154$	1386.14	0.725311
$155$	490.440	0.254149
$156$	−218.507	−0.112145
$157$	2669.11	1.35681	0.678403	−	0.734690i	$-0.262672\pi$
$157$	2669.11	1.35681	0.678403	+	0.734690i	$0.262672\pi$
$158$	1520.81	0.765752
$159$	535.615	0.267151
$160$	−2288.70	−1.13086
$161$	2288.31	1.12015
$162$	−171.894	−0.0833658
$163$	2397.28	1.15196	0.575980	−	0.817464i	$-0.304620\pi$
$163$	2397.28	1.15196	0.575980	+	0.817464i	$0.304620\pi$
$164$	754.454	0.359225
$165$	−900.341	−0.424796
$166$	−2172.72	−1.01588
$167$	1472.00	0.682075	0.341037	−	0.940050i	$-0.389222\pi$
$167$	1472.00	0.682075	0.341037	+	0.940050i	$0.389222\pi$
$168$	2520.18	1.15736
$169$	−1763.07	−0.802488
$170$	2527.12	1.14012
$171$	−171.000	−0.0764719
$172$	−317.646	−0.140816
$173$	4099.05	1.80142	0.900708	−	0.434426i	$-0.143049\pi$
$173$	4099.05	1.80142	0.900708	+	0.434426i	$0.143049\pi$
$174$	173.669	0.0756657
$175$	4314.16	1.86354
$176$	451.529	0.193382
$177$	2099.81	0.891703
$178$	−2493.92	−1.05015
$179$	812.689	0.339348	0.169674	−	0.985500i	$-0.445729\pi$
$179$	812.689	0.339348	0.169674	+	0.985500i	$0.445729\pi$
$180$	−497.851	−0.206153
$181$	−859.993	−0.353165	−0.176582	−	0.984286i	$-0.556504\pi$
$181$	−859.993	−0.353165	−0.176582	+	0.984286i	$0.556504\pi$
$182$	−1522.14	−0.619939
$183$	−7.59115	−0.00306641
$184$	1621.39	0.649620
$185$	4241.41	1.68559
$186$	−197.360	−0.0778017
$187$	1427.86	0.558373
$188$	30.8679	0.0119749
$189$	929.678	0.357800
$190$	637.901	0.243570
$191$	393.400	0.149033	0.0745167	−	0.997220i	$-0.476259\pi$
$191$	393.400	0.149033	0.0745167	+	0.997220i	$0.476259\pi$
$192$	1492.27	0.560912
$193$	−1794.37	−0.669229	−0.334615	−	0.942355i	$-0.608606\pi$
$193$	−1794.37	−0.669229	−0.334615	+	0.942355i	$0.608606\pi$
$194$	−1631.16	−0.603663
$195$	988.683	0.363082
$196$	−2946.14	−1.07367
$197$	−3461.71	−1.25196	−0.625982	−	0.779838i	$-0.715302\pi$
$197$	−3461.71	−1.25196	−0.625982	+	0.779838i	$0.715302\pi$
$198$	362.309	0.130041
$199$	1507.54	0.537020	0.268510	−	0.963277i	$-0.413469\pi$
$199$	1507.54	0.537020	0.268510	+	0.963277i	$0.413469\pi$
$200$	3056.80	1.08074
$201$	1594.86	0.559667
$202$	2617.25	0.911629
$203$	−939.280	−0.324751
$204$	789.549	0.270978
$205$	−3413.69	−1.16304
$206$	368.121	0.124506
$207$	598.120	0.200832
$208$	−495.834	−0.165288
$209$	360.425	0.119288
$210$	−3468.09	−1.13962
$211$	4386.44	1.43116	0.715580	−	0.698530i	$-0.246162\pi$
$211$	4386.44	1.43116	0.715580	+	0.698530i	$0.246162\pi$
$212$	−624.258	−0.202237
$213$	−1159.85	−0.373105
$214$	−166.687	−0.0532453
$215$	1437.26	0.455909
$216$	658.726	0.207503
$217$	1067.41	0.333919
$218$	2531.19	0.786393
$219$	661.760	0.204190
$220$	1049.34	0.321576
$221$	−1567.97	−0.477253
$222$	−1706.80	−0.516004
$223$	−4619.00	−1.38705	−0.693523	−	0.720434i	$-0.743943\pi$
$223$	−4619.00	−1.38705	−0.693523	+	0.720434i	$0.743943\pi$
$224$	−4981.19	−1.48580
$225$	1127.64	0.334115
$226$	1062.09	0.312608
$227$	−3787.36	−1.10738	−0.553691	−	0.832722i	$-0.686781\pi$
$227$	−3787.36	−1.10738	−0.553691	+	0.832722i	$0.686781\pi$
$228$	199.300	0.0578902
$229$	5202.24	1.50119	0.750597	−	0.660760i	$-0.229766\pi$
$229$	5202.24	1.50119	0.750597	+	0.660760i	$0.229766\pi$
$230$	−2231.24	−0.639666
$231$	−1959.53	−0.558127
$232$	−665.529	−0.188337
$233$	−4536.04	−1.27539	−0.637694	−	0.770289i	$-0.720112\pi$
$233$	−4536.04	−1.27539	−0.637694	+	0.770289i	$0.720112\pi$
$234$	−397.859	−0.111149
$235$	−139.669	−0.0387702
$236$	−2447.32	−0.675031
$237$	−2149.91	−0.589247
$238$	5500.09	1.49797
$239$	−537.836	−0.145564	−0.0727819	−	0.997348i	$-0.523188\pi$
$239$	−537.836	−0.145564	−0.0727819	+	0.997348i	$0.523188\pi$
$240$	−1129.72	−0.303846
$241$	3229.96	0.863318	0.431659	−	0.902037i	$-0.357928\pi$
$241$	3229.96	0.863318	0.431659	+	0.902037i	$0.357928\pi$
$242$	2060.92	0.547442
$243$	243.000	0.0641500
$244$	8.84746	0.00232131
$245$	13330.5	3.47613
$246$	1373.72	0.356036
$247$	−395.790	−0.101958
$248$	756.315	0.193653
$249$	3071.49	0.781718
$250$	−9.83777	−0.00248878
$251$	4120.44	1.03617	0.518087	−	0.855328i	$-0.326644\pi$
$251$	4120.44	1.03617	0.518087	+	0.855328i	$0.326644\pi$
$252$	−1083.54	−0.270859
$253$	−1260.69	−0.313275
$254$	2646.13	0.653673
$255$	−3572.49	−0.877325
$256$	−4195.24	−1.02423
$257$	−187.290	−0.0454584	−0.0227292	−	0.999742i	$-0.507236\pi$
$257$	−187.290	−0.0454584	−0.0227292	+	0.999742i	$0.507236\pi$
$258$	−578.373	−0.139566
$259$	9231.13	2.21465
$260$	−1152.31	−0.274858
$261$	−245.510	−0.0582248
$262$	1713.95	0.404153
$263$	−6141.08	−1.43983	−0.719915	−	0.694063i	$-0.755819\pi$
$263$	−6141.08	−1.43983	−0.719915	+	0.694063i	$0.755819\pi$
$264$	−1388.43	−0.323681
$265$	2824.59	0.654768
$266$	1388.35	0.320019
$267$	3525.56	0.808092
$268$	−1858.81	−0.423675
$269$	6727.88	1.52493	0.762465	−	0.647029i	$-0.223989\pi$
$269$	6727.88	1.52493	0.762465	+	0.647029i	$0.223989\pi$
$270$	−906.491	−0.204323
$271$	6840.75	1.53338	0.766690	−	0.642018i	$-0.221902\pi$
$271$	6840.75	1.53338	0.766690	+	0.642018i	$0.221902\pi$
$272$	1791.64	0.399390
$273$	2151.80	0.477043
$274$	−5585.69	−1.23155
$275$	−2376.77	−0.521182
$276$	−697.107	−0.152032
$277$	−4860.56	−1.05431	−0.527153	−	0.849771i	$-0.676740\pi$
$277$	−4860.56	−1.05431	−0.527153	+	0.849771i	$0.676740\pi$
$278$	−1727.23	−0.372634
$279$	279.000	0.0598684
$280$	13290.3	2.83659
$281$	−4292.89	−0.911361	−0.455680	−	0.890144i	$-0.650604\pi$
$281$	−4292.89	−0.911361	−0.455680	+	0.890144i	$0.650604\pi$
$282$	56.2046	0.0118686
$283$	2854.67	0.599619	0.299810	−	0.953999i	$-0.403077\pi$
$283$	2854.67	0.599619	0.299810	+	0.953999i	$0.403077\pi$
$284$	1351.80	0.282445
$285$	−901.777	−0.187427
$286$	838.587	0.173380
$287$	−7429.66	−1.52808
$288$	−1301.99	−0.266390
$289$	752.663	0.153198
$290$	915.853	0.185451
$291$	2305.91	0.464519
$292$	−771.279	−0.154574
$293$	−2339.03	−0.466375	−0.233187	−	0.972432i	$-0.574916\pi$
$293$	−2339.03	−0.466375	−0.233187	+	0.972432i	$0.574916\pi$
$294$	−5364.36	−1.06413
$295$	11073.5	2.18550
$296$	6540.74	1.28437
$297$	−512.183	−0.100067
$298$	4779.74	0.929137
$299$	1384.39	0.267763
$300$	−1314.26	−0.252929
$301$	3128.10	0.599005
$302$	1813.52	0.345550
$303$	−3699.91	−0.701499
$304$	452.250	0.0853233
$305$	−40.0323	−0.00751555
$306$	1437.62	0.268572
$307$	5808.81	1.07989	0.539946	−	0.841700i	$-0.318445\pi$
$307$	5808.81	1.07989	0.539946	+	0.841700i	$0.318445\pi$
$308$	2283.82	0.422510
$309$	−520.399	−0.0958073
$310$	−1040.79	−0.190686
$311$	5640.18	1.02838	0.514189	−	0.857677i	$-0.328093\pi$
$311$	5640.18	1.02838	0.514189	+	0.857677i	$0.328093\pi$
$312$	1524.66	0.276657
$313$	3319.94	0.599534	0.299767	−	0.954012i	$-0.403091\pi$
$313$	3319.94	0.599534	0.299767	+	0.954012i	$0.403091\pi$
$314$	−5664.25	−1.01800
$315$	4902.71	0.876940
$316$	2505.71	0.446067
$317$	−4679.03	−0.829024	−0.414512	−	0.910044i	$-0.636048\pi$
$317$	−4679.03	−0.829024	−0.414512	+	0.910044i	$0.636048\pi$
$318$	−1136.65	−0.200442
$319$	517.473	0.0908241
$320$	7869.54	1.37475
$321$	235.639	0.0409723
$322$	−4856.13	−0.840439
$323$	1430.14	0.246363
$324$	−283.216	−0.0485624
$325$	2609.99	0.445465
$326$	−5087.38	−0.864307
$327$	−3578.25	−0.605130
$328$	−5264.30	−0.886197
$329$	−303.979	−0.0509390
$330$	1910.66	0.318722
$331$	−3467.98	−0.575884	−0.287942	−	0.957648i	$-0.592971\pi$
$331$	−3467.98	−0.575884	−0.287942	+	0.957648i	$0.592971\pi$
$332$	−3579.81	−0.591770
$333$	2412.84	0.397066
$334$	−3123.79	−0.511755
$335$	8410.60	1.37170
$336$	−2458.75	−0.399214
$337$	−7520.92	−1.21570	−0.607850	−	0.794052i	$-0.707968\pi$
$337$	−7520.92	−1.21570	−0.607850	+	0.794052i	$0.707968\pi$
$338$	3741.49	0.602101
$339$	−1501.44	−0.240552
$340$	4163.73	0.664146
$341$	−588.062	−0.0933881
$342$	362.887	0.0573763
$343$	17202.5	2.70800
$344$	2216.42	0.347388
$345$	3154.21	0.492224
$346$	−8698.78	−1.35159
$347$	−10449.9	−1.61666	−0.808331	−	0.588728i	$-0.799629\pi$
$347$	−10449.9	−1.61666	−0.808331	+	0.588728i	$0.799629\pi$
$348$	286.141	0.0440769
$349$	−7567.80	−1.16073	−0.580366	−	0.814356i	$-0.697090\pi$
$349$	−7567.80	−1.16073	−0.580366	+	0.814356i	$0.697090\pi$
$350$	−9155.27	−1.39820
$351$	562.439	0.0855292
$352$	2744.26	0.415539
$353$	1445.40	0.217934	0.108967	−	0.994045i	$-0.465246\pi$
$353$	1445.40	0.217934	0.108967	+	0.994045i	$0.465246\pi$
$354$	−4456.11	−0.669038
$355$	−6116.51	−0.914453
$356$	−4109.03	−0.611736
$357$	−7775.27	−1.15269
$358$	−1724.65	−0.254610
$359$	−11907.2	−1.75053	−0.875264	−	0.483646i	$-0.839312\pi$
$359$	−11907.2	−1.75053	−0.875264	+	0.483646i	$0.839312\pi$
$360$	3473.82	0.508574
$361$	361.000	0.0526316
$362$	1825.03	0.264977
$363$	−2913.45	−0.421257
$364$	−2507.92	−0.361128
$365$	3489.82	0.500454
$366$	16.1095	0.00230071
$367$	−221.469	−0.0315002	−0.0157501	−	0.999876i	$-0.505014\pi$
$367$	−221.469	−0.0315002	−0.0157501	+	0.999876i	$0.505014\pi$
$368$	−1581.87	−0.224078
$369$	−1941.97	−0.273970
$370$	−9000.90	−1.26469
$371$	6147.53	0.860280
$372$	−325.174	−0.0453212
$373$	−3782.40	−0.525054	−0.262527	−	0.964925i	$-0.584556\pi$
$373$	−3782.40	−0.525054	−0.262527	+	0.964925i	$0.584556\pi$
$374$	−3030.14	−0.418943
$375$	13.9073	0.00191512
$376$	−215.385	−0.0295416
$377$	−568.248	−0.0776293
$378$	−1972.91	−0.268454
$379$	11589.2	1.57070	0.785350	−	0.619052i	$-0.212483\pi$
$379$	11589.2	1.57070	0.785350	+	0.619052i	$0.212483\pi$
$380$	1051.02	0.141885
$381$	−3740.74	−0.503002
$382$	−834.852	−0.111819
$383$	−14507.3	−1.93548	−0.967740	−	0.251952i	$-0.918928\pi$
$383$	−14507.3	−1.93548	−0.967740	+	0.251952i	$0.918928\pi$
$384$	305.160	0.0405537
$385$	−10333.7	−1.36793
$386$	3807.91	0.502118
$387$	817.625	0.107396
$388$	−2687.53	−0.351647
$389$	4174.22	0.544065	0.272032	−	0.962288i	$-0.412304\pi$
$389$	4174.22	0.544065	0.272032	+	0.962288i	$0.412304\pi$
$390$	−2098.13	−0.272418
$391$	−5002.31	−0.647002
$392$	20557.1	2.64870
$393$	−2422.95	−0.310996
$394$	7346.27	0.939339
$395$	−11337.6	−1.44420
$396$	596.948	0.0757519
$397$	9603.57	1.21408	0.607040	−	0.794671i	$-0.292357\pi$
$397$	9603.57	1.21408	0.607040	+	0.794671i	$0.292357\pi$
$398$	−3199.23	−0.402922
$399$	−1962.65	−0.246255
$400$	−2982.30	−0.372788
$401$	2174.31	0.270773	0.135386	−	0.990793i	$-0.456772\pi$
$401$	2174.31	0.270773	0.135386	+	0.990793i	$0.456772\pi$
$402$	−3384.54	−0.419914
$403$	645.763	0.0798207
$404$	4312.23	0.531043
$405$	1281.47	0.157227
$406$	1993.29	0.243658
$407$	−5085.66	−0.619378
$408$	−5509.19	−0.668494
$409$	8481.29	1.02536	0.512681	−	0.858579i	$-0.328652\pi$
$409$	8481.29	1.02536	0.512681	+	0.858579i	$0.328652\pi$
$410$	7244.36	0.872618
$411$	7896.28	0.947676
$412$	606.523	0.0725273
$413$	24100.6	2.87146
$414$	−1269.30	−0.150683
$415$	16197.7	1.91593
$416$	−3013.53	−0.355170
$417$	2441.72	0.286742
$418$	−764.875	−0.0895006
$419$	−1705.23	−0.198821	−0.0994104	−	0.995047i	$-0.531696\pi$
$419$	−1705.23	−0.198821	−0.0994104	+	0.995047i	$0.531696\pi$
$420$	−5714.09	−0.663855
$421$	14429.7	1.67045	0.835224	−	0.549910i	$-0.185338\pi$
$421$	14429.7	1.67045	0.835224	+	0.549910i	$0.185338\pi$
$422$	−9308.67	−1.07379
$423$	−79.4544	−0.00913287
$424$	4355.85	0.498912
$425$	−9430.88	−1.07639
$426$	2461.37	0.279938
$427$	−87.1275	−0.00987446
$428$	−274.637	−0.0310166
$429$	−1185.48	−0.133416
$430$	−3050.08	−0.342065
$431$	491.695	0.0549515	0.0274758	−	0.999622i	$-0.491253\pi$
$431$	491.695	0.0549515	0.0274758	+	0.999622i	$0.491253\pi$
$432$	−642.671	−0.0715752
$433$	1122.03	0.124530	0.0622649	−	0.998060i	$-0.480168\pi$
$433$	1122.03	0.124530	0.0622649	+	0.998060i	$0.480168\pi$
$434$	−2265.20	−0.250537
$435$	−1294.71	−0.142705
$436$	4170.44	0.458091
$437$	−1262.70	−0.138222
$438$	−1404.35	−0.153202
$439$	−2475.33	−0.269114	−0.134557	−	0.990906i	$-0.542961\pi$
$439$	−2475.33	−0.269114	−0.134557	+	0.990906i	$0.542961\pi$
$440$	−7321.94	−0.793318
$441$	7583.39	0.818852
$442$	3327.46	0.358079
$443$	11342.1	1.21643	0.608215	−	0.793773i	$-0.291886\pi$
$443$	11342.1	1.21643	0.608215	+	0.793773i	$0.291886\pi$
$444$	−2812.16	−0.300584
$445$	18592.2	1.98057
$446$	9802.21	1.04069
$447$	−6756.94	−0.714971
$448$	17127.5	1.80625
$449$	−4041.38	−0.424776	−0.212388	−	0.977185i	$-0.568124\pi$
$449$	−4041.38	−0.424776	−0.212388	+	0.977185i	$0.568124\pi$
$450$	−2393.01	−0.250684
$451$	4093.18	0.427363
$452$	1749.92	0.182101
$453$	−2563.70	−0.265901
$454$	8037.33	0.830861
$455$	11347.6	1.16920
$456$	−1390.64	−0.142813
$457$	7301.67	0.747391	0.373695	−	0.927551i	$-0.378091\pi$
$457$	7301.67	0.747391	0.373695	+	0.927551i	$0.378091\pi$
$458$	−11039.9	−1.12633
$459$	−2032.31	−0.206667
$460$	−3676.23	−0.372620
$461$	−7375.74	−0.745168	−0.372584	−	0.927999i	$-0.621528\pi$
$461$	−7375.74	−0.745168	−0.372584	+	0.927999i	$0.621528\pi$
$462$	4158.41	0.418759
$463$	4775.43	0.479338	0.239669	−	0.970855i	$-0.422961\pi$
$463$	4775.43	0.479338	0.239669	+	0.970855i	$0.422961\pi$
$464$	649.308	0.0649642
$465$	1471.32	0.146733
$466$	9626.14	0.956914
$467$	−2901.64	−0.287520	−0.143760	−	0.989613i	$-0.545919\pi$
$467$	−2901.64	−0.287520	−0.143760	+	0.989613i	$0.545919\pi$
$468$	−655.521	−0.0647467
$469$	18305.1	1.80224
$470$	296.398	0.0290890
$471$	8007.34	0.783352
$472$	17076.5	1.66528
$473$	−1723.35	−0.167525
$474$	4562.42	0.442107
$475$	−2380.57	−0.229954
$476$	9062.06	0.872602
$477$	1606.85	0.154240
$478$	1141.37	0.109215
$479$	−17295.9	−1.64983	−0.824916	−	0.565255i	$-0.808778\pi$
$479$	−17295.9	−1.64983	−0.824916	+	0.565255i	$0.808778\pi$
$480$	−6866.10	−0.652902
$481$	5584.67	0.529395
$482$	−6854.44	−0.647741
$483$	6864.92	0.646718
$484$	3395.62	0.318897
$485$	12160.3	1.13850
$486$	−515.682	−0.0481313
$487$	419.066	0.0389933	0.0194966	−	0.999810i	$-0.493794\pi$
$487$	419.066	0.0389933	0.0194966	+	0.999810i	$0.493794\pi$
$488$	−61.7344	−0.00572660
$489$	7191.85	0.665085
$490$	−28289.2	−2.60811
$491$	−1480.81	−0.136106	−0.0680530	−	0.997682i	$-0.521679\pi$
$491$	−1480.81	−0.136106	−0.0680530	+	0.997682i	$0.521679\pi$
$492$	2263.36	0.207399
$493$	2053.30	0.187578
$494$	839.925	0.0764980
$495$	−2701.02	−0.245256
$496$	−737.881	−0.0667981
$497$	−13312.2	−1.20147
$498$	−6518.15	−0.586517
$499$	−17780.6	−1.59513	−0.797565	−	0.603233i	$-0.793879\pi$
$499$	−17780.6	−1.59513	−0.797565	+	0.603233i	$0.793879\pi$
$500$	−16.2089	−0.00144977
$501$	4415.99	0.393796
$502$	−8744.17	−0.777433
$503$	7209.20	0.639051	0.319525	−	0.947578i	$-0.396477\pi$
$503$	7209.20	0.639051	0.319525	+	0.947578i	$0.396477\pi$
$504$	7560.53	0.668200
$505$	−19511.6	−1.71932
$506$	2675.36	0.235048
$507$	−5289.20	−0.463317
$508$	4359.82	0.380779
$509$	4407.55	0.383813	0.191907	−	0.981413i	$-0.438533\pi$
$509$	4407.55	0.383813	0.191907	+	0.981413i	$0.438533\pi$
$510$	7581.35	0.658251
$511$	7595.36	0.657532
$512$	8089.16	0.698230
$513$	−513.000	−0.0441511
$514$	397.456	0.0341071
$515$	−2744.35	−0.234816
$516$	−952.939	−0.0813000
$517$	167.470	0.0142463
$518$	−19589.8	−1.66164
$519$	12297.1	1.04005
$520$	8040.38	0.678066
$521$	18844.8	1.58466	0.792328	−	0.610096i	$-0.208869\pi$
$521$	18844.8	1.58466	0.792328	+	0.610096i	$0.208869\pi$
$522$	521.008	0.0436856
$523$	−12315.8	−1.02970	−0.514851	−	0.857280i	$-0.672153\pi$
$523$	−12315.8	−1.02970	−0.514851	+	0.857280i	$0.672153\pi$
$524$	2823.94	0.235428
$525$	12942.5	1.07592
$526$	13032.3	1.08029
$527$	−2333.39	−0.192873
$528$	1354.59	0.111649
$529$	−7750.37	−0.636999
$530$	−5994.21	−0.491267
$531$	6299.43	0.514825
$532$	2287.47	0.186418
$533$	−4494.81	−0.365276
$534$	−7481.75	−0.606305
$535$	1242.66	0.100420
$536$	12970.1	1.04519
$537$	2438.07	0.195922
$538$	−14277.6	−1.14414
$539$	−15983.9	−1.27732
$540$	−1493.55	−0.119023
$541$	−21161.0	−1.68167	−0.840833	−	0.541295i	$-0.817934\pi$
$541$	−21161.0	−1.68167	−0.840833	+	0.541295i	$0.817934\pi$
$542$	−14517.1	−1.15048
$543$	−2579.98	−0.203900
$544$	10889.0	0.858206
$545$	−18870.1	−1.48313
$546$	−4566.43	−0.357922
$547$	16396.1	1.28162	0.640811	−	0.767699i	$-0.278598\pi$
$547$	16396.1	1.28162	0.640811	+	0.767699i	$0.278598\pi$
$548$	−9203.10	−0.717403
$549$	−22.7734	−0.00177039
$550$	5043.87	0.391039
$551$	518.298	0.0400730
$552$	4864.16	0.375058
$553$	−24675.6	−1.89749
$554$	10314.8	0.791037
$555$	12724.2	0.973178
$556$	−2845.81	−0.217067
$557$	−4399.38	−0.334664	−0.167332	−	0.985901i	$-0.553515\pi$
$557$	−4399.38	−0.334664	−0.167332	+	0.985901i	$0.553515\pi$
$558$	−592.079	−0.0449188
$559$	1892.44	0.143188
$560$	−12966.4	−0.978444
$561$	4283.59	0.322377
$562$	9110.14	0.683787
$563$	9109.33	0.681905	0.340953	−	0.940081i	$-0.389250\pi$
$563$	9109.33	0.681905	0.340953	+	0.940081i	$0.389250\pi$
$564$	92.6038	0.00691370
$565$	−7917.92	−0.589574
$566$	−6058.02	−0.449890
$567$	2789.03	0.206576
$568$	−9432.36	−0.696783
$569$	1644.49	0.121161	0.0605804	−	0.998163i	$-0.480705\pi$
$569$	1644.49	0.121161	0.0605804	+	0.998163i	$0.480705\pi$
$570$	1913.70	0.140625
$571$	10032.5	0.735286	0.367643	−	0.929967i	$-0.380165\pi$
$571$	10032.5	0.735286	0.367643	+	0.929967i	$0.380165\pi$
$572$	1381.67	0.100998
$573$	1180.20	0.0860445
$574$	15766.8	1.14651
$575$	8326.69	0.603908
$576$	4476.80	0.323842
$577$	11252.1	0.811838	0.405919	−	0.913909i	$-0.366951\pi$
$577$	11252.1	0.811838	0.405919	+	0.913909i	$0.366951\pi$
$578$	−1597.26	−0.114944
$579$	−5383.10	−0.386380
$580$	1508.98	0.108029
$581$	35253.1	2.51729
$582$	−4893.49	−0.348525
$583$	−3386.83	−0.240597
$584$	5381.71	0.381330
$585$	2966.05	0.209626
$586$	4963.77	0.349917
$587$	−4450.72	−0.312949	−0.156474	−	0.987682i	$-0.550013\pi$
$587$	−4450.72	−0.312949	−0.156474	+	0.987682i	$0.550013\pi$
$588$	−8838.42	−0.619882
$589$	−589.000	−0.0412043
$590$	−23499.5	−1.63976
$591$	−10385.1	−0.722822
$592$	−6381.32	−0.443025
$593$	−18189.1	−1.25959	−0.629794	−	0.776762i	$-0.716861\pi$
$593$	−18189.1	−1.25959	−0.629794	+	0.776762i	$0.716861\pi$
$594$	1086.93	0.0750794
$595$	−41003.3	−2.82516
$596$	7875.19	0.541242
$597$	4522.63	0.310049
$598$	−2937.87	−0.200900
$599$	7673.02	0.523391	0.261695	−	0.965150i	$-0.415718\pi$
$599$	7673.02	0.523391	0.261695	+	0.965150i	$0.415718\pi$
$600$	9170.41	0.623968
$601$	20252.7	1.37458	0.687291	−	0.726382i	$-0.258800\pi$
$601$	20252.7	1.37458	0.687291	+	0.726382i	$0.258800\pi$
$602$	−6638.28	−0.449429
$603$	4784.59	0.323124
$604$	2987.99	0.201290
$605$	−15364.2	−1.03247
$606$	7851.75	0.526329
$607$	7611.57	0.508969	0.254485	−	0.967077i	$-0.418094\pi$
$607$	7611.57	0.508969	0.254485	+	0.967077i	$0.418094\pi$
$608$	2748.64	0.183342
$609$	−2817.84	−0.187495
$610$	84.9544	0.00563886
$611$	−183.902	−0.0121766
$612$	2368.65	0.156449
$613$	6272.17	0.413264	0.206632	−	0.978419i	$-0.433750\pi$
$613$	6272.17	0.413264	0.206632	+	0.978419i	$0.433750\pi$
$614$	−12327.2	−0.810234
$615$	−10241.1	−0.671480
$616$	−15935.7	−1.04232
$617$	−3786.11	−0.247039	−0.123520	−	0.992342i	$-0.539418\pi$
$617$	−3786.11	−0.247039	−0.123520	+	0.992342i	$0.539418\pi$
$618$	1104.36	0.0718835
$619$	9785.61	0.635407	0.317704	−	0.948190i	$-0.397088\pi$
$619$	9785.61	0.635407	0.317704	+	0.948190i	$0.397088\pi$
$620$	−1714.82	−0.111079
$621$	1794.36	0.115950
$622$	−11969.3	−0.771584
$623$	40464.6	2.60222
$624$	−1487.50	−0.0954290
$625$	−15588.3	−0.997650
$626$	−7045.40	−0.449826
$627$	1081.27	0.0688707
$628$	−9332.53	−0.593007
$629$	−20179.6	−1.27919
$630$	−10404.3	−0.657961
$631$	5524.83	0.348558	0.174279	−	0.984696i	$-0.444241\pi$
$631$	5524.83	0.348558	0.174279	+	0.984696i	$0.444241\pi$
$632$	−17483.9	−1.10043
$633$	13159.3	0.826281
$634$	9929.59	0.622010
$635$	−19727.0	−1.23282
$636$	−1872.77	−0.116762
$637$	17552.2	1.09175
$638$	−1098.15	−0.0681447
$639$	−3479.54	−0.215412
$640$	1609.28	0.0993941
$641$	−26311.4	−1.62127	−0.810637	−	0.585549i	$-0.800879\pi$
$641$	−26311.4	−1.62127	−0.810637	+	0.585549i	$0.800879\pi$
$642$	−500.062	−0.0307412
$643$	5230.94	0.320821	0.160411	−	0.987050i	$-0.448718\pi$
$643$	5230.94	0.320821	0.160411	+	0.987050i	$0.448718\pi$
$644$	−8001.05	−0.489574
$645$	4311.78	0.263219
$646$	−3034.97	−0.184844
$647$	−9330.44	−0.566951	−0.283476	−	0.958979i	$-0.591488\pi$
$647$	−9330.44	−0.566951	−0.283476	+	0.958979i	$0.591488\pi$
$648$	1976.18	0.119802
$649$	−13277.6	−0.803069
$650$	−5538.78	−0.334229
$651$	3202.23	0.192788
$652$	−8382.08	−0.503478
$653$	−12518.5	−0.750211	−0.375106	−	0.926982i	$-0.622394\pi$
$653$	−12518.5	−0.750211	−0.375106	+	0.926982i	$0.622394\pi$
$654$	7593.57	0.454024
$655$	−12777.5	−0.762228
$656$	5136.00	0.305681
$657$	1985.28	0.117889
$658$	645.089	0.0382191
$659$	−3820.34	−0.225826	−0.112913	−	0.993605i	$-0.536018\pi$
$659$	−3820.34	−0.225826	−0.112913	+	0.993605i	$0.536018\pi$
$660$	3148.03	0.185662
$661$	22208.5	1.30682	0.653411	−	0.757003i	$-0.273337\pi$
$661$	22208.5	1.30682	0.653411	+	0.757003i	$0.273337\pi$
$662$	7359.57	0.432082
$663$	−4703.90	−0.275542
$664$	24978.6	1.45988
$665$	−10350.2	−0.603552
$666$	−5120.40	−0.297915
$667$	−1812.89	−0.105240
$668$	−5146.82	−0.298108
$669$	−13857.0	−0.800812
$670$	−17848.5	−1.02918
$671$	48.0007	0.00276162
$672$	−14943.6	−0.857829
$673$	−33176.0	−1.90021	−0.950105	−	0.311931i	$-0.899024\pi$
$673$	−33176.0	−1.90021	−0.950105	+	0.311931i	$0.899024\pi$
$674$	15960.5	0.912130
$675$	3382.91	0.192901
$676$	6164.55	0.350737
$677$	−9624.51	−0.546381	−0.273191	−	0.961960i	$-0.588079\pi$
$677$	−9624.51	−0.546381	−0.273191	+	0.961960i	$0.588079\pi$
$678$	3186.28	0.180484
$679$	26466.1	1.49584
$680$	−29053.0	−1.63843
$681$	−11362.1	−0.639348
$682$	1247.95	0.0700683
$683$	−22910.3	−1.28351	−0.641756	−	0.766909i	$-0.721794\pi$
$683$	−22910.3	−1.28351	−0.641756	+	0.766909i	$0.721794\pi$
$684$	597.900	0.0334229
$685$	41641.5	2.32268
$686$	−36506.1	−2.03179
$687$	15606.7	0.866715
$688$	−2162.40	−0.119827
$689$	3719.15	0.205643
$690$	−6693.71	−0.369312
$691$	−17368.4	−0.956186	−0.478093	−	0.878309i	$-0.658672\pi$
$691$	−17368.4	−0.956186	−0.478093	+	0.878309i	$0.658672\pi$
$692$	−14332.3	−0.787329
$693$	−5878.58	−0.322235
$694$	22176.3	1.21297
$695$	12876.5	0.702783
$696$	−1996.59	−0.108736
$697$	16241.5	0.882625
$698$	16060.0	0.870888
$699$	−13608.1	−0.736346
$700$	−15084.4	−0.814482
$701$	−17471.4	−0.941347	−0.470674	−	0.882307i	$-0.655989\pi$
$701$	−17471.4	−0.941347	−0.470674	+	0.882307i	$0.655989\pi$
$702$	−1193.58	−0.0641719
$703$	−5093.77	−0.273279
$704$	−9435.96	−0.505158
$705$	−419.007	−0.0223840
$706$	−3067.35	−0.163514
$707$	−42465.7	−2.25896
$708$	−7341.97	−0.389729
$709$	7333.60	0.388462	0.194231	−	0.980956i	$-0.437779\pi$
$709$	7333.60	0.388462	0.194231	+	0.980956i	$0.437779\pi$
$710$	12980.1	0.686107
$711$	−6449.72	−0.340202
$712$	28671.3	1.50913
$713$	2060.19	0.108211
$714$	16500.3	0.864856
$715$	−6251.68	−0.326993
$716$	−2841.56	−0.148316
$717$	−1613.51	−0.0840413
$718$	25268.9	1.31341
$719$	−21467.8	−1.11351	−0.556754	−	0.830677i	$-0.687953\pi$
$719$	−21467.8	−1.11351	−0.556754	+	0.830677i	$0.687953\pi$
$720$	−3389.16	−0.175426
$721$	−5972.88	−0.308518
$722$	−766.095	−0.0394891
$723$	9689.87	0.498437
$724$	3006.96	0.154355
$725$	−3417.85	−0.175084
$726$	6182.76	0.316066
$727$	−14127.0	−0.720691	−0.360345	−	0.932819i	$-0.617341\pi$
$727$	−14127.0	−0.720691	−0.360345	+	0.932819i	$0.617341\pi$
$728$	17499.3	0.890890
$729$	729.000	0.0370370
$730$	−7405.92	−0.375487
$731$	−6838.12	−0.345988
$732$	26.5424	0.00134021
$733$	−20422.2	−1.02907	−0.514537	−	0.857468i	$-0.672036\pi$
$733$	−20422.2	−1.02907	−0.514537	+	0.857468i	$0.672036\pi$
$734$	469.990	0.0236344
$735$	39991.4	2.00695
$736$	−9614.13	−0.481497
$737$	−10084.7	−0.504037
$738$	4121.15	0.205558
$739$	14838.8	0.738639	0.369319	−	0.929303i	$-0.379591\pi$
$739$	14838.8	0.738639	0.369319	+	0.929303i	$0.379591\pi$
$740$	−14830.1	−0.736708
$741$	−1187.37	−0.0588653
$742$	−13046.0	−0.645461
$743$	−6929.23	−0.342139	−0.171069	−	0.985259i	$-0.554722\pi$
$743$	−6929.23	−0.342139	−0.171069	+	0.985259i	$0.554722\pi$
$744$	2268.94	0.111806
$745$	−35633.0	−1.75234
$746$	8026.80	0.393944
$747$	9214.47	0.451325
$748$	−4992.51	−0.244043
$749$	2704.55	0.131939
$750$	−29.5133	−0.00143690
$751$	14911.6	0.724544	0.362272	−	0.932072i	$-0.382001\pi$
$751$	14911.6	0.724544	0.362272	+	0.932072i	$0.382001\pi$
$752$	210.136	0.0101900
$753$	12361.3	0.598235
$754$	1205.91	0.0582447
$755$	−13519.8	−0.651703
$756$	−3250.61	−0.156380
$757$	−32602.1	−1.56531	−0.782657	−	0.622453i	$-0.786136\pi$
$757$	−32602.1	−1.56531	−0.782657	+	0.622453i	$0.786136\pi$
$758$	−24593.9	−1.17848
$759$	−3782.06	−0.180869
$760$	−7333.63	−0.350024
$761$	−27228.6	−1.29703	−0.648514	−	0.761203i	$-0.724609\pi$
$761$	−27228.6	−1.29703	−0.648514	+	0.761203i	$0.724609\pi$
$762$	7938.39	0.377398
$763$	−41069.4	−1.94864
$764$	−1375.52	−0.0651368
$765$	−10717.5	−0.506524
$766$	30786.6	1.45218
$767$	14580.4	0.686400
$768$	−12585.7	−0.591339
$769$	−20244.4	−0.949328	−0.474664	−	0.880167i	$-0.657430\pi$
$769$	−20244.4	−0.949328	−0.474664	+	0.880167i	$0.657430\pi$
$770$	21929.6	1.02635
$771$	−561.869	−0.0262454
$772$	6273.99	0.292494
$773$	31588.2	1.46979	0.734896	−	0.678179i	$-0.237231\pi$
$773$	31588.2	1.46979	0.734896	+	0.678179i	$0.237231\pi$
$774$	−1735.12	−0.0805783
$775$	3884.08	0.180026
$776$	18752.6	0.867501
$777$	27693.4	1.27863
$778$	−8858.30	−0.408207
$779$	4099.72	0.188559
$780$	−3456.92	−0.158689
$781$	7333.99	0.336019
$782$	10615.6	0.485441
$783$	−736.529	−0.0336161
$784$	−20056.1	−0.913632
$785$	42227.1	1.91994
$786$	5141.85	0.233338
$787$	14462.3	0.655052	0.327526	−	0.944842i	$-0.393785\pi$
$787$	14462.3	0.655052	0.327526	+	0.944842i	$0.393785\pi$
$788$	12103.9	0.547185
$789$	−18423.2	−0.831286
$790$	24060.1	1.08357
$791$	−17232.8	−0.774624
$792$	−4165.28	−0.186877
$793$	−52.7106	−0.00236041
$794$	−20380.2	−0.910914
$795$	8473.78	0.378030
$796$	−5271.11	−0.234711
$797$	−42308.4	−1.88035	−0.940177	−	0.340687i	$-0.889340\pi$
$797$	−42308.4	−1.88035	−0.940177	+	0.340687i	$0.889340\pi$
$798$	4165.04	0.184763
$799$	664.509	0.0294226
$800$	−18125.6	−0.801044
$801$	10576.7	0.466552
$802$	−4614.21	−0.203159
$803$	−4184.47	−0.183894
$804$	−5576.43	−0.244609
$805$	36202.5	1.58506
$806$	−1370.40	−0.0598889
$807$	20183.7	0.880419
$808$	−30089.2	−1.31007
$809$	2080.96	0.0904360	0.0452180	−	0.998977i	$-0.485602\pi$
$809$	2080.96	0.0904360	0.0452180	+	0.998977i	$0.485602\pi$
$810$	−2719.47	−0.117966
$811$	30146.6	1.30529	0.652645	−	0.757664i	$-0.273659\pi$
$811$	30146.6	1.30529	0.652645	+	0.757664i	$0.273659\pi$
$812$	3284.18	0.141936
$813$	20522.2	0.885297
$814$	10792.5	0.464714
$815$	37926.6	1.63007
$816$	5374.91	0.230588
$817$	−1726.10	−0.0739149
$818$	−17998.5	−0.769321
$819$	6455.40	0.275421
$820$	11936.0	0.508319
$821$	−19270.6	−0.819184	−0.409592	−	0.912269i	$-0.634329\pi$
$821$	−19270.6	−0.819184	−0.409592	+	0.912269i	$0.634329\pi$
$822$	−16757.1	−0.711034
$823$	−3981.15	−0.168620	−0.0843100	−	0.996440i	$-0.526869\pi$
$823$	−3981.15	−0.168620	−0.0843100	+	0.996440i	$0.526869\pi$
$824$	−4232.10	−0.178923
$825$	−7130.32	−0.300904
$826$	−51145.0	−2.15443
$827$	34753.8	1.46132	0.730658	−	0.682743i	$-0.239213\pi$
$827$	34753.8	1.46132	0.730658	+	0.682743i	$0.239213\pi$
$828$	−2091.32	−0.0877758
$829$	46032.9	1.92858	0.964288	−	0.264856i	$-0.0853244\pi$
$829$	46032.9	1.92858	0.964288	+	0.264856i	$0.0853244\pi$
$830$	−34373.8	−1.43751
$831$	−14581.7	−0.608704
$832$	10361.8	0.431769
$833$	−63422.9	−2.63802
$834$	−5181.68	−0.215140
$835$	23287.9	0.965164
$836$	−1260.22	−0.0521360
$837$	837.000	0.0345651
$838$	3618.75	0.149174
$839$	11202.4	0.460967	0.230484	−	0.973076i	$-0.425969\pi$
$839$	11202.4	0.460967	0.230484	+	0.973076i	$0.425969\pi$
$840$	39870.8	1.63771
$841$	−23644.9	−0.969489
$842$	−30621.9	−1.25332
$843$	−12878.7	−0.526174
$844$	−15337.1	−0.625505
$845$	−27892.9	−1.13555
$846$	168.614	0.00685232
$847$	−33439.1	−1.35653
$848$	−4249.68	−0.172093
$849$	8564.00	0.346190
$850$	20013.7	0.807606
$851$	17816.9	0.717691
$852$	4055.39	0.163070
$853$	−31206.8	−1.25264	−0.626319	−	0.779567i	$-0.715439\pi$
$853$	−31206.8	−1.25264	−0.626319	+	0.779567i	$0.715439\pi$
$854$	184.897	0.00740873
$855$	−2705.33	−0.108211
$856$	1916.32	0.0765168
$857$	−9175.37	−0.365723	−0.182862	−	0.983139i	$-0.558536\pi$
$857$	−9175.37	−0.365723	−0.182862	+	0.983139i	$0.558536\pi$
$858$	2515.76	0.100101
$859$	−34790.5	−1.38188	−0.690941	−	0.722912i	$-0.742803\pi$
$859$	−34790.5	−1.38188	−0.690941	+	0.722912i	$0.742803\pi$
$860$	−5025.37	−0.199260
$861$	−22289.0	−0.882238
$862$	−1043.45	−0.0412297
$863$	−30460.0	−1.20147	−0.600736	−	0.799447i	$-0.705126\pi$
$863$	−30460.0	−1.20147	−0.600736	+	0.799447i	$0.705126\pi$
$864$	−3905.96	−0.153800
$865$	64849.6	2.54908
$866$	−2381.12	−0.0934338
$867$	2257.99	0.0884491
$868$	−3732.18	−0.145943
$869$	13594.4	0.530677
$870$	2747.56	0.107070
$871$	11074.2	0.430811
$872$	−29099.8	−1.13010
$873$	6917.74	0.268190
$874$	2679.63	0.103707
$875$	159.621	0.00616706
$876$	−2313.84	−0.0892436
$877$	−5116.24	−0.196993	−0.0984967	−	0.995137i	$-0.531403\pi$
$877$	−5116.24	−0.196993	−0.0984967	+	0.995137i	$0.531403\pi$
$878$	5253.01	0.201914
$879$	−7017.10	−0.269262
$880$	7143.49	0.273644
$881$	27678.6	1.05847	0.529237	−	0.848474i	$-0.322478\pi$
$881$	27678.6	1.05847	0.529237	+	0.848474i	$0.322478\pi$
$882$	−16093.1	−0.614379
$883$	−6040.64	−0.230219	−0.115110	−	0.993353i	$-0.536722\pi$
$883$	−6040.64	−0.230219	−0.115110	+	0.993353i	$0.536722\pi$
$884$	5482.38	0.208589
$885$	33220.4	1.26180
$886$	−24069.6	−0.912678
$887$	3964.14	0.150060	0.0750298	−	0.997181i	$-0.476095\pi$
$887$	3964.14	0.150060	0.0750298	+	0.997181i	$0.476095\pi$
$888$	19622.2	0.741530
$889$	−42934.3	−1.61977
$890$	−39455.4	−1.48601
$891$	−1536.55	−0.0577736
$892$	16150.3	0.606225
$893$	167.737	0.00628567
$894$	14339.2	0.536437
$895$	12857.3	0.480191
$896$	3502.48	0.130591
$897$	4153.16	0.154593
$898$	8576.40	0.318706
$899$	−845.644	−0.0313724
$900$	−3942.77	−0.146029
$901$	−13438.7	−0.496901
$902$	−8686.34	−0.320647
$903$	9384.29	0.345836
$904$	−12210.3	−0.449236
$905$	−13605.7	−0.499743
$906$	5440.55	0.199503
$907$	3413.64	0.124970	0.0624851	−	0.998046i	$-0.480097\pi$
$907$	3413.64	0.124970	0.0624851	+	0.998046i	$0.480097\pi$
$908$	13242.5	0.483994
$909$	−11099.7	−0.405011
$910$	−24081.3	−0.877240
$911$	12679.5	0.461130	0.230565	−	0.973057i	$-0.425943\pi$
$911$	12679.5	0.461130	0.230565	+	0.973057i	$0.425943\pi$
$912$	1356.75	0.0492615
$913$	−19421.8	−0.704017
$914$	−15495.2	−0.560762
$915$	−120.097	−0.00433910
$916$	−18189.6	−0.656114
$917$	−27809.4	−1.00147
$918$	4312.85	0.155060
$919$	−3002.21	−0.107763	−0.0538813	−	0.998547i	$-0.517159\pi$
$919$	−3002.21	−0.107763	−0.0538813	+	0.998547i	$0.517159\pi$
$920$	25651.4	0.919240
$921$	17426.4	0.623475
$922$	15652.4	0.559094
$923$	−8053.61	−0.287203
$924$	6851.47	0.243936
$925$	33590.2	1.19399
$926$	−10134.2	−0.359643
$927$	−1561.20	−0.0553144
$928$	3946.30	0.139595
$929$	6154.39	0.217351	0.108675	−	0.994077i	$-0.465339\pi$
$929$	6154.39	0.217351	0.108675	+	0.994077i	$0.465339\pi$
$930$	−3122.36	−0.110093
$931$	−16009.4	−0.563573
$932$	15860.2	0.557423
$933$	16920.5	0.593734
$934$	6157.70	0.215724
$935$	22589.7	0.790121
$936$	4573.99	0.159728
$937$	15818.8	0.551525	0.275763	−	0.961226i	$-0.411070\pi$
$937$	15818.8	0.551525	0.275763	+	0.961226i	$0.411070\pi$
$938$	−38846.1	−1.35221
$939$	9959.82	0.346141
$940$	488.351	0.0169450
$941$	47799.0	1.65590	0.827951	−	0.560800i	$-0.189506\pi$
$941$	47799.0	1.65590	0.827951	+	0.560800i	$0.189506\pi$
$942$	−16992.8	−0.587743
$943$	−14339.9	−0.495197
$944$	−16660.3	−0.574415
$945$	14708.1	0.506302
$946$	3657.19	0.125693
$947$	33198.2	1.13917	0.569586	−	0.821931i	$-0.307103\pi$
$947$	33198.2	1.13917	0.569586	+	0.821931i	$0.307103\pi$
$948$	7517.13	0.257537
$949$	4595.06	0.157178
$950$	5051.91	0.172532
$951$	−14037.1	−0.478637
$952$	−63231.7	−2.15268
$953$	20169.1	0.685564	0.342782	−	0.939415i	$-0.388631\pi$
$953$	20169.1	0.685564	0.342782	+	0.939415i	$0.388631\pi$
$954$	−3409.96	−0.115725
$955$	6223.84	0.210889
$956$	1880.54	0.0636203
$957$	1552.42	0.0524373
$958$	36704.4	1.23786
$959$	90629.7	3.05171
$960$	23608.6	0.793713
$961$	961.000	0.0322581
$962$	−11851.5	−0.397201
$963$	706.918	0.0236554
$964$	−11293.5	−0.377323
$965$	−28388.0	−0.946988
$966$	−14568.4	−0.485228
$967$	−53705.2	−1.78598	−0.892990	−	0.450077i	$-0.851396\pi$
$967$	−53705.2	−1.78598	−0.892990	+	0.450077i	$0.851396\pi$
$968$	−23693.4	−0.786708
$969$	4290.42	0.142238
$970$	−25806.0	−0.854208
$971$	−44327.6	−1.46503	−0.732513	−	0.680753i	$-0.761653\pi$
$971$	−44327.6	−1.46503	−0.732513	+	0.680753i	$0.761653\pi$
$972$	−849.647	−0.0280375
$973$	28024.8	0.923365
$974$	−889.321	−0.0292563
$975$	7829.96	0.257189
$976$	60.2297	0.00197531
$977$	14142.9	0.463122	0.231561	−	0.972820i	$-0.425617\pi$
$977$	14142.9	0.463122	0.231561	+	0.972820i	$0.425617\pi$
$978$	−15262.2	−0.499008
$979$	−22293.0	−0.727769
$980$	−46609.9	−1.51928
$981$	−10734.7	−0.349372
$982$	3142.50	0.102119
$983$	9523.83	0.309016	0.154508	−	0.987992i	$-0.450621\pi$
$983$	9523.83	0.309016	0.154508	+	0.987992i	$0.450621\pi$
$984$	−15792.9	−0.511646
$985$	−54766.6	−1.77158
$986$	−4357.40	−0.140738
$987$	−911.938	−0.0294096
$988$	1383.88	0.0445617
$989$	6037.50	0.194117
$990$	5731.97	0.184014
$991$	−20749.2	−0.665106	−0.332553	−	0.943085i	$-0.607910\pi$
$991$	−20749.2	−0.665106	−0.332553	+	0.943085i	$0.607910\pi$
$992$	−4484.63	−0.143535
$993$	−10404.0	−0.332487
$994$	28250.3	0.901455
$995$	23850.3	0.759906
$996$	−10739.4	−0.341659
$997$	37504.4	1.19135	0.595675	−	0.803226i	$-0.296885\pi$
$997$	37504.4	1.19135	0.595675	+	0.803226i	$0.296885\pi$
$998$	37733.1	1.19681
$999$	7238.52	0.229246

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1767.4.a.h.1.13	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1767.4.a.h.1.13	✓	40	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1767 = 3 \cdot 19 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1767.a (trivial)

\(f(q)\)	\(=\)	\(q-2.12215 q^{2} +3.00000 q^{3} -3.49649 q^{4} +15.8207 q^{5} -6.36644 q^{6} +34.4325 q^{7} +24.3972 q^{8} +9.00000 q^{9} -33.5738 q^{10} -18.9697 q^{11} -10.4895 q^{12} +20.8311 q^{13} -73.0709 q^{14} +47.4620 q^{15} -23.8026 q^{16} -75.2706 q^{17} -19.0993 q^{18} -19.0000 q^{19} -55.3168 q^{20} +103.298 q^{21} +40.2566 q^{22} +66.4577 q^{23} +73.1917 q^{24} +125.293 q^{25} -44.2066 q^{26} +27.0000 q^{27} -120.393 q^{28} -27.2789 q^{29} -100.721 q^{30} +31.0000 q^{31} -144.665 q^{32} -56.9092 q^{33} +159.735 q^{34} +544.745 q^{35} -31.4684 q^{36} +268.093 q^{37} +40.3208 q^{38} +62.4932 q^{39} +385.980 q^{40} -215.775 q^{41} -219.213 q^{42} +90.8472 q^{43} +66.3275 q^{44} +142.386 q^{45} -141.033 q^{46} -8.82826 q^{47} -71.4078 q^{48} +842.599 q^{49} -265.890 q^{50} -225.812 q^{51} -72.8356 q^{52} +178.538 q^{53} -57.2980 q^{54} -300.114 q^{55} +840.059 q^{56} -57.0000 q^{57} +57.8897 q^{58} +699.937 q^{59} -165.950 q^{60} -2.53038 q^{61} -65.7866 q^{62} +309.893 q^{63} +497.422 q^{64} +329.561 q^{65} +120.770 q^{66} +531.622 q^{67} +263.183 q^{68} +199.373 q^{69} -1156.03 q^{70} -386.616 q^{71} +219.575 q^{72} +220.587 q^{73} -568.934 q^{74} +375.879 q^{75} +66.4333 q^{76} -653.176 q^{77} -132.620 q^{78} -716.636 q^{79} -376.573 q^{80} +81.0000 q^{81} +457.905 q^{82} +1023.83 q^{83} -361.179 q^{84} -1190.83 q^{85} -192.791 q^{86} -81.8366 q^{87} -462.809 q^{88} +1175.19 q^{89} -302.164 q^{90} +717.266 q^{91} -232.369 q^{92} +93.0000 q^{93} +18.7349 q^{94} -300.592 q^{95} -433.996 q^{96} +768.638 q^{97} -1788.12 q^{98} -170.728 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 7 q^{2} + 120 q^{3} + 195 q^{4} + 5 q^{5} + 21 q^{6} + 23 q^{7} + 90 q^{8} + 360 q^{9} + 98 q^{10} + 50 q^{11} + 585 q^{12} + 222 q^{13} + 89 q^{14} + 15 q^{15} + 1155 q^{16} + 165 q^{17} + 63 q^{18}+ \cdots + 450 q^{99}+O(q^{100}) \) 40 * q + 7 * q^2 + 120 * q^3 + 195 * q^4 + 5 * q^5 + 21 * q^6 + 23 * q^7 + 90 * q^8 + 360 * q^9 + 98 * q^10 + 50 * q^11 + 585 * q^12 + 222 * q^13 + 89 * q^14 + 15 * q^15 + 1155 * q^16 + 165 * q^17 + 63 * q^18 - 760 * q^19 - 236 * q^20 + 69 * q^21 + 384 * q^22 + 159 * q^23 + 270 * q^24 + 2013 * q^25 + 531 * q^26 + 1080 * q^27 + 382 * q^28 + 355 * q^29 + 294 * q^30 + 1240 * q^31 + 1947 * q^32 + 150 * q^33 + 1323 * q^34 - 34 * q^35 + 1755 * q^36 + 870 * q^37 - 133 * q^38 + 666 * q^39 + 1333 * q^40 + 1227 * q^41 + 267 * q^42 + 907 * q^43 + 1889 * q^44 + 45 * q^45 + 817 * q^46 + 128 * q^47 + 3465 * q^48 + 3403 * q^49 + 1368 * q^50 + 495 * q^51 + 3686 * q^52 + 2331 * q^53 + 189 * q^54 + 834 * q^55 + 1516 * q^56 - 2280 * q^57 + 2768 * q^58 + 272 * q^59 - 708 * q^60 + 2243 * q^61 + 217 * q^62 + 207 * q^63 + 8968 * q^64 + 1958 * q^65 + 1152 * q^66 + 2201 * q^67 + 1335 * q^68 + 477 * q^69 + 1406 * q^70 + 1839 * q^71 + 810 * q^72 + 2648 * q^73 + 819 * q^74 + 6039 * q^75 - 3705 * q^76 + 4422 * q^77 + 1593 * q^78 + 2413 * q^79 - 1751 * q^80 + 3240 * q^81 + 2661 * q^82 - 94 * q^83 + 1146 * q^84 + 2620 * q^85 + 96 * q^86 + 1065 * q^87 + 3089 * q^88 + 2578 * q^89 + 882 * q^90 + 1736 * q^91 + 1408 * q^92 + 3720 * q^93 + 3275 * q^94 - 95 * q^95 + 5841 * q^96 + 7780 * q^97 + 4040 * q^98 + 450 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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