LMFDB - Embedded newform 1849.4.a.m.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,4,Mod(1,1849)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1849.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$109.094531601$
Analytic rank:	$0$
Dimension:	$110$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.51127 q^{2} +1.26223 q^{3} +22.3741 q^{4} +19.4467 q^{5} -6.95647 q^{6} +10.3981 q^{7} -79.2194 q^{8} -25.4068 q^{9} +O(q^{10})$	\(q-5.51127 q^{2} +1.26223 q^{3} +22.3741 q^{4} +19.4467 q^{5} -6.95647 q^{6} +10.3981 q^{7} -79.2194 q^{8} -25.4068 q^{9} -107.176 q^{10} -22.9792 q^{11} +28.2411 q^{12} +28.1139 q^{13} -57.3065 q^{14} +24.5461 q^{15} +257.607 q^{16} +54.8789 q^{17} +140.024 q^{18} -54.7943 q^{19} +435.101 q^{20} +13.1247 q^{21} +126.645 q^{22} -70.2313 q^{23} -99.9928 q^{24} +253.172 q^{25} -154.943 q^{26} -66.1492 q^{27} +232.647 q^{28} -73.7205 q^{29} -135.280 q^{30} -141.186 q^{31} -785.985 q^{32} -29.0049 q^{33} -302.453 q^{34} +202.207 q^{35} -568.453 q^{36} -201.065 q^{37} +301.986 q^{38} +35.4861 q^{39} -1540.55 q^{40} +291.747 q^{41} -72.3338 q^{42} -514.138 q^{44} -494.077 q^{45} +387.064 q^{46} +130.363 q^{47} +325.158 q^{48} -234.880 q^{49} -1395.30 q^{50} +69.2696 q^{51} +629.022 q^{52} +199.277 q^{53} +364.566 q^{54} -446.869 q^{55} -823.728 q^{56} -69.1628 q^{57} +406.293 q^{58} +398.571 q^{59} +549.196 q^{60} -298.891 q^{61} +778.112 q^{62} -264.181 q^{63} +2270.92 q^{64} +546.721 q^{65} +159.854 q^{66} +897.516 q^{67} +1227.87 q^{68} -88.6478 q^{69} -1114.42 q^{70} +292.202 q^{71} +2012.71 q^{72} +148.103 q^{73} +1108.12 q^{74} +319.561 q^{75} -1225.97 q^{76} -238.939 q^{77} -195.573 q^{78} -891.632 q^{79} +5009.59 q^{80} +602.488 q^{81} -1607.90 q^{82} +1373.20 q^{83} +293.653 q^{84} +1067.21 q^{85} -93.0519 q^{87} +1820.40 q^{88} +820.045 q^{89} +2722.99 q^{90} +292.330 q^{91} -1571.36 q^{92} -178.208 q^{93} -718.468 q^{94} -1065.57 q^{95} -992.091 q^{96} -883.202 q^{97} +1294.49 q^{98} +583.828 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 110 q + 492 q^{4} + 102 q^{6} + 1234 q^{9}+O(q^{10}) $ 110 * q + 492 * q^4 + 102 * q^6 + 1234 * q^9	$ 110 q + 492 q^{4} + 102 q^{6} + 1234 q^{9} + 102 q^{10} + 360 q^{11} + 166 q^{13} + 496 q^{14} + 540 q^{15} + 2204 q^{16} + 610 q^{17} + 896 q^{21} + 1508 q^{23} + 1086 q^{24} + 3168 q^{25} + 2312 q^{31} + 2760 q^{35} + 8334 q^{36} + 3626 q^{38} + 1462 q^{40} + 3598 q^{41} + 1596 q^{44} + 4448 q^{47} + 7194 q^{49} + 3620 q^{52} + 3818 q^{53} - 2570 q^{54} - 714 q^{56} + 3236 q^{57} + 3242 q^{58} + 8556 q^{59} + 178 q^{60} + 7308 q^{64} + 4202 q^{66} + 1992 q^{67} + 8994 q^{68} + 8256 q^{74} + 4784 q^{78} + 13752 q^{79} + 19678 q^{81} + 7620 q^{83} + 11390 q^{84} + 6012 q^{87} - 476 q^{90} + 8022 q^{92} + 7392 q^{95} + 16760 q^{96} - 1186 q^{97} + 11068 q^{99}+O(q^{100}) $ 110 * q + 492 * q^4 + 102 * q^6 + 1234 * q^9 + 102 * q^10 + 360 * q^11 + 166 * q^13 + 496 * q^14 + 540 * q^15 + 2204 * q^16 + 610 * q^17 + 896 * q^21 + 1508 * q^23 + 1086 * q^24 + 3168 * q^25 + 2312 * q^31 + 2760 * q^35 + 8334 * q^36 + 3626 * q^38 + 1462 * q^40 + 3598 * q^41 + 1596 * q^44 + 4448 * q^47 + 7194 * q^49 + 3620 * q^52 + 3818 * q^53 - 2570 * q^54 - 714 * q^56 + 3236 * q^57 + 3242 * q^58 + 8556 * q^59 + 178 * q^60 + 7308 * q^64 + 4202 * q^66 + 1992 * q^67 + 8994 * q^68 + 8256 * q^74 + 4784 * q^78 + 13752 * q^79 + 19678 * q^81 + 7620 * q^83 + 11390 * q^84 + 6012 * q^87 - 476 * q^90 + 8022 * q^92 + 7392 * q^95 + 16760 * q^96 - 1186 * q^97 + 11068 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−5.51127	−1.94853	−0.974264	−	0.225411i	$-0.927628\pi$
$2$	−5.51127	−1.94853	−0.974264	+	0.225411i	$0.927628\pi$
$3$	1.26223	0.242915	0.121458	−	0.992597i	$-0.461243\pi$
$3$	1.26223	0.242915	0.121458	+	0.992597i	$0.461243\pi$
$4$	22.3741	2.79676
$5$	19.4467	1.73936	0.869681	−	0.493614i	$-0.164325\pi$
$5$	19.4467	1.73936	0.869681	+	0.493614i	$0.164325\pi$
$6$	−6.95647	−0.473328
$7$	10.3981	0.561442	0.280721	−	0.959789i	$-0.409426\pi$
$7$	10.3981	0.561442	0.280721	+	0.959789i	$0.409426\pi$
$8$	−79.2194	−3.50104
$9$	−25.4068	−0.940992
$10$	−107.176	−3.38919
$11$	−22.9792	−0.629863	−0.314931	−	0.949114i	$-0.601981\pi$
$11$	−22.9792	−0.629863	−0.314931	+	0.949114i	$0.601981\pi$
$12$	28.2411	0.679376
$13$	28.1139	0.599799	0.299899	−	0.953971i	$-0.403047\pi$
$13$	28.1139	0.599799	0.299899	+	0.953971i	$0.403047\pi$
$14$	−57.3065	−1.09399
$15$	24.5461	0.422518
$16$	257.607	4.02511
$17$	54.8789	0.782947	0.391473	−	0.920189i	$-0.371966\pi$
$17$	54.8789	0.782947	0.391473	+	0.920189i	$0.371966\pi$
$18$	140.024	1.83355
$19$	−54.7943	−0.661615	−0.330807	−	0.943698i	$-0.607321\pi$
$19$	−54.7943	−0.661615	−0.330807	+	0.943698i	$0.607321\pi$
$20$	435.101	4.86458
$21$	13.1247	0.136383
$22$	126.645	1.22730
$23$	−70.2313	−0.636706	−0.318353	−	0.947972i	$-0.603130\pi$
$23$	−70.2313	−0.636706	−0.318353	+	0.947972i	$0.603130\pi$
$24$	−99.9928	−0.850456
$25$	253.172	2.02538
$26$	−154.943	−1.16872
$27$	−66.1492	−0.471497
$28$	232.647	1.57022
$29$	−73.7205	−0.472053	−0.236027	−	0.971747i	$-0.575845\pi$
$29$	−73.7205	−0.472053	−0.236027	+	0.971747i	$0.575845\pi$
$30$	−135.280	−0.823288
$31$	−141.186	−0.817990	−0.408995	−	0.912537i	$-0.634121\pi$
$31$	−141.186	−0.817990	−0.408995	+	0.912537i	$0.634121\pi$
$32$	−785.985	−4.34199
$33$	−29.0049	−0.153003
$34$	−302.453	−1.52559
$35$	202.207	0.976552
$36$	−568.453	−2.63173
$37$	−201.065	−0.893373	−0.446687	−	0.894690i	$-0.647396\pi$
$37$	−201.065	−0.893373	−0.446687	+	0.894690i	$0.647396\pi$
$38$	301.986	1.28917
$39$	35.4861	0.145700
$40$	−1540.55	−6.08957
$41$	291.747	1.11130	0.555649	−	0.831417i	$-0.312470\pi$
$41$	291.747	1.11130	0.555649	+	0.831417i	$0.312470\pi$
$42$	−72.3338	−0.265746
$43$	0	0
$43$	0	0
$44$	−514.138	−1.76157
$45$	−494.077	−1.63673
$46$	387.064	1.24064
$47$	130.363	0.404584	0.202292	−	0.979325i	$-0.435161\pi$
$47$	130.363	0.404584	0.202292	+	0.979325i	$0.435161\pi$
$48$	325.158	0.977761
$49$	−234.880	−0.684782
$50$	−1395.30	−3.94651
$51$	69.2696	0.190190
$52$	629.022	1.67749
$53$	199.277	0.516467	0.258234	−	0.966082i	$-0.416860\pi$
$53$	199.277	0.516467	0.258234	+	0.966082i	$0.416860\pi$
$54$	364.566	0.918725
$55$	−446.869	−1.09556
$56$	−823.728	−1.96563
$57$	−69.1628	−0.160716
$58$	406.293	0.919809
$59$	398.571	0.879482	0.439741	−	0.898125i	$-0.355070\pi$
$59$	398.571	0.879482	0.439741	+	0.898125i	$0.355070\pi$
$60$	549.196	1.18168
$61$	−298.891	−0.627363	−0.313681	−	0.949528i	$-0.601562\pi$
$61$	−298.891	−0.627363	−0.313681	+	0.949528i	$0.601562\pi$
$62$	778.112	1.59388
$63$	−264.181	−0.528313
$64$	2270.92	4.43539
$65$	546.721	1.04327
$66$	159.854	0.298131
$67$	897.516	1.63655	0.818276	−	0.574826i	$-0.194930\pi$
$67$	897.516	1.63655	0.818276	+	0.574826i	$0.194930\pi$
$68$	1227.87	2.18971
$69$	−88.6478	−0.154666
$70$	−1114.42	−1.90284
$71$	292.202	0.488422	0.244211	−	0.969722i	$-0.421471\pi$
$71$	292.202	0.488422	0.244211	+	0.969722i	$0.421471\pi$
$72$	2012.71	3.29445
$73$	148.103	0.237455	0.118727	−	0.992927i	$-0.462119\pi$
$73$	148.103	0.237455	0.118727	+	0.992927i	$0.462119\pi$
$74$	1108.12	1.74076
$75$	319.561	0.491996
$76$	−1225.97	−1.85038
$77$	−238.939	−0.353632
$78$	−195.573	−0.283901
$79$	−891.632	−1.26983	−0.634914	−	0.772583i	$-0.718965\pi$
$79$	−891.632	−1.26983	−0.634914	+	0.772583i	$0.718965\pi$
$80$	5009.59	7.00112
$81$	602.488	0.826458
$82$	−1607.90	−2.16540
$83$	1373.20	1.81600	0.907999	−	0.418972i	$-0.137609\pi$
$83$	1373.20	1.81600	0.907999	+	0.418972i	$0.137609\pi$
$84$	293.653	0.381431
$85$	1067.21	1.36183
$86$	0	0
$87$	−93.0519	−0.114669
$88$	1820.40	2.20517
$89$	820.045	0.976681	0.488340	−	0.872653i	$-0.337602\pi$
$89$	820.045	0.976681	0.488340	+	0.872653i	$0.337602\pi$
$90$	2722.99	3.18921
$91$	292.330	0.336753
$92$	−1571.36	−1.78071
$93$	−178.208	−0.198702
$94$	−718.468	−0.788344
$95$	−1065.57	−1.15079
$96$	−992.091	−1.05474
$97$	−883.202	−0.924490	−0.462245	−	0.886752i	$-0.652956\pi$
$97$	−883.202	−0.924490	−0.462245	+	0.886752i	$0.652956\pi$
$98$	1294.49	1.33432
$99$	583.828	0.592696
$100$	5664.50	5.66450
$101$	105.585	0.104020	0.0520102	−	0.998647i	$-0.483437\pi$
$101$	105.585	0.104020	0.0520102	+	0.998647i	$0.483437\pi$
$102$	−381.763	−0.370590
$103$	1872.38	1.79117	0.895587	−	0.444886i	$-0.146756\pi$
$103$	1872.38	1.79117	0.895587	+	0.444886i	$0.146756\pi$
$104$	−2227.16	−2.09992
$105$	255.232	0.237220
$106$	−1098.27	−1.00635
$107$	484.492	0.437735	0.218867	−	0.975755i	$-0.429764\pi$
$107$	484.492	0.437735	0.218867	+	0.975755i	$0.429764\pi$
$108$	−1480.03	−1.31866
$109$	2056.05	1.80673	0.903367	−	0.428868i	$-0.141087\pi$
$109$	2056.05	1.80673	0.903367	+	0.428868i	$0.141087\pi$
$110$	2462.81	2.13473
$111$	−253.789	−0.217014
$112$	2678.61	2.25987
$113$	−1454.66	−1.21100	−0.605498	−	0.795847i	$-0.707026\pi$
$113$	−1454.66	−1.21100	−0.605498	+	0.795847i	$0.707026\pi$
$114$	381.175	0.313161
$115$	−1365.76	−1.10746
$116$	−1649.43	−1.32022
$117$	−714.283	−0.564406
$118$	−2196.63	−1.71370
$119$	570.634	0.439580
$120$	−1944.53	−1.47925
$121$	−802.957	−0.603273
$122$	1647.27	1.22243
$123$	368.251	0.269952
$124$	−3158.90	−2.28772
$125$	2492.52	1.78351
$126$	1455.97	1.02943
$127$	1990.62	1.39086	0.695429	−	0.718595i	$-0.255214\pi$
$127$	1990.62	1.39086	0.695429	+	0.718595i	$0.255214\pi$
$128$	−6227.77	−4.30049
$129$	0	0
$130$	−3013.13	−2.03284
$131$	−478.581	−0.319189	−0.159595	−	0.987183i	$-0.551019\pi$
$131$	−478.581	−0.319189	−0.159595	+	0.987183i	$0.551019\pi$
$132$	−648.959	−0.427914
$133$	−569.755	−0.371459
$134$	−4946.45	−3.18887
$135$	−1286.38	−0.820104
$136$	−4347.48	−2.74113
$137$	2496.59	1.55692	0.778459	−	0.627695i	$-0.216002\pi$
$137$	2496.59	1.55692	0.778459	+	0.627695i	$0.216002\pi$
$138$	488.562	0.301370
$139$	591.235	0.360777	0.180388	−	0.983595i	$-0.442265\pi$
$139$	591.235	0.360777	0.180388	+	0.983595i	$0.442265\pi$
$140$	4524.21	2.73118
$141$	164.548	0.0982798
$142$	−1610.40	−0.951704
$143$	−646.034	−0.377791
$144$	−6544.96	−3.78759
$145$	−1433.62	−0.821071
$146$	−816.238	−0.462687
$147$	−296.472	−0.166344
$148$	−4498.64	−2.49855
$149$	654.395	0.359800	0.179900	−	0.983685i	$-0.442423\pi$
$149$	654.395	0.359800	0.179900	+	0.983685i	$0.442423\pi$
$150$	−1761.19	−0.958668
$151$	2392.15	1.28921	0.644604	−	0.764517i	$-0.277022\pi$
$151$	2392.15	1.28921	0.644604	+	0.764517i	$0.277022\pi$
$152$	4340.77	2.31634
$153$	−1394.30	−0.736747
$154$	1316.86	0.689061
$155$	−2745.59	−1.42278
$156$	793.968	0.407489
$157$	379.978	0.193157	0.0965783	−	0.995325i	$-0.469210\pi$
$157$	379.978	0.193157	0.0965783	+	0.995325i	$0.469210\pi$
$158$	4914.02	2.47430
$159$	251.532	0.125458
$160$	−15284.8	−7.55230
$161$	−730.269	−0.357474
$162$	−3320.47	−1.61038
$163$	922.723	0.443394	0.221697	−	0.975116i	$-0.428840\pi$
$163$	922.723	0.443394	0.221697	+	0.975116i	$0.428840\pi$
$164$	6527.57	3.10804
$165$	−564.049	−0.266128
$166$	−7568.05	−3.53852
$167$	2212.00	1.02497	0.512484	−	0.858697i	$-0.328725\pi$
$167$	2212.00	1.02497	0.512484	+	0.858697i	$0.328725\pi$
$168$	−1039.73	−0.477482
$169$	−1406.61	−0.640241
$170$	−5881.69	−2.65356
$171$	1392.15	0.622574
$172$	0	0
$173$	3286.65	1.44439	0.722195	−	0.691690i	$-0.243133\pi$
$173$	3286.65	1.44439	0.722195	+	0.691690i	$0.243133\pi$
$174$	512.834	0.223436
$175$	2632.50	1.13713
$176$	−5919.60	−2.53526
$177$	503.086	0.213640
$178$	−4519.49	−1.90309
$179$	3125.24	1.30498	0.652491	−	0.757797i	$-0.273724\pi$
$179$	3125.24	1.30498	0.652491	+	0.757797i	$0.273724\pi$
$180$	−11054.5	−4.57753
$181$	−206.748	−0.0849033	−0.0424516	−	0.999099i	$-0.513517\pi$
$181$	−206.748	−0.0849033	−0.0424516	+	0.999099i	$0.513517\pi$
$182$	−1611.11	−0.656172
$183$	−377.269	−0.152396
$184$	5563.68	2.22913
$185$	−3910.03	−1.55390
$186$	982.153	0.387177
$187$	−1261.07	−0.493149
$188$	2916.76	1.13153
$189$	−687.823	−0.264718
$190$	5872.62	2.24234
$191$	−751.083	−0.284537	−0.142268	−	0.989828i	$-0.545440\pi$
$191$	−751.083	−0.284537	−0.142268	+	0.989828i	$0.545440\pi$
$192$	2866.41	1.07743
$193$	−2614.96	−0.975278	−0.487639	−	0.873045i	$-0.662142\pi$
$193$	−2614.96	−0.975278	−0.487639	+	0.873045i	$0.662142\pi$
$194$	4867.56	1.80140
$195$	690.085	0.253426
$196$	−5255.23	−1.91517
$197$	−1214.32	−0.439170	−0.219585	−	0.975593i	$-0.570470\pi$
$197$	−1214.32	−0.439170	−0.219585	+	0.975593i	$0.570470\pi$
$198$	−3217.63	−1.15488
$199$	5315.66	1.89355	0.946777	−	0.321890i	$-0.104318\pi$
$199$	5315.66	1.89355	0.946777	+	0.321890i	$0.104318\pi$
$200$	−20056.2	−7.09093
$201$	1132.87	0.397544
$202$	−581.905	−0.202687
$203$	−766.550	−0.265031
$204$	1549.84	0.531916
$205$	5673.51	1.93295
$206$	−10319.2	−3.49015
$207$	1784.35	0.599135
$208$	7242.33	2.41425
$209$	1259.13	0.416726
$210$	−1406.65	−0.462229
$211$	1541.29	0.502876	0.251438	−	0.967873i	$-0.419097\pi$
$211$	1541.29	0.502876	0.251438	+	0.967873i	$0.419097\pi$
$212$	4458.63	1.44444
$213$	368.825	0.118645
$214$	−2670.17	−0.852939
$215$	0	0
$216$	5240.30	1.65073
$217$	−1468.06	−0.459254
$218$	−11331.5	−3.52047
$219$	186.940	0.0576815
$220$	−9998.27	−3.06402
$221$	1542.86	0.469611
$222$	1398.70	0.422858
$223$	−1717.86	−0.515860	−0.257930	−	0.966164i	$-0.583040\pi$
$223$	−1717.86	−0.515860	−0.257930	+	0.966164i	$0.583040\pi$
$224$	−8172.72	−2.43778
$225$	−6432.30	−1.90587
$226$	8017.00	2.35966
$227$	−1912.32	−0.559142	−0.279571	−	0.960125i	$-0.590192\pi$
$227$	−1912.32	−0.559142	−0.279571	+	0.960125i	$0.590192\pi$
$228$	−1547.45	−0.449485
$229$	693.989	0.200263	0.100131	−	0.994974i	$-0.468074\pi$
$229$	693.989	0.200263	0.100131	+	0.994974i	$0.468074\pi$
$230$	7527.09	2.15792
$231$	−301.595	−0.0859026
$232$	5840.09	1.65268
$233$	−2148.08	−0.603971	−0.301986	−	0.953313i	$-0.597649\pi$
$233$	−2148.08	−0.603971	−0.301986	+	0.953313i	$0.597649\pi$
$234$	3936.61	1.09976
$235$	2535.13	0.703719
$236$	8917.65	2.45970
$237$	−1125.44	−0.308461
$238$	−3144.92	−0.856533
$239$	2989.96	0.809222	0.404611	−	0.914489i	$-0.367407\pi$
$239$	2989.96	0.809222	0.404611	+	0.914489i	$0.367407\pi$
$240$	6323.24	1.70068
$241$	1983.11	0.530056	0.265028	−	0.964241i	$-0.414619\pi$
$241$	1983.11	0.530056	0.265028	+	0.964241i	$0.414619\pi$
$242$	4425.31	1.17549
$243$	2546.50	0.672257
$244$	−6687.42	−1.75458
$245$	−4567.64	−1.19108
$246$	−2029.53	−0.526008
$247$	−1540.48	−0.396836
$248$	11184.6	2.86381
$249$	1733.28	0.441134
$250$	−13737.0	−3.47521
$251$	6296.33	1.58335	0.791675	−	0.610942i	$-0.209209\pi$
$251$	6296.33	1.58335	0.791675	+	0.610942i	$0.209209\pi$
$252$	−5910.81	−1.47756
$253$	1613.86	0.401037
$254$	−10970.8	−2.71012
$255$	1347.06	0.330809
$256$	16155.5	3.94423
$257$	40.5174	0.00983426	0.00491713	−	0.999988i	$-0.498435\pi$
$257$	40.5174	0.00983426	0.00491713	+	0.999988i	$0.498435\pi$
$258$	0	0
$259$	−2090.68	−0.501578
$260$	12232.4	2.91777
$261$	1873.00	0.444198
$262$	2637.59	0.621949
$263$	1494.88	0.350489	0.175244	−	0.984525i	$-0.443928\pi$
$263$	1494.88	0.350489	0.175244	+	0.984525i	$0.443928\pi$
$264$	2297.75	0.535670
$265$	3875.27	0.898324
$266$	3140.07	0.723797
$267$	1035.08	0.237251
$268$	20081.1	4.57704
$269$	−3407.78	−0.772401	−0.386201	−	0.922415i	$-0.626213\pi$
$269$	−3407.78	−0.772401	−0.386201	+	0.922415i	$0.626213\pi$
$270$	7089.59	1.59800
$271$	−1066.80	−0.239128	−0.119564	−	0.992826i	$-0.538150\pi$
$271$	−1066.80	−0.239128	−0.119564	+	0.992826i	$0.538150\pi$
$272$	14137.2	3.15144
$273$	368.986	0.0818024
$274$	−13759.4	−3.03370
$275$	−5817.70	−1.27571
$276$	−1983.41	−0.432563
$277$	−8765.38	−1.90130	−0.950651	−	0.310261i	$-0.899584\pi$
$277$	−8765.38	−1.90130	−0.950651	+	0.310261i	$0.899584\pi$
$278$	−3258.46	−0.702983
$279$	3587.07	0.769722
$280$	−16018.8	−3.41894
$281$	−5716.43	−1.21357	−0.606786	−	0.794865i	$-0.707542\pi$
$281$	−5716.43	−1.21357	−0.606786	+	0.794865i	$0.707542\pi$
$282$	−906.869	−0.191501
$283$	−5891.72	−1.23755	−0.618775	−	0.785568i	$-0.712371\pi$
$283$	−5891.72	−1.23755	−0.618775	+	0.785568i	$0.712371\pi$
$284$	6537.74	1.36600
$285$	−1344.99	−0.279544
$286$	3560.47	0.736136
$287$	3033.60	0.623930
$288$	19969.4	4.08578
$289$	−1901.30	−0.386994
$290$	7901.04	1.59988
$291$	−1114.80	−0.224573
$292$	3313.68	0.664104
$293$	1101.20	0.219566	0.109783	−	0.993956i	$-0.464984\pi$
$293$	1101.20	0.219566	0.109783	+	0.993956i	$0.464984\pi$
$294$	1633.94	0.324126
$295$	7750.86	1.52974
$296$	15928.2	3.12773
$297$	1520.06	0.296978
$298$	−3606.55	−0.701080
$299$	−1974.47	−0.381896
$300$	7149.88	1.37599
$301$	0	0
$302$	−13183.8	−2.51206
$303$	133.272	0.0252682
$304$	−14115.4	−2.66307
$305$	−5812.44	−1.09121
$306$	7684.35	1.43557
$307$	2947.72	0.547997	0.273999	−	0.961730i	$-0.411654\pi$
$307$	2947.72	0.547997	0.273999	+	0.961730i	$0.411654\pi$
$308$	−5346.04	−0.989023
$309$	2363.37	0.435104
$310$	15131.7	2.77233
$311$	−4412.55	−0.804542	−0.402271	−	0.915521i	$-0.631779\pi$
$311$	−4412.55	−0.804542	−0.402271	+	0.915521i	$0.631779\pi$
$312$	−2811.18	−0.510103
$313$	−9321.71	−1.68337	−0.841684	−	0.539971i	$-0.818435\pi$
$313$	−9321.71	−1.68337	−0.841684	+	0.539971i	$0.818435\pi$
$314$	−2094.16	−0.376371
$315$	−5137.44	−0.918927
$316$	−19949.4	−3.55141
$317$	−1970.25	−0.349086	−0.174543	−	0.984650i	$-0.555845\pi$
$317$	−1970.25	−0.349086	−0.174543	+	0.984650i	$0.555845\pi$
$318$	−1386.26	−0.244458
$319$	1694.04	0.297329
$320$	44161.8	7.71475
$321$	611.539	0.106333
$322$	4024.71	0.696548
$323$	−3007.05	−0.518009
$324$	13480.1	2.31140
$325$	7117.66	1.21482
$326$	−5085.38	−0.863966
$327$	2595.20	0.438884
$328$	−23112.0	−3.89070
$329$	1355.53	0.227151
$330$	3108.63	0.518558
$331$	−4376.46	−0.726743	−0.363372	−	0.931644i	$-0.618374\pi$
$331$	−4376.46	−0.726743	−0.363372	+	0.931644i	$0.618374\pi$
$332$	30724.0	5.07891
$333$	5108.41	0.840657
$334$	−12190.9	−1.99718
$335$	17453.7	2.84656
$336$	3381.01	0.548956
$337$	2193.62	0.354583	0.177291	−	0.984158i	$-0.443267\pi$
$337$	2193.62	0.354583	0.177291	+	0.984158i	$0.443267\pi$
$338$	7752.21	1.24753
$339$	−1836.11	−0.294170
$340$	23877.9	3.80871
$341$	3244.33	0.515221
$342$	−7672.50	−1.21310
$343$	−6008.83	−0.945908
$344$	0	0
$345$	−1723.90	−0.269020
$346$	−18113.6	−2.81443
$347$	8264.85	1.27862	0.639309	−	0.768950i	$-0.279221\pi$
$347$	8264.85	1.27862	0.639309	+	0.768950i	$0.279221\pi$
$348$	−2081.95	−0.320702
$349$	5553.54	0.851789	0.425895	−	0.904773i	$-0.359959\pi$
$349$	5553.54	0.851789	0.425895	+	0.904773i	$0.359959\pi$
$350$	−14508.4	−2.21574
$351$	−1859.71	−0.282803
$352$	18061.3	2.73486
$353$	6658.15	1.00390	0.501951	−	0.864896i	$-0.332616\pi$
$353$	6658.15	1.00390	0.501951	+	0.864896i	$0.332616\pi$
$354$	−2772.64	−0.416283
$355$	5682.34	0.849542
$356$	18347.7	2.73154
$357$	720.270	0.106781
$358$	−17224.1	−2.54279
$359$	1731.90	0.254613	0.127307	−	0.991863i	$-0.459367\pi$
$359$	1731.90	0.254613	0.127307	+	0.991863i	$0.459367\pi$
$360$	39140.5	5.73024
$361$	−3856.58	−0.562266
$362$	1139.45	0.165436
$363$	−1013.51	−0.146544
$364$	6540.61	0.941816
$365$	2880.12	0.413020
$366$	2079.23	0.296948
$367$	7772.68	1.10553	0.552766	−	0.833336i	$-0.313572\pi$
$367$	7772.68	1.10553	0.552766	+	0.833336i	$0.313572\pi$
$368$	−18092.1	−2.56281
$369$	−7412.36	−1.04572
$370$	21549.2	3.02782
$371$	2072.09	0.289967
$372$	−3987.24	−0.555723
$373$	7625.43	1.05853	0.529263	−	0.848458i	$-0.322469\pi$
$373$	7625.43	1.05853	0.529263	+	0.848458i	$0.322469\pi$
$374$	6950.12	0.960914
$375$	3146.13	0.433241
$376$	−10327.3	−1.41646
$377$	−2072.57	−0.283137
$378$	3790.78	0.515811
$379$	722.651	0.0979422	0.0489711	−	0.998800i	$-0.484406\pi$
$379$	722.651	0.0979422	0.0489711	+	0.998800i	$0.484406\pi$
$380$	−23841.1	−3.21848
$381$	2512.61	0.337861
$382$	4139.42	0.554427
$383$	−7800.58	−1.04071	−0.520354	−	0.853951i	$-0.674200\pi$
$383$	−7800.58	−1.04071	−0.520354	+	0.853951i	$0.674200\pi$
$384$	−7860.85	−1.04465
$385$	−4646.57	−0.615093
$386$	14411.7	1.90036
$387$	0	0
$388$	−19760.8	−2.58558
$389$	−4803.56	−0.626093	−0.313047	−	0.949738i	$-0.601350\pi$
$389$	−4803.56	−0.626093	−0.313047	+	0.949738i	$0.601350\pi$
$390$	−3803.24	−0.493807
$391$	−3854.22	−0.498507
$392$	18607.1	2.39745
$393$	−604.077	−0.0775360
$394$	6692.42	0.855734
$395$	−17339.3	−2.20869
$396$	13062.6	1.65763
$397$	−4573.94	−0.578236	−0.289118	−	0.957294i	$-0.593362\pi$
$397$	−4573.94	−0.578236	−0.289118	+	0.957294i	$0.593362\pi$
$398$	−29296.0	−3.68964
$399$	−719.159	−0.0902331
$400$	65218.9	8.15237
$401$	7435.57	0.925971	0.462986	−	0.886366i	$-0.346778\pi$
$401$	7435.57	0.925971	0.462986	+	0.886366i	$0.346778\pi$
$402$	−6243.54	−0.774625
$403$	−3969.27	−0.490629
$404$	2362.36	0.290920
$405$	11716.4	1.43751
$406$	4224.66	0.516420
$407$	4620.30	0.562703
$408$	−5487.50	−0.665862
$409$	−8211.52	−0.992747	−0.496374	−	0.868109i	$-0.665335\pi$
$409$	−8211.52	−0.992747	−0.496374	+	0.868109i	$0.665335\pi$
$410$	−31268.2	−3.76641
$411$	3151.26	0.378200
$412$	41892.8	5.00949
$413$	4144.36	0.493779
$414$	−9834.04	−1.16743
$415$	26704.1	3.15868
$416$	−22097.1	−2.60432
$417$	746.273	0.0876382
$418$	−6939.40	−0.812003
$419$	−9.52353	−0.00111039	−0.000555197	−	1.00000i	$-0.500177\pi$
$419$	−9.52353	−0.00111039	−0.000555197		1.00000i	$0.500177\pi$
$420$	5710.57	0.663446
$421$	−15353.9	−1.77744	−0.888719	−	0.458451i	$-0.848404\pi$
$421$	−15353.9	−1.77744	−0.888719	+	0.458451i	$0.848404\pi$
$422$	−8494.47	−0.979868
$423$	−3312.12	−0.380711
$424$	−15786.6	−1.80817
$425$	13893.8	1.58576
$426$	−2032.69	−0.231184
$427$	−3107.89	−0.352228
$428$	10840.1	1.22424
$429$	−815.441	−0.0917713
$430$	0	0
$431$	−544.776	−0.0608838	−0.0304419	−	0.999537i	$-0.509691\pi$
$431$	−544.776	−0.0608838	−0.0304419	+	0.999537i	$0.509691\pi$
$432$	−17040.5	−1.89783
$433$	−4150.46	−0.460643	−0.230321	−	0.973115i	$-0.573978\pi$
$433$	−4150.46	−0.460643	−0.230321	+	0.973115i	$0.573978\pi$
$434$	8090.85	0.894869
$435$	−1809.55	−0.199451
$436$	46002.3	5.05300
$437$	3848.28	0.421254
$438$	−1030.28	−0.112394
$439$	13182.2	1.43315	0.716575	−	0.697510i	$-0.245709\pi$
$439$	13182.2	1.43315	0.716575	+	0.697510i	$0.245709\pi$
$440$	35400.7	3.83559
$441$	5967.55	0.644375
$442$	−8503.11	−0.915049
$443$	−12662.6	−1.35806	−0.679028	−	0.734113i	$-0.737598\pi$
$443$	−12662.6	−1.35806	−0.679028	+	0.734113i	$0.737598\pi$
$444$	−5678.29	−0.606937
$445$	15947.1	1.69880
$446$	9467.61	1.00517
$447$	825.995	0.0874009
$448$	23613.2	2.49022
$449$	−12227.7	−1.28522	−0.642608	−	0.766195i	$-0.722148\pi$
$449$	−12227.7	−1.28522	−0.642608	+	0.766195i	$0.722148\pi$
$450$	35450.1	3.71363
$451$	−6704.12	−0.699966
$452$	−32546.6	−3.38687
$453$	3019.43	0.313169
$454$	10539.3	1.08950
$455$	5684.84	0.585735
$456$	5479.04	0.562674
$457$	991.432	0.101482	0.0507409	−	0.998712i	$-0.483842\pi$
$457$	991.432	0.101482	0.0507409	+	0.998712i	$0.483842\pi$
$458$	−3824.76	−0.390217
$459$	−3630.20	−0.369157
$460$	−30557.7	−3.09731
$461$	11785.3	1.19067	0.595334	−	0.803478i	$-0.297020\pi$
$461$	11785.3	1.19067	0.595334	+	0.803478i	$0.297020\pi$
$462$	1662.17	0.167384
$463$	18190.4	1.82588	0.912939	−	0.408096i	$-0.133807\pi$
$463$	18190.4	1.82588	0.912939	+	0.408096i	$0.133807\pi$
$464$	−18990.9	−1.90006
$465$	−3465.55	−0.345615
$466$	11838.6	1.17685
$467$	1442.23	0.142909	0.0714545	−	0.997444i	$-0.477236\pi$
$467$	1442.23	0.142909	0.0714545	+	0.997444i	$0.477236\pi$
$468$	−15981.4	−1.57851
$469$	9332.42	0.918830
$470$	−13971.8	−1.37122
$471$	479.619	0.0469207
$472$	−31574.5	−3.07910
$473$	0	0
$474$	6202.61	0.601045
$475$	−13872.4	−1.34002
$476$	12767.4	1.22940
$477$	−5062.98	−0.485992
$478$	−16478.4	−1.57679
$479$	271.103	0.0258602	0.0129301	−	0.999916i	$-0.495884\pi$
$479$	271.103	0.0258602	0.0129301	+	0.999916i	$0.495884\pi$
$480$	−19292.8	−1.83457
$481$	−5652.70	−0.535844
$482$	−10929.5	−1.03283
$483$	−921.765	−0.0868359
$484$	−17965.4	−1.68721
$485$	−17175.3	−1.60802
$486$	−14034.5	−1.30991
$487$	−12180.7	−1.13339	−0.566693	−	0.823929i	$-0.691778\pi$
$487$	−12180.7	−1.13339	−0.566693	+	0.823929i	$0.691778\pi$
$488$	23678.0	2.19642
$489$	1164.69	0.107707
$490$	25173.5	2.32086
$491$	11473.4	1.05456	0.527280	−	0.849692i	$-0.323212\pi$
$491$	11473.4	1.05456	0.527280	+	0.849692i	$0.323212\pi$
$492$	8239.27	0.754990
$493$	−4045.70	−0.369593
$494$	8490.00	0.773246
$495$	11353.5	1.03091
$496$	−36370.4	−3.29250
$497$	3038.33	0.274221
$498$	−9552.59	−0.859562
$499$	−14435.7	−1.29505	−0.647527	−	0.762042i	$-0.724197\pi$
$499$	−14435.7	−1.29505	−0.647527	+	0.762042i	$0.724197\pi$
$500$	55767.9	4.98804
$501$	2792.04	0.248981
$502$	−34700.8	−3.08520
$503$	−12471.4	−1.10551	−0.552756	−	0.833343i	$-0.686424\pi$
$503$	−12471.4	−1.10551	−0.552756	+	0.833343i	$0.686424\pi$
$504$	20928.3	1.84964
$505$	2053.27	0.180929
$506$	−8894.41	−0.781432
$507$	−1775.46	−0.155525
$508$	44538.3	3.88989
$509$	11300.9	0.984093	0.492046	−	0.870569i	$-0.336249\pi$
$509$	11300.9	0.984093	0.492046	+	0.870569i	$0.336249\pi$
$510$	−7424.02	−0.644591
$511$	1539.99	0.133317
$512$	−39215.4	−3.38495
$513$	3624.60	0.311949
$514$	−223.302	−0.0191623
$515$	36411.5	3.11550
$516$	0	0
$517$	−2995.65	−0.254833
$518$	11522.3	0.977338
$519$	4148.50	0.350865
$520$	−43310.9	−3.65252
$521$	11935.7	1.00367	0.501837	−	0.864962i	$-0.332658\pi$
$521$	11935.7	1.00367	0.501837	+	0.864962i	$0.332658\pi$
$522$	−10322.6	−0.865533
$523$	−635.431	−0.0531271	−0.0265635	−	0.999647i	$-0.508456\pi$
$523$	−635.431	−0.0531271	−0.0265635	+	0.999647i	$0.508456\pi$
$524$	−10707.8	−0.892696
$525$	3322.81	0.276227
$526$	−8238.71	−0.682937
$527$	−7748.11	−0.640442
$528$	−7471.87	−0.615855
$529$	−7234.56	−0.594605
$530$	−21357.6	−1.75041
$531$	−10126.4	−0.827586
$532$	−12747.7	−1.03888
$533$	8202.14	0.666556
$534$	−5704.61	−0.462290
$535$	9421.75	0.761379
$536$	−71100.7	−5.72963
$537$	3944.76	0.317000
$538$	18781.2	1.50505
$539$	5397.36	0.431319
$540$	−28781.6	−2.29363
$541$	−3261.58	−0.259199	−0.129599	−	0.991566i	$-0.541369\pi$
$541$	−3261.58	−0.259199	−0.129599	+	0.991566i	$0.541369\pi$
$542$	5879.45	0.465948
$543$	−260.963	−0.0206243
$544$	−43134.0	−3.39955
$545$	39983.3	3.14256
$546$	−2033.58	−0.159394
$547$	−5544.11	−0.433362	−0.216681	−	0.976242i	$-0.569523\pi$
$547$	−5544.11	−0.433362	−0.216681	+	0.976242i	$0.569523\pi$
$548$	55858.8	4.35433
$549$	7593.87	0.590343
$550$	32062.9	2.48576
$551$	4039.46	0.312317
$552$	7022.62	0.541490
$553$	−9271.24	−0.712936
$554$	48308.4	3.70474
$555$	−4935.35	−0.377466
$556$	13228.3	1.00901
$557$	4131.59	0.314292	0.157146	−	0.987575i	$-0.449771\pi$
$557$	4131.59	0.314292	0.157146	+	0.987575i	$0.449771\pi$
$558$	−19769.3	−1.49982
$559$	0	0
$560$	52090.0	3.93072
$561$	−1591.76	−0.119794
$562$	31504.8	2.36468
$563$	23026.8	1.72374	0.861870	−	0.507130i	$-0.169293\pi$
$563$	23026.8	1.72374	0.861870	+	0.507130i	$0.169293\pi$
$564$	3681.61	0.274865
$565$	−28288.2	−2.10636
$566$	32470.9	2.41140
$567$	6264.71	0.464009
$568$	−23148.0	−1.70998
$569$	21722.4	1.60044	0.800219	−	0.599708i	$-0.204717\pi$
$569$	21722.4	1.60044	0.800219	+	0.599708i	$0.204717\pi$
$570$	7412.58	0.544699
$571$	18609.0	1.36386	0.681928	−	0.731420i	$-0.261142\pi$
$571$	18609.0	1.36386	0.681928	+	0.731420i	$0.261142\pi$
$572$	−14454.4	−1.05659
$573$	−948.037	−0.0691183
$574$	−16719.0	−1.21575
$575$	−17780.6	−1.28957
$576$	−57696.8	−4.17367
$577$	14495.3	1.04584	0.522919	−	0.852382i	$-0.324843\pi$
$577$	14495.3	1.04584	0.522919	+	0.852382i	$0.324843\pi$
$578$	10478.6	0.754069
$579$	−3300.67	−0.236910
$580$	−32075.8	−2.29634
$581$	14278.6	1.01958
$582$	6143.96	0.437587
$583$	−4579.22	−0.325303
$584$	−11732.7	−0.831338
$585$	−13890.4	−0.981706
$586$	−6069.01	−0.427830
$587$	−20159.9	−1.41753	−0.708764	−	0.705445i	$-0.750747\pi$
$587$	−20159.9	−1.41753	−0.708764	+	0.705445i	$0.750747\pi$
$588$	−6633.29	−0.465225
$589$	7736.17	0.541194
$590$	−42717.1	−2.98074
$591$	−1532.74	−0.106681
$592$	−51795.6	−3.59592
$593$	6343.84	0.439309	0.219654	−	0.975578i	$-0.429507\pi$
$593$	6343.84	0.439309	0.219654	+	0.975578i	$0.429507\pi$
$594$	−8377.43	−0.578671
$595$	11096.9	0.764588
$596$	14641.5	1.00627
$597$	6709.57	0.459974
$598$	10881.9	0.744134
$599$	21188.0	1.44527	0.722636	−	0.691229i	$-0.242931\pi$
$599$	21188.0	1.44527	0.722636	+	0.691229i	$0.242931\pi$
$600$	−25315.4	−1.72250
$601$	23048.8	1.56436	0.782179	−	0.623053i	$-0.214108\pi$
$601$	23048.8	1.56436	0.782179	+	0.623053i	$0.214108\pi$
$602$	0	0
$603$	−22803.0	−1.53998
$604$	53522.2	3.60561
$605$	−15614.8	−1.04931
$606$	−734.495	−0.0492357
$607$	−24720.4	−1.65300	−0.826498	−	0.562940i	$-0.809670\pi$
$607$	−24720.4	−1.65300	−0.826498	+	0.562940i	$0.809670\pi$
$608$	43067.5	2.87273
$609$	−967.559	−0.0643801
$610$	32033.9	2.12625
$611$	3665.02	0.242669
$612$	−31196.1	−2.06050
$613$	−8105.30	−0.534045	−0.267023	−	0.963690i	$-0.586040\pi$
$613$	−8105.30	−0.534045	−0.267023	+	0.963690i	$0.586040\pi$
$614$	−16245.7	−1.06779
$615$	7161.25	0.469544
$616$	18928.6	1.23808
$617$	15419.9	1.00613	0.503064	−	0.864249i	$-0.332206\pi$
$617$	15419.9	1.00613	0.503064	+	0.864249i	$0.332206\pi$
$618$	−13025.1	−0.847812
$619$	−8709.17	−0.565511	−0.282755	−	0.959192i	$-0.591248\pi$
$619$	−8709.17	−0.565511	−0.282755	+	0.959192i	$0.591248\pi$
$620$	−61430.0	−3.97917
$621$	4645.74	0.300205
$622$	24318.7	1.56767
$623$	8526.87	0.548350
$624$	9141.45	0.586460
$625$	16824.7	1.07678
$626$	51374.4	3.28009
$627$	1589.31	0.101229
$628$	8501.67	0.540212
$629$	−11034.2	−0.699464
$630$	28313.8	1.79056
$631$	−12138.9	−0.765833	−0.382916	−	0.923783i	$-0.625080\pi$
$631$	−12138.9	−0.765833	−0.382916	+	0.923783i	$0.625080\pi$
$632$	70634.6	4.44572
$633$	1945.46	0.122156
$634$	10858.6	0.680203
$635$	38710.9	2.41920
$636$	5627.80	0.350876
$637$	−6603.40	−0.410732
$638$	−9336.29	−0.579353
$639$	−7423.90	−0.459601
$640$	−121109.	−7.48010
$641$	18811.4	1.15913	0.579567	−	0.814925i	$-0.303222\pi$
$641$	18811.4	1.15913	0.579567	+	0.814925i	$0.303222\pi$
$642$	−3370.35	−0.207192
$643$	−4950.02	−0.303592	−0.151796	−	0.988412i	$-0.548506\pi$
$643$	−4950.02	−0.303592	−0.151796	+	0.988412i	$0.548506\pi$
$644$	−16339.1	−0.999768
$645$	0	0
$646$	16572.7	1.00936
$647$	−21765.7	−1.32256	−0.661282	−	0.750137i	$-0.729988\pi$
$647$	−21765.7	−1.32256	−0.661282	+	0.750137i	$0.729988\pi$
$648$	−47728.7	−2.89346
$649$	−9158.83	−0.553953
$650$	−39227.3	−2.36711
$651$	−1853.02	−0.111560
$652$	20645.1	1.24007
$653$	2283.51	0.136846	0.0684231	−	0.997656i	$-0.478203\pi$
$653$	2283.51	0.136846	0.0684231	+	0.997656i	$0.478203\pi$
$654$	−14302.9	−0.855177
$655$	−9306.80	−0.555186
$656$	75156.1	4.47310
$657$	−3762.83	−0.223443
$658$	−7470.68	−0.442610
$659$	22450.8	1.32710	0.663551	−	0.748131i	$-0.269049\pi$
$659$	22450.8	1.32710	0.663551	+	0.748131i	$0.269049\pi$
$660$	−12620.1	−0.744297
$661$	3560.88	0.209534	0.104767	−	0.994497i	$-0.466590\pi$
$661$	3560.88	0.209534	0.104767	+	0.994497i	$0.466590\pi$
$662$	24119.9	1.41608
$663$	1947.44	0.114076
$664$	−108784.	−6.35788
$665$	−11079.8	−0.646101
$666$	−28153.8	−1.63804
$667$	5177.48	0.300559
$668$	49491.4	2.86659
$669$	−2168.33	−0.125310
$670$	−96191.9	−5.54659
$671$	6868.29	0.395152
$672$	−10315.8	−0.592175
$673$	3921.66	0.224619	0.112310	−	0.993673i	$-0.464175\pi$
$673$	3921.66	0.224619	0.112310	+	0.993673i	$0.464175\pi$
$674$	−12089.7	−0.690914
$675$	−16747.2	−0.954960
$676$	−31471.6	−1.79060
$677$	−18502.2	−1.05036	−0.525182	−	0.850990i	$-0.676003\pi$
$677$	−18502.2	−1.05036	−0.525182	+	0.850990i	$0.676003\pi$
$678$	10119.3	0.573198
$679$	−9183.59	−0.519048
$680$	−84543.9	−4.76781
$681$	−2413.78	−0.135824
$682$	−17880.4	−1.00392
$683$	−31340.6	−1.75580	−0.877902	−	0.478840i	$-0.841057\pi$
$683$	−31340.6	−1.75580	−0.877902	+	0.478840i	$0.841057\pi$
$684$	31148.0	1.74119
$685$	48550.3	2.70804
$686$	33116.3	1.84313
$687$	875.972	0.0486469
$688$	0	0
$689$	5602.44	0.309777
$690$	9500.89	0.524192
$691$	12379.8	0.681547	0.340773	−	0.940145i	$-0.389311\pi$
$691$	12379.8	0.681547	0.340773	+	0.940145i	$0.389311\pi$
$692$	73535.8	4.03961
$693$	6070.67	0.332765
$694$	−45549.8	−2.49142
$695$	11497.6	0.627521
$696$	7371.52	0.401461
$697$	16010.8	0.870088
$698$	−30607.1	−1.65973
$699$	−2711.36	−0.146714
$700$	58899.8	3.18029
$701$	−10286.0	−0.554202	−0.277101	−	0.960841i	$-0.589374\pi$
$701$	−10286.0	−0.554202	−0.277101	+	0.960841i	$0.589374\pi$
$702$	10249.4	0.551050
$703$	11017.2	0.591069
$704$	−52183.9	−2.79369
$705$	3199.91	0.170944
$706$	−36694.9	−1.95613
$707$	1097.87	0.0584015
$708$	11256.1	0.597500
$709$	−21727.8	−1.15092	−0.575462	−	0.817829i	$-0.695178\pi$
$709$	−21727.8	−1.15092	−0.575462	+	0.817829i	$0.695178\pi$
$710$	−31316.9	−1.65536
$711$	22653.5	1.19490
$712$	−64963.5	−3.41939
$713$	9915.65	0.520819
$714$	−3969.60	−0.208065
$715$	−12563.2	−0.657115
$716$	69924.5	3.64972
$717$	3774.00	0.196573
$718$	−9544.96	−0.496121
$719$	18857.2	0.978101	0.489050	−	0.872256i	$-0.337343\pi$
$719$	18857.2	0.978101	0.489050	+	0.872256i	$0.337343\pi$
$720$	−127278.	−6.58799
$721$	19469.1	1.00564
$722$	21254.7	1.09559
$723$	2503.14	0.128759
$724$	−4625.81	−0.237454
$725$	−18664.0	−0.956087
$726$	5585.74	0.285546
$727$	−27556.3	−1.40578	−0.702892	−	0.711297i	$-0.748108\pi$
$727$	−27556.3	−1.40578	−0.702892	+	0.711297i	$0.748108\pi$
$728$	−23158.2	−1.17898
$729$	−13052.9	−0.663157
$730$	−15873.1	−0.804781
$731$	0	0
$732$	−8441.04	−0.426215
$733$	−13260.9	−0.668214	−0.334107	−	0.942535i	$-0.608435\pi$
$733$	−13260.9	−0.668214	−0.334107	+	0.942535i	$0.608435\pi$
$734$	−42837.3	−2.15416
$735$	−5765.39	−0.289333
$736$	55200.7	2.76457
$737$	−20624.2	−1.03080
$738$	40851.5	2.03762
$739$	−20819.0	−1.03632	−0.518160	−	0.855284i	$-0.673383\pi$
$739$	−20819.0	−1.03632	−0.518160	+	0.855284i	$0.673383\pi$
$740$	−87483.4	−4.34588
$741$	−1944.43	−0.0963976
$742$	−11419.9	−0.565008
$743$	−155.122	−0.00765934	−0.00382967	−	0.999993i	$-0.501219\pi$
$743$	−155.122	−0.00765934	−0.00382967	+	0.999993i	$0.501219\pi$
$744$	14117.5	0.695664
$745$	12725.8	0.625822
$746$	−42025.8	−2.06257
$747$	−34888.5	−1.70884
$748$	−28215.4	−1.37922
$749$	5037.78	0.245763
$750$	−17339.2	−0.844182
$751$	2137.45	0.103857	0.0519286	−	0.998651i	$-0.483463\pi$
$751$	2137.45	0.103857	0.0519286	+	0.998651i	$0.483463\pi$
$752$	33582.5	1.62850
$753$	7947.39	0.384620
$754$	11422.5	0.551700
$755$	46519.3	2.24240
$756$	−15389.4	−0.740354
$757$	−23470.6	−1.12689	−0.563443	−	0.826155i	$-0.690524\pi$
$757$	−23470.6	−1.12689	−0.563443	+	0.826155i	$0.690524\pi$
$758$	−3982.72	−0.190843
$759$	2037.05	0.0974182
$760$	84413.5	4.02895
$761$	−6294.02	−0.299814	−0.149907	−	0.988700i	$-0.547897\pi$
$761$	−6294.02	−0.299814	−0.149907	+	0.988700i	$0.547897\pi$
$762$	−13847.7	−0.658331
$763$	21378.9	1.01438
$764$	−16804.8	−0.795780
$765$	−27114.4	−1.28147
$766$	42991.1	2.02785
$767$	11205.4	0.527513
$768$	20391.9	0.958113
$769$	19131.8	0.897155	0.448577	−	0.893744i	$-0.351931\pi$
$769$	19131.8	0.897155	0.448577	+	0.893744i	$0.351931\pi$
$770$	25608.5	1.19853
$771$	51.1421	0.00238889
$772$	−58507.2	−2.72762
$773$	19442.7	0.904665	0.452333	−	0.891849i	$-0.350592\pi$
$773$	19442.7	0.904665	0.452333	+	0.891849i	$0.350592\pi$
$774$	0	0
$775$	−35744.3	−1.65674
$776$	69966.7	3.23667
$777$	−2638.91	−0.121841
$778$	26473.7	1.21996
$779$	−15986.1	−0.735252
$780$	15440.0	0.708771
$781$	−6714.56	−0.307639
$782$	21241.6	0.971354
$783$	4876.55	0.222572
$784$	−60506.8	−2.75632
$785$	7389.31	0.335969
$786$	3329.23	0.151081
$787$	−9619.42	−0.435699	−0.217850	−	0.975982i	$-0.569904\pi$
$787$	−9619.42	−0.435699	−0.217850	+	0.975982i	$0.569904\pi$
$788$	−27169.2	−1.22825
$789$	1886.88	0.0851391
$790$	95561.3	4.30370
$791$	−15125.6	−0.679905
$792$	−46250.5	−2.07505
$793$	−8403.00	−0.376292
$794$	25208.2	1.12671
$795$	4891.46	0.218217
$796$	118933.	5.29582
$797$	−19389.8	−0.861758	−0.430879	−	0.902410i	$-0.641796\pi$
$797$	−19389.8	−0.861758	−0.430879	+	0.902410i	$0.641796\pi$
$798$	3963.48	0.175822
$799$	7154.21	0.316768
$800$	−198990.	−8.79419
$801$	−20834.7	−0.919049
$802$	−40979.4	−1.80428
$803$	−3403.30	−0.149564
$804$	25346.9	1.11183
$805$	−14201.3	−0.621776
$806$	21875.7	0.956005
$807$	−4301.39	−0.187628
$808$	−8364.35	−0.364179
$809$	1344.98	0.0584510	0.0292255	−	0.999573i	$-0.490696\pi$
$809$	1344.98	0.0584510	0.0292255	+	0.999573i	$0.490696\pi$
$810$	−64572.1	−2.80103
$811$	34793.3	1.50649	0.753243	−	0.657743i	$-0.228489\pi$
$811$	34793.3	1.50649	0.753243	+	0.657743i	$0.228489\pi$
$812$	−17150.8	−0.741227
$813$	−1346.55	−0.0580880
$814$	−25463.7	−1.09644
$815$	17943.9	0.771223
$816$	17844.3	0.765535
$817$	0	0
$818$	45255.9	1.93440
$819$	−7427.16	−0.316882
$820$	126939.	5.40600
$821$	−39432.0	−1.67623	−0.838116	−	0.545493i	$-0.816343\pi$
$821$	−39432.0	−1.67623	−0.838116	+	0.545493i	$0.816343\pi$
$822$	−17367.4	−0.736932
$823$	−18167.6	−0.769483	−0.384741	−	0.923024i	$-0.625709\pi$
$823$	−18167.6	−0.769483	−0.384741	+	0.923024i	$0.625709\pi$
$824$	−148329.	−6.27097
$825$	−7343.25	−0.309890
$826$	−22840.7	−0.962142
$827$	16418.4	0.690355	0.345177	−	0.938537i	$-0.387819\pi$
$827$	16418.4	0.690355	0.345177	+	0.938537i	$0.387819\pi$
$828$	39923.2	1.67564
$829$	−840.398	−0.0352090	−0.0176045	−	0.999845i	$-0.505604\pi$
$829$	−840.398	−0.0352090	−0.0176045	+	0.999845i	$0.505604\pi$
$830$	−147173.	−6.15477
$831$	−11063.9	−0.461856
$832$	63844.3	2.66034
$833$	−12890.0	−0.536148
$834$	−4112.91	−0.170765
$835$	43016.0	1.78279
$836$	28171.9	1.16548
$837$	9339.31	0.385680
$838$	52.4867	0.00216363
$839$	19652.8	0.808690	0.404345	−	0.914606i	$-0.367499\pi$
$839$	19652.8	0.808690	0.404345	+	0.914606i	$0.367499\pi$
$840$	−20219.3	−0.830514
$841$	−18954.3	−0.777166
$842$	84619.3	3.46339
$843$	−7215.43	−0.294795
$844$	34485.0	1.40642
$845$	−27353.9	−1.11361
$846$	18254.0	0.741825
$847$	−8349.19	−0.338703
$848$	51335.1	2.07884
$849$	−7436.69	−0.300620
$850$	−76572.6	−3.08991
$851$	14121.0	0.568816
$852$	8252.11	0.331822
$853$	10821.7	0.434384	0.217192	−	0.976129i	$-0.430310\pi$
$853$	10821.7	0.434384	0.217192	+	0.976129i	$0.430310\pi$
$854$	17128.4	0.686326
$855$	27072.6	1.08288
$856$	−38381.2	−1.53253
$857$	−2824.74	−0.112592	−0.0562960	−	0.998414i	$-0.517929\pi$
$857$	−2824.74	−0.112592	−0.0562960	+	0.998414i	$0.517929\pi$
$858$	4494.11	0.178819
$859$	−17086.4	−0.678672	−0.339336	−	0.940665i	$-0.610202\pi$
$859$	−17086.4	−0.678672	−0.339336	+	0.940665i	$0.610202\pi$
$860$	0	0
$861$	3829.09	0.151562
$862$	3002.41	0.118634
$863$	9239.60	0.364449	0.182225	−	0.983257i	$-0.441670\pi$
$863$	9239.60	0.364449	0.182225	+	0.983257i	$0.441670\pi$
$864$	51992.3	2.04724
$865$	63914.4	2.51232
$866$	22874.3	0.897575
$867$	−2399.87	−0.0940069
$868$	−32846.4	−1.28442
$869$	20489.0	0.799817
$870$	9972.90	0.388636
$871$	25232.6	0.981602
$872$	−162879.	−6.32544
$873$	22439.3	0.869938
$874$	−21208.9	−0.820825
$875$	25917.4	1.00134
$876$	4182.61	0.161321
$877$	27489.7	1.05845	0.529225	−	0.848482i	$-0.322483\pi$
$877$	27489.7	1.05845	0.529225	+	0.848482i	$0.322483\pi$
$878$	−72650.7	−2.79253
$879$	1389.96	0.0533359
$880$	−115116.	−4.40974
$881$	30826.3	1.17885	0.589424	−	0.807824i	$-0.299355\pi$
$881$	30826.3	1.17885	0.589424	+	0.807824i	$0.299355\pi$
$882$	−32888.8	−1.25558
$883$	9893.65	0.377064	0.188532	−	0.982067i	$-0.439627\pi$
$883$	9893.65	0.377064	0.188532	+	0.982067i	$0.439627\pi$
$884$	34520.1	1.31339
$885$	9783.34	0.371597
$886$	69787.0	2.64621
$887$	37494.5	1.41933	0.709663	−	0.704542i	$-0.248847\pi$
$887$	37494.5	1.41933	0.709663	+	0.704542i	$0.248847\pi$
$888$	20105.0	0.759775
$889$	20698.6	0.780887
$890$	−87888.9	−3.31016
$891$	−13844.7	−0.520555
$892$	−38435.6	−1.44274
$893$	−7143.18	−0.267679
$894$	−4552.28	−0.170303
$895$	60775.5	2.26983
$896$	−64756.7	−2.41448
$897$	−2492.23	−0.0927683
$898$	67390.3	2.50428
$899$	10408.3	0.386135
$900$	−143917.	−5.33025
$901$	10936.1	0.404366
$902$	36948.2	1.36390
$903$	0	0
$904$	115237.	4.23974
$905$	−4020.57	−0.147678
$906$	−16640.9	−0.610218
$907$	−15239.3	−0.557896	−0.278948	−	0.960306i	$-0.589986\pi$
$907$	−15239.3	−0.557896	−0.278948	+	0.960306i	$0.589986\pi$
$908$	−42786.4	−1.56378
$909$	−2682.56	−0.0978823
$910$	−31330.7	−1.14132
$911$	−32986.5	−1.19966	−0.599831	−	0.800127i	$-0.704766\pi$
$911$	−32986.5	−1.19966	−0.599831	+	0.800127i	$0.704766\pi$
$912$	−17816.8	−0.646901
$913$	−31554.9	−1.14383
$914$	−5464.05	−0.197740
$915$	−7336.61	−0.265072
$916$	15527.4	0.560086
$917$	−4976.31	−0.179206
$918$	20007.0	0.719313
$919$	−40520.3	−1.45445	−0.727226	−	0.686398i	$-0.759191\pi$
$919$	−40520.3	−1.45445	−0.727226	+	0.686398i	$0.759191\pi$
$920$	108195.	3.87726
$921$	3720.68	0.133117
$922$	−64952.2	−2.32005
$923$	8214.92	0.292955
$924$	−6747.91	−0.240249
$925$	−50904.0	−1.80942
$926$	−100252.	−3.55777
$927$	−47571.1	−1.68548
$928$	57943.2	2.04965
$929$	17342.0	0.612457	0.306229	−	0.951958i	$-0.400933\pi$
$929$	17342.0	0.612457	0.306229	+	0.951958i	$0.400933\pi$
$930$	19099.6	0.673441
$931$	12870.1	0.453062
$932$	−48061.3	−1.68916
$933$	−5569.63	−0.195436
$934$	−7948.52	−0.278462
$935$	−24523.7	−0.857764
$936$	56585.1	1.97601
$937$	−134.615	−0.00469337	−0.00234668	−	0.999997i	$-0.500747\pi$
$937$	−134.615	−0.00469337	−0.00234668	+	0.999997i	$0.500747\pi$
$938$	−51433.5	−1.79037
$939$	−11766.1	−0.408916
$940$	56721.3	1.96813
$941$	−14325.2	−0.496270	−0.248135	−	0.968726i	$-0.579818\pi$
$941$	−14325.2	−0.496270	−0.248135	+	0.968726i	$0.579818\pi$
$942$	−2643.31	−0.0914263
$943$	−20489.8	−0.707571
$944$	102674.	3.54001
$945$	−13375.9	−0.460441
$946$	0	0
$947$	−38764.9	−1.33019	−0.665095	−	0.746759i	$-0.731609\pi$
$947$	−38764.9	−1.33019	−0.665095	+	0.746759i	$0.731609\pi$
$948$	−25180.7	−0.862691
$949$	4163.76	0.142425
$950$	76454.6	2.61107
$951$	−2486.90	−0.0847983
$952$	−45205.3	−1.53898
$953$	−42964.8	−1.46041	−0.730203	−	0.683230i	$-0.760574\pi$
$953$	−42964.8	−1.46041	−0.730203	+	0.683230i	$0.760574\pi$
$954$	27903.5	0.946968
$955$	−14606.1	−0.494912
$956$	66897.5	2.26320
$957$	2138.26	0.0722258
$958$	−1494.12	−0.0503893
$959$	25959.7	0.874120
$960$	55742.2	1.87403
$961$	−9857.64	−0.330893
$962$	31153.6	1.04411
$963$	−12309.4	−0.411905
$964$	44370.3	1.48244
$965$	−50852.2	−1.69636
$966$	5080.09	0.169202
$967$	35355.5	1.17576	0.587878	−	0.808950i	$-0.299964\pi$
$967$	35355.5	1.17576	0.587878	+	0.808950i	$0.299964\pi$
$968$	63609.7	2.11208
$969$	−3795.58	−0.125832
$970$	94657.8	3.13328
$971$	−13699.8	−0.452778	−0.226389	−	0.974037i	$-0.572692\pi$
$971$	−13699.8	−0.452778	−0.226389	+	0.974037i	$0.572692\pi$
$972$	56975.7	1.88014
$973$	6147.70	0.202555
$974$	67131.0	2.20844
$975$	8984.09	0.295099
$976$	−76996.5	−2.52520
$977$	18726.7	0.613224	0.306612	−	0.951835i	$-0.400805\pi$
$977$	18726.7	0.613224	0.306612	+	0.951835i	$0.400805\pi$
$978$	−6418.89	−0.209871
$979$	−18844.0	−0.615175
$980$	−102197.	−3.33118
$981$	−52237.7	−1.70012
$982$	−63233.2	−2.05484
$983$	45198.0	1.46652	0.733262	−	0.679946i	$-0.237997\pi$
$983$	45198.0	1.46652	0.733262	+	0.679946i	$0.237997\pi$
$984$	−29172.6	−0.945111
$985$	−23614.4	−0.763875
$986$	22296.9	0.720161
$987$	1710.98	0.0551785
$988$	−34466.8	−1.10985
$989$	0	0
$990$	−62572.1	−2.00876
$991$	4117.21	0.131975	0.0659876	−	0.997820i	$-0.478980\pi$
$991$	4117.21	0.131975	0.0659876	+	0.997820i	$0.478980\pi$
$992$	110970.	3.55171
$993$	−5524.08	−0.176537
$994$	−16745.1	−0.534327
$995$	103372.	3.29358
$996$	38780.6	1.23375
$997$	3485.72	0.110726	0.0553629	−	0.998466i	$-0.482368\pi$
$997$	3485.72	0.110726	0.0553629	+	0.998466i	$0.482368\pi$
$998$	79559.2	2.52345
$999$	13300.3	0.421223

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.m.1.2	✓	110
43.42	odd	2	inner	1849.4.a.m.1.109	yes	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.m.1.2	✓	110	1.1	even	1	trivial
1849.4.a.m.1.109	yes	110	43.42	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q-5.51127 q^{2} +1.26223 q^{3} +22.3741 q^{4} +19.4467 q^{5} -6.95647 q^{6} +10.3981 q^{7} -79.2194 q^{8} -25.4068 q^{9} +O(q^{10})\)	\(q-5.51127 q^{2} +1.26223 q^{3} +22.3741 q^{4} +19.4467 q^{5} -6.95647 q^{6} +10.3981 q^{7} -79.2194 q^{8} -25.4068 q^{9} -107.176 q^{10} -22.9792 q^{11} +28.2411 q^{12} +28.1139 q^{13} -57.3065 q^{14} +24.5461 q^{15} +257.607 q^{16} +54.8789 q^{17} +140.024 q^{18} -54.7943 q^{19} +435.101 q^{20} +13.1247 q^{21} +126.645 q^{22} -70.2313 q^{23} -99.9928 q^{24} +253.172 q^{25} -154.943 q^{26} -66.1492 q^{27} +232.647 q^{28} -73.7205 q^{29} -135.280 q^{30} -141.186 q^{31} -785.985 q^{32} -29.0049 q^{33} -302.453 q^{34} +202.207 q^{35} -568.453 q^{36} -201.065 q^{37} +301.986 q^{38} +35.4861 q^{39} -1540.55 q^{40} +291.747 q^{41} -72.3338 q^{42} -514.138 q^{44} -494.077 q^{45} +387.064 q^{46} +130.363 q^{47} +325.158 q^{48} -234.880 q^{49} -1395.30 q^{50} +69.2696 q^{51} +629.022 q^{52} +199.277 q^{53} +364.566 q^{54} -446.869 q^{55} -823.728 q^{56} -69.1628 q^{57} +406.293 q^{58} +398.571 q^{59} +549.196 q^{60} -298.891 q^{61} +778.112 q^{62} -264.181 q^{63} +2270.92 q^{64} +546.721 q^{65} +159.854 q^{66} +897.516 q^{67} +1227.87 q^{68} -88.6478 q^{69} -1114.42 q^{70} +292.202 q^{71} +2012.71 q^{72} +148.103 q^{73} +1108.12 q^{74} +319.561 q^{75} -1225.97 q^{76} -238.939 q^{77} -195.573 q^{78} -891.632 q^{79} +5009.59 q^{80} +602.488 q^{81} -1607.90 q^{82} +1373.20 q^{83} +293.653 q^{84} +1067.21 q^{85} -93.0519 q^{87} +1820.40 q^{88} +820.045 q^{89} +2722.99 q^{90} +292.330 q^{91} -1571.36 q^{92} -178.208 q^{93} -718.468 q^{94} -1065.57 q^{95} -992.091 q^{96} -883.202 q^{97} +1294.49 q^{98} +583.828 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q + 492 q^{4} + 102 q^{6} + 1234 q^{9}+O(q^{10}) \) 110 * q + 492 * q^4 + 102 * q^6 + 1234 * q^9	\( 110 q + 492 q^{4} + 102 q^{6} + 1234 q^{9} + 102 q^{10} + 360 q^{11} + 166 q^{13} + 496 q^{14} + 540 q^{15} + 2204 q^{16} + 610 q^{17} + 896 q^{21} + 1508 q^{23} + 1086 q^{24} + 3168 q^{25} + 2312 q^{31} + 2760 q^{35} + 8334 q^{36} + 3626 q^{38} + 1462 q^{40} + 3598 q^{41} + 1596 q^{44} + 4448 q^{47} + 7194 q^{49} + 3620 q^{52} + 3818 q^{53} - 2570 q^{54} - 714 q^{56} + 3236 q^{57} + 3242 q^{58} + 8556 q^{59} + 178 q^{60} + 7308 q^{64} + 4202 q^{66} + 1992 q^{67} + 8994 q^{68} + 8256 q^{74} + 4784 q^{78} + 13752 q^{79} + 19678 q^{81} + 7620 q^{83} + 11390 q^{84} + 6012 q^{87} - 476 q^{90} + 8022 q^{92} + 7392 q^{95} + 16760 q^{96} - 1186 q^{97} + 11068 q^{99}+O(q^{100}) \) 110 * q + 492 * q^4 + 102 * q^6 + 1234 * q^9 + 102 * q^10 + 360 * q^11 + 166 * q^13 + 496 * q^14 + 540 * q^15 + 2204 * q^16 + 610 * q^17 + 896 * q^21 + 1508 * q^23 + 1086 * q^24 + 3168 * q^25 + 2312 * q^31 + 2760 * q^35 + 8334 * q^36 + 3626 * q^38 + 1462 * q^40 + 3598 * q^41 + 1596 * q^44 + 4448 * q^47 + 7194 * q^49 + 3620 * q^52 + 3818 * q^53 - 2570 * q^54 - 714 * q^56 + 3236 * q^57 + 3242 * q^58 + 8556 * q^59 + 178 * q^60 + 7308 * q^64 + 4202 * q^66 + 1992 * q^67 + 8994 * q^68 + 8256 * q^74 + 4784 * q^78 + 13752 * q^79 + 19678 * q^81 + 7620 * q^83 + 11390 * q^84 + 6012 * q^87 - 476 * q^90 + 8022 * q^92 + 7392 * q^95 + 16760 * q^96 - 1186 * q^97 + 11068 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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