LMFDB - Embedded newform 1849.4.a.m.1.109

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			1.109
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	$-0.0723724\pi$
$2$	5.51127	1.94853	0.974264	+	0.225411i	$0.0723724\pi$
$3$	−1.26223	−0.242915	−0.121458	−	0.992597i	$-0.538757\pi$
$3$	−1.26223	−0.242915	−0.121458	+	0.992597i	$0.538757\pi$
$4$	22.3741	2.79676
$5$	−19.4467	−1.73936	−0.869681	−	0.493614i	$-0.835675\pi$
$5$	−19.4467	−1.73936	−0.869681	+	0.493614i	$0.835675\pi$
$6$	−6.95647	−0.473328
$7$	−10.3981	−0.561442	−0.280721	−	0.959789i	$-0.590574\pi$
$7$	−10.3981	−0.561442	−0.280721	+	0.959789i	$0.590574\pi$
$8$	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	$-0.392679\pi$
$19$	54.7943	0.661615	0.330807	+	0.943698i	$0.392679\pi$
$20$	−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	$-0.424155\pi$
$29$	73.7205	0.472053	0.236027	+	0.971747i	$0.424155\pi$
$30$	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	$-0.352604\pi$
$37$	201.065	0.893373	0.446687	+	0.894690i	$0.352604\pi$
$38$	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	$-0.398438\pi$
$61$	298.891	0.627363	0.313681	+	0.949528i	$0.398438\pi$
$62$	−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	$-0.578529\pi$
$71$	−292.202	−0.488422	−0.244211	+	0.969722i	$0.578529\pi$
$72$	−2012.71	−3.29445
$73$	−148.103	−0.237455	−0.118727	−	0.992927i	$-0.537881\pi$
$73$	−148.103	−0.237455	−0.118727	+	0.992927i	$0.537881\pi$
$74$	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	$-0.662398\pi$
$89$	−820.045	−0.976681	−0.488340	+	0.872653i	$0.662398\pi$
$90$	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	$-0.292974\pi$
$113$	1454.66	1.21100	0.605498	+	0.795847i	$0.292974\pi$
$114$	−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	$-0.448981\pi$
$131$	478.581	0.319189	0.159595	+	0.987183i	$0.448981\pi$
$132$	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	$-0.783998\pi$
$137$	−2496.59	−1.55692	−0.778459	+	0.627695i	$0.783998\pi$
$138$	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	$-0.557577\pi$
$149$	−654.395	−0.359800	−0.179900	+	0.983685i	$0.557577\pi$
$150$	−1761.19	−0.958668
$151$	−2392.15	−1.28921	−0.644604	−	0.764517i	$-0.722978\pi$
$151$	−2392.15	−1.28921	−0.644604	+	0.764517i	$0.722978\pi$
$152$	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	$-0.530790\pi$
$157$	−379.978	−0.193157	−0.0965783	+	0.995325i	$0.530790\pi$
$158$	−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	$-0.571160\pi$
$163$	−922.723	−0.443394	−0.221697	+	0.975116i	$0.571160\pi$
$164$	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	$-0.726276\pi$
$179$	−3125.24	−1.30498	−0.652491	+	0.757797i	$0.726276\pi$
$180$	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	$-0.454560\pi$
$191$	751.083	0.284537	0.142268	+	0.989828i	$0.454560\pi$
$192$	−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	$-0.895682\pi$
$199$	−5315.66	−1.89355	−0.946777	+	0.321890i	$0.895682\pi$
$200$	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	$-0.580903\pi$
$211$	−1541.29	−0.502876	−0.251438	+	0.967873i	$0.580903\pi$
$212$	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	$-0.416960\pi$
$223$	1717.86	0.515860	0.257930	+	0.966164i	$0.416960\pi$
$224$	−8172.72	−2.43778
$225$	−6432.30	−1.90587
$226$	8017.00	2.35966
$227$	1912.32	0.559142	0.279571	−	0.960125i	$-0.409808\pi$
$227$	1912.32	0.559142	0.279571	+	0.960125i	$0.409808\pi$
$228$	−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	$-0.402351\pi$
$233$	2148.08	0.603971	0.301986	+	0.953313i	$0.402351\pi$
$234$	−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	$-0.585381\pi$
$241$	−1983.11	−0.530056	−0.265028	+	0.964241i	$0.585381\pi$
$242$	−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	$-0.501565\pi$
$257$	−40.5174	−0.00983426	−0.00491713	+	0.999988i	$0.501565\pi$
$258$	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	$-0.556072\pi$
$263$	−1494.88	−0.350489	−0.175244	+	0.984525i	$0.556072\pi$
$264$	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	$-0.100416\pi$
$277$	8765.38	1.90130	0.950651	+	0.310261i	$0.100416\pi$
$278$	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	$-0.181565\pi$
$313$	9321.71	1.68337	0.841684	+	0.539971i	$0.181565\pi$
$314$	−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	$-0.381626\pi$
$331$	4376.46	0.726743	0.363372	+	0.931644i	$0.381626\pi$
$332$	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	$-0.720779\pi$
$347$	−8264.85	−1.27862	−0.639309	+	0.768950i	$0.720779\pi$
$348$	−2081.95	−0.320702
$349$	−5553.54	−0.851789	−0.425895	−	0.904773i	$-0.640041\pi$
$349$	−5553.54	−0.851789	−0.425895	+	0.904773i	$0.640041\pi$
$350$	−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	$-0.677531\pi$
$373$	−7625.43	−1.05853	−0.529263	+	0.848458i	$0.677531\pi$
$374$	−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	$-0.325800\pi$
$383$	7800.58	1.04071	0.520354	+	0.853951i	$0.325800\pi$
$384$	−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	$-0.398650\pi$
$389$	4803.56	0.626093	0.313047	+	0.949738i	$0.398650\pi$
$390$	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	$-0.334665\pi$
$409$	8211.52	0.992747	0.496374	+	0.868109i	$0.334665\pi$
$410$	−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	$-0.499823\pi$
$419$	9.52353	0.00111039	0.000555197		1.00000i	$0.499823\pi$
$420$	−5710.57	−0.663446
$421$	15353.9	1.77744	0.888719	−	0.458451i	$-0.151596\pi$
$421$	15353.9	1.77744	0.888719	+	0.458451i	$0.151596\pi$
$422$	−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	$-0.426022\pi$
$433$	4150.46	0.460643	0.230321	+	0.973115i	$0.426022\pi$
$434$	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	$-0.277852\pi$
$449$	12227.7	1.28522	0.642608	+	0.766195i	$0.277852\pi$
$450$	−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	$-0.516158\pi$
$457$	−991.432	−0.101482	−0.0507409	+	0.998712i	$0.516158\pi$
$458$	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	$-0.866193\pi$
$463$	−18190.4	−1.82588	−0.912939	+	0.408096i	$0.866193\pi$
$464$	18990.9	1.90006
$465$	−3465.55	−0.345615
$466$	11838.6	1.17685
$467$	−1442.23	−0.142909	−0.0714545	−	0.997444i	$-0.522764\pi$
$467$	−1442.23	−0.142909	−0.0714545	+	0.997444i	$0.522764\pi$
$468$	−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	$-0.676788\pi$
$491$	−11473.4	−1.05456	−0.527280	+	0.849692i	$0.676788\pi$
$492$	−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	$-0.275803\pi$
$499$	14435.7	1.29505	0.647527	+	0.762042i	$0.275803\pi$
$500$	−55767.9	−4.98804
$501$	−2792.04	−0.248981
$502$	34700.8	3.08520
$503$	12471.4	1.10551	0.552756	−	0.833343i	$-0.313576\pi$
$503$	12471.4	1.10551	0.552756	+	0.833343i	$0.313576\pi$
$504$	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	$-0.667342\pi$
$521$	−11935.7	−1.00367	−0.501837	+	0.864962i	$0.667342\pi$
$522$	−10322.6	−0.865533
$523$	635.431	0.0531271	0.0265635	−	0.999647i	$-0.491544\pi$
$523$	635.431	0.0531271	0.0265635	+	0.999647i	$0.491544\pi$
$524$	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	$-0.738858\pi$
$571$	−18609.0	−1.36386	−0.681928	+	0.731420i	$0.738858\pi$
$572$	−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	$-0.675157\pi$
$577$	−14495.3	−1.04584	−0.522919	+	0.852382i	$0.675157\pi$
$578$	−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	$-0.249253\pi$
$587$	20159.9	1.41753	0.708764	+	0.705445i	$0.249253\pi$
$588$	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	$-0.570493\pi$
$593$	−6343.84	−0.439309	−0.219654	+	0.975578i	$0.570493\pi$
$594$	−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	$-0.785892\pi$
$601$	−23048.8	−1.56436	−0.782179	+	0.623053i	$0.785892\pi$
$602$	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	$-0.190330\pi$
$607$	24720.4	1.65300	0.826498	+	0.562940i	$0.190330\pi$
$608$	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	$-0.374920\pi$
$631$	12138.9	0.765833	0.382916	+	0.923783i	$0.374920\pi$
$632$	−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	$-0.696778\pi$
$641$	−18811.4	−1.15913	−0.579567	+	0.814925i	$0.696778\pi$
$642$	−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	$-0.270012\pi$
$647$	21765.7	1.32256	0.661282	+	0.750137i	$0.270012\pi$
$648$	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	$-0.521797\pi$
$653$	−2283.51	−0.136846	−0.0684231	+	0.997656i	$0.521797\pi$
$654$	−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	$-0.535825\pi$
$673$	−3921.66	−0.224619	−0.112310	+	0.993673i	$0.535825\pi$
$674$	12089.7	0.690914
$675$	16747.2	0.954960
$676$	−31471.6	−1.79060
$677$	18502.2	1.05036	0.525182	−	0.850990i	$-0.323997\pi$
$677$	18502.2	1.05036	0.525182	+	0.850990i	$0.323997\pi$
$678$	−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	$-0.610689\pi$
$691$	−12379.8	−0.681547	−0.340773	+	0.940145i	$0.610689\pi$
$692$	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	$-0.251892\pi$
$727$	27556.3	1.40578	0.702892	+	0.711297i	$0.251892\pi$
$728$	−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	$-0.391565\pi$
$733$	13260.9	0.668214	0.334107	+	0.942535i	$0.391565\pi$
$734$	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	$-0.326617\pi$
$739$	20819.0	1.03632	0.518160	+	0.855284i	$0.326617\pi$
$740$	−87483.4	−4.34588
$741$	−1944.43	−0.0963976
$742$	−11419.9	−0.565008
$743$	155.122	0.00765934	0.00382967	−	0.999993i	$-0.498781\pi$
$743$	155.122	0.00765934	0.00382967	+	0.999993i	$0.498781\pi$
$744$	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	$-0.516537\pi$
$751$	−2137.45	−0.103857	−0.0519286	+	0.998651i	$0.516537\pi$
$752$	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	$-0.309476\pi$
$757$	23470.6	1.12689	0.563443	+	0.826155i	$0.309476\pi$
$758$	3982.72	0.190843
$759$	−2037.05	−0.0974182
$760$	−84413.5	−4.02895
$761$	6294.02	0.299814	0.149907	−	0.988700i	$-0.452103\pi$
$761$	6294.02	0.299814	0.149907	+	0.988700i	$0.452103\pi$
$762$	−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	$-0.649408\pi$
$773$	−19442.7	−0.904665	−0.452333	+	0.891849i	$0.649408\pi$
$774$	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	$-0.771511\pi$
$811$	−34793.3	−1.50649	−0.753243	+	0.657743i	$0.771511\pi$
$812$	−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	$-0.494396\pi$
$829$	840.398	0.0352090	0.0176045	+	0.999845i	$0.494396\pi$
$830$	−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	$-0.632501\pi$
$839$	−19652.8	−0.808690	−0.404345	+	0.914606i	$0.632501\pi$
$840$	−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	$-0.389798\pi$
$859$	17086.4	0.678672	0.339336	+	0.940665i	$0.389798\pi$
$860$	0	0
$861$	3829.09	0.151562
$862$	−3002.41	−0.118634
$863$	−9239.60	−0.364449	−0.182225	−	0.983257i	$-0.558330\pi$
$863$	−9239.60	−0.364449	−0.182225	+	0.983257i	$0.558330\pi$
$864$	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	$-0.751153\pi$
$887$	−37494.5	−1.41933	−0.709663	+	0.704542i	$0.751153\pi$
$888$	−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	$-0.295234\pi$
$911$	32986.5	1.19966	0.599831	+	0.800127i	$0.295234\pi$
$912$	−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	$-0.599067\pi$
$929$	−17342.0	−0.612457	−0.306229	+	0.951958i	$0.599067\pi$
$930$	−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	$-0.499253\pi$
$937$	134.615	0.00469337	0.00234668	+	0.999997i	$0.499253\pi$
$938$	−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	$-0.239426\pi$
$953$	42964.8	1.46041	0.730203	+	0.683230i	$0.239426\pi$
$954$	−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	$-0.762003\pi$
$983$	−45198.0	−1.46652	−0.733262	+	0.679946i	$0.762003\pi$
$984$	−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	$-0.521020\pi$
$991$	−4117.21	−0.131975	−0.0659876	+	0.997820i	$0.521020\pi$
$992$	−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	$-0.517632\pi$
$997$	−3485.72	−0.110726	−0.0553629	+	0.998466i	$0.517632\pi$
$998$	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.1.109	yes	110
43.42	odd	2	inner	1849.4.a.m.1.2	✓	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.m.1.2	✓	110	43.42	odd	2	inner
1849.4.a.m.1.109	yes	110	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 $\F_{q}$

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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