LMFDB - Embedded newform 1849.4.a.m.1.1

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			1.1
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)

$f(q)$	$=$	$q-5.53180 q^{2} -6.46364 q^{3} +22.6009 q^{4} +8.28125 q^{5} +35.7556 q^{6} -25.9073 q^{7} -80.7691 q^{8} +14.7786 q^{9} +O(q^{10})$	\(q-5.53180 q^{2} -6.46364 q^{3} +22.6009 q^{4} +8.28125 q^{5} +35.7556 q^{6} -25.9073 q^{7} -80.7691 q^{8} +14.7786 q^{9} -45.8102 q^{10} +1.13801 q^{11} -146.084 q^{12} -22.9917 q^{13} +143.314 q^{14} -53.5270 q^{15} +265.992 q^{16} +79.3978 q^{17} -81.7523 q^{18} +17.3266 q^{19} +187.163 q^{20} +167.456 q^{21} -6.29527 q^{22} -162.461 q^{23} +522.062 q^{24} -56.4209 q^{25} +127.186 q^{26} +78.9947 q^{27} -585.528 q^{28} -242.090 q^{29} +296.101 q^{30} +57.4002 q^{31} -825.264 q^{32} -7.35570 q^{33} -439.213 q^{34} -214.545 q^{35} +334.009 q^{36} -64.1627 q^{37} -95.8471 q^{38} +148.610 q^{39} -668.869 q^{40} +1.97486 q^{41} -926.331 q^{42} +25.7201 q^{44} +122.385 q^{45} +898.703 q^{46} +228.071 q^{47} -1719.28 q^{48} +328.189 q^{49} +312.110 q^{50} -513.198 q^{51} -519.633 q^{52} -568.321 q^{53} -436.983 q^{54} +9.42417 q^{55} +2092.51 q^{56} -111.993 q^{57} +1339.19 q^{58} -1.47509 q^{59} -1209.76 q^{60} +14.6908 q^{61} -317.527 q^{62} -382.874 q^{63} +2437.26 q^{64} -190.400 q^{65} +40.6903 q^{66} -521.511 q^{67} +1794.46 q^{68} +1050.09 q^{69} +1186.82 q^{70} +708.351 q^{71} -1193.65 q^{72} -592.620 q^{73} +354.936 q^{74} +364.684 q^{75} +391.595 q^{76} -29.4829 q^{77} -822.082 q^{78} +831.348 q^{79} +2202.75 q^{80} -909.615 q^{81} -10.9245 q^{82} -130.281 q^{83} +3784.64 q^{84} +657.513 q^{85} +1564.78 q^{87} -91.9164 q^{88} +458.740 q^{89} -677.011 q^{90} +595.654 q^{91} -3671.76 q^{92} -371.014 q^{93} -1261.65 q^{94} +143.485 q^{95} +5334.20 q^{96} +79.6178 q^{97} -1815.48 q^{98} +16.8182 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.53180	−1.95579	−0.977894	−	0.209100i	$-0.932946\pi$
$2$	−5.53180	−1.95579	−0.977894	+	0.209100i	$0.932946\pi$
$3$	−6.46364	−1.24393	−0.621964	−	0.783046i	$-0.713665\pi$
$3$	−6.46364	−1.24393	−0.621964	+	0.783046i	$0.713665\pi$
$4$	22.6009	2.82511
$5$	8.28125	0.740697	0.370349	−	0.928893i	$-0.379238\pi$
$5$	8.28125	0.740697	0.370349	+	0.928893i	$0.379238\pi$
$6$	35.7556	2.43286
$7$	−25.9073	−1.39886	−0.699432	−	0.714699i	$-0.746564\pi$
$7$	−25.9073	−1.39886	−0.699432	+	0.714699i	$0.746564\pi$
$8$	−80.7691	−3.56953
$9$	14.7786	0.547355
$10$	−45.8102	−1.44865
$11$	1.13801	0.0311931	0.0155965	−	0.999878i	$-0.495035\pi$
$11$	1.13801	0.0311931	0.0155965	+	0.999878i	$0.495035\pi$
$12$	−146.084	−3.51423
$13$	−22.9917	−0.490520	−0.245260	−	0.969457i	$-0.578873\pi$
$13$	−22.9917	−0.490520	−0.245260	+	0.969457i	$0.578873\pi$
$14$	143.314	2.73588
$15$	−53.5270	−0.921374
$16$	265.992	4.15613
$17$	79.3978	1.13275	0.566376	−	0.824147i	$-0.308345\pi$
$17$	79.3978	1.13275	0.566376	+	0.824147i	$0.308345\pi$
$18$	−81.7523	−1.07051
$19$	17.3266	0.209210	0.104605	−	0.994514i	$-0.466642\pi$
$19$	17.3266	0.209210	0.104605	+	0.994514i	$0.466642\pi$
$20$	187.163	2.09255
$21$	167.456	1.74009
$22$	−6.29527	−0.0610071
$23$	−162.461	−1.47285	−0.736424	−	0.676521i	$-0.763487\pi$
$23$	−162.461	−1.47285	−0.736424	+	0.676521i	$0.763487\pi$
$24$	522.062	4.44023
$25$	−56.4209	−0.451368
$26$	127.186	0.959353
$27$	78.9947	0.563057
$28$	−585.528	−3.95194
$29$	−242.090	−1.55017	−0.775084	−	0.631858i	$-0.782293\pi$
$29$	−242.090	−1.55017	−0.775084	+	0.631858i	$0.782293\pi$
$30$	296.101	1.80201
$31$	57.4002	0.332561	0.166280	−	0.986079i	$-0.446824\pi$
$31$	57.4002	0.332561	0.166280	+	0.986079i	$0.446824\pi$
$32$	−825.264	−4.55898
$33$	−7.35570	−0.0388019
$34$	−439.213	−2.21542
$35$	−214.545	−1.03613
$36$	334.009	1.54634
$37$	−64.1627	−0.285089	−0.142544	−	0.989788i	$-0.545528\pi$
$37$	−64.1627	−0.285089	−0.142544	+	0.989788i	$0.545528\pi$
$38$	−95.8471	−0.409170
$39$	148.610	0.610171
$40$	−668.869	−2.64394
$41$	1.97486	0.00752248	0.00376124	−	0.999993i	$-0.498803\pi$
$41$	1.97486	0.00752248	0.00376124	+	0.999993i	$0.498803\pi$
$42$	−926.331	−3.40324
$43$	0	0
$43$	0	0
$44$	25.7201	0.0881238
$45$	122.385	0.405425
$46$	898.703	2.88058
$47$	228.071	0.707822	0.353911	−	0.935279i	$-0.384852\pi$
$47$	228.071	0.707822	0.353911	+	0.935279i	$0.384852\pi$
$48$	−1719.28	−5.16992
$49$	328.189	0.956821
$50$	312.110	0.882779
$51$	−513.198	−1.40906
$52$	−519.633	−1.38577
$53$	−568.321	−1.47292	−0.736461	−	0.676480i	$-0.763505\pi$
$53$	−568.321	−1.47292	−0.736461	+	0.676480i	$0.763505\pi$
$54$	−436.983	−1.10122
$55$	9.42417	0.0231046
$56$	2092.51	4.99328
$57$	−111.993	−0.260242
$58$	1339.19	3.03180
$59$	−1.47509	−0.00325493	−0.00162747	−	0.999999i	$-0.500518\pi$
$59$	−1.47509	−0.00325493	−0.00162747	+	0.999999i	$0.500518\pi$
$60$	−1209.76	−2.60298
$61$	14.6908	0.0308354	0.0154177	−	0.999881i	$-0.495092\pi$
$61$	14.6908	0.0308354	0.0154177	+	0.999881i	$0.495092\pi$
$62$	−317.527	−0.650418
$63$	−382.874	−0.765676
$64$	2437.26	4.76027
$65$	−190.400	−0.363327
$66$	40.6903	0.0758884
$67$	−521.511	−0.950935	−0.475468	−	0.879733i	$-0.657721\pi$
$67$	−521.511	−0.950935	−0.475468	+	0.879733i	$0.657721\pi$
$68$	1794.46	3.20015
$69$	1050.09	1.83212
$70$	1186.82	2.02646
$71$	708.351	1.18402	0.592012	−	0.805929i	$-0.298334\pi$
$71$	708.351	1.18402	0.592012	+	0.805929i	$0.298334\pi$
$72$	−1193.65	−1.95380
$73$	−592.620	−0.950150	−0.475075	−	0.879945i	$-0.657579\pi$
$73$	−592.620	−0.950150	−0.475075	+	0.879945i	$0.657579\pi$
$74$	354.936	0.557573
$75$	364.684	0.561468
$76$	391.595	0.591040
$77$	−29.4829	−0.0436349
$78$	−822.082	−1.19337
$79$	831.348	1.18397	0.591987	−	0.805947i	$-0.298344\pi$
$79$	831.348	1.18397	0.591987	+	0.805947i	$0.298344\pi$
$80$	2202.75	3.07843
$81$	−909.615	−1.24776
$82$	−10.9245	−0.0147124
$83$	−130.281	−0.172292	−0.0861461	−	0.996283i	$-0.527455\pi$
$83$	−130.281	−0.172292	−0.0861461	+	0.996283i	$0.527455\pi$
$84$	3784.64	4.91593
$85$	657.513	0.839027
$86$	0	0
$87$	1564.78	1.92830
$88$	−91.9164	−0.111345
$89$	458.740	0.546364	0.273182	−	0.961962i	$-0.411924\pi$
$89$	458.740	0.546364	0.273182	+	0.961962i	$0.411924\pi$
$90$	−677.011	−0.792925
$91$	595.654	0.686171
$92$	−3671.76	−4.16095
$93$	−371.014	−0.413681
$94$	−1261.65	−1.38435
$95$	143.485	0.154961
$96$	5334.20	5.67104
$97$	79.6178	0.0833398	0.0416699	−	0.999131i	$-0.486732\pi$
$97$	79.6178	0.0833398	0.0416699	+	0.999131i	$0.486732\pi$
$98$	−1815.48	−1.87134
$99$	16.8182	0.0170737
$100$	−1275.16	−1.27516
$101$	−870.099	−0.857208	−0.428604	−	0.903492i	$-0.640994\pi$
$101$	−870.099	−0.857208	−0.428604	+	0.903492i	$0.640994\pi$
$102$	2838.91	2.75583
$103$	−1935.83	−1.85187	−0.925935	−	0.377683i	$-0.876721\pi$
$103$	−1935.83	−1.85187	−0.925935	+	0.377683i	$0.876721\pi$
$104$	1857.02	1.75092
$105$	1386.74	1.28888
$106$	3143.84	2.88073
$107$	593.787	0.536482	0.268241	−	0.963352i	$-0.413558\pi$
$107$	593.787	0.536482	0.268241	+	0.963352i	$0.413558\pi$
$108$	1785.35	1.59070
$109$	316.510	0.278130	0.139065	−	0.990283i	$-0.455590\pi$
$109$	316.510	0.278130	0.139065	+	0.990283i	$0.455590\pi$
$110$	−52.1327	−0.0451878
$111$	414.724	0.354630
$112$	−6891.15	−5.81386
$113$	−1123.20	−0.935057	−0.467528	−	0.883978i	$-0.654855\pi$
$113$	−1123.20	−0.935057	−0.467528	+	0.883978i	$0.654855\pi$
$114$	619.521	0.508978
$115$	−1345.38	−1.09093
$116$	−5471.43	−4.37939
$117$	−339.785	−0.268489
$118$	8.15993	0.00636596
$119$	−2056.98	−1.58457
$120$	4323.33	3.28887
$121$	−1329.70	−0.999027
$122$	−81.2665	−0.0603076
$123$	−12.7648	−0.00935741
$124$	1297.29	0.939520
$125$	−1502.39	−1.07502
$126$	2117.98	1.49750
$127$	16.3974	0.0114569	0.00572847	−	0.999984i	$-0.498177\pi$
$127$	16.3974	0.0114569	0.00572847	+	0.999984i	$0.498177\pi$
$128$	−6880.34	−4.75111
$129$	0	0
$130$	1053.26	0.710590
$131$	605.734	0.403994	0.201997	−	0.979386i	$-0.435257\pi$
$131$	605.734	0.403994	0.201997	+	0.979386i	$0.435257\pi$
$132$	−166.245	−0.109620
$133$	−448.885	−0.292656
$134$	2884.89	1.85983
$135$	654.175	0.417055
$136$	−6412.89	−4.04339
$137$	865.018	0.539441	0.269721	−	0.962939i	$-0.413069\pi$
$137$	865.018	0.539441	0.269721	+	0.962939i	$0.413069\pi$
$138$	−5808.89	−3.58323
$139$	−1372.00	−0.837206	−0.418603	−	0.908169i	$-0.637480\pi$
$139$	−1372.00	−0.837206	−0.418603	+	0.908169i	$0.637480\pi$
$140$	−4848.90	−2.92719
$141$	−1474.17	−0.880479
$142$	−3918.46	−2.31570
$143$	−26.1649	−0.0153008
$144$	3930.99	2.27488
$145$	−2004.80	−1.14821
$146$	3278.26	1.85829
$147$	−2121.30	−1.19022
$148$	−1450.13	−0.805406
$149$	−2920.59	−1.60580	−0.802899	−	0.596115i	$-0.796710\pi$
$149$	−2920.59	−1.60580	−0.802899	+	0.596115i	$0.796710\pi$
$150$	−2017.36	−1.09811
$151$	1467.00	0.790612	0.395306	−	0.918550i	$-0.370639\pi$
$151$	1467.00	0.790612	0.395306	+	0.918550i	$0.370639\pi$
$152$	−1399.45	−0.746779
$153$	1173.39	0.620018
$154$	163.094	0.0853406
$155$	475.345	0.246327
$156$	3358.72	1.72380
$157$	2551.74	1.29714	0.648570	−	0.761155i	$-0.275368\pi$
$157$	2551.74	1.29714	0.648570	+	0.761155i	$0.275368\pi$
$158$	−4598.86	−2.31560
$159$	3673.42	1.83221
$160$	−6834.21	−3.37683
$161$	4208.93	2.06031
$162$	5031.81	2.44035
$163$	−3077.50	−1.47883	−0.739413	−	0.673252i	$-0.764897\pi$
$163$	−3077.50	−1.47883	−0.739413	+	0.673252i	$0.764897\pi$
$164$	44.6336	0.0212518
$165$	−60.9144	−0.0287405
$166$	720.692	0.336967
$167$	3280.45	1.52005	0.760027	−	0.649892i	$-0.225186\pi$
$167$	3280.45	1.52005	0.760027	+	0.649892i	$0.225186\pi$
$168$	−13525.2	−6.21128
$169$	−1668.38	−0.759390
$170$	−3637.23	−1.64096
$171$	256.062	0.114512
$172$	0	0
$173$	−3002.63	−1.31957	−0.659786	−	0.751453i	$-0.729353\pi$
$173$	−3002.63	−1.31957	−0.659786	+	0.751453i	$0.729353\pi$
$174$	−8656.05	−3.77134
$175$	1461.72	0.631402
$176$	302.703	0.129642
$177$	9.53447	0.00404890
$178$	−2537.66	−1.06857
$179$	1708.92	0.713578	0.356789	−	0.934185i	$-0.383871\pi$
$179$	1708.92	0.713578	0.356789	+	0.934185i	$0.383871\pi$
$180$	2766.01	1.14537
$181$	−2156.22	−0.885472	−0.442736	−	0.896652i	$-0.645992\pi$
$181$	−2156.22	−0.885472	−0.442736	+	0.896652i	$0.645992\pi$
$182$	−3295.04	−1.34200
$183$	−94.9559	−0.0383570
$184$	13121.8	5.25737
$185$	−531.347	−0.211164
$186$	2052.38	0.809073
$187$	90.3557	0.0353340
$188$	5154.61	1.99967
$189$	−2046.54	−0.787640
$190$	−793.734	−0.303071
$191$	−649.327	−0.245988	−0.122994	−	0.992407i	$-0.539250\pi$
$191$	−649.327	−0.245988	−0.122994	+	0.992407i	$0.539250\pi$
$192$	−15753.6	−5.92144
$193$	3205.26	1.19544	0.597719	−	0.801706i	$-0.296074\pi$
$193$	3205.26	1.19544	0.597719	+	0.801706i	$0.296074\pi$
$194$	−440.430	−0.162995
$195$	1230.68	0.451952
$196$	7417.37	2.70312
$197$	−2017.66	−0.729709	−0.364854	−	0.931065i	$-0.618881\pi$
$197$	−2017.66	−0.729709	−0.364854	+	0.931065i	$0.618881\pi$
$198$	−93.0352	−0.0333925
$199$	−5098.07	−1.81604	−0.908022	−	0.418924i	$-0.862408\pi$
$199$	−5098.07	−1.81604	−0.908022	+	0.418924i	$0.862408\pi$
$200$	4557.07	1.61117
$201$	3370.85	1.18289
$202$	4813.22	1.67652
$203$	6271.89	2.16848
$204$	−11598.7	−3.98075
$205$	16.3543	0.00557188
$206$	10708.6	3.62187
$207$	−2400.95	−0.806171
$208$	−6115.62	−2.03866
$209$	19.7178	0.00652589
$210$	−7671.18	−2.52077
$211$	382.902	0.124929	0.0624646	−	0.998047i	$-0.480104\pi$
$211$	382.902	0.124929	0.0624646	+	0.998047i	$0.480104\pi$
$212$	−12844.5	−4.16117
$213$	−4578.52	−1.47284
$214$	−3284.72	−1.04925
$215$	0	0
$216$	−6380.34	−2.00985
$217$	−1487.09	−0.465207
$218$	−1750.87	−0.543963
$219$	3830.48	1.18192
$220$	212.994	0.0652731
$221$	−1825.49	−0.555638
$222$	−2294.17	−0.693581
$223$	−3420.81	−1.02724	−0.513620	−	0.858018i	$-0.671696\pi$
$223$	−3420.81	−1.02724	−0.513620	+	0.858018i	$0.671696\pi$
$224$	21380.4	6.37740
$225$	−833.822	−0.247058
$226$	6213.30	1.82877
$227$	−4076.92	−1.19205	−0.596024	−	0.802967i	$-0.703254\pi$
$227$	−4076.92	−1.19205	−0.596024	+	0.802967i	$0.703254\pi$
$228$	−2531.13	−0.735211
$229$	−5959.29	−1.71966	−0.859828	−	0.510584i	$-0.829429\pi$
$229$	−5959.29	−1.71966	−0.859828	+	0.510584i	$0.829429\pi$
$230$	7442.39	2.13364
$231$	190.567	0.0542786
$232$	19553.4	5.53337
$233$	−4161.25	−1.17001	−0.585006	−	0.811029i	$-0.698908\pi$
$233$	−4161.25	−1.17001	−0.585006	+	0.811029i	$0.698908\pi$
$234$	1879.63	0.525107
$235$	1888.72	0.524282
$236$	−33.3384	−0.00919553
$237$	−5373.53	−1.47278
$238$	11378.8	3.09908
$239$	−492.696	−0.133347	−0.0666733	−	0.997775i	$-0.521239\pi$
$239$	−492.696	−0.133347	−0.0666733	+	0.997775i	$0.521239\pi$
$240$	−14237.8	−3.82935
$241$	−5763.04	−1.54037	−0.770187	−	0.637818i	$-0.779837\pi$
$241$	−5763.04	−1.54037	−0.770187	+	0.637818i	$0.779837\pi$
$242$	7355.67	1.95389
$243$	3746.56	0.989062
$244$	332.024	0.0871134
$245$	2717.82	0.708714
$246$	70.6123	0.0183011
$247$	−398.367	−0.102622
$248$	−4636.16	−1.18708
$249$	842.092	0.214319
$250$	8310.94	2.10252
$251$	−2116.05	−0.532126	−0.266063	−	0.963956i	$-0.585723\pi$
$251$	−2116.05	−0.532126	−0.266063	+	0.963956i	$0.585723\pi$
$252$	−8653.28	−2.16312
$253$	−184.883	−0.0459427
$254$	−90.7070	−0.0224073
$255$	−4249.92	−1.04369
$256$	18562.6	4.53189
$257$	7383.90	1.79220	0.896099	−	0.443855i	$-0.146389\pi$
$257$	7383.90	1.79220	0.896099	+	0.443855i	$0.146389\pi$
$258$	0	0
$259$	1662.28	0.398800
$260$	−4303.21	−1.02644
$261$	−3577.74	−0.848493
$262$	−3350.80	−0.790127
$263$	1291.08	0.302705	0.151353	−	0.988480i	$-0.451637\pi$
$263$	1291.08	0.302705	0.151353	+	0.988480i	$0.451637\pi$
$264$	594.114	0.138504
$265$	−4706.41	−1.09099
$266$	2483.14	0.572373
$267$	−2965.13	−0.679637
$268$	−11786.6	−2.68649
$269$	3341.36	0.757347	0.378673	−	0.925530i	$-0.376380\pi$
$269$	3341.36	0.757347	0.378673	+	0.925530i	$0.376380\pi$
$270$	−3618.77	−0.815671
$271$	4989.16	1.11834	0.559169	−	0.829054i	$-0.311120\pi$
$271$	4989.16	1.11834	0.559169	+	0.829054i	$0.311120\pi$
$272$	21119.2	4.70786
$273$	−3850.09	−0.853546
$274$	−4785.11	−1.05503
$275$	−64.2078	−0.0140795
$276$	23732.9	5.17592
$277$	5126.05	1.11189	0.555947	−	0.831218i	$-0.312356\pi$
$277$	5126.05	1.11189	0.555947	+	0.831218i	$0.312356\pi$
$278$	7589.64	1.63740
$279$	848.294	0.182029
$280$	17328.6	3.69851
$281$	4263.19	0.905056	0.452528	−	0.891750i	$-0.350522\pi$
$281$	4263.19	0.905056	0.452528	+	0.891750i	$0.350522\pi$
$282$	8154.83	1.72203
$283$	−3931.33	−0.825772	−0.412886	−	0.910783i	$-0.635479\pi$
$283$	−3931.33	−0.825772	−0.412886	+	0.910783i	$0.635479\pi$
$284$	16009.3	3.34500
$285$	−927.438	−0.192760
$286$	144.739	0.0299252
$287$	−51.1634	−0.0105229
$288$	−12196.2	−2.49538
$289$	1391.01	0.283129
$290$	11090.2	2.24565
$291$	−514.620	−0.103669
$292$	−13393.7	−2.68428
$293$	−4950.75	−0.987120	−0.493560	−	0.869712i	$-0.664305\pi$
$293$	−4950.75	−0.987120	−0.493560	+	0.869712i	$0.664305\pi$
$294$	11734.6	2.32781
$295$	−12.2156	−0.00241092
$296$	5182.37	1.01763
$297$	89.8971	0.0175635
$298$	16156.1	3.14060
$299$	3735.26	0.722461
$300$	8242.18	1.58621
$301$	0	0
$302$	−8115.13	−1.54627
$303$	5624.00	1.06630
$304$	4608.73	0.869502
$305$	121.658	0.0228397
$306$	−6490.95	−1.21262
$307$	2585.13	0.480591	0.240295	−	0.970700i	$-0.422756\pi$
$307$	2585.13	0.480591	0.240295	+	0.970700i	$0.422756\pi$
$308$	−666.339	−0.123273
$309$	12512.5	2.30359
$310$	−2629.52	−0.481763
$311$	7231.31	1.31849	0.659245	−	0.751929i	$-0.270876\pi$
$311$	7231.31	1.31849	0.659245	+	0.751929i	$0.270876\pi$
$312$	−12003.1	−2.17802
$313$	−7307.62	−1.31965	−0.659826	−	0.751418i	$-0.729370\pi$
$313$	−7307.62	−1.31965	−0.659826	+	0.751418i	$0.729370\pi$
$314$	−14115.7	−2.53693
$315$	−3170.67	−0.567134
$316$	18789.2	3.34486
$317$	735.218	0.130265	0.0651324	−	0.997877i	$-0.479253\pi$
$317$	735.218	0.130265	0.0651324	+	0.997877i	$0.479253\pi$
$318$	−20320.6	−3.58341
$319$	−275.501	−0.0483545
$320$	20183.6	3.52592
$321$	−3838.03	−0.667345
$322$	−23283.0	−4.02954
$323$	1375.69	0.236983
$324$	−20558.1	−3.52505
$325$	1297.22	0.221405
$326$	17024.2	2.89227
$327$	−2045.80	−0.345973
$328$	−159.508	−0.0268517
$329$	−5908.72	−0.990147
$330$	336.967	0.0562103
$331$	454.622	0.0754933	0.0377467	−	0.999287i	$-0.487982\pi$
$331$	454.622	0.0754933	0.0377467	+	0.999287i	$0.487982\pi$
$332$	−2944.47	−0.486744
$333$	−948.234	−0.156045
$334$	−18146.8	−2.97290
$335$	−4318.76	−0.704355
$336$	44541.9	7.23202
$337$	−3821.78	−0.617762	−0.308881	−	0.951101i	$-0.599954\pi$
$337$	−3821.78	−0.617762	−0.308881	+	0.951101i	$0.599954\pi$
$338$	9229.15	1.48521
$339$	7259.93	1.16314
$340$	14860.4	2.37034
$341$	65.3222	0.0103736
$342$	−1416.49	−0.223961
$343$	383.701	0.0604021
$344$	0	0
$345$	8696.05	1.35704
$346$	16610.0	2.58080
$347$	11364.6	1.75817	0.879083	−	0.476669i	$-0.158156\pi$
$347$	11364.6	1.75817	0.879083	+	0.476669i	$0.158156\pi$
$348$	35365.3	5.44765
$349$	1064.34	0.163245	0.0816227	−	0.996663i	$-0.473990\pi$
$349$	1064.34	0.163245	0.0816227	+	0.996663i	$0.473990\pi$
$350$	−8085.93	−1.23489
$351$	−1816.23	−0.276191
$352$	−939.161	−0.142209
$353$	−2573.50	−0.388027	−0.194014	−	0.980999i	$-0.562151\pi$
$353$	−2573.50	−0.388027	−0.194014	+	0.980999i	$0.562151\pi$
$354$	−52.7428	−0.00791879
$355$	5866.03	0.877004
$356$	10367.9	1.54354
$357$	13295.6	1.97109
$358$	−9453.40	−1.39561
$359$	−11714.6	−1.72221	−0.861105	−	0.508427i	$-0.830227\pi$
$359$	−11714.6	−1.72221	−0.861105	+	0.508427i	$0.830227\pi$
$360$	−9884.94	−1.44717
$361$	−6558.79	−0.956231
$362$	11927.8	1.73180
$363$	8594.73	1.24272
$364$	13462.3	1.93851
$365$	−4907.63	−0.703773
$366$	525.277	0.0750183
$367$	−8600.08	−1.22322	−0.611608	−	0.791161i	$-0.709477\pi$
$367$	−8600.08	−1.22322	−0.611608	+	0.791161i	$0.709477\pi$
$368$	−43213.4	−6.12134
$369$	29.1857	0.00411747
$370$	2939.31	0.412993
$371$	14723.7	2.06042
$372$	−8385.24	−1.16869
$373$	−4637.56	−0.643763	−0.321882	−	0.946780i	$-0.604315\pi$
$373$	−4637.56	−0.643763	−0.321882	+	0.946780i	$0.604315\pi$
$374$	−499.830	−0.0691059
$375$	9710.91	1.33725
$376$	−18421.1	−2.52659
$377$	5566.06	0.760389
$378$	11321.1	1.54046
$379$	−6856.29	−0.929245	−0.464623	−	0.885509i	$-0.653810\pi$
$379$	−6856.29	−0.929245	−0.464623	+	0.885509i	$0.653810\pi$
$380$	3242.90	0.437782
$381$	−105.987	−0.0142516
$382$	3591.95	0.481100
$383$	6705.64	0.894627	0.447313	−	0.894377i	$-0.352381\pi$
$383$	6705.64	0.894627	0.447313	+	0.894377i	$0.352381\pi$
$384$	44472.0	5.91003
$385$	−244.155	−0.0323202
$386$	−17730.9	−2.33802
$387$	0	0
$388$	1799.43	0.235444
$389$	−1091.32	−0.142241	−0.0711207	−	0.997468i	$-0.522658\pi$
$389$	−1091.32	−0.142241	−0.0711207	+	0.997468i	$0.522658\pi$
$390$	−6807.87	−0.883923
$391$	−12899.1	−1.66837
$392$	−26507.6	−3.41540
$393$	−3915.25	−0.502539
$394$	11161.3	1.42716
$395$	6884.60	0.876967
$396$	380.107	0.0482350
$397$	−1954.42	−0.247076	−0.123538	−	0.992340i	$-0.539424\pi$
$397$	−1954.42	−0.247076	−0.123538	+	0.992340i	$0.539424\pi$
$398$	28201.5	3.55180
$399$	2901.43	0.364043
$400$	−15007.5	−1.87594
$401$	−2756.19	−0.343235	−0.171618	−	0.985164i	$-0.554899\pi$
$401$	−2756.19	−0.343235	−0.171618	+	0.985164i	$0.554899\pi$
$402$	−18646.9	−2.31349
$403$	−1319.73	−0.163128
$404$	−19665.0	−2.42171
$405$	−7532.75	−0.924211
$406$	−34694.9	−4.24108
$407$	−73.0180	−0.00889280
$408$	41450.6	5.02968
$409$	4904.93	0.592991	0.296496	−	0.955034i	$-0.404182\pi$
$409$	4904.93	0.592991	0.296496	+	0.955034i	$0.404182\pi$
$410$	−90.4689	−0.0108974
$411$	−5591.16	−0.671026
$412$	−43751.3	−5.23173
$413$	38.2157	0.00455321
$414$	13281.6	1.57670
$415$	−1078.89	−0.127616
$416$	18974.2	2.23627
$417$	8868.11	1.04142
$418$	−109.075	−0.0127633
$419$	4995.27	0.582422	0.291211	−	0.956659i	$-0.405942\pi$
$419$	4995.27	0.582422	0.291211	+	0.956659i	$0.405942\pi$
$420$	31341.5	3.64122
$421$	−4894.76	−0.566641	−0.283321	−	0.959025i	$-0.591436\pi$
$421$	−4894.76	−0.566641	−0.283321	+	0.959025i	$0.591436\pi$
$422$	−2118.14	−0.244335
$423$	3370.58	0.387430
$424$	45902.8	5.25763
$425$	−4479.70	−0.511288
$426$	25327.5	2.88056
$427$	−380.599	−0.0431346
$428$	13420.1	1.51562
$429$	169.120	0.0190331
$430$	0	0
$431$	12639.8	1.41262	0.706309	−	0.707904i	$-0.250359\pi$
$431$	12639.8	1.41262	0.706309	+	0.707904i	$0.250359\pi$
$432$	21012.0	2.34014
$433$	−5585.63	−0.619927	−0.309963	−	0.950748i	$-0.600317\pi$
$433$	−5585.63	−0.619927	−0.309963	+	0.950748i	$0.600317\pi$
$434$	8226.27	0.909847
$435$	12958.3	1.42828
$436$	7153.39	0.785746
$437$	−2814.89	−0.308134
$438$	−21189.5	−2.31158
$439$	14142.7	1.53757	0.768785	−	0.639507i	$-0.220862\pi$
$439$	14142.7	1.53757	0.768785	+	0.639507i	$0.220862\pi$
$440$	−761.182	−0.0824726
$441$	4850.18	0.523721
$442$	10098.3	1.08671
$443$	2209.03	0.236916	0.118458	−	0.992959i	$-0.462205\pi$
$443$	2209.03	0.236916	0.118458	+	0.992959i	$0.462205\pi$
$444$	9373.13	1.00187
$445$	3798.94	0.404690
$446$	18923.3	2.00906
$447$	18877.6	1.99750
$448$	−63142.9	−6.65898
$449$	3115.97	0.327510	0.163755	−	0.986501i	$-0.447639\pi$
$449$	3115.97	0.327510	0.163755	+	0.986501i	$0.447639\pi$
$450$	4612.54	0.483194
$451$	2.24742	0.000234649 0
$452$	−25385.2	−2.64164
$453$	−9482.12	−0.983463
$454$	22552.7	2.33139
$455$	4932.76	0.508245
$456$	9045.54	0.928939
$457$	12049.3	1.23335	0.616677	−	0.787216i	$-0.288479\pi$
$457$	12049.3	1.23335	0.616677	+	0.787216i	$0.288479\pi$
$458$	32965.6	3.36328
$459$	6272.01	0.637805
$460$	−30406.8	−3.08201
$461$	2951.30	0.298169	0.149084	−	0.988824i	$-0.452367\pi$
$461$	2951.30	0.298169	0.149084	+	0.988824i	$0.452367\pi$
$462$	−1054.18	−0.106158
$463$	904.973	0.0908373	0.0454186	−	0.998968i	$-0.485538\pi$
$463$	904.973	0.0908373	0.0454186	+	0.998968i	$0.485538\pi$
$464$	−64393.9	−6.44270
$465$	−3072.46	−0.306413
$466$	23019.2	2.28829
$467$	−692.068	−0.0685762	−0.0342881	−	0.999412i	$-0.510916\pi$
$467$	−692.068	−0.0685762	−0.0342881	+	0.999412i	$0.510916\pi$
$468$	−7679.44	−0.758509
$469$	13510.9	1.33023
$470$	−10448.0	−1.02538
$471$	−16493.5	−1.61355
$472$	119.142	0.0116186
$473$	0	0
$474$	29725.3	2.88044
$475$	−977.581	−0.0944305
$476$	−46489.6	−4.47657
$477$	−8398.98	−0.806212
$478$	2725.50	0.260798
$479$	13386.0	1.27688	0.638438	−	0.769674i	$-0.279581\pi$
$479$	13386.0	1.27688	0.638438	+	0.769674i	$0.279581\pi$
$480$	44173.9	4.20052
$481$	1475.21	0.139842
$482$	31880.0	3.01265
$483$	−27205.0	−2.56288
$484$	−30052.5	−2.82236
$485$	659.335	0.0617296
$486$	−20725.3	−1.93440
$487$	−12652.0	−1.17725	−0.588623	−	0.808408i	$-0.700330\pi$
$487$	−12652.0	−1.17725	−0.588623	+	0.808408i	$0.700330\pi$
$488$	−1186.56	−0.110068
$489$	19891.9	1.83955
$490$	−15034.4	−1.38610
$491$	20281.9	1.86418	0.932089	−	0.362230i	$-0.117984\pi$
$491$	20281.9	1.86418	0.932089	+	0.362230i	$0.117984\pi$
$492$	−288.495	−0.0264357
$493$	−19221.4	−1.75596
$494$	2203.69	0.200706
$495$	139.276	0.0126464
$496$	15268.0	1.38216
$497$	−18351.5	−1.65629
$498$	−4658.29	−0.419163
$499$	−13298.1	−1.19299	−0.596497	−	0.802615i	$-0.703441\pi$
$499$	−13298.1	−1.19299	−0.596497	+	0.802615i	$0.703441\pi$
$500$	−33955.4	−3.03706
$501$	−21203.6	−1.89084
$502$	11705.6	1.04073
$503$	16243.0	1.43984	0.719922	−	0.694055i	$-0.244178\pi$
$503$	16243.0	1.43984	0.719922	+	0.694055i	$0.244178\pi$
$504$	30924.4	2.73310
$505$	−7205.50	−0.634932
$506$	1022.74	0.0898541
$507$	10783.8	0.944626
$508$	370.595	0.0323671
$509$	19395.7	1.68900	0.844500	−	0.535555i	$-0.179897\pi$
$509$	19395.7	1.68900	0.844500	+	0.535555i	$0.179897\pi$
$510$	23509.7	2.04123
$511$	15353.2	1.32913
$512$	−47642.0	−4.11231
$513$	1368.71	0.117797
$514$	−40846.3	−3.50516
$515$	−16031.1	−1.37167
$516$	0	0
$517$	259.548	0.0220792
$518$	−9195.43	−0.779969
$519$	19407.9	1.64145
$520$	15378.5	1.29690
$521$	−14225.5	−1.19622	−0.598111	−	0.801413i	$-0.704082\pi$
$521$	−14225.5	−1.19622	−0.598111	+	0.801413i	$0.704082\pi$
$522$	19791.4	1.65947
$523$	−12794.5	−1.06972	−0.534861	−	0.844940i	$-0.679636\pi$
$523$	−12794.5	−1.06972	−0.534861	+	0.844940i	$0.679636\pi$
$524$	13690.1	1.14133
$525$	−9448.00	−0.785418
$526$	−7142.01	−0.592028
$527$	4557.45	0.376709
$528$	−1956.56	−0.161266
$529$	14226.6	1.16928
$530$	26034.9	2.13375
$531$	−21.7998	−0.00178160
$532$	−10145.2	−0.826785
$533$	−45.4055	−0.00368992
$534$	16402.5	1.32923
$535$	4917.30	0.397371
$536$	42122.0	3.39439
$537$	−11045.8	−0.887640
$538$	−18483.8	−1.48121
$539$	373.484	0.0298462
$540$	14784.9	1.17823
$541$	4464.91	0.354827	0.177414	−	0.984136i	$-0.443227\pi$
$541$	4464.91	0.354827	0.177414	+	0.984136i	$0.443227\pi$
$542$	−27599.0	−2.18723
$543$	13937.0	1.10146
$544$	−65524.1	−5.16420
$545$	2621.10	0.206010
$546$	21298.0	1.66936
$547$	−4191.68	−0.327647	−0.163824	−	0.986490i	$-0.552383\pi$
$547$	−4191.68	−0.327647	−0.163824	+	0.986490i	$0.552383\pi$
$548$	19550.2	1.52398
$549$	217.109	0.0168779
$550$	355.185	0.0275366
$551$	−4194.58	−0.324310
$552$	−84814.8	−6.53978
$553$	−21538.0	−1.65622
$554$	−28356.3	−2.17463
$555$	3434.43	0.262673
$556$	−31008.4	−2.36520
$557$	13393.0	1.01881	0.509407	−	0.860526i	$-0.329865\pi$
$557$	13393.0	1.01881	0.509407	+	0.860526i	$0.329865\pi$
$558$	−4692.60	−0.356010
$559$	0	0
$560$	−57067.3	−4.30631
$561$	−584.027	−0.0439530
$562$	−23583.2	−1.77010
$563$	4005.09	0.299812	0.149906	−	0.988700i	$-0.452103\pi$
$563$	4005.09	0.299812	0.149906	+	0.988700i	$0.452103\pi$
$564$	−33317.5	−2.48745
$565$	−9301.47	−0.692594
$566$	21747.4	1.61503
$567$	23565.7	1.74544
$568$	−57212.9	−4.22641
$569$	19010.3	1.40062	0.700309	−	0.713840i	$-0.253046\pi$
$569$	19010.3	1.40062	0.700309	+	0.713840i	$0.253046\pi$
$570$	5130.40	0.376998
$571$	−12513.0	−0.917083	−0.458542	−	0.888673i	$-0.651628\pi$
$571$	−12513.0	−0.917083	−0.458542	+	0.888673i	$0.651628\pi$
$572$	−591.349	−0.0432265
$573$	4197.01	0.305991
$574$	283.026	0.0205806
$575$	9166.21	0.664796
$576$	36019.3	2.60556
$577$	2560.16	0.184715	0.0923576	−	0.995726i	$-0.470560\pi$
$577$	2560.16	0.184715	0.0923576	+	0.995726i	$0.470560\pi$
$578$	−7694.80	−0.553739
$579$	−20717.6	−1.48704
$580$	−45310.3	−3.24381
$581$	3375.25	0.241013
$582$	2846.78	0.202754
$583$	−646.757	−0.0459450
$584$	47865.4	3.39158
$585$	−2813.85	−0.198869
$586$	27386.6	1.93060
$587$	1666.95	0.117210	0.0586052	−	0.998281i	$-0.481335\pi$
$587$	1666.95	0.117210	0.0586052	+	0.998281i	$0.481335\pi$
$588$	−47943.2	−3.36249
$589$	994.548	0.0695749
$590$	67.5744	0.00471525
$591$	13041.5	0.907705
$592$	−17066.8	−1.18487
$593$	−19206.9	−1.33008	−0.665038	−	0.746810i	$-0.731585\pi$
$593$	−19206.9	−1.33008	−0.665038	+	0.746810i	$0.731585\pi$
$594$	−497.293	−0.0343505
$595$	−17034.4	−1.17368
$596$	−66007.8	−4.53655
$597$	32952.1	2.25903
$598$	−20662.7	−1.41298
$599$	−7226.07	−0.492903	−0.246452	−	0.969155i	$-0.579265\pi$
$599$	−7226.07	−0.492903	−0.246452	+	0.969155i	$0.579265\pi$
$600$	−29455.3	−2.00418
$601$	−73.6411	−0.00499814	−0.00249907	−	0.999997i	$-0.500795\pi$
$601$	−73.6411	−0.00499814	−0.00249907	+	0.999997i	$0.500795\pi$
$602$	0	0
$603$	−7707.19	−0.520499
$604$	33155.4	2.23356
$605$	−11011.6	−0.739977
$606$	−31110.9	−2.08547
$607$	26845.4	1.79510	0.897548	−	0.440917i	$-0.145347\pi$
$607$	26845.4	1.79510	0.897548	+	0.440917i	$0.145347\pi$
$608$	−14299.0	−0.953783
$609$	−40539.2	−2.69743
$610$	−672.988	−0.0446697
$611$	−5243.76	−0.347201
$612$	26519.6	1.75162
$613$	10381.0	0.683989	0.341995	−	0.939702i	$-0.388898\pi$
$613$	10381.0	0.683989	0.341995	+	0.939702i	$0.388898\pi$
$614$	−14300.5	−0.939934
$615$	−105.708	−0.00693101
$616$	2381.31	0.155756
$617$	830.395	0.0541822	0.0270911	−	0.999633i	$-0.491376\pi$
$617$	830.395	0.0541822	0.0270911	+	0.999633i	$0.491376\pi$
$618$	−69216.6	−4.50534
$619$	17107.7	1.11085	0.555427	−	0.831565i	$-0.312555\pi$
$619$	17107.7	1.11085	0.555427	+	0.831565i	$0.312555\pi$
$620$	10743.2	0.695900
$621$	−12833.6	−0.829297
$622$	−40002.2	−2.57869
$623$	−11884.7	−0.764289
$624$	39529.1	2.53595
$625$	−5389.06	−0.344900
$626$	40424.3	2.58096
$627$	−127.449	−0.00811774
$628$	57671.5	3.66456
$629$	−5094.38	−0.322935
$630$	17539.5	1.10919
$631$	19885.0	1.25453	0.627265	−	0.778806i	$-0.284174\pi$
$631$	19885.0	1.25453	0.627265	+	0.778806i	$0.284174\pi$
$632$	−67147.3	−4.22623
$633$	−2474.94	−0.155403
$634$	−4067.08	−0.254770
$635$	135.791	0.00848612
$636$	83022.5	5.17619
$637$	−7545.64	−0.469340
$638$	1524.02	0.0945713
$639$	10468.4	0.648082
$640$	−56977.8	−3.51913
$641$	15584.0	0.960266	0.480133	−	0.877196i	$-0.340588\pi$
$641$	15584.0	0.960266	0.480133	+	0.877196i	$0.340588\pi$
$642$	21231.2	1.30519
$643$	3656.84	0.224280	0.112140	−	0.993692i	$-0.464230\pi$
$643$	3656.84	0.224280	0.112140	+	0.993692i	$0.464230\pi$
$644$	95125.6	5.82061
$645$	0	0
$646$	−7610.05	−0.463488
$647$	−24997.8	−1.51896	−0.759479	−	0.650532i	$-0.774546\pi$
$647$	−24997.8	−1.51896	−0.759479	+	0.650532i	$0.774546\pi$
$648$	73468.8	4.45390
$649$	−1.67868	−0.000101531 0
$650$	−7175.94	−0.433021
$651$	9611.98	0.578684
$652$	−69554.3	−4.17785
$653$	26500.2	1.58810	0.794051	−	0.607851i	$-0.207968\pi$
$653$	26500.2	1.58810	0.794051	+	0.607851i	$0.207968\pi$
$654$	11317.0	0.676650
$655$	5016.23	0.299237
$656$	525.298	0.0312644
$657$	−8758.09	−0.520069
$658$	32685.9	1.93652
$659$	7783.62	0.460101	0.230051	−	0.973179i	$-0.426111\pi$
$659$	7783.62	0.460101	0.230051	+	0.973179i	$0.426111\pi$
$660$	−1376.72	−0.0811950
$661$	18450.6	1.08570	0.542849	−	0.839831i	$-0.317346\pi$
$661$	18450.6	1.08570	0.542849	+	0.839831i	$0.317346\pi$
$662$	−2514.88	−0.147649
$663$	11799.3	0.691173
$664$	10522.7	0.615001
$665$	−3717.32	−0.216769
$666$	5245.45	0.305191
$667$	39330.1	2.28316
$668$	74141.0	4.29431
$669$	22110.9	1.27781
$670$	23890.5	1.37757
$671$	16.7183	0.000961852 0
$672$	−138195.	−7.93302
$673$	27963.2	1.60164	0.800818	−	0.598907i	$-0.204398\pi$
$673$	27963.2	1.60164	0.800818	+	0.598907i	$0.204398\pi$
$674$	21141.3	1.20821
$675$	−4456.96	−0.254146
$676$	−37706.8	−2.14536
$677$	4625.91	0.262612	0.131306	−	0.991342i	$-0.458083\pi$
$677$	4625.91	0.262612	0.131306	+	0.991342i	$0.458083\pi$
$678$	−40160.5	−2.27486
$679$	−2062.68	−0.116581
$680$	−53106.7	−2.99493
$681$	26351.7	1.48282
$682$	−361.350	−0.0202885
$683$	19227.2	1.07717	0.538587	−	0.842570i	$-0.318958\pi$
$683$	19227.2	1.07717	0.538587	+	0.842570i	$0.318958\pi$
$684$	5787.22	0.323509
$685$	7163.43	0.399563
$686$	−2122.56	−0.118134
$687$	38518.7	2.13913
$688$	0	0
$689$	13066.7	0.722498
$690$	−48104.9	−2.65409
$691$	−26995.1	−1.48617	−0.743083	−	0.669199i	$-0.766637\pi$
$691$	−26995.1	−1.48617	−0.743083	+	0.669199i	$0.766637\pi$
$692$	−67862.1	−3.72793
$693$	−435.715	−0.0238838
$694$	−62866.7	−3.43860
$695$	−11361.9	−0.620116
$696$	−126386.	−6.88311
$697$	156.800	0.00852111
$698$	−5887.71	−0.319274
$699$	26896.8	1.45541
$700$	33036.0	1.78378
$701$	27588.8	1.48647	0.743234	−	0.669032i	$-0.233291\pi$
$701$	27588.8	1.48647	0.743234	+	0.669032i	$0.233291\pi$
$702$	10047.0	0.540171
$703$	−1111.72	−0.0596433
$704$	2773.64	0.148488
$705$	−12208.0	−0.652169
$706$	14236.1	0.758899
$707$	22541.9	1.19912
$708$	215.487	0.0114386
$709$	2204.19	0.116756	0.0583781	−	0.998295i	$-0.481407\pi$
$709$	2204.19	0.116756	0.0583781	+	0.998295i	$0.481407\pi$
$710$	−32449.7	−1.71523
$711$	12286.2	0.648055
$712$	−37052.1	−1.95026
$713$	−9325.30	−0.489811
$714$	−73548.7	−3.85503
$715$	−216.678	−0.0113333
$716$	38623.0	2.01594
$717$	3184.61	0.165873
$718$	64802.9	3.36828
$719$	−2121.76	−0.110053	−0.0550267	−	0.998485i	$-0.517524\pi$
$719$	−2121.76	−0.110053	−0.0550267	+	0.998485i	$0.517524\pi$
$720$	32553.5	1.68500
$721$	50152.1	2.59051
$722$	36281.9	1.87019
$723$	37250.2	1.91611
$724$	−48732.4	−2.50155
$725$	13658.9	0.699696
$726$	−47544.4	−2.43049
$727$	−3435.42	−0.175258	−0.0876291	−	0.996153i	$-0.527929\pi$
$727$	−3435.42	−0.175258	−0.0876291	+	0.996153i	$0.527929\pi$
$728$	−48110.5	−2.44930
$729$	343.187	0.0174357
$730$	27148.1	1.37643
$731$	0	0
$732$	−2146.08	−0.108363
$733$	23806.5	1.19961	0.599804	−	0.800147i	$-0.295245\pi$
$733$	23806.5	1.19961	0.599804	+	0.800147i	$0.295245\pi$
$734$	47574.0	2.39235
$735$	−17567.0	−0.881589
$736$	134073.	6.71468
$737$	−593.486	−0.0296626
$738$	−161.449	−0.00805289
$739$	−14415.3	−0.717560	−0.358780	−	0.933422i	$-0.616807\pi$
$739$	−14415.3	−0.717560	−0.358780	+	0.933422i	$0.616807\pi$
$740$	−12008.9	−0.596562
$741$	2574.90	0.127654
$742$	−81448.5	−4.02974
$743$	−12562.2	−0.620272	−0.310136	−	0.950692i	$-0.600375\pi$
$743$	−12562.2	−0.620272	−0.310136	+	0.950692i	$0.600375\pi$
$744$	29966.5	1.47665
$745$	−24186.1	−1.18941
$746$	25654.1	1.25906
$747$	−1925.38	−0.0943050
$748$	2042.12	0.0998225
$749$	−15383.4	−0.750466
$750$	−53718.9	−2.61538
$751$	17368.1	0.843901	0.421950	−	0.906619i	$-0.361346\pi$
$751$	17368.1	0.843901	0.421950	+	0.906619i	$0.361346\pi$
$752$	60665.2	2.94180
$753$	13677.3	0.661926
$754$	−30790.3	−1.48716
$755$	12148.5	0.585604
$756$	−46253.6	−2.22517
$757$	7082.76	0.340063	0.170031	−	0.985439i	$-0.445613\pi$
$757$	7082.76	0.340063	0.170031	+	0.985439i	$0.445613\pi$
$758$	37927.7	1.81741
$759$	1195.02	0.0571493
$760$	−11589.2	−0.553137
$761$	−10682.2	−0.508841	−0.254421	−	0.967094i	$-0.581885\pi$
$761$	−10682.2	−0.508841	−0.254421	+	0.967094i	$0.581885\pi$
$762$	586.297	0.0278731
$763$	−8199.92	−0.389066
$764$	−14675.4	−0.694942
$765$	9717.11	0.459246
$766$	−37094.3	−1.74970
$767$	33.9150	0.00159661
$768$	−119982.	−5.63734
$769$	−11288.0	−0.529330	−0.264665	−	0.964340i	$-0.585261\pi$
$769$	−11288.0	−0.529330	−0.264665	+	0.964340i	$0.585261\pi$
$770$	1350.62	0.0632115
$771$	−47726.8	−2.22936
$772$	72441.6	3.37724
$773$	−33574.4	−1.56221	−0.781103	−	0.624402i	$-0.785343\pi$
$773$	−33574.4	−1.56221	−0.781103	+	0.624402i	$0.785343\pi$
$774$	0	0
$775$	−3238.57	−0.150107
$776$	−6430.66	−0.297484
$777$	−10744.4	−0.496079
$778$	6036.94	0.278194
$779$	34.2175	0.00157377
$780$	27814.4	1.27681
$781$	806.112	0.0369334
$782$	71355.1	3.26298
$783$	−19123.8	−0.872834
$784$	87295.8	3.97667
$785$	21131.6	0.960788
$786$	21658.4	0.982861
$787$	−19632.3	−0.889219	−0.444610	−	0.895724i	$-0.646658\pi$
$787$	−19632.3	−0.889219	−0.444610	+	0.895724i	$0.646658\pi$
$788$	−45601.0	−2.06151
$789$	−8345.08	−0.376544
$790$	−38084.3	−1.71516
$791$	29099.0	1.30802
$792$	−1358.39	−0.0609450
$793$	−337.766	−0.0151254
$794$	10811.4	0.483229
$795$	30420.5	1.35711
$796$	−115221.	−5.13052
$797$	40200.2	1.78666	0.893328	−	0.449405i	$-0.148364\pi$
$797$	40200.2	1.78666	0.893328	+	0.449405i	$0.148364\pi$
$798$	−16050.1	−0.711990
$799$	18108.4	0.801787
$800$	46562.2	2.05778
$801$	6779.54	0.299055
$802$	15246.7	0.671296
$803$	−674.410	−0.0296381
$804$	76184.2	3.34180
$805$	34855.2	1.52607
$806$	7300.49	0.319043
$807$	−21597.3	−0.942084
$808$	70277.1	3.05983
$809$	−4461.03	−0.193871	−0.0969354	−	0.995291i	$-0.530904\pi$
$809$	−4461.03	−0.193871	−0.0969354	+	0.995291i	$0.530904\pi$
$810$	41669.7	1.80756
$811$	21550.8	0.933108	0.466554	−	0.884493i	$-0.345495\pi$
$811$	21550.8	0.933108	0.466554	+	0.884493i	$0.345495\pi$
$812$	141750.	6.12618
$813$	−32248.1	−1.39113
$814$	403.921	0.0173924
$815$	−25485.6	−1.09536
$816$	−136507.	−5.85624
$817$	0	0
$818$	−27133.1	−1.15977
$819$	8802.93	0.375579
$820$	369.622	0.0157412
$821$	29867.4	1.26965	0.634824	−	0.772657i	$-0.281073\pi$
$821$	29867.4	1.26965	0.634824	+	0.772657i	$0.281073\pi$
$822$	30929.2	1.31238
$823$	18179.7	0.769995	0.384997	−	0.922918i	$-0.374202\pi$
$823$	18179.7	0.769995	0.384997	+	0.922918i	$0.374202\pi$
$824$	156355.	6.61030
$825$	415.016	0.0175139
$826$	−211.402	−0.00890511
$827$	−4265.73	−0.179364	−0.0896821	−	0.995970i	$-0.528585\pi$
$827$	−4265.73	−0.179364	−0.0896821	+	0.995970i	$0.528585\pi$
$828$	−54263.5	−2.27752
$829$	−7720.33	−0.323448	−0.161724	−	0.986836i	$-0.551705\pi$
$829$	−7720.33	−0.323448	−0.161724	+	0.986836i	$0.551705\pi$
$830$	5968.23	0.249591
$831$	−33132.9	−1.38312
$832$	−56036.8	−2.33501
$833$	26057.5	1.08384
$834$	−49056.7	−2.03680
$835$	27166.2	1.12590
$836$	445.640	0.0184364
$837$	4534.31	0.187251
$838$	−27632.8	−1.13909
$839$	−6307.72	−0.259555	−0.129778	−	0.991543i	$-0.541426\pi$
$839$	−6307.72	−0.259555	−0.129778	+	0.991543i	$0.541426\pi$
$840$	−112006.	−4.60068
$841$	34218.3	1.40302
$842$	27076.9	1.10823
$843$	−27555.7	−1.12582
$844$	8653.92	0.352938
$845$	−13816.3	−0.562478
$846$	−18645.4	−0.757731
$847$	34449.1	1.39750
$848$	−151169.	−6.12166
$849$	25410.7	1.02720
$850$	24780.8	0.999971
$851$	10423.9	0.419892
$852$	−103479.	−4.16093
$853$	18044.6	0.724308	0.362154	−	0.932118i	$-0.382041\pi$
$853$	18044.6	0.724308	0.362154	+	0.932118i	$0.382041\pi$
$854$	2105.40	0.0843621
$855$	2120.51	0.0848187
$856$	−47959.7	−1.91499
$857$	10579.9	0.421708	0.210854	−	0.977518i	$-0.432375\pi$
$857$	10579.9	0.421708	0.210854	+	0.977518i	$0.432375\pi$
$858$	−935.541	−0.0372248
$859$	−32828.7	−1.30396	−0.651980	−	0.758236i	$-0.726061\pi$
$859$	−32828.7	−1.30396	−0.651980	+	0.758236i	$0.726061\pi$
$860$	0	0
$861$	330.701	0.0130898
$862$	−69920.9	−2.76278
$863$	24972.9	0.985036	0.492518	−	0.870302i	$-0.336077\pi$
$863$	24972.9	0.985036	0.492518	+	0.870302i	$0.336077\pi$
$864$	−65191.5	−2.56697
$865$	−24865.5	−0.977403
$866$	30898.6	1.21245
$867$	−8990.98	−0.352191
$868$	−33609.4	−1.31426
$869$	946.085	0.0369318
$870$	−71682.9	−2.79342
$871$	11990.4	0.466453
$872$	−25564.2	−0.992791
$873$	1176.64	0.0456165
$874$	15571.4	0.602645
$875$	38922.9	1.50381
$876$	86572.2	3.33904
$877$	−36581.1	−1.40850	−0.704251	−	0.709951i	$-0.748717\pi$
$877$	−36581.1	−1.40850	−0.704251	+	0.709951i	$0.748717\pi$
$878$	−78234.6	−3.00716
$879$	31999.9	1.22790
$880$	2506.76	0.0960258
$881$	−24079.2	−0.920828	−0.460414	−	0.887704i	$-0.652299\pi$
$881$	−24079.2	−0.920828	−0.460414	+	0.887704i	$0.652299\pi$
$882$	−26830.2	−1.02429
$883$	−42315.0	−1.61270	−0.806349	−	0.591440i	$-0.798559\pi$
$883$	−42315.0	−1.61270	−0.806349	+	0.591440i	$0.798559\pi$
$884$	−41257.7	−1.56974
$885$	78.9573	0.00299901
$886$	−12219.9	−0.463358
$887$	−47087.8	−1.78247	−0.891236	−	0.453539i	$-0.850161\pi$
$887$	−47087.8	−1.78247	−0.891236	+	0.453539i	$0.850161\pi$
$888$	−33496.9	−1.26586
$889$	−424.812	−0.0160267
$890$	−21015.0	−0.791488
$891$	−1035.15	−0.0389214
$892$	−77313.3	−2.90206
$893$	3951.69	0.148083
$894$	−104427.	−3.90668
$895$	14152.0	0.528545
$896$	178251.	6.64616
$897$	−24143.4	−0.898689
$898$	−17237.0	−0.640540
$899$	−13896.0	−0.515525
$900$	−18845.1	−0.697967
$901$	−45123.4	−1.66846
$902$	−12.4323	−0.000458924 0
$903$	0	0
$904$	90719.6	3.33771
$905$	−17856.2	−0.655866
$906$	52453.2	1.92345
$907$	43470.3	1.59141	0.795704	−	0.605685i	$-0.207101\pi$
$907$	43470.3	1.59141	0.795704	+	0.605685i	$0.207101\pi$
$908$	−92142.0	−3.36766
$909$	−12858.8	−0.469197
$910$	−27287.1	−0.994019
$911$	−28977.5	−1.05386	−0.526931	−	0.849908i	$-0.676657\pi$
$911$	−28977.5	−1.05386	−0.526931	+	0.849908i	$0.676657\pi$
$912$	−29789.1	−1.08160
$913$	−148.262	−0.00537432
$914$	−66654.4	−2.41218
$915$	−786.353	−0.0284110
$916$	−134685.	−4.85821
$917$	−15693.0	−0.565133
$918$	−34695.5	−1.24741
$919$	−7071.53	−0.253828	−0.126914	−	0.991914i	$-0.540507\pi$
$919$	−7071.53	−0.253828	−0.126914	+	0.991914i	$0.540507\pi$
$920$	108665.	3.89412
$921$	−16709.4	−0.597820
$922$	−16326.0	−0.583155
$923$	−16286.2	−0.580788
$924$	4306.97	0.153343
$925$	3620.12	0.128680
$926$	−5006.13	−0.177658
$927$	−28608.8	−1.01363
$928$	199788.	7.06719
$929$	−1251.98	−0.0442155	−0.0221077	−	0.999756i	$-0.507038\pi$
$929$	−1251.98	−0.0442155	−0.0221077	+	0.999756i	$0.507038\pi$
$930$	16996.2	0.599278
$931$	5686.39	0.200176
$932$	−94047.9	−3.30541
$933$	−46740.6	−1.64010
$934$	3828.39	0.134121
$935$	748.258	0.0261718
$936$	27444.2	0.958377
$937$	−36027.3	−1.25610	−0.628048	−	0.778175i	$-0.716146\pi$
$937$	−36027.3	−1.25610	−0.628048	+	0.778175i	$0.716146\pi$
$938$	−74739.9	−2.60165
$939$	47233.8	1.64155
$940$	42686.6	1.48115
$941$	−7477.71	−0.259051	−0.129525	−	0.991576i	$-0.541345\pi$
$941$	−7477.71	−0.259051	−0.129525	+	0.991576i	$0.541345\pi$
$942$	91238.9	3.15576
$943$	−320.838	−0.0110795
$944$	−392.364	−0.0135279
$945$	−16947.9	−0.583403
$946$	0	0
$947$	23249.2	0.797780	0.398890	−	0.916999i	$-0.369395\pi$
$947$	23249.2	0.797780	0.398890	+	0.916999i	$0.369395\pi$
$948$	−121446.	−4.16076
$949$	13625.4	0.466067
$950$	5407.78	0.184686
$951$	−4752.18	−0.162040
$952$	166141.	5.65615
$953$	7735.85	0.262947	0.131474	−	0.991320i	$-0.458029\pi$
$953$	7735.85	0.262947	0.131474	+	0.991320i	$0.458029\pi$
$954$	46461.5	1.57678
$955$	−5377.24	−0.182202
$956$	−11135.3	−0.376719
$957$	1780.74	0.0601495
$958$	−74048.9	−2.49730
$959$	−22410.3	−0.754605
$960$	−130459.	−4.38599
$961$	−26496.2	−0.889403
$962$	−8160.58	−0.273501
$963$	8775.34	0.293646
$964$	−130250.	−4.35172
$965$	26543.5	0.885457
$966$	150493.	5.01245
$967$	52702.6	1.75264	0.876320	−	0.481730i	$-0.159991\pi$
$967$	52702.6	1.75264	0.876320	+	0.481730i	$0.159991\pi$
$968$	107399.	3.56605
$969$	−8891.96	−0.294789
$970$	−3647.31	−0.120730
$971$	−16955.0	−0.560364	−0.280182	−	0.959947i	$-0.590395\pi$
$971$	−16955.0	−0.560364	−0.280182	+	0.959947i	$0.590395\pi$
$972$	84675.6	2.79421
$973$	35544.9	1.17114
$974$	69988.6	2.30244
$975$	−8384.73	−0.275411
$976$	3907.63	0.128156
$977$	36227.0	1.18629	0.593145	−	0.805095i	$-0.297886\pi$
$977$	36227.0	1.18629	0.593145	+	0.805095i	$0.297886\pi$
$978$	−110038.	−3.59778
$979$	522.053	0.0170428
$980$	61425.0	2.00219
$981$	4677.57	0.152236
$982$	−112196.	−3.64594
$983$	3488.52	0.113191	0.0565953	−	0.998397i	$-0.481976\pi$
$983$	3488.52	0.113191	0.0565953	+	0.998397i	$0.481976\pi$
$984$	1031.00	0.0334015
$985$	−16708.8	−0.540493
$986$	106329.	3.43428
$987$	38191.8	1.23167
$988$	−9003.45	−0.289917
$989$	0	0
$990$	−770.447	−0.0247338
$991$	51827.9	1.66132	0.830659	−	0.556781i	$-0.187964\pi$
$991$	51827.9	1.66132	0.830659	+	0.556781i	$0.187964\pi$
$992$	−47370.3	−1.51614
$993$	−2938.51	−0.0939082
$994$	101517.	3.23935
$995$	−42218.4	−1.34514
$996$	19032.0	0.605474
$997$	−20587.0	−0.653960	−0.326980	−	0.945031i	$-0.606031\pi$
$997$	−20587.0	−0.653960	−0.326980	+	0.945031i	$0.606031\pi$
$998$	73562.5	2.33325
$999$	−5068.52	−0.160521

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.m.1.1	✓	110
43.42	odd	2	inner	1849.4.a.m.1.110	yes	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.m.1.1	✓	110	1.1	even	1	trivial
1849.4.a.m.1.110	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)

\(f(q)\)	\(=\)	\(q-5.53180 q^{2} -6.46364 q^{3} +22.6009 q^{4} +8.28125 q^{5} +35.7556 q^{6} -25.9073 q^{7} -80.7691 q^{8} +14.7786 q^{9} +O(q^{10})\)	\(q-5.53180 q^{2} -6.46364 q^{3} +22.6009 q^{4} +8.28125 q^{5} +35.7556 q^{6} -25.9073 q^{7} -80.7691 q^{8} +14.7786 q^{9} -45.8102 q^{10} +1.13801 q^{11} -146.084 q^{12} -22.9917 q^{13} +143.314 q^{14} -53.5270 q^{15} +265.992 q^{16} +79.3978 q^{17} -81.7523 q^{18} +17.3266 q^{19} +187.163 q^{20} +167.456 q^{21} -6.29527 q^{22} -162.461 q^{23} +522.062 q^{24} -56.4209 q^{25} +127.186 q^{26} +78.9947 q^{27} -585.528 q^{28} -242.090 q^{29} +296.101 q^{30} +57.4002 q^{31} -825.264 q^{32} -7.35570 q^{33} -439.213 q^{34} -214.545 q^{35} +334.009 q^{36} -64.1627 q^{37} -95.8471 q^{38} +148.610 q^{39} -668.869 q^{40} +1.97486 q^{41} -926.331 q^{42} +25.7201 q^{44} +122.385 q^{45} +898.703 q^{46} +228.071 q^{47} -1719.28 q^{48} +328.189 q^{49} +312.110 q^{50} -513.198 q^{51} -519.633 q^{52} -568.321 q^{53} -436.983 q^{54} +9.42417 q^{55} +2092.51 q^{56} -111.993 q^{57} +1339.19 q^{58} -1.47509 q^{59} -1209.76 q^{60} +14.6908 q^{61} -317.527 q^{62} -382.874 q^{63} +2437.26 q^{64} -190.400 q^{65} +40.6903 q^{66} -521.511 q^{67} +1794.46 q^{68} +1050.09 q^{69} +1186.82 q^{70} +708.351 q^{71} -1193.65 q^{72} -592.620 q^{73} +354.936 q^{74} +364.684 q^{75} +391.595 q^{76} -29.4829 q^{77} -822.082 q^{78} +831.348 q^{79} +2202.75 q^{80} -909.615 q^{81} -10.9245 q^{82} -130.281 q^{83} +3784.64 q^{84} +657.513 q^{85} +1564.78 q^{87} -91.9164 q^{88} +458.740 q^{89} -677.011 q^{90} +595.654 q^{91} -3671.76 q^{92} -371.014 q^{93} -1261.65 q^{94} +143.485 q^{95} +5334.20 q^{96} +79.6178 q^{97} -1815.48 q^{98} +16.8182 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q + 492 q^{4} + 102 q^{6} + 1234 q^{9}+O(q^{10}) \) 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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