LMFDB - Embedded newform 1849.4.a.m.1.20

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			1.20
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)

$f(q)$	$=$	$q-4.17102 q^{2} -0.918823 q^{3} +9.39743 q^{4} -18.4602 q^{5} +3.83243 q^{6} -23.0342 q^{7} -5.82873 q^{8} -26.1558 q^{9} +O(q^{10})$	\(q-4.17102 q^{2} -0.918823 q^{3} +9.39743 q^{4} -18.4602 q^{5} +3.83243 q^{6} -23.0342 q^{7} -5.82873 q^{8} -26.1558 q^{9} +76.9977 q^{10} +54.4265 q^{11} -8.63458 q^{12} +32.0693 q^{13} +96.0763 q^{14} +16.9616 q^{15} -50.8677 q^{16} -116.385 q^{17} +109.096 q^{18} -6.07996 q^{19} -173.478 q^{20} +21.1644 q^{21} -227.014 q^{22} +78.6277 q^{23} +5.35558 q^{24} +215.777 q^{25} -133.762 q^{26} +48.8407 q^{27} -216.463 q^{28} -106.305 q^{29} -70.7473 q^{30} +132.505 q^{31} +258.800 q^{32} -50.0083 q^{33} +485.446 q^{34} +425.216 q^{35} -245.797 q^{36} -343.011 q^{37} +25.3596 q^{38} -29.4660 q^{39} +107.599 q^{40} -162.289 q^{41} -88.2772 q^{42} +511.469 q^{44} +482.839 q^{45} -327.958 q^{46} +53.1606 q^{47} +46.7384 q^{48} +187.576 q^{49} -900.012 q^{50} +106.937 q^{51} +301.369 q^{52} -442.625 q^{53} -203.716 q^{54} -1004.72 q^{55} +134.260 q^{56} +5.58641 q^{57} +443.402 q^{58} +44.7353 q^{59} +159.396 q^{60} -113.889 q^{61} -552.682 q^{62} +602.478 q^{63} -672.520 q^{64} -592.005 q^{65} +208.586 q^{66} -658.098 q^{67} -1093.72 q^{68} -72.2449 q^{69} -1773.58 q^{70} -870.116 q^{71} +152.455 q^{72} -655.222 q^{73} +1430.71 q^{74} -198.261 q^{75} -57.1360 q^{76} -1253.67 q^{77} +122.904 q^{78} -408.092 q^{79} +939.025 q^{80} +661.330 q^{81} +676.911 q^{82} -520.142 q^{83} +198.891 q^{84} +2148.49 q^{85} +97.6758 q^{87} -317.237 q^{88} -397.802 q^{89} -2013.93 q^{90} -738.693 q^{91} +738.899 q^{92} -121.749 q^{93} -221.734 q^{94} +112.237 q^{95} -237.792 q^{96} -1006.55 q^{97} -782.384 q^{98} -1423.57 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.17102	−1.47468	−0.737340	−	0.675522i	$-0.763918\pi$
$2$	−4.17102	−1.47468	−0.737340	+	0.675522i	$0.763918\pi$
$3$	−0.918823	−0.176828	−0.0884138	−	0.996084i	$-0.528180\pi$
$3$	−0.918823	−0.176828	−0.0884138	+	0.996084i	$0.528180\pi$
$4$	9.39743	1.17468
$5$	−18.4602	−1.65113	−0.825563	−	0.564310i	$-0.809142\pi$
$5$	−18.4602	−1.65113	−0.825563	+	0.564310i	$0.809142\pi$
$6$	3.83243	0.260764
$7$	−23.0342	−1.24373	−0.621866	−	0.783124i	$-0.713625\pi$
$7$	−23.0342	−1.24373	−0.621866	+	0.783124i	$0.713625\pi$
$8$	−5.82873	−0.257596
$9$	−26.1558	−0.968732
$10$	76.9977	2.43488
$11$	54.4265	1.49184	0.745918	−	0.666038i	$-0.232011\pi$
$11$	54.4265	1.49184	0.745918	+	0.666038i	$0.232011\pi$
$12$	−8.63458	−0.207716
$13$	32.0693	0.684187	0.342094	−	0.939666i	$-0.388864\pi$
$13$	32.0693	0.684187	0.342094	+	0.939666i	$0.388864\pi$
$14$	96.0763	1.83411
$15$	16.9616	0.291965
$16$	−50.8677	−0.794808
$17$	−116.385	−1.66045	−0.830223	−	0.557432i	$-0.811787\pi$
$17$	−116.385	−1.66045	−0.830223	+	0.557432i	$0.811787\pi$
$18$	109.096	1.42857
$19$	−6.07996	−0.0734125	−0.0367063	−	0.999326i	$-0.511687\pi$
$19$	−6.07996	−0.0734125	−0.0367063	+	0.999326i	$0.511687\pi$
$20$	−173.478	−1.93954
$21$	21.1644	0.219926
$22$	−227.014	−2.19998
$23$	78.6277	0.712826	0.356413	−	0.934328i	$-0.384000\pi$
$23$	78.6277	0.712826	0.356413	+	0.934328i	$0.384000\pi$
$24$	5.35558	0.0455501
$25$	215.777	1.72622
$26$	−133.762	−1.00896
$27$	48.8407	0.348126
$28$	−216.463	−1.46099
$29$	−106.305	−0.680704	−0.340352	−	0.940298i	$-0.610546\pi$
$29$	−106.305	−0.680704	−0.340352	+	0.940298i	$0.610546\pi$
$30$	−70.7473	−0.430554
$31$	132.505	0.767697	0.383849	−	0.923396i	$-0.374598\pi$
$31$	132.505	0.767697	0.383849	+	0.923396i	$0.374598\pi$
$32$	258.800	1.42968
$33$	−50.0083	−0.263798
$34$	485.446	2.44862
$35$	425.216	2.05356
$36$	−245.797	−1.13795
$37$	−343.011	−1.52407	−0.762036	−	0.647535i	$-0.775800\pi$
$37$	−343.011	−1.52407	−0.762036	+	0.647535i	$0.775800\pi$
$38$	25.3596	0.108260
$39$	−29.4660	−0.120983
$40$	107.599	0.425324
$41$	−162.289	−0.618177	−0.309089	−	0.951033i	$-0.600024\pi$
$41$	−162.289	−0.618177	−0.309089	+	0.951033i	$0.600024\pi$
$42$	−88.2772	−0.324321
$43$	0	0
$43$	0	0
$44$	511.469	1.75243
$45$	482.839	1.59950
$46$	−327.958	−1.05119
$47$	53.1606	0.164985	0.0824923	−	0.996592i	$-0.473712\pi$
$47$	53.1606	0.164985	0.0824923	+	0.996592i	$0.473712\pi$
$48$	46.7384	0.140544
$49$	187.576	0.546869
$50$	−900.012	−2.54562
$51$	106.937	0.293613
$52$	301.369	0.803700
$53$	−442.625	−1.14715	−0.573577	−	0.819152i	$-0.694445\pi$
$53$	−442.625	−1.14715	−0.573577	+	0.819152i	$0.694445\pi$
$54$	−203.716	−0.513374
$55$	−1004.72	−2.46321
$56$	134.260	0.320380
$57$	5.58641	0.0129814
$58$	443.402	1.00382
$59$	44.7353	0.0987126	0.0493563	−	0.998781i	$-0.484283\pi$
$59$	44.7353	0.0987126	0.0493563	+	0.998781i	$0.484283\pi$
$60$	159.396	0.342965
$61$	−113.889	−0.239048	−0.119524	−	0.992831i	$-0.538137\pi$
$61$	−113.889	−0.239048	−0.119524	+	0.992831i	$0.538137\pi$
$62$	−552.682	−1.13211
$63$	602.478	1.20484
$64$	−672.520	−1.31352
$65$	−592.005	−1.12968
$66$	208.586	0.389017
$67$	−658.098	−1.19999	−0.599996	−	0.800003i	$-0.704831\pi$
$67$	−658.098	−1.19999	−0.599996	+	0.800003i	$0.704831\pi$
$68$	−1093.72	−1.95049
$69$	−72.2449	−0.126047
$70$	−1773.58	−3.02834
$71$	−870.116	−1.45442	−0.727209	−	0.686416i	$-0.759183\pi$
$71$	−870.116	−1.45442	−0.727209	+	0.686416i	$0.759183\pi$
$72$	152.455	0.249542
$73$	−655.222	−1.05052	−0.525260	−	0.850942i	$-0.676032\pi$
$73$	−655.222	−1.05052	−0.525260	+	0.850942i	$0.676032\pi$
$74$	1430.71	2.24752
$75$	−198.261	−0.305243
$76$	−57.1360	−0.0862362
$77$	−1253.67	−1.85544
$78$	122.904	0.178411
$79$	−408.092	−0.581189	−0.290595	−	0.956846i	$-0.593853\pi$
$79$	−408.092	−0.581189	−0.290595	+	0.956846i	$0.593853\pi$
$80$	939.025	1.31233
$81$	661.330	0.907174
$82$	676.911	0.911613
$83$	−520.142	−0.687867	−0.343933	−	0.938994i	$-0.611759\pi$
$83$	−520.142	−0.687867	−0.343933	+	0.938994i	$0.611759\pi$
$84$	198.891	0.258343
$85$	2148.49	2.74160
$86$	0	0
$87$	97.6758	0.120367
$88$	−317.237	−0.384291
$89$	−397.802	−0.473786	−0.236893	−	0.971536i	$-0.576129\pi$
$89$	−397.802	−0.473786	−0.236893	+	0.971536i	$0.576129\pi$
$90$	−2013.93	−2.35875
$91$	−738.693	−0.850945
$92$	738.899	0.837342
$93$	−121.749	−0.135750
$94$	−221.734	−0.243299
$95$	112.237	0.121213
$96$	−237.792	−0.252807
$97$	−1006.55	−1.05361	−0.526803	−	0.849988i	$-0.676609\pi$
$97$	−1006.55	−1.05361	−0.526803	+	0.849988i	$0.676609\pi$
$98$	−782.384	−0.806456
$99$	−1423.57	−1.44519
$100$	2027.75	2.02775
$101$	755.315	0.744125	0.372062	−	0.928208i	$-0.378651\pi$
$101$	755.315	0.744125	0.372062	+	0.928208i	$0.378651\pi$
$102$	−446.039	−0.432984
$103$	−711.552	−0.680692	−0.340346	−	0.940300i	$-0.610544\pi$
$103$	−711.552	−0.680692	−0.340346	+	0.940300i	$0.610544\pi$
$104$	−186.924	−0.176244
$105$	−390.698	−0.363126
$106$	1846.20	1.69168
$107$	−1855.28	−1.67623	−0.838116	−	0.545492i	$-0.816343\pi$
$107$	−1855.28	−1.67623	−0.838116	+	0.545492i	$0.816343\pi$
$108$	458.978	0.408937
$109$	1120.32	0.984472	0.492236	−	0.870462i	$-0.336180\pi$
$109$	1120.32	0.984472	0.492236	+	0.870462i	$0.336180\pi$
$110$	4190.71	3.63244
$111$	315.166	0.269498
$112$	1171.70	0.988528
$113$	2126.92	1.77065	0.885327	−	0.464968i	$-0.153934\pi$
$113$	2126.92	1.77065	0.885327	+	0.464968i	$0.153934\pi$
$114$	−23.3010	−0.0191433
$115$	−1451.48	−1.17697
$116$	−998.998	−0.799609
$117$	−838.798	−0.662794
$118$	−186.592	−0.145569
$119$	2680.85	2.06515
$120$	−98.8647	−0.0752090
$121$	1631.24	1.22557
$122$	475.032	0.352520
$123$	149.115	0.109311
$124$	1245.21	0.901798
$125$	−1675.76	−1.19908
$126$	−2512.95	−1.77676
$127$	−2388.40	−1.66879	−0.834393	−	0.551170i	$-0.814182\pi$
$127$	−2388.40	−1.66879	−0.834393	+	0.551170i	$0.814182\pi$
$128$	734.695	0.507332
$129$	0	0
$130$	2469.27	1.66591
$131$	−578.107	−0.385568	−0.192784	−	0.981241i	$-0.561752\pi$
$131$	−578.107	−0.385568	−0.192784	+	0.981241i	$0.561752\pi$
$132$	−469.950	−0.309878
$133$	140.047	0.0913055
$134$	2744.94	1.76960
$135$	−901.608	−0.574800
$136$	678.379	0.427724
$137$	771.386	0.481050	0.240525	−	0.970643i	$-0.422680\pi$
$137$	771.386	0.481050	0.240525	+	0.970643i	$0.422680\pi$
$138$	301.335	0.185879
$139$	−1676.30	−1.02289	−0.511446	−	0.859315i	$-0.670890\pi$
$139$	−1676.30	−1.02289	−0.511446	+	0.859315i	$0.670890\pi$
$140$	3995.94	2.41227
$141$	−48.8452	−0.0291738
$142$	3629.27	2.14480
$143$	1745.42	1.02069
$144$	1330.48	0.769956
$145$	1962.41	1.12393
$146$	2732.95	1.54918
$147$	−172.349	−0.0967015
$148$	−3223.42	−1.79029
$149$	−2809.91	−1.54494	−0.772472	−	0.635048i	$-0.780980\pi$
$149$	−2809.91	−1.54494	−0.772472	+	0.635048i	$0.780980\pi$
$150$	826.952	0.450136
$151$	−788.106	−0.424736	−0.212368	−	0.977190i	$-0.568118\pi$
$151$	−788.106	−0.424736	−0.212368	+	0.977190i	$0.568118\pi$
$152$	35.4385	0.0189108
$153$	3044.15	1.60853
$154$	5229.09	2.73618
$155$	−2446.06	−1.26757
$156$	−276.905	−0.142116
$157$	−1215.63	−0.617949	−0.308974	−	0.951070i	$-0.599986\pi$
$157$	−1215.63	−0.617949	−0.308974	+	0.951070i	$0.599986\pi$
$158$	1702.16	0.857068
$159$	406.694	0.202849
$160$	−4777.49	−2.36059
$161$	−1811.13	−0.886565
$162$	−2758.42	−1.33779
$163$	−382.617	−0.183858	−0.0919290	−	0.995766i	$-0.529303\pi$
$163$	−382.617	−0.183858	−0.0919290	+	0.995766i	$0.529303\pi$
$164$	−1525.10	−0.726160
$165$	923.161	0.435563
$166$	2169.52	1.01438
$167$	3010.48	1.39496	0.697478	−	0.716606i	$-0.254305\pi$
$167$	3010.48	1.39496	0.697478	+	0.716606i	$0.254305\pi$
$168$	−123.362	−0.0566521
$169$	−1168.56	−0.531888
$170$	−8961.40	−4.04299
$171$	159.026	0.0711171
$172$	0	0
$173$	−1953.54	−0.858527	−0.429264	−	0.903179i	$-0.641227\pi$
$173$	−1953.54	−0.858527	−0.429264	+	0.903179i	$0.641227\pi$
$174$	−407.408	−0.177503
$175$	−4970.26	−2.14695
$176$	−2768.55	−1.18572
$177$	−41.1039	−0.0174551
$178$	1659.24	0.698683
$179$	47.9467	0.0200207	0.0100103	−	0.999950i	$-0.496814\pi$
$179$	47.9467	0.0200207	0.0100103	+	0.999950i	$0.496814\pi$
$180$	4537.45	1.87890
$181$	−599.017	−0.245992	−0.122996	−	0.992407i	$-0.539250\pi$
$181$	−599.017	−0.245992	−0.122996	+	0.992407i	$0.539250\pi$
$182$	3081.10	1.25487
$183$	104.644	0.0422703
$184$	−458.300	−0.183621
$185$	6332.03	2.51643
$186$	507.817	0.200188
$187$	−6334.44	−2.47711
$188$	499.574	0.193804
$189$	−1125.01	−0.432976
$190$	−468.143	−0.178751
$191$	−3909.36	−1.48100	−0.740500	−	0.672056i	$-0.765411\pi$
$191$	−3909.36	−1.48100	−0.740500	+	0.672056i	$0.765411\pi$
$192$	617.927	0.232266
$193$	673.998	0.251375	0.125688	−	0.992070i	$-0.459886\pi$
$193$	673.998	0.251375	0.125688	+	0.992070i	$0.459886\pi$
$194$	4198.34	1.55373
$195$	543.948	0.199758
$196$	1762.73	0.642396
$197$	−1260.12	−0.455735	−0.227867	−	0.973692i	$-0.573175\pi$
$197$	−1260.12	−0.455735	−0.227867	+	0.973692i	$0.573175\pi$
$198$	5937.72	2.13119
$199$	−1036.86	−0.369353	−0.184676	−	0.982799i	$-0.559124\pi$
$199$	−1036.86	−0.369353	−0.184676	+	0.982799i	$0.559124\pi$
$200$	−1257.71	−0.444667
$201$	604.675	0.212192
$202$	−3150.44	−1.09735
$203$	2448.66	0.846613
$204$	1004.94	0.344901
$205$	2995.88	1.02069
$206$	2967.90	1.00380
$207$	−2056.57	−0.690538
$208$	−1631.29	−0.543797
$209$	−330.911	−0.109519
$210$	1629.61	0.535494
$211$	−1361.64	−0.444262	−0.222131	−	0.975017i	$-0.571301\pi$
$211$	−1361.64	−0.444262	−0.222131	+	0.975017i	$0.571301\pi$
$212$	−4159.54	−1.34754
$213$	799.482	0.257181
$214$	7738.42	2.47190
$215$	0	0
$216$	−284.680	−0.0896759
$217$	−3052.15	−0.954810
$218$	−4672.89	−1.45178
$219$	602.033	0.185761
$220$	−9441.80	−2.89348
$221$	−3732.40	−1.13606
$222$	−1314.57	−0.397423
$223$	−1235.39	−0.370977	−0.185489	−	0.982646i	$-0.559387\pi$
$223$	−1235.39	−0.370977	−0.185489	+	0.982646i	$0.559387\pi$
$224$	−5961.27	−1.77814
$225$	−5643.82	−1.67224
$226$	−8871.44	−2.61115
$227$	6055.18	1.77047	0.885234	−	0.465146i	$-0.153998\pi$
$227$	6055.18	1.77047	0.885234	+	0.465146i	$0.153998\pi$
$228$	52.4979	0.0152489
$229$	119.641	0.0345246	0.0172623	−	0.999851i	$-0.494505\pi$
$229$	119.641	0.0345246	0.0172623	+	0.999851i	$0.494505\pi$
$230$	6054.15	1.73565
$231$	1151.90	0.328094
$232$	619.626	0.175347
$233$	−2344.78	−0.659278	−0.329639	−	0.944107i	$-0.606927\pi$
$233$	−2344.78	−0.659278	−0.329639	+	0.944107i	$0.606927\pi$
$234$	3498.65	0.977409
$235$	−981.354	−0.272410
$236$	420.397	0.115956
$237$	374.965	0.102770
$238$	−11181.9	−3.04543
$239$	450.550	0.121940	0.0609700	−	0.998140i	$-0.480581\pi$
$239$	450.550	0.121940	0.0609700	+	0.998140i	$0.480581\pi$
$240$	−862.798	−0.232056
$241$	730.395	0.195224	0.0976118	−	0.995225i	$-0.468880\pi$
$241$	730.395	0.195224	0.0976118	+	0.995225i	$0.468880\pi$
$242$	−6803.94	−1.80733
$243$	−1926.35	−0.508540
$244$	−1070.26	−0.280805
$245$	−3462.68	−0.902950
$246$	−621.961	−0.161198
$247$	−194.980	−0.0502279
$248$	−772.337	−0.197756
$249$	477.918	0.121634
$250$	6989.64	1.76825
$251$	−4257.31	−1.07059	−0.535297	−	0.844664i	$-0.679800\pi$
$251$	−4257.31	−1.07059	−0.535297	+	0.844664i	$0.679800\pi$
$252$	5661.75	1.41530
$253$	4279.43	1.06342
$254$	9962.05	2.46092
$255$	−1974.08	−0.484791
$256$	2315.73	0.565364
$257$	−3974.86	−0.964766	−0.482383	−	0.875960i	$-0.660229\pi$
$257$	−3974.86	−0.964766	−0.482383	+	0.875960i	$0.660229\pi$
$258$	0	0
$259$	7900.99	1.89554
$260$	−5563.33	−1.32701
$261$	2780.50	0.659420
$262$	2411.30	0.568589
$263$	4688.06	1.09916	0.549578	−	0.835442i	$-0.314788\pi$
$263$	4688.06	1.09916	0.549578	+	0.835442i	$0.314788\pi$
$264$	291.485	0.0679533
$265$	8170.92	1.89410
$266$	−584.140	−0.134646
$267$	365.510	0.0837785
$268$	−6184.43	−1.40961
$269$	4527.81	1.02626	0.513132	−	0.858310i	$-0.328485\pi$
$269$	4527.81	1.02626	0.513132	+	0.858310i	$0.328485\pi$
$270$	3760.63	0.847646
$271$	−6159.59	−1.38069	−0.690347	−	0.723478i	$-0.742542\pi$
$271$	−6159.59	−1.38069	−0.690347	+	0.723478i	$0.742542\pi$
$272$	5920.25	1.31973
$273$	678.728	0.150471
$274$	−3217.47	−0.709395
$275$	11744.0	2.57523
$276$	−678.917	−0.148065
$277$	3855.18	0.836228	0.418114	−	0.908395i	$-0.362691\pi$
$277$	3855.18	0.836228	0.418114	+	0.908395i	$0.362691\pi$
$278$	6991.89	1.50844
$279$	−3465.77	−0.743693
$280$	−2478.47	−0.528989
$281$	−3324.51	−0.705779	−0.352889	−	0.935665i	$-0.614801\pi$
$281$	−3324.51	−0.705779	−0.352889	+	0.935665i	$0.614801\pi$
$282$	203.735	0.0430220
$283$	−4159.29	−0.873654	−0.436827	−	0.899545i	$-0.643898\pi$
$283$	−4159.29	−0.873654	−0.436827	+	0.899545i	$0.643898\pi$
$284$	−8176.86	−1.70848
$285$	−103.126	−0.0214339
$286$	−7280.19	−1.50520
$287$	3738.20	0.768847
$288$	−6769.12	−1.38498
$289$	8632.53	1.75708
$290$	−8185.27	−1.65743
$291$	924.842	0.186306
$292$	−6157.41	−1.23402
$293$	7353.48	1.46619	0.733097	−	0.680125i	$-0.238074\pi$
$293$	7353.48	1.46619	0.733097	+	0.680125i	$0.238074\pi$
$294$	718.873	0.142604
$295$	−825.821	−0.162987
$296$	1999.32	0.392595
$297$	2658.23	0.519347
$298$	11720.2	2.27830
$299$	2521.54	0.487707
$300$	−1863.15	−0.358563
$301$	0	0
$302$	3287.21	0.626350
$303$	−694.001	−0.131582
$304$	309.273	0.0583488
$305$	2102.40	0.394699
$306$	−12697.2	−2.37206
$307$	1174.76	0.218395	0.109197	−	0.994020i	$-0.465172\pi$
$307$	1174.76	0.218395	0.109197	+	0.994020i	$0.465172\pi$
$308$	−11781.3	−2.17955
$309$	653.791	0.120365
$310$	10202.6	1.86925
$311$	9650.83	1.75964	0.879821	−	0.475306i	$-0.157663\pi$
$311$	9650.83	1.75964	0.879821	+	0.475306i	$0.157663\pi$
$312$	171.750	0.0311648
$313$	−5956.13	−1.07559	−0.537796	−	0.843075i	$-0.680743\pi$
$313$	−5956.13	−1.07559	−0.537796	+	0.843075i	$0.680743\pi$
$314$	5070.43	0.911276
$315$	−11121.8	−1.98935
$316$	−3835.02	−0.682711
$317$	−5589.77	−0.990388	−0.495194	−	0.868782i	$-0.664903\pi$
$317$	−5589.77	−0.990388	−0.495194	+	0.868782i	$0.664903\pi$
$318$	−1696.33	−0.299137
$319$	−5785.82	−1.01550
$320$	12414.8	2.16878
$321$	1704.68	0.296404
$322$	7554.26	1.30740
$323$	707.617	0.121897
$324$	6214.80	1.06564
$325$	6919.83	1.18106
$326$	1595.90	0.271132
$327$	−1029.38	−0.174082
$328$	945.939	0.159240
$329$	−1224.51	−0.205197
$330$	−3850.52	−0.642316
$331$	9097.55	1.51072	0.755358	−	0.655313i	$-0.227463\pi$
$331$	9097.55	1.51072	0.755358	+	0.655313i	$0.227463\pi$
$332$	−4888.00	−0.808023
$333$	8971.71	1.47642
$334$	−12556.8	−2.05711
$335$	12148.6	1.98134
$336$	−1076.58	−0.174799
$337$	−2936.83	−0.474716	−0.237358	−	0.971422i	$-0.576282\pi$
$337$	−2936.83	−0.474716	−0.237358	+	0.971422i	$0.576282\pi$
$338$	4874.08	0.784364
$339$	−1954.27	−0.313101
$340$	20190.3	3.22051
$341$	7211.78	1.14528
$342$	−663.301	−0.104875
$343$	3580.07	0.563574
$344$	0	0
$345$	1333.65	0.208120
$346$	8148.28	1.26605
$347$	−3259.34	−0.504238	−0.252119	−	0.967696i	$-0.581128\pi$
$347$	−3259.34	−0.504238	−0.252119	+	0.967696i	$0.581128\pi$
$348$	917.902	0.141393
$349$	1394.04	0.213814	0.106907	−	0.994269i	$-0.465905\pi$
$349$	1394.04	0.213814	0.106907	+	0.994269i	$0.465905\pi$
$350$	20731.1	3.16607
$351$	1566.29	0.238183
$352$	14085.6	2.13285
$353$	−13096.6	−1.97468	−0.987342	−	0.158606i	$-0.949300\pi$
$353$	−13096.6	−1.97468	−0.987342	+	0.158606i	$0.949300\pi$
$354$	171.445	0.0257407
$355$	16062.5	2.40143
$356$	−3738.32	−0.556547
$357$	−2463.22	−0.365175
$358$	−199.987	−0.0295241
$359$	5716.76	0.840443	0.420222	−	0.907422i	$-0.361952\pi$
$359$	5716.76	0.840443	0.420222	+	0.907422i	$0.361952\pi$
$360$	−2814.34	−0.412025
$361$	−6822.03	−0.994611
$362$	2498.51	0.362760
$363$	−1498.82	−0.216715
$364$	−6941.81	−0.999588
$365$	12095.5	1.73454
$366$	−436.471	−0.0623352
$367$	−6811.92	−0.968881	−0.484441	−	0.874824i	$-0.660977\pi$
$367$	−6811.92	−0.968881	−0.484441	+	0.874824i	$0.660977\pi$
$368$	−3999.61	−0.566560
$369$	4244.79	0.598848
$370$	−26411.1	−3.71093
$371$	10195.5	1.42675
$372$	−1144.13	−0.159463
$373$	1309.37	0.181760	0.0908799	−	0.995862i	$-0.471032\pi$
$373$	1309.37	0.181760	0.0908799	+	0.995862i	$0.471032\pi$
$374$	26421.1	3.65295
$375$	1539.73	0.212030
$376$	−309.859	−0.0424994
$377$	−3409.14	−0.465729
$378$	4692.44	0.638500
$379$	1104.66	0.149717	0.0748586	−	0.997194i	$-0.476149\pi$
$379$	1104.66	0.149717	0.0748586	+	0.997194i	$0.476149\pi$
$380$	1054.74	0.142387
$381$	2194.51	0.295087
$382$	16306.0	2.18400
$383$	−4201.76	−0.560574	−0.280287	−	0.959916i	$-0.590430\pi$
$383$	−4201.76	−0.560574	−0.280287	+	0.959916i	$0.590430\pi$
$384$	−675.055	−0.0897103
$385$	23143.0	3.06357
$386$	−2811.26	−0.370698
$387$	0	0
$388$	−9458.99	−1.23765
$389$	9046.05	1.17906	0.589528	−	0.807748i	$-0.299314\pi$
$389$	9046.05	1.17906	0.589528	+	0.807748i	$0.299314\pi$
$390$	−2268.82	−0.294580
$391$	−9151.10	−1.18361
$392$	−1093.33	−0.140871
$393$	531.178	0.0681791
$394$	5255.99	0.672063
$395$	7533.45	0.959617
$396$	−13377.9	−1.69763
$397$	−8692.48	−1.09890	−0.549450	−	0.835527i	$-0.685163\pi$
$397$	−8692.48	−1.09890	−0.549450	+	0.835527i	$0.685163\pi$
$398$	4324.77	0.544677
$399$	−128.679	−0.0161453
$400$	−10976.1	−1.37201
$401$	11634.6	1.44888	0.724442	−	0.689336i	$-0.242097\pi$
$401$	11634.6	1.44888	0.724442	+	0.689336i	$0.242097\pi$
$402$	−2522.12	−0.312915
$403$	4249.35	0.525249
$404$	7098.02	0.874108
$405$	−12208.2	−1.49786
$406$	−10213.4	−1.24848
$407$	−18668.9	−2.27366
$408$	−623.310	−0.0756334
$409$	−7680.49	−0.928547	−0.464274	−	0.885692i	$-0.653685\pi$
$409$	−7680.49	−0.928547	−0.464274	+	0.885692i	$0.653685\pi$
$410$	−12495.9	−1.50519
$411$	−708.767	−0.0850630
$412$	−6686.77	−0.799595
$413$	−1030.44	−0.122772
$414$	8577.99	1.01832
$415$	9601.89	1.13576
$416$	8299.55	0.978170
$417$	1540.22	0.180876
$418$	1380.24	0.161506
$419$	14585.1	1.70054	0.850271	−	0.526346i	$-0.176438\pi$
$419$	14585.1	1.70054	0.850271	+	0.526346i	$0.176438\pi$
$420$	−3671.56	−0.426556
$421$	4478.99	0.518510	0.259255	−	0.965809i	$-0.416523\pi$
$421$	4478.99	0.518510	0.259255	+	0.965809i	$0.416523\pi$
$422$	5679.43	0.655143
$423$	−1390.46	−0.159826
$424$	2579.94	0.295502
$425$	−25113.3	−2.86629
$426$	−3334.66	−0.379260
$427$	2623.34	0.297312
$428$	−17434.9	−1.96903
$429$	−1603.73	−0.180487
$430$	0	0
$431$	−3110.01	−0.347572	−0.173786	−	0.984783i	$-0.555600\pi$
$431$	−3110.01	−0.347572	−0.173786	+	0.984783i	$0.555600\pi$
$432$	−2484.42	−0.276693
$433$	651.877	0.0723492	0.0361746	−	0.999345i	$-0.488483\pi$
$433$	651.877	0.0723492	0.0361746	+	0.999345i	$0.488483\pi$
$434$	12730.6	1.40804
$435$	−1803.11	−0.198741
$436$	10528.2	1.15644
$437$	−478.053	−0.0523304
$438$	−2511.09	−0.273938
$439$	−6474.40	−0.703887	−0.351944	−	0.936021i	$-0.614479\pi$
$439$	−6474.40	−0.703887	−0.351944	+	0.936021i	$0.614479\pi$
$440$	5856.25	0.634513
$441$	−4906.19	−0.529769
$442$	15567.9	1.67532
$443$	−12200.0	−1.30844	−0.654219	−	0.756305i	$-0.727003\pi$
$443$	−12200.0	−1.30844	−0.654219	+	0.756305i	$0.727003\pi$
$444$	2961.75	0.316574
$445$	7343.49	0.782281
$446$	5152.85	0.547072
$447$	2581.81	0.273189
$448$	15491.0	1.63366
$449$	5260.37	0.552900	0.276450	−	0.961028i	$-0.410842\pi$
$449$	5260.37	0.552900	0.276450	+	0.961028i	$0.410842\pi$
$450$	23540.5	2.46602
$451$	−8832.81	−0.922219
$452$	19987.6	2.07995
$453$	724.130	0.0751051
$454$	−25256.3	−2.61087
$455$	13636.4	1.40502
$456$	−32.5617	−0.00334395
$457$	9881.41	1.01145	0.505725	−	0.862695i	$-0.331225\pi$
$457$	9881.41	1.01145	0.505725	+	0.862695i	$0.331225\pi$
$458$	−499.027	−0.0509127
$459$	−5684.34	−0.578044
$460$	−13640.2	−1.38256
$461$	2556.87	0.258319	0.129160	−	0.991624i	$-0.458772\pi$
$461$	2556.87	0.258319	0.129160	+	0.991624i	$0.458772\pi$
$462$	−4804.61	−0.483833
$463$	−12947.9	−1.29966	−0.649829	−	0.760080i	$-0.725160\pi$
$463$	−12947.9	−1.29966	−0.649829	+	0.760080i	$0.725160\pi$
$464$	5407.51	0.541029
$465$	2247.50	0.224141
$466$	9780.14	0.972224
$467$	−7817.82	−0.774658	−0.387329	−	0.921942i	$-0.626602\pi$
$467$	−7817.82	−0.774658	−0.387329	+	0.921942i	$0.626602\pi$
$468$	−7882.55	−0.778570
$469$	15158.8	1.49247
$470$	4093.25	0.401718
$471$	1116.95	0.109270
$472$	−260.750	−0.0254280
$473$	0	0
$474$	−1563.99	−0.151553
$475$	−1311.92	−0.126726
$476$	25193.1	2.42589
$477$	11577.2	1.11129
$478$	−1879.25	−0.179822
$479$	8649.91	0.825104	0.412552	−	0.910934i	$-0.364638\pi$
$479$	8649.91	0.825104	0.412552	+	0.910934i	$0.364638\pi$
$480$	4389.67	0.417417
$481$	−11000.1	−1.04275
$482$	−3046.49	−0.287892
$483$	1664.11	0.156769
$484$	15329.5	1.43966
$485$	18581.1	1.73964
$486$	8034.83	0.749933
$487$	−11901.4	−1.10740	−0.553699	−	0.832717i	$-0.686784\pi$
$487$	−11901.4	−1.10740	−0.553699	+	0.832717i	$0.686784\pi$
$488$	663.827	0.0615779
$489$	351.557	0.0325112
$490$	14442.9	1.33156
$491$	−4066.27	−0.373743	−0.186872	−	0.982384i	$-0.559835\pi$
$491$	−4066.27	−0.373743	−0.186872	+	0.982384i	$0.559835\pi$
$492$	1401.30	0.128405
$493$	12372.4	1.13027
$494$	813.267	0.0740701
$495$	26279.2	2.38619
$496$	−6740.23	−0.610172
$497$	20042.5	1.80891
$498$	−1993.41	−0.179371
$499$	736.731	0.0660934	0.0330467	−	0.999454i	$-0.489479\pi$
$499$	736.731	0.0660934	0.0330467	+	0.999454i	$0.489479\pi$
$500$	−15747.9	−1.40853
$501$	−2766.10	−0.246667
$502$	17757.3	1.57878
$503$	−1123.91	−0.0996273	−0.0498137	−	0.998759i	$-0.515863\pi$
$503$	−1123.91	−0.0996273	−0.0498137	+	0.998759i	$0.515863\pi$
$504$	−3511.68	−0.310363
$505$	−13943.2	−1.22864
$506$	−17849.6	−1.56820
$507$	1073.70	0.0940525
$508$	−22444.8	−1.96029
$509$	21029.6	1.83128	0.915638	−	0.402004i	$-0.131686\pi$
$509$	21029.6	1.83128	0.915638	+	0.402004i	$0.131686\pi$
$510$	8233.94	0.714912
$511$	15092.5	1.30656
$512$	−15536.5	−1.34106
$513$	−296.950	−0.0255568
$514$	16579.2	1.42272
$515$	13135.4	1.12391
$516$	0	0
$517$	2893.35	0.246130
$518$	−32955.2	−2.79531
$519$	1794.96	0.151811
$520$	3450.64	0.291001
$521$	−7390.23	−0.621443	−0.310722	−	0.950501i	$-0.600571\pi$
$521$	−7390.23	−0.621443	−0.310722	+	0.950501i	$0.600571\pi$
$522$	−11597.5	−0.972432
$523$	−6900.94	−0.576974	−0.288487	−	0.957484i	$-0.593152\pi$
$523$	−6900.94	−0.576974	−0.288487	+	0.957484i	$0.593152\pi$
$524$	−5432.72	−0.452919
$525$	4566.79	0.379640
$526$	−19554.0	−1.62090
$527$	−15421.6	−1.27472
$528$	2543.81	0.209668
$529$	−5984.69	−0.491879
$530$	−34081.1	−2.79319
$531$	−1170.09	−0.0956261
$532$	1316.08	0.107255
$533$	−5204.50	−0.422949
$534$	−1524.55	−0.123546
$535$	34248.8	2.76767
$536$	3835.88	0.309113
$537$	−44.0545	−0.00354021
$538$	−18885.6	−1.51341
$539$	10209.1	0.815839
$540$	−8472.80	−0.675206
$541$	14325.3	1.13843	0.569215	−	0.822189i	$-0.307247\pi$
$541$	14325.3	1.13843	0.569215	+	0.822189i	$0.307247\pi$
$542$	25691.8	2.03608
$543$	550.391	0.0434982
$544$	−30120.5	−2.37391
$545$	−20681.3	−1.62549
$546$	−2830.99	−0.221896
$547$	−3074.19	−0.240297	−0.120149	−	0.992756i	$-0.538337\pi$
$547$	−3074.19	−0.240297	−0.120149	+	0.992756i	$0.538337\pi$
$548$	7249.05	0.565080
$549$	2978.85	0.231574
$550$	−48984.5	−3.79764
$551$	646.332	0.0499722
$552$	421.096	0.0324693
$553$	9400.09	0.722844
$554$	−16080.0	−1.23317
$555$	−5818.02	−0.444975
$556$	−15752.9	−1.20157
$557$	8152.84	0.620192	0.310096	−	0.950705i	$-0.399639\pi$
$557$	8152.84	0.620192	0.310096	+	0.950705i	$0.399639\pi$
$558$	14455.8	1.09671
$559$	0	0
$560$	−21629.7	−1.63218
$561$	5820.23	0.438022
$562$	13866.6	1.04080
$563$	−3331.24	−0.249370	−0.124685	−	0.992196i	$-0.539792\pi$
$563$	−3331.24	−0.249370	−0.124685	+	0.992196i	$0.539792\pi$
$564$	−459.020	−0.0342699
$565$	−39263.3	−2.92357
$566$	17348.5	1.28836
$567$	−15233.2	−1.12828
$568$	5071.67	0.374653
$569$	5572.79	0.410586	0.205293	−	0.978701i	$-0.434185\pi$
$569$	5572.79	0.410586	0.205293	+	0.978701i	$0.434185\pi$
$570$	430.141	0.0316081
$571$	87.4735	0.00641095	0.00320548	−	0.999995i	$-0.498980\pi$
$571$	87.4735	0.00641095	0.00320548	+	0.999995i	$0.498980\pi$
$572$	16402.5	1.19899
$573$	3592.01	0.261882
$574$	−15592.1	−1.13380
$575$	16966.1	1.23049
$576$	17590.3	1.27244
$577$	−7443.69	−0.537062	−0.268531	−	0.963271i	$-0.586538\pi$
$577$	−7443.69	−0.537062	−0.268531	+	0.963271i	$0.586538\pi$
$578$	−36006.5	−2.59113
$579$	−619.285	−0.0444501
$580$	18441.7	1.32025
$581$	11981.1	0.855522
$582$	−3857.54	−0.274742
$583$	−24090.5	−1.71137
$584$	3819.12	0.270610
$585$	15484.3	1.09436
$586$	−30671.5	−2.16216
$587$	24921.3	1.75232	0.876162	−	0.482018i	$-0.160096\pi$
$587$	24921.3	1.75232	0.876162	+	0.482018i	$0.160096\pi$
$588$	−1619.64	−0.113593
$589$	−805.625	−0.0563586
$590$	3444.52	0.240354
$591$	1157.83	0.0805865
$592$	17448.2	1.21134
$593$	13448.0	0.931269	0.465634	−	0.884977i	$-0.345826\pi$
$593$	13448.0	0.931269	0.465634	+	0.884977i	$0.345826\pi$
$594$	−11087.5	−0.765870
$595$	−49488.8	−3.40982
$596$	−26405.9	−1.81481
$597$	952.693	0.0653117
$598$	−10517.4	−0.719211
$599$	3398.75	0.231835	0.115918	−	0.993259i	$-0.463019\pi$
$599$	3398.75	0.231835	0.115918	+	0.993259i	$0.463019\pi$
$600$	1155.61	0.0786294
$601$	−16525.0	−1.12158	−0.560791	−	0.827957i	$-0.689503\pi$
$601$	−16525.0	−1.12158	−0.560791	+	0.827957i	$0.689503\pi$
$602$	0	0
$603$	17213.1	1.16247
$604$	−7406.18	−0.498929
$605$	−30112.9	−2.02358
$606$	2894.69	0.194041
$607$	27823.1	1.86047	0.930234	−	0.366967i	$-0.119604\pi$
$607$	27823.1	1.86047	0.930234	+	0.366967i	$0.119604\pi$
$608$	−1573.49	−0.104957
$609$	−2249.89	−0.149705
$610$	−8769.17	−0.582055
$611$	1704.83	0.112880
$612$	28607.2	1.88950
$613$	−18027.5	−1.18780	−0.593902	−	0.804537i	$-0.702413\pi$
$613$	−18027.5	−1.18780	−0.593902	+	0.804537i	$0.702413\pi$
$614$	−4899.96	−0.322062
$615$	−2752.68	−0.180486
$616$	7307.32	0.477955
$617$	−8998.57	−0.587146	−0.293573	−	0.955937i	$-0.594844\pi$
$617$	−8998.57	−0.587146	−0.293573	+	0.955937i	$0.594844\pi$
$618$	−2726.98	−0.177500
$619$	119.912	0.00778621	0.00389311	−	0.999992i	$-0.498761\pi$
$619$	119.912	0.00778621	0.00389311	+	0.999992i	$0.498761\pi$
$620$	−22986.7	−1.48898
$621$	3840.23	0.248153
$622$	−40253.8	−2.59491
$623$	9163.07	0.589263
$624$	1498.87	0.0961584
$625$	3962.66	0.253610
$626$	24843.1	1.58615
$627$	304.048	0.0193661
$628$	−11423.8	−0.725892
$629$	39921.4	2.53064
$630$	46389.4	2.93365
$631$	−7482.88	−0.472090	−0.236045	−	0.971742i	$-0.575851\pi$
$631$	−7482.88	−0.472090	−0.236045	+	0.971742i	$0.575851\pi$
$632$	2378.66	0.149712
$633$	1251.11	0.0785577
$634$	23315.1	1.46050
$635$	44090.1	2.75538
$636$	3821.88	0.238282
$637$	6015.44	0.374161
$638$	24132.8	1.49753
$639$	22758.5	1.40894
$640$	−13562.6	−0.837669
$641$	1461.44	0.0900522	0.0450261	−	0.998986i	$-0.485663\pi$
$641$	1461.44	0.0900522	0.0450261	+	0.998986i	$0.485663\pi$
$642$	−7110.24	−0.437101
$643$	−30694.1	−1.88252	−0.941258	−	0.337690i	$-0.890355\pi$
$643$	−30694.1	−1.88252	−0.941258	+	0.337690i	$0.890355\pi$
$644$	−17020.0	−1.04143
$645$	0	0
$646$	−2951.49	−0.179760
$647$	28736.3	1.74612	0.873059	−	0.487614i	$-0.162133\pi$
$647$	28736.3	1.74612	0.873059	+	0.487614i	$0.162133\pi$
$648$	−3854.71	−0.233684
$649$	2434.79	0.147263
$650$	−28862.8	−1.74168
$651$	2804.39	0.168837
$652$	−3595.62	−0.215974
$653$	24660.0	1.47783	0.738914	−	0.673800i	$-0.235339\pi$
$653$	24660.0	1.47783	0.738914	+	0.673800i	$0.235339\pi$
$654$	4293.56	0.256715
$655$	10671.9	0.636622
$656$	8255.26	0.491332
$657$	17137.8	1.01767
$658$	5107.48	0.302599
$659$	6137.88	0.362819	0.181410	−	0.983408i	$-0.441934\pi$
$659$	6137.88	0.362819	0.181410	+	0.983408i	$0.441934\pi$
$660$	8675.34	0.511647
$661$	7831.81	0.460851	0.230425	−	0.973090i	$-0.425988\pi$
$661$	7831.81	0.460851	0.230425	+	0.973090i	$0.425988\pi$
$662$	−37946.1	−2.22782
$663$	3429.41	0.200886
$664$	3031.77	0.177192
$665$	−2585.29	−0.150757
$666$	−37421.2	−2.17724
$667$	−8358.54	−0.485224
$668$	28290.8	1.63863
$669$	1135.11	0.0655990
$670$	−50672.0	−2.92184
$671$	−6198.56	−0.356621
$672$	5477.35	0.314425
$673$	7595.89	0.435067	0.217534	−	0.976053i	$-0.430199\pi$
$673$	7595.89	0.435067	0.217534	+	0.976053i	$0.430199\pi$
$674$	12249.6	0.700054
$675$	10538.7	0.600942
$676$	−10981.4	−0.624798
$677$	−11611.0	−0.659154	−0.329577	−	0.944129i	$-0.606906\pi$
$677$	−11611.0	−0.659154	−0.329577	+	0.944129i	$0.606906\pi$
$678$	8151.29	0.461723
$679$	23185.1	1.31040
$680$	−12523.0	−0.706227
$681$	−5563.64	−0.313068
$682$	−30080.5	−1.68892
$683$	20797.5	1.16514	0.582571	−	0.812779i	$-0.302047\pi$
$683$	20797.5	1.16514	0.582571	+	0.812779i	$0.302047\pi$
$684$	1494.44	0.0835397
$685$	−14239.9	−0.794275
$686$	−14932.6	−0.831090
$687$	−109.929	−0.00610489
$688$	0	0
$689$	−14194.7	−0.784868
$690$	−5562.70	−0.306910
$691$	−18199.9	−1.00197	−0.500983	−	0.865457i	$-0.667028\pi$
$691$	−18199.9	−1.00197	−0.500983	+	0.865457i	$0.667028\pi$
$692$	−18358.3	−1.00849
$693$	32790.7	1.79743
$694$	13594.8	0.743590
$695$	30944.8	1.68892
$696$	−569.326	−0.0310061
$697$	18888.0	1.02645
$698$	−5814.56	−0.315307
$699$	2154.44	0.116579
$700$	−46707.7	−2.52198
$701$	27169.3	1.46386	0.731932	−	0.681377i	$-0.238619\pi$
$701$	27169.3	1.46386	0.731932	+	0.681377i	$0.238619\pi$
$702$	−6533.03	−0.351244
$703$	2085.49	0.111886
$704$	−36602.9	−1.95955
$705$	901.690	0.0481697
$706$	54626.4	2.91203
$707$	−17398.1	−0.925492
$708$	−386.271	−0.0205042
$709$	17361.0	0.919614	0.459807	−	0.888019i	$-0.347919\pi$
$709$	17361.0	0.919614	0.459807	+	0.888019i	$0.347919\pi$
$710$	−66996.9	−3.54134
$711$	10674.0	0.563017
$712$	2318.68	0.122045
$713$	10418.6	0.547235
$714$	10274.2	0.538516
$715$	−32220.7	−1.68530
$716$	450.576	0.0235179
$717$	−413.976	−0.0215623
$718$	−23844.7	−1.23938
$719$	−36955.9	−1.91686	−0.958430	−	0.285327i	$-0.907898\pi$
$719$	−36955.9	−1.91686	−0.958430	+	0.285327i	$0.907898\pi$
$720$	−24560.9	−1.27129
$721$	16390.1	0.846599
$722$	28454.9	1.46673
$723$	−671.104	−0.0345209
$724$	−5629.22	−0.288962
$725$	−22938.3	−1.17504
$726$	6251.61	0.319586
$727$	8748.46	0.446303	0.223151	−	0.974784i	$-0.428366\pi$
$727$	8748.46	0.446303	0.223151	+	0.974784i	$0.428366\pi$
$728$	4305.64	0.219200
$729$	−16085.9	−0.817250
$730$	−50450.6	−2.55789
$731$	0	0
$732$	983.381	0.0496541
$733$	15305.7	0.771252	0.385626	−	0.922655i	$-0.373985\pi$
$733$	15305.7	0.771252	0.385626	+	0.922655i	$0.373985\pi$
$734$	28412.7	1.42879
$735$	3181.59	0.159666
$736$	20348.9	1.01912
$737$	−35817.9	−1.79019
$738$	−17705.1	−0.883109
$739$	−36570.0	−1.82037	−0.910183	−	0.414206i	$-0.864059\pi$
$739$	−36570.0	−1.82037	−0.910183	+	0.414206i	$0.864059\pi$
$740$	59504.9	2.95600
$741$	179.152	0.00888168
$742$	−42525.8	−2.10400
$743$	−33001.6	−1.62949	−0.814745	−	0.579820i	$-0.803123\pi$
$743$	−33001.6	−1.62949	−0.814745	+	0.579820i	$0.803123\pi$
$744$	709.641	0.0349687
$745$	51871.4	2.55090
$746$	−5461.40	−0.268038
$747$	13604.7	0.666359
$748$	−59527.5	−2.90981
$749$	42735.0	2.08478
$750$	−6422.24	−0.312676
$751$	−33182.5	−1.61231	−0.806156	−	0.591703i	$-0.798456\pi$
$751$	−33182.5	−1.61231	−0.806156	+	0.591703i	$0.798456\pi$
$752$	−2704.16	−0.131131
$753$	3911.71	0.189310
$754$	14219.6	0.686801
$755$	14548.6	0.701293
$756$	−10572.2	−0.508607
$757$	−14327.6	−0.687906	−0.343953	−	0.938987i	$-0.611766\pi$
$757$	−14327.6	−0.687906	−0.343953	+	0.938987i	$0.611766\pi$
$758$	−4607.58	−0.220785
$759$	−3932.04	−0.188042
$760$	−654.199	−0.0312241
$761$	10567.0	0.503355	0.251677	−	0.967811i	$-0.419018\pi$
$761$	10567.0	0.503355	0.251677	+	0.967811i	$0.419018\pi$
$762$	−9153.36	−0.435159
$763$	−25805.8	−1.22442
$764$	−36737.9	−1.73970
$765$	−56195.4	−2.65588
$766$	17525.6	0.826666
$767$	1434.63	0.0675379
$768$	−2127.75	−0.0999719
$769$	−6788.88	−0.318353	−0.159176	−	0.987250i	$-0.550884\pi$
$769$	−6788.88	−0.318353	−0.159176	+	0.987250i	$0.550884\pi$
$770$	−96529.9	−4.51779
$771$	3652.19	0.170597
$772$	6333.86	0.295286
$773$	−574.639	−0.0267378	−0.0133689	−	0.999911i	$-0.504256\pi$
$773$	−574.639	−0.0267378	−0.0133689	+	0.999911i	$0.504256\pi$
$774$	0	0
$775$	28591.6	1.32521
$776$	5866.91	0.271405
$777$	−7259.61	−0.335183
$778$	−37731.3	−1.73873
$779$	986.710	0.0453820
$780$	5111.71	0.234652
$781$	−47357.3	−2.16975
$782$	38169.5	1.74544
$783$	−5192.03	−0.236971
$784$	−9541.56	−0.434656
$785$	22440.7	1.02031
$786$	−2215.56	−0.100542
$787$	−25600.4	−1.15954	−0.579769	−	0.814781i	$-0.696857\pi$
$787$	−25600.4	−1.15954	−0.579769	+	0.814781i	$0.696857\pi$
$788$	−11841.9	−0.535342
$789$	−4307.50	−0.194361
$790$	−31422.2	−1.41513
$791$	−48992.0	−2.20222
$792$	8297.58	0.372275
$793$	−3652.33	−0.163554
$794$	36256.5	1.62052
$795$	−7507.63	−0.334929
$796$	−9743.84	−0.433871
$797$	−6270.59	−0.278690	−0.139345	−	0.990244i	$-0.544500\pi$
$797$	−6270.59	−0.278690	−0.139345	+	0.990244i	$0.544500\pi$
$798$	536.721	0.0238092
$799$	−6187.11	−0.273948
$800$	55843.2	2.46794
$801$	10404.8	0.458972
$802$	−48528.0	−2.13664
$803$	−35661.4	−1.56720
$804$	5682.40	0.249257
$805$	33433.7	1.46383
$806$	−17724.1	−0.774573
$807$	−4160.25	−0.181472
$808$	−4402.53	−0.191684
$809$	1819.58	0.0790766	0.0395383	−	0.999218i	$-0.487411\pi$
$809$	1819.58	0.0790766	0.0395383	+	0.999218i	$0.487411\pi$
$810$	50920.9	2.20886
$811$	−6228.52	−0.269683	−0.134841	−	0.990867i	$-0.543053\pi$
$811$	−6228.52	−0.269683	−0.134841	+	0.990867i	$0.543053\pi$
$812$	23011.1	0.994499
$813$	5659.57	0.244145
$814$	77868.3	3.35293
$815$	7063.16	0.303573
$816$	−5439.66	−0.233366
$817$	0	0
$818$	32035.5	1.36931
$819$	19321.1	0.824338
$820$	28153.6	1.19898
$821$	−34997.6	−1.48773	−0.743864	−	0.668331i	$-0.767009\pi$
$821$	−34997.6	−1.48773	−0.743864	+	0.668331i	$0.767009\pi$
$822$	2956.28	0.125441
$823$	−9400.04	−0.398135	−0.199067	−	0.979986i	$-0.563791\pi$
$823$	−9400.04	−0.398135	−0.199067	+	0.979986i	$0.563791\pi$
$824$	4147.45	0.175344
$825$	−10790.7	−0.455372
$826$	4298.01	0.181049
$827$	5005.10	0.210452	0.105226	−	0.994448i	$-0.466443\pi$
$827$	5005.10	0.210452	0.105226	+	0.994448i	$0.466443\pi$
$828$	−19326.5	−0.811160
$829$	−32661.7	−1.36838	−0.684190	−	0.729304i	$-0.739844\pi$
$829$	−32661.7	−1.36838	−0.684190	+	0.729304i	$0.739844\pi$
$830$	−40049.7	−1.67487
$831$	−3542.22	−0.147868
$832$	−21567.3	−0.898691
$833$	−21831.1	−0.908046
$834$	−6424.31	−0.266734
$835$	−55573.9	−2.30325
$836$	−3109.71	−0.128650
$837$	6471.65	0.267256
$838$	−60834.6	−2.50775
$839$	11753.6	0.483648	0.241824	−	0.970320i	$-0.422254\pi$
$839$	11753.6	0.483648	0.241824	+	0.970320i	$0.422254\pi$
$840$	2277.27	0.0935398
$841$	−13088.2	−0.536642
$842$	−18682.0	−0.764636
$843$	3054.64	0.124801
$844$	−12795.9	−0.521865
$845$	21571.8	0.878214
$846$	5799.63	0.235692
$847$	−37574.3	−1.52429
$848$	22515.3	0.911767
$849$	3821.65	0.154486
$850$	104748.	4.22686
$851$	−26970.1	−1.08640
$852$	7513.08	0.302106
$853$	−29813.4	−1.19671	−0.598353	−	0.801232i	$-0.704178\pi$
$853$	−29813.4	−1.19671	−0.598353	+	0.801232i	$0.704178\pi$
$854$	−10942.0	−0.438440
$855$	−2935.64	−0.117423
$856$	10813.9	0.431791
$857$	−34595.8	−1.37896	−0.689481	−	0.724304i	$-0.742161\pi$
$857$	−34595.8	−1.37896	−0.689481	+	0.724304i	$0.742161\pi$
$858$	6689.20	0.266160
$859$	−6449.40	−0.256171	−0.128085	−	0.991763i	$-0.540883\pi$
$859$	−6449.40	−0.256171	−0.128085	+	0.991763i	$0.540883\pi$
$860$	0	0
$861$	−3434.75	−0.135953
$862$	12971.9	0.512558
$863$	−12375.4	−0.488140	−0.244070	−	0.969758i	$-0.578483\pi$
$863$	−12375.4	−0.488140	−0.244070	+	0.969758i	$0.578483\pi$
$864$	12640.0	0.497710
$865$	36062.7	1.41754
$866$	−2718.99	−0.106692
$867$	−7931.77	−0.310700
$868$	−28682.4	−1.12160
$869$	−22211.0	−0.867039
$870$	7520.82	0.293080
$871$	−21104.8	−0.821019
$872$	−6530.06	−0.253596
$873$	26327.1	1.02066
$874$	1993.97	0.0771705
$875$	38599.9	1.49133
$876$	5657.57	0.218209
$877$	16051.9	0.618056	0.309028	−	0.951053i	$-0.399996\pi$
$877$	16051.9	0.618056	0.309028	+	0.951053i	$0.399996\pi$
$878$	27004.9	1.03801
$879$	−6756.54	−0.259263
$880$	51107.8	1.95778
$881$	−35168.8	−1.34491	−0.672456	−	0.740137i	$-0.734761\pi$
$881$	−35168.8	−1.34491	−0.672456	+	0.740137i	$0.734761\pi$
$882$	20463.9	0.781240
$883$	24992.2	0.952497	0.476249	−	0.879311i	$-0.341996\pi$
$883$	24992.2	0.952497	0.476249	+	0.879311i	$0.341996\pi$
$884$	−35075.0	−1.33450
$885$	758.784	0.0288206
$886$	50886.4	1.92953
$887$	−19117.9	−0.723695	−0.361847	−	0.932237i	$-0.617854\pi$
$887$	−19117.9	−0.723695	−0.361847	+	0.932237i	$0.617854\pi$
$888$	−1837.02	−0.0694216
$889$	55014.9	2.07552
$890$	−30629.9	−1.15361
$891$	35993.8	1.35335
$892$	−11609.5	−0.435779
$893$	−323.214	−0.0121119
$894$	−10768.8	−0.402866
$895$	−885.103	−0.0330567
$896$	−16923.1	−0.630985
$897$	−2316.85	−0.0862400
$898$	−21941.1	−0.815351
$899$	−14086.0	−0.522574
$900$	−53037.4	−1.96435
$901$	51515.0	1.90479
$902$	36841.9	1.35998
$903$	0	0
$904$	−12397.3	−0.456114
$905$	11057.9	0.406164
$906$	−3020.36	−0.110756
$907$	9880.51	0.361717	0.180858	−	0.983509i	$-0.442112\pi$
$907$	9880.51	0.361717	0.180858	+	0.983509i	$0.442112\pi$
$908$	56903.1	2.07973
$909$	−19755.8	−0.720858
$910$	−56877.6	−2.07195
$911$	−25267.9	−0.918949	−0.459474	−	0.888191i	$-0.651962\pi$
$911$	−25267.9	−0.918949	−0.459474	+	0.888191i	$0.651962\pi$
$912$	−284.168	−0.0103177
$913$	−28309.5	−1.02618
$914$	−41215.6	−1.49157
$915$	−1931.74	−0.0697937
$916$	1124.32	0.0405553
$917$	13316.2	0.479543
$918$	23709.5	0.852430
$919$	21380.4	0.767436	0.383718	−	0.923450i	$-0.374643\pi$
$919$	21380.4	0.767436	0.383718	+	0.923450i	$0.374643\pi$
$920$	8460.28	0.303182
$921$	−1079.40	−0.0386182
$922$	−10664.7	−0.380938
$923$	−27904.0	−0.995095
$924$	10824.9	0.385405
$925$	−74013.9	−2.63088
$926$	54006.1	1.91658
$927$	18611.2	0.659409
$928$	−27511.8	−0.973190
$929$	8792.54	0.310521	0.155260	−	0.987874i	$-0.450378\pi$
$929$	8792.54	0.310521	0.155260	+	0.987874i	$0.450378\pi$
$930$	−9374.38	−0.330535
$931$	−1140.45	−0.0401470
$932$	−22034.9	−0.774440
$933$	−8867.41	−0.311153
$934$	32608.3	1.14237
$935$	116935.	4.09002
$936$	4889.13	0.170733
$937$	21243.0	0.740640	0.370320	−	0.928904i	$-0.379248\pi$
$937$	21243.0	0.740640	0.370320	+	0.928904i	$0.379248\pi$
$938$	−63227.6	−2.20091
$939$	5472.63	0.190194
$940$	−9222.21	−0.319995
$941$	−49059.8	−1.69958	−0.849789	−	0.527122i	$-0.823271\pi$
$941$	−49059.8	−1.69958	−0.849789	+	0.527122i	$0.823271\pi$
$942$	−4658.83	−0.161139
$943$	−12760.4	−0.440653
$944$	−2275.58	−0.0784576
$945$	20767.8	0.714897
$946$	0	0
$947$	−19388.8	−0.665314	−0.332657	−	0.943048i	$-0.607945\pi$
$947$	−19388.8	−0.665314	−0.332657	+	0.943048i	$0.607945\pi$
$948$	3523.71	0.120722
$949$	−21012.5	−0.718752
$950$	5472.03	0.186880
$951$	5136.01	0.175128
$952$	−15625.9	−0.531974
$953$	42158.7	1.43301	0.716503	−	0.697584i	$-0.245741\pi$
$953$	42158.7	1.43301	0.716503	+	0.697584i	$0.245741\pi$
$954$	−48288.7	−1.63879
$955$	72167.3	2.44532
$956$	4234.01	0.143240
$957$	5316.15	0.179568
$958$	−36079.0	−1.21676
$959$	−17768.3	−0.598298
$960$	−11407.0	−0.383500
$961$	−12233.4	−0.410641
$962$	45881.8	1.53772
$963$	48526.3	1.62382
$964$	6863.84	0.229325
$965$	−12442.1	−0.415053
$966$	−6941.03	−0.231184
$967$	−47691.0	−1.58598	−0.792988	−	0.609237i	$-0.791476\pi$
$967$	−47691.0	−1.58598	−0.792988	+	0.609237i	$0.791476\pi$
$968$	−9508.06	−0.315703
$969$	−650.175	−0.0215548
$970$	−77502.1	−2.56540
$971$	31569.6	1.04337	0.521687	−	0.853137i	$-0.325303\pi$
$971$	31569.6	1.04337	0.521687	+	0.853137i	$0.325303\pi$
$972$	−18102.7	−0.597371
$973$	38612.3	1.27220
$974$	49640.9	1.63306
$975$	−6358.10	−0.208843
$976$	5793.25	0.189997
$977$	−48558.2	−1.59009	−0.795043	−	0.606553i	$-0.792552\pi$
$977$	−48558.2	−1.59009	−0.795043	+	0.606553i	$0.792552\pi$
$978$	−1466.35	−0.0479435
$979$	−21651.0	−0.706811
$980$	−32540.3	−1.06068
$981$	−29302.9	−0.953690
$982$	16960.5	0.551152
$983$	5649.14	0.183296	0.0916479	−	0.995791i	$-0.470787\pi$
$983$	5649.14	0.183296	0.0916479	+	0.995791i	$0.470787\pi$
$984$	−869.150	−0.0281580
$985$	23262.0	0.752476
$986$	−51605.5	−1.66679
$987$	1125.11	0.0362844
$988$	−1832.31	−0.0590017
$989$	0	0
$990$	−109611.	−3.51886
$991$	−16667.2	−0.534259	−0.267129	−	0.963661i	$-0.586075\pi$
$991$	−16667.2	−0.534259	−0.267129	+	0.963661i	$0.586075\pi$
$992$	34292.3	1.09756
$993$	−8359.04	−0.267136
$994$	−83597.5	−2.66756
$995$	19140.6	0.609848
$996$	4491.20	0.142881
$997$	21585.1	0.685663	0.342832	−	0.939397i	$-0.388614\pi$
$997$	21585.1	0.685663	0.342832	+	0.939397i	$0.388614\pi$
$998$	−3072.92	−0.0974666
$999$	−16752.9	−0.530569

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.m.1.20	✓	110
43.42	odd	2	inner	1849.4.a.m.1.91	yes	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.m.1.20	✓	110	1.1	even	1	trivial
1849.4.a.m.1.91	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)

\(f(q)\)	\(=\)	\(q-4.17102 q^{2} -0.918823 q^{3} +9.39743 q^{4} -18.4602 q^{5} +3.83243 q^{6} -23.0342 q^{7} -5.82873 q^{8} -26.1558 q^{9} +O(q^{10})\)	\(q-4.17102 q^{2} -0.918823 q^{3} +9.39743 q^{4} -18.4602 q^{5} +3.83243 q^{6} -23.0342 q^{7} -5.82873 q^{8} -26.1558 q^{9} +76.9977 q^{10} +54.4265 q^{11} -8.63458 q^{12} +32.0693 q^{13} +96.0763 q^{14} +16.9616 q^{15} -50.8677 q^{16} -116.385 q^{17} +109.096 q^{18} -6.07996 q^{19} -173.478 q^{20} +21.1644 q^{21} -227.014 q^{22} +78.6277 q^{23} +5.35558 q^{24} +215.777 q^{25} -133.762 q^{26} +48.8407 q^{27} -216.463 q^{28} -106.305 q^{29} -70.7473 q^{30} +132.505 q^{31} +258.800 q^{32} -50.0083 q^{33} +485.446 q^{34} +425.216 q^{35} -245.797 q^{36} -343.011 q^{37} +25.3596 q^{38} -29.4660 q^{39} +107.599 q^{40} -162.289 q^{41} -88.2772 q^{42} +511.469 q^{44} +482.839 q^{45} -327.958 q^{46} +53.1606 q^{47} +46.7384 q^{48} +187.576 q^{49} -900.012 q^{50} +106.937 q^{51} +301.369 q^{52} -442.625 q^{53} -203.716 q^{54} -1004.72 q^{55} +134.260 q^{56} +5.58641 q^{57} +443.402 q^{58} +44.7353 q^{59} +159.396 q^{60} -113.889 q^{61} -552.682 q^{62} +602.478 q^{63} -672.520 q^{64} -592.005 q^{65} +208.586 q^{66} -658.098 q^{67} -1093.72 q^{68} -72.2449 q^{69} -1773.58 q^{70} -870.116 q^{71} +152.455 q^{72} -655.222 q^{73} +1430.71 q^{74} -198.261 q^{75} -57.1360 q^{76} -1253.67 q^{77} +122.904 q^{78} -408.092 q^{79} +939.025 q^{80} +661.330 q^{81} +676.911 q^{82} -520.142 q^{83} +198.891 q^{84} +2148.49 q^{85} +97.6758 q^{87} -317.237 q^{88} -397.802 q^{89} -2013.93 q^{90} -738.693 q^{91} +738.899 q^{92} -121.749 q^{93} -221.734 q^{94} +112.237 q^{95} -237.792 q^{96} -1006.55 q^{97} -782.384 q^{98} -1423.57 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q + 492 q^{4} + 102 q^{6} + 1234 q^{9}+O(q^{10}) \) 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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