LMFDB - Embedded newform 1870.4.a.j.1.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1870,4,Mod(1,1870)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1870, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1870.1"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 1870 = 2 \cdot 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1870.a (trivial)

Newform invariants

comment:select newform

sage:traces = [10,-20,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$110.333571711$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} - 168 x^{8} + 138 x^{7} + 9025 x^{6} - 8357 x^{5} - 177203 x^{4} + 269951 x^{3} + \cdots + 1239820 $ x^10 - x^9 - 168x^8 + 138x^7 + 9025x^6 - 8357x^5 - 177203x^4 + 269951x^3 + 1064495x^2 - 2545931x + 1239820
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-6.75882$ of defining polynomial
Character	$\chi$	$=$	1870.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.00000 q^{2} +6.75882 q^{3} +4.00000 q^{4} -5.00000 q^{5} -13.5176 q^{6} -13.5453 q^{7} -8.00000 q^{8} +18.6817 q^{9} +10.0000 q^{10} -11.0000 q^{11} +27.0353 q^{12} -22.3689 q^{13} +27.0906 q^{14} -33.7941 q^{15} +16.0000 q^{16} +17.0000 q^{17} -37.3633 q^{18} +151.863 q^{19} -20.0000 q^{20} -91.5504 q^{21} +22.0000 q^{22} -79.5943 q^{23} -54.0706 q^{24} +25.0000 q^{25} +44.7379 q^{26} -56.2222 q^{27} -54.1813 q^{28} +116.745 q^{29} +67.5882 q^{30} +61.9413 q^{31} -32.0000 q^{32} -74.3470 q^{33} -34.0000 q^{34} +67.7266 q^{35} +74.7266 q^{36} +403.396 q^{37} -303.725 q^{38} -151.188 q^{39} +40.0000 q^{40} -491.912 q^{41} +183.101 q^{42} +22.8081 q^{43} -44.0000 q^{44} -93.4083 q^{45} +159.189 q^{46} +94.1471 q^{47} +108.141 q^{48} -159.524 q^{49} -50.0000 q^{50} +114.900 q^{51} -89.4757 q^{52} +329.027 q^{53} +112.444 q^{54} +55.0000 q^{55} +108.363 q^{56} +1026.41 q^{57} -233.491 q^{58} +408.048 q^{59} -135.176 q^{60} -687.911 q^{61} -123.883 q^{62} -253.049 q^{63} +64.0000 q^{64} +111.845 q^{65} +148.694 q^{66} -223.762 q^{67} +68.0000 q^{68} -537.963 q^{69} -135.453 q^{70} -959.473 q^{71} -149.453 q^{72} +321.116 q^{73} -806.791 q^{74} +168.971 q^{75} +607.451 q^{76} +148.999 q^{77} +302.375 q^{78} +259.901 q^{79} -80.0000 q^{80} -884.400 q^{81} +983.824 q^{82} -816.371 q^{83} -366.202 q^{84} -85.0000 q^{85} -45.6161 q^{86} +789.062 q^{87} +88.0000 q^{88} -461.285 q^{89} +186.817 q^{90} +302.994 q^{91} -318.377 q^{92} +418.650 q^{93} -188.294 q^{94} -759.314 q^{95} -216.282 q^{96} +5.85796 q^{97} +319.049 q^{98} -205.498 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 20 q^{2} - q^{3} + 40 q^{4} - 50 q^{5} + 2 q^{6} + 4 q^{7} - 80 q^{8} + 67 q^{9} + 100 q^{10} - 110 q^{11} - 4 q^{12} - 7 q^{13} - 8 q^{14} + 5 q^{15} + 160 q^{16} + 170 q^{17} - 134 q^{18} + 11 q^{19}+ \cdots - 737 q^{99}+O(q^{100}) $ 10 * q - 20 * q^2 - q^3 + 40 * q^4 - 50 * q^5 + 2 * q^6 + 4 * q^7 - 80 * q^8 + 67 * q^9 + 100 * q^10 - 110 * q^11 - 4 * q^12 - 7 * q^13 - 8 * q^14 + 5 * q^15 + 160 * q^16 + 170 * q^17 - 134 * q^18 + 11 * q^19 - 200 * q^20 - 162 * q^21 + 220 * q^22 - 124 * q^23 + 8 * q^24 + 250 * q^25 + 14 * q^26 - 37 * q^27 + 16 * q^28 + 91 * q^29 - 10 * q^30 + 29 * q^31 - 320 * q^32 + 11 * q^33 - 340 * q^34 - 20 * q^35 + 268 * q^36 + 468 * q^37 - 22 * q^38 + 161 * q^39 + 400 * q^40 - 698 * q^41 + 324 * q^42 + 726 * q^43 - 440 * q^44 - 335 * q^45 + 248 * q^46 - 181 * q^47 - 16 * q^48 + 638 * q^49 - 500 * q^50 - 17 * q^51 - 28 * q^52 - 335 * q^53 + 74 * q^54 + 550 * q^55 - 32 * q^56 + 11 * q^57 - 182 * q^58 + 649 * q^59 + 20 * q^60 + 13 * q^61 - 58 * q^62 - 460 * q^63 + 640 * q^64 + 35 * q^65 - 22 * q^66 + 1384 * q^67 + 680 * q^68 + 1304 * q^69 + 40 * q^70 - 1655 * q^71 - 536 * q^72 - 1185 * q^73 - 936 * q^74 - 25 * q^75 + 44 * q^76 - 44 * q^77 - 322 * q^78 + 364 * q^79 - 800 * q^80 + 462 * q^81 + 1396 * q^82 - 120 * q^83 - 648 * q^84 - 850 * q^85 - 1452 * q^86 + 3429 * q^87 + 880 * q^88 - 651 * q^89 + 670 * q^90 - 42 * q^91 - 496 * q^92 - 355 * q^93 + 362 * q^94 - 55 * q^95 + 32 * q^96 + 73 * q^97 - 1276 * q^98 - 737 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	6.75882	1.30074	0.650368	−	0.759619i	$-0.274615\pi$
$3$	6.75882	1.30074	0.650368	+	0.759619i	$0.274615\pi$
$4$	4.00000	0.500000
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−13.5176	−0.919759
$7$	−13.5453	−0.731379	−0.365689	−	0.930737i	$-0.619167\pi$
$7$	−13.5453	−0.731379	−0.365689	+	0.930737i	$0.619167\pi$
$8$	−8.00000	−0.353553
$9$	18.6817	0.691913
$10$	10.0000	0.316228
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	27.0353	0.650368
$13$	−22.3689	−0.477233	−0.238616	−	0.971114i	$-0.576694\pi$
$13$	−22.3689	−0.477233	−0.238616	+	0.971114i	$0.576694\pi$
$14$	27.0906	0.517163
$15$	−33.7941	−0.581707
$16$	16.0000	0.250000
$17$	17.0000	0.242536
$17$	17.0000	0.242536
$18$	−37.3633	−0.489256
$19$	151.863	1.83367	0.916834	−	0.399268i	$-0.130736\pi$
$19$	151.863	1.83367	0.916834	+	0.399268i	$0.130736\pi$
$20$	−20.0000	−0.223607
$21$	−91.5504	−0.951330
$22$	22.0000	0.213201
$23$	−79.5943	−0.721589	−0.360795	−	0.932645i	$-0.617494\pi$
$23$	−79.5943	−0.721589	−0.360795	+	0.932645i	$0.617494\pi$
$24$	−54.0706	−0.459879
$25$	25.0000	0.200000
$26$	44.7379	0.337455
$27$	−56.2222	−0.400740
$28$	−54.1813	−0.365689
$29$	116.745	0.747555	0.373777	−	0.927518i	$-0.378062\pi$
$29$	116.745	0.747555	0.373777	+	0.927518i	$0.378062\pi$
$30$	67.5882	0.411329
$31$	61.9413	0.358871	0.179435	−	0.983770i	$-0.442573\pi$
$31$	61.9413	0.358871	0.179435	+	0.983770i	$0.442573\pi$
$32$	−32.0000	−0.176777
$33$	−74.3470	−0.392187
$34$	−34.0000	−0.171499
$35$	67.7266	0.327082
$36$	74.7266	0.345957
$37$	403.396	1.79237	0.896187	−	0.443677i	$-0.146326\pi$
$37$	403.396	1.79237	0.896187	+	0.443677i	$0.146326\pi$
$38$	−303.725	−1.29660
$39$	−151.188	−0.620754
$40$	40.0000	0.158114
$41$	−491.912	−1.87375	−0.936875	−	0.349664i	$-0.886296\pi$
$41$	−491.912	−1.87375	−0.936875	+	0.349664i	$0.886296\pi$
$42$	183.101	0.672692
$43$	22.8081	0.0808883	0.0404442	−	0.999182i	$-0.487123\pi$
$43$	22.8081	0.0808883	0.0404442	+	0.999182i	$0.487123\pi$
$44$	−44.0000	−0.150756
$45$	−93.4083	−0.309433
$46$	159.189	0.510241
$47$	94.1471	0.292186	0.146093	−	0.989271i	$-0.453330\pi$
$47$	94.1471	0.292186	0.146093	+	0.989271i	$0.453330\pi$
$48$	108.141	0.325184
$49$	−159.524	−0.465085
$50$	−50.0000	−0.141421
$51$	114.900	0.315475
$52$	−89.4757	−0.238616
$53$	329.027	0.852743	0.426371	−	0.904548i	$-0.359792\pi$
$53$	329.027	0.852743	0.426371	+	0.904548i	$0.359792\pi$
$54$	112.444	0.283366
$55$	55.0000	0.134840
$56$	108.363	0.258581
$57$	1026.41	2.38512
$58$	−233.491	−0.528601
$59$	408.048	0.900395	0.450197	−	0.892929i	$-0.351354\pi$
$59$	408.048	0.900395	0.450197	+	0.892929i	$0.351354\pi$
$60$	−135.176	−0.290853
$61$	−687.911	−1.44390	−0.721951	−	0.691944i	$-0.756754\pi$
$61$	−687.911	−1.44390	−0.721951	+	0.691944i	$0.756754\pi$
$62$	−123.883	−0.253760
$63$	−253.049	−0.506050
$64$	64.0000	0.125000
$65$	111.845	0.213425
$66$	148.694	0.277318
$67$	−223.762	−0.408013	−0.204006	−	0.978970i	$-0.565396\pi$
$67$	−223.762	−0.408013	−0.204006	+	0.978970i	$0.565396\pi$
$68$	68.0000	0.121268
$69$	−537.963	−0.938597
$70$	−135.453	−0.231282
$71$	−959.473	−1.60378	−0.801891	−	0.597471i	$-0.796172\pi$
$71$	−959.473	−1.60378	−0.801891	+	0.597471i	$0.796172\pi$
$72$	−149.453	−0.244628
$73$	321.116	0.514847	0.257424	−	0.966299i	$-0.417126\pi$
$73$	321.116	0.514847	0.257424	+	0.966299i	$0.417126\pi$
$74$	−806.791	−1.26740
$75$	168.971	0.260147
$76$	607.451	0.916834
$77$	148.999	0.220519
$78$	302.375	0.438939
$79$	259.901	0.370141	0.185070	−	0.982725i	$-0.440749\pi$
$79$	259.901	0.370141	0.185070	+	0.982725i	$0.440749\pi$
$80$	−80.0000	−0.111803
$81$	−884.400	−1.21317
$82$	983.824	1.32494
$83$	−816.371	−1.07962	−0.539810	−	0.841787i	$-0.681504\pi$
$83$	−816.371	−1.07962	−0.539810	+	0.841787i	$0.681504\pi$
$84$	−366.202	−0.475665
$85$	−85.0000	−0.108465
$86$	−45.6161	−0.0571967
$87$	789.062	0.972371
$88$	88.0000	0.106600
$89$	−461.285	−0.549395	−0.274697	−	0.961531i	$-0.588578\pi$
$89$	−461.285	−0.549395	−0.274697	+	0.961531i	$0.588578\pi$
$90$	186.817	0.218802
$91$	302.994	0.349038
$92$	−318.377	−0.360795
$93$	418.650	0.466796
$94$	−188.294	−0.206607
$95$	−759.314	−0.820041
$96$	−216.282	−0.229940
$97$	5.85796	0.00613181	0.00306591	−	0.999995i	$-0.499024\pi$
$97$	5.85796	0.00613181	0.00306591	+	0.999995i	$0.499024\pi$
$98$	319.049	0.328865
$99$	−205.498	−0.208620
$100$	100.000	0.100000
$101$	170.428	0.167903	0.0839516	−	0.996470i	$-0.473246\pi$
$101$	170.428	0.167903	0.0839516	+	0.996470i	$0.473246\pi$
$102$	−229.800	−0.223074
$103$	−654.386	−0.626006	−0.313003	−	0.949752i	$-0.601335\pi$
$103$	−654.386	−0.626006	−0.313003	+	0.949752i	$0.601335\pi$
$104$	178.951	0.168727
$105$	457.752	0.425448
$106$	−658.054	−0.602980
$107$	−10.0987	−0.00912414	−0.00456207	−	0.999990i	$-0.501452\pi$
$107$	−10.0987	−0.00912414	−0.00456207	+	0.999990i	$0.501452\pi$
$108$	−224.889	−0.200370
$109$	−1030.90	−0.905889	−0.452945	−	0.891539i	$-0.649626\pi$
$109$	−1030.90	−0.905889	−0.452945	+	0.891539i	$0.649626\pi$
$110$	−110.000	−0.0953463
$111$	2726.48	2.33140
$112$	−216.725	−0.182845
$113$	−1445.50	−1.20337	−0.601687	−	0.798732i	$-0.705505\pi$
$113$	−1445.50	−1.20337	−0.601687	+	0.798732i	$0.705505\pi$
$114$	−2052.83	−1.68653
$115$	397.971	0.322704
$116$	466.982	0.373777
$117$	−417.889	−0.330204
$118$	−816.096	−0.636675
$119$	−230.270	−0.177385
$120$	270.353	0.205664
$121$	121.000	0.0909091
$122$	1375.82	1.02099
$123$	−3324.75	−2.43725
$124$	247.765	0.179435
$125$	−125.000	−0.0894427
$126$	506.098	0.357832
$127$	−2019.43	−1.41099	−0.705493	−	0.708717i	$-0.749274\pi$
$127$	−2019.43	−1.41099	−0.705493	+	0.708717i	$0.749274\pi$
$128$	−128.000	−0.0883883
$129$	154.156	0.105214
$130$	−223.689	−0.150914
$131$	−2614.85	−1.74397	−0.871985	−	0.489533i	$-0.837167\pi$
$131$	−2614.85	−1.74397	−0.871985	+	0.489533i	$0.837167\pi$
$132$	−297.388	−0.196093
$133$	−2057.03	−1.34111
$134$	447.523	0.288508
$135$	281.111	0.179216
$136$	−136.000	−0.0857493
$137$	−1359.91	−0.848063	−0.424032	−	0.905647i	$-0.639385\pi$
$137$	−1359.91	−0.848063	−0.424032	+	0.905647i	$0.639385\pi$
$138$	1075.93	0.663688
$139$	−1926.84	−1.17577	−0.587886	−	0.808944i	$-0.700040\pi$
$139$	−1926.84	−1.17577	−0.587886	+	0.808944i	$0.700040\pi$
$140$	270.906	0.163541
$141$	636.323	0.380057
$142$	1918.95	1.13404
$143$	246.058	0.143891
$144$	298.906	0.172978
$145$	−583.727	−0.334317
$146$	−642.233	−0.364052
$147$	−1078.20	−0.604953
$148$	1613.58	0.896187
$149$	−1761.68	−0.968605	−0.484303	−	0.874901i	$-0.660927\pi$
$149$	−1761.68	−0.968605	−0.484303	+	0.874901i	$0.660927\pi$
$150$	−337.941	−0.183952
$151$	−539.773	−0.290901	−0.145451	−	0.989366i	$-0.546463\pi$
$151$	−539.773	−0.290901	−0.145451	+	0.989366i	$0.546463\pi$
$152$	−1214.90	−0.648300
$153$	317.588	0.167814
$154$	−297.997	−0.155930
$155$	−309.707	−0.160492
$156$	−604.750	−0.310377
$157$	1435.83	0.729885	0.364942	−	0.931030i	$-0.381089\pi$
$157$	1435.83	0.729885	0.364942	+	0.931030i	$0.381089\pi$
$158$	−519.801	−0.261729
$159$	2223.84	1.10919
$160$	160.000	0.0790569
$161$	1078.13	0.527755
$162$	1768.80	0.857840
$163$	260.042	0.124957	0.0624787	−	0.998046i	$-0.480099\pi$
$163$	260.042	0.124957	0.0624787	+	0.998046i	$0.480099\pi$
$164$	−1967.65	−0.936875
$165$	371.735	0.175391
$166$	1632.74	0.763406
$167$	−304.465	−0.141079	−0.0705395	−	0.997509i	$-0.522472\pi$
$167$	−304.465	−0.141079	−0.0705395	+	0.997509i	$0.522472\pi$
$168$	732.403	0.336346
$169$	−1696.63	−0.772249
$170$	170.000	0.0766965
$171$	2837.05	1.26874
$172$	91.2323	0.0404442
$173$	2306.83	1.01379	0.506893	−	0.862009i	$-0.330794\pi$
$173$	2306.83	1.01379	0.506893	+	0.862009i	$0.330794\pi$
$174$	−1578.12	−0.687570
$175$	−338.633	−0.146276
$176$	−176.000	−0.0753778
$177$	2757.92	1.17118
$178$	922.571	0.388481
$179$	1393.68	0.581948	0.290974	−	0.956731i	$-0.406021\pi$
$179$	1393.68	0.581948	0.290974	+	0.956731i	$0.406021\pi$
$180$	−373.633	−0.154716
$181$	−915.395	−0.375916	−0.187958	−	0.982177i	$-0.560187\pi$
$181$	−915.395	−0.375916	−0.187958	+	0.982177i	$0.560187\pi$
$182$	−605.989	−0.246807
$183$	−4649.47	−1.87813
$184$	636.754	0.255120
$185$	−2016.98	−0.801574
$186$	−837.301	−0.330075
$187$	−187.000	−0.0731272
$188$	376.588	0.146093
$189$	761.548	0.293092
$190$	1518.63	0.579857
$191$	743.146	0.281529	0.140765	−	0.990043i	$-0.455044\pi$
$191$	743.146	0.281529	0.140765	+	0.990043i	$0.455044\pi$
$192$	432.565	0.162592
$193$	125.566	0.0468313	0.0234157	−	0.999726i	$-0.492546\pi$
$193$	125.566	0.0468313	0.0234157	+	0.999726i	$0.492546\pi$
$194$	−11.7159	−0.00433585
$195$	755.938	0.277609
$196$	−638.097	−0.232543
$197$	−4303.89	−1.55655	−0.778274	−	0.627925i	$-0.783904\pi$
$197$	−4303.89	−1.55655	−0.778274	+	0.627925i	$0.783904\pi$
$198$	410.996	0.147516
$199$	2456.43	0.875033	0.437516	−	0.899210i	$-0.355858\pi$
$199$	2456.43	0.875033	0.437516	+	0.899210i	$0.355858\pi$
$200$	−200.000	−0.0707107
$201$	−1512.37	−0.530716
$202$	−340.856	−0.118725
$203$	−1581.36	−0.546746
$204$	459.600	0.157737
$205$	2459.56	0.837967
$206$	1308.77	0.442653
$207$	−1486.95	−0.499277
$208$	−357.903	−0.119308
$209$	−1670.49	−0.552872
$210$	−915.504	−0.300837
$211$	−3118.02	−1.01731	−0.508657	−	0.860969i	$-0.669858\pi$
$211$	−3118.02	−1.01731	−0.508657	+	0.860969i	$0.669858\pi$
$212$	1316.11	0.426371
$213$	−6484.90	−2.08610
$214$	20.1975	0.00645174
$215$	−114.040	−0.0361744
$216$	449.778	0.141683
$217$	−839.015	−0.262470
$218$	2061.79	0.640560
$219$	2170.37	0.669680
$220$	220.000	0.0674200
$221$	−380.272	−0.115746
$222$	−5452.96	−1.64855
$223$	4296.53	1.29021	0.645105	−	0.764094i	$-0.276813\pi$
$223$	4296.53	1.29021	0.645105	+	0.764094i	$0.276813\pi$
$224$	433.450	0.129291
$225$	467.041	0.138383
$226$	2891.00	0.850914
$227$	−1676.69	−0.490245	−0.245123	−	0.969492i	$-0.578828\pi$
$227$	−1676.69	−0.490245	−0.245123	+	0.969492i	$0.578828\pi$
$228$	4105.65	1.19256
$229$	−2750.10	−0.793588	−0.396794	−	0.917908i	$-0.629877\pi$
$229$	−2750.10	−0.793588	−0.396794	+	0.917908i	$0.629877\pi$
$230$	−795.943	−0.228187
$231$	1007.05	0.286837
$232$	−933.964	−0.264301
$233$	2624.96	0.738056	0.369028	−	0.929418i	$-0.379691\pi$
$233$	2624.96	0.738056	0.369028	+	0.929418i	$0.379691\pi$
$234$	835.777	0.233489
$235$	−470.735	−0.130670
$236$	1632.19	0.450197
$237$	1756.62	0.481455
$238$	460.541	0.125430
$239$	4062.01	1.09937	0.549685	−	0.835372i	$-0.314748\pi$
$239$	4062.01	1.09937	0.549685	+	0.835372i	$0.314748\pi$
$240$	−540.706	−0.145427
$241$	3235.21	0.864723	0.432362	−	0.901700i	$-0.357680\pi$
$241$	3235.21	0.864723	0.432362	+	0.901700i	$0.357680\pi$
$242$	−242.000	−0.0642824
$243$	−4459.50	−1.17727
$244$	−2751.64	−0.721951
$245$	797.621	0.207992
$246$	6649.49	1.72340
$247$	−3397.01	−0.875087
$248$	−495.531	−0.126880
$249$	−5517.71	−1.40430
$250$	250.000	0.0632456
$251$	3925.65	0.987190	0.493595	−	0.869692i	$-0.335682\pi$
$251$	3925.65	0.987190	0.493595	+	0.869692i	$0.335682\pi$
$252$	−1012.20	−0.253025
$253$	875.537	0.217567
$254$	4038.86	0.997718
$255$	−574.500	−0.141085
$256$	256.000	0.0625000
$257$	3615.49	0.877540	0.438770	−	0.898599i	$-0.355414\pi$
$257$	3615.49	0.877540	0.438770	+	0.898599i	$0.355414\pi$
$258$	−308.311	−0.0743978
$259$	−5464.12	−1.31090
$260$	447.379	0.106712
$261$	2181.00	0.517243
$262$	5229.69	1.23317
$263$	5875.14	1.37748	0.688739	−	0.725009i	$-0.258165\pi$
$263$	5875.14	1.37748	0.688739	+	0.725009i	$0.258165\pi$
$264$	594.776	0.138659
$265$	−1645.14	−0.381358
$266$	4114.06	0.948305
$267$	−3117.75	−0.714618
$268$	−895.047	−0.204006
$269$	−3528.62	−0.799792	−0.399896	−	0.916561i	$-0.630954\pi$
$269$	−3528.62	−0.799792	−0.399896	+	0.916561i	$0.630954\pi$
$270$	−562.222	−0.126725
$271$	1140.78	0.255709	0.127855	−	0.991793i	$-0.459191\pi$
$271$	1140.78	0.255709	0.127855	+	0.991793i	$0.459191\pi$
$272$	272.000	0.0606339
$273$	2047.88	0.454006
$274$	2719.81	0.599671
$275$	−275.000	−0.0603023
$276$	−2151.85	−0.469298
$277$	7928.71	1.71982	0.859910	−	0.510445i	$-0.170519\pi$
$277$	7928.71	1.71982	0.859910	+	0.510445i	$0.170519\pi$
$278$	3853.68	0.831396
$279$	1157.17	0.248307
$280$	−541.813	−0.115641
$281$	−3202.47	−0.679869	−0.339935	−	0.940449i	$-0.610405\pi$
$281$	−3202.47	−0.679869	−0.339935	+	0.940449i	$0.610405\pi$
$282$	−1272.65	−0.268741
$283$	−7887.69	−1.65680	−0.828400	−	0.560137i	$-0.810749\pi$
$283$	−7887.69	−1.65680	−0.828400	+	0.560137i	$0.810749\pi$
$284$	−3837.89	−0.801891
$285$	−5132.06	−1.06666
$286$	−492.117	−0.101746
$287$	6663.11	1.37042
$288$	−597.813	−0.122314
$289$	289.000	0.0588235
$290$	1167.45	0.236398
$291$	39.5929	0.00797587
$292$	1284.47	0.257424
$293$	1366.96	0.272555	0.136277	−	0.990671i	$-0.456486\pi$
$293$	1366.96	0.272555	0.136277	+	0.990671i	$0.456486\pi$
$294$	2156.39	0.427766
$295$	−2040.24	−0.402669
$296$	−3227.17	−0.633700
$297$	618.444	0.120828
$298$	3523.35	0.684907
$299$	1780.44	0.344366
$300$	675.882	0.130074
$301$	−308.943	−0.0591600
$302$	1079.55	0.205698
$303$	1151.89	0.218398
$304$	2429.80	0.458417
$305$	3439.56	0.645732
$306$	−635.176	−0.118662
$307$	−3078.43	−0.572298	−0.286149	−	0.958185i	$-0.592375\pi$
$307$	−3078.43	−0.572298	−0.286149	+	0.958185i	$0.592375\pi$
$308$	595.994	0.110259
$309$	−4422.88	−0.814268
$310$	619.413	0.113485
$311$	4222.02	0.769804	0.384902	−	0.922958i	$-0.374235\pi$
$311$	4222.02	0.769804	0.384902	+	0.922958i	$0.374235\pi$
$312$	1209.50	0.219470
$313$	3049.54	0.550704	0.275352	−	0.961344i	$-0.411206\pi$
$313$	3049.54	0.550704	0.275352	+	0.961344i	$0.411206\pi$
$314$	−2871.66	−0.516106
$315$	1265.25	0.226313
$316$	1039.60	0.185070
$317$	2878.98	0.510093	0.255046	−	0.966929i	$-0.417909\pi$
$317$	2878.98	0.510093	0.255046	+	0.966929i	$0.417909\pi$
$318$	−4447.67	−0.784318
$319$	−1284.20	−0.225396
$320$	−320.000	−0.0559017
$321$	−68.2556	−0.0118681
$322$	−2156.26	−0.373179
$323$	2581.67	0.444730
$324$	−3537.60	−0.606585
$325$	−559.223	−0.0954466
$326$	−520.084	−0.0883582
$327$	−6967.64	−1.17832
$328$	3935.30	0.662471
$329$	−1275.25	−0.213699
$330$	−743.470	−0.124020
$331$	2885.34	0.479132	0.239566	−	0.970880i	$-0.422995\pi$
$331$	2885.34	0.479132	0.239566	+	0.970880i	$0.422995\pi$
$332$	−3265.49	−0.539810
$333$	7536.10	1.24017
$334$	608.930	0.0997580
$335$	1118.81	0.182469
$336$	−1464.81	−0.237833
$337$	−4275.07	−0.691032	−0.345516	−	0.938413i	$-0.612296\pi$
$337$	−4275.07	−0.691032	−0.345516	+	0.938413i	$0.612296\pi$
$338$	3393.26	0.546062
$339$	−9769.88	−1.56527
$340$	−340.000	−0.0542326
$341$	−681.355	−0.108204
$342$	−5674.09	−0.897134
$343$	6806.85	1.07153
$344$	−182.465	−0.0285983
$345$	2689.82	0.419753
$346$	−4613.66	−0.716856
$347$	−6754.63	−1.04498	−0.522489	−	0.852646i	$-0.674996\pi$
$347$	−6754.63	−1.04498	−0.522489	+	0.852646i	$0.674996\pi$
$348$	3156.25	0.486186
$349$	−9241.25	−1.41740	−0.708700	−	0.705510i	$-0.750718\pi$
$349$	−9241.25	−1.41740	−0.708700	+	0.705510i	$0.750718\pi$
$350$	677.266	0.103433
$351$	1257.63	0.191246
$352$	352.000	0.0533002
$353$	−6370.31	−0.960502	−0.480251	−	0.877131i	$-0.659455\pi$
$353$	−6370.31	−0.960502	−0.480251	+	0.877131i	$0.659455\pi$
$354$	−5515.84	−0.828146
$355$	4797.36	0.717233
$356$	−1845.14	−0.274697
$357$	−1556.36	−0.230731
$358$	−2787.36	−0.411499
$359$	−1023.31	−0.150441	−0.0752207	−	0.997167i	$-0.523966\pi$
$359$	−1023.31	−0.150441	−0.0752207	+	0.997167i	$0.523966\pi$
$360$	747.266	0.109401
$361$	16203.3	2.36234
$362$	1830.79	0.265813
$363$	817.817	0.118249
$364$	1211.98	0.174519
$365$	−1605.58	−0.230247
$366$	9298.94	1.32804
$367$	−2889.17	−0.410936	−0.205468	−	0.978664i	$-0.565872\pi$
$367$	−2889.17	−0.410936	−0.205468	+	0.978664i	$0.565872\pi$
$368$	−1273.51	−0.180397
$369$	−9189.73	−1.29647
$370$	4033.96	0.566798
$371$	−4456.78	−0.623678
$372$	1674.60	0.233398
$373$	−5977.62	−0.829784	−0.414892	−	0.909871i	$-0.636181\pi$
$373$	−5977.62	−0.829784	−0.414892	+	0.909871i	$0.636181\pi$
$374$	374.000	0.0517088
$375$	−844.853	−0.116341
$376$	−753.177	−0.103304
$377$	−2611.47	−0.356758
$378$	−1523.10	−0.207248
$379$	738.455	0.100084	0.0500421	−	0.998747i	$-0.484064\pi$
$379$	738.455	0.100084	0.0500421	+	0.998747i	$0.484064\pi$
$380$	−3037.25	−0.410021
$381$	−13648.9	−1.83532
$382$	−1486.29	−0.199071
$383$	−10225.5	−1.36423	−0.682115	−	0.731245i	$-0.738940\pi$
$383$	−10225.5	−1.36423	−0.682115	+	0.731245i	$0.738940\pi$
$384$	−865.129	−0.114970
$385$	−744.993	−0.0986191
$386$	−251.132	−0.0331147
$387$	426.092	0.0559677
$388$	23.4318	0.00306591
$389$	−6493.43	−0.846350	−0.423175	−	0.906048i	$-0.639084\pi$
$389$	−6493.43	−0.846350	−0.423175	+	0.906048i	$0.639084\pi$
$390$	−1511.88	−0.196300
$391$	−1353.10	−0.175011
$392$	1276.19	0.164432
$393$	−17673.3	−2.26844
$394$	8607.79	1.10065
$395$	−1299.50	−0.165532
$396$	−821.993	−0.104310
$397$	−3842.04	−0.485709	−0.242855	−	0.970063i	$-0.578084\pi$
$397$	−3842.04	−0.485709	−0.242855	+	0.970063i	$0.578084\pi$
$398$	−4912.86	−0.618742
$399$	−13903.1	−1.74442
$400$	400.000	0.0500000
$401$	10128.4	1.26132	0.630660	−	0.776059i	$-0.282784\pi$
$401$	10128.4	1.26132	0.630660	+	0.776059i	$0.282784\pi$
$402$	3024.73	0.375273
$403$	−1385.56	−0.171265
$404$	681.712	0.0839516
$405$	4422.00	0.542546
$406$	3162.71	0.386608
$407$	−4437.35	−0.540421
$408$	−919.200	−0.111537
$409$	−14703.2	−1.77757	−0.888783	−	0.458329i	$-0.848448\pi$
$409$	−14703.2	−1.77757	−0.888783	+	0.458329i	$0.848448\pi$
$410$	−4919.12	−0.592532
$411$	−9191.37	−1.10311
$412$	−2617.54	−0.313003
$413$	−5527.14	−0.658530
$414$	2973.91	0.353042
$415$	4081.86	0.482820
$416$	715.806	0.0843636
$417$	−13023.2	−1.52937
$418$	3340.98	0.390939
$419$	−10674.5	−1.24458	−0.622292	−	0.782785i	$-0.713799\pi$
$419$	−10674.5	−1.24458	−0.622292	+	0.782785i	$0.713799\pi$
$420$	1831.01	0.212724
$421$	10823.9	1.25302	0.626512	−	0.779412i	$-0.284482\pi$
$421$	10823.9	1.25302	0.626512	+	0.779412i	$0.284482\pi$
$422$	6236.04	0.719350
$423$	1758.82	0.202168
$424$	−2632.22	−0.301490
$425$	425.000	0.0485071
$426$	12969.8	1.47509
$427$	9317.98	1.05604
$428$	−40.3950	−0.00456207
$429$	1663.06	0.187164
$430$	228.081	0.0255791
$431$	−7772.91	−0.868696	−0.434348	−	0.900745i	$-0.643021\pi$
$431$	−7772.91	−0.868696	−0.434348	+	0.900745i	$0.643021\pi$
$432$	−899.555	−0.100185
$433$	5310.75	0.589419	0.294710	−	0.955587i	$-0.404777\pi$
$433$	5310.75	0.589419	0.294710	+	0.955587i	$0.404777\pi$
$434$	1678.03	0.185595
$435$	−3945.31	−0.434858
$436$	−4123.58	−0.452945
$437$	−12087.4	−1.32316
$438$	−4340.74	−0.473535
$439$	2456.03	0.267016	0.133508	−	0.991048i	$-0.457376\pi$
$439$	2456.03	0.267016	0.133508	+	0.991048i	$0.457376\pi$
$440$	−440.000	−0.0476731
$441$	−2980.18	−0.321799
$442$	760.544	0.0818448
$443$	6091.14	0.653271	0.326635	−	0.945150i	$-0.394085\pi$
$443$	6091.14	0.653271	0.326635	+	0.945150i	$0.394085\pi$
$444$	10905.9	1.16570
$445$	2306.43	0.245697
$446$	−8593.06	−0.912317
$447$	−11906.9	−1.25990
$448$	−866.901	−0.0914223
$449$	−7342.12	−0.771706	−0.385853	−	0.922560i	$-0.626093\pi$
$449$	−7342.12	−0.771706	−0.385853	+	0.922560i	$0.626093\pi$
$450$	−934.083	−0.0978513
$451$	5411.03	0.564957
$452$	−5782.00	−0.601687
$453$	−3648.23	−0.378385
$454$	3353.38	0.346656
$455$	−1514.97	−0.156094
$456$	−8211.30	−0.843266
$457$	3095.08	0.316809	0.158404	−	0.987374i	$-0.449365\pi$
$457$	3095.08	0.316809	0.158404	+	0.987374i	$0.449365\pi$
$458$	5500.20	0.561151
$459$	−955.778	−0.0971936
$460$	1591.89	0.161352
$461$	−10041.3	−1.01447	−0.507233	−	0.861809i	$-0.669332\pi$
$461$	−10041.3	−1.01447	−0.507233	+	0.861809i	$0.669332\pi$
$462$	−2014.11	−0.202824
$463$	−3726.25	−0.374024	−0.187012	−	0.982358i	$-0.559880\pi$
$463$	−3726.25	−0.374024	−0.187012	+	0.982358i	$0.559880\pi$
$464$	1867.93	0.186889
$465$	−2093.25	−0.208758
$466$	−5249.93	−0.521885
$467$	−8836.46	−0.875594	−0.437797	−	0.899074i	$-0.644241\pi$
$467$	−8836.46	−0.875594	−0.437797	+	0.899074i	$0.644241\pi$
$468$	−1671.55	−0.165102
$469$	3030.92	0.298412
$470$	941.471	0.0923975
$471$	9704.53	0.949387
$472$	−3264.38	−0.318338
$473$	−250.889	−0.0243887
$474$	−3513.24	−0.340440
$475$	3796.57	0.366734
$476$	−921.082	−0.0886927
$477$	6146.77	0.590024
$478$	−8124.01	−0.777372
$479$	−15932.7	−1.51980	−0.759902	−	0.650038i	$-0.774753\pi$
$479$	−15932.7	−1.51980	−0.759902	+	0.650038i	$0.774753\pi$
$480$	1081.41	0.102832
$481$	−9023.53	−0.855380
$482$	−6470.42	−0.611452
$483$	7286.89	0.686470
$484$	484.000	0.0454545
$485$	−29.2898	−0.00274223
$486$	8919.01	0.832458
$487$	17676.7	1.64478	0.822390	−	0.568925i	$-0.192640\pi$
$487$	17676.7	1.64478	0.822390	+	0.568925i	$0.192640\pi$
$488$	5503.29	0.510496
$489$	1757.58	0.162537
$490$	−1595.24	−0.147073
$491$	−5360.92	−0.492740	−0.246370	−	0.969176i	$-0.579238\pi$
$491$	−5360.92	−0.492740	−0.246370	+	0.969176i	$0.579238\pi$
$492$	−13299.0	−1.21863
$493$	1984.67	0.181309
$494$	6794.01	0.618780
$495$	1027.49	0.0932975
$496$	991.062	0.0897177
$497$	12996.4	1.17297
$498$	11035.4	0.992989
$499$	3491.18	0.313200	0.156600	−	0.987662i	$-0.449947\pi$
$499$	3491.18	0.313200	0.156600	+	0.987662i	$0.449947\pi$
$500$	−500.000	−0.0447214
$501$	−2057.82	−0.183507
$502$	−7851.30	−0.698049
$503$	−17824.6	−1.58003	−0.790017	−	0.613084i	$-0.789929\pi$
$503$	−17824.6	−1.58003	−0.790017	+	0.613084i	$0.789929\pi$
$504$	2024.39	0.178916
$505$	−852.140	−0.0750886
$506$	−1751.07	−0.153843
$507$	−11467.2	−1.00449
$508$	−8077.71	−0.705493
$509$	6862.03	0.597552	0.298776	−	0.954323i	$-0.403422\pi$
$509$	6862.03	0.597552	0.298776	+	0.954323i	$0.403422\pi$
$510$	1149.00	0.0997619
$511$	−4349.63	−0.376548
$512$	−512.000	−0.0441942
$513$	−8538.06	−0.734823
$514$	−7230.97	−0.620515
$515$	3271.93	0.279958
$516$	616.623	0.0526072
$517$	−1035.62	−0.0880975
$518$	10928.2	0.926949
$519$	15591.5	1.31867
$520$	−894.757	−0.0754571
$521$	2507.98	0.210896	0.105448	−	0.994425i	$-0.466372\pi$
$521$	2507.98	0.210896	0.105448	+	0.994425i	$0.466372\pi$
$522$	−4362.00	−0.365746
$523$	13285.9	1.11081	0.555403	−	0.831582i	$-0.312564\pi$
$523$	13285.9	1.11081	0.555403	+	0.831582i	$0.312564\pi$
$524$	−10459.4	−0.871985
$525$	−2288.76	−0.190266
$526$	−11750.3	−0.974024
$527$	1053.00	0.0870390
$528$	−1189.55	−0.0980466
$529$	−5831.75	−0.479309
$530$	3290.27	0.269661
$531$	7623.01	0.622995
$532$	−8228.12	−0.670553
$533$	11003.5	0.894215
$534$	6235.49	0.505311
$535$	50.4937	0.00408044
$536$	1790.09	0.144254
$537$	9419.65	0.756961
$538$	7057.25	0.565538
$539$	1754.77	0.140228
$540$	1124.44	0.0896081
$541$	21242.1	1.68811	0.844055	−	0.536256i	$-0.180162\pi$
$541$	21242.1	1.68811	0.844055	+	0.536256i	$0.180162\pi$
$542$	−2281.55	−0.180814
$543$	−6186.99	−0.488967
$544$	−544.000	−0.0428746
$545$	5154.48	0.405126
$546$	−4095.77	−0.321031
$547$	−17444.0	−1.36353	−0.681766	−	0.731570i	$-0.738788\pi$
$547$	−17444.0	−1.36353	−0.681766	+	0.731570i	$0.738788\pi$
$548$	−5439.63	−0.424032
$549$	−12851.3	−0.999055
$550$	550.000	0.0426401
$551$	17729.3	1.37077
$552$	4303.71	0.331844
$553$	−3520.44	−0.270713
$554$	−15857.4	−1.21610
$555$	−13632.4	−1.04264
$556$	−7707.35	−0.587886
$557$	−13208.6	−1.00479	−0.502394	−	0.864639i	$-0.667547\pi$
$557$	−13208.6	−1.00479	−0.502394	+	0.864639i	$0.667547\pi$
$558$	−2314.33	−0.175580
$559$	−510.192	−0.0386026
$560$	1083.63	0.0817706
$561$	−1263.90	−0.0951192
$562$	6404.94	0.480740
$563$	5498.89	0.411635	0.205818	−	0.978590i	$-0.434015\pi$
$563$	5498.89	0.411635	0.205818	+	0.978590i	$0.434015\pi$
$564$	2545.29	0.190029
$565$	7227.51	0.538165
$566$	15775.4	1.17153
$567$	11979.5	0.887286
$568$	7675.78	0.567022
$569$	6646.65	0.489705	0.244853	−	0.969560i	$-0.421260\pi$
$569$	6646.65	0.489705	0.244853	+	0.969560i	$0.421260\pi$
$570$	10264.1	0.754240
$571$	−16849.5	−1.23490	−0.617450	−	0.786610i	$-0.711834\pi$
$571$	−16849.5	−1.23490	−0.617450	+	0.786610i	$0.711834\pi$
$572$	984.233	0.0719456
$573$	5022.79	0.366195
$574$	−13326.2	−0.969034
$575$	−1989.86	−0.144318
$576$	1195.63	0.0864891
$577$	−3297.41	−0.237908	−0.118954	−	0.992900i	$-0.537954\pi$
$577$	−3297.41	−0.237908	−0.118954	+	0.992900i	$0.537954\pi$
$578$	−578.000	−0.0415945
$579$	848.679	0.0609152
$580$	−2334.91	−0.167158
$581$	11058.0	0.789610
$582$	−79.1858	−0.00563979
$583$	−3619.30	−0.257112
$584$	−2568.93	−0.182026
$585$	2089.44	0.147672
$586$	−2733.92	−0.192725
$587$	1730.96	0.121711	0.0608555	−	0.998147i	$-0.480617\pi$
$587$	1730.96	0.121711	0.0608555	+	0.998147i	$0.480617\pi$
$588$	−4312.78	−0.302477
$589$	9406.58	0.658050
$590$	4080.48	0.284730
$591$	−29089.2	−2.02466
$592$	6454.33	0.448093
$593$	13272.7	0.919134	0.459567	−	0.888143i	$-0.348005\pi$
$593$	13272.7	0.919134	0.459567	+	0.888143i	$0.348005\pi$
$594$	−1236.89	−0.0854380
$595$	1151.35	0.0793292
$596$	−7046.71	−0.484303
$597$	16602.6	1.13819
$598$	−3560.88	−0.243504
$599$	19964.8	1.36183	0.680917	−	0.732360i	$-0.261581\pi$
$599$	19964.8	1.36183	0.680917	+	0.732360i	$0.261581\pi$
$600$	−1351.76	−0.0919759
$601$	4639.53	0.314893	0.157446	−	0.987528i	$-0.449674\pi$
$601$	4639.53	0.314893	0.157446	+	0.987528i	$0.449674\pi$
$602$	617.885	0.0418324
$603$	−4180.24	−0.282309
$604$	−2159.09	−0.145451
$605$	−605.000	−0.0406558
$606$	−2303.78	−0.154430
$607$	−5503.34	−0.367996	−0.183998	−	0.982927i	$-0.558904\pi$
$607$	−5503.34	−0.367996	−0.183998	+	0.982927i	$0.558904\pi$
$608$	−4859.61	−0.324150
$609$	−10688.1	−0.711172
$610$	−6879.11	−0.456602
$611$	−2105.97	−0.139441
$612$	1270.35	0.0839068
$613$	18205.7	1.19954	0.599772	−	0.800171i	$-0.295258\pi$
$613$	18205.7	1.19954	0.599772	+	0.800171i	$0.295258\pi$
$614$	6156.87	0.404676
$615$	16623.7	1.08997
$616$	−1191.99	−0.0779652
$617$	−6814.59	−0.444644	−0.222322	−	0.974973i	$-0.571364\pi$
$617$	−6814.59	−0.444644	−0.222322	+	0.974973i	$0.571364\pi$
$618$	8845.76	0.575774
$619$	−21410.1	−1.39022	−0.695110	−	0.718903i	$-0.744644\pi$
$619$	−21410.1	−1.39022	−0.695110	+	0.718903i	$0.744644\pi$
$620$	−1238.83	−0.0802459
$621$	4474.97	0.289169
$622$	−8444.04	−0.544333
$623$	6248.26	0.401816
$624$	−2419.00	−0.155188
$625$	625.000	0.0400000
$626$	−6099.08	−0.389406
$627$	−11290.5	−0.719140
$628$	5743.33	0.364942
$629$	6857.73	0.434715
$630$	−2530.49	−0.160027
$631$	−3608.27	−0.227644	−0.113822	−	0.993501i	$-0.536309\pi$
$631$	−3608.27	−0.227644	−0.113822	+	0.993501i	$0.536309\pi$
$632$	−2079.20	−0.130864
$633$	−21074.1	−1.32326
$634$	−5757.95	−0.360690
$635$	10097.1	0.631012
$636$	8895.34	0.554596
$637$	3568.39	0.221954
$638$	2568.40	0.159379
$639$	−17924.5	−1.10968
$640$	640.000	0.0395285
$641$	3085.65	0.190134	0.0950671	−	0.995471i	$-0.469693\pi$
$641$	3085.65	0.190134	0.0950671	+	0.995471i	$0.469693\pi$
$642$	136.511	0.00839201
$643$	−8758.73	−0.537186	−0.268593	−	0.963254i	$-0.586559\pi$
$643$	−8758.73	−0.537186	−0.268593	+	0.963254i	$0.586559\pi$
$644$	4312.52	0.263877
$645$	−770.778	−0.0470533
$646$	−5163.33	−0.314471
$647$	24180.6	1.46930	0.734649	−	0.678448i	$-0.237347\pi$
$647$	24180.6	1.46930	0.734649	+	0.678448i	$0.237347\pi$
$648$	7075.20	0.428920
$649$	−4488.53	−0.271479
$650$	1118.45	0.0674909
$651$	−5670.76	−0.341405
$652$	1040.17	0.0624787
$653$	22276.3	1.33498	0.667488	−	0.744620i	$-0.267369\pi$
$653$	22276.3	1.33498	0.667488	+	0.744620i	$0.267369\pi$
$654$	13935.3	0.833200
$655$	13074.2	0.779927
$656$	−7870.59	−0.468438
$657$	5998.99	0.356229
$658$	2550.50	0.151108
$659$	−31697.9	−1.87371	−0.936855	−	0.349718i	$-0.886277\pi$
$659$	−31697.9	−1.87371	−0.936855	+	0.349718i	$0.886277\pi$
$660$	1486.94	0.0876956
$661$	19930.0	1.17275	0.586374	−	0.810040i	$-0.300555\pi$
$661$	19930.0	1.17275	0.586374	+	0.810040i	$0.300555\pi$
$662$	−5770.68	−0.338798
$663$	−2570.19	−0.150555
$664$	6530.97	0.381703
$665$	10285.1	0.599761
$666$	−15072.2	−0.876930
$667$	−9292.27	−0.539428
$668$	−1217.86	−0.0705395
$669$	29039.5	1.67822
$670$	−2237.62	−0.129025
$671$	7567.02	0.435353
$672$	2929.61	0.168173
$673$	14226.1	0.814826	0.407413	−	0.913244i	$-0.366431\pi$
$673$	14226.1	0.814826	0.407413	+	0.913244i	$0.366431\pi$
$674$	8550.13	0.488633
$675$	−1405.56	−0.0801479
$676$	−6786.52	−0.386124
$677$	−23389.5	−1.32782	−0.663908	−	0.747814i	$-0.731104\pi$
$677$	−23389.5	−1.32782	−0.663908	+	0.747814i	$0.731104\pi$
$678$	19539.8	1.10681
$679$	−79.3480	−0.00448468
$680$	680.000	0.0383482
$681$	−11332.4	−0.637680
$682$	1362.71	0.0765115
$683$	−11702.6	−0.655618	−0.327809	−	0.944744i	$-0.606310\pi$
$683$	−11702.6	−0.655618	−0.327809	+	0.944744i	$0.606310\pi$
$684$	11348.2	0.634370
$685$	6799.53	0.379265
$686$	−13613.7	−0.757688
$687$	−18587.4	−1.03225
$688$	364.929	0.0202221
$689$	−7359.99	−0.406957
$690$	−5379.63	−0.296810
$691$	8239.72	0.453623	0.226812	−	0.973939i	$-0.427170\pi$
$691$	8239.72	0.453623	0.226812	+	0.973939i	$0.427170\pi$
$692$	9227.32	0.506893
$693$	2783.54	0.152580
$694$	13509.3	0.738911
$695$	9634.19	0.525821
$696$	−6312.49	−0.343785
$697$	−8362.50	−0.454451
$698$	18482.5	1.00225
$699$	17741.7	0.960016
$700$	−1354.53	−0.0731379
$701$	12402.5	0.668238	0.334119	−	0.942531i	$-0.391561\pi$
$701$	12402.5	0.668238	0.334119	+	0.942531i	$0.391561\pi$
$702$	−2515.26	−0.135231
$703$	61260.8	3.28662
$704$	−704.000	−0.0376889
$705$	−3181.62	−0.169967
$706$	12740.6	0.679178
$707$	−2308.50	−0.122801
$708$	11031.7	0.585588
$709$	22956.5	1.21601	0.608004	−	0.793934i	$-0.291971\pi$
$709$	22956.5	1.21601	0.608004	+	0.793934i	$0.291971\pi$
$710$	−9594.73	−0.507160
$711$	4855.37	0.256105
$712$	3690.28	0.194240
$713$	−4930.18	−0.258957
$714$	3112.71	0.163152
$715$	−1230.29	−0.0643501
$716$	5574.73	0.290974
$717$	27454.4	1.42999
$718$	2046.63	0.106378
$719$	−7697.35	−0.399253	−0.199626	−	0.979872i	$-0.563973\pi$
$719$	−7697.35	−0.399253	−0.199626	+	0.979872i	$0.563973\pi$
$720$	−1494.53	−0.0773582
$721$	8863.87	0.457847
$722$	−32406.6	−1.67043
$723$	21866.2	1.12478
$724$	−3661.58	−0.187958
$725$	2918.64	0.149511
$726$	−1635.63	−0.0836145
$727$	5111.26	0.260751	0.130376	−	0.991465i	$-0.458382\pi$
$727$	5111.26	0.260751	0.130376	+	0.991465i	$0.458382\pi$
$728$	−2423.96	−0.123404
$729$	−6262.18	−0.318152
$730$	3211.16	0.162809
$731$	387.737	0.0196183
$732$	−18597.9	−0.939067
$733$	13590.4	0.684818	0.342409	−	0.939551i	$-0.388757\pi$
$733$	13590.4	0.684818	0.342409	+	0.939551i	$0.388757\pi$
$734$	5778.34	0.290575
$735$	5390.98	0.270543
$736$	2547.02	0.127560
$737$	2461.38	0.123020
$738$	18379.5	0.916744
$739$	−27412.0	−1.36450	−0.682252	−	0.731117i	$-0.738999\pi$
$739$	−27412.0	−1.36450	−0.682252	+	0.731117i	$0.738999\pi$
$740$	−8067.91	−0.400787
$741$	−22959.8	−1.13826
$742$	8913.56	0.441007
$743$	−1543.20	−0.0761970	−0.0380985	−	0.999274i	$-0.512130\pi$
$743$	−1543.20	−0.0761970	−0.0380985	+	0.999274i	$0.512130\pi$
$744$	−3349.20	−0.165037
$745$	8808.38	0.433173
$746$	11955.2	0.586746
$747$	−15251.2	−0.747003
$748$	−748.000	−0.0365636
$749$	136.791	0.00667320
$750$	1689.71	0.0822657
$751$	−12374.1	−0.601246	−0.300623	−	0.953743i	$-0.597195\pi$
$751$	−12374.1	−0.601246	−0.300623	+	0.953743i	$0.597195\pi$
$752$	1506.35	0.0730466
$753$	26532.8	1.28407
$754$	5222.94	0.252266
$755$	2698.86	0.130095
$756$	3046.19	0.146546
$757$	25188.7	1.20938	0.604689	−	0.796462i	$-0.293297\pi$
$757$	25188.7	1.20938	0.604689	+	0.796462i	$0.293297\pi$
$758$	−1476.91	−0.0707702
$759$	5917.60	0.282998
$760$	6074.51	0.289928
$761$	−14631.9	−0.696986	−0.348493	−	0.937311i	$-0.613307\pi$
$761$	−14631.9	−0.696986	−0.348493	+	0.937311i	$0.613307\pi$
$762$	27297.9	1.29777
$763$	13963.8	0.662548
$764$	2972.58	0.140765
$765$	−1587.94	−0.0750485
$766$	20451.1	0.964657
$767$	−9127.59	−0.429698
$768$	1730.26	0.0812960
$769$	32817.3	1.53891	0.769455	−	0.638701i	$-0.220528\pi$
$769$	32817.3	1.53891	0.769455	+	0.638701i	$0.220528\pi$
$770$	1489.99	0.0697342
$771$	24436.4	1.14145
$772$	502.264	0.0234157
$773$	11519.4	0.535993	0.267996	−	0.963420i	$-0.413638\pi$
$773$	11519.4	0.535993	0.267996	+	0.963420i	$0.413638\pi$
$774$	−852.185	−0.0395751
$775$	1548.53	0.0717742
$776$	−46.8637	−0.00216792
$777$	−36931.0	−1.70514
$778$	12986.9	0.598460
$779$	−74703.1	−3.43584
$780$	3023.75	0.138805
$781$	10554.2	0.483558
$782$	2706.21	0.123752
$783$	−6563.69	−0.299575
$784$	−2552.39	−0.116271
$785$	−7179.16	−0.326414
$786$	35346.5	1.60403
$787$	16217.8	0.734562	0.367281	−	0.930110i	$-0.380289\pi$
$787$	16217.8	0.734562	0.367281	+	0.930110i	$0.380289\pi$
$788$	−17215.6	−0.778274
$789$	39709.0	1.79174
$790$	2599.01	0.117049
$791$	19579.8	0.880122
$792$	1643.99	0.0737582
$793$	15387.8	0.689077
$794$	7684.09	0.343448
$795$	−11119.2	−0.496046
$796$	9825.71	0.437516
$797$	−13350.6	−0.593352	−0.296676	−	0.954978i	$-0.595878\pi$
$797$	−13350.6	−0.593352	−0.296676	+	0.954978i	$0.595878\pi$
$798$	27806.2	1.23349
$799$	1600.50	0.0708656
$800$	−800.000	−0.0353553
$801$	−8617.57	−0.380134
$802$	−20256.8	−0.891888
$803$	−3532.28	−0.155232
$804$	−6049.46	−0.265358
$805$	−5390.65	−0.236019
$806$	2771.12	0.121103
$807$	−23849.3	−1.04032
$808$	−1363.42	−0.0593627
$809$	−981.564	−0.0426576	−0.0213288	−	0.999773i	$-0.506790\pi$
$809$	−981.564	−0.0426576	−0.0213288	+	0.999773i	$0.506790\pi$
$810$	−8844.00	−0.383638
$811$	−37571.7	−1.62678	−0.813392	−	0.581717i	$-0.802381\pi$
$811$	−37571.7	−1.62678	−0.813392	+	0.581717i	$0.802381\pi$
$812$	−6325.42	−0.273373
$813$	7710.31	0.332610
$814$	8874.70	0.382135
$815$	−1300.21	−0.0558826
$816$	1838.40	0.0788687
$817$	3463.69	0.148322
$818$	29406.3	1.25693
$819$	5660.44	0.241504
$820$	9838.24	0.418983
$821$	10468.0	0.444987	0.222493	−	0.974934i	$-0.428580\pi$
$821$	10468.0	0.444987	0.222493	+	0.974934i	$0.428580\pi$
$822$	18382.7	0.780014
$823$	−17683.1	−0.748962	−0.374481	−	0.927235i	$-0.622179\pi$
$823$	−17683.1	−0.748962	−0.374481	+	0.927235i	$0.622179\pi$
$824$	5235.09	0.221326
$825$	−1858.68	−0.0784373
$826$	11054.3	0.465651
$827$	−12366.5	−0.519983	−0.259992	−	0.965611i	$-0.583720\pi$
$827$	−12366.5	−0.519983	−0.259992	+	0.965611i	$0.583720\pi$
$828$	−5947.81	−0.249639
$829$	−16335.2	−0.684371	−0.342185	−	0.939632i	$-0.611167\pi$
$829$	−16335.2	−0.684371	−0.342185	+	0.939632i	$0.611167\pi$
$830$	−8163.71	−0.341406
$831$	53588.8	2.23703
$832$	−1431.61	−0.0596541
$833$	−2711.91	−0.112800
$834$	26046.3	1.08143
$835$	1522.32	0.0630925
$836$	−6681.96	−0.276436
$837$	−3482.48	−0.143814
$838$	21348.9	0.880054
$839$	−25617.8	−1.05414	−0.527070	−	0.849822i	$-0.676709\pi$
$839$	−25617.8	−1.05414	−0.527070	+	0.849822i	$0.676709\pi$
$840$	−3662.02	−0.150419
$841$	−10759.5	−0.441162
$842$	−21647.7	−0.886022
$843$	−21644.9	−0.884330
$844$	−12472.1	−0.508657
$845$	8483.15	0.345360
$846$	−3517.65	−0.142954
$847$	−1638.98	−0.0664890
$848$	5264.44	0.213186
$849$	−53311.5	−2.15506
$850$	−850.000	−0.0342997
$851$	−32108.0	−1.29336
$852$	−25939.6	−1.04305
$853$	−14578.8	−0.585193	−0.292596	−	0.956236i	$-0.594519\pi$
$853$	−14578.8	−0.585193	−0.292596	+	0.956236i	$0.594519\pi$
$854$	−18636.0	−0.746732
$855$	−14185.2	−0.567397
$856$	80.7900	0.00322587
$857$	37064.5	1.47736	0.738681	−	0.674056i	$-0.235449\pi$
$857$	37064.5	1.47736	0.738681	+	0.674056i	$0.235449\pi$
$858$	−3326.13	−0.132345
$859$	13609.0	0.540551	0.270275	−	0.962783i	$-0.412885\pi$
$859$	13609.0	0.540551	0.270275	+	0.962783i	$0.412885\pi$
$860$	−456.161	−0.0180872
$861$	45034.7	1.78256
$862$	15545.8	0.614261
$863$	−32778.2	−1.29291	−0.646457	−	0.762951i	$-0.723750\pi$
$863$	−32778.2	−1.29291	−0.646457	+	0.762951i	$0.723750\pi$
$864$	1799.11	0.0708414
$865$	−11534.2	−0.453379
$866$	−10621.5	−0.416782
$867$	1953.30	0.0765139
$868$	−3356.06	−0.131235
$869$	−2858.91	−0.111602
$870$	7890.62	0.307491
$871$	5005.31	0.194717
$872$	8247.17	0.320280
$873$	109.436	0.00424268
$874$	24174.8	0.935612
$875$	1693.17	0.0654165
$876$	8681.47	0.334840
$877$	35970.7	1.38500	0.692499	−	0.721419i	$-0.256510\pi$
$877$	35970.7	1.38500	0.692499	+	0.721419i	$0.256510\pi$
$878$	−4912.06	−0.188809
$879$	9239.02	0.354522
$880$	880.000	0.0337100
$881$	−20493.7	−0.783714	−0.391857	−	0.920026i	$-0.628167\pi$
$881$	−20493.7	−0.783714	−0.391857	+	0.920026i	$0.628167\pi$
$882$	5960.35	0.227546
$883$	38559.0	1.46955	0.734776	−	0.678310i	$-0.237287\pi$
$883$	38559.0	1.46955	0.734776	+	0.678310i	$0.237287\pi$
$884$	−1521.09	−0.0578730
$885$	−13789.6	−0.523766
$886$	−12182.3	−0.461932
$887$	9193.53	0.348014	0.174007	−	0.984744i	$-0.444328\pi$
$887$	9193.53	0.348014	0.174007	+	0.984744i	$0.444328\pi$
$888$	−21811.8	−0.824276
$889$	27353.8	1.03197
$890$	−4612.85	−0.173734
$891$	9728.41	0.365784
$892$	17186.1	0.645105
$893$	14297.4	0.535773
$894$	23813.7	0.890883
$895$	−6968.41	−0.260255
$896$	1733.80	0.0646453
$897$	12033.7	0.447929
$898$	14684.2	0.545679
$899$	7231.37	0.268276
$900$	1868.17	0.0691913
$901$	5593.46	0.206821
$902$	−10822.1	−0.399485
$903$	−2088.09	−0.0769515
$904$	11564.0	0.425457
$905$	4576.97	0.168115
$906$	7296.45	0.267559
$907$	41125.4	1.50557	0.752783	−	0.658269i	$-0.228711\pi$
$907$	41125.4	1.50557	0.752783	+	0.658269i	$0.228711\pi$
$908$	−6706.75	−0.245123
$909$	3183.88	0.116174
$910$	3029.94	0.110375
$911$	−23781.0	−0.864875	−0.432437	−	0.901664i	$-0.642346\pi$
$911$	−23781.0	−0.864875	−0.432437	+	0.901664i	$0.642346\pi$
$912$	16422.6	0.596279
$913$	8980.08	0.325517
$914$	−6190.16	−0.224018
$915$	23247.3	0.839927
$916$	−11000.4	−0.396794
$917$	35418.9	1.27550
$918$	1911.56	0.0687263
$919$	50146.6	1.79998	0.899991	−	0.435908i	$-0.143573\pi$
$919$	50146.6	1.79998	0.899991	+	0.435908i	$0.143573\pi$
$920$	−3183.77	−0.114093
$921$	−20806.6	−0.744409
$922$	20082.5	0.717336
$923$	21462.4	0.765377
$924$	4028.22	0.143418
$925$	10084.9	0.358475
$926$	7452.49	0.264475
$927$	−12225.0	−0.433142
$928$	−3735.86	−0.132150
$929$	−4263.08	−0.150557	−0.0752783	−	0.997163i	$-0.523985\pi$
$929$	−4263.08	−0.150557	−0.0752783	+	0.997163i	$0.523985\pi$
$930$	4186.50	0.147614
$931$	−24225.8	−0.852812
$932$	10499.9	0.369028
$933$	28535.9	1.00131
$934$	17672.9	0.619139
$935$	935.000	0.0327035
$936$	3343.11	0.116745
$937$	−17901.3	−0.624130	−0.312065	−	0.950061i	$-0.601021\pi$
$937$	−17901.3	−0.624130	−0.312065	+	0.950061i	$0.601021\pi$
$938$	−6061.85	−0.211009
$939$	20611.3	0.716320
$940$	−1882.94	−0.0653349
$941$	−52622.0	−1.82299	−0.911493	−	0.411316i	$-0.865069\pi$
$941$	−52622.0	−1.82299	−0.911493	+	0.411316i	$0.865069\pi$
$942$	−19409.1	−0.671318
$943$	39153.4	1.35208
$944$	6528.76	0.225099
$945$	−3807.74	−0.131075
$946$	501.777	0.0172454
$947$	31333.3	1.07518	0.537591	−	0.843206i	$-0.319335\pi$
$947$	31333.3	1.07518	0.537591	+	0.843206i	$0.319335\pi$
$948$	7026.49	0.240727
$949$	−7183.03	−0.245702
$950$	−7593.14	−0.259320
$951$	19458.5	0.663496
$952$	1842.16	0.0627152
$953$	−50541.9	−1.71796	−0.858978	−	0.512012i	$-0.828900\pi$
$953$	−50541.9	−1.71796	−0.858978	+	0.512012i	$0.828900\pi$
$954$	−12293.5	−0.417210
$955$	−3715.73	−0.125904
$956$	16248.0	0.549685
$957$	−8679.68	−0.293181
$958$	31865.5	1.07466
$959$	18420.4	0.620255
$960$	−2162.82	−0.0727133
$961$	−25954.3	−0.871212
$962$	18047.1	0.604845
$963$	−188.661	−0.00631311
$964$	12940.8	0.432362
$965$	−627.830	−0.0209436
$966$	−14573.8	−0.485407
$967$	55.8682	0.00185791	0.000928955	−	1.00000i	$-0.499704\pi$
$967$	55.8682	0.00185791	0.000928955		1.00000i	$0.499704\pi$
$968$	−968.000	−0.0321412
$969$	17449.0	0.578476
$970$	58.5796	0.00193905
$971$	42149.5	1.39304	0.696520	−	0.717537i	$-0.254731\pi$
$971$	42149.5	1.39304	0.696520	+	0.717537i	$0.254731\pi$
$972$	−17838.0	−0.588636
$973$	26099.6	0.859934
$974$	−35353.4	−1.16303
$975$	−3779.69	−0.124151
$976$	−11006.6	−0.360975
$977$	12761.9	0.417902	0.208951	−	0.977926i	$-0.432995\pi$
$977$	12761.9	0.417902	0.208951	+	0.977926i	$0.432995\pi$
$978$	−3515.15	−0.114931
$979$	5074.14	0.165649
$980$	3190.49	0.103996
$981$	−19258.8	−0.626797
$982$	10721.8	0.348420
$983$	−34889.6	−1.13205	−0.566025	−	0.824388i	$-0.691519\pi$
$983$	−34889.6	−1.13205	−0.566025	+	0.824388i	$0.691519\pi$
$984$	26598.0	0.861699
$985$	21519.5	0.696109
$986$	−3969.35	−0.128205
$987$	−8619.20	−0.277966
$988$	−13588.0	−0.437543
$989$	−1815.39	−0.0583681
$990$	−2054.98	−0.0659713
$991$	−33085.0	−1.06053	−0.530263	−	0.847833i	$-0.677907\pi$
$991$	−33085.0	−1.06053	−0.530263	+	0.847833i	$0.677907\pi$
$992$	−1982.12	−0.0634400
$993$	19501.5	0.623224
$994$	−25992.7	−0.829416
$995$	−12282.1	−0.391327
$996$	−22070.8	−0.702150
$997$	34857.2	1.10726	0.553631	−	0.832762i	$-0.313242\pi$
$997$	34857.2	1.10726	0.553631	+	0.832762i	$0.313242\pi$
$998$	−6982.36	−0.221466
$999$	−22679.8	−0.718275

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1870.4.a.j.1.9	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1870.4.a.j.1.9	✓	10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1870 = 2 \cdot 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1870.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +6.75882 q^{3} +4.00000 q^{4} -5.00000 q^{5} -13.5176 q^{6} -13.5453 q^{7} -8.00000 q^{8} +18.6817 q^{9} +10.0000 q^{10} -11.0000 q^{11} +27.0353 q^{12} -22.3689 q^{13} +27.0906 q^{14} -33.7941 q^{15} +16.0000 q^{16} +17.0000 q^{17} -37.3633 q^{18} +151.863 q^{19} -20.0000 q^{20} -91.5504 q^{21} +22.0000 q^{22} -79.5943 q^{23} -54.0706 q^{24} +25.0000 q^{25} +44.7379 q^{26} -56.2222 q^{27} -54.1813 q^{28} +116.745 q^{29} +67.5882 q^{30} +61.9413 q^{31} -32.0000 q^{32} -74.3470 q^{33} -34.0000 q^{34} +67.7266 q^{35} +74.7266 q^{36} +403.396 q^{37} -303.725 q^{38} -151.188 q^{39} +40.0000 q^{40} -491.912 q^{41} +183.101 q^{42} +22.8081 q^{43} -44.0000 q^{44} -93.4083 q^{45} +159.189 q^{46} +94.1471 q^{47} +108.141 q^{48} -159.524 q^{49} -50.0000 q^{50} +114.900 q^{51} -89.4757 q^{52} +329.027 q^{53} +112.444 q^{54} +55.0000 q^{55} +108.363 q^{56} +1026.41 q^{57} -233.491 q^{58} +408.048 q^{59} -135.176 q^{60} -687.911 q^{61} -123.883 q^{62} -253.049 q^{63} +64.0000 q^{64} +111.845 q^{65} +148.694 q^{66} -223.762 q^{67} +68.0000 q^{68} -537.963 q^{69} -135.453 q^{70} -959.473 q^{71} -149.453 q^{72} +321.116 q^{73} -806.791 q^{74} +168.971 q^{75} +607.451 q^{76} +148.999 q^{77} +302.375 q^{78} +259.901 q^{79} -80.0000 q^{80} -884.400 q^{81} +983.824 q^{82} -816.371 q^{83} -366.202 q^{84} -85.0000 q^{85} -45.6161 q^{86} +789.062 q^{87} +88.0000 q^{88} -461.285 q^{89} +186.817 q^{90} +302.994 q^{91} -318.377 q^{92} +418.650 q^{93} -188.294 q^{94} -759.314 q^{95} -216.282 q^{96} +5.85796 q^{97} +319.049 q^{98} -205.498 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 20 q^{2} - q^{3} + 40 q^{4} - 50 q^{5} + 2 q^{6} + 4 q^{7} - 80 q^{8} + 67 q^{9} + 100 q^{10} - 110 q^{11} - 4 q^{12} - 7 q^{13} - 8 q^{14} + 5 q^{15} + 160 q^{16} + 170 q^{17} - 134 q^{18} + 11 q^{19}+ \cdots - 737 q^{99}+O(q^{100}) \) 10 * q - 20 * q^2 - q^3 + 40 * q^4 - 50 * q^5 + 2 * q^6 + 4 * q^7 - 80 * q^8 + 67 * q^9 + 100 * q^10 - 110 * q^11 - 4 * q^12 - 7 * q^13 - 8 * q^14 + 5 * q^15 + 160 * q^16 + 170 * q^17 - 134 * q^18 + 11 * q^19 - 200 * q^20 - 162 * q^21 + 220 * q^22 - 124 * q^23 + 8 * q^24 + 250 * q^25 + 14 * q^26 - 37 * q^27 + 16 * q^28 + 91 * q^29 - 10 * q^30 + 29 * q^31 - 320 * q^32 + 11 * q^33 - 340 * q^34 - 20 * q^35 + 268 * q^36 + 468 * q^37 - 22 * q^38 + 161 * q^39 + 400 * q^40 - 698 * q^41 + 324 * q^42 + 726 * q^43 - 440 * q^44 - 335 * q^45 + 248 * q^46 - 181 * q^47 - 16 * q^48 + 638 * q^49 - 500 * q^50 - 17 * q^51 - 28 * q^52 - 335 * q^53 + 74 * q^54 + 550 * q^55 - 32 * q^56 + 11 * q^57 - 182 * q^58 + 649 * q^59 + 20 * q^60 + 13 * q^61 - 58 * q^62 - 460 * q^63 + 640 * q^64 + 35 * q^65 - 22 * q^66 + 1384 * q^67 + 680 * q^68 + 1304 * q^69 + 40 * q^70 - 1655 * q^71 - 536 * q^72 - 1185 * q^73 - 936 * q^74 - 25 * q^75 + 44 * q^76 - 44 * q^77 - 322 * q^78 + 364 * q^79 - 800 * q^80 + 462 * q^81 + 1396 * q^82 - 120 * q^83 - 648 * q^84 - 850 * q^85 - 1452 * q^86 + 3429 * q^87 + 880 * q^88 - 651 * q^89 + 670 * q^90 - 42 * q^91 - 496 * q^92 - 355 * q^93 + 362 * q^94 - 55 * q^95 + 32 * q^96 + 73 * q^97 - 1276 * q^98 - 737 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more