LMFDB - Embedded newform 161.4.a.a.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [161,4,Mod(1,161)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(161, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("161.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 161 = 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	161.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:	$9.49930751092$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 18x^{3} - 4x^{2} + 44x + 24 $ x^5 - x^4 - 18x^3 - 4x^2 + 44*x + 24
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$4.59776$ of defining polynomial
Character	$\chi$	$=$	161.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.59776 q^{2} -4.68651 q^{3} +4.94388 q^{4} -3.25737 q^{5} -16.8609 q^{6} +7.00000 q^{7} -10.9952 q^{8} -5.03662 q^{9} -11.7192 q^{10} -52.7424 q^{11} -23.1695 q^{12} -2.09755 q^{13} +25.1843 q^{14} +15.2657 q^{15} -79.1091 q^{16} -14.6489 q^{17} -18.1205 q^{18} +6.38490 q^{19} -16.1040 q^{20} -32.8056 q^{21} -189.754 q^{22} -23.0000 q^{23} +51.5291 q^{24} -114.390 q^{25} -7.54647 q^{26} +150.140 q^{27} +34.6071 q^{28} +101.423 q^{29} +54.9223 q^{30} -96.9377 q^{31} -196.654 q^{32} +247.178 q^{33} -52.7033 q^{34} -22.8016 q^{35} -24.9004 q^{36} -219.426 q^{37} +22.9713 q^{38} +9.83018 q^{39} +35.8154 q^{40} +462.118 q^{41} -118.027 q^{42} +148.234 q^{43} -260.752 q^{44} +16.4061 q^{45} -82.7485 q^{46} -16.0617 q^{47} +370.746 q^{48} +49.0000 q^{49} -411.546 q^{50} +68.6523 q^{51} -10.3700 q^{52} +408.417 q^{53} +540.168 q^{54} +171.801 q^{55} -76.9664 q^{56} -29.9229 q^{57} +364.895 q^{58} +194.836 q^{59} +75.4717 q^{60} +272.396 q^{61} -348.759 q^{62} -35.2563 q^{63} -74.6411 q^{64} +6.83248 q^{65} +889.286 q^{66} -811.909 q^{67} -72.4224 q^{68} +107.790 q^{69} -82.0346 q^{70} -867.936 q^{71} +55.3786 q^{72} -948.048 q^{73} -789.441 q^{74} +536.088 q^{75} +31.5662 q^{76} -369.197 q^{77} +35.3666 q^{78} -149.385 q^{79} +257.687 q^{80} -567.644 q^{81} +1662.59 q^{82} -824.893 q^{83} -162.187 q^{84} +47.7169 q^{85} +533.312 q^{86} -475.319 q^{87} +579.913 q^{88} +370.815 q^{89} +59.0253 q^{90} -14.6828 q^{91} -113.709 q^{92} +454.300 q^{93} -57.7863 q^{94} -20.7980 q^{95} +921.621 q^{96} -1648.19 q^{97} +176.290 q^{98} +265.643 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 4 q^{2} - 11 q^{3} - 4 q^{5} + 35 q^{7} + 18 q^{8} + 14 q^{9} + 26 q^{10} - 36 q^{11} - 28 q^{12} - 69 q^{13} - 28 q^{14} - 88 q^{15} - 124 q^{16} - 42 q^{17} - 94 q^{18} - 140 q^{19} - 168 q^{20}+ \cdots - 990 q^{99}+O(q^{100}) $ 5 * q - 4 * q^2 - 11 * q^3 - 4 * q^5 + 35 * q^7 + 18 * q^8 + 14 * q^9 + 26 * q^10 - 36 * q^11 - 28 * q^12 - 69 * q^13 - 28 * q^14 - 88 * q^15 - 124 * q^16 - 42 * q^17 - 94 * q^18 - 140 * q^19 - 168 * q^20 - 77 * q^21 - 346 * q^22 - 115 * q^23 + 18 * q^24 - 357 * q^25 + 68 * q^26 - 35 * q^27 - 383 * q^29 + 184 * q^30 - 319 * q^31 - 50 * q^32 - 108 * q^33 - 376 * q^34 - 28 * q^35 - 180 * q^36 - 154 * q^37 + 8 * q^38 - 235 * q^39 + 90 * q^40 + 277 * q^41 - 718 * q^43 + 422 * q^44 + 470 * q^45 + 92 * q^46 + 53 * q^47 + 248 * q^48 + 245 * q^49 - 60 * q^50 + 232 * q^51 + 178 * q^52 + 450 * q^53 + 468 * q^54 - 206 * q^55 + 126 * q^56 - 560 * q^57 + 1738 * q^58 + 936 * q^59 + 944 * q^60 - 522 * q^61 + 788 * q^62 + 98 * q^63 - 252 * q^64 + 264 * q^65 + 2310 * q^66 - 810 * q^67 + 1326 * q^68 + 253 * q^69 + 182 * q^70 - 1373 * q^71 + 1590 * q^72 + 459 * q^73 + 330 * q^74 + 333 * q^75 + 1168 * q^76 - 252 * q^77 + 462 * q^78 - 728 * q^79 + 1368 * q^80 - 895 * q^81 + 1034 * q^82 - 500 * q^83 - 196 * q^84 - 1432 * q^85 + 3138 * q^86 + 1803 * q^87 - 722 * q^88 - 586 * q^89 - 1024 * q^90 - 483 * q^91 + 2149 * q^93 + 316 * q^94 - 188 * q^95 + 1210 * q^96 - 2150 * q^97 - 196 * q^98 - 990 * 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 $

$2$	3.59776	1.27200	0.636000	−	0.771689i	$-0.280588\pi$
$2$	3.59776	1.27200	0.636000	+	0.771689i	$0.280588\pi$
$3$	−4.68651	−0.901919	−0.450960	−	0.892544i	$-0.648918\pi$
$3$	−4.68651	−0.901919	−0.450960	+	0.892544i	$0.648918\pi$
$4$	4.94388	0.617985
$5$	−3.25737	−0.291348	−0.145674	−	0.989333i	$-0.546535\pi$
$5$	−3.25737	−0.291348	−0.145674	+	0.989333i	$0.546535\pi$
$6$	−16.8609	−1.14724
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−10.9952	−0.485924
$9$	−5.03662	−0.186541
$10$	−11.7192	−0.370594
$11$	−52.7424	−1.44568	−0.722838	−	0.691018i	$-0.757163\pi$
$11$	−52.7424	−1.44568	−0.722838	+	0.691018i	$0.757163\pi$
$12$	−23.1695	−0.557372
$13$	−2.09755	−0.0447504	−0.0223752	−	0.999750i	$-0.507123\pi$
$13$	−2.09755	−0.0447504	−0.0223752	+	0.999750i	$0.507123\pi$
$14$	25.1843	0.480771
$15$	15.2657	0.262772
$16$	−79.1091	−1.23608
$17$	−14.6489	−0.208993	−0.104497	−	0.994525i	$-0.533323\pi$
$17$	−14.6489	−0.208993	−0.104497	+	0.994525i	$0.533323\pi$
$18$	−18.1205	−0.237281
$19$	6.38490	0.0770945	0.0385473	−	0.999257i	$-0.487727\pi$
$19$	6.38490	0.0770945	0.0385473	+	0.999257i	$0.487727\pi$
$20$	−16.1040	−0.180048
$21$	−32.8056	−0.340893
$22$	−189.754	−1.83890
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	51.5291	0.438264
$25$	−114.390	−0.915116
$26$	−7.54647	−0.0569225
$27$	150.140	1.07016
$28$	34.6071	0.233576
$29$	101.423	0.649439	0.324720	−	0.945810i	$-0.394730\pi$
$29$	101.423	0.649439	0.324720	+	0.945810i	$0.394730\pi$
$30$	54.9223	0.334246
$31$	−96.9377	−0.561630	−0.280815	−	0.959762i	$-0.590605\pi$
$31$	−96.9377	−0.561630	−0.280815	+	0.959762i	$0.590605\pi$
$32$	−196.654	−1.08637
$33$	247.178	1.30388
$34$	−52.7033	−0.265839
$35$	−22.8016	−0.110119
$36$	−24.9004	−0.115280
$37$	−219.426	−0.974956	−0.487478	−	0.873135i	$-0.662083\pi$
$37$	−219.426	−0.974956	−0.487478	+	0.873135i	$0.662083\pi$
$38$	22.9713	0.0980643
$39$	9.83018	0.0403612
$40$	35.8154	0.141573
$41$	462.118	1.76026	0.880131	−	0.474730i	$-0.157454\pi$
$41$	462.118	1.76026	0.880131	+	0.474730i	$0.157454\pi$
$42$	−118.027	−0.433617
$43$	148.234	0.525710	0.262855	−	0.964835i	$-0.415336\pi$
$43$	148.234	0.525710	0.262855	+	0.964835i	$0.415336\pi$
$44$	−260.752	−0.893405
$45$	16.4061	0.0543484
$46$	−82.7485	−0.265230
$47$	−16.0617	−0.0498478	−0.0249239	−	0.999689i	$-0.507934\pi$
$47$	−16.0617	−0.0498478	−0.0249239	+	0.999689i	$0.507934\pi$
$48$	370.746	1.11484
$49$	49.0000	0.142857
$50$	−411.546	−1.16403
$51$	68.6523	0.188495
$52$	−10.3700	−0.0276551
$53$	408.417	1.05850	0.529249	−	0.848466i	$-0.322474\pi$
$53$	408.417	1.05850	0.529249	+	0.848466i	$0.322474\pi$
$54$	540.168	1.36125
$55$	171.801	0.421194
$56$	−76.9664	−0.183662
$57$	−29.9229	−0.0695330
$58$	364.895	0.826087
$59$	194.836	0.429923	0.214962	−	0.976622i	$-0.431037\pi$
$59$	194.836	0.429923	0.214962	+	0.976622i	$0.431037\pi$
$60$	75.4717	0.162389
$61$	272.396	0.571749	0.285875	−	0.958267i	$-0.407716\pi$
$61$	272.396	0.571749	0.285875	+	0.958267i	$0.407716\pi$
$62$	−348.759	−0.714394
$63$	−35.2563	−0.0705060
$64$	−74.6411	−0.145783
$65$	6.83248	0.0130379
$66$	889.286	1.65854
$67$	−811.909	−1.48045	−0.740227	−	0.672357i	$-0.765282\pi$
$67$	−811.909	−1.48045	−0.740227	+	0.672357i	$0.765282\pi$
$68$	−72.4224	−0.129155
$69$	107.790	0.188063
$70$	−82.0346	−0.140072
$71$	−867.936	−1.45078	−0.725388	−	0.688340i	$-0.758340\pi$
$71$	−867.936	−1.45078	−0.725388	+	0.688340i	$0.758340\pi$
$72$	55.3786	0.0906449
$73$	−948.048	−1.52001	−0.760004	−	0.649918i	$-0.774803\pi$
$73$	−948.048	−1.52001	−0.760004	+	0.649918i	$0.774803\pi$
$74$	−789.441	−1.24014
$75$	536.088	0.825361
$76$	31.5662	0.0476432
$77$	−369.197	−0.546414
$78$	35.3666	0.0513395
$79$	−149.385	−0.212748	−0.106374	−	0.994326i	$-0.533924\pi$
$79$	−149.385	−0.212748	−0.106374	+	0.994326i	$0.533924\pi$
$80$	257.687	0.360129
$81$	−567.644	−0.778661
$82$	1662.59	2.23906
$83$	−824.893	−1.09089	−0.545445	−	0.838147i	$-0.683639\pi$
$83$	−824.893	−1.09089	−0.545445	+	0.838147i	$0.683639\pi$
$84$	−162.187	−0.210667
$85$	47.7169	0.0608897
$86$	533.312	0.668704
$87$	−475.319	−0.585742
$88$	579.913	0.702488
$89$	370.815	0.441644	0.220822	−	0.975314i	$-0.429126\pi$
$89$	370.815	0.441644	0.220822	+	0.975314i	$0.429126\pi$
$90$	59.0253	0.0691312
$91$	−14.6828	−0.0169141
$92$	−113.709	−0.128859
$93$	454.300	0.506545
$94$	−57.7863	−0.0634064
$95$	−20.7980	−0.0224613
$96$	921.621	0.979818
$97$	−1648.19	−1.72524	−0.862619	−	0.505854i	$-0.831177\pi$
$97$	−1648.19	−1.72524	−0.862619	+	0.505854i	$0.831177\pi$
$98$	176.290	0.181714
$99$	265.643	0.269678
$100$	−565.528	−0.565528
$101$	−153.058	−0.150790	−0.0753952	−	0.997154i	$-0.524022\pi$
$101$	−153.058	−0.150790	−0.0753952	+	0.997154i	$0.524022\pi$
$102$	246.994	0.239766
$103$	624.753	0.597657	0.298829	−	0.954307i	$-0.403404\pi$
$103$	624.753	0.597657	0.298829	+	0.954307i	$0.403404\pi$
$104$	23.0629	0.0217453
$105$	106.860	0.0993186
$106$	1469.39	1.34641
$107$	−16.5010	−0.0149085	−0.00745427	−	0.999972i	$-0.502373\pi$
$107$	−16.5010	−0.0149085	−0.00745427	+	0.999972i	$0.502373\pi$
$108$	742.274	0.661345
$109$	−242.588	−0.213172	−0.106586	−	0.994303i	$-0.533992\pi$
$109$	−242.588	−0.213172	−0.106586	+	0.994303i	$0.533992\pi$
$110$	618.100	0.535759
$111$	1028.34	0.879331
$112$	−553.764	−0.467194
$113$	728.565	0.606528	0.303264	−	0.952907i	$-0.401924\pi$
$113$	728.565	0.606528	0.303264	+	0.952907i	$0.401924\pi$
$114$	−107.655	−0.0884460
$115$	74.9195	0.0607502
$116$	501.422	0.401344
$117$	10.5645	0.00834780
$118$	700.973	0.546862
$119$	−102.542	−0.0789920
$120$	−167.849	−0.127687
$121$	1450.76	1.08998
$122$	980.014	0.727265
$123$	−2165.72	−1.58762
$124$	−479.248	−0.347079
$125$	779.780	0.557965
$126$	−126.844	−0.0896837
$127$	1197.87	0.836959	0.418479	−	0.908226i	$-0.362563\pi$
$127$	1197.87	0.836959	0.418479	+	0.908226i	$0.362563\pi$
$128$	1304.69	0.900933
$129$	−694.702	−0.474148
$130$	24.5816	0.0165842
$131$	−1602.54	−1.06881	−0.534405	−	0.845228i	$-0.679464\pi$
$131$	−1602.54	−1.06881	−0.534405	+	0.845228i	$0.679464\pi$
$132$	1222.02	0.805780
$133$	44.6943	0.0291390
$134$	−2921.05	−1.88314
$135$	−489.061	−0.311790
$136$	161.068	0.101555
$137$	−2757.17	−1.71942	−0.859710	−	0.510782i	$-0.829356\pi$
$137$	−2757.17	−1.71942	−0.859710	+	0.510782i	$0.829356\pi$
$138$	387.802	0.239216
$139$	−2212.09	−1.34984	−0.674918	−	0.737892i	$-0.735821\pi$
$139$	−2212.09	−1.34984	−0.674918	+	0.737892i	$0.735821\pi$
$140$	−112.728	−0.0680519
$141$	75.2735	0.0449587
$142$	−3122.63	−1.84539
$143$	110.630	0.0646945
$144$	398.442	0.230580
$145$	−330.371	−0.189213
$146$	−3410.85	−1.93345
$147$	−229.639	−0.128846
$148$	−1084.81	−0.602508
$149$	1365.23	0.750632	0.375316	−	0.926897i	$-0.377534\pi$
$149$	1365.23	0.750632	0.375316	+	0.926897i	$0.377534\pi$
$150$	1928.72	1.04986
$151$	−1429.58	−0.770445	−0.385223	−	0.922824i	$-0.625875\pi$
$151$	−1429.58	−0.770445	−0.385223	+	0.922824i	$0.625875\pi$
$152$	−70.2032	−0.0374620
$153$	73.7810	0.0389859
$154$	−1328.28	−0.695039
$155$	315.762	0.163630
$156$	48.5992	0.0249426
$157$	2969.39	1.50945	0.754723	−	0.656043i	$-0.227771\pi$
$157$	2969.39	1.50945	0.754723	+	0.656043i	$0.227771\pi$
$158$	−537.451	−0.270616
$159$	−1914.05	−0.954680
$160$	640.574	0.316512
$161$	−161.000	−0.0788110
$162$	−2042.25	−0.990457
$163$	−645.541	−0.310200	−0.155100	−	0.987899i	$-0.549570\pi$
$163$	−645.541	−0.310200	−0.155100	+	0.987899i	$0.549570\pi$
$164$	2284.66	1.08782
$165$	−805.149	−0.379883
$166$	−2967.77	−1.38761
$167$	−3579.97	−1.65884	−0.829420	−	0.558625i	$-0.811329\pi$
$167$	−3579.97	−1.65884	−0.829420	+	0.558625i	$0.811329\pi$
$168$	360.704	0.165648
$169$	−2192.60	−0.997997
$170$	171.674	0.0774517
$171$	−32.1583	−0.0143813
$172$	732.853	0.324881
$173$	1548.06	0.680327	0.340163	−	0.940366i	$-0.389518\pi$
$173$	1548.06	0.680327	0.340163	+	0.940366i	$0.389518\pi$
$174$	−1710.08	−0.745064
$175$	−800.727	−0.345882
$176$	4172.40	1.78697
$177$	−913.100	−0.387756
$178$	1334.10	0.561771
$179$	−786.566	−0.328440	−0.164220	−	0.986424i	$-0.552511\pi$
$179$	−786.566	−0.328440	−0.164220	+	0.986424i	$0.552511\pi$
$180$	81.1099	0.0335865
$181$	3192.62	1.31108	0.655539	−	0.755161i	$-0.272441\pi$
$181$	3192.62	1.31108	0.655539	+	0.755161i	$0.272441\pi$
$182$	−52.8253	−0.0215147
$183$	−1276.59	−0.515672
$184$	252.889	0.101322
$185$	714.750	0.284051
$186$	1634.46	0.644325
$187$	772.619	0.302136
$188$	−79.4073	−0.0308052
$189$	1050.98	0.404484
$190$	−74.8261	−0.0285708
$191$	−656.034	−0.248528	−0.124264	−	0.992249i	$-0.539657\pi$
$191$	−656.034	−0.248528	−0.124264	+	0.992249i	$0.539657\pi$
$192$	349.807	0.131485
$193$	−2138.50	−0.797580	−0.398790	−	0.917042i	$-0.630570\pi$
$193$	−2138.50	−0.797580	−0.398790	+	0.917042i	$0.630570\pi$
$194$	−5929.78	−2.19450
$195$	−32.0205	−0.0117592
$196$	242.250	0.0882835
$197$	3550.69	1.28414	0.642071	−	0.766645i	$-0.278075\pi$
$197$	3550.69	1.28414	0.642071	+	0.766645i	$0.278075\pi$
$198$	955.721	0.343031
$199$	−644.764	−0.229679	−0.114839	−	0.993384i	$-0.536635\pi$
$199$	−644.764	−0.229679	−0.114839	+	0.993384i	$0.536635\pi$
$200$	1257.74	0.444677
$201$	3805.02	1.33525
$202$	−550.666	−0.191805
$203$	709.960	0.245465
$204$	339.409	0.116487
$205$	−1505.29	−0.512849
$206$	2247.71	0.760220
$207$	115.842	0.0388966
$208$	165.935	0.0553150
$209$	−336.755	−0.111454
$210$	384.456	0.126333
$211$	532.889	0.173865	0.0869326	−	0.996214i	$-0.472294\pi$
$211$	532.889	0.173865	0.0869326	+	0.996214i	$0.472294\pi$
$212$	2019.16	0.654136
$213$	4067.59	1.30848
$214$	−59.3667	−0.0189637
$215$	−482.854	−0.153165
$216$	−1650.82	−0.520018
$217$	−678.564	−0.212276
$218$	−872.774	−0.271155
$219$	4443.04	1.37092
$220$	849.365	0.260292
$221$	30.7268	0.00935252
$222$	3699.72	1.11851
$223$	1075.23	0.322882	0.161441	−	0.986882i	$-0.448386\pi$
$223$	1075.23	0.322882	0.161441	+	0.986882i	$0.448386\pi$
$224$	−1376.58	−0.410609
$225$	576.137	0.170707
$226$	2621.20	0.771504
$227$	5265.86	1.53968	0.769840	−	0.638237i	$-0.220336\pi$
$227$	5265.86	1.53968	0.769840	+	0.638237i	$0.220336\pi$
$228$	−147.935	−0.0429704
$229$	170.334	0.0491528	0.0245764	−	0.999698i	$-0.492176\pi$
$229$	170.334	0.0491528	0.0245764	+	0.999698i	$0.492176\pi$
$230$	269.542	0.0772743
$231$	1730.24	0.492821
$232$	−1115.16	−0.315578
$233$	5383.24	1.51359	0.756797	−	0.653650i	$-0.226763\pi$
$233$	5383.24	1.51359	0.756797	+	0.653650i	$0.226763\pi$
$234$	38.0087	0.0106184
$235$	52.3190	0.0145230
$236$	963.245	0.265686
$237$	700.094	0.191882
$238$	−368.923	−0.100478
$239$	−5437.23	−1.47157	−0.735785	−	0.677216i	$-0.763186\pi$
$239$	−5437.23	−1.47157	−0.735785	+	0.677216i	$0.763186\pi$
$240$	−1207.65	−0.324807
$241$	1193.11	0.318901	0.159450	−	0.987206i	$-0.449028\pi$
$241$	1193.11	0.318901	0.159450	+	0.987206i	$0.449028\pi$
$242$	5219.49	1.38645
$243$	−1393.51	−0.367875
$244$	1346.69	0.353332
$245$	−159.611	−0.0416211
$246$	−7791.75	−2.01945
$247$	−13.3926	−0.00345001
$248$	1065.85	0.272909
$249$	3865.87	0.983894
$250$	2805.46	0.709732
$251$	−2527.45	−0.635583	−0.317791	−	0.948161i	$-0.602941\pi$
$251$	−2527.45	−0.635583	−0.317791	+	0.948161i	$0.602941\pi$
$252$	−174.303	−0.0435717
$253$	1213.08	0.301444
$254$	4309.65	1.06461
$255$	−223.626	−0.0549176
$256$	5291.09	1.29177
$257$	−707.247	−0.171661	−0.0858305	−	0.996310i	$-0.527354\pi$
$257$	−707.247	−0.171661	−0.0858305	+	0.996310i	$0.527354\pi$
$258$	−2499.37	−0.603117
$259$	−1535.98	−0.368499
$260$	33.7790	0.00805724
$261$	−510.828	−0.121147
$262$	−5765.54	−1.35953
$263$	4383.54	1.02776	0.513880	−	0.857862i	$-0.328208\pi$
$263$	4383.54	1.02776	0.513880	+	0.857862i	$0.328208\pi$
$264$	−2717.77	−0.633587
$265$	−1330.36	−0.308391
$266$	160.799	0.0370648
$267$	−1737.83	−0.398327
$268$	−4013.98	−0.914899
$269$	6451.97	1.46239	0.731196	−	0.682167i	$-0.238962\pi$
$269$	6451.97	1.46239	0.731196	+	0.682167i	$0.238962\pi$
$270$	−1759.52	−0.396597
$271$	−7434.30	−1.66643	−0.833213	−	0.552952i	$-0.813501\pi$
$271$	−7434.30	−1.66643	−0.833213	+	0.552952i	$0.813501\pi$
$272$	1158.86	0.258332
$273$	68.8112	0.0152551
$274$	−9919.62	−2.18710
$275$	6033.18	1.32296
$276$	532.899	0.116220
$277$	−4459.88	−0.967394	−0.483697	−	0.875236i	$-0.660706\pi$
$277$	−4459.88	−0.967394	−0.483697	+	0.875236i	$0.660706\pi$
$278$	−7958.58	−1.71699
$279$	488.239	0.104767
$280$	250.708	0.0535095
$281$	6116.73	1.29855	0.649277	−	0.760552i	$-0.275072\pi$
$281$	6116.73	1.29855	0.649277	+	0.760552i	$0.275072\pi$
$282$	270.816	0.0571875
$283$	−2037.96	−0.428071	−0.214036	−	0.976826i	$-0.568661\pi$
$283$	−2037.96	−0.428071	−0.214036	+	0.976826i	$0.568661\pi$
$284$	−4290.97	−0.896557
$285$	97.4698	0.0202583
$286$	398.019	0.0822915
$287$	3234.83	0.665317
$288$	990.471	0.202653
$289$	−4698.41	−0.956322
$290$	−1188.60	−0.240679
$291$	7724.25	1.55603
$292$	−4687.03	−0.939342
$293$	1234.28	0.246099	0.123050	−	0.992401i	$-0.460733\pi$
$293$	1234.28	0.246099	0.123050	+	0.992401i	$0.460733\pi$
$294$	−826.186	−0.163892
$295$	−634.652	−0.125257
$296$	2412.63	0.473754
$297$	−7918.74	−1.54711
$298$	4911.77	0.954804
$299$	48.2436	0.00933110
$300$	2650.35	0.510061
$301$	1037.64	0.198700
$302$	−5143.27	−0.980006
$303$	717.308	0.136001
$304$	−505.103	−0.0952950
$305$	−887.293	−0.166578
$306$	265.446	0.0495901
$307$	−2544.58	−0.473052	−0.236526	−	0.971625i	$-0.576009\pi$
$307$	−2544.58	−0.473052	−0.236526	+	0.971625i	$0.576009\pi$
$308$	−1825.26	−0.337675
$309$	−2927.91	−0.539039
$310$	1136.04	0.208137
$311$	3924.86	0.715621	0.357811	−	0.933794i	$-0.383523\pi$
$311$	3924.86	0.715621	0.357811	+	0.933794i	$0.383523\pi$
$312$	−108.085	−0.0196125
$313$	8598.16	1.55271	0.776353	−	0.630299i	$-0.217068\pi$
$313$	8598.16	1.55271	0.776353	+	0.630299i	$0.217068\pi$
$314$	10683.2	1.92002
$315$	114.843	0.0205418
$316$	−738.540	−0.131475
$317$	1329.20	0.235506	0.117753	−	0.993043i	$-0.462431\pi$
$317$	1329.20	0.235506	0.117753	+	0.993043i	$0.462431\pi$
$318$	−6886.30	−1.21435
$319$	−5349.28	−0.938878
$320$	243.134	0.0424737
$321$	77.3322	0.0134463
$322$	−579.239	−0.100248
$323$	−93.5318	−0.0161122
$324$	−2806.36	−0.481201
$325$	239.937	0.0409518
$326$	−2322.50	−0.394575
$327$	1136.89	0.192264
$328$	−5081.08	−0.855353
$329$	−112.432	−0.0188407
$330$	−2896.73	−0.483212
$331$	−4479.47	−0.743848	−0.371924	−	0.928263i	$-0.621302\pi$
$331$	−4479.47	−0.743848	−0.371924	+	0.928263i	$0.621302\pi$
$332$	−4078.17	−0.674153
$333$	1105.16	0.181870
$334$	−12879.9	−2.11005
$335$	2644.69	0.431327
$336$	2595.22	0.421371
$337$	6045.75	0.977248	0.488624	−	0.872494i	$-0.337499\pi$
$337$	6045.75	0.977248	0.488624	+	0.872494i	$0.337499\pi$
$338$	−7888.45	−1.26945
$339$	−3414.43	−0.547039
$340$	235.906	0.0376289
$341$	5112.73	0.811935
$342$	−115.698	−0.0182930
$343$	343.000	0.0539949
$344$	−1629.87	−0.255455
$345$	−351.111	−0.0547918
$346$	5569.54	0.865376
$347$	967.191	0.149630	0.0748149	−	0.997197i	$-0.476163\pi$
$347$	967.191	0.149630	0.0748149	+	0.997197i	$0.476163\pi$
$348$	−2349.92	−0.361980
$349$	−2803.90	−0.430056	−0.215028	−	0.976608i	$-0.568984\pi$
$349$	−2803.90	−0.430056	−0.215028	+	0.976608i	$0.568984\pi$
$350$	−2880.82	−0.439961
$351$	−314.926	−0.0478903
$352$	10372.0	1.57054
$353$	−6866.98	−1.03539	−0.517695	−	0.855565i	$-0.673210\pi$
$353$	−6866.98	−1.03539	−0.517695	+	0.855565i	$0.673210\pi$
$354$	−3285.12	−0.493226
$355$	2827.19	0.422680
$356$	1833.26	0.272929
$357$	480.566	0.0712444
$358$	−2829.88	−0.417775
$359$	−4023.27	−0.591476	−0.295738	−	0.955269i	$-0.595566\pi$
$359$	−4023.27	−0.591476	−0.295738	+	0.955269i	$0.595566\pi$
$360$	−180.388	−0.0264092
$361$	−6818.23	−0.994056
$362$	11486.3	1.66769
$363$	−6799.00	−0.983072
$364$	−72.5901	−0.0104526
$365$	3088.14	0.442851
$366$	−4592.85	−0.655934
$367$	4280.70	0.608857	0.304428	−	0.952535i	$-0.401535\pi$
$367$	4280.70	0.608857	0.304428	+	0.952535i	$0.401535\pi$
$368$	1819.51	0.257740
$369$	−2327.51	−0.328362
$370$	2571.50	0.361313
$371$	2858.92	0.400075
$372$	2246.00	0.313037
$373$	−5482.90	−0.761109	−0.380555	−	0.924758i	$-0.624267\pi$
$373$	−5482.90	−0.761109	−0.380555	+	0.924758i	$0.624267\pi$
$374$	2779.70	0.384317
$375$	−3654.45	−0.503239
$376$	176.602	0.0242222
$377$	−212.739	−0.0290627
$378$	3781.17	0.514504
$379$	−1569.38	−0.212700	−0.106350	−	0.994329i	$-0.533916\pi$
$379$	−1569.38	−0.212700	−0.106350	+	0.994329i	$0.533916\pi$
$380$	−102.823	−0.0138808
$381$	−5613.83	−0.754869
$382$	−2360.25	−0.316128
$383$	7169.92	0.956569	0.478285	−	0.878205i	$-0.341259\pi$
$383$	7169.92	0.956569	0.478285	+	0.878205i	$0.341259\pi$
$384$	−6114.45	−0.812569
$385$	1202.61	0.159197
$386$	−7693.82	−1.01452
$387$	−746.601	−0.0980668
$388$	−8148.44	−1.06617
$389$	−10328.4	−1.34620	−0.673100	−	0.739552i	$-0.735037\pi$
$389$	−10328.4	−1.34620	−0.673100	+	0.739552i	$0.735037\pi$
$390$	−115.202	−0.0149577
$391$	336.925	0.0435781
$392$	−538.765	−0.0694176
$393$	7510.30	0.963981
$394$	12774.5	1.63343
$395$	486.601	0.0619837
$396$	1313.31	0.166657
$397$	−6608.31	−0.835419	−0.417710	−	0.908581i	$-0.637167\pi$
$397$	−6608.31	−0.835419	−0.417710	+	0.908581i	$0.637167\pi$
$398$	−2319.71	−0.292152
$399$	−209.460	−0.0262810
$400$	9049.25	1.13116
$401$	8742.74	1.08876	0.544379	−	0.838840i	$-0.316765\pi$
$401$	8742.74	1.08876	0.544379	+	0.838840i	$0.316765\pi$
$402$	13689.6	1.69844
$403$	203.332	0.0251332
$404$	−756.700	−0.0931862
$405$	1849.02	0.226861
$406$	2554.26	0.312232
$407$	11573.0	1.40947
$408$	−754.845	−0.0915941
$409$	−10270.5	−1.24167	−0.620836	−	0.783941i	$-0.713207\pi$
$409$	−10270.5	−1.24167	−0.620836	+	0.783941i	$0.713207\pi$
$410$	−5415.67	−0.652344
$411$	12921.5	1.55078
$412$	3088.70	0.369343
$413$	1363.85	0.162496
$414$	416.773	0.0494765
$415$	2686.98	0.317828
$416$	412.491	0.0486155
$417$	10367.0	1.21744
$418$	−1211.56	−0.141769
$419$	−204.055	−0.0237917	−0.0118958	−	0.999929i	$-0.503787\pi$
$419$	−204.055	−0.0237917	−0.0118958	+	0.999929i	$0.503787\pi$
$420$	528.302	0.0613774
$421$	12498.8	1.44693	0.723464	−	0.690363i	$-0.242549\pi$
$421$	12498.8	1.44693	0.723464	+	0.690363i	$0.242549\pi$
$422$	1917.21	0.221157
$423$	80.8969	0.00929868
$424$	−4490.63	−0.514349
$425$	1675.68	0.191253
$426$	14634.2	1.66439
$427$	1906.77	0.216101
$428$	−81.5790	−0.00921325
$429$	−518.467	−0.0583492
$430$	−1737.19	−0.194825
$431$	−11136.3	−1.24459	−0.622294	−	0.782784i	$-0.713799\pi$
$431$	−11136.3	−1.24459	−0.622294	+	0.782784i	$0.713799\pi$
$432$	−11877.4	−1.32281
$433$	−7168.61	−0.795615	−0.397807	−	0.917469i	$-0.630229\pi$
$433$	−7168.61	−0.795615	−0.397807	+	0.917469i	$0.630229\pi$
$434$	−2441.31	−0.270015
$435$	1548.29	0.170655
$436$	−1199.33	−0.131737
$437$	−146.853	−0.0160753
$438$	15985.0	1.74382
$439$	8307.02	0.903126	0.451563	−	0.892239i	$-0.350867\pi$
$439$	8307.02	0.903126	0.451563	+	0.892239i	$0.350867\pi$
$440$	−1888.99	−0.204668
$441$	−246.794	−0.0266488
$442$	110.548	0.0118964
$443$	−11823.7	−1.26808	−0.634042	−	0.773298i	$-0.718606\pi$
$443$	−11823.7	−1.26808	−0.634042	+	0.773298i	$0.718606\pi$
$444$	5083.99	0.543413
$445$	−1207.88	−0.128672
$446$	3868.42	0.410706
$447$	−6398.17	−0.677009
$448$	−522.488	−0.0551010
$449$	6407.90	0.673513	0.336757	−	0.941592i	$-0.390670\pi$
$449$	6407.90	0.673513	0.336757	+	0.941592i	$0.390670\pi$
$450$	2072.80	0.217140
$451$	−24373.2	−2.54477
$452$	3601.94	0.374825
$453$	6699.72	0.694879
$454$	18945.3	1.95847
$455$	47.8274	0.00492787
$456$	329.008	0.0337877
$457$	−1254.46	−0.128406	−0.0642028	−	0.997937i	$-0.520450\pi$
$457$	−1254.46	−0.128406	−0.0642028	+	0.997937i	$0.520450\pi$
$458$	612.821	0.0625224
$459$	−2199.39	−0.223657
$460$	370.393	0.0375427
$461$	8438.67	0.852555	0.426277	−	0.904592i	$-0.359825\pi$
$461$	8438.67	0.852555	0.426277	+	0.904592i	$0.359825\pi$
$462$	6225.00	0.626869
$463$	−4172.97	−0.418864	−0.209432	−	0.977823i	$-0.567162\pi$
$463$	−4172.97	−0.418864	−0.209432	+	0.977823i	$0.567162\pi$
$464$	−8023.47	−0.802759
$465$	−1479.82	−0.147581
$466$	19367.6	1.92529
$467$	−1053.51	−0.104391	−0.0521956	−	0.998637i	$-0.516622\pi$
$467$	−1053.51	−0.104391	−0.0521956	+	0.998637i	$0.516622\pi$
$468$	52.2298	0.00515881
$469$	−5683.36	−0.559559
$470$	188.231	0.0184733
$471$	−13916.1	−1.36140
$472$	−2142.26	−0.208910
$473$	−7818.24	−0.760007
$474$	2518.77	0.244074
$475$	−730.366	−0.0705505
$476$	−506.957	−0.0488158
$477$	−2057.04	−0.197454
$478$	−19561.8	−1.87184
$479$	−6309.22	−0.601828	−0.300914	−	0.953651i	$-0.597292\pi$
$479$	−6309.22	−0.601828	−0.300914	+	0.953651i	$0.597292\pi$
$480$	−3002.06	−0.285468
$481$	460.256	0.0436296
$482$	4292.53	0.405642
$483$	754.528	0.0710812
$484$	7172.38	0.673589
$485$	5368.75	0.502644
$486$	−5013.52	−0.467938
$487$	−5294.18	−0.492612	−0.246306	−	0.969192i	$-0.579217\pi$
$487$	−5294.18	−0.492612	−0.246306	+	0.969192i	$0.579217\pi$
$488$	−2995.04	−0.277826
$489$	3025.33	0.279776
$490$	−574.242	−0.0529421
$491$	4030.46	0.370453	0.185226	−	0.982696i	$-0.440698\pi$
$491$	4030.46	0.370453	0.185226	+	0.982696i	$0.440698\pi$
$492$	−10707.1	−0.981122
$493$	−1485.73	−0.135728
$494$	−48.1834	−0.00438841
$495$	−865.298	−0.0785702
$496$	7668.66	0.694220
$497$	−6075.55	−0.548342
$498$	13908.5	1.25151
$499$	793.983	0.0712296	0.0356148	−	0.999366i	$-0.488661\pi$
$499$	793.983	0.0712296	0.0356148	+	0.999366i	$0.488661\pi$
$500$	3855.14	0.344814
$501$	16777.6	1.49614
$502$	−9093.16	−0.808461
$503$	−15179.8	−1.34559	−0.672796	−	0.739828i	$-0.734907\pi$
$503$	−15179.8	−1.34559	−0.672796	+	0.739828i	$0.734907\pi$
$504$	387.650	0.0342605
$505$	498.566	0.0439325
$506$	4364.35	0.383437
$507$	10275.6	0.900113
$508$	5922.12	0.517228
$509$	8692.69	0.756968	0.378484	−	0.925608i	$-0.376446\pi$
$509$	8692.69	0.756968	0.378484	+	0.925608i	$0.376446\pi$
$510$	−804.552	−0.0698552
$511$	−6636.33	−0.574509
$512$	8598.56	0.742200
$513$	958.628	0.0825038
$514$	−2544.51	−0.218353
$515$	−2035.05	−0.174126
$516$	−3434.52	−0.293016
$517$	847.135	0.0720637
$518$	−5526.09	−0.468730
$519$	−7254.98	−0.613600
$520$	−75.1245	−0.00633543
$521$	10817.9	0.909679	0.454840	−	0.890573i	$-0.349697\pi$
$521$	10817.9	0.909679	0.454840	+	0.890573i	$0.349697\pi$
$522$	−1837.84	−0.154099
$523$	19439.4	1.62529	0.812645	−	0.582759i	$-0.198027\pi$
$523$	19439.4	1.62529	0.812645	+	0.582759i	$0.198027\pi$
$524$	−7922.74	−0.660508
$525$	3752.62	0.311957
$526$	15770.9	1.30731
$527$	1420.03	0.117377
$528$	−19554.0	−1.61170
$529$	529.000	0.0434783
$530$	−4786.33	−0.392274
$531$	−981.314	−0.0801985
$532$	220.963	0.0180075
$533$	−969.315	−0.0787724
$534$	−6252.29	−0.506672
$535$	53.7499	0.00434357
$536$	8927.10	0.719388
$537$	3686.25	0.296226
$538$	23212.6	1.86016
$539$	−2584.38	−0.206525
$540$	−2417.86	−0.192682
$541$	−18392.4	−1.46165	−0.730823	−	0.682567i	$-0.760864\pi$
$541$	−18392.4	−1.46165	−0.730823	+	0.682567i	$0.760864\pi$
$542$	−26746.8	−2.11969
$543$	−14962.2	−1.18249
$544$	2880.77	0.227044
$545$	790.199	0.0621072
$546$	247.566	0.0194045
$547$	20954.3	1.63792	0.818960	−	0.573851i	$-0.194551\pi$
$547$	20954.3	1.63792	0.818960	+	0.573851i	$0.194551\pi$
$548$	−13631.1	−1.06258
$549$	−1371.95	−0.106655
$550$	21705.9	1.68281
$551$	647.574	0.0500682
$552$	−1185.17	−0.0913843
$553$	−1045.69	−0.0804113
$554$	−16045.6	−1.23053
$555$	−3349.68	−0.256191
$556$	−10936.3	−0.834178
$557$	1419.22	0.107961	0.0539807	−	0.998542i	$-0.482809\pi$
$557$	1419.22	0.107961	0.0539807	+	0.998542i	$0.482809\pi$
$558$	1756.57	0.133264
$559$	−310.929	−0.0235257
$560$	1803.81	0.136116
$561$	−3620.89	−0.272503
$562$	22006.5	1.65176
$563$	654.698	0.0490093	0.0245046	−	0.999700i	$-0.492199\pi$
$563$	654.698	0.0490093	0.0245046	+	0.999700i	$0.492199\pi$
$564$	372.143	0.0277838
$565$	−2373.21	−0.176711
$566$	−7332.09	−0.544507
$567$	−3973.51	−0.294306
$568$	9543.13	0.704966
$569$	−4848.16	−0.357198	−0.178599	−	0.983922i	$-0.557156\pi$
$569$	−4848.16	−0.357198	−0.178599	+	0.983922i	$0.557156\pi$
$570$	350.673	0.0257686
$571$	−1580.00	−0.115798	−0.0578991	−	0.998322i	$-0.518440\pi$
$571$	−1580.00	−0.115798	−0.0578991	+	0.998322i	$0.518440\pi$
$572$	546.940	0.0399802
$573$	3074.51	0.224153
$574$	11638.1	0.846283
$575$	2630.96	0.190815
$576$	375.939	0.0271947
$577$	−7858.33	−0.566978	−0.283489	−	0.958975i	$-0.591492\pi$
$577$	−7858.33	−0.566978	−0.283489	+	0.958975i	$0.591492\pi$
$578$	−16903.7	−1.21644
$579$	10022.1	0.719352
$580$	−1633.32	−0.116931
$581$	−5774.25	−0.412317
$582$	27790.0	1.97926
$583$	−21540.9	−1.53024
$584$	10424.0	0.738608
$585$	−34.4126	−0.00243211
$586$	4440.63	0.313039
$587$	−24973.6	−1.75600	−0.878001	−	0.478660i	$-0.841123\pi$
$587$	−24973.6	−1.75600	−0.878001	+	0.478660i	$0.841123\pi$
$588$	−1135.31	−0.0796246
$589$	−618.938	−0.0432986
$590$	−2283.33	−0.159327
$591$	−16640.3	−1.15819
$592$	17358.6	1.20512
$593$	−12820.2	−0.887796	−0.443898	−	0.896077i	$-0.646405\pi$
$593$	−12820.2	−0.887796	−0.443898	+	0.896077i	$0.646405\pi$
$594$	−28489.7	−1.96793
$595$	334.018	0.0230141
$596$	6749.54	0.463879
$597$	3021.69	0.207152
$598$	173.569	0.0118692
$599$	11113.4	0.758067	0.379034	−	0.925383i	$-0.376257\pi$
$599$	11113.4	0.758067	0.379034	+	0.925383i	$0.376257\pi$
$600$	−5894.39	−0.401062
$601$	27135.9	1.84176	0.920880	−	0.389845i	$-0.127471\pi$
$601$	27135.9	1.84176	0.920880	+	0.389845i	$0.127471\pi$
$602$	3733.18	0.252746
$603$	4089.28	0.276166
$604$	−7067.65	−0.476123
$605$	−4725.66	−0.317563
$606$	2580.70	0.172993
$607$	−16202.8	−1.08345	−0.541724	−	0.840556i	$-0.682228\pi$
$607$	−16202.8	−1.08345	−0.541724	+	0.840556i	$0.682228\pi$
$608$	−1255.62	−0.0837532
$609$	−3327.23	−0.221390
$610$	−3192.27	−0.211887
$611$	33.6903	0.00223071
$612$	364.764	0.0240927
$613$	11802.4	0.777645	0.388822	−	0.921313i	$-0.372882\pi$
$613$	11802.4	0.777645	0.388822	+	0.921313i	$0.372882\pi$
$614$	−9154.80	−0.601723
$615$	7054.56	0.462548
$616$	4059.39	0.265515
$617$	−26758.7	−1.74597	−0.872986	−	0.487746i	$-0.837819\pi$
$617$	−26758.7	−1.74597	−0.872986	+	0.487746i	$0.837819\pi$
$618$	−10533.9	−0.685657
$619$	−2640.23	−0.171438	−0.0857189	−	0.996319i	$-0.527319\pi$
$619$	−2640.23	−0.171438	−0.0857189	+	0.996319i	$0.527319\pi$
$620$	1561.09	0.101121
$621$	−3453.22	−0.223145
$622$	14120.7	0.910270
$623$	2595.71	0.166926
$624$	−777.656	−0.0498897
$625$	11758.7	0.752555
$626$	30934.1	1.97504
$627$	1578.20	0.100522
$628$	14680.3	0.932815
$629$	3214.35	0.203759
$630$	413.177	0.0261292
$631$	2832.03	0.178671	0.0893354	−	0.996002i	$-0.471526\pi$
$631$	2832.03	0.178671	0.0893354	+	0.996002i	$0.471526\pi$
$632$	1642.52	0.103379
$633$	−2497.39	−0.156812
$634$	4782.15	0.299564
$635$	−3901.90	−0.243846
$636$	−9462.84	−0.589978
$637$	−102.780	−0.00639291
$638$	−19245.4	−1.19425
$639$	4371.46	0.270630
$640$	−4249.86	−0.262485
$641$	−28217.3	−1.73872	−0.869359	−	0.494181i	$-0.835468\pi$
$641$	−28217.3	−1.73872	−0.869359	+	0.494181i	$0.835468\pi$
$642$	278.223	0.0171037
$643$	21931.3	1.34508	0.672539	−	0.740062i	$-0.265204\pi$
$643$	21931.3	1.34508	0.672539	+	0.740062i	$0.265204\pi$
$644$	−795.964	−0.0487040
$645$	2262.90	0.138142
$646$	−336.505	−0.0204948
$647$	8915.68	0.541749	0.270874	−	0.962615i	$-0.412687\pi$
$647$	8915.68	0.541749	0.270874	+	0.962615i	$0.412687\pi$
$648$	6241.35	0.378370
$649$	−10276.1	−0.621529
$650$	863.238	0.0520907
$651$	3180.10	0.191456
$652$	−3191.48	−0.191699
$653$	28323.0	1.69735	0.848673	−	0.528918i	$-0.177402\pi$
$653$	28323.0	1.69735	0.848673	+	0.528918i	$0.177402\pi$
$654$	4090.27	0.244560
$655$	5220.05	0.311396
$656$	−36557.8	−2.17583
$657$	4774.95	0.283544
$658$	−404.504	−0.0239654
$659$	15096.9	0.892400	0.446200	−	0.894933i	$-0.352777\pi$
$659$	15096.9	0.892400	0.446200	+	0.894933i	$0.352777\pi$
$660$	−3980.56	−0.234762
$661$	−30098.5	−1.77110	−0.885549	−	0.464546i	$-0.846218\pi$
$661$	−30098.5	−1.77110	−0.885549	+	0.464546i	$0.846218\pi$
$662$	−16116.1	−0.946175
$663$	−144.001	−0.00843522
$664$	9069.86	0.530089
$665$	−145.586	−0.00848958
$666$	3976.11	0.231338
$667$	−2332.72	−0.135417
$668$	−17698.9	−1.02514
$669$	−5039.07	−0.291213
$670$	9514.95	0.548648
$671$	−14366.8	−0.826564
$672$	6451.35	0.370336
$673$	−642.804	−0.0368176	−0.0184088	−	0.999831i	$-0.505860\pi$
$673$	−642.804	−0.0368176	−0.0184088	+	0.999831i	$0.505860\pi$
$674$	21751.1	1.24306
$675$	−17174.4	−0.979325
$676$	−10839.9	−0.616747
$677$	29128.6	1.65363	0.826813	−	0.562477i	$-0.190151\pi$
$677$	29128.6	1.65363	0.826813	+	0.562477i	$0.190151\pi$
$678$	−12284.3	−0.695834
$679$	−11537.3	−0.652079
$680$	−524.656	−0.0295877
$681$	−24678.5	−1.38867
$682$	18394.4	1.03278
$683$	10168.8	0.569692	0.284846	−	0.958573i	$-0.408057\pi$
$683$	10168.8	0.569692	0.284846	+	0.958573i	$0.408057\pi$
$684$	−158.987	−0.00888744
$685$	8981.10	0.500949
$686$	1234.03	0.0686816
$687$	−798.273	−0.0443319
$688$	−11726.7	−0.649820
$689$	−856.674	−0.0473682
$690$	−1263.21	−0.0696952
$691$	5.34100	0.000294039 0	0.000147020	−	1.00000i	$-0.499953\pi$
$691$	5.34100	0.000294039 0	0.000147020		1.00000i	$0.499953\pi$
$692$	7653.40	0.420432
$693$	1859.50	0.101929
$694$	3479.72	0.190329
$695$	7205.60	0.393272
$696$	5226.22	0.284626
$697$	−6769.53	−0.367883
$698$	−10087.8	−0.547031
$699$	−25228.6	−1.36514
$700$	−3958.70	−0.213749
$701$	−32821.1	−1.76838	−0.884192	−	0.467124i	$-0.845290\pi$
$701$	−32821.1	−1.76838	−0.884192	+	0.467124i	$0.845290\pi$
$702$	−1133.03	−0.0609164
$703$	−1401.01	−0.0751637
$704$	3936.75	0.210756
$705$	−245.194	−0.0130986
$706$	−24705.8	−1.31702
$707$	−1071.41	−0.0569934
$708$	−4514.26	−0.239627
$709$	29044.4	1.53848	0.769242	−	0.638957i	$-0.220634\pi$
$709$	29044.4	1.53848	0.769242	+	0.638957i	$0.220634\pi$
$710$	10171.5	0.537649
$711$	752.395	0.0396864
$712$	−4077.18	−0.214605
$713$	2229.57	0.117108
$714$	1728.96	0.0906229
$715$	−360.361	−0.0188486
$716$	−3888.69	−0.202971
$717$	25481.6	1.32724
$718$	−14474.8	−0.752358
$719$	13087.0	0.678810	0.339405	−	0.940640i	$-0.389774\pi$
$719$	13087.0	0.678810	0.339405	+	0.940640i	$0.389774\pi$
$720$	−1297.87	−0.0671790
$721$	4373.27	0.225893
$722$	−24530.4	−1.26444
$723$	−5591.53	−0.287623
$724$	15783.9	0.810227
$725$	−11601.7	−0.594313
$726$	−24461.2	−1.25047
$727$	26656.1	1.35986	0.679931	−	0.733276i	$-0.262010\pi$
$727$	26656.1	1.35986	0.679931	+	0.733276i	$0.262010\pi$
$728$	161.441	0.00821894
$729$	21857.1	1.11045
$730$	11110.4	0.563307
$731$	−2171.47	−0.109870
$732$	−6311.28	−0.318677
$733$	−8999.08	−0.453463	−0.226732	−	0.973957i	$-0.572804\pi$
$733$	−8999.08	−0.453463	−0.226732	+	0.973957i	$0.572804\pi$
$734$	15400.9	0.774466
$735$	748.019	0.0375389
$736$	4523.04	0.226524
$737$	42822.0	2.14026
$738$	−8373.84	−0.417677
$739$	−26287.2	−1.30851	−0.654257	−	0.756273i	$-0.727018\pi$
$739$	−26287.2	−1.30851	−0.654257	+	0.756273i	$0.727018\pi$
$740$	3533.64	0.175539
$741$	62.7647	0.00311163
$742$	10285.7	0.508895
$743$	−13784.3	−0.680615	−0.340308	−	0.940314i	$-0.610531\pi$
$743$	−13784.3	−0.680615	−0.340308	+	0.940314i	$0.610531\pi$
$744$	−4995.11	−0.246142
$745$	−4447.06	−0.218695
$746$	−19726.2	−0.968131
$747$	4154.67	0.203496
$748$	3819.73	0.186716
$749$	−115.507	−0.00563490
$750$	−13147.8	−0.640121
$751$	−34412.8	−1.67209	−0.836046	−	0.548660i	$-0.815138\pi$
$751$	−34412.8	−1.67209	−0.836046	+	0.548660i	$0.815138\pi$
$752$	1270.63	0.0616158
$753$	11844.9	0.573244
$754$	−765.384	−0.0369677
$755$	4656.65	0.224468
$756$	5195.92	0.249965
$757$	−1047.44	−0.0502905	−0.0251453	−	0.999684i	$-0.508005\pi$
$757$	−1047.44	−0.0502905	−0.0251453	+	0.999684i	$0.508005\pi$
$758$	−5646.24	−0.270555
$759$	−5685.09	−0.271878
$760$	228.678	0.0109145
$761$	−29611.6	−1.41054	−0.705269	−	0.708940i	$-0.749174\pi$
$761$	−29611.6	−1.41054	−0.705269	+	0.708940i	$0.749174\pi$
$762$	−20197.2	−0.960194
$763$	−1698.12	−0.0805714
$764$	−3243.35	−0.153587
$765$	−240.332	−0.0113585
$766$	25795.7	1.21676
$767$	−408.677	−0.0192392
$768$	−24796.8	−1.16507
$769$	33154.6	1.55473	0.777364	−	0.629051i	$-0.216556\pi$
$769$	33154.6	1.55473	0.777364	+	0.629051i	$0.216556\pi$
$770$	4326.70	0.202498
$771$	3314.52	0.154824
$772$	−10572.5	−0.492892
$773$	27270.2	1.26887	0.634437	−	0.772975i	$-0.281232\pi$
$773$	27270.2	1.26887	0.634437	+	0.772975i	$0.281232\pi$
$774$	−2686.09	−0.124741
$775$	11088.7	0.513957
$776$	18122.1	0.838334
$777$	7198.39	0.332356
$778$	−37159.2	−1.71237
$779$	2950.58	0.135707
$780$	−158.305	−0.00726698
$781$	45777.0	2.09735
$782$	1212.18	0.0554313
$783$	15227.6	0.695007
$784$	−3876.35	−0.176583
$785$	−9672.39	−0.439774
$786$	27020.3	1.22618
$787$	26185.8	1.18605	0.593026	−	0.805183i	$-0.297933\pi$
$787$	26185.8	1.18605	0.593026	+	0.805183i	$0.297933\pi$
$788$	17554.2	0.793580
$789$	−20543.5	−0.926957
$790$	1750.67	0.0788433
$791$	5099.96	0.229246
$792$	−2920.80	−0.131043
$793$	−571.363	−0.0255860
$794$	−23775.1	−1.06265
$795$	6234.77	0.278144
$796$	−3187.63	−0.141938
$797$	78.4109	0.00348489	0.00174244	−	0.999998i	$-0.499445\pi$
$797$	78.4109	0.00348489	0.00174244	+	0.999998i	$0.499445\pi$
$798$	−753.588	−0.0334295
$799$	235.287	0.0104178
$800$	22495.2	0.994155
$801$	−1867.65	−0.0823849
$802$	31454.3	1.38490
$803$	50002.3	2.19744
$804$	18811.6	0.825165
$805$	524.436	0.0229614
$806$	731.538	0.0319694
$807$	−30237.2	−1.31896
$808$	1682.90	0.0732726
$809$	10096.4	0.438778	0.219389	−	0.975637i	$-0.429594\pi$
$809$	10096.4	0.438778	0.219389	+	0.975637i	$0.429594\pi$
$810$	6652.35	0.288567
$811$	−15893.9	−0.688175	−0.344087	−	0.938938i	$-0.611812\pi$
$811$	−15893.9	−0.688175	−0.344087	+	0.938938i	$0.611812\pi$
$812$	3509.95	0.151694
$813$	34840.9	1.50298
$814$	41637.0	1.79285
$815$	2102.76	0.0903762
$816$	−5431.02	−0.232995
$817$	946.462	0.0405294
$818$	−36950.8	−1.57941
$819$	73.9518	0.00315517
$820$	−7441.97	−0.316933
$821$	−19073.2	−0.810791	−0.405395	−	0.914141i	$-0.632866\pi$
$821$	−19073.2	−0.810791	−0.405395	+	0.914141i	$0.632866\pi$
$822$	46488.4	1.97259
$823$	44059.6	1.86612	0.933062	−	0.359716i	$-0.117126\pi$
$823$	44059.6	1.86612	0.933062	+	0.359716i	$0.117126\pi$
$824$	−6869.28	−0.290416
$825$	−28274.6	−1.19320
$826$	4906.81	0.206695
$827$	6393.67	0.268839	0.134419	−	0.990925i	$-0.457083\pi$
$827$	6393.67	0.268839	0.134419	+	0.990925i	$0.457083\pi$
$828$	572.710	0.0240375
$829$	−22741.4	−0.952762	−0.476381	−	0.879239i	$-0.658052\pi$
$829$	−22741.4	−0.952762	−0.476381	+	0.879239i	$0.658052\pi$
$830$	9667.11	0.404278
$831$	20901.3	0.872511
$832$	156.563	0.00652387
$833$	−717.797	−0.0298562
$834$	37298.0	1.54859
$835$	11661.3	0.483299
$836$	−1664.87	−0.0688767
$837$	−14554.2	−0.601037
$838$	−734.139	−0.0302630
$839$	−12609.1	−0.518851	−0.259426	−	0.965763i	$-0.583533\pi$
$839$	−12609.1	−0.518851	−0.259426	+	0.965763i	$0.583533\pi$
$840$	−1174.94	−0.0482612
$841$	−14102.4	−0.578229
$842$	44967.8	1.84049
$843$	−28666.1	−1.17119
$844$	2634.54	0.107446
$845$	7142.10	0.290764
$846$	291.048	0.0118279
$847$	10155.3	0.411973
$848$	−32309.5	−1.30839
$849$	9550.92	0.386086
$850$	6028.70	0.243274
$851$	5046.79	0.203292
$852$	20109.7	0.808622
$853$	−2992.93	−0.120136	−0.0600680	−	0.998194i	$-0.519132\pi$
$853$	−2992.93	−0.120136	−0.0600680	+	0.998194i	$0.519132\pi$
$854$	6860.10	0.274880
$855$	104.751	0.00418997
$856$	181.432	0.00724441
$857$	31106.6	1.23988	0.619942	−	0.784648i	$-0.287156\pi$
$857$	31106.6	1.23988	0.619942	+	0.784648i	$0.287156\pi$
$858$	−1865.32	−0.0742203
$859$	−11227.2	−0.445946	−0.222973	−	0.974825i	$-0.571576\pi$
$859$	−11227.2	−0.445946	−0.222973	+	0.974825i	$0.571576\pi$
$860$	−2387.17	−0.0946534
$861$	−15160.1	−0.600062
$862$	−40065.8	−1.58312
$863$	37362.5	1.47374	0.736869	−	0.676036i	$-0.236303\pi$
$863$	37362.5	1.47374	0.736869	+	0.676036i	$0.236303\pi$
$864$	−29525.6	−1.16259
$865$	−5042.59	−0.198212
$866$	−25790.9	−1.01202
$867$	22019.1	0.862525
$868$	−3354.74	−0.131183
$869$	7878.91	0.307565
$870$	5570.37	0.217073
$871$	1703.02	0.0662509
$872$	2667.30	0.103585
$873$	8301.29	0.321828
$874$	−528.341	−0.0204478
$875$	5458.46	0.210891
$876$	21965.8	0.847210
$877$	2132.02	0.0820904	0.0410452	−	0.999157i	$-0.486931\pi$
$877$	2132.02	0.0820904	0.0410452	+	0.999157i	$0.486931\pi$
$878$	29886.7	1.14878
$879$	−5784.44	−0.221962
$880$	−13591.0	−0.520630
$881$	−18579.6	−0.710514	−0.355257	−	0.934769i	$-0.615607\pi$
$881$	−18579.6	−0.710514	−0.355257	+	0.934769i	$0.615607\pi$
$882$	−887.907	−0.0338973
$883$	−41495.9	−1.58148	−0.790740	−	0.612152i	$-0.790304\pi$
$883$	−41495.9	−1.58148	−0.790740	+	0.612152i	$0.790304\pi$
$884$	151.909	0.00577972
$885$	2974.30	0.112972
$886$	−42538.9	−1.61300
$887$	10693.1	0.404780	0.202390	−	0.979305i	$-0.435129\pi$
$887$	10693.1	0.404780	0.202390	+	0.979305i	$0.435129\pi$
$888$	−11306.8	−0.427288
$889$	8385.09	0.316341
$890$	−4345.67	−0.163671
$891$	29938.9	1.12569
$892$	5315.80	0.199536
$893$	−102.553	−0.00384299
$894$	−23019.1	−0.861156
$895$	2562.13	0.0956902
$896$	9132.84	0.340521
$897$	−226.094	−0.00841590
$898$	23054.1	0.856709
$899$	−9831.70	−0.364745
$900$	2848.35	0.105494
$901$	−5982.87	−0.221219
$902$	−87689.1	−3.23695
$903$	−4862.92	−0.179211
$904$	−8010.72	−0.294726
$905$	−10399.5	−0.381980
$906$	24104.0	0.883887
$907$	2676.02	0.0979665	0.0489833	−	0.998800i	$-0.484402\pi$
$907$	2676.02	0.0979665	0.0489833	+	0.998800i	$0.484402\pi$
$908$	26033.8	0.951499
$909$	770.894	0.0281287
$910$	172.071	0.00626826
$911$	−8827.86	−0.321054	−0.160527	−	0.987031i	$-0.551319\pi$
$911$	−8827.86	−0.321054	−0.160527	+	0.987031i	$0.551319\pi$
$912$	2367.17	0.0859484
$913$	43506.8	1.57707
$914$	−4513.26	−0.163332
$915$	4158.31	0.150240
$916$	842.111	0.0303757
$917$	−11217.7	−0.403972
$918$	−7912.87	−0.284492
$919$	−36542.5	−1.31167	−0.655836	−	0.754903i	$-0.727684\pi$
$919$	−36542.5	−1.31167	−0.655836	+	0.754903i	$0.727684\pi$
$920$	−823.754	−0.0295200
$921$	11925.2	0.426655
$922$	30360.3	1.08445
$923$	1820.54	0.0649228
$924$	8554.12	0.304556
$925$	25100.0	0.892198
$926$	−15013.3	−0.532795
$927$	−3146.64	−0.111488
$928$	−19945.2	−0.705531
$929$	−44400.7	−1.56807	−0.784036	−	0.620715i	$-0.786842\pi$
$929$	−44400.7	−1.56807	−0.784036	+	0.620715i	$0.786842\pi$
$930$	−5324.04	−0.187723
$931$	312.860	0.0110135
$932$	26614.1	0.935378
$933$	−18393.9	−0.645433
$934$	−3790.28	−0.132786
$935$	−2516.70	−0.0880267
$936$	−116.159	−0.00405639
$937$	−16762.4	−0.584422	−0.292211	−	0.956354i	$-0.594391\pi$
$937$	−16762.4	−0.584422	−0.292211	+	0.956354i	$0.594391\pi$
$938$	−20447.4	−0.711760
$939$	−40295.4	−1.40041
$940$	258.659	0.00897502
$941$	9953.32	0.344813	0.172406	−	0.985026i	$-0.444846\pi$
$941$	9953.32	0.344813	0.172406	+	0.985026i	$0.444846\pi$
$942$	−50066.7	−1.73170
$943$	−10628.7	−0.367040
$944$	−15413.3	−0.531419
$945$	−3423.43	−0.117846
$946$	−28128.2	−0.966729
$947$	25529.1	0.876013	0.438006	−	0.898972i	$-0.355685\pi$
$947$	25529.1	0.876013	0.438006	+	0.898972i	$0.355685\pi$
$948$	3461.18	0.118580
$949$	1988.57	0.0680209
$950$	−2627.68	−0.0897402
$951$	−6229.32	−0.212408
$952$	1127.47	0.0383841
$953$	−10158.3	−0.345287	−0.172644	−	0.984984i	$-0.555231\pi$
$953$	−10158.3	−0.345287	−0.172644	+	0.984984i	$0.555231\pi$
$954$	−7400.74	−0.251161
$955$	2136.94	0.0724082
$956$	−26881.0	−0.909407
$957$	25069.5	0.846793
$958$	−22699.0	−0.765525
$959$	−19300.2	−0.649880
$960$	−1139.45	−0.0383079
$961$	−20394.1	−0.684572
$962$	1655.89	0.0554969
$963$	83.1094	0.00278106
$964$	5898.60	0.197076
$965$	6965.89	0.232373
$966$	2714.61	0.0904153
$967$	−15351.4	−0.510513	−0.255257	−	0.966873i	$-0.582160\pi$
$967$	−15351.4	−0.510513	−0.255257	+	0.966873i	$0.582160\pi$
$968$	−15951.4	−0.529646
$969$	438.338	0.0145319
$970$	19315.5	0.639364
$971$	30905.9	1.02144	0.510720	−	0.859747i	$-0.329379\pi$
$971$	30905.9	1.02144	0.510720	+	0.859747i	$0.329379\pi$
$972$	−6889.34	−0.227341
$973$	−15484.7	−0.510190
$974$	−19047.2	−0.626603
$975$	−1124.47	−0.0369352
$976$	−21549.0	−0.706727
$977$	−7476.01	−0.244809	−0.122405	−	0.992480i	$-0.539061\pi$
$977$	−7476.01	−0.244809	−0.122405	+	0.992480i	$0.539061\pi$
$978$	10884.4	0.355875
$979$	−19557.7	−0.638474
$980$	−789.097	−0.0257212
$981$	1221.82	0.0397654
$982$	14500.6	0.471216
$983$	6166.16	0.200071	0.100036	−	0.994984i	$-0.468104\pi$
$983$	6166.16	0.200071	0.100036	+	0.994984i	$0.468104\pi$
$984$	23812.5	0.771460
$985$	−11565.9	−0.374132
$986$	−5345.31	−0.172647
$987$	526.915	0.0169928
$988$	−66.2115	−0.00213205
$989$	−3409.39	−0.109618
$990$	−3113.13	−0.0999413
$991$	−34122.5	−1.09378	−0.546891	−	0.837204i	$-0.684189\pi$
$991$	−34122.5	−1.09378	−0.546891	+	0.837204i	$0.684189\pi$
$992$	19063.2	0.610138
$993$	20993.1	0.670891
$994$	−21858.4	−0.697491
$995$	2100.23	0.0669164
$996$	19112.4	0.608032
$997$	−54763.7	−1.73960	−0.869801	−	0.493403i	$-0.835753\pi$
$997$	−54763.7	−1.73960	−0.869801	+	0.493403i	$0.835753\pi$
$998$	2856.56	0.0906040
$999$	−32944.6	−1.04336

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	161.4.a.a.1.5	✓	5
3.2	odd	2		1449.4.a.e.1.1		5
7.6	odd	2		1127.4.a.d.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.4.a.a.1.5	✓	5	1.1	even	1	trivial
1127.4.a.d.1.5		5	7.6	odd	2
1449.4.a.e.1.1		5	3.2	odd	2

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:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	161.a (trivial)

\(f(q)\)	\(=\)	\(q+3.59776 q^{2} -4.68651 q^{3} +4.94388 q^{4} -3.25737 q^{5} -16.8609 q^{6} +7.00000 q^{7} -10.9952 q^{8} -5.03662 q^{9} -11.7192 q^{10} -52.7424 q^{11} -23.1695 q^{12} -2.09755 q^{13} +25.1843 q^{14} +15.2657 q^{15} -79.1091 q^{16} -14.6489 q^{17} -18.1205 q^{18} +6.38490 q^{19} -16.1040 q^{20} -32.8056 q^{21} -189.754 q^{22} -23.0000 q^{23} +51.5291 q^{24} -114.390 q^{25} -7.54647 q^{26} +150.140 q^{27} +34.6071 q^{28} +101.423 q^{29} +54.9223 q^{30} -96.9377 q^{31} -196.654 q^{32} +247.178 q^{33} -52.7033 q^{34} -22.8016 q^{35} -24.9004 q^{36} -219.426 q^{37} +22.9713 q^{38} +9.83018 q^{39} +35.8154 q^{40} +462.118 q^{41} -118.027 q^{42} +148.234 q^{43} -260.752 q^{44} +16.4061 q^{45} -82.7485 q^{46} -16.0617 q^{47} +370.746 q^{48} +49.0000 q^{49} -411.546 q^{50} +68.6523 q^{51} -10.3700 q^{52} +408.417 q^{53} +540.168 q^{54} +171.801 q^{55} -76.9664 q^{56} -29.9229 q^{57} +364.895 q^{58} +194.836 q^{59} +75.4717 q^{60} +272.396 q^{61} -348.759 q^{62} -35.2563 q^{63} -74.6411 q^{64} +6.83248 q^{65} +889.286 q^{66} -811.909 q^{67} -72.4224 q^{68} +107.790 q^{69} -82.0346 q^{70} -867.936 q^{71} +55.3786 q^{72} -948.048 q^{73} -789.441 q^{74} +536.088 q^{75} +31.5662 q^{76} -369.197 q^{77} +35.3666 q^{78} -149.385 q^{79} +257.687 q^{80} -567.644 q^{81} +1662.59 q^{82} -824.893 q^{83} -162.187 q^{84} +47.7169 q^{85} +533.312 q^{86} -475.319 q^{87} +579.913 q^{88} +370.815 q^{89} +59.0253 q^{90} -14.6828 q^{91} -113.709 q^{92} +454.300 q^{93} -57.7863 q^{94} -20.7980 q^{95} +921.621 q^{96} -1648.19 q^{97} +176.290 q^{98} +265.643 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 4 q^{2} - 11 q^{3} - 4 q^{5} + 35 q^{7} + 18 q^{8} + 14 q^{9} + 26 q^{10} - 36 q^{11} - 28 q^{12} - 69 q^{13} - 28 q^{14} - 88 q^{15} - 124 q^{16} - 42 q^{17} - 94 q^{18} - 140 q^{19} - 168 q^{20}+ \cdots - 990 q^{99}+O(q^{100}) \) 5 * q - 4 * q^2 - 11 * q^3 - 4 * q^5 + 35 * q^7 + 18 * q^8 + 14 * q^9 + 26 * q^10 - 36 * q^11 - 28 * q^12 - 69 * q^13 - 28 * q^14 - 88 * q^15 - 124 * q^16 - 42 * q^17 - 94 * q^18 - 140 * q^19 - 168 * q^20 - 77 * q^21 - 346 * q^22 - 115 * q^23 + 18 * q^24 - 357 * q^25 + 68 * q^26 - 35 * q^27 - 383 * q^29 + 184 * q^30 - 319 * q^31 - 50 * q^32 - 108 * q^33 - 376 * q^34 - 28 * q^35 - 180 * q^36 - 154 * q^37 + 8 * q^38 - 235 * q^39 + 90 * q^40 + 277 * q^41 - 718 * q^43 + 422 * q^44 + 470 * q^45 + 92 * q^46 + 53 * q^47 + 248 * q^48 + 245 * q^49 - 60 * q^50 + 232 * q^51 + 178 * q^52 + 450 * q^53 + 468 * q^54 - 206 * q^55 + 126 * q^56 - 560 * q^57 + 1738 * q^58 + 936 * q^59 + 944 * q^60 - 522 * q^61 + 788 * q^62 + 98 * q^63 - 252 * q^64 + 264 * q^65 + 2310 * q^66 - 810 * q^67 + 1326 * q^68 + 253 * q^69 + 182 * q^70 - 1373 * q^71 + 1590 * q^72 + 459 * q^73 + 330 * q^74 + 333 * q^75 + 1168 * q^76 - 252 * q^77 + 462 * q^78 - 728 * q^79 + 1368 * q^80 - 895 * q^81 + 1034 * q^82 - 500 * q^83 - 196 * q^84 - 1432 * q^85 + 3138 * q^86 + 1803 * q^87 - 722 * q^88 - 586 * q^89 - 1024 * q^90 - 483 * q^91 + 2149 * q^93 + 316 * q^94 - 188 * q^95 + 1210 * q^96 - 2150 * q^97 - 196 * q^98 - 990 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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