LMFDB - Embedded newform 2166.4.a.bj.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2166,4,Mod(1,2166)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2166, 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("2166.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2166 = 2 \cdot 3 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2166.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:	$127.798137072$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 603 x^{7} - 764 x^{6} + 123192 x^{5} + 325506 x^{4} - 10023031 x^{3} - 37119420 x^{2} + \cdots + 1077539768 $ x^9 - 603x^7 - 764x^6 + 123192x^5 + 325506x^4 - 10023031x^3 - 37119420x^2 + 258857220*x + 1077539768
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3\cdot 19 $
Twist minimal:	no (minimal twist has level 114)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$11.1773$ of defining polynomial
Character	$\chi$	$=$	2166.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +14.5246 q^{5} +6.00000 q^{6} +22.7843 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +14.5246 q^{5} +6.00000 q^{6} +22.7843 q^{7} -8.00000 q^{8} +9.00000 q^{9} -29.0491 q^{10} -33.2063 q^{11} -12.0000 q^{12} -10.0169 q^{13} -45.5685 q^{14} -43.5737 q^{15} +16.0000 q^{16} +51.2381 q^{17} -18.0000 q^{18} +58.0983 q^{20} -68.3528 q^{21} +66.4125 q^{22} -102.813 q^{23} +24.0000 q^{24} +85.9631 q^{25} +20.0339 q^{26} -27.0000 q^{27} +91.1370 q^{28} +216.242 q^{29} +87.1474 q^{30} -84.8381 q^{31} -32.0000 q^{32} +99.6188 q^{33} -102.476 q^{34} +330.932 q^{35} +36.0000 q^{36} -269.416 q^{37} +30.0508 q^{39} -116.197 q^{40} -474.753 q^{41} +136.706 q^{42} +37.8505 q^{43} -132.825 q^{44} +130.721 q^{45} +205.627 q^{46} +293.769 q^{47} -48.0000 q^{48} +176.122 q^{49} -171.926 q^{50} -153.714 q^{51} -40.0677 q^{52} -524.961 q^{53} +54.0000 q^{54} -482.307 q^{55} -182.274 q^{56} -432.484 q^{58} -637.513 q^{59} -174.295 q^{60} -453.262 q^{61} +169.676 q^{62} +205.058 q^{63} +64.0000 q^{64} -145.492 q^{65} -199.238 q^{66} -70.7179 q^{67} +204.953 q^{68} +308.440 q^{69} -661.863 q^{70} +287.989 q^{71} -72.0000 q^{72} -1017.49 q^{73} +538.832 q^{74} -257.889 q^{75} -756.580 q^{77} -60.1016 q^{78} -608.168 q^{79} +232.393 q^{80} +81.0000 q^{81} +949.506 q^{82} -199.418 q^{83} -273.411 q^{84} +744.212 q^{85} -75.7009 q^{86} -648.726 q^{87} +265.650 q^{88} +1109.37 q^{89} -261.442 q^{90} -228.228 q^{91} -411.254 q^{92} +254.514 q^{93} -587.537 q^{94} +96.0000 q^{96} -1472.51 q^{97} -352.245 q^{98} -298.856 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 18 q^{2} - 27 q^{3} + 36 q^{4} + 27 q^{5} + 54 q^{6} - 72 q^{8} + 81 q^{9}+O(q^{10}) $ 9 * q - 18 * q^2 - 27 * q^3 + 36 * q^4 + 27 * q^5 + 54 * q^6 - 72 * q^8 + 81 * q^9	\( 9 q - 18 q^{2} - 27 q^{3} + 36 q^{4} + 27 q^{5} + 54 q^{6} - 72 q^{8} + 81 q^{9} - 54 q^{10} + 39 q^{11} - 108 q^{12} - 99 q^{13} - 81 q^{15} + 144 q^{16} + 57 q^{17} - 162 q^{18} + 108 q^{20} - 78 q^{22} + 228 q^{23} + 216 q^{24} + 174 q^{25} + 198 q^{26} - 243 q^{27} - 459 q^{29} + 162 q^{30} - 243 q^{31} - 288 q^{32} - 117 q^{33} - 114 q^{34} + 324 q^{35} + 324 q^{36} - 711 q^{37} + 297 q^{39} - 216 q^{40} - 459 q^{41} + 252 q^{43} + 156 q^{44} + 243 q^{45} - 456 q^{46} - 66 q^{47} - 432 q^{48} + 2229 q^{49} - 348 q^{50} - 171 q^{51} - 396 q^{52} - 1197 q^{53} + 486 q^{54} + 762 q^{55} + 918 q^{58} - 1221 q^{59} - 324 q^{60} - 780 q^{61} + 486 q^{62} + 576 q^{64} + 237 q^{65} + 234 q^{66} - 1596 q^{67} + 228 q^{68} - 684 q^{69} - 648 q^{70} - 2538 q^{71} - 648 q^{72} + 225 q^{73} + 1422 q^{74} - 522 q^{75} - 135 q^{77} - 594 q^{78} - 834 q^{79} + 432 q^{80} + 729 q^{81} + 918 q^{82} + 2490 q^{83} - 1653 q^{85} - 504 q^{86} + 1377 q^{87} - 312 q^{88} + 507 q^{89} - 486 q^{90} - 6423 q^{91} + 912 q^{92} + 729 q^{93} + 132 q^{94} + 864 q^{96} - 2529 q^{97} - 4458 q^{98} + 351 q^{99}+O(q^{100}) \) 9 * q - 18 * q^2 - 27 * q^3 + 36 * q^4 + 27 * q^5 + 54 * q^6 - 72 * q^8 + 81 * q^9 - 54 * q^10 + 39 * q^11 - 108 * q^12 - 99 * q^13 - 81 * q^15 + 144 * q^16 + 57 * q^17 - 162 * q^18 + 108 * q^20 - 78 * q^22 + 228 * q^23 + 216 * q^24 + 174 * q^25 + 198 * q^26 - 243 * q^27 - 459 * q^29 + 162 * q^30 - 243 * q^31 - 288 * q^32 - 117 * q^33 - 114 * q^34 + 324 * q^35 + 324 * q^36 - 711 * q^37 + 297 * q^39 - 216 * q^40 - 459 * q^41 + 252 * q^43 + 156 * q^44 + 243 * q^45 - 456 * q^46 - 66 * q^47 - 432 * q^48 + 2229 * q^49 - 348 * q^50 - 171 * q^51 - 396 * q^52 - 1197 * q^53 + 486 * q^54 + 762 * q^55 + 918 * q^58 - 1221 * q^59 - 324 * q^60 - 780 * q^61 + 486 * q^62 + 576 * q^64 + 237 * q^65 + 234 * q^66 - 1596 * q^67 + 228 * q^68 - 684 * q^69 - 648 * q^70 - 2538 * q^71 - 648 * q^72 + 225 * q^73 + 1422 * q^74 - 522 * q^75 - 135 * q^77 - 594 * q^78 - 834 * q^79 + 432 * q^80 + 729 * q^81 + 918 * q^82 + 2490 * q^83 - 1653 * q^85 - 504 * q^86 + 1377 * q^87 - 312 * q^88 + 507 * q^89 - 486 * q^90 - 6423 * q^91 + 912 * q^92 + 729 * q^93 + 132 * q^94 + 864 * q^96 - 2529 * q^97 - 4458 * q^98 + 351 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	4.00000	0.500000
$5$	14.5246	1.29912	0.649559	−	0.760312i	$-0.274954\pi$
$5$	14.5246	1.29912	0.649559	+	0.760312i	$0.274954\pi$
$6$	6.00000	0.408248
$7$	22.7843	1.23023	0.615117	−	0.788436i	$-0.289109\pi$
$7$	22.7843	1.23023	0.615117	+	0.788436i	$0.289109\pi$
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	−29.0491	−0.918614
$11$	−33.2063	−0.910188	−0.455094	−	0.890443i	$-0.650394\pi$
$11$	−33.2063	−0.910188	−0.455094	+	0.890443i	$0.650394\pi$
$12$	−12.0000	−0.288675
$13$	−10.0169	−0.213708	−0.106854	−	0.994275i	$-0.534078\pi$
$13$	−10.0169	−0.213708	−0.106854	+	0.994275i	$0.534078\pi$
$14$	−45.5685	−0.869907
$15$	−43.5737	−0.750046
$16$	16.0000	0.250000
$17$	51.2381	0.731004	0.365502	−	0.930810i	$-0.380897\pi$
$17$	51.2381	0.731004	0.365502	+	0.930810i	$0.380897\pi$
$18$	−18.0000	−0.235702
$19$	0	0
$19$	0	0
$20$	58.0983	0.649559
$21$	−68.3528	−0.710276
$22$	66.4125	0.643600
$23$	−102.813	−0.932091	−0.466045	−	0.884761i	$-0.654322\pi$
$23$	−102.813	−0.932091	−0.466045	+	0.884761i	$0.654322\pi$
$24$	24.0000	0.204124
$25$	85.9631	0.687705
$26$	20.0339	0.151114
$27$	−27.0000	−0.192450
$28$	91.1370	0.615117
$29$	216.242	1.38466	0.692330	−	0.721581i	$-0.256584\pi$
$29$	216.242	1.38466	0.692330	+	0.721581i	$0.256584\pi$
$30$	87.1474	0.530362
$31$	−84.8381	−0.491528	−0.245764	−	0.969330i	$-0.579039\pi$
$31$	−84.8381	−0.491528	−0.245764	+	0.969330i	$0.579039\pi$
$32$	−32.0000	−0.176777
$33$	99.6188	0.525497
$34$	−102.476	−0.516898
$35$	330.932	1.59822
$36$	36.0000	0.166667
$37$	−269.416	−1.19707	−0.598537	−	0.801095i	$-0.704251\pi$
$37$	−269.416	−1.19707	−0.598537	+	0.801095i	$0.704251\pi$
$38$	0	0
$39$	30.0508	0.123384
$40$	−116.197	−0.459307
$41$	−474.753	−1.80839	−0.904195	−	0.427120i	$-0.859528\pi$
$41$	−474.753	−1.80839	−0.904195	+	0.427120i	$0.859528\pi$
$42$	136.706	0.502241
$43$	37.8505	0.134236	0.0671179	−	0.997745i	$-0.478620\pi$
$43$	37.8505	0.134236	0.0671179	+	0.997745i	$0.478620\pi$
$44$	−132.825	−0.455094
$45$	130.721	0.433039
$46$	205.627	0.659088
$47$	293.769	0.911714	0.455857	−	0.890053i	$-0.349333\pi$
$47$	293.769	0.911714	0.455857	+	0.890053i	$0.349333\pi$
$48$	−48.0000	−0.144338
$49$	176.122	0.513476
$50$	−171.926	−0.486281
$51$	−153.714	−0.422046
$52$	−40.0677	−0.106854
$53$	−524.961	−1.36055	−0.680273	−	0.732958i	$-0.738139\pi$
$53$	−524.961	−1.36055	−0.680273	+	0.732958i	$0.738139\pi$
$54$	54.0000	0.136083
$55$	−482.307	−1.18244
$56$	−182.274	−0.434953
$57$	0	0
$58$	−432.484	−0.979103
$59$	−637.513	−1.40673	−0.703365	−	0.710829i	$-0.748320\pi$
$59$	−637.513	−1.40673	−0.703365	+	0.710829i	$0.748320\pi$
$60$	−174.295	−0.375023
$61$	−453.262	−0.951380	−0.475690	−	0.879613i	$-0.657802\pi$
$61$	−453.262	−0.951380	−0.475690	+	0.879613i	$0.657802\pi$
$62$	169.676	0.347563
$63$	205.058	0.410078
$64$	64.0000	0.125000
$65$	−145.492	−0.277631
$66$	−199.238	−0.371583
$67$	−70.7179	−0.128949	−0.0644744	−	0.997919i	$-0.520537\pi$
$67$	−70.7179	−0.128949	−0.0644744	+	0.997919i	$0.520537\pi$
$68$	204.953	0.365502
$69$	308.440	0.538143
$70$	−661.863	−1.13011
$71$	287.989	0.481381	0.240690	−	0.970602i	$-0.422626\pi$
$71$	287.989	0.481381	0.240690	+	0.970602i	$0.422626\pi$
$72$	−72.0000	−0.117851
$73$	−1017.49	−1.63134	−0.815669	−	0.578519i	$-0.803631\pi$
$73$	−1017.49	−1.63134	−0.815669	+	0.578519i	$0.803631\pi$
$74$	538.832	0.846459
$75$	−257.889	−0.397047
$76$	0	0
$77$	−756.580	−1.11974
$78$	−60.1016	−0.0872457
$79$	−608.168	−0.866130	−0.433065	−	0.901363i	$-0.642568\pi$
$79$	−608.168	−0.866130	−0.433065	+	0.901363i	$0.642568\pi$
$80$	232.393	0.324779
$81$	81.0000	0.111111
$82$	949.506	1.27872
$83$	−199.418	−0.263722	−0.131861	−	0.991268i	$-0.542095\pi$
$83$	−199.418	−0.263722	−0.131861	+	0.991268i	$0.542095\pi$
$84$	−273.411	−0.355138
$85$	744.212	0.949660
$86$	−75.7009	−0.0949191
$87$	−648.726	−0.799434
$88$	265.650	0.321800
$89$	1109.37	1.32127	0.660633	−	0.750709i	$-0.270288\pi$
$89$	1109.37	1.32127	0.660633	+	0.750709i	$0.270288\pi$
$90$	−261.442	−0.306205
$91$	−228.228	−0.262910
$92$	−411.254	−0.466045
$93$	254.514	0.283784
$94$	−587.537	−0.644679
$95$	0	0
$96$	96.0000	0.102062
$97$	−1472.51	−1.54135	−0.770673	−	0.637231i	$-0.780080\pi$
$97$	−1472.51	−1.54135	−0.770673	+	0.637231i	$0.780080\pi$
$98$	−352.245	−0.363082
$99$	−298.856	−0.303396
$100$	343.853	0.343853
$101$	−367.775	−0.362326	−0.181163	−	0.983453i	$-0.557986\pi$
$101$	−367.775	−0.362326	−0.181163	+	0.983453i	$0.557986\pi$
$102$	307.429	0.298431
$103$	1345.72	1.28736	0.643678	−	0.765296i	$-0.277408\pi$
$103$	1345.72	1.28736	0.643678	+	0.765296i	$0.277408\pi$
$104$	80.1355	0.0755570
$105$	−992.795	−0.922732
$106$	1049.92	0.962052
$107$	−1496.55	−1.35212	−0.676062	−	0.736845i	$-0.736315\pi$
$107$	−1496.55	−1.35212	−0.676062	+	0.736845i	$0.736315\pi$
$108$	−108.000	−0.0962250
$109$	−1566.99	−1.37698	−0.688488	−	0.725248i	$-0.741725\pi$
$109$	−1566.99	−1.37698	−0.688488	+	0.725248i	$0.741725\pi$
$110$	964.614	0.836112
$111$	808.248	0.691131
$112$	364.548	0.307559
$113$	428.237	0.356505	0.178253	−	0.983985i	$-0.442956\pi$
$113$	428.237	0.356505	0.178253	+	0.983985i	$0.442956\pi$
$114$	0	0
$115$	−1493.32	−1.21089
$116$	864.968	0.692330
$117$	−90.1524	−0.0712358
$118$	1275.03	0.994709
$119$	1167.42	0.899306
$120$	348.590	0.265181
$121$	−228.343	−0.171558
$122$	906.523	0.672727
$123$	1424.26	1.04407
$124$	−339.352	−0.245764
$125$	−566.994	−0.405708
$126$	−410.117	−0.289969
$127$	1236.90	0.864228	0.432114	−	0.901819i	$-0.357768\pi$
$127$	1236.90	0.864228	0.432114	+	0.901819i	$0.357768\pi$
$128$	−128.000	−0.0883883
$129$	−113.551	−0.0775011
$130$	290.983	0.196315
$131$	2408.01	1.60602	0.803010	−	0.595965i	$-0.203230\pi$
$131$	2408.01	1.60602	0.803010	+	0.595965i	$0.203230\pi$
$132$	398.475	0.262749
$133$	0	0
$134$	141.436	0.0911806
$135$	−392.163	−0.250015
$136$	−409.905	−0.258449
$137$	1227.21	0.765311	0.382655	−	0.923891i	$-0.375010\pi$
$137$	1227.21	0.765311	0.382655	+	0.923891i	$0.375010\pi$
$138$	−616.881	−0.380524
$139$	−350.884	−0.214112	−0.107056	−	0.994253i	$-0.534142\pi$
$139$	−350.884	−0.214112	−0.107056	+	0.994253i	$0.534142\pi$
$140$	1323.73	0.799109
$141$	−881.306	−0.526378
$142$	−575.978	−0.340388
$143$	332.625	0.194514
$144$	144.000	0.0833333
$145$	3140.82	1.79884
$146$	2034.97	1.15353
$147$	−528.367	−0.296456
$148$	−1077.66	−0.598537
$149$	−39.0516	−0.0214714	−0.0107357	−	0.999942i	$-0.503417\pi$
$149$	−39.0516	−0.0214714	−0.0107357	+	0.999942i	$0.503417\pi$
$150$	515.779	0.280754
$151$	1441.23	0.776728	0.388364	−	0.921506i	$-0.373040\pi$
$151$	1441.23	0.776728	0.388364	+	0.921506i	$0.373040\pi$
$152$	0	0
$153$	461.143	0.243668
$154$	1513.16	0.791779
$155$	−1232.24	−0.638553
$156$	120.203	0.0616920
$157$	−2856.59	−1.45211	−0.726053	−	0.687639i	$-0.758647\pi$
$157$	−2856.59	−1.45211	−0.726053	+	0.687639i	$0.758647\pi$
$158$	1216.34	0.612447
$159$	1574.88	0.785512
$160$	−464.786	−0.229654
$161$	−2342.53	−1.14669
$162$	−162.000	−0.0785674
$163$	2413.33	1.15967	0.579837	−	0.814733i	$-0.303116\pi$
$163$	2413.33	1.15967	0.579837	+	0.814733i	$0.303116\pi$
$164$	−1899.01	−0.904195
$165$	1446.92	0.682683
$166$	398.835	0.186480
$167$	1621.63	0.751411	0.375706	−	0.926739i	$-0.377400\pi$
$167$	1621.63	0.751411	0.375706	+	0.926739i	$0.377400\pi$
$168$	546.822	0.251120
$169$	−2096.66	−0.954329
$170$	−1488.42	−0.671511
$171$	0	0
$172$	151.402	0.0671179
$173$	1132.31	0.497617	0.248809	−	0.968553i	$-0.419961\pi$
$173$	1132.31	0.497617	0.248809	+	0.968553i	$0.419961\pi$
$174$	1297.45	0.565285
$175$	1958.61	0.846038
$176$	−531.300	−0.227547
$177$	1912.54	0.812176
$178$	−2218.73	−0.934276
$179$	−920.853	−0.384513	−0.192256	−	0.981345i	$-0.561581\pi$
$179$	−920.853	−0.384513	−0.192256	+	0.981345i	$0.561581\pi$
$180$	522.885	0.216520
$181$	3905.57	1.60386	0.801930	−	0.597419i	$-0.203807\pi$
$181$	3905.57	1.60386	0.801930	+	0.597419i	$0.203807\pi$
$182$	456.457	0.185906
$183$	1359.78	0.549280
$184$	822.508	0.329544
$185$	−3913.15	−1.55514
$186$	−509.029	−0.200666
$187$	−1701.43	−0.665351
$188$	1175.07	0.455857
$189$	−615.175	−0.236759
$190$	0	0
$191$	−4321.73	−1.63722	−0.818610	−	0.574349i	$-0.805255\pi$
$191$	−4321.73	−1.63722	−0.818610	+	0.574349i	$0.805255\pi$
$192$	−192.000	−0.0721688
$193$	4012.46	1.49649	0.748247	−	0.663420i	$-0.230896\pi$
$193$	4012.46	1.49649	0.748247	+	0.663420i	$0.230896\pi$
$194$	2945.02	1.08990
$195$	436.475	0.160290
$196$	704.489	0.256738
$197$	−133.787	−0.0483854	−0.0241927	−	0.999707i	$-0.507702\pi$
$197$	−133.787	−0.0483854	−0.0241927	+	0.999707i	$0.507702\pi$
$198$	597.713	0.214533
$199$	4033.94	1.43698	0.718488	−	0.695540i	$-0.244835\pi$
$199$	4033.94	1.43698	0.718488	+	0.695540i	$0.244835\pi$
$200$	−687.705	−0.243140
$201$	212.154	0.0744486
$202$	735.549	0.256203
$203$	4926.92	1.70346
$204$	−614.858	−0.211023
$205$	−6895.58	−2.34931
$206$	−2691.44	−0.910298
$207$	−925.321	−0.310697
$208$	−160.271	−0.0534269
$209$	0	0
$210$	1985.59	0.652470
$211$	3697.95	1.20653	0.603264	−	0.797542i	$-0.293867\pi$
$211$	3697.95	1.20653	0.603264	+	0.797542i	$0.293867\pi$
$212$	−2099.85	−0.680273
$213$	−863.968	−0.277925
$214$	2993.10	0.956096
$215$	549.762	0.174388
$216$	216.000	0.0680414
$217$	−1932.97	−0.604695
$218$	3133.98	0.973669
$219$	3052.46	0.941853
$220$	−1929.23	−0.591220
$221$	−513.249	−0.156221
$222$	−1616.50	−0.488703
$223$	−5059.33	−1.51927	−0.759636	−	0.650349i	$-0.774623\pi$
$223$	−5059.33	−1.51927	−0.759636	+	0.650349i	$0.774623\pi$
$224$	−729.096	−0.217477
$225$	773.668	0.229235
$226$	−856.473	−0.252087
$227$	3124.48	0.913563	0.456781	−	0.889579i	$-0.349002\pi$
$227$	3124.48	0.913563	0.456781	+	0.889579i	$0.349002\pi$
$228$	0	0
$229$	−2197.05	−0.633997	−0.316998	−	0.948426i	$-0.602675\pi$
$229$	−2197.05	−0.633997	−0.316998	+	0.948426i	$0.602675\pi$
$230$	2986.64	0.856232
$231$	2269.74	0.646485
$232$	−1729.94	−0.489551
$233$	−1753.75	−0.493100	−0.246550	−	0.969130i	$-0.579297\pi$
$233$	−1753.75	−0.493100	−0.246550	+	0.969130i	$0.579297\pi$
$234$	180.305	0.0503713
$235$	4266.86	1.18442
$236$	−2550.05	−0.703365
$237$	1824.51	0.500061
$238$	−2334.85	−0.635906
$239$	−3649.36	−0.987689	−0.493844	−	0.869550i	$-0.664409\pi$
$239$	−3649.36	−0.987689	−0.493844	+	0.869550i	$0.664409\pi$
$240$	−697.179	−0.187511
$241$	−1539.68	−0.411533	−0.205767	−	0.978601i	$-0.565969\pi$
$241$	−1539.68	−0.411533	−0.205767	+	0.978601i	$0.565969\pi$
$242$	456.687	0.121310
$243$	−243.000	−0.0641500
$244$	−1813.05	−0.475690
$245$	2558.10	0.667065
$246$	−2848.52	−0.738272
$247$	0	0
$248$	678.705	0.173781
$249$	598.253	0.152260
$250$	1133.99	0.286879
$251$	7451.60	1.87387	0.936934	−	0.349506i	$-0.113650\pi$
$251$	7451.60	1.87387	0.936934	+	0.349506i	$0.113650\pi$
$252$	820.233	0.205039
$253$	3414.05	0.848378
$254$	−2473.80	−0.611101
$255$	−2232.64	−0.548287
$256$	256.000	0.0625000
$257$	−6423.38	−1.55906	−0.779532	−	0.626362i	$-0.784543\pi$
$257$	−6423.38	−1.55906	−0.779532	+	0.626362i	$0.784543\pi$
$258$	227.103	0.0548016
$259$	−6138.44	−1.47268
$260$	−581.967	−0.138816
$261$	1946.18	0.461553
$262$	−4816.02	−1.13563
$263$	−4737.63	−1.11078	−0.555389	−	0.831591i	$-0.687431\pi$
$263$	−4737.63	−1.11078	−0.555389	+	0.831591i	$0.687431\pi$
$264$	−796.951	−0.185791
$265$	−7624.84	−1.76751
$266$	0	0
$267$	−3328.10	−0.762833
$268$	−282.872	−0.0644744
$269$	5614.53	1.27258	0.636290	−	0.771450i	$-0.280468\pi$
$269$	5614.53	1.27258	0.636290	+	0.771450i	$0.280468\pi$
$270$	784.327	0.176787
$271$	−5230.76	−1.17250	−0.586248	−	0.810132i	$-0.699395\pi$
$271$	−5230.76	−1.17250	−0.586248	+	0.810132i	$0.699395\pi$
$272$	819.810	0.182751
$273$	684.685	0.151791
$274$	−2454.42	−0.541156
$275$	−2854.52	−0.625941
$276$	1233.76	0.269071
$277$	−7239.91	−1.57041	−0.785205	−	0.619235i	$-0.787443\pi$
$277$	−7239.91	−1.57041	−0.785205	+	0.619235i	$0.787443\pi$
$278$	701.768	0.151400
$279$	−763.543	−0.163843
$280$	−2647.45	−0.565055
$281$	1844.11	0.391496	0.195748	−	0.980654i	$-0.437287\pi$
$281$	1844.11	0.391496	0.195748	+	0.980654i	$0.437287\pi$
$282$	1762.61	0.372206
$283$	−1394.93	−0.293004	−0.146502	−	0.989210i	$-0.546802\pi$
$283$	−1394.93	−0.293004	−0.146502	+	0.989210i	$0.546802\pi$
$284$	1151.96	0.240690
$285$	0	0
$286$	−665.250	−0.137542
$287$	−10816.9	−2.22474
$288$	−288.000	−0.0589256
$289$	−2287.65	−0.465633
$290$	−6281.65	−1.27197
$291$	4417.53	0.889897
$292$	−4069.94	−0.815669
$293$	−4587.06	−0.914603	−0.457301	−	0.889312i	$-0.651184\pi$
$293$	−4587.06	−0.914603	−0.457301	+	0.889312i	$0.651184\pi$
$294$	1056.73	0.209626
$295$	−9259.60	−1.82751
$296$	2155.33	0.423229
$297$	896.569	0.175166
$298$	78.1032	0.0151825
$299$	1029.88	0.199195
$300$	−1031.56	−0.198523
$301$	862.395	0.165142
$302$	−2882.47	−0.549230
$303$	1103.32	0.209189
$304$	0	0
$305$	−6583.43	−1.23595
$306$	−922.286	−0.172299
$307$	−6072.06	−1.12883	−0.564415	−	0.825491i	$-0.690898\pi$
$307$	−6072.06	−1.12883	−0.564415	+	0.825491i	$0.690898\pi$
$308$	−3026.32	−0.559872
$309$	−4037.16	−0.743256
$310$	2464.47	0.451525
$311$	2640.11	0.481373	0.240687	−	0.970603i	$-0.422627\pi$
$311$	2640.11	0.481373	0.240687	+	0.970603i	$0.422627\pi$
$312$	−240.406	−0.0436229
$313$	3789.21	0.684278	0.342139	−	0.939649i	$-0.388849\pi$
$313$	3789.21	0.684278	0.342139	+	0.939649i	$0.388849\pi$
$314$	5713.18	1.02679
$315$	2978.38	0.532739
$316$	−2432.67	−0.433065
$317$	−813.211	−0.144083	−0.0720417	−	0.997402i	$-0.522951\pi$
$317$	−813.211	−0.144083	−0.0720417	+	0.997402i	$0.522951\pi$
$318$	−3149.77	−0.555441
$319$	−7180.59	−1.26030
$320$	929.572	0.162390
$321$	4489.66	0.780649
$322$	4685.06	0.810832
$323$	0	0
$324$	324.000	0.0555556
$325$	−861.087	−0.146968
$326$	−4826.67	−0.820013
$327$	4700.97	0.794998
$328$	3798.02	0.639362
$329$	6693.30	1.12162
$330$	−2893.84	−0.482729
$331$	−1582.97	−0.262864	−0.131432	−	0.991325i	$-0.541958\pi$
$331$	−1582.97	−0.262864	−0.131432	+	0.991325i	$0.541958\pi$
$332$	−797.671	−0.131861
$333$	−2424.74	−0.399024
$334$	−3243.27	−0.531328
$335$	−1027.15	−0.167520
$336$	−1093.64	−0.177569
$337$	7259.00	1.17336	0.586681	−	0.809818i	$-0.300434\pi$
$337$	7259.00	1.17336	0.586681	+	0.809818i	$0.300434\pi$
$338$	4193.32	0.674813
$339$	−1284.71	−0.205828
$340$	2976.85	0.474830
$341$	2817.16	0.447383
$342$	0	0
$343$	−3802.18	−0.598538
$344$	−302.804	−0.0474595
$345$	4479.96	0.699110
$346$	−2264.62	−0.351869
$347$	−806.201	−0.124724	−0.0623618	−	0.998054i	$-0.519863\pi$
$347$	−806.201	−0.124724	−0.0623618	+	0.998054i	$0.519863\pi$
$348$	−2594.91	−0.399717
$349$	7907.34	1.21281	0.606404	−	0.795157i	$-0.292611\pi$
$349$	7907.34	1.21281	0.606404	+	0.795157i	$0.292611\pi$
$350$	−3917.21	−0.598239
$351$	270.457	0.0411280
$352$	1062.60	0.160900
$353$	5567.57	0.839468	0.419734	−	0.907647i	$-0.362123\pi$
$353$	5567.57	0.839468	0.419734	+	0.907647i	$0.362123\pi$
$354$	−3825.08	−0.574295
$355$	4182.92	0.625370
$356$	4437.47	0.660633
$357$	−3502.27	−0.519215
$358$	1841.71	0.271892
$359$	9603.05	1.41178	0.705891	−	0.708321i	$-0.250547\pi$
$359$	9603.05	1.41178	0.705891	+	0.708321i	$0.250547\pi$
$360$	−1045.77	−0.153102
$361$	0	0
$362$	−7811.13	−1.13410
$363$	685.030	0.0990489
$364$	−912.914	−0.131455
$365$	−14778.5	−2.11930
$366$	−2719.57	−0.388399
$367$	−604.304	−0.0859520	−0.0429760	−	0.999076i	$-0.513684\pi$
$367$	−604.304	−0.0859520	−0.0429760	+	0.999076i	$0.513684\pi$
$368$	−1645.02	−0.233023
$369$	−4272.78	−0.602797
$370$	7826.30	1.09965
$371$	−11960.9	−1.67379
$372$	1018.06	0.141892
$373$	−2130.66	−0.295768	−0.147884	−	0.989005i	$-0.547246\pi$
$373$	−2130.66	−0.295768	−0.147884	+	0.989005i	$0.547246\pi$
$374$	3402.86	0.470474
$375$	1700.98	0.234235
$376$	−2350.15	−0.322339
$377$	−2166.08	−0.295912
$378$	1230.35	0.167414
$379$	−2326.95	−0.315376	−0.157688	−	0.987489i	$-0.550404\pi$
$379$	−2326.95	−0.315376	−0.157688	+	0.987489i	$0.550404\pi$
$380$	0	0
$381$	−3710.69	−0.498962
$382$	8643.45	1.15769
$383$	6421.79	0.856758	0.428379	−	0.903599i	$-0.359085\pi$
$383$	6421.79	0.856758	0.428379	+	0.903599i	$0.359085\pi$
$384$	384.000	0.0510310
$385$	−10989.0	−1.45468
$386$	−8024.92	−1.05818
$387$	340.654	0.0447453
$388$	−5890.03	−0.770673
$389$	−8234.22	−1.07324	−0.536621	−	0.843823i	$-0.680300\pi$
$389$	−8234.22	−1.07324	−0.536621	+	0.843823i	$0.680300\pi$
$390$	−872.950	−0.113342
$391$	−5267.97	−0.681362
$392$	−1408.98	−0.181541
$393$	−7224.03	−0.927236
$394$	267.574	0.0342137
$395$	−8833.39	−1.12520
$396$	−1195.43	−0.151698
$397$	9921.33	1.25425	0.627125	−	0.778918i	$-0.284231\pi$
$397$	9921.33	1.25425	0.627125	+	0.778918i	$0.284231\pi$
$398$	−8067.87	−1.01609
$399$	0	0
$400$	1375.41	0.171926
$401$	11106.2	1.38309	0.691543	−	0.722335i	$-0.256931\pi$
$401$	11106.2	1.38309	0.691543	+	0.722335i	$0.256931\pi$
$402$	−424.308	−0.0526431
$403$	849.818	0.105043
$404$	−1471.10	−0.181163
$405$	1176.49	0.144346
$406$	−9853.83	−1.20453
$407$	8946.30	1.08956
$408$	1229.72	0.149216
$409$	−7784.68	−0.941143	−0.470571	−	0.882362i	$-0.655952\pi$
$409$	−7784.68	−0.941143	−0.470571	+	0.882362i	$0.655952\pi$
$410$	13791.2	1.66121
$411$	−3681.63	−0.441852
$412$	5382.88	0.643678
$413$	−14525.3	−1.73061
$414$	1850.64	0.219696
$415$	−2896.46	−0.342606
$416$	320.542	0.0377785
$417$	1052.65	0.123618
$418$	0	0
$419$	−12224.7	−1.42534	−0.712669	−	0.701500i	$-0.752514\pi$
$419$	−12224.7	−1.42534	−0.712669	+	0.701500i	$0.752514\pi$
$420$	−3971.18	−0.461366
$421$	−9194.34	−1.06438	−0.532191	−	0.846624i	$-0.678631\pi$
$421$	−9194.34	−1.06438	−0.532191	+	0.846624i	$0.678631\pi$
$422$	−7395.90	−0.853144
$423$	2643.92	0.303905
$424$	4199.69	0.481026
$425$	4404.59	0.502715
$426$	1727.94	0.196523
$427$	−10327.2	−1.17042
$428$	−5986.21	−0.676062
$429$	−997.875	−0.112303
$430$	−1099.52	−0.123311
$431$	13737.1	1.53525	0.767624	−	0.640901i	$-0.221439\pi$
$431$	13737.1	1.53525	0.767624	+	0.640901i	$0.221439\pi$
$432$	−432.000	−0.0481125
$433$	−798.640	−0.0886378	−0.0443189	−	0.999017i	$-0.514112\pi$
$433$	−798.640	−0.0886378	−0.0443189	+	0.999017i	$0.514112\pi$
$434$	3865.95	0.427584
$435$	−9422.47	−1.03856
$436$	−6267.96	−0.688488
$437$	0	0
$438$	−6104.91	−0.665991
$439$	−10694.2	−1.16266	−0.581328	−	0.813669i	$-0.697467\pi$
$439$	−10694.2	−1.16266	−0.581328	+	0.813669i	$0.697467\pi$
$440$	3858.45	0.418056
$441$	1585.10	0.171159
$442$	1026.50	0.110465
$443$	−9477.92	−1.01650	−0.508250	−	0.861210i	$-0.669707\pi$
$443$	−9477.92	−1.01650	−0.508250	+	0.861210i	$0.669707\pi$
$444$	3232.99	0.345565
$445$	16113.1	1.71648
$446$	10118.7	1.07429
$447$	117.155	0.0123965
$448$	1458.19	0.153779
$449$	3241.40	0.340693	0.170347	−	0.985384i	$-0.445511\pi$
$449$	3241.40	0.340693	0.170347	+	0.985384i	$0.445511\pi$
$450$	−1547.34	−0.162094
$451$	15764.8	1.64597
$452$	1712.95	0.178253
$453$	−4323.70	−0.448444
$454$	−6248.95	−0.645986
$455$	−3314.92	−0.341551
$456$	0	0
$457$	3617.76	0.370310	0.185155	−	0.982709i	$-0.440721\pi$
$457$	3617.76	0.370310	0.185155	+	0.982709i	$0.440721\pi$
$458$	4394.10	0.448303
$459$	−1383.43	−0.140682
$460$	−5973.28	−0.605447
$461$	−5909.37	−0.597021	−0.298511	−	0.954406i	$-0.596490\pi$
$461$	−5909.37	−0.597021	−0.298511	+	0.954406i	$0.596490\pi$
$462$	−4539.48	−0.457134
$463$	−5073.99	−0.509305	−0.254653	−	0.967033i	$-0.581961\pi$
$463$	−5073.99	−0.509305	−0.254653	+	0.967033i	$0.581961\pi$
$464$	3459.87	0.346165
$465$	3696.71	0.368669
$466$	3507.51	0.348674
$467$	18935.9	1.87634	0.938169	−	0.346179i	$-0.112521\pi$
$467$	18935.9	1.87634	0.938169	+	0.346179i	$0.112521\pi$
$468$	−360.610	−0.0356179
$469$	−1611.26	−0.158637
$470$	−8533.72	−0.837513
$471$	8569.77	0.838374
$472$	5100.10	0.497354
$473$	−1256.87	−0.122180
$474$	−3649.01	−0.353596
$475$	0	0
$476$	4669.69	0.449653
$477$	−4724.65	−0.453516
$478$	7298.73	0.698402
$479$	6251.73	0.596344	0.298172	−	0.954512i	$-0.403623\pi$
$479$	6251.73	0.596344	0.298172	+	0.954512i	$0.403623\pi$
$480$	1394.36	0.132591
$481$	2698.72	0.255824
$482$	3079.36	0.290998
$483$	7027.58	0.662042
$484$	−913.373	−0.0857789
$485$	−21387.6	−2.00239
$486$	486.000	0.0453609
$487$	−14384.3	−1.33842	−0.669212	−	0.743071i	$-0.733368\pi$
$487$	−14384.3	−1.33842	−0.669212	+	0.743071i	$0.733368\pi$
$488$	3626.09	0.336364
$489$	−7240.00	−0.669538
$490$	−5116.20	−0.471687
$491$	16356.0	1.50333	0.751666	−	0.659544i	$-0.229250\pi$
$491$	16356.0	1.50333	0.751666	+	0.659544i	$0.229250\pi$
$492$	5697.04	0.522037
$493$	11079.8	1.01219
$494$	0	0
$495$	−4340.76	−0.394147
$496$	−1357.41	−0.122882
$497$	6561.62	0.592211
$498$	−1196.51	−0.107664
$499$	−20023.5	−1.79635	−0.898173	−	0.439642i	$-0.855105\pi$
$499$	−20023.5	−1.79635	−0.898173	+	0.439642i	$0.855105\pi$
$500$	−2267.97	−0.202854
$501$	−4864.90	−0.433828
$502$	−14903.2	−1.32503
$503$	3003.49	0.266241	0.133120	−	0.991100i	$-0.457500\pi$
$503$	3003.49	0.266241	0.133120	+	0.991100i	$0.457500\pi$
$504$	−1640.47	−0.144984
$505$	−5341.77	−0.470704
$506$	−6828.10	−0.599894
$507$	6289.98	0.550982
$508$	4947.59	0.432114
$509$	−3107.69	−0.270620	−0.135310	−	0.990803i	$-0.543203\pi$
$509$	−3107.69	−0.270620	−0.135310	+	0.990803i	$0.543203\pi$
$510$	4465.27	0.387697
$511$	−23182.6	−2.00693
$512$	−512.000	−0.0441942
$513$	0	0
$514$	12846.8	1.10242
$515$	19546.0	1.67243
$516$	−454.206	−0.0387506
$517$	−9754.96	−0.829831
$518$	12276.9	1.04134
$519$	−3396.93	−0.287300
$520$	1163.93	0.0981574
$521$	−19805.1	−1.66541	−0.832703	−	0.553720i	$-0.813208\pi$
$521$	−19805.1	−1.66541	−0.832703	+	0.553720i	$0.813208\pi$
$522$	−3892.36	−0.326368
$523$	−12775.2	−1.06811	−0.534053	−	0.845451i	$-0.679332\pi$
$523$	−12775.2	−1.06811	−0.534053	+	0.845451i	$0.679332\pi$
$524$	9632.04	0.803010
$525$	−5875.82	−0.488460
$526$	9475.26	0.785439
$527$	−4346.95	−0.359309
$528$	1593.90	0.131374
$529$	−1596.40	−0.131207
$530$	15249.7	1.24982
$531$	−5737.62	−0.468910
$532$	0	0
$533$	4755.57	0.386466
$534$	6656.20	0.539404
$535$	−21736.8	−1.75657
$536$	565.743	0.0455903
$537$	2762.56	0.221999
$538$	−11229.1	−0.899850
$539$	−5848.37	−0.467360
$540$	−1568.65	−0.125008
$541$	540.246	0.0429334	0.0214667	−	0.999770i	$-0.493166\pi$
$541$	540.246	0.0429334	0.0214667	+	0.999770i	$0.493166\pi$
$542$	10461.5	0.829079
$543$	−11716.7	−0.925989
$544$	−1639.62	−0.129225
$545$	−22759.9	−1.78885
$546$	−1369.37	−0.107333
$547$	−4078.04	−0.318765	−0.159382	−	0.987217i	$-0.550950\pi$
$547$	−4078.04	−0.318765	−0.159382	+	0.987217i	$0.550950\pi$
$548$	4908.84	0.382655
$549$	−4079.35	−0.317127
$550$	5709.03	0.442607
$551$	0	0
$552$	−2467.52	−0.190262
$553$	−13856.7	−1.06554
$554$	14479.8	1.11045
$555$	11739.5	0.897859
$556$	−1403.54	−0.107056
$557$	7469.80	0.568233	0.284116	−	0.958790i	$-0.408300\pi$
$557$	7469.80	0.568233	0.284116	+	0.958790i	$0.408300\pi$
$558$	1527.09	0.115854
$559$	−379.146	−0.0286872
$560$	5294.90	0.399555
$561$	5104.28	0.384141
$562$	−3688.22	−0.276829
$563$	19780.7	1.48074	0.740371	−	0.672199i	$-0.234650\pi$
$563$	19780.7	1.48074	0.740371	+	0.672199i	$0.234650\pi$
$564$	−3525.22	−0.263189
$565$	6219.95	0.463142
$566$	2789.87	0.207185
$567$	1845.52	0.136693
$568$	−2303.91	−0.170194
$569$	7544.98	0.555891	0.277945	−	0.960597i	$-0.410347\pi$
$569$	7544.98	0.555891	0.277945	+	0.960597i	$0.410347\pi$
$570$	0	0
$571$	1405.02	0.102974	0.0514871	−	0.998674i	$-0.483604\pi$
$571$	1405.02	0.102974	0.0514871	+	0.998674i	$0.483604\pi$
$572$	1330.50	0.0972570
$573$	12965.2	0.945250
$574$	21633.8	1.57313
$575$	−8838.17	−0.641004
$576$	576.000	0.0416667
$577$	−20989.4	−1.51438	−0.757191	−	0.653194i	$-0.773429\pi$
$577$	−20989.4	−1.51438	−0.757191	+	0.653194i	$0.773429\pi$
$578$	4575.31	0.329252
$579$	−12037.4	−0.864001
$580$	12563.3	0.899418
$581$	−4543.58	−0.324440
$582$	−8835.05	−0.629252
$583$	17432.0	1.23835
$584$	8139.88	0.576765
$585$	−1309.43	−0.0925437
$586$	9174.11	0.646722
$587$	−7317.64	−0.514534	−0.257267	−	0.966340i	$-0.582822\pi$
$587$	−7317.64	−0.514534	−0.257267	+	0.966340i	$0.582822\pi$
$588$	−2113.47	−0.148228
$589$	0	0
$590$	18519.2	1.29224
$591$	401.361	0.0279353
$592$	−4310.66	−0.299268
$593$	6436.66	0.445737	0.222868	−	0.974849i	$-0.428458\pi$
$593$	6436.66	0.445737	0.222868	+	0.974849i	$0.428458\pi$
$594$	−1793.14	−0.123861
$595$	16956.3	1.16830
$596$	−156.206	−0.0107357
$597$	−12101.8	−0.829638
$598$	−2059.75	−0.140852
$599$	−1729.42	−0.117967	−0.0589834	−	0.998259i	$-0.518786\pi$
$599$	−1729.42	−0.117967	−0.0589834	+	0.998259i	$0.518786\pi$
$600$	2063.12	0.140377
$601$	6310.57	0.428309	0.214155	−	0.976800i	$-0.431300\pi$
$601$	6310.57	0.428309	0.214155	+	0.976800i	$0.431300\pi$
$602$	−1724.79	−0.116773
$603$	−636.461	−0.0429829
$604$	5764.94	0.388364
$605$	−3316.59	−0.222874
$606$	−2206.65	−0.147919
$607$	777.764	0.0520074	0.0260037	−	0.999662i	$-0.491722\pi$
$607$	777.764	0.0520074	0.0260037	+	0.999662i	$0.491722\pi$
$608$	0	0
$609$	−14780.7	−0.983491
$610$	13166.9	0.873952
$611$	−2942.66	−0.194840
$612$	1844.57	0.121834
$613$	−28084.2	−1.85043	−0.925213	−	0.379448i	$-0.876114\pi$
$613$	−28084.2	−1.85043	−0.925213	+	0.379448i	$0.876114\pi$
$614$	12144.1	0.798203
$615$	20686.8	1.35637
$616$	6052.64	0.395889
$617$	10348.6	0.675231	0.337615	−	0.941284i	$-0.390380\pi$
$617$	10348.6	0.675231	0.337615	+	0.941284i	$0.390380\pi$
$618$	8074.32	0.525561
$619$	−20559.6	−1.33499	−0.667495	−	0.744614i	$-0.732634\pi$
$619$	−20559.6	−1.33499	−0.667495	+	0.744614i	$0.732634\pi$
$620$	−4928.95	−0.319276
$621$	2775.96	0.179381
$622$	−5280.22	−0.340382
$623$	25276.1	1.62547
$624$	480.813	0.0308460
$625$	−18980.7	−1.21477
$626$	−7578.43	−0.483858
$627$	0	0
$628$	−11426.4	−0.726053
$629$	−13804.4	−0.875066
$630$	−5956.77	−0.376704
$631$	10287.3	0.649022	0.324511	−	0.945882i	$-0.394800\pi$
$631$	10287.3	0.649022	0.324511	+	0.945882i	$0.394800\pi$
$632$	4865.35	0.306223
$633$	−11093.8	−0.696589
$634$	1626.42	0.101882
$635$	17965.4	1.12273
$636$	6299.54	0.392756
$637$	−1764.21	−0.109734
$638$	14361.2	0.891168
$639$	2591.90	0.160460
$640$	−1859.14	−0.114827
$641$	1188.13	0.0732110	0.0366055	−	0.999330i	$-0.488346\pi$
$641$	1188.13	0.0732110	0.0366055	+	0.999330i	$0.488346\pi$
$642$	−8979.31	−0.552002
$643$	−18019.0	−1.10513	−0.552566	−	0.833469i	$-0.686351\pi$
$643$	−18019.0	−1.10513	−0.552566	+	0.833469i	$0.686351\pi$
$644$	−9370.11	−0.573345
$645$	−1649.29	−0.100683
$646$	0	0
$647$	3288.22	0.199804	0.0999019	−	0.994997i	$-0.468147\pi$
$647$	3288.22	0.199804	0.0999019	+	0.994997i	$0.468147\pi$
$648$	−648.000	−0.0392837
$649$	21169.4	1.28039
$650$	1722.17	0.103922
$651$	5798.92	0.349121
$652$	9653.33	0.579837
$653$	14159.6	0.848557	0.424278	−	0.905532i	$-0.360528\pi$
$653$	14159.6	0.848557	0.424278	+	0.905532i	$0.360528\pi$
$654$	−9401.94	−0.562148
$655$	34975.3	2.08641
$656$	−7596.05	−0.452097
$657$	−9157.37	−0.543779
$658$	−13386.6	−0.793106
$659$	10661.5	0.630217	0.315109	−	0.949056i	$-0.397959\pi$
$659$	10661.5	0.630217	0.315109	+	0.949056i	$0.397959\pi$
$660$	5787.68	0.341341
$661$	3115.39	0.183320	0.0916602	−	0.995790i	$-0.470783\pi$
$661$	3115.39	0.183320	0.0916602	+	0.995790i	$0.470783\pi$
$662$	3165.94	0.185873
$663$	1539.75	0.0901943
$664$	1595.34	0.0932399
$665$	0	0
$666$	4849.49	0.282153
$667$	−22232.6	−1.29063
$668$	6486.53	0.375706
$669$	15178.0	0.877152
$670$	2054.29	0.118454
$671$	15051.1	0.865935
$672$	2187.29	0.125560
$673$	27282.0	1.56262	0.781309	−	0.624144i	$-0.214552\pi$
$673$	27282.0	1.56262	0.781309	+	0.624144i	$0.214552\pi$
$674$	−14518.0	−0.829692
$675$	−2321.00	−0.132349
$676$	−8386.64	−0.477165
$677$	2009.29	0.114067	0.0570333	−	0.998372i	$-0.481836\pi$
$677$	2009.29	0.114067	0.0570333	+	0.998372i	$0.481836\pi$
$678$	2569.42	0.145543
$679$	−33550.0	−1.89622
$680$	−5953.70	−0.335756
$681$	−9373.43	−0.527446
$682$	−5634.32	−0.316348
$683$	19205.3	1.07595	0.537973	−	0.842962i	$-0.319190\pi$
$683$	19205.3	1.07595	0.537973	+	0.842962i	$0.319190\pi$
$684$	0	0
$685$	17824.7	0.994228
$686$	7604.37	0.423231
$687$	6591.15	0.366038
$688$	605.607	0.0335590
$689$	5258.50	0.290759
$690$	−8959.93	−0.494346
$691$	1343.96	0.0739892	0.0369946	−	0.999315i	$-0.488222\pi$
$691$	1343.96	0.0739892	0.0369946	+	0.999315i	$0.488222\pi$
$692$	4529.23	0.248809
$693$	−6809.22	−0.373248
$694$	1612.40	0.0881930
$695$	−5096.44	−0.278157
$696$	5189.81	0.282643
$697$	−24325.5	−1.32194
$698$	−15814.7	−0.857585
$699$	5261.26	0.284691
$700$	7834.42	0.423019
$701$	−12078.5	−0.650784	−0.325392	−	0.945579i	$-0.605496\pi$
$701$	−12078.5	−0.650784	−0.325392	+	0.945579i	$0.605496\pi$
$702$	−540.914	−0.0290819
$703$	0	0
$704$	−2125.20	−0.113774
$705$	−12800.6	−0.683827
$706$	−11135.1	−0.593593
$707$	−8379.47	−0.445746
$708$	7650.16	0.406088
$709$	−27766.7	−1.47081	−0.735403	−	0.677630i	$-0.763007\pi$
$709$	−27766.7	−1.47081	−0.735403	+	0.677630i	$0.763007\pi$
$710$	−8365.84	−0.442203
$711$	−5473.52	−0.288710
$712$	−8874.93	−0.467138
$713$	8722.50	0.458149
$714$	7004.54	0.367140
$715$	4831.24	0.252696
$716$	−3683.41	−0.192256
$717$	10948.1	0.570242
$718$	−19206.1	−0.998280
$719$	−12655.9	−0.656446	−0.328223	−	0.944600i	$-0.606450\pi$
$719$	−12655.9	−0.656446	−0.328223	+	0.944600i	$0.606450\pi$
$720$	2091.54	0.108260
$721$	30661.2	1.58375
$722$	0	0
$723$	4619.04	0.237599
$724$	15622.3	0.801930
$725$	18588.9	0.952238
$726$	−1370.06	−0.0700381
$727$	37368.2	1.90634	0.953171	−	0.302433i	$-0.0977990\pi$
$727$	37368.2	1.90634	0.953171	+	0.302433i	$0.0977990\pi$
$728$	1825.83	0.0929528
$729$	729.000	0.0370370
$730$	29557.1	1.49857
$731$	1939.39	0.0981270
$732$	5439.14	0.274640
$733$	−24478.5	−1.23347	−0.616736	−	0.787170i	$-0.711545\pi$
$733$	−24478.5	−1.23347	−0.616736	+	0.787170i	$0.711545\pi$
$734$	1208.61	0.0607773
$735$	−7674.30	−0.385130
$736$	3290.03	0.164772
$737$	2348.28	0.117368
$738$	8545.56	0.426242
$739$	−23685.6	−1.17901	−0.589504	−	0.807765i	$-0.700677\pi$
$739$	−23685.6	−1.17901	−0.589504	+	0.807765i	$0.700677\pi$
$740$	−15652.6	−0.777569
$741$	0	0
$742$	23921.7	1.18355
$743$	6209.28	0.306590	0.153295	−	0.988180i	$-0.451011\pi$
$743$	6209.28	0.306590	0.153295	+	0.988180i	$0.451011\pi$
$744$	−2036.11	−0.100333
$745$	−567.208	−0.0278938
$746$	4261.33	0.209140
$747$	−1794.76	−0.0879074
$748$	−6805.71	−0.332676
$749$	−34097.8	−1.66343
$750$	−3401.96	−0.165629
$751$	28071.8	1.36399	0.681994	−	0.731358i	$-0.261113\pi$
$751$	28071.8	1.36399	0.681994	+	0.731358i	$0.261113\pi$
$752$	4700.30	0.227928
$753$	−22354.8	−1.08188
$754$	4332.17	0.209242
$755$	20933.3	1.00906
$756$	−2460.70	−0.118379
$757$	−3520.39	−0.169024	−0.0845118	−	0.996422i	$-0.526933\pi$
$757$	−3520.39	−0.169024	−0.0845118	+	0.996422i	$0.526933\pi$
$758$	4653.91	0.223005
$759$	−10242.2	−0.489811
$760$	0	0
$761$	−23591.6	−1.12378	−0.561890	−	0.827212i	$-0.689926\pi$
$761$	−23591.6	−1.12378	−0.561890	+	0.827212i	$0.689926\pi$
$762$	7421.39	0.352820
$763$	−35702.7	−1.69400
$764$	−17286.9	−0.818610
$765$	6697.91	0.316553
$766$	−12843.6	−0.605819
$767$	6385.93	0.300629
$768$	−768.000	−0.0360844
$769$	−29847.3	−1.39964	−0.699819	−	0.714321i	$-0.746736\pi$
$769$	−29847.3	−1.39964	−0.699819	+	0.714321i	$0.746736\pi$
$770$	21978.0	1.02861
$771$	19270.1	0.900126
$772$	16049.8	0.748247
$773$	18286.4	0.850862	0.425431	−	0.904991i	$-0.360123\pi$
$773$	18286.4	0.850862	0.425431	+	0.904991i	$0.360123\pi$
$774$	−681.308	−0.0316397
$775$	−7292.95	−0.338026
$776$	11780.1	0.544948
$777$	18415.3	0.850252
$778$	16468.4	0.758897
$779$	0	0
$780$	1745.90	0.0801452
$781$	−9563.05	−0.438147
$782$	10535.9	0.481796
$783$	−5838.54	−0.266478
$784$	2817.96	0.128369
$785$	−41490.7	−1.88646
$786$	14448.1	0.655655
$787$	1421.91	0.0644037	0.0322019	−	0.999481i	$-0.489748\pi$
$787$	1421.91	0.0644037	0.0322019	+	0.999481i	$0.489748\pi$
$788$	−535.148	−0.0241927
$789$	14212.9	0.641308
$790$	17666.8	0.795640
$791$	9757.05	0.438585
$792$	2390.85	0.107267
$793$	4540.29	0.203317
$794$	−19842.7	−0.886889
$795$	22874.5	1.02047
$796$	16135.7	0.718488
$797$	−14172.5	−0.629881	−0.314941	−	0.949111i	$-0.601985\pi$
$797$	−14172.5	−0.629881	−0.314941	+	0.949111i	$0.601985\pi$
$798$	0	0
$799$	15052.2	0.666467
$800$	−2750.82	−0.121570
$801$	9984.30	0.440422
$802$	−22212.4	−0.977990
$803$	33786.9	1.48482
$804$	848.615	0.0372243
$805$	−34024.2	−1.48968
$806$	−1699.64	−0.0742768
$807$	−16843.6	−0.734724
$808$	2942.20	0.128102
$809$	−1174.32	−0.0510345	−0.0255172	−	0.999674i	$-0.508123\pi$
$809$	−1174.32	−0.0510345	−0.0255172	+	0.999674i	$0.508123\pi$
$810$	−2352.98	−0.102068
$811$	−7303.74	−0.316238	−0.158119	−	0.987420i	$-0.550543\pi$
$811$	−7303.74	−0.316238	−0.158119	+	0.987420i	$0.550543\pi$
$812$	19707.7	0.851728
$813$	15692.3	0.676940
$814$	−17892.6	−0.770436
$815$	35052.6	1.50655
$816$	−2459.43	−0.105511
$817$	0	0
$818$	15569.4	0.665489
$819$	−2054.06	−0.0876368
$820$	−27582.3	−1.17465
$821$	892.416	0.0379361	0.0189680	−	0.999820i	$-0.493962\pi$
$821$	892.416	0.0379361	0.0189680	+	0.999820i	$0.493962\pi$
$822$	7363.26	0.312437
$823$	34180.1	1.44768	0.723841	−	0.689967i	$-0.242375\pi$
$823$	34180.1	1.44768	0.723841	+	0.689967i	$0.242375\pi$
$824$	−10765.8	−0.455149
$825$	8563.55	0.361387
$826$	29050.5	1.22372
$827$	−1530.00	−0.0643329	−0.0321664	−	0.999483i	$-0.510241\pi$
$827$	−1530.00	−0.0643329	−0.0321664	+	0.999483i	$0.510241\pi$
$828$	−3701.28	−0.155348
$829$	36456.0	1.52735	0.763673	−	0.645603i	$-0.223394\pi$
$829$	36456.0	1.52735	0.763673	+	0.645603i	$0.223394\pi$
$830$	5792.91	0.242259
$831$	21719.7	0.906677
$832$	−641.084	−0.0267134
$833$	9024.18	0.375353
$834$	−2105.30	−0.0874109
$835$	23553.5	0.976171
$836$	0	0
$837$	2290.63	0.0945947
$838$	24449.5	1.00787
$839$	−16341.3	−0.672423	−0.336212	−	0.941786i	$-0.609146\pi$
$839$	−16341.3	−0.672423	−0.336212	+	0.941786i	$0.609146\pi$
$840$	7942.36	0.326235
$841$	22371.6	0.917284
$842$	18388.7	0.752631
$843$	−5532.32	−0.226030
$844$	14791.8	0.603264
$845$	−30453.1	−1.23979
$846$	−5287.83	−0.214893
$847$	−5202.63	−0.211056
$848$	−8399.38	−0.340137
$849$	4184.80	0.169166
$850$	−8809.18	−0.355473
$851$	27699.6	1.11578
$852$	−3455.87	−0.138963
$853$	−73.6836	−0.00295766	−0.00147883	−	0.999999i	$-0.500471\pi$
$853$	−73.6836	−0.00295766	−0.00147883	+	0.999999i	$0.500471\pi$
$854$	20654.5	0.827612
$855$	0	0
$856$	11972.4	0.478048
$857$	−32919.1	−1.31213	−0.656064	−	0.754705i	$-0.727780\pi$
$857$	−32919.1	−1.31213	−0.656064	+	0.754705i	$0.727780\pi$
$858$	1995.75	0.0794100
$859$	−39405.7	−1.56520	−0.782599	−	0.622526i	$-0.786106\pi$
$859$	−39405.7	−1.56520	−0.782599	+	0.622526i	$0.786106\pi$
$860$	2199.05	0.0871941
$861$	32450.7	1.28446
$862$	−27474.2	−1.08558
$863$	3381.53	0.133382	0.0666910	−	0.997774i	$-0.478756\pi$
$863$	3381.53	0.133382	0.0666910	+	0.997774i	$0.478756\pi$
$864$	864.000	0.0340207
$865$	16446.3	0.646463
$866$	1597.28	0.0626764
$867$	6862.96	0.268833
$868$	−7731.89	−0.302347
$869$	20195.0	0.788341
$870$	18844.9	0.734372
$871$	708.377	0.0275573
$872$	12535.9	0.486835
$873$	−13252.6	−0.513782
$874$	0	0
$875$	−12918.5	−0.499115
$876$	12209.8	0.470926
$877$	−30677.6	−1.18120	−0.590598	−	0.806966i	$-0.701108\pi$
$877$	−30677.6	−1.18120	−0.590598	+	0.806966i	$0.701108\pi$
$878$	21388.4	0.822122
$879$	13761.2	0.528046
$880$	−7716.91	−0.295610
$881$	50730.6	1.94002	0.970010	−	0.243065i	$-0.0781529\pi$
$881$	50730.6	1.94002	0.970010	+	0.243065i	$0.0781529\pi$
$882$	−3170.20	−0.121027
$883$	−31963.5	−1.21819	−0.609093	−	0.793099i	$-0.708466\pi$
$883$	−31963.5	−1.21819	−0.609093	+	0.793099i	$0.708466\pi$
$884$	−2053.00	−0.0781106
$885$	27778.8	1.05511
$886$	18955.8	0.718774
$887$	−46289.7	−1.75226	−0.876131	−	0.482073i	$-0.839884\pi$
$887$	−46289.7	−1.75226	−0.876131	+	0.482073i	$0.839884\pi$
$888$	−6465.98	−0.244352
$889$	28181.8	1.06320
$890$	−32226.2	−1.21373
$891$	−2689.71	−0.101132
$892$	−20237.3	−0.759636
$893$	0	0
$894$	−234.310	−0.00876565
$895$	−13375.0	−0.499527
$896$	−2916.38	−0.108738
$897$	−3089.63	−0.115005
$898$	−6482.80	−0.240906
$899$	−18345.6	−0.680600
$900$	3094.67	0.114618
$901$	−26898.0	−0.994566
$902$	−31529.6	−1.16388
$903$	−2587.18	−0.0953445
$904$	−3425.89	−0.126044
$905$	56726.7	2.08360
$906$	8647.40	0.317098
$907$	−2332.70	−0.0853981	−0.0426990	−	0.999088i	$-0.513596\pi$
$907$	−2332.70	−0.0853981	−0.0426990	+	0.999088i	$0.513596\pi$
$908$	12497.9	0.456781
$909$	−3309.97	−0.120775
$910$	6629.84	0.241513
$911$	−1536.03	−0.0558629	−0.0279314	−	0.999610i	$-0.508892\pi$
$911$	−1536.03	−0.0558629	−0.0279314	+	0.999610i	$0.508892\pi$
$912$	0	0
$913$	6621.92	0.240037
$914$	−7235.53	−0.261849
$915$	19750.3	0.713578
$916$	−8788.20	−0.316998
$917$	54864.7	1.97578
$918$	2766.86	0.0994771
$919$	−15608.9	−0.560272	−0.280136	−	0.959960i	$-0.590379\pi$
$919$	−15608.9	−0.560272	−0.280136	+	0.959960i	$0.590379\pi$
$920$	11946.6	0.428116
$921$	18216.2	0.651730
$922$	11818.7	0.422158
$923$	−2884.77	−0.102875
$924$	9078.96	0.323242
$925$	−23159.8	−0.823233
$926$	10148.0	0.360133
$927$	12111.5	0.429119
$928$	−6919.75	−0.244776
$929$	37308.4	1.31760	0.658800	−	0.752318i	$-0.271064\pi$
$929$	37308.4	1.31760	0.658800	+	0.752318i	$0.271064\pi$
$930$	−7393.42	−0.260688
$931$	0	0
$932$	−7015.02	−0.246550
$933$	−7920.34	−0.277921
$934$	−37871.8	−1.32677
$935$	−24712.5	−0.864369
$936$	721.219	0.0251857
$937$	−22520.2	−0.785168	−0.392584	−	0.919716i	$-0.628419\pi$
$937$	−22520.2	−0.785168	−0.392584	+	0.919716i	$0.628419\pi$
$938$	3222.51	0.112173
$939$	−11367.6	−0.395068
$940$	17067.4	0.592211
$941$	−8269.06	−0.286465	−0.143232	−	0.989689i	$-0.545750\pi$
$941$	−8269.06	−0.286465	−0.143232	+	0.989689i	$0.545750\pi$
$942$	−17139.5	−0.592820
$943$	48811.0	1.68558
$944$	−10200.2	−0.351683
$945$	−8935.15	−0.307577
$946$	2513.75	0.0863942
$947$	−1951.26	−0.0669559	−0.0334780	−	0.999439i	$-0.510658\pi$
$947$	−1951.26	−0.0669559	−0.0334780	+	0.999439i	$0.510658\pi$
$948$	7298.02	0.250030
$949$	10192.1	0.348629
$950$	0	0
$951$	2439.63	0.0831866
$952$	−9339.38	−0.317953
$953$	−27769.0	−0.943889	−0.471945	−	0.881628i	$-0.656448\pi$
$953$	−27769.0	−0.943889	−0.471945	+	0.881628i	$0.656448\pi$
$954$	9449.30	0.320684
$955$	−62771.2	−2.12694
$956$	−14597.5	−0.493844
$957$	21541.8	0.727635
$958$	−12503.5	−0.421679
$959$	27961.0	0.941511
$960$	−2788.72	−0.0937557
$961$	−22593.5	−0.758400
$962$	−5397.44	−0.180895
$963$	−13469.0	−0.450708
$964$	−6158.72	−0.205767
$965$	58279.3	1.94412
$966$	−14055.2	−0.468134
$967$	26286.7	0.874170	0.437085	−	0.899420i	$-0.356011\pi$
$967$	26286.7	0.874170	0.437085	+	0.899420i	$0.356011\pi$
$968$	1826.75	0.0606548
$969$	0	0
$970$	42775.1	1.41590
$971$	9469.93	0.312981	0.156490	−	0.987679i	$-0.449982\pi$
$971$	9469.93	0.312981	0.156490	+	0.987679i	$0.449982\pi$
$972$	−972.000	−0.0320750
$973$	−7994.63	−0.263408
$974$	28768.5	0.946409
$975$	2583.26	0.0848519
$976$	−7252.18	−0.237845
$977$	7414.97	0.242811	0.121405	−	0.992603i	$-0.461260\pi$
$977$	7414.97	0.242811	0.121405	+	0.992603i	$0.461260\pi$
$978$	14480.0	0.473435
$979$	−36837.9	−1.20260
$980$	10232.4	0.333533
$981$	−14102.9	−0.458992
$982$	−32712.0	−1.06302
$983$	−1718.32	−0.0557536	−0.0278768	−	0.999611i	$-0.508875\pi$
$983$	−1718.32	−0.0557536	−0.0278768	+	0.999611i	$0.508875\pi$
$984$	−11394.1	−0.369136
$985$	−1943.20	−0.0628583
$986$	−22159.7	−0.715728
$987$	−20079.9	−0.647568
$988$	0	0
$989$	−3891.54	−0.125120
$990$	8681.52	0.278704
$991$	−12737.9	−0.408309	−0.204155	−	0.978939i	$-0.565444\pi$
$991$	−12737.9	−0.408309	−0.204155	+	0.978939i	$0.565444\pi$
$992$	2714.82	0.0868907
$993$	4748.92	0.151765
$994$	−13123.2	−0.418756
$995$	58591.2	1.86680
$996$	2393.01	0.0761300
$997$	−4754.98	−0.151045	−0.0755224	−	0.997144i	$-0.524062\pi$
$997$	−4754.98	−0.151045	−0.0755224	+	0.997144i	$0.524062\pi$
$998$	40047.1	1.27021
$999$	7274.23	0.230377

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2166.4.a.bj.1.7		9
19.14	odd	18		114.4.i.d.25.3	✓	18
19.15	odd	18		114.4.i.d.73.3	yes	18
19.18	odd	2		2166.4.a.bm.1.7		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.4.i.d.25.3	✓	18	19.14	odd	18
114.4.i.d.73.3	yes	18	19.15	odd	18
2166.4.a.bj.1.7		9	1.1	even	1	trivial
2166.4.a.bm.1.7		9	19.18	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 2166 = 2 \cdot 3 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2166.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +14.5246 q^{5} +6.00000 q^{6} +22.7843 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +14.5246 q^{5} +6.00000 q^{6} +22.7843 q^{7} -8.00000 q^{8} +9.00000 q^{9} -29.0491 q^{10} -33.2063 q^{11} -12.0000 q^{12} -10.0169 q^{13} -45.5685 q^{14} -43.5737 q^{15} +16.0000 q^{16} +51.2381 q^{17} -18.0000 q^{18} +58.0983 q^{20} -68.3528 q^{21} +66.4125 q^{22} -102.813 q^{23} +24.0000 q^{24} +85.9631 q^{25} +20.0339 q^{26} -27.0000 q^{27} +91.1370 q^{28} +216.242 q^{29} +87.1474 q^{30} -84.8381 q^{31} -32.0000 q^{32} +99.6188 q^{33} -102.476 q^{34} +330.932 q^{35} +36.0000 q^{36} -269.416 q^{37} +30.0508 q^{39} -116.197 q^{40} -474.753 q^{41} +136.706 q^{42} +37.8505 q^{43} -132.825 q^{44} +130.721 q^{45} +205.627 q^{46} +293.769 q^{47} -48.0000 q^{48} +176.122 q^{49} -171.926 q^{50} -153.714 q^{51} -40.0677 q^{52} -524.961 q^{53} +54.0000 q^{54} -482.307 q^{55} -182.274 q^{56} -432.484 q^{58} -637.513 q^{59} -174.295 q^{60} -453.262 q^{61} +169.676 q^{62} +205.058 q^{63} +64.0000 q^{64} -145.492 q^{65} -199.238 q^{66} -70.7179 q^{67} +204.953 q^{68} +308.440 q^{69} -661.863 q^{70} +287.989 q^{71} -72.0000 q^{72} -1017.49 q^{73} +538.832 q^{74} -257.889 q^{75} -756.580 q^{77} -60.1016 q^{78} -608.168 q^{79} +232.393 q^{80} +81.0000 q^{81} +949.506 q^{82} -199.418 q^{83} -273.411 q^{84} +744.212 q^{85} -75.7009 q^{86} -648.726 q^{87} +265.650 q^{88} +1109.37 q^{89} -261.442 q^{90} -228.228 q^{91} -411.254 q^{92} +254.514 q^{93} -587.537 q^{94} +96.0000 q^{96} -1472.51 q^{97} -352.245 q^{98} -298.856 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 18 q^{2} - 27 q^{3} + 36 q^{4} + 27 q^{5} + 54 q^{6} - 72 q^{8} + 81 q^{9}+O(q^{10}) \) 9 * q - 18 * q^2 - 27 * q^3 + 36 * q^4 + 27 * q^5 + 54 * q^6 - 72 * q^8 + 81 * q^9	\( 9 q - 18 q^{2} - 27 q^{3} + 36 q^{4} + 27 q^{5} + 54 q^{6} - 72 q^{8} + 81 q^{9} - 54 q^{10} + 39 q^{11} - 108 q^{12} - 99 q^{13} - 81 q^{15} + 144 q^{16} + 57 q^{17} - 162 q^{18} + 108 q^{20} - 78 q^{22} + 228 q^{23} + 216 q^{24} + 174 q^{25} + 198 q^{26} - 243 q^{27} - 459 q^{29} + 162 q^{30} - 243 q^{31} - 288 q^{32} - 117 q^{33} - 114 q^{34} + 324 q^{35} + 324 q^{36} - 711 q^{37} + 297 q^{39} - 216 q^{40} - 459 q^{41} + 252 q^{43} + 156 q^{44} + 243 q^{45} - 456 q^{46} - 66 q^{47} - 432 q^{48} + 2229 q^{49} - 348 q^{50} - 171 q^{51} - 396 q^{52} - 1197 q^{53} + 486 q^{54} + 762 q^{55} + 918 q^{58} - 1221 q^{59} - 324 q^{60} - 780 q^{61} + 486 q^{62} + 576 q^{64} + 237 q^{65} + 234 q^{66} - 1596 q^{67} + 228 q^{68} - 684 q^{69} - 648 q^{70} - 2538 q^{71} - 648 q^{72} + 225 q^{73} + 1422 q^{74} - 522 q^{75} - 135 q^{77} - 594 q^{78} - 834 q^{79} + 432 q^{80} + 729 q^{81} + 918 q^{82} + 2490 q^{83} - 1653 q^{85} - 504 q^{86} + 1377 q^{87} - 312 q^{88} + 507 q^{89} - 486 q^{90} - 6423 q^{91} + 912 q^{92} + 729 q^{93} + 132 q^{94} + 864 q^{96} - 2529 q^{97} - 4458 q^{98} + 351 q^{99}+O(q^{100}) \) 9 * q - 18 * q^2 - 27 * q^3 + 36 * q^4 + 27 * q^5 + 54 * q^6 - 72 * q^8 + 81 * q^9 - 54 * q^10 + 39 * q^11 - 108 * q^12 - 99 * q^13 - 81 * q^15 + 144 * q^16 + 57 * q^17 - 162 * q^18 + 108 * q^20 - 78 * q^22 + 228 * q^23 + 216 * q^24 + 174 * q^25 + 198 * q^26 - 243 * q^27 - 459 * q^29 + 162 * q^30 - 243 * q^31 - 288 * q^32 - 117 * q^33 - 114 * q^34 + 324 * q^35 + 324 * q^36 - 711 * q^37 + 297 * q^39 - 216 * q^40 - 459 * q^41 + 252 * q^43 + 156 * q^44 + 243 * q^45 - 456 * q^46 - 66 * q^47 - 432 * q^48 + 2229 * q^49 - 348 * q^50 - 171 * q^51 - 396 * q^52 - 1197 * q^53 + 486 * q^54 + 762 * q^55 + 918 * q^58 - 1221 * q^59 - 324 * q^60 - 780 * q^61 + 486 * q^62 + 576 * q^64 + 237 * q^65 + 234 * q^66 - 1596 * q^67 + 228 * q^68 - 684 * q^69 - 648 * q^70 - 2538 * q^71 - 648 * q^72 + 225 * q^73 + 1422 * q^74 - 522 * q^75 - 135 * q^77 - 594 * q^78 - 834 * q^79 + 432 * q^80 + 729 * q^81 + 918 * q^82 + 2490 * q^83 - 1653 * q^85 - 504 * q^86 + 1377 * q^87 - 312 * q^88 + 507 * q^89 - 486 * q^90 - 6423 * q^91 + 912 * q^92 + 729 * q^93 + 132 * q^94 + 864 * q^96 - 2529 * q^97 - 4458 * q^98 + 351 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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