LMFDB - Embedded newform 2166.4.a.bj.1.9

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			1.9
Root			$16.8589$ 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)

$f(q)$	$=$	$q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +21.3910 q^{5} +6.00000 q^{6} +12.1690 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +21.3910 q^{5} +6.00000 q^{6} +12.1690 q^{7} -8.00000 q^{8} +9.00000 q^{9} -42.7821 q^{10} -2.11696 q^{11} -12.0000 q^{12} -63.2918 q^{13} -24.3379 q^{14} -64.1731 q^{15} +16.0000 q^{16} -89.3230 q^{17} -18.0000 q^{18} +85.5641 q^{20} -36.5069 q^{21} +4.23392 q^{22} +75.0245 q^{23} +24.0000 q^{24} +332.576 q^{25} +126.584 q^{26} -27.0000 q^{27} +48.6759 q^{28} +39.0079 q^{29} +128.346 q^{30} -15.6234 q^{31} -32.0000 q^{32} +6.35088 q^{33} +178.646 q^{34} +260.307 q^{35} +36.0000 q^{36} +98.1199 q^{37} +189.875 q^{39} -171.128 q^{40} -37.7348 q^{41} +73.0138 q^{42} -387.145 q^{43} -8.46784 q^{44} +192.519 q^{45} -150.049 q^{46} -294.553 q^{47} -48.0000 q^{48} -194.916 q^{49} -665.153 q^{50} +267.969 q^{51} -253.167 q^{52} -126.721 q^{53} +54.0000 q^{54} -45.2840 q^{55} -97.3518 q^{56} -78.0158 q^{58} -572.701 q^{59} -256.692 q^{60} -734.609 q^{61} +31.2469 q^{62} +109.521 q^{63} +64.0000 q^{64} -1353.88 q^{65} -12.7018 q^{66} -829.355 q^{67} -357.292 q^{68} -225.074 q^{69} -520.614 q^{70} -444.891 q^{71} -72.0000 q^{72} +1136.11 q^{73} -196.240 q^{74} -997.729 q^{75} -25.7612 q^{77} -379.751 q^{78} +1242.40 q^{79} +342.257 q^{80} +81.0000 q^{81} +75.4695 q^{82} +726.036 q^{83} -146.028 q^{84} -1910.71 q^{85} +774.290 q^{86} -117.024 q^{87} +16.9357 q^{88} +117.045 q^{89} -385.039 q^{90} -770.196 q^{91} +300.098 q^{92} +46.8703 q^{93} +589.107 q^{94} +96.0000 q^{96} -1082.86 q^{97} +389.832 q^{98} -19.0526 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	21.3910	1.91327	0.956636	−	0.291285i	$-0.0940829\pi$
$5$	21.3910	1.91327	0.956636	+	0.291285i	$0.0940829\pi$
$6$	6.00000	0.408248
$7$	12.1690	0.657063	0.328531	−	0.944493i	$-0.393446\pi$
$7$	12.1690	0.657063	0.328531	+	0.944493i	$0.393446\pi$
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	−42.7821	−1.35289
$11$	−2.11696	−0.0580262	−0.0290131	−	0.999579i	$-0.509236\pi$
$11$	−2.11696	−0.0580262	−0.0290131	+	0.999579i	$0.509236\pi$
$12$	−12.0000	−0.288675
$13$	−63.2918	−1.35031	−0.675153	−	0.737677i	$-0.735923\pi$
$13$	−63.2918	−1.35031	−0.675153	+	0.737677i	$0.735923\pi$
$14$	−24.3379	−0.464614
$15$	−64.1731	−1.10463
$16$	16.0000	0.250000
$17$	−89.3230	−1.27435	−0.637177	−	0.770718i	$-0.719898\pi$
$17$	−89.3230	−1.27435	−0.637177	+	0.770718i	$0.719898\pi$
$18$	−18.0000	−0.235702
$19$	0	0
$19$	0	0
$20$	85.5641	0.956636
$21$	−36.5069	−0.379355
$22$	4.23392	0.0410307
$23$	75.0245	0.680161	0.340080	−	0.940396i	$-0.389546\pi$
$23$	75.0245	0.680161	0.340080	+	0.940396i	$0.389546\pi$
$24$	24.0000	0.204124
$25$	332.576	2.66061
$26$	126.584	0.954811
$27$	−27.0000	−0.192450
$28$	48.6759	0.328531
$29$	39.0079	0.249779	0.124889	−	0.992171i	$-0.460142\pi$
$29$	39.0079	0.249779	0.124889	+	0.992171i	$0.460142\pi$
$30$	128.346	0.781090
$31$	−15.6234	−0.0905178	−0.0452589	−	0.998975i	$-0.514411\pi$
$31$	−15.6234	−0.0905178	−0.0452589	+	0.998975i	$0.514411\pi$
$32$	−32.0000	−0.176777
$33$	6.35088	0.0335014
$34$	178.646	0.901104
$35$	260.307	1.25714
$36$	36.0000	0.166667
$37$	98.1199	0.435968	0.217984	−	0.975952i	$-0.430052\pi$
$37$	98.1199	0.435968	0.217984	+	0.975952i	$0.430052\pi$
$38$	0	0
$39$	189.875	0.779600
$40$	−171.128	−0.676444
$41$	−37.7348	−0.143736	−0.0718680	−	0.997414i	$-0.522896\pi$
$41$	−37.7348	−0.143736	−0.0718680	+	0.997414i	$0.522896\pi$
$42$	73.0138	0.268245
$43$	−387.145	−1.37300	−0.686501	−	0.727129i	$-0.740854\pi$
$43$	−387.145	−1.37300	−0.686501	+	0.727129i	$0.740854\pi$
$44$	−8.46784	−0.0290131
$45$	192.519	0.637757
$46$	−150.049	−0.480946
$47$	−294.553	−0.914150	−0.457075	−	0.889428i	$-0.651103\pi$
$47$	−294.553	−0.914150	−0.457075	+	0.889428i	$0.651103\pi$
$48$	−48.0000	−0.144338
$49$	−194.916	−0.568269
$50$	−665.153	−1.88134
$51$	267.969	0.735748
$52$	−253.167	−0.675153
$53$	−126.721	−0.328423	−0.164212	−	0.986425i	$-0.552508\pi$
$53$	−126.721	−0.328423	−0.164212	+	0.986425i	$0.552508\pi$
$54$	54.0000	0.136083
$55$	−45.2840	−0.111020
$56$	−97.3518	−0.232307
$57$	0	0
$58$	−78.0158	−0.176620
$59$	−572.701	−1.26372	−0.631859	−	0.775084i	$-0.717708\pi$
$59$	−572.701	−1.26372	−0.631859	+	0.775084i	$0.717708\pi$
$60$	−256.692	−0.552314
$61$	−734.609	−1.54192	−0.770960	−	0.636884i	$-0.780223\pi$
$61$	−734.609	−1.54192	−0.770960	+	0.636884i	$0.780223\pi$
$62$	31.2469	0.0640058
$63$	109.521	0.219021
$64$	64.0000	0.125000
$65$	−1353.88	−2.58350
$66$	−12.7018	−0.0236891
$67$	−829.355	−1.51227	−0.756133	−	0.654418i	$-0.772914\pi$
$67$	−829.355	−1.51227	−0.756133	+	0.654418i	$0.772914\pi$
$68$	−357.292	−0.637177
$69$	−225.074	−0.392691
$70$	−520.614	−0.888932
$71$	−444.891	−0.743645	−0.371823	−	0.928304i	$-0.621267\pi$
$71$	−444.891	−0.743645	−0.371823	+	0.928304i	$0.621267\pi$
$72$	−72.0000	−0.117851
$73$	1136.11	1.82153	0.910766	−	0.412923i	$-0.135492\pi$
$73$	1136.11	1.82153	0.910766	+	0.412923i	$0.135492\pi$
$74$	−196.240	−0.308276
$75$	−997.729	−1.53610
$76$	0	0
$77$	−25.7612	−0.0381268
$78$	−379.751	−0.551260
$79$	1242.40	1.76937	0.884686	−	0.466187i	$-0.154372\pi$
$79$	1242.40	1.76937	0.884686	+	0.466187i	$0.154372\pi$
$80$	342.257	0.478318
$81$	81.0000	0.111111
$82$	75.4695	0.101637
$83$	726.036	0.960154	0.480077	−	0.877226i	$-0.340609\pi$
$83$	726.036	0.960154	0.480077	+	0.877226i	$0.340609\pi$
$84$	−146.028	−0.189678
$85$	−1910.71	−2.43819
$86$	774.290	0.970859
$87$	−117.024	−0.144210
$88$	16.9357	0.0205153
$89$	117.045	0.139402	0.0697010	−	0.997568i	$-0.477795\pi$
$89$	117.045	0.139402	0.0697010	+	0.997568i	$0.477795\pi$
$90$	−385.039	−0.450963
$91$	−770.196	−0.887236
$92$	300.098	0.340080
$93$	46.8703	0.0522605
$94$	589.107	0.646402
$95$	0	0
$96$	96.0000	0.102062
$97$	−1082.86	−1.13348	−0.566742	−	0.823895i	$-0.691797\pi$
$97$	−1082.86	−1.13348	−0.566742	+	0.823895i	$0.691797\pi$
$98$	389.832	0.401827
$99$	−19.0526	−0.0193421
$100$	1330.31	1.33031
$101$	−1903.61	−1.87541	−0.937705	−	0.347433i	$-0.887053\pi$
$101$	−1903.61	−1.87541	−0.937705	+	0.347433i	$0.887053\pi$
$102$	−535.938	−0.520253
$103$	99.5734	0.0952549	0.0476275	−	0.998865i	$-0.484834\pi$
$103$	99.5734	0.0952549	0.0476275	+	0.998865i	$0.484834\pi$
$104$	506.334	0.477406
$105$	−780.921	−0.725810
$106$	253.442	0.232230
$107$	−6.74057	−0.00609006	−0.00304503	−	0.999995i	$-0.500969\pi$
$107$	−6.74057	−0.00609006	−0.00304503	+	0.999995i	$0.500969\pi$
$108$	−108.000	−0.0962250
$109$	1122.56	0.986436	0.493218	−	0.869906i	$-0.335821\pi$
$109$	1122.56	0.986436	0.493218	+	0.869906i	$0.335821\pi$
$110$	90.5680	0.0785029
$111$	−294.360	−0.251706
$112$	194.704	0.164266
$113$	236.297	0.196716	0.0983580	−	0.995151i	$-0.468641\pi$
$113$	236.297	0.196716	0.0983580	+	0.995151i	$0.468641\pi$
$114$	0	0
$115$	1604.85	1.30133
$116$	156.032	0.124889
$117$	−569.626	−0.450102
$118$	1145.40	0.893583
$119$	−1086.97	−0.837330
$120$	513.385	0.390545
$121$	−1326.52	−0.996633
$122$	1469.22	1.09030
$123$	113.204	0.0829861
$124$	−62.4938	−0.0452589
$125$	4440.28	3.17720
$126$	−219.042	−0.154871
$127$	2354.74	1.64527	0.822634	−	0.568571i	$-0.192504\pi$
$127$	2354.74	1.64527	0.822634	+	0.568571i	$0.192504\pi$
$128$	−128.000	−0.0883883
$129$	1161.44	0.792703
$130$	2707.75	1.82681
$131$	−1446.93	−0.965032	−0.482516	−	0.875887i	$-0.660277\pi$
$131$	−1446.93	−0.965032	−0.482516	+	0.875887i	$0.660277\pi$
$132$	25.4035	0.0167507
$133$	0	0
$134$	1658.71	1.06933
$135$	−577.558	−0.368209
$136$	714.584	0.450552
$137$	−780.571	−0.486779	−0.243389	−	0.969929i	$-0.578259\pi$
$137$	−780.571	−0.486779	−0.243389	+	0.969929i	$0.578259\pi$
$138$	450.147	0.277674
$139$	−1636.73	−0.998745	−0.499373	−	0.866387i	$-0.666436\pi$
$139$	−1636.73	−0.998745	−0.499373	+	0.866387i	$0.666436\pi$
$140$	1041.23	0.628570
$141$	883.660	0.527785
$142$	889.781	0.525837
$143$	133.986	0.0783531
$144$	144.000	0.0833333
$145$	834.419	0.477895
$146$	−2272.22	−1.28802
$147$	584.748	0.328090
$148$	392.479	0.217984
$149$	−2682.73	−1.47502	−0.737508	−	0.675338i	$-0.763998\pi$
$149$	−2682.73	−1.47502	−0.737508	+	0.675338i	$0.763998\pi$
$150$	1995.46	1.08619
$151$	271.572	0.146359	0.0731796	−	0.997319i	$-0.476685\pi$
$151$	271.572	0.146359	0.0731796	+	0.997319i	$0.476685\pi$
$152$	0	0
$153$	−803.907	−0.424784
$154$	51.5225	0.0269597
$155$	−334.202	−0.173185
$156$	759.502	0.389800
$157$	1403.65	0.713527	0.356764	−	0.934195i	$-0.383880\pi$
$157$	1403.65	0.713527	0.356764	+	0.934195i	$0.383880\pi$
$158$	−2484.79	−1.25114
$159$	380.162	0.189615
$160$	−684.513	−0.338222
$161$	912.971	0.446908
$162$	−162.000	−0.0785674
$163$	566.263	0.272105	0.136053	−	0.990702i	$-0.456558\pi$
$163$	566.263	0.272105	0.136053	+	0.990702i	$0.456558\pi$
$164$	−150.939	−0.0718680
$165$	135.852	0.0640973
$166$	−1452.07	−0.678932
$167$	−2688.00	−1.24553	−0.622766	−	0.782408i	$-0.713991\pi$
$167$	−2688.00	−1.24553	−0.622766	+	0.782408i	$0.713991\pi$
$168$	292.055	0.134122
$169$	1808.85	0.823328
$170$	3821.42	1.72406
$171$	0	0
$172$	−1548.58	−0.686501
$173$	2885.59	1.26813	0.634067	−	0.773278i	$-0.281384\pi$
$173$	2885.59	1.26813	0.634067	+	0.773278i	$0.281384\pi$
$174$	234.047	0.101972
$175$	4047.11	1.74819
$176$	−33.8714	−0.0145065
$177$	1718.10	0.729607
$178$	−234.091	−0.0985721
$179$	−2105.39	−0.879132	−0.439566	−	0.898210i	$-0.644868\pi$
$179$	−2105.39	−0.879132	−0.439566	+	0.898210i	$0.644868\pi$
$180$	770.077	0.318879
$181$	−4295.22	−1.76388	−0.881938	−	0.471366i	$-0.843761\pi$
$181$	−4295.22	−1.76388	−0.881938	+	0.471366i	$0.843761\pi$
$182$	1540.39	0.627371
$183$	2203.83	0.890228
$184$	−600.196	−0.240473
$185$	2098.89	0.834125
$186$	−93.7406	−0.0369537
$187$	189.093	0.0739458
$188$	−1178.21	−0.457075
$189$	−328.562	−0.126452
$190$	0	0
$191$	1511.70	0.572684	0.286342	−	0.958127i	$-0.407561\pi$
$191$	1511.70	0.572684	0.286342	+	0.958127i	$0.407561\pi$
$192$	−192.000	−0.0721688
$193$	−4389.76	−1.63721	−0.818607	−	0.574354i	$-0.805253\pi$
$193$	−4389.76	−1.63721	−0.818607	+	0.574354i	$0.805253\pi$
$194$	2165.73	0.801495
$195$	4061.63	1.49159
$196$	−779.664	−0.284134
$197$	−1360.97	−0.492208	−0.246104	−	0.969243i	$-0.579150\pi$
$197$	−1360.97	−0.492208	−0.246104	+	0.969243i	$0.579150\pi$
$198$	38.1053	0.0136769
$199$	−3824.73	−1.36245	−0.681226	−	0.732073i	$-0.738553\pi$
$199$	−3824.73	−1.36245	−0.681226	+	0.732073i	$0.738553\pi$
$200$	−2660.61	−0.940668
$201$	2488.06	0.873107
$202$	3807.22	1.32611
$203$	474.686	0.164120
$204$	1071.88	0.367874
$205$	−807.186	−0.275006
$206$	−199.147	−0.0673554
$207$	675.221	0.226720
$208$	−1012.67	−0.337577
$209$	0	0
$210$	1561.84	0.513225
$211$	527.696	0.172171	0.0860856	−	0.996288i	$-0.472564\pi$
$211$	527.696	0.172171	0.0860856	+	0.996288i	$0.472564\pi$
$212$	−506.883	−0.164212
$213$	1334.67	0.429344
$214$	13.4811	0.00430632
$215$	−8281.44	−2.62693
$216$	216.000	0.0680414
$217$	−190.121	−0.0594759
$218$	−2245.12	−0.697516
$219$	−3408.34	−1.05166
$220$	−181.136	−0.0555099
$221$	5653.41	1.72077
$222$	588.719	0.177983
$223$	−1184.16	−0.355592	−0.177796	−	0.984067i	$-0.556897\pi$
$223$	−1184.16	−0.355592	−0.177796	+	0.984067i	$0.556897\pi$
$224$	−389.407	−0.116153
$225$	2993.19	0.886871
$226$	−472.593	−0.139099
$227$	4993.75	1.46012	0.730059	−	0.683384i	$-0.239493\pi$
$227$	4993.75	1.46012	0.730059	+	0.683384i	$0.239493\pi$
$228$	0	0
$229$	−3568.76	−1.02983	−0.514914	−	0.857242i	$-0.672176\pi$
$229$	−3568.76	−1.02983	−0.514914	+	0.857242i	$0.672176\pi$
$230$	−3209.70	−0.920181
$231$	77.2837	0.0220125
$232$	−312.063	−0.0883101
$233$	2055.11	0.577832	0.288916	−	0.957354i	$-0.406705\pi$
$233$	2055.11	0.577832	0.288916	+	0.957354i	$0.406705\pi$
$234$	1139.25	0.318270
$235$	−6300.80	−1.74902
$236$	−2290.80	−0.631859
$237$	−3727.19	−1.02155
$238$	2173.94	0.592082
$239$	6173.61	1.67087	0.835434	−	0.549590i	$-0.185216\pi$
$239$	6173.61	1.67087	0.835434	+	0.549590i	$0.185216\pi$
$240$	−1026.77	−0.276157
$241$	987.440	0.263928	0.131964	−	0.991255i	$-0.457872\pi$
$241$	987.440	0.263928	0.131964	+	0.991255i	$0.457872\pi$
$242$	2653.04	0.704726
$243$	−243.000	−0.0641500
$244$	−2938.44	−0.770960
$245$	−4169.46	−1.08725
$246$	−226.409	−0.0586800
$247$	0	0
$248$	124.988	0.0320029
$249$	−2178.11	−0.554345
$250$	−8880.55	−2.24662
$251$	−1398.52	−0.351689	−0.175845	−	0.984418i	$-0.556266\pi$
$251$	−1398.52	−0.351689	−0.175845	+	0.984418i	$0.556266\pi$
$252$	438.083	0.109510
$253$	−158.824	−0.0394671
$254$	−4709.47	−1.16338
$255$	5732.13	1.40769
$256$	256.000	0.0625000
$257$	6012.06	1.45923	0.729614	−	0.683859i	$-0.239700\pi$
$257$	6012.06	1.45923	0.729614	+	0.683859i	$0.239700\pi$
$258$	−2322.87	−0.560526
$259$	1194.02	0.286458
$260$	−5415.51	−1.29175
$261$	351.071	0.0832596
$262$	2893.87	0.682381
$263$	7110.33	1.66708	0.833540	−	0.552459i	$-0.186311\pi$
$263$	7110.33	1.66708	0.833540	+	0.552459i	$0.186311\pi$
$264$	−50.8071	−0.0118445
$265$	−2710.69	−0.628363
$266$	0	0
$267$	−351.136	−0.0804838
$268$	−3317.42	−0.756133
$269$	−381.888	−0.0865580	−0.0432790	−	0.999063i	$-0.513780\pi$
$269$	−381.888	−0.0865580	−0.0432790	+	0.999063i	$0.513780\pi$
$270$	1155.12	0.260363
$271$	5288.95	1.18554	0.592769	−	0.805373i	$-0.298035\pi$
$271$	5288.95	1.18554	0.592769	+	0.805373i	$0.298035\pi$
$272$	−1429.17	−0.318588
$273$	2310.59	0.512246
$274$	1561.14	0.344205
$275$	−704.051	−0.154385
$276$	−900.294	−0.196345
$277$	−335.159	−0.0726996	−0.0363498	−	0.999339i	$-0.511573\pi$
$277$	−335.159	−0.0726996	−0.0363498	+	0.999339i	$0.511573\pi$
$278$	3273.46	0.706219
$279$	−140.611	−0.0301726
$280$	−2082.46	−0.444466
$281$	−767.694	−0.162978	−0.0814890	−	0.996674i	$-0.525968\pi$
$281$	−767.694	−0.162978	−0.0814890	+	0.996674i	$0.525968\pi$
$282$	−1767.32	−0.373200
$283$	1928.31	0.405040	0.202520	−	0.979278i	$-0.435087\pi$
$283$	1928.31	0.405040	0.202520	+	0.979278i	$0.435087\pi$
$284$	−1779.56	−0.371823
$285$	0	0
$286$	−267.973	−0.0554040
$287$	−459.193	−0.0944436
$288$	−288.000	−0.0589256
$289$	3065.60	0.623977
$290$	−1668.84	−0.337923
$291$	3248.59	0.654418
$292$	4544.45	0.910766
$293$	6839.03	1.36362	0.681810	−	0.731529i	$-0.261193\pi$
$293$	6839.03	1.36362	0.681810	+	0.731529i	$0.261193\pi$
$294$	−1169.50	−0.231995
$295$	−12250.7	−2.41784
$296$	−784.959	−0.154138
$297$	57.1579	0.0111671
$298$	5365.45	1.04299
$299$	−4748.44	−0.918425
$300$	−3990.92	−0.768052
$301$	−4711.16	−0.902149
$302$	−543.145	−0.103492
$303$	5710.83	1.08277
$304$	0	0
$305$	−15714.1	−2.95011
$306$	1607.81	0.300368
$307$	4112.14	0.764469	0.382235	−	0.924065i	$-0.375155\pi$
$307$	4112.14	0.764469	0.382235	+	0.924065i	$0.375155\pi$
$308$	−103.045	−0.0190634
$309$	−298.720	−0.0549954
$310$	668.403	0.122460
$311$	7174.67	1.30816	0.654080	−	0.756425i	$-0.273056\pi$
$311$	7174.67	1.30816	0.654080	+	0.756425i	$0.273056\pi$
$312$	−1519.00	−0.275630
$313$	−1889.65	−0.341244	−0.170622	−	0.985337i	$-0.554578\pi$
$313$	−1889.65	−0.341244	−0.170622	+	0.985337i	$0.554578\pi$
$314$	−2807.31	−0.504540
$315$	2342.76	0.419047
$316$	4969.58	0.884686
$317$	−4751.63	−0.841887	−0.420944	−	0.907087i	$-0.638301\pi$
$317$	−4751.63	−0.841887	−0.420944	+	0.907087i	$0.638301\pi$
$318$	−760.325	−0.134078
$319$	−82.5782	−0.0144937
$320$	1369.03	0.239159
$321$	20.2217	0.00351610
$322$	−1825.94	−0.316012
$323$	0	0
$324$	324.000	0.0555556
$325$	−21049.4	−3.59264
$326$	−1132.53	−0.192407
$327$	−3367.67	−0.569519
$328$	301.878	0.0508184
$329$	−3584.41	−0.600654
$330$	−271.704	−0.0453237
$331$	−7691.90	−1.27730	−0.638648	−	0.769499i	$-0.720506\pi$
$331$	−7691.90	−1.27730	−0.638648	+	0.769499i	$0.720506\pi$
$332$	2904.14	0.480077
$333$	883.079	0.145323
$334$	5376.00	0.880724
$335$	−17740.8	−2.89338
$336$	−584.111	−0.0948388
$337$	367.161	0.0593487	0.0296743	−	0.999560i	$-0.490553\pi$
$337$	367.161	0.0593487	0.0296743	+	0.999560i	$0.490553\pi$
$338$	−3617.70	−0.582181
$339$	−708.890	−0.113574
$340$	−7642.85	−1.21909
$341$	33.0742	0.00525240
$342$	0	0
$343$	−6545.89	−1.03045
$344$	3097.16	0.485430
$345$	−4814.56	−0.751325
$346$	−5771.18	−0.896706
$347$	−5485.91	−0.848700	−0.424350	−	0.905498i	$-0.639497\pi$
$347$	−5485.91	−0.848700	−0.424350	+	0.905498i	$0.639497\pi$
$348$	−468.095	−0.0721049
$349$	363.584	0.0557657	0.0278828	−	0.999611i	$-0.491123\pi$
$349$	363.584	0.0557657	0.0278828	+	0.999611i	$0.491123\pi$
$350$	−8094.23	−1.23616
$351$	1708.88	0.259867
$352$	67.7427	0.0102577
$353$	973.496	0.146782	0.0733909	−	0.997303i	$-0.476618\pi$
$353$	973.496	0.146782	0.0733909	+	0.997303i	$0.476618\pi$
$354$	−3436.21	−0.515910
$355$	−9516.67	−1.42280
$356$	468.181	0.0697010
$357$	3260.91	0.483433
$358$	4210.79	0.621640
$359$	−2833.11	−0.416507	−0.208253	−	0.978075i	$-0.566778\pi$
$359$	−2833.11	−0.416507	−0.208253	+	0.978075i	$0.566778\pi$
$360$	−1540.15	−0.225481
$361$	0	0
$362$	8590.45	1.24725
$363$	3979.56	0.575406
$364$	−3080.78	−0.443618
$365$	24302.6	3.48509
$366$	−4407.66	−0.629486
$367$	−4286.17	−0.609635	−0.304818	−	0.952411i	$-0.598596\pi$
$367$	−4286.17	−0.609635	−0.304818	+	0.952411i	$0.598596\pi$
$368$	1200.39	0.170040
$369$	−339.613	−0.0479120
$370$	−4197.77	−0.589815
$371$	−1542.06	−0.215795
$372$	187.481	0.0261302
$373$	−13506.7	−1.87493	−0.937466	−	0.348077i	$-0.886835\pi$
$373$	−13506.7	−1.87493	−0.937466	+	0.348077i	$0.886835\pi$
$374$	−378.187	−0.0522876
$375$	−13320.8	−1.83436
$376$	2356.43	0.323201
$377$	−2468.88	−0.337278
$378$	657.125	0.0894149
$379$	1924.60	0.260845	0.130422	−	0.991459i	$-0.458367\pi$
$379$	1924.60	0.260845	0.130422	+	0.991459i	$0.458367\pi$
$380$	0	0
$381$	−7064.21	−0.949896
$382$	−3023.40	−0.404949
$383$	−5439.42	−0.725696	−0.362848	−	0.931848i	$-0.618196\pi$
$383$	−5439.42	−0.725696	−0.362848	+	0.931848i	$0.618196\pi$
$384$	384.000	0.0510310
$385$	−551.060	−0.0729470
$386$	8779.53	1.15768
$387$	−3484.31	−0.457667
$388$	−4331.45	−0.566742
$389$	−7238.10	−0.943409	−0.471705	−	0.881757i	$-0.656361\pi$
$389$	−7238.10	−0.943409	−0.471705	+	0.881757i	$0.656361\pi$
$390$	−8123.26	−1.05471
$391$	−6701.41	−0.866765
$392$	1559.33	0.200913
$393$	4340.80	0.557161
$394$	2721.94	0.348044
$395$	26576.1	3.38529
$396$	−76.2106	−0.00967103
$397$	−4101.14	−0.518464	−0.259232	−	0.965815i	$-0.583469\pi$
$397$	−4101.14	−0.518464	−0.259232	+	0.965815i	$0.583469\pi$
$398$	7649.46	0.963399
$399$	0	0
$400$	5321.22	0.665153
$401$	−8727.08	−1.08681	−0.543403	−	0.839472i	$-0.682865\pi$
$401$	−8727.08	−1.08681	−0.543403	+	0.839472i	$0.682865\pi$
$402$	−4976.13	−0.617380
$403$	988.835	0.122227
$404$	−7614.44	−0.937705
$405$	1732.67	0.212586
$406$	−949.372	−0.116051
$407$	−207.716	−0.0252975
$408$	−2143.75	−0.260126
$409$	12095.2	1.46228	0.731138	−	0.682229i	$-0.238989\pi$
$409$	12095.2	1.46228	0.731138	+	0.682229i	$0.238989\pi$
$410$	1614.37	0.194459
$411$	2341.71	0.281042
$412$	398.293	0.0476275
$413$	−6969.18	−0.830341
$414$	−1350.44	−0.160315
$415$	15530.7	1.83704
$416$	2025.34	0.238703
$417$	4910.19	0.576626
$418$	0	0
$419$	6332.87	0.738379	0.369190	−	0.929354i	$-0.379635\pi$
$419$	6332.87	0.738379	0.369190	+	0.929354i	$0.379635\pi$
$420$	−3123.68	−0.362905
$421$	−4182.79	−0.484220	−0.242110	−	0.970249i	$-0.577840\pi$
$421$	−4182.79	−0.484220	−0.242110	+	0.970249i	$0.577840\pi$
$422$	−1055.39	−0.121743
$423$	−2650.98	−0.304717
$424$	1013.77	0.116115
$425$	−29706.7	−3.39056
$426$	−2669.34	−0.303592
$427$	−8939.44	−1.01314
$428$	−26.9623	−0.00304503
$429$	−401.959	−0.0452372
$430$	16562.9	1.85752
$431$	−6892.39	−0.770289	−0.385145	−	0.922856i	$-0.625848\pi$
$431$	−6892.39	−0.770289	−0.385145	+	0.922856i	$0.625848\pi$
$432$	−432.000	−0.0481125
$433$	−14320.5	−1.58937	−0.794685	−	0.607021i	$-0.792364\pi$
$433$	−14320.5	−1.58937	−0.794685	+	0.607021i	$0.792364\pi$
$434$	380.242	0.0420558
$435$	−2503.26	−0.275913
$436$	4490.23	0.493218
$437$	0	0
$438$	6816.67	0.743637
$439$	1500.59	0.163142	0.0815709	−	0.996668i	$-0.474006\pi$
$439$	1500.59	0.163142	0.0815709	+	0.996668i	$0.474006\pi$
$440$	362.272	0.0392514
$441$	−1754.24	−0.189423
$442$	−11306.8	−1.21677
$443$	−3265.45	−0.350217	−0.175109	−	0.984549i	$-0.556028\pi$
$443$	−3265.45	−0.350217	−0.175109	+	0.984549i	$0.556028\pi$
$444$	−1177.44	−0.125853
$445$	2503.72	0.266714
$446$	2368.31	0.251442
$447$	8048.18	0.851601
$448$	778.814	0.0821328
$449$	2539.97	0.266968	0.133484	−	0.991051i	$-0.457384\pi$
$449$	2539.97	0.266968	0.133484	+	0.991051i	$0.457384\pi$
$450$	−5986.38	−0.627112
$451$	79.8830	0.00834045
$452$	945.186	0.0983580
$453$	−814.717	−0.0845005
$454$	−9987.49	−1.03246
$455$	−16475.3	−1.69752
$456$	0	0
$457$	600.612	0.0614780	0.0307390	−	0.999527i	$-0.490214\pi$
$457$	600.612	0.0614780	0.0307390	+	0.999527i	$0.490214\pi$
$458$	7137.52	0.728198
$459$	2411.72	0.245249
$460$	6419.41	0.650666
$461$	1706.43	0.172400	0.0862002	−	0.996278i	$-0.472528\pi$
$461$	1706.43	0.172400	0.0862002	+	0.996278i	$0.472528\pi$
$462$	−154.567	−0.0155652
$463$	4467.57	0.448435	0.224218	−	0.974539i	$-0.428017\pi$
$463$	4467.57	0.448435	0.224218	+	0.974539i	$0.428017\pi$
$464$	624.126	0.0624447
$465$	1002.60	0.0999885
$466$	−4110.23	−0.408589
$467$	12331.4	1.22191	0.610954	−	0.791666i	$-0.290786\pi$
$467$	12331.4	1.22191	0.610954	+	0.791666i	$0.290786\pi$
$468$	−2278.50	−0.225051
$469$	−10092.4	−0.993653
$470$	12601.6	1.23674
$471$	−4210.96	−0.411955
$472$	4581.61	0.446791
$473$	819.571	0.0796700
$474$	7454.38	0.722343
$475$	0	0
$476$	−4347.88	−0.418665
$477$	−1140.49	−0.109474
$478$	−12347.2	−1.18148
$479$	−4454.20	−0.424880	−0.212440	−	0.977174i	$-0.568141\pi$
$479$	−4454.20	−0.424880	−0.212440	+	0.977174i	$0.568141\pi$
$480$	2053.54	0.195273
$481$	−6210.18	−0.588690
$482$	−1974.88	−0.186625
$483$	−2738.91	−0.258023
$484$	−5306.07	−0.498316
$485$	−23163.6	−2.16867
$486$	486.000	0.0453609
$487$	10919.8	1.01607	0.508034	−	0.861337i	$-0.330373\pi$
$487$	10919.8	1.01607	0.508034	+	0.861337i	$0.330373\pi$
$488$	5876.87	0.545151
$489$	−1698.79	−0.157100
$490$	8338.91	0.768804
$491$	11229.5	1.03214	0.516071	−	0.856546i	$-0.327394\pi$
$491$	11229.5	1.03214	0.516071	+	0.856546i	$0.327394\pi$
$492$	452.817	0.0414930
$493$	−3484.30	−0.318306
$494$	0	0
$495$	−407.556	−0.0370066
$496$	−249.975	−0.0226295
$497$	−5413.86	−0.488622
$498$	4356.22	0.391981
$499$	−9821.59	−0.881112	−0.440556	−	0.897725i	$-0.645219\pi$
$499$	−9821.59	−0.881112	−0.440556	+	0.897725i	$0.645219\pi$
$500$	17761.1	1.58860
$501$	8064.00	0.719108
$502$	2797.05	0.248682
$503$	17123.7	1.51791	0.758956	−	0.651142i	$-0.225710\pi$
$503$	17123.7	1.51791	0.758956	+	0.651142i	$0.225710\pi$
$504$	−876.166	−0.0774356
$505$	−40720.2	−3.58817
$506$	317.648	0.0279075
$507$	−5426.56	−0.475349
$508$	9418.94	0.822634
$509$	13865.6	1.20743	0.603715	−	0.797201i	$-0.293687\pi$
$509$	13865.6	1.20743	0.603715	+	0.797201i	$0.293687\pi$
$510$	−11464.3	−0.995385
$511$	13825.3	1.19686
$512$	−512.000	−0.0441942
$513$	0	0
$514$	−12024.1	−1.03183
$515$	2129.98	0.182249
$516$	4645.74	0.396352
$517$	623.558	0.0530446
$518$	−2388.04	−0.202557
$519$	−8656.76	−0.732157
$520$	10831.0	0.913407
$521$	−5692.46	−0.478678	−0.239339	−	0.970936i	$-0.576931\pi$
$521$	−5692.46	−0.478678	−0.239339	+	0.970936i	$0.576931\pi$
$522$	−702.142	−0.0588734
$523$	−6132.02	−0.512686	−0.256343	−	0.966586i	$-0.582518\pi$
$523$	−6132.02	−0.512686	−0.256343	+	0.966586i	$0.582518\pi$
$524$	−5787.73	−0.482516
$525$	−12141.3	−1.00932
$526$	−14220.7	−1.17880
$527$	1395.53	0.115352
$528$	101.614	0.00837535
$529$	−6538.32	−0.537382
$530$	5421.38	0.444320
$531$	−5154.31	−0.421239
$532$	0	0
$533$	2388.30	0.194088
$534$	702.272	0.0569106
$535$	−144.188	−0.0116519
$536$	6634.84	0.534667
$537$	6316.18	0.507567
$538$	763.776	0.0612058
$539$	412.630	0.0329744
$540$	−2310.23	−0.184105
$541$	−6558.08	−0.521172	−0.260586	−	0.965451i	$-0.583916\pi$
$541$	−6558.08	−0.521172	−0.260586	+	0.965451i	$0.583916\pi$
$542$	−10577.9	−0.838302
$543$	12885.7	1.01837
$544$	2858.34	0.225276
$545$	24012.7	1.88732
$546$	−4621.18	−0.362213
$547$	−6692.88	−0.523157	−0.261578	−	0.965182i	$-0.584243\pi$
$547$	−6692.88	−0.523157	−0.261578	+	0.965182i	$0.584243\pi$
$548$	−3122.28	−0.243389
$549$	−6611.48	−0.513973
$550$	1408.10	0.109167
$551$	0	0
$552$	1800.59	0.138837
$553$	15118.7	1.16259
$554$	670.319	0.0514063
$555$	−6296.66	−0.481582
$556$	−6546.92	−0.499373
$557$	−2138.25	−0.162658	−0.0813289	−	0.996687i	$-0.525916\pi$
$557$	−2138.25	−0.162658	−0.0813289	+	0.996687i	$0.525916\pi$
$558$	281.222	0.0213353
$559$	24503.1	1.85397
$560$	4164.91	0.314285
$561$	−567.280	−0.0426926
$562$	1535.39	0.115243
$563$	11288.6	0.845042	0.422521	−	0.906353i	$-0.361145\pi$
$563$	11288.6	0.845042	0.422521	+	0.906353i	$0.361145\pi$
$564$	3534.64	0.263892
$565$	5054.63	0.376371
$566$	−3856.63	−0.286407
$567$	985.687	0.0730070
$568$	3559.13	0.262918
$569$	−10164.6	−0.748899	−0.374450	−	0.927247i	$-0.622168\pi$
$569$	−10164.6	−0.748899	−0.374450	+	0.927247i	$0.622168\pi$
$570$	0	0
$571$	−19104.8	−1.40019	−0.700096	−	0.714049i	$-0.746859\pi$
$571$	−19104.8	−1.40019	−0.700096	+	0.714049i	$0.746859\pi$
$572$	535.945	0.0391766
$573$	−4535.10	−0.330639
$574$	918.387	0.0667817
$575$	24951.4	1.80964
$576$	576.000	0.0416667
$577$	−11569.4	−0.834729	−0.417365	−	0.908739i	$-0.637046\pi$
$577$	−11569.4	−0.834729	−0.417365	+	0.908739i	$0.637046\pi$
$578$	−6131.19	−0.441218
$579$	13169.3	0.945246
$580$	3337.68	0.238947
$581$	8835.11	0.630882
$582$	−6497.18	−0.462743
$583$	268.263	0.0190571
$584$	−9088.89	−0.644009
$585$	−12184.9	−0.861168
$586$	−13678.1	−0.964225
$587$	23990.8	1.68689	0.843447	−	0.537212i	$-0.180522\pi$
$587$	23990.8	1.68689	0.843447	+	0.537212i	$0.180522\pi$
$588$	2338.99	0.164045
$589$	0	0
$590$	24501.3	1.70967
$591$	4082.90	0.284176
$592$	1569.92	0.108992
$593$	−11233.0	−0.777881	−0.388940	−	0.921263i	$-0.627159\pi$
$593$	−11233.0	−0.777881	−0.388940	+	0.921263i	$0.627159\pi$
$594$	−114.316	−0.00789636
$595$	−23251.4	−1.60204
$596$	−10730.9	−0.737508
$597$	11474.2	0.786612
$598$	9496.87	0.649425
$599$	−13778.8	−0.939878	−0.469939	−	0.882699i	$-0.655724\pi$
$599$	−13778.8	−0.939878	−0.469939	+	0.882699i	$0.655724\pi$
$600$	7981.83	0.543095
$601$	9502.60	0.644957	0.322478	−	0.946577i	$-0.395484\pi$
$601$	9502.60	0.644957	0.322478	+	0.946577i	$0.395484\pi$
$602$	9422.32	0.637915
$603$	−7464.19	−0.504089
$604$	1086.29	0.0731796
$605$	−28375.6	−1.90683
$606$	−11421.7	−0.765633
$607$	1737.13	0.116158	0.0580791	−	0.998312i	$-0.481502\pi$
$607$	1737.13	0.116158	0.0580791	+	0.998312i	$0.481502\pi$
$608$	0	0
$609$	−1424.06	−0.0947549
$610$	31428.1	2.08604
$611$	18642.8	1.23438
$612$	−3215.63	−0.212392
$613$	−16093.3	−1.06036	−0.530181	−	0.847885i	$-0.677876\pi$
$613$	−16093.3	−1.06036	−0.530181	+	0.847885i	$0.677876\pi$
$614$	−8224.28	−0.540562
$615$	2421.56	0.158775
$616$	206.090	0.0134799
$617$	3836.13	0.250303	0.125151	−	0.992138i	$-0.460058\pi$
$617$	3836.13	0.250303	0.125151	+	0.992138i	$0.460058\pi$
$618$	597.440	0.0388877
$619$	19825.1	1.28730	0.643650	−	0.765320i	$-0.277419\pi$
$619$	19825.1	1.28730	0.643650	+	0.765320i	$0.277419\pi$
$620$	−1336.81	−0.0865926
$621$	−2025.66	−0.130897
$622$	−14349.3	−0.925009
$623$	1424.32	0.0915958
$624$	3038.01	0.194900
$625$	53410.0	3.41824
$626$	3779.31	0.241296
$627$	0	0
$628$	5614.62	0.356764
$629$	−8764.36	−0.555577
$630$	−4685.52	−0.296311
$631$	−12653.9	−0.798328	−0.399164	−	0.916880i	$-0.630700\pi$
$631$	−12653.9	−0.798328	−0.399164	+	0.916880i	$0.630700\pi$
$632$	−9939.17	−0.625568
$633$	−1583.09	−0.0994030
$634$	9503.26	0.595304
$635$	50370.2	3.14785
$636$	1520.65	0.0948076
$637$	12336.6	0.767337
$638$	165.156	0.0102486
$639$	−4004.02	−0.247882
$640$	−2738.05	−0.169111
$641$	1095.79	0.0675213	0.0337606	−	0.999430i	$-0.489252\pi$
$641$	1095.79	0.0675213	0.0337606	+	0.999430i	$0.489252\pi$
$642$	−40.4434	−0.00248625
$643$	10839.2	0.664785	0.332393	−	0.943141i	$-0.392144\pi$
$643$	10839.2	0.664785	0.332393	+	0.943141i	$0.392144\pi$
$644$	3651.89	0.223454
$645$	24844.3	1.51666
$646$	0	0
$647$	−2242.23	−0.136246	−0.0681231	−	0.997677i	$-0.521701\pi$
$647$	−2242.23	−0.136246	−0.0681231	+	0.997677i	$0.521701\pi$
$648$	−648.000	−0.0392837
$649$	1212.39	0.0733286
$650$	42098.7	2.54038
$651$	570.364	0.0343384
$652$	2265.05	0.136053
$653$	−31828.9	−1.90744	−0.953722	−	0.300690i	$-0.902783\pi$
$653$	−31828.9	−1.90744	−0.953722	+	0.300690i	$0.902783\pi$
$654$	6735.35	0.402711
$655$	−30951.4	−1.84637
$656$	−603.756	−0.0359340
$657$	10225.0	0.607177
$658$	7168.83	0.424726
$659$	10994.2	0.649884	0.324942	−	0.945734i	$-0.394655\pi$
$659$	10994.2	0.649884	0.324942	+	0.945734i	$0.394655\pi$
$660$	543.408	0.0320487
$661$	−13667.2	−0.804226	−0.402113	−	0.915590i	$-0.631724\pi$
$661$	−13667.2	−0.804226	−0.402113	+	0.915590i	$0.631724\pi$
$662$	15383.8	0.903185
$663$	−16960.2	−0.993486
$664$	−5808.29	−0.339466
$665$	0	0
$666$	−1766.16	−0.102759
$667$	2926.55	0.169890
$668$	−10752.0	−0.622766
$669$	3552.47	0.205301
$670$	35481.5	2.04593
$671$	1555.14	0.0894717
$672$	1168.22	0.0670612
$673$	−19357.4	−1.10872	−0.554362	−	0.832275i	$-0.687038\pi$
$673$	−19357.4	−1.10872	−0.554362	+	0.832275i	$0.687038\pi$
$674$	−734.321	−0.0419659
$675$	−8979.56	−0.512035
$676$	7235.41	0.411664
$677$	4164.98	0.236445	0.118222	−	0.992987i	$-0.462280\pi$
$677$	4164.98	0.236445	0.118222	+	0.992987i	$0.462280\pi$
$678$	1417.78	0.0803090
$679$	−13177.3	−0.744771
$680$	15285.7	0.862029
$681$	−14981.2	−0.842999
$682$	−66.1484	−0.00371401
$683$	−19434.0	−1.08876	−0.544378	−	0.838840i	$-0.683234\pi$
$683$	−19434.0	−1.08876	−0.544378	+	0.838840i	$0.683234\pi$
$684$	0	0
$685$	−16697.2	−0.931340
$686$	13091.8	0.728639
$687$	10706.3	0.594571
$688$	−6194.32	−0.343251
$689$	8020.39	0.443472
$690$	9629.11	0.531267
$691$	15820.1	0.870946	0.435473	−	0.900202i	$-0.356581\pi$
$691$	15820.1	0.870946	0.435473	+	0.900202i	$0.356581\pi$
$692$	11542.4	0.634067
$693$	−231.851	−0.0127089
$694$	10971.8	0.600122
$695$	−35011.3	−1.91087
$696$	936.189	0.0509859
$697$	3370.58	0.183171
$698$	−727.169	−0.0394323
$699$	−6165.34	−0.333612
$700$	16188.5	0.874094
$701$	−18750.8	−1.01028	−0.505140	−	0.863037i	$-0.668559\pi$
$701$	−18750.8	−1.01028	−0.505140	+	0.863037i	$0.668559\pi$
$702$	−3417.76	−0.183753
$703$	0	0
$704$	−135.485	−0.00725327
$705$	18902.4	1.00980
$706$	−1946.99	−0.103790
$707$	−23165.0	−1.23226
$708$	6872.41	0.364804
$709$	−25042.8	−1.32652	−0.663261	−	0.748388i	$-0.730828\pi$
$709$	−25042.8	−1.32652	−0.663261	+	0.748388i	$0.730828\pi$
$710$	19033.3	1.00607
$711$	11181.6	0.589791
$712$	−936.362	−0.0492860
$713$	−1172.14	−0.0615666
$714$	−6521.81	−0.341839
$715$	2866.10	0.149911
$716$	−8421.58	−0.439566
$717$	−18520.8	−0.964676
$718$	5666.23	0.294515
$719$	−3267.61	−0.169487	−0.0847437	−	0.996403i	$-0.527007\pi$
$719$	−3267.61	−0.169487	−0.0847437	+	0.996403i	$0.527007\pi$
$720$	3080.31	0.159439
$721$	1211.71	0.0625884
$722$	0	0
$723$	−2962.32	−0.152379
$724$	−17180.9	−0.881938
$725$	12973.1	0.664564
$726$	−7959.11	−0.406874
$727$	9242.83	0.471523	0.235762	−	0.971811i	$-0.424242\pi$
$727$	9242.83	0.471523	0.235762	+	0.971811i	$0.424242\pi$
$728$	6161.57	0.313685
$729$	729.000	0.0370370
$730$	−48605.2	−2.46433
$731$	34581.0	1.74969
$732$	8815.31	0.445114
$733$	9829.38	0.495302	0.247651	−	0.968849i	$-0.420341\pi$
$733$	9829.38	0.495302	0.247651	+	0.968849i	$0.420341\pi$
$734$	8572.34	0.431077
$735$	12508.4	0.627726
$736$	−2400.78	−0.120237
$737$	1755.71	0.0877510
$738$	679.226	0.0338789
$739$	−26225.2	−1.30543	−0.652714	−	0.757605i	$-0.726370\pi$
$739$	−26225.2	−1.30543	−0.652714	+	0.757605i	$0.726370\pi$
$740$	8395.54	0.417063
$741$	0	0
$742$	3084.12	0.152590
$743$	24816.4	1.22533	0.612667	−	0.790341i	$-0.290097\pi$
$743$	24816.4	1.22533	0.612667	+	0.790341i	$0.290097\pi$
$744$	−374.963	−0.0184769
$745$	−57386.3	−2.82211
$746$	27013.4	1.32578
$747$	6534.32	0.320051
$748$	756.373	0.0369729
$749$	−82.0259	−0.00400155
$750$	26641.7	1.29709
$751$	7397.68	0.359447	0.179724	−	0.983717i	$-0.442480\pi$
$751$	7397.68	0.359447	0.179724	+	0.983717i	$0.442480\pi$
$752$	−4712.86	−0.228537
$753$	4195.57	0.203048
$754$	4937.76	0.238491
$755$	5809.21	0.280025
$756$	−1314.25	−0.0632259
$757$	−32823.1	−1.57592	−0.787962	−	0.615723i	$-0.788864\pi$
$757$	−32823.1	−1.57592	−0.787962	+	0.615723i	$0.788864\pi$
$758$	−3849.20	−0.184445
$759$	476.472	0.0227863
$760$	0	0
$761$	1239.56	0.0590460	0.0295230	−	0.999564i	$-0.490601\pi$
$761$	1239.56	0.0590460	0.0295230	+	0.999564i	$0.490601\pi$
$762$	14128.4	0.671678
$763$	13660.4	0.648150
$764$	6046.80	0.286342
$765$	−17196.4	−0.812728
$766$	10878.8	0.513144
$767$	36247.3	1.70641
$768$	−768.000	−0.0360844
$769$	−29780.5	−1.39650	−0.698252	−	0.715852i	$-0.746039\pi$
$769$	−29780.5	−1.39650	−0.698252	+	0.715852i	$0.746039\pi$
$770$	1102.12	0.0515813
$771$	−18036.2	−0.842486
$772$	−17559.1	−0.818607
$773$	2539.89	0.118180	0.0590902	−	0.998253i	$-0.481180\pi$
$773$	2539.89	0.118180	0.0590902	+	0.998253i	$0.481180\pi$
$774$	6968.61	0.323620
$775$	−5195.99	−0.240833
$776$	8662.90	0.400747
$777$	−3582.05	−0.165387
$778$	14476.2	0.667091
$779$	0	0
$780$	16246.5	0.745794
$781$	941.816	0.0431509
$782$	13402.8	0.612895
$783$	−1053.21	−0.0480699
$784$	−3118.66	−0.142067
$785$	30025.6	1.36517
$786$	−8681.60	−0.393973
$787$	−39991.2	−1.81135	−0.905674	−	0.423975i	$-0.860634\pi$
$787$	−39991.2	−1.81135	−0.905674	+	0.423975i	$0.860634\pi$
$788$	−5443.87	−0.246104
$789$	−21331.0	−0.962489
$790$	−53152.3	−2.39376
$791$	2875.49	0.129255
$792$	152.421	0.00683845
$793$	46494.7	2.08206
$794$	8202.27	0.366609
$795$	8132.07	0.362786
$796$	−15298.9	−0.681226
$797$	−12485.1	−0.554887	−0.277444	−	0.960742i	$-0.589487\pi$
$797$	−12485.1	−0.554887	−0.277444	+	0.960742i	$0.589487\pi$
$798$	0	0
$799$	26310.4	1.16495
$800$	−10642.4	−0.470334
$801$	1053.41	0.0464673
$802$	17454.2	0.768488
$803$	−2405.10	−0.105696
$804$	9952.26	0.436553
$805$	19529.4	0.855057
$806$	−1977.67	−0.0864274
$807$	1145.66	0.0499743
$808$	15228.9	0.663057
$809$	4250.78	0.184734	0.0923668	−	0.995725i	$-0.470557\pi$
$809$	4250.78	0.184734	0.0923668	+	0.995725i	$0.470557\pi$
$810$	−3465.35	−0.150321
$811$	−3410.65	−0.147674	−0.0738372	−	0.997270i	$-0.523525\pi$
$811$	−3410.65	−0.147674	−0.0738372	+	0.997270i	$0.523525\pi$
$812$	1898.74	0.0820602
$813$	−15866.8	−0.684470
$814$	415.432	0.0178881
$815$	12113.0	0.520611
$816$	4287.50	0.183937
$817$	0	0
$818$	−24190.5	−1.03399
$819$	−6931.77	−0.295745
$820$	−3228.74	−0.137503
$821$	−5328.70	−0.226520	−0.113260	−	0.993565i	$-0.536129\pi$
$821$	−5328.70	−0.226520	−0.113260	+	0.993565i	$0.536129\pi$
$822$	−4683.43	−0.198727
$823$	−7325.02	−0.310248	−0.155124	−	0.987895i	$-0.549578\pi$
$823$	−7325.02	−0.310248	−0.155124	+	0.987895i	$0.549578\pi$
$824$	−796.587	−0.0336777
$825$	2112.15	0.0891343
$826$	13938.4	0.587140
$827$	35885.9	1.50892	0.754458	−	0.656348i	$-0.227900\pi$
$827$	35885.9	1.50892	0.754458	+	0.656348i	$0.227900\pi$
$828$	2700.88	0.113360
$829$	13361.9	0.559803	0.279901	−	0.960029i	$-0.409698\pi$
$829$	13361.9	0.559803	0.279901	+	0.960029i	$0.409698\pi$
$830$	−31061.3	−1.29898
$831$	1005.48	0.0419731
$832$	−4050.68	−0.168788
$833$	17410.5	0.724175
$834$	−9820.38	−0.407736
$835$	−57499.1	−2.38304
$836$	0	0
$837$	421.833	0.0174202
$838$	−12665.7	−0.522113
$839$	33872.4	1.39381	0.696903	−	0.717165i	$-0.254561\pi$
$839$	33872.4	1.39381	0.696903	+	0.717165i	$0.254561\pi$
$840$	6247.37	0.256613
$841$	−22867.4	−0.937611
$842$	8365.58	0.342395
$843$	2303.08	0.0940954
$844$	2110.78	0.0860856
$845$	38693.2	1.57525
$846$	5301.96	0.215467
$847$	−16142.4	−0.654850
$848$	−2027.53	−0.0821058
$849$	−5784.94	−0.233850
$850$	59413.4	2.39749
$851$	7361.40	0.296528
$852$	5338.69	0.214672
$853$	10425.0	0.418460	0.209230	−	0.977866i	$-0.432904\pi$
$853$	10425.0	0.418460	0.209230	+	0.977866i	$0.432904\pi$
$854$	17878.9	0.716397
$855$	0	0
$856$	53.9246	0.00215316
$857$	−29022.6	−1.15682	−0.578409	−	0.815747i	$-0.696326\pi$
$857$	−29022.6	−1.15682	−0.578409	+	0.815747i	$0.696326\pi$
$858$	803.918	0.0319875
$859$	−17679.4	−0.702227	−0.351113	−	0.936333i	$-0.614197\pi$
$859$	−17679.4	−0.702227	−0.351113	+	0.936333i	$0.614197\pi$
$860$	−33125.7	−1.31346
$861$	1377.58	0.0545271
$862$	13784.8	0.544677
$863$	−27435.9	−1.08219	−0.541094	−	0.840962i	$-0.681990\pi$
$863$	−27435.9	−1.08219	−0.541094	+	0.840962i	$0.681990\pi$
$864$	864.000	0.0340207
$865$	61725.7	2.42629
$866$	28640.9	1.12385
$867$	−9196.79	−0.360253
$868$	−760.485	−0.0297379
$869$	−2630.10	−0.102670
$870$	5006.52	0.195100
$871$	52491.3	2.04202
$872$	−8980.46	−0.348758
$873$	−9745.76	−0.377828
$874$	0	0
$875$	54033.6	2.08762
$876$	−13633.3	−0.525831
$877$	−2951.40	−0.113639	−0.0568196	−	0.998384i	$-0.518096\pi$
$877$	−2951.40	−0.113639	−0.0568196	+	0.998384i	$0.518096\pi$
$878$	−3001.18	−0.115359
$879$	−20517.1	−0.787286
$880$	−724.544	−0.0277550
$881$	31058.2	1.18771	0.593857	−	0.804571i	$-0.297605\pi$
$881$	31058.2	1.18771	0.593857	+	0.804571i	$0.297605\pi$
$882$	3508.49	0.133942
$883$	−16218.7	−0.618124	−0.309062	−	0.951042i	$-0.600015\pi$
$883$	−16218.7	−0.618124	−0.309062	+	0.951042i	$0.600015\pi$
$884$	22613.7	0.860384
$885$	36752.0	1.39594
$886$	6530.90	0.247641
$887$	47549.8	1.79996	0.899980	−	0.435930i	$-0.143581\pi$
$887$	47549.8	1.79996	0.899980	+	0.435930i	$0.143581\pi$
$888$	2354.88	0.0889915
$889$	28654.7	1.08104
$890$	−5007.44	−0.188595
$891$	−171.474	−0.00644735
$892$	−4736.63	−0.177796
$893$	0	0
$894$	−16096.4	−0.602173
$895$	−45036.6	−1.68202
$896$	−1557.63	−0.0580767
$897$	14245.3	0.530253
$898$	−5079.93	−0.188775
$899$	−609.437	−0.0226094
$900$	11972.8	0.443435
$901$	11319.1	0.418527
$902$	−159.766	−0.00589759
$903$	14133.5	0.520856
$904$	−1890.37	−0.0695496
$905$	−91879.3	−3.37477
$906$	1629.43	0.0597509
$907$	−11930.0	−0.436746	−0.218373	−	0.975865i	$-0.570075\pi$
$907$	−11930.0	−0.436746	−0.218373	+	0.975865i	$0.570075\pi$
$908$	19975.0	0.730059
$909$	−17132.5	−0.625137
$910$	32950.6	1.20033
$911$	34938.4	1.27065	0.635324	−	0.772246i	$-0.280866\pi$
$911$	34938.4	1.27065	0.635324	+	0.772246i	$0.280866\pi$
$912$	0	0
$913$	−1536.99	−0.0557141
$914$	−1201.22	−0.0434715
$915$	47142.2	1.70325
$916$	−14275.0	−0.514914
$917$	−17607.7	−0.634087
$918$	−4823.44	−0.173418
$919$	−20037.1	−0.719220	−0.359610	−	0.933103i	$-0.617090\pi$
$919$	−20037.1	−0.719220	−0.359610	+	0.933103i	$0.617090\pi$
$920$	−12838.8	−0.460091
$921$	−12336.4	−0.441367
$922$	−3412.87	−0.121905
$923$	28157.9	1.00415
$924$	309.135	0.0110063
$925$	32632.4	1.15994
$926$	−8935.14	−0.317092
$927$	896.160	0.0317516
$928$	−1248.25	−0.0441551
$929$	−42395.7	−1.49726	−0.748632	−	0.662986i	$-0.769289\pi$
$929$	−42395.7	−1.49726	−0.748632	+	0.662986i	$0.769289\pi$
$930$	−2005.21	−0.0707026
$931$	0	0
$932$	8220.45	0.288916
$933$	−21524.0	−0.755267
$934$	−24662.9	−0.864019
$935$	4044.90	0.141479
$936$	4557.01	0.159135
$937$	24297.8	0.847145	0.423573	−	0.905862i	$-0.360776\pi$
$937$	24297.8	0.847145	0.423573	+	0.905862i	$0.360776\pi$
$938$	20184.8	0.702619
$939$	5668.96	0.197018
$940$	−25203.2	−0.874509
$941$	35530.2	1.23087	0.615437	−	0.788186i	$-0.288980\pi$
$941$	35530.2	1.23087	0.615437	+	0.788186i	$0.288980\pi$
$942$	8421.92	0.291296
$943$	−2831.03	−0.0977636
$944$	−9163.21	−0.315929
$945$	−7028.29	−0.241937
$946$	−1639.14	−0.0563352
$947$	−26605.7	−0.912956	−0.456478	−	0.889735i	$-0.650889\pi$
$947$	−26605.7	−0.912956	−0.456478	+	0.889735i	$0.650889\pi$
$948$	−14908.8	−0.510774
$949$	−71906.6	−2.45963
$950$	0	0
$951$	14254.9	0.486064
$952$	8695.75	0.296041
$953$	8588.04	0.291914	0.145957	−	0.989291i	$-0.453374\pi$
$953$	8588.04	0.291914	0.145957	+	0.989291i	$0.453374\pi$
$954$	2280.97	0.0774101
$955$	32336.8	1.09570
$956$	24694.4	0.835434
$957$	247.735	0.00836794
$958$	8908.40	0.300435
$959$	−9498.75	−0.319844
$960$	−4107.08	−0.138079
$961$	−29546.9	−0.991807
$962$	12420.4	0.416267
$963$	−60.6652	−0.00203002
$964$	3949.76	0.131964
$965$	−93901.6	−3.13244
$966$	5477.83	0.182449
$967$	−23018.2	−0.765475	−0.382738	−	0.923857i	$-0.625019\pi$
$967$	−23018.2	−0.765475	−0.382738	+	0.923857i	$0.625019\pi$
$968$	10612.1	0.352363
$969$	0	0
$970$	46327.1	1.53348
$971$	18916.0	0.625173	0.312586	−	0.949889i	$-0.398805\pi$
$971$	18916.0	0.625173	0.312586	+	0.949889i	$0.398805\pi$
$972$	−972.000	−0.0320750
$973$	−19917.3	−0.656238
$974$	−21839.7	−0.718468
$975$	63148.1	2.07421
$976$	−11753.7	−0.385480
$977$	−18663.7	−0.611160	−0.305580	−	0.952166i	$-0.598850\pi$
$977$	−18663.7	−0.611160	−0.305580	+	0.952166i	$0.598850\pi$
$978$	3397.58	0.111086
$979$	−247.780	−0.00808896
$980$	−16677.8	−0.543626
$981$	10103.0	0.328812
$982$	−22459.1	−0.729835
$983$	−3134.24	−0.101695	−0.0508477	−	0.998706i	$-0.516192\pi$
$983$	−3134.24	−0.101695	−0.0508477	+	0.998706i	$0.516192\pi$
$984$	−905.634	−0.0293400
$985$	−29112.5	−0.941728
$986$	6968.60	0.225077
$987$	10753.2	0.346788
$988$	0	0
$989$	−29045.4	−0.933862
$990$	815.112	0.0261676
$991$	−41605.7	−1.33365	−0.666826	−	0.745214i	$-0.732347\pi$
$991$	−41605.7	−1.33365	−0.666826	+	0.745214i	$0.732347\pi$
$992$	499.950	0.0160014
$993$	23075.7	0.737447
$994$	10827.7	0.345508
$995$	−81815.0	−2.60674
$996$	−8712.43	−0.277173
$997$	31942.2	1.01466	0.507332	−	0.861751i	$-0.330632\pi$
$997$	31942.2	1.01466	0.507332	+	0.861751i	$0.330632\pi$
$998$	19643.2	0.623040
$999$	−2649.24	−0.0839020

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2166.4.a.bj.1.9		9
19.2	odd	18		114.4.i.d.61.3	yes	18
19.10	odd	18		114.4.i.d.43.3	✓	18
19.18	odd	2		2166.4.a.bm.1.9		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.4.i.d.43.3	✓	18	19.10	odd	18
114.4.i.d.61.3	yes	18	19.2	odd	18
2166.4.a.bj.1.9		9	1.1	even	1	trivial
2166.4.a.bm.1.9		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)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +21.3910 q^{5} +6.00000 q^{6} +12.1690 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +21.3910 q^{5} +6.00000 q^{6} +12.1690 q^{7} -8.00000 q^{8} +9.00000 q^{9} -42.7821 q^{10} -2.11696 q^{11} -12.0000 q^{12} -63.2918 q^{13} -24.3379 q^{14} -64.1731 q^{15} +16.0000 q^{16} -89.3230 q^{17} -18.0000 q^{18} +85.5641 q^{20} -36.5069 q^{21} +4.23392 q^{22} +75.0245 q^{23} +24.0000 q^{24} +332.576 q^{25} +126.584 q^{26} -27.0000 q^{27} +48.6759 q^{28} +39.0079 q^{29} +128.346 q^{30} -15.6234 q^{31} -32.0000 q^{32} +6.35088 q^{33} +178.646 q^{34} +260.307 q^{35} +36.0000 q^{36} +98.1199 q^{37} +189.875 q^{39} -171.128 q^{40} -37.7348 q^{41} +73.0138 q^{42} -387.145 q^{43} -8.46784 q^{44} +192.519 q^{45} -150.049 q^{46} -294.553 q^{47} -48.0000 q^{48} -194.916 q^{49} -665.153 q^{50} +267.969 q^{51} -253.167 q^{52} -126.721 q^{53} +54.0000 q^{54} -45.2840 q^{55} -97.3518 q^{56} -78.0158 q^{58} -572.701 q^{59} -256.692 q^{60} -734.609 q^{61} +31.2469 q^{62} +109.521 q^{63} +64.0000 q^{64} -1353.88 q^{65} -12.7018 q^{66} -829.355 q^{67} -357.292 q^{68} -225.074 q^{69} -520.614 q^{70} -444.891 q^{71} -72.0000 q^{72} +1136.11 q^{73} -196.240 q^{74} -997.729 q^{75} -25.7612 q^{77} -379.751 q^{78} +1242.40 q^{79} +342.257 q^{80} +81.0000 q^{81} +75.4695 q^{82} +726.036 q^{83} -146.028 q^{84} -1910.71 q^{85} +774.290 q^{86} -117.024 q^{87} +16.9357 q^{88} +117.045 q^{89} -385.039 q^{90} -770.196 q^{91} +300.098 q^{92} +46.8703 q^{93} +589.107 q^{94} +96.0000 q^{96} -1082.86 q^{97} +389.832 q^{98} -19.0526 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 18 q^{2} - 27 q^{3} + 36 q^{4} + 27 q^{5} + 54 q^{6} - 72 q^{8} + 81 q^{9}+O(q^{10}) \) 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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