LMFDB - Embedded newform 483.4.a.i.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,4,Mod(1,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("483.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	483.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:	$28.4979225328$
Analytic rank:	$0$
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} - x^{8} - 51x^{7} + 34x^{6} + 861x^{5} - 401x^{4} - 5403x^{3} + 1772x^{2} + 8716x - 192 $ x^9 - x^8 - 51x^7 + 34x^6 + 861x^5 - 401x^4 - 5403x^3 + 1772x^2 + 8716*x - 192
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-4.47249$ of defining polynomial
Character	$\chi$	$=$	483.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+5.47249 q^{2} +3.00000 q^{3} +21.9481 q^{4} +8.93744 q^{5} +16.4175 q^{6} +7.00000 q^{7} +76.3311 q^{8} +9.00000 q^{9} +48.9100 q^{10} -64.9462 q^{11} +65.8444 q^{12} +34.6747 q^{13} +38.3074 q^{14} +26.8123 q^{15} +242.136 q^{16} -30.9018 q^{17} +49.2524 q^{18} -138.470 q^{19} +196.160 q^{20} +21.0000 q^{21} -355.417 q^{22} -23.0000 q^{23} +228.993 q^{24} -45.1222 q^{25} +189.757 q^{26} +27.0000 q^{27} +153.637 q^{28} +16.0755 q^{29} +146.730 q^{30} -142.943 q^{31} +714.437 q^{32} -194.839 q^{33} -169.110 q^{34} +62.5621 q^{35} +197.533 q^{36} +368.798 q^{37} -757.774 q^{38} +104.024 q^{39} +682.204 q^{40} -79.8823 q^{41} +114.922 q^{42} -441.379 q^{43} -1425.45 q^{44} +80.4369 q^{45} -125.867 q^{46} +197.161 q^{47} +726.408 q^{48} +49.0000 q^{49} -246.931 q^{50} -92.7055 q^{51} +761.046 q^{52} +38.9761 q^{53} +147.757 q^{54} -580.453 q^{55} +534.317 q^{56} -415.409 q^{57} +87.9728 q^{58} +854.084 q^{59} +588.480 q^{60} +435.416 q^{61} -782.257 q^{62} +63.0000 q^{63} +1972.66 q^{64} +309.903 q^{65} -1066.25 q^{66} -796.063 q^{67} -678.238 q^{68} -69.0000 q^{69} +342.370 q^{70} -236.179 q^{71} +686.980 q^{72} +646.398 q^{73} +2018.25 q^{74} -135.367 q^{75} -3039.15 q^{76} -454.623 q^{77} +569.271 q^{78} -859.016 q^{79} +2164.07 q^{80} +81.0000 q^{81} -437.155 q^{82} +821.976 q^{83} +460.911 q^{84} -276.183 q^{85} -2415.44 q^{86} +48.2264 q^{87} -4957.41 q^{88} +576.608 q^{89} +440.190 q^{90} +242.723 q^{91} -504.807 q^{92} -428.830 q^{93} +1078.96 q^{94} -1237.56 q^{95} +2143.31 q^{96} +1651.08 q^{97} +268.152 q^{98} -584.516 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 8 q^{2} + 27 q^{3} + 38 q^{4} + 39 q^{5} + 24 q^{6} + 63 q^{7} + 135 q^{8} + 81 q^{9} + 81 q^{10} + 38 q^{11} + 114 q^{12} + 107 q^{13} + 56 q^{14} + 117 q^{15} + 178 q^{16} + 170 q^{17} + 72 q^{18}+ \cdots + 342 q^{99}+O(q^{100}) $ 9 * q + 8 * q^2 + 27 * q^3 + 38 * q^4 + 39 * q^5 + 24 * q^6 + 63 * q^7 + 135 * q^8 + 81 * q^9 + 81 * q^10 + 38 * q^11 + 114 * q^12 + 107 * q^13 + 56 * q^14 + 117 * q^15 + 178 * q^16 + 170 * q^17 + 72 * q^18 + 20 * q^19 + 300 * q^20 + 189 * q^21 - 129 * q^22 - 207 * q^23 + 405 * q^24 + 354 * q^25 - 114 * q^26 + 243 * q^27 + 266 * q^28 + 405 * q^29 + 243 * q^30 - 182 * q^31 + 648 * q^32 + 114 * q^33 - 277 * q^34 + 273 * q^35 + 342 * q^36 + 347 * q^37 - 291 * q^38 + 321 * q^39 + 1066 * q^40 + 717 * q^41 + 168 * q^42 - 77 * q^43 - 705 * q^44 + 351 * q^45 - 184 * q^46 + 799 * q^47 + 534 * q^48 + 441 * q^49 + 406 * q^50 + 510 * q^51 + 519 * q^52 + 780 * q^53 + 216 * q^54 - 754 * q^55 + 945 * q^56 + 60 * q^57 - 508 * q^58 + 766 * q^59 + 900 * q^60 + 1836 * q^61 + 173 * q^62 + 567 * q^63 + 805 * q^64 + 655 * q^65 - 387 * q^66 - 1290 * q^67 + 317 * q^68 - 621 * q^69 + 567 * q^70 + 1802 * q^71 + 1215 * q^72 + 598 * q^73 + 578 * q^74 + 1062 * q^75 - 1323 * q^76 + 266 * q^77 - 342 * q^78 - 1150 * q^79 + 795 * q^80 + 729 * q^81 - 1040 * q^82 + 1758 * q^83 + 798 * q^84 + 1078 * q^85 - 1920 * q^86 + 1215 * q^87 - 3056 * q^88 + 1400 * q^89 + 729 * q^90 + 749 * q^91 - 874 * q^92 - 546 * q^93 + 799 * q^94 + 2186 * q^95 + 1944 * q^96 + 1123 * q^97 + 392 * q^98 + 342 * q^99

Coefficient data

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

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

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

$2$	5.47249	1.93482	0.967409	−	0.253220i	$-0.0814898\pi$
$2$	5.47249	1.93482	0.967409	+	0.253220i	$0.0814898\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	21.9481	2.74352
$5$	8.93744	0.799389	0.399694	−	0.916648i	$-0.369116\pi$
$5$	8.93744	0.799389	0.399694	+	0.916648i	$0.369116\pi$
$6$	16.4175	1.11707
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	76.3311	3.37339
$9$	9.00000	0.333333
$10$	48.9100	1.54667
$11$	−64.9462	−1.78018	−0.890092	−	0.455782i	$-0.849360\pi$
$11$	−64.9462	−1.78018	−0.890092	+	0.455782i	$0.849360\pi$
$12$	65.8444	1.58397
$13$	34.6747	0.739772	0.369886	−	0.929077i	$-0.379397\pi$
$13$	34.6747	0.739772	0.369886	+	0.929077i	$0.379397\pi$
$14$	38.3074	0.731292
$15$	26.8123	0.461527
$16$	242.136	3.78337
$17$	−30.9018	−0.440870	−0.220435	−	0.975402i	$-0.570748\pi$
$17$	−30.9018	−0.440870	−0.220435	+	0.975402i	$0.570748\pi$
$18$	49.2524	0.644939
$19$	−138.470	−1.67195	−0.835977	−	0.548765i	$-0.815098\pi$
$19$	−138.470	−1.67195	−0.835977	+	0.548765i	$0.815098\pi$
$20$	196.160	2.19314
$21$	21.0000	0.218218
$22$	−355.417	−3.44433
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	228.993	1.94763
$25$	−45.1222	−0.360978
$26$	189.757	1.43132
$27$	27.0000	0.192450
$28$	153.637	1.03695
$29$	16.0755	0.102936	0.0514679	−	0.998675i	$-0.483610\pi$
$29$	16.0755	0.102936	0.0514679	+	0.998675i	$0.483610\pi$
$30$	146.730	0.892971
$31$	−142.943	−0.828174	−0.414087	−	0.910237i	$-0.635899\pi$
$31$	−142.943	−0.828174	−0.414087	+	0.910237i	$0.635899\pi$
$32$	714.437	3.94675
$33$	−194.839	−1.02779
$34$	−169.110	−0.853003
$35$	62.5621	0.302141
$36$	197.533	0.914506
$37$	368.798	1.63865	0.819325	−	0.573329i	$-0.194348\pi$
$37$	368.798	1.63865	0.819325	+	0.573329i	$0.194348\pi$
$38$	−757.774	−3.23493
$39$	104.024	0.427108
$40$	682.204	2.69665
$41$	−79.8823	−0.304281	−0.152140	−	0.988359i	$-0.548617\pi$
$41$	−79.8823	−0.304281	−0.152140	+	0.988359i	$0.548617\pi$
$42$	114.922	0.422212
$43$	−441.379	−1.56534	−0.782670	−	0.622437i	$-0.786143\pi$
$43$	−441.379	−1.56534	−0.782670	+	0.622437i	$0.786143\pi$
$44$	−1425.45	−4.88396
$45$	80.4369	0.266463
$46$	−125.867	−0.403437
$47$	197.161	0.611893	0.305946	−	0.952049i	$-0.401027\pi$
$47$	197.161	0.611893	0.305946	+	0.952049i	$0.401027\pi$
$48$	726.408	2.18433
$49$	49.0000	0.142857
$50$	−246.931	−0.698426
$51$	−92.7055	−0.254537
$52$	761.046	2.02958
$53$	38.9761	0.101015	0.0505073	−	0.998724i	$-0.483916\pi$
$53$	38.9761	0.101015	0.0505073	+	0.998724i	$0.483916\pi$
$54$	147.757	0.372356
$55$	−580.453	−1.42306
$56$	534.317	1.27502
$57$	−415.409	−0.965303
$58$	87.9728	0.199162
$59$	854.084	1.88461	0.942307	−	0.334750i	$-0.108652\pi$
$59$	854.084	1.88461	0.942307	+	0.334750i	$0.108652\pi$
$60$	588.480	1.26621
$61$	435.416	0.913923	0.456962	−	0.889486i	$-0.348938\pi$
$61$	435.416	0.913923	0.456962	+	0.889486i	$0.348938\pi$
$62$	−782.257	−1.60237
$63$	63.0000	0.125988
$64$	1972.66	3.85286
$65$	309.903	0.591366
$66$	−1066.25	−1.98858
$67$	−796.063	−1.45156	−0.725781	−	0.687926i	$-0.758521\pi$
$67$	−796.063	−1.45156	−0.725781	+	0.687926i	$0.758521\pi$
$68$	−678.238	−1.20954
$69$	−69.0000	−0.120386
$70$	342.370	0.584587
$71$	−236.179	−0.394779	−0.197389	−	0.980325i	$-0.563246\pi$
$71$	−236.179	−0.394779	−0.197389	+	0.980325i	$0.563246\pi$
$72$	686.980	1.12446
$73$	646.398	1.03637	0.518186	−	0.855268i	$-0.326608\pi$
$73$	646.398	1.03637	0.518186	+	0.855268i	$0.326608\pi$
$74$	2018.25	3.17049
$75$	−135.367	−0.208411
$76$	−3039.15	−4.58704
$77$	−454.623	−0.672846
$78$	569.271	0.826375
$79$	−859.016	−1.22338	−0.611689	−	0.791098i	$-0.709510\pi$
$79$	−859.016	−1.22338	−0.611689	+	0.791098i	$0.709510\pi$
$80$	2164.07	3.02439
$81$	81.0000	0.111111
$82$	−437.155	−0.588728
$83$	821.976	1.08703	0.543516	−	0.839399i	$-0.317093\pi$
$83$	821.976	1.08703	0.543516	+	0.839399i	$0.317093\pi$
$84$	460.911	0.598685
$85$	−276.183	−0.352427
$86$	−2415.44	−3.02865
$87$	48.2264	0.0594300
$88$	−4957.41	−6.00525
$89$	576.608	0.686745	0.343373	−	0.939199i	$-0.388431\pi$
$89$	576.608	0.686745	0.343373	+	0.939199i	$0.388431\pi$
$90$	440.190	0.515557
$91$	242.723	0.279608
$92$	−504.807	−0.572063
$93$	−428.830	−0.478147
$94$	1078.96	1.18390
$95$	−1237.56	−1.33654
$96$	2143.31	2.27865
$97$	1651.08	1.72826	0.864131	−	0.503268i	$-0.167869\pi$
$97$	1651.08	1.72826	0.864131	+	0.503268i	$0.167869\pi$
$98$	268.152	0.276402
$99$	−584.516	−0.593394
$100$	−990.349	−0.990349
$101$	−1177.39	−1.15995	−0.579974	−	0.814635i	$-0.696937\pi$
$101$	−1177.39	−1.15995	−0.579974	+	0.814635i	$0.696937\pi$
$102$	−507.330	−0.492482
$103$	1358.79	1.29986	0.649930	−	0.759994i	$-0.274798\pi$
$103$	1358.79	1.29986	0.649930	+	0.759994i	$0.274798\pi$
$104$	2646.76	2.49554
$105$	187.686	0.174441
$106$	213.296	0.195445
$107$	−550.175	−0.497079	−0.248539	−	0.968622i	$-0.579951\pi$
$107$	−550.175	−0.497079	−0.248539	+	0.968622i	$0.579951\pi$
$108$	592.600	0.527990
$109$	−996.931	−0.876042	−0.438021	−	0.898965i	$-0.644321\pi$
$109$	−996.931	−0.876042	−0.438021	+	0.898965i	$0.644321\pi$
$110$	−3176.52	−2.75336
$111$	1106.40	0.946075
$112$	1694.95	1.42998
$113$	1890.29	1.57366	0.786828	−	0.617172i	$-0.211722\pi$
$113$	1890.29	1.57366	0.786828	+	0.617172i	$0.211722\pi$
$114$	−2273.32	−1.86768
$115$	−205.561	−0.166684
$116$	352.827	0.282406
$117$	312.073	0.246591
$118$	4673.96	3.64638
$119$	−216.313	−0.166633
$120$	2046.61	1.55691
$121$	2887.01	2.16905
$122$	2382.81	1.76827
$123$	−239.647	−0.175677
$124$	−3137.34	−2.27211
$125$	−1520.46	−1.08795
$126$	344.767	0.243764
$127$	−2062.71	−1.44123	−0.720613	−	0.693337i	$-0.756140\pi$
$127$	−2062.71	−1.44123	−0.720613	+	0.693337i	$0.756140\pi$
$128$	5079.89	3.50783
$129$	−1324.14	−0.903750
$130$	1695.94	1.14418
$131$	−1112.85	−0.742218	−0.371109	−	0.928589i	$-0.621022\pi$
$131$	−1112.85	−0.742218	−0.371109	+	0.928589i	$0.621022\pi$
$132$	−4276.35	−2.81976
$133$	−969.288	−0.631939
$134$	−4356.45	−2.80851
$135$	241.311	0.153842
$136$	−2358.77	−1.48723
$137$	−456.121	−0.284446	−0.142223	−	0.989835i	$-0.545425\pi$
$137$	−456.121	−0.284446	−0.142223	+	0.989835i	$0.545425\pi$
$138$	−377.602	−0.232925
$139$	618.754	0.377569	0.188784	−	0.982019i	$-0.439545\pi$
$139$	618.754	0.377569	0.188784	+	0.982019i	$0.439545\pi$
$140$	1373.12	0.828928
$141$	591.484	0.353276
$142$	−1292.49	−0.763824
$143$	−2251.99	−1.31693
$144$	2179.22	1.26112
$145$	143.674	0.0822858
$146$	3537.40	2.00519
$147$	147.000	0.0824786
$148$	8094.44	4.49567
$149$	191.696	0.105398	0.0526992	−	0.998610i	$-0.483218\pi$
$149$	191.696	0.105398	0.0526992	+	0.998610i	$0.483218\pi$
$150$	−740.792	−0.403236
$151$	−1503.50	−0.810288	−0.405144	−	0.914253i	$-0.632779\pi$
$151$	−1503.50	−0.810288	−0.405144	+	0.914253i	$0.632779\pi$
$152$	−10569.5	−5.64015
$153$	−278.116	−0.146957
$154$	−2487.92	−1.30183
$155$	−1277.55	−0.662033
$156$	2283.14	1.17178
$157$	−1360.53	−0.691605	−0.345803	−	0.938307i	$-0.612393\pi$
$157$	−1360.53	−0.691605	−0.345803	+	0.938307i	$0.612393\pi$
$158$	−4700.96	−2.36701
$159$	116.928	0.0583209
$160$	6385.24	3.15498
$161$	−161.000	−0.0788110
$162$	443.272	0.214980
$163$	2283.61	1.09734	0.548670	−	0.836039i	$-0.315134\pi$
$163$	2283.61	1.09734	0.548670	+	0.836039i	$0.315134\pi$
$164$	−1753.27	−0.834800
$165$	−1741.36	−0.821603
$166$	4498.26	2.10321
$167$	−970.287	−0.449599	−0.224800	−	0.974405i	$-0.572173\pi$
$167$	−970.287	−0.449599	−0.224800	+	0.974405i	$0.572173\pi$
$168$	1602.95	0.736134
$169$	−994.664	−0.452737
$170$	−1511.41	−0.681881
$171$	−1246.23	−0.557318
$172$	−9687.45	−4.29454
$173$	−2175.48	−0.956062	−0.478031	−	0.878343i	$-0.658649\pi$
$173$	−2175.48	−0.956062	−0.478031	+	0.878343i	$0.658649\pi$
$174$	263.919	0.114986
$175$	−315.855	−0.136437
$176$	−15725.8	−6.73510
$177$	2562.25	1.08808
$178$	3155.48	1.32873
$179$	3254.30	1.35887	0.679435	−	0.733736i	$-0.262225\pi$
$179$	3254.30	1.35887	0.679435	+	0.733736i	$0.262225\pi$
$180$	1765.44	0.731046
$181$	1147.73	0.471325	0.235663	−	0.971835i	$-0.424274\pi$
$181$	1147.73	0.471325	0.235663	+	0.971835i	$0.424274\pi$
$182$	1328.30	0.540990
$183$	1306.25	0.527654
$184$	−1755.61	−0.703400
$185$	3296.11	1.30992
$186$	−2346.77	−0.925126
$187$	2006.96	0.784830
$188$	4327.33	1.67874
$189$	189.000	0.0727393
$190$	−6772.56	−2.58596
$191$	−865.071	−0.327719	−0.163859	−	0.986484i	$-0.552394\pi$
$191$	−865.071	−0.327719	−0.163859	+	0.986484i	$0.552394\pi$
$192$	5917.99	2.22445
$193$	−2005.48	−0.747969	−0.373984	−	0.927435i	$-0.622009\pi$
$193$	−2005.48	−0.747969	−0.373984	+	0.927435i	$0.622009\pi$
$194$	9035.49	3.34387
$195$	929.710	0.341425
$196$	1075.46	0.391931
$197$	−218.707	−0.0790975	−0.0395488	−	0.999218i	$-0.512592\pi$
$197$	−218.707	−0.0790975	−0.0395488	+	0.999218i	$0.512592\pi$
$198$	−3198.76	−1.14811
$199$	−273.538	−0.0974401	−0.0487201	−	0.998812i	$-0.515514\pi$
$199$	−273.538	−0.0974401	−0.0487201	+	0.998812i	$0.515514\pi$
$200$	−3444.23	−1.21772
$201$	−2388.19	−0.838059
$202$	−6443.26	−2.24429
$203$	112.528	0.0389061
$204$	−2034.71	−0.698326
$205$	−713.943	−0.243239
$206$	7435.96	2.51499
$207$	−207.000	−0.0695048
$208$	8395.99	2.79883
$209$	8993.08	2.97638
$210$	1027.11	0.337511
$211$	899.743	0.293559	0.146779	−	0.989169i	$-0.453109\pi$
$211$	899.743	0.293559	0.146779	+	0.989169i	$0.453109\pi$
$212$	855.453	0.277136
$213$	−708.537	−0.227926
$214$	−3010.83	−0.961756
$215$	−3944.80	−1.25132
$216$	2060.94	0.649209
$217$	−1000.60	−0.313020
$218$	−5455.69	−1.69498
$219$	1939.19	0.598349
$220$	−12739.9	−3.90419
$221$	−1071.51	−0.326144
$222$	6054.74	1.83048
$223$	−827.023	−0.248348	−0.124174	−	0.992260i	$-0.539628\pi$
$223$	−827.023	−0.248348	−0.124174	+	0.992260i	$0.539628\pi$
$224$	5001.06	1.49173
$225$	−406.100	−0.120326
$226$	10344.6	3.04474
$227$	−3323.67	−0.971806	−0.485903	−	0.874013i	$-0.661509\pi$
$227$	−3323.67	−0.971806	−0.485903	+	0.874013i	$0.661509\pi$
$228$	−9117.46	−2.64833
$229$	4620.63	1.33336	0.666681	−	0.745343i	$-0.267714\pi$
$229$	4620.63	1.33336	0.666681	+	0.745343i	$0.267714\pi$
$230$	−1124.93	−0.322503
$231$	−1363.87	−0.388468
$232$	1227.06	0.347243
$233$	−2523.32	−0.709478	−0.354739	−	0.934965i	$-0.615430\pi$
$233$	−2523.32	−0.709478	−0.354739	+	0.934965i	$0.615430\pi$
$234$	1707.81	0.477108
$235$	1762.12	0.489140
$236$	18745.5	5.17047
$237$	−2577.05	−0.706318
$238$	−1183.77	−0.322405
$239$	4250.48	1.15038	0.575190	−	0.818020i	$-0.304928\pi$
$239$	4250.48	1.15038	0.575190	+	0.818020i	$0.304928\pi$
$240$	6492.22	1.74613
$241$	−7054.93	−1.88568	−0.942838	−	0.333250i	$-0.891855\pi$
$241$	−7054.93	−1.88568	−0.942838	+	0.333250i	$0.891855\pi$
$242$	15799.1	4.19672
$243$	243.000	0.0641500
$244$	9556.58	2.50736
$245$	437.934	0.114198
$246$	−1311.46	−0.339902
$247$	−4801.40	−1.23686
$248$	−10911.0	−2.79375
$249$	2465.93	0.627598
$250$	−8320.68	−2.10498
$251$	5829.72	1.46601	0.733005	−	0.680223i	$-0.238117\pi$
$251$	5829.72	1.46601	0.733005	+	0.680223i	$0.238117\pi$
$252$	1382.73	0.345651
$253$	1493.76	0.371194
$254$	−11288.2	−2.78851
$255$	−828.550	−0.203474
$256$	12018.3	2.93416
$257$	−1639.22	−0.397866	−0.198933	−	0.980013i	$-0.563748\pi$
$257$	−1639.22	−0.397866	−0.198933	+	0.980013i	$0.563748\pi$
$258$	−7246.32	−1.74859
$259$	2581.59	0.619352
$260$	6801.80	1.62242
$261$	144.679	0.0343120
$262$	−6090.09	−1.43606
$263$	−273.365	−0.0640927	−0.0320464	−	0.999486i	$-0.510202\pi$
$263$	−273.365	−0.0640927	−0.0320464	+	0.999486i	$0.510202\pi$
$264$	−14872.2	−3.46713
$265$	348.346	0.0807500
$266$	−5304.42	−1.22269
$267$	1729.82	0.396492
$268$	−17472.1	−3.98238
$269$	7443.39	1.68711	0.843553	−	0.537046i	$-0.180460\pi$
$269$	7443.39	1.68711	0.843553	+	0.537046i	$0.180460\pi$
$270$	1320.57	0.297657
$271$	3102.28	0.695388	0.347694	−	0.937608i	$-0.386965\pi$
$271$	3102.28	0.695388	0.347694	+	0.937608i	$0.386965\pi$
$272$	−7482.44	−1.66798
$273$	728.169	0.161432
$274$	−2496.12	−0.550350
$275$	2930.52	0.642606
$276$	−1514.42	−0.330281
$277$	2151.15	0.466608	0.233304	−	0.972404i	$-0.425046\pi$
$277$	2151.15	0.466608	0.233304	+	0.972404i	$0.425046\pi$
$278$	3386.13	0.730527
$279$	−1286.49	−0.276058
$280$	4775.43	1.01924
$281$	664.784	0.141131	0.0705653	−	0.997507i	$-0.477520\pi$
$281$	664.784	0.141131	0.0705653	+	0.997507i	$0.477520\pi$
$282$	3236.89	0.683525
$283$	2923.45	0.614067	0.307033	−	0.951699i	$-0.400664\pi$
$283$	2923.45	0.614067	0.307033	+	0.951699i	$0.400664\pi$
$284$	−5183.69	−1.08308
$285$	−3712.69	−0.771652
$286$	−12324.0	−2.54802
$287$	−559.176	−0.115007
$288$	6429.94	1.31558
$289$	−3958.08	−0.805633
$290$	786.252	0.159208
$291$	4953.23	0.997812
$292$	14187.2	2.84330
$293$	−1765.02	−0.351924	−0.175962	−	0.984397i	$-0.556304\pi$
$293$	−1765.02	−0.351924	−0.175962	+	0.984397i	$0.556304\pi$
$294$	804.456	0.159581
$295$	7633.32	1.50654
$296$	28150.8	5.52781
$297$	−1753.55	−0.342596
$298$	1049.06	0.203927
$299$	−797.519	−0.154253
$300$	−2971.05	−0.571778
$301$	−3089.65	−0.591643
$302$	−8227.91	−1.56776
$303$	−3532.17	−0.669696
$304$	−33528.5	−6.32562
$305$	3891.50	0.730580
$306$	−1521.99	−0.284334
$307$	−4091.63	−0.760657	−0.380328	−	0.924852i	$-0.624189\pi$
$307$	−4091.63	−0.760657	−0.380328	+	0.924852i	$0.624189\pi$
$308$	−9978.14	−1.84596
$309$	4076.37	0.750474
$310$	−6991.37	−1.28091
$311$	2508.33	0.457346	0.228673	−	0.973503i	$-0.426561\pi$
$311$	2508.33	0.457346	0.228673	+	0.973503i	$0.426561\pi$
$312$	7940.28	1.44080
$313$	−2276.71	−0.411142	−0.205571	−	0.978642i	$-0.565905\pi$
$313$	−2276.71	−0.411142	−0.205571	+	0.978642i	$0.565905\pi$
$314$	−7445.48	−1.33813
$315$	563.059	0.100714
$316$	−18853.8	−3.35636
$317$	2282.31	0.404377	0.202188	−	0.979347i	$-0.435195\pi$
$317$	2282.31	0.404377	0.202188	+	0.979347i	$0.435195\pi$
$318$	639.889	0.112840
$319$	−1044.04	−0.183245
$320$	17630.6	3.07993
$321$	−1650.52	−0.286988
$322$	−881.071	−0.152485
$323$	4278.97	0.737115
$324$	1777.80	0.304835
$325$	−1564.60	−0.267041
$326$	12497.0	2.12315
$327$	−2990.79	−0.505783
$328$	−6097.50	−1.02646
$329$	1380.13	0.231274
$330$	−9529.56	−1.58965
$331$	−6834.36	−1.13490	−0.567448	−	0.823409i	$-0.692069\pi$
$331$	−6834.36	−1.13490	−0.567448	+	0.823409i	$0.692069\pi$
$332$	18040.9	2.98229
$333$	3319.19	0.546217
$334$	−5309.89	−0.869892
$335$	−7114.76	−1.16036
$336$	5084.85	0.825600
$337$	−2946.37	−0.476258	−0.238129	−	0.971234i	$-0.576534\pi$
$337$	−2946.37	−0.476258	−0.238129	+	0.971234i	$0.576534\pi$
$338$	−5443.29	−0.875964
$339$	5670.86	0.908551
$340$	−6061.71	−0.966889
$341$	9283.63	1.47430
$342$	−6819.96	−1.07831
$343$	343.000	0.0539949
$344$	−33690.9	−5.28050
$345$	−616.683	−0.0962351
$346$	−11905.3	−1.84981
$347$	10980.7	1.69878	0.849391	−	0.527764i	$-0.176970\pi$
$347$	10980.7	1.69878	0.849391	+	0.527764i	$0.176970\pi$
$348$	1058.48	0.163047
$349$	−1299.92	−0.199379	−0.0996894	−	0.995019i	$-0.531785\pi$
$349$	−1299.92	−0.199379	−0.0996894	+	0.995019i	$0.531785\pi$
$350$	−1728.52	−0.263980
$351$	936.218	0.142369
$352$	−46400.0	−7.02593
$353$	−5177.82	−0.780702	−0.390351	−	0.920666i	$-0.627646\pi$
$353$	−5177.82	−0.780702	−0.390351	+	0.920666i	$0.627646\pi$
$354$	14021.9	2.10524
$355$	−2110.83	−0.315582
$356$	12655.5	1.88410
$357$	−648.938	−0.0962058
$358$	17809.1	2.62916
$359$	11913.7	1.75148	0.875740	−	0.482784i	$-0.160374\pi$
$359$	11913.7	1.75148	0.875740	+	0.482784i	$0.160374\pi$
$360$	6139.84	0.898883
$361$	12314.9	1.79543
$362$	6280.93	0.911929
$363$	8661.02	1.25230
$364$	5327.32	0.767108
$365$	5777.14	0.828464
$366$	7148.43	1.02091
$367$	2003.44	0.284956	0.142478	−	0.989798i	$-0.454493\pi$
$367$	2003.44	0.284956	0.142478	+	0.989798i	$0.454493\pi$
$368$	−5569.12	−0.788888
$369$	−718.940	−0.101427
$370$	18037.9	2.53445
$371$	272.833	0.0381800
$372$	−9412.03	−1.31180
$373$	5882.77	0.816618	0.408309	−	0.912844i	$-0.366119\pi$
$373$	5882.77	0.816618	0.408309	+	0.912844i	$0.366119\pi$
$374$	10983.0	1.51850
$375$	−4561.37	−0.628128
$376$	15049.5	2.06415
$377$	557.412	0.0761491
$378$	1034.30	0.140737
$379$	−11601.1	−1.57232	−0.786162	−	0.618020i	$-0.787935\pi$
$379$	−11601.1	−1.57232	−0.786162	+	0.618020i	$0.787935\pi$
$380$	−27162.2	−3.66682
$381$	−6188.13	−0.832093
$382$	−4734.09	−0.634076
$383$	−1653.63	−0.220618	−0.110309	−	0.993897i	$-0.535184\pi$
$383$	−1653.63	−0.220618	−0.110309	+	0.993897i	$0.535184\pi$
$384$	15239.7	2.02525
$385$	−4063.17	−0.537865
$386$	−10975.0	−1.44718
$387$	−3972.41	−0.521780
$388$	36238.0	4.74152
$389$	−11585.3	−1.51002	−0.755008	−	0.655716i	$-0.772367\pi$
$389$	−11585.3	−1.51002	−0.755008	+	0.655716i	$0.772367\pi$
$390$	5087.83	0.660595
$391$	710.742	0.0919278
$392$	3740.22	0.481913
$393$	−3338.56	−0.428520
$394$	−1196.87	−0.153039
$395$	−7677.41	−0.977955
$396$	−12829.0	−1.62799
$397$	−2639.48	−0.333682	−0.166841	−	0.985984i	$-0.553357\pi$
$397$	−2639.48	−0.333682	−0.166841	+	0.985984i	$0.553357\pi$
$398$	−1496.93	−0.188529
$399$	−2907.86	−0.364850
$400$	−10925.7	−1.36571
$401$	2043.37	0.254466	0.127233	−	0.991873i	$-0.459390\pi$
$401$	2043.37	0.254466	0.127233	+	0.991873i	$0.459390\pi$
$402$	−13069.3	−1.62149
$403$	−4956.52	−0.612660
$404$	−25841.5	−3.18234
$405$	723.932	0.0888210
$406$	615.810	0.0752762
$407$	−23952.0	−2.91710
$408$	−7076.31	−0.858651
$409$	2054.04	0.248327	0.124163	−	0.992262i	$-0.460375\pi$
$409$	2054.04	0.248327	0.124163	+	0.992262i	$0.460375\pi$
$410$	−3907.04	−0.470622
$411$	−1368.36	−0.164225
$412$	29822.9	3.56619
$413$	5978.59	0.712317
$414$	−1132.81	−0.134479
$415$	7346.36	0.868961
$416$	24772.9	2.91969
$417$	1856.26	0.217989
$418$	49214.5	5.75876
$419$	−3741.09	−0.436191	−0.218095	−	0.975927i	$-0.569984\pi$
$419$	−3741.09	−0.436191	−0.218095	+	0.975927i	$0.569984\pi$
$420$	4119.36	0.478582
$421$	−7830.25	−0.906468	−0.453234	−	0.891392i	$-0.649730\pi$
$421$	−7830.25	−0.906468	−0.453234	+	0.891392i	$0.649730\pi$
$422$	4923.83	0.567982
$423$	1774.45	0.203964
$424$	2975.09	0.340762
$425$	1394.36	0.159144
$426$	−3877.46	−0.440994
$427$	3047.91	0.345431
$428$	−12075.3	−1.36374
$429$	−6755.97	−0.760330
$430$	−21587.9	−2.42107
$431$	14614.5	1.63331	0.816654	−	0.577128i	$-0.195827\pi$
$431$	14614.5	1.63331	0.816654	+	0.577128i	$0.195827\pi$
$432$	6537.67	0.728110
$433$	−1920.46	−0.213144	−0.106572	−	0.994305i	$-0.533987\pi$
$433$	−1920.46	−0.213144	−0.106572	+	0.994305i	$0.533987\pi$
$434$	−5475.80	−0.605637
$435$	431.021	0.0475077
$436$	−21880.8	−2.40344
$437$	3184.80	0.348626
$438$	10612.2	1.15770
$439$	4703.07	0.511310	0.255655	−	0.966768i	$-0.417709\pi$
$439$	4703.07	0.511310	0.255655	+	0.966768i	$0.417709\pi$
$440$	−44306.6	−4.80053
$441$	441.000	0.0476190
$442$	−5863.84	−0.631028
$443$	5855.09	0.627954	0.313977	−	0.949431i	$-0.398338\pi$
$443$	5855.09	0.627954	0.313977	+	0.949431i	$0.398338\pi$
$444$	24283.3	2.59557
$445$	5153.40	0.548976
$446$	−4525.87	−0.480507
$447$	575.088	0.0608518
$448$	13808.6	1.45624
$449$	14581.6	1.53262	0.766312	−	0.642469i	$-0.222090\pi$
$449$	14581.6	1.53262	0.766312	+	0.642469i	$0.222090\pi$
$450$	−2222.38	−0.232809
$451$	5188.05	0.541676
$452$	41488.3	4.31735
$453$	−4510.51	−0.467820
$454$	−18188.8	−1.88027
$455$	2169.32	0.223515
$456$	−31708.6	−3.25634
$457$	−1552.87	−0.158950	−0.0794752	−	0.996837i	$-0.525324\pi$
$457$	−1552.87	−0.158950	−0.0794752	+	0.996837i	$0.525324\pi$
$458$	25286.4	2.57981
$459$	−834.349	−0.0848455
$460$	−4511.68	−0.457301
$461$	11609.2	1.17287	0.586436	−	0.809996i	$-0.300531\pi$
$461$	11609.2	1.17287	0.586436	+	0.809996i	$0.300531\pi$
$462$	−7463.76	−0.751614
$463$	−15818.5	−1.58779	−0.793897	−	0.608053i	$-0.791951\pi$
$463$	−15818.5	−1.58779	−0.793897	+	0.608053i	$0.791951\pi$
$464$	3892.45	0.389445
$465$	−3832.64	−0.382225
$466$	−13808.9	−1.37271
$467$	11797.8	1.16903	0.584516	−	0.811382i	$-0.301285\pi$
$467$	11797.8	1.16903	0.584516	+	0.811382i	$0.301285\pi$
$468$	6849.41	0.676526
$469$	−5572.44	−0.548639
$470$	9643.17	0.946397
$471$	−4081.59	−0.399298
$472$	65193.1	6.35753
$473$	28665.9	2.78659
$474$	−14102.9	−1.36660
$475$	6248.06	0.603538
$476$	−4747.66	−0.457161
$477$	350.785	0.0336716
$478$	23260.7	2.22578
$479$	−9158.14	−0.873582	−0.436791	−	0.899563i	$-0.643885\pi$
$479$	−9158.14	−0.873582	−0.436791	+	0.899563i	$0.643885\pi$
$480$	19155.7	1.82153
$481$	12788.0	1.21223
$482$	−38608.0	−3.64844
$483$	−483.000	−0.0455016
$484$	63364.5	5.95083
$485$	14756.4	1.38155
$486$	1329.81	0.124119
$487$	16332.9	1.51974	0.759871	−	0.650074i	$-0.225262\pi$
$487$	16332.9	1.51974	0.759871	+	0.650074i	$0.225262\pi$
$488$	33235.8	3.08302
$489$	6850.84	0.633549
$490$	2396.59	0.220953
$491$	17333.9	1.59321	0.796607	−	0.604498i	$-0.206626\pi$
$491$	17333.9	1.59321	0.796607	+	0.604498i	$0.206626\pi$
$492$	−5259.80	−0.481972
$493$	−496.761	−0.0453814
$494$	−26275.6	−2.39311
$495$	−5224.07	−0.474353
$496$	−34611.7	−3.13329
$497$	−1653.25	−0.149212
$498$	13494.8	1.21429
$499$	9399.30	0.843227	0.421614	−	0.906776i	$-0.361464\pi$
$499$	9399.30	0.843227	0.421614	+	0.906776i	$0.361464\pi$
$500$	−33371.2	−2.98481
$501$	−2910.86	−0.259576
$502$	31903.1	2.83646
$503$	16313.9	1.44612	0.723062	−	0.690783i	$-0.242734\pi$
$503$	16313.9	1.44612	0.723062	+	0.690783i	$0.242734\pi$
$504$	4808.86	0.425007
$505$	−10522.9	−0.927249
$506$	8174.60	0.718192
$507$	−2983.99	−0.261388
$508$	−45272.6	−3.95403
$509$	14553.0	1.26729	0.633643	−	0.773626i	$-0.281559\pi$
$509$	14553.0	1.26729	0.633643	+	0.773626i	$0.281559\pi$
$510$	−4534.23	−0.393684
$511$	4524.78	0.391712
$512$	25131.0	2.16922
$513$	−3738.68	−0.321768
$514$	−8970.59	−0.769797
$515$	12144.1	1.03909
$516$	−29062.3	−2.47945
$517$	−12804.9	−1.08928
$518$	14127.7	1.19833
$519$	−6526.44	−0.551983
$520$	23655.2	1.99491
$521$	3658.55	0.307647	0.153823	−	0.988098i	$-0.450841\pi$
$521$	3658.55	0.307647	0.153823	+	0.988098i	$0.450841\pi$
$522$	791.756	0.0663874
$523$	9660.17	0.807667	0.403834	−	0.914832i	$-0.367677\pi$
$523$	9660.17	0.807667	0.403834	+	0.914832i	$0.367677\pi$
$524$	−24425.1	−2.03629
$525$	−947.566	−0.0787718
$526$	−1495.99	−0.124008
$527$	4417.21	0.365117
$528$	−47177.4	−3.88851
$529$	529.000	0.0434783
$530$	1906.32	0.156236
$531$	7686.75	0.628205
$532$	−21274.1	−1.73374
$533$	−2769.90	−0.225098
$534$	9466.44	0.767140
$535$	−4917.15	−0.397359
$536$	−60764.4	−4.89668
$537$	9762.89	0.784544
$538$	40733.9	3.26424
$539$	−3182.36	−0.254312
$540$	5296.32	0.422069
$541$	−11525.7	−0.915950	−0.457975	−	0.888965i	$-0.651425\pi$
$541$	−11525.7	−0.915950	−0.457975	+	0.888965i	$0.651425\pi$
$542$	16977.2	1.34545
$543$	3443.18	0.272120
$544$	−22077.4	−1.74000
$545$	−8910.00	−0.700298
$546$	3984.90	0.312340
$547$	−18887.0	−1.47633	−0.738163	−	0.674623i	$-0.764306\pi$
$547$	−18887.0	−1.47633	−0.738163	+	0.674623i	$0.764306\pi$
$548$	−10011.0	−0.780381
$549$	3918.75	0.304641
$550$	16037.2	1.24333
$551$	−2225.97	−0.172104
$552$	−5266.84	−0.406108
$553$	−6013.11	−0.462394
$554$	11772.2	0.902801
$555$	9888.34	0.756282
$556$	13580.5	1.03587
$557$	−13486.0	−1.02589	−0.512943	−	0.858423i	$-0.671445\pi$
$557$	−13486.0	−1.02589	−0.512943	+	0.858423i	$0.671445\pi$
$558$	−7040.31	−0.534122
$559$	−15304.7	−1.15800
$560$	15148.5	1.14311
$561$	6020.87	0.453122
$562$	3638.02	0.273062
$563$	−16192.7	−1.21215	−0.606075	−	0.795408i	$-0.707257\pi$
$563$	−16192.7	−1.21215	−0.606075	+	0.795408i	$0.707257\pi$
$564$	12982.0	0.969220
$565$	16894.3	1.25796
$566$	15998.5	1.18811
$567$	567.000	0.0419961
$568$	−18027.8	−1.33174
$569$	9293.58	0.684722	0.342361	−	0.939568i	$-0.388773\pi$
$569$	9293.58	0.684722	0.342361	+	0.939568i	$0.388773\pi$
$570$	−20317.7	−1.49301
$571$	15286.5	1.12035	0.560175	−	0.828374i	$-0.310734\pi$
$571$	15286.5	1.12035	0.560175	+	0.828374i	$0.310734\pi$
$572$	−49427.0	−3.61302
$573$	−2595.21	−0.189209
$574$	−3060.08	−0.222518
$575$	1037.81	0.0752690
$576$	17754.0	1.28429
$577$	−10993.2	−0.793161	−0.396581	−	0.918000i	$-0.629803\pi$
$577$	−10993.2	−0.793161	−0.396581	+	0.918000i	$0.629803\pi$
$578$	−21660.5	−1.55875
$579$	−6016.45	−0.431840
$580$	3153.37	0.225752
$581$	5753.83	0.410859
$582$	27106.5	1.93058
$583$	−2531.35	−0.179825
$584$	49340.2	3.49608
$585$	2789.13	0.197122
$586$	−9659.06	−0.680908
$587$	−5939.95	−0.417663	−0.208831	−	0.977952i	$-0.566966\pi$
$587$	−5939.95	−0.417663	−0.208831	+	0.977952i	$0.566966\pi$
$588$	3226.38	0.226282
$589$	19793.3	1.38467
$590$	41773.3	2.91488
$591$	−656.120	−0.0456670
$592$	89299.3	6.19963
$593$	−11704.3	−0.810518	−0.405259	−	0.914202i	$-0.632819\pi$
$593$	−11704.3	−0.810518	−0.405259	+	0.914202i	$0.632819\pi$
$594$	−9596.27	−0.662861
$595$	−1933.28	−0.133205
$596$	4207.37	0.289162
$597$	−820.614	−0.0562571
$598$	−4364.41	−0.298452
$599$	−3212.92	−0.219159	−0.109580	−	0.993978i	$-0.534950\pi$
$599$	−3212.92	−0.219159	−0.109580	+	0.993978i	$0.534950\pi$
$600$	−10332.7	−0.703050
$601$	24141.0	1.63849	0.819246	−	0.573442i	$-0.194392\pi$
$601$	24141.0	1.63849	0.819246	+	0.573442i	$0.194392\pi$
$602$	−16908.1	−1.14472
$603$	−7164.57	−0.483854
$604$	−32999.1	−2.22304
$605$	25802.5	1.73392
$606$	−19329.8	−1.29574
$607$	−8240.03	−0.550993	−0.275496	−	0.961302i	$-0.588842\pi$
$607$	−8240.03	−0.550993	−0.275496	+	0.961302i	$0.588842\pi$
$608$	−98927.9	−6.59878
$609$	337.585	0.0224624
$610$	21296.2	1.41354
$611$	6836.52	0.452661
$612$	−6104.14	−0.403178
$613$	−24760.8	−1.63145	−0.815726	−	0.578438i	$-0.803662\pi$
$613$	−24760.8	−1.63145	−0.815726	+	0.578438i	$0.803662\pi$
$614$	−22391.4	−1.47173
$615$	−2141.83	−0.140434
$616$	−34701.9	−2.26977
$617$	−4624.30	−0.301730	−0.150865	−	0.988554i	$-0.548206\pi$
$617$	−4624.30	−0.301730	−0.150865	+	0.988554i	$0.548206\pi$
$618$	22307.9	1.45203
$619$	−1330.77	−0.0864103	−0.0432051	−	0.999066i	$-0.513757\pi$
$619$	−1330.77	−0.0864103	−0.0432051	+	0.999066i	$0.513757\pi$
$620$	−28039.8	−1.81630
$621$	−621.000	−0.0401286
$622$	13726.8	0.884880
$623$	4036.25	0.259565
$624$	25188.0	1.61591
$625$	−7948.71	−0.508717
$626$	−12459.3	−0.795484
$627$	26979.2	1.71842
$628$	−29861.1	−1.89743
$629$	−11396.5	−0.722432
$630$	3081.33	0.194862
$631$	−29390.6	−1.85423	−0.927117	−	0.374773i	$-0.877721\pi$
$631$	−29390.6	−1.85423	−0.927117	+	0.374773i	$0.877721\pi$
$632$	−65569.6	−4.12693
$633$	2699.23	0.169486
$634$	12489.9	0.782396
$635$	−18435.3	−1.15210
$636$	2566.36	0.160004
$637$	1699.06	0.105682
$638$	−5713.50	−0.354545
$639$	−2125.61	−0.131593
$640$	45401.2	2.80412
$641$	−8899.76	−0.548392	−0.274196	−	0.961674i	$-0.588412\pi$
$641$	−8899.76	−0.548392	−0.274196	+	0.961674i	$0.588412\pi$
$642$	−9032.48	−0.555270
$643$	24093.0	1.47766	0.738830	−	0.673892i	$-0.235379\pi$
$643$	24093.0	1.47766	0.738830	+	0.673892i	$0.235379\pi$
$644$	−3533.65	−0.216219
$645$	−11834.4	−0.722447
$646$	23416.6	1.42618
$647$	−15696.8	−0.953796	−0.476898	−	0.878959i	$-0.658239\pi$
$647$	−15696.8	−0.953796	−0.476898	+	0.878959i	$0.658239\pi$
$648$	6182.82	0.374821
$649$	−55469.5	−3.35496
$650$	−8562.26	−0.516676
$651$	−3001.81	−0.180722
$652$	50121.1	3.01057
$653$	8664.84	0.519267	0.259634	−	0.965707i	$-0.416398\pi$
$653$	8664.84	0.519267	0.259634	+	0.965707i	$0.416398\pi$
$654$	−16367.1	−0.978598
$655$	−9946.07	−0.593321
$656$	−19342.4	−1.15121
$657$	5817.58	0.345457
$658$	7552.75	0.447472
$659$	−18667.0	−1.10343	−0.551716	−	0.834032i	$-0.686027\pi$
$659$	−18667.0	−1.10343	−0.551716	+	0.834032i	$0.686027\pi$
$660$	−38219.6	−2.25408
$661$	14121.6	0.830964	0.415482	−	0.909601i	$-0.363613\pi$
$661$	14121.6	0.830964	0.415482	+	0.909601i	$0.363613\pi$
$662$	−37401.0	−2.19582
$663$	−3214.54	−0.188299
$664$	62742.3	3.66698
$665$	−8662.95	−0.505165
$666$	18164.2	1.05683
$667$	−369.736	−0.0214636
$668$	−21296.0	−1.23348
$669$	−2481.07	−0.143384
$670$	−38935.5	−2.24509
$671$	−28278.6	−1.62695
$672$	15003.2	0.861251
$673$	31238.5	1.78923	0.894617	−	0.446833i	$-0.147448\pi$
$673$	31238.5	1.78923	0.894617	+	0.446833i	$0.147448\pi$
$674$	−16124.0	−0.921473
$675$	−1218.30	−0.0694702
$676$	−21831.0	−1.24209
$677$	23202.3	1.31719	0.658596	−	0.752497i	$-0.271151\pi$
$677$	23202.3	1.31719	0.658596	+	0.752497i	$0.271151\pi$
$678$	31033.7	1.75788
$679$	11557.5	0.653221
$680$	−21081.4	−1.18887
$681$	−9971.02	−0.561073
$682$	50804.6	2.85250
$683$	−11108.7	−0.622348	−0.311174	−	0.950353i	$-0.600722\pi$
$683$	−11108.7	−0.622348	−0.311174	+	0.950353i	$0.600722\pi$
$684$	−27352.4	−1.52901
$685$	−4076.55	−0.227383
$686$	1877.06	0.104470
$687$	13861.9	0.769817
$688$	−106874.	−5.92227
$689$	1351.49	0.0747278
$690$	−3374.79	−0.186197
$691$	−32784.6	−1.80490	−0.902449	−	0.430797i	$-0.858233\pi$
$691$	−32784.6	−1.80490	−0.902449	+	0.430797i	$0.858233\pi$
$692$	−47747.8	−2.62297
$693$	−4091.61	−0.224282
$694$	60092.0	3.28683
$695$	5530.08	0.301824
$696$	3681.17	0.200481
$697$	2468.51	0.134148
$698$	−7113.80	−0.385761
$699$	−7569.97	−0.409618
$700$	−6932.44	−0.374317
$701$	−2027.49	−0.109240	−0.0546200	−	0.998507i	$-0.517395\pi$
$701$	−2027.49	−0.109240	−0.0546200	+	0.998507i	$0.517395\pi$
$702$	5123.44	0.275458
$703$	−51067.4	−2.73975
$704$	−128117.	−6.85880
$705$	5286.35	0.282405
$706$	−28335.6	−1.51052
$707$	−8241.73	−0.438419
$708$	56236.6	2.98517
$709$	−31315.4	−1.65878	−0.829389	−	0.558671i	$-0.811311\pi$
$709$	−31315.4	−1.65878	−0.829389	+	0.558671i	$0.811311\pi$
$710$	−11551.5	−0.610593
$711$	−7731.15	−0.407793
$712$	44013.1	2.31666
$713$	3287.70	0.172686
$714$	−3551.31	−0.186141
$715$	−20127.0	−1.05274
$716$	71425.8	3.72808
$717$	12751.5	0.664173
$718$	65197.6	3.38879
$719$	13785.9	0.715060	0.357530	−	0.933902i	$-0.383619\pi$
$719$	13785.9	0.715060	0.357530	+	0.933902i	$0.383619\pi$
$720$	19476.7	1.00813
$721$	9511.53	0.491301
$722$	67392.9	3.47383
$723$	−21164.8	−1.08870
$724$	25190.5	1.29309
$725$	−725.361	−0.0371575
$726$	47397.4	2.42298
$727$	11853.4	0.604700	0.302350	−	0.953197i	$-0.402229\pi$
$727$	11853.4	0.604700	0.302350	+	0.953197i	$0.402229\pi$
$728$	18527.3	0.943225
$729$	729.000	0.0370370
$730$	31615.3	1.60293
$731$	13639.4	0.690112
$732$	28669.7	1.44763
$733$	−6857.02	−0.345525	−0.172762	−	0.984964i	$-0.555269\pi$
$733$	−6857.02	−0.345525	−0.172762	+	0.984964i	$0.555269\pi$
$734$	10963.8	0.551338
$735$	1313.80	0.0659325
$736$	−16432.1	−0.822953
$737$	51701.3	2.58404
$738$	−3934.39	−0.196243
$739$	7095.95	0.353219	0.176609	−	0.984281i	$-0.443487\pi$
$739$	7095.95	0.353219	0.176609	+	0.984281i	$0.443487\pi$
$740$	72343.5	3.59379
$741$	−14404.2	−0.714104
$742$	1493.07	0.0738712
$743$	−26319.1	−1.29953	−0.649767	−	0.760133i	$-0.725134\pi$
$743$	−26319.1	−1.29953	−0.649767	+	0.760133i	$0.725134\pi$
$744$	−32733.1	−1.61297
$745$	1713.27	0.0842543
$746$	32193.4	1.58001
$747$	7397.79	0.362344
$748$	44049.0	2.15319
$749$	−3851.22	−0.187878
$750$	−24962.0	−1.21531
$751$	27498.1	1.33611	0.668055	−	0.744112i	$-0.267127\pi$
$751$	27498.1	1.33611	0.668055	+	0.744112i	$0.267127\pi$
$752$	47739.9	2.31502
$753$	17489.1	0.846401
$754$	3050.43	0.147335
$755$	−13437.5	−0.647735
$756$	4148.20	0.199562
$757$	28018.2	1.34523	0.672614	−	0.739994i	$-0.265172\pi$
$757$	28018.2	1.34523	0.672614	+	0.739994i	$0.265172\pi$
$758$	−63487.2	−3.04216
$759$	4481.29	0.214309
$760$	−94464.6	−4.50867
$761$	−30614.8	−1.45833	−0.729163	−	0.684340i	$-0.760091\pi$
$761$	−30614.8	−1.45833	−0.729163	+	0.684340i	$0.760091\pi$
$762$	−33864.5	−1.60995
$763$	−6978.51	−0.331113
$764$	−18986.7	−0.899103
$765$	−2485.65	−0.117476
$766$	−9049.48	−0.426855
$767$	29615.1	1.39418
$768$	36054.9	1.69404
$769$	−36535.2	−1.71326	−0.856628	−	0.515935i	$-0.827445\pi$
$769$	−36535.2	−1.71326	−0.856628	+	0.515935i	$0.827445\pi$
$770$	−22235.6	−1.04067
$771$	−4917.65	−0.229708
$772$	−44016.7	−2.05207
$773$	−2926.76	−0.136181	−0.0680907	−	0.997679i	$-0.521691\pi$
$773$	−2926.76	−0.136181	−0.0680907	+	0.997679i	$0.521691\pi$
$774$	−21739.0	−1.00955
$775$	6449.92	0.298952
$776$	126028.	5.83010
$777$	7744.77	0.357583
$778$	−63400.2	−2.92160
$779$	11061.3	0.508743
$780$	20405.4	0.936706
$781$	15338.9	0.702778
$782$	3889.53	0.177864
$783$	434.038	0.0198100
$784$	11864.7	0.540482
$785$	−12159.6	−0.552861
$786$	−18270.3	−0.829108
$787$	−15882.5	−0.719376	−0.359688	−	0.933073i	$-0.617117\pi$
$787$	−15882.5	−0.719376	−0.359688	+	0.933073i	$0.617117\pi$
$788$	−4800.21	−0.217005
$789$	−820.094	−0.0370040
$790$	−42014.5	−1.89216
$791$	13232.0	0.594786
$792$	−44616.7	−2.00175
$793$	15097.9	0.676095
$794$	−14444.5	−0.645614
$795$	1045.04	0.0466210
$796$	−6003.65	−0.267329
$797$	−16842.7	−0.748556	−0.374278	−	0.927316i	$-0.622109\pi$
$797$	−16842.7	−0.748556	−0.374278	+	0.927316i	$0.622109\pi$
$798$	−15913.3	−0.705919
$799$	−6092.65	−0.269765
$800$	−32237.0	−1.42469
$801$	5189.47	0.228915
$802$	11182.3	0.492345
$803$	−41981.1	−1.84493
$804$	−52416.3	−2.29923
$805$	−1438.93	−0.0630007
$806$	−27124.5	−1.18539
$807$	22330.2	0.974051
$808$	−89871.4	−3.91295
$809$	18173.9	0.789815	0.394907	−	0.918721i	$-0.370777\pi$
$809$	18173.9	0.789815	0.394907	+	0.918721i	$0.370777\pi$
$810$	3961.71	0.171852
$811$	−13426.0	−0.581321	−0.290661	−	0.956826i	$-0.593875\pi$
$811$	−13426.0	−0.581321	−0.290661	+	0.956826i	$0.593875\pi$
$812$	2469.79	0.106740
$813$	9306.84	0.401482
$814$	−131077.	−5.64405
$815$	20409.7	0.877201
$816$	−22447.3	−0.963007
$817$	61117.6	2.61718
$818$	11240.7	0.480467
$819$	2184.51	0.0932025
$820$	−15669.7	−0.667330
$821$	−21961.4	−0.933569	−0.466784	−	0.884371i	$-0.654588\pi$
$821$	−21961.4	−0.933569	−0.466784	+	0.884371i	$0.654588\pi$
$822$	−7488.35	−0.317745
$823$	−5614.14	−0.237784	−0.118892	−	0.992907i	$-0.537934\pi$
$823$	−5614.14	−0.237784	−0.118892	+	0.992907i	$0.537934\pi$
$824$	103718.	4.38493
$825$	8791.55	0.371009
$826$	32717.7	1.37820
$827$	10174.5	0.427815	0.213907	−	0.976854i	$-0.431381\pi$
$827$	10174.5	0.427815	0.213907	+	0.976854i	$0.431381\pi$
$828$	−4543.27	−0.190688
$829$	−27711.0	−1.16097	−0.580485	−	0.814271i	$-0.697137\pi$
$829$	−27711.0	−1.16097	−0.580485	+	0.814271i	$0.697137\pi$
$830$	40202.9	1.68128
$831$	6453.46	0.269396
$832$	68401.6	2.85024
$833$	−1514.19	−0.0629815
$834$	10158.4	0.421770
$835$	−8671.88	−0.359404
$836$	197381.	8.16576
$837$	−3859.47	−0.159382
$838$	−20473.1	−0.843950
$839$	−1474.25	−0.0606637	−0.0303319	−	0.999540i	$-0.509656\pi$
$839$	−1474.25	−0.0606637	−0.0303319	+	0.999540i	$0.509656\pi$
$840$	14326.3	0.588457
$841$	−24130.6	−0.989404
$842$	−42850.9	−1.75385
$843$	1994.35	0.0814818
$844$	19747.7	0.805383
$845$	−8889.74	−0.361913
$846$	9710.68	0.394633
$847$	20209.1	0.819825
$848$	9437.51	0.382176
$849$	8770.34	0.354532
$850$	7630.61	0.307915
$851$	−8482.36	−0.341682
$852$	−15551.1	−0.625318
$853$	−31045.8	−1.24617	−0.623087	−	0.782152i	$-0.714122\pi$
$853$	−31045.8	−1.24617	−0.623087	+	0.782152i	$0.714122\pi$
$854$	16679.7	0.668345
$855$	−11138.1	−0.445514
$856$	−41995.4	−1.67684
$857$	−41409.9	−1.65057	−0.825283	−	0.564720i	$-0.808984\pi$
$857$	−41409.9	−1.65057	−0.825283	+	0.564720i	$0.808984\pi$
$858$	−36972.0	−1.47110
$859$	4188.80	0.166380	0.0831898	−	0.996534i	$-0.473489\pi$
$859$	4188.80	0.166380	0.0831898	+	0.996534i	$0.473489\pi$
$860$	−86580.9	−3.43301
$861$	−1677.53	−0.0663995
$862$	79977.7	3.16015
$863$	−14097.9	−0.556082	−0.278041	−	0.960569i	$-0.589685\pi$
$863$	−14097.9	−0.556082	−0.278041	+	0.960569i	$0.589685\pi$
$864$	19289.8	0.759552
$865$	−19443.2	−0.764265
$866$	−10509.7	−0.412395
$867$	−11874.2	−0.465133
$868$	−21961.4	−0.858777
$869$	55789.8	2.17784
$870$	2358.76	0.0919187
$871$	−27603.3	−1.07382
$872$	−76096.8	−2.95523
$873$	14859.7	0.576087
$874$	17428.8	0.674528
$875$	−10643.2	−0.411207
$876$	42561.7	1.64158
$877$	−26701.7	−1.02811	−0.514055	−	0.857757i	$-0.671857\pi$
$877$	−26701.7	−1.02811	−0.514055	+	0.857757i	$0.671857\pi$
$878$	25737.5	0.989291
$879$	−5295.06	−0.203183
$880$	−140548.	−5.38396
$881$	−12186.4	−0.466029	−0.233014	−	0.972473i	$-0.574859\pi$
$881$	−12186.4	−0.466029	−0.233014	+	0.972473i	$0.574859\pi$
$882$	2413.37	0.0921342
$883$	−43820.5	−1.67008	−0.835039	−	0.550191i	$-0.814555\pi$
$883$	−43820.5	−1.67008	−0.835039	+	0.550191i	$0.814555\pi$
$884$	−23517.7	−0.894781
$885$	22900.0	0.869801
$886$	32041.9	1.21498
$887$	−12779.0	−0.483741	−0.241871	−	0.970309i	$-0.577761\pi$
$887$	−12779.0	−0.483741	−0.241871	+	0.970309i	$0.577761\pi$
$888$	84452.3	3.19148
$889$	−14439.0	−0.544732
$890$	28201.9	1.06217
$891$	−5260.64	−0.197798
$892$	−18151.6	−0.681346
$893$	−27300.9	−1.02306
$894$	3147.17	0.117737
$895$	29085.1	1.08626
$896$	35559.2	1.32584
$897$	−2392.56	−0.0890581
$898$	79797.6	2.96535
$899$	−2297.88	−0.0852488
$900$	−8913.14	−0.330116
$901$	−1204.43	−0.0445344
$902$	28391.5	1.04804
$903$	−9268.96	−0.341585
$904$	144288.	5.30855
$905$	10257.7	0.376772
$906$	−24683.7	−0.905146
$907$	−7244.34	−0.265209	−0.132604	−	0.991169i	$-0.542334\pi$
$907$	−7244.34	−0.265209	−0.132604	+	0.991169i	$0.542334\pi$
$908$	−72948.5	−2.66617
$909$	−10596.5	−0.386649
$910$	11871.6	0.432461
$911$	−19922.1	−0.724531	−0.362266	−	0.932075i	$-0.617997\pi$
$911$	−19922.1	−0.724531	−0.362266	+	0.932075i	$0.617997\pi$
$912$	−100585.	−3.65210
$913$	−53384.2	−1.93512
$914$	−8498.09	−0.307540
$915$	11674.5	0.421801
$916$	101414.	3.65810
$917$	−7789.98	−0.280532
$918$	−4565.97	−0.164161
$919$	−12768.2	−0.458306	−0.229153	−	0.973390i	$-0.573596\pi$
$919$	−12768.2	−0.458306	−0.229153	+	0.973390i	$0.573596\pi$
$920$	−15690.7	−0.562290
$921$	−12274.9	−0.439165
$922$	63531.2	2.26929
$923$	−8189.44	−0.292046
$924$	−29934.4	−1.06577
$925$	−16641.0	−0.591516
$926$	−86566.6	−3.07209
$927$	12229.1	0.433287
$928$	11484.9	0.406262
$929$	27889.7	0.984964	0.492482	−	0.870323i	$-0.336090\pi$
$929$	27889.7	0.984964	0.492482	+	0.870323i	$0.336090\pi$
$930$	−20974.1	−0.739536
$931$	−6785.01	−0.238851
$932$	−55382.3	−1.94647
$933$	7525.00	0.264049
$934$	64563.4	2.26186
$935$	17937.0	0.627384
$936$	23820.8	0.831846
$937$	−33958.2	−1.18395	−0.591977	−	0.805955i	$-0.701652\pi$
$937$	−33958.2	−1.18395	−0.591977	+	0.805955i	$0.701652\pi$
$938$	−30495.1	−1.06152
$939$	−6830.14	−0.237373
$940$	38675.2	1.34196
$941$	39002.5	1.35116	0.675582	−	0.737285i	$-0.263892\pi$
$941$	39002.5	1.35116	0.675582	+	0.737285i	$0.263892\pi$
$942$	−22336.4	−0.772570
$943$	1837.29	0.0634469
$944$	206804.	7.13020
$945$	1689.18	0.0581470
$946$	156874.	5.39155
$947$	−6375.90	−0.218784	−0.109392	−	0.993999i	$-0.534890\pi$
$947$	−6375.90	−0.218784	−0.109392	+	0.993999i	$0.534890\pi$
$948$	−56561.4	−1.93780
$949$	22413.7	0.766679
$950$	34192.4	1.16774
$951$	6846.94	0.233467
$952$	−16511.4	−0.562119
$953$	11469.9	0.389871	0.194935	−	0.980816i	$-0.437550\pi$
$953$	11469.9	0.389871	0.194935	+	0.980816i	$0.437550\pi$
$954$	1919.67	0.0651483
$955$	−7731.52	−0.261975
$956$	93290.2	3.15609
$957$	−3132.12	−0.105796
$958$	−50117.8	−1.69022
$959$	−3192.85	−0.107510
$960$	52891.7	1.77820
$961$	−9358.17	−0.314127
$962$	69982.1	2.34544
$963$	−4951.57	−0.165693
$964$	−154843.	−5.17339
$965$	−17923.9	−0.597918
$966$	−2643.21	−0.0880372
$967$	−11097.4	−0.369045	−0.184523	−	0.982828i	$-0.559074\pi$
$967$	−11097.4	−0.369045	−0.184523	+	0.982828i	$0.559074\pi$
$968$	220368.	7.31705
$969$	12836.9	0.425573
$970$	80754.2	2.67305
$971$	19350.8	0.639545	0.319773	−	0.947494i	$-0.396394\pi$
$971$	19350.8	0.639545	0.319773	+	0.947494i	$0.396394\pi$
$972$	5333.40	0.175997
$973$	4331.28	0.142708
$974$	89381.7	2.94042
$975$	−4693.80	−0.154176
$976$	105430.	3.45771
$977$	19020.2	0.622834	0.311417	−	0.950273i	$-0.399196\pi$
$977$	19020.2	0.622834	0.311417	+	0.950273i	$0.399196\pi$
$978$	37491.1	1.22580
$979$	−37448.5	−1.22253
$980$	9611.85	0.313305
$981$	−8972.37	−0.292014
$982$	94859.6	3.08258
$983$	48405.2	1.57059	0.785293	−	0.619125i	$-0.212512\pi$
$983$	48405.2	1.57059	0.785293	+	0.619125i	$0.212512\pi$
$984$	−18292.5	−0.592626
$985$	−1954.68	−0.0632297
$986$	−2718.52	−0.0878046
$987$	4140.39	0.133526
$988$	−105382.	−3.39336
$989$	10151.7	0.326396
$990$	−28588.7	−0.917786
$991$	31822.7	1.02006	0.510031	−	0.860156i	$-0.329634\pi$
$991$	31822.7	1.02006	0.510031	+	0.860156i	$0.329634\pi$
$992$	−102124.	−3.26859
$993$	−20503.1	−0.655233
$994$	−9047.41	−0.288699
$995$	−2444.73	−0.0778926
$996$	54122.6	1.72183
$997$	−7520.08	−0.238880	−0.119440	−	0.992841i	$-0.538110\pi$
$997$	−7520.08	−0.238880	−0.119440	+	0.992841i	$0.538110\pi$
$998$	51437.6	1.63149
$999$	9957.56	0.315358

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.4.a.i.1.9	✓	9
3.2	odd	2		1449.4.a.j.1.1		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.4.a.i.1.9	✓	9	1.1	even	1	trivial
1449.4.a.j.1.1		9	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	483.a (trivial)

\(f(q)\)	\(=\)	\(q+5.47249 q^{2} +3.00000 q^{3} +21.9481 q^{4} +8.93744 q^{5} +16.4175 q^{6} +7.00000 q^{7} +76.3311 q^{8} +9.00000 q^{9} +48.9100 q^{10} -64.9462 q^{11} +65.8444 q^{12} +34.6747 q^{13} +38.3074 q^{14} +26.8123 q^{15} +242.136 q^{16} -30.9018 q^{17} +49.2524 q^{18} -138.470 q^{19} +196.160 q^{20} +21.0000 q^{21} -355.417 q^{22} -23.0000 q^{23} +228.993 q^{24} -45.1222 q^{25} +189.757 q^{26} +27.0000 q^{27} +153.637 q^{28} +16.0755 q^{29} +146.730 q^{30} -142.943 q^{31} +714.437 q^{32} -194.839 q^{33} -169.110 q^{34} +62.5621 q^{35} +197.533 q^{36} +368.798 q^{37} -757.774 q^{38} +104.024 q^{39} +682.204 q^{40} -79.8823 q^{41} +114.922 q^{42} -441.379 q^{43} -1425.45 q^{44} +80.4369 q^{45} -125.867 q^{46} +197.161 q^{47} +726.408 q^{48} +49.0000 q^{49} -246.931 q^{50} -92.7055 q^{51} +761.046 q^{52} +38.9761 q^{53} +147.757 q^{54} -580.453 q^{55} +534.317 q^{56} -415.409 q^{57} +87.9728 q^{58} +854.084 q^{59} +588.480 q^{60} +435.416 q^{61} -782.257 q^{62} +63.0000 q^{63} +1972.66 q^{64} +309.903 q^{65} -1066.25 q^{66} -796.063 q^{67} -678.238 q^{68} -69.0000 q^{69} +342.370 q^{70} -236.179 q^{71} +686.980 q^{72} +646.398 q^{73} +2018.25 q^{74} -135.367 q^{75} -3039.15 q^{76} -454.623 q^{77} +569.271 q^{78} -859.016 q^{79} +2164.07 q^{80} +81.0000 q^{81} -437.155 q^{82} +821.976 q^{83} +460.911 q^{84} -276.183 q^{85} -2415.44 q^{86} +48.2264 q^{87} -4957.41 q^{88} +576.608 q^{89} +440.190 q^{90} +242.723 q^{91} -504.807 q^{92} -428.830 q^{93} +1078.96 q^{94} -1237.56 q^{95} +2143.31 q^{96} +1651.08 q^{97} +268.152 q^{98} -584.516 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 8 q^{2} + 27 q^{3} + 38 q^{4} + 39 q^{5} + 24 q^{6} + 63 q^{7} + 135 q^{8} + 81 q^{9} + 81 q^{10} + 38 q^{11} + 114 q^{12} + 107 q^{13} + 56 q^{14} + 117 q^{15} + 178 q^{16} + 170 q^{17} + 72 q^{18}+ \cdots + 342 q^{99}+O(q^{100}) \) 9 * q + 8 * q^2 + 27 * q^3 + 38 * q^4 + 39 * q^5 + 24 * q^6 + 63 * q^7 + 135 * q^8 + 81 * q^9 + 81 * q^10 + 38 * q^11 + 114 * q^12 + 107 * q^13 + 56 * q^14 + 117 * q^15 + 178 * q^16 + 170 * q^17 + 72 * q^18 + 20 * q^19 + 300 * q^20 + 189 * q^21 - 129 * q^22 - 207 * q^23 + 405 * q^24 + 354 * q^25 - 114 * q^26 + 243 * q^27 + 266 * q^28 + 405 * q^29 + 243 * q^30 - 182 * q^31 + 648 * q^32 + 114 * q^33 - 277 * q^34 + 273 * q^35 + 342 * q^36 + 347 * q^37 - 291 * q^38 + 321 * q^39 + 1066 * q^40 + 717 * q^41 + 168 * q^42 - 77 * q^43 - 705 * q^44 + 351 * q^45 - 184 * q^46 + 799 * q^47 + 534 * q^48 + 441 * q^49 + 406 * q^50 + 510 * q^51 + 519 * q^52 + 780 * q^53 + 216 * q^54 - 754 * q^55 + 945 * q^56 + 60 * q^57 - 508 * q^58 + 766 * q^59 + 900 * q^60 + 1836 * q^61 + 173 * q^62 + 567 * q^63 + 805 * q^64 + 655 * q^65 - 387 * q^66 - 1290 * q^67 + 317 * q^68 - 621 * q^69 + 567 * q^70 + 1802 * q^71 + 1215 * q^72 + 598 * q^73 + 578 * q^74 + 1062 * q^75 - 1323 * q^76 + 266 * q^77 - 342 * q^78 - 1150 * q^79 + 795 * q^80 + 729 * q^81 - 1040 * q^82 + 1758 * q^83 + 798 * q^84 + 1078 * q^85 - 1920 * q^86 + 1215 * q^87 - 3056 * q^88 + 1400 * q^89 + 729 * q^90 + 749 * q^91 - 874 * q^92 - 546 * q^93 + 799 * q^94 + 2186 * q^95 + 1944 * q^96 + 1123 * q^97 + 392 * q^98 + 342 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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