LMFDB - Embedded newform 546.4.a.p.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [546,4,Mod(1,546)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("546.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(546, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	546.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,6,-9,12,7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$32.2150428631$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.118088.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 50x - 32 $ x^3 - 50*x - 32
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.645376$ of defining polynomial
Character	$\chi$	$=$	546.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +17.5010 q^{5} -6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +35.0020 q^{10} -3.08051 q^{11} -12.0000 q^{12} +13.0000 q^{13} -14.0000 q^{14} -52.5030 q^{15} +16.0000 q^{16} +124.540 q^{17} +18.0000 q^{18} -78.9607 q^{19} +70.0040 q^{20} +21.0000 q^{21} -6.16102 q^{22} +126.218 q^{23} -24.0000 q^{24} +181.285 q^{25} +26.0000 q^{26} -27.0000 q^{27} -28.0000 q^{28} -25.3812 q^{29} -105.006 q^{30} -215.249 q^{31} +32.0000 q^{32} +9.24154 q^{33} +249.080 q^{34} -122.507 q^{35} +36.0000 q^{36} +370.949 q^{37} -157.921 q^{38} -39.0000 q^{39} +140.008 q^{40} -215.291 q^{41} +42.0000 q^{42} -461.369 q^{43} -12.3220 q^{44} +157.509 q^{45} +252.436 q^{46} +478.874 q^{47} -48.0000 q^{48} +49.0000 q^{49} +362.569 q^{50} -373.621 q^{51} +52.0000 q^{52} +503.038 q^{53} -54.0000 q^{54} -53.9120 q^{55} -56.0000 q^{56} +236.882 q^{57} -50.7624 q^{58} +681.315 q^{59} -210.012 q^{60} -96.3991 q^{61} -430.499 q^{62} -63.0000 q^{63} +64.0000 q^{64} +227.513 q^{65} +18.4831 q^{66} +489.363 q^{67} +498.161 q^{68} -378.655 q^{69} -245.014 q^{70} +271.106 q^{71} +72.0000 q^{72} -529.647 q^{73} +741.897 q^{74} -543.854 q^{75} -315.843 q^{76} +21.5636 q^{77} -78.0000 q^{78} -910.161 q^{79} +280.016 q^{80} +81.0000 q^{81} -430.581 q^{82} +1051.22 q^{83} +84.0000 q^{84} +2179.58 q^{85} -922.738 q^{86} +76.1436 q^{87} -24.6441 q^{88} -305.279 q^{89} +315.018 q^{90} -91.0000 q^{91} +504.873 q^{92} +645.748 q^{93} +957.748 q^{94} -1381.89 q^{95} -96.0000 q^{96} +1128.48 q^{97} +98.0000 q^{98} -27.7246 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 6 q^{2} - 9 q^{3} + 12 q^{4} + 7 q^{5} - 18 q^{6} - 21 q^{7} + 24 q^{8} + 27 q^{9} + 14 q^{10} - 47 q^{11} - 36 q^{12} + 39 q^{13} - 42 q^{14} - 21 q^{15} + 48 q^{16} + 119 q^{17} + 54 q^{18} + 101 q^{19}+ \cdots - 423 q^{99}+O(q^{100}) $ 3 * q + 6 * q^2 - 9 * q^3 + 12 * q^4 + 7 * q^5 - 18 * q^6 - 21 * q^7 + 24 * q^8 + 27 * q^9 + 14 * q^10 - 47 * q^11 - 36 * q^12 + 39 * q^13 - 42 * q^14 - 21 * q^15 + 48 * q^16 + 119 * q^17 + 54 * q^18 + 101 * q^19 + 28 * q^20 + 63 * q^21 - 94 * q^22 - 27 * q^23 - 72 * q^24 + 266 * q^25 + 78 * q^26 - 81 * q^27 - 84 * q^28 + 345 * q^29 - 42 * q^30 + 152 * q^31 + 96 * q^32 + 141 * q^33 + 238 * q^34 - 49 * q^35 + 108 * q^36 + 227 * q^37 + 202 * q^38 - 117 * q^39 + 56 * q^40 + 452 * q^41 + 126 * q^42 - 415 * q^43 - 188 * q^44 + 63 * q^45 - 54 * q^46 + 240 * q^47 - 144 * q^48 + 147 * q^49 + 532 * q^50 - 357 * q^51 + 156 * q^52 + 874 * q^53 - 162 * q^54 + 1123 * q^55 - 168 * q^56 - 303 * q^57 + 690 * q^58 + 948 * q^59 - 84 * q^60 + 951 * q^61 + 304 * q^62 - 189 * q^63 + 192 * q^64 + 91 * q^65 + 282 * q^66 + 742 * q^67 + 476 * q^68 + 81 * q^69 - 98 * q^70 + 732 * q^71 + 216 * q^72 - 585 * q^73 + 454 * q^74 - 798 * q^75 + 404 * q^76 + 329 * q^77 - 234 * q^78 - 618 * q^79 + 112 * q^80 + 243 * q^81 + 904 * q^82 + 774 * q^83 + 252 * q^84 + 1273 * q^85 - 830 * q^86 - 1035 * q^87 - 376 * q^88 + 730 * q^89 + 126 * q^90 - 273 * q^91 - 108 * q^92 - 456 * q^93 + 480 * q^94 - 2617 * q^95 - 288 * q^96 + 2518 * q^97 + 294 * q^98 - 423 * q^99

Coefficient data

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

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

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

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	4.00000	0.500000
$5$	17.5010	1.56534	0.782668	−	0.622439i	$-0.213858\pi$
$5$	17.5010	1.56534	0.782668	+	0.622439i	$0.213858\pi$
$6$	−6.00000	−0.408248
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	35.0020	1.10686
$11$	−3.08051	−0.0844372	−0.0422186	−	0.999108i	$-0.513443\pi$
$11$	−3.08051	−0.0844372	−0.0422186	+	0.999108i	$0.513443\pi$
$12$	−12.0000	−0.288675
$13$	13.0000	0.277350
$13$	13.0000	0.277350
$14$	−14.0000	−0.267261
$15$	−52.5030	−0.903747
$16$	16.0000	0.250000
$17$	124.540	1.77679	0.888395	−	0.459079i	$-0.151821\pi$
$17$	124.540	1.77679	0.888395	+	0.459079i	$0.151821\pi$
$18$	18.0000	0.235702
$19$	−78.9607	−0.953412	−0.476706	−	0.879063i	$-0.658169\pi$
$19$	−78.9607	−0.953412	−0.476706	+	0.879063i	$0.658169\pi$
$20$	70.0040	0.782668
$21$	21.0000	0.218218
$22$	−6.16102	−0.0597061
$23$	126.218	1.14427	0.572137	−	0.820158i	$-0.306114\pi$
$23$	126.218	1.14427	0.572137	+	0.820158i	$0.306114\pi$
$24$	−24.0000	−0.204124
$25$	181.285	1.45028
$26$	26.0000	0.196116
$27$	−27.0000	−0.192450
$28$	−28.0000	−0.188982
$29$	−25.3812	−0.162523	−0.0812615	−	0.996693i	$-0.525895\pi$
$29$	−25.3812	−0.162523	−0.0812615	+	0.996693i	$0.525895\pi$
$30$	−105.006	−0.639046
$31$	−215.249	−1.24709	−0.623547	−	0.781786i	$-0.714309\pi$
$31$	−215.249	−1.24709	−0.623547	+	0.781786i	$0.714309\pi$
$32$	32.0000	0.176777
$33$	9.24154	0.0487498
$34$	249.080	1.25638
$35$	−122.507	−0.591642
$36$	36.0000	0.166667
$37$	370.949	1.64821	0.824103	−	0.566441i	$-0.191680\pi$
$37$	370.949	1.64821	0.824103	+	0.566441i	$0.191680\pi$
$38$	−157.921	−0.674164
$39$	−39.0000	−0.160128
$40$	140.008	0.553430
$41$	−215.291	−0.820067	−0.410034	−	0.912070i	$-0.634483\pi$
$41$	−215.291	−0.820067	−0.410034	+	0.912070i	$0.634483\pi$
$42$	42.0000	0.154303
$43$	−461.369	−1.63624	−0.818118	−	0.575051i	$-0.804982\pi$
$43$	−461.369	−1.63624	−0.818118	+	0.575051i	$0.804982\pi$
$44$	−12.3220	−0.0422186
$45$	157.509	0.521779
$46$	252.436	0.809124
$47$	478.874	1.48619	0.743095	−	0.669185i	$-0.233357\pi$
$47$	478.874	1.48619	0.743095	+	0.669185i	$0.233357\pi$
$48$	−48.0000	−0.144338
$49$	49.0000	0.142857
$50$	362.569	1.02550
$51$	−373.621	−1.02583
$52$	52.0000	0.138675
$53$	503.038	1.30373	0.651864	−	0.758336i	$-0.273987\pi$
$53$	503.038	1.30373	0.651864	+	0.758336i	$0.273987\pi$
$54$	−54.0000	−0.136083
$55$	−53.9120	−0.132173
$56$	−56.0000	−0.133631
$57$	236.882	0.550453
$58$	−50.7624	−0.114921
$59$	681.315	1.50338	0.751692	−	0.659515i	$-0.229238\pi$
$59$	681.315	1.50338	0.751692	+	0.659515i	$0.229238\pi$
$60$	−210.012	−0.451874
$61$	−96.3991	−0.202338	−0.101169	−	0.994869i	$-0.532258\pi$
$61$	−96.3991	−0.202338	−0.101169	+	0.994869i	$0.532258\pi$
$62$	−430.499	−0.881829
$63$	−63.0000	−0.125988
$64$	64.0000	0.125000
$65$	227.513	0.434146
$66$	18.4831	0.0344713
$67$	489.363	0.892316	0.446158	−	0.894954i	$-0.352792\pi$
$67$	489.363	0.892316	0.446158	+	0.894954i	$0.352792\pi$
$68$	498.161	0.888395
$69$	−378.655	−0.660647
$70$	−245.014	−0.418354
$71$	271.106	0.453160	0.226580	−	0.973993i	$-0.427246\pi$
$71$	271.106	0.453160	0.226580	+	0.973993i	$0.427246\pi$
$72$	72.0000	0.117851
$73$	−529.647	−0.849185	−0.424593	−	0.905384i	$-0.639583\pi$
$73$	−529.647	−0.849185	−0.424593	+	0.905384i	$0.639583\pi$
$74$	741.897	1.16546
$75$	−543.854	−0.837318
$76$	−315.843	−0.476706
$77$	21.5636	0.0319143
$78$	−78.0000	−0.113228
$79$	−910.161	−1.29622	−0.648108	−	0.761548i	$-0.724440\pi$
$79$	−910.161	−1.29622	−0.648108	+	0.761548i	$0.724440\pi$
$80$	280.016	0.391334
$81$	81.0000	0.111111
$82$	−430.581	−0.579875
$83$	1051.22	1.39020	0.695100	−	0.718913i	$-0.255360\pi$
$83$	1051.22	1.39020	0.695100	+	0.718913i	$0.255360\pi$
$84$	84.0000	0.109109
$85$	2179.58	2.78128
$86$	−922.738	−1.15699
$87$	76.1436	0.0938327
$88$	−24.6441	−0.0298531
$89$	−305.279	−0.363590	−0.181795	−	0.983336i	$-0.558191\pi$
$89$	−305.279	−0.363590	−0.181795	+	0.983336i	$0.558191\pi$
$90$	315.018	0.368953
$91$	−91.0000	−0.104828
$92$	504.873	0.572137
$93$	645.748	0.720010
$94$	957.748	1.05090
$95$	−1381.89	−1.49241
$96$	−96.0000	−0.102062
$97$	1128.48	1.18124	0.590619	−	0.806951i	$-0.298884\pi$
$97$	1128.48	1.18124	0.590619	+	0.806951i	$0.298884\pi$
$98$	98.0000	0.101015
$99$	−27.7246	−0.0281457
$100$	725.139	0.725139
$101$	1802.10	1.77540	0.887700	−	0.460422i	$-0.152302\pi$
$101$	1802.10	1.77540	0.887700	+	0.460422i	$0.152302\pi$
$102$	−747.241	−0.725372
$103$	642.894	0.615012	0.307506	−	0.951546i	$-0.400506\pi$
$103$	642.894	0.615012	0.307506	+	0.951546i	$0.400506\pi$
$104$	104.000	0.0980581
$105$	367.521	0.341584
$106$	1006.08	0.921875
$107$	−1546.98	−1.39768	−0.698841	−	0.715277i	$-0.746301\pi$
$107$	−1546.98	−1.39768	−0.698841	+	0.715277i	$0.746301\pi$
$108$	−108.000	−0.0962250
$109$	−1341.11	−1.17849	−0.589244	−	0.807955i	$-0.700574\pi$
$109$	−1341.11	−1.17849	−0.589244	+	0.807955i	$0.700574\pi$
$110$	−107.824	−0.0934602
$111$	−1112.85	−0.951592
$112$	−112.000	−0.0944911
$113$	−175.661	−0.146237	−0.0731184	−	0.997323i	$-0.523295\pi$
$113$	−175.661	−0.146237	−0.0731184	+	0.997323i	$0.523295\pi$
$114$	473.764	0.389229
$115$	2208.94	1.79117
$116$	−101.525	−0.0812615
$117$	117.000	0.0924500
$118$	1362.63	1.06305
$119$	−871.782	−0.671564
$120$	−420.024	−0.319523
$121$	−1321.51	−0.992870
$122$	−192.798	−0.143075
$123$	645.872	0.473466
$124$	−860.998	−0.623547
$125$	985.039	0.704836
$126$	−126.000	−0.0890871
$127$	1815.10	1.26822	0.634110	−	0.773243i	$-0.281367\pi$
$127$	1815.10	1.26822	0.634110	+	0.773243i	$0.281367\pi$
$128$	128.000	0.0883883
$129$	1384.11	0.944681
$130$	455.026	0.306988
$131$	1906.15	1.27130	0.635652	−	0.771976i	$-0.280731\pi$
$131$	1906.15	1.27130	0.635652	+	0.771976i	$0.280731\pi$
$132$	36.9661	0.0243749
$133$	552.725	0.360356
$134$	978.725	0.630963
$135$	−472.527	−0.301249
$136$	996.322	0.628190
$137$	−1018.48	−0.635142	−0.317571	−	0.948235i	$-0.602867\pi$
$137$	−1018.48	−0.635142	−0.317571	+	0.948235i	$0.602867\pi$
$138$	−757.309	−0.467148
$139$	−1780.42	−1.08643	−0.543213	−	0.839595i	$-0.682792\pi$
$139$	−1780.42	−1.08643	−0.543213	+	0.839595i	$0.682792\pi$
$140$	−490.028	−0.295821
$141$	−1436.62	−0.858053
$142$	542.212	0.320432
$143$	−40.0467	−0.0234187
$144$	144.000	0.0833333
$145$	−444.196	−0.254403
$146$	−1059.29	−0.600465
$147$	−147.000	−0.0824786
$148$	1483.79	0.824103
$149$	−3259.79	−1.79230	−0.896150	−	0.443751i	$-0.853647\pi$
$149$	−3259.79	−1.79230	−0.896150	+	0.443751i	$0.853647\pi$
$150$	−1087.71	−0.592073
$151$	−1198.37	−0.645842	−0.322921	−	0.946426i	$-0.604665\pi$
$151$	−1198.37	−0.645842	−0.322921	+	0.946426i	$0.604665\pi$
$152$	−631.686	−0.337082
$153$	1120.86	0.592264
$154$	43.1272	0.0225668
$155$	−3767.08	−1.95212
$156$	−156.000	−0.0800641
$157$	−1739.38	−0.884191	−0.442096	−	0.896968i	$-0.645765\pi$
$157$	−1739.38	−0.884191	−0.442096	+	0.896968i	$0.645765\pi$
$158$	−1820.32	−0.916563
$159$	−1509.11	−0.752707
$160$	560.032	0.276715
$161$	−883.527	−0.432495
$162$	162.000	0.0785674
$163$	−2260.00	−1.08599	−0.542997	−	0.839735i	$-0.682711\pi$
$163$	−2260.00	−1.08599	−0.542997	+	0.839735i	$0.682711\pi$
$164$	−861.163	−0.410034
$165$	161.736	0.0763099
$166$	2102.45	0.983021
$167$	−4230.60	−1.96032	−0.980160	−	0.198208i	$-0.936488\pi$
$167$	−4230.60	−1.96032	−0.980160	+	0.198208i	$0.936488\pi$
$168$	168.000	0.0771517
$169$	169.000	0.0769231
$170$	4359.16	1.96666
$171$	−710.646	−0.317804
$172$	−1845.48	−0.818118
$173$	−3493.30	−1.53521	−0.767604	−	0.640925i	$-0.778551\pi$
$173$	−3493.30	−1.53521	−0.767604	+	0.640925i	$0.778551\pi$
$174$	152.287	0.0663498
$175$	−1268.99	−0.548154
$176$	−49.2882	−0.0211093
$177$	−2043.94	−0.867979
$178$	−610.557	−0.257097
$179$	−1364.24	−0.569653	−0.284826	−	0.958579i	$-0.591936\pi$
$179$	−1364.24	−0.569653	−0.284826	+	0.958579i	$0.591936\pi$
$180$	630.036	0.260889
$181$	427.903	0.175722	0.0878612	−	0.996133i	$-0.471997\pi$
$181$	427.903	0.175722	0.0878612	+	0.996133i	$0.471997\pi$
$182$	−182.000	−0.0741249
$183$	289.197	0.116820
$184$	1009.75	0.404562
$185$	6491.97	2.58000
$186$	1291.50	0.509124
$187$	−383.648	−0.150027
$188$	1915.50	0.743095
$189$	189.000	0.0727393
$190$	−2763.78	−1.05529
$191$	−360.185	−0.136451	−0.0682253	−	0.997670i	$-0.521734\pi$
$191$	−360.185	−0.136451	−0.0682253	+	0.997670i	$0.521734\pi$
$192$	−192.000	−0.0721688
$193$	440.997	0.164475	0.0822375	−	0.996613i	$-0.473793\pi$
$193$	440.997	0.164475	0.0822375	+	0.996613i	$0.473793\pi$
$194$	2256.97	0.835261
$195$	−682.539	−0.250654
$196$	196.000	0.0714286
$197$	2861.57	1.03492	0.517459	−	0.855708i	$-0.326878\pi$
$197$	2861.57	1.03492	0.517459	+	0.855708i	$0.326878\pi$
$198$	−55.4492	−0.0199020
$199$	−1618.55	−0.576564	−0.288282	−	0.957546i	$-0.593084\pi$
$199$	−1618.55	−0.576564	−0.288282	+	0.957546i	$0.593084\pi$
$200$	1450.28	0.512751
$201$	−1468.09	−0.515179
$202$	3604.20	1.25540
$203$	177.668	0.0614279
$204$	−1494.48	−0.512915
$205$	−3767.80	−1.28368
$206$	1285.79	0.434879
$207$	1135.96	0.381425
$208$	208.000	0.0693375
$209$	243.239	0.0805035
$210$	735.042	0.241537
$211$	−1177.74	−0.384259	−0.192130	−	0.981370i	$-0.561539\pi$
$211$	−1177.74	−0.384259	−0.192130	+	0.981370i	$0.561539\pi$
$212$	2012.15	0.651864
$213$	−813.317	−0.261632
$214$	−3093.96	−0.988311
$215$	−8074.42	−2.56126
$216$	−216.000	−0.0680414
$217$	1506.75	0.471358
$218$	−2682.22	−0.833317
$219$	1588.94	0.490277
$220$	−215.648	−0.0660863
$221$	1619.02	0.492793
$222$	−2225.69	−0.672877
$223$	3038.67	0.912487	0.456243	−	0.889855i	$-0.349195\pi$
$223$	3038.67	0.912487	0.456243	+	0.889855i	$0.349195\pi$
$224$	−224.000	−0.0668153
$225$	1631.56	0.483426
$226$	−351.321	−0.103405
$227$	−528.647	−0.154571	−0.0772853	−	0.997009i	$-0.524625\pi$
$227$	−528.647	−0.154571	−0.0772853	+	0.997009i	$0.524625\pi$
$228$	947.529	0.275226
$229$	4075.81	1.17615	0.588073	−	0.808808i	$-0.299887\pi$
$229$	4075.81	1.17615	0.588073	+	0.808808i	$0.299887\pi$
$230$	4417.89	1.26655
$231$	−64.6907	−0.0184257
$232$	−203.050	−0.0574606
$233$	−2711.73	−0.762451	−0.381226	−	0.924482i	$-0.624498\pi$
$233$	−2711.73	−0.762451	−0.381226	+	0.924482i	$0.624498\pi$
$234$	234.000	0.0653720
$235$	8380.77	2.32639
$236$	2725.26	0.751692
$237$	2730.48	0.748371
$238$	−1743.56	−0.474867
$239$	2645.97	0.716123	0.358061	−	0.933698i	$-0.383438\pi$
$239$	2645.97	0.716123	0.358061	+	0.933698i	$0.383438\pi$
$240$	−840.048	−0.225937
$241$	−2842.96	−0.759879	−0.379940	−	0.925011i	$-0.624055\pi$
$241$	−2842.96	−0.759879	−0.379940	+	0.925011i	$0.624055\pi$
$242$	−2643.02	−0.702065
$243$	−243.000	−0.0641500
$244$	−385.596	−0.101169
$245$	857.549	0.223619
$246$	1291.74	0.334791
$247$	−1026.49	−0.264429
$248$	−1722.00	−0.440915
$249$	−3153.67	−0.802633
$250$	1970.08	0.498395
$251$	−6081.75	−1.52939	−0.764695	−	0.644393i	$-0.777110\pi$
$251$	−6081.75	−1.52939	−0.764695	+	0.644393i	$0.777110\pi$
$252$	−252.000	−0.0629941
$253$	−388.817	−0.0966193
$254$	3630.19	0.896766
$255$	−6538.73	−1.60577
$256$	256.000	0.0625000
$257$	3593.93	0.872309	0.436154	−	0.899872i	$-0.356340\pi$
$257$	3593.93	0.872309	0.436154	+	0.899872i	$0.356340\pi$
$258$	2768.22	0.667990
$259$	−2596.64	−0.622963
$260$	910.052	0.217073
$261$	−228.431	−0.0541744
$262$	3812.29	0.898947
$263$	−6555.80	−1.53706	−0.768532	−	0.639812i	$-0.779012\pi$
$263$	−6555.80	−1.53706	−0.768532	+	0.639812i	$0.779012\pi$
$264$	73.9323	0.0172357
$265$	8803.66	2.04077
$266$	1105.45	0.254810
$267$	915.836	0.209919
$268$	1957.45	0.446158
$269$	1206.16	0.273385	0.136693	−	0.990614i	$-0.456353\pi$
$269$	1206.16	0.273385	0.136693	+	0.990614i	$0.456353\pi$
$270$	−945.054	−0.213015
$271$	7204.84	1.61499	0.807496	−	0.589873i	$-0.200822\pi$
$271$	7204.84	1.61499	0.807496	+	0.589873i	$0.200822\pi$
$272$	1992.64	0.444198
$273$	273.000	0.0605228
$274$	−2036.95	−0.449113
$275$	−558.450	−0.122457
$276$	−1514.62	−0.330324
$277$	−5382.72	−1.16757	−0.583784	−	0.811909i	$-0.698428\pi$
$277$	−5382.72	−1.16757	−0.583784	+	0.811909i	$0.698428\pi$
$278$	−3560.84	−0.768219
$279$	−1937.24	−0.415698
$280$	−980.056	−0.209177
$281$	−7232.51	−1.53543	−0.767714	−	0.640793i	$-0.778606\pi$
$281$	−7232.51	−1.53543	−0.767714	+	0.640793i	$0.778606\pi$
$282$	−2873.24	−0.606735
$283$	−1033.41	−0.217066	−0.108533	−	0.994093i	$-0.534615\pi$
$283$	−1033.41	−0.217066	−0.108533	+	0.994093i	$0.534615\pi$
$284$	1084.42	0.226580
$285$	4145.67	0.861644
$286$	−80.0933	−0.0165595
$287$	1507.03	0.309956
$288$	288.000	0.0589256
$289$	10597.3	2.15699
$290$	−888.392	−0.179890
$291$	−3385.45	−0.681988
$292$	−2118.59	−0.424593
$293$	−1698.95	−0.338750	−0.169375	−	0.985552i	$-0.554175\pi$
$293$	−1698.95	−0.338750	−0.169375	+	0.985552i	$0.554175\pi$
$294$	−294.000	−0.0583212
$295$	11923.7	2.35330
$296$	2967.59	0.582729
$297$	83.1738	0.0162499
$298$	−6519.59	−1.26735
$299$	1640.84	0.317365
$300$	−2175.42	−0.418659
$301$	3229.58	0.618439
$302$	−2396.75	−0.456679
$303$	−5406.29	−1.02503
$304$	−1263.37	−0.238353
$305$	−1687.08	−0.316727
$306$	2241.72	0.418794
$307$	−5906.06	−1.09797	−0.548984	−	0.835833i	$-0.684985\pi$
$307$	−5906.06	−1.09797	−0.548984	+	0.835833i	$0.684985\pi$
$308$	86.2543	0.0159571
$309$	−1928.68	−0.355077
$310$	−7534.16	−1.38036
$311$	7047.32	1.28494	0.642471	−	0.766310i	$-0.277909\pi$
$311$	7047.32	1.28494	0.642471	+	0.766310i	$0.277909\pi$
$312$	−312.000	−0.0566139
$313$	−3424.01	−0.618327	−0.309164	−	0.951009i	$-0.600049\pi$
$313$	−3424.01	−0.618327	−0.309164	+	0.951009i	$0.600049\pi$
$314$	−3478.77	−0.625217
$315$	−1102.56	−0.197214
$316$	−3640.64	−0.648108
$317$	−6110.29	−1.08261	−0.541306	−	0.840826i	$-0.682070\pi$
$317$	−6110.29	−1.08261	−0.541306	+	0.840826i	$0.682070\pi$
$318$	−3018.23	−0.532245
$319$	78.1871	0.0137230
$320$	1120.06	0.195667
$321$	4640.93	0.806952
$322$	−1767.05	−0.305820
$323$	−9833.78	−1.69401
$324$	324.000	0.0555556
$325$	2356.70	0.402235
$326$	−4520.00	−0.767914
$327$	4023.34	0.680401
$328$	−1722.33	−0.289937
$329$	−3352.12	−0.561727
$330$	323.472	0.0539593
$331$	−8243.20	−1.36884	−0.684422	−	0.729086i	$-0.739945\pi$
$331$	−8243.20	−1.36884	−0.684422	+	0.729086i	$0.739945\pi$
$332$	4204.89	0.695100
$333$	3338.54	0.549402
$334$	−8461.19	−1.38616
$335$	8564.33	1.39677
$336$	336.000	0.0545545
$337$	−370.624	−0.0599086	−0.0299543	−	0.999551i	$-0.509536\pi$
$337$	−370.624	−0.0599086	−0.0299543	+	0.999551i	$0.509536\pi$
$338$	338.000	0.0543928
$339$	526.982	0.0844299
$340$	8718.31	1.39064
$341$	663.078	0.105301
$342$	−1421.29	−0.224721
$343$	−343.000	−0.0539949
$344$	−3690.95	−0.578497
$345$	−6626.83	−1.03413
$346$	−6986.60	−1.08556
$347$	8500.86	1.31513	0.657565	−	0.753398i	$-0.271587\pi$
$347$	8500.86	1.31513	0.657565	+	0.753398i	$0.271587\pi$
$348$	304.574	0.0469164
$349$	10345.7	1.58679	0.793397	−	0.608704i	$-0.208310\pi$
$349$	10345.7	1.58679	0.793397	+	0.608704i	$0.208310\pi$
$350$	−2537.99	−0.387603
$351$	−351.000	−0.0533761
$352$	−98.5764	−0.0149265
$353$	−10703.4	−1.61383	−0.806917	−	0.590665i	$-0.798865\pi$
$353$	−10703.4	−1.61383	−0.806917	+	0.590665i	$0.798865\pi$
$354$	−4087.89	−0.613754
$355$	4744.62	0.709347
$356$	−1221.11	−0.181795
$357$	2615.34	0.387728
$358$	−2728.47	−0.402805
$359$	−2409.71	−0.354261	−0.177131	−	0.984187i	$-0.556682\pi$
$359$	−2409.71	−0.354261	−0.177131	+	0.984187i	$0.556682\pi$
$360$	1260.07	0.184477
$361$	−624.206	−0.0910054
$362$	855.805	0.124254
$363$	3964.53	0.573234
$364$	−364.000	−0.0524142
$365$	−9269.35	−1.32926
$366$	578.394	0.0826043
$367$	−1895.62	−0.269620	−0.134810	−	0.990871i	$-0.543042\pi$
$367$	−1895.62	−0.269620	−0.134810	+	0.990871i	$0.543042\pi$
$368$	2019.49	0.286069
$369$	−1937.62	−0.273356
$370$	12983.9	1.82433
$371$	−3521.26	−0.492763
$372$	2582.99	0.360005
$373$	−3312.84	−0.459872	−0.229936	−	0.973206i	$-0.573852\pi$
$373$	−3312.84	−0.459872	−0.229936	+	0.973206i	$0.573852\pi$
$374$	−767.295	−0.106085
$375$	−2955.12	−0.406938
$376$	3830.99	0.525448
$377$	−329.955	−0.0450758
$378$	378.000	0.0514344
$379$	5795.41	0.785462	0.392731	−	0.919653i	$-0.371530\pi$
$379$	5795.41	0.785462	0.392731	+	0.919653i	$0.371530\pi$
$380$	−5527.56	−0.746205
$381$	−5445.29	−0.732207
$382$	−720.370	−0.0964851
$383$	10767.6	1.43655	0.718276	−	0.695758i	$-0.244931\pi$
$383$	10767.6	1.43655	0.718276	+	0.695758i	$0.244931\pi$
$384$	−384.000	−0.0510310
$385$	377.384	0.0499566
$386$	881.994	0.116301
$387$	−4152.32	−0.545412
$388$	4513.93	0.590619
$389$	162.786	0.0212174	0.0106087	−	0.999944i	$-0.496623\pi$
$389$	162.786	0.0212174	0.0106087	+	0.999944i	$0.496623\pi$
$390$	−1365.08	−0.177239
$391$	15719.2	2.03314
$392$	392.000	0.0505076
$393$	−5718.44	−0.733987
$394$	5723.15	0.731797
$395$	−15928.7	−2.02901
$396$	−110.898	−0.0140729
$397$	6644.79	0.840031	0.420016	−	0.907517i	$-0.362025\pi$
$397$	6644.79	0.840031	0.420016	+	0.907517i	$0.362025\pi$
$398$	−3237.11	−0.407692
$399$	−1658.17	−0.208052
$400$	2900.56	0.362569
$401$	7449.38	0.927691	0.463846	−	0.885916i	$-0.346469\pi$
$401$	7449.38	0.927691	0.463846	+	0.885916i	$0.346469\pi$
$402$	−2936.18	−0.364286
$403$	−2798.24	−0.345882
$404$	7208.39	0.887700
$405$	1417.58	0.173926
$406$	355.337	0.0434361
$407$	−1142.71	−0.139170
$408$	−2988.97	−0.362686
$409$	−5490.61	−0.663798	−0.331899	−	0.943315i	$-0.607689\pi$
$409$	−5490.61	−0.663798	−0.331899	+	0.943315i	$0.607689\pi$
$410$	−7535.60	−0.907699
$411$	3055.43	0.366699
$412$	2571.58	0.307506
$413$	−4769.20	−0.568225
$414$	2271.93	0.269708
$415$	18397.4	2.17613
$416$	416.000	0.0490290
$417$	5341.26	0.627249
$418$	486.479	0.0569245
$419$	1600.56	0.186617	0.0933087	−	0.995637i	$-0.470256\pi$
$419$	1600.56	0.186617	0.0933087	+	0.995637i	$0.470256\pi$
$420$	1470.08	0.170792
$421$	3112.21	0.360285	0.180142	−	0.983641i	$-0.442344\pi$
$421$	3112.21	0.360285	0.180142	+	0.983641i	$0.442344\pi$
$422$	−2355.47	−0.271712
$423$	4309.87	0.495397
$424$	4024.30	0.460937
$425$	22577.2	2.57684
$426$	−1626.63	−0.185002
$427$	674.793	0.0764767
$428$	−6187.91	−0.698841
$429$	120.140	0.0135208
$430$	−16148.8	−1.81108
$431$	−586.221	−0.0655158	−0.0327579	−	0.999463i	$-0.510429\pi$
$431$	−586.221	−0.0655158	−0.0327579	+	0.999463i	$0.510429\pi$
$432$	−432.000	−0.0481125
$433$	−2888.50	−0.320583	−0.160292	−	0.987070i	$-0.551243\pi$
$433$	−2888.50	−0.320583	−0.160292	+	0.987070i	$0.551243\pi$
$434$	3013.49	0.333300
$435$	1332.59	0.146880
$436$	−5364.45	−0.589244
$437$	−9966.28	−1.09096
$438$	3177.88	0.346678
$439$	−8487.06	−0.922700	−0.461350	−	0.887218i	$-0.652635\pi$
$439$	−8487.06	−0.922700	−0.461350	+	0.887218i	$0.652635\pi$
$440$	−431.296	−0.0467301
$441$	441.000	0.0476190
$442$	3238.05	0.348457
$443$	−16021.2	−1.71826	−0.859129	−	0.511758i	$-0.828994\pi$
$443$	−16021.2	−1.71826	−0.859129	+	0.511758i	$0.828994\pi$
$444$	−4451.38	−0.475796
$445$	−5342.68	−0.569140
$446$	6077.34	0.645225
$447$	9779.38	1.03478
$448$	−448.000	−0.0472456
$449$	−10427.6	−1.09602	−0.548008	−	0.836473i	$-0.684614\pi$
$449$	−10427.6	−1.09602	−0.548008	+	0.836473i	$0.684614\pi$
$450$	3263.13	0.341834
$451$	663.205	0.0692442
$452$	−702.643	−0.0731184
$453$	3595.12	0.372877
$454$	−1057.29	−0.109298
$455$	−1592.59	−0.164092
$456$	1895.06	0.194614
$457$	−12167.7	−1.24547	−0.622736	−	0.782432i	$-0.713979\pi$
$457$	−12167.7	−1.24547	−0.622736	+	0.782432i	$0.713979\pi$
$458$	8151.62	0.831660
$459$	−3362.59	−0.341944
$460$	8835.77	0.895587
$461$	8258.92	0.834395	0.417198	−	0.908816i	$-0.363012\pi$
$461$	8258.92	0.834395	0.417198	+	0.908816i	$0.363012\pi$
$462$	−129.381	−0.0130289
$463$	13810.1	1.38620	0.693098	−	0.720843i	$-0.256245\pi$
$463$	13810.1	1.38620	0.693098	+	0.720843i	$0.256245\pi$
$464$	−406.099	−0.0406308
$465$	11301.2	1.12706
$466$	−5423.45	−0.539134
$467$	−3244.95	−0.321538	−0.160769	−	0.986992i	$-0.551397\pi$
$467$	−3244.95	−0.321538	−0.160769	+	0.986992i	$0.551397\pi$
$468$	468.000	0.0462250
$469$	−3425.54	−0.337264
$470$	16761.5	1.64501
$471$	5218.15	0.510488
$472$	5450.52	0.531526
$473$	1421.25	0.138159
$474$	5460.96	0.529178
$475$	−14314.4	−1.38271
$476$	−3487.13	−0.335782
$477$	4527.34	0.434576
$478$	5291.93	0.506375
$479$	233.921	0.0223134	0.0111567	−	0.999938i	$-0.496449\pi$
$479$	233.921	0.0223134	0.0111567	+	0.999938i	$0.496449\pi$
$480$	−1680.10	−0.159761
$481$	4822.33	0.457130
$482$	−5685.91	−0.537316
$483$	2650.58	0.249701
$484$	−5286.04	−0.496435
$485$	19749.6	1.84903
$486$	−486.000	−0.0453609
$487$	1438.64	0.133862	0.0669312	−	0.997758i	$-0.478679\pi$
$487$	1438.64	0.133862	0.0669312	+	0.997758i	$0.478679\pi$
$488$	−771.192	−0.0715374
$489$	6780.01	0.626999
$490$	1715.10	0.158123
$491$	−1743.79	−0.160277	−0.0801385	−	0.996784i	$-0.525536\pi$
$491$	−1743.79	−0.160277	−0.0801385	+	0.996784i	$0.525536\pi$
$492$	2583.49	0.236733
$493$	−3160.98	−0.288769
$494$	−2052.98	−0.186979
$495$	−485.208	−0.0440575
$496$	−3443.99	−0.311774
$497$	−1897.74	−0.171278
$498$	−6307.34	−0.567547
$499$	5389.51	0.483502	0.241751	−	0.970338i	$-0.422278\pi$
$499$	5389.51	0.483502	0.241751	+	0.970338i	$0.422278\pi$
$500$	3940.16	0.352418
$501$	12691.8	1.13179
$502$	−12163.5	−1.08144
$503$	−2553.60	−0.226361	−0.113180	−	0.993574i	$-0.536104\pi$
$503$	−2553.60	−0.226361	−0.113180	+	0.993574i	$0.536104\pi$
$504$	−504.000	−0.0445435
$505$	31538.5	2.77910
$506$	−777.633	−0.0683202
$507$	−507.000	−0.0444116
$508$	7260.39	0.634110
$509$	5135.74	0.447226	0.223613	−	0.974678i	$-0.428215\pi$
$509$	5135.74	0.447226	0.223613	+	0.974678i	$0.428215\pi$
$510$	−13077.5	−1.13545
$511$	3707.53	0.320962
$512$	512.000	0.0441942
$513$	2131.94	0.183484
$514$	7187.86	0.616815
$515$	11251.3	0.962701
$516$	5536.43	0.472341
$517$	−1475.18	−0.125490
$518$	−5193.28	−0.440501
$519$	10479.9	0.886352
$520$	1820.10	0.153494
$521$	12293.5	1.03376	0.516880	−	0.856058i	$-0.327093\pi$
$521$	12293.5	1.03376	0.516880	+	0.856058i	$0.327093\pi$
$522$	−456.861	−0.0383071
$523$	767.695	0.0641854	0.0320927	−	0.999485i	$-0.489783\pi$
$523$	767.695	0.0641854	0.0320927	+	0.999485i	$0.489783\pi$
$524$	7624.58	0.635652
$525$	3806.98	0.316477
$526$	−13111.6	−1.08687
$527$	−26807.2	−2.21583
$528$	147.865	0.0121875
$529$	3764.03	0.309364
$530$	17607.3	1.44304
$531$	6131.83	0.501128
$532$	2210.90	0.180178
$533$	−2798.78	−0.227446
$534$	1831.67	0.148435
$535$	−27073.6	−2.18784
$536$	3914.90	0.315481
$537$	4092.71	0.328889
$538$	2412.31	0.193313
$539$	−150.945	−0.0120625
$540$	−1890.11	−0.150625
$541$	−4911.09	−0.390285	−0.195143	−	0.980775i	$-0.562517\pi$
$541$	−4911.09	−0.390285	−0.195143	+	0.980775i	$0.562517\pi$
$542$	14409.7	1.14197
$543$	−1283.71	−0.101453
$544$	3985.29	0.314095
$545$	−23470.8	−1.84473
$546$	546.000	0.0427960
$547$	12903.1	1.00859	0.504293	−	0.863533i	$-0.331753\pi$
$547$	12903.1	1.00859	0.504293	+	0.863533i	$0.331753\pi$
$548$	−4073.91	−0.317571
$549$	−867.592	−0.0674461
$550$	−1116.90	−0.0865905
$551$	2004.12	0.154951
$552$	−3029.24	−0.233574
$553$	6371.13	0.489924
$554$	−10765.4	−0.825595
$555$	−19475.9	−1.48956
$556$	−7121.68	−0.543213
$557$	−1487.99	−0.113193	−0.0565963	−	0.998397i	$-0.518025\pi$
$557$	−1487.99	−0.113193	−0.0565963	+	0.998397i	$0.518025\pi$
$558$	−3874.49	−0.293943
$559$	−5997.80	−0.453810
$560$	−1960.11	−0.147910
$561$	1150.94	0.0866183
$562$	−14465.0	−1.08571
$563$	12717.7	0.952022	0.476011	−	0.879439i	$-0.342082\pi$
$563$	12717.7	0.952022	0.476011	+	0.879439i	$0.342082\pi$
$564$	−5746.49	−0.429026
$565$	−3074.24	−0.228910
$566$	−2066.82	−0.153489
$567$	−567.000	−0.0419961
$568$	2168.85	0.160216
$569$	−6292.11	−0.463584	−0.231792	−	0.972765i	$-0.574459\pi$
$569$	−6292.11	−0.463584	−0.231792	+	0.972765i	$0.574459\pi$
$570$	8291.34	0.609274
$571$	−11686.0	−0.856467	−0.428234	−	0.903668i	$-0.640864\pi$
$571$	−11686.0	−0.856467	−0.428234	+	0.903668i	$0.640864\pi$
$572$	−160.187	−0.0117093
$573$	1080.55	0.0787798
$574$	3014.07	0.219172
$575$	22881.4	1.65952
$576$	576.000	0.0416667
$577$	22460.2	1.62050	0.810250	−	0.586085i	$-0.199331\pi$
$577$	22460.2	1.62050	0.810250	+	0.586085i	$0.199331\pi$
$578$	21194.5	1.52522
$579$	−1322.99	−0.0949597
$580$	−1776.78	−0.127202
$581$	−7358.56	−0.525447
$582$	−6770.90	−0.482238
$583$	−1549.61	−0.110083
$584$	−4237.18	−0.300232
$585$	2047.62	0.144715
$586$	−3397.91	−0.239533
$587$	2120.31	0.149088	0.0745438	−	0.997218i	$-0.476250\pi$
$587$	2120.31	0.149088	0.0745438	+	0.997218i	$0.476250\pi$
$588$	−588.000	−0.0412393
$589$	16996.2	1.18900
$590$	23847.4	1.66403
$591$	−8584.72	−0.597510
$592$	5935.18	0.412051
$593$	12568.2	0.870344	0.435172	−	0.900347i	$-0.356688\pi$
$593$	12568.2	0.870344	0.435172	+	0.900347i	$0.356688\pi$
$594$	166.348	0.0114904
$595$	−15257.0	−1.05122
$596$	−13039.2	−0.896150
$597$	4855.66	0.332879
$598$	3281.67	0.224411
$599$	−1115.60	−0.0760969	−0.0380485	−	0.999276i	$-0.512114\pi$
$599$	−1115.60	−0.0760969	−0.0380485	+	0.999276i	$0.512114\pi$
$600$	−4350.83	−0.296037
$601$	−18330.1	−1.24409	−0.622046	−	0.782980i	$-0.713698\pi$
$601$	−18330.1	−1.24409	−0.622046	+	0.782980i	$0.713698\pi$
$602$	6459.17	0.437302
$603$	4404.26	0.297439
$604$	−4793.49	−0.322921
$605$	−23127.7	−1.55418
$606$	−10812.6	−0.724804
$607$	−8933.61	−0.597370	−0.298685	−	0.954352i	$-0.596548\pi$
$607$	−8933.61	−0.597370	−0.298685	+	0.954352i	$0.596548\pi$
$608$	−2526.74	−0.168541
$609$	−533.005	−0.0354654
$610$	−3374.16	−0.223960
$611$	6225.36	0.412195
$612$	4483.45	0.296132
$613$	−5461.96	−0.359880	−0.179940	−	0.983678i	$-0.557590\pi$
$613$	−5461.96	−0.359880	−0.179940	+	0.983678i	$0.557590\pi$
$614$	−11812.1	−0.776381
$615$	11303.4	0.741133
$616$	172.509	0.0112834
$617$	22936.9	1.49661	0.748303	−	0.663357i	$-0.230869\pi$
$617$	22936.9	1.49661	0.748303	+	0.663357i	$0.230869\pi$
$618$	−3857.36	−0.251078
$619$	20204.7	1.31195	0.655974	−	0.754784i	$-0.272258\pi$
$619$	20204.7	1.31195	0.655974	+	0.754784i	$0.272258\pi$
$620$	−15068.3	−0.976061
$621$	−3407.89	−0.220216
$622$	14094.6	0.908591
$623$	2136.95	0.137424
$624$	−624.000	−0.0400320
$625$	−5421.44	−0.346972
$626$	−6848.02	−0.437223
$627$	−729.718	−0.0464787
$628$	−6957.54	−0.442096
$629$	46198.0	2.92852
$630$	−2205.13	−0.139451
$631$	−29155.9	−1.83943	−0.919714	−	0.392589i	$-0.871579\pi$
$631$	−29155.9	−1.83943	−0.919714	+	0.392589i	$0.871579\pi$
$632$	−7281.29	−0.458282
$633$	3533.21	0.221852
$634$	−12220.6	−0.765522
$635$	31766.0	1.98519
$636$	−6036.45	−0.376354
$637$	637.000	0.0396214
$638$	156.374	0.00970362
$639$	2439.95	0.151053
$640$	2240.13	0.138357
$641$	−532.914	−0.0328375	−0.0164188	−	0.999865i	$-0.505226\pi$
$641$	−532.914	−0.0328375	−0.0164188	+	0.999865i	$0.505226\pi$
$642$	9281.87	0.570601
$643$	1464.36	0.0898113	0.0449056	−	0.998991i	$-0.485701\pi$
$643$	1464.36	0.0898113	0.0449056	+	0.998991i	$0.485701\pi$
$644$	−3534.11	−0.216248
$645$	24223.3	1.47874
$646$	−19667.6	−1.19785
$647$	16260.7	0.988056	0.494028	−	0.869446i	$-0.335524\pi$
$647$	16260.7	0.988056	0.494028	+	0.869446i	$0.335524\pi$
$648$	648.000	0.0392837
$649$	−2098.80	−0.126941
$650$	4713.40	0.284423
$651$	−4520.24	−0.272138
$652$	−9040.01	−0.542997
$653$	22089.7	1.32380	0.661898	−	0.749594i	$-0.269751\pi$
$653$	22089.7	1.32380	0.661898	+	0.749594i	$0.269751\pi$
$654$	8046.67	0.481116
$655$	33359.4	1.99002
$656$	−3444.65	−0.205017
$657$	−4766.83	−0.283062
$658$	−6704.24	−0.397201
$659$	24416.3	1.44329	0.721643	−	0.692266i	$-0.243387\pi$
$659$	24416.3	1.44329	0.721643	+	0.692266i	$0.243387\pi$
$660$	646.944	0.0381550
$661$	12583.1	0.740433	0.370216	−	0.928946i	$-0.379284\pi$
$661$	12583.1	0.740433	0.370216	+	0.928946i	$0.379284\pi$
$662$	−16486.4	−0.967919
$663$	−4857.07	−0.284514
$664$	8409.78	0.491510
$665$	9673.24	0.564078
$666$	6677.08	0.388486
$667$	−3203.57	−0.185971
$668$	−16922.4	−0.980160
$669$	−9116.02	−0.526824
$670$	17128.7	0.987669
$671$	296.958	0.0170849
$672$	672.000	0.0385758
$673$	14986.3	0.858363	0.429181	−	0.903218i	$-0.358802\pi$
$673$	14986.3	0.858363	0.429181	+	0.903218i	$0.358802\pi$
$674$	−741.249	−0.0423618
$675$	−4894.69	−0.279106
$676$	676.000	0.0384615
$677$	14413.0	0.818224	0.409112	−	0.912484i	$-0.365838\pi$
$677$	14413.0	0.818224	0.409112	+	0.912484i	$0.365838\pi$
$678$	1053.96	0.0597010
$679$	−7899.38	−0.446466
$680$	17436.6	0.983329
$681$	1585.94	0.0892414
$682$	1326.16	0.0744592
$683$	−29101.8	−1.63038	−0.815190	−	0.579194i	$-0.803367\pi$
$683$	−29101.8	−1.63038	−0.815190	+	0.579194i	$0.803367\pi$
$684$	−2842.59	−0.158902
$685$	−17824.4	−0.994210
$686$	−686.000	−0.0381802
$687$	−12227.4	−0.679048
$688$	−7381.91	−0.409059
$689$	6539.49	0.361589
$690$	−13253.7	−0.731244
$691$	−21241.9	−1.16943	−0.584717	−	0.811238i	$-0.698794\pi$
$691$	−21241.9	−1.16943	−0.584717	+	0.811238i	$0.698794\pi$
$692$	−13973.2	−0.767604
$693$	194.072	0.0106381
$694$	17001.7	0.929937
$695$	−31159.1	−1.70062
$696$	609.149	0.0331749
$697$	−26812.3	−1.45709
$698$	20691.3	1.12203
$699$	8135.18	0.440201
$700$	−5075.97	−0.274077
$701$	21407.5	1.15342	0.576711	−	0.816948i	$-0.304336\pi$
$701$	21407.5	1.15342	0.576711	+	0.816948i	$0.304336\pi$
$702$	−702.000	−0.0377426
$703$	−29290.4	−1.57142
$704$	−197.153	−0.0105547
$705$	−25142.3	−1.34314
$706$	−21406.8	−1.14115
$707$	−12614.7	−0.671038
$708$	−8175.77	−0.433989
$709$	14533.0	0.769816	0.384908	−	0.922955i	$-0.374233\pi$
$709$	14533.0	0.769816	0.384908	+	0.922955i	$0.374233\pi$
$710$	9489.24	0.501584
$711$	−8191.45	−0.432072
$712$	−2442.23	−0.128548
$713$	−27168.4	−1.42702
$714$	5230.69	0.274165
$715$	−700.856	−0.0366581
$716$	−5456.95	−0.284826
$717$	−7937.90	−0.413454
$718$	−4819.43	−0.250501
$719$	−96.3244	−0.00499624	−0.00249812	−	0.999997i	$-0.500795\pi$
$719$	−96.3244	−0.00499624	−0.00249812	+	0.999997i	$0.500795\pi$
$720$	2520.14	0.130445
$721$	−4500.26	−0.232453
$722$	−1248.41	−0.0643506
$723$	8528.87	0.438716
$724$	1711.61	0.0878612
$725$	−4601.22	−0.235704
$726$	7929.06	0.405338
$727$	−18844.6	−0.961359	−0.480680	−	0.876896i	$-0.659610\pi$
$727$	−18844.6	−0.961359	−0.480680	+	0.876896i	$0.659610\pi$
$728$	−728.000	−0.0370625
$729$	729.000	0.0370370
$730$	−18538.7	−0.939929
$731$	−57459.0	−2.90725
$732$	1156.79	0.0584100
$733$	−10522.5	−0.530231	−0.265115	−	0.964217i	$-0.585410\pi$
$733$	−10522.5	−0.530231	−0.265115	+	0.964217i	$0.585410\pi$
$734$	−3791.25	−0.190650
$735$	−2572.65	−0.129107
$736$	4038.98	0.202281
$737$	−1507.49	−0.0753446
$738$	−3875.23	−0.193292
$739$	6962.26	0.346564	0.173282	−	0.984872i	$-0.444563\pi$
$739$	6962.26	0.346564	0.173282	+	0.984872i	$0.444563\pi$
$740$	25967.9	1.29000
$741$	3079.47	0.152668
$742$	−7042.53	−0.348436
$743$	12884.2	0.636171	0.318085	−	0.948062i	$-0.396960\pi$
$743$	12884.2	0.636171	0.318085	+	0.948062i	$0.396960\pi$
$744$	5165.99	0.254562
$745$	−57049.6	−2.80555
$746$	−6625.68	−0.325179
$747$	9461.00	0.463400
$748$	−1534.59	−0.0750136
$749$	10828.8	0.528274
$750$	−5910.23	−0.287748
$751$	6403.18	0.311126	0.155563	−	0.987826i	$-0.450281\pi$
$751$	6403.18	0.311126	0.155563	+	0.987826i	$0.450281\pi$
$752$	7661.99	0.371548
$753$	18245.3	0.882994
$754$	−659.911	−0.0318734
$755$	−20972.7	−1.01096
$756$	756.000	0.0363696
$757$	−30018.1	−1.44125	−0.720624	−	0.693326i	$-0.756145\pi$
$757$	−30018.1	−1.44125	−0.720624	+	0.693326i	$0.756145\pi$
$758$	11590.8	0.555406
$759$	1166.45	0.0557832
$760$	−11055.1	−0.527647
$761$	−30647.9	−1.45990	−0.729952	−	0.683498i	$-0.760458\pi$
$761$	−30647.9	−1.45990	−0.729952	+	0.683498i	$0.760458\pi$
$762$	−10890.6	−0.517748
$763$	9387.79	0.445427
$764$	−1440.74	−0.0682253
$765$	19616.2	0.927092
$766$	21535.2	1.01580
$767$	8857.09	0.416963
$768$	−768.000	−0.0360844
$769$	−34598.8	−1.62245	−0.811225	−	0.584734i	$-0.801199\pi$
$769$	−34598.8	−1.62245	−0.811225	+	0.584734i	$0.801199\pi$
$770$	754.768	0.0353246
$771$	−10781.8	−0.503628
$772$	1763.99	0.0822375
$773$	−32387.7	−1.50699	−0.753495	−	0.657454i	$-0.771633\pi$
$773$	−32387.7	−1.50699	−0.753495	+	0.657454i	$0.771633\pi$
$774$	−8304.65	−0.385664
$775$	−39021.4	−1.80863
$776$	9027.86	0.417631
$777$	7789.92	0.359668
$778$	325.571	0.0150030
$779$	16999.5	0.781862
$780$	−2730.15	−0.125327
$781$	−835.145	−0.0382635
$782$	31438.5	1.43764
$783$	685.292	0.0312776
$784$	784.000	0.0357143
$785$	−30441.0	−1.38406
$786$	−11436.9	−0.519007
$787$	11338.0	0.513540	0.256770	−	0.966472i	$-0.417342\pi$
$787$	11338.0	0.513540	0.256770	+	0.966472i	$0.417342\pi$
$788$	11446.3	0.517459
$789$	19667.4	0.887424
$790$	−31857.4	−1.43473
$791$	1229.62	0.0552723
$792$	−221.797	−0.00995102
$793$	−1253.19	−0.0561185
$794$	13289.6	0.593992
$795$	−26411.0	−1.17824
$796$	−6474.21	−0.288282
$797$	18132.0	0.805856	0.402928	−	0.915232i	$-0.367992\pi$
$797$	18132.0	0.805856	0.402928	+	0.915232i	$0.367992\pi$
$798$	−3316.35	−0.147115
$799$	59639.1	2.64065
$800$	5801.11	0.256375
$801$	−2747.51	−0.121197
$802$	14898.8	0.655977
$803$	1631.58	0.0717028
$804$	−5872.35	−0.257589
$805$	−15462.6	−0.677000
$806$	−5596.48	−0.244575
$807$	−3618.47	−0.157839
$808$	14416.8	0.627699
$809$	34658.2	1.50620	0.753100	−	0.657906i	$-0.228558\pi$
$809$	34658.2	1.50620	0.753100	+	0.657906i	$0.228558\pi$
$810$	2835.16	0.122984
$811$	−27092.8	−1.17306	−0.586532	−	0.809926i	$-0.699507\pi$
$811$	−27092.8	−1.17306	−0.586532	+	0.809926i	$0.699507\pi$
$812$	710.673	0.0307140
$813$	−21614.5	−0.932416
$814$	−2285.42	−0.0984079
$815$	−39552.3	−1.69995
$816$	−5977.93	−0.256458
$817$	36430.0	1.56001
$818$	−10981.2	−0.469376
$819$	−819.000	−0.0349428
$820$	−15071.2	−0.641840
$821$	11640.6	0.494837	0.247419	−	0.968909i	$-0.420418\pi$
$821$	11640.6	0.494837	0.247419	+	0.968909i	$0.420418\pi$
$822$	6110.86	0.259295
$823$	−28317.7	−1.19938	−0.599692	−	0.800231i	$-0.704710\pi$
$823$	−28317.7	−1.19938	−0.599692	+	0.800231i	$0.704710\pi$
$824$	5143.15	0.217440
$825$	1675.35	0.0707008
$826$	−9538.40	−0.401796
$827$	−24252.5	−1.01976	−0.509881	−	0.860245i	$-0.670311\pi$
$827$	−24252.5	−1.01976	−0.509881	+	0.860245i	$0.670311\pi$
$828$	4543.85	0.190712
$829$	165.611	0.00693837	0.00346919	−	0.999994i	$-0.498896\pi$
$829$	165.611	0.00693837	0.00346919	+	0.999994i	$0.498896\pi$
$830$	36794.9	1.53876
$831$	16148.2	0.674096
$832$	832.000	0.0346688
$833$	6102.47	0.253827
$834$	10682.5	0.443532
$835$	−74039.7	−3.06856
$836$	972.958	0.0402517
$837$	5811.73	0.240003
$838$	3201.13	0.131958
$839$	10872.1	0.447374	0.223687	−	0.974661i	$-0.428191\pi$
$839$	10872.1	0.447374	0.223687	+	0.974661i	$0.428191\pi$
$840$	2940.17	0.120768
$841$	−23744.8	−0.973586
$842$	6224.42	0.254760
$843$	21697.5	0.886480
$844$	−4710.94	−0.192130
$845$	2957.67	0.120410
$846$	8619.73	0.350299
$847$	9250.57	0.375270
$848$	8048.61	0.325932
$849$	3100.22	0.125323
$850$	45154.5	1.82210
$851$	46820.5	1.88600
$852$	−3253.27	−0.130816
$853$	41897.4	1.68176	0.840879	−	0.541223i	$-0.182039\pi$
$853$	41897.4	1.68176	0.840879	+	0.541223i	$0.182039\pi$
$854$	1349.59	0.0540772
$855$	−12437.0	−0.497470
$856$	−12375.8	−0.494155
$857$	−19962.3	−0.795682	−0.397841	−	0.917454i	$-0.630240\pi$
$857$	−19962.3	−0.795682	−0.397841	+	0.917454i	$0.630240\pi$
$858$	240.280	0.00956063
$859$	−21620.5	−0.858769	−0.429384	−	0.903122i	$-0.641269\pi$
$859$	−21620.5	−0.858769	−0.429384	+	0.903122i	$0.641269\pi$
$860$	−32297.7	−1.28063
$861$	−4521.10	−0.178953
$862$	−1172.44	−0.0463266
$863$	−7226.93	−0.285061	−0.142530	−	0.989790i	$-0.545524\pi$
$863$	−7226.93	−0.285061	−0.142530	+	0.989790i	$0.545524\pi$
$864$	−864.000	−0.0340207
$865$	−61136.3	−2.40312
$866$	−5777.01	−0.226687
$867$	−31791.8	−1.24534
$868$	6026.98	0.235679
$869$	2803.76	0.109449
$870$	2665.18	0.103860
$871$	6361.71	0.247484
$872$	−10728.9	−0.416659
$873$	10156.3	0.393746
$874$	−19932.6	−0.771429
$875$	−6895.27	−0.266403
$876$	6355.77	0.245139
$877$	22915.5	0.882327	0.441164	−	0.897427i	$-0.354566\pi$
$877$	22915.5	0.882327	0.441164	+	0.897427i	$0.354566\pi$
$878$	−16974.1	−0.652448
$879$	5096.86	0.195578
$880$	−862.592	−0.0330432
$881$	−6518.09	−0.249262	−0.124631	−	0.992203i	$-0.539775\pi$
$881$	−6518.09	−0.249262	−0.124631	+	0.992203i	$0.539775\pi$
$882$	882.000	0.0336718
$883$	34272.9	1.30620	0.653101	−	0.757271i	$-0.273468\pi$
$883$	34272.9	1.30620	0.653101	+	0.757271i	$0.273468\pi$
$884$	6476.09	0.246397
$885$	−35771.0	−1.35868
$886$	−32042.3	−1.21499
$887$	13489.3	0.510626	0.255313	−	0.966858i	$-0.417821\pi$
$887$	13489.3	0.510626	0.255313	+	0.966858i	$0.417821\pi$
$888$	−8902.77	−0.336438
$889$	−12705.7	−0.479342
$890$	−10685.4	−0.402443
$891$	−249.521	−0.00938191
$892$	12154.7	0.456243
$893$	−37812.2	−1.41695
$894$	19558.8	0.731703
$895$	−23875.5	−0.891698
$896$	−896.000	−0.0334077
$897$	−4922.51	−0.183231
$898$	−20855.3	−0.775000
$899$	5463.29	0.202682
$900$	6526.25	0.241713
$901$	62648.4	2.31645
$902$	1326.41	0.0489630
$903$	−9688.75	−0.357056
$904$	−1405.29	−0.0517025
$905$	7488.72	0.275065
$906$	7190.24	0.263664
$907$	5606.09	0.205234	0.102617	−	0.994721i	$-0.467278\pi$
$907$	5606.09	0.205234	0.102617	+	0.994721i	$0.467278\pi$
$908$	−2114.59	−0.0772853
$909$	16218.9	0.591800
$910$	−3185.18	−0.116030
$911$	7406.18	0.269350	0.134675	−	0.990890i	$-0.457001\pi$
$911$	7406.18	0.269350	0.134675	+	0.990890i	$0.457001\pi$
$912$	3790.11	0.137613
$913$	−3238.30	−0.117385
$914$	−24335.4	−0.880682
$915$	5061.24	0.182863
$916$	16303.2	0.588073
$917$	−13343.0	−0.480508
$918$	−6725.17	−0.241791
$919$	19474.7	0.699032	0.349516	−	0.936930i	$-0.386346\pi$
$919$	19474.7	0.699032	0.349516	+	0.936930i	$0.386346\pi$
$920$	17671.5	0.633276
$921$	17718.2	0.633912
$922$	16517.8	0.590006
$923$	3524.38	0.125684
$924$	−258.763	−0.00921285
$925$	67247.3	2.39036
$926$	27620.2	0.980189
$927$	5786.05	0.205004
$928$	−812.198	−0.0287303
$929$	8071.60	0.285060	0.142530	−	0.989791i	$-0.454476\pi$
$929$	8071.60	0.285060	0.142530	+	0.989791i	$0.454476\pi$
$930$	22602.5	0.796951
$931$	−3869.07	−0.136202
$932$	−10846.9	−0.381226
$933$	−21142.0	−0.741862
$934$	−6489.89	−0.227362
$935$	−6714.21	−0.234843
$936$	936.000	0.0326860
$937$	31783.6	1.10814	0.554069	−	0.832471i	$-0.313074\pi$
$937$	31783.6	1.10814	0.554069	+	0.832471i	$0.313074\pi$
$938$	−6851.08	−0.238481
$939$	10272.0	0.356991
$940$	33523.1	1.16319
$941$	11718.2	0.405954	0.202977	−	0.979183i	$-0.434938\pi$
$941$	11718.2	0.405954	0.202977	+	0.979183i	$0.434938\pi$
$942$	10436.3	0.360969
$943$	−27173.6	−0.938382
$944$	10901.0	0.375846
$945$	3307.69	0.113861
$946$	2842.51	0.0976933
$947$	−14845.1	−0.509399	−0.254699	−	0.967020i	$-0.581977\pi$
$947$	−14845.1	−0.509399	−0.254699	+	0.967020i	$0.581977\pi$
$948$	10921.9	0.374185
$949$	−6885.42	−0.235522
$950$	−28628.7	−0.977725
$951$	18330.9	0.625046
$952$	−6974.25	−0.237434
$953$	−24372.9	−0.828452	−0.414226	−	0.910174i	$-0.635948\pi$
$953$	−24372.9	−0.828452	−0.414226	+	0.910174i	$0.635948\pi$
$954$	9054.68	0.307292
$955$	−6303.59	−0.213591
$956$	10583.9	0.358061
$957$	−234.561	−0.00792297
$958$	467.842	0.0157779
$959$	7129.34	0.240061
$960$	−3360.19	−0.112968
$961$	16541.3	0.555245
$962$	9644.67	0.323240
$963$	−13922.8	−0.465894
$964$	−11371.8	−0.379940
$965$	7717.89	0.257459
$966$	5301.16	0.176565
$967$	−46387.0	−1.54261	−0.771306	−	0.636465i	$-0.780396\pi$
$967$	−46387.0	−1.54261	−0.771306	+	0.636465i	$0.780396\pi$
$968$	−10572.1	−0.351033
$969$	29501.4	0.978039
$970$	39499.1	1.30747
$971$	−36510.7	−1.20668	−0.603339	−	0.797485i	$-0.706163\pi$
$971$	−36510.7	−1.20668	−0.603339	+	0.797485i	$0.706163\pi$
$972$	−972.000	−0.0320750
$973$	12462.9	0.410631
$974$	2877.28	0.0946550
$975$	−7070.10	−0.232230
$976$	−1542.38	−0.0505846
$977$	56123.2	1.83781	0.918904	−	0.394480i	$-0.129075\pi$
$977$	56123.2	1.83781	0.918904	+	0.394480i	$0.129075\pi$
$978$	13560.0	0.443355
$979$	940.414	0.0307005
$980$	3430.19	0.111810
$981$	−12070.0	−0.392830
$982$	−3487.57	−0.113333
$983$	1935.03	0.0627852	0.0313926	−	0.999507i	$-0.490006\pi$
$983$	1935.03	0.0627852	0.0313926	+	0.999507i	$0.490006\pi$
$984$	5166.98	0.167395
$985$	50080.4	1.61999
$986$	−6321.96	−0.204191
$987$	10056.4	0.324313
$988$	−4105.96	−0.132214
$989$	−58233.2	−1.87230
$990$	−970.416	−0.0311534
$991$	−13544.5	−0.434162	−0.217081	−	0.976154i	$-0.569654\pi$
$991$	−13544.5	−0.434162	−0.217081	+	0.976154i	$0.569654\pi$
$992$	−6887.98	−0.220457
$993$	24729.6	0.790302
$994$	−3795.48	−0.121112
$995$	−28326.3	−0.902517
$996$	−12614.7	−0.401316
$997$	17740.0	0.563522	0.281761	−	0.959485i	$-0.409081\pi$
$997$	17740.0	0.563522	0.281761	+	0.959485i	$0.409081\pi$
$998$	10779.0	0.341888
$999$	−10015.6	−0.317197

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.4.a.p.1.3	✓	3
3.2	odd	2		1638.4.a.v.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.4.a.p.1.3	✓	3	1.1	even	1	trivial
1638.4.a.v.1.1		3	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	546.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +17.5010 q^{5} -6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +35.0020 q^{10} -3.08051 q^{11} -12.0000 q^{12} +13.0000 q^{13} -14.0000 q^{14} -52.5030 q^{15} +16.0000 q^{16} +124.540 q^{17} +18.0000 q^{18} -78.9607 q^{19} +70.0040 q^{20} +21.0000 q^{21} -6.16102 q^{22} +126.218 q^{23} -24.0000 q^{24} +181.285 q^{25} +26.0000 q^{26} -27.0000 q^{27} -28.0000 q^{28} -25.3812 q^{29} -105.006 q^{30} -215.249 q^{31} +32.0000 q^{32} +9.24154 q^{33} +249.080 q^{34} -122.507 q^{35} +36.0000 q^{36} +370.949 q^{37} -157.921 q^{38} -39.0000 q^{39} +140.008 q^{40} -215.291 q^{41} +42.0000 q^{42} -461.369 q^{43} -12.3220 q^{44} +157.509 q^{45} +252.436 q^{46} +478.874 q^{47} -48.0000 q^{48} +49.0000 q^{49} +362.569 q^{50} -373.621 q^{51} +52.0000 q^{52} +503.038 q^{53} -54.0000 q^{54} -53.9120 q^{55} -56.0000 q^{56} +236.882 q^{57} -50.7624 q^{58} +681.315 q^{59} -210.012 q^{60} -96.3991 q^{61} -430.499 q^{62} -63.0000 q^{63} +64.0000 q^{64} +227.513 q^{65} +18.4831 q^{66} +489.363 q^{67} +498.161 q^{68} -378.655 q^{69} -245.014 q^{70} +271.106 q^{71} +72.0000 q^{72} -529.647 q^{73} +741.897 q^{74} -543.854 q^{75} -315.843 q^{76} +21.5636 q^{77} -78.0000 q^{78} -910.161 q^{79} +280.016 q^{80} +81.0000 q^{81} -430.581 q^{82} +1051.22 q^{83} +84.0000 q^{84} +2179.58 q^{85} -922.738 q^{86} +76.1436 q^{87} -24.6441 q^{88} -305.279 q^{89} +315.018 q^{90} -91.0000 q^{91} +504.873 q^{92} +645.748 q^{93} +957.748 q^{94} -1381.89 q^{95} -96.0000 q^{96} +1128.48 q^{97} +98.0000 q^{98} -27.7246 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 6 q^{2} - 9 q^{3} + 12 q^{4} + 7 q^{5} - 18 q^{6} - 21 q^{7} + 24 q^{8} + 27 q^{9} + 14 q^{10} - 47 q^{11} - 36 q^{12} + 39 q^{13} - 42 q^{14} - 21 q^{15} + 48 q^{16} + 119 q^{17} + 54 q^{18} + 101 q^{19}+ \cdots - 423 q^{99}+O(q^{100}) \) 3 * q + 6 * q^2 - 9 * q^3 + 12 * q^4 + 7 * q^5 - 18 * q^6 - 21 * q^7 + 24 * q^8 + 27 * q^9 + 14 * q^10 - 47 * q^11 - 36 * q^12 + 39 * q^13 - 42 * q^14 - 21 * q^15 + 48 * q^16 + 119 * q^17 + 54 * q^18 + 101 * q^19 + 28 * q^20 + 63 * q^21 - 94 * q^22 - 27 * q^23 - 72 * q^24 + 266 * q^25 + 78 * q^26 - 81 * q^27 - 84 * q^28 + 345 * q^29 - 42 * q^30 + 152 * q^31 + 96 * q^32 + 141 * q^33 + 238 * q^34 - 49 * q^35 + 108 * q^36 + 227 * q^37 + 202 * q^38 - 117 * q^39 + 56 * q^40 + 452 * q^41 + 126 * q^42 - 415 * q^43 - 188 * q^44 + 63 * q^45 - 54 * q^46 + 240 * q^47 - 144 * q^48 + 147 * q^49 + 532 * q^50 - 357 * q^51 + 156 * q^52 + 874 * q^53 - 162 * q^54 + 1123 * q^55 - 168 * q^56 - 303 * q^57 + 690 * q^58 + 948 * q^59 - 84 * q^60 + 951 * q^61 + 304 * q^62 - 189 * q^63 + 192 * q^64 + 91 * q^65 + 282 * q^66 + 742 * q^67 + 476 * q^68 + 81 * q^69 - 98 * q^70 + 732 * q^71 + 216 * q^72 - 585 * q^73 + 454 * q^74 - 798 * q^75 + 404 * q^76 + 329 * q^77 - 234 * q^78 - 618 * q^79 + 112 * q^80 + 243 * q^81 + 904 * q^82 + 774 * q^83 + 252 * q^84 + 1273 * q^85 - 830 * q^86 - 1035 * q^87 - 376 * q^88 + 730 * q^89 + 126 * q^90 - 273 * q^91 - 108 * q^92 - 456 * q^93 + 480 * q^94 - 2617 * q^95 - 288 * q^96 + 2518 * q^97 + 294 * q^98 - 423 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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