Properties

Label 462.4.a.g.1.1
Level $462$
Weight $4$
Character 462.1
Self dual yes
Analytic conductor $27.259$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 462.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(27.2588824227\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 462.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +3.00000 q^{5} -6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +3.00000 q^{5} -6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +6.00000 q^{10} -11.0000 q^{11} -12.0000 q^{12} +41.0000 q^{13} +14.0000 q^{14} -9.00000 q^{15} +16.0000 q^{16} +6.00000 q^{17} +18.0000 q^{18} -43.0000 q^{19} +12.0000 q^{20} -21.0000 q^{21} -22.0000 q^{22} +120.000 q^{23} -24.0000 q^{24} -116.000 q^{25} +82.0000 q^{26} -27.0000 q^{27} +28.0000 q^{28} +111.000 q^{29} -18.0000 q^{30} +266.000 q^{31} +32.0000 q^{32} +33.0000 q^{33} +12.0000 q^{34} +21.0000 q^{35} +36.0000 q^{36} -79.0000 q^{37} -86.0000 q^{38} -123.000 q^{39} +24.0000 q^{40} +216.000 q^{41} -42.0000 q^{42} +284.000 q^{43} -44.0000 q^{44} +27.0000 q^{45} +240.000 q^{46} +213.000 q^{47} -48.0000 q^{48} +49.0000 q^{49} -232.000 q^{50} -18.0000 q^{51} +164.000 q^{52} -216.000 q^{53} -54.0000 q^{54} -33.0000 q^{55} +56.0000 q^{56} +129.000 q^{57} +222.000 q^{58} +393.000 q^{59} -36.0000 q^{60} +350.000 q^{61} +532.000 q^{62} +63.0000 q^{63} +64.0000 q^{64} +123.000 q^{65} +66.0000 q^{66} +821.000 q^{67} +24.0000 q^{68} -360.000 q^{69} +42.0000 q^{70} -264.000 q^{71} +72.0000 q^{72} -865.000 q^{73} -158.000 q^{74} +348.000 q^{75} -172.000 q^{76} -77.0000 q^{77} -246.000 q^{78} -484.000 q^{79} +48.0000 q^{80} +81.0000 q^{81} +432.000 q^{82} +1158.00 q^{83} -84.0000 q^{84} +18.0000 q^{85} +568.000 q^{86} -333.000 q^{87} -88.0000 q^{88} +330.000 q^{89} +54.0000 q^{90} +287.000 q^{91} +480.000 q^{92} -798.000 q^{93} +426.000 q^{94} -129.000 q^{95} -96.0000 q^{96} +980.000 q^{97} +98.0000 q^{98} -99.0000 q^{99} +O(q^{100})\)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 0.707107
\(3\) −3.00000 −0.577350
\(4\) 4.00000 0.500000
\(5\) 3.00000 0.268328 0.134164 0.990959i \(-0.457165\pi\)
0.134164 + 0.990959i \(0.457165\pi\)
\(6\) −6.00000 −0.408248
\(7\) 7.00000 0.377964
\(8\) 8.00000 0.353553
\(9\) 9.00000 0.333333
\(10\) 6.00000 0.189737
\(11\) −11.0000 −0.301511
\(12\) −12.0000 −0.288675
\(13\) 41.0000 0.874720 0.437360 0.899287i \(-0.355914\pi\)
0.437360 + 0.899287i \(0.355914\pi\)
\(14\) 14.0000 0.267261
\(15\) −9.00000 −0.154919
\(16\) 16.0000 0.250000
\(17\) 6.00000 0.0856008 0.0428004 0.999084i \(-0.486372\pi\)
0.0428004 + 0.999084i \(0.486372\pi\)
\(18\) 18.0000 0.235702
\(19\) −43.0000 −0.519204 −0.259602 0.965716i \(-0.583591\pi\)
−0.259602 + 0.965716i \(0.583591\pi\)
\(20\) 12.0000 0.134164
\(21\) −21.0000 −0.218218
\(22\) −22.0000 −0.213201
\(23\) 120.000 1.08790 0.543951 0.839117i \(-0.316928\pi\)
0.543951 + 0.839117i \(0.316928\pi\)
\(24\) −24.0000 −0.204124
\(25\) −116.000 −0.928000
\(26\) 82.0000 0.618520
\(27\) −27.0000 −0.192450
\(28\) 28.0000 0.188982
\(29\) 111.000 0.710765 0.355382 0.934721i \(-0.384351\pi\)
0.355382 + 0.934721i \(0.384351\pi\)
\(30\) −18.0000 −0.109545
\(31\) 266.000 1.54113 0.770565 0.637362i \(-0.219974\pi\)
0.770565 + 0.637362i \(0.219974\pi\)
\(32\) 32.0000 0.176777
\(33\) 33.0000 0.174078
\(34\) 12.0000 0.0605289
\(35\) 21.0000 0.101419
\(36\) 36.0000 0.166667
\(37\) −79.0000 −0.351014 −0.175507 0.984478i \(-0.556156\pi\)
−0.175507 + 0.984478i \(0.556156\pi\)
\(38\) −86.0000 −0.367133
\(39\) −123.000 −0.505020
\(40\) 24.0000 0.0948683
\(41\) 216.000 0.822769 0.411385 0.911462i \(-0.365045\pi\)
0.411385 + 0.911462i \(0.365045\pi\)
\(42\) −42.0000 −0.154303
\(43\) 284.000 1.00720 0.503600 0.863937i \(-0.332009\pi\)
0.503600 + 0.863937i \(0.332009\pi\)
\(44\) −44.0000 −0.150756
\(45\) 27.0000 0.0894427
\(46\) 240.000 0.769262
\(47\) 213.000 0.661048 0.330524 0.943798i \(-0.392775\pi\)
0.330524 + 0.943798i \(0.392775\pi\)
\(48\) −48.0000 −0.144338
\(49\) 49.0000 0.142857
\(50\) −232.000 −0.656195
\(51\) −18.0000 −0.0494217
\(52\) 164.000 0.437360
\(53\) −216.000 −0.559809 −0.279905 0.960028i \(-0.590303\pi\)
−0.279905 + 0.960028i \(0.590303\pi\)
\(54\) −54.0000 −0.136083
\(55\) −33.0000 −0.0809040
\(56\) 56.0000 0.133631
\(57\) 129.000 0.299763
\(58\) 222.000 0.502587
\(59\) 393.000 0.867191 0.433595 0.901108i \(-0.357245\pi\)
0.433595 + 0.901108i \(0.357245\pi\)
\(60\) −36.0000 −0.0774597
\(61\) 350.000 0.734638 0.367319 0.930095i \(-0.380276\pi\)
0.367319 + 0.930095i \(0.380276\pi\)
\(62\) 532.000 1.08974
\(63\) 63.0000 0.125988
\(64\) 64.0000 0.125000
\(65\) 123.000 0.234712
\(66\) 66.0000 0.123091
\(67\) 821.000 1.49703 0.748516 0.663117i \(-0.230767\pi\)
0.748516 + 0.663117i \(0.230767\pi\)
\(68\) 24.0000 0.0428004
\(69\) −360.000 −0.628100
\(70\) 42.0000 0.0717137
\(71\) −264.000 −0.441282 −0.220641 0.975355i \(-0.570815\pi\)
−0.220641 + 0.975355i \(0.570815\pi\)
\(72\) 72.0000 0.117851
\(73\) −865.000 −1.38686 −0.693429 0.720525i \(-0.743901\pi\)
−0.693429 + 0.720525i \(0.743901\pi\)
\(74\) −158.000 −0.248204
\(75\) 348.000 0.535781
\(76\) −172.000 −0.259602
\(77\) −77.0000 −0.113961
\(78\) −246.000 −0.357103
\(79\) −484.000 −0.689294 −0.344647 0.938732i \(-0.612001\pi\)
−0.344647 + 0.938732i \(0.612001\pi\)
\(80\) 48.0000 0.0670820
\(81\) 81.0000 0.111111
\(82\) 432.000 0.581786
\(83\) 1158.00 1.53141 0.765705 0.643192i \(-0.222390\pi\)
0.765705 + 0.643192i \(0.222390\pi\)
\(84\) −84.0000 −0.109109
\(85\) 18.0000 0.0229691
\(86\) 568.000 0.712198
\(87\) −333.000 −0.410360
\(88\) −88.0000 −0.106600
\(89\) 330.000 0.393033 0.196516 0.980501i \(-0.437037\pi\)
0.196516 + 0.980501i \(0.437037\pi\)
\(90\) 54.0000 0.0632456
\(91\) 287.000 0.330613
\(92\) 480.000 0.543951
\(93\) −798.000 −0.889771
\(94\) 426.000 0.467431
\(95\) −129.000 −0.139317
\(96\) −96.0000 −0.102062
\(97\) 980.000 1.02581 0.512907 0.858444i \(-0.328569\pi\)
0.512907 + 0.858444i \(0.328569\pi\)
\(98\) 98.0000 0.101015
\(99\) −99.0000 −0.100504
\(100\) −464.000 −0.464000
\(101\) 210.000 0.206889 0.103444 0.994635i \(-0.467014\pi\)
0.103444 + 0.994635i \(0.467014\pi\)
\(102\) −36.0000 −0.0349464
\(103\) −1330.00 −1.27232 −0.636159 0.771558i \(-0.719478\pi\)
−0.636159 + 0.771558i \(0.719478\pi\)
\(104\) 328.000 0.309260
\(105\) −63.0000 −0.0585540
\(106\) −432.000 −0.395845
\(107\) −1329.00 −1.20074 −0.600370 0.799722i \(-0.704980\pi\)
−0.600370 + 0.799722i \(0.704980\pi\)
\(108\) −108.000 −0.0962250
\(109\) −94.0000 −0.0826015 −0.0413008 0.999147i \(-0.513150\pi\)
−0.0413008 + 0.999147i \(0.513150\pi\)
\(110\) −66.0000 −0.0572078
\(111\) 237.000 0.202658
\(112\) 112.000 0.0944911
\(113\) 198.000 0.164834 0.0824171 0.996598i \(-0.473736\pi\)
0.0824171 + 0.996598i \(0.473736\pi\)
\(114\) 258.000 0.211964
\(115\) 360.000 0.291915
\(116\) 444.000 0.355382
\(117\) 369.000 0.291573
\(118\) 786.000 0.613196
\(119\) 42.0000 0.0323541
\(120\) −72.0000 −0.0547723
\(121\) 121.000 0.0909091
\(122\) 700.000 0.519467
\(123\) −648.000 −0.475026
\(124\) 1064.00 0.770565
\(125\) −723.000 −0.517337
\(126\) 126.000 0.0890871
\(127\) −1066.00 −0.744821 −0.372410 0.928068i \(-0.621469\pi\)
−0.372410 + 0.928068i \(0.621469\pi\)
\(128\) 128.000 0.0883883
\(129\) −852.000 −0.581507
\(130\) 246.000 0.165966
\(131\) −120.000 −0.0800340 −0.0400170 0.999199i \(-0.512741\pi\)
−0.0400170 + 0.999199i \(0.512741\pi\)
\(132\) 132.000 0.0870388
\(133\) −301.000 −0.196241
\(134\) 1642.00 1.05856
\(135\) −81.0000 −0.0516398
\(136\) 48.0000 0.0302645
\(137\) −1938.00 −1.20857 −0.604287 0.796767i \(-0.706542\pi\)
−0.604287 + 0.796767i \(0.706542\pi\)
\(138\) −720.000 −0.444134
\(139\) 1712.00 1.04468 0.522338 0.852739i \(-0.325060\pi\)
0.522338 + 0.852739i \(0.325060\pi\)
\(140\) 84.0000 0.0507093
\(141\) −639.000 −0.381656
\(142\) −528.000 −0.312034
\(143\) −451.000 −0.263738
\(144\) 144.000 0.0833333
\(145\) 333.000 0.190718
\(146\) −1730.00 −0.980656
\(147\) −147.000 −0.0824786
\(148\) −316.000 −0.175507
\(149\) −1917.00 −1.05401 −0.527003 0.849864i \(-0.676684\pi\)
−0.527003 + 0.849864i \(0.676684\pi\)
\(150\) 696.000 0.378854
\(151\) −3022.00 −1.62865 −0.814327 0.580406i \(-0.802894\pi\)
−0.814327 + 0.580406i \(0.802894\pi\)
\(152\) −344.000 −0.183566
\(153\) 54.0000 0.0285336
\(154\) −154.000 −0.0805823
\(155\) 798.000 0.413528
\(156\) −492.000 −0.252510
\(157\) −2200.00 −1.11834 −0.559169 0.829054i \(-0.688880\pi\)
−0.559169 + 0.829054i \(0.688880\pi\)
\(158\) −968.000 −0.487405
\(159\) 648.000 0.323206
\(160\) 96.0000 0.0474342
\(161\) 840.000 0.411188
\(162\) 162.000 0.0785674
\(163\) −3715.00 −1.78516 −0.892581 0.450888i \(-0.851107\pi\)
−0.892581 + 0.450888i \(0.851107\pi\)
\(164\) 864.000 0.411385
\(165\) 99.0000 0.0467099
\(166\) 2316.00 1.08287
\(167\) 84.0000 0.0389228 0.0194614 0.999811i \(-0.493805\pi\)
0.0194614 + 0.999811i \(0.493805\pi\)
\(168\) −168.000 −0.0771517
\(169\) −516.000 −0.234866
\(170\) 36.0000 0.0162416
\(171\) −387.000 −0.173068
\(172\) 1136.00 0.503600
\(173\) 1812.00 0.796323 0.398161 0.917315i \(-0.369648\pi\)
0.398161 + 0.917315i \(0.369648\pi\)
\(174\) −666.000 −0.290169
\(175\) −812.000 −0.350751
\(176\) −176.000 −0.0753778
\(177\) −1179.00 −0.500673
\(178\) 660.000 0.277916
\(179\) 192.000 0.0801718 0.0400859 0.999196i \(-0.487237\pi\)
0.0400859 + 0.999196i \(0.487237\pi\)
\(180\) 108.000 0.0447214
\(181\) −3148.00 −1.29276 −0.646378 0.763017i \(-0.723717\pi\)
−0.646378 + 0.763017i \(0.723717\pi\)
\(182\) 574.000 0.233779
\(183\) −1050.00 −0.424143
\(184\) 960.000 0.384631
\(185\) −237.000 −0.0941870
\(186\) −1596.00 −0.629163
\(187\) −66.0000 −0.0258096
\(188\) 852.000 0.330524
\(189\) −189.000 −0.0727393
\(190\) −258.000 −0.0985120
\(191\) 4554.00 1.72521 0.862607 0.505875i \(-0.168830\pi\)
0.862607 + 0.505875i \(0.168830\pi\)
\(192\) −192.000 −0.0721688
\(193\) −940.000 −0.350584 −0.175292 0.984517i \(-0.556087\pi\)
−0.175292 + 0.984517i \(0.556087\pi\)
\(194\) 1960.00 0.725360
\(195\) −369.000 −0.135511
\(196\) 196.000 0.0714286
\(197\) −1122.00 −0.405783 −0.202891 0.979201i \(-0.565034\pi\)
−0.202891 + 0.979201i \(0.565034\pi\)
\(198\) −198.000 −0.0710669
\(199\) 3956.00 1.40921 0.704607 0.709598i \(-0.251124\pi\)
0.704607 + 0.709598i \(0.251124\pi\)
\(200\) −928.000 −0.328098
\(201\) −2463.00 −0.864312
\(202\) 420.000 0.146293
\(203\) 777.000 0.268644
\(204\) −72.0000 −0.0247108
\(205\) 648.000 0.220772
\(206\) −2660.00 −0.899665
\(207\) 1080.00 0.362634
\(208\) 656.000 0.218680
\(209\) 473.000 0.156546
\(210\) −126.000 −0.0414039
\(211\) 122.000 0.0398049 0.0199024 0.999802i \(-0.493664\pi\)
0.0199024 + 0.999802i \(0.493664\pi\)
\(212\) −864.000 −0.279905
\(213\) 792.000 0.254774
\(214\) −2658.00 −0.849052
\(215\) 852.000 0.270260
\(216\) −216.000 −0.0680414
\(217\) 1862.00 0.582492
\(218\) −188.000 −0.0584081
\(219\) 2595.00 0.800703
\(220\) −132.000 −0.0404520
\(221\) 246.000 0.0748767
\(222\) 474.000 0.143301
\(223\) 602.000 0.180775 0.0903877 0.995907i \(-0.471189\pi\)
0.0903877 + 0.995907i \(0.471189\pi\)
\(224\) 224.000 0.0668153
\(225\) −1044.00 −0.309333
\(226\) 396.000 0.116555
\(227\) −426.000 −0.124558 −0.0622789 0.998059i \(-0.519837\pi\)
−0.0622789 + 0.998059i \(0.519837\pi\)
\(228\) 516.000 0.149881
\(229\) −4396.00 −1.26854 −0.634270 0.773111i \(-0.718699\pi\)
−0.634270 + 0.773111i \(0.718699\pi\)
\(230\) 720.000 0.206415
\(231\) 231.000 0.0657952
\(232\) 888.000 0.251293
\(233\) 3198.00 0.899176 0.449588 0.893236i \(-0.351571\pi\)
0.449588 + 0.893236i \(0.351571\pi\)
\(234\) 738.000 0.206173
\(235\) 639.000 0.177378
\(236\) 1572.00 0.433595
\(237\) 1452.00 0.397964
\(238\) 84.0000 0.0228778
\(239\) 2997.00 0.811129 0.405564 0.914066i \(-0.367075\pi\)
0.405564 + 0.914066i \(0.367075\pi\)
\(240\) −144.000 −0.0387298
\(241\) −6235.00 −1.66652 −0.833261 0.552880i \(-0.813529\pi\)
−0.833261 + 0.552880i \(0.813529\pi\)
\(242\) 242.000 0.0642824
\(243\) −243.000 −0.0641500
\(244\) 1400.00 0.367319
\(245\) 147.000 0.0383326
\(246\) −1296.00 −0.335894
\(247\) −1763.00 −0.454158
\(248\) 2128.00 0.544872
\(249\) −3474.00 −0.884160
\(250\) −1446.00 −0.365812
\(251\) 3735.00 0.939247 0.469624 0.882867i \(-0.344390\pi\)
0.469624 + 0.882867i \(0.344390\pi\)
\(252\) 252.000 0.0629941
\(253\) −1320.00 −0.328015
\(254\) −2132.00 −0.526668
\(255\) −54.0000 −0.0132612
\(256\) 256.000 0.0625000
\(257\) 1515.00 0.367716 0.183858 0.982953i \(-0.441141\pi\)
0.183858 + 0.982953i \(0.441141\pi\)
\(258\) −1704.00 −0.411188
\(259\) −553.000 −0.132671
\(260\) 492.000 0.117356
\(261\) 999.000 0.236922
\(262\) −240.000 −0.0565926
\(263\) −4317.00 −1.01216 −0.506079 0.862487i \(-0.668906\pi\)
−0.506079 + 0.862487i \(0.668906\pi\)
\(264\) 264.000 0.0615457
\(265\) −648.000 −0.150213
\(266\) −602.000 −0.138763
\(267\) −990.000 −0.226918
\(268\) 3284.00 0.748516
\(269\) −1434.00 −0.325028 −0.162514 0.986706i \(-0.551960\pi\)
−0.162514 + 0.986706i \(0.551960\pi\)
\(270\) −162.000 −0.0365148
\(271\) −943.000 −0.211377 −0.105689 0.994399i \(-0.533705\pi\)
−0.105689 + 0.994399i \(0.533705\pi\)
\(272\) 96.0000 0.0214002
\(273\) −861.000 −0.190879
\(274\) −3876.00 −0.854590
\(275\) 1276.00 0.279803
\(276\) −1440.00 −0.314050
\(277\) −5776.00 −1.25287 −0.626437 0.779472i \(-0.715488\pi\)
−0.626437 + 0.779472i \(0.715488\pi\)
\(278\) 3424.00 0.738697
\(279\) 2394.00 0.513710
\(280\) 168.000 0.0358569
\(281\) −1653.00 −0.350924 −0.175462 0.984486i \(-0.556142\pi\)
−0.175462 + 0.984486i \(0.556142\pi\)
\(282\) −1278.00 −0.269872
\(283\) 677.000 0.142203 0.0711015 0.997469i \(-0.477349\pi\)
0.0711015 + 0.997469i \(0.477349\pi\)
\(284\) −1056.00 −0.220641
\(285\) 387.000 0.0804347
\(286\) −902.000 −0.186491
\(287\) 1512.00 0.310977
\(288\) 288.000 0.0589256
\(289\) −4877.00 −0.992673
\(290\) 666.000 0.134858
\(291\) −2940.00 −0.592254
\(292\) −3460.00 −0.693429
\(293\) 4752.00 0.947491 0.473745 0.880662i \(-0.342902\pi\)
0.473745 + 0.880662i \(0.342902\pi\)
\(294\) −294.000 −0.0583212
\(295\) 1179.00 0.232692
\(296\) −632.000 −0.124102
\(297\) 297.000 0.0580259
\(298\) −3834.00 −0.745294
\(299\) 4920.00 0.951609
\(300\) 1392.00 0.267891
\(301\) 1988.00 0.380686
\(302\) −6044.00 −1.15163
\(303\) −630.000 −0.119447
\(304\) −688.000 −0.129801
\(305\) 1050.00 0.197124
\(306\) 108.000 0.0201763
\(307\) 1676.00 0.311578 0.155789 0.987790i \(-0.450208\pi\)
0.155789 + 0.987790i \(0.450208\pi\)
\(308\) −308.000 −0.0569803
\(309\) 3990.00 0.734573
\(310\) 1596.00 0.292409
\(311\) −6288.00 −1.14649 −0.573247 0.819382i \(-0.694317\pi\)
−0.573247 + 0.819382i \(0.694317\pi\)
\(312\) −984.000 −0.178551
\(313\) −430.000 −0.0776519 −0.0388259 0.999246i \(-0.512362\pi\)
−0.0388259 + 0.999246i \(0.512362\pi\)
\(314\) −4400.00 −0.790785
\(315\) 189.000 0.0338062
\(316\) −1936.00 −0.344647
\(317\) 7176.00 1.27143 0.635717 0.771923i \(-0.280705\pi\)
0.635717 + 0.771923i \(0.280705\pi\)
\(318\) 1296.00 0.228541
\(319\) −1221.00 −0.214304
\(320\) 192.000 0.0335410
\(321\) 3987.00 0.693248
\(322\) 1680.00 0.290754
\(323\) −258.000 −0.0444443
\(324\) 324.000 0.0555556
\(325\) −4756.00 −0.811740
\(326\) −7430.00 −1.26230
\(327\) 282.000 0.0476900
\(328\) 1728.00 0.290893
\(329\) 1491.00 0.249853
\(330\) 198.000 0.0330289
\(331\) 5360.00 0.890067 0.445034 0.895514i \(-0.353192\pi\)
0.445034 + 0.895514i \(0.353192\pi\)
\(332\) 4632.00 0.765705
\(333\) −711.000 −0.117005
\(334\) 168.000 0.0275226
\(335\) 2463.00 0.401696
\(336\) −336.000 −0.0545545
\(337\) −9376.00 −1.51556 −0.757779 0.652511i \(-0.773716\pi\)
−0.757779 + 0.652511i \(0.773716\pi\)
\(338\) −1032.00 −0.166075
\(339\) −594.000 −0.0951671
\(340\) 72.0000 0.0114846
\(341\) −2926.00 −0.464668
\(342\) −774.000 −0.122378
\(343\) 343.000 0.0539949
\(344\) 2272.00 0.356099
\(345\) −1080.00 −0.168537
\(346\) 3624.00 0.563085
\(347\) 1608.00 0.248766 0.124383 0.992234i \(-0.460305\pi\)
0.124383 + 0.992234i \(0.460305\pi\)
\(348\) −1332.00 −0.205180
\(349\) 2477.00 0.379916 0.189958 0.981792i \(-0.439165\pi\)
0.189958 + 0.981792i \(0.439165\pi\)
\(350\) −1624.00 −0.248018
\(351\) −1107.00 −0.168340
\(352\) −352.000 −0.0533002
\(353\) −975.000 −0.147009 −0.0735043 0.997295i \(-0.523418\pi\)
−0.0735043 + 0.997295i \(0.523418\pi\)
\(354\) −2358.00 −0.354029
\(355\) −792.000 −0.118408
\(356\) 1320.00 0.196516
\(357\) −126.000 −0.0186796
\(358\) 384.000 0.0566900
\(359\) 4116.00 0.605109 0.302555 0.953132i \(-0.402161\pi\)
0.302555 + 0.953132i \(0.402161\pi\)
\(360\) 216.000 0.0316228
\(361\) −5010.00 −0.730427
\(362\) −6296.00 −0.914117
\(363\) −363.000 −0.0524864
\(364\) 1148.00 0.165306
\(365\) −2595.00 −0.372133
\(366\) −2100.00 −0.299915
\(367\) 2066.00 0.293854 0.146927 0.989147i \(-0.453062\pi\)
0.146927 + 0.989147i \(0.453062\pi\)
\(368\) 1920.00 0.271975
\(369\) 1944.00 0.274256
\(370\) −474.000 −0.0666002
\(371\) −1512.00 −0.211588
\(372\) −3192.00 −0.444886
\(373\) 1778.00 0.246813 0.123407 0.992356i \(-0.460618\pi\)
0.123407 + 0.992356i \(0.460618\pi\)
\(374\) −132.000 −0.0182502
\(375\) 2169.00 0.298684
\(376\) 1704.00 0.233716
\(377\) 4551.00 0.621720
\(378\) −378.000 −0.0514344
\(379\) −10717.0 −1.45249 −0.726247 0.687434i \(-0.758737\pi\)
−0.726247 + 0.687434i \(0.758737\pi\)
\(380\) −516.000 −0.0696585
\(381\) 3198.00 0.430022
\(382\) 9108.00 1.21991
\(383\) 9360.00 1.24876 0.624378 0.781122i \(-0.285352\pi\)
0.624378 + 0.781122i \(0.285352\pi\)
\(384\) −384.000 −0.0510310
\(385\) −231.000 −0.0305788
\(386\) −1880.00 −0.247900
\(387\) 2556.00 0.335733
\(388\) 3920.00 0.512907
\(389\) 8364.00 1.09016 0.545079 0.838385i \(-0.316500\pi\)
0.545079 + 0.838385i \(0.316500\pi\)
\(390\) −738.000 −0.0958207
\(391\) 720.000 0.0931252
\(392\) 392.000 0.0505076
\(393\) 360.000 0.0462076
\(394\) −2244.00 −0.286932
\(395\) −1452.00 −0.184957
\(396\) −396.000 −0.0502519
\(397\) −646.000 −0.0816670 −0.0408335 0.999166i \(-0.513001\pi\)
−0.0408335 + 0.999166i \(0.513001\pi\)
\(398\) 7912.00 0.996464
\(399\) 903.000 0.113300
\(400\) −1856.00 −0.232000
\(401\) 2808.00 0.349688 0.174844 0.984596i \(-0.444058\pi\)
0.174844 + 0.984596i \(0.444058\pi\)
\(402\) −4926.00 −0.611161
\(403\) 10906.0 1.34806
\(404\) 840.000 0.103444
\(405\) 243.000 0.0298142
\(406\) 1554.00 0.189960
\(407\) 869.000 0.105835
\(408\) −144.000 −0.0174732
\(409\) 8750.00 1.05785 0.528924 0.848669i \(-0.322596\pi\)
0.528924 + 0.848669i \(0.322596\pi\)
\(410\) 1296.00 0.156109
\(411\) 5814.00 0.697770
\(412\) −5320.00 −0.636159
\(413\) 2751.00 0.327767
\(414\) 2160.00 0.256421
\(415\) 3474.00 0.410920
\(416\) 1312.00 0.154630
\(417\) −5136.00 −0.603144
\(418\) 946.000 0.110695
\(419\) 13263.0 1.54640 0.773198 0.634165i \(-0.218656\pi\)
0.773198 + 0.634165i \(0.218656\pi\)
\(420\) −252.000 −0.0292770
\(421\) −5785.00 −0.669700 −0.334850 0.942271i \(-0.608686\pi\)
−0.334850 + 0.942271i \(0.608686\pi\)
\(422\) 244.000 0.0281463
\(423\) 1917.00 0.220349
\(424\) −1728.00 −0.197922
\(425\) −696.000 −0.0794376
\(426\) 1584.00 0.180153
\(427\) 2450.00 0.277667
\(428\) −5316.00 −0.600370
\(429\) 1353.00 0.152269
\(430\) 1704.00 0.191103
\(431\) 5019.00 0.560920 0.280460 0.959866i \(-0.409513\pi\)
0.280460 + 0.959866i \(0.409513\pi\)
\(432\) −432.000 −0.0481125
\(433\) 14768.0 1.63904 0.819521 0.573050i \(-0.194240\pi\)
0.819521 + 0.573050i \(0.194240\pi\)
\(434\) 3724.00 0.411884
\(435\) −999.000 −0.110111
\(436\) −376.000 −0.0413008
\(437\) −5160.00 −0.564843
\(438\) 5190.00 0.566182
\(439\) −2311.00 −0.251248 −0.125624 0.992078i \(-0.540093\pi\)
−0.125624 + 0.992078i \(0.540093\pi\)
\(440\) −264.000 −0.0286039
\(441\) 441.000 0.0476190
\(442\) 492.000 0.0529458
\(443\) −252.000 −0.0270268 −0.0135134 0.999909i \(-0.504302\pi\)
−0.0135134 + 0.999909i \(0.504302\pi\)
\(444\) 948.000 0.101329
\(445\) 990.000 0.105462
\(446\) 1204.00 0.127827
\(447\) 5751.00 0.608530
\(448\) 448.000 0.0472456
\(449\) 1980.00 0.208111 0.104056 0.994571i \(-0.466818\pi\)
0.104056 + 0.994571i \(0.466818\pi\)
\(450\) −2088.00 −0.218732
\(451\) −2376.00 −0.248074
\(452\) 792.000 0.0824171
\(453\) 9066.00 0.940304
\(454\) −852.000 −0.0880756
\(455\) 861.000 0.0887128
\(456\) 1032.00 0.105982
\(457\) 12164.0 1.24509 0.622547 0.782582i \(-0.286098\pi\)
0.622547 + 0.782582i \(0.286098\pi\)
\(458\) −8792.00 −0.896994
\(459\) −162.000 −0.0164739
\(460\) 1440.00 0.145957
\(461\) −18732.0 −1.89249 −0.946243 0.323456i \(-0.895155\pi\)
−0.946243 + 0.323456i \(0.895155\pi\)
\(462\) 462.000 0.0465242
\(463\) −13051.0 −1.31000 −0.655002 0.755628i \(-0.727332\pi\)
−0.655002 + 0.755628i \(0.727332\pi\)
\(464\) 1776.00 0.177691
\(465\) −2394.00 −0.238751
\(466\) 6396.00 0.635813
\(467\) 6717.00 0.665580 0.332790 0.943001i \(-0.392010\pi\)
0.332790 + 0.943001i \(0.392010\pi\)
\(468\) 1476.00 0.145787
\(469\) 5747.00 0.565825
\(470\) 1278.00 0.125425
\(471\) 6600.00 0.645673
\(472\) 3144.00 0.306598
\(473\) −3124.00 −0.303682
\(474\) 2904.00 0.281403
\(475\) 4988.00 0.481821
\(476\) 168.000 0.0161770
\(477\) −1944.00 −0.186603
\(478\) 5994.00 0.573555
\(479\) −18438.0 −1.75878 −0.879388 0.476106i \(-0.842048\pi\)
−0.879388 + 0.476106i \(0.842048\pi\)
\(480\) −288.000 −0.0273861
\(481\) −3239.00 −0.307039
\(482\) −12470.0 −1.17841
\(483\) −2520.00 −0.237400
\(484\) 484.000 0.0454545
\(485\) 2940.00 0.275255
\(486\) −486.000 −0.0453609
\(487\) −10648.0 −0.990774 −0.495387 0.868672i \(-0.664974\pi\)
−0.495387 + 0.868672i \(0.664974\pi\)
\(488\) 2800.00 0.259734
\(489\) 11145.0 1.03066
\(490\) 294.000 0.0271052
\(491\) 16863.0 1.54993 0.774966 0.632003i \(-0.217767\pi\)
0.774966 + 0.632003i \(0.217767\pi\)
\(492\) −2592.00 −0.237513
\(493\) 666.000 0.0608421
\(494\) −3526.00 −0.321138
\(495\) −297.000 −0.0269680
\(496\) 4256.00 0.385282
\(497\) −1848.00 −0.166789
\(498\) −6948.00 −0.625195
\(499\) 12683.0 1.13781 0.568907 0.822402i \(-0.307366\pi\)
0.568907 + 0.822402i \(0.307366\pi\)
\(500\) −2892.00 −0.258668
\(501\) −252.000 −0.0224721
\(502\) 7470.00 0.664148
\(503\) 14472.0 1.28285 0.641426 0.767185i \(-0.278343\pi\)
0.641426 + 0.767185i \(0.278343\pi\)
\(504\) 504.000 0.0445435
\(505\) 630.000 0.0555141
\(506\) −2640.00 −0.231941
\(507\) 1548.00 0.135600
\(508\) −4264.00 −0.372410
\(509\) −10722.0 −0.933682 −0.466841 0.884341i \(-0.654608\pi\)
−0.466841 + 0.884341i \(0.654608\pi\)
\(510\) −108.000 −0.00937710
\(511\) −6055.00 −0.524183
\(512\) 512.000 0.0441942
\(513\) 1161.00 0.0999209
\(514\) 3030.00 0.260015
\(515\) −3990.00 −0.341399
\(516\) −3408.00 −0.290754
\(517\) −2343.00 −0.199313
\(518\) −1106.00 −0.0938125
\(519\) −5436.00 −0.459757
\(520\) 984.000 0.0829832
\(521\) −10341.0 −0.869573 −0.434786 0.900534i \(-0.643176\pi\)
−0.434786 + 0.900534i \(0.643176\pi\)
\(522\) 1998.00 0.167529
\(523\) 5819.00 0.486515 0.243257 0.969962i \(-0.421784\pi\)
0.243257 + 0.969962i \(0.421784\pi\)
\(524\) −480.000 −0.0400170
\(525\) 2436.00 0.202506
\(526\) −8634.00 −0.715704
\(527\) 1596.00 0.131922
\(528\) 528.000 0.0435194
\(529\) 2233.00 0.183529
\(530\) −1296.00 −0.106216
\(531\) 3537.00 0.289064
\(532\) −1204.00 −0.0981203
\(533\) 8856.00 0.719692
\(534\) −1980.00 −0.160455
\(535\) −3987.00 −0.322193
\(536\) 6568.00 0.529281
\(537\) −576.000 −0.0462872
\(538\) −2868.00 −0.229829
\(539\) −539.000 −0.0430730
\(540\) −324.000 −0.0258199
\(541\) 9668.00 0.768318 0.384159 0.923267i \(-0.374492\pi\)
0.384159 + 0.923267i \(0.374492\pi\)
\(542\) −1886.00 −0.149466
\(543\) 9444.00 0.746374
\(544\) 192.000 0.0151322
\(545\) −282.000 −0.0221643
\(546\) −1722.00 −0.134972
\(547\) 13160.0 1.02867 0.514334 0.857590i \(-0.328039\pi\)
0.514334 + 0.857590i \(0.328039\pi\)
\(548\) −7752.00 −0.604287
\(549\) 3150.00 0.244879
\(550\) 2552.00 0.197850
\(551\) −4773.00 −0.369032
\(552\) −2880.00 −0.222067
\(553\) −3388.00 −0.260529
\(554\) −11552.0 −0.885916
\(555\) 711.000 0.0543789
\(556\) 6848.00 0.522338
\(557\) −2253.00 −0.171387 −0.0856936 0.996322i \(-0.527311\pi\)
−0.0856936 + 0.996322i \(0.527311\pi\)
\(558\) 4788.00 0.363248
\(559\) 11644.0 0.881017
\(560\) 336.000 0.0253546
\(561\) 198.000 0.0149012
\(562\) −3306.00 −0.248141
\(563\) −984.000 −0.0736601 −0.0368301 0.999322i \(-0.511726\pi\)
−0.0368301 + 0.999322i \(0.511726\pi\)
\(564\) −2556.00 −0.190828
\(565\) 594.000 0.0442297
\(566\) 1354.00 0.100553
\(567\) 567.000 0.0419961
\(568\) −2112.00 −0.156017
\(569\) −16878.0 −1.24352 −0.621760 0.783208i \(-0.713582\pi\)
−0.621760 + 0.783208i \(0.713582\pi\)
\(570\) 774.000 0.0568760
\(571\) 4736.00 0.347102 0.173551 0.984825i \(-0.444476\pi\)
0.173551 + 0.984825i \(0.444476\pi\)
\(572\) −1804.00 −0.131869
\(573\) −13662.0 −0.996053
\(574\) 3024.00 0.219894
\(575\) −13920.0 −1.00957
\(576\) 576.000 0.0416667
\(577\) −3694.00 −0.266522 −0.133261 0.991081i \(-0.542545\pi\)
−0.133261 + 0.991081i \(0.542545\pi\)
\(578\) −9754.00 −0.701925
\(579\) 2820.00 0.202410
\(580\) 1332.00 0.0953591
\(581\) 8106.00 0.578818
\(582\) −5880.00 −0.418787
\(583\) 2376.00 0.168789
\(584\) −6920.00 −0.490328
\(585\) 1107.00 0.0782373
\(586\) 9504.00 0.669977
\(587\) −21237.0 −1.49326 −0.746631 0.665238i \(-0.768330\pi\)
−0.746631 + 0.665238i \(0.768330\pi\)
\(588\) −588.000 −0.0412393
\(589\) −11438.0 −0.800161
\(590\) 2358.00 0.164538
\(591\) 3366.00 0.234279
\(592\) −1264.00 −0.0877535
\(593\) −7416.00 −0.513556 −0.256778 0.966470i \(-0.582661\pi\)
−0.256778 + 0.966470i \(0.582661\pi\)
\(594\) 594.000 0.0410305
\(595\) 126.000 0.00868151
\(596\) −7668.00 −0.527003
\(597\) −11868.0 −0.813610
\(598\) 9840.00 0.672889
\(599\) −5484.00 −0.374074 −0.187037 0.982353i \(-0.559888\pi\)
−0.187037 + 0.982353i \(0.559888\pi\)
\(600\) 2784.00 0.189427
\(601\) −11077.0 −0.751814 −0.375907 0.926657i \(-0.622669\pi\)
−0.375907 + 0.926657i \(0.622669\pi\)
\(602\) 3976.00 0.269185
\(603\) 7389.00 0.499011
\(604\) −12088.0 −0.814327
\(605\) 363.000 0.0243935
\(606\) −1260.00 −0.0844620
\(607\) −5047.00 −0.337482 −0.168741 0.985660i \(-0.553970\pi\)
−0.168741 + 0.985660i \(0.553970\pi\)
\(608\) −1376.00 −0.0917832
\(609\) −2331.00 −0.155102
\(610\) 2100.00 0.139388
\(611\) 8733.00 0.578231
\(612\) 216.000 0.0142668
\(613\) 20066.0 1.32212 0.661059 0.750334i \(-0.270107\pi\)
0.661059 + 0.750334i \(0.270107\pi\)
\(614\) 3352.00 0.220319
\(615\) −1944.00 −0.127463
\(616\) −616.000 −0.0402911
\(617\) −16626.0 −1.08483 −0.542413 0.840112i \(-0.682489\pi\)
−0.542413 + 0.840112i \(0.682489\pi\)
\(618\) 7980.00 0.519422
\(619\) −10162.0 −0.659847 −0.329923 0.944008i \(-0.607023\pi\)
−0.329923 + 0.944008i \(0.607023\pi\)
\(620\) 3192.00 0.206764
\(621\) −3240.00 −0.209367
\(622\) −12576.0 −0.810694
\(623\) 2310.00 0.148552
\(624\) −1968.00 −0.126255
\(625\) 12331.0 0.789184
\(626\) −860.000 −0.0549082
\(627\) −1419.00 −0.0903818
\(628\) −8800.00 −0.559169
\(629\) −474.000 −0.0300471
\(630\) 378.000 0.0239046
\(631\) −16108.0 −1.01624 −0.508122 0.861285i \(-0.669660\pi\)
−0.508122 + 0.861285i \(0.669660\pi\)
\(632\) −3872.00 −0.243702
\(633\) −366.000 −0.0229813
\(634\) 14352.0 0.899039
\(635\) −3198.00 −0.199856
\(636\) 2592.00 0.161603
\(637\) 2009.00 0.124960
\(638\) −2442.00 −0.151536
\(639\) −2376.00 −0.147094
\(640\) 384.000 0.0237171
\(641\) −19950.0 −1.22929 −0.614647 0.788802i \(-0.710702\pi\)
−0.614647 + 0.788802i \(0.710702\pi\)
\(642\) 7974.00 0.490200
\(643\) −8260.00 −0.506598 −0.253299 0.967388i \(-0.581516\pi\)
−0.253299 + 0.967388i \(0.581516\pi\)
\(644\) 3360.00 0.205594
\(645\) −2556.00 −0.156035
\(646\) −516.000 −0.0314269
\(647\) −28833.0 −1.75200 −0.875999 0.482314i \(-0.839797\pi\)
−0.875999 + 0.482314i \(0.839797\pi\)
\(648\) 648.000 0.0392837
\(649\) −4323.00 −0.261468
\(650\) −9512.00 −0.573987
\(651\) −5586.00 −0.336302
\(652\) −14860.0 −0.892581
\(653\) −13152.0 −0.788174 −0.394087 0.919073i \(-0.628939\pi\)
−0.394087 + 0.919073i \(0.628939\pi\)
\(654\) 564.000 0.0337219
\(655\) −360.000 −0.0214754
\(656\) 3456.00 0.205692
\(657\) −7785.00 −0.462286
\(658\) 2982.00 0.176672
\(659\) −32229.0 −1.90510 −0.952552 0.304376i \(-0.901552\pi\)
−0.952552 + 0.304376i \(0.901552\pi\)
\(660\) 396.000 0.0233550
\(661\) −460.000 −0.0270680 −0.0135340 0.999908i \(-0.504308\pi\)
−0.0135340 + 0.999908i \(0.504308\pi\)
\(662\) 10720.0 0.629373
\(663\) −738.000 −0.0432301
\(664\) 9264.00 0.541435
\(665\) −903.000 −0.0526569
\(666\) −1422.00 −0.0827348
\(667\) 13320.0 0.773242
\(668\) 336.000 0.0194614
\(669\) −1806.00 −0.104371
\(670\) 4926.00 0.284042
\(671\) −3850.00 −0.221502
\(672\) −672.000 −0.0385758
\(673\) −12784.0 −0.732224 −0.366112 0.930571i \(-0.619311\pi\)
−0.366112 + 0.930571i \(0.619311\pi\)
\(674\) −18752.0 −1.07166
\(675\) 3132.00 0.178594
\(676\) −2064.00 −0.117433
\(677\) 2190.00 0.124326 0.0621629 0.998066i \(-0.480200\pi\)
0.0621629 + 0.998066i \(0.480200\pi\)
\(678\) −1188.00 −0.0672933
\(679\) 6860.00 0.387721
\(680\) 144.000 0.00812081
\(681\) 1278.00 0.0719135
\(682\) −5852.00 −0.328570
\(683\) 11514.0 0.645053 0.322526 0.946560i \(-0.395468\pi\)
0.322526 + 0.946560i \(0.395468\pi\)
\(684\) −1548.00 −0.0865340
\(685\) −5814.00 −0.324294
\(686\) 686.000 0.0381802
\(687\) 13188.0 0.732392
\(688\) 4544.00 0.251800
\(689\) −8856.00 −0.489676
\(690\) −2160.00 −0.119174
\(691\) −11554.0 −0.636085 −0.318043 0.948076i \(-0.603026\pi\)
−0.318043 + 0.948076i \(0.603026\pi\)
\(692\) 7248.00 0.398161
\(693\) −693.000 −0.0379869
\(694\) 3216.00 0.175904
\(695\) 5136.00 0.280316
\(696\) −2664.00 −0.145084
\(697\) 1296.00 0.0704297
\(698\) 4954.00 0.268641
\(699\) −9594.00 −0.519139
\(700\) −3248.00 −0.175376
\(701\) −18450.0 −0.994075 −0.497038 0.867729i \(-0.665579\pi\)
−0.497038 + 0.867729i \(0.665579\pi\)
\(702\) −2214.00 −0.119034
\(703\) 3397.00 0.182248
\(704\) −704.000 −0.0376889
\(705\) −1917.00 −0.102409
\(706\) −1950.00 −0.103951
\(707\) 1470.00 0.0781967
\(708\) −4716.00 −0.250336
\(709\) 15203.0 0.805304 0.402652 0.915353i \(-0.368088\pi\)
0.402652 + 0.915353i \(0.368088\pi\)
\(710\) −1584.00 −0.0837274
\(711\) −4356.00 −0.229765
\(712\) 2640.00 0.138958
\(713\) 31920.0 1.67660
\(714\) −252.000 −0.0132085
\(715\) −1353.00 −0.0707683
\(716\) 768.000 0.0400859
\(717\) −8991.00 −0.468306
\(718\) 8232.00 0.427877
\(719\) 28515.0 1.47904 0.739520 0.673134i \(-0.235052\pi\)
0.739520 + 0.673134i \(0.235052\pi\)
\(720\) 432.000 0.0223607
\(721\) −9310.00 −0.480891
\(722\) −10020.0 −0.516490
\(723\) 18705.0 0.962167
\(724\) −12592.0 −0.646378
\(725\) −12876.0 −0.659590
\(726\) −726.000 −0.0371135
\(727\) 15932.0 0.812772 0.406386 0.913702i \(-0.366789\pi\)
0.406386 + 0.913702i \(0.366789\pi\)
\(728\) 2296.00 0.116889
\(729\) 729.000 0.0370370
\(730\) −5190.00 −0.263138
\(731\) 1704.00 0.0862171
\(732\) −4200.00 −0.212072
\(733\) 26630.0 1.34188 0.670942 0.741510i \(-0.265890\pi\)
0.670942 + 0.741510i \(0.265890\pi\)
\(734\) 4132.00 0.207786
\(735\) −441.000 −0.0221313
\(736\) 3840.00 0.192316
\(737\) −9031.00 −0.451372
\(738\) 3888.00 0.193929
\(739\) −3940.00 −0.196123 −0.0980617 0.995180i \(-0.531264\pi\)
−0.0980617 + 0.995180i \(0.531264\pi\)
\(740\) −948.000 −0.0470935
\(741\) 5289.00 0.262208
\(742\) −3024.00 −0.149615
\(743\) 25203.0 1.24443 0.622213 0.782848i \(-0.286234\pi\)
0.622213 + 0.782848i \(0.286234\pi\)
\(744\) −6384.00 −0.314582
\(745\) −5751.00 −0.282819
\(746\) 3556.00 0.174523
\(747\) 10422.0 0.510470
\(748\) −264.000 −0.0129048
\(749\) −9303.00 −0.453837
\(750\) 4338.00 0.211202
\(751\) −17611.0 −0.855705 −0.427853 0.903849i \(-0.640730\pi\)
−0.427853 + 0.903849i \(0.640730\pi\)
\(752\) 3408.00 0.165262
\(753\) −11205.0 −0.542275
\(754\) 9102.00 0.439622
\(755\) −9066.00 −0.437014
\(756\) −756.000 −0.0363696
\(757\) −28543.0 −1.37043 −0.685213 0.728342i \(-0.740291\pi\)
−0.685213 + 0.728342i \(0.740291\pi\)
\(758\) −21434.0 −1.02707
\(759\) 3960.00 0.189379
\(760\) −1032.00 −0.0492560
\(761\) −16884.0 −0.804263 −0.402132 0.915582i \(-0.631731\pi\)
−0.402132 + 0.915582i \(0.631731\pi\)
\(762\) 6396.00 0.304072
\(763\) −658.000 −0.0312204
\(764\) 18216.0 0.862607
\(765\) 162.000 0.00765637
\(766\) 18720.0 0.883004
\(767\) 16113.0 0.758549
\(768\) −768.000 −0.0360844
\(769\) −22963.0 −1.07681 −0.538405 0.842686i \(-0.680973\pi\)
−0.538405 + 0.842686i \(0.680973\pi\)
\(770\) −462.000 −0.0216225
\(771\) −4545.00 −0.212301
\(772\) −3760.00 −0.175292
\(773\) −32601.0 −1.51692 −0.758458 0.651722i \(-0.774047\pi\)
−0.758458 + 0.651722i \(0.774047\pi\)
\(774\) 5112.00 0.237399
\(775\) −30856.0 −1.43017
\(776\) 7840.00 0.362680
\(777\) 1659.00 0.0765975
\(778\) 16728.0 0.770858
\(779\) −9288.00 −0.427185
\(780\) −1476.00 −0.0677555
\(781\) 2904.00 0.133052
\(782\) 1440.00 0.0658495
\(783\) −2997.00 −0.136787
\(784\) 784.000 0.0357143
\(785\) −6600.00 −0.300082
\(786\) 720.000 0.0326737
\(787\) 17867.0 0.809263 0.404631 0.914480i \(-0.367400\pi\)
0.404631 + 0.914480i \(0.367400\pi\)
\(788\) −4488.00 −0.202891
\(789\) 12951.0 0.584370
\(790\) −2904.00 −0.130784
\(791\) 1386.00 0.0623015
\(792\) −792.000 −0.0355335
\(793\) 14350.0 0.642602
\(794\) −1292.00 −0.0577473
\(795\) 1944.00 0.0867253
\(796\) 15824.0 0.704607
\(797\) 17505.0 0.777991 0.388996 0.921240i \(-0.372822\pi\)
0.388996 + 0.921240i \(0.372822\pi\)
\(798\) 1806.00 0.0801149
\(799\) 1278.00 0.0565862
\(800\) −3712.00 −0.164049
\(801\) 2970.00 0.131011
\(802\) 5616.00 0.247267
\(803\) 9515.00 0.418153
\(804\) −9852.00 −0.432156
\(805\) 2520.00 0.110333
\(806\) 21812.0 0.953220
\(807\) 4302.00 0.187655
\(808\) 1680.00 0.0731463
\(809\) 11079.0 0.481479 0.240740 0.970590i \(-0.422610\pi\)
0.240740 + 0.970590i \(0.422610\pi\)
\(810\) 486.000 0.0210819
\(811\) −28021.0 −1.21326 −0.606628 0.794986i \(-0.707478\pi\)
−0.606628 + 0.794986i \(0.707478\pi\)
\(812\) 3108.00 0.134322
\(813\) 2829.00 0.122039
\(814\) 1738.00 0.0748364
\(815\) −11145.0 −0.479009
\(816\) −288.000 −0.0123554
\(817\) −12212.0 −0.522942
\(818\) 17500.0 0.748011
\(819\) 2583.00 0.110204
\(820\) 2592.00 0.110386
\(821\) 12309.0 0.523249 0.261624 0.965170i \(-0.415742\pi\)
0.261624 + 0.965170i \(0.415742\pi\)
\(822\) 11628.0 0.493398
\(823\) 3893.00 0.164886 0.0824432 0.996596i \(-0.473728\pi\)
0.0824432 + 0.996596i \(0.473728\pi\)
\(824\) −10640.0 −0.449832
\(825\) −3828.00 −0.161544
\(826\) 5502.00 0.231766
\(827\) 45063.0 1.89479 0.947397 0.320062i \(-0.103704\pi\)
0.947397 + 0.320062i \(0.103704\pi\)
\(828\) 4320.00 0.181317
\(829\) −15136.0 −0.634131 −0.317066 0.948404i \(-0.602698\pi\)
−0.317066 + 0.948404i \(0.602698\pi\)
\(830\) 6948.00 0.290565
\(831\) 17328.0 0.723347
\(832\) 2624.00 0.109340
\(833\) 294.000 0.0122287
\(834\) −10272.0 −0.426487
\(835\) 252.000 0.0104441
\(836\) 1892.00 0.0782730
\(837\) −7182.00 −0.296590
\(838\) 26526.0 1.09347
\(839\) −20739.0 −0.853385 −0.426692 0.904397i \(-0.640321\pi\)
−0.426692 + 0.904397i \(0.640321\pi\)
\(840\) −504.000 −0.0207020
\(841\) −12068.0 −0.494813
\(842\) −11570.0 −0.473549
\(843\) 4959.00 0.202606
\(844\) 488.000 0.0199024
\(845\) −1548.00 −0.0630211
\(846\) 3834.00 0.155810
\(847\) 847.000 0.0343604
\(848\) −3456.00 −0.139952
\(849\) −2031.00 −0.0821010
\(850\) −1392.00 −0.0561708
\(851\) −9480.00 −0.381869
\(852\) 3168.00 0.127387
\(853\) 37610.0 1.50966 0.754831 0.655919i \(-0.227719\pi\)
0.754831 + 0.655919i \(0.227719\pi\)
\(854\) 4900.00 0.196340
\(855\) −1161.00 −0.0464390
\(856\) −10632.0 −0.424526
\(857\) −37470.0 −1.49352 −0.746762 0.665091i \(-0.768393\pi\)
−0.746762 + 0.665091i \(0.768393\pi\)
\(858\) 2706.00 0.107671
\(859\) −15604.0 −0.619792 −0.309896 0.950770i \(-0.600294\pi\)
−0.309896 + 0.950770i \(0.600294\pi\)
\(860\) 3408.00 0.135130
\(861\) −4536.00 −0.179543
\(862\) 10038.0 0.396631
\(863\) 20004.0 0.789043 0.394521 0.918887i \(-0.370910\pi\)
0.394521 + 0.918887i \(0.370910\pi\)
\(864\) −864.000 −0.0340207
\(865\) 5436.00 0.213676
\(866\) 29536.0 1.15898
\(867\) 14631.0 0.573120
\(868\) 7448.00 0.291246
\(869\) 5324.00 0.207830
\(870\) −1998.00 −0.0778604
\(871\) 33661.0 1.30948
\(872\) −752.000 −0.0292041
\(873\) 8820.00 0.341938
\(874\) −10320.0 −0.399404
\(875\) −5061.00 −0.195535
\(876\) 10380.0 0.400351
\(877\) 1064.00 0.0409678 0.0204839 0.999790i \(-0.493479\pi\)
0.0204839 + 0.999790i \(0.493479\pi\)
\(878\) −4622.00 −0.177659
\(879\) −14256.0 −0.547034
\(880\) −528.000 −0.0202260
\(881\) 4179.00 0.159812 0.0799058 0.996802i \(-0.474538\pi\)
0.0799058 + 0.996802i \(0.474538\pi\)
\(882\) 882.000 0.0336718
\(883\) −44509.0 −1.69632 −0.848158 0.529743i \(-0.822288\pi\)
−0.848158 + 0.529743i \(0.822288\pi\)
\(884\) 984.000 0.0374384
\(885\) −3537.00 −0.134345
\(886\) −504.000 −0.0191108
\(887\) 12642.0 0.478553 0.239277 0.970951i \(-0.423090\pi\)
0.239277 + 0.970951i \(0.423090\pi\)
\(888\) 1896.00 0.0716504
\(889\) −7462.00 −0.281516
\(890\) 1980.00 0.0745728
\(891\) −891.000 −0.0335013
\(892\) 2408.00 0.0903877
\(893\) −9159.00 −0.343219
\(894\) 11502.0 0.430296
\(895\) 576.000 0.0215124
\(896\) 896.000 0.0334077
\(897\) −14760.0 −0.549411
\(898\) 3960.00 0.147157
\(899\) 29526.0 1.09538
\(900\) −4176.00 −0.154667
\(901\) −1296.00 −0.0479201
\(902\) −4752.00 −0.175415
\(903\) −5964.00 −0.219789
\(904\) 1584.00 0.0582777
\(905\) −9444.00 −0.346883
\(906\) 18132.0 0.664896
\(907\) −28.0000 −0.00102505 −0.000512527 1.00000i \(-0.500163\pi\)
−0.000512527 1.00000i \(0.500163\pi\)
\(908\) −1704.00 −0.0622789
\(909\) 1890.00 0.0689630
\(910\) 1722.00 0.0627294
\(911\) −9774.00 −0.355463 −0.177732 0.984079i \(-0.556876\pi\)
−0.177732 + 0.984079i \(0.556876\pi\)
\(912\) 2064.00 0.0749406
\(913\) −12738.0 −0.461737
\(914\) 24328.0 0.880414
\(915\) −3150.00 −0.113810
\(916\) −17584.0 −0.634270
\(917\) −840.000 −0.0302500
\(918\) −324.000 −0.0116488
\(919\) 23204.0 0.832894 0.416447 0.909160i \(-0.363275\pi\)
0.416447 + 0.909160i \(0.363275\pi\)
\(920\) 2880.00 0.103207
\(921\) −5028.00 −0.179890
\(922\) −37464.0 −1.33819
\(923\) −10824.0 −0.385998
\(924\) 924.000 0.0328976
\(925\) 9164.00 0.325741
\(926\) −26102.0 −0.926312
\(927\) −11970.0 −0.424106
\(928\) 3552.00 0.125647
\(929\) 3633.00 0.128304 0.0641522 0.997940i \(-0.479566\pi\)
0.0641522 + 0.997940i \(0.479566\pi\)
\(930\) −4788.00 −0.168822
\(931\) −2107.00 −0.0741720
\(932\) 12792.0 0.449588
\(933\) 18864.0 0.661929
\(934\) 13434.0 0.470636
\(935\) −198.000 −0.00692545
\(936\) 2952.00 0.103087
\(937\) 18938.0 0.660275 0.330137 0.943933i \(-0.392905\pi\)
0.330137 + 0.943933i \(0.392905\pi\)
\(938\) 11494.0 0.400099
\(939\) 1290.00 0.0448323
\(940\) 2556.00 0.0886889
\(941\) 14784.0 0.512162 0.256081 0.966655i \(-0.417569\pi\)
0.256081 + 0.966655i \(0.417569\pi\)
\(942\) 13200.0 0.456560
\(943\) 25920.0 0.895092
\(944\) 6288.00 0.216798
\(945\) −567.000 −0.0195180
\(946\) −6248.00 −0.214736
\(947\) −31266.0 −1.07287 −0.536435 0.843941i \(-0.680229\pi\)
−0.536435 + 0.843941i \(0.680229\pi\)
\(948\) 5808.00 0.198982
\(949\) −35465.0 −1.21311
\(950\) 9976.00 0.340699
\(951\) −21528.0 −0.734062
\(952\) 336.000 0.0114389
\(953\) 33951.0 1.15402 0.577010 0.816737i \(-0.304219\pi\)
0.577010 + 0.816737i \(0.304219\pi\)
\(954\) −3888.00 −0.131948
\(955\) 13662.0 0.462923
\(956\) 11988.0 0.405564
\(957\) 3663.00 0.123728
\(958\) −36876.0 −1.24364
\(959\) −13566.0 −0.456798
\(960\) −576.000 −0.0193649
\(961\) 40965.0 1.37508
\(962\) −6478.00 −0.217109
\(963\) −11961.0 −0.400247
\(964\) −24940.0 −0.833261
\(965\) −2820.00 −0.0940715
\(966\) −5040.00 −0.167867
\(967\) 16322.0 0.542792 0.271396 0.962468i \(-0.412515\pi\)
0.271396 + 0.962468i \(0.412515\pi\)
\(968\) 968.000 0.0321412
\(969\) 774.000 0.0256599
\(970\) 5880.00 0.194634
\(971\) 40779.0 1.34774 0.673872 0.738848i \(-0.264630\pi\)
0.673872 + 0.738848i \(0.264630\pi\)
\(972\) −972.000 −0.0320750
\(973\) 11984.0 0.394850
\(974\) −21296.0 −0.700583
\(975\) 14268.0 0.468658
\(976\) 5600.00 0.183659
\(977\) 21804.0 0.713994 0.356997 0.934106i \(-0.383801\pi\)
0.356997 + 0.934106i \(0.383801\pi\)
\(978\) 22290.0 0.728789
\(979\) −3630.00 −0.118504
\(980\) 588.000 0.0191663
\(981\) −846.000 −0.0275338
\(982\) 33726.0 1.09597
\(983\) −35424.0 −1.14939 −0.574695 0.818368i \(-0.694879\pi\)
−0.574695 + 0.818368i \(0.694879\pi\)
\(984\) −5184.00 −0.167947
\(985\) −3366.00 −0.108883
\(986\) 1332.00 0.0430218
\(987\) −4473.00 −0.144252
\(988\) −7052.00 −0.227079
\(989\) 34080.0 1.09573
\(990\) −594.000 −0.0190693
\(991\) −37315.0 −1.19612 −0.598058 0.801453i \(-0.704061\pi\)
−0.598058 + 0.801453i \(0.704061\pi\)
\(992\) 8512.00 0.272436
\(993\) −16080.0 −0.513881
\(994\) −3696.00 −0.117938
\(995\) 11868.0 0.378132
\(996\) −13896.0 −0.442080
\(997\) 30674.0 0.974378 0.487189 0.873296i \(-0.338022\pi\)
0.487189 + 0.873296i \(0.338022\pi\)
\(998\) 25366.0 0.804556
\(999\) 2133.00 0.0675527
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 462.4.a.g.1.1 1
3.2 odd 2 1386.4.a.c.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
462.4.a.g.1.1 1 1.1 even 1 trivial
1386.4.a.c.1.1 1 3.2 odd 2