Properties

Label 1386.4.a.l.1.1
Level $1386$
Weight $4$
Character 1386.1
Self dual yes
Analytic conductor $81.777$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1386.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(81.7766472680\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 462)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1386.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000 q^{2} +4.00000 q^{4} +7.00000 q^{5} +7.00000 q^{7} +8.00000 q^{8} +O(q^{10})\) \(q+2.00000 q^{2} +4.00000 q^{4} +7.00000 q^{5} +7.00000 q^{7} +8.00000 q^{8} +14.0000 q^{10} -11.0000 q^{11} -67.0000 q^{13} +14.0000 q^{14} +16.0000 q^{16} -30.0000 q^{17} -7.00000 q^{19} +28.0000 q^{20} -22.0000 q^{22} -28.0000 q^{23} -76.0000 q^{25} -134.000 q^{26} +28.0000 q^{28} -121.000 q^{29} -310.000 q^{31} +32.0000 q^{32} -60.0000 q^{34} +49.0000 q^{35} -71.0000 q^{37} -14.0000 q^{38} +56.0000 q^{40} +180.000 q^{41} -108.000 q^{43} -44.0000 q^{44} -56.0000 q^{46} -71.0000 q^{47} +49.0000 q^{49} -152.000 q^{50} -268.000 q^{52} -128.000 q^{53} -77.0000 q^{55} +56.0000 q^{56} -242.000 q^{58} +429.000 q^{59} +22.0000 q^{61} -620.000 q^{62} +64.0000 q^{64} -469.000 q^{65} -803.000 q^{67} -120.000 q^{68} +98.0000 q^{70} -468.000 q^{71} -117.000 q^{73} -142.000 q^{74} -28.0000 q^{76} -77.0000 q^{77} -96.0000 q^{79} +112.000 q^{80} +360.000 q^{82} +1122.00 q^{83} -210.000 q^{85} -216.000 q^{86} -88.0000 q^{88} +1146.00 q^{89} -469.000 q^{91} -112.000 q^{92} -142.000 q^{94} -49.0000 q^{95} -92.0000 q^{97} +98.0000 q^{98} +O(q^{100})\)

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
\(3\) 0 0
\(4\) 4.00000 0.500000
\(5\) 7.00000 0.626099 0.313050 0.949737i \(-0.398649\pi\)
0.313050 + 0.949737i \(0.398649\pi\)
\(6\) 0 0
\(7\) 7.00000 0.377964
\(8\) 8.00000 0.353553
\(9\) 0 0
\(10\) 14.0000 0.442719
\(11\) −11.0000 −0.301511
\(12\) 0 0
\(13\) −67.0000 −1.42942 −0.714710 0.699421i \(-0.753441\pi\)
−0.714710 + 0.699421i \(0.753441\pi\)
\(14\) 14.0000 0.267261
\(15\) 0 0
\(16\) 16.0000 0.250000
\(17\) −30.0000 −0.428004 −0.214002 0.976833i \(-0.568650\pi\)
−0.214002 + 0.976833i \(0.568650\pi\)
\(18\) 0 0
\(19\) −7.00000 −0.0845216 −0.0422608 0.999107i \(-0.513456\pi\)
−0.0422608 + 0.999107i \(0.513456\pi\)
\(20\) 28.0000 0.313050
\(21\) 0 0
\(22\) −22.0000 −0.213201
\(23\) −28.0000 −0.253844 −0.126922 0.991913i \(-0.540510\pi\)
−0.126922 + 0.991913i \(0.540510\pi\)
\(24\) 0 0
\(25\) −76.0000 −0.608000
\(26\) −134.000 −1.01075
\(27\) 0 0
\(28\) 28.0000 0.188982
\(29\) −121.000 −0.774798 −0.387399 0.921912i \(-0.626626\pi\)
−0.387399 + 0.921912i \(0.626626\pi\)
\(30\) 0 0
\(31\) −310.000 −1.79605 −0.898027 0.439941i \(-0.854999\pi\)
−0.898027 + 0.439941i \(0.854999\pi\)
\(32\) 32.0000 0.176777
\(33\) 0 0
\(34\) −60.0000 −0.302645
\(35\) 49.0000 0.236643
\(36\) 0 0
\(37\) −71.0000 −0.315468 −0.157734 0.987482i \(-0.550419\pi\)
−0.157734 + 0.987482i \(0.550419\pi\)
\(38\) −14.0000 −0.0597658
\(39\) 0 0
\(40\) 56.0000 0.221359
\(41\) 180.000 0.685641 0.342820 0.939401i \(-0.388618\pi\)
0.342820 + 0.939401i \(0.388618\pi\)
\(42\) 0 0
\(43\) −108.000 −0.383020 −0.191510 0.981491i \(-0.561338\pi\)
−0.191510 + 0.981491i \(0.561338\pi\)
\(44\) −44.0000 −0.150756
\(45\) 0 0
\(46\) −56.0000 −0.179495
\(47\) −71.0000 −0.220349 −0.110175 0.993912i \(-0.535141\pi\)
−0.110175 + 0.993912i \(0.535141\pi\)
\(48\) 0 0
\(49\) 49.0000 0.142857
\(50\) −152.000 −0.429921
\(51\) 0 0
\(52\) −268.000 −0.714710
\(53\) −128.000 −0.331739 −0.165869 0.986148i \(-0.553043\pi\)
−0.165869 + 0.986148i \(0.553043\pi\)
\(54\) 0 0
\(55\) −77.0000 −0.188776
\(56\) 56.0000 0.133631
\(57\) 0 0
\(58\) −242.000 −0.547865
\(59\) 429.000 0.946628 0.473314 0.880894i \(-0.343058\pi\)
0.473314 + 0.880894i \(0.343058\pi\)
\(60\) 0 0
\(61\) 22.0000 0.0461772 0.0230886 0.999733i \(-0.492650\pi\)
0.0230886 + 0.999733i \(0.492650\pi\)
\(62\) −620.000 −1.27000
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −469.000 −0.894958
\(66\) 0 0
\(67\) −803.000 −1.46421 −0.732105 0.681192i \(-0.761462\pi\)
−0.732105 + 0.681192i \(0.761462\pi\)
\(68\) −120.000 −0.214002
\(69\) 0 0
\(70\) 98.0000 0.167332
\(71\) −468.000 −0.782273 −0.391136 0.920333i \(-0.627918\pi\)
−0.391136 + 0.920333i \(0.627918\pi\)
\(72\) 0 0
\(73\) −117.000 −0.187586 −0.0937932 0.995592i \(-0.529899\pi\)
−0.0937932 + 0.995592i \(0.529899\pi\)
\(74\) −142.000 −0.223070
\(75\) 0 0
\(76\) −28.0000 −0.0422608
\(77\) −77.0000 −0.113961
\(78\) 0 0
\(79\) −96.0000 −0.136720 −0.0683598 0.997661i \(-0.521777\pi\)
−0.0683598 + 0.997661i \(0.521777\pi\)
\(80\) 112.000 0.156525
\(81\) 0 0
\(82\) 360.000 0.484821
\(83\) 1122.00 1.48380 0.741901 0.670510i \(-0.233925\pi\)
0.741901 + 0.670510i \(0.233925\pi\)
\(84\) 0 0
\(85\) −210.000 −0.267973
\(86\) −216.000 −0.270836
\(87\) 0 0
\(88\) −88.0000 −0.106600
\(89\) 1146.00 1.36490 0.682448 0.730934i \(-0.260915\pi\)
0.682448 + 0.730934i \(0.260915\pi\)
\(90\) 0 0
\(91\) −469.000 −0.540270
\(92\) −112.000 −0.126922
\(93\) 0 0
\(94\) −142.000 −0.155810
\(95\) −49.0000 −0.0529189
\(96\) 0 0
\(97\) −92.0000 −0.0963009 −0.0481504 0.998840i \(-0.515333\pi\)
−0.0481504 + 0.998840i \(0.515333\pi\)
\(98\) 98.0000 0.101015
\(99\) 0 0
\(100\) −304.000 −0.304000
\(101\) 202.000 0.199007 0.0995037 0.995037i \(-0.468274\pi\)
0.0995037 + 0.995037i \(0.468274\pi\)
\(102\) 0 0
\(103\) −1798.00 −1.72002 −0.860011 0.510276i \(-0.829543\pi\)
−0.860011 + 0.510276i \(0.829543\pi\)
\(104\) −536.000 −0.505376
\(105\) 0 0
\(106\) −256.000 −0.234575
\(107\) 1431.00 1.29290 0.646449 0.762958i \(-0.276253\pi\)
0.646449 + 0.762958i \(0.276253\pi\)
\(108\) 0 0
\(109\) −278.000 −0.244290 −0.122145 0.992512i \(-0.538977\pi\)
−0.122145 + 0.992512i \(0.538977\pi\)
\(110\) −154.000 −0.133485
\(111\) 0 0
\(112\) 112.000 0.0944911
\(113\) 2322.00 1.93306 0.966528 0.256560i \(-0.0825892\pi\)
0.966528 + 0.256560i \(0.0825892\pi\)
\(114\) 0 0
\(115\) −196.000 −0.158931
\(116\) −484.000 −0.387399
\(117\) 0 0
\(118\) 858.000 0.669367
\(119\) −210.000 −0.161770
\(120\) 0 0
\(121\) 121.000 0.0909091
\(122\) 44.0000 0.0326522
\(123\) 0 0
\(124\) −1240.00 −0.898027
\(125\) −1407.00 −1.00677
\(126\) 0 0
\(127\) 2254.00 1.57488 0.787442 0.616389i \(-0.211405\pi\)
0.787442 + 0.616389i \(0.211405\pi\)
\(128\) 128.000 0.0883883
\(129\) 0 0
\(130\) −938.000 −0.632831
\(131\) −2196.00 −1.46462 −0.732311 0.680971i \(-0.761558\pi\)
−0.732311 + 0.680971i \(0.761558\pi\)
\(132\) 0 0
\(133\) −49.0000 −0.0319462
\(134\) −1606.00 −1.03535
\(135\) 0 0
\(136\) −240.000 −0.151322
\(137\) −766.000 −0.477692 −0.238846 0.971057i \(-0.576769\pi\)
−0.238846 + 0.971057i \(0.576769\pi\)
\(138\) 0 0
\(139\) −1080.00 −0.659024 −0.329512 0.944151i \(-0.606884\pi\)
−0.329512 + 0.944151i \(0.606884\pi\)
\(140\) 196.000 0.118322
\(141\) 0 0
\(142\) −936.000 −0.553151
\(143\) 737.000 0.430986
\(144\) 0 0
\(145\) −847.000 −0.485100
\(146\) −234.000 −0.132644
\(147\) 0 0
\(148\) −284.000 −0.157734
\(149\) −1373.00 −0.754903 −0.377451 0.926029i \(-0.623200\pi\)
−0.377451 + 0.926029i \(0.623200\pi\)
\(150\) 0 0
\(151\) −3210.00 −1.72997 −0.864987 0.501794i \(-0.832673\pi\)
−0.864987 + 0.501794i \(0.832673\pi\)
\(152\) −56.0000 −0.0298829
\(153\) 0 0
\(154\) −154.000 −0.0805823
\(155\) −2170.00 −1.12451
\(156\) 0 0
\(157\) 452.000 0.229768 0.114884 0.993379i \(-0.463350\pi\)
0.114884 + 0.993379i \(0.463350\pi\)
\(158\) −192.000 −0.0966753
\(159\) 0 0
\(160\) 224.000 0.110680
\(161\) −196.000 −0.0959439
\(162\) 0 0
\(163\) −11.0000 −0.00528581 −0.00264290 0.999997i \(-0.500841\pi\)
−0.00264290 + 0.999997i \(0.500841\pi\)
\(164\) 720.000 0.342820
\(165\) 0 0
\(166\) 2244.00 1.04921
\(167\) −504.000 −0.233537 −0.116769 0.993159i \(-0.537254\pi\)
−0.116769 + 0.993159i \(0.537254\pi\)
\(168\) 0 0
\(169\) 2292.00 1.04324
\(170\) −420.000 −0.189485
\(171\) 0 0
\(172\) −432.000 −0.191510
\(173\) −1688.00 −0.741828 −0.370914 0.928667i \(-0.620956\pi\)
−0.370914 + 0.928667i \(0.620956\pi\)
\(174\) 0 0
\(175\) −532.000 −0.229802
\(176\) −176.000 −0.0753778
\(177\) 0 0
\(178\) 2292.00 0.965127
\(179\) −460.000 −0.192078 −0.0960391 0.995378i \(-0.530617\pi\)
−0.0960391 + 0.995378i \(0.530617\pi\)
\(180\) 0 0
\(181\) 2296.00 0.942875 0.471437 0.881900i \(-0.343735\pi\)
0.471437 + 0.881900i \(0.343735\pi\)
\(182\) −938.000 −0.382028
\(183\) 0 0
\(184\) −224.000 −0.0897473
\(185\) −497.000 −0.197514
\(186\) 0 0
\(187\) 330.000 0.129048
\(188\) −284.000 −0.110175
\(189\) 0 0
\(190\) −98.0000 −0.0374193
\(191\) −878.000 −0.332617 −0.166309 0.986074i \(-0.553185\pi\)
−0.166309 + 0.986074i \(0.553185\pi\)
\(192\) 0 0
\(193\) −2268.00 −0.845877 −0.422938 0.906158i \(-0.639001\pi\)
−0.422938 + 0.906158i \(0.639001\pi\)
\(194\) −184.000 −0.0680950
\(195\) 0 0
\(196\) 196.000 0.0714286
\(197\) −5298.00 −1.91608 −0.958038 0.286642i \(-0.907461\pi\)
−0.958038 + 0.286642i \(0.907461\pi\)
\(198\) 0 0
\(199\) 1044.00 0.371895 0.185948 0.982560i \(-0.440464\pi\)
0.185948 + 0.982560i \(0.440464\pi\)
\(200\) −608.000 −0.214960
\(201\) 0 0
\(202\) 404.000 0.140720
\(203\) −847.000 −0.292846
\(204\) 0 0
\(205\) 1260.00 0.429279
\(206\) −3596.00 −1.21624
\(207\) 0 0
\(208\) −1072.00 −0.357355
\(209\) 77.0000 0.0254842
\(210\) 0 0
\(211\) 4566.00 1.48975 0.744873 0.667206i \(-0.232510\pi\)
0.744873 + 0.667206i \(0.232510\pi\)
\(212\) −512.000 −0.165869
\(213\) 0 0
\(214\) 2862.00 0.914216
\(215\) −756.000 −0.239808
\(216\) 0 0
\(217\) −2170.00 −0.678844
\(218\) −556.000 −0.172739
\(219\) 0 0
\(220\) −308.000 −0.0943880
\(221\) 2010.00 0.611797
\(222\) 0 0
\(223\) 198.000 0.0594577 0.0297288 0.999558i \(-0.490536\pi\)
0.0297288 + 0.999558i \(0.490536\pi\)
\(224\) 224.000 0.0668153
\(225\) 0 0
\(226\) 4644.00 1.36688
\(227\) −3762.00 −1.09997 −0.549984 0.835175i \(-0.685366\pi\)
−0.549984 + 0.835175i \(0.685366\pi\)
\(228\) 0 0
\(229\) −704.000 −0.203151 −0.101576 0.994828i \(-0.532388\pi\)
−0.101576 + 0.994828i \(0.532388\pi\)
\(230\) −392.000 −0.112381
\(231\) 0 0
\(232\) −968.000 −0.273932
\(233\) −2210.00 −0.621382 −0.310691 0.950511i \(-0.600560\pi\)
−0.310691 + 0.950511i \(0.600560\pi\)
\(234\) 0 0
\(235\) −497.000 −0.137960
\(236\) 1716.00 0.473314
\(237\) 0 0
\(238\) −420.000 −0.114389
\(239\) −2451.00 −0.663356 −0.331678 0.943393i \(-0.607615\pi\)
−0.331678 + 0.943393i \(0.607615\pi\)
\(240\) 0 0
\(241\) 25.0000 0.00668212 0.00334106 0.999994i \(-0.498937\pi\)
0.00334106 + 0.999994i \(0.498937\pi\)
\(242\) 242.000 0.0642824
\(243\) 0 0
\(244\) 88.0000 0.0230886
\(245\) 343.000 0.0894427
\(246\) 0 0
\(247\) 469.000 0.120817
\(248\) −2480.00 −0.635001
\(249\) 0 0
\(250\) −2814.00 −0.711892
\(251\) 5267.00 1.32450 0.662251 0.749282i \(-0.269601\pi\)
0.662251 + 0.749282i \(0.269601\pi\)
\(252\) 0 0
\(253\) 308.000 0.0765367
\(254\) 4508.00 1.11361
\(255\) 0 0
\(256\) 256.000 0.0625000
\(257\) 1623.00 0.393930 0.196965 0.980411i \(-0.436891\pi\)
0.196965 + 0.980411i \(0.436891\pi\)
\(258\) 0 0
\(259\) −497.000 −0.119236
\(260\) −1876.00 −0.447479
\(261\) 0 0
\(262\) −4392.00 −1.03564
\(263\) 2475.00 0.580285 0.290143 0.956983i \(-0.406297\pi\)
0.290143 + 0.956983i \(0.406297\pi\)
\(264\) 0 0
\(265\) −896.000 −0.207701
\(266\) −98.0000 −0.0225893
\(267\) 0 0
\(268\) −3212.00 −0.732105
\(269\) −1746.00 −0.395745 −0.197873 0.980228i \(-0.563403\pi\)
−0.197873 + 0.980228i \(0.563403\pi\)
\(270\) 0 0
\(271\) 1653.00 0.370526 0.185263 0.982689i \(-0.440686\pi\)
0.185263 + 0.982689i \(0.440686\pi\)
\(272\) −480.000 −0.107001
\(273\) 0 0
\(274\) −1532.00 −0.337779
\(275\) 836.000 0.183319
\(276\) 0 0
\(277\) −2056.00 −0.445968 −0.222984 0.974822i \(-0.571580\pi\)
−0.222984 + 0.974822i \(0.571580\pi\)
\(278\) −2160.00 −0.466001
\(279\) 0 0
\(280\) 392.000 0.0836660
\(281\) −837.000 −0.177691 −0.0888456 0.996045i \(-0.528318\pi\)
−0.0888456 + 0.996045i \(0.528318\pi\)
\(282\) 0 0
\(283\) 8969.00 1.88393 0.941964 0.335713i \(-0.108977\pi\)
0.941964 + 0.335713i \(0.108977\pi\)
\(284\) −1872.00 −0.391136
\(285\) 0 0
\(286\) 1474.00 0.304753
\(287\) 1260.00 0.259148
\(288\) 0 0
\(289\) −4013.00 −0.816813
\(290\) −1694.00 −0.343018
\(291\) 0 0
\(292\) −468.000 −0.0937932
\(293\) −5120.00 −1.02087 −0.510433 0.859918i \(-0.670515\pi\)
−0.510433 + 0.859918i \(0.670515\pi\)
\(294\) 0 0
\(295\) 3003.00 0.592683
\(296\) −568.000 −0.111535
\(297\) 0 0
\(298\) −2746.00 −0.533797
\(299\) 1876.00 0.362849
\(300\) 0 0
\(301\) −756.000 −0.144768
\(302\) −6420.00 −1.22328
\(303\) 0 0
\(304\) −112.000 −0.0211304
\(305\) 154.000 0.0289115
\(306\) 0 0
\(307\) −2892.00 −0.537639 −0.268819 0.963191i \(-0.586634\pi\)
−0.268819 + 0.963191i \(0.586634\pi\)
\(308\) −308.000 −0.0569803
\(309\) 0 0
\(310\) −4340.00 −0.795147
\(311\) −3208.00 −0.584916 −0.292458 0.956278i \(-0.594473\pi\)
−0.292458 + 0.956278i \(0.594473\pi\)
\(312\) 0 0
\(313\) 3550.00 0.641079 0.320540 0.947235i \(-0.396136\pi\)
0.320540 + 0.947235i \(0.396136\pi\)
\(314\) 904.000 0.162470
\(315\) 0 0
\(316\) −384.000 −0.0683598
\(317\) 5524.00 0.978734 0.489367 0.872078i \(-0.337228\pi\)
0.489367 + 0.872078i \(0.337228\pi\)
\(318\) 0 0
\(319\) 1331.00 0.233610
\(320\) 448.000 0.0782624
\(321\) 0 0
\(322\) −392.000 −0.0678426
\(323\) 210.000 0.0361756
\(324\) 0 0
\(325\) 5092.00 0.869087
\(326\) −22.0000 −0.00373763
\(327\) 0 0
\(328\) 1440.00 0.242411
\(329\) −497.000 −0.0832842
\(330\) 0 0
\(331\) −2144.00 −0.356027 −0.178013 0.984028i \(-0.556967\pi\)
−0.178013 + 0.984028i \(0.556967\pi\)
\(332\) 4488.00 0.741901
\(333\) 0 0
\(334\) −1008.00 −0.165136
\(335\) −5621.00 −0.916740
\(336\) 0 0
\(337\) −884.000 −0.142892 −0.0714459 0.997444i \(-0.522761\pi\)
−0.0714459 + 0.997444i \(0.522761\pi\)
\(338\) 4584.00 0.737683
\(339\) 0 0
\(340\) −840.000 −0.133986
\(341\) 3410.00 0.541530
\(342\) 0 0
\(343\) 343.000 0.0539949
\(344\) −864.000 −0.135418
\(345\) 0 0
\(346\) −3376.00 −0.524552
\(347\) 4040.00 0.625010 0.312505 0.949916i \(-0.398832\pi\)
0.312505 + 0.949916i \(0.398832\pi\)
\(348\) 0 0
\(349\) 1225.00 0.187888 0.0939438 0.995578i \(-0.470053\pi\)
0.0939438 + 0.995578i \(0.470053\pi\)
\(350\) −1064.00 −0.162495
\(351\) 0 0
\(352\) −352.000 −0.0533002
\(353\) −2483.00 −0.374382 −0.187191 0.982324i \(-0.559938\pi\)
−0.187191 + 0.982324i \(0.559938\pi\)
\(354\) 0 0
\(355\) −3276.00 −0.489780
\(356\) 4584.00 0.682448
\(357\) 0 0
\(358\) −920.000 −0.135820
\(359\) −7804.00 −1.14730 −0.573648 0.819102i \(-0.694472\pi\)
−0.573648 + 0.819102i \(0.694472\pi\)
\(360\) 0 0
\(361\) −6810.00 −0.992856
\(362\) 4592.00 0.666713
\(363\) 0 0
\(364\) −1876.00 −0.270135
\(365\) −819.000 −0.117448
\(366\) 0 0
\(367\) 3074.00 0.437225 0.218612 0.975812i \(-0.429847\pi\)
0.218612 + 0.975812i \(0.429847\pi\)
\(368\) −448.000 −0.0634609
\(369\) 0 0
\(370\) −994.000 −0.139664
\(371\) −896.000 −0.125385
\(372\) 0 0
\(373\) 674.000 0.0935614 0.0467807 0.998905i \(-0.485104\pi\)
0.0467807 + 0.998905i \(0.485104\pi\)
\(374\) 660.000 0.0912508
\(375\) 0 0
\(376\) −568.000 −0.0779052
\(377\) 8107.00 1.10751
\(378\) 0 0
\(379\) 12051.0 1.63329 0.816647 0.577138i \(-0.195830\pi\)
0.816647 + 0.577138i \(0.195830\pi\)
\(380\) −196.000 −0.0264594
\(381\) 0 0
\(382\) −1756.00 −0.235196
\(383\) 12664.0 1.68956 0.844778 0.535116i \(-0.179732\pi\)
0.844778 + 0.535116i \(0.179732\pi\)
\(384\) 0 0
\(385\) −539.000 −0.0713506
\(386\) −4536.00 −0.598125
\(387\) 0 0
\(388\) −368.000 −0.0481504
\(389\) −264.000 −0.0344096 −0.0172048 0.999852i \(-0.505477\pi\)
−0.0172048 + 0.999852i \(0.505477\pi\)
\(390\) 0 0
\(391\) 840.000 0.108646
\(392\) 392.000 0.0505076
\(393\) 0 0
\(394\) −10596.0 −1.35487
\(395\) −672.000 −0.0856000
\(396\) 0 0
\(397\) −14394.0 −1.81968 −0.909842 0.414956i \(-0.863797\pi\)
−0.909842 + 0.414956i \(0.863797\pi\)
\(398\) 2088.00 0.262970
\(399\) 0 0
\(400\) −1216.00 −0.152000
\(401\) 12304.0 1.53225 0.766125 0.642691i \(-0.222182\pi\)
0.766125 + 0.642691i \(0.222182\pi\)
\(402\) 0 0
\(403\) 20770.0 2.56731
\(404\) 808.000 0.0995037
\(405\) 0 0
\(406\) −1694.00 −0.207073
\(407\) 781.000 0.0951173
\(408\) 0 0
\(409\) −3154.00 −0.381309 −0.190654 0.981657i \(-0.561061\pi\)
−0.190654 + 0.981657i \(0.561061\pi\)
\(410\) 2520.00 0.303546
\(411\) 0 0
\(412\) −7192.00 −0.860011
\(413\) 3003.00 0.357792
\(414\) 0 0
\(415\) 7854.00 0.929006
\(416\) −2144.00 −0.252688
\(417\) 0 0
\(418\) 154.000 0.0180201
\(419\) 4635.00 0.540417 0.270208 0.962802i \(-0.412907\pi\)
0.270208 + 0.962802i \(0.412907\pi\)
\(420\) 0 0
\(421\) −7265.00 −0.841032 −0.420516 0.907285i \(-0.638151\pi\)
−0.420516 + 0.907285i \(0.638151\pi\)
\(422\) 9132.00 1.05341
\(423\) 0 0
\(424\) −1024.00 −0.117287
\(425\) 2280.00 0.260226
\(426\) 0 0
\(427\) 154.000 0.0174534
\(428\) 5724.00 0.646449
\(429\) 0 0
\(430\) −1512.00 −0.169570
\(431\) −7589.00 −0.848142 −0.424071 0.905629i \(-0.639399\pi\)
−0.424071 + 0.905629i \(0.639399\pi\)
\(432\) 0 0
\(433\) 5164.00 0.573132 0.286566 0.958061i \(-0.407486\pi\)
0.286566 + 0.958061i \(0.407486\pi\)
\(434\) −4340.00 −0.480015
\(435\) 0 0
\(436\) −1112.00 −0.122145
\(437\) 196.000 0.0214553
\(438\) 0 0
\(439\) 14221.0 1.54608 0.773042 0.634354i \(-0.218734\pi\)
0.773042 + 0.634354i \(0.218734\pi\)
\(440\) −616.000 −0.0667424
\(441\) 0 0
\(442\) 4020.00 0.432606
\(443\) −6924.00 −0.742594 −0.371297 0.928514i \(-0.621087\pi\)
−0.371297 + 0.928514i \(0.621087\pi\)
\(444\) 0 0
\(445\) 8022.00 0.854560
\(446\) 396.000 0.0420429
\(447\) 0 0
\(448\) 448.000 0.0472456
\(449\) −2524.00 −0.265289 −0.132645 0.991164i \(-0.542347\pi\)
−0.132645 + 0.991164i \(0.542347\pi\)
\(450\) 0 0
\(451\) −1980.00 −0.206729
\(452\) 9288.00 0.966528
\(453\) 0 0
\(454\) −7524.00 −0.777795
\(455\) −3283.00 −0.338262
\(456\) 0 0
\(457\) 1928.00 0.197348 0.0986740 0.995120i \(-0.468540\pi\)
0.0986740 + 0.995120i \(0.468540\pi\)
\(458\) −1408.00 −0.143650
\(459\) 0 0
\(460\) −784.000 −0.0794656
\(461\) 12852.0 1.29843 0.649216 0.760604i \(-0.275097\pi\)
0.649216 + 0.760604i \(0.275097\pi\)
\(462\) 0 0
\(463\) 4741.00 0.475881 0.237941 0.971280i \(-0.423528\pi\)
0.237941 + 0.971280i \(0.423528\pi\)
\(464\) −1936.00 −0.193699
\(465\) 0 0
\(466\) −4420.00 −0.439383
\(467\) 6809.00 0.674696 0.337348 0.941380i \(-0.390470\pi\)
0.337348 + 0.941380i \(0.390470\pi\)
\(468\) 0 0
\(469\) −5621.00 −0.553419
\(470\) −994.000 −0.0975528
\(471\) 0 0
\(472\) 3432.00 0.334683
\(473\) 1188.00 0.115485
\(474\) 0 0
\(475\) 532.000 0.0513891
\(476\) −840.000 −0.0808852
\(477\) 0 0
\(478\) −4902.00 −0.469063
\(479\) −1734.00 −0.165404 −0.0827020 0.996574i \(-0.526355\pi\)
−0.0827020 + 0.996574i \(0.526355\pi\)
\(480\) 0 0
\(481\) 4757.00 0.450937
\(482\) 50.0000 0.00472497
\(483\) 0 0
\(484\) 484.000 0.0454545
\(485\) −644.000 −0.0602939
\(486\) 0 0
\(487\) −7368.00 −0.685577 −0.342788 0.939413i \(-0.611371\pi\)
−0.342788 + 0.939413i \(0.611371\pi\)
\(488\) 176.000 0.0163261
\(489\) 0 0
\(490\) 686.000 0.0632456
\(491\) −13201.0 −1.21335 −0.606673 0.794952i \(-0.707496\pi\)
−0.606673 + 0.794952i \(0.707496\pi\)
\(492\) 0 0
\(493\) 3630.00 0.331617
\(494\) 938.000 0.0854304
\(495\) 0 0
\(496\) −4960.00 −0.449013
\(497\) −3276.00 −0.295671
\(498\) 0 0
\(499\) 16539.0 1.48374 0.741871 0.670543i \(-0.233939\pi\)
0.741871 + 0.670543i \(0.233939\pi\)
\(500\) −5628.00 −0.503384
\(501\) 0 0
\(502\) 10534.0 0.936565
\(503\) 14780.0 1.31015 0.655077 0.755562i \(-0.272636\pi\)
0.655077 + 0.755562i \(0.272636\pi\)
\(504\) 0 0
\(505\) 1414.00 0.124598
\(506\) 616.000 0.0541196
\(507\) 0 0
\(508\) 9016.00 0.787442
\(509\) 11766.0 1.02459 0.512297 0.858808i \(-0.328795\pi\)
0.512297 + 0.858808i \(0.328795\pi\)
\(510\) 0 0
\(511\) −819.000 −0.0709010
\(512\) 512.000 0.0441942
\(513\) 0 0
\(514\) 3246.00 0.278550
\(515\) −12586.0 −1.07690
\(516\) 0 0
\(517\) 781.000 0.0664378
\(518\) −994.000 −0.0843125
\(519\) 0 0
\(520\) −3752.00 −0.316416
\(521\) 13503.0 1.13546 0.567732 0.823213i \(-0.307821\pi\)
0.567732 + 0.823213i \(0.307821\pi\)
\(522\) 0 0
\(523\) −18681.0 −1.56188 −0.780940 0.624606i \(-0.785259\pi\)
−0.780940 + 0.624606i \(0.785259\pi\)
\(524\) −8784.00 −0.732311
\(525\) 0 0
\(526\) 4950.00 0.410324
\(527\) 9300.00 0.768718
\(528\) 0 0
\(529\) −11383.0 −0.935563
\(530\) −1792.00 −0.146867
\(531\) 0 0
\(532\) −196.000 −0.0159731
\(533\) −12060.0 −0.980069
\(534\) 0 0
\(535\) 10017.0 0.809482
\(536\) −6424.00 −0.517676
\(537\) 0 0
\(538\) −3492.00 −0.279834
\(539\) −539.000 −0.0430730
\(540\) 0 0
\(541\) −2000.00 −0.158940 −0.0794702 0.996837i \(-0.525323\pi\)
−0.0794702 + 0.996837i \(0.525323\pi\)
\(542\) 3306.00 0.262002
\(543\) 0 0
\(544\) −960.000 −0.0756611
\(545\) −1946.00 −0.152950
\(546\) 0 0
\(547\) 19368.0 1.51392 0.756961 0.653459i \(-0.226683\pi\)
0.756961 + 0.653459i \(0.226683\pi\)
\(548\) −3064.00 −0.238846
\(549\) 0 0
\(550\) 1672.00 0.129626
\(551\) 847.000 0.0654871
\(552\) 0 0
\(553\) −672.000 −0.0516751
\(554\) −4112.00 −0.315347
\(555\) 0 0
\(556\) −4320.00 −0.329512
\(557\) −4669.00 −0.355174 −0.177587 0.984105i \(-0.556829\pi\)
−0.177587 + 0.984105i \(0.556829\pi\)
\(558\) 0 0
\(559\) 7236.00 0.547496
\(560\) 784.000 0.0591608
\(561\) 0 0
\(562\) −1674.00 −0.125647
\(563\) 9324.00 0.697975 0.348987 0.937127i \(-0.386526\pi\)
0.348987 + 0.937127i \(0.386526\pi\)
\(564\) 0 0
\(565\) 16254.0 1.21028
\(566\) 17938.0 1.33214
\(567\) 0 0
\(568\) −3744.00 −0.276575
\(569\) −25646.0 −1.88952 −0.944759 0.327765i \(-0.893705\pi\)
−0.944759 + 0.327765i \(0.893705\pi\)
\(570\) 0 0
\(571\) −12928.0 −0.947496 −0.473748 0.880661i \(-0.657099\pi\)
−0.473748 + 0.880661i \(0.657099\pi\)
\(572\) 2948.00 0.215493
\(573\) 0 0
\(574\) 2520.00 0.183245
\(575\) 2128.00 0.154337
\(576\) 0 0
\(577\) −14862.0 −1.07229 −0.536147 0.844125i \(-0.680121\pi\)
−0.536147 + 0.844125i \(0.680121\pi\)
\(578\) −8026.00 −0.577574
\(579\) 0 0
\(580\) −3388.00 −0.242550
\(581\) 7854.00 0.560824
\(582\) 0 0
\(583\) 1408.00 0.100023
\(584\) −936.000 −0.0663218
\(585\) 0 0
\(586\) −10240.0 −0.721861
\(587\) 13383.0 0.941015 0.470507 0.882396i \(-0.344071\pi\)
0.470507 + 0.882396i \(0.344071\pi\)
\(588\) 0 0
\(589\) 2170.00 0.151805
\(590\) 6006.00 0.419090
\(591\) 0 0
\(592\) −1136.00 −0.0788671
\(593\) 10152.0 0.703023 0.351512 0.936184i \(-0.385668\pi\)
0.351512 + 0.936184i \(0.385668\pi\)
\(594\) 0 0
\(595\) −1470.00 −0.101284
\(596\) −5492.00 −0.377451
\(597\) 0 0
\(598\) 3752.00 0.256573
\(599\) −16592.0 −1.13177 −0.565885 0.824484i \(-0.691466\pi\)
−0.565885 + 0.824484i \(0.691466\pi\)
\(600\) 0 0
\(601\) −1001.00 −0.0679395 −0.0339698 0.999423i \(-0.510815\pi\)
−0.0339698 + 0.999423i \(0.510815\pi\)
\(602\) −1512.00 −0.102366
\(603\) 0 0
\(604\) −12840.0 −0.864987
\(605\) 847.000 0.0569181
\(606\) 0 0
\(607\) −18427.0 −1.23217 −0.616086 0.787679i \(-0.711283\pi\)
−0.616086 + 0.787679i \(0.711283\pi\)
\(608\) −224.000 −0.0149414
\(609\) 0 0
\(610\) 308.000 0.0204435
\(611\) 4757.00 0.314972
\(612\) 0 0
\(613\) 5606.00 0.369371 0.184685 0.982798i \(-0.440873\pi\)
0.184685 + 0.982798i \(0.440873\pi\)
\(614\) −5784.00 −0.380168
\(615\) 0 0
\(616\) −616.000 −0.0402911
\(617\) −6378.00 −0.416157 −0.208078 0.978112i \(-0.566721\pi\)
−0.208078 + 0.978112i \(0.566721\pi\)
\(618\) 0 0
\(619\) −4070.00 −0.264276 −0.132138 0.991231i \(-0.542184\pi\)
−0.132138 + 0.991231i \(0.542184\pi\)
\(620\) −8680.00 −0.562254
\(621\) 0 0
\(622\) −6416.00 −0.413598
\(623\) 8022.00 0.515882
\(624\) 0 0
\(625\) −349.000 −0.0223360
\(626\) 7100.00 0.453312
\(627\) 0 0
\(628\) 1808.00 0.114884
\(629\) 2130.00 0.135022
\(630\) 0 0
\(631\) 23252.0 1.46695 0.733477 0.679715i \(-0.237896\pi\)
0.733477 + 0.679715i \(0.237896\pi\)
\(632\) −768.000 −0.0483377
\(633\) 0 0
\(634\) 11048.0 0.692070
\(635\) 15778.0 0.986033
\(636\) 0 0
\(637\) −3283.00 −0.204203
\(638\) 2662.00 0.165187
\(639\) 0 0
\(640\) 896.000 0.0553399
\(641\) −3758.00 −0.231563 −0.115782 0.993275i \(-0.536937\pi\)
−0.115782 + 0.993275i \(0.536937\pi\)
\(642\) 0 0
\(643\) 13068.0 0.801480 0.400740 0.916192i \(-0.368753\pi\)
0.400740 + 0.916192i \(0.368753\pi\)
\(644\) −784.000 −0.0479719
\(645\) 0 0
\(646\) 420.000 0.0255800
\(647\) 31027.0 1.88531 0.942656 0.333765i \(-0.108319\pi\)
0.942656 + 0.333765i \(0.108319\pi\)
\(648\) 0 0
\(649\) −4719.00 −0.285419
\(650\) 10184.0 0.614537
\(651\) 0 0
\(652\) −44.0000 −0.00264290
\(653\) 18456.0 1.10603 0.553016 0.833171i \(-0.313477\pi\)
0.553016 + 0.833171i \(0.313477\pi\)
\(654\) 0 0
\(655\) −15372.0 −0.916998
\(656\) 2880.00 0.171410
\(657\) 0 0
\(658\) −994.000 −0.0588908
\(659\) −11141.0 −0.658561 −0.329281 0.944232i \(-0.606806\pi\)
−0.329281 + 0.944232i \(0.606806\pi\)
\(660\) 0 0
\(661\) 5172.00 0.304338 0.152169 0.988354i \(-0.451374\pi\)
0.152169 + 0.988354i \(0.451374\pi\)
\(662\) −4288.00 −0.251749
\(663\) 0 0
\(664\) 8976.00 0.524603
\(665\) −343.000 −0.0200015
\(666\) 0 0
\(667\) 3388.00 0.196677
\(668\) −2016.00 −0.116769
\(669\) 0 0
\(670\) −11242.0 −0.648233
\(671\) −242.000 −0.0139230
\(672\) 0 0
\(673\) −10460.0 −0.599113 −0.299557 0.954078i \(-0.596839\pi\)
−0.299557 + 0.954078i \(0.596839\pi\)
\(674\) −1768.00 −0.101040
\(675\) 0 0
\(676\) 9168.00 0.521620
\(677\) 15546.0 0.882543 0.441271 0.897374i \(-0.354528\pi\)
0.441271 + 0.897374i \(0.354528\pi\)
\(678\) 0 0
\(679\) −644.000 −0.0363983
\(680\) −1680.00 −0.0947427
\(681\) 0 0
\(682\) 6820.00 0.382920
\(683\) −31138.0 −1.74445 −0.872227 0.489101i \(-0.837325\pi\)
−0.872227 + 0.489101i \(0.837325\pi\)
\(684\) 0 0
\(685\) −5362.00 −0.299082
\(686\) 686.000 0.0381802
\(687\) 0 0
\(688\) −1728.00 −0.0957549
\(689\) 8576.00 0.474194
\(690\) 0 0
\(691\) 21574.0 1.18772 0.593859 0.804569i \(-0.297604\pi\)
0.593859 + 0.804569i \(0.297604\pi\)
\(692\) −6752.00 −0.370914
\(693\) 0 0
\(694\) 8080.00 0.441949
\(695\) −7560.00 −0.412615
\(696\) 0 0
\(697\) −5400.00 −0.293457
\(698\) 2450.00 0.132857
\(699\) 0 0
\(700\) −2128.00 −0.114901
\(701\) −2074.00 −0.111746 −0.0558730 0.998438i \(-0.517794\pi\)
−0.0558730 + 0.998438i \(0.517794\pi\)
\(702\) 0 0
\(703\) 497.000 0.0266639
\(704\) −704.000 −0.0376889
\(705\) 0 0
\(706\) −4966.00 −0.264728
\(707\) 1414.00 0.0752177
\(708\) 0 0
\(709\) −6829.00 −0.361733 −0.180866 0.983508i \(-0.557890\pi\)
−0.180866 + 0.983508i \(0.557890\pi\)
\(710\) −6552.00 −0.346327
\(711\) 0 0
\(712\) 9168.00 0.482564
\(713\) 8680.00 0.455917
\(714\) 0 0
\(715\) 5159.00 0.269840
\(716\) −1840.00 −0.0960391
\(717\) 0 0
\(718\) −15608.0 −0.811261
\(719\) −6921.00 −0.358984 −0.179492 0.983759i \(-0.557445\pi\)
−0.179492 + 0.983759i \(0.557445\pi\)
\(720\) 0 0
\(721\) −12586.0 −0.650107
\(722\) −13620.0 −0.702055
\(723\) 0 0
\(724\) 9184.00 0.471437
\(725\) 9196.00 0.471077
\(726\) 0 0
\(727\) 24064.0 1.22763 0.613813 0.789451i \(-0.289635\pi\)
0.613813 + 0.789451i \(0.289635\pi\)
\(728\) −3752.00 −0.191014
\(729\) 0 0
\(730\) −1638.00 −0.0830481
\(731\) 3240.00 0.163934
\(732\) 0 0
\(733\) 30262.0 1.52490 0.762451 0.647047i \(-0.223996\pi\)
0.762451 + 0.647047i \(0.223996\pi\)
\(734\) 6148.00 0.309165
\(735\) 0 0
\(736\) −896.000 −0.0448736
\(737\) 8833.00 0.441476
\(738\) 0 0
\(739\) 24024.0 1.19586 0.597928 0.801550i \(-0.295991\pi\)
0.597928 + 0.801550i \(0.295991\pi\)
\(740\) −1988.00 −0.0987572
\(741\) 0 0
\(742\) −1792.00 −0.0886609
\(743\) 227.000 0.0112084 0.00560419 0.999984i \(-0.498216\pi\)
0.00560419 + 0.999984i \(0.498216\pi\)
\(744\) 0 0
\(745\) −9611.00 −0.472644
\(746\) 1348.00 0.0661579
\(747\) 0 0
\(748\) 1320.00 0.0645240
\(749\) 10017.0 0.488669
\(750\) 0 0
\(751\) −23435.0 −1.13869 −0.569344 0.822099i \(-0.692803\pi\)
−0.569344 + 0.822099i \(0.692803\pi\)
\(752\) −1136.00 −0.0550873
\(753\) 0 0
\(754\) 16214.0 0.783129
\(755\) −22470.0 −1.08314
\(756\) 0 0
\(757\) 1609.00 0.0772524 0.0386262 0.999254i \(-0.487702\pi\)
0.0386262 + 0.999254i \(0.487702\pi\)
\(758\) 24102.0 1.15491
\(759\) 0 0
\(760\) −392.000 −0.0187097
\(761\) −6976.00 −0.332299 −0.166150 0.986101i \(-0.553133\pi\)
−0.166150 + 0.986101i \(0.553133\pi\)
\(762\) 0 0
\(763\) −1946.00 −0.0923328
\(764\) −3512.00 −0.166309
\(765\) 0 0
\(766\) 25328.0 1.19470
\(767\) −28743.0 −1.35313
\(768\) 0 0
\(769\) −36079.0 −1.69186 −0.845931 0.533292i \(-0.820955\pi\)
−0.845931 + 0.533292i \(0.820955\pi\)
\(770\) −1078.00 −0.0504525
\(771\) 0 0
\(772\) −9072.00 −0.422938
\(773\) 23507.0 1.09377 0.546887 0.837206i \(-0.315813\pi\)
0.546887 + 0.837206i \(0.315813\pi\)
\(774\) 0 0
\(775\) 23560.0 1.09200
\(776\) −736.000 −0.0340475
\(777\) 0 0
\(778\) −528.000 −0.0243313
\(779\) −1260.00 −0.0579515
\(780\) 0 0
\(781\) 5148.00 0.235864
\(782\) 1680.00 0.0768244
\(783\) 0 0
\(784\) 784.000 0.0357143
\(785\) 3164.00 0.143857
\(786\) 0 0
\(787\) −35145.0 −1.59185 −0.795924 0.605397i \(-0.793014\pi\)
−0.795924 + 0.605397i \(0.793014\pi\)
\(788\) −21192.0 −0.958038
\(789\) 0 0
\(790\) −1344.00 −0.0605283
\(791\) 16254.0 0.730627
\(792\) 0 0
\(793\) −1474.00 −0.0660067
\(794\) −28788.0 −1.28671
\(795\) 0 0
\(796\) 4176.00 0.185948
\(797\) −34155.0 −1.51798 −0.758991 0.651101i \(-0.774308\pi\)
−0.758991 + 0.651101i \(0.774308\pi\)
\(798\) 0 0
\(799\) 2130.00 0.0943104
\(800\) −2432.00 −0.107480
\(801\) 0 0
\(802\) 24608.0 1.08346
\(803\) 1287.00 0.0565595
\(804\) 0 0
\(805\) −1372.00 −0.0600704
\(806\) 41540.0 1.81536
\(807\) 0 0
\(808\) 1616.00 0.0703598
\(809\) 3439.00 0.149455 0.0747273 0.997204i \(-0.476191\pi\)
0.0747273 + 0.997204i \(0.476191\pi\)
\(810\) 0 0
\(811\) −1625.00 −0.0703594 −0.0351797 0.999381i \(-0.511200\pi\)
−0.0351797 + 0.999381i \(0.511200\pi\)
\(812\) −3388.00 −0.146423
\(813\) 0 0
\(814\) 1562.00 0.0672581
\(815\) −77.0000 −0.00330944
\(816\) 0 0
\(817\) 756.000 0.0323734
\(818\) −6308.00 −0.269626
\(819\) 0 0
\(820\) 5040.00 0.214640
\(821\) −31531.0 −1.34036 −0.670182 0.742196i \(-0.733784\pi\)
−0.670182 + 0.742196i \(0.733784\pi\)
\(822\) 0 0
\(823\) −31003.0 −1.31312 −0.656559 0.754274i \(-0.727989\pi\)
−0.656559 + 0.754274i \(0.727989\pi\)
\(824\) −14384.0 −0.608119
\(825\) 0 0
\(826\) 6006.00 0.252997
\(827\) 15015.0 0.631345 0.315673 0.948868i \(-0.397770\pi\)
0.315673 + 0.948868i \(0.397770\pi\)
\(828\) 0 0
\(829\) 12280.0 0.514478 0.257239 0.966348i \(-0.417187\pi\)
0.257239 + 0.966348i \(0.417187\pi\)
\(830\) 15708.0 0.656907
\(831\) 0 0
\(832\) −4288.00 −0.178677
\(833\) −1470.00 −0.0611434
\(834\) 0 0
\(835\) −3528.00 −0.146217
\(836\) 308.000 0.0127421
\(837\) 0 0
\(838\) 9270.00 0.382132
\(839\) −26599.0 −1.09452 −0.547258 0.836964i \(-0.684328\pi\)
−0.547258 + 0.836964i \(0.684328\pi\)
\(840\) 0 0
\(841\) −9748.00 −0.399688
\(842\) −14530.0 −0.594699
\(843\) 0 0
\(844\) 18264.0 0.744873
\(845\) 16044.0 0.653172
\(846\) 0 0
\(847\) 847.000 0.0343604
\(848\) −2048.00 −0.0829347
\(849\) 0 0
\(850\) 4560.00 0.184008
\(851\) 1988.00 0.0800796
\(852\) 0 0
\(853\) −3798.00 −0.152451 −0.0762257 0.997091i \(-0.524287\pi\)
−0.0762257 + 0.997091i \(0.524287\pi\)
\(854\) 308.000 0.0123414
\(855\) 0 0
\(856\) 11448.0 0.457108
\(857\) 38726.0 1.54359 0.771794 0.635873i \(-0.219360\pi\)
0.771794 + 0.635873i \(0.219360\pi\)
\(858\) 0 0
\(859\) 3296.00 0.130917 0.0654587 0.997855i \(-0.479149\pi\)
0.0654587 + 0.997855i \(0.479149\pi\)
\(860\) −3024.00 −0.119904
\(861\) 0 0
\(862\) −15178.0 −0.599727
\(863\) −13488.0 −0.532024 −0.266012 0.963970i \(-0.585706\pi\)
−0.266012 + 0.963970i \(0.585706\pi\)
\(864\) 0 0
\(865\) −11816.0 −0.464458
\(866\) 10328.0 0.405265
\(867\) 0 0
\(868\) −8680.00 −0.339422
\(869\) 1056.00 0.0412225
\(870\) 0 0
\(871\) 53801.0 2.09297
\(872\) −2224.00 −0.0863694
\(873\) 0 0
\(874\) 392.000 0.0151712
\(875\) −9849.00 −0.380522
\(876\) 0 0
\(877\) −17144.0 −0.660105 −0.330052 0.943963i \(-0.607066\pi\)
−0.330052 + 0.943963i \(0.607066\pi\)
\(878\) 28442.0 1.09325
\(879\) 0 0
\(880\) −1232.00 −0.0471940
\(881\) −11993.0 −0.458632 −0.229316 0.973352i \(-0.573649\pi\)
−0.229316 + 0.973352i \(0.573649\pi\)
\(882\) 0 0
\(883\) 10483.0 0.399526 0.199763 0.979844i \(-0.435983\pi\)
0.199763 + 0.979844i \(0.435983\pi\)
\(884\) 8040.00 0.305899
\(885\) 0 0
\(886\) −13848.0 −0.525093
\(887\) −4562.00 −0.172691 −0.0863455 0.996265i \(-0.527519\pi\)
−0.0863455 + 0.996265i \(0.527519\pi\)
\(888\) 0 0
\(889\) 15778.0 0.595250
\(890\) 16044.0 0.604265
\(891\) 0 0
\(892\) 792.000 0.0297288
\(893\) 497.000 0.0186243
\(894\) 0 0
\(895\) −3220.00 −0.120260
\(896\) 896.000 0.0334077
\(897\) 0 0
\(898\) −5048.00 −0.187588
\(899\) 37510.0 1.39158
\(900\) 0 0
\(901\) 3840.00 0.141986
\(902\) −3960.00 −0.146179
\(903\) 0 0
\(904\) 18576.0 0.683439
\(905\) 16072.0 0.590333
\(906\) 0 0
\(907\) 18556.0 0.679318 0.339659 0.940549i \(-0.389688\pi\)
0.339659 + 0.940549i \(0.389688\pi\)
\(908\) −15048.0 −0.549984
\(909\) 0 0
\(910\) −6566.00 −0.239188
\(911\) −5826.00 −0.211881 −0.105941 0.994372i \(-0.533785\pi\)
−0.105941 + 0.994372i \(0.533785\pi\)
\(912\) 0 0
\(913\) −12342.0 −0.447383
\(914\) 3856.00 0.139546
\(915\) 0 0
\(916\) −2816.00 −0.101576
\(917\) −15372.0 −0.553575
\(918\) 0 0
\(919\) 41492.0 1.48933 0.744665 0.667438i \(-0.232609\pi\)
0.744665 + 0.667438i \(0.232609\pi\)
\(920\) −1568.00 −0.0561907
\(921\) 0 0
\(922\) 25704.0 0.918130
\(923\) 31356.0 1.11820
\(924\) 0 0
\(925\) 5396.00 0.191805
\(926\) 9482.00 0.336499
\(927\) 0 0
\(928\) −3872.00 −0.136966
\(929\) 15381.0 0.543202 0.271601 0.962410i \(-0.412447\pi\)
0.271601 + 0.962410i \(0.412447\pi\)
\(930\) 0 0
\(931\) −343.000 −0.0120745
\(932\) −8840.00 −0.310691
\(933\) 0 0
\(934\) 13618.0 0.477082
\(935\) 2310.00 0.0807969
\(936\) 0 0
\(937\) −55054.0 −1.91946 −0.959731 0.280921i \(-0.909360\pi\)
−0.959731 + 0.280921i \(0.909360\pi\)
\(938\) −11242.0 −0.391327
\(939\) 0 0
\(940\) −1988.00 −0.0689802
\(941\) 3892.00 0.134831 0.0674153 0.997725i \(-0.478525\pi\)
0.0674153 + 0.997725i \(0.478525\pi\)
\(942\) 0 0
\(943\) −5040.00 −0.174046
\(944\) 6864.00 0.236657
\(945\) 0 0
\(946\) 2376.00 0.0816601
\(947\) 36158.0 1.24074 0.620368 0.784311i \(-0.286983\pi\)
0.620368 + 0.784311i \(0.286983\pi\)
\(948\) 0 0
\(949\) 7839.00 0.268140
\(950\) 1064.00 0.0363376
\(951\) 0 0
\(952\) −1680.00 −0.0571944
\(953\) 23959.0 0.814384 0.407192 0.913343i \(-0.366508\pi\)
0.407192 + 0.913343i \(0.366508\pi\)
\(954\) 0 0
\(955\) −6146.00 −0.208251
\(956\) −9804.00 −0.331678
\(957\) 0 0
\(958\) −3468.00 −0.116958
\(959\) −5362.00 −0.180551
\(960\) 0 0
\(961\) 66309.0 2.22581
\(962\) 9514.00 0.318860
\(963\) 0 0
\(964\) 100.000 0.00334106
\(965\) −15876.0 −0.529603
\(966\) 0 0
\(967\) −56106.0 −1.86582 −0.932910 0.360110i \(-0.882739\pi\)
−0.932910 + 0.360110i \(0.882739\pi\)
\(968\) 968.000 0.0321412
\(969\) 0 0
\(970\) −1288.00 −0.0426342
\(971\) 35079.0 1.15936 0.579680 0.814844i \(-0.303178\pi\)
0.579680 + 0.814844i \(0.303178\pi\)
\(972\) 0 0
\(973\) −7560.00 −0.249088
\(974\) −14736.0 −0.484776
\(975\) 0 0
\(976\) 352.000 0.0115443
\(977\) 26184.0 0.857421 0.428711 0.903442i \(-0.358968\pi\)
0.428711 + 0.903442i \(0.358968\pi\)
\(978\) 0 0
\(979\) −12606.0 −0.411532
\(980\) 1372.00 0.0447214
\(981\) 0 0
\(982\) −26402.0 −0.857965
\(983\) 8584.00 0.278522 0.139261 0.990256i \(-0.455527\pi\)
0.139261 + 0.990256i \(0.455527\pi\)
\(984\) 0 0
\(985\) −37086.0 −1.19965
\(986\) 7260.00 0.234488
\(987\) 0 0
\(988\) 1876.00 0.0604084
\(989\) 3024.00 0.0972271
\(990\) 0 0
\(991\) −51331.0 −1.64539 −0.822696 0.568482i \(-0.807531\pi\)
−0.822696 + 0.568482i \(0.807531\pi\)
\(992\) −9920.00 −0.317500
\(993\) 0 0
\(994\) −6552.00 −0.209071
\(995\) 7308.00 0.232843
\(996\) 0 0
\(997\) −38542.0 −1.22431 −0.612155 0.790738i \(-0.709697\pi\)
−0.612155 + 0.790738i \(0.709697\pi\)
\(998\) 33078.0 1.04916
\(999\) 0 0
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 1386.4.a.l.1.1 1
3.2 odd 2 462.4.a.d.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
462.4.a.d.1.1 1 3.2 odd 2
1386.4.a.l.1.1 1 1.1 even 1 trivial