Properties

Label 1386.4.a.j.1.1
Level $1386$
Weight $4$
Character 1386.1
Self dual yes
Analytic conductor $81.777$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

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: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 154)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000 q^{2} +4.00000 q^{4} -2.00000 q^{5} -7.00000 q^{7} +8.00000 q^{8} +O(q^{10})\) \(q+2.00000 q^{2} +4.00000 q^{4} -2.00000 q^{5} -7.00000 q^{7} +8.00000 q^{8} -4.00000 q^{10} -11.0000 q^{11} +26.0000 q^{13} -14.0000 q^{14} +16.0000 q^{16} +46.0000 q^{17} -48.0000 q^{19} -8.00000 q^{20} -22.0000 q^{22} +128.000 q^{23} -121.000 q^{25} +52.0000 q^{26} -28.0000 q^{28} +146.000 q^{29} -128.000 q^{31} +32.0000 q^{32} +92.0000 q^{34} +14.0000 q^{35} -26.0000 q^{37} -96.0000 q^{38} -16.0000 q^{40} -10.0000 q^{41} +52.0000 q^{43} -44.0000 q^{44} +256.000 q^{46} +544.000 q^{47} +49.0000 q^{49} -242.000 q^{50} +104.000 q^{52} -318.000 q^{53} +22.0000 q^{55} -56.0000 q^{56} +292.000 q^{58} +48.0000 q^{59} +466.000 q^{61} -256.000 q^{62} +64.0000 q^{64} -52.0000 q^{65} +516.000 q^{67} +184.000 q^{68} +28.0000 q^{70} +392.000 q^{71} +754.000 q^{73} -52.0000 q^{74} -192.000 q^{76} +77.0000 q^{77} -32.0000 q^{80} -20.0000 q^{82} -624.000 q^{83} -92.0000 q^{85} +104.000 q^{86} -88.0000 q^{88} +1590.00 q^{89} -182.000 q^{91} +512.000 q^{92} +1088.00 q^{94} +96.0000 q^{95} +1018.00 q^{97} +98.0000 q^{98} +O(q^{100})\)

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
\(5\) −2.00000 −0.178885 −0.0894427 0.995992i \(-0.528509\pi\)
−0.0894427 + 0.995992i \(0.528509\pi\)
\(6\) 0 0
\(7\) −7.00000 −0.377964
\(8\) 8.00000 0.353553
\(9\) 0 0
\(10\) −4.00000 −0.126491
\(11\) −11.0000 −0.301511
\(12\) 0 0
\(13\) 26.0000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) −14.0000 −0.267261
\(15\) 0 0
\(16\) 16.0000 0.250000
\(17\) 46.0000 0.656273 0.328136 0.944630i \(-0.393579\pi\)
0.328136 + 0.944630i \(0.393579\pi\)
\(18\) 0 0
\(19\) −48.0000 −0.579577 −0.289788 0.957091i \(-0.593585\pi\)
−0.289788 + 0.957091i \(0.593585\pi\)
\(20\) −8.00000 −0.0894427
\(21\) 0 0
\(22\) −22.0000 −0.213201
\(23\) 128.000 1.16043 0.580214 0.814464i \(-0.302969\pi\)
0.580214 + 0.814464i \(0.302969\pi\)
\(24\) 0 0
\(25\) −121.000 −0.968000
\(26\) 52.0000 0.392232
\(27\) 0 0
\(28\) −28.0000 −0.188982
\(29\) 146.000 0.934880 0.467440 0.884025i \(-0.345176\pi\)
0.467440 + 0.884025i \(0.345176\pi\)
\(30\) 0 0
\(31\) −128.000 −0.741596 −0.370798 0.928714i \(-0.620916\pi\)
−0.370798 + 0.928714i \(0.620916\pi\)
\(32\) 32.0000 0.176777
\(33\) 0 0
\(34\) 92.0000 0.464055
\(35\) 14.0000 0.0676123
\(36\) 0 0
\(37\) −26.0000 −0.115524 −0.0577618 0.998330i \(-0.518396\pi\)
−0.0577618 + 0.998330i \(0.518396\pi\)
\(38\) −96.0000 −0.409823
\(39\) 0 0
\(40\) −16.0000 −0.0632456
\(41\) −10.0000 −0.0380912 −0.0190456 0.999819i \(-0.506063\pi\)
−0.0190456 + 0.999819i \(0.506063\pi\)
\(42\) 0 0
\(43\) 52.0000 0.184417 0.0922084 0.995740i \(-0.470607\pi\)
0.0922084 + 0.995740i \(0.470607\pi\)
\(44\) −44.0000 −0.150756
\(45\) 0 0
\(46\) 256.000 0.820547
\(47\) 544.000 1.68831 0.844155 0.536099i \(-0.180103\pi\)
0.844155 + 0.536099i \(0.180103\pi\)
\(48\) 0 0
\(49\) 49.0000 0.142857
\(50\) −242.000 −0.684479
\(51\) 0 0
\(52\) 104.000 0.277350
\(53\) −318.000 −0.824163 −0.412082 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) 0 0
\(55\) 22.0000 0.0539360
\(56\) −56.0000 −0.133631
\(57\) 0 0
\(58\) 292.000 0.661060
\(59\) 48.0000 0.105916 0.0529582 0.998597i \(-0.483135\pi\)
0.0529582 + 0.998597i \(0.483135\pi\)
\(60\) 0 0
\(61\) 466.000 0.978118 0.489059 0.872251i \(-0.337340\pi\)
0.489059 + 0.872251i \(0.337340\pi\)
\(62\) −256.000 −0.524388
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −52.0000 −0.0992278
\(66\) 0 0
\(67\) 516.000 0.940887 0.470444 0.882430i \(-0.344094\pi\)
0.470444 + 0.882430i \(0.344094\pi\)
\(68\) 184.000 0.328136
\(69\) 0 0
\(70\) 28.0000 0.0478091
\(71\) 392.000 0.655237 0.327619 0.944810i \(-0.393754\pi\)
0.327619 + 0.944810i \(0.393754\pi\)
\(72\) 0 0
\(73\) 754.000 1.20889 0.604445 0.796647i \(-0.293395\pi\)
0.604445 + 0.796647i \(0.293395\pi\)
\(74\) −52.0000 −0.0816875
\(75\) 0 0
\(76\) −192.000 −0.289788
\(77\) 77.0000 0.113961
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) −32.0000 −0.0447214
\(81\) 0 0
\(82\) −20.0000 −0.0269345
\(83\) −624.000 −0.825216 −0.412608 0.910909i \(-0.635382\pi\)
−0.412608 + 0.910909i \(0.635382\pi\)
\(84\) 0 0
\(85\) −92.0000 −0.117398
\(86\) 104.000 0.130402
\(87\) 0 0
\(88\) −88.0000 −0.106600
\(89\) 1590.00 1.89370 0.946852 0.321669i \(-0.104244\pi\)
0.946852 + 0.321669i \(0.104244\pi\)
\(90\) 0 0
\(91\) −182.000 −0.209657
\(92\) 512.000 0.580214
\(93\) 0 0
\(94\) 1088.00 1.19382
\(95\) 96.0000 0.103678
\(96\) 0 0
\(97\) 1018.00 1.06559 0.532795 0.846244i \(-0.321142\pi\)
0.532795 + 0.846244i \(0.321142\pi\)
\(98\) 98.0000 0.101015
\(99\) 0 0
\(100\) −484.000 −0.484000
\(101\) −474.000 −0.466978 −0.233489 0.972359i \(-0.575014\pi\)
−0.233489 + 0.972359i \(0.575014\pi\)
\(102\) 0 0
\(103\) −984.000 −0.941324 −0.470662 0.882314i \(-0.655985\pi\)
−0.470662 + 0.882314i \(0.655985\pi\)
\(104\) 208.000 0.196116
\(105\) 0 0
\(106\) −636.000 −0.582772
\(107\) −92.0000 −0.0831213 −0.0415606 0.999136i \(-0.513233\pi\)
−0.0415606 + 0.999136i \(0.513233\pi\)
\(108\) 0 0
\(109\) 1246.00 1.09491 0.547455 0.836835i \(-0.315597\pi\)
0.547455 + 0.836835i \(0.315597\pi\)
\(110\) 44.0000 0.0381385
\(111\) 0 0
\(112\) −112.000 −0.0944911
\(113\) 1630.00 1.35697 0.678485 0.734615i \(-0.262637\pi\)
0.678485 + 0.734615i \(0.262637\pi\)
\(114\) 0 0
\(115\) −256.000 −0.207584
\(116\) 584.000 0.467440
\(117\) 0 0
\(118\) 96.0000 0.0748942
\(119\) −322.000 −0.248048
\(120\) 0 0
\(121\) 121.000 0.0909091
\(122\) 932.000 0.691634
\(123\) 0 0
\(124\) −512.000 −0.370798
\(125\) 492.000 0.352047
\(126\) 0 0
\(127\) 1016.00 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 128.000 0.0883883
\(129\) 0 0
\(130\) −104.000 −0.0701646
\(131\) 1920.00 1.28054 0.640272 0.768149i \(-0.278822\pi\)
0.640272 + 0.768149i \(0.278822\pi\)
\(132\) 0 0
\(133\) 336.000 0.219059
\(134\) 1032.00 0.665308
\(135\) 0 0
\(136\) 368.000 0.232027
\(137\) −1482.00 −0.924203 −0.462101 0.886827i \(-0.652904\pi\)
−0.462101 + 0.886827i \(0.652904\pi\)
\(138\) 0 0
\(139\) −2608.00 −1.59142 −0.795711 0.605676i \(-0.792903\pi\)
−0.795711 + 0.605676i \(0.792903\pi\)
\(140\) 56.0000 0.0338062
\(141\) 0 0
\(142\) 784.000 0.463323
\(143\) −286.000 −0.167248
\(144\) 0 0
\(145\) −292.000 −0.167236
\(146\) 1508.00 0.854815
\(147\) 0 0
\(148\) −104.000 −0.0577618
\(149\) −1310.00 −0.720264 −0.360132 0.932901i \(-0.617268\pi\)
−0.360132 + 0.932901i \(0.617268\pi\)
\(150\) 0 0
\(151\) −192.000 −0.103475 −0.0517375 0.998661i \(-0.516476\pi\)
−0.0517375 + 0.998661i \(0.516476\pi\)
\(152\) −384.000 −0.204911
\(153\) 0 0
\(154\) 154.000 0.0805823
\(155\) 256.000 0.132661
\(156\) 0 0
\(157\) 658.000 0.334485 0.167242 0.985916i \(-0.446514\pi\)
0.167242 + 0.985916i \(0.446514\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) −64.0000 −0.0316228
\(161\) −896.000 −0.438601
\(162\) 0 0
\(163\) 2236.00 1.07446 0.537230 0.843436i \(-0.319471\pi\)
0.537230 + 0.843436i \(0.319471\pi\)
\(164\) −40.0000 −0.0190456
\(165\) 0 0
\(166\) −1248.00 −0.583516
\(167\) 1664.00 0.771043 0.385522 0.922699i \(-0.374022\pi\)
0.385522 + 0.922699i \(0.374022\pi\)
\(168\) 0 0
\(169\) −1521.00 −0.692308
\(170\) −184.000 −0.0830127
\(171\) 0 0
\(172\) 208.000 0.0922084
\(173\) 662.000 0.290930 0.145465 0.989363i \(-0.453532\pi\)
0.145465 + 0.989363i \(0.453532\pi\)
\(174\) 0 0
\(175\) 847.000 0.365870
\(176\) −176.000 −0.0753778
\(177\) 0 0
\(178\) 3180.00 1.33905
\(179\) 2540.00 1.06061 0.530303 0.847808i \(-0.322078\pi\)
0.530303 + 0.847808i \(0.322078\pi\)
\(180\) 0 0
\(181\) 2762.00 1.13424 0.567121 0.823634i \(-0.308057\pi\)
0.567121 + 0.823634i \(0.308057\pi\)
\(182\) −364.000 −0.148250
\(183\) 0 0
\(184\) 1024.00 0.410273
\(185\) 52.0000 0.0206655
\(186\) 0 0
\(187\) −506.000 −0.197874
\(188\) 2176.00 0.844155
\(189\) 0 0
\(190\) 192.000 0.0733113
\(191\) 16.0000 0.00606136 0.00303068 0.999995i \(-0.499035\pi\)
0.00303068 + 0.999995i \(0.499035\pi\)
\(192\) 0 0
\(193\) 5138.00 1.91628 0.958138 0.286306i \(-0.0924275\pi\)
0.958138 + 0.286306i \(0.0924275\pi\)
\(194\) 2036.00 0.753486
\(195\) 0 0
\(196\) 196.000 0.0714286
\(197\) −4350.00 −1.57322 −0.786611 0.617449i \(-0.788166\pi\)
−0.786611 + 0.617449i \(0.788166\pi\)
\(198\) 0 0
\(199\) −4040.00 −1.43914 −0.719568 0.694422i \(-0.755660\pi\)
−0.719568 + 0.694422i \(0.755660\pi\)
\(200\) −968.000 −0.342240
\(201\) 0 0
\(202\) −948.000 −0.330203
\(203\) −1022.00 −0.353351
\(204\) 0 0
\(205\) 20.0000 0.00681395
\(206\) −1968.00 −0.665617
\(207\) 0 0
\(208\) 416.000 0.138675
\(209\) 528.000 0.174749
\(210\) 0 0
\(211\) −1820.00 −0.593810 −0.296905 0.954907i \(-0.595955\pi\)
−0.296905 + 0.954907i \(0.595955\pi\)
\(212\) −1272.00 −0.412082
\(213\) 0 0
\(214\) −184.000 −0.0587756
\(215\) −104.000 −0.0329895
\(216\) 0 0
\(217\) 896.000 0.280297
\(218\) 2492.00 0.774218
\(219\) 0 0
\(220\) 88.0000 0.0269680
\(221\) 1196.00 0.364035
\(222\) 0 0
\(223\) −2360.00 −0.708687 −0.354344 0.935115i \(-0.615296\pi\)
−0.354344 + 0.935115i \(0.615296\pi\)
\(224\) −224.000 −0.0668153
\(225\) 0 0
\(226\) 3260.00 0.959522
\(227\) 6416.00 1.87597 0.937984 0.346678i \(-0.112690\pi\)
0.937984 + 0.346678i \(0.112690\pi\)
\(228\) 0 0
\(229\) −1558.00 −0.449588 −0.224794 0.974406i \(-0.572171\pi\)
−0.224794 + 0.974406i \(0.572171\pi\)
\(230\) −512.000 −0.146784
\(231\) 0 0
\(232\) 1168.00 0.330530
\(233\) −522.000 −0.146770 −0.0733849 0.997304i \(-0.523380\pi\)
−0.0733849 + 0.997304i \(0.523380\pi\)
\(234\) 0 0
\(235\) −1088.00 −0.302014
\(236\) 192.000 0.0529582
\(237\) 0 0
\(238\) −644.000 −0.175396
\(239\) −2152.00 −0.582432 −0.291216 0.956657i \(-0.594060\pi\)
−0.291216 + 0.956657i \(0.594060\pi\)
\(240\) 0 0
\(241\) −606.000 −0.161975 −0.0809873 0.996715i \(-0.525807\pi\)
−0.0809873 + 0.996715i \(0.525807\pi\)
\(242\) 242.000 0.0642824
\(243\) 0 0
\(244\) 1864.00 0.489059
\(245\) −98.0000 −0.0255551
\(246\) 0 0
\(247\) −1248.00 −0.321491
\(248\) −1024.00 −0.262194
\(249\) 0 0
\(250\) 984.000 0.248934
\(251\) 1608.00 0.404367 0.202183 0.979348i \(-0.435196\pi\)
0.202183 + 0.979348i \(0.435196\pi\)
\(252\) 0 0
\(253\) −1408.00 −0.349882
\(254\) 2032.00 0.501965
\(255\) 0 0
\(256\) 256.000 0.0625000
\(257\) 4446.00 1.07912 0.539560 0.841947i \(-0.318591\pi\)
0.539560 + 0.841947i \(0.318591\pi\)
\(258\) 0 0
\(259\) 182.000 0.0436638
\(260\) −208.000 −0.0496139
\(261\) 0 0
\(262\) 3840.00 0.905481
\(263\) −6600.00 −1.54743 −0.773714 0.633535i \(-0.781603\pi\)
−0.773714 + 0.633535i \(0.781603\pi\)
\(264\) 0 0
\(265\) 636.000 0.147431
\(266\) 672.000 0.154898
\(267\) 0 0
\(268\) 2064.00 0.470444
\(269\) 1854.00 0.420224 0.210112 0.977677i \(-0.432617\pi\)
0.210112 + 0.977677i \(0.432617\pi\)
\(270\) 0 0
\(271\) −272.000 −0.0609698 −0.0304849 0.999535i \(-0.509705\pi\)
−0.0304849 + 0.999535i \(0.509705\pi\)
\(272\) 736.000 0.164068
\(273\) 0 0
\(274\) −2964.00 −0.653510
\(275\) 1331.00 0.291863
\(276\) 0 0
\(277\) −5010.00 −1.08672 −0.543361 0.839499i \(-0.682848\pi\)
−0.543361 + 0.839499i \(0.682848\pi\)
\(278\) −5216.00 −1.12531
\(279\) 0 0
\(280\) 112.000 0.0239046
\(281\) −314.000 −0.0666607 −0.0333304 0.999444i \(-0.510611\pi\)
−0.0333304 + 0.999444i \(0.510611\pi\)
\(282\) 0 0
\(283\) 3480.00 0.730970 0.365485 0.930817i \(-0.380903\pi\)
0.365485 + 0.930817i \(0.380903\pi\)
\(284\) 1568.00 0.327619
\(285\) 0 0
\(286\) −572.000 −0.118262
\(287\) 70.0000 0.0143971
\(288\) 0 0
\(289\) −2797.00 −0.569306
\(290\) −584.000 −0.118254
\(291\) 0 0
\(292\) 3016.00 0.604445
\(293\) 4230.00 0.843410 0.421705 0.906733i \(-0.361432\pi\)
0.421705 + 0.906733i \(0.361432\pi\)
\(294\) 0 0
\(295\) −96.0000 −0.0189469
\(296\) −208.000 −0.0408438
\(297\) 0 0
\(298\) −2620.00 −0.509304
\(299\) 3328.00 0.643690
\(300\) 0 0
\(301\) −364.000 −0.0697030
\(302\) −384.000 −0.0731679
\(303\) 0 0
\(304\) −768.000 −0.144894
\(305\) −932.000 −0.174971
\(306\) 0 0
\(307\) −1552.00 −0.288525 −0.144263 0.989539i \(-0.546081\pi\)
−0.144263 + 0.989539i \(0.546081\pi\)
\(308\) 308.000 0.0569803
\(309\) 0 0
\(310\) 512.000 0.0938053
\(311\) 4864.00 0.886856 0.443428 0.896310i \(-0.353762\pi\)
0.443428 + 0.896310i \(0.353762\pi\)
\(312\) 0 0
\(313\) 4786.00 0.864283 0.432142 0.901806i \(-0.357758\pi\)
0.432142 + 0.901806i \(0.357758\pi\)
\(314\) 1316.00 0.236516
\(315\) 0 0
\(316\) 0 0
\(317\) 1530.00 0.271083 0.135542 0.990772i \(-0.456723\pi\)
0.135542 + 0.990772i \(0.456723\pi\)
\(318\) 0 0
\(319\) −1606.00 −0.281877
\(320\) −128.000 −0.0223607
\(321\) 0 0
\(322\) −1792.00 −0.310137
\(323\) −2208.00 −0.380360
\(324\) 0 0
\(325\) −3146.00 −0.536950
\(326\) 4472.00 0.759758
\(327\) 0 0
\(328\) −80.0000 −0.0134673
\(329\) −3808.00 −0.638121
\(330\) 0 0
\(331\) −10844.0 −1.80073 −0.900363 0.435140i \(-0.856699\pi\)
−0.900363 + 0.435140i \(0.856699\pi\)
\(332\) −2496.00 −0.412608
\(333\) 0 0
\(334\) 3328.00 0.545210
\(335\) −1032.00 −0.168311
\(336\) 0 0
\(337\) 402.000 0.0649802 0.0324901 0.999472i \(-0.489656\pi\)
0.0324901 + 0.999472i \(0.489656\pi\)
\(338\) −3042.00 −0.489535
\(339\) 0 0
\(340\) −368.000 −0.0586988
\(341\) 1408.00 0.223600
\(342\) 0 0
\(343\) −343.000 −0.0539949
\(344\) 416.000 0.0652012
\(345\) 0 0
\(346\) 1324.00 0.205719
\(347\) 5980.00 0.925139 0.462569 0.886583i \(-0.346928\pi\)
0.462569 + 0.886583i \(0.346928\pi\)
\(348\) 0 0
\(349\) −3094.00 −0.474550 −0.237275 0.971442i \(-0.576254\pi\)
−0.237275 + 0.971442i \(0.576254\pi\)
\(350\) 1694.00 0.258709
\(351\) 0 0
\(352\) −352.000 −0.0533002
\(353\) 4494.00 0.677596 0.338798 0.940859i \(-0.389980\pi\)
0.338798 + 0.940859i \(0.389980\pi\)
\(354\) 0 0
\(355\) −784.000 −0.117212
\(356\) 6360.00 0.946852
\(357\) 0 0
\(358\) 5080.00 0.749962
\(359\) 2752.00 0.404582 0.202291 0.979325i \(-0.435161\pi\)
0.202291 + 0.979325i \(0.435161\pi\)
\(360\) 0 0
\(361\) −4555.00 −0.664091
\(362\) 5524.00 0.802030
\(363\) 0 0
\(364\) −728.000 −0.104828
\(365\) −1508.00 −0.216253
\(366\) 0 0
\(367\) −2024.00 −0.287880 −0.143940 0.989586i \(-0.545977\pi\)
−0.143940 + 0.989586i \(0.545977\pi\)
\(368\) 2048.00 0.290107
\(369\) 0 0
\(370\) 104.000 0.0146127
\(371\) 2226.00 0.311504
\(372\) 0 0
\(373\) 5246.00 0.728224 0.364112 0.931355i \(-0.381373\pi\)
0.364112 + 0.931355i \(0.381373\pi\)
\(374\) −1012.00 −0.139918
\(375\) 0 0
\(376\) 4352.00 0.596908
\(377\) 3796.00 0.518578
\(378\) 0 0
\(379\) 3892.00 0.527490 0.263745 0.964592i \(-0.415042\pi\)
0.263745 + 0.964592i \(0.415042\pi\)
\(380\) 384.000 0.0518389
\(381\) 0 0
\(382\) 32.0000 0.00428603
\(383\) −6752.00 −0.900812 −0.450406 0.892824i \(-0.648721\pi\)
−0.450406 + 0.892824i \(0.648721\pi\)
\(384\) 0 0
\(385\) −154.000 −0.0203859
\(386\) 10276.0 1.35501
\(387\) 0 0
\(388\) 4072.00 0.532795
\(389\) −12486.0 −1.62742 −0.813709 0.581273i \(-0.802555\pi\)
−0.813709 + 0.581273i \(0.802555\pi\)
\(390\) 0 0
\(391\) 5888.00 0.761557
\(392\) 392.000 0.0505076
\(393\) 0 0
\(394\) −8700.00 −1.11244
\(395\) 0 0
\(396\) 0 0
\(397\) 1938.00 0.245001 0.122501 0.992468i \(-0.460909\pi\)
0.122501 + 0.992468i \(0.460909\pi\)
\(398\) −8080.00 −1.01762
\(399\) 0 0
\(400\) −1936.00 −0.242000
\(401\) −4530.00 −0.564133 −0.282067 0.959395i \(-0.591020\pi\)
−0.282067 + 0.959395i \(0.591020\pi\)
\(402\) 0 0
\(403\) −3328.00 −0.411363
\(404\) −1896.00 −0.233489
\(405\) 0 0
\(406\) −2044.00 −0.249857
\(407\) 286.000 0.0348317
\(408\) 0 0
\(409\) −13718.0 −1.65846 −0.829232 0.558905i \(-0.811222\pi\)
−0.829232 + 0.558905i \(0.811222\pi\)
\(410\) 40.0000 0.00481819
\(411\) 0 0
\(412\) −3936.00 −0.470662
\(413\) −336.000 −0.0400326
\(414\) 0 0
\(415\) 1248.00 0.147619
\(416\) 832.000 0.0980581
\(417\) 0 0
\(418\) 1056.00 0.123566
\(419\) −15280.0 −1.78157 −0.890784 0.454427i \(-0.849844\pi\)
−0.890784 + 0.454427i \(0.849844\pi\)
\(420\) 0 0
\(421\) 478.000 0.0553356 0.0276678 0.999617i \(-0.491192\pi\)
0.0276678 + 0.999617i \(0.491192\pi\)
\(422\) −3640.00 −0.419887
\(423\) 0 0
\(424\) −2544.00 −0.291386
\(425\) −5566.00 −0.635272
\(426\) 0 0
\(427\) −3262.00 −0.369694
\(428\) −368.000 −0.0415606
\(429\) 0 0
\(430\) −208.000 −0.0233271
\(431\) −6280.00 −0.701849 −0.350925 0.936404i \(-0.614133\pi\)
−0.350925 + 0.936404i \(0.614133\pi\)
\(432\) 0 0
\(433\) 13802.0 1.53183 0.765914 0.642943i \(-0.222287\pi\)
0.765914 + 0.642943i \(0.222287\pi\)
\(434\) 1792.00 0.198200
\(435\) 0 0
\(436\) 4984.00 0.547455
\(437\) −6144.00 −0.672557
\(438\) 0 0
\(439\) 8728.00 0.948895 0.474447 0.880284i \(-0.342648\pi\)
0.474447 + 0.880284i \(0.342648\pi\)
\(440\) 176.000 0.0190693
\(441\) 0 0
\(442\) 2392.00 0.257411
\(443\) 3540.00 0.379662 0.189831 0.981817i \(-0.439206\pi\)
0.189831 + 0.981817i \(0.439206\pi\)
\(444\) 0 0
\(445\) −3180.00 −0.338756
\(446\) −4720.00 −0.501118
\(447\) 0 0
\(448\) −448.000 −0.0472456
\(449\) −4194.00 −0.440818 −0.220409 0.975408i \(-0.570739\pi\)
−0.220409 + 0.975408i \(0.570739\pi\)
\(450\) 0 0
\(451\) 110.000 0.0114849
\(452\) 6520.00 0.678485
\(453\) 0 0
\(454\) 12832.0 1.32651
\(455\) 364.000 0.0375046
\(456\) 0 0
\(457\) −14134.0 −1.44674 −0.723370 0.690460i \(-0.757408\pi\)
−0.723370 + 0.690460i \(0.757408\pi\)
\(458\) −3116.00 −0.317906
\(459\) 0 0
\(460\) −1024.00 −0.103792
\(461\) −234.000 −0.0236409 −0.0118205 0.999930i \(-0.503763\pi\)
−0.0118205 + 0.999930i \(0.503763\pi\)
\(462\) 0 0
\(463\) 13696.0 1.37475 0.687373 0.726305i \(-0.258764\pi\)
0.687373 + 0.726305i \(0.258764\pi\)
\(464\) 2336.00 0.233720
\(465\) 0 0
\(466\) −1044.00 −0.103782
\(467\) −16104.0 −1.59573 −0.797863 0.602839i \(-0.794036\pi\)
−0.797863 + 0.602839i \(0.794036\pi\)
\(468\) 0 0
\(469\) −3612.00 −0.355622
\(470\) −2176.00 −0.213556
\(471\) 0 0
\(472\) 384.000 0.0374471
\(473\) −572.000 −0.0556038
\(474\) 0 0
\(475\) 5808.00 0.561030
\(476\) −1288.00 −0.124024
\(477\) 0 0
\(478\) −4304.00 −0.411842
\(479\) 11272.0 1.07522 0.537610 0.843193i \(-0.319327\pi\)
0.537610 + 0.843193i \(0.319327\pi\)
\(480\) 0 0
\(481\) −676.000 −0.0640810
\(482\) −1212.00 −0.114533
\(483\) 0 0
\(484\) 484.000 0.0454545
\(485\) −2036.00 −0.190619
\(486\) 0 0
\(487\) −304.000 −0.0282866 −0.0141433 0.999900i \(-0.504502\pi\)
−0.0141433 + 0.999900i \(0.504502\pi\)
\(488\) 3728.00 0.345817
\(489\) 0 0
\(490\) −196.000 −0.0180702
\(491\) −10572.0 −0.971706 −0.485853 0.874041i \(-0.661491\pi\)
−0.485853 + 0.874041i \(0.661491\pi\)
\(492\) 0 0
\(493\) 6716.00 0.613536
\(494\) −2496.00 −0.227329
\(495\) 0 0
\(496\) −2048.00 −0.185399
\(497\) −2744.00 −0.247656
\(498\) 0 0
\(499\) −15004.0 −1.34603 −0.673017 0.739627i \(-0.735002\pi\)
−0.673017 + 0.739627i \(0.735002\pi\)
\(500\) 1968.00 0.176023
\(501\) 0 0
\(502\) 3216.00 0.285930
\(503\) −16872.0 −1.49560 −0.747799 0.663926i \(-0.768889\pi\)
−0.747799 + 0.663926i \(0.768889\pi\)
\(504\) 0 0
\(505\) 948.000 0.0835355
\(506\) −2816.00 −0.247404
\(507\) 0 0
\(508\) 4064.00 0.354943
\(509\) −818.000 −0.0712322 −0.0356161 0.999366i \(-0.511339\pi\)
−0.0356161 + 0.999366i \(0.511339\pi\)
\(510\) 0 0
\(511\) −5278.00 −0.456918
\(512\) 512.000 0.0441942
\(513\) 0 0
\(514\) 8892.00 0.763053
\(515\) 1968.00 0.168389
\(516\) 0 0
\(517\) −5984.00 −0.509045
\(518\) 364.000 0.0308750
\(519\) 0 0
\(520\) −416.000 −0.0350823
\(521\) 2270.00 0.190884 0.0954419 0.995435i \(-0.469574\pi\)
0.0954419 + 0.995435i \(0.469574\pi\)
\(522\) 0 0
\(523\) 12776.0 1.06817 0.534087 0.845429i \(-0.320655\pi\)
0.534087 + 0.845429i \(0.320655\pi\)
\(524\) 7680.00 0.640272
\(525\) 0 0
\(526\) −13200.0 −1.09420
\(527\) −5888.00 −0.486689
\(528\) 0 0
\(529\) 4217.00 0.346593
\(530\) 1272.00 0.104249
\(531\) 0 0
\(532\) 1344.00 0.109530
\(533\) −260.000 −0.0211292
\(534\) 0 0
\(535\) 184.000 0.0148692
\(536\) 4128.00 0.332654
\(537\) 0 0
\(538\) 3708.00 0.297144
\(539\) −539.000 −0.0430730
\(540\) 0 0
\(541\) −23050.0 −1.83179 −0.915894 0.401421i \(-0.868516\pi\)
−0.915894 + 0.401421i \(0.868516\pi\)
\(542\) −544.000 −0.0431122
\(543\) 0 0
\(544\) 1472.00 0.116014
\(545\) −2492.00 −0.195863
\(546\) 0 0
\(547\) −6564.00 −0.513083 −0.256541 0.966533i \(-0.582583\pi\)
−0.256541 + 0.966533i \(0.582583\pi\)
\(548\) −5928.00 −0.462101
\(549\) 0 0
\(550\) 2662.00 0.206378
\(551\) −7008.00 −0.541835
\(552\) 0 0
\(553\) 0 0
\(554\) −10020.0 −0.768428
\(555\) 0 0
\(556\) −10432.0 −0.795711
\(557\) 4522.00 0.343992 0.171996 0.985098i \(-0.444978\pi\)
0.171996 + 0.985098i \(0.444978\pi\)
\(558\) 0 0
\(559\) 1352.00 0.102296
\(560\) 224.000 0.0169031
\(561\) 0 0
\(562\) −628.000 −0.0471363
\(563\) 20440.0 1.53009 0.765047 0.643974i \(-0.222716\pi\)
0.765047 + 0.643974i \(0.222716\pi\)
\(564\) 0 0
\(565\) −3260.00 −0.242742
\(566\) 6960.00 0.516874
\(567\) 0 0
\(568\) 3136.00 0.231661
\(569\) 16518.0 1.21700 0.608498 0.793556i \(-0.291772\pi\)
0.608498 + 0.793556i \(0.291772\pi\)
\(570\) 0 0
\(571\) −8828.00 −0.647006 −0.323503 0.946227i \(-0.604861\pi\)
−0.323503 + 0.946227i \(0.604861\pi\)
\(572\) −1144.00 −0.0836242
\(573\) 0 0
\(574\) 140.000 0.0101803
\(575\) −15488.0 −1.12329
\(576\) 0 0
\(577\) −15550.0 −1.12193 −0.560966 0.827839i \(-0.689570\pi\)
−0.560966 + 0.827839i \(0.689570\pi\)
\(578\) −5594.00 −0.402560
\(579\) 0 0
\(580\) −1168.00 −0.0836182
\(581\) 4368.00 0.311902
\(582\) 0 0
\(583\) 3498.00 0.248495
\(584\) 6032.00 0.427407
\(585\) 0 0
\(586\) 8460.00 0.596381
\(587\) 4536.00 0.318945 0.159473 0.987202i \(-0.449021\pi\)
0.159473 + 0.987202i \(0.449021\pi\)
\(588\) 0 0
\(589\) 6144.00 0.429812
\(590\) −192.000 −0.0133975
\(591\) 0 0
\(592\) −416.000 −0.0288809
\(593\) 11142.0 0.771580 0.385790 0.922587i \(-0.373929\pi\)
0.385790 + 0.922587i \(0.373929\pi\)
\(594\) 0 0
\(595\) 644.000 0.0443721
\(596\) −5240.00 −0.360132
\(597\) 0 0
\(598\) 6656.00 0.455157
\(599\) 16248.0 1.10831 0.554153 0.832415i \(-0.313042\pi\)
0.554153 + 0.832415i \(0.313042\pi\)
\(600\) 0 0
\(601\) −9646.00 −0.654690 −0.327345 0.944905i \(-0.606154\pi\)
−0.327345 + 0.944905i \(0.606154\pi\)
\(602\) −728.000 −0.0492875
\(603\) 0 0
\(604\) −768.000 −0.0517375
\(605\) −242.000 −0.0162623
\(606\) 0 0
\(607\) 4064.00 0.271751 0.135875 0.990726i \(-0.456615\pi\)
0.135875 + 0.990726i \(0.456615\pi\)
\(608\) −1536.00 −0.102456
\(609\) 0 0
\(610\) −1864.00 −0.123723
\(611\) 14144.0 0.936506
\(612\) 0 0
\(613\) −15098.0 −0.994784 −0.497392 0.867526i \(-0.665709\pi\)
−0.497392 + 0.867526i \(0.665709\pi\)
\(614\) −3104.00 −0.204018
\(615\) 0 0
\(616\) 616.000 0.0402911
\(617\) 4470.00 0.291662 0.145831 0.989310i \(-0.453414\pi\)
0.145831 + 0.989310i \(0.453414\pi\)
\(618\) 0 0
\(619\) −21184.0 −1.37554 −0.687768 0.725931i \(-0.741409\pi\)
−0.687768 + 0.725931i \(0.741409\pi\)
\(620\) 1024.00 0.0663304
\(621\) 0 0
\(622\) 9728.00 0.627102
\(623\) −11130.0 −0.715753
\(624\) 0 0
\(625\) 14141.0 0.905024
\(626\) 9572.00 0.611141
\(627\) 0 0
\(628\) 2632.00 0.167242
\(629\) −1196.00 −0.0758150
\(630\) 0 0
\(631\) −8760.00 −0.552663 −0.276331 0.961062i \(-0.589119\pi\)
−0.276331 + 0.961062i \(0.589119\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 3060.00 0.191685
\(635\) −2032.00 −0.126988
\(636\) 0 0
\(637\) 1274.00 0.0792429
\(638\) −3212.00 −0.199317
\(639\) 0 0
\(640\) −256.000 −0.0158114
\(641\) 3582.00 0.220718 0.110359 0.993892i \(-0.464800\pi\)
0.110359 + 0.993892i \(0.464800\pi\)
\(642\) 0 0
\(643\) −23168.0 −1.42093 −0.710464 0.703734i \(-0.751515\pi\)
−0.710464 + 0.703734i \(0.751515\pi\)
\(644\) −3584.00 −0.219300
\(645\) 0 0
\(646\) −4416.00 −0.268955
\(647\) −30216.0 −1.83603 −0.918017 0.396542i \(-0.870210\pi\)
−0.918017 + 0.396542i \(0.870210\pi\)
\(648\) 0 0
\(649\) −528.000 −0.0319350
\(650\) −6292.00 −0.379681
\(651\) 0 0
\(652\) 8944.00 0.537230
\(653\) −8158.00 −0.488893 −0.244447 0.969663i \(-0.578606\pi\)
−0.244447 + 0.969663i \(0.578606\pi\)
\(654\) 0 0
\(655\) −3840.00 −0.229071
\(656\) −160.000 −0.00952279
\(657\) 0 0
\(658\) −7616.00 −0.451220
\(659\) −11932.0 −0.705318 −0.352659 0.935752i \(-0.614722\pi\)
−0.352659 + 0.935752i \(0.614722\pi\)
\(660\) 0 0
\(661\) 26882.0 1.58183 0.790914 0.611927i \(-0.209605\pi\)
0.790914 + 0.611927i \(0.209605\pi\)
\(662\) −21688.0 −1.27331
\(663\) 0 0
\(664\) −4992.00 −0.291758
\(665\) −672.000 −0.0391865
\(666\) 0 0
\(667\) 18688.0 1.08486
\(668\) 6656.00 0.385522
\(669\) 0 0
\(670\) −2064.00 −0.119014
\(671\) −5126.00 −0.294914
\(672\) 0 0
\(673\) 13090.0 0.749751 0.374875 0.927075i \(-0.377685\pi\)
0.374875 + 0.927075i \(0.377685\pi\)
\(674\) 804.000 0.0459480
\(675\) 0 0
\(676\) −6084.00 −0.346154
\(677\) 33790.0 1.91825 0.959125 0.282983i \(-0.0913240\pi\)
0.959125 + 0.282983i \(0.0913240\pi\)
\(678\) 0 0
\(679\) −7126.00 −0.402755
\(680\) −736.000 −0.0415063
\(681\) 0 0
\(682\) 2816.00 0.158109
\(683\) −24588.0 −1.37750 −0.688751 0.724998i \(-0.741841\pi\)
−0.688751 + 0.724998i \(0.741841\pi\)
\(684\) 0 0
\(685\) 2964.00 0.165326
\(686\) −686.000 −0.0381802
\(687\) 0 0
\(688\) 832.000 0.0461042
\(689\) −8268.00 −0.457164
\(690\) 0 0
\(691\) −1128.00 −0.0621001 −0.0310500 0.999518i \(-0.509885\pi\)
−0.0310500 + 0.999518i \(0.509885\pi\)
\(692\) 2648.00 0.145465
\(693\) 0 0
\(694\) 11960.0 0.654172
\(695\) 5216.00 0.284682
\(696\) 0 0
\(697\) −460.000 −0.0249982
\(698\) −6188.00 −0.335558
\(699\) 0 0
\(700\) 3388.00 0.182935
\(701\) 18786.0 1.01218 0.506089 0.862481i \(-0.331091\pi\)
0.506089 + 0.862481i \(0.331091\pi\)
\(702\) 0 0
\(703\) 1248.00 0.0669548
\(704\) −704.000 −0.0376889
\(705\) 0 0
\(706\) 8988.00 0.479133
\(707\) 3318.00 0.176501
\(708\) 0 0
\(709\) 12102.0 0.641044 0.320522 0.947241i \(-0.396142\pi\)
0.320522 + 0.947241i \(0.396142\pi\)
\(710\) −1568.00 −0.0828817
\(711\) 0 0
\(712\) 12720.0 0.669525
\(713\) −16384.0 −0.860569
\(714\) 0 0
\(715\) 572.000 0.0299183
\(716\) 10160.0 0.530303
\(717\) 0 0
\(718\) 5504.00 0.286083
\(719\) −18112.0 −0.939449 −0.469724 0.882813i \(-0.655647\pi\)
−0.469724 + 0.882813i \(0.655647\pi\)
\(720\) 0 0
\(721\) 6888.00 0.355787
\(722\) −9110.00 −0.469583
\(723\) 0 0
\(724\) 11048.0 0.567121
\(725\) −17666.0 −0.904964
\(726\) 0 0
\(727\) 12728.0 0.649320 0.324660 0.945831i \(-0.394750\pi\)
0.324660 + 0.945831i \(0.394750\pi\)
\(728\) −1456.00 −0.0741249
\(729\) 0 0
\(730\) −3016.00 −0.152914
\(731\) 2392.00 0.121028
\(732\) 0 0
\(733\) 17138.0 0.863583 0.431792 0.901973i \(-0.357882\pi\)
0.431792 + 0.901973i \(0.357882\pi\)
\(734\) −4048.00 −0.203562
\(735\) 0 0
\(736\) 4096.00 0.205137
\(737\) −5676.00 −0.283688
\(738\) 0 0
\(739\) −8340.00 −0.415145 −0.207572 0.978220i \(-0.566556\pi\)
−0.207572 + 0.978220i \(0.566556\pi\)
\(740\) 208.000 0.0103327
\(741\) 0 0
\(742\) 4452.00 0.220267
\(743\) −8304.00 −0.410019 −0.205010 0.978760i \(-0.565723\pi\)
−0.205010 + 0.978760i \(0.565723\pi\)
\(744\) 0 0
\(745\) 2620.00 0.128845
\(746\) 10492.0 0.514932
\(747\) 0 0
\(748\) −2024.00 −0.0989369
\(749\) 644.000 0.0314169
\(750\) 0 0
\(751\) 2152.00 0.104564 0.0522820 0.998632i \(-0.483351\pi\)
0.0522820 + 0.998632i \(0.483351\pi\)
\(752\) 8704.00 0.422077
\(753\) 0 0
\(754\) 7592.00 0.366690
\(755\) 384.000 0.0185102
\(756\) 0 0
\(757\) −25594.0 −1.22884 −0.614419 0.788980i \(-0.710609\pi\)
−0.614419 + 0.788980i \(0.710609\pi\)
\(758\) 7784.00 0.372992
\(759\) 0 0
\(760\) 768.000 0.0366556
\(761\) 17190.0 0.818840 0.409420 0.912346i \(-0.365731\pi\)
0.409420 + 0.912346i \(0.365731\pi\)
\(762\) 0 0
\(763\) −8722.00 −0.413837
\(764\) 64.0000 0.00303068
\(765\) 0 0
\(766\) −13504.0 −0.636970
\(767\) 1248.00 0.0587518
\(768\) 0 0
\(769\) −15086.0 −0.707432 −0.353716 0.935353i \(-0.615082\pi\)
−0.353716 + 0.935353i \(0.615082\pi\)
\(770\) −308.000 −0.0144150
\(771\) 0 0
\(772\) 20552.0 0.958138
\(773\) −14178.0 −0.659699 −0.329849 0.944034i \(-0.606998\pi\)
−0.329849 + 0.944034i \(0.606998\pi\)
\(774\) 0 0
\(775\) 15488.0 0.717865
\(776\) 8144.00 0.376743
\(777\) 0 0
\(778\) −24972.0 −1.15076
\(779\) 480.000 0.0220767
\(780\) 0 0
\(781\) −4312.00 −0.197561
\(782\) 11776.0 0.538502
\(783\) 0 0
\(784\) 784.000 0.0357143
\(785\) −1316.00 −0.0598345
\(786\) 0 0
\(787\) −18304.0 −0.829056 −0.414528 0.910037i \(-0.636053\pi\)
−0.414528 + 0.910037i \(0.636053\pi\)
\(788\) −17400.0 −0.786611
\(789\) 0 0
\(790\) 0 0
\(791\) −11410.0 −0.512886
\(792\) 0 0
\(793\) 12116.0 0.542562
\(794\) 3876.00 0.173242
\(795\) 0 0
\(796\) −16160.0 −0.719568
\(797\) 38206.0 1.69803 0.849013 0.528373i \(-0.177198\pi\)
0.849013 + 0.528373i \(0.177198\pi\)
\(798\) 0 0
\(799\) 25024.0 1.10799
\(800\) −3872.00 −0.171120
\(801\) 0 0
\(802\) −9060.00 −0.398902
\(803\) −8294.00 −0.364494
\(804\) 0 0
\(805\) 1792.00 0.0784593
\(806\) −6656.00 −0.290878
\(807\) 0 0
\(808\) −3792.00 −0.165102
\(809\) −7146.00 −0.310556 −0.155278 0.987871i \(-0.549627\pi\)
−0.155278 + 0.987871i \(0.549627\pi\)
\(810\) 0 0
\(811\) −21256.0 −0.920344 −0.460172 0.887830i \(-0.652212\pi\)
−0.460172 + 0.887830i \(0.652212\pi\)
\(812\) −4088.00 −0.176676
\(813\) 0 0
\(814\) 572.000 0.0246297
\(815\) −4472.00 −0.192205
\(816\) 0 0
\(817\) −2496.00 −0.106884
\(818\) −27436.0 −1.17271
\(819\) 0 0
\(820\) 80.0000 0.00340698
\(821\) −38670.0 −1.64384 −0.821920 0.569603i \(-0.807097\pi\)
−0.821920 + 0.569603i \(0.807097\pi\)
\(822\) 0 0
\(823\) −21112.0 −0.894190 −0.447095 0.894487i \(-0.647541\pi\)
−0.447095 + 0.894487i \(0.647541\pi\)
\(824\) −7872.00 −0.332808
\(825\) 0 0
\(826\) −672.000 −0.0283073
\(827\) 3172.00 0.133375 0.0666876 0.997774i \(-0.478757\pi\)
0.0666876 + 0.997774i \(0.478757\pi\)
\(828\) 0 0
\(829\) 30346.0 1.27136 0.635682 0.771951i \(-0.280719\pi\)
0.635682 + 0.771951i \(0.280719\pi\)
\(830\) 2496.00 0.104382
\(831\) 0 0
\(832\) 1664.00 0.0693375
\(833\) 2254.00 0.0937533
\(834\) 0 0
\(835\) −3328.00 −0.137928
\(836\) 2112.00 0.0873745
\(837\) 0 0
\(838\) −30560.0 −1.25976
\(839\) 9480.00 0.390091 0.195045 0.980794i \(-0.437515\pi\)
0.195045 + 0.980794i \(0.437515\pi\)
\(840\) 0 0
\(841\) −3073.00 −0.125999
\(842\) 956.000 0.0391282
\(843\) 0 0
\(844\) −7280.00 −0.296905
\(845\) 3042.00 0.123844
\(846\) 0 0
\(847\) −847.000 −0.0343604
\(848\) −5088.00 −0.206041
\(849\) 0 0
\(850\) −11132.0 −0.449205
\(851\) −3328.00 −0.134057
\(852\) 0 0
\(853\) −24958.0 −1.00181 −0.500906 0.865502i \(-0.667000\pi\)
−0.500906 + 0.865502i \(0.667000\pi\)
\(854\) −6524.00 −0.261413
\(855\) 0 0
\(856\) −736.000 −0.0293878
\(857\) 26806.0 1.06847 0.534233 0.845337i \(-0.320600\pi\)
0.534233 + 0.845337i \(0.320600\pi\)
\(858\) 0 0
\(859\) 23128.0 0.918646 0.459323 0.888269i \(-0.348092\pi\)
0.459323 + 0.888269i \(0.348092\pi\)
\(860\) −416.000 −0.0164947
\(861\) 0 0
\(862\) −12560.0 −0.496282
\(863\) −12496.0 −0.492895 −0.246448 0.969156i \(-0.579263\pi\)
−0.246448 + 0.969156i \(0.579263\pi\)
\(864\) 0 0
\(865\) −1324.00 −0.0520432
\(866\) 27604.0 1.08317
\(867\) 0 0
\(868\) 3584.00 0.140148
\(869\) 0 0
\(870\) 0 0
\(871\) 13416.0 0.521910
\(872\) 9968.00 0.387109
\(873\) 0 0
\(874\) −12288.0 −0.475570
\(875\) −3444.00 −0.133061
\(876\) 0 0
\(877\) 30478.0 1.17351 0.586755 0.809764i \(-0.300405\pi\)
0.586755 + 0.809764i \(0.300405\pi\)
\(878\) 17456.0 0.670970
\(879\) 0 0
\(880\) 352.000 0.0134840
\(881\) −25506.0 −0.975390 −0.487695 0.873014i \(-0.662162\pi\)
−0.487695 + 0.873014i \(0.662162\pi\)
\(882\) 0 0
\(883\) −13244.0 −0.504752 −0.252376 0.967629i \(-0.581212\pi\)
−0.252376 + 0.967629i \(0.581212\pi\)
\(884\) 4784.00 0.182017
\(885\) 0 0
\(886\) 7080.00 0.268462
\(887\) −25456.0 −0.963618 −0.481809 0.876276i \(-0.660020\pi\)
−0.481809 + 0.876276i \(0.660020\pi\)
\(888\) 0 0
\(889\) −7112.00 −0.268311
\(890\) −6360.00 −0.239537
\(891\) 0 0
\(892\) −9440.00 −0.354344
\(893\) −26112.0 −0.978505
\(894\) 0 0
\(895\) −5080.00 −0.189727
\(896\) −896.000 −0.0334077
\(897\) 0 0
\(898\) −8388.00 −0.311705
\(899\) −18688.0 −0.693303
\(900\) 0 0
\(901\) −14628.0 −0.540876
\(902\) 220.000 0.00812106
\(903\) 0 0
\(904\) 13040.0 0.479761
\(905\) −5524.00 −0.202899
\(906\) 0 0
\(907\) −51652.0 −1.89093 −0.945467 0.325719i \(-0.894394\pi\)
−0.945467 + 0.325719i \(0.894394\pi\)
\(908\) 25664.0 0.937984
\(909\) 0 0
\(910\) 728.000 0.0265197
\(911\) 46392.0 1.68720 0.843598 0.536975i \(-0.180433\pi\)
0.843598 + 0.536975i \(0.180433\pi\)
\(912\) 0 0
\(913\) 6864.00 0.248812
\(914\) −28268.0 −1.02300
\(915\) 0 0
\(916\) −6232.00 −0.224794
\(917\) −13440.0 −0.484000
\(918\) 0 0
\(919\) 17832.0 0.640069 0.320034 0.947406i \(-0.396305\pi\)
0.320034 + 0.947406i \(0.396305\pi\)
\(920\) −2048.00 −0.0733919
\(921\) 0 0
\(922\) −468.000 −0.0167167
\(923\) 10192.0 0.363460
\(924\) 0 0
\(925\) 3146.00 0.111827
\(926\) 27392.0 0.972092
\(927\) 0 0
\(928\) 4672.00 0.165265
\(929\) 41334.0 1.45977 0.729884 0.683571i \(-0.239574\pi\)
0.729884 + 0.683571i \(0.239574\pi\)
\(930\) 0 0
\(931\) −2352.00 −0.0827967
\(932\) −2088.00 −0.0733849
\(933\) 0 0
\(934\) −32208.0 −1.12835
\(935\) 1012.00 0.0353967
\(936\) 0 0
\(937\) 23058.0 0.803919 0.401959 0.915657i \(-0.368329\pi\)
0.401959 + 0.915657i \(0.368329\pi\)
\(938\) −7224.00 −0.251463
\(939\) 0 0
\(940\) −4352.00 −0.151007
\(941\) 11678.0 0.404561 0.202281 0.979328i \(-0.435165\pi\)
0.202281 + 0.979328i \(0.435165\pi\)
\(942\) 0 0
\(943\) −1280.00 −0.0442021
\(944\) 768.000 0.0264791
\(945\) 0 0
\(946\) −1144.00 −0.0393178
\(947\) 36436.0 1.25028 0.625138 0.780514i \(-0.285043\pi\)
0.625138 + 0.780514i \(0.285043\pi\)
\(948\) 0 0
\(949\) 19604.0 0.670572
\(950\) 11616.0 0.396708
\(951\) 0 0
\(952\) −2576.00 −0.0876982
\(953\) −21098.0 −0.717137 −0.358568 0.933503i \(-0.616735\pi\)
−0.358568 + 0.933503i \(0.616735\pi\)
\(954\) 0 0
\(955\) −32.0000 −0.00108429
\(956\) −8608.00 −0.291216
\(957\) 0 0
\(958\) 22544.0 0.760296
\(959\) 10374.0 0.349316
\(960\) 0 0
\(961\) −13407.0 −0.450035
\(962\) −1352.00 −0.0453121
\(963\) 0 0
\(964\) −2424.00 −0.0809873
\(965\) −10276.0 −0.342794
\(966\) 0 0
\(967\) 7184.00 0.238906 0.119453 0.992840i \(-0.461886\pi\)
0.119453 + 0.992840i \(0.461886\pi\)
\(968\) 968.000 0.0321412
\(969\) 0 0
\(970\) −4072.00 −0.134788
\(971\) 40048.0 1.32359 0.661793 0.749687i \(-0.269796\pi\)
0.661793 + 0.749687i \(0.269796\pi\)
\(972\) 0 0
\(973\) 18256.0 0.601501
\(974\) −608.000 −0.0200016
\(975\) 0 0
\(976\) 7456.00 0.244529
\(977\) −51938.0 −1.70076 −0.850381 0.526168i \(-0.823628\pi\)
−0.850381 + 0.526168i \(0.823628\pi\)
\(978\) 0 0
\(979\) −17490.0 −0.570973
\(980\) −392.000 −0.0127775
\(981\) 0 0
\(982\) −21144.0 −0.687100
\(983\) 28968.0 0.939914 0.469957 0.882689i \(-0.344269\pi\)
0.469957 + 0.882689i \(0.344269\pi\)
\(984\) 0 0
\(985\) 8700.00 0.281426
\(986\) 13432.0 0.433836
\(987\) 0 0
\(988\) −4992.00 −0.160746
\(989\) 6656.00 0.214003
\(990\) 0 0
\(991\) 37504.0 1.20217 0.601087 0.799184i \(-0.294735\pi\)
0.601087 + 0.799184i \(0.294735\pi\)
\(992\) −4096.00 −0.131097
\(993\) 0 0
\(994\) −5488.00 −0.175120
\(995\) 8080.00 0.257440
\(996\) 0 0
\(997\) 20298.0 0.644778 0.322389 0.946607i \(-0.395514\pi\)
0.322389 + 0.946607i \(0.395514\pi\)
\(998\) −30008.0 −0.951790
\(999\) 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.j.1.1 1
3.2 odd 2 154.4.a.b.1.1 1
12.11 even 2 1232.4.a.e.1.1 1
21.20 even 2 1078.4.a.b.1.1 1
33.32 even 2 1694.4.a.f.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
154.4.a.b.1.1 1 3.2 odd 2
1078.4.a.b.1.1 1 21.20 even 2
1232.4.a.e.1.1 1 12.11 even 2
1386.4.a.j.1.1 1 1.1 even 1 trivial
1694.4.a.f.1.1 1 33.32 even 2