Properties

Label 2394.4.a.c.1.1
Level $2394$
Weight $4$
Character 2394.1
Self dual yes
Analytic conductor $141.251$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2394.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(141.250572554\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 798)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 2394.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000 q^{2} +4.00000 q^{4} +10.0000 q^{5} +7.00000 q^{7} -8.00000 q^{8} +O(q^{10})\) \(q-2.00000 q^{2} +4.00000 q^{4} +10.0000 q^{5} +7.00000 q^{7} -8.00000 q^{8} -20.0000 q^{10} -8.00000 q^{11} -50.0000 q^{13} -14.0000 q^{14} +16.0000 q^{16} -114.000 q^{17} +19.0000 q^{19} +40.0000 q^{20} +16.0000 q^{22} +148.000 q^{23} -25.0000 q^{25} +100.000 q^{26} +28.0000 q^{28} +30.0000 q^{29} +304.000 q^{31} -32.0000 q^{32} +228.000 q^{34} +70.0000 q^{35} -274.000 q^{37} -38.0000 q^{38} -80.0000 q^{40} +202.000 q^{41} -116.000 q^{43} -32.0000 q^{44} -296.000 q^{46} +324.000 q^{47} +49.0000 q^{49} +50.0000 q^{50} -200.000 q^{52} +550.000 q^{53} -80.0000 q^{55} -56.0000 q^{56} -60.0000 q^{58} -628.000 q^{59} -58.0000 q^{61} -608.000 q^{62} +64.0000 q^{64} -500.000 q^{65} -756.000 q^{67} -456.000 q^{68} -140.000 q^{70} +216.000 q^{71} -278.000 q^{73} +548.000 q^{74} +76.0000 q^{76} -56.0000 q^{77} -952.000 q^{79} +160.000 q^{80} -404.000 q^{82} +1184.00 q^{83} -1140.00 q^{85} +232.000 q^{86} +64.0000 q^{88} -1542.00 q^{89} -350.000 q^{91} +592.000 q^{92} -648.000 q^{94} +190.000 q^{95} -870.000 q^{97} -98.0000 q^{98} +O(q^{100})\)

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
\(5\) 10.0000 0.894427 0.447214 0.894427i \(-0.352416\pi\)
0.447214 + 0.894427i \(0.352416\pi\)
\(6\) 0 0
\(7\) 7.00000 0.377964
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) −20.0000 −0.632456
\(11\) −8.00000 −0.219281 −0.109640 0.993971i \(-0.534970\pi\)
−0.109640 + 0.993971i \(0.534970\pi\)
\(12\) 0 0
\(13\) −50.0000 −1.06673 −0.533366 0.845885i \(-0.679073\pi\)
−0.533366 + 0.845885i \(0.679073\pi\)
\(14\) −14.0000 −0.267261
\(15\) 0 0
\(16\) 16.0000 0.250000
\(17\) −114.000 −1.62642 −0.813208 0.581974i \(-0.802281\pi\)
−0.813208 + 0.581974i \(0.802281\pi\)
\(18\) 0 0
\(19\) 19.0000 0.229416
\(20\) 40.0000 0.447214
\(21\) 0 0
\(22\) 16.0000 0.155055
\(23\) 148.000 1.34174 0.670872 0.741573i \(-0.265920\pi\)
0.670872 + 0.741573i \(0.265920\pi\)
\(24\) 0 0
\(25\) −25.0000 −0.200000
\(26\) 100.000 0.754293
\(27\) 0 0
\(28\) 28.0000 0.188982
\(29\) 30.0000 0.192099 0.0960493 0.995377i \(-0.469379\pi\)
0.0960493 + 0.995377i \(0.469379\pi\)
\(30\) 0 0
\(31\) 304.000 1.76129 0.880645 0.473776i \(-0.157109\pi\)
0.880645 + 0.473776i \(0.157109\pi\)
\(32\) −32.0000 −0.176777
\(33\) 0 0
\(34\) 228.000 1.15005
\(35\) 70.0000 0.338062
\(36\) 0 0
\(37\) −274.000 −1.21744 −0.608721 0.793385i \(-0.708317\pi\)
−0.608721 + 0.793385i \(0.708317\pi\)
\(38\) −38.0000 −0.162221
\(39\) 0 0
\(40\) −80.0000 −0.316228
\(41\) 202.000 0.769441 0.384721 0.923033i \(-0.374298\pi\)
0.384721 + 0.923033i \(0.374298\pi\)
\(42\) 0 0
\(43\) −116.000 −0.411391 −0.205696 0.978616i \(-0.565946\pi\)
−0.205696 + 0.978616i \(0.565946\pi\)
\(44\) −32.0000 −0.109640
\(45\) 0 0
\(46\) −296.000 −0.948757
\(47\) 324.000 1.00554 0.502769 0.864421i \(-0.332315\pi\)
0.502769 + 0.864421i \(0.332315\pi\)
\(48\) 0 0
\(49\) 49.0000 0.142857
\(50\) 50.0000 0.141421
\(51\) 0 0
\(52\) −200.000 −0.533366
\(53\) 550.000 1.42544 0.712720 0.701449i \(-0.247463\pi\)
0.712720 + 0.701449i \(0.247463\pi\)
\(54\) 0 0
\(55\) −80.0000 −0.196131
\(56\) −56.0000 −0.133631
\(57\) 0 0
\(58\) −60.0000 −0.135834
\(59\) −628.000 −1.38574 −0.692870 0.721063i \(-0.743654\pi\)
−0.692870 + 0.721063i \(0.743654\pi\)
\(60\) 0 0
\(61\) −58.0000 −0.121740 −0.0608700 0.998146i \(-0.519388\pi\)
−0.0608700 + 0.998146i \(0.519388\pi\)
\(62\) −608.000 −1.24542
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −500.000 −0.954113
\(66\) 0 0
\(67\) −756.000 −1.37851 −0.689254 0.724519i \(-0.742062\pi\)
−0.689254 + 0.724519i \(0.742062\pi\)
\(68\) −456.000 −0.813208
\(69\) 0 0
\(70\) −140.000 −0.239046
\(71\) 216.000 0.361049 0.180525 0.983570i \(-0.442220\pi\)
0.180525 + 0.983570i \(0.442220\pi\)
\(72\) 0 0
\(73\) −278.000 −0.445718 −0.222859 0.974851i \(-0.571539\pi\)
−0.222859 + 0.974851i \(0.571539\pi\)
\(74\) 548.000 0.860861
\(75\) 0 0
\(76\) 76.0000 0.114708
\(77\) −56.0000 −0.0828804
\(78\) 0 0
\(79\) −952.000 −1.35580 −0.677901 0.735153i \(-0.737110\pi\)
−0.677901 + 0.735153i \(0.737110\pi\)
\(80\) 160.000 0.223607
\(81\) 0 0
\(82\) −404.000 −0.544077
\(83\) 1184.00 1.56579 0.782897 0.622151i \(-0.213741\pi\)
0.782897 + 0.622151i \(0.213741\pi\)
\(84\) 0 0
\(85\) −1140.00 −1.45471
\(86\) 232.000 0.290898
\(87\) 0 0
\(88\) 64.0000 0.0775275
\(89\) −1542.00 −1.83654 −0.918268 0.395960i \(-0.870412\pi\)
−0.918268 + 0.395960i \(0.870412\pi\)
\(90\) 0 0
\(91\) −350.000 −0.403186
\(92\) 592.000 0.670872
\(93\) 0 0
\(94\) −648.000 −0.711022
\(95\) 190.000 0.205196
\(96\) 0 0
\(97\) −870.000 −0.910671 −0.455336 0.890320i \(-0.650481\pi\)
−0.455336 + 0.890320i \(0.650481\pi\)
\(98\) −98.0000 −0.101015
\(99\) 0 0
\(100\) −100.000 −0.100000
\(101\) 594.000 0.585200 0.292600 0.956235i \(-0.405480\pi\)
0.292600 + 0.956235i \(0.405480\pi\)
\(102\) 0 0
\(103\) −288.000 −0.275510 −0.137755 0.990466i \(-0.543989\pi\)
−0.137755 + 0.990466i \(0.543989\pi\)
\(104\) 400.000 0.377146
\(105\) 0 0
\(106\) −1100.00 −1.00794
\(107\) 276.000 0.249364 0.124682 0.992197i \(-0.460209\pi\)
0.124682 + 0.992197i \(0.460209\pi\)
\(108\) 0 0
\(109\) −1714.00 −1.50616 −0.753080 0.657929i \(-0.771433\pi\)
−0.753080 + 0.657929i \(0.771433\pi\)
\(110\) 160.000 0.138685
\(111\) 0 0
\(112\) 112.000 0.0944911
\(113\) 730.000 0.607722 0.303861 0.952716i \(-0.401724\pi\)
0.303861 + 0.952716i \(0.401724\pi\)
\(114\) 0 0
\(115\) 1480.00 1.20009
\(116\) 120.000 0.0960493
\(117\) 0 0
\(118\) 1256.00 0.979866
\(119\) −798.000 −0.614727
\(120\) 0 0
\(121\) −1267.00 −0.951916
\(122\) 116.000 0.0860832
\(123\) 0 0
\(124\) 1216.00 0.880645
\(125\) −1500.00 −1.07331
\(126\) 0 0
\(127\) 784.000 0.547785 0.273893 0.961760i \(-0.411689\pi\)
0.273893 + 0.961760i \(0.411689\pi\)
\(128\) −128.000 −0.0883883
\(129\) 0 0
\(130\) 1000.00 0.674660
\(131\) 120.000 0.0800340 0.0400170 0.999199i \(-0.487259\pi\)
0.0400170 + 0.999199i \(0.487259\pi\)
\(132\) 0 0
\(133\) 133.000 0.0867110
\(134\) 1512.00 0.974753
\(135\) 0 0
\(136\) 912.000 0.575025
\(137\) 30.0000 0.0187086 0.00935428 0.999956i \(-0.497022\pi\)
0.00935428 + 0.999956i \(0.497022\pi\)
\(138\) 0 0
\(139\) 1140.00 0.695637 0.347818 0.937562i \(-0.386923\pi\)
0.347818 + 0.937562i \(0.386923\pi\)
\(140\) 280.000 0.169031
\(141\) 0 0
\(142\) −432.000 −0.255300
\(143\) 400.000 0.233914
\(144\) 0 0
\(145\) 300.000 0.171818
\(146\) 556.000 0.315170
\(147\) 0 0
\(148\) −1096.00 −0.608721
\(149\) −406.000 −0.223227 −0.111613 0.993752i \(-0.535602\pi\)
−0.111613 + 0.993752i \(0.535602\pi\)
\(150\) 0 0
\(151\) 2320.00 1.25032 0.625162 0.780495i \(-0.285033\pi\)
0.625162 + 0.780495i \(0.285033\pi\)
\(152\) −152.000 −0.0811107
\(153\) 0 0
\(154\) 112.000 0.0586053
\(155\) 3040.00 1.57535
\(156\) 0 0
\(157\) −3194.00 −1.62362 −0.811812 0.583919i \(-0.801519\pi\)
−0.811812 + 0.583919i \(0.801519\pi\)
\(158\) 1904.00 0.958697
\(159\) 0 0
\(160\) −320.000 −0.158114
\(161\) 1036.00 0.507132
\(162\) 0 0
\(163\) −4.00000 −0.00192211 −0.000961056 1.00000i \(-0.500306\pi\)
−0.000961056 1.00000i \(0.500306\pi\)
\(164\) 808.000 0.384721
\(165\) 0 0
\(166\) −2368.00 −1.10718
\(167\) 632.000 0.292848 0.146424 0.989222i \(-0.453224\pi\)
0.146424 + 0.989222i \(0.453224\pi\)
\(168\) 0 0
\(169\) 303.000 0.137915
\(170\) 2280.00 1.02864
\(171\) 0 0
\(172\) −464.000 −0.205696
\(173\) −3682.00 −1.61813 −0.809067 0.587716i \(-0.800027\pi\)
−0.809067 + 0.587716i \(0.800027\pi\)
\(174\) 0 0
\(175\) −175.000 −0.0755929
\(176\) −128.000 −0.0548202
\(177\) 0 0
\(178\) 3084.00 1.29863
\(179\) −2196.00 −0.916965 −0.458483 0.888703i \(-0.651607\pi\)
−0.458483 + 0.888703i \(0.651607\pi\)
\(180\) 0 0
\(181\) −3802.00 −1.56133 −0.780664 0.624951i \(-0.785119\pi\)
−0.780664 + 0.624951i \(0.785119\pi\)
\(182\) 700.000 0.285096
\(183\) 0 0
\(184\) −1184.00 −0.474378
\(185\) −2740.00 −1.08891
\(186\) 0 0
\(187\) 912.000 0.356642
\(188\) 1296.00 0.502769
\(189\) 0 0
\(190\) −380.000 −0.145095
\(191\) −1852.00 −0.701602 −0.350801 0.936450i \(-0.614091\pi\)
−0.350801 + 0.936450i \(0.614091\pi\)
\(192\) 0 0
\(193\) 4242.00 1.58210 0.791051 0.611750i \(-0.209534\pi\)
0.791051 + 0.611750i \(0.209534\pi\)
\(194\) 1740.00 0.643942
\(195\) 0 0
\(196\) 196.000 0.0714286
\(197\) −670.000 −0.242312 −0.121156 0.992633i \(-0.538660\pi\)
−0.121156 + 0.992633i \(0.538660\pi\)
\(198\) 0 0
\(199\) −4672.00 −1.66427 −0.832134 0.554575i \(-0.812881\pi\)
−0.832134 + 0.554575i \(0.812881\pi\)
\(200\) 200.000 0.0707107
\(201\) 0 0
\(202\) −1188.00 −0.413799
\(203\) 210.000 0.0726065
\(204\) 0 0
\(205\) 2020.00 0.688209
\(206\) 576.000 0.194815
\(207\) 0 0
\(208\) −800.000 −0.266683
\(209\) −152.000 −0.0503065
\(210\) 0 0
\(211\) 1852.00 0.604251 0.302125 0.953268i \(-0.402304\pi\)
0.302125 + 0.953268i \(0.402304\pi\)
\(212\) 2200.00 0.712720
\(213\) 0 0
\(214\) −552.000 −0.176327
\(215\) −1160.00 −0.367960
\(216\) 0 0
\(217\) 2128.00 0.665705
\(218\) 3428.00 1.06502
\(219\) 0 0
\(220\) −320.000 −0.0980654
\(221\) 5700.00 1.73495
\(222\) 0 0
\(223\) 4312.00 1.29486 0.647428 0.762127i \(-0.275845\pi\)
0.647428 + 0.762127i \(0.275845\pi\)
\(224\) −224.000 −0.0668153
\(225\) 0 0
\(226\) −1460.00 −0.429725
\(227\) −1476.00 −0.431566 −0.215783 0.976441i \(-0.569230\pi\)
−0.215783 + 0.976441i \(0.569230\pi\)
\(228\) 0 0
\(229\) −3042.00 −0.877821 −0.438911 0.898531i \(-0.644635\pi\)
−0.438911 + 0.898531i \(0.644635\pi\)
\(230\) −2960.00 −0.848594
\(231\) 0 0
\(232\) −240.000 −0.0679171
\(233\) −938.000 −0.263736 −0.131868 0.991267i \(-0.542097\pi\)
−0.131868 + 0.991267i \(0.542097\pi\)
\(234\) 0 0
\(235\) 3240.00 0.899380
\(236\) −2512.00 −0.692870
\(237\) 0 0
\(238\) 1596.00 0.434678
\(239\) −812.000 −0.219765 −0.109883 0.993945i \(-0.535048\pi\)
−0.109883 + 0.993945i \(0.535048\pi\)
\(240\) 0 0
\(241\) 842.000 0.225054 0.112527 0.993649i \(-0.464106\pi\)
0.112527 + 0.993649i \(0.464106\pi\)
\(242\) 2534.00 0.673106
\(243\) 0 0
\(244\) −232.000 −0.0608700
\(245\) 490.000 0.127775
\(246\) 0 0
\(247\) −950.000 −0.244725
\(248\) −2432.00 −0.622710
\(249\) 0 0
\(250\) 3000.00 0.758947
\(251\) 3288.00 0.826840 0.413420 0.910541i \(-0.364334\pi\)
0.413420 + 0.910541i \(0.364334\pi\)
\(252\) 0 0
\(253\) −1184.00 −0.294219
\(254\) −1568.00 −0.387343
\(255\) 0 0
\(256\) 256.000 0.0625000
\(257\) 2522.00 0.612132 0.306066 0.952010i \(-0.400987\pi\)
0.306066 + 0.952010i \(0.400987\pi\)
\(258\) 0 0
\(259\) −1918.00 −0.460150
\(260\) −2000.00 −0.477057
\(261\) 0 0
\(262\) −240.000 −0.0565926
\(263\) 3228.00 0.756833 0.378416 0.925635i \(-0.376469\pi\)
0.378416 + 0.925635i \(0.376469\pi\)
\(264\) 0 0
\(265\) 5500.00 1.27495
\(266\) −266.000 −0.0613139
\(267\) 0 0
\(268\) −3024.00 −0.689254
\(269\) −8434.00 −1.91164 −0.955818 0.293959i \(-0.905027\pi\)
−0.955818 + 0.293959i \(0.905027\pi\)
\(270\) 0 0
\(271\) −7400.00 −1.65874 −0.829369 0.558701i \(-0.811300\pi\)
−0.829369 + 0.558701i \(0.811300\pi\)
\(272\) −1824.00 −0.406604
\(273\) 0 0
\(274\) −60.0000 −0.0132290
\(275\) 200.000 0.0438562
\(276\) 0 0
\(277\) −1442.00 −0.312785 −0.156392 0.987695i \(-0.549986\pi\)
−0.156392 + 0.987695i \(0.549986\pi\)
\(278\) −2280.00 −0.491890
\(279\) 0 0
\(280\) −560.000 −0.119523
\(281\) −6262.00 −1.32939 −0.664697 0.747113i \(-0.731439\pi\)
−0.664697 + 0.747113i \(0.731439\pi\)
\(282\) 0 0
\(283\) −3796.00 −0.797346 −0.398673 0.917093i \(-0.630529\pi\)
−0.398673 + 0.917093i \(0.630529\pi\)
\(284\) 864.000 0.180525
\(285\) 0 0
\(286\) −800.000 −0.165402
\(287\) 1414.00 0.290822
\(288\) 0 0
\(289\) 8083.00 1.64523
\(290\) −600.000 −0.121494
\(291\) 0 0
\(292\) −1112.00 −0.222859
\(293\) 5046.00 1.00611 0.503055 0.864254i \(-0.332209\pi\)
0.503055 + 0.864254i \(0.332209\pi\)
\(294\) 0 0
\(295\) −6280.00 −1.23944
\(296\) 2192.00 0.430430
\(297\) 0 0
\(298\) 812.000 0.157845
\(299\) −7400.00 −1.43128
\(300\) 0 0
\(301\) −812.000 −0.155491
\(302\) −4640.00 −0.884113
\(303\) 0 0
\(304\) 304.000 0.0573539
\(305\) −580.000 −0.108888
\(306\) 0 0
\(307\) 244.000 0.0453610 0.0226805 0.999743i \(-0.492780\pi\)
0.0226805 + 0.999743i \(0.492780\pi\)
\(308\) −224.000 −0.0414402
\(309\) 0 0
\(310\) −6080.00 −1.11394
\(311\) 8028.00 1.46375 0.731875 0.681439i \(-0.238646\pi\)
0.731875 + 0.681439i \(0.238646\pi\)
\(312\) 0 0
\(313\) 9178.00 1.65742 0.828708 0.559681i \(-0.189076\pi\)
0.828708 + 0.559681i \(0.189076\pi\)
\(314\) 6388.00 1.14808
\(315\) 0 0
\(316\) −3808.00 −0.677901
\(317\) −1514.00 −0.268248 −0.134124 0.990965i \(-0.542822\pi\)
−0.134124 + 0.990965i \(0.542822\pi\)
\(318\) 0 0
\(319\) −240.000 −0.0421236
\(320\) 640.000 0.111803
\(321\) 0 0
\(322\) −2072.00 −0.358596
\(323\) −2166.00 −0.373125
\(324\) 0 0
\(325\) 1250.00 0.213346
\(326\) 8.00000 0.00135914
\(327\) 0 0
\(328\) −1616.00 −0.272039
\(329\) 2268.00 0.380057
\(330\) 0 0
\(331\) −2196.00 −0.364662 −0.182331 0.983237i \(-0.558364\pi\)
−0.182331 + 0.983237i \(0.558364\pi\)
\(332\) 4736.00 0.782897
\(333\) 0 0
\(334\) −1264.00 −0.207075
\(335\) −7560.00 −1.23298
\(336\) 0 0
\(337\) 7594.00 1.22751 0.613756 0.789496i \(-0.289658\pi\)
0.613756 + 0.789496i \(0.289658\pi\)
\(338\) −606.000 −0.0975209
\(339\) 0 0
\(340\) −4560.00 −0.727355
\(341\) −2432.00 −0.386218
\(342\) 0 0
\(343\) 343.000 0.0539949
\(344\) 928.000 0.145449
\(345\) 0 0
\(346\) 7364.00 1.14419
\(347\) −4632.00 −0.716596 −0.358298 0.933607i \(-0.616643\pi\)
−0.358298 + 0.933607i \(0.616643\pi\)
\(348\) 0 0
\(349\) 1798.00 0.275773 0.137886 0.990448i \(-0.455969\pi\)
0.137886 + 0.990448i \(0.455969\pi\)
\(350\) 350.000 0.0534522
\(351\) 0 0
\(352\) 256.000 0.0387638
\(353\) −3666.00 −0.552752 −0.276376 0.961050i \(-0.589134\pi\)
−0.276376 + 0.961050i \(0.589134\pi\)
\(354\) 0 0
\(355\) 2160.00 0.322932
\(356\) −6168.00 −0.918268
\(357\) 0 0
\(358\) 4392.00 0.648392
\(359\) −12004.0 −1.76475 −0.882377 0.470543i \(-0.844058\pi\)
−0.882377 + 0.470543i \(0.844058\pi\)
\(360\) 0 0
\(361\) 361.000 0.0526316
\(362\) 7604.00 1.10403
\(363\) 0 0
\(364\) −1400.00 −0.201593
\(365\) −2780.00 −0.398663
\(366\) 0 0
\(367\) 120.000 0.0170680 0.00853399 0.999964i \(-0.497284\pi\)
0.00853399 + 0.999964i \(0.497284\pi\)
\(368\) 2368.00 0.335436
\(369\) 0 0
\(370\) 5480.00 0.769977
\(371\) 3850.00 0.538766
\(372\) 0 0
\(373\) −7954.00 −1.10414 −0.552068 0.833799i \(-0.686161\pi\)
−0.552068 + 0.833799i \(0.686161\pi\)
\(374\) −1824.00 −0.252184
\(375\) 0 0
\(376\) −2592.00 −0.355511
\(377\) −1500.00 −0.204918
\(378\) 0 0
\(379\) −11268.0 −1.52717 −0.763586 0.645706i \(-0.776563\pi\)
−0.763586 + 0.645706i \(0.776563\pi\)
\(380\) 760.000 0.102598
\(381\) 0 0
\(382\) 3704.00 0.496108
\(383\) −1224.00 −0.163299 −0.0816494 0.996661i \(-0.526019\pi\)
−0.0816494 + 0.996661i \(0.526019\pi\)
\(384\) 0 0
\(385\) −560.000 −0.0741305
\(386\) −8484.00 −1.11872
\(387\) 0 0
\(388\) −3480.00 −0.455336
\(389\) −7038.00 −0.917328 −0.458664 0.888610i \(-0.651672\pi\)
−0.458664 + 0.888610i \(0.651672\pi\)
\(390\) 0 0
\(391\) −16872.0 −2.18223
\(392\) −392.000 −0.0505076
\(393\) 0 0
\(394\) 1340.00 0.171341
\(395\) −9520.00 −1.21267
\(396\) 0 0
\(397\) 13110.0 1.65736 0.828680 0.559722i \(-0.189092\pi\)
0.828680 + 0.559722i \(0.189092\pi\)
\(398\) 9344.00 1.17682
\(399\) 0 0
\(400\) −400.000 −0.0500000
\(401\) 4346.00 0.541219 0.270610 0.962689i \(-0.412775\pi\)
0.270610 + 0.962689i \(0.412775\pi\)
\(402\) 0 0
\(403\) −15200.0 −1.87882
\(404\) 2376.00 0.292600
\(405\) 0 0
\(406\) −420.000 −0.0513405
\(407\) 2192.00 0.266962
\(408\) 0 0
\(409\) −14734.0 −1.78129 −0.890647 0.454695i \(-0.849748\pi\)
−0.890647 + 0.454695i \(0.849748\pi\)
\(410\) −4040.00 −0.486638
\(411\) 0 0
\(412\) −1152.00 −0.137755
\(413\) −4396.00 −0.523760
\(414\) 0 0
\(415\) 11840.0 1.40049
\(416\) 1600.00 0.188573
\(417\) 0 0
\(418\) 304.000 0.0355721
\(419\) −7528.00 −0.877725 −0.438863 0.898554i \(-0.644619\pi\)
−0.438863 + 0.898554i \(0.644619\pi\)
\(420\) 0 0
\(421\) −11018.0 −1.27550 −0.637749 0.770244i \(-0.720134\pi\)
−0.637749 + 0.770244i \(0.720134\pi\)
\(422\) −3704.00 −0.427270
\(423\) 0 0
\(424\) −4400.00 −0.503969
\(425\) 2850.00 0.325283
\(426\) 0 0
\(427\) −406.000 −0.0460134
\(428\) 1104.00 0.124682
\(429\) 0 0
\(430\) 2320.00 0.260187
\(431\) 2448.00 0.273587 0.136794 0.990600i \(-0.456320\pi\)
0.136794 + 0.990600i \(0.456320\pi\)
\(432\) 0 0
\(433\) −46.0000 −0.00510536 −0.00255268 0.999997i \(-0.500813\pi\)
−0.00255268 + 0.999997i \(0.500813\pi\)
\(434\) −4256.00 −0.470725
\(435\) 0 0
\(436\) −6856.00 −0.753080
\(437\) 2812.00 0.307817
\(438\) 0 0
\(439\) 16672.0 1.81255 0.906277 0.422684i \(-0.138912\pi\)
0.906277 + 0.422684i \(0.138912\pi\)
\(440\) 640.000 0.0693427
\(441\) 0 0
\(442\) −11400.0 −1.22679
\(443\) 4232.00 0.453879 0.226939 0.973909i \(-0.427128\pi\)
0.226939 + 0.973909i \(0.427128\pi\)
\(444\) 0 0
\(445\) −15420.0 −1.64265
\(446\) −8624.00 −0.915601
\(447\) 0 0
\(448\) 448.000 0.0472456
\(449\) −11150.0 −1.17194 −0.585970 0.810333i \(-0.699286\pi\)
−0.585970 + 0.810333i \(0.699286\pi\)
\(450\) 0 0
\(451\) −1616.00 −0.168724
\(452\) 2920.00 0.303861
\(453\) 0 0
\(454\) 2952.00 0.305163
\(455\) −3500.00 −0.360621
\(456\) 0 0
\(457\) 2538.00 0.259787 0.129893 0.991528i \(-0.458536\pi\)
0.129893 + 0.991528i \(0.458536\pi\)
\(458\) 6084.00 0.620713
\(459\) 0 0
\(460\) 5920.00 0.600047
\(461\) −7078.00 −0.715087 −0.357544 0.933896i \(-0.616386\pi\)
−0.357544 + 0.933896i \(0.616386\pi\)
\(462\) 0 0
\(463\) −11432.0 −1.14749 −0.573747 0.819032i \(-0.694511\pi\)
−0.573747 + 0.819032i \(0.694511\pi\)
\(464\) 480.000 0.0480247
\(465\) 0 0
\(466\) 1876.00 0.186489
\(467\) −9984.00 −0.989303 −0.494651 0.869091i \(-0.664704\pi\)
−0.494651 + 0.869091i \(0.664704\pi\)
\(468\) 0 0
\(469\) −5292.00 −0.521027
\(470\) −6480.00 −0.635958
\(471\) 0 0
\(472\) 5024.00 0.489933
\(473\) 928.000 0.0902103
\(474\) 0 0
\(475\) −475.000 −0.0458831
\(476\) −3192.00 −0.307364
\(477\) 0 0
\(478\) 1624.00 0.155398
\(479\) 9276.00 0.884825 0.442413 0.896812i \(-0.354123\pi\)
0.442413 + 0.896812i \(0.354123\pi\)
\(480\) 0 0
\(481\) 13700.0 1.29868
\(482\) −1684.00 −0.159137
\(483\) 0 0
\(484\) −5068.00 −0.475958
\(485\) −8700.00 −0.814529
\(486\) 0 0
\(487\) −19240.0 −1.79024 −0.895121 0.445824i \(-0.852911\pi\)
−0.895121 + 0.445824i \(0.852911\pi\)
\(488\) 464.000 0.0430416
\(489\) 0 0
\(490\) −980.000 −0.0903508
\(491\) 11384.0 1.04634 0.523170 0.852228i \(-0.324749\pi\)
0.523170 + 0.852228i \(0.324749\pi\)
\(492\) 0 0
\(493\) −3420.00 −0.312432
\(494\) 1900.00 0.173047
\(495\) 0 0
\(496\) 4864.00 0.440323
\(497\) 1512.00 0.136464
\(498\) 0 0
\(499\) 6204.00 0.556572 0.278286 0.960498i \(-0.410234\pi\)
0.278286 + 0.960498i \(0.410234\pi\)
\(500\) −6000.00 −0.536656
\(501\) 0 0
\(502\) −6576.00 −0.584664
\(503\) 17332.0 1.53637 0.768187 0.640226i \(-0.221159\pi\)
0.768187 + 0.640226i \(0.221159\pi\)
\(504\) 0 0
\(505\) 5940.00 0.523419
\(506\) 2368.00 0.208044
\(507\) 0 0
\(508\) 3136.00 0.273893
\(509\) −4930.00 −0.429309 −0.214655 0.976690i \(-0.568863\pi\)
−0.214655 + 0.976690i \(0.568863\pi\)
\(510\) 0 0
\(511\) −1946.00 −0.168466
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) −5044.00 −0.432843
\(515\) −2880.00 −0.246423
\(516\) 0 0
\(517\) −2592.00 −0.220495
\(518\) 3836.00 0.325375
\(519\) 0 0
\(520\) 4000.00 0.337330
\(521\) −21014.0 −1.76706 −0.883532 0.468371i \(-0.844841\pi\)
−0.883532 + 0.468371i \(0.844841\pi\)
\(522\) 0 0
\(523\) −4828.00 −0.403659 −0.201830 0.979421i \(-0.564689\pi\)
−0.201830 + 0.979421i \(0.564689\pi\)
\(524\) 480.000 0.0400170
\(525\) 0 0
\(526\) −6456.00 −0.535162
\(527\) −34656.0 −2.86459
\(528\) 0 0
\(529\) 9737.00 0.800279
\(530\) −11000.0 −0.901527
\(531\) 0 0
\(532\) 532.000 0.0433555
\(533\) −10100.0 −0.820787
\(534\) 0 0
\(535\) 2760.00 0.223038
\(536\) 6048.00 0.487377
\(537\) 0 0
\(538\) 16868.0 1.35173
\(539\) −392.000 −0.0313259
\(540\) 0 0
\(541\) 16038.0 1.27454 0.637271 0.770640i \(-0.280063\pi\)
0.637271 + 0.770640i \(0.280063\pi\)
\(542\) 14800.0 1.17290
\(543\) 0 0
\(544\) 3648.00 0.287512
\(545\) −17140.0 −1.34715
\(546\) 0 0
\(547\) −14524.0 −1.13529 −0.567643 0.823275i \(-0.692145\pi\)
−0.567643 + 0.823275i \(0.692145\pi\)
\(548\) 120.000 0.00935428
\(549\) 0 0
\(550\) −400.000 −0.0310110
\(551\) 570.000 0.0440704
\(552\) 0 0
\(553\) −6664.00 −0.512445
\(554\) 2884.00 0.221172
\(555\) 0 0
\(556\) 4560.00 0.347818
\(557\) 12322.0 0.937343 0.468671 0.883373i \(-0.344733\pi\)
0.468671 + 0.883373i \(0.344733\pi\)
\(558\) 0 0
\(559\) 5800.00 0.438844
\(560\) 1120.00 0.0845154
\(561\) 0 0
\(562\) 12524.0 0.940023
\(563\) 11100.0 0.830922 0.415461 0.909611i \(-0.363620\pi\)
0.415461 + 0.909611i \(0.363620\pi\)
\(564\) 0 0
\(565\) 7300.00 0.543563
\(566\) 7592.00 0.563808
\(567\) 0 0
\(568\) −1728.00 −0.127650
\(569\) 9418.00 0.693889 0.346945 0.937886i \(-0.387219\pi\)
0.346945 + 0.937886i \(0.387219\pi\)
\(570\) 0 0
\(571\) −16452.0 −1.20577 −0.602885 0.797828i \(-0.705982\pi\)
−0.602885 + 0.797828i \(0.705982\pi\)
\(572\) 1600.00 0.116957
\(573\) 0 0
\(574\) −2828.00 −0.205642
\(575\) −3700.00 −0.268349
\(576\) 0 0
\(577\) 16658.0 1.20187 0.600937 0.799296i \(-0.294794\pi\)
0.600937 + 0.799296i \(0.294794\pi\)
\(578\) −16166.0 −1.16335
\(579\) 0 0
\(580\) 1200.00 0.0859091
\(581\) 8288.00 0.591814
\(582\) 0 0
\(583\) −4400.00 −0.312572
\(584\) 2224.00 0.157585
\(585\) 0 0
\(586\) −10092.0 −0.711428
\(587\) 5544.00 0.389822 0.194911 0.980821i \(-0.437558\pi\)
0.194911 + 0.980821i \(0.437558\pi\)
\(588\) 0 0
\(589\) 5776.00 0.404068
\(590\) 12560.0 0.876419
\(591\) 0 0
\(592\) −4384.00 −0.304360
\(593\) −14058.0 −0.973512 −0.486756 0.873538i \(-0.661820\pi\)
−0.486756 + 0.873538i \(0.661820\pi\)
\(594\) 0 0
\(595\) −7980.00 −0.549829
\(596\) −1624.00 −0.111613
\(597\) 0 0
\(598\) 14800.0 1.01207
\(599\) −4720.00 −0.321960 −0.160980 0.986958i \(-0.551465\pi\)
−0.160980 + 0.986958i \(0.551465\pi\)
\(600\) 0 0
\(601\) −3558.00 −0.241487 −0.120744 0.992684i \(-0.538528\pi\)
−0.120744 + 0.992684i \(0.538528\pi\)
\(602\) 1624.00 0.109949
\(603\) 0 0
\(604\) 9280.00 0.625162
\(605\) −12670.0 −0.851419
\(606\) 0 0
\(607\) −23744.0 −1.58771 −0.793854 0.608108i \(-0.791929\pi\)
−0.793854 + 0.608108i \(0.791929\pi\)
\(608\) −608.000 −0.0405554
\(609\) 0 0
\(610\) 1160.00 0.0769951
\(611\) −16200.0 −1.07264
\(612\) 0 0
\(613\) 16062.0 1.05830 0.529150 0.848528i \(-0.322511\pi\)
0.529150 + 0.848528i \(0.322511\pi\)
\(614\) −488.000 −0.0320750
\(615\) 0 0
\(616\) 448.000 0.0293027
\(617\) −14498.0 −0.945977 −0.472988 0.881069i \(-0.656825\pi\)
−0.472988 + 0.881069i \(0.656825\pi\)
\(618\) 0 0
\(619\) −6764.00 −0.439205 −0.219603 0.975589i \(-0.570476\pi\)
−0.219603 + 0.975589i \(0.570476\pi\)
\(620\) 12160.0 0.787673
\(621\) 0 0
\(622\) −16056.0 −1.03503
\(623\) −10794.0 −0.694145
\(624\) 0 0
\(625\) −11875.0 −0.760000
\(626\) −18356.0 −1.17197
\(627\) 0 0
\(628\) −12776.0 −0.811812
\(629\) 31236.0 1.98006
\(630\) 0 0
\(631\) 15016.0 0.947349 0.473675 0.880700i \(-0.342927\pi\)
0.473675 + 0.880700i \(0.342927\pi\)
\(632\) 7616.00 0.479348
\(633\) 0 0
\(634\) 3028.00 0.189680
\(635\) 7840.00 0.489954
\(636\) 0 0
\(637\) −2450.00 −0.152390
\(638\) 480.000 0.0297859
\(639\) 0 0
\(640\) −1280.00 −0.0790569
\(641\) 18906.0 1.16496 0.582482 0.812844i \(-0.302082\pi\)
0.582482 + 0.812844i \(0.302082\pi\)
\(642\) 0 0
\(643\) −29532.0 −1.81124 −0.905621 0.424088i \(-0.860595\pi\)
−0.905621 + 0.424088i \(0.860595\pi\)
\(644\) 4144.00 0.253566
\(645\) 0 0
\(646\) 4332.00 0.263839
\(647\) −3636.00 −0.220936 −0.110468 0.993880i \(-0.535235\pi\)
−0.110468 + 0.993880i \(0.535235\pi\)
\(648\) 0 0
\(649\) 5024.00 0.303866
\(650\) −2500.00 −0.150859
\(651\) 0 0
\(652\) −16.0000 −0.000961056 0
\(653\) −12126.0 −0.726688 −0.363344 0.931655i \(-0.618365\pi\)
−0.363344 + 0.931655i \(0.618365\pi\)
\(654\) 0 0
\(655\) 1200.00 0.0715845
\(656\) 3232.00 0.192360
\(657\) 0 0
\(658\) −4536.00 −0.268741
\(659\) 4580.00 0.270731 0.135365 0.990796i \(-0.456779\pi\)
0.135365 + 0.990796i \(0.456779\pi\)
\(660\) 0 0
\(661\) −18178.0 −1.06966 −0.534828 0.844961i \(-0.679623\pi\)
−0.534828 + 0.844961i \(0.679623\pi\)
\(662\) 4392.00 0.257855
\(663\) 0 0
\(664\) −9472.00 −0.553592
\(665\) 1330.00 0.0775567
\(666\) 0 0
\(667\) 4440.00 0.257747
\(668\) 2528.00 0.146424
\(669\) 0 0
\(670\) 15120.0 0.871846
\(671\) 464.000 0.0266953
\(672\) 0 0
\(673\) 10802.0 0.618702 0.309351 0.950948i \(-0.399888\pi\)
0.309351 + 0.950948i \(0.399888\pi\)
\(674\) −15188.0 −0.867982
\(675\) 0 0
\(676\) 1212.00 0.0689577
\(677\) −11186.0 −0.635026 −0.317513 0.948254i \(-0.602848\pi\)
−0.317513 + 0.948254i \(0.602848\pi\)
\(678\) 0 0
\(679\) −6090.00 −0.344201
\(680\) 9120.00 0.514318
\(681\) 0 0
\(682\) 4864.00 0.273097
\(683\) 29940.0 1.67734 0.838669 0.544641i \(-0.183334\pi\)
0.838669 + 0.544641i \(0.183334\pi\)
\(684\) 0 0
\(685\) 300.000 0.0167334
\(686\) −686.000 −0.0381802
\(687\) 0 0
\(688\) −1856.00 −0.102848
\(689\) −27500.0 −1.52056
\(690\) 0 0
\(691\) −17036.0 −0.937887 −0.468944 0.883228i \(-0.655365\pi\)
−0.468944 + 0.883228i \(0.655365\pi\)
\(692\) −14728.0 −0.809067
\(693\) 0 0
\(694\) 9264.00 0.506710
\(695\) 11400.0 0.622197
\(696\) 0 0
\(697\) −23028.0 −1.25143
\(698\) −3596.00 −0.195001
\(699\) 0 0
\(700\) −700.000 −0.0377964
\(701\) 15762.0 0.849248 0.424624 0.905370i \(-0.360406\pi\)
0.424624 + 0.905370i \(0.360406\pi\)
\(702\) 0 0
\(703\) −5206.00 −0.279300
\(704\) −512.000 −0.0274101
\(705\) 0 0
\(706\) 7332.00 0.390855
\(707\) 4158.00 0.221185
\(708\) 0 0
\(709\) −16210.0 −0.858645 −0.429323 0.903151i \(-0.641248\pi\)
−0.429323 + 0.903151i \(0.641248\pi\)
\(710\) −4320.00 −0.228347
\(711\) 0 0
\(712\) 12336.0 0.649313
\(713\) 44992.0 2.36320
\(714\) 0 0
\(715\) 4000.00 0.209219
\(716\) −8784.00 −0.458483
\(717\) 0 0
\(718\) 24008.0 1.24787
\(719\) −3916.00 −0.203118 −0.101559 0.994829i \(-0.532383\pi\)
−0.101559 + 0.994829i \(0.532383\pi\)
\(720\) 0 0
\(721\) −2016.00 −0.104133
\(722\) −722.000 −0.0372161
\(723\) 0 0
\(724\) −15208.0 −0.780664
\(725\) −750.000 −0.0384197
\(726\) 0 0
\(727\) −25520.0 −1.30190 −0.650952 0.759119i \(-0.725630\pi\)
−0.650952 + 0.759119i \(0.725630\pi\)
\(728\) 2800.00 0.142548
\(729\) 0 0
\(730\) 5560.00 0.281897
\(731\) 13224.0 0.669093
\(732\) 0 0
\(733\) 16726.0 0.842823 0.421411 0.906870i \(-0.361535\pi\)
0.421411 + 0.906870i \(0.361535\pi\)
\(734\) −240.000 −0.0120689
\(735\) 0 0
\(736\) −4736.00 −0.237189
\(737\) 6048.00 0.302281
\(738\) 0 0
\(739\) 3436.00 0.171036 0.0855178 0.996337i \(-0.472746\pi\)
0.0855178 + 0.996337i \(0.472746\pi\)
\(740\) −10960.0 −0.544456
\(741\) 0 0
\(742\) −7700.00 −0.380965
\(743\) −24664.0 −1.21781 −0.608906 0.793242i \(-0.708391\pi\)
−0.608906 + 0.793242i \(0.708391\pi\)
\(744\) 0 0
\(745\) −4060.00 −0.199660
\(746\) 15908.0 0.780742
\(747\) 0 0
\(748\) 3648.00 0.178321
\(749\) 1932.00 0.0942507
\(750\) 0 0
\(751\) −29208.0 −1.41919 −0.709597 0.704608i \(-0.751123\pi\)
−0.709597 + 0.704608i \(0.751123\pi\)
\(752\) 5184.00 0.251384
\(753\) 0 0
\(754\) 3000.00 0.144899
\(755\) 23200.0 1.11832
\(756\) 0 0
\(757\) 20686.0 0.993191 0.496595 0.867982i \(-0.334583\pi\)
0.496595 + 0.867982i \(0.334583\pi\)
\(758\) 22536.0 1.07987
\(759\) 0 0
\(760\) −1520.00 −0.0725476
\(761\) 40182.0 1.91406 0.957028 0.289996i \(-0.0936540\pi\)
0.957028 + 0.289996i \(0.0936540\pi\)
\(762\) 0 0
\(763\) −11998.0 −0.569275
\(764\) −7408.00 −0.350801
\(765\) 0 0
\(766\) 2448.00 0.115470
\(767\) 31400.0 1.47821
\(768\) 0 0
\(769\) −4686.00 −0.219742 −0.109871 0.993946i \(-0.535044\pi\)
−0.109871 + 0.993946i \(0.535044\pi\)
\(770\) 1120.00 0.0524182
\(771\) 0 0
\(772\) 16968.0 0.791051
\(773\) −31114.0 −1.44773 −0.723863 0.689943i \(-0.757635\pi\)
−0.723863 + 0.689943i \(0.757635\pi\)
\(774\) 0 0
\(775\) −7600.00 −0.352258
\(776\) 6960.00 0.321971
\(777\) 0 0
\(778\) 14076.0 0.648649
\(779\) 3838.00 0.176522
\(780\) 0 0
\(781\) −1728.00 −0.0791712
\(782\) 33744.0 1.54307
\(783\) 0 0
\(784\) 784.000 0.0357143
\(785\) −31940.0 −1.45221
\(786\) 0 0
\(787\) 25708.0 1.16441 0.582205 0.813042i \(-0.302190\pi\)
0.582205 + 0.813042i \(0.302190\pi\)
\(788\) −2680.00 −0.121156
\(789\) 0 0
\(790\) 19040.0 0.857485
\(791\) 5110.00 0.229697
\(792\) 0 0
\(793\) 2900.00 0.129864
\(794\) −26220.0 −1.17193
\(795\) 0 0
\(796\) −18688.0 −0.832134
\(797\) 41326.0 1.83669 0.918345 0.395781i \(-0.129526\pi\)
0.918345 + 0.395781i \(0.129526\pi\)
\(798\) 0 0
\(799\) −36936.0 −1.63542
\(800\) 800.000 0.0353553
\(801\) 0 0
\(802\) −8692.00 −0.382700
\(803\) 2224.00 0.0977376
\(804\) 0 0
\(805\) 10360.0 0.453593
\(806\) 30400.0 1.32853
\(807\) 0 0
\(808\) −4752.00 −0.206899
\(809\) 34086.0 1.48133 0.740667 0.671872i \(-0.234509\pi\)
0.740667 + 0.671872i \(0.234509\pi\)
\(810\) 0 0
\(811\) 15564.0 0.673891 0.336946 0.941524i \(-0.390606\pi\)
0.336946 + 0.941524i \(0.390606\pi\)
\(812\) 840.000 0.0363032
\(813\) 0 0
\(814\) −4384.00 −0.188770
\(815\) −40.0000 −0.00171919
\(816\) 0 0
\(817\) −2204.00 −0.0943797
\(818\) 29468.0 1.25957
\(819\) 0 0
\(820\) 8080.00 0.344105
\(821\) 16074.0 0.683297 0.341648 0.939828i \(-0.389015\pi\)
0.341648 + 0.939828i \(0.389015\pi\)
\(822\) 0 0
\(823\) −22840.0 −0.967378 −0.483689 0.875240i \(-0.660703\pi\)
−0.483689 + 0.875240i \(0.660703\pi\)
\(824\) 2304.00 0.0974073
\(825\) 0 0
\(826\) 8792.00 0.370354
\(827\) 32628.0 1.37193 0.685965 0.727634i \(-0.259380\pi\)
0.685965 + 0.727634i \(0.259380\pi\)
\(828\) 0 0
\(829\) 27326.0 1.14484 0.572419 0.819961i \(-0.306005\pi\)
0.572419 + 0.819961i \(0.306005\pi\)
\(830\) −23680.0 −0.990295
\(831\) 0 0
\(832\) −3200.00 −0.133341
\(833\) −5586.00 −0.232345
\(834\) 0 0
\(835\) 6320.00 0.261931
\(836\) −608.000 −0.0251533
\(837\) 0 0
\(838\) 15056.0 0.620645
\(839\) −26400.0 −1.08633 −0.543164 0.839627i \(-0.682774\pi\)
−0.543164 + 0.839627i \(0.682774\pi\)
\(840\) 0 0
\(841\) −23489.0 −0.963098
\(842\) 22036.0 0.901913
\(843\) 0 0
\(844\) 7408.00 0.302125
\(845\) 3030.00 0.123355
\(846\) 0 0
\(847\) −8869.00 −0.359790
\(848\) 8800.00 0.356360
\(849\) 0 0
\(850\) −5700.00 −0.230010
\(851\) −40552.0 −1.63350
\(852\) 0 0
\(853\) 20078.0 0.805929 0.402965 0.915216i \(-0.367980\pi\)
0.402965 + 0.915216i \(0.367980\pi\)
\(854\) 812.000 0.0325364
\(855\) 0 0
\(856\) −2208.00 −0.0881634
\(857\) −24214.0 −0.965151 −0.482576 0.875854i \(-0.660299\pi\)
−0.482576 + 0.875854i \(0.660299\pi\)
\(858\) 0 0
\(859\) 34708.0 1.37860 0.689302 0.724474i \(-0.257917\pi\)
0.689302 + 0.724474i \(0.257917\pi\)
\(860\) −4640.00 −0.183980
\(861\) 0 0
\(862\) −4896.00 −0.193455
\(863\) −11072.0 −0.436727 −0.218363 0.975868i \(-0.570072\pi\)
−0.218363 + 0.975868i \(0.570072\pi\)
\(864\) 0 0
\(865\) −36820.0 −1.44730
\(866\) 92.0000 0.00361003
\(867\) 0 0
\(868\) 8512.00 0.332853
\(869\) 7616.00 0.297302
\(870\) 0 0
\(871\) 37800.0 1.47050
\(872\) 13712.0 0.532508
\(873\) 0 0
\(874\) −5624.00 −0.217660
\(875\) −10500.0 −0.405674
\(876\) 0 0
\(877\) −8314.00 −0.320118 −0.160059 0.987107i \(-0.551169\pi\)
−0.160059 + 0.987107i \(0.551169\pi\)
\(878\) −33344.0 −1.28167
\(879\) 0 0
\(880\) −1280.00 −0.0490327
\(881\) 7710.00 0.294843 0.147421 0.989074i \(-0.452903\pi\)
0.147421 + 0.989074i \(0.452903\pi\)
\(882\) 0 0
\(883\) −37748.0 −1.43864 −0.719321 0.694678i \(-0.755547\pi\)
−0.719321 + 0.694678i \(0.755547\pi\)
\(884\) 22800.0 0.867474
\(885\) 0 0
\(886\) −8464.00 −0.320941
\(887\) 45624.0 1.72706 0.863531 0.504296i \(-0.168248\pi\)
0.863531 + 0.504296i \(0.168248\pi\)
\(888\) 0 0
\(889\) 5488.00 0.207043
\(890\) 30840.0 1.16153
\(891\) 0 0
\(892\) 17248.0 0.647428
\(893\) 6156.00 0.230686
\(894\) 0 0
\(895\) −21960.0 −0.820158
\(896\) −896.000 −0.0334077
\(897\) 0 0
\(898\) 22300.0 0.828687
\(899\) 9120.00 0.338342
\(900\) 0 0
\(901\) −62700.0 −2.31836
\(902\) 3232.00 0.119306
\(903\) 0 0
\(904\) −5840.00 −0.214862
\(905\) −38020.0 −1.39649
\(906\) 0 0
\(907\) 11732.0 0.429498 0.214749 0.976669i \(-0.431107\pi\)
0.214749 + 0.976669i \(0.431107\pi\)
\(908\) −5904.00 −0.215783
\(909\) 0 0
\(910\) 7000.00 0.254998
\(911\) −18696.0 −0.679941 −0.339970 0.940436i \(-0.610417\pi\)
−0.339970 + 0.940436i \(0.610417\pi\)
\(912\) 0 0
\(913\) −9472.00 −0.343349
\(914\) −5076.00 −0.183697
\(915\) 0 0
\(916\) −12168.0 −0.438911
\(917\) 840.000 0.0302500
\(918\) 0 0
\(919\) 37512.0 1.34647 0.673235 0.739428i \(-0.264904\pi\)
0.673235 + 0.739428i \(0.264904\pi\)
\(920\) −11840.0 −0.424297
\(921\) 0 0
\(922\) 14156.0 0.505643
\(923\) −10800.0 −0.385142
\(924\) 0 0
\(925\) 6850.00 0.243488
\(926\) 22864.0 0.811401
\(927\) 0 0
\(928\) −960.000 −0.0339586
\(929\) 14838.0 0.524025 0.262012 0.965065i \(-0.415614\pi\)
0.262012 + 0.965065i \(0.415614\pi\)
\(930\) 0 0
\(931\) 931.000 0.0327737
\(932\) −3752.00 −0.131868
\(933\) 0 0
\(934\) 19968.0 0.699543
\(935\) 9120.00 0.318990
\(936\) 0 0
\(937\) 45754.0 1.59522 0.797608 0.603176i \(-0.206098\pi\)
0.797608 + 0.603176i \(0.206098\pi\)
\(938\) 10584.0 0.368422
\(939\) 0 0
\(940\) 12960.0 0.449690
\(941\) −28018.0 −0.970628 −0.485314 0.874340i \(-0.661295\pi\)
−0.485314 + 0.874340i \(0.661295\pi\)
\(942\) 0 0
\(943\) 29896.0 1.03239
\(944\) −10048.0 −0.346435
\(945\) 0 0
\(946\) −1856.00 −0.0637883
\(947\) −14064.0 −0.482596 −0.241298 0.970451i \(-0.577573\pi\)
−0.241298 + 0.970451i \(0.577573\pi\)
\(948\) 0 0
\(949\) 13900.0 0.475462
\(950\) 950.000 0.0324443
\(951\) 0 0
\(952\) 6384.00 0.217339
\(953\) 12218.0 0.415299 0.207649 0.978203i \(-0.433419\pi\)
0.207649 + 0.978203i \(0.433419\pi\)
\(954\) 0 0
\(955\) −18520.0 −0.627532
\(956\) −3248.00 −0.109883
\(957\) 0 0
\(958\) −18552.0 −0.625666
\(959\) 210.000 0.00707117
\(960\) 0 0
\(961\) 62625.0 2.10214
\(962\) −27400.0 −0.918307
\(963\) 0 0
\(964\) 3368.00 0.112527
\(965\) 42420.0 1.41508
\(966\) 0 0
\(967\) 23256.0 0.773384 0.386692 0.922209i \(-0.373618\pi\)
0.386692 + 0.922209i \(0.373618\pi\)
\(968\) 10136.0 0.336553
\(969\) 0 0
\(970\) 17400.0 0.575959
\(971\) −15836.0 −0.523379 −0.261690 0.965152i \(-0.584280\pi\)
−0.261690 + 0.965152i \(0.584280\pi\)
\(972\) 0 0
\(973\) 7980.00 0.262926
\(974\) 38480.0 1.26589
\(975\) 0 0
\(976\) −928.000 −0.0304350
\(977\) −33718.0 −1.10413 −0.552065 0.833801i \(-0.686160\pi\)
−0.552065 + 0.833801i \(0.686160\pi\)
\(978\) 0 0
\(979\) 12336.0 0.402717
\(980\) 1960.00 0.0638877
\(981\) 0 0
\(982\) −22768.0 −0.739874
\(983\) −59832.0 −1.94135 −0.970674 0.240401i \(-0.922721\pi\)
−0.970674 + 0.240401i \(0.922721\pi\)
\(984\) 0 0
\(985\) −6700.00 −0.216731
\(986\) 6840.00 0.220923
\(987\) 0 0
\(988\) −3800.00 −0.122362
\(989\) −17168.0 −0.551982
\(990\) 0 0
\(991\) −6304.00 −0.202072 −0.101036 0.994883i \(-0.532216\pi\)
−0.101036 + 0.994883i \(0.532216\pi\)
\(992\) −9728.00 −0.311355
\(993\) 0 0
\(994\) −3024.00 −0.0964944
\(995\) −46720.0 −1.48857
\(996\) 0 0
\(997\) −23266.0 −0.739059 −0.369529 0.929219i \(-0.620481\pi\)
−0.369529 + 0.929219i \(0.620481\pi\)
\(998\) −12408.0 −0.393555
\(999\) 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 2394.4.a.c.1.1 1
3.2 odd 2 798.4.a.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
798.4.a.b.1.1 1 3.2 odd 2
2394.4.a.c.1.1 1 1.1 even 1 trivial