Properties

Label 1386.4.a.h.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

\(f(q)\) \(=\) \(q-2.00000 q^{2} +4.00000 q^{4} +17.0000 q^{5} +7.00000 q^{7} -8.00000 q^{8} +O(q^{10})\) \(q-2.00000 q^{2} +4.00000 q^{4} +17.0000 q^{5} +7.00000 q^{7} -8.00000 q^{8} -34.0000 q^{10} +11.0000 q^{11} -21.0000 q^{13} -14.0000 q^{14} +16.0000 q^{16} +104.000 q^{17} -161.000 q^{19} +68.0000 q^{20} -22.0000 q^{22} -194.000 q^{23} +164.000 q^{25} +42.0000 q^{26} +28.0000 q^{28} -9.00000 q^{29} -180.000 q^{31} -32.0000 q^{32} -208.000 q^{34} +119.000 q^{35} -363.000 q^{37} +322.000 q^{38} -136.000 q^{40} +108.000 q^{41} -386.000 q^{43} +44.0000 q^{44} +388.000 q^{46} -333.000 q^{47} +49.0000 q^{49} -328.000 q^{50} -84.0000 q^{52} +122.000 q^{53} +187.000 q^{55} -56.0000 q^{56} +18.0000 q^{58} -537.000 q^{59} -950.000 q^{61} +360.000 q^{62} +64.0000 q^{64} -357.000 q^{65} -83.0000 q^{67} +416.000 q^{68} -238.000 q^{70} -180.000 q^{71} +177.000 q^{73} +726.000 q^{74} -644.000 q^{76} +77.0000 q^{77} -220.000 q^{79} +272.000 q^{80} -216.000 q^{82} -1112.00 q^{83} +1768.00 q^{85} +772.000 q^{86} -88.0000 q^{88} +394.000 q^{89} -147.000 q^{91} -776.000 q^{92} +666.000 q^{94} -2737.00 q^{95} +826.000 q^{97} -98.0000 q^{98} +O(q^{100})\)

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
\(5\) 17.0000 1.52053 0.760263 0.649615i \(-0.225070\pi\)
0.760263 + 0.649615i \(0.225070\pi\)
\(6\) 0 0
\(7\) 7.00000 0.377964
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) −34.0000 −1.07517
\(11\) 11.0000 0.301511
\(12\) 0 0
\(13\) −21.0000 −0.448027 −0.224014 0.974586i \(-0.571916\pi\)
−0.224014 + 0.974586i \(0.571916\pi\)
\(14\) −14.0000 −0.267261
\(15\) 0 0
\(16\) 16.0000 0.250000
\(17\) 104.000 1.48375 0.741874 0.670540i \(-0.233937\pi\)
0.741874 + 0.670540i \(0.233937\pi\)
\(18\) 0 0
\(19\) −161.000 −1.94400 −0.971998 0.234988i \(-0.924495\pi\)
−0.971998 + 0.234988i \(0.924495\pi\)
\(20\) 68.0000 0.760263
\(21\) 0 0
\(22\) −22.0000 −0.213201
\(23\) −194.000 −1.75877 −0.879387 0.476108i \(-0.842047\pi\)
−0.879387 + 0.476108i \(0.842047\pi\)
\(24\) 0 0
\(25\) 164.000 1.31200
\(26\) 42.0000 0.316803
\(27\) 0 0
\(28\) 28.0000 0.188982
\(29\) −9.00000 −0.0576296 −0.0288148 0.999585i \(-0.509173\pi\)
−0.0288148 + 0.999585i \(0.509173\pi\)
\(30\) 0 0
\(31\) −180.000 −1.04287 −0.521435 0.853291i \(-0.674603\pi\)
−0.521435 + 0.853291i \(0.674603\pi\)
\(32\) −32.0000 −0.176777
\(33\) 0 0
\(34\) −208.000 −1.04917
\(35\) 119.000 0.574705
\(36\) 0 0
\(37\) −363.000 −1.61289 −0.806444 0.591311i \(-0.798611\pi\)
−0.806444 + 0.591311i \(0.798611\pi\)
\(38\) 322.000 1.37461
\(39\) 0 0
\(40\) −136.000 −0.537587
\(41\) 108.000 0.411385 0.205692 0.978617i \(-0.434055\pi\)
0.205692 + 0.978617i \(0.434055\pi\)
\(42\) 0 0
\(43\) −386.000 −1.36894 −0.684470 0.729041i \(-0.739966\pi\)
−0.684470 + 0.729041i \(0.739966\pi\)
\(44\) 44.0000 0.150756
\(45\) 0 0
\(46\) 388.000 1.24364
\(47\) −333.000 −1.03347 −0.516734 0.856146i \(-0.672853\pi\)
−0.516734 + 0.856146i \(0.672853\pi\)
\(48\) 0 0
\(49\) 49.0000 0.142857
\(50\) −328.000 −0.927724
\(51\) 0 0
\(52\) −84.0000 −0.224014
\(53\) 122.000 0.316188 0.158094 0.987424i \(-0.449465\pi\)
0.158094 + 0.987424i \(0.449465\pi\)
\(54\) 0 0
\(55\) 187.000 0.458456
\(56\) −56.0000 −0.133631
\(57\) 0 0
\(58\) 18.0000 0.0407503
\(59\) −537.000 −1.18494 −0.592470 0.805593i \(-0.701847\pi\)
−0.592470 + 0.805593i \(0.701847\pi\)
\(60\) 0 0
\(61\) −950.000 −1.99402 −0.997008 0.0772921i \(-0.975373\pi\)
−0.997008 + 0.0772921i \(0.975373\pi\)
\(62\) 360.000 0.737420
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −357.000 −0.681237
\(66\) 0 0
\(67\) −83.0000 −0.151344 −0.0756721 0.997133i \(-0.524110\pi\)
−0.0756721 + 0.997133i \(0.524110\pi\)
\(68\) 416.000 0.741874
\(69\) 0 0
\(70\) −238.000 −0.406378
\(71\) −180.000 −0.300874 −0.150437 0.988620i \(-0.548068\pi\)
−0.150437 + 0.988620i \(0.548068\pi\)
\(72\) 0 0
\(73\) 177.000 0.283785 0.141892 0.989882i \(-0.454681\pi\)
0.141892 + 0.989882i \(0.454681\pi\)
\(74\) 726.000 1.14048
\(75\) 0 0
\(76\) −644.000 −0.971998
\(77\) 77.0000 0.113961
\(78\) 0 0
\(79\) −220.000 −0.313316 −0.156658 0.987653i \(-0.550072\pi\)
−0.156658 + 0.987653i \(0.550072\pi\)
\(80\) 272.000 0.380132
\(81\) 0 0
\(82\) −216.000 −0.290893
\(83\) −1112.00 −1.47058 −0.735288 0.677754i \(-0.762953\pi\)
−0.735288 + 0.677754i \(0.762953\pi\)
\(84\) 0 0
\(85\) 1768.00 2.25608
\(86\) 772.000 0.967987
\(87\) 0 0
\(88\) −88.0000 −0.106600
\(89\) 394.000 0.469257 0.234629 0.972085i \(-0.424613\pi\)
0.234629 + 0.972085i \(0.424613\pi\)
\(90\) 0 0
\(91\) −147.000 −0.169338
\(92\) −776.000 −0.879387
\(93\) 0 0
\(94\) 666.000 0.730773
\(95\) −2737.00 −2.95590
\(96\) 0 0
\(97\) 826.000 0.864614 0.432307 0.901726i \(-0.357700\pi\)
0.432307 + 0.901726i \(0.357700\pi\)
\(98\) −98.0000 −0.101015
\(99\) 0 0
\(100\) 656.000 0.656000
\(101\) 1688.00 1.66299 0.831496 0.555530i \(-0.187485\pi\)
0.831496 + 0.555530i \(0.187485\pi\)
\(102\) 0 0
\(103\) 1338.00 1.27997 0.639986 0.768387i \(-0.278940\pi\)
0.639986 + 0.768387i \(0.278940\pi\)
\(104\) 168.000 0.158401
\(105\) 0 0
\(106\) −244.000 −0.223579
\(107\) 535.000 0.483368 0.241684 0.970355i \(-0.422300\pi\)
0.241684 + 0.970355i \(0.422300\pi\)
\(108\) 0 0
\(109\) 216.000 0.189808 0.0949039 0.995486i \(-0.469746\pi\)
0.0949039 + 0.995486i \(0.469746\pi\)
\(110\) −374.000 −0.324177
\(111\) 0 0
\(112\) 112.000 0.0944911
\(113\) −502.000 −0.417913 −0.208957 0.977925i \(-0.567007\pi\)
−0.208957 + 0.977925i \(0.567007\pi\)
\(114\) 0 0
\(115\) −3298.00 −2.67426
\(116\) −36.0000 −0.0288148
\(117\) 0 0
\(118\) 1074.00 0.837879
\(119\) 728.000 0.560804
\(120\) 0 0
\(121\) 121.000 0.0909091
\(122\) 1900.00 1.40998
\(123\) 0 0
\(124\) −720.000 −0.521435
\(125\) 663.000 0.474404
\(126\) 0 0
\(127\) 1752.00 1.22413 0.612066 0.790806i \(-0.290339\pi\)
0.612066 + 0.790806i \(0.290339\pi\)
\(128\) −128.000 −0.0883883
\(129\) 0 0
\(130\) 714.000 0.481707
\(131\) 112.000 0.0746984 0.0373492 0.999302i \(-0.488109\pi\)
0.0373492 + 0.999302i \(0.488109\pi\)
\(132\) 0 0
\(133\) −1127.00 −0.734762
\(134\) 166.000 0.107017
\(135\) 0 0
\(136\) −832.000 −0.524584
\(137\) 1724.00 1.07512 0.537559 0.843226i \(-0.319346\pi\)
0.537559 + 0.843226i \(0.319346\pi\)
\(138\) 0 0
\(139\) 2516.00 1.53528 0.767641 0.640880i \(-0.221430\pi\)
0.767641 + 0.640880i \(0.221430\pi\)
\(140\) 476.000 0.287352
\(141\) 0 0
\(142\) 360.000 0.212750
\(143\) −231.000 −0.135085
\(144\) 0 0
\(145\) −153.000 −0.0876273
\(146\) −354.000 −0.200666
\(147\) 0 0
\(148\) −1452.00 −0.806444
\(149\) 251.000 0.138005 0.0690024 0.997616i \(-0.478018\pi\)
0.0690024 + 0.997616i \(0.478018\pi\)
\(150\) 0 0
\(151\) 3040.00 1.63836 0.819178 0.573540i \(-0.194430\pi\)
0.819178 + 0.573540i \(0.194430\pi\)
\(152\) 1288.00 0.687307
\(153\) 0 0
\(154\) −154.000 −0.0805823
\(155\) −3060.00 −1.58571
\(156\) 0 0
\(157\) −496.000 −0.252134 −0.126067 0.992022i \(-0.540236\pi\)
−0.126067 + 0.992022i \(0.540236\pi\)
\(158\) 440.000 0.221548
\(159\) 0 0
\(160\) −544.000 −0.268794
\(161\) −1358.00 −0.664754
\(162\) 0 0
\(163\) −1259.00 −0.604985 −0.302492 0.953152i \(-0.597819\pi\)
−0.302492 + 0.953152i \(0.597819\pi\)
\(164\) 432.000 0.205692
\(165\) 0 0
\(166\) 2224.00 1.03985
\(167\) 2130.00 0.986972 0.493486 0.869754i \(-0.335722\pi\)
0.493486 + 0.869754i \(0.335722\pi\)
\(168\) 0 0
\(169\) −1756.00 −0.799272
\(170\) −3536.00 −1.59529
\(171\) 0 0
\(172\) −1544.00 −0.684470
\(173\) −988.000 −0.434198 −0.217099 0.976150i \(-0.569659\pi\)
−0.217099 + 0.976150i \(0.569659\pi\)
\(174\) 0 0
\(175\) 1148.00 0.495889
\(176\) 176.000 0.0753778
\(177\) 0 0
\(178\) −788.000 −0.331815
\(179\) −4276.00 −1.78549 −0.892746 0.450559i \(-0.851225\pi\)
−0.892746 + 0.450559i \(0.851225\pi\)
\(180\) 0 0
\(181\) 370.000 0.151944 0.0759721 0.997110i \(-0.475794\pi\)
0.0759721 + 0.997110i \(0.475794\pi\)
\(182\) 294.000 0.119740
\(183\) 0 0
\(184\) 1552.00 0.621820
\(185\) −6171.00 −2.45244
\(186\) 0 0
\(187\) 1144.00 0.447367
\(188\) −1332.00 −0.516734
\(189\) 0 0
\(190\) 5474.00 2.09014
\(191\) 3384.00 1.28198 0.640989 0.767550i \(-0.278525\pi\)
0.640989 + 0.767550i \(0.278525\pi\)
\(192\) 0 0
\(193\) −2894.00 −1.07935 −0.539675 0.841873i \(-0.681453\pi\)
−0.539675 + 0.841873i \(0.681453\pi\)
\(194\) −1652.00 −0.611375
\(195\) 0 0
\(196\) 196.000 0.0714286
\(197\) −2654.00 −0.959846 −0.479923 0.877311i \(-0.659335\pi\)
−0.479923 + 0.877311i \(0.659335\pi\)
\(198\) 0 0
\(199\) −4114.00 −1.46550 −0.732748 0.680500i \(-0.761763\pi\)
−0.732748 + 0.680500i \(0.761763\pi\)
\(200\) −1312.00 −0.463862
\(201\) 0 0
\(202\) −3376.00 −1.17591
\(203\) −63.0000 −0.0217819
\(204\) 0 0
\(205\) 1836.00 0.625521
\(206\) −2676.00 −0.905076
\(207\) 0 0
\(208\) −336.000 −0.112007
\(209\) −1771.00 −0.586137
\(210\) 0 0
\(211\) 470.000 0.153347 0.0766733 0.997056i \(-0.475570\pi\)
0.0766733 + 0.997056i \(0.475570\pi\)
\(212\) 488.000 0.158094
\(213\) 0 0
\(214\) −1070.00 −0.341793
\(215\) −6562.00 −2.08151
\(216\) 0 0
\(217\) −1260.00 −0.394168
\(218\) −432.000 −0.134214
\(219\) 0 0
\(220\) 748.000 0.229228
\(221\) −2184.00 −0.664759
\(222\) 0 0
\(223\) 2958.00 0.888262 0.444131 0.895962i \(-0.353513\pi\)
0.444131 + 0.895962i \(0.353513\pi\)
\(224\) −224.000 −0.0668153
\(225\) 0 0
\(226\) 1004.00 0.295509
\(227\) −4878.00 −1.42627 −0.713137 0.701025i \(-0.752726\pi\)
−0.713137 + 0.701025i \(0.752726\pi\)
\(228\) 0 0
\(229\) −6538.00 −1.88665 −0.943326 0.331868i \(-0.892321\pi\)
−0.943326 + 0.331868i \(0.892321\pi\)
\(230\) 6596.00 1.89099
\(231\) 0 0
\(232\) 72.0000 0.0203751
\(233\) 3262.00 0.917170 0.458585 0.888650i \(-0.348356\pi\)
0.458585 + 0.888650i \(0.348356\pi\)
\(234\) 0 0
\(235\) −5661.00 −1.57142
\(236\) −2148.00 −0.592470
\(237\) 0 0
\(238\) −1456.00 −0.396548
\(239\) 2609.00 0.706118 0.353059 0.935601i \(-0.385142\pi\)
0.353059 + 0.935601i \(0.385142\pi\)
\(240\) 0 0
\(241\) 6559.00 1.75312 0.876561 0.481291i \(-0.159832\pi\)
0.876561 + 0.481291i \(0.159832\pi\)
\(242\) −242.000 −0.0642824
\(243\) 0 0
\(244\) −3800.00 −0.997008
\(245\) 833.000 0.217218
\(246\) 0 0
\(247\) 3381.00 0.870963
\(248\) 1440.00 0.368710
\(249\) 0 0
\(250\) −1326.00 −0.335454
\(251\) 2705.00 0.680231 0.340116 0.940384i \(-0.389534\pi\)
0.340116 + 0.940384i \(0.389534\pi\)
\(252\) 0 0
\(253\) −2134.00 −0.530290
\(254\) −3504.00 −0.865593
\(255\) 0 0
\(256\) 256.000 0.0625000
\(257\) −2995.00 −0.726938 −0.363469 0.931606i \(-0.618408\pi\)
−0.363469 + 0.931606i \(0.618408\pi\)
\(258\) 0 0
\(259\) −2541.00 −0.609614
\(260\) −1428.00 −0.340618
\(261\) 0 0
\(262\) −224.000 −0.0528197
\(263\) 39.0000 0.00914389 0.00457194 0.999990i \(-0.498545\pi\)
0.00457194 + 0.999990i \(0.498545\pi\)
\(264\) 0 0
\(265\) 2074.00 0.480773
\(266\) 2254.00 0.519555
\(267\) 0 0
\(268\) −332.000 −0.0756721
\(269\) −2494.00 −0.565286 −0.282643 0.959225i \(-0.591211\pi\)
−0.282643 + 0.959225i \(0.591211\pi\)
\(270\) 0 0
\(271\) −1681.00 −0.376803 −0.188401 0.982092i \(-0.560331\pi\)
−0.188401 + 0.982092i \(0.560331\pi\)
\(272\) 1664.00 0.370937
\(273\) 0 0
\(274\) −3448.00 −0.760224
\(275\) 1804.00 0.395583
\(276\) 0 0
\(277\) 272.000 0.0589996 0.0294998 0.999565i \(-0.490609\pi\)
0.0294998 + 0.999565i \(0.490609\pi\)
\(278\) −5032.00 −1.08561
\(279\) 0 0
\(280\) −952.000 −0.203189
\(281\) −1813.00 −0.384892 −0.192446 0.981308i \(-0.561642\pi\)
−0.192446 + 0.981308i \(0.561642\pi\)
\(282\) 0 0
\(283\) −2513.00 −0.527853 −0.263926 0.964543i \(-0.585018\pi\)
−0.263926 + 0.964543i \(0.585018\pi\)
\(284\) −720.000 −0.150437
\(285\) 0 0
\(286\) 462.000 0.0955197
\(287\) 756.000 0.155489
\(288\) 0 0
\(289\) 5903.00 1.20151
\(290\) 306.000 0.0619619
\(291\) 0 0
\(292\) 708.000 0.141892
\(293\) 7648.00 1.52492 0.762459 0.647037i \(-0.223992\pi\)
0.762459 + 0.647037i \(0.223992\pi\)
\(294\) 0 0
\(295\) −9129.00 −1.80173
\(296\) 2904.00 0.570242
\(297\) 0 0
\(298\) −502.000 −0.0975842
\(299\) 4074.00 0.787978
\(300\) 0 0
\(301\) −2702.00 −0.517411
\(302\) −6080.00 −1.15849
\(303\) 0 0
\(304\) −2576.00 −0.485999
\(305\) −16150.0 −3.03196
\(306\) 0 0
\(307\) −5444.00 −1.01207 −0.506035 0.862513i \(-0.668889\pi\)
−0.506035 + 0.862513i \(0.668889\pi\)
\(308\) 308.000 0.0569803
\(309\) 0 0
\(310\) 6120.00 1.12127
\(311\) 3400.00 0.619924 0.309962 0.950749i \(-0.399684\pi\)
0.309962 + 0.950749i \(0.399684\pi\)
\(312\) 0 0
\(313\) −7348.00 −1.32694 −0.663472 0.748201i \(-0.730918\pi\)
−0.663472 + 0.748201i \(0.730918\pi\)
\(314\) 992.000 0.178286
\(315\) 0 0
\(316\) −880.000 −0.156658
\(317\) 486.000 0.0861088 0.0430544 0.999073i \(-0.486291\pi\)
0.0430544 + 0.999073i \(0.486291\pi\)
\(318\) 0 0
\(319\) −99.0000 −0.0173760
\(320\) 1088.00 0.190066
\(321\) 0 0
\(322\) 2716.00 0.470052
\(323\) −16744.0 −2.88440
\(324\) 0 0
\(325\) −3444.00 −0.587812
\(326\) 2518.00 0.427789
\(327\) 0 0
\(328\) −864.000 −0.145446
\(329\) −2331.00 −0.390615
\(330\) 0 0
\(331\) −4468.00 −0.741944 −0.370972 0.928644i \(-0.620975\pi\)
−0.370972 + 0.928644i \(0.620975\pi\)
\(332\) −4448.00 −0.735288
\(333\) 0 0
\(334\) −4260.00 −0.697895
\(335\) −1411.00 −0.230123
\(336\) 0 0
\(337\) 450.000 0.0727391 0.0363695 0.999338i \(-0.488421\pi\)
0.0363695 + 0.999338i \(0.488421\pi\)
\(338\) 3512.00 0.565170
\(339\) 0 0
\(340\) 7072.00 1.12804
\(341\) −1980.00 −0.314437
\(342\) 0 0
\(343\) 343.000 0.0539949
\(344\) 3088.00 0.483994
\(345\) 0 0
\(346\) 1976.00 0.307024
\(347\) 11288.0 1.74632 0.873158 0.487437i \(-0.162068\pi\)
0.873158 + 0.487437i \(0.162068\pi\)
\(348\) 0 0
\(349\) −11121.0 −1.70571 −0.852856 0.522146i \(-0.825132\pi\)
−0.852856 + 0.522146i \(0.825132\pi\)
\(350\) −2296.00 −0.350647
\(351\) 0 0
\(352\) −352.000 −0.0533002
\(353\) −8853.00 −1.33484 −0.667419 0.744683i \(-0.732601\pi\)
−0.667419 + 0.744683i \(0.732601\pi\)
\(354\) 0 0
\(355\) −3060.00 −0.457487
\(356\) 1576.00 0.234629
\(357\) 0 0
\(358\) 8552.00 1.26253
\(359\) 5400.00 0.793875 0.396937 0.917846i \(-0.370073\pi\)
0.396937 + 0.917846i \(0.370073\pi\)
\(360\) 0 0
\(361\) 19062.0 2.77912
\(362\) −740.000 −0.107441
\(363\) 0 0
\(364\) −588.000 −0.0846692
\(365\) 3009.00 0.431502
\(366\) 0 0
\(367\) 8570.00 1.21894 0.609469 0.792810i \(-0.291383\pi\)
0.609469 + 0.792810i \(0.291383\pi\)
\(368\) −3104.00 −0.439693
\(369\) 0 0
\(370\) 12342.0 1.73414
\(371\) 854.000 0.119508
\(372\) 0 0
\(373\) 12244.0 1.69965 0.849826 0.527063i \(-0.176707\pi\)
0.849826 + 0.527063i \(0.176707\pi\)
\(374\) −2288.00 −0.316336
\(375\) 0 0
\(376\) 2664.00 0.365386
\(377\) 189.000 0.0258196
\(378\) 0 0
\(379\) 323.000 0.0437768 0.0218884 0.999760i \(-0.493032\pi\)
0.0218884 + 0.999760i \(0.493032\pi\)
\(380\) −10948.0 −1.47795
\(381\) 0 0
\(382\) −6768.00 −0.906495
\(383\) 6920.00 0.923226 0.461613 0.887081i \(-0.347271\pi\)
0.461613 + 0.887081i \(0.347271\pi\)
\(384\) 0 0
\(385\) 1309.00 0.173280
\(386\) 5788.00 0.763216
\(387\) 0 0
\(388\) 3304.00 0.432307
\(389\) 5388.00 0.702268 0.351134 0.936325i \(-0.385796\pi\)
0.351134 + 0.936325i \(0.385796\pi\)
\(390\) 0 0
\(391\) −20176.0 −2.60958
\(392\) −392.000 −0.0505076
\(393\) 0 0
\(394\) 5308.00 0.678714
\(395\) −3740.00 −0.476405
\(396\) 0 0
\(397\) −12392.0 −1.56659 −0.783296 0.621650i \(-0.786463\pi\)
−0.783296 + 0.621650i \(0.786463\pi\)
\(398\) 8228.00 1.03626
\(399\) 0 0
\(400\) 2624.00 0.328000
\(401\) 3826.00 0.476462 0.238231 0.971209i \(-0.423432\pi\)
0.238231 + 0.971209i \(0.423432\pi\)
\(402\) 0 0
\(403\) 3780.00 0.467234
\(404\) 6752.00 0.831496
\(405\) 0 0
\(406\) 126.000 0.0154022
\(407\) −3993.00 −0.486304
\(408\) 0 0
\(409\) −7094.00 −0.857642 −0.428821 0.903389i \(-0.641071\pi\)
−0.428821 + 0.903389i \(0.641071\pi\)
\(410\) −3672.00 −0.442310
\(411\) 0 0
\(412\) 5352.00 0.639986
\(413\) −3759.00 −0.447865
\(414\) 0 0
\(415\) −18904.0 −2.23605
\(416\) 672.000 0.0792007
\(417\) 0 0
\(418\) 3542.00 0.414461
\(419\) −8283.00 −0.965754 −0.482877 0.875688i \(-0.660408\pi\)
−0.482877 + 0.875688i \(0.660408\pi\)
\(420\) 0 0
\(421\) 7043.00 0.815332 0.407666 0.913131i \(-0.366343\pi\)
0.407666 + 0.913131i \(0.366343\pi\)
\(422\) −940.000 −0.108432
\(423\) 0 0
\(424\) −976.000 −0.111790
\(425\) 17056.0 1.94668
\(426\) 0 0
\(427\) −6650.00 −0.753668
\(428\) 2140.00 0.241684
\(429\) 0 0
\(430\) 13124.0 1.47185
\(431\) 16623.0 1.85778 0.928888 0.370360i \(-0.120766\pi\)
0.928888 + 0.370360i \(0.120766\pi\)
\(432\) 0 0
\(433\) 6896.00 0.765359 0.382680 0.923881i \(-0.375001\pi\)
0.382680 + 0.923881i \(0.375001\pi\)
\(434\) 2520.00 0.278719
\(435\) 0 0
\(436\) 864.000 0.0949039
\(437\) 31234.0 3.41905
\(438\) 0 0
\(439\) −15809.0 −1.71873 −0.859365 0.511363i \(-0.829141\pi\)
−0.859365 + 0.511363i \(0.829141\pi\)
\(440\) −1496.00 −0.162089
\(441\) 0 0
\(442\) 4368.00 0.470056
\(443\) 628.000 0.0673526 0.0336763 0.999433i \(-0.489278\pi\)
0.0336763 + 0.999433i \(0.489278\pi\)
\(444\) 0 0
\(445\) 6698.00 0.713518
\(446\) −5916.00 −0.628096
\(447\) 0 0
\(448\) 448.000 0.0472456
\(449\) −6616.00 −0.695386 −0.347693 0.937608i \(-0.613035\pi\)
−0.347693 + 0.937608i \(0.613035\pi\)
\(450\) 0 0
\(451\) 1188.00 0.124037
\(452\) −2008.00 −0.208957
\(453\) 0 0
\(454\) 9756.00 1.00853
\(455\) −2499.00 −0.257483
\(456\) 0 0
\(457\) −7238.00 −0.740874 −0.370437 0.928858i \(-0.620792\pi\)
−0.370437 + 0.928858i \(0.620792\pi\)
\(458\) 13076.0 1.33406
\(459\) 0 0
\(460\) −13192.0 −1.33713
\(461\) 7400.00 0.747619 0.373810 0.927506i \(-0.378051\pi\)
0.373810 + 0.927506i \(0.378051\pi\)
\(462\) 0 0
\(463\) −18447.0 −1.85163 −0.925815 0.377977i \(-0.876620\pi\)
−0.925815 + 0.377977i \(0.876620\pi\)
\(464\) −144.000 −0.0144074
\(465\) 0 0
\(466\) −6524.00 −0.648537
\(467\) −12393.0 −1.22801 −0.614004 0.789303i \(-0.710442\pi\)
−0.614004 + 0.789303i \(0.710442\pi\)
\(468\) 0 0
\(469\) −581.000 −0.0572027
\(470\) 11322.0 1.11116
\(471\) 0 0
\(472\) 4296.00 0.418939
\(473\) −4246.00 −0.412751
\(474\) 0 0
\(475\) −26404.0 −2.55052
\(476\) 2912.00 0.280402
\(477\) 0 0
\(478\) −5218.00 −0.499301
\(479\) −2628.00 −0.250681 −0.125341 0.992114i \(-0.540002\pi\)
−0.125341 + 0.992114i \(0.540002\pi\)
\(480\) 0 0
\(481\) 7623.00 0.722617
\(482\) −13118.0 −1.23964
\(483\) 0 0
\(484\) 484.000 0.0454545
\(485\) 14042.0 1.31467
\(486\) 0 0
\(487\) −6712.00 −0.624537 −0.312269 0.949994i \(-0.601089\pi\)
−0.312269 + 0.949994i \(0.601089\pi\)
\(488\) 7600.00 0.704991
\(489\) 0 0
\(490\) −1666.00 −0.153596
\(491\) 5423.00 0.498445 0.249223 0.968446i \(-0.419825\pi\)
0.249223 + 0.968446i \(0.419825\pi\)
\(492\) 0 0
\(493\) −936.000 −0.0855077
\(494\) −6762.00 −0.615864
\(495\) 0 0
\(496\) −2880.00 −0.260717
\(497\) −1260.00 −0.113720
\(498\) 0 0
\(499\) −709.000 −0.0636056 −0.0318028 0.999494i \(-0.510125\pi\)
−0.0318028 + 0.999494i \(0.510125\pi\)
\(500\) 2652.00 0.237202
\(501\) 0 0
\(502\) −5410.00 −0.480996
\(503\) −3118.00 −0.276391 −0.138196 0.990405i \(-0.544130\pi\)
−0.138196 + 0.990405i \(0.544130\pi\)
\(504\) 0 0
\(505\) 28696.0 2.52862
\(506\) 4268.00 0.374972
\(507\) 0 0
\(508\) 7008.00 0.612066
\(509\) −6214.00 −0.541121 −0.270561 0.962703i \(-0.587209\pi\)
−0.270561 + 0.962703i \(0.587209\pi\)
\(510\) 0 0
\(511\) 1239.00 0.107261
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) 5990.00 0.514023
\(515\) 22746.0 1.94623
\(516\) 0 0
\(517\) −3663.00 −0.311603
\(518\) 5082.00 0.431062
\(519\) 0 0
\(520\) 2856.00 0.240854
\(521\) 4377.00 0.368061 0.184031 0.982921i \(-0.441085\pi\)
0.184031 + 0.982921i \(0.441085\pi\)
\(522\) 0 0
\(523\) 701.000 0.0586092 0.0293046 0.999571i \(-0.490671\pi\)
0.0293046 + 0.999571i \(0.490671\pi\)
\(524\) 448.000 0.0373492
\(525\) 0 0
\(526\) −78.0000 −0.00646571
\(527\) −18720.0 −1.54735
\(528\) 0 0
\(529\) 25469.0 2.09329
\(530\) −4148.00 −0.339958
\(531\) 0 0
\(532\) −4508.00 −0.367381
\(533\) −2268.00 −0.184311
\(534\) 0 0
\(535\) 9095.00 0.734974
\(536\) 664.000 0.0535083
\(537\) 0 0
\(538\) 4988.00 0.399717
\(539\) 539.000 0.0430730
\(540\) 0 0
\(541\) −6668.00 −0.529907 −0.264954 0.964261i \(-0.585357\pi\)
−0.264954 + 0.964261i \(0.585357\pi\)
\(542\) 3362.00 0.266440
\(543\) 0 0
\(544\) −3328.00 −0.262292
\(545\) 3672.00 0.288608
\(546\) 0 0
\(547\) 10628.0 0.830750 0.415375 0.909650i \(-0.363650\pi\)
0.415375 + 0.909650i \(0.363650\pi\)
\(548\) 6896.00 0.537559
\(549\) 0 0
\(550\) −3608.00 −0.279719
\(551\) 1449.00 0.112032
\(552\) 0 0
\(553\) −1540.00 −0.118422
\(554\) −544.000 −0.0417190
\(555\) 0 0
\(556\) 10064.0 0.767641
\(557\) 1191.00 0.0906002 0.0453001 0.998973i \(-0.485576\pi\)
0.0453001 + 0.998973i \(0.485576\pi\)
\(558\) 0 0
\(559\) 8106.00 0.613322
\(560\) 1904.00 0.143676
\(561\) 0 0
\(562\) 3626.00 0.272159
\(563\) 550.000 0.0411718 0.0205859 0.999788i \(-0.493447\pi\)
0.0205859 + 0.999788i \(0.493447\pi\)
\(564\) 0 0
\(565\) −8534.00 −0.635448
\(566\) 5026.00 0.373248
\(567\) 0 0
\(568\) 1440.00 0.106375
\(569\) 8074.00 0.594868 0.297434 0.954742i \(-0.403869\pi\)
0.297434 + 0.954742i \(0.403869\pi\)
\(570\) 0 0
\(571\) 1264.00 0.0926388 0.0463194 0.998927i \(-0.485251\pi\)
0.0463194 + 0.998927i \(0.485251\pi\)
\(572\) −924.000 −0.0675426
\(573\) 0 0
\(574\) −1512.00 −0.109947
\(575\) −31816.0 −2.30751
\(576\) 0 0
\(577\) 12764.0 0.920922 0.460461 0.887680i \(-0.347684\pi\)
0.460461 + 0.887680i \(0.347684\pi\)
\(578\) −11806.0 −0.849593
\(579\) 0 0
\(580\) −612.000 −0.0438136
\(581\) −7784.00 −0.555826
\(582\) 0 0
\(583\) 1342.00 0.0953344
\(584\) −1416.00 −0.100333
\(585\) 0 0
\(586\) −15296.0 −1.07828
\(587\) 1821.00 0.128042 0.0640211 0.997949i \(-0.479608\pi\)
0.0640211 + 0.997949i \(0.479608\pi\)
\(588\) 0 0
\(589\) 28980.0 2.02733
\(590\) 18258.0 1.27402
\(591\) 0 0
\(592\) −5808.00 −0.403222
\(593\) 16284.0 1.12766 0.563831 0.825890i \(-0.309327\pi\)
0.563831 + 0.825890i \(0.309327\pi\)
\(594\) 0 0
\(595\) 12376.0 0.852717
\(596\) 1004.00 0.0690024
\(597\) 0 0
\(598\) −8148.00 −0.557185
\(599\) −14508.0 −0.989617 −0.494809 0.869002i \(-0.664762\pi\)
−0.494809 + 0.869002i \(0.664762\pi\)
\(600\) 0 0
\(601\) −10607.0 −0.719914 −0.359957 0.932969i \(-0.617209\pi\)
−0.359957 + 0.932969i \(0.617209\pi\)
\(602\) 5404.00 0.365865
\(603\) 0 0
\(604\) 12160.0 0.819178
\(605\) 2057.00 0.138230
\(606\) 0 0
\(607\) 26707.0 1.78584 0.892919 0.450217i \(-0.148653\pi\)
0.892919 + 0.450217i \(0.148653\pi\)
\(608\) 5152.00 0.343653
\(609\) 0 0
\(610\) 32300.0 2.14392
\(611\) 6993.00 0.463022
\(612\) 0 0
\(613\) −10848.0 −0.714758 −0.357379 0.933959i \(-0.616330\pi\)
−0.357379 + 0.933959i \(0.616330\pi\)
\(614\) 10888.0 0.715642
\(615\) 0 0
\(616\) −616.000 −0.0402911
\(617\) −2974.00 −0.194050 −0.0970249 0.995282i \(-0.530933\pi\)
−0.0970249 + 0.995282i \(0.530933\pi\)
\(618\) 0 0
\(619\) 6776.00 0.439985 0.219992 0.975502i \(-0.429397\pi\)
0.219992 + 0.975502i \(0.429397\pi\)
\(620\) −12240.0 −0.792855
\(621\) 0 0
\(622\) −6800.00 −0.438352
\(623\) 2758.00 0.177363
\(624\) 0 0
\(625\) −9229.00 −0.590656
\(626\) 14696.0 0.938291
\(627\) 0 0
\(628\) −1984.00 −0.126067
\(629\) −37752.0 −2.39312
\(630\) 0 0
\(631\) −29600.0 −1.86744 −0.933722 0.357998i \(-0.883459\pi\)
−0.933722 + 0.357998i \(0.883459\pi\)
\(632\) 1760.00 0.110774
\(633\) 0 0
\(634\) −972.000 −0.0608881
\(635\) 29784.0 1.86133
\(636\) 0 0
\(637\) −1029.00 −0.0640039
\(638\) 198.000 0.0122867
\(639\) 0 0
\(640\) −2176.00 −0.134397
\(641\) −7200.00 −0.443655 −0.221828 0.975086i \(-0.571202\pi\)
−0.221828 + 0.975086i \(0.571202\pi\)
\(642\) 0 0
\(643\) −25246.0 −1.54837 −0.774187 0.632956i \(-0.781841\pi\)
−0.774187 + 0.632956i \(0.781841\pi\)
\(644\) −5432.00 −0.332377
\(645\) 0 0
\(646\) 33488.0 2.03958
\(647\) 28181.0 1.71238 0.856190 0.516662i \(-0.172825\pi\)
0.856190 + 0.516662i \(0.172825\pi\)
\(648\) 0 0
\(649\) −5907.00 −0.357273
\(650\) 6888.00 0.415646
\(651\) 0 0
\(652\) −5036.00 −0.302492
\(653\) 2664.00 0.159648 0.0798242 0.996809i \(-0.474564\pi\)
0.0798242 + 0.996809i \(0.474564\pi\)
\(654\) 0 0
\(655\) 1904.00 0.113581
\(656\) 1728.00 0.102846
\(657\) 0 0
\(658\) 4662.00 0.276206
\(659\) −2205.00 −0.130341 −0.0651704 0.997874i \(-0.520759\pi\)
−0.0651704 + 0.997874i \(0.520759\pi\)
\(660\) 0 0
\(661\) −10770.0 −0.633743 −0.316872 0.948468i \(-0.602632\pi\)
−0.316872 + 0.948468i \(0.602632\pi\)
\(662\) 8936.00 0.524634
\(663\) 0 0
\(664\) 8896.00 0.519927
\(665\) −19159.0 −1.11722
\(666\) 0 0
\(667\) 1746.00 0.101357
\(668\) 8520.00 0.493486
\(669\) 0 0
\(670\) 2822.00 0.162721
\(671\) −10450.0 −0.601219
\(672\) 0 0
\(673\) −274.000 −0.0156938 −0.00784690 0.999969i \(-0.502498\pi\)
−0.00784690 + 0.999969i \(0.502498\pi\)
\(674\) −900.000 −0.0514343
\(675\) 0 0
\(676\) −7024.00 −0.399636
\(677\) −3290.00 −0.186772 −0.0933862 0.995630i \(-0.529769\pi\)
−0.0933862 + 0.995630i \(0.529769\pi\)
\(678\) 0 0
\(679\) 5782.00 0.326794
\(680\) −14144.0 −0.797644
\(681\) 0 0
\(682\) 3960.00 0.222341
\(683\) −24780.0 −1.38826 −0.694129 0.719851i \(-0.744210\pi\)
−0.694129 + 0.719851i \(0.744210\pi\)
\(684\) 0 0
\(685\) 29308.0 1.63475
\(686\) −686.000 −0.0381802
\(687\) 0 0
\(688\) −6176.00 −0.342235
\(689\) −2562.00 −0.141661
\(690\) 0 0
\(691\) 4014.00 0.220984 0.110492 0.993877i \(-0.464757\pi\)
0.110492 + 0.993877i \(0.464757\pi\)
\(692\) −3952.00 −0.217099
\(693\) 0 0
\(694\) −22576.0 −1.23483
\(695\) 42772.0 2.33444
\(696\) 0 0
\(697\) 11232.0 0.610391
\(698\) 22242.0 1.20612
\(699\) 0 0
\(700\) 4592.00 0.247945
\(701\) −27378.0 −1.47511 −0.737555 0.675287i \(-0.764020\pi\)
−0.737555 + 0.675287i \(0.764020\pi\)
\(702\) 0 0
\(703\) 58443.0 3.13545
\(704\) 704.000 0.0376889
\(705\) 0 0
\(706\) 17706.0 0.943873
\(707\) 11816.0 0.628552
\(708\) 0 0
\(709\) −11289.0 −0.597979 −0.298990 0.954256i \(-0.596650\pi\)
−0.298990 + 0.954256i \(0.596650\pi\)
\(710\) 6120.00 0.323492
\(711\) 0 0
\(712\) −3152.00 −0.165908
\(713\) 34920.0 1.83417
\(714\) 0 0
\(715\) −3927.00 −0.205401
\(716\) −17104.0 −0.892746
\(717\) 0 0
\(718\) −10800.0 −0.561354
\(719\) 21573.0 1.11897 0.559483 0.828842i \(-0.311000\pi\)
0.559483 + 0.828842i \(0.311000\pi\)
\(720\) 0 0
\(721\) 9366.00 0.483784
\(722\) −38124.0 −1.96514
\(723\) 0 0
\(724\) 1480.00 0.0759721
\(725\) −1476.00 −0.0756100
\(726\) 0 0
\(727\) 31590.0 1.61157 0.805783 0.592211i \(-0.201745\pi\)
0.805783 + 0.592211i \(0.201745\pi\)
\(728\) 1176.00 0.0598701
\(729\) 0 0
\(730\) −6018.00 −0.305118
\(731\) −40144.0 −2.03116
\(732\) 0 0
\(733\) −27814.0 −1.40155 −0.700773 0.713384i \(-0.747162\pi\)
−0.700773 + 0.713384i \(0.747162\pi\)
\(734\) −17140.0 −0.861920
\(735\) 0 0
\(736\) 6208.00 0.310910
\(737\) −913.000 −0.0456320
\(738\) 0 0
\(739\) −4942.00 −0.246001 −0.123000 0.992407i \(-0.539252\pi\)
−0.123000 + 0.992407i \(0.539252\pi\)
\(740\) −24684.0 −1.22622
\(741\) 0 0
\(742\) −1708.00 −0.0845049
\(743\) −17897.0 −0.883684 −0.441842 0.897093i \(-0.645675\pi\)
−0.441842 + 0.897093i \(0.645675\pi\)
\(744\) 0 0
\(745\) 4267.00 0.209840
\(746\) −24488.0 −1.20184
\(747\) 0 0
\(748\) 4576.00 0.223683
\(749\) 3745.00 0.182696
\(750\) 0 0
\(751\) −2443.00 −0.118704 −0.0593518 0.998237i \(-0.518903\pi\)
−0.0593518 + 0.998237i \(0.518903\pi\)
\(752\) −5328.00 −0.258367
\(753\) 0 0
\(754\) −378.000 −0.0182572
\(755\) 51680.0 2.49116
\(756\) 0 0
\(757\) 16589.0 0.796483 0.398241 0.917281i \(-0.369621\pi\)
0.398241 + 0.917281i \(0.369621\pi\)
\(758\) −646.000 −0.0309549
\(759\) 0 0
\(760\) 21896.0 1.04507
\(761\) −17040.0 −0.811695 −0.405847 0.913941i \(-0.633024\pi\)
−0.405847 + 0.913941i \(0.633024\pi\)
\(762\) 0 0
\(763\) 1512.00 0.0717406
\(764\) 13536.0 0.640989
\(765\) 0 0
\(766\) −13840.0 −0.652819
\(767\) 11277.0 0.530885
\(768\) 0 0
\(769\) 23527.0 1.10326 0.551629 0.834090i \(-0.314006\pi\)
0.551629 + 0.834090i \(0.314006\pi\)
\(770\) −2618.00 −0.122527
\(771\) 0 0
\(772\) −11576.0 −0.539675
\(773\) −16287.0 −0.757830 −0.378915 0.925431i \(-0.623703\pi\)
−0.378915 + 0.925431i \(0.623703\pi\)
\(774\) 0 0
\(775\) −29520.0 −1.36824
\(776\) −6608.00 −0.305687
\(777\) 0 0
\(778\) −10776.0 −0.496579
\(779\) −17388.0 −0.799730
\(780\) 0 0
\(781\) −1980.00 −0.0907170
\(782\) 40352.0 1.84525
\(783\) 0 0
\(784\) 784.000 0.0357143
\(785\) −8432.00 −0.383377
\(786\) 0 0
\(787\) 31753.0 1.43821 0.719106 0.694901i \(-0.244552\pi\)
0.719106 + 0.694901i \(0.244552\pi\)
\(788\) −10616.0 −0.479923
\(789\) 0 0
\(790\) 7480.00 0.336869
\(791\) −3514.00 −0.157956
\(792\) 0 0
\(793\) 19950.0 0.893374
\(794\) 24784.0 1.10775
\(795\) 0 0
\(796\) −16456.0 −0.732748
\(797\) 12879.0 0.572393 0.286197 0.958171i \(-0.407609\pi\)
0.286197 + 0.958171i \(0.407609\pi\)
\(798\) 0 0
\(799\) −34632.0 −1.53341
\(800\) −5248.00 −0.231931
\(801\) 0 0
\(802\) −7652.00 −0.336910
\(803\) 1947.00 0.0855643
\(804\) 0 0
\(805\) −23086.0 −1.01078
\(806\) −7560.00 −0.330384
\(807\) 0 0
\(808\) −13504.0 −0.587957
\(809\) −7601.00 −0.330330 −0.165165 0.986266i \(-0.552816\pi\)
−0.165165 + 0.986266i \(0.552816\pi\)
\(810\) 0 0
\(811\) −28363.0 −1.22806 −0.614032 0.789281i \(-0.710453\pi\)
−0.614032 + 0.789281i \(0.710453\pi\)
\(812\) −252.000 −0.0108910
\(813\) 0 0
\(814\) 7986.00 0.343869
\(815\) −21403.0 −0.919895
\(816\) 0 0
\(817\) 62146.0 2.66122
\(818\) 14188.0 0.606445
\(819\) 0 0
\(820\) 7344.00 0.312760
\(821\) 13369.0 0.568309 0.284154 0.958779i \(-0.408287\pi\)
0.284154 + 0.958779i \(0.408287\pi\)
\(822\) 0 0
\(823\) 5669.00 0.240108 0.120054 0.992767i \(-0.461693\pi\)
0.120054 + 0.992767i \(0.461693\pi\)
\(824\) −10704.0 −0.452538
\(825\) 0 0
\(826\) 7518.00 0.316688
\(827\) 20171.0 0.848143 0.424072 0.905629i \(-0.360600\pi\)
0.424072 + 0.905629i \(0.360600\pi\)
\(828\) 0 0
\(829\) 41152.0 1.72409 0.862043 0.506834i \(-0.169184\pi\)
0.862043 + 0.506834i \(0.169184\pi\)
\(830\) 37808.0 1.58113
\(831\) 0 0
\(832\) −1344.00 −0.0560034
\(833\) 5096.00 0.211964
\(834\) 0 0
\(835\) 36210.0 1.50072
\(836\) −7084.00 −0.293068
\(837\) 0 0
\(838\) 16566.0 0.682891
\(839\) 17091.0 0.703274 0.351637 0.936136i \(-0.385625\pi\)
0.351637 + 0.936136i \(0.385625\pi\)
\(840\) 0 0
\(841\) −24308.0 −0.996679
\(842\) −14086.0 −0.576527
\(843\) 0 0
\(844\) 1880.00 0.0766733
\(845\) −29852.0 −1.21531
\(846\) 0 0
\(847\) 847.000 0.0343604
\(848\) 1952.00 0.0790471
\(849\) 0 0
\(850\) −34112.0 −1.37651
\(851\) 70422.0 2.83670
\(852\) 0 0
\(853\) 37314.0 1.49778 0.748890 0.662694i \(-0.230587\pi\)
0.748890 + 0.662694i \(0.230587\pi\)
\(854\) 13300.0 0.532923
\(855\) 0 0
\(856\) −4280.00 −0.170896
\(857\) 14594.0 0.581705 0.290853 0.956768i \(-0.406061\pi\)
0.290853 + 0.956768i \(0.406061\pi\)
\(858\) 0 0
\(859\) 19024.0 0.755635 0.377818 0.925880i \(-0.376675\pi\)
0.377818 + 0.925880i \(0.376675\pi\)
\(860\) −26248.0 −1.04076
\(861\) 0 0
\(862\) −33246.0 −1.31365
\(863\) 2414.00 0.0952184 0.0476092 0.998866i \(-0.484840\pi\)
0.0476092 + 0.998866i \(0.484840\pi\)
\(864\) 0 0
\(865\) −16796.0 −0.660209
\(866\) −13792.0 −0.541191
\(867\) 0 0
\(868\) −5040.00 −0.197084
\(869\) −2420.00 −0.0944682
\(870\) 0 0
\(871\) 1743.00 0.0678063
\(872\) −1728.00 −0.0671072
\(873\) 0 0
\(874\) −62468.0 −2.41763
\(875\) 4641.00 0.179308
\(876\) 0 0
\(877\) 9756.00 0.375640 0.187820 0.982203i \(-0.439858\pi\)
0.187820 + 0.982203i \(0.439858\pi\)
\(878\) 31618.0 1.21533
\(879\) 0 0
\(880\) 2992.00 0.114614
\(881\) −31283.0 −1.19631 −0.598156 0.801380i \(-0.704100\pi\)
−0.598156 + 0.801380i \(0.704100\pi\)
\(882\) 0 0
\(883\) 11479.0 0.437485 0.218742 0.975783i \(-0.429805\pi\)
0.218742 + 0.975783i \(0.429805\pi\)
\(884\) −8736.00 −0.332379
\(885\) 0 0
\(886\) −1256.00 −0.0476254
\(887\) −33672.0 −1.27463 −0.637314 0.770604i \(-0.719955\pi\)
−0.637314 + 0.770604i \(0.719955\pi\)
\(888\) 0 0
\(889\) 12264.0 0.462679
\(890\) −13396.0 −0.504534
\(891\) 0 0
\(892\) 11832.0 0.444131
\(893\) 53613.0 2.00906
\(894\) 0 0
\(895\) −72692.0 −2.71489
\(896\) −896.000 −0.0334077
\(897\) 0 0
\(898\) 13232.0 0.491712
\(899\) 1620.00 0.0601001
\(900\) 0 0
\(901\) 12688.0 0.469144
\(902\) −2376.00 −0.0877075
\(903\) 0 0
\(904\) 4016.00 0.147755
\(905\) 6290.00 0.231035
\(906\) 0 0
\(907\) 39004.0 1.42790 0.713951 0.700196i \(-0.246904\pi\)
0.713951 + 0.700196i \(0.246904\pi\)
\(908\) −19512.0 −0.713137
\(909\) 0 0
\(910\) 4998.00 0.182068
\(911\) 5850.00 0.212754 0.106377 0.994326i \(-0.466075\pi\)
0.106377 + 0.994326i \(0.466075\pi\)
\(912\) 0 0
\(913\) −12232.0 −0.443396
\(914\) 14476.0 0.523877
\(915\) 0 0
\(916\) −26152.0 −0.943326
\(917\) 784.000 0.0282333
\(918\) 0 0
\(919\) −49054.0 −1.76076 −0.880382 0.474265i \(-0.842714\pi\)
−0.880382 + 0.474265i \(0.842714\pi\)
\(920\) 26384.0 0.945494
\(921\) 0 0
\(922\) −14800.0 −0.528646
\(923\) 3780.00 0.134800
\(924\) 0 0
\(925\) −59532.0 −2.11611
\(926\) 36894.0 1.30930
\(927\) 0 0
\(928\) 288.000 0.0101876
\(929\) 17799.0 0.628597 0.314298 0.949324i \(-0.398231\pi\)
0.314298 + 0.949324i \(0.398231\pi\)
\(930\) 0 0
\(931\) −7889.00 −0.277714
\(932\) 13048.0 0.458585
\(933\) 0 0
\(934\) 24786.0 0.868333
\(935\) 19448.0 0.680233
\(936\) 0 0
\(937\) −12938.0 −0.451084 −0.225542 0.974233i \(-0.572415\pi\)
−0.225542 + 0.974233i \(0.572415\pi\)
\(938\) 1162.00 0.0404484
\(939\) 0 0
\(940\) −22644.0 −0.785708
\(941\) 16200.0 0.561217 0.280608 0.959822i \(-0.409464\pi\)
0.280608 + 0.959822i \(0.409464\pi\)
\(942\) 0 0
\(943\) −20952.0 −0.723532
\(944\) −8592.00 −0.296235
\(945\) 0 0
\(946\) 8492.00 0.291859
\(947\) 28302.0 0.971163 0.485582 0.874191i \(-0.338608\pi\)
0.485582 + 0.874191i \(0.338608\pi\)
\(948\) 0 0
\(949\) −3717.00 −0.127143
\(950\) 52808.0 1.80349
\(951\) 0 0
\(952\) −5824.00 −0.198274
\(953\) 17787.0 0.604593 0.302297 0.953214i \(-0.402247\pi\)
0.302297 + 0.953214i \(0.402247\pi\)
\(954\) 0 0
\(955\) 57528.0 1.94928
\(956\) 10436.0 0.353059
\(957\) 0 0
\(958\) 5256.00 0.177259
\(959\) 12068.0 0.406357
\(960\) 0 0
\(961\) 2609.00 0.0875768
\(962\) −15246.0 −0.510968
\(963\) 0 0
\(964\) 26236.0 0.876561
\(965\) −49198.0 −1.64118
\(966\) 0 0
\(967\) −11990.0 −0.398731 −0.199365 0.979925i \(-0.563888\pi\)
−0.199365 + 0.979925i \(0.563888\pi\)
\(968\) −968.000 −0.0321412
\(969\) 0 0
\(970\) −28084.0 −0.929611
\(971\) −44763.0 −1.47942 −0.739708 0.672928i \(-0.765036\pi\)
−0.739708 + 0.672928i \(0.765036\pi\)
\(972\) 0 0
\(973\) 17612.0 0.580282
\(974\) 13424.0 0.441615
\(975\) 0 0
\(976\) −15200.0 −0.498504
\(977\) −49474.0 −1.62008 −0.810038 0.586378i \(-0.800553\pi\)
−0.810038 + 0.586378i \(0.800553\pi\)
\(978\) 0 0
\(979\) 4334.00 0.141486
\(980\) 3332.00 0.108609
\(981\) 0 0
\(982\) −10846.0 −0.352454
\(983\) 36276.0 1.17703 0.588517 0.808485i \(-0.299712\pi\)
0.588517 + 0.808485i \(0.299712\pi\)
\(984\) 0 0
\(985\) −45118.0 −1.45947
\(986\) 1872.00 0.0604631
\(987\) 0 0
\(988\) 13524.0 0.435482
\(989\) 74884.0 2.40766
\(990\) 0 0
\(991\) −47035.0 −1.50769 −0.753843 0.657055i \(-0.771802\pi\)
−0.753843 + 0.657055i \(0.771802\pi\)
\(992\) 5760.00 0.184355
\(993\) 0 0
\(994\) 2520.00 0.0804120
\(995\) −69938.0 −2.22833
\(996\) 0 0
\(997\) −20450.0 −0.649607 −0.324803 0.945782i \(-0.605298\pi\)
−0.324803 + 0.945782i \(0.605298\pi\)
\(998\) 1418.00 0.0449760
\(999\) 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.h.1.1 1
3.2 odd 2 462.4.a.h.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
462.4.a.h.1.1 1 3.2 odd 2
1386.4.a.h.1.1 1 1.1 even 1 trivial