Properties

Label 1638.4.a.b.1.1
Level $1638$
Weight $4$
Character 1638.1
Self dual yes
Analytic conductor $96.645$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1638.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(96.6451285894\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 546)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1638.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000 q^{2} +4.00000 q^{4} -9.00000 q^{5} -7.00000 q^{7} -8.00000 q^{8} +O(q^{10})\) \(q-2.00000 q^{2} +4.00000 q^{4} -9.00000 q^{5} -7.00000 q^{7} -8.00000 q^{8} +18.0000 q^{10} -62.0000 q^{11} -13.0000 q^{13} +14.0000 q^{14} +16.0000 q^{16} +16.0000 q^{17} +79.0000 q^{19} -36.0000 q^{20} +124.000 q^{22} +155.000 q^{23} -44.0000 q^{25} +26.0000 q^{26} -28.0000 q^{28} -51.0000 q^{29} +243.000 q^{31} -32.0000 q^{32} -32.0000 q^{34} +63.0000 q^{35} +412.000 q^{37} -158.000 q^{38} +72.0000 q^{40} +406.000 q^{41} -103.000 q^{43} -248.000 q^{44} -310.000 q^{46} -429.000 q^{47} +49.0000 q^{49} +88.0000 q^{50} -52.0000 q^{52} +169.000 q^{53} +558.000 q^{55} +56.0000 q^{56} +102.000 q^{58} -320.000 q^{59} -614.000 q^{61} -486.000 q^{62} +64.0000 q^{64} +117.000 q^{65} +258.000 q^{67} +64.0000 q^{68} -126.000 q^{70} +264.000 q^{71} -121.000 q^{73} -824.000 q^{74} +316.000 q^{76} +434.000 q^{77} -967.000 q^{79} -144.000 q^{80} -812.000 q^{82} +679.000 q^{83} -144.000 q^{85} +206.000 q^{86} +496.000 q^{88} -1059.00 q^{89} +91.0000 q^{91} +620.000 q^{92} +858.000 q^{94} -711.000 q^{95} -21.0000 q^{97} -98.0000 q^{98} +O(q^{100})\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 −0.707107
\(3\) 0 0
\(4\) 4.00000 0.500000
\(5\) −9.00000 −0.804984 −0.402492 0.915423i \(-0.631856\pi\)
−0.402492 + 0.915423i \(0.631856\pi\)
\(6\) 0 0
\(7\) −7.00000 −0.377964
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) 18.0000 0.569210
\(11\) −62.0000 −1.69943 −0.849714 0.527244i \(-0.823225\pi\)
−0.849714 + 0.527244i \(0.823225\pi\)
\(12\) 0 0
\(13\) −13.0000 −0.277350
\(14\) 14.0000 0.267261
\(15\) 0 0
\(16\) 16.0000 0.250000
\(17\) 16.0000 0.228269 0.114134 0.993465i \(-0.463591\pi\)
0.114134 + 0.993465i \(0.463591\pi\)
\(18\) 0 0
\(19\) 79.0000 0.953886 0.476943 0.878934i \(-0.341745\pi\)
0.476943 + 0.878934i \(0.341745\pi\)
\(20\) −36.0000 −0.402492
\(21\) 0 0
\(22\) 124.000 1.20168
\(23\) 155.000 1.40521 0.702603 0.711582i \(-0.252021\pi\)
0.702603 + 0.711582i \(0.252021\pi\)
\(24\) 0 0
\(25\) −44.0000 −0.352000
\(26\) 26.0000 0.196116
\(27\) 0 0
\(28\) −28.0000 −0.188982
\(29\) −51.0000 −0.326568 −0.163284 0.986579i \(-0.552209\pi\)
−0.163284 + 0.986579i \(0.552209\pi\)
\(30\) 0 0
\(31\) 243.000 1.40787 0.703937 0.710263i \(-0.251424\pi\)
0.703937 + 0.710263i \(0.251424\pi\)
\(32\) −32.0000 −0.176777
\(33\) 0 0
\(34\) −32.0000 −0.161410
\(35\) 63.0000 0.304256
\(36\) 0 0
\(37\) 412.000 1.83060 0.915302 0.402767i \(-0.131952\pi\)
0.915302 + 0.402767i \(0.131952\pi\)
\(38\) −158.000 −0.674500
\(39\) 0 0
\(40\) 72.0000 0.284605
\(41\) 406.000 1.54650 0.773251 0.634101i \(-0.218629\pi\)
0.773251 + 0.634101i \(0.218629\pi\)
\(42\) 0 0
\(43\) −103.000 −0.365287 −0.182644 0.983179i \(-0.558465\pi\)
−0.182644 + 0.983179i \(0.558465\pi\)
\(44\) −248.000 −0.849714
\(45\) 0 0
\(46\) −310.000 −0.993631
\(47\) −429.000 −1.33141 −0.665703 0.746217i \(-0.731868\pi\)
−0.665703 + 0.746217i \(0.731868\pi\)
\(48\) 0 0
\(49\) 49.0000 0.142857
\(50\) 88.0000 0.248902
\(51\) 0 0
\(52\) −52.0000 −0.138675
\(53\) 169.000 0.437999 0.218999 0.975725i \(-0.429721\pi\)
0.218999 + 0.975725i \(0.429721\pi\)
\(54\) 0 0
\(55\) 558.000 1.36801
\(56\) 56.0000 0.133631
\(57\) 0 0
\(58\) 102.000 0.230918
\(59\) −320.000 −0.706109 −0.353055 0.935603i \(-0.614857\pi\)
−0.353055 + 0.935603i \(0.614857\pi\)
\(60\) 0 0
\(61\) −614.000 −1.28876 −0.644382 0.764703i \(-0.722885\pi\)
−0.644382 + 0.764703i \(0.722885\pi\)
\(62\) −486.000 −0.995517
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 117.000 0.223263
\(66\) 0 0
\(67\) 258.000 0.470444 0.235222 0.971942i \(-0.424418\pi\)
0.235222 + 0.971942i \(0.424418\pi\)
\(68\) 64.0000 0.114134
\(69\) 0 0
\(70\) −126.000 −0.215141
\(71\) 264.000 0.441282 0.220641 0.975355i \(-0.429185\pi\)
0.220641 + 0.975355i \(0.429185\pi\)
\(72\) 0 0
\(73\) −121.000 −0.194000 −0.0969999 0.995284i \(-0.530925\pi\)
−0.0969999 + 0.995284i \(0.530925\pi\)
\(74\) −824.000 −1.29443
\(75\) 0 0
\(76\) 316.000 0.476943
\(77\) 434.000 0.642323
\(78\) 0 0
\(79\) −967.000 −1.37716 −0.688582 0.725158i \(-0.741767\pi\)
−0.688582 + 0.725158i \(0.741767\pi\)
\(80\) −144.000 −0.201246
\(81\) 0 0
\(82\) −812.000 −1.09354
\(83\) 679.000 0.897951 0.448975 0.893544i \(-0.351789\pi\)
0.448975 + 0.893544i \(0.351789\pi\)
\(84\) 0 0
\(85\) −144.000 −0.183753
\(86\) 206.000 0.258297
\(87\) 0 0
\(88\) 496.000 0.600838
\(89\) −1059.00 −1.26128 −0.630639 0.776076i \(-0.717207\pi\)
−0.630639 + 0.776076i \(0.717207\pi\)
\(90\) 0 0
\(91\) 91.0000 0.104828
\(92\) 620.000 0.702603
\(93\) 0 0
\(94\) 858.000 0.941446
\(95\) −711.000 −0.767864
\(96\) 0 0
\(97\) −21.0000 −0.0219817 −0.0109909 0.999940i \(-0.503499\pi\)
−0.0109909 + 0.999940i \(0.503499\pi\)
\(98\) −98.0000 −0.101015
\(99\) 0 0
\(100\) −176.000 −0.176000
\(101\) −894.000 −0.880756 −0.440378 0.897813i \(-0.645156\pi\)
−0.440378 + 0.897813i \(0.645156\pi\)
\(102\) 0 0
\(103\) 128.000 0.122449 0.0612243 0.998124i \(-0.480499\pi\)
0.0612243 + 0.998124i \(0.480499\pi\)
\(104\) 104.000 0.0980581
\(105\) 0 0
\(106\) −338.000 −0.309712
\(107\) 708.000 0.639672 0.319836 0.947473i \(-0.396372\pi\)
0.319836 + 0.947473i \(0.396372\pi\)
\(108\) 0 0
\(109\) 1238.00 1.08788 0.543940 0.839124i \(-0.316932\pi\)
0.543940 + 0.839124i \(0.316932\pi\)
\(110\) −1116.00 −0.967331
\(111\) 0 0
\(112\) −112.000 −0.0944911
\(113\) −1073.00 −0.893269 −0.446634 0.894717i \(-0.647377\pi\)
−0.446634 + 0.894717i \(0.647377\pi\)
\(114\) 0 0
\(115\) −1395.00 −1.13117
\(116\) −204.000 −0.163284
\(117\) 0 0
\(118\) 640.000 0.499295
\(119\) −112.000 −0.0862775
\(120\) 0 0
\(121\) 2513.00 1.88805
\(122\) 1228.00 0.911294
\(123\) 0 0
\(124\) 972.000 0.703937
\(125\) 1521.00 1.08834
\(126\) 0 0
\(127\) −1748.00 −1.22134 −0.610669 0.791886i \(-0.709099\pi\)
−0.610669 + 0.791886i \(0.709099\pi\)
\(128\) −128.000 −0.0883883
\(129\) 0 0
\(130\) −234.000 −0.157870
\(131\) 936.000 0.624265 0.312132 0.950039i \(-0.398957\pi\)
0.312132 + 0.950039i \(0.398957\pi\)
\(132\) 0 0
\(133\) −553.000 −0.360535
\(134\) −516.000 −0.332654
\(135\) 0 0
\(136\) −128.000 −0.0807052
\(137\) 1128.00 0.703442 0.351721 0.936105i \(-0.385597\pi\)
0.351721 + 0.936105i \(0.385597\pi\)
\(138\) 0 0
\(139\) −854.000 −0.521118 −0.260559 0.965458i \(-0.583907\pi\)
−0.260559 + 0.965458i \(0.583907\pi\)
\(140\) 252.000 0.152128
\(141\) 0 0
\(142\) −528.000 −0.312034
\(143\) 806.000 0.471336
\(144\) 0 0
\(145\) 459.000 0.262882
\(146\) 242.000 0.137179
\(147\) 0 0
\(148\) 1648.00 0.915302
\(149\) 442.000 0.243020 0.121510 0.992590i \(-0.461226\pi\)
0.121510 + 0.992590i \(0.461226\pi\)
\(150\) 0 0
\(151\) −1016.00 −0.547556 −0.273778 0.961793i \(-0.588273\pi\)
−0.273778 + 0.961793i \(0.588273\pi\)
\(152\) −632.000 −0.337250
\(153\) 0 0
\(154\) −868.000 −0.454191
\(155\) −2187.00 −1.13332
\(156\) 0 0
\(157\) −3880.00 −1.97234 −0.986171 0.165731i \(-0.947002\pi\)
−0.986171 + 0.165731i \(0.947002\pi\)
\(158\) 1934.00 0.973802
\(159\) 0 0
\(160\) 288.000 0.142302
\(161\) −1085.00 −0.531118
\(162\) 0 0
\(163\) −1604.00 −0.770767 −0.385383 0.922757i \(-0.625931\pi\)
−0.385383 + 0.922757i \(0.625931\pi\)
\(164\) 1624.00 0.773251
\(165\) 0 0
\(166\) −1358.00 −0.634947
\(167\) −959.000 −0.444369 −0.222185 0.975005i \(-0.571319\pi\)
−0.222185 + 0.975005i \(0.571319\pi\)
\(168\) 0 0
\(169\) 169.000 0.0769231
\(170\) 288.000 0.129933
\(171\) 0 0
\(172\) −412.000 −0.182644
\(173\) 488.000 0.214462 0.107231 0.994234i \(-0.465802\pi\)
0.107231 + 0.994234i \(0.465802\pi\)
\(174\) 0 0
\(175\) 308.000 0.133043
\(176\) −992.000 −0.424857
\(177\) 0 0
\(178\) 2118.00 0.891858
\(179\) −2533.00 −1.05768 −0.528842 0.848721i \(-0.677373\pi\)
−0.528842 + 0.848721i \(0.677373\pi\)
\(180\) 0 0
\(181\) −3626.00 −1.48905 −0.744526 0.667593i \(-0.767325\pi\)
−0.744526 + 0.667593i \(0.767325\pi\)
\(182\) −182.000 −0.0741249
\(183\) 0 0
\(184\) −1240.00 −0.496815
\(185\) −3708.00 −1.47361
\(186\) 0 0
\(187\) −992.000 −0.387926
\(188\) −1716.00 −0.665703
\(189\) 0 0
\(190\) 1422.00 0.542962
\(191\) 4992.00 1.89114 0.945572 0.325413i \(-0.105503\pi\)
0.945572 + 0.325413i \(0.105503\pi\)
\(192\) 0 0
\(193\) −470.000 −0.175292 −0.0876460 0.996152i \(-0.527934\pi\)
−0.0876460 + 0.996152i \(0.527934\pi\)
\(194\) 42.0000 0.0155434
\(195\) 0 0
\(196\) 196.000 0.0714286
\(197\) 3190.00 1.15370 0.576848 0.816852i \(-0.304283\pi\)
0.576848 + 0.816852i \(0.304283\pi\)
\(198\) 0 0
\(199\) 1944.00 0.692495 0.346248 0.938143i \(-0.387456\pi\)
0.346248 + 0.938143i \(0.387456\pi\)
\(200\) 352.000 0.124451
\(201\) 0 0
\(202\) 1788.00 0.622788
\(203\) 357.000 0.123431
\(204\) 0 0
\(205\) −3654.00 −1.24491
\(206\) −256.000 −0.0865843
\(207\) 0 0
\(208\) −208.000 −0.0693375
\(209\) −4898.00 −1.62106
\(210\) 0 0
\(211\) −1139.00 −0.371621 −0.185810 0.982586i \(-0.559491\pi\)
−0.185810 + 0.982586i \(0.559491\pi\)
\(212\) 676.000 0.218999
\(213\) 0 0
\(214\) −1416.00 −0.452317
\(215\) 927.000 0.294051
\(216\) 0 0
\(217\) −1701.00 −0.532126
\(218\) −2476.00 −0.769247
\(219\) 0 0
\(220\) 2232.00 0.684006
\(221\) −208.000 −0.0633104
\(222\) 0 0
\(223\) 833.000 0.250143 0.125071 0.992148i \(-0.460084\pi\)
0.125071 + 0.992148i \(0.460084\pi\)
\(224\) 224.000 0.0668153
\(225\) 0 0
\(226\) 2146.00 0.631636
\(227\) 3516.00 1.02804 0.514020 0.857778i \(-0.328156\pi\)
0.514020 + 0.857778i \(0.328156\pi\)
\(228\) 0 0
\(229\) 3222.00 0.929763 0.464882 0.885373i \(-0.346097\pi\)
0.464882 + 0.885373i \(0.346097\pi\)
\(230\) 2790.00 0.799857
\(231\) 0 0
\(232\) 408.000 0.115459
\(233\) 477.000 0.134117 0.0670586 0.997749i \(-0.478639\pi\)
0.0670586 + 0.997749i \(0.478639\pi\)
\(234\) 0 0
\(235\) 3861.00 1.07176
\(236\) −1280.00 −0.353055
\(237\) 0 0
\(238\) 224.000 0.0610074
\(239\) 6368.00 1.72348 0.861740 0.507350i \(-0.169375\pi\)
0.861740 + 0.507350i \(0.169375\pi\)
\(240\) 0 0
\(241\) 747.000 0.199662 0.0998309 0.995004i \(-0.468170\pi\)
0.0998309 + 0.995004i \(0.468170\pi\)
\(242\) −5026.00 −1.33506
\(243\) 0 0
\(244\) −2456.00 −0.644382
\(245\) −441.000 −0.114998
\(246\) 0 0
\(247\) −1027.00 −0.264561
\(248\) −1944.00 −0.497759
\(249\) 0 0
\(250\) −3042.00 −0.769572
\(251\) −7518.00 −1.89057 −0.945283 0.326252i \(-0.894214\pi\)
−0.945283 + 0.326252i \(0.894214\pi\)
\(252\) 0 0
\(253\) −9610.00 −2.38805
\(254\) 3496.00 0.863616
\(255\) 0 0
\(256\) 256.000 0.0625000
\(257\) −1094.00 −0.265532 −0.132766 0.991147i \(-0.542386\pi\)
−0.132766 + 0.991147i \(0.542386\pi\)
\(258\) 0 0
\(259\) −2884.00 −0.691904
\(260\) 468.000 0.111631
\(261\) 0 0
\(262\) −1872.00 −0.441422
\(263\) 1289.00 0.302217 0.151109 0.988517i \(-0.451716\pi\)
0.151109 + 0.988517i \(0.451716\pi\)
\(264\) 0 0
\(265\) −1521.00 −0.352582
\(266\) 1106.00 0.254937
\(267\) 0 0
\(268\) 1032.00 0.235222
\(269\) 2060.00 0.466916 0.233458 0.972367i \(-0.424996\pi\)
0.233458 + 0.972367i \(0.424996\pi\)
\(270\) 0 0
\(271\) 576.000 0.129113 0.0645563 0.997914i \(-0.479437\pi\)
0.0645563 + 0.997914i \(0.479437\pi\)
\(272\) 256.000 0.0570672
\(273\) 0 0
\(274\) −2256.00 −0.497409
\(275\) 2728.00 0.598199
\(276\) 0 0
\(277\) −5699.00 −1.23617 −0.618086 0.786110i \(-0.712092\pi\)
−0.618086 + 0.786110i \(0.712092\pi\)
\(278\) 1708.00 0.368486
\(279\) 0 0
\(280\) −504.000 −0.107571
\(281\) −4062.00 −0.862344 −0.431172 0.902270i \(-0.641900\pi\)
−0.431172 + 0.902270i \(0.641900\pi\)
\(282\) 0 0
\(283\) −772.000 −0.162158 −0.0810789 0.996708i \(-0.525837\pi\)
−0.0810789 + 0.996708i \(0.525837\pi\)
\(284\) 1056.00 0.220641
\(285\) 0 0
\(286\) −1612.00 −0.333285
\(287\) −2842.00 −0.584522
\(288\) 0 0
\(289\) −4657.00 −0.947893
\(290\) −918.000 −0.185886
\(291\) 0 0
\(292\) −484.000 −0.0969999
\(293\) −7833.00 −1.56180 −0.780902 0.624653i \(-0.785240\pi\)
−0.780902 + 0.624653i \(0.785240\pi\)
\(294\) 0 0
\(295\) 2880.00 0.568407
\(296\) −3296.00 −0.647217
\(297\) 0 0
\(298\) −884.000 −0.171841
\(299\) −2015.00 −0.389734
\(300\) 0 0
\(301\) 721.000 0.138066
\(302\) 2032.00 0.387180
\(303\) 0 0
\(304\) 1264.00 0.238472
\(305\) 5526.00 1.03744
\(306\) 0 0
\(307\) −2891.00 −0.537453 −0.268727 0.963217i \(-0.586603\pi\)
−0.268727 + 0.963217i \(0.586603\pi\)
\(308\) 1736.00 0.321162
\(309\) 0 0
\(310\) 4374.00 0.801376
\(311\) 3530.00 0.643627 0.321813 0.946803i \(-0.395708\pi\)
0.321813 + 0.946803i \(0.395708\pi\)
\(312\) 0 0
\(313\) 5490.00 0.991416 0.495708 0.868489i \(-0.334909\pi\)
0.495708 + 0.868489i \(0.334909\pi\)
\(314\) 7760.00 1.39466
\(315\) 0 0
\(316\) −3868.00 −0.688582
\(317\) 5636.00 0.998578 0.499289 0.866435i \(-0.333595\pi\)
0.499289 + 0.866435i \(0.333595\pi\)
\(318\) 0 0
\(319\) 3162.00 0.554978
\(320\) −576.000 −0.100623
\(321\) 0 0
\(322\) 2170.00 0.375557
\(323\) 1264.00 0.217743
\(324\) 0 0
\(325\) 572.000 0.0976272
\(326\) 3208.00 0.545014
\(327\) 0 0
\(328\) −3248.00 −0.546771
\(329\) 3003.00 0.503224
\(330\) 0 0
\(331\) −9962.00 −1.65426 −0.827131 0.562008i \(-0.810029\pi\)
−0.827131 + 0.562008i \(0.810029\pi\)
\(332\) 2716.00 0.448975
\(333\) 0 0
\(334\) 1918.00 0.314216
\(335\) −2322.00 −0.378700
\(336\) 0 0
\(337\) −11415.0 −1.84515 −0.922574 0.385821i \(-0.873918\pi\)
−0.922574 + 0.385821i \(0.873918\pi\)
\(338\) −338.000 −0.0543928
\(339\) 0 0
\(340\) −576.000 −0.0918764
\(341\) −15066.0 −2.39258
\(342\) 0 0
\(343\) −343.000 −0.0539949
\(344\) 824.000 0.129149
\(345\) 0 0
\(346\) −976.000 −0.151648
\(347\) −4864.00 −0.752488 −0.376244 0.926521i \(-0.622784\pi\)
−0.376244 + 0.926521i \(0.622784\pi\)
\(348\) 0 0
\(349\) −469.000 −0.0719341 −0.0359670 0.999353i \(-0.511451\pi\)
−0.0359670 + 0.999353i \(0.511451\pi\)
\(350\) −616.000 −0.0940760
\(351\) 0 0
\(352\) 1984.00 0.300419
\(353\) −4198.00 −0.632966 −0.316483 0.948598i \(-0.602502\pi\)
−0.316483 + 0.948598i \(0.602502\pi\)
\(354\) 0 0
\(355\) −2376.00 −0.355225
\(356\) −4236.00 −0.630639
\(357\) 0 0
\(358\) 5066.00 0.747895
\(359\) −3408.00 −0.501023 −0.250512 0.968114i \(-0.580599\pi\)
−0.250512 + 0.968114i \(0.580599\pi\)
\(360\) 0 0
\(361\) −618.000 −0.0901006
\(362\) 7252.00 1.05292
\(363\) 0 0
\(364\) 364.000 0.0524142
\(365\) 1089.00 0.156167
\(366\) 0 0
\(367\) −8290.00 −1.17911 −0.589557 0.807727i \(-0.700697\pi\)
−0.589557 + 0.807727i \(0.700697\pi\)
\(368\) 2480.00 0.351301
\(369\) 0 0
\(370\) 7416.00 1.04200
\(371\) −1183.00 −0.165548
\(372\) 0 0
\(373\) −9906.00 −1.37510 −0.687551 0.726136i \(-0.741314\pi\)
−0.687551 + 0.726136i \(0.741314\pi\)
\(374\) 1984.00 0.274305
\(375\) 0 0
\(376\) 3432.00 0.470723
\(377\) 663.000 0.0905736
\(378\) 0 0
\(379\) −9238.00 −1.25204 −0.626021 0.779806i \(-0.715318\pi\)
−0.626021 + 0.779806i \(0.715318\pi\)
\(380\) −2844.00 −0.383932
\(381\) 0 0
\(382\) −9984.00 −1.33724
\(383\) −4972.00 −0.663335 −0.331668 0.943396i \(-0.607611\pi\)
−0.331668 + 0.943396i \(0.607611\pi\)
\(384\) 0 0
\(385\) −3906.00 −0.517060
\(386\) 940.000 0.123950
\(387\) 0 0
\(388\) −84.0000 −0.0109909
\(389\) −7454.00 −0.971550 −0.485775 0.874084i \(-0.661462\pi\)
−0.485775 + 0.874084i \(0.661462\pi\)
\(390\) 0 0
\(391\) 2480.00 0.320765
\(392\) −392.000 −0.0505076
\(393\) 0 0
\(394\) −6380.00 −0.815786
\(395\) 8703.00 1.10860
\(396\) 0 0
\(397\) 7219.00 0.912623 0.456311 0.889820i \(-0.349170\pi\)
0.456311 + 0.889820i \(0.349170\pi\)
\(398\) −3888.00 −0.489668
\(399\) 0 0
\(400\) −704.000 −0.0880000
\(401\) −10772.0 −1.34147 −0.670733 0.741699i \(-0.734020\pi\)
−0.670733 + 0.741699i \(0.734020\pi\)
\(402\) 0 0
\(403\) −3159.00 −0.390474
\(404\) −3576.00 −0.440378
\(405\) 0 0
\(406\) −714.000 −0.0872789
\(407\) −25544.0 −3.11098
\(408\) 0 0
\(409\) 13151.0 1.58991 0.794957 0.606665i \(-0.207493\pi\)
0.794957 + 0.606665i \(0.207493\pi\)
\(410\) 7308.00 0.880284
\(411\) 0 0
\(412\) 512.000 0.0612243
\(413\) 2240.00 0.266884
\(414\) 0 0
\(415\) −6111.00 −0.722837
\(416\) 416.000 0.0490290
\(417\) 0 0
\(418\) 9796.00 1.14626
\(419\) −6034.00 −0.703533 −0.351766 0.936088i \(-0.614419\pi\)
−0.351766 + 0.936088i \(0.614419\pi\)
\(420\) 0 0
\(421\) 8864.00 1.02614 0.513070 0.858347i \(-0.328508\pi\)
0.513070 + 0.858347i \(0.328508\pi\)
\(422\) 2278.00 0.262776
\(423\) 0 0
\(424\) −1352.00 −0.154856
\(425\) −704.000 −0.0803506
\(426\) 0 0
\(427\) 4298.00 0.487107
\(428\) 2832.00 0.319836
\(429\) 0 0
\(430\) −1854.00 −0.207925
\(431\) 134.000 0.0149758 0.00748788 0.999972i \(-0.497617\pi\)
0.00748788 + 0.999972i \(0.497617\pi\)
\(432\) 0 0
\(433\) 12376.0 1.37356 0.686781 0.726864i \(-0.259023\pi\)
0.686781 + 0.726864i \(0.259023\pi\)
\(434\) 3402.00 0.376270
\(435\) 0 0
\(436\) 4952.00 0.543940
\(437\) 12245.0 1.34041
\(438\) 0 0
\(439\) 14198.0 1.54358 0.771792 0.635875i \(-0.219361\pi\)
0.771792 + 0.635875i \(0.219361\pi\)
\(440\) −4464.00 −0.483666
\(441\) 0 0
\(442\) 416.000 0.0447672
\(443\) −7657.00 −0.821208 −0.410604 0.911814i \(-0.634682\pi\)
−0.410604 + 0.911814i \(0.634682\pi\)
\(444\) 0 0
\(445\) 9531.00 1.01531
\(446\) −1666.00 −0.176878
\(447\) 0 0
\(448\) −448.000 −0.0472456
\(449\) −15500.0 −1.62915 −0.814577 0.580055i \(-0.803031\pi\)
−0.814577 + 0.580055i \(0.803031\pi\)
\(450\) 0 0
\(451\) −25172.0 −2.62817
\(452\) −4292.00 −0.446634
\(453\) 0 0
\(454\) −7032.00 −0.726934
\(455\) −819.000 −0.0843853
\(456\) 0 0
\(457\) 10184.0 1.04242 0.521212 0.853427i \(-0.325480\pi\)
0.521212 + 0.853427i \(0.325480\pi\)
\(458\) −6444.00 −0.657442
\(459\) 0 0
\(460\) −5580.00 −0.565584
\(461\) −19250.0 −1.94482 −0.972410 0.233279i \(-0.925054\pi\)
−0.972410 + 0.233279i \(0.925054\pi\)
\(462\) 0 0
\(463\) −15622.0 −1.56807 −0.784034 0.620717i \(-0.786841\pi\)
−0.784034 + 0.620717i \(0.786841\pi\)
\(464\) −816.000 −0.0816419
\(465\) 0 0
\(466\) −954.000 −0.0948352
\(467\) 15594.0 1.54519 0.772596 0.634898i \(-0.218958\pi\)
0.772596 + 0.634898i \(0.218958\pi\)
\(468\) 0 0
\(469\) −1806.00 −0.177811
\(470\) −7722.00 −0.757850
\(471\) 0 0
\(472\) 2560.00 0.249647
\(473\) 6386.00 0.620779
\(474\) 0 0
\(475\) −3476.00 −0.335768
\(476\) −448.000 −0.0431388
\(477\) 0 0
\(478\) −12736.0 −1.21868
\(479\) −3239.00 −0.308964 −0.154482 0.987996i \(-0.549371\pi\)
−0.154482 + 0.987996i \(0.549371\pi\)
\(480\) 0 0
\(481\) −5356.00 −0.507718
\(482\) −1494.00 −0.141182
\(483\) 0 0
\(484\) 10052.0 0.944027
\(485\) 189.000 0.0176949
\(486\) 0 0
\(487\) 1798.00 0.167300 0.0836501 0.996495i \(-0.473342\pi\)
0.0836501 + 0.996495i \(0.473342\pi\)
\(488\) 4912.00 0.455647
\(489\) 0 0
\(490\) 882.000 0.0813157
\(491\) −13708.0 −1.25995 −0.629973 0.776617i \(-0.716934\pi\)
−0.629973 + 0.776617i \(0.716934\pi\)
\(492\) 0 0
\(493\) −816.000 −0.0745452
\(494\) 2054.00 0.187073
\(495\) 0 0
\(496\) 3888.00 0.351968
\(497\) −1848.00 −0.166789
\(498\) 0 0
\(499\) −11936.0 −1.07080 −0.535400 0.844599i \(-0.679839\pi\)
−0.535400 + 0.844599i \(0.679839\pi\)
\(500\) 6084.00 0.544170
\(501\) 0 0
\(502\) 15036.0 1.33683
\(503\) −2562.00 −0.227105 −0.113553 0.993532i \(-0.536223\pi\)
−0.113553 + 0.993532i \(0.536223\pi\)
\(504\) 0 0
\(505\) 8046.00 0.708995
\(506\) 19220.0 1.68860
\(507\) 0 0
\(508\) −6992.00 −0.610669
\(509\) 8055.00 0.701437 0.350719 0.936481i \(-0.385937\pi\)
0.350719 + 0.936481i \(0.385937\pi\)
\(510\) 0 0
\(511\) 847.000 0.0733250
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) 2188.00 0.187760
\(515\) −1152.00 −0.0985693
\(516\) 0 0
\(517\) 26598.0 2.26263
\(518\) 5768.00 0.489250
\(519\) 0 0
\(520\) −936.000 −0.0789352
\(521\) 5980.00 0.502857 0.251429 0.967876i \(-0.419100\pi\)
0.251429 + 0.967876i \(0.419100\pi\)
\(522\) 0 0
\(523\) 19238.0 1.60845 0.804225 0.594325i \(-0.202581\pi\)
0.804225 + 0.594325i \(0.202581\pi\)
\(524\) 3744.00 0.312132
\(525\) 0 0
\(526\) −2578.00 −0.213700
\(527\) 3888.00 0.321374
\(528\) 0 0
\(529\) 11858.0 0.974603
\(530\) 3042.00 0.249313
\(531\) 0 0
\(532\) −2212.00 −0.180268
\(533\) −5278.00 −0.428922
\(534\) 0 0
\(535\) −6372.00 −0.514926
\(536\) −2064.00 −0.166327
\(537\) 0 0
\(538\) −4120.00 −0.330160
\(539\) −3038.00 −0.242775
\(540\) 0 0
\(541\) 13012.0 1.03407 0.517033 0.855966i \(-0.327036\pi\)
0.517033 + 0.855966i \(0.327036\pi\)
\(542\) −1152.00 −0.0912964
\(543\) 0 0
\(544\) −512.000 −0.0403526
\(545\) −11142.0 −0.875726
\(546\) 0 0
\(547\) 18055.0 1.41129 0.705645 0.708565i \(-0.250657\pi\)
0.705645 + 0.708565i \(0.250657\pi\)
\(548\) 4512.00 0.351721
\(549\) 0 0
\(550\) −5456.00 −0.422990
\(551\) −4029.00 −0.311508
\(552\) 0 0
\(553\) 6769.00 0.520519
\(554\) 11398.0 0.874106
\(555\) 0 0
\(556\) −3416.00 −0.260559
\(557\) 19608.0 1.49159 0.745797 0.666174i \(-0.232069\pi\)
0.745797 + 0.666174i \(0.232069\pi\)
\(558\) 0 0
\(559\) 1339.00 0.101312
\(560\) 1008.00 0.0760639
\(561\) 0 0
\(562\) 8124.00 0.609769
\(563\) 13512.0 1.01148 0.505740 0.862686i \(-0.331220\pi\)
0.505740 + 0.862686i \(0.331220\pi\)
\(564\) 0 0
\(565\) 9657.00 0.719067
\(566\) 1544.00 0.114663
\(567\) 0 0
\(568\) −2112.00 −0.156017
\(569\) 4061.00 0.299202 0.149601 0.988746i \(-0.452201\pi\)
0.149601 + 0.988746i \(0.452201\pi\)
\(570\) 0 0
\(571\) −2255.00 −0.165269 −0.0826347 0.996580i \(-0.526333\pi\)
−0.0826347 + 0.996580i \(0.526333\pi\)
\(572\) 3224.00 0.235668
\(573\) 0 0
\(574\) 5684.00 0.413320
\(575\) −6820.00 −0.494632
\(576\) 0 0
\(577\) −254.000 −0.0183261 −0.00916305 0.999958i \(-0.502917\pi\)
−0.00916305 + 0.999958i \(0.502917\pi\)
\(578\) 9314.00 0.670262
\(579\) 0 0
\(580\) 1836.00 0.131441
\(581\) −4753.00 −0.339394
\(582\) 0 0
\(583\) −10478.0 −0.744347
\(584\) 968.000 0.0685893
\(585\) 0 0
\(586\) 15666.0 1.10436
\(587\) −15057.0 −1.05872 −0.529360 0.848397i \(-0.677568\pi\)
−0.529360 + 0.848397i \(0.677568\pi\)
\(588\) 0 0
\(589\) 19197.0 1.34295
\(590\) −5760.00 −0.401924
\(591\) 0 0
\(592\) 6592.00 0.457651
\(593\) −19917.0 −1.37925 −0.689623 0.724168i \(-0.742224\pi\)
−0.689623 + 0.724168i \(0.742224\pi\)
\(594\) 0 0
\(595\) 1008.00 0.0694521
\(596\) 1768.00 0.121510
\(597\) 0 0
\(598\) 4030.00 0.275584
\(599\) 15107.0 1.03048 0.515238 0.857047i \(-0.327703\pi\)
0.515238 + 0.857047i \(0.327703\pi\)
\(600\) 0 0
\(601\) 23674.0 1.60679 0.803397 0.595444i \(-0.203024\pi\)
0.803397 + 0.595444i \(0.203024\pi\)
\(602\) −1442.00 −0.0976271
\(603\) 0 0
\(604\) −4064.00 −0.273778
\(605\) −22617.0 −1.51985
\(606\) 0 0
\(607\) 23746.0 1.58784 0.793921 0.608021i \(-0.208036\pi\)
0.793921 + 0.608021i \(0.208036\pi\)
\(608\) −2528.00 −0.168625
\(609\) 0 0
\(610\) −11052.0 −0.733578
\(611\) 5577.00 0.369266
\(612\) 0 0
\(613\) −19216.0 −1.26611 −0.633056 0.774106i \(-0.718200\pi\)
−0.633056 + 0.774106i \(0.718200\pi\)
\(614\) 5782.00 0.380037
\(615\) 0 0
\(616\) −3472.00 −0.227096
\(617\) −20862.0 −1.36122 −0.680610 0.732646i \(-0.738285\pi\)
−0.680610 + 0.732646i \(0.738285\pi\)
\(618\) 0 0
\(619\) 124.000 0.00805167 0.00402583 0.999992i \(-0.498719\pi\)
0.00402583 + 0.999992i \(0.498719\pi\)
\(620\) −8748.00 −0.566658
\(621\) 0 0
\(622\) −7060.00 −0.455113
\(623\) 7413.00 0.476718
\(624\) 0 0
\(625\) −8189.00 −0.524096
\(626\) −10980.0 −0.701037
\(627\) 0 0
\(628\) −15520.0 −0.986171
\(629\) 6592.00 0.417870
\(630\) 0 0
\(631\) 23942.0 1.51048 0.755242 0.655446i \(-0.227519\pi\)
0.755242 + 0.655446i \(0.227519\pi\)
\(632\) 7736.00 0.486901
\(633\) 0 0
\(634\) −11272.0 −0.706101
\(635\) 15732.0 0.983158
\(636\) 0 0
\(637\) −637.000 −0.0396214
\(638\) −6324.00 −0.392429
\(639\) 0 0
\(640\) 1152.00 0.0711512
\(641\) 15723.0 0.968832 0.484416 0.874838i \(-0.339032\pi\)
0.484416 + 0.874838i \(0.339032\pi\)
\(642\) 0 0
\(643\) −5544.00 −0.340022 −0.170011 0.985442i \(-0.554380\pi\)
−0.170011 + 0.985442i \(0.554380\pi\)
\(644\) −4340.00 −0.265559
\(645\) 0 0
\(646\) −2528.00 −0.153967
\(647\) 6078.00 0.369321 0.184661 0.982802i \(-0.440881\pi\)
0.184661 + 0.982802i \(0.440881\pi\)
\(648\) 0 0
\(649\) 19840.0 1.19998
\(650\) −1144.00 −0.0690329
\(651\) 0 0
\(652\) −6416.00 −0.385383
\(653\) −30778.0 −1.84447 −0.922233 0.386635i \(-0.873637\pi\)
−0.922233 + 0.386635i \(0.873637\pi\)
\(654\) 0 0
\(655\) −8424.00 −0.502524
\(656\) 6496.00 0.386625
\(657\) 0 0
\(658\) −6006.00 −0.355833
\(659\) 11205.0 0.662344 0.331172 0.943570i \(-0.392556\pi\)
0.331172 + 0.943570i \(0.392556\pi\)
\(660\) 0 0
\(661\) −20785.0 −1.22306 −0.611530 0.791221i \(-0.709446\pi\)
−0.611530 + 0.791221i \(0.709446\pi\)
\(662\) 19924.0 1.16974
\(663\) 0 0
\(664\) −5432.00 −0.317474
\(665\) 4977.00 0.290225
\(666\) 0 0
\(667\) −7905.00 −0.458895
\(668\) −3836.00 −0.222185
\(669\) 0 0
\(670\) 4644.00 0.267781
\(671\) 38068.0 2.19016
\(672\) 0 0
\(673\) 1297.00 0.0742878 0.0371439 0.999310i \(-0.488174\pi\)
0.0371439 + 0.999310i \(0.488174\pi\)
\(674\) 22830.0 1.30472
\(675\) 0 0
\(676\) 676.000 0.0384615
\(677\) −7310.00 −0.414987 −0.207493 0.978236i \(-0.566531\pi\)
−0.207493 + 0.978236i \(0.566531\pi\)
\(678\) 0 0
\(679\) 147.000 0.00830831
\(680\) 1152.00 0.0649664
\(681\) 0 0
\(682\) 30132.0 1.69181
\(683\) 26384.0 1.47812 0.739060 0.673640i \(-0.235270\pi\)
0.739060 + 0.673640i \(0.235270\pi\)
\(684\) 0 0
\(685\) −10152.0 −0.566260
\(686\) 686.000 0.0381802
\(687\) 0 0
\(688\) −1648.00 −0.0913218
\(689\) −2197.00 −0.121479
\(690\) 0 0
\(691\) −27823.0 −1.53175 −0.765873 0.642992i \(-0.777693\pi\)
−0.765873 + 0.642992i \(0.777693\pi\)
\(692\) 1952.00 0.107231
\(693\) 0 0
\(694\) 9728.00 0.532089
\(695\) 7686.00 0.419492
\(696\) 0 0
\(697\) 6496.00 0.353018
\(698\) 938.000 0.0508651
\(699\) 0 0
\(700\) 1232.00 0.0665217
\(701\) −24117.0 −1.29941 −0.649705 0.760186i \(-0.725108\pi\)
−0.649705 + 0.760186i \(0.725108\pi\)
\(702\) 0 0
\(703\) 32548.0 1.74619
\(704\) −3968.00 −0.212428
\(705\) 0 0
\(706\) 8396.00 0.447575
\(707\) 6258.00 0.332894
\(708\) 0 0
\(709\) 28286.0 1.49831 0.749156 0.662394i \(-0.230459\pi\)
0.749156 + 0.662394i \(0.230459\pi\)
\(710\) 4752.00 0.251182
\(711\) 0 0
\(712\) 8472.00 0.445929
\(713\) 37665.0 1.97835
\(714\) 0 0
\(715\) −7254.00 −0.379418
\(716\) −10132.0 −0.528842
\(717\) 0 0
\(718\) 6816.00 0.354277
\(719\) 26346.0 1.36654 0.683268 0.730167i \(-0.260558\pi\)
0.683268 + 0.730167i \(0.260558\pi\)
\(720\) 0 0
\(721\) −896.000 −0.0462813
\(722\) 1236.00 0.0637107
\(723\) 0 0
\(724\) −14504.0 −0.744526
\(725\) 2244.00 0.114952
\(726\) 0 0
\(727\) −22862.0 −1.16631 −0.583153 0.812362i \(-0.698181\pi\)
−0.583153 + 0.812362i \(0.698181\pi\)
\(728\) −728.000 −0.0370625
\(729\) 0 0
\(730\) −2178.00 −0.110427
\(731\) −1648.00 −0.0833837
\(732\) 0 0
\(733\) 18587.0 0.936598 0.468299 0.883570i \(-0.344867\pi\)
0.468299 + 0.883570i \(0.344867\pi\)
\(734\) 16580.0 0.833759
\(735\) 0 0
\(736\) −4960.00 −0.248408
\(737\) −15996.0 −0.799485
\(738\) 0 0
\(739\) 5102.00 0.253965 0.126982 0.991905i \(-0.459471\pi\)
0.126982 + 0.991905i \(0.459471\pi\)
\(740\) −14832.0 −0.736804
\(741\) 0 0
\(742\) 2366.00 0.117060
\(743\) −27428.0 −1.35429 −0.677144 0.735851i \(-0.736783\pi\)
−0.677144 + 0.735851i \(0.736783\pi\)
\(744\) 0 0
\(745\) −3978.00 −0.195628
\(746\) 19812.0 0.972344
\(747\) 0 0
\(748\) −3968.00 −0.193963
\(749\) −4956.00 −0.241773
\(750\) 0 0
\(751\) 125.000 0.00607365 0.00303683 0.999995i \(-0.499033\pi\)
0.00303683 + 0.999995i \(0.499033\pi\)
\(752\) −6864.00 −0.332851
\(753\) 0 0
\(754\) −1326.00 −0.0640452
\(755\) 9144.00 0.440774
\(756\) 0 0
\(757\) −27907.0 −1.33989 −0.669945 0.742410i \(-0.733682\pi\)
−0.669945 + 0.742410i \(0.733682\pi\)
\(758\) 18476.0 0.885328
\(759\) 0 0
\(760\) 5688.00 0.271481
\(761\) −7793.00 −0.371217 −0.185608 0.982624i \(-0.559426\pi\)
−0.185608 + 0.982624i \(0.559426\pi\)
\(762\) 0 0
\(763\) −8666.00 −0.411180
\(764\) 19968.0 0.945572
\(765\) 0 0
\(766\) 9944.00 0.469049
\(767\) 4160.00 0.195839
\(768\) 0 0
\(769\) 29393.0 1.37833 0.689167 0.724603i \(-0.257977\pi\)
0.689167 + 0.724603i \(0.257977\pi\)
\(770\) 7812.00 0.365617
\(771\) 0 0
\(772\) −1880.00 −0.0876460
\(773\) −20326.0 −0.945764 −0.472882 0.881126i \(-0.656786\pi\)
−0.472882 + 0.881126i \(0.656786\pi\)
\(774\) 0 0
\(775\) −10692.0 −0.495572
\(776\) 168.000 0.00777171
\(777\) 0 0
\(778\) 14908.0 0.686989
\(779\) 32074.0 1.47519
\(780\) 0 0
\(781\) −16368.0 −0.749927
\(782\) −4960.00 −0.226815
\(783\) 0 0
\(784\) 784.000 0.0357143
\(785\) 34920.0 1.58770
\(786\) 0 0
\(787\) 16679.0 0.755454 0.377727 0.925917i \(-0.376706\pi\)
0.377727 + 0.925917i \(0.376706\pi\)
\(788\) 12760.0 0.576848
\(789\) 0 0
\(790\) −17406.0 −0.783896
\(791\) 7511.00 0.337624
\(792\) 0 0
\(793\) 7982.00 0.357439
\(794\) −14438.0 −0.645322
\(795\) 0 0
\(796\) 7776.00 0.346248
\(797\) 9282.00 0.412529 0.206264 0.978496i \(-0.433869\pi\)
0.206264 + 0.978496i \(0.433869\pi\)
\(798\) 0 0
\(799\) −6864.00 −0.303918
\(800\) 1408.00 0.0622254
\(801\) 0 0
\(802\) 21544.0 0.948560
\(803\) 7502.00 0.329688
\(804\) 0 0
\(805\) 9765.00 0.427542
\(806\) 6318.00 0.276107
\(807\) 0 0
\(808\) 7152.00 0.311394
\(809\) 883.000 0.0383741 0.0191870 0.999816i \(-0.493892\pi\)
0.0191870 + 0.999816i \(0.493892\pi\)
\(810\) 0 0
\(811\) −12684.0 −0.549193 −0.274596 0.961560i \(-0.588544\pi\)
−0.274596 + 0.961560i \(0.588544\pi\)
\(812\) 1428.00 0.0617155
\(813\) 0 0
\(814\) 51088.0 2.19980
\(815\) 14436.0 0.620455
\(816\) 0 0
\(817\) −8137.00 −0.348443
\(818\) −26302.0 −1.12424
\(819\) 0 0
\(820\) −14616.0 −0.622455
\(821\) 34126.0 1.45068 0.725338 0.688393i \(-0.241683\pi\)
0.725338 + 0.688393i \(0.241683\pi\)
\(822\) 0 0
\(823\) −7568.00 −0.320539 −0.160270 0.987073i \(-0.551236\pi\)
−0.160270 + 0.987073i \(0.551236\pi\)
\(824\) −1024.00 −0.0432921
\(825\) 0 0
\(826\) −4480.00 −0.188716
\(827\) −32076.0 −1.34872 −0.674360 0.738403i \(-0.735580\pi\)
−0.674360 + 0.738403i \(0.735580\pi\)
\(828\) 0 0
\(829\) −22598.0 −0.946756 −0.473378 0.880859i \(-0.656966\pi\)
−0.473378 + 0.880859i \(0.656966\pi\)
\(830\) 12222.0 0.511123
\(831\) 0 0
\(832\) −832.000 −0.0346688
\(833\) 784.000 0.0326098
\(834\) 0 0
\(835\) 8631.00 0.357710
\(836\) −19592.0 −0.810530
\(837\) 0 0
\(838\) 12068.0 0.497473
\(839\) −25480.0 −1.04847 −0.524236 0.851573i \(-0.675649\pi\)
−0.524236 + 0.851573i \(0.675649\pi\)
\(840\) 0 0
\(841\) −21788.0 −0.893354
\(842\) −17728.0 −0.725591
\(843\) 0 0
\(844\) −4556.00 −0.185810
\(845\) −1521.00 −0.0619219
\(846\) 0 0
\(847\) −17591.0 −0.713617
\(848\) 2704.00 0.109500
\(849\) 0 0
\(850\) 1408.00 0.0568165
\(851\) 63860.0 2.57238
\(852\) 0 0
\(853\) −22939.0 −0.920770 −0.460385 0.887719i \(-0.652289\pi\)
−0.460385 + 0.887719i \(0.652289\pi\)
\(854\) −8596.00 −0.344437
\(855\) 0 0
\(856\) −5664.00 −0.226158
\(857\) 38782.0 1.54582 0.772910 0.634516i \(-0.218800\pi\)
0.772910 + 0.634516i \(0.218800\pi\)
\(858\) 0 0
\(859\) −13970.0 −0.554890 −0.277445 0.960742i \(-0.589488\pi\)
−0.277445 + 0.960742i \(0.589488\pi\)
\(860\) 3708.00 0.147025
\(861\) 0 0
\(862\) −268.000 −0.0105895
\(863\) 22212.0 0.876136 0.438068 0.898942i \(-0.355663\pi\)
0.438068 + 0.898942i \(0.355663\pi\)
\(864\) 0 0
\(865\) −4392.00 −0.172639
\(866\) −24752.0 −0.971255
\(867\) 0 0
\(868\) −6804.00 −0.266063
\(869\) 59954.0 2.34039
\(870\) 0 0
\(871\) −3354.00 −0.130478
\(872\) −9904.00 −0.384624
\(873\) 0 0
\(874\) −24490.0 −0.947811
\(875\) −10647.0 −0.411353
\(876\) 0 0
\(877\) −24816.0 −0.955504 −0.477752 0.878495i \(-0.658548\pi\)
−0.477752 + 0.878495i \(0.658548\pi\)
\(878\) −28396.0 −1.09148
\(879\) 0 0
\(880\) 8928.00 0.342003
\(881\) −7490.00 −0.286430 −0.143215 0.989692i \(-0.545744\pi\)
−0.143215 + 0.989692i \(0.545744\pi\)
\(882\) 0 0
\(883\) 6092.00 0.232177 0.116088 0.993239i \(-0.462964\pi\)
0.116088 + 0.993239i \(0.462964\pi\)
\(884\) −832.000 −0.0316552
\(885\) 0 0
\(886\) 15314.0 0.580682
\(887\) 6480.00 0.245295 0.122648 0.992450i \(-0.460861\pi\)
0.122648 + 0.992450i \(0.460861\pi\)
\(888\) 0 0
\(889\) 12236.0 0.461622
\(890\) −19062.0 −0.717932
\(891\) 0 0
\(892\) 3332.00 0.125071
\(893\) −33891.0 −1.27001
\(894\) 0 0
\(895\) 22797.0 0.851419
\(896\) 896.000 0.0334077
\(897\) 0 0
\(898\) 31000.0 1.15199
\(899\) −12393.0 −0.459766
\(900\) 0 0
\(901\) 2704.00 0.0999815
\(902\) 50344.0 1.85839
\(903\) 0 0
\(904\) 8584.00 0.315818
\(905\) 32634.0 1.19866
\(906\) 0 0
\(907\) −12111.0 −0.443373 −0.221686 0.975118i \(-0.571156\pi\)
−0.221686 + 0.975118i \(0.571156\pi\)
\(908\) 14064.0 0.514020
\(909\) 0 0
\(910\) 1638.00 0.0596694
\(911\) −7191.00 −0.261524 −0.130762 0.991414i \(-0.541742\pi\)
−0.130762 + 0.991414i \(0.541742\pi\)
\(912\) 0 0
\(913\) −42098.0 −1.52600
\(914\) −20368.0 −0.737105
\(915\) 0 0
\(916\) 12888.0 0.464882
\(917\) −6552.00 −0.235950
\(918\) 0 0
\(919\) −12272.0 −0.440496 −0.220248 0.975444i \(-0.570687\pi\)
−0.220248 + 0.975444i \(0.570687\pi\)
\(920\) 11160.0 0.399929
\(921\) 0 0
\(922\) 38500.0 1.37520
\(923\) −3432.00 −0.122390
\(924\) 0 0
\(925\) −18128.0 −0.644373
\(926\) 31244.0 1.10879
\(927\) 0 0
\(928\) 1632.00 0.0577296
\(929\) −3285.00 −0.116014 −0.0580072 0.998316i \(-0.518475\pi\)
−0.0580072 + 0.998316i \(0.518475\pi\)
\(930\) 0 0
\(931\) 3871.00 0.136269
\(932\) 1908.00 0.0670586
\(933\) 0 0
\(934\) −31188.0 −1.09262
\(935\) 8928.00 0.312275
\(936\) 0 0
\(937\) −5068.00 −0.176696 −0.0883481 0.996090i \(-0.528159\pi\)
−0.0883481 + 0.996090i \(0.528159\pi\)
\(938\) 3612.00 0.125731
\(939\) 0 0
\(940\) 15444.0 0.535881
\(941\) −13571.0 −0.470140 −0.235070 0.971978i \(-0.575532\pi\)
−0.235070 + 0.971978i \(0.575532\pi\)
\(942\) 0 0
\(943\) 62930.0 2.17315
\(944\) −5120.00 −0.176527
\(945\) 0 0
\(946\) −12772.0 −0.438957
\(947\) 17662.0 0.606059 0.303030 0.952981i \(-0.402002\pi\)
0.303030 + 0.952981i \(0.402002\pi\)
\(948\) 0 0
\(949\) 1573.00 0.0538058
\(950\) 6952.00 0.237424
\(951\) 0 0
\(952\) 896.000 0.0305037
\(953\) −37893.0 −1.28801 −0.644006 0.765021i \(-0.722729\pi\)
−0.644006 + 0.765021i \(0.722729\pi\)
\(954\) 0 0
\(955\) −44928.0 −1.52234
\(956\) 25472.0 0.861740
\(957\) 0 0
\(958\) 6478.00 0.218470
\(959\) −7896.00 −0.265876
\(960\) 0 0
\(961\) 29258.0 0.982109
\(962\) 10712.0 0.359011
\(963\) 0 0
\(964\) 2988.00 0.0998309
\(965\) 4230.00 0.141107
\(966\) 0 0
\(967\) −48914.0 −1.62665 −0.813324 0.581811i \(-0.802344\pi\)
−0.813324 + 0.581811i \(0.802344\pi\)
\(968\) −20104.0 −0.667528
\(969\) 0 0
\(970\) −378.000 −0.0125122
\(971\) −31110.0 −1.02818 −0.514092 0.857735i \(-0.671871\pi\)
−0.514092 + 0.857735i \(0.671871\pi\)
\(972\) 0 0
\(973\) 5978.00 0.196964
\(974\) −3596.00 −0.118299
\(975\) 0 0
\(976\) −9824.00 −0.322191
\(977\) −22294.0 −0.730039 −0.365020 0.931000i \(-0.618938\pi\)
−0.365020 + 0.931000i \(0.618938\pi\)
\(978\) 0 0
\(979\) 65658.0 2.14345
\(980\) −1764.00 −0.0574989
\(981\) 0 0
\(982\) 27416.0 0.890916
\(983\) 317.000 0.0102856 0.00514279 0.999987i \(-0.498363\pi\)
0.00514279 + 0.999987i \(0.498363\pi\)
\(984\) 0 0
\(985\) −28710.0 −0.928707
\(986\) 1632.00 0.0527114
\(987\) 0 0
\(988\) −4108.00 −0.132280
\(989\) −15965.0 −0.513304
\(990\) 0 0
\(991\) 40564.0 1.30026 0.650130 0.759823i \(-0.274714\pi\)
0.650130 + 0.759823i \(0.274714\pi\)
\(992\) −7776.00 −0.248879
\(993\) 0 0
\(994\) 3696.00 0.117938
\(995\) −17496.0 −0.557448
\(996\) 0 0
\(997\) −57528.0 −1.82741 −0.913706 0.406376i \(-0.866792\pi\)
−0.913706 + 0.406376i \(0.866792\pi\)
\(998\) 23872.0 0.757169
\(999\) 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 1638.4.a.b.1.1 1
3.2 odd 2 546.4.a.e.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.4.a.e.1.1 1 3.2 odd 2
1638.4.a.b.1.1 1 1.1 even 1 trivial