Properties

Label 100.4.a.b.1.1
Level $100$
Weight $4$
Character 100.1
Self dual yes
Analytic conductor $5.900$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 100.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(5.90019100057\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 100.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} -26.0000 q^{7} -26.0000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} -26.0000 q^{7} -26.0000 q^{9} +45.0000 q^{11} -44.0000 q^{13} -117.000 q^{17} -91.0000 q^{19} +26.0000 q^{21} +18.0000 q^{23} +53.0000 q^{27} +144.000 q^{29} +26.0000 q^{31} -45.0000 q^{33} +214.000 q^{37} +44.0000 q^{39} -459.000 q^{41} +460.000 q^{43} +468.000 q^{47} +333.000 q^{49} +117.000 q^{51} -558.000 q^{53} +91.0000 q^{57} -72.0000 q^{59} -118.000 q^{61} +676.000 q^{63} -251.000 q^{67} -18.0000 q^{69} +108.000 q^{71} -299.000 q^{73} -1170.00 q^{77} -898.000 q^{79} +649.000 q^{81} -927.000 q^{83} -144.000 q^{87} +351.000 q^{89} +1144.00 q^{91} -26.0000 q^{93} -386.000 q^{97} -1170.00 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.00000 −0.192450 −0.0962250 0.995360i \(-0.530677\pi\)
−0.0962250 + 0.995360i \(0.530677\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −26.0000 −1.40387 −0.701934 0.712242i \(-0.747680\pi\)
−0.701934 + 0.712242i \(0.747680\pi\)
\(8\) 0 0
\(9\) −26.0000 −0.962963
\(10\) 0 0
\(11\) 45.0000 1.23346 0.616728 0.787177i \(-0.288458\pi\)
0.616728 + 0.787177i \(0.288458\pi\)
\(12\) 0 0
\(13\) −44.0000 −0.938723 −0.469362 0.883006i \(-0.655516\pi\)
−0.469362 + 0.883006i \(0.655516\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −117.000 −1.66922 −0.834608 0.550845i \(-0.814306\pi\)
−0.834608 + 0.550845i \(0.814306\pi\)
\(18\) 0 0
\(19\) −91.0000 −1.09878 −0.549390 0.835566i \(-0.685140\pi\)
−0.549390 + 0.835566i \(0.685140\pi\)
\(20\) 0 0
\(21\) 26.0000 0.270175
\(22\) 0 0
\(23\) 18.0000 0.163185 0.0815926 0.996666i \(-0.473999\pi\)
0.0815926 + 0.996666i \(0.473999\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 53.0000 0.377772
\(28\) 0 0
\(29\) 144.000 0.922073 0.461037 0.887381i \(-0.347478\pi\)
0.461037 + 0.887381i \(0.347478\pi\)
\(30\) 0 0
\(31\) 26.0000 0.150637 0.0753184 0.997160i \(-0.476003\pi\)
0.0753184 + 0.997160i \(0.476003\pi\)
\(32\) 0 0
\(33\) −45.0000 −0.237379
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 214.000 0.950848 0.475424 0.879757i \(-0.342295\pi\)
0.475424 + 0.879757i \(0.342295\pi\)
\(38\) 0 0
\(39\) 44.0000 0.180657
\(40\) 0 0
\(41\) −459.000 −1.74838 −0.874192 0.485580i \(-0.838608\pi\)
−0.874192 + 0.485580i \(0.838608\pi\)
\(42\) 0 0
\(43\) 460.000 1.63138 0.815690 0.578489i \(-0.196358\pi\)
0.815690 + 0.578489i \(0.196358\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 468.000 1.45244 0.726221 0.687461i \(-0.241275\pi\)
0.726221 + 0.687461i \(0.241275\pi\)
\(48\) 0 0
\(49\) 333.000 0.970845
\(50\) 0 0
\(51\) 117.000 0.321241
\(52\) 0 0
\(53\) −558.000 −1.44617 −0.723087 0.690757i \(-0.757277\pi\)
−0.723087 + 0.690757i \(0.757277\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 91.0000 0.211460
\(58\) 0 0
\(59\) −72.0000 −0.158875 −0.0794373 0.996840i \(-0.525312\pi\)
−0.0794373 + 0.996840i \(0.525312\pi\)
\(60\) 0 0
\(61\) −118.000 −0.247678 −0.123839 0.992302i \(-0.539521\pi\)
−0.123839 + 0.992302i \(0.539521\pi\)
\(62\) 0 0
\(63\) 676.000 1.35187
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −251.000 −0.457680 −0.228840 0.973464i \(-0.573493\pi\)
−0.228840 + 0.973464i \(0.573493\pi\)
\(68\) 0 0
\(69\) −18.0000 −0.0314050
\(70\) 0 0
\(71\) 108.000 0.180525 0.0902623 0.995918i \(-0.471229\pi\)
0.0902623 + 0.995918i \(0.471229\pi\)
\(72\) 0 0
\(73\) −299.000 −0.479388 −0.239694 0.970849i \(-0.577047\pi\)
−0.239694 + 0.970849i \(0.577047\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −1170.00 −1.73161
\(78\) 0 0
\(79\) −898.000 −1.27890 −0.639449 0.768834i \(-0.720837\pi\)
−0.639449 + 0.768834i \(0.720837\pi\)
\(80\) 0 0
\(81\) 649.000 0.890261
\(82\) 0 0
\(83\) −927.000 −1.22592 −0.612961 0.790113i \(-0.710022\pi\)
−0.612961 + 0.790113i \(0.710022\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −144.000 −0.177453
\(88\) 0 0
\(89\) 351.000 0.418044 0.209022 0.977911i \(-0.432972\pi\)
0.209022 + 0.977911i \(0.432972\pi\)
\(90\) 0 0
\(91\) 1144.00 1.31784
\(92\) 0 0
\(93\) −26.0000 −0.0289900
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −386.000 −0.404045 −0.202022 0.979381i \(-0.564751\pi\)
−0.202022 + 0.979381i \(0.564751\pi\)
\(98\) 0 0
\(99\) −1170.00 −1.18777
\(100\) 0 0
\(101\) −954.000 −0.939867 −0.469933 0.882702i \(-0.655722\pi\)
−0.469933 + 0.882702i \(0.655722\pi\)
\(102\) 0 0
\(103\) 772.000 0.738519 0.369259 0.929326i \(-0.379611\pi\)
0.369259 + 0.929326i \(0.379611\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1197.00 −1.08148 −0.540740 0.841190i \(-0.681856\pi\)
−0.540740 + 0.841190i \(0.681856\pi\)
\(108\) 0 0
\(109\) −802.000 −0.704749 −0.352375 0.935859i \(-0.614626\pi\)
−0.352375 + 0.935859i \(0.614626\pi\)
\(110\) 0 0
\(111\) −214.000 −0.182991
\(112\) 0 0
\(113\) −1143.00 −0.951543 −0.475772 0.879569i \(-0.657831\pi\)
−0.475772 + 0.879569i \(0.657831\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 1144.00 0.903956
\(118\) 0 0
\(119\) 3042.00 2.34336
\(120\) 0 0
\(121\) 694.000 0.521412
\(122\) 0 0
\(123\) 459.000 0.336477
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 2374.00 1.65873 0.829364 0.558709i \(-0.188703\pi\)
0.829364 + 0.558709i \(0.188703\pi\)
\(128\) 0 0
\(129\) −460.000 −0.313959
\(130\) 0 0
\(131\) −1260.00 −0.840357 −0.420178 0.907442i \(-0.638032\pi\)
−0.420178 + 0.907442i \(0.638032\pi\)
\(132\) 0 0
\(133\) 2366.00 1.54254
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 891.000 0.555644 0.277822 0.960633i \(-0.410387\pi\)
0.277822 + 0.960633i \(0.410387\pi\)
\(138\) 0 0
\(139\) 389.000 0.237371 0.118685 0.992932i \(-0.462132\pi\)
0.118685 + 0.992932i \(0.462132\pi\)
\(140\) 0 0
\(141\) −468.000 −0.279523
\(142\) 0 0
\(143\) −1980.00 −1.15787
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −333.000 −0.186839
\(148\) 0 0
\(149\) 1296.00 0.712567 0.356283 0.934378i \(-0.384044\pi\)
0.356283 + 0.934378i \(0.384044\pi\)
\(150\) 0 0
\(151\) −2710.00 −1.46051 −0.730254 0.683176i \(-0.760598\pi\)
−0.730254 + 0.683176i \(0.760598\pi\)
\(152\) 0 0
\(153\) 3042.00 1.60739
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 1846.00 0.938388 0.469194 0.883095i \(-0.344545\pi\)
0.469194 + 0.883095i \(0.344545\pi\)
\(158\) 0 0
\(159\) 558.000 0.278316
\(160\) 0 0
\(161\) −468.000 −0.229090
\(162\) 0 0
\(163\) −1475.00 −0.708779 −0.354389 0.935098i \(-0.615311\pi\)
−0.354389 + 0.935098i \(0.615311\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1476.00 0.683930 0.341965 0.939713i \(-0.388908\pi\)
0.341965 + 0.939713i \(0.388908\pi\)
\(168\) 0 0
\(169\) −261.000 −0.118798
\(170\) 0 0
\(171\) 2366.00 1.05809
\(172\) 0 0
\(173\) −1368.00 −0.601197 −0.300599 0.953751i \(-0.597186\pi\)
−0.300599 + 0.953751i \(0.597186\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 72.0000 0.0305754
\(178\) 0 0
\(179\) −1503.00 −0.627595 −0.313797 0.949490i \(-0.601601\pi\)
−0.313797 + 0.949490i \(0.601601\pi\)
\(180\) 0 0
\(181\) 3770.00 1.54819 0.774094 0.633071i \(-0.218206\pi\)
0.774094 + 0.633071i \(0.218206\pi\)
\(182\) 0 0
\(183\) 118.000 0.0476656
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −5265.00 −2.05890
\(188\) 0 0
\(189\) −1378.00 −0.530343
\(190\) 0 0
\(191\) −4122.00 −1.56156 −0.780779 0.624808i \(-0.785177\pi\)
−0.780779 + 0.624808i \(0.785177\pi\)
\(192\) 0 0
\(193\) 1963.00 0.732123 0.366062 0.930591i \(-0.380706\pi\)
0.366062 + 0.930591i \(0.380706\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −2934.00 −1.06111 −0.530555 0.847650i \(-0.678017\pi\)
−0.530555 + 0.847650i \(0.678017\pi\)
\(198\) 0 0
\(199\) 1412.00 0.502985 0.251493 0.967859i \(-0.419079\pi\)
0.251493 + 0.967859i \(0.419079\pi\)
\(200\) 0 0
\(201\) 251.000 0.0880805
\(202\) 0 0
\(203\) −3744.00 −1.29447
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −468.000 −0.157141
\(208\) 0 0
\(209\) −4095.00 −1.35530
\(210\) 0 0
\(211\) 3419.00 1.11552 0.557758 0.830004i \(-0.311662\pi\)
0.557758 + 0.830004i \(0.311662\pi\)
\(212\) 0 0
\(213\) −108.000 −0.0347420
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −676.000 −0.211474
\(218\) 0 0
\(219\) 299.000 0.0922582
\(220\) 0 0
\(221\) 5148.00 1.56693
\(222\) 0 0
\(223\) 100.000 0.0300291 0.0150146 0.999887i \(-0.495221\pi\)
0.0150146 + 0.999887i \(0.495221\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −4212.00 −1.23154 −0.615771 0.787925i \(-0.711156\pi\)
−0.615771 + 0.787925i \(0.711156\pi\)
\(228\) 0 0
\(229\) −3484.00 −1.00537 −0.502684 0.864470i \(-0.667654\pi\)
−0.502684 + 0.864470i \(0.667654\pi\)
\(230\) 0 0
\(231\) 1170.00 0.333248
\(232\) 0 0
\(233\) −918.000 −0.258112 −0.129056 0.991637i \(-0.541195\pi\)
−0.129056 + 0.991637i \(0.541195\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 898.000 0.246124
\(238\) 0 0
\(239\) 3744.00 1.01330 0.506651 0.862151i \(-0.330883\pi\)
0.506651 + 0.862151i \(0.330883\pi\)
\(240\) 0 0
\(241\) −4231.00 −1.13088 −0.565441 0.824789i \(-0.691294\pi\)
−0.565441 + 0.824789i \(0.691294\pi\)
\(242\) 0 0
\(243\) −2080.00 −0.549103
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 4004.00 1.03145
\(248\) 0 0
\(249\) 927.000 0.235929
\(250\) 0 0
\(251\) −2925.00 −0.735555 −0.367778 0.929914i \(-0.619881\pi\)
−0.367778 + 0.929914i \(0.619881\pi\)
\(252\) 0 0
\(253\) 810.000 0.201282
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 18.0000 0.00436891 0.00218445 0.999998i \(-0.499305\pi\)
0.00218445 + 0.999998i \(0.499305\pi\)
\(258\) 0 0
\(259\) −5564.00 −1.33487
\(260\) 0 0
\(261\) −3744.00 −0.887923
\(262\) 0 0
\(263\) 6786.00 1.59104 0.795518 0.605929i \(-0.207199\pi\)
0.795518 + 0.605929i \(0.207199\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −351.000 −0.0804526
\(268\) 0 0
\(269\) 7632.00 1.72986 0.864928 0.501896i \(-0.167364\pi\)
0.864928 + 0.501896i \(0.167364\pi\)
\(270\) 0 0
\(271\) 650.000 0.145700 0.0728500 0.997343i \(-0.476791\pi\)
0.0728500 + 0.997343i \(0.476791\pi\)
\(272\) 0 0
\(273\) −1144.00 −0.253619
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 3232.00 0.701054 0.350527 0.936553i \(-0.386002\pi\)
0.350527 + 0.936553i \(0.386002\pi\)
\(278\) 0 0
\(279\) −676.000 −0.145058
\(280\) 0 0
\(281\) 4446.00 0.943865 0.471933 0.881635i \(-0.343557\pi\)
0.471933 + 0.881635i \(0.343557\pi\)
\(282\) 0 0
\(283\) −2483.00 −0.521551 −0.260776 0.965399i \(-0.583978\pi\)
−0.260776 + 0.965399i \(0.583978\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 11934.0 2.45450
\(288\) 0 0
\(289\) 8776.00 1.78628
\(290\) 0 0
\(291\) 386.000 0.0777585
\(292\) 0 0
\(293\) 4050.00 0.807521 0.403760 0.914865i \(-0.367703\pi\)
0.403760 + 0.914865i \(0.367703\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 2385.00 0.465965
\(298\) 0 0
\(299\) −792.000 −0.153186
\(300\) 0 0
\(301\) −11960.0 −2.29024
\(302\) 0 0
\(303\) 954.000 0.180877
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −2321.00 −0.431487 −0.215743 0.976450i \(-0.569217\pi\)
−0.215743 + 0.976450i \(0.569217\pi\)
\(308\) 0 0
\(309\) −772.000 −0.142128
\(310\) 0 0
\(311\) −3258.00 −0.594033 −0.297016 0.954872i \(-0.595992\pi\)
−0.297016 + 0.954872i \(0.595992\pi\)
\(312\) 0 0
\(313\) −3626.00 −0.654804 −0.327402 0.944885i \(-0.606173\pi\)
−0.327402 + 0.944885i \(0.606173\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −3852.00 −0.682492 −0.341246 0.939974i \(-0.610849\pi\)
−0.341246 + 0.939974i \(0.610849\pi\)
\(318\) 0 0
\(319\) 6480.00 1.13734
\(320\) 0 0
\(321\) 1197.00 0.208131
\(322\) 0 0
\(323\) 10647.0 1.83410
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 802.000 0.135629
\(328\) 0 0
\(329\) −12168.0 −2.03904
\(330\) 0 0
\(331\) 7553.00 1.25423 0.627115 0.778926i \(-0.284235\pi\)
0.627115 + 0.778926i \(0.284235\pi\)
\(332\) 0 0
\(333\) −5564.00 −0.915632
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 109.000 0.0176190 0.00880951 0.999961i \(-0.497196\pi\)
0.00880951 + 0.999961i \(0.497196\pi\)
\(338\) 0 0
\(339\) 1143.00 0.183125
\(340\) 0 0
\(341\) 1170.00 0.185804
\(342\) 0 0
\(343\) 260.000 0.0409291
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2835.00 0.438590 0.219295 0.975659i \(-0.429624\pi\)
0.219295 + 0.975659i \(0.429624\pi\)
\(348\) 0 0
\(349\) 2990.00 0.458599 0.229299 0.973356i \(-0.426356\pi\)
0.229299 + 0.973356i \(0.426356\pi\)
\(350\) 0 0
\(351\) −2332.00 −0.354624
\(352\) 0 0
\(353\) −9126.00 −1.37600 −0.688000 0.725711i \(-0.741511\pi\)
−0.688000 + 0.725711i \(0.741511\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −3042.00 −0.450980
\(358\) 0 0
\(359\) −9594.00 −1.41045 −0.705226 0.708983i \(-0.749154\pi\)
−0.705226 + 0.708983i \(0.749154\pi\)
\(360\) 0 0
\(361\) 1422.00 0.207319
\(362\) 0 0
\(363\) −694.000 −0.100346
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −9764.00 −1.38876 −0.694382 0.719606i \(-0.744322\pi\)
−0.694382 + 0.719606i \(0.744322\pi\)
\(368\) 0 0
\(369\) 11934.0 1.68363
\(370\) 0 0
\(371\) 14508.0 2.03024
\(372\) 0 0
\(373\) −6722.00 −0.933115 −0.466558 0.884491i \(-0.654506\pi\)
−0.466558 + 0.884491i \(0.654506\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −6336.00 −0.865572
\(378\) 0 0
\(379\) −13537.0 −1.83469 −0.917347 0.398089i \(-0.869674\pi\)
−0.917347 + 0.398089i \(0.869674\pi\)
\(380\) 0 0
\(381\) −2374.00 −0.319222
\(382\) 0 0
\(383\) 8658.00 1.15510 0.577550 0.816355i \(-0.304009\pi\)
0.577550 + 0.816355i \(0.304009\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −11960.0 −1.57096
\(388\) 0 0
\(389\) −8874.00 −1.15663 −0.578316 0.815813i \(-0.696290\pi\)
−0.578316 + 0.815813i \(0.696290\pi\)
\(390\) 0 0
\(391\) −2106.00 −0.272391
\(392\) 0 0
\(393\) 1260.00 0.161727
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −5876.00 −0.742841 −0.371421 0.928465i \(-0.621129\pi\)
−0.371421 + 0.928465i \(0.621129\pi\)
\(398\) 0 0
\(399\) −2366.00 −0.296863
\(400\) 0 0
\(401\) −1755.00 −0.218555 −0.109277 0.994011i \(-0.534854\pi\)
−0.109277 + 0.994011i \(0.534854\pi\)
\(402\) 0 0
\(403\) −1144.00 −0.141406
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 9630.00 1.17283
\(408\) 0 0
\(409\) 4589.00 0.554796 0.277398 0.960755i \(-0.410528\pi\)
0.277398 + 0.960755i \(0.410528\pi\)
\(410\) 0 0
\(411\) −891.000 −0.106934
\(412\) 0 0
\(413\) 1872.00 0.223039
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −389.000 −0.0456820
\(418\) 0 0
\(419\) 5409.00 0.630661 0.315330 0.948982i \(-0.397885\pi\)
0.315330 + 0.948982i \(0.397885\pi\)
\(420\) 0 0
\(421\) 12116.0 1.40261 0.701304 0.712863i \(-0.252602\pi\)
0.701304 + 0.712863i \(0.252602\pi\)
\(422\) 0 0
\(423\) −12168.0 −1.39865
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 3068.00 0.347707
\(428\) 0 0
\(429\) 1980.00 0.222833
\(430\) 0 0
\(431\) 9126.00 1.01992 0.509958 0.860199i \(-0.329661\pi\)
0.509958 + 0.860199i \(0.329661\pi\)
\(432\) 0 0
\(433\) −629.000 −0.0698102 −0.0349051 0.999391i \(-0.511113\pi\)
−0.0349051 + 0.999391i \(0.511113\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1638.00 −0.179305
\(438\) 0 0
\(439\) 4472.00 0.486189 0.243094 0.970003i \(-0.421838\pi\)
0.243094 + 0.970003i \(0.421838\pi\)
\(440\) 0 0
\(441\) −8658.00 −0.934888
\(442\) 0 0
\(443\) 3393.00 0.363897 0.181948 0.983308i \(-0.441760\pi\)
0.181948 + 0.983308i \(0.441760\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −1296.00 −0.137134
\(448\) 0 0
\(449\) −5031.00 −0.528792 −0.264396 0.964414i \(-0.585173\pi\)
−0.264396 + 0.964414i \(0.585173\pi\)
\(450\) 0 0
\(451\) −20655.0 −2.15655
\(452\) 0 0
\(453\) 2710.00 0.281075
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 6487.00 0.664002 0.332001 0.943279i \(-0.392276\pi\)
0.332001 + 0.943279i \(0.392276\pi\)
\(458\) 0 0
\(459\) −6201.00 −0.630584
\(460\) 0 0
\(461\) 2700.00 0.272780 0.136390 0.990655i \(-0.456450\pi\)
0.136390 + 0.990655i \(0.456450\pi\)
\(462\) 0 0
\(463\) 2932.00 0.294302 0.147151 0.989114i \(-0.452990\pi\)
0.147151 + 0.989114i \(0.452990\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 15660.0 1.55173 0.775866 0.630898i \(-0.217314\pi\)
0.775866 + 0.630898i \(0.217314\pi\)
\(468\) 0 0
\(469\) 6526.00 0.642522
\(470\) 0 0
\(471\) −1846.00 −0.180593
\(472\) 0 0
\(473\) 20700.0 2.01223
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 14508.0 1.39261
\(478\) 0 0
\(479\) 10134.0 0.966669 0.483334 0.875436i \(-0.339426\pi\)
0.483334 + 0.875436i \(0.339426\pi\)
\(480\) 0 0
\(481\) −9416.00 −0.892583
\(482\) 0 0
\(483\) 468.000 0.0440885
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −1898.00 −0.176605 −0.0883025 0.996094i \(-0.528144\pi\)
−0.0883025 + 0.996094i \(0.528144\pi\)
\(488\) 0 0
\(489\) 1475.00 0.136405
\(490\) 0 0
\(491\) −6300.00 −0.579053 −0.289526 0.957170i \(-0.593498\pi\)
−0.289526 + 0.957170i \(0.593498\pi\)
\(492\) 0 0
\(493\) −16848.0 −1.53914
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −2808.00 −0.253433
\(498\) 0 0
\(499\) 18044.0 1.61876 0.809379 0.587286i \(-0.199804\pi\)
0.809379 + 0.587286i \(0.199804\pi\)
\(500\) 0 0
\(501\) −1476.00 −0.131622
\(502\) 0 0
\(503\) 6876.00 0.609514 0.304757 0.952430i \(-0.401425\pi\)
0.304757 + 0.952430i \(0.401425\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 261.000 0.0228628
\(508\) 0 0
\(509\) −4806.00 −0.418511 −0.209256 0.977861i \(-0.567104\pi\)
−0.209256 + 0.977861i \(0.567104\pi\)
\(510\) 0 0
\(511\) 7774.00 0.672997
\(512\) 0 0
\(513\) −4823.00 −0.415089
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 21060.0 1.79152
\(518\) 0 0
\(519\) 1368.00 0.115700
\(520\) 0 0
\(521\) 7749.00 0.651612 0.325806 0.945437i \(-0.394364\pi\)
0.325806 + 0.945437i \(0.394364\pi\)
\(522\) 0 0
\(523\) −8153.00 −0.681655 −0.340828 0.940126i \(-0.610707\pi\)
−0.340828 + 0.940126i \(0.610707\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −3042.00 −0.251445
\(528\) 0 0
\(529\) −11843.0 −0.973371
\(530\) 0 0
\(531\) 1872.00 0.152990
\(532\) 0 0
\(533\) 20196.0 1.64125
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 1503.00 0.120781
\(538\) 0 0
\(539\) 14985.0 1.19749
\(540\) 0 0
\(541\) −10576.0 −0.840476 −0.420238 0.907414i \(-0.638053\pi\)
−0.420238 + 0.907414i \(0.638053\pi\)
\(542\) 0 0
\(543\) −3770.00 −0.297949
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −7553.00 −0.590389 −0.295195 0.955437i \(-0.595385\pi\)
−0.295195 + 0.955437i \(0.595385\pi\)
\(548\) 0 0
\(549\) 3068.00 0.238505
\(550\) 0 0
\(551\) −13104.0 −1.01316
\(552\) 0 0
\(553\) 23348.0 1.79540
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −13500.0 −1.02695 −0.513477 0.858103i \(-0.671643\pi\)
−0.513477 + 0.858103i \(0.671643\pi\)
\(558\) 0 0
\(559\) −20240.0 −1.53141
\(560\) 0 0
\(561\) 5265.00 0.396236
\(562\) 0 0
\(563\) −23184.0 −1.73550 −0.867752 0.496997i \(-0.834436\pi\)
−0.867752 + 0.496997i \(0.834436\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −16874.0 −1.24981
\(568\) 0 0
\(569\) −8055.00 −0.593468 −0.296734 0.954960i \(-0.595897\pi\)
−0.296734 + 0.954960i \(0.595897\pi\)
\(570\) 0 0
\(571\) 3068.00 0.224854 0.112427 0.993660i \(-0.464138\pi\)
0.112427 + 0.993660i \(0.464138\pi\)
\(572\) 0 0
\(573\) 4122.00 0.300522
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −12419.0 −0.896031 −0.448015 0.894026i \(-0.647869\pi\)
−0.448015 + 0.894026i \(0.647869\pi\)
\(578\) 0 0
\(579\) −1963.00 −0.140897
\(580\) 0 0
\(581\) 24102.0 1.72103
\(582\) 0 0
\(583\) −25110.0 −1.78379
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 12393.0 0.871403 0.435702 0.900091i \(-0.356500\pi\)
0.435702 + 0.900091i \(0.356500\pi\)
\(588\) 0 0
\(589\) −2366.00 −0.165517
\(590\) 0 0
\(591\) 2934.00 0.204211
\(592\) 0 0
\(593\) −23751.0 −1.64475 −0.822375 0.568946i \(-0.807351\pi\)
−0.822375 + 0.568946i \(0.807351\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −1412.00 −0.0967995
\(598\) 0 0
\(599\) −11610.0 −0.791939 −0.395970 0.918264i \(-0.629591\pi\)
−0.395970 + 0.918264i \(0.629591\pi\)
\(600\) 0 0
\(601\) 26675.0 1.81048 0.905238 0.424905i \(-0.139693\pi\)
0.905238 + 0.424905i \(0.139693\pi\)
\(602\) 0 0
\(603\) 6526.00 0.440728
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −17264.0 −1.15441 −0.577203 0.816601i \(-0.695856\pi\)
−0.577203 + 0.816601i \(0.695856\pi\)
\(608\) 0 0
\(609\) 3744.00 0.249121
\(610\) 0 0
\(611\) −20592.0 −1.36344
\(612\) 0 0
\(613\) 26026.0 1.71481 0.857406 0.514640i \(-0.172074\pi\)
0.857406 + 0.514640i \(0.172074\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −5022.00 −0.327679 −0.163840 0.986487i \(-0.552388\pi\)
−0.163840 + 0.986487i \(0.552388\pi\)
\(618\) 0 0
\(619\) 7820.00 0.507774 0.253887 0.967234i \(-0.418291\pi\)
0.253887 + 0.967234i \(0.418291\pi\)
\(620\) 0 0
\(621\) 954.000 0.0616469
\(622\) 0 0
\(623\) −9126.00 −0.586879
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 4095.00 0.260827
\(628\) 0 0
\(629\) −25038.0 −1.58717
\(630\) 0 0
\(631\) 15002.0 0.946466 0.473233 0.880937i \(-0.343087\pi\)
0.473233 + 0.880937i \(0.343087\pi\)
\(632\) 0 0
\(633\) −3419.00 −0.214681
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −14652.0 −0.911355
\(638\) 0 0
\(639\) −2808.00 −0.173838
\(640\) 0 0
\(641\) −918.000 −0.0565660 −0.0282830 0.999600i \(-0.509004\pi\)
−0.0282830 + 0.999600i \(0.509004\pi\)
\(642\) 0 0
\(643\) 23452.0 1.43835 0.719173 0.694831i \(-0.244521\pi\)
0.719173 + 0.694831i \(0.244521\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −20556.0 −1.24906 −0.624528 0.781002i \(-0.714709\pi\)
−0.624528 + 0.781002i \(0.714709\pi\)
\(648\) 0 0
\(649\) −3240.00 −0.195965
\(650\) 0 0
\(651\) 676.000 0.0406982
\(652\) 0 0
\(653\) −30654.0 −1.83703 −0.918517 0.395381i \(-0.870613\pi\)
−0.918517 + 0.395381i \(0.870613\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 7774.00 0.461633
\(658\) 0 0
\(659\) 8919.00 0.527215 0.263608 0.964630i \(-0.415088\pi\)
0.263608 + 0.964630i \(0.415088\pi\)
\(660\) 0 0
\(661\) −22912.0 −1.34822 −0.674110 0.738631i \(-0.735473\pi\)
−0.674110 + 0.738631i \(0.735473\pi\)
\(662\) 0 0
\(663\) −5148.00 −0.301556
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 2592.00 0.150469
\(668\) 0 0
\(669\) −100.000 −0.00577911
\(670\) 0 0
\(671\) −5310.00 −0.305500
\(672\) 0 0
\(673\) 1222.00 0.0699920 0.0349960 0.999387i \(-0.488858\pi\)
0.0349960 + 0.999387i \(0.488858\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −144.000 −0.00817484 −0.00408742 0.999992i \(-0.501301\pi\)
−0.00408742 + 0.999992i \(0.501301\pi\)
\(678\) 0 0
\(679\) 10036.0 0.567226
\(680\) 0 0
\(681\) 4212.00 0.237011
\(682\) 0 0
\(683\) 12519.0 0.701356 0.350678 0.936496i \(-0.385951\pi\)
0.350678 + 0.936496i \(0.385951\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 3484.00 0.193483
\(688\) 0 0
\(689\) 24552.0 1.35756
\(690\) 0 0
\(691\) 11873.0 0.653647 0.326824 0.945085i \(-0.394022\pi\)
0.326824 + 0.945085i \(0.394022\pi\)
\(692\) 0 0
\(693\) 30420.0 1.66748
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 53703.0 2.91843
\(698\) 0 0
\(699\) 918.000 0.0496737
\(700\) 0 0
\(701\) −3060.00 −0.164871 −0.0824355 0.996596i \(-0.526270\pi\)
−0.0824355 + 0.996596i \(0.526270\pi\)
\(702\) 0 0
\(703\) −19474.0 −1.04477
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 24804.0 1.31945
\(708\) 0 0
\(709\) 4004.00 0.212092 0.106046 0.994361i \(-0.466181\pi\)
0.106046 + 0.994361i \(0.466181\pi\)
\(710\) 0 0
\(711\) 23348.0 1.23153
\(712\) 0 0
\(713\) 468.000 0.0245817
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −3744.00 −0.195010
\(718\) 0 0
\(719\) 10314.0 0.534975 0.267488 0.963561i \(-0.413807\pi\)
0.267488 + 0.963561i \(0.413807\pi\)
\(720\) 0 0
\(721\) −20072.0 −1.03678
\(722\) 0 0
\(723\) 4231.00 0.217638
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −9872.00 −0.503621 −0.251810 0.967777i \(-0.581026\pi\)
−0.251810 + 0.967777i \(0.581026\pi\)
\(728\) 0 0
\(729\) −15443.0 −0.784586
\(730\) 0 0
\(731\) −53820.0 −2.72313
\(732\) 0 0
\(733\) −7436.00 −0.374700 −0.187350 0.982293i \(-0.559990\pi\)
−0.187350 + 0.982293i \(0.559990\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −11295.0 −0.564527
\(738\) 0 0
\(739\) −16900.0 −0.841240 −0.420620 0.907237i \(-0.638187\pi\)
−0.420620 + 0.907237i \(0.638187\pi\)
\(740\) 0 0
\(741\) −4004.00 −0.198503
\(742\) 0 0
\(743\) 23058.0 1.13851 0.569257 0.822160i \(-0.307231\pi\)
0.569257 + 0.822160i \(0.307231\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 24102.0 1.18052
\(748\) 0 0
\(749\) 31122.0 1.51826
\(750\) 0 0
\(751\) −8224.00 −0.399598 −0.199799 0.979837i \(-0.564029\pi\)
−0.199799 + 0.979837i \(0.564029\pi\)
\(752\) 0 0
\(753\) 2925.00 0.141558
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 7696.00 0.369506 0.184753 0.982785i \(-0.440852\pi\)
0.184753 + 0.982785i \(0.440852\pi\)
\(758\) 0 0
\(759\) −810.000 −0.0387367
\(760\) 0 0
\(761\) −6363.00 −0.303099 −0.151550 0.988450i \(-0.548426\pi\)
−0.151550 + 0.988450i \(0.548426\pi\)
\(762\) 0 0
\(763\) 20852.0 0.989375
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 3168.00 0.149139
\(768\) 0 0
\(769\) 8333.00 0.390762 0.195381 0.980727i \(-0.437406\pi\)
0.195381 + 0.980727i \(0.437406\pi\)
\(770\) 0 0
\(771\) −18.0000 −0.000840797 0
\(772\) 0 0
\(773\) −32760.0 −1.52431 −0.762157 0.647392i \(-0.775860\pi\)
−0.762157 + 0.647392i \(0.775860\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 5564.00 0.256895
\(778\) 0 0
\(779\) 41769.0 1.92109
\(780\) 0 0
\(781\) 4860.00 0.222669
\(782\) 0 0
\(783\) 7632.00 0.348334
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 43732.0 1.98078 0.990392 0.138286i \(-0.0441595\pi\)
0.990392 + 0.138286i \(0.0441595\pi\)
\(788\) 0 0
\(789\) −6786.00 −0.306195
\(790\) 0 0
\(791\) 29718.0 1.33584
\(792\) 0 0
\(793\) 5192.00 0.232501
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −16866.0 −0.749591 −0.374796 0.927107i \(-0.622287\pi\)
−0.374796 + 0.927107i \(0.622287\pi\)
\(798\) 0 0
\(799\) −54756.0 −2.42444
\(800\) 0 0
\(801\) −9126.00 −0.402561
\(802\) 0 0
\(803\) −13455.0 −0.591303
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −7632.00 −0.332911
\(808\) 0 0
\(809\) 16146.0 0.701685 0.350842 0.936434i \(-0.385895\pi\)
0.350842 + 0.936434i \(0.385895\pi\)
\(810\) 0 0
\(811\) 32444.0 1.40476 0.702382 0.711801i \(-0.252120\pi\)
0.702382 + 0.711801i \(0.252120\pi\)
\(812\) 0 0
\(813\) −650.000 −0.0280400
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −41860.0 −1.79253
\(818\) 0 0
\(819\) −29744.0 −1.26903
\(820\) 0 0
\(821\) −2574.00 −0.109419 −0.0547096 0.998502i \(-0.517423\pi\)
−0.0547096 + 0.998502i \(0.517423\pi\)
\(822\) 0 0
\(823\) 27604.0 1.16916 0.584578 0.811338i \(-0.301260\pi\)
0.584578 + 0.811338i \(0.301260\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −11655.0 −0.490065 −0.245033 0.969515i \(-0.578799\pi\)
−0.245033 + 0.969515i \(0.578799\pi\)
\(828\) 0 0
\(829\) 33428.0 1.40049 0.700243 0.713905i \(-0.253075\pi\)
0.700243 + 0.713905i \(0.253075\pi\)
\(830\) 0 0
\(831\) −3232.00 −0.134918
\(832\) 0 0
\(833\) −38961.0 −1.62055
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 1378.00 0.0569064
\(838\) 0 0
\(839\) −17712.0 −0.728827 −0.364414 0.931237i \(-0.618731\pi\)
−0.364414 + 0.931237i \(0.618731\pi\)
\(840\) 0 0
\(841\) −3653.00 −0.149781
\(842\) 0 0
\(843\) −4446.00 −0.181647
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −18044.0 −0.731994
\(848\) 0 0
\(849\) 2483.00 0.100373
\(850\) 0 0
\(851\) 3852.00 0.155164
\(852\) 0 0
\(853\) 10270.0 0.412237 0.206118 0.978527i \(-0.433917\pi\)
0.206118 + 0.978527i \(0.433917\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −38709.0 −1.54291 −0.771455 0.636284i \(-0.780471\pi\)
−0.771455 + 0.636284i \(0.780471\pi\)
\(858\) 0 0
\(859\) 15509.0 0.616019 0.308009 0.951383i \(-0.400337\pi\)
0.308009 + 0.951383i \(0.400337\pi\)
\(860\) 0 0
\(861\) −11934.0 −0.472369
\(862\) 0 0
\(863\) −15912.0 −0.627637 −0.313819 0.949483i \(-0.601608\pi\)
−0.313819 + 0.949483i \(0.601608\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −8776.00 −0.343770
\(868\) 0 0
\(869\) −40410.0 −1.57746
\(870\) 0 0
\(871\) 11044.0 0.429635
\(872\) 0 0
\(873\) 10036.0 0.389080
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 10972.0 0.422461 0.211230 0.977436i \(-0.432253\pi\)
0.211230 + 0.977436i \(0.432253\pi\)
\(878\) 0 0
\(879\) −4050.00 −0.155407
\(880\) 0 0
\(881\) −18738.0 −0.716571 −0.358286 0.933612i \(-0.616639\pi\)
−0.358286 + 0.933612i \(0.616639\pi\)
\(882\) 0 0
\(883\) 21367.0 0.814334 0.407167 0.913354i \(-0.366517\pi\)
0.407167 + 0.913354i \(0.366517\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −20124.0 −0.761779 −0.380889 0.924621i \(-0.624382\pi\)
−0.380889 + 0.924621i \(0.624382\pi\)
\(888\) 0 0
\(889\) −61724.0 −2.32864
\(890\) 0 0
\(891\) 29205.0 1.09810
\(892\) 0 0
\(893\) −42588.0 −1.59592
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 792.000 0.0294806
\(898\) 0 0
\(899\) 3744.00 0.138898
\(900\) 0 0
\(901\) 65286.0 2.41398
\(902\) 0 0
\(903\) 11960.0 0.440757
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −23132.0 −0.846842 −0.423421 0.905933i \(-0.639171\pi\)
−0.423421 + 0.905933i \(0.639171\pi\)
\(908\) 0 0
\(909\) 24804.0 0.905057
\(910\) 0 0
\(911\) 31212.0 1.13513 0.567563 0.823330i \(-0.307886\pi\)
0.567563 + 0.823330i \(0.307886\pi\)
\(912\) 0 0
\(913\) −41715.0 −1.51212
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 32760.0 1.17975
\(918\) 0 0
\(919\) −6994.00 −0.251045 −0.125523 0.992091i \(-0.540061\pi\)
−0.125523 + 0.992091i \(0.540061\pi\)
\(920\) 0 0
\(921\) 2321.00 0.0830397
\(922\) 0 0
\(923\) −4752.00 −0.169463
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −20072.0 −0.711166
\(928\) 0 0
\(929\) 19422.0 0.685915 0.342958 0.939351i \(-0.388571\pi\)
0.342958 + 0.939351i \(0.388571\pi\)
\(930\) 0 0
\(931\) −30303.0 −1.06675
\(932\) 0 0
\(933\) 3258.00 0.114322
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −11699.0 −0.407887 −0.203943 0.978983i \(-0.565376\pi\)
−0.203943 + 0.978983i \(0.565376\pi\)
\(938\) 0 0
\(939\) 3626.00 0.126017
\(940\) 0 0
\(941\) −42948.0 −1.48785 −0.743924 0.668264i \(-0.767038\pi\)
−0.743924 + 0.668264i \(0.767038\pi\)
\(942\) 0 0
\(943\) −8262.00 −0.285310
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 3816.00 0.130943 0.0654717 0.997854i \(-0.479145\pi\)
0.0654717 + 0.997854i \(0.479145\pi\)
\(948\) 0 0
\(949\) 13156.0 0.450012
\(950\) 0 0
\(951\) 3852.00 0.131346
\(952\) 0 0
\(953\) 43407.0 1.47544 0.737718 0.675109i \(-0.235903\pi\)
0.737718 + 0.675109i \(0.235903\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −6480.00 −0.218881
\(958\) 0 0
\(959\) −23166.0 −0.780051
\(960\) 0 0
\(961\) −29115.0 −0.977309
\(962\) 0 0
\(963\) 31122.0 1.04143
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 43216.0 1.43716 0.718580 0.695445i \(-0.244793\pi\)
0.718580 + 0.695445i \(0.244793\pi\)
\(968\) 0 0
\(969\) −10647.0 −0.352973
\(970\) 0 0
\(971\) −47619.0 −1.57381 −0.786903 0.617076i \(-0.788317\pi\)
−0.786903 + 0.617076i \(0.788317\pi\)
\(972\) 0 0
\(973\) −10114.0 −0.333237
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 4671.00 0.152957 0.0764783 0.997071i \(-0.475632\pi\)
0.0764783 + 0.997071i \(0.475632\pi\)
\(978\) 0 0
\(979\) 15795.0 0.515639
\(980\) 0 0
\(981\) 20852.0 0.678647
\(982\) 0 0
\(983\) −9054.00 −0.293772 −0.146886 0.989153i \(-0.546925\pi\)
−0.146886 + 0.989153i \(0.546925\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 12168.0 0.392413
\(988\) 0 0
\(989\) 8280.00 0.266217
\(990\) 0 0
\(991\) 8126.00 0.260475 0.130238 0.991483i \(-0.458426\pi\)
0.130238 + 0.991483i \(0.458426\pi\)
\(992\) 0 0
\(993\) −7553.00 −0.241377
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −38468.0 −1.22196 −0.610980 0.791646i \(-0.709224\pi\)
−0.610980 + 0.791646i \(0.709224\pi\)
\(998\) 0 0
\(999\) 11342.0 0.359204
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 100.4.a.b.1.1 1
3.2 odd 2 900.4.a.c.1.1 1
4.3 odd 2 400.4.a.l.1.1 1
5.2 odd 4 100.4.c.b.49.2 2
5.3 odd 4 100.4.c.b.49.1 2
5.4 even 2 100.4.a.c.1.1 yes 1
8.3 odd 2 1600.4.a.y.1.1 1
8.5 even 2 1600.4.a.bc.1.1 1
15.2 even 4 900.4.d.a.649.1 2
15.8 even 4 900.4.d.a.649.2 2
15.14 odd 2 900.4.a.p.1.1 1
20.3 even 4 400.4.c.l.49.2 2
20.7 even 4 400.4.c.l.49.1 2
20.19 odd 2 400.4.a.i.1.1 1
40.19 odd 2 1600.4.a.bd.1.1 1
40.29 even 2 1600.4.a.x.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
100.4.a.b.1.1 1 1.1 even 1 trivial
100.4.a.c.1.1 yes 1 5.4 even 2
100.4.c.b.49.1 2 5.3 odd 4
100.4.c.b.49.2 2 5.2 odd 4
400.4.a.i.1.1 1 20.19 odd 2
400.4.a.l.1.1 1 4.3 odd 2
400.4.c.l.49.1 2 20.7 even 4
400.4.c.l.49.2 2 20.3 even 4
900.4.a.c.1.1 1 3.2 odd 2
900.4.a.p.1.1 1 15.14 odd 2
900.4.d.a.649.1 2 15.2 even 4
900.4.d.a.649.2 2 15.8 even 4
1600.4.a.x.1.1 1 40.29 even 2
1600.4.a.y.1.1 1 8.3 odd 2
1600.4.a.bc.1.1 1 8.5 even 2
1600.4.a.bd.1.1 1 40.19 odd 2