Properties

Label 720.4.a.y.1.1
Level $720$
Weight $4$
Character 720.1
Self dual yes
Analytic conductor $42.481$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 720.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(42.4813752041\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 30)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 720.1

$q$-expansion

\(f(q)\) \(=\) \(q+5.00000 q^{5} +4.00000 q^{7} +O(q^{10})\) \(q+5.00000 q^{5} +4.00000 q^{7} -48.0000 q^{11} +2.00000 q^{13} +114.000 q^{17} -140.000 q^{19} +72.0000 q^{23} +25.0000 q^{25} -210.000 q^{29} -272.000 q^{31} +20.0000 q^{35} -334.000 q^{37} +198.000 q^{41} +268.000 q^{43} +216.000 q^{47} -327.000 q^{49} +78.0000 q^{53} -240.000 q^{55} +240.000 q^{59} +302.000 q^{61} +10.0000 q^{65} -596.000 q^{67} -768.000 q^{71} -478.000 q^{73} -192.000 q^{77} +640.000 q^{79} -348.000 q^{83} +570.000 q^{85} -210.000 q^{89} +8.00000 q^{91} -700.000 q^{95} -1534.00 q^{97} +O(q^{100})\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) 5.00000 0.447214
\(6\) 0 0
\(7\) 4.00000 0.215980 0.107990 0.994152i \(-0.465559\pi\)
0.107990 + 0.994152i \(0.465559\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −48.0000 −1.31569 −0.657843 0.753155i \(-0.728531\pi\)
−0.657843 + 0.753155i \(0.728531\pi\)
\(12\) 0 0
\(13\) 2.00000 0.0426692 0.0213346 0.999772i \(-0.493208\pi\)
0.0213346 + 0.999772i \(0.493208\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 114.000 1.62642 0.813208 0.581974i \(-0.197719\pi\)
0.813208 + 0.581974i \(0.197719\pi\)
\(18\) 0 0
\(19\) −140.000 −1.69043 −0.845216 0.534425i \(-0.820528\pi\)
−0.845216 + 0.534425i \(0.820528\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 72.0000 0.652741 0.326370 0.945242i \(-0.394174\pi\)
0.326370 + 0.945242i \(0.394174\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −210.000 −1.34469 −0.672345 0.740238i \(-0.734713\pi\)
−0.672345 + 0.740238i \(0.734713\pi\)
\(30\) 0 0
\(31\) −272.000 −1.57589 −0.787946 0.615745i \(-0.788855\pi\)
−0.787946 + 0.615745i \(0.788855\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 20.0000 0.0965891
\(36\) 0 0
\(37\) −334.000 −1.48403 −0.742017 0.670381i \(-0.766131\pi\)
−0.742017 + 0.670381i \(0.766131\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 198.000 0.754205 0.377102 0.926172i \(-0.376920\pi\)
0.377102 + 0.926172i \(0.376920\pi\)
\(42\) 0 0
\(43\) 268.000 0.950456 0.475228 0.879863i \(-0.342366\pi\)
0.475228 + 0.879863i \(0.342366\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 216.000 0.670358 0.335179 0.942154i \(-0.391203\pi\)
0.335179 + 0.942154i \(0.391203\pi\)
\(48\) 0 0
\(49\) −327.000 −0.953353
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 78.0000 0.202153 0.101077 0.994879i \(-0.467771\pi\)
0.101077 + 0.994879i \(0.467771\pi\)
\(54\) 0 0
\(55\) −240.000 −0.588393
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 240.000 0.529582 0.264791 0.964306i \(-0.414697\pi\)
0.264791 + 0.964306i \(0.414697\pi\)
\(60\) 0 0
\(61\) 302.000 0.633888 0.316944 0.948444i \(-0.397343\pi\)
0.316944 + 0.948444i \(0.397343\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 10.0000 0.0190823
\(66\) 0 0
\(67\) −596.000 −1.08676 −0.543381 0.839487i \(-0.682856\pi\)
−0.543381 + 0.839487i \(0.682856\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −768.000 −1.28373 −0.641865 0.766818i \(-0.721839\pi\)
−0.641865 + 0.766818i \(0.721839\pi\)
\(72\) 0 0
\(73\) −478.000 −0.766379 −0.383190 0.923670i \(-0.625174\pi\)
−0.383190 + 0.923670i \(0.625174\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −192.000 −0.284161
\(78\) 0 0
\(79\) 640.000 0.911464 0.455732 0.890117i \(-0.349378\pi\)
0.455732 + 0.890117i \(0.349378\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −348.000 −0.460216 −0.230108 0.973165i \(-0.573908\pi\)
−0.230108 + 0.973165i \(0.573908\pi\)
\(84\) 0 0
\(85\) 570.000 0.727355
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −210.000 −0.250112 −0.125056 0.992150i \(-0.539911\pi\)
−0.125056 + 0.992150i \(0.539911\pi\)
\(90\) 0 0
\(91\) 8.00000 0.00921569
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −700.000 −0.755984
\(96\) 0 0
\(97\) −1534.00 −1.60571 −0.802856 0.596173i \(-0.796687\pi\)
−0.802856 + 0.596173i \(0.796687\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −1722.00 −1.69649 −0.848245 0.529605i \(-0.822340\pi\)
−0.848245 + 0.529605i \(0.822340\pi\)
\(102\) 0 0
\(103\) −1052.00 −1.00638 −0.503188 0.864177i \(-0.667840\pi\)
−0.503188 + 0.864177i \(0.667840\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −564.000 −0.509570 −0.254785 0.966998i \(-0.582005\pi\)
−0.254785 + 0.966998i \(0.582005\pi\)
\(108\) 0 0
\(109\) −610.000 −0.536031 −0.268016 0.963415i \(-0.586368\pi\)
−0.268016 + 0.963415i \(0.586368\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1302.00 −1.08391 −0.541955 0.840407i \(-0.682316\pi\)
−0.541955 + 0.840407i \(0.682316\pi\)
\(114\) 0 0
\(115\) 360.000 0.291915
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 456.000 0.351273
\(120\) 0 0
\(121\) 973.000 0.731029
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) 124.000 0.0866395 0.0433198 0.999061i \(-0.486207\pi\)
0.0433198 + 0.999061i \(0.486207\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 192.000 0.128054 0.0640272 0.997948i \(-0.479606\pi\)
0.0640272 + 0.997948i \(0.479606\pi\)
\(132\) 0 0
\(133\) −560.000 −0.365099
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2514.00 1.56778 0.783889 0.620901i \(-0.213233\pi\)
0.783889 + 0.620901i \(0.213233\pi\)
\(138\) 0 0
\(139\) −1340.00 −0.817679 −0.408839 0.912606i \(-0.634066\pi\)
−0.408839 + 0.912606i \(0.634066\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −96.0000 −0.0561393
\(144\) 0 0
\(145\) −1050.00 −0.601364
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1410.00 −0.775246 −0.387623 0.921818i \(-0.626704\pi\)
−0.387623 + 0.921818i \(0.626704\pi\)
\(150\) 0 0
\(151\) 2128.00 1.14685 0.573424 0.819258i \(-0.305615\pi\)
0.573424 + 0.819258i \(0.305615\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1360.00 −0.704760
\(156\) 0 0
\(157\) 3026.00 1.53822 0.769112 0.639114i \(-0.220699\pi\)
0.769112 + 0.639114i \(0.220699\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 288.000 0.140979
\(162\) 0 0
\(163\) −2612.00 −1.25514 −0.627569 0.778561i \(-0.715950\pi\)
−0.627569 + 0.778561i \(0.715950\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −24.0000 −0.0111208 −0.00556041 0.999985i \(-0.501770\pi\)
−0.00556041 + 0.999985i \(0.501770\pi\)
\(168\) 0 0
\(169\) −2193.00 −0.998179
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1962.00 −0.862243 −0.431122 0.902294i \(-0.641882\pi\)
−0.431122 + 0.902294i \(0.641882\pi\)
\(174\) 0 0
\(175\) 100.000 0.0431959
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −120.000 −0.0501074 −0.0250537 0.999686i \(-0.507976\pi\)
−0.0250537 + 0.999686i \(0.507976\pi\)
\(180\) 0 0
\(181\) 902.000 0.370415 0.185208 0.982699i \(-0.440704\pi\)
0.185208 + 0.982699i \(0.440704\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1670.00 −0.663680
\(186\) 0 0
\(187\) −5472.00 −2.13985
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −168.000 −0.0636443 −0.0318221 0.999494i \(-0.510131\pi\)
−0.0318221 + 0.999494i \(0.510131\pi\)
\(192\) 0 0
\(193\) −1318.00 −0.491563 −0.245782 0.969325i \(-0.579045\pi\)
−0.245782 + 0.969325i \(0.579045\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 4014.00 1.45170 0.725852 0.687851i \(-0.241446\pi\)
0.725852 + 0.687851i \(0.241446\pi\)
\(198\) 0 0
\(199\) −2000.00 −0.712443 −0.356222 0.934401i \(-0.615935\pi\)
−0.356222 + 0.934401i \(0.615935\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −840.000 −0.290426
\(204\) 0 0
\(205\) 990.000 0.337291
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 6720.00 2.22408
\(210\) 0 0
\(211\) 3868.00 1.26201 0.631005 0.775779i \(-0.282643\pi\)
0.631005 + 0.775779i \(0.282643\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1340.00 0.425057
\(216\) 0 0
\(217\) −1088.00 −0.340361
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 228.000 0.0693979
\(222\) 0 0
\(223\) 3148.00 0.945317 0.472658 0.881246i \(-0.343294\pi\)
0.472658 + 0.881246i \(0.343294\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 2556.00 0.747347 0.373673 0.927560i \(-0.378098\pi\)
0.373673 + 0.927560i \(0.378098\pi\)
\(228\) 0 0
\(229\) −610.000 −0.176026 −0.0880130 0.996119i \(-0.528052\pi\)
−0.0880130 + 0.996119i \(0.528052\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2058.00 0.578644 0.289322 0.957232i \(-0.406570\pi\)
0.289322 + 0.957232i \(0.406570\pi\)
\(234\) 0 0
\(235\) 1080.00 0.299793
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 4920.00 1.33158 0.665792 0.746138i \(-0.268094\pi\)
0.665792 + 0.746138i \(0.268094\pi\)
\(240\) 0 0
\(241\) −1438.00 −0.384356 −0.192178 0.981360i \(-0.561555\pi\)
−0.192178 + 0.981360i \(0.561555\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1635.00 −0.426352
\(246\) 0 0
\(247\) −280.000 −0.0721294
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 792.000 0.199166 0.0995829 0.995029i \(-0.468249\pi\)
0.0995829 + 0.995029i \(0.468249\pi\)
\(252\) 0 0
\(253\) −3456.00 −0.858802
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2166.00 −0.525725 −0.262863 0.964833i \(-0.584667\pi\)
−0.262863 + 0.964833i \(0.584667\pi\)
\(258\) 0 0
\(259\) −1336.00 −0.320521
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 3192.00 0.748392 0.374196 0.927350i \(-0.377919\pi\)
0.374196 + 0.927350i \(0.377919\pi\)
\(264\) 0 0
\(265\) 390.000 0.0904057
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −5490.00 −1.24435 −0.622177 0.782877i \(-0.713752\pi\)
−0.622177 + 0.782877i \(0.713752\pi\)
\(270\) 0 0
\(271\) 6328.00 1.41845 0.709223 0.704985i \(-0.249046\pi\)
0.709223 + 0.704985i \(0.249046\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1200.00 −0.263137
\(276\) 0 0
\(277\) −574.000 −0.124507 −0.0622533 0.998060i \(-0.519829\pi\)
−0.0622533 + 0.998060i \(0.519829\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −4242.00 −0.900557 −0.450278 0.892888i \(-0.648675\pi\)
−0.450278 + 0.892888i \(0.648675\pi\)
\(282\) 0 0
\(283\) 628.000 0.131911 0.0659553 0.997823i \(-0.478991\pi\)
0.0659553 + 0.997823i \(0.478991\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 792.000 0.162893
\(288\) 0 0
\(289\) 8083.00 1.64523
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 558.000 0.111258 0.0556292 0.998451i \(-0.482284\pi\)
0.0556292 + 0.998451i \(0.482284\pi\)
\(294\) 0 0
\(295\) 1200.00 0.236836
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 144.000 0.0278520
\(300\) 0 0
\(301\) 1072.00 0.205279
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1510.00 0.283483
\(306\) 0 0
\(307\) 6964.00 1.29465 0.647323 0.762216i \(-0.275888\pi\)
0.647323 + 0.762216i \(0.275888\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 2832.00 0.516360 0.258180 0.966097i \(-0.416877\pi\)
0.258180 + 0.966097i \(0.416877\pi\)
\(312\) 0 0
\(313\) 8642.00 1.56062 0.780311 0.625392i \(-0.215061\pi\)
0.780311 + 0.625392i \(0.215061\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2214.00 0.392273 0.196137 0.980577i \(-0.437160\pi\)
0.196137 + 0.980577i \(0.437160\pi\)
\(318\) 0 0
\(319\) 10080.0 1.76919
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −15960.0 −2.74934
\(324\) 0 0
\(325\) 50.0000 0.00853385
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 864.000 0.144784
\(330\) 0 0
\(331\) −10772.0 −1.78877 −0.894385 0.447299i \(-0.852386\pi\)
−0.894385 + 0.447299i \(0.852386\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −2980.00 −0.486014
\(336\) 0 0
\(337\) −1654.00 −0.267356 −0.133678 0.991025i \(-0.542679\pi\)
−0.133678 + 0.991025i \(0.542679\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 13056.0 2.07338
\(342\) 0 0
\(343\) −2680.00 −0.421885
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2196.00 0.339733 0.169867 0.985467i \(-0.445666\pi\)
0.169867 + 0.985467i \(0.445666\pi\)
\(348\) 0 0
\(349\) 8270.00 1.26843 0.634216 0.773156i \(-0.281323\pi\)
0.634216 + 0.773156i \(0.281323\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −10302.0 −1.55331 −0.776657 0.629923i \(-0.783086\pi\)
−0.776657 + 0.629923i \(0.783086\pi\)
\(354\) 0 0
\(355\) −3840.00 −0.574102
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −2280.00 −0.335192 −0.167596 0.985856i \(-0.553600\pi\)
−0.167596 + 0.985856i \(0.553600\pi\)
\(360\) 0 0
\(361\) 12741.0 1.85756
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −2390.00 −0.342735
\(366\) 0 0
\(367\) 8764.00 1.24653 0.623266 0.782010i \(-0.285805\pi\)
0.623266 + 0.782010i \(0.285805\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 312.000 0.0436610
\(372\) 0 0
\(373\) −1318.00 −0.182958 −0.0914792 0.995807i \(-0.529159\pi\)
−0.0914792 + 0.995807i \(0.529159\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −420.000 −0.0573769
\(378\) 0 0
\(379\) −1100.00 −0.149085 −0.0745425 0.997218i \(-0.523750\pi\)
−0.0745425 + 0.997218i \(0.523750\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −3528.00 −0.470685 −0.235343 0.971912i \(-0.575621\pi\)
−0.235343 + 0.971912i \(0.575621\pi\)
\(384\) 0 0
\(385\) −960.000 −0.127081
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 9630.00 1.25517 0.627584 0.778549i \(-0.284044\pi\)
0.627584 + 0.778549i \(0.284044\pi\)
\(390\) 0 0
\(391\) 8208.00 1.06163
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 3200.00 0.407619
\(396\) 0 0
\(397\) −3094.00 −0.391142 −0.195571 0.980690i \(-0.562656\pi\)
−0.195571 + 0.980690i \(0.562656\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1638.00 0.203985 0.101992 0.994785i \(-0.467478\pi\)
0.101992 + 0.994785i \(0.467478\pi\)
\(402\) 0 0
\(403\) −544.000 −0.0672421
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 16032.0 1.95252
\(408\) 0 0
\(409\) −13750.0 −1.66233 −0.831166 0.556024i \(-0.812326\pi\)
−0.831166 + 0.556024i \(0.812326\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 960.000 0.114379
\(414\) 0 0
\(415\) −1740.00 −0.205815
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −12480.0 −1.45510 −0.727551 0.686053i \(-0.759342\pi\)
−0.727551 + 0.686053i \(0.759342\pi\)
\(420\) 0 0
\(421\) 7262.00 0.840685 0.420342 0.907366i \(-0.361910\pi\)
0.420342 + 0.907366i \(0.361910\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 2850.00 0.325283
\(426\) 0 0
\(427\) 1208.00 0.136907
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 9792.00 1.09435 0.547174 0.837019i \(-0.315704\pi\)
0.547174 + 0.837019i \(0.315704\pi\)
\(432\) 0 0
\(433\) 1802.00 0.199997 0.0999984 0.994988i \(-0.468116\pi\)
0.0999984 + 0.994988i \(0.468116\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −10080.0 −1.10341
\(438\) 0 0
\(439\) 2320.00 0.252227 0.126113 0.992016i \(-0.459750\pi\)
0.126113 + 0.992016i \(0.459750\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 11172.0 1.19819 0.599095 0.800678i \(-0.295527\pi\)
0.599095 + 0.800678i \(0.295527\pi\)
\(444\) 0 0
\(445\) −1050.00 −0.111853
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −6810.00 −0.715777 −0.357888 0.933764i \(-0.616503\pi\)
−0.357888 + 0.933764i \(0.616503\pi\)
\(450\) 0 0
\(451\) −9504.00 −0.992297
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 40.0000 0.00412138
\(456\) 0 0
\(457\) 17066.0 1.74686 0.873429 0.486952i \(-0.161891\pi\)
0.873429 + 0.486952i \(0.161891\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 18918.0 1.91128 0.955639 0.294541i \(-0.0951667\pi\)
0.955639 + 0.294541i \(0.0951667\pi\)
\(462\) 0 0
\(463\) −1052.00 −0.105595 −0.0527976 0.998605i \(-0.516814\pi\)
−0.0527976 + 0.998605i \(0.516814\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 11076.0 1.09751 0.548754 0.835984i \(-0.315102\pi\)
0.548754 + 0.835984i \(0.315102\pi\)
\(468\) 0 0
\(469\) −2384.00 −0.234718
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −12864.0 −1.25050
\(474\) 0 0
\(475\) −3500.00 −0.338086
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −9000.00 −0.858498 −0.429249 0.903186i \(-0.641222\pi\)
−0.429249 + 0.903186i \(0.641222\pi\)
\(480\) 0 0
\(481\) −668.000 −0.0633226
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −7670.00 −0.718096
\(486\) 0 0
\(487\) 8764.00 0.815472 0.407736 0.913100i \(-0.366318\pi\)
0.407736 + 0.913100i \(0.366318\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 5592.00 0.513978 0.256989 0.966414i \(-0.417270\pi\)
0.256989 + 0.966414i \(0.417270\pi\)
\(492\) 0 0
\(493\) −23940.0 −2.18703
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −3072.00 −0.277260
\(498\) 0 0
\(499\) −4700.00 −0.421645 −0.210823 0.977524i \(-0.567614\pi\)
−0.210823 + 0.977524i \(0.567614\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −11808.0 −1.04671 −0.523353 0.852116i \(-0.675319\pi\)
−0.523353 + 0.852116i \(0.675319\pi\)
\(504\) 0 0
\(505\) −8610.00 −0.758693
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −1170.00 −0.101885 −0.0509424 0.998702i \(-0.516222\pi\)
−0.0509424 + 0.998702i \(0.516222\pi\)
\(510\) 0 0
\(511\) −1912.00 −0.165522
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −5260.00 −0.450065
\(516\) 0 0
\(517\) −10368.0 −0.881981
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 16638.0 1.39909 0.699543 0.714590i \(-0.253387\pi\)
0.699543 + 0.714590i \(0.253387\pi\)
\(522\) 0 0
\(523\) −15692.0 −1.31198 −0.655988 0.754771i \(-0.727748\pi\)
−0.655988 + 0.754771i \(0.727748\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −31008.0 −2.56305
\(528\) 0 0
\(529\) −6983.00 −0.573929
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 396.000 0.0321814
\(534\) 0 0
\(535\) −2820.00 −0.227886
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 15696.0 1.25431
\(540\) 0 0
\(541\) −22018.0 −1.74977 −0.874887 0.484327i \(-0.839064\pi\)
−0.874887 + 0.484327i \(0.839064\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −3050.00 −0.239720
\(546\) 0 0
\(547\) 4564.00 0.356751 0.178375 0.983963i \(-0.442916\pi\)
0.178375 + 0.983963i \(0.442916\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 29400.0 2.27311
\(552\) 0 0
\(553\) 2560.00 0.196858
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 7734.00 0.588331 0.294165 0.955755i \(-0.404958\pi\)
0.294165 + 0.955755i \(0.404958\pi\)
\(558\) 0 0
\(559\) 536.000 0.0405552
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −20148.0 −1.50824 −0.754118 0.656739i \(-0.771935\pi\)
−0.754118 + 0.656739i \(0.771935\pi\)
\(564\) 0 0
\(565\) −6510.00 −0.484739
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 24030.0 1.77046 0.885228 0.465156i \(-0.154002\pi\)
0.885228 + 0.465156i \(0.154002\pi\)
\(570\) 0 0
\(571\) −2372.00 −0.173844 −0.0869222 0.996215i \(-0.527703\pi\)
−0.0869222 + 0.996215i \(0.527703\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1800.00 0.130548
\(576\) 0 0
\(577\) 8546.00 0.616594 0.308297 0.951290i \(-0.400241\pi\)
0.308297 + 0.951290i \(0.400241\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1392.00 −0.0993974
\(582\) 0 0
\(583\) −3744.00 −0.265970
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −15444.0 −1.08593 −0.542966 0.839755i \(-0.682699\pi\)
−0.542966 + 0.839755i \(0.682699\pi\)
\(588\) 0 0
\(589\) 38080.0 2.66394
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −18342.0 −1.27018 −0.635089 0.772439i \(-0.719037\pi\)
−0.635089 + 0.772439i \(0.719037\pi\)
\(594\) 0 0
\(595\) 2280.00 0.157094
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 24600.0 1.67801 0.839006 0.544123i \(-0.183137\pi\)
0.839006 + 0.544123i \(0.183137\pi\)
\(600\) 0 0
\(601\) −8998.00 −0.610709 −0.305354 0.952239i \(-0.598775\pi\)
−0.305354 + 0.952239i \(0.598775\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 4865.00 0.326926
\(606\) 0 0
\(607\) −4076.00 −0.272553 −0.136277 0.990671i \(-0.543514\pi\)
−0.136277 + 0.990671i \(0.543514\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 432.000 0.0286037
\(612\) 0 0
\(613\) −4078.00 −0.268693 −0.134347 0.990934i \(-0.542894\pi\)
−0.134347 + 0.990934i \(0.542894\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −10086.0 −0.658099 −0.329049 0.944313i \(-0.606728\pi\)
−0.329049 + 0.944313i \(0.606728\pi\)
\(618\) 0 0
\(619\) −8780.00 −0.570110 −0.285055 0.958511i \(-0.592012\pi\)
−0.285055 + 0.958511i \(0.592012\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −840.000 −0.0540191
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −38076.0 −2.41366
\(630\) 0 0
\(631\) −2792.00 −0.176145 −0.0880727 0.996114i \(-0.528071\pi\)
−0.0880727 + 0.996114i \(0.528071\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 620.000 0.0387464
\(636\) 0 0
\(637\) −654.000 −0.0406788
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −7602.00 −0.468426 −0.234213 0.972185i \(-0.575251\pi\)
−0.234213 + 0.972185i \(0.575251\pi\)
\(642\) 0 0
\(643\) −24212.0 −1.48496 −0.742479 0.669869i \(-0.766350\pi\)
−0.742479 + 0.669869i \(0.766350\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 9456.00 0.574581 0.287290 0.957844i \(-0.407246\pi\)
0.287290 + 0.957844i \(0.407246\pi\)
\(648\) 0 0
\(649\) −11520.0 −0.696764
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 9558.00 0.572792 0.286396 0.958111i \(-0.407543\pi\)
0.286396 + 0.958111i \(0.407543\pi\)
\(654\) 0 0
\(655\) 960.000 0.0572676
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −29280.0 −1.73078 −0.865392 0.501095i \(-0.832931\pi\)
−0.865392 + 0.501095i \(0.832931\pi\)
\(660\) 0 0
\(661\) −29098.0 −1.71223 −0.856113 0.516789i \(-0.827127\pi\)
−0.856113 + 0.516789i \(0.827127\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −2800.00 −0.163277
\(666\) 0 0
\(667\) −15120.0 −0.877734
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −14496.0 −0.833997
\(672\) 0 0
\(673\) −11638.0 −0.666585 −0.333293 0.942823i \(-0.608160\pi\)
−0.333293 + 0.942823i \(0.608160\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −3426.00 −0.194493 −0.0972466 0.995260i \(-0.531004\pi\)
−0.0972466 + 0.995260i \(0.531004\pi\)
\(678\) 0 0
\(679\) −6136.00 −0.346801
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −20148.0 −1.12876 −0.564379 0.825516i \(-0.690884\pi\)
−0.564379 + 0.825516i \(0.690884\pi\)
\(684\) 0 0
\(685\) 12570.0 0.701131
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 156.000 0.00862573
\(690\) 0 0
\(691\) 29428.0 1.62011 0.810053 0.586356i \(-0.199438\pi\)
0.810053 + 0.586356i \(0.199438\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −6700.00 −0.365677
\(696\) 0 0
\(697\) 22572.0 1.22665
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −16242.0 −0.875110 −0.437555 0.899192i \(-0.644155\pi\)
−0.437555 + 0.899192i \(0.644155\pi\)
\(702\) 0 0
\(703\) 46760.0 2.50866
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −6888.00 −0.366407
\(708\) 0 0
\(709\) 2030.00 0.107529 0.0537646 0.998554i \(-0.482878\pi\)
0.0537646 + 0.998554i \(0.482878\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −19584.0 −1.02865
\(714\) 0 0
\(715\) −480.000 −0.0251063
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 6960.00 0.361007 0.180504 0.983574i \(-0.442227\pi\)
0.180504 + 0.983574i \(0.442227\pi\)
\(720\) 0 0
\(721\) −4208.00 −0.217357
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −5250.00 −0.268938
\(726\) 0 0
\(727\) −18596.0 −0.948676 −0.474338 0.880343i \(-0.657313\pi\)
−0.474338 + 0.880343i \(0.657313\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 30552.0 1.54584
\(732\) 0 0
\(733\) 21242.0 1.07038 0.535192 0.844731i \(-0.320239\pi\)
0.535192 + 0.844731i \(0.320239\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 28608.0 1.42984
\(738\) 0 0
\(739\) 340.000 0.0169244 0.00846218 0.999964i \(-0.497306\pi\)
0.00846218 + 0.999964i \(0.497306\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −21888.0 −1.08074 −0.540372 0.841426i \(-0.681716\pi\)
−0.540372 + 0.841426i \(0.681716\pi\)
\(744\) 0 0
\(745\) −7050.00 −0.346701
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −2256.00 −0.110057
\(750\) 0 0
\(751\) −17792.0 −0.864500 −0.432250 0.901754i \(-0.642280\pi\)
−0.432250 + 0.901754i \(0.642280\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 10640.0 0.512886
\(756\) 0 0
\(757\) 37346.0 1.79308 0.896541 0.442960i \(-0.146072\pi\)
0.896541 + 0.442960i \(0.146072\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 11358.0 0.541034 0.270517 0.962715i \(-0.412805\pi\)
0.270517 + 0.962715i \(0.412805\pi\)
\(762\) 0 0
\(763\) −2440.00 −0.115772
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 480.000 0.0225969
\(768\) 0 0
\(769\) −34270.0 −1.60703 −0.803516 0.595283i \(-0.797040\pi\)
−0.803516 + 0.595283i \(0.797040\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 13278.0 0.617822 0.308911 0.951091i \(-0.400035\pi\)
0.308911 + 0.951091i \(0.400035\pi\)
\(774\) 0 0
\(775\) −6800.00 −0.315178
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −27720.0 −1.27493
\(780\) 0 0
\(781\) 36864.0 1.68899
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 15130.0 0.687914
\(786\) 0 0
\(787\) 11164.0 0.505659 0.252829 0.967511i \(-0.418639\pi\)
0.252829 + 0.967511i \(0.418639\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −5208.00 −0.234103
\(792\) 0 0
\(793\) 604.000 0.0270475
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 5094.00 0.226397 0.113199 0.993572i \(-0.463890\pi\)
0.113199 + 0.993572i \(0.463890\pi\)
\(798\) 0 0
\(799\) 24624.0 1.09028
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 22944.0 1.00831
\(804\) 0 0
\(805\) 1440.00 0.0630476
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 8790.00 0.382002 0.191001 0.981590i \(-0.438827\pi\)
0.191001 + 0.981590i \(0.438827\pi\)
\(810\) 0 0
\(811\) −5852.00 −0.253380 −0.126690 0.991942i \(-0.540435\pi\)
−0.126690 + 0.991942i \(0.540435\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −13060.0 −0.561315
\(816\) 0 0
\(817\) −37520.0 −1.60668
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 29478.0 1.25309 0.626546 0.779384i \(-0.284468\pi\)
0.626546 + 0.779384i \(0.284468\pi\)
\(822\) 0 0
\(823\) −39332.0 −1.66589 −0.832945 0.553356i \(-0.813347\pi\)
−0.832945 + 0.553356i \(0.813347\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 6756.00 0.284074 0.142037 0.989861i \(-0.454635\pi\)
0.142037 + 0.989861i \(0.454635\pi\)
\(828\) 0 0
\(829\) 3950.00 0.165488 0.0827438 0.996571i \(-0.473632\pi\)
0.0827438 + 0.996571i \(0.473632\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −37278.0 −1.55055
\(834\) 0 0
\(835\) −120.000 −0.00497338
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 12360.0 0.508599 0.254300 0.967126i \(-0.418155\pi\)
0.254300 + 0.967126i \(0.418155\pi\)
\(840\) 0 0
\(841\) 19711.0 0.808192
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −10965.0 −0.446399
\(846\) 0 0
\(847\) 3892.00 0.157887
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −24048.0 −0.968690
\(852\) 0 0
\(853\) −35998.0 −1.44496 −0.722478 0.691394i \(-0.756997\pi\)
−0.722478 + 0.691394i \(0.756997\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 21594.0 0.860720 0.430360 0.902657i \(-0.358387\pi\)
0.430360 + 0.902657i \(0.358387\pi\)
\(858\) 0 0
\(859\) −9260.00 −0.367808 −0.183904 0.982944i \(-0.558874\pi\)
−0.183904 + 0.982944i \(0.558874\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 31632.0 1.24770 0.623850 0.781544i \(-0.285567\pi\)
0.623850 + 0.781544i \(0.285567\pi\)
\(864\) 0 0
\(865\) −9810.00 −0.385607
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −30720.0 −1.19920
\(870\) 0 0
\(871\) −1192.00 −0.0463713
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 500.000 0.0193178
\(876\) 0 0
\(877\) −39694.0 −1.52836 −0.764180 0.645003i \(-0.776856\pi\)
−0.764180 + 0.645003i \(0.776856\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −1242.00 −0.0474961 −0.0237480 0.999718i \(-0.507560\pi\)
−0.0237480 + 0.999718i \(0.507560\pi\)
\(882\) 0 0
\(883\) 2668.00 0.101682 0.0508411 0.998707i \(-0.483810\pi\)
0.0508411 + 0.998707i \(0.483810\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −4344.00 −0.164439 −0.0822194 0.996614i \(-0.526201\pi\)
−0.0822194 + 0.996614i \(0.526201\pi\)
\(888\) 0 0
\(889\) 496.000 0.0187124
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −30240.0 −1.13319
\(894\) 0 0
\(895\) −600.000 −0.0224087
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 57120.0 2.11909
\(900\) 0 0
\(901\) 8892.00 0.328785
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 4510.00 0.165655
\(906\) 0 0
\(907\) −4436.00 −0.162398 −0.0811990 0.996698i \(-0.525875\pi\)
−0.0811990 + 0.996698i \(0.525875\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 22752.0 0.827450 0.413725 0.910402i \(-0.364227\pi\)
0.413725 + 0.910402i \(0.364227\pi\)
\(912\) 0 0
\(913\) 16704.0 0.605500
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 768.000 0.0276571
\(918\) 0 0
\(919\) 27160.0 0.974892 0.487446 0.873153i \(-0.337929\pi\)
0.487446 + 0.873153i \(0.337929\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −1536.00 −0.0547758
\(924\) 0 0
\(925\) −8350.00 −0.296807
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 33030.0 1.16650 0.583250 0.812292i \(-0.301781\pi\)
0.583250 + 0.812292i \(0.301781\pi\)
\(930\) 0 0
\(931\) 45780.0 1.61158
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −27360.0 −0.956971
\(936\) 0 0
\(937\) −29974.0 −1.04505 −0.522523 0.852625i \(-0.675009\pi\)
−0.522523 + 0.852625i \(0.675009\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −13962.0 −0.483686 −0.241843 0.970315i \(-0.577752\pi\)
−0.241843 + 0.970315i \(0.577752\pi\)
\(942\) 0 0
\(943\) 14256.0 0.492300
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 35196.0 1.20773 0.603863 0.797088i \(-0.293627\pi\)
0.603863 + 0.797088i \(0.293627\pi\)
\(948\) 0 0
\(949\) −956.000 −0.0327008
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 28338.0 0.963230 0.481615 0.876383i \(-0.340050\pi\)
0.481615 + 0.876383i \(0.340050\pi\)
\(954\) 0 0
\(955\) −840.000 −0.0284626
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 10056.0 0.338608
\(960\) 0 0
\(961\) 44193.0 1.48343
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −6590.00 −0.219834
\(966\) 0 0
\(967\) 17524.0 0.582765 0.291383 0.956607i \(-0.405885\pi\)
0.291383 + 0.956607i \(0.405885\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −26808.0 −0.886004 −0.443002 0.896521i \(-0.646087\pi\)
−0.443002 + 0.896521i \(0.646087\pi\)
\(972\) 0 0
\(973\) −5360.00 −0.176602
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 10914.0 0.357390 0.178695 0.983905i \(-0.442813\pi\)
0.178695 + 0.983905i \(0.442813\pi\)
\(978\) 0 0
\(979\) 10080.0 0.329069
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 22272.0 0.722652 0.361326 0.932440i \(-0.382324\pi\)
0.361326 + 0.932440i \(0.382324\pi\)
\(984\) 0 0
\(985\) 20070.0 0.649222
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 19296.0 0.620402
\(990\) 0 0
\(991\) −14072.0 −0.451071 −0.225536 0.974235i \(-0.572413\pi\)
−0.225536 + 0.974235i \(0.572413\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −10000.0 −0.318614
\(996\) 0 0
\(997\) 4826.00 0.153301 0.0766504 0.997058i \(-0.475577\pi\)
0.0766504 + 0.997058i \(0.475577\pi\)
\(998\) 0 0
\(999\) 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 720.4.a.y.1.1 1
3.2 odd 2 240.4.a.b.1.1 1
4.3 odd 2 90.4.a.c.1.1 1
12.11 even 2 30.4.a.b.1.1 1
15.2 even 4 1200.4.f.r.49.2 2
15.8 even 4 1200.4.f.r.49.1 2
15.14 odd 2 1200.4.a.ba.1.1 1
20.3 even 4 450.4.c.j.199.2 2
20.7 even 4 450.4.c.j.199.1 2
20.19 odd 2 450.4.a.r.1.1 1
24.5 odd 2 960.4.a.bg.1.1 1
24.11 even 2 960.4.a.n.1.1 1
36.7 odd 6 810.4.e.p.271.1 2
36.11 even 6 810.4.e.i.271.1 2
36.23 even 6 810.4.e.i.541.1 2
36.31 odd 6 810.4.e.p.541.1 2
60.23 odd 4 150.4.c.c.49.1 2
60.47 odd 4 150.4.c.c.49.2 2
60.59 even 2 150.4.a.b.1.1 1
84.83 odd 2 1470.4.a.r.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
30.4.a.b.1.1 1 12.11 even 2
90.4.a.c.1.1 1 4.3 odd 2
150.4.a.b.1.1 1 60.59 even 2
150.4.c.c.49.1 2 60.23 odd 4
150.4.c.c.49.2 2 60.47 odd 4
240.4.a.b.1.1 1 3.2 odd 2
450.4.a.r.1.1 1 20.19 odd 2
450.4.c.j.199.1 2 20.7 even 4
450.4.c.j.199.2 2 20.3 even 4
720.4.a.y.1.1 1 1.1 even 1 trivial
810.4.e.i.271.1 2 36.11 even 6
810.4.e.i.541.1 2 36.23 even 6
810.4.e.p.271.1 2 36.7 odd 6
810.4.e.p.541.1 2 36.31 odd 6
960.4.a.n.1.1 1 24.11 even 2
960.4.a.bg.1.1 1 24.5 odd 2
1200.4.a.ba.1.1 1 15.14 odd 2
1200.4.f.r.49.1 2 15.8 even 4
1200.4.f.r.49.2 2 15.2 even 4
1470.4.a.r.1.1 1 84.83 odd 2