Properties

Label 1960.4.a.h.1.1
Level $1960$
Weight $4$
Character 1960.1
Self dual yes
Analytic conductor $115.644$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1960.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(115.643743611\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 40)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1960.1

$q$-expansion

\(f(q)\) \(=\) \(q+6.00000 q^{3} +5.00000 q^{5} +9.00000 q^{9} +O(q^{10})\) \(q+6.00000 q^{3} +5.00000 q^{5} +9.00000 q^{9} +16.0000 q^{11} -58.0000 q^{13} +30.0000 q^{15} +70.0000 q^{17} -4.00000 q^{19} -134.000 q^{23} +25.0000 q^{25} -108.000 q^{27} -242.000 q^{29} -100.000 q^{31} +96.0000 q^{33} -438.000 q^{37} -348.000 q^{39} +138.000 q^{41} +178.000 q^{43} +45.0000 q^{45} -22.0000 q^{47} +420.000 q^{51} +162.000 q^{53} +80.0000 q^{55} -24.0000 q^{57} +268.000 q^{59} -250.000 q^{61} -290.000 q^{65} +422.000 q^{67} -804.000 q^{69} -852.000 q^{71} -306.000 q^{73} +150.000 q^{75} -456.000 q^{79} -891.000 q^{81} -434.000 q^{83} +350.000 q^{85} -1452.00 q^{87} +726.000 q^{89} -600.000 q^{93} -20.0000 q^{95} -1378.00 q^{97} +144.000 q^{99} +O(q^{100})\)

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
\(3\) 6.00000 1.15470 0.577350 0.816497i \(-0.304087\pi\)
0.577350 + 0.816497i \(0.304087\pi\)
\(4\) 0 0
\(5\) 5.00000 0.447214
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 9.00000 0.333333
\(10\) 0 0
\(11\) 16.0000 0.438562 0.219281 0.975662i \(-0.429629\pi\)
0.219281 + 0.975662i \(0.429629\pi\)
\(12\) 0 0
\(13\) −58.0000 −1.23741 −0.618704 0.785624i \(-0.712342\pi\)
−0.618704 + 0.785624i \(0.712342\pi\)
\(14\) 0 0
\(15\) 30.0000 0.516398
\(16\) 0 0
\(17\) 70.0000 0.998676 0.499338 0.866407i \(-0.333577\pi\)
0.499338 + 0.866407i \(0.333577\pi\)
\(18\) 0 0
\(19\) −4.00000 −0.0482980 −0.0241490 0.999708i \(-0.507688\pi\)
−0.0241490 + 0.999708i \(0.507688\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −134.000 −1.21482 −0.607412 0.794387i \(-0.707792\pi\)
−0.607412 + 0.794387i \(0.707792\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) −108.000 −0.769800
\(28\) 0 0
\(29\) −242.000 −1.54960 −0.774798 0.632209i \(-0.782148\pi\)
−0.774798 + 0.632209i \(0.782148\pi\)
\(30\) 0 0
\(31\) −100.000 −0.579372 −0.289686 0.957122i \(-0.593551\pi\)
−0.289686 + 0.957122i \(0.593551\pi\)
\(32\) 0 0
\(33\) 96.0000 0.506408
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −438.000 −1.94613 −0.973064 0.230534i \(-0.925953\pi\)
−0.973064 + 0.230534i \(0.925953\pi\)
\(38\) 0 0
\(39\) −348.000 −1.42884
\(40\) 0 0
\(41\) 138.000 0.525658 0.262829 0.964842i \(-0.415344\pi\)
0.262829 + 0.964842i \(0.415344\pi\)
\(42\) 0 0
\(43\) 178.000 0.631273 0.315637 0.948880i \(-0.397782\pi\)
0.315637 + 0.948880i \(0.397782\pi\)
\(44\) 0 0
\(45\) 45.0000 0.149071
\(46\) 0 0
\(47\) −22.0000 −0.0682772 −0.0341386 0.999417i \(-0.510869\pi\)
−0.0341386 + 0.999417i \(0.510869\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 420.000 1.15317
\(52\) 0 0
\(53\) 162.000 0.419857 0.209928 0.977717i \(-0.432677\pi\)
0.209928 + 0.977717i \(0.432677\pi\)
\(54\) 0 0
\(55\) 80.0000 0.196131
\(56\) 0 0
\(57\) −24.0000 −0.0557698
\(58\) 0 0
\(59\) 268.000 0.591367 0.295683 0.955286i \(-0.404453\pi\)
0.295683 + 0.955286i \(0.404453\pi\)
\(60\) 0 0
\(61\) −250.000 −0.524741 −0.262371 0.964967i \(-0.584504\pi\)
−0.262371 + 0.964967i \(0.584504\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −290.000 −0.553386
\(66\) 0 0
\(67\) 422.000 0.769485 0.384743 0.923024i \(-0.374290\pi\)
0.384743 + 0.923024i \(0.374290\pi\)
\(68\) 0 0
\(69\) −804.000 −1.40276
\(70\) 0 0
\(71\) −852.000 −1.42414 −0.712069 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) 0 0
\(73\) −306.000 −0.490611 −0.245305 0.969446i \(-0.578888\pi\)
−0.245305 + 0.969446i \(0.578888\pi\)
\(74\) 0 0
\(75\) 150.000 0.230940
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −456.000 −0.649418 −0.324709 0.945814i \(-0.605266\pi\)
−0.324709 + 0.945814i \(0.605266\pi\)
\(80\) 0 0
\(81\) −891.000 −1.22222
\(82\) 0 0
\(83\) −434.000 −0.573948 −0.286974 0.957938i \(-0.592649\pi\)
−0.286974 + 0.957938i \(0.592649\pi\)
\(84\) 0 0
\(85\) 350.000 0.446622
\(86\) 0 0
\(87\) −1452.00 −1.78932
\(88\) 0 0
\(89\) 726.000 0.864672 0.432336 0.901712i \(-0.357689\pi\)
0.432336 + 0.901712i \(0.357689\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −600.000 −0.669001
\(94\) 0 0
\(95\) −20.0000 −0.0215995
\(96\) 0 0
\(97\) −1378.00 −1.44242 −0.721210 0.692717i \(-0.756414\pi\)
−0.721210 + 0.692717i \(0.756414\pi\)
\(98\) 0 0
\(99\) 144.000 0.146187
\(100\) 0 0
\(101\) −126.000 −0.124133 −0.0620667 0.998072i \(-0.519769\pi\)
−0.0620667 + 0.998072i \(0.519769\pi\)
\(102\) 0 0
\(103\) 1262.00 1.20727 0.603634 0.797262i \(-0.293719\pi\)
0.603634 + 0.797262i \(0.293719\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 510.000 0.460781 0.230390 0.973098i \(-0.426000\pi\)
0.230390 + 0.973098i \(0.426000\pi\)
\(108\) 0 0
\(109\) 26.0000 0.0228472 0.0114236 0.999935i \(-0.496364\pi\)
0.0114236 + 0.999935i \(0.496364\pi\)
\(110\) 0 0
\(111\) −2628.00 −2.24720
\(112\) 0 0
\(113\) 1242.00 1.03396 0.516980 0.855997i \(-0.327056\pi\)
0.516980 + 0.855997i \(0.327056\pi\)
\(114\) 0 0
\(115\) −670.000 −0.543285
\(116\) 0 0
\(117\) −522.000 −0.412469
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −1075.00 −0.807663
\(122\) 0 0
\(123\) 828.000 0.606978
\(124\) 0 0
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) −978.000 −0.683334 −0.341667 0.939821i \(-0.610992\pi\)
−0.341667 + 0.939821i \(0.610992\pi\)
\(128\) 0 0
\(129\) 1068.00 0.728931
\(130\) 0 0
\(131\) 912.000 0.608258 0.304129 0.952631i \(-0.401635\pi\)
0.304129 + 0.952631i \(0.401635\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −540.000 −0.344265
\(136\) 0 0
\(137\) −926.000 −0.577471 −0.288735 0.957409i \(-0.593235\pi\)
−0.288735 + 0.957409i \(0.593235\pi\)
\(138\) 0 0
\(139\) −516.000 −0.314867 −0.157434 0.987530i \(-0.550322\pi\)
−0.157434 + 0.987530i \(0.550322\pi\)
\(140\) 0 0
\(141\) −132.000 −0.0788398
\(142\) 0 0
\(143\) −928.000 −0.542680
\(144\) 0 0
\(145\) −1210.00 −0.693000
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −958.000 −0.526728 −0.263364 0.964697i \(-0.584832\pi\)
−0.263364 + 0.964697i \(0.584832\pi\)
\(150\) 0 0
\(151\) 332.000 0.178926 0.0894628 0.995990i \(-0.471485\pi\)
0.0894628 + 0.995990i \(0.471485\pi\)
\(152\) 0 0
\(153\) 630.000 0.332892
\(154\) 0 0
\(155\) −500.000 −0.259103
\(156\) 0 0
\(157\) 1022.00 0.519519 0.259759 0.965673i \(-0.416357\pi\)
0.259759 + 0.965673i \(0.416357\pi\)
\(158\) 0 0
\(159\) 972.000 0.484809
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −926.000 −0.444969 −0.222484 0.974936i \(-0.571417\pi\)
−0.222484 + 0.974936i \(0.571417\pi\)
\(164\) 0 0
\(165\) 480.000 0.226472
\(166\) 0 0
\(167\) −654.000 −0.303042 −0.151521 0.988454i \(-0.548417\pi\)
−0.151521 + 0.988454i \(0.548417\pi\)
\(168\) 0 0
\(169\) 1167.00 0.531179
\(170\) 0 0
\(171\) −36.0000 −0.0160993
\(172\) 0 0
\(173\) 1294.00 0.568676 0.284338 0.958724i \(-0.408226\pi\)
0.284338 + 0.958724i \(0.408226\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 1608.00 0.682851
\(178\) 0 0
\(179\) −2836.00 −1.18420 −0.592102 0.805863i \(-0.701702\pi\)
−0.592102 + 0.805863i \(0.701702\pi\)
\(180\) 0 0
\(181\) −1742.00 −0.715369 −0.357685 0.933842i \(-0.616434\pi\)
−0.357685 + 0.933842i \(0.616434\pi\)
\(182\) 0 0
\(183\) −1500.00 −0.605919
\(184\) 0 0
\(185\) −2190.00 −0.870335
\(186\) 0 0
\(187\) 1120.00 0.437981
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 4460.00 1.68960 0.844802 0.535079i \(-0.179718\pi\)
0.844802 + 0.535079i \(0.179718\pi\)
\(192\) 0 0
\(193\) −3782.00 −1.41054 −0.705270 0.708939i \(-0.749174\pi\)
−0.705270 + 0.708939i \(0.749174\pi\)
\(194\) 0 0
\(195\) −1740.00 −0.638995
\(196\) 0 0
\(197\) 4474.00 1.61807 0.809034 0.587762i \(-0.199991\pi\)
0.809034 + 0.587762i \(0.199991\pi\)
\(198\) 0 0
\(199\) −3608.00 −1.28525 −0.642624 0.766182i \(-0.722154\pi\)
−0.642624 + 0.766182i \(0.722154\pi\)
\(200\) 0 0
\(201\) 2532.00 0.888525
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 690.000 0.235081
\(206\) 0 0
\(207\) −1206.00 −0.404941
\(208\) 0 0
\(209\) −64.0000 −0.0211817
\(210\) 0 0
\(211\) −256.000 −0.0835250 −0.0417625 0.999128i \(-0.513297\pi\)
−0.0417625 + 0.999128i \(0.513297\pi\)
\(212\) 0 0
\(213\) −5112.00 −1.64445
\(214\) 0 0
\(215\) 890.000 0.282314
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −1836.00 −0.566509
\(220\) 0 0
\(221\) −4060.00 −1.23577
\(222\) 0 0
\(223\) 5158.00 1.54890 0.774451 0.632634i \(-0.218026\pi\)
0.774451 + 0.632634i \(0.218026\pi\)
\(224\) 0 0
\(225\) 225.000 0.0666667
\(226\) 0 0
\(227\) 2226.00 0.650858 0.325429 0.945566i \(-0.394491\pi\)
0.325429 + 0.945566i \(0.394491\pi\)
\(228\) 0 0
\(229\) −2086.00 −0.601951 −0.300975 0.953632i \(-0.597312\pi\)
−0.300975 + 0.953632i \(0.597312\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −5718.00 −1.60772 −0.803860 0.594819i \(-0.797224\pi\)
−0.803860 + 0.594819i \(0.797224\pi\)
\(234\) 0 0
\(235\) −110.000 −0.0305345
\(236\) 0 0
\(237\) −2736.00 −0.749883
\(238\) 0 0
\(239\) −3624.00 −0.980825 −0.490412 0.871491i \(-0.663154\pi\)
−0.490412 + 0.871491i \(0.663154\pi\)
\(240\) 0 0
\(241\) 82.0000 0.0219174 0.0109587 0.999940i \(-0.496512\pi\)
0.0109587 + 0.999940i \(0.496512\pi\)
\(242\) 0 0
\(243\) −2430.00 −0.641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 232.000 0.0597644
\(248\) 0 0
\(249\) −2604.00 −0.662738
\(250\) 0 0
\(251\) 5040.00 1.26742 0.633709 0.773571i \(-0.281532\pi\)
0.633709 + 0.773571i \(0.281532\pi\)
\(252\) 0 0
\(253\) −2144.00 −0.532775
\(254\) 0 0
\(255\) 2100.00 0.515714
\(256\) 0 0
\(257\) 2310.00 0.560676 0.280338 0.959901i \(-0.409553\pi\)
0.280338 + 0.959901i \(0.409553\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −2178.00 −0.516532
\(262\) 0 0
\(263\) −4110.00 −0.963625 −0.481813 0.876274i \(-0.660021\pi\)
−0.481813 + 0.876274i \(0.660021\pi\)
\(264\) 0 0
\(265\) 810.000 0.187766
\(266\) 0 0
\(267\) 4356.00 0.998438
\(268\) 0 0
\(269\) −746.000 −0.169087 −0.0845435 0.996420i \(-0.526943\pi\)
−0.0845435 + 0.996420i \(0.526943\pi\)
\(270\) 0 0
\(271\) 4596.00 1.03021 0.515105 0.857127i \(-0.327753\pi\)
0.515105 + 0.857127i \(0.327753\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 400.000 0.0877124
\(276\) 0 0
\(277\) −2206.00 −0.478504 −0.239252 0.970957i \(-0.576902\pi\)
−0.239252 + 0.970957i \(0.576902\pi\)
\(278\) 0 0
\(279\) −900.000 −0.193124
\(280\) 0 0
\(281\) 8278.00 1.75738 0.878691 0.477392i \(-0.158418\pi\)
0.878691 + 0.477392i \(0.158418\pi\)
\(282\) 0 0
\(283\) −1178.00 −0.247438 −0.123719 0.992317i \(-0.539482\pi\)
−0.123719 + 0.992317i \(0.539482\pi\)
\(284\) 0 0
\(285\) −120.000 −0.0249410
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −13.0000 −0.00264604
\(290\) 0 0
\(291\) −8268.00 −1.66556
\(292\) 0 0
\(293\) −106.000 −0.0211351 −0.0105676 0.999944i \(-0.503364\pi\)
−0.0105676 + 0.999944i \(0.503364\pi\)
\(294\) 0 0
\(295\) 1340.00 0.264467
\(296\) 0 0
\(297\) −1728.00 −0.337605
\(298\) 0 0
\(299\) 7772.00 1.50323
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −756.000 −0.143337
\(304\) 0 0
\(305\) −1250.00 −0.234671
\(306\) 0 0
\(307\) −8134.00 −1.51216 −0.756078 0.654482i \(-0.772887\pi\)
−0.756078 + 0.654482i \(0.772887\pi\)
\(308\) 0 0
\(309\) 7572.00 1.39403
\(310\) 0 0
\(311\) 4396.00 0.801525 0.400763 0.916182i \(-0.368745\pi\)
0.400763 + 0.916182i \(0.368745\pi\)
\(312\) 0 0
\(313\) −4826.00 −0.871507 −0.435753 0.900066i \(-0.643518\pi\)
−0.435753 + 0.900066i \(0.643518\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 7026.00 1.24486 0.622428 0.782677i \(-0.286146\pi\)
0.622428 + 0.782677i \(0.286146\pi\)
\(318\) 0 0
\(319\) −3872.00 −0.679594
\(320\) 0 0
\(321\) 3060.00 0.532064
\(322\) 0 0
\(323\) −280.000 −0.0482341
\(324\) 0 0
\(325\) −1450.00 −0.247482
\(326\) 0 0
\(327\) 156.000 0.0263817
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 8808.00 1.46263 0.731316 0.682038i \(-0.238906\pi\)
0.731316 + 0.682038i \(0.238906\pi\)
\(332\) 0 0
\(333\) −3942.00 −0.648710
\(334\) 0 0
\(335\) 2110.00 0.344124
\(336\) 0 0
\(337\) 5602.00 0.905520 0.452760 0.891632i \(-0.350439\pi\)
0.452760 + 0.891632i \(0.350439\pi\)
\(338\) 0 0
\(339\) 7452.00 1.19391
\(340\) 0 0
\(341\) −1600.00 −0.254090
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −4020.00 −0.627332
\(346\) 0 0
\(347\) −6634.00 −1.02632 −0.513158 0.858294i \(-0.671525\pi\)
−0.513158 + 0.858294i \(0.671525\pi\)
\(348\) 0 0
\(349\) −3198.00 −0.490501 −0.245251 0.969460i \(-0.578870\pi\)
−0.245251 + 0.969460i \(0.578870\pi\)
\(350\) 0 0
\(351\) 6264.00 0.952557
\(352\) 0 0
\(353\) 5230.00 0.788569 0.394284 0.918988i \(-0.370992\pi\)
0.394284 + 0.918988i \(0.370992\pi\)
\(354\) 0 0
\(355\) −4260.00 −0.636894
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −312.000 −0.0458683 −0.0229342 0.999737i \(-0.507301\pi\)
−0.0229342 + 0.999737i \(0.507301\pi\)
\(360\) 0 0
\(361\) −6843.00 −0.997667
\(362\) 0 0
\(363\) −6450.00 −0.932609
\(364\) 0 0
\(365\) −1530.00 −0.219408
\(366\) 0 0
\(367\) −10790.0 −1.53470 −0.767348 0.641231i \(-0.778424\pi\)
−0.767348 + 0.641231i \(0.778424\pi\)
\(368\) 0 0
\(369\) 1242.00 0.175219
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −4190.00 −0.581635 −0.290818 0.956778i \(-0.593927\pi\)
−0.290818 + 0.956778i \(0.593927\pi\)
\(374\) 0 0
\(375\) 750.000 0.103280
\(376\) 0 0
\(377\) 14036.0 1.91748
\(378\) 0 0
\(379\) −6980.00 −0.946012 −0.473006 0.881059i \(-0.656831\pi\)
−0.473006 + 0.881059i \(0.656831\pi\)
\(380\) 0 0
\(381\) −5868.00 −0.789047
\(382\) 0 0
\(383\) −13962.0 −1.86273 −0.931364 0.364089i \(-0.881380\pi\)
−0.931364 + 0.364089i \(0.881380\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 1602.00 0.210424
\(388\) 0 0
\(389\) 3810.00 0.496593 0.248296 0.968684i \(-0.420129\pi\)
0.248296 + 0.968684i \(0.420129\pi\)
\(390\) 0 0
\(391\) −9380.00 −1.21321
\(392\) 0 0
\(393\) 5472.00 0.702356
\(394\) 0 0
\(395\) −2280.00 −0.290428
\(396\) 0 0
\(397\) 9158.00 1.15775 0.578875 0.815416i \(-0.303492\pi\)
0.578875 + 0.815416i \(0.303492\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 4866.00 0.605976 0.302988 0.952994i \(-0.402016\pi\)
0.302988 + 0.952994i \(0.402016\pi\)
\(402\) 0 0
\(403\) 5800.00 0.716920
\(404\) 0 0
\(405\) −4455.00 −0.546594
\(406\) 0 0
\(407\) −7008.00 −0.853498
\(408\) 0 0
\(409\) −13486.0 −1.63042 −0.815208 0.579169i \(-0.803377\pi\)
−0.815208 + 0.579169i \(0.803377\pi\)
\(410\) 0 0
\(411\) −5556.00 −0.666806
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −2170.00 −0.256677
\(416\) 0 0
\(417\) −3096.00 −0.363577
\(418\) 0 0
\(419\) −5628.00 −0.656195 −0.328098 0.944644i \(-0.606407\pi\)
−0.328098 + 0.944644i \(0.606407\pi\)
\(420\) 0 0
\(421\) 7938.00 0.918942 0.459471 0.888193i \(-0.348039\pi\)
0.459471 + 0.888193i \(0.348039\pi\)
\(422\) 0 0
\(423\) −198.000 −0.0227591
\(424\) 0 0
\(425\) 1750.00 0.199735
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −5568.00 −0.626633
\(430\) 0 0
\(431\) 1916.00 0.214131 0.107066 0.994252i \(-0.465855\pi\)
0.107066 + 0.994252i \(0.465855\pi\)
\(432\) 0 0
\(433\) 16510.0 1.83238 0.916189 0.400746i \(-0.131249\pi\)
0.916189 + 0.400746i \(0.131249\pi\)
\(434\) 0 0
\(435\) −7260.00 −0.800208
\(436\) 0 0
\(437\) 536.000 0.0586736
\(438\) 0 0
\(439\) 1256.00 0.136550 0.0682752 0.997667i \(-0.478250\pi\)
0.0682752 + 0.997667i \(0.478250\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −12222.0 −1.31080 −0.655400 0.755282i \(-0.727500\pi\)
−0.655400 + 0.755282i \(0.727500\pi\)
\(444\) 0 0
\(445\) 3630.00 0.386693
\(446\) 0 0
\(447\) −5748.00 −0.608213
\(448\) 0 0
\(449\) −5946.00 −0.624965 −0.312482 0.949924i \(-0.601160\pi\)
−0.312482 + 0.949924i \(0.601160\pi\)
\(450\) 0 0
\(451\) 2208.00 0.230534
\(452\) 0 0
\(453\) 1992.00 0.206606
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 1258.00 0.128768 0.0643838 0.997925i \(-0.479492\pi\)
0.0643838 + 0.997925i \(0.479492\pi\)
\(458\) 0 0
\(459\) −7560.00 −0.768781
\(460\) 0 0
\(461\) −16422.0 −1.65911 −0.829554 0.558426i \(-0.811405\pi\)
−0.829554 + 0.558426i \(0.811405\pi\)
\(462\) 0 0
\(463\) 2658.00 0.266799 0.133399 0.991062i \(-0.457411\pi\)
0.133399 + 0.991062i \(0.457411\pi\)
\(464\) 0 0
\(465\) −3000.00 −0.299186
\(466\) 0 0
\(467\) −3686.00 −0.365241 −0.182621 0.983183i \(-0.558458\pi\)
−0.182621 + 0.983183i \(0.558458\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 6132.00 0.599889
\(472\) 0 0
\(473\) 2848.00 0.276852
\(474\) 0 0
\(475\) −100.000 −0.00965961
\(476\) 0 0
\(477\) 1458.00 0.139952
\(478\) 0 0
\(479\) −88.0000 −0.00839420 −0.00419710 0.999991i \(-0.501336\pi\)
−0.00419710 + 0.999991i \(0.501336\pi\)
\(480\) 0 0
\(481\) 25404.0 2.40816
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −6890.00 −0.645070
\(486\) 0 0
\(487\) −14714.0 −1.36911 −0.684553 0.728963i \(-0.740003\pi\)
−0.684553 + 0.728963i \(0.740003\pi\)
\(488\) 0 0
\(489\) −5556.00 −0.513806
\(490\) 0 0
\(491\) −7344.00 −0.675010 −0.337505 0.941324i \(-0.609583\pi\)
−0.337505 + 0.941324i \(0.609583\pi\)
\(492\) 0 0
\(493\) −16940.0 −1.54754
\(494\) 0 0
\(495\) 720.000 0.0653770
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 1604.00 0.143898 0.0719488 0.997408i \(-0.477078\pi\)
0.0719488 + 0.997408i \(0.477078\pi\)
\(500\) 0 0
\(501\) −3924.00 −0.349923
\(502\) 0 0
\(503\) −14802.0 −1.31210 −0.656052 0.754715i \(-0.727775\pi\)
−0.656052 + 0.754715i \(0.727775\pi\)
\(504\) 0 0
\(505\) −630.000 −0.0555141
\(506\) 0 0
\(507\) 7002.00 0.613353
\(508\) 0 0
\(509\) 22514.0 1.96054 0.980271 0.197660i \(-0.0633342\pi\)
0.980271 + 0.197660i \(0.0633342\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 432.000 0.0371799
\(514\) 0 0
\(515\) 6310.00 0.539906
\(516\) 0 0
\(517\) −352.000 −0.0299438
\(518\) 0 0
\(519\) 7764.00 0.656651
\(520\) 0 0
\(521\) 6710.00 0.564243 0.282121 0.959379i \(-0.408962\pi\)
0.282121 + 0.959379i \(0.408962\pi\)
\(522\) 0 0
\(523\) −7930.00 −0.663011 −0.331505 0.943453i \(-0.607557\pi\)
−0.331505 + 0.943453i \(0.607557\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −7000.00 −0.578605
\(528\) 0 0
\(529\) 5789.00 0.475795
\(530\) 0 0
\(531\) 2412.00 0.197122
\(532\) 0 0
\(533\) −8004.00 −0.650454
\(534\) 0 0
\(535\) 2550.00 0.206068
\(536\) 0 0
\(537\) −17016.0 −1.36740
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 4918.00 0.390834 0.195417 0.980720i \(-0.437394\pi\)
0.195417 + 0.980720i \(0.437394\pi\)
\(542\) 0 0
\(543\) −10452.0 −0.826037
\(544\) 0 0
\(545\) 130.000 0.0102176
\(546\) 0 0
\(547\) −3922.00 −0.306568 −0.153284 0.988182i \(-0.548985\pi\)
−0.153284 + 0.988182i \(0.548985\pi\)
\(548\) 0 0
\(549\) −2250.00 −0.174914
\(550\) 0 0
\(551\) 968.000 0.0748424
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −13140.0 −1.00498
\(556\) 0 0
\(557\) 17786.0 1.35299 0.676496 0.736446i \(-0.263497\pi\)
0.676496 + 0.736446i \(0.263497\pi\)
\(558\) 0 0
\(559\) −10324.0 −0.781143
\(560\) 0 0
\(561\) 6720.00 0.505737
\(562\) 0 0
\(563\) −20266.0 −1.51707 −0.758535 0.651633i \(-0.774084\pi\)
−0.758535 + 0.651633i \(0.774084\pi\)
\(564\) 0 0
\(565\) 6210.00 0.462401
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 13358.0 0.984177 0.492088 0.870545i \(-0.336234\pi\)
0.492088 + 0.870545i \(0.336234\pi\)
\(570\) 0 0
\(571\) 16360.0 1.19903 0.599514 0.800364i \(-0.295361\pi\)
0.599514 + 0.800364i \(0.295361\pi\)
\(572\) 0 0
\(573\) 26760.0 1.95099
\(574\) 0 0
\(575\) −3350.00 −0.242965
\(576\) 0 0
\(577\) 15574.0 1.12366 0.561832 0.827251i \(-0.310097\pi\)
0.561832 + 0.827251i \(0.310097\pi\)
\(578\) 0 0
\(579\) −22692.0 −1.62875
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 2592.00 0.184133
\(584\) 0 0
\(585\) −2610.00 −0.184462
\(586\) 0 0
\(587\) −6654.00 −0.467870 −0.233935 0.972252i \(-0.575160\pi\)
−0.233935 + 0.972252i \(0.575160\pi\)
\(588\) 0 0
\(589\) 400.000 0.0279825
\(590\) 0 0
\(591\) 26844.0 1.86838
\(592\) 0 0
\(593\) 17742.0 1.22863 0.614314 0.789062i \(-0.289433\pi\)
0.614314 + 0.789062i \(0.289433\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −21648.0 −1.48408
\(598\) 0 0
\(599\) 15840.0 1.08048 0.540238 0.841512i \(-0.318334\pi\)
0.540238 + 0.841512i \(0.318334\pi\)
\(600\) 0 0
\(601\) 3002.00 0.203751 0.101875 0.994797i \(-0.467516\pi\)
0.101875 + 0.994797i \(0.467516\pi\)
\(602\) 0 0
\(603\) 3798.00 0.256495
\(604\) 0 0
\(605\) −5375.00 −0.361198
\(606\) 0 0
\(607\) 23610.0 1.57875 0.789374 0.613912i \(-0.210405\pi\)
0.789374 + 0.613912i \(0.210405\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1276.00 0.0844868
\(612\) 0 0
\(613\) 23850.0 1.57144 0.785720 0.618583i \(-0.212293\pi\)
0.785720 + 0.618583i \(0.212293\pi\)
\(614\) 0 0
\(615\) 4140.00 0.271449
\(616\) 0 0
\(617\) −5334.00 −0.348037 −0.174018 0.984742i \(-0.555675\pi\)
−0.174018 + 0.984742i \(0.555675\pi\)
\(618\) 0 0
\(619\) 2164.00 0.140515 0.0702573 0.997529i \(-0.477618\pi\)
0.0702573 + 0.997529i \(0.477618\pi\)
\(620\) 0 0
\(621\) 14472.0 0.935171
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) −384.000 −0.0244585
\(628\) 0 0
\(629\) −30660.0 −1.94355
\(630\) 0 0
\(631\) −25220.0 −1.59111 −0.795557 0.605879i \(-0.792821\pi\)
−0.795557 + 0.605879i \(0.792821\pi\)
\(632\) 0 0
\(633\) −1536.00 −0.0964463
\(634\) 0 0
\(635\) −4890.00 −0.305596
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −7668.00 −0.474713
\(640\) 0 0
\(641\) −12306.0 −0.758280 −0.379140 0.925339i \(-0.623780\pi\)
−0.379140 + 0.925339i \(0.623780\pi\)
\(642\) 0 0
\(643\) 27414.0 1.68134 0.840671 0.541547i \(-0.182161\pi\)
0.840671 + 0.541547i \(0.182161\pi\)
\(644\) 0 0
\(645\) 5340.00 0.325988
\(646\) 0 0
\(647\) 21834.0 1.32671 0.663356 0.748304i \(-0.269131\pi\)
0.663356 + 0.748304i \(0.269131\pi\)
\(648\) 0 0
\(649\) 4288.00 0.259351
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −23998.0 −1.43815 −0.719077 0.694931i \(-0.755435\pi\)
−0.719077 + 0.694931i \(0.755435\pi\)
\(654\) 0 0
\(655\) 4560.00 0.272021
\(656\) 0 0
\(657\) −2754.00 −0.163537
\(658\) 0 0
\(659\) −32004.0 −1.89180 −0.945902 0.324452i \(-0.894820\pi\)
−0.945902 + 0.324452i \(0.894820\pi\)
\(660\) 0 0
\(661\) 8526.00 0.501699 0.250849 0.968026i \(-0.419290\pi\)
0.250849 + 0.968026i \(0.419290\pi\)
\(662\) 0 0
\(663\) −24360.0 −1.42694
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 32428.0 1.88248
\(668\) 0 0
\(669\) 30948.0 1.78852
\(670\) 0 0
\(671\) −4000.00 −0.230132
\(672\) 0 0
\(673\) 8178.00 0.468408 0.234204 0.972187i \(-0.424752\pi\)
0.234204 + 0.972187i \(0.424752\pi\)
\(674\) 0 0
\(675\) −2700.00 −0.153960
\(676\) 0 0
\(677\) 16646.0 0.944989 0.472495 0.881334i \(-0.343354\pi\)
0.472495 + 0.881334i \(0.343354\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 13356.0 0.751546
\(682\) 0 0
\(683\) −22446.0 −1.25750 −0.628750 0.777608i \(-0.716433\pi\)
−0.628750 + 0.777608i \(0.716433\pi\)
\(684\) 0 0
\(685\) −4630.00 −0.258253
\(686\) 0 0
\(687\) −12516.0 −0.695073
\(688\) 0 0
\(689\) −9396.00 −0.519534
\(690\) 0 0
\(691\) −35336.0 −1.94536 −0.972681 0.232147i \(-0.925425\pi\)
−0.972681 + 0.232147i \(0.925425\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −2580.00 −0.140813
\(696\) 0 0
\(697\) 9660.00 0.524962
\(698\) 0 0
\(699\) −34308.0 −1.85643
\(700\) 0 0
\(701\) 3482.00 0.187608 0.0938041 0.995591i \(-0.470097\pi\)
0.0938041 + 0.995591i \(0.470097\pi\)
\(702\) 0 0
\(703\) 1752.00 0.0939942
\(704\) 0 0
\(705\) −660.000 −0.0352582
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −19402.0 −1.02773 −0.513863 0.857872i \(-0.671786\pi\)
−0.513863 + 0.857872i \(0.671786\pi\)
\(710\) 0 0
\(711\) −4104.00 −0.216473
\(712\) 0 0
\(713\) 13400.0 0.703834
\(714\) 0 0
\(715\) −4640.00 −0.242694
\(716\) 0 0
\(717\) −21744.0 −1.13256
\(718\) 0 0
\(719\) 9896.00 0.513294 0.256647 0.966505i \(-0.417382\pi\)
0.256647 + 0.966505i \(0.417382\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 492.000 0.0253080
\(724\) 0 0
\(725\) −6050.00 −0.309919
\(726\) 0 0
\(727\) −494.000 −0.0252014 −0.0126007 0.999921i \(-0.504011\pi\)
−0.0126007 + 0.999921i \(0.504011\pi\)
\(728\) 0 0
\(729\) 9477.00 0.481481
\(730\) 0 0
\(731\) 12460.0 0.630437
\(732\) 0 0
\(733\) −9282.00 −0.467720 −0.233860 0.972270i \(-0.575136\pi\)
−0.233860 + 0.972270i \(0.575136\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 6752.00 0.337467
\(738\) 0 0
\(739\) −3252.00 −0.161877 −0.0809383 0.996719i \(-0.525792\pi\)
−0.0809383 + 0.996719i \(0.525792\pi\)
\(740\) 0 0
\(741\) 1392.00 0.0690100
\(742\) 0 0
\(743\) −4710.00 −0.232561 −0.116281 0.993216i \(-0.537097\pi\)
−0.116281 + 0.993216i \(0.537097\pi\)
\(744\) 0 0
\(745\) −4790.00 −0.235560
\(746\) 0 0
\(747\) −3906.00 −0.191316
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 25764.0 1.25185 0.625927 0.779882i \(-0.284721\pi\)
0.625927 + 0.779882i \(0.284721\pi\)
\(752\) 0 0
\(753\) 30240.0 1.46349
\(754\) 0 0
\(755\) 1660.00 0.0800180
\(756\) 0 0
\(757\) −30094.0 −1.44489 −0.722447 0.691426i \(-0.756983\pi\)
−0.722447 + 0.691426i \(0.756983\pi\)
\(758\) 0 0
\(759\) −12864.0 −0.615196
\(760\) 0 0
\(761\) −22362.0 −1.06521 −0.532603 0.846365i \(-0.678786\pi\)
−0.532603 + 0.846365i \(0.678786\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 3150.00 0.148874
\(766\) 0 0
\(767\) −15544.0 −0.731762
\(768\) 0 0
\(769\) 30398.0 1.42546 0.712731 0.701438i \(-0.247458\pi\)
0.712731 + 0.701438i \(0.247458\pi\)
\(770\) 0 0
\(771\) 13860.0 0.647413
\(772\) 0 0
\(773\) −1290.00 −0.0600234 −0.0300117 0.999550i \(-0.509554\pi\)
−0.0300117 + 0.999550i \(0.509554\pi\)
\(774\) 0 0
\(775\) −2500.00 −0.115874
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −552.000 −0.0253883
\(780\) 0 0
\(781\) −13632.0 −0.624573
\(782\) 0 0
\(783\) 26136.0 1.19288
\(784\) 0 0
\(785\) 5110.00 0.232336
\(786\) 0 0
\(787\) −14.0000 −0.000634112 0 −0.000317056 1.00000i \(-0.500101\pi\)
−0.000317056 1.00000i \(0.500101\pi\)
\(788\) 0 0
\(789\) −24660.0 −1.11270
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 14500.0 0.649319
\(794\) 0 0
\(795\) 4860.00 0.216813
\(796\) 0 0
\(797\) 38814.0 1.72505 0.862523 0.506017i \(-0.168883\pi\)
0.862523 + 0.506017i \(0.168883\pi\)
\(798\) 0 0
\(799\) −1540.00 −0.0681868
\(800\) 0 0
\(801\) 6534.00 0.288224
\(802\) 0 0
\(803\) −4896.00 −0.215163
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −4476.00 −0.195245
\(808\) 0 0
\(809\) 27402.0 1.19086 0.595428 0.803408i \(-0.296982\pi\)
0.595428 + 0.803408i \(0.296982\pi\)
\(810\) 0 0
\(811\) 28576.0 1.23729 0.618643 0.785672i \(-0.287683\pi\)
0.618643 + 0.785672i \(0.287683\pi\)
\(812\) 0 0
\(813\) 27576.0 1.18958
\(814\) 0 0
\(815\) −4630.00 −0.198996
\(816\) 0 0
\(817\) −712.000 −0.0304893
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 31762.0 1.35018 0.675092 0.737733i \(-0.264104\pi\)
0.675092 + 0.737733i \(0.264104\pi\)
\(822\) 0 0
\(823\) 20506.0 0.868523 0.434261 0.900787i \(-0.357009\pi\)
0.434261 + 0.900787i \(0.357009\pi\)
\(824\) 0 0
\(825\) 2400.00 0.101282
\(826\) 0 0
\(827\) 13014.0 0.547208 0.273604 0.961842i \(-0.411784\pi\)
0.273604 + 0.961842i \(0.411784\pi\)
\(828\) 0 0
\(829\) 22790.0 0.954800 0.477400 0.878686i \(-0.341579\pi\)
0.477400 + 0.878686i \(0.341579\pi\)
\(830\) 0 0
\(831\) −13236.0 −0.552529
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −3270.00 −0.135525
\(836\) 0 0
\(837\) 10800.0 0.446001
\(838\) 0 0
\(839\) −23696.0 −0.975062 −0.487531 0.873106i \(-0.662102\pi\)
−0.487531 + 0.873106i \(0.662102\pi\)
\(840\) 0 0
\(841\) 34175.0 1.40125
\(842\) 0 0
\(843\) 49668.0 2.02925
\(844\) 0 0
\(845\) 5835.00 0.237550
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −7068.00 −0.285716
\(850\) 0 0
\(851\) 58692.0 2.36420
\(852\) 0 0
\(853\) −5306.00 −0.212982 −0.106491 0.994314i \(-0.533962\pi\)
−0.106491 + 0.994314i \(0.533962\pi\)
\(854\) 0 0
\(855\) −180.000 −0.00719985
\(856\) 0 0
\(857\) 21054.0 0.839196 0.419598 0.907710i \(-0.362171\pi\)
0.419598 + 0.907710i \(0.362171\pi\)
\(858\) 0 0
\(859\) −7364.00 −0.292499 −0.146249 0.989248i \(-0.546720\pi\)
−0.146249 + 0.989248i \(0.546720\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 17226.0 0.679467 0.339733 0.940522i \(-0.389663\pi\)
0.339733 + 0.940522i \(0.389663\pi\)
\(864\) 0 0
\(865\) 6470.00 0.254320
\(866\) 0 0
\(867\) −78.0000 −0.00305539
\(868\) 0 0
\(869\) −7296.00 −0.284810
\(870\) 0 0
\(871\) −24476.0 −0.952167
\(872\) 0 0
\(873\) −12402.0 −0.480807
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 21202.0 0.816352 0.408176 0.912903i \(-0.366165\pi\)
0.408176 + 0.912903i \(0.366165\pi\)
\(878\) 0 0
\(879\) −636.000 −0.0244047
\(880\) 0 0
\(881\) 29490.0 1.12774 0.563872 0.825862i \(-0.309311\pi\)
0.563872 + 0.825862i \(0.309311\pi\)
\(882\) 0 0
\(883\) 2570.00 0.0979472 0.0489736 0.998800i \(-0.484405\pi\)
0.0489736 + 0.998800i \(0.484405\pi\)
\(884\) 0 0
\(885\) 8040.00 0.305380
\(886\) 0 0
\(887\) −36334.0 −1.37540 −0.687698 0.725997i \(-0.741379\pi\)
−0.687698 + 0.725997i \(0.741379\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −14256.0 −0.536020
\(892\) 0 0
\(893\) 88.0000 0.00329766
\(894\) 0 0
\(895\) −14180.0 −0.529592
\(896\) 0 0
\(897\) 46632.0 1.73578
\(898\) 0 0
\(899\) 24200.0 0.897792
\(900\) 0 0
\(901\) 11340.0 0.419301
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −8710.00 −0.319923
\(906\) 0 0
\(907\) −12474.0 −0.456662 −0.228331 0.973584i \(-0.573327\pi\)
−0.228331 + 0.973584i \(0.573327\pi\)
\(908\) 0 0
\(909\) −1134.00 −0.0413778
\(910\) 0 0
\(911\) −41132.0 −1.49590 −0.747949 0.663756i \(-0.768961\pi\)
−0.747949 + 0.663756i \(0.768961\pi\)
\(912\) 0 0
\(913\) −6944.00 −0.251712
\(914\) 0 0
\(915\) −7500.00 −0.270975
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −38416.0 −1.37892 −0.689460 0.724324i \(-0.742152\pi\)
−0.689460 + 0.724324i \(0.742152\pi\)
\(920\) 0 0
\(921\) −48804.0 −1.74609
\(922\) 0 0
\(923\) 49416.0 1.76224
\(924\) 0 0
\(925\) −10950.0 −0.389226
\(926\) 0 0
\(927\) 11358.0 0.402423
\(928\) 0 0
\(929\) −41302.0 −1.45864 −0.729319 0.684174i \(-0.760163\pi\)
−0.729319 + 0.684174i \(0.760163\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 26376.0 0.925521
\(934\) 0 0
\(935\) 5600.00 0.195871
\(936\) 0 0
\(937\) 26150.0 0.911722 0.455861 0.890051i \(-0.349331\pi\)
0.455861 + 0.890051i \(0.349331\pi\)
\(938\) 0 0
\(939\) −28956.0 −1.00633
\(940\) 0 0
\(941\) −35254.0 −1.22130 −0.610652 0.791899i \(-0.709093\pi\)
−0.610652 + 0.791899i \(0.709093\pi\)
\(942\) 0 0
\(943\) −18492.0 −0.638582
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 18550.0 0.636530 0.318265 0.948002i \(-0.396900\pi\)
0.318265 + 0.948002i \(0.396900\pi\)
\(948\) 0 0
\(949\) 17748.0 0.607086
\(950\) 0 0
\(951\) 42156.0 1.43744
\(952\) 0 0
\(953\) 17322.0 0.588788 0.294394 0.955684i \(-0.404882\pi\)
0.294394 + 0.955684i \(0.404882\pi\)
\(954\) 0 0
\(955\) 22300.0 0.755614
\(956\) 0 0
\(957\) −23232.0 −0.784727
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −19791.0 −0.664328
\(962\) 0 0
\(963\) 4590.00 0.153594
\(964\) 0 0
\(965\) −18910.0 −0.630813
\(966\) 0 0
\(967\) 35190.0 1.17025 0.585126 0.810942i \(-0.301045\pi\)
0.585126 + 0.810942i \(0.301045\pi\)
\(968\) 0 0
\(969\) −1680.00 −0.0556960
\(970\) 0 0
\(971\) 40696.0 1.34500 0.672501 0.740096i \(-0.265220\pi\)
0.672501 + 0.740096i \(0.265220\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −8700.00 −0.285767
\(976\) 0 0
\(977\) 44306.0 1.45084 0.725422 0.688304i \(-0.241645\pi\)
0.725422 + 0.688304i \(0.241645\pi\)
\(978\) 0 0
\(979\) 11616.0 0.379212
\(980\) 0 0
\(981\) 234.000 0.00761574
\(982\) 0 0
\(983\) 18798.0 0.609932 0.304966 0.952363i \(-0.401355\pi\)
0.304966 + 0.952363i \(0.401355\pi\)
\(984\) 0 0
\(985\) 22370.0 0.723622
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −23852.0 −0.766885
\(990\) 0 0
\(991\) 2468.00 0.0791106 0.0395553 0.999217i \(-0.487406\pi\)
0.0395553 + 0.999217i \(0.487406\pi\)
\(992\) 0 0
\(993\) 52848.0 1.68890
\(994\) 0 0
\(995\) −18040.0 −0.574780
\(996\) 0 0
\(997\) 61086.0 1.94043 0.970217 0.242237i \(-0.0778811\pi\)
0.970217 + 0.242237i \(0.0778811\pi\)
\(998\) 0 0
\(999\) 47304.0 1.49813
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 1960.4.a.h.1.1 1
7.6 odd 2 40.4.a.a.1.1 1
21.20 even 2 360.4.a.h.1.1 1
28.27 even 2 80.4.a.e.1.1 1
35.13 even 4 200.4.c.c.49.1 2
35.27 even 4 200.4.c.c.49.2 2
35.34 odd 2 200.4.a.i.1.1 1
56.13 odd 2 320.4.a.l.1.1 1
56.27 even 2 320.4.a.c.1.1 1
84.83 odd 2 720.4.a.bd.1.1 1
105.62 odd 4 1800.4.f.j.649.1 2
105.83 odd 4 1800.4.f.j.649.2 2
105.104 even 2 1800.4.a.bi.1.1 1
112.13 odd 4 1280.4.d.p.641.1 2
112.27 even 4 1280.4.d.a.641.1 2
112.69 odd 4 1280.4.d.p.641.2 2
112.83 even 4 1280.4.d.a.641.2 2
140.27 odd 4 400.4.c.f.49.1 2
140.83 odd 4 400.4.c.f.49.2 2
140.139 even 2 400.4.a.e.1.1 1
280.69 odd 2 1600.4.a.j.1.1 1
280.139 even 2 1600.4.a.br.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
40.4.a.a.1.1 1 7.6 odd 2
80.4.a.e.1.1 1 28.27 even 2
200.4.a.i.1.1 1 35.34 odd 2
200.4.c.c.49.1 2 35.13 even 4
200.4.c.c.49.2 2 35.27 even 4
320.4.a.c.1.1 1 56.27 even 2
320.4.a.l.1.1 1 56.13 odd 2
360.4.a.h.1.1 1 21.20 even 2
400.4.a.e.1.1 1 140.139 even 2
400.4.c.f.49.1 2 140.27 odd 4
400.4.c.f.49.2 2 140.83 odd 4
720.4.a.bd.1.1 1 84.83 odd 2
1280.4.d.a.641.1 2 112.27 even 4
1280.4.d.a.641.2 2 112.83 even 4
1280.4.d.p.641.1 2 112.13 odd 4
1280.4.d.p.641.2 2 112.69 odd 4
1600.4.a.j.1.1 1 280.69 odd 2
1600.4.a.br.1.1 1 280.139 even 2
1800.4.a.bi.1.1 1 105.104 even 2
1800.4.f.j.649.1 2 105.62 odd 4
1800.4.f.j.649.2 2 105.83 odd 4
1960.4.a.h.1.1 1 1.1 even 1 trivial