Properties

Label 9800.2.a.bx.1.1
Level $9800$
Weight $2$
Character 9800.1
Self dual yes
Analytic conductor $78.253$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9800.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(78.2533939809\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{17}) \)
Defining polynomial: \(x^{2} - x - 4\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1400)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.56155\) of defining polynomial
Character \(\chi\) \(=\) 9800.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.56155 q^{3} -0.561553 q^{9} +O(q^{10})\) \(q-1.56155 q^{3} -0.561553 q^{9} -6.12311 q^{11} +2.00000 q^{13} +1.56155 q^{17} -3.56155 q^{19} -1.43845 q^{23} +5.56155 q^{27} +3.43845 q^{29} +9.12311 q^{31} +9.56155 q^{33} -8.80776 q^{37} -3.12311 q^{39} +2.43845 q^{41} -6.56155 q^{43} -8.24621 q^{47} -2.43845 q^{51} +1.12311 q^{53} +5.56155 q^{57} -11.3693 q^{59} -11.1231 q^{61} -7.87689 q^{67} +2.24621 q^{69} +1.68466 q^{71} +6.43845 q^{73} -5.68466 q^{79} -7.00000 q^{81} -1.31534 q^{83} -5.36932 q^{87} -9.80776 q^{89} -14.2462 q^{93} +6.00000 q^{97} +3.43845 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{3} + 3q^{9} + O(q^{10}) \) \( 2q + q^{3} + 3q^{9} - 4q^{11} + 4q^{13} - q^{17} - 3q^{19} - 7q^{23} + 7q^{27} + 11q^{29} + 10q^{31} + 15q^{33} + 3q^{37} + 2q^{39} + 9q^{41} - 9q^{43} - 9q^{51} - 6q^{53} + 7q^{57} + 2q^{59} - 14q^{61} - 24q^{67} - 12q^{69} - 9q^{71} + 17q^{73} + q^{79} - 14q^{81} - 15q^{83} + 14q^{87} + q^{89} - 12q^{93} + 12q^{97} + 11q^{99} + O(q^{100}) \)

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
\(3\) −1.56155 −0.901563 −0.450781 0.892634i \(-0.648855\pi\)
−0.450781 + 0.892634i \(0.648855\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −0.561553 −0.187184
\(10\) 0 0
\(11\) −6.12311 −1.84619 −0.923093 0.384577i \(-0.874347\pi\)
−0.923093 + 0.384577i \(0.874347\pi\)
\(12\) 0 0
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.56155 0.378732 0.189366 0.981907i \(-0.439357\pi\)
0.189366 + 0.981907i \(0.439357\pi\)
\(18\) 0 0
\(19\) −3.56155 −0.817076 −0.408538 0.912741i \(-0.633961\pi\)
−0.408538 + 0.912741i \(0.633961\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.43845 −0.299937 −0.149968 0.988691i \(-0.547917\pi\)
−0.149968 + 0.988691i \(0.547917\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 5.56155 1.07032
\(28\) 0 0
\(29\) 3.43845 0.638504 0.319252 0.947670i \(-0.396568\pi\)
0.319252 + 0.947670i \(0.396568\pi\)
\(30\) 0 0
\(31\) 9.12311 1.63856 0.819279 0.573395i \(-0.194374\pi\)
0.819279 + 0.573395i \(0.194374\pi\)
\(32\) 0 0
\(33\) 9.56155 1.66445
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −8.80776 −1.44799 −0.723994 0.689807i \(-0.757696\pi\)
−0.723994 + 0.689807i \(0.757696\pi\)
\(38\) 0 0
\(39\) −3.12311 −0.500097
\(40\) 0 0
\(41\) 2.43845 0.380821 0.190411 0.981705i \(-0.439018\pi\)
0.190411 + 0.981705i \(0.439018\pi\)
\(42\) 0 0
\(43\) −6.56155 −1.00063 −0.500314 0.865844i \(-0.666782\pi\)
−0.500314 + 0.865844i \(0.666782\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −8.24621 −1.20283 −0.601417 0.798935i \(-0.705397\pi\)
−0.601417 + 0.798935i \(0.705397\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −2.43845 −0.341451
\(52\) 0 0
\(53\) 1.12311 0.154270 0.0771352 0.997021i \(-0.475423\pi\)
0.0771352 + 0.997021i \(0.475423\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 5.56155 0.736646
\(58\) 0 0
\(59\) −11.3693 −1.48016 −0.740079 0.672519i \(-0.765212\pi\)
−0.740079 + 0.672519i \(0.765212\pi\)
\(60\) 0 0
\(61\) −11.1231 −1.42417 −0.712084 0.702094i \(-0.752248\pi\)
−0.712084 + 0.702094i \(0.752248\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −7.87689 −0.962316 −0.481158 0.876634i \(-0.659784\pi\)
−0.481158 + 0.876634i \(0.659784\pi\)
\(68\) 0 0
\(69\) 2.24621 0.270412
\(70\) 0 0
\(71\) 1.68466 0.199932 0.0999661 0.994991i \(-0.468127\pi\)
0.0999661 + 0.994991i \(0.468127\pi\)
\(72\) 0 0
\(73\) 6.43845 0.753563 0.376782 0.926302i \(-0.377031\pi\)
0.376782 + 0.926302i \(0.377031\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −5.68466 −0.639574 −0.319787 0.947489i \(-0.603611\pi\)
−0.319787 + 0.947489i \(0.603611\pi\)
\(80\) 0 0
\(81\) −7.00000 −0.777778
\(82\) 0 0
\(83\) −1.31534 −0.144377 −0.0721887 0.997391i \(-0.522998\pi\)
−0.0721887 + 0.997391i \(0.522998\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −5.36932 −0.575651
\(88\) 0 0
\(89\) −9.80776 −1.03962 −0.519810 0.854282i \(-0.673997\pi\)
−0.519810 + 0.854282i \(0.673997\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −14.2462 −1.47726
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 6.00000 0.609208 0.304604 0.952479i \(-0.401476\pi\)
0.304604 + 0.952479i \(0.401476\pi\)
\(98\) 0 0
\(99\) 3.43845 0.345577
\(100\) 0 0
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) −1.12311 −0.110663 −0.0553314 0.998468i \(-0.517622\pi\)
−0.0553314 + 0.998468i \(0.517622\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −7.80776 −0.754805 −0.377403 0.926049i \(-0.623183\pi\)
−0.377403 + 0.926049i \(0.623183\pi\)
\(108\) 0 0
\(109\) 19.9309 1.90903 0.954516 0.298161i \(-0.0963733\pi\)
0.954516 + 0.298161i \(0.0963733\pi\)
\(110\) 0 0
\(111\) 13.7538 1.30545
\(112\) 0 0
\(113\) −17.2462 −1.62239 −0.811194 0.584778i \(-0.801182\pi\)
−0.811194 + 0.584778i \(0.801182\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −1.12311 −0.103831
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 26.4924 2.40840
\(122\) 0 0
\(123\) −3.80776 −0.343335
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −10.8078 −0.959034 −0.479517 0.877533i \(-0.659188\pi\)
−0.479517 + 0.877533i \(0.659188\pi\)
\(128\) 0 0
\(129\) 10.2462 0.902129
\(130\) 0 0
\(131\) 18.2462 1.59418 0.797089 0.603861i \(-0.206372\pi\)
0.797089 + 0.603861i \(0.206372\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 14.6847 1.25460 0.627298 0.778780i \(-0.284161\pi\)
0.627298 + 0.778780i \(0.284161\pi\)
\(138\) 0 0
\(139\) 7.31534 0.620479 0.310240 0.950658i \(-0.399591\pi\)
0.310240 + 0.950658i \(0.399591\pi\)
\(140\) 0 0
\(141\) 12.8769 1.08443
\(142\) 0 0
\(143\) −12.2462 −1.02408
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 13.4384 1.10092 0.550460 0.834861i \(-0.314452\pi\)
0.550460 + 0.834861i \(0.314452\pi\)
\(150\) 0 0
\(151\) −1.43845 −0.117059 −0.0585296 0.998286i \(-0.518641\pi\)
−0.0585296 + 0.998286i \(0.518641\pi\)
\(152\) 0 0
\(153\) −0.876894 −0.0708927
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −8.49242 −0.677769 −0.338885 0.940828i \(-0.610050\pi\)
−0.338885 + 0.940828i \(0.610050\pi\)
\(158\) 0 0
\(159\) −1.75379 −0.139084
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −14.9309 −1.16948 −0.584738 0.811222i \(-0.698803\pi\)
−0.584738 + 0.811222i \(0.698803\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 21.6155 1.67266 0.836330 0.548227i \(-0.184697\pi\)
0.836330 + 0.548227i \(0.184697\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) 2.00000 0.152944
\(172\) 0 0
\(173\) −18.4924 −1.40595 −0.702976 0.711213i \(-0.748146\pi\)
−0.702976 + 0.711213i \(0.748146\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 17.7538 1.33446
\(178\) 0 0
\(179\) −20.6847 −1.54604 −0.773022 0.634379i \(-0.781256\pi\)
−0.773022 + 0.634379i \(0.781256\pi\)
\(180\) 0 0
\(181\) 11.1231 0.826774 0.413387 0.910555i \(-0.364346\pi\)
0.413387 + 0.910555i \(0.364346\pi\)
\(182\) 0 0
\(183\) 17.3693 1.28398
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −9.56155 −0.699210
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 25.3693 1.83566 0.917830 0.396974i \(-0.129940\pi\)
0.917830 + 0.396974i \(0.129940\pi\)
\(192\) 0 0
\(193\) 20.6155 1.48394 0.741969 0.670434i \(-0.233892\pi\)
0.741969 + 0.670434i \(0.233892\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −0.561553 −0.0400090 −0.0200045 0.999800i \(-0.506368\pi\)
−0.0200045 + 0.999800i \(0.506368\pi\)
\(198\) 0 0
\(199\) 4.87689 0.345714 0.172857 0.984947i \(-0.444700\pi\)
0.172857 + 0.984947i \(0.444700\pi\)
\(200\) 0 0
\(201\) 12.3002 0.867588
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0.807764 0.0561435
\(208\) 0 0
\(209\) 21.8078 1.50847
\(210\) 0 0
\(211\) 6.43845 0.443241 0.221620 0.975133i \(-0.428865\pi\)
0.221620 + 0.975133i \(0.428865\pi\)
\(212\) 0 0
\(213\) −2.63068 −0.180251
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −10.0540 −0.679385
\(220\) 0 0
\(221\) 3.12311 0.210083
\(222\) 0 0
\(223\) −25.3693 −1.69886 −0.849428 0.527705i \(-0.823053\pi\)
−0.849428 + 0.527705i \(0.823053\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 11.3693 0.754608 0.377304 0.926089i \(-0.376851\pi\)
0.377304 + 0.926089i \(0.376851\pi\)
\(228\) 0 0
\(229\) 14.0000 0.925146 0.462573 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0.561553 0.0367885 0.0183943 0.999831i \(-0.494145\pi\)
0.0183943 + 0.999831i \(0.494145\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 8.87689 0.576616
\(238\) 0 0
\(239\) −4.00000 −0.258738 −0.129369 0.991596i \(-0.541295\pi\)
−0.129369 + 0.991596i \(0.541295\pi\)
\(240\) 0 0
\(241\) 12.0540 0.776465 0.388232 0.921562i \(-0.373086\pi\)
0.388232 + 0.921562i \(0.373086\pi\)
\(242\) 0 0
\(243\) −5.75379 −0.369106
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −7.12311 −0.453232
\(248\) 0 0
\(249\) 2.05398 0.130165
\(250\) 0 0
\(251\) 24.6847 1.55808 0.779041 0.626973i \(-0.215706\pi\)
0.779041 + 0.626973i \(0.215706\pi\)
\(252\) 0 0
\(253\) 8.80776 0.553739
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 12.2462 0.763898 0.381949 0.924183i \(-0.375253\pi\)
0.381949 + 0.924183i \(0.375253\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −1.93087 −0.119518
\(262\) 0 0
\(263\) −1.68466 −0.103880 −0.0519402 0.998650i \(-0.516541\pi\)
−0.0519402 + 0.998650i \(0.516541\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 15.3153 0.937284
\(268\) 0 0
\(269\) −28.2462 −1.72220 −0.861101 0.508434i \(-0.830225\pi\)
−0.861101 + 0.508434i \(0.830225\pi\)
\(270\) 0 0
\(271\) 0.246211 0.0149563 0.00747813 0.999972i \(-0.497620\pi\)
0.00747813 + 0.999972i \(0.497620\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −22.4924 −1.35144 −0.675719 0.737159i \(-0.736167\pi\)
−0.675719 + 0.737159i \(0.736167\pi\)
\(278\) 0 0
\(279\) −5.12311 −0.306712
\(280\) 0 0
\(281\) 7.43845 0.443741 0.221870 0.975076i \(-0.428784\pi\)
0.221870 + 0.975076i \(0.428784\pi\)
\(282\) 0 0
\(283\) −1.31534 −0.0781889 −0.0390945 0.999236i \(-0.512447\pi\)
−0.0390945 + 0.999236i \(0.512447\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −14.5616 −0.856562
\(290\) 0 0
\(291\) −9.36932 −0.549239
\(292\) 0 0
\(293\) −30.0000 −1.75262 −0.876309 0.481749i \(-0.840002\pi\)
−0.876309 + 0.481749i \(0.840002\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −34.0540 −1.97601
\(298\) 0 0
\(299\) −2.87689 −0.166375
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 16.6847 0.952244 0.476122 0.879379i \(-0.342042\pi\)
0.476122 + 0.879379i \(0.342042\pi\)
\(308\) 0 0
\(309\) 1.75379 0.0997696
\(310\) 0 0
\(311\) −11.1231 −0.630733 −0.315367 0.948970i \(-0.602128\pi\)
−0.315367 + 0.948970i \(0.602128\pi\)
\(312\) 0 0
\(313\) 22.0000 1.24351 0.621757 0.783210i \(-0.286419\pi\)
0.621757 + 0.783210i \(0.286419\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 8.31534 0.467036 0.233518 0.972352i \(-0.424976\pi\)
0.233518 + 0.972352i \(0.424976\pi\)
\(318\) 0 0
\(319\) −21.0540 −1.17880
\(320\) 0 0
\(321\) 12.1922 0.680504
\(322\) 0 0
\(323\) −5.56155 −0.309453
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −31.1231 −1.72111
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 27.0000 1.48405 0.742027 0.670370i \(-0.233865\pi\)
0.742027 + 0.670370i \(0.233865\pi\)
\(332\) 0 0
\(333\) 4.94602 0.271040
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −6.68466 −0.364137 −0.182068 0.983286i \(-0.558279\pi\)
−0.182068 + 0.983286i \(0.558279\pi\)
\(338\) 0 0
\(339\) 26.9309 1.46268
\(340\) 0 0
\(341\) −55.8617 −3.02508
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 18.6155 0.999334 0.499667 0.866218i \(-0.333456\pi\)
0.499667 + 0.866218i \(0.333456\pi\)
\(348\) 0 0
\(349\) 21.1231 1.13069 0.565347 0.824853i \(-0.308742\pi\)
0.565347 + 0.824853i \(0.308742\pi\)
\(350\) 0 0
\(351\) 11.1231 0.593707
\(352\) 0 0
\(353\) −28.2462 −1.50339 −0.751697 0.659509i \(-0.770764\pi\)
−0.751697 + 0.659509i \(0.770764\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −2.31534 −0.122199 −0.0610995 0.998132i \(-0.519461\pi\)
−0.0610995 + 0.998132i \(0.519461\pi\)
\(360\) 0 0
\(361\) −6.31534 −0.332386
\(362\) 0 0
\(363\) −41.3693 −2.17133
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 34.2462 1.78764 0.893819 0.448428i \(-0.148016\pi\)
0.893819 + 0.448428i \(0.148016\pi\)
\(368\) 0 0
\(369\) −1.36932 −0.0712838
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 23.0540 1.19369 0.596845 0.802357i \(-0.296421\pi\)
0.596845 + 0.802357i \(0.296421\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 6.87689 0.354178
\(378\) 0 0
\(379\) 32.8617 1.68799 0.843997 0.536348i \(-0.180196\pi\)
0.843997 + 0.536348i \(0.180196\pi\)
\(380\) 0 0
\(381\) 16.8769 0.864629
\(382\) 0 0
\(383\) −3.75379 −0.191810 −0.0959048 0.995391i \(-0.530574\pi\)
−0.0959048 + 0.995391i \(0.530574\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 3.68466 0.187302
\(388\) 0 0
\(389\) 6.56155 0.332684 0.166342 0.986068i \(-0.446804\pi\)
0.166342 + 0.986068i \(0.446804\pi\)
\(390\) 0 0
\(391\) −2.24621 −0.113596
\(392\) 0 0
\(393\) −28.4924 −1.43725
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 5.50758 0.276417 0.138209 0.990403i \(-0.455866\pi\)
0.138209 + 0.990403i \(0.455866\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1.49242 0.0745280 0.0372640 0.999305i \(-0.488136\pi\)
0.0372640 + 0.999305i \(0.488136\pi\)
\(402\) 0 0
\(403\) 18.2462 0.908909
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 53.9309 2.67325
\(408\) 0 0
\(409\) 25.8078 1.27611 0.638056 0.769990i \(-0.279739\pi\)
0.638056 + 0.769990i \(0.279739\pi\)
\(410\) 0 0
\(411\) −22.9309 −1.13110
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −11.4233 −0.559401
\(418\) 0 0
\(419\) −1.80776 −0.0883151 −0.0441575 0.999025i \(-0.514060\pi\)
−0.0441575 + 0.999025i \(0.514060\pi\)
\(420\) 0 0
\(421\) 33.9309 1.65369 0.826845 0.562430i \(-0.190134\pi\)
0.826845 + 0.562430i \(0.190134\pi\)
\(422\) 0 0
\(423\) 4.63068 0.225152
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 19.1231 0.923272
\(430\) 0 0
\(431\) −30.2462 −1.45691 −0.728454 0.685094i \(-0.759761\pi\)
−0.728454 + 0.685094i \(0.759761\pi\)
\(432\) 0 0
\(433\) 34.5464 1.66019 0.830097 0.557619i \(-0.188285\pi\)
0.830097 + 0.557619i \(0.188285\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 5.12311 0.245071
\(438\) 0 0
\(439\) −1.12311 −0.0536029 −0.0268015 0.999641i \(-0.508532\pi\)
−0.0268015 + 0.999641i \(0.508532\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −18.4384 −0.876037 −0.438019 0.898966i \(-0.644320\pi\)
−0.438019 + 0.898966i \(0.644320\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −20.9848 −0.992549
\(448\) 0 0
\(449\) −14.3693 −0.678130 −0.339065 0.940763i \(-0.610111\pi\)
−0.339065 + 0.940763i \(0.610111\pi\)
\(450\) 0 0
\(451\) −14.9309 −0.703067
\(452\) 0 0
\(453\) 2.24621 0.105536
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 37.1080 1.73584 0.867918 0.496707i \(-0.165458\pi\)
0.867918 + 0.496707i \(0.165458\pi\)
\(458\) 0 0
\(459\) 8.68466 0.405365
\(460\) 0 0
\(461\) 26.4924 1.23388 0.616938 0.787012i \(-0.288373\pi\)
0.616938 + 0.787012i \(0.288373\pi\)
\(462\) 0 0
\(463\) −12.4924 −0.580572 −0.290286 0.956940i \(-0.593750\pi\)
−0.290286 + 0.956940i \(0.593750\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −33.1231 −1.53275 −0.766377 0.642391i \(-0.777943\pi\)
−0.766377 + 0.642391i \(0.777943\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 13.2614 0.611052
\(472\) 0 0
\(473\) 40.1771 1.84734
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −0.630683 −0.0288770
\(478\) 0 0
\(479\) −8.73863 −0.399278 −0.199639 0.979869i \(-0.563977\pi\)
−0.199639 + 0.979869i \(0.563977\pi\)
\(480\) 0 0
\(481\) −17.6155 −0.803199
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −31.4384 −1.42461 −0.712306 0.701869i \(-0.752349\pi\)
−0.712306 + 0.701869i \(0.752349\pi\)
\(488\) 0 0
\(489\) 23.3153 1.05436
\(490\) 0 0
\(491\) 8.31534 0.375266 0.187633 0.982239i \(-0.439918\pi\)
0.187633 + 0.982239i \(0.439918\pi\)
\(492\) 0 0
\(493\) 5.36932 0.241822
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 16.4924 0.738302 0.369151 0.929369i \(-0.379648\pi\)
0.369151 + 0.929369i \(0.379648\pi\)
\(500\) 0 0
\(501\) −33.7538 −1.50801
\(502\) 0 0
\(503\) 36.2462 1.61614 0.808069 0.589087i \(-0.200513\pi\)
0.808069 + 0.589087i \(0.200513\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 14.0540 0.624159
\(508\) 0 0
\(509\) −26.0000 −1.15243 −0.576215 0.817298i \(-0.695471\pi\)
−0.576215 + 0.817298i \(0.695471\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −19.8078 −0.874534
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 50.4924 2.22065
\(518\) 0 0
\(519\) 28.8769 1.26755
\(520\) 0 0
\(521\) 31.5616 1.38274 0.691368 0.722502i \(-0.257008\pi\)
0.691368 + 0.722502i \(0.257008\pi\)
\(522\) 0 0
\(523\) 40.6847 1.77902 0.889508 0.456920i \(-0.151047\pi\)
0.889508 + 0.456920i \(0.151047\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 14.2462 0.620575
\(528\) 0 0
\(529\) −20.9309 −0.910038
\(530\) 0 0
\(531\) 6.38447 0.277062
\(532\) 0 0
\(533\) 4.87689 0.211242
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 32.3002 1.39386
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −20.4233 −0.878066 −0.439033 0.898471i \(-0.644679\pi\)
−0.439033 + 0.898471i \(0.644679\pi\)
\(542\) 0 0
\(543\) −17.3693 −0.745389
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 15.7386 0.672935 0.336468 0.941695i \(-0.390768\pi\)
0.336468 + 0.941695i \(0.390768\pi\)
\(548\) 0 0
\(549\) 6.24621 0.266582
\(550\) 0 0
\(551\) −12.2462 −0.521706
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −5.43845 −0.230434 −0.115217 0.993340i \(-0.536756\pi\)
−0.115217 + 0.993340i \(0.536756\pi\)
\(558\) 0 0
\(559\) −13.1231 −0.555048
\(560\) 0 0
\(561\) 14.9309 0.630382
\(562\) 0 0
\(563\) 1.12311 0.0473333 0.0236666 0.999720i \(-0.492466\pi\)
0.0236666 + 0.999720i \(0.492466\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 45.9848 1.92778 0.963892 0.266292i \(-0.0857984\pi\)
0.963892 + 0.266292i \(0.0857984\pi\)
\(570\) 0 0
\(571\) 39.6847 1.66075 0.830376 0.557204i \(-0.188126\pi\)
0.830376 + 0.557204i \(0.188126\pi\)
\(572\) 0 0
\(573\) −39.6155 −1.65496
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 24.5464 1.02188 0.510940 0.859616i \(-0.329297\pi\)
0.510940 + 0.859616i \(0.329297\pi\)
\(578\) 0 0
\(579\) −32.1922 −1.33786
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −6.87689 −0.284812
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −37.1771 −1.53446 −0.767231 0.641371i \(-0.778366\pi\)
−0.767231 + 0.641371i \(0.778366\pi\)
\(588\) 0 0
\(589\) −32.4924 −1.33883
\(590\) 0 0
\(591\) 0.876894 0.0360706
\(592\) 0 0
\(593\) 24.6847 1.01368 0.506839 0.862041i \(-0.330814\pi\)
0.506839 + 0.862041i \(0.330814\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −7.61553 −0.311683
\(598\) 0 0
\(599\) −29.3002 −1.19717 −0.598587 0.801058i \(-0.704271\pi\)
−0.598587 + 0.801058i \(0.704271\pi\)
\(600\) 0 0
\(601\) 42.0540 1.71542 0.857709 0.514136i \(-0.171887\pi\)
0.857709 + 0.514136i \(0.171887\pi\)
\(602\) 0 0
\(603\) 4.42329 0.180130
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −12.6307 −0.512664 −0.256332 0.966589i \(-0.582514\pi\)
−0.256332 + 0.966589i \(0.582514\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −16.4924 −0.667212
\(612\) 0 0
\(613\) −5.68466 −0.229601 −0.114801 0.993389i \(-0.536623\pi\)
−0.114801 + 0.993389i \(0.536623\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 2.80776 0.113036 0.0565182 0.998402i \(-0.482000\pi\)
0.0565182 + 0.998402i \(0.482000\pi\)
\(618\) 0 0
\(619\) −4.63068 −0.186123 −0.0930614 0.995660i \(-0.529665\pi\)
−0.0930614 + 0.995660i \(0.529665\pi\)
\(620\) 0 0
\(621\) −8.00000 −0.321029
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −34.0540 −1.35998
\(628\) 0 0
\(629\) −13.7538 −0.548399
\(630\) 0 0
\(631\) −3.05398 −0.121577 −0.0607884 0.998151i \(-0.519361\pi\)
−0.0607884 + 0.998151i \(0.519361\pi\)
\(632\) 0 0
\(633\) −10.0540 −0.399610
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −0.946025 −0.0374242
\(640\) 0 0
\(641\) −20.5616 −0.812133 −0.406066 0.913844i \(-0.633100\pi\)
−0.406066 + 0.913844i \(0.633100\pi\)
\(642\) 0 0
\(643\) −46.7386 −1.84319 −0.921596 0.388151i \(-0.873114\pi\)
−0.921596 + 0.388151i \(0.873114\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −0.630683 −0.0247947 −0.0123974 0.999923i \(-0.503946\pi\)
−0.0123974 + 0.999923i \(0.503946\pi\)
\(648\) 0 0
\(649\) 69.6155 2.73265
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 23.8617 0.933782 0.466891 0.884315i \(-0.345374\pi\)
0.466891 + 0.884315i \(0.345374\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −3.61553 −0.141055
\(658\) 0 0
\(659\) 14.4384 0.562442 0.281221 0.959643i \(-0.409261\pi\)
0.281221 + 0.959643i \(0.409261\pi\)
\(660\) 0 0
\(661\) −10.4924 −0.408108 −0.204054 0.978960i \(-0.565412\pi\)
−0.204054 + 0.978960i \(0.565412\pi\)
\(662\) 0 0
\(663\) −4.87689 −0.189403
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −4.94602 −0.191511
\(668\) 0 0
\(669\) 39.6155 1.53162
\(670\) 0 0
\(671\) 68.1080 2.62928
\(672\) 0 0
\(673\) −13.5076 −0.520679 −0.260339 0.965517i \(-0.583834\pi\)
−0.260339 + 0.965517i \(0.583834\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 39.3693 1.51309 0.756543 0.653944i \(-0.226887\pi\)
0.756543 + 0.653944i \(0.226887\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −17.7538 −0.680327
\(682\) 0 0
\(683\) −25.8769 −0.990152 −0.495076 0.868850i \(-0.664860\pi\)
−0.495076 + 0.868850i \(0.664860\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −21.8617 −0.834077
\(688\) 0 0
\(689\) 2.24621 0.0855738
\(690\) 0 0
\(691\) 21.5616 0.820240 0.410120 0.912032i \(-0.365487\pi\)
0.410120 + 0.912032i \(0.365487\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 3.80776 0.144229
\(698\) 0 0
\(699\) −0.876894 −0.0331672
\(700\) 0 0
\(701\) −30.1080 −1.13716 −0.568581 0.822627i \(-0.692507\pi\)
−0.568581 + 0.822627i \(0.692507\pi\)
\(702\) 0 0
\(703\) 31.3693 1.18312
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 12.6307 0.474355 0.237178 0.971466i \(-0.423778\pi\)
0.237178 + 0.971466i \(0.423778\pi\)
\(710\) 0 0
\(711\) 3.19224 0.119718
\(712\) 0 0
\(713\) −13.1231 −0.491464
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 6.24621 0.233269
\(718\) 0 0
\(719\) −21.7538 −0.811279 −0.405640 0.914033i \(-0.632951\pi\)
−0.405640 + 0.914033i \(0.632951\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −18.8229 −0.700032
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 39.6155 1.46926 0.734629 0.678469i \(-0.237356\pi\)
0.734629 + 0.678469i \(0.237356\pi\)
\(728\) 0 0
\(729\) 29.9848 1.11055
\(730\) 0 0
\(731\) −10.2462 −0.378970
\(732\) 0 0
\(733\) 5.75379 0.212521 0.106261 0.994338i \(-0.466112\pi\)
0.106261 + 0.994338i \(0.466112\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 48.2311 1.77661
\(738\) 0 0
\(739\) −28.1771 −1.03651 −0.518255 0.855226i \(-0.673418\pi\)
−0.518255 + 0.855226i \(0.673418\pi\)
\(740\) 0 0
\(741\) 11.1231 0.408617
\(742\) 0 0
\(743\) −30.7386 −1.12769 −0.563846 0.825880i \(-0.690679\pi\)
−0.563846 + 0.825880i \(0.690679\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0.738634 0.0270252
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 2.63068 0.0959950 0.0479975 0.998847i \(-0.484716\pi\)
0.0479975 + 0.998847i \(0.484716\pi\)
\(752\) 0 0
\(753\) −38.5464 −1.40471
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −25.6847 −0.933525 −0.466762 0.884383i \(-0.654580\pi\)
−0.466762 + 0.884383i \(0.654580\pi\)
\(758\) 0 0
\(759\) −13.7538 −0.499231
\(760\) 0 0
\(761\) 27.4233 0.994094 0.497047 0.867724i \(-0.334418\pi\)
0.497047 + 0.867724i \(0.334418\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −22.7386 −0.821044
\(768\) 0 0
\(769\) −20.3002 −0.732043 −0.366022 0.930606i \(-0.619280\pi\)
−0.366022 + 0.930606i \(0.619280\pi\)
\(770\) 0 0
\(771\) −19.1231 −0.688702
\(772\) 0 0
\(773\) 29.6155 1.06520 0.532598 0.846368i \(-0.321216\pi\)
0.532598 + 0.846368i \(0.321216\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −8.68466 −0.311160
\(780\) 0 0
\(781\) −10.3153 −0.369112
\(782\) 0 0
\(783\) 19.1231 0.683404
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 9.75379 0.347685 0.173843 0.984773i \(-0.444382\pi\)
0.173843 + 0.984773i \(0.444382\pi\)
\(788\) 0 0
\(789\) 2.63068 0.0936548
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −22.2462 −0.789986
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0.384472 0.0136187 0.00680935 0.999977i \(-0.497833\pi\)
0.00680935 + 0.999977i \(0.497833\pi\)
\(798\) 0 0
\(799\) −12.8769 −0.455552
\(800\) 0 0
\(801\) 5.50758 0.194601
\(802\) 0 0
\(803\) −39.4233 −1.39122
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 44.1080 1.55267
\(808\) 0 0
\(809\) −12.4233 −0.436780 −0.218390 0.975862i \(-0.570080\pi\)
−0.218390 + 0.975862i \(0.570080\pi\)
\(810\) 0 0
\(811\) −2.38447 −0.0837301 −0.0418651 0.999123i \(-0.513330\pi\)
−0.0418651 + 0.999123i \(0.513330\pi\)
\(812\) 0 0
\(813\) −0.384472 −0.0134840
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 23.3693 0.817589
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −11.8617 −0.413978 −0.206989 0.978343i \(-0.566366\pi\)
−0.206989 + 0.978343i \(0.566366\pi\)
\(822\) 0 0
\(823\) −16.5616 −0.577299 −0.288650 0.957435i \(-0.593206\pi\)
−0.288650 + 0.957435i \(0.593206\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −7.24621 −0.251975 −0.125988 0.992032i \(-0.540210\pi\)
−0.125988 + 0.992032i \(0.540210\pi\)
\(828\) 0 0
\(829\) −14.2462 −0.494791 −0.247396 0.968915i \(-0.579575\pi\)
−0.247396 + 0.968915i \(0.579575\pi\)
\(830\) 0 0
\(831\) 35.1231 1.21841
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 50.7386 1.75378
\(838\) 0 0
\(839\) −7.12311 −0.245917 −0.122958 0.992412i \(-0.539238\pi\)
−0.122958 + 0.992412i \(0.539238\pi\)
\(840\) 0 0
\(841\) −17.1771 −0.592313
\(842\) 0 0
\(843\) −11.6155 −0.400060
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 2.05398 0.0704923
\(850\) 0 0
\(851\) 12.6695 0.434305
\(852\) 0 0
\(853\) 19.1231 0.654763 0.327381 0.944892i \(-0.393834\pi\)
0.327381 + 0.944892i \(0.393834\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 42.0540 1.43654 0.718268 0.695766i \(-0.244935\pi\)
0.718268 + 0.695766i \(0.244935\pi\)
\(858\) 0 0
\(859\) 11.1771 0.381357 0.190679 0.981653i \(-0.438931\pi\)
0.190679 + 0.981653i \(0.438931\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 3.19224 0.108665 0.0543325 0.998523i \(-0.482697\pi\)
0.0543325 + 0.998523i \(0.482697\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 22.7386 0.772244
\(868\) 0 0
\(869\) 34.8078 1.18077
\(870\) 0 0
\(871\) −15.7538 −0.533797
\(872\) 0 0
\(873\) −3.36932 −0.114034
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 17.6155 0.594834 0.297417 0.954748i \(-0.403875\pi\)
0.297417 + 0.954748i \(0.403875\pi\)
\(878\) 0 0
\(879\) 46.8466 1.58010
\(880\) 0 0
\(881\) −8.73863 −0.294412 −0.147206 0.989106i \(-0.547028\pi\)
−0.147206 + 0.989106i \(0.547028\pi\)
\(882\) 0 0
\(883\) −31.4924 −1.05980 −0.529902 0.848059i \(-0.677771\pi\)
−0.529902 + 0.848059i \(0.677771\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −8.38447 −0.281523 −0.140762 0.990044i \(-0.544955\pi\)
−0.140762 + 0.990044i \(0.544955\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 42.8617 1.43592
\(892\) 0 0
\(893\) 29.3693 0.982807
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 4.49242 0.149998
\(898\) 0 0
\(899\) 31.3693 1.04623
\(900\) 0 0
\(901\) 1.75379 0.0584272
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −4.00000 −0.132818 −0.0664089 0.997792i \(-0.521154\pi\)
−0.0664089 + 0.997792i \(0.521154\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 22.4233 0.742917 0.371458 0.928450i \(-0.378858\pi\)
0.371458 + 0.928450i \(0.378858\pi\)
\(912\) 0 0
\(913\) 8.05398 0.266548
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 38.8078 1.28015 0.640075 0.768312i \(-0.278903\pi\)
0.640075 + 0.768312i \(0.278903\pi\)
\(920\) 0 0
\(921\) −26.0540 −0.858508
\(922\) 0 0
\(923\) 3.36932 0.110902
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0.630683 0.0207144
\(928\) 0 0
\(929\) 34.3542 1.12712 0.563562 0.826074i \(-0.309431\pi\)
0.563562 + 0.826074i \(0.309431\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 17.3693 0.568646
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −32.3002 −1.05520 −0.527601 0.849493i \(-0.676908\pi\)
−0.527601 + 0.849493i \(0.676908\pi\)
\(938\) 0 0
\(939\) −34.3542 −1.12111
\(940\) 0 0
\(941\) −23.3693 −0.761818 −0.380909 0.924613i \(-0.624389\pi\)
−0.380909 + 0.924613i \(0.624389\pi\)
\(942\) 0 0
\(943\) −3.50758 −0.114222
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 16.4924 0.535932 0.267966 0.963428i \(-0.413649\pi\)
0.267966 + 0.963428i \(0.413649\pi\)
\(948\) 0 0
\(949\) 12.8769 0.418002
\(950\) 0 0
\(951\) −12.9848 −0.421062
\(952\) 0 0
\(953\) 36.1231 1.17014 0.585071 0.810982i \(-0.301067\pi\)
0.585071 + 0.810982i \(0.301067\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 32.8769 1.06276
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 52.2311 1.68487
\(962\) 0 0
\(963\) 4.38447 0.141288
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 41.3693 1.33035 0.665174 0.746689i \(-0.268357\pi\)
0.665174 + 0.746689i \(0.268357\pi\)
\(968\) 0 0
\(969\) 8.68466 0.278991
\(970\) 0 0
\(971\) 14.6847 0.471253 0.235627 0.971844i \(-0.424286\pi\)
0.235627 + 0.971844i \(0.424286\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 16.7538 0.536001 0.268001 0.963419i \(-0.413637\pi\)
0.268001 + 0.963419i \(0.413637\pi\)
\(978\) 0 0
\(979\) 60.0540 1.91933
\(980\) 0 0
\(981\) −11.1922 −0.357341
\(982\) 0 0
\(983\) 28.3542 0.904357 0.452179 0.891927i \(-0.350647\pi\)
0.452179 + 0.891927i \(0.350647\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 9.43845 0.300125
\(990\) 0 0
\(991\) 48.6695 1.54604 0.773019 0.634383i \(-0.218746\pi\)
0.773019 + 0.634383i \(0.218746\pi\)
\(992\) 0 0
\(993\) −42.1619 −1.33797
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −4.24621 −0.134479 −0.0672394 0.997737i \(-0.521419\pi\)
−0.0672394 + 0.997737i \(0.521419\pi\)
\(998\) 0 0
\(999\) −48.9848 −1.54981
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 9800.2.a.bx.1.1 2
5.4 even 2 9800.2.a.bt.1.2 2
7.6 odd 2 1400.2.a.o.1.2 2
28.27 even 2 2800.2.a.bo.1.1 2
35.13 even 4 1400.2.g.j.449.3 4
35.27 even 4 1400.2.g.j.449.2 4
35.34 odd 2 1400.2.a.q.1.1 yes 2
140.27 odd 4 2800.2.g.v.449.3 4
140.83 odd 4 2800.2.g.v.449.2 4
140.139 even 2 2800.2.a.bj.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1400.2.a.o.1.2 2 7.6 odd 2
1400.2.a.q.1.1 yes 2 35.34 odd 2
1400.2.g.j.449.2 4 35.27 even 4
1400.2.g.j.449.3 4 35.13 even 4
2800.2.a.bj.1.2 2 140.139 even 2
2800.2.a.bo.1.1 2 28.27 even 2
2800.2.g.v.449.2 4 140.83 odd 4
2800.2.g.v.449.3 4 140.27 odd 4
9800.2.a.bt.1.2 2 5.4 even 2
9800.2.a.bx.1.1 2 1.1 even 1 trivial