Properties

Label 4900.2.a.ba.1.1
Level $4900$
Weight $2$
Character 4900.1
Self dual yes
Analytic conductor $39.127$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4900 = 2^{2} \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4900.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(39.1266969904\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.257.1
Defining polynomial: \(x^{3} - x^{2} - 4 x + 3\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 700)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(0.713538\) of defining polynomial
Character \(\chi\) \(=\) 4900.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.20440 q^{3} +7.26819 q^{9} +O(q^{10})\) \(q-3.20440 q^{3} +7.26819 q^{9} +4.20440 q^{11} +0.204402 q^{13} -5.06379 q^{17} +1.06379 q^{19} +2.14061 q^{23} -13.6770 q^{27} -7.47259 q^{29} -8.47259 q^{31} -13.4726 q^{33} -10.6132 q^{37} -0.654985 q^{39} +10.5494 q^{41} +8.26819 q^{43} +3.26819 q^{47} +16.2264 q^{51} +5.67699 q^{53} -3.40880 q^{57} +1.20440 q^{59} +1.65498 q^{61} -12.4088 q^{67} -6.85939 q^{69} -0.591197 q^{71} -4.00000 q^{73} +6.54942 q^{79} +22.0220 q^{81} +3.88139 q^{83} +23.9452 q^{87} -9.26819 q^{89} +27.1496 q^{93} +1.33198 q^{97} +30.5584 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - q^{3} + 8 q^{9} + O(q^{10}) \) \( 3 q - q^{3} + 8 q^{9} + 4 q^{11} - 8 q^{13} - 10 q^{17} - 2 q^{19} + 3 q^{23} - 10 q^{27} - 3 q^{31} - 18 q^{33} - 6 q^{37} - 14 q^{39} + 11 q^{41} + 11 q^{43} - 4 q^{47} - 3 q^{51} - 14 q^{53} + 7 q^{57} - 5 q^{59} + 17 q^{61} - 20 q^{67} - 24 q^{69} - 19 q^{71} - 12 q^{73} - q^{79} + 23 q^{81} - 28 q^{83} + 27 q^{87} - 14 q^{89} + 28 q^{93} - 15 q^{97} + 21 q^{99} + O(q^{100}) \)

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
\(3\) −3.20440 −1.85006 −0.925031 0.379892i \(-0.875961\pi\)
−0.925031 + 0.379892i \(0.875961\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 7.26819 2.42273
\(10\) 0 0
\(11\) 4.20440 1.26767 0.633837 0.773466i \(-0.281479\pi\)
0.633837 + 0.773466i \(0.281479\pi\)
\(12\) 0 0
\(13\) 0.204402 0.0566908 0.0283454 0.999598i \(-0.490976\pi\)
0.0283454 + 0.999598i \(0.490976\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −5.06379 −1.22815 −0.614074 0.789248i \(-0.710471\pi\)
−0.614074 + 0.789248i \(0.710471\pi\)
\(18\) 0 0
\(19\) 1.06379 0.244050 0.122025 0.992527i \(-0.461061\pi\)
0.122025 + 0.992527i \(0.461061\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.14061 0.446349 0.223174 0.974779i \(-0.428358\pi\)
0.223174 + 0.974779i \(0.428358\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −13.6770 −2.63214
\(28\) 0 0
\(29\) −7.47259 −1.38763 −0.693813 0.720156i \(-0.744070\pi\)
−0.693813 + 0.720156i \(0.744070\pi\)
\(30\) 0 0
\(31\) −8.47259 −1.52172 −0.760861 0.648915i \(-0.775223\pi\)
−0.760861 + 0.648915i \(0.775223\pi\)
\(32\) 0 0
\(33\) −13.4726 −2.34528
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −10.6132 −1.74480 −0.872400 0.488793i \(-0.837437\pi\)
−0.872400 + 0.488793i \(0.837437\pi\)
\(38\) 0 0
\(39\) −0.654985 −0.104881
\(40\) 0 0
\(41\) 10.5494 1.64754 0.823771 0.566923i \(-0.191866\pi\)
0.823771 + 0.566923i \(0.191866\pi\)
\(42\) 0 0
\(43\) 8.26819 1.26089 0.630444 0.776235i \(-0.282873\pi\)
0.630444 + 0.776235i \(0.282873\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 3.26819 0.476714 0.238357 0.971178i \(-0.423391\pi\)
0.238357 + 0.971178i \(0.423391\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 16.2264 2.27215
\(52\) 0 0
\(53\) 5.67699 0.779795 0.389897 0.920858i \(-0.372510\pi\)
0.389897 + 0.920858i \(0.372510\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −3.40880 −0.451507
\(58\) 0 0
\(59\) 1.20440 0.156800 0.0783999 0.996922i \(-0.475019\pi\)
0.0783999 + 0.996922i \(0.475019\pi\)
\(60\) 0 0
\(61\) 1.65498 0.211899 0.105950 0.994372i \(-0.466212\pi\)
0.105950 + 0.994372i \(0.466212\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −12.4088 −1.51598 −0.757988 0.652268i \(-0.773818\pi\)
−0.757988 + 0.652268i \(0.773818\pi\)
\(68\) 0 0
\(69\) −6.85939 −0.825773
\(70\) 0 0
\(71\) −0.591197 −0.0701622 −0.0350811 0.999384i \(-0.511169\pi\)
−0.0350811 + 0.999384i \(0.511169\pi\)
\(72\) 0 0
\(73\) −4.00000 −0.468165 −0.234082 0.972217i \(-0.575209\pi\)
−0.234082 + 0.972217i \(0.575209\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 6.54942 0.736867 0.368433 0.929654i \(-0.379894\pi\)
0.368433 + 0.929654i \(0.379894\pi\)
\(80\) 0 0
\(81\) 22.0220 2.44689
\(82\) 0 0
\(83\) 3.88139 0.426038 0.213019 0.977048i \(-0.431670\pi\)
0.213019 + 0.977048i \(0.431670\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 23.9452 2.56719
\(88\) 0 0
\(89\) −9.26819 −0.982426 −0.491213 0.871039i \(-0.663446\pi\)
−0.491213 + 0.871039i \(0.663446\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 27.1496 2.81528
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 1.33198 0.135242 0.0676209 0.997711i \(-0.478459\pi\)
0.0676209 + 0.997711i \(0.478459\pi\)
\(98\) 0 0
\(99\) 30.5584 3.07123
\(100\) 0 0
\(101\) 6.19136 0.616064 0.308032 0.951376i \(-0.400330\pi\)
0.308032 + 0.951376i \(0.400330\pi\)
\(102\) 0 0
\(103\) 9.74078 0.959788 0.479894 0.877327i \(-0.340675\pi\)
0.479894 + 0.877327i \(0.340675\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 9.85939 0.953143 0.476571 0.879136i \(-0.341879\pi\)
0.476571 + 0.879136i \(0.341879\pi\)
\(108\) 0 0
\(109\) −4.07683 −0.390489 −0.195245 0.980755i \(-0.562550\pi\)
−0.195245 + 0.980755i \(0.562550\pi\)
\(110\) 0 0
\(111\) 34.0090 3.22799
\(112\) 0 0
\(113\) 2.21744 0.208599 0.104300 0.994546i \(-0.466740\pi\)
0.104300 + 0.994546i \(0.466740\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 1.48563 0.137346
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 6.67699 0.606999
\(122\) 0 0
\(123\) −33.8046 −3.04806
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 6.54942 0.581167 0.290583 0.956850i \(-0.406151\pi\)
0.290583 + 0.956850i \(0.406151\pi\)
\(128\) 0 0
\(129\) −26.4946 −2.33272
\(130\) 0 0
\(131\) −17.0090 −1.48608 −0.743040 0.669247i \(-0.766617\pi\)
−0.743040 + 0.669247i \(0.766617\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −17.0858 −1.45974 −0.729869 0.683587i \(-0.760419\pi\)
−0.729869 + 0.683587i \(0.760419\pi\)
\(138\) 0 0
\(139\) 0.740780 0.0628322 0.0314161 0.999506i \(-0.489998\pi\)
0.0314161 + 0.999506i \(0.489998\pi\)
\(140\) 0 0
\(141\) −10.4726 −0.881951
\(142\) 0 0
\(143\) 0.859386 0.0718655
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −16.4178 −1.34500 −0.672498 0.740099i \(-0.734779\pi\)
−0.672498 + 0.740099i \(0.734779\pi\)
\(150\) 0 0
\(151\) 0.527409 0.0429199 0.0214600 0.999770i \(-0.493169\pi\)
0.0214600 + 0.999770i \(0.493169\pi\)
\(152\) 0 0
\(153\) −36.8046 −2.97547
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −9.48563 −0.757036 −0.378518 0.925594i \(-0.623566\pi\)
−0.378518 + 0.925594i \(0.623566\pi\)
\(158\) 0 0
\(159\) −18.1914 −1.44267
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 8.85939 0.693921 0.346960 0.937880i \(-0.387214\pi\)
0.346960 + 0.937880i \(0.387214\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 8.33198 0.644748 0.322374 0.946612i \(-0.395519\pi\)
0.322374 + 0.946612i \(0.395519\pi\)
\(168\) 0 0
\(169\) −12.9582 −0.996786
\(170\) 0 0
\(171\) 7.73181 0.591266
\(172\) 0 0
\(173\) −18.3450 −1.39475 −0.697373 0.716709i \(-0.745648\pi\)
−0.697373 + 0.716709i \(0.745648\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −3.85939 −0.290089
\(178\) 0 0
\(179\) −4.28123 −0.319994 −0.159997 0.987118i \(-0.551148\pi\)
−0.159997 + 0.987118i \(0.551148\pi\)
\(180\) 0 0
\(181\) 2.93621 0.218247 0.109123 0.994028i \(-0.465196\pi\)
0.109123 + 0.994028i \(0.465196\pi\)
\(182\) 0 0
\(183\) −5.30324 −0.392026
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −21.2902 −1.55689
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −11.9452 −0.864323 −0.432162 0.901796i \(-0.642249\pi\)
−0.432162 + 0.901796i \(0.642249\pi\)
\(192\) 0 0
\(193\) 7.08580 0.510047 0.255023 0.966935i \(-0.417917\pi\)
0.255023 + 0.966935i \(0.417917\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −5.48563 −0.390835 −0.195417 0.980720i \(-0.562606\pi\)
−0.195417 + 0.980720i \(0.562606\pi\)
\(198\) 0 0
\(199\) 16.0858 1.14029 0.570146 0.821543i \(-0.306887\pi\)
0.570146 + 0.821543i \(0.306887\pi\)
\(200\) 0 0
\(201\) 39.7628 2.80465
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 15.5584 1.08138
\(208\) 0 0
\(209\) 4.47259 0.309376
\(210\) 0 0
\(211\) 16.6002 1.14280 0.571401 0.820671i \(-0.306400\pi\)
0.571401 + 0.820671i \(0.306400\pi\)
\(212\) 0 0
\(213\) 1.89443 0.129804
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 12.8176 0.866134
\(220\) 0 0
\(221\) −1.03505 −0.0696247
\(222\) 0 0
\(223\) −15.4856 −1.03699 −0.518497 0.855079i \(-0.673508\pi\)
−0.518497 + 0.855079i \(0.673508\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −3.78256 −0.251057 −0.125529 0.992090i \(-0.540063\pi\)
−0.125529 + 0.992090i \(0.540063\pi\)
\(228\) 0 0
\(229\) −11.2044 −0.740408 −0.370204 0.928951i \(-0.620712\pi\)
−0.370204 + 0.928951i \(0.620712\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −11.9452 −0.782555 −0.391277 0.920273i \(-0.627967\pi\)
−0.391277 + 0.920273i \(0.627967\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −20.9870 −1.36325
\(238\) 0 0
\(239\) 15.3450 0.992587 0.496293 0.868155i \(-0.334694\pi\)
0.496293 + 0.868155i \(0.334694\pi\)
\(240\) 0 0
\(241\) −14.3958 −0.927313 −0.463656 0.886015i \(-0.653463\pi\)
−0.463656 + 0.886015i \(0.653463\pi\)
\(242\) 0 0
\(243\) −29.5364 −1.89476
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0.217440 0.0138354
\(248\) 0 0
\(249\) −12.4375 −0.788197
\(250\) 0 0
\(251\) −19.4178 −1.22564 −0.612819 0.790223i \(-0.709965\pi\)
−0.612819 + 0.790223i \(0.709965\pi\)
\(252\) 0 0
\(253\) 9.00000 0.565825
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −13.8724 −0.865338 −0.432669 0.901553i \(-0.642428\pi\)
−0.432669 + 0.901553i \(0.642428\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −54.3122 −3.36184
\(262\) 0 0
\(263\) 3.45955 0.213325 0.106663 0.994295i \(-0.465984\pi\)
0.106663 + 0.994295i \(0.465984\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 29.6990 1.81755
\(268\) 0 0
\(269\) 25.6640 1.56476 0.782379 0.622802i \(-0.214006\pi\)
0.782379 + 0.622802i \(0.214006\pi\)
\(270\) 0 0
\(271\) 19.6770 1.19529 0.597646 0.801760i \(-0.296103\pi\)
0.597646 + 0.801760i \(0.296103\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 18.1496 1.09050 0.545251 0.838273i \(-0.316434\pi\)
0.545251 + 0.838273i \(0.316434\pi\)
\(278\) 0 0
\(279\) −61.5804 −3.68672
\(280\) 0 0
\(281\) −18.5364 −1.10579 −0.552894 0.833252i \(-0.686476\pi\)
−0.552894 + 0.833252i \(0.686476\pi\)
\(282\) 0 0
\(283\) −28.5584 −1.69762 −0.848810 0.528698i \(-0.822680\pi\)
−0.848810 + 0.528698i \(0.822680\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 8.64195 0.508350
\(290\) 0 0
\(291\) −4.26819 −0.250206
\(292\) 0 0
\(293\) −25.5494 −1.49261 −0.746306 0.665603i \(-0.768175\pi\)
−0.746306 + 0.665603i \(0.768175\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −57.5036 −3.33670
\(298\) 0 0
\(299\) 0.437545 0.0253039
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −19.8396 −1.13976
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −10.1145 −0.577267 −0.288634 0.957440i \(-0.593201\pi\)
−0.288634 + 0.957440i \(0.593201\pi\)
\(308\) 0 0
\(309\) −31.2134 −1.77567
\(310\) 0 0
\(311\) 34.1716 1.93769 0.968847 0.247662i \(-0.0796621\pi\)
0.968847 + 0.247662i \(0.0796621\pi\)
\(312\) 0 0
\(313\) 8.61320 0.486847 0.243424 0.969920i \(-0.421730\pi\)
0.243424 + 0.969920i \(0.421730\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 7.81761 0.439081 0.219540 0.975603i \(-0.429544\pi\)
0.219540 + 0.975603i \(0.429544\pi\)
\(318\) 0 0
\(319\) −31.4178 −1.75906
\(320\) 0 0
\(321\) −31.5934 −1.76337
\(322\) 0 0
\(323\) −5.38680 −0.299729
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 13.0638 0.722429
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −22.0988 −1.21466 −0.607331 0.794449i \(-0.707760\pi\)
−0.607331 + 0.794449i \(0.707760\pi\)
\(332\) 0 0
\(333\) −77.1388 −4.22718
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −1.29020 −0.0702815 −0.0351408 0.999382i \(-0.511188\pi\)
−0.0351408 + 0.999382i \(0.511188\pi\)
\(338\) 0 0
\(339\) −7.10557 −0.385921
\(340\) 0 0
\(341\) −35.6222 −1.92905
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −9.45955 −0.507815 −0.253908 0.967228i \(-0.581716\pi\)
−0.253908 + 0.967228i \(0.581716\pi\)
\(348\) 0 0
\(349\) 15.5494 0.832341 0.416171 0.909287i \(-0.363372\pi\)
0.416171 + 0.909287i \(0.363372\pi\)
\(350\) 0 0
\(351\) −2.79560 −0.149218
\(352\) 0 0
\(353\) 15.1365 0.805637 0.402818 0.915280i \(-0.368031\pi\)
0.402818 + 0.915280i \(0.368031\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 10.3189 0.544613 0.272306 0.962211i \(-0.412214\pi\)
0.272306 + 0.962211i \(0.412214\pi\)
\(360\) 0 0
\(361\) −17.8684 −0.940440
\(362\) 0 0
\(363\) −21.3958 −1.12299
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 17.9362 0.936263 0.468131 0.883659i \(-0.344927\pi\)
0.468131 + 0.883659i \(0.344927\pi\)
\(368\) 0 0
\(369\) 76.6752 3.99155
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −16.1914 −0.838357 −0.419179 0.907904i \(-0.637682\pi\)
−0.419179 + 0.907904i \(0.637682\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −1.52741 −0.0786656
\(378\) 0 0
\(379\) −12.6002 −0.647227 −0.323614 0.946189i \(-0.604898\pi\)
−0.323614 + 0.946189i \(0.604898\pi\)
\(380\) 0 0
\(381\) −20.9870 −1.07519
\(382\) 0 0
\(383\) 15.1757 0.775440 0.387720 0.921777i \(-0.373263\pi\)
0.387720 + 0.921777i \(0.373263\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 60.0948 3.05479
\(388\) 0 0
\(389\) −29.2394 −1.48250 −0.741249 0.671230i \(-0.765766\pi\)
−0.741249 + 0.671230i \(0.765766\pi\)
\(390\) 0 0
\(391\) −10.8396 −0.548183
\(392\) 0 0
\(393\) 54.5036 2.74934
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 11.2682 0.565534 0.282767 0.959189i \(-0.408748\pi\)
0.282767 + 0.959189i \(0.408748\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −18.0220 −0.899976 −0.449988 0.893035i \(-0.648572\pi\)
−0.449988 + 0.893035i \(0.648572\pi\)
\(402\) 0 0
\(403\) −1.73181 −0.0862676
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −44.6222 −2.21184
\(408\) 0 0
\(409\) −15.7915 −0.780841 −0.390420 0.920637i \(-0.627670\pi\)
−0.390420 + 0.920637i \(0.627670\pi\)
\(410\) 0 0
\(411\) 54.7497 2.70061
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −2.37376 −0.116243
\(418\) 0 0
\(419\) −13.4726 −0.658179 −0.329090 0.944299i \(-0.606742\pi\)
−0.329090 + 0.944299i \(0.606742\pi\)
\(420\) 0 0
\(421\) −26.8396 −1.30808 −0.654041 0.756459i \(-0.726928\pi\)
−0.654041 + 0.756459i \(0.726928\pi\)
\(422\) 0 0
\(423\) 23.7538 1.15495
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −2.75382 −0.132956
\(430\) 0 0
\(431\) 16.0507 0.773137 0.386569 0.922261i \(-0.373660\pi\)
0.386569 + 0.922261i \(0.373660\pi\)
\(432\) 0 0
\(433\) 0.910136 0.0437383 0.0218692 0.999761i \(-0.493038\pi\)
0.0218692 + 0.999761i \(0.493038\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.27716 0.108931
\(438\) 0 0
\(439\) −37.9034 −1.80903 −0.904515 0.426441i \(-0.859767\pi\)
−0.904515 + 0.426441i \(0.859767\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −6.88139 −0.326945 −0.163472 0.986548i \(-0.552269\pi\)
−0.163472 + 0.986548i \(0.552269\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 52.6091 2.48833
\(448\) 0 0
\(449\) 6.43754 0.303807 0.151903 0.988395i \(-0.451460\pi\)
0.151903 + 0.988395i \(0.451460\pi\)
\(450\) 0 0
\(451\) 44.3540 2.08855
\(452\) 0 0
\(453\) −1.69003 −0.0794046
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −9.29427 −0.434767 −0.217384 0.976086i \(-0.569752\pi\)
−0.217384 + 0.976086i \(0.569752\pi\)
\(458\) 0 0
\(459\) 69.2574 3.23266
\(460\) 0 0
\(461\) 9.29020 0.432688 0.216344 0.976317i \(-0.430587\pi\)
0.216344 + 0.976317i \(0.430587\pi\)
\(462\) 0 0
\(463\) −29.6091 −1.37605 −0.688027 0.725685i \(-0.741523\pi\)
−0.688027 + 0.725685i \(0.741523\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −26.0638 −1.20609 −0.603044 0.797708i \(-0.706046\pi\)
−0.603044 + 0.797708i \(0.706046\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 30.3958 1.40056
\(472\) 0 0
\(473\) 34.7628 1.59839
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 41.2615 1.88923
\(478\) 0 0
\(479\) −1.10557 −0.0505147 −0.0252573 0.999681i \(-0.508041\pi\)
−0.0252573 + 0.999681i \(0.508041\pi\)
\(480\) 0 0
\(481\) −2.16936 −0.0989141
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 5.19136 0.235243 0.117622 0.993058i \(-0.462473\pi\)
0.117622 + 0.993058i \(0.462473\pi\)
\(488\) 0 0
\(489\) −28.3890 −1.28380
\(490\) 0 0
\(491\) −28.6640 −1.29359 −0.646793 0.762666i \(-0.723890\pi\)
−0.646793 + 0.762666i \(0.723890\pi\)
\(492\) 0 0
\(493\) 37.8396 1.70421
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −26.0728 −1.16718 −0.583588 0.812050i \(-0.698352\pi\)
−0.583588 + 0.812050i \(0.698352\pi\)
\(500\) 0 0
\(501\) −26.6990 −1.19282
\(502\) 0 0
\(503\) 8.80864 0.392758 0.196379 0.980528i \(-0.437082\pi\)
0.196379 + 0.980528i \(0.437082\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 41.5233 1.84412
\(508\) 0 0
\(509\) −22.0179 −0.975928 −0.487964 0.872864i \(-0.662260\pi\)
−0.487964 + 0.872864i \(0.662260\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −14.5494 −0.642372
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 13.7408 0.604319
\(518\) 0 0
\(519\) 58.7848 2.58037
\(520\) 0 0
\(521\) −15.0988 −0.661492 −0.330746 0.943720i \(-0.607300\pi\)
−0.330746 + 0.943720i \(0.607300\pi\)
\(522\) 0 0
\(523\) −4.59120 −0.200759 −0.100380 0.994949i \(-0.532006\pi\)
−0.100380 + 0.994949i \(0.532006\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 42.9034 1.86890
\(528\) 0 0
\(529\) −18.4178 −0.800773
\(530\) 0 0
\(531\) 8.75382 0.379883
\(532\) 0 0
\(533\) 2.15632 0.0934005
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 13.7188 0.592009
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 13.6770 0.588020 0.294010 0.955802i \(-0.405010\pi\)
0.294010 + 0.955802i \(0.405010\pi\)
\(542\) 0 0
\(543\) −9.40880 −0.403770
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −11.3581 −0.485635 −0.242818 0.970072i \(-0.578072\pi\)
−0.242818 + 0.970072i \(0.578072\pi\)
\(548\) 0 0
\(549\) 12.0287 0.513374
\(550\) 0 0
\(551\) −7.94925 −0.338649
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 16.3958 0.694711 0.347355 0.937734i \(-0.387080\pi\)
0.347355 + 0.937734i \(0.387080\pi\)
\(558\) 0 0
\(559\) 1.69003 0.0714807
\(560\) 0 0
\(561\) 68.2223 2.88035
\(562\) 0 0
\(563\) −4.87242 −0.205348 −0.102674 0.994715i \(-0.532740\pi\)
−0.102674 + 0.994715i \(0.532740\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −37.8553 −1.58698 −0.793489 0.608585i \(-0.791737\pi\)
−0.793489 + 0.608585i \(0.791737\pi\)
\(570\) 0 0
\(571\) −41.7408 −1.74680 −0.873399 0.487006i \(-0.838089\pi\)
−0.873399 + 0.487006i \(0.838089\pi\)
\(572\) 0 0
\(573\) 38.2772 1.59905
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 43.0530 1.79232 0.896160 0.443732i \(-0.146346\pi\)
0.896160 + 0.443732i \(0.146346\pi\)
\(578\) 0 0
\(579\) −22.7057 −0.943618
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 23.8684 0.988526
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −5.67699 −0.234315 −0.117157 0.993113i \(-0.537378\pi\)
−0.117157 + 0.993113i \(0.537378\pi\)
\(588\) 0 0
\(589\) −9.01304 −0.371376
\(590\) 0 0
\(591\) 17.5782 0.723069
\(592\) 0 0
\(593\) 8.94518 0.367335 0.183667 0.982988i \(-0.441203\pi\)
0.183667 + 0.982988i \(0.441203\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −51.5453 −2.10961
\(598\) 0 0
\(599\) −25.2264 −1.03072 −0.515362 0.856973i \(-0.672342\pi\)
−0.515362 + 0.856973i \(0.672342\pi\)
\(600\) 0 0
\(601\) 15.3409 0.625770 0.312885 0.949791i \(-0.398705\pi\)
0.312885 + 0.949791i \(0.398705\pi\)
\(602\) 0 0
\(603\) −90.1895 −3.67280
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 20.9362 0.849775 0.424887 0.905246i \(-0.360314\pi\)
0.424887 + 0.905246i \(0.360314\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0.668023 0.0270253
\(612\) 0 0
\(613\) −5.31894 −0.214830 −0.107415 0.994214i \(-0.534257\pi\)
−0.107415 + 0.994214i \(0.534257\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −28.6262 −1.15245 −0.576225 0.817291i \(-0.695475\pi\)
−0.576225 + 0.817291i \(0.695475\pi\)
\(618\) 0 0
\(619\) −21.5625 −0.866668 −0.433334 0.901233i \(-0.642663\pi\)
−0.433334 + 0.901233i \(0.642663\pi\)
\(620\) 0 0
\(621\) −29.2772 −1.17485
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −14.3320 −0.572364
\(628\) 0 0
\(629\) 53.7430 2.14287
\(630\) 0 0
\(631\) −25.1365 −1.00067 −0.500335 0.865832i \(-0.666790\pi\)
−0.500335 + 0.865832i \(0.666790\pi\)
\(632\) 0 0
\(633\) −53.1936 −2.11426
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −4.29693 −0.169984
\(640\) 0 0
\(641\) 44.1078 1.74215 0.871077 0.491147i \(-0.163422\pi\)
0.871077 + 0.491147i \(0.163422\pi\)
\(642\) 0 0
\(643\) −16.4816 −0.649969 −0.324985 0.945719i \(-0.605359\pi\)
−0.324985 + 0.945719i \(0.605359\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −31.4398 −1.23603 −0.618013 0.786168i \(-0.712062\pi\)
−0.618013 + 0.786168i \(0.712062\pi\)
\(648\) 0 0
\(649\) 5.06379 0.198771
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 40.8773 1.59965 0.799827 0.600231i \(-0.204925\pi\)
0.799827 + 0.600231i \(0.204925\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −29.0728 −1.13424
\(658\) 0 0
\(659\) −46.6860 −1.81863 −0.909313 0.416112i \(-0.863392\pi\)
−0.909313 + 0.416112i \(0.863392\pi\)
\(660\) 0 0
\(661\) 0.127575 0.00496211 0.00248106 0.999997i \(-0.499210\pi\)
0.00248106 + 0.999997i \(0.499210\pi\)
\(662\) 0 0
\(663\) 3.31670 0.128810
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −15.9959 −0.619365
\(668\) 0 0
\(669\) 49.6222 1.91850
\(670\) 0 0
\(671\) 6.95822 0.268619
\(672\) 0 0
\(673\) 48.1936 1.85773 0.928863 0.370423i \(-0.120787\pi\)
0.928863 + 0.370423i \(0.120787\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −46.4178 −1.78398 −0.891990 0.452055i \(-0.850691\pi\)
−0.891990 + 0.452055i \(0.850691\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 12.1208 0.464472
\(682\) 0 0
\(683\) 43.5494 1.66637 0.833186 0.552993i \(-0.186514\pi\)
0.833186 + 0.552993i \(0.186514\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 35.9034 1.36980
\(688\) 0 0
\(689\) 1.16039 0.0442072
\(690\) 0 0
\(691\) −26.0948 −0.992692 −0.496346 0.868125i \(-0.665325\pi\)
−0.496346 + 0.868125i \(0.665325\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −53.4200 −2.02343
\(698\) 0 0
\(699\) 38.2772 1.44778
\(700\) 0 0
\(701\) 21.7277 0.820645 0.410323 0.911940i \(-0.365416\pi\)
0.410323 + 0.911940i \(0.365416\pi\)
\(702\) 0 0
\(703\) −11.2902 −0.425818
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 17.0768 0.641334 0.320667 0.947192i \(-0.396093\pi\)
0.320667 + 0.947192i \(0.396093\pi\)
\(710\) 0 0
\(711\) 47.6024 1.78523
\(712\) 0 0
\(713\) −18.1365 −0.679219
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −49.1716 −1.83635
\(718\) 0 0
\(719\) 27.2462 1.01611 0.508056 0.861324i \(-0.330364\pi\)
0.508056 + 0.861324i \(0.330364\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 46.1298 1.71559
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 19.9232 0.738910 0.369455 0.929249i \(-0.379544\pi\)
0.369455 + 0.929249i \(0.379544\pi\)
\(728\) 0 0
\(729\) 28.5804 1.05853
\(730\) 0 0
\(731\) −41.8684 −1.54856
\(732\) 0 0
\(733\) 31.1626 1.15102 0.575509 0.817796i \(-0.304804\pi\)
0.575509 + 0.817796i \(0.304804\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −52.1716 −1.92177
\(738\) 0 0
\(739\) 1.90117 0.0699355 0.0349678 0.999388i \(-0.488867\pi\)
0.0349678 + 0.999388i \(0.488867\pi\)
\(740\) 0 0
\(741\) −0.696765 −0.0255963
\(742\) 0 0
\(743\) 36.0660 1.32313 0.661567 0.749886i \(-0.269892\pi\)
0.661567 + 0.749886i \(0.269892\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 28.2107 1.03218
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −0.769522 −0.0280803 −0.0140401 0.999901i \(-0.504469\pi\)
−0.0140401 + 0.999901i \(0.504469\pi\)
\(752\) 0 0
\(753\) 62.2223 2.26751
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −14.9542 −0.543518 −0.271759 0.962365i \(-0.587605\pi\)
−0.271759 + 0.962365i \(0.587605\pi\)
\(758\) 0 0
\(759\) −28.8396 −1.04681
\(760\) 0 0
\(761\) 19.1716 0.694970 0.347485 0.937686i \(-0.387036\pi\)
0.347485 + 0.937686i \(0.387036\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0.246182 0.00888910
\(768\) 0 0
\(769\) 36.3189 1.30969 0.654847 0.755761i \(-0.272733\pi\)
0.654847 + 0.755761i \(0.272733\pi\)
\(770\) 0 0
\(771\) 44.4528 1.60093
\(772\) 0 0
\(773\) −47.4685 −1.70732 −0.853662 0.520827i \(-0.825624\pi\)
−0.853662 + 0.520827i \(0.825624\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 11.2223 0.402082
\(780\) 0 0
\(781\) −2.48563 −0.0889428
\(782\) 0 0
\(783\) 102.203 3.65242
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 7.88546 0.281086 0.140543 0.990075i \(-0.455115\pi\)
0.140543 + 0.990075i \(0.455115\pi\)
\(788\) 0 0
\(789\) −11.0858 −0.394665
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0.338281 0.0120127
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −33.6132 −1.19064 −0.595320 0.803488i \(-0.702975\pi\)
−0.595320 + 0.803488i \(0.702975\pi\)
\(798\) 0 0
\(799\) −16.5494 −0.585476
\(800\) 0 0
\(801\) −67.3630 −2.38015
\(802\) 0 0
\(803\) −16.8176 −0.593480
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −82.2376 −2.89490
\(808\) 0 0
\(809\) −9.19136 −0.323151 −0.161576 0.986860i \(-0.551658\pi\)
−0.161576 + 0.986860i \(0.551658\pi\)
\(810\) 0 0
\(811\) 21.6483 0.760173 0.380086 0.924951i \(-0.375894\pi\)
0.380086 + 0.924951i \(0.375894\pi\)
\(812\) 0 0
\(813\) −63.0530 −2.21136
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 8.79560 0.307719
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 32.2615 1.12593 0.562966 0.826480i \(-0.309660\pi\)
0.562966 + 0.826480i \(0.309660\pi\)
\(822\) 0 0
\(823\) 11.4438 0.398908 0.199454 0.979907i \(-0.436083\pi\)
0.199454 + 0.979907i \(0.436083\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 9.82658 0.341704 0.170852 0.985297i \(-0.445348\pi\)
0.170852 + 0.985297i \(0.445348\pi\)
\(828\) 0 0
\(829\) 38.2574 1.32873 0.664367 0.747407i \(-0.268701\pi\)
0.664367 + 0.747407i \(0.268701\pi\)
\(830\) 0 0
\(831\) −58.1586 −2.01750
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 115.880 4.00538
\(838\) 0 0
\(839\) 30.6900 1.05954 0.529769 0.848142i \(-0.322279\pi\)
0.529769 + 0.848142i \(0.322279\pi\)
\(840\) 0 0
\(841\) 26.8396 0.925504
\(842\) 0 0
\(843\) 59.3980 2.04578
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 91.5125 3.14070
\(850\) 0 0
\(851\) −22.7188 −0.778789
\(852\) 0 0
\(853\) 39.4569 1.35098 0.675489 0.737370i \(-0.263933\pi\)
0.675489 + 0.737370i \(0.263933\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −39.8594 −1.36157 −0.680785 0.732483i \(-0.738361\pi\)
−0.680785 + 0.732483i \(0.738361\pi\)
\(858\) 0 0
\(859\) −19.5144 −0.665822 −0.332911 0.942958i \(-0.608031\pi\)
−0.332911 + 0.942958i \(0.608031\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −37.9321 −1.29123 −0.645613 0.763665i \(-0.723398\pi\)
−0.645613 + 0.763665i \(0.723398\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −27.6923 −0.940479
\(868\) 0 0
\(869\) 27.5364 0.934108
\(870\) 0 0
\(871\) −2.53638 −0.0859419
\(872\) 0 0
\(873\) 9.68106 0.327654
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 10.9452 0.369593 0.184796 0.982777i \(-0.440837\pi\)
0.184796 + 0.982777i \(0.440837\pi\)
\(878\) 0 0
\(879\) 81.8706 2.76143
\(880\) 0 0
\(881\) −16.2592 −0.547787 −0.273894 0.961760i \(-0.588312\pi\)
−0.273894 + 0.961760i \(0.588312\pi\)
\(882\) 0 0
\(883\) 23.2511 0.782461 0.391231 0.920293i \(-0.372049\pi\)
0.391231 + 0.920293i \(0.372049\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −23.2394 −0.780304 −0.390152 0.920750i \(-0.627578\pi\)
−0.390152 + 0.920750i \(0.627578\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 92.5894 3.10186
\(892\) 0 0
\(893\) 3.47666 0.116342
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −1.40207 −0.0468137
\(898\) 0 0
\(899\) 63.3122 2.11158
\(900\) 0 0
\(901\) −28.7471 −0.957704
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −44.2264 −1.46851 −0.734257 0.678872i \(-0.762469\pi\)
−0.734257 + 0.678872i \(0.762469\pi\)
\(908\) 0 0
\(909\) 45.0000 1.49256
\(910\) 0 0
\(911\) −27.4218 −0.908526 −0.454263 0.890868i \(-0.650097\pi\)
−0.454263 + 0.890868i \(0.650097\pi\)
\(912\) 0 0
\(913\) 16.3189 0.540078
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −33.3163 −1.09900 −0.549501 0.835493i \(-0.685182\pi\)
−0.549501 + 0.835493i \(0.685182\pi\)
\(920\) 0 0
\(921\) 32.4110 1.06798
\(922\) 0 0
\(923\) −0.120842 −0.00397755
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 70.7978 2.32531
\(928\) 0 0
\(929\) −13.2484 −0.434666 −0.217333 0.976097i \(-0.569736\pi\)
−0.217333 + 0.976097i \(0.569736\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −109.499 −3.58485
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −10.1365 −0.331146 −0.165573 0.986197i \(-0.552947\pi\)
−0.165573 + 0.986197i \(0.552947\pi\)
\(938\) 0 0
\(939\) −27.6002 −0.900697
\(940\) 0 0
\(941\) −32.8684 −1.07148 −0.535739 0.844384i \(-0.679967\pi\)
−0.535739 + 0.844384i \(0.679967\pi\)
\(942\) 0 0
\(943\) 22.5822 0.735379
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −22.3252 −0.725473 −0.362736 0.931892i \(-0.618157\pi\)
−0.362736 + 0.931892i \(0.618157\pi\)
\(948\) 0 0
\(949\) −0.817606 −0.0265406
\(950\) 0 0
\(951\) −25.0507 −0.812326
\(952\) 0 0
\(953\) −47.4685 −1.53766 −0.768828 0.639455i \(-0.779160\pi\)
−0.768828 + 0.639455i \(0.779160\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 100.675 3.25437
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 40.7848 1.31564
\(962\) 0 0
\(963\) 71.6599 2.30921
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 21.3189 0.685571 0.342785 0.939414i \(-0.388630\pi\)
0.342785 + 0.939414i \(0.388630\pi\)
\(968\) 0 0
\(969\) 17.2615 0.554518
\(970\) 0 0
\(971\) −29.5625 −0.948704 −0.474352 0.880335i \(-0.657318\pi\)
−0.474352 + 0.880335i \(0.657318\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −1.83961 −0.0588545 −0.0294272 0.999567i \(-0.509368\pi\)
−0.0294272 + 0.999567i \(0.509368\pi\)
\(978\) 0 0
\(979\) −38.9672 −1.24540
\(980\) 0 0
\(981\) −29.6311 −0.946050
\(982\) 0 0
\(983\) −11.3760 −0.362838 −0.181419 0.983406i \(-0.558069\pi\)
−0.181419 + 0.983406i \(0.558069\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 17.6990 0.562795
\(990\) 0 0
\(991\) 7.79153 0.247506 0.123753 0.992313i \(-0.460507\pi\)
0.123753 + 0.992313i \(0.460507\pi\)
\(992\) 0 0
\(993\) 70.8135 2.24720
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 11.4218 0.361733 0.180867 0.983508i \(-0.442110\pi\)
0.180867 + 0.983508i \(0.442110\pi\)
\(998\) 0 0
\(999\) 145.157 4.59256
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 4900.2.a.ba.1.1 3
5.2 odd 4 4900.2.e.t.2549.6 6
5.3 odd 4 4900.2.e.t.2549.1 6
5.4 even 2 4900.2.a.bc.1.3 3
7.2 even 3 700.2.i.e.501.3 yes 6
7.4 even 3 700.2.i.e.401.3 yes 6
7.6 odd 2 4900.2.a.bd.1.3 3
35.2 odd 12 700.2.r.d.249.1 12
35.4 even 6 700.2.i.d.401.1 6
35.9 even 6 700.2.i.d.501.1 yes 6
35.13 even 4 4900.2.e.s.2549.6 6
35.18 odd 12 700.2.r.d.149.1 12
35.23 odd 12 700.2.r.d.249.6 12
35.27 even 4 4900.2.e.s.2549.1 6
35.32 odd 12 700.2.r.d.149.6 12
35.34 odd 2 4900.2.a.bb.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
700.2.i.d.401.1 6 35.4 even 6
700.2.i.d.501.1 yes 6 35.9 even 6
700.2.i.e.401.3 yes 6 7.4 even 3
700.2.i.e.501.3 yes 6 7.2 even 3
700.2.r.d.149.1 12 35.18 odd 12
700.2.r.d.149.6 12 35.32 odd 12
700.2.r.d.249.1 12 35.2 odd 12
700.2.r.d.249.6 12 35.23 odd 12
4900.2.a.ba.1.1 3 1.1 even 1 trivial
4900.2.a.bb.1.1 3 35.34 odd 2
4900.2.a.bc.1.3 3 5.4 even 2
4900.2.a.bd.1.3 3 7.6 odd 2
4900.2.e.s.2549.1 6 35.27 even 4
4900.2.e.s.2549.6 6 35.13 even 4
4900.2.e.t.2549.1 6 5.3 odd 4
4900.2.e.t.2549.6 6 5.2 odd 4