Properties

Label 4900.2.a.ba.1.2
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 1.2
Root \(2.19869\) of defining polynomial
Character \(\chi\) \(=\) 4900.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.364448 q^{3} -2.86718 q^{9} +O(q^{10})\) \(q-0.364448 q^{3} -2.86718 q^{9} +1.36445 q^{11} -2.63555 q^{13} +2.23163 q^{17} -6.23163 q^{19} +6.59607 q^{23} +2.13828 q^{27} +5.50273 q^{29} +4.50273 q^{31} -0.497270 q^{33} -2.09334 q^{37} +0.960522 q^{39} +9.32497 q^{41} -1.86718 q^{43} -6.86718 q^{47} -0.813312 q^{51} -10.1383 q^{53} +2.27110 q^{57} -1.63555 q^{59} +0.0394782 q^{61} -6.72890 q^{67} -2.40393 q^{69} -6.27110 q^{71} -4.00000 q^{73} +5.32497 q^{79} +7.82224 q^{81} -14.7738 q^{83} -2.00546 q^{87} +0.867178 q^{89} -1.64101 q^{93} -16.0988 q^{97} -3.91211 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - q^{3} + 8 q^{9} + O(q^{10}) \) \( 3 q - q^{3} + 8 q^{9} + 4 q^{11} - 8 q^{13} - 10 q^{17} - 2 q^{19} + 3 q^{23} - 10 q^{27} - 3 q^{31} - 18 q^{33} - 6 q^{37} - 14 q^{39} + 11 q^{41} + 11 q^{43} - 4 q^{47} - 3 q^{51} - 14 q^{53} + 7 q^{57} - 5 q^{59} + 17 q^{61} - 20 q^{67} - 24 q^{69} - 19 q^{71} - 12 q^{73} - q^{79} + 23 q^{81} - 28 q^{83} + 27 q^{87} - 14 q^{89} + 28 q^{93} - 15 q^{97} + 21 q^{99} + O(q^{100}) \)

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
\(3\) −0.364448 −0.210414 −0.105207 0.994450i \(-0.533551\pi\)
−0.105207 + 0.994450i \(0.533551\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −2.86718 −0.955726
\(10\) 0 0
\(11\) 1.36445 0.411397 0.205698 0.978615i \(-0.434053\pi\)
0.205698 + 0.978615i \(0.434053\pi\)
\(12\) 0 0
\(13\) −2.63555 −0.730971 −0.365485 0.930817i \(-0.619097\pi\)
−0.365485 + 0.930817i \(0.619097\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.23163 0.541249 0.270624 0.962685i \(-0.412770\pi\)
0.270624 + 0.962685i \(0.412770\pi\)
\(18\) 0 0
\(19\) −6.23163 −1.42963 −0.714816 0.699312i \(-0.753490\pi\)
−0.714816 + 0.699312i \(0.753490\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 6.59607 1.37538 0.687688 0.726006i \(-0.258626\pi\)
0.687688 + 0.726006i \(0.258626\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 2.13828 0.411512
\(28\) 0 0
\(29\) 5.50273 1.02183 0.510916 0.859631i \(-0.329306\pi\)
0.510916 + 0.859631i \(0.329306\pi\)
\(30\) 0 0
\(31\) 4.50273 0.808714 0.404357 0.914601i \(-0.367495\pi\)
0.404357 + 0.914601i \(0.367495\pi\)
\(32\) 0 0
\(33\) −0.497270 −0.0865637
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −2.09334 −0.344144 −0.172072 0.985084i \(-0.555046\pi\)
−0.172072 + 0.985084i \(0.555046\pi\)
\(38\) 0 0
\(39\) 0.960522 0.153807
\(40\) 0 0
\(41\) 9.32497 1.45632 0.728158 0.685410i \(-0.240377\pi\)
0.728158 + 0.685410i \(0.240377\pi\)
\(42\) 0 0
\(43\) −1.86718 −0.284742 −0.142371 0.989813i \(-0.545473\pi\)
−0.142371 + 0.989813i \(0.545473\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −6.86718 −1.00168 −0.500840 0.865540i \(-0.666976\pi\)
−0.500840 + 0.865540i \(0.666976\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −0.813312 −0.113886
\(52\) 0 0
\(53\) −10.1383 −1.39260 −0.696300 0.717751i \(-0.745172\pi\)
−0.696300 + 0.717751i \(0.745172\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 2.27110 0.300815
\(58\) 0 0
\(59\) −1.63555 −0.212931 −0.106465 0.994316i \(-0.533953\pi\)
−0.106465 + 0.994316i \(0.533953\pi\)
\(60\) 0 0
\(61\) 0.0394782 0.00505467 0.00252733 0.999997i \(-0.499196\pi\)
0.00252733 + 0.999997i \(0.499196\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −6.72890 −0.822065 −0.411033 0.911621i \(-0.634832\pi\)
−0.411033 + 0.911621i \(0.634832\pi\)
\(68\) 0 0
\(69\) −2.40393 −0.289399
\(70\) 0 0
\(71\) −6.27110 −0.744243 −0.372122 0.928184i \(-0.621370\pi\)
−0.372122 + 0.928184i \(0.621370\pi\)
\(72\) 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
\(79\) 5.32497 0.599106 0.299553 0.954080i \(-0.403162\pi\)
0.299553 + 0.954080i \(0.403162\pi\)
\(80\) 0 0
\(81\) 7.82224 0.869138
\(82\) 0 0
\(83\) −14.7738 −1.62164 −0.810819 0.585296i \(-0.800978\pi\)
−0.810819 + 0.585296i \(0.800978\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −2.00546 −0.215008
\(88\) 0 0
\(89\) 0.867178 0.0919206 0.0459603 0.998943i \(-0.485365\pi\)
0.0459603 + 0.998943i \(0.485365\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −1.64101 −0.170165
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −16.0988 −1.63459 −0.817293 0.576222i \(-0.804526\pi\)
−0.817293 + 0.576222i \(0.804526\pi\)
\(98\) 0 0
\(99\) −3.91211 −0.393182
\(100\) 0 0
\(101\) −15.6949 −1.56170 −0.780849 0.624719i \(-0.785213\pi\)
−0.780849 + 0.624719i \(0.785213\pi\)
\(102\) 0 0
\(103\) −13.3699 −1.31738 −0.658688 0.752416i \(-0.728888\pi\)
−0.658688 + 0.752416i \(0.728888\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 5.40393 0.522417 0.261209 0.965282i \(-0.415879\pi\)
0.261209 + 0.965282i \(0.415879\pi\)
\(108\) 0 0
\(109\) −15.8277 −1.51602 −0.758009 0.652244i \(-0.773828\pi\)
−0.758009 + 0.652244i \(0.773828\pi\)
\(110\) 0 0
\(111\) 0.762915 0.0724127
\(112\) 0 0
\(113\) 18.4238 1.73316 0.866581 0.499036i \(-0.166312\pi\)
0.866581 + 0.499036i \(0.166312\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 7.55660 0.698608
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −9.13828 −0.830753
\(122\) 0 0
\(123\) −3.39847 −0.306429
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 5.32497 0.472515 0.236257 0.971691i \(-0.424079\pi\)
0.236257 + 0.971691i \(0.424079\pi\)
\(128\) 0 0
\(129\) 0.680489 0.0599137
\(130\) 0 0
\(131\) 16.2371 1.41864 0.709320 0.704886i \(-0.249002\pi\)
0.709320 + 0.704886i \(0.249002\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 4.40939 0.376719 0.188360 0.982100i \(-0.439683\pi\)
0.188360 + 0.982100i \(0.439683\pi\)
\(138\) 0 0
\(139\) −22.3699 −1.89739 −0.948695 0.316192i \(-0.897596\pi\)
−0.948695 + 0.316192i \(0.897596\pi\)
\(140\) 0 0
\(141\) 2.50273 0.210768
\(142\) 0 0
\(143\) −3.59607 −0.300719
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 22.5082 1.84394 0.921971 0.387258i \(-0.126578\pi\)
0.921971 + 0.387258i \(0.126578\pi\)
\(150\) 0 0
\(151\) 13.5027 1.09884 0.549418 0.835547i \(-0.314849\pi\)
0.549418 + 0.835547i \(0.314849\pi\)
\(152\) 0 0
\(153\) −6.39847 −0.517285
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −15.5566 −1.24155 −0.620776 0.783988i \(-0.713182\pi\)
−0.620776 + 0.783988i \(0.713182\pi\)
\(158\) 0 0
\(159\) 3.69488 0.293023
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 4.40393 0.344942 0.172471 0.985015i \(-0.444825\pi\)
0.172471 + 0.985015i \(0.444825\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −9.09880 −0.704087 −0.352043 0.935984i \(-0.614513\pi\)
−0.352043 + 0.935984i \(0.614513\pi\)
\(168\) 0 0
\(169\) −6.05387 −0.465682
\(170\) 0 0
\(171\) 17.8672 1.36634
\(172\) 0 0
\(173\) −19.9605 −1.51757 −0.758785 0.651341i \(-0.774207\pi\)
−0.758785 + 0.651341i \(0.774207\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0.596074 0.0448036
\(178\) 0 0
\(179\) −13.1921 −0.986027 −0.493014 0.870022i \(-0.664105\pi\)
−0.493014 + 0.870022i \(0.664105\pi\)
\(180\) 0 0
\(181\) 10.2316 0.760511 0.380255 0.924882i \(-0.375836\pi\)
0.380255 + 0.924882i \(0.375836\pi\)
\(182\) 0 0
\(183\) −0.0143878 −0.00106357
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 3.04494 0.222668
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 14.0055 1.01340 0.506700 0.862123i \(-0.330865\pi\)
0.506700 + 0.862123i \(0.330865\pi\)
\(192\) 0 0
\(193\) −14.4094 −1.03721 −0.518605 0.855014i \(-0.673549\pi\)
−0.518605 + 0.855014i \(0.673549\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −11.5566 −0.823373 −0.411687 0.911325i \(-0.635060\pi\)
−0.411687 + 0.911325i \(0.635060\pi\)
\(198\) 0 0
\(199\) −5.40939 −0.383461 −0.191731 0.981448i \(-0.561410\pi\)
−0.191731 + 0.981448i \(0.561410\pi\)
\(200\) 0 0
\(201\) 2.45233 0.172974
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −18.9121 −1.31448
\(208\) 0 0
\(209\) −8.50273 −0.588146
\(210\) 0 0
\(211\) −10.9660 −0.754929 −0.377465 0.926024i \(-0.623204\pi\)
−0.377465 + 0.926024i \(0.623204\pi\)
\(212\) 0 0
\(213\) 2.28549 0.156599
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 1.45779 0.0985085
\(220\) 0 0
\(221\) −5.88157 −0.395637
\(222\) 0 0
\(223\) −21.5566 −1.44354 −0.721768 0.692135i \(-0.756670\pi\)
−0.721768 + 0.692135i \(0.756670\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 12.4238 0.824595 0.412297 0.911049i \(-0.364726\pi\)
0.412297 + 0.911049i \(0.364726\pi\)
\(228\) 0 0
\(229\) −8.36445 −0.552738 −0.276369 0.961052i \(-0.589131\pi\)
−0.276369 + 0.961052i \(0.589131\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 14.0055 0.917528 0.458764 0.888558i \(-0.348292\pi\)
0.458764 + 0.888558i \(0.348292\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −1.94067 −0.126060
\(238\) 0 0
\(239\) 16.9605 1.09708 0.548542 0.836123i \(-0.315183\pi\)
0.548542 + 0.836123i \(0.315183\pi\)
\(240\) 0 0
\(241\) 10.3304 0.665441 0.332721 0.943025i \(-0.392033\pi\)
0.332721 + 0.943025i \(0.392033\pi\)
\(242\) 0 0
\(243\) −9.26564 −0.594391
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 16.4238 1.04502
\(248\) 0 0
\(249\) 5.38429 0.341216
\(250\) 0 0
\(251\) 19.5082 1.23135 0.615673 0.788002i \(-0.288884\pi\)
0.615673 + 0.788002i \(0.288884\pi\)
\(252\) 0 0
\(253\) 9.00000 0.565825
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −28.4633 −1.77549 −0.887744 0.460337i \(-0.847729\pi\)
−0.887744 + 0.460337i \(0.847729\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −15.7773 −0.976591
\(262\) 0 0
\(263\) −28.5621 −1.76121 −0.880606 0.473849i \(-0.842864\pi\)
−0.880606 + 0.473849i \(0.842864\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −0.316041 −0.0193414
\(268\) 0 0
\(269\) −9.19761 −0.560788 −0.280394 0.959885i \(-0.590465\pi\)
−0.280394 + 0.959885i \(0.590465\pi\)
\(270\) 0 0
\(271\) 3.86172 0.234583 0.117291 0.993098i \(-0.462579\pi\)
0.117291 + 0.993098i \(0.462579\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −10.6410 −0.639356 −0.319678 0.947526i \(-0.603575\pi\)
−0.319678 + 0.947526i \(0.603575\pi\)
\(278\) 0 0
\(279\) −12.9101 −0.772909
\(280\) 0 0
\(281\) 1.73436 0.103463 0.0517315 0.998661i \(-0.483526\pi\)
0.0517315 + 0.998661i \(0.483526\pi\)
\(282\) 0 0
\(283\) 5.91211 0.351439 0.175719 0.984440i \(-0.443775\pi\)
0.175719 + 0.984440i \(0.443775\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −12.0198 −0.707050
\(290\) 0 0
\(291\) 5.86718 0.343940
\(292\) 0 0
\(293\) −24.3250 −1.42108 −0.710540 0.703657i \(-0.751549\pi\)
−0.710540 + 0.703657i \(0.751549\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 2.91757 0.169295
\(298\) 0 0
\(299\) −17.3843 −1.00536
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 5.71997 0.328604
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 23.5226 1.34250 0.671252 0.741229i \(-0.265757\pi\)
0.671252 + 0.741229i \(0.265757\pi\)
\(308\) 0 0
\(309\) 4.87264 0.277195
\(310\) 0 0
\(311\) −8.81877 −0.500067 −0.250033 0.968237i \(-0.580442\pi\)
−0.250033 + 0.968237i \(0.580442\pi\)
\(312\) 0 0
\(313\) 0.0933442 0.00527612 0.00263806 0.999997i \(-0.499160\pi\)
0.00263806 + 0.999997i \(0.499160\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −3.54221 −0.198950 −0.0994751 0.995040i \(-0.531716\pi\)
−0.0994751 + 0.995040i \(0.531716\pi\)
\(318\) 0 0
\(319\) 7.50819 0.420378
\(320\) 0 0
\(321\) −1.96945 −0.109924
\(322\) 0 0
\(323\) −13.9067 −0.773787
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 5.76837 0.318992
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −19.6499 −1.08006 −0.540029 0.841646i \(-0.681587\pi\)
−0.540029 + 0.841646i \(0.681587\pi\)
\(332\) 0 0
\(333\) 6.00199 0.328907
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 23.0449 1.25534 0.627669 0.778480i \(-0.284009\pi\)
0.627669 + 0.778480i \(0.284009\pi\)
\(338\) 0 0
\(339\) −6.71451 −0.364682
\(340\) 0 0
\(341\) 6.14374 0.332702
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 22.5621 1.21119 0.605597 0.795771i \(-0.292934\pi\)
0.605597 + 0.795771i \(0.292934\pi\)
\(348\) 0 0
\(349\) 14.3250 0.766798 0.383399 0.923583i \(-0.374753\pi\)
0.383399 + 0.923583i \(0.374753\pi\)
\(350\) 0 0
\(351\) −5.63555 −0.300804
\(352\) 0 0
\(353\) −32.7003 −1.74046 −0.870232 0.492643i \(-0.836031\pi\)
−0.870232 + 0.492643i \(0.836031\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −26.1581 −1.38057 −0.690287 0.723536i \(-0.742516\pi\)
−0.690287 + 0.723536i \(0.742516\pi\)
\(360\) 0 0
\(361\) 19.8332 1.04385
\(362\) 0 0
\(363\) 3.33043 0.174802
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 25.2316 1.31708 0.658540 0.752546i \(-0.271174\pi\)
0.658540 + 0.752546i \(0.271174\pi\)
\(368\) 0 0
\(369\) −26.7363 −1.39184
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 5.69488 0.294870 0.147435 0.989072i \(-0.452898\pi\)
0.147435 + 0.989072i \(0.452898\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −14.5027 −0.746929
\(378\) 0 0
\(379\) 14.9660 0.768751 0.384375 0.923177i \(-0.374417\pi\)
0.384375 + 0.923177i \(0.374417\pi\)
\(380\) 0 0
\(381\) −1.94067 −0.0994238
\(382\) 0 0
\(383\) 24.4776 1.25075 0.625374 0.780325i \(-0.284946\pi\)
0.625374 + 0.780325i \(0.284946\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 5.35353 0.272135
\(388\) 0 0
\(389\) −31.2460 −1.58424 −0.792118 0.610368i \(-0.791022\pi\)
−0.792118 + 0.610368i \(0.791022\pi\)
\(390\) 0 0
\(391\) 14.7200 0.744421
\(392\) 0 0
\(393\) −5.91757 −0.298502
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 1.13282 0.0568547 0.0284274 0.999596i \(-0.490950\pi\)
0.0284274 + 0.999596i \(0.490950\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −3.82224 −0.190874 −0.0954368 0.995435i \(-0.530425\pi\)
−0.0954368 + 0.995435i \(0.530425\pi\)
\(402\) 0 0
\(403\) −11.8672 −0.591146
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −2.85626 −0.141580
\(408\) 0 0
\(409\) 33.6609 1.66442 0.832211 0.554459i \(-0.187075\pi\)
0.832211 + 0.554459i \(0.187075\pi\)
\(410\) 0 0
\(411\) −1.60699 −0.0792671
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 8.15267 0.399238
\(418\) 0 0
\(419\) −0.497270 −0.0242933 −0.0121466 0.999926i \(-0.503866\pi\)
−0.0121466 + 0.999926i \(0.503866\pi\)
\(420\) 0 0
\(421\) −1.28003 −0.0623850 −0.0311925 0.999513i \(-0.509930\pi\)
−0.0311925 + 0.999513i \(0.509930\pi\)
\(422\) 0 0
\(423\) 19.6894 0.957332
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 1.31058 0.0632755
\(430\) 0 0
\(431\) −10.2910 −0.495698 −0.247849 0.968799i \(-0.579724\pi\)
−0.247849 + 0.968799i \(0.579724\pi\)
\(432\) 0 0
\(433\) −29.8870 −1.43628 −0.718139 0.695899i \(-0.755006\pi\)
−0.718139 + 0.695899i \(0.755006\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −41.1043 −1.96628
\(438\) 0 0
\(439\) −5.04841 −0.240947 −0.120474 0.992717i \(-0.538441\pi\)
−0.120474 + 0.992717i \(0.538441\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 11.7738 0.559392 0.279696 0.960089i \(-0.409766\pi\)
0.279696 + 0.960089i \(0.409766\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −8.20307 −0.387992
\(448\) 0 0
\(449\) −11.3843 −0.537258 −0.268629 0.963244i \(-0.586571\pi\)
−0.268629 + 0.963244i \(0.586571\pi\)
\(450\) 0 0
\(451\) 12.7234 0.599123
\(452\) 0 0
\(453\) −4.92104 −0.231211
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −37.2515 −1.74255 −0.871275 0.490795i \(-0.836706\pi\)
−0.871275 + 0.490795i \(0.836706\pi\)
\(458\) 0 0
\(459\) 4.77184 0.222731
\(460\) 0 0
\(461\) −15.0449 −0.700713 −0.350356 0.936616i \(-0.613939\pi\)
−0.350356 + 0.936616i \(0.613939\pi\)
\(462\) 0 0
\(463\) 31.2031 1.45013 0.725065 0.688681i \(-0.241810\pi\)
0.725065 + 0.688681i \(0.241810\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −18.7684 −0.868497 −0.434248 0.900793i \(-0.642986\pi\)
−0.434248 + 0.900793i \(0.642986\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 5.66957 0.261240
\(472\) 0 0
\(473\) −2.54767 −0.117142
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 29.0683 1.33094
\(478\) 0 0
\(479\) −0.714508 −0.0326467 −0.0163234 0.999867i \(-0.505196\pi\)
−0.0163234 + 0.999867i \(0.505196\pi\)
\(480\) 0 0
\(481\) 5.51712 0.251559
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −16.6949 −0.756517 −0.378259 0.925700i \(-0.623477\pi\)
−0.378259 + 0.925700i \(0.623477\pi\)
\(488\) 0 0
\(489\) −1.60500 −0.0725807
\(490\) 0 0
\(491\) 6.19761 0.279694 0.139847 0.990173i \(-0.455339\pi\)
0.139847 + 0.990173i \(0.455339\pi\)
\(492\) 0 0
\(493\) 12.2800 0.553065
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 14.4687 0.647708 0.323854 0.946107i \(-0.395021\pi\)
0.323854 + 0.946107i \(0.395021\pi\)
\(500\) 0 0
\(501\) 3.31604 0.148150
\(502\) 0 0
\(503\) 30.6949 1.36862 0.684308 0.729193i \(-0.260104\pi\)
0.684308 + 0.729193i \(0.260104\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 2.20632 0.0979861
\(508\) 0 0
\(509\) 44.4742 1.97128 0.985641 0.168852i \(-0.0540059\pi\)
0.985641 + 0.168852i \(0.0540059\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −13.3250 −0.588312
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −9.36991 −0.412088
\(518\) 0 0
\(519\) 7.27457 0.319318
\(520\) 0 0
\(521\) −12.6499 −0.554204 −0.277102 0.960841i \(-0.589374\pi\)
−0.277102 + 0.960841i \(0.589374\pi\)
\(522\) 0 0
\(523\) −10.2711 −0.449124 −0.224562 0.974460i \(-0.572095\pi\)
−0.224562 + 0.974460i \(0.572095\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 10.0484 0.437715
\(528\) 0 0
\(529\) 20.5082 0.891660
\(530\) 0 0
\(531\) 4.68942 0.203503
\(532\) 0 0
\(533\) −24.5764 −1.06452
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 4.80785 0.207474
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −2.13828 −0.0919319 −0.0459660 0.998943i \(-0.514637\pi\)
−0.0459660 + 0.998943i \(0.514637\pi\)
\(542\) 0 0
\(543\) −3.72890 −0.160022
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −32.0198 −1.36907 −0.684535 0.728980i \(-0.739995\pi\)
−0.684535 + 0.728980i \(0.739995\pi\)
\(548\) 0 0
\(549\) −0.113191 −0.00483088
\(550\) 0 0
\(551\) −34.2910 −1.46084
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −8.33043 −0.352972 −0.176486 0.984303i \(-0.556473\pi\)
−0.176486 + 0.984303i \(0.556473\pi\)
\(558\) 0 0
\(559\) 4.92104 0.208138
\(560\) 0 0
\(561\) −1.10972 −0.0468525
\(562\) 0 0
\(563\) −19.4633 −0.820278 −0.410139 0.912023i \(-0.634520\pi\)
−0.410139 + 0.912023i \(0.634520\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 18.8925 0.792014 0.396007 0.918247i \(-0.370396\pi\)
0.396007 + 0.918247i \(0.370396\pi\)
\(570\) 0 0
\(571\) −18.6301 −0.779645 −0.389823 0.920890i \(-0.627464\pi\)
−0.389823 + 0.920890i \(0.627464\pi\)
\(572\) 0 0
\(573\) −5.10426 −0.213234
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −18.5926 −0.774020 −0.387010 0.922075i \(-0.626492\pi\)
−0.387010 + 0.922075i \(0.626492\pi\)
\(578\) 0 0
\(579\) 5.25147 0.218244
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −13.8332 −0.572911
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 10.1383 0.418452 0.209226 0.977867i \(-0.432906\pi\)
0.209226 + 0.977867i \(0.432906\pi\)
\(588\) 0 0
\(589\) −28.0593 −1.15616
\(590\) 0 0
\(591\) 4.21178 0.173249
\(592\) 0 0
\(593\) −17.0055 −0.698331 −0.349165 0.937061i \(-0.613535\pi\)
−0.349165 + 0.937061i \(0.613535\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 1.97144 0.0806857
\(598\) 0 0
\(599\) −8.18669 −0.334499 −0.167250 0.985915i \(-0.553489\pi\)
−0.167250 + 0.985915i \(0.553489\pi\)
\(600\) 0 0
\(601\) −35.3359 −1.44138 −0.720690 0.693257i \(-0.756175\pi\)
−0.720690 + 0.693257i \(0.756175\pi\)
\(602\) 0 0
\(603\) 19.2929 0.785669
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 28.2316 1.14589 0.572943 0.819595i \(-0.305802\pi\)
0.572943 + 0.819595i \(0.305802\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 18.0988 0.732199
\(612\) 0 0
\(613\) 31.1581 1.25846 0.629232 0.777217i \(-0.283369\pi\)
0.629232 + 0.777217i \(0.283369\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −39.1527 −1.57623 −0.788114 0.615530i \(-0.788942\pi\)
−0.788114 + 0.615530i \(0.788942\pi\)
\(618\) 0 0
\(619\) −39.3843 −1.58299 −0.791494 0.611177i \(-0.790696\pi\)
−0.791494 + 0.611177i \(0.790696\pi\)
\(620\) 0 0
\(621\) 14.1043 0.565985
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 3.09880 0.123754
\(628\) 0 0
\(629\) −4.67156 −0.186267
\(630\) 0 0
\(631\) 22.7003 0.903686 0.451843 0.892097i \(-0.350767\pi\)
0.451843 + 0.892097i \(0.350767\pi\)
\(632\) 0 0
\(633\) 3.99653 0.158848
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 17.9804 0.711292
\(640\) 0 0
\(641\) 8.41285 0.332288 0.166144 0.986102i \(-0.446868\pi\)
0.166144 + 0.986102i \(0.446868\pi\)
\(642\) 0 0
\(643\) 29.7398 1.17282 0.586412 0.810013i \(-0.300540\pi\)
0.586412 + 0.810013i \(0.300540\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 21.6859 0.852563 0.426281 0.904591i \(-0.359823\pi\)
0.426281 + 0.904591i \(0.359823\pi\)
\(648\) 0 0
\(649\) −2.23163 −0.0875990
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −30.0702 −1.17674 −0.588370 0.808592i \(-0.700230\pi\)
−0.588370 + 0.808592i \(0.700230\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 11.4687 0.447437
\(658\) 0 0
\(659\) 2.37537 0.0925311 0.0462656 0.998929i \(-0.485268\pi\)
0.0462656 + 0.998929i \(0.485268\pi\)
\(660\) 0 0
\(661\) −14.4633 −0.562555 −0.281278 0.959626i \(-0.590758\pi\)
−0.281278 + 0.959626i \(0.590758\pi\)
\(662\) 0 0
\(663\) 2.14353 0.0832476
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 36.2964 1.40540
\(668\) 0 0
\(669\) 7.85626 0.303741
\(670\) 0 0
\(671\) 0.0538660 0.00207947
\(672\) 0 0
\(673\) −8.99653 −0.346791 −0.173395 0.984852i \(-0.555474\pi\)
−0.173395 + 0.984852i \(0.555474\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −7.49181 −0.287934 −0.143967 0.989583i \(-0.545986\pi\)
−0.143967 + 0.989583i \(0.545986\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −4.52782 −0.173506
\(682\) 0 0
\(683\) 42.3250 1.61952 0.809760 0.586761i \(-0.199597\pi\)
0.809760 + 0.586761i \(0.199597\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 3.04841 0.116304
\(688\) 0 0
\(689\) 26.7200 1.01795
\(690\) 0 0
\(691\) 28.6465 1.08976 0.544882 0.838513i \(-0.316575\pi\)
0.544882 + 0.838513i \(0.316575\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 20.8098 0.788229
\(698\) 0 0
\(699\) −5.10426 −0.193061
\(700\) 0 0
\(701\) −20.4292 −0.771601 −0.385801 0.922582i \(-0.626075\pi\)
−0.385801 + 0.922582i \(0.626075\pi\)
\(702\) 0 0
\(703\) 13.0449 0.491999
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 28.8277 1.08265 0.541323 0.840814i \(-0.317923\pi\)
0.541323 + 0.840814i \(0.317923\pi\)
\(710\) 0 0
\(711\) −15.2676 −0.572581
\(712\) 0 0
\(713\) 29.7003 1.11229
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −6.18123 −0.230842
\(718\) 0 0
\(719\) 31.3106 1.16769 0.583844 0.811866i \(-0.301548\pi\)
0.583844 + 0.811866i \(0.301548\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −3.76490 −0.140018
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 8.17230 0.303094 0.151547 0.988450i \(-0.451575\pi\)
0.151547 + 0.988450i \(0.451575\pi\)
\(728\) 0 0
\(729\) −20.0899 −0.744069
\(730\) 0 0
\(731\) −4.16684 −0.154116
\(732\) 0 0
\(733\) 21.4183 0.791103 0.395552 0.918444i \(-0.370553\pi\)
0.395552 + 0.918444i \(0.370553\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −9.18123 −0.338195
\(738\) 0 0
\(739\) 4.35006 0.160020 0.0800098 0.996794i \(-0.474505\pi\)
0.0800098 + 0.996794i \(0.474505\pi\)
\(740\) 0 0
\(741\) −5.98561 −0.219887
\(742\) 0 0
\(743\) −6.53328 −0.239683 −0.119841 0.992793i \(-0.538239\pi\)
−0.119841 + 0.992793i \(0.538239\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 42.3592 1.54984
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 34.4831 1.25831 0.629153 0.777281i \(-0.283402\pi\)
0.629153 + 0.777281i \(0.283402\pi\)
\(752\) 0 0
\(753\) −7.10972 −0.259093
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 44.2425 1.60802 0.804011 0.594614i \(-0.202695\pi\)
0.804011 + 0.594614i \(0.202695\pi\)
\(758\) 0 0
\(759\) −3.28003 −0.119058
\(760\) 0 0
\(761\) −23.8188 −0.863430 −0.431715 0.902010i \(-0.642091\pi\)
−0.431715 + 0.902010i \(0.642091\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 4.31058 0.155646
\(768\) 0 0
\(769\) −0.158128 −0.00570225 −0.00285113 0.999996i \(-0.500908\pi\)
−0.00285113 + 0.999996i \(0.500908\pi\)
\(770\) 0 0
\(771\) 10.3734 0.373588
\(772\) 0 0
\(773\) 17.7991 0.640191 0.320095 0.947385i \(-0.396285\pi\)
0.320095 + 0.947385i \(0.396285\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −58.1097 −2.08200
\(780\) 0 0
\(781\) −8.55660 −0.306179
\(782\) 0 0
\(783\) 11.7664 0.420496
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 41.5226 1.48012 0.740060 0.672541i \(-0.234797\pi\)
0.740060 + 0.672541i \(0.234797\pi\)
\(788\) 0 0
\(789\) 10.4094 0.370584
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −0.104047 −0.00369481
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −25.0933 −0.888852 −0.444426 0.895816i \(-0.646592\pi\)
−0.444426 + 0.895816i \(0.646592\pi\)
\(798\) 0 0
\(799\) −15.3250 −0.542158
\(800\) 0 0
\(801\) −2.48635 −0.0878509
\(802\) 0 0
\(803\) −5.45779 −0.192601
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 3.35205 0.117998
\(808\) 0 0
\(809\) 12.6949 0.446328 0.223164 0.974781i \(-0.428361\pi\)
0.223164 + 0.974781i \(0.428361\pi\)
\(810\) 0 0
\(811\) 17.9749 0.631184 0.315592 0.948895i \(-0.397797\pi\)
0.315592 + 0.948895i \(0.397797\pi\)
\(812\) 0 0
\(813\) −1.40740 −0.0493595
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 11.6356 0.407076
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 20.0683 0.700387 0.350193 0.936677i \(-0.386116\pi\)
0.350193 + 0.936677i \(0.386116\pi\)
\(822\) 0 0
\(823\) 10.6105 0.369857 0.184929 0.982752i \(-0.440795\pi\)
0.184929 + 0.982752i \(0.440795\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −34.7793 −1.20939 −0.604697 0.796455i \(-0.706706\pi\)
−0.604697 + 0.796455i \(0.706706\pi\)
\(828\) 0 0
\(829\) −26.2282 −0.910942 −0.455471 0.890251i \(-0.650529\pi\)
−0.455471 + 0.890251i \(0.650529\pi\)
\(830\) 0 0
\(831\) 3.87810 0.134530
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 9.62810 0.332796
\(838\) 0 0
\(839\) 33.9210 1.17108 0.585542 0.810642i \(-0.300882\pi\)
0.585542 + 0.810642i \(0.300882\pi\)
\(840\) 0 0
\(841\) 1.28003 0.0441391
\(842\) 0 0
\(843\) −0.632082 −0.0217701
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −2.15466 −0.0739477
\(850\) 0 0
\(851\) −13.8079 −0.473327
\(852\) 0 0
\(853\) 57.6698 1.97458 0.987288 0.158942i \(-0.0508082\pi\)
0.987288 + 0.158942i \(0.0508082\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −35.4039 −1.20938 −0.604688 0.796463i \(-0.706702\pi\)
−0.604688 + 0.796463i \(0.706702\pi\)
\(858\) 0 0
\(859\) −13.4434 −0.458683 −0.229342 0.973346i \(-0.573657\pi\)
−0.229342 + 0.973346i \(0.573657\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 7.06478 0.240488 0.120244 0.992744i \(-0.461632\pi\)
0.120244 + 0.992744i \(0.461632\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 4.38061 0.148773
\(868\) 0 0
\(869\) 7.26564 0.246470
\(870\) 0 0
\(871\) 17.7344 0.600906
\(872\) 0 0
\(873\) 46.1581 1.56222
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −15.0055 −0.506698 −0.253349 0.967375i \(-0.581532\pi\)
−0.253349 + 0.967375i \(0.581532\pi\)
\(878\) 0 0
\(879\) 8.86519 0.299015
\(880\) 0 0
\(881\) −39.3699 −1.32641 −0.663203 0.748440i \(-0.730803\pi\)
−0.663203 + 0.748440i \(0.730803\pi\)
\(882\) 0 0
\(883\) −58.2229 −1.95936 −0.979679 0.200574i \(-0.935719\pi\)
−0.979679 + 0.200574i \(0.935719\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −25.2460 −0.847678 −0.423839 0.905738i \(-0.639318\pi\)
−0.423839 + 0.905738i \(0.639318\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 10.6730 0.357560
\(892\) 0 0
\(893\) 42.7937 1.43204
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 6.33567 0.211542
\(898\) 0 0
\(899\) 24.7773 0.826369
\(900\) 0 0
\(901\) −22.6248 −0.753743
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −27.1867 −0.902719 −0.451360 0.892342i \(-0.649061\pi\)
−0.451360 + 0.892342i \(0.649061\pi\)
\(908\) 0 0
\(909\) 45.0000 1.49256
\(910\) 0 0
\(911\) −40.7882 −1.35137 −0.675687 0.737189i \(-0.736153\pi\)
−0.675687 + 0.737189i \(0.736153\pi\)
\(912\) 0 0
\(913\) −20.1581 −0.667137
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −47.0737 −1.55282 −0.776409 0.630229i \(-0.782961\pi\)
−0.776409 + 0.630229i \(0.782961\pi\)
\(920\) 0 0
\(921\) −8.57276 −0.282482
\(922\) 0 0
\(923\) 16.5278 0.544020
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 38.3339 1.25905
\(928\) 0 0
\(929\) 17.9911 0.590268 0.295134 0.955456i \(-0.404636\pi\)
0.295134 + 0.955456i \(0.404636\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 3.21398 0.105221
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 37.7003 1.23162 0.615808 0.787896i \(-0.288830\pi\)
0.615808 + 0.787896i \(0.288830\pi\)
\(938\) 0 0
\(939\) −0.0340191 −0.00111017
\(940\) 0 0
\(941\) 4.83316 0.157556 0.0787782 0.996892i \(-0.474898\pi\)
0.0787782 + 0.996892i \(0.474898\pi\)
\(942\) 0 0
\(943\) 61.5082 2.00298
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −2.83663 −0.0921780 −0.0460890 0.998937i \(-0.514676\pi\)
−0.0460890 + 0.998937i \(0.514676\pi\)
\(948\) 0 0
\(949\) 10.5422 0.342215
\(950\) 0 0
\(951\) 1.29095 0.0418619
\(952\) 0 0
\(953\) 17.7991 0.576571 0.288285 0.957545i \(-0.406915\pi\)
0.288285 + 0.957545i \(0.406915\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −2.73634 −0.0884535
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −10.7254 −0.345982
\(962\) 0 0
\(963\) −15.4940 −0.499288
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −15.1581 −0.487453 −0.243726 0.969844i \(-0.578370\pi\)
−0.243726 + 0.969844i \(0.578370\pi\)
\(968\) 0 0
\(969\) 5.06825 0.162816
\(970\) 0 0
\(971\) −47.3843 −1.52063 −0.760317 0.649552i \(-0.774956\pi\)
−0.760317 + 0.649552i \(0.774956\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 23.7200 0.758869 0.379434 0.925219i \(-0.376119\pi\)
0.379434 + 0.925219i \(0.376119\pi\)
\(978\) 0 0
\(979\) 1.18322 0.0378158
\(980\) 0 0
\(981\) 45.3808 1.44890
\(982\) 0 0
\(983\) 34.4543 1.09892 0.549461 0.835519i \(-0.314833\pi\)
0.549461 + 0.835519i \(0.314833\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −12.3160 −0.391627
\(990\) 0 0
\(991\) −41.6609 −1.32340 −0.661700 0.749768i \(-0.730165\pi\)
−0.661700 + 0.749768i \(0.730165\pi\)
\(992\) 0 0
\(993\) 7.16138 0.227260
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 24.7882 0.785051 0.392525 0.919741i \(-0.371601\pi\)
0.392525 + 0.919741i \(0.371601\pi\)
\(998\) 0 0
\(999\) −4.47616 −0.141619
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.1.2 3
5.2 odd 4 4900.2.e.t.2549.4 6
5.3 odd 4 4900.2.e.t.2549.3 6
5.4 even 2 4900.2.a.bc.1.2 3
7.2 even 3 700.2.i.e.501.2 yes 6
7.4 even 3 700.2.i.e.401.2 yes 6
7.6 odd 2 4900.2.a.bd.1.2 3
35.2 odd 12 700.2.r.d.249.3 12
35.4 even 6 700.2.i.d.401.2 6
35.9 even 6 700.2.i.d.501.2 yes 6
35.13 even 4 4900.2.e.s.2549.4 6
35.18 odd 12 700.2.r.d.149.3 12
35.23 odd 12 700.2.r.d.249.4 12
35.27 even 4 4900.2.e.s.2549.3 6
35.32 odd 12 700.2.r.d.149.4 12
35.34 odd 2 4900.2.a.bb.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
700.2.i.d.401.2 6 35.4 even 6
700.2.i.d.501.2 yes 6 35.9 even 6
700.2.i.e.401.2 yes 6 7.4 even 3
700.2.i.e.501.2 yes 6 7.2 even 3
700.2.r.d.149.3 12 35.18 odd 12
700.2.r.d.149.4 12 35.32 odd 12
700.2.r.d.249.3 12 35.2 odd 12
700.2.r.d.249.4 12 35.23 odd 12
4900.2.a.ba.1.2 3 1.1 even 1 trivial
4900.2.a.bb.1.2 3 35.34 odd 2
4900.2.a.bc.1.2 3 5.4 even 2
4900.2.a.bd.1.2 3 7.6 odd 2
4900.2.e.s.2549.3 6 35.27 even 4
4900.2.e.s.2549.4 6 35.13 even 4
4900.2.e.t.2549.3 6 5.3 odd 4
4900.2.e.t.2549.4 6 5.2 odd 4