Properties

Label 3640.2.a.y.1.4
Level $3640$
Weight $2$
Character 3640.1
Self dual yes
Analytic conductor $29.066$
Analytic rank $1$
Dimension $5$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 3640 = 2^{3} \cdot 5 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3640.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(29.0655463357\)
Analytic rank: \(1\)
Dimension: \(5\)
Coefficient field: 5.5.1194649.1
Defining polynomial: \( x^{5} - 8x^{3} - 3x^{2} + 10x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-1.32400\) of defining polynomial
Character \(\chi\) \(=\) 3640.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.32400 q^{3} -1.00000 q^{5} +1.00000 q^{7} -1.24704 q^{9} +O(q^{10})\) \(q+1.32400 q^{3} -1.00000 q^{5} +1.00000 q^{7} -1.24704 q^{9} +2.54610 q^{11} -1.00000 q^{13} -1.32400 q^{15} -3.92589 q^{17} -4.79313 q^{19} +1.32400 q^{21} -4.70002 q^{23} +1.00000 q^{25} -5.62306 q^{27} +4.32185 q^{29} +8.37387 q^{31} +3.37102 q^{33} -1.00000 q^{35} -1.69716 q^{37} -1.32400 q^{39} +4.84516 q^{41} -11.8188 q^{43} +1.24704 q^{45} -10.8209 q^{47} +1.00000 q^{49} -5.19786 q^{51} -9.04988 q^{53} -2.54610 q^{55} -6.34609 q^{57} -4.69502 q^{59} -5.37102 q^{61} -1.24704 q^{63} +1.00000 q^{65} +6.59289 q^{67} -6.22280 q^{69} -0.527086 q^{71} +4.27128 q^{73} +1.32400 q^{75} +2.54610 q^{77} -15.0870 q^{79} -3.70379 q^{81} +1.95013 q^{83} +3.92589 q^{85} +5.72211 q^{87} -7.91996 q^{89} -1.00000 q^{91} +11.0870 q^{93} +4.79313 q^{95} +4.32685 q^{97} -3.17508 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 5 q^{5} + 5 q^{7} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 5 q - 5 q^{5} + 5 q^{7} + q^{9} - 7 q^{11} - 5 q^{13} + q^{17} + 3 q^{19} - 5 q^{23} + 5 q^{25} - 9 q^{27} - 9 q^{29} + 6 q^{31} + q^{33} - 5 q^{35} - 10 q^{37} - 8 q^{41} + 6 q^{43} - q^{45} - 13 q^{47} + 5 q^{49} - 4 q^{51} - 16 q^{53} + 7 q^{55} - 10 q^{57} - q^{59} - 11 q^{61} + q^{63} + 5 q^{65} - 30 q^{67} - 15 q^{69} - 12 q^{71} + 23 q^{73} - 7 q^{77} + 2 q^{79} - 11 q^{81} - 2 q^{83} - q^{85} - 5 q^{87} - 25 q^{89} - 5 q^{91} - 22 q^{93} - 3 q^{95} - 5 q^{97} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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
\(3\) 1.32400 0.764409 0.382205 0.924078i \(-0.375165\pi\)
0.382205 + 0.924078i \(0.375165\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) −1.24704 −0.415679
\(10\) 0 0
\(11\) 2.54610 0.767677 0.383839 0.923400i \(-0.374602\pi\)
0.383839 + 0.923400i \(0.374602\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −1.32400 −0.341854
\(16\) 0 0
\(17\) −3.92589 −0.952169 −0.476084 0.879400i \(-0.657944\pi\)
−0.476084 + 0.879400i \(0.657944\pi\)
\(18\) 0 0
\(19\) −4.79313 −1.09962 −0.549810 0.835290i \(-0.685300\pi\)
−0.549810 + 0.835290i \(0.685300\pi\)
\(20\) 0 0
\(21\) 1.32400 0.288919
\(22\) 0 0
\(23\) −4.70002 −0.980021 −0.490010 0.871717i \(-0.663007\pi\)
−0.490010 + 0.871717i \(0.663007\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −5.62306 −1.08216
\(28\) 0 0
\(29\) 4.32185 0.802547 0.401274 0.915958i \(-0.368568\pi\)
0.401274 + 0.915958i \(0.368568\pi\)
\(30\) 0 0
\(31\) 8.37387 1.50399 0.751996 0.659168i \(-0.229091\pi\)
0.751996 + 0.659168i \(0.229091\pi\)
\(32\) 0 0
\(33\) 3.37102 0.586819
\(34\) 0 0
\(35\) −1.00000 −0.169031
\(36\) 0 0
\(37\) −1.69716 −0.279012 −0.139506 0.990221i \(-0.544551\pi\)
−0.139506 + 0.990221i \(0.544551\pi\)
\(38\) 0 0
\(39\) −1.32400 −0.212009
\(40\) 0 0
\(41\) 4.84516 0.756687 0.378343 0.925665i \(-0.376494\pi\)
0.378343 + 0.925665i \(0.376494\pi\)
\(42\) 0 0
\(43\) −11.8188 −1.80235 −0.901173 0.433460i \(-0.857293\pi\)
−0.901173 + 0.433460i \(0.857293\pi\)
\(44\) 0 0
\(45\) 1.24704 0.185897
\(46\) 0 0
\(47\) −10.8209 −1.57839 −0.789197 0.614141i \(-0.789503\pi\)
−0.789197 + 0.614141i \(0.789503\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −5.19786 −0.727846
\(52\) 0 0
\(53\) −9.04988 −1.24310 −0.621548 0.783376i \(-0.713496\pi\)
−0.621548 + 0.783376i \(0.713496\pi\)
\(54\) 0 0
\(55\) −2.54610 −0.343316
\(56\) 0 0
\(57\) −6.34609 −0.840560
\(58\) 0 0
\(59\) −4.69502 −0.611239 −0.305620 0.952154i \(-0.598864\pi\)
−0.305620 + 0.952154i \(0.598864\pi\)
\(60\) 0 0
\(61\) −5.37102 −0.687689 −0.343844 0.939027i \(-0.611729\pi\)
−0.343844 + 0.939027i \(0.611729\pi\)
\(62\) 0 0
\(63\) −1.24704 −0.157112
\(64\) 0 0
\(65\) 1.00000 0.124035
\(66\) 0 0
\(67\) 6.59289 0.805450 0.402725 0.915321i \(-0.368063\pi\)
0.402725 + 0.915321i \(0.368063\pi\)
\(68\) 0 0
\(69\) −6.22280 −0.749137
\(70\) 0 0
\(71\) −0.527086 −0.0625536 −0.0312768 0.999511i \(-0.509957\pi\)
−0.0312768 + 0.999511i \(0.509957\pi\)
\(72\) 0 0
\(73\) 4.27128 0.499915 0.249957 0.968257i \(-0.419583\pi\)
0.249957 + 0.968257i \(0.419583\pi\)
\(74\) 0 0
\(75\) 1.32400 0.152882
\(76\) 0 0
\(77\) 2.54610 0.290155
\(78\) 0 0
\(79\) −15.0870 −1.69742 −0.848708 0.528861i \(-0.822619\pi\)
−0.848708 + 0.528861i \(0.822619\pi\)
\(80\) 0 0
\(81\) −3.70379 −0.411532
\(82\) 0 0
\(83\) 1.95013 0.214055 0.107027 0.994256i \(-0.465867\pi\)
0.107027 + 0.994256i \(0.465867\pi\)
\(84\) 0 0
\(85\) 3.92589 0.425823
\(86\) 0 0
\(87\) 5.72211 0.613474
\(88\) 0 0
\(89\) −7.91996 −0.839514 −0.419757 0.907636i \(-0.637885\pi\)
−0.419757 + 0.907636i \(0.637885\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) 11.0870 1.14967
\(94\) 0 0
\(95\) 4.79313 0.491765
\(96\) 0 0
\(97\) 4.32685 0.439325 0.219662 0.975576i \(-0.429504\pi\)
0.219662 + 0.975576i \(0.429504\pi\)
\(98\) 0 0
\(99\) −3.17508 −0.319107
\(100\) 0 0
\(101\) 4.51308 0.449069 0.224534 0.974466i \(-0.427914\pi\)
0.224534 + 0.974466i \(0.427914\pi\)
\(102\) 0 0
\(103\) 14.2948 1.40851 0.704253 0.709949i \(-0.251282\pi\)
0.704253 + 0.709949i \(0.251282\pi\)
\(104\) 0 0
\(105\) −1.32400 −0.129209
\(106\) 0 0
\(107\) 4.67671 0.452115 0.226057 0.974114i \(-0.427416\pi\)
0.226057 + 0.974114i \(0.427416\pi\)
\(108\) 0 0
\(109\) −6.98815 −0.669343 −0.334671 0.942335i \(-0.608625\pi\)
−0.334671 + 0.942335i \(0.608625\pi\)
\(110\) 0 0
\(111\) −2.24704 −0.213279
\(112\) 0 0
\(113\) −2.72303 −0.256161 −0.128081 0.991764i \(-0.540882\pi\)
−0.128081 + 0.991764i \(0.540882\pi\)
\(114\) 0 0
\(115\) 4.70002 0.438279
\(116\) 0 0
\(117\) 1.24704 0.115289
\(118\) 0 0
\(119\) −3.92589 −0.359886
\(120\) 0 0
\(121\) −4.51739 −0.410672
\(122\) 0 0
\(123\) 6.41497 0.578418
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −1.05388 −0.0935168 −0.0467584 0.998906i \(-0.514889\pi\)
−0.0467584 + 0.998906i \(0.514889\pi\)
\(128\) 0 0
\(129\) −15.6480 −1.37773
\(130\) 0 0
\(131\) 5.40758 0.472463 0.236231 0.971697i \(-0.424088\pi\)
0.236231 + 0.971697i \(0.424088\pi\)
\(132\) 0 0
\(133\) −4.79313 −0.415617
\(134\) 0 0
\(135\) 5.62306 0.483956
\(136\) 0 0
\(137\) −11.5124 −0.983570 −0.491785 0.870717i \(-0.663655\pi\)
−0.491785 + 0.870717i \(0.663655\pi\)
\(138\) 0 0
\(139\) 10.4898 0.889731 0.444866 0.895597i \(-0.353251\pi\)
0.444866 + 0.895597i \(0.353251\pi\)
\(140\) 0 0
\(141\) −14.3268 −1.20654
\(142\) 0 0
\(143\) −2.54610 −0.212915
\(144\) 0 0
\(145\) −4.32185 −0.358910
\(146\) 0 0
\(147\) 1.32400 0.109201
\(148\) 0 0
\(149\) 2.77105 0.227013 0.113507 0.993537i \(-0.463792\pi\)
0.113507 + 0.993537i \(0.463792\pi\)
\(150\) 0 0
\(151\) −12.1266 −0.986849 −0.493425 0.869789i \(-0.664255\pi\)
−0.493425 + 0.869789i \(0.664255\pi\)
\(152\) 0 0
\(153\) 4.89573 0.395796
\(154\) 0 0
\(155\) −8.37387 −0.672606
\(156\) 0 0
\(157\) 6.54465 0.522320 0.261160 0.965296i \(-0.415895\pi\)
0.261160 + 0.965296i \(0.415895\pi\)
\(158\) 0 0
\(159\) −11.9820 −0.950234
\(160\) 0 0
\(161\) −4.70002 −0.370413
\(162\) 0 0
\(163\) −18.1736 −1.42347 −0.711734 0.702449i \(-0.752090\pi\)
−0.711734 + 0.702449i \(0.752090\pi\)
\(164\) 0 0
\(165\) −3.37102 −0.262434
\(166\) 0 0
\(167\) −16.9515 −1.31175 −0.655874 0.754870i \(-0.727700\pi\)
−0.655874 + 0.754870i \(0.727700\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 5.97721 0.457089
\(172\) 0 0
\(173\) −11.8202 −0.898675 −0.449338 0.893362i \(-0.648340\pi\)
−0.449338 + 0.893362i \(0.648340\pi\)
\(174\) 0 0
\(175\) 1.00000 0.0755929
\(176\) 0 0
\(177\) −6.21618 −0.467237
\(178\) 0 0
\(179\) 13.5545 1.01311 0.506555 0.862208i \(-0.330919\pi\)
0.506555 + 0.862208i \(0.330919\pi\)
\(180\) 0 0
\(181\) −13.9767 −1.03888 −0.519440 0.854507i \(-0.673859\pi\)
−0.519440 + 0.854507i \(0.673859\pi\)
\(182\) 0 0
\(183\) −7.11121 −0.525676
\(184\) 0 0
\(185\) 1.69716 0.124778
\(186\) 0 0
\(187\) −9.99571 −0.730958
\(188\) 0 0
\(189\) −5.62306 −0.409017
\(190\) 0 0
\(191\) −16.2160 −1.17335 −0.586673 0.809824i \(-0.699562\pi\)
−0.586673 + 0.809824i \(0.699562\pi\)
\(192\) 0 0
\(193\) −9.37009 −0.674474 −0.337237 0.941420i \(-0.609492\pi\)
−0.337237 + 0.941420i \(0.609492\pi\)
\(194\) 0 0
\(195\) 1.32400 0.0948133
\(196\) 0 0
\(197\) −1.21064 −0.0862546 −0.0431273 0.999070i \(-0.513732\pi\)
−0.0431273 + 0.999070i \(0.513732\pi\)
\(198\) 0 0
\(199\) 17.5938 1.24719 0.623596 0.781746i \(-0.285671\pi\)
0.623596 + 0.781746i \(0.285671\pi\)
\(200\) 0 0
\(201\) 8.72896 0.615694
\(202\) 0 0
\(203\) 4.32185 0.303334
\(204\) 0 0
\(205\) −4.84516 −0.338401
\(206\) 0 0
\(207\) 5.86109 0.407374
\(208\) 0 0
\(209\) −12.2038 −0.844154
\(210\) 0 0
\(211\) 23.5677 1.62247 0.811235 0.584721i \(-0.198796\pi\)
0.811235 + 0.584721i \(0.198796\pi\)
\(212\) 0 0
\(213\) −0.697859 −0.0478165
\(214\) 0 0
\(215\) 11.8188 0.806034
\(216\) 0 0
\(217\) 8.37387 0.568456
\(218\) 0 0
\(219\) 5.65515 0.382139
\(220\) 0 0
\(221\) 3.92589 0.264084
\(222\) 0 0
\(223\) 0.376715 0.0252267 0.0126134 0.999920i \(-0.495985\pi\)
0.0126134 + 0.999920i \(0.495985\pi\)
\(224\) 0 0
\(225\) −1.24704 −0.0831358
\(226\) 0 0
\(227\) −3.59998 −0.238939 −0.119469 0.992838i \(-0.538119\pi\)
−0.119469 + 0.992838i \(0.538119\pi\)
\(228\) 0 0
\(229\) −17.2219 −1.13805 −0.569027 0.822319i \(-0.692680\pi\)
−0.569027 + 0.822319i \(0.692680\pi\)
\(230\) 0 0
\(231\) 3.37102 0.221797
\(232\) 0 0
\(233\) 6.88265 0.450897 0.225449 0.974255i \(-0.427615\pi\)
0.225449 + 0.974255i \(0.427615\pi\)
\(234\) 0 0
\(235\) 10.8209 0.705879
\(236\) 0 0
\(237\) −19.9751 −1.29752
\(238\) 0 0
\(239\) 3.52849 0.228239 0.114119 0.993467i \(-0.463595\pi\)
0.114119 + 0.993467i \(0.463595\pi\)
\(240\) 0 0
\(241\) 4.02563 0.259314 0.129657 0.991559i \(-0.458612\pi\)
0.129657 + 0.991559i \(0.458612\pi\)
\(242\) 0 0
\(243\) 11.9654 0.767579
\(244\) 0 0
\(245\) −1.00000 −0.0638877
\(246\) 0 0
\(247\) 4.79313 0.304980
\(248\) 0 0
\(249\) 2.58196 0.163625
\(250\) 0 0
\(251\) 18.1231 1.14392 0.571959 0.820282i \(-0.306184\pi\)
0.571959 + 0.820282i \(0.306184\pi\)
\(252\) 0 0
\(253\) −11.9667 −0.752340
\(254\) 0 0
\(255\) 5.19786 0.325503
\(256\) 0 0
\(257\) 13.4423 0.838511 0.419255 0.907868i \(-0.362291\pi\)
0.419255 + 0.907868i \(0.362291\pi\)
\(258\) 0 0
\(259\) −1.69716 −0.105457
\(260\) 0 0
\(261\) −5.38950 −0.333602
\(262\) 0 0
\(263\) −27.5514 −1.69889 −0.849446 0.527675i \(-0.823064\pi\)
−0.849446 + 0.527675i \(0.823064\pi\)
\(264\) 0 0
\(265\) 9.04988 0.555930
\(266\) 0 0
\(267\) −10.4860 −0.641732
\(268\) 0 0
\(269\) −16.5131 −1.00682 −0.503410 0.864048i \(-0.667922\pi\)
−0.503410 + 0.864048i \(0.667922\pi\)
\(270\) 0 0
\(271\) −0.0458648 −0.00278609 −0.00139305 0.999999i \(-0.500443\pi\)
−0.00139305 + 0.999999i \(0.500443\pi\)
\(272\) 0 0
\(273\) −1.32400 −0.0801318
\(274\) 0 0
\(275\) 2.54610 0.153535
\(276\) 0 0
\(277\) 25.2375 1.51638 0.758188 0.652036i \(-0.226085\pi\)
0.758188 + 0.652036i \(0.226085\pi\)
\(278\) 0 0
\(279\) −10.4425 −0.625178
\(280\) 0 0
\(281\) 16.4437 0.980952 0.490476 0.871455i \(-0.336823\pi\)
0.490476 + 0.871455i \(0.336823\pi\)
\(282\) 0 0
\(283\) 7.36038 0.437529 0.218765 0.975778i \(-0.429797\pi\)
0.218765 + 0.975778i \(0.429797\pi\)
\(284\) 0 0
\(285\) 6.34609 0.375910
\(286\) 0 0
\(287\) 4.84516 0.286001
\(288\) 0 0
\(289\) −1.58737 −0.0933745
\(290\) 0 0
\(291\) 5.72872 0.335824
\(292\) 0 0
\(293\) −20.8442 −1.21773 −0.608866 0.793273i \(-0.708375\pi\)
−0.608866 + 0.793273i \(0.708375\pi\)
\(294\) 0 0
\(295\) 4.69502 0.273354
\(296\) 0 0
\(297\) −14.3168 −0.830748
\(298\) 0 0
\(299\) 4.70002 0.271809
\(300\) 0 0
\(301\) −11.8188 −0.681223
\(302\) 0 0
\(303\) 5.97530 0.343272
\(304\) 0 0
\(305\) 5.37102 0.307544
\(306\) 0 0
\(307\) −0.504070 −0.0287688 −0.0143844 0.999897i \(-0.504579\pi\)
−0.0143844 + 0.999897i \(0.504579\pi\)
\(308\) 0 0
\(309\) 18.9262 1.07667
\(310\) 0 0
\(311\) −15.6860 −0.889473 −0.444736 0.895662i \(-0.646703\pi\)
−0.444736 + 0.895662i \(0.646703\pi\)
\(312\) 0 0
\(313\) 0.227797 0.0128758 0.00643791 0.999979i \(-0.497951\pi\)
0.00643791 + 0.999979i \(0.497951\pi\)
\(314\) 0 0
\(315\) 1.24704 0.0702625
\(316\) 0 0
\(317\) 5.76349 0.323710 0.161855 0.986815i \(-0.448252\pi\)
0.161855 + 0.986815i \(0.448252\pi\)
\(318\) 0 0
\(319\) 11.0038 0.616097
\(320\) 0 0
\(321\) 6.19194 0.345600
\(322\) 0 0
\(323\) 18.8173 1.04702
\(324\) 0 0
\(325\) −1.00000 −0.0554700
\(326\) 0 0
\(327\) −9.25227 −0.511652
\(328\) 0 0
\(329\) −10.8209 −0.596577
\(330\) 0 0
\(331\) 0.800209 0.0439835 0.0219917 0.999758i \(-0.492999\pi\)
0.0219917 + 0.999758i \(0.492999\pi\)
\(332\) 0 0
\(333\) 2.11642 0.115979
\(334\) 0 0
\(335\) −6.59289 −0.360208
\(336\) 0 0
\(337\) 20.1051 1.09519 0.547596 0.836743i \(-0.315543\pi\)
0.547596 + 0.836743i \(0.315543\pi\)
\(338\) 0 0
\(339\) −3.60528 −0.195812
\(340\) 0 0
\(341\) 21.3207 1.15458
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 6.22280 0.335024
\(346\) 0 0
\(347\) −34.1048 −1.83084 −0.915420 0.402500i \(-0.868141\pi\)
−0.915420 + 0.402500i \(0.868141\pi\)
\(348\) 0 0
\(349\) −29.4240 −1.57503 −0.787516 0.616294i \(-0.788633\pi\)
−0.787516 + 0.616294i \(0.788633\pi\)
\(350\) 0 0
\(351\) 5.62306 0.300137
\(352\) 0 0
\(353\) 29.1592 1.55199 0.775995 0.630740i \(-0.217248\pi\)
0.775995 + 0.630740i \(0.217248\pi\)
\(354\) 0 0
\(355\) 0.527086 0.0279748
\(356\) 0 0
\(357\) −5.19786 −0.275100
\(358\) 0 0
\(359\) 14.1148 0.744949 0.372474 0.928042i \(-0.378509\pi\)
0.372474 + 0.928042i \(0.378509\pi\)
\(360\) 0 0
\(361\) 3.97413 0.209165
\(362\) 0 0
\(363\) −5.98100 −0.313921
\(364\) 0 0
\(365\) −4.27128 −0.223569
\(366\) 0 0
\(367\) 35.9708 1.87766 0.938831 0.344377i \(-0.111910\pi\)
0.938831 + 0.344377i \(0.111910\pi\)
\(368\) 0 0
\(369\) −6.04209 −0.314539
\(370\) 0 0
\(371\) −9.04988 −0.469846
\(372\) 0 0
\(373\) −13.9634 −0.722997 −0.361498 0.932373i \(-0.617735\pi\)
−0.361498 + 0.932373i \(0.617735\pi\)
\(374\) 0 0
\(375\) −1.32400 −0.0683708
\(376\) 0 0
\(377\) −4.32185 −0.222587
\(378\) 0 0
\(379\) −6.02872 −0.309674 −0.154837 0.987940i \(-0.549485\pi\)
−0.154837 + 0.987940i \(0.549485\pi\)
\(380\) 0 0
\(381\) −1.39533 −0.0714851
\(382\) 0 0
\(383\) −29.2034 −1.49222 −0.746112 0.665820i \(-0.768082\pi\)
−0.746112 + 0.665820i \(0.768082\pi\)
\(384\) 0 0
\(385\) −2.54610 −0.129761
\(386\) 0 0
\(387\) 14.7384 0.749197
\(388\) 0 0
\(389\) −33.4461 −1.69579 −0.847893 0.530167i \(-0.822129\pi\)
−0.847893 + 0.530167i \(0.822129\pi\)
\(390\) 0 0
\(391\) 18.4518 0.933145
\(392\) 0 0
\(393\) 7.15961 0.361155
\(394\) 0 0
\(395\) 15.0870 0.759108
\(396\) 0 0
\(397\) −13.4133 −0.673193 −0.336597 0.941649i \(-0.609276\pi\)
−0.336597 + 0.941649i \(0.609276\pi\)
\(398\) 0 0
\(399\) −6.34609 −0.317702
\(400\) 0 0
\(401\) 7.29785 0.364437 0.182219 0.983258i \(-0.441672\pi\)
0.182219 + 0.983258i \(0.441672\pi\)
\(402\) 0 0
\(403\) −8.37387 −0.417132
\(404\) 0 0
\(405\) 3.70379 0.184043
\(406\) 0 0
\(407\) −4.32114 −0.214191
\(408\) 0 0
\(409\) 25.0879 1.24052 0.620258 0.784398i \(-0.287028\pi\)
0.620258 + 0.784398i \(0.287028\pi\)
\(410\) 0 0
\(411\) −15.2423 −0.751850
\(412\) 0 0
\(413\) −4.69502 −0.231027
\(414\) 0 0
\(415\) −1.95013 −0.0957282
\(416\) 0 0
\(417\) 13.8884 0.680119
\(418\) 0 0
\(419\) −10.2727 −0.501853 −0.250927 0.968006i \(-0.580735\pi\)
−0.250927 + 0.968006i \(0.580735\pi\)
\(420\) 0 0
\(421\) 7.32870 0.357179 0.178590 0.983924i \(-0.442847\pi\)
0.178590 + 0.983924i \(0.442847\pi\)
\(422\) 0 0
\(423\) 13.4941 0.656105
\(424\) 0 0
\(425\) −3.92589 −0.190434
\(426\) 0 0
\(427\) −5.37102 −0.259922
\(428\) 0 0
\(429\) −3.37102 −0.162754
\(430\) 0 0
\(431\) 7.89235 0.380161 0.190081 0.981768i \(-0.439125\pi\)
0.190081 + 0.981768i \(0.439125\pi\)
\(432\) 0 0
\(433\) −18.2100 −0.875118 −0.437559 0.899190i \(-0.644157\pi\)
−0.437559 + 0.899190i \(0.644157\pi\)
\(434\) 0 0
\(435\) −5.72211 −0.274354
\(436\) 0 0
\(437\) 22.5278 1.07765
\(438\) 0 0
\(439\) 29.0262 1.38534 0.692672 0.721253i \(-0.256433\pi\)
0.692672 + 0.721253i \(0.256433\pi\)
\(440\) 0 0
\(441\) −1.24704 −0.0593827
\(442\) 0 0
\(443\) 31.0549 1.47546 0.737731 0.675095i \(-0.235897\pi\)
0.737731 + 0.675095i \(0.235897\pi\)
\(444\) 0 0
\(445\) 7.91996 0.375442
\(446\) 0 0
\(447\) 3.66886 0.173531
\(448\) 0 0
\(449\) −18.4090 −0.868774 −0.434387 0.900726i \(-0.643035\pi\)
−0.434387 + 0.900726i \(0.643035\pi\)
\(450\) 0 0
\(451\) 12.3362 0.580891
\(452\) 0 0
\(453\) −16.0556 −0.754357
\(454\) 0 0
\(455\) 1.00000 0.0468807
\(456\) 0 0
\(457\) −36.8958 −1.72591 −0.862957 0.505278i \(-0.831390\pi\)
−0.862957 + 0.505278i \(0.831390\pi\)
\(458\) 0 0
\(459\) 22.0755 1.03040
\(460\) 0 0
\(461\) −2.22641 −0.103694 −0.0518470 0.998655i \(-0.516511\pi\)
−0.0518470 + 0.998655i \(0.516511\pi\)
\(462\) 0 0
\(463\) 26.9564 1.25277 0.626384 0.779514i \(-0.284534\pi\)
0.626384 + 0.779514i \(0.284534\pi\)
\(464\) 0 0
\(465\) −11.0870 −0.514146
\(466\) 0 0
\(467\) −13.3532 −0.617914 −0.308957 0.951076i \(-0.599980\pi\)
−0.308957 + 0.951076i \(0.599980\pi\)
\(468\) 0 0
\(469\) 6.59289 0.304432
\(470\) 0 0
\(471\) 8.66508 0.399266
\(472\) 0 0
\(473\) −30.0917 −1.38362
\(474\) 0 0
\(475\) −4.79313 −0.219924
\(476\) 0 0
\(477\) 11.2855 0.516729
\(478\) 0 0
\(479\) 34.1331 1.55958 0.779790 0.626041i \(-0.215326\pi\)
0.779790 + 0.626041i \(0.215326\pi\)
\(480\) 0 0
\(481\) 1.69716 0.0773840
\(482\) 0 0
\(483\) −6.22280 −0.283147
\(484\) 0 0
\(485\) −4.32685 −0.196472
\(486\) 0 0
\(487\) 25.0103 1.13333 0.566663 0.823950i \(-0.308234\pi\)
0.566663 + 0.823950i \(0.308234\pi\)
\(488\) 0 0
\(489\) −24.0618 −1.08811
\(490\) 0 0
\(491\) 21.5227 0.971305 0.485653 0.874152i \(-0.338582\pi\)
0.485653 + 0.874152i \(0.338582\pi\)
\(492\) 0 0
\(493\) −16.9671 −0.764160
\(494\) 0 0
\(495\) 3.17508 0.142709
\(496\) 0 0
\(497\) −0.527086 −0.0236430
\(498\) 0 0
\(499\) 7.70432 0.344893 0.172446 0.985019i \(-0.444833\pi\)
0.172446 + 0.985019i \(0.444833\pi\)
\(500\) 0 0
\(501\) −22.4437 −1.00271
\(502\) 0 0
\(503\) −1.57835 −0.0703754 −0.0351877 0.999381i \(-0.511203\pi\)
−0.0351877 + 0.999381i \(0.511203\pi\)
\(504\) 0 0
\(505\) −4.51308 −0.200830
\(506\) 0 0
\(507\) 1.32400 0.0588007
\(508\) 0 0
\(509\) −10.2566 −0.454617 −0.227309 0.973823i \(-0.572993\pi\)
−0.227309 + 0.973823i \(0.572993\pi\)
\(510\) 0 0
\(511\) 4.27128 0.188950
\(512\) 0 0
\(513\) 26.9521 1.18996
\(514\) 0 0
\(515\) −14.2948 −0.629903
\(516\) 0 0
\(517\) −27.5511 −1.21170
\(518\) 0 0
\(519\) −15.6499 −0.686955
\(520\) 0 0
\(521\) 27.6343 1.21068 0.605340 0.795967i \(-0.293037\pi\)
0.605340 + 0.795967i \(0.293037\pi\)
\(522\) 0 0
\(523\) 22.8725 1.00015 0.500073 0.865983i \(-0.333306\pi\)
0.500073 + 0.865983i \(0.333306\pi\)
\(524\) 0 0
\(525\) 1.32400 0.0577839
\(526\) 0 0
\(527\) −32.8749 −1.43205
\(528\) 0 0
\(529\) −0.909858 −0.0395590
\(530\) 0 0
\(531\) 5.85486 0.254079
\(532\) 0 0
\(533\) −4.84516 −0.209867
\(534\) 0 0
\(535\) −4.67671 −0.202192
\(536\) 0 0
\(537\) 17.9461 0.774430
\(538\) 0 0
\(539\) 2.54610 0.109668
\(540\) 0 0
\(541\) 36.3440 1.56255 0.781276 0.624186i \(-0.214569\pi\)
0.781276 + 0.624186i \(0.214569\pi\)
\(542\) 0 0
\(543\) −18.5051 −0.794129
\(544\) 0 0
\(545\) 6.98815 0.299339
\(546\) 0 0
\(547\) −14.7090 −0.628913 −0.314456 0.949272i \(-0.601822\pi\)
−0.314456 + 0.949272i \(0.601822\pi\)
\(548\) 0 0
\(549\) 6.69786 0.285858
\(550\) 0 0
\(551\) −20.7152 −0.882497
\(552\) 0 0
\(553\) −15.0870 −0.641563
\(554\) 0 0
\(555\) 2.24704 0.0953814
\(556\) 0 0
\(557\) −36.7791 −1.55838 −0.779191 0.626787i \(-0.784370\pi\)
−0.779191 + 0.626787i \(0.784370\pi\)
\(558\) 0 0
\(559\) 11.8188 0.499881
\(560\) 0 0
\(561\) −13.2343 −0.558751
\(562\) 0 0
\(563\) 4.92804 0.207692 0.103846 0.994593i \(-0.466885\pi\)
0.103846 + 0.994593i \(0.466885\pi\)
\(564\) 0 0
\(565\) 2.72303 0.114559
\(566\) 0 0
\(567\) −3.70379 −0.155545
\(568\) 0 0
\(569\) 7.05627 0.295814 0.147907 0.989001i \(-0.452746\pi\)
0.147907 + 0.989001i \(0.452746\pi\)
\(570\) 0 0
\(571\) −10.4183 −0.435994 −0.217997 0.975949i \(-0.569952\pi\)
−0.217997 + 0.975949i \(0.569952\pi\)
\(572\) 0 0
\(573\) −21.4698 −0.896916
\(574\) 0 0
\(575\) −4.70002 −0.196004
\(576\) 0 0
\(577\) 28.3146 1.17875 0.589376 0.807859i \(-0.299374\pi\)
0.589376 + 0.807859i \(0.299374\pi\)
\(578\) 0 0
\(579\) −12.4060 −0.515574
\(580\) 0 0
\(581\) 1.95013 0.0809051
\(582\) 0 0
\(583\) −23.0419 −0.954297
\(584\) 0 0
\(585\) −1.24704 −0.0515586
\(586\) 0 0
\(587\) 23.5510 0.972056 0.486028 0.873943i \(-0.338445\pi\)
0.486028 + 0.873943i \(0.338445\pi\)
\(588\) 0 0
\(589\) −40.1371 −1.65382
\(590\) 0 0
\(591\) −1.60288 −0.0659338
\(592\) 0 0
\(593\) 3.39617 0.139464 0.0697321 0.997566i \(-0.477786\pi\)
0.0697321 + 0.997566i \(0.477786\pi\)
\(594\) 0 0
\(595\) 3.92589 0.160946
\(596\) 0 0
\(597\) 23.2941 0.953365
\(598\) 0 0
\(599\) 9.15921 0.374235 0.187118 0.982338i \(-0.440085\pi\)
0.187118 + 0.982338i \(0.440085\pi\)
\(600\) 0 0
\(601\) 30.1707 1.23069 0.615344 0.788259i \(-0.289017\pi\)
0.615344 + 0.788259i \(0.289017\pi\)
\(602\) 0 0
\(603\) −8.22158 −0.334809
\(604\) 0 0
\(605\) 4.51739 0.183658
\(606\) 0 0
\(607\) 20.4832 0.831388 0.415694 0.909504i \(-0.363539\pi\)
0.415694 + 0.909504i \(0.363539\pi\)
\(608\) 0 0
\(609\) 5.72211 0.231871
\(610\) 0 0
\(611\) 10.8209 0.437768
\(612\) 0 0
\(613\) 7.15493 0.288985 0.144493 0.989506i \(-0.453845\pi\)
0.144493 + 0.989506i \(0.453845\pi\)
\(614\) 0 0
\(615\) −6.41497 −0.258676
\(616\) 0 0
\(617\) −30.7640 −1.23851 −0.619256 0.785190i \(-0.712565\pi\)
−0.619256 + 0.785190i \(0.712565\pi\)
\(618\) 0 0
\(619\) 14.9971 0.602786 0.301393 0.953500i \(-0.402548\pi\)
0.301393 + 0.953500i \(0.402548\pi\)
\(620\) 0 0
\(621\) 26.4284 1.06054
\(622\) 0 0
\(623\) −7.91996 −0.317307
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −16.1578 −0.645279
\(628\) 0 0
\(629\) 6.66288 0.265667
\(630\) 0 0
\(631\) 42.5258 1.69293 0.846464 0.532447i \(-0.178727\pi\)
0.846464 + 0.532447i \(0.178727\pi\)
\(632\) 0 0
\(633\) 31.2036 1.24023
\(634\) 0 0
\(635\) 1.05388 0.0418220
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) 0.657295 0.0260022
\(640\) 0 0
\(641\) −1.93897 −0.0765848 −0.0382924 0.999267i \(-0.512192\pi\)
−0.0382924 + 0.999267i \(0.512192\pi\)
\(642\) 0 0
\(643\) 10.7539 0.424093 0.212046 0.977260i \(-0.431987\pi\)
0.212046 + 0.977260i \(0.431987\pi\)
\(644\) 0 0
\(645\) 15.6480 0.616139
\(646\) 0 0
\(647\) −0.201400 −0.00791785 −0.00395892 0.999992i \(-0.501260\pi\)
−0.00395892 + 0.999992i \(0.501260\pi\)
\(648\) 0 0
\(649\) −11.9540 −0.469234
\(650\) 0 0
\(651\) 11.0870 0.434533
\(652\) 0 0
\(653\) 17.7520 0.694691 0.347346 0.937737i \(-0.387083\pi\)
0.347346 + 0.937737i \(0.387083\pi\)
\(654\) 0 0
\(655\) −5.40758 −0.211292
\(656\) 0 0
\(657\) −5.32644 −0.207804
\(658\) 0 0
\(659\) −28.7235 −1.11891 −0.559454 0.828861i \(-0.688989\pi\)
−0.559454 + 0.828861i \(0.688989\pi\)
\(660\) 0 0
\(661\) −27.6076 −1.07381 −0.536906 0.843642i \(-0.680407\pi\)
−0.536906 + 0.843642i \(0.680407\pi\)
\(662\) 0 0
\(663\) 5.19786 0.201868
\(664\) 0 0
\(665\) 4.79313 0.185870
\(666\) 0 0
\(667\) −20.3128 −0.786513
\(668\) 0 0
\(669\) 0.498770 0.0192835
\(670\) 0 0
\(671\) −13.6751 −0.527923
\(672\) 0 0
\(673\) 21.1668 0.815919 0.407960 0.913000i \(-0.366240\pi\)
0.407960 + 0.913000i \(0.366240\pi\)
\(674\) 0 0
\(675\) −5.62306 −0.216432
\(676\) 0 0
\(677\) −8.12016 −0.312083 −0.156042 0.987750i \(-0.549873\pi\)
−0.156042 + 0.987750i \(0.549873\pi\)
\(678\) 0 0
\(679\) 4.32685 0.166049
\(680\) 0 0
\(681\) −4.76635 −0.182647
\(682\) 0 0
\(683\) 17.9886 0.688316 0.344158 0.938912i \(-0.388164\pi\)
0.344158 + 0.938912i \(0.388164\pi\)
\(684\) 0 0
\(685\) 11.5124 0.439866
\(686\) 0 0
\(687\) −22.8017 −0.869938
\(688\) 0 0
\(689\) 9.04988 0.344773
\(690\) 0 0
\(691\) 34.2442 1.30271 0.651356 0.758773i \(-0.274201\pi\)
0.651356 + 0.758773i \(0.274201\pi\)
\(692\) 0 0
\(693\) −3.17508 −0.120611
\(694\) 0 0
\(695\) −10.4898 −0.397900
\(696\) 0 0
\(697\) −19.0216 −0.720493
\(698\) 0 0
\(699\) 9.11260 0.344670
\(700\) 0 0
\(701\) 1.63131 0.0616138 0.0308069 0.999525i \(-0.490192\pi\)
0.0308069 + 0.999525i \(0.490192\pi\)
\(702\) 0 0
\(703\) 8.13473 0.306807
\(704\) 0 0
\(705\) 14.3268 0.539580
\(706\) 0 0
\(707\) 4.51308 0.169732
\(708\) 0 0
\(709\) 17.7093 0.665088 0.332544 0.943088i \(-0.392093\pi\)
0.332544 + 0.943088i \(0.392093\pi\)
\(710\) 0 0
\(711\) 18.8140 0.705580
\(712\) 0 0
\(713\) −39.3573 −1.47394
\(714\) 0 0
\(715\) 2.54610 0.0952186
\(716\) 0 0
\(717\) 4.67170 0.174468
\(718\) 0 0
\(719\) −17.3710 −0.647828 −0.323914 0.946087i \(-0.604999\pi\)
−0.323914 + 0.946087i \(0.604999\pi\)
\(720\) 0 0
\(721\) 14.2948 0.532365
\(722\) 0 0
\(723\) 5.32992 0.198222
\(724\) 0 0
\(725\) 4.32185 0.160509
\(726\) 0 0
\(727\) 12.3161 0.456777 0.228389 0.973570i \(-0.426654\pi\)
0.228389 + 0.973570i \(0.426654\pi\)
\(728\) 0 0
\(729\) 26.9535 0.998276
\(730\) 0 0
\(731\) 46.3992 1.71614
\(732\) 0 0
\(733\) 38.2101 1.41132 0.705661 0.708549i \(-0.250650\pi\)
0.705661 + 0.708549i \(0.250650\pi\)
\(734\) 0 0
\(735\) −1.32400 −0.0488363
\(736\) 0 0
\(737\) 16.7862 0.618326
\(738\) 0 0
\(739\) −20.3072 −0.747011 −0.373505 0.927628i \(-0.621844\pi\)
−0.373505 + 0.927628i \(0.621844\pi\)
\(740\) 0 0
\(741\) 6.34609 0.233129
\(742\) 0 0
\(743\) −18.4200 −0.675763 −0.337882 0.941189i \(-0.609710\pi\)
−0.337882 + 0.941189i \(0.609710\pi\)
\(744\) 0 0
\(745\) −2.77105 −0.101523
\(746\) 0 0
\(747\) −2.43189 −0.0889780
\(748\) 0 0
\(749\) 4.67671 0.170883
\(750\) 0 0
\(751\) −21.5352 −0.785832 −0.392916 0.919574i \(-0.628534\pi\)
−0.392916 + 0.919574i \(0.628534\pi\)
\(752\) 0 0
\(753\) 23.9948 0.874421
\(754\) 0 0
\(755\) 12.1266 0.441332
\(756\) 0 0
\(757\) −18.6537 −0.677980 −0.338990 0.940790i \(-0.610085\pi\)
−0.338990 + 0.940790i \(0.610085\pi\)
\(758\) 0 0
\(759\) −15.8438 −0.575095
\(760\) 0 0
\(761\) 12.1471 0.440330 0.220165 0.975463i \(-0.429340\pi\)
0.220165 + 0.975463i \(0.429340\pi\)
\(762\) 0 0
\(763\) −6.98815 −0.252988
\(764\) 0 0
\(765\) −4.89573 −0.177006
\(766\) 0 0
\(767\) 4.69502 0.169527
\(768\) 0 0
\(769\) −19.8123 −0.714451 −0.357225 0.934018i \(-0.616277\pi\)
−0.357225 + 0.934018i \(0.616277\pi\)
\(770\) 0 0
\(771\) 17.7976 0.640965
\(772\) 0 0
\(773\) −50.7217 −1.82433 −0.912167 0.409819i \(-0.865592\pi\)
−0.912167 + 0.409819i \(0.865592\pi\)
\(774\) 0 0
\(775\) 8.37387 0.300798
\(776\) 0 0
\(777\) −2.24704 −0.0806120
\(778\) 0 0
\(779\) −23.2235 −0.832068
\(780\) 0 0
\(781\) −1.34201 −0.0480210
\(782\) 0 0
\(783\) −24.3020 −0.868482
\(784\) 0 0
\(785\) −6.54465 −0.233588
\(786\) 0 0
\(787\) −3.14961 −0.112272 −0.0561358 0.998423i \(-0.517878\pi\)
−0.0561358 + 0.998423i \(0.517878\pi\)
\(788\) 0 0
\(789\) −36.4779 −1.29865
\(790\) 0 0
\(791\) −2.72303 −0.0968198
\(792\) 0 0
\(793\) 5.37102 0.190731
\(794\) 0 0
\(795\) 11.9820 0.424958
\(796\) 0 0
\(797\) −3.38503 −0.119904 −0.0599520 0.998201i \(-0.519095\pi\)
−0.0599520 + 0.998201i \(0.519095\pi\)
\(798\) 0 0
\(799\) 42.4818 1.50290
\(800\) 0 0
\(801\) 9.87648 0.348968
\(802\) 0 0
\(803\) 10.8751 0.383773
\(804\) 0 0
\(805\) 4.70002 0.165654
\(806\) 0 0
\(807\) −21.8632 −0.769623
\(808\) 0 0
\(809\) −4.89543 −0.172114 −0.0860571 0.996290i \(-0.527427\pi\)
−0.0860571 + 0.996290i \(0.527427\pi\)
\(810\) 0 0
\(811\) −21.6544 −0.760389 −0.380194 0.924907i \(-0.624143\pi\)
−0.380194 + 0.924907i \(0.624143\pi\)
\(812\) 0 0
\(813\) −0.0607248 −0.00212971
\(814\) 0 0
\(815\) 18.1736 0.636595
\(816\) 0 0
\(817\) 56.6490 1.98190
\(818\) 0 0
\(819\) 1.24704 0.0435750
\(820\) 0 0
\(821\) 7.35956 0.256850 0.128425 0.991719i \(-0.459008\pi\)
0.128425 + 0.991719i \(0.459008\pi\)
\(822\) 0 0
\(823\) 36.8948 1.28607 0.643035 0.765837i \(-0.277675\pi\)
0.643035 + 0.765837i \(0.277675\pi\)
\(824\) 0 0
\(825\) 3.37102 0.117364
\(826\) 0 0
\(827\) −50.2841 −1.74855 −0.874275 0.485431i \(-0.838663\pi\)
−0.874275 + 0.485431i \(0.838663\pi\)
\(828\) 0 0
\(829\) −27.7254 −0.962944 −0.481472 0.876461i \(-0.659898\pi\)
−0.481472 + 0.876461i \(0.659898\pi\)
\(830\) 0 0
\(831\) 33.4144 1.15913
\(832\) 0 0
\(833\) −3.92589 −0.136024
\(834\) 0 0
\(835\) 16.9515 0.586632
\(836\) 0 0
\(837\) −47.0868 −1.62756
\(838\) 0 0
\(839\) 39.6877 1.37017 0.685086 0.728462i \(-0.259765\pi\)
0.685086 + 0.728462i \(0.259765\pi\)
\(840\) 0 0
\(841\) −10.3216 −0.355918
\(842\) 0 0
\(843\) 21.7714 0.749848
\(844\) 0 0
\(845\) −1.00000 −0.0344010
\(846\) 0 0
\(847\) −4.51739 −0.155219
\(848\) 0 0
\(849\) 9.74511 0.334451
\(850\) 0 0
\(851\) 7.97669 0.273438
\(852\) 0 0
\(853\) 0.599513 0.0205269 0.0102635 0.999947i \(-0.496733\pi\)
0.0102635 + 0.999947i \(0.496733\pi\)
\(854\) 0 0
\(855\) −5.97721 −0.204416
\(856\) 0 0
\(857\) −37.7333 −1.28894 −0.644472 0.764628i \(-0.722923\pi\)
−0.644472 + 0.764628i \(0.722923\pi\)
\(858\) 0 0
\(859\) 14.5805 0.497481 0.248740 0.968570i \(-0.419983\pi\)
0.248740 + 0.968570i \(0.419983\pi\)
\(860\) 0 0
\(861\) 6.41497 0.218621
\(862\) 0 0
\(863\) −35.9402 −1.22342 −0.611709 0.791083i \(-0.709518\pi\)
−0.611709 + 0.791083i \(0.709518\pi\)
\(864\) 0 0
\(865\) 11.8202 0.401900
\(866\) 0 0
\(867\) −2.10166 −0.0713763
\(868\) 0 0
\(869\) −38.4129 −1.30307
\(870\) 0 0
\(871\) −6.59289 −0.223392
\(872\) 0 0
\(873\) −5.39574 −0.182618
\(874\) 0 0
\(875\) −1.00000 −0.0338062
\(876\) 0 0
\(877\) 43.3174 1.46272 0.731362 0.681989i \(-0.238885\pi\)
0.731362 + 0.681989i \(0.238885\pi\)
\(878\) 0 0
\(879\) −27.5977 −0.930846
\(880\) 0 0
\(881\) −33.5858 −1.13154 −0.565768 0.824565i \(-0.691420\pi\)
−0.565768 + 0.824565i \(0.691420\pi\)
\(882\) 0 0
\(883\) −23.6436 −0.795670 −0.397835 0.917457i \(-0.630238\pi\)
−0.397835 + 0.917457i \(0.630238\pi\)
\(884\) 0 0
\(885\) 6.21618 0.208955
\(886\) 0 0
\(887\) 12.7330 0.427534 0.213767 0.976885i \(-0.431427\pi\)
0.213767 + 0.976885i \(0.431427\pi\)
\(888\) 0 0
\(889\) −1.05388 −0.0353460
\(890\) 0 0
\(891\) −9.43021 −0.315924
\(892\) 0 0
\(893\) 51.8661 1.73563
\(894\) 0 0
\(895\) −13.5545 −0.453076
\(896\) 0 0
\(897\) 6.22280 0.207773
\(898\) 0 0
\(899\) 36.1906 1.20702
\(900\) 0 0
\(901\) 35.5288 1.18364
\(902\) 0 0
\(903\) −15.6480 −0.520733
\(904\) 0 0
\(905\) 13.9767 0.464601
\(906\) 0 0
\(907\) −17.7514 −0.589424 −0.294712 0.955586i \(-0.595224\pi\)
−0.294712 + 0.955586i \(0.595224\pi\)
\(908\) 0 0
\(909\) −5.62798 −0.186668
\(910\) 0 0
\(911\) 7.76256 0.257185 0.128593 0.991698i \(-0.458954\pi\)
0.128593 + 0.991698i \(0.458954\pi\)
\(912\) 0 0
\(913\) 4.96522 0.164325
\(914\) 0 0
\(915\) 7.11121 0.235089
\(916\) 0 0
\(917\) 5.40758 0.178574
\(918\) 0 0
\(919\) 36.5271 1.20492 0.602459 0.798150i \(-0.294188\pi\)
0.602459 + 0.798150i \(0.294188\pi\)
\(920\) 0 0
\(921\) −0.667387 −0.0219911
\(922\) 0 0
\(923\) 0.527086 0.0173492
\(924\) 0 0
\(925\) −1.69716 −0.0558024
\(926\) 0 0
\(927\) −17.8261 −0.585486
\(928\) 0 0
\(929\) −51.2973 −1.68301 −0.841505 0.540249i \(-0.818330\pi\)
−0.841505 + 0.540249i \(0.818330\pi\)
\(930\) 0 0
\(931\) −4.79313 −0.157089
\(932\) 0 0
\(933\) −20.7682 −0.679921
\(934\) 0 0
\(935\) 9.99571 0.326895
\(936\) 0 0
\(937\) 16.6195 0.542935 0.271467 0.962448i \(-0.412491\pi\)
0.271467 + 0.962448i \(0.412491\pi\)
\(938\) 0 0
\(939\) 0.301602 0.00984240
\(940\) 0 0
\(941\) −2.23375 −0.0728180 −0.0364090 0.999337i \(-0.511592\pi\)
−0.0364090 + 0.999337i \(0.511592\pi\)
\(942\) 0 0
\(943\) −22.7723 −0.741569
\(944\) 0 0
\(945\) 5.62306 0.182918
\(946\) 0 0
\(947\) −40.7174 −1.32314 −0.661568 0.749885i \(-0.730109\pi\)
−0.661568 + 0.749885i \(0.730109\pi\)
\(948\) 0 0
\(949\) −4.27128 −0.138651
\(950\) 0 0
\(951\) 7.63084 0.247447
\(952\) 0 0
\(953\) 31.6803 1.02623 0.513113 0.858321i \(-0.328492\pi\)
0.513113 + 0.858321i \(0.328492\pi\)
\(954\) 0 0
\(955\) 16.2160 0.524736
\(956\) 0 0
\(957\) 14.5690 0.470950
\(958\) 0 0
\(959\) −11.5124 −0.371754
\(960\) 0 0
\(961\) 39.1217 1.26199
\(962\) 0 0
\(963\) −5.83203 −0.187934
\(964\) 0 0
\(965\) 9.37009 0.301634
\(966\) 0 0
\(967\) −37.8987 −1.21874 −0.609370 0.792886i \(-0.708578\pi\)
−0.609370 + 0.792886i \(0.708578\pi\)
\(968\) 0 0
\(969\) 24.9141 0.800355
\(970\) 0 0
\(971\) 13.9824 0.448716 0.224358 0.974507i \(-0.427971\pi\)
0.224358 + 0.974507i \(0.427971\pi\)
\(972\) 0 0
\(973\) 10.4898 0.336287
\(974\) 0 0
\(975\) −1.32400 −0.0424018
\(976\) 0 0
\(977\) 41.7478 1.33563 0.667816 0.744327i \(-0.267229\pi\)
0.667816 + 0.744327i \(0.267229\pi\)
\(978\) 0 0
\(979\) −20.1650 −0.644476
\(980\) 0 0
\(981\) 8.71447 0.278232
\(982\) 0 0
\(983\) −32.4144 −1.03386 −0.516929 0.856028i \(-0.672925\pi\)
−0.516929 + 0.856028i \(0.672925\pi\)
\(984\) 0 0
\(985\) 1.21064 0.0385742
\(986\) 0 0
\(987\) −14.3268 −0.456029
\(988\) 0 0
\(989\) 55.5484 1.76634
\(990\) 0 0
\(991\) −22.5373 −0.715922 −0.357961 0.933737i \(-0.616528\pi\)
−0.357961 + 0.933737i \(0.616528\pi\)
\(992\) 0 0
\(993\) 1.05947 0.0336213
\(994\) 0 0
\(995\) −17.5938 −0.557762
\(996\) 0 0
\(997\) −34.0690 −1.07898 −0.539488 0.841994i \(-0.681382\pi\)
−0.539488 + 0.841994i \(0.681382\pi\)
\(998\) 0 0
\(999\) 9.54325 0.301935
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 3640.2.a.y.1.4 5
4.3 odd 2 7280.2.a.cc.1.2 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3640.2.a.y.1.4 5 1.1 even 1 trivial
7280.2.a.cc.1.2 5 4.3 odd 2