Properties

Label 3640.2.a.p.1.3
Level $3640$
Weight $2$
Character 3640.1
Self dual yes
Analytic conductor $29.066$
Analytic rank $0$
Dimension $3$
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: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.1101.1
Defining polynomial: \( x^{3} - x^{2} - 9x + 12 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-3.11903\) of defining polynomial
Character \(\chi\) \(=\) 3640.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.11903 q^{3} -1.00000 q^{5} +1.00000 q^{7} +6.72833 q^{9} +O(q^{10})\) \(q+3.11903 q^{3} -1.00000 q^{5} +1.00000 q^{7} +6.72833 q^{9} -1.00000 q^{13} -3.11903 q^{15} +3.72833 q^{17} +1.72833 q^{19} +3.11903 q^{21} +1.21860 q^{23} +1.00000 q^{25} +11.6288 q^{27} -6.33763 q^{29} +7.11903 q^{31} -1.00000 q^{35} +3.90043 q^{37} -3.11903 q^{39} +3.72833 q^{41} -10.2381 q^{43} -6.72833 q^{45} +2.78140 q^{47} +1.00000 q^{49} +11.6288 q^{51} +2.00000 q^{53} +5.39070 q^{57} +13.3571 q^{59} -10.0000 q^{61} +6.72833 q^{63} +1.00000 q^{65} -3.29112 q^{67} +3.80085 q^{69} -6.23805 q^{71} +15.6947 q^{73} +3.11903 q^{75} -1.72833 q^{79} +16.0854 q^{81} -1.21860 q^{83} -3.72833 q^{85} -19.7672 q^{87} +10.1385 q^{89} -1.00000 q^{91} +22.2044 q^{93} -1.72833 q^{95} -5.80085 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - q^{3} - 3 q^{5} + 3 q^{7} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - q^{3} - 3 q^{5} + 3 q^{7} + 10 q^{9} - 3 q^{13} + q^{15} + q^{17} - 5 q^{19} - q^{21} + 4 q^{23} + 3 q^{25} + 14 q^{27} - 9 q^{29} + 11 q^{31} - 3 q^{35} + q^{37} + q^{39} + q^{41} - 10 q^{43} - 10 q^{45} + 8 q^{47} + 3 q^{49} + 14 q^{51} + 6 q^{53} + 16 q^{57} + 9 q^{59} - 30 q^{61} + 10 q^{63} + 3 q^{65} + q^{67} - 10 q^{69} + 2 q^{71} + 6 q^{73} - q^{75} + 5 q^{79} + 7 q^{81} - 4 q^{83} - q^{85} - 7 q^{87} - q^{89} - 3 q^{91} + 15 q^{93} + 5 q^{95} + 4 q^{97}+O(q^{100}) \) 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
\(3\) 3.11903 1.80077 0.900385 0.435093i \(-0.143285\pi\)
0.900385 + 0.435093i \(0.143285\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) 6.72833 2.24278
\(10\) 0 0
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −3.11903 −0.805329
\(16\) 0 0
\(17\) 3.72833 0.904252 0.452126 0.891954i \(-0.350666\pi\)
0.452126 + 0.891954i \(0.350666\pi\)
\(18\) 0 0
\(19\) 1.72833 0.396505 0.198253 0.980151i \(-0.436473\pi\)
0.198253 + 0.980151i \(0.436473\pi\)
\(20\) 0 0
\(21\) 3.11903 0.680627
\(22\) 0 0
\(23\) 1.21860 0.254096 0.127048 0.991897i \(-0.459450\pi\)
0.127048 + 0.991897i \(0.459450\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 11.6288 2.23795
\(28\) 0 0
\(29\) −6.33763 −1.17687 −0.588434 0.808545i \(-0.700255\pi\)
−0.588434 + 0.808545i \(0.700255\pi\)
\(30\) 0 0
\(31\) 7.11903 1.27861 0.639307 0.768951i \(-0.279221\pi\)
0.639307 + 0.768951i \(0.279221\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1.00000 −0.169031
\(36\) 0 0
\(37\) 3.90043 0.641226 0.320613 0.947210i \(-0.396111\pi\)
0.320613 + 0.947210i \(0.396111\pi\)
\(38\) 0 0
\(39\) −3.11903 −0.499444
\(40\) 0 0
\(41\) 3.72833 0.582267 0.291133 0.956682i \(-0.405968\pi\)
0.291133 + 0.956682i \(0.405968\pi\)
\(42\) 0 0
\(43\) −10.2381 −1.56129 −0.780644 0.624976i \(-0.785109\pi\)
−0.780644 + 0.624976i \(0.785109\pi\)
\(44\) 0 0
\(45\) −6.72833 −1.00300
\(46\) 0 0
\(47\) 2.78140 0.405709 0.202854 0.979209i \(-0.434978\pi\)
0.202854 + 0.979209i \(0.434978\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 11.6288 1.62835
\(52\) 0 0
\(53\) 2.00000 0.274721 0.137361 0.990521i \(-0.456138\pi\)
0.137361 + 0.990521i \(0.456138\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 5.39070 0.714016
\(58\) 0 0
\(59\) 13.3571 1.73894 0.869472 0.493982i \(-0.164459\pi\)
0.869472 + 0.493982i \(0.164459\pi\)
\(60\) 0 0
\(61\) −10.0000 −1.28037 −0.640184 0.768221i \(-0.721142\pi\)
−0.640184 + 0.768221i \(0.721142\pi\)
\(62\) 0 0
\(63\) 6.72833 0.847690
\(64\) 0 0
\(65\) 1.00000 0.124035
\(66\) 0 0
\(67\) −3.29112 −0.402075 −0.201037 0.979584i \(-0.564431\pi\)
−0.201037 + 0.979584i \(0.564431\pi\)
\(68\) 0 0
\(69\) 3.80085 0.457569
\(70\) 0 0
\(71\) −6.23805 −0.740321 −0.370160 0.928968i \(-0.620697\pi\)
−0.370160 + 0.928968i \(0.620697\pi\)
\(72\) 0 0
\(73\) 15.6947 1.83693 0.918463 0.395506i \(-0.129431\pi\)
0.918463 + 0.395506i \(0.129431\pi\)
\(74\) 0 0
\(75\) 3.11903 0.360154
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −1.72833 −0.194452 −0.0972260 0.995262i \(-0.530997\pi\)
−0.0972260 + 0.995262i \(0.530997\pi\)
\(80\) 0 0
\(81\) 16.0854 1.78727
\(82\) 0 0
\(83\) −1.21860 −0.133759 −0.0668794 0.997761i \(-0.521304\pi\)
−0.0668794 + 0.997761i \(0.521304\pi\)
\(84\) 0 0
\(85\) −3.72833 −0.404394
\(86\) 0 0
\(87\) −19.7672 −2.11927
\(88\) 0 0
\(89\) 10.1385 1.07468 0.537338 0.843367i \(-0.319430\pi\)
0.537338 + 0.843367i \(0.319430\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) 22.2044 2.30249
\(94\) 0 0
\(95\) −1.72833 −0.177323
\(96\) 0 0
\(97\) −5.80085 −0.588987 −0.294494 0.955653i \(-0.595151\pi\)
−0.294494 + 0.955653i \(0.595151\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 3.21860 0.320263 0.160131 0.987096i \(-0.448808\pi\)
0.160131 + 0.987096i \(0.448808\pi\)
\(102\) 0 0
\(103\) 3.29112 0.324284 0.162142 0.986767i \(-0.448160\pi\)
0.162142 + 0.986767i \(0.448160\pi\)
\(104\) 0 0
\(105\) −3.11903 −0.304386
\(106\) 0 0
\(107\) −5.01945 −0.485249 −0.242624 0.970120i \(-0.578008\pi\)
−0.242624 + 0.970120i \(0.578008\pi\)
\(108\) 0 0
\(109\) −3.56280 −0.341254 −0.170627 0.985336i \(-0.554579\pi\)
−0.170627 + 0.985336i \(0.554579\pi\)
\(110\) 0 0
\(111\) 12.1655 1.15470
\(112\) 0 0
\(113\) 13.8009 1.29827 0.649137 0.760671i \(-0.275130\pi\)
0.649137 + 0.760671i \(0.275130\pi\)
\(114\) 0 0
\(115\) −1.21860 −0.113635
\(116\) 0 0
\(117\) −6.72833 −0.622034
\(118\) 0 0
\(119\) 3.72833 0.341775
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) 0 0
\(123\) 11.6288 1.04853
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −5.69471 −0.505324 −0.252662 0.967555i \(-0.581306\pi\)
−0.252662 + 0.967555i \(0.581306\pi\)
\(128\) 0 0
\(129\) −31.9328 −2.81152
\(130\) 0 0
\(131\) −13.6947 −1.19651 −0.598256 0.801305i \(-0.704139\pi\)
−0.598256 + 0.801305i \(0.704139\pi\)
\(132\) 0 0
\(133\) 1.72833 0.149865
\(134\) 0 0
\(135\) −11.6288 −1.00084
\(136\) 0 0
\(137\) 9.66237 0.825512 0.412756 0.910842i \(-0.364566\pi\)
0.412756 + 0.910842i \(0.364566\pi\)
\(138\) 0 0
\(139\) −7.45665 −0.632465 −0.316233 0.948682i \(-0.602418\pi\)
−0.316233 + 0.948682i \(0.602418\pi\)
\(140\) 0 0
\(141\) 8.67526 0.730588
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 6.33763 0.526311
\(146\) 0 0
\(147\) 3.11903 0.257253
\(148\) 0 0
\(149\) 2.00000 0.163846 0.0819232 0.996639i \(-0.473894\pi\)
0.0819232 + 0.996639i \(0.473894\pi\)
\(150\) 0 0
\(151\) −0.675256 −0.0549516 −0.0274758 0.999622i \(-0.508747\pi\)
−0.0274758 + 0.999622i \(0.508747\pi\)
\(152\) 0 0
\(153\) 25.0854 2.02803
\(154\) 0 0
\(155\) −7.11903 −0.571814
\(156\) 0 0
\(157\) −16.5757 −1.32288 −0.661442 0.749997i \(-0.730055\pi\)
−0.661442 + 0.749997i \(0.730055\pi\)
\(158\) 0 0
\(159\) 6.23805 0.494710
\(160\) 0 0
\(161\) 1.21860 0.0960392
\(162\) 0 0
\(163\) 4.88097 0.382307 0.191154 0.981560i \(-0.438777\pi\)
0.191154 + 0.981560i \(0.438777\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −21.1514 −1.63674 −0.818371 0.574691i \(-0.805122\pi\)
−0.818371 + 0.574691i \(0.805122\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 11.6288 0.889273
\(172\) 0 0
\(173\) 7.01288 0.533180 0.266590 0.963810i \(-0.414103\pi\)
0.266590 + 0.963810i \(0.414103\pi\)
\(174\) 0 0
\(175\) 1.00000 0.0755929
\(176\) 0 0
\(177\) 41.6611 3.13144
\(178\) 0 0
\(179\) 13.7283 1.02610 0.513052 0.858358i \(-0.328515\pi\)
0.513052 + 0.858358i \(0.328515\pi\)
\(180\) 0 0
\(181\) 9.80085 0.728491 0.364246 0.931303i \(-0.381327\pi\)
0.364246 + 0.931303i \(0.381327\pi\)
\(182\) 0 0
\(183\) −31.1903 −2.30565
\(184\) 0 0
\(185\) −3.90043 −0.286765
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 11.6288 0.845867
\(190\) 0 0
\(191\) 8.88097 0.642605 0.321302 0.946977i \(-0.395879\pi\)
0.321302 + 0.946977i \(0.395879\pi\)
\(192\) 0 0
\(193\) 27.1850 1.95682 0.978409 0.206678i \(-0.0662654\pi\)
0.978409 + 0.206678i \(0.0662654\pi\)
\(194\) 0 0
\(195\) 3.11903 0.223358
\(196\) 0 0
\(197\) −19.2898 −1.37434 −0.687172 0.726495i \(-0.741148\pi\)
−0.687172 + 0.726495i \(0.741148\pi\)
\(198\) 0 0
\(199\) 11.8009 0.836540 0.418270 0.908323i \(-0.362637\pi\)
0.418270 + 0.908323i \(0.362637\pi\)
\(200\) 0 0
\(201\) −10.2651 −0.724045
\(202\) 0 0
\(203\) −6.33763 −0.444814
\(204\) 0 0
\(205\) −3.72833 −0.260398
\(206\) 0 0
\(207\) 8.19915 0.569880
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −15.7672 −1.08546 −0.542730 0.839907i \(-0.682609\pi\)
−0.542730 + 0.839907i \(0.682609\pi\)
\(212\) 0 0
\(213\) −19.4567 −1.33315
\(214\) 0 0
\(215\) 10.2381 0.698229
\(216\) 0 0
\(217\) 7.11903 0.483271
\(218\) 0 0
\(219\) 48.9522 3.30788
\(220\) 0 0
\(221\) −3.72833 −0.250794
\(222\) 0 0
\(223\) −1.01945 −0.0682675 −0.0341338 0.999417i \(-0.510867\pi\)
−0.0341338 + 0.999417i \(0.510867\pi\)
\(224\) 0 0
\(225\) 6.72833 0.448555
\(226\) 0 0
\(227\) 9.21860 0.611860 0.305930 0.952054i \(-0.401033\pi\)
0.305930 + 0.952054i \(0.401033\pi\)
\(228\) 0 0
\(229\) −4.27167 −0.282280 −0.141140 0.989990i \(-0.545077\pi\)
−0.141140 + 0.989990i \(0.545077\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −8.78140 −0.575289 −0.287644 0.957737i \(-0.592872\pi\)
−0.287644 + 0.957737i \(0.592872\pi\)
\(234\) 0 0
\(235\) −2.78140 −0.181438
\(236\) 0 0
\(237\) −5.39070 −0.350164
\(238\) 0 0
\(239\) 2.78140 0.179914 0.0899569 0.995946i \(-0.471327\pi\)
0.0899569 + 0.995946i \(0.471327\pi\)
\(240\) 0 0
\(241\) −14.6416 −0.943151 −0.471575 0.881826i \(-0.656314\pi\)
−0.471575 + 0.881826i \(0.656314\pi\)
\(242\) 0 0
\(243\) 15.2846 0.980505
\(244\) 0 0
\(245\) −1.00000 −0.0638877
\(246\) 0 0
\(247\) −1.72833 −0.109971
\(248\) 0 0
\(249\) −3.80085 −0.240869
\(250\) 0 0
\(251\) 25.1514 1.58754 0.793770 0.608218i \(-0.208115\pi\)
0.793770 + 0.608218i \(0.208115\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) −11.6288 −0.728221
\(256\) 0 0
\(257\) −14.9522 −0.932693 −0.466347 0.884602i \(-0.654430\pi\)
−0.466347 + 0.884602i \(0.654430\pi\)
\(258\) 0 0
\(259\) 3.90043 0.242361
\(260\) 0 0
\(261\) −42.6416 −2.63945
\(262\) 0 0
\(263\) 14.7814 0.911460 0.455730 0.890118i \(-0.349378\pi\)
0.455730 + 0.890118i \(0.349378\pi\)
\(264\) 0 0
\(265\) −2.00000 −0.122859
\(266\) 0 0
\(267\) 31.6222 1.93525
\(268\) 0 0
\(269\) −17.2575 −1.05221 −0.526104 0.850420i \(-0.676348\pi\)
−0.526104 + 0.850420i \(0.676348\pi\)
\(270\) 0 0
\(271\) −5.56280 −0.337916 −0.168958 0.985623i \(-0.554040\pi\)
−0.168958 + 0.985623i \(0.554040\pi\)
\(272\) 0 0
\(273\) −3.11903 −0.188772
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −21.2575 −1.27724 −0.638620 0.769522i \(-0.720494\pi\)
−0.638620 + 0.769522i \(0.720494\pi\)
\(278\) 0 0
\(279\) 47.8991 2.86765
\(280\) 0 0
\(281\) 10.3311 0.616299 0.308150 0.951338i \(-0.400290\pi\)
0.308150 + 0.951338i \(0.400290\pi\)
\(282\) 0 0
\(283\) −31.7672 −1.88837 −0.944183 0.329422i \(-0.893146\pi\)
−0.944183 + 0.329422i \(0.893146\pi\)
\(284\) 0 0
\(285\) −5.39070 −0.319317
\(286\) 0 0
\(287\) 3.72833 0.220076
\(288\) 0 0
\(289\) −3.09957 −0.182328
\(290\) 0 0
\(291\) −18.0930 −1.06063
\(292\) 0 0
\(293\) −15.0195 −0.877446 −0.438723 0.898622i \(-0.644569\pi\)
−0.438723 + 0.898622i \(0.644569\pi\)
\(294\) 0 0
\(295\) −13.3571 −0.777679
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1.21860 −0.0704735
\(300\) 0 0
\(301\) −10.2381 −0.590112
\(302\) 0 0
\(303\) 10.0389 0.576720
\(304\) 0 0
\(305\) 10.0000 0.572598
\(306\) 0 0
\(307\) 9.21860 0.526133 0.263067 0.964778i \(-0.415266\pi\)
0.263067 + 0.964778i \(0.415266\pi\)
\(308\) 0 0
\(309\) 10.2651 0.583961
\(310\) 0 0
\(311\) −21.4956 −1.21890 −0.609451 0.792824i \(-0.708610\pi\)
−0.609451 + 0.792824i \(0.708610\pi\)
\(312\) 0 0
\(313\) −3.01288 −0.170298 −0.0851491 0.996368i \(-0.527137\pi\)
−0.0851491 + 0.996368i \(0.527137\pi\)
\(314\) 0 0
\(315\) −6.72833 −0.379098
\(316\) 0 0
\(317\) −20.9133 −1.17461 −0.587304 0.809366i \(-0.699811\pi\)
−0.587304 + 0.809366i \(0.699811\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −15.6558 −0.873822
\(322\) 0 0
\(323\) 6.44377 0.358541
\(324\) 0 0
\(325\) −1.00000 −0.0554700
\(326\) 0 0
\(327\) −11.1125 −0.614520
\(328\) 0 0
\(329\) 2.78140 0.153343
\(330\) 0 0
\(331\) −5.56280 −0.305759 −0.152879 0.988245i \(-0.548855\pi\)
−0.152879 + 0.988245i \(0.548855\pi\)
\(332\) 0 0
\(333\) 26.2433 1.43813
\(334\) 0 0
\(335\) 3.29112 0.179813
\(336\) 0 0
\(337\) −10.4761 −0.570670 −0.285335 0.958428i \(-0.592105\pi\)
−0.285335 + 0.958428i \(0.592105\pi\)
\(338\) 0 0
\(339\) 43.0452 2.33790
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) −3.80085 −0.204631
\(346\) 0 0
\(347\) −18.5691 −0.996842 −0.498421 0.866935i \(-0.666087\pi\)
−0.498421 + 0.866935i \(0.666087\pi\)
\(348\) 0 0
\(349\) 27.4890 1.47145 0.735726 0.677279i \(-0.236841\pi\)
0.735726 + 0.677279i \(0.236841\pi\)
\(350\) 0 0
\(351\) −11.6288 −0.620697
\(352\) 0 0
\(353\) −37.3894 −1.99004 −0.995019 0.0996863i \(-0.968216\pi\)
−0.995019 + 0.0996863i \(0.968216\pi\)
\(354\) 0 0
\(355\) 6.23805 0.331081
\(356\) 0 0
\(357\) 11.6288 0.615459
\(358\) 0 0
\(359\) 8.33106 0.439697 0.219848 0.975534i \(-0.429444\pi\)
0.219848 + 0.975534i \(0.429444\pi\)
\(360\) 0 0
\(361\) −16.0129 −0.842783
\(362\) 0 0
\(363\) −34.3093 −1.80077
\(364\) 0 0
\(365\) −15.6947 −0.821499
\(366\) 0 0
\(367\) 17.5628 0.916771 0.458385 0.888754i \(-0.348428\pi\)
0.458385 + 0.888754i \(0.348428\pi\)
\(368\) 0 0
\(369\) 25.0854 1.30589
\(370\) 0 0
\(371\) 2.00000 0.103835
\(372\) 0 0
\(373\) 33.1903 1.71853 0.859263 0.511533i \(-0.170922\pi\)
0.859263 + 0.511533i \(0.170922\pi\)
\(374\) 0 0
\(375\) −3.11903 −0.161066
\(376\) 0 0
\(377\) 6.33763 0.326404
\(378\) 0 0
\(379\) 0.344196 0.0176801 0.00884007 0.999961i \(-0.497186\pi\)
0.00884007 + 0.999961i \(0.497186\pi\)
\(380\) 0 0
\(381\) −17.7619 −0.909972
\(382\) 0 0
\(383\) −31.9328 −1.63169 −0.815844 0.578272i \(-0.803727\pi\)
−0.815844 + 0.578272i \(0.803727\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −68.8850 −3.50162
\(388\) 0 0
\(389\) −23.1177 −1.17212 −0.586058 0.810269i \(-0.699321\pi\)
−0.586058 + 0.810269i \(0.699321\pi\)
\(390\) 0 0
\(391\) 4.54335 0.229767
\(392\) 0 0
\(393\) −42.7142 −2.15464
\(394\) 0 0
\(395\) 1.72833 0.0869616
\(396\) 0 0
\(397\) −29.9328 −1.50228 −0.751141 0.660142i \(-0.770496\pi\)
−0.751141 + 0.660142i \(0.770496\pi\)
\(398\) 0 0
\(399\) 5.39070 0.269873
\(400\) 0 0
\(401\) 21.0584 1.05160 0.525802 0.850607i \(-0.323765\pi\)
0.525802 + 0.850607i \(0.323765\pi\)
\(402\) 0 0
\(403\) −7.11903 −0.354624
\(404\) 0 0
\(405\) −16.0854 −0.799290
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −36.9133 −1.82525 −0.912623 0.408803i \(-0.865946\pi\)
−0.912623 + 0.408803i \(0.865946\pi\)
\(410\) 0 0
\(411\) 30.1372 1.48656
\(412\) 0 0
\(413\) 13.3571 0.657259
\(414\) 0 0
\(415\) 1.21860 0.0598188
\(416\) 0 0
\(417\) −23.2575 −1.13892
\(418\) 0 0
\(419\) 0.543345 0.0265441 0.0132721 0.999912i \(-0.495775\pi\)
0.0132721 + 0.999912i \(0.495775\pi\)
\(420\) 0 0
\(421\) −18.4761 −0.900470 −0.450235 0.892910i \(-0.648660\pi\)
−0.450235 + 0.892910i \(0.648660\pi\)
\(422\) 0 0
\(423\) 18.7142 0.909914
\(424\) 0 0
\(425\) 3.72833 0.180850
\(426\) 0 0
\(427\) −10.0000 −0.483934
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −14.5822 −0.702402 −0.351201 0.936300i \(-0.614227\pi\)
−0.351201 + 0.936300i \(0.614227\pi\)
\(432\) 0 0
\(433\) −14.7089 −0.706863 −0.353432 0.935460i \(-0.614985\pi\)
−0.353432 + 0.935460i \(0.614985\pi\)
\(434\) 0 0
\(435\) 19.7672 0.947766
\(436\) 0 0
\(437\) 2.10614 0.100750
\(438\) 0 0
\(439\) 6.91331 0.329954 0.164977 0.986297i \(-0.447245\pi\)
0.164977 + 0.986297i \(0.447245\pi\)
\(440\) 0 0
\(441\) 6.72833 0.320397
\(442\) 0 0
\(443\) −1.21860 −0.0578975 −0.0289488 0.999581i \(-0.509216\pi\)
−0.0289488 + 0.999581i \(0.509216\pi\)
\(444\) 0 0
\(445\) −10.1385 −0.480610
\(446\) 0 0
\(447\) 6.23805 0.295050
\(448\) 0 0
\(449\) 6.19915 0.292556 0.146278 0.989244i \(-0.453271\pi\)
0.146278 + 0.989244i \(0.453271\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −2.10614 −0.0989552
\(454\) 0 0
\(455\) 1.00000 0.0468807
\(456\) 0 0
\(457\) 1.66237 0.0777625 0.0388812 0.999244i \(-0.487621\pi\)
0.0388812 + 0.999244i \(0.487621\pi\)
\(458\) 0 0
\(459\) 43.3558 2.02368
\(460\) 0 0
\(461\) 31.2898 1.45731 0.728657 0.684879i \(-0.240145\pi\)
0.728657 + 0.684879i \(0.240145\pi\)
\(462\) 0 0
\(463\) −16.6416 −0.773402 −0.386701 0.922205i \(-0.626386\pi\)
−0.386701 + 0.922205i \(0.626386\pi\)
\(464\) 0 0
\(465\) −22.2044 −1.02971
\(466\) 0 0
\(467\) 32.0983 1.48533 0.742666 0.669662i \(-0.233561\pi\)
0.742666 + 0.669662i \(0.233561\pi\)
\(468\) 0 0
\(469\) −3.29112 −0.151970
\(470\) 0 0
\(471\) −51.7000 −2.38221
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 1.72833 0.0793011
\(476\) 0 0
\(477\) 13.4567 0.616138
\(478\) 0 0
\(479\) 17.5562 0.802165 0.401082 0.916042i \(-0.368634\pi\)
0.401082 + 0.916042i \(0.368634\pi\)
\(480\) 0 0
\(481\) −3.90043 −0.177844
\(482\) 0 0
\(483\) 3.80085 0.172945
\(484\) 0 0
\(485\) 5.80085 0.263403
\(486\) 0 0
\(487\) 4.27039 0.193510 0.0967549 0.995308i \(-0.469154\pi\)
0.0967549 + 0.995308i \(0.469154\pi\)
\(488\) 0 0
\(489\) 15.2239 0.688448
\(490\) 0 0
\(491\) 14.0389 0.633567 0.316783 0.948498i \(-0.397397\pi\)
0.316783 + 0.948498i \(0.397397\pi\)
\(492\) 0 0
\(493\) −23.6288 −1.06419
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −6.23805 −0.279815
\(498\) 0 0
\(499\) −33.3505 −1.49297 −0.746487 0.665400i \(-0.768261\pi\)
−0.746487 + 0.665400i \(0.768261\pi\)
\(500\) 0 0
\(501\) −65.9717 −2.94740
\(502\) 0 0
\(503\) 17.5628 0.783086 0.391543 0.920160i \(-0.371941\pi\)
0.391543 + 0.920160i \(0.371941\pi\)
\(504\) 0 0
\(505\) −3.21860 −0.143226
\(506\) 0 0
\(507\) 3.11903 0.138521
\(508\) 0 0
\(509\) 25.2911 1.12101 0.560505 0.828151i \(-0.310607\pi\)
0.560505 + 0.828151i \(0.310607\pi\)
\(510\) 0 0
\(511\) 15.6947 0.694293
\(512\) 0 0
\(513\) 20.0983 0.887361
\(514\) 0 0
\(515\) −3.29112 −0.145024
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 21.8734 0.960135
\(520\) 0 0
\(521\) −11.9070 −0.521655 −0.260827 0.965385i \(-0.583995\pi\)
−0.260827 + 0.965385i \(0.583995\pi\)
\(522\) 0 0
\(523\) 39.3894 1.72238 0.861189 0.508284i \(-0.169720\pi\)
0.861189 + 0.508284i \(0.169720\pi\)
\(524\) 0 0
\(525\) 3.11903 0.136125
\(526\) 0 0
\(527\) 26.5421 1.15619
\(528\) 0 0
\(529\) −21.5150 −0.935435
\(530\) 0 0
\(531\) 89.8708 3.90006
\(532\) 0 0
\(533\) −3.72833 −0.161492
\(534\) 0 0
\(535\) 5.01945 0.217010
\(536\) 0 0
\(537\) 42.8190 1.84778
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −12.9805 −0.558077 −0.279039 0.960280i \(-0.590016\pi\)
−0.279039 + 0.960280i \(0.590016\pi\)
\(542\) 0 0
\(543\) 30.5691 1.31185
\(544\) 0 0
\(545\) 3.56280 0.152613
\(546\) 0 0
\(547\) 21.6947 0.927599 0.463799 0.885940i \(-0.346486\pi\)
0.463799 + 0.885940i \(0.346486\pi\)
\(548\) 0 0
\(549\) −67.2833 −2.87158
\(550\) 0 0
\(551\) −10.9535 −0.466635
\(552\) 0 0
\(553\) −1.72833 −0.0734960
\(554\) 0 0
\(555\) −12.1655 −0.516398
\(556\) 0 0
\(557\) −14.6416 −0.620386 −0.310193 0.950674i \(-0.600394\pi\)
−0.310193 + 0.950674i \(0.600394\pi\)
\(558\) 0 0
\(559\) 10.2381 0.433024
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 25.1177 1.05859 0.529293 0.848439i \(-0.322457\pi\)
0.529293 + 0.848439i \(0.322457\pi\)
\(564\) 0 0
\(565\) −13.8009 −0.580606
\(566\) 0 0
\(567\) 16.0854 0.675524
\(568\) 0 0
\(569\) 21.2509 0.890886 0.445443 0.895310i \(-0.353046\pi\)
0.445443 + 0.895310i \(0.353046\pi\)
\(570\) 0 0
\(571\) −12.8810 −0.539052 −0.269526 0.962993i \(-0.586867\pi\)
−0.269526 + 0.962993i \(0.586867\pi\)
\(572\) 0 0
\(573\) 27.7000 1.15718
\(574\) 0 0
\(575\) 1.21860 0.0508192
\(576\) 0 0
\(577\) −12.3831 −0.515515 −0.257758 0.966210i \(-0.582984\pi\)
−0.257758 + 0.966210i \(0.582984\pi\)
\(578\) 0 0
\(579\) 84.7907 3.52378
\(580\) 0 0
\(581\) −1.21860 −0.0505561
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 6.72833 0.278182
\(586\) 0 0
\(587\) −22.3700 −0.923307 −0.461654 0.887060i \(-0.652744\pi\)
−0.461654 + 0.887060i \(0.652744\pi\)
\(588\) 0 0
\(589\) 12.3040 0.506978
\(590\) 0 0
\(591\) −60.1655 −2.47488
\(592\) 0 0
\(593\) 14.3442 0.589046 0.294523 0.955644i \(-0.404839\pi\)
0.294523 + 0.955644i \(0.404839\pi\)
\(594\) 0 0
\(595\) −3.72833 −0.152847
\(596\) 0 0
\(597\) 36.8072 1.50642
\(598\) 0 0
\(599\) 13.5628 0.554161 0.277080 0.960847i \(-0.410633\pi\)
0.277080 + 0.960847i \(0.410633\pi\)
\(600\) 0 0
\(601\) −45.1903 −1.84335 −0.921675 0.387964i \(-0.873179\pi\)
−0.921675 + 0.387964i \(0.873179\pi\)
\(602\) 0 0
\(603\) −22.1438 −0.901764
\(604\) 0 0
\(605\) 11.0000 0.447214
\(606\) 0 0
\(607\) −12.8810 −0.522823 −0.261411 0.965228i \(-0.584188\pi\)
−0.261411 + 0.965228i \(0.584188\pi\)
\(608\) 0 0
\(609\) −19.7672 −0.801009
\(610\) 0 0
\(611\) −2.78140 −0.112523
\(612\) 0 0
\(613\) −8.03890 −0.324688 −0.162344 0.986734i \(-0.551905\pi\)
−0.162344 + 0.986734i \(0.551905\pi\)
\(614\) 0 0
\(615\) −11.6288 −0.468917
\(616\) 0 0
\(617\) 24.8150 0.999015 0.499507 0.866310i \(-0.333514\pi\)
0.499507 + 0.866310i \(0.333514\pi\)
\(618\) 0 0
\(619\) −13.0801 −0.525735 −0.262867 0.964832i \(-0.584668\pi\)
−0.262867 + 0.964832i \(0.584668\pi\)
\(620\) 0 0
\(621\) 14.1708 0.568655
\(622\) 0 0
\(623\) 10.1385 0.406190
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 14.5421 0.579830
\(630\) 0 0
\(631\) −18.3700 −0.731297 −0.365648 0.930753i \(-0.619153\pi\)
−0.365648 + 0.930753i \(0.619153\pi\)
\(632\) 0 0
\(633\) −49.1784 −1.95467
\(634\) 0 0
\(635\) 5.69471 0.225988
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) −41.9717 −1.66037
\(640\) 0 0
\(641\) −29.0518 −1.14748 −0.573738 0.819039i \(-0.694507\pi\)
−0.573738 + 0.819039i \(0.694507\pi\)
\(642\) 0 0
\(643\) 40.8203 1.60980 0.804898 0.593413i \(-0.202220\pi\)
0.804898 + 0.593413i \(0.202220\pi\)
\(644\) 0 0
\(645\) 31.9328 1.25735
\(646\) 0 0
\(647\) 11.1190 0.437134 0.218567 0.975822i \(-0.429862\pi\)
0.218567 + 0.975822i \(0.429862\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 22.2044 0.870260
\(652\) 0 0
\(653\) 35.9717 1.40768 0.703840 0.710359i \(-0.251467\pi\)
0.703840 + 0.710359i \(0.251467\pi\)
\(654\) 0 0
\(655\) 13.6947 0.535097
\(656\) 0 0
\(657\) 105.599 4.11981
\(658\) 0 0
\(659\) 22.0594 0.859312 0.429656 0.902993i \(-0.358635\pi\)
0.429656 + 0.902993i \(0.358635\pi\)
\(660\) 0 0
\(661\) 4.05939 0.157892 0.0789459 0.996879i \(-0.474845\pi\)
0.0789459 + 0.996879i \(0.474845\pi\)
\(662\) 0 0
\(663\) −11.6288 −0.451623
\(664\) 0 0
\(665\) −1.72833 −0.0670217
\(666\) 0 0
\(667\) −7.72304 −0.299037
\(668\) 0 0
\(669\) −3.17970 −0.122934
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −36.1708 −1.39428 −0.697141 0.716934i \(-0.745545\pi\)
−0.697141 + 0.716934i \(0.745545\pi\)
\(674\) 0 0
\(675\) 11.6288 0.447591
\(676\) 0 0
\(677\) −8.03890 −0.308960 −0.154480 0.987996i \(-0.549370\pi\)
−0.154480 + 0.987996i \(0.549370\pi\)
\(678\) 0 0
\(679\) −5.80085 −0.222616
\(680\) 0 0
\(681\) 28.7531 1.10182
\(682\) 0 0
\(683\) 20.3106 0.777163 0.388581 0.921414i \(-0.372965\pi\)
0.388581 + 0.921414i \(0.372965\pi\)
\(684\) 0 0
\(685\) −9.66237 −0.369180
\(686\) 0 0
\(687\) −13.3235 −0.508322
\(688\) 0 0
\(689\) −2.00000 −0.0761939
\(690\) 0 0
\(691\) 19.5951 0.745434 0.372717 0.927945i \(-0.378426\pi\)
0.372717 + 0.927945i \(0.378426\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 7.45665 0.282847
\(696\) 0 0
\(697\) 13.9004 0.526516
\(698\) 0 0
\(699\) −27.3894 −1.03596
\(700\) 0 0
\(701\) 44.2044 1.66958 0.834789 0.550570i \(-0.185589\pi\)
0.834789 + 0.550570i \(0.185589\pi\)
\(702\) 0 0
\(703\) 6.74121 0.254250
\(704\) 0 0
\(705\) −8.67526 −0.326729
\(706\) 0 0
\(707\) 3.21860 0.121048
\(708\) 0 0
\(709\) −12.1708 −0.457085 −0.228542 0.973534i \(-0.573396\pi\)
−0.228542 + 0.973534i \(0.573396\pi\)
\(710\) 0 0
\(711\) −11.6288 −0.436112
\(712\) 0 0
\(713\) 8.67526 0.324891
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 8.67526 0.323983
\(718\) 0 0
\(719\) 32.8850 1.22640 0.613201 0.789927i \(-0.289881\pi\)
0.613201 + 0.789927i \(0.289881\pi\)
\(720\) 0 0
\(721\) 3.29112 0.122568
\(722\) 0 0
\(723\) −45.6677 −1.69840
\(724\) 0 0
\(725\) −6.33763 −0.235374
\(726\) 0 0
\(727\) 27.7943 1.03083 0.515416 0.856940i \(-0.327637\pi\)
0.515416 + 0.856940i \(0.327637\pi\)
\(728\) 0 0
\(729\) −0.583281 −0.0216030
\(730\) 0 0
\(731\) −38.1708 −1.41180
\(732\) 0 0
\(733\) 0.649487 0.0239894 0.0119947 0.999928i \(-0.496182\pi\)
0.0119947 + 0.999928i \(0.496182\pi\)
\(734\) 0 0
\(735\) −3.11903 −0.115047
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 25.0195 0.920355 0.460178 0.887827i \(-0.347786\pi\)
0.460178 + 0.887827i \(0.347786\pi\)
\(740\) 0 0
\(741\) −5.39070 −0.198032
\(742\) 0 0
\(743\) −14.8928 −0.546365 −0.273182 0.961962i \(-0.588076\pi\)
−0.273182 + 0.961962i \(0.588076\pi\)
\(744\) 0 0
\(745\) −2.00000 −0.0732743
\(746\) 0 0
\(747\) −8.19915 −0.299991
\(748\) 0 0
\(749\) −5.01945 −0.183407
\(750\) 0 0
\(751\) −46.7076 −1.70438 −0.852192 0.523229i \(-0.824727\pi\)
−0.852192 + 0.523229i \(0.824727\pi\)
\(752\) 0 0
\(753\) 78.4478 2.85880
\(754\) 0 0
\(755\) 0.675256 0.0245751
\(756\) 0 0
\(757\) 7.56280 0.274875 0.137437 0.990510i \(-0.456113\pi\)
0.137437 + 0.990510i \(0.456113\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −45.3287 −1.64317 −0.821583 0.570089i \(-0.806909\pi\)
−0.821583 + 0.570089i \(0.806909\pi\)
\(762\) 0 0
\(763\) −3.56280 −0.128982
\(764\) 0 0
\(765\) −25.0854 −0.906965
\(766\) 0 0
\(767\) −13.3571 −0.482296
\(768\) 0 0
\(769\) −35.4283 −1.27758 −0.638789 0.769382i \(-0.720564\pi\)
−0.638789 + 0.769382i \(0.720564\pi\)
\(770\) 0 0
\(771\) −46.6364 −1.67957
\(772\) 0 0
\(773\) −48.9911 −1.76209 −0.881044 0.473034i \(-0.843159\pi\)
−0.881044 + 0.473034i \(0.843159\pi\)
\(774\) 0 0
\(775\) 7.11903 0.255723
\(776\) 0 0
\(777\) 12.1655 0.436436
\(778\) 0 0
\(779\) 6.44377 0.230872
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −73.6987 −2.63378
\(784\) 0 0
\(785\) 16.5757 0.591611
\(786\) 0 0
\(787\) −52.9522 −1.88754 −0.943771 0.330599i \(-0.892749\pi\)
−0.943771 + 0.330599i \(0.892749\pi\)
\(788\) 0 0
\(789\) 46.1036 1.64133
\(790\) 0 0
\(791\) 13.8009 0.490702
\(792\) 0 0
\(793\) 10.0000 0.355110
\(794\) 0 0
\(795\) −6.23805 −0.221241
\(796\) 0 0
\(797\) −7.22517 −0.255929 −0.127964 0.991779i \(-0.540844\pi\)
−0.127964 + 0.991779i \(0.540844\pi\)
\(798\) 0 0
\(799\) 10.3700 0.366863
\(800\) 0 0
\(801\) 68.2150 2.41026
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) −1.21860 −0.0429501
\(806\) 0 0
\(807\) −53.8266 −1.89479
\(808\) 0 0
\(809\) −37.2239 −1.30872 −0.654361 0.756182i \(-0.727062\pi\)
−0.654361 + 0.756182i \(0.727062\pi\)
\(810\) 0 0
\(811\) −8.68839 −0.305091 −0.152545 0.988296i \(-0.548747\pi\)
−0.152545 + 0.988296i \(0.548747\pi\)
\(812\) 0 0
\(813\) −17.3505 −0.608509
\(814\) 0 0
\(815\) −4.88097 −0.170973
\(816\) 0 0
\(817\) −17.6947 −0.619059
\(818\) 0 0
\(819\) −6.72833 −0.235107
\(820\) 0 0
\(821\) 4.36996 0.152513 0.0762564 0.997088i \(-0.475703\pi\)
0.0762564 + 0.997088i \(0.475703\pi\)
\(822\) 0 0
\(823\) 52.9522 1.84580 0.922899 0.385042i \(-0.125813\pi\)
0.922899 + 0.385042i \(0.125813\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −26.5150 −0.922017 −0.461009 0.887396i \(-0.652512\pi\)
−0.461009 + 0.887396i \(0.652512\pi\)
\(828\) 0 0
\(829\) −35.2964 −1.22589 −0.612947 0.790124i \(-0.710016\pi\)
−0.612947 + 0.790124i \(0.710016\pi\)
\(830\) 0 0
\(831\) −66.3027 −2.30002
\(832\) 0 0
\(833\) 3.72833 0.129179
\(834\) 0 0
\(835\) 21.1514 0.731973
\(836\) 0 0
\(837\) 82.7854 2.86148
\(838\) 0 0
\(839\) −18.4372 −0.636523 −0.318261 0.948003i \(-0.603099\pi\)
−0.318261 + 0.948003i \(0.603099\pi\)
\(840\) 0 0
\(841\) 11.1655 0.385018
\(842\) 0 0
\(843\) 32.2229 1.10981
\(844\) 0 0
\(845\) −1.00000 −0.0344010
\(846\) 0 0
\(847\) −11.0000 −0.377964
\(848\) 0 0
\(849\) −99.0828 −3.40051
\(850\) 0 0
\(851\) 4.75306 0.162933
\(852\) 0 0
\(853\) −20.3053 −0.695240 −0.347620 0.937636i \(-0.613010\pi\)
−0.347620 + 0.937636i \(0.613010\pi\)
\(854\) 0 0
\(855\) −11.6288 −0.397695
\(856\) 0 0
\(857\) 50.4154 1.72216 0.861079 0.508471i \(-0.169789\pi\)
0.861079 + 0.508471i \(0.169789\pi\)
\(858\) 0 0
\(859\) 17.8939 0.610531 0.305265 0.952267i \(-0.401255\pi\)
0.305265 + 0.952267i \(0.401255\pi\)
\(860\) 0 0
\(861\) 11.6288 0.396307
\(862\) 0 0
\(863\) 9.33003 0.317598 0.158799 0.987311i \(-0.449238\pi\)
0.158799 + 0.987311i \(0.449238\pi\)
\(864\) 0 0
\(865\) −7.01288 −0.238445
\(866\) 0 0
\(867\) −9.66766 −0.328331
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 3.29112 0.111515
\(872\) 0 0
\(873\) −39.0300 −1.32097
\(874\) 0 0
\(875\) −1.00000 −0.0338062
\(876\) 0 0
\(877\) 25.5549 0.862929 0.431465 0.902130i \(-0.357997\pi\)
0.431465 + 0.902130i \(0.357997\pi\)
\(878\) 0 0
\(879\) −46.8461 −1.58008
\(880\) 0 0
\(881\) −41.4026 −1.39489 −0.697444 0.716640i \(-0.745679\pi\)
−0.697444 + 0.716640i \(0.745679\pi\)
\(882\) 0 0
\(883\) 29.3505 0.987723 0.493862 0.869540i \(-0.335585\pi\)
0.493862 + 0.869540i \(0.335585\pi\)
\(884\) 0 0
\(885\) −41.6611 −1.40042
\(886\) 0 0
\(887\) −26.4438 −0.887895 −0.443947 0.896053i \(-0.646422\pi\)
−0.443947 + 0.896053i \(0.646422\pi\)
\(888\) 0 0
\(889\) −5.69471 −0.190994
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 4.80717 0.160866
\(894\) 0 0
\(895\) −13.7283 −0.458887
\(896\) 0 0
\(897\) −3.80085 −0.126907
\(898\) 0 0
\(899\) −45.1177 −1.50476
\(900\) 0 0
\(901\) 7.45665 0.248417
\(902\) 0 0
\(903\) −31.9328 −1.06266
\(904\) 0 0
\(905\) −9.80085 −0.325791
\(906\) 0 0
\(907\) 0.610584 0.0202741 0.0101370 0.999949i \(-0.496773\pi\)
0.0101370 + 0.999949i \(0.496773\pi\)
\(908\) 0 0
\(909\) 21.6558 0.718278
\(910\) 0 0
\(911\) −6.53549 −0.216531 −0.108265 0.994122i \(-0.534530\pi\)
−0.108265 + 0.994122i \(0.534530\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 31.1903 1.03112
\(916\) 0 0
\(917\) −13.6947 −0.452239
\(918\) 0 0
\(919\) −17.5562 −0.579127 −0.289563 0.957159i \(-0.593510\pi\)
−0.289563 + 0.957159i \(0.593510\pi\)
\(920\) 0 0
\(921\) 28.7531 0.947446
\(922\) 0 0
\(923\) 6.23805 0.205328
\(924\) 0 0
\(925\) 3.90043 0.128245
\(926\) 0 0
\(927\) 22.1438 0.727297
\(928\) 0 0
\(929\) −33.2509 −1.09093 −0.545464 0.838134i \(-0.683647\pi\)
−0.545464 + 0.838134i \(0.683647\pi\)
\(930\) 0 0
\(931\) 1.72833 0.0566436
\(932\) 0 0
\(933\) −67.0452 −2.19496
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −35.1850 −1.14944 −0.574722 0.818349i \(-0.694890\pi\)
−0.574722 + 0.818349i \(0.694890\pi\)
\(938\) 0 0
\(939\) −9.39727 −0.306668
\(940\) 0 0
\(941\) 27.3300 0.890933 0.445467 0.895298i \(-0.353038\pi\)
0.445467 + 0.895298i \(0.353038\pi\)
\(942\) 0 0
\(943\) 4.54335 0.147952
\(944\) 0 0
\(945\) −11.6288 −0.378283
\(946\) 0 0
\(947\) 0.853922 0.0277487 0.0138744 0.999904i \(-0.495584\pi\)
0.0138744 + 0.999904i \(0.495584\pi\)
\(948\) 0 0
\(949\) −15.6947 −0.509472
\(950\) 0 0
\(951\) −65.2292 −2.11520
\(952\) 0 0
\(953\) 60.2486 1.95164 0.975822 0.218566i \(-0.0701379\pi\)
0.975822 + 0.218566i \(0.0701379\pi\)
\(954\) 0 0
\(955\) −8.88097 −0.287382
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 9.66237 0.312014
\(960\) 0 0
\(961\) 19.6805 0.634856
\(962\) 0 0
\(963\) −33.7725 −1.08830
\(964\) 0 0
\(965\) −27.1850 −0.875116
\(966\) 0 0
\(967\) 46.0323 1.48030 0.740150 0.672442i \(-0.234754\pi\)
0.740150 + 0.672442i \(0.234754\pi\)
\(968\) 0 0
\(969\) 20.0983 0.645650
\(970\) 0 0
\(971\) −15.3894 −0.493870 −0.246935 0.969032i \(-0.579423\pi\)
−0.246935 + 0.969032i \(0.579423\pi\)
\(972\) 0 0
\(973\) −7.45665 −0.239049
\(974\) 0 0
\(975\) −3.11903 −0.0998888
\(976\) 0 0
\(977\) −30.0311 −0.960779 −0.480389 0.877055i \(-0.659505\pi\)
−0.480389 + 0.877055i \(0.659505\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) −23.9717 −0.765356
\(982\) 0 0
\(983\) −22.3053 −0.711428 −0.355714 0.934595i \(-0.615762\pi\)
−0.355714 + 0.934595i \(0.615762\pi\)
\(984\) 0 0
\(985\) 19.2898 0.614625
\(986\) 0 0
\(987\) 8.67526 0.276136
\(988\) 0 0
\(989\) −12.4761 −0.396717
\(990\) 0 0
\(991\) −8.24334 −0.261858 −0.130929 0.991392i \(-0.541796\pi\)
−0.130929 + 0.991392i \(0.541796\pi\)
\(992\) 0 0
\(993\) −17.3505 −0.550602
\(994\) 0 0
\(995\) −11.8009 −0.374112
\(996\) 0 0
\(997\) −33.1461 −1.04975 −0.524873 0.851180i \(-0.675887\pi\)
−0.524873 + 0.851180i \(0.675887\pi\)
\(998\) 0 0
\(999\) 45.3571 1.43503
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.p.1.3 3
4.3 odd 2 7280.2.a.bn.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3640.2.a.p.1.3 3 1.1 even 1 trivial
7280.2.a.bn.1.1 3 4.3 odd 2