Properties

Label 260.2.a.b.1.3
Level $260$
Weight $2$
Character 260.1
Self dual yes
Analytic conductor $2.076$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 260.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(2.07611045255\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.564.1
Defining polynomial: \( x^{3} - x^{2} - 5x + 3 \) 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 1.3
Root \(2.51414\) of defining polynomial
Character \(\chi\) \(=\) 260.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.32088 q^{3} +1.00000 q^{5} -5.02827 q^{7} +8.02827 q^{9} +O(q^{10})\) \(q+3.32088 q^{3} +1.00000 q^{5} -5.02827 q^{7} +8.02827 q^{9} +1.70739 q^{11} +1.00000 q^{13} +3.32088 q^{15} -4.64177 q^{17} -4.34916 q^{19} -16.6983 q^{21} -0.679116 q^{23} +1.00000 q^{25} +16.6983 q^{27} -1.02827 q^{29} -2.29261 q^{31} +5.67004 q^{33} -5.02827 q^{35} -1.61350 q^{37} +3.32088 q^{39} +4.64177 q^{41} -3.32088 q^{43} +8.02827 q^{45} +1.02827 q^{47} +18.2835 q^{49} -15.4148 q^{51} -9.41478 q^{53} +1.70739 q^{55} -14.4431 q^{57} -8.93438 q^{59} +9.02827 q^{61} -40.3684 q^{63} +1.00000 q^{65} +5.61350 q^{67} -2.25526 q^{69} +1.70739 q^{71} +12.4431 q^{73} +3.32088 q^{75} -8.58522 q^{77} -2.64177 q^{79} +31.3684 q^{81} -8.25526 q^{83} -4.64177 q^{85} -3.41478 q^{87} +1.22699 q^{89} -5.02827 q^{91} -7.61350 q^{93} -4.34916 q^{95} -0.0565477 q^{97} +13.7074 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 2 q^{3} + 3 q^{5} - 2 q^{7} + 11 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + 2 q^{3} + 3 q^{5} - 2 q^{7} + 11 q^{9} + 3 q^{13} + 2 q^{15} + 2 q^{17} + 8 q^{19} - 8 q^{21} - 10 q^{23} + 3 q^{25} + 8 q^{27} + 10 q^{29} - 12 q^{31} - 12 q^{33} - 2 q^{35} - 2 q^{37} + 2 q^{39} - 2 q^{41} - 2 q^{43} + 11 q^{45} - 10 q^{47} + 23 q^{49} - 36 q^{51} - 18 q^{53} - 20 q^{57} - 16 q^{59} + 14 q^{61} - 50 q^{63} + 3 q^{65} + 14 q^{67} + 12 q^{69} + 14 q^{73} + 2 q^{75} - 36 q^{77} + 8 q^{79} + 23 q^{81} - 6 q^{83} + 2 q^{85} - 2 q^{89} - 2 q^{91} - 20 q^{93} + 8 q^{95} + 26 q^{97} + 36 q^{99}+O(q^{100}) \) 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
\(3\) 3.32088 1.91731 0.958657 0.284565i \(-0.0918491\pi\)
0.958657 + 0.284565i \(0.0918491\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −5.02827 −1.90051 −0.950254 0.311475i \(-0.899177\pi\)
−0.950254 + 0.311475i \(0.899177\pi\)
\(8\) 0 0
\(9\) 8.02827 2.67609
\(10\) 0 0
\(11\) 1.70739 0.514797 0.257399 0.966305i \(-0.417135\pi\)
0.257399 + 0.966305i \(0.417135\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 3.32088 0.857449
\(16\) 0 0
\(17\) −4.64177 −1.12579 −0.562897 0.826527i \(-0.690313\pi\)
−0.562897 + 0.826527i \(0.690313\pi\)
\(18\) 0 0
\(19\) −4.34916 −0.997765 −0.498883 0.866670i \(-0.666256\pi\)
−0.498883 + 0.866670i \(0.666256\pi\)
\(20\) 0 0
\(21\) −16.6983 −3.64387
\(22\) 0 0
\(23\) −0.679116 −0.141605 −0.0708027 0.997490i \(-0.522556\pi\)
−0.0708027 + 0.997490i \(0.522556\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 16.6983 3.21359
\(28\) 0 0
\(29\) −1.02827 −0.190946 −0.0954728 0.995432i \(-0.530436\pi\)
−0.0954728 + 0.995432i \(0.530436\pi\)
\(30\) 0 0
\(31\) −2.29261 −0.411765 −0.205883 0.978577i \(-0.566006\pi\)
−0.205883 + 0.978577i \(0.566006\pi\)
\(32\) 0 0
\(33\) 5.67004 0.987028
\(34\) 0 0
\(35\) −5.02827 −0.849933
\(36\) 0 0
\(37\) −1.61350 −0.265257 −0.132628 0.991166i \(-0.542342\pi\)
−0.132628 + 0.991166i \(0.542342\pi\)
\(38\) 0 0
\(39\) 3.32088 0.531767
\(40\) 0 0
\(41\) 4.64177 0.724923 0.362461 0.931999i \(-0.381937\pi\)
0.362461 + 0.931999i \(0.381937\pi\)
\(42\) 0 0
\(43\) −3.32088 −0.506430 −0.253215 0.967410i \(-0.581488\pi\)
−0.253215 + 0.967410i \(0.581488\pi\)
\(44\) 0 0
\(45\) 8.02827 1.19678
\(46\) 0 0
\(47\) 1.02827 0.149989 0.0749946 0.997184i \(-0.476106\pi\)
0.0749946 + 0.997184i \(0.476106\pi\)
\(48\) 0 0
\(49\) 18.2835 2.61193
\(50\) 0 0
\(51\) −15.4148 −2.15850
\(52\) 0 0
\(53\) −9.41478 −1.29322 −0.646610 0.762821i \(-0.723814\pi\)
−0.646610 + 0.762821i \(0.723814\pi\)
\(54\) 0 0
\(55\) 1.70739 0.230224
\(56\) 0 0
\(57\) −14.4431 −1.91303
\(58\) 0 0
\(59\) −8.93438 −1.16316 −0.581579 0.813490i \(-0.697565\pi\)
−0.581579 + 0.813490i \(0.697565\pi\)
\(60\) 0 0
\(61\) 9.02827 1.15595 0.577976 0.816054i \(-0.303843\pi\)
0.577976 + 0.816054i \(0.303843\pi\)
\(62\) 0 0
\(63\) −40.3684 −5.08594
\(64\) 0 0
\(65\) 1.00000 0.124035
\(66\) 0 0
\(67\) 5.61350 0.685798 0.342899 0.939372i \(-0.388591\pi\)
0.342899 + 0.939372i \(0.388591\pi\)
\(68\) 0 0
\(69\) −2.25526 −0.271502
\(70\) 0 0
\(71\) 1.70739 0.202630 0.101315 0.994854i \(-0.467695\pi\)
0.101315 + 0.994854i \(0.467695\pi\)
\(72\) 0 0
\(73\) 12.4431 1.45635 0.728175 0.685392i \(-0.240369\pi\)
0.728175 + 0.685392i \(0.240369\pi\)
\(74\) 0 0
\(75\) 3.32088 0.383463
\(76\) 0 0
\(77\) −8.58522 −0.978377
\(78\) 0 0
\(79\) −2.64177 −0.297222 −0.148611 0.988896i \(-0.547480\pi\)
−0.148611 + 0.988896i \(0.547480\pi\)
\(80\) 0 0
\(81\) 31.3684 3.48537
\(82\) 0 0
\(83\) −8.25526 −0.906133 −0.453066 0.891477i \(-0.649670\pi\)
−0.453066 + 0.891477i \(0.649670\pi\)
\(84\) 0 0
\(85\) −4.64177 −0.503471
\(86\) 0 0
\(87\) −3.41478 −0.366103
\(88\) 0 0
\(89\) 1.22699 0.130061 0.0650304 0.997883i \(-0.479286\pi\)
0.0650304 + 0.997883i \(0.479286\pi\)
\(90\) 0 0
\(91\) −5.02827 −0.527106
\(92\) 0 0
\(93\) −7.61350 −0.789483
\(94\) 0 0
\(95\) −4.34916 −0.446214
\(96\) 0 0
\(97\) −0.0565477 −0.00574155 −0.00287078 0.999996i \(-0.500914\pi\)
−0.00287078 + 0.999996i \(0.500914\pi\)
\(98\) 0 0
\(99\) 13.7074 1.37764
\(100\) 0 0
\(101\) 6.00000 0.597022 0.298511 0.954406i \(-0.403510\pi\)
0.298511 + 0.954406i \(0.403510\pi\)
\(102\) 0 0
\(103\) 9.37743 0.923986 0.461993 0.886884i \(-0.347135\pi\)
0.461993 + 0.886884i \(0.347135\pi\)
\(104\) 0 0
\(105\) −16.6983 −1.62959
\(106\) 0 0
\(107\) −13.3774 −1.29325 −0.646623 0.762810i \(-0.723819\pi\)
−0.646623 + 0.762810i \(0.723819\pi\)
\(108\) 0 0
\(109\) 11.2835 1.08077 0.540383 0.841419i \(-0.318279\pi\)
0.540383 + 0.841419i \(0.318279\pi\)
\(110\) 0 0
\(111\) −5.35823 −0.508581
\(112\) 0 0
\(113\) −18.6983 −1.75899 −0.879495 0.475908i \(-0.842119\pi\)
−0.879495 + 0.475908i \(0.842119\pi\)
\(114\) 0 0
\(115\) −0.679116 −0.0633278
\(116\) 0 0
\(117\) 8.02827 0.742214
\(118\) 0 0
\(119\) 23.3401 2.13958
\(120\) 0 0
\(121\) −8.08482 −0.734984
\(122\) 0 0
\(123\) 15.4148 1.38990
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 10.7357 0.952636 0.476318 0.879273i \(-0.341971\pi\)
0.476318 + 0.879273i \(0.341971\pi\)
\(128\) 0 0
\(129\) −11.0283 −0.970985
\(130\) 0 0
\(131\) 7.22699 0.631425 0.315713 0.948855i \(-0.397756\pi\)
0.315713 + 0.948855i \(0.397756\pi\)
\(132\) 0 0
\(133\) 21.8688 1.89626
\(134\) 0 0
\(135\) 16.6983 1.43716
\(136\) 0 0
\(137\) 17.3401 1.48146 0.740732 0.671801i \(-0.234479\pi\)
0.740732 + 0.671801i \(0.234479\pi\)
\(138\) 0 0
\(139\) 9.35823 0.793755 0.396877 0.917872i \(-0.370094\pi\)
0.396877 + 0.917872i \(0.370094\pi\)
\(140\) 0 0
\(141\) 3.41478 0.287576
\(142\) 0 0
\(143\) 1.70739 0.142779
\(144\) 0 0
\(145\) −1.02827 −0.0853935
\(146\) 0 0
\(147\) 60.7175 5.00790
\(148\) 0 0
\(149\) 17.3401 1.42056 0.710278 0.703922i \(-0.248569\pi\)
0.710278 + 0.703922i \(0.248569\pi\)
\(150\) 0 0
\(151\) 3.57615 0.291023 0.145511 0.989357i \(-0.453517\pi\)
0.145511 + 0.989357i \(0.453517\pi\)
\(152\) 0 0
\(153\) −37.2654 −3.01273
\(154\) 0 0
\(155\) −2.29261 −0.184147
\(156\) 0 0
\(157\) −7.28354 −0.581290 −0.290645 0.956831i \(-0.593870\pi\)
−0.290645 + 0.956831i \(0.593870\pi\)
\(158\) 0 0
\(159\) −31.2654 −2.47951
\(160\) 0 0
\(161\) 3.41478 0.269122
\(162\) 0 0
\(163\) 0.840485 0.0658319 0.0329159 0.999458i \(-0.489521\pi\)
0.0329159 + 0.999458i \(0.489521\pi\)
\(164\) 0 0
\(165\) 5.67004 0.441412
\(166\) 0 0
\(167\) −13.0283 −1.00816 −0.504079 0.863658i \(-0.668168\pi\)
−0.504079 + 0.863658i \(0.668168\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −34.9162 −2.67011
\(172\) 0 0
\(173\) 25.9253 1.97106 0.985532 0.169488i \(-0.0542113\pi\)
0.985532 + 0.169488i \(0.0542113\pi\)
\(174\) 0 0
\(175\) −5.02827 −0.380102
\(176\) 0 0
\(177\) −29.6700 −2.23014
\(178\) 0 0
\(179\) −4.77301 −0.356751 −0.178376 0.983962i \(-0.557084\pi\)
−0.178376 + 0.983962i \(0.557084\pi\)
\(180\) 0 0
\(181\) −14.3118 −1.06379 −0.531894 0.846811i \(-0.678520\pi\)
−0.531894 + 0.846811i \(0.678520\pi\)
\(182\) 0 0
\(183\) 29.9819 2.21632
\(184\) 0 0
\(185\) −1.61350 −0.118627
\(186\) 0 0
\(187\) −7.92531 −0.579556
\(188\) 0 0
\(189\) −83.9637 −6.10746
\(190\) 0 0
\(191\) 12.0000 0.868290 0.434145 0.900843i \(-0.357051\pi\)
0.434145 + 0.900843i \(0.357051\pi\)
\(192\) 0 0
\(193\) 4.05655 0.291997 0.145998 0.989285i \(-0.453361\pi\)
0.145998 + 0.989285i \(0.453361\pi\)
\(194\) 0 0
\(195\) 3.32088 0.237813
\(196\) 0 0
\(197\) −15.2835 −1.08891 −0.544453 0.838791i \(-0.683263\pi\)
−0.544453 + 0.838791i \(0.683263\pi\)
\(198\) 0 0
\(199\) −8.77301 −0.621902 −0.310951 0.950426i \(-0.600648\pi\)
−0.310951 + 0.950426i \(0.600648\pi\)
\(200\) 0 0
\(201\) 18.6418 1.31489
\(202\) 0 0
\(203\) 5.17044 0.362894
\(204\) 0 0
\(205\) 4.64177 0.324195
\(206\) 0 0
\(207\) −5.45213 −0.378949
\(208\) 0 0
\(209\) −7.42571 −0.513647
\(210\) 0 0
\(211\) 0.773010 0.0532162 0.0266081 0.999646i \(-0.491529\pi\)
0.0266081 + 0.999646i \(0.491529\pi\)
\(212\) 0 0
\(213\) 5.67004 0.388505
\(214\) 0 0
\(215\) −3.32088 −0.226482
\(216\) 0 0
\(217\) 11.5279 0.782563
\(218\) 0 0
\(219\) 41.3219 2.79228
\(220\) 0 0
\(221\) −4.64177 −0.312239
\(222\) 0 0
\(223\) −14.3118 −0.958390 −0.479195 0.877709i \(-0.659071\pi\)
−0.479195 + 0.877709i \(0.659071\pi\)
\(224\) 0 0
\(225\) 8.02827 0.535218
\(226\) 0 0
\(227\) −13.7266 −0.911066 −0.455533 0.890219i \(-0.650551\pi\)
−0.455533 + 0.890219i \(0.650551\pi\)
\(228\) 0 0
\(229\) 21.9253 1.44887 0.724433 0.689346i \(-0.242102\pi\)
0.724433 + 0.689346i \(0.242102\pi\)
\(230\) 0 0
\(231\) −28.5105 −1.87586
\(232\) 0 0
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 0 0
\(235\) 1.02827 0.0670772
\(236\) 0 0
\(237\) −8.77301 −0.569868
\(238\) 0 0
\(239\) −15.7639 −1.01968 −0.509842 0.860268i \(-0.670296\pi\)
−0.509842 + 0.860268i \(0.670296\pi\)
\(240\) 0 0
\(241\) 9.92531 0.639345 0.319673 0.947528i \(-0.396427\pi\)
0.319673 + 0.947528i \(0.396427\pi\)
\(242\) 0 0
\(243\) 54.0757 3.46896
\(244\) 0 0
\(245\) 18.2835 1.16809
\(246\) 0 0
\(247\) −4.34916 −0.276730
\(248\) 0 0
\(249\) −27.4148 −1.73734
\(250\) 0 0
\(251\) 24.6983 1.55894 0.779472 0.626437i \(-0.215487\pi\)
0.779472 + 0.626437i \(0.215487\pi\)
\(252\) 0 0
\(253\) −1.15951 −0.0728981
\(254\) 0 0
\(255\) −15.4148 −0.965311
\(256\) 0 0
\(257\) −20.0565 −1.25109 −0.625547 0.780187i \(-0.715124\pi\)
−0.625547 + 0.780187i \(0.715124\pi\)
\(258\) 0 0
\(259\) 8.11310 0.504123
\(260\) 0 0
\(261\) −8.25526 −0.510988
\(262\) 0 0
\(263\) 26.0757 1.60790 0.803950 0.594697i \(-0.202728\pi\)
0.803950 + 0.594697i \(0.202728\pi\)
\(264\) 0 0
\(265\) −9.41478 −0.578345
\(266\) 0 0
\(267\) 4.07469 0.249367
\(268\) 0 0
\(269\) −12.8296 −0.782232 −0.391116 0.920341i \(-0.627911\pi\)
−0.391116 + 0.920341i \(0.627911\pi\)
\(270\) 0 0
\(271\) −17.7074 −1.07565 −0.537824 0.843057i \(-0.680753\pi\)
−0.537824 + 0.843057i \(0.680753\pi\)
\(272\) 0 0
\(273\) −16.6983 −1.01063
\(274\) 0 0
\(275\) 1.70739 0.102959
\(276\) 0 0
\(277\) −15.4713 −0.929582 −0.464791 0.885420i \(-0.653871\pi\)
−0.464791 + 0.885420i \(0.653871\pi\)
\(278\) 0 0
\(279\) −18.4057 −1.10192
\(280\) 0 0
\(281\) 7.35823 0.438955 0.219478 0.975618i \(-0.429565\pi\)
0.219478 + 0.975618i \(0.429565\pi\)
\(282\) 0 0
\(283\) −0.604422 −0.0359292 −0.0179646 0.999839i \(-0.505719\pi\)
−0.0179646 + 0.999839i \(0.505719\pi\)
\(284\) 0 0
\(285\) −14.4431 −0.855533
\(286\) 0 0
\(287\) −23.3401 −1.37772
\(288\) 0 0
\(289\) 4.54602 0.267413
\(290\) 0 0
\(291\) −0.187788 −0.0110084
\(292\) 0 0
\(293\) 23.0101 1.34427 0.672133 0.740430i \(-0.265378\pi\)
0.672133 + 0.740430i \(0.265378\pi\)
\(294\) 0 0
\(295\) −8.93438 −0.520180
\(296\) 0 0
\(297\) 28.5105 1.65435
\(298\) 0 0
\(299\) −0.679116 −0.0392743
\(300\) 0 0
\(301\) 16.6983 0.962475
\(302\) 0 0
\(303\) 19.9253 1.14468
\(304\) 0 0
\(305\) 9.02827 0.516957
\(306\) 0 0
\(307\) 20.3684 1.16248 0.581242 0.813731i \(-0.302567\pi\)
0.581242 + 0.813731i \(0.302567\pi\)
\(308\) 0 0
\(309\) 31.1414 1.77157
\(310\) 0 0
\(311\) −19.9253 −1.12986 −0.564930 0.825139i \(-0.691097\pi\)
−0.564930 + 0.825139i \(0.691097\pi\)
\(312\) 0 0
\(313\) 31.4713 1.77886 0.889432 0.457067i \(-0.151100\pi\)
0.889432 + 0.457067i \(0.151100\pi\)
\(314\) 0 0
\(315\) −40.3684 −2.27450
\(316\) 0 0
\(317\) 1.72659 0.0969750 0.0484875 0.998824i \(-0.484560\pi\)
0.0484875 + 0.998824i \(0.484560\pi\)
\(318\) 0 0
\(319\) −1.75566 −0.0982983
\(320\) 0 0
\(321\) −44.4249 −2.47956
\(322\) 0 0
\(323\) 20.1878 1.12328
\(324\) 0 0
\(325\) 1.00000 0.0554700
\(326\) 0 0
\(327\) 37.4713 2.07217
\(328\) 0 0
\(329\) −5.17044 −0.285056
\(330\) 0 0
\(331\) 10.4057 0.571949 0.285975 0.958237i \(-0.407683\pi\)
0.285975 + 0.958237i \(0.407683\pi\)
\(332\) 0 0
\(333\) −12.9536 −0.709852
\(334\) 0 0
\(335\) 5.61350 0.306698
\(336\) 0 0
\(337\) −10.6983 −0.582774 −0.291387 0.956605i \(-0.594117\pi\)
−0.291387 + 0.956605i \(0.594117\pi\)
\(338\) 0 0
\(339\) −62.0950 −3.37253
\(340\) 0 0
\(341\) −3.91438 −0.211976
\(342\) 0 0
\(343\) −56.7367 −3.06349
\(344\) 0 0
\(345\) −2.25526 −0.121419
\(346\) 0 0
\(347\) −32.6044 −1.75030 −0.875149 0.483854i \(-0.839236\pi\)
−0.875149 + 0.483854i \(0.839236\pi\)
\(348\) 0 0
\(349\) −13.4148 −0.718077 −0.359038 0.933323i \(-0.616895\pi\)
−0.359038 + 0.933323i \(0.616895\pi\)
\(350\) 0 0
\(351\) 16.6983 0.891290
\(352\) 0 0
\(353\) −35.0101 −1.86340 −0.931701 0.363227i \(-0.881675\pi\)
−0.931701 + 0.363227i \(0.881675\pi\)
\(354\) 0 0
\(355\) 1.70739 0.0906188
\(356\) 0 0
\(357\) 77.5097 4.10225
\(358\) 0 0
\(359\) 20.9344 1.10487 0.552437 0.833555i \(-0.313698\pi\)
0.552437 + 0.833555i \(0.313698\pi\)
\(360\) 0 0
\(361\) −0.0848216 −0.00446429
\(362\) 0 0
\(363\) −26.8488 −1.40919
\(364\) 0 0
\(365\) 12.4431 0.651299
\(366\) 0 0
\(367\) 11.4340 0.596849 0.298424 0.954433i \(-0.403539\pi\)
0.298424 + 0.954433i \(0.403539\pi\)
\(368\) 0 0
\(369\) 37.2654 1.93996
\(370\) 0 0
\(371\) 47.3401 2.45777
\(372\) 0 0
\(373\) −14.1131 −0.730748 −0.365374 0.930861i \(-0.619059\pi\)
−0.365374 + 0.930861i \(0.619059\pi\)
\(374\) 0 0
\(375\) 3.32088 0.171490
\(376\) 0 0
\(377\) −1.02827 −0.0529588
\(378\) 0 0
\(379\) −1.89518 −0.0973487 −0.0486744 0.998815i \(-0.515500\pi\)
−0.0486744 + 0.998815i \(0.515500\pi\)
\(380\) 0 0
\(381\) 35.6519 1.82650
\(382\) 0 0
\(383\) −22.3118 −1.14008 −0.570040 0.821617i \(-0.693072\pi\)
−0.570040 + 0.821617i \(0.693072\pi\)
\(384\) 0 0
\(385\) −8.58522 −0.437543
\(386\) 0 0
\(387\) −26.6610 −1.35525
\(388\) 0 0
\(389\) −28.6802 −1.45414 −0.727071 0.686562i \(-0.759119\pi\)
−0.727071 + 0.686562i \(0.759119\pi\)
\(390\) 0 0
\(391\) 3.15230 0.159419
\(392\) 0 0
\(393\) 24.0000 1.21064
\(394\) 0 0
\(395\) −2.64177 −0.132922
\(396\) 0 0
\(397\) 15.5569 0.780781 0.390390 0.920649i \(-0.372340\pi\)
0.390390 + 0.920649i \(0.372340\pi\)
\(398\) 0 0
\(399\) 72.6236 3.63573
\(400\) 0 0
\(401\) −24.1696 −1.20697 −0.603487 0.797373i \(-0.706223\pi\)
−0.603487 + 0.797373i \(0.706223\pi\)
\(402\) 0 0
\(403\) −2.29261 −0.114203
\(404\) 0 0
\(405\) 31.3684 1.55871
\(406\) 0 0
\(407\) −2.75486 −0.136554
\(408\) 0 0
\(409\) −29.9253 −1.47971 −0.739856 0.672766i \(-0.765106\pi\)
−0.739856 + 0.672766i \(0.765106\pi\)
\(410\) 0 0
\(411\) 57.5844 2.84043
\(412\) 0 0
\(413\) 44.9245 2.21059
\(414\) 0 0
\(415\) −8.25526 −0.405235
\(416\) 0 0
\(417\) 31.0776 1.52188
\(418\) 0 0
\(419\) −8.58522 −0.419416 −0.209708 0.977764i \(-0.567251\pi\)
−0.209708 + 0.977764i \(0.567251\pi\)
\(420\) 0 0
\(421\) −21.7375 −1.05942 −0.529711 0.848178i \(-0.677700\pi\)
−0.529711 + 0.848178i \(0.677700\pi\)
\(422\) 0 0
\(423\) 8.25526 0.401385
\(424\) 0 0
\(425\) −4.64177 −0.225159
\(426\) 0 0
\(427\) −45.3966 −2.19690
\(428\) 0 0
\(429\) 5.67004 0.273752
\(430\) 0 0
\(431\) 13.7074 0.660262 0.330131 0.943935i \(-0.392907\pi\)
0.330131 + 0.943935i \(0.392907\pi\)
\(432\) 0 0
\(433\) −40.5671 −1.94953 −0.974765 0.223235i \(-0.928338\pi\)
−0.974765 + 0.223235i \(0.928338\pi\)
\(434\) 0 0
\(435\) −3.41478 −0.163726
\(436\) 0 0
\(437\) 2.95358 0.141289
\(438\) 0 0
\(439\) 26.5671 1.26798 0.633989 0.773342i \(-0.281417\pi\)
0.633989 + 0.773342i \(0.281417\pi\)
\(440\) 0 0
\(441\) 146.785 6.98977
\(442\) 0 0
\(443\) −16.7922 −0.797822 −0.398911 0.916990i \(-0.630612\pi\)
−0.398911 + 0.916990i \(0.630612\pi\)
\(444\) 0 0
\(445\) 1.22699 0.0581649
\(446\) 0 0
\(447\) 57.5844 2.72365
\(448\) 0 0
\(449\) −16.2443 −0.766618 −0.383309 0.923620i \(-0.625215\pi\)
−0.383309 + 0.923620i \(0.625215\pi\)
\(450\) 0 0
\(451\) 7.92531 0.373188
\(452\) 0 0
\(453\) 11.8760 0.557982
\(454\) 0 0
\(455\) −5.02827 −0.235729
\(456\) 0 0
\(457\) 6.77301 0.316828 0.158414 0.987373i \(-0.449362\pi\)
0.158414 + 0.987373i \(0.449362\pi\)
\(458\) 0 0
\(459\) −77.5097 −3.61784
\(460\) 0 0
\(461\) −22.8114 −1.06243 −0.531217 0.847236i \(-0.678265\pi\)
−0.531217 + 0.847236i \(0.678265\pi\)
\(462\) 0 0
\(463\) −16.3300 −0.758917 −0.379459 0.925209i \(-0.623890\pi\)
−0.379459 + 0.925209i \(0.623890\pi\)
\(464\) 0 0
\(465\) −7.61350 −0.353067
\(466\) 0 0
\(467\) 10.6610 0.493331 0.246665 0.969101i \(-0.420665\pi\)
0.246665 + 0.969101i \(0.420665\pi\)
\(468\) 0 0
\(469\) −28.2262 −1.30336
\(470\) 0 0
\(471\) −24.1878 −1.11451
\(472\) 0 0
\(473\) −5.67004 −0.260709
\(474\) 0 0
\(475\) −4.34916 −0.199553
\(476\) 0 0
\(477\) −75.5844 −3.46077
\(478\) 0 0
\(479\) 6.48040 0.296097 0.148048 0.988980i \(-0.452701\pi\)
0.148048 + 0.988980i \(0.452701\pi\)
\(480\) 0 0
\(481\) −1.61350 −0.0735690
\(482\) 0 0
\(483\) 11.3401 0.515992
\(484\) 0 0
\(485\) −0.0565477 −0.00256770
\(486\) 0 0
\(487\) 23.7831 1.07772 0.538858 0.842396i \(-0.318856\pi\)
0.538858 + 0.842396i \(0.318856\pi\)
\(488\) 0 0
\(489\) 2.79116 0.126220
\(490\) 0 0
\(491\) −6.13124 −0.276699 −0.138350 0.990383i \(-0.544180\pi\)
−0.138350 + 0.990383i \(0.544180\pi\)
\(492\) 0 0
\(493\) 4.77301 0.214966
\(494\) 0 0
\(495\) 13.7074 0.616101
\(496\) 0 0
\(497\) −8.58522 −0.385100
\(498\) 0 0
\(499\) 21.0475 0.942214 0.471107 0.882076i \(-0.343854\pi\)
0.471107 + 0.882076i \(0.343854\pi\)
\(500\) 0 0
\(501\) −43.2654 −1.93296
\(502\) 0 0
\(503\) 33.5652 1.49660 0.748300 0.663361i \(-0.230871\pi\)
0.748300 + 0.663361i \(0.230871\pi\)
\(504\) 0 0
\(505\) 6.00000 0.266996
\(506\) 0 0
\(507\) 3.32088 0.147486
\(508\) 0 0
\(509\) −14.5852 −0.646479 −0.323239 0.946317i \(-0.604772\pi\)
−0.323239 + 0.946317i \(0.604772\pi\)
\(510\) 0 0
\(511\) −62.5671 −2.76780
\(512\) 0 0
\(513\) −72.6236 −3.20641
\(514\) 0 0
\(515\) 9.37743 0.413219
\(516\) 0 0
\(517\) 1.75566 0.0772140
\(518\) 0 0
\(519\) 86.0950 3.77915
\(520\) 0 0
\(521\) −3.48225 −0.152560 −0.0762802 0.997086i \(-0.524304\pi\)
−0.0762802 + 0.997086i \(0.524304\pi\)
\(522\) 0 0
\(523\) −11.5087 −0.503239 −0.251620 0.967826i \(-0.580963\pi\)
−0.251620 + 0.967826i \(0.580963\pi\)
\(524\) 0 0
\(525\) −16.6983 −0.728774
\(526\) 0 0
\(527\) 10.6418 0.463563
\(528\) 0 0
\(529\) −22.5388 −0.979948
\(530\) 0 0
\(531\) −71.7276 −3.11271
\(532\) 0 0
\(533\) 4.64177 0.201057
\(534\) 0 0
\(535\) −13.3774 −0.578357
\(536\) 0 0
\(537\) −15.8506 −0.684004
\(538\) 0 0
\(539\) 31.2171 1.34462
\(540\) 0 0
\(541\) −13.8122 −0.593833 −0.296917 0.954903i \(-0.595958\pi\)
−0.296917 + 0.954903i \(0.595958\pi\)
\(542\) 0 0
\(543\) −47.5279 −2.03962
\(544\) 0 0
\(545\) 11.2835 0.483334
\(546\) 0 0
\(547\) −5.37743 −0.229922 −0.114961 0.993370i \(-0.536674\pi\)
−0.114961 + 0.993370i \(0.536674\pi\)
\(548\) 0 0
\(549\) 72.4815 3.09343
\(550\) 0 0
\(551\) 4.47213 0.190519
\(552\) 0 0
\(553\) 13.2835 0.564873
\(554\) 0 0
\(555\) −5.35823 −0.227444
\(556\) 0 0
\(557\) −0.0674757 −0.00285904 −0.00142952 0.999999i \(-0.500455\pi\)
−0.00142952 + 0.999999i \(0.500455\pi\)
\(558\) 0 0
\(559\) −3.32088 −0.140458
\(560\) 0 0
\(561\) −26.3190 −1.11119
\(562\) 0 0
\(563\) −7.20779 −0.303772 −0.151886 0.988398i \(-0.548535\pi\)
−0.151886 + 0.988398i \(0.548535\pi\)
\(564\) 0 0
\(565\) −18.6983 −0.786644
\(566\) 0 0
\(567\) −157.729 −6.62398
\(568\) 0 0
\(569\) −7.85783 −0.329417 −0.164709 0.986342i \(-0.552668\pi\)
−0.164709 + 0.986342i \(0.552668\pi\)
\(570\) 0 0
\(571\) −23.9253 −1.00124 −0.500621 0.865666i \(-0.666895\pi\)
−0.500621 + 0.865666i \(0.666895\pi\)
\(572\) 0 0
\(573\) 39.8506 1.66478
\(574\) 0 0
\(575\) −0.679116 −0.0283211
\(576\) 0 0
\(577\) 31.0101 1.29097 0.645484 0.763774i \(-0.276656\pi\)
0.645484 + 0.763774i \(0.276656\pi\)
\(578\) 0 0
\(579\) 13.4713 0.559849
\(580\) 0 0
\(581\) 41.5097 1.72211
\(582\) 0 0
\(583\) −16.0747 −0.665746
\(584\) 0 0
\(585\) 8.02827 0.331928
\(586\) 0 0
\(587\) 47.4076 1.95672 0.978360 0.206911i \(-0.0663411\pi\)
0.978360 + 0.206911i \(0.0663411\pi\)
\(588\) 0 0
\(589\) 9.97093 0.410845
\(590\) 0 0
\(591\) −50.7549 −2.08778
\(592\) 0 0
\(593\) −14.8861 −0.611299 −0.305650 0.952144i \(-0.598874\pi\)
−0.305650 + 0.952144i \(0.598874\pi\)
\(594\) 0 0
\(595\) 23.3401 0.956850
\(596\) 0 0
\(597\) −29.1342 −1.19238
\(598\) 0 0
\(599\) 42.8680 1.75154 0.875769 0.482731i \(-0.160355\pi\)
0.875769 + 0.482731i \(0.160355\pi\)
\(600\) 0 0
\(601\) −10.0000 −0.407909 −0.203954 0.978980i \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) 0 0
\(603\) 45.0667 1.83526
\(604\) 0 0
\(605\) −8.08482 −0.328695
\(606\) 0 0
\(607\) −18.7357 −0.760457 −0.380229 0.924893i \(-0.624155\pi\)
−0.380229 + 0.924893i \(0.624155\pi\)
\(608\) 0 0
\(609\) 17.1704 0.695781
\(610\) 0 0
\(611\) 1.02827 0.0415995
\(612\) 0 0
\(613\) 36.6802 1.48150 0.740749 0.671782i \(-0.234471\pi\)
0.740749 + 0.671782i \(0.234471\pi\)
\(614\) 0 0
\(615\) 15.4148 0.621584
\(616\) 0 0
\(617\) −8.05655 −0.324344 −0.162172 0.986762i \(-0.551850\pi\)
−0.162172 + 0.986762i \(0.551850\pi\)
\(618\) 0 0
\(619\) −33.1606 −1.33284 −0.666418 0.745578i \(-0.732173\pi\)
−0.666418 + 0.745578i \(0.732173\pi\)
\(620\) 0 0
\(621\) −11.3401 −0.455062
\(622\) 0 0
\(623\) −6.16964 −0.247182
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −24.6599 −0.984822
\(628\) 0 0
\(629\) 7.48947 0.298625
\(630\) 0 0
\(631\) −33.8205 −1.34637 −0.673186 0.739473i \(-0.735075\pi\)
−0.673186 + 0.739473i \(0.735075\pi\)
\(632\) 0 0
\(633\) 2.56708 0.102032
\(634\) 0 0
\(635\) 10.7357 0.426032
\(636\) 0 0
\(637\) 18.2835 0.724420
\(638\) 0 0
\(639\) 13.7074 0.542256
\(640\) 0 0
\(641\) 12.8296 0.506737 0.253369 0.967370i \(-0.418461\pi\)
0.253369 + 0.967370i \(0.418461\pi\)
\(642\) 0 0
\(643\) 43.7084 1.72369 0.861846 0.507169i \(-0.169308\pi\)
0.861846 + 0.507169i \(0.169308\pi\)
\(644\) 0 0
\(645\) −11.0283 −0.434238
\(646\) 0 0
\(647\) 25.4158 0.999200 0.499600 0.866256i \(-0.333480\pi\)
0.499600 + 0.866256i \(0.333480\pi\)
\(648\) 0 0
\(649\) −15.2545 −0.598790
\(650\) 0 0
\(651\) 38.2827 1.50042
\(652\) 0 0
\(653\) −3.94345 −0.154319 −0.0771596 0.997019i \(-0.524585\pi\)
−0.0771596 + 0.997019i \(0.524585\pi\)
\(654\) 0 0
\(655\) 7.22699 0.282382
\(656\) 0 0
\(657\) 99.8962 3.89732
\(658\) 0 0
\(659\) −38.0950 −1.48397 −0.741984 0.670417i \(-0.766115\pi\)
−0.741984 + 0.670417i \(0.766115\pi\)
\(660\) 0 0
\(661\) 18.1131 0.704518 0.352259 0.935903i \(-0.385414\pi\)
0.352259 + 0.935903i \(0.385414\pi\)
\(662\) 0 0
\(663\) −15.4148 −0.598660
\(664\) 0 0
\(665\) 21.8688 0.848034
\(666\) 0 0
\(667\) 0.698317 0.0270389
\(668\) 0 0
\(669\) −47.5279 −1.83753
\(670\) 0 0
\(671\) 15.4148 0.595081
\(672\) 0 0
\(673\) 43.2088 1.66558 0.832789 0.553590i \(-0.186743\pi\)
0.832789 + 0.553590i \(0.186743\pi\)
\(674\) 0 0
\(675\) 16.6983 0.642719
\(676\) 0 0
\(677\) −30.6983 −1.17983 −0.589916 0.807465i \(-0.700839\pi\)
−0.589916 + 0.807465i \(0.700839\pi\)
\(678\) 0 0
\(679\) 0.284337 0.0109119
\(680\) 0 0
\(681\) −45.5844 −1.74680
\(682\) 0 0
\(683\) −32.9536 −1.26093 −0.630467 0.776216i \(-0.717137\pi\)
−0.630467 + 0.776216i \(0.717137\pi\)
\(684\) 0 0
\(685\) 17.3401 0.662531
\(686\) 0 0
\(687\) 72.8114 2.77793
\(688\) 0 0
\(689\) −9.41478 −0.358675
\(690\) 0 0
\(691\) 37.1222 1.41219 0.706097 0.708115i \(-0.250454\pi\)
0.706097 + 0.708115i \(0.250454\pi\)
\(692\) 0 0
\(693\) −68.9245 −2.61823
\(694\) 0 0
\(695\) 9.35823 0.354978
\(696\) 0 0
\(697\) −21.5460 −0.816114
\(698\) 0 0
\(699\) −19.9253 −0.753644
\(700\) 0 0
\(701\) −7.39663 −0.279367 −0.139683 0.990196i \(-0.544609\pi\)
−0.139683 + 0.990196i \(0.544609\pi\)
\(702\) 0 0
\(703\) 7.01735 0.264664
\(704\) 0 0
\(705\) 3.41478 0.128608
\(706\) 0 0
\(707\) −30.1696 −1.13465
\(708\) 0 0
\(709\) 28.7549 1.07991 0.539956 0.841693i \(-0.318441\pi\)
0.539956 + 0.841693i \(0.318441\pi\)
\(710\) 0 0
\(711\) −21.2088 −0.795394
\(712\) 0 0
\(713\) 1.55695 0.0583081
\(714\) 0 0
\(715\) 1.70739 0.0638527
\(716\) 0 0
\(717\) −52.3502 −1.95505
\(718\) 0 0
\(719\) −39.4532 −1.47136 −0.735678 0.677332i \(-0.763136\pi\)
−0.735678 + 0.677332i \(0.763136\pi\)
\(720\) 0 0
\(721\) −47.1523 −1.75604
\(722\) 0 0
\(723\) 32.9608 1.22583
\(724\) 0 0
\(725\) −1.02827 −0.0381891
\(726\) 0 0
\(727\) −0.866904 −0.0321517 −0.0160758 0.999871i \(-0.505117\pi\)
−0.0160758 + 0.999871i \(0.505117\pi\)
\(728\) 0 0
\(729\) 85.4742 3.16571
\(730\) 0 0
\(731\) 15.4148 0.570136
\(732\) 0 0
\(733\) −10.0000 −0.369358 −0.184679 0.982799i \(-0.559125\pi\)
−0.184679 + 0.982799i \(0.559125\pi\)
\(734\) 0 0
\(735\) 60.7175 2.23960
\(736\) 0 0
\(737\) 9.58442 0.353047
\(738\) 0 0
\(739\) −31.5015 −1.15880 −0.579400 0.815043i \(-0.696713\pi\)
−0.579400 + 0.815043i \(0.696713\pi\)
\(740\) 0 0
\(741\) −14.4431 −0.530579
\(742\) 0 0
\(743\) −31.8578 −1.16875 −0.584375 0.811484i \(-0.698660\pi\)
−0.584375 + 0.811484i \(0.698660\pi\)
\(744\) 0 0
\(745\) 17.3401 0.635292
\(746\) 0 0
\(747\) −66.2755 −2.42489
\(748\) 0 0
\(749\) 67.2654 2.45782
\(750\) 0 0
\(751\) 46.0950 1.68203 0.841014 0.541013i \(-0.181959\pi\)
0.841014 + 0.541013i \(0.181959\pi\)
\(752\) 0 0
\(753\) 82.0203 2.98898
\(754\) 0 0
\(755\) 3.57615 0.130149
\(756\) 0 0
\(757\) 5.01735 0.182359 0.0911793 0.995834i \(-0.470936\pi\)
0.0911793 + 0.995834i \(0.470936\pi\)
\(758\) 0 0
\(759\) −3.85061 −0.139768
\(760\) 0 0
\(761\) 24.8296 0.900071 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(762\) 0 0
\(763\) −56.7367 −2.05401
\(764\) 0 0
\(765\) −37.2654 −1.34733
\(766\) 0 0
\(767\) −8.93438 −0.322602
\(768\) 0 0
\(769\) 36.9427 1.33219 0.666093 0.745869i \(-0.267965\pi\)
0.666093 + 0.745869i \(0.267965\pi\)
\(770\) 0 0
\(771\) −66.6055 −2.39874
\(772\) 0 0
\(773\) −16.4431 −0.591415 −0.295708 0.955278i \(-0.595555\pi\)
−0.295708 + 0.955278i \(0.595555\pi\)
\(774\) 0 0
\(775\) −2.29261 −0.0823530
\(776\) 0 0
\(777\) 26.9427 0.966562
\(778\) 0 0
\(779\) −20.1878 −0.723303
\(780\) 0 0
\(781\) 2.91518 0.104313
\(782\) 0 0
\(783\) −17.1704 −0.613622
\(784\) 0 0
\(785\) −7.28354 −0.259961
\(786\) 0 0
\(787\) 40.2553 1.43495 0.717473 0.696587i \(-0.245299\pi\)
0.717473 + 0.696587i \(0.245299\pi\)
\(788\) 0 0
\(789\) 86.5946 3.08285
\(790\) 0 0
\(791\) 94.0203 3.34298
\(792\) 0 0
\(793\) 9.02827 0.320603
\(794\) 0 0
\(795\) −31.2654 −1.10887
\(796\) 0 0
\(797\) 27.2835 0.966432 0.483216 0.875501i \(-0.339468\pi\)
0.483216 + 0.875501i \(0.339468\pi\)
\(798\) 0 0
\(799\) −4.77301 −0.168857
\(800\) 0 0
\(801\) 9.85061 0.348054
\(802\) 0 0
\(803\) 21.2451 0.749725
\(804\) 0 0
\(805\) 3.41478 0.120355
\(806\) 0 0
\(807\) −42.6055 −1.49978
\(808\) 0 0
\(809\) −28.4815 −1.00135 −0.500677 0.865634i \(-0.666916\pi\)
−0.500677 + 0.865634i \(0.666916\pi\)
\(810\) 0 0
\(811\) 31.6892 1.11276 0.556380 0.830928i \(-0.312190\pi\)
0.556380 + 0.830928i \(0.312190\pi\)
\(812\) 0 0
\(813\) −58.8042 −2.06235
\(814\) 0 0
\(815\) 0.840485 0.0294409
\(816\) 0 0
\(817\) 14.4431 0.505298
\(818\) 0 0
\(819\) −40.3684 −1.41058
\(820\) 0 0
\(821\) −6.65991 −0.232433 −0.116216 0.993224i \(-0.537077\pi\)
−0.116216 + 0.993224i \(0.537077\pi\)
\(822\) 0 0
\(823\) −7.79301 −0.271647 −0.135824 0.990733i \(-0.543368\pi\)
−0.135824 + 0.990733i \(0.543368\pi\)
\(824\) 0 0
\(825\) 5.67004 0.197406
\(826\) 0 0
\(827\) 26.4249 0.918884 0.459442 0.888208i \(-0.348049\pi\)
0.459442 + 0.888208i \(0.348049\pi\)
\(828\) 0 0
\(829\) 11.7447 0.407912 0.203956 0.978980i \(-0.434620\pi\)
0.203956 + 0.978980i \(0.434620\pi\)
\(830\) 0 0
\(831\) −51.3785 −1.78230
\(832\) 0 0
\(833\) −84.8680 −2.94050
\(834\) 0 0
\(835\) −13.0283 −0.450862
\(836\) 0 0
\(837\) −38.2827 −1.32325
\(838\) 0 0
\(839\) −44.5753 −1.53891 −0.769456 0.638700i \(-0.779473\pi\)
−0.769456 + 0.638700i \(0.779473\pi\)
\(840\) 0 0
\(841\) −27.9427 −0.963540
\(842\) 0 0
\(843\) 24.4358 0.841615
\(844\) 0 0
\(845\) 1.00000 0.0344010
\(846\) 0 0
\(847\) 40.6527 1.39684
\(848\) 0 0
\(849\) −2.00722 −0.0688875
\(850\) 0 0
\(851\) 1.09575 0.0375618
\(852\) 0 0
\(853\) 29.6135 1.01395 0.506973 0.861962i \(-0.330764\pi\)
0.506973 + 0.861962i \(0.330764\pi\)
\(854\) 0 0
\(855\) −34.9162 −1.19411
\(856\) 0 0
\(857\) 22.5105 0.768945 0.384472 0.923136i \(-0.374383\pi\)
0.384472 + 0.923136i \(0.374383\pi\)
\(858\) 0 0
\(859\) −0.585221 −0.0199675 −0.00998375 0.999950i \(-0.503178\pi\)
−0.00998375 + 0.999950i \(0.503178\pi\)
\(860\) 0 0
\(861\) −77.5097 −2.64152
\(862\) 0 0
\(863\) 45.6519 1.55401 0.777004 0.629495i \(-0.216738\pi\)
0.777004 + 0.629495i \(0.216738\pi\)
\(864\) 0 0
\(865\) 25.9253 0.881487
\(866\) 0 0
\(867\) 15.0968 0.512714
\(868\) 0 0
\(869\) −4.51053 −0.153009
\(870\) 0 0
\(871\) 5.61350 0.190206
\(872\) 0 0
\(873\) −0.453981 −0.0153649
\(874\) 0 0
\(875\) −5.02827 −0.169987
\(876\) 0 0
\(877\) −10.0000 −0.337676 −0.168838 0.985644i \(-0.554001\pi\)
−0.168838 + 0.985644i \(0.554001\pi\)
\(878\) 0 0
\(879\) 76.4140 2.57738
\(880\) 0 0
\(881\) 42.5380 1.43314 0.716571 0.697514i \(-0.245711\pi\)
0.716571 + 0.697514i \(0.245711\pi\)
\(882\) 0 0
\(883\) 6.22513 0.209492 0.104746 0.994499i \(-0.466597\pi\)
0.104746 + 0.994499i \(0.466597\pi\)
\(884\) 0 0
\(885\) −29.6700 −0.997348
\(886\) 0 0
\(887\) 22.0011 0.738723 0.369362 0.929286i \(-0.379576\pi\)
0.369362 + 0.929286i \(0.379576\pi\)
\(888\) 0 0
\(889\) −53.9819 −1.81049
\(890\) 0 0
\(891\) 53.5580 1.79426
\(892\) 0 0
\(893\) −4.47213 −0.149654
\(894\) 0 0
\(895\) −4.77301 −0.159544
\(896\) 0 0
\(897\) −2.25526 −0.0753011
\(898\) 0 0
\(899\) 2.35743 0.0786247
\(900\) 0 0
\(901\) 43.7012 1.45590
\(902\) 0 0
\(903\) 55.4532 1.84537
\(904\) 0 0
\(905\) −14.3118 −0.475741
\(906\) 0 0
\(907\) 28.2070 0.936598 0.468299 0.883570i \(-0.344867\pi\)
0.468299 + 0.883570i \(0.344867\pi\)
\(908\) 0 0
\(909\) 48.1696 1.59769
\(910\) 0 0
\(911\) 40.5105 1.34217 0.671087 0.741379i \(-0.265828\pi\)
0.671087 + 0.741379i \(0.265828\pi\)
\(912\) 0 0
\(913\) −14.0950 −0.466475
\(914\) 0 0
\(915\) 29.9819 0.991170
\(916\) 0 0
\(917\) −36.3393 −1.20003
\(918\) 0 0
\(919\) 0.0746930 0.00246389 0.00123195 0.999999i \(-0.499608\pi\)
0.00123195 + 0.999999i \(0.499608\pi\)
\(920\) 0 0
\(921\) 67.6410 2.22885
\(922\) 0 0
\(923\) 1.70739 0.0561994
\(924\) 0 0
\(925\) −1.61350 −0.0530514
\(926\) 0 0
\(927\) 75.2846 2.47267
\(928\) 0 0
\(929\) 53.6410 1.75990 0.879952 0.475063i \(-0.157575\pi\)
0.879952 + 0.475063i \(0.157575\pi\)
\(930\) 0 0
\(931\) −79.5180 −2.60610
\(932\) 0 0
\(933\) −66.1696 −2.16630
\(934\) 0 0
\(935\) −7.92531 −0.259185
\(936\) 0 0
\(937\) 26.0000 0.849383 0.424691 0.905338i \(-0.360383\pi\)
0.424691 + 0.905338i \(0.360383\pi\)
\(938\) 0 0
\(939\) 104.513 3.41064
\(940\) 0 0
\(941\) −49.9253 −1.62752 −0.813759 0.581202i \(-0.802583\pi\)
−0.813759 + 0.581202i \(0.802583\pi\)
\(942\) 0 0
\(943\) −3.15230 −0.102653
\(944\) 0 0
\(945\) −83.9637 −2.73134
\(946\) 0 0
\(947\) −5.80128 −0.188516 −0.0942582 0.995548i \(-0.530048\pi\)
−0.0942582 + 0.995548i \(0.530048\pi\)
\(948\) 0 0
\(949\) 12.4431 0.403919
\(950\) 0 0
\(951\) 5.73381 0.185931
\(952\) 0 0
\(953\) −13.2270 −0.428464 −0.214232 0.976783i \(-0.568725\pi\)
−0.214232 + 0.976783i \(0.568725\pi\)
\(954\) 0 0
\(955\) 12.0000 0.388311
\(956\) 0 0
\(957\) −5.83036 −0.188469
\(958\) 0 0
\(959\) −87.1907 −2.81553
\(960\) 0 0
\(961\) −25.7439 −0.830450
\(962\) 0 0
\(963\) −107.398 −3.46084
\(964\) 0 0
\(965\) 4.05655 0.130585
\(966\) 0 0
\(967\) −1.61350 −0.0518865 −0.0259433 0.999663i \(-0.508259\pi\)
−0.0259433 + 0.999663i \(0.508259\pi\)
\(968\) 0 0
\(969\) 67.0413 2.15368
\(970\) 0 0
\(971\) 16.7730 0.538271 0.269136 0.963102i \(-0.413262\pi\)
0.269136 + 0.963102i \(0.413262\pi\)
\(972\) 0 0
\(973\) −47.0557 −1.50854
\(974\) 0 0
\(975\) 3.32088 0.106353
\(976\) 0 0
\(977\) −47.6700 −1.52510 −0.762550 0.646929i \(-0.776053\pi\)
−0.762550 + 0.646929i \(0.776053\pi\)
\(978\) 0 0
\(979\) 2.09495 0.0669549
\(980\) 0 0
\(981\) 90.5873 2.89223
\(982\) 0 0
\(983\) 30.4996 0.972786 0.486393 0.873740i \(-0.338312\pi\)
0.486393 + 0.873740i \(0.338312\pi\)
\(984\) 0 0
\(985\) −15.2835 −0.486974
\(986\) 0 0
\(987\) −17.1704 −0.546541
\(988\) 0 0
\(989\) 2.25526 0.0717132
\(990\) 0 0
\(991\) −19.8506 −0.630576 −0.315288 0.948996i \(-0.602101\pi\)
−0.315288 + 0.948996i \(0.602101\pi\)
\(992\) 0 0
\(993\) 34.5561 1.09661
\(994\) 0 0
\(995\) −8.77301 −0.278123
\(996\) 0 0
\(997\) −33.6410 −1.06542 −0.532710 0.846298i \(-0.678826\pi\)
−0.532710 + 0.846298i \(0.678826\pi\)
\(998\) 0 0
\(999\) −26.9427 −0.852428
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 260.2.a.b.1.3 3
3.2 odd 2 2340.2.a.n.1.1 3
4.3 odd 2 1040.2.a.o.1.1 3
5.2 odd 4 1300.2.c.f.1249.1 6
5.3 odd 4 1300.2.c.f.1249.6 6
5.4 even 2 1300.2.a.i.1.1 3
8.3 odd 2 4160.2.a.br.1.3 3
8.5 even 2 4160.2.a.bo.1.1 3
12.11 even 2 9360.2.a.da.1.3 3
13.5 odd 4 3380.2.f.h.3041.5 6
13.8 odd 4 3380.2.f.h.3041.6 6
13.12 even 2 3380.2.a.o.1.3 3
20.19 odd 2 5200.2.a.ci.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
260.2.a.b.1.3 3 1.1 even 1 trivial
1040.2.a.o.1.1 3 4.3 odd 2
1300.2.a.i.1.1 3 5.4 even 2
1300.2.c.f.1249.1 6 5.2 odd 4
1300.2.c.f.1249.6 6 5.3 odd 4
2340.2.a.n.1.1 3 3.2 odd 2
3380.2.a.o.1.3 3 13.12 even 2
3380.2.f.h.3041.5 6 13.5 odd 4
3380.2.f.h.3041.6 6 13.8 odd 4
4160.2.a.bo.1.1 3 8.5 even 2
4160.2.a.br.1.3 3 8.3 odd 2
5200.2.a.ci.1.3 3 20.19 odd 2
9360.2.a.da.1.3 3 12.11 even 2