Properties

Label 2960.2.a.s.1.1
Level $2960$
Weight $2$
Character 2960.1
Self dual yes
Analytic conductor $23.636$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2960 = 2^{4} \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2960.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(23.6357189983\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.568.1
Defining polynomial: \(x^{3} - x^{2} - 6 x - 2\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1480)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(3.12489\) of defining polynomial
Character \(\chi\) \(=\) 2960.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.12489 q^{3} +1.00000 q^{5} +3.12489 q^{7} +6.76491 q^{9} +O(q^{10})\) \(q-3.12489 q^{3} +1.00000 q^{5} +3.12489 q^{7} +6.76491 q^{9} -1.51514 q^{11} -3.12489 q^{15} -5.60975 q^{19} -9.76491 q^{21} -4.00000 q^{23} +1.00000 q^{25} -11.7649 q^{27} -1.03028 q^{29} +0.640023 q^{31} +4.73463 q^{33} +3.12489 q^{35} +1.00000 q^{37} -5.76491 q^{41} -3.03028 q^{43} +6.76491 q^{45} +1.18544 q^{47} +2.76491 q^{49} +8.79518 q^{53} -1.51514 q^{55} +17.5298 q^{57} +3.67030 q^{59} -14.4995 q^{61} +21.1396 q^{63} -11.6703 q^{67} +12.4995 q^{69} +0.734633 q^{71} +7.70436 q^{73} -3.12489 q^{75} -4.73463 q^{77} +2.57947 q^{79} +16.4693 q^{81} +12.5942 q^{83} +3.21949 q^{87} +8.56009 q^{89} -2.00000 q^{93} -5.60975 q^{95} +6.00000 q^{97} -10.2498 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q - q^{3} + 3q^{5} + q^{7} + 4q^{9} + O(q^{10}) \) \( 3q - q^{3} + 3q^{5} + q^{7} + 4q^{9} - 5q^{11} - q^{15} - 8q^{19} - 13q^{21} - 12q^{23} + 3q^{25} - 19q^{27} - 4q^{29} - 6q^{31} - 3q^{33} + q^{35} + 3q^{37} - q^{41} - 10q^{43} + 4q^{45} - 3q^{47} - 8q^{49} + 11q^{53} - 5q^{55} + 20q^{57} + 4q^{59} - 10q^{61} + 22q^{63} - 28q^{67} + 4q^{69} - 15q^{71} + 5q^{73} - q^{75} + 3q^{77} - 2q^{79} + 15q^{81} - 5q^{83} - 8q^{87} - 6q^{89} - 6q^{93} - 8q^{95} + 18q^{97} - 14q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −3.12489 −1.80415 −0.902077 0.431576i \(-0.857958\pi\)
−0.902077 + 0.431576i \(0.857958\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 3.12489 1.18110 0.590548 0.807003i \(-0.298912\pi\)
0.590548 + 0.807003i \(0.298912\pi\)
\(8\) 0 0
\(9\) 6.76491 2.25497
\(10\) 0 0
\(11\) −1.51514 −0.456831 −0.228416 0.973564i \(-0.573355\pi\)
−0.228416 + 0.973564i \(0.573355\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) −3.12489 −0.806842
\(16\) 0 0
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 0 0
\(19\) −5.60975 −1.28696 −0.643482 0.765461i \(-0.722511\pi\)
−0.643482 + 0.765461i \(0.722511\pi\)
\(20\) 0 0
\(21\) −9.76491 −2.13088
\(22\) 0 0
\(23\) −4.00000 −0.834058 −0.417029 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −11.7649 −2.26416
\(28\) 0 0
\(29\) −1.03028 −0.191317 −0.0956587 0.995414i \(-0.530496\pi\)
−0.0956587 + 0.995414i \(0.530496\pi\)
\(30\) 0 0
\(31\) 0.640023 0.114952 0.0574758 0.998347i \(-0.481695\pi\)
0.0574758 + 0.998347i \(0.481695\pi\)
\(32\) 0 0
\(33\) 4.73463 0.824194
\(34\) 0 0
\(35\) 3.12489 0.528202
\(36\) 0 0
\(37\) 1.00000 0.164399
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −5.76491 −0.900328 −0.450164 0.892946i \(-0.648634\pi\)
−0.450164 + 0.892946i \(0.648634\pi\)
\(42\) 0 0
\(43\) −3.03028 −0.462113 −0.231056 0.972940i \(-0.574218\pi\)
−0.231056 + 0.972940i \(0.574218\pi\)
\(44\) 0 0
\(45\) 6.76491 1.00845
\(46\) 0 0
\(47\) 1.18544 0.172914 0.0864569 0.996256i \(-0.472446\pi\)
0.0864569 + 0.996256i \(0.472446\pi\)
\(48\) 0 0
\(49\) 2.76491 0.394987
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 8.79518 1.20811 0.604056 0.796942i \(-0.293550\pi\)
0.604056 + 0.796942i \(0.293550\pi\)
\(54\) 0 0
\(55\) −1.51514 −0.204301
\(56\) 0 0
\(57\) 17.5298 2.32188
\(58\) 0 0
\(59\) 3.67030 0.477832 0.238916 0.971040i \(-0.423208\pi\)
0.238916 + 0.971040i \(0.423208\pi\)
\(60\) 0 0
\(61\) −14.4995 −1.85648 −0.928238 0.371987i \(-0.878677\pi\)
−0.928238 + 0.371987i \(0.878677\pi\)
\(62\) 0 0
\(63\) 21.1396 2.66333
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −11.6703 −1.42575 −0.712877 0.701289i \(-0.752608\pi\)
−0.712877 + 0.701289i \(0.752608\pi\)
\(68\) 0 0
\(69\) 12.4995 1.50477
\(70\) 0 0
\(71\) 0.734633 0.0871849 0.0435924 0.999049i \(-0.486120\pi\)
0.0435924 + 0.999049i \(0.486120\pi\)
\(72\) 0 0
\(73\) 7.70436 0.901727 0.450863 0.892593i \(-0.351116\pi\)
0.450863 + 0.892593i \(0.351116\pi\)
\(74\) 0 0
\(75\) −3.12489 −0.360831
\(76\) 0 0
\(77\) −4.73463 −0.539561
\(78\) 0 0
\(79\) 2.57947 0.290213 0.145107 0.989416i \(-0.453647\pi\)
0.145107 + 0.989416i \(0.453647\pi\)
\(80\) 0 0
\(81\) 16.4693 1.82992
\(82\) 0 0
\(83\) 12.5942 1.38239 0.691194 0.722669i \(-0.257085\pi\)
0.691194 + 0.722669i \(0.257085\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 3.21949 0.345166
\(88\) 0 0
\(89\) 8.56009 0.907368 0.453684 0.891163i \(-0.350109\pi\)
0.453684 + 0.891163i \(0.350109\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −2.00000 −0.207390
\(94\) 0 0
\(95\) −5.60975 −0.575548
\(96\) 0 0
\(97\) 6.00000 0.609208 0.304604 0.952479i \(-0.401476\pi\)
0.304604 + 0.952479i \(0.401476\pi\)
\(98\) 0 0
\(99\) −10.2498 −1.03014
\(100\) 0 0
\(101\) −15.2947 −1.52188 −0.760941 0.648821i \(-0.775262\pi\)
−0.760941 + 0.648821i \(0.775262\pi\)
\(102\) 0 0
\(103\) 14.7493 1.45329 0.726646 0.687012i \(-0.241078\pi\)
0.726646 + 0.687012i \(0.241078\pi\)
\(104\) 0 0
\(105\) −9.76491 −0.952958
\(106\) 0 0
\(107\) 4.95035 0.478568 0.239284 0.970950i \(-0.423087\pi\)
0.239284 + 0.970950i \(0.423087\pi\)
\(108\) 0 0
\(109\) −18.4995 −1.77193 −0.885967 0.463748i \(-0.846504\pi\)
−0.885967 + 0.463748i \(0.846504\pi\)
\(110\) 0 0
\(111\) −3.12489 −0.296601
\(112\) 0 0
\(113\) −17.4693 −1.64337 −0.821685 0.569942i \(-0.806966\pi\)
−0.821685 + 0.569942i \(0.806966\pi\)
\(114\) 0 0
\(115\) −4.00000 −0.373002
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −8.70436 −0.791305
\(122\) 0 0
\(123\) 18.0147 1.62433
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −17.5639 −1.55854 −0.779271 0.626687i \(-0.784410\pi\)
−0.779271 + 0.626687i \(0.784410\pi\)
\(128\) 0 0
\(129\) 9.46927 0.833722
\(130\) 0 0
\(131\) −0.640023 −0.0559191 −0.0279596 0.999609i \(-0.508901\pi\)
−0.0279596 + 0.999609i \(0.508901\pi\)
\(132\) 0 0
\(133\) −17.5298 −1.52003
\(134\) 0 0
\(135\) −11.7649 −1.01256
\(136\) 0 0
\(137\) −10.4995 −0.897036 −0.448518 0.893774i \(-0.648048\pi\)
−0.448518 + 0.893774i \(0.648048\pi\)
\(138\) 0 0
\(139\) 14.5601 1.23497 0.617486 0.786582i \(-0.288151\pi\)
0.617486 + 0.786582i \(0.288151\pi\)
\(140\) 0 0
\(141\) −3.70436 −0.311963
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) −1.03028 −0.0855598
\(146\) 0 0
\(147\) −8.64002 −0.712617
\(148\) 0 0
\(149\) 7.76491 0.636126 0.318063 0.948070i \(-0.396968\pi\)
0.318063 + 0.948070i \(0.396968\pi\)
\(150\) 0 0
\(151\) −21.7796 −1.77240 −0.886199 0.463305i \(-0.846663\pi\)
−0.886199 + 0.463305i \(0.846663\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0.640023 0.0514079
\(156\) 0 0
\(157\) −19.3553 −1.54472 −0.772360 0.635185i \(-0.780924\pi\)
−0.772360 + 0.635185i \(0.780924\pi\)
\(158\) 0 0
\(159\) −27.4839 −2.17962
\(160\) 0 0
\(161\) −12.4995 −0.985102
\(162\) 0 0
\(163\) −11.2195 −0.878779 −0.439389 0.898297i \(-0.644805\pi\)
−0.439389 + 0.898297i \(0.644805\pi\)
\(164\) 0 0
\(165\) 4.73463 0.368591
\(166\) 0 0
\(167\) 12.1892 0.943230 0.471615 0.881805i \(-0.343671\pi\)
0.471615 + 0.881805i \(0.343671\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) 0 0
\(171\) −37.9494 −2.90207
\(172\) 0 0
\(173\) 6.23509 0.474045 0.237023 0.971504i \(-0.423828\pi\)
0.237023 + 0.971504i \(0.423828\pi\)
\(174\) 0 0
\(175\) 3.12489 0.236219
\(176\) 0 0
\(177\) −11.4693 −0.862083
\(178\) 0 0
\(179\) −0.450805 −0.0336947 −0.0168474 0.999858i \(-0.505363\pi\)
−0.0168474 + 0.999858i \(0.505363\pi\)
\(180\) 0 0
\(181\) −7.64380 −0.568160 −0.284080 0.958801i \(-0.591688\pi\)
−0.284080 + 0.958801i \(0.591688\pi\)
\(182\) 0 0
\(183\) 45.3094 3.34937
\(184\) 0 0
\(185\) 1.00000 0.0735215
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −36.7640 −2.67419
\(190\) 0 0
\(191\) −18.1093 −1.31034 −0.655171 0.755481i \(-0.727403\pi\)
−0.655171 + 0.755481i \(0.727403\pi\)
\(192\) 0 0
\(193\) 17.5298 1.26182 0.630912 0.775854i \(-0.282681\pi\)
0.630912 + 0.775854i \(0.282681\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −6.73463 −0.479823 −0.239911 0.970795i \(-0.577118\pi\)
−0.239911 + 0.970795i \(0.577118\pi\)
\(198\) 0 0
\(199\) −11.8595 −0.840699 −0.420349 0.907362i \(-0.638093\pi\)
−0.420349 + 0.907362i \(0.638093\pi\)
\(200\) 0 0
\(201\) 36.4683 2.57228
\(202\) 0 0
\(203\) −3.21949 −0.225964
\(204\) 0 0
\(205\) −5.76491 −0.402639
\(206\) 0 0
\(207\) −27.0596 −1.88077
\(208\) 0 0
\(209\) 8.49954 0.587926
\(210\) 0 0
\(211\) 21.8255 1.50253 0.751263 0.660003i \(-0.229445\pi\)
0.751263 + 0.660003i \(0.229445\pi\)
\(212\) 0 0
\(213\) −2.29564 −0.157295
\(214\) 0 0
\(215\) −3.03028 −0.206663
\(216\) 0 0
\(217\) 2.00000 0.135769
\(218\) 0 0
\(219\) −24.0752 −1.62685
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 6.62534 0.443666 0.221833 0.975085i \(-0.428796\pi\)
0.221833 + 0.975085i \(0.428796\pi\)
\(224\) 0 0
\(225\) 6.76491 0.450994
\(226\) 0 0
\(227\) −17.2800 −1.14692 −0.573458 0.819235i \(-0.694399\pi\)
−0.573458 + 0.819235i \(0.694399\pi\)
\(228\) 0 0
\(229\) 11.3553 0.750378 0.375189 0.926948i \(-0.377578\pi\)
0.375189 + 0.926948i \(0.377578\pi\)
\(230\) 0 0
\(231\) 14.7952 0.973452
\(232\) 0 0
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 0 0
\(235\) 1.18544 0.0773294
\(236\) 0 0
\(237\) −8.06055 −0.523589
\(238\) 0 0
\(239\) −23.6997 −1.53300 −0.766502 0.642242i \(-0.778004\pi\)
−0.766502 + 0.642242i \(0.778004\pi\)
\(240\) 0 0
\(241\) −27.5904 −1.77725 −0.888626 0.458633i \(-0.848339\pi\)
−0.888626 + 0.458633i \(0.848339\pi\)
\(242\) 0 0
\(243\) −16.1698 −1.03730
\(244\) 0 0
\(245\) 2.76491 0.176644
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −39.3553 −2.49404
\(250\) 0 0
\(251\) −3.04965 −0.192492 −0.0962462 0.995358i \(-0.530684\pi\)
−0.0962462 + 0.995358i \(0.530684\pi\)
\(252\) 0 0
\(253\) 6.06055 0.381024
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 25.4693 1.58873 0.794365 0.607441i \(-0.207804\pi\)
0.794365 + 0.607441i \(0.207804\pi\)
\(258\) 0 0
\(259\) 3.12489 0.194171
\(260\) 0 0
\(261\) −6.96972 −0.431415
\(262\) 0 0
\(263\) −0.0946093 −0.00583386 −0.00291693 0.999996i \(-0.500928\pi\)
−0.00291693 + 0.999996i \(0.500928\pi\)
\(264\) 0 0
\(265\) 8.79518 0.540284
\(266\) 0 0
\(267\) −26.7493 −1.63703
\(268\) 0 0
\(269\) −17.5904 −1.07250 −0.536252 0.844058i \(-0.680160\pi\)
−0.536252 + 0.844058i \(0.680160\pi\)
\(270\) 0 0
\(271\) −6.32500 −0.384217 −0.192108 0.981374i \(-0.561532\pi\)
−0.192108 + 0.981374i \(0.561532\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.51514 −0.0913663
\(276\) 0 0
\(277\) 13.5904 0.816566 0.408283 0.912855i \(-0.366128\pi\)
0.408283 + 0.912855i \(0.366128\pi\)
\(278\) 0 0
\(279\) 4.32970 0.259212
\(280\) 0 0
\(281\) 18.9991 1.13339 0.566695 0.823928i \(-0.308222\pi\)
0.566695 + 0.823928i \(0.308222\pi\)
\(282\) 0 0
\(283\) −7.34060 −0.436353 −0.218177 0.975909i \(-0.570011\pi\)
−0.218177 + 0.975909i \(0.570011\pi\)
\(284\) 0 0
\(285\) 17.5298 1.03838
\(286\) 0 0
\(287\) −18.0147 −1.06337
\(288\) 0 0
\(289\) −17.0000 −1.00000
\(290\) 0 0
\(291\) −18.7493 −1.09910
\(292\) 0 0
\(293\) −10.0000 −0.584206 −0.292103 0.956387i \(-0.594355\pi\)
−0.292103 + 0.956387i \(0.594355\pi\)
\(294\) 0 0
\(295\) 3.67030 0.213693
\(296\) 0 0
\(297\) 17.8255 1.03434
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) −9.46927 −0.545799
\(302\) 0 0
\(303\) 47.7943 2.74571
\(304\) 0 0
\(305\) −14.4995 −0.830241
\(306\) 0 0
\(307\) 4.40493 0.251403 0.125701 0.992068i \(-0.459882\pi\)
0.125701 + 0.992068i \(0.459882\pi\)
\(308\) 0 0
\(309\) −46.0899 −2.62196
\(310\) 0 0
\(311\) 24.1698 1.37055 0.685273 0.728286i \(-0.259683\pi\)
0.685273 + 0.728286i \(0.259683\pi\)
\(312\) 0 0
\(313\) 14.9991 0.847798 0.423899 0.905709i \(-0.360661\pi\)
0.423899 + 0.905709i \(0.360661\pi\)
\(314\) 0 0
\(315\) 21.1396 1.19108
\(316\) 0 0
\(317\) 24.5601 1.37943 0.689716 0.724080i \(-0.257735\pi\)
0.689716 + 0.724080i \(0.257735\pi\)
\(318\) 0 0
\(319\) 1.56101 0.0873998
\(320\) 0 0
\(321\) −15.4693 −0.863410
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 57.8089 3.19684
\(328\) 0 0
\(329\) 3.70436 0.204228
\(330\) 0 0
\(331\) 16.1698 0.888775 0.444387 0.895835i \(-0.353421\pi\)
0.444387 + 0.895835i \(0.353421\pi\)
\(332\) 0 0
\(333\) 6.76491 0.370715
\(334\) 0 0
\(335\) −11.6703 −0.637617
\(336\) 0 0
\(337\) −27.8548 −1.51735 −0.758674 0.651470i \(-0.774153\pi\)
−0.758674 + 0.651470i \(0.774153\pi\)
\(338\) 0 0
\(339\) 54.5895 2.96489
\(340\) 0 0
\(341\) −0.969724 −0.0525135
\(342\) 0 0
\(343\) −13.2342 −0.714578
\(344\) 0 0
\(345\) 12.4995 0.672953
\(346\) 0 0
\(347\) 4.49954 0.241548 0.120774 0.992680i \(-0.461462\pi\)
0.120774 + 0.992680i \(0.461462\pi\)
\(348\) 0 0
\(349\) −35.5298 −1.90187 −0.950934 0.309395i \(-0.899874\pi\)
−0.950934 + 0.309395i \(0.899874\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 16.0606 0.854817 0.427408 0.904059i \(-0.359427\pi\)
0.427408 + 0.904059i \(0.359427\pi\)
\(354\) 0 0
\(355\) 0.734633 0.0389903
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 5.51514 0.291078 0.145539 0.989353i \(-0.453508\pi\)
0.145539 + 0.989353i \(0.453508\pi\)
\(360\) 0 0
\(361\) 12.4693 0.656277
\(362\) 0 0
\(363\) 27.2001 1.42764
\(364\) 0 0
\(365\) 7.70436 0.403264
\(366\) 0 0
\(367\) 5.60975 0.292826 0.146413 0.989224i \(-0.453227\pi\)
0.146413 + 0.989224i \(0.453227\pi\)
\(368\) 0 0
\(369\) −38.9991 −2.03021
\(370\) 0 0
\(371\) 27.4839 1.42690
\(372\) 0 0
\(373\) −19.8255 −1.02652 −0.513262 0.858232i \(-0.671563\pi\)
−0.513262 + 0.858232i \(0.671563\pi\)
\(374\) 0 0
\(375\) −3.12489 −0.161368
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −17.5151 −0.899692 −0.449846 0.893106i \(-0.648521\pi\)
−0.449846 + 0.893106i \(0.648521\pi\)
\(380\) 0 0
\(381\) 54.8851 2.81185
\(382\) 0 0
\(383\) −11.5298 −0.589146 −0.294573 0.955629i \(-0.595177\pi\)
−0.294573 + 0.955629i \(0.595177\pi\)
\(384\) 0 0
\(385\) −4.73463 −0.241299
\(386\) 0 0
\(387\) −20.4995 −1.04205
\(388\) 0 0
\(389\) 28.0899 1.42422 0.712108 0.702070i \(-0.247741\pi\)
0.712108 + 0.702070i \(0.247741\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 2.00000 0.100887
\(394\) 0 0
\(395\) 2.57947 0.129787
\(396\) 0 0
\(397\) 1.26537 0.0635070 0.0317535 0.999496i \(-0.489891\pi\)
0.0317535 + 0.999496i \(0.489891\pi\)
\(398\) 0 0
\(399\) 54.7787 2.74236
\(400\) 0 0
\(401\) −4.43899 −0.221673 −0.110836 0.993839i \(-0.535353\pi\)
−0.110836 + 0.993839i \(0.535353\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 16.4693 0.818364
\(406\) 0 0
\(407\) −1.51514 −0.0751026
\(408\) 0 0
\(409\) −0.909172 −0.0449556 −0.0224778 0.999747i \(-0.507156\pi\)
−0.0224778 + 0.999747i \(0.507156\pi\)
\(410\) 0 0
\(411\) 32.8099 1.61839
\(412\) 0 0
\(413\) 11.4693 0.564366
\(414\) 0 0
\(415\) 12.5942 0.618223
\(416\) 0 0
\(417\) −45.4986 −2.22808
\(418\) 0 0
\(419\) 19.6050 0.957769 0.478885 0.877878i \(-0.341041\pi\)
0.478885 + 0.877878i \(0.341041\pi\)
\(420\) 0 0
\(421\) 0.909172 0.0443103 0.0221552 0.999755i \(-0.492947\pi\)
0.0221552 + 0.999755i \(0.492947\pi\)
\(422\) 0 0
\(423\) 8.01938 0.389915
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −45.3094 −2.19268
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −13.3288 −0.642025 −0.321012 0.947075i \(-0.604023\pi\)
−0.321012 + 0.947075i \(0.604023\pi\)
\(432\) 0 0
\(433\) −11.8255 −0.568295 −0.284148 0.958781i \(-0.591711\pi\)
−0.284148 + 0.958781i \(0.591711\pi\)
\(434\) 0 0
\(435\) 3.21949 0.154363
\(436\) 0 0
\(437\) 22.4390 1.07340
\(438\) 0 0
\(439\) 15.5492 0.742123 0.371061 0.928608i \(-0.378994\pi\)
0.371061 + 0.928608i \(0.378994\pi\)
\(440\) 0 0
\(441\) 18.7044 0.890684
\(442\) 0 0
\(443\) −27.4646 −1.30488 −0.652441 0.757840i \(-0.726255\pi\)
−0.652441 + 0.757840i \(0.726255\pi\)
\(444\) 0 0
\(445\) 8.56009 0.405787
\(446\) 0 0
\(447\) −24.2645 −1.14767
\(448\) 0 0
\(449\) 14.0000 0.660701 0.330350 0.943858i \(-0.392833\pi\)
0.330350 + 0.943858i \(0.392833\pi\)
\(450\) 0 0
\(451\) 8.73463 0.411298
\(452\) 0 0
\(453\) 68.0587 3.19768
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −36.9385 −1.72791 −0.863956 0.503568i \(-0.832020\pi\)
−0.863956 + 0.503568i \(0.832020\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −21.1807 −0.986485 −0.493243 0.869892i \(-0.664189\pi\)
−0.493243 + 0.869892i \(0.664189\pi\)
\(462\) 0 0
\(463\) −6.08991 −0.283022 −0.141511 0.989937i \(-0.545196\pi\)
−0.141511 + 0.989937i \(0.545196\pi\)
\(464\) 0 0
\(465\) −2.00000 −0.0927478
\(466\) 0 0
\(467\) −14.6282 −0.676913 −0.338456 0.940982i \(-0.609905\pi\)
−0.338456 + 0.940982i \(0.609905\pi\)
\(468\) 0 0
\(469\) −36.4683 −1.68395
\(470\) 0 0
\(471\) 60.4830 2.78691
\(472\) 0 0
\(473\) 4.59129 0.211108
\(474\) 0 0
\(475\) −5.60975 −0.257393
\(476\) 0 0
\(477\) 59.4986 2.72425
\(478\) 0 0
\(479\) −19.6703 −0.898759 −0.449379 0.893341i \(-0.648355\pi\)
−0.449379 + 0.893341i \(0.648355\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 39.0596 1.77727
\(484\) 0 0
\(485\) 6.00000 0.272446
\(486\) 0 0
\(487\) 4.65940 0.211138 0.105569 0.994412i \(-0.466334\pi\)
0.105569 + 0.994412i \(0.466334\pi\)
\(488\) 0 0
\(489\) 35.0596 1.58545
\(490\) 0 0
\(491\) −37.6197 −1.69775 −0.848877 0.528590i \(-0.822721\pi\)
−0.848877 + 0.528590i \(0.822721\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) −10.2498 −0.460693
\(496\) 0 0
\(497\) 2.29564 0.102974
\(498\) 0 0
\(499\) 0.359060 0.0160737 0.00803686 0.999968i \(-0.497442\pi\)
0.00803686 + 0.999968i \(0.497442\pi\)
\(500\) 0 0
\(501\) −38.0899 −1.70173
\(502\) 0 0
\(503\) −8.49954 −0.378976 −0.189488 0.981883i \(-0.560683\pi\)
−0.189488 + 0.981883i \(0.560683\pi\)
\(504\) 0 0
\(505\) −15.2947 −0.680606
\(506\) 0 0
\(507\) 40.6235 1.80415
\(508\) 0 0
\(509\) −16.1745 −0.716924 −0.358462 0.933544i \(-0.616699\pi\)
−0.358462 + 0.933544i \(0.616699\pi\)
\(510\) 0 0
\(511\) 24.0752 1.06503
\(512\) 0 0
\(513\) 65.9982 2.91389
\(514\) 0 0
\(515\) 14.7493 0.649932
\(516\) 0 0
\(517\) −1.79610 −0.0789925
\(518\) 0 0
\(519\) −19.4839 −0.855250
\(520\) 0 0
\(521\) −11.2947 −0.494831 −0.247415 0.968909i \(-0.579581\pi\)
−0.247415 + 0.968909i \(0.579581\pi\)
\(522\) 0 0
\(523\) 11.0303 0.482320 0.241160 0.970485i \(-0.422472\pi\)
0.241160 + 0.970485i \(0.422472\pi\)
\(524\) 0 0
\(525\) −9.76491 −0.426176
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −7.00000 −0.304348
\(530\) 0 0
\(531\) 24.8292 1.07750
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 4.95035 0.214022
\(536\) 0 0
\(537\) 1.40871 0.0607905
\(538\) 0 0
\(539\) −4.18922 −0.180442
\(540\) 0 0
\(541\) 18.9991 0.816834 0.408417 0.912795i \(-0.366081\pi\)
0.408417 + 0.912795i \(0.366081\pi\)
\(542\) 0 0
\(543\) 23.8860 1.02505
\(544\) 0 0
\(545\) −18.4995 −0.792433
\(546\) 0 0
\(547\) 33.9982 1.45366 0.726828 0.686819i \(-0.240994\pi\)
0.726828 + 0.686819i \(0.240994\pi\)
\(548\) 0 0
\(549\) −98.0881 −4.18630
\(550\) 0 0
\(551\) 5.77959 0.246219
\(552\) 0 0
\(553\) 8.06055 0.342770
\(554\) 0 0
\(555\) −3.12489 −0.132644
\(556\) 0 0
\(557\) 19.8789 0.842296 0.421148 0.906992i \(-0.361627\pi\)
0.421148 + 0.906992i \(0.361627\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −28.4995 −1.20111 −0.600556 0.799583i \(-0.705054\pi\)
−0.600556 + 0.799583i \(0.705054\pi\)
\(564\) 0 0
\(565\) −17.4693 −0.734938
\(566\) 0 0
\(567\) 51.4646 2.16131
\(568\) 0 0
\(569\) 38.4995 1.61398 0.806992 0.590562i \(-0.201094\pi\)
0.806992 + 0.590562i \(0.201094\pi\)
\(570\) 0 0
\(571\) −21.3553 −0.893691 −0.446845 0.894611i \(-0.647453\pi\)
−0.446845 + 0.894611i \(0.647453\pi\)
\(572\) 0 0
\(573\) 56.5895 2.36406
\(574\) 0 0
\(575\) −4.00000 −0.166812
\(576\) 0 0
\(577\) 26.9385 1.12147 0.560733 0.827997i \(-0.310519\pi\)
0.560733 + 0.827997i \(0.310519\pi\)
\(578\) 0 0
\(579\) −54.7787 −2.27652
\(580\) 0 0
\(581\) 39.3553 1.63273
\(582\) 0 0
\(583\) −13.3259 −0.551903
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −24.1505 −0.996796 −0.498398 0.866948i \(-0.666078\pi\)
−0.498398 + 0.866948i \(0.666078\pi\)
\(588\) 0 0
\(589\) −3.59037 −0.147939
\(590\) 0 0
\(591\) 21.0450 0.865674
\(592\) 0 0
\(593\) 7.58325 0.311407 0.155703 0.987804i \(-0.450236\pi\)
0.155703 + 0.987804i \(0.450236\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 37.0596 1.51675
\(598\) 0 0
\(599\) 38.5142 1.57365 0.786824 0.617177i \(-0.211724\pi\)
0.786824 + 0.617177i \(0.211724\pi\)
\(600\) 0 0
\(601\) −23.4087 −0.954861 −0.477431 0.878669i \(-0.658432\pi\)
−0.477431 + 0.878669i \(0.658432\pi\)
\(602\) 0 0
\(603\) −78.9485 −3.21503
\(604\) 0 0
\(605\) −8.70436 −0.353882
\(606\) 0 0
\(607\) 15.5005 0.629144 0.314572 0.949234i \(-0.398139\pi\)
0.314572 + 0.949234i \(0.398139\pi\)
\(608\) 0 0
\(609\) 10.0606 0.407674
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 22.2645 0.899253 0.449626 0.893217i \(-0.351557\pi\)
0.449626 + 0.893217i \(0.351557\pi\)
\(614\) 0 0
\(615\) 18.0147 0.726422
\(616\) 0 0
\(617\) −46.3232 −1.86490 −0.932450 0.361298i \(-0.882334\pi\)
−0.932450 + 0.361298i \(0.882334\pi\)
\(618\) 0 0
\(619\) 26.7034 1.07330 0.536651 0.843804i \(-0.319689\pi\)
0.536651 + 0.843804i \(0.319689\pi\)
\(620\) 0 0
\(621\) 47.0596 1.88844
\(622\) 0 0
\(623\) 26.7493 1.07169
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −26.5601 −1.06071
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 9.29942 0.370204 0.185102 0.982719i \(-0.440738\pi\)
0.185102 + 0.982719i \(0.440738\pi\)
\(632\) 0 0
\(633\) −68.2021 −2.71079
\(634\) 0 0
\(635\) −17.5639 −0.697001
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 4.96972 0.196599
\(640\) 0 0
\(641\) −21.1131 −0.833916 −0.416958 0.908926i \(-0.636904\pi\)
−0.416958 + 0.908926i \(0.636904\pi\)
\(642\) 0 0
\(643\) 17.9007 0.705934 0.352967 0.935636i \(-0.385173\pi\)
0.352967 + 0.935636i \(0.385173\pi\)
\(644\) 0 0
\(645\) 9.46927 0.372852
\(646\) 0 0
\(647\) 32.6500 1.28360 0.641802 0.766870i \(-0.278187\pi\)
0.641802 + 0.766870i \(0.278187\pi\)
\(648\) 0 0
\(649\) −5.56101 −0.218289
\(650\) 0 0
\(651\) −6.24977 −0.244948
\(652\) 0 0
\(653\) −42.0587 −1.64588 −0.822942 0.568125i \(-0.807669\pi\)
−0.822942 + 0.568125i \(0.807669\pi\)
\(654\) 0 0
\(655\) −0.640023 −0.0250078
\(656\) 0 0
\(657\) 52.1193 2.03337
\(658\) 0 0
\(659\) 0.613528 0.0238997 0.0119498 0.999929i \(-0.496196\pi\)
0.0119498 + 0.999929i \(0.496196\pi\)
\(660\) 0 0
\(661\) −41.6803 −1.62118 −0.810588 0.585617i \(-0.800852\pi\)
−0.810588 + 0.585617i \(0.800852\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −17.5298 −0.679777
\(666\) 0 0
\(667\) 4.12110 0.159570
\(668\) 0 0
\(669\) −20.7034 −0.800441
\(670\) 0 0
\(671\) 21.9688 0.848096
\(672\) 0 0
\(673\) 36.2039 1.39556 0.697779 0.716313i \(-0.254172\pi\)
0.697779 + 0.716313i \(0.254172\pi\)
\(674\) 0 0
\(675\) −11.7649 −0.452832
\(676\) 0 0
\(677\) 41.6732 1.60163 0.800815 0.598912i \(-0.204400\pi\)
0.800815 + 0.598912i \(0.204400\pi\)
\(678\) 0 0
\(679\) 18.7493 0.719533
\(680\) 0 0
\(681\) 53.9982 2.06921
\(682\) 0 0
\(683\) 11.5005 0.440053 0.220026 0.975494i \(-0.429386\pi\)
0.220026 + 0.975494i \(0.429386\pi\)
\(684\) 0 0
\(685\) −10.4995 −0.401167
\(686\) 0 0
\(687\) −35.4839 −1.35380
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −44.7181 −1.70116 −0.850579 0.525848i \(-0.823748\pi\)
−0.850579 + 0.525848i \(0.823748\pi\)
\(692\) 0 0
\(693\) −32.0294 −1.21669
\(694\) 0 0
\(695\) 14.5601 0.552296
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 18.7493 0.709164
\(700\) 0 0
\(701\) 41.9083 1.58285 0.791426 0.611264i \(-0.209339\pi\)
0.791426 + 0.611264i \(0.209339\pi\)
\(702\) 0 0
\(703\) −5.60975 −0.211576
\(704\) 0 0
\(705\) −3.70436 −0.139514
\(706\) 0 0
\(707\) −47.7943 −1.79749
\(708\) 0 0
\(709\) 35.0284 1.31552 0.657760 0.753227i \(-0.271504\pi\)
0.657760 + 0.753227i \(0.271504\pi\)
\(710\) 0 0
\(711\) 17.4499 0.654422
\(712\) 0 0
\(713\) −2.56009 −0.0958763
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 74.0587 2.76577
\(718\) 0 0
\(719\) −13.8936 −0.518143 −0.259071 0.965858i \(-0.583417\pi\)
−0.259071 + 0.965858i \(0.583417\pi\)
\(720\) 0 0
\(721\) 46.0899 1.71648
\(722\) 0 0
\(723\) 86.2167 3.20644
\(724\) 0 0
\(725\) −1.03028 −0.0382635
\(726\) 0 0
\(727\) −25.0284 −0.928254 −0.464127 0.885769i \(-0.653632\pi\)
−0.464127 + 0.885769i \(0.653632\pi\)
\(728\) 0 0
\(729\) 1.12110 0.0415224
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 17.7649 0.656162 0.328081 0.944650i \(-0.393598\pi\)
0.328081 + 0.944650i \(0.393598\pi\)
\(734\) 0 0
\(735\) −8.64002 −0.318692
\(736\) 0 0
\(737\) 17.6821 0.651329
\(738\) 0 0
\(739\) −43.7943 −1.61100 −0.805499 0.592597i \(-0.798103\pi\)
−0.805499 + 0.592597i \(0.798103\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −19.4646 −0.714086 −0.357043 0.934088i \(-0.616215\pi\)
−0.357043 + 0.934088i \(0.616215\pi\)
\(744\) 0 0
\(745\) 7.76491 0.284484
\(746\) 0 0
\(747\) 85.1983 3.11724
\(748\) 0 0
\(749\) 15.4693 0.565235
\(750\) 0 0
\(751\) 13.5151 0.493174 0.246587 0.969121i \(-0.420691\pi\)
0.246587 + 0.969121i \(0.420691\pi\)
\(752\) 0 0
\(753\) 9.52982 0.347286
\(754\) 0 0
\(755\) −21.7796 −0.792640
\(756\) 0 0
\(757\) 40.7106 1.47965 0.739825 0.672799i \(-0.234908\pi\)
0.739825 + 0.672799i \(0.234908\pi\)
\(758\) 0 0
\(759\) −18.9385 −0.687425
\(760\) 0 0
\(761\) −4.17454 −0.151327 −0.0756635 0.997133i \(-0.524107\pi\)
−0.0756635 + 0.997133i \(0.524107\pi\)
\(762\) 0 0
\(763\) −57.8089 −2.09282
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −7.09083 −0.255702 −0.127851 0.991793i \(-0.540808\pi\)
−0.127851 + 0.991793i \(0.540808\pi\)
\(770\) 0 0
\(771\) −79.5885 −2.86631
\(772\) 0 0
\(773\) 1.26537 0.0455121 0.0227560 0.999741i \(-0.492756\pi\)
0.0227560 + 0.999741i \(0.492756\pi\)
\(774\) 0 0
\(775\) 0.640023 0.0229903
\(776\) 0 0
\(777\) −9.76491 −0.350314
\(778\) 0 0
\(779\) 32.3397 1.15869
\(780\) 0 0
\(781\) −1.11307 −0.0398288
\(782\) 0 0
\(783\) 12.1211 0.433173
\(784\) 0 0
\(785\) −19.3553 −0.690820
\(786\) 0 0
\(787\) −27.3141 −0.973643 −0.486821 0.873502i \(-0.661844\pi\)
−0.486821 + 0.873502i \(0.661844\pi\)
\(788\) 0 0
\(789\) 0.295643 0.0105252
\(790\) 0 0
\(791\) −54.5895 −1.94098
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) −27.4839 −0.974755
\(796\) 0 0
\(797\) 24.9991 0.885513 0.442756 0.896642i \(-0.354001\pi\)
0.442756 + 0.896642i \(0.354001\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 57.9083 2.04609
\(802\) 0 0
\(803\) −11.6732 −0.411937
\(804\) 0 0
\(805\) −12.4995 −0.440551
\(806\) 0 0
\(807\) 54.9679 1.93496
\(808\) 0 0
\(809\) 11.4693 0.403238 0.201619 0.979464i \(-0.435380\pi\)
0.201619 + 0.979464i \(0.435380\pi\)
\(810\) 0 0
\(811\) 20.8851 0.733375 0.366687 0.930344i \(-0.380492\pi\)
0.366687 + 0.930344i \(0.380492\pi\)
\(812\) 0 0
\(813\) 19.7649 0.693186
\(814\) 0 0
\(815\) −11.2195 −0.393002
\(816\) 0 0
\(817\) 16.9991 0.594723
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 12.7034 0.443353 0.221677 0.975120i \(-0.428847\pi\)
0.221677 + 0.975120i \(0.428847\pi\)
\(822\) 0 0
\(823\) 20.2909 0.707298 0.353649 0.935378i \(-0.384941\pi\)
0.353649 + 0.935378i \(0.384941\pi\)
\(824\) 0 0
\(825\) 4.73463 0.164839
\(826\) 0 0
\(827\) −23.7190 −0.824792 −0.412396 0.911005i \(-0.635308\pi\)
−0.412396 + 0.911005i \(0.635308\pi\)
\(828\) 0 0
\(829\) 52.5895 1.82651 0.913254 0.407392i \(-0.133562\pi\)
0.913254 + 0.407392i \(0.133562\pi\)
\(830\) 0 0
\(831\) −42.4683 −1.47321
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 12.1892 0.421825
\(836\) 0 0
\(837\) −7.52982 −0.260269
\(838\) 0 0
\(839\) −34.5601 −1.19315 −0.596573 0.802558i \(-0.703472\pi\)
−0.596573 + 0.802558i \(0.703472\pi\)
\(840\) 0 0
\(841\) −27.9385 −0.963398
\(842\) 0 0
\(843\) −59.3700 −2.04481
\(844\) 0 0
\(845\) −13.0000 −0.447214
\(846\) 0 0
\(847\) −27.2001 −0.934607
\(848\) 0 0
\(849\) 22.9385 0.787248
\(850\) 0 0
\(851\) −4.00000 −0.137118
\(852\) 0 0
\(853\) −31.7115 −1.08578 −0.542890 0.839804i \(-0.682670\pi\)
−0.542890 + 0.839804i \(0.682670\pi\)
\(854\) 0 0
\(855\) −37.9494 −1.29784
\(856\) 0 0
\(857\) 7.93945 0.271206 0.135603 0.990763i \(-0.456703\pi\)
0.135603 + 0.990763i \(0.456703\pi\)
\(858\) 0 0
\(859\) −30.8898 −1.05395 −0.526973 0.849882i \(-0.676673\pi\)
−0.526973 + 0.849882i \(0.676673\pi\)
\(860\) 0 0
\(861\) 56.2938 1.91849
\(862\) 0 0
\(863\) 20.7081 0.704913 0.352457 0.935828i \(-0.385346\pi\)
0.352457 + 0.935828i \(0.385346\pi\)
\(864\) 0 0
\(865\) 6.23509 0.211999
\(866\) 0 0
\(867\) 53.1231 1.80415
\(868\) 0 0
\(869\) −3.90826 −0.132578
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 40.5895 1.37374
\(874\) 0 0
\(875\) 3.12489 0.105640
\(876\) 0 0
\(877\) −39.1202 −1.32099 −0.660497 0.750828i \(-0.729655\pi\)
−0.660497 + 0.750828i \(0.729655\pi\)
\(878\) 0 0
\(879\) 31.2489 1.05400
\(880\) 0 0
\(881\) 12.3491 0.416051 0.208026 0.978123i \(-0.433296\pi\)
0.208026 + 0.978123i \(0.433296\pi\)
\(882\) 0 0
\(883\) −35.2195 −1.18523 −0.592615 0.805486i \(-0.701904\pi\)
−0.592615 + 0.805486i \(0.701904\pi\)
\(884\) 0 0
\(885\) −11.4693 −0.385535
\(886\) 0 0
\(887\) −51.8043 −1.73942 −0.869708 0.493566i \(-0.835693\pi\)
−0.869708 + 0.493566i \(0.835693\pi\)
\(888\) 0 0
\(889\) −54.8851 −1.84079
\(890\) 0 0
\(891\) −24.9532 −0.835964
\(892\) 0 0
\(893\) −6.65001 −0.222534
\(894\) 0 0
\(895\) −0.450805 −0.0150687
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −0.659401 −0.0219923
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 29.5904 0.984706
\(904\) 0 0
\(905\) −7.64380 −0.254089
\(906\) 0 0
\(907\) −55.8695 −1.85512 −0.927558 0.373679i \(-0.878096\pi\)
−0.927558 + 0.373679i \(0.878096\pi\)
\(908\) 0 0
\(909\) −103.467 −3.43180
\(910\) 0 0
\(911\) −33.2607 −1.10198 −0.550988 0.834513i \(-0.685749\pi\)
−0.550988 + 0.834513i \(0.685749\pi\)
\(912\) 0 0
\(913\) −19.0819 −0.631518
\(914\) 0 0
\(915\) 45.3094 1.49788
\(916\) 0 0
\(917\) −2.00000 −0.0660458
\(918\) 0 0
\(919\) −4.98910 −0.164575 −0.0822876 0.996609i \(-0.526223\pi\)
−0.0822876 + 0.996609i \(0.526223\pi\)
\(920\) 0 0
\(921\) −13.7649 −0.453569
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 1.00000 0.0328798
\(926\) 0 0
\(927\) 99.7778 3.27713
\(928\) 0 0
\(929\) 30.0000 0.984268 0.492134 0.870519i \(-0.336217\pi\)
0.492134 + 0.870519i \(0.336217\pi\)
\(930\) 0 0
\(931\) −15.5104 −0.508334
\(932\) 0 0
\(933\) −75.5280 −2.47268
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −58.8851 −1.92369 −0.961846 0.273591i \(-0.911789\pi\)
−0.961846 + 0.273591i \(0.911789\pi\)
\(938\) 0 0
\(939\) −46.8704 −1.52956
\(940\) 0 0
\(941\) 19.6509 0.640602 0.320301 0.947316i \(-0.396216\pi\)
0.320301 + 0.947316i \(0.396216\pi\)
\(942\) 0 0
\(943\) 23.0596 0.750925
\(944\) 0 0
\(945\) −36.7640 −1.19593
\(946\) 0 0
\(947\) 32.3397 1.05090 0.525449 0.850825i \(-0.323897\pi\)
0.525449 + 0.850825i \(0.323897\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) −76.7475 −2.48871
\(952\) 0 0
\(953\) −48.8245 −1.58158 −0.790791 0.612086i \(-0.790331\pi\)
−0.790791 + 0.612086i \(0.790331\pi\)
\(954\) 0 0
\(955\) −18.1093 −0.586003
\(956\) 0 0
\(957\) −4.87798 −0.157683
\(958\) 0 0
\(959\) −32.8099 −1.05949
\(960\) 0 0
\(961\) −30.5904 −0.986786
\(962\) 0 0
\(963\) 33.4886 1.07916
\(964\) 0 0
\(965\) 17.5298 0.564305
\(966\) 0 0
\(967\) 14.9915 0.482095 0.241047 0.970513i \(-0.422509\pi\)
0.241047 + 0.970513i \(0.422509\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 18.4390 0.591735 0.295868 0.955229i \(-0.404391\pi\)
0.295868 + 0.955229i \(0.404391\pi\)
\(972\) 0 0
\(973\) 45.4986 1.45862
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 29.5298 0.944743 0.472371 0.881400i \(-0.343398\pi\)
0.472371 + 0.881400i \(0.343398\pi\)
\(978\) 0 0
\(979\) −12.9697 −0.414514
\(980\) 0 0
\(981\) −125.148 −3.99566
\(982\) 0 0
\(983\) 27.9348 0.890980 0.445490 0.895287i \(-0.353029\pi\)
0.445490 + 0.895287i \(0.353029\pi\)
\(984\) 0 0
\(985\) −6.73463 −0.214583
\(986\) 0 0
\(987\) −11.5757 −0.368458
\(988\) 0 0
\(989\) 12.1211 0.385429
\(990\) 0 0
\(991\) 3.85952 0.122602 0.0613008 0.998119i \(-0.480475\pi\)
0.0613008 + 0.998119i \(0.480475\pi\)
\(992\) 0 0
\(993\) −50.5289 −1.60349
\(994\) 0 0
\(995\) −11.8595 −0.375972
\(996\) 0 0
\(997\) 18.6500 0.590652 0.295326 0.955397i \(-0.404572\pi\)
0.295326 + 0.955397i \(0.404572\pi\)
\(998\) 0 0
\(999\) −11.7649 −0.372225
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 2960.2.a.s.1.1 3
4.3 odd 2 1480.2.a.f.1.3 3
20.19 odd 2 7400.2.a.m.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1480.2.a.f.1.3 3 4.3 odd 2
2960.2.a.s.1.1 3 1.1 even 1 trivial
7400.2.a.m.1.1 3 20.19 odd 2