Properties

Label 2960.2.a.s.1.3
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 1.3
Root \(-1.76156\) of defining polynomial
Character \(\chi\) \(=\) 2960.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.76156 q^{3} +1.00000 q^{5} -1.76156 q^{7} +0.103084 q^{9} +O(q^{10})\) \(q+1.76156 q^{3} +1.00000 q^{5} -1.76156 q^{7} +0.103084 q^{9} -4.62620 q^{11} +1.76156 q^{15} +2.38776 q^{19} -3.10308 q^{21} -4.00000 q^{23} +1.00000 q^{25} -5.10308 q^{27} -7.25240 q^{29} -1.13536 q^{31} -8.14931 q^{33} -1.76156 q^{35} +1.00000 q^{37} +0.896916 q^{41} -9.25240 q^{43} +0.103084 q^{45} +8.74324 q^{47} -3.89692 q^{49} +8.35548 q^{53} -4.62620 q^{55} +4.20617 q^{57} +8.11704 q^{59} +5.04623 q^{61} -0.181588 q^{63} -16.1170 q^{67} -7.04623 q^{69} -12.1493 q^{71} -11.4017 q^{73} +1.76156 q^{75} +8.14931 q^{77} -11.6402 q^{79} -9.29862 q^{81} -18.0602 q^{83} -12.7755 q^{87} +1.45856 q^{89} -2.00000 q^{93} +2.38776 q^{95} +6.00000 q^{97} -0.476886 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q - q^{3} + 3q^{5} + q^{7} + 4q^{9} + O(q^{10}) \) \( 3q - q^{3} + 3q^{5} + q^{7} + 4q^{9} - 5q^{11} - q^{15} - 8q^{19} - 13q^{21} - 12q^{23} + 3q^{25} - 19q^{27} - 4q^{29} - 6q^{31} - 3q^{33} + q^{35} + 3q^{37} - q^{41} - 10q^{43} + 4q^{45} - 3q^{47} - 8q^{49} + 11q^{53} - 5q^{55} + 20q^{57} + 4q^{59} - 10q^{61} + 22q^{63} - 28q^{67} + 4q^{69} - 15q^{71} + 5q^{73} - q^{75} + 3q^{77} - 2q^{79} + 15q^{81} - 5q^{83} - 8q^{87} - 6q^{89} - 6q^{93} - 8q^{95} + 18q^{97} - 14q^{99} + O(q^{100}) \)

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
\(3\) 1.76156 1.01704 0.508518 0.861052i \(-0.330194\pi\)
0.508518 + 0.861052i \(0.330194\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −1.76156 −0.665806 −0.332903 0.942961i \(-0.608028\pi\)
−0.332903 + 0.942961i \(0.608028\pi\)
\(8\) 0 0
\(9\) 0.103084 0.0343612
\(10\) 0 0
\(11\) −4.62620 −1.39485 −0.697426 0.716657i \(-0.745671\pi\)
−0.697426 + 0.716657i \(0.745671\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) 1.76156 0.454832
\(16\) 0 0
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 0 0
\(19\) 2.38776 0.547789 0.273894 0.961760i \(-0.411688\pi\)
0.273894 + 0.961760i \(0.411688\pi\)
\(20\) 0 0
\(21\) −3.10308 −0.677148
\(22\) 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
\(27\) −5.10308 −0.982089
\(28\) 0 0
\(29\) −7.25240 −1.34674 −0.673368 0.739307i \(-0.735153\pi\)
−0.673368 + 0.739307i \(0.735153\pi\)
\(30\) 0 0
\(31\) −1.13536 −0.203917 −0.101958 0.994789i \(-0.532511\pi\)
−0.101958 + 0.994789i \(0.532511\pi\)
\(32\) 0 0
\(33\) −8.14931 −1.41861
\(34\) 0 0
\(35\) −1.76156 −0.297758
\(36\) 0 0
\(37\) 1.00000 0.164399
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0.896916 0.140075 0.0700374 0.997544i \(-0.477688\pi\)
0.0700374 + 0.997544i \(0.477688\pi\)
\(42\) 0 0
\(43\) −9.25240 −1.41098 −0.705489 0.708721i \(-0.749272\pi\)
−0.705489 + 0.708721i \(0.749272\pi\)
\(44\) 0 0
\(45\) 0.103084 0.0153668
\(46\) 0 0
\(47\) 8.74324 1.27533 0.637666 0.770313i \(-0.279900\pi\)
0.637666 + 0.770313i \(0.279900\pi\)
\(48\) 0 0
\(49\) −3.89692 −0.556702
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 8.35548 1.14771 0.573857 0.818956i \(-0.305447\pi\)
0.573857 + 0.818956i \(0.305447\pi\)
\(54\) 0 0
\(55\) −4.62620 −0.623796
\(56\) 0 0
\(57\) 4.20617 0.557120
\(58\) 0 0
\(59\) 8.11704 1.05675 0.528374 0.849012i \(-0.322802\pi\)
0.528374 + 0.849012i \(0.322802\pi\)
\(60\) 0 0
\(61\) 5.04623 0.646103 0.323052 0.946381i \(-0.395291\pi\)
0.323052 + 0.946381i \(0.395291\pi\)
\(62\) 0 0
\(63\) −0.181588 −0.0228779
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −16.1170 −1.96901 −0.984505 0.175358i \(-0.943892\pi\)
−0.984505 + 0.175358i \(0.943892\pi\)
\(68\) 0 0
\(69\) −7.04623 −0.848266
\(70\) 0 0
\(71\) −12.1493 −1.44186 −0.720929 0.693009i \(-0.756285\pi\)
−0.720929 + 0.693009i \(0.756285\pi\)
\(72\) 0 0
\(73\) −11.4017 −1.33447 −0.667235 0.744848i \(-0.732522\pi\)
−0.667235 + 0.744848i \(0.732522\pi\)
\(74\) 0 0
\(75\) 1.76156 0.203407
\(76\) 0 0
\(77\) 8.14931 0.928700
\(78\) 0 0
\(79\) −11.6402 −1.30962 −0.654810 0.755794i \(-0.727251\pi\)
−0.654810 + 0.755794i \(0.727251\pi\)
\(80\) 0 0
\(81\) −9.29862 −1.03318
\(82\) 0 0
\(83\) −18.0602 −1.98236 −0.991181 0.132513i \(-0.957695\pi\)
−0.991181 + 0.132513i \(0.957695\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −12.7755 −1.36968
\(88\) 0 0
\(89\) 1.45856 0.154607 0.0773037 0.997008i \(-0.475369\pi\)
0.0773037 + 0.997008i \(0.475369\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −2.00000 −0.207390
\(94\) 0 0
\(95\) 2.38776 0.244979
\(96\) 0 0
\(97\) 6.00000 0.609208 0.304604 0.952479i \(-0.401476\pi\)
0.304604 + 0.952479i \(0.401476\pi\)
\(98\) 0 0
\(99\) −0.476886 −0.0479288
\(100\) 0 0
\(101\) 4.69075 0.466747 0.233373 0.972387i \(-0.425024\pi\)
0.233373 + 0.972387i \(0.425024\pi\)
\(102\) 0 0
\(103\) −14.5693 −1.43556 −0.717780 0.696270i \(-0.754842\pi\)
−0.717780 + 0.696270i \(0.754842\pi\)
\(104\) 0 0
\(105\) −3.10308 −0.302830
\(106\) 0 0
\(107\) 5.84632 0.565185 0.282592 0.959240i \(-0.408806\pi\)
0.282592 + 0.959240i \(0.408806\pi\)
\(108\) 0 0
\(109\) 1.04623 0.100211 0.0501053 0.998744i \(-0.484044\pi\)
0.0501053 + 0.998744i \(0.484044\pi\)
\(110\) 0 0
\(111\) 1.76156 0.167200
\(112\) 0 0
\(113\) 8.29862 0.780669 0.390334 0.920673i \(-0.372359\pi\)
0.390334 + 0.920673i \(0.372359\pi\)
\(114\) 0 0
\(115\) −4.00000 −0.373002
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 10.4017 0.945610
\(122\) 0 0
\(123\) 1.57997 0.142461
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 19.3126 1.71371 0.856857 0.515554i \(-0.172414\pi\)
0.856857 + 0.515554i \(0.172414\pi\)
\(128\) 0 0
\(129\) −16.2986 −1.43501
\(130\) 0 0
\(131\) 1.13536 0.0991968 0.0495984 0.998769i \(-0.484206\pi\)
0.0495984 + 0.998769i \(0.484206\pi\)
\(132\) 0 0
\(133\) −4.20617 −0.364721
\(134\) 0 0
\(135\) −5.10308 −0.439204
\(136\) 0 0
\(137\) 9.04623 0.772871 0.386436 0.922316i \(-0.373706\pi\)
0.386436 + 0.922316i \(0.373706\pi\)
\(138\) 0 0
\(139\) 7.45856 0.632627 0.316314 0.948655i \(-0.397555\pi\)
0.316314 + 0.948655i \(0.397555\pi\)
\(140\) 0 0
\(141\) 15.4017 1.29706
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) −7.25240 −0.602279
\(146\) 0 0
\(147\) −6.86464 −0.566186
\(148\) 0 0
\(149\) 1.10308 0.0903681 0.0451841 0.998979i \(-0.485613\pi\)
0.0451841 + 0.998979i \(0.485613\pi\)
\(150\) 0 0
\(151\) 1.31695 0.107172 0.0535858 0.998563i \(-0.482935\pi\)
0.0535858 + 0.998563i \(0.482935\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1.13536 −0.0911942
\(156\) 0 0
\(157\) −11.8140 −0.942863 −0.471432 0.881903i \(-0.656263\pi\)
−0.471432 + 0.881903i \(0.656263\pi\)
\(158\) 0 0
\(159\) 14.7187 1.16727
\(160\) 0 0
\(161\) 7.04623 0.555321
\(162\) 0 0
\(163\) 4.77551 0.374047 0.187023 0.982355i \(-0.440116\pi\)
0.187023 + 0.982355i \(0.440116\pi\)
\(164\) 0 0
\(165\) −8.14931 −0.634423
\(166\) 0 0
\(167\) −10.0279 −0.775983 −0.387991 0.921663i \(-0.626831\pi\)
−0.387991 + 0.921663i \(0.626831\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) 0 0
\(171\) 0.246139 0.0188227
\(172\) 0 0
\(173\) 12.8969 0.980534 0.490267 0.871572i \(-0.336899\pi\)
0.490267 + 0.871572i \(0.336899\pi\)
\(174\) 0 0
\(175\) −1.76156 −0.133161
\(176\) 0 0
\(177\) 14.2986 1.07475
\(178\) 0 0
\(179\) −20.8925 −1.56158 −0.780791 0.624792i \(-0.785184\pi\)
−0.780791 + 0.624792i \(0.785184\pi\)
\(180\) 0 0
\(181\) 23.9065 1.77696 0.888478 0.458919i \(-0.151763\pi\)
0.888478 + 0.458919i \(0.151763\pi\)
\(182\) 0 0
\(183\) 8.88922 0.657110
\(184\) 0 0
\(185\) 1.00000 0.0735215
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 8.98937 0.653881
\(190\) 0 0
\(191\) 9.43398 0.682619 0.341310 0.939951i \(-0.389130\pi\)
0.341310 + 0.939951i \(0.389130\pi\)
\(192\) 0 0
\(193\) 4.20617 0.302767 0.151383 0.988475i \(-0.451627\pi\)
0.151383 + 0.988475i \(0.451627\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 6.14931 0.438120 0.219060 0.975711i \(-0.429701\pi\)
0.219060 + 0.975711i \(0.429701\pi\)
\(198\) 0 0
\(199\) 5.91087 0.419010 0.209505 0.977808i \(-0.432815\pi\)
0.209505 + 0.977808i \(0.432815\pi\)
\(200\) 0 0
\(201\) −28.3911 −2.00255
\(202\) 0 0
\(203\) 12.7755 0.896665
\(204\) 0 0
\(205\) 0.896916 0.0626434
\(206\) 0 0
\(207\) −0.412335 −0.0286593
\(208\) 0 0
\(209\) −11.0462 −0.764084
\(210\) 0 0
\(211\) 27.6079 1.90060 0.950302 0.311329i \(-0.100774\pi\)
0.950302 + 0.311329i \(0.100774\pi\)
\(212\) 0 0
\(213\) −21.4017 −1.46642
\(214\) 0 0
\(215\) −9.25240 −0.631008
\(216\) 0 0
\(217\) 2.00000 0.135769
\(218\) 0 0
\(219\) −20.0848 −1.35720
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 21.2847 1.42533 0.712664 0.701506i \(-0.247489\pi\)
0.712664 + 0.701506i \(0.247489\pi\)
\(224\) 0 0
\(225\) 0.103084 0.00687225
\(226\) 0 0
\(227\) −13.7293 −0.911244 −0.455622 0.890173i \(-0.650583\pi\)
−0.455622 + 0.890173i \(0.650583\pi\)
\(228\) 0 0
\(229\) 3.81404 0.252039 0.126020 0.992028i \(-0.459780\pi\)
0.126020 + 0.992028i \(0.459780\pi\)
\(230\) 0 0
\(231\) 14.3555 0.944521
\(232\) 0 0
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 0 0
\(235\) 8.74324 0.570346
\(236\) 0 0
\(237\) −20.5048 −1.33193
\(238\) 0 0
\(239\) 4.72302 0.305507 0.152754 0.988264i \(-0.451186\pi\)
0.152754 + 0.988264i \(0.451186\pi\)
\(240\) 0 0
\(241\) −26.7110 −1.72060 −0.860302 0.509785i \(-0.829725\pi\)
−0.860302 + 0.509785i \(0.829725\pi\)
\(242\) 0 0
\(243\) −1.07081 −0.0686924
\(244\) 0 0
\(245\) −3.89692 −0.248965
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −31.8140 −2.01613
\(250\) 0 0
\(251\) −2.15368 −0.135939 −0.0679696 0.997687i \(-0.521652\pi\)
−0.0679696 + 0.997687i \(0.521652\pi\)
\(252\) 0 0
\(253\) 18.5048 1.16339
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −0.298625 −0.0186277 −0.00931385 0.999957i \(-0.502965\pi\)
−0.00931385 + 0.999957i \(0.502965\pi\)
\(258\) 0 0
\(259\) −1.76156 −0.109458
\(260\) 0 0
\(261\) −0.747604 −0.0462755
\(262\) 0 0
\(263\) 11.0140 0.679149 0.339575 0.940579i \(-0.389717\pi\)
0.339575 + 0.940579i \(0.389717\pi\)
\(264\) 0 0
\(265\) 8.35548 0.513273
\(266\) 0 0
\(267\) 2.56934 0.157241
\(268\) 0 0
\(269\) −16.7110 −1.01889 −0.509443 0.860505i \(-0.670148\pi\)
−0.509443 + 0.860505i \(0.670148\pi\)
\(270\) 0 0
\(271\) 7.43835 0.451848 0.225924 0.974145i \(-0.427460\pi\)
0.225924 + 0.974145i \(0.427460\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −4.62620 −0.278970
\(276\) 0 0
\(277\) 12.7110 0.763728 0.381864 0.924219i \(-0.375282\pi\)
0.381864 + 0.924219i \(0.375282\pi\)
\(278\) 0 0
\(279\) −0.117037 −0.00700682
\(280\) 0 0
\(281\) −20.0925 −1.19862 −0.599308 0.800519i \(-0.704557\pi\)
−0.599308 + 0.800519i \(0.704557\pi\)
\(282\) 0 0
\(283\) −16.2341 −0.965016 −0.482508 0.875892i \(-0.660274\pi\)
−0.482508 + 0.875892i \(0.660274\pi\)
\(284\) 0 0
\(285\) 4.20617 0.249152
\(286\) 0 0
\(287\) −1.57997 −0.0932626
\(288\) 0 0
\(289\) −17.0000 −1.00000
\(290\) 0 0
\(291\) 10.5693 0.619586
\(292\) 0 0
\(293\) −10.0000 −0.584206 −0.292103 0.956387i \(-0.594355\pi\)
−0.292103 + 0.956387i \(0.594355\pi\)
\(294\) 0 0
\(295\) 8.11704 0.472592
\(296\) 0 0
\(297\) 23.6079 1.36987
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 16.2986 0.939437
\(302\) 0 0
\(303\) 8.26302 0.474698
\(304\) 0 0
\(305\) 5.04623 0.288946
\(306\) 0 0
\(307\) −4.03228 −0.230134 −0.115067 0.993358i \(-0.536708\pi\)
−0.115067 + 0.993358i \(0.536708\pi\)
\(308\) 0 0
\(309\) −25.6647 −1.46002
\(310\) 0 0
\(311\) 9.07081 0.514358 0.257179 0.966364i \(-0.417207\pi\)
0.257179 + 0.966364i \(0.417207\pi\)
\(312\) 0 0
\(313\) −24.0925 −1.36179 −0.680893 0.732383i \(-0.738408\pi\)
−0.680893 + 0.732383i \(0.738408\pi\)
\(314\) 0 0
\(315\) −0.181588 −0.0102313
\(316\) 0 0
\(317\) 17.4586 0.980571 0.490285 0.871562i \(-0.336893\pi\)
0.490285 + 0.871562i \(0.336893\pi\)
\(318\) 0 0
\(319\) 33.5510 1.87850
\(320\) 0 0
\(321\) 10.2986 0.574813
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 1.84299 0.101918
\(328\) 0 0
\(329\) −15.4017 −0.849124
\(330\) 0 0
\(331\) 1.07081 0.0588569 0.0294285 0.999567i \(-0.490631\pi\)
0.0294285 + 0.999567i \(0.490631\pi\)
\(332\) 0 0
\(333\) 0.103084 0.00564895
\(334\) 0 0
\(335\) −16.1170 −0.880568
\(336\) 0 0
\(337\) −0.767815 −0.0418255 −0.0209128 0.999781i \(-0.506657\pi\)
−0.0209128 + 0.999781i \(0.506657\pi\)
\(338\) 0 0
\(339\) 14.6185 0.793968
\(340\) 0 0
\(341\) 5.25240 0.284433
\(342\) 0 0
\(343\) 19.1955 1.03646
\(344\) 0 0
\(345\) −7.04623 −0.379356
\(346\) 0 0
\(347\) −15.0462 −0.807724 −0.403862 0.914820i \(-0.632332\pi\)
−0.403862 + 0.914820i \(0.632332\pi\)
\(348\) 0 0
\(349\) −22.2062 −1.18867 −0.594334 0.804218i \(-0.702584\pi\)
−0.594334 + 0.804218i \(0.702584\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 28.5048 1.51716 0.758579 0.651582i \(-0.225894\pi\)
0.758579 + 0.651582i \(0.225894\pi\)
\(354\) 0 0
\(355\) −12.1493 −0.644819
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 8.62620 0.455273 0.227637 0.973746i \(-0.426900\pi\)
0.227637 + 0.973746i \(0.426900\pi\)
\(360\) 0 0
\(361\) −13.2986 −0.699928
\(362\) 0 0
\(363\) 18.3232 0.961719
\(364\) 0 0
\(365\) −11.4017 −0.596793
\(366\) 0 0
\(367\) −2.38776 −0.124640 −0.0623199 0.998056i \(-0.519850\pi\)
−0.0623199 + 0.998056i \(0.519850\pi\)
\(368\) 0 0
\(369\) 0.0924575 0.00481314
\(370\) 0 0
\(371\) −14.7187 −0.764155
\(372\) 0 0
\(373\) −25.6079 −1.32593 −0.662963 0.748652i \(-0.730701\pi\)
−0.662963 + 0.748652i \(0.730701\pi\)
\(374\) 0 0
\(375\) 1.76156 0.0909664
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −20.6262 −1.05950 −0.529748 0.848155i \(-0.677714\pi\)
−0.529748 + 0.848155i \(0.677714\pi\)
\(380\) 0 0
\(381\) 34.0202 1.74291
\(382\) 0 0
\(383\) 1.79383 0.0916606 0.0458303 0.998949i \(-0.485407\pi\)
0.0458303 + 0.998949i \(0.485407\pi\)
\(384\) 0 0
\(385\) 8.14931 0.415327
\(386\) 0 0
\(387\) −0.953771 −0.0484829
\(388\) 0 0
\(389\) 7.66473 0.388617 0.194309 0.980940i \(-0.437754\pi\)
0.194309 + 0.980940i \(0.437754\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 2.00000 0.100887
\(394\) 0 0
\(395\) −11.6402 −0.585680
\(396\) 0 0
\(397\) 14.1493 0.710134 0.355067 0.934841i \(-0.384458\pi\)
0.355067 + 0.934841i \(0.384458\pi\)
\(398\) 0 0
\(399\) −7.40940 −0.370934
\(400\) 0 0
\(401\) 27.5510 1.37583 0.687916 0.725790i \(-0.258526\pi\)
0.687916 + 0.725790i \(0.258526\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −9.29862 −0.462052
\(406\) 0 0
\(407\) −4.62620 −0.229312
\(408\) 0 0
\(409\) 17.7572 0.878036 0.439018 0.898478i \(-0.355326\pi\)
0.439018 + 0.898478i \(0.355326\pi\)
\(410\) 0 0
\(411\) 15.9354 0.786038
\(412\) 0 0
\(413\) −14.2986 −0.703589
\(414\) 0 0
\(415\) −18.0602 −0.886539
\(416\) 0 0
\(417\) 13.1387 0.643404
\(418\) 0 0
\(419\) 2.29093 0.111919 0.0559596 0.998433i \(-0.482178\pi\)
0.0559596 + 0.998433i \(0.482178\pi\)
\(420\) 0 0
\(421\) −17.7572 −0.865432 −0.432716 0.901530i \(-0.642445\pi\)
−0.432716 + 0.901530i \(0.642445\pi\)
\(422\) 0 0
\(423\) 0.901285 0.0438220
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −8.88922 −0.430180
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 30.2095 1.45514 0.727570 0.686033i \(-0.240650\pi\)
0.727570 + 0.686033i \(0.240650\pi\)
\(432\) 0 0
\(433\) −17.6079 −0.846181 −0.423090 0.906088i \(-0.639055\pi\)
−0.423090 + 0.906088i \(0.639055\pi\)
\(434\) 0 0
\(435\) −12.7755 −0.612539
\(436\) 0 0
\(437\) −9.55102 −0.456887
\(438\) 0 0
\(439\) −4.89255 −0.233509 −0.116754 0.993161i \(-0.537249\pi\)
−0.116754 + 0.993161i \(0.537249\pi\)
\(440\) 0 0
\(441\) −0.401709 −0.0191290
\(442\) 0 0
\(443\) 7.61994 0.362034 0.181017 0.983480i \(-0.442061\pi\)
0.181017 + 0.983480i \(0.442061\pi\)
\(444\) 0 0
\(445\) 1.45856 0.0691425
\(446\) 0 0
\(447\) 1.94315 0.0919076
\(448\) 0 0
\(449\) 14.0000 0.660701 0.330350 0.943858i \(-0.392833\pi\)
0.330350 + 0.943858i \(0.392833\pi\)
\(450\) 0 0
\(451\) −4.14931 −0.195383
\(452\) 0 0
\(453\) 2.31988 0.108997
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 14.5972 0.682831 0.341415 0.939913i \(-0.389094\pi\)
0.341415 + 0.939913i \(0.389094\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −19.4219 −0.904569 −0.452284 0.891874i \(-0.649391\pi\)
−0.452284 + 0.891874i \(0.649391\pi\)
\(462\) 0 0
\(463\) 14.3353 0.666216 0.333108 0.942889i \(-0.391903\pi\)
0.333108 + 0.942889i \(0.391903\pi\)
\(464\) 0 0
\(465\) −2.00000 −0.0927478
\(466\) 0 0
\(467\) 39.5789 1.83149 0.915747 0.401755i \(-0.131600\pi\)
0.915747 + 0.401755i \(0.131600\pi\)
\(468\) 0 0
\(469\) 28.3911 1.31098
\(470\) 0 0
\(471\) −20.8111 −0.958925
\(472\) 0 0
\(473\) 42.8034 1.96810
\(474\) 0 0
\(475\) 2.38776 0.109558
\(476\) 0 0
\(477\) 0.861314 0.0394369
\(478\) 0 0
\(479\) −24.1170 −1.10194 −0.550968 0.834527i \(-0.685741\pi\)
−0.550968 + 0.834527i \(0.685741\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 12.4123 0.564781
\(484\) 0 0
\(485\) 6.00000 0.272446
\(486\) 0 0
\(487\) −4.23407 −0.191864 −0.0959321 0.995388i \(-0.530583\pi\)
−0.0959321 + 0.995388i \(0.530583\pi\)
\(488\) 0 0
\(489\) 8.41233 0.380419
\(490\) 0 0
\(491\) −3.87090 −0.174691 −0.0873456 0.996178i \(-0.527838\pi\)
−0.0873456 + 0.996178i \(0.527838\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) −0.476886 −0.0214344
\(496\) 0 0
\(497\) 21.4017 0.959998
\(498\) 0 0
\(499\) −36.9571 −1.65443 −0.827213 0.561888i \(-0.810075\pi\)
−0.827213 + 0.561888i \(0.810075\pi\)
\(500\) 0 0
\(501\) −17.6647 −0.789202
\(502\) 0 0
\(503\) 11.0462 0.492527 0.246263 0.969203i \(-0.420797\pi\)
0.246263 + 0.969203i \(0.420797\pi\)
\(504\) 0 0
\(505\) 4.69075 0.208736
\(506\) 0 0
\(507\) −22.9002 −1.01704
\(508\) 0 0
\(509\) −10.3921 −0.460623 −0.230311 0.973117i \(-0.573974\pi\)
−0.230311 + 0.973117i \(0.573974\pi\)
\(510\) 0 0
\(511\) 20.0848 0.888498
\(512\) 0 0
\(513\) −12.1849 −0.537977
\(514\) 0 0
\(515\) −14.5693 −0.642002
\(516\) 0 0
\(517\) −40.4479 −1.77890
\(518\) 0 0
\(519\) 22.7187 0.997238
\(520\) 0 0
\(521\) 8.69075 0.380749 0.190374 0.981712i \(-0.439030\pi\)
0.190374 + 0.981712i \(0.439030\pi\)
\(522\) 0 0
\(523\) 17.2524 0.754395 0.377197 0.926133i \(-0.376888\pi\)
0.377197 + 0.926133i \(0.376888\pi\)
\(524\) 0 0
\(525\) −3.10308 −0.135430
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −7.00000 −0.304348
\(530\) 0 0
\(531\) 0.836734 0.0363112
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 5.84632 0.252758
\(536\) 0 0
\(537\) −36.8034 −1.58818
\(538\) 0 0
\(539\) 18.0279 0.776517
\(540\) 0 0
\(541\) −20.0925 −0.863842 −0.431921 0.901911i \(-0.642164\pi\)
−0.431921 + 0.901911i \(0.642164\pi\)
\(542\) 0 0
\(543\) 42.1127 1.80723
\(544\) 0 0
\(545\) 1.04623 0.0448155
\(546\) 0 0
\(547\) −44.1849 −1.88921 −0.944605 0.328209i \(-0.893555\pi\)
−0.944605 + 0.328209i \(0.893555\pi\)
\(548\) 0 0
\(549\) 0.520184 0.0222009
\(550\) 0 0
\(551\) −17.3169 −0.737727
\(552\) 0 0
\(553\) 20.5048 0.871952
\(554\) 0 0
\(555\) 1.76156 0.0747739
\(556\) 0 0
\(557\) −5.00958 −0.212263 −0.106131 0.994352i \(-0.533846\pi\)
−0.106131 + 0.994352i \(0.533846\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −8.95377 −0.377356 −0.188678 0.982039i \(-0.560420\pi\)
−0.188678 + 0.982039i \(0.560420\pi\)
\(564\) 0 0
\(565\) 8.29862 0.349126
\(566\) 0 0
\(567\) 16.3801 0.687898
\(568\) 0 0
\(569\) 18.9538 0.794583 0.397292 0.917692i \(-0.369950\pi\)
0.397292 + 0.917692i \(0.369950\pi\)
\(570\) 0 0
\(571\) −13.8140 −0.578100 −0.289050 0.957314i \(-0.593339\pi\)
−0.289050 + 0.957314i \(0.593339\pi\)
\(572\) 0 0
\(573\) 16.6185 0.694248
\(574\) 0 0
\(575\) −4.00000 −0.166812
\(576\) 0 0
\(577\) −24.5972 −1.02400 −0.511998 0.858986i \(-0.671095\pi\)
−0.511998 + 0.858986i \(0.671095\pi\)
\(578\) 0 0
\(579\) 7.40940 0.307924
\(580\) 0 0
\(581\) 31.8140 1.31987
\(582\) 0 0
\(583\) −38.6541 −1.60089
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −16.1695 −0.667388 −0.333694 0.942682i \(-0.608295\pi\)
−0.333694 + 0.942682i \(0.608295\pi\)
\(588\) 0 0
\(589\) −2.71096 −0.111703
\(590\) 0 0
\(591\) 10.8324 0.445584
\(592\) 0 0
\(593\) −36.4113 −1.49523 −0.747616 0.664131i \(-0.768802\pi\)
−0.747616 + 0.664131i \(0.768802\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 10.4123 0.426148
\(598\) 0 0
\(599\) 2.53374 0.103526 0.0517629 0.998659i \(-0.483516\pi\)
0.0517629 + 0.998659i \(0.483516\pi\)
\(600\) 0 0
\(601\) 14.8034 0.603844 0.301922 0.953333i \(-0.402372\pi\)
0.301922 + 0.953333i \(0.402372\pi\)
\(602\) 0 0
\(603\) −1.66140 −0.0676576
\(604\) 0 0
\(605\) 10.4017 0.422890
\(606\) 0 0
\(607\) 35.0462 1.42248 0.711241 0.702948i \(-0.248133\pi\)
0.711241 + 0.702948i \(0.248133\pi\)
\(608\) 0 0
\(609\) 22.5048 0.911940
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −3.94315 −0.159262 −0.0796311 0.996824i \(-0.525374\pi\)
−0.0796311 + 0.996824i \(0.525374\pi\)
\(614\) 0 0
\(615\) 1.57997 0.0637105
\(616\) 0 0
\(617\) 45.6233 1.83672 0.918362 0.395742i \(-0.129512\pi\)
0.918362 + 0.395742i \(0.129512\pi\)
\(618\) 0 0
\(619\) −31.4942 −1.26586 −0.632929 0.774210i \(-0.718147\pi\)
−0.632929 + 0.774210i \(0.718147\pi\)
\(620\) 0 0
\(621\) 20.4123 0.819119
\(622\) 0 0
\(623\) −2.56934 −0.102939
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −19.4586 −0.777100
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) −1.36943 −0.0545163 −0.0272581 0.999628i \(-0.508678\pi\)
−0.0272581 + 0.999628i \(0.508678\pi\)
\(632\) 0 0
\(633\) 48.6329 1.93298
\(634\) 0 0
\(635\) 19.3126 0.766396
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −1.25240 −0.0495440
\(640\) 0 0
\(641\) 36.2051 1.43002 0.715008 0.699116i \(-0.246423\pi\)
0.715008 + 0.699116i \(0.246423\pi\)
\(642\) 0 0
\(643\) 19.6926 0.776602 0.388301 0.921533i \(-0.373062\pi\)
0.388301 + 0.921533i \(0.373062\pi\)
\(644\) 0 0
\(645\) −16.2986 −0.641758
\(646\) 0 0
\(647\) 5.12329 0.201417 0.100709 0.994916i \(-0.467889\pi\)
0.100709 + 0.994916i \(0.467889\pi\)
\(648\) 0 0
\(649\) −37.5510 −1.47401
\(650\) 0 0
\(651\) 3.52311 0.138082
\(652\) 0 0
\(653\) 23.6801 0.926675 0.463337 0.886182i \(-0.346652\pi\)
0.463337 + 0.886182i \(0.346652\pi\)
\(654\) 0 0
\(655\) 1.13536 0.0443622
\(656\) 0 0
\(657\) −1.17533 −0.0458540
\(658\) 0 0
\(659\) −37.1589 −1.44751 −0.723753 0.690060i \(-0.757584\pi\)
−0.723753 + 0.690060i \(0.757584\pi\)
\(660\) 0 0
\(661\) −20.3757 −0.792523 −0.396261 0.918138i \(-0.629693\pi\)
−0.396261 + 0.918138i \(0.629693\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −4.20617 −0.163108
\(666\) 0 0
\(667\) 29.0096 1.12326
\(668\) 0 0
\(669\) 37.4942 1.44961
\(670\) 0 0
\(671\) −23.3449 −0.901218
\(672\) 0 0
\(673\) −2.44794 −0.0943610 −0.0471805 0.998886i \(-0.515024\pi\)
−0.0471805 + 0.998886i \(0.515024\pi\)
\(674\) 0 0
\(675\) −5.10308 −0.196418
\(676\) 0 0
\(677\) −22.7466 −0.874221 −0.437111 0.899408i \(-0.643998\pi\)
−0.437111 + 0.899408i \(0.643998\pi\)
\(678\) 0 0
\(679\) −10.5693 −0.405614
\(680\) 0 0
\(681\) −24.1849 −0.926768
\(682\) 0 0
\(683\) 31.0462 1.18795 0.593975 0.804483i \(-0.297558\pi\)
0.593975 + 0.804483i \(0.297558\pi\)
\(684\) 0 0
\(685\) 9.04623 0.345639
\(686\) 0 0
\(687\) 6.71866 0.256333
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 29.9142 1.13799 0.568995 0.822341i \(-0.307332\pi\)
0.568995 + 0.822341i \(0.307332\pi\)
\(692\) 0 0
\(693\) 0.840061 0.0319113
\(694\) 0 0
\(695\) 7.45856 0.282919
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) −10.5693 −0.399769
\(700\) 0 0
\(701\) −15.8496 −0.598633 −0.299316 0.954154i \(-0.596759\pi\)
−0.299316 + 0.954154i \(0.596759\pi\)
\(702\) 0 0
\(703\) 2.38776 0.0900559
\(704\) 0 0
\(705\) 15.4017 0.580062
\(706\) 0 0
\(707\) −8.26302 −0.310763
\(708\) 0 0
\(709\) −36.9325 −1.38703 −0.693515 0.720442i \(-0.743939\pi\)
−0.693515 + 0.720442i \(0.743939\pi\)
\(710\) 0 0
\(711\) −1.19991 −0.0450001
\(712\) 0 0
\(713\) 4.54144 0.170078
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 8.31988 0.310712
\(718\) 0 0
\(719\) 27.4296 1.02295 0.511476 0.859298i \(-0.329099\pi\)
0.511476 + 0.859298i \(0.329099\pi\)
\(720\) 0 0
\(721\) 25.6647 0.955805
\(722\) 0 0
\(723\) −47.0529 −1.74992
\(724\) 0 0
\(725\) −7.25240 −0.269347
\(726\) 0 0
\(727\) 46.9325 1.74063 0.870315 0.492495i \(-0.163915\pi\)
0.870315 + 0.492495i \(0.163915\pi\)
\(728\) 0 0
\(729\) 26.0096 0.963318
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 11.1031 0.410102 0.205051 0.978751i \(-0.434264\pi\)
0.205051 + 0.978751i \(0.434264\pi\)
\(734\) 0 0
\(735\) −6.86464 −0.253206
\(736\) 0 0
\(737\) 74.5606 2.74648
\(738\) 0 0
\(739\) −4.26302 −0.156818 −0.0784089 0.996921i \(-0.524984\pi\)
−0.0784089 + 0.996921i \(0.524984\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 15.6199 0.573040 0.286520 0.958074i \(-0.407502\pi\)
0.286520 + 0.958074i \(0.407502\pi\)
\(744\) 0 0
\(745\) 1.10308 0.0404139
\(746\) 0 0
\(747\) −1.86171 −0.0681164
\(748\) 0 0
\(749\) −10.2986 −0.376304
\(750\) 0 0
\(751\) 16.6262 0.606699 0.303349 0.952879i \(-0.401895\pi\)
0.303349 + 0.952879i \(0.401895\pi\)
\(752\) 0 0
\(753\) −3.79383 −0.138255
\(754\) 0 0
\(755\) 1.31695 0.0479286
\(756\) 0 0
\(757\) 25.6281 0.931469 0.465734 0.884925i \(-0.345790\pi\)
0.465734 + 0.884925i \(0.345790\pi\)
\(758\) 0 0
\(759\) 32.5972 1.18321
\(760\) 0 0
\(761\) 1.60788 0.0582855 0.0291427 0.999575i \(-0.490722\pi\)
0.0291427 + 0.999575i \(0.490722\pi\)
\(762\) 0 0
\(763\) −1.84299 −0.0667208
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −25.7572 −0.928828 −0.464414 0.885618i \(-0.653735\pi\)
−0.464414 + 0.885618i \(0.653735\pi\)
\(770\) 0 0
\(771\) −0.526045 −0.0189450
\(772\) 0 0
\(773\) 14.1493 0.508915 0.254458 0.967084i \(-0.418103\pi\)
0.254458 + 0.967084i \(0.418103\pi\)
\(774\) 0 0
\(775\) −1.13536 −0.0407833
\(776\) 0 0
\(777\) −3.10308 −0.111323
\(778\) 0 0
\(779\) 2.14162 0.0767314
\(780\) 0 0
\(781\) 56.2051 2.01118
\(782\) 0 0
\(783\) 37.0096 1.32261
\(784\) 0 0
\(785\) −11.8140 −0.421661
\(786\) 0 0
\(787\) −0.210536 −0.00750480 −0.00375240 0.999993i \(-0.501194\pi\)
−0.00375240 + 0.999993i \(0.501194\pi\)
\(788\) 0 0
\(789\) 19.4017 0.690719
\(790\) 0 0
\(791\) −14.6185 −0.519774
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 14.7187 0.522017
\(796\) 0 0
\(797\) −14.0925 −0.499180 −0.249590 0.968352i \(-0.580296\pi\)
−0.249590 + 0.968352i \(0.580296\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0.150354 0.00531250
\(802\) 0 0
\(803\) 52.7466 1.86139
\(804\) 0 0
\(805\) 7.04623 0.248347
\(806\) 0 0
\(807\) −29.4373 −1.03624
\(808\) 0 0
\(809\) −14.2986 −0.502713 −0.251356 0.967895i \(-0.580877\pi\)
−0.251356 + 0.967895i \(0.580877\pi\)
\(810\) 0 0
\(811\) 0.0202108 0.000709697 0 0.000354849 1.00000i \(-0.499887\pi\)
0.000354849 1.00000i \(0.499887\pi\)
\(812\) 0 0
\(813\) 13.1031 0.459545
\(814\) 0 0
\(815\) 4.77551 0.167279
\(816\) 0 0
\(817\) −22.0925 −0.772917
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −45.4942 −1.58776 −0.793879 0.608076i \(-0.791942\pi\)
−0.793879 + 0.608076i \(0.791942\pi\)
\(822\) 0 0
\(823\) 30.0804 1.04854 0.524268 0.851553i \(-0.324339\pi\)
0.524268 + 0.851553i \(0.324339\pi\)
\(824\) 0 0
\(825\) −8.14931 −0.283723
\(826\) 0 0
\(827\) 11.8217 0.411082 0.205541 0.978648i \(-0.434105\pi\)
0.205541 + 0.978648i \(0.434105\pi\)
\(828\) 0 0
\(829\) 12.6185 0.438259 0.219129 0.975696i \(-0.429678\pi\)
0.219129 + 0.975696i \(0.429678\pi\)
\(830\) 0 0
\(831\) 22.3911 0.776738
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −10.0279 −0.347030
\(836\) 0 0
\(837\) 5.79383 0.200264
\(838\) 0 0
\(839\) −27.4586 −0.947975 −0.473987 0.880532i \(-0.657186\pi\)
−0.473987 + 0.880532i \(0.657186\pi\)
\(840\) 0 0
\(841\) 23.5972 0.813698
\(842\) 0 0
\(843\) −35.3940 −1.21903
\(844\) 0 0
\(845\) −13.0000 −0.447214
\(846\) 0 0
\(847\) −18.3232 −0.629593
\(848\) 0 0
\(849\) −28.5972 −0.981455
\(850\) 0 0
\(851\) −4.00000 −0.137118
\(852\) 0 0
\(853\) −55.7205 −1.90784 −0.953918 0.300069i \(-0.902990\pi\)
−0.953918 + 0.300069i \(0.902990\pi\)
\(854\) 0 0
\(855\) 0.246139 0.00841776
\(856\) 0 0
\(857\) −4.50479 −0.153881 −0.0769404 0.997036i \(-0.524515\pi\)
−0.0769404 + 0.997036i \(0.524515\pi\)
\(858\) 0 0
\(859\) −19.3415 −0.659924 −0.329962 0.943994i \(-0.607036\pi\)
−0.329962 + 0.943994i \(0.607036\pi\)
\(860\) 0 0
\(861\) −2.78321 −0.0948514
\(862\) 0 0
\(863\) −28.1729 −0.959015 −0.479507 0.877538i \(-0.659185\pi\)
−0.479507 + 0.877538i \(0.659185\pi\)
\(864\) 0 0
\(865\) 12.8969 0.438508
\(866\) 0 0
\(867\) −29.9465 −1.01704
\(868\) 0 0
\(869\) 53.8496 1.82672
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0.618502 0.0209331
\(874\) 0 0
\(875\) −1.76156 −0.0595515
\(876\) 0 0
\(877\) −24.9171 −0.841392 −0.420696 0.907202i \(-0.638214\pi\)
−0.420696 + 0.907202i \(0.638214\pi\)
\(878\) 0 0
\(879\) −17.6156 −0.594158
\(880\) 0 0
\(881\) 0.784248 0.0264220 0.0132110 0.999913i \(-0.495795\pi\)
0.0132110 + 0.999913i \(0.495795\pi\)
\(882\) 0 0
\(883\) −19.2245 −0.646956 −0.323478 0.946236i \(-0.604852\pi\)
−0.323478 + 0.946236i \(0.604852\pi\)
\(884\) 0 0
\(885\) 14.2986 0.480643
\(886\) 0 0
\(887\) 13.4783 0.452558 0.226279 0.974063i \(-0.427344\pi\)
0.226279 + 0.974063i \(0.427344\pi\)
\(888\) 0 0
\(889\) −34.0202 −1.14100
\(890\) 0 0
\(891\) 43.0173 1.44113
\(892\) 0 0
\(893\) 20.8767 0.698612
\(894\) 0 0
\(895\) −20.8925 −0.698361
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 8.23407 0.274622
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 28.7110 0.955441
\(904\) 0 0
\(905\) 23.9065 0.794679
\(906\) 0 0
\(907\) −12.3478 −0.410001 −0.205001 0.978762i \(-0.565720\pi\)
−0.205001 + 0.978762i \(0.565720\pi\)
\(908\) 0 0
\(909\) 0.483540 0.0160380
\(910\) 0 0
\(911\) −36.8280 −1.22017 −0.610083 0.792338i \(-0.708864\pi\)
−0.610083 + 0.792338i \(0.708864\pi\)
\(912\) 0 0
\(913\) 83.5500 2.76510
\(914\) 0 0
\(915\) 8.88922 0.293869
\(916\) 0 0
\(917\) −2.00000 −0.0660458
\(918\) 0 0
\(919\) 8.35111 0.275478 0.137739 0.990469i \(-0.456017\pi\)
0.137739 + 0.990469i \(0.456017\pi\)
\(920\) 0 0
\(921\) −7.10308 −0.234055
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 1.00000 0.0328798
\(926\) 0 0
\(927\) −1.50186 −0.0493276
\(928\) 0 0
\(929\) 30.0000 0.984268 0.492134 0.870519i \(-0.336217\pi\)
0.492134 + 0.870519i \(0.336217\pi\)
\(930\) 0 0
\(931\) −9.30488 −0.304955
\(932\) 0 0
\(933\) 15.9787 0.523121
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −38.0202 −1.24207 −0.621033 0.783784i \(-0.713287\pi\)
−0.621033 + 0.783784i \(0.713287\pi\)
\(938\) 0 0
\(939\) −42.4402 −1.38498
\(940\) 0 0
\(941\) 31.2158 1.01760 0.508802 0.860883i \(-0.330088\pi\)
0.508802 + 0.860883i \(0.330088\pi\)
\(942\) 0 0
\(943\) −3.58767 −0.116830
\(944\) 0 0
\(945\) 8.98937 0.292424
\(946\) 0 0
\(947\) 2.14162 0.0695932 0.0347966 0.999394i \(-0.488922\pi\)
0.0347966 + 0.999394i \(0.488922\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 30.7543 0.997275
\(952\) 0 0
\(953\) −15.5154 −0.502594 −0.251297 0.967910i \(-0.580857\pi\)
−0.251297 + 0.967910i \(0.580857\pi\)
\(954\) 0 0
\(955\) 9.43398 0.305277
\(956\) 0 0
\(957\) 59.1020 1.91050
\(958\) 0 0
\(959\) −15.9354 −0.514582
\(960\) 0 0
\(961\) −29.7110 −0.958418
\(962\) 0 0
\(963\) 0.602660 0.0194205
\(964\) 0 0
\(965\) 4.20617 0.135401
\(966\) 0 0
\(967\) 35.4498 1.13999 0.569995 0.821648i \(-0.306945\pi\)
0.569995 + 0.821648i \(0.306945\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −13.5510 −0.434873 −0.217436 0.976074i \(-0.569769\pi\)
−0.217436 + 0.976074i \(0.569769\pi\)
\(972\) 0 0
\(973\) −13.1387 −0.421207
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 16.2062 0.518481 0.259241 0.965813i \(-0.416528\pi\)
0.259241 + 0.965813i \(0.416528\pi\)
\(978\) 0 0
\(979\) −6.74760 −0.215654
\(980\) 0 0
\(981\) 0.107849 0.00344336
\(982\) 0 0
\(983\) 6.17389 0.196917 0.0984583 0.995141i \(-0.468609\pi\)
0.0984583 + 0.995141i \(0.468609\pi\)
\(984\) 0 0
\(985\) 6.14931 0.195933
\(986\) 0 0
\(987\) −27.1310 −0.863589
\(988\) 0 0
\(989\) 37.0096 1.17684
\(990\) 0 0
\(991\) −13.9109 −0.441893 −0.220947 0.975286i \(-0.570915\pi\)
−0.220947 + 0.975286i \(0.570915\pi\)
\(992\) 0 0
\(993\) 1.88629 0.0598596
\(994\) 0 0
\(995\) 5.91087 0.187387
\(996\) 0 0
\(997\) −8.87671 −0.281128 −0.140564 0.990072i \(-0.544892\pi\)
−0.140564 + 0.990072i \(0.544892\pi\)
\(998\) 0 0
\(999\) −5.10308 −0.161454
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.1.3 3
4.3 odd 2 1480.2.a.f.1.1 3
20.19 odd 2 7400.2.a.m.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1480.2.a.f.1.1 3 4.3 odd 2
2960.2.a.s.1.3 3 1.1 even 1 trivial
7400.2.a.m.1.3 3 20.19 odd 2