Properties

Label 9360.2.a.dd.1.3
Level $9360$
Weight $2$
Character 9360.1
Self dual yes
Analytic conductor $74.740$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 9360 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9360.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(74.7399762919\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.316.1
Defining polynomial: \( x^{3} - x^{2} - 4x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 195)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(0.470683\) of defining polynomial
Character \(\chi\) \(=\) 9360.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{5} +2.71982 q^{7} +O(q^{10})\) \(q+1.00000 q^{5} +2.71982 q^{7} -2.71982 q^{11} +1.00000 q^{13} +2.83709 q^{17} +3.55691 q^{19} -4.83709 q^{23} +1.00000 q^{25} -6.00000 q^{29} -7.55691 q^{31} +2.71982 q^{35} -4.27674 q^{37} -2.83709 q^{41} -11.1138 q^{43} -11.5569 q^{47} +0.397442 q^{49} -1.16291 q^{53} -2.71982 q^{55} -2.11727 q^{59} +6.60256 q^{61} +1.00000 q^{65} -1.88273 q^{67} -6.71982 q^{71} +9.11383 q^{73} -7.39744 q^{77} -10.2767 q^{79} +2.11727 q^{83} +2.83709 q^{85} -1.16291 q^{89} +2.71982 q^{91} +3.55691 q^{95} -10.8371 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 3 q^{5} - q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + 3 q^{5} - q^{7} + q^{11} + 3 q^{13} + q^{17} - 6 q^{19} - 7 q^{23} + 3 q^{25} - 18 q^{29} - 6 q^{31} - q^{35} + 13 q^{37} - q^{41} - 18 q^{47} + 12 q^{49} - 11 q^{53} + q^{55} - 8 q^{59} + 9 q^{61} + 3 q^{65} - 4 q^{67} - 11 q^{71} - 6 q^{73} - 33 q^{77} - 5 q^{79} + 8 q^{83} + q^{85} - 11 q^{89} - q^{91} - 6 q^{95} - 25 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 2.71982 1.02800 0.513998 0.857791i \(-0.328164\pi\)
0.513998 + 0.857791i \(0.328164\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.71982 −0.820058 −0.410029 0.912073i \(-0.634481\pi\)
−0.410029 + 0.912073i \(0.634481\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.83709 0.688095 0.344048 0.938952i \(-0.388202\pi\)
0.344048 + 0.938952i \(0.388202\pi\)
\(18\) 0 0
\(19\) 3.55691 0.816012 0.408006 0.912979i \(-0.366224\pi\)
0.408006 + 0.912979i \(0.366224\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4.83709 −1.00860 −0.504302 0.863528i \(-0.668250\pi\)
−0.504302 + 0.863528i \(0.668250\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 0 0
\(31\) −7.55691 −1.35726 −0.678631 0.734479i \(-0.737426\pi\)
−0.678631 + 0.734479i \(0.737426\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.71982 0.459734
\(36\) 0 0
\(37\) −4.27674 −0.703091 −0.351546 0.936171i \(-0.614344\pi\)
−0.351546 + 0.936171i \(0.614344\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2.83709 −0.443079 −0.221540 0.975151i \(-0.571108\pi\)
−0.221540 + 0.975151i \(0.571108\pi\)
\(42\) 0 0
\(43\) −11.1138 −1.69484 −0.847421 0.530921i \(-0.821846\pi\)
−0.847421 + 0.530921i \(0.821846\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −11.5569 −1.68575 −0.842875 0.538110i \(-0.819138\pi\)
−0.842875 + 0.538110i \(0.819138\pi\)
\(48\) 0 0
\(49\) 0.397442 0.0567775
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −1.16291 −0.159738 −0.0798690 0.996805i \(-0.525450\pi\)
−0.0798690 + 0.996805i \(0.525450\pi\)
\(54\) 0 0
\(55\) −2.71982 −0.366741
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −2.11727 −0.275645 −0.137822 0.990457i \(-0.544010\pi\)
−0.137822 + 0.990457i \(0.544010\pi\)
\(60\) 0 0
\(61\) 6.60256 0.845371 0.422685 0.906276i \(-0.361088\pi\)
0.422685 + 0.906276i \(0.361088\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1.00000 0.124035
\(66\) 0 0
\(67\) −1.88273 −0.230013 −0.115006 0.993365i \(-0.536689\pi\)
−0.115006 + 0.993365i \(0.536689\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −6.71982 −0.797496 −0.398748 0.917060i \(-0.630555\pi\)
−0.398748 + 0.917060i \(0.630555\pi\)
\(72\) 0 0
\(73\) 9.11383 1.06669 0.533346 0.845897i \(-0.320934\pi\)
0.533346 + 0.845897i \(0.320934\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −7.39744 −0.843017
\(78\) 0 0
\(79\) −10.2767 −1.15622 −0.578112 0.815958i \(-0.696210\pi\)
−0.578112 + 0.815958i \(0.696210\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 2.11727 0.232400 0.116200 0.993226i \(-0.462929\pi\)
0.116200 + 0.993226i \(0.462929\pi\)
\(84\) 0 0
\(85\) 2.83709 0.307726
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1.16291 −0.123268 −0.0616341 0.998099i \(-0.519631\pi\)
−0.0616341 + 0.998099i \(0.519631\pi\)
\(90\) 0 0
\(91\) 2.71982 0.285115
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 3.55691 0.364932
\(96\) 0 0
\(97\) −10.8371 −1.10034 −0.550170 0.835053i \(-0.685437\pi\)
−0.550170 + 0.835053i \(0.685437\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −7.67418 −0.763610 −0.381805 0.924243i \(-0.624697\pi\)
−0.381805 + 0.924243i \(0.624697\pi\)
\(102\) 0 0
\(103\) −3.76547 −0.371023 −0.185511 0.982642i \(-0.559394\pi\)
−0.185511 + 0.982642i \(0.559394\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −12.6026 −1.21834 −0.609168 0.793041i \(-0.708496\pi\)
−0.609168 + 0.793041i \(0.708496\pi\)
\(108\) 0 0
\(109\) 11.4396 1.09572 0.547860 0.836570i \(-0.315443\pi\)
0.547860 + 0.836570i \(0.315443\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 13.1138 1.23365 0.616823 0.787102i \(-0.288420\pi\)
0.616823 + 0.787102i \(0.288420\pi\)
\(114\) 0 0
\(115\) −4.83709 −0.451061
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 7.71639 0.707360
\(120\) 0 0
\(121\) −3.60256 −0.327505
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 13.4396 1.19258 0.596288 0.802771i \(-0.296642\pi\)
0.596288 + 0.802771i \(0.296642\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −9.43965 −0.824746 −0.412373 0.911015i \(-0.635300\pi\)
−0.412373 + 0.911015i \(0.635300\pi\)
\(132\) 0 0
\(133\) 9.67418 0.838858
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1.76547 −0.150834 −0.0754170 0.997152i \(-0.524029\pi\)
−0.0754170 + 0.997152i \(0.524029\pi\)
\(138\) 0 0
\(139\) 6.27674 0.532386 0.266193 0.963920i \(-0.414234\pi\)
0.266193 + 0.963920i \(0.414234\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −2.71982 −0.227443
\(144\) 0 0
\(145\) −6.00000 −0.498273
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 20.8302 1.70648 0.853239 0.521520i \(-0.174635\pi\)
0.853239 + 0.521520i \(0.174635\pi\)
\(150\) 0 0
\(151\) −4.99656 −0.406614 −0.203307 0.979115i \(-0.565169\pi\)
−0.203307 + 0.979115i \(0.565169\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −7.55691 −0.606986
\(156\) 0 0
\(157\) 8.87930 0.708645 0.354322 0.935123i \(-0.384712\pi\)
0.354322 + 0.935123i \(0.384712\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −13.1560 −1.03684
\(162\) 0 0
\(163\) 13.8337 1.08354 0.541768 0.840528i \(-0.317755\pi\)
0.541768 + 0.840528i \(0.317755\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −9.88273 −0.764749 −0.382374 0.924007i \(-0.624894\pi\)
−0.382374 + 0.924007i \(0.624894\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −13.1138 −0.997026 −0.498513 0.866882i \(-0.666120\pi\)
−0.498513 + 0.866882i \(0.666120\pi\)
\(174\) 0 0
\(175\) 2.71982 0.205599
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 8.55348 0.639317 0.319658 0.947533i \(-0.396432\pi\)
0.319658 + 0.947533i \(0.396432\pi\)
\(180\) 0 0
\(181\) 3.72326 0.276748 0.138374 0.990380i \(-0.455812\pi\)
0.138374 + 0.990380i \(0.455812\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −4.27674 −0.314432
\(186\) 0 0
\(187\) −7.71639 −0.564278
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −4.23453 −0.306400 −0.153200 0.988195i \(-0.548958\pi\)
−0.153200 + 0.988195i \(0.548958\pi\)
\(192\) 0 0
\(193\) −23.3906 −1.68369 −0.841845 0.539719i \(-0.818530\pi\)
−0.841845 + 0.539719i \(0.818530\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −14.5535 −1.03689 −0.518446 0.855110i \(-0.673489\pi\)
−0.518446 + 0.855110i \(0.673489\pi\)
\(198\) 0 0
\(199\) 15.1138 1.07139 0.535695 0.844411i \(-0.320050\pi\)
0.535695 + 0.844411i \(0.320050\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −16.3189 −1.14537
\(204\) 0 0
\(205\) −2.83709 −0.198151
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −9.67418 −0.669177
\(210\) 0 0
\(211\) 18.2277 1.25484 0.627422 0.778680i \(-0.284110\pi\)
0.627422 + 0.778680i \(0.284110\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −11.1138 −0.757957
\(216\) 0 0
\(217\) −20.5535 −1.39526
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 2.83709 0.190843
\(222\) 0 0
\(223\) −10.1173 −0.677502 −0.338751 0.940876i \(-0.610004\pi\)
−0.338751 + 0.940876i \(0.610004\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 11.3224 0.751493 0.375746 0.926723i \(-0.377386\pi\)
0.375746 + 0.926723i \(0.377386\pi\)
\(228\) 0 0
\(229\) −6.23453 −0.411990 −0.205995 0.978553i \(-0.566043\pi\)
−0.205995 + 0.978553i \(0.566043\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −6.83709 −0.447913 −0.223956 0.974599i \(-0.571897\pi\)
−0.223956 + 0.974599i \(0.571897\pi\)
\(234\) 0 0
\(235\) −11.5569 −0.753890
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1.28018 0.0828077 0.0414039 0.999142i \(-0.486817\pi\)
0.0414039 + 0.999142i \(0.486817\pi\)
\(240\) 0 0
\(241\) −6.00000 −0.386494 −0.193247 0.981150i \(-0.561902\pi\)
−0.193247 + 0.981150i \(0.561902\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0.397442 0.0253917
\(246\) 0 0
\(247\) 3.55691 0.226321
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 18.2277 1.15052 0.575260 0.817971i \(-0.304901\pi\)
0.575260 + 0.817971i \(0.304901\pi\)
\(252\) 0 0
\(253\) 13.1560 0.827113
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1.11383 −0.0694787 −0.0347394 0.999396i \(-0.511060\pi\)
−0.0347394 + 0.999396i \(0.511060\pi\)
\(258\) 0 0
\(259\) −11.6320 −0.722776
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 8.00000 0.493301 0.246651 0.969104i \(-0.420670\pi\)
0.246651 + 0.969104i \(0.420670\pi\)
\(264\) 0 0
\(265\) −1.16291 −0.0714370
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −15.6742 −0.955672 −0.477836 0.878449i \(-0.658579\pi\)
−0.477836 + 0.878449i \(0.658579\pi\)
\(270\) 0 0
\(271\) −0.443086 −0.0269155 −0.0134578 0.999909i \(-0.504284\pi\)
−0.0134578 + 0.999909i \(0.504284\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2.71982 −0.164012
\(276\) 0 0
\(277\) −4.87930 −0.293168 −0.146584 0.989198i \(-0.546828\pi\)
−0.146584 + 0.989198i \(0.546828\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 9.11383 0.543685 0.271843 0.962342i \(-0.412367\pi\)
0.271843 + 0.962342i \(0.412367\pi\)
\(282\) 0 0
\(283\) −33.3415 −1.98195 −0.990973 0.134063i \(-0.957198\pi\)
−0.990973 + 0.134063i \(0.957198\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −7.71639 −0.455484
\(288\) 0 0
\(289\) −8.95092 −0.526525
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 29.4328 1.71948 0.859740 0.510731i \(-0.170625\pi\)
0.859740 + 0.510731i \(0.170625\pi\)
\(294\) 0 0
\(295\) −2.11727 −0.123272
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −4.83709 −0.279736
\(300\) 0 0
\(301\) −30.2277 −1.74229
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 6.60256 0.378061
\(306\) 0 0
\(307\) 21.8337 1.24611 0.623056 0.782177i \(-0.285891\pi\)
0.623056 + 0.782177i \(0.285891\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 25.1070 1.42368 0.711842 0.702339i \(-0.247861\pi\)
0.711842 + 0.702339i \(0.247861\pi\)
\(312\) 0 0
\(313\) 8.22766 0.465055 0.232527 0.972590i \(-0.425300\pi\)
0.232527 + 0.972590i \(0.425300\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −27.6742 −1.55434 −0.777168 0.629293i \(-0.783345\pi\)
−0.777168 + 0.629293i \(0.783345\pi\)
\(318\) 0 0
\(319\) 16.3189 0.913685
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 10.0913 0.561494
\(324\) 0 0
\(325\) 1.00000 0.0554700
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −31.4328 −1.73294
\(330\) 0 0
\(331\) 13.2311 0.727247 0.363623 0.931546i \(-0.381540\pi\)
0.363623 + 0.931546i \(0.381540\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −1.88273 −0.102865
\(336\) 0 0
\(337\) −4.32582 −0.235642 −0.117821 0.993035i \(-0.537591\pi\)
−0.117821 + 0.993035i \(0.537591\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 20.5535 1.11303
\(342\) 0 0
\(343\) −17.9578 −0.969630
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 6.27674 0.336953 0.168476 0.985706i \(-0.446115\pi\)
0.168476 + 0.985706i \(0.446115\pi\)
\(348\) 0 0
\(349\) 17.6673 0.945709 0.472855 0.881140i \(-0.343224\pi\)
0.472855 + 0.881140i \(0.343224\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 13.7655 0.732662 0.366331 0.930485i \(-0.380614\pi\)
0.366331 + 0.930485i \(0.380614\pi\)
\(354\) 0 0
\(355\) −6.71982 −0.356651
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0.996562 0.0525965 0.0262983 0.999654i \(-0.491628\pi\)
0.0262983 + 0.999654i \(0.491628\pi\)
\(360\) 0 0
\(361\) −6.34836 −0.334124
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 9.11383 0.477040
\(366\) 0 0
\(367\) −14.2277 −0.742678 −0.371339 0.928497i \(-0.621101\pi\)
−0.371339 + 0.928497i \(0.621101\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −3.16291 −0.164210
\(372\) 0 0
\(373\) 15.6742 0.811578 0.405789 0.913967i \(-0.366997\pi\)
0.405789 + 0.913967i \(0.366997\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −6.00000 −0.309016
\(378\) 0 0
\(379\) −26.2017 −1.34589 −0.672945 0.739693i \(-0.734971\pi\)
−0.672945 + 0.739693i \(0.734971\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 22.4362 1.14644 0.573218 0.819403i \(-0.305695\pi\)
0.573218 + 0.819403i \(0.305695\pi\)
\(384\) 0 0
\(385\) −7.39744 −0.377009
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −31.6742 −1.60594 −0.802972 0.596016i \(-0.796749\pi\)
−0.802972 + 0.596016i \(0.796749\pi\)
\(390\) 0 0
\(391\) −13.7233 −0.694015
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −10.2767 −0.517079
\(396\) 0 0
\(397\) 17.9509 0.900931 0.450465 0.892794i \(-0.351258\pi\)
0.450465 + 0.892794i \(0.351258\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −13.5829 −0.678297 −0.339149 0.940733i \(-0.610139\pi\)
−0.339149 + 0.940733i \(0.610139\pi\)
\(402\) 0 0
\(403\) −7.55691 −0.376437
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 11.6320 0.576576
\(408\) 0 0
\(409\) −14.0000 −0.692255 −0.346128 0.938187i \(-0.612504\pi\)
−0.346128 + 0.938187i \(0.612504\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −5.75859 −0.283362
\(414\) 0 0
\(415\) 2.11727 0.103933
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 12.3189 0.601820 0.300910 0.953653i \(-0.402710\pi\)
0.300910 + 0.953653i \(0.402710\pi\)
\(420\) 0 0
\(421\) 22.7880 1.11062 0.555310 0.831644i \(-0.312600\pi\)
0.555310 + 0.831644i \(0.312600\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 2.83709 0.137619
\(426\) 0 0
\(427\) 17.9578 0.869039
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −8.99656 −0.433349 −0.216675 0.976244i \(-0.569521\pi\)
−0.216675 + 0.976244i \(0.569521\pi\)
\(432\) 0 0
\(433\) −20.3258 −0.976797 −0.488398 0.872621i \(-0.662419\pi\)
−0.488398 + 0.872621i \(0.662419\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −17.2051 −0.823032
\(438\) 0 0
\(439\) 25.3906 1.21183 0.605913 0.795531i \(-0.292808\pi\)
0.605913 + 0.795531i \(0.292808\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 10.9284 0.519223 0.259611 0.965713i \(-0.416406\pi\)
0.259611 + 0.965713i \(0.416406\pi\)
\(444\) 0 0
\(445\) −1.16291 −0.0551272
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −2.83709 −0.133891 −0.0669453 0.997757i \(-0.521325\pi\)
−0.0669453 + 0.997757i \(0.521325\pi\)
\(450\) 0 0
\(451\) 7.71639 0.363350
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 2.71982 0.127507
\(456\) 0 0
\(457\) −13.7164 −0.641625 −0.320813 0.947143i \(-0.603956\pi\)
−0.320813 + 0.947143i \(0.603956\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 19.6251 0.914032 0.457016 0.889458i \(-0.348918\pi\)
0.457016 + 0.889458i \(0.348918\pi\)
\(462\) 0 0
\(463\) −27.0388 −1.25660 −0.628299 0.777972i \(-0.716249\pi\)
−0.628299 + 0.777972i \(0.716249\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 28.9215 1.33833 0.669164 0.743115i \(-0.266652\pi\)
0.669164 + 0.743115i \(0.266652\pi\)
\(468\) 0 0
\(469\) −5.12070 −0.236452
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 30.2277 1.38987
\(474\) 0 0
\(475\) 3.55691 0.163202
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −12.1595 −0.555580 −0.277790 0.960642i \(-0.589602\pi\)
−0.277790 + 0.960642i \(0.589602\pi\)
\(480\) 0 0
\(481\) −4.27674 −0.195002
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −10.8371 −0.492087
\(486\) 0 0
\(487\) 0.159472 0.00722636 0.00361318 0.999993i \(-0.498850\pi\)
0.00361318 + 0.999993i \(0.498850\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −42.2277 −1.90571 −0.952854 0.303430i \(-0.901868\pi\)
−0.952854 + 0.303430i \(0.901868\pi\)
\(492\) 0 0
\(493\) −17.0225 −0.766657
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −18.2767 −0.819824
\(498\) 0 0
\(499\) −7.79145 −0.348793 −0.174397 0.984676i \(-0.555797\pi\)
−0.174397 + 0.984676i \(0.555797\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 27.3484 1.21940 0.609702 0.792631i \(-0.291289\pi\)
0.609702 + 0.792631i \(0.291289\pi\)
\(504\) 0 0
\(505\) −7.67418 −0.341497
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 33.4819 1.48406 0.742029 0.670368i \(-0.233864\pi\)
0.742029 + 0.670368i \(0.233864\pi\)
\(510\) 0 0
\(511\) 24.7880 1.09656
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −3.76547 −0.165926
\(516\) 0 0
\(517\) 31.4328 1.38241
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 17.3484 0.760045 0.380023 0.924977i \(-0.375916\pi\)
0.380023 + 0.924977i \(0.375916\pi\)
\(522\) 0 0
\(523\) 4.00000 0.174908 0.0874539 0.996169i \(-0.472127\pi\)
0.0874539 + 0.996169i \(0.472127\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −21.4396 −0.933926
\(528\) 0 0
\(529\) 0.397442 0.0172801
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −2.83709 −0.122888
\(534\) 0 0
\(535\) −12.6026 −0.544856
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1.08097 −0.0465608
\(540\) 0 0
\(541\) −32.6448 −1.40351 −0.701754 0.712419i \(-0.747599\pi\)
−0.701754 + 0.712419i \(0.747599\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 11.4396 0.490021
\(546\) 0 0
\(547\) −34.2277 −1.46347 −0.731734 0.681590i \(-0.761289\pi\)
−0.731734 + 0.681590i \(0.761289\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −21.3415 −0.909178
\(552\) 0 0
\(553\) −27.9509 −1.18859
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −6.65164 −0.281839 −0.140919 0.990021i \(-0.545006\pi\)
−0.140919 + 0.990021i \(0.545006\pi\)
\(558\) 0 0
\(559\) −11.1138 −0.470065
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 40.2699 1.69717 0.848586 0.529057i \(-0.177454\pi\)
0.848586 + 0.529057i \(0.177454\pi\)
\(564\) 0 0
\(565\) 13.1138 0.551703
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 13.4328 0.563131 0.281566 0.959542i \(-0.409146\pi\)
0.281566 + 0.959542i \(0.409146\pi\)
\(570\) 0 0
\(571\) 35.7164 1.49468 0.747342 0.664439i \(-0.231330\pi\)
0.747342 + 0.664439i \(0.231330\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −4.83709 −0.201721
\(576\) 0 0
\(577\) −13.7164 −0.571021 −0.285510 0.958376i \(-0.592163\pi\)
−0.285510 + 0.958376i \(0.592163\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 5.75859 0.238907
\(582\) 0 0
\(583\) 3.16291 0.130994
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 30.6707 1.26592 0.632959 0.774186i \(-0.281840\pi\)
0.632959 + 0.774186i \(0.281840\pi\)
\(588\) 0 0
\(589\) −26.8793 −1.10754
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 45.6673 1.87533 0.937666 0.347538i \(-0.112982\pi\)
0.937666 + 0.347538i \(0.112982\pi\)
\(594\) 0 0
\(595\) 7.71639 0.316341
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −40.2208 −1.64338 −0.821688 0.569937i \(-0.806968\pi\)
−0.821688 + 0.569937i \(0.806968\pi\)
\(600\) 0 0
\(601\) 17.3974 0.709656 0.354828 0.934932i \(-0.384539\pi\)
0.354828 + 0.934932i \(0.384539\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −3.60256 −0.146465
\(606\) 0 0
\(607\) 14.2277 0.577483 0.288741 0.957407i \(-0.406763\pi\)
0.288741 + 0.957407i \(0.406763\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −11.5569 −0.467543
\(612\) 0 0
\(613\) −40.8302 −1.64912 −0.824558 0.565777i \(-0.808576\pi\)
−0.824558 + 0.565777i \(0.808576\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −5.11383 −0.205875 −0.102937 0.994688i \(-0.532824\pi\)
−0.102937 + 0.994688i \(0.532824\pi\)
\(618\) 0 0
\(619\) −11.5569 −0.464512 −0.232256 0.972655i \(-0.574611\pi\)
−0.232256 + 0.972655i \(0.574611\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −3.16291 −0.126719
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −12.1335 −0.483794
\(630\) 0 0
\(631\) −35.2242 −1.40225 −0.701127 0.713036i \(-0.747319\pi\)
−0.701127 + 0.713036i \(0.747319\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 13.4396 0.533336
\(636\) 0 0
\(637\) 0.397442 0.0157472
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 21.9018 0.865071 0.432535 0.901617i \(-0.357619\pi\)
0.432535 + 0.901617i \(0.357619\pi\)
\(642\) 0 0
\(643\) −7.50783 −0.296080 −0.148040 0.988981i \(-0.547296\pi\)
−0.148040 + 0.988981i \(0.547296\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −14.0422 −0.552056 −0.276028 0.961150i \(-0.589018\pi\)
−0.276028 + 0.961150i \(0.589018\pi\)
\(648\) 0 0
\(649\) 5.75859 0.226044
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −7.99312 −0.312795 −0.156398 0.987694i \(-0.549988\pi\)
−0.156398 + 0.987694i \(0.549988\pi\)
\(654\) 0 0
\(655\) −9.43965 −0.368838
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −25.3415 −0.987164 −0.493582 0.869699i \(-0.664313\pi\)
−0.493582 + 0.869699i \(0.664313\pi\)
\(660\) 0 0
\(661\) 27.4396 1.06728 0.533639 0.845712i \(-0.320824\pi\)
0.533639 + 0.845712i \(0.320824\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 9.67418 0.375149
\(666\) 0 0
\(667\) 29.0225 1.12376
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −17.9578 −0.693253
\(672\) 0 0
\(673\) 27.1070 1.04490 0.522448 0.852671i \(-0.325019\pi\)
0.522448 + 0.852671i \(0.325019\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 36.5957 1.40649 0.703243 0.710949i \(-0.251735\pi\)
0.703243 + 0.710949i \(0.251735\pi\)
\(678\) 0 0
\(679\) −29.4750 −1.13115
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −13.4656 −0.515248 −0.257624 0.966245i \(-0.582940\pi\)
−0.257624 + 0.966245i \(0.582940\pi\)
\(684\) 0 0
\(685\) −1.76547 −0.0674550
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −1.16291 −0.0443033
\(690\) 0 0
\(691\) −29.5500 −1.12414 −0.562068 0.827091i \(-0.689994\pi\)
−0.562068 + 0.827091i \(0.689994\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 6.27674 0.238090
\(696\) 0 0
\(697\) −8.04908 −0.304881
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −43.6604 −1.64903 −0.824516 0.565839i \(-0.808552\pi\)
−0.824516 + 0.565839i \(0.808552\pi\)
\(702\) 0 0
\(703\) −15.2120 −0.573731
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −20.8724 −0.784988
\(708\) 0 0
\(709\) −26.7880 −1.00604 −0.503022 0.864273i \(-0.667779\pi\)
−0.503022 + 0.864273i \(0.667779\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 36.5535 1.36894
\(714\) 0 0
\(715\) −2.71982 −0.101716
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −34.8793 −1.30078 −0.650389 0.759601i \(-0.725394\pi\)
−0.650389 + 0.759601i \(0.725394\pi\)
\(720\) 0 0
\(721\) −10.2414 −0.381410
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −6.00000 −0.222834
\(726\) 0 0
\(727\) −37.4396 −1.38856 −0.694280 0.719705i \(-0.744277\pi\)
−0.694280 + 0.719705i \(0.744277\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −31.5309 −1.16621
\(732\) 0 0
\(733\) −47.1560 −1.74175 −0.870874 0.491506i \(-0.836446\pi\)
−0.870874 + 0.491506i \(0.836446\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 5.12070 0.188624
\(738\) 0 0
\(739\) 31.7914 1.16947 0.584734 0.811225i \(-0.301199\pi\)
0.584734 + 0.811225i \(0.301199\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 16.6776 0.611842 0.305921 0.952057i \(-0.401036\pi\)
0.305921 + 0.952057i \(0.401036\pi\)
\(744\) 0 0
\(745\) 20.8302 0.763160
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −34.2767 −1.25244
\(750\) 0 0
\(751\) −16.1855 −0.590616 −0.295308 0.955402i \(-0.595422\pi\)
−0.295308 + 0.955402i \(0.595422\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −4.99656 −0.181844
\(756\) 0 0
\(757\) 12.3258 0.447990 0.223995 0.974590i \(-0.428090\pi\)
0.223995 + 0.974590i \(0.428090\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0.00687569 0.000249244 0 0.000124622 1.00000i \(-0.499960\pi\)
0.000124622 1.00000i \(0.499960\pi\)
\(762\) 0 0
\(763\) 31.1138 1.12640
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −2.11727 −0.0764501
\(768\) 0 0
\(769\) −20.3258 −0.732968 −0.366484 0.930424i \(-0.619439\pi\)
−0.366484 + 0.930424i \(0.619439\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −9.90184 −0.356144 −0.178072 0.984017i \(-0.556986\pi\)
−0.178072 + 0.984017i \(0.556986\pi\)
\(774\) 0 0
\(775\) −7.55691 −0.271452
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −10.0913 −0.361558
\(780\) 0 0
\(781\) 18.2767 0.653993
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 8.87930 0.316916
\(786\) 0 0
\(787\) −36.3449 −1.29556 −0.647778 0.761829i \(-0.724302\pi\)
−0.647778 + 0.761829i \(0.724302\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 35.6673 1.26818
\(792\) 0 0
\(793\) 6.60256 0.234464
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −18.8371 −0.667244 −0.333622 0.942707i \(-0.608271\pi\)
−0.333622 + 0.942707i \(0.608271\pi\)
\(798\) 0 0
\(799\) −32.7880 −1.15996
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −24.7880 −0.874750
\(804\) 0 0
\(805\) −13.1560 −0.463689
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −32.2277 −1.13306 −0.566532 0.824040i \(-0.691715\pi\)
−0.566532 + 0.824040i \(0.691715\pi\)
\(810\) 0 0
\(811\) 23.0034 0.807760 0.403880 0.914812i \(-0.367661\pi\)
0.403880 + 0.914812i \(0.367661\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 13.8337 0.484572
\(816\) 0 0
\(817\) −39.5309 −1.38301
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −49.9372 −1.74282 −0.871410 0.490556i \(-0.836794\pi\)
−0.871410 + 0.490556i \(0.836794\pi\)
\(822\) 0 0
\(823\) −28.2345 −0.984194 −0.492097 0.870540i \(-0.663769\pi\)
−0.492097 + 0.870540i \(0.663769\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −9.55004 −0.332087 −0.166044 0.986118i \(-0.553099\pi\)
−0.166044 + 0.986118i \(0.553099\pi\)
\(828\) 0 0
\(829\) −37.9862 −1.31932 −0.659658 0.751565i \(-0.729299\pi\)
−0.659658 + 0.751565i \(0.729299\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 1.12758 0.0390683
\(834\) 0 0
\(835\) −9.88273 −0.342006
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −4.72670 −0.163184 −0.0815919 0.996666i \(-0.526000\pi\)
−0.0815919 + 0.996666i \(0.526000\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 1.00000 0.0344010
\(846\) 0 0
\(847\) −9.79832 −0.336674
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 20.6870 0.709140
\(852\) 0 0
\(853\) −48.3611 −1.65585 −0.827927 0.560836i \(-0.810480\pi\)
−0.827927 + 0.560836i \(0.810480\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −6.83709 −0.233551 −0.116775 0.993158i \(-0.537256\pi\)
−0.116775 + 0.993158i \(0.537256\pi\)
\(858\) 0 0
\(859\) −12.6026 −0.429994 −0.214997 0.976615i \(-0.568974\pi\)
−0.214997 + 0.976615i \(0.568974\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 8.20855 0.279422 0.139711 0.990192i \(-0.455383\pi\)
0.139711 + 0.990192i \(0.455383\pi\)
\(864\) 0 0
\(865\) −13.1138 −0.445884
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 27.9509 0.948170
\(870\) 0 0
\(871\) −1.88273 −0.0637940
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 2.71982 0.0919468
\(876\) 0 0
\(877\) 13.5309 0.456907 0.228454 0.973555i \(-0.426633\pi\)
0.228454 + 0.973555i \(0.426633\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 9.34836 0.314954 0.157477 0.987523i \(-0.449664\pi\)
0.157477 + 0.987523i \(0.449664\pi\)
\(882\) 0 0
\(883\) 55.1001 1.85427 0.927133 0.374733i \(-0.122266\pi\)
0.927133 + 0.374733i \(0.122266\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0.133492 0.00448223 0.00224112 0.999997i \(-0.499287\pi\)
0.00224112 + 0.999997i \(0.499287\pi\)
\(888\) 0 0
\(889\) 36.5535 1.22596
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −41.1070 −1.37559
\(894\) 0 0
\(895\) 8.55348 0.285911
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 45.3415 1.51222
\(900\) 0 0
\(901\) −3.29928 −0.109915
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 3.72326 0.123765
\(906\) 0 0
\(907\) 58.5466 1.94401 0.972004 0.234964i \(-0.0754973\pi\)
0.972004 + 0.234964i \(0.0754973\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 50.4622 1.67189 0.835943 0.548816i \(-0.184921\pi\)
0.835943 + 0.548816i \(0.184921\pi\)
\(912\) 0 0
\(913\) −5.75859 −0.190582
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −25.6742 −0.847836
\(918\) 0 0
\(919\) −56.9735 −1.87938 −0.939691 0.342026i \(-0.888887\pi\)
−0.939691 + 0.342026i \(0.888887\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −6.71982 −0.221186
\(924\) 0 0
\(925\) −4.27674 −0.140618
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 36.5957 1.20067 0.600333 0.799750i \(-0.295035\pi\)
0.600333 + 0.799750i \(0.295035\pi\)
\(930\) 0 0
\(931\) 1.41367 0.0463311
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −7.71639 −0.252353
\(936\) 0 0
\(937\) −47.1070 −1.53892 −0.769459 0.638697i \(-0.779474\pi\)
−0.769459 + 0.638697i \(0.779474\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 36.3611 1.18534 0.592670 0.805446i \(-0.298074\pi\)
0.592670 + 0.805446i \(0.298074\pi\)
\(942\) 0 0
\(943\) 13.7233 0.446891
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 44.5795 1.44864 0.724319 0.689465i \(-0.242154\pi\)
0.724319 + 0.689465i \(0.242154\pi\)
\(948\) 0 0
\(949\) 9.11383 0.295847
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −19.8596 −0.643317 −0.321658 0.946856i \(-0.604240\pi\)
−0.321658 + 0.946856i \(0.604240\pi\)
\(954\) 0 0
\(955\) −4.23453 −0.137026
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −4.80176 −0.155057
\(960\) 0 0
\(961\) 26.1070 0.842160
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −23.3906 −0.752969
\(966\) 0 0
\(967\) −47.4068 −1.52450 −0.762250 0.647283i \(-0.775905\pi\)
−0.762250 + 0.647283i \(0.775905\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −10.6448 −0.341607 −0.170803 0.985305i \(-0.554636\pi\)
−0.170803 + 0.985305i \(0.554636\pi\)
\(972\) 0 0
\(973\) 17.0716 0.547291
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 1.21199 0.0387750 0.0193875 0.999812i \(-0.493828\pi\)
0.0193875 + 0.999812i \(0.493828\pi\)
\(978\) 0 0
\(979\) 3.16291 0.101087
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 51.8759 1.65458 0.827291 0.561773i \(-0.189881\pi\)
0.827291 + 0.561773i \(0.189881\pi\)
\(984\) 0 0
\(985\) −14.5535 −0.463712
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 53.7586 1.70942
\(990\) 0 0
\(991\) 21.6251 0.686944 0.343472 0.939163i \(-0.388397\pi\)
0.343472 + 0.939163i \(0.388397\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 15.1138 0.479141
\(996\) 0 0
\(997\) 23.2051 0.734913 0.367457 0.930041i \(-0.380229\pi\)
0.367457 + 0.930041i \(0.380229\pi\)
\(998\) 0 0
\(999\) 0 0
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 9360.2.a.dd.1.3 3
3.2 odd 2 3120.2.a.bj.1.3 3
4.3 odd 2 585.2.a.n.1.1 3
12.11 even 2 195.2.a.e.1.3 3
20.3 even 4 2925.2.c.w.2224.6 6
20.7 even 4 2925.2.c.w.2224.1 6
20.19 odd 2 2925.2.a.bh.1.3 3
52.51 odd 2 7605.2.a.bx.1.3 3
60.23 odd 4 975.2.c.i.274.1 6
60.47 odd 4 975.2.c.i.274.6 6
60.59 even 2 975.2.a.o.1.1 3
84.83 odd 2 9555.2.a.bq.1.3 3
156.155 even 2 2535.2.a.bc.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
195.2.a.e.1.3 3 12.11 even 2
585.2.a.n.1.1 3 4.3 odd 2
975.2.a.o.1.1 3 60.59 even 2
975.2.c.i.274.1 6 60.23 odd 4
975.2.c.i.274.6 6 60.47 odd 4
2535.2.a.bc.1.1 3 156.155 even 2
2925.2.a.bh.1.3 3 20.19 odd 2
2925.2.c.w.2224.1 6 20.7 even 4
2925.2.c.w.2224.6 6 20.3 even 4
3120.2.a.bj.1.3 3 3.2 odd 2
7605.2.a.bx.1.3 3 52.51 odd 2
9360.2.a.dd.1.3 3 1.1 even 1 trivial
9555.2.a.bq.1.3 3 84.83 odd 2