Properties

Label 8280.2.a.bk.1.2
Level $8280$
Weight $2$
Character 8280.1
Self dual yes
Analytic conductor $66.116$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 8280 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8280.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(66.1161328736\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.568.1
Defining polynomial: \( x^{3} - x^{2} - 6x - 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-0.363328\) of defining polynomial
Character \(\chi\) \(=\) 8280.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{5} +0.636672 q^{7} +O(q^{10})\) \(q-1.00000 q^{5} +0.636672 q^{7} +1.50466 q^{11} -3.50466 q^{13} -0.636672 q^{17} -0.778008 q^{19} +1.00000 q^{23} +1.00000 q^{25} +4.14134 q^{29} +2.14134 q^{31} -0.636672 q^{35} +1.36333 q^{37} -1.85866 q^{41} -7.00933 q^{43} -3.22199 q^{47} -6.59465 q^{49} -0.636672 q^{53} -1.50466 q^{55} -11.1507 q^{59} +13.7873 q^{61} +3.50466 q^{65} +13.9287 q^{67} -8.97070 q^{71} +15.2406 q^{73} +0.957977 q^{77} -12.5653 q^{79} -9.64600 q^{83} +0.636672 q^{85} +2.44398 q^{89} -2.23132 q^{91} +0.778008 q^{95} -7.55602 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 3 q^{5} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 3 q^{5} + 4 q^{7} - 6 q^{11} - 4 q^{17} + 4 q^{19} + 3 q^{23} + 3 q^{25} + 4 q^{29} - 2 q^{31} - 4 q^{35} + 2 q^{37} - 14 q^{41} - 16 q^{47} - 3 q^{49} - 4 q^{53} + 6 q^{55} - 4 q^{59} + 14 q^{61} + 6 q^{67} - 10 q^{71} + 10 q^{73} - 16 q^{77} - 4 q^{79} - 10 q^{83} + 4 q^{85} + 20 q^{89} + 8 q^{91} - 4 q^{95} - 10 q^{97}+O(q^{100}) \) 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
\(7\) 0.636672 0.240639 0.120320 0.992735i \(-0.461608\pi\)
0.120320 + 0.992735i \(0.461608\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.50466 0.453673 0.226837 0.973933i \(-0.427162\pi\)
0.226837 + 0.973933i \(0.427162\pi\)
\(12\) 0 0
\(13\) −3.50466 −0.972019 −0.486010 0.873954i \(-0.661548\pi\)
−0.486010 + 0.873954i \(0.661548\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.636672 −0.154416 −0.0772078 0.997015i \(-0.524600\pi\)
−0.0772078 + 0.997015i \(0.524600\pi\)
\(18\) 0 0
\(19\) −0.778008 −0.178487 −0.0892436 0.996010i \(-0.528445\pi\)
−0.0892436 + 0.996010i \(0.528445\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 4.14134 0.769027 0.384513 0.923119i \(-0.374369\pi\)
0.384513 + 0.923119i \(0.374369\pi\)
\(30\) 0 0
\(31\) 2.14134 0.384595 0.192298 0.981337i \(-0.438406\pi\)
0.192298 + 0.981337i \(0.438406\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −0.636672 −0.107617
\(36\) 0 0
\(37\) 1.36333 0.224130 0.112065 0.993701i \(-0.464254\pi\)
0.112065 + 0.993701i \(0.464254\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −1.85866 −0.290275 −0.145137 0.989412i \(-0.546362\pi\)
−0.145137 + 0.989412i \(0.546362\pi\)
\(42\) 0 0
\(43\) −7.00933 −1.06891 −0.534456 0.845196i \(-0.679484\pi\)
−0.534456 + 0.845196i \(0.679484\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −3.22199 −0.469976 −0.234988 0.971998i \(-0.575505\pi\)
−0.234988 + 0.971998i \(0.575505\pi\)
\(48\) 0 0
\(49\) −6.59465 −0.942093
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −0.636672 −0.0874536 −0.0437268 0.999044i \(-0.513923\pi\)
−0.0437268 + 0.999044i \(0.513923\pi\)
\(54\) 0 0
\(55\) −1.50466 −0.202889
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −11.1507 −1.45169 −0.725846 0.687857i \(-0.758552\pi\)
−0.725846 + 0.687857i \(0.758552\pi\)
\(60\) 0 0
\(61\) 13.7873 1.76529 0.882644 0.470043i \(-0.155761\pi\)
0.882644 + 0.470043i \(0.155761\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 3.50466 0.434700
\(66\) 0 0
\(67\) 13.9287 1.70166 0.850829 0.525443i \(-0.176100\pi\)
0.850829 + 0.525443i \(0.176100\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −8.97070 −1.06463 −0.532313 0.846548i \(-0.678677\pi\)
−0.532313 + 0.846548i \(0.678677\pi\)
\(72\) 0 0
\(73\) 15.2406 1.78378 0.891892 0.452249i \(-0.149378\pi\)
0.891892 + 0.452249i \(0.149378\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0.957977 0.109172
\(78\) 0 0
\(79\) −12.5653 −1.41371 −0.706856 0.707358i \(-0.749887\pi\)
−0.706856 + 0.707358i \(0.749887\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −9.64600 −1.05879 −0.529393 0.848377i \(-0.677580\pi\)
−0.529393 + 0.848377i \(0.677580\pi\)
\(84\) 0 0
\(85\) 0.636672 0.0690567
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 2.44398 0.259062 0.129531 0.991575i \(-0.458653\pi\)
0.129531 + 0.991575i \(0.458653\pi\)
\(90\) 0 0
\(91\) −2.23132 −0.233906
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0.778008 0.0798219
\(96\) 0 0
\(97\) −7.55602 −0.767197 −0.383599 0.923500i \(-0.625315\pi\)
−0.383599 + 0.923500i \(0.625315\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −10.8680 −1.08141 −0.540703 0.841214i \(-0.681842\pi\)
−0.540703 + 0.841214i \(0.681842\pi\)
\(102\) 0 0
\(103\) 17.1893 1.69371 0.846856 0.531822i \(-0.178493\pi\)
0.846856 + 0.531822i \(0.178493\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 13.9287 1.34654 0.673268 0.739399i \(-0.264890\pi\)
0.673268 + 0.739399i \(0.264890\pi\)
\(108\) 0 0
\(109\) −12.5140 −1.19862 −0.599312 0.800516i \(-0.704559\pi\)
−0.599312 + 0.800516i \(0.704559\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 6.47536 0.609151 0.304575 0.952488i \(-0.401485\pi\)
0.304575 + 0.952488i \(0.401485\pi\)
\(114\) 0 0
\(115\) −1.00000 −0.0932505
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −0.405351 −0.0371585
\(120\) 0 0
\(121\) −8.73599 −0.794180
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −9.60737 −0.852516 −0.426258 0.904602i \(-0.640168\pi\)
−0.426258 + 0.904602i \(0.640168\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1.00933 −0.0881855 −0.0440927 0.999027i \(-0.514040\pi\)
−0.0440927 + 0.999027i \(0.514040\pi\)
\(132\) 0 0
\(133\) −0.495336 −0.0429510
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −17.2920 −1.47736 −0.738678 0.674059i \(-0.764549\pi\)
−0.738678 + 0.674059i \(0.764549\pi\)
\(138\) 0 0
\(139\) 17.7160 1.50265 0.751326 0.659931i \(-0.229415\pi\)
0.751326 + 0.659931i \(0.229415\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −5.27334 −0.440979
\(144\) 0 0
\(145\) −4.14134 −0.343919
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −15.2406 −1.24856 −0.624281 0.781200i \(-0.714608\pi\)
−0.624281 + 0.781200i \(0.714608\pi\)
\(150\) 0 0
\(151\) −4.28267 −0.348519 −0.174259 0.984700i \(-0.555753\pi\)
−0.174259 + 0.984700i \(0.555753\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −2.14134 −0.171996
\(156\) 0 0
\(157\) 11.2020 0.894018 0.447009 0.894529i \(-0.352489\pi\)
0.447009 + 0.894529i \(0.352489\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0.636672 0.0501768
\(162\) 0 0
\(163\) 9.83869 0.770626 0.385313 0.922786i \(-0.374094\pi\)
0.385313 + 0.922786i \(0.374094\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −15.6846 −1.21371 −0.606857 0.794811i \(-0.707570\pi\)
−0.606857 + 0.794811i \(0.707570\pi\)
\(168\) 0 0
\(169\) −0.717328 −0.0551791
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −22.8480 −1.73710 −0.868551 0.495599i \(-0.834948\pi\)
−0.868551 + 0.495599i \(0.834948\pi\)
\(174\) 0 0
\(175\) 0.636672 0.0481279
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −21.1893 −1.58376 −0.791881 0.610675i \(-0.790898\pi\)
−0.791881 + 0.610675i \(0.790898\pi\)
\(180\) 0 0
\(181\) −0.161312 −0.0119902 −0.00599511 0.999982i \(-0.501908\pi\)
−0.00599511 + 0.999982i \(0.501908\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1.36333 −0.100234
\(186\) 0 0
\(187\) −0.957977 −0.0700542
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −18.5140 −1.33963 −0.669813 0.742530i \(-0.733626\pi\)
−0.669813 + 0.742530i \(0.733626\pi\)
\(192\) 0 0
\(193\) −22.2827 −1.60394 −0.801971 0.597363i \(-0.796215\pi\)
−0.801971 + 0.597363i \(0.796215\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 24.5840 1.75154 0.875769 0.482731i \(-0.160355\pi\)
0.875769 + 0.482731i \(0.160355\pi\)
\(198\) 0 0
\(199\) 1.73599 0.123061 0.0615304 0.998105i \(-0.480402\pi\)
0.0615304 + 0.998105i \(0.480402\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 2.63667 0.185058
\(204\) 0 0
\(205\) 1.85866 0.129815
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −1.17064 −0.0809749
\(210\) 0 0
\(211\) −3.69735 −0.254536 −0.127268 0.991868i \(-0.540621\pi\)
−0.127268 + 0.991868i \(0.540621\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 7.00933 0.478032
\(216\) 0 0
\(217\) 1.36333 0.0925488
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 2.23132 0.150095
\(222\) 0 0
\(223\) 0.443984 0.0297314 0.0148657 0.999889i \(-0.495268\pi\)
0.0148657 + 0.999889i \(0.495268\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −22.0187 −1.46143 −0.730715 0.682683i \(-0.760813\pi\)
−0.730715 + 0.682683i \(0.760813\pi\)
\(228\) 0 0
\(229\) 4.62395 0.305559 0.152780 0.988260i \(-0.451177\pi\)
0.152780 + 0.988260i \(0.451177\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −7.83869 −0.513530 −0.256765 0.966474i \(-0.582657\pi\)
−0.256765 + 0.966474i \(0.582657\pi\)
\(234\) 0 0
\(235\) 3.22199 0.210180
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 23.1693 1.49870 0.749349 0.662175i \(-0.230366\pi\)
0.749349 + 0.662175i \(0.230366\pi\)
\(240\) 0 0
\(241\) 1.60737 0.103540 0.0517698 0.998659i \(-0.483514\pi\)
0.0517698 + 0.998659i \(0.483514\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 6.59465 0.421317
\(246\) 0 0
\(247\) 2.72666 0.173493
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −2.99067 −0.188769 −0.0943847 0.995536i \(-0.530088\pi\)
−0.0943847 + 0.995536i \(0.530088\pi\)
\(252\) 0 0
\(253\) 1.50466 0.0945974
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −11.9486 −0.745336 −0.372668 0.927965i \(-0.621557\pi\)
−0.372668 + 0.927965i \(0.621557\pi\)
\(258\) 0 0
\(259\) 0.867993 0.0539344
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 25.5033 1.57260 0.786302 0.617843i \(-0.211993\pi\)
0.786302 + 0.617843i \(0.211993\pi\)
\(264\) 0 0
\(265\) 0.636672 0.0391104
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −7.33063 −0.446957 −0.223478 0.974709i \(-0.571741\pi\)
−0.223478 + 0.974709i \(0.571741\pi\)
\(270\) 0 0
\(271\) 14.5267 0.882435 0.441217 0.897400i \(-0.354547\pi\)
0.441217 + 0.897400i \(0.354547\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.50466 0.0907347
\(276\) 0 0
\(277\) 2.72666 0.163829 0.0819145 0.996639i \(-0.473897\pi\)
0.0819145 + 0.996639i \(0.473897\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 23.3620 1.39366 0.696830 0.717236i \(-0.254593\pi\)
0.696830 + 0.717236i \(0.254593\pi\)
\(282\) 0 0
\(283\) −18.2113 −1.08255 −0.541276 0.840845i \(-0.682059\pi\)
−0.541276 + 0.840845i \(0.682059\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1.18336 −0.0698515
\(288\) 0 0
\(289\) −16.5946 −0.976156
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −3.26063 −0.190488 −0.0952439 0.995454i \(-0.530363\pi\)
−0.0952439 + 0.995454i \(0.530363\pi\)
\(294\) 0 0
\(295\) 11.1507 0.649217
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −3.50466 −0.202680
\(300\) 0 0
\(301\) −4.46264 −0.257222
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −13.7873 −0.789461
\(306\) 0 0
\(307\) 28.9580 1.65272 0.826360 0.563143i \(-0.190408\pi\)
0.826360 + 0.563143i \(0.190408\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 12.3854 0.702310 0.351155 0.936317i \(-0.385789\pi\)
0.351155 + 0.936317i \(0.385789\pi\)
\(312\) 0 0
\(313\) −28.2886 −1.59897 −0.799483 0.600688i \(-0.794893\pi\)
−0.799483 + 0.600688i \(0.794893\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 19.4206 1.09077 0.545385 0.838185i \(-0.316383\pi\)
0.545385 + 0.838185i \(0.316383\pi\)
\(318\) 0 0
\(319\) 6.23132 0.348887
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0.495336 0.0275612
\(324\) 0 0
\(325\) −3.50466 −0.194404
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −2.05135 −0.113095
\(330\) 0 0
\(331\) 24.9707 1.37251 0.686257 0.727359i \(-0.259253\pi\)
0.686257 + 0.727359i \(0.259253\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −13.9287 −0.761005
\(336\) 0 0
\(337\) −23.8387 −1.29858 −0.649288 0.760543i \(-0.724933\pi\)
−0.649288 + 0.760543i \(0.724933\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 3.22199 0.174481
\(342\) 0 0
\(343\) −8.65533 −0.467344
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(348\) 0 0
\(349\) −21.8773 −1.17107 −0.585533 0.810649i \(-0.699115\pi\)
−0.585533 + 0.810649i \(0.699115\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −35.9860 −1.91534 −0.957670 0.287869i \(-0.907053\pi\)
−0.957670 + 0.287869i \(0.907053\pi\)
\(354\) 0 0
\(355\) 8.97070 0.476115
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −21.9486 −1.15841 −0.579203 0.815184i \(-0.696636\pi\)
−0.579203 + 0.815184i \(0.696636\pi\)
\(360\) 0 0
\(361\) −18.3947 −0.968142
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −15.2406 −0.797732
\(366\) 0 0
\(367\) 2.79798 0.146054 0.0730268 0.997330i \(-0.476734\pi\)
0.0730268 + 0.997330i \(0.476734\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −0.405351 −0.0210448
\(372\) 0 0
\(373\) 36.8853 1.90985 0.954925 0.296847i \(-0.0959352\pi\)
0.954925 + 0.296847i \(0.0959352\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −14.5140 −0.747509
\(378\) 0 0
\(379\) −28.9253 −1.48579 −0.742896 0.669407i \(-0.766548\pi\)
−0.742896 + 0.669407i \(0.766548\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −24.1927 −1.23619 −0.618094 0.786104i \(-0.712095\pi\)
−0.618094 + 0.786104i \(0.712095\pi\)
\(384\) 0 0
\(385\) −0.957977 −0.0488230
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −24.6867 −1.25167 −0.625833 0.779957i \(-0.715241\pi\)
−0.625833 + 0.779957i \(0.715241\pi\)
\(390\) 0 0
\(391\) −0.636672 −0.0321979
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 12.5653 0.632231
\(396\) 0 0
\(397\) −5.65872 −0.284003 −0.142001 0.989866i \(-0.545354\pi\)
−0.142001 + 0.989866i \(0.545354\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −25.8387 −1.29032 −0.645161 0.764046i \(-0.723210\pi\)
−0.645161 + 0.764046i \(0.723210\pi\)
\(402\) 0 0
\(403\) −7.50466 −0.373834
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 2.05135 0.101682
\(408\) 0 0
\(409\) −25.9800 −1.28463 −0.642315 0.766441i \(-0.722026\pi\)
−0.642315 + 0.766441i \(0.722026\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −7.09931 −0.349334
\(414\) 0 0
\(415\) 9.64600 0.473504
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 1.96731 0.0961092 0.0480546 0.998845i \(-0.484698\pi\)
0.0480546 + 0.998845i \(0.484698\pi\)
\(420\) 0 0
\(421\) −1.14473 −0.0557905 −0.0278953 0.999611i \(-0.508880\pi\)
−0.0278953 + 0.999611i \(0.508880\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −0.636672 −0.0308831
\(426\) 0 0
\(427\) 8.77801 0.424798
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −19.4720 −0.937932 −0.468966 0.883216i \(-0.655373\pi\)
−0.468966 + 0.883216i \(0.655373\pi\)
\(432\) 0 0
\(433\) −11.1834 −0.537438 −0.268719 0.963219i \(-0.586600\pi\)
−0.268719 + 0.963219i \(0.586600\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −0.778008 −0.0372172
\(438\) 0 0
\(439\) −13.2733 −0.633502 −0.316751 0.948509i \(-0.602592\pi\)
−0.316751 + 0.948509i \(0.602592\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −14.8994 −0.707890 −0.353945 0.935266i \(-0.615160\pi\)
−0.353945 + 0.935266i \(0.615160\pi\)
\(444\) 0 0
\(445\) −2.44398 −0.115856
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 23.1693 1.09343 0.546714 0.837319i \(-0.315879\pi\)
0.546714 + 0.837319i \(0.315879\pi\)
\(450\) 0 0
\(451\) −2.79667 −0.131690
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 2.23132 0.104606
\(456\) 0 0
\(457\) 10.9380 0.511658 0.255829 0.966722i \(-0.417652\pi\)
0.255829 + 0.966722i \(0.417652\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 13.2920 0.619070 0.309535 0.950888i \(-0.399827\pi\)
0.309535 + 0.950888i \(0.399827\pi\)
\(462\) 0 0
\(463\) 0.436726 0.0202964 0.0101482 0.999949i \(-0.496770\pi\)
0.0101482 + 0.999949i \(0.496770\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 29.1180 1.34742 0.673709 0.738996i \(-0.264700\pi\)
0.673709 + 0.738996i \(0.264700\pi\)
\(468\) 0 0
\(469\) 8.86799 0.409486
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −10.5467 −0.484937
\(474\) 0 0
\(475\) −0.778008 −0.0356974
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −10.1541 −0.463951 −0.231975 0.972722i \(-0.574519\pi\)
−0.231975 + 0.972722i \(0.574519\pi\)
\(480\) 0 0
\(481\) −4.77801 −0.217858
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 7.55602 0.343101
\(486\) 0 0
\(487\) 18.5980 0.842758 0.421379 0.906885i \(-0.361546\pi\)
0.421379 + 0.906885i \(0.361546\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −35.0080 −1.57989 −0.789945 0.613178i \(-0.789891\pi\)
−0.789945 + 0.613178i \(0.789891\pi\)
\(492\) 0 0
\(493\) −2.63667 −0.118750
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −5.71139 −0.256191
\(498\) 0 0
\(499\) −8.40535 −0.376275 −0.188138 0.982143i \(-0.560245\pi\)
−0.188138 + 0.982143i \(0.560245\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 37.5806 1.67564 0.837818 0.545949i \(-0.183831\pi\)
0.837818 + 0.545949i \(0.183831\pi\)
\(504\) 0 0
\(505\) 10.8680 0.483619
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 34.2427 1.51778 0.758891 0.651218i \(-0.225742\pi\)
0.758891 + 0.651218i \(0.225742\pi\)
\(510\) 0 0
\(511\) 9.70329 0.429248
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −17.1893 −0.757451
\(516\) 0 0
\(517\) −4.84802 −0.213216
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −0.572602 −0.0250862 −0.0125431 0.999921i \(-0.503993\pi\)
−0.0125431 + 0.999921i \(0.503993\pi\)
\(522\) 0 0
\(523\) 13.3760 0.584894 0.292447 0.956282i \(-0.405531\pi\)
0.292447 + 0.956282i \(0.405531\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.36333 −0.0593875
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 6.51399 0.282152
\(534\) 0 0
\(535\) −13.9287 −0.602189
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −9.92273 −0.427402
\(540\) 0 0
\(541\) −36.4040 −1.56513 −0.782566 0.622568i \(-0.786089\pi\)
−0.782566 + 0.622568i \(0.786089\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 12.5140 0.536041
\(546\) 0 0
\(547\) −14.5840 −0.623567 −0.311783 0.950153i \(-0.600926\pi\)
−0.311783 + 0.950153i \(0.600926\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −3.22199 −0.137261
\(552\) 0 0
\(553\) −8.00000 −0.340195
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −46.4100 −1.96645 −0.983227 0.182387i \(-0.941618\pi\)
−0.983227 + 0.182387i \(0.941618\pi\)
\(558\) 0 0
\(559\) 24.5653 1.03900
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −9.36333 −0.394617 −0.197309 0.980341i \(-0.563220\pi\)
−0.197309 + 0.980341i \(0.563220\pi\)
\(564\) 0 0
\(565\) −6.47536 −0.272420
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0.282672 0.0118502 0.00592512 0.999982i \(-0.498114\pi\)
0.00592512 + 0.999982i \(0.498114\pi\)
\(570\) 0 0
\(571\) −24.1073 −1.00886 −0.504430 0.863453i \(-0.668297\pi\)
−0.504430 + 0.863453i \(0.668297\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.00000 0.0417029
\(576\) 0 0
\(577\) 22.4227 0.933469 0.466734 0.884398i \(-0.345430\pi\)
0.466734 + 0.884398i \(0.345430\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −6.14134 −0.254786
\(582\) 0 0
\(583\) −0.957977 −0.0396754
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −19.1893 −0.792027 −0.396014 0.918245i \(-0.629607\pi\)
−0.396014 + 0.918245i \(0.629607\pi\)
\(588\) 0 0
\(589\) −1.66598 −0.0686454
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −9.04202 −0.371311 −0.185656 0.982615i \(-0.559441\pi\)
−0.185656 + 0.982615i \(0.559441\pi\)
\(594\) 0 0
\(595\) 0.405351 0.0166178
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −46.3386 −1.89335 −0.946673 0.322196i \(-0.895579\pi\)
−0.946673 + 0.322196i \(0.895579\pi\)
\(600\) 0 0
\(601\) −17.6974 −0.721890 −0.360945 0.932587i \(-0.617546\pi\)
−0.360945 + 0.932587i \(0.617546\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 8.73599 0.355168
\(606\) 0 0
\(607\) 42.5327 1.72635 0.863174 0.504907i \(-0.168473\pi\)
0.863174 + 0.504907i \(0.168473\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 11.2920 0.456825
\(612\) 0 0
\(613\) −31.5747 −1.27529 −0.637645 0.770331i \(-0.720091\pi\)
−0.637645 + 0.770331i \(0.720091\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −45.2393 −1.82127 −0.910633 0.413215i \(-0.864406\pi\)
−0.910633 + 0.413215i \(0.864406\pi\)
\(618\) 0 0
\(619\) 29.4906 1.18533 0.592664 0.805450i \(-0.298076\pi\)
0.592664 + 0.805450i \(0.298076\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 1.55602 0.0623405
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −0.867993 −0.0346091
\(630\) 0 0
\(631\) 43.6447 1.73747 0.868734 0.495280i \(-0.164934\pi\)
0.868734 + 0.495280i \(0.164934\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 9.60737 0.381257
\(636\) 0 0
\(637\) 23.1120 0.915732
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −28.3527 −1.11986 −0.559932 0.828539i \(-0.689173\pi\)
−0.559932 + 0.828539i \(0.689173\pi\)
\(642\) 0 0
\(643\) 22.1086 0.871880 0.435940 0.899976i \(-0.356416\pi\)
0.435940 + 0.899976i \(0.356416\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −9.42062 −0.370363 −0.185181 0.982704i \(-0.559287\pi\)
−0.185181 + 0.982704i \(0.559287\pi\)
\(648\) 0 0
\(649\) −16.7780 −0.658594
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −3.76868 −0.147480 −0.0737399 0.997278i \(-0.523493\pi\)
−0.0737399 + 0.997278i \(0.523493\pi\)
\(654\) 0 0
\(655\) 1.00933 0.0394377
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −16.9393 −0.659862 −0.329931 0.944005i \(-0.607026\pi\)
−0.329931 + 0.944005i \(0.607026\pi\)
\(660\) 0 0
\(661\) 35.6960 1.38841 0.694207 0.719775i \(-0.255755\pi\)
0.694207 + 0.719775i \(0.255755\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0.495336 0.0192083
\(666\) 0 0
\(667\) 4.14134 0.160353
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 20.7453 0.800864
\(672\) 0 0
\(673\) 2.53265 0.0976265 0.0488133 0.998808i \(-0.484456\pi\)
0.0488133 + 0.998808i \(0.484456\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −31.3633 −1.20539 −0.602695 0.797971i \(-0.705907\pi\)
−0.602695 + 0.797971i \(0.705907\pi\)
\(678\) 0 0
\(679\) −4.81070 −0.184618
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 23.7873 0.910197 0.455099 0.890441i \(-0.349604\pi\)
0.455099 + 0.890441i \(0.349604\pi\)
\(684\) 0 0
\(685\) 17.2920 0.660693
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 2.23132 0.0850066
\(690\) 0 0
\(691\) −22.6613 −0.862075 −0.431038 0.902334i \(-0.641852\pi\)
−0.431038 + 0.902334i \(0.641852\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −17.7160 −0.672007
\(696\) 0 0
\(697\) 1.18336 0.0448229
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 13.2593 0.500797 0.250399 0.968143i \(-0.419438\pi\)
0.250399 + 0.968143i \(0.419438\pi\)
\(702\) 0 0
\(703\) −1.06068 −0.0400043
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −6.91934 −0.260229
\(708\) 0 0
\(709\) −40.6940 −1.52829 −0.764147 0.645042i \(-0.776840\pi\)
−0.764147 + 0.645042i \(0.776840\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 2.14134 0.0801937
\(714\) 0 0
\(715\) 5.27334 0.197212
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −4.79073 −0.178664 −0.0893320 0.996002i \(-0.528473\pi\)
−0.0893320 + 0.996002i \(0.528473\pi\)
\(720\) 0 0
\(721\) 10.9439 0.407574
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 4.14134 0.153805
\(726\) 0 0
\(727\) −17.9473 −0.665630 −0.332815 0.942992i \(-0.607998\pi\)
−0.332815 + 0.942992i \(0.607998\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 4.46264 0.165057
\(732\) 0 0
\(733\) −17.9287 −0.662211 −0.331105 0.943594i \(-0.607422\pi\)
−0.331105 + 0.943594i \(0.607422\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 20.9580 0.771997
\(738\) 0 0
\(739\) 16.5853 0.610101 0.305050 0.952336i \(-0.401327\pi\)
0.305050 + 0.952336i \(0.401327\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −2.90663 −0.106634 −0.0533169 0.998578i \(-0.516979\pi\)
−0.0533169 + 0.998578i \(0.516979\pi\)
\(744\) 0 0
\(745\) 15.2406 0.558374
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 8.86799 0.324029
\(750\) 0 0
\(751\) −18.8994 −0.689648 −0.344824 0.938667i \(-0.612061\pi\)
−0.344824 + 0.938667i \(0.612061\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 4.28267 0.155862
\(756\) 0 0
\(757\) 3.34467 0.121564 0.0607821 0.998151i \(-0.480641\pi\)
0.0607821 + 0.998151i \(0.480641\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −23.5946 −0.855305 −0.427653 0.903943i \(-0.640659\pi\)
−0.427653 + 0.903943i \(0.640659\pi\)
\(762\) 0 0
\(763\) −7.96731 −0.288436
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 39.0793 1.41107
\(768\) 0 0
\(769\) 44.8340 1.61675 0.808377 0.588665i \(-0.200346\pi\)
0.808377 + 0.588665i \(0.200346\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 19.9160 0.716327 0.358164 0.933659i \(-0.383403\pi\)
0.358164 + 0.933659i \(0.383403\pi\)
\(774\) 0 0
\(775\) 2.14134 0.0769191
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1.44606 0.0518103
\(780\) 0 0
\(781\) −13.4979 −0.482992
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −11.2020 −0.399817
\(786\) 0 0
\(787\) 33.2207 1.18419 0.592095 0.805868i \(-0.298301\pi\)
0.592095 + 0.805868i \(0.298301\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 4.12268 0.146586
\(792\) 0 0
\(793\) −48.3200 −1.71589
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 23.8633 0.845281 0.422640 0.906297i \(-0.361103\pi\)
0.422640 + 0.906297i \(0.361103\pi\)
\(798\) 0 0
\(799\) 2.05135 0.0725716
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 22.9321 0.809255
\(804\) 0 0
\(805\) −0.636672 −0.0224397
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 35.1693 1.23649 0.618244 0.785986i \(-0.287844\pi\)
0.618244 + 0.785986i \(0.287844\pi\)
\(810\) 0 0
\(811\) 29.0480 1.02001 0.510006 0.860171i \(-0.329643\pi\)
0.510006 + 0.860171i \(0.329643\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −9.83869 −0.344634
\(816\) 0 0
\(817\) 5.45331 0.190787
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −38.6027 −1.34724 −0.673621 0.739077i \(-0.735262\pi\)
−0.673621 + 0.739077i \(0.735262\pi\)
\(822\) 0 0
\(823\) −16.4040 −0.571809 −0.285904 0.958258i \(-0.592294\pi\)
−0.285904 + 0.958258i \(0.592294\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −27.2393 −0.947204 −0.473602 0.880739i \(-0.657047\pi\)
−0.473602 + 0.880739i \(0.657047\pi\)
\(828\) 0 0
\(829\) 31.1107 1.08052 0.540260 0.841498i \(-0.318326\pi\)
0.540260 + 0.841498i \(0.318326\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 4.19863 0.145474
\(834\) 0 0
\(835\) 15.6846 0.542789
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −3.71733 −0.128336 −0.0641682 0.997939i \(-0.520439\pi\)
−0.0641682 + 0.997939i \(0.520439\pi\)
\(840\) 0 0
\(841\) −11.8493 −0.408598
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0.717328 0.0246768
\(846\) 0 0
\(847\) −5.56196 −0.191111
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 1.36333 0.0467343
\(852\) 0 0
\(853\) 9.17064 0.313997 0.156998 0.987599i \(-0.449818\pi\)
0.156998 + 0.987599i \(0.449818\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 14.9907 0.512072 0.256036 0.966667i \(-0.417584\pi\)
0.256036 + 0.966667i \(0.417584\pi\)
\(858\) 0 0
\(859\) −6.98935 −0.238474 −0.119237 0.992866i \(-0.538045\pi\)
−0.119237 + 0.992866i \(0.538045\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −21.2080 −0.721927 −0.360964 0.932580i \(-0.617552\pi\)
−0.360964 + 0.932580i \(0.617552\pi\)
\(864\) 0 0
\(865\) 22.8480 0.776856
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −18.9066 −0.641363
\(870\) 0 0
\(871\) −48.8153 −1.65404
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −0.636672 −0.0215234
\(876\) 0 0
\(877\) 29.3760 0.991959 0.495979 0.868334i \(-0.334809\pi\)
0.495979 + 0.868334i \(0.334809\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −39.1820 −1.32008 −0.660038 0.751232i \(-0.729460\pi\)
−0.660038 + 0.751232i \(0.729460\pi\)
\(882\) 0 0
\(883\) 1.13795 0.0382950 0.0191475 0.999817i \(-0.493905\pi\)
0.0191475 + 0.999817i \(0.493905\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 19.1520 0.643061 0.321530 0.946899i \(-0.395803\pi\)
0.321530 + 0.946899i \(0.395803\pi\)
\(888\) 0 0
\(889\) −6.11674 −0.205149
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 2.50674 0.0838847
\(894\) 0 0
\(895\) 21.1893 0.708280
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 8.86799 0.295764
\(900\) 0 0
\(901\) 0.405351 0.0135042
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0.161312 0.00536219
\(906\) 0 0
\(907\) 21.4406 0.711923 0.355962 0.934501i \(-0.384153\pi\)
0.355962 + 0.934501i \(0.384153\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 39.9346 1.32309 0.661546 0.749904i \(-0.269900\pi\)
0.661546 + 0.749904i \(0.269900\pi\)
\(912\) 0 0
\(913\) −14.5140 −0.480343
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −0.642611 −0.0212209
\(918\) 0 0
\(919\) −47.4066 −1.56380 −0.781899 0.623405i \(-0.785749\pi\)
−0.781899 + 0.623405i \(0.785749\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 31.4393 1.03484
\(924\) 0 0
\(925\) 1.36333 0.0448260
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 40.9053 1.34206 0.671030 0.741430i \(-0.265852\pi\)
0.671030 + 0.741430i \(0.265852\pi\)
\(930\) 0 0
\(931\) 5.13069 0.168152
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0.957977 0.0313292
\(936\) 0 0
\(937\) −25.6120 −0.836707 −0.418354 0.908284i \(-0.637393\pi\)
−0.418354 + 0.908284i \(0.637393\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 6.21266 0.202527 0.101264 0.994860i \(-0.467711\pi\)
0.101264 + 0.994860i \(0.467711\pi\)
\(942\) 0 0
\(943\) −1.85866 −0.0605264
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −37.7987 −1.22829 −0.614147 0.789192i \(-0.710500\pi\)
−0.614147 + 0.789192i \(0.710500\pi\)
\(948\) 0 0
\(949\) −53.4134 −1.73387
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −2.32262 −0.0752372 −0.0376186 0.999292i \(-0.511977\pi\)
−0.0376186 + 0.999292i \(0.511977\pi\)
\(954\) 0 0
\(955\) 18.5140 0.599099
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −11.0093 −0.355510
\(960\) 0 0
\(961\) −26.4147 −0.852086
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 22.2827 0.717305
\(966\) 0 0
\(967\) 9.14473 0.294075 0.147037 0.989131i \(-0.453026\pi\)
0.147037 + 0.989131i \(0.453026\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 38.7453 1.24340 0.621698 0.783257i \(-0.286443\pi\)
0.621698 + 0.783257i \(0.286443\pi\)
\(972\) 0 0
\(973\) 11.2793 0.361597
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 32.8794 1.05190 0.525952 0.850514i \(-0.323709\pi\)
0.525952 + 0.850514i \(0.323709\pi\)
\(978\) 0 0
\(979\) 3.67738 0.117529
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −2.13408 −0.0680665 −0.0340333 0.999421i \(-0.510835\pi\)
−0.0340333 + 0.999421i \(0.510835\pi\)
\(984\) 0 0
\(985\) −24.5840 −0.783311
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −7.00933 −0.222884
\(990\) 0 0
\(991\) 58.3586 1.85382 0.926911 0.375280i \(-0.122454\pi\)
0.926911 + 0.375280i \(0.122454\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −1.73599 −0.0550344
\(996\) 0 0
\(997\) 11.4347 0.362139 0.181070 0.983470i \(-0.442044\pi\)
0.181070 + 0.983470i \(0.442044\pi\)
\(998\) 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 8280.2.a.bk.1.2 3
3.2 odd 2 8280.2.a.bp.1.2 yes 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8280.2.a.bk.1.2 3 1.1 even 1 trivial
8280.2.a.bp.1.2 yes 3 3.2 odd 2