Properties

Label 6012.2.a.f.1.1
Level 6012
Weight 2
Character 6012.1
Self dual yes
Analytic conductor 48.006
Analytic rank 0
Dimension 5
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 6012 = 2^{2} \cdot 3^{2} \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6012.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.0060616952\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: 5.5.161121.1
Defining polynomial: \(x^{5} - x^{4} - 6 x^{3} + 3 x^{2} + 5 x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 2004)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(1.31991\) of defining polynomial
Character \(\chi\) \(=\) 6012.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.28459 q^{5} -1.96468 q^{7} +O(q^{10})\) \(q-1.28459 q^{5} -1.96468 q^{7} +2.40916 q^{11} -3.92621 q^{13} +3.63982 q^{17} +2.30861 q^{19} +4.55057 q^{23} -3.34982 q^{25} +5.81156 q^{29} -4.65708 q^{31} +2.52381 q^{35} +4.09300 q^{37} -7.34227 q^{41} -3.88636 q^{43} -7.51721 q^{47} -3.14003 q^{49} +10.6471 q^{53} -3.09479 q^{55} -10.8022 q^{59} -14.0025 q^{61} +5.04358 q^{65} +0.286799 q^{67} +10.1569 q^{71} +3.44823 q^{73} -4.73323 q^{77} +5.99698 q^{79} -10.0713 q^{83} -4.67569 q^{85} +9.05989 q^{89} +7.71375 q^{91} -2.96563 q^{95} +4.02676 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q + 7q^{5} - 2q^{7} + O(q^{10}) \) \( 5q + 7q^{5} - 2q^{7} + 5q^{11} - 8q^{13} + 7q^{17} + 2q^{19} + 13q^{23} + 2q^{25} + 11q^{29} - 12q^{31} + 12q^{35} - 7q^{37} + 12q^{41} + 19q^{47} - 9q^{49} + 21q^{53} - q^{55} + 7q^{59} - 6q^{61} - 14q^{65} + 10q^{67} + 35q^{71} - 8q^{73} + 6q^{77} + 11q^{83} + 5q^{85} + 32q^{89} + 5q^{91} + 19q^{95} + 11q^{97} + O(q^{100}) \)

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
\(3\) 0 0
\(4\) 0 0
\(5\) −1.28459 −0.574487 −0.287244 0.957858i \(-0.592739\pi\)
−0.287244 + 0.957858i \(0.592739\pi\)
\(6\) 0 0
\(7\) −1.96468 −0.742579 −0.371290 0.928517i \(-0.621084\pi\)
−0.371290 + 0.928517i \(0.621084\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.40916 0.726390 0.363195 0.931713i \(-0.381686\pi\)
0.363195 + 0.931713i \(0.381686\pi\)
\(12\) 0 0
\(13\) −3.92621 −1.08893 −0.544467 0.838782i \(-0.683268\pi\)
−0.544467 + 0.838782i \(0.683268\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.63982 0.882787 0.441393 0.897314i \(-0.354484\pi\)
0.441393 + 0.897314i \(0.354484\pi\)
\(18\) 0 0
\(19\) 2.30861 0.529632 0.264816 0.964299i \(-0.414689\pi\)
0.264816 + 0.964299i \(0.414689\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 4.55057 0.948860 0.474430 0.880293i \(-0.342654\pi\)
0.474430 + 0.880293i \(0.342654\pi\)
\(24\) 0 0
\(25\) −3.34982 −0.669965
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 5.81156 1.07918 0.539590 0.841928i \(-0.318579\pi\)
0.539590 + 0.841928i \(0.318579\pi\)
\(30\) 0 0
\(31\) −4.65708 −0.836436 −0.418218 0.908347i \(-0.637345\pi\)
−0.418218 + 0.908347i \(0.637345\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.52381 0.426602
\(36\) 0 0
\(37\) 4.09300 0.672885 0.336442 0.941704i \(-0.390776\pi\)
0.336442 + 0.941704i \(0.390776\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −7.34227 −1.14667 −0.573335 0.819321i \(-0.694351\pi\)
−0.573335 + 0.819321i \(0.694351\pi\)
\(42\) 0 0
\(43\) −3.88636 −0.592664 −0.296332 0.955085i \(-0.595763\pi\)
−0.296332 + 0.955085i \(0.595763\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −7.51721 −1.09650 −0.548249 0.836315i \(-0.684705\pi\)
−0.548249 + 0.836315i \(0.684705\pi\)
\(48\) 0 0
\(49\) −3.14003 −0.448576
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 10.6471 1.46250 0.731248 0.682111i \(-0.238938\pi\)
0.731248 + 0.682111i \(0.238938\pi\)
\(54\) 0 0
\(55\) −3.09479 −0.417302
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −10.8022 −1.40633 −0.703164 0.711028i \(-0.748230\pi\)
−0.703164 + 0.711028i \(0.748230\pi\)
\(60\) 0 0
\(61\) −14.0025 −1.79284 −0.896418 0.443209i \(-0.853840\pi\)
−0.896418 + 0.443209i \(0.853840\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 5.04358 0.625579
\(66\) 0 0
\(67\) 0.286799 0.0350381 0.0175191 0.999847i \(-0.494423\pi\)
0.0175191 + 0.999847i \(0.494423\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 10.1569 1.20540 0.602699 0.797968i \(-0.294092\pi\)
0.602699 + 0.797968i \(0.294092\pi\)
\(72\) 0 0
\(73\) 3.44823 0.403585 0.201792 0.979428i \(-0.435323\pi\)
0.201792 + 0.979428i \(0.435323\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −4.73323 −0.539402
\(78\) 0 0
\(79\) 5.99698 0.674713 0.337356 0.941377i \(-0.390467\pi\)
0.337356 + 0.941377i \(0.390467\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −10.0713 −1.10547 −0.552737 0.833356i \(-0.686417\pi\)
−0.552737 + 0.833356i \(0.686417\pi\)
\(84\) 0 0
\(85\) −4.67569 −0.507150
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 9.05989 0.960346 0.480173 0.877174i \(-0.340574\pi\)
0.480173 + 0.877174i \(0.340574\pi\)
\(90\) 0 0
\(91\) 7.71375 0.808620
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −2.96563 −0.304267
\(96\) 0 0
\(97\) 4.02676 0.408855 0.204428 0.978882i \(-0.434467\pi\)
0.204428 + 0.978882i \(0.434467\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −1.06980 −0.106450 −0.0532248 0.998583i \(-0.516950\pi\)
−0.0532248 + 0.998583i \(0.516950\pi\)
\(102\) 0 0
\(103\) 15.5422 1.53142 0.765709 0.643188i \(-0.222388\pi\)
0.765709 + 0.643188i \(0.222388\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 2.54641 0.246171 0.123085 0.992396i \(-0.460721\pi\)
0.123085 + 0.992396i \(0.460721\pi\)
\(108\) 0 0
\(109\) 15.5695 1.49129 0.745646 0.666343i \(-0.232141\pi\)
0.745646 + 0.666343i \(0.232141\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 3.22887 0.303746 0.151873 0.988400i \(-0.451469\pi\)
0.151873 + 0.988400i \(0.451469\pi\)
\(114\) 0 0
\(115\) −5.84563 −0.545108
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −7.15109 −0.655539
\(120\) 0 0
\(121\) −5.19594 −0.472358
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 10.7261 0.959373
\(126\) 0 0
\(127\) 0.940660 0.0834701 0.0417351 0.999129i \(-0.486711\pi\)
0.0417351 + 0.999129i \(0.486711\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 13.7284 1.19946 0.599729 0.800203i \(-0.295275\pi\)
0.599729 + 0.800203i \(0.295275\pi\)
\(132\) 0 0
\(133\) −4.53569 −0.393294
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 17.2672 1.47524 0.737620 0.675216i \(-0.235950\pi\)
0.737620 + 0.675216i \(0.235950\pi\)
\(138\) 0 0
\(139\) 10.0634 0.853570 0.426785 0.904353i \(-0.359646\pi\)
0.426785 + 0.904353i \(0.359646\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −9.45888 −0.790991
\(144\) 0 0
\(145\) −7.46548 −0.619975
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 18.8300 1.54261 0.771306 0.636464i \(-0.219604\pi\)
0.771306 + 0.636464i \(0.219604\pi\)
\(150\) 0 0
\(151\) 10.6354 0.865498 0.432749 0.901514i \(-0.357544\pi\)
0.432749 + 0.901514i \(0.357544\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 5.98244 0.480521
\(156\) 0 0
\(157\) 22.2179 1.77318 0.886592 0.462553i \(-0.153066\pi\)
0.886592 + 0.462553i \(0.153066\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −8.94042 −0.704604
\(162\) 0 0
\(163\) −21.9987 −1.72307 −0.861535 0.507699i \(-0.830496\pi\)
−0.861535 + 0.507699i \(0.830496\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1.00000 0.0773823
\(168\) 0 0
\(169\) 2.41512 0.185778
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −15.8426 −1.20449 −0.602246 0.798311i \(-0.705727\pi\)
−0.602246 + 0.798311i \(0.705727\pi\)
\(174\) 0 0
\(175\) 6.58133 0.497502
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 3.43373 0.256649 0.128324 0.991732i \(-0.459040\pi\)
0.128324 + 0.991732i \(0.459040\pi\)
\(180\) 0 0
\(181\) −11.3243 −0.841725 −0.420863 0.907124i \(-0.638273\pi\)
−0.420863 + 0.907124i \(0.638273\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −5.25783 −0.386564
\(186\) 0 0
\(187\) 8.76893 0.641247
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 26.0824 1.88726 0.943628 0.331007i \(-0.107388\pi\)
0.943628 + 0.331007i \(0.107388\pi\)
\(192\) 0 0
\(193\) 25.5074 1.83606 0.918031 0.396508i \(-0.129778\pi\)
0.918031 + 0.396508i \(0.129778\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 4.73730 0.337519 0.168759 0.985657i \(-0.446024\pi\)
0.168759 + 0.985657i \(0.446024\pi\)
\(198\) 0 0
\(199\) −13.8698 −0.983206 −0.491603 0.870819i \(-0.663589\pi\)
−0.491603 + 0.870819i \(0.663589\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −11.4179 −0.801376
\(204\) 0 0
\(205\) 9.43182 0.658747
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 5.56182 0.384719
\(210\) 0 0
\(211\) 17.5267 1.20659 0.603294 0.797519i \(-0.293854\pi\)
0.603294 + 0.797519i \(0.293854\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 4.99238 0.340478
\(216\) 0 0
\(217\) 9.14967 0.621120
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −14.2907 −0.961297
\(222\) 0 0
\(223\) 17.9825 1.20420 0.602099 0.798422i \(-0.294331\pi\)
0.602099 + 0.798422i \(0.294331\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −4.80164 −0.318696 −0.159348 0.987222i \(-0.550939\pi\)
−0.159348 + 0.987222i \(0.550939\pi\)
\(228\) 0 0
\(229\) −27.8758 −1.84208 −0.921041 0.389465i \(-0.872660\pi\)
−0.921041 + 0.389465i \(0.872660\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −5.52381 −0.361877 −0.180939 0.983494i \(-0.557914\pi\)
−0.180939 + 0.983494i \(0.557914\pi\)
\(234\) 0 0
\(235\) 9.65655 0.629924
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 23.2120 1.50146 0.750729 0.660611i \(-0.229703\pi\)
0.750729 + 0.660611i \(0.229703\pi\)
\(240\) 0 0
\(241\) 3.27780 0.211142 0.105571 0.994412i \(-0.466333\pi\)
0.105571 + 0.994412i \(0.466333\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 4.03366 0.257701
\(246\) 0 0
\(247\) −9.06410 −0.576735
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 11.2250 0.708518 0.354259 0.935147i \(-0.384733\pi\)
0.354259 + 0.935147i \(0.384733\pi\)
\(252\) 0 0
\(253\) 10.9631 0.689242
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −12.9517 −0.807907 −0.403954 0.914779i \(-0.632364\pi\)
−0.403954 + 0.914779i \(0.632364\pi\)
\(258\) 0 0
\(259\) −8.04143 −0.499670
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 4.16998 0.257132 0.128566 0.991701i \(-0.458963\pi\)
0.128566 + 0.991701i \(0.458963\pi\)
\(264\) 0 0
\(265\) −13.6772 −0.840185
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 31.2329 1.90430 0.952152 0.305625i \(-0.0988654\pi\)
0.952152 + 0.305625i \(0.0988654\pi\)
\(270\) 0 0
\(271\) 19.9256 1.21039 0.605197 0.796076i \(-0.293095\pi\)
0.605197 + 0.796076i \(0.293095\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −8.07027 −0.486655
\(276\) 0 0
\(277\) 2.20031 0.132204 0.0661021 0.997813i \(-0.478944\pi\)
0.0661021 + 0.997813i \(0.478944\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −26.4717 −1.57917 −0.789585 0.613641i \(-0.789704\pi\)
−0.789585 + 0.613641i \(0.789704\pi\)
\(282\) 0 0
\(283\) 14.2466 0.846870 0.423435 0.905926i \(-0.360824\pi\)
0.423435 + 0.905926i \(0.360824\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 14.4252 0.851494
\(288\) 0 0
\(289\) −3.75169 −0.220687
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −12.2255 −0.714221 −0.357111 0.934062i \(-0.616238\pi\)
−0.357111 + 0.934062i \(0.616238\pi\)
\(294\) 0 0
\(295\) 13.8764 0.807917
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −17.8665 −1.03325
\(300\) 0 0
\(301\) 7.63545 0.440100
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 17.9875 1.02996
\(306\) 0 0
\(307\) 1.04146 0.0594395 0.0297197 0.999558i \(-0.490539\pi\)
0.0297197 + 0.999558i \(0.490539\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1.61814 0.0917564 0.0458782 0.998947i \(-0.485391\pi\)
0.0458782 + 0.998947i \(0.485391\pi\)
\(312\) 0 0
\(313\) −25.1205 −1.41990 −0.709948 0.704254i \(-0.751281\pi\)
−0.709948 + 0.704254i \(0.751281\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 25.6518 1.44075 0.720374 0.693586i \(-0.243970\pi\)
0.720374 + 0.693586i \(0.243970\pi\)
\(318\) 0 0
\(319\) 14.0010 0.783905
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 8.40294 0.467552
\(324\) 0 0
\(325\) 13.1521 0.729547
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 14.7689 0.814236
\(330\) 0 0
\(331\) 17.7667 0.976544 0.488272 0.872691i \(-0.337627\pi\)
0.488272 + 0.872691i \(0.337627\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −0.368420 −0.0201290
\(336\) 0 0
\(337\) −19.2213 −1.04705 −0.523526 0.852010i \(-0.675384\pi\)
−0.523526 + 0.852010i \(0.675384\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −11.2197 −0.607578
\(342\) 0 0
\(343\) 19.9219 1.07568
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −14.1326 −0.758677 −0.379339 0.925258i \(-0.623848\pi\)
−0.379339 + 0.925258i \(0.623848\pi\)
\(348\) 0 0
\(349\) −28.1862 −1.50877 −0.754387 0.656429i \(-0.772066\pi\)
−0.754387 + 0.656429i \(0.772066\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 16.0991 0.856870 0.428435 0.903573i \(-0.359065\pi\)
0.428435 + 0.903573i \(0.359065\pi\)
\(354\) 0 0
\(355\) −13.0474 −0.692486
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 3.09816 0.163515 0.0817574 0.996652i \(-0.473947\pi\)
0.0817574 + 0.996652i \(0.473947\pi\)
\(360\) 0 0
\(361\) −13.6703 −0.719490
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −4.42957 −0.231854
\(366\) 0 0
\(367\) −15.5041 −0.809307 −0.404654 0.914470i \(-0.632608\pi\)
−0.404654 + 0.914470i \(0.632608\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −20.9182 −1.08602
\(372\) 0 0
\(373\) −8.04456 −0.416532 −0.208266 0.978072i \(-0.566782\pi\)
−0.208266 + 0.978072i \(0.566782\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −22.8174 −1.17516
\(378\) 0 0
\(379\) 18.3818 0.944210 0.472105 0.881542i \(-0.343494\pi\)
0.472105 + 0.881542i \(0.343494\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −1.38490 −0.0707649 −0.0353825 0.999374i \(-0.511265\pi\)
−0.0353825 + 0.999374i \(0.511265\pi\)
\(384\) 0 0
\(385\) 6.08028 0.309880
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −18.6320 −0.944680 −0.472340 0.881416i \(-0.656591\pi\)
−0.472340 + 0.881416i \(0.656591\pi\)
\(390\) 0 0
\(391\) 16.5633 0.837641
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −7.70367 −0.387614
\(396\) 0 0
\(397\) 36.8598 1.84994 0.924969 0.380042i \(-0.124090\pi\)
0.924969 + 0.380042i \(0.124090\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 5.06368 0.252868 0.126434 0.991975i \(-0.459647\pi\)
0.126434 + 0.991975i \(0.459647\pi\)
\(402\) 0 0
\(403\) 18.2847 0.910824
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 9.86070 0.488777
\(408\) 0 0
\(409\) 24.0361 1.18851 0.594254 0.804278i \(-0.297447\pi\)
0.594254 + 0.804278i \(0.297447\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 21.2229 1.04431
\(414\) 0 0
\(415\) 12.9376 0.635080
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −10.8318 −0.529170 −0.264585 0.964362i \(-0.585235\pi\)
−0.264585 + 0.964362i \(0.585235\pi\)
\(420\) 0 0
\(421\) 2.18637 0.106557 0.0532785 0.998580i \(-0.483033\pi\)
0.0532785 + 0.998580i \(0.483033\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −12.1928 −0.591436
\(426\) 0 0
\(427\) 27.5104 1.33132
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −19.3902 −0.933994 −0.466997 0.884259i \(-0.654664\pi\)
−0.466997 + 0.884259i \(0.654664\pi\)
\(432\) 0 0
\(433\) 18.7996 0.903449 0.451725 0.892157i \(-0.350809\pi\)
0.451725 + 0.892157i \(0.350809\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 10.5055 0.502547
\(438\) 0 0
\(439\) −8.05917 −0.384643 −0.192322 0.981332i \(-0.561602\pi\)
−0.192322 + 0.981332i \(0.561602\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 28.1425 1.33709 0.668546 0.743671i \(-0.266917\pi\)
0.668546 + 0.743671i \(0.266917\pi\)
\(444\) 0 0
\(445\) −11.6383 −0.551706
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −28.9364 −1.36559 −0.682797 0.730608i \(-0.739237\pi\)
−0.682797 + 0.730608i \(0.739237\pi\)
\(450\) 0 0
\(451\) −17.6887 −0.832929
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −9.90902 −0.464542
\(456\) 0 0
\(457\) −7.80085 −0.364909 −0.182454 0.983214i \(-0.558404\pi\)
−0.182454 + 0.983214i \(0.558404\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 13.6981 0.637984 0.318992 0.947757i \(-0.396656\pi\)
0.318992 + 0.947757i \(0.396656\pi\)
\(462\) 0 0
\(463\) 39.1886 1.82125 0.910625 0.413235i \(-0.135601\pi\)
0.910625 + 0.413235i \(0.135601\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −17.2581 −0.798610 −0.399305 0.916818i \(-0.630748\pi\)
−0.399305 + 0.916818i \(0.630748\pi\)
\(468\) 0 0
\(469\) −0.563469 −0.0260186
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −9.36287 −0.430505
\(474\) 0 0
\(475\) −7.73344 −0.354835
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 2.46912 0.112817 0.0564084 0.998408i \(-0.482035\pi\)
0.0564084 + 0.998408i \(0.482035\pi\)
\(480\) 0 0
\(481\) −16.0700 −0.732727
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −5.17274 −0.234882
\(486\) 0 0
\(487\) 17.6955 0.801861 0.400930 0.916108i \(-0.368687\pi\)
0.400930 + 0.916108i \(0.368687\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −14.9043 −0.672623 −0.336312 0.941751i \(-0.609180\pi\)
−0.336312 + 0.941751i \(0.609180\pi\)
\(492\) 0 0
\(493\) 21.1530 0.952685
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −19.9550 −0.895104
\(498\) 0 0
\(499\) 14.7483 0.660226 0.330113 0.943941i \(-0.392913\pi\)
0.330113 + 0.943941i \(0.392913\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −21.6170 −0.963856 −0.481928 0.876211i \(-0.660063\pi\)
−0.481928 + 0.876211i \(0.660063\pi\)
\(504\) 0 0
\(505\) 1.37426 0.0611539
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 11.3422 0.502735 0.251368 0.967892i \(-0.419120\pi\)
0.251368 + 0.967892i \(0.419120\pi\)
\(510\) 0 0
\(511\) −6.77467 −0.299694
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −19.9654 −0.879779
\(516\) 0 0
\(517\) −18.1102 −0.796484
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 5.90072 0.258515 0.129258 0.991611i \(-0.458741\pi\)
0.129258 + 0.991611i \(0.458741\pi\)
\(522\) 0 0
\(523\) 7.21958 0.315690 0.157845 0.987464i \(-0.449545\pi\)
0.157845 + 0.987464i \(0.449545\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −16.9509 −0.738394
\(528\) 0 0
\(529\) −2.29229 −0.0996648
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 28.8273 1.24865
\(534\) 0 0
\(535\) −3.27110 −0.141422
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −7.56484 −0.325841
\(540\) 0 0
\(541\) −4.15094 −0.178463 −0.0892314 0.996011i \(-0.528441\pi\)
−0.0892314 + 0.996011i \(0.528441\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −20.0005 −0.856728
\(546\) 0 0
\(547\) −5.37704 −0.229906 −0.114953 0.993371i \(-0.536672\pi\)
−0.114953 + 0.993371i \(0.536672\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 13.4166 0.571568
\(552\) 0 0
\(553\) −11.7822 −0.501028
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 13.1551 0.557399 0.278700 0.960378i \(-0.410097\pi\)
0.278700 + 0.960378i \(0.410097\pi\)
\(558\) 0 0
\(559\) 15.2587 0.645372
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −5.08117 −0.214146 −0.107073 0.994251i \(-0.534148\pi\)
−0.107073 + 0.994251i \(0.534148\pi\)
\(564\) 0 0
\(565\) −4.14778 −0.174498
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 16.5777 0.694972 0.347486 0.937685i \(-0.387035\pi\)
0.347486 + 0.937685i \(0.387035\pi\)
\(570\) 0 0
\(571\) 30.5518 1.27855 0.639277 0.768977i \(-0.279234\pi\)
0.639277 + 0.768977i \(0.279234\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −15.2436 −0.635703
\(576\) 0 0
\(577\) −23.2441 −0.967663 −0.483832 0.875161i \(-0.660755\pi\)
−0.483832 + 0.875161i \(0.660755\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 19.7870 0.820902
\(582\) 0 0
\(583\) 25.6507 1.06234
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 19.3846 0.800088 0.400044 0.916496i \(-0.368995\pi\)
0.400044 + 0.916496i \(0.368995\pi\)
\(588\) 0 0
\(589\) −10.7514 −0.443003
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −9.34754 −0.383857 −0.191929 0.981409i \(-0.561474\pi\)
−0.191929 + 0.981409i \(0.561474\pi\)
\(594\) 0 0
\(595\) 9.18623 0.376599
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −1.66606 −0.0680732 −0.0340366 0.999421i \(-0.510836\pi\)
−0.0340366 + 0.999421i \(0.510836\pi\)
\(600\) 0 0
\(601\) −26.5815 −1.08428 −0.542141 0.840287i \(-0.682386\pi\)
−0.542141 + 0.840287i \(0.682386\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 6.67466 0.271363
\(606\) 0 0
\(607\) −30.8790 −1.25334 −0.626670 0.779285i \(-0.715583\pi\)
−0.626670 + 0.779285i \(0.715583\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 29.5141 1.19401
\(612\) 0 0
\(613\) 14.9530 0.603947 0.301973 0.953316i \(-0.402355\pi\)
0.301973 + 0.953316i \(0.402355\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −20.3705 −0.820087 −0.410043 0.912066i \(-0.634486\pi\)
−0.410043 + 0.912066i \(0.634486\pi\)
\(618\) 0 0
\(619\) 0.534153 0.0214694 0.0107347 0.999942i \(-0.496583\pi\)
0.0107347 + 0.999942i \(0.496583\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −17.7998 −0.713133
\(624\) 0 0
\(625\) 2.97043 0.118817
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 14.8978 0.594014
\(630\) 0 0
\(631\) −16.3425 −0.650583 −0.325292 0.945614i \(-0.605462\pi\)
−0.325292 + 0.945614i \(0.605462\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1.20836 −0.0479525
\(636\) 0 0
\(637\) 12.3284 0.488470
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −45.9146 −1.81352 −0.906759 0.421649i \(-0.861452\pi\)
−0.906759 + 0.421649i \(0.861452\pi\)
\(642\) 0 0
\(643\) −2.16517 −0.0853860 −0.0426930 0.999088i \(-0.513594\pi\)
−0.0426930 + 0.999088i \(0.513594\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 29.7954 1.17138 0.585688 0.810536i \(-0.300824\pi\)
0.585688 + 0.810536i \(0.300824\pi\)
\(648\) 0 0
\(649\) −26.0243 −1.02154
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −9.26237 −0.362464 −0.181232 0.983440i \(-0.558009\pi\)
−0.181232 + 0.983440i \(0.558009\pi\)
\(654\) 0 0
\(655\) −17.6354 −0.689073
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −0.492474 −0.0191841 −0.00959203 0.999954i \(-0.503053\pi\)
−0.00959203 + 0.999954i \(0.503053\pi\)
\(660\) 0 0
\(661\) −8.06786 −0.313804 −0.156902 0.987614i \(-0.550151\pi\)
−0.156902 + 0.987614i \(0.550151\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 5.82651 0.225942
\(666\) 0 0
\(667\) 26.4459 1.02399
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −33.7343 −1.30230
\(672\) 0 0
\(673\) 6.59943 0.254389 0.127195 0.991878i \(-0.459403\pi\)
0.127195 + 0.991878i \(0.459403\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 14.6380 0.562584 0.281292 0.959622i \(-0.409237\pi\)
0.281292 + 0.959622i \(0.409237\pi\)
\(678\) 0 0
\(679\) −7.91130 −0.303608
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 10.3419 0.395724 0.197862 0.980230i \(-0.436600\pi\)
0.197862 + 0.980230i \(0.436600\pi\)
\(684\) 0 0
\(685\) −22.1814 −0.847506
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −41.8029 −1.59256
\(690\) 0 0
\(691\) −34.5829 −1.31559 −0.657797 0.753195i \(-0.728512\pi\)
−0.657797 + 0.753195i \(0.728512\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −12.9274 −0.490365
\(696\) 0 0
\(697\) −26.7246 −1.01227
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 38.5480 1.45594 0.727969 0.685610i \(-0.240465\pi\)
0.727969 + 0.685610i \(0.240465\pi\)
\(702\) 0 0
\(703\) 9.44915 0.356381
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 2.10183 0.0790473
\(708\) 0 0
\(709\) 16.9239 0.635592 0.317796 0.948159i \(-0.397057\pi\)
0.317796 + 0.948159i \(0.397057\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −21.1924 −0.793660
\(714\) 0 0
\(715\) 12.1508 0.454414
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −16.1218 −0.601241 −0.300621 0.953744i \(-0.597194\pi\)
−0.300621 + 0.953744i \(0.597194\pi\)
\(720\) 0 0
\(721\) −30.5354 −1.13720
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −19.4677 −0.723012
\(726\) 0 0
\(727\) 10.8925 0.403980 0.201990 0.979388i \(-0.435259\pi\)
0.201990 + 0.979388i \(0.435259\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −14.1457 −0.523196
\(732\) 0 0
\(733\) 39.2054 1.44809 0.724043 0.689755i \(-0.242282\pi\)
0.724043 + 0.689755i \(0.242282\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0.690946 0.0254513
\(738\) 0 0
\(739\) −46.8075 −1.72184 −0.860921 0.508738i \(-0.830112\pi\)
−0.860921 + 0.508738i \(0.830112\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 33.4808 1.22829 0.614145 0.789193i \(-0.289501\pi\)
0.614145 + 0.789193i \(0.289501\pi\)
\(744\) 0 0
\(745\) −24.1888 −0.886211
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −5.00289 −0.182801
\(750\) 0 0
\(751\) −24.7166 −0.901922 −0.450961 0.892544i \(-0.648919\pi\)
−0.450961 + 0.892544i \(0.648919\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −13.6622 −0.497218
\(756\) 0 0
\(757\) −26.5140 −0.963667 −0.481834 0.876263i \(-0.660029\pi\)
−0.481834 + 0.876263i \(0.660029\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −25.2602 −0.915681 −0.457840 0.889034i \(-0.651377\pi\)
−0.457840 + 0.889034i \(0.651377\pi\)
\(762\) 0 0
\(763\) −30.5892 −1.10740
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 42.4117 1.53140
\(768\) 0 0
\(769\) −19.6768 −0.709564 −0.354782 0.934949i \(-0.615445\pi\)
−0.354782 + 0.934949i \(0.615445\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 36.8440 1.32519 0.662594 0.748979i \(-0.269456\pi\)
0.662594 + 0.748979i \(0.269456\pi\)
\(774\) 0 0
\(775\) 15.6004 0.560382
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −16.9505 −0.607313
\(780\) 0 0
\(781\) 24.4695 0.875589
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −28.5410 −1.01867
\(786\) 0 0
\(787\) 5.36433 0.191218 0.0956088 0.995419i \(-0.469520\pi\)
0.0956088 + 0.995419i \(0.469520\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −6.34369 −0.225556
\(792\) 0 0
\(793\) 54.9767 1.95228
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 7.20815 0.255326 0.127663 0.991818i \(-0.459252\pi\)
0.127663 + 0.991818i \(0.459252\pi\)
\(798\) 0 0
\(799\) −27.3613 −0.967973
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 8.30734 0.293160
\(804\) 0 0
\(805\) 11.4848 0.404786
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −23.3611 −0.821334 −0.410667 0.911785i \(-0.634704\pi\)
−0.410667 + 0.911785i \(0.634704\pi\)
\(810\) 0 0
\(811\) 47.5681 1.67034 0.835170 0.549991i \(-0.185369\pi\)
0.835170 + 0.549991i \(0.185369\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 28.2593 0.989881
\(816\) 0 0
\(817\) −8.97209 −0.313894
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −1.28529 −0.0448568 −0.0224284 0.999748i \(-0.507140\pi\)
−0.0224284 + 0.999748i \(0.507140\pi\)
\(822\) 0 0
\(823\) 15.1103 0.526712 0.263356 0.964699i \(-0.415171\pi\)
0.263356 + 0.964699i \(0.415171\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 32.1009 1.11626 0.558129 0.829754i \(-0.311519\pi\)
0.558129 + 0.829754i \(0.311519\pi\)
\(828\) 0 0
\(829\) −39.5385 −1.37323 −0.686614 0.727022i \(-0.740904\pi\)
−0.686614 + 0.727022i \(0.740904\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −11.4292 −0.395997
\(834\) 0 0
\(835\) −1.28459 −0.0444551
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 2.69426 0.0930161 0.0465081 0.998918i \(-0.485191\pi\)
0.0465081 + 0.998918i \(0.485191\pi\)
\(840\) 0 0
\(841\) 4.77421 0.164628
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −3.10244 −0.106727
\(846\) 0 0
\(847\) 10.2084 0.350763
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 18.6255 0.638473
\(852\) 0 0
\(853\) 48.3525 1.65556 0.827779 0.561054i \(-0.189604\pi\)
0.827779 + 0.561054i \(0.189604\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 36.9684 1.26282 0.631408 0.775450i \(-0.282477\pi\)
0.631408 + 0.775450i \(0.282477\pi\)
\(858\) 0 0
\(859\) 57.7504 1.97042 0.985210 0.171352i \(-0.0548136\pi\)
0.985210 + 0.171352i \(0.0548136\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −0.667087 −0.0227079 −0.0113540 0.999936i \(-0.503614\pi\)
−0.0113540 + 0.999936i \(0.503614\pi\)
\(864\) 0 0
\(865\) 20.3513 0.691965
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 14.4477 0.490105
\(870\) 0 0
\(871\) −1.12603 −0.0381542
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −21.0734 −0.712411
\(876\) 0 0
\(877\) −17.1291 −0.578407 −0.289204 0.957268i \(-0.593390\pi\)
−0.289204 + 0.957268i \(0.593390\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 18.5491 0.624935 0.312468 0.949928i \(-0.398844\pi\)
0.312468 + 0.949928i \(0.398844\pi\)
\(882\) 0 0
\(883\) −18.0598 −0.607761 −0.303880 0.952710i \(-0.598282\pi\)
−0.303880 + 0.952710i \(0.598282\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 14.4311 0.484549 0.242274 0.970208i \(-0.422107\pi\)
0.242274 + 0.970208i \(0.422107\pi\)
\(888\) 0 0
\(889\) −1.84810 −0.0619832
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −17.3543 −0.580740
\(894\) 0 0
\(895\) −4.41094 −0.147442
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −27.0649 −0.902664
\(900\) 0 0
\(901\) 38.7537 1.29107
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 14.5470 0.483560
\(906\) 0 0
\(907\) 53.6448 1.78125 0.890624 0.454741i \(-0.150268\pi\)
0.890624 + 0.454741i \(0.150268\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 39.7916 1.31835 0.659177 0.751988i \(-0.270905\pi\)
0.659177 + 0.751988i \(0.270905\pi\)
\(912\) 0 0
\(913\) −24.2635 −0.803005
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −26.9720 −0.890693
\(918\) 0 0
\(919\) −25.7644 −0.849889 −0.424945 0.905219i \(-0.639706\pi\)
−0.424945 + 0.905219i \(0.639706\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −39.8780 −1.31260
\(924\) 0 0
\(925\) −13.7108 −0.450809
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 24.8575 0.815549 0.407775 0.913083i \(-0.366305\pi\)
0.407775 + 0.913083i \(0.366305\pi\)
\(930\) 0 0
\(931\) −7.24911 −0.237580
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −11.2645 −0.368388
\(936\) 0 0
\(937\) 12.4739 0.407505 0.203752 0.979022i \(-0.434686\pi\)
0.203752 + 0.979022i \(0.434686\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 8.43127 0.274852 0.137426 0.990512i \(-0.456117\pi\)
0.137426 + 0.990512i \(0.456117\pi\)
\(942\) 0 0
\(943\) −33.4115 −1.08803
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 46.1816 1.50070 0.750350 0.661041i \(-0.229885\pi\)
0.750350 + 0.661041i \(0.229885\pi\)
\(948\) 0 0
\(949\) −13.5385 −0.439477
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 27.1218 0.878563 0.439281 0.898350i \(-0.355233\pi\)
0.439281 + 0.898350i \(0.355233\pi\)
\(954\) 0 0
\(955\) −33.5053 −1.08420
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −33.9246 −1.09548
\(960\) 0 0
\(961\) −9.31164 −0.300375
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −32.7666 −1.05479
\(966\) 0 0
\(967\) −51.9680 −1.67118 −0.835590 0.549354i \(-0.814874\pi\)
−0.835590 + 0.549354i \(0.814874\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 36.3326 1.16597 0.582985 0.812483i \(-0.301885\pi\)
0.582985 + 0.812483i \(0.301885\pi\)
\(972\) 0 0
\(973\) −19.7714 −0.633843
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 56.2379 1.79921 0.899605 0.436704i \(-0.143854\pi\)
0.899605 + 0.436704i \(0.143854\pi\)
\(978\) 0 0
\(979\) 21.8267 0.697586
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 45.9094 1.46428 0.732141 0.681153i \(-0.238521\pi\)
0.732141 + 0.681153i \(0.238521\pi\)
\(984\) 0 0
\(985\) −6.08550 −0.193900
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −17.6852 −0.562355
\(990\) 0 0
\(991\) −23.0349 −0.731726 −0.365863 0.930669i \(-0.619226\pi\)
−0.365863 + 0.930669i \(0.619226\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 17.8171 0.564839
\(996\) 0 0
\(997\) −49.2868 −1.56093 −0.780464 0.625201i \(-0.785017\pi\)
−0.780464 + 0.625201i \(0.785017\pi\)
\(998\) 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 6012.2.a.f.1.1 5
3.2 odd 2 2004.2.a.b.1.5 5
12.11 even 2 8016.2.a.q.1.5 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2004.2.a.b.1.5 5 3.2 odd 2
6012.2.a.f.1.1 5 1.1 even 1 trivial
8016.2.a.q.1.5 5 12.11 even 2