Properties

Label 5184.2.d.r.2593.3
Level $5184$
Weight $2$
Character 5184.2593
Analytic conductor $41.394$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 5184 = 2^{6} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5184.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(41.3944484078\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \( x^{12} - 16x^{8} - 24x^{7} + 96x^{5} + 304x^{4} + 384x^{3} + 288x^{2} + 144x + 36 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{12}\cdot 3^{4} \)
Twist minimal: no (minimal twist has level 576)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 2593.3
Root \(-1.50511 + 0.403293i\) of defining polynomial
Character \(\chi\) \(=\) 5184.2593
Dual form 5184.2.d.r.2593.9

$q$-expansion

\(f(q)\) \(=\) \(q-1.73205i q^{5} -0.990721 q^{7} +O(q^{10})\) \(q-1.73205i q^{5} -0.990721 q^{7} -2.10083i q^{11} +6.36152i q^{13} -3.81681 q^{17} +2.00000i q^{19} +7.10285 q^{23} +2.00000 q^{25} -8.34296i q^{29} +2.15609 q^{31} +1.71598i q^{35} -4.62947i q^{37} -0.816810 q^{41} +2.28402i q^{43} -6.78555 q^{47} -6.01847 q^{49} +3.14681i q^{53} -3.63875 q^{55} +11.9176i q^{59} -4.87886i q^{61} +11.0185 q^{65} +13.7345i q^{67} +13.5391 q^{71} +10.0185 q^{73} +2.08134i q^{77} -9.08429 q^{79} +4.28402i q^{83} +6.61091i q^{85} +14.0185 q^{89} -6.30249i q^{91} +3.46410 q^{95} +12.4504 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 24 q^{25} + 36 q^{41} + 48 q^{49} + 12 q^{65} + 48 q^{89} + 12 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5184\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(1217\) \(2431\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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
\(5\) − 1.73205i − 0.774597i −0.921954 0.387298i \(-0.873408\pi\)
0.921954 0.387298i \(-0.126592\pi\)
\(6\) 0 0
\(7\) −0.990721 −0.374457 −0.187229 0.982316i \(-0.559951\pi\)
−0.187229 + 0.982316i \(0.559951\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) − 2.10083i − 0.633424i −0.948522 0.316712i \(-0.897421\pi\)
0.948522 0.316712i \(-0.102579\pi\)
\(12\) 0 0
\(13\) 6.36152i 1.76437i 0.470905 + 0.882184i \(0.343927\pi\)
−0.470905 + 0.882184i \(0.656073\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −3.81681 −0.925712 −0.462856 0.886433i \(-0.653175\pi\)
−0.462856 + 0.886433i \(0.653175\pi\)
\(18\) 0 0
\(19\) 2.00000i 0.458831i 0.973329 + 0.229416i \(0.0736815\pi\)
−0.973329 + 0.229416i \(0.926318\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 7.10285 1.48105 0.740523 0.672031i \(-0.234578\pi\)
0.740523 + 0.672031i \(0.234578\pi\)
\(24\) 0 0
\(25\) 2.00000 0.400000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) − 8.34296i − 1.54925i −0.632422 0.774624i \(-0.717939\pi\)
0.632422 0.774624i \(-0.282061\pi\)
\(30\) 0 0
\(31\) 2.15609 0.387245 0.193622 0.981076i \(-0.437976\pi\)
0.193622 + 0.981076i \(0.437976\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1.71598i 0.290054i
\(36\) 0 0
\(37\) − 4.62947i − 0.761080i −0.924765 0.380540i \(-0.875738\pi\)
0.924765 0.380540i \(-0.124262\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −0.816810 −0.127564 −0.0637822 0.997964i \(-0.520316\pi\)
−0.0637822 + 0.997964i \(0.520316\pi\)
\(42\) 0 0
\(43\) 2.28402i 0.348310i 0.984718 + 0.174155i \(0.0557193\pi\)
−0.984718 + 0.174155i \(0.944281\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −6.78555 −0.989775 −0.494887 0.868957i \(-0.664791\pi\)
−0.494887 + 0.868957i \(0.664791\pi\)
\(48\) 0 0
\(49\) −6.01847 −0.859782
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 3.14681i 0.432247i 0.976366 + 0.216124i \(0.0693414\pi\)
−0.976366 + 0.216124i \(0.930659\pi\)
\(54\) 0 0
\(55\) −3.63875 −0.490648
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 11.9176i 1.55154i 0.631013 + 0.775772i \(0.282639\pi\)
−0.631013 + 0.775772i \(0.717361\pi\)
\(60\) 0 0
\(61\) − 4.87886i − 0.624674i −0.949971 0.312337i \(-0.898888\pi\)
0.949971 0.312337i \(-0.101112\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 11.0185 1.36667
\(66\) 0 0
\(67\) 13.7345i 1.67793i 0.544185 + 0.838965i \(0.316839\pi\)
−0.544185 + 0.838965i \(0.683161\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 13.5391 1.60680 0.803399 0.595442i \(-0.203023\pi\)
0.803399 + 0.595442i \(0.203023\pi\)
\(72\) 0 0
\(73\) 10.0185 1.17257 0.586287 0.810104i \(-0.300589\pi\)
0.586287 + 0.810104i \(0.300589\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 2.08134i 0.237190i
\(78\) 0 0
\(79\) −9.08429 −1.02206 −0.511031 0.859562i \(-0.670736\pi\)
−0.511031 + 0.859562i \(0.670736\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 4.28402i 0.470232i 0.971967 + 0.235116i \(0.0755471\pi\)
−0.971967 + 0.235116i \(0.924453\pi\)
\(84\) 0 0
\(85\) 6.61091i 0.717054i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 14.0185 1.48595 0.742977 0.669316i \(-0.233413\pi\)
0.742977 + 0.669316i \(0.233413\pi\)
\(90\) 0 0
\(91\) − 6.30249i − 0.660681i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 3.46410 0.355409
\(96\) 0 0
\(97\) 12.4504 1.26415 0.632075 0.774907i \(-0.282204\pi\)
0.632075 + 0.774907i \(0.282204\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) − 15.9377i − 1.58586i −0.609310 0.792932i \(-0.708553\pi\)
0.609310 0.792932i \(-0.291447\pi\)
\(102\) 0 0
\(103\) 17.1779 1.69258 0.846292 0.532719i \(-0.178830\pi\)
0.846292 + 0.532719i \(0.178830\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 16.2017i 1.56627i 0.621849 + 0.783137i \(0.286382\pi\)
−0.621849 + 0.783137i \(0.713618\pi\)
\(108\) 0 0
\(109\) 0.816078i 0.0781661i 0.999236 + 0.0390830i \(0.0124437\pi\)
−0.999236 + 0.0390830i \(0.987556\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 6.43196 0.605068 0.302534 0.953139i \(-0.402167\pi\)
0.302534 + 0.953139i \(0.402167\pi\)
\(114\) 0 0
\(115\) − 12.3025i − 1.14721i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 3.78140 0.346640
\(120\) 0 0
\(121\) 6.58651 0.598774
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) − 12.1244i − 1.08444i
\(126\) 0 0
\(127\) −16.1871 −1.43638 −0.718188 0.695849i \(-0.755028\pi\)
−0.718188 + 0.695849i \(0.755028\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) − 7.71598i − 0.674148i −0.941478 0.337074i \(-0.890563\pi\)
0.941478 0.337074i \(-0.109437\pi\)
\(132\) 0 0
\(133\) − 1.98144i − 0.171813i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 8.61515 0.736042 0.368021 0.929818i \(-0.380035\pi\)
0.368021 + 0.929818i \(0.380035\pi\)
\(138\) 0 0
\(139\) − 5.71598i − 0.484823i −0.970174 0.242412i \(-0.922062\pi\)
0.970174 0.242412i \(-0.0779384\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 13.3645 1.11759
\(144\) 0 0
\(145\) −14.4504 −1.20004
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1.41476i 0.115901i 0.998319 + 0.0579507i \(0.0184566\pi\)
−0.998319 + 0.0579507i \(0.981543\pi\)
\(150\) 0 0
\(151\) 3.28946 0.267692 0.133846 0.991002i \(-0.457267\pi\)
0.133846 + 0.991002i \(0.457267\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) − 3.73445i − 0.299958i
\(156\) 0 0
\(157\) − 6.67881i − 0.533027i −0.963831 0.266514i \(-0.914128\pi\)
0.963831 0.266514i \(-0.0858717\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −7.03694 −0.554589
\(162\) 0 0
\(163\) − 7.43196i − 0.582116i −0.956705 0.291058i \(-0.905993\pi\)
0.956705 0.291058i \(-0.0940073\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 9.90037 0.766113 0.383057 0.923725i \(-0.374871\pi\)
0.383057 + 0.923725i \(0.374871\pi\)
\(168\) 0 0
\(169\) −27.4689 −2.11299
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) − 12.1244i − 0.921798i −0.887453 0.460899i \(-0.847527\pi\)
0.887453 0.460899i \(-0.152473\pi\)
\(174\) 0 0
\(175\) −1.98144 −0.149783
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) − 6.00000i − 0.448461i −0.974536 0.224231i \(-0.928013\pi\)
0.974536 0.224231i \(-0.0719869\pi\)
\(180\) 0 0
\(181\) 4.62947i 0.344106i 0.985088 + 0.172053i \(0.0550400\pi\)
−0.985088 + 0.172053i \(0.944960\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −8.01847 −0.589530
\(186\) 0 0
\(187\) 8.01847i 0.586369i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 17.1779 1.24295 0.621473 0.783436i \(-0.286535\pi\)
0.621473 + 0.783436i \(0.286535\pi\)
\(192\) 0 0
\(193\) −11.5865 −0.834015 −0.417008 0.908903i \(-0.636921\pi\)
−0.417008 + 0.908903i \(0.636921\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) − 17.6698i − 1.25892i −0.777033 0.629460i \(-0.783276\pi\)
0.777033 0.629460i \(-0.216724\pi\)
\(198\) 0 0
\(199\) 16.5044 1.16997 0.584984 0.811045i \(-0.301101\pi\)
0.584984 + 0.811045i \(0.301101\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 8.26555i 0.580128i
\(204\) 0 0
\(205\) 1.41476i 0.0988109i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 4.20166 0.290635
\(210\) 0 0
\(211\) − 11.7345i − 0.807833i −0.914796 0.403916i \(-0.867649\pi\)
0.914796 0.403916i \(-0.132351\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 3.95604 0.269800
\(216\) 0 0
\(217\) −2.13608 −0.145007
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) − 24.2807i − 1.63330i
\(222\) 0 0
\(223\) 1.34001 0.0897336 0.0448668 0.998993i \(-0.485714\pi\)
0.0448668 + 0.998993i \(0.485714\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) − 3.89917i − 0.258797i −0.991593 0.129398i \(-0.958695\pi\)
0.991593 0.129398i \(-0.0413046\pi\)
\(228\) 0 0
\(229\) − 2.23083i − 0.147418i −0.997280 0.0737089i \(-0.976516\pi\)
0.997280 0.0737089i \(-0.0234836\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 9.26724 0.607117 0.303559 0.952813i \(-0.401825\pi\)
0.303559 + 0.952813i \(0.401825\pi\)
\(234\) 0 0
\(235\) 11.7529i 0.766676i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 20.9593 1.35574 0.677871 0.735181i \(-0.262903\pi\)
0.677871 + 0.735181i \(0.262903\pi\)
\(240\) 0 0
\(241\) 15.0369 0.968615 0.484307 0.874898i \(-0.339072\pi\)
0.484307 + 0.874898i \(0.339072\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 10.4243i 0.665984i
\(246\) 0 0
\(247\) −12.7230 −0.809547
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0.164719i 0.0103969i 0.999986 + 0.00519847i \(0.00165473\pi\)
−0.999986 + 0.00519847i \(0.998345\pi\)
\(252\) 0 0
\(253\) − 14.9219i − 0.938130i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 26.8353 1.67394 0.836969 0.547250i \(-0.184325\pi\)
0.836969 + 0.547250i \(0.184325\pi\)
\(258\) 0 0
\(259\) 4.58651i 0.284992i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 19.9754 1.23173 0.615867 0.787850i \(-0.288806\pi\)
0.615867 + 0.787850i \(0.288806\pi\)
\(264\) 0 0
\(265\) 5.45043 0.334817
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0.666581i 0.0406422i 0.999794 + 0.0203211i \(0.00646884\pi\)
−0.999794 + 0.0203211i \(0.993531\pi\)
\(270\) 0 0
\(271\) 17.0352 1.03482 0.517408 0.855739i \(-0.326897\pi\)
0.517408 + 0.855739i \(0.326897\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) − 4.20166i − 0.253370i
\(276\) 0 0
\(277\) 3.71349i 0.223122i 0.993758 + 0.111561i \(0.0355851\pi\)
−0.993758 + 0.111561i \(0.964415\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −27.0554 −1.61399 −0.806995 0.590558i \(-0.798908\pi\)
−0.806995 + 0.590558i \(0.798908\pi\)
\(282\) 0 0
\(283\) 1.14794i 0.0682379i 0.999418 + 0.0341190i \(0.0108625\pi\)
−0.999418 + 0.0341190i \(0.989137\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0.809231 0.0477674
\(288\) 0 0
\(289\) −2.43196 −0.143056
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) − 26.3300i − 1.53822i −0.639118 0.769109i \(-0.720700\pi\)
0.639118 0.769109i \(-0.279300\pi\)
\(294\) 0 0
\(295\) 20.6420 1.20182
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 45.1849i 2.61311i
\(300\) 0 0
\(301\) − 2.26283i − 0.130427i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −8.45043 −0.483870
\(306\) 0 0
\(307\) 7.43196i 0.424164i 0.977252 + 0.212082i \(0.0680244\pi\)
−0.977252 + 0.212082i \(0.931976\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −9.93236 −0.563212 −0.281606 0.959530i \(-0.590867\pi\)
−0.281606 + 0.959530i \(0.590867\pi\)
\(312\) 0 0
\(313\) −9.03694 −0.510798 −0.255399 0.966836i \(-0.582207\pi\)
−0.255399 + 0.966836i \(0.582207\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 8.69225i 0.488205i 0.969749 + 0.244103i \(0.0784934\pi\)
−0.969749 + 0.244103i \(0.921507\pi\)
\(318\) 0 0
\(319\) −17.5271 −0.981332
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) − 7.63362i − 0.424746i
\(324\) 0 0
\(325\) 12.7230i 0.705747i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 6.72259 0.370629
\(330\) 0 0
\(331\) − 12.8705i − 0.707428i −0.935354 0.353714i \(-0.884919\pi\)
0.935354 0.353714i \(-0.115081\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 23.7888 1.29972
\(336\) 0 0
\(337\) −2.43196 −0.132477 −0.0662386 0.997804i \(-0.521100\pi\)
−0.0662386 + 0.997804i \(0.521100\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) − 4.52957i − 0.245290i
\(342\) 0 0
\(343\) 12.8977 0.696409
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 23.3681i 1.25446i 0.778833 + 0.627232i \(0.215812\pi\)
−0.778833 + 0.627232i \(0.784188\pi\)
\(348\) 0 0
\(349\) 10.0071i 0.535668i 0.963465 + 0.267834i \(0.0863079\pi\)
−0.963465 + 0.267834i \(0.913692\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 21.3849 1.13820 0.569100 0.822268i \(-0.307292\pi\)
0.569100 + 0.822268i \(0.307292\pi\)
\(354\) 0 0
\(355\) − 23.4504i − 1.24462i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −23.9634 −1.26474 −0.632370 0.774666i \(-0.717918\pi\)
−0.632370 + 0.774666i \(0.717918\pi\)
\(360\) 0 0
\(361\) 15.0000 0.789474
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) − 17.3525i − 0.908271i
\(366\) 0 0
\(367\) 16.5113 0.861882 0.430941 0.902380i \(-0.358182\pi\)
0.430941 + 0.902380i \(0.358182\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) − 3.11761i − 0.161858i
\(372\) 0 0
\(373\) − 24.5301i − 1.27012i −0.772463 0.635060i \(-0.780975\pi\)
0.772463 0.635060i \(-0.219025\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 53.0739 2.73344
\(378\) 0 0
\(379\) − 10.8824i − 0.558991i −0.960147 0.279495i \(-0.909833\pi\)
0.960147 0.279495i \(-0.0901672\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −3.32145 −0.169718 −0.0848591 0.996393i \(-0.527044\pi\)
−0.0848591 + 0.996393i \(0.527044\pi\)
\(384\) 0 0
\(385\) 3.60498 0.183727
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) − 1.38276i − 0.0701089i −0.999385 0.0350545i \(-0.988840\pi\)
0.999385 0.0350545i \(-0.0111605\pi\)
\(390\) 0 0
\(391\) −27.1102 −1.37102
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 15.7345i 0.791686i
\(396\) 0 0
\(397\) 19.9685i 1.00219i 0.865392 + 0.501096i \(0.167070\pi\)
−0.865392 + 0.501096i \(0.832930\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 0.652092 0.0325639 0.0162819 0.999867i \(-0.494817\pi\)
0.0162819 + 0.999867i \(0.494817\pi\)
\(402\) 0 0
\(403\) 13.7160i 0.683242i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −9.72572 −0.482086
\(408\) 0 0
\(409\) 15.0369 0.743529 0.371764 0.928327i \(-0.378753\pi\)
0.371764 + 0.928327i \(0.378753\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) − 11.8071i − 0.580988i
\(414\) 0 0
\(415\) 7.42014 0.364240
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 13.1664i 0.643221i 0.946872 + 0.321611i \(0.104224\pi\)
−0.946872 + 0.321611i \(0.895776\pi\)
\(420\) 0 0
\(421\) − 3.88129i − 0.189163i −0.995517 0.0945813i \(-0.969849\pi\)
0.995517 0.0945813i \(-0.0301512\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −7.63362 −0.370285
\(426\) 0 0
\(427\) 4.83359i 0.233914i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 3.81339 0.183684 0.0918422 0.995774i \(-0.470724\pi\)
0.0918422 + 0.995774i \(0.470724\pi\)
\(432\) 0 0
\(433\) −10.0185 −0.481457 −0.240728 0.970592i \(-0.577386\pi\)
−0.240728 + 0.970592i \(0.577386\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 14.2057i 0.679550i
\(438\) 0 0
\(439\) −24.4234 −1.16566 −0.582832 0.812593i \(-0.698055\pi\)
−0.582832 + 0.812593i \(0.698055\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 24.6873i 1.17293i 0.809974 + 0.586466i \(0.199481\pi\)
−0.809974 + 0.586466i \(0.800519\pi\)
\(444\) 0 0
\(445\) − 24.2807i − 1.15102i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −21.6521 −1.02183 −0.510913 0.859633i \(-0.670692\pi\)
−0.510913 + 0.859633i \(0.670692\pi\)
\(450\) 0 0
\(451\) 1.71598i 0.0808023i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −10.9162 −0.511761
\(456\) 0 0
\(457\) −22.4874 −1.05191 −0.525957 0.850511i \(-0.676293\pi\)
−0.525957 + 0.850511i \(0.676293\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 25.0289i 1.16571i 0.812576 + 0.582856i \(0.198065\pi\)
−0.812576 + 0.582856i \(0.801935\pi\)
\(462\) 0 0
\(463\) −19.4766 −0.905154 −0.452577 0.891725i \(-0.649495\pi\)
−0.452577 + 0.891725i \(0.649495\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 2.40332i 0.111212i 0.998453 + 0.0556062i \(0.0177091\pi\)
−0.998453 + 0.0556062i \(0.982291\pi\)
\(468\) 0 0
\(469\) − 13.6070i − 0.628314i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 4.79834 0.220628
\(474\) 0 0
\(475\) 4.00000i 0.183533i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 21.3085 0.973612 0.486806 0.873510i \(-0.338162\pi\)
0.486806 + 0.873510i \(0.338162\pi\)
\(480\) 0 0
\(481\) 29.4504 1.34282
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) − 21.5648i − 0.979206i
\(486\) 0 0
\(487\) −40.7851 −1.84815 −0.924075 0.382210i \(-0.875163\pi\)
−0.924075 + 0.382210i \(0.875163\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) − 35.4235i − 1.59864i −0.600906 0.799320i \(-0.705193\pi\)
0.600906 0.799320i \(-0.294807\pi\)
\(492\) 0 0
\(493\) 31.8435i 1.43416i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −13.4135 −0.601677
\(498\) 0 0
\(499\) − 4.32096i − 0.193433i −0.995312 0.0967164i \(-0.969166\pi\)
0.995312 0.0967164i \(-0.0308340\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 7.24550 0.323061 0.161530 0.986868i \(-0.448357\pi\)
0.161530 + 0.986868i \(0.448357\pi\)
\(504\) 0 0
\(505\) −27.6050 −1.22841
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 8.34296i 0.369795i 0.982758 + 0.184898i \(0.0591953\pi\)
−0.982758 + 0.184898i \(0.940805\pi\)
\(510\) 0 0
\(511\) −9.92551 −0.439079
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) − 29.7529i − 1.31107i
\(516\) 0 0
\(517\) 14.2553i 0.626947i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −16.9714 −0.743529 −0.371764 0.928327i \(-0.621247\pi\)
−0.371764 + 0.928327i \(0.621247\pi\)
\(522\) 0 0
\(523\) 40.0554i 1.75150i 0.482764 + 0.875750i \(0.339633\pi\)
−0.482764 + 0.875750i \(0.660367\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −8.22937 −0.358477
\(528\) 0 0
\(529\) 27.4504 1.19350
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) − 5.19615i − 0.225070i
\(534\) 0 0
\(535\) 28.0621 1.21323
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 12.6438i 0.544606i
\(540\) 0 0
\(541\) 25.5956i 1.10044i 0.835020 + 0.550220i \(0.185456\pi\)
−0.835020 + 0.550220i \(0.814544\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1.41349 0.0605472
\(546\) 0 0
\(547\) 33.7714i 1.44396i 0.691914 + 0.721980i \(0.256768\pi\)
−0.691914 + 0.721980i \(0.743232\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 16.6859 0.710844
\(552\) 0 0
\(553\) 9.00000 0.382719
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) − 18.3364i − 0.776937i −0.921462 0.388469i \(-0.873004\pi\)
0.921462 0.388469i \(-0.126996\pi\)
\(558\) 0 0
\(559\) −14.5298 −0.614546
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) − 41.3681i − 1.74346i −0.489990 0.871728i \(-0.663000\pi\)
0.489990 0.871728i \(-0.337000\pi\)
\(564\) 0 0
\(565\) − 11.1405i − 0.468684i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 1.36638 0.0572816 0.0286408 0.999590i \(-0.490882\pi\)
0.0286408 + 0.999590i \(0.490882\pi\)
\(570\) 0 0
\(571\) 17.7345i 0.742164i 0.928600 + 0.371082i \(0.121013\pi\)
−0.928600 + 0.371082i \(0.878987\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 14.2057 0.592418
\(576\) 0 0
\(577\) 20.5865 0.857028 0.428514 0.903535i \(-0.359037\pi\)
0.428514 + 0.903535i \(0.359037\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) − 4.24427i − 0.176082i
\(582\) 0 0
\(583\) 6.61091 0.273796
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 14.4857i 0.597888i 0.954271 + 0.298944i \(0.0966344\pi\)
−0.954271 + 0.298944i \(0.903366\pi\)
\(588\) 0 0
\(589\) 4.31217i 0.177680i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −4.58651 −0.188345 −0.0941727 0.995556i \(-0.530021\pi\)
−0.0941727 + 0.995556i \(0.530021\pi\)
\(594\) 0 0
\(595\) − 6.54957i − 0.268506i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −2.62288 −0.107168 −0.0535839 0.998563i \(-0.517064\pi\)
−0.0535839 + 0.998563i \(0.517064\pi\)
\(600\) 0 0
\(601\) 7.01847 0.286289 0.143145 0.989702i \(-0.454279\pi\)
0.143145 + 0.989702i \(0.454279\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) − 11.4082i − 0.463808i
\(606\) 0 0
\(607\) 37.1784 1.50902 0.754512 0.656286i \(-0.227874\pi\)
0.754512 + 0.656286i \(0.227874\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) − 43.1664i − 1.74633i
\(612\) 0 0
\(613\) 10.7096i 0.432557i 0.976332 + 0.216278i \(0.0693919\pi\)
−0.976332 + 0.216278i \(0.930608\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −33.2201 −1.33739 −0.668696 0.743536i \(-0.733147\pi\)
−0.668696 + 0.743536i \(0.733147\pi\)
\(618\) 0 0
\(619\) − 26.3394i − 1.05867i −0.848413 0.529336i \(-0.822441\pi\)
0.848413 0.529336i \(-0.177559\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −13.8884 −0.556427
\(624\) 0 0
\(625\) −11.0000 −0.440000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 17.6698i 0.704541i
\(630\) 0 0
\(631\) 21.6327 0.861183 0.430592 0.902547i \(-0.358305\pi\)
0.430592 + 0.902547i \(0.358305\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 28.0369i 1.11261i
\(636\) 0 0
\(637\) − 38.2866i − 1.51697i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −3.76970 −0.148894 −0.0744471 0.997225i \(-0.523719\pi\)
−0.0744471 + 0.997225i \(0.523719\pi\)
\(642\) 0 0
\(643\) 33.7714i 1.33181i 0.746035 + 0.665907i \(0.231955\pi\)
−0.746035 + 0.665907i \(0.768045\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 15.7020 0.617311 0.308656 0.951174i \(-0.400121\pi\)
0.308656 + 0.951174i \(0.400121\pi\)
\(648\) 0 0
\(649\) 25.0369 0.982786
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 31.6398i 1.23816i 0.785328 + 0.619080i \(0.212494\pi\)
−0.785328 + 0.619080i \(0.787506\pi\)
\(654\) 0 0
\(655\) −13.3645 −0.522193
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) − 36.3025i − 1.41414i −0.707141 0.707072i \(-0.750016\pi\)
0.707141 0.707072i \(-0.249984\pi\)
\(660\) 0 0
\(661\) − 14.6046i − 0.568052i −0.958817 0.284026i \(-0.908330\pi\)
0.958817 0.284026i \(-0.0916703\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −3.43196 −0.133086
\(666\) 0 0
\(667\) − 59.2588i − 2.29451i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −10.2497 −0.395684
\(672\) 0 0
\(673\) −3.58651 −0.138250 −0.0691249 0.997608i \(-0.522021\pi\)
−0.0691249 + 0.997608i \(0.522021\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) − 1.44675i − 0.0556031i −0.999613 0.0278016i \(-0.991149\pi\)
0.999613 0.0278016i \(-0.00885065\pi\)
\(678\) 0 0
\(679\) −12.3349 −0.473370
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 16.9714i 0.649391i 0.945819 + 0.324696i \(0.105262\pi\)
−0.945819 + 0.324696i \(0.894738\pi\)
\(684\) 0 0
\(685\) − 14.9219i − 0.570136i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −20.0185 −0.762643
\(690\) 0 0
\(691\) − 9.75292i − 0.371019i −0.982643 0.185509i \(-0.940607\pi\)
0.982643 0.185509i \(-0.0593935\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −9.90037 −0.375542
\(696\) 0 0
\(697\) 3.11761 0.118088
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 33.3398i 1.25923i 0.776908 + 0.629614i \(0.216787\pi\)
−0.776908 + 0.629614i \(0.783213\pi\)
\(702\) 0 0
\(703\) 9.25893 0.349207
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 15.7899i 0.593839i
\(708\) 0 0
\(709\) 51.4268i 1.93138i 0.259707 + 0.965688i \(0.416374\pi\)
−0.259707 + 0.965688i \(0.583626\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 15.3143 0.573527
\(714\) 0 0
\(715\) − 23.1479i − 0.865684i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −22.1178 −0.824854 −0.412427 0.910991i \(-0.635319\pi\)
−0.412427 + 0.910991i \(0.635319\pi\)
\(720\) 0 0
\(721\) −17.0185 −0.633801
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) − 16.6859i − 0.619700i
\(726\) 0 0
\(727\) 28.5860 1.06020 0.530099 0.847936i \(-0.322155\pi\)
0.530099 + 0.847936i \(0.322155\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) − 8.71767i − 0.322435i
\(732\) 0 0
\(733\) 45.5145i 1.68112i 0.541721 + 0.840558i \(0.317773\pi\)
−0.541721 + 0.840558i \(0.682227\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 28.8538 1.06284
\(738\) 0 0
\(739\) 19.9815i 0.735032i 0.930017 + 0.367516i \(0.119792\pi\)
−0.930017 + 0.367516i \(0.880208\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 37.6772 1.38224 0.691121 0.722739i \(-0.257117\pi\)
0.691121 + 0.722739i \(0.257117\pi\)
\(744\) 0 0
\(745\) 2.45043 0.0897768
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) − 16.0513i − 0.586503i
\(750\) 0 0
\(751\) 12.5164 0.456730 0.228365 0.973576i \(-0.426662\pi\)
0.228365 + 0.973576i \(0.426662\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) − 5.69751i − 0.207354i
\(756\) 0 0
\(757\) − 12.5872i − 0.457491i −0.973486 0.228745i \(-0.926538\pi\)
0.973486 0.228745i \(-0.0734623\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 11.8824 0.430736 0.215368 0.976533i \(-0.430905\pi\)
0.215368 + 0.976533i \(0.430905\pi\)
\(762\) 0 0
\(763\) − 0.808506i − 0.0292699i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −75.8143 −2.73749
\(768\) 0 0
\(769\) −45.0739 −1.62541 −0.812703 0.582678i \(-0.802005\pi\)
−0.812703 + 0.582678i \(0.802005\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 34.0384i 1.22428i 0.790751 + 0.612138i \(0.209690\pi\)
−0.790751 + 0.612138i \(0.790310\pi\)
\(774\) 0 0
\(775\) 4.31217 0.154898
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) − 1.63362i − 0.0585305i
\(780\) 0 0
\(781\) − 28.4434i − 1.01778i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −11.5680 −0.412881
\(786\) 0 0
\(787\) − 4.24708i − 0.151392i −0.997131 0.0756960i \(-0.975882\pi\)
0.997131 0.0756960i \(-0.0241179\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −6.37228 −0.226572
\(792\) 0 0
\(793\) 31.0369 1.10215
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 43.0480i 1.52484i 0.647084 + 0.762419i \(0.275988\pi\)
−0.647084 + 0.762419i \(0.724012\pi\)
\(798\) 0 0
\(799\) 25.8992 0.916247
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) − 21.0471i − 0.742736i
\(804\) 0 0
\(805\) 12.1883i 0.429583i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −25.2488 −0.887699 −0.443850 0.896101i \(-0.646388\pi\)
−0.443850 + 0.896101i \(0.646388\pi\)
\(810\) 0 0
\(811\) 36.9378i 1.29706i 0.761188 + 0.648531i \(0.224616\pi\)
−0.761188 + 0.648531i \(0.775384\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −12.8725 −0.450905
\(816\) 0 0
\(817\) −4.56804 −0.159816
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 12.4416i 0.434217i 0.976148 + 0.217108i \(0.0696625\pi\)
−0.976148 + 0.217108i \(0.930338\pi\)
\(822\) 0 0
\(823\) 1.52150 0.0530361 0.0265180 0.999648i \(-0.491558\pi\)
0.0265180 + 0.999648i \(0.491558\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) − 10.0369i − 0.349019i −0.984656 0.174509i \(-0.944166\pi\)
0.984656 0.174509i \(-0.0558339\pi\)
\(828\) 0 0
\(829\) − 43.7824i − 1.52063i −0.649556 0.760314i \(-0.725045\pi\)
0.649556 0.760314i \(-0.274955\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 22.9714 0.795911
\(834\) 0 0
\(835\) − 17.1479i − 0.593429i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −42.1251 −1.45432 −0.727161 0.686467i \(-0.759161\pi\)
−0.727161 + 0.686467i \(0.759161\pi\)
\(840\) 0 0
\(841\) −40.6050 −1.40017
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 47.5775i 1.63672i
\(846\) 0 0
\(847\) −6.52540 −0.224215
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) − 32.8824i − 1.12719i
\(852\) 0 0
\(853\) − 26.2981i − 0.900428i −0.892921 0.450214i \(-0.851348\pi\)
0.892921 0.450214i \(-0.148652\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 18.4874 0.631517 0.315758 0.948840i \(-0.397741\pi\)
0.315758 + 0.948840i \(0.397741\pi\)
\(858\) 0 0
\(859\) 46.0673i 1.57180i 0.618357 + 0.785898i \(0.287799\pi\)
−0.618357 + 0.785898i \(0.712201\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −46.0812 −1.56862 −0.784311 0.620368i \(-0.786983\pi\)
−0.784311 + 0.620368i \(0.786983\pi\)
\(864\) 0 0
\(865\) −21.0000 −0.714021
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 19.0846i 0.647399i
\(870\) 0 0
\(871\) −87.3719 −2.96049
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 12.0119i 0.406075i
\(876\) 0 0
\(877\) 32.9547i 1.11280i 0.830915 + 0.556400i \(0.187818\pi\)
−0.830915 + 0.556400i \(0.812182\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −21.9815 −0.740577 −0.370288 0.928917i \(-0.620741\pi\)
−0.370288 + 0.928917i \(0.620741\pi\)
\(882\) 0 0
\(883\) − 10.0000i − 0.336527i −0.985742 0.168263i \(-0.946184\pi\)
0.985742 0.168263i \(-0.0538159\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 3.35344 0.112598 0.0562988 0.998414i \(-0.482070\pi\)
0.0562988 + 0.998414i \(0.482070\pi\)
\(888\) 0 0
\(889\) 16.0369 0.537862
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) − 13.5711i − 0.454140i
\(894\) 0 0
\(895\) −10.3923 −0.347376
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) − 17.9881i − 0.599938i
\(900\) 0 0
\(901\) − 12.0108i − 0.400137i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 8.01847 0.266543
\(906\) 0 0
\(907\) 10.2471i 0.340249i 0.985423 + 0.170124i \(0.0544169\pi\)
−0.985423 + 0.170124i \(0.945583\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −25.4072 −0.841779 −0.420890 0.907112i \(-0.638282\pi\)
−0.420890 + 0.907112i \(0.638282\pi\)
\(912\) 0 0
\(913\) 9.00000 0.297857
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 7.64439i 0.252440i
\(918\) 0 0
\(919\) −44.1134 −1.45517 −0.727584 0.686019i \(-0.759357\pi\)
−0.727584 + 0.686019i \(0.759357\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 86.1293i 2.83498i
\(924\) 0 0
\(925\) − 9.25893i − 0.304432i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 35.6235 1.16877 0.584384 0.811477i \(-0.301336\pi\)
0.584384 + 0.811477i \(0.301336\pi\)
\(930\) 0 0
\(931\) − 12.0369i − 0.394495i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 13.8884 0.454199
\(936\) 0 0
\(937\) −15.4135 −0.503537 −0.251768 0.967788i \(-0.581012\pi\)
−0.251768 + 0.967788i \(0.581012\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) − 8.72424i − 0.284402i −0.989838 0.142201i \(-0.954582\pi\)
0.989838 0.142201i \(-0.0454180\pi\)
\(942\) 0 0
\(943\) −5.80168 −0.188929
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) − 15.8992i − 0.516654i −0.966058 0.258327i \(-0.916829\pi\)
0.966058 0.258327i \(-0.0831711\pi\)
\(948\) 0 0
\(949\) 63.7327i 2.06885i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −25.6890 −0.832149 −0.416075 0.909330i \(-0.636595\pi\)
−0.416075 + 0.909330i \(0.636595\pi\)
\(954\) 0 0
\(955\) − 29.7529i − 0.962782i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −8.53521 −0.275616
\(960\) 0 0
\(961\) −26.3513 −0.850042
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 20.0684i 0.646026i
\(966\) 0 0
\(967\) 30.7170 0.987791 0.493896 0.869521i \(-0.335572\pi\)
0.493896 + 0.869521i \(0.335572\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 40.0924i 1.28662i 0.765604 + 0.643312i \(0.222440\pi\)
−0.765604 + 0.643312i \(0.777560\pi\)
\(972\) 0 0
\(973\) 5.66294i 0.181546i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −48.8722 −1.56356 −0.781780 0.623554i \(-0.785688\pi\)
−0.781780 + 0.623554i \(0.785688\pi\)
\(978\) 0 0
\(979\) − 29.4504i − 0.941240i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 11.2015 0.357274 0.178637 0.983915i \(-0.442831\pi\)
0.178637 + 0.983915i \(0.442831\pi\)
\(984\) 0 0
\(985\) −30.6050 −0.975156
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 16.2230i 0.515863i
\(990\) 0 0
\(991\) 15.7020 0.498792 0.249396 0.968402i \(-0.419768\pi\)
0.249396 + 0.968402i \(0.419768\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) − 28.5865i − 0.906253i
\(996\) 0 0
\(997\) − 24.3623i − 0.771562i −0.922590 0.385781i \(-0.873932\pi\)
0.922590 0.385781i \(-0.126068\pi\)
\(998\) 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 5184.2.d.r.2593.3 12
3.2 odd 2 5184.2.d.q.2593.9 12
4.3 odd 2 inner 5184.2.d.r.2593.4 12
8.3 odd 2 inner 5184.2.d.r.2593.10 12
8.5 even 2 inner 5184.2.d.r.2593.9 12
9.2 odd 6 576.2.r.e.481.2 yes 12
9.4 even 3 1728.2.r.e.289.4 12
9.5 odd 6 576.2.r.f.97.5 yes 12
9.7 even 3 1728.2.r.f.1441.4 12
12.11 even 2 5184.2.d.q.2593.10 12
24.5 odd 2 5184.2.d.q.2593.3 12
24.11 even 2 5184.2.d.q.2593.4 12
36.7 odd 6 1728.2.r.f.1441.3 12
36.11 even 6 576.2.r.e.481.5 yes 12
36.23 even 6 576.2.r.f.97.2 yes 12
36.31 odd 6 1728.2.r.e.289.3 12
72.5 odd 6 576.2.r.e.97.2 12
72.11 even 6 576.2.r.f.481.2 yes 12
72.13 even 6 1728.2.r.f.289.4 12
72.29 odd 6 576.2.r.f.481.5 yes 12
72.43 odd 6 1728.2.r.e.1441.3 12
72.59 even 6 576.2.r.e.97.5 yes 12
72.61 even 6 1728.2.r.e.1441.4 12
72.67 odd 6 1728.2.r.f.289.3 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
576.2.r.e.97.2 12 72.5 odd 6
576.2.r.e.97.5 yes 12 72.59 even 6
576.2.r.e.481.2 yes 12 9.2 odd 6
576.2.r.e.481.5 yes 12 36.11 even 6
576.2.r.f.97.2 yes 12 36.23 even 6
576.2.r.f.97.5 yes 12 9.5 odd 6
576.2.r.f.481.2 yes 12 72.11 even 6
576.2.r.f.481.5 yes 12 72.29 odd 6
1728.2.r.e.289.3 12 36.31 odd 6
1728.2.r.e.289.4 12 9.4 even 3
1728.2.r.e.1441.3 12 72.43 odd 6
1728.2.r.e.1441.4 12 72.61 even 6
1728.2.r.f.289.3 12 72.67 odd 6
1728.2.r.f.289.4 12 72.13 even 6
1728.2.r.f.1441.3 12 36.7 odd 6
1728.2.r.f.1441.4 12 9.7 even 3
5184.2.d.q.2593.3 12 24.5 odd 2
5184.2.d.q.2593.4 12 24.11 even 2
5184.2.d.q.2593.9 12 3.2 odd 2
5184.2.d.q.2593.10 12 12.11 even 2
5184.2.d.r.2593.3 12 1.1 even 1 trivial
5184.2.d.r.2593.4 12 4.3 odd 2 inner
5184.2.d.r.2593.9 12 8.5 even 2 inner
5184.2.d.r.2593.10 12 8.3 odd 2 inner