Properties

Label 5184.2.d.r.2593.2
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 2593.2
Root \(0.583700 + 2.17840i\) of defining polynomial
Character \(\chi\) \(=\) 5184.2593
Dual form 5184.2.d.r.2593.8

$q$-expansion

\(f(q)\) \(=\) \(q-1.73205i q^{5} -3.61328 q^{7} +O(q^{10})\) \(q-1.73205i q^{5} -3.61328 q^{7} +0.734191i q^{11} -0.609577i q^{13} +5.52420 q^{17} -2.00000i q^{19} -4.73576 q^{23} +2.00000 q^{25} +7.83614i q^{29} +9.41901 q^{31} +6.25839i q^{35} +2.34163i q^{37} +8.52420 q^{41} -10.2584i q^{43} -11.7606 q^{47} +6.05582 q^{49} -13.0323i q^{53} +1.27166 q^{55} -1.20999i q^{59} +11.3002i q^{61} -1.05582 q^{65} +6.31421i q^{67} +2.63999 q^{71} -2.05582 q^{73} -2.65284i q^{77} -2.49081 q^{79} -12.2584i q^{83} -9.56819i q^{85} +1.94418 q^{89} +2.20257i q^{91} -3.46410 q^{95} -15.5726 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q+O(q^{10}) \) 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
\(7\) −3.61328 −1.36569 −0.682846 0.730562i \(-0.739258\pi\)
−0.682846 + 0.730562i \(0.739258\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0.734191i 0.221367i 0.993856 + 0.110683i \(0.0353040\pi\)
−0.993856 + 0.110683i \(0.964696\pi\)
\(12\) 0 0
\(13\) − 0.609577i − 0.169066i −0.996421 0.0845331i \(-0.973060\pi\)
0.996421 0.0845331i \(-0.0269399\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 5.52420 1.33982 0.669908 0.742444i \(-0.266334\pi\)
0.669908 + 0.742444i \(0.266334\pi\)
\(18\) 0 0
\(19\) − 2.00000i − 0.458831i −0.973329 0.229416i \(-0.926318\pi\)
0.973329 0.229416i \(-0.0736815\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4.73576 −0.987474 −0.493737 0.869611i \(-0.664369\pi\)
−0.493737 + 0.869611i \(0.664369\pi\)
\(24\) 0 0
\(25\) 2.00000 0.400000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 7.83614i 1.45514i 0.686036 + 0.727568i \(0.259349\pi\)
−0.686036 + 0.727568i \(0.740651\pi\)
\(30\) 0 0
\(31\) 9.41901 1.69170 0.845852 0.533417i \(-0.179092\pi\)
0.845852 + 0.533417i \(0.179092\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 6.25839i 1.05786i
\(36\) 0 0
\(37\) 2.34163i 0.384961i 0.981301 + 0.192481i \(0.0616532\pi\)
−0.981301 + 0.192481i \(0.938347\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 8.52420 1.33126 0.665628 0.746284i \(-0.268164\pi\)
0.665628 + 0.746284i \(0.268164\pi\)
\(42\) 0 0
\(43\) − 10.2584i − 1.56439i −0.623034 0.782195i \(-0.714100\pi\)
0.623034 0.782195i \(-0.285900\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −11.7606 −1.71547 −0.857733 0.514096i \(-0.828128\pi\)
−0.857733 + 0.514096i \(0.828128\pi\)
\(48\) 0 0
\(49\) 6.05582 0.865117
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) − 13.0323i − 1.79012i −0.445942 0.895062i \(-0.647131\pi\)
0.445942 0.895062i \(-0.352869\pi\)
\(54\) 0 0
\(55\) 1.27166 0.171470
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) − 1.20999i − 0.157527i −0.996893 0.0787637i \(-0.974903\pi\)
0.996893 0.0787637i \(-0.0250973\pi\)
\(60\) 0 0
\(61\) 11.3002i 1.44685i 0.690404 + 0.723424i \(0.257433\pi\)
−0.690404 + 0.723424i \(0.742567\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.05582 −0.130958
\(66\) 0 0
\(67\) 6.31421i 0.771403i 0.922624 + 0.385702i \(0.126041\pi\)
−0.922624 + 0.385702i \(0.873959\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 2.63999 0.313309 0.156655 0.987653i \(-0.449929\pi\)
0.156655 + 0.987653i \(0.449929\pi\)
\(72\) 0 0
\(73\) −2.05582 −0.240615 −0.120308 0.992737i \(-0.538388\pi\)
−0.120308 + 0.992737i \(0.538388\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) − 2.65284i − 0.302319i
\(78\) 0 0
\(79\) −2.49081 −0.280238 −0.140119 0.990135i \(-0.544749\pi\)
−0.140119 + 0.990135i \(0.544749\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) − 12.2584i − 1.34553i −0.739855 0.672767i \(-0.765106\pi\)
0.739855 0.672767i \(-0.234894\pi\)
\(84\) 0 0
\(85\) − 9.56819i − 1.03782i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 1.94418 0.206083 0.103041 0.994677i \(-0.467143\pi\)
0.103041 + 0.994677i \(0.467143\pi\)
\(90\) 0 0
\(91\) 2.20257i 0.230892i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −3.46410 −0.355409
\(96\) 0 0
\(97\) −15.5726 −1.58116 −0.790579 0.612360i \(-0.790220\pi\)
−0.790579 + 0.612360i \(0.790220\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) − 11.2036i − 1.11480i −0.830245 0.557398i \(-0.811800\pi\)
0.830245 0.557398i \(-0.188200\pi\)
\(102\) 0 0
\(103\) 1.36834 0.134826 0.0674130 0.997725i \(-0.478525\pi\)
0.0674130 + 0.997725i \(0.478525\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) − 13.4684i − 1.30204i −0.759062 0.651019i \(-0.774342\pi\)
0.759062 0.651019i \(-0.225658\pi\)
\(108\) 0 0
\(109\) − 1.42084i − 0.136092i −0.997682 0.0680458i \(-0.978324\pi\)
0.997682 0.0680458i \(-0.0216764\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −9.51678 −0.895263 −0.447632 0.894218i \(-0.647732\pi\)
−0.447632 + 0.894218i \(0.647732\pi\)
\(114\) 0 0
\(115\) 8.20257i 0.764894i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −19.9605 −1.82978
\(120\) 0 0
\(121\) 10.4610 0.950997
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) − 12.1244i − 1.08444i
\(126\) 0 0
\(127\) 2.24495 0.199207 0.0996035 0.995027i \(-0.468243\pi\)
0.0996035 + 0.995027i \(0.468243\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) − 0.258391i − 0.0225757i −0.999936 0.0112878i \(-0.996407\pi\)
0.999936 0.0112878i \(-0.00359311\pi\)
\(132\) 0 0
\(133\) 7.22657i 0.626623i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2.00742 0.171505 0.0857527 0.996316i \(-0.472671\pi\)
0.0857527 + 0.996316i \(0.472671\pi\)
\(138\) 0 0
\(139\) − 2.25839i − 0.191554i −0.995403 0.0957771i \(-0.969466\pi\)
0.995403 0.0957771i \(-0.0305336\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0.447546 0.0374256
\(144\) 0 0
\(145\) 13.5726 1.12714
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) − 14.7643i − 1.20954i −0.796399 0.604771i \(-0.793265\pi\)
0.796399 0.604771i \(-0.206735\pi\)
\(150\) 0 0
\(151\) −5.65655 −0.460323 −0.230162 0.973152i \(-0.573925\pi\)
−0.230162 + 0.973152i \(0.573925\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) − 16.3142i − 1.31039i
\(156\) 0 0
\(157\) − 15.8868i − 1.26791i −0.773371 0.633953i \(-0.781431\pi\)
0.773371 0.633953i \(-0.218569\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 17.1116 1.34859
\(162\) 0 0
\(163\) − 8.51678i − 0.667086i −0.942735 0.333543i \(-0.891756\pi\)
0.942735 0.333543i \(-0.108244\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 3.91165 0.302692 0.151346 0.988481i \(-0.451639\pi\)
0.151346 + 0.988481i \(0.451639\pi\)
\(168\) 0 0
\(169\) 12.6284 0.971417
\(170\) 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
\(175\) −7.22657 −0.546277
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 6.00000i 0.448461i 0.974536 + 0.224231i \(0.0719869\pi\)
−0.974536 + 0.224231i \(0.928013\pi\)
\(180\) 0 0
\(181\) − 2.34163i − 0.174052i −0.996206 0.0870259i \(-0.972264\pi\)
0.996206 0.0870259i \(-0.0277363\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 4.05582 0.298190
\(186\) 0 0
\(187\) 4.05582i 0.296591i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1.36834 0.0990092 0.0495046 0.998774i \(-0.484236\pi\)
0.0495046 + 0.998774i \(0.484236\pi\)
\(192\) 0 0
\(193\) −15.4610 −1.11290 −0.556452 0.830880i \(-0.687838\pi\)
−0.556452 + 0.830880i \(0.687838\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) − 12.9356i − 0.921625i −0.887498 0.460812i \(-0.847558\pi\)
0.887498 0.460812i \(-0.152442\pi\)
\(198\) 0 0
\(199\) −18.7413 −1.32854 −0.664269 0.747493i \(-0.731257\pi\)
−0.664269 + 0.747493i \(0.731257\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) − 28.3142i − 1.98727i
\(204\) 0 0
\(205\) − 14.7643i − 1.03119i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1.46838 0.101570
\(210\) 0 0
\(211\) − 8.31421i − 0.572374i −0.958174 0.286187i \(-0.907612\pi\)
0.958174 0.286187i \(-0.0923878\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −17.7681 −1.21177
\(216\) 0 0
\(217\) −34.0336 −2.31035
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) − 3.36742i − 0.226517i
\(222\) 0 0
\(223\) 7.99817 0.535597 0.267799 0.963475i \(-0.413704\pi\)
0.267799 + 0.963475i \(0.413704\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 5.26581i 0.349504i 0.984612 + 0.174752i \(0.0559124\pi\)
−0.984612 + 0.174752i \(0.944088\pi\)
\(228\) 0 0
\(229\) 16.1852i 1.06955i 0.844995 + 0.534774i \(0.179603\pi\)
−0.844995 + 0.534774i \(0.820397\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −28.0968 −1.84068 −0.920341 0.391116i \(-0.872089\pi\)
−0.920341 + 0.391116i \(0.872089\pi\)
\(234\) 0 0
\(235\) 20.3700i 1.32879i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −18.5922 −1.20263 −0.601314 0.799013i \(-0.705356\pi\)
−0.601314 + 0.799013i \(0.705356\pi\)
\(240\) 0 0
\(241\) −9.11164 −0.586932 −0.293466 0.955970i \(-0.594809\pi\)
−0.293466 + 0.955970i \(0.594809\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) − 10.4890i − 0.670117i
\(246\) 0 0
\(247\) −1.21915 −0.0775729
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) − 21.5800i − 1.36212i −0.732228 0.681059i \(-0.761520\pi\)
0.732228 0.681059i \(-0.238480\pi\)
\(252\) 0 0
\(253\) − 3.47695i − 0.218594i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 5.41998 0.338089 0.169045 0.985608i \(-0.445932\pi\)
0.169045 + 0.985608i \(0.445932\pi\)
\(258\) 0 0
\(259\) − 8.46096i − 0.525739i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 10.0157 0.617597 0.308798 0.951127i \(-0.400073\pi\)
0.308798 + 0.951127i \(0.400073\pi\)
\(264\) 0 0
\(265\) −22.5726 −1.38662
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 12.1115i 0.738452i 0.929340 + 0.369226i \(0.120377\pi\)
−0.929340 + 0.369226i \(0.879623\pi\)
\(270\) 0 0
\(271\) 20.0572 1.21839 0.609193 0.793022i \(-0.291493\pi\)
0.609193 + 0.793022i \(0.291493\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.46838i 0.0885468i
\(276\) 0 0
\(277\) − 5.49452i − 0.330133i −0.986282 0.165067i \(-0.947216\pi\)
0.986282 0.165067i \(-0.0527840\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 9.16745 0.546884 0.273442 0.961888i \(-0.411838\pi\)
0.273442 + 0.961888i \(0.411838\pi\)
\(282\) 0 0
\(283\) 22.7752i 1.35384i 0.736055 + 0.676922i \(0.236686\pi\)
−0.736055 + 0.676922i \(0.763314\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −30.8003 −1.81809
\(288\) 0 0
\(289\) 13.5168 0.795105
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) − 21.5959i − 1.26164i −0.775927 0.630822i \(-0.782718\pi\)
0.775927 0.630822i \(-0.217282\pi\)
\(294\) 0 0
\(295\) −2.09577 −0.122020
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2.88681i 0.166948i
\(300\) 0 0
\(301\) 37.0665i 2.13648i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 19.5726 1.12072
\(306\) 0 0
\(307\) 8.51678i 0.486078i 0.970016 + 0.243039i \(0.0781444\pi\)
−0.970016 + 0.243039i \(0.921856\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −24.7929 −1.40588 −0.702939 0.711250i \(-0.748129\pi\)
−0.702939 + 0.711250i \(0.748129\pi\)
\(312\) 0 0
\(313\) 15.1116 0.854160 0.427080 0.904214i \(-0.359542\pi\)
0.427080 + 0.904214i \(0.359542\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) − 12.2210i − 0.686402i −0.939262 0.343201i \(-0.888489\pi\)
0.939262 0.343201i \(-0.111511\pi\)
\(318\) 0 0
\(319\) −5.75323 −0.322119
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) − 11.0484i − 0.614749i
\(324\) 0 0
\(325\) − 1.21915i − 0.0676264i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 42.4945 2.34280
\(330\) 0 0
\(331\) 24.7194i 1.35870i 0.733815 + 0.679349i \(0.237738\pi\)
−0.733815 + 0.679349i \(0.762262\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 10.9365 0.597526
\(336\) 0 0
\(337\) 13.5168 0.736306 0.368153 0.929765i \(-0.379990\pi\)
0.368153 + 0.929765i \(0.379990\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 6.91535i 0.374487i
\(342\) 0 0
\(343\) 3.41160 0.184209
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 15.3626i 0.824708i 0.911024 + 0.412354i \(0.135293\pi\)
−0.911024 + 0.412354i \(0.864707\pi\)
\(348\) 0 0
\(349\) − 31.5591i − 1.68932i −0.535303 0.844660i \(-0.679803\pi\)
0.535303 0.844660i \(-0.320197\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 27.9926 1.48989 0.744947 0.667123i \(-0.232475\pi\)
0.744947 + 0.667123i \(0.232475\pi\)
\(354\) 0 0
\(355\) − 4.57260i − 0.242688i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −13.1290 −0.692921 −0.346460 0.938065i \(-0.612616\pi\)
−0.346460 + 0.938065i \(0.612616\pi\)
\(360\) 0 0
\(361\) 15.0000 0.789474
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 3.56078i 0.186380i
\(366\) 0 0
\(367\) 13.4798 0.703642 0.351821 0.936067i \(-0.385563\pi\)
0.351821 + 0.936067i \(0.385563\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 47.0894i 2.44476i
\(372\) 0 0
\(373\) 5.59120i 0.289501i 0.989468 + 0.144751i \(0.0462380\pi\)
−0.989468 + 0.144751i \(0.953762\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 4.77673 0.246014
\(378\) 0 0
\(379\) − 33.0894i − 1.69969i −0.527035 0.849844i \(-0.676696\pi\)
0.527035 0.849844i \(-0.323304\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −15.2247 −0.777948 −0.388974 0.921249i \(-0.627170\pi\)
−0.388974 + 0.921249i \(0.627170\pi\)
\(384\) 0 0
\(385\) −4.59485 −0.234175
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) − 6.11694i − 0.310141i −0.987903 0.155071i \(-0.950439\pi\)
0.987903 0.155071i \(-0.0495605\pi\)
\(390\) 0 0
\(391\) −26.1613 −1.32303
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 4.31421i 0.217071i
\(396\) 0 0
\(397\) 22.2054i 1.11446i 0.830358 + 0.557230i \(0.188136\pi\)
−0.830358 + 0.557230i \(0.811864\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −30.1042 −1.50333 −0.751666 0.659543i \(-0.770750\pi\)
−0.751666 + 0.659543i \(0.770750\pi\)
\(402\) 0 0
\(403\) − 5.74161i − 0.286010i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −1.71920 −0.0852177
\(408\) 0 0
\(409\) −9.11164 −0.450541 −0.225271 0.974296i \(-0.572327\pi\)
−0.225271 + 0.974296i \(0.572327\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 4.37204i 0.215134i
\(414\) 0 0
\(415\) −21.2322 −1.04225
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 22.8310i 1.11537i 0.830054 + 0.557683i \(0.188310\pi\)
−0.830054 + 0.557683i \(0.811690\pi\)
\(420\) 0 0
\(421\) − 24.5342i − 1.19573i −0.801599 0.597863i \(-0.796017\pi\)
0.801599 0.597863i \(-0.203983\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 11.0484 0.535926
\(426\) 0 0
\(427\) − 40.8310i − 1.97595i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0.920789 0.0443529 0.0221764 0.999754i \(-0.492940\pi\)
0.0221764 + 0.999754i \(0.492940\pi\)
\(432\) 0 0
\(433\) 2.05582 0.0987963 0.0493981 0.998779i \(-0.484270\pi\)
0.0493981 + 0.998779i \(0.484270\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 9.47152i 0.453084i
\(438\) 0 0
\(439\) 22.0563 1.05269 0.526344 0.850272i \(-0.323562\pi\)
0.526344 + 0.850272i \(0.323562\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) − 27.1952i − 1.29208i −0.763303 0.646040i \(-0.776424\pi\)
0.763303 0.646040i \(-0.223576\pi\)
\(444\) 0 0
\(445\) − 3.36742i − 0.159631i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 9.10422 0.429655 0.214827 0.976652i \(-0.431081\pi\)
0.214827 + 0.976652i \(0.431081\pi\)
\(450\) 0 0
\(451\) 6.25839i 0.294696i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 3.81497 0.178848
\(456\) 0 0
\(457\) 29.6842 1.38857 0.694285 0.719700i \(-0.255721\pi\)
0.694285 + 0.719700i \(0.255721\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) − 23.5084i − 1.09490i −0.836839 0.547448i \(-0.815599\pi\)
0.836839 0.547448i \(-0.184401\pi\)
\(462\) 0 0
\(463\) 7.90150 0.367214 0.183607 0.983000i \(-0.441223\pi\)
0.183607 + 0.983000i \(0.441223\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 3.06324i 0.141750i 0.997485 + 0.0708748i \(0.0225791\pi\)
−0.997485 + 0.0708748i \(0.977421\pi\)
\(468\) 0 0
\(469\) − 22.8150i − 1.05350i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 7.53162 0.346304
\(474\) 0 0
\(475\) − 4.00000i − 0.183533i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −14.2073 −0.649147 −0.324573 0.945860i \(-0.605221\pi\)
−0.324573 + 0.945860i \(0.605221\pi\)
\(480\) 0 0
\(481\) 1.42740 0.0650839
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 26.9725i 1.22476i
\(486\) 0 0
\(487\) 22.1088 1.00184 0.500922 0.865492i \(-0.332994\pi\)
0.500922 + 0.865492i \(0.332994\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) − 39.5301i − 1.78397i −0.452068 0.891983i \(-0.649314\pi\)
0.452068 0.891983i \(-0.350686\pi\)
\(492\) 0 0
\(493\) 43.2884i 1.94961i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −9.53904 −0.427884
\(498\) 0 0
\(499\) − 11.8532i − 0.530624i −0.964163 0.265312i \(-0.914525\pi\)
0.964163 0.265312i \(-0.0854750\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −23.4246 −1.04445 −0.522226 0.852807i \(-0.674898\pi\)
−0.522226 + 0.852807i \(0.674898\pi\)
\(504\) 0 0
\(505\) −19.4051 −0.863518
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) − 7.83614i − 0.347331i −0.984805 0.173665i \(-0.944439\pi\)
0.984805 0.173665i \(-0.0555611\pi\)
\(510\) 0 0
\(511\) 7.42825 0.328607
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) − 2.37003i − 0.104436i
\(516\) 0 0
\(517\) − 8.63456i − 0.379747i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −27.4535 −1.20276 −0.601381 0.798963i \(-0.705383\pi\)
−0.601381 + 0.798963i \(0.705383\pi\)
\(522\) 0 0
\(523\) − 3.83255i − 0.167586i −0.996483 0.0837928i \(-0.973297\pi\)
0.996483 0.0837928i \(-0.0267034\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 52.0325 2.26657
\(528\) 0 0
\(529\) −0.572599 −0.0248956
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) − 5.19615i − 0.225070i
\(534\) 0 0
\(535\) −23.3279 −1.00855
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 4.44613i 0.191508i
\(540\) 0 0
\(541\) − 15.9707i − 0.686632i −0.939220 0.343316i \(-0.888450\pi\)
0.939220 0.343316i \(-0.111550\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −2.46096 −0.105416
\(546\) 0 0
\(547\) 10.4258i 0.445777i 0.974844 + 0.222888i \(0.0715486\pi\)
−0.974844 + 0.222888i \(0.928451\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 15.6723 0.667662
\(552\) 0 0
\(553\) 9.00000 0.382719
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) − 25.0471i − 1.06128i −0.847597 0.530640i \(-0.821951\pi\)
0.847597 0.530640i \(-0.178049\pi\)
\(558\) 0 0
\(559\) −6.25327 −0.264485
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 2.63739i 0.111153i 0.998454 + 0.0555764i \(0.0176996\pi\)
−0.998454 + 0.0555764i \(0.982300\pi\)
\(564\) 0 0
\(565\) 16.4835i 0.693468i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 20.0484 0.840473 0.420236 0.907415i \(-0.361947\pi\)
0.420236 + 0.907415i \(0.361947\pi\)
\(570\) 0 0
\(571\) 2.31421i 0.0968466i 0.998827 + 0.0484233i \(0.0154196\pi\)
−0.998827 + 0.0484233i \(0.984580\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −9.47152 −0.394989
\(576\) 0 0
\(577\) 24.4610 1.01832 0.509162 0.860671i \(-0.329956\pi\)
0.509162 + 0.860671i \(0.329956\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 44.2930i 1.83758i
\(582\) 0 0
\(583\) 9.56819 0.396274
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) − 19.7268i − 0.814211i −0.913381 0.407106i \(-0.866538\pi\)
0.913381 0.407106i \(-0.133462\pi\)
\(588\) 0 0
\(589\) − 18.8380i − 0.776207i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −8.46096 −0.347450 −0.173725 0.984794i \(-0.555580\pi\)
−0.173725 + 0.984794i \(0.555580\pi\)
\(594\) 0 0
\(595\) 34.5726i 1.41734i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −6.45496 −0.263742 −0.131871 0.991267i \(-0.542099\pi\)
−0.131871 + 0.991267i \(0.542099\pi\)
\(600\) 0 0
\(601\) −5.05582 −0.206231 −0.103116 0.994669i \(-0.532881\pi\)
−0.103116 + 0.994669i \(0.532881\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) − 18.1189i − 0.736639i
\(606\) 0 0
\(607\) 0.0441760 0.00179305 0.000896524 1.00000i \(-0.499715\pi\)
0.000896524 1.00000i \(0.499715\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 7.16901i 0.290027i
\(612\) 0 0
\(613\) 26.8887i 1.08602i 0.839725 + 0.543012i \(0.182716\pi\)
−0.839725 + 0.543012i \(0.817284\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −18.4126 −0.741262 −0.370631 0.928780i \(-0.620859\pi\)
−0.370631 + 0.928780i \(0.620859\pi\)
\(618\) 0 0
\(619\) − 1.90906i − 0.0767317i −0.999264 0.0383658i \(-0.987785\pi\)
0.999264 0.0383658i \(-0.0122152\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −7.02488 −0.281446
\(624\) 0 0
\(625\) −11.0000 −0.440000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 12.9356i 0.515777i
\(630\) 0 0
\(631\) 1.51752 0.0604114 0.0302057 0.999544i \(-0.490384\pi\)
0.0302057 + 0.999544i \(0.490384\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) − 3.88836i − 0.154305i
\(636\) 0 0
\(637\) − 3.69148i − 0.146262i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −16.9852 −0.670874 −0.335437 0.942063i \(-0.608884\pi\)
−0.335437 + 0.942063i \(0.608884\pi\)
\(642\) 0 0
\(643\) 10.4258i 0.411155i 0.978641 + 0.205578i \(0.0659073\pi\)
−0.978641 + 0.205578i \(0.934093\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 44.2802 1.74083 0.870417 0.492315i \(-0.163849\pi\)
0.870417 + 0.492315i \(0.163849\pi\)
\(648\) 0 0
\(649\) 0.888365 0.0348714
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) − 33.0766i − 1.29439i −0.762325 0.647194i \(-0.775942\pi\)
0.762325 0.647194i \(-0.224058\pi\)
\(654\) 0 0
\(655\) −0.447546 −0.0174871
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 32.2026i 1.25443i 0.778844 + 0.627217i \(0.215806\pi\)
−0.778844 + 0.627217i \(0.784194\pi\)
\(660\) 0 0
\(661\) 13.0194i 0.506398i 0.967414 + 0.253199i \(0.0814827\pi\)
−0.967414 + 0.253199i \(0.918517\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 12.5168 0.485380
\(666\) 0 0
\(667\) − 37.1101i − 1.43691i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −8.29654 −0.320284
\(672\) 0 0
\(673\) −7.46096 −0.287599 −0.143800 0.989607i \(-0.545932\pi\)
−0.143800 + 0.989607i \(0.545932\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 35.6456i 1.36997i 0.728556 + 0.684987i \(0.240192\pi\)
−0.728556 + 0.684987i \(0.759808\pi\)
\(678\) 0 0
\(679\) 56.2682 2.15938
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) − 27.4535i − 1.05048i −0.850954 0.525240i \(-0.823975\pi\)
0.850954 0.525240i \(-0.176025\pi\)
\(684\) 0 0
\(685\) − 3.47695i − 0.132847i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −7.94418 −0.302649
\(690\) 0 0
\(691\) − 22.3700i − 0.850996i −0.904959 0.425498i \(-0.860099\pi\)
0.904959 0.425498i \(-0.139901\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −3.91165 −0.148377
\(696\) 0 0
\(697\) 47.0894 1.78364
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) − 10.4633i − 0.395193i −0.980283 0.197596i \(-0.936686\pi\)
0.980283 0.197596i \(-0.0633136\pi\)
\(702\) 0 0
\(703\) 4.68325 0.176632
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 40.4817i 1.52247i
\(708\) 0 0
\(709\) 23.5425i 0.884155i 0.896977 + 0.442078i \(0.145758\pi\)
−0.896977 + 0.442078i \(0.854242\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −44.6062 −1.67051
\(714\) 0 0
\(715\) − 0.775172i − 0.0289898i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 45.0076 1.67850 0.839251 0.543745i \(-0.182994\pi\)
0.839251 + 0.543745i \(0.182994\pi\)
\(720\) 0 0
\(721\) −4.94418 −0.184131
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 15.6723i 0.582054i
\(726\) 0 0
\(727\) −16.7506 −0.621245 −0.310622 0.950533i \(-0.600537\pi\)
−0.310622 + 0.950533i \(0.600537\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) − 56.6694i − 2.09599i
\(732\) 0 0
\(733\) 24.3409i 0.899050i 0.893268 + 0.449525i \(0.148407\pi\)
−0.893268 + 0.449525i \(0.851593\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −4.63583 −0.170763
\(738\) 0 0
\(739\) − 32.0558i − 1.17919i −0.807698 0.589596i \(-0.799287\pi\)
0.807698 0.589596i \(-0.200713\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 17.9614 0.658940 0.329470 0.944166i \(-0.393130\pi\)
0.329470 + 0.944166i \(0.393130\pi\)
\(744\) 0 0
\(745\) −25.5726 −0.936908
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 48.6651i 1.77818i
\(750\) 0 0
\(751\) −21.8546 −0.797485 −0.398742 0.917063i \(-0.630553\pi\)
−0.398742 + 0.917063i \(0.630553\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 9.79743i 0.356565i
\(756\) 0 0
\(757\) 52.1292i 1.89467i 0.320248 + 0.947334i \(0.396234\pi\)
−0.320248 + 0.947334i \(0.603766\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −32.0894 −1.16324 −0.581620 0.813461i \(-0.697581\pi\)
−0.581620 + 0.813461i \(0.697581\pi\)
\(762\) 0 0
\(763\) 5.13389i 0.185859i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −0.737582 −0.0266326
\(768\) 0 0
\(769\) 3.22327 0.116234 0.0581171 0.998310i \(-0.481490\pi\)
0.0581171 + 0.998310i \(0.481490\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) − 19.2331i − 0.691765i −0.938278 0.345883i \(-0.887580\pi\)
0.938278 0.345883i \(-0.112420\pi\)
\(774\) 0 0
\(775\) 18.8380 0.676682
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) − 17.0484i − 0.610822i
\(780\) 0 0
\(781\) 1.93826i 0.0693563i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −27.5168 −0.982116
\(786\) 0 0
\(787\) 36.3700i 1.29645i 0.761448 + 0.648226i \(0.224489\pi\)
−0.761448 + 0.648226i \(0.775511\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 34.3868 1.22265
\(792\) 0 0
\(793\) 6.88836 0.244613
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) − 14.9577i − 0.529829i −0.964272 0.264915i \(-0.914656\pi\)
0.964272 0.264915i \(-0.0853437\pi\)
\(798\) 0 0
\(799\) −64.9681 −2.29841
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) − 1.50936i − 0.0532643i
\(804\) 0 0
\(805\) − 29.6382i − 1.04461i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0.0409808 0.00144081 0.000720404 1.00000i \(-0.499771\pi\)
0.000720404 1.00000i \(0.499771\pi\)
\(810\) 0 0
\(811\) 43.2568i 1.51895i 0.650535 + 0.759476i \(0.274545\pi\)
−0.650535 + 0.759476i \(0.725455\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −14.7515 −0.516722
\(816\) 0 0
\(817\) −20.5168 −0.717791
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 28.6208i 0.998871i 0.866351 + 0.499436i \(0.166459\pi\)
−0.866351 + 0.499436i \(0.833541\pi\)
\(822\) 0 0
\(823\) 42.4118 1.47838 0.739191 0.673495i \(-0.235208\pi\)
0.739191 + 0.673495i \(0.235208\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) − 14.1116i − 0.490710i −0.969433 0.245355i \(-0.921096\pi\)
0.969433 0.245355i \(-0.0789045\pi\)
\(828\) 0 0
\(829\) − 22.6088i − 0.785237i −0.919701 0.392618i \(-0.871569\pi\)
0.919701 0.392618i \(-0.128431\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 33.4535 1.15910
\(834\) 0 0
\(835\) − 6.77517i − 0.234464i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 14.1106 0.487152 0.243576 0.969882i \(-0.421680\pi\)
0.243576 + 0.969882i \(0.421680\pi\)
\(840\) 0 0
\(841\) −32.4051 −1.11742
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) − 21.8731i − 0.752456i
\(846\) 0 0
\(847\) −37.7984 −1.29877
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) − 11.0894i − 0.380139i
\(852\) 0 0
\(853\) − 42.4772i − 1.45439i −0.686431 0.727195i \(-0.740824\pi\)
0.686431 0.727195i \(-0.259176\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −33.6842 −1.15063 −0.575316 0.817931i \(-0.695121\pi\)
−0.575316 + 0.817931i \(0.695121\pi\)
\(858\) 0 0
\(859\) 45.9762i 1.56869i 0.620327 + 0.784344i \(0.287000\pi\)
−0.620327 + 0.784344i \(0.713000\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 31.8786 1.08516 0.542581 0.840004i \(-0.317447\pi\)
0.542581 + 0.840004i \(0.317447\pi\)
\(864\) 0 0
\(865\) −21.0000 −0.714021
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) − 1.82873i − 0.0620354i
\(870\) 0 0
\(871\) 3.84899 0.130418
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 43.8087i 1.48101i
\(876\) 0 0
\(877\) − 52.4147i − 1.76992i −0.465668 0.884959i \(-0.654186\pi\)
0.465668 0.884959i \(-0.345814\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −34.0558 −1.14737 −0.573685 0.819076i \(-0.694487\pi\)
−0.573685 + 0.819076i \(0.694487\pi\)
\(882\) 0 0
\(883\) 10.0000i 0.336527i 0.985742 + 0.168263i \(0.0538159\pi\)
−0.985742 + 0.168263i \(0.946184\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 36.1060 1.21232 0.606161 0.795342i \(-0.292709\pi\)
0.606161 + 0.795342i \(0.292709\pi\)
\(888\) 0 0
\(889\) −8.11164 −0.272056
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 23.5213i 0.787110i
\(894\) 0 0
\(895\) 10.3923 0.347376
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 73.8087i 2.46166i
\(900\) 0 0
\(901\) − 71.9930i − 2.39843i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −4.05582 −0.134820
\(906\) 0 0
\(907\) − 42.3700i − 1.40687i −0.710758 0.703437i \(-0.751648\pi\)
0.710758 0.703437i \(-0.248352\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 50.6642 1.67858 0.839289 0.543685i \(-0.182971\pi\)
0.839289 + 0.543685i \(0.182971\pi\)
\(912\) 0 0
\(913\) 9.00000 0.297857
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0.933638i 0.0308315i
\(918\) 0 0
\(919\) −25.3372 −0.835796 −0.417898 0.908494i \(-0.637233\pi\)
−0.417898 + 0.908494i \(0.637233\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) − 1.60928i − 0.0529700i
\(924\) 0 0
\(925\) 4.68325i 0.153984i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 15.3493 0.503595 0.251798 0.967780i \(-0.418978\pi\)
0.251798 + 0.967780i \(0.418978\pi\)
\(930\) 0 0
\(931\) − 12.1116i − 0.396943i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 7.02488 0.229738
\(936\) 0 0
\(937\) −11.5390 −0.376964 −0.188482 0.982077i \(-0.560357\pi\)
−0.188482 + 0.982077i \(0.560357\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 33.1023i 1.07910i 0.841952 + 0.539552i \(0.181407\pi\)
−0.841952 + 0.539552i \(0.818593\pi\)
\(942\) 0 0
\(943\) −40.3685 −1.31458
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 17.2658i 0.561063i 0.959845 + 0.280532i \(0.0905108\pi\)
−0.959845 + 0.280532i \(0.909489\pi\)
\(948\) 0 0
\(949\) 1.25318i 0.0406799i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 29.2159 0.946394 0.473197 0.880957i \(-0.343100\pi\)
0.473197 + 0.880957i \(0.343100\pi\)
\(954\) 0 0
\(955\) − 2.37003i − 0.0766922i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −7.25337 −0.234224
\(960\) 0 0
\(961\) 57.7178 1.86186
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 26.7792i 0.862052i
\(966\) 0 0
\(967\) 4.00833 0.128899 0.0644495 0.997921i \(-0.479471\pi\)
0.0644495 + 0.997921i \(0.479471\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 20.2791i 0.650787i 0.945579 + 0.325393i \(0.105497\pi\)
−0.945579 + 0.325393i \(0.894503\pi\)
\(972\) 0 0
\(973\) 8.16021i 0.261604i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −3.30835 −0.105843 −0.0529217 0.998599i \(-0.516853\pi\)
−0.0529217 + 0.998599i \(0.516853\pi\)
\(978\) 0 0
\(979\) 1.42740i 0.0456199i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −41.1927 −1.31384 −0.656921 0.753960i \(-0.728141\pi\)
−0.656921 + 0.753960i \(0.728141\pi\)
\(984\) 0 0
\(985\) −22.4051 −0.713887
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 48.5813i 1.54479i
\(990\) 0 0
\(991\) 44.2802 1.40661 0.703303 0.710890i \(-0.251708\pi\)
0.703303 + 0.710890i \(0.251708\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 32.4610i 1.02908i
\(996\) 0 0
\(997\) 35.6199i 1.12809i 0.825742 + 0.564047i \(0.190756\pi\)
−0.825742 + 0.564047i \(0.809244\pi\)
\(998\) 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.2593.2 12
3.2 odd 2 5184.2.d.q.2593.8 12
4.3 odd 2 inner 5184.2.d.r.2593.5 12
8.3 odd 2 inner 5184.2.d.r.2593.11 12
8.5 even 2 inner 5184.2.d.r.2593.8 12
9.2 odd 6 576.2.r.e.481.1 yes 12
9.4 even 3 1728.2.r.e.289.5 12
9.5 odd 6 576.2.r.f.97.6 yes 12
9.7 even 3 1728.2.r.f.1441.5 12
12.11 even 2 5184.2.d.q.2593.11 12
24.5 odd 2 5184.2.d.q.2593.2 12
24.11 even 2 5184.2.d.q.2593.5 12
36.7 odd 6 1728.2.r.f.1441.2 12
36.11 even 6 576.2.r.e.481.6 yes 12
36.23 even 6 576.2.r.f.97.1 yes 12
36.31 odd 6 1728.2.r.e.289.2 12
72.5 odd 6 576.2.r.e.97.1 12
72.11 even 6 576.2.r.f.481.1 yes 12
72.13 even 6 1728.2.r.f.289.5 12
72.29 odd 6 576.2.r.f.481.6 yes 12
72.43 odd 6 1728.2.r.e.1441.2 12
72.59 even 6 576.2.r.e.97.6 yes 12
72.61 even 6 1728.2.r.e.1441.5 12
72.67 odd 6 1728.2.r.f.289.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
576.2.r.e.97.1 12 72.5 odd 6
576.2.r.e.97.6 yes 12 72.59 even 6
576.2.r.e.481.1 yes 12 9.2 odd 6
576.2.r.e.481.6 yes 12 36.11 even 6
576.2.r.f.97.1 yes 12 36.23 even 6
576.2.r.f.97.6 yes 12 9.5 odd 6
576.2.r.f.481.1 yes 12 72.11 even 6
576.2.r.f.481.6 yes 12 72.29 odd 6
1728.2.r.e.289.2 12 36.31 odd 6
1728.2.r.e.289.5 12 9.4 even 3
1728.2.r.e.1441.2 12 72.43 odd 6
1728.2.r.e.1441.5 12 72.61 even 6
1728.2.r.f.289.2 12 72.67 odd 6
1728.2.r.f.289.5 12 72.13 even 6
1728.2.r.f.1441.2 12 36.7 odd 6
1728.2.r.f.1441.5 12 9.7 even 3
5184.2.d.q.2593.2 12 24.5 odd 2
5184.2.d.q.2593.5 12 24.11 even 2
5184.2.d.q.2593.8 12 3.2 odd 2
5184.2.d.q.2593.11 12 12.11 even 2
5184.2.d.r.2593.2 12 1.1 even 1 trivial
5184.2.d.r.2593.5 12 4.3 odd 2 inner
5184.2.d.r.2593.8 12 8.5 even 2 inner
5184.2.d.r.2593.11 12 8.3 odd 2 inner