Properties

Label 5184.2.f.b.2591.15
Level $5184$
Weight $2$
Character 5184.2591
Analytic conductor $41.394$
Analytic rank $0$
Dimension $16$
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.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(41.3944484078\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \( x^{16} - 8x^{14} + 49x^{12} - 104x^{10} + 160x^{8} - 104x^{6} + 49x^{4} - 8x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{37}]\)
Coefficient ring index: \( 2^{12}\cdot 3^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 2591.15
Root \(-1.11871 - 0.645885i\) of defining polynomial
Character \(\chi\) \(=\) 5184.2591
Dual form 5184.2.f.b.2591.16

$q$-expansion

\(f(q)\) \(=\) \(q+4.04682 q^{5} -3.89623i q^{7} +O(q^{10})\) \(q+4.04682 q^{5} -3.89623i q^{7} +0.468572i q^{11} -4.89623i q^{13} -3.57825i q^{17} +1.89623 q^{19} -8.56221 q^{23} +11.3767 q^{25} -2.36451 q^{29} +7.18059i q^{31} -15.7673i q^{35} -6.16418i q^{37} -5.13116i q^{41} +10.5409 q^{43} -9.37380 q^{47} -8.18059 q^{49} +5.52280 q^{53} +1.89623i q^{55} +6.26797i q^{59} -0.983586i q^{61} -19.8141i q^{65} -12.7485 q^{67} +3.02890 q^{71} +4.58429 q^{73} +1.82566 q^{77} -11.6767i q^{79} +5.66616i q^{83} -14.4805i q^{85} +3.17610i q^{89} -19.0768 q^{91} +7.67369 q^{95} +0.611865 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 24 q^{19} + 16 q^{25} - 24 q^{43} - 48 q^{49} - 120 q^{67} + 16 q^{73} - 168 q^{91} - 16 q^{97}+O(q^{100}) \) 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
\(5\) 4.04682 1.80979 0.904896 0.425632i \(-0.139948\pi\)
0.904896 + 0.425632i \(0.139948\pi\)
\(6\) 0 0
\(7\) − 3.89623i − 1.47264i −0.676636 0.736318i \(-0.736563\pi\)
0.676636 0.736318i \(-0.263437\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0.468572i 0.141280i 0.997502 + 0.0706400i \(0.0225041\pi\)
−0.997502 + 0.0706400i \(0.977496\pi\)
\(12\) 0 0
\(13\) − 4.89623i − 1.35797i −0.734152 0.678985i \(-0.762420\pi\)
0.734152 0.678985i \(-0.237580\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) − 3.57825i − 0.867852i −0.900948 0.433926i \(-0.857128\pi\)
0.900948 0.433926i \(-0.142872\pi\)
\(18\) 0 0
\(19\) 1.89623 0.435024 0.217512 0.976058i \(-0.430206\pi\)
0.217512 + 0.976058i \(0.430206\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −8.56221 −1.78534 −0.892672 0.450707i \(-0.851172\pi\)
−0.892672 + 0.450707i \(0.851172\pi\)
\(24\) 0 0
\(25\) 11.3767 2.27535
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −2.36451 −0.439078 −0.219539 0.975604i \(-0.570455\pi\)
−0.219539 + 0.975604i \(0.570455\pi\)
\(30\) 0 0
\(31\) 7.18059i 1.28967i 0.764321 + 0.644836i \(0.223074\pi\)
−0.764321 + 0.644836i \(0.776926\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) − 15.7673i − 2.66516i
\(36\) 0 0
\(37\) − 6.16418i − 1.01338i −0.862127 0.506692i \(-0.830868\pi\)
0.862127 0.506692i \(-0.169132\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) − 5.13116i − 0.801353i −0.916220 0.400676i \(-0.868775\pi\)
0.916220 0.400676i \(-0.131225\pi\)
\(42\) 0 0
\(43\) 10.5409 1.60748 0.803738 0.594984i \(-0.202842\pi\)
0.803738 + 0.594984i \(0.202842\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −9.37380 −1.36731 −0.683655 0.729806i \(-0.739611\pi\)
−0.683655 + 0.729806i \(0.739611\pi\)
\(48\) 0 0
\(49\) −8.18059 −1.16866
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 5.52280 0.758616 0.379308 0.925271i \(-0.376162\pi\)
0.379308 + 0.925271i \(0.376162\pi\)
\(54\) 0 0
\(55\) 1.89623i 0.255687i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 6.26797i 0.816021i 0.912977 + 0.408010i \(0.133777\pi\)
−0.912977 + 0.408010i \(0.866223\pi\)
\(60\) 0 0
\(61\) − 0.983586i − 0.125935i −0.998016 0.0629677i \(-0.979943\pi\)
0.998016 0.0629677i \(-0.0200565\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) − 19.8141i − 2.45764i
\(66\) 0 0
\(67\) −12.7485 −1.55747 −0.778736 0.627351i \(-0.784139\pi\)
−0.778736 + 0.627351i \(0.784139\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 3.02890 0.359464 0.179732 0.983716i \(-0.442477\pi\)
0.179732 + 0.983716i \(0.442477\pi\)
\(72\) 0 0
\(73\) 4.58429 0.536550 0.268275 0.963342i \(-0.413546\pi\)
0.268275 + 0.963342i \(0.413546\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1.82566 0.208054
\(78\) 0 0
\(79\) − 11.6767i − 1.31373i −0.754009 0.656864i \(-0.771883\pi\)
0.754009 0.656864i \(-0.228117\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 5.66616i 0.621941i 0.950419 + 0.310971i \(0.100654\pi\)
−0.950419 + 0.310971i \(0.899346\pi\)
\(84\) 0 0
\(85\) − 14.4805i − 1.57063i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 3.17610i 0.336666i 0.985730 + 0.168333i \(0.0538383\pi\)
−0.985730 + 0.168333i \(0.946162\pi\)
\(90\) 0 0
\(91\) −19.0768 −1.99979
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 7.67369 0.787304
\(96\) 0 0
\(97\) 0.611865 0.0621255 0.0310627 0.999517i \(-0.490111\pi\)
0.0310627 + 0.999517i \(0.490111\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −8.28561 −0.824449 −0.412225 0.911082i \(-0.635248\pi\)
−0.412225 + 0.911082i \(0.635248\pi\)
\(102\) 0 0
\(103\) 2.00000i 0.197066i 0.995134 + 0.0985329i \(0.0314150\pi\)
−0.995134 + 0.0985329i \(0.968585\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 4.25315i 0.411167i 0.978640 + 0.205584i \(0.0659092\pi\)
−0.978640 + 0.205584i \(0.934091\pi\)
\(108\) 0 0
\(109\) − 9.42011i − 0.902283i −0.892452 0.451141i \(-0.851017\pi\)
0.892452 0.451141i \(-0.148983\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 9.84622i 0.926254i 0.886292 + 0.463127i \(0.153273\pi\)
−0.886292 + 0.463127i \(0.846727\pi\)
\(114\) 0 0
\(115\) −34.6497 −3.23110
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −13.9417 −1.27803
\(120\) 0 0
\(121\) 10.7804 0.980040
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 25.8055 2.30812
\(126\) 0 0
\(127\) − 14.2885i − 1.26790i −0.773373 0.633951i \(-0.781432\pi\)
0.773373 0.633951i \(-0.218568\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) − 17.5444i − 1.53286i −0.642329 0.766429i \(-0.722032\pi\)
0.642329 0.766429i \(-0.277968\pi\)
\(132\) 0 0
\(133\) − 7.38814i − 0.640633i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 11.7310i 1.00225i 0.865375 + 0.501124i \(0.167080\pi\)
−0.865375 + 0.501124i \(0.832920\pi\)
\(138\) 0 0
\(139\) −5.75963 −0.488525 −0.244263 0.969709i \(-0.578546\pi\)
−0.244263 + 0.969709i \(0.578546\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 2.29424 0.191854
\(144\) 0 0
\(145\) −9.56873 −0.794639
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −19.2022 −1.57311 −0.786554 0.617522i \(-0.788137\pi\)
−0.786554 + 0.617522i \(0.788137\pi\)
\(150\) 0 0
\(151\) 7.79246i 0.634141i 0.948402 + 0.317071i \(0.102699\pi\)
−0.948402 + 0.317071i \(0.897301\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 29.0585i 2.33404i
\(156\) 0 0
\(157\) 9.73707i 0.777103i 0.921427 + 0.388551i \(0.127024\pi\)
−0.921427 + 0.388551i \(0.872976\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 33.3603i 2.62916i
\(162\) 0 0
\(163\) 9.21342 0.721651 0.360825 0.932633i \(-0.382495\pi\)
0.360825 + 0.932633i \(0.382495\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 7.88386 0.610072 0.305036 0.952341i \(-0.401332\pi\)
0.305036 + 0.952341i \(0.401332\pi\)
\(168\) 0 0
\(169\) −10.9730 −0.844080
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −20.4747 −1.55666 −0.778331 0.627854i \(-0.783933\pi\)
−0.778331 + 0.627854i \(0.783933\pi\)
\(174\) 0 0
\(175\) − 44.3264i − 3.35076i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) − 19.1392i − 1.43053i −0.698851 0.715267i \(-0.746305\pi\)
0.698851 0.715267i \(-0.253695\pi\)
\(180\) 0 0
\(181\) 11.2894i 0.839133i 0.907725 + 0.419567i \(0.137818\pi\)
−0.907725 + 0.419567i \(0.862182\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) − 24.9453i − 1.83402i
\(186\) 0 0
\(187\) 1.67667 0.122610
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 19.7694 1.43046 0.715231 0.698889i \(-0.246322\pi\)
0.715231 + 0.698889i \(0.246322\pi\)
\(192\) 0 0
\(193\) 18.5849 1.33777 0.668886 0.743365i \(-0.266772\pi\)
0.668886 + 0.743365i \(0.266772\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 25.8055 1.83857 0.919284 0.393596i \(-0.128769\pi\)
0.919284 + 0.393596i \(0.128769\pi\)
\(198\) 0 0
\(199\) − 1.79246i − 0.127064i −0.997980 0.0635319i \(-0.979764\pi\)
0.997980 0.0635319i \(-0.0202365\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 9.21265i 0.646601i
\(204\) 0 0
\(205\) − 20.7649i − 1.45028i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0.888520i 0.0614602i
\(210\) 0 0
\(211\) 0.288533 0.0198634 0.00993170 0.999951i \(-0.496839\pi\)
0.00993170 + 0.999951i \(0.496839\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 42.6572 2.90920
\(216\) 0 0
\(217\) 27.9772 1.89922
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −17.5199 −1.17852
\(222\) 0 0
\(223\) 1.85309i 0.124092i 0.998073 + 0.0620460i \(0.0197625\pi\)
−0.998073 + 0.0620460i \(0.980237\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 6.13473i 0.407176i 0.979057 + 0.203588i \(0.0652603\pi\)
−0.979057 + 0.203588i \(0.934740\pi\)
\(228\) 0 0
\(229\) 21.3662i 1.41192i 0.708253 + 0.705959i \(0.249484\pi\)
−0.708253 + 0.705959i \(0.750516\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 14.0325i 0.919303i 0.888099 + 0.459651i \(0.152026\pi\)
−0.888099 + 0.459651i \(0.847974\pi\)
\(234\) 0 0
\(235\) −37.9341 −2.47455
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 6.35219 0.410889 0.205445 0.978669i \(-0.434136\pi\)
0.205445 + 0.978669i \(0.434136\pi\)
\(240\) 0 0
\(241\) −11.7769 −0.758616 −0.379308 0.925270i \(-0.623838\pi\)
−0.379308 + 0.925270i \(0.623838\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −33.1054 −2.11502
\(246\) 0 0
\(247\) − 9.28436i − 0.590750i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) − 5.24621i − 0.331138i −0.986198 0.165569i \(-0.947054\pi\)
0.986198 0.165569i \(-0.0529460\pi\)
\(252\) 0 0
\(253\) − 4.01202i − 0.252233i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 21.8395i 1.36231i 0.732140 + 0.681155i \(0.238522\pi\)
−0.732140 + 0.681155i \(0.761478\pi\)
\(258\) 0 0
\(259\) −24.0170 −1.49235
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 9.52766 0.587501 0.293750 0.955882i \(-0.405097\pi\)
0.293750 + 0.955882i \(0.405097\pi\)
\(264\) 0 0
\(265\) 22.3498 1.37294
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −15.4565 −0.942397 −0.471198 0.882027i \(-0.656178\pi\)
−0.471198 + 0.882027i \(0.656178\pi\)
\(270\) 0 0
\(271\) − 16.2765i − 0.988728i −0.869255 0.494364i \(-0.835401\pi\)
0.869255 0.494364i \(-0.164599\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 5.33083i 0.321461i
\(276\) 0 0
\(277\) − 12.6878i − 0.762338i −0.924505 0.381169i \(-0.875522\pi\)
0.924505 0.381169i \(-0.124478\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) − 7.33452i − 0.437541i −0.975776 0.218770i \(-0.929795\pi\)
0.975776 0.218770i \(-0.0702045\pi\)
\(282\) 0 0
\(283\) −6.84022 −0.406609 −0.203304 0.979116i \(-0.565168\pi\)
−0.203304 + 0.979116i \(0.565168\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −19.9922 −1.18010
\(288\) 0 0
\(289\) 4.19615 0.246832
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 22.9969 1.34349 0.671747 0.740781i \(-0.265544\pi\)
0.671747 + 0.740781i \(0.265544\pi\)
\(294\) 0 0
\(295\) 25.3654i 1.47683i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 41.9225i 2.42444i
\(300\) 0 0
\(301\) − 41.0698i − 2.36723i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) − 3.98040i − 0.227917i
\(306\) 0 0
\(307\) 19.3654 1.10524 0.552619 0.833434i \(-0.313628\pi\)
0.552619 + 0.833434i \(0.313628\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −16.9142 −0.959119 −0.479559 0.877509i \(-0.659204\pi\)
−0.479559 + 0.877509i \(0.659204\pi\)
\(312\) 0 0
\(313\) 6.78044 0.383253 0.191627 0.981468i \(-0.438624\pi\)
0.191627 + 0.981468i \(0.438624\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −8.77583 −0.492900 −0.246450 0.969156i \(-0.579264\pi\)
−0.246450 + 0.969156i \(0.579264\pi\)
\(318\) 0 0
\(319\) − 1.10794i − 0.0620328i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) − 6.78517i − 0.377537i
\(324\) 0 0
\(325\) − 55.7031i − 3.08985i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 36.5225i 2.01355i
\(330\) 0 0
\(331\) −17.8722 −0.982345 −0.491172 0.871062i \(-0.663431\pi\)
−0.491172 + 0.871062i \(0.663431\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −51.5907 −2.81870
\(336\) 0 0
\(337\) 3.98798 0.217239 0.108620 0.994083i \(-0.465357\pi\)
0.108620 + 0.994083i \(0.465357\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −3.36463 −0.182205
\(342\) 0 0
\(343\) 4.59985i 0.248369i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 22.0353i 1.18292i 0.806335 + 0.591458i \(0.201448\pi\)
−0.806335 + 0.591458i \(0.798552\pi\)
\(348\) 0 0
\(349\) − 4.25239i − 0.227625i −0.993502 0.113813i \(-0.963694\pi\)
0.993502 0.113813i \(-0.0363063\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) − 1.81516i − 0.0966112i −0.998833 0.0483056i \(-0.984618\pi\)
0.998833 0.0483056i \(-0.0153821\pi\)
\(354\) 0 0
\(355\) 12.2574 0.650556
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 20.8880 1.10243 0.551213 0.834365i \(-0.314165\pi\)
0.551213 + 0.834365i \(0.314165\pi\)
\(360\) 0 0
\(361\) −15.4043 −0.810754
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 18.5518 0.971045
\(366\) 0 0
\(367\) − 14.1727i − 0.739811i −0.929069 0.369906i \(-0.879390\pi\)
0.929069 0.369906i \(-0.120610\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) − 21.5181i − 1.11716i
\(372\) 0 0
\(373\) − 29.3462i − 1.51949i −0.650221 0.759745i \(-0.725324\pi\)
0.650221 0.759745i \(-0.274676\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 11.5772i 0.596254i
\(378\) 0 0
\(379\) −7.74761 −0.397968 −0.198984 0.980003i \(-0.563764\pi\)
−0.198984 + 0.980003i \(0.563764\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 36.0948 1.84436 0.922180 0.386762i \(-0.126406\pi\)
0.922180 + 0.386762i \(0.126406\pi\)
\(384\) 0 0
\(385\) 7.38814 0.376534
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 29.3765 1.48945 0.744723 0.667373i \(-0.232581\pi\)
0.744723 + 0.667373i \(0.232581\pi\)
\(390\) 0 0
\(391\) 30.6377i 1.54941i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) − 47.2534i − 2.37757i
\(396\) 0 0
\(397\) 1.33275i 0.0668889i 0.999441 + 0.0334444i \(0.0106477\pi\)
−0.999441 + 0.0334444i \(0.989352\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) − 31.2133i − 1.55872i −0.626578 0.779358i \(-0.715545\pi\)
0.626578 0.779358i \(-0.284455\pi\)
\(402\) 0 0
\(403\) 35.1578 1.75134
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 2.88836 0.143171
\(408\) 0 0
\(409\) −10.9575 −0.541813 −0.270906 0.962606i \(-0.587323\pi\)
−0.270906 + 0.962606i \(0.587323\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 24.4214 1.20170
\(414\) 0 0
\(415\) 22.9299i 1.12558i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 18.1535i 0.886855i 0.896310 + 0.443428i \(0.146238\pi\)
−0.896310 + 0.443428i \(0.853762\pi\)
\(420\) 0 0
\(421\) − 18.6127i − 0.907128i −0.891224 0.453564i \(-0.850152\pi\)
0.891224 0.453564i \(-0.149848\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) − 40.7088i − 1.97467i
\(426\) 0 0
\(427\) −3.83228 −0.185457
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 25.0852 1.20831 0.604156 0.796866i \(-0.293510\pi\)
0.604156 + 0.796866i \(0.293510\pi\)
\(432\) 0 0
\(433\) 25.3492 1.21820 0.609102 0.793092i \(-0.291530\pi\)
0.609102 + 0.793092i \(0.291530\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −16.2359 −0.776668
\(438\) 0 0
\(439\) − 29.3342i − 1.40005i −0.714120 0.700023i \(-0.753173\pi\)
0.714120 0.700023i \(-0.246827\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) − 20.4404i − 0.971154i −0.874194 0.485577i \(-0.838610\pi\)
0.874194 0.485577i \(-0.161390\pi\)
\(444\) 0 0
\(445\) 12.8531i 0.609295i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) − 40.0304i − 1.88915i −0.328291 0.944577i \(-0.606473\pi\)
0.328291 0.944577i \(-0.393527\pi\)
\(450\) 0 0
\(451\) 2.40432 0.113215
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −77.2004 −3.61921
\(456\) 0 0
\(457\) 19.9737 0.934329 0.467164 0.884170i \(-0.345276\pi\)
0.467164 + 0.884170i \(0.345276\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −11.6016 −0.540341 −0.270171 0.962812i \(-0.587080\pi\)
−0.270171 + 0.962812i \(0.587080\pi\)
\(462\) 0 0
\(463\) 12.3732i 0.575031i 0.957776 + 0.287516i \(0.0928293\pi\)
−0.957776 + 0.287516i \(0.907171\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) − 16.1873i − 0.749058i −0.927215 0.374529i \(-0.877804\pi\)
0.927215 0.374529i \(-0.122196\pi\)
\(468\) 0 0
\(469\) 49.6709i 2.29359i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 4.93918i 0.227104i
\(474\) 0 0
\(475\) 21.5729 0.989832
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 1.46203 0.0668020 0.0334010 0.999442i \(-0.489366\pi\)
0.0334010 + 0.999442i \(0.489366\pi\)
\(480\) 0 0
\(481\) −30.1812 −1.37614
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 2.47611 0.112434
\(486\) 0 0
\(487\) 15.7577i 0.714048i 0.934095 + 0.357024i \(0.116208\pi\)
−0.934095 + 0.357024i \(0.883792\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) − 5.79940i − 0.261723i −0.991401 0.130862i \(-0.958226\pi\)
0.991401 0.130862i \(-0.0417744\pi\)
\(492\) 0 0
\(493\) 8.46078i 0.381055i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) − 11.8013i − 0.529360i
\(498\) 0 0
\(499\) −37.0540 −1.65877 −0.829383 0.558680i \(-0.811308\pi\)
−0.829383 + 0.558680i \(0.811308\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −1.98721 −0.0886055 −0.0443027 0.999018i \(-0.514107\pi\)
−0.0443027 + 0.999018i \(0.514107\pi\)
\(504\) 0 0
\(505\) −33.5304 −1.49208
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 19.8358 0.879206 0.439603 0.898192i \(-0.355119\pi\)
0.439603 + 0.898192i \(0.355119\pi\)
\(510\) 0 0
\(511\) − 17.8614i − 0.790143i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 8.09364i 0.356648i
\(516\) 0 0
\(517\) − 4.39230i − 0.193173i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) − 10.8050i − 0.473376i −0.971586 0.236688i \(-0.923938\pi\)
0.971586 0.236688i \(-0.0760619\pi\)
\(522\) 0 0
\(523\) 35.0092 1.53085 0.765423 0.643528i \(-0.222530\pi\)
0.765423 + 0.643528i \(0.222530\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 25.6939 1.11924
\(528\) 0 0
\(529\) 50.3114 2.18745
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −25.1233 −1.08821
\(534\) 0 0
\(535\) 17.2117i 0.744127i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) − 3.83320i − 0.165108i
\(540\) 0 0
\(541\) − 33.3973i − 1.43586i −0.696114 0.717932i \(-0.745089\pi\)
0.696114 0.717932i \(-0.254911\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) − 38.1215i − 1.63294i
\(546\) 0 0
\(547\) 1.11664 0.0477441 0.0238720 0.999715i \(-0.492401\pi\)
0.0238720 + 0.999715i \(0.492401\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −4.48364 −0.191010
\(552\) 0 0
\(553\) −45.4950 −1.93464
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 7.55480 0.320107 0.160054 0.987108i \(-0.448833\pi\)
0.160054 + 0.987108i \(0.448833\pi\)
\(558\) 0 0
\(559\) − 51.6107i − 2.18290i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) − 43.3715i − 1.82789i −0.405836 0.913946i \(-0.633019\pi\)
0.405836 0.913946i \(-0.366981\pi\)
\(564\) 0 0
\(565\) 39.8459i 1.67633i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 25.8719i 1.08461i 0.840182 + 0.542304i \(0.182448\pi\)
−0.840182 + 0.542304i \(0.817552\pi\)
\(570\) 0 0
\(571\) −19.0370 −0.796674 −0.398337 0.917239i \(-0.630412\pi\)
−0.398337 + 0.917239i \(0.630412\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −97.4101 −4.06228
\(576\) 0 0
\(577\) 16.5418 0.688643 0.344321 0.938852i \(-0.388109\pi\)
0.344321 + 0.938852i \(0.388109\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 22.0766 0.915893
\(582\) 0 0
\(583\) 2.58783i 0.107177i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) − 15.8160i − 0.652794i −0.945233 0.326397i \(-0.894165\pi\)
0.945233 0.326397i \(-0.105835\pi\)
\(588\) 0 0
\(589\) 13.6160i 0.561039i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 26.7787i 1.09967i 0.835274 + 0.549834i \(0.185309\pi\)
−0.835274 + 0.549834i \(0.814691\pi\)
\(594\) 0 0
\(595\) −56.4194 −2.31297
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −16.6199 −0.679069 −0.339534 0.940594i \(-0.610269\pi\)
−0.339534 + 0.940594i \(0.610269\pi\)
\(600\) 0 0
\(601\) 20.0042 0.815987 0.407994 0.912985i \(-0.366229\pi\)
0.407994 + 0.912985i \(0.366229\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 43.6265 1.77367
\(606\) 0 0
\(607\) 2.42181i 0.0982984i 0.998791 + 0.0491492i \(0.0156510\pi\)
−0.998791 + 0.0491492i \(0.984349\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 45.8963i 1.85676i
\(612\) 0 0
\(613\) − 15.4102i − 0.622412i −0.950343 0.311206i \(-0.899267\pi\)
0.950343 0.311206i \(-0.100733\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) − 7.00200i − 0.281890i −0.990017 0.140945i \(-0.954986\pi\)
0.990017 0.140945i \(-0.0450141\pi\)
\(618\) 0 0
\(619\) −11.9253 −0.479317 −0.239659 0.970857i \(-0.577036\pi\)
−0.239659 + 0.970857i \(0.577036\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 12.3748 0.495786
\(624\) 0 0
\(625\) 47.5466 1.90186
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −22.0569 −0.879468
\(630\) 0 0
\(631\) 6.65500i 0.264932i 0.991188 + 0.132466i \(0.0422895\pi\)
−0.991188 + 0.132466i \(0.957711\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) − 57.8231i − 2.29464i
\(636\) 0 0
\(637\) 40.0540i 1.58700i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 38.6695i 1.52735i 0.645599 + 0.763677i \(0.276608\pi\)
−0.645599 + 0.763677i \(0.723392\pi\)
\(642\) 0 0
\(643\) 27.8236 1.09725 0.548627 0.836067i \(-0.315151\pi\)
0.548627 + 0.836067i \(0.315151\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 5.30252 0.208464 0.104232 0.994553i \(-0.466762\pi\)
0.104232 + 0.994553i \(0.466762\pi\)
\(648\) 0 0
\(649\) −2.93700 −0.115287
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −24.0403 −0.940770 −0.470385 0.882461i \(-0.655885\pi\)
−0.470385 + 0.882461i \(0.655885\pi\)
\(654\) 0 0
\(655\) − 70.9989i − 2.77416i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 32.5078i 1.26632i 0.774019 + 0.633162i \(0.218243\pi\)
−0.774019 + 0.633162i \(0.781757\pi\)
\(660\) 0 0
\(661\) − 43.8787i − 1.70668i −0.521352 0.853342i \(-0.674572\pi\)
0.521352 0.853342i \(-0.325428\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) − 29.8984i − 1.15941i
\(666\) 0 0
\(667\) 20.2454 0.783905
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0.460881 0.0177921
\(672\) 0 0
\(673\) −24.0162 −0.925756 −0.462878 0.886422i \(-0.653183\pi\)
−0.462878 + 0.886422i \(0.653183\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 18.3455 0.705073 0.352537 0.935798i \(-0.385319\pi\)
0.352537 + 0.935798i \(0.385319\pi\)
\(678\) 0 0
\(679\) − 2.38397i − 0.0914882i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 50.4847i 1.93174i 0.259018 + 0.965872i \(0.416601\pi\)
−0.259018 + 0.965872i \(0.583399\pi\)
\(684\) 0 0
\(685\) 47.4733i 1.81386i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) − 27.0409i − 1.03018i
\(690\) 0 0
\(691\) 27.5020 1.04622 0.523112 0.852264i \(-0.324771\pi\)
0.523112 + 0.852264i \(0.324771\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −23.3082 −0.884129
\(696\) 0 0
\(697\) −18.3606 −0.695456
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 6.33376 0.239223 0.119611 0.992821i \(-0.461835\pi\)
0.119611 + 0.992821i \(0.461835\pi\)
\(702\) 0 0
\(703\) − 11.6887i − 0.440847i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 32.2826i 1.21411i
\(708\) 0 0
\(709\) 12.1008i 0.454457i 0.973841 + 0.227228i \(0.0729664\pi\)
−0.973841 + 0.227228i \(0.927034\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) − 61.4817i − 2.30251i
\(714\) 0 0
\(715\) 9.28436 0.347215
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −9.82136 −0.366275 −0.183137 0.983087i \(-0.558625\pi\)
−0.183137 + 0.983087i \(0.558625\pi\)
\(720\) 0 0
\(721\) 7.79246 0.290206
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −26.9004 −0.999055
\(726\) 0 0
\(727\) 39.8494i 1.47793i 0.673742 + 0.738966i \(0.264686\pi\)
−0.673742 + 0.738966i \(0.735314\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) − 37.7180i − 1.39505i
\(732\) 0 0
\(733\) 21.4330i 0.791645i 0.918327 + 0.395823i \(0.129540\pi\)
−0.918327 + 0.395823i \(0.870460\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) − 5.97358i − 0.220040i
\(738\) 0 0
\(739\) −27.3791 −1.00716 −0.503578 0.863950i \(-0.667983\pi\)
−0.503578 + 0.863950i \(0.667983\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 14.8229 0.543799 0.271900 0.962326i \(-0.412348\pi\)
0.271900 + 0.962326i \(0.412348\pi\)
\(744\) 0 0
\(745\) −77.7079 −2.84700
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 16.5712 0.605499
\(750\) 0 0
\(751\) − 11.4571i − 0.418076i −0.977908 0.209038i \(-0.932967\pi\)
0.977908 0.209038i \(-0.0670332\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 31.5347i 1.14766i
\(756\) 0 0
\(757\) 33.0507i 1.20125i 0.799531 + 0.600624i \(0.205081\pi\)
−0.799531 + 0.600624i \(0.794919\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 8.12860i 0.294662i 0.989087 + 0.147331i \(0.0470682\pi\)
−0.989087 + 0.147331i \(0.952932\pi\)
\(762\) 0 0
\(763\) −36.7029 −1.32873
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 30.6894 1.10813
\(768\) 0 0
\(769\) −19.5771 −0.705967 −0.352984 0.935630i \(-0.614833\pi\)
−0.352984 + 0.935630i \(0.614833\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 37.7684 1.35843 0.679217 0.733938i \(-0.262320\pi\)
0.679217 + 0.733938i \(0.262320\pi\)
\(774\) 0 0
\(775\) 81.6917i 2.93445i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) − 9.72985i − 0.348608i
\(780\) 0 0
\(781\) 1.41926i 0.0507851i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 39.4042i 1.40640i
\(786\) 0 0
\(787\) −2.03615 −0.0725807 −0.0362904 0.999341i \(-0.511554\pi\)
−0.0362904 + 0.999341i \(0.511554\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 38.3631 1.36404
\(792\) 0 0
\(793\) −4.81586 −0.171016
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −33.2487 −1.17773 −0.588865 0.808231i \(-0.700425\pi\)
−0.588865 + 0.808231i \(0.700425\pi\)
\(798\) 0 0
\(799\) 33.5418i 1.18662i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 2.14807i 0.0758038i
\(804\) 0 0
\(805\) 135.003i 4.75824i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 17.3485i 0.609942i 0.952362 + 0.304971i \(0.0986468\pi\)
−0.952362 + 0.304971i \(0.901353\pi\)
\(810\) 0 0
\(811\) 40.9868 1.43924 0.719620 0.694368i \(-0.244316\pi\)
0.719620 + 0.694368i \(0.244316\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 37.2850 1.30604
\(816\) 0 0
\(817\) 19.9880 0.699291
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 4.85801 0.169546 0.0847729 0.996400i \(-0.472984\pi\)
0.0847729 + 0.996400i \(0.472984\pi\)
\(822\) 0 0
\(823\) 28.0083i 0.976309i 0.872757 + 0.488155i \(0.162330\pi\)
−0.872757 + 0.488155i \(0.837670\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 3.46917i 0.120635i 0.998179 + 0.0603174i \(0.0192113\pi\)
−0.998179 + 0.0603174i \(0.980789\pi\)
\(828\) 0 0
\(829\) 14.6239i 0.507908i 0.967216 + 0.253954i \(0.0817312\pi\)
−0.967216 + 0.253954i \(0.918269\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 29.2722i 1.01422i
\(834\) 0 0
\(835\) 31.9046 1.10410
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 15.3680 0.530562 0.265281 0.964171i \(-0.414535\pi\)
0.265281 + 0.964171i \(0.414535\pi\)
\(840\) 0 0
\(841\) −23.4091 −0.807211
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −44.4059 −1.52761
\(846\) 0 0
\(847\) − 42.0030i − 1.44324i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 52.7790i 1.80924i
\(852\) 0 0
\(853\) − 0.874295i − 0.0299353i −0.999888 0.0149676i \(-0.995235\pi\)
0.999888 0.0149676i \(-0.00476453\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 34.7031i 1.18543i 0.805411 + 0.592717i \(0.201945\pi\)
−0.805411 + 0.592717i \(0.798055\pi\)
\(858\) 0 0
\(859\) 39.4933 1.34749 0.673746 0.738963i \(-0.264684\pi\)
0.673746 + 0.738963i \(0.264684\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −28.1903 −0.959611 −0.479805 0.877375i \(-0.659293\pi\)
−0.479805 + 0.877375i \(0.659293\pi\)
\(864\) 0 0
\(865\) −82.8574 −2.81724
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 5.47136 0.185603
\(870\) 0 0
\(871\) 62.4194i 2.11500i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) − 100.544i − 3.39901i
\(876\) 0 0
\(877\) − 34.5026i − 1.16507i −0.812806 0.582535i \(-0.802061\pi\)
0.812806 0.582535i \(-0.197939\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 21.7178i 0.731690i 0.930676 + 0.365845i \(0.119220\pi\)
−0.930676 + 0.365845i \(0.880780\pi\)
\(882\) 0 0
\(883\) 10.8314 0.364506 0.182253 0.983252i \(-0.441661\pi\)
0.182253 + 0.983252i \(0.441661\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 11.1435 0.374164 0.187082 0.982344i \(-0.440097\pi\)
0.187082 + 0.982344i \(0.440097\pi\)
\(888\) 0 0
\(889\) −55.6714 −1.86716
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −17.7749 −0.594813
\(894\) 0 0
\(895\) − 77.4531i − 2.58897i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) − 16.9785i − 0.566266i
\(900\) 0 0
\(901\) − 19.7620i − 0.658366i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 45.6861i 1.51866i
\(906\) 0 0
\(907\) −10.7103 −0.355631 −0.177816 0.984064i \(-0.556903\pi\)
−0.177816 + 0.984064i \(0.556903\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 21.5384 0.713600 0.356800 0.934181i \(-0.383868\pi\)
0.356800 + 0.934181i \(0.383868\pi\)
\(912\) 0 0
\(913\) −2.65500 −0.0878678
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −68.3569 −2.25734
\(918\) 0 0
\(919\) − 15.5159i − 0.511824i −0.966700 0.255912i \(-0.917624\pi\)
0.966700 0.255912i \(-0.0823757\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) − 14.8302i − 0.488141i
\(924\) 0 0
\(925\) − 70.1283i − 2.30580i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 31.9098i 1.04693i 0.852048 + 0.523464i \(0.175360\pi\)
−0.852048 + 0.523464i \(0.824640\pi\)
\(930\) 0 0
\(931\) −15.5123 −0.508394
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 6.78517 0.221899
\(936\) 0 0
\(937\) −7.01911 −0.229304 −0.114652 0.993406i \(-0.536575\pi\)
−0.114652 + 0.993406i \(0.536575\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −11.7306 −0.382407 −0.191204 0.981550i \(-0.561239\pi\)
−0.191204 + 0.981550i \(0.561239\pi\)
\(942\) 0 0
\(943\) 43.9341i 1.43069i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 5.92535i 0.192548i 0.995355 + 0.0962741i \(0.0306925\pi\)
−0.995355 + 0.0962741i \(0.969307\pi\)
\(948\) 0 0
\(949\) − 22.4457i − 0.728619i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) − 8.28906i − 0.268509i −0.990947 0.134255i \(-0.957136\pi\)
0.990947 0.134255i \(-0.0428640\pi\)
\(954\) 0 0
\(955\) 80.0030 2.58884
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 45.7067 1.47595
\(960\) 0 0
\(961\) −20.5609 −0.663254
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 75.2098 2.42109
\(966\) 0 0
\(967\) 38.6688i 1.24351i 0.783214 + 0.621753i \(0.213579\pi\)
−0.783214 + 0.621753i \(0.786421\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 36.9214i 1.18486i 0.805620 + 0.592432i \(0.201832\pi\)
−0.805620 + 0.592432i \(0.798168\pi\)
\(972\) 0 0
\(973\) 22.4408i 0.719420i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 41.9613i 1.34246i 0.741248 + 0.671231i \(0.234234\pi\)
−0.741248 + 0.671231i \(0.765766\pi\)
\(978\) 0 0
\(979\) −1.48823 −0.0475641
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 34.8430 1.11132 0.555659 0.831410i \(-0.312466\pi\)
0.555659 + 0.831410i \(0.312466\pi\)
\(984\) 0 0
\(985\) 104.430 3.32743
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −90.2536 −2.86990
\(990\) 0 0
\(991\) 36.9678i 1.17432i 0.809471 + 0.587160i \(0.199754\pi\)
−0.809471 + 0.587160i \(0.800246\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) − 7.25374i − 0.229959i
\(996\) 0 0
\(997\) − 9.65401i − 0.305746i −0.988246 0.152873i \(-0.951148\pi\)
0.988246 0.152873i \(-0.0488525\pi\)
\(998\) 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.f.b.2591.15 yes 16
3.2 odd 2 inner 5184.2.f.b.2591.1 16
4.3 odd 2 5184.2.f.e.2591.16 yes 16
8.3 odd 2 inner 5184.2.f.b.2591.2 yes 16
8.5 even 2 5184.2.f.e.2591.1 yes 16
12.11 even 2 5184.2.f.e.2591.2 yes 16
24.5 odd 2 5184.2.f.e.2591.15 yes 16
24.11 even 2 inner 5184.2.f.b.2591.16 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5184.2.f.b.2591.1 16 3.2 odd 2 inner
5184.2.f.b.2591.2 yes 16 8.3 odd 2 inner
5184.2.f.b.2591.15 yes 16 1.1 even 1 trivial
5184.2.f.b.2591.16 yes 16 24.11 even 2 inner
5184.2.f.e.2591.1 yes 16 8.5 even 2
5184.2.f.e.2591.2 yes 16 12.11 even 2
5184.2.f.e.2591.15 yes 16 24.5 odd 2
5184.2.f.e.2591.16 yes 16 4.3 odd 2