Properties

Label 5184.2.f.e.2591.6
Level $5184$
Weight $2$
Character 5184.2591
Analytic conductor $41.394$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

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 2591.6
Root \(0.670418 + 0.387066i\) of defining polynomial
Character \(\chi\) \(=\) 5184.2591
Dual form 5184.2.f.e.2591.5

$q$-expansion

\(f(q)\) \(=\) \(q-1.59733 q^{5} +1.16418i q^{7} +O(q^{10})\) \(q-1.59733 q^{5} +1.16418i q^{7} +1.98092i q^{11} -0.164177i q^{13} -3.57825i q^{17} +3.16418 q^{19} -1.21374 q^{23} -2.44854 q^{25} -4.98396 q^{29} -6.64469i q^{31} -1.85957i q^{35} +1.10377i q^{37} -2.02533i q^{41} +8.34477 q^{43} +2.21731 q^{47} +5.64469 q^{49} +9.65461 q^{53} -3.16418i q^{55} -0.888520i q^{59} +9.74846i q^{61} +0.262245i q^{65} +3.98359 q^{67} -12.8049 q^{71} +0.879814 q^{73} -2.30614 q^{77} -2.91179i q^{79} +13.9298i q^{83} +5.71564i q^{85} -8.41501i q^{89} +0.191131 q^{91} -5.05423 q^{95} +4.31634 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q+O(q^{10}) \) 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
\(5\) −1.59733 −0.714347 −0.357174 0.934038i \(-0.616260\pi\)
−0.357174 + 0.934038i \(0.616260\pi\)
\(6\) 0 0
\(7\) 1.16418i 0.440018i 0.975498 + 0.220009i \(0.0706086\pi\)
−0.975498 + 0.220009i \(0.929391\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.98092i 0.597269i 0.954368 + 0.298635i \(0.0965312\pi\)
−0.954368 + 0.298635i \(0.903469\pi\)
\(12\) 0 0
\(13\) − 0.164177i − 0.0455345i −0.999741 0.0227672i \(-0.992752\pi\)
0.999741 0.0227672i \(-0.00724766\pi\)
\(14\) 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
\(19\) 3.16418 0.725912 0.362956 0.931806i \(-0.381768\pi\)
0.362956 + 0.931806i \(0.381768\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.21374 −0.253082 −0.126541 0.991961i \(-0.540388\pi\)
−0.126541 + 0.991961i \(0.540388\pi\)
\(24\) 0 0
\(25\) −2.44854 −0.489708
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −4.98396 −0.925499 −0.462749 0.886489i \(-0.653137\pi\)
−0.462749 + 0.886489i \(0.653137\pi\)
\(30\) 0 0
\(31\) − 6.64469i − 1.19342i −0.802456 0.596711i \(-0.796474\pi\)
0.802456 0.596711i \(-0.203526\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) − 1.85957i − 0.314325i
\(36\) 0 0
\(37\) 1.10377i 0.181459i 0.995876 + 0.0907295i \(0.0289199\pi\)
−0.995876 + 0.0907295i \(0.971080\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) − 2.02533i − 0.316304i −0.987415 0.158152i \(-0.949446\pi\)
0.987415 0.158152i \(-0.0505536\pi\)
\(42\) 0 0
\(43\) 8.34477 1.27257 0.636283 0.771456i \(-0.280471\pi\)
0.636283 + 0.771456i \(0.280471\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 2.21731 0.323428 0.161714 0.986838i \(-0.448298\pi\)
0.161714 + 0.986838i \(0.448298\pi\)
\(48\) 0 0
\(49\) 5.64469 0.806385
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 9.65461 1.32616 0.663081 0.748548i \(-0.269248\pi\)
0.663081 + 0.748548i \(0.269248\pi\)
\(54\) 0 0
\(55\) − 3.16418i − 0.426658i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) − 0.888520i − 0.115675i −0.998326 0.0578377i \(-0.981579\pi\)
0.998326 0.0578377i \(-0.0184206\pi\)
\(60\) 0 0
\(61\) 9.74846i 1.24816i 0.781359 + 0.624081i \(0.214527\pi\)
−0.781359 + 0.624081i \(0.785473\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0.262245i 0.0325274i
\(66\) 0 0
\(67\) 3.98359 0.486673 0.243336 0.969942i \(-0.421758\pi\)
0.243336 + 0.969942i \(0.421758\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −12.8049 −1.51966 −0.759828 0.650124i \(-0.774717\pi\)
−0.759828 + 0.650124i \(0.774717\pi\)
\(72\) 0 0
\(73\) 0.879814 0.102974 0.0514872 0.998674i \(-0.483604\pi\)
0.0514872 + 0.998674i \(0.483604\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −2.30614 −0.262809
\(78\) 0 0
\(79\) − 2.91179i − 0.327602i −0.986493 0.163801i \(-0.947625\pi\)
0.986493 0.163801i \(-0.0523755\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 13.9298i 1.52899i 0.644630 + 0.764495i \(0.277012\pi\)
−0.644630 + 0.764495i \(0.722988\pi\)
\(84\) 0 0
\(85\) 5.71564i 0.619948i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) − 8.41501i − 0.891990i −0.895036 0.445995i \(-0.852850\pi\)
0.895036 0.445995i \(-0.147150\pi\)
\(90\) 0 0
\(91\) 0.191131 0.0200360
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −5.05423 −0.518553
\(96\) 0 0
\(97\) 4.31634 0.438258 0.219129 0.975696i \(-0.429678\pi\)
0.219129 + 0.975696i \(0.429678\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −11.3103 −1.12542 −0.562709 0.826655i \(-0.690241\pi\)
−0.562709 + 0.826655i \(0.690241\pi\)
\(102\) 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
\(107\) − 19.4306i − 1.87842i −0.343339 0.939211i \(-0.611558\pi\)
0.343339 0.939211i \(-0.388442\pi\)
\(108\) 0 0
\(109\) 10.7760i 1.03216i 0.856541 + 0.516079i \(0.172609\pi\)
−0.856541 + 0.516079i \(0.827391\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 4.46677i 0.420198i 0.977680 + 0.210099i \(0.0673786\pi\)
−0.977680 + 0.210099i \(0.932621\pi\)
\(114\) 0 0
\(115\) 1.93874 0.180789
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 4.16571 0.381870
\(120\) 0 0
\(121\) 7.07597 0.643270
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 11.8978 1.06417
\(126\) 0 0
\(127\) − 9.22813i − 0.818864i −0.912341 0.409432i \(-0.865727\pi\)
0.912341 0.409432i \(-0.134273\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 10.6764i 0.932799i 0.884574 + 0.466399i \(0.154449\pi\)
−0.884574 + 0.466399i \(0.845551\pi\)
\(132\) 0 0
\(133\) 3.68366i 0.319414i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 20.2163i 1.72719i 0.504182 + 0.863597i \(0.331794\pi\)
−0.504182 + 0.863597i \(0.668206\pi\)
\(138\) 0 0
\(139\) 13.1686 1.11694 0.558472 0.829523i \(-0.311388\pi\)
0.558472 + 0.829523i \(0.311388\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0.325221 0.0271963
\(144\) 0 0
\(145\) 7.96103 0.661128
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 5.99383 0.491033 0.245517 0.969392i \(-0.421042\pi\)
0.245517 + 0.969392i \(0.421042\pi\)
\(150\) 0 0
\(151\) − 2.32835i − 0.189479i −0.995502 0.0947394i \(-0.969798\pi\)
0.995502 0.0947394i \(-0.0302018\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 10.6138i 0.852518i
\(156\) 0 0
\(157\) 9.14861i 0.730139i 0.930980 + 0.365069i \(0.118955\pi\)
−0.930980 + 0.365069i \(0.881045\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) − 1.41301i − 0.111361i
\(162\) 0 0
\(163\) 22.1416 1.73427 0.867133 0.498077i \(-0.165960\pi\)
0.867133 + 0.498077i \(0.165960\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 21.4440 1.65939 0.829693 0.558220i \(-0.188516\pi\)
0.829693 + 0.558220i \(0.188516\pi\)
\(168\) 0 0
\(169\) 12.9730 0.997927
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −16.7481 −1.27334 −0.636668 0.771138i \(-0.719688\pi\)
−0.636668 + 0.771138i \(0.719688\pi\)
\(174\) 0 0
\(175\) − 2.85053i − 0.215480i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) − 16.1146i − 1.20446i −0.798323 0.602229i \(-0.794279\pi\)
0.798323 0.602229i \(-0.205721\pi\)
\(180\) 0 0
\(181\) 16.3612i 1.21612i 0.793892 + 0.608059i \(0.208051\pi\)
−0.793892 + 0.608059i \(0.791949\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) − 1.76309i − 0.129625i
\(186\) 0 0
\(187\) 7.08821 0.518341
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 18.6326 1.34820 0.674102 0.738638i \(-0.264531\pi\)
0.674102 + 0.738638i \(0.264531\pi\)
\(192\) 0 0
\(193\) −1.65671 −0.119252 −0.0596262 0.998221i \(-0.518991\pi\)
−0.0596262 + 0.998221i \(0.518991\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 11.8978 0.847681 0.423840 0.905737i \(-0.360682\pi\)
0.423840 + 0.905737i \(0.360682\pi\)
\(198\) 0 0
\(199\) 8.32835i 0.590381i 0.955438 + 0.295191i \(0.0953832\pi\)
−0.955438 + 0.295191i \(0.904617\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) − 5.80222i − 0.407236i
\(204\) 0 0
\(205\) 3.23512i 0.225951i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 6.26797i 0.433565i
\(210\) 0 0
\(211\) 4.77187 0.328509 0.164255 0.986418i \(-0.447478\pi\)
0.164255 + 0.986418i \(0.447478\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −13.3293 −0.909053
\(216\) 0 0
\(217\) 7.73560 0.525127
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −0.587465 −0.0395172
\(222\) 0 0
\(223\) − 24.4415i − 1.63673i −0.574701 0.818363i \(-0.694882\pi\)
0.574701 0.818363i \(-0.305118\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 15.9107i 1.05603i 0.849235 + 0.528014i \(0.177063\pi\)
−0.849235 + 0.528014i \(0.822937\pi\)
\(228\) 0 0
\(229\) 25.1700i 1.66328i 0.555312 + 0.831642i \(0.312599\pi\)
−0.555312 + 0.831642i \(0.687401\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) − 6.87605i − 0.450465i −0.974305 0.225233i \(-0.927686\pi\)
0.974305 0.225233i \(-0.0723142\pi\)
\(234\) 0 0
\(235\) −3.54177 −0.231040
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −16.8300 −1.08864 −0.544322 0.838876i \(-0.683213\pi\)
−0.544322 + 0.838876i \(0.683213\pi\)
\(240\) 0 0
\(241\) 12.1692 0.783887 0.391943 0.919989i \(-0.371803\pi\)
0.391943 + 0.919989i \(0.371803\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −9.01643 −0.576039
\(246\) 0 0
\(247\) − 0.519485i − 0.0330540i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) − 22.1787i − 1.39990i −0.714190 0.699952i \(-0.753205\pi\)
0.714190 0.699952i \(-0.246795\pi\)
\(252\) 0 0
\(253\) − 2.40432i − 0.151158i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 4.86892i 0.303715i 0.988402 + 0.151857i \(0.0485254\pi\)
−0.988402 + 0.151857i \(0.951475\pi\)
\(258\) 0 0
\(259\) −1.28499 −0.0798452
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 17.1807 1.05941 0.529705 0.848182i \(-0.322303\pi\)
0.529705 + 0.848182i \(0.322303\pi\)
\(264\) 0 0
\(265\) −15.4216 −0.947340
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 28.1844 1.71843 0.859216 0.511613i \(-0.170952\pi\)
0.859216 + 0.511613i \(0.170952\pi\)
\(270\) 0 0
\(271\) − 17.6324i − 1.07109i −0.844505 0.535547i \(-0.820105\pi\)
0.844505 0.535547i \(-0.179895\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) − 4.85035i − 0.292487i
\(276\) 0 0
\(277\) 20.0968i 1.20750i 0.797174 + 0.603749i \(0.206327\pi\)
−0.797174 + 0.603749i \(0.793673\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) − 5.06089i − 0.301908i −0.988541 0.150954i \(-0.951766\pi\)
0.988541 0.150954i \(-0.0482345\pi\)
\(282\) 0 0
\(283\) 9.55208 0.567812 0.283906 0.958852i \(-0.408370\pi\)
0.283906 + 0.958852i \(0.408370\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 2.35784 0.139179
\(288\) 0 0
\(289\) 4.19615 0.246832
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −6.33095 −0.369858 −0.184929 0.982752i \(-0.559206\pi\)
−0.184929 + 0.982752i \(0.559206\pi\)
\(294\) 0 0
\(295\) 1.41926i 0.0826324i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0.199268i 0.0115240i
\(300\) 0 0
\(301\) 9.71479i 0.559951i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) − 15.5715i − 0.891622i
\(306\) 0 0
\(307\) 4.58074 0.261437 0.130718 0.991420i \(-0.458272\pi\)
0.130718 + 0.991420i \(0.458272\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 24.0707 1.36493 0.682463 0.730920i \(-0.260909\pi\)
0.682463 + 0.730920i \(0.260909\pi\)
\(312\) 0 0
\(313\) 3.07597 0.173864 0.0869320 0.996214i \(-0.472294\pi\)
0.0869320 + 0.996214i \(0.472294\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −8.37060 −0.470140 −0.235070 0.971978i \(-0.575532\pi\)
−0.235070 + 0.971978i \(0.575532\pi\)
\(318\) 0 0
\(319\) − 9.87282i − 0.552772i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) − 11.3222i − 0.629984i
\(324\) 0 0
\(325\) 0.401994i 0.0222986i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 2.58134i 0.142314i
\(330\) 0 0
\(331\) 25.6445 1.40955 0.704774 0.709432i \(-0.251049\pi\)
0.704774 + 0.709432i \(0.251049\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −6.36310 −0.347653
\(336\) 0 0
\(337\) 10.4043 0.566759 0.283380 0.959008i \(-0.408544\pi\)
0.283380 + 0.959008i \(0.408544\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 13.1626 0.712794
\(342\) 0 0
\(343\) 14.7207i 0.794841i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0.971054i 0.0521289i 0.999660 + 0.0260644i \(0.00829751\pi\)
−0.999660 + 0.0260644i \(0.991702\pi\)
\(348\) 0 0
\(349\) − 9.57290i − 0.512425i −0.966620 0.256213i \(-0.917525\pi\)
0.966620 0.256213i \(-0.0824747\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 21.3671i 1.13725i 0.822596 + 0.568627i \(0.192525\pi\)
−0.822596 + 0.568627i \(0.807475\pi\)
\(354\) 0 0
\(355\) 20.4536 1.08556
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −23.5074 −1.24068 −0.620338 0.784335i \(-0.713004\pi\)
−0.620338 + 0.784335i \(0.713004\pi\)
\(360\) 0 0
\(361\) −8.98798 −0.473052
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −1.40535 −0.0735595
\(366\) 0 0
\(367\) − 10.4683i − 0.546439i −0.961952 0.273220i \(-0.911911\pi\)
0.961952 0.273220i \(-0.0880886\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 11.2397i 0.583535i
\(372\) 0 0
\(373\) − 28.6668i − 1.48431i −0.670229 0.742154i \(-0.733804\pi\)
0.670229 0.742154i \(-0.266196\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0.818252i 0.0421421i
\(378\) 0 0
\(379\) 21.5729 1.10813 0.554063 0.832475i \(-0.313077\pi\)
0.554063 + 0.832475i \(0.313077\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −22.9975 −1.17512 −0.587560 0.809181i \(-0.699911\pi\)
−0.587560 + 0.809181i \(0.699911\pi\)
\(384\) 0 0
\(385\) 3.68366 0.187737
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −19.0980 −0.968309 −0.484155 0.874982i \(-0.660873\pi\)
−0.484155 + 0.874982i \(0.660873\pi\)
\(390\) 0 0
\(391\) 4.34306i 0.219638i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 4.65109i 0.234022i
\(396\) 0 0
\(397\) 11.1366i 0.558930i 0.960156 + 0.279465i \(0.0901571\pi\)
−0.960156 + 0.279465i \(0.909843\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) − 2.65161i − 0.132415i −0.997806 0.0662075i \(-0.978910\pi\)
0.997806 0.0662075i \(-0.0210899\pi\)
\(402\) 0 0
\(403\) −1.09091 −0.0543419
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −2.18648 −0.108380
\(408\) 0 0
\(409\) 26.8139 1.32586 0.662931 0.748681i \(-0.269312\pi\)
0.662931 + 0.748681i \(0.269312\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 1.03439 0.0508992
\(414\) 0 0
\(415\) − 22.2504i − 1.09223i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 1.92291i 0.0939405i 0.998896 + 0.0469703i \(0.0149566\pi\)
−0.998896 + 0.0469703i \(0.985043\pi\)
\(420\) 0 0
\(421\) − 0.272971i − 0.0133038i −0.999978 0.00665189i \(-0.997883\pi\)
0.999978 0.00665189i \(-0.00211738\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 8.76148i 0.424994i
\(426\) 0 0
\(427\) −11.3489 −0.549214
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 33.5705 1.61703 0.808517 0.588473i \(-0.200271\pi\)
0.808517 + 0.588473i \(0.200271\pi\)
\(432\) 0 0
\(433\) 4.11494 0.197751 0.0988756 0.995100i \(-0.468475\pi\)
0.0988756 + 0.995100i \(0.468475\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −3.84049 −0.183716
\(438\) 0 0
\(439\) 22.2624i 1.06253i 0.847206 + 0.531264i \(0.178283\pi\)
−0.847206 + 0.531264i \(0.821717\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 25.8199i 1.22674i 0.789796 + 0.613370i \(0.210186\pi\)
−0.789796 + 0.613370i \(0.789814\pi\)
\(444\) 0 0
\(445\) 13.4415i 0.637190i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) − 11.4688i − 0.541245i −0.962686 0.270622i \(-0.912771\pi\)
0.962686 0.270622i \(-0.0872295\pi\)
\(450\) 0 0
\(451\) 4.01202 0.188918
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −0.305299 −0.0143126
\(456\) 0 0
\(457\) −20.5096 −0.959397 −0.479699 0.877433i \(-0.659254\pi\)
−0.479699 + 0.877433i \(0.659254\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 12.0821 0.562719 0.281359 0.959602i \(-0.409215\pi\)
0.281359 + 0.959602i \(0.409215\pi\)
\(462\) 0 0
\(463\) − 21.6937i − 1.00819i −0.863648 0.504096i \(-0.831826\pi\)
0.863648 0.504096i \(-0.168174\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 6.38932i 0.295662i 0.989013 + 0.147831i \(0.0472292\pi\)
−0.989013 + 0.147831i \(0.952771\pi\)
\(468\) 0 0
\(469\) 4.63760i 0.214144i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 16.5303i 0.760064i
\(474\) 0 0
\(475\) −7.74761 −0.355485
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 1.15743 0.0528841 0.0264421 0.999650i \(-0.491582\pi\)
0.0264421 + 0.999650i \(0.491582\pi\)
\(480\) 0 0
\(481\) 0.181214 0.00826264
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −6.89461 −0.313068
\(486\) 0 0
\(487\) − 8.18844i − 0.371053i −0.982639 0.185527i \(-0.940601\pi\)
0.982639 0.185527i \(-0.0593991\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 2.86944i 0.129496i 0.997902 + 0.0647479i \(0.0206243\pi\)
−0.997902 + 0.0647479i \(0.979376\pi\)
\(492\) 0 0
\(493\) 17.8339i 0.803196i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) − 14.9071i − 0.668675i
\(498\) 0 0
\(499\) −2.07327 −0.0928124 −0.0464062 0.998923i \(-0.514777\pi\)
−0.0464062 + 0.998923i \(0.514777\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −39.0342 −1.74045 −0.870224 0.492657i \(-0.836026\pi\)
−0.870224 + 0.492657i \(0.836026\pi\)
\(504\) 0 0
\(505\) 18.0663 0.803939
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −4.65838 −0.206479 −0.103239 0.994657i \(-0.532921\pi\)
−0.103239 + 0.994657i \(0.532921\pi\)
\(510\) 0 0
\(511\) 1.02426i 0.0453106i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) − 3.19466i − 0.140773i
\(516\) 0 0
\(517\) 4.39230i 0.193173i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) − 5.42555i − 0.237698i −0.992912 0.118849i \(-0.962080\pi\)
0.992912 0.118849i \(-0.0379204\pi\)
\(522\) 0 0
\(523\) −19.8280 −0.867017 −0.433508 0.901149i \(-0.642725\pi\)
−0.433508 + 0.901149i \(0.642725\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −23.7763 −1.03571
\(528\) 0 0
\(529\) −21.5268 −0.935949
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −0.332513 −0.0144027
\(534\) 0 0
\(535\) 31.0370i 1.34185i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 11.1817i 0.481629i
\(540\) 0 0
\(541\) 14.5116i 0.623904i 0.950098 + 0.311952i \(0.100983\pi\)
−0.950098 + 0.311952i \(0.899017\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) − 17.2129i − 0.737319i
\(546\) 0 0
\(547\) 22.8295 0.976117 0.488058 0.872811i \(-0.337705\pi\)
0.488058 + 0.872811i \(0.337705\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −15.7701 −0.671831
\(552\) 0 0
\(553\) 3.38984 0.144151
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −10.4848 −0.444254 −0.222127 0.975018i \(-0.571300\pi\)
−0.222127 + 0.975018i \(0.571300\pi\)
\(558\) 0 0
\(559\) − 1.37002i − 0.0579456i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 3.69923i 0.155904i 0.996957 + 0.0779519i \(0.0248381\pi\)
−0.996957 + 0.0779519i \(0.975162\pi\)
\(564\) 0 0
\(565\) − 7.13490i − 0.300167i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) − 25.8719i − 1.08461i −0.840182 0.542304i \(-0.817552\pi\)
0.840182 0.542304i \(-0.182448\pi\)
\(570\) 0 0
\(571\) 5.21171 0.218103 0.109052 0.994036i \(-0.465219\pi\)
0.109052 + 0.994036i \(0.465219\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 2.97189 0.123936
\(576\) 0 0
\(577\) −24.9341 −1.03802 −0.519010 0.854768i \(-0.673699\pi\)
−0.519010 + 0.854768i \(0.673699\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −16.2167 −0.672782
\(582\) 0 0
\(583\) 19.1250i 0.792076i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) − 12.0894i − 0.498982i −0.968377 0.249491i \(-0.919737\pi\)
0.968377 0.249491i \(-0.0802633\pi\)
\(588\) 0 0
\(589\) − 21.0250i − 0.866319i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 21.3992i 0.878760i 0.898301 + 0.439380i \(0.144802\pi\)
−0.898301 + 0.439380i \(0.855198\pi\)
\(594\) 0 0
\(595\) −6.65401 −0.272788
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 32.8504 1.34223 0.671116 0.741353i \(-0.265815\pi\)
0.671116 + 0.741353i \(0.265815\pi\)
\(600\) 0 0
\(601\) 23.7086 0.967096 0.483548 0.875318i \(-0.339348\pi\)
0.483548 + 0.875318i \(0.339348\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −11.3026 −0.459518
\(606\) 0 0
\(607\) − 41.4026i − 1.68048i −0.542216 0.840239i \(-0.682414\pi\)
0.542216 0.840239i \(-0.317586\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) − 0.364031i − 0.0147271i
\(612\) 0 0
\(613\) − 32.4820i − 1.31194i −0.754789 0.655968i \(-0.772261\pi\)
0.754789 0.655968i \(-0.227739\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) − 30.1842i − 1.21517i −0.794254 0.607586i \(-0.792138\pi\)
0.794254 0.607586i \(-0.207862\pi\)
\(618\) 0 0
\(619\) −24.8535 −0.998946 −0.499473 0.866329i \(-0.666473\pi\)
−0.499473 + 0.866329i \(0.666473\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 9.79656 0.392491
\(624\) 0 0
\(625\) −6.76196 −0.270478
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 3.94957 0.157480
\(630\) 0 0
\(631\) 31.5937i 1.25773i 0.777516 + 0.628863i \(0.216479\pi\)
−0.777516 + 0.628863i \(0.783521\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 14.7404i 0.584953i
\(636\) 0 0
\(637\) − 0.926728i − 0.0367183i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) − 1.48328i − 0.0585859i −0.999571 0.0292930i \(-0.990674\pi\)
0.999571 0.0292930i \(-0.00932558\pi\)
\(642\) 0 0
\(643\) −45.3533 −1.78856 −0.894280 0.447507i \(-0.852312\pi\)
−0.894280 + 0.447507i \(0.852312\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −15.0785 −0.592796 −0.296398 0.955065i \(-0.595785\pi\)
−0.296398 + 0.955065i \(0.595785\pi\)
\(648\) 0 0
\(649\) 1.76008 0.0690894
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 34.3187 1.34300 0.671498 0.741006i \(-0.265651\pi\)
0.671498 + 0.741006i \(0.265651\pi\)
\(654\) 0 0
\(655\) − 17.0537i − 0.666342i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) − 29.5778i − 1.15219i −0.817383 0.576094i \(-0.804576\pi\)
0.817383 0.576094i \(-0.195424\pi\)
\(660\) 0 0
\(661\) − 6.36203i − 0.247454i −0.992316 0.123727i \(-0.960515\pi\)
0.992316 0.123727i \(-0.0394848\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) − 5.88402i − 0.228173i
\(666\) 0 0
\(667\) 6.04924 0.234228
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −19.3109 −0.745489
\(672\) 0 0
\(673\) −21.3043 −0.821221 −0.410611 0.911811i \(-0.634684\pi\)
−0.410611 + 0.911811i \(0.634684\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 16.4279 0.631375 0.315687 0.948863i \(-0.397765\pi\)
0.315687 + 0.948863i \(0.397765\pi\)
\(678\) 0 0
\(679\) 5.02498i 0.192841i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) − 1.01447i − 0.0388177i −0.999812 0.0194089i \(-0.993822\pi\)
0.999812 0.0194089i \(-0.00617842\pi\)
\(684\) 0 0
\(685\) − 32.2921i − 1.23382i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) − 1.58506i − 0.0603861i
\(690\) 0 0
\(691\) 8.91349 0.339085 0.169543 0.985523i \(-0.445771\pi\)
0.169543 + 0.985523i \(0.445771\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −21.0345 −0.797886
\(696\) 0 0
\(697\) −7.24714 −0.274505
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −29.3401 −1.10816 −0.554080 0.832463i \(-0.686930\pi\)
−0.554080 + 0.832463i \(0.686930\pi\)
\(702\) 0 0
\(703\) 3.49253i 0.131723i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) − 13.1672i − 0.495203i
\(708\) 0 0
\(709\) 19.6175i 0.736751i 0.929677 + 0.368376i \(0.120086\pi\)
−0.929677 + 0.368376i \(0.879914\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 8.06493i 0.302034i
\(714\) 0 0
\(715\) −0.519485 −0.0194276
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 51.5446 1.92229 0.961145 0.276044i \(-0.0890235\pi\)
0.961145 + 0.276044i \(0.0890235\pi\)
\(720\) 0 0
\(721\) −2.32835 −0.0867124
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 12.2034 0.453224
\(726\) 0 0
\(727\) 27.3801i 1.01547i 0.861513 + 0.507735i \(0.169517\pi\)
−0.861513 + 0.507735i \(0.830483\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) − 29.8596i − 1.10440i
\(732\) 0 0
\(733\) 6.21759i 0.229652i 0.993386 + 0.114826i \(0.0366310\pi\)
−0.993386 + 0.114826i \(0.963369\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 7.89116i 0.290674i
\(738\) 0 0
\(739\) −48.1637 −1.77173 −0.885865 0.463943i \(-0.846434\pi\)
−0.885865 + 0.463943i \(0.846434\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 29.5198 1.08298 0.541489 0.840708i \(-0.317861\pi\)
0.541489 + 0.840708i \(0.317861\pi\)
\(744\) 0 0
\(745\) −9.57411 −0.350768
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 22.6206 0.826539
\(750\) 0 0
\(751\) 1.01224i 0.0369373i 0.999829 + 0.0184686i \(0.00587909\pi\)
−0.999829 + 0.0184686i \(0.994121\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 3.71915i 0.135354i
\(756\) 0 0
\(757\) 32.3712i 1.17655i 0.808660 + 0.588276i \(0.200193\pi\)
−0.808660 + 0.588276i \(0.799807\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 38.1317i 1.38227i 0.722724 + 0.691136i \(0.242890\pi\)
−0.722724 + 0.691136i \(0.757110\pi\)
\(762\) 0 0
\(763\) −12.5452 −0.454167
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −0.145874 −0.00526722
\(768\) 0 0
\(769\) −9.45626 −0.341001 −0.170501 0.985358i \(-0.554538\pi\)
−0.170501 + 0.985358i \(0.554538\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −39.7374 −1.42925 −0.714627 0.699506i \(-0.753404\pi\)
−0.714627 + 0.699506i \(0.753404\pi\)
\(774\) 0 0
\(775\) 16.2698i 0.584428i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) − 6.40851i − 0.229609i
\(780\) 0 0
\(781\) − 25.3654i − 0.907644i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) − 14.6133i − 0.521573i
\(786\) 0 0
\(787\) 10.8010 0.385015 0.192507 0.981296i \(-0.438338\pi\)
0.192507 + 0.981296i \(0.438338\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −5.20011 −0.184894
\(792\) 0 0
\(793\) 1.60047 0.0568345
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −13.2916 −0.470812 −0.235406 0.971897i \(-0.575642\pi\)
−0.235406 + 0.971897i \(0.575642\pi\)
\(798\) 0 0
\(799\) − 7.93408i − 0.280687i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 1.74284i 0.0615035i
\(804\) 0 0
\(805\) 2.25704i 0.0795502i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 16.5163i 0.580684i 0.956923 + 0.290342i \(0.0937690\pi\)
−0.956923 + 0.290342i \(0.906231\pi\)
\(810\) 0 0
\(811\) 34.5560 1.21342 0.606712 0.794921i \(-0.292488\pi\)
0.606712 + 0.794921i \(0.292488\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −35.3675 −1.23887
\(816\) 0 0
\(817\) 26.4043 0.923770
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 46.5813 1.62570 0.812849 0.582475i \(-0.197915\pi\)
0.812849 + 0.582475i \(0.197915\pi\)
\(822\) 0 0
\(823\) 35.4173i 1.23457i 0.786740 + 0.617284i \(0.211767\pi\)
−0.786740 + 0.617284i \(0.788233\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 34.7146i 1.20714i 0.797308 + 0.603572i \(0.206257\pi\)
−0.797308 + 0.603572i \(0.793743\pi\)
\(828\) 0 0
\(829\) − 11.9120i − 0.413721i −0.978370 0.206861i \(-0.933675\pi\)
0.978370 0.206861i \(-0.0663247\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) − 20.1981i − 0.699823i
\(834\) 0 0
\(835\) −34.2531 −1.18538
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −7.50962 −0.259261 −0.129630 0.991562i \(-0.541379\pi\)
−0.129630 + 0.991562i \(0.541379\pi\)
\(840\) 0 0
\(841\) −4.16011 −0.143452
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −20.7222 −0.712866
\(846\) 0 0
\(847\) 8.23768i 0.283050i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) − 1.33969i − 0.0459241i
\(852\) 0 0
\(853\) − 47.0179i − 1.60986i −0.593369 0.804931i \(-0.702202\pi\)
0.593369 0.804931i \(-0.297798\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) − 29.4641i − 1.00648i −0.864148 0.503238i \(-0.832142\pi\)
0.864148 0.503238i \(-0.167858\pi\)
\(858\) 0 0
\(859\) −35.7888 −1.22110 −0.610549 0.791979i \(-0.709051\pi\)
−0.610549 + 0.791979i \(0.709051\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 47.0404 1.60127 0.800636 0.599151i \(-0.204495\pi\)
0.800636 + 0.599151i \(0.204495\pi\)
\(864\) 0 0
\(865\) 26.7523 0.909604
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 5.76801 0.195666
\(870\) 0 0
\(871\) − 0.654013i − 0.0221604i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 13.8511i 0.468253i
\(876\) 0 0
\(877\) − 18.4500i − 0.623013i −0.950244 0.311506i \(-0.899166\pi\)
0.950244 0.311506i \(-0.100834\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 14.0647i 0.473852i 0.971528 + 0.236926i \(0.0761398\pi\)
−0.971528 + 0.236926i \(0.923860\pi\)
\(882\) 0 0
\(883\) −18.2404 −0.613837 −0.306919 0.951736i \(-0.599298\pi\)
−0.306919 + 0.951736i \(0.599298\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 37.7362 1.26706 0.633529 0.773719i \(-0.281606\pi\)
0.633529 + 0.773719i \(0.281606\pi\)
\(888\) 0 0
\(889\) 10.7432 0.360314
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 7.01596 0.234780
\(894\) 0 0
\(895\) 25.7403i 0.860402i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 33.1169i 1.10451i
\(900\) 0 0
\(901\) − 34.5466i − 1.15091i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) − 26.1342i − 0.868730i
\(906\) 0 0
\(907\) −38.1744 −1.26756 −0.633781 0.773513i \(-0.718498\pi\)
−0.633781 + 0.773513i \(0.718498\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −18.9190 −0.626813 −0.313407 0.949619i \(-0.601470\pi\)
−0.313407 + 0.949619i \(0.601470\pi\)
\(912\) 0 0
\(913\) −27.5937 −0.913218
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −12.4292 −0.410448
\(918\) 0 0
\(919\) − 4.03920i − 0.133241i −0.997778 0.0666204i \(-0.978778\pi\)
0.997778 0.0666204i \(-0.0212217\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 2.10226i 0.0691968i
\(924\) 0 0
\(925\) − 2.70263i − 0.0888619i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 23.4245i 0.768534i 0.923222 + 0.384267i \(0.125546\pi\)
−0.923222 + 0.384267i \(0.874454\pi\)
\(930\) 0 0
\(931\) 17.8608 0.585364
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −11.3222 −0.370276
\(936\) 0 0
\(937\) −41.0860 −1.34222 −0.671111 0.741357i \(-0.734182\pi\)
−0.671111 + 0.741357i \(0.734182\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −24.5313 −0.799696 −0.399848 0.916581i \(-0.630937\pi\)
−0.399848 + 0.916581i \(0.630937\pi\)
\(942\) 0 0
\(943\) 2.45823i 0.0800509i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) − 47.0862i − 1.53010i −0.643973 0.765048i \(-0.722715\pi\)
0.643973 0.765048i \(-0.277285\pi\)
\(948\) 0 0
\(949\) − 0.144445i − 0.00468889i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 47.3929i 1.53521i 0.640926 + 0.767603i \(0.278551\pi\)
−0.640926 + 0.767603i \(0.721449\pi\)
\(954\) 0 0
\(955\) −29.7623 −0.963086
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −23.5353 −0.759996
\(960\) 0 0
\(961\) −13.1519 −0.424256
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 2.64631 0.0851876
\(966\) 0 0
\(967\) 40.0248i 1.28711i 0.765400 + 0.643555i \(0.222541\pi\)
−0.765400 + 0.643555i \(0.777459\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 36.5162i 1.17186i 0.810362 + 0.585930i \(0.199271\pi\)
−0.810362 + 0.585930i \(0.800729\pi\)
\(972\) 0 0
\(973\) 15.3306i 0.491475i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 43.4028i 1.38858i 0.719697 + 0.694289i \(0.244281\pi\)
−0.719697 + 0.694289i \(0.755719\pi\)
\(978\) 0 0
\(979\) 16.6694 0.532758
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 2.34326 0.0747384 0.0373692 0.999302i \(-0.488102\pi\)
0.0373692 + 0.999302i \(0.488102\pi\)
\(984\) 0 0
\(985\) −19.0047 −0.605539
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −10.1284 −0.322064
\(990\) 0 0
\(991\) − 44.6280i − 1.41766i −0.705382 0.708828i \(-0.749224\pi\)
0.705382 0.708828i \(-0.250776\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) − 13.3031i − 0.421737i
\(996\) 0 0
\(997\) − 53.4194i − 1.69181i −0.533334 0.845904i \(-0.679061\pi\)
0.533334 0.845904i \(-0.320939\pi\)
\(998\) 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.e.2591.6 yes 16
3.2 odd 2 inner 5184.2.f.e.2591.12 yes 16
4.3 odd 2 5184.2.f.b.2591.5 16
8.3 odd 2 inner 5184.2.f.e.2591.11 yes 16
8.5 even 2 5184.2.f.b.2591.12 yes 16
12.11 even 2 5184.2.f.b.2591.11 yes 16
24.5 odd 2 5184.2.f.b.2591.6 yes 16
24.11 even 2 inner 5184.2.f.e.2591.5 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5184.2.f.b.2591.5 16 4.3 odd 2
5184.2.f.b.2591.6 yes 16 24.5 odd 2
5184.2.f.b.2591.11 yes 16 12.11 even 2
5184.2.f.b.2591.12 yes 16 8.5 even 2
5184.2.f.e.2591.5 yes 16 24.11 even 2 inner
5184.2.f.e.2591.6 yes 16 1.1 even 1 trivial
5184.2.f.e.2591.11 yes 16 8.3 odd 2 inner
5184.2.f.e.2591.12 yes 16 3.2 odd 2 inner