Properties

Label 8280.2.a.be.1.2
Level $8280$
Weight $2$
Character 8280.1
Self dual yes
Analytic conductor $66.116$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 8280 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8280.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(66.1161328736\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{17}) \)
Defining polynomial: \( x^{2} - x - 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 2760)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-1.56155\) of defining polynomial
Character \(\chi\) \(=\) 8280.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{5} +1.56155 q^{7} +O(q^{10})\) \(q+1.00000 q^{5} +1.56155 q^{7} -3.12311 q^{11} +2.00000 q^{13} -0.438447 q^{17} -7.12311 q^{19} +1.00000 q^{23} +1.00000 q^{25} -4.43845 q^{29} +8.68466 q^{31} +1.56155 q^{35} -3.56155 q^{37} -7.56155 q^{41} +10.2462 q^{43} -8.00000 q^{47} -4.56155 q^{49} +3.56155 q^{53} -3.12311 q^{55} -2.43845 q^{59} -11.3693 q^{61} +2.00000 q^{65} +1.56155 q^{67} +0.684658 q^{71} +2.00000 q^{73} -4.87689 q^{77} -6.24621 q^{79} +12.6847 q^{83} -0.438447 q^{85} -5.12311 q^{89} +3.12311 q^{91} -7.12311 q^{95} -6.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{5} - q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{5} - q^{7} + 2 q^{11} + 4 q^{13} - 5 q^{17} - 6 q^{19} + 2 q^{23} + 2 q^{25} - 13 q^{29} + 5 q^{31} - q^{35} - 3 q^{37} - 11 q^{41} + 4 q^{43} - 16 q^{47} - 5 q^{49} + 3 q^{53} + 2 q^{55} - 9 q^{59} + 2 q^{61} + 4 q^{65} - q^{67} - 11 q^{71} + 4 q^{73} - 18 q^{77} + 4 q^{79} + 13 q^{83} - 5 q^{85} - 2 q^{89} - 2 q^{91} - 6 q^{95} - 12 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 1.56155 0.590211 0.295106 0.955465i \(-0.404645\pi\)
0.295106 + 0.955465i \(0.404645\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −3.12311 −0.941652 −0.470826 0.882226i \(-0.656044\pi\)
−0.470826 + 0.882226i \(0.656044\pi\)
\(12\) 0 0
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.438447 −0.106339 −0.0531695 0.998586i \(-0.516932\pi\)
−0.0531695 + 0.998586i \(0.516932\pi\)
\(18\) 0 0
\(19\) −7.12311 −1.63415 −0.817076 0.576530i \(-0.804407\pi\)
−0.817076 + 0.576530i \(0.804407\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −4.43845 −0.824199 −0.412099 0.911139i \(-0.635204\pi\)
−0.412099 + 0.911139i \(0.635204\pi\)
\(30\) 0 0
\(31\) 8.68466 1.55981 0.779905 0.625897i \(-0.215267\pi\)
0.779905 + 0.625897i \(0.215267\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1.56155 0.263951
\(36\) 0 0
\(37\) −3.56155 −0.585516 −0.292758 0.956187i \(-0.594573\pi\)
−0.292758 + 0.956187i \(0.594573\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −7.56155 −1.18092 −0.590458 0.807068i \(-0.701053\pi\)
−0.590458 + 0.807068i \(0.701053\pi\)
\(42\) 0 0
\(43\) 10.2462 1.56253 0.781266 0.624198i \(-0.214574\pi\)
0.781266 + 0.624198i \(0.214574\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −8.00000 −1.16692 −0.583460 0.812142i \(-0.698301\pi\)
−0.583460 + 0.812142i \(0.698301\pi\)
\(48\) 0 0
\(49\) −4.56155 −0.651650
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 3.56155 0.489217 0.244608 0.969622i \(-0.421341\pi\)
0.244608 + 0.969622i \(0.421341\pi\)
\(54\) 0 0
\(55\) −3.12311 −0.421119
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −2.43845 −0.317459 −0.158729 0.987322i \(-0.550740\pi\)
−0.158729 + 0.987322i \(0.550740\pi\)
\(60\) 0 0
\(61\) −11.3693 −1.45569 −0.727846 0.685741i \(-0.759478\pi\)
−0.727846 + 0.685741i \(0.759478\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 2.00000 0.248069
\(66\) 0 0
\(67\) 1.56155 0.190774 0.0953870 0.995440i \(-0.469591\pi\)
0.0953870 + 0.995440i \(0.469591\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0.684658 0.0812540 0.0406270 0.999174i \(-0.487064\pi\)
0.0406270 + 0.999174i \(0.487064\pi\)
\(72\) 0 0
\(73\) 2.00000 0.234082 0.117041 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −4.87689 −0.555774
\(78\) 0 0
\(79\) −6.24621 −0.702754 −0.351377 0.936234i \(-0.614286\pi\)
−0.351377 + 0.936234i \(0.614286\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 12.6847 1.39232 0.696161 0.717886i \(-0.254890\pi\)
0.696161 + 0.717886i \(0.254890\pi\)
\(84\) 0 0
\(85\) −0.438447 −0.0475563
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −5.12311 −0.543048 −0.271524 0.962432i \(-0.587528\pi\)
−0.271524 + 0.962432i \(0.587528\pi\)
\(90\) 0 0
\(91\) 3.12311 0.327390
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −7.12311 −0.730815
\(96\) 0 0
\(97\) −6.00000 −0.609208 −0.304604 0.952479i \(-0.598524\pi\)
−0.304604 + 0.952479i \(0.598524\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −18.6847 −1.85919 −0.929597 0.368579i \(-0.879844\pi\)
−0.929597 + 0.368579i \(0.879844\pi\)
\(102\) 0 0
\(103\) −2.24621 −0.221326 −0.110663 0.993858i \(-0.535297\pi\)
−0.110663 + 0.993858i \(0.535297\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 4.68466 0.452883 0.226442 0.974025i \(-0.427291\pi\)
0.226442 + 0.974025i \(0.427291\pi\)
\(108\) 0 0
\(109\) 12.2462 1.17297 0.586487 0.809959i \(-0.300510\pi\)
0.586487 + 0.809959i \(0.300510\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −14.6847 −1.38142 −0.690708 0.723134i \(-0.742701\pi\)
−0.690708 + 0.723134i \(0.742701\pi\)
\(114\) 0 0
\(115\) 1.00000 0.0932505
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −0.684658 −0.0627625
\(120\) 0 0
\(121\) −1.24621 −0.113292
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −2.24621 −0.199319 −0.0996595 0.995022i \(-0.531775\pi\)
−0.0996595 + 0.995022i \(0.531775\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −6.24621 −0.545734 −0.272867 0.962052i \(-0.587972\pi\)
−0.272867 + 0.962052i \(0.587972\pi\)
\(132\) 0 0
\(133\) −11.1231 −0.964496
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −14.0000 −1.19610 −0.598050 0.801459i \(-0.704058\pi\)
−0.598050 + 0.801459i \(0.704058\pi\)
\(138\) 0 0
\(139\) 7.80776 0.662246 0.331123 0.943588i \(-0.392573\pi\)
0.331123 + 0.943588i \(0.392573\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −6.24621 −0.522334
\(144\) 0 0
\(145\) −4.43845 −0.368593
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −11.3693 −0.931411 −0.465705 0.884940i \(-0.654199\pi\)
−0.465705 + 0.884940i \(0.654199\pi\)
\(150\) 0 0
\(151\) −6.24621 −0.508309 −0.254155 0.967164i \(-0.581797\pi\)
−0.254155 + 0.967164i \(0.581797\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 8.68466 0.697569
\(156\) 0 0
\(157\) 20.0540 1.60048 0.800241 0.599679i \(-0.204705\pi\)
0.800241 + 0.599679i \(0.204705\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1.56155 0.123068
\(162\) 0 0
\(163\) −5.36932 −0.420557 −0.210279 0.977641i \(-0.567437\pi\)
−0.210279 + 0.977641i \(0.567437\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −20.4924 −1.58575 −0.792876 0.609383i \(-0.791417\pi\)
−0.792876 + 0.609383i \(0.791417\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −6.87689 −0.522841 −0.261420 0.965225i \(-0.584191\pi\)
−0.261420 + 0.965225i \(0.584191\pi\)
\(174\) 0 0
\(175\) 1.56155 0.118042
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 20.4924 1.53168 0.765838 0.643034i \(-0.222325\pi\)
0.765838 + 0.643034i \(0.222325\pi\)
\(180\) 0 0
\(181\) 9.12311 0.678115 0.339058 0.940766i \(-0.389892\pi\)
0.339058 + 0.940766i \(0.389892\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −3.56155 −0.261851
\(186\) 0 0
\(187\) 1.36932 0.100134
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −20.4924 −1.48278 −0.741390 0.671075i \(-0.765833\pi\)
−0.741390 + 0.671075i \(0.765833\pi\)
\(192\) 0 0
\(193\) 11.3693 0.818381 0.409191 0.912449i \(-0.365811\pi\)
0.409191 + 0.912449i \(0.365811\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −3.75379 −0.267446 −0.133723 0.991019i \(-0.542693\pi\)
−0.133723 + 0.991019i \(0.542693\pi\)
\(198\) 0 0
\(199\) −11.1231 −0.788496 −0.394248 0.919004i \(-0.628995\pi\)
−0.394248 + 0.919004i \(0.628995\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −6.93087 −0.486452
\(204\) 0 0
\(205\) −7.56155 −0.528122
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 22.2462 1.53880
\(210\) 0 0
\(211\) −17.5616 −1.20899 −0.604494 0.796610i \(-0.706624\pi\)
−0.604494 + 0.796610i \(0.706624\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 10.2462 0.698786
\(216\) 0 0
\(217\) 13.5616 0.920618
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −0.876894 −0.0589863
\(222\) 0 0
\(223\) 5.36932 0.359556 0.179778 0.983707i \(-0.442462\pi\)
0.179778 + 0.983707i \(0.442462\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 24.4924 1.62562 0.812810 0.582529i \(-0.197937\pi\)
0.812810 + 0.582529i \(0.197937\pi\)
\(228\) 0 0
\(229\) 1.12311 0.0742169 0.0371085 0.999311i \(-0.488185\pi\)
0.0371085 + 0.999311i \(0.488185\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 11.3693 0.744829 0.372414 0.928067i \(-0.378530\pi\)
0.372414 + 0.928067i \(0.378530\pi\)
\(234\) 0 0
\(235\) −8.00000 −0.521862
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 7.31534 0.473190 0.236595 0.971608i \(-0.423969\pi\)
0.236595 + 0.971608i \(0.423969\pi\)
\(240\) 0 0
\(241\) 2.00000 0.128831 0.0644157 0.997923i \(-0.479482\pi\)
0.0644157 + 0.997923i \(0.479482\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −4.56155 −0.291427
\(246\) 0 0
\(247\) −14.2462 −0.906465
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 20.8769 1.31774 0.658869 0.752258i \(-0.271035\pi\)
0.658869 + 0.752258i \(0.271035\pi\)
\(252\) 0 0
\(253\) −3.12311 −0.196348
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 17.6155 1.09883 0.549413 0.835551i \(-0.314851\pi\)
0.549413 + 0.835551i \(0.314851\pi\)
\(258\) 0 0
\(259\) −5.56155 −0.345578
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −26.4384 −1.63026 −0.815132 0.579275i \(-0.803336\pi\)
−0.815132 + 0.579275i \(0.803336\pi\)
\(264\) 0 0
\(265\) 3.56155 0.218784
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −15.5616 −0.948805 −0.474402 0.880308i \(-0.657336\pi\)
−0.474402 + 0.880308i \(0.657336\pi\)
\(270\) 0 0
\(271\) −0.684658 −0.0415900 −0.0207950 0.999784i \(-0.506620\pi\)
−0.0207950 + 0.999784i \(0.506620\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −3.12311 −0.188330
\(276\) 0 0
\(277\) 8.24621 0.495467 0.247733 0.968828i \(-0.420314\pi\)
0.247733 + 0.968828i \(0.420314\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −10.0000 −0.596550 −0.298275 0.954480i \(-0.596411\pi\)
−0.298275 + 0.954480i \(0.596411\pi\)
\(282\) 0 0
\(283\) −1.56155 −0.0928247 −0.0464123 0.998922i \(-0.514779\pi\)
−0.0464123 + 0.998922i \(0.514779\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −11.8078 −0.696990
\(288\) 0 0
\(289\) −16.8078 −0.988692
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 20.9309 1.22279 0.611397 0.791324i \(-0.290608\pi\)
0.611397 + 0.791324i \(0.290608\pi\)
\(294\) 0 0
\(295\) −2.43845 −0.141972
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2.00000 0.115663
\(300\) 0 0
\(301\) 16.0000 0.922225
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −11.3693 −0.651005
\(306\) 0 0
\(307\) 11.6155 0.662933 0.331467 0.943467i \(-0.392457\pi\)
0.331467 + 0.943467i \(0.392457\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 8.00000 0.453638 0.226819 0.973937i \(-0.427167\pi\)
0.226819 + 0.973937i \(0.427167\pi\)
\(312\) 0 0
\(313\) 7.56155 0.427404 0.213702 0.976899i \(-0.431448\pi\)
0.213702 + 0.976899i \(0.431448\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2.87689 0.161582 0.0807912 0.996731i \(-0.474255\pi\)
0.0807912 + 0.996731i \(0.474255\pi\)
\(318\) 0 0
\(319\) 13.8617 0.776108
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 3.12311 0.173774
\(324\) 0 0
\(325\) 2.00000 0.110940
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −12.4924 −0.688730
\(330\) 0 0
\(331\) −23.8078 −1.30859 −0.654297 0.756238i \(-0.727035\pi\)
−0.654297 + 0.756238i \(0.727035\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1.56155 0.0853167
\(336\) 0 0
\(337\) −14.0000 −0.762629 −0.381314 0.924445i \(-0.624528\pi\)
−0.381314 + 0.924445i \(0.624528\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −27.1231 −1.46880
\(342\) 0 0
\(343\) −18.0540 −0.974823
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 22.7386 1.22067 0.610337 0.792142i \(-0.291034\pi\)
0.610337 + 0.792142i \(0.291034\pi\)
\(348\) 0 0
\(349\) −36.0540 −1.92993 −0.964963 0.262388i \(-0.915490\pi\)
−0.964963 + 0.262388i \(0.915490\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −2.87689 −0.153122 −0.0765608 0.997065i \(-0.524394\pi\)
−0.0765608 + 0.997065i \(0.524394\pi\)
\(354\) 0 0
\(355\) 0.684658 0.0363379
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 24.0000 1.26667 0.633336 0.773877i \(-0.281685\pi\)
0.633336 + 0.773877i \(0.281685\pi\)
\(360\) 0 0
\(361\) 31.7386 1.67045
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 2.00000 0.104685
\(366\) 0 0
\(367\) −36.3002 −1.89485 −0.947427 0.319972i \(-0.896327\pi\)
−0.947427 + 0.319972i \(0.896327\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 5.56155 0.288741
\(372\) 0 0
\(373\) −36.2462 −1.87676 −0.938379 0.345608i \(-0.887673\pi\)
−0.938379 + 0.345608i \(0.887673\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −8.87689 −0.457183
\(378\) 0 0
\(379\) −18.2462 −0.937245 −0.468622 0.883399i \(-0.655250\pi\)
−0.468622 + 0.883399i \(0.655250\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −6.93087 −0.354151 −0.177075 0.984197i \(-0.556664\pi\)
−0.177075 + 0.984197i \(0.556664\pi\)
\(384\) 0 0
\(385\) −4.87689 −0.248550
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 2.49242 0.126371 0.0631854 0.998002i \(-0.479874\pi\)
0.0631854 + 0.998002i \(0.479874\pi\)
\(390\) 0 0
\(391\) −0.438447 −0.0221732
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −6.24621 −0.314281
\(396\) 0 0
\(397\) 17.6155 0.884098 0.442049 0.896991i \(-0.354252\pi\)
0.442049 + 0.896991i \(0.354252\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −18.0000 −0.898877 −0.449439 0.893311i \(-0.648376\pi\)
−0.449439 + 0.893311i \(0.648376\pi\)
\(402\) 0 0
\(403\) 17.3693 0.865227
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 11.1231 0.551352
\(408\) 0 0
\(409\) −14.6847 −0.726110 −0.363055 0.931768i \(-0.618266\pi\)
−0.363055 + 0.931768i \(0.618266\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −3.80776 −0.187368
\(414\) 0 0
\(415\) 12.6847 0.622665
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 35.1231 1.71588 0.857938 0.513753i \(-0.171745\pi\)
0.857938 + 0.513753i \(0.171745\pi\)
\(420\) 0 0
\(421\) −6.49242 −0.316421 −0.158211 0.987405i \(-0.550573\pi\)
−0.158211 + 0.987405i \(0.550573\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −0.438447 −0.0212678
\(426\) 0 0
\(427\) −17.7538 −0.859166
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 12.4924 0.601739 0.300869 0.953665i \(-0.402723\pi\)
0.300869 + 0.953665i \(0.402723\pi\)
\(432\) 0 0
\(433\) −11.5616 −0.555613 −0.277806 0.960637i \(-0.589607\pi\)
−0.277806 + 0.960637i \(0.589607\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −7.12311 −0.340744
\(438\) 0 0
\(439\) 16.0000 0.763638 0.381819 0.924237i \(-0.375298\pi\)
0.381819 + 0.924237i \(0.375298\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 16.4924 0.783579 0.391789 0.920055i \(-0.371856\pi\)
0.391789 + 0.920055i \(0.371856\pi\)
\(444\) 0 0
\(445\) −5.12311 −0.242858
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −21.4233 −1.01103 −0.505514 0.862818i \(-0.668697\pi\)
−0.505514 + 0.862818i \(0.668697\pi\)
\(450\) 0 0
\(451\) 23.6155 1.11201
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 3.12311 0.146413
\(456\) 0 0
\(457\) −22.6847 −1.06114 −0.530572 0.847640i \(-0.678023\pi\)
−0.530572 + 0.847640i \(0.678023\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −3.75379 −0.174831 −0.0874157 0.996172i \(-0.527861\pi\)
−0.0874157 + 0.996172i \(0.527861\pi\)
\(462\) 0 0
\(463\) 29.3693 1.36491 0.682454 0.730929i \(-0.260913\pi\)
0.682454 + 0.730929i \(0.260913\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −19.3153 −0.893807 −0.446904 0.894582i \(-0.647473\pi\)
−0.446904 + 0.894582i \(0.647473\pi\)
\(468\) 0 0
\(469\) 2.43845 0.112597
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −32.0000 −1.47136
\(474\) 0 0
\(475\) −7.12311 −0.326831
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 26.7386 1.22172 0.610860 0.791739i \(-0.290824\pi\)
0.610860 + 0.791739i \(0.290824\pi\)
\(480\) 0 0
\(481\) −7.12311 −0.324786
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −6.00000 −0.272446
\(486\) 0 0
\(487\) −30.7386 −1.39290 −0.696450 0.717605i \(-0.745238\pi\)
−0.696450 + 0.717605i \(0.745238\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 16.6847 0.752968 0.376484 0.926423i \(-0.377133\pi\)
0.376484 + 0.926423i \(0.377133\pi\)
\(492\) 0 0
\(493\) 1.94602 0.0876445
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1.06913 0.0479570
\(498\) 0 0
\(499\) −39.4233 −1.76483 −0.882414 0.470473i \(-0.844083\pi\)
−0.882414 + 0.470473i \(0.844083\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −24.6847 −1.10063 −0.550317 0.834956i \(-0.685493\pi\)
−0.550317 + 0.834956i \(0.685493\pi\)
\(504\) 0 0
\(505\) −18.6847 −0.831456
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 26.4924 1.17426 0.587128 0.809494i \(-0.300259\pi\)
0.587128 + 0.809494i \(0.300259\pi\)
\(510\) 0 0
\(511\) 3.12311 0.138158
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −2.24621 −0.0989799
\(516\) 0 0
\(517\) 24.9848 1.09883
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −38.4924 −1.68638 −0.843192 0.537613i \(-0.819326\pi\)
−0.843192 + 0.537613i \(0.819326\pi\)
\(522\) 0 0
\(523\) −32.4924 −1.42079 −0.710397 0.703801i \(-0.751485\pi\)
−0.710397 + 0.703801i \(0.751485\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −3.80776 −0.165869
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −15.1231 −0.655054
\(534\) 0 0
\(535\) 4.68466 0.202535
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 14.2462 0.613628
\(540\) 0 0
\(541\) 6.00000 0.257960 0.128980 0.991647i \(-0.458830\pi\)
0.128980 + 0.991647i \(0.458830\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 12.2462 0.524570
\(546\) 0 0
\(547\) 26.2462 1.12221 0.561103 0.827746i \(-0.310377\pi\)
0.561103 + 0.827746i \(0.310377\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 31.6155 1.34687
\(552\) 0 0
\(553\) −9.75379 −0.414773
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −16.9309 −0.717384 −0.358692 0.933456i \(-0.616777\pi\)
−0.358692 + 0.933456i \(0.616777\pi\)
\(558\) 0 0
\(559\) 20.4924 0.866737
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 3.31534 0.139725 0.0698625 0.997557i \(-0.477744\pi\)
0.0698625 + 0.997557i \(0.477744\pi\)
\(564\) 0 0
\(565\) −14.6847 −0.617788
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 22.0000 0.922288 0.461144 0.887325i \(-0.347439\pi\)
0.461144 + 0.887325i \(0.347439\pi\)
\(570\) 0 0
\(571\) −20.0000 −0.836974 −0.418487 0.908223i \(-0.637439\pi\)
−0.418487 + 0.908223i \(0.637439\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.00000 0.0417029
\(576\) 0 0
\(577\) −11.8617 −0.493811 −0.246905 0.969040i \(-0.579414\pi\)
−0.246905 + 0.969040i \(0.579414\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 19.8078 0.821765
\(582\) 0 0
\(583\) −11.1231 −0.460672
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −17.8617 −0.737233 −0.368616 0.929582i \(-0.620168\pi\)
−0.368616 + 0.929582i \(0.620168\pi\)
\(588\) 0 0
\(589\) −61.8617 −2.54897
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 21.1231 0.867422 0.433711 0.901052i \(-0.357204\pi\)
0.433711 + 0.901052i \(0.357204\pi\)
\(594\) 0 0
\(595\) −0.684658 −0.0280683
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 32.0000 1.30748 0.653742 0.756717i \(-0.273198\pi\)
0.653742 + 0.756717i \(0.273198\pi\)
\(600\) 0 0
\(601\) −3.56155 −0.145279 −0.0726394 0.997358i \(-0.523142\pi\)
−0.0726394 + 0.997358i \(0.523142\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1.24621 −0.0506657
\(606\) 0 0
\(607\) 28.0000 1.13648 0.568242 0.822861i \(-0.307624\pi\)
0.568242 + 0.822861i \(0.307624\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −16.0000 −0.647291
\(612\) 0 0
\(613\) 3.75379 0.151614 0.0758070 0.997123i \(-0.475847\pi\)
0.0758070 + 0.997123i \(0.475847\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −13.3153 −0.536055 −0.268028 0.963411i \(-0.586372\pi\)
−0.268028 + 0.963411i \(0.586372\pi\)
\(618\) 0 0
\(619\) 35.2311 1.41606 0.708028 0.706185i \(-0.249585\pi\)
0.708028 + 0.706185i \(0.249585\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −8.00000 −0.320513
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1.56155 0.0622632
\(630\) 0 0
\(631\) −1.75379 −0.0698172 −0.0349086 0.999391i \(-0.511114\pi\)
−0.0349086 + 0.999391i \(0.511114\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −2.24621 −0.0891382
\(636\) 0 0
\(637\) −9.12311 −0.361471
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 15.7538 0.622237 0.311119 0.950371i \(-0.399296\pi\)
0.311119 + 0.950371i \(0.399296\pi\)
\(642\) 0 0
\(643\) 20.3002 0.800561 0.400281 0.916393i \(-0.368913\pi\)
0.400281 + 0.916393i \(0.368913\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −43.1231 −1.69534 −0.847672 0.530520i \(-0.821997\pi\)
−0.847672 + 0.530520i \(0.821997\pi\)
\(648\) 0 0
\(649\) 7.61553 0.298936
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.50758 0.0589961 0.0294980 0.999565i \(-0.490609\pi\)
0.0294980 + 0.999565i \(0.490609\pi\)
\(654\) 0 0
\(655\) −6.24621 −0.244060
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −9.36932 −0.364977 −0.182488 0.983208i \(-0.558415\pi\)
−0.182488 + 0.983208i \(0.558415\pi\)
\(660\) 0 0
\(661\) 32.7386 1.27339 0.636693 0.771118i \(-0.280302\pi\)
0.636693 + 0.771118i \(0.280302\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −11.1231 −0.431336
\(666\) 0 0
\(667\) −4.43845 −0.171857
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 35.5076 1.37075
\(672\) 0 0
\(673\) 43.3693 1.67176 0.835882 0.548909i \(-0.184957\pi\)
0.835882 + 0.548909i \(0.184957\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −42.3002 −1.62573 −0.812864 0.582453i \(-0.802093\pi\)
−0.812864 + 0.582453i \(0.802093\pi\)
\(678\) 0 0
\(679\) −9.36932 −0.359561
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −10.2462 −0.392060 −0.196030 0.980598i \(-0.562805\pi\)
−0.196030 + 0.980598i \(0.562805\pi\)
\(684\) 0 0
\(685\) −14.0000 −0.534913
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 7.12311 0.271369
\(690\) 0 0
\(691\) −40.4924 −1.54040 −0.770202 0.637800i \(-0.779845\pi\)
−0.770202 + 0.637800i \(0.779845\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 7.80776 0.296165
\(696\) 0 0
\(697\) 3.31534 0.125578
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 19.8617 0.750168 0.375084 0.926991i \(-0.377614\pi\)
0.375084 + 0.926991i \(0.377614\pi\)
\(702\) 0 0
\(703\) 25.3693 0.956822
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −29.1771 −1.09732
\(708\) 0 0
\(709\) −37.1231 −1.39419 −0.697094 0.716980i \(-0.745524\pi\)
−0.697094 + 0.716980i \(0.745524\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 8.68466 0.325243
\(714\) 0 0
\(715\) −6.24621 −0.233595
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 40.3002 1.50294 0.751472 0.659765i \(-0.229344\pi\)
0.751472 + 0.659765i \(0.229344\pi\)
\(720\) 0 0
\(721\) −3.50758 −0.130629
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −4.43845 −0.164840
\(726\) 0 0
\(727\) −7.80776 −0.289574 −0.144787 0.989463i \(-0.546250\pi\)
−0.144787 + 0.989463i \(0.546250\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −4.49242 −0.166158
\(732\) 0 0
\(733\) 0.930870 0.0343825 0.0171912 0.999852i \(-0.494528\pi\)
0.0171912 + 0.999852i \(0.494528\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −4.87689 −0.179643
\(738\) 0 0
\(739\) 2.93087 0.107814 0.0539069 0.998546i \(-0.482833\pi\)
0.0539069 + 0.998546i \(0.482833\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −19.5076 −0.715664 −0.357832 0.933786i \(-0.616484\pi\)
−0.357832 + 0.933786i \(0.616484\pi\)
\(744\) 0 0
\(745\) −11.3693 −0.416540
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 7.31534 0.267297
\(750\) 0 0
\(751\) −39.6155 −1.44559 −0.722796 0.691062i \(-0.757143\pi\)
−0.722796 + 0.691062i \(0.757143\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −6.24621 −0.227323
\(756\) 0 0
\(757\) −43.1771 −1.56930 −0.784649 0.619940i \(-0.787157\pi\)
−0.784649 + 0.619940i \(0.787157\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −21.8078 −0.790531 −0.395265 0.918567i \(-0.629347\pi\)
−0.395265 + 0.918567i \(0.629347\pi\)
\(762\) 0 0
\(763\) 19.1231 0.692303
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −4.87689 −0.176094
\(768\) 0 0
\(769\) 0.630683 0.0227430 0.0113715 0.999935i \(-0.496380\pi\)
0.0113715 + 0.999935i \(0.496380\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 3.26137 0.117303 0.0586516 0.998279i \(-0.481320\pi\)
0.0586516 + 0.998279i \(0.481320\pi\)
\(774\) 0 0
\(775\) 8.68466 0.311962
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 53.8617 1.92980
\(780\) 0 0
\(781\) −2.13826 −0.0765130
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 20.0540 0.715757
\(786\) 0 0
\(787\) −45.6695 −1.62794 −0.813971 0.580906i \(-0.802699\pi\)
−0.813971 + 0.580906i \(0.802699\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −22.9309 −0.815328
\(792\) 0 0
\(793\) −22.7386 −0.807473
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −30.7926 −1.09073 −0.545365 0.838199i \(-0.683609\pi\)
−0.545365 + 0.838199i \(0.683609\pi\)
\(798\) 0 0
\(799\) 3.50758 0.124089
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −6.24621 −0.220424
\(804\) 0 0
\(805\) 1.56155 0.0550375
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 41.8078 1.46988 0.734941 0.678131i \(-0.237210\pi\)
0.734941 + 0.678131i \(0.237210\pi\)
\(810\) 0 0
\(811\) −50.5464 −1.77492 −0.887462 0.460881i \(-0.847534\pi\)
−0.887462 + 0.460881i \(0.847534\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −5.36932 −0.188079
\(816\) 0 0
\(817\) −72.9848 −2.55342
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 38.0000 1.32621 0.663105 0.748527i \(-0.269238\pi\)
0.663105 + 0.748527i \(0.269238\pi\)
\(822\) 0 0
\(823\) 52.0000 1.81261 0.906303 0.422628i \(-0.138892\pi\)
0.906303 + 0.422628i \(0.138892\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 46.0540 1.60145 0.800727 0.599030i \(-0.204447\pi\)
0.800727 + 0.599030i \(0.204447\pi\)
\(828\) 0 0
\(829\) 25.8078 0.896341 0.448170 0.893948i \(-0.352076\pi\)
0.448170 + 0.893948i \(0.352076\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 2.00000 0.0692959
\(834\) 0 0
\(835\) −20.4924 −0.709170
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −3.12311 −0.107822 −0.0539108 0.998546i \(-0.517169\pi\)
−0.0539108 + 0.998546i \(0.517169\pi\)
\(840\) 0 0
\(841\) −9.30019 −0.320696
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −9.00000 −0.309609
\(846\) 0 0
\(847\) −1.94602 −0.0668662
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −3.56155 −0.122088
\(852\) 0 0
\(853\) 33.2311 1.13781 0.568905 0.822403i \(-0.307367\pi\)
0.568905 + 0.822403i \(0.307367\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −9.50758 −0.324773 −0.162386 0.986727i \(-0.551919\pi\)
−0.162386 + 0.986727i \(0.551919\pi\)
\(858\) 0 0
\(859\) 25.1771 0.859031 0.429515 0.903060i \(-0.358684\pi\)
0.429515 + 0.903060i \(0.358684\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −45.8617 −1.56115 −0.780576 0.625061i \(-0.785074\pi\)
−0.780576 + 0.625061i \(0.785074\pi\)
\(864\) 0 0
\(865\) −6.87689 −0.233821
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 19.5076 0.661749
\(870\) 0 0
\(871\) 3.12311 0.105822
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 1.56155 0.0527901
\(876\) 0 0
\(877\) −29.2311 −0.987063 −0.493531 0.869728i \(-0.664294\pi\)
−0.493531 + 0.869728i \(0.664294\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −51.3693 −1.73068 −0.865338 0.501189i \(-0.832896\pi\)
−0.865338 + 0.501189i \(0.832896\pi\)
\(882\) 0 0
\(883\) 12.0000 0.403832 0.201916 0.979403i \(-0.435283\pi\)
0.201916 + 0.979403i \(0.435283\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 12.8769 0.432364 0.216182 0.976353i \(-0.430640\pi\)
0.216182 + 0.976353i \(0.430640\pi\)
\(888\) 0 0
\(889\) −3.50758 −0.117640
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 56.9848 1.90693
\(894\) 0 0
\(895\) 20.4924 0.684986
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −38.5464 −1.28559
\(900\) 0 0
\(901\) −1.56155 −0.0520229
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 9.12311 0.303262
\(906\) 0 0
\(907\) −42.9309 −1.42550 −0.712748 0.701420i \(-0.752550\pi\)
−0.712748 + 0.701420i \(0.752550\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 18.7386 0.620839 0.310419 0.950600i \(-0.399531\pi\)
0.310419 + 0.950600i \(0.399531\pi\)
\(912\) 0 0
\(913\) −39.6155 −1.31108
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −9.75379 −0.322098
\(918\) 0 0
\(919\) 16.9848 0.560278 0.280139 0.959959i \(-0.409619\pi\)
0.280139 + 0.959959i \(0.409619\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 1.36932 0.0450716
\(924\) 0 0
\(925\) −3.56155 −0.117103
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 16.0540 0.526714 0.263357 0.964698i \(-0.415170\pi\)
0.263357 + 0.964698i \(0.415170\pi\)
\(930\) 0 0
\(931\) 32.4924 1.06490
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 1.36932 0.0447815
\(936\) 0 0
\(937\) −1.50758 −0.0492504 −0.0246252 0.999697i \(-0.507839\pi\)
−0.0246252 + 0.999697i \(0.507839\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −3.36932 −0.109837 −0.0549183 0.998491i \(-0.517490\pi\)
−0.0549183 + 0.998491i \(0.517490\pi\)
\(942\) 0 0
\(943\) −7.56155 −0.246238
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 12.0000 0.389948 0.194974 0.980808i \(-0.437538\pi\)
0.194974 + 0.980808i \(0.437538\pi\)
\(948\) 0 0
\(949\) 4.00000 0.129845
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −36.2462 −1.17413 −0.587065 0.809540i \(-0.699717\pi\)
−0.587065 + 0.809540i \(0.699717\pi\)
\(954\) 0 0
\(955\) −20.4924 −0.663119
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −21.8617 −0.705952
\(960\) 0 0
\(961\) 44.4233 1.43301
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 11.3693 0.365991
\(966\) 0 0
\(967\) 52.9848 1.70388 0.851939 0.523641i \(-0.175427\pi\)
0.851939 + 0.523641i \(0.175427\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 2.73863 0.0878869 0.0439435 0.999034i \(-0.486008\pi\)
0.0439435 + 0.999034i \(0.486008\pi\)
\(972\) 0 0
\(973\) 12.1922 0.390865
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 13.4233 0.429449 0.214725 0.976675i \(-0.431115\pi\)
0.214725 + 0.976675i \(0.431115\pi\)
\(978\) 0 0
\(979\) 16.0000 0.511362
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 21.1771 0.675444 0.337722 0.941246i \(-0.390344\pi\)
0.337722 + 0.941246i \(0.390344\pi\)
\(984\) 0 0
\(985\) −3.75379 −0.119606
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 10.2462 0.325811
\(990\) 0 0
\(991\) −50.0540 −1.59002 −0.795008 0.606598i \(-0.792534\pi\)
−0.795008 + 0.606598i \(0.792534\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −11.1231 −0.352626
\(996\) 0 0
\(997\) −19.8617 −0.629028 −0.314514 0.949253i \(-0.601841\pi\)
−0.314514 + 0.949253i \(0.601841\pi\)
\(998\) 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 8280.2.a.be.1.2 2
3.2 odd 2 2760.2.a.p.1.2 2
12.11 even 2 5520.2.a.bh.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2760.2.a.p.1.2 2 3.2 odd 2
5520.2.a.bh.1.1 2 12.11 even 2
8280.2.a.be.1.2 2 1.1 even 1 trivial