Properties

Label 8280.2.a.bs.1.4
Level $8280$
Weight $2$
Character 8280.1
Self dual yes
Analytic conductor $66.116$
Analytic rank $0$
Dimension $5$
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: \(0\)
Dimension: \(5\)
Coefficient field: 5.5.13955077.1
Defining polynomial: \(x^{5} - 14 x^{3} - x^{2} + 32 x + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 920)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(1.93283\) of defining polynomial
Character \(\chi\) \(=\) 8280.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{5} +2.38236 q^{7} +O(q^{10})\) \(q+1.00000 q^{5} +2.38236 q^{7} -5.33368 q^{11} -4.53752 q^{13} -1.81464 q^{17} +7.00233 q^{19} +1.00000 q^{23} +1.00000 q^{25} +0.118188 q^{29} -0.884147 q^{31} +2.38236 q^{35} +7.51903 q^{37} +1.45186 q^{41} -10.4389 q^{47} -1.32437 q^{49} +9.42167 q^{53} -5.33368 q^{55} -7.79239 q^{59} -2.80533 q^{61} -4.53752 q^{65} -3.11134 q^{67} +13.5909 q^{71} +12.4389 q^{73} -12.7067 q^{77} +6.80169 q^{79} +13.5190 q^{83} -1.81464 q^{85} -2.89906 q^{89} -10.8100 q^{91} +7.00233 q^{95} -1.97774 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q + 5q^{5} - 2q^{7} + O(q^{10}) \) \( 5q + 5q^{5} - 2q^{7} + q^{11} + 4q^{13} - 4q^{17} + 7q^{19} + 5q^{23} + 5q^{25} - 4q^{29} + 19q^{31} - 2q^{35} + 15q^{37} - 25q^{41} + 11q^{47} + 25q^{49} - 3q^{53} + q^{55} + q^{59} - 5q^{61} + 4q^{65} + 9q^{67} - q^{71} - q^{73} - 18q^{77} - 2q^{79} + 45q^{83} - 4q^{85} - 6q^{89} + 11q^{91} + 7q^{95} + 25q^{97} + O(q^{100}) \)

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
\(7\) 2.38236 0.900447 0.450223 0.892916i \(-0.351344\pi\)
0.450223 + 0.892916i \(0.351344\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −5.33368 −1.60816 −0.804082 0.594519i \(-0.797343\pi\)
−0.804082 + 0.594519i \(0.797343\pi\)
\(12\) 0 0
\(13\) −4.53752 −1.25848 −0.629241 0.777210i \(-0.716634\pi\)
−0.629241 + 0.777210i \(0.716634\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.81464 −0.440115 −0.220058 0.975487i \(-0.570625\pi\)
−0.220058 + 0.975487i \(0.570625\pi\)
\(18\) 0 0
\(19\) 7.00233 1.60645 0.803223 0.595679i \(-0.203117\pi\)
0.803223 + 0.595679i \(0.203117\pi\)
\(20\) 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
\(29\) 0.118188 0.0219469 0.0109735 0.999940i \(-0.496507\pi\)
0.0109735 + 0.999940i \(0.496507\pi\)
\(30\) 0 0
\(31\) −0.884147 −0.158797 −0.0793987 0.996843i \(-0.525300\pi\)
−0.0793987 + 0.996843i \(0.525300\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.38236 0.402692
\(36\) 0 0
\(37\) 7.51903 1.23612 0.618061 0.786130i \(-0.287919\pi\)
0.618061 + 0.786130i \(0.287919\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 1.45186 0.226743 0.113371 0.993553i \(-0.463835\pi\)
0.113371 + 0.993553i \(0.463835\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −10.4389 −1.52267 −0.761336 0.648357i \(-0.775456\pi\)
−0.761336 + 0.648357i \(0.775456\pi\)
\(48\) 0 0
\(49\) −1.32437 −0.189195
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 9.42167 1.29417 0.647083 0.762420i \(-0.275989\pi\)
0.647083 + 0.762420i \(0.275989\pi\)
\(54\) 0 0
\(55\) −5.33368 −0.719193
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −7.79239 −1.01448 −0.507241 0.861804i \(-0.669335\pi\)
−0.507241 + 0.861804i \(0.669335\pi\)
\(60\) 0 0
\(61\) −2.80533 −0.359186 −0.179593 0.983741i \(-0.557478\pi\)
−0.179593 + 0.983741i \(0.557478\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −4.53752 −0.562810
\(66\) 0 0
\(67\) −3.11134 −0.380111 −0.190055 0.981773i \(-0.560867\pi\)
−0.190055 + 0.981773i \(0.560867\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 13.5909 1.61294 0.806470 0.591275i \(-0.201375\pi\)
0.806470 + 0.591275i \(0.201375\pi\)
\(72\) 0 0
\(73\) 12.4389 1.45586 0.727932 0.685649i \(-0.240481\pi\)
0.727932 + 0.685649i \(0.240481\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −12.7067 −1.44807
\(78\) 0 0
\(79\) 6.80169 0.765250 0.382625 0.923904i \(-0.375020\pi\)
0.382625 + 0.923904i \(0.375020\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 13.5190 1.48391 0.741953 0.670451i \(-0.233900\pi\)
0.741953 + 0.670451i \(0.233900\pi\)
\(84\) 0 0
\(85\) −1.81464 −0.196826
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −2.89906 −0.307300 −0.153650 0.988125i \(-0.549103\pi\)
−0.153650 + 0.988125i \(0.549103\pi\)
\(90\) 0 0
\(91\) −10.8100 −1.13320
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 7.00233 0.718424
\(96\) 0 0
\(97\) −1.97774 −0.200809 −0.100405 0.994947i \(-0.532014\pi\)
−0.100405 + 0.994947i \(0.532014\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 12.2838 1.22228 0.611139 0.791523i \(-0.290711\pi\)
0.611139 + 0.791523i \(0.290711\pi\)
\(102\) 0 0
\(103\) −12.5061 −1.23226 −0.616131 0.787644i \(-0.711301\pi\)
−0.616131 + 0.787644i \(0.711301\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 17.3847 1.68064 0.840321 0.542089i \(-0.182367\pi\)
0.840321 + 0.542089i \(0.182367\pi\)
\(108\) 0 0
\(109\) 4.30908 0.412735 0.206368 0.978475i \(-0.433836\pi\)
0.206368 + 0.978475i \(0.433836\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 12.1494 1.14292 0.571460 0.820630i \(-0.306377\pi\)
0.571460 + 0.820630i \(0.306377\pi\)
\(114\) 0 0
\(115\) 1.00000 0.0932505
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −4.32313 −0.396300
\(120\) 0 0
\(121\) 17.4481 1.58619
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −1.22953 −0.109103 −0.0545515 0.998511i \(-0.517373\pi\)
−0.0545515 + 0.998511i \(0.517373\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1.97345 −0.172421 −0.0862104 0.996277i \(-0.527476\pi\)
−0.0862104 + 0.996277i \(0.527476\pi\)
\(132\) 0 0
\(133\) 16.6821 1.44652
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −13.7671 −1.17620 −0.588099 0.808789i \(-0.700124\pi\)
−0.588099 + 0.808789i \(0.700124\pi\)
\(138\) 0 0
\(139\) 5.30280 0.449778 0.224889 0.974384i \(-0.427798\pi\)
0.224889 + 0.974384i \(0.427798\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 24.2017 2.02385
\(144\) 0 0
\(145\) 0.118188 0.00981497
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −7.73256 −0.633476 −0.316738 0.948513i \(-0.602588\pi\)
−0.316738 + 0.948513i \(0.602588\pi\)
\(150\) 0 0
\(151\) 21.4156 1.74277 0.871387 0.490596i \(-0.163221\pi\)
0.871387 + 0.490596i \(0.163221\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −0.884147 −0.0710164
\(156\) 0 0
\(157\) −4.04738 −0.323016 −0.161508 0.986871i \(-0.551636\pi\)
−0.161508 + 0.986871i \(0.551636\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 2.38236 0.187756
\(162\) 0 0
\(163\) 9.04725 0.708635 0.354318 0.935125i \(-0.384713\pi\)
0.354318 + 0.935125i \(0.384713\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 12.5467 0.970893 0.485446 0.874266i \(-0.338657\pi\)
0.485446 + 0.874266i \(0.338657\pi\)
\(168\) 0 0
\(169\) 7.58910 0.583777
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 14.1354 1.07469 0.537346 0.843362i \(-0.319427\pi\)
0.537346 + 0.843362i \(0.319427\pi\)
\(174\) 0 0
\(175\) 2.38236 0.180089
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 26.2442 1.96158 0.980791 0.195061i \(-0.0624904\pi\)
0.980791 + 0.195061i \(0.0624904\pi\)
\(180\) 0 0
\(181\) −18.3461 −1.36365 −0.681826 0.731514i \(-0.738814\pi\)
−0.681826 + 0.731514i \(0.738814\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 7.51903 0.552810
\(186\) 0 0
\(187\) 9.67871 0.707777
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 3.86566 0.279709 0.139855 0.990172i \(-0.455336\pi\)
0.139855 + 0.990172i \(0.455336\pi\)
\(192\) 0 0
\(193\) −23.8599 −1.71747 −0.858737 0.512417i \(-0.828750\pi\)
−0.858737 + 0.512417i \(0.828750\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −11.7356 −0.836128 −0.418064 0.908418i \(-0.637291\pi\)
−0.418064 + 0.908418i \(0.637291\pi\)
\(198\) 0 0
\(199\) −8.89906 −0.630838 −0.315419 0.948953i \(-0.602145\pi\)
−0.315419 + 0.948953i \(0.602145\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0.281566 0.0197620
\(204\) 0 0
\(205\) 1.45186 0.101403
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −37.3482 −2.58343
\(210\) 0 0
\(211\) 23.1224 1.59181 0.795906 0.605420i \(-0.206995\pi\)
0.795906 + 0.605420i \(0.206995\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −2.10635 −0.142989
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 8.23398 0.553877
\(222\) 0 0
\(223\) 1.50863 0.101026 0.0505128 0.998723i \(-0.483914\pi\)
0.0505128 + 0.998723i \(0.483914\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 22.0047 1.46050 0.730251 0.683179i \(-0.239403\pi\)
0.730251 + 0.683179i \(0.239403\pi\)
\(228\) 0 0
\(229\) −11.2931 −0.746266 −0.373133 0.927778i \(-0.621717\pi\)
−0.373133 + 0.927778i \(0.621717\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 17.6789 1.15818 0.579091 0.815263i \(-0.303408\pi\)
0.579091 + 0.815263i \(0.303408\pi\)
\(234\) 0 0
\(235\) −10.4389 −0.680960
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 25.2583 1.63382 0.816911 0.576763i \(-0.195684\pi\)
0.816911 + 0.576763i \(0.195684\pi\)
\(240\) 0 0
\(241\) 0.790615 0.0509280 0.0254640 0.999676i \(-0.491894\pi\)
0.0254640 + 0.999676i \(0.491894\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1.32437 −0.0846108
\(246\) 0 0
\(247\) −31.7732 −2.02168
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −12.3461 −0.779276 −0.389638 0.920968i \(-0.627400\pi\)
−0.389638 + 0.920968i \(0.627400\pi\)
\(252\) 0 0
\(253\) −5.33368 −0.335325
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −6.40442 −0.399497 −0.199748 0.979847i \(-0.564012\pi\)
−0.199748 + 0.979847i \(0.564012\pi\)
\(258\) 0 0
\(259\) 17.9130 1.11306
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −19.6914 −1.21422 −0.607111 0.794617i \(-0.707672\pi\)
−0.607111 + 0.794617i \(0.707672\pi\)
\(264\) 0 0
\(265\) 9.42167 0.578768
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 3.42494 0.208822 0.104411 0.994534i \(-0.466704\pi\)
0.104411 + 0.994534i \(0.466704\pi\)
\(270\) 0 0
\(271\) 13.7197 0.833411 0.416705 0.909042i \(-0.363185\pi\)
0.416705 + 0.909042i \(0.363185\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −5.33368 −0.321633
\(276\) 0 0
\(277\) 0.636129 0.0382213 0.0191107 0.999817i \(-0.493917\pi\)
0.0191107 + 0.999817i \(0.493917\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −18.4124 −1.09839 −0.549195 0.835694i \(-0.685065\pi\)
−0.549195 + 0.835694i \(0.685065\pi\)
\(282\) 0 0
\(283\) −7.95729 −0.473012 −0.236506 0.971630i \(-0.576002\pi\)
−0.236506 + 0.971630i \(0.576002\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 3.45886 0.204170
\(288\) 0 0
\(289\) −13.7071 −0.806299
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 20.9166 1.22196 0.610981 0.791645i \(-0.290775\pi\)
0.610981 + 0.791645i \(0.290775\pi\)
\(294\) 0 0
\(295\) −7.79239 −0.453690
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −4.53752 −0.262412
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −2.80533 −0.160633
\(306\) 0 0
\(307\) −5.78807 −0.330342 −0.165171 0.986265i \(-0.552818\pi\)
−0.165171 + 0.986265i \(0.552818\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −18.3674 −1.04152 −0.520761 0.853702i \(-0.674352\pi\)
−0.520761 + 0.853702i \(0.674352\pi\)
\(312\) 0 0
\(313\) 9.85869 0.557246 0.278623 0.960401i \(-0.410122\pi\)
0.278623 + 0.960401i \(0.410122\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 32.9488 1.85059 0.925294 0.379250i \(-0.123818\pi\)
0.925294 + 0.379250i \(0.123818\pi\)
\(318\) 0 0
\(319\) −0.630376 −0.0352943
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −12.7067 −0.707021
\(324\) 0 0
\(325\) −4.53752 −0.251696
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −24.8692 −1.37109
\(330\) 0 0
\(331\) −6.85308 −0.376679 −0.188340 0.982104i \(-0.560311\pi\)
−0.188340 + 0.982104i \(0.560311\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −3.11134 −0.169991
\(336\) 0 0
\(337\) 35.8432 1.95250 0.976251 0.216641i \(-0.0695100\pi\)
0.976251 + 0.216641i \(0.0695100\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 4.71575 0.255372
\(342\) 0 0
\(343\) −19.8316 −1.07081
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 4.09198 0.219669 0.109835 0.993950i \(-0.464968\pi\)
0.109835 + 0.993950i \(0.464968\pi\)
\(348\) 0 0
\(349\) −11.3229 −0.606101 −0.303051 0.952974i \(-0.598005\pi\)
−0.303051 + 0.952974i \(0.598005\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −26.1443 −1.39152 −0.695761 0.718273i \(-0.744933\pi\)
−0.695761 + 0.718273i \(0.744933\pi\)
\(354\) 0 0
\(355\) 13.5909 0.721329
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 12.2058 0.644198 0.322099 0.946706i \(-0.395612\pi\)
0.322099 + 0.946706i \(0.395612\pi\)
\(360\) 0 0
\(361\) 30.0327 1.58067
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 12.4389 0.651083
\(366\) 0 0
\(367\) −3.15299 −0.164585 −0.0822923 0.996608i \(-0.526224\pi\)
−0.0822923 + 0.996608i \(0.526224\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 22.4458 1.16533
\(372\) 0 0
\(373\) 9.59872 0.497003 0.248501 0.968632i \(-0.420062\pi\)
0.248501 + 0.968632i \(0.420062\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −0.536280 −0.0276198
\(378\) 0 0
\(379\) 32.7841 1.68401 0.842003 0.539473i \(-0.181376\pi\)
0.842003 + 0.539473i \(0.181376\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −34.7378 −1.77502 −0.887508 0.460792i \(-0.847565\pi\)
−0.887508 + 0.460792i \(0.847565\pi\)
\(384\) 0 0
\(385\) −12.7067 −0.647595
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −13.8965 −0.704581 −0.352290 0.935891i \(-0.614597\pi\)
−0.352290 + 0.935891i \(0.614597\pi\)
\(390\) 0 0
\(391\) −1.81464 −0.0917704
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 6.80169 0.342230
\(396\) 0 0
\(397\) −26.1135 −1.31060 −0.655299 0.755370i \(-0.727457\pi\)
−0.655299 + 0.755370i \(0.727457\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −18.0715 −0.902446 −0.451223 0.892411i \(-0.649012\pi\)
−0.451223 + 0.892411i \(0.649012\pi\)
\(402\) 0 0
\(403\) 4.01183 0.199844
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −40.1041 −1.98789
\(408\) 0 0
\(409\) −0.865532 −0.0427978 −0.0213989 0.999771i \(-0.506812\pi\)
−0.0213989 + 0.999771i \(0.506812\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −18.5643 −0.913487
\(414\) 0 0
\(415\) 13.5190 0.663623
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 20.5675 1.00479 0.502394 0.864639i \(-0.332453\pi\)
0.502394 + 0.864639i \(0.332453\pi\)
\(420\) 0 0
\(421\) 26.2423 1.27897 0.639485 0.768803i \(-0.279147\pi\)
0.639485 + 0.768803i \(0.279147\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1.81464 −0.0880230
\(426\) 0 0
\(427\) −6.68331 −0.323428
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −23.2654 −1.12066 −0.560328 0.828271i \(-0.689325\pi\)
−0.560328 + 0.828271i \(0.689325\pi\)
\(432\) 0 0
\(433\) −34.7365 −1.66933 −0.834665 0.550758i \(-0.814339\pi\)
−0.834665 + 0.550758i \(0.814339\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 7.00233 0.334967
\(438\) 0 0
\(439\) 28.5238 1.36137 0.680684 0.732577i \(-0.261683\pi\)
0.680684 + 0.732577i \(0.261683\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −26.3428 −1.25158 −0.625792 0.779990i \(-0.715224\pi\)
−0.625792 + 0.779990i \(0.715224\pi\)
\(444\) 0 0
\(445\) −2.89906 −0.137429
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −29.5411 −1.39413 −0.697065 0.717008i \(-0.745511\pi\)
−0.697065 + 0.717008i \(0.745511\pi\)
\(450\) 0 0
\(451\) −7.74377 −0.364640
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −10.8100 −0.506781
\(456\) 0 0
\(457\) 3.16668 0.148131 0.0740655 0.997253i \(-0.476403\pi\)
0.0740655 + 0.997253i \(0.476403\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −8.43891 −0.393039 −0.196520 0.980500i \(-0.562964\pi\)
−0.196520 + 0.980500i \(0.562964\pi\)
\(462\) 0 0
\(463\) 9.62461 0.447294 0.223647 0.974670i \(-0.428204\pi\)
0.223647 + 0.974670i \(0.428204\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 23.1041 1.06913 0.534564 0.845128i \(-0.320476\pi\)
0.534564 + 0.845128i \(0.320476\pi\)
\(468\) 0 0
\(469\) −7.41233 −0.342270
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 7.00233 0.321289
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −20.5981 −0.941150 −0.470575 0.882360i \(-0.655953\pi\)
−0.470575 + 0.882360i \(0.655953\pi\)
\(480\) 0 0
\(481\) −34.1178 −1.55564
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.97774 −0.0898047
\(486\) 0 0
\(487\) 40.1145 1.81776 0.908881 0.417056i \(-0.136938\pi\)
0.908881 + 0.417056i \(0.136938\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 18.4799 0.833985 0.416993 0.908910i \(-0.363084\pi\)
0.416993 + 0.908910i \(0.363084\pi\)
\(492\) 0 0
\(493\) −0.214469 −0.00965918
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 32.3783 1.45237
\(498\) 0 0
\(499\) 0.0506452 0.00226719 0.00113360 0.999999i \(-0.499639\pi\)
0.00113360 + 0.999999i \(0.499639\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 31.1887 1.39064 0.695318 0.718702i \(-0.255263\pi\)
0.695318 + 0.718702i \(0.255263\pi\)
\(504\) 0 0
\(505\) 12.2838 0.546620
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −3.42426 −0.151778 −0.0758888 0.997116i \(-0.524179\pi\)
−0.0758888 + 0.997116i \(0.524179\pi\)
\(510\) 0 0
\(511\) 29.6340 1.31093
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −12.5061 −0.551084
\(516\) 0 0
\(517\) 55.6778 2.44871
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 9.78442 0.428663 0.214332 0.976761i \(-0.431243\pi\)
0.214332 + 0.976761i \(0.431243\pi\)
\(522\) 0 0
\(523\) 6.22884 0.272368 0.136184 0.990684i \(-0.456516\pi\)
0.136184 + 0.990684i \(0.456516\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.60441 0.0698892
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −6.58786 −0.285352
\(534\) 0 0
\(535\) 17.3847 0.751606
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 7.06375 0.304257
\(540\) 0 0
\(541\) 19.8477 0.853319 0.426660 0.904412i \(-0.359690\pi\)
0.426660 + 0.904412i \(0.359690\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 4.30908 0.184581
\(546\) 0 0
\(547\) −7.68024 −0.328383 −0.164192 0.986428i \(-0.552502\pi\)
−0.164192 + 0.986428i \(0.552502\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0.827591 0.0352566
\(552\) 0 0
\(553\) 16.2041 0.689067
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −18.1260 −0.768023 −0.384012 0.923328i \(-0.625458\pi\)
−0.384012 + 0.923328i \(0.625458\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 16.8772 0.711287 0.355644 0.934622i \(-0.384262\pi\)
0.355644 + 0.934622i \(0.384262\pi\)
\(564\) 0 0
\(565\) 12.1494 0.511130
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −36.0022 −1.50929 −0.754645 0.656133i \(-0.772191\pi\)
−0.754645 + 0.656133i \(0.772191\pi\)
\(570\) 0 0
\(571\) 26.6267 1.11429 0.557147 0.830414i \(-0.311896\pi\)
0.557147 + 0.830414i \(0.311896\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.00000 0.0417029
\(576\) 0 0
\(577\) 30.0190 1.24971 0.624854 0.780742i \(-0.285158\pi\)
0.624854 + 0.780742i \(0.285158\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 32.2072 1.33618
\(582\) 0 0
\(583\) −50.2521 −2.08123
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 31.1814 1.28699 0.643497 0.765449i \(-0.277483\pi\)
0.643497 + 0.765449i \(0.277483\pi\)
\(588\) 0 0
\(589\) −6.19109 −0.255099
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −15.0334 −0.617348 −0.308674 0.951168i \(-0.599885\pi\)
−0.308674 + 0.951168i \(0.599885\pi\)
\(594\) 0 0
\(595\) −4.32313 −0.177231
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −20.3534 −0.831617 −0.415808 0.909452i \(-0.636501\pi\)
−0.415808 + 0.909452i \(0.636501\pi\)
\(600\) 0 0
\(601\) 46.5338 1.89816 0.949078 0.315043i \(-0.102019\pi\)
0.949078 + 0.315043i \(0.102019\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 17.4481 0.709366
\(606\) 0 0
\(607\) −7.52725 −0.305522 −0.152761 0.988263i \(-0.548816\pi\)
−0.152761 + 0.988263i \(0.548816\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 47.3668 1.91626
\(612\) 0 0
\(613\) 32.2643 1.30314 0.651572 0.758587i \(-0.274110\pi\)
0.651572 + 0.758587i \(0.274110\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −4.52158 −0.182032 −0.0910161 0.995849i \(-0.529011\pi\)
−0.0910161 + 0.995849i \(0.529011\pi\)
\(618\) 0 0
\(619\) 17.7807 0.714668 0.357334 0.933977i \(-0.383686\pi\)
0.357334 + 0.933977i \(0.383686\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −6.90660 −0.276707
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −13.6444 −0.544036
\(630\) 0 0
\(631\) 27.4554 1.09298 0.546490 0.837466i \(-0.315964\pi\)
0.546490 + 0.837466i \(0.315964\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1.22953 −0.0487924
\(636\) 0 0
\(637\) 6.00935 0.238099
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 48.9270 1.93250 0.966250 0.257605i \(-0.0829333\pi\)
0.966250 + 0.257605i \(0.0829333\pi\)
\(642\) 0 0
\(643\) 2.89333 0.114102 0.0570508 0.998371i \(-0.481830\pi\)
0.0570508 + 0.998371i \(0.481830\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −15.0877 −0.593157 −0.296578 0.955009i \(-0.595846\pi\)
−0.296578 + 0.955009i \(0.595846\pi\)
\(648\) 0 0
\(649\) 41.5621 1.63145
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 13.3255 0.521468 0.260734 0.965411i \(-0.416035\pi\)
0.260734 + 0.965411i \(0.416035\pi\)
\(654\) 0 0
\(655\) −1.97345 −0.0771090
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 39.9000 1.55428 0.777142 0.629325i \(-0.216669\pi\)
0.777142 + 0.629325i \(0.216669\pi\)
\(660\) 0 0
\(661\) −37.3060 −1.45104 −0.725518 0.688203i \(-0.758400\pi\)
−0.725518 + 0.688203i \(0.758400\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 16.6821 0.646903
\(666\) 0 0
\(667\) 0.118188 0.00457625
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 14.9627 0.577630
\(672\) 0 0
\(673\) −18.6641 −0.719447 −0.359724 0.933059i \(-0.617129\pi\)
−0.359724 + 0.933059i \(0.617129\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −19.4978 −0.749361 −0.374681 0.927154i \(-0.622248\pi\)
−0.374681 + 0.927154i \(0.622248\pi\)
\(678\) 0 0
\(679\) −4.71169 −0.180818
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 41.6331 1.59305 0.796523 0.604608i \(-0.206670\pi\)
0.796523 + 0.604608i \(0.206670\pi\)
\(684\) 0 0
\(685\) −13.7671 −0.526012
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −42.7510 −1.62868
\(690\) 0 0
\(691\) −9.53192 −0.362611 −0.181306 0.983427i \(-0.558032\pi\)
−0.181306 + 0.983427i \(0.558032\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 5.30280 0.201147
\(696\) 0 0
\(697\) −2.63461 −0.0997930
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −27.9897 −1.05716 −0.528579 0.848884i \(-0.677275\pi\)
−0.528579 + 0.848884i \(0.677275\pi\)
\(702\) 0 0
\(703\) 52.6508 1.98576
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 29.2643 1.10060
\(708\) 0 0
\(709\) 27.6832 1.03966 0.519831 0.854269i \(-0.325995\pi\)
0.519831 + 0.854269i \(0.325995\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −0.884147 −0.0331115
\(714\) 0 0
\(715\) 24.2017 0.905091
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −50.8364 −1.89588 −0.947938 0.318454i \(-0.896836\pi\)
−0.947938 + 0.318454i \(0.896836\pi\)
\(720\) 0 0
\(721\) −29.7940 −1.10959
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0.118188 0.00438939
\(726\) 0 0
\(727\) 37.5061 1.39102 0.695512 0.718514i \(-0.255177\pi\)
0.695512 + 0.718514i \(0.255177\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −36.9374 −1.36431 −0.682157 0.731206i \(-0.738958\pi\)
−0.682157 + 0.731206i \(0.738958\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 16.5949 0.611281
\(738\) 0 0
\(739\) −12.3287 −0.453517 −0.226759 0.973951i \(-0.572813\pi\)
−0.226759 + 0.973951i \(0.572813\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 29.7534 1.09154 0.545772 0.837933i \(-0.316236\pi\)
0.545772 + 0.837933i \(0.316236\pi\)
\(744\) 0 0
\(745\) −7.73256 −0.283299
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 41.4166 1.51333
\(750\) 0 0
\(751\) −41.9834 −1.53200 −0.765999 0.642842i \(-0.777755\pi\)
−0.765999 + 0.642842i \(0.777755\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 21.4156 0.779392
\(756\) 0 0
\(757\) 11.4708 0.416915 0.208458 0.978031i \(-0.433156\pi\)
0.208458 + 0.978031i \(0.433156\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 13.4122 0.486193 0.243097 0.970002i \(-0.421837\pi\)
0.243097 + 0.970002i \(0.421837\pi\)
\(762\) 0 0
\(763\) 10.2658 0.371646
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 35.3581 1.27671
\(768\) 0 0
\(769\) 2.18327 0.0787307 0.0393654 0.999225i \(-0.487466\pi\)
0.0393654 + 0.999225i \(0.487466\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −5.73306 −0.206204 −0.103102 0.994671i \(-0.532877\pi\)
−0.103102 + 0.994671i \(0.532877\pi\)
\(774\) 0 0
\(775\) −0.884147 −0.0317595
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 10.1664 0.364250
\(780\) 0 0
\(781\) −72.4893 −2.59387
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −4.04738 −0.144457
\(786\) 0 0
\(787\) −8.13502 −0.289982 −0.144991 0.989433i \(-0.546315\pi\)
−0.144991 + 0.989433i \(0.546315\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 28.9442 1.02914
\(792\) 0 0
\(793\) 12.7293 0.452029
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 41.5139 1.47050 0.735250 0.677797i \(-0.237065\pi\)
0.735250 + 0.677797i \(0.237065\pi\)
\(798\) 0 0
\(799\) 18.9429 0.670151
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −66.3451 −2.34127
\(804\) 0 0
\(805\) 2.38236 0.0839671
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 22.8566 0.803596 0.401798 0.915728i \(-0.368385\pi\)
0.401798 + 0.915728i \(0.368385\pi\)
\(810\) 0 0
\(811\) −42.1917 −1.48155 −0.740776 0.671753i \(-0.765542\pi\)
−0.740776 + 0.671753i \(0.765542\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 9.04725 0.316911
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −27.0195 −0.942985 −0.471493 0.881870i \(-0.656285\pi\)
−0.471493 + 0.881870i \(0.656285\pi\)
\(822\) 0 0
\(823\) 27.2435 0.949650 0.474825 0.880080i \(-0.342511\pi\)
0.474825 + 0.880080i \(0.342511\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −10.5732 −0.367667 −0.183834 0.982957i \(-0.558851\pi\)
−0.183834 + 0.982957i \(0.558851\pi\)
\(828\) 0 0
\(829\) −1.16445 −0.0404429 −0.0202215 0.999796i \(-0.506437\pi\)
−0.0202215 + 0.999796i \(0.506437\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 2.40325 0.0832678
\(834\) 0 0
\(835\) 12.5467 0.434197
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 20.2920 0.700556 0.350278 0.936646i \(-0.386087\pi\)
0.350278 + 0.936646i \(0.386087\pi\)
\(840\) 0 0
\(841\) −28.9860 −0.999518
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 7.58910 0.261073
\(846\) 0 0
\(847\) 41.5676 1.42828
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 7.51903 0.257749
\(852\) 0 0
\(853\) 26.6154 0.911295 0.455648 0.890160i \(-0.349408\pi\)
0.455648 + 0.890160i \(0.349408\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 10.4342 0.356427 0.178214 0.983992i \(-0.442968\pi\)
0.178214 + 0.983992i \(0.442968\pi\)
\(858\) 0 0
\(859\) −24.6623 −0.841466 −0.420733 0.907185i \(-0.638227\pi\)
−0.420733 + 0.907185i \(0.638227\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −8.48317 −0.288771 −0.144385 0.989522i \(-0.546120\pi\)
−0.144385 + 0.989522i \(0.546120\pi\)
\(864\) 0 0
\(865\) 14.1354 0.480617
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −36.2780 −1.23065
\(870\) 0 0
\(871\) 14.1178 0.478363
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 2.38236 0.0805384
\(876\) 0 0
\(877\) 3.08796 0.104273 0.0521365 0.998640i \(-0.483397\pi\)
0.0521365 + 0.998640i \(0.483397\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −42.5879 −1.43482 −0.717412 0.696649i \(-0.754673\pi\)
−0.717412 + 0.696649i \(0.754673\pi\)
\(882\) 0 0
\(883\) −48.3342 −1.62657 −0.813287 0.581863i \(-0.802324\pi\)
−0.813287 + 0.581863i \(0.802324\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 2.12173 0.0712408 0.0356204 0.999365i \(-0.488659\pi\)
0.0356204 + 0.999365i \(0.488659\pi\)
\(888\) 0 0
\(889\) −2.92918 −0.0982415
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −73.0968 −2.44609
\(894\) 0 0
\(895\) 26.2442 0.877246
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −0.104495 −0.00348512
\(900\) 0 0
\(901\) −17.0970 −0.569582
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −18.3461 −0.609844
\(906\) 0 0
\(907\) 28.6914 0.952684 0.476342 0.879260i \(-0.341962\pi\)
0.476342 + 0.879260i \(0.341962\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 1.14899 0.0380679 0.0190339 0.999819i \(-0.493941\pi\)
0.0190339 + 0.999819i \(0.493941\pi\)
\(912\) 0 0
\(913\) −72.1061 −2.38636
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −4.70146 −0.155256
\(918\) 0 0
\(919\) −55.4798 −1.83011 −0.915055 0.403329i \(-0.867853\pi\)
−0.915055 + 0.403329i \(0.867853\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −61.6689 −2.02986
\(924\) 0 0
\(925\) 7.51903 0.247224
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 4.05780 0.133132 0.0665660 0.997782i \(-0.478796\pi\)
0.0665660 + 0.997782i \(0.478796\pi\)
\(930\) 0 0
\(931\) −9.27367 −0.303932
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 9.67871 0.316528
\(936\) 0 0
\(937\) 16.0588 0.524617 0.262308 0.964984i \(-0.415516\pi\)
0.262308 + 0.964984i \(0.415516\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −4.73779 −0.154448 −0.0772238 0.997014i \(-0.524606\pi\)
−0.0772238 + 0.997014i \(0.524606\pi\)
\(942\) 0 0
\(943\) 1.45186 0.0472792
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 3.38634 0.110041 0.0550207 0.998485i \(-0.482478\pi\)
0.0550207 + 0.998485i \(0.482478\pi\)
\(948\) 0 0
\(949\) −56.4418 −1.83218
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −29.2967 −0.949013 −0.474507 0.880252i \(-0.657373\pi\)
−0.474507 + 0.880252i \(0.657373\pi\)
\(954\) 0 0
\(955\) 3.86566 0.125090
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −32.7981 −1.05910
\(960\) 0 0
\(961\) −30.2183 −0.974783
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −23.8599 −0.768078
\(966\) 0 0
\(967\) −15.5743 −0.500837 −0.250419 0.968138i \(-0.580568\pi\)
−0.250419 + 0.968138i \(0.580568\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −51.5951 −1.65577 −0.827883 0.560900i \(-0.810455\pi\)
−0.827883 + 0.560900i \(0.810455\pi\)
\(972\) 0 0
\(973\) 12.6332 0.405001
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −9.04984 −0.289530 −0.144765 0.989466i \(-0.546243\pi\)
−0.144765 + 0.989466i \(0.546243\pi\)
\(978\) 0 0
\(979\) 15.4626 0.494188
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 39.3855 1.25620 0.628101 0.778132i \(-0.283833\pi\)
0.628101 + 0.778132i \(0.283833\pi\)
\(984\) 0 0
\(985\) −11.7356 −0.373928
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −18.9152 −0.600860 −0.300430 0.953804i \(-0.597130\pi\)
−0.300430 + 0.953804i \(0.597130\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −8.89906 −0.282119
\(996\) 0 0
\(997\) −12.2966 −0.389438 −0.194719 0.980859i \(-0.562380\pi\)
−0.194719 + 0.980859i \(0.562380\pi\)
\(998\) 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.bs.1.4 5
3.2 odd 2 920.2.a.j.1.4 5
12.11 even 2 1840.2.a.v.1.2 5
15.2 even 4 4600.2.e.u.4049.3 10
15.8 even 4 4600.2.e.u.4049.8 10
15.14 odd 2 4600.2.a.be.1.2 5
24.5 odd 2 7360.2.a.co.1.2 5
24.11 even 2 7360.2.a.cp.1.4 5
60.59 even 2 9200.2.a.cu.1.4 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
920.2.a.j.1.4 5 3.2 odd 2
1840.2.a.v.1.2 5 12.11 even 2
4600.2.a.be.1.2 5 15.14 odd 2
4600.2.e.u.4049.3 10 15.2 even 4
4600.2.e.u.4049.8 10 15.8 even 4
7360.2.a.co.1.2 5 24.5 odd 2
7360.2.a.cp.1.4 5 24.11 even 2
8280.2.a.bs.1.4 5 1.1 even 1 trivial
9200.2.a.cu.1.4 5 60.59 even 2