Properties

Label 8280.2.a.br.1.2
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: 5.5.20087896.1
Defining polynomial: \( x^{5} - x^{4} - 21x^{3} + 5x^{2} + 84x - 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 2760)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.27399\) of defining polynomial
Character \(\chi\) \(=\) 8280.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{5} -3.55148 q^{7} +O(q^{10})\) \(q-1.00000 q^{5} -3.55148 q^{7} +2.79304 q^{11} +3.73151 q^{13} +7.83097 q^{17} +6.27949 q^{19} +1.00000 q^{23} +1.00000 q^{25} -2.75844 q^{29} -2.48995 q^{31} +3.55148 q^{35} -1.55148 q^{37} -5.78954 q^{41} -4.54798 q^{43} +6.27949 q^{47} +5.61301 q^{49} -8.89250 q^{53} -2.79304 q^{55} -3.31342 q^{59} +11.2180 q^{61} -3.73151 q^{65} +5.52105 q^{67} -6.34452 q^{71} +15.3824 q^{73} -9.91943 q^{77} -9.62051 q^{79} -5.83097 q^{83} -7.83097 q^{85} -0.390487 q^{89} -13.2524 q^{91} -6.27949 q^{95} +0.961896 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 5 q^{5} - 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 5 q - 5 q^{5} - 4 q^{7} + 4 q^{11} + 4 q^{13} - 10 q^{17} - 4 q^{19} + 5 q^{23} + 5 q^{25} - 10 q^{29} + 6 q^{31} + 4 q^{35} + 6 q^{37} - 12 q^{41} - 2 q^{43} - 4 q^{47} + 19 q^{49} - 4 q^{55} - 6 q^{59} + 16 q^{61} - 4 q^{65} - 4 q^{67} - 8 q^{71} + 14 q^{73} - 16 q^{77} + 18 q^{79} + 20 q^{83} + 10 q^{85} - 18 q^{89} + 20 q^{91} + 4 q^{95} + 4 q^{97}+O(q^{100}) \) 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
\(7\) −3.55148 −1.34233 −0.671167 0.741306i \(-0.734207\pi\)
−0.671167 + 0.741306i \(0.734207\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.79304 0.842134 0.421067 0.907030i \(-0.361656\pi\)
0.421067 + 0.907030i \(0.361656\pi\)
\(12\) 0 0
\(13\) 3.73151 1.03493 0.517467 0.855703i \(-0.326875\pi\)
0.517467 + 0.855703i \(0.326875\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 7.83097 1.89929 0.949644 0.313330i \(-0.101445\pi\)
0.949644 + 0.313330i \(0.101445\pi\)
\(18\) 0 0
\(19\) 6.27949 1.44061 0.720307 0.693656i \(-0.244001\pi\)
0.720307 + 0.693656i \(0.244001\pi\)
\(20\) 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
\(29\) −2.75844 −0.512229 −0.256115 0.966646i \(-0.582442\pi\)
−0.256115 + 0.966646i \(0.582442\pi\)
\(30\) 0 0
\(31\) −2.48995 −0.447208 −0.223604 0.974680i \(-0.571782\pi\)
−0.223604 + 0.974680i \(0.571782\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 3.55148 0.600310
\(36\) 0 0
\(37\) −1.55148 −0.255062 −0.127531 0.991835i \(-0.540705\pi\)
−0.127531 + 0.991835i \(0.540705\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −5.78954 −0.904174 −0.452087 0.891974i \(-0.649320\pi\)
−0.452087 + 0.891974i \(0.649320\pi\)
\(42\) 0 0
\(43\) −4.54798 −0.693560 −0.346780 0.937946i \(-0.612725\pi\)
−0.346780 + 0.937946i \(0.612725\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 6.27949 0.915957 0.457979 0.888963i \(-0.348574\pi\)
0.457979 + 0.888963i \(0.348574\pi\)
\(48\) 0 0
\(49\) 5.61301 0.801859
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −8.89250 −1.22148 −0.610739 0.791832i \(-0.709128\pi\)
−0.610739 + 0.791832i \(0.709128\pi\)
\(54\) 0 0
\(55\) −2.79304 −0.376614
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −3.31342 −0.431371 −0.215685 0.976463i \(-0.569199\pi\)
−0.215685 + 0.976463i \(0.569199\pi\)
\(60\) 0 0
\(61\) 11.2180 1.43631 0.718156 0.695882i \(-0.244986\pi\)
0.718156 + 0.695882i \(0.244986\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −3.73151 −0.462837
\(66\) 0 0
\(67\) 5.52105 0.674503 0.337252 0.941415i \(-0.390503\pi\)
0.337252 + 0.941415i \(0.390503\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −6.34452 −0.752956 −0.376478 0.926426i \(-0.622865\pi\)
−0.376478 + 0.926426i \(0.622865\pi\)
\(72\) 0 0
\(73\) 15.3824 1.80038 0.900190 0.435498i \(-0.143428\pi\)
0.900190 + 0.435498i \(0.143428\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −9.91943 −1.13042
\(78\) 0 0
\(79\) −9.62051 −1.08239 −0.541196 0.840897i \(-0.682028\pi\)
−0.541196 + 0.840897i \(0.682028\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −5.83097 −0.640032 −0.320016 0.947412i \(-0.603688\pi\)
−0.320016 + 0.947412i \(0.603688\pi\)
\(84\) 0 0
\(85\) −7.83097 −0.849388
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −0.390487 −0.0413915 −0.0206958 0.999786i \(-0.506588\pi\)
−0.0206958 + 0.999786i \(0.506588\pi\)
\(90\) 0 0
\(91\) −13.2524 −1.38923
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −6.27949 −0.644262
\(96\) 0 0
\(97\) 0.961896 0.0976657 0.0488329 0.998807i \(-0.484450\pi\)
0.0488329 + 0.998807i \(0.484450\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 16.9035 1.68196 0.840980 0.541066i \(-0.181979\pi\)
0.840980 + 0.541066i \(0.181979\pi\)
\(102\) 0 0
\(103\) −6.04143 −0.595280 −0.297640 0.954678i \(-0.596199\pi\)
−0.297640 + 0.954678i \(0.596199\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −12.3141 −1.19045 −0.595224 0.803560i \(-0.702937\pi\)
−0.595224 + 0.803560i \(0.702937\pi\)
\(108\) 0 0
\(109\) 14.8579 1.42313 0.711564 0.702621i \(-0.247987\pi\)
0.711564 + 0.702621i \(0.247987\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −3.21113 −0.302077 −0.151039 0.988528i \(-0.548262\pi\)
−0.151039 + 0.988528i \(0.548262\pi\)
\(114\) 0 0
\(115\) −1.00000 −0.0932505
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −27.8115 −2.54948
\(120\) 0 0
\(121\) −3.19892 −0.290811
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 0.145425 0.0129043 0.00645217 0.999979i \(-0.497946\pi\)
0.00645217 + 0.999979i \(0.497946\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) −22.3015 −1.93378
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 6.16450 0.526668 0.263334 0.964705i \(-0.415178\pi\)
0.263334 + 0.964705i \(0.415178\pi\)
\(138\) 0 0
\(139\) 14.0690 1.19332 0.596660 0.802494i \(-0.296494\pi\)
0.596660 + 0.802494i \(0.296494\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 10.4223 0.871553
\(144\) 0 0
\(145\) 2.75844 0.229076
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −13.7964 −1.13024 −0.565121 0.825008i \(-0.691171\pi\)
−0.565121 + 0.825008i \(0.691171\pi\)
\(150\) 0 0
\(151\) 16.1989 1.31825 0.659125 0.752034i \(-0.270927\pi\)
0.659125 + 0.752034i \(0.270927\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 2.48995 0.199997
\(156\) 0 0
\(157\) −14.1105 −1.12614 −0.563068 0.826410i \(-0.690379\pi\)
−0.563068 + 0.826410i \(0.690379\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −3.55148 −0.279896
\(162\) 0 0
\(163\) 21.2480 1.66427 0.832137 0.554571i \(-0.187118\pi\)
0.832137 + 0.554571i \(0.187118\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −19.3895 −1.50040 −0.750200 0.661211i \(-0.770043\pi\)
−0.750200 + 0.661211i \(0.770043\pi\)
\(168\) 0 0
\(169\) 0.924149 0.0710884
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 13.1030 0.996200 0.498100 0.867120i \(-0.334031\pi\)
0.498100 + 0.867120i \(0.334031\pi\)
\(174\) 0 0
\(175\) −3.55148 −0.268467
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 14.0759 1.05208 0.526039 0.850460i \(-0.323676\pi\)
0.526039 + 0.850460i \(0.323676\pi\)
\(180\) 0 0
\(181\) 21.1374 1.57113 0.785565 0.618779i \(-0.212373\pi\)
0.785565 + 0.618779i \(0.212373\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1.55148 0.114067
\(186\) 0 0
\(187\) 21.8722 1.59945
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −2.81647 −0.203793 −0.101896 0.994795i \(-0.532491\pi\)
−0.101896 + 0.994795i \(0.532491\pi\)
\(192\) 0 0
\(193\) 15.4560 1.11255 0.556274 0.830999i \(-0.312230\pi\)
0.556274 + 0.830999i \(0.312230\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −25.7311 −1.83327 −0.916634 0.399728i \(-0.869105\pi\)
−0.916634 + 0.399728i \(0.869105\pi\)
\(198\) 0 0
\(199\) 5.95857 0.422392 0.211196 0.977444i \(-0.432264\pi\)
0.211196 + 0.977444i \(0.432264\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 9.79654 0.687583
\(204\) 0 0
\(205\) 5.78954 0.404359
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 17.5389 1.21319
\(210\) 0 0
\(211\) −6.06903 −0.417809 −0.208905 0.977936i \(-0.566990\pi\)
−0.208905 + 0.977936i \(0.566990\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 4.54798 0.310170
\(216\) 0 0
\(217\) 8.84300 0.600302
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 29.2213 1.96564
\(222\) 0 0
\(223\) −1.57509 −0.105476 −0.0527379 0.998608i \(-0.516795\pi\)
−0.0527379 + 0.998608i \(0.516795\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 21.7034 1.44050 0.720251 0.693713i \(-0.244026\pi\)
0.720251 + 0.693713i \(0.244026\pi\)
\(228\) 0 0
\(229\) 23.2136 1.53400 0.766999 0.641649i \(-0.221749\pi\)
0.766999 + 0.641649i \(0.221749\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 18.1989 1.19225 0.596125 0.802891i \(-0.296706\pi\)
0.596125 + 0.802891i \(0.296706\pi\)
\(234\) 0 0
\(235\) −6.27949 −0.409629
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −21.9236 −1.41812 −0.709060 0.705148i \(-0.750880\pi\)
−0.709060 + 0.705148i \(0.750880\pi\)
\(240\) 0 0
\(241\) 17.7964 1.14636 0.573182 0.819428i \(-0.305709\pi\)
0.573182 + 0.819428i \(0.305709\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −5.61301 −0.358602
\(246\) 0 0
\(247\) 23.4320 1.49094
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 23.2785 1.46932 0.734661 0.678434i \(-0.237341\pi\)
0.734661 + 0.678434i \(0.237341\pi\)
\(252\) 0 0
\(253\) 2.79304 0.175597
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −25.5884 −1.59616 −0.798079 0.602552i \(-0.794150\pi\)
−0.798079 + 0.602552i \(0.794150\pi\)
\(258\) 0 0
\(259\) 5.51005 0.342378
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 8.57051 0.528481 0.264240 0.964457i \(-0.414879\pi\)
0.264240 + 0.964457i \(0.414879\pi\)
\(264\) 0 0
\(265\) 8.89250 0.546262
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 13.4405 0.819481 0.409740 0.912202i \(-0.365619\pi\)
0.409740 + 0.912202i \(0.365619\pi\)
\(270\) 0 0
\(271\) 3.38699 0.205745 0.102872 0.994695i \(-0.467197\pi\)
0.102872 + 0.994695i \(0.467197\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2.79304 0.168427
\(276\) 0 0
\(277\) −18.7469 −1.12639 −0.563196 0.826323i \(-0.690428\pi\)
−0.563196 + 0.826323i \(0.690428\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 5.21396 0.311039 0.155519 0.987833i \(-0.450295\pi\)
0.155519 + 0.987833i \(0.450295\pi\)
\(282\) 0 0
\(283\) −18.9771 −1.12807 −0.564035 0.825751i \(-0.690752\pi\)
−0.564035 + 0.825751i \(0.690752\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 20.5614 1.21370
\(288\) 0 0
\(289\) 44.3240 2.60730
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 27.3976 1.60059 0.800293 0.599609i \(-0.204677\pi\)
0.800293 + 0.599609i \(0.204677\pi\)
\(294\) 0 0
\(295\) 3.31342 0.192915
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 3.73151 0.215799
\(300\) 0 0
\(301\) 16.1521 0.930989
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −11.2180 −0.642338
\(306\) 0 0
\(307\) 1.18353 0.0675475 0.0337738 0.999430i \(-0.489247\pi\)
0.0337738 + 0.999430i \(0.489247\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −18.5770 −1.05340 −0.526702 0.850050i \(-0.676572\pi\)
−0.526702 + 0.850050i \(0.676572\pi\)
\(312\) 0 0
\(313\) −8.50094 −0.480502 −0.240251 0.970711i \(-0.577230\pi\)
−0.240251 + 0.970711i \(0.577230\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −21.5884 −1.21252 −0.606262 0.795265i \(-0.707332\pi\)
−0.606262 + 0.795265i \(0.707332\pi\)
\(318\) 0 0
\(319\) −7.70443 −0.431366
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 49.1745 2.73614
\(324\) 0 0
\(325\) 3.73151 0.206987
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −22.3015 −1.22952
\(330\) 0 0
\(331\) 24.0288 1.32074 0.660372 0.750939i \(-0.270399\pi\)
0.660372 + 0.750939i \(0.270399\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −5.52105 −0.301647
\(336\) 0 0
\(337\) −19.7960 −1.07836 −0.539178 0.842192i \(-0.681265\pi\)
−0.539178 + 0.842192i \(0.681265\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −6.95452 −0.376609
\(342\) 0 0
\(343\) 4.92585 0.265971
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −3.52388 −0.189172 −0.0945859 0.995517i \(-0.530153\pi\)
−0.0945859 + 0.995517i \(0.530153\pi\)
\(348\) 0 0
\(349\) 9.10979 0.487636 0.243818 0.969821i \(-0.421600\pi\)
0.243818 + 0.969821i \(0.421600\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 24.7224 1.31584 0.657920 0.753088i \(-0.271436\pi\)
0.657920 + 0.753088i \(0.271436\pi\)
\(354\) 0 0
\(355\) 6.34452 0.336732
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −11.3895 −0.601112 −0.300556 0.953764i \(-0.597172\pi\)
−0.300556 + 0.953764i \(0.597172\pi\)
\(360\) 0 0
\(361\) 20.4320 1.07537
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −15.3824 −0.805154
\(366\) 0 0
\(367\) 11.1306 0.581011 0.290505 0.956873i \(-0.406177\pi\)
0.290505 + 0.956873i \(0.406177\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 31.5815 1.63963
\(372\) 0 0
\(373\) 8.51755 0.441022 0.220511 0.975385i \(-0.429228\pi\)
0.220511 + 0.975385i \(0.429228\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −10.2931 −0.530123
\(378\) 0 0
\(379\) −21.1320 −1.08548 −0.542738 0.839902i \(-0.682612\pi\)
−0.542738 + 0.839902i \(0.682612\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −9.37562 −0.479072 −0.239536 0.970887i \(-0.576995\pi\)
−0.239536 + 0.970887i \(0.576995\pi\)
\(384\) 0 0
\(385\) 9.91943 0.505541
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 16.6352 0.843437 0.421719 0.906727i \(-0.361427\pi\)
0.421719 + 0.906727i \(0.361427\pi\)
\(390\) 0 0
\(391\) 7.83097 0.396029
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 9.62051 0.484060
\(396\) 0 0
\(397\) 23.9261 1.20081 0.600407 0.799694i \(-0.295005\pi\)
0.600407 + 0.799694i \(0.295005\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 12.4457 0.621508 0.310754 0.950490i \(-0.399418\pi\)
0.310754 + 0.950490i \(0.399418\pi\)
\(402\) 0 0
\(403\) −9.29125 −0.462830
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −4.33335 −0.214796
\(408\) 0 0
\(409\) 27.0419 1.33714 0.668568 0.743651i \(-0.266907\pi\)
0.668568 + 0.743651i \(0.266907\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 11.7676 0.579043
\(414\) 0 0
\(415\) 5.83097 0.286231
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −10.0949 −0.493169 −0.246585 0.969121i \(-0.579308\pi\)
−0.246585 + 0.969121i \(0.579308\pi\)
\(420\) 0 0
\(421\) −28.5268 −1.39031 −0.695156 0.718858i \(-0.744665\pi\)
−0.695156 + 0.718858i \(0.744665\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 7.83097 0.379858
\(426\) 0 0
\(427\) −39.8403 −1.92801
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −21.6081 −1.04082 −0.520412 0.853915i \(-0.674222\pi\)
−0.520412 + 0.853915i \(0.674222\pi\)
\(432\) 0 0
\(433\) −8.21009 −0.394552 −0.197276 0.980348i \(-0.563209\pi\)
−0.197276 + 0.980348i \(0.563209\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 6.27949 0.300389
\(438\) 0 0
\(439\) 24.4429 1.16660 0.583298 0.812258i \(-0.301762\pi\)
0.583298 + 0.812258i \(0.301762\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −32.5074 −1.54447 −0.772237 0.635335i \(-0.780862\pi\)
−0.772237 + 0.635335i \(0.780862\pi\)
\(444\) 0 0
\(445\) 0.390487 0.0185109
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 24.5635 1.15922 0.579612 0.814893i \(-0.303204\pi\)
0.579612 + 0.814893i \(0.303204\pi\)
\(450\) 0 0
\(451\) −16.1704 −0.761436
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 13.2524 0.621281
\(456\) 0 0
\(457\) −29.6798 −1.38836 −0.694180 0.719801i \(-0.744233\pi\)
−0.694180 + 0.719801i \(0.744233\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 34.2239 1.59397 0.796983 0.604001i \(-0.206428\pi\)
0.796983 + 0.604001i \(0.206428\pi\)
\(462\) 0 0
\(463\) −27.8074 −1.29232 −0.646159 0.763203i \(-0.723626\pi\)
−0.646159 + 0.763203i \(0.723626\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −22.3207 −1.03288 −0.516440 0.856323i \(-0.672743\pi\)
−0.516440 + 0.856323i \(0.672743\pi\)
\(468\) 0 0
\(469\) −19.6079 −0.905408
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −12.7027 −0.584070
\(474\) 0 0
\(475\) 6.27949 0.288123
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 32.7535 1.49655 0.748274 0.663390i \(-0.230883\pi\)
0.748274 + 0.663390i \(0.230883\pi\)
\(480\) 0 0
\(481\) −5.78936 −0.263972
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −0.961896 −0.0436774
\(486\) 0 0
\(487\) −25.9996 −1.17816 −0.589078 0.808076i \(-0.700509\pi\)
−0.589078 + 0.808076i \(0.700509\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 7.67348 0.346299 0.173150 0.984896i \(-0.444606\pi\)
0.173150 + 0.984896i \(0.444606\pi\)
\(492\) 0 0
\(493\) −21.6012 −0.972871
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 22.5324 1.01072
\(498\) 0 0
\(499\) 15.2951 0.684701 0.342350 0.939572i \(-0.388777\pi\)
0.342350 + 0.939572i \(0.388777\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 9.79654 0.436806 0.218403 0.975859i \(-0.429915\pi\)
0.218403 + 0.975859i \(0.429915\pi\)
\(504\) 0 0
\(505\) −16.9035 −0.752196
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −6.25713 −0.277342 −0.138671 0.990338i \(-0.544283\pi\)
−0.138671 + 0.990338i \(0.544283\pi\)
\(510\) 0 0
\(511\) −54.6305 −2.41671
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 6.04143 0.266217
\(516\) 0 0
\(517\) 17.5389 0.771358
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 8.72384 0.382198 0.191099 0.981571i \(-0.438795\pi\)
0.191099 + 0.981571i \(0.438795\pi\)
\(522\) 0 0
\(523\) −8.66404 −0.378852 −0.189426 0.981895i \(-0.560663\pi\)
−0.189426 + 0.981895i \(0.560663\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −19.4987 −0.849376
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −21.6037 −0.935761
\(534\) 0 0
\(535\) 12.3141 0.532384
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 15.6774 0.675273
\(540\) 0 0
\(541\) −36.5660 −1.57209 −0.786047 0.618167i \(-0.787876\pi\)
−0.786047 + 0.618167i \(0.787876\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −14.8579 −0.636442
\(546\) 0 0
\(547\) −0.827834 −0.0353956 −0.0176978 0.999843i \(-0.505634\pi\)
−0.0176978 + 0.999843i \(0.505634\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −17.3216 −0.737924
\(552\) 0 0
\(553\) 34.1670 1.45293
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −0.125533 −0.00531902 −0.00265951 0.999996i \(-0.500847\pi\)
−0.00265951 + 0.999996i \(0.500847\pi\)
\(558\) 0 0
\(559\) −16.9708 −0.717789
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 38.3207 1.61503 0.807513 0.589849i \(-0.200813\pi\)
0.807513 + 0.589849i \(0.200813\pi\)
\(564\) 0 0
\(565\) 3.21113 0.135093
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 28.8715 1.21036 0.605179 0.796090i \(-0.293102\pi\)
0.605179 + 0.796090i \(0.293102\pi\)
\(570\) 0 0
\(571\) 15.0514 0.629881 0.314940 0.949111i \(-0.398015\pi\)
0.314940 + 0.949111i \(0.398015\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.00000 0.0417029
\(576\) 0 0
\(577\) −21.0561 −0.876577 −0.438288 0.898834i \(-0.644415\pi\)
−0.438288 + 0.898834i \(0.644415\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 20.7086 0.859136
\(582\) 0 0
\(583\) −24.8371 −1.02865
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −22.2751 −0.919393 −0.459696 0.888076i \(-0.652042\pi\)
−0.459696 + 0.888076i \(0.652042\pi\)
\(588\) 0 0
\(589\) −15.6356 −0.644253
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 8.45642 0.347263 0.173632 0.984811i \(-0.444450\pi\)
0.173632 + 0.984811i \(0.444450\pi\)
\(594\) 0 0
\(595\) 27.8115 1.14016
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 10.0040 0.408752 0.204376 0.978892i \(-0.434483\pi\)
0.204376 + 0.978892i \(0.434483\pi\)
\(600\) 0 0
\(601\) 14.8119 0.604191 0.302096 0.953278i \(-0.402314\pi\)
0.302096 + 0.953278i \(0.402314\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 3.19892 0.130055
\(606\) 0 0
\(607\) 10.8883 0.441944 0.220972 0.975280i \(-0.429077\pi\)
0.220972 + 0.975280i \(0.429077\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 23.4320 0.947955
\(612\) 0 0
\(613\) 3.35238 0.135401 0.0677007 0.997706i \(-0.478434\pi\)
0.0677007 + 0.997706i \(0.478434\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 21.8848 0.881050 0.440525 0.897740i \(-0.354792\pi\)
0.440525 + 0.897740i \(0.354792\pi\)
\(618\) 0 0
\(619\) −10.0762 −0.404997 −0.202498 0.979283i \(-0.564906\pi\)
−0.202498 + 0.979283i \(0.564906\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 1.38681 0.0555613
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −12.1496 −0.484436
\(630\) 0 0
\(631\) 6.50485 0.258954 0.129477 0.991582i \(-0.458670\pi\)
0.129477 + 0.991582i \(0.458670\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −0.145425 −0.00577100
\(636\) 0 0
\(637\) 20.9450 0.829871
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.60723 0.0634816 0.0317408 0.999496i \(-0.489895\pi\)
0.0317408 + 0.999496i \(0.489895\pi\)
\(642\) 0 0
\(643\) −7.73605 −0.305080 −0.152540 0.988297i \(-0.548745\pi\)
−0.152540 + 0.988297i \(0.548745\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 8.89232 0.349593 0.174797 0.984605i \(-0.444073\pi\)
0.174797 + 0.984605i \(0.444073\pi\)
\(648\) 0 0
\(649\) −9.25452 −0.363272
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −31.2055 −1.22117 −0.610583 0.791952i \(-0.709065\pi\)
−0.610583 + 0.791952i \(0.709065\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 21.7051 0.845509 0.422755 0.906244i \(-0.361063\pi\)
0.422755 + 0.906244i \(0.361063\pi\)
\(660\) 0 0
\(661\) 30.0564 1.16906 0.584529 0.811372i \(-0.301279\pi\)
0.584529 + 0.811372i \(0.301279\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 22.3015 0.864814
\(666\) 0 0
\(667\) −2.75844 −0.106807
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 31.3322 1.20957
\(672\) 0 0
\(673\) 16.2795 0.627528 0.313764 0.949501i \(-0.398410\pi\)
0.313764 + 0.949501i \(0.398410\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 4.70723 0.180914 0.0904568 0.995900i \(-0.471167\pi\)
0.0904568 + 0.995900i \(0.471167\pi\)
\(678\) 0 0
\(679\) −3.41616 −0.131100
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −9.82536 −0.375957 −0.187978 0.982173i \(-0.560193\pi\)
−0.187978 + 0.982173i \(0.560193\pi\)
\(684\) 0 0
\(685\) −6.16450 −0.235533
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −33.1824 −1.26415
\(690\) 0 0
\(691\) −43.1718 −1.64233 −0.821167 0.570689i \(-0.806676\pi\)
−0.821167 + 0.570689i \(0.806676\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −14.0690 −0.533669
\(696\) 0 0
\(697\) −45.3377 −1.71729
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 1.44539 0.0545915 0.0272957 0.999627i \(-0.491310\pi\)
0.0272957 + 0.999627i \(0.491310\pi\)
\(702\) 0 0
\(703\) −9.74250 −0.367445
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −60.0324 −2.25775
\(708\) 0 0
\(709\) −28.9697 −1.08798 −0.543991 0.839091i \(-0.683087\pi\)
−0.543991 + 0.839091i \(0.683087\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −2.48995 −0.0932492
\(714\) 0 0
\(715\) −10.4223 −0.389770
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −42.4742 −1.58402 −0.792011 0.610507i \(-0.790966\pi\)
−0.792011 + 0.610507i \(0.790966\pi\)
\(720\) 0 0
\(721\) 21.4560 0.799064
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −2.75844 −0.102446
\(726\) 0 0
\(727\) −3.10857 −0.115291 −0.0576453 0.998337i \(-0.518359\pi\)
−0.0576453 + 0.998337i \(0.518359\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −35.6151 −1.31727
\(732\) 0 0
\(733\) 6.20453 0.229170 0.114585 0.993413i \(-0.463446\pi\)
0.114585 + 0.993413i \(0.463446\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 15.4205 0.568022
\(738\) 0 0
\(739\) −21.5010 −0.790926 −0.395463 0.918482i \(-0.629416\pi\)
−0.395463 + 0.918482i \(0.629416\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 25.4469 0.933558 0.466779 0.884374i \(-0.345414\pi\)
0.466779 + 0.884374i \(0.345414\pi\)
\(744\) 0 0
\(745\) 13.7964 0.505460
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 43.7332 1.59798
\(750\) 0 0
\(751\) 49.9066 1.82112 0.910560 0.413378i \(-0.135651\pi\)
0.910560 + 0.413378i \(0.135651\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −16.1989 −0.589539
\(756\) 0 0
\(757\) 31.8486 1.15756 0.578778 0.815485i \(-0.303530\pi\)
0.578778 + 0.815485i \(0.303530\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −7.63541 −0.276783 −0.138392 0.990378i \(-0.544193\pi\)
−0.138392 + 0.990378i \(0.544193\pi\)
\(762\) 0 0
\(763\) −52.7675 −1.91031
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −12.3641 −0.446440
\(768\) 0 0
\(769\) −3.36880 −0.121482 −0.0607410 0.998154i \(-0.519346\pi\)
−0.0607410 + 0.998154i \(0.519346\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −5.77800 −0.207820 −0.103910 0.994587i \(-0.533135\pi\)
−0.103910 + 0.994587i \(0.533135\pi\)
\(774\) 0 0
\(775\) −2.48995 −0.0894415
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −36.3553 −1.30257
\(780\) 0 0
\(781\) −17.7205 −0.634090
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 14.1105 0.503624
\(786\) 0 0
\(787\) 6.46988 0.230626 0.115313 0.993329i \(-0.463213\pi\)
0.115313 + 0.993329i \(0.463213\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 11.4043 0.405489
\(792\) 0 0
\(793\) 41.8599 1.48649
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 21.9636 0.777990 0.388995 0.921240i \(-0.372822\pi\)
0.388995 + 0.921240i \(0.372822\pi\)
\(798\) 0 0
\(799\) 49.1745 1.73967
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 42.9638 1.51616
\(804\) 0 0
\(805\) 3.55148 0.125173
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 42.7222 1.50203 0.751017 0.660283i \(-0.229564\pi\)
0.751017 + 0.660283i \(0.229564\pi\)
\(810\) 0 0
\(811\) −30.2347 −1.06169 −0.530843 0.847470i \(-0.678124\pi\)
−0.530843 + 0.847470i \(0.678124\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −21.2480 −0.744286
\(816\) 0 0
\(817\) −28.5590 −0.999152
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 18.3260 0.639581 0.319791 0.947488i \(-0.396387\pi\)
0.319791 + 0.947488i \(0.396387\pi\)
\(822\) 0 0
\(823\) −14.5081 −0.505721 −0.252861 0.967503i \(-0.581371\pi\)
−0.252861 + 0.967503i \(0.581371\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 28.0452 0.975228 0.487614 0.873059i \(-0.337867\pi\)
0.487614 + 0.873059i \(0.337867\pi\)
\(828\) 0 0
\(829\) −26.2281 −0.910939 −0.455470 0.890251i \(-0.650529\pi\)
−0.455470 + 0.890251i \(0.650529\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 43.9553 1.52296
\(834\) 0 0
\(835\) 19.3895 0.671000
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −12.2129 −0.421637 −0.210819 0.977525i \(-0.567613\pi\)
−0.210819 + 0.977525i \(0.567613\pi\)
\(840\) 0 0
\(841\) −21.3910 −0.737621
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −0.924149 −0.0317917
\(846\) 0 0
\(847\) 11.3609 0.390365
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −1.55148 −0.0531841
\(852\) 0 0
\(853\) 54.2928 1.85895 0.929474 0.368886i \(-0.120261\pi\)
0.929474 + 0.368886i \(0.120261\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −15.0491 −0.514067 −0.257034 0.966402i \(-0.582745\pi\)
−0.257034 + 0.966402i \(0.582745\pi\)
\(858\) 0 0
\(859\) 34.2351 1.16809 0.584043 0.811723i \(-0.301470\pi\)
0.584043 + 0.811723i \(0.301470\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −14.6488 −0.498652 −0.249326 0.968420i \(-0.580209\pi\)
−0.249326 + 0.968420i \(0.580209\pi\)
\(864\) 0 0
\(865\) −13.1030 −0.445514
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −26.8705 −0.911518
\(870\) 0 0
\(871\) 20.6018 0.698066
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 3.55148 0.120062
\(876\) 0 0
\(877\) −54.2319 −1.83128 −0.915641 0.401998i \(-0.868316\pi\)
−0.915641 + 0.401998i \(0.868316\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −44.3162 −1.49305 −0.746525 0.665357i \(-0.768279\pi\)
−0.746525 + 0.665357i \(0.768279\pi\)
\(882\) 0 0
\(883\) 38.2704 1.28790 0.643951 0.765067i \(-0.277294\pi\)
0.643951 + 0.765067i \(0.277294\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 5.80699 0.194980 0.0974898 0.995237i \(-0.468919\pi\)
0.0974898 + 0.995237i \(0.468919\pi\)
\(888\) 0 0
\(889\) −0.516473 −0.0173219
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 39.4320 1.31954
\(894\) 0 0
\(895\) −14.0759 −0.470504
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 6.86837 0.229073
\(900\) 0 0
\(901\) −69.6369 −2.31994
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −21.1374 −0.702630
\(906\) 0 0
\(907\) −12.3419 −0.409805 −0.204903 0.978782i \(-0.565688\pi\)
−0.204903 + 0.978782i \(0.565688\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −27.2190 −0.901807 −0.450903 0.892573i \(-0.648898\pi\)
−0.450903 + 0.892573i \(0.648898\pi\)
\(912\) 0 0
\(913\) −16.2861 −0.538992
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 38.6836 1.27605 0.638027 0.770014i \(-0.279751\pi\)
0.638027 + 0.770014i \(0.279751\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −23.6746 −0.779260
\(924\) 0 0
\(925\) −1.55148 −0.0510124
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 17.1365 0.562230 0.281115 0.959674i \(-0.409296\pi\)
0.281115 + 0.959674i \(0.409296\pi\)
\(930\) 0 0
\(931\) 35.2468 1.15517
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −21.8722 −0.715298
\(936\) 0 0
\(937\) 44.4382 1.45173 0.725866 0.687836i \(-0.241439\pi\)
0.725866 + 0.687836i \(0.241439\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 19.1745 0.625069 0.312535 0.949906i \(-0.398822\pi\)
0.312535 + 0.949906i \(0.398822\pi\)
\(942\) 0 0
\(943\) −5.78954 −0.188533
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −56.7662 −1.84465 −0.922327 0.386410i \(-0.873715\pi\)
−0.922327 + 0.386410i \(0.873715\pi\)
\(948\) 0 0
\(949\) 57.3997 1.86327
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −37.8953 −1.22755 −0.613774 0.789482i \(-0.710349\pi\)
−0.613774 + 0.789482i \(0.710349\pi\)
\(954\) 0 0
\(955\) 2.81647 0.0911389
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −21.8931 −0.706965
\(960\) 0 0
\(961\) −24.8002 −0.800005
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −15.4560 −0.497547
\(966\) 0 0
\(967\) 58.9924 1.89707 0.948534 0.316674i \(-0.102566\pi\)
0.948534 + 0.316674i \(0.102566\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −19.9675 −0.640787 −0.320394 0.947284i \(-0.603815\pi\)
−0.320394 + 0.947284i \(0.603815\pi\)
\(972\) 0 0
\(973\) −49.9659 −1.60183
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 5.54712 0.177468 0.0887341 0.996055i \(-0.471718\pi\)
0.0887341 + 0.996055i \(0.471718\pi\)
\(978\) 0 0
\(979\) −1.09065 −0.0348572
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −12.1636 −0.387959 −0.193979 0.981006i \(-0.562139\pi\)
−0.193979 + 0.981006i \(0.562139\pi\)
\(984\) 0 0
\(985\) 25.7311 0.819862
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −4.54798 −0.144617
\(990\) 0 0
\(991\) 18.1991 0.578113 0.289057 0.957312i \(-0.406658\pi\)
0.289057 + 0.957312i \(0.406658\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −5.95857 −0.188899
\(996\) 0 0
\(997\) 49.4097 1.56482 0.782411 0.622762i \(-0.213990\pi\)
0.782411 + 0.622762i \(0.213990\pi\)
\(998\) 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.br.1.2 5
3.2 odd 2 2760.2.a.w.1.2 5
12.11 even 2 5520.2.a.cc.1.4 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2760.2.a.w.1.2 5 3.2 odd 2
5520.2.a.cc.1.4 5 12.11 even 2
8280.2.a.br.1.2 5 1.1 even 1 trivial