Properties

Label 8280.2.a.br.1.5
Level $8280$
Weight $2$
Character 8280.1
Self dual yes
Analytic conductor $66.116$
Analytic rank $0$
Dimension $5$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

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 1.5
Root \(4.50582\) of defining polynomial
Character \(\chi\) \(=\) 8280.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{5} +2.89831 q^{7} +O(q^{10})\) \(q-1.00000 q^{5} +2.89831 q^{7} -3.43123 q^{11} -4.72973 q^{13} -2.61639 q^{17} +2.28192 q^{19} +1.00000 q^{23} +1.00000 q^{25} -2.53292 q^{29} +6.19681 q^{31} -2.89831 q^{35} +4.89831 q^{37} -10.4787 q^{41} -9.01165 q^{43} +2.28192 q^{47} +1.40019 q^{49} -0.682109 q^{53} +3.43123 q^{55} +14.2753 q^{59} +4.98342 q^{61} +4.72973 q^{65} +1.74900 q^{67} +6.32954 q^{71} -1.51470 q^{73} -9.94476 q^{77} -3.86234 q^{79} +4.61639 q^{83} +2.61639 q^{85} +6.31015 q^{89} -13.7082 q^{91} -2.28192 q^{95} +17.8741 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 5 q^{5} - 4 q^{7}+O(q^{10}) \) 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
\(7\) 2.89831 1.09546 0.547729 0.836656i \(-0.315493\pi\)
0.547729 + 0.836656i \(0.315493\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −3.43123 −1.03455 −0.517277 0.855818i \(-0.673054\pi\)
−0.517277 + 0.855818i \(0.673054\pi\)
\(12\) 0 0
\(13\) −4.72973 −1.31179 −0.655895 0.754852i \(-0.727709\pi\)
−0.655895 + 0.754852i \(0.727709\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2.61639 −0.634568 −0.317284 0.948331i \(-0.602771\pi\)
−0.317284 + 0.948331i \(0.602771\pi\)
\(18\) 0 0
\(19\) 2.28192 0.523508 0.261754 0.965135i \(-0.415699\pi\)
0.261754 + 0.965135i \(0.415699\pi\)
\(20\) 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
\(29\) −2.53292 −0.470351 −0.235176 0.971953i \(-0.575567\pi\)
−0.235176 + 0.971953i \(0.575567\pi\)
\(30\) 0 0
\(31\) 6.19681 1.11298 0.556490 0.830854i \(-0.312148\pi\)
0.556490 + 0.830854i \(0.312148\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −2.89831 −0.489904
\(36\) 0 0
\(37\) 4.89831 0.805277 0.402638 0.915359i \(-0.368093\pi\)
0.402638 + 0.915359i \(0.368093\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −10.4787 −1.63650 −0.818251 0.574861i \(-0.805056\pi\)
−0.818251 + 0.574861i \(0.805056\pi\)
\(42\) 0 0
\(43\) −9.01165 −1.37426 −0.687132 0.726533i \(-0.741130\pi\)
−0.687132 + 0.726533i \(0.741130\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 2.28192 0.332852 0.166426 0.986054i \(-0.446777\pi\)
0.166426 + 0.986054i \(0.446777\pi\)
\(48\) 0 0
\(49\) 1.40019 0.200027
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −0.682109 −0.0936949 −0.0468475 0.998902i \(-0.514917\pi\)
−0.0468475 + 0.998902i \(0.514917\pi\)
\(54\) 0 0
\(55\) 3.43123 0.462667
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 14.2753 1.85849 0.929246 0.369462i \(-0.120458\pi\)
0.929246 + 0.369462i \(0.120458\pi\)
\(60\) 0 0
\(61\) 4.98342 0.638061 0.319031 0.947744i \(-0.396643\pi\)
0.319031 + 0.947744i \(0.396643\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 4.72973 0.586651
\(66\) 0 0
\(67\) 1.74900 0.213674 0.106837 0.994277i \(-0.465928\pi\)
0.106837 + 0.994277i \(0.465928\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 6.32954 0.751178 0.375589 0.926786i \(-0.377440\pi\)
0.375589 + 0.926786i \(0.377440\pi\)
\(72\) 0 0
\(73\) −1.51470 −0.177282 −0.0886410 0.996064i \(-0.528252\pi\)
−0.0886410 + 0.996064i \(0.528252\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −9.94476 −1.13331
\(78\) 0 0
\(79\) −3.86234 −0.434547 −0.217273 0.976111i \(-0.569716\pi\)
−0.217273 + 0.976111i \(0.569716\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 4.61639 0.506715 0.253357 0.967373i \(-0.418465\pi\)
0.253357 + 0.967373i \(0.418465\pi\)
\(84\) 0 0
\(85\) 2.61639 0.283787
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 6.31015 0.668874 0.334437 0.942418i \(-0.391454\pi\)
0.334437 + 0.942418i \(0.391454\pi\)
\(90\) 0 0
\(91\) −13.7082 −1.43701
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −2.28192 −0.234120
\(96\) 0 0
\(97\) 17.8741 1.81484 0.907420 0.420225i \(-0.138049\pi\)
0.907420 + 0.420225i \(0.138049\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −3.76570 −0.374701 −0.187351 0.982293i \(-0.559990\pi\)
−0.187351 + 0.982293i \(0.559990\pi\)
\(102\) 0 0
\(103\) 9.09512 0.896168 0.448084 0.893991i \(-0.352106\pi\)
0.448084 + 0.893991i \(0.352106\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −2.31777 −0.224067 −0.112034 0.993704i \(-0.535736\pi\)
−0.112034 + 0.993704i \(0.535736\pi\)
\(108\) 0 0
\(109\) 12.6463 1.21129 0.605646 0.795734i \(-0.292915\pi\)
0.605646 + 0.795734i \(0.292915\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −6.11439 −0.575193 −0.287597 0.957752i \(-0.592856\pi\)
−0.287597 + 0.957752i \(0.592856\pi\)
\(114\) 0 0
\(115\) −1.00000 −0.0932505
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −7.58311 −0.695142
\(120\) 0 0
\(121\) 0.773325 0.0703023
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 4.13273 0.366720 0.183360 0.983046i \(-0.441303\pi\)
0.183360 + 0.983046i \(0.441303\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) 6.61370 0.573481
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −4.49812 −0.384300 −0.192150 0.981366i \(-0.561546\pi\)
−0.192150 + 0.981366i \(0.561546\pi\)
\(138\) 0 0
\(139\) 14.7606 1.25198 0.625991 0.779830i \(-0.284695\pi\)
0.625991 + 0.779830i \(0.284695\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 16.2288 1.35712
\(144\) 0 0
\(145\) 2.53292 0.210348
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −9.34776 −0.765798 −0.382899 0.923790i \(-0.625074\pi\)
−0.382899 + 0.923790i \(0.625074\pi\)
\(150\) 0 0
\(151\) 12.2267 0.994993 0.497496 0.867466i \(-0.334253\pi\)
0.497496 + 0.867466i \(0.334253\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −6.19681 −0.497740
\(156\) 0 0
\(157\) 0.334473 0.0266938 0.0133469 0.999911i \(-0.495751\pi\)
0.0133469 + 0.999911i \(0.495751\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 2.89831 0.228419
\(162\) 0 0
\(163\) −12.0952 −0.947372 −0.473686 0.880694i \(-0.657077\pi\)
−0.473686 + 0.880694i \(0.657077\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 19.3346 1.49616 0.748078 0.663610i \(-0.230977\pi\)
0.748078 + 0.663610i \(0.230977\pi\)
\(168\) 0 0
\(169\) 9.37032 0.720794
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0.203383 0.0154629 0.00773147 0.999970i \(-0.497539\pi\)
0.00773147 + 0.999970i \(0.497539\pi\)
\(174\) 0 0
\(175\) 2.89831 0.219092
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 5.62968 0.420782 0.210391 0.977617i \(-0.432526\pi\)
0.210391 + 0.977617i \(0.432526\pi\)
\(180\) 0 0
\(181\) 14.9282 1.10960 0.554801 0.831983i \(-0.312794\pi\)
0.554801 + 0.831983i \(0.312794\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −4.89831 −0.360131
\(186\) 0 0
\(187\) 8.97743 0.656495
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −15.7414 −1.13901 −0.569503 0.821989i \(-0.692864\pi\)
−0.569503 + 0.821989i \(0.692864\pi\)
\(192\) 0 0
\(193\) 20.3605 1.46558 0.732789 0.680456i \(-0.238218\pi\)
0.732789 + 0.680456i \(0.238218\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 7.16108 0.510206 0.255103 0.966914i \(-0.417891\pi\)
0.255103 + 0.966914i \(0.417891\pi\)
\(198\) 0 0
\(199\) 21.0951 1.49539 0.747697 0.664041i \(-0.231160\pi\)
0.747697 + 0.664041i \(0.231160\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −7.34118 −0.515250
\(204\) 0 0
\(205\) 10.4787 0.731866
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −7.82978 −0.541597
\(210\) 0 0
\(211\) −6.76064 −0.465422 −0.232711 0.972546i \(-0.574760\pi\)
−0.232711 + 0.972546i \(0.574760\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 9.01165 0.614589
\(216\) 0 0
\(217\) 17.9603 1.21922
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 12.3748 0.832420
\(222\) 0 0
\(223\) −1.58535 −0.106163 −0.0530816 0.998590i \(-0.516904\pi\)
−0.0530816 + 0.998590i \(0.516904\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −14.3279 −0.950976 −0.475488 0.879722i \(-0.657728\pi\)
−0.475488 + 0.879722i \(0.657728\pi\)
\(228\) 0 0
\(229\) −16.8200 −1.11150 −0.555749 0.831350i \(-0.687569\pi\)
−0.555749 + 0.831350i \(0.687569\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 14.2267 0.932020 0.466010 0.884779i \(-0.345691\pi\)
0.466010 + 0.884779i \(0.345691\pi\)
\(234\) 0 0
\(235\) −2.28192 −0.148856
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −18.6279 −1.20494 −0.602470 0.798142i \(-0.705817\pi\)
−0.602470 + 0.798142i \(0.705817\pi\)
\(240\) 0 0
\(241\) 13.3478 0.859805 0.429902 0.902875i \(-0.358548\pi\)
0.429902 + 0.902875i \(0.358548\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1.40019 −0.0894550
\(246\) 0 0
\(247\) −10.7929 −0.686733
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −12.7425 −0.804302 −0.402151 0.915573i \(-0.631737\pi\)
−0.402151 + 0.915573i \(0.631737\pi\)
\(252\) 0 0
\(253\) −3.43123 −0.215719
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 17.1079 1.06716 0.533582 0.845748i \(-0.320846\pi\)
0.533582 + 0.845748i \(0.320846\pi\)
\(258\) 0 0
\(259\) 14.1968 0.882147
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −0.141565 −0.00872927 −0.00436463 0.999990i \(-0.501389\pi\)
−0.00436463 + 0.999990i \(0.501389\pi\)
\(264\) 0 0
\(265\) 0.682109 0.0419016
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 9.69376 0.591039 0.295519 0.955337i \(-0.404507\pi\)
0.295519 + 0.955337i \(0.404507\pi\)
\(270\) 0 0
\(271\) 7.59981 0.461655 0.230828 0.972995i \(-0.425857\pi\)
0.230828 + 0.972995i \(0.425857\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −3.43123 −0.206911
\(276\) 0 0
\(277\) −19.2383 −1.15592 −0.577959 0.816066i \(-0.696151\pi\)
−0.577959 + 0.816066i \(0.696151\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −10.3887 −0.619737 −0.309868 0.950779i \(-0.600285\pi\)
−0.309868 + 0.950779i \(0.600285\pi\)
\(282\) 0 0
\(283\) −20.1095 −1.19538 −0.597691 0.801726i \(-0.703915\pi\)
−0.597691 + 0.801726i \(0.703915\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −30.3706 −1.79272
\(288\) 0 0
\(289\) −10.1545 −0.597324
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −5.27935 −0.308423 −0.154211 0.988038i \(-0.549284\pi\)
−0.154211 + 0.988038i \(0.549284\pi\)
\(294\) 0 0
\(295\) −14.2753 −0.831143
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −4.72973 −0.273527
\(300\) 0 0
\(301\) −26.1185 −1.50545
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −4.98342 −0.285350
\(306\) 0 0
\(307\) −11.7414 −0.670116 −0.335058 0.942198i \(-0.608756\pi\)
−0.335058 + 0.942198i \(0.608756\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 23.7039 1.34412 0.672062 0.740495i \(-0.265409\pi\)
0.672062 + 0.740495i \(0.265409\pi\)
\(312\) 0 0
\(313\) 12.6446 0.714716 0.357358 0.933967i \(-0.383678\pi\)
0.357358 + 0.933967i \(0.383678\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 21.1079 1.18554 0.592770 0.805372i \(-0.298034\pi\)
0.592770 + 0.805372i \(0.298034\pi\)
\(318\) 0 0
\(319\) 8.69102 0.486604
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −5.97039 −0.332201
\(324\) 0 0
\(325\) −4.72973 −0.262358
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 6.61370 0.364625
\(330\) 0 0
\(331\) −10.0266 −0.551111 −0.275556 0.961285i \(-0.588862\pi\)
−0.275556 + 0.961285i \(0.588862\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −1.74900 −0.0955580
\(336\) 0 0
\(337\) 9.08359 0.494815 0.247407 0.968912i \(-0.420421\pi\)
0.247407 + 0.968912i \(0.420421\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −21.2627 −1.15144
\(342\) 0 0
\(343\) −16.2300 −0.876336
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 18.7541 1.00677 0.503386 0.864062i \(-0.332088\pi\)
0.503386 + 0.864062i \(0.332088\pi\)
\(348\) 0 0
\(349\) −12.9276 −0.691998 −0.345999 0.938235i \(-0.612460\pi\)
−0.345999 + 0.938235i \(0.612460\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −13.5712 −0.722320 −0.361160 0.932504i \(-0.617619\pi\)
−0.361160 + 0.932504i \(0.617619\pi\)
\(354\) 0 0
\(355\) −6.32954 −0.335937
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 27.3346 1.44267 0.721333 0.692589i \(-0.243530\pi\)
0.721333 + 0.692589i \(0.243530\pi\)
\(360\) 0 0
\(361\) −13.7929 −0.725940
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1.51470 0.0792830
\(366\) 0 0
\(367\) 14.0591 0.733881 0.366941 0.930244i \(-0.380405\pi\)
0.366941 + 0.930244i \(0.380405\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −1.97696 −0.102639
\(372\) 0 0
\(373\) 15.6590 0.810790 0.405395 0.914142i \(-0.367134\pi\)
0.405395 + 0.914142i \(0.367134\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 11.9800 0.617002
\(378\) 0 0
\(379\) 38.5121 1.97824 0.989118 0.147124i \(-0.0470018\pi\)
0.989118 + 0.147124i \(0.0470018\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −1.61627 −0.0825875 −0.0412938 0.999147i \(-0.513148\pi\)
−0.0412938 + 0.999147i \(0.513148\pi\)
\(384\) 0 0
\(385\) 9.94476 0.506832
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −25.1844 −1.27690 −0.638449 0.769664i \(-0.720424\pi\)
−0.638449 + 0.769664i \(0.720424\pi\)
\(390\) 0 0
\(391\) −2.61639 −0.132317
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 3.86234 0.194335
\(396\) 0 0
\(397\) −22.3065 −1.11953 −0.559766 0.828651i \(-0.689109\pi\)
−0.559766 + 0.828651i \(0.689109\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 37.4014 1.86774 0.933868 0.357618i \(-0.116411\pi\)
0.933868 + 0.357618i \(0.116411\pi\)
\(402\) 0 0
\(403\) −29.3092 −1.46000
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −16.8072 −0.833103
\(408\) 0 0
\(409\) 32.1869 1.59154 0.795771 0.605598i \(-0.207066\pi\)
0.795771 + 0.605598i \(0.207066\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 41.3743 2.03590
\(414\) 0 0
\(415\) −4.61639 −0.226610
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 13.0012 0.635149 0.317574 0.948233i \(-0.397132\pi\)
0.317574 + 0.948233i \(0.397132\pi\)
\(420\) 0 0
\(421\) 16.4064 0.799601 0.399800 0.916602i \(-0.369079\pi\)
0.399800 + 0.916602i \(0.369079\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −2.61639 −0.126914
\(426\) 0 0
\(427\) 14.4435 0.698969
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 15.7581 0.759040 0.379520 0.925184i \(-0.376089\pi\)
0.379520 + 0.925184i \(0.376089\pi\)
\(432\) 0 0
\(433\) 20.9101 1.00487 0.502437 0.864614i \(-0.332437\pi\)
0.502437 + 0.864614i \(0.332437\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.28192 0.109159
\(438\) 0 0
\(439\) −9.85307 −0.470261 −0.235131 0.971964i \(-0.575552\pi\)
−0.235131 + 0.971964i \(0.575552\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 22.2069 1.05508 0.527542 0.849529i \(-0.323114\pi\)
0.527542 + 0.849529i \(0.323114\pi\)
\(444\) 0 0
\(445\) −6.31015 −0.299130
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 37.6783 1.77815 0.889075 0.457761i \(-0.151348\pi\)
0.889075 + 0.457761i \(0.151348\pi\)
\(450\) 0 0
\(451\) 35.9549 1.69305
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 13.7082 0.642651
\(456\) 0 0
\(457\) 12.8116 0.599299 0.299650 0.954049i \(-0.403130\pi\)
0.299650 + 0.954049i \(0.403130\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −25.8610 −1.20446 −0.602232 0.798321i \(-0.705722\pi\)
−0.602232 + 0.798321i \(0.705722\pi\)
\(462\) 0 0
\(463\) −10.8999 −0.506564 −0.253282 0.967393i \(-0.581510\pi\)
−0.253282 + 0.967393i \(0.581510\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −15.8757 −0.734642 −0.367321 0.930094i \(-0.619725\pi\)
−0.367321 + 0.930094i \(0.619725\pi\)
\(468\) 0 0
\(469\) 5.06914 0.234071
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 30.9210 1.42175
\(474\) 0 0
\(475\) 2.28192 0.104702
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −13.0129 −0.594576 −0.297288 0.954788i \(-0.596082\pi\)
−0.297288 + 0.954788i \(0.596082\pi\)
\(480\) 0 0
\(481\) −23.1677 −1.05635
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −17.8741 −0.811621
\(486\) 0 0
\(487\) −1.56865 −0.0710824 −0.0355412 0.999368i \(-0.511315\pi\)
−0.0355412 + 0.999368i \(0.511315\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −13.9382 −0.629021 −0.314511 0.949254i \(-0.601840\pi\)
−0.314511 + 0.949254i \(0.601840\pi\)
\(492\) 0 0
\(493\) 6.62711 0.298470
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 18.3449 0.822883
\(498\) 0 0
\(499\) 7.56103 0.338478 0.169239 0.985575i \(-0.445869\pi\)
0.169239 + 0.985575i \(0.445869\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −7.34118 −0.327327 −0.163664 0.986516i \(-0.552331\pi\)
−0.163664 + 0.986516i \(0.552331\pi\)
\(504\) 0 0
\(505\) 3.76570 0.167571
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −2.74619 −0.121723 −0.0608614 0.998146i \(-0.519385\pi\)
−0.0608614 + 0.998146i \(0.519385\pi\)
\(510\) 0 0
\(511\) −4.39006 −0.194205
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −9.09512 −0.400779
\(516\) 0 0
\(517\) −7.82978 −0.344353
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 14.4971 0.635128 0.317564 0.948237i \(-0.397135\pi\)
0.317564 + 0.948237i \(0.397135\pi\)
\(522\) 0 0
\(523\) −39.4286 −1.72409 −0.862045 0.506832i \(-0.830817\pi\)
−0.862045 + 0.506832i \(0.830817\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −16.2133 −0.706261
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 49.5615 2.14675
\(534\) 0 0
\(535\) 2.31777 0.100206
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −4.80438 −0.206939
\(540\) 0 0
\(541\) −6.74393 −0.289944 −0.144972 0.989436i \(-0.546309\pi\)
−0.144972 + 0.989436i \(0.546309\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −12.6463 −0.541706
\(546\) 0 0
\(547\) −25.7249 −1.09992 −0.549959 0.835192i \(-0.685357\pi\)
−0.549959 + 0.835192i \(0.685357\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −5.77991 −0.246233
\(552\) 0 0
\(553\) −11.1942 −0.476027
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 38.3374 1.62441 0.812204 0.583373i \(-0.198267\pi\)
0.812204 + 0.583373i \(0.198267\pi\)
\(558\) 0 0
\(559\) 42.6226 1.80275
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 31.8757 1.34340 0.671701 0.740822i \(-0.265564\pi\)
0.671701 + 0.740822i \(0.265564\pi\)
\(564\) 0 0
\(565\) 6.11439 0.257234
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −41.4249 −1.73662 −0.868311 0.496020i \(-0.834794\pi\)
−0.868311 + 0.496020i \(0.834794\pi\)
\(570\) 0 0
\(571\) −44.5674 −1.86509 −0.932544 0.361057i \(-0.882416\pi\)
−0.932544 + 0.361057i \(0.882416\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.00000 0.0417029
\(576\) 0 0
\(577\) 30.1418 1.25482 0.627410 0.778689i \(-0.284115\pi\)
0.627410 + 0.778689i \(0.284115\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 13.3797 0.555084
\(582\) 0 0
\(583\) 2.34047 0.0969325
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 15.5215 0.640642 0.320321 0.947309i \(-0.396209\pi\)
0.320321 + 0.947309i \(0.396209\pi\)
\(588\) 0 0
\(589\) 14.1406 0.582654
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 25.4042 1.04323 0.521613 0.853182i \(-0.325331\pi\)
0.521613 + 0.853182i \(0.325331\pi\)
\(594\) 0 0
\(595\) 7.58311 0.310877
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 19.3721 0.791522 0.395761 0.918353i \(-0.370481\pi\)
0.395761 + 0.918353i \(0.370481\pi\)
\(600\) 0 0
\(601\) 6.62687 0.270316 0.135158 0.990824i \(-0.456846\pi\)
0.135158 + 0.990824i \(0.456846\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −0.773325 −0.0314401
\(606\) 0 0
\(607\) 5.99895 0.243490 0.121745 0.992561i \(-0.461151\pi\)
0.121745 + 0.992561i \(0.461151\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −10.7929 −0.436632
\(612\) 0 0
\(613\) 13.5640 0.547843 0.273922 0.961752i \(-0.411679\pi\)
0.273922 + 0.961752i \(0.411679\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 27.9089 1.12357 0.561785 0.827283i \(-0.310115\pi\)
0.561785 + 0.827283i \(0.310115\pi\)
\(618\) 0 0
\(619\) 23.7482 0.954521 0.477260 0.878762i \(-0.341630\pi\)
0.477260 + 0.878762i \(0.341630\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 18.2887 0.732723
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −12.8159 −0.511003
\(630\) 0 0
\(631\) −13.5108 −0.537857 −0.268928 0.963160i \(-0.586670\pi\)
−0.268928 + 0.963160i \(0.586670\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −4.13273 −0.164002
\(636\) 0 0
\(637\) −6.62252 −0.262394
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 38.5556 1.52286 0.761428 0.648250i \(-0.224499\pi\)
0.761428 + 0.648250i \(0.224499\pi\)
\(642\) 0 0
\(643\) −20.3848 −0.803897 −0.401949 0.915662i \(-0.631667\pi\)
−0.401949 + 0.915662i \(0.631667\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 13.3710 0.525670 0.262835 0.964841i \(-0.415342\pi\)
0.262835 + 0.964841i \(0.415342\pi\)
\(648\) 0 0
\(649\) −48.9820 −1.92271
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 6.63699 0.259726 0.129863 0.991532i \(-0.458546\pi\)
0.129863 + 0.991532i \(0.458546\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 25.2897 0.985146 0.492573 0.870271i \(-0.336056\pi\)
0.492573 + 0.870271i \(0.336056\pi\)
\(660\) 0 0
\(661\) 11.8292 0.460101 0.230051 0.973179i \(-0.426111\pi\)
0.230051 + 0.973179i \(0.426111\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −6.61370 −0.256468
\(666\) 0 0
\(667\) −2.53292 −0.0980750
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −17.0992 −0.660109
\(672\) 0 0
\(673\) 12.2819 0.473433 0.236717 0.971579i \(-0.423929\pi\)
0.236717 + 0.971579i \(0.423929\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −17.8065 −0.684360 −0.342180 0.939635i \(-0.611165\pi\)
−0.342180 + 0.939635i \(0.611165\pi\)
\(678\) 0 0
\(679\) 51.8047 1.98808
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 41.3678 1.58289 0.791447 0.611238i \(-0.209328\pi\)
0.791447 + 0.611238i \(0.209328\pi\)
\(684\) 0 0
\(685\) 4.49812 0.171864
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 3.22619 0.122908
\(690\) 0 0
\(691\) −43.6530 −1.66064 −0.830319 0.557289i \(-0.811842\pi\)
−0.830319 + 0.557289i \(0.811842\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −14.7606 −0.559903
\(696\) 0 0
\(697\) 27.4164 1.03847
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 43.2396 1.63314 0.816569 0.577248i \(-0.195873\pi\)
0.816569 + 0.577248i \(0.195873\pi\)
\(702\) 0 0
\(703\) 11.1775 0.421569
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −10.9142 −0.410469
\(708\) 0 0
\(709\) 50.2595 1.88754 0.943768 0.330609i \(-0.107254\pi\)
0.943768 + 0.330609i \(0.107254\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 6.19681 0.232072
\(714\) 0 0
\(715\) −16.2288 −0.606922
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −37.8254 −1.41065 −0.705325 0.708884i \(-0.749199\pi\)
−0.705325 + 0.708884i \(0.749199\pi\)
\(720\) 0 0
\(721\) 26.3605 0.981715
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −2.53292 −0.0940703
\(726\) 0 0
\(727\) −30.9548 −1.14805 −0.574024 0.818838i \(-0.694619\pi\)
−0.574024 + 0.818838i \(0.694619\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 23.5780 0.872063
\(732\) 0 0
\(733\) 42.9781 1.58743 0.793715 0.608289i \(-0.208144\pi\)
0.793715 + 0.608289i \(0.208144\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −6.00121 −0.221057
\(738\) 0 0
\(739\) 12.0322 0.442612 0.221306 0.975204i \(-0.428968\pi\)
0.221306 + 0.975204i \(0.428968\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −11.8686 −0.435415 −0.217708 0.976014i \(-0.569858\pi\)
−0.217708 + 0.976014i \(0.569858\pi\)
\(744\) 0 0
\(745\) 9.34776 0.342475
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −6.71761 −0.245456
\(750\) 0 0
\(751\) 43.7022 1.59472 0.797358 0.603506i \(-0.206230\pi\)
0.797358 + 0.603506i \(0.206230\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −12.2267 −0.444974
\(756\) 0 0
\(757\) −37.3155 −1.35625 −0.678127 0.734945i \(-0.737208\pi\)
−0.678127 + 0.734945i \(0.737208\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 9.45167 0.342623 0.171311 0.985217i \(-0.445200\pi\)
0.171311 + 0.985217i \(0.445200\pi\)
\(762\) 0 0
\(763\) 36.6528 1.32692
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −67.5185 −2.43795
\(768\) 0 0
\(769\) −4.74724 −0.171190 −0.0855949 0.996330i \(-0.527279\pi\)
−0.0855949 + 0.996330i \(0.527279\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −11.1841 −0.402265 −0.201133 0.979564i \(-0.564462\pi\)
−0.201133 + 0.979564i \(0.564462\pi\)
\(774\) 0 0
\(775\) 6.19681 0.222596
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −23.9116 −0.856722
\(780\) 0 0
\(781\) −21.7181 −0.777134
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −0.334473 −0.0119378
\(786\) 0 0
\(787\) −31.9780 −1.13989 −0.569947 0.821682i \(-0.693036\pi\)
−0.569947 + 0.821682i \(0.693036\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −17.7214 −0.630100
\(792\) 0 0
\(793\) −23.5702 −0.837003
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −40.5354 −1.43584 −0.717919 0.696126i \(-0.754905\pi\)
−0.717919 + 0.696126i \(0.754905\pi\)
\(798\) 0 0
\(799\) −5.97039 −0.211217
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 5.19728 0.183408
\(804\) 0 0
\(805\) −2.89831 −0.102152
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 17.1178 0.601829 0.300915 0.953651i \(-0.402708\pi\)
0.300915 + 0.953651i \(0.402708\pi\)
\(810\) 0 0
\(811\) 29.6198 1.04009 0.520046 0.854138i \(-0.325915\pi\)
0.520046 + 0.854138i \(0.325915\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 12.0952 0.423678
\(816\) 0 0
\(817\) −20.5638 −0.719438
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 28.1958 0.984039 0.492020 0.870584i \(-0.336259\pi\)
0.492020 + 0.870584i \(0.336259\pi\)
\(822\) 0 0
\(823\) 41.1535 1.43452 0.717260 0.696806i \(-0.245396\pi\)
0.717260 + 0.696806i \(0.245396\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −14.8433 −0.516152 −0.258076 0.966125i \(-0.583089\pi\)
−0.258076 + 0.966125i \(0.583089\pi\)
\(828\) 0 0
\(829\) 37.1778 1.29124 0.645619 0.763660i \(-0.276599\pi\)
0.645619 + 0.763660i \(0.276599\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −3.66345 −0.126931
\(834\) 0 0
\(835\) −19.3346 −0.669102
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 35.4131 1.22260 0.611299 0.791400i \(-0.290647\pi\)
0.611299 + 0.791400i \(0.290647\pi\)
\(840\) 0 0
\(841\) −22.5843 −0.778770
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −9.37032 −0.322349
\(846\) 0 0
\(847\) 2.24134 0.0770132
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 4.89831 0.167912
\(852\) 0 0
\(853\) 7.58863 0.259830 0.129915 0.991525i \(-0.458530\pi\)
0.129915 + 0.991525i \(0.458530\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 14.3219 0.489227 0.244614 0.969621i \(-0.421339\pi\)
0.244614 + 0.969621i \(0.421339\pi\)
\(858\) 0 0
\(859\) −50.9977 −1.74002 −0.870010 0.493035i \(-0.835887\pi\)
−0.870010 + 0.493035i \(0.835887\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 45.4463 1.54701 0.773505 0.633790i \(-0.218502\pi\)
0.773505 + 0.633790i \(0.218502\pi\)
\(864\) 0 0
\(865\) −0.203383 −0.00691524
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 13.2526 0.449562
\(870\) 0 0
\(871\) −8.27229 −0.280296
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −2.89831 −0.0979807
\(876\) 0 0
\(877\) −12.8832 −0.435036 −0.217518 0.976056i \(-0.569796\pi\)
−0.217518 + 0.976056i \(0.569796\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 33.0480 1.11342 0.556708 0.830709i \(-0.312064\pi\)
0.556708 + 0.830709i \(0.312064\pi\)
\(882\) 0 0
\(883\) −7.94710 −0.267441 −0.133721 0.991019i \(-0.542692\pi\)
−0.133721 + 0.991019i \(0.542692\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −35.5314 −1.19303 −0.596514 0.802603i \(-0.703448\pi\)
−0.596514 + 0.802603i \(0.703448\pi\)
\(888\) 0 0
\(889\) 11.9779 0.401727
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 5.20715 0.174251
\(894\) 0 0
\(895\) −5.62968 −0.188179
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −15.6960 −0.523491
\(900\) 0 0
\(901\) 1.78466 0.0594558
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −14.9282 −0.496229
\(906\) 0 0
\(907\) −55.2938 −1.83600 −0.918001 0.396579i \(-0.870197\pi\)
−0.918001 + 0.396579i \(0.870197\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −40.6203 −1.34581 −0.672905 0.739729i \(-0.734954\pi\)
−0.672905 + 0.739729i \(0.734954\pi\)
\(912\) 0 0
\(913\) −15.8399 −0.524224
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −40.0994 −1.32276 −0.661378 0.750052i \(-0.730028\pi\)
−0.661378 + 0.750052i \(0.730028\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −29.9370 −0.985388
\(924\) 0 0
\(925\) 4.89831 0.161055
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −21.3976 −0.702034 −0.351017 0.936369i \(-0.614164\pi\)
−0.351017 + 0.936369i \(0.614164\pi\)
\(930\) 0 0
\(931\) 3.19512 0.104716
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −8.97743 −0.293593
\(936\) 0 0
\(937\) −48.0879 −1.57096 −0.785481 0.618886i \(-0.787584\pi\)
−0.785481 + 0.618886i \(0.787584\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −35.9704 −1.17260 −0.586301 0.810094i \(-0.699416\pi\)
−0.586301 + 0.810094i \(0.699416\pi\)
\(942\) 0 0
\(943\) −10.4787 −0.341234
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −38.1568 −1.23993 −0.619965 0.784629i \(-0.712853\pi\)
−0.619965 + 0.784629i \(0.712853\pi\)
\(948\) 0 0
\(949\) 7.16411 0.232557
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −19.7187 −0.638751 −0.319375 0.947628i \(-0.603473\pi\)
−0.319375 + 0.947628i \(0.603473\pi\)
\(954\) 0 0
\(955\) 15.7414 0.509379
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −13.0369 −0.420984
\(960\) 0 0
\(961\) 7.40043 0.238724
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −20.3605 −0.655426
\(966\) 0 0
\(967\) −49.9496 −1.60627 −0.803135 0.595797i \(-0.796836\pi\)
−0.803135 + 0.595797i \(0.796836\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 41.4016 1.32864 0.664321 0.747448i \(-0.268721\pi\)
0.664321 + 0.747448i \(0.268721\pi\)
\(972\) 0 0
\(973\) 42.7809 1.37149
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −34.7018 −1.11021 −0.555104 0.831781i \(-0.687321\pi\)
−0.555104 + 0.831781i \(0.687321\pi\)
\(978\) 0 0
\(979\) −21.6515 −0.691986
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 30.8239 0.983131 0.491565 0.870841i \(-0.336425\pi\)
0.491565 + 0.870841i \(0.336425\pi\)
\(984\) 0 0
\(985\) −7.16108 −0.228171
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −9.01165 −0.286554
\(990\) 0 0
\(991\) 1.53774 0.0488478 0.0244239 0.999702i \(-0.492225\pi\)
0.0244239 + 0.999702i \(0.492225\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −21.0951 −0.668760
\(996\) 0 0
\(997\) −53.8478 −1.70538 −0.852688 0.522420i \(-0.825029\pi\)
−0.852688 + 0.522420i \(0.825029\pi\)
\(998\) 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.1.5 5
3.2 odd 2 2760.2.a.w.1.5 5
12.11 even 2 5520.2.a.cc.1.1 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2760.2.a.w.1.5 5 3.2 odd 2
5520.2.a.cc.1.1 5 12.11 even 2
8280.2.a.br.1.5 5 1.1 even 1 trivial