Properties

Label 8280.2.a.bl.1.2
Level $8280$
Weight $2$
Character 8280.1
Self dual yes
Analytic conductor $66.116$
Analytic rank $0$
Dimension $3$
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: \(3\)
Coefficient field: 3.3.229.1
Defining polynomial: \( x^{3} - 4x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
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 1.2
Root \(-1.86081\) of defining polynomial
Character \(\chi\) \(=\) 8280.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{5} +1.53740 q^{7} +O(q^{10})\) \(q-1.00000 q^{5} +1.53740 q^{7} +0.860806 q^{11} +0.139194 q^{13} -5.50761 q^{17} +5.25901 q^{19} +1.00000 q^{23} +1.00000 q^{25} -9.76663 q^{29} +6.78600 q^{31} -1.53740 q^{35} -12.0900 q^{37} +9.98062 q^{41} +11.4432 q^{43} +2.32340 q^{47} -4.63640 q^{49} -0.149606 q^{53} -0.860806 q^{55} +11.0152 q^{59} +4.43281 q^{61} -0.139194 q^{65} -10.4972 q^{67} -7.31299 q^{71} +7.11982 q^{73} +1.32340 q^{77} +6.79641 q^{79} -10.6468 q^{83} +5.50761 q^{85} +17.2936 q^{89} +0.213997 q^{91} -5.25901 q^{95} +1.93561 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 3 q^{5} + 7 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 3 q^{5} + 7 q^{7} - 3 q^{11} + 6 q^{13} + 5 q^{17} + 7 q^{19} + 3 q^{23} + 3 q^{25} + q^{29} + 10 q^{31} - 7 q^{35} + 2 q^{37} + 10 q^{41} + 12 q^{43} - q^{47} + 6 q^{49} - 10 q^{53} + 3 q^{55} - 10 q^{59} - 13 q^{61} - 6 q^{65} - 6 q^{67} - 10 q^{71} + 7 q^{73} - 4 q^{77} + 14 q^{79} - 16 q^{83} - 5 q^{85} + 20 q^{89} + 11 q^{91} - 7 q^{95} + 5 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 1.53740 0.581083 0.290542 0.956862i \(-0.406165\pi\)
0.290542 + 0.956862i \(0.406165\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0.860806 0.259543 0.129771 0.991544i \(-0.458576\pi\)
0.129771 + 0.991544i \(0.458576\pi\)
\(12\) 0 0
\(13\) 0.139194 0.0386055 0.0193028 0.999814i \(-0.493855\pi\)
0.0193028 + 0.999814i \(0.493855\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −5.50761 −1.33579 −0.667896 0.744254i \(-0.732805\pi\)
−0.667896 + 0.744254i \(0.732805\pi\)
\(18\) 0 0
\(19\) 5.25901 1.20650 0.603250 0.797552i \(-0.293872\pi\)
0.603250 + 0.797552i \(0.293872\pi\)
\(20\) 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
\(29\) −9.76663 −1.81362 −0.906809 0.421543i \(-0.861489\pi\)
−0.906809 + 0.421543i \(0.861489\pi\)
\(30\) 0 0
\(31\) 6.78600 1.21880 0.609401 0.792862i \(-0.291410\pi\)
0.609401 + 0.792862i \(0.291410\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1.53740 −0.259868
\(36\) 0 0
\(37\) −12.0900 −1.98759 −0.993795 0.111232i \(-0.964520\pi\)
−0.993795 + 0.111232i \(0.964520\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 9.98062 1.55871 0.779356 0.626582i \(-0.215546\pi\)
0.779356 + 0.626582i \(0.215546\pi\)
\(42\) 0 0
\(43\) 11.4432 1.74508 0.872538 0.488547i \(-0.162473\pi\)
0.872538 + 0.488547i \(0.162473\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 2.32340 0.338903 0.169452 0.985538i \(-0.445800\pi\)
0.169452 + 0.985538i \(0.445800\pi\)
\(48\) 0 0
\(49\) −4.63640 −0.662342
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −0.149606 −0.0205500 −0.0102750 0.999947i \(-0.503271\pi\)
−0.0102750 + 0.999947i \(0.503271\pi\)
\(54\) 0 0
\(55\) −0.860806 −0.116071
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 11.0152 1.43406 0.717030 0.697042i \(-0.245501\pi\)
0.717030 + 0.697042i \(0.245501\pi\)
\(60\) 0 0
\(61\) 4.43281 0.567563 0.283782 0.958889i \(-0.408411\pi\)
0.283782 + 0.958889i \(0.408411\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −0.139194 −0.0172649
\(66\) 0 0
\(67\) −10.4972 −1.28244 −0.641219 0.767358i \(-0.721571\pi\)
−0.641219 + 0.767358i \(0.721571\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −7.31299 −0.867892 −0.433946 0.900939i \(-0.642879\pi\)
−0.433946 + 0.900939i \(0.642879\pi\)
\(72\) 0 0
\(73\) 7.11982 0.833312 0.416656 0.909064i \(-0.363202\pi\)
0.416656 + 0.909064i \(0.363202\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1.32340 0.150816
\(78\) 0 0
\(79\) 6.79641 0.764656 0.382328 0.924027i \(-0.375122\pi\)
0.382328 + 0.924027i \(0.375122\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −10.6468 −1.16864 −0.584320 0.811524i \(-0.698639\pi\)
−0.584320 + 0.811524i \(0.698639\pi\)
\(84\) 0 0
\(85\) 5.50761 0.597385
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 17.2936 1.83312 0.916560 0.399897i \(-0.130954\pi\)
0.916560 + 0.399897i \(0.130954\pi\)
\(90\) 0 0
\(91\) 0.213997 0.0224330
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −5.25901 −0.539563
\(96\) 0 0
\(97\) 1.93561 0.196531 0.0982657 0.995160i \(-0.468671\pi\)
0.0982657 + 0.995160i \(0.468671\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 15.4224 1.53459 0.767293 0.641297i \(-0.221603\pi\)
0.767293 + 0.641297i \(0.221603\pi\)
\(102\) 0 0
\(103\) 7.91478 0.779867 0.389933 0.920843i \(-0.372498\pi\)
0.389933 + 0.920843i \(0.372498\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 4.27839 0.413607 0.206804 0.978382i \(-0.433694\pi\)
0.206804 + 0.978382i \(0.433694\pi\)
\(108\) 0 0
\(109\) −17.7770 −1.70273 −0.851366 0.524572i \(-0.824225\pi\)
−0.851366 + 0.524572i \(0.824225\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 3.20359 0.301368 0.150684 0.988582i \(-0.451852\pi\)
0.150684 + 0.988582i \(0.451852\pi\)
\(114\) 0 0
\(115\) −1.00000 −0.0932505
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −8.46742 −0.776207
\(120\) 0 0
\(121\) −10.2590 −0.932638
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −15.2099 −1.34966 −0.674828 0.737975i \(-0.735782\pi\)
−0.674828 + 0.737975i \(0.735782\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −12.6918 −1.10889 −0.554445 0.832220i \(-0.687069\pi\)
−0.554445 + 0.832220i \(0.687069\pi\)
\(132\) 0 0
\(133\) 8.08522 0.701077
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 14.0346 1.19906 0.599529 0.800353i \(-0.295355\pi\)
0.599529 + 0.800353i \(0.295355\pi\)
\(138\) 0 0
\(139\) 14.2638 1.20984 0.604921 0.796285i \(-0.293205\pi\)
0.604921 + 0.796285i \(0.293205\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0.119819 0.0100198
\(144\) 0 0
\(145\) 9.76663 0.811074
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 4.46260 0.365590 0.182795 0.983151i \(-0.441485\pi\)
0.182795 + 0.983151i \(0.441485\pi\)
\(150\) 0 0
\(151\) 10.7562 0.875328 0.437664 0.899139i \(-0.355806\pi\)
0.437664 + 0.899139i \(0.355806\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −6.78600 −0.545065
\(156\) 0 0
\(157\) 14.5180 1.15866 0.579332 0.815091i \(-0.303313\pi\)
0.579332 + 0.815091i \(0.303313\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1.53740 0.121164
\(162\) 0 0
\(163\) −1.30403 −0.102139 −0.0510697 0.998695i \(-0.516263\pi\)
−0.0510697 + 0.998695i \(0.516263\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −3.44322 −0.266445 −0.133222 0.991086i \(-0.542532\pi\)
−0.133222 + 0.991086i \(0.542532\pi\)
\(168\) 0 0
\(169\) −12.9806 −0.998510
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −9.35801 −0.711476 −0.355738 0.934586i \(-0.615770\pi\)
−0.355738 + 0.934586i \(0.615770\pi\)
\(174\) 0 0
\(175\) 1.53740 0.116217
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 18.4134 1.37628 0.688142 0.725576i \(-0.258426\pi\)
0.688142 + 0.725576i \(0.258426\pi\)
\(180\) 0 0
\(181\) −1.94457 −0.144539 −0.0722694 0.997385i \(-0.523024\pi\)
−0.0722694 + 0.997385i \(0.523024\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 12.0900 0.888877
\(186\) 0 0
\(187\) −4.74099 −0.346695
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0.775591 0.0561198 0.0280599 0.999606i \(-0.491067\pi\)
0.0280599 + 0.999606i \(0.491067\pi\)
\(192\) 0 0
\(193\) −11.7666 −0.846980 −0.423490 0.905901i \(-0.639195\pi\)
−0.423490 + 0.905901i \(0.639195\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −9.68141 −0.689772 −0.344886 0.938645i \(-0.612082\pi\)
−0.344886 + 0.938645i \(0.612082\pi\)
\(198\) 0 0
\(199\) −3.29362 −0.233478 −0.116739 0.993163i \(-0.537244\pi\)
−0.116739 + 0.993163i \(0.537244\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −15.0152 −1.05386
\(204\) 0 0
\(205\) −9.98062 −0.697077
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 4.52699 0.313138
\(210\) 0 0
\(211\) −16.2396 −1.11798 −0.558991 0.829173i \(-0.688812\pi\)
−0.558991 + 0.829173i \(0.688812\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −11.4432 −0.780421
\(216\) 0 0
\(217\) 10.4328 0.708225
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −0.766628 −0.0515690
\(222\) 0 0
\(223\) 21.2936 1.42593 0.712963 0.701202i \(-0.247353\pi\)
0.712963 + 0.701202i \(0.247353\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 29.6620 1.96874 0.984369 0.176117i \(-0.0563536\pi\)
0.984369 + 0.176117i \(0.0563536\pi\)
\(228\) 0 0
\(229\) 19.6829 1.30068 0.650340 0.759643i \(-0.274626\pi\)
0.650340 + 0.759643i \(0.274626\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 5.52699 0.362085 0.181043 0.983475i \(-0.442053\pi\)
0.181043 + 0.983475i \(0.442053\pi\)
\(234\) 0 0
\(235\) −2.32340 −0.151562
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 17.3982 1.12540 0.562698 0.826662i \(-0.309763\pi\)
0.562698 + 0.826662i \(0.309763\pi\)
\(240\) 0 0
\(241\) −16.0900 −1.03645 −0.518225 0.855244i \(-0.673407\pi\)
−0.518225 + 0.855244i \(0.673407\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 4.63640 0.296209
\(246\) 0 0
\(247\) 0.732024 0.0465776
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 29.0498 1.83361 0.916805 0.399336i \(-0.130759\pi\)
0.916805 + 0.399336i \(0.130759\pi\)
\(252\) 0 0
\(253\) 0.860806 0.0541184
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 6.56304 0.409391 0.204696 0.978826i \(-0.434380\pi\)
0.204696 + 0.978826i \(0.434380\pi\)
\(258\) 0 0
\(259\) −18.5872 −1.15495
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0.561593 0.0346293 0.0173147 0.999850i \(-0.494488\pi\)
0.0173147 + 0.999850i \(0.494488\pi\)
\(264\) 0 0
\(265\) 0.149606 0.00919024
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 7.26943 0.443225 0.221612 0.975135i \(-0.428868\pi\)
0.221612 + 0.975135i \(0.428868\pi\)
\(270\) 0 0
\(271\) 0.184210 0.0111900 0.00559498 0.999984i \(-0.498219\pi\)
0.00559498 + 0.999984i \(0.498219\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0.860806 0.0519085
\(276\) 0 0
\(277\) 25.8954 1.55590 0.777952 0.628323i \(-0.216259\pi\)
0.777952 + 0.628323i \(0.216259\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 26.7756 1.59730 0.798649 0.601797i \(-0.205548\pi\)
0.798649 + 0.601797i \(0.205548\pi\)
\(282\) 0 0
\(283\) 5.70079 0.338877 0.169438 0.985541i \(-0.445805\pi\)
0.169438 + 0.985541i \(0.445805\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 15.3442 0.905741
\(288\) 0 0
\(289\) 13.3338 0.784342
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1.05398 −0.0615741 −0.0307871 0.999526i \(-0.509801\pi\)
−0.0307871 + 0.999526i \(0.509801\pi\)
\(294\) 0 0
\(295\) −11.0152 −0.641331
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0.139194 0.00804981
\(300\) 0 0
\(301\) 17.5928 1.01403
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −4.43281 −0.253822
\(306\) 0 0
\(307\) 17.8760 1.02024 0.510120 0.860103i \(-0.329601\pi\)
0.510120 + 0.860103i \(0.329601\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −16.9315 −0.960095 −0.480048 0.877242i \(-0.659381\pi\)
−0.480048 + 0.877242i \(0.659381\pi\)
\(312\) 0 0
\(313\) −19.9959 −1.13023 −0.565116 0.825011i \(-0.691169\pi\)
−0.565116 + 0.825011i \(0.691169\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −3.29776 −0.185221 −0.0926104 0.995702i \(-0.529521\pi\)
−0.0926104 + 0.995702i \(0.529521\pi\)
\(318\) 0 0
\(319\) −8.40717 −0.470711
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −28.9646 −1.61163
\(324\) 0 0
\(325\) 0.139194 0.00772110
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 3.57201 0.196931
\(330\) 0 0
\(331\) −12.8802 −0.707959 −0.353979 0.935253i \(-0.615172\pi\)
−0.353979 + 0.935253i \(0.615172\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 10.4972 0.573523
\(336\) 0 0
\(337\) −9.22026 −0.502260 −0.251130 0.967953i \(-0.580802\pi\)
−0.251130 + 0.967953i \(0.580802\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 5.84143 0.316331
\(342\) 0 0
\(343\) −17.8898 −0.965959
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −31.2984 −1.68019 −0.840094 0.542441i \(-0.817500\pi\)
−0.840094 + 0.542441i \(0.817500\pi\)
\(348\) 0 0
\(349\) 9.89541 0.529689 0.264845 0.964291i \(-0.414679\pi\)
0.264845 + 0.964291i \(0.414679\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −19.4287 −1.03408 −0.517042 0.855960i \(-0.672967\pi\)
−0.517042 + 0.855960i \(0.672967\pi\)
\(354\) 0 0
\(355\) 7.31299 0.388133
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 13.1440 0.693714 0.346857 0.937918i \(-0.387249\pi\)
0.346857 + 0.937918i \(0.387249\pi\)
\(360\) 0 0
\(361\) 8.65722 0.455643
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −7.11982 −0.372668
\(366\) 0 0
\(367\) −15.7424 −0.821748 −0.410874 0.911692i \(-0.634776\pi\)
−0.410874 + 0.911692i \(0.634776\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −0.230005 −0.0119413
\(372\) 0 0
\(373\) 27.6620 1.43229 0.716143 0.697954i \(-0.245906\pi\)
0.716143 + 0.697954i \(0.245906\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −1.35946 −0.0700156
\(378\) 0 0
\(379\) 28.2140 1.44926 0.724628 0.689140i \(-0.242012\pi\)
0.724628 + 0.689140i \(0.242012\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 21.5928 1.10334 0.551671 0.834062i \(-0.313990\pi\)
0.551671 + 0.834062i \(0.313990\pi\)
\(384\) 0 0
\(385\) −1.32340 −0.0674469
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −17.2501 −0.874612 −0.437306 0.899313i \(-0.644067\pi\)
−0.437306 + 0.899313i \(0.644067\pi\)
\(390\) 0 0
\(391\) −5.50761 −0.278532
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −6.79641 −0.341965
\(396\) 0 0
\(397\) 34.8850 1.75083 0.875414 0.483374i \(-0.160589\pi\)
0.875414 + 0.483374i \(0.160589\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −4.21881 −0.210678 −0.105339 0.994436i \(-0.533593\pi\)
−0.105339 + 0.994436i \(0.533593\pi\)
\(402\) 0 0
\(403\) 0.944572 0.0470525
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −10.4072 −0.515864
\(408\) 0 0
\(409\) 38.8165 1.91935 0.959675 0.281111i \(-0.0907030\pi\)
0.959675 + 0.281111i \(0.0907030\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 16.9348 0.833309
\(414\) 0 0
\(415\) 10.6468 0.522631
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −22.0305 −1.07626 −0.538129 0.842862i \(-0.680869\pi\)
−0.538129 + 0.842862i \(0.680869\pi\)
\(420\) 0 0
\(421\) −17.2203 −0.839264 −0.419632 0.907694i \(-0.637841\pi\)
−0.419632 + 0.907694i \(0.637841\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −5.50761 −0.267159
\(426\) 0 0
\(427\) 6.81501 0.329801
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 11.8116 0.568947 0.284473 0.958684i \(-0.408181\pi\)
0.284473 + 0.958684i \(0.408181\pi\)
\(432\) 0 0
\(433\) 19.8642 0.954611 0.477306 0.878737i \(-0.341613\pi\)
0.477306 + 0.878737i \(0.341613\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 5.25901 0.251573
\(438\) 0 0
\(439\) −5.04647 −0.240855 −0.120427 0.992722i \(-0.538426\pi\)
−0.120427 + 0.992722i \(0.538426\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 14.3193 0.680328 0.340164 0.940366i \(-0.389517\pi\)
0.340164 + 0.940366i \(0.389517\pi\)
\(444\) 0 0
\(445\) −17.2936 −0.819796
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 13.3699 0.630963 0.315482 0.948932i \(-0.397834\pi\)
0.315482 + 0.948932i \(0.397834\pi\)
\(450\) 0 0
\(451\) 8.59138 0.404552
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −0.213997 −0.0100323
\(456\) 0 0
\(457\) 2.38924 0.111764 0.0558821 0.998437i \(-0.482203\pi\)
0.0558821 + 0.998437i \(0.482203\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −21.2278 −0.988676 −0.494338 0.869270i \(-0.664590\pi\)
−0.494338 + 0.869270i \(0.664590\pi\)
\(462\) 0 0
\(463\) 35.1261 1.63245 0.816224 0.577736i \(-0.196064\pi\)
0.816224 + 0.577736i \(0.196064\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −16.7756 −0.776282 −0.388141 0.921600i \(-0.626883\pi\)
−0.388141 + 0.921600i \(0.626883\pi\)
\(468\) 0 0
\(469\) −16.1384 −0.745203
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 9.85039 0.452922
\(474\) 0 0
\(475\) 5.25901 0.241300
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 5.61076 0.256362 0.128181 0.991751i \(-0.459086\pi\)
0.128181 + 0.991751i \(0.459086\pi\)
\(480\) 0 0
\(481\) −1.68286 −0.0767319
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.93561 −0.0878915
\(486\) 0 0
\(487\) 10.2638 0.465099 0.232549 0.972585i \(-0.425293\pi\)
0.232549 + 0.972585i \(0.425293\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −9.28735 −0.419132 −0.209566 0.977794i \(-0.567205\pi\)
−0.209566 + 0.977794i \(0.567205\pi\)
\(492\) 0 0
\(493\) 53.7908 2.42262
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −11.2430 −0.504318
\(498\) 0 0
\(499\) 13.3082 0.595756 0.297878 0.954604i \(-0.403721\pi\)
0.297878 + 0.954604i \(0.403721\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 37.7383 1.68267 0.841334 0.540516i \(-0.181771\pi\)
0.841334 + 0.540516i \(0.181771\pi\)
\(504\) 0 0
\(505\) −15.4224 −0.686288
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 1.11982 0.0496351 0.0248176 0.999692i \(-0.492100\pi\)
0.0248176 + 0.999692i \(0.492100\pi\)
\(510\) 0 0
\(511\) 10.9460 0.484223
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −7.91478 −0.348767
\(516\) 0 0
\(517\) 2.00000 0.0879599
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 13.9100 0.609407 0.304703 0.952447i \(-0.401443\pi\)
0.304703 + 0.952447i \(0.401443\pi\)
\(522\) 0 0
\(523\) 8.19799 0.358473 0.179237 0.983806i \(-0.442637\pi\)
0.179237 + 0.983806i \(0.442637\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −37.3747 −1.62807
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1.38924 0.0601749
\(534\) 0 0
\(535\) −4.27839 −0.184971
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −3.99104 −0.171906
\(540\) 0 0
\(541\) 23.5478 1.01240 0.506200 0.862416i \(-0.331050\pi\)
0.506200 + 0.862416i \(0.331050\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 17.7770 0.761485
\(546\) 0 0
\(547\) 1.77077 0.0757128 0.0378564 0.999283i \(-0.487947\pi\)
0.0378564 + 0.999283i \(0.487947\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −51.3628 −2.18813
\(552\) 0 0
\(553\) 10.4488 0.444329
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 22.5872 0.957052 0.478526 0.878073i \(-0.341171\pi\)
0.478526 + 0.878073i \(0.341171\pi\)
\(558\) 0 0
\(559\) 1.59283 0.0673695
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −21.8504 −0.920884 −0.460442 0.887690i \(-0.652309\pi\)
−0.460442 + 0.887690i \(0.652309\pi\)
\(564\) 0 0
\(565\) −3.20359 −0.134776
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −11.4737 −0.481002 −0.240501 0.970649i \(-0.577312\pi\)
−0.240501 + 0.970649i \(0.577312\pi\)
\(570\) 0 0
\(571\) 27.7085 1.15956 0.579782 0.814771i \(-0.303138\pi\)
0.579782 + 0.814771i \(0.303138\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.00000 0.0417029
\(576\) 0 0
\(577\) 20.3442 0.846941 0.423471 0.905910i \(-0.360812\pi\)
0.423471 + 0.905910i \(0.360812\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −16.3684 −0.679076
\(582\) 0 0
\(583\) −0.128782 −0.00533360
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −12.1690 −0.502268 −0.251134 0.967952i \(-0.580803\pi\)
−0.251134 + 0.967952i \(0.580803\pi\)
\(588\) 0 0
\(589\) 35.6877 1.47049
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 40.5180 1.66388 0.831938 0.554869i \(-0.187231\pi\)
0.831938 + 0.554869i \(0.187231\pi\)
\(594\) 0 0
\(595\) 8.46742 0.347130
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 28.8913 1.18047 0.590233 0.807233i \(-0.299036\pi\)
0.590233 + 0.807233i \(0.299036\pi\)
\(600\) 0 0
\(601\) 5.34278 0.217937 0.108968 0.994045i \(-0.465245\pi\)
0.108968 + 0.994045i \(0.465245\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 10.2590 0.417088
\(606\) 0 0
\(607\) −40.4376 −1.64131 −0.820656 0.571422i \(-0.806392\pi\)
−0.820656 + 0.571422i \(0.806392\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0.323404 0.0130835
\(612\) 0 0
\(613\) −5.31154 −0.214531 −0.107266 0.994230i \(-0.534210\pi\)
−0.107266 + 0.994230i \(0.534210\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −9.71680 −0.391183 −0.195592 0.980685i \(-0.562663\pi\)
−0.195592 + 0.980685i \(0.562663\pi\)
\(618\) 0 0
\(619\) −23.7562 −0.954843 −0.477421 0.878674i \(-0.658428\pi\)
−0.477421 + 0.878674i \(0.658428\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 26.5872 1.06520
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 66.5872 2.65501
\(630\) 0 0
\(631\) 1.24234 0.0494566 0.0247283 0.999694i \(-0.492128\pi\)
0.0247283 + 0.999694i \(0.492128\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 15.2099 0.603585
\(636\) 0 0
\(637\) −0.645359 −0.0255701
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 34.8864 1.37793 0.688966 0.724794i \(-0.258065\pi\)
0.688966 + 0.724794i \(0.258065\pi\)
\(642\) 0 0
\(643\) 32.1592 1.26824 0.634118 0.773236i \(-0.281363\pi\)
0.634118 + 0.773236i \(0.281363\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −23.9550 −0.941768 −0.470884 0.882195i \(-0.656065\pi\)
−0.470884 + 0.882195i \(0.656065\pi\)
\(648\) 0 0
\(649\) 9.48197 0.372200
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −4.31926 −0.169026 −0.0845128 0.996422i \(-0.526933\pi\)
−0.0845128 + 0.996422i \(0.526933\pi\)
\(654\) 0 0
\(655\) 12.6918 0.495911
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 6.14961 0.239555 0.119777 0.992801i \(-0.461782\pi\)
0.119777 + 0.992801i \(0.461782\pi\)
\(660\) 0 0
\(661\) −15.7473 −0.612497 −0.306249 0.951952i \(-0.599074\pi\)
−0.306249 + 0.951952i \(0.599074\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −8.08522 −0.313531
\(666\) 0 0
\(667\) −9.76663 −0.378165
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 3.81579 0.147307
\(672\) 0 0
\(673\) 43.5783 1.67982 0.839909 0.542727i \(-0.182608\pi\)
0.839909 + 0.542727i \(0.182608\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −30.1801 −1.15991 −0.579957 0.814647i \(-0.696931\pi\)
−0.579957 + 0.814647i \(0.696931\pi\)
\(678\) 0 0
\(679\) 2.97581 0.114201
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −29.2832 −1.12049 −0.560245 0.828327i \(-0.689293\pi\)
−0.560245 + 0.828327i \(0.689293\pi\)
\(684\) 0 0
\(685\) −14.0346 −0.536235
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −0.0208243 −0.000793344 0
\(690\) 0 0
\(691\) −14.9557 −0.568940 −0.284470 0.958685i \(-0.591818\pi\)
−0.284470 + 0.958685i \(0.591818\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −14.2638 −0.541058
\(696\) 0 0
\(697\) −54.9694 −2.08212
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −24.9627 −0.942828 −0.471414 0.881912i \(-0.656256\pi\)
−0.471414 + 0.881912i \(0.656256\pi\)
\(702\) 0 0
\(703\) −63.5816 −2.39803
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 23.7104 0.891722
\(708\) 0 0
\(709\) −38.9717 −1.46361 −0.731806 0.681513i \(-0.761322\pi\)
−0.731806 + 0.681513i \(0.761322\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 6.78600 0.254138
\(714\) 0 0
\(715\) −0.119819 −0.00448098
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 25.2978 0.943447 0.471724 0.881746i \(-0.343632\pi\)
0.471724 + 0.881746i \(0.343632\pi\)
\(720\) 0 0
\(721\) 12.1682 0.453168
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −9.76663 −0.362723
\(726\) 0 0
\(727\) 12.7417 0.472562 0.236281 0.971685i \(-0.424071\pi\)
0.236281 + 0.971685i \(0.424071\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −63.0249 −2.33106
\(732\) 0 0
\(733\) −9.83247 −0.363170 −0.181585 0.983375i \(-0.558123\pi\)
−0.181585 + 0.983375i \(0.558123\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −9.03605 −0.332847
\(738\) 0 0
\(739\) 22.6918 0.834732 0.417366 0.908738i \(-0.362953\pi\)
0.417366 + 0.908738i \(0.362953\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −3.08858 −0.113309 −0.0566546 0.998394i \(-0.518043\pi\)
−0.0566546 + 0.998394i \(0.518043\pi\)
\(744\) 0 0
\(745\) −4.46260 −0.163497
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 6.57760 0.240340
\(750\) 0 0
\(751\) −10.7577 −0.392553 −0.196276 0.980549i \(-0.562885\pi\)
−0.196276 + 0.980549i \(0.562885\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −10.7562 −0.391459
\(756\) 0 0
\(757\) −19.5333 −0.709948 −0.354974 0.934876i \(-0.615510\pi\)
−0.354974 + 0.934876i \(0.615510\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 15.6933 0.568881 0.284440 0.958694i \(-0.408192\pi\)
0.284440 + 0.958694i \(0.408192\pi\)
\(762\) 0 0
\(763\) −27.3304 −0.989429
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1.53326 0.0553626
\(768\) 0 0
\(769\) 11.4128 0.411555 0.205777 0.978599i \(-0.434028\pi\)
0.205777 + 0.978599i \(0.434028\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 22.5872 0.812406 0.406203 0.913783i \(-0.366853\pi\)
0.406203 + 0.913783i \(0.366853\pi\)
\(774\) 0 0
\(775\) 6.78600 0.243760
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 52.4882 1.88059
\(780\) 0 0
\(781\) −6.29507 −0.225255
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −14.5180 −0.518171
\(786\) 0 0
\(787\) −4.42799 −0.157841 −0.0789205 0.996881i \(-0.525147\pi\)
−0.0789205 + 0.996881i \(0.525147\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 4.92520 0.175120
\(792\) 0 0
\(793\) 0.617021 0.0219111
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −21.5124 −0.762009 −0.381005 0.924573i \(-0.624422\pi\)
−0.381005 + 0.924573i \(0.624422\pi\)
\(798\) 0 0
\(799\) −12.7964 −0.452705
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 6.12878 0.216280
\(804\) 0 0
\(805\) −1.53740 −0.0541863
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −7.37883 −0.259426 −0.129713 0.991552i \(-0.541406\pi\)
−0.129713 + 0.991552i \(0.541406\pi\)
\(810\) 0 0
\(811\) 29.0423 1.01981 0.509907 0.860230i \(-0.329680\pi\)
0.509907 + 0.860230i \(0.329680\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 1.30403 0.0456782
\(816\) 0 0
\(817\) 60.1801 2.10543
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −5.70079 −0.198959 −0.0994794 0.995040i \(-0.531718\pi\)
−0.0994794 + 0.995040i \(0.531718\pi\)
\(822\) 0 0
\(823\) −16.0034 −0.557842 −0.278921 0.960314i \(-0.589977\pi\)
−0.278921 + 0.960314i \(0.589977\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −39.7937 −1.38376 −0.691882 0.722011i \(-0.743218\pi\)
−0.691882 + 0.722011i \(0.743218\pi\)
\(828\) 0 0
\(829\) −23.3353 −0.810467 −0.405234 0.914213i \(-0.632810\pi\)
−0.405234 + 0.914213i \(0.632810\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 25.5355 0.884752
\(834\) 0 0
\(835\) 3.44322 0.119158
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −37.1469 −1.28245 −0.641227 0.767351i \(-0.721574\pi\)
−0.641227 + 0.767351i \(0.721574\pi\)
\(840\) 0 0
\(841\) 66.3870 2.28921
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 12.9806 0.446547
\(846\) 0 0
\(847\) −15.7722 −0.541940
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −12.0900 −0.414441
\(852\) 0 0
\(853\) −53.7658 −1.84091 −0.920454 0.390851i \(-0.872181\pi\)
−0.920454 + 0.390851i \(0.872181\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 23.9675 0.818715 0.409357 0.912374i \(-0.365753\pi\)
0.409357 + 0.912374i \(0.365753\pi\)
\(858\) 0 0
\(859\) 3.70705 0.126483 0.0632415 0.997998i \(-0.479856\pi\)
0.0632415 + 0.997998i \(0.479856\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −49.6296 −1.68941 −0.844705 0.535232i \(-0.820224\pi\)
−0.844705 + 0.535232i \(0.820224\pi\)
\(864\) 0 0
\(865\) 9.35801 0.318182
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 5.85039 0.198461
\(870\) 0 0
\(871\) −1.46115 −0.0495091
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −1.53740 −0.0519737
\(876\) 0 0
\(877\) −13.1004 −0.442371 −0.221185 0.975232i \(-0.570993\pi\)
−0.221185 + 0.975232i \(0.570993\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −3.88085 −0.130749 −0.0653746 0.997861i \(-0.520824\pi\)
−0.0653746 + 0.997861i \(0.520824\pi\)
\(882\) 0 0
\(883\) −10.8131 −0.363890 −0.181945 0.983309i \(-0.558239\pi\)
−0.181945 + 0.983309i \(0.558239\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 8.58387 0.288218 0.144109 0.989562i \(-0.453968\pi\)
0.144109 + 0.989562i \(0.453968\pi\)
\(888\) 0 0
\(889\) −23.3836 −0.784262
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 12.2188 0.408887
\(894\) 0 0
\(895\) −18.4134 −0.615493
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −66.2764 −2.21044
\(900\) 0 0
\(901\) 0.823974 0.0274505
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 1.94457 0.0646398
\(906\) 0 0
\(907\) −21.2728 −0.706351 −0.353176 0.935557i \(-0.614898\pi\)
−0.353176 + 0.935557i \(0.614898\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 27.6441 0.915890 0.457945 0.888980i \(-0.348586\pi\)
0.457945 + 0.888980i \(0.348586\pi\)
\(912\) 0 0
\(913\) −9.16484 −0.303312
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −19.5124 −0.644357
\(918\) 0 0
\(919\) −0.994404 −0.0328024 −0.0164012 0.999865i \(-0.505221\pi\)
−0.0164012 + 0.999865i \(0.505221\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −1.01793 −0.0335054
\(924\) 0 0
\(925\) −12.0900 −0.397518
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 18.3747 0.602854 0.301427 0.953489i \(-0.402537\pi\)
0.301427 + 0.953489i \(0.402537\pi\)
\(930\) 0 0
\(931\) −24.3829 −0.799116
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 4.74099 0.155047
\(936\) 0 0
\(937\) −24.0942 −0.787122 −0.393561 0.919298i \(-0.628757\pi\)
−0.393561 + 0.919298i \(0.628757\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −51.9244 −1.69269 −0.846344 0.532637i \(-0.821201\pi\)
−0.846344 + 0.532637i \(0.821201\pi\)
\(942\) 0 0
\(943\) 9.98062 0.325014
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 4.72643 0.153588 0.0767941 0.997047i \(-0.475532\pi\)
0.0767941 + 0.997047i \(0.475532\pi\)
\(948\) 0 0
\(949\) 0.991037 0.0321704
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −3.57682 −0.115865 −0.0579323 0.998321i \(-0.518451\pi\)
−0.0579323 + 0.998321i \(0.518451\pi\)
\(954\) 0 0
\(955\) −0.775591 −0.0250975
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 21.5768 0.696752
\(960\) 0 0
\(961\) 15.0498 0.485478
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 11.7666 0.378781
\(966\) 0 0
\(967\) 33.9646 1.09223 0.546114 0.837711i \(-0.316106\pi\)
0.546114 + 0.837711i \(0.316106\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 56.0561 1.79893 0.899463 0.436997i \(-0.143958\pi\)
0.899463 + 0.436997i \(0.143958\pi\)
\(972\) 0 0
\(973\) 21.9292 0.703019
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 53.1219 1.69952 0.849761 0.527169i \(-0.176746\pi\)
0.849761 + 0.527169i \(0.176746\pi\)
\(978\) 0 0
\(979\) 14.8864 0.475773
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −28.7833 −0.918045 −0.459022 0.888425i \(-0.651800\pi\)
−0.459022 + 0.888425i \(0.651800\pi\)
\(984\) 0 0
\(985\) 9.68141 0.308475
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 11.4432 0.363873
\(990\) 0 0
\(991\) 48.1641 1.52998 0.764991 0.644041i \(-0.222743\pi\)
0.764991 + 0.644041i \(0.222743\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 3.29362 0.104415
\(996\) 0 0
\(997\) 43.5153 1.37814 0.689072 0.724693i \(-0.258018\pi\)
0.689072 + 0.724693i \(0.258018\pi\)
\(998\) 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.bl.1.2 3
3.2 odd 2 920.2.a.i.1.2 3
12.11 even 2 1840.2.a.q.1.2 3
15.2 even 4 4600.2.e.q.4049.3 6
15.8 even 4 4600.2.e.q.4049.4 6
15.14 odd 2 4600.2.a.v.1.2 3
24.5 odd 2 7360.2.a.bw.1.2 3
24.11 even 2 7360.2.a.cf.1.2 3
60.59 even 2 9200.2.a.ci.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
920.2.a.i.1.2 3 3.2 odd 2
1840.2.a.q.1.2 3 12.11 even 2
4600.2.a.v.1.2 3 15.14 odd 2
4600.2.e.q.4049.3 6 15.2 even 4
4600.2.e.q.4049.4 6 15.8 even 4
7360.2.a.bw.1.2 3 24.5 odd 2
7360.2.a.cf.1.2 3 24.11 even 2
8280.2.a.bl.1.2 3 1.1 even 1 trivial
9200.2.a.ci.1.2 3 60.59 even 2