Properties

Label 4140.2.a.s.1.1
Level $4140$
Weight $2$
Character 4140.1
Self dual yes
Analytic conductor $33.058$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4140.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(33.0580664368\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.3144.1
Defining polynomial: \( x^{3} - x^{2} - 16x - 8 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1380)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(4.73549\) of defining polynomial
Character \(\chi\) \(=\) 4140.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{5} -3.73549 q^{7} +O(q^{10})\) \(q+1.00000 q^{5} -3.73549 q^{7} -4.84469 q^{11} -2.84469 q^{13} -0.890804 q^{17} +6.84469 q^{19} -1.00000 q^{23} +1.00000 q^{25} +0.890804 q^{29} +7.73549 q^{31} -3.73549 q^{35} -1.95388 q^{37} -12.3618 q^{41} -3.47098 q^{43} +6.62629 q^{47} +6.95388 q^{49} -12.3618 q^{53} -4.84469 q^{55} -0.890804 q^{59} +8.62629 q^{61} -2.84469 q^{65} +7.73549 q^{67} +12.3618 q^{71} +16.5341 q^{73} +18.0973 q^{77} +13.4710 q^{79} +4.58018 q^{83} -0.890804 q^{85} +15.1604 q^{89} +10.6263 q^{91} +6.84469 q^{95} -17.2526 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 3 q^{5} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + 3 q^{5} + 2 q^{7} - 4 q^{11} + 2 q^{13} + 10 q^{19} - 3 q^{23} + 3 q^{25} + 10 q^{31} + 2 q^{35} + 2 q^{37} - 8 q^{41} + 16 q^{43} + 4 q^{47} + 13 q^{49} - 8 q^{53} - 4 q^{55} + 10 q^{61} + 2 q^{65} + 10 q^{67} + 8 q^{71} + 18 q^{73} + 12 q^{77} + 14 q^{79} - 10 q^{83} - 2 q^{89} + 16 q^{91} + 10 q^{95} - 20 q^{97}+O(q^{100}) \) 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
\(7\) −3.73549 −1.41188 −0.705941 0.708270i \(-0.749476\pi\)
−0.705941 + 0.708270i \(0.749476\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −4.84469 −1.46073 −0.730364 0.683058i \(-0.760649\pi\)
−0.730364 + 0.683058i \(0.760649\pi\)
\(12\) 0 0
\(13\) −2.84469 −0.788974 −0.394487 0.918902i \(-0.629078\pi\)
−0.394487 + 0.918902i \(0.629078\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.890804 −0.216052 −0.108026 0.994148i \(-0.534453\pi\)
−0.108026 + 0.994148i \(0.534453\pi\)
\(18\) 0 0
\(19\) 6.84469 1.57028 0.785139 0.619319i \(-0.212591\pi\)
0.785139 + 0.619319i \(0.212591\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 0.890804 0.165418 0.0827091 0.996574i \(-0.473643\pi\)
0.0827091 + 0.996574i \(0.473643\pi\)
\(30\) 0 0
\(31\) 7.73549 1.38933 0.694667 0.719331i \(-0.255552\pi\)
0.694667 + 0.719331i \(0.255552\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −3.73549 −0.631413
\(36\) 0 0
\(37\) −1.95388 −0.321216 −0.160608 0.987018i \(-0.551346\pi\)
−0.160608 + 0.987018i \(0.551346\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −12.3618 −1.93059 −0.965293 0.261169i \(-0.915892\pi\)
−0.965293 + 0.261169i \(0.915892\pi\)
\(42\) 0 0
\(43\) −3.47098 −0.529319 −0.264660 0.964342i \(-0.585260\pi\)
−0.264660 + 0.964342i \(0.585260\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 6.62629 0.966544 0.483272 0.875470i \(-0.339448\pi\)
0.483272 + 0.875470i \(0.339448\pi\)
\(48\) 0 0
\(49\) 6.95388 0.993412
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −12.3618 −1.69802 −0.849011 0.528376i \(-0.822801\pi\)
−0.849011 + 0.528376i \(0.822801\pi\)
\(54\) 0 0
\(55\) −4.84469 −0.653257
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −0.890804 −0.115973 −0.0579864 0.998317i \(-0.518468\pi\)
−0.0579864 + 0.998317i \(0.518468\pi\)
\(60\) 0 0
\(61\) 8.62629 1.10448 0.552242 0.833684i \(-0.313773\pi\)
0.552242 + 0.833684i \(0.313773\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −2.84469 −0.352840
\(66\) 0 0
\(67\) 7.73549 0.945040 0.472520 0.881320i \(-0.343344\pi\)
0.472520 + 0.881320i \(0.343344\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 12.3618 1.46707 0.733537 0.679650i \(-0.237868\pi\)
0.733537 + 0.679650i \(0.237868\pi\)
\(72\) 0 0
\(73\) 16.5341 1.93516 0.967582 0.252555i \(-0.0812709\pi\)
0.967582 + 0.252555i \(0.0812709\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 18.0973 2.06238
\(78\) 0 0
\(79\) 13.4710 1.51560 0.757802 0.652485i \(-0.226273\pi\)
0.757802 + 0.652485i \(0.226273\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 4.58018 0.502740 0.251370 0.967891i \(-0.419119\pi\)
0.251370 + 0.967891i \(0.419119\pi\)
\(84\) 0 0
\(85\) −0.890804 −0.0966212
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 15.1604 1.60699 0.803497 0.595309i \(-0.202970\pi\)
0.803497 + 0.595309i \(0.202970\pi\)
\(90\) 0 0
\(91\) 10.6263 1.11394
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 6.84469 0.702250
\(96\) 0 0
\(97\) −17.2526 −1.75173 −0.875867 0.482552i \(-0.839710\pi\)
−0.875867 + 0.482552i \(0.839710\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 2.67241 0.265915 0.132957 0.991122i \(-0.457553\pi\)
0.132957 + 0.991122i \(0.457553\pi\)
\(102\) 0 0
\(103\) 6.21839 0.612716 0.306358 0.951916i \(-0.400889\pi\)
0.306358 + 0.951916i \(0.400889\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 14.7986 1.43063 0.715316 0.698801i \(-0.246283\pi\)
0.715316 + 0.698801i \(0.246283\pi\)
\(108\) 0 0
\(109\) −12.5341 −1.20054 −0.600272 0.799796i \(-0.704941\pi\)
−0.600272 + 0.799796i \(0.704941\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −12.3618 −1.16290 −0.581449 0.813583i \(-0.697514\pi\)
−0.581449 + 0.813583i \(0.697514\pi\)
\(114\) 0 0
\(115\) −1.00000 −0.0932505
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 3.32759 0.305040
\(120\) 0 0
\(121\) 12.4710 1.13373
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 11.7866 1.04590 0.522948 0.852365i \(-0.324832\pi\)
0.522948 + 0.852365i \(0.324832\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 17.4710 1.52645 0.763223 0.646135i \(-0.223616\pi\)
0.763223 + 0.646135i \(0.223616\pi\)
\(132\) 0 0
\(133\) −25.5683 −2.21705
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −15.1604 −1.29524 −0.647618 0.761965i \(-0.724235\pi\)
−0.647618 + 0.761965i \(0.724235\pi\)
\(138\) 0 0
\(139\) −5.51710 −0.467954 −0.233977 0.972242i \(-0.575174\pi\)
−0.233977 + 0.972242i \(0.575174\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 13.7816 1.15248
\(144\) 0 0
\(145\) 0.890804 0.0739772
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1.15531 −0.0946470 −0.0473235 0.998880i \(-0.515069\pi\)
−0.0473235 + 0.998880i \(0.515069\pi\)
\(150\) 0 0
\(151\) −15.4710 −1.25901 −0.629505 0.776996i \(-0.716742\pi\)
−0.629505 + 0.776996i \(0.716742\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 7.73549 0.621329
\(156\) 0 0
\(157\) 18.6774 1.49062 0.745311 0.666717i \(-0.232301\pi\)
0.745311 + 0.666717i \(0.232301\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 3.73549 0.294398
\(162\) 0 0
\(163\) 0.0922364 0.00722451 0.00361226 0.999993i \(-0.498850\pi\)
0.00361226 + 0.999993i \(0.498850\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 5.37371 0.415830 0.207915 0.978147i \(-0.433332\pi\)
0.207915 + 0.978147i \(0.433332\pi\)
\(168\) 0 0
\(169\) −4.90776 −0.377520
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(174\) 0 0
\(175\) −3.73549 −0.282376
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 9.56322 0.714788 0.357394 0.933954i \(-0.383665\pi\)
0.357394 + 0.933954i \(0.383665\pi\)
\(180\) 0 0
\(181\) −7.16035 −0.532225 −0.266112 0.963942i \(-0.585739\pi\)
−0.266112 + 0.963942i \(0.585739\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1.95388 −0.143652
\(186\) 0 0
\(187\) 4.31566 0.315593
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −14.0050 −1.01337 −0.506684 0.862132i \(-0.669129\pi\)
−0.506684 + 0.862132i \(0.669129\pi\)
\(192\) 0 0
\(193\) 26.7236 1.92360 0.961802 0.273745i \(-0.0882626\pi\)
0.961802 + 0.273745i \(0.0882626\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −9.16035 −0.652648 −0.326324 0.945258i \(-0.605810\pi\)
−0.326324 + 0.945258i \(0.605810\pi\)
\(198\) 0 0
\(199\) −0.310629 −0.0220199 −0.0110099 0.999939i \(-0.503505\pi\)
−0.0110099 + 0.999939i \(0.503505\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −3.32759 −0.233551
\(204\) 0 0
\(205\) −12.3618 −0.863384
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −33.1604 −2.29375
\(210\) 0 0
\(211\) 5.95388 0.409882 0.204941 0.978774i \(-0.434300\pi\)
0.204941 + 0.978774i \(0.434300\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −3.47098 −0.236719
\(216\) 0 0
\(217\) −28.8958 −1.96158
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 2.53406 0.170459
\(222\) 0 0
\(223\) −11.9078 −0.797403 −0.398701 0.917081i \(-0.630539\pi\)
−0.398701 + 0.917081i \(0.630539\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −7.37874 −0.489744 −0.244872 0.969555i \(-0.578746\pi\)
−0.244872 + 0.969555i \(0.578746\pi\)
\(228\) 0 0
\(229\) 23.1604 1.53048 0.765240 0.643746i \(-0.222621\pi\)
0.765240 + 0.643746i \(0.222621\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 22.9420 1.50298 0.751489 0.659746i \(-0.229336\pi\)
0.751489 + 0.659746i \(0.229336\pi\)
\(234\) 0 0
\(235\) 6.62629 0.432252
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −0.361783 −0.0234018 −0.0117009 0.999932i \(-0.503725\pi\)
−0.0117009 + 0.999932i \(0.503725\pi\)
\(240\) 0 0
\(241\) 28.5341 1.83804 0.919020 0.394211i \(-0.128982\pi\)
0.919020 + 0.394211i \(0.128982\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 6.95388 0.444267
\(246\) 0 0
\(247\) −19.4710 −1.23891
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 30.8497 1.94722 0.973609 0.228224i \(-0.0732920\pi\)
0.973609 + 0.228224i \(0.0732920\pi\)
\(252\) 0 0
\(253\) 4.84469 0.304583
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 12.7524 0.795476 0.397738 0.917499i \(-0.369795\pi\)
0.397738 + 0.917499i \(0.369795\pi\)
\(258\) 0 0
\(259\) 7.29870 0.453519
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −6.36178 −0.392284 −0.196142 0.980575i \(-0.562841\pi\)
−0.196142 + 0.980575i \(0.562841\pi\)
\(264\) 0 0
\(265\) −12.3618 −0.759378
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −10.5802 −0.645085 −0.322542 0.946555i \(-0.604537\pi\)
−0.322542 + 0.946555i \(0.604537\pi\)
\(270\) 0 0
\(271\) −4.26451 −0.259051 −0.129525 0.991576i \(-0.541345\pi\)
−0.129525 + 0.991576i \(0.541345\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −4.84469 −0.292146
\(276\) 0 0
\(277\) −29.3787 −1.76520 −0.882599 0.470127i \(-0.844208\pi\)
−0.882599 + 0.470127i \(0.844208\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 18.7524 1.11868 0.559339 0.828939i \(-0.311055\pi\)
0.559339 + 0.828939i \(0.311055\pi\)
\(282\) 0 0
\(283\) −12.8958 −0.766578 −0.383289 0.923628i \(-0.625209\pi\)
−0.383289 + 0.923628i \(0.625209\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 46.1773 2.72576
\(288\) 0 0
\(289\) −16.2065 −0.953322
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −8.79857 −0.514018 −0.257009 0.966409i \(-0.582737\pi\)
−0.257009 + 0.966409i \(0.582737\pi\)
\(294\) 0 0
\(295\) −0.890804 −0.0518646
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2.84469 0.164512
\(300\) 0 0
\(301\) 12.9658 0.747337
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 8.62629 0.493940
\(306\) 0 0
\(307\) 10.0050 0.571018 0.285509 0.958376i \(-0.407837\pi\)
0.285509 + 0.958376i \(0.407837\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 18.5290 1.05068 0.525342 0.850891i \(-0.323937\pi\)
0.525342 + 0.850891i \(0.323937\pi\)
\(312\) 0 0
\(313\) 2.39067 0.135128 0.0675642 0.997715i \(-0.478477\pi\)
0.0675642 + 0.997715i \(0.478477\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 16.3157 0.916379 0.458190 0.888855i \(-0.348498\pi\)
0.458190 + 0.888855i \(0.348498\pi\)
\(318\) 0 0
\(319\) −4.31566 −0.241631
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −6.09727 −0.339261
\(324\) 0 0
\(325\) −2.84469 −0.157795
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −24.7524 −1.36465
\(330\) 0 0
\(331\) −24.8958 −1.36840 −0.684200 0.729295i \(-0.739848\pi\)
−0.684200 + 0.729295i \(0.739848\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 7.73549 0.422635
\(336\) 0 0
\(337\) −27.4710 −1.49644 −0.748220 0.663451i \(-0.769091\pi\)
−0.748220 + 0.663451i \(0.769091\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −37.4760 −2.02944
\(342\) 0 0
\(343\) 0.172274 0.00930193
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.25259 0.0672424 0.0336212 0.999435i \(-0.489296\pi\)
0.0336212 + 0.999435i \(0.489296\pi\)
\(348\) 0 0
\(349\) 9.64325 0.516192 0.258096 0.966119i \(-0.416905\pi\)
0.258096 + 0.966119i \(0.416905\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 12.7524 0.678744 0.339372 0.940652i \(-0.389785\pi\)
0.339372 + 0.940652i \(0.389785\pi\)
\(354\) 0 0
\(355\) 12.3618 0.656095
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 6.62629 0.349722 0.174861 0.984593i \(-0.444052\pi\)
0.174861 + 0.984593i \(0.444052\pi\)
\(360\) 0 0
\(361\) 27.8497 1.46577
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 16.5341 0.865432
\(366\) 0 0
\(367\) −9.60933 −0.501603 −0.250802 0.968039i \(-0.580694\pi\)
−0.250802 + 0.968039i \(0.580694\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 46.1773 2.39741
\(372\) 0 0
\(373\) 29.8839 1.54733 0.773665 0.633595i \(-0.218421\pi\)
0.773665 + 0.633595i \(0.218421\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −2.53406 −0.130511
\(378\) 0 0
\(379\) 2.52902 0.129907 0.0649535 0.997888i \(-0.479310\pi\)
0.0649535 + 0.997888i \(0.479310\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −25.2115 −1.28825 −0.644124 0.764921i \(-0.722778\pi\)
−0.644124 + 0.764921i \(0.722778\pi\)
\(384\) 0 0
\(385\) 18.0973 0.922322
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −35.0681 −1.77802 −0.889012 0.457884i \(-0.848608\pi\)
−0.889012 + 0.457884i \(0.848608\pi\)
\(390\) 0 0
\(391\) 0.890804 0.0450499
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 13.4710 0.677799
\(396\) 0 0
\(397\) 8.84972 0.444155 0.222077 0.975029i \(-0.428716\pi\)
0.222077 + 0.975029i \(0.428716\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 23.0681 1.15197 0.575983 0.817461i \(-0.304619\pi\)
0.575983 + 0.817461i \(0.304619\pi\)
\(402\) 0 0
\(403\) −22.0050 −1.09615
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 9.46594 0.469209
\(408\) 0 0
\(409\) 5.29870 0.262004 0.131002 0.991382i \(-0.458181\pi\)
0.131002 + 0.991382i \(0.458181\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 3.32759 0.163740
\(414\) 0 0
\(415\) 4.58018 0.224832
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −2.53406 −0.123797 −0.0618984 0.998082i \(-0.519715\pi\)
−0.0618984 + 0.998082i \(0.519715\pi\)
\(420\) 0 0
\(421\) 22.4079 1.09209 0.546047 0.837754i \(-0.316132\pi\)
0.546047 + 0.837754i \(0.316132\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −0.890804 −0.0432103
\(426\) 0 0
\(427\) −32.2234 −1.55940
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −31.5733 −1.52083 −0.760416 0.649436i \(-0.775005\pi\)
−0.760416 + 0.649436i \(0.775005\pi\)
\(432\) 0 0
\(433\) 7.20647 0.346321 0.173160 0.984894i \(-0.444602\pi\)
0.173160 + 0.984894i \(0.444602\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −6.84469 −0.327426
\(438\) 0 0
\(439\) −4.72357 −0.225443 −0.112722 0.993627i \(-0.535957\pi\)
−0.112722 + 0.993627i \(0.535957\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 7.87888 0.374337 0.187168 0.982328i \(-0.440069\pi\)
0.187168 + 0.982328i \(0.440069\pi\)
\(444\) 0 0
\(445\) 15.1604 0.718670
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 4.70633 0.222105 0.111053 0.993815i \(-0.464578\pi\)
0.111053 + 0.993815i \(0.464578\pi\)
\(450\) 0 0
\(451\) 59.8890 2.82006
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 10.6263 0.498168
\(456\) 0 0
\(457\) −6.04612 −0.282825 −0.141413 0.989951i \(-0.545164\pi\)
−0.141413 + 0.989951i \(0.545164\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 19.2526 0.896682 0.448341 0.893863i \(-0.352015\pi\)
0.448341 + 0.893863i \(0.352015\pi\)
\(462\) 0 0
\(463\) −26.4418 −1.22886 −0.614428 0.788973i \(-0.710613\pi\)
−0.614428 + 0.788973i \(0.710613\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −9.20143 −0.425792 −0.212896 0.977075i \(-0.568289\pi\)
−0.212896 + 0.977075i \(0.568289\pi\)
\(468\) 0 0
\(469\) −28.8958 −1.33429
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 16.8158 0.773191
\(474\) 0 0
\(475\) 6.84469 0.314056
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 12.7524 0.582674 0.291337 0.956620i \(-0.405900\pi\)
0.291337 + 0.956620i \(0.405900\pi\)
\(480\) 0 0
\(481\) 5.55818 0.253431
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −17.2526 −0.783400
\(486\) 0 0
\(487\) −30.5341 −1.38363 −0.691815 0.722075i \(-0.743189\pi\)
−0.691815 + 0.722075i \(0.743189\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 2.67241 0.120604 0.0603021 0.998180i \(-0.480794\pi\)
0.0603021 + 0.998180i \(0.480794\pi\)
\(492\) 0 0
\(493\) −0.793532 −0.0357389
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −46.1773 −2.07134
\(498\) 0 0
\(499\) −20.8036 −0.931297 −0.465649 0.884970i \(-0.654179\pi\)
−0.465649 + 0.884970i \(0.654179\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −3.32759 −0.148370 −0.0741849 0.997245i \(-0.523636\pi\)
−0.0741849 + 0.997245i \(0.523636\pi\)
\(504\) 0 0
\(505\) 2.67241 0.118921
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −16.2184 −0.718868 −0.359434 0.933171i \(-0.617030\pi\)
−0.359434 + 0.933171i \(0.617030\pi\)
\(510\) 0 0
\(511\) −61.7628 −2.73223
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 6.21839 0.274015
\(516\) 0 0
\(517\) −32.1023 −1.41186
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −3.18923 −0.139723 −0.0698614 0.997557i \(-0.522256\pi\)
−0.0698614 + 0.997557i \(0.522256\pi\)
\(522\) 0 0
\(523\) 23.8155 1.04138 0.520690 0.853746i \(-0.325675\pi\)
0.520690 + 0.853746i \(0.325675\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −6.89080 −0.300168
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 35.1654 1.52318
\(534\) 0 0
\(535\) 14.7986 0.639798
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −33.6894 −1.45110
\(540\) 0 0
\(541\) 15.7816 0.678504 0.339252 0.940695i \(-0.389826\pi\)
0.339252 + 0.940695i \(0.389826\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −12.5341 −0.536900
\(546\) 0 0
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 6.09727 0.259753
\(552\) 0 0
\(553\) −50.3207 −2.13985
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −31.7405 −1.34489 −0.672445 0.740147i \(-0.734756\pi\)
−0.672445 + 0.740147i \(0.734756\pi\)
\(558\) 0 0
\(559\) 9.87384 0.417619
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −21.9250 −0.924029 −0.462014 0.886872i \(-0.652873\pi\)
−0.462014 + 0.886872i \(0.652873\pi\)
\(564\) 0 0
\(565\) −12.3618 −0.520064
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 14.6313 0.613377 0.306689 0.951810i \(-0.400779\pi\)
0.306689 + 0.951810i \(0.400779\pi\)
\(570\) 0 0
\(571\) 1.24755 0.0522084 0.0261042 0.999659i \(-0.491690\pi\)
0.0261042 + 0.999659i \(0.491690\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1.00000 −0.0417029
\(576\) 0 0
\(577\) 18.0922 0.753190 0.376595 0.926378i \(-0.377095\pi\)
0.376595 + 0.926378i \(0.377095\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −17.1092 −0.709809
\(582\) 0 0
\(583\) 59.8890 2.48035
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −12.5290 −0.517128 −0.258564 0.965994i \(-0.583249\pi\)
−0.258564 + 0.965994i \(0.583249\pi\)
\(588\) 0 0
\(589\) 52.9470 2.18164
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 24.9470 1.02445 0.512225 0.858851i \(-0.328821\pi\)
0.512225 + 0.858851i \(0.328821\pi\)
\(594\) 0 0
\(595\) 3.32759 0.136418
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 34.5391 1.41123 0.705615 0.708596i \(-0.250671\pi\)
0.705615 + 0.708596i \(0.250671\pi\)
\(600\) 0 0
\(601\) 37.9300 1.54720 0.773599 0.633675i \(-0.218454\pi\)
0.773599 + 0.633675i \(0.218454\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 12.4710 0.507017
\(606\) 0 0
\(607\) 26.0973 1.05926 0.529628 0.848230i \(-0.322332\pi\)
0.529628 + 0.848230i \(0.322332\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −18.8497 −0.762578
\(612\) 0 0
\(613\) 2.84972 0.115099 0.0575496 0.998343i \(-0.481671\pi\)
0.0575496 + 0.998343i \(0.481671\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 9.52213 0.383347 0.191673 0.981459i \(-0.438609\pi\)
0.191673 + 0.981459i \(0.438609\pi\)
\(618\) 0 0
\(619\) −23.9762 −0.963683 −0.481841 0.876258i \(-0.660032\pi\)
−0.481841 + 0.876258i \(0.660032\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −56.6313 −2.26889
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1.74053 0.0693993
\(630\) 0 0
\(631\) −17.8789 −0.711747 −0.355873 0.934534i \(-0.615817\pi\)
−0.355873 + 0.934534i \(0.615817\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 11.7866 0.467739
\(636\) 0 0
\(637\) −19.7816 −0.783776
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −2.93692 −0.116001 −0.0580007 0.998317i \(-0.518473\pi\)
−0.0580007 + 0.998317i \(0.518473\pi\)
\(642\) 0 0
\(643\) −0.895840 −0.0353285 −0.0176642 0.999844i \(-0.505623\pi\)
−0.0176642 + 0.999844i \(0.505623\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 21.4659 0.843913 0.421957 0.906616i \(-0.361343\pi\)
0.421957 + 0.906616i \(0.361343\pi\)
\(648\) 0 0
\(649\) 4.31566 0.169405
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 4.84469 0.189587 0.0947936 0.995497i \(-0.469781\pi\)
0.0947936 + 0.995497i \(0.469781\pi\)
\(654\) 0 0
\(655\) 17.4710 0.682648
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 18.0973 0.704970 0.352485 0.935818i \(-0.385337\pi\)
0.352485 + 0.935818i \(0.385337\pi\)
\(660\) 0 0
\(661\) 0.747413 0.0290710 0.0145355 0.999894i \(-0.495373\pi\)
0.0145355 + 0.999894i \(0.495373\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −25.5683 −0.991494
\(666\) 0 0
\(667\) −0.890804 −0.0344921
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −41.7917 −1.61335
\(672\) 0 0
\(673\) −19.1892 −0.739691 −0.369845 0.929093i \(-0.620589\pi\)
−0.369845 + 0.929093i \(0.620589\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 4.17731 0.160547 0.0802735 0.996773i \(-0.474421\pi\)
0.0802735 + 0.996773i \(0.474421\pi\)
\(678\) 0 0
\(679\) 64.4469 2.47324
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 26.0050 0.995055 0.497528 0.867448i \(-0.334241\pi\)
0.497528 + 0.867448i \(0.334241\pi\)
\(684\) 0 0
\(685\) −15.1604 −0.579247
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 35.1654 1.33969
\(690\) 0 0
\(691\) 26.8497 1.02141 0.510706 0.859756i \(-0.329384\pi\)
0.510706 + 0.859756i \(0.329384\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −5.51710 −0.209275
\(696\) 0 0
\(697\) 11.0119 0.417106
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −11.9027 −0.449560 −0.224780 0.974410i \(-0.572166\pi\)
−0.224780 + 0.974410i \(0.572166\pi\)
\(702\) 0 0
\(703\) −13.3737 −0.504399
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −9.98277 −0.375441
\(708\) 0 0
\(709\) −39.3737 −1.47871 −0.739355 0.673315i \(-0.764870\pi\)
−0.739355 + 0.673315i \(0.764870\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −7.73549 −0.289696
\(714\) 0 0
\(715\) 13.7816 0.515403
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −23.6382 −0.881557 −0.440778 0.897616i \(-0.645298\pi\)
−0.440778 + 0.897616i \(0.645298\pi\)
\(720\) 0 0
\(721\) −23.2287 −0.865083
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0.890804 0.0330836
\(726\) 0 0
\(727\) 12.5513 0.465502 0.232751 0.972536i \(-0.425227\pi\)
0.232751 + 0.972536i \(0.425227\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 3.09196 0.114360
\(732\) 0 0
\(733\) 39.1142 1.44472 0.722359 0.691519i \(-0.243058\pi\)
0.722359 + 0.691519i \(0.243058\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −37.4760 −1.38045
\(738\) 0 0
\(739\) 35.7456 1.31492 0.657461 0.753489i \(-0.271630\pi\)
0.657461 + 0.753489i \(0.271630\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −20.4368 −0.749753 −0.374876 0.927075i \(-0.622315\pi\)
−0.374876 + 0.927075i \(0.622315\pi\)
\(744\) 0 0
\(745\) −1.15531 −0.0423274
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −55.2799 −2.01988
\(750\) 0 0
\(751\) −0.534057 −0.0194880 −0.00974401 0.999953i \(-0.503102\pi\)
−0.00974401 + 0.999953i \(0.503102\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −15.4710 −0.563047
\(756\) 0 0
\(757\) −29.5171 −1.07282 −0.536409 0.843958i \(-0.680219\pi\)
−0.536409 + 0.843958i \(0.680219\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −38.1434 −1.38270 −0.691348 0.722522i \(-0.742983\pi\)
−0.691348 + 0.722522i \(0.742983\pi\)
\(762\) 0 0
\(763\) 46.8208 1.69503
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 2.53406 0.0914995
\(768\) 0 0
\(769\) 20.8786 0.752902 0.376451 0.926437i \(-0.377144\pi\)
0.376451 + 0.926437i \(0.377144\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −8.31063 −0.298913 −0.149456 0.988768i \(-0.547752\pi\)
−0.149456 + 0.988768i \(0.547752\pi\)
\(774\) 0 0
\(775\) 7.73549 0.277867
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −84.6125 −3.03156
\(780\) 0 0
\(781\) −59.8890 −2.14300
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 18.6774 0.666627
\(786\) 0 0
\(787\) −1.95388 −0.0696484 −0.0348242 0.999393i \(-0.511087\pi\)
−0.0348242 + 0.999393i \(0.511087\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 46.1773 1.64188
\(792\) 0 0
\(793\) −24.5391 −0.871409
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 16.1773 0.573030 0.286515 0.958076i \(-0.407503\pi\)
0.286515 + 0.958076i \(0.407503\pi\)
\(798\) 0 0
\(799\) −5.90273 −0.208823
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −80.1023 −2.82675
\(804\) 0 0
\(805\) 3.73549 0.131659
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 26.8670 0.944592 0.472296 0.881440i \(-0.343425\pi\)
0.472296 + 0.881440i \(0.343425\pi\)
\(810\) 0 0
\(811\) 2.13835 0.0750878 0.0375439 0.999295i \(-0.488047\pi\)
0.0375439 + 0.999295i \(0.488047\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0.0922364 0.00323090
\(816\) 0 0
\(817\) −23.7578 −0.831179
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −15.1604 −0.529100 −0.264550 0.964372i \(-0.585223\pi\)
−0.264550 + 0.964372i \(0.585223\pi\)
\(822\) 0 0
\(823\) −23.1264 −0.806137 −0.403068 0.915170i \(-0.632056\pi\)
−0.403068 + 0.915170i \(0.632056\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −47.4299 −1.64930 −0.824650 0.565644i \(-0.808628\pi\)
−0.824650 + 0.565644i \(0.808628\pi\)
\(828\) 0 0
\(829\) −30.1723 −1.04793 −0.523963 0.851741i \(-0.675547\pi\)
−0.523963 + 0.851741i \(0.675547\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −6.19454 −0.214628
\(834\) 0 0
\(835\) 5.37371 0.185965
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −18.8497 −0.650765 −0.325382 0.945583i \(-0.605493\pi\)
−0.325382 + 0.945583i \(0.605493\pi\)
\(840\) 0 0
\(841\) −28.2065 −0.972637
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −4.90776 −0.168832
\(846\) 0 0
\(847\) −46.5852 −1.60069
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 1.95388 0.0669782
\(852\) 0 0
\(853\) 29.7578 1.01889 0.509443 0.860504i \(-0.329851\pi\)
0.509443 + 0.860504i \(0.329851\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 15.2865 0.522177 0.261089 0.965315i \(-0.415919\pi\)
0.261089 + 0.965315i \(0.415919\pi\)
\(858\) 0 0
\(859\) 33.5171 1.14359 0.571794 0.820397i \(-0.306248\pi\)
0.571794 + 0.820397i \(0.306248\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 31.0443 1.05676 0.528380 0.849008i \(-0.322800\pi\)
0.528380 + 0.849008i \(0.322800\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −65.2627 −2.21388
\(870\) 0 0
\(871\) −22.0050 −0.745612
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −3.73549 −0.126283
\(876\) 0 0
\(877\) 10.6313 0.358994 0.179497 0.983758i \(-0.442553\pi\)
0.179497 + 0.983758i \(0.442553\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −20.5341 −0.691810 −0.345905 0.938270i \(-0.612428\pi\)
−0.345905 + 0.938270i \(0.612428\pi\)
\(882\) 0 0
\(883\) 36.0390 1.21281 0.606404 0.795157i \(-0.292612\pi\)
0.606404 + 0.795157i \(0.292612\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 24.9759 0.838608 0.419304 0.907846i \(-0.362274\pi\)
0.419304 + 0.907846i \(0.362274\pi\)
\(888\) 0 0
\(889\) −44.0289 −1.47668
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 45.3549 1.51774
\(894\) 0 0
\(895\) 9.56322 0.319663
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 6.89080 0.229821
\(900\) 0 0
\(901\) 11.0119 0.366860
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −7.16035 −0.238018
\(906\) 0 0
\(907\) 41.6194 1.38195 0.690975 0.722879i \(-0.257182\pi\)
0.690975 + 0.722879i \(0.257182\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −3.81553 −0.126414 −0.0632070 0.998000i \(-0.520133\pi\)
−0.0632070 + 0.998000i \(0.520133\pi\)
\(912\) 0 0
\(913\) −22.1895 −0.734366
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −65.2627 −2.15516
\(918\) 0 0
\(919\) −39.7917 −1.31261 −0.656303 0.754497i \(-0.727881\pi\)
−0.656303 + 0.754497i \(0.727881\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −35.1654 −1.15748
\(924\) 0 0
\(925\) −1.95388 −0.0642432
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −12.6141 −0.413855 −0.206928 0.978356i \(-0.566346\pi\)
−0.206928 + 0.978356i \(0.566346\pi\)
\(930\) 0 0
\(931\) 47.5971 1.55993
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 4.31566 0.141137
\(936\) 0 0
\(937\) −22.1262 −0.722830 −0.361415 0.932405i \(-0.617706\pi\)
−0.361415 + 0.932405i \(0.617706\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 11.0392 0.359869 0.179934 0.983679i \(-0.442411\pi\)
0.179934 + 0.983679i \(0.442411\pi\)
\(942\) 0 0
\(943\) 12.3618 0.402555
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −9.68937 −0.314862 −0.157431 0.987530i \(-0.550321\pi\)
−0.157431 + 0.987530i \(0.550321\pi\)
\(948\) 0 0
\(949\) −47.0342 −1.52679
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 14.1845 0.459480 0.229740 0.973252i \(-0.426212\pi\)
0.229740 + 0.973252i \(0.426212\pi\)
\(954\) 0 0
\(955\) −14.0050 −0.453192
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 56.6313 1.82872
\(960\) 0 0
\(961\) 28.8378 0.930252
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 26.7236 0.860262
\(966\) 0 0
\(967\) 12.8447 0.413057 0.206529 0.978441i \(-0.433783\pi\)
0.206529 + 0.978441i \(0.433783\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 24.1945 0.776440 0.388220 0.921567i \(-0.373090\pi\)
0.388220 + 0.921567i \(0.373090\pi\)
\(972\) 0 0
\(973\) 20.6091 0.660696
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −18.4879 −0.591482 −0.295741 0.955268i \(-0.595566\pi\)
−0.295741 + 0.955268i \(0.595566\pi\)
\(978\) 0 0
\(979\) −73.4471 −2.34738
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 28.8325 0.919614 0.459807 0.888019i \(-0.347919\pi\)
0.459807 + 0.888019i \(0.347919\pi\)
\(984\) 0 0
\(985\) −9.16035 −0.291873
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 3.47098 0.110371
\(990\) 0 0
\(991\) 40.8958 1.29910 0.649550 0.760319i \(-0.274957\pi\)
0.649550 + 0.760319i \(0.274957\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −0.310629 −0.00984759
\(996\) 0 0
\(997\) −4.65518 −0.147431 −0.0737155 0.997279i \(-0.523486\pi\)
−0.0737155 + 0.997279i \(0.523486\pi\)
\(998\) 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 4140.2.a.s.1.1 3
3.2 odd 2 1380.2.a.j.1.1 3
12.11 even 2 5520.2.a.bv.1.3 3
15.2 even 4 6900.2.f.r.6349.1 6
15.8 even 4 6900.2.f.r.6349.6 6
15.14 odd 2 6900.2.a.x.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1380.2.a.j.1.1 3 3.2 odd 2
4140.2.a.s.1.1 3 1.1 even 1 trivial
5520.2.a.bv.1.3 3 12.11 even 2
6900.2.a.x.1.3 3 15.14 odd 2
6900.2.f.r.6349.1 6 15.2 even 4
6900.2.f.r.6349.6 6 15.8 even 4