Properties

Label 8280.2.a.bj.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: 3.3.2597.1
Defining polynomial: \( x^{3} - x^{2} - 9x + 8 \) 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 \(0.878468\) of defining polynomial
Character \(\chi\) \(=\) 8280.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{5} +0.121532 q^{7} +O(q^{10})\) \(q-1.00000 q^{5} +0.121532 q^{7} -2.87847 q^{11} +5.22829 q^{13} +2.22829 q^{17} +1.22829 q^{19} -1.00000 q^{23} +1.00000 q^{25} -9.34983 q^{29} -2.12153 q^{31} -0.121532 q^{35} +5.59289 q^{37} -8.22829 q^{41} +8.00000 q^{43} +10.4566 q^{47} -6.98523 q^{49} +3.59289 q^{53} +2.87847 q^{55} +0.650174 q^{59} -7.33506 q^{61} -5.22829 q^{65} +5.59289 q^{67} +13.9852 q^{71} +12.9427 q^{73} -0.349826 q^{77} -3.51387 q^{79} +11.1068 q^{83} -2.22829 q^{85} +0.486128 q^{89} +0.635404 q^{91} -1.22829 q^{95} +0.635404 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 3 q^{5} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 3 q^{5} + 2 q^{7} - 7 q^{11} - q^{13} - 10 q^{17} - 13 q^{19} - 3 q^{23} + 3 q^{25} - 13 q^{29} - 8 q^{31} - 2 q^{35} + 5 q^{37} - 8 q^{41} + 24 q^{43} - 2 q^{47} - q^{49} - q^{53} + 7 q^{55} + 17 q^{59} + 13 q^{61} + q^{65} + 5 q^{67} + 22 q^{71} + 12 q^{73} + 14 q^{77} - 4 q^{79} + 15 q^{83} + 10 q^{85} + 8 q^{89} - 3 q^{91} + 13 q^{95} - 3 q^{97}+O(q^{100}) \) 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
\(7\) 0.121532 0.0459347 0.0229674 0.999736i \(-0.492689\pi\)
0.0229674 + 0.999736i \(0.492689\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.87847 −0.867891 −0.433945 0.900939i \(-0.642879\pi\)
−0.433945 + 0.900939i \(0.642879\pi\)
\(12\) 0 0
\(13\) 5.22829 1.45007 0.725034 0.688713i \(-0.241824\pi\)
0.725034 + 0.688713i \(0.241824\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.22829 0.540441 0.270220 0.962799i \(-0.412903\pi\)
0.270220 + 0.962799i \(0.412903\pi\)
\(18\) 0 0
\(19\) 1.22829 0.281790 0.140895 0.990025i \(-0.455002\pi\)
0.140895 + 0.990025i \(0.455002\pi\)
\(20\) 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
\(29\) −9.34983 −1.73622 −0.868110 0.496373i \(-0.834665\pi\)
−0.868110 + 0.496373i \(0.834665\pi\)
\(30\) 0 0
\(31\) −2.12153 −0.381038 −0.190519 0.981683i \(-0.561017\pi\)
−0.190519 + 0.981683i \(0.561017\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −0.121532 −0.0205426
\(36\) 0 0
\(37\) 5.59289 0.919465 0.459733 0.888057i \(-0.347945\pi\)
0.459733 + 0.888057i \(0.347945\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −8.22829 −1.28504 −0.642522 0.766267i \(-0.722112\pi\)
−0.642522 + 0.766267i \(0.722112\pi\)
\(42\) 0 0
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 10.4566 1.52525 0.762625 0.646841i \(-0.223910\pi\)
0.762625 + 0.646841i \(0.223910\pi\)
\(48\) 0 0
\(49\) −6.98523 −0.997890
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 3.59289 0.493521 0.246761 0.969076i \(-0.420634\pi\)
0.246761 + 0.969076i \(0.420634\pi\)
\(54\) 0 0
\(55\) 2.87847 0.388133
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0.650174 0.0846455 0.0423227 0.999104i \(-0.486524\pi\)
0.0423227 + 0.999104i \(0.486524\pi\)
\(60\) 0 0
\(61\) −7.33506 −0.939158 −0.469579 0.882891i \(-0.655594\pi\)
−0.469579 + 0.882891i \(0.655594\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −5.22829 −0.648490
\(66\) 0 0
\(67\) 5.59289 0.683280 0.341640 0.939831i \(-0.389018\pi\)
0.341640 + 0.939831i \(0.389018\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 13.9852 1.65974 0.829871 0.557956i \(-0.188414\pi\)
0.829871 + 0.557956i \(0.188414\pi\)
\(72\) 0 0
\(73\) 12.9427 1.51483 0.757415 0.652934i \(-0.226462\pi\)
0.757415 + 0.652934i \(0.226462\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −0.349826 −0.0398663
\(78\) 0 0
\(79\) −3.51387 −0.395342 −0.197671 0.980268i \(-0.563338\pi\)
−0.197671 + 0.980268i \(0.563338\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 11.1068 1.21913 0.609563 0.792738i \(-0.291345\pi\)
0.609563 + 0.792738i \(0.291345\pi\)
\(84\) 0 0
\(85\) −2.22829 −0.241692
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0.486128 0.0515294 0.0257647 0.999668i \(-0.491798\pi\)
0.0257647 + 0.999668i \(0.491798\pi\)
\(90\) 0 0
\(91\) 0.635404 0.0666085
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1.22829 −0.126020
\(96\) 0 0
\(97\) 0.635404 0.0645155 0.0322578 0.999480i \(-0.489730\pi\)
0.0322578 + 0.999480i \(0.489730\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −13.3498 −1.32836 −0.664179 0.747574i \(-0.731219\pi\)
−0.664179 + 0.747574i \(0.731219\pi\)
\(102\) 0 0
\(103\) −7.33506 −0.722745 −0.361372 0.932422i \(-0.617692\pi\)
−0.361372 + 0.932422i \(0.617692\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −16.0495 −1.55156 −0.775781 0.631003i \(-0.782644\pi\)
−0.775781 + 0.631003i \(0.782644\pi\)
\(108\) 0 0
\(109\) 1.01477 0.0971973 0.0485987 0.998818i \(-0.484524\pi\)
0.0485987 + 0.998818i \(0.484524\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −17.3203 −1.62936 −0.814678 0.579914i \(-0.803086\pi\)
−0.814678 + 0.579914i \(0.803086\pi\)
\(114\) 0 0
\(115\) 1.00000 0.0932505
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0.270809 0.0248250
\(120\) 0 0
\(121\) −2.71442 −0.246766
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 1.75694 0.155903 0.0779514 0.996957i \(-0.475162\pi\)
0.0779514 + 0.996957i \(0.475162\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 20.2135 1.76606 0.883032 0.469313i \(-0.155498\pi\)
0.883032 + 0.469313i \(0.155498\pi\)
\(132\) 0 0
\(133\) 0.149277 0.0129439
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 17.9279 1.53169 0.765844 0.643027i \(-0.222322\pi\)
0.765844 + 0.643027i \(0.222322\pi\)
\(138\) 0 0
\(139\) −10.8637 −0.921447 −0.460723 0.887544i \(-0.652410\pi\)
−0.460723 + 0.887544i \(0.652410\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −15.0495 −1.25850
\(144\) 0 0
\(145\) 9.34983 0.776461
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 15.7144 1.28738 0.643688 0.765288i \(-0.277404\pi\)
0.643688 + 0.765288i \(0.277404\pi\)
\(150\) 0 0
\(151\) −8.39234 −0.682959 −0.341479 0.939889i \(-0.610928\pi\)
−0.341479 + 0.939889i \(0.610928\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 2.12153 0.170406
\(156\) 0 0
\(157\) −19.5633 −1.56133 −0.780663 0.624953i \(-0.785118\pi\)
−0.780663 + 0.624953i \(0.785118\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −0.121532 −0.00957805
\(162\) 0 0
\(163\) 1.01477 0.0794829 0.0397415 0.999210i \(-0.487347\pi\)
0.0397415 + 0.999210i \(0.487347\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 8.00000 0.619059 0.309529 0.950890i \(-0.399829\pi\)
0.309529 + 0.950890i \(0.399829\pi\)
\(168\) 0 0
\(169\) 14.3351 1.10270
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 2.63540 0.200366 0.100183 0.994969i \(-0.468057\pi\)
0.100183 + 0.994969i \(0.468057\pi\)
\(174\) 0 0
\(175\) 0.121532 0.00918695
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 14.4566 1.08054 0.540268 0.841493i \(-0.318323\pi\)
0.540268 + 0.841493i \(0.318323\pi\)
\(180\) 0 0
\(181\) 10.7422 0.798459 0.399229 0.916851i \(-0.369278\pi\)
0.399229 + 0.916851i \(0.369278\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −5.59289 −0.411197
\(186\) 0 0
\(187\) −6.41407 −0.469043
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 22.6701 1.64035 0.820176 0.572112i \(-0.193876\pi\)
0.820176 + 0.572112i \(0.193876\pi\)
\(192\) 0 0
\(193\) 2.24306 0.161459 0.0807296 0.996736i \(-0.474275\pi\)
0.0807296 + 0.996736i \(0.474275\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 7.57812 0.539919 0.269959 0.962872i \(-0.412990\pi\)
0.269959 + 0.962872i \(0.412990\pi\)
\(198\) 0 0
\(199\) −14.0000 −0.992434 −0.496217 0.868199i \(-0.665278\pi\)
−0.496217 + 0.868199i \(0.665278\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1.13630 −0.0797528
\(204\) 0 0
\(205\) 8.22829 0.574689
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −3.53560 −0.244563
\(210\) 0 0
\(211\) −3.10676 −0.213878 −0.106939 0.994266i \(-0.534105\pi\)
−0.106939 + 0.994266i \(0.534105\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −8.00000 −0.545595
\(216\) 0 0
\(217\) −0.257834 −0.0175029
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 11.6502 0.783676
\(222\) 0 0
\(223\) 18.2135 1.21967 0.609834 0.792529i \(-0.291236\pi\)
0.609834 + 0.792529i \(0.291236\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −13.9705 −0.927252 −0.463626 0.886031i \(-0.653452\pi\)
−0.463626 + 0.886031i \(0.653452\pi\)
\(228\) 0 0
\(229\) 12.2135 0.807092 0.403546 0.914959i \(-0.367777\pi\)
0.403546 + 0.914959i \(0.367777\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −9.75694 −0.639198 −0.319599 0.947553i \(-0.603548\pi\)
−0.319599 + 0.947553i \(0.603548\pi\)
\(234\) 0 0
\(235\) −10.4566 −0.682113
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −8.62063 −0.557622 −0.278811 0.960346i \(-0.589940\pi\)
−0.278811 + 0.960346i \(0.589940\pi\)
\(240\) 0 0
\(241\) 3.18578 0.205214 0.102607 0.994722i \(-0.467282\pi\)
0.102607 + 0.994722i \(0.467282\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 6.98523 0.446270
\(246\) 0 0
\(247\) 6.42188 0.408614
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 25.2283 1.59240 0.796198 0.605036i \(-0.206841\pi\)
0.796198 + 0.605036i \(0.206841\pi\)
\(252\) 0 0
\(253\) 2.87847 0.180968
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 10.6701 0.665583 0.332792 0.943000i \(-0.392009\pi\)
0.332792 + 0.943000i \(0.392009\pi\)
\(258\) 0 0
\(259\) 0.679714 0.0422354
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 18.6849 1.15216 0.576080 0.817394i \(-0.304582\pi\)
0.576080 + 0.817394i \(0.304582\pi\)
\(264\) 0 0
\(265\) −3.59289 −0.220709
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 24.8637 1.51597 0.757983 0.652274i \(-0.226185\pi\)
0.757983 + 0.652274i \(0.226185\pi\)
\(270\) 0 0
\(271\) 0.578119 0.0351183 0.0175591 0.999846i \(-0.494410\pi\)
0.0175591 + 0.999846i \(0.494410\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2.87847 −0.173578
\(276\) 0 0
\(277\) −9.51387 −0.571633 −0.285817 0.958284i \(-0.592265\pi\)
−0.285817 + 0.958284i \(0.592265\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 13.1562 0.784835 0.392418 0.919787i \(-0.371639\pi\)
0.392418 + 0.919787i \(0.371639\pi\)
\(282\) 0 0
\(283\) 24.5061 1.45673 0.728367 0.685187i \(-0.240280\pi\)
0.728367 + 0.685187i \(0.240280\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1.00000 −0.0590281
\(288\) 0 0
\(289\) −12.0347 −0.707924
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 6.29254 0.367614 0.183807 0.982962i \(-0.441158\pi\)
0.183807 + 0.982962i \(0.441158\pi\)
\(294\) 0 0
\(295\) −0.650174 −0.0378546
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −5.22829 −0.302360
\(300\) 0 0
\(301\) 0.972255 0.0560398
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 7.33506 0.420004
\(306\) 0 0
\(307\) 13.3351 0.761072 0.380536 0.924766i \(-0.375740\pi\)
0.380536 + 0.924766i \(0.375740\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 24.4270 1.38513 0.692565 0.721355i \(-0.256480\pi\)
0.692565 + 0.721355i \(0.256480\pi\)
\(312\) 0 0
\(313\) 26.5486 1.50061 0.750307 0.661089i \(-0.229906\pi\)
0.750307 + 0.661089i \(0.229906\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 16.9852 0.953986 0.476993 0.878907i \(-0.341727\pi\)
0.476993 + 0.878907i \(0.341727\pi\)
\(318\) 0 0
\(319\) 26.9132 1.50685
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 2.73700 0.152291
\(324\) 0 0
\(325\) 5.22829 0.290014
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1.27081 0.0700620
\(330\) 0 0
\(331\) 17.8914 0.983403 0.491701 0.870764i \(-0.336375\pi\)
0.491701 + 0.870764i \(0.336375\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −5.59289 −0.305572
\(336\) 0 0
\(337\) −4.52864 −0.246691 −0.123345 0.992364i \(-0.539362\pi\)
−0.123345 + 0.992364i \(0.539362\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 6.10676 0.330700
\(342\) 0 0
\(343\) −1.69965 −0.0917725
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0.0937869 0.00503475 0.00251737 0.999997i \(-0.499199\pi\)
0.00251737 + 0.999997i \(0.499199\pi\)
\(348\) 0 0
\(349\) 8.07902 0.432460 0.216230 0.976342i \(-0.430624\pi\)
0.216230 + 0.976342i \(0.430624\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 8.00000 0.425797 0.212899 0.977074i \(-0.431710\pi\)
0.212899 + 0.977074i \(0.431710\pi\)
\(354\) 0 0
\(355\) −13.9852 −0.742259
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −8.69965 −0.459150 −0.229575 0.973291i \(-0.573734\pi\)
−0.229575 + 0.973291i \(0.573734\pi\)
\(360\) 0 0
\(361\) −17.4913 −0.920594
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −12.9427 −0.677453
\(366\) 0 0
\(367\) 31.8064 1.66028 0.830141 0.557554i \(-0.188260\pi\)
0.830141 + 0.557554i \(0.188260\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0.436651 0.0226698
\(372\) 0 0
\(373\) −13.4288 −0.695319 −0.347660 0.937621i \(-0.613023\pi\)
−0.347660 + 0.937621i \(0.613023\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −48.8836 −2.51764
\(378\) 0 0
\(379\) 31.8212 1.63454 0.817272 0.576252i \(-0.195485\pi\)
0.817272 + 0.576252i \(0.195485\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −34.3480 −1.75510 −0.877551 0.479483i \(-0.840824\pi\)
−0.877551 + 0.479483i \(0.840824\pi\)
\(384\) 0 0
\(385\) 0.349826 0.0178288
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −8.14928 −0.413185 −0.206592 0.978427i \(-0.566237\pi\)
−0.206592 + 0.978427i \(0.566237\pi\)
\(390\) 0 0
\(391\) −2.22829 −0.112690
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 3.51387 0.176802
\(396\) 0 0
\(397\) 19.0625 0.956717 0.478359 0.878165i \(-0.341232\pi\)
0.478359 + 0.878165i \(0.341232\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −19.9705 −0.997277 −0.498639 0.866810i \(-0.666167\pi\)
−0.498639 + 0.866810i \(0.666167\pi\)
\(402\) 0 0
\(403\) −11.0920 −0.552531
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −16.0990 −0.797996
\(408\) 0 0
\(409\) −10.3351 −0.511036 −0.255518 0.966804i \(-0.582246\pi\)
−0.255518 + 0.966804i \(0.582246\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0.0790169 0.00388817
\(414\) 0 0
\(415\) −11.1068 −0.545209
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −5.72740 −0.279802 −0.139901 0.990166i \(-0.544678\pi\)
−0.139901 + 0.990166i \(0.544678\pi\)
\(420\) 0 0
\(421\) −8.44361 −0.411516 −0.205758 0.978603i \(-0.565966\pi\)
−0.205758 + 0.978603i \(0.565966\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 2.22829 0.108088
\(426\) 0 0
\(427\) −0.891443 −0.0431400
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −35.3698 −1.70370 −0.851851 0.523785i \(-0.824520\pi\)
−0.851851 + 0.523785i \(0.824520\pi\)
\(432\) 0 0
\(433\) 13.3923 0.643595 0.321797 0.946809i \(-0.395713\pi\)
0.321797 + 0.946809i \(0.395713\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1.22829 −0.0587573
\(438\) 0 0
\(439\) −21.1137 −1.00770 −0.503852 0.863790i \(-0.668084\pi\)
−0.503852 + 0.863790i \(0.668084\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 31.1692 1.48089 0.740447 0.672115i \(-0.234614\pi\)
0.740447 + 0.672115i \(0.234614\pi\)
\(444\) 0 0
\(445\) −0.486128 −0.0230447
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 6.09199 0.287499 0.143749 0.989614i \(-0.454084\pi\)
0.143749 + 0.989614i \(0.454084\pi\)
\(450\) 0 0
\(451\) 23.6849 1.11528
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −0.635404 −0.0297882
\(456\) 0 0
\(457\) 22.1345 1.03541 0.517704 0.855560i \(-0.326787\pi\)
0.517704 + 0.855560i \(0.326787\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 11.5434 0.537630 0.268815 0.963192i \(-0.413368\pi\)
0.268815 + 0.963192i \(0.413368\pi\)
\(462\) 0 0
\(463\) 30.4270 1.41406 0.707032 0.707181i \(-0.250033\pi\)
0.707032 + 0.707181i \(0.250033\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −10.3776 −0.480217 −0.240108 0.970746i \(-0.577183\pi\)
−0.240108 + 0.970746i \(0.577183\pi\)
\(468\) 0 0
\(469\) 0.679714 0.0313863
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −23.0277 −1.05882
\(474\) 0 0
\(475\) 1.22829 0.0563580
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 29.6128 1.35304 0.676522 0.736422i \(-0.263486\pi\)
0.676522 + 0.736422i \(0.263486\pi\)
\(480\) 0 0
\(481\) 29.2413 1.33329
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −0.635404 −0.0288522
\(486\) 0 0
\(487\) 11.1562 0.505537 0.252769 0.967527i \(-0.418659\pi\)
0.252769 + 0.967527i \(0.418659\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −38.2630 −1.72679 −0.863393 0.504533i \(-0.831665\pi\)
−0.863393 + 0.504533i \(0.831665\pi\)
\(492\) 0 0
\(493\) −20.8342 −0.938323
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1.69965 0.0762398
\(498\) 0 0
\(499\) 6.40711 0.286822 0.143411 0.989663i \(-0.454193\pi\)
0.143411 + 0.989663i \(0.454193\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 18.0920 0.806682 0.403341 0.915050i \(-0.367849\pi\)
0.403341 + 0.915050i \(0.367849\pi\)
\(504\) 0 0
\(505\) 13.3498 0.594059
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 34.1285 1.51272 0.756359 0.654156i \(-0.226976\pi\)
0.756359 + 0.654156i \(0.226976\pi\)
\(510\) 0 0
\(511\) 1.57295 0.0695833
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 7.33506 0.323221
\(516\) 0 0
\(517\) −30.0990 −1.32375
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −35.8854 −1.57217 −0.786085 0.618119i \(-0.787895\pi\)
−0.786085 + 0.618119i \(0.787895\pi\)
\(522\) 0 0
\(523\) 11.7865 0.515387 0.257693 0.966227i \(-0.417038\pi\)
0.257693 + 0.966227i \(0.417038\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −4.72740 −0.205929
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −43.0199 −1.86340
\(534\) 0 0
\(535\) 16.0495 0.693879
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 20.1068 0.866060
\(540\) 0 0
\(541\) −17.2413 −0.741260 −0.370630 0.928781i \(-0.620858\pi\)
−0.370630 + 0.928781i \(0.620858\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −1.01477 −0.0434680
\(546\) 0 0
\(547\) 14.6571 0.626694 0.313347 0.949639i \(-0.398550\pi\)
0.313347 + 0.949639i \(0.398550\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −11.4843 −0.489249
\(552\) 0 0
\(553\) −0.427048 −0.0181599
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −2.07902 −0.0880908 −0.0440454 0.999030i \(-0.514025\pi\)
−0.0440454 + 0.999030i \(0.514025\pi\)
\(558\) 0 0
\(559\) 41.8264 1.76907
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 5.10676 0.215224 0.107612 0.994193i \(-0.465680\pi\)
0.107612 + 0.994193i \(0.465680\pi\)
\(564\) 0 0
\(565\) 17.3203 0.728670
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −6.00000 −0.251533 −0.125767 0.992060i \(-0.540139\pi\)
−0.125767 + 0.992060i \(0.540139\pi\)
\(570\) 0 0
\(571\) 10.0642 0.421176 0.210588 0.977575i \(-0.432462\pi\)
0.210588 + 0.977575i \(0.432462\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1.00000 −0.0417029
\(576\) 0 0
\(577\) −15.7274 −0.654740 −0.327370 0.944896i \(-0.606162\pi\)
−0.327370 + 0.944896i \(0.606162\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 1.34983 0.0560002
\(582\) 0 0
\(583\) −10.3420 −0.428323
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 18.7344 0.773250 0.386625 0.922237i \(-0.373641\pi\)
0.386625 + 0.922237i \(0.373641\pi\)
\(588\) 0 0
\(589\) −2.60586 −0.107373
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 3.21532 0.132037 0.0660187 0.997818i \(-0.478970\pi\)
0.0660187 + 0.997818i \(0.478970\pi\)
\(594\) 0 0
\(595\) −0.270809 −0.0111021
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −22.7639 −0.930108 −0.465054 0.885282i \(-0.653965\pi\)
−0.465054 + 0.885282i \(0.653965\pi\)
\(600\) 0 0
\(601\) 4.30552 0.175626 0.0878128 0.996137i \(-0.472012\pi\)
0.0878128 + 0.996137i \(0.472012\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 2.71442 0.110357
\(606\) 0 0
\(607\) 11.0868 0.450000 0.225000 0.974359i \(-0.427762\pi\)
0.225000 + 0.974359i \(0.427762\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 54.6701 2.21172
\(612\) 0 0
\(613\) 29.9409 1.20930 0.604651 0.796490i \(-0.293313\pi\)
0.604651 + 0.796490i \(0.293313\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −35.0130 −1.40957 −0.704785 0.709421i \(-0.748956\pi\)
−0.704785 + 0.709421i \(0.748956\pi\)
\(618\) 0 0
\(619\) 4.98523 0.200373 0.100187 0.994969i \(-0.468056\pi\)
0.100187 + 0.994969i \(0.468056\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0.0590800 0.00236699
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 12.4626 0.496916
\(630\) 0 0
\(631\) −3.64237 −0.145000 −0.0725002 0.997368i \(-0.523098\pi\)
−0.0725002 + 0.997368i \(0.523098\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1.75694 −0.0697219
\(636\) 0 0
\(637\) −36.5208 −1.44701
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −38.6997 −1.52854 −0.764272 0.644894i \(-0.776902\pi\)
−0.764272 + 0.644894i \(0.776902\pi\)
\(642\) 0 0
\(643\) −28.8637 −1.13827 −0.569137 0.822243i \(-0.692722\pi\)
−0.569137 + 0.822243i \(0.692722\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 19.8854 0.781777 0.390888 0.920438i \(-0.372168\pi\)
0.390888 + 0.920438i \(0.372168\pi\)
\(648\) 0 0
\(649\) −1.87151 −0.0734630
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 27.1988 1.06437 0.532185 0.846628i \(-0.321371\pi\)
0.532185 + 0.846628i \(0.321371\pi\)
\(654\) 0 0
\(655\) −20.2135 −0.789808
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 17.7274 0.690561 0.345281 0.938499i \(-0.387784\pi\)
0.345281 + 0.938499i \(0.387784\pi\)
\(660\) 0 0
\(661\) 40.7048 1.58323 0.791617 0.611018i \(-0.209240\pi\)
0.791617 + 0.611018i \(0.209240\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −0.149277 −0.00578871
\(666\) 0 0
\(667\) 9.34983 0.362027
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 21.1137 0.815086
\(672\) 0 0
\(673\) 12.2135 0.470797 0.235398 0.971899i \(-0.424361\pi\)
0.235398 + 0.971899i \(0.424361\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −16.5061 −0.634380 −0.317190 0.948362i \(-0.602739\pi\)
−0.317190 + 0.948362i \(0.602739\pi\)
\(678\) 0 0
\(679\) 0.0772219 0.00296350
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 29.1988 1.11726 0.558630 0.829417i \(-0.311327\pi\)
0.558630 + 0.829417i \(0.311327\pi\)
\(684\) 0 0
\(685\) −17.9279 −0.684992
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 18.7847 0.715639
\(690\) 0 0
\(691\) −15.9150 −0.605434 −0.302717 0.953080i \(-0.597894\pi\)
−0.302717 + 0.953080i \(0.597894\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 10.8637 0.412084
\(696\) 0 0
\(697\) −18.3351 −0.694490
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −34.5981 −1.30675 −0.653375 0.757034i \(-0.726648\pi\)
−0.653375 + 0.757034i \(0.726648\pi\)
\(702\) 0 0
\(703\) 6.86971 0.259096
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1.62243 −0.0610177
\(708\) 0 0
\(709\) 35.8212 1.34529 0.672646 0.739964i \(-0.265158\pi\)
0.672646 + 0.739964i \(0.265158\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 2.12153 0.0794520
\(714\) 0 0
\(715\) 15.0495 0.562819
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 32.5781 1.21496 0.607479 0.794335i \(-0.292181\pi\)
0.607479 + 0.794335i \(0.292181\pi\)
\(720\) 0 0
\(721\) −0.891443 −0.0331991
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −9.34983 −0.347244
\(726\) 0 0
\(727\) −31.9557 −1.18517 −0.592585 0.805508i \(-0.701893\pi\)
−0.592585 + 0.805508i \(0.701893\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 17.8264 0.659331
\(732\) 0 0
\(733\) −2.19359 −0.0810220 −0.0405110 0.999179i \(-0.512899\pi\)
−0.0405110 + 0.999179i \(0.512899\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −16.0990 −0.593013
\(738\) 0 0
\(739\) −51.7473 −1.90356 −0.951778 0.306787i \(-0.900746\pi\)
−0.951778 + 0.306787i \(0.900746\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 14.4436 0.529885 0.264942 0.964264i \(-0.414647\pi\)
0.264942 + 0.964264i \(0.414647\pi\)
\(744\) 0 0
\(745\) −15.7144 −0.575732
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −1.95052 −0.0712706
\(750\) 0 0
\(751\) 17.4288 0.635987 0.317994 0.948093i \(-0.396991\pi\)
0.317994 + 0.948093i \(0.396991\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 8.39234 0.305429
\(756\) 0 0
\(757\) −34.9331 −1.26967 −0.634833 0.772650i \(-0.718931\pi\)
−0.634833 + 0.772650i \(0.718931\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 23.2482 0.842748 0.421374 0.906887i \(-0.361548\pi\)
0.421374 + 0.906887i \(0.361548\pi\)
\(762\) 0 0
\(763\) 0.123327 0.00446473
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 3.39930 0.122742
\(768\) 0 0
\(769\) −48.6997 −1.75615 −0.878077 0.478519i \(-0.841174\pi\)
−0.878077 + 0.478519i \(0.841174\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 15.6128 0.561554 0.280777 0.959773i \(-0.409408\pi\)
0.280777 + 0.959773i \(0.409408\pi\)
\(774\) 0 0
\(775\) −2.12153 −0.0762077
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −10.1068 −0.362112
\(780\) 0 0
\(781\) −40.2560 −1.44047
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 19.5633 0.698246
\(786\) 0 0
\(787\) 24.2630 0.864883 0.432441 0.901662i \(-0.357652\pi\)
0.432441 + 0.901662i \(0.357652\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −2.10497 −0.0748440
\(792\) 0 0
\(793\) −38.3498 −1.36184
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −44.5911 −1.57950 −0.789749 0.613430i \(-0.789789\pi\)
−0.789749 + 0.613430i \(0.789789\pi\)
\(798\) 0 0
\(799\) 23.3003 0.824307
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −37.2552 −1.31471
\(804\) 0 0
\(805\) 0.121532 0.00428344
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 44.7144 1.57208 0.786038 0.618179i \(-0.212129\pi\)
0.786038 + 0.618179i \(0.212129\pi\)
\(810\) 0 0
\(811\) 1.19179 0.0418495 0.0209247 0.999781i \(-0.493339\pi\)
0.0209247 + 0.999781i \(0.493339\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −1.01477 −0.0355458
\(816\) 0 0
\(817\) 9.82635 0.343780
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −10.0000 −0.349002 −0.174501 0.984657i \(-0.555831\pi\)
−0.174501 + 0.984657i \(0.555831\pi\)
\(822\) 0 0
\(823\) 26.7551 0.932626 0.466313 0.884620i \(-0.345582\pi\)
0.466313 + 0.884620i \(0.345582\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 27.2907 0.948992 0.474496 0.880258i \(-0.342630\pi\)
0.474496 + 0.880258i \(0.342630\pi\)
\(828\) 0 0
\(829\) 34.2925 1.19103 0.595515 0.803344i \(-0.296948\pi\)
0.595515 + 0.803344i \(0.296948\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −15.5651 −0.539300
\(834\) 0 0
\(835\) −8.00000 −0.276851
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 40.6701 1.40409 0.702044 0.712133i \(-0.252271\pi\)
0.702044 + 0.712133i \(0.252271\pi\)
\(840\) 0 0
\(841\) 58.4192 2.01446
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −14.3351 −0.493141
\(846\) 0 0
\(847\) −0.329889 −0.0113351
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −5.59289 −0.191722
\(852\) 0 0
\(853\) −34.6276 −1.18563 −0.592813 0.805340i \(-0.701983\pi\)
−0.592813 + 0.805340i \(0.701983\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −26.4861 −0.904749 −0.452374 0.891828i \(-0.649423\pi\)
−0.452374 + 0.891828i \(0.649423\pi\)
\(858\) 0 0
\(859\) 40.9627 1.39763 0.698814 0.715304i \(-0.253712\pi\)
0.698814 + 0.715304i \(0.253712\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 18.5712 0.632170 0.316085 0.948731i \(-0.397632\pi\)
0.316085 + 0.948731i \(0.397632\pi\)
\(864\) 0 0
\(865\) −2.63540 −0.0896064
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 10.1146 0.343113
\(870\) 0 0
\(871\) 29.2413 0.990803
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −0.121532 −0.00410853
\(876\) 0 0
\(877\) −28.4913 −0.962083 −0.481041 0.876698i \(-0.659741\pi\)
−0.481041 + 0.876698i \(0.659741\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 4.91318 0.165529 0.0827645 0.996569i \(-0.473625\pi\)
0.0827645 + 0.996569i \(0.473625\pi\)
\(882\) 0 0
\(883\) 30.1710 1.01534 0.507668 0.861553i \(-0.330508\pi\)
0.507668 + 0.861553i \(0.330508\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −25.7865 −0.865825 −0.432913 0.901436i \(-0.642514\pi\)
−0.432913 + 0.901436i \(0.642514\pi\)
\(888\) 0 0
\(889\) 0.213524 0.00716136
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 12.8438 0.429800
\(894\) 0 0
\(895\) −14.4566 −0.483230
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 19.8360 0.661566
\(900\) 0 0
\(901\) 8.00601 0.266719
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −10.7422 −0.357082
\(906\) 0 0
\(907\) −44.3776 −1.47353 −0.736767 0.676147i \(-0.763648\pi\)
−0.736767 + 0.676147i \(0.763648\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −47.7968 −1.58358 −0.791789 0.610794i \(-0.790850\pi\)
−0.791789 + 0.610794i \(0.790850\pi\)
\(912\) 0 0
\(913\) −31.9705 −1.05807
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 2.45659 0.0811237
\(918\) 0 0
\(919\) 8.00000 0.263896 0.131948 0.991257i \(-0.457877\pi\)
0.131948 + 0.991257i \(0.457877\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 73.1189 2.40674
\(924\) 0 0
\(925\) 5.59289 0.183893
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −24.0199 −0.788069 −0.394034 0.919096i \(-0.628921\pi\)
−0.394034 + 0.919096i \(0.628921\pi\)
\(930\) 0 0
\(931\) −8.57991 −0.281195
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 6.41407 0.209763
\(936\) 0 0
\(937\) 0.384533 0.0125621 0.00628107 0.999980i \(-0.498001\pi\)
0.00628107 + 0.999980i \(0.498001\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −25.0920 −0.817976 −0.408988 0.912540i \(-0.634118\pi\)
−0.408988 + 0.912540i \(0.634118\pi\)
\(942\) 0 0
\(943\) 8.22829 0.267950
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −44.7126 −1.45297 −0.726483 0.687185i \(-0.758846\pi\)
−0.726483 + 0.687185i \(0.758846\pi\)
\(948\) 0 0
\(949\) 67.6683 2.19661
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 21.2500 0.688356 0.344178 0.938904i \(-0.388158\pi\)
0.344178 + 0.938904i \(0.388158\pi\)
\(954\) 0 0
\(955\) −22.6701 −0.733588
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 2.17882 0.0703577
\(960\) 0 0
\(961\) −26.4991 −0.854810
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −2.24306 −0.0722068
\(966\) 0 0
\(967\) −41.0417 −1.31981 −0.659906 0.751349i \(-0.729404\pi\)
−0.659906 + 0.751349i \(0.729404\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −35.2760 −1.13206 −0.566030 0.824385i \(-0.691521\pi\)
−0.566030 + 0.824385i \(0.691521\pi\)
\(972\) 0 0
\(973\) −1.32029 −0.0423264
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 6.79164 0.217284 0.108642 0.994081i \(-0.465350\pi\)
0.108642 + 0.994081i \(0.465350\pi\)
\(978\) 0 0
\(979\) −1.39930 −0.0447219
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −19.5981 −0.625081 −0.312540 0.949904i \(-0.601180\pi\)
−0.312540 + 0.949904i \(0.601180\pi\)
\(984\) 0 0
\(985\) −7.57812 −0.241459
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −8.00000 −0.254385
\(990\) 0 0
\(991\) −37.2995 −1.18486 −0.592429 0.805623i \(-0.701831\pi\)
−0.592429 + 0.805623i \(0.701831\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 14.0000 0.443830
\(996\) 0 0
\(997\) −19.7274 −0.624773 −0.312386 0.949955i \(-0.601128\pi\)
−0.312386 + 0.949955i \(0.601128\pi\)
\(998\) 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.bj.1.2 3
3.2 odd 2 920.2.a.h.1.2 3
12.11 even 2 1840.2.a.s.1.2 3
15.2 even 4 4600.2.e.p.4049.3 6
15.8 even 4 4600.2.e.p.4049.4 6
15.14 odd 2 4600.2.a.x.1.2 3
24.5 odd 2 7360.2.a.by.1.2 3
24.11 even 2 7360.2.a.cc.1.2 3
60.59 even 2 9200.2.a.ce.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
920.2.a.h.1.2 3 3.2 odd 2
1840.2.a.s.1.2 3 12.11 even 2
4600.2.a.x.1.2 3 15.14 odd 2
4600.2.e.p.4049.3 6 15.2 even 4
4600.2.e.p.4049.4 6 15.8 even 4
7360.2.a.by.1.2 3 24.5 odd 2
7360.2.a.cc.1.2 3 24.11 even 2
8280.2.a.bj.1.2 3 1.1 even 1 trivial
9200.2.a.ce.1.2 3 60.59 even 2