Properties

Label 6048.2.j.c.5615.20
Level 6048
Weight 2
Character 6048.5615
Analytic conductor 48.294
Analytic rank 0
Dimension 32
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6048.j (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(48.2935231425\)
Analytic rank: \(0\)
Dimension: \(32\)
Coefficient ring index: multiple of None
Twist minimal: no (minimal twist has level 1512)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 5615.20
Character \(\chi\) = 6048.5615
Dual form 6048.2.j.c.5615.19

$q$-expansion

\(f(q)\) \(=\) \(q+0.206991 q^{5} +1.00000i q^{7} +O(q^{10})\) \(q+0.206991 q^{5} +1.00000i q^{7} -6.42190i q^{11} -3.52336i q^{13} +3.90616i q^{17} +5.48691 q^{19} +0.880512 q^{23} -4.95715 q^{25} -3.20814 q^{29} +0.0631261i q^{31} +0.206991i q^{35} -9.91837i q^{37} -5.94221i q^{41} +1.13960 q^{43} -6.81266 q^{47} -1.00000 q^{49} -12.6324 q^{53} -1.32928i q^{55} +4.23338i q^{59} +12.3006i q^{61} -0.729305i q^{65} +5.74666 q^{67} +10.1795 q^{71} +8.27618 q^{73} +6.42190 q^{77} -4.86426i q^{79} -7.51539i q^{83} +0.808542i q^{85} +4.44682i q^{89} +3.52336 q^{91} +1.13574 q^{95} -17.3929 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + O(q^{10}) \) \( 32q + 64q^{19} - 16q^{25} + 48q^{43} - 32q^{49} - 16q^{67} - 16q^{73} - 16q^{91} + 64q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).

\(n\) \(2593\) \(3781\) \(3809\) \(4159\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(-1\)

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
\(5\) 0.206991 0.0925694 0.0462847 0.998928i \(-0.485262\pi\)
0.0462847 + 0.998928i \(0.485262\pi\)
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) − 6.42190i − 1.93628i −0.250418 0.968138i \(-0.580568\pi\)
0.250418 0.968138i \(-0.419432\pi\)
\(12\) 0 0
\(13\) − 3.52336i − 0.977204i −0.872507 0.488602i \(-0.837507\pi\)
0.872507 0.488602i \(-0.162493\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.90616i 0.947383i 0.880691 + 0.473692i \(0.157079\pi\)
−0.880691 + 0.473692i \(0.842921\pi\)
\(18\) 0 0
\(19\) 5.48691 1.25878 0.629392 0.777088i \(-0.283304\pi\)
0.629392 + 0.777088i \(0.283304\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.880512 0.183599 0.0917997 0.995777i \(-0.470738\pi\)
0.0917997 + 0.995777i \(0.470738\pi\)
\(24\) 0 0
\(25\) −4.95715 −0.991431
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −3.20814 −0.595737 −0.297868 0.954607i \(-0.596276\pi\)
−0.297868 + 0.954607i \(0.596276\pi\)
\(30\) 0 0
\(31\) 0.0631261i 0.0113378i 0.999984 + 0.00566890i \(0.00180448\pi\)
−0.999984 + 0.00566890i \(0.998196\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0.206991i 0.0349879i
\(36\) 0 0
\(37\) − 9.91837i − 1.63057i −0.579060 0.815285i \(-0.696580\pi\)
0.579060 0.815285i \(-0.303420\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) − 5.94221i − 0.928017i −0.885831 0.464009i \(-0.846411\pi\)
0.885831 0.464009i \(-0.153589\pi\)
\(42\) 0 0
\(43\) 1.13960 0.173788 0.0868938 0.996218i \(-0.472306\pi\)
0.0868938 + 0.996218i \(0.472306\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −6.81266 −0.993729 −0.496864 0.867828i \(-0.665515\pi\)
−0.496864 + 0.867828i \(0.665515\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −12.6324 −1.73520 −0.867598 0.497265i \(-0.834338\pi\)
−0.867598 + 0.497265i \(0.834338\pi\)
\(54\) 0 0
\(55\) − 1.32928i − 0.179240i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 4.23338i 0.551139i 0.961281 + 0.275570i \(0.0888664\pi\)
−0.961281 + 0.275570i \(0.911134\pi\)
\(60\) 0 0
\(61\) 12.3006i 1.57493i 0.616359 + 0.787465i \(0.288607\pi\)
−0.616359 + 0.787465i \(0.711393\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) − 0.729305i − 0.0904591i
\(66\) 0 0
\(67\) 5.74666 0.702067 0.351033 0.936363i \(-0.385830\pi\)
0.351033 + 0.936363i \(0.385830\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 10.1795 1.20809 0.604043 0.796952i \(-0.293556\pi\)
0.604043 + 0.796952i \(0.293556\pi\)
\(72\) 0 0
\(73\) 8.27618 0.968653 0.484327 0.874887i \(-0.339065\pi\)
0.484327 + 0.874887i \(0.339065\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 6.42190 0.731843
\(78\) 0 0
\(79\) − 4.86426i − 0.547272i −0.961833 0.273636i \(-0.911774\pi\)
0.961833 0.273636i \(-0.0882264\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) − 7.51539i − 0.824921i −0.910976 0.412460i \(-0.864669\pi\)
0.910976 0.412460i \(-0.135331\pi\)
\(84\) 0 0
\(85\) 0.808542i 0.0876987i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 4.44682i 0.471362i 0.971830 + 0.235681i \(0.0757320\pi\)
−0.971830 + 0.235681i \(0.924268\pi\)
\(90\) 0 0
\(91\) 3.52336 0.369348
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1.13574 0.116525
\(96\) 0 0
\(97\) −17.3929 −1.76599 −0.882993 0.469387i \(-0.844475\pi\)
−0.882993 + 0.469387i \(0.844475\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −19.0273 −1.89329 −0.946643 0.322284i \(-0.895550\pi\)
−0.946643 + 0.322284i \(0.895550\pi\)
\(102\) 0 0
\(103\) 10.7903i 1.06320i 0.846995 + 0.531601i \(0.178409\pi\)
−0.846995 + 0.531601i \(0.821591\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) − 4.97087i − 0.480553i −0.970705 0.240276i \(-0.922762\pi\)
0.970705 0.240276i \(-0.0772380\pi\)
\(108\) 0 0
\(109\) − 2.84810i − 0.272798i −0.990654 0.136399i \(-0.956447\pi\)
0.990654 0.136399i \(-0.0435530\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) − 2.88561i − 0.271455i −0.990746 0.135728i \(-0.956663\pi\)
0.990746 0.135728i \(-0.0433372\pi\)
\(114\) 0 0
\(115\) 0.182258 0.0169957
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −3.90616 −0.358077
\(120\) 0 0
\(121\) −30.2408 −2.74916
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −2.06105 −0.184345
\(126\) 0 0
\(127\) − 7.23082i − 0.641631i −0.947142 0.320816i \(-0.896043\pi\)
0.947142 0.320816i \(-0.103957\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) − 12.8026i − 1.11857i −0.828975 0.559286i \(-0.811076\pi\)
0.828975 0.559286i \(-0.188924\pi\)
\(132\) 0 0
\(133\) 5.48691i 0.475776i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0.363873i 0.0310878i 0.999879 + 0.0155439i \(0.00494798\pi\)
−0.999879 + 0.0155439i \(0.995052\pi\)
\(138\) 0 0
\(139\) 9.32338 0.790799 0.395399 0.918509i \(-0.370606\pi\)
0.395399 + 0.918509i \(0.370606\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −22.6266 −1.89214
\(144\) 0 0
\(145\) −0.664057 −0.0551470
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −4.82519 −0.395295 −0.197648 0.980273i \(-0.563330\pi\)
−0.197648 + 0.980273i \(0.563330\pi\)
\(150\) 0 0
\(151\) 12.7969i 1.04140i 0.853740 + 0.520700i \(0.174329\pi\)
−0.853740 + 0.520700i \(0.825671\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0.0130666i 0.00104953i
\(156\) 0 0
\(157\) 15.5455i 1.24067i 0.784337 + 0.620335i \(0.213003\pi\)
−0.784337 + 0.620335i \(0.786997\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0.880512i 0.0693940i
\(162\) 0 0
\(163\) −18.4630 −1.44613 −0.723067 0.690778i \(-0.757268\pi\)
−0.723067 + 0.690778i \(0.757268\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −12.5320 −0.969754 −0.484877 0.874582i \(-0.661136\pi\)
−0.484877 + 0.874582i \(0.661136\pi\)
\(168\) 0 0
\(169\) 0.585951 0.0450731
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 5.49171 0.417527 0.208763 0.977966i \(-0.433056\pi\)
0.208763 + 0.977966i \(0.433056\pi\)
\(174\) 0 0
\(175\) − 4.95715i − 0.374726i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) − 14.5830i − 1.08998i −0.838441 0.544992i \(-0.816533\pi\)
0.838441 0.544992i \(-0.183467\pi\)
\(180\) 0 0
\(181\) 17.2753i 1.28407i 0.766677 + 0.642033i \(0.221909\pi\)
−0.766677 + 0.642033i \(0.778091\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) − 2.05302i − 0.150941i
\(186\) 0 0
\(187\) 25.0850 1.83440
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 7.29828 0.528085 0.264042 0.964511i \(-0.414944\pi\)
0.264042 + 0.964511i \(0.414944\pi\)
\(192\) 0 0
\(193\) 12.1106 0.871742 0.435871 0.900009i \(-0.356440\pi\)
0.435871 + 0.900009i \(0.356440\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −17.3925 −1.23917 −0.619584 0.784931i \(-0.712699\pi\)
−0.619584 + 0.784931i \(0.712699\pi\)
\(198\) 0 0
\(199\) 3.07583i 0.218040i 0.994040 + 0.109020i \(0.0347712\pi\)
−0.994040 + 0.109020i \(0.965229\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) − 3.20814i − 0.225167i
\(204\) 0 0
\(205\) − 1.22999i − 0.0859060i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) − 35.2364i − 2.43735i
\(210\) 0 0
\(211\) −9.57154 −0.658932 −0.329466 0.944167i \(-0.606869\pi\)
−0.329466 + 0.944167i \(0.606869\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0.235888 0.0160874
\(216\) 0 0
\(217\) −0.0631261 −0.00428528
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 13.7628 0.925786
\(222\) 0 0
\(223\) − 26.5694i − 1.77922i −0.456722 0.889610i \(-0.650976\pi\)
0.456722 0.889610i \(-0.349024\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) − 20.7345i − 1.37620i −0.725616 0.688100i \(-0.758445\pi\)
0.725616 0.688100i \(-0.241555\pi\)
\(228\) 0 0
\(229\) − 19.2625i − 1.27290i −0.771316 0.636452i \(-0.780401\pi\)
0.771316 0.636452i \(-0.219599\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) − 25.0038i − 1.63805i −0.573756 0.819027i \(-0.694514\pi\)
0.573756 0.819027i \(-0.305486\pi\)
\(234\) 0 0
\(235\) −1.41016 −0.0919889
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −15.0439 −0.973107 −0.486553 0.873651i \(-0.661746\pi\)
−0.486553 + 0.873651i \(0.661746\pi\)
\(240\) 0 0
\(241\) −3.23274 −0.208239 −0.104120 0.994565i \(-0.533203\pi\)
−0.104120 + 0.994565i \(0.533203\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −0.206991 −0.0132242
\(246\) 0 0
\(247\) − 19.3324i − 1.23009i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) − 10.4258i − 0.658071i −0.944318 0.329036i \(-0.893276\pi\)
0.944318 0.329036i \(-0.106724\pi\)
\(252\) 0 0
\(253\) − 5.65456i − 0.355499i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) − 8.12452i − 0.506794i −0.967362 0.253397i \(-0.918452\pi\)
0.967362 0.253397i \(-0.0815479\pi\)
\(258\) 0 0
\(259\) 9.91837 0.616297
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −14.7639 −0.910382 −0.455191 0.890394i \(-0.650429\pi\)
−0.455191 + 0.890394i \(0.650429\pi\)
\(264\) 0 0
\(265\) −2.61480 −0.160626
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 26.8961 1.63989 0.819943 0.572445i \(-0.194005\pi\)
0.819943 + 0.572445i \(0.194005\pi\)
\(270\) 0 0
\(271\) 17.5914i 1.06860i 0.845295 + 0.534301i \(0.179425\pi\)
−0.845295 + 0.534301i \(0.820575\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 31.8343i 1.91968i
\(276\) 0 0
\(277\) − 24.8383i − 1.49239i −0.665729 0.746194i \(-0.731879\pi\)
0.665729 0.746194i \(-0.268121\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) − 4.13370i − 0.246596i −0.992370 0.123298i \(-0.960653\pi\)
0.992370 0.123298i \(-0.0393471\pi\)
\(282\) 0 0
\(283\) 23.9297 1.42247 0.711236 0.702954i \(-0.248136\pi\)
0.711236 + 0.702954i \(0.248136\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 5.94221 0.350758
\(288\) 0 0
\(289\) 1.74190 0.102465
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −12.0225 −0.702360 −0.351180 0.936308i \(-0.614219\pi\)
−0.351180 + 0.936308i \(0.614219\pi\)
\(294\) 0 0
\(295\) 0.876273i 0.0510186i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) − 3.10236i − 0.179414i
\(300\) 0 0
\(301\) 1.13960i 0.0656855i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 2.54612i 0.145790i
\(306\) 0 0
\(307\) 5.82060 0.332199 0.166100 0.986109i \(-0.446883\pi\)
0.166100 + 0.986109i \(0.446883\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −12.7884 −0.725161 −0.362580 0.931952i \(-0.618104\pi\)
−0.362580 + 0.931952i \(0.618104\pi\)
\(312\) 0 0
\(313\) 1.74881 0.0988483 0.0494242 0.998778i \(-0.484261\pi\)
0.0494242 + 0.998778i \(0.484261\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −30.5938 −1.71832 −0.859159 0.511709i \(-0.829013\pi\)
−0.859159 + 0.511709i \(0.829013\pi\)
\(318\) 0 0
\(319\) 20.6024i 1.15351i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 21.4328i 1.19255i
\(324\) 0 0
\(325\) 17.4658i 0.968830i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) − 6.81266i − 0.375594i
\(330\) 0 0
\(331\) 20.7269 1.13925 0.569627 0.821904i \(-0.307088\pi\)
0.569627 + 0.821904i \(0.307088\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1.18951 0.0649899
\(336\) 0 0
\(337\) 19.9716 1.08792 0.543961 0.839110i \(-0.316924\pi\)
0.543961 + 0.839110i \(0.316924\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0.405390 0.0219531
\(342\) 0 0
\(343\) − 1.00000i − 0.0539949i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 10.6443i 0.571414i 0.958317 + 0.285707i \(0.0922284\pi\)
−0.958317 + 0.285707i \(0.907772\pi\)
\(348\) 0 0
\(349\) − 21.1575i − 1.13254i −0.824221 0.566268i \(-0.808387\pi\)
0.824221 0.566268i \(-0.191613\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) − 7.85498i − 0.418079i −0.977907 0.209039i \(-0.932966\pi\)
0.977907 0.209039i \(-0.0670337\pi\)
\(354\) 0 0
\(355\) 2.10707 0.111832
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 22.0102 1.16165 0.580826 0.814028i \(-0.302730\pi\)
0.580826 + 0.814028i \(0.302730\pi\)
\(360\) 0 0
\(361\) 11.1062 0.584537
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1.71310 0.0896676
\(366\) 0 0
\(367\) − 5.61196i − 0.292942i −0.989215 0.146471i \(-0.953209\pi\)
0.989215 0.146471i \(-0.0467915\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) − 12.6324i − 0.655843i
\(372\) 0 0
\(373\) − 21.5334i − 1.11496i −0.830192 0.557478i \(-0.811769\pi\)
0.830192 0.557478i \(-0.188231\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 11.3034i 0.582156i
\(378\) 0 0
\(379\) −36.2973 −1.86447 −0.932233 0.361858i \(-0.882143\pi\)
−0.932233 + 0.361858i \(0.882143\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 12.4362 0.635462 0.317731 0.948181i \(-0.397079\pi\)
0.317731 + 0.948181i \(0.397079\pi\)
\(384\) 0 0
\(385\) 1.32928 0.0677463
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −5.47648 −0.277669 −0.138834 0.990316i \(-0.544336\pi\)
−0.138834 + 0.990316i \(0.544336\pi\)
\(390\) 0 0
\(391\) 3.43942i 0.173939i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) − 1.00686i − 0.0506606i
\(396\) 0 0
\(397\) − 9.58947i − 0.481282i −0.970614 0.240641i \(-0.922642\pi\)
0.970614 0.240641i \(-0.0773576\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) − 1.76702i − 0.0882408i −0.999026 0.0441204i \(-0.985951\pi\)
0.999026 0.0441204i \(-0.0140485\pi\)
\(402\) 0 0
\(403\) 0.222416 0.0110793
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −63.6948 −3.15723
\(408\) 0 0
\(409\) −5.87490 −0.290495 −0.145248 0.989395i \(-0.546398\pi\)
−0.145248 + 0.989395i \(0.546398\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −4.23338 −0.208311
\(414\) 0 0
\(415\) − 1.55562i − 0.0763624i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 18.9459i 0.925567i 0.886471 + 0.462783i \(0.153149\pi\)
−0.886471 + 0.462783i \(0.846851\pi\)
\(420\) 0 0
\(421\) 25.2598i 1.23109i 0.788103 + 0.615544i \(0.211064\pi\)
−0.788103 + 0.615544i \(0.788936\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) − 19.3634i − 0.939265i
\(426\) 0 0
\(427\) −12.3006 −0.595268
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −37.5774 −1.81004 −0.905020 0.425369i \(-0.860144\pi\)
−0.905020 + 0.425369i \(0.860144\pi\)
\(432\) 0 0
\(433\) 21.1040 1.01419 0.507097 0.861889i \(-0.330719\pi\)
0.507097 + 0.861889i \(0.330719\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 4.83129 0.231112
\(438\) 0 0
\(439\) 2.88405i 0.137648i 0.997629 + 0.0688240i \(0.0219247\pi\)
−0.997629 + 0.0688240i \(0.978075\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) − 34.5978i − 1.64379i −0.569640 0.821895i \(-0.692917\pi\)
0.569640 0.821895i \(-0.307083\pi\)
\(444\) 0 0
\(445\) 0.920453i 0.0436337i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 14.8661i 0.701575i 0.936455 + 0.350787i \(0.114086\pi\)
−0.936455 + 0.350787i \(0.885914\pi\)
\(450\) 0 0
\(451\) −38.1603 −1.79690
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0.729305 0.0341903
\(456\) 0 0
\(457\) 11.0037 0.514730 0.257365 0.966314i \(-0.417146\pi\)
0.257365 + 0.966314i \(0.417146\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −32.9687 −1.53551 −0.767753 0.640746i \(-0.778625\pi\)
−0.767753 + 0.640746i \(0.778625\pi\)
\(462\) 0 0
\(463\) − 12.3348i − 0.573245i −0.958044 0.286622i \(-0.907468\pi\)
0.958044 0.286622i \(-0.0925325\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) − 33.5264i − 1.55142i −0.631091 0.775709i \(-0.717393\pi\)
0.631091 0.775709i \(-0.282607\pi\)
\(468\) 0 0
\(469\) 5.74666i 0.265356i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) − 7.31840i − 0.336501i
\(474\) 0 0
\(475\) −27.1995 −1.24800
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −9.65791 −0.441281 −0.220641 0.975355i \(-0.570815\pi\)
−0.220641 + 0.975355i \(0.570815\pi\)
\(480\) 0 0
\(481\) −34.9460 −1.59340
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −3.60019 −0.163476
\(486\) 0 0
\(487\) 25.1008i 1.13742i 0.822537 + 0.568712i \(0.192558\pi\)
−0.822537 + 0.568712i \(0.807442\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 10.5524i 0.476224i 0.971238 + 0.238112i \(0.0765285\pi\)
−0.971238 + 0.238112i \(0.923471\pi\)
\(492\) 0 0
\(493\) − 12.5315i − 0.564391i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 10.1795i 0.456613i
\(498\) 0 0
\(499\) 11.6619 0.522059 0.261029 0.965331i \(-0.415938\pi\)
0.261029 + 0.965331i \(0.415938\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 29.0202 1.29394 0.646972 0.762513i \(-0.276035\pi\)
0.646972 + 0.762513i \(0.276035\pi\)
\(504\) 0 0
\(505\) −3.93849 −0.175260
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 22.0894 0.979096 0.489548 0.871976i \(-0.337162\pi\)
0.489548 + 0.871976i \(0.337162\pi\)
\(510\) 0 0
\(511\) 8.27618i 0.366116i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 2.23350i 0.0984199i
\(516\) 0 0
\(517\) 43.7502i 1.92413i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 14.5460i 0.637273i 0.947877 + 0.318636i \(0.103225\pi\)
−0.947877 + 0.318636i \(0.896775\pi\)
\(522\) 0 0
\(523\) −31.6350 −1.38330 −0.691651 0.722232i \(-0.743116\pi\)
−0.691651 + 0.722232i \(0.743116\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −0.246581 −0.0107412
\(528\) 0 0
\(529\) −22.2247 −0.966291
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −20.9365 −0.906862
\(534\) 0 0
\(535\) − 1.02893i − 0.0444844i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 6.42190i 0.276611i
\(540\) 0 0
\(541\) 22.7160i 0.976639i 0.872665 + 0.488319i \(0.162390\pi\)
−0.872665 + 0.488319i \(0.837610\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) − 0.589532i − 0.0252528i
\(546\) 0 0
\(547\) 22.2601 0.951774 0.475887 0.879506i \(-0.342127\pi\)
0.475887 + 0.879506i \(0.342127\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −17.6028 −0.749904
\(552\) 0 0
\(553\) 4.86426 0.206849
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −2.99670 −0.126974 −0.0634872 0.997983i \(-0.520222\pi\)
−0.0634872 + 0.997983i \(0.520222\pi\)
\(558\) 0 0
\(559\) − 4.01522i − 0.169826i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) − 13.4913i − 0.568589i −0.958737 0.284295i \(-0.908241\pi\)
0.958737 0.284295i \(-0.0917594\pi\)
\(564\) 0 0
\(565\) − 0.597296i − 0.0251284i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) − 40.7445i − 1.70810i −0.520191 0.854050i \(-0.674139\pi\)
0.520191 0.854050i \(-0.325861\pi\)
\(570\) 0 0
\(571\) −18.0110 −0.753739 −0.376869 0.926266i \(-0.622999\pi\)
−0.376869 + 0.926266i \(0.622999\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −4.36483 −0.182026
\(576\) 0 0
\(577\) 29.3495 1.22184 0.610919 0.791693i \(-0.290800\pi\)
0.610919 + 0.791693i \(0.290800\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 7.51539 0.311791
\(582\) 0 0
\(583\) 81.1242i 3.35982i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) − 11.1732i − 0.461168i −0.973052 0.230584i \(-0.925936\pi\)
0.973052 0.230584i \(-0.0740637\pi\)
\(588\) 0 0
\(589\) 0.346368i 0.0142718i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) − 29.9792i − 1.23110i −0.788099 0.615549i \(-0.788934\pi\)
0.788099 0.615549i \(-0.211066\pi\)
\(594\) 0 0
\(595\) −0.808542 −0.0331470
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −6.38388 −0.260838 −0.130419 0.991459i \(-0.541632\pi\)
−0.130419 + 0.991459i \(0.541632\pi\)
\(600\) 0 0
\(601\) −23.5445 −0.960402 −0.480201 0.877159i \(-0.659436\pi\)
−0.480201 + 0.877159i \(0.659436\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −6.25958 −0.254488
\(606\) 0 0
\(607\) − 33.9599i − 1.37839i −0.724577 0.689194i \(-0.757965\pi\)
0.724577 0.689194i \(-0.242035\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 24.0034i 0.971076i
\(612\) 0 0
\(613\) − 20.6042i − 0.832197i −0.909320 0.416098i \(-0.863397\pi\)
0.909320 0.416098i \(-0.136603\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 37.4489i 1.50764i 0.657083 + 0.753818i \(0.271790\pi\)
−0.657083 + 0.753818i \(0.728210\pi\)
\(618\) 0 0
\(619\) −14.2766 −0.573825 −0.286913 0.957957i \(-0.592629\pi\)
−0.286913 + 0.957957i \(0.592629\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −4.44682 −0.178158
\(624\) 0 0
\(625\) 24.3592 0.974366
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 38.7427 1.54477
\(630\) 0 0
\(631\) − 7.00448i − 0.278844i −0.990233 0.139422i \(-0.955476\pi\)
0.990233 0.139422i \(-0.0445244\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) − 1.49672i − 0.0593954i
\(636\) 0 0
\(637\) 3.52336i 0.139601i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 9.23092i 0.364599i 0.983243 + 0.182300i \(0.0583541\pi\)
−0.983243 + 0.182300i \(0.941646\pi\)
\(642\) 0 0
\(643\) −1.48603 −0.0586031 −0.0293016 0.999571i \(-0.509328\pi\)
−0.0293016 + 0.999571i \(0.509328\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 16.2654 0.639457 0.319729 0.947509i \(-0.396408\pi\)
0.319729 + 0.947509i \(0.396408\pi\)
\(648\) 0 0
\(649\) 27.1863 1.06716
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −6.92310 −0.270922 −0.135461 0.990783i \(-0.543252\pi\)
−0.135461 + 0.990783i \(0.543252\pi\)
\(654\) 0 0
\(655\) − 2.65003i − 0.103545i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 11.3057i 0.440407i 0.975454 + 0.220203i \(0.0706721\pi\)
−0.975454 + 0.220203i \(0.929328\pi\)
\(660\) 0 0
\(661\) 18.9877i 0.738536i 0.929323 + 0.369268i \(0.120392\pi\)
−0.929323 + 0.369268i \(0.879608\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1.13574i 0.0440422i
\(666\) 0 0
\(667\) −2.82481 −0.109377
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 78.9932 3.04950
\(672\) 0 0
\(673\) 17.6164 0.679061 0.339531 0.940595i \(-0.389732\pi\)
0.339531 + 0.940595i \(0.389732\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 7.42579 0.285396 0.142698 0.989766i \(-0.454422\pi\)
0.142698 + 0.989766i \(0.454422\pi\)
\(678\) 0 0
\(679\) − 17.3929i − 0.667480i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 22.8832i 0.875600i 0.899072 + 0.437800i \(0.144242\pi\)
−0.899072 + 0.437800i \(0.855758\pi\)
\(684\) 0 0
\(685\) 0.0753186i 0.00287778i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 44.5086i 1.69564i
\(690\) 0 0
\(691\) −33.6439 −1.27987 −0.639936 0.768428i \(-0.721039\pi\)
−0.639936 + 0.768428i \(0.721039\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.92986 0.0732038
\(696\) 0 0
\(697\) 23.2112 0.879188
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −35.4474 −1.33883 −0.669414 0.742890i \(-0.733455\pi\)
−0.669414 + 0.742890i \(0.733455\pi\)
\(702\) 0 0
\(703\) − 54.4212i − 2.05253i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) − 19.0273i − 0.715595i
\(708\) 0 0
\(709\) 8.71118i 0.327155i 0.986530 + 0.163578i \(0.0523034\pi\)
−0.986530 + 0.163578i \(0.947697\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0.0555833i 0.00208161i
\(714\) 0 0
\(715\) −4.68352 −0.175154
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −0.821108 −0.0306222 −0.0153111 0.999883i \(-0.504874\pi\)
−0.0153111 + 0.999883i \(0.504874\pi\)
\(720\) 0 0
\(721\) −10.7903 −0.401853
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 15.9032 0.590632
\(726\) 0 0
\(727\) − 28.0509i − 1.04035i −0.854059 0.520176i \(-0.825866\pi\)
0.854059 0.520176i \(-0.174134\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 4.45147i 0.164643i
\(732\) 0 0
\(733\) − 21.9677i − 0.811395i −0.914007 0.405697i \(-0.867029\pi\)
0.914007 0.405697i \(-0.132971\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) − 36.9045i − 1.35939i
\(738\) 0 0
\(739\) 18.6044 0.684374 0.342187 0.939632i \(-0.388832\pi\)
0.342187 + 0.939632i \(0.388832\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 29.0849 1.06702 0.533512 0.845793i \(-0.320872\pi\)
0.533512 + 0.845793i \(0.320872\pi\)
\(744\) 0 0
\(745\) −0.998774 −0.0365922
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 4.97087 0.181632
\(750\) 0 0
\(751\) 14.4693i 0.527991i 0.964524 + 0.263995i \(0.0850403\pi\)
−0.964524 + 0.263995i \(0.914960\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 2.64886i 0.0964018i
\(756\) 0 0
\(757\) − 13.6988i − 0.497891i −0.968517 0.248946i \(-0.919916\pi\)
0.968517 0.248946i \(-0.0800840\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 46.5579i 1.68772i 0.536562 + 0.843861i \(0.319723\pi\)
−0.536562 + 0.843861i \(0.680277\pi\)
\(762\) 0 0
\(763\) 2.84810 0.103108
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 14.9157 0.538575
\(768\) 0 0
\(769\) 50.6427 1.82622 0.913111 0.407711i \(-0.133673\pi\)
0.913111 + 0.407711i \(0.133673\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 6.66928 0.239877 0.119939 0.992781i \(-0.461730\pi\)
0.119939 + 0.992781i \(0.461730\pi\)
\(774\) 0 0
\(775\) − 0.312926i − 0.0112406i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) − 32.6044i − 1.16817i
\(780\) 0 0
\(781\) − 65.3718i − 2.33919i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 3.21779i 0.114848i
\(786\) 0 0
\(787\) 0.759732 0.0270815 0.0135408 0.999908i \(-0.495690\pi\)
0.0135408 + 0.999908i \(0.495690\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 2.88561 0.102600
\(792\) 0 0
\(793\) 43.3394 1.53903
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 26.1758 0.927194 0.463597 0.886046i \(-0.346559\pi\)
0.463597 + 0.886046i \(0.346559\pi\)
\(798\) 0 0
\(799\) − 26.6114i − 0.941442i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) − 53.1488i − 1.87558i
\(804\) 0 0
\(805\) 0.182258i 0.00642376i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 14.6876i 0.516388i 0.966093 + 0.258194i \(0.0831273\pi\)
−0.966093 + 0.258194i \(0.916873\pi\)
\(810\) 0 0
\(811\) 4.13912 0.145344 0.0726721 0.997356i \(-0.476847\pi\)
0.0726721 + 0.997356i \(0.476847\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −3.82168 −0.133868
\(816\) 0 0
\(817\) 6.25289 0.218761
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 30.7760 1.07409 0.537045 0.843554i \(-0.319540\pi\)
0.537045 + 0.843554i \(0.319540\pi\)
\(822\) 0 0
\(823\) 28.3750i 0.989090i 0.869152 + 0.494545i \(0.164665\pi\)
−0.869152 + 0.494545i \(0.835335\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 26.2522i 0.912880i 0.889754 + 0.456440i \(0.150876\pi\)
−0.889754 + 0.456440i \(0.849124\pi\)
\(828\) 0 0
\(829\) − 8.40833i − 0.292033i −0.989282 0.146017i \(-0.953355\pi\)
0.989282 0.146017i \(-0.0466453\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) − 3.90616i − 0.135340i
\(834\) 0 0
\(835\) −2.59401 −0.0897695
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 10.3099 0.355936 0.177968 0.984036i \(-0.443048\pi\)
0.177968 + 0.984036i \(0.443048\pi\)
\(840\) 0 0
\(841\) −18.7078 −0.645098
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0.121287 0.00417239
\(846\) 0 0
\(847\) − 30.2408i − 1.03909i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) − 8.73324i − 0.299372i
\(852\) 0 0
\(853\) 42.6992i 1.46199i 0.682382 + 0.730996i \(0.260944\pi\)
−0.682382 + 0.730996i \(0.739056\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 5.06990i 0.173185i 0.996244 + 0.0865923i \(0.0275977\pi\)
−0.996244 + 0.0865923i \(0.972402\pi\)
\(858\) 0 0
\(859\) −10.9220 −0.372654 −0.186327 0.982488i \(-0.559658\pi\)
−0.186327 + 0.982488i \(0.559658\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 38.1030 1.29704 0.648520 0.761197i \(-0.275388\pi\)
0.648520 + 0.761197i \(0.275388\pi\)
\(864\) 0 0
\(865\) 1.13674 0.0386502
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −31.2378 −1.05967
\(870\) 0 0
\(871\) − 20.2476i − 0.686062i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) − 2.06105i − 0.0696760i
\(876\) 0 0
\(877\) 26.1674i 0.883610i 0.897111 + 0.441805i \(0.145662\pi\)
−0.897111 + 0.441805i \(0.854338\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 29.2903i 0.986817i 0.869798 + 0.493408i \(0.164249\pi\)
−0.869798 + 0.493408i \(0.835751\pi\)
\(882\) 0 0
\(883\) 49.0887 1.65197 0.825983 0.563696i \(-0.190621\pi\)
0.825983 + 0.563696i \(0.190621\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 20.0617 0.673606 0.336803 0.941575i \(-0.390654\pi\)
0.336803 + 0.941575i \(0.390654\pi\)
\(888\) 0 0
\(889\) 7.23082 0.242514
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −37.3805 −1.25089
\(894\) 0 0
\(895\) − 3.01855i − 0.100899i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) − 0.202518i − 0.00675434i
\(900\) 0 0
\(901\) − 49.3443i − 1.64390i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 3.57585i 0.118865i
\(906\) 0 0
\(907\) −17.0142 −0.564948 −0.282474 0.959275i \(-0.591155\pi\)
−0.282474 + 0.959275i \(0.591155\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 8.54462 0.283096 0.141548 0.989931i \(-0.454792\pi\)
0.141548 + 0.989931i \(0.454792\pi\)
\(912\) 0 0
\(913\) −48.2631 −1.59727
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 12.8026 0.422780
\(918\) 0 0
\(919\) 6.49841i 0.214363i 0.994239 + 0.107181i \(0.0341826\pi\)
−0.994239 + 0.107181i \(0.965817\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) − 35.8660i − 1.18055i
\(924\) 0 0
\(925\) 49.1669i 1.61660i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) − 16.9216i − 0.555181i −0.960699 0.277591i \(-0.910464\pi\)
0.960699 0.277591i \(-0.0895358\pi\)
\(930\) 0 0
\(931\) −5.48691 −0.179826
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 5.19237 0.169809
\(936\) 0 0
\(937\) 14.4249 0.471240 0.235620 0.971845i \(-0.424288\pi\)
0.235620 + 0.971845i \(0.424288\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −58.5364 −1.90823 −0.954116 0.299436i \(-0.903201\pi\)
−0.954116 + 0.299436i \(0.903201\pi\)
\(942\) 0 0
\(943\) − 5.23218i − 0.170383i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 15.3006i 0.497201i 0.968606 + 0.248601i \(0.0799707\pi\)
−0.968606 + 0.248601i \(0.920029\pi\)
\(948\) 0 0
\(949\) − 29.1599i − 0.946571i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 14.9133i 0.483089i 0.970390 + 0.241544i \(0.0776539\pi\)
−0.970390 + 0.241544i \(0.922346\pi\)
\(954\) 0 0
\(955\) 1.51068 0.0488845
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −0.363873 −0.0117501
\(960\) 0 0
\(961\) 30.9960 0.999871
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 2.50680 0.0806966
\(966\) 0 0
\(967\) 27.1896i 0.874358i 0.899375 + 0.437179i \(0.144022\pi\)
−0.899375 + 0.437179i \(0.855978\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 35.0892i 1.12607i 0.826434 + 0.563034i \(0.190366\pi\)
−0.826434 + 0.563034i \(0.809634\pi\)
\(972\) 0 0
\(973\) 9.32338i 0.298894i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 32.0438i 1.02517i 0.858636 + 0.512586i \(0.171312\pi\)
−0.858636 + 0.512586i \(0.828688\pi\)
\(978\) 0 0
\(979\) 28.5570 0.912687
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −43.5719 −1.38973 −0.694864 0.719142i \(-0.744535\pi\)
−0.694864 + 0.719142i \(0.744535\pi\)
\(984\) 0 0
\(985\) −3.60011 −0.114709
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 1.00343 0.0319073
\(990\) 0 0
\(991\) 15.2929i 0.485794i 0.970052 + 0.242897i \(0.0780978\pi\)
−0.970052 + 0.242897i \(0.921902\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0.636670i 0.0201838i
\(996\) 0 0
\(997\) 29.8050i 0.943933i 0.881616 + 0.471967i \(0.156456\pi\)
−0.881616 + 0.471967i \(0.843544\pi\)
\(998\) 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 6048.2.j.c.5615.20 32
3.2 odd 2 inner 6048.2.j.c.5615.13 32
4.3 odd 2 1512.2.j.c.323.9 32
8.3 odd 2 inner 6048.2.j.c.5615.14 32
8.5 even 2 1512.2.j.c.323.23 yes 32
12.11 even 2 1512.2.j.c.323.24 yes 32
24.5 odd 2 1512.2.j.c.323.10 yes 32
24.11 even 2 inner 6048.2.j.c.5615.19 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1512.2.j.c.323.9 32 4.3 odd 2
1512.2.j.c.323.10 yes 32 24.5 odd 2
1512.2.j.c.323.23 yes 32 8.5 even 2
1512.2.j.c.323.24 yes 32 12.11 even 2
6048.2.j.c.5615.13 32 3.2 odd 2 inner
6048.2.j.c.5615.14 32 8.3 odd 2 inner
6048.2.j.c.5615.19 32 24.11 even 2 inner
6048.2.j.c.5615.20 32 1.1 even 1 trivial