Properties

Label 6048.2.a.br.1.4
Level 6048
Weight 2
Character 6048.1
Self dual yes
Analytic conductor 48.294
Analytic rank 0
Dimension 4
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6048.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.2935231425\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.4.22896.1
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(0.398683\)
Character \(\chi\) = 6048.1

$q$-expansion

\(f(q)\) \(=\) \(q+4.38773 q^{5} -1.00000 q^{7} +O(q^{10})\) \(q+4.38773 q^{5} -1.00000 q^{7} -3.59037 q^{11} +0.797366 q^{13} +0.295993 q^{17} -0.704007 q^{19} +7.86446 q^{23} +14.2522 q^{25} +4.50137 q^{29} +1.50137 q^{31} -4.38773 q^{35} -0.202634 q^{37} -8.66182 q^{41} +2.79737 q^{43} -8.27409 q^{47} +1.00000 q^{49} +4.00000 q^{53} -15.7536 q^{55} -8.27409 q^{59} +11.9562 q^{61} +3.49863 q^{65} -13.3455 q^{67} +6.79300 q^{71} +6.20538 q^{73} +3.59037 q^{77} +14.7536 q^{79} +14.6443 q^{83} +1.29874 q^{85} -4.66182 q^{89} -0.797366 q^{91} -3.08899 q^{95} -8.54818 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{5} - 4q^{7} + O(q^{10}) \) \( 4q + 2q^{5} - 4q^{7} - 2q^{11} + 8q^{17} + 4q^{19} - 2q^{23} + 8q^{25} + 8q^{29} - 4q^{31} - 2q^{35} - 4q^{37} + 2q^{41} + 8q^{43} - 12q^{47} + 4q^{49} + 16q^{53} - 4q^{55} - 12q^{59} - 8q^{61} + 24q^{65} - 8q^{67} + 18q^{71} + 8q^{73} + 2q^{77} - 8q^{85} + 18q^{89} - 10q^{95} + 8q^{97} + O(q^{100}) \)

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
\(5\) 4.38773 1.96225 0.981127 0.193367i \(-0.0619407\pi\)
0.981127 + 0.193367i \(0.0619407\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −3.59037 −1.08254 −0.541268 0.840850i \(-0.682056\pi\)
−0.541268 + 0.840850i \(0.682056\pi\)
\(12\) 0 0
\(13\) 0.797366 0.221150 0.110575 0.993868i \(-0.464731\pi\)
0.110575 + 0.993868i \(0.464731\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.295993 0.0717889 0.0358944 0.999356i \(-0.488572\pi\)
0.0358944 + 0.999356i \(0.488572\pi\)
\(18\) 0 0
\(19\) −0.704007 −0.161510 −0.0807551 0.996734i \(-0.525733\pi\)
−0.0807551 + 0.996734i \(0.525733\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 7.86446 1.63985 0.819926 0.572469i \(-0.194014\pi\)
0.819926 + 0.572469i \(0.194014\pi\)
\(24\) 0 0
\(25\) 14.2522 2.85044
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 4.50137 0.835884 0.417942 0.908474i \(-0.362752\pi\)
0.417942 + 0.908474i \(0.362752\pi\)
\(30\) 0 0
\(31\) 1.50137 0.269654 0.134827 0.990869i \(-0.456952\pi\)
0.134827 + 0.990869i \(0.456952\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −4.38773 −0.741662
\(36\) 0 0
\(37\) −0.202634 −0.0333128 −0.0166564 0.999861i \(-0.505302\pi\)
−0.0166564 + 0.999861i \(0.505302\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −8.66182 −1.35275 −0.676375 0.736558i \(-0.736450\pi\)
−0.676375 + 0.736558i \(0.736450\pi\)
\(42\) 0 0
\(43\) 2.79737 0.426594 0.213297 0.976987i \(-0.431580\pi\)
0.213297 + 0.976987i \(0.431580\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −8.27409 −1.20690 −0.603450 0.797401i \(-0.706208\pi\)
−0.603450 + 0.797401i \(0.706208\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 4.00000 0.549442 0.274721 0.961524i \(-0.411414\pi\)
0.274721 + 0.961524i \(0.411414\pi\)
\(54\) 0 0
\(55\) −15.7536 −2.12421
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −8.27409 −1.07719 −0.538597 0.842563i \(-0.681046\pi\)
−0.538597 + 0.842563i \(0.681046\pi\)
\(60\) 0 0
\(61\) 11.9562 1.53083 0.765417 0.643535i \(-0.222533\pi\)
0.765417 + 0.643535i \(0.222533\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 3.49863 0.433951
\(66\) 0 0
\(67\) −13.3455 −1.63042 −0.815209 0.579167i \(-0.803378\pi\)
−0.815209 + 0.579167i \(0.803378\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 6.79300 0.806181 0.403090 0.915160i \(-0.367936\pi\)
0.403090 + 0.915160i \(0.367936\pi\)
\(72\) 0 0
\(73\) 6.20538 0.726285 0.363142 0.931734i \(-0.381704\pi\)
0.363142 + 0.931734i \(0.381704\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 3.59037 0.409160
\(78\) 0 0
\(79\) 14.7536 1.65991 0.829953 0.557834i \(-0.188367\pi\)
0.829953 + 0.557834i \(0.188367\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 14.6443 1.60742 0.803710 0.595022i \(-0.202857\pi\)
0.803710 + 0.595022i \(0.202857\pi\)
\(84\) 0 0
\(85\) 1.29874 0.140868
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −4.66182 −0.494152 −0.247076 0.968996i \(-0.579470\pi\)
−0.247076 + 0.968996i \(0.579470\pi\)
\(90\) 0 0
\(91\) −0.797366 −0.0835867
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −3.08899 −0.316924
\(96\) 0 0
\(97\) −8.54818 −0.867936 −0.433968 0.900928i \(-0.642887\pi\)
−0.433968 + 0.900928i \(0.642887\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 8.29599 0.825482 0.412741 0.910848i \(-0.364571\pi\)
0.412741 + 0.910848i \(0.364571\pi\)
\(102\) 0 0
\(103\) 9.04681 0.891408 0.445704 0.895180i \(-0.352953\pi\)
0.445704 + 0.895180i \(0.352953\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 10.8847 1.05227 0.526134 0.850402i \(-0.323641\pi\)
0.526134 + 0.850402i \(0.323641\pi\)
\(108\) 0 0
\(109\) 6.45482 0.618260 0.309130 0.951020i \(-0.399962\pi\)
0.309130 + 0.951020i \(0.399962\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 11.1807 1.05179 0.525897 0.850548i \(-0.323730\pi\)
0.525897 + 0.850548i \(0.323730\pi\)
\(114\) 0 0
\(115\) 34.5071 3.21781
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −0.295993 −0.0271337
\(120\) 0 0
\(121\) 1.89072 0.171884
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 40.5961 3.63103
\(126\) 0 0
\(127\) −14.3483 −1.27320 −0.636602 0.771192i \(-0.719661\pi\)
−0.636602 + 0.771192i \(0.719661\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −17.2768 −1.50948 −0.754742 0.656022i \(-0.772238\pi\)
−0.754742 + 0.656022i \(0.772238\pi\)
\(132\) 0 0
\(133\) 0.704007 0.0610451
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 5.31191 0.453827 0.226914 0.973915i \(-0.427137\pi\)
0.226914 + 0.973915i \(0.427137\pi\)
\(138\) 0 0
\(139\) 10.9534 0.929059 0.464530 0.885558i \(-0.346223\pi\)
0.464530 + 0.885558i \(0.346223\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −2.86283 −0.239402
\(144\) 0 0
\(145\) 19.7508 1.64022
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 13.3674 1.09510 0.547552 0.836772i \(-0.315560\pi\)
0.547552 + 0.836772i \(0.315560\pi\)
\(150\) 0 0
\(151\) 9.95619 0.810224 0.405112 0.914267i \(-0.367233\pi\)
0.405112 + 0.914267i \(0.367233\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 6.58762 0.529130
\(156\) 0 0
\(157\) −9.80011 −0.782134 −0.391067 0.920362i \(-0.627894\pi\)
−0.391067 + 0.920362i \(0.627894\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −7.86446 −0.619806
\(162\) 0 0
\(163\) −5.38935 −0.422127 −0.211063 0.977472i \(-0.567693\pi\)
−0.211063 + 0.977472i \(0.567693\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −15.1807 −1.17472 −0.587360 0.809326i \(-0.699833\pi\)
−0.587360 + 0.809326i \(0.699833\pi\)
\(168\) 0 0
\(169\) −12.3642 −0.951093
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 12.6837 0.964326 0.482163 0.876082i \(-0.339851\pi\)
0.482163 + 0.876082i \(0.339851\pi\)
\(174\) 0 0
\(175\) −14.2522 −1.07736
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 17.0715 1.27598 0.637990 0.770044i \(-0.279766\pi\)
0.637990 + 0.770044i \(0.279766\pi\)
\(180\) 0 0
\(181\) −21.3642 −1.58799 −0.793995 0.607925i \(-0.792002\pi\)
−0.793995 + 0.607925i \(0.792002\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −0.889104 −0.0653682
\(186\) 0 0
\(187\) −1.06272 −0.0777141
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −4.31902 −0.312513 −0.156257 0.987716i \(-0.549943\pi\)
−0.156257 + 0.987716i \(0.549943\pi\)
\(192\) 0 0
\(193\) −8.14291 −0.586140 −0.293070 0.956091i \(-0.594677\pi\)
−0.293070 + 0.956091i \(0.594677\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −9.32364 −0.664282 −0.332141 0.943230i \(-0.607771\pi\)
−0.332141 + 0.943230i \(0.607771\pi\)
\(198\) 0 0
\(199\) 17.3483 1.22979 0.614894 0.788610i \(-0.289199\pi\)
0.614894 + 0.788610i \(0.289199\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −4.50137 −0.315934
\(204\) 0 0
\(205\) −38.0057 −2.65444
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 2.52764 0.174841
\(210\) 0 0
\(211\) −22.9589 −1.58056 −0.790279 0.612747i \(-0.790065\pi\)
−0.790279 + 0.612747i \(0.790065\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 12.2741 0.837086
\(216\) 0 0
\(217\) −1.50137 −0.101920
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0.236015 0.0158761
\(222\) 0 0
\(223\) 1.79737 0.120361 0.0601803 0.998188i \(-0.480832\pi\)
0.0601803 + 0.998188i \(0.480832\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 12.1835 0.808646 0.404323 0.914616i \(-0.367507\pi\)
0.404323 + 0.914616i \(0.367507\pi\)
\(228\) 0 0
\(229\) −23.1457 −1.52951 −0.764754 0.644322i \(-0.777140\pi\)
−0.764754 + 0.644322i \(0.777140\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −11.7289 −0.768387 −0.384193 0.923253i \(-0.625520\pi\)
−0.384193 + 0.923253i \(0.625520\pi\)
\(234\) 0 0
\(235\) −36.3045 −2.36824
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 17.4822 1.13083 0.565415 0.824806i \(-0.308716\pi\)
0.565415 + 0.824806i \(0.308716\pi\)
\(240\) 0 0
\(241\) 21.7508 1.40109 0.700547 0.713607i \(-0.252940\pi\)
0.700547 + 0.713607i \(0.252940\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 4.38773 0.280322
\(246\) 0 0
\(247\) −0.561351 −0.0357179
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 10.5975 0.668907 0.334453 0.942412i \(-0.391448\pi\)
0.334453 + 0.942412i \(0.391448\pi\)
\(252\) 0 0
\(253\) −28.2363 −1.77520
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 20.9578 1.30731 0.653656 0.756792i \(-0.273234\pi\)
0.653656 + 0.756792i \(0.273234\pi\)
\(258\) 0 0
\(259\) 0.202634 0.0125911
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −2.27846 −0.140496 −0.0702478 0.997530i \(-0.522379\pi\)
−0.0702478 + 0.997530i \(0.522379\pi\)
\(264\) 0 0
\(265\) 17.5509 1.07814
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 16.8672 1.02841 0.514206 0.857667i \(-0.328087\pi\)
0.514206 + 0.857667i \(0.328087\pi\)
\(270\) 0 0
\(271\) 5.81328 0.353132 0.176566 0.984289i \(-0.443501\pi\)
0.176566 + 0.984289i \(0.443501\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −51.1706 −3.08570
\(276\) 0 0
\(277\) −16.1588 −0.970890 −0.485445 0.874267i \(-0.661342\pi\)
−0.485445 + 0.874267i \(0.661342\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 4.86608 0.290286 0.145143 0.989411i \(-0.453636\pi\)
0.145143 + 0.989411i \(0.453636\pi\)
\(282\) 0 0
\(283\) 21.5509 1.28107 0.640535 0.767929i \(-0.278713\pi\)
0.640535 + 0.767929i \(0.278713\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 8.66182 0.511291
\(288\) 0 0
\(289\) −16.9124 −0.994846
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −23.3978 −1.36692 −0.683458 0.729990i \(-0.739525\pi\)
−0.683458 + 0.729990i \(0.739525\pi\)
\(294\) 0 0
\(295\) −36.3045 −2.11373
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 6.27085 0.362653
\(300\) 0 0
\(301\) −2.79737 −0.161237
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 52.4606 3.00388
\(306\) 0 0
\(307\) −34.0189 −1.94156 −0.970781 0.239967i \(-0.922863\pi\)
−0.970781 + 0.239967i \(0.922863\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 21.5977 1.22470 0.612348 0.790589i \(-0.290225\pi\)
0.612348 + 0.790589i \(0.290225\pi\)
\(312\) 0 0
\(313\) −8.34280 −0.471563 −0.235781 0.971806i \(-0.575765\pi\)
−0.235781 + 0.971806i \(0.575765\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 23.0901 1.29687 0.648435 0.761270i \(-0.275424\pi\)
0.648435 + 0.761270i \(0.275424\pi\)
\(318\) 0 0
\(319\) −16.1616 −0.904874
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −0.208381 −0.0115946
\(324\) 0 0
\(325\) 11.3642 0.630373
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 8.27409 0.456165
\(330\) 0 0
\(331\) 30.0991 1.65440 0.827198 0.561910i \(-0.189933\pi\)
0.827198 + 0.561910i \(0.189933\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −58.5567 −3.19929
\(336\) 0 0
\(337\) 25.3615 1.38153 0.690763 0.723081i \(-0.257275\pi\)
0.690763 + 0.723081i \(0.257275\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −5.39048 −0.291911
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 8.43454 0.452790 0.226395 0.974036i \(-0.427306\pi\)
0.226395 + 0.974036i \(0.427306\pi\)
\(348\) 0 0
\(349\) −19.5947 −1.04888 −0.524441 0.851447i \(-0.675726\pi\)
−0.524441 + 0.851447i \(0.675726\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 18.7111 0.995892 0.497946 0.867208i \(-0.334088\pi\)
0.497946 + 0.867208i \(0.334088\pi\)
\(354\) 0 0
\(355\) 29.8059 1.58193
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −7.02216 −0.370615 −0.185308 0.982681i \(-0.559328\pi\)
−0.185308 + 0.982681i \(0.559328\pi\)
\(360\) 0 0
\(361\) −18.5044 −0.973914
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 27.2275 1.42515
\(366\) 0 0
\(367\) 19.4912 1.01743 0.508716 0.860934i \(-0.330120\pi\)
0.508716 + 0.860934i \(0.330120\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −4.00000 −0.207670
\(372\) 0 0
\(373\) 25.0085 1.29489 0.647445 0.762112i \(-0.275837\pi\)
0.647445 + 0.762112i \(0.275837\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 3.58924 0.184855
\(378\) 0 0
\(379\) −16.3921 −0.842005 −0.421003 0.907059i \(-0.638322\pi\)
−0.421003 + 0.907059i \(0.638322\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 13.2798 0.678568 0.339284 0.940684i \(-0.389815\pi\)
0.339284 + 0.940684i \(0.389815\pi\)
\(384\) 0 0
\(385\) 15.7536 0.802876
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −22.5537 −1.14352 −0.571758 0.820422i \(-0.693738\pi\)
−0.571758 + 0.820422i \(0.693738\pi\)
\(390\) 0 0
\(391\) 2.32783 0.117723
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 64.7347 3.25715
\(396\) 0 0
\(397\) −35.3149 −1.77240 −0.886202 0.463299i \(-0.846666\pi\)
−0.886202 + 0.463299i \(0.846666\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 35.8218 1.78885 0.894427 0.447214i \(-0.147584\pi\)
0.894427 + 0.447214i \(0.147584\pi\)
\(402\) 0 0
\(403\) 1.19714 0.0596340
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0.727531 0.0360624
\(408\) 0 0
\(409\) −21.9430 −1.08501 −0.542506 0.840052i \(-0.682525\pi\)
−0.542506 + 0.840052i \(0.682525\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 8.27409 0.407141
\(414\) 0 0
\(415\) 64.2552 3.15416
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −2.67636 −0.130749 −0.0653743 0.997861i \(-0.520824\pi\)
−0.0653743 + 0.997861i \(0.520824\pi\)
\(420\) 0 0
\(421\) 7.93479 0.386718 0.193359 0.981128i \(-0.438062\pi\)
0.193359 + 0.981128i \(0.438062\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 4.21855 0.204630
\(426\) 0 0
\(427\) −11.9562 −0.578601
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 3.13280 0.150902 0.0754508 0.997150i \(-0.475960\pi\)
0.0754508 + 0.997150i \(0.475960\pi\)
\(432\) 0 0
\(433\) 26.1561 1.25698 0.628491 0.777817i \(-0.283673\pi\)
0.628491 + 0.777817i \(0.283673\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −5.53663 −0.264853
\(438\) 0 0
\(439\) −9.18397 −0.438327 −0.219164 0.975688i \(-0.570333\pi\)
−0.219164 + 0.975688i \(0.570333\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −38.1353 −1.81186 −0.905931 0.423424i \(-0.860828\pi\)
−0.905931 + 0.423424i \(0.860828\pi\)
\(444\) 0 0
\(445\) −20.4548 −0.969652
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 10.4140 0.491467 0.245734 0.969337i \(-0.420971\pi\)
0.245734 + 0.969337i \(0.420971\pi\)
\(450\) 0 0
\(451\) 31.0991 1.46440
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −3.49863 −0.164018
\(456\) 0 0
\(457\) −14.1457 −0.661706 −0.330853 0.943682i \(-0.607336\pi\)
−0.330853 + 0.943682i \(0.607336\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −4.91101 −0.228728 −0.114364 0.993439i \(-0.536483\pi\)
−0.114364 + 0.993439i \(0.536483\pi\)
\(462\) 0 0
\(463\) −3.59473 −0.167061 −0.0835307 0.996505i \(-0.526620\pi\)
−0.0835307 + 0.996505i \(0.526620\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −23.0463 −1.06646 −0.533228 0.845972i \(-0.679021\pi\)
−0.533228 + 0.845972i \(0.679021\pi\)
\(468\) 0 0
\(469\) 13.3455 0.616240
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −10.0436 −0.461804
\(474\) 0 0
\(475\) −10.0336 −0.460375
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −12.7404 −0.582123 −0.291062 0.956704i \(-0.594008\pi\)
−0.291062 + 0.956704i \(0.594008\pi\)
\(480\) 0 0
\(481\) −0.161574 −0.00736712
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −37.5071 −1.70311
\(486\) 0 0
\(487\) −29.1150 −1.31933 −0.659664 0.751561i \(-0.729301\pi\)
−0.659664 + 0.751561i \(0.729301\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −31.2155 −1.40874 −0.704368 0.709835i \(-0.748769\pi\)
−0.704368 + 0.709835i \(0.748769\pi\)
\(492\) 0 0
\(493\) 1.33238 0.0600072
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −6.79300 −0.304708
\(498\) 0 0
\(499\) −29.1588 −1.30533 −0.652664 0.757647i \(-0.726349\pi\)
−0.652664 + 0.757647i \(0.726349\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −17.8337 −0.795168 −0.397584 0.917566i \(-0.630151\pi\)
−0.397584 + 0.917566i \(0.630151\pi\)
\(504\) 0 0
\(505\) 36.4006 1.61980
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −5.65471 −0.250641 −0.125320 0.992116i \(-0.539996\pi\)
−0.125320 + 0.992116i \(0.539996\pi\)
\(510\) 0 0
\(511\) −6.20538 −0.274510
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 39.6950 1.74917
\(516\) 0 0
\(517\) 29.7070 1.30651
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −9.00162 −0.394368 −0.197184 0.980366i \(-0.563180\pi\)
−0.197184 + 0.980366i \(0.563180\pi\)
\(522\) 0 0
\(523\) 13.9589 0.610382 0.305191 0.952291i \(-0.401280\pi\)
0.305191 + 0.952291i \(0.401280\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0.444396 0.0193582
\(528\) 0 0
\(529\) 38.8497 1.68912
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −6.90664 −0.299160
\(534\) 0 0
\(535\) 47.7593 2.06481
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −3.59037 −0.154648
\(540\) 0 0
\(541\) −1.24919 −0.0537067 −0.0268533 0.999639i \(-0.508549\pi\)
−0.0268533 + 0.999639i \(0.508549\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 28.3220 1.21318
\(546\) 0 0
\(547\) −18.6911 −0.799173 −0.399587 0.916695i \(-0.630846\pi\)
−0.399587 + 0.916695i \(0.630846\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −3.16900 −0.135004
\(552\) 0 0
\(553\) −14.7536 −0.627385
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −42.2388 −1.78971 −0.894857 0.446353i \(-0.852723\pi\)
−0.894857 + 0.446353i \(0.852723\pi\)
\(558\) 0 0
\(559\) 2.23052 0.0943411
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −20.0030 −0.843026 −0.421513 0.906822i \(-0.638501\pi\)
−0.421513 + 0.906822i \(0.638501\pi\)
\(564\) 0 0
\(565\) 49.0580 2.06389
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 8.36470 0.350667 0.175333 0.984509i \(-0.443900\pi\)
0.175333 + 0.984509i \(0.443900\pi\)
\(570\) 0 0
\(571\) 19.7695 0.827327 0.413663 0.910430i \(-0.364249\pi\)
0.413663 + 0.910430i \(0.364249\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 112.086 4.67430
\(576\) 0 0
\(577\) 12.1867 0.507340 0.253670 0.967291i \(-0.418362\pi\)
0.253670 + 0.967291i \(0.418362\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −14.6443 −0.607547
\(582\) 0 0
\(583\) −14.3615 −0.594791
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 9.54219 0.393848 0.196924 0.980419i \(-0.436905\pi\)
0.196924 + 0.980419i \(0.436905\pi\)
\(588\) 0 0
\(589\) −1.05698 −0.0435520
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 30.1002 1.23607 0.618034 0.786151i \(-0.287929\pi\)
0.618034 + 0.786151i \(0.287929\pi\)
\(594\) 0 0
\(595\) −1.29874 −0.0532431
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −39.0101 −1.59391 −0.796955 0.604039i \(-0.793557\pi\)
−0.796955 + 0.604039i \(0.793557\pi\)
\(600\) 0 0
\(601\) 3.20263 0.130638 0.0653191 0.997864i \(-0.479193\pi\)
0.0653191 + 0.997864i \(0.479193\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 8.29599 0.337280
\(606\) 0 0
\(607\) −22.1429 −0.898753 −0.449377 0.893342i \(-0.648354\pi\)
−0.449377 + 0.893342i \(0.648354\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −6.59748 −0.266905
\(612\) 0 0
\(613\) 1.50137 0.0606399 0.0303199 0.999540i \(-0.490347\pi\)
0.0303199 + 0.999540i \(0.490347\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −11.2275 −0.452004 −0.226002 0.974127i \(-0.572566\pi\)
−0.226002 + 0.974127i \(0.572566\pi\)
\(618\) 0 0
\(619\) −7.09911 −0.285337 −0.142669 0.989771i \(-0.545568\pi\)
−0.142669 + 0.989771i \(0.545568\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 4.66182 0.186772
\(624\) 0 0
\(625\) 106.864 4.27456
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −0.0599783 −0.00239149
\(630\) 0 0
\(631\) 46.7098 1.85949 0.929743 0.368209i \(-0.120029\pi\)
0.929743 + 0.368209i \(0.120029\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −62.9565 −2.49835
\(636\) 0 0
\(637\) 0.797366 0.0315928
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 3.13693 0.123901 0.0619505 0.998079i \(-0.480268\pi\)
0.0619505 + 0.998079i \(0.480268\pi\)
\(642\) 0 0
\(643\) −29.2522 −1.15359 −0.576797 0.816888i \(-0.695698\pi\)
−0.576797 + 0.816888i \(0.695698\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −6.37320 −0.250556 −0.125278 0.992122i \(-0.539982\pi\)
−0.125278 + 0.992122i \(0.539982\pi\)
\(648\) 0 0
\(649\) 29.7070 1.16610
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −11.0901 −0.433990 −0.216995 0.976173i \(-0.569626\pi\)
−0.216995 + 0.976173i \(0.569626\pi\)
\(654\) 0 0
\(655\) −75.8061 −2.96199
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 34.9633 1.36198 0.680989 0.732294i \(-0.261550\pi\)
0.680989 + 0.732294i \(0.261550\pi\)
\(660\) 0 0
\(661\) −35.2524 −1.37116 −0.685581 0.727997i \(-0.740452\pi\)
−0.685581 + 0.727997i \(0.740452\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 3.08899 0.119786
\(666\) 0 0
\(667\) 35.4008 1.37073
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −42.9271 −1.65718
\(672\) 0 0
\(673\) −4.14291 −0.159698 −0.0798488 0.996807i \(-0.525444\pi\)
−0.0798488 + 0.996807i \(0.525444\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −14.5306 −0.558458 −0.279229 0.960225i \(-0.590079\pi\)
−0.279229 + 0.960225i \(0.590079\pi\)
\(678\) 0 0
\(679\) 8.54818 0.328049
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 23.0422 0.881685 0.440842 0.897585i \(-0.354680\pi\)
0.440842 + 0.897585i \(0.354680\pi\)
\(684\) 0 0
\(685\) 23.3072 0.890524
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 3.18946 0.121509
\(690\) 0 0
\(691\) 25.3587 0.964691 0.482346 0.875981i \(-0.339785\pi\)
0.482346 + 0.875981i \(0.339785\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 48.0608 1.82305
\(696\) 0 0
\(697\) −2.56384 −0.0971124
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 34.1459 1.28967 0.644837 0.764320i \(-0.276925\pi\)
0.644837 + 0.764320i \(0.276925\pi\)
\(702\) 0 0
\(703\) 0.142656 0.00538037
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −8.29599 −0.312003
\(708\) 0 0
\(709\) −39.9301 −1.49961 −0.749803 0.661661i \(-0.769852\pi\)
−0.749803 + 0.661661i \(0.769852\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 11.8075 0.442194
\(714\) 0 0
\(715\) −12.5614 −0.469768
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 5.49539 0.204943 0.102472 0.994736i \(-0.467325\pi\)
0.102472 + 0.994736i \(0.467325\pi\)
\(720\) 0 0
\(721\) −9.04681 −0.336921
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 64.1544 2.38263
\(726\) 0 0
\(727\) −35.5564 −1.31871 −0.659357 0.751830i \(-0.729172\pi\)
−0.659357 + 0.751830i \(0.729172\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0.828001 0.0306247
\(732\) 0 0
\(733\) −34.7536 −1.28365 −0.641826 0.766850i \(-0.721823\pi\)
−0.641826 + 0.766850i \(0.721823\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 47.9154 1.76499
\(738\) 0 0
\(739\) 47.8367 1.75970 0.879852 0.475248i \(-0.157642\pi\)
0.879852 + 0.475248i \(0.157642\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 17.5717 0.644643 0.322322 0.946630i \(-0.395537\pi\)
0.322322 + 0.946630i \(0.395537\pi\)
\(744\) 0 0
\(745\) 58.6528 2.14887
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −10.8847 −0.397720
\(750\) 0 0
\(751\) 25.7508 0.939661 0.469830 0.882757i \(-0.344315\pi\)
0.469830 + 0.882757i \(0.344315\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 43.6851 1.58986
\(756\) 0 0
\(757\) 5.21580 0.189572 0.0947858 0.995498i \(-0.469783\pi\)
0.0947858 + 0.995498i \(0.469783\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −26.0655 −0.944873 −0.472436 0.881365i \(-0.656625\pi\)
−0.472436 + 0.881365i \(0.656625\pi\)
\(762\) 0 0
\(763\) −6.45482 −0.233680
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −6.59748 −0.238221
\(768\) 0 0
\(769\) 16.9896 0.612660 0.306330 0.951925i \(-0.400899\pi\)
0.306330 + 0.951925i \(0.400899\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −15.8396 −0.569709 −0.284855 0.958571i \(-0.591945\pi\)
−0.284855 + 0.958571i \(0.591945\pi\)
\(774\) 0 0
\(775\) 21.3978 0.768633
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 6.09798 0.218483
\(780\) 0 0
\(781\) −24.3894 −0.872720
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −43.0003 −1.53474
\(786\) 0 0
\(787\) 27.7376 0.988740 0.494370 0.869252i \(-0.335399\pi\)
0.494370 + 0.869252i \(0.335399\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −11.1807 −0.397541
\(792\) 0 0
\(793\) 9.53346 0.338543
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 21.5192 0.762248 0.381124 0.924524i \(-0.375537\pi\)
0.381124 + 0.924524i \(0.375537\pi\)
\(798\) 0 0
\(799\) −2.44907 −0.0866420
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −22.2796 −0.786229
\(804\) 0 0
\(805\) −34.5071 −1.21622
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 7.90939 0.278079 0.139040 0.990287i \(-0.455598\pi\)
0.139040 + 0.990287i \(0.455598\pi\)
\(810\) 0 0
\(811\) −26.5947 −0.933867 −0.466934 0.884292i \(-0.654641\pi\)
−0.466934 + 0.884292i \(0.654641\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −23.6470 −0.828319
\(816\) 0 0
\(817\) −1.96936 −0.0688993
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −35.7757 −1.24858 −0.624291 0.781192i \(-0.714612\pi\)
−0.624291 + 0.781192i \(0.714612\pi\)
\(822\) 0 0
\(823\) −8.00549 −0.279054 −0.139527 0.990218i \(-0.544558\pi\)
−0.139527 + 0.990218i \(0.544558\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 7.60927 0.264600 0.132300 0.991210i \(-0.457764\pi\)
0.132300 + 0.991210i \(0.457764\pi\)
\(828\) 0 0
\(829\) −23.2081 −0.806051 −0.403026 0.915189i \(-0.632041\pi\)
−0.403026 + 0.915189i \(0.632041\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0.295993 0.0102556
\(834\) 0 0
\(835\) −66.6090 −2.30510
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −24.9121 −0.860062 −0.430031 0.902814i \(-0.641497\pi\)
−0.430031 + 0.902814i \(0.641497\pi\)
\(840\) 0 0
\(841\) −8.73764 −0.301298
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −54.2508 −1.86629
\(846\) 0 0
\(847\) −1.89072 −0.0649661
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −1.59361 −0.0546281
\(852\) 0 0
\(853\) −19.7376 −0.675804 −0.337902 0.941181i \(-0.609717\pi\)
−0.337902 + 0.941181i \(0.609717\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 22.2916 0.761467 0.380734 0.924685i \(-0.375671\pi\)
0.380734 + 0.924685i \(0.375671\pi\)
\(858\) 0 0
\(859\) −25.1646 −0.858604 −0.429302 0.903161i \(-0.641240\pi\)
−0.429302 + 0.903161i \(0.641240\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 51.7625 1.76202 0.881009 0.473100i \(-0.156865\pi\)
0.881009 + 0.473100i \(0.156865\pi\)
\(864\) 0 0
\(865\) 55.6528 1.89225
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −52.9707 −1.79691
\(870\) 0 0
\(871\) −10.6413 −0.360566
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −40.5961 −1.37240
\(876\) 0 0
\(877\) 58.7464 1.98372 0.991862 0.127315i \(-0.0406358\pi\)
0.991862 + 0.127315i \(0.0406358\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −56.1284 −1.89101 −0.945507 0.325603i \(-0.894433\pi\)
−0.945507 + 0.325603i \(0.894433\pi\)
\(882\) 0 0
\(883\) −9.14017 −0.307591 −0.153796 0.988103i \(-0.549150\pi\)
−0.153796 + 0.988103i \(0.549150\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −46.4083 −1.55824 −0.779119 0.626877i \(-0.784333\pi\)
−0.779119 + 0.626877i \(0.784333\pi\)
\(888\) 0 0
\(889\) 14.3483 0.481226
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 5.82502 0.194927
\(894\) 0 0
\(895\) 74.9050 2.50380
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 6.75824 0.225400
\(900\) 0 0
\(901\) 1.18397 0.0394438
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −93.7404 −3.11604
\(906\) 0 0
\(907\) 28.1867 0.935925 0.467962 0.883748i \(-0.344988\pi\)
0.467962 + 0.883748i \(0.344988\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 40.1235 1.32935 0.664675 0.747132i \(-0.268570\pi\)
0.664675 + 0.747132i \(0.268570\pi\)
\(912\) 0 0
\(913\) −52.5783 −1.74009
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 17.2768 0.570531
\(918\) 0 0
\(919\) −17.6445 −0.582040 −0.291020 0.956717i \(-0.593995\pi\)
−0.291020 + 0.956717i \(0.593995\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 5.41651 0.178286
\(924\) 0 0
\(925\) −2.88798 −0.0949562
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 21.3924 0.701860 0.350930 0.936402i \(-0.385865\pi\)
0.350930 + 0.936402i \(0.385865\pi\)
\(930\) 0 0
\(931\) −0.704007 −0.0230729
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −4.66295 −0.152495
\(936\) 0 0
\(937\) −47.0580 −1.53732 −0.768660 0.639658i \(-0.779076\pi\)
−0.768660 + 0.639658i \(0.779076\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −16.0668 −0.523764 −0.261882 0.965100i \(-0.584343\pi\)
−0.261882 + 0.965100i \(0.584343\pi\)
\(942\) 0 0
\(943\) −68.1205 −2.21831
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −26.4838 −0.860609 −0.430305 0.902684i \(-0.641594\pi\)
−0.430305 + 0.902684i \(0.641594\pi\)
\(948\) 0 0
\(949\) 4.94796 0.160618
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −17.8337 −0.577692 −0.288846 0.957376i \(-0.593272\pi\)
−0.288846 + 0.957376i \(0.593272\pi\)
\(954\) 0 0
\(955\) −18.9507 −0.613230
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −5.31191 −0.171530
\(960\) 0 0
\(961\) −28.7459 −0.927286
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −35.7289 −1.15015
\(966\) 0 0
\(967\) −28.4113 −0.913645 −0.456822 0.889558i \(-0.651013\pi\)
−0.456822 + 0.889558i \(0.651013\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 19.0550 0.611505 0.305753 0.952111i \(-0.401092\pi\)
0.305753 + 0.952111i \(0.401092\pi\)
\(972\) 0 0
\(973\) −10.9534 −0.351151
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −44.1046 −1.41103 −0.705516 0.708694i \(-0.749284\pi\)
−0.705516 + 0.708694i \(0.749284\pi\)
\(978\) 0 0
\(979\) 16.7376 0.534937
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 47.7867 1.52416 0.762080 0.647483i \(-0.224179\pi\)
0.762080 + 0.647483i \(0.224179\pi\)
\(984\) 0 0
\(985\) −40.9096 −1.30349
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 21.9998 0.699552
\(990\) 0 0
\(991\) 20.6161 0.654893 0.327447 0.944870i \(-0.393812\pi\)
0.327447 + 0.944870i \(0.393812\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 76.1196 2.41315
\(996\) 0 0
\(997\) 16.8160 0.532569 0.266284 0.963894i \(-0.414204\pi\)
0.266284 + 0.963894i \(0.414204\pi\)
\(998\) 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.a.br.1.4 yes 4
3.2 odd 2 6048.2.a.bm.1.1 4
4.3 odd 2 6048.2.a.bv.1.4 yes 4
12.11 even 2 6048.2.a.bo.1.1 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6048.2.a.bm.1.1 4 3.2 odd 2
6048.2.a.bo.1.1 yes 4 12.11 even 2
6048.2.a.br.1.4 yes 4 1.1 even 1 trivial
6048.2.a.bv.1.4 yes 4 4.3 odd 2