Properties

Label 324.6.a.d.1.3
Level 324
Weight 6
Character 324.1
Self dual yes
Analytic conductor 51.964
Analytic rank 1
Dimension 5
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 324.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(51.9643576194\)
Analytic rank: \(1\)
Dimension: \(5\)
Coefficient field: \(\mathbb{Q}[x]/(x^{5} - \cdots)\)
Defining polynomial: \(x^{5} - 2 x^{4} - 110 x^{3} + 39 x^{2} + 2214 x - 1944\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{4}\cdot 3^{7} \)
Twist minimal: no (minimal twist has level 36)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(4.43077\) of defining polynomial
Character \(\chi\) \(=\) 324.1

$q$-expansion

\(f(q)\) \(=\) \(q+9.76844 q^{5} +136.668 q^{7} +O(q^{10})\) \(q+9.76844 q^{5} +136.668 q^{7} -653.321 q^{11} +250.494 q^{13} -249.768 q^{17} -1754.03 q^{19} +1654.88 q^{23} -3029.58 q^{25} -4247.92 q^{29} +8987.43 q^{31} +1335.03 q^{35} -6000.33 q^{37} +10745.2 q^{41} +10046.6 q^{43} -23486.6 q^{47} +1871.16 q^{49} -9411.34 q^{53} -6381.93 q^{55} -44166.8 q^{59} -22404.9 q^{61} +2446.93 q^{65} -36003.0 q^{67} -78538.5 q^{71} +61305.5 q^{73} -89288.1 q^{77} +27490.1 q^{79} +64806.4 q^{83} -2439.85 q^{85} +34652.4 q^{89} +34234.5 q^{91} -17134.1 q^{95} +16112.3 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q - 21q^{5} - 29q^{7} + O(q^{10}) \) \( 5q - 21q^{5} - 29q^{7} + 177q^{11} + 181q^{13} - 1140q^{17} - 416q^{19} + 399q^{23} + 4778q^{25} - 6033q^{29} - 2759q^{31} - 18573q^{35} - 7586q^{37} - 18435q^{41} - 1469q^{43} - 25155q^{47} + 4056q^{49} - 58422q^{53} + 7389q^{55} - 90537q^{59} - 1403q^{61} - 148407q^{65} - 13907q^{67} - 114684q^{71} + 7600q^{73} - 211983q^{77} - 29993q^{79} - 228951q^{83} + 49662q^{85} - 299166q^{89} + 62465q^{91} - 394764q^{95} - 40541q^{97} + O(q^{100}) \)

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
\(5\) 9.76844 0.174743 0.0873716 0.996176i \(-0.472153\pi\)
0.0873716 + 0.996176i \(0.472153\pi\)
\(6\) 0 0
\(7\) 136.668 1.05420 0.527099 0.849804i \(-0.323280\pi\)
0.527099 + 0.849804i \(0.323280\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −653.321 −1.62796 −0.813982 0.580890i \(-0.802705\pi\)
−0.813982 + 0.580890i \(0.802705\pi\)
\(12\) 0 0
\(13\) 250.494 0.411092 0.205546 0.978647i \(-0.434103\pi\)
0.205546 + 0.978647i \(0.434103\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −249.768 −0.209611 −0.104806 0.994493i \(-0.533422\pi\)
−0.104806 + 0.994493i \(0.533422\pi\)
\(18\) 0 0
\(19\) −1754.03 −1.11469 −0.557343 0.830282i \(-0.688179\pi\)
−0.557343 + 0.830282i \(0.688179\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1654.88 0.652300 0.326150 0.945318i \(-0.394249\pi\)
0.326150 + 0.945318i \(0.394249\pi\)
\(24\) 0 0
\(25\) −3029.58 −0.969465
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −4247.92 −0.937954 −0.468977 0.883211i \(-0.655377\pi\)
−0.468977 + 0.883211i \(0.655377\pi\)
\(30\) 0 0
\(31\) 8987.43 1.67970 0.839849 0.542820i \(-0.182643\pi\)
0.839849 + 0.542820i \(0.182643\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1335.03 0.184214
\(36\) 0 0
\(37\) −6000.33 −0.720561 −0.360280 0.932844i \(-0.617319\pi\)
−0.360280 + 0.932844i \(0.617319\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 10745.2 0.998285 0.499142 0.866520i \(-0.333648\pi\)
0.499142 + 0.866520i \(0.333648\pi\)
\(42\) 0 0
\(43\) 10046.6 0.828606 0.414303 0.910139i \(-0.364025\pi\)
0.414303 + 0.910139i \(0.364025\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −23486.6 −1.55087 −0.775435 0.631427i \(-0.782469\pi\)
−0.775435 + 0.631427i \(0.782469\pi\)
\(48\) 0 0
\(49\) 1871.16 0.111332
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −9411.34 −0.460216 −0.230108 0.973165i \(-0.573908\pi\)
−0.230108 + 0.973165i \(0.573908\pi\)
\(54\) 0 0
\(55\) −6381.93 −0.284476
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −44166.8 −1.65183 −0.825915 0.563794i \(-0.809341\pi\)
−0.825915 + 0.563794i \(0.809341\pi\)
\(60\) 0 0
\(61\) −22404.9 −0.770935 −0.385467 0.922721i \(-0.625960\pi\)
−0.385467 + 0.922721i \(0.625960\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 2446.93 0.0718355
\(66\) 0 0
\(67\) −36003.0 −0.979832 −0.489916 0.871770i \(-0.662973\pi\)
−0.489916 + 0.871770i \(0.662973\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −78538.5 −1.84900 −0.924499 0.381184i \(-0.875517\pi\)
−0.924499 + 0.381184i \(0.875517\pi\)
\(72\) 0 0
\(73\) 61305.5 1.34646 0.673229 0.739434i \(-0.264907\pi\)
0.673229 + 0.739434i \(0.264907\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −89288.1 −1.71620
\(78\) 0 0
\(79\) 27490.1 0.495574 0.247787 0.968815i \(-0.420297\pi\)
0.247787 + 0.968815i \(0.420297\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 64806.4 1.03258 0.516289 0.856415i \(-0.327313\pi\)
0.516289 + 0.856415i \(0.327313\pi\)
\(84\) 0 0
\(85\) −2439.85 −0.0366282
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 34652.4 0.463722 0.231861 0.972749i \(-0.425518\pi\)
0.231861 + 0.972749i \(0.425518\pi\)
\(90\) 0 0
\(91\) 34234.5 0.433372
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −17134.1 −0.194784
\(96\) 0 0
\(97\) 16112.3 0.173871 0.0869356 0.996214i \(-0.472293\pi\)
0.0869356 + 0.996214i \(0.472293\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −186939. −1.82346 −0.911731 0.410787i \(-0.865254\pi\)
−0.911731 + 0.410787i \(0.865254\pi\)
\(102\) 0 0
\(103\) −168588. −1.56579 −0.782893 0.622156i \(-0.786257\pi\)
−0.782893 + 0.622156i \(0.786257\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −155131. −1.30991 −0.654953 0.755669i \(-0.727312\pi\)
−0.654953 + 0.755669i \(0.727312\pi\)
\(108\) 0 0
\(109\) −115289. −0.929439 −0.464720 0.885458i \(-0.653845\pi\)
−0.464720 + 0.885458i \(0.653845\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −125388. −0.923759 −0.461880 0.886943i \(-0.652825\pi\)
−0.461880 + 0.886943i \(0.652825\pi\)
\(114\) 0 0
\(115\) 16165.6 0.113985
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −34135.4 −0.220972
\(120\) 0 0
\(121\) 265777. 1.65027
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −60120.6 −0.344151
\(126\) 0 0
\(127\) 17459.4 0.0960548 0.0480274 0.998846i \(-0.484707\pi\)
0.0480274 + 0.998846i \(0.484707\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 28928.1 0.147279 0.0736395 0.997285i \(-0.476539\pi\)
0.0736395 + 0.997285i \(0.476539\pi\)
\(132\) 0 0
\(133\) −239720. −1.17510
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −408554. −1.85972 −0.929862 0.367910i \(-0.880074\pi\)
−0.929862 + 0.367910i \(0.880074\pi\)
\(138\) 0 0
\(139\) 289155. 1.26939 0.634693 0.772765i \(-0.281127\pi\)
0.634693 + 0.772765i \(0.281127\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −163653. −0.669243
\(144\) 0 0
\(145\) −41495.6 −0.163901
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 339.345 0.00125221 0.000626104 1.00000i \(-0.499801\pi\)
0.000626104 1.00000i \(0.499801\pi\)
\(150\) 0 0
\(151\) 357474. 1.27586 0.637928 0.770096i \(-0.279792\pi\)
0.637928 + 0.770096i \(0.279792\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 87793.2 0.293516
\(156\) 0 0
\(157\) −752.621 −0.00243684 −0.00121842 0.999999i \(-0.500388\pi\)
−0.00121842 + 0.999999i \(0.500388\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 226169. 0.687653
\(162\) 0 0
\(163\) −358488. −1.05683 −0.528416 0.848986i \(-0.677214\pi\)
−0.528416 + 0.848986i \(0.677214\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 493751. 1.36999 0.684994 0.728549i \(-0.259805\pi\)
0.684994 + 0.728549i \(0.259805\pi\)
\(168\) 0 0
\(169\) −308546. −0.831004
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −167849. −0.426387 −0.213193 0.977010i \(-0.568386\pi\)
−0.213193 + 0.977010i \(0.568386\pi\)
\(174\) 0 0
\(175\) −414047. −1.02201
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 483862. 1.12873 0.564364 0.825526i \(-0.309122\pi\)
0.564364 + 0.825526i \(0.309122\pi\)
\(180\) 0 0
\(181\) 74732.3 0.169555 0.0847777 0.996400i \(-0.472982\pi\)
0.0847777 + 0.996400i \(0.472982\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −58613.8 −0.125913
\(186\) 0 0
\(187\) 163179. 0.341240
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 594260. 1.17867 0.589337 0.807888i \(-0.299389\pi\)
0.589337 + 0.807888i \(0.299389\pi\)
\(192\) 0 0
\(193\) −89899.6 −0.173726 −0.0868630 0.996220i \(-0.527684\pi\)
−0.0868630 + 0.996220i \(0.527684\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −425161. −0.780527 −0.390263 0.920703i \(-0.627616\pi\)
−0.390263 + 0.920703i \(0.627616\pi\)
\(198\) 0 0
\(199\) 374339. 0.670089 0.335044 0.942202i \(-0.391249\pi\)
0.335044 + 0.942202i \(0.391249\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −580555. −0.988788
\(204\) 0 0
\(205\) 104964. 0.174443
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1.14594e6 1.81467
\(210\) 0 0
\(211\) −164605. −0.254529 −0.127265 0.991869i \(-0.540620\pi\)
−0.127265 + 0.991869i \(0.540620\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 98139.7 0.144793
\(216\) 0 0
\(217\) 1.22829e6 1.77073
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −62565.4 −0.0861695
\(222\) 0 0
\(223\) −324678. −0.437211 −0.218605 0.975813i \(-0.570151\pi\)
−0.218605 + 0.975813i \(0.570151\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 709768. 0.914222 0.457111 0.889410i \(-0.348884\pi\)
0.457111 + 0.889410i \(0.348884\pi\)
\(228\) 0 0
\(229\) −253906. −0.319952 −0.159976 0.987121i \(-0.551142\pi\)
−0.159976 + 0.987121i \(0.551142\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 557666. 0.672952 0.336476 0.941692i \(-0.390765\pi\)
0.336476 + 0.941692i \(0.390765\pi\)
\(234\) 0 0
\(235\) −229427. −0.271004
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 532295. 0.602778 0.301389 0.953501i \(-0.402550\pi\)
0.301389 + 0.953501i \(0.402550\pi\)
\(240\) 0 0
\(241\) 665089. 0.737627 0.368814 0.929503i \(-0.379764\pi\)
0.368814 + 0.929503i \(0.379764\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 18278.3 0.0194546
\(246\) 0 0
\(247\) −439373. −0.458238
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 906446. 0.908150 0.454075 0.890963i \(-0.349970\pi\)
0.454075 + 0.890963i \(0.349970\pi\)
\(252\) 0 0
\(253\) −1.08117e6 −1.06192
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 724841. 0.684557 0.342279 0.939598i \(-0.388801\pi\)
0.342279 + 0.939598i \(0.388801\pi\)
\(258\) 0 0
\(259\) −820053. −0.759613
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −252523. −0.225119 −0.112560 0.993645i \(-0.535905\pi\)
−0.112560 + 0.993645i \(0.535905\pi\)
\(264\) 0 0
\(265\) −91934.2 −0.0804197
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 191107. 0.161026 0.0805131 0.996754i \(-0.474344\pi\)
0.0805131 + 0.996754i \(0.474344\pi\)
\(270\) 0 0
\(271\) 86694.8 0.0717084 0.0358542 0.999357i \(-0.488585\pi\)
0.0358542 + 0.999357i \(0.488585\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.97929e6 1.57825
\(276\) 0 0
\(277\) 1.27048e6 0.994873 0.497437 0.867500i \(-0.334275\pi\)
0.497437 + 0.867500i \(0.334275\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 56829.7 0.0429348 0.0214674 0.999770i \(-0.493166\pi\)
0.0214674 + 0.999770i \(0.493166\pi\)
\(282\) 0 0
\(283\) 1.35360e6 1.00467 0.502335 0.864673i \(-0.332475\pi\)
0.502335 + 0.864673i \(0.332475\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1.46852e6 1.05239
\(288\) 0 0
\(289\) −1.35747e6 −0.956063
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 527702. 0.359103 0.179552 0.983749i \(-0.442535\pi\)
0.179552 + 0.983749i \(0.442535\pi\)
\(294\) 0 0
\(295\) −431440. −0.288646
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 414537. 0.268155
\(300\) 0 0
\(301\) 1.37305e6 0.873515
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −218861. −0.134716
\(306\) 0 0
\(307\) 1.15348e6 0.698497 0.349249 0.937030i \(-0.386437\pi\)
0.349249 + 0.937030i \(0.386437\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1.51767e6 0.889765 0.444883 0.895589i \(-0.353245\pi\)
0.444883 + 0.895589i \(0.353245\pi\)
\(312\) 0 0
\(313\) −1.95992e6 −1.13078 −0.565388 0.824825i \(-0.691274\pi\)
−0.565388 + 0.824825i \(0.691274\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.83228e6 −1.02410 −0.512052 0.858955i \(-0.671114\pi\)
−0.512052 + 0.858955i \(0.671114\pi\)
\(318\) 0 0
\(319\) 2.77525e6 1.52695
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 438100. 0.233651
\(324\) 0 0
\(325\) −758891. −0.398539
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −3.20987e6 −1.63492
\(330\) 0 0
\(331\) −720112. −0.361269 −0.180634 0.983550i \(-0.557815\pi\)
−0.180634 + 0.983550i \(0.557815\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −351693. −0.171219
\(336\) 0 0
\(337\) −3.10867e6 −1.49107 −0.745537 0.666464i \(-0.767807\pi\)
−0.745537 + 0.666464i \(0.767807\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −5.87168e6 −2.73449
\(342\) 0 0
\(343\) −2.04125e6 −0.936831
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −272068. −0.121298 −0.0606490 0.998159i \(-0.519317\pi\)
−0.0606490 + 0.998159i \(0.519317\pi\)
\(348\) 0 0
\(349\) 3.02049e6 1.32744 0.663718 0.747983i \(-0.268978\pi\)
0.663718 + 0.747983i \(0.268978\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −1.05389e6 −0.450151 −0.225075 0.974341i \(-0.572263\pi\)
−0.225075 + 0.974341i \(0.572263\pi\)
\(354\) 0 0
\(355\) −767198. −0.323100
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 4.26085e6 1.74486 0.872430 0.488739i \(-0.162543\pi\)
0.872430 + 0.488739i \(0.162543\pi\)
\(360\) 0 0
\(361\) 600514. 0.242524
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 598860. 0.235284
\(366\) 0 0
\(367\) −311300. −0.120646 −0.0603231 0.998179i \(-0.519213\pi\)
−0.0603231 + 0.998179i \(0.519213\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −1.28623e6 −0.485159
\(372\) 0 0
\(373\) −2.27536e6 −0.846794 −0.423397 0.905944i \(-0.639162\pi\)
−0.423397 + 0.905944i \(0.639162\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −1.06408e6 −0.385585
\(378\) 0 0
\(379\) 3.28710e6 1.17548 0.587739 0.809050i \(-0.300018\pi\)
0.587739 + 0.809050i \(0.300018\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −2.24672e6 −0.782621 −0.391311 0.920259i \(-0.627978\pi\)
−0.391311 + 0.920259i \(0.627978\pi\)
\(384\) 0 0
\(385\) −872206. −0.299893
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 1.36745e6 0.458180 0.229090 0.973405i \(-0.426425\pi\)
0.229090 + 0.973405i \(0.426425\pi\)
\(390\) 0 0
\(391\) −413337. −0.136729
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 268535. 0.0865982
\(396\) 0 0
\(397\) 1.52652e6 0.486099 0.243050 0.970014i \(-0.421852\pi\)
0.243050 + 0.970014i \(0.421852\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −4.73997e6 −1.47202 −0.736011 0.676969i \(-0.763293\pi\)
−0.736011 + 0.676969i \(0.763293\pi\)
\(402\) 0 0
\(403\) 2.25130e6 0.690510
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 3.92014e6 1.17305
\(408\) 0 0
\(409\) 956937. 0.282862 0.141431 0.989948i \(-0.454830\pi\)
0.141431 + 0.989948i \(0.454830\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −6.03619e6 −1.74136
\(414\) 0 0
\(415\) 633057. 0.180436
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −1.77084e6 −0.492769 −0.246384 0.969172i \(-0.579243\pi\)
−0.246384 + 0.969172i \(0.579243\pi\)
\(420\) 0 0
\(421\) 3.08529e6 0.848381 0.424190 0.905573i \(-0.360559\pi\)
0.424190 + 0.905573i \(0.360559\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 756692. 0.203211
\(426\) 0 0
\(427\) −3.06203e6 −0.812718
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −2.16873e6 −0.562356 −0.281178 0.959656i \(-0.590725\pi\)
−0.281178 + 0.959656i \(0.590725\pi\)
\(432\) 0 0
\(433\) 6.69677e6 1.71651 0.858253 0.513226i \(-0.171550\pi\)
0.858253 + 0.513226i \(0.171550\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −2.90271e6 −0.727109
\(438\) 0 0
\(439\) −6.46259e6 −1.60046 −0.800231 0.599691i \(-0.795290\pi\)
−0.800231 + 0.599691i \(0.795290\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −1.75472e6 −0.424815 −0.212407 0.977181i \(-0.568130\pi\)
−0.212407 + 0.977181i \(0.568130\pi\)
\(444\) 0 0
\(445\) 338500. 0.0810323
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 515131. 0.120587 0.0602937 0.998181i \(-0.480796\pi\)
0.0602937 + 0.998181i \(0.480796\pi\)
\(450\) 0 0
\(451\) −7.02006e6 −1.62517
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 334418. 0.0757288
\(456\) 0 0
\(457\) −4.93389e6 −1.10509 −0.552546 0.833482i \(-0.686344\pi\)
−0.552546 + 0.833482i \(0.686344\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −8.25863e6 −1.80991 −0.904953 0.425512i \(-0.860094\pi\)
−0.904953 + 0.425512i \(0.860094\pi\)
\(462\) 0 0
\(463\) 2.19085e6 0.474964 0.237482 0.971392i \(-0.423678\pi\)
0.237482 + 0.971392i \(0.423678\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −2.29374e6 −0.486691 −0.243345 0.969940i \(-0.578245\pi\)
−0.243345 + 0.969940i \(0.578245\pi\)
\(468\) 0 0
\(469\) −4.92046e6 −1.03294
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −6.56366e6 −1.34894
\(474\) 0 0
\(475\) 5.31396e6 1.08065
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −92886.5 −0.0184975 −0.00924876 0.999957i \(-0.502944\pi\)
−0.00924876 + 0.999957i \(0.502944\pi\)
\(480\) 0 0
\(481\) −1.50304e6 −0.296217
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 157392. 0.0303828
\(486\) 0 0
\(487\) −1.13899e6 −0.217620 −0.108810 0.994063i \(-0.534704\pi\)
−0.108810 + 0.994063i \(0.534704\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 8.72946e6 1.63412 0.817060 0.576553i \(-0.195603\pi\)
0.817060 + 0.576553i \(0.195603\pi\)
\(492\) 0 0
\(493\) 1.06100e6 0.196606
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.07337e7 −1.94921
\(498\) 0 0
\(499\) −1.47762e6 −0.265651 −0.132825 0.991139i \(-0.542405\pi\)
−0.132825 + 0.991139i \(0.542405\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 743514. 0.131029 0.0655147 0.997852i \(-0.479131\pi\)
0.0655147 + 0.997852i \(0.479131\pi\)
\(504\) 0 0
\(505\) −1.82610e6 −0.318638
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 8.87120e6 1.51771 0.758854 0.651261i \(-0.225760\pi\)
0.758854 + 0.651261i \(0.225760\pi\)
\(510\) 0 0
\(511\) 8.37851e6 1.41943
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.64684e6 −0.273610
\(516\) 0 0
\(517\) 1.53443e7 2.52476
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 2.00935e6 0.324311 0.162155 0.986765i \(-0.448155\pi\)
0.162155 + 0.986765i \(0.448155\pi\)
\(522\) 0 0
\(523\) 6.39895e6 1.02295 0.511475 0.859298i \(-0.329099\pi\)
0.511475 + 0.859298i \(0.329099\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2.24478e6 −0.352084
\(528\) 0 0
\(529\) −3.69771e6 −0.574505
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 2.69160e6 0.410387
\(534\) 0 0
\(535\) −1.51539e6 −0.228897
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1.22247e6 −0.181245
\(540\) 0 0
\(541\) −1.26335e7 −1.85580 −0.927899 0.372832i \(-0.878387\pi\)
−0.927899 + 0.372832i \(0.878387\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −1.12619e6 −0.162413
\(546\) 0 0
\(547\) −1.10355e7 −1.57697 −0.788487 0.615052i \(-0.789135\pi\)
−0.788487 + 0.615052i \(0.789135\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 7.45097e6 1.04552
\(552\) 0 0
\(553\) 3.75702e6 0.522433
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 1.08374e7 1.48009 0.740046 0.672557i \(-0.234804\pi\)
0.740046 + 0.672557i \(0.234804\pi\)
\(558\) 0 0
\(559\) 2.51661e6 0.340633
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 3.31377e6 0.440607 0.220303 0.975431i \(-0.429295\pi\)
0.220303 + 0.975431i \(0.429295\pi\)
\(564\) 0 0
\(565\) −1.22484e6 −0.161421
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 1.54951e6 0.200639 0.100319 0.994955i \(-0.468014\pi\)
0.100319 + 0.994955i \(0.468014\pi\)
\(570\) 0 0
\(571\) 3.19114e6 0.409595 0.204798 0.978804i \(-0.434346\pi\)
0.204798 + 0.978804i \(0.434346\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −5.01359e6 −0.632381
\(576\) 0 0
\(577\) 9.55234e6 1.19446 0.597228 0.802072i \(-0.296269\pi\)
0.597228 + 0.802072i \(0.296269\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 8.85696e6 1.08854
\(582\) 0 0
\(583\) 6.14863e6 0.749216
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.12882e7 1.35217 0.676083 0.736826i \(-0.263676\pi\)
0.676083 + 0.736826i \(0.263676\pi\)
\(588\) 0 0
\(589\) −1.57642e7 −1.87234
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 7.91815e6 0.924671 0.462336 0.886705i \(-0.347012\pi\)
0.462336 + 0.886705i \(0.347012\pi\)
\(594\) 0 0
\(595\) −333449. −0.0386133
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 3.21828e6 0.366485 0.183242 0.983068i \(-0.441341\pi\)
0.183242 + 0.983068i \(0.441341\pi\)
\(600\) 0 0
\(601\) −7.48609e6 −0.845413 −0.422706 0.906267i \(-0.638920\pi\)
−0.422706 + 0.906267i \(0.638920\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 2.59623e6 0.288373
\(606\) 0 0
\(607\) −1.01212e7 −1.11497 −0.557483 0.830189i \(-0.688233\pi\)
−0.557483 + 0.830189i \(0.688233\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −5.88325e6 −0.637550
\(612\) 0 0
\(613\) −4.34715e6 −0.467254 −0.233627 0.972326i \(-0.575059\pi\)
−0.233627 + 0.972326i \(0.575059\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1.85918e7 −1.96611 −0.983056 0.183305i \(-0.941320\pi\)
−0.983056 + 0.183305i \(0.941320\pi\)
\(618\) 0 0
\(619\) 1.36603e7 1.43296 0.716478 0.697610i \(-0.245753\pi\)
0.716478 + 0.697610i \(0.245753\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 4.73588e6 0.488855
\(624\) 0 0
\(625\) 8.88015e6 0.909327
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1.49869e6 0.151038
\(630\) 0 0
\(631\) −3.33121e6 −0.333065 −0.166532 0.986036i \(-0.553257\pi\)
−0.166532 + 0.986036i \(0.553257\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 170551. 0.0167849
\(636\) 0 0
\(637\) 468715. 0.0457678
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −2.28954e6 −0.220091 −0.110046 0.993927i \(-0.535100\pi\)
−0.110046 + 0.993927i \(0.535100\pi\)
\(642\) 0 0
\(643\) −6.81039e6 −0.649597 −0.324799 0.945783i \(-0.605297\pi\)
−0.324799 + 0.945783i \(0.605297\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.48250e7 1.39231 0.696153 0.717894i \(-0.254894\pi\)
0.696153 + 0.717894i \(0.254894\pi\)
\(648\) 0 0
\(649\) 2.88551e7 2.68912
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 8.12712e6 0.745854 0.372927 0.927861i \(-0.378354\pi\)
0.372927 + 0.927861i \(0.378354\pi\)
\(654\) 0 0
\(655\) 282582. 0.0257360
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 8.15231e6 0.731253 0.365626 0.930762i \(-0.380855\pi\)
0.365626 + 0.930762i \(0.380855\pi\)
\(660\) 0 0
\(661\) −8.75916e6 −0.779756 −0.389878 0.920867i \(-0.627483\pi\)
−0.389878 + 0.920867i \(0.627483\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −2.34169e6 −0.205341
\(666\) 0 0
\(667\) −7.02980e6 −0.611827
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1.46376e7 1.25505
\(672\) 0 0
\(673\) 8.53489e6 0.726374 0.363187 0.931716i \(-0.381689\pi\)
0.363187 + 0.931716i \(0.381689\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 1.51632e7 1.27151 0.635755 0.771891i \(-0.280689\pi\)
0.635755 + 0.771891i \(0.280689\pi\)
\(678\) 0 0
\(679\) 2.20203e6 0.183295
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.33221e7 1.09275 0.546376 0.837540i \(-0.316007\pi\)
0.546376 + 0.837540i \(0.316007\pi\)
\(684\) 0 0
\(685\) −3.99094e6 −0.324974
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −2.35748e6 −0.189191
\(690\) 0 0
\(691\) −1.96348e6 −0.156434 −0.0782169 0.996936i \(-0.524923\pi\)
−0.0782169 + 0.996936i \(0.524923\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 2.82459e6 0.221816
\(696\) 0 0
\(697\) −2.68381e6 −0.209252
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −2.36605e7 −1.81856 −0.909282 0.416180i \(-0.863369\pi\)
−0.909282 + 0.416180i \(0.863369\pi\)
\(702\) 0 0
\(703\) 1.05247e7 0.803199
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −2.55486e7 −1.92229
\(708\) 0 0
\(709\) −1.67839e7 −1.25394 −0.626970 0.779043i \(-0.715705\pi\)
−0.626970 + 0.779043i \(0.715705\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 1.48731e7 1.09567
\(714\) 0 0
\(715\) −1.59863e6 −0.116946
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 5.89621e6 0.425355 0.212677 0.977123i \(-0.431782\pi\)
0.212677 + 0.977123i \(0.431782\pi\)
\(720\) 0 0
\(721\) −2.30405e7 −1.65065
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 1.28694e7 0.909313
\(726\) 0 0
\(727\) −1.03092e7 −0.723415 −0.361708 0.932292i \(-0.617806\pi\)
−0.361708 + 0.932292i \(0.617806\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −2.50932e6 −0.173685
\(732\) 0 0
\(733\) 1.53374e7 1.05436 0.527182 0.849752i \(-0.323249\pi\)
0.527182 + 0.849752i \(0.323249\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 2.35215e7 1.59513
\(738\) 0 0
\(739\) −1.97929e6 −0.133321 −0.0666606 0.997776i \(-0.521234\pi\)
−0.0666606 + 0.997776i \(0.521234\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 2.89747e7 1.92552 0.962758 0.270363i \(-0.0871437\pi\)
0.962758 + 0.270363i \(0.0871437\pi\)
\(744\) 0 0
\(745\) 3314.88 0.000218815 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −2.12015e7 −1.38090
\(750\) 0 0
\(751\) 1.04365e7 0.675238 0.337619 0.941283i \(-0.390379\pi\)
0.337619 + 0.941283i \(0.390379\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 3.49196e6 0.222947
\(756\) 0 0
\(757\) 1.51464e7 0.960661 0.480331 0.877087i \(-0.340517\pi\)
0.480331 + 0.877087i \(0.340517\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 2.21800e7 1.38835 0.694176 0.719806i \(-0.255769\pi\)
0.694176 + 0.719806i \(0.255769\pi\)
\(762\) 0 0
\(763\) −1.57563e7 −0.979812
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −1.10635e7 −0.679054
\(768\) 0 0
\(769\) −6.42382e6 −0.391722 −0.195861 0.980632i \(-0.562750\pi\)
−0.195861 + 0.980632i \(0.562750\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −2.34346e6 −0.141062 −0.0705308 0.997510i \(-0.522469\pi\)
−0.0705308 + 0.997510i \(0.522469\pi\)
\(774\) 0 0
\(775\) −2.72281e7 −1.62841
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1.88474e7 −1.11277
\(780\) 0 0
\(781\) 5.13108e7 3.01010
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −7351.93 −0.000425821 0
\(786\) 0 0
\(787\) 2.85081e7 1.64071 0.820354 0.571856i \(-0.193776\pi\)
0.820354 + 0.571856i \(0.193776\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −1.71365e7 −0.973824
\(792\) 0 0
\(793\) −5.61228e6 −0.316925
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −7.54995e6 −0.421016 −0.210508 0.977592i \(-0.567512\pi\)
−0.210508 + 0.977592i \(0.567512\pi\)
\(798\) 0 0
\(799\) 5.86621e6 0.325080
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −4.00522e7 −2.19198
\(804\) 0 0
\(805\) 2.20932e6 0.120163
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −5.98225e6 −0.321361 −0.160680 0.987006i \(-0.551369\pi\)
−0.160680 + 0.987006i \(0.551369\pi\)
\(810\) 0 0
\(811\) 9.22339e6 0.492423 0.246212 0.969216i \(-0.420814\pi\)
0.246212 + 0.969216i \(0.420814\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −3.50187e6 −0.184674
\(816\) 0 0
\(817\) −1.76220e7 −0.923636
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −1.29602e7 −0.671049 −0.335525 0.942031i \(-0.608914\pi\)
−0.335525 + 0.942031i \(0.608914\pi\)
\(822\) 0 0
\(823\) −7.53351e6 −0.387702 −0.193851 0.981031i \(-0.562098\pi\)
−0.193851 + 0.981031i \(0.562098\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −1.59694e7 −0.811942 −0.405971 0.913886i \(-0.633067\pi\)
−0.405971 + 0.913886i \(0.633067\pi\)
\(828\) 0 0
\(829\) −2.71049e7 −1.36981 −0.684907 0.728631i \(-0.740157\pi\)
−0.684907 + 0.728631i \(0.740157\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −467357. −0.0233365
\(834\) 0 0
\(835\) 4.82318e6 0.239396
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −2.76275e7 −1.35499 −0.677497 0.735526i \(-0.736935\pi\)
−0.677497 + 0.735526i \(0.736935\pi\)
\(840\) 0 0
\(841\) −2.46633e6 −0.120243
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −3.01401e6 −0.145212
\(846\) 0 0
\(847\) 3.63233e7 1.73971
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −9.92982e6 −0.470021
\(852\) 0 0
\(853\) −1.93396e7 −0.910072 −0.455036 0.890473i \(-0.650374\pi\)
−0.455036 + 0.890473i \(0.650374\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 2.74898e7 1.27855 0.639277 0.768977i \(-0.279234\pi\)
0.639277 + 0.768977i \(0.279234\pi\)
\(858\) 0 0
\(859\) 4.66389e6 0.215658 0.107829 0.994169i \(-0.465610\pi\)
0.107829 + 0.994169i \(0.465610\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 3.10059e6 0.141716 0.0708578 0.997486i \(-0.477426\pi\)
0.0708578 + 0.997486i \(0.477426\pi\)
\(864\) 0 0
\(865\) −1.63962e6 −0.0745082
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −1.79599e7 −0.806777
\(870\) 0 0
\(871\) −9.01853e6 −0.402801
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −8.21657e6 −0.362803
\(876\) 0 0
\(877\) −1.64543e7 −0.722405 −0.361202 0.932487i \(-0.617634\pi\)
−0.361202 + 0.932487i \(0.617634\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −2.06332e6 −0.0895626 −0.0447813 0.998997i \(-0.514259\pi\)
−0.0447813 + 0.998997i \(0.514259\pi\)
\(882\) 0 0
\(883\) −2.00336e7 −0.864683 −0.432342 0.901710i \(-0.642313\pi\)
−0.432342 + 0.901710i \(0.642313\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −2.83243e7 −1.20879 −0.604393 0.796686i \(-0.706584\pi\)
−0.604393 + 0.796686i \(0.706584\pi\)
\(888\) 0 0
\(889\) 2.38614e6 0.101261
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 4.11961e7 1.72873
\(894\) 0 0
\(895\) 4.72658e6 0.197237
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −3.81779e7 −1.57548
\(900\) 0 0
\(901\) 2.35066e6 0.0964666
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 730018. 0.0296287
\(906\) 0 0
\(907\) −2.80750e7 −1.13319 −0.566593 0.823998i \(-0.691739\pi\)
−0.566593 + 0.823998i \(0.691739\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 2.71729e7 1.08477 0.542387 0.840128i \(-0.317520\pi\)
0.542387 + 0.840128i \(0.317520\pi\)
\(912\) 0 0
\(913\) −4.23394e7 −1.68100
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 3.95354e6 0.155261
\(918\) 0 0
\(919\) 4.48360e7 1.75121 0.875604 0.483029i \(-0.160464\pi\)
0.875604 + 0.483029i \(0.160464\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −1.96734e7 −0.760108
\(924\) 0 0
\(925\) 1.81785e7 0.698558
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 1.57318e6 0.0598054 0.0299027 0.999553i \(-0.490480\pi\)
0.0299027 + 0.999553i \(0.490480\pi\)
\(930\) 0 0
\(931\) −3.28207e6 −0.124101
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 1.59400e6 0.0596293
\(936\) 0 0
\(937\) 2.08278e6 0.0774986 0.0387493 0.999249i \(-0.487663\pi\)
0.0387493 + 0.999249i \(0.487663\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 8.30903e6 0.305898 0.152949 0.988234i \(-0.451123\pi\)
0.152949 + 0.988234i \(0.451123\pi\)
\(942\) 0 0
\(943\) 1.77820e7 0.651181
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −4.69140e7 −1.69992 −0.849958 0.526851i \(-0.823373\pi\)
−0.849958 + 0.526851i \(0.823373\pi\)
\(948\) 0 0
\(949\) 1.53567e7 0.553517
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −1.19875e7 −0.427559 −0.213779 0.976882i \(-0.568577\pi\)
−0.213779 + 0.976882i \(0.568577\pi\)
\(954\) 0 0
\(955\) 5.80500e6 0.205965
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −5.58363e7 −1.96052
\(960\) 0 0
\(961\) 5.21448e7 1.82139
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −878179. −0.0303574
\(966\) 0 0
\(967\) −2.88381e7 −0.991745 −0.495872 0.868395i \(-0.665152\pi\)
−0.495872 + 0.868395i \(0.665152\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −1.30199e7 −0.443158 −0.221579 0.975142i \(-0.571121\pi\)
−0.221579 + 0.975142i \(0.571121\pi\)
\(972\) 0 0
\(973\) 3.95182e7 1.33818
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 1.82908e7 0.613050 0.306525 0.951863i \(-0.400834\pi\)
0.306525 + 0.951863i \(0.400834\pi\)
\(978\) 0 0
\(979\) −2.26391e7 −0.754924
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −969801. −0.0320110 −0.0160055 0.999872i \(-0.505095\pi\)
−0.0160055 + 0.999872i \(0.505095\pi\)
\(984\) 0 0
\(985\) −4.15316e6 −0.136392
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 1.66259e7 0.540500
\(990\) 0 0
\(991\) −5.04589e7 −1.63213 −0.816063 0.577962i \(-0.803848\pi\)
−0.816063 + 0.577962i \(0.803848\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 3.65671e6 0.117093
\(996\) 0 0
\(997\) 1.78125e7 0.567528 0.283764 0.958894i \(-0.408417\pi\)
0.283764 + 0.958894i \(0.408417\pi\)
\(998\) 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 324.6.a.d.1.3 5
3.2 odd 2 324.6.a.e.1.3 5
9.2 odd 6 36.6.e.a.13.2 10
9.4 even 3 108.6.e.a.73.3 10
9.5 odd 6 36.6.e.a.25.2 yes 10
9.7 even 3 108.6.e.a.37.3 10
36.7 odd 6 432.6.i.d.145.3 10
36.11 even 6 144.6.i.d.49.4 10
36.23 even 6 144.6.i.d.97.4 10
36.31 odd 6 432.6.i.d.289.3 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
36.6.e.a.13.2 10 9.2 odd 6
36.6.e.a.25.2 yes 10 9.5 odd 6
108.6.e.a.37.3 10 9.7 even 3
108.6.e.a.73.3 10 9.4 even 3
144.6.i.d.49.4 10 36.11 even 6
144.6.i.d.97.4 10 36.23 even 6
324.6.a.d.1.3 5 1.1 even 1 trivial
324.6.a.e.1.3 5 3.2 odd 2
432.6.i.d.145.3 10 36.7 odd 6
432.6.i.d.289.3 10 36.31 odd 6