Properties

Label 108.6.a.d.1.2
Level 108
Weight 6
Character 108.1
Self dual yes
Analytic conductor 17.321
Analytic rank 0
Dimension 2
CM no
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 108.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(17.3214525398\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{6}) \)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.44949\) of \(x^{2} - 6\)
Character \(\chi\) \(=\) 108.1

$q$-expansion

\(f(q)\) \(=\) \(q+88.1816 q^{5} +29.0000 q^{7} +O(q^{10})\) \(q+88.1816 q^{5} +29.0000 q^{7} +88.1816 q^{11} +329.000 q^{13} -2204.54 q^{17} +1799.00 q^{19} +3615.45 q^{23} +4651.00 q^{25} +1410.91 q^{29} +5228.00 q^{31} +2557.27 q^{35} +8783.00 q^{37} -15520.0 q^{41} +19976.0 q^{43} -10846.3 q^{47} -15966.0 q^{49} +29452.7 q^{53} +7776.00 q^{55} +5731.81 q^{59} -1069.00 q^{61} +29011.8 q^{65} -62077.0 q^{67} -46383.5 q^{71} -48079.0 q^{73} +2557.27 q^{77} +49979.0 q^{79} -57670.8 q^{83} -194400. q^{85} -87917.1 q^{89} +9541.00 q^{91} +158639. q^{95} +12917.0 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 58q^{7} + O(q^{10}) \) \( 2q + 58q^{7} + 658q^{13} + 3598q^{19} + 9302q^{25} + 10456q^{31} + 17566q^{37} + 39952q^{43} - 31932q^{49} + 15552q^{55} - 2138q^{61} - 124154q^{67} - 96158q^{73} + 99958q^{79} - 388800q^{85} + 19082q^{91} + 25834q^{97} + O(q^{100}) \)

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
\(5\) 88.1816 1.57744 0.788720 0.614752i \(-0.210744\pi\)
0.788720 + 0.614752i \(0.210744\pi\)
\(6\) 0 0
\(7\) 29.0000 0.223693 0.111847 0.993725i \(-0.464323\pi\)
0.111847 + 0.993725i \(0.464323\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 88.1816 0.219734 0.109867 0.993946i \(-0.464958\pi\)
0.109867 + 0.993946i \(0.464958\pi\)
\(12\) 0 0
\(13\) 329.000 0.539930 0.269965 0.962870i \(-0.412988\pi\)
0.269965 + 0.962870i \(0.412988\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2204.54 −1.85010 −0.925051 0.379842i \(-0.875978\pi\)
−0.925051 + 0.379842i \(0.875978\pi\)
\(18\) 0 0
\(19\) 1799.00 1.14327 0.571633 0.820510i \(-0.306310\pi\)
0.571633 + 0.820510i \(0.306310\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3615.45 1.42509 0.712545 0.701626i \(-0.247542\pi\)
0.712545 + 0.701626i \(0.247542\pi\)
\(24\) 0 0
\(25\) 4651.00 1.48832
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 1410.91 0.311532 0.155766 0.987794i \(-0.450215\pi\)
0.155766 + 0.987794i \(0.450215\pi\)
\(30\) 0 0
\(31\) 5228.00 0.977083 0.488541 0.872541i \(-0.337529\pi\)
0.488541 + 0.872541i \(0.337529\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2557.27 0.352863
\(36\) 0 0
\(37\) 8783.00 1.05472 0.527362 0.849641i \(-0.323181\pi\)
0.527362 + 0.849641i \(0.323181\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −15520.0 −1.44189 −0.720943 0.692994i \(-0.756291\pi\)
−0.720943 + 0.692994i \(0.756291\pi\)
\(42\) 0 0
\(43\) 19976.0 1.64755 0.823773 0.566920i \(-0.191865\pi\)
0.823773 + 0.566920i \(0.191865\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −10846.3 −0.716207 −0.358104 0.933682i \(-0.616577\pi\)
−0.358104 + 0.933682i \(0.616577\pi\)
\(48\) 0 0
\(49\) −15966.0 −0.949961
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 29452.7 1.44024 0.720120 0.693849i \(-0.244087\pi\)
0.720120 + 0.693849i \(0.244087\pi\)
\(54\) 0 0
\(55\) 7776.00 0.346617
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 5731.81 0.214369 0.107184 0.994239i \(-0.465816\pi\)
0.107184 + 0.994239i \(0.465816\pi\)
\(60\) 0 0
\(61\) −1069.00 −0.0367835 −0.0183918 0.999831i \(-0.505855\pi\)
−0.0183918 + 0.999831i \(0.505855\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 29011.8 0.851708
\(66\) 0 0
\(67\) −62077.0 −1.68944 −0.844722 0.535206i \(-0.820234\pi\)
−0.844722 + 0.535206i \(0.820234\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −46383.5 −1.09199 −0.545994 0.837789i \(-0.683848\pi\)
−0.545994 + 0.837789i \(0.683848\pi\)
\(72\) 0 0
\(73\) −48079.0 −1.05596 −0.527981 0.849256i \(-0.677051\pi\)
−0.527981 + 0.849256i \(0.677051\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 2557.27 0.0491529
\(78\) 0 0
\(79\) 49979.0 0.900990 0.450495 0.892779i \(-0.351248\pi\)
0.450495 + 0.892779i \(0.351248\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −57670.8 −0.918884 −0.459442 0.888208i \(-0.651951\pi\)
−0.459442 + 0.888208i \(0.651951\pi\)
\(84\) 0 0
\(85\) −194400. −2.91843
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −87917.1 −1.17652 −0.588259 0.808673i \(-0.700186\pi\)
−0.588259 + 0.808673i \(0.700186\pi\)
\(90\) 0 0
\(91\) 9541.00 0.120779
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 158639. 1.80343
\(96\) 0 0
\(97\) 12917.0 0.139390 0.0696951 0.997568i \(-0.477797\pi\)
0.0696951 + 0.997568i \(0.477797\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 112872. 1.10099 0.550497 0.834837i \(-0.314438\pi\)
0.550497 + 0.834837i \(0.314438\pi\)
\(102\) 0 0
\(103\) −77503.0 −0.719823 −0.359911 0.932987i \(-0.617193\pi\)
−0.359911 + 0.932987i \(0.617193\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 111726. 0.943399 0.471699 0.881759i \(-0.343641\pi\)
0.471699 + 0.881759i \(0.343641\pi\)
\(108\) 0 0
\(109\) −17710.0 −0.142775 −0.0713875 0.997449i \(-0.522743\pi\)
−0.0713875 + 0.997449i \(0.522743\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −251582. −1.85346 −0.926731 0.375725i \(-0.877394\pi\)
−0.926731 + 0.375725i \(0.877394\pi\)
\(114\) 0 0
\(115\) 318816. 2.24800
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −63931.7 −0.413855
\(120\) 0 0
\(121\) −153275. −0.951717
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 134565. 0.770296
\(126\) 0 0
\(127\) 269444. 1.48238 0.741189 0.671296i \(-0.234262\pi\)
0.741189 + 0.671296i \(0.234262\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −154141. −0.784768 −0.392384 0.919801i \(-0.628350\pi\)
−0.392384 + 0.919801i \(0.628350\pi\)
\(132\) 0 0
\(133\) 52171.0 0.255741
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −271864. −1.23751 −0.618757 0.785582i \(-0.712364\pi\)
−0.618757 + 0.785582i \(0.712364\pi\)
\(138\) 0 0
\(139\) 182705. 0.802072 0.401036 0.916062i \(-0.368650\pi\)
0.401036 + 0.916062i \(0.368650\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 29011.8 0.118641
\(144\) 0 0
\(145\) 124416. 0.491424
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 347259. 1.28141 0.640705 0.767787i \(-0.278642\pi\)
0.640705 + 0.767787i \(0.278642\pi\)
\(150\) 0 0
\(151\) 434351. 1.55024 0.775119 0.631815i \(-0.217690\pi\)
0.775119 + 0.631815i \(0.217690\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 461014. 1.54129
\(156\) 0 0
\(157\) −22978.0 −0.0743983 −0.0371992 0.999308i \(-0.511844\pi\)
−0.0371992 + 0.999308i \(0.511844\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 104848. 0.318783
\(162\) 0 0
\(163\) 109961. 0.324168 0.162084 0.986777i \(-0.448179\pi\)
0.162084 + 0.986777i \(0.448179\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −307137. −0.852198 −0.426099 0.904677i \(-0.640112\pi\)
−0.426099 + 0.904677i \(0.640112\pi\)
\(168\) 0 0
\(169\) −263052. −0.708476
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −4232.72 −0.0107524 −0.00537618 0.999986i \(-0.501711\pi\)
−0.00537618 + 0.999986i \(0.501711\pi\)
\(174\) 0 0
\(175\) 134879. 0.332927
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −831906. −1.94062 −0.970312 0.241856i \(-0.922244\pi\)
−0.970312 + 0.241856i \(0.922244\pi\)
\(180\) 0 0
\(181\) −327187. −0.742334 −0.371167 0.928566i \(-0.621042\pi\)
−0.371167 + 0.928566i \(0.621042\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 774499. 1.66376
\(186\) 0 0
\(187\) −194400. −0.406530
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −468862. −0.929954 −0.464977 0.885323i \(-0.653937\pi\)
−0.464977 + 0.885323i \(0.653937\pi\)
\(192\) 0 0
\(193\) 152231. 0.294178 0.147089 0.989123i \(-0.453010\pi\)
0.147089 + 0.989123i \(0.453010\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −653514. −1.19975 −0.599873 0.800095i \(-0.704782\pi\)
−0.599873 + 0.800095i \(0.704782\pi\)
\(198\) 0 0
\(199\) −645895. −1.15619 −0.578095 0.815969i \(-0.696204\pi\)
−0.578095 + 0.815969i \(0.696204\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 40916.3 0.0696877
\(204\) 0 0
\(205\) −1.36858e6 −2.27449
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 158639. 0.251214
\(210\) 0 0
\(211\) 169637. 0.262310 0.131155 0.991362i \(-0.458131\pi\)
0.131155 + 0.991362i \(0.458131\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.76152e6 2.59891
\(216\) 0 0
\(217\) 151612. 0.218567
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −725294. −0.998926
\(222\) 0 0
\(223\) −691276. −0.930871 −0.465435 0.885082i \(-0.654102\pi\)
−0.465435 + 0.885082i \(0.654102\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 989927. 1.27508 0.637542 0.770416i \(-0.279951\pi\)
0.637542 + 0.770416i \(0.279951\pi\)
\(228\) 0 0
\(229\) 352250. 0.443877 0.221938 0.975061i \(-0.428762\pi\)
0.221938 + 0.975061i \(0.428762\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 381297. 0.460123 0.230062 0.973176i \(-0.426107\pi\)
0.230062 + 0.973176i \(0.426107\pi\)
\(234\) 0 0
\(235\) −956448. −1.12977
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −785698. −0.889736 −0.444868 0.895596i \(-0.646749\pi\)
−0.444868 + 0.895596i \(0.646749\pi\)
\(240\) 0 0
\(241\) −1.20262e6 −1.33379 −0.666894 0.745152i \(-0.732377\pi\)
−0.666894 + 0.745152i \(0.732377\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1.40791e6 −1.49851
\(246\) 0 0
\(247\) 591871. 0.617284
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −416570. −0.417353 −0.208677 0.977985i \(-0.566916\pi\)
−0.208677 + 0.977985i \(0.566916\pi\)
\(252\) 0 0
\(253\) 318816. 0.313140
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −44972.6 −0.0424732 −0.0212366 0.999774i \(-0.506760\pi\)
−0.0212366 + 0.999774i \(0.506760\pi\)
\(258\) 0 0
\(259\) 254707. 0.235935
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −515157. −0.459251 −0.229626 0.973279i \(-0.573750\pi\)
−0.229626 + 0.973279i \(0.573750\pi\)
\(264\) 0 0
\(265\) 2.59718e6 2.27189
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 197439. 0.166361 0.0831805 0.996534i \(-0.473492\pi\)
0.0831805 + 0.996534i \(0.473492\pi\)
\(270\) 0 0
\(271\) −1.01499e6 −0.839530 −0.419765 0.907633i \(-0.637888\pi\)
−0.419765 + 0.907633i \(0.637888\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 410133. 0.327034
\(276\) 0 0
\(277\) −379318. −0.297033 −0.148516 0.988910i \(-0.547450\pi\)
−0.148516 + 0.988910i \(0.547450\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 955889. 0.722174 0.361087 0.932532i \(-0.382406\pi\)
0.361087 + 0.932532i \(0.382406\pi\)
\(282\) 0 0
\(283\) 662912. 0.492028 0.246014 0.969266i \(-0.420879\pi\)
0.246014 + 0.969266i \(0.420879\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −450079. −0.322540
\(288\) 0 0
\(289\) 3.44014e6 2.42288
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 447522. 0.304541 0.152270 0.988339i \(-0.451342\pi\)
0.152270 + 0.988339i \(0.451342\pi\)
\(294\) 0 0
\(295\) 505440. 0.338154
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1.18948e6 0.769449
\(300\) 0 0
\(301\) 579304. 0.368545
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −94266.2 −0.0580238
\(306\) 0 0
\(307\) −1.17362e6 −0.710690 −0.355345 0.934735i \(-0.615637\pi\)
−0.355345 + 0.934735i \(0.615637\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 2.41221e6 1.41421 0.707105 0.707109i \(-0.250001\pi\)
0.707105 + 0.707109i \(0.250001\pi\)
\(312\) 0 0
\(313\) 1.72967e6 0.997934 0.498967 0.866621i \(-0.333713\pi\)
0.498967 + 0.866621i \(0.333713\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.17476e6 0.656598 0.328299 0.944574i \(-0.393525\pi\)
0.328299 + 0.944574i \(0.393525\pi\)
\(318\) 0 0
\(319\) 124416. 0.0684541
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −3.96597e6 −2.11516
\(324\) 0 0
\(325\) 1.53018e6 0.803589
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −314544. −0.160211
\(330\) 0 0
\(331\) 451001. 0.226260 0.113130 0.993580i \(-0.463912\pi\)
0.113130 + 0.993580i \(0.463912\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −5.47405e6 −2.66500
\(336\) 0 0
\(337\) 2.17937e6 1.04534 0.522669 0.852536i \(-0.324936\pi\)
0.522669 + 0.852536i \(0.324936\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 461014. 0.214698
\(342\) 0 0
\(343\) −950417. −0.436193
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −381474. −0.170075 −0.0850376 0.996378i \(-0.527101\pi\)
−0.0850376 + 0.996378i \(0.527101\pi\)
\(348\) 0 0
\(349\) −2.29596e6 −1.00902 −0.504511 0.863405i \(-0.668327\pi\)
−0.504511 + 0.863405i \(0.668327\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 3.24103e6 1.38435 0.692175 0.721730i \(-0.256653\pi\)
0.692175 + 0.721730i \(0.256653\pi\)
\(354\) 0 0
\(355\) −4.09018e6 −1.72255
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 4.15044e6 1.69965 0.849823 0.527068i \(-0.176709\pi\)
0.849823 + 0.527068i \(0.176709\pi\)
\(360\) 0 0
\(361\) 760302. 0.307056
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −4.23968e6 −1.66572
\(366\) 0 0
\(367\) 3.39911e6 1.31735 0.658674 0.752429i \(-0.271118\pi\)
0.658674 + 0.752429i \(0.271118\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 854127. 0.322172
\(372\) 0 0
\(373\) −3.14494e6 −1.17041 −0.585207 0.810884i \(-0.698987\pi\)
−0.585207 + 0.810884i \(0.698987\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 464188. 0.168206
\(378\) 0 0
\(379\) −2.76635e6 −0.989257 −0.494628 0.869105i \(-0.664696\pi\)
−0.494628 + 0.869105i \(0.664696\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 2.24898e6 0.783411 0.391705 0.920091i \(-0.371885\pi\)
0.391705 + 0.920091i \(0.371885\pi\)
\(384\) 0 0
\(385\) 225504. 0.0775358
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 555985. 0.186290 0.0931449 0.995653i \(-0.470308\pi\)
0.0931449 + 0.995653i \(0.470308\pi\)
\(390\) 0 0
\(391\) −7.97040e6 −2.63656
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 4.40723e6 1.42126
\(396\) 0 0
\(397\) 836174. 0.266269 0.133134 0.991098i \(-0.457496\pi\)
0.133134 + 0.991098i \(0.457496\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −2.01283e6 −0.625096 −0.312548 0.949902i \(-0.601183\pi\)
−0.312548 + 0.949902i \(0.601183\pi\)
\(402\) 0 0
\(403\) 1.72001e6 0.527556
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 774499. 0.231758
\(408\) 0 0
\(409\) −1.37271e6 −0.405762 −0.202881 0.979203i \(-0.565030\pi\)
−0.202881 + 0.979203i \(0.565030\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 166222. 0.0479528
\(414\) 0 0
\(415\) −5.08550e6 −1.44949
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −3.54305e6 −0.985921 −0.492961 0.870052i \(-0.664085\pi\)
−0.492961 + 0.870052i \(0.664085\pi\)
\(420\) 0 0
\(421\) −3.48884e6 −0.959347 −0.479673 0.877447i \(-0.659245\pi\)
−0.479673 + 0.877447i \(0.659245\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1.02533e7 −2.75354
\(426\) 0 0
\(427\) −31001.0 −0.00822822
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −5.43754e6 −1.40997 −0.704985 0.709223i \(-0.749046\pi\)
−0.704985 + 0.709223i \(0.749046\pi\)
\(432\) 0 0
\(433\) 4.96023e6 1.27140 0.635699 0.771937i \(-0.280712\pi\)
0.635699 + 0.771937i \(0.280712\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 6.50419e6 1.62926
\(438\) 0 0
\(439\) 5.75071e6 1.42416 0.712082 0.702096i \(-0.247752\pi\)
0.712082 + 0.702096i \(0.247752\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 5.63110e6 1.36328 0.681639 0.731689i \(-0.261268\pi\)
0.681639 + 0.731689i \(0.261268\pi\)
\(444\) 0 0
\(445\) −7.75267e6 −1.85589
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −3.45310e6 −0.808340 −0.404170 0.914684i \(-0.632440\pi\)
−0.404170 + 0.914684i \(0.632440\pi\)
\(450\) 0 0
\(451\) −1.36858e6 −0.316831
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 841341. 0.190521
\(456\) 0 0
\(457\) 1.96799e6 0.440791 0.220395 0.975411i \(-0.429265\pi\)
0.220395 + 0.975411i \(0.429265\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 6.63329e6 1.45371 0.726853 0.686793i \(-0.240982\pi\)
0.726853 + 0.686793i \(0.240982\pi\)
\(462\) 0 0
\(463\) −1.62568e6 −0.352439 −0.176219 0.984351i \(-0.556387\pi\)
−0.176219 + 0.984351i \(0.556387\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −2.48346e6 −0.526944 −0.263472 0.964667i \(-0.584868\pi\)
−0.263472 + 0.964667i \(0.584868\pi\)
\(468\) 0 0
\(469\) −1.80023e6 −0.377917
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1.76152e6 0.362021
\(474\) 0 0
\(475\) 8.36715e6 1.70155
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 1.59626e6 0.317882 0.158941 0.987288i \(-0.449192\pi\)
0.158941 + 0.987288i \(0.449192\pi\)
\(480\) 0 0
\(481\) 2.88961e6 0.569477
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1.13904e6 0.219880
\(486\) 0 0
\(487\) 7.95245e6 1.51942 0.759712 0.650260i \(-0.225340\pi\)
0.759712 + 0.650260i \(0.225340\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 2.05595e6 0.384866 0.192433 0.981310i \(-0.438362\pi\)
0.192433 + 0.981310i \(0.438362\pi\)
\(492\) 0 0
\(493\) −3.11040e6 −0.576367
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.34512e6 −0.244270
\(498\) 0 0
\(499\) 4.93539e6 0.887300 0.443650 0.896200i \(-0.353683\pi\)
0.443650 + 0.896200i \(0.353683\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 836755. 0.147461 0.0737307 0.997278i \(-0.476509\pi\)
0.0737307 + 0.997278i \(0.476509\pi\)
\(504\) 0 0
\(505\) 9.95328e6 1.73675
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 5.90156e6 1.00965 0.504826 0.863221i \(-0.331557\pi\)
0.504826 + 0.863221i \(0.331557\pi\)
\(510\) 0 0
\(511\) −1.39429e6 −0.236212
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −6.83434e6 −1.13548
\(516\) 0 0
\(517\) −956448. −0.157375
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −163577. −0.0264014 −0.0132007 0.999913i \(-0.504202\pi\)
−0.0132007 + 0.999913i \(0.504202\pi\)
\(522\) 0 0
\(523\) −2.95232e6 −0.471965 −0.235983 0.971757i \(-0.575831\pi\)
−0.235983 + 0.971757i \(0.575831\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.15253e7 −1.80770
\(528\) 0 0
\(529\) 6.63511e6 1.03088
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −5.10607e6 −0.778518
\(534\) 0 0
\(535\) 9.85219e6 1.48816
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1.40791e6 −0.208738
\(540\) 0 0
\(541\) −9.58390e6 −1.40783 −0.703913 0.710286i \(-0.748566\pi\)
−0.703913 + 0.710286i \(0.748566\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −1.56170e6 −0.225219
\(546\) 0 0
\(547\) 1.21781e7 1.74025 0.870127 0.492827i \(-0.164036\pi\)
0.870127 + 0.492827i \(0.164036\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 2.53822e6 0.356164
\(552\) 0 0
\(553\) 1.44939e6 0.201545
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 5.32679e6 0.727491 0.363745 0.931498i \(-0.381498\pi\)
0.363745 + 0.931498i \(0.381498\pi\)
\(558\) 0 0
\(559\) 6.57210e6 0.889559
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −8.23899e6 −1.09548 −0.547738 0.836650i \(-0.684511\pi\)
−0.547738 + 0.836650i \(0.684511\pi\)
\(564\) 0 0
\(565\) −2.21849e7 −2.92373
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 7.42410e6 0.961309 0.480655 0.876910i \(-0.340399\pi\)
0.480655 + 0.876910i \(0.340399\pi\)
\(570\) 0 0
\(571\) −288553. −0.0370370 −0.0185185 0.999829i \(-0.505895\pi\)
−0.0185185 + 0.999829i \(0.505895\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.68154e7 2.12099
\(576\) 0 0
\(577\) 933299. 0.116703 0.0583514 0.998296i \(-0.481416\pi\)
0.0583514 + 0.998296i \(0.481416\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1.67245e6 −0.205548
\(582\) 0 0
\(583\) 2.59718e6 0.316469
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 8.15424e6 0.976761 0.488381 0.872631i \(-0.337588\pi\)
0.488381 + 0.872631i \(0.337588\pi\)
\(588\) 0 0
\(589\) 9.40517e6 1.11707
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 2.18214e6 0.254828 0.127414 0.991850i \(-0.459332\pi\)
0.127414 + 0.991850i \(0.459332\pi\)
\(594\) 0 0
\(595\) −5.63760e6 −0.652833
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 2.85991e6 0.325675 0.162838 0.986653i \(-0.447935\pi\)
0.162838 + 0.986653i \(0.447935\pi\)
\(600\) 0 0
\(601\) −1.52613e7 −1.72347 −0.861737 0.507355i \(-0.830623\pi\)
−0.861737 + 0.507355i \(0.830623\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1.35160e7 −1.50128
\(606\) 0 0
\(607\) 2.37356e6 0.261474 0.130737 0.991417i \(-0.458266\pi\)
0.130737 + 0.991417i \(0.458266\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −3.56845e6 −0.386702
\(612\) 0 0
\(613\) −4.21002e6 −0.452515 −0.226258 0.974068i \(-0.572649\pi\)
−0.226258 + 0.974068i \(0.572649\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 3.19579e6 0.337960 0.168980 0.985619i \(-0.445953\pi\)
0.168980 + 0.985619i \(0.445953\pi\)
\(618\) 0 0
\(619\) −1.30206e7 −1.36586 −0.682930 0.730484i \(-0.739294\pi\)
−0.682930 + 0.730484i \(0.739294\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −2.54960e6 −0.263179
\(624\) 0 0
\(625\) −2.66820e6 −0.273224
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −1.93625e7 −1.95135
\(630\) 0 0
\(631\) −1.44185e7 −1.44161 −0.720803 0.693140i \(-0.756227\pi\)
−0.720803 + 0.693140i \(0.756227\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 2.37600e7 2.33837
\(636\) 0 0
\(637\) −5.25281e6 −0.512913
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 3.40822e6 0.327629 0.163815 0.986491i \(-0.447620\pi\)
0.163815 + 0.986491i \(0.447620\pi\)
\(642\) 0 0
\(643\) 1.43017e7 1.36414 0.682070 0.731287i \(-0.261080\pi\)
0.682070 + 0.731287i \(0.261080\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.59891e7 −1.50163 −0.750815 0.660512i \(-0.770339\pi\)
−0.750815 + 0.660512i \(0.770339\pi\)
\(648\) 0 0
\(649\) 505440. 0.0471040
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −1.83032e7 −1.67974 −0.839872 0.542785i \(-0.817370\pi\)
−0.839872 + 0.542785i \(0.817370\pi\)
\(654\) 0 0
\(655\) −1.35924e7 −1.23793
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −4.82724e6 −0.432997 −0.216499 0.976283i \(-0.569464\pi\)
−0.216499 + 0.976283i \(0.569464\pi\)
\(660\) 0 0
\(661\) −1.45127e7 −1.29195 −0.645973 0.763360i \(-0.723548\pi\)
−0.645973 + 0.763360i \(0.723548\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 4.60052e6 0.403416
\(666\) 0 0
\(667\) 5.10106e6 0.443962
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −94266.2 −0.00808257
\(672\) 0 0
\(673\) −5.23273e6 −0.445339 −0.222670 0.974894i \(-0.571477\pi\)
−0.222670 + 0.974894i \(0.571477\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 3.31889e6 0.278305 0.139153 0.990271i \(-0.455562\pi\)
0.139153 + 0.990271i \(0.455562\pi\)
\(678\) 0 0
\(679\) 374593. 0.0311807
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 350257. 0.0287300 0.0143650 0.999897i \(-0.495427\pi\)
0.0143650 + 0.999897i \(0.495427\pi\)
\(684\) 0 0
\(685\) −2.39734e7 −1.95211
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 9.68993e6 0.777629
\(690\) 0 0
\(691\) −9.62745e6 −0.767037 −0.383518 0.923533i \(-0.625288\pi\)
−0.383518 + 0.923533i \(0.625288\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.61112e7 1.26522
\(696\) 0 0
\(697\) 3.42144e7 2.66764
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 1.75325e7 1.34756 0.673782 0.738930i \(-0.264668\pi\)
0.673782 + 0.738930i \(0.264668\pi\)
\(702\) 0 0
\(703\) 1.58006e7 1.20583
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 3.27330e6 0.246285
\(708\) 0 0
\(709\) 5.32159e6 0.397581 0.198790 0.980042i \(-0.436299\pi\)
0.198790 + 0.980042i \(0.436299\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 1.89016e7 1.39243
\(714\) 0 0
\(715\) 2.55830e6 0.187149
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −1.74700e7 −1.26029 −0.630146 0.776477i \(-0.717005\pi\)
−0.630146 + 0.776477i \(0.717005\pi\)
\(720\) 0 0
\(721\) −2.24759e6 −0.161019
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 6.56212e6 0.463660
\(726\) 0 0
\(727\) −5.86973e6 −0.411891 −0.205945 0.978563i \(-0.566027\pi\)
−0.205945 + 0.978563i \(0.566027\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −4.40379e7 −3.04813
\(732\) 0 0
\(733\) −5.60294e6 −0.385173 −0.192587 0.981280i \(-0.561688\pi\)
−0.192587 + 0.981280i \(0.561688\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −5.47405e6 −0.371227
\(738\) 0 0
\(739\) −5.56792e6 −0.375044 −0.187522 0.982260i \(-0.560046\pi\)
−0.187522 + 0.982260i \(0.560046\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 3.78484e6 0.251522 0.125761 0.992061i \(-0.459863\pi\)
0.125761 + 0.992061i \(0.459863\pi\)
\(744\) 0 0
\(745\) 3.06219e7 2.02135
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 3.24006e6 0.211032
\(750\) 0 0
\(751\) −6.76657e6 −0.437793 −0.218897 0.975748i \(-0.570246\pi\)
−0.218897 + 0.975748i \(0.570246\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 3.83018e7 2.44541
\(756\) 0 0
\(757\) 2.46970e7 1.56640 0.783202 0.621768i \(-0.213585\pi\)
0.783202 + 0.621768i \(0.213585\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −3.00870e7 −1.88329 −0.941644 0.336611i \(-0.890719\pi\)
−0.941644 + 0.336611i \(0.890719\pi\)
\(762\) 0 0
\(763\) −513590. −0.0319378
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1.88576e6 0.115744
\(768\) 0 0
\(769\) 3.25118e6 0.198256 0.0991278 0.995075i \(-0.468395\pi\)
0.0991278 + 0.995075i \(0.468395\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −3.30628e6 −0.199017 −0.0995087 0.995037i \(-0.531727\pi\)
−0.0995087 + 0.995037i \(0.531727\pi\)
\(774\) 0 0
\(775\) 2.43154e7 1.45421
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −2.79204e7 −1.64846
\(780\) 0 0
\(781\) −4.09018e6 −0.239946
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −2.02624e6 −0.117359
\(786\) 0 0
\(787\) 1.70156e7 0.979286 0.489643 0.871923i \(-0.337127\pi\)
0.489643 + 0.871923i \(0.337127\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −7.29588e6 −0.414607
\(792\) 0 0
\(793\) −351701. −0.0198605
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −1.31267e7 −0.731999 −0.365999 0.930615i \(-0.619273\pi\)
−0.365999 + 0.930615i \(0.619273\pi\)
\(798\) 0 0
\(799\) 2.39112e7 1.32506
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −4.23968e6 −0.232030
\(804\) 0 0
\(805\) 9.24566e6 0.502862
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 2.90313e7 1.55954 0.779768 0.626068i \(-0.215337\pi\)
0.779768 + 0.626068i \(0.215337\pi\)
\(810\) 0 0
\(811\) −2.70345e7 −1.44333 −0.721666 0.692241i \(-0.756623\pi\)
−0.721666 + 0.692241i \(0.756623\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 9.69654e6 0.511355
\(816\) 0 0
\(817\) 3.59368e7 1.88358
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 2.14836e7 1.11237 0.556185 0.831059i \(-0.312265\pi\)
0.556185 + 0.831059i \(0.312265\pi\)
\(822\) 0 0
\(823\) −2.46282e7 −1.26745 −0.633727 0.773557i \(-0.718476\pi\)
−0.633727 + 0.773557i \(0.718476\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 5.10933e6 0.259777 0.129888 0.991529i \(-0.458538\pi\)
0.129888 + 0.991529i \(0.458538\pi\)
\(828\) 0 0
\(829\) 3.04805e7 1.54041 0.770205 0.637797i \(-0.220154\pi\)
0.770205 + 0.637797i \(0.220154\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 3.51977e7 1.75753
\(834\) 0 0
\(835\) −2.70838e7 −1.34429
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 1.36807e7 0.670969 0.335485 0.942046i \(-0.391100\pi\)
0.335485 + 0.942046i \(0.391100\pi\)
\(840\) 0 0
\(841\) −1.85205e7 −0.902948
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −2.31964e7 −1.11758
\(846\) 0 0
\(847\) −4.44498e6 −0.212893
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 3.17545e7 1.50308
\(852\) 0 0
\(853\) 3.44079e7 1.61914 0.809572 0.587020i \(-0.199699\pi\)
0.809572 + 0.587020i \(0.199699\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −2.73555e7 −1.27231 −0.636155 0.771561i \(-0.719476\pi\)
−0.636155 + 0.771561i \(0.719476\pi\)
\(858\) 0 0
\(859\) −5.37818e6 −0.248687 −0.124343 0.992239i \(-0.539682\pi\)
−0.124343 + 0.992239i \(0.539682\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −2.64604e7 −1.20940 −0.604699 0.796454i \(-0.706707\pi\)
−0.604699 + 0.796454i \(0.706707\pi\)
\(864\) 0 0
\(865\) −373248. −0.0169612
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 4.40723e6 0.197978
\(870\) 0 0
\(871\) −2.04233e7 −0.912181
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 3.90239e6 0.172310
\(876\) 0 0
\(877\) −1.77108e7 −0.777571 −0.388785 0.921328i \(-0.627105\pi\)
−0.388785 + 0.921328i \(0.627105\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −3.04035e7 −1.31973 −0.659864 0.751385i \(-0.729386\pi\)
−0.659864 + 0.751385i \(0.729386\pi\)
\(882\) 0 0
\(883\) 2.93557e7 1.26704 0.633521 0.773726i \(-0.281609\pi\)
0.633521 + 0.773726i \(0.281609\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −2.64563e6 −0.112907 −0.0564533 0.998405i \(-0.517979\pi\)
−0.0564533 + 0.998405i \(0.517979\pi\)
\(888\) 0 0
\(889\) 7.81388e6 0.331598
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −1.95126e7 −0.818815
\(894\) 0 0
\(895\) −7.33588e7 −3.06122
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 7.37622e6 0.304393
\(900\) 0 0
\(901\) −6.49296e7 −2.66459
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −2.88519e7 −1.17099
\(906\) 0 0
\(907\) 2.07393e7 0.837095 0.418548 0.908195i \(-0.362539\pi\)
0.418548 + 0.908195i \(0.362539\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 4.55091e7 1.81678 0.908390 0.418123i \(-0.137312\pi\)
0.908390 + 0.418123i \(0.137312\pi\)
\(912\) 0 0
\(913\) −5.08550e6 −0.201910
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −4.47010e6 −0.175547
\(918\) 0 0
\(919\) 1.89012e7 0.738247 0.369123 0.929380i \(-0.379658\pi\)
0.369123 + 0.929380i \(0.379658\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −1.52602e7 −0.589597
\(924\) 0 0
\(925\) 4.08497e7 1.56977
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −3.08391e7 −1.17236 −0.586181 0.810180i \(-0.699369\pi\)
−0.586181 + 0.810180i \(0.699369\pi\)
\(930\) 0 0
\(931\) −2.87228e7 −1.08606
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −1.71425e7 −0.641277
\(936\) 0 0
\(937\) −5.36296e6 −0.199552 −0.0997758 0.995010i \(-0.531813\pi\)
−0.0997758 + 0.995010i \(0.531813\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 3.76785e7 1.38714 0.693569 0.720390i \(-0.256037\pi\)
0.693569 + 0.720390i \(0.256037\pi\)
\(942\) 0 0
\(943\) −5.61116e7 −2.05482
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 1.96221e7 0.711001 0.355501 0.934676i \(-0.384310\pi\)
0.355501 + 0.934676i \(0.384310\pi\)
\(948\) 0 0
\(949\) −1.58180e7 −0.570146
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 1.36730e7 0.487676 0.243838 0.969816i \(-0.421593\pi\)
0.243838 + 0.969816i \(0.421593\pi\)
\(954\) 0 0
\(955\) −4.13450e7 −1.46695
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −7.88406e6 −0.276824
\(960\) 0 0
\(961\) −1.29717e6 −0.0453093
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 1.34240e7 0.464048
\(966\) 0 0
\(967\) 3.63824e7 1.25119 0.625597 0.780146i \(-0.284855\pi\)
0.625597 + 0.780146i \(0.284855\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 9.46886e6 0.322292 0.161146 0.986931i \(-0.448481\pi\)
0.161146 + 0.986931i \(0.448481\pi\)
\(972\) 0 0
\(973\) 5.29844e6 0.179418
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 3.59889e7 1.20623 0.603117 0.797653i \(-0.293925\pi\)
0.603117 + 0.797653i \(0.293925\pi\)
\(978\) 0 0
\(979\) −7.75267e6 −0.258520
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −2.60556e7 −0.860039 −0.430019 0.902820i \(-0.641493\pi\)
−0.430019 + 0.902820i \(0.641493\pi\)
\(984\) 0 0
\(985\) −5.76279e7 −1.89253
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 7.22222e7 2.34790
\(990\) 0 0
\(991\) 1.92232e7 0.621788 0.310894 0.950445i \(-0.399372\pi\)
0.310894 + 0.950445i \(0.399372\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −5.69561e7 −1.82382
\(996\) 0 0
\(997\) 2.93287e7 0.934448 0.467224 0.884139i \(-0.345254\pi\)
0.467224 + 0.884139i \(0.345254\pi\)
\(998\) 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 108.6.a.d.1.2 yes 2
3.2 odd 2 inner 108.6.a.d.1.1 2
4.3 odd 2 432.6.a.p.1.2 2
9.2 odd 6 324.6.e.e.109.2 4
9.4 even 3 324.6.e.e.217.1 4
9.5 odd 6 324.6.e.e.217.2 4
9.7 even 3 324.6.e.e.109.1 4
12.11 even 2 432.6.a.p.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
108.6.a.d.1.1 2 3.2 odd 2 inner
108.6.a.d.1.2 yes 2 1.1 even 1 trivial
324.6.e.e.109.1 4 9.7 even 3
324.6.e.e.109.2 4 9.2 odd 6
324.6.e.e.217.1 4 9.4 even 3
324.6.e.e.217.2 4 9.5 odd 6
432.6.a.p.1.1 2 12.11 even 2
432.6.a.p.1.2 2 4.3 odd 2