Properties

Label 7800.2.a.bg.1.2
Level $7800$
Weight $2$
Character 7800.1
Self dual yes
Analytic conductor $62.283$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7800.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(62.2833135766\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.788.1
Defining polynomial: \( x^{3} - x^{2} - 7x - 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-0.476452\) of defining polynomial
Character \(\chi\) \(=\) 7800.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} +0.476452 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} +0.476452 q^{7} +1.00000 q^{9} -3.34364 q^{11} +1.00000 q^{13} +1.00000 q^{17} -6.77299 q^{19} -0.476452 q^{21} -4.77299 q^{23} -1.00000 q^{27} +7.59308 q^{29} +7.93672 q^{31} +3.34364 q^{33} +7.82009 q^{37} -1.00000 q^{39} +9.46027 q^{41} +1.82009 q^{43} -9.06953 q^{47} -6.77299 q^{49} -1.00000 q^{51} +9.50736 q^{53} +6.77299 q^{57} +3.16373 q^{59} -9.59308 q^{61} +0.476452 q^{63} -1.34364 q^{67} +4.77299 q^{69} -4.86719 q^{71} -14.4132 q^{73} -1.59308 q^{77} -2.17991 q^{79} +1.00000 q^{81} +9.16373 q^{83} -7.59308 q^{87} -10.5931 q^{89} +0.476452 q^{91} -7.93672 q^{93} +7.04710 q^{97} -3.34364 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 3 q^{3} - q^{7} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 3 q^{3} - q^{7} + 3 q^{9} - 3 q^{11} + 3 q^{13} + 3 q^{17} - 6 q^{19} + q^{21} - 3 q^{27} - q^{29} - 7 q^{31} + 3 q^{33} + 14 q^{37} - 3 q^{39} - 4 q^{43} - q^{47} - 6 q^{49} - 3 q^{51} + 5 q^{53} + 6 q^{57} - 7 q^{59} - 5 q^{61} - q^{63} + 3 q^{67} - 10 q^{71} - 10 q^{73} + 19 q^{77} - 16 q^{79} + 3 q^{81} + 11 q^{83} + q^{87} - 8 q^{89} - q^{91} + 7 q^{93} + 26 q^{97} - 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 0.476452 0.180082 0.0900410 0.995938i \(-0.471300\pi\)
0.0900410 + 0.995938i \(0.471300\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −3.34364 −1.00814 −0.504072 0.863661i \(-0.668165\pi\)
−0.504072 + 0.863661i \(0.668165\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.00000 0.242536 0.121268 0.992620i \(-0.461304\pi\)
0.121268 + 0.992620i \(0.461304\pi\)
\(18\) 0 0
\(19\) −6.77299 −1.55383 −0.776916 0.629605i \(-0.783217\pi\)
−0.776916 + 0.629605i \(0.783217\pi\)
\(20\) 0 0
\(21\) −0.476452 −0.103970
\(22\) 0 0
\(23\) −4.77299 −0.995238 −0.497619 0.867396i \(-0.665792\pi\)
−0.497619 + 0.867396i \(0.665792\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 7.59308 1.41000 0.705000 0.709207i \(-0.250947\pi\)
0.705000 + 0.709207i \(0.250947\pi\)
\(30\) 0 0
\(31\) 7.93672 1.42548 0.712739 0.701430i \(-0.247455\pi\)
0.712739 + 0.701430i \(0.247455\pi\)
\(32\) 0 0
\(33\) 3.34364 0.582053
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 7.82009 1.28561 0.642807 0.766028i \(-0.277770\pi\)
0.642807 + 0.766028i \(0.277770\pi\)
\(38\) 0 0
\(39\) −1.00000 −0.160128
\(40\) 0 0
\(41\) 9.46027 1.47745 0.738723 0.674009i \(-0.235429\pi\)
0.738723 + 0.674009i \(0.235429\pi\)
\(42\) 0 0
\(43\) 1.82009 0.277561 0.138781 0.990323i \(-0.455682\pi\)
0.138781 + 0.990323i \(0.455682\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −9.06953 −1.32293 −0.661464 0.749977i \(-0.730064\pi\)
−0.661464 + 0.749977i \(0.730064\pi\)
\(48\) 0 0
\(49\) −6.77299 −0.967570
\(50\) 0 0
\(51\) −1.00000 −0.140028
\(52\) 0 0
\(53\) 9.50736 1.30594 0.652968 0.757385i \(-0.273523\pi\)
0.652968 + 0.757385i \(0.273523\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 6.77299 0.897105
\(58\) 0 0
\(59\) 3.16373 0.411882 0.205941 0.978564i \(-0.433974\pi\)
0.205941 + 0.978564i \(0.433974\pi\)
\(60\) 0 0
\(61\) −9.59308 −1.22827 −0.614134 0.789202i \(-0.710495\pi\)
−0.614134 + 0.789202i \(0.710495\pi\)
\(62\) 0 0
\(63\) 0.476452 0.0600273
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −1.34364 −0.164151 −0.0820757 0.996626i \(-0.526155\pi\)
−0.0820757 + 0.996626i \(0.526155\pi\)
\(68\) 0 0
\(69\) 4.77299 0.574601
\(70\) 0 0
\(71\) −4.86719 −0.577629 −0.288814 0.957385i \(-0.593261\pi\)
−0.288814 + 0.957385i \(0.593261\pi\)
\(72\) 0 0
\(73\) −14.4132 −1.68693 −0.843467 0.537181i \(-0.819489\pi\)
−0.843467 + 0.537181i \(0.819489\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −1.59308 −0.181549
\(78\) 0 0
\(79\) −2.17991 −0.245259 −0.122630 0.992453i \(-0.539133\pi\)
−0.122630 + 0.992453i \(0.539133\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 9.16373 1.00585 0.502925 0.864330i \(-0.332257\pi\)
0.502925 + 0.864330i \(0.332257\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −7.59308 −0.814064
\(88\) 0 0
\(89\) −10.5931 −1.12286 −0.561432 0.827523i \(-0.689749\pi\)
−0.561432 + 0.827523i \(0.689749\pi\)
\(90\) 0 0
\(91\) 0.476452 0.0499457
\(92\) 0 0
\(93\) −7.93672 −0.823000
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 7.04710 0.715524 0.357762 0.933813i \(-0.383540\pi\)
0.357762 + 0.933813i \(0.383540\pi\)
\(98\) 0 0
\(99\) −3.34364 −0.336048
\(100\) 0 0
\(101\) −18.3661 −1.82749 −0.913746 0.406285i \(-0.866824\pi\)
−0.913746 + 0.406285i \(0.866824\pi\)
\(102\) 0 0
\(103\) −13.5545 −1.33556 −0.667780 0.744358i \(-0.732755\pi\)
−0.667780 + 0.744358i \(0.732755\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 16.2333 1.56933 0.784664 0.619921i \(-0.212835\pi\)
0.784664 + 0.619921i \(0.212835\pi\)
\(108\) 0 0
\(109\) −16.4132 −1.57210 −0.786048 0.618165i \(-0.787876\pi\)
−0.786048 + 0.618165i \(0.787876\pi\)
\(110\) 0 0
\(111\) −7.82009 −0.742250
\(112\) 0 0
\(113\) 8.59308 0.808369 0.404185 0.914677i \(-0.367555\pi\)
0.404185 + 0.914677i \(0.367555\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 1.00000 0.0924500
\(118\) 0 0
\(119\) 0.476452 0.0436763
\(120\) 0 0
\(121\) 0.179911 0.0163555
\(122\) 0 0
\(123\) −9.46027 −0.853004
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 2.86719 0.254422 0.127211 0.991876i \(-0.459398\pi\)
0.127211 + 0.991876i \(0.459398\pi\)
\(128\) 0 0
\(129\) −1.82009 −0.160250
\(130\) 0 0
\(131\) −16.1475 −1.41082 −0.705409 0.708801i \(-0.749237\pi\)
−0.705409 + 0.708801i \(0.749237\pi\)
\(132\) 0 0
\(133\) −3.22701 −0.279817
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 22.2333 1.89952 0.949758 0.312986i \(-0.101329\pi\)
0.949758 + 0.312986i \(0.101329\pi\)
\(138\) 0 0
\(139\) 9.28036 0.787150 0.393575 0.919293i \(-0.371238\pi\)
0.393575 + 0.919293i \(0.371238\pi\)
\(140\) 0 0
\(141\) 9.06953 0.763793
\(142\) 0 0
\(143\) −3.34364 −0.279609
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 6.77299 0.558627
\(148\) 0 0
\(149\) −22.1391 −1.81370 −0.906852 0.421450i \(-0.861521\pi\)
−0.906852 + 0.421450i \(0.861521\pi\)
\(150\) 0 0
\(151\) −16.0224 −1.30389 −0.651944 0.758267i \(-0.726046\pi\)
−0.651944 + 0.758267i \(0.726046\pi\)
\(152\) 0 0
\(153\) 1.00000 0.0808452
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 6.22701 0.496969 0.248485 0.968636i \(-0.420067\pi\)
0.248485 + 0.968636i \(0.420067\pi\)
\(158\) 0 0
\(159\) −9.50736 −0.753983
\(160\) 0 0
\(161\) −2.27410 −0.179224
\(162\) 0 0
\(163\) 17.6935 1.38586 0.692932 0.721003i \(-0.256319\pi\)
0.692932 + 0.721003i \(0.256319\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0.179911 0.0139219 0.00696095 0.999976i \(-0.497784\pi\)
0.00696095 + 0.999976i \(0.497784\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −6.77299 −0.517944
\(172\) 0 0
\(173\) −12.4603 −0.947337 −0.473668 0.880703i \(-0.657070\pi\)
−0.473668 + 0.880703i \(0.657070\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −3.16373 −0.237800
\(178\) 0 0
\(179\) −5.55446 −0.415160 −0.207580 0.978218i \(-0.566559\pi\)
−0.207580 + 0.978218i \(0.566559\pi\)
\(180\) 0 0
\(181\) 24.0063 1.78437 0.892185 0.451669i \(-0.149171\pi\)
0.892185 + 0.451669i \(0.149171\pi\)
\(182\) 0 0
\(183\) 9.59308 0.709141
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −3.34364 −0.244511
\(188\) 0 0
\(189\) −0.476452 −0.0346568
\(190\) 0 0
\(191\) 3.18617 0.230543 0.115271 0.993334i \(-0.463226\pi\)
0.115271 + 0.993334i \(0.463226\pi\)
\(192\) 0 0
\(193\) −14.8672 −1.07016 −0.535082 0.844800i \(-0.679719\pi\)
−0.535082 + 0.844800i \(0.679719\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 23.7259 1.69040 0.845200 0.534450i \(-0.179481\pi\)
0.845200 + 0.534450i \(0.179481\pi\)
\(198\) 0 0
\(199\) −9.64018 −0.683374 −0.341687 0.939814i \(-0.610998\pi\)
−0.341687 + 0.939814i \(0.610998\pi\)
\(200\) 0 0
\(201\) 1.34364 0.0947729
\(202\) 0 0
\(203\) 3.61774 0.253916
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −4.77299 −0.331746
\(208\) 0 0
\(209\) 22.6464 1.56649
\(210\) 0 0
\(211\) −10.8672 −0.748128 −0.374064 0.927403i \(-0.622036\pi\)
−0.374064 + 0.927403i \(0.622036\pi\)
\(212\) 0 0
\(213\) 4.86719 0.333494
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 3.78147 0.256703
\(218\) 0 0
\(219\) 14.4132 0.973952
\(220\) 0 0
\(221\) 1.00000 0.0672673
\(222\) 0 0
\(223\) −22.2417 −1.48942 −0.744708 0.667390i \(-0.767411\pi\)
−0.744708 + 0.667390i \(0.767411\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 23.4827 1.55860 0.779301 0.626650i \(-0.215574\pi\)
0.779301 + 0.626650i \(0.215574\pi\)
\(228\) 0 0
\(229\) 28.3723 1.87490 0.937448 0.348125i \(-0.113181\pi\)
0.937448 + 0.348125i \(0.113181\pi\)
\(230\) 0 0
\(231\) 1.59308 0.104817
\(232\) 0 0
\(233\) −16.5931 −1.08705 −0.543524 0.839393i \(-0.682911\pi\)
−0.543524 + 0.839393i \(0.682911\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 2.17991 0.141600
\(238\) 0 0
\(239\) 12.0224 0.777667 0.388833 0.921308i \(-0.372878\pi\)
0.388833 + 0.921308i \(0.372878\pi\)
\(240\) 0 0
\(241\) −23.6935 −1.52623 −0.763117 0.646260i \(-0.776332\pi\)
−0.763117 + 0.646260i \(0.776332\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −6.77299 −0.430955
\(248\) 0 0
\(249\) −9.16373 −0.580728
\(250\) 0 0
\(251\) 18.7406 1.18290 0.591449 0.806342i \(-0.298556\pi\)
0.591449 + 0.806342i \(0.298556\pi\)
\(252\) 0 0
\(253\) 15.9592 1.00334
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −9.24173 −0.576484 −0.288242 0.957558i \(-0.593071\pi\)
−0.288242 + 0.957558i \(0.593071\pi\)
\(258\) 0 0
\(259\) 3.72590 0.231516
\(260\) 0 0
\(261\) 7.59308 0.470000
\(262\) 0 0
\(263\) −17.9143 −1.10464 −0.552321 0.833632i \(-0.686258\pi\)
−0.552321 + 0.833632i \(0.686258\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 10.5931 0.648286
\(268\) 0 0
\(269\) −6.28036 −0.382920 −0.191460 0.981500i \(-0.561322\pi\)
−0.191460 + 0.981500i \(0.561322\pi\)
\(270\) 0 0
\(271\) −18.2881 −1.11092 −0.555461 0.831543i \(-0.687458\pi\)
−0.555461 + 0.831543i \(0.687458\pi\)
\(272\) 0 0
\(273\) −0.476452 −0.0288362
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 12.7645 0.766946 0.383473 0.923552i \(-0.374728\pi\)
0.383473 + 0.923552i \(0.374728\pi\)
\(278\) 0 0
\(279\) 7.93672 0.475159
\(280\) 0 0
\(281\) −26.8263 −1.60033 −0.800163 0.599783i \(-0.795254\pi\)
−0.800163 + 0.599783i \(0.795254\pi\)
\(282\) 0 0
\(283\) −21.4518 −1.27518 −0.637588 0.770377i \(-0.720068\pi\)
−0.637588 + 0.770377i \(0.720068\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 4.50736 0.266061
\(288\) 0 0
\(289\) −16.0000 −0.941176
\(290\) 0 0
\(291\) −7.04710 −0.413108
\(292\) 0 0
\(293\) −11.3745 −0.664508 −0.332254 0.943190i \(-0.607809\pi\)
−0.332254 + 0.943190i \(0.607809\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 3.34364 0.194018
\(298\) 0 0
\(299\) −4.77299 −0.276029
\(300\) 0 0
\(301\) 0.867185 0.0499837
\(302\) 0 0
\(303\) 18.3661 1.05510
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −14.0857 −0.803914 −0.401957 0.915658i \(-0.631670\pi\)
−0.401957 + 0.915658i \(0.631670\pi\)
\(308\) 0 0
\(309\) 13.5545 0.771086
\(310\) 0 0
\(311\) −17.4518 −0.989601 −0.494800 0.869007i \(-0.664759\pi\)
−0.494800 + 0.869007i \(0.664759\pi\)
\(312\) 0 0
\(313\) −6.39844 −0.361661 −0.180831 0.983514i \(-0.557879\pi\)
−0.180831 + 0.983514i \(0.557879\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 5.58683 0.313788 0.156894 0.987615i \(-0.449852\pi\)
0.156894 + 0.987615i \(0.449852\pi\)
\(318\) 0 0
\(319\) −25.3885 −1.42148
\(320\) 0 0
\(321\) −16.2333 −0.906052
\(322\) 0 0
\(323\) −6.77299 −0.376859
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 16.4132 0.907650
\(328\) 0 0
\(329\) −4.32120 −0.238235
\(330\) 0 0
\(331\) 10.4132 0.572360 0.286180 0.958176i \(-0.407615\pi\)
0.286180 + 0.958176i \(0.407615\pi\)
\(332\) 0 0
\(333\) 7.82009 0.428538
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −16.3661 −0.891517 −0.445758 0.895153i \(-0.647066\pi\)
−0.445758 + 0.895153i \(0.647066\pi\)
\(338\) 0 0
\(339\) −8.59308 −0.466712
\(340\) 0 0
\(341\) −26.5375 −1.43709
\(342\) 0 0
\(343\) −6.56217 −0.354324
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −36.3723 −1.95257 −0.976285 0.216491i \(-0.930539\pi\)
−0.976285 + 0.216491i \(0.930539\pi\)
\(348\) 0 0
\(349\) −17.7259 −0.948846 −0.474423 0.880297i \(-0.657343\pi\)
−0.474423 + 0.880297i \(0.657343\pi\)
\(350\) 0 0
\(351\) −1.00000 −0.0533761
\(352\) 0 0
\(353\) 19.5375 1.03988 0.519938 0.854204i \(-0.325955\pi\)
0.519938 + 0.854204i \(0.325955\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −0.476452 −0.0252165
\(358\) 0 0
\(359\) −5.92825 −0.312881 −0.156440 0.987687i \(-0.550002\pi\)
−0.156440 + 0.987687i \(0.550002\pi\)
\(360\) 0 0
\(361\) 26.8734 1.41439
\(362\) 0 0
\(363\) −0.179911 −0.00944286
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −27.2804 −1.42402 −0.712012 0.702168i \(-0.752216\pi\)
−0.712012 + 0.702168i \(0.752216\pi\)
\(368\) 0 0
\(369\) 9.46027 0.492482
\(370\) 0 0
\(371\) 4.52980 0.235176
\(372\) 0 0
\(373\) −27.2866 −1.41285 −0.706424 0.707789i \(-0.749693\pi\)
−0.706424 + 0.707789i \(0.749693\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 7.59308 0.391064
\(378\) 0 0
\(379\) −33.4503 −1.71823 −0.859114 0.511784i \(-0.828985\pi\)
−0.859114 + 0.511784i \(0.828985\pi\)
\(380\) 0 0
\(381\) −2.86719 −0.146890
\(382\) 0 0
\(383\) 2.60156 0.132933 0.0664666 0.997789i \(-0.478827\pi\)
0.0664666 + 0.997789i \(0.478827\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 1.82009 0.0925203
\(388\) 0 0
\(389\) −0.781467 −0.0396219 −0.0198110 0.999804i \(-0.506306\pi\)
−0.0198110 + 0.999804i \(0.506306\pi\)
\(390\) 0 0
\(391\) −4.77299 −0.241381
\(392\) 0 0
\(393\) 16.1475 0.814536
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −6.49889 −0.326170 −0.163085 0.986612i \(-0.552144\pi\)
−0.163085 + 0.986612i \(0.552144\pi\)
\(398\) 0 0
\(399\) 3.22701 0.161552
\(400\) 0 0
\(401\) 21.0063 1.04900 0.524501 0.851410i \(-0.324252\pi\)
0.524501 + 0.851410i \(0.324252\pi\)
\(402\) 0 0
\(403\) 7.93672 0.395356
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −26.1475 −1.29609
\(408\) 0 0
\(409\) −8.08572 −0.399813 −0.199907 0.979815i \(-0.564064\pi\)
−0.199907 + 0.979815i \(0.564064\pi\)
\(410\) 0 0
\(411\) −22.2333 −1.09669
\(412\) 0 0
\(413\) 1.50736 0.0741725
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −9.28036 −0.454461
\(418\) 0 0
\(419\) 1.91428 0.0935188 0.0467594 0.998906i \(-0.485111\pi\)
0.0467594 + 0.998906i \(0.485111\pi\)
\(420\) 0 0
\(421\) −27.1089 −1.32121 −0.660604 0.750735i \(-0.729700\pi\)
−0.660604 + 0.750735i \(0.729700\pi\)
\(422\) 0 0
\(423\) −9.06953 −0.440976
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −4.57064 −0.221189
\(428\) 0 0
\(429\) 3.34364 0.161432
\(430\) 0 0
\(431\) −13.0386 −0.628048 −0.314024 0.949415i \(-0.601677\pi\)
−0.314024 + 0.949415i \(0.601677\pi\)
\(432\) 0 0
\(433\) −26.3275 −1.26522 −0.632608 0.774472i \(-0.718016\pi\)
−0.632608 + 0.774472i \(0.718016\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 32.3275 1.54643
\(438\) 0 0
\(439\) 7.69353 0.367192 0.183596 0.983002i \(-0.441226\pi\)
0.183596 + 0.983002i \(0.441226\pi\)
\(440\) 0 0
\(441\) −6.77299 −0.322523
\(442\) 0 0
\(443\) 23.7259 1.12725 0.563626 0.826030i \(-0.309406\pi\)
0.563626 + 0.826030i \(0.309406\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 22.1391 1.04714
\(448\) 0 0
\(449\) 9.73437 0.459393 0.229697 0.973262i \(-0.426227\pi\)
0.229697 + 0.973262i \(0.426227\pi\)
\(450\) 0 0
\(451\) −31.6317 −1.48948
\(452\) 0 0
\(453\) 16.0224 0.752800
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −5.64865 −0.264233 −0.132116 0.991234i \(-0.542177\pi\)
−0.132116 + 0.991234i \(0.542177\pi\)
\(458\) 0 0
\(459\) −1.00000 −0.0466760
\(460\) 0 0
\(461\) −12.4540 −0.580041 −0.290021 0.957020i \(-0.593662\pi\)
−0.290021 + 0.957020i \(0.593662\pi\)
\(462\) 0 0
\(463\) 14.2642 0.662912 0.331456 0.943471i \(-0.392460\pi\)
0.331456 + 0.943471i \(0.392460\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −18.7815 −0.869103 −0.434551 0.900647i \(-0.643093\pi\)
−0.434551 + 0.900647i \(0.643093\pi\)
\(468\) 0 0
\(469\) −0.640179 −0.0295607
\(470\) 0 0
\(471\) −6.22701 −0.286925
\(472\) 0 0
\(473\) −6.08572 −0.279822
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 9.50736 0.435312
\(478\) 0 0
\(479\) −12.7954 −0.584638 −0.292319 0.956321i \(-0.594427\pi\)
−0.292319 + 0.956321i \(0.594427\pi\)
\(480\) 0 0
\(481\) 7.82009 0.356565
\(482\) 0 0
\(483\) 2.27410 0.103475
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 15.4378 0.699555 0.349777 0.936833i \(-0.386257\pi\)
0.349777 + 0.936833i \(0.386257\pi\)
\(488\) 0 0
\(489\) −17.6935 −0.800129
\(490\) 0 0
\(491\) −11.3745 −0.513326 −0.256663 0.966501i \(-0.582623\pi\)
−0.256663 + 0.966501i \(0.582623\pi\)
\(492\) 0 0
\(493\) 7.59308 0.341975
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −2.31898 −0.104020
\(498\) 0 0
\(499\) 43.7075 1.95662 0.978308 0.207155i \(-0.0664205\pi\)
0.978308 + 0.207155i \(0.0664205\pi\)
\(500\) 0 0
\(501\) −0.179911 −0.00803781
\(502\) 0 0
\(503\) 10.5846 0.471944 0.235972 0.971760i \(-0.424173\pi\)
0.235972 + 0.971760i \(0.424173\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −1.00000 −0.0444116
\(508\) 0 0
\(509\) 4.05335 0.179662 0.0898308 0.995957i \(-0.471367\pi\)
0.0898308 + 0.995957i \(0.471367\pi\)
\(510\) 0 0
\(511\) −6.86719 −0.303786
\(512\) 0 0
\(513\) 6.77299 0.299035
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 30.3252 1.33370
\(518\) 0 0
\(519\) 12.4603 0.546945
\(520\) 0 0
\(521\) 19.1862 0.840561 0.420281 0.907394i \(-0.361932\pi\)
0.420281 + 0.907394i \(0.361932\pi\)
\(522\) 0 0
\(523\) −40.2333 −1.75928 −0.879639 0.475642i \(-0.842216\pi\)
−0.879639 + 0.475642i \(0.842216\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 7.93672 0.345729
\(528\) 0 0
\(529\) −0.218533 −0.00950146
\(530\) 0 0
\(531\) 3.16373 0.137294
\(532\) 0 0
\(533\) 9.46027 0.409770
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 5.55446 0.239693
\(538\) 0 0
\(539\) 22.6464 0.975451
\(540\) 0 0
\(541\) 43.7708 1.88185 0.940926 0.338611i \(-0.109957\pi\)
0.940926 + 0.338611i \(0.109957\pi\)
\(542\) 0 0
\(543\) −24.0063 −1.03021
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 1.72590 0.0737940 0.0368970 0.999319i \(-0.488253\pi\)
0.0368970 + 0.999319i \(0.488253\pi\)
\(548\) 0 0
\(549\) −9.59308 −0.409423
\(550\) 0 0
\(551\) −51.4279 −2.19090
\(552\) 0 0
\(553\) −1.03862 −0.0441667
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 16.6016 0.703430 0.351715 0.936107i \(-0.385599\pi\)
0.351715 + 0.936107i \(0.385599\pi\)
\(558\) 0 0
\(559\) 1.82009 0.0769816
\(560\) 0 0
\(561\) 3.34364 0.141168
\(562\) 0 0
\(563\) −27.1453 −1.14404 −0.572020 0.820240i \(-0.693840\pi\)
−0.572020 + 0.820240i \(0.693840\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0.476452 0.0200091
\(568\) 0 0
\(569\) −24.0232 −1.00710 −0.503552 0.863965i \(-0.667974\pi\)
−0.503552 + 0.863965i \(0.667974\pi\)
\(570\) 0 0
\(571\) 37.9592 1.58854 0.794271 0.607564i \(-0.207853\pi\)
0.794271 + 0.607564i \(0.207853\pi\)
\(572\) 0 0
\(573\) −3.18617 −0.133104
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 39.7020 1.65282 0.826408 0.563072i \(-0.190381\pi\)
0.826408 + 0.563072i \(0.190381\pi\)
\(578\) 0 0
\(579\) 14.8672 0.617859
\(580\) 0 0
\(581\) 4.36608 0.181135
\(582\) 0 0
\(583\) −31.7892 −1.31657
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −32.6070 −1.34584 −0.672918 0.739717i \(-0.734960\pi\)
−0.672918 + 0.739717i \(0.734960\pi\)
\(588\) 0 0
\(589\) −53.7554 −2.21495
\(590\) 0 0
\(591\) −23.7259 −0.975953
\(592\) 0 0
\(593\) −0.454013 −0.0186441 −0.00932204 0.999957i \(-0.502967\pi\)
−0.00932204 + 0.999957i \(0.502967\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 9.64018 0.394546
\(598\) 0 0
\(599\) −8.31898 −0.339904 −0.169952 0.985452i \(-0.554361\pi\)
−0.169952 + 0.985452i \(0.554361\pi\)
\(600\) 0 0
\(601\) 36.3337 1.48208 0.741041 0.671459i \(-0.234332\pi\)
0.741041 + 0.671459i \(0.234332\pi\)
\(602\) 0 0
\(603\) −1.34364 −0.0547171
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 34.9654 1.41920 0.709601 0.704604i \(-0.248875\pi\)
0.709601 + 0.704604i \(0.248875\pi\)
\(608\) 0 0
\(609\) −3.61774 −0.146598
\(610\) 0 0
\(611\) −9.06953 −0.366914
\(612\) 0 0
\(613\) 15.3745 0.620972 0.310486 0.950578i \(-0.399508\pi\)
0.310486 + 0.950578i \(0.399508\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −11.8734 −0.478007 −0.239003 0.971019i \(-0.576821\pi\)
−0.239003 + 0.971019i \(0.576821\pi\)
\(618\) 0 0
\(619\) 13.1946 0.530337 0.265169 0.964202i \(-0.414572\pi\)
0.265169 + 0.964202i \(0.414572\pi\)
\(620\) 0 0
\(621\) 4.77299 0.191534
\(622\) 0 0
\(623\) −5.04710 −0.202208
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −22.6464 −0.904411
\(628\) 0 0
\(629\) 7.82009 0.311807
\(630\) 0 0
\(631\) −2.63392 −0.104855 −0.0524274 0.998625i \(-0.516696\pi\)
−0.0524274 + 0.998625i \(0.516696\pi\)
\(632\) 0 0
\(633\) 10.8672 0.431932
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −6.77299 −0.268356
\(638\) 0 0
\(639\) −4.86719 −0.192543
\(640\) 0 0
\(641\) −18.4687 −0.729471 −0.364736 0.931111i \(-0.618841\pi\)
−0.364736 + 0.931111i \(0.618841\pi\)
\(642\) 0 0
\(643\) −36.5074 −1.43971 −0.719855 0.694125i \(-0.755792\pi\)
−0.719855 + 0.694125i \(0.755792\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.40692 −0.0553116 −0.0276558 0.999618i \(-0.508804\pi\)
−0.0276558 + 0.999618i \(0.508804\pi\)
\(648\) 0 0
\(649\) −10.5784 −0.415237
\(650\) 0 0
\(651\) −3.78147 −0.148207
\(652\) 0 0
\(653\) −38.7469 −1.51628 −0.758141 0.652090i \(-0.773892\pi\)
−0.758141 + 0.652090i \(0.773892\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −14.4132 −0.562311
\(658\) 0 0
\(659\) 28.0857 1.09406 0.547032 0.837112i \(-0.315758\pi\)
0.547032 + 0.837112i \(0.315758\pi\)
\(660\) 0 0
\(661\) −45.2071 −1.75835 −0.879177 0.476495i \(-0.841907\pi\)
−0.879177 + 0.476495i \(0.841907\pi\)
\(662\) 0 0
\(663\) −1.00000 −0.0388368
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −36.2417 −1.40329
\(668\) 0 0
\(669\) 22.2417 0.859915
\(670\) 0 0
\(671\) 32.0758 1.23827
\(672\) 0 0
\(673\) −21.2741 −0.820056 −0.410028 0.912073i \(-0.634481\pi\)
−0.410028 + 0.912073i \(0.634481\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 19.5460 0.751213 0.375607 0.926779i \(-0.377434\pi\)
0.375607 + 0.926779i \(0.377434\pi\)
\(678\) 0 0
\(679\) 3.35760 0.128853
\(680\) 0 0
\(681\) −23.4827 −0.899859
\(682\) 0 0
\(683\) 7.79765 0.298369 0.149184 0.988809i \(-0.452335\pi\)
0.149184 + 0.988809i \(0.452335\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −28.3723 −1.08247
\(688\) 0 0
\(689\) 9.50736 0.362202
\(690\) 0 0
\(691\) −20.7267 −0.788479 −0.394240 0.919008i \(-0.628992\pi\)
−0.394240 + 0.919008i \(0.628992\pi\)
\(692\) 0 0
\(693\) −1.59308 −0.0605162
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 9.46027 0.358333
\(698\) 0 0
\(699\) 16.5931 0.627608
\(700\) 0 0
\(701\) −32.7792 −1.23806 −0.619028 0.785369i \(-0.712473\pi\)
−0.619028 + 0.785369i \(0.712473\pi\)
\(702\) 0 0
\(703\) −52.9654 −1.99763
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −8.75055 −0.329098
\(708\) 0 0
\(709\) 4.08572 0.153442 0.0767212 0.997053i \(-0.475555\pi\)
0.0767212 + 0.997053i \(0.475555\pi\)
\(710\) 0 0
\(711\) −2.17991 −0.0817530
\(712\) 0 0
\(713\) −37.8819 −1.41869
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −12.0224 −0.448986
\(718\) 0 0
\(719\) 30.0857 1.12201 0.561004 0.827813i \(-0.310415\pi\)
0.561004 + 0.827813i \(0.310415\pi\)
\(720\) 0 0
\(721\) −6.45805 −0.240510
\(722\) 0 0
\(723\) 23.6935 0.881172
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 18.9121 0.701410 0.350705 0.936486i \(-0.385942\pi\)
0.350705 + 0.936486i \(0.385942\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 1.82009 0.0673184
\(732\) 0 0
\(733\) 30.3893 1.12245 0.561227 0.827662i \(-0.310330\pi\)
0.561227 + 0.827662i \(0.310330\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 4.49264 0.165488
\(738\) 0 0
\(739\) −5.60927 −0.206340 −0.103170 0.994664i \(-0.532899\pi\)
−0.103170 + 0.994664i \(0.532899\pi\)
\(740\) 0 0
\(741\) 6.77299 0.248812
\(742\) 0 0
\(743\) 9.51507 0.349074 0.174537 0.984651i \(-0.444157\pi\)
0.174537 + 0.984651i \(0.444157\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 9.16373 0.335283
\(748\) 0 0
\(749\) 7.73437 0.282608
\(750\) 0 0
\(751\) −31.5221 −1.15026 −0.575129 0.818063i \(-0.695048\pi\)
−0.575129 + 0.818063i \(0.695048\pi\)
\(752\) 0 0
\(753\) −18.7406 −0.682946
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −25.5607 −0.929020 −0.464510 0.885568i \(-0.653770\pi\)
−0.464510 + 0.885568i \(0.653770\pi\)
\(758\) 0 0
\(759\) −15.9592 −0.579281
\(760\) 0 0
\(761\) 10.4132 0.377477 0.188739 0.982027i \(-0.439560\pi\)
0.188739 + 0.982027i \(0.439560\pi\)
\(762\) 0 0
\(763\) −7.82009 −0.283106
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 3.16373 0.114236
\(768\) 0 0
\(769\) −2.95290 −0.106484 −0.0532422 0.998582i \(-0.516956\pi\)
−0.0532422 + 0.998582i \(0.516956\pi\)
\(770\) 0 0
\(771\) 9.24173 0.332833
\(772\) 0 0
\(773\) 11.0471 0.397336 0.198668 0.980067i \(-0.436338\pi\)
0.198668 + 0.980067i \(0.436338\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −3.72590 −0.133666
\(778\) 0 0
\(779\) −64.0743 −2.29570
\(780\) 0 0
\(781\) 16.2741 0.582333
\(782\) 0 0
\(783\) −7.59308 −0.271355
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −15.1553 −0.540226 −0.270113 0.962829i \(-0.587061\pi\)
−0.270113 + 0.962829i \(0.587061\pi\)
\(788\) 0 0
\(789\) 17.9143 0.637765
\(790\) 0 0
\(791\) 4.09419 0.145573
\(792\) 0 0
\(793\) −9.59308 −0.340660
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 38.7962 1.37423 0.687116 0.726548i \(-0.258876\pi\)
0.687116 + 0.726548i \(0.258876\pi\)
\(798\) 0 0
\(799\) −9.06953 −0.320857
\(800\) 0 0
\(801\) −10.5931 −0.374288
\(802\) 0 0
\(803\) 48.1924 1.70067
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 6.28036 0.221079
\(808\) 0 0
\(809\) −50.1391 −1.76280 −0.881398 0.472375i \(-0.843397\pi\)
−0.881398 + 0.472375i \(0.843397\pi\)
\(810\) 0 0
\(811\) −17.5684 −0.616911 −0.308455 0.951239i \(-0.599812\pi\)
−0.308455 + 0.951239i \(0.599812\pi\)
\(812\) 0 0
\(813\) 18.2881 0.641391
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −12.3275 −0.431283
\(818\) 0 0
\(819\) 0.476452 0.0166486
\(820\) 0 0
\(821\) 1.19464 0.0416932 0.0208466 0.999783i \(-0.493364\pi\)
0.0208466 + 0.999783i \(0.493364\pi\)
\(822\) 0 0
\(823\) 44.2458 1.54231 0.771155 0.636647i \(-0.219679\pi\)
0.771155 + 0.636647i \(0.219679\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −6.84475 −0.238015 −0.119008 0.992893i \(-0.537971\pi\)
−0.119008 + 0.992893i \(0.537971\pi\)
\(828\) 0 0
\(829\) 1.04488 0.0362901 0.0181451 0.999835i \(-0.494224\pi\)
0.0181451 + 0.999835i \(0.494224\pi\)
\(830\) 0 0
\(831\) −12.7645 −0.442796
\(832\) 0 0
\(833\) −6.77299 −0.234670
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −7.93672 −0.274333
\(838\) 0 0
\(839\) 38.2417 1.32025 0.660126 0.751155i \(-0.270503\pi\)
0.660126 + 0.751155i \(0.270503\pi\)
\(840\) 0 0
\(841\) 28.6549 0.988100
\(842\) 0 0
\(843\) 26.8263 0.923948
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0.0857188 0.00294533
\(848\) 0 0
\(849\) 21.4518 0.736224
\(850\) 0 0
\(851\) −37.3252 −1.27949
\(852\) 0 0
\(853\) 44.9978 1.54069 0.770347 0.637624i \(-0.220083\pi\)
0.770347 + 0.637624i \(0.220083\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 12.3723 0.422631 0.211315 0.977418i \(-0.432225\pi\)
0.211315 + 0.977418i \(0.432225\pi\)
\(858\) 0 0
\(859\) −22.4750 −0.766837 −0.383418 0.923575i \(-0.625253\pi\)
−0.383418 + 0.923575i \(0.625253\pi\)
\(860\) 0 0
\(861\) −4.50736 −0.153611
\(862\) 0 0
\(863\) 12.1251 0.412743 0.206372 0.978474i \(-0.433834\pi\)
0.206372 + 0.978474i \(0.433834\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 16.0000 0.543388
\(868\) 0 0
\(869\) 7.28883 0.247257
\(870\) 0 0
\(871\) −1.34364 −0.0455274
\(872\) 0 0
\(873\) 7.04710 0.238508
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −26.0449 −0.879473 −0.439737 0.898127i \(-0.644928\pi\)
−0.439737 + 0.898127i \(0.644928\pi\)
\(878\) 0 0
\(879\) 11.3745 0.383654
\(880\) 0 0
\(881\) −13.4132 −0.451901 −0.225951 0.974139i \(-0.572549\pi\)
−0.225951 + 0.974139i \(0.572549\pi\)
\(882\) 0 0
\(883\) −28.5158 −0.959634 −0.479817 0.877369i \(-0.659297\pi\)
−0.479817 + 0.877369i \(0.659297\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 30.6464 1.02901 0.514503 0.857488i \(-0.327976\pi\)
0.514503 + 0.857488i \(0.327976\pi\)
\(888\) 0 0
\(889\) 1.36608 0.0458167
\(890\) 0 0
\(891\) −3.34364 −0.112016
\(892\) 0 0
\(893\) 61.4279 2.05561
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 4.77299 0.159366
\(898\) 0 0
\(899\) 60.2642 2.00992
\(900\) 0 0
\(901\) 9.50736 0.316736
\(902\) 0 0
\(903\) −0.867185 −0.0288581
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −36.9978 −1.22849 −0.614246 0.789115i \(-0.710540\pi\)
−0.614246 + 0.789115i \(0.710540\pi\)
\(908\) 0 0
\(909\) −18.3661 −0.609164
\(910\) 0 0
\(911\) 35.3337 1.17066 0.585329 0.810796i \(-0.300965\pi\)
0.585329 + 0.810796i \(0.300965\pi\)
\(912\) 0 0
\(913\) −30.6402 −1.01404
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −7.69353 −0.254063
\(918\) 0 0
\(919\) −35.6851 −1.17714 −0.588571 0.808446i \(-0.700309\pi\)
−0.588571 + 0.808446i \(0.700309\pi\)
\(920\) 0 0
\(921\) 14.0857 0.464140
\(922\) 0 0
\(923\) −4.86719 −0.160205
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −13.5545 −0.445187
\(928\) 0 0
\(929\) −48.2009 −1.58142 −0.790710 0.612191i \(-0.790288\pi\)
−0.790710 + 0.612191i \(0.790288\pi\)
\(930\) 0 0
\(931\) 45.8734 1.50344
\(932\) 0 0
\(933\) 17.4518 0.571346
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 36.1538 1.18109 0.590547 0.807004i \(-0.298912\pi\)
0.590547 + 0.807004i \(0.298912\pi\)
\(938\) 0 0
\(939\) 6.39844 0.208805
\(940\) 0 0
\(941\) −6.66629 −0.217315 −0.108657 0.994079i \(-0.534655\pi\)
−0.108657 + 0.994079i \(0.534655\pi\)
\(942\) 0 0
\(943\) −45.1538 −1.47041
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −15.3760 −0.499653 −0.249827 0.968291i \(-0.580374\pi\)
−0.249827 + 0.968291i \(0.580374\pi\)
\(948\) 0 0
\(949\) −14.4132 −0.467871
\(950\) 0 0
\(951\) −5.58683 −0.181165
\(952\) 0 0
\(953\) 7.10266 0.230078 0.115039 0.993361i \(-0.463301\pi\)
0.115039 + 0.993361i \(0.463301\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 25.3885 0.820694
\(958\) 0 0
\(959\) 10.5931 0.342068
\(960\) 0 0
\(961\) 31.9915 1.03198
\(962\) 0 0
\(963\) 16.2333 0.523110
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −28.8573 −0.927987 −0.463993 0.885839i \(-0.653584\pi\)
−0.463993 + 0.885839i \(0.653584\pi\)
\(968\) 0 0
\(969\) 6.77299 0.217580
\(970\) 0 0
\(971\) −25.5909 −0.821250 −0.410625 0.911804i \(-0.634689\pi\)
−0.410625 + 0.911804i \(0.634689\pi\)
\(972\) 0 0
\(973\) 4.42165 0.141751
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 31.6402 1.01226 0.506129 0.862457i \(-0.331076\pi\)
0.506129 + 0.862457i \(0.331076\pi\)
\(978\) 0 0
\(979\) 35.4194 1.13201
\(980\) 0 0
\(981\) −16.4132 −0.524032
\(982\) 0 0
\(983\) −5.12289 −0.163395 −0.0816973 0.996657i \(-0.526034\pi\)
−0.0816973 + 0.996657i \(0.526034\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 4.32120 0.137545
\(988\) 0 0
\(989\) −8.68727 −0.276239
\(990\) 0 0
\(991\) −26.3359 −0.836588 −0.418294 0.908312i \(-0.637372\pi\)
−0.418294 + 0.908312i \(0.637372\pi\)
\(992\) 0 0
\(993\) −10.4132 −0.330452
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −42.0766 −1.33258 −0.666289 0.745694i \(-0.732118\pi\)
−0.666289 + 0.745694i \(0.732118\pi\)
\(998\) 0 0
\(999\) −7.82009 −0.247417
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 7800.2.a.bg.1.2 3
5.4 even 2 7800.2.a.br.1.2 yes 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7800.2.a.bg.1.2 3 1.1 even 1 trivial
7800.2.a.br.1.2 yes 3 5.4 even 2