Properties

Label 7800.2.a.bo.1.3
Level $7800$
Weight $2$
Character 7800.1
Self dual yes
Analytic conductor $62.283$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

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: 3.3.148.1
Defining polynomial: \(x^{3} - x^{2} - 3 x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(0.311108\) of defining polynomial
Character \(\chi\) \(=\) 7800.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} +4.11753 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} +4.11753 q^{7} +1.00000 q^{9} -3.21432 q^{11} +1.00000 q^{13} -6.05086 q^{17} -2.90321 q^{19} +4.11753 q^{21} -3.65878 q^{23} +1.00000 q^{27} -0.377784 q^{29} -1.40790 q^{31} -3.21432 q^{33} -10.0874 q^{37} +1.00000 q^{39} +1.33185 q^{41} -6.57628 q^{43} +8.11753 q^{47} +9.95407 q^{49} -6.05086 q^{51} -4.09679 q^{53} -2.90321 q^{57} -14.2192 q^{59} -2.57136 q^{61} +4.11753 q^{63} -7.02074 q^{67} -3.65878 q^{69} +7.19850 q^{71} -7.46520 q^{73} -13.2351 q^{77} +7.13828 q^{79} +1.00000 q^{81} -10.9748 q^{83} -0.377784 q^{87} -18.5303 q^{89} +4.11753 q^{91} -1.40790 q^{93} +12.2351 q^{97} -3.21432 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 3 q^{3} - q^{7} + 3 q^{9} + O(q^{10}) \) \( 3 q + 3 q^{3} - q^{7} + 3 q^{9} - 3 q^{11} + 3 q^{13} - 5 q^{17} - 2 q^{19} - q^{21} - 4 q^{23} + 3 q^{27} - q^{29} - 11 q^{31} - 3 q^{33} - 10 q^{37} + 3 q^{39} - 16 q^{41} + 11 q^{47} + 10 q^{49} - 5 q^{51} - 19 q^{53} - 2 q^{57} - 3 q^{59} - 21 q^{61} - q^{63} - q^{67} - 4 q^{69} + 2 q^{71} - 2 q^{73} - 13 q^{77} - 12 q^{79} + 3 q^{81} + 7 q^{83} - q^{87} - 16 q^{89} - q^{91} - 11 q^{93} + 10 q^{97} - 3 q^{99} + O(q^{100}) \)

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
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 4.11753 1.55628 0.778140 0.628090i \(-0.216163\pi\)
0.778140 + 0.628090i \(0.216163\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −3.21432 −0.969154 −0.484577 0.874749i \(-0.661026\pi\)
−0.484577 + 0.874749i \(0.661026\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −6.05086 −1.46755 −0.733774 0.679394i \(-0.762243\pi\)
−0.733774 + 0.679394i \(0.762243\pi\)
\(18\) 0 0
\(19\) −2.90321 −0.666042 −0.333021 0.942919i \(-0.608068\pi\)
−0.333021 + 0.942919i \(0.608068\pi\)
\(20\) 0 0
\(21\) 4.11753 0.898519
\(22\) 0 0
\(23\) −3.65878 −0.762909 −0.381454 0.924388i \(-0.624577\pi\)
−0.381454 + 0.924388i \(0.624577\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −0.377784 −0.0701528 −0.0350764 0.999385i \(-0.511167\pi\)
−0.0350764 + 0.999385i \(0.511167\pi\)
\(30\) 0 0
\(31\) −1.40790 −0.252866 −0.126433 0.991975i \(-0.540353\pi\)
−0.126433 + 0.991975i \(0.540353\pi\)
\(32\) 0 0
\(33\) −3.21432 −0.559541
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −10.0874 −1.65836 −0.829181 0.558980i \(-0.811193\pi\)
−0.829181 + 0.558980i \(0.811193\pi\)
\(38\) 0 0
\(39\) 1.00000 0.160128
\(40\) 0 0
\(41\) 1.33185 0.208000 0.104000 0.994577i \(-0.466836\pi\)
0.104000 + 0.994577i \(0.466836\pi\)
\(42\) 0 0
\(43\) −6.57628 −1.00287 −0.501437 0.865194i \(-0.667195\pi\)
−0.501437 + 0.865194i \(0.667195\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 8.11753 1.18406 0.592032 0.805915i \(-0.298326\pi\)
0.592032 + 0.805915i \(0.298326\pi\)
\(48\) 0 0
\(49\) 9.95407 1.42201
\(50\) 0 0
\(51\) −6.05086 −0.847289
\(52\) 0 0
\(53\) −4.09679 −0.562737 −0.281369 0.959600i \(-0.590788\pi\)
−0.281369 + 0.959600i \(0.590788\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −2.90321 −0.384540
\(58\) 0 0
\(59\) −14.2192 −1.85119 −0.925594 0.378518i \(-0.876434\pi\)
−0.925594 + 0.378518i \(0.876434\pi\)
\(60\) 0 0
\(61\) −2.57136 −0.329229 −0.164614 0.986358i \(-0.552638\pi\)
−0.164614 + 0.986358i \(0.552638\pi\)
\(62\) 0 0
\(63\) 4.11753 0.518760
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −7.02074 −0.857720 −0.428860 0.903371i \(-0.641085\pi\)
−0.428860 + 0.903371i \(0.641085\pi\)
\(68\) 0 0
\(69\) −3.65878 −0.440465
\(70\) 0 0
\(71\) 7.19850 0.854305 0.427152 0.904180i \(-0.359517\pi\)
0.427152 + 0.904180i \(0.359517\pi\)
\(72\) 0 0
\(73\) −7.46520 −0.873736 −0.436868 0.899526i \(-0.643912\pi\)
−0.436868 + 0.899526i \(0.643912\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −13.2351 −1.50828
\(78\) 0 0
\(79\) 7.13828 0.803119 0.401559 0.915833i \(-0.368468\pi\)
0.401559 + 0.915833i \(0.368468\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −10.9748 −1.20464 −0.602321 0.798254i \(-0.705757\pi\)
−0.602321 + 0.798254i \(0.705757\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −0.377784 −0.0405027
\(88\) 0 0
\(89\) −18.5303 −1.96421 −0.982107 0.188326i \(-0.939694\pi\)
−0.982107 + 0.188326i \(0.939694\pi\)
\(90\) 0 0
\(91\) 4.11753 0.431635
\(92\) 0 0
\(93\) −1.40790 −0.145992
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 12.2351 1.24228 0.621141 0.783699i \(-0.286669\pi\)
0.621141 + 0.783699i \(0.286669\pi\)
\(98\) 0 0
\(99\) −3.21432 −0.323051
\(100\) 0 0
\(101\) −8.03657 −0.799668 −0.399834 0.916588i \(-0.630932\pi\)
−0.399834 + 0.916588i \(0.630932\pi\)
\(102\) 0 0
\(103\) −4.57628 −0.450915 −0.225457 0.974253i \(-0.572388\pi\)
−0.225457 + 0.974253i \(0.572388\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −14.9906 −1.44920 −0.724600 0.689170i \(-0.757975\pi\)
−0.724600 + 0.689170i \(0.757975\pi\)
\(108\) 0 0
\(109\) 19.2716 1.84589 0.922944 0.384935i \(-0.125776\pi\)
0.922944 + 0.384935i \(0.125776\pi\)
\(110\) 0 0
\(111\) −10.0874 −0.957456
\(112\) 0 0
\(113\) 6.04149 0.568335 0.284168 0.958775i \(-0.408283\pi\)
0.284168 + 0.958775i \(0.408283\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 1.00000 0.0924500
\(118\) 0 0
\(119\) −24.9146 −2.28392
\(120\) 0 0
\(121\) −0.668149 −0.0607408
\(122\) 0 0
\(123\) 1.33185 0.120089
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 19.2716 1.71008 0.855040 0.518562i \(-0.173532\pi\)
0.855040 + 0.518562i \(0.173532\pi\)
\(128\) 0 0
\(129\) −6.57628 −0.579009
\(130\) 0 0
\(131\) −14.2494 −1.24497 −0.622486 0.782631i \(-0.713877\pi\)
−0.622486 + 0.782631i \(0.713877\pi\)
\(132\) 0 0
\(133\) −11.9541 −1.03655
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 5.37778 0.459455 0.229728 0.973255i \(-0.426216\pi\)
0.229728 + 0.973255i \(0.426216\pi\)
\(138\) 0 0
\(139\) 7.24443 0.614465 0.307232 0.951635i \(-0.400597\pi\)
0.307232 + 0.951635i \(0.400597\pi\)
\(140\) 0 0
\(141\) 8.11753 0.683619
\(142\) 0 0
\(143\) −3.21432 −0.268795
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 9.95407 0.820998
\(148\) 0 0
\(149\) 17.4795 1.43198 0.715988 0.698113i \(-0.245977\pi\)
0.715988 + 0.698113i \(0.245977\pi\)
\(150\) 0 0
\(151\) −22.6795 −1.84563 −0.922817 0.385239i \(-0.874119\pi\)
−0.922817 + 0.385239i \(0.874119\pi\)
\(152\) 0 0
\(153\) −6.05086 −0.489183
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 13.3225 1.06325 0.531625 0.846980i \(-0.321582\pi\)
0.531625 + 0.846980i \(0.321582\pi\)
\(158\) 0 0
\(159\) −4.09679 −0.324896
\(160\) 0 0
\(161\) −15.0651 −1.18730
\(162\) 0 0
\(163\) 16.0558 1.25759 0.628793 0.777573i \(-0.283549\pi\)
0.628793 + 0.777573i \(0.283549\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 8.84299 0.684291 0.342146 0.939647i \(-0.388846\pi\)
0.342146 + 0.939647i \(0.388846\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −2.90321 −0.222014
\(172\) 0 0
\(173\) −15.7699 −1.19896 −0.599480 0.800390i \(-0.704626\pi\)
−0.599480 + 0.800390i \(0.704626\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −14.2192 −1.06878
\(178\) 0 0
\(179\) 2.38271 0.178092 0.0890459 0.996028i \(-0.471618\pi\)
0.0890459 + 0.996028i \(0.471618\pi\)
\(180\) 0 0
\(181\) −14.8207 −1.10161 −0.550807 0.834632i \(-0.685680\pi\)
−0.550807 + 0.834632i \(0.685680\pi\)
\(182\) 0 0
\(183\) −2.57136 −0.190080
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 19.4494 1.42228
\(188\) 0 0
\(189\) 4.11753 0.299506
\(190\) 0 0
\(191\) −8.10171 −0.586219 −0.293110 0.956079i \(-0.594690\pi\)
−0.293110 + 0.956079i \(0.594690\pi\)
\(192\) 0 0
\(193\) −7.65878 −0.551291 −0.275646 0.961259i \(-0.588892\pi\)
−0.275646 + 0.961259i \(0.588892\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 11.5254 0.821153 0.410576 0.911826i \(-0.365328\pi\)
0.410576 + 0.911826i \(0.365328\pi\)
\(198\) 0 0
\(199\) 13.5210 0.958477 0.479238 0.877685i \(-0.340913\pi\)
0.479238 + 0.877685i \(0.340913\pi\)
\(200\) 0 0
\(201\) −7.02074 −0.495205
\(202\) 0 0
\(203\) −1.55554 −0.109177
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −3.65878 −0.254303
\(208\) 0 0
\(209\) 9.33185 0.645498
\(210\) 0 0
\(211\) 6.44293 0.443550 0.221775 0.975098i \(-0.428815\pi\)
0.221775 + 0.975098i \(0.428815\pi\)
\(212\) 0 0
\(213\) 7.19850 0.493233
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −5.79706 −0.393530
\(218\) 0 0
\(219\) −7.46520 −0.504452
\(220\) 0 0
\(221\) −6.05086 −0.407025
\(222\) 0 0
\(223\) −2.51606 −0.168488 −0.0842439 0.996445i \(-0.526847\pi\)
−0.0842439 + 0.996445i \(0.526847\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 2.22369 0.147591 0.0737957 0.997273i \(-0.476489\pi\)
0.0737957 + 0.997273i \(0.476489\pi\)
\(228\) 0 0
\(229\) 4.48886 0.296632 0.148316 0.988940i \(-0.452615\pi\)
0.148316 + 0.988940i \(0.452615\pi\)
\(230\) 0 0
\(231\) −13.2351 −0.870803
\(232\) 0 0
\(233\) 10.8988 0.714002 0.357001 0.934104i \(-0.383799\pi\)
0.357001 + 0.934104i \(0.383799\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 7.13828 0.463681
\(238\) 0 0
\(239\) 22.5877 1.46107 0.730537 0.682873i \(-0.239270\pi\)
0.730537 + 0.682873i \(0.239270\pi\)
\(240\) 0 0
\(241\) −16.3412 −1.05263 −0.526315 0.850290i \(-0.676427\pi\)
−0.526315 + 0.850290i \(0.676427\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −2.90321 −0.184727
\(248\) 0 0
\(249\) −10.9748 −0.695500
\(250\) 0 0
\(251\) 10.6780 0.673989 0.336994 0.941507i \(-0.390590\pi\)
0.336994 + 0.941507i \(0.390590\pi\)
\(252\) 0 0
\(253\) 11.7605 0.739376
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 10.8622 0.677565 0.338783 0.940865i \(-0.389985\pi\)
0.338783 + 0.940865i \(0.389985\pi\)
\(258\) 0 0
\(259\) −41.5353 −2.58088
\(260\) 0 0
\(261\) −0.377784 −0.0233843
\(262\) 0 0
\(263\) −16.2810 −1.00393 −0.501965 0.864888i \(-0.667389\pi\)
−0.501965 + 0.864888i \(0.667389\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −18.5303 −1.13404
\(268\) 0 0
\(269\) 2.80642 0.171111 0.0855553 0.996333i \(-0.472734\pi\)
0.0855553 + 0.996333i \(0.472734\pi\)
\(270\) 0 0
\(271\) −21.4637 −1.30383 −0.651913 0.758294i \(-0.726033\pi\)
−0.651913 + 0.758294i \(0.726033\pi\)
\(272\) 0 0
\(273\) 4.11753 0.249204
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 31.1941 1.87427 0.937134 0.348968i \(-0.113468\pi\)
0.937134 + 0.348968i \(0.113468\pi\)
\(278\) 0 0
\(279\) −1.40790 −0.0842885
\(280\) 0 0
\(281\) −17.3176 −1.03308 −0.516540 0.856263i \(-0.672780\pi\)
−0.516540 + 0.856263i \(0.672780\pi\)
\(282\) 0 0
\(283\) 21.5210 1.27929 0.639645 0.768671i \(-0.279081\pi\)
0.639645 + 0.768671i \(0.279081\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 5.48394 0.323707
\(288\) 0 0
\(289\) 19.6128 1.15370
\(290\) 0 0
\(291\) 12.2351 0.717232
\(292\) 0 0
\(293\) 2.47013 0.144306 0.0721532 0.997394i \(-0.477013\pi\)
0.0721532 + 0.997394i \(0.477013\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −3.21432 −0.186514
\(298\) 0 0
\(299\) −3.65878 −0.211593
\(300\) 0 0
\(301\) −27.0781 −1.56075
\(302\) 0 0
\(303\) −8.03657 −0.461689
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 16.2810 0.929206 0.464603 0.885519i \(-0.346197\pi\)
0.464603 + 0.885519i \(0.346197\pi\)
\(308\) 0 0
\(309\) −4.57628 −0.260336
\(310\) 0 0
\(311\) 11.4193 0.647527 0.323764 0.946138i \(-0.395052\pi\)
0.323764 + 0.946138i \(0.395052\pi\)
\(312\) 0 0
\(313\) 17.2208 0.973376 0.486688 0.873576i \(-0.338205\pi\)
0.486688 + 0.873576i \(0.338205\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.00492 0.0564421 0.0282210 0.999602i \(-0.491016\pi\)
0.0282210 + 0.999602i \(0.491016\pi\)
\(318\) 0 0
\(319\) 1.21432 0.0679889
\(320\) 0 0
\(321\) −14.9906 −0.836695
\(322\) 0 0
\(323\) 17.5669 0.977449
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 19.2716 1.06572
\(328\) 0 0
\(329\) 33.4242 1.84274
\(330\) 0 0
\(331\) −10.2494 −0.563355 −0.281678 0.959509i \(-0.590891\pi\)
−0.281678 + 0.959509i \(0.590891\pi\)
\(332\) 0 0
\(333\) −10.0874 −0.552787
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0.423717 0.0230814 0.0115407 0.999933i \(-0.496326\pi\)
0.0115407 + 0.999933i \(0.496326\pi\)
\(338\) 0 0
\(339\) 6.04149 0.328129
\(340\) 0 0
\(341\) 4.52543 0.245066
\(342\) 0 0
\(343\) 12.1635 0.656765
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −22.4701 −1.20626 −0.603130 0.797643i \(-0.706080\pi\)
−0.603130 + 0.797643i \(0.706080\pi\)
\(348\) 0 0
\(349\) −6.38271 −0.341658 −0.170829 0.985301i \(-0.554645\pi\)
−0.170829 + 0.985301i \(0.554645\pi\)
\(350\) 0 0
\(351\) 1.00000 0.0533761
\(352\) 0 0
\(353\) −11.7003 −0.622742 −0.311371 0.950288i \(-0.600788\pi\)
−0.311371 + 0.950288i \(0.600788\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −24.9146 −1.31862
\(358\) 0 0
\(359\) −4.99355 −0.263549 −0.131775 0.991280i \(-0.542068\pi\)
−0.131775 + 0.991280i \(0.542068\pi\)
\(360\) 0 0
\(361\) −10.5714 −0.556387
\(362\) 0 0
\(363\) −0.668149 −0.0350687
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −5.12399 −0.267470 −0.133735 0.991017i \(-0.542697\pi\)
−0.133735 + 0.991017i \(0.542697\pi\)
\(368\) 0 0
\(369\) 1.33185 0.0693334
\(370\) 0 0
\(371\) −16.8687 −0.875777
\(372\) 0 0
\(373\) −0.258721 −0.0133961 −0.00669804 0.999978i \(-0.502132\pi\)
−0.00669804 + 0.999978i \(0.502132\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −0.377784 −0.0194569
\(378\) 0 0
\(379\) 18.0114 0.925182 0.462591 0.886572i \(-0.346920\pi\)
0.462591 + 0.886572i \(0.346920\pi\)
\(380\) 0 0
\(381\) 19.2716 0.987315
\(382\) 0 0
\(383\) 17.8336 0.911255 0.455628 0.890170i \(-0.349415\pi\)
0.455628 + 0.890170i \(0.349415\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −6.57628 −0.334291
\(388\) 0 0
\(389\) −8.32693 −0.422192 −0.211096 0.977465i \(-0.567703\pi\)
−0.211096 + 0.977465i \(0.567703\pi\)
\(390\) 0 0
\(391\) 22.1388 1.11960
\(392\) 0 0
\(393\) −14.2494 −0.718785
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −16.2636 −0.816249 −0.408124 0.912926i \(-0.633817\pi\)
−0.408124 + 0.912926i \(0.633817\pi\)
\(398\) 0 0
\(399\) −11.9541 −0.598452
\(400\) 0 0
\(401\) −3.98571 −0.199037 −0.0995184 0.995036i \(-0.531730\pi\)
−0.0995184 + 0.995036i \(0.531730\pi\)
\(402\) 0 0
\(403\) −1.40790 −0.0701323
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 32.4242 1.60721
\(408\) 0 0
\(409\) −30.0687 −1.48680 −0.743400 0.668847i \(-0.766788\pi\)
−0.743400 + 0.668847i \(0.766788\pi\)
\(410\) 0 0
\(411\) 5.37778 0.265267
\(412\) 0 0
\(413\) −58.5482 −2.88097
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 7.24443 0.354761
\(418\) 0 0
\(419\) −30.9447 −1.51175 −0.755874 0.654717i \(-0.772788\pi\)
−0.755874 + 0.654717i \(0.772788\pi\)
\(420\) 0 0
\(421\) 23.2543 1.13334 0.566672 0.823943i \(-0.308231\pi\)
0.566672 + 0.823943i \(0.308231\pi\)
\(422\) 0 0
\(423\) 8.11753 0.394688
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −10.5877 −0.512373
\(428\) 0 0
\(429\) −3.21432 −0.155189
\(430\) 0 0
\(431\) 34.9862 1.68523 0.842613 0.538520i \(-0.181016\pi\)
0.842613 + 0.538520i \(0.181016\pi\)
\(432\) 0 0
\(433\) −35.0736 −1.68553 −0.842765 0.538282i \(-0.819074\pi\)
−0.842765 + 0.538282i \(0.819074\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 10.6222 0.508129
\(438\) 0 0
\(439\) 17.6686 0.843277 0.421639 0.906764i \(-0.361455\pi\)
0.421639 + 0.906764i \(0.361455\pi\)
\(440\) 0 0
\(441\) 9.95407 0.474003
\(442\) 0 0
\(443\) −13.2114 −0.627693 −0.313846 0.949474i \(-0.601618\pi\)
−0.313846 + 0.949474i \(0.601618\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 17.4795 0.826752
\(448\) 0 0
\(449\) −32.6450 −1.54061 −0.770306 0.637675i \(-0.779896\pi\)
−0.770306 + 0.637675i \(0.779896\pi\)
\(450\) 0 0
\(451\) −4.28100 −0.201584
\(452\) 0 0
\(453\) −22.6795 −1.06558
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −27.9037 −1.30528 −0.652640 0.757668i \(-0.726338\pi\)
−0.652640 + 0.757668i \(0.726338\pi\)
\(458\) 0 0
\(459\) −6.05086 −0.282430
\(460\) 0 0
\(461\) −25.5210 −1.18863 −0.594315 0.804232i \(-0.702577\pi\)
−0.594315 + 0.804232i \(0.702577\pi\)
\(462\) 0 0
\(463\) 0.0715987 0.00332747 0.00166374 0.999999i \(-0.499470\pi\)
0.00166374 + 0.999999i \(0.499470\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 2.59364 0.120019 0.0600096 0.998198i \(-0.480887\pi\)
0.0600096 + 0.998198i \(0.480887\pi\)
\(468\) 0 0
\(469\) −28.9081 −1.33485
\(470\) 0 0
\(471\) 13.3225 0.613868
\(472\) 0 0
\(473\) 21.1383 0.971939
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −4.09679 −0.187579
\(478\) 0 0
\(479\) −14.1635 −0.647145 −0.323573 0.946203i \(-0.604884\pi\)
−0.323573 + 0.946203i \(0.604884\pi\)
\(480\) 0 0
\(481\) −10.0874 −0.459947
\(482\) 0 0
\(483\) −15.0651 −0.685488
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 12.9190 0.585417 0.292709 0.956202i \(-0.405443\pi\)
0.292709 + 0.956202i \(0.405443\pi\)
\(488\) 0 0
\(489\) 16.0558 0.726067
\(490\) 0 0
\(491\) 35.3274 1.59430 0.797152 0.603779i \(-0.206339\pi\)
0.797152 + 0.603779i \(0.206339\pi\)
\(492\) 0 0
\(493\) 2.28592 0.102953
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 29.6400 1.32954
\(498\) 0 0
\(499\) −35.4449 −1.58673 −0.793367 0.608744i \(-0.791674\pi\)
−0.793367 + 0.608744i \(0.791674\pi\)
\(500\) 0 0
\(501\) 8.84299 0.395076
\(502\) 0 0
\(503\) 1.18865 0.0529995 0.0264997 0.999649i \(-0.491564\pi\)
0.0264997 + 0.999649i \(0.491564\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 1.00000 0.0444116
\(508\) 0 0
\(509\) −10.0558 −0.445714 −0.222857 0.974851i \(-0.571538\pi\)
−0.222857 + 0.974851i \(0.571538\pi\)
\(510\) 0 0
\(511\) −30.7382 −1.35978
\(512\) 0 0
\(513\) −2.90321 −0.128180
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −26.0923 −1.14754
\(518\) 0 0
\(519\) −15.7699 −0.692220
\(520\) 0 0
\(521\) −26.8573 −1.17664 −0.588319 0.808629i \(-0.700210\pi\)
−0.588319 + 0.808629i \(0.700210\pi\)
\(522\) 0 0
\(523\) −14.3368 −0.626903 −0.313452 0.949604i \(-0.601485\pi\)
−0.313452 + 0.949604i \(0.601485\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 8.51897 0.371092
\(528\) 0 0
\(529\) −9.61332 −0.417971
\(530\) 0 0
\(531\) −14.2192 −0.617063
\(532\) 0 0
\(533\) 1.33185 0.0576889
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 2.38271 0.102821
\(538\) 0 0
\(539\) −31.9956 −1.37815
\(540\) 0 0
\(541\) −18.9318 −0.813941 −0.406971 0.913441i \(-0.633415\pi\)
−0.406971 + 0.913441i \(0.633415\pi\)
\(542\) 0 0
\(543\) −14.8207 −0.636018
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 45.7288 1.95522 0.977612 0.210415i \(-0.0674815\pi\)
0.977612 + 0.210415i \(0.0674815\pi\)
\(548\) 0 0
\(549\) −2.57136 −0.109743
\(550\) 0 0
\(551\) 1.09679 0.0467247
\(552\) 0 0
\(553\) 29.3921 1.24988
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −44.3323 −1.87842 −0.939211 0.343342i \(-0.888441\pi\)
−0.939211 + 0.343342i \(0.888441\pi\)
\(558\) 0 0
\(559\) −6.57628 −0.278147
\(560\) 0 0
\(561\) 19.4494 0.821154
\(562\) 0 0
\(563\) −22.3511 −0.941985 −0.470993 0.882137i \(-0.656104\pi\)
−0.470993 + 0.882137i \(0.656104\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 4.11753 0.172920
\(568\) 0 0
\(569\) 1.45584 0.0610318 0.0305159 0.999534i \(-0.490285\pi\)
0.0305159 + 0.999534i \(0.490285\pi\)
\(570\) 0 0
\(571\) 7.12537 0.298187 0.149094 0.988823i \(-0.452364\pi\)
0.149094 + 0.988823i \(0.452364\pi\)
\(572\) 0 0
\(573\) −8.10171 −0.338454
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 42.4197 1.76596 0.882979 0.469413i \(-0.155535\pi\)
0.882979 + 0.469413i \(0.155535\pi\)
\(578\) 0 0
\(579\) −7.65878 −0.318288
\(580\) 0 0
\(581\) −45.1891 −1.87476
\(582\) 0 0
\(583\) 13.1684 0.545379
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 4.59210 0.189536 0.0947682 0.995499i \(-0.469789\pi\)
0.0947682 + 0.995499i \(0.469789\pi\)
\(588\) 0 0
\(589\) 4.08742 0.168419
\(590\) 0 0
\(591\) 11.5254 0.474093
\(592\) 0 0
\(593\) 13.9081 0.571139 0.285569 0.958358i \(-0.407817\pi\)
0.285569 + 0.958358i \(0.407817\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 13.5210 0.553377
\(598\) 0 0
\(599\) −2.22077 −0.0907383 −0.0453692 0.998970i \(-0.514446\pi\)
−0.0453692 + 0.998970i \(0.514446\pi\)
\(600\) 0 0
\(601\) −3.54464 −0.144589 −0.0722944 0.997383i \(-0.523032\pi\)
−0.0722944 + 0.997383i \(0.523032\pi\)
\(602\) 0 0
\(603\) −7.02074 −0.285907
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 25.5714 1.03791 0.518955 0.854802i \(-0.326321\pi\)
0.518955 + 0.854802i \(0.326321\pi\)
\(608\) 0 0
\(609\) −1.55554 −0.0630336
\(610\) 0 0
\(611\) 8.11753 0.328400
\(612\) 0 0
\(613\) −28.5718 −1.15401 −0.577003 0.816742i \(-0.695778\pi\)
−0.577003 + 0.816742i \(0.695778\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 7.67307 0.308906 0.154453 0.988000i \(-0.450638\pi\)
0.154453 + 0.988000i \(0.450638\pi\)
\(618\) 0 0
\(619\) 12.8716 0.517352 0.258676 0.965964i \(-0.416714\pi\)
0.258676 + 0.965964i \(0.416714\pi\)
\(620\) 0 0
\(621\) −3.65878 −0.146822
\(622\) 0 0
\(623\) −76.2993 −3.05687
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 9.33185 0.372678
\(628\) 0 0
\(629\) 61.0375 2.43373
\(630\) 0 0
\(631\) −19.8938 −0.791961 −0.395981 0.918259i \(-0.629595\pi\)
−0.395981 + 0.918259i \(0.629595\pi\)
\(632\) 0 0
\(633\) 6.44293 0.256083
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 9.95407 0.394394
\(638\) 0 0
\(639\) 7.19850 0.284768
\(640\) 0 0
\(641\) 0.0508551 0.00200866 0.00100433 0.999999i \(-0.499680\pi\)
0.00100433 + 0.999999i \(0.499680\pi\)
\(642\) 0 0
\(643\) 34.5161 1.36118 0.680590 0.732664i \(-0.261723\pi\)
0.680590 + 0.732664i \(0.261723\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 36.6321 1.44015 0.720077 0.693894i \(-0.244106\pi\)
0.720077 + 0.693894i \(0.244106\pi\)
\(648\) 0 0
\(649\) 45.7052 1.79409
\(650\) 0 0
\(651\) −5.79706 −0.227205
\(652\) 0 0
\(653\) −24.6860 −0.966037 −0.483018 0.875610i \(-0.660460\pi\)
−0.483018 + 0.875610i \(0.660460\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −7.46520 −0.291245
\(658\) 0 0
\(659\) −12.2623 −0.477670 −0.238835 0.971060i \(-0.576765\pi\)
−0.238835 + 0.971060i \(0.576765\pi\)
\(660\) 0 0
\(661\) 34.0973 1.32623 0.663115 0.748518i \(-0.269234\pi\)
0.663115 + 0.748518i \(0.269234\pi\)
\(662\) 0 0
\(663\) −6.05086 −0.234996
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 1.38223 0.0535202
\(668\) 0 0
\(669\) −2.51606 −0.0972765
\(670\) 0 0
\(671\) 8.26517 0.319074
\(672\) 0 0
\(673\) −23.3926 −0.901717 −0.450858 0.892596i \(-0.648882\pi\)
−0.450858 + 0.892596i \(0.648882\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 9.31756 0.358103 0.179051 0.983840i \(-0.442697\pi\)
0.179051 + 0.983840i \(0.442697\pi\)
\(678\) 0 0
\(679\) 50.3783 1.93334
\(680\) 0 0
\(681\) 2.22369 0.0852119
\(682\) 0 0
\(683\) 30.3669 1.16196 0.580978 0.813919i \(-0.302670\pi\)
0.580978 + 0.813919i \(0.302670\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 4.48886 0.171261
\(688\) 0 0
\(689\) −4.09679 −0.156075
\(690\) 0 0
\(691\) −26.5462 −1.00986 −0.504932 0.863159i \(-0.668482\pi\)
−0.504932 + 0.863159i \(0.668482\pi\)
\(692\) 0 0
\(693\) −13.2351 −0.502758
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −8.05884 −0.305250
\(698\) 0 0
\(699\) 10.8988 0.412229
\(700\) 0 0
\(701\) −32.0923 −1.21211 −0.606056 0.795422i \(-0.707249\pi\)
−0.606056 + 0.795422i \(0.707249\pi\)
\(702\) 0 0
\(703\) 29.2859 1.10454
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −33.0908 −1.24451
\(708\) 0 0
\(709\) −29.3230 −1.10125 −0.550623 0.834754i \(-0.685610\pi\)
−0.550623 + 0.834754i \(0.685610\pi\)
\(710\) 0 0
\(711\) 7.13828 0.267706
\(712\) 0 0
\(713\) 5.15118 0.192913
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 22.5877 0.843552
\(718\) 0 0
\(719\) −3.54416 −0.132175 −0.0660875 0.997814i \(-0.521052\pi\)
−0.0660875 + 0.997814i \(0.521052\pi\)
\(720\) 0 0
\(721\) −18.8430 −0.701750
\(722\) 0 0
\(723\) −16.3412 −0.607736
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −20.2721 −0.751851 −0.375925 0.926650i \(-0.622675\pi\)
−0.375925 + 0.926650i \(0.622675\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 39.7921 1.47177
\(732\) 0 0
\(733\) 33.5397 1.23882 0.619409 0.785069i \(-0.287372\pi\)
0.619409 + 0.785069i \(0.287372\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 22.5669 0.831263
\(738\) 0 0
\(739\) −49.0119 −1.80293 −0.901465 0.432852i \(-0.857507\pi\)
−0.901465 + 0.432852i \(0.857507\pi\)
\(740\) 0 0
\(741\) −2.90321 −0.106652
\(742\) 0 0
\(743\) 35.6943 1.30950 0.654748 0.755847i \(-0.272775\pi\)
0.654748 + 0.755847i \(0.272775\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −10.9748 −0.401547
\(748\) 0 0
\(749\) −61.7244 −2.25536
\(750\) 0 0
\(751\) −1.49378 −0.0545090 −0.0272545 0.999629i \(-0.508676\pi\)
−0.0272545 + 0.999629i \(0.508676\pi\)
\(752\) 0 0
\(753\) 10.6780 0.389128
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −43.0830 −1.56588 −0.782939 0.622099i \(-0.786280\pi\)
−0.782939 + 0.622099i \(0.786280\pi\)
\(758\) 0 0
\(759\) 11.7605 0.426879
\(760\) 0 0
\(761\) −5.57581 −0.202123 −0.101061 0.994880i \(-0.532224\pi\)
−0.101061 + 0.994880i \(0.532224\pi\)
\(762\) 0 0
\(763\) 79.3515 2.87272
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −14.2192 −0.513427
\(768\) 0 0
\(769\) 33.4608 1.20663 0.603313 0.797505i \(-0.293847\pi\)
0.603313 + 0.797505i \(0.293847\pi\)
\(770\) 0 0
\(771\) 10.8622 0.391193
\(772\) 0 0
\(773\) −27.3778 −0.984710 −0.492355 0.870394i \(-0.663864\pi\)
−0.492355 + 0.870394i \(0.663864\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −41.5353 −1.49007
\(778\) 0 0
\(779\) −3.86665 −0.138537
\(780\) 0 0
\(781\) −23.1383 −0.827953
\(782\) 0 0
\(783\) −0.377784 −0.0135009
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 30.5288 1.08823 0.544117 0.839009i \(-0.316865\pi\)
0.544117 + 0.839009i \(0.316865\pi\)
\(788\) 0 0
\(789\) −16.2810 −0.579619
\(790\) 0 0
\(791\) 24.8760 0.884489
\(792\) 0 0
\(793\) −2.57136 −0.0913117
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −5.54909 −0.196559 −0.0982793 0.995159i \(-0.531334\pi\)
−0.0982793 + 0.995159i \(0.531334\pi\)
\(798\) 0 0
\(799\) −49.1180 −1.73767
\(800\) 0 0
\(801\) −18.5303 −0.654738
\(802\) 0 0
\(803\) 23.9956 0.846785
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 2.80642 0.0987908
\(808\) 0 0
\(809\) 1.86665 0.0656278 0.0328139 0.999461i \(-0.489553\pi\)
0.0328139 + 0.999461i \(0.489553\pi\)
\(810\) 0 0
\(811\) 0.721011 0.0253181 0.0126591 0.999920i \(-0.495970\pi\)
0.0126591 + 0.999920i \(0.495970\pi\)
\(812\) 0 0
\(813\) −21.4637 −0.752764
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 19.0923 0.667957
\(818\) 0 0
\(819\) 4.11753 0.143878
\(820\) 0 0
\(821\) 2.05884 0.0718540 0.0359270 0.999354i \(-0.488562\pi\)
0.0359270 + 0.999354i \(0.488562\pi\)
\(822\) 0 0
\(823\) −27.9210 −0.973266 −0.486633 0.873606i \(-0.661775\pi\)
−0.486633 + 0.873606i \(0.661775\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 4.94761 0.172045 0.0860227 0.996293i \(-0.472584\pi\)
0.0860227 + 0.996293i \(0.472584\pi\)
\(828\) 0 0
\(829\) −3.70519 −0.128687 −0.0643433 0.997928i \(-0.520495\pi\)
−0.0643433 + 0.997928i \(0.520495\pi\)
\(830\) 0 0
\(831\) 31.1941 1.08211
\(832\) 0 0
\(833\) −60.2306 −2.08687
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −1.40790 −0.0486640
\(838\) 0 0
\(839\) 38.3956 1.32556 0.662782 0.748813i \(-0.269376\pi\)
0.662782 + 0.748813i \(0.269376\pi\)
\(840\) 0 0
\(841\) −28.8573 −0.995079
\(842\) 0 0
\(843\) −17.3176 −0.596448
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −2.75112 −0.0945297
\(848\) 0 0
\(849\) 21.5210 0.738598
\(850\) 0 0
\(851\) 36.9077 1.26518
\(852\) 0 0
\(853\) 41.5941 1.42416 0.712078 0.702101i \(-0.247754\pi\)
0.712078 + 0.702101i \(0.247754\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 3.71456 0.126887 0.0634434 0.997985i \(-0.479792\pi\)
0.0634434 + 0.997985i \(0.479792\pi\)
\(858\) 0 0
\(859\) −9.89384 −0.337574 −0.168787 0.985653i \(-0.553985\pi\)
−0.168787 + 0.985653i \(0.553985\pi\)
\(860\) 0 0
\(861\) 5.48394 0.186892
\(862\) 0 0
\(863\) −25.7862 −0.877771 −0.438885 0.898543i \(-0.644627\pi\)
−0.438885 + 0.898543i \(0.644627\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 19.6128 0.666087
\(868\) 0 0
\(869\) −22.9447 −0.778346
\(870\) 0 0
\(871\) −7.02074 −0.237889
\(872\) 0 0
\(873\) 12.2351 0.414094
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −49.5812 −1.67424 −0.837119 0.547021i \(-0.815762\pi\)
−0.837119 + 0.547021i \(0.815762\pi\)
\(878\) 0 0
\(879\) 2.47013 0.0833153
\(880\) 0 0
\(881\) 42.0593 1.41701 0.708507 0.705704i \(-0.249369\pi\)
0.708507 + 0.705704i \(0.249369\pi\)
\(882\) 0 0
\(883\) −47.1753 −1.58758 −0.793788 0.608195i \(-0.791894\pi\)
−0.793788 + 0.608195i \(0.791894\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −30.0143 −1.00778 −0.503891 0.863767i \(-0.668099\pi\)
−0.503891 + 0.863767i \(0.668099\pi\)
\(888\) 0 0
\(889\) 79.3515 2.66137
\(890\) 0 0
\(891\) −3.21432 −0.107684
\(892\) 0 0
\(893\) −23.5669 −0.788637
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −3.65878 −0.122163
\(898\) 0 0
\(899\) 0.531881 0.0177392
\(900\) 0 0
\(901\) 24.7891 0.825844
\(902\) 0 0
\(903\) −27.0781 −0.901101
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 33.5941 1.11547 0.557737 0.830018i \(-0.311670\pi\)
0.557737 + 0.830018i \(0.311670\pi\)
\(908\) 0 0
\(909\) −8.03657 −0.266556
\(910\) 0 0
\(911\) −1.07805 −0.0357175 −0.0178587 0.999841i \(-0.505685\pi\)
−0.0178587 + 0.999841i \(0.505685\pi\)
\(912\) 0 0
\(913\) 35.2766 1.16748
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −58.6722 −1.93753
\(918\) 0 0
\(919\) −32.6133 −1.07581 −0.537907 0.843004i \(-0.680785\pi\)
−0.537907 + 0.843004i \(0.680785\pi\)
\(920\) 0 0
\(921\) 16.2810 0.536477
\(922\) 0 0
\(923\) 7.19850 0.236941
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −4.57628 −0.150305
\(928\) 0 0
\(929\) 2.35857 0.0773822 0.0386911 0.999251i \(-0.487681\pi\)
0.0386911 + 0.999251i \(0.487681\pi\)
\(930\) 0 0
\(931\) −28.8988 −0.947119
\(932\) 0 0
\(933\) 11.4193 0.373850
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −26.2859 −0.858724 −0.429362 0.903133i \(-0.641261\pi\)
−0.429362 + 0.903133i \(0.641261\pi\)
\(938\) 0 0
\(939\) 17.2208 0.561979
\(940\) 0 0
\(941\) −7.07805 −0.230738 −0.115369 0.993323i \(-0.536805\pi\)
−0.115369 + 0.993323i \(0.536805\pi\)
\(942\) 0 0
\(943\) −4.87295 −0.158685
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 23.3990 0.760365 0.380183 0.924911i \(-0.375861\pi\)
0.380183 + 0.924911i \(0.375861\pi\)
\(948\) 0 0
\(949\) −7.46520 −0.242331
\(950\) 0 0
\(951\) 1.00492 0.0325868
\(952\) 0 0
\(953\) 44.6815 1.44738 0.723688 0.690127i \(-0.242445\pi\)
0.723688 + 0.690127i \(0.242445\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 1.21432 0.0392534
\(958\) 0 0
\(959\) 22.1432 0.715041
\(960\) 0 0
\(961\) −29.0178 −0.936059
\(962\) 0 0
\(963\) −14.9906 −0.483066
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 41.5640 1.33661 0.668304 0.743888i \(-0.267021\pi\)
0.668304 + 0.743888i \(0.267021\pi\)
\(968\) 0 0
\(969\) 17.5669 0.564331
\(970\) 0 0
\(971\) 10.8988 0.349758 0.174879 0.984590i \(-0.444047\pi\)
0.174879 + 0.984590i \(0.444047\pi\)
\(972\) 0 0
\(973\) 29.8292 0.956279
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 40.9688 1.31071 0.655355 0.755321i \(-0.272519\pi\)
0.655355 + 0.755321i \(0.272519\pi\)
\(978\) 0 0
\(979\) 59.5625 1.90362
\(980\) 0 0
\(981\) 19.2716 0.615296
\(982\) 0 0
\(983\) 47.5640 1.51706 0.758528 0.651640i \(-0.225919\pi\)
0.758528 + 0.651640i \(0.225919\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 33.4242 1.06390
\(988\) 0 0
\(989\) 24.0612 0.765101
\(990\) 0 0
\(991\) −10.8845 −0.345757 −0.172878 0.984943i \(-0.555307\pi\)
−0.172878 + 0.984943i \(0.555307\pi\)
\(992\) 0 0
\(993\) −10.2494 −0.325253
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −20.9684 −0.664075 −0.332037 0.943266i \(-0.607736\pi\)
−0.332037 + 0.943266i \(0.607736\pi\)
\(998\) 0 0
\(999\) −10.0874 −0.319152
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.bo.1.3 yes 3
5.4 even 2 7800.2.a.bl.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7800.2.a.bl.1.1 3 5.4 even 2
7800.2.a.bo.1.3 yes 3 1.1 even 1 trivial