Properties

Label 7800.2.a.bl.1.1
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: 3.3.148.1
Defining polynomial: \( x^{3} - x^{2} - 3x + 1 \) Copy content Toggle raw display
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 1.1
Root \(0.311108\) of defining polynomial
Character \(\chi\) \(=\) 7800.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} -4.11753 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} -4.11753 q^{7} +1.00000 q^{9} -3.21432 q^{11} -1.00000 q^{13} +6.05086 q^{17} -2.90321 q^{19} +4.11753 q^{21} +3.65878 q^{23} -1.00000 q^{27} -0.377784 q^{29} -1.40790 q^{31} +3.21432 q^{33} +10.0874 q^{37} +1.00000 q^{39} +1.33185 q^{41} +6.57628 q^{43} -8.11753 q^{47} +9.95407 q^{49} -6.05086 q^{51} +4.09679 q^{53} +2.90321 q^{57} -14.2192 q^{59} -2.57136 q^{61} -4.11753 q^{63} +7.02074 q^{67} -3.65878 q^{69} +7.19850 q^{71} +7.46520 q^{73} +13.2351 q^{77} +7.13828 q^{79} +1.00000 q^{81} +10.9748 q^{83} +0.377784 q^{87} -18.5303 q^{89} +4.11753 q^{91} +1.40790 q^{93} -12.2351 q^{97} -3.21432 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 3 q^{3} + q^{7} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 3 q^{3} + q^{7} + 3 q^{9} - 3 q^{11} - 3 q^{13} + 5 q^{17} - 2 q^{19} - q^{21} + 4 q^{23} - 3 q^{27} - q^{29} - 11 q^{31} + 3 q^{33} + 10 q^{37} + 3 q^{39} - 16 q^{41} - 11 q^{47} + 10 q^{49} - 5 q^{51} + 19 q^{53} + 2 q^{57} - 3 q^{59} - 21 q^{61} + q^{63} + q^{67} - 4 q^{69} + 2 q^{71} + 2 q^{73} + 13 q^{77} - 12 q^{79} + 3 q^{81} - 7 q^{83} + q^{87} - 16 q^{89} - q^{91} + 11 q^{93} - 10 q^{97} - 3 q^{99}+O(q^{100}) \) 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
\(7\) −4.11753 −1.55628 −0.778140 0.628090i \(-0.783837\pi\)
−0.778140 + 0.628090i \(0.783837\pi\)
\(8\) 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 \(-0.237757\pi\)
0.733774 + 0.679394i \(0.237757\pi\)
\(18\) 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 \(-0.375423\pi\)
0.381454 + 0.924388i \(0.375423\pi\)
\(24\) 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 \(-0.188807\pi\)
0.829181 + 0.558980i \(0.188807\pi\)
\(38\) 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 \(-0.332805\pi\)
0.501437 + 0.865194i \(0.332805\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −8.11753 −1.18406 −0.592032 0.805915i \(-0.701674\pi\)
−0.592032 + 0.805915i \(0.701674\pi\)
\(48\) 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 \(-0.409212\pi\)
0.281369 + 0.959600i \(0.409212\pi\)
\(54\) 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 \(-0.358915\pi\)
0.428860 + 0.903371i \(0.358915\pi\)
\(68\) 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 \(-0.356088\pi\)
0.436868 + 0.899526i \(0.356088\pi\)
\(74\) 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 \(-0.294243\pi\)
0.602321 + 0.798254i \(0.294243\pi\)
\(84\) 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 \(-0.713331\pi\)
−0.621141 + 0.783699i \(0.713331\pi\)
\(98\) 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 \(-0.427612\pi\)
0.225457 + 0.974253i \(0.427612\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 14.9906 1.44920 0.724600 0.689170i \(-0.242025\pi\)
0.724600 + 0.689170i \(0.242025\pi\)
\(108\) 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 \(-0.591717\pi\)
−0.284168 + 0.958775i \(0.591717\pi\)
\(114\) 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 \(-0.826468\pi\)
−0.855040 + 0.518562i \(0.826468\pi\)
\(128\) 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 \(-0.573784\pi\)
−0.229728 + 0.973255i \(0.573784\pi\)
\(138\) 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 \(-0.678418\pi\)
−0.531625 + 0.846980i \(0.678418\pi\)
\(158\) 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 \(-0.716451\pi\)
−0.628793 + 0.777573i \(0.716451\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −8.84299 −0.684291 −0.342146 0.939647i \(-0.611154\pi\)
−0.342146 + 0.939647i \(0.611154\pi\)
\(168\) 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 \(-0.295374\pi\)
0.599480 + 0.800390i \(0.295374\pi\)
\(174\) 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 \(-0.411108\pi\)
0.275646 + 0.961259i \(0.411108\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −11.5254 −0.821153 −0.410576 0.911826i \(-0.634672\pi\)
−0.410576 + 0.911826i \(0.634672\pi\)
\(198\) 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 \(-0.473153\pi\)
0.0842439 + 0.996445i \(0.473153\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −2.22369 −0.147591 −0.0737957 0.997273i \(-0.523511\pi\)
−0.0737957 + 0.997273i \(0.523511\pi\)
\(228\) 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 \(-0.616201\pi\)
−0.357001 + 0.934104i \(0.616201\pi\)
\(234\) 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 \(-0.610015\pi\)
−0.338783 + 0.940865i \(0.610015\pi\)
\(258\) 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 \(-0.332611\pi\)
0.501965 + 0.864888i \(0.332611\pi\)
\(264\) 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 \(-0.886532\pi\)
−0.937134 + 0.348968i \(0.886532\pi\)
\(278\) 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 \(-0.720919\pi\)
−0.639645 + 0.768671i \(0.720919\pi\)
\(284\) 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 \(-0.522987\pi\)
−0.0721532 + 0.997394i \(0.522987\pi\)
\(294\) 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 \(-0.653803\pi\)
−0.464603 + 0.885519i \(0.653803\pi\)
\(308\) 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 \(-0.661795\pi\)
−0.486688 + 0.873576i \(0.661795\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.00492 −0.0564421 −0.0282210 0.999602i \(-0.508984\pi\)
−0.0282210 + 0.999602i \(0.508984\pi\)
\(318\) 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 \(-0.503674\pi\)
−0.0115407 + 0.999933i \(0.503674\pi\)
\(338\) 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 \(-0.293920\pi\)
0.603130 + 0.797643i \(0.293920\pi\)
\(348\) 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 \(-0.399212\pi\)
0.311371 + 0.950288i \(0.399212\pi\)
\(354\) 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 \(-0.457303\pi\)
0.133735 + 0.991017i \(0.457303\pi\)
\(368\) 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 \(-0.497868\pi\)
0.00669804 + 0.999978i \(0.497868\pi\)
\(374\) 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 \(-0.650585\pi\)
−0.455628 + 0.890170i \(0.650585\pi\)
\(384\) 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 \(-0.366183\pi\)
0.408124 + 0.912926i \(0.366183\pi\)
\(398\) 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 \(-0.180926\pi\)
0.842765 + 0.538282i \(0.180926\pi\)
\(434\) 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 \(-0.398382\pi\)
0.313846 + 0.949474i \(0.398382\pi\)
\(444\) 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 \(-0.273662\pi\)
0.652640 + 0.757668i \(0.273662\pi\)
\(458\) 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 \(-0.500530\pi\)
−0.00166374 + 0.999999i \(0.500530\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −2.59364 −0.120019 −0.0600096 0.998198i \(-0.519113\pi\)
−0.0600096 + 0.998198i \(0.519113\pi\)
\(468\) 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 \(-0.594557\pi\)
−0.292709 + 0.956202i \(0.594557\pi\)
\(488\) 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 \(-0.508436\pi\)
−0.0264997 + 0.999649i \(0.508436\pi\)
\(504\) 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 \(-0.398515\pi\)
0.313452 + 0.949604i \(0.398515\pi\)
\(524\) 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 \(-0.932519\pi\)
−0.977612 + 0.210415i \(0.932519\pi\)
\(548\) 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 \(-0.111559\pi\)
0.939211 + 0.343342i \(0.111559\pi\)
\(558\) 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 \(-0.343896\pi\)
0.470993 + 0.882137i \(0.343896\pi\)
\(564\) 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 \(-0.844465\pi\)
−0.882979 + 0.469413i \(0.844465\pi\)
\(578\) 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 \(-0.530211\pi\)
−0.0947682 + 0.995499i \(0.530211\pi\)
\(588\) 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 \(-0.592183\pi\)
−0.285569 + 0.958358i \(0.592183\pi\)
\(594\) 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 \(-0.673679\pi\)
−0.518955 + 0.854802i \(0.673679\pi\)
\(608\) 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 \(-0.304222\pi\)
0.577003 + 0.816742i \(0.304222\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −7.67307 −0.308906 −0.154453 0.988000i \(-0.549362\pi\)
−0.154453 + 0.988000i \(0.549362\pi\)
\(618\) 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 \(-0.738277\pi\)
−0.680590 + 0.732664i \(0.738277\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −36.6321 −1.44015 −0.720077 0.693894i \(-0.755894\pi\)
−0.720077 + 0.693894i \(0.755894\pi\)
\(648\) 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 \(-0.339540\pi\)
0.483018 + 0.875610i \(0.339540\pi\)
\(654\) 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 \(-0.351118\pi\)
0.450858 + 0.892596i \(0.351118\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −9.31756 −0.358103 −0.179051 0.983840i \(-0.557303\pi\)
−0.179051 + 0.983840i \(0.557303\pi\)
\(678\) 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 \(-0.697330\pi\)
−0.580978 + 0.813919i \(0.697330\pi\)
\(684\) 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 \(-0.377325\pi\)
0.375925 + 0.926650i \(0.377325\pi\)
\(728\) 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 \(-0.712628\pi\)
−0.619409 + 0.785069i \(0.712628\pi\)
\(734\) 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 \(-0.727225\pi\)
−0.654748 + 0.755847i \(0.727225\pi\)
\(744\) 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 \(-0.213720\pi\)
0.782939 + 0.622099i \(0.213720\pi\)
\(758\) 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 \(-0.336136\pi\)
0.492355 + 0.870394i \(0.336136\pi\)
\(774\) 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 \(-0.683135\pi\)
−0.544117 + 0.839009i \(0.683135\pi\)
\(788\) 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 \(-0.468666\pi\)
0.0982793 + 0.995159i \(0.468666\pi\)
\(798\) 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 \(-0.338225\pi\)
0.486633 + 0.873606i \(0.338225\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −4.94761 −0.172045 −0.0860227 0.996293i \(-0.527416\pi\)
−0.0860227 + 0.996293i \(0.527416\pi\)
\(828\) 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 \(-0.752246\pi\)
−0.712078 + 0.702101i \(0.752246\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −3.71456 −0.126887 −0.0634434 0.997985i \(-0.520208\pi\)
−0.0634434 + 0.997985i \(0.520208\pi\)
\(858\) 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 \(-0.355373\pi\)
0.438885 + 0.898543i \(0.355373\pi\)
\(864\) 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 \(-0.184238\pi\)
0.837119 + 0.547021i \(0.184238\pi\)
\(878\) 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 \(-0.208106\pi\)
0.793788 + 0.608195i \(0.208106\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 30.0143 1.00778 0.503891 0.863767i \(-0.331901\pi\)
0.503891 + 0.863767i \(0.331901\pi\)
\(888\) 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 \(-0.688330\pi\)
−0.557737 + 0.830018i \(0.688330\pi\)
\(908\) 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 \(-0.358739\pi\)
0.429362 + 0.903133i \(0.358739\pi\)
\(938\) 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 \(-0.624139\pi\)
−0.380183 + 0.924911i \(0.624139\pi\)
\(948\) 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 \(-0.757555\pi\)
−0.723688 + 0.690127i \(0.757555\pi\)
\(954\) 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 \(-0.732979\pi\)
−0.668304 + 0.743888i \(0.732979\pi\)
\(968\) 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 \(-0.727481\pi\)
−0.655355 + 0.755321i \(0.727481\pi\)
\(978\) 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 \(-0.774081\pi\)
−0.758528 + 0.651640i \(0.774081\pi\)
\(984\) 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 \(-0.392264\pi\)
0.332037 + 0.943266i \(0.392264\pi\)
\(998\) 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.bl.1.1 3
5.4 even 2 7800.2.a.bo.1.3 yes 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7800.2.a.bl.1.1 3 1.1 even 1 trivial
7800.2.a.bo.1.3 yes 3 5.4 even 2