Properties

Label 9360.2.a.cl.1.1
Level $9360$
Weight $2$
Character 9360.1
Self dual yes
Analytic conductor $74.740$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 9360 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9360.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(74.7399762919\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{17}) \)
Defining polynomial: \( x^{2} - x - 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 585)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.56155\) of defining polynomial
Character \(\chi\) \(=\) 9360.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{5} +0.438447 q^{7} +O(q^{10})\) \(q-1.00000 q^{5} +0.438447 q^{7} -1.56155 q^{11} -1.00000 q^{13} -1.56155 q^{17} +5.12311 q^{19} +2.43845 q^{23} +1.00000 q^{25} +7.12311 q^{29} -6.00000 q^{31} -0.438447 q^{35} -10.6847 q^{37} -3.56155 q^{41} -3.12311 q^{43} +11.1231 q^{47} -6.80776 q^{49} +4.68466 q^{53} +1.56155 q^{55} +12.0000 q^{59} -6.68466 q^{61} +1.00000 q^{65} +11.3693 q^{67} +10.4384 q^{71} -6.00000 q^{73} -0.684658 q^{77} -4.68466 q^{79} -16.4924 q^{83} +1.56155 q^{85} -10.6847 q^{89} -0.438447 q^{91} -5.12311 q^{95} +16.9309 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{5} + 5 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{5} + 5 q^{7} + q^{11} - 2 q^{13} + q^{17} + 2 q^{19} + 9 q^{23} + 2 q^{25} + 6 q^{29} - 12 q^{31} - 5 q^{35} - 9 q^{37} - 3 q^{41} + 2 q^{43} + 14 q^{47} + 7 q^{49} - 3 q^{53} - q^{55} + 24 q^{59} - q^{61} + 2 q^{65} - 2 q^{67} + 25 q^{71} - 12 q^{73} + 11 q^{77} + 3 q^{79} - q^{85} - 9 q^{89} - 5 q^{91} - 2 q^{95} + 5 q^{97}+O(q^{100}) \) 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
\(3\) 0 0
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 0.438447 0.165717 0.0828587 0.996561i \(-0.473595\pi\)
0.0828587 + 0.996561i \(0.473595\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.56155 −0.470826 −0.235413 0.971895i \(-0.575644\pi\)
−0.235413 + 0.971895i \(0.575644\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.56155 −0.378732 −0.189366 0.981907i \(-0.560643\pi\)
−0.189366 + 0.981907i \(0.560643\pi\)
\(18\) 0 0
\(19\) 5.12311 1.17532 0.587661 0.809108i \(-0.300049\pi\)
0.587661 + 0.809108i \(0.300049\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.43845 0.508451 0.254226 0.967145i \(-0.418179\pi\)
0.254226 + 0.967145i \(0.418179\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 7.12311 1.32273 0.661364 0.750065i \(-0.269978\pi\)
0.661364 + 0.750065i \(0.269978\pi\)
\(30\) 0 0
\(31\) −6.00000 −1.07763 −0.538816 0.842424i \(-0.681128\pi\)
−0.538816 + 0.842424i \(0.681128\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −0.438447 −0.0741111
\(36\) 0 0
\(37\) −10.6847 −1.75655 −0.878274 0.478159i \(-0.841304\pi\)
−0.878274 + 0.478159i \(0.841304\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −3.56155 −0.556221 −0.278111 0.960549i \(-0.589708\pi\)
−0.278111 + 0.960549i \(0.589708\pi\)
\(42\) 0 0
\(43\) −3.12311 −0.476269 −0.238135 0.971232i \(-0.576536\pi\)
−0.238135 + 0.971232i \(0.576536\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 11.1231 1.62247 0.811236 0.584719i \(-0.198795\pi\)
0.811236 + 0.584719i \(0.198795\pi\)
\(48\) 0 0
\(49\) −6.80776 −0.972538
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 4.68466 0.643487 0.321744 0.946827i \(-0.395731\pi\)
0.321744 + 0.946827i \(0.395731\pi\)
\(54\) 0 0
\(55\) 1.56155 0.210560
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 12.0000 1.56227 0.781133 0.624364i \(-0.214642\pi\)
0.781133 + 0.624364i \(0.214642\pi\)
\(60\) 0 0
\(61\) −6.68466 −0.855883 −0.427941 0.903806i \(-0.640761\pi\)
−0.427941 + 0.903806i \(0.640761\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1.00000 0.124035
\(66\) 0 0
\(67\) 11.3693 1.38898 0.694492 0.719501i \(-0.255629\pi\)
0.694492 + 0.719501i \(0.255629\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 10.4384 1.23882 0.619408 0.785069i \(-0.287373\pi\)
0.619408 + 0.785069i \(0.287373\pi\)
\(72\) 0 0
\(73\) −6.00000 −0.702247 −0.351123 0.936329i \(-0.614200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −0.684658 −0.0780241
\(78\) 0 0
\(79\) −4.68466 −0.527065 −0.263533 0.964650i \(-0.584888\pi\)
−0.263533 + 0.964650i \(0.584888\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −16.4924 −1.81028 −0.905139 0.425115i \(-0.860234\pi\)
−0.905139 + 0.425115i \(0.860234\pi\)
\(84\) 0 0
\(85\) 1.56155 0.169374
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −10.6847 −1.13257 −0.566286 0.824209i \(-0.691620\pi\)
−0.566286 + 0.824209i \(0.691620\pi\)
\(90\) 0 0
\(91\) −0.438447 −0.0459618
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −5.12311 −0.525620
\(96\) 0 0
\(97\) 16.9309 1.71907 0.859535 0.511077i \(-0.170753\pi\)
0.859535 + 0.511077i \(0.170753\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −10.2462 −1.01954 −0.509768 0.860312i \(-0.670269\pi\)
−0.509768 + 0.860312i \(0.670269\pi\)
\(102\) 0 0
\(103\) 15.1231 1.49012 0.745062 0.666995i \(-0.232420\pi\)
0.745062 + 0.666995i \(0.232420\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 10.9309 1.05673 0.528364 0.849018i \(-0.322806\pi\)
0.528364 + 0.849018i \(0.322806\pi\)
\(108\) 0 0
\(109\) −2.00000 −0.191565 −0.0957826 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 4.87689 0.458780 0.229390 0.973335i \(-0.426327\pi\)
0.229390 + 0.973335i \(0.426327\pi\)
\(114\) 0 0
\(115\) −2.43845 −0.227386
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −0.684658 −0.0627625
\(120\) 0 0
\(121\) −8.56155 −0.778323
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −1.75379 −0.155624 −0.0778118 0.996968i \(-0.524793\pi\)
−0.0778118 + 0.996968i \(0.524793\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) 2.24621 0.194771
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1.12311 −0.0959534 −0.0479767 0.998848i \(-0.515277\pi\)
−0.0479767 + 0.998848i \(0.515277\pi\)
\(138\) 0 0
\(139\) −3.31534 −0.281204 −0.140602 0.990066i \(-0.544904\pi\)
−0.140602 + 0.990066i \(0.544904\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 1.56155 0.130584
\(144\) 0 0
\(145\) −7.12311 −0.591542
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 17.8078 1.45887 0.729434 0.684051i \(-0.239783\pi\)
0.729434 + 0.684051i \(0.239783\pi\)
\(150\) 0 0
\(151\) −11.3693 −0.925222 −0.462611 0.886561i \(-0.653087\pi\)
−0.462611 + 0.886561i \(0.653087\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 6.00000 0.481932
\(156\) 0 0
\(157\) 3.36932 0.268901 0.134450 0.990920i \(-0.457073\pi\)
0.134450 + 0.990920i \(0.457073\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1.06913 0.0842593
\(162\) 0 0
\(163\) −16.0540 −1.25744 −0.628722 0.777630i \(-0.716422\pi\)
−0.628722 + 0.777630i \(0.716422\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 4.87689 0.377385 0.188693 0.982036i \(-0.439575\pi\)
0.188693 + 0.982036i \(0.439575\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −12.8769 −0.979012 −0.489506 0.872000i \(-0.662823\pi\)
−0.489506 + 0.872000i \(0.662823\pi\)
\(174\) 0 0
\(175\) 0.438447 0.0331435
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −4.87689 −0.364516 −0.182258 0.983251i \(-0.558341\pi\)
−0.182258 + 0.983251i \(0.558341\pi\)
\(180\) 0 0
\(181\) 13.3153 0.989722 0.494861 0.868972i \(-0.335219\pi\)
0.494861 + 0.868972i \(0.335219\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 10.6847 0.785552
\(186\) 0 0
\(187\) 2.43845 0.178317
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 19.6155 1.41933 0.709665 0.704539i \(-0.248846\pi\)
0.709665 + 0.704539i \(0.248846\pi\)
\(192\) 0 0
\(193\) 19.5616 1.40807 0.704036 0.710165i \(-0.251379\pi\)
0.704036 + 0.710165i \(0.251379\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 3.36932 0.240054 0.120027 0.992771i \(-0.461702\pi\)
0.120027 + 0.992771i \(0.461702\pi\)
\(198\) 0 0
\(199\) 8.00000 0.567105 0.283552 0.958957i \(-0.408487\pi\)
0.283552 + 0.958957i \(0.408487\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 3.12311 0.219199
\(204\) 0 0
\(205\) 3.56155 0.248750
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −8.00000 −0.553372
\(210\) 0 0
\(211\) −6.24621 −0.430007 −0.215003 0.976613i \(-0.568976\pi\)
−0.215003 + 0.976613i \(0.568976\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 3.12311 0.212994
\(216\) 0 0
\(217\) −2.63068 −0.178582
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 1.56155 0.105041
\(222\) 0 0
\(223\) 15.3693 1.02921 0.514603 0.857429i \(-0.327939\pi\)
0.514603 + 0.857429i \(0.327939\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 5.75379 0.381892 0.190946 0.981601i \(-0.438844\pi\)
0.190946 + 0.981601i \(0.438844\pi\)
\(228\) 0 0
\(229\) 17.1231 1.13153 0.565763 0.824568i \(-0.308582\pi\)
0.565763 + 0.824568i \(0.308582\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 27.8078 1.82175 0.910874 0.412685i \(-0.135409\pi\)
0.910874 + 0.412685i \(0.135409\pi\)
\(234\) 0 0
\(235\) −11.1231 −0.725591
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 22.9309 1.48327 0.741637 0.670801i \(-0.234050\pi\)
0.741637 + 0.670801i \(0.234050\pi\)
\(240\) 0 0
\(241\) 24.7386 1.59356 0.796778 0.604272i \(-0.206536\pi\)
0.796778 + 0.604272i \(0.206536\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 6.80776 0.434932
\(246\) 0 0
\(247\) −5.12311 −0.325975
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 26.2462 1.65665 0.828323 0.560251i \(-0.189295\pi\)
0.828323 + 0.560251i \(0.189295\pi\)
\(252\) 0 0
\(253\) −3.80776 −0.239392
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 12.8769 0.803239 0.401619 0.915807i \(-0.368448\pi\)
0.401619 + 0.915807i \(0.368448\pi\)
\(258\) 0 0
\(259\) −4.68466 −0.291091
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −2.24621 −0.138507 −0.0692537 0.997599i \(-0.522062\pi\)
−0.0692537 + 0.997599i \(0.522062\pi\)
\(264\) 0 0
\(265\) −4.68466 −0.287776
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0.876894 0.0534652 0.0267326 0.999643i \(-0.491490\pi\)
0.0267326 + 0.999643i \(0.491490\pi\)
\(270\) 0 0
\(271\) 19.3693 1.17660 0.588301 0.808642i \(-0.299797\pi\)
0.588301 + 0.808642i \(0.299797\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.56155 −0.0941652
\(276\) 0 0
\(277\) −12.2462 −0.735804 −0.367902 0.929865i \(-0.619924\pi\)
−0.367902 + 0.929865i \(0.619924\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −4.24621 −0.253308 −0.126654 0.991947i \(-0.540424\pi\)
−0.126654 + 0.991947i \(0.540424\pi\)
\(282\) 0 0
\(283\) 4.00000 0.237775 0.118888 0.992908i \(-0.462067\pi\)
0.118888 + 0.992908i \(0.462067\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1.56155 −0.0921755
\(288\) 0 0
\(289\) −14.5616 −0.856562
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 20.2462 1.18280 0.591398 0.806380i \(-0.298576\pi\)
0.591398 + 0.806380i \(0.298576\pi\)
\(294\) 0 0
\(295\) −12.0000 −0.698667
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −2.43845 −0.141019
\(300\) 0 0
\(301\) −1.36932 −0.0789261
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 6.68466 0.382762
\(306\) 0 0
\(307\) −7.56155 −0.431561 −0.215780 0.976442i \(-0.569230\pi\)
−0.215780 + 0.976442i \(0.569230\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 2.63068 0.149172 0.0745862 0.997215i \(-0.476236\pi\)
0.0745862 + 0.997215i \(0.476236\pi\)
\(312\) 0 0
\(313\) 29.1231 1.64614 0.823068 0.567943i \(-0.192261\pi\)
0.823068 + 0.567943i \(0.192261\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.50758 −0.0846740 −0.0423370 0.999103i \(-0.513480\pi\)
−0.0423370 + 0.999103i \(0.513480\pi\)
\(318\) 0 0
\(319\) −11.1231 −0.622774
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −8.00000 −0.445132
\(324\) 0 0
\(325\) −1.00000 −0.0554700
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 4.87689 0.268872
\(330\) 0 0
\(331\) −29.1231 −1.60075 −0.800375 0.599499i \(-0.795366\pi\)
−0.800375 + 0.599499i \(0.795366\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −11.3693 −0.621172
\(336\) 0 0
\(337\) −30.4924 −1.66103 −0.830514 0.556998i \(-0.811953\pi\)
−0.830514 + 0.556998i \(0.811953\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 9.36932 0.507377
\(342\) 0 0
\(343\) −6.05398 −0.326884
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −26.0540 −1.39865 −0.699325 0.714804i \(-0.746516\pi\)
−0.699325 + 0.714804i \(0.746516\pi\)
\(348\) 0 0
\(349\) −23.3693 −1.25093 −0.625465 0.780252i \(-0.715091\pi\)
−0.625465 + 0.780252i \(0.715091\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 22.4924 1.19715 0.598575 0.801066i \(-0.295734\pi\)
0.598575 + 0.801066i \(0.295734\pi\)
\(354\) 0 0
\(355\) −10.4384 −0.554015
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −14.2462 −0.751886 −0.375943 0.926643i \(-0.622681\pi\)
−0.375943 + 0.926643i \(0.622681\pi\)
\(360\) 0 0
\(361\) 7.24621 0.381380
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 6.00000 0.314054
\(366\) 0 0
\(367\) 1.75379 0.0915470 0.0457735 0.998952i \(-0.485425\pi\)
0.0457735 + 0.998952i \(0.485425\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 2.05398 0.106637
\(372\) 0 0
\(373\) 12.2462 0.634085 0.317042 0.948411i \(-0.397310\pi\)
0.317042 + 0.948411i \(0.397310\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −7.12311 −0.366859
\(378\) 0 0
\(379\) 30.4924 1.56629 0.783145 0.621839i \(-0.213614\pi\)
0.783145 + 0.621839i \(0.213614\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 3.50758 0.179229 0.0896144 0.995977i \(-0.471437\pi\)
0.0896144 + 0.995977i \(0.471437\pi\)
\(384\) 0 0
\(385\) 0.684658 0.0348934
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −37.8617 −1.91967 −0.959833 0.280571i \(-0.909476\pi\)
−0.959833 + 0.280571i \(0.909476\pi\)
\(390\) 0 0
\(391\) −3.80776 −0.192567
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 4.68466 0.235711
\(396\) 0 0
\(397\) −4.43845 −0.222759 −0.111380 0.993778i \(-0.535527\pi\)
−0.111380 + 0.993778i \(0.535527\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −3.75379 −0.187455 −0.0937276 0.995598i \(-0.529878\pi\)
−0.0937276 + 0.995598i \(0.529878\pi\)
\(402\) 0 0
\(403\) 6.00000 0.298881
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 16.6847 0.827028
\(408\) 0 0
\(409\) −6.87689 −0.340041 −0.170020 0.985441i \(-0.554383\pi\)
−0.170020 + 0.985441i \(0.554383\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 5.26137 0.258895
\(414\) 0 0
\(415\) 16.4924 0.809581
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 7.61553 0.372043 0.186021 0.982546i \(-0.440441\pi\)
0.186021 + 0.982546i \(0.440441\pi\)
\(420\) 0 0
\(421\) 39.3693 1.91874 0.959372 0.282146i \(-0.0910462\pi\)
0.959372 + 0.282146i \(0.0910462\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1.56155 −0.0757464
\(426\) 0 0
\(427\) −2.93087 −0.141835
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −3.50758 −0.168954 −0.0844770 0.996425i \(-0.526922\pi\)
−0.0844770 + 0.996425i \(0.526922\pi\)
\(432\) 0 0
\(433\) −9.61553 −0.462093 −0.231046 0.972943i \(-0.574215\pi\)
−0.231046 + 0.972943i \(0.574215\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 12.4924 0.597594
\(438\) 0 0
\(439\) −22.0540 −1.05258 −0.526289 0.850306i \(-0.676417\pi\)
−0.526289 + 0.850306i \(0.676417\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −7.80776 −0.370958 −0.185479 0.982648i \(-0.559384\pi\)
−0.185479 + 0.982648i \(0.559384\pi\)
\(444\) 0 0
\(445\) 10.6847 0.506501
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 35.1771 1.66011 0.830055 0.557682i \(-0.188309\pi\)
0.830055 + 0.557682i \(0.188309\pi\)
\(450\) 0 0
\(451\) 5.56155 0.261883
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0.438447 0.0205547
\(456\) 0 0
\(457\) −13.3153 −0.622865 −0.311433 0.950268i \(-0.600809\pi\)
−0.311433 + 0.950268i \(0.600809\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −8.05398 −0.375111 −0.187556 0.982254i \(-0.560056\pi\)
−0.187556 + 0.982254i \(0.560056\pi\)
\(462\) 0 0
\(463\) 28.9309 1.34453 0.672266 0.740310i \(-0.265321\pi\)
0.672266 + 0.740310i \(0.265321\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 6.93087 0.320722 0.160361 0.987058i \(-0.448734\pi\)
0.160361 + 0.987058i \(0.448734\pi\)
\(468\) 0 0
\(469\) 4.98485 0.230179
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 4.87689 0.224240
\(474\) 0 0
\(475\) 5.12311 0.235064
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 26.0540 1.19044 0.595218 0.803564i \(-0.297066\pi\)
0.595218 + 0.803564i \(0.297066\pi\)
\(480\) 0 0
\(481\) 10.6847 0.487178
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −16.9309 −0.768791
\(486\) 0 0
\(487\) 32.0540 1.45250 0.726252 0.687428i \(-0.241260\pi\)
0.726252 + 0.687428i \(0.241260\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −27.6155 −1.24627 −0.623136 0.782114i \(-0.714142\pi\)
−0.623136 + 0.782114i \(0.714142\pi\)
\(492\) 0 0
\(493\) −11.1231 −0.500959
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 4.57671 0.205293
\(498\) 0 0
\(499\) −34.9848 −1.56614 −0.783068 0.621936i \(-0.786347\pi\)
−0.783068 + 0.621936i \(0.786347\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 13.7538 0.613251 0.306626 0.951830i \(-0.400800\pi\)
0.306626 + 0.951830i \(0.400800\pi\)
\(504\) 0 0
\(505\) 10.2462 0.455950
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 23.5616 1.04435 0.522174 0.852839i \(-0.325121\pi\)
0.522174 + 0.852839i \(0.325121\pi\)
\(510\) 0 0
\(511\) −2.63068 −0.116375
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −15.1231 −0.666404
\(516\) 0 0
\(517\) −17.3693 −0.763902
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 25.8617 1.13302 0.566512 0.824054i \(-0.308293\pi\)
0.566512 + 0.824054i \(0.308293\pi\)
\(522\) 0 0
\(523\) 30.7386 1.34411 0.672053 0.740503i \(-0.265413\pi\)
0.672053 + 0.740503i \(0.265413\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 9.36932 0.408134
\(528\) 0 0
\(529\) −17.0540 −0.741477
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 3.56155 0.154268
\(534\) 0 0
\(535\) −10.9309 −0.472583
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 10.6307 0.457896
\(540\) 0 0
\(541\) 18.8769 0.811581 0.405791 0.913966i \(-0.366996\pi\)
0.405791 + 0.913966i \(0.366996\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 2.00000 0.0856706
\(546\) 0 0
\(547\) 5.36932 0.229575 0.114788 0.993390i \(-0.463381\pi\)
0.114788 + 0.993390i \(0.463381\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 36.4924 1.55463
\(552\) 0 0
\(553\) −2.05398 −0.0873439
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −6.49242 −0.275093 −0.137546 0.990495i \(-0.543922\pi\)
−0.137546 + 0.990495i \(0.543922\pi\)
\(558\) 0 0
\(559\) 3.12311 0.132093
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −19.3153 −0.814045 −0.407022 0.913418i \(-0.633433\pi\)
−0.407022 + 0.913418i \(0.633433\pi\)
\(564\) 0 0
\(565\) −4.87689 −0.205172
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 32.8769 1.37827 0.689136 0.724632i \(-0.257990\pi\)
0.689136 + 0.724632i \(0.257990\pi\)
\(570\) 0 0
\(571\) 22.0540 0.922930 0.461465 0.887158i \(-0.347324\pi\)
0.461465 + 0.887158i \(0.347324\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 2.43845 0.101690
\(576\) 0 0
\(577\) 24.4384 1.01739 0.508693 0.860948i \(-0.330129\pi\)
0.508693 + 0.860948i \(0.330129\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −7.23106 −0.299995
\(582\) 0 0
\(583\) −7.31534 −0.302970
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −32.4924 −1.34111 −0.670553 0.741862i \(-0.733943\pi\)
−0.670553 + 0.741862i \(0.733943\pi\)
\(588\) 0 0
\(589\) −30.7386 −1.26656
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −24.2462 −0.995673 −0.497836 0.867271i \(-0.665872\pi\)
−0.497836 + 0.867271i \(0.665872\pi\)
\(594\) 0 0
\(595\) 0.684658 0.0280683
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −9.36932 −0.382820 −0.191410 0.981510i \(-0.561306\pi\)
−0.191410 + 0.981510i \(0.561306\pi\)
\(600\) 0 0
\(601\) −28.5464 −1.16443 −0.582216 0.813034i \(-0.697814\pi\)
−0.582216 + 0.813034i \(0.697814\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 8.56155 0.348077
\(606\) 0 0
\(607\) 24.0000 0.974130 0.487065 0.873366i \(-0.338067\pi\)
0.487065 + 0.873366i \(0.338067\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −11.1231 −0.449993
\(612\) 0 0
\(613\) −32.5464 −1.31454 −0.657268 0.753657i \(-0.728288\pi\)
−0.657268 + 0.753657i \(0.728288\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −0.738634 −0.0297363 −0.0148681 0.999889i \(-0.504733\pi\)
−0.0148681 + 0.999889i \(0.504733\pi\)
\(618\) 0 0
\(619\) 8.63068 0.346896 0.173448 0.984843i \(-0.444509\pi\)
0.173448 + 0.984843i \(0.444509\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −4.68466 −0.187687
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 16.6847 0.665261
\(630\) 0 0
\(631\) 32.7386 1.30330 0.651652 0.758518i \(-0.274076\pi\)
0.651652 + 0.758518i \(0.274076\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1.75379 0.0695970
\(636\) 0 0
\(637\) 6.80776 0.269733
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 32.9848 1.30282 0.651412 0.758725i \(-0.274177\pi\)
0.651412 + 0.758725i \(0.274177\pi\)
\(642\) 0 0
\(643\) 10.6847 0.421362 0.210681 0.977555i \(-0.432432\pi\)
0.210681 + 0.977555i \(0.432432\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 31.8078 1.25049 0.625246 0.780428i \(-0.284999\pi\)
0.625246 + 0.780428i \(0.284999\pi\)
\(648\) 0 0
\(649\) −18.7386 −0.735556
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 33.3693 1.30584 0.652921 0.757426i \(-0.273543\pi\)
0.652921 + 0.757426i \(0.273543\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0.876894 0.0341590 0.0170795 0.999854i \(-0.494563\pi\)
0.0170795 + 0.999854i \(0.494563\pi\)
\(660\) 0 0
\(661\) 6.49242 0.252526 0.126263 0.991997i \(-0.459702\pi\)
0.126263 + 0.991997i \(0.459702\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −2.24621 −0.0871043
\(666\) 0 0
\(667\) 17.3693 0.672543
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 10.4384 0.402972
\(672\) 0 0
\(673\) 16.7386 0.645227 0.322613 0.946531i \(-0.395439\pi\)
0.322613 + 0.946531i \(0.395439\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 14.4384 0.554915 0.277457 0.960738i \(-0.410508\pi\)
0.277457 + 0.960738i \(0.410508\pi\)
\(678\) 0 0
\(679\) 7.42329 0.284880
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 32.4924 1.24329 0.621644 0.783300i \(-0.286465\pi\)
0.621644 + 0.783300i \(0.286465\pi\)
\(684\) 0 0
\(685\) 1.12311 0.0429117
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −4.68466 −0.178471
\(690\) 0 0
\(691\) 21.6155 0.822293 0.411147 0.911569i \(-0.365128\pi\)
0.411147 + 0.911569i \(0.365128\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 3.31534 0.125758
\(696\) 0 0
\(697\) 5.56155 0.210659
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 48.9848 1.85013 0.925066 0.379806i \(-0.124009\pi\)
0.925066 + 0.379806i \(0.124009\pi\)
\(702\) 0 0
\(703\) −54.7386 −2.06451
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −4.49242 −0.168955
\(708\) 0 0
\(709\) 9.12311 0.342625 0.171313 0.985217i \(-0.445199\pi\)
0.171313 + 0.985217i \(0.445199\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −14.6307 −0.547923
\(714\) 0 0
\(715\) −1.56155 −0.0583988
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 36.0000 1.34257 0.671287 0.741198i \(-0.265742\pi\)
0.671287 + 0.741198i \(0.265742\pi\)
\(720\) 0 0
\(721\) 6.63068 0.246940
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 7.12311 0.264546
\(726\) 0 0
\(727\) −12.8769 −0.477578 −0.238789 0.971072i \(-0.576750\pi\)
−0.238789 + 0.971072i \(0.576750\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 4.87689 0.180378
\(732\) 0 0
\(733\) −16.4384 −0.607168 −0.303584 0.952805i \(-0.598183\pi\)
−0.303584 + 0.952805i \(0.598183\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −17.7538 −0.653969
\(738\) 0 0
\(739\) −48.7386 −1.79288 −0.896440 0.443166i \(-0.853855\pi\)
−0.896440 + 0.443166i \(0.853855\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 18.7386 0.687454 0.343727 0.939070i \(-0.388311\pi\)
0.343727 + 0.939070i \(0.388311\pi\)
\(744\) 0 0
\(745\) −17.8078 −0.652426
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 4.79261 0.175118
\(750\) 0 0
\(751\) −14.0540 −0.512837 −0.256418 0.966566i \(-0.582542\pi\)
−0.256418 + 0.966566i \(0.582542\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 11.3693 0.413772
\(756\) 0 0
\(757\) −14.4924 −0.526736 −0.263368 0.964695i \(-0.584833\pi\)
−0.263368 + 0.964695i \(0.584833\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −45.2311 −1.63962 −0.819812 0.572632i \(-0.805922\pi\)
−0.819812 + 0.572632i \(0.805922\pi\)
\(762\) 0 0
\(763\) −0.876894 −0.0317457
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −12.0000 −0.433295
\(768\) 0 0
\(769\) −30.0000 −1.08183 −0.540914 0.841078i \(-0.681921\pi\)
−0.540914 + 0.841078i \(0.681921\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 9.12311 0.328135 0.164068 0.986449i \(-0.447538\pi\)
0.164068 + 0.986449i \(0.447538\pi\)
\(774\) 0 0
\(775\) −6.00000 −0.215526
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −18.2462 −0.653738
\(780\) 0 0
\(781\) −16.3002 −0.583267
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −3.36932 −0.120256
\(786\) 0 0
\(787\) −11.3693 −0.405272 −0.202636 0.979254i \(-0.564951\pi\)
−0.202636 + 0.979254i \(0.564951\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 2.13826 0.0760278
\(792\) 0 0
\(793\) 6.68466 0.237379
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −4.68466 −0.165939 −0.0829696 0.996552i \(-0.526440\pi\)
−0.0829696 + 0.996552i \(0.526440\pi\)
\(798\) 0 0
\(799\) −17.3693 −0.614482
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 9.36932 0.330636
\(804\) 0 0
\(805\) −1.06913 −0.0376819
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −7.50758 −0.263952 −0.131976 0.991253i \(-0.542132\pi\)
−0.131976 + 0.991253i \(0.542132\pi\)
\(810\) 0 0
\(811\) −4.24621 −0.149105 −0.0745523 0.997217i \(-0.523753\pi\)
−0.0745523 + 0.997217i \(0.523753\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 16.0540 0.562346
\(816\) 0 0
\(817\) −16.0000 −0.559769
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −48.5464 −1.69428 −0.847140 0.531369i \(-0.821678\pi\)
−0.847140 + 0.531369i \(0.821678\pi\)
\(822\) 0 0
\(823\) 29.7538 1.03715 0.518576 0.855032i \(-0.326462\pi\)
0.518576 + 0.855032i \(0.326462\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 7.12311 0.247695 0.123847 0.992301i \(-0.460477\pi\)
0.123847 + 0.992301i \(0.460477\pi\)
\(828\) 0 0
\(829\) 0.738634 0.0256538 0.0128269 0.999918i \(-0.495917\pi\)
0.0128269 + 0.999918i \(0.495917\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 10.6307 0.368331
\(834\) 0 0
\(835\) −4.87689 −0.168772
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −44.7926 −1.54641 −0.773206 0.634155i \(-0.781348\pi\)
−0.773206 + 0.634155i \(0.781348\pi\)
\(840\) 0 0
\(841\) 21.7386 0.749608
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −1.00000 −0.0344010
\(846\) 0 0
\(847\) −3.75379 −0.128982
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −26.0540 −0.893119
\(852\) 0 0
\(853\) 41.4233 1.41831 0.709153 0.705054i \(-0.249077\pi\)
0.709153 + 0.705054i \(0.249077\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −2.43845 −0.0832958 −0.0416479 0.999132i \(-0.513261\pi\)
−0.0416479 + 0.999132i \(0.513261\pi\)
\(858\) 0 0
\(859\) −3.80776 −0.129919 −0.0649596 0.997888i \(-0.520692\pi\)
−0.0649596 + 0.997888i \(0.520692\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −9.36932 −0.318935 −0.159468 0.987203i \(-0.550978\pi\)
−0.159468 + 0.987203i \(0.550978\pi\)
\(864\) 0 0
\(865\) 12.8769 0.437828
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 7.31534 0.248156
\(870\) 0 0
\(871\) −11.3693 −0.385235
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −0.438447 −0.0148222
\(876\) 0 0
\(877\) 46.9848 1.58657 0.793283 0.608853i \(-0.208370\pi\)
0.793283 + 0.608853i \(0.208370\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 21.3693 0.719951 0.359975 0.932962i \(-0.382785\pi\)
0.359975 + 0.932962i \(0.382785\pi\)
\(882\) 0 0
\(883\) 56.1080 1.88818 0.944091 0.329684i \(-0.106942\pi\)
0.944091 + 0.329684i \(0.106942\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 5.56155 0.186739 0.0933693 0.995632i \(-0.470236\pi\)
0.0933693 + 0.995632i \(0.470236\pi\)
\(888\) 0 0
\(889\) −0.768944 −0.0257895
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 56.9848 1.90693
\(894\) 0 0
\(895\) 4.87689 0.163017
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −42.7386 −1.42541
\(900\) 0 0
\(901\) −7.31534 −0.243709
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −13.3153 −0.442617
\(906\) 0 0
\(907\) 2.63068 0.0873504 0.0436752 0.999046i \(-0.486093\pi\)
0.0436752 + 0.999046i \(0.486093\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −12.0000 −0.397578 −0.198789 0.980042i \(-0.563701\pi\)
−0.198789 + 0.980042i \(0.563701\pi\)
\(912\) 0 0
\(913\) 25.7538 0.852326
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −1.94602 −0.0641934 −0.0320967 0.999485i \(-0.510218\pi\)
−0.0320967 + 0.999485i \(0.510218\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −10.4384 −0.343586
\(924\) 0 0
\(925\) −10.6847 −0.351309
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −39.6695 −1.30151 −0.650757 0.759286i \(-0.725548\pi\)
−0.650757 + 0.759286i \(0.725548\pi\)
\(930\) 0 0
\(931\) −34.8769 −1.14304
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −2.43845 −0.0797458
\(936\) 0 0
\(937\) −27.3693 −0.894117 −0.447058 0.894505i \(-0.647528\pi\)
−0.447058 + 0.894505i \(0.647528\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 41.8078 1.36289 0.681447 0.731867i \(-0.261351\pi\)
0.681447 + 0.731867i \(0.261351\pi\)
\(942\) 0 0
\(943\) −8.68466 −0.282811
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 60.6004 1.96925 0.984624 0.174688i \(-0.0558918\pi\)
0.984624 + 0.174688i \(0.0558918\pi\)
\(948\) 0 0
\(949\) 6.00000 0.194768
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −29.5616 −0.957593 −0.478796 0.877926i \(-0.658927\pi\)
−0.478796 + 0.877926i \(0.658927\pi\)
\(954\) 0 0
\(955\) −19.6155 −0.634744
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −0.492423 −0.0159012
\(960\) 0 0
\(961\) 5.00000 0.161290
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −19.5616 −0.629709
\(966\) 0 0
\(967\) 7.36932 0.236981 0.118491 0.992955i \(-0.462194\pi\)
0.118491 + 0.992955i \(0.462194\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −24.4924 −0.785999 −0.393000 0.919539i \(-0.628563\pi\)
−0.393000 + 0.919539i \(0.628563\pi\)
\(972\) 0 0
\(973\) −1.45360 −0.0466003
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 43.4773 1.39096 0.695481 0.718545i \(-0.255192\pi\)
0.695481 + 0.718545i \(0.255192\pi\)
\(978\) 0 0
\(979\) 16.6847 0.533244
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 42.7386 1.36315 0.681575 0.731748i \(-0.261295\pi\)
0.681575 + 0.731748i \(0.261295\pi\)
\(984\) 0 0
\(985\) −3.36932 −0.107355
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −7.61553 −0.242160
\(990\) 0 0
\(991\) −10.0540 −0.319375 −0.159688 0.987168i \(-0.551049\pi\)
−0.159688 + 0.987168i \(0.551049\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −8.00000 −0.253617
\(996\) 0 0
\(997\) 28.2462 0.894566 0.447283 0.894392i \(-0.352392\pi\)
0.447283 + 0.894392i \(0.352392\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 9360.2.a.cl.1.1 2
3.2 odd 2 9360.2.a.cw.1.1 2
4.3 odd 2 585.2.a.j.1.1 2
12.11 even 2 585.2.a.l.1.2 yes 2
20.3 even 4 2925.2.c.o.2224.4 4
20.7 even 4 2925.2.c.o.2224.1 4
20.19 odd 2 2925.2.a.bc.1.2 2
52.51 odd 2 7605.2.a.bi.1.2 2
60.23 odd 4 2925.2.c.p.2224.1 4
60.47 odd 4 2925.2.c.p.2224.4 4
60.59 even 2 2925.2.a.x.1.1 2
156.155 even 2 7605.2.a.bd.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
585.2.a.j.1.1 2 4.3 odd 2
585.2.a.l.1.2 yes 2 12.11 even 2
2925.2.a.x.1.1 2 60.59 even 2
2925.2.a.bc.1.2 2 20.19 odd 2
2925.2.c.o.2224.1 4 20.7 even 4
2925.2.c.o.2224.4 4 20.3 even 4
2925.2.c.p.2224.1 4 60.23 odd 4
2925.2.c.p.2224.4 4 60.47 odd 4
7605.2.a.bd.1.1 2 156.155 even 2
7605.2.a.bi.1.2 2 52.51 odd 2
9360.2.a.cl.1.1 2 1.1 even 1 trivial
9360.2.a.cw.1.1 2 3.2 odd 2