Properties

Label 7800.2.a.be.1.2
Level $7800$
Weight $2$
Character 7800.1
Self dual yes
Analytic conductor $62.283$
Analytic rank $1$
Dimension $2$
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: \(2\)
Coefficient field: \(\Q(\sqrt{41}) \)
Defining polynomial: \( x^{2} - x - 10 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1560)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(3.70156\) of defining polynomial
Character \(\chi\) \(=\) 7800.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} +3.70156 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} +3.70156 q^{7} +1.00000 q^{9} -5.70156 q^{11} +1.00000 q^{13} -5.70156 q^{17} -2.00000 q^{19} +3.70156 q^{21} -0.298438 q^{23} +1.00000 q^{27} -3.40312 q^{29} +3.40312 q^{31} -5.70156 q^{33} +0.298438 q^{37} +1.00000 q^{39} +4.29844 q^{41} -4.00000 q^{43} -11.4031 q^{47} +6.70156 q^{49} -5.70156 q^{51} -4.29844 q^{53} -2.00000 q^{57} +10.8062 q^{59} -3.70156 q^{61} +3.70156 q^{63} +4.00000 q^{67} -0.298438 q^{69} -16.5078 q^{71} -0.596876 q^{73} -21.1047 q^{77} -1.70156 q^{79} +1.00000 q^{81} -4.00000 q^{83} -3.40312 q^{87} -11.1047 q^{89} +3.70156 q^{91} +3.40312 q^{93} +1.10469 q^{97} -5.70156 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{3} + q^{7} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{3} + q^{7} + 2 q^{9} - 5 q^{11} + 2 q^{13} - 5 q^{17} - 4 q^{19} + q^{21} - 7 q^{23} + 2 q^{27} + 6 q^{29} - 6 q^{31} - 5 q^{33} + 7 q^{37} + 2 q^{39} + 15 q^{41} - 8 q^{43} - 10 q^{47} + 7 q^{49} - 5 q^{51} - 15 q^{53} - 4 q^{57} - 4 q^{59} - q^{61} + q^{63} + 8 q^{67} - 7 q^{69} - q^{71} - 14 q^{73} - 23 q^{77} + 3 q^{79} + 2 q^{81} - 8 q^{83} + 6 q^{87} - 3 q^{89} + q^{91} - 6 q^{93} - 17 q^{97} - 5 q^{99}+O(q^{100}) \) 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
\(7\) 3.70156 1.39906 0.699529 0.714604i \(-0.253393\pi\)
0.699529 + 0.714604i \(0.253393\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −5.70156 −1.71909 −0.859543 0.511064i \(-0.829252\pi\)
−0.859543 + 0.511064i \(0.829252\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −5.70156 −1.38283 −0.691416 0.722457i \(-0.743013\pi\)
−0.691416 + 0.722457i \(0.743013\pi\)
\(18\) 0 0
\(19\) −2.00000 −0.458831 −0.229416 0.973329i \(-0.573682\pi\)
−0.229416 + 0.973329i \(0.573682\pi\)
\(20\) 0 0
\(21\) 3.70156 0.807747
\(22\) 0 0
\(23\) −0.298438 −0.0622286 −0.0311143 0.999516i \(-0.509906\pi\)
−0.0311143 + 0.999516i \(0.509906\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −3.40312 −0.631944 −0.315972 0.948768i \(-0.602331\pi\)
−0.315972 + 0.948768i \(0.602331\pi\)
\(30\) 0 0
\(31\) 3.40312 0.611219 0.305610 0.952157i \(-0.401140\pi\)
0.305610 + 0.952157i \(0.401140\pi\)
\(32\) 0 0
\(33\) −5.70156 −0.992515
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 0.298438 0.0490629 0.0245314 0.999699i \(-0.492191\pi\)
0.0245314 + 0.999699i \(0.492191\pi\)
\(38\) 0 0
\(39\) 1.00000 0.160128
\(40\) 0 0
\(41\) 4.29844 0.671303 0.335652 0.941986i \(-0.391044\pi\)
0.335652 + 0.941986i \(0.391044\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −11.4031 −1.66332 −0.831658 0.555288i \(-0.812608\pi\)
−0.831658 + 0.555288i \(0.812608\pi\)
\(48\) 0 0
\(49\) 6.70156 0.957366
\(50\) 0 0
\(51\) −5.70156 −0.798378
\(52\) 0 0
\(53\) −4.29844 −0.590436 −0.295218 0.955430i \(-0.595392\pi\)
−0.295218 + 0.955430i \(0.595392\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −2.00000 −0.264906
\(58\) 0 0
\(59\) 10.8062 1.40685 0.703427 0.710768i \(-0.251652\pi\)
0.703427 + 0.710768i \(0.251652\pi\)
\(60\) 0 0
\(61\) −3.70156 −0.473936 −0.236968 0.971517i \(-0.576154\pi\)
−0.236968 + 0.971517i \(0.576154\pi\)
\(62\) 0 0
\(63\) 3.70156 0.466353
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 4.00000 0.488678 0.244339 0.969690i \(-0.421429\pi\)
0.244339 + 0.969690i \(0.421429\pi\)
\(68\) 0 0
\(69\) −0.298438 −0.0359277
\(70\) 0 0
\(71\) −16.5078 −1.95912 −0.979558 0.201160i \(-0.935529\pi\)
−0.979558 + 0.201160i \(0.935529\pi\)
\(72\) 0 0
\(73\) −0.596876 −0.0698590 −0.0349295 0.999390i \(-0.511121\pi\)
−0.0349295 + 0.999390i \(0.511121\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −21.1047 −2.40510
\(78\) 0 0
\(79\) −1.70156 −0.191441 −0.0957203 0.995408i \(-0.530515\pi\)
−0.0957203 + 0.995408i \(0.530515\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −4.00000 −0.439057 −0.219529 0.975606i \(-0.570452\pi\)
−0.219529 + 0.975606i \(0.570452\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −3.40312 −0.364853
\(88\) 0 0
\(89\) −11.1047 −1.17709 −0.588547 0.808463i \(-0.700300\pi\)
−0.588547 + 0.808463i \(0.700300\pi\)
\(90\) 0 0
\(91\) 3.70156 0.388029
\(92\) 0 0
\(93\) 3.40312 0.352888
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 1.10469 0.112164 0.0560820 0.998426i \(-0.482139\pi\)
0.0560820 + 0.998426i \(0.482139\pi\)
\(98\) 0 0
\(99\) −5.70156 −0.573029
\(100\) 0 0
\(101\) 18.8062 1.87129 0.935646 0.352940i \(-0.114818\pi\)
0.935646 + 0.352940i \(0.114818\pi\)
\(102\) 0 0
\(103\) −12.0000 −1.18240 −0.591198 0.806527i \(-0.701345\pi\)
−0.591198 + 0.806527i \(0.701345\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1.10469 0.106794 0.0533970 0.998573i \(-0.482995\pi\)
0.0533970 + 0.998573i \(0.482995\pi\)
\(108\) 0 0
\(109\) −14.8062 −1.41818 −0.709091 0.705117i \(-0.750894\pi\)
−0.709091 + 0.705117i \(0.750894\pi\)
\(110\) 0 0
\(111\) 0.298438 0.0283265
\(112\) 0 0
\(113\) −19.4031 −1.82529 −0.912646 0.408750i \(-0.865965\pi\)
−0.912646 + 0.408750i \(0.865965\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 1.00000 0.0924500
\(118\) 0 0
\(119\) −21.1047 −1.93466
\(120\) 0 0
\(121\) 21.5078 1.95526
\(122\) 0 0
\(123\) 4.29844 0.387577
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0.596876 0.0529642 0.0264821 0.999649i \(-0.491570\pi\)
0.0264821 + 0.999649i \(0.491570\pi\)
\(128\) 0 0
\(129\) −4.00000 −0.352180
\(130\) 0 0
\(131\) 12.8062 1.11889 0.559444 0.828868i \(-0.311015\pi\)
0.559444 + 0.828868i \(0.311015\pi\)
\(132\) 0 0
\(133\) −7.40312 −0.641932
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −18.0000 −1.53784 −0.768922 0.639343i \(-0.779207\pi\)
−0.768922 + 0.639343i \(0.779207\pi\)
\(138\) 0 0
\(139\) 1.70156 0.144325 0.0721623 0.997393i \(-0.477010\pi\)
0.0721623 + 0.997393i \(0.477010\pi\)
\(140\) 0 0
\(141\) −11.4031 −0.960316
\(142\) 0 0
\(143\) −5.70156 −0.476789
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 6.70156 0.552736
\(148\) 0 0
\(149\) 7.70156 0.630937 0.315468 0.948936i \(-0.397838\pi\)
0.315468 + 0.948936i \(0.397838\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) −5.70156 −0.460944
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 16.8062 1.34128 0.670642 0.741781i \(-0.266019\pi\)
0.670642 + 0.741781i \(0.266019\pi\)
\(158\) 0 0
\(159\) −4.29844 −0.340888
\(160\) 0 0
\(161\) −1.10469 −0.0870615
\(162\) 0 0
\(163\) −17.7016 −1.38649 −0.693247 0.720700i \(-0.743820\pi\)
−0.693247 + 0.720700i \(0.743820\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −2.80625 −0.217154 −0.108577 0.994088i \(-0.534629\pi\)
−0.108577 + 0.994088i \(0.534629\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −2.00000 −0.152944
\(172\) 0 0
\(173\) 2.00000 0.152057 0.0760286 0.997106i \(-0.475776\pi\)
0.0760286 + 0.997106i \(0.475776\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 10.8062 0.812247
\(178\) 0 0
\(179\) −22.0000 −1.64436 −0.822179 0.569230i \(-0.807242\pi\)
−0.822179 + 0.569230i \(0.807242\pi\)
\(180\) 0 0
\(181\) −7.70156 −0.572453 −0.286226 0.958162i \(-0.592401\pi\)
−0.286226 + 0.958162i \(0.592401\pi\)
\(182\) 0 0
\(183\) −3.70156 −0.273627
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 32.5078 2.37721
\(188\) 0 0
\(189\) 3.70156 0.269249
\(190\) 0 0
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 0 0
\(193\) 2.89531 0.208409 0.104205 0.994556i \(-0.466770\pi\)
0.104205 + 0.994556i \(0.466770\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −24.2094 −1.72485 −0.862423 0.506188i \(-0.831054\pi\)
−0.862423 + 0.506188i \(0.831054\pi\)
\(198\) 0 0
\(199\) −22.8062 −1.61669 −0.808346 0.588708i \(-0.799637\pi\)
−0.808346 + 0.588708i \(0.799637\pi\)
\(200\) 0 0
\(201\) 4.00000 0.282138
\(202\) 0 0
\(203\) −12.5969 −0.884127
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −0.298438 −0.0207429
\(208\) 0 0
\(209\) 11.4031 0.788771
\(210\) 0 0
\(211\) 20.0000 1.37686 0.688428 0.725304i \(-0.258301\pi\)
0.688428 + 0.725304i \(0.258301\pi\)
\(212\) 0 0
\(213\) −16.5078 −1.13110
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 12.5969 0.855132
\(218\) 0 0
\(219\) −0.596876 −0.0403331
\(220\) 0 0
\(221\) −5.70156 −0.383529
\(222\) 0 0
\(223\) 9.40312 0.629680 0.314840 0.949145i \(-0.398049\pi\)
0.314840 + 0.949145i \(0.398049\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 23.4031 1.55332 0.776660 0.629920i \(-0.216912\pi\)
0.776660 + 0.629920i \(0.216912\pi\)
\(228\) 0 0
\(229\) −12.5969 −0.832425 −0.416212 0.909267i \(-0.636643\pi\)
−0.416212 + 0.909267i \(0.636643\pi\)
\(230\) 0 0
\(231\) −21.1047 −1.38859
\(232\) 0 0
\(233\) −9.10469 −0.596468 −0.298234 0.954493i \(-0.596398\pi\)
−0.298234 + 0.954493i \(0.596398\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −1.70156 −0.110528
\(238\) 0 0
\(239\) 13.1047 0.847672 0.423836 0.905739i \(-0.360683\pi\)
0.423836 + 0.905739i \(0.360683\pi\)
\(240\) 0 0
\(241\) 2.00000 0.128831 0.0644157 0.997923i \(-0.479482\pi\)
0.0644157 + 0.997923i \(0.479482\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −2.00000 −0.127257
\(248\) 0 0
\(249\) −4.00000 −0.253490
\(250\) 0 0
\(251\) 20.2094 1.27560 0.637802 0.770200i \(-0.279844\pi\)
0.637802 + 0.770200i \(0.279844\pi\)
\(252\) 0 0
\(253\) 1.70156 0.106976
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 18.2094 1.13587 0.567935 0.823074i \(-0.307743\pi\)
0.567935 + 0.823074i \(0.307743\pi\)
\(258\) 0 0
\(259\) 1.10469 0.0686419
\(260\) 0 0
\(261\) −3.40312 −0.210648
\(262\) 0 0
\(263\) −17.4031 −1.07312 −0.536561 0.843861i \(-0.680277\pi\)
−0.536561 + 0.843861i \(0.680277\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −11.1047 −0.679596
\(268\) 0 0
\(269\) 10.8062 0.658869 0.329434 0.944179i \(-0.393142\pi\)
0.329434 + 0.944179i \(0.393142\pi\)
\(270\) 0 0
\(271\) −19.4031 −1.17866 −0.589328 0.807894i \(-0.700607\pi\)
−0.589328 + 0.807894i \(0.700607\pi\)
\(272\) 0 0
\(273\) 3.70156 0.224029
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 16.8062 1.00979 0.504895 0.863181i \(-0.331531\pi\)
0.504895 + 0.863181i \(0.331531\pi\)
\(278\) 0 0
\(279\) 3.40312 0.203740
\(280\) 0 0
\(281\) 10.0000 0.596550 0.298275 0.954480i \(-0.403589\pi\)
0.298275 + 0.954480i \(0.403589\pi\)
\(282\) 0 0
\(283\) −20.0000 −1.18888 −0.594438 0.804141i \(-0.702626\pi\)
−0.594438 + 0.804141i \(0.702626\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 15.9109 0.939193
\(288\) 0 0
\(289\) 15.5078 0.912224
\(290\) 0 0
\(291\) 1.10469 0.0647579
\(292\) 0 0
\(293\) −2.59688 −0.151711 −0.0758556 0.997119i \(-0.524169\pi\)
−0.0758556 + 0.997119i \(0.524169\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −5.70156 −0.330838
\(298\) 0 0
\(299\) −0.298438 −0.0172591
\(300\) 0 0
\(301\) −14.8062 −0.853418
\(302\) 0 0
\(303\) 18.8062 1.08039
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 33.1047 1.88938 0.944692 0.327959i \(-0.106361\pi\)
0.944692 + 0.327959i \(0.106361\pi\)
\(308\) 0 0
\(309\) −12.0000 −0.682656
\(310\) 0 0
\(311\) 8.00000 0.453638 0.226819 0.973937i \(-0.427167\pi\)
0.226819 + 0.973937i \(0.427167\pi\)
\(312\) 0 0
\(313\) 8.80625 0.497759 0.248879 0.968535i \(-0.419938\pi\)
0.248879 + 0.968535i \(0.419938\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 24.2094 1.35973 0.679867 0.733336i \(-0.262038\pi\)
0.679867 + 0.733336i \(0.262038\pi\)
\(318\) 0 0
\(319\) 19.4031 1.08637
\(320\) 0 0
\(321\) 1.10469 0.0616576
\(322\) 0 0
\(323\) 11.4031 0.634487
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −14.8062 −0.818787
\(328\) 0 0
\(329\) −42.2094 −2.32708
\(330\) 0 0
\(331\) 24.2094 1.33067 0.665334 0.746546i \(-0.268289\pi\)
0.665334 + 0.746546i \(0.268289\pi\)
\(332\) 0 0
\(333\) 0.298438 0.0163543
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −32.2094 −1.75456 −0.877278 0.479982i \(-0.840643\pi\)
−0.877278 + 0.479982i \(0.840643\pi\)
\(338\) 0 0
\(339\) −19.4031 −1.05383
\(340\) 0 0
\(341\) −19.4031 −1.05074
\(342\) 0 0
\(343\) −1.10469 −0.0596475
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 13.1047 0.703496 0.351748 0.936095i \(-0.385587\pi\)
0.351748 + 0.936095i \(0.385587\pi\)
\(348\) 0 0
\(349\) −9.19375 −0.492130 −0.246065 0.969253i \(-0.579138\pi\)
−0.246065 + 0.969253i \(0.579138\pi\)
\(350\) 0 0
\(351\) 1.00000 0.0533761
\(352\) 0 0
\(353\) 12.8062 0.681608 0.340804 0.940134i \(-0.389301\pi\)
0.340804 + 0.940134i \(0.389301\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −21.1047 −1.11698
\(358\) 0 0
\(359\) 29.6125 1.56289 0.781444 0.623975i \(-0.214484\pi\)
0.781444 + 0.623975i \(0.214484\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) 0 0
\(363\) 21.5078 1.12887
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −26.8062 −1.39927 −0.699637 0.714498i \(-0.746655\pi\)
−0.699637 + 0.714498i \(0.746655\pi\)
\(368\) 0 0
\(369\) 4.29844 0.223768
\(370\) 0 0
\(371\) −15.9109 −0.826055
\(372\) 0 0
\(373\) 21.4031 1.10821 0.554106 0.832446i \(-0.313060\pi\)
0.554106 + 0.832446i \(0.313060\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −3.40312 −0.175270
\(378\) 0 0
\(379\) −35.6125 −1.82929 −0.914646 0.404257i \(-0.867530\pi\)
−0.914646 + 0.404257i \(0.867530\pi\)
\(380\) 0 0
\(381\) 0.596876 0.0305789
\(382\) 0 0
\(383\) −7.40312 −0.378282 −0.189141 0.981950i \(-0.560570\pi\)
−0.189141 + 0.981950i \(0.560570\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −4.00000 −0.203331
\(388\) 0 0
\(389\) −25.6125 −1.29861 −0.649303 0.760530i \(-0.724939\pi\)
−0.649303 + 0.760530i \(0.724939\pi\)
\(390\) 0 0
\(391\) 1.70156 0.0860517
\(392\) 0 0
\(393\) 12.8062 0.645990
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 16.2984 0.817995 0.408998 0.912535i \(-0.365878\pi\)
0.408998 + 0.912535i \(0.365878\pi\)
\(398\) 0 0
\(399\) −7.40312 −0.370620
\(400\) 0 0
\(401\) −24.8062 −1.23876 −0.619382 0.785089i \(-0.712617\pi\)
−0.619382 + 0.785089i \(0.712617\pi\)
\(402\) 0 0
\(403\) 3.40312 0.169522
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −1.70156 −0.0843433
\(408\) 0 0
\(409\) 20.8062 1.02880 0.514401 0.857550i \(-0.328014\pi\)
0.514401 + 0.857550i \(0.328014\pi\)
\(410\) 0 0
\(411\) −18.0000 −0.887875
\(412\) 0 0
\(413\) 40.0000 1.96827
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 1.70156 0.0833259
\(418\) 0 0
\(419\) −23.6125 −1.15355 −0.576773 0.816904i \(-0.695688\pi\)
−0.576773 + 0.816904i \(0.695688\pi\)
\(420\) 0 0
\(421\) 25.6125 1.24828 0.624138 0.781314i \(-0.285450\pi\)
0.624138 + 0.781314i \(0.285450\pi\)
\(422\) 0 0
\(423\) −11.4031 −0.554439
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −13.7016 −0.663065
\(428\) 0 0
\(429\) −5.70156 −0.275274
\(430\) 0 0
\(431\) −16.0000 −0.770693 −0.385346 0.922772i \(-0.625918\pi\)
−0.385346 + 0.922772i \(0.625918\pi\)
\(432\) 0 0
\(433\) −25.4031 −1.22080 −0.610398 0.792095i \(-0.708991\pi\)
−0.610398 + 0.792095i \(0.708991\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0.596876 0.0285524
\(438\) 0 0
\(439\) −21.1047 −1.00727 −0.503636 0.863916i \(-0.668005\pi\)
−0.503636 + 0.863916i \(0.668005\pi\)
\(440\) 0 0
\(441\) 6.70156 0.319122
\(442\) 0 0
\(443\) −31.3141 −1.48778 −0.743888 0.668304i \(-0.767020\pi\)
−0.743888 + 0.668304i \(0.767020\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 7.70156 0.364271
\(448\) 0 0
\(449\) 23.1047 1.09038 0.545189 0.838313i \(-0.316458\pi\)
0.545189 + 0.838313i \(0.316458\pi\)
\(450\) 0 0
\(451\) −24.5078 −1.15403
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −13.7016 −0.640932 −0.320466 0.947260i \(-0.603840\pi\)
−0.320466 + 0.947260i \(0.603840\pi\)
\(458\) 0 0
\(459\) −5.70156 −0.266126
\(460\) 0 0
\(461\) 39.1047 1.82129 0.910643 0.413193i \(-0.135587\pi\)
0.910643 + 0.413193i \(0.135587\pi\)
\(462\) 0 0
\(463\) −15.1047 −0.701974 −0.350987 0.936380i \(-0.614154\pi\)
−0.350987 + 0.936380i \(0.614154\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 1.10469 0.0511188 0.0255594 0.999673i \(-0.491863\pi\)
0.0255594 + 0.999673i \(0.491863\pi\)
\(468\) 0 0
\(469\) 14.8062 0.683689
\(470\) 0 0
\(471\) 16.8062 0.774391
\(472\) 0 0
\(473\) 22.8062 1.04863
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −4.29844 −0.196812
\(478\) 0 0
\(479\) −22.2984 −1.01884 −0.509421 0.860518i \(-0.670140\pi\)
−0.509421 + 0.860518i \(0.670140\pi\)
\(480\) 0 0
\(481\) 0.298438 0.0136076
\(482\) 0 0
\(483\) −1.10469 −0.0502650
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −21.3141 −0.965832 −0.482916 0.875667i \(-0.660422\pi\)
−0.482916 + 0.875667i \(0.660422\pi\)
\(488\) 0 0
\(489\) −17.7016 −0.800492
\(490\) 0 0
\(491\) 32.2094 1.45359 0.726794 0.686855i \(-0.241009\pi\)
0.726794 + 0.686855i \(0.241009\pi\)
\(492\) 0 0
\(493\) 19.4031 0.873873
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −61.1047 −2.74092
\(498\) 0 0
\(499\) 40.8062 1.82674 0.913369 0.407132i \(-0.133471\pi\)
0.913369 + 0.407132i \(0.133471\pi\)
\(500\) 0 0
\(501\) −2.80625 −0.125374
\(502\) 0 0
\(503\) −18.5969 −0.829194 −0.414597 0.910005i \(-0.636077\pi\)
−0.414597 + 0.910005i \(0.636077\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 1.00000 0.0444116
\(508\) 0 0
\(509\) 25.3141 1.12203 0.561013 0.827807i \(-0.310412\pi\)
0.561013 + 0.827807i \(0.310412\pi\)
\(510\) 0 0
\(511\) −2.20937 −0.0977369
\(512\) 0 0
\(513\) −2.00000 −0.0883022
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 65.0156 2.85938
\(518\) 0 0
\(519\) 2.00000 0.0877903
\(520\) 0 0
\(521\) 30.0000 1.31432 0.657162 0.753749i \(-0.271757\pi\)
0.657162 + 0.753749i \(0.271757\pi\)
\(522\) 0 0
\(523\) −20.0000 −0.874539 −0.437269 0.899331i \(-0.644054\pi\)
−0.437269 + 0.899331i \(0.644054\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −19.4031 −0.845213
\(528\) 0 0
\(529\) −22.9109 −0.996128
\(530\) 0 0
\(531\) 10.8062 0.468951
\(532\) 0 0
\(533\) 4.29844 0.186186
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −22.0000 −0.949370
\(538\) 0 0
\(539\) −38.2094 −1.64579
\(540\) 0 0
\(541\) 1.79063 0.0769851 0.0384925 0.999259i \(-0.487744\pi\)
0.0384925 + 0.999259i \(0.487744\pi\)
\(542\) 0 0
\(543\) −7.70156 −0.330506
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −25.6125 −1.09511 −0.547556 0.836769i \(-0.684442\pi\)
−0.547556 + 0.836769i \(0.684442\pi\)
\(548\) 0 0
\(549\) −3.70156 −0.157979
\(550\) 0 0
\(551\) 6.80625 0.289956
\(552\) 0 0
\(553\) −6.29844 −0.267837
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −2.00000 −0.0847427 −0.0423714 0.999102i \(-0.513491\pi\)
−0.0423714 + 0.999102i \(0.513491\pi\)
\(558\) 0 0
\(559\) −4.00000 −0.169182
\(560\) 0 0
\(561\) 32.5078 1.37248
\(562\) 0 0
\(563\) −2.89531 −0.122023 −0.0610115 0.998137i \(-0.519433\pi\)
−0.0610115 + 0.998137i \(0.519433\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 3.70156 0.155451
\(568\) 0 0
\(569\) −14.5969 −0.611933 −0.305966 0.952042i \(-0.598980\pi\)
−0.305966 + 0.952042i \(0.598980\pi\)
\(570\) 0 0
\(571\) −31.3141 −1.31045 −0.655226 0.755433i \(-0.727427\pi\)
−0.655226 + 0.755433i \(0.727427\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −0.507811 −0.0211404 −0.0105702 0.999944i \(-0.503365\pi\)
−0.0105702 + 0.999944i \(0.503365\pi\)
\(578\) 0 0
\(579\) 2.89531 0.120325
\(580\) 0 0
\(581\) −14.8062 −0.614267
\(582\) 0 0
\(583\) 24.5078 1.01501
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −14.2094 −0.586484 −0.293242 0.956038i \(-0.594734\pi\)
−0.293242 + 0.956038i \(0.594734\pi\)
\(588\) 0 0
\(589\) −6.80625 −0.280447
\(590\) 0 0
\(591\) −24.2094 −0.995841
\(592\) 0 0
\(593\) −9.40312 −0.386140 −0.193070 0.981185i \(-0.561844\pi\)
−0.193070 + 0.981185i \(0.561844\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −22.8062 −0.933398
\(598\) 0 0
\(599\) −17.1938 −0.702518 −0.351259 0.936278i \(-0.614246\pi\)
−0.351259 + 0.936278i \(0.614246\pi\)
\(600\) 0 0
\(601\) 15.7016 0.640480 0.320240 0.947336i \(-0.396236\pi\)
0.320240 + 0.947336i \(0.396236\pi\)
\(602\) 0 0
\(603\) 4.00000 0.162893
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −9.61250 −0.390159 −0.195080 0.980787i \(-0.562497\pi\)
−0.195080 + 0.980787i \(0.562497\pi\)
\(608\) 0 0
\(609\) −12.5969 −0.510451
\(610\) 0 0
\(611\) −11.4031 −0.461321
\(612\) 0 0
\(613\) −24.7172 −0.998318 −0.499159 0.866511i \(-0.666358\pi\)
−0.499159 + 0.866511i \(0.666358\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −2.00000 −0.0805170 −0.0402585 0.999189i \(-0.512818\pi\)
−0.0402585 + 0.999189i \(0.512818\pi\)
\(618\) 0 0
\(619\) −11.6125 −0.466746 −0.233373 0.972387i \(-0.574976\pi\)
−0.233373 + 0.972387i \(0.574976\pi\)
\(620\) 0 0
\(621\) −0.298438 −0.0119759
\(622\) 0 0
\(623\) −41.1047 −1.64682
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 11.4031 0.455397
\(628\) 0 0
\(629\) −1.70156 −0.0678457
\(630\) 0 0
\(631\) 20.0000 0.796187 0.398094 0.917345i \(-0.369672\pi\)
0.398094 + 0.917345i \(0.369672\pi\)
\(632\) 0 0
\(633\) 20.0000 0.794929
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 6.70156 0.265526
\(638\) 0 0
\(639\) −16.5078 −0.653039
\(640\) 0 0
\(641\) 28.2094 1.11420 0.557102 0.830444i \(-0.311913\pi\)
0.557102 + 0.830444i \(0.311913\pi\)
\(642\) 0 0
\(643\) −37.7016 −1.48680 −0.743402 0.668845i \(-0.766789\pi\)
−0.743402 + 0.668845i \(0.766789\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −0.895314 −0.0351984 −0.0175992 0.999845i \(-0.505602\pi\)
−0.0175992 + 0.999845i \(0.505602\pi\)
\(648\) 0 0
\(649\) −61.6125 −2.41850
\(650\) 0 0
\(651\) 12.5969 0.493710
\(652\) 0 0
\(653\) 35.6125 1.39362 0.696812 0.717253i \(-0.254601\pi\)
0.696812 + 0.717253i \(0.254601\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −0.596876 −0.0232863
\(658\) 0 0
\(659\) −14.5969 −0.568614 −0.284307 0.958733i \(-0.591763\pi\)
−0.284307 + 0.958733i \(0.591763\pi\)
\(660\) 0 0
\(661\) −12.0000 −0.466746 −0.233373 0.972387i \(-0.574976\pi\)
−0.233373 + 0.972387i \(0.574976\pi\)
\(662\) 0 0
\(663\) −5.70156 −0.221430
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 1.01562 0.0393250
\(668\) 0 0
\(669\) 9.40312 0.363546
\(670\) 0 0
\(671\) 21.1047 0.814737
\(672\) 0 0
\(673\) 28.8062 1.11040 0.555200 0.831717i \(-0.312642\pi\)
0.555200 + 0.831717i \(0.312642\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −15.1047 −0.580520 −0.290260 0.956948i \(-0.593742\pi\)
−0.290260 + 0.956948i \(0.593742\pi\)
\(678\) 0 0
\(679\) 4.08907 0.156924
\(680\) 0 0
\(681\) 23.4031 0.896810
\(682\) 0 0
\(683\) −28.0000 −1.07139 −0.535695 0.844411i \(-0.679950\pi\)
−0.535695 + 0.844411i \(0.679950\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −12.5969 −0.480601
\(688\) 0 0
\(689\) −4.29844 −0.163757
\(690\) 0 0
\(691\) −10.0000 −0.380418 −0.190209 0.981744i \(-0.560917\pi\)
−0.190209 + 0.981744i \(0.560917\pi\)
\(692\) 0 0
\(693\) −21.1047 −0.801701
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −24.5078 −0.928300
\(698\) 0 0
\(699\) −9.10469 −0.344371
\(700\) 0 0
\(701\) 25.6125 0.967371 0.483685 0.875242i \(-0.339298\pi\)
0.483685 + 0.875242i \(0.339298\pi\)
\(702\) 0 0
\(703\) −0.596876 −0.0225116
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 69.6125 2.61805
\(708\) 0 0
\(709\) 17.1938 0.645725 0.322862 0.946446i \(-0.395355\pi\)
0.322862 + 0.946446i \(0.395355\pi\)
\(710\) 0 0
\(711\) −1.70156 −0.0638136
\(712\) 0 0
\(713\) −1.01562 −0.0380353
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 13.1047 0.489403
\(718\) 0 0
\(719\) 34.8062 1.29805 0.649027 0.760765i \(-0.275176\pi\)
0.649027 + 0.760765i \(0.275176\pi\)
\(720\) 0 0
\(721\) −44.4187 −1.65424
\(722\) 0 0
\(723\) 2.00000 0.0743808
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −3.40312 −0.126215 −0.0631074 0.998007i \(-0.520101\pi\)
−0.0631074 + 0.998007i \(0.520101\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 22.8062 0.843520
\(732\) 0 0
\(733\) 28.7172 1.06069 0.530347 0.847781i \(-0.322062\pi\)
0.530347 + 0.847781i \(0.322062\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −22.8062 −0.840079
\(738\) 0 0
\(739\) 16.8062 0.618228 0.309114 0.951025i \(-0.399968\pi\)
0.309114 + 0.951025i \(0.399968\pi\)
\(740\) 0 0
\(741\) −2.00000 −0.0734718
\(742\) 0 0
\(743\) 23.4031 0.858577 0.429289 0.903167i \(-0.358764\pi\)
0.429289 + 0.903167i \(0.358764\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −4.00000 −0.146352
\(748\) 0 0
\(749\) 4.08907 0.149411
\(750\) 0 0
\(751\) 15.3141 0.558818 0.279409 0.960172i \(-0.409861\pi\)
0.279409 + 0.960172i \(0.409861\pi\)
\(752\) 0 0
\(753\) 20.2094 0.736470
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 34.5969 1.25744 0.628722 0.777630i \(-0.283578\pi\)
0.628722 + 0.777630i \(0.283578\pi\)
\(758\) 0 0
\(759\) 1.70156 0.0617628
\(760\) 0 0
\(761\) −10.0000 −0.362500 −0.181250 0.983437i \(-0.558014\pi\)
−0.181250 + 0.983437i \(0.558014\pi\)
\(762\) 0 0
\(763\) −54.8062 −1.98412
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 10.8062 0.390191
\(768\) 0 0
\(769\) 38.5969 1.39184 0.695919 0.718120i \(-0.254997\pi\)
0.695919 + 0.718120i \(0.254997\pi\)
\(770\) 0 0
\(771\) 18.2094 0.655795
\(772\) 0 0
\(773\) 45.4031 1.63304 0.816518 0.577319i \(-0.195901\pi\)
0.816518 + 0.577319i \(0.195901\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 1.10469 0.0396304
\(778\) 0 0
\(779\) −8.59688 −0.308015
\(780\) 0 0
\(781\) 94.1203 3.36789
\(782\) 0 0
\(783\) −3.40312 −0.121618
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −30.8062 −1.09812 −0.549062 0.835782i \(-0.685015\pi\)
−0.549062 + 0.835782i \(0.685015\pi\)
\(788\) 0 0
\(789\) −17.4031 −0.619568
\(790\) 0 0
\(791\) −71.8219 −2.55369
\(792\) 0 0
\(793\) −3.70156 −0.131446
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 8.29844 0.293946 0.146973 0.989141i \(-0.453047\pi\)
0.146973 + 0.989141i \(0.453047\pi\)
\(798\) 0 0
\(799\) 65.0156 2.30009
\(800\) 0 0
\(801\) −11.1047 −0.392365
\(802\) 0 0
\(803\) 3.40312 0.120094
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 10.8062 0.380398
\(808\) 0 0
\(809\) 24.8062 0.872141 0.436071 0.899912i \(-0.356370\pi\)
0.436071 + 0.899912i \(0.356370\pi\)
\(810\) 0 0
\(811\) 24.2094 0.850106 0.425053 0.905168i \(-0.360255\pi\)
0.425053 + 0.905168i \(0.360255\pi\)
\(812\) 0 0
\(813\) −19.4031 −0.680497
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 8.00000 0.279885
\(818\) 0 0
\(819\) 3.70156 0.129343
\(820\) 0 0
\(821\) −34.5078 −1.20433 −0.602165 0.798371i \(-0.705695\pi\)
−0.602165 + 0.798371i \(0.705695\pi\)
\(822\) 0 0
\(823\) −4.00000 −0.139431 −0.0697156 0.997567i \(-0.522209\pi\)
−0.0697156 + 0.997567i \(0.522209\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −47.4031 −1.64837 −0.824184 0.566322i \(-0.808366\pi\)
−0.824184 + 0.566322i \(0.808366\pi\)
\(828\) 0 0
\(829\) 3.61250 0.125467 0.0627336 0.998030i \(-0.480018\pi\)
0.0627336 + 0.998030i \(0.480018\pi\)
\(830\) 0 0
\(831\) 16.8062 0.583002
\(832\) 0 0
\(833\) −38.2094 −1.32388
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 3.40312 0.117629
\(838\) 0 0
\(839\) −38.1203 −1.31606 −0.658030 0.752992i \(-0.728610\pi\)
−0.658030 + 0.752992i \(0.728610\pi\)
\(840\) 0 0
\(841\) −17.4187 −0.600646
\(842\) 0 0
\(843\) 10.0000 0.344418
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 79.6125 2.73552
\(848\) 0 0
\(849\) −20.0000 −0.686398
\(850\) 0 0
\(851\) −0.0890652 −0.00305311
\(852\) 0 0
\(853\) −48.7172 −1.66804 −0.834022 0.551731i \(-0.813968\pi\)
−0.834022 + 0.551731i \(0.813968\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −6.29844 −0.215151 −0.107575 0.994197i \(-0.534309\pi\)
−0.107575 + 0.994197i \(0.534309\pi\)
\(858\) 0 0
\(859\) 37.7016 1.28636 0.643180 0.765715i \(-0.277615\pi\)
0.643180 + 0.765715i \(0.277615\pi\)
\(860\) 0 0
\(861\) 15.9109 0.542243
\(862\) 0 0
\(863\) −0.596876 −0.0203179 −0.0101589 0.999948i \(-0.503234\pi\)
−0.0101589 + 0.999948i \(0.503234\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 15.5078 0.526673
\(868\) 0 0
\(869\) 9.70156 0.329103
\(870\) 0 0
\(871\) 4.00000 0.135535
\(872\) 0 0
\(873\) 1.10469 0.0373880
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −47.6125 −1.60776 −0.803880 0.594792i \(-0.797235\pi\)
−0.803880 + 0.594792i \(0.797235\pi\)
\(878\) 0 0
\(879\) −2.59688 −0.0875904
\(880\) 0 0
\(881\) 12.8062 0.431453 0.215727 0.976454i \(-0.430788\pi\)
0.215727 + 0.976454i \(0.430788\pi\)
\(882\) 0 0
\(883\) −33.6125 −1.13115 −0.565575 0.824697i \(-0.691346\pi\)
−0.565575 + 0.824697i \(0.691346\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −50.5078 −1.69589 −0.847943 0.530087i \(-0.822159\pi\)
−0.847943 + 0.530087i \(0.822159\pi\)
\(888\) 0 0
\(889\) 2.20937 0.0741000
\(890\) 0 0
\(891\) −5.70156 −0.191010
\(892\) 0 0
\(893\) 22.8062 0.763182
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −0.298438 −0.00996455
\(898\) 0 0
\(899\) −11.5813 −0.386256
\(900\) 0 0
\(901\) 24.5078 0.816474
\(902\) 0 0
\(903\) −14.8062 −0.492721
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −22.2094 −0.737450 −0.368725 0.929539i \(-0.620206\pi\)
−0.368725 + 0.929539i \(0.620206\pi\)
\(908\) 0 0
\(909\) 18.8062 0.623764
\(910\) 0 0
\(911\) −18.8062 −0.623079 −0.311539 0.950233i \(-0.600845\pi\)
−0.311539 + 0.950233i \(0.600845\pi\)
\(912\) 0 0
\(913\) 22.8062 0.754777
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 47.4031 1.56539
\(918\) 0 0
\(919\) 51.9109 1.71238 0.856192 0.516658i \(-0.172824\pi\)
0.856192 + 0.516658i \(0.172824\pi\)
\(920\) 0 0
\(921\) 33.1047 1.09084
\(922\) 0 0
\(923\) −16.5078 −0.543361
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −12.0000 −0.394132
\(928\) 0 0
\(929\) −11.1047 −0.364333 −0.182166 0.983268i \(-0.558311\pi\)
−0.182166 + 0.983268i \(0.558311\pi\)
\(930\) 0 0
\(931\) −13.4031 −0.439270
\(932\) 0 0
\(933\) 8.00000 0.261908
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −27.1938 −0.888381 −0.444191 0.895932i \(-0.646509\pi\)
−0.444191 + 0.895932i \(0.646509\pi\)
\(938\) 0 0
\(939\) 8.80625 0.287381
\(940\) 0 0
\(941\) −48.2984 −1.57448 −0.787242 0.616644i \(-0.788492\pi\)
−0.787242 + 0.616644i \(0.788492\pi\)
\(942\) 0 0
\(943\) −1.28282 −0.0417743
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −41.6125 −1.35222 −0.676112 0.736799i \(-0.736337\pi\)
−0.676112 + 0.736799i \(0.736337\pi\)
\(948\) 0 0
\(949\) −0.596876 −0.0193754
\(950\) 0 0
\(951\) 24.2094 0.785043
\(952\) 0 0
\(953\) 39.9109 1.29284 0.646421 0.762981i \(-0.276265\pi\)
0.646421 + 0.762981i \(0.276265\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 19.4031 0.627214
\(958\) 0 0
\(959\) −66.6281 −2.15153
\(960\) 0 0
\(961\) −19.4187 −0.626411
\(962\) 0 0
\(963\) 1.10469 0.0355980
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 49.8219 1.60216 0.801082 0.598555i \(-0.204258\pi\)
0.801082 + 0.598555i \(0.204258\pi\)
\(968\) 0 0
\(969\) 11.4031 0.366321
\(970\) 0 0
\(971\) −7.01562 −0.225142 −0.112571 0.993644i \(-0.535909\pi\)
−0.112571 + 0.993644i \(0.535909\pi\)
\(972\) 0 0
\(973\) 6.29844 0.201919
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 12.2094 0.390612 0.195306 0.980742i \(-0.437430\pi\)
0.195306 + 0.980742i \(0.437430\pi\)
\(978\) 0 0
\(979\) 63.3141 2.02353
\(980\) 0 0
\(981\) −14.8062 −0.472727
\(982\) 0 0
\(983\) 20.0000 0.637901 0.318950 0.947771i \(-0.396670\pi\)
0.318950 + 0.947771i \(0.396670\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −42.2094 −1.34354
\(988\) 0 0
\(989\) 1.19375 0.0379591
\(990\) 0 0
\(991\) −42.7172 −1.35696 −0.678478 0.734621i \(-0.737360\pi\)
−0.678478 + 0.734621i \(0.737360\pi\)
\(992\) 0 0
\(993\) 24.2094 0.768261
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 38.5969 1.22238 0.611188 0.791486i \(-0.290692\pi\)
0.611188 + 0.791486i \(0.290692\pi\)
\(998\) 0 0
\(999\) 0.298438 0.00944216
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.be.1.2 2
5.4 even 2 1560.2.a.m.1.1 2
15.14 odd 2 4680.2.a.bb.1.1 2
20.19 odd 2 3120.2.a.bf.1.2 2
60.59 even 2 9360.2.a.ct.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1560.2.a.m.1.1 2 5.4 even 2
3120.2.a.bf.1.2 2 20.19 odd 2
4680.2.a.bb.1.1 2 15.14 odd 2
7800.2.a.be.1.2 2 1.1 even 1 trivial
9360.2.a.ct.1.2 2 60.59 even 2