Properties

Label 1449.2.a.a.1.1
Level $1449$
Weight $2$
Character 1449.1
Self dual yes
Analytic conductor $11.570$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1449 = 3^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1449.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(11.5703232529\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 483)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1449.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000 q^{2} +2.00000 q^{4} -4.00000 q^{5} -1.00000 q^{7} +O(q^{10})\) \(q-2.00000 q^{2} +2.00000 q^{4} -4.00000 q^{5} -1.00000 q^{7} +8.00000 q^{10} +5.00000 q^{11} -2.00000 q^{13} +2.00000 q^{14} -4.00000 q^{16} -5.00000 q^{19} -8.00000 q^{20} -10.0000 q^{22} +1.00000 q^{23} +11.0000 q^{25} +4.00000 q^{26} -2.00000 q^{28} +2.00000 q^{29} +6.00000 q^{31} +8.00000 q^{32} +4.00000 q^{35} +6.00000 q^{37} +10.0000 q^{38} -5.00000 q^{41} +8.00000 q^{43} +10.0000 q^{44} -2.00000 q^{46} +9.00000 q^{47} +1.00000 q^{49} -22.0000 q^{50} -4.00000 q^{52} -9.00000 q^{53} -20.0000 q^{55} -4.00000 q^{58} -9.00000 q^{59} -5.00000 q^{61} -12.0000 q^{62} -8.00000 q^{64} +8.00000 q^{65} +4.00000 q^{67} -8.00000 q^{70} -12.0000 q^{71} -12.0000 q^{74} -10.0000 q^{76} -5.00000 q^{77} -10.0000 q^{79} +16.0000 q^{80} +10.0000 q^{82} +18.0000 q^{83} -16.0000 q^{86} -10.0000 q^{89} +2.00000 q^{91} +2.00000 q^{92} -18.0000 q^{94} +20.0000 q^{95} -18.0000 q^{97} -2.00000 q^{98} +O(q^{100})\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(3\) 0 0
\(4\) 2.00000 1.00000
\(5\) −4.00000 −1.78885 −0.894427 0.447214i \(-0.852416\pi\)
−0.894427 + 0.447214i \(0.852416\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 8.00000 2.52982
\(11\) 5.00000 1.50756 0.753778 0.657129i \(-0.228229\pi\)
0.753778 + 0.657129i \(0.228229\pi\)
\(12\) 0 0
\(13\) −2.00000 −0.554700 −0.277350 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 2.00000 0.534522
\(15\) 0 0
\(16\) −4.00000 −1.00000
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 0 0
\(19\) −5.00000 −1.14708 −0.573539 0.819178i \(-0.694430\pi\)
−0.573539 + 0.819178i \(0.694430\pi\)
\(20\) −8.00000 −1.78885
\(21\) 0 0
\(22\) −10.0000 −2.13201
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 11.0000 2.20000
\(26\) 4.00000 0.784465
\(27\) 0 0
\(28\) −2.00000 −0.377964
\(29\) 2.00000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) 0 0
\(31\) 6.00000 1.07763 0.538816 0.842424i \(-0.318872\pi\)
0.538816 + 0.842424i \(0.318872\pi\)
\(32\) 8.00000 1.41421
\(33\) 0 0
\(34\) 0 0
\(35\) 4.00000 0.676123
\(36\) 0 0
\(37\) 6.00000 0.986394 0.493197 0.869918i \(-0.335828\pi\)
0.493197 + 0.869918i \(0.335828\pi\)
\(38\) 10.0000 1.62221
\(39\) 0 0
\(40\) 0 0
\(41\) −5.00000 −0.780869 −0.390434 0.920631i \(-0.627675\pi\)
−0.390434 + 0.920631i \(0.627675\pi\)
\(42\) 0 0
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 10.0000 1.50756
\(45\) 0 0
\(46\) −2.00000 −0.294884
\(47\) 9.00000 1.31278 0.656392 0.754420i \(-0.272082\pi\)
0.656392 + 0.754420i \(0.272082\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −22.0000 −3.11127
\(51\) 0 0
\(52\) −4.00000 −0.554700
\(53\) −9.00000 −1.23625 −0.618123 0.786082i \(-0.712106\pi\)
−0.618123 + 0.786082i \(0.712106\pi\)
\(54\) 0 0
\(55\) −20.0000 −2.69680
\(56\) 0 0
\(57\) 0 0
\(58\) −4.00000 −0.525226
\(59\) −9.00000 −1.17170 −0.585850 0.810419i \(-0.699239\pi\)
−0.585850 + 0.810419i \(0.699239\pi\)
\(60\) 0 0
\(61\) −5.00000 −0.640184 −0.320092 0.947386i \(-0.603714\pi\)
−0.320092 + 0.947386i \(0.603714\pi\)
\(62\) −12.0000 −1.52400
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) 8.00000 0.992278
\(66\) 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 0
\(70\) −8.00000 −0.956183
\(71\) −12.0000 −1.42414 −0.712069 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(74\) −12.0000 −1.39497
\(75\) 0 0
\(76\) −10.0000 −1.14708
\(77\) −5.00000 −0.569803
\(78\) 0 0
\(79\) −10.0000 −1.12509 −0.562544 0.826767i \(-0.690177\pi\)
−0.562544 + 0.826767i \(0.690177\pi\)
\(80\) 16.0000 1.78885
\(81\) 0 0
\(82\) 10.0000 1.10432
\(83\) 18.0000 1.97576 0.987878 0.155230i \(-0.0496119\pi\)
0.987878 + 0.155230i \(0.0496119\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −16.0000 −1.72532
\(87\) 0 0
\(88\) 0 0
\(89\) −10.0000 −1.06000 −0.529999 0.847998i \(-0.677808\pi\)
−0.529999 + 0.847998i \(0.677808\pi\)
\(90\) 0 0
\(91\) 2.00000 0.209657
\(92\) 2.00000 0.208514
\(93\) 0 0
\(94\) −18.0000 −1.85656
\(95\) 20.0000 2.05196
\(96\) 0 0
\(97\) −18.0000 −1.82762 −0.913812 0.406138i \(-0.866875\pi\)
−0.913812 + 0.406138i \(0.866875\pi\)
\(98\) −2.00000 −0.202031
\(99\) 0 0
\(100\) 22.0000 2.20000
\(101\) −5.00000 −0.497519 −0.248759 0.968565i \(-0.580023\pi\)
−0.248759 + 0.968565i \(0.580023\pi\)
\(102\) 0 0
\(103\) −19.0000 −1.87213 −0.936063 0.351833i \(-0.885559\pi\)
−0.936063 + 0.351833i \(0.885559\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 18.0000 1.74831
\(107\) −4.00000 −0.386695 −0.193347 0.981130i \(-0.561934\pi\)
−0.193347 + 0.981130i \(0.561934\pi\)
\(108\) 0 0
\(109\) −12.0000 −1.14939 −0.574696 0.818367i \(-0.694880\pi\)
−0.574696 + 0.818367i \(0.694880\pi\)
\(110\) 40.0000 3.81385
\(111\) 0 0
\(112\) 4.00000 0.377964
\(113\) 2.00000 0.188144 0.0940721 0.995565i \(-0.470012\pi\)
0.0940721 + 0.995565i \(0.470012\pi\)
\(114\) 0 0
\(115\) −4.00000 −0.373002
\(116\) 4.00000 0.371391
\(117\) 0 0
\(118\) 18.0000 1.65703
\(119\) 0 0
\(120\) 0 0
\(121\) 14.0000 1.27273
\(122\) 10.0000 0.905357
\(123\) 0 0
\(124\) 12.0000 1.07763
\(125\) −24.0000 −2.14663
\(126\) 0 0
\(127\) 9.00000 0.798621 0.399310 0.916816i \(-0.369250\pi\)
0.399310 + 0.916816i \(0.369250\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) −16.0000 −1.40329
\(131\) 5.00000 0.436852 0.218426 0.975854i \(-0.429908\pi\)
0.218426 + 0.975854i \(0.429908\pi\)
\(132\) 0 0
\(133\) 5.00000 0.433555
\(134\) −8.00000 −0.691095
\(135\) 0 0
\(136\) 0 0
\(137\) −9.00000 −0.768922 −0.384461 0.923141i \(-0.625613\pi\)
−0.384461 + 0.923141i \(0.625613\pi\)
\(138\) 0 0
\(139\) 12.0000 1.01783 0.508913 0.860818i \(-0.330047\pi\)
0.508913 + 0.860818i \(0.330047\pi\)
\(140\) 8.00000 0.676123
\(141\) 0 0
\(142\) 24.0000 2.01404
\(143\) −10.0000 −0.836242
\(144\) 0 0
\(145\) −8.00000 −0.664364
\(146\) 0 0
\(147\) 0 0
\(148\) 12.0000 0.986394
\(149\) −3.00000 −0.245770 −0.122885 0.992421i \(-0.539215\pi\)
−0.122885 + 0.992421i \(0.539215\pi\)
\(150\) 0 0
\(151\) −19.0000 −1.54620 −0.773099 0.634285i \(-0.781294\pi\)
−0.773099 + 0.634285i \(0.781294\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 10.0000 0.805823
\(155\) −24.0000 −1.92773
\(156\) 0 0
\(157\) 7.00000 0.558661 0.279330 0.960195i \(-0.409888\pi\)
0.279330 + 0.960195i \(0.409888\pi\)
\(158\) 20.0000 1.59111
\(159\) 0 0
\(160\) −32.0000 −2.52982
\(161\) −1.00000 −0.0788110
\(162\) 0 0
\(163\) 13.0000 1.01824 0.509119 0.860696i \(-0.329971\pi\)
0.509119 + 0.860696i \(0.329971\pi\)
\(164\) −10.0000 −0.780869
\(165\) 0 0
\(166\) −36.0000 −2.79414
\(167\) −19.0000 −1.47026 −0.735132 0.677924i \(-0.762880\pi\)
−0.735132 + 0.677924i \(0.762880\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) 0 0
\(172\) 16.0000 1.21999
\(173\) −2.00000 −0.152057 −0.0760286 0.997106i \(-0.524224\pi\)
−0.0760286 + 0.997106i \(0.524224\pi\)
\(174\) 0 0
\(175\) −11.0000 −0.831522
\(176\) −20.0000 −1.50756
\(177\) 0 0
\(178\) 20.0000 1.49906
\(179\) −8.00000 −0.597948 −0.298974 0.954261i \(-0.596644\pi\)
−0.298974 + 0.954261i \(0.596644\pi\)
\(180\) 0 0
\(181\) −14.0000 −1.04061 −0.520306 0.853980i \(-0.674182\pi\)
−0.520306 + 0.853980i \(0.674182\pi\)
\(182\) −4.00000 −0.296500
\(183\) 0 0
\(184\) 0 0
\(185\) −24.0000 −1.76452
\(186\) 0 0
\(187\) 0 0
\(188\) 18.0000 1.31278
\(189\) 0 0
\(190\) −40.0000 −2.90191
\(191\) 23.0000 1.66422 0.832111 0.554609i \(-0.187132\pi\)
0.832111 + 0.554609i \(0.187132\pi\)
\(192\) 0 0
\(193\) −19.0000 −1.36765 −0.683825 0.729646i \(-0.739685\pi\)
−0.683825 + 0.729646i \(0.739685\pi\)
\(194\) 36.0000 2.58465
\(195\) 0 0
\(196\) 2.00000 0.142857
\(197\) 2.00000 0.142494 0.0712470 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) 0 0
\(199\) 3.00000 0.212664 0.106332 0.994331i \(-0.466089\pi\)
0.106332 + 0.994331i \(0.466089\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 10.0000 0.703598
\(203\) −2.00000 −0.140372
\(204\) 0 0
\(205\) 20.0000 1.39686
\(206\) 38.0000 2.64759
\(207\) 0 0
\(208\) 8.00000 0.554700
\(209\) −25.0000 −1.72929
\(210\) 0 0
\(211\) 13.0000 0.894957 0.447478 0.894295i \(-0.352322\pi\)
0.447478 + 0.894295i \(0.352322\pi\)
\(212\) −18.0000 −1.23625
\(213\) 0 0
\(214\) 8.00000 0.546869
\(215\) −32.0000 −2.18238
\(216\) 0 0
\(217\) −6.00000 −0.407307
\(218\) 24.0000 1.62549
\(219\) 0 0
\(220\) −40.0000 −2.69680
\(221\) 0 0
\(222\) 0 0
\(223\) 10.0000 0.669650 0.334825 0.942280i \(-0.391323\pi\)
0.334825 + 0.942280i \(0.391323\pi\)
\(224\) −8.00000 −0.534522
\(225\) 0 0
\(226\) −4.00000 −0.266076
\(227\) 18.0000 1.19470 0.597351 0.801980i \(-0.296220\pi\)
0.597351 + 0.801980i \(0.296220\pi\)
\(228\) 0 0
\(229\) −13.0000 −0.859064 −0.429532 0.903052i \(-0.641321\pi\)
−0.429532 + 0.903052i \(0.641321\pi\)
\(230\) 8.00000 0.527504
\(231\) 0 0
\(232\) 0 0
\(233\) 12.0000 0.786146 0.393073 0.919507i \(-0.371412\pi\)
0.393073 + 0.919507i \(0.371412\pi\)
\(234\) 0 0
\(235\) −36.0000 −2.34838
\(236\) −18.0000 −1.17170
\(237\) 0 0
\(238\) 0 0
\(239\) −12.0000 −0.776215 −0.388108 0.921614i \(-0.626871\pi\)
−0.388108 + 0.921614i \(0.626871\pi\)
\(240\) 0 0
\(241\) 17.0000 1.09507 0.547533 0.836784i \(-0.315567\pi\)
0.547533 + 0.836784i \(0.315567\pi\)
\(242\) −28.0000 −1.79991
\(243\) 0 0
\(244\) −10.0000 −0.640184
\(245\) −4.00000 −0.255551
\(246\) 0 0
\(247\) 10.0000 0.636285
\(248\) 0 0
\(249\) 0 0
\(250\) 48.0000 3.03579
\(251\) −10.0000 −0.631194 −0.315597 0.948893i \(-0.602205\pi\)
−0.315597 + 0.948893i \(0.602205\pi\)
\(252\) 0 0
\(253\) 5.00000 0.314347
\(254\) −18.0000 −1.12942
\(255\) 0 0
\(256\) 16.0000 1.00000
\(257\) −17.0000 −1.06043 −0.530215 0.847863i \(-0.677889\pi\)
−0.530215 + 0.847863i \(0.677889\pi\)
\(258\) 0 0
\(259\) −6.00000 −0.372822
\(260\) 16.0000 0.992278
\(261\) 0 0
\(262\) −10.0000 −0.617802
\(263\) −7.00000 −0.431638 −0.215819 0.976433i \(-0.569242\pi\)
−0.215819 + 0.976433i \(0.569242\pi\)
\(264\) 0 0
\(265\) 36.0000 2.21146
\(266\) −10.0000 −0.613139
\(267\) 0 0
\(268\) 8.00000 0.488678
\(269\) 18.0000 1.09748 0.548740 0.835993i \(-0.315108\pi\)
0.548740 + 0.835993i \(0.315108\pi\)
\(270\) 0 0
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 18.0000 1.08742
\(275\) 55.0000 3.31662
\(276\) 0 0
\(277\) 7.00000 0.420589 0.210295 0.977638i \(-0.432558\pi\)
0.210295 + 0.977638i \(0.432558\pi\)
\(278\) −24.0000 −1.43942
\(279\) 0 0
\(280\) 0 0
\(281\) −2.00000 −0.119310 −0.0596550 0.998219i \(-0.519000\pi\)
−0.0596550 + 0.998219i \(0.519000\pi\)
\(282\) 0 0
\(283\) −20.0000 −1.18888 −0.594438 0.804141i \(-0.702626\pi\)
−0.594438 + 0.804141i \(0.702626\pi\)
\(284\) −24.0000 −1.42414
\(285\) 0 0
\(286\) 20.0000 1.18262
\(287\) 5.00000 0.295141
\(288\) 0 0
\(289\) −17.0000 −1.00000
\(290\) 16.0000 0.939552
\(291\) 0 0
\(292\) 0 0
\(293\) 4.00000 0.233682 0.116841 0.993151i \(-0.462723\pi\)
0.116841 + 0.993151i \(0.462723\pi\)
\(294\) 0 0
\(295\) 36.0000 2.09600
\(296\) 0 0
\(297\) 0 0
\(298\) 6.00000 0.347571
\(299\) −2.00000 −0.115663
\(300\) 0 0
\(301\) −8.00000 −0.461112
\(302\) 38.0000 2.18665
\(303\) 0 0
\(304\) 20.0000 1.14708
\(305\) 20.0000 1.14520
\(306\) 0 0
\(307\) −8.00000 −0.456584 −0.228292 0.973593i \(-0.573314\pi\)
−0.228292 + 0.973593i \(0.573314\pi\)
\(308\) −10.0000 −0.569803
\(309\) 0 0
\(310\) 48.0000 2.72622
\(311\) 15.0000 0.850572 0.425286 0.905059i \(-0.360174\pi\)
0.425286 + 0.905059i \(0.360174\pi\)
\(312\) 0 0
\(313\) −25.0000 −1.41308 −0.706542 0.707671i \(-0.749746\pi\)
−0.706542 + 0.707671i \(0.749746\pi\)
\(314\) −14.0000 −0.790066
\(315\) 0 0
\(316\) −20.0000 −1.12509
\(317\) −30.0000 −1.68497 −0.842484 0.538721i \(-0.818908\pi\)
−0.842484 + 0.538721i \(0.818908\pi\)
\(318\) 0 0
\(319\) 10.0000 0.559893
\(320\) 32.0000 1.78885
\(321\) 0 0
\(322\) 2.00000 0.111456
\(323\) 0 0
\(324\) 0 0
\(325\) −22.0000 −1.22034
\(326\) −26.0000 −1.44001
\(327\) 0 0
\(328\) 0 0
\(329\) −9.00000 −0.496186
\(330\) 0 0
\(331\) 29.0000 1.59398 0.796992 0.603990i \(-0.206423\pi\)
0.796992 + 0.603990i \(0.206423\pi\)
\(332\) 36.0000 1.97576
\(333\) 0 0
\(334\) 38.0000 2.07927
\(335\) −16.0000 −0.874173
\(336\) 0 0
\(337\) 22.0000 1.19842 0.599208 0.800593i \(-0.295482\pi\)
0.599208 + 0.800593i \(0.295482\pi\)
\(338\) 18.0000 0.979071
\(339\) 0 0
\(340\) 0 0
\(341\) 30.0000 1.62459
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 4.00000 0.215041
\(347\) −2.00000 −0.107366 −0.0536828 0.998558i \(-0.517096\pi\)
−0.0536828 + 0.998558i \(0.517096\pi\)
\(348\) 0 0
\(349\) −2.00000 −0.107058 −0.0535288 0.998566i \(-0.517047\pi\)
−0.0535288 + 0.998566i \(0.517047\pi\)
\(350\) 22.0000 1.17595
\(351\) 0 0
\(352\) 40.0000 2.13201
\(353\) 14.0000 0.745145 0.372572 0.928003i \(-0.378476\pi\)
0.372572 + 0.928003i \(0.378476\pi\)
\(354\) 0 0
\(355\) 48.0000 2.54758
\(356\) −20.0000 −1.06000
\(357\) 0 0
\(358\) 16.0000 0.845626
\(359\) −32.0000 −1.68890 −0.844448 0.535638i \(-0.820071\pi\)
−0.844448 + 0.535638i \(0.820071\pi\)
\(360\) 0 0
\(361\) 6.00000 0.315789
\(362\) 28.0000 1.47165
\(363\) 0 0
\(364\) 4.00000 0.209657
\(365\) 0 0
\(366\) 0 0
\(367\) 27.0000 1.40939 0.704694 0.709511i \(-0.251084\pi\)
0.704694 + 0.709511i \(0.251084\pi\)
\(368\) −4.00000 −0.208514
\(369\) 0 0
\(370\) 48.0000 2.49540
\(371\) 9.00000 0.467257
\(372\) 0 0
\(373\) −34.0000 −1.76045 −0.880227 0.474554i \(-0.842610\pi\)
−0.880227 + 0.474554i \(0.842610\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −4.00000 −0.206010
\(378\) 0 0
\(379\) −30.0000 −1.54100 −0.770498 0.637442i \(-0.779993\pi\)
−0.770498 + 0.637442i \(0.779993\pi\)
\(380\) 40.0000 2.05196
\(381\) 0 0
\(382\) −46.0000 −2.35356
\(383\) −6.00000 −0.306586 −0.153293 0.988181i \(-0.548988\pi\)
−0.153293 + 0.988181i \(0.548988\pi\)
\(384\) 0 0
\(385\) 20.0000 1.01929
\(386\) 38.0000 1.93415
\(387\) 0 0
\(388\) −36.0000 −1.82762
\(389\) −6.00000 −0.304212 −0.152106 0.988364i \(-0.548606\pi\)
−0.152106 + 0.988364i \(0.548606\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) −4.00000 −0.201517
\(395\) 40.0000 2.01262
\(396\) 0 0
\(397\) 30.0000 1.50566 0.752828 0.658217i \(-0.228689\pi\)
0.752828 + 0.658217i \(0.228689\pi\)
\(398\) −6.00000 −0.300753
\(399\) 0 0
\(400\) −44.0000 −2.20000
\(401\) −3.00000 −0.149813 −0.0749064 0.997191i \(-0.523866\pi\)
−0.0749064 + 0.997191i \(0.523866\pi\)
\(402\) 0 0
\(403\) −12.0000 −0.597763
\(404\) −10.0000 −0.497519
\(405\) 0 0
\(406\) 4.00000 0.198517
\(407\) 30.0000 1.48704
\(408\) 0 0
\(409\) 14.0000 0.692255 0.346128 0.938187i \(-0.387496\pi\)
0.346128 + 0.938187i \(0.387496\pi\)
\(410\) −40.0000 −1.97546
\(411\) 0 0
\(412\) −38.0000 −1.87213
\(413\) 9.00000 0.442861
\(414\) 0 0
\(415\) −72.0000 −3.53434
\(416\) −16.0000 −0.784465
\(417\) 0 0
\(418\) 50.0000 2.44558
\(419\) 18.0000 0.879358 0.439679 0.898155i \(-0.355092\pi\)
0.439679 + 0.898155i \(0.355092\pi\)
\(420\) 0 0
\(421\) 8.00000 0.389896 0.194948 0.980814i \(-0.437546\pi\)
0.194948 + 0.980814i \(0.437546\pi\)
\(422\) −26.0000 −1.26566
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 5.00000 0.241967
\(428\) −8.00000 −0.386695
\(429\) 0 0
\(430\) 64.0000 3.08635
\(431\) −27.0000 −1.30054 −0.650272 0.759701i \(-0.725345\pi\)
−0.650272 + 0.759701i \(0.725345\pi\)
\(432\) 0 0
\(433\) −11.0000 −0.528626 −0.264313 0.964437i \(-0.585145\pi\)
−0.264313 + 0.964437i \(0.585145\pi\)
\(434\) 12.0000 0.576018
\(435\) 0 0
\(436\) −24.0000 −1.14939
\(437\) −5.00000 −0.239182
\(438\) 0 0
\(439\) −36.0000 −1.71819 −0.859093 0.511819i \(-0.828972\pi\)
−0.859093 + 0.511819i \(0.828972\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 36.0000 1.71041 0.855206 0.518289i \(-0.173431\pi\)
0.855206 + 0.518289i \(0.173431\pi\)
\(444\) 0 0
\(445\) 40.0000 1.89618
\(446\) −20.0000 −0.947027
\(447\) 0 0
\(448\) 8.00000 0.377964
\(449\) −6.00000 −0.283158 −0.141579 0.989927i \(-0.545218\pi\)
−0.141579 + 0.989927i \(0.545218\pi\)
\(450\) 0 0
\(451\) −25.0000 −1.17720
\(452\) 4.00000 0.188144
\(453\) 0 0
\(454\) −36.0000 −1.68956
\(455\) −8.00000 −0.375046
\(456\) 0 0
\(457\) 10.0000 0.467780 0.233890 0.972263i \(-0.424854\pi\)
0.233890 + 0.972263i \(0.424854\pi\)
\(458\) 26.0000 1.21490
\(459\) 0 0
\(460\) −8.00000 −0.373002
\(461\) −2.00000 −0.0931493 −0.0465746 0.998915i \(-0.514831\pi\)
−0.0465746 + 0.998915i \(0.514831\pi\)
\(462\) 0 0
\(463\) −35.0000 −1.62659 −0.813294 0.581853i \(-0.802328\pi\)
−0.813294 + 0.581853i \(0.802328\pi\)
\(464\) −8.00000 −0.371391
\(465\) 0 0
\(466\) −24.0000 −1.11178
\(467\) 6.00000 0.277647 0.138823 0.990317i \(-0.455668\pi\)
0.138823 + 0.990317i \(0.455668\pi\)
\(468\) 0 0
\(469\) −4.00000 −0.184703
\(470\) 72.0000 3.32111
\(471\) 0 0
\(472\) 0 0
\(473\) 40.0000 1.83920
\(474\) 0 0
\(475\) −55.0000 −2.52357
\(476\) 0 0
\(477\) 0 0
\(478\) 24.0000 1.09773
\(479\) −32.0000 −1.46212 −0.731059 0.682315i \(-0.760973\pi\)
−0.731059 + 0.682315i \(0.760973\pi\)
\(480\) 0 0
\(481\) −12.0000 −0.547153
\(482\) −34.0000 −1.54866
\(483\) 0 0
\(484\) 28.0000 1.27273
\(485\) 72.0000 3.26935
\(486\) 0 0
\(487\) −20.0000 −0.906287 −0.453143 0.891438i \(-0.649697\pi\)
−0.453143 + 0.891438i \(0.649697\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 8.00000 0.361403
\(491\) −14.0000 −0.631811 −0.315906 0.948791i \(-0.602308\pi\)
−0.315906 + 0.948791i \(0.602308\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −20.0000 −0.899843
\(495\) 0 0
\(496\) −24.0000 −1.07763
\(497\) 12.0000 0.538274
\(498\) 0 0
\(499\) −20.0000 −0.895323 −0.447661 0.894203i \(-0.647743\pi\)
−0.447661 + 0.894203i \(0.647743\pi\)
\(500\) −48.0000 −2.14663
\(501\) 0 0
\(502\) 20.0000 0.892644
\(503\) 36.0000 1.60516 0.802580 0.596544i \(-0.203460\pi\)
0.802580 + 0.596544i \(0.203460\pi\)
\(504\) 0 0
\(505\) 20.0000 0.889988
\(506\) −10.0000 −0.444554
\(507\) 0 0
\(508\) 18.0000 0.798621
\(509\) 19.0000 0.842160 0.421080 0.907023i \(-0.361651\pi\)
0.421080 + 0.907023i \(0.361651\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −32.0000 −1.41421
\(513\) 0 0
\(514\) 34.0000 1.49968
\(515\) 76.0000 3.34896
\(516\) 0 0
\(517\) 45.0000 1.97910
\(518\) 12.0000 0.527250
\(519\) 0 0
\(520\) 0 0
\(521\) 30.0000 1.31432 0.657162 0.753749i \(-0.271757\pi\)
0.657162 + 0.753749i \(0.271757\pi\)
\(522\) 0 0
\(523\) 19.0000 0.830812 0.415406 0.909636i \(-0.363640\pi\)
0.415406 + 0.909636i \(0.363640\pi\)
\(524\) 10.0000 0.436852
\(525\) 0 0
\(526\) 14.0000 0.610429
\(527\) 0 0
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) −72.0000 −3.12748
\(531\) 0 0
\(532\) 10.0000 0.433555
\(533\) 10.0000 0.433148
\(534\) 0 0
\(535\) 16.0000 0.691740
\(536\) 0 0
\(537\) 0 0
\(538\) −36.0000 −1.55207
\(539\) 5.00000 0.215365
\(540\) 0 0
\(541\) 11.0000 0.472927 0.236463 0.971640i \(-0.424012\pi\)
0.236463 + 0.971640i \(0.424012\pi\)
\(542\) 16.0000 0.687259
\(543\) 0 0
\(544\) 0 0
\(545\) 48.0000 2.05609
\(546\) 0 0
\(547\) −8.00000 −0.342055 −0.171028 0.985266i \(-0.554709\pi\)
−0.171028 + 0.985266i \(0.554709\pi\)
\(548\) −18.0000 −0.768922
\(549\) 0 0
\(550\) −110.000 −4.69042
\(551\) −10.0000 −0.426014
\(552\) 0 0
\(553\) 10.0000 0.425243
\(554\) −14.0000 −0.594803
\(555\) 0 0
\(556\) 24.0000 1.01783
\(557\) −46.0000 −1.94908 −0.974541 0.224208i \(-0.928020\pi\)
−0.974541 + 0.224208i \(0.928020\pi\)
\(558\) 0 0
\(559\) −16.0000 −0.676728
\(560\) −16.0000 −0.676123
\(561\) 0 0
\(562\) 4.00000 0.168730
\(563\) −40.0000 −1.68580 −0.842900 0.538071i \(-0.819153\pi\)
−0.842900 + 0.538071i \(0.819153\pi\)
\(564\) 0 0
\(565\) −8.00000 −0.336563
\(566\) 40.0000 1.68133
\(567\) 0 0
\(568\) 0 0
\(569\) 17.0000 0.712677 0.356339 0.934357i \(-0.384025\pi\)
0.356339 + 0.934357i \(0.384025\pi\)
\(570\) 0 0
\(571\) 8.00000 0.334790 0.167395 0.985890i \(-0.446465\pi\)
0.167395 + 0.985890i \(0.446465\pi\)
\(572\) −20.0000 −0.836242
\(573\) 0 0
\(574\) −10.0000 −0.417392
\(575\) 11.0000 0.458732
\(576\) 0 0
\(577\) −2.00000 −0.0832611 −0.0416305 0.999133i \(-0.513255\pi\)
−0.0416305 + 0.999133i \(0.513255\pi\)
\(578\) 34.0000 1.41421
\(579\) 0 0
\(580\) −16.0000 −0.664364
\(581\) −18.0000 −0.746766
\(582\) 0 0
\(583\) −45.0000 −1.86371
\(584\) 0 0
\(585\) 0 0
\(586\) −8.00000 −0.330477
\(587\) 17.0000 0.701665 0.350833 0.936438i \(-0.385899\pi\)
0.350833 + 0.936438i \(0.385899\pi\)
\(588\) 0 0
\(589\) −30.0000 −1.23613
\(590\) −72.0000 −2.96419
\(591\) 0 0
\(592\) −24.0000 −0.986394
\(593\) 18.0000 0.739171 0.369586 0.929197i \(-0.379500\pi\)
0.369586 + 0.929197i \(0.379500\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −6.00000 −0.245770
\(597\) 0 0
\(598\) 4.00000 0.163572
\(599\) −42.0000 −1.71607 −0.858037 0.513588i \(-0.828316\pi\)
−0.858037 + 0.513588i \(0.828316\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(602\) 16.0000 0.652111
\(603\) 0 0
\(604\) −38.0000 −1.54620
\(605\) −56.0000 −2.27672
\(606\) 0 0
\(607\) 8.00000 0.324710 0.162355 0.986732i \(-0.448091\pi\)
0.162355 + 0.986732i \(0.448091\pi\)
\(608\) −40.0000 −1.62221
\(609\) 0 0
\(610\) −40.0000 −1.61955
\(611\) −18.0000 −0.728202
\(612\) 0 0
\(613\) 34.0000 1.37325 0.686624 0.727013i \(-0.259092\pi\)
0.686624 + 0.727013i \(0.259092\pi\)
\(614\) 16.0000 0.645707
\(615\) 0 0
\(616\) 0 0
\(617\) −18.0000 −0.724653 −0.362326 0.932051i \(-0.618017\pi\)
−0.362326 + 0.932051i \(0.618017\pi\)
\(618\) 0 0
\(619\) −20.0000 −0.803868 −0.401934 0.915669i \(-0.631662\pi\)
−0.401934 + 0.915669i \(0.631662\pi\)
\(620\) −48.0000 −1.92773
\(621\) 0 0
\(622\) −30.0000 −1.20289
\(623\) 10.0000 0.400642
\(624\) 0 0
\(625\) 41.0000 1.64000
\(626\) 50.0000 1.99840
\(627\) 0 0
\(628\) 14.0000 0.558661
\(629\) 0 0
\(630\) 0 0
\(631\) −10.0000 −0.398094 −0.199047 0.979990i \(-0.563785\pi\)
−0.199047 + 0.979990i \(0.563785\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 60.0000 2.38290
\(635\) −36.0000 −1.42862
\(636\) 0 0
\(637\) −2.00000 −0.0792429
\(638\) −20.0000 −0.791808
\(639\) 0 0
\(640\) 0 0
\(641\) 9.00000 0.355479 0.177739 0.984078i \(-0.443122\pi\)
0.177739 + 0.984078i \(0.443122\pi\)
\(642\) 0 0
\(643\) −31.0000 −1.22252 −0.611260 0.791430i \(-0.709337\pi\)
−0.611260 + 0.791430i \(0.709337\pi\)
\(644\) −2.00000 −0.0788110
\(645\) 0 0
\(646\) 0 0
\(647\) 28.0000 1.10079 0.550397 0.834903i \(-0.314476\pi\)
0.550397 + 0.834903i \(0.314476\pi\)
\(648\) 0 0
\(649\) −45.0000 −1.76640
\(650\) 44.0000 1.72582
\(651\) 0 0
\(652\) 26.0000 1.01824
\(653\) −24.0000 −0.939193 −0.469596 0.882881i \(-0.655601\pi\)
−0.469596 + 0.882881i \(0.655601\pi\)
\(654\) 0 0
\(655\) −20.0000 −0.781465
\(656\) 20.0000 0.780869
\(657\) 0 0
\(658\) 18.0000 0.701713
\(659\) −24.0000 −0.934907 −0.467454 0.884018i \(-0.654829\pi\)
−0.467454 + 0.884018i \(0.654829\pi\)
\(660\) 0 0
\(661\) −5.00000 −0.194477 −0.0972387 0.995261i \(-0.531001\pi\)
−0.0972387 + 0.995261i \(0.531001\pi\)
\(662\) −58.0000 −2.25423
\(663\) 0 0
\(664\) 0 0
\(665\) −20.0000 −0.775567
\(666\) 0 0
\(667\) 2.00000 0.0774403
\(668\) −38.0000 −1.47026
\(669\) 0 0
\(670\) 32.0000 1.23627
\(671\) −25.0000 −0.965114
\(672\) 0 0
\(673\) 49.0000 1.88881 0.944406 0.328783i \(-0.106638\pi\)
0.944406 + 0.328783i \(0.106638\pi\)
\(674\) −44.0000 −1.69482
\(675\) 0 0
\(676\) −18.0000 −0.692308
\(677\) −36.0000 −1.38359 −0.691796 0.722093i \(-0.743180\pi\)
−0.691796 + 0.722093i \(0.743180\pi\)
\(678\) 0 0
\(679\) 18.0000 0.690777
\(680\) 0 0
\(681\) 0 0
\(682\) −60.0000 −2.29752
\(683\) −36.0000 −1.37750 −0.688751 0.724998i \(-0.741841\pi\)
−0.688751 + 0.724998i \(0.741841\pi\)
\(684\) 0 0
\(685\) 36.0000 1.37549
\(686\) 2.00000 0.0763604
\(687\) 0 0
\(688\) −32.0000 −1.21999
\(689\) 18.0000 0.685745
\(690\) 0 0
\(691\) −4.00000 −0.152167 −0.0760836 0.997101i \(-0.524242\pi\)
−0.0760836 + 0.997101i \(0.524242\pi\)
\(692\) −4.00000 −0.152057
\(693\) 0 0
\(694\) 4.00000 0.151838
\(695\) −48.0000 −1.82074
\(696\) 0 0
\(697\) 0 0
\(698\) 4.00000 0.151402
\(699\) 0 0
\(700\) −22.0000 −0.831522
\(701\) 15.0000 0.566542 0.283271 0.959040i \(-0.408580\pi\)
0.283271 + 0.959040i \(0.408580\pi\)
\(702\) 0 0
\(703\) −30.0000 −1.13147
\(704\) −40.0000 −1.50756
\(705\) 0 0
\(706\) −28.0000 −1.05379
\(707\) 5.00000 0.188044
\(708\) 0 0
\(709\) −6.00000 −0.225335 −0.112667 0.993633i \(-0.535939\pi\)
−0.112667 + 0.993633i \(0.535939\pi\)
\(710\) −96.0000 −3.60282
\(711\) 0 0
\(712\) 0 0
\(713\) 6.00000 0.224702
\(714\) 0 0
\(715\) 40.0000 1.49592
\(716\) −16.0000 −0.597948
\(717\) 0 0
\(718\) 64.0000 2.38846
\(719\) 24.0000 0.895049 0.447524 0.894272i \(-0.352306\pi\)
0.447524 + 0.894272i \(0.352306\pi\)
\(720\) 0 0
\(721\) 19.0000 0.707597
\(722\) −12.0000 −0.446594
\(723\) 0 0
\(724\) −28.0000 −1.04061
\(725\) 22.0000 0.817059
\(726\) 0 0
\(727\) 41.0000 1.52061 0.760303 0.649569i \(-0.225051\pi\)
0.760303 + 0.649569i \(0.225051\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −6.00000 −0.221615 −0.110808 0.993842i \(-0.535344\pi\)
−0.110808 + 0.993842i \(0.535344\pi\)
\(734\) −54.0000 −1.99318
\(735\) 0 0
\(736\) 8.00000 0.294884
\(737\) 20.0000 0.736709
\(738\) 0 0
\(739\) 12.0000 0.441427 0.220714 0.975339i \(-0.429161\pi\)
0.220714 + 0.975339i \(0.429161\pi\)
\(740\) −48.0000 −1.76452
\(741\) 0 0
\(742\) −18.0000 −0.660801
\(743\) −15.0000 −0.550297 −0.275148 0.961402i \(-0.588727\pi\)
−0.275148 + 0.961402i \(0.588727\pi\)
\(744\) 0 0
\(745\) 12.0000 0.439646
\(746\) 68.0000 2.48966
\(747\) 0 0
\(748\) 0 0
\(749\) 4.00000 0.146157
\(750\) 0 0
\(751\) −32.0000 −1.16770 −0.583848 0.811863i \(-0.698454\pi\)
−0.583848 + 0.811863i \(0.698454\pi\)
\(752\) −36.0000 −1.31278
\(753\) 0 0
\(754\) 8.00000 0.291343
\(755\) 76.0000 2.76592
\(756\) 0 0
\(757\) 8.00000 0.290765 0.145382 0.989376i \(-0.453559\pi\)
0.145382 + 0.989376i \(0.453559\pi\)
\(758\) 60.0000 2.17930
\(759\) 0 0
\(760\) 0 0
\(761\) 21.0000 0.761249 0.380625 0.924730i \(-0.375709\pi\)
0.380625 + 0.924730i \(0.375709\pi\)
\(762\) 0 0
\(763\) 12.0000 0.434429
\(764\) 46.0000 1.66422
\(765\) 0 0
\(766\) 12.0000 0.433578
\(767\) 18.0000 0.649942
\(768\) 0 0
\(769\) 14.0000 0.504853 0.252426 0.967616i \(-0.418771\pi\)
0.252426 + 0.967616i \(0.418771\pi\)
\(770\) −40.0000 −1.44150
\(771\) 0 0
\(772\) −38.0000 −1.36765
\(773\) −20.0000 −0.719350 −0.359675 0.933078i \(-0.617112\pi\)
−0.359675 + 0.933078i \(0.617112\pi\)
\(774\) 0 0
\(775\) 66.0000 2.37079
\(776\) 0 0
\(777\) 0 0
\(778\) 12.0000 0.430221
\(779\) 25.0000 0.895718
\(780\) 0 0
\(781\) −60.0000 −2.14697
\(782\) 0 0
\(783\) 0 0
\(784\) −4.00000 −0.142857
\(785\) −28.0000 −0.999363
\(786\) 0 0
\(787\) −23.0000 −0.819861 −0.409931 0.912117i \(-0.634447\pi\)
−0.409931 + 0.912117i \(0.634447\pi\)
\(788\) 4.00000 0.142494
\(789\) 0 0
\(790\) −80.0000 −2.84627
\(791\) −2.00000 −0.0711118
\(792\) 0 0
\(793\) 10.0000 0.355110
\(794\) −60.0000 −2.12932
\(795\) 0 0
\(796\) 6.00000 0.212664
\(797\) −46.0000 −1.62940 −0.814702 0.579880i \(-0.803099\pi\)
−0.814702 + 0.579880i \(0.803099\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 88.0000 3.11127
\(801\) 0 0
\(802\) 6.00000 0.211867
\(803\) 0 0
\(804\) 0 0
\(805\) 4.00000 0.140981
\(806\) 24.0000 0.845364
\(807\) 0 0
\(808\) 0 0
\(809\) 6.00000 0.210949 0.105474 0.994422i \(-0.466364\pi\)
0.105474 + 0.994422i \(0.466364\pi\)
\(810\) 0 0
\(811\) 2.00000 0.0702295 0.0351147 0.999383i \(-0.488820\pi\)
0.0351147 + 0.999383i \(0.488820\pi\)
\(812\) −4.00000 −0.140372
\(813\) 0 0
\(814\) −60.0000 −2.10300
\(815\) −52.0000 −1.82148
\(816\) 0 0
\(817\) −40.0000 −1.39942
\(818\) −28.0000 −0.978997
\(819\) 0 0
\(820\) 40.0000 1.39686
\(821\) 4.00000 0.139601 0.0698005 0.997561i \(-0.477764\pi\)
0.0698005 + 0.997561i \(0.477764\pi\)
\(822\) 0 0
\(823\) 27.0000 0.941161 0.470580 0.882357i \(-0.344045\pi\)
0.470580 + 0.882357i \(0.344045\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) −18.0000 −0.626300
\(827\) 21.0000 0.730242 0.365121 0.930960i \(-0.381028\pi\)
0.365121 + 0.930960i \(0.381028\pi\)
\(828\) 0 0
\(829\) 26.0000 0.903017 0.451509 0.892267i \(-0.350886\pi\)
0.451509 + 0.892267i \(0.350886\pi\)
\(830\) 144.000 4.99831
\(831\) 0 0
\(832\) 16.0000 0.554700
\(833\) 0 0
\(834\) 0 0
\(835\) 76.0000 2.63009
\(836\) −50.0000 −1.72929
\(837\) 0 0
\(838\) −36.0000 −1.24360
\(839\) −46.0000 −1.58810 −0.794048 0.607855i \(-0.792030\pi\)
−0.794048 + 0.607855i \(0.792030\pi\)
\(840\) 0 0
\(841\) −25.0000 −0.862069
\(842\) −16.0000 −0.551396
\(843\) 0 0
\(844\) 26.0000 0.894957
\(845\) 36.0000 1.23844
\(846\) 0 0
\(847\) −14.0000 −0.481046
\(848\) 36.0000 1.23625
\(849\) 0 0
\(850\) 0 0
\(851\) 6.00000 0.205677
\(852\) 0 0
\(853\) 8.00000 0.273915 0.136957 0.990577i \(-0.456268\pi\)
0.136957 + 0.990577i \(0.456268\pi\)
\(854\) −10.0000 −0.342193
\(855\) 0 0
\(856\) 0 0
\(857\) −1.00000 −0.0341593 −0.0170797 0.999854i \(-0.505437\pi\)
−0.0170797 + 0.999854i \(0.505437\pi\)
\(858\) 0 0
\(859\) −40.0000 −1.36478 −0.682391 0.730987i \(-0.739060\pi\)
−0.682391 + 0.730987i \(0.739060\pi\)
\(860\) −64.0000 −2.18238
\(861\) 0 0
\(862\) 54.0000 1.83925
\(863\) 30.0000 1.02121 0.510606 0.859815i \(-0.329421\pi\)
0.510606 + 0.859815i \(0.329421\pi\)
\(864\) 0 0
\(865\) 8.00000 0.272008
\(866\) 22.0000 0.747590
\(867\) 0 0
\(868\) −12.0000 −0.407307
\(869\) −50.0000 −1.69613
\(870\) 0 0
\(871\) −8.00000 −0.271070
\(872\) 0 0
\(873\) 0 0
\(874\) 10.0000 0.338255
\(875\) 24.0000 0.811348
\(876\) 0 0
\(877\) −17.0000 −0.574049 −0.287025 0.957923i \(-0.592666\pi\)
−0.287025 + 0.957923i \(0.592666\pi\)
\(878\) 72.0000 2.42988
\(879\) 0 0
\(880\) 80.0000 2.69680
\(881\) −6.00000 −0.202145 −0.101073 0.994879i \(-0.532227\pi\)
−0.101073 + 0.994879i \(0.532227\pi\)
\(882\) 0 0
\(883\) 32.0000 1.07689 0.538443 0.842662i \(-0.319013\pi\)
0.538443 + 0.842662i \(0.319013\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −72.0000 −2.41889
\(887\) 16.0000 0.537227 0.268614 0.963248i \(-0.413434\pi\)
0.268614 + 0.963248i \(0.413434\pi\)
\(888\) 0 0
\(889\) −9.00000 −0.301850
\(890\) −80.0000 −2.68161
\(891\) 0 0
\(892\) 20.0000 0.669650
\(893\) −45.0000 −1.50587
\(894\) 0 0
\(895\) 32.0000 1.06964
\(896\) 0 0
\(897\) 0 0
\(898\) 12.0000 0.400445
\(899\) 12.0000 0.400222
\(900\) 0 0
\(901\) 0 0
\(902\) 50.0000 1.66482
\(903\) 0 0
\(904\) 0 0
\(905\) 56.0000 1.86150
\(906\) 0 0
\(907\) 44.0000 1.46100 0.730498 0.682915i \(-0.239288\pi\)
0.730498 + 0.682915i \(0.239288\pi\)
\(908\) 36.0000 1.19470
\(909\) 0 0
\(910\) 16.0000 0.530395
\(911\) −24.0000 −0.795155 −0.397578 0.917568i \(-0.630149\pi\)
−0.397578 + 0.917568i \(0.630149\pi\)
\(912\) 0 0
\(913\) 90.0000 2.97857
\(914\) −20.0000 −0.661541
\(915\) 0 0
\(916\) −26.0000 −0.859064
\(917\) −5.00000 −0.165115
\(918\) 0 0
\(919\) 2.00000 0.0659739 0.0329870 0.999456i \(-0.489498\pi\)
0.0329870 + 0.999456i \(0.489498\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 4.00000 0.131733
\(923\) 24.0000 0.789970
\(924\) 0 0
\(925\) 66.0000 2.17007
\(926\) 70.0000 2.30034
\(927\) 0 0
\(928\) 16.0000 0.525226
\(929\) −26.0000 −0.853032 −0.426516 0.904480i \(-0.640259\pi\)
−0.426516 + 0.904480i \(0.640259\pi\)
\(930\) 0 0
\(931\) −5.00000 −0.163868
\(932\) 24.0000 0.786146
\(933\) 0 0
\(934\) −12.0000 −0.392652
\(935\) 0 0
\(936\) 0 0
\(937\) −27.0000 −0.882052 −0.441026 0.897494i \(-0.645385\pi\)
−0.441026 + 0.897494i \(0.645385\pi\)
\(938\) 8.00000 0.261209
\(939\) 0 0
\(940\) −72.0000 −2.34838
\(941\) −20.0000 −0.651981 −0.325991 0.945373i \(-0.605698\pi\)
−0.325991 + 0.945373i \(0.605698\pi\)
\(942\) 0 0
\(943\) −5.00000 −0.162822
\(944\) 36.0000 1.17170
\(945\) 0 0
\(946\) −80.0000 −2.60102
\(947\) −32.0000 −1.03986 −0.519930 0.854209i \(-0.674042\pi\)
−0.519930 + 0.854209i \(0.674042\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 110.000 3.56887
\(951\) 0 0
\(952\) 0 0
\(953\) 55.0000 1.78162 0.890812 0.454371i \(-0.150136\pi\)
0.890812 + 0.454371i \(0.150136\pi\)
\(954\) 0 0
\(955\) −92.0000 −2.97705
\(956\) −24.0000 −0.776215
\(957\) 0 0
\(958\) 64.0000 2.06775
\(959\) 9.00000 0.290625
\(960\) 0 0
\(961\) 5.00000 0.161290
\(962\) 24.0000 0.773791
\(963\) 0 0
\(964\) 34.0000 1.09507
\(965\) 76.0000 2.44653
\(966\) 0 0
\(967\) 28.0000 0.900419 0.450210 0.892923i \(-0.351349\pi\)
0.450210 + 0.892923i \(0.351349\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) −144.000 −4.62356
\(971\) 18.0000 0.577647 0.288824 0.957382i \(-0.406736\pi\)
0.288824 + 0.957382i \(0.406736\pi\)
\(972\) 0 0
\(973\) −12.0000 −0.384702
\(974\) 40.0000 1.28168
\(975\) 0 0
\(976\) 20.0000 0.640184
\(977\) 3.00000 0.0959785 0.0479893 0.998848i \(-0.484719\pi\)
0.0479893 + 0.998848i \(0.484719\pi\)
\(978\) 0 0
\(979\) −50.0000 −1.59801
\(980\) −8.00000 −0.255551
\(981\) 0 0
\(982\) 28.0000 0.893516
\(983\) −42.0000 −1.33959 −0.669796 0.742545i \(-0.733618\pi\)
−0.669796 + 0.742545i \(0.733618\pi\)
\(984\) 0 0
\(985\) −8.00000 −0.254901
\(986\) 0 0
\(987\) 0 0
\(988\) 20.0000 0.636285
\(989\) 8.00000 0.254385
\(990\) 0 0
\(991\) 5.00000 0.158830 0.0794151 0.996842i \(-0.474695\pi\)
0.0794151 + 0.996842i \(0.474695\pi\)
\(992\) 48.0000 1.52400
\(993\) 0 0
\(994\) −24.0000 −0.761234
\(995\) −12.0000 −0.380426
\(996\) 0 0
\(997\) −56.0000 −1.77354 −0.886769 0.462213i \(-0.847056\pi\)
−0.886769 + 0.462213i \(0.847056\pi\)
\(998\) 40.0000 1.26618
\(999\) 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 1449.2.a.a.1.1 1
3.2 odd 2 483.2.a.b.1.1 1
12.11 even 2 7728.2.a.l.1.1 1
21.20 even 2 3381.2.a.l.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
483.2.a.b.1.1 1 3.2 odd 2
1449.2.a.a.1.1 1 1.1 even 1 trivial
3381.2.a.l.1.1 1 21.20 even 2
7728.2.a.l.1.1 1 12.11 even 2