Properties

Label 3200.2.a.bt.1.1
Level $3200$
Weight $2$
Character 3200.1
Self dual yes
Analytic conductor $25.552$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 3200 = 2^{7} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3200.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(25.5521286468\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.148.1
Defining polynomial: \( x^{3} - x^{2} - 3x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 640)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.17009\) of defining polynomial
Character \(\chi\) \(=\) 3200.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.70928 q^{3} -2.63090 q^{7} -0.0783777 q^{9} +O(q^{10})\) \(q-1.70928 q^{3} -2.63090 q^{7} -0.0783777 q^{9} +5.41855 q^{11} -6.34017 q^{13} +3.41855 q^{17} +3.26180 q^{19} +4.49693 q^{21} -1.36910 q^{23} +5.26180 q^{27} -2.00000 q^{29} +4.68035 q^{31} -9.26180 q^{33} +5.75872 q^{37} +10.8371 q^{39} -7.75872 q^{41} +4.44748 q^{43} -4.78765 q^{47} -0.0783777 q^{49} -5.84324 q^{51} -1.65983 q^{53} -5.57531 q^{57} -3.26180 q^{59} +2.49693 q^{61} +0.206204 q^{63} +7.86603 q^{67} +2.34017 q^{69} +6.15676 q^{71} -13.5753 q^{73} -14.2557 q^{77} -12.6803 q^{79} -8.75872 q^{81} +14.9711 q^{83} +3.41855 q^{87} -8.52359 q^{89} +16.6803 q^{91} -8.00000 q^{93} -4.58145 q^{97} -0.424694 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 2 q^{3} - 4 q^{7} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + 2 q^{3} - 4 q^{7} + 3 q^{9} + 2 q^{11} - 8 q^{13} - 4 q^{17} + 2 q^{19} - 4 q^{21} - 8 q^{23} + 8 q^{27} - 6 q^{29} - 8 q^{31} - 20 q^{33} - 8 q^{37} + 4 q^{39} + 2 q^{41} + 14 q^{43} - 4 q^{47} + 3 q^{49} - 24 q^{51} - 16 q^{53} + 4 q^{57} - 2 q^{59} - 10 q^{61} - 24 q^{63} + 10 q^{67} - 4 q^{69} + 12 q^{71} - 20 q^{73} - 16 q^{79} - q^{81} + 30 q^{83} - 4 q^{87} - 10 q^{89} + 28 q^{91} - 24 q^{93} - 28 q^{97} - 22 q^{99}+O(q^{100}) \) 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
\(3\) −1.70928 −0.986851 −0.493425 0.869788i \(-0.664255\pi\)
−0.493425 + 0.869788i \(0.664255\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −2.63090 −0.994386 −0.497193 0.867640i \(-0.665636\pi\)
−0.497193 + 0.867640i \(0.665636\pi\)
\(8\) 0 0
\(9\) −0.0783777 −0.0261259
\(10\) 0 0
\(11\) 5.41855 1.63375 0.816877 0.576812i \(-0.195703\pi\)
0.816877 + 0.576812i \(0.195703\pi\)
\(12\) 0 0
\(13\) −6.34017 −1.75845 −0.879224 0.476409i \(-0.841938\pi\)
−0.879224 + 0.476409i \(0.841938\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.41855 0.829120 0.414560 0.910022i \(-0.363935\pi\)
0.414560 + 0.910022i \(0.363935\pi\)
\(18\) 0 0
\(19\) 3.26180 0.748307 0.374154 0.927367i \(-0.377933\pi\)
0.374154 + 0.927367i \(0.377933\pi\)
\(20\) 0 0
\(21\) 4.49693 0.981310
\(22\) 0 0
\(23\) −1.36910 −0.285478 −0.142739 0.989760i \(-0.545591\pi\)
−0.142739 + 0.989760i \(0.545591\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 5.26180 1.01263
\(28\) 0 0
\(29\) −2.00000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) 0 0
\(31\) 4.68035 0.840615 0.420307 0.907382i \(-0.361922\pi\)
0.420307 + 0.907382i \(0.361922\pi\)
\(32\) 0 0
\(33\) −9.26180 −1.61227
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 5.75872 0.946728 0.473364 0.880867i \(-0.343039\pi\)
0.473364 + 0.880867i \(0.343039\pi\)
\(38\) 0 0
\(39\) 10.8371 1.73533
\(40\) 0 0
\(41\) −7.75872 −1.21171 −0.605855 0.795575i \(-0.707169\pi\)
−0.605855 + 0.795575i \(0.707169\pi\)
\(42\) 0 0
\(43\) 4.44748 0.678234 0.339117 0.940744i \(-0.389872\pi\)
0.339117 + 0.940744i \(0.389872\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −4.78765 −0.698351 −0.349175 0.937057i \(-0.613538\pi\)
−0.349175 + 0.937057i \(0.613538\pi\)
\(48\) 0 0
\(49\) −0.0783777 −0.0111968
\(50\) 0 0
\(51\) −5.84324 −0.818218
\(52\) 0 0
\(53\) −1.65983 −0.227995 −0.113997 0.993481i \(-0.536366\pi\)
−0.113997 + 0.993481i \(0.536366\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −5.57531 −0.738467
\(58\) 0 0
\(59\) −3.26180 −0.424650 −0.212325 0.977199i \(-0.568103\pi\)
−0.212325 + 0.977199i \(0.568103\pi\)
\(60\) 0 0
\(61\) 2.49693 0.319699 0.159849 0.987141i \(-0.448899\pi\)
0.159849 + 0.987141i \(0.448899\pi\)
\(62\) 0 0
\(63\) 0.206204 0.0259792
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 7.86603 0.960989 0.480494 0.876998i \(-0.340457\pi\)
0.480494 + 0.876998i \(0.340457\pi\)
\(68\) 0 0
\(69\) 2.34017 0.281724
\(70\) 0 0
\(71\) 6.15676 0.730672 0.365336 0.930876i \(-0.380954\pi\)
0.365336 + 0.930876i \(0.380954\pi\)
\(72\) 0 0
\(73\) −13.5753 −1.58887 −0.794435 0.607350i \(-0.792233\pi\)
−0.794435 + 0.607350i \(0.792233\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −14.2557 −1.62458
\(78\) 0 0
\(79\) −12.6803 −1.42665 −0.713325 0.700833i \(-0.752812\pi\)
−0.713325 + 0.700833i \(0.752812\pi\)
\(80\) 0 0
\(81\) −8.75872 −0.973192
\(82\) 0 0
\(83\) 14.9711 1.64329 0.821644 0.570001i \(-0.193057\pi\)
0.821644 + 0.570001i \(0.193057\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 3.41855 0.366507
\(88\) 0 0
\(89\) −8.52359 −0.903499 −0.451749 0.892145i \(-0.649200\pi\)
−0.451749 + 0.892145i \(0.649200\pi\)
\(90\) 0 0
\(91\) 16.6803 1.74858
\(92\) 0 0
\(93\) −8.00000 −0.829561
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −4.58145 −0.465176 −0.232588 0.972575i \(-0.574719\pi\)
−0.232588 + 0.972575i \(0.574719\pi\)
\(98\) 0 0
\(99\) −0.424694 −0.0426833
\(100\) 0 0
\(101\) −2.31351 −0.230203 −0.115101 0.993354i \(-0.536719\pi\)
−0.115101 + 0.993354i \(0.536719\pi\)
\(102\) 0 0
\(103\) −16.2062 −1.59684 −0.798422 0.602098i \(-0.794332\pi\)
−0.798422 + 0.602098i \(0.794332\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −15.6514 −1.51308 −0.756540 0.653948i \(-0.773112\pi\)
−0.756540 + 0.653948i \(0.773112\pi\)
\(108\) 0 0
\(109\) 12.3402 1.18197 0.590987 0.806681i \(-0.298738\pi\)
0.590987 + 0.806681i \(0.298738\pi\)
\(110\) 0 0
\(111\) −9.84324 −0.934279
\(112\) 0 0
\(113\) 9.36069 0.880580 0.440290 0.897856i \(-0.354876\pi\)
0.440290 + 0.897856i \(0.354876\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0.496928 0.0459411
\(118\) 0 0
\(119\) −8.99386 −0.824466
\(120\) 0 0
\(121\) 18.3607 1.66915
\(122\) 0 0
\(123\) 13.2618 1.19578
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −1.95055 −0.173083 −0.0865417 0.996248i \(-0.527582\pi\)
−0.0865417 + 0.996248i \(0.527582\pi\)
\(128\) 0 0
\(129\) −7.60197 −0.669316
\(130\) 0 0
\(131\) −15.5753 −1.36082 −0.680410 0.732831i \(-0.738198\pi\)
−0.680410 + 0.732831i \(0.738198\pi\)
\(132\) 0 0
\(133\) −8.58145 −0.744106
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −15.2039 −1.29896 −0.649480 0.760379i \(-0.725013\pi\)
−0.649480 + 0.760379i \(0.725013\pi\)
\(138\) 0 0
\(139\) 2.58145 0.218956 0.109478 0.993989i \(-0.465082\pi\)
0.109478 + 0.993989i \(0.465082\pi\)
\(140\) 0 0
\(141\) 8.18342 0.689168
\(142\) 0 0
\(143\) −34.3545 −2.87287
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0.133969 0.0110496
\(148\) 0 0
\(149\) 1.81658 0.148820 0.0744101 0.997228i \(-0.476293\pi\)
0.0744101 + 0.997228i \(0.476293\pi\)
\(150\) 0 0
\(151\) 5.16290 0.420151 0.210075 0.977685i \(-0.432629\pi\)
0.210075 + 0.977685i \(0.432629\pi\)
\(152\) 0 0
\(153\) −0.267938 −0.0216615
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −13.7587 −1.09807 −0.549033 0.835801i \(-0.685004\pi\)
−0.549033 + 0.835801i \(0.685004\pi\)
\(158\) 0 0
\(159\) 2.83710 0.224997
\(160\) 0 0
\(161\) 3.60197 0.283875
\(162\) 0 0
\(163\) 6.29072 0.492728 0.246364 0.969177i \(-0.420764\pi\)
0.246364 + 0.969177i \(0.420764\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 3.89269 0.301226 0.150613 0.988593i \(-0.451875\pi\)
0.150613 + 0.988593i \(0.451875\pi\)
\(168\) 0 0
\(169\) 27.1978 2.09214
\(170\) 0 0
\(171\) −0.255652 −0.0195502
\(172\) 0 0
\(173\) 1.44521 0.109877 0.0549387 0.998490i \(-0.482504\pi\)
0.0549387 + 0.998490i \(0.482504\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 5.57531 0.419066
\(178\) 0 0
\(179\) −11.9421 −0.892598 −0.446299 0.894884i \(-0.647258\pi\)
−0.446299 + 0.894884i \(0.647258\pi\)
\(180\) 0 0
\(181\) −15.3607 −1.14175 −0.570876 0.821037i \(-0.693396\pi\)
−0.570876 + 0.821037i \(0.693396\pi\)
\(182\) 0 0
\(183\) −4.26794 −0.315495
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 18.5236 1.35458
\(188\) 0 0
\(189\) −13.8432 −1.00695
\(190\) 0 0
\(191\) −25.3607 −1.83504 −0.917518 0.397695i \(-0.869810\pi\)
−0.917518 + 0.397695i \(0.869810\pi\)
\(192\) 0 0
\(193\) −4.58145 −0.329780 −0.164890 0.986312i \(-0.552727\pi\)
−0.164890 + 0.986312i \(0.552727\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −16.8638 −1.20149 −0.600747 0.799439i \(-0.705130\pi\)
−0.600747 + 0.799439i \(0.705130\pi\)
\(198\) 0 0
\(199\) 9.84324 0.697769 0.348885 0.937166i \(-0.386561\pi\)
0.348885 + 0.937166i \(0.386561\pi\)
\(200\) 0 0
\(201\) −13.4452 −0.948352
\(202\) 0 0
\(203\) 5.26180 0.369306
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0.107307 0.00745836
\(208\) 0 0
\(209\) 17.6742 1.22255
\(210\) 0 0
\(211\) −15.5753 −1.07225 −0.536124 0.844139i \(-0.680112\pi\)
−0.536124 + 0.844139i \(0.680112\pi\)
\(212\) 0 0
\(213\) −10.5236 −0.721065
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −12.3135 −0.835896
\(218\) 0 0
\(219\) 23.2039 1.56798
\(220\) 0 0
\(221\) −21.6742 −1.45796
\(222\) 0 0
\(223\) 16.9854 1.13743 0.568715 0.822535i \(-0.307441\pi\)
0.568715 + 0.822535i \(0.307441\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −19.9649 −1.32512 −0.662559 0.749009i \(-0.730530\pi\)
−0.662559 + 0.749009i \(0.730530\pi\)
\(228\) 0 0
\(229\) −23.6742 −1.56444 −0.782218 0.623005i \(-0.785912\pi\)
−0.782218 + 0.623005i \(0.785912\pi\)
\(230\) 0 0
\(231\) 24.3668 1.60322
\(232\) 0 0
\(233\) −13.5753 −0.889348 −0.444674 0.895693i \(-0.646680\pi\)
−0.444674 + 0.895693i \(0.646680\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 21.6742 1.40789
\(238\) 0 0
\(239\) 8.36683 0.541206 0.270603 0.962691i \(-0.412777\pi\)
0.270603 + 0.962691i \(0.412777\pi\)
\(240\) 0 0
\(241\) 9.91548 0.638712 0.319356 0.947635i \(-0.396533\pi\)
0.319356 + 0.947635i \(0.396533\pi\)
\(242\) 0 0
\(243\) −0.814315 −0.0522383
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −20.6803 −1.31586
\(248\) 0 0
\(249\) −25.5897 −1.62168
\(250\) 0 0
\(251\) −17.6163 −1.11193 −0.555967 0.831204i \(-0.687652\pi\)
−0.555967 + 0.831204i \(0.687652\pi\)
\(252\) 0 0
\(253\) −7.41855 −0.466400
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 3.68649 0.229957 0.114978 0.993368i \(-0.463320\pi\)
0.114978 + 0.993368i \(0.463320\pi\)
\(258\) 0 0
\(259\) −15.1506 −0.941413
\(260\) 0 0
\(261\) 0.156755 0.00970292
\(262\) 0 0
\(263\) 0.107307 0.00661684 0.00330842 0.999995i \(-0.498947\pi\)
0.00330842 + 0.999995i \(0.498947\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 14.5692 0.891618
\(268\) 0 0
\(269\) −3.85762 −0.235203 −0.117602 0.993061i \(-0.537521\pi\)
−0.117602 + 0.993061i \(0.537521\pi\)
\(270\) 0 0
\(271\) −21.3074 −1.29433 −0.647165 0.762350i \(-0.724046\pi\)
−0.647165 + 0.762350i \(0.724046\pi\)
\(272\) 0 0
\(273\) −28.5113 −1.72558
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 1.44521 0.0868344 0.0434172 0.999057i \(-0.486176\pi\)
0.0434172 + 0.999057i \(0.486176\pi\)
\(278\) 0 0
\(279\) −0.366835 −0.0219618
\(280\) 0 0
\(281\) 12.4391 0.742053 0.371026 0.928622i \(-0.379006\pi\)
0.371026 + 0.928622i \(0.379006\pi\)
\(282\) 0 0
\(283\) 6.29072 0.373945 0.186972 0.982365i \(-0.440133\pi\)
0.186972 + 0.982365i \(0.440133\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 20.4124 1.20491
\(288\) 0 0
\(289\) −5.31351 −0.312559
\(290\) 0 0
\(291\) 7.83096 0.459059
\(292\) 0 0
\(293\) 1.07838 0.0629995 0.0314998 0.999504i \(-0.489972\pi\)
0.0314998 + 0.999504i \(0.489972\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 28.5113 1.65439
\(298\) 0 0
\(299\) 8.68035 0.501997
\(300\) 0 0
\(301\) −11.7009 −0.674427
\(302\) 0 0
\(303\) 3.95443 0.227176
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 25.2267 1.43977 0.719883 0.694096i \(-0.244196\pi\)
0.719883 + 0.694096i \(0.244196\pi\)
\(308\) 0 0
\(309\) 27.7009 1.57585
\(310\) 0 0
\(311\) 18.8371 1.06815 0.534077 0.845436i \(-0.320659\pi\)
0.534077 + 0.845436i \(0.320659\pi\)
\(312\) 0 0
\(313\) −15.2039 −0.859377 −0.429689 0.902977i \(-0.641377\pi\)
−0.429689 + 0.902977i \(0.641377\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 16.8638 0.947163 0.473582 0.880750i \(-0.342961\pi\)
0.473582 + 0.880750i \(0.342961\pi\)
\(318\) 0 0
\(319\) −10.8371 −0.606761
\(320\) 0 0
\(321\) 26.7526 1.49318
\(322\) 0 0
\(323\) 11.1506 0.620437
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −21.0928 −1.16643
\(328\) 0 0
\(329\) 12.5958 0.694430
\(330\) 0 0
\(331\) 23.5753 1.29582 0.647908 0.761719i \(-0.275644\pi\)
0.647908 + 0.761719i \(0.275644\pi\)
\(332\) 0 0
\(333\) −0.451356 −0.0247341
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −14.8371 −0.808228 −0.404114 0.914709i \(-0.632420\pi\)
−0.404114 + 0.914709i \(0.632420\pi\)
\(338\) 0 0
\(339\) −16.0000 −0.869001
\(340\) 0 0
\(341\) 25.3607 1.37336
\(342\) 0 0
\(343\) 18.6225 1.00552
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −0.133969 −0.00719184 −0.00359592 0.999994i \(-0.501145\pi\)
−0.00359592 + 0.999994i \(0.501145\pi\)
\(348\) 0 0
\(349\) −22.3135 −1.19441 −0.597207 0.802087i \(-0.703723\pi\)
−0.597207 + 0.802087i \(0.703723\pi\)
\(350\) 0 0
\(351\) −33.3607 −1.78066
\(352\) 0 0
\(353\) 22.8371 1.21550 0.607748 0.794130i \(-0.292073\pi\)
0.607748 + 0.794130i \(0.292073\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 15.3730 0.813624
\(358\) 0 0
\(359\) −31.8843 −1.68279 −0.841394 0.540422i \(-0.818265\pi\)
−0.841394 + 0.540422i \(0.818265\pi\)
\(360\) 0 0
\(361\) −8.36069 −0.440036
\(362\) 0 0
\(363\) −31.3835 −1.64721
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −30.4619 −1.59010 −0.795048 0.606547i \(-0.792554\pi\)
−0.795048 + 0.606547i \(0.792554\pi\)
\(368\) 0 0
\(369\) 0.608111 0.0316570
\(370\) 0 0
\(371\) 4.36683 0.226715
\(372\) 0 0
\(373\) −10.0722 −0.521521 −0.260760 0.965404i \(-0.583973\pi\)
−0.260760 + 0.965404i \(0.583973\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 12.6803 0.653071
\(378\) 0 0
\(379\) −14.7792 −0.759159 −0.379579 0.925159i \(-0.623931\pi\)
−0.379579 + 0.925159i \(0.623931\pi\)
\(380\) 0 0
\(381\) 3.33403 0.170808
\(382\) 0 0
\(383\) 14.4619 0.738966 0.369483 0.929237i \(-0.379535\pi\)
0.369483 + 0.929237i \(0.379535\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −0.348583 −0.0177195
\(388\) 0 0
\(389\) 3.17727 0.161094 0.0805471 0.996751i \(-0.474333\pi\)
0.0805471 + 0.996751i \(0.474333\pi\)
\(390\) 0 0
\(391\) −4.68035 −0.236695
\(392\) 0 0
\(393\) 26.6225 1.34293
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −10.8227 −0.543177 −0.271589 0.962413i \(-0.587549\pi\)
−0.271589 + 0.962413i \(0.587549\pi\)
\(398\) 0 0
\(399\) 14.6681 0.734321
\(400\) 0 0
\(401\) −12.5236 −0.625398 −0.312699 0.949852i \(-0.601233\pi\)
−0.312699 + 0.949852i \(0.601233\pi\)
\(402\) 0 0
\(403\) −29.6742 −1.47818
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 31.2039 1.54672
\(408\) 0 0
\(409\) −13.2885 −0.657072 −0.328536 0.944491i \(-0.606555\pi\)
−0.328536 + 0.944491i \(0.606555\pi\)
\(410\) 0 0
\(411\) 25.9877 1.28188
\(412\) 0 0
\(413\) 8.58145 0.422266
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −4.41241 −0.216077
\(418\) 0 0
\(419\) −0.255652 −0.0124894 −0.00624471 0.999981i \(-0.501988\pi\)
−0.00624471 + 0.999981i \(0.501988\pi\)
\(420\) 0 0
\(421\) 2.49693 0.121693 0.0608464 0.998147i \(-0.480620\pi\)
0.0608464 + 0.998147i \(0.480620\pi\)
\(422\) 0 0
\(423\) 0.375245 0.0182451
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −6.56916 −0.317904
\(428\) 0 0
\(429\) 58.7214 2.83510
\(430\) 0 0
\(431\) 0.993857 0.0478724 0.0239362 0.999713i \(-0.492380\pi\)
0.0239362 + 0.999713i \(0.492380\pi\)
\(432\) 0 0
\(433\) −17.6286 −0.847178 −0.423589 0.905855i \(-0.639230\pi\)
−0.423589 + 0.905855i \(0.639230\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −4.46573 −0.213625
\(438\) 0 0
\(439\) 40.5113 1.93350 0.966750 0.255725i \(-0.0823142\pi\)
0.966750 + 0.255725i \(0.0823142\pi\)
\(440\) 0 0
\(441\) 0.00614307 0.000292527 0
\(442\) 0 0
\(443\) −17.7093 −0.841393 −0.420697 0.907201i \(-0.638214\pi\)
−0.420697 + 0.907201i \(0.638214\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −3.10504 −0.146863
\(448\) 0 0
\(449\) −1.28846 −0.0608061 −0.0304030 0.999538i \(-0.509679\pi\)
−0.0304030 + 0.999538i \(0.509679\pi\)
\(450\) 0 0
\(451\) −42.0410 −1.97964
\(452\) 0 0
\(453\) −8.82482 −0.414626
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 26.3545 1.23281 0.616407 0.787428i \(-0.288588\pi\)
0.616407 + 0.787428i \(0.288588\pi\)
\(458\) 0 0
\(459\) 17.9877 0.839595
\(460\) 0 0
\(461\) 41.0349 1.91119 0.955593 0.294690i \(-0.0952165\pi\)
0.955593 + 0.294690i \(0.0952165\pi\)
\(462\) 0 0
\(463\) −28.7708 −1.33709 −0.668547 0.743670i \(-0.733083\pi\)
−0.668547 + 0.743670i \(0.733083\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −5.12783 −0.237287 −0.118644 0.992937i \(-0.537855\pi\)
−0.118644 + 0.992937i \(0.537855\pi\)
\(468\) 0 0
\(469\) −20.6947 −0.955593
\(470\) 0 0
\(471\) 23.5174 1.08363
\(472\) 0 0
\(473\) 24.0989 1.10807
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0.130094 0.00595657
\(478\) 0 0
\(479\) −13.6742 −0.624790 −0.312395 0.949952i \(-0.601131\pi\)
−0.312395 + 0.949952i \(0.601131\pi\)
\(480\) 0 0
\(481\) −36.5113 −1.66477
\(482\) 0 0
\(483\) −6.15676 −0.280142
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 8.51971 0.386065 0.193033 0.981192i \(-0.438168\pi\)
0.193033 + 0.981192i \(0.438168\pi\)
\(488\) 0 0
\(489\) −10.7526 −0.486249
\(490\) 0 0
\(491\) −4.73820 −0.213832 −0.106916 0.994268i \(-0.534098\pi\)
−0.106916 + 0.994268i \(0.534098\pi\)
\(492\) 0 0
\(493\) −6.83710 −0.307928
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −16.1978 −0.726570
\(498\) 0 0
\(499\) 11.0928 0.496580 0.248290 0.968686i \(-0.420131\pi\)
0.248290 + 0.968686i \(0.420131\pi\)
\(500\) 0 0
\(501\) −6.65368 −0.297265
\(502\) 0 0
\(503\) 8.42082 0.375466 0.187733 0.982220i \(-0.439886\pi\)
0.187733 + 0.982220i \(0.439886\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −46.4885 −2.06463
\(508\) 0 0
\(509\) −26.0000 −1.15243 −0.576215 0.817298i \(-0.695471\pi\)
−0.576215 + 0.817298i \(0.695471\pi\)
\(510\) 0 0
\(511\) 35.7152 1.57995
\(512\) 0 0
\(513\) 17.1629 0.757760
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −25.9421 −1.14093
\(518\) 0 0
\(519\) −2.47027 −0.108433
\(520\) 0 0
\(521\) −10.3135 −0.451843 −0.225922 0.974145i \(-0.572539\pi\)
−0.225922 + 0.974145i \(0.572539\pi\)
\(522\) 0 0
\(523\) 16.2784 0.711806 0.355903 0.934523i \(-0.384173\pi\)
0.355903 + 0.934523i \(0.384173\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 16.0000 0.696971
\(528\) 0 0
\(529\) −21.1256 −0.918503
\(530\) 0 0
\(531\) 0.255652 0.0110944
\(532\) 0 0
\(533\) 49.1917 2.13073
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 20.4124 0.880860
\(538\) 0 0
\(539\) −0.424694 −0.0182929
\(540\) 0 0
\(541\) 3.36069 0.144487 0.0722437 0.997387i \(-0.476984\pi\)
0.0722437 + 0.997387i \(0.476984\pi\)
\(542\) 0 0
\(543\) 26.2557 1.12674
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 1.51148 0.0646263 0.0323132 0.999478i \(-0.489713\pi\)
0.0323132 + 0.999478i \(0.489713\pi\)
\(548\) 0 0
\(549\) −0.195704 −0.00835243
\(550\) 0 0
\(551\) −6.52359 −0.277914
\(552\) 0 0
\(553\) 33.3607 1.41864
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 36.2290 1.53507 0.767536 0.641006i \(-0.221483\pi\)
0.767536 + 0.641006i \(0.221483\pi\)
\(558\) 0 0
\(559\) −28.1978 −1.19264
\(560\) 0 0
\(561\) −31.6619 −1.33677
\(562\) 0 0
\(563\) 2.17501 0.0916656 0.0458328 0.998949i \(-0.485406\pi\)
0.0458328 + 0.998949i \(0.485406\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 23.0433 0.967728
\(568\) 0 0
\(569\) 33.1194 1.38844 0.694219 0.719764i \(-0.255750\pi\)
0.694219 + 0.719764i \(0.255750\pi\)
\(570\) 0 0
\(571\) 18.4657 0.772767 0.386383 0.922338i \(-0.373724\pi\)
0.386383 + 0.922338i \(0.373724\pi\)
\(572\) 0 0
\(573\) 43.3484 1.81091
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −14.2101 −0.591573 −0.295787 0.955254i \(-0.595582\pi\)
−0.295787 + 0.955254i \(0.595582\pi\)
\(578\) 0 0
\(579\) 7.83096 0.325444
\(580\) 0 0
\(581\) −39.3874 −1.63406
\(582\) 0 0
\(583\) −8.99386 −0.372487
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 11.7503 0.484987 0.242494 0.970153i \(-0.422035\pi\)
0.242494 + 0.970153i \(0.422035\pi\)
\(588\) 0 0
\(589\) 15.2663 0.629038
\(590\) 0 0
\(591\) 28.8248 1.18569
\(592\) 0 0
\(593\) 8.00000 0.328521 0.164260 0.986417i \(-0.447476\pi\)
0.164260 + 0.986417i \(0.447476\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −16.8248 −0.688594
\(598\) 0 0
\(599\) 20.5646 0.840248 0.420124 0.907467i \(-0.361987\pi\)
0.420124 + 0.907467i \(0.361987\pi\)
\(600\) 0 0
\(601\) −8.60811 −0.351132 −0.175566 0.984468i \(-0.556176\pi\)
−0.175566 + 0.984468i \(0.556176\pi\)
\(602\) 0 0
\(603\) −0.616522 −0.0251067
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0.259528 0.0105339 0.00526695 0.999986i \(-0.498323\pi\)
0.00526695 + 0.999986i \(0.498323\pi\)
\(608\) 0 0
\(609\) −8.99386 −0.364449
\(610\) 0 0
\(611\) 30.3545 1.22801
\(612\) 0 0
\(613\) 47.1650 1.90498 0.952488 0.304576i \(-0.0985148\pi\)
0.952488 + 0.304576i \(0.0985148\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −40.2967 −1.62228 −0.811142 0.584849i \(-0.801154\pi\)
−0.811142 + 0.584849i \(0.801154\pi\)
\(618\) 0 0
\(619\) −30.6102 −1.23033 −0.615164 0.788399i \(-0.710910\pi\)
−0.615164 + 0.788399i \(0.710910\pi\)
\(620\) 0 0
\(621\) −7.20394 −0.289084
\(622\) 0 0
\(623\) 22.4247 0.898426
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −30.2101 −1.20647
\(628\) 0 0
\(629\) 19.6865 0.784952
\(630\) 0 0
\(631\) −2.21008 −0.0879819 −0.0439909 0.999032i \(-0.514007\pi\)
−0.0439909 + 0.999032i \(0.514007\pi\)
\(632\) 0 0
\(633\) 26.6225 1.05815
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0.496928 0.0196890
\(638\) 0 0
\(639\) −0.482553 −0.0190895
\(640\) 0 0
\(641\) 7.92777 0.313128 0.156564 0.987668i \(-0.449958\pi\)
0.156564 + 0.987668i \(0.449958\pi\)
\(642\) 0 0
\(643\) 5.18115 0.204325 0.102162 0.994768i \(-0.467424\pi\)
0.102162 + 0.994768i \(0.467424\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 12.2062 0.479875 0.239938 0.970788i \(-0.422873\pi\)
0.239938 + 0.970788i \(0.422873\pi\)
\(648\) 0 0
\(649\) −17.6742 −0.693773
\(650\) 0 0
\(651\) 21.0472 0.824904
\(652\) 0 0
\(653\) 32.4969 1.27170 0.635852 0.771811i \(-0.280649\pi\)
0.635852 + 0.771811i \(0.280649\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 1.06400 0.0415107
\(658\) 0 0
\(659\) 29.4186 1.14598 0.572992 0.819561i \(-0.305783\pi\)
0.572992 + 0.819561i \(0.305783\pi\)
\(660\) 0 0
\(661\) 26.0677 1.01392 0.506958 0.861971i \(-0.330770\pi\)
0.506958 + 0.861971i \(0.330770\pi\)
\(662\) 0 0
\(663\) 37.0472 1.43879
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 2.73820 0.106024
\(668\) 0 0
\(669\) −29.0328 −1.12247
\(670\) 0 0
\(671\) 13.5297 0.522310
\(672\) 0 0
\(673\) 9.62863 0.371156 0.185578 0.982629i \(-0.440584\pi\)
0.185578 + 0.982629i \(0.440584\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 19.0205 0.731018 0.365509 0.930808i \(-0.380895\pi\)
0.365509 + 0.930808i \(0.380895\pi\)
\(678\) 0 0
\(679\) 12.0533 0.462564
\(680\) 0 0
\(681\) 34.1256 1.30769
\(682\) 0 0
\(683\) 17.4947 0.669415 0.334707 0.942322i \(-0.391363\pi\)
0.334707 + 0.942322i \(0.391363\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 40.4657 1.54386
\(688\) 0 0
\(689\) 10.5236 0.400917
\(690\) 0 0
\(691\) −16.3090 −0.620423 −0.310211 0.950668i \(-0.600400\pi\)
−0.310211 + 0.950668i \(0.600400\pi\)
\(692\) 0 0
\(693\) 1.11733 0.0424437
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −26.5236 −1.00465
\(698\) 0 0
\(699\) 23.2039 0.877653
\(700\) 0 0
\(701\) −12.9672 −0.489764 −0.244882 0.969553i \(-0.578749\pi\)
−0.244882 + 0.969553i \(0.578749\pi\)
\(702\) 0 0
\(703\) 18.7838 0.708444
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 6.08661 0.228911
\(708\) 0 0
\(709\) 7.36069 0.276437 0.138218 0.990402i \(-0.455862\pi\)
0.138218 + 0.990402i \(0.455862\pi\)
\(710\) 0 0
\(711\) 0.993857 0.0372725
\(712\) 0 0
\(713\) −6.40787 −0.239977
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −14.3012 −0.534089
\(718\) 0 0
\(719\) 19.3197 0.720502 0.360251 0.932856i \(-0.382691\pi\)
0.360251 + 0.932856i \(0.382691\pi\)
\(720\) 0 0
\(721\) 42.6369 1.58788
\(722\) 0 0
\(723\) −16.9483 −0.630313
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −21.1545 −0.784577 −0.392288 0.919842i \(-0.628316\pi\)
−0.392288 + 0.919842i \(0.628316\pi\)
\(728\) 0 0
\(729\) 27.6681 1.02474
\(730\) 0 0
\(731\) 15.2039 0.562338
\(732\) 0 0
\(733\) −22.7526 −0.840386 −0.420193 0.907435i \(-0.638038\pi\)
−0.420193 + 0.907435i \(0.638038\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 42.6225 1.57002
\(738\) 0 0
\(739\) 28.4534 1.04668 0.523338 0.852125i \(-0.324686\pi\)
0.523338 + 0.852125i \(0.324686\pi\)
\(740\) 0 0
\(741\) 35.3484 1.29856
\(742\) 0 0
\(743\) 3.79380 0.139181 0.0695904 0.997576i \(-0.477831\pi\)
0.0695904 + 0.997576i \(0.477831\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −1.17340 −0.0429324
\(748\) 0 0
\(749\) 41.1773 1.50458
\(750\) 0 0
\(751\) −17.3607 −0.633501 −0.316750 0.948509i \(-0.602592\pi\)
−0.316750 + 0.948509i \(0.602592\pi\)
\(752\) 0 0
\(753\) 30.1112 1.09731
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −4.76487 −0.173182 −0.0865910 0.996244i \(-0.527597\pi\)
−0.0865910 + 0.996244i \(0.527597\pi\)
\(758\) 0 0
\(759\) 12.6803 0.460267
\(760\) 0 0
\(761\) −14.1978 −0.514670 −0.257335 0.966322i \(-0.582844\pi\)
−0.257335 + 0.966322i \(0.582844\pi\)
\(762\) 0 0
\(763\) −32.4657 −1.17534
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 20.6803 0.746724
\(768\) 0 0
\(769\) 54.7091 1.97286 0.986430 0.164181i \(-0.0524981\pi\)
0.986430 + 0.164181i \(0.0524981\pi\)
\(770\) 0 0
\(771\) −6.30122 −0.226933
\(772\) 0 0
\(773\) −11.0205 −0.396381 −0.198190 0.980164i \(-0.563506\pi\)
−0.198190 + 0.980164i \(0.563506\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 25.8966 0.929034
\(778\) 0 0
\(779\) −25.3074 −0.906731
\(780\) 0 0
\(781\) 33.3607 1.19374
\(782\) 0 0
\(783\) −10.5236 −0.376082
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −33.6925 −1.20101 −0.600503 0.799622i \(-0.705033\pi\)
−0.600503 + 0.799622i \(0.705033\pi\)
\(788\) 0 0
\(789\) −0.183417 −0.00652984
\(790\) 0 0
\(791\) −24.6270 −0.875636
\(792\) 0 0
\(793\) −15.8310 −0.562174
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 23.7009 0.839528 0.419764 0.907633i \(-0.362113\pi\)
0.419764 + 0.907633i \(0.362113\pi\)
\(798\) 0 0
\(799\) −16.3668 −0.579017
\(800\) 0 0
\(801\) 0.668060 0.0236047
\(802\) 0 0
\(803\) −73.5585 −2.59582
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 6.59374 0.232110
\(808\) 0 0
\(809\) −33.0349 −1.16145 −0.580723 0.814102i \(-0.697230\pi\)
−0.580723 + 0.814102i \(0.697230\pi\)
\(810\) 0 0
\(811\) −6.26794 −0.220097 −0.110049 0.993926i \(-0.535101\pi\)
−0.110049 + 0.993926i \(0.535101\pi\)
\(812\) 0 0
\(813\) 36.4202 1.27731
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 14.5068 0.507528
\(818\) 0 0
\(819\) −1.30737 −0.0456831
\(820\) 0 0
\(821\) −15.0616 −0.525652 −0.262826 0.964843i \(-0.584655\pi\)
−0.262826 + 0.964843i \(0.584655\pi\)
\(822\) 0 0
\(823\) −33.5669 −1.17007 −0.585034 0.811009i \(-0.698919\pi\)
−0.585034 + 0.811009i \(0.698919\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −10.6576 −0.370600 −0.185300 0.982682i \(-0.559326\pi\)
−0.185300 + 0.982682i \(0.559326\pi\)
\(828\) 0 0
\(829\) −52.4846 −1.82287 −0.911433 0.411447i \(-0.865023\pi\)
−0.911433 + 0.411447i \(0.865023\pi\)
\(830\) 0 0
\(831\) −2.47027 −0.0856926
\(832\) 0 0
\(833\) −0.267938 −0.00928351
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 24.6270 0.851234
\(838\) 0 0
\(839\) −18.2101 −0.628682 −0.314341 0.949310i \(-0.601783\pi\)
−0.314341 + 0.949310i \(0.601783\pi\)
\(840\) 0 0
\(841\) −25.0000 −0.862069
\(842\) 0 0
\(843\) −21.2618 −0.732295
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −48.3051 −1.65978
\(848\) 0 0
\(849\) −10.7526 −0.369028
\(850\) 0 0
\(851\) −7.88428 −0.270270
\(852\) 0 0
\(853\) −19.7542 −0.676371 −0.338185 0.941080i \(-0.609813\pi\)
−0.338185 + 0.941080i \(0.609813\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 48.9939 1.67360 0.836799 0.547510i \(-0.184424\pi\)
0.836799 + 0.547510i \(0.184424\pi\)
\(858\) 0 0
\(859\) −24.3090 −0.829412 −0.414706 0.909956i \(-0.636115\pi\)
−0.414706 + 0.909956i \(0.636115\pi\)
\(860\) 0 0
\(861\) −34.8904 −1.18906
\(862\) 0 0
\(863\) 44.3584 1.50998 0.754989 0.655737i \(-0.227642\pi\)
0.754989 + 0.655737i \(0.227642\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 9.08225 0.308449
\(868\) 0 0
\(869\) −68.7091 −2.33080
\(870\) 0 0
\(871\) −49.8720 −1.68985
\(872\) 0 0
\(873\) 0.359084 0.0121531
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −37.9565 −1.28170 −0.640850 0.767666i \(-0.721418\pi\)
−0.640850 + 0.767666i \(0.721418\pi\)
\(878\) 0 0
\(879\) −1.84324 −0.0621711
\(880\) 0 0
\(881\) 25.0661 0.844498 0.422249 0.906480i \(-0.361241\pi\)
0.422249 + 0.906480i \(0.361241\pi\)
\(882\) 0 0
\(883\) 21.1278 0.711008 0.355504 0.934675i \(-0.384309\pi\)
0.355504 + 0.934675i \(0.384309\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −36.1894 −1.21512 −0.607560 0.794274i \(-0.707852\pi\)
−0.607560 + 0.794274i \(0.707852\pi\)
\(888\) 0 0
\(889\) 5.13170 0.172112
\(890\) 0 0
\(891\) −47.4596 −1.58996
\(892\) 0 0
\(893\) −15.6163 −0.522581
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −14.8371 −0.495396
\(898\) 0 0
\(899\) −9.36069 −0.312197
\(900\) 0 0
\(901\) −5.67420 −0.189035
\(902\) 0 0
\(903\) 20.0000 0.665558
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 35.2678 1.17105 0.585523 0.810656i \(-0.300889\pi\)
0.585523 + 0.810656i \(0.300889\pi\)
\(908\) 0 0
\(909\) 0.181328 0.00601426
\(910\) 0 0
\(911\) 15.0061 0.497176 0.248588 0.968609i \(-0.420034\pi\)
0.248588 + 0.968609i \(0.420034\pi\)
\(912\) 0 0
\(913\) 81.1215 2.68473
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 40.9770 1.35318
\(918\) 0 0
\(919\) −32.8781 −1.08455 −0.542275 0.840201i \(-0.682437\pi\)
−0.542275 + 0.840201i \(0.682437\pi\)
\(920\) 0 0
\(921\) −43.1194 −1.42083
\(922\) 0 0
\(923\) −39.0349 −1.28485
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 1.27021 0.0417190
\(928\) 0 0
\(929\) −30.2290 −0.991781 −0.495890 0.868385i \(-0.665158\pi\)
−0.495890 + 0.868385i \(0.665158\pi\)
\(930\) 0 0
\(931\) −0.255652 −0.00837866
\(932\) 0 0
\(933\) −32.1978 −1.05411
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −28.4124 −0.928193 −0.464096 0.885785i \(-0.653621\pi\)
−0.464096 + 0.885785i \(0.653621\pi\)
\(938\) 0 0
\(939\) 25.9877 0.848077
\(940\) 0 0
\(941\) −42.0821 −1.37184 −0.685918 0.727679i \(-0.740599\pi\)
−0.685918 + 0.727679i \(0.740599\pi\)
\(942\) 0 0
\(943\) 10.6225 0.345916
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 22.2739 0.723805 0.361902 0.932216i \(-0.382127\pi\)
0.361902 + 0.932216i \(0.382127\pi\)
\(948\) 0 0
\(949\) 86.0698 2.79394
\(950\) 0 0
\(951\) −28.8248 −0.934709
\(952\) 0 0
\(953\) −14.6681 −0.475145 −0.237573 0.971370i \(-0.576352\pi\)
−0.237573 + 0.971370i \(0.576352\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 18.5236 0.598783
\(958\) 0 0
\(959\) 40.0000 1.29167
\(960\) 0 0
\(961\) −9.09436 −0.293367
\(962\) 0 0
\(963\) 1.22672 0.0395306
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0.403997 0.0129917 0.00649584 0.999979i \(-0.497932\pi\)
0.00649584 + 0.999979i \(0.497932\pi\)
\(968\) 0 0
\(969\) −19.0595 −0.612278
\(970\) 0 0
\(971\) −46.8326 −1.50293 −0.751464 0.659774i \(-0.770652\pi\)
−0.751464 + 0.659774i \(0.770652\pi\)
\(972\) 0 0
\(973\) −6.79153 −0.217726
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 53.6041 1.71495 0.857473 0.514529i \(-0.172033\pi\)
0.857473 + 0.514529i \(0.172033\pi\)
\(978\) 0 0
\(979\) −46.1855 −1.47610
\(980\) 0 0
\(981\) −0.967195 −0.0308802
\(982\) 0 0
\(983\) 19.9916 0.637633 0.318816 0.947817i \(-0.396715\pi\)
0.318816 + 0.947817i \(0.396715\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −21.5297 −0.685299
\(988\) 0 0
\(989\) −6.08906 −0.193621
\(990\) 0 0
\(991\) 24.6270 0.782303 0.391152 0.920326i \(-0.372077\pi\)
0.391152 + 0.920326i \(0.372077\pi\)
\(992\) 0 0
\(993\) −40.2967 −1.27878
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −20.9795 −0.664427 −0.332213 0.943204i \(-0.607795\pi\)
−0.332213 + 0.943204i \(0.607795\pi\)
\(998\) 0 0
\(999\) 30.3012 0.958688
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 3200.2.a.bt.1.1 3
4.3 odd 2 3200.2.a.bq.1.3 3
5.2 odd 4 640.2.c.b.129.5 yes 6
5.3 odd 4 640.2.c.b.129.2 yes 6
5.4 even 2 3200.2.a.br.1.3 3
8.3 odd 2 3200.2.a.bv.1.1 3
8.5 even 2 3200.2.a.bo.1.3 3
20.3 even 4 640.2.c.a.129.5 yes 6
20.7 even 4 640.2.c.a.129.2 6
20.19 odd 2 3200.2.a.bs.1.1 3
40.3 even 4 640.2.c.d.129.2 yes 6
40.13 odd 4 640.2.c.c.129.5 yes 6
40.19 odd 2 3200.2.a.bp.1.3 3
40.27 even 4 640.2.c.d.129.5 yes 6
40.29 even 2 3200.2.a.bu.1.1 3
40.37 odd 4 640.2.c.c.129.2 yes 6
80.3 even 4 1280.2.f.l.129.2 6
80.13 odd 4 1280.2.f.j.129.6 6
80.27 even 4 1280.2.f.l.129.1 6
80.37 odd 4 1280.2.f.j.129.5 6
80.43 even 4 1280.2.f.i.129.5 6
80.53 odd 4 1280.2.f.k.129.1 6
80.67 even 4 1280.2.f.i.129.6 6
80.77 odd 4 1280.2.f.k.129.2 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
640.2.c.a.129.2 6 20.7 even 4
640.2.c.a.129.5 yes 6 20.3 even 4
640.2.c.b.129.2 yes 6 5.3 odd 4
640.2.c.b.129.5 yes 6 5.2 odd 4
640.2.c.c.129.2 yes 6 40.37 odd 4
640.2.c.c.129.5 yes 6 40.13 odd 4
640.2.c.d.129.2 yes 6 40.3 even 4
640.2.c.d.129.5 yes 6 40.27 even 4
1280.2.f.i.129.5 6 80.43 even 4
1280.2.f.i.129.6 6 80.67 even 4
1280.2.f.j.129.5 6 80.37 odd 4
1280.2.f.j.129.6 6 80.13 odd 4
1280.2.f.k.129.1 6 80.53 odd 4
1280.2.f.k.129.2 6 80.77 odd 4
1280.2.f.l.129.1 6 80.27 even 4
1280.2.f.l.129.2 6 80.3 even 4
3200.2.a.bo.1.3 3 8.5 even 2
3200.2.a.bp.1.3 3 40.19 odd 2
3200.2.a.bq.1.3 3 4.3 odd 2
3200.2.a.br.1.3 3 5.4 even 2
3200.2.a.bs.1.1 3 20.19 odd 2
3200.2.a.bt.1.1 3 1.1 even 1 trivial
3200.2.a.bu.1.1 3 40.29 even 2
3200.2.a.bv.1.1 3 8.3 odd 2