Properties

Label 1932.2.a.d.1.2
Level $1932$
Weight $2$
Character 1932.1
Self dual yes
Analytic conductor $15.427$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1932 = 2^{2} \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1932.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(15.4270976705\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
Defining polynomial: \( x^{2} - x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(1.61803\) of defining polynomial
Character \(\chi\) \(=\) 1932.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} +1.61803 q^{5} -1.00000 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} +1.61803 q^{5} -1.00000 q^{7} +1.00000 q^{9} -4.23607 q^{11} +2.61803 q^{13} -1.61803 q^{15} +2.23607 q^{17} -5.47214 q^{19} +1.00000 q^{21} +1.00000 q^{23} -2.38197 q^{25} -1.00000 q^{27} -3.47214 q^{29} -6.23607 q^{31} +4.23607 q^{33} -1.61803 q^{35} +3.47214 q^{37} -2.61803 q^{39} -1.47214 q^{41} +7.56231 q^{43} +1.61803 q^{45} -5.23607 q^{47} +1.00000 q^{49} -2.23607 q^{51} +4.09017 q^{53} -6.85410 q^{55} +5.47214 q^{57} -5.61803 q^{59} -10.3262 q^{61} -1.00000 q^{63} +4.23607 q^{65} -5.61803 q^{67} -1.00000 q^{69} -4.14590 q^{71} -15.9443 q^{73} +2.38197 q^{75} +4.23607 q^{77} -3.76393 q^{79} +1.00000 q^{81} +9.94427 q^{83} +3.61803 q^{85} +3.47214 q^{87} +3.85410 q^{89} -2.61803 q^{91} +6.23607 q^{93} -8.85410 q^{95} +4.23607 q^{97} -4.23607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{3} + q^{5} - 2 q^{7} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{3} + q^{5} - 2 q^{7} + 2 q^{9} - 4 q^{11} + 3 q^{13} - q^{15} - 2 q^{19} + 2 q^{21} + 2 q^{23} - 7 q^{25} - 2 q^{27} + 2 q^{29} - 8 q^{31} + 4 q^{33} - q^{35} - 2 q^{37} - 3 q^{39} + 6 q^{41} - 5 q^{43} + q^{45} - 6 q^{47} + 2 q^{49} - 3 q^{53} - 7 q^{55} + 2 q^{57} - 9 q^{59} - 5 q^{61} - 2 q^{63} + 4 q^{65} - 9 q^{67} - 2 q^{69} - 15 q^{71} - 14 q^{73} + 7 q^{75} + 4 q^{77} - 12 q^{79} + 2 q^{81} + 2 q^{83} + 5 q^{85} - 2 q^{87} + q^{89} - 3 q^{91} + 8 q^{93} - 11 q^{95} + 4 q^{97} - 4 q^{99}+O(q^{100}) \) 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
\(5\) 1.61803 0.723607 0.361803 0.932254i \(-0.382161\pi\)
0.361803 + 0.932254i \(0.382161\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −4.23607 −1.27722 −0.638611 0.769529i \(-0.720491\pi\)
−0.638611 + 0.769529i \(0.720491\pi\)
\(12\) 0 0
\(13\) 2.61803 0.726112 0.363056 0.931767i \(-0.381733\pi\)
0.363056 + 0.931767i \(0.381733\pi\)
\(14\) 0 0
\(15\) −1.61803 −0.417775
\(16\) 0 0
\(17\) 2.23607 0.542326 0.271163 0.962533i \(-0.412592\pi\)
0.271163 + 0.962533i \(0.412592\pi\)
\(18\) 0 0
\(19\) −5.47214 −1.25539 −0.627697 0.778458i \(-0.716002\pi\)
−0.627697 + 0.778458i \(0.716002\pi\)
\(20\) 0 0
\(21\) 1.00000 0.218218
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) −2.38197 −0.476393
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −3.47214 −0.644759 −0.322380 0.946610i \(-0.604483\pi\)
−0.322380 + 0.946610i \(0.604483\pi\)
\(30\) 0 0
\(31\) −6.23607 −1.12003 −0.560015 0.828482i \(-0.689205\pi\)
−0.560015 + 0.828482i \(0.689205\pi\)
\(32\) 0 0
\(33\) 4.23607 0.737405
\(34\) 0 0
\(35\) −1.61803 −0.273498
\(36\) 0 0
\(37\) 3.47214 0.570816 0.285408 0.958406i \(-0.407871\pi\)
0.285408 + 0.958406i \(0.407871\pi\)
\(38\) 0 0
\(39\) −2.61803 −0.419221
\(40\) 0 0
\(41\) −1.47214 −0.229909 −0.114955 0.993371i \(-0.536672\pi\)
−0.114955 + 0.993371i \(0.536672\pi\)
\(42\) 0 0
\(43\) 7.56231 1.15324 0.576620 0.817012i \(-0.304371\pi\)
0.576620 + 0.817012i \(0.304371\pi\)
\(44\) 0 0
\(45\) 1.61803 0.241202
\(46\) 0 0
\(47\) −5.23607 −0.763759 −0.381880 0.924212i \(-0.624723\pi\)
−0.381880 + 0.924212i \(0.624723\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −2.23607 −0.313112
\(52\) 0 0
\(53\) 4.09017 0.561828 0.280914 0.959733i \(-0.409362\pi\)
0.280914 + 0.959733i \(0.409362\pi\)
\(54\) 0 0
\(55\) −6.85410 −0.924207
\(56\) 0 0
\(57\) 5.47214 0.724802
\(58\) 0 0
\(59\) −5.61803 −0.731406 −0.365703 0.930732i \(-0.619171\pi\)
−0.365703 + 0.930732i \(0.619171\pi\)
\(60\) 0 0
\(61\) −10.3262 −1.32214 −0.661070 0.750325i \(-0.729897\pi\)
−0.661070 + 0.750325i \(0.729897\pi\)
\(62\) 0 0
\(63\) −1.00000 −0.125988
\(64\) 0 0
\(65\) 4.23607 0.525420
\(66\) 0 0
\(67\) −5.61803 −0.686352 −0.343176 0.939271i \(-0.611503\pi\)
−0.343176 + 0.939271i \(0.611503\pi\)
\(68\) 0 0
\(69\) −1.00000 −0.120386
\(70\) 0 0
\(71\) −4.14590 −0.492028 −0.246014 0.969266i \(-0.579121\pi\)
−0.246014 + 0.969266i \(0.579121\pi\)
\(72\) 0 0
\(73\) −15.9443 −1.86614 −0.933068 0.359700i \(-0.882879\pi\)
−0.933068 + 0.359700i \(0.882879\pi\)
\(74\) 0 0
\(75\) 2.38197 0.275046
\(76\) 0 0
\(77\) 4.23607 0.482745
\(78\) 0 0
\(79\) −3.76393 −0.423475 −0.211738 0.977327i \(-0.567912\pi\)
−0.211738 + 0.977327i \(0.567912\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 9.94427 1.09153 0.545763 0.837940i \(-0.316240\pi\)
0.545763 + 0.837940i \(0.316240\pi\)
\(84\) 0 0
\(85\) 3.61803 0.392431
\(86\) 0 0
\(87\) 3.47214 0.372252
\(88\) 0 0
\(89\) 3.85410 0.408534 0.204267 0.978915i \(-0.434519\pi\)
0.204267 + 0.978915i \(0.434519\pi\)
\(90\) 0 0
\(91\) −2.61803 −0.274445
\(92\) 0 0
\(93\) 6.23607 0.646650
\(94\) 0 0
\(95\) −8.85410 −0.908412
\(96\) 0 0
\(97\) 4.23607 0.430108 0.215054 0.976602i \(-0.431007\pi\)
0.215054 + 0.976602i \(0.431007\pi\)
\(98\) 0 0
\(99\) −4.23607 −0.425741
\(100\) 0 0
\(101\) −3.61803 −0.360008 −0.180004 0.983666i \(-0.557611\pi\)
−0.180004 + 0.983666i \(0.557611\pi\)
\(102\) 0 0
\(103\) 8.94427 0.881305 0.440653 0.897678i \(-0.354747\pi\)
0.440653 + 0.897678i \(0.354747\pi\)
\(104\) 0 0
\(105\) 1.61803 0.157904
\(106\) 0 0
\(107\) −12.6180 −1.21983 −0.609916 0.792466i \(-0.708797\pi\)
−0.609916 + 0.792466i \(0.708797\pi\)
\(108\) 0 0
\(109\) −4.38197 −0.419716 −0.209858 0.977732i \(-0.567300\pi\)
−0.209858 + 0.977732i \(0.567300\pi\)
\(110\) 0 0
\(111\) −3.47214 −0.329561
\(112\) 0 0
\(113\) −12.5623 −1.18176 −0.590881 0.806759i \(-0.701220\pi\)
−0.590881 + 0.806759i \(0.701220\pi\)
\(114\) 0 0
\(115\) 1.61803 0.150882
\(116\) 0 0
\(117\) 2.61803 0.242037
\(118\) 0 0
\(119\) −2.23607 −0.204980
\(120\) 0 0
\(121\) 6.94427 0.631297
\(122\) 0 0
\(123\) 1.47214 0.132738
\(124\) 0 0
\(125\) −11.9443 −1.06833
\(126\) 0 0
\(127\) −13.8541 −1.22935 −0.614676 0.788779i \(-0.710713\pi\)
−0.614676 + 0.788779i \(0.710713\pi\)
\(128\) 0 0
\(129\) −7.56231 −0.665824
\(130\) 0 0
\(131\) 17.9443 1.56780 0.783899 0.620888i \(-0.213228\pi\)
0.783899 + 0.620888i \(0.213228\pi\)
\(132\) 0 0
\(133\) 5.47214 0.474494
\(134\) 0 0
\(135\) −1.61803 −0.139258
\(136\) 0 0
\(137\) 4.23607 0.361912 0.180956 0.983491i \(-0.442081\pi\)
0.180956 + 0.983491i \(0.442081\pi\)
\(138\) 0 0
\(139\) 17.0344 1.44484 0.722421 0.691453i \(-0.243029\pi\)
0.722421 + 0.691453i \(0.243029\pi\)
\(140\) 0 0
\(141\) 5.23607 0.440956
\(142\) 0 0
\(143\) −11.0902 −0.927407
\(144\) 0 0
\(145\) −5.61803 −0.466552
\(146\) 0 0
\(147\) −1.00000 −0.0824786
\(148\) 0 0
\(149\) −16.6525 −1.36422 −0.682112 0.731248i \(-0.738938\pi\)
−0.682112 + 0.731248i \(0.738938\pi\)
\(150\) 0 0
\(151\) −15.7082 −1.27832 −0.639158 0.769076i \(-0.720717\pi\)
−0.639158 + 0.769076i \(0.720717\pi\)
\(152\) 0 0
\(153\) 2.23607 0.180775
\(154\) 0 0
\(155\) −10.0902 −0.810462
\(156\) 0 0
\(157\) −12.7639 −1.01867 −0.509336 0.860568i \(-0.670109\pi\)
−0.509336 + 0.860568i \(0.670109\pi\)
\(158\) 0 0
\(159\) −4.09017 −0.324372
\(160\) 0 0
\(161\) −1.00000 −0.0788110
\(162\) 0 0
\(163\) −16.5623 −1.29726 −0.648630 0.761104i \(-0.724658\pi\)
−0.648630 + 0.761104i \(0.724658\pi\)
\(164\) 0 0
\(165\) 6.85410 0.533591
\(166\) 0 0
\(167\) 20.8885 1.61640 0.808202 0.588905i \(-0.200441\pi\)
0.808202 + 0.588905i \(0.200441\pi\)
\(168\) 0 0
\(169\) −6.14590 −0.472761
\(170\) 0 0
\(171\) −5.47214 −0.418465
\(172\) 0 0
\(173\) 2.05573 0.156294 0.0781471 0.996942i \(-0.475100\pi\)
0.0781471 + 0.996942i \(0.475100\pi\)
\(174\) 0 0
\(175\) 2.38197 0.180060
\(176\) 0 0
\(177\) 5.61803 0.422277
\(178\) 0 0
\(179\) 21.7984 1.62929 0.814643 0.579962i \(-0.196933\pi\)
0.814643 + 0.579962i \(0.196933\pi\)
\(180\) 0 0
\(181\) 0.236068 0.0175468 0.00877340 0.999962i \(-0.497207\pi\)
0.00877340 + 0.999962i \(0.497207\pi\)
\(182\) 0 0
\(183\) 10.3262 0.763337
\(184\) 0 0
\(185\) 5.61803 0.413046
\(186\) 0 0
\(187\) −9.47214 −0.692671
\(188\) 0 0
\(189\) 1.00000 0.0727393
\(190\) 0 0
\(191\) −19.1246 −1.38381 −0.691904 0.721989i \(-0.743228\pi\)
−0.691904 + 0.721989i \(0.743228\pi\)
\(192\) 0 0
\(193\) −17.7082 −1.27466 −0.637332 0.770589i \(-0.719962\pi\)
−0.637332 + 0.770589i \(0.719962\pi\)
\(194\) 0 0
\(195\) −4.23607 −0.303351
\(196\) 0 0
\(197\) −8.61803 −0.614009 −0.307005 0.951708i \(-0.599327\pi\)
−0.307005 + 0.951708i \(0.599327\pi\)
\(198\) 0 0
\(199\) −21.3262 −1.51178 −0.755888 0.654700i \(-0.772795\pi\)
−0.755888 + 0.654700i \(0.772795\pi\)
\(200\) 0 0
\(201\) 5.61803 0.396266
\(202\) 0 0
\(203\) 3.47214 0.243696
\(204\) 0 0
\(205\) −2.38197 −0.166364
\(206\) 0 0
\(207\) 1.00000 0.0695048
\(208\) 0 0
\(209\) 23.1803 1.60342
\(210\) 0 0
\(211\) 2.23607 0.153937 0.0769686 0.997034i \(-0.475476\pi\)
0.0769686 + 0.997034i \(0.475476\pi\)
\(212\) 0 0
\(213\) 4.14590 0.284072
\(214\) 0 0
\(215\) 12.2361 0.834493
\(216\) 0 0
\(217\) 6.23607 0.423332
\(218\) 0 0
\(219\) 15.9443 1.07741
\(220\) 0 0
\(221\) 5.85410 0.393790
\(222\) 0 0
\(223\) −25.2148 −1.68851 −0.844253 0.535944i \(-0.819956\pi\)
−0.844253 + 0.535944i \(0.819956\pi\)
\(224\) 0 0
\(225\) −2.38197 −0.158798
\(226\) 0 0
\(227\) −10.0902 −0.669708 −0.334854 0.942270i \(-0.608687\pi\)
−0.334854 + 0.942270i \(0.608687\pi\)
\(228\) 0 0
\(229\) 12.3820 0.818223 0.409112 0.912484i \(-0.365839\pi\)
0.409112 + 0.912484i \(0.365839\pi\)
\(230\) 0 0
\(231\) −4.23607 −0.278713
\(232\) 0 0
\(233\) 2.09017 0.136932 0.0684658 0.997653i \(-0.478190\pi\)
0.0684658 + 0.997653i \(0.478190\pi\)
\(234\) 0 0
\(235\) −8.47214 −0.552661
\(236\) 0 0
\(237\) 3.76393 0.244494
\(238\) 0 0
\(239\) 7.03444 0.455020 0.227510 0.973776i \(-0.426942\pi\)
0.227510 + 0.973776i \(0.426942\pi\)
\(240\) 0 0
\(241\) −11.2918 −0.727369 −0.363684 0.931522i \(-0.618481\pi\)
−0.363684 + 0.931522i \(0.618481\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 1.61803 0.103372
\(246\) 0 0
\(247\) −14.3262 −0.911557
\(248\) 0 0
\(249\) −9.94427 −0.630193
\(250\) 0 0
\(251\) −0.180340 −0.0113830 −0.00569148 0.999984i \(-0.501812\pi\)
−0.00569148 + 0.999984i \(0.501812\pi\)
\(252\) 0 0
\(253\) −4.23607 −0.266319
\(254\) 0 0
\(255\) −3.61803 −0.226570
\(256\) 0 0
\(257\) 12.2918 0.766741 0.383371 0.923595i \(-0.374763\pi\)
0.383371 + 0.923595i \(0.374763\pi\)
\(258\) 0 0
\(259\) −3.47214 −0.215748
\(260\) 0 0
\(261\) −3.47214 −0.214920
\(262\) 0 0
\(263\) 9.94427 0.613190 0.306595 0.951840i \(-0.400810\pi\)
0.306595 + 0.951840i \(0.400810\pi\)
\(264\) 0 0
\(265\) 6.61803 0.406543
\(266\) 0 0
\(267\) −3.85410 −0.235867
\(268\) 0 0
\(269\) 23.0902 1.40783 0.703916 0.710283i \(-0.251433\pi\)
0.703916 + 0.710283i \(0.251433\pi\)
\(270\) 0 0
\(271\) 31.3607 1.90503 0.952513 0.304499i \(-0.0984889\pi\)
0.952513 + 0.304499i \(0.0984889\pi\)
\(272\) 0 0
\(273\) 2.61803 0.158451
\(274\) 0 0
\(275\) 10.0902 0.608460
\(276\) 0 0
\(277\) 8.61803 0.517807 0.258904 0.965903i \(-0.416639\pi\)
0.258904 + 0.965903i \(0.416639\pi\)
\(278\) 0 0
\(279\) −6.23607 −0.373344
\(280\) 0 0
\(281\) 22.6525 1.35133 0.675667 0.737207i \(-0.263856\pi\)
0.675667 + 0.737207i \(0.263856\pi\)
\(282\) 0 0
\(283\) −7.90983 −0.470191 −0.235095 0.971972i \(-0.575540\pi\)
−0.235095 + 0.971972i \(0.575540\pi\)
\(284\) 0 0
\(285\) 8.85410 0.524472
\(286\) 0 0
\(287\) 1.47214 0.0868974
\(288\) 0 0
\(289\) −12.0000 −0.705882
\(290\) 0 0
\(291\) −4.23607 −0.248323
\(292\) 0 0
\(293\) 24.9443 1.45726 0.728630 0.684908i \(-0.240157\pi\)
0.728630 + 0.684908i \(0.240157\pi\)
\(294\) 0 0
\(295\) −9.09017 −0.529250
\(296\) 0 0
\(297\) 4.23607 0.245802
\(298\) 0 0
\(299\) 2.61803 0.151405
\(300\) 0 0
\(301\) −7.56231 −0.435884
\(302\) 0 0
\(303\) 3.61803 0.207851
\(304\) 0 0
\(305\) −16.7082 −0.956709
\(306\) 0 0
\(307\) 10.2361 0.584203 0.292102 0.956387i \(-0.405645\pi\)
0.292102 + 0.956387i \(0.405645\pi\)
\(308\) 0 0
\(309\) −8.94427 −0.508822
\(310\) 0 0
\(311\) 30.9787 1.75664 0.878321 0.478072i \(-0.158664\pi\)
0.878321 + 0.478072i \(0.158664\pi\)
\(312\) 0 0
\(313\) −2.47214 −0.139733 −0.0698667 0.997556i \(-0.522257\pi\)
−0.0698667 + 0.997556i \(0.522257\pi\)
\(314\) 0 0
\(315\) −1.61803 −0.0911659
\(316\) 0 0
\(317\) 4.96556 0.278894 0.139447 0.990230i \(-0.455468\pi\)
0.139447 + 0.990230i \(0.455468\pi\)
\(318\) 0 0
\(319\) 14.7082 0.823501
\(320\) 0 0
\(321\) 12.6180 0.704270
\(322\) 0 0
\(323\) −12.2361 −0.680833
\(324\) 0 0
\(325\) −6.23607 −0.345915
\(326\) 0 0
\(327\) 4.38197 0.242323
\(328\) 0 0
\(329\) 5.23607 0.288674
\(330\) 0 0
\(331\) 18.9443 1.04127 0.520636 0.853779i \(-0.325695\pi\)
0.520636 + 0.853779i \(0.325695\pi\)
\(332\) 0 0
\(333\) 3.47214 0.190272
\(334\) 0 0
\(335\) −9.09017 −0.496649
\(336\) 0 0
\(337\) 5.56231 0.302998 0.151499 0.988457i \(-0.451590\pi\)
0.151499 + 0.988457i \(0.451590\pi\)
\(338\) 0 0
\(339\) 12.5623 0.682291
\(340\) 0 0
\(341\) 26.4164 1.43053
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −1.61803 −0.0871120
\(346\) 0 0
\(347\) −3.18034 −0.170730 −0.0853648 0.996350i \(-0.527206\pi\)
−0.0853648 + 0.996350i \(0.527206\pi\)
\(348\) 0 0
\(349\) 11.9098 0.637519 0.318759 0.947836i \(-0.396734\pi\)
0.318759 + 0.947836i \(0.396734\pi\)
\(350\) 0 0
\(351\) −2.61803 −0.139740
\(352\) 0 0
\(353\) 25.9443 1.38087 0.690437 0.723392i \(-0.257418\pi\)
0.690437 + 0.723392i \(0.257418\pi\)
\(354\) 0 0
\(355\) −6.70820 −0.356034
\(356\) 0 0
\(357\) 2.23607 0.118345
\(358\) 0 0
\(359\) −7.32624 −0.386664 −0.193332 0.981133i \(-0.561929\pi\)
−0.193332 + 0.981133i \(0.561929\pi\)
\(360\) 0 0
\(361\) 10.9443 0.576014
\(362\) 0 0
\(363\) −6.94427 −0.364480
\(364\) 0 0
\(365\) −25.7984 −1.35035
\(366\) 0 0
\(367\) 12.7984 0.668070 0.334035 0.942561i \(-0.391590\pi\)
0.334035 + 0.942561i \(0.391590\pi\)
\(368\) 0 0
\(369\) −1.47214 −0.0766363
\(370\) 0 0
\(371\) −4.09017 −0.212351
\(372\) 0 0
\(373\) 8.05573 0.417110 0.208555 0.978011i \(-0.433124\pi\)
0.208555 + 0.978011i \(0.433124\pi\)
\(374\) 0 0
\(375\) 11.9443 0.616800
\(376\) 0 0
\(377\) −9.09017 −0.468168
\(378\) 0 0
\(379\) −26.8328 −1.37831 −0.689155 0.724614i \(-0.742018\pi\)
−0.689155 + 0.724614i \(0.742018\pi\)
\(380\) 0 0
\(381\) 13.8541 0.709767
\(382\) 0 0
\(383\) 9.47214 0.484004 0.242002 0.970276i \(-0.422196\pi\)
0.242002 + 0.970276i \(0.422196\pi\)
\(384\) 0 0
\(385\) 6.85410 0.349317
\(386\) 0 0
\(387\) 7.56231 0.384414
\(388\) 0 0
\(389\) 26.4164 1.33937 0.669683 0.742648i \(-0.266430\pi\)
0.669683 + 0.742648i \(0.266430\pi\)
\(390\) 0 0
\(391\) 2.23607 0.113083
\(392\) 0 0
\(393\) −17.9443 −0.905169
\(394\) 0 0
\(395\) −6.09017 −0.306430
\(396\) 0 0
\(397\) 5.81966 0.292080 0.146040 0.989279i \(-0.453347\pi\)
0.146040 + 0.989279i \(0.453347\pi\)
\(398\) 0 0
\(399\) −5.47214 −0.273949
\(400\) 0 0
\(401\) 33.3607 1.66595 0.832976 0.553308i \(-0.186635\pi\)
0.832976 + 0.553308i \(0.186635\pi\)
\(402\) 0 0
\(403\) −16.3262 −0.813268
\(404\) 0 0
\(405\) 1.61803 0.0804008
\(406\) 0 0
\(407\) −14.7082 −0.729059
\(408\) 0 0
\(409\) 0.236068 0.0116728 0.00583641 0.999983i \(-0.498142\pi\)
0.00583641 + 0.999983i \(0.498142\pi\)
\(410\) 0 0
\(411\) −4.23607 −0.208950
\(412\) 0 0
\(413\) 5.61803 0.276445
\(414\) 0 0
\(415\) 16.0902 0.789835
\(416\) 0 0
\(417\) −17.0344 −0.834180
\(418\) 0 0
\(419\) −11.2148 −0.547878 −0.273939 0.961747i \(-0.588327\pi\)
−0.273939 + 0.961747i \(0.588327\pi\)
\(420\) 0 0
\(421\) −20.5066 −0.999429 −0.499715 0.866190i \(-0.666562\pi\)
−0.499715 + 0.866190i \(0.666562\pi\)
\(422\) 0 0
\(423\) −5.23607 −0.254586
\(424\) 0 0
\(425\) −5.32624 −0.258360
\(426\) 0 0
\(427\) 10.3262 0.499722
\(428\) 0 0
\(429\) 11.0902 0.535438
\(430\) 0 0
\(431\) −2.43769 −0.117420 −0.0587098 0.998275i \(-0.518699\pi\)
−0.0587098 + 0.998275i \(0.518699\pi\)
\(432\) 0 0
\(433\) −10.2918 −0.494592 −0.247296 0.968940i \(-0.579542\pi\)
−0.247296 + 0.968940i \(0.579542\pi\)
\(434\) 0 0
\(435\) 5.61803 0.269364
\(436\) 0 0
\(437\) −5.47214 −0.261768
\(438\) 0 0
\(439\) 29.1803 1.39270 0.696351 0.717702i \(-0.254806\pi\)
0.696351 + 0.717702i \(0.254806\pi\)
\(440\) 0 0
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) 21.8885 1.03996 0.519978 0.854180i \(-0.325940\pi\)
0.519978 + 0.854180i \(0.325940\pi\)
\(444\) 0 0
\(445\) 6.23607 0.295618
\(446\) 0 0
\(447\) 16.6525 0.787635
\(448\) 0 0
\(449\) −2.09017 −0.0986412 −0.0493206 0.998783i \(-0.515706\pi\)
−0.0493206 + 0.998783i \(0.515706\pi\)
\(450\) 0 0
\(451\) 6.23607 0.293645
\(452\) 0 0
\(453\) 15.7082 0.738036
\(454\) 0 0
\(455\) −4.23607 −0.198590
\(456\) 0 0
\(457\) 2.85410 0.133509 0.0667546 0.997769i \(-0.478736\pi\)
0.0667546 + 0.997769i \(0.478736\pi\)
\(458\) 0 0
\(459\) −2.23607 −0.104371
\(460\) 0 0
\(461\) −4.56231 −0.212488 −0.106244 0.994340i \(-0.533882\pi\)
−0.106244 + 0.994340i \(0.533882\pi\)
\(462\) 0 0
\(463\) −1.11146 −0.0516537 −0.0258269 0.999666i \(-0.508222\pi\)
−0.0258269 + 0.999666i \(0.508222\pi\)
\(464\) 0 0
\(465\) 10.0902 0.467920
\(466\) 0 0
\(467\) −12.4164 −0.574563 −0.287281 0.957846i \(-0.592751\pi\)
−0.287281 + 0.957846i \(0.592751\pi\)
\(468\) 0 0
\(469\) 5.61803 0.259417
\(470\) 0 0
\(471\) 12.7639 0.588131
\(472\) 0 0
\(473\) −32.0344 −1.47295
\(474\) 0 0
\(475\) 13.0344 0.598061
\(476\) 0 0
\(477\) 4.09017 0.187276
\(478\) 0 0
\(479\) −15.1803 −0.693607 −0.346804 0.937938i \(-0.612733\pi\)
−0.346804 + 0.937938i \(0.612733\pi\)
\(480\) 0 0
\(481\) 9.09017 0.414476
\(482\) 0 0
\(483\) 1.00000 0.0455016
\(484\) 0 0
\(485\) 6.85410 0.311229
\(486\) 0 0
\(487\) 29.4721 1.33551 0.667755 0.744381i \(-0.267255\pi\)
0.667755 + 0.744381i \(0.267255\pi\)
\(488\) 0 0
\(489\) 16.5623 0.748973
\(490\) 0 0
\(491\) 5.85410 0.264192 0.132096 0.991237i \(-0.457829\pi\)
0.132096 + 0.991237i \(0.457829\pi\)
\(492\) 0 0
\(493\) −7.76393 −0.349670
\(494\) 0 0
\(495\) −6.85410 −0.308069
\(496\) 0 0
\(497\) 4.14590 0.185969
\(498\) 0 0
\(499\) 32.2705 1.44463 0.722313 0.691566i \(-0.243079\pi\)
0.722313 + 0.691566i \(0.243079\pi\)
\(500\) 0 0
\(501\) −20.8885 −0.933231
\(502\) 0 0
\(503\) −24.5623 −1.09518 −0.547590 0.836747i \(-0.684454\pi\)
−0.547590 + 0.836747i \(0.684454\pi\)
\(504\) 0 0
\(505\) −5.85410 −0.260504
\(506\) 0 0
\(507\) 6.14590 0.272949
\(508\) 0 0
\(509\) 15.7082 0.696254 0.348127 0.937447i \(-0.386818\pi\)
0.348127 + 0.937447i \(0.386818\pi\)
\(510\) 0 0
\(511\) 15.9443 0.705333
\(512\) 0 0
\(513\) 5.47214 0.241601
\(514\) 0 0
\(515\) 14.4721 0.637719
\(516\) 0 0
\(517\) 22.1803 0.975490
\(518\) 0 0
\(519\) −2.05573 −0.0902364
\(520\) 0 0
\(521\) −0.472136 −0.0206847 −0.0103423 0.999947i \(-0.503292\pi\)
−0.0103423 + 0.999947i \(0.503292\pi\)
\(522\) 0 0
\(523\) 9.41641 0.411751 0.205875 0.978578i \(-0.433996\pi\)
0.205875 + 0.978578i \(0.433996\pi\)
\(524\) 0 0
\(525\) −2.38197 −0.103958
\(526\) 0 0
\(527\) −13.9443 −0.607422
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −5.61803 −0.243802
\(532\) 0 0
\(533\) −3.85410 −0.166940
\(534\) 0 0
\(535\) −20.4164 −0.882678
\(536\) 0 0
\(537\) −21.7984 −0.940669
\(538\) 0 0
\(539\) −4.23607 −0.182460
\(540\) 0 0
\(541\) −15.7082 −0.675348 −0.337674 0.941263i \(-0.609640\pi\)
−0.337674 + 0.941263i \(0.609640\pi\)
\(542\) 0 0
\(543\) −0.236068 −0.0101306
\(544\) 0 0
\(545\) −7.09017 −0.303710
\(546\) 0 0
\(547\) −8.09017 −0.345911 −0.172955 0.984930i \(-0.555332\pi\)
−0.172955 + 0.984930i \(0.555332\pi\)
\(548\) 0 0
\(549\) −10.3262 −0.440713
\(550\) 0 0
\(551\) 19.0000 0.809427
\(552\) 0 0
\(553\) 3.76393 0.160059
\(554\) 0 0
\(555\) −5.61803 −0.238472
\(556\) 0 0
\(557\) −26.6525 −1.12930 −0.564651 0.825330i \(-0.690989\pi\)
−0.564651 + 0.825330i \(0.690989\pi\)
\(558\) 0 0
\(559\) 19.7984 0.837382
\(560\) 0 0
\(561\) 9.47214 0.399914
\(562\) 0 0
\(563\) 0.506578 0.0213497 0.0106749 0.999943i \(-0.496602\pi\)
0.0106749 + 0.999943i \(0.496602\pi\)
\(564\) 0 0
\(565\) −20.3262 −0.855131
\(566\) 0 0
\(567\) −1.00000 −0.0419961
\(568\) 0 0
\(569\) 17.5279 0.734806 0.367403 0.930062i \(-0.380247\pi\)
0.367403 + 0.930062i \(0.380247\pi\)
\(570\) 0 0
\(571\) 16.7082 0.699217 0.349608 0.936896i \(-0.386315\pi\)
0.349608 + 0.936896i \(0.386315\pi\)
\(572\) 0 0
\(573\) 19.1246 0.798942
\(574\) 0 0
\(575\) −2.38197 −0.0993348
\(576\) 0 0
\(577\) −13.0557 −0.543517 −0.271759 0.962365i \(-0.587605\pi\)
−0.271759 + 0.962365i \(0.587605\pi\)
\(578\) 0 0
\(579\) 17.7082 0.735928
\(580\) 0 0
\(581\) −9.94427 −0.412558
\(582\) 0 0
\(583\) −17.3262 −0.717579
\(584\) 0 0
\(585\) 4.23607 0.175140
\(586\) 0 0
\(587\) 12.0344 0.496715 0.248357 0.968668i \(-0.420109\pi\)
0.248357 + 0.968668i \(0.420109\pi\)
\(588\) 0 0
\(589\) 34.1246 1.40608
\(590\) 0 0
\(591\) 8.61803 0.354499
\(592\) 0 0
\(593\) 7.23607 0.297150 0.148575 0.988901i \(-0.452531\pi\)
0.148575 + 0.988901i \(0.452531\pi\)
\(594\) 0 0
\(595\) −3.61803 −0.148325
\(596\) 0 0
\(597\) 21.3262 0.872825
\(598\) 0 0
\(599\) −36.3951 −1.48706 −0.743532 0.668700i \(-0.766851\pi\)
−0.743532 + 0.668700i \(0.766851\pi\)
\(600\) 0 0
\(601\) −25.6869 −1.04779 −0.523896 0.851782i \(-0.675522\pi\)
−0.523896 + 0.851782i \(0.675522\pi\)
\(602\) 0 0
\(603\) −5.61803 −0.228784
\(604\) 0 0
\(605\) 11.2361 0.456811
\(606\) 0 0
\(607\) −37.6312 −1.52740 −0.763701 0.645570i \(-0.776620\pi\)
−0.763701 + 0.645570i \(0.776620\pi\)
\(608\) 0 0
\(609\) −3.47214 −0.140698
\(610\) 0 0
\(611\) −13.7082 −0.554575
\(612\) 0 0
\(613\) −22.2361 −0.898106 −0.449053 0.893505i \(-0.648239\pi\)
−0.449053 + 0.893505i \(0.648239\pi\)
\(614\) 0 0
\(615\) 2.38197 0.0960501
\(616\) 0 0
\(617\) −27.0902 −1.09061 −0.545305 0.838238i \(-0.683586\pi\)
−0.545305 + 0.838238i \(0.683586\pi\)
\(618\) 0 0
\(619\) −22.0344 −0.885639 −0.442819 0.896611i \(-0.646022\pi\)
−0.442819 + 0.896611i \(0.646022\pi\)
\(620\) 0 0
\(621\) −1.00000 −0.0401286
\(622\) 0 0
\(623\) −3.85410 −0.154411
\(624\) 0 0
\(625\) −7.41641 −0.296656
\(626\) 0 0
\(627\) −23.1803 −0.925734
\(628\) 0 0
\(629\) 7.76393 0.309568
\(630\) 0 0
\(631\) −0.527864 −0.0210139 −0.0105070 0.999945i \(-0.503345\pi\)
−0.0105070 + 0.999945i \(0.503345\pi\)
\(632\) 0 0
\(633\) −2.23607 −0.0888757
\(634\) 0 0
\(635\) −22.4164 −0.889568
\(636\) 0 0
\(637\) 2.61803 0.103730
\(638\) 0 0
\(639\) −4.14590 −0.164009
\(640\) 0 0
\(641\) −28.1459 −1.11170 −0.555848 0.831284i \(-0.687606\pi\)
−0.555848 + 0.831284i \(0.687606\pi\)
\(642\) 0 0
\(643\) −26.9787 −1.06394 −0.531968 0.846764i \(-0.678547\pi\)
−0.531968 + 0.846764i \(0.678547\pi\)
\(644\) 0 0
\(645\) −12.2361 −0.481795
\(646\) 0 0
\(647\) −42.0902 −1.65474 −0.827368 0.561661i \(-0.810163\pi\)
−0.827368 + 0.561661i \(0.810163\pi\)
\(648\) 0 0
\(649\) 23.7984 0.934168
\(650\) 0 0
\(651\) −6.23607 −0.244411
\(652\) 0 0
\(653\) 19.0344 0.744875 0.372438 0.928057i \(-0.378522\pi\)
0.372438 + 0.928057i \(0.378522\pi\)
\(654\) 0 0
\(655\) 29.0344 1.13447
\(656\) 0 0
\(657\) −15.9443 −0.622045
\(658\) 0 0
\(659\) 17.0689 0.664909 0.332455 0.943119i \(-0.392123\pi\)
0.332455 + 0.943119i \(0.392123\pi\)
\(660\) 0 0
\(661\) −31.1803 −1.21277 −0.606387 0.795169i \(-0.707382\pi\)
−0.606387 + 0.795169i \(0.707382\pi\)
\(662\) 0 0
\(663\) −5.85410 −0.227354
\(664\) 0 0
\(665\) 8.85410 0.343347
\(666\) 0 0
\(667\) −3.47214 −0.134442
\(668\) 0 0
\(669\) 25.2148 0.974860
\(670\) 0 0
\(671\) 43.7426 1.68867
\(672\) 0 0
\(673\) −7.58359 −0.292326 −0.146163 0.989261i \(-0.546692\pi\)
−0.146163 + 0.989261i \(0.546692\pi\)
\(674\) 0 0
\(675\) 2.38197 0.0916819
\(676\) 0 0
\(677\) 24.9787 0.960010 0.480005 0.877266i \(-0.340635\pi\)
0.480005 + 0.877266i \(0.340635\pi\)
\(678\) 0 0
\(679\) −4.23607 −0.162565
\(680\) 0 0
\(681\) 10.0902 0.386656
\(682\) 0 0
\(683\) −20.2361 −0.774312 −0.387156 0.922014i \(-0.626542\pi\)
−0.387156 + 0.922014i \(0.626542\pi\)
\(684\) 0 0
\(685\) 6.85410 0.261882
\(686\) 0 0
\(687\) −12.3820 −0.472401
\(688\) 0 0
\(689\) 10.7082 0.407950
\(690\) 0 0
\(691\) −17.5623 −0.668102 −0.334051 0.942555i \(-0.608416\pi\)
−0.334051 + 0.942555i \(0.608416\pi\)
\(692\) 0 0
\(693\) 4.23607 0.160915
\(694\) 0 0
\(695\) 27.5623 1.04550
\(696\) 0 0
\(697\) −3.29180 −0.124686
\(698\) 0 0
\(699\) −2.09017 −0.0790575
\(700\) 0 0
\(701\) 5.21478 0.196960 0.0984798 0.995139i \(-0.468602\pi\)
0.0984798 + 0.995139i \(0.468602\pi\)
\(702\) 0 0
\(703\) −19.0000 −0.716599
\(704\) 0 0
\(705\) 8.47214 0.319079
\(706\) 0 0
\(707\) 3.61803 0.136070
\(708\) 0 0
\(709\) −25.2705 −0.949054 −0.474527 0.880241i \(-0.657381\pi\)
−0.474527 + 0.880241i \(0.657381\pi\)
\(710\) 0 0
\(711\) −3.76393 −0.141158
\(712\) 0 0
\(713\) −6.23607 −0.233543
\(714\) 0 0
\(715\) −17.9443 −0.671078
\(716\) 0 0
\(717\) −7.03444 −0.262706
\(718\) 0 0
\(719\) −6.23607 −0.232566 −0.116283 0.993216i \(-0.537098\pi\)
−0.116283 + 0.993216i \(0.537098\pi\)
\(720\) 0 0
\(721\) −8.94427 −0.333102
\(722\) 0 0
\(723\) 11.2918 0.419946
\(724\) 0 0
\(725\) 8.27051 0.307159
\(726\) 0 0
\(727\) 36.5279 1.35474 0.677372 0.735641i \(-0.263119\pi\)
0.677372 + 0.735641i \(0.263119\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 16.9098 0.625433
\(732\) 0 0
\(733\) 7.59675 0.280592 0.140296 0.990110i \(-0.455195\pi\)
0.140296 + 0.990110i \(0.455195\pi\)
\(734\) 0 0
\(735\) −1.61803 −0.0596821
\(736\) 0 0
\(737\) 23.7984 0.876624
\(738\) 0 0
\(739\) −24.5967 −0.904806 −0.452403 0.891814i \(-0.649433\pi\)
−0.452403 + 0.891814i \(0.649433\pi\)
\(740\) 0 0
\(741\) 14.3262 0.526288
\(742\) 0 0
\(743\) −53.7984 −1.97367 −0.986835 0.161727i \(-0.948293\pi\)
−0.986835 + 0.161727i \(0.948293\pi\)
\(744\) 0 0
\(745\) −26.9443 −0.987162
\(746\) 0 0
\(747\) 9.94427 0.363842
\(748\) 0 0
\(749\) 12.6180 0.461053
\(750\) 0 0
\(751\) −8.96556 −0.327158 −0.163579 0.986530i \(-0.552304\pi\)
−0.163579 + 0.986530i \(0.552304\pi\)
\(752\) 0 0
\(753\) 0.180340 0.00657195
\(754\) 0 0
\(755\) −25.4164 −0.924998
\(756\) 0 0
\(757\) 35.0000 1.27210 0.636048 0.771649i \(-0.280568\pi\)
0.636048 + 0.771649i \(0.280568\pi\)
\(758\) 0 0
\(759\) 4.23607 0.153760
\(760\) 0 0
\(761\) −42.8328 −1.55269 −0.776344 0.630309i \(-0.782928\pi\)
−0.776344 + 0.630309i \(0.782928\pi\)
\(762\) 0 0
\(763\) 4.38197 0.158638
\(764\) 0 0
\(765\) 3.61803 0.130810
\(766\) 0 0
\(767\) −14.7082 −0.531082
\(768\) 0 0
\(769\) 7.81966 0.281984 0.140992 0.990011i \(-0.454971\pi\)
0.140992 + 0.990011i \(0.454971\pi\)
\(770\) 0 0
\(771\) −12.2918 −0.442678
\(772\) 0 0
\(773\) 15.4721 0.556494 0.278247 0.960510i \(-0.410247\pi\)
0.278247 + 0.960510i \(0.410247\pi\)
\(774\) 0 0
\(775\) 14.8541 0.533575
\(776\) 0 0
\(777\) 3.47214 0.124562
\(778\) 0 0
\(779\) 8.05573 0.288626
\(780\) 0 0
\(781\) 17.5623 0.628429
\(782\) 0 0
\(783\) 3.47214 0.124084
\(784\) 0 0
\(785\) −20.6525 −0.737118
\(786\) 0 0
\(787\) 38.4508 1.37062 0.685312 0.728249i \(-0.259666\pi\)
0.685312 + 0.728249i \(0.259666\pi\)
\(788\) 0 0
\(789\) −9.94427 −0.354025
\(790\) 0 0
\(791\) 12.5623 0.446664
\(792\) 0 0
\(793\) −27.0344 −0.960021
\(794\) 0 0
\(795\) −6.61803 −0.234717
\(796\) 0 0
\(797\) −38.5410 −1.36519 −0.682596 0.730795i \(-0.739149\pi\)
−0.682596 + 0.730795i \(0.739149\pi\)
\(798\) 0 0
\(799\) −11.7082 −0.414206
\(800\) 0 0
\(801\) 3.85410 0.136178
\(802\) 0 0
\(803\) 67.5410 2.38347
\(804\) 0 0
\(805\) −1.61803 −0.0570282
\(806\) 0 0
\(807\) −23.0902 −0.812812
\(808\) 0 0
\(809\) 18.6180 0.654575 0.327288 0.944925i \(-0.393865\pi\)
0.327288 + 0.944925i \(0.393865\pi\)
\(810\) 0 0
\(811\) 32.4164 1.13829 0.569147 0.822236i \(-0.307274\pi\)
0.569147 + 0.822236i \(0.307274\pi\)
\(812\) 0 0
\(813\) −31.3607 −1.09987
\(814\) 0 0
\(815\) −26.7984 −0.938706
\(816\) 0 0
\(817\) −41.3820 −1.44777
\(818\) 0 0
\(819\) −2.61803 −0.0914815
\(820\) 0 0
\(821\) 0.875388 0.0305513 0.0152756 0.999883i \(-0.495137\pi\)
0.0152756 + 0.999883i \(0.495137\pi\)
\(822\) 0 0
\(823\) 15.7295 0.548296 0.274148 0.961688i \(-0.411604\pi\)
0.274148 + 0.961688i \(0.411604\pi\)
\(824\) 0 0
\(825\) −10.0902 −0.351295
\(826\) 0 0
\(827\) −3.43769 −0.119540 −0.0597702 0.998212i \(-0.519037\pi\)
−0.0597702 + 0.998212i \(0.519037\pi\)
\(828\) 0 0
\(829\) 20.1246 0.698957 0.349478 0.936944i \(-0.386359\pi\)
0.349478 + 0.936944i \(0.386359\pi\)
\(830\) 0 0
\(831\) −8.61803 −0.298956
\(832\) 0 0
\(833\) 2.23607 0.0774752
\(834\) 0 0
\(835\) 33.7984 1.16964
\(836\) 0 0
\(837\) 6.23607 0.215550
\(838\) 0 0
\(839\) 29.9230 1.03306 0.516528 0.856270i \(-0.327224\pi\)
0.516528 + 0.856270i \(0.327224\pi\)
\(840\) 0 0
\(841\) −16.9443 −0.584285
\(842\) 0 0
\(843\) −22.6525 −0.780193
\(844\) 0 0
\(845\) −9.94427 −0.342093
\(846\) 0 0
\(847\) −6.94427 −0.238608
\(848\) 0 0
\(849\) 7.90983 0.271465
\(850\) 0 0
\(851\) 3.47214 0.119023
\(852\) 0 0
\(853\) 2.65248 0.0908190 0.0454095 0.998968i \(-0.485541\pi\)
0.0454095 + 0.998968i \(0.485541\pi\)
\(854\) 0 0
\(855\) −8.85410 −0.302804
\(856\) 0 0
\(857\) 41.1246 1.40479 0.702395 0.711787i \(-0.252114\pi\)
0.702395 + 0.711787i \(0.252114\pi\)
\(858\) 0 0
\(859\) 2.94427 0.100457 0.0502286 0.998738i \(-0.484005\pi\)
0.0502286 + 0.998738i \(0.484005\pi\)
\(860\) 0 0
\(861\) −1.47214 −0.0501703
\(862\) 0 0
\(863\) −37.1246 −1.26374 −0.631868 0.775076i \(-0.717712\pi\)
−0.631868 + 0.775076i \(0.717712\pi\)
\(864\) 0 0
\(865\) 3.32624 0.113095
\(866\) 0 0
\(867\) 12.0000 0.407541
\(868\) 0 0
\(869\) 15.9443 0.540872
\(870\) 0 0
\(871\) −14.7082 −0.498368
\(872\) 0 0
\(873\) 4.23607 0.143369
\(874\) 0 0
\(875\) 11.9443 0.403790
\(876\) 0 0
\(877\) 51.1935 1.72868 0.864341 0.502907i \(-0.167736\pi\)
0.864341 + 0.502907i \(0.167736\pi\)
\(878\) 0 0
\(879\) −24.9443 −0.841349
\(880\) 0 0
\(881\) −22.2918 −0.751030 −0.375515 0.926816i \(-0.622534\pi\)
−0.375515 + 0.926816i \(0.622534\pi\)
\(882\) 0 0
\(883\) 9.74265 0.327866 0.163933 0.986471i \(-0.447582\pi\)
0.163933 + 0.986471i \(0.447582\pi\)
\(884\) 0 0
\(885\) 9.09017 0.305563
\(886\) 0 0
\(887\) −0.437694 −0.0146963 −0.00734816 0.999973i \(-0.502339\pi\)
−0.00734816 + 0.999973i \(0.502339\pi\)
\(888\) 0 0
\(889\) 13.8541 0.464652
\(890\) 0 0
\(891\) −4.23607 −0.141914
\(892\) 0 0
\(893\) 28.6525 0.958819
\(894\) 0 0
\(895\) 35.2705 1.17896
\(896\) 0 0
\(897\) −2.61803 −0.0874136
\(898\) 0 0
\(899\) 21.6525 0.722151
\(900\) 0 0
\(901\) 9.14590 0.304694
\(902\) 0 0
\(903\) 7.56231 0.251658
\(904\) 0 0
\(905\) 0.381966 0.0126970
\(906\) 0 0
\(907\) 47.0344 1.56175 0.780877 0.624685i \(-0.214773\pi\)
0.780877 + 0.624685i \(0.214773\pi\)
\(908\) 0 0
\(909\) −3.61803 −0.120003
\(910\) 0 0
\(911\) −34.5410 −1.14440 −0.572198 0.820116i \(-0.693909\pi\)
−0.572198 + 0.820116i \(0.693909\pi\)
\(912\) 0 0
\(913\) −42.1246 −1.39412
\(914\) 0 0
\(915\) 16.7082 0.552356
\(916\) 0 0
\(917\) −17.9443 −0.592572
\(918\) 0 0
\(919\) 20.4164 0.673475 0.336738 0.941599i \(-0.390676\pi\)
0.336738 + 0.941599i \(0.390676\pi\)
\(920\) 0 0
\(921\) −10.2361 −0.337290
\(922\) 0 0
\(923\) −10.8541 −0.357267
\(924\) 0 0
\(925\) −8.27051 −0.271933
\(926\) 0 0
\(927\) 8.94427 0.293768
\(928\) 0 0
\(929\) 7.50658 0.246283 0.123141 0.992389i \(-0.460703\pi\)
0.123141 + 0.992389i \(0.460703\pi\)
\(930\) 0 0
\(931\) −5.47214 −0.179342
\(932\) 0 0
\(933\) −30.9787 −1.01420
\(934\) 0 0
\(935\) −15.3262 −0.501222
\(936\) 0 0
\(937\) 22.5279 0.735953 0.367977 0.929835i \(-0.380051\pi\)
0.367977 + 0.929835i \(0.380051\pi\)
\(938\) 0 0
\(939\) 2.47214 0.0806751
\(940\) 0 0
\(941\) 28.0000 0.912774 0.456387 0.889781i \(-0.349143\pi\)
0.456387 + 0.889781i \(0.349143\pi\)
\(942\) 0 0
\(943\) −1.47214 −0.0479393
\(944\) 0 0
\(945\) 1.61803 0.0526346
\(946\) 0 0
\(947\) 59.8885 1.94612 0.973058 0.230560i \(-0.0740558\pi\)
0.973058 + 0.230560i \(0.0740558\pi\)
\(948\) 0 0
\(949\) −41.7426 −1.35502
\(950\) 0 0
\(951\) −4.96556 −0.161019
\(952\) 0 0
\(953\) −33.5623 −1.08719 −0.543595 0.839348i \(-0.682937\pi\)
−0.543595 + 0.839348i \(0.682937\pi\)
\(954\) 0 0
\(955\) −30.9443 −1.00133
\(956\) 0 0
\(957\) −14.7082 −0.475449
\(958\) 0 0
\(959\) −4.23607 −0.136790
\(960\) 0 0
\(961\) 7.88854 0.254469
\(962\) 0 0
\(963\) −12.6180 −0.406610
\(964\) 0 0
\(965\) −28.6525 −0.922356
\(966\) 0 0
\(967\) 7.52786 0.242080 0.121040 0.992648i \(-0.461377\pi\)
0.121040 + 0.992648i \(0.461377\pi\)
\(968\) 0 0
\(969\) 12.2361 0.393079
\(970\) 0 0
\(971\) −13.6738 −0.438812 −0.219406 0.975634i \(-0.570412\pi\)
−0.219406 + 0.975634i \(0.570412\pi\)
\(972\) 0 0
\(973\) −17.0344 −0.546099
\(974\) 0 0
\(975\) 6.23607 0.199714
\(976\) 0 0
\(977\) −57.0902 −1.82648 −0.913238 0.407426i \(-0.866426\pi\)
−0.913238 + 0.407426i \(0.866426\pi\)
\(978\) 0 0
\(979\) −16.3262 −0.521789
\(980\) 0 0
\(981\) −4.38197 −0.139905
\(982\) 0 0
\(983\) −48.7771 −1.55575 −0.777874 0.628421i \(-0.783702\pi\)
−0.777874 + 0.628421i \(0.783702\pi\)
\(984\) 0 0
\(985\) −13.9443 −0.444301
\(986\) 0 0
\(987\) −5.23607 −0.166666
\(988\) 0 0
\(989\) 7.56231 0.240467
\(990\) 0 0
\(991\) 59.1591 1.87925 0.939625 0.342207i \(-0.111174\pi\)
0.939625 + 0.342207i \(0.111174\pi\)
\(992\) 0 0
\(993\) −18.9443 −0.601178
\(994\) 0 0
\(995\) −34.5066 −1.09393
\(996\) 0 0
\(997\) 28.1246 0.890715 0.445358 0.895353i \(-0.353077\pi\)
0.445358 + 0.895353i \(0.353077\pi\)
\(998\) 0 0
\(999\) −3.47214 −0.109854
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 1932.2.a.d.1.2 2
3.2 odd 2 5796.2.a.i.1.1 2
4.3 odd 2 7728.2.a.bo.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1932.2.a.d.1.2 2 1.1 even 1 trivial
5796.2.a.i.1.1 2 3.2 odd 2
7728.2.a.bo.1.2 2 4.3 odd 2