Properties

Label 3200.2.a.bs.1.2
Level $3200$
Weight $2$
Character 3200.1
Self dual yes
Analytic conductor $25.552$
Analytic rank $0$
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: \(0\)
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 1.2
Root \(-1.48119\) of defining polynomial
Character \(\chi\) \(=\) 3200.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.806063 q^{3} +2.15633 q^{7} -2.35026 q^{9} +O(q^{10})\) \(q+0.806063 q^{3} +2.15633 q^{7} -2.35026 q^{9} -0.387873 q^{11} -0.962389 q^{13} +1.61213 q^{17} +6.31265 q^{19} +1.73813 q^{21} -6.15633 q^{23} -4.31265 q^{27} -2.00000 q^{29} +9.92478 q^{31} -0.312650 q^{33} +6.57452 q^{37} -0.775746 q^{39} +4.57452 q^{41} +11.5066 q^{43} -4.54420 q^{47} -2.35026 q^{49} +1.29948 q^{51} +8.96239 q^{53} +5.08840 q^{57} -6.31265 q^{59} -0.261865 q^{61} -5.06793 q^{63} +9.89446 q^{67} -4.96239 q^{69} -10.7005 q^{71} +13.0884 q^{73} -0.836381 q^{77} -1.92478 q^{79} +3.57452 q^{81} +2.88129 q^{83} -1.61213 q^{87} +10.6253 q^{89} -2.07522 q^{91} +8.00000 q^{93} +9.61213 q^{97} +0.911603 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 2 q^{3} - 4 q^{7} + 3 q^{9}+O(q^{10}) \) 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
\(3\) 0.806063 0.465381 0.232690 0.972551i \(-0.425247\pi\)
0.232690 + 0.972551i \(0.425247\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 2.15633 0.815014 0.407507 0.913202i \(-0.366398\pi\)
0.407507 + 0.913202i \(0.366398\pi\)
\(8\) 0 0
\(9\) −2.35026 −0.783421
\(10\) 0 0
\(11\) −0.387873 −0.116948 −0.0584741 0.998289i \(-0.518623\pi\)
−0.0584741 + 0.998289i \(0.518623\pi\)
\(12\) 0 0
\(13\) −0.962389 −0.266919 −0.133459 0.991054i \(-0.542609\pi\)
−0.133459 + 0.991054i \(0.542609\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.61213 0.390998 0.195499 0.980704i \(-0.437367\pi\)
0.195499 + 0.980704i \(0.437367\pi\)
\(18\) 0 0
\(19\) 6.31265 1.44822 0.724111 0.689684i \(-0.242250\pi\)
0.724111 + 0.689684i \(0.242250\pi\)
\(20\) 0 0
\(21\) 1.73813 0.379292
\(22\) 0 0
\(23\) −6.15633 −1.28368 −0.641841 0.766838i \(-0.721829\pi\)
−0.641841 + 0.766838i \(0.721829\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −4.31265 −0.829970
\(28\) 0 0
\(29\) −2.00000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) 0 0
\(31\) 9.92478 1.78254 0.891271 0.453470i \(-0.149814\pi\)
0.891271 + 0.453470i \(0.149814\pi\)
\(32\) 0 0
\(33\) −0.312650 −0.0544254
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 6.57452 1.08084 0.540422 0.841394i \(-0.318265\pi\)
0.540422 + 0.841394i \(0.318265\pi\)
\(38\) 0 0
\(39\) −0.775746 −0.124219
\(40\) 0 0
\(41\) 4.57452 0.714419 0.357210 0.934024i \(-0.383728\pi\)
0.357210 + 0.934024i \(0.383728\pi\)
\(42\) 0 0
\(43\) 11.5066 1.75474 0.877369 0.479816i \(-0.159297\pi\)
0.877369 + 0.479816i \(0.159297\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −4.54420 −0.662839 −0.331420 0.943483i \(-0.607528\pi\)
−0.331420 + 0.943483i \(0.607528\pi\)
\(48\) 0 0
\(49\) −2.35026 −0.335752
\(50\) 0 0
\(51\) 1.29948 0.181963
\(52\) 0 0
\(53\) 8.96239 1.23108 0.615539 0.788106i \(-0.288938\pi\)
0.615539 + 0.788106i \(0.288938\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 5.08840 0.673975
\(58\) 0 0
\(59\) −6.31265 −0.821837 −0.410919 0.911672i \(-0.634792\pi\)
−0.410919 + 0.911672i \(0.634792\pi\)
\(60\) 0 0
\(61\) −0.261865 −0.0335284 −0.0167642 0.999859i \(-0.505336\pi\)
−0.0167642 + 0.999859i \(0.505336\pi\)
\(62\) 0 0
\(63\) −5.06793 −0.638499
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 9.89446 1.20880 0.604400 0.796681i \(-0.293413\pi\)
0.604400 + 0.796681i \(0.293413\pi\)
\(68\) 0 0
\(69\) −4.96239 −0.597401
\(70\) 0 0
\(71\) −10.7005 −1.26992 −0.634959 0.772546i \(-0.718983\pi\)
−0.634959 + 0.772546i \(0.718983\pi\)
\(72\) 0 0
\(73\) 13.0884 1.53188 0.765940 0.642911i \(-0.222274\pi\)
0.765940 + 0.642911i \(0.222274\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −0.836381 −0.0953144
\(78\) 0 0
\(79\) −1.92478 −0.216554 −0.108277 0.994121i \(-0.534533\pi\)
−0.108277 + 0.994121i \(0.534533\pi\)
\(80\) 0 0
\(81\) 3.57452 0.397168
\(82\) 0 0
\(83\) 2.88129 0.316262 0.158131 0.987418i \(-0.449453\pi\)
0.158131 + 0.987418i \(0.449453\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −1.61213 −0.172838
\(88\) 0 0
\(89\) 10.6253 1.12628 0.563140 0.826362i \(-0.309593\pi\)
0.563140 + 0.826362i \(0.309593\pi\)
\(90\) 0 0
\(91\) −2.07522 −0.217542
\(92\) 0 0
\(93\) 8.00000 0.829561
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 9.61213 0.975964 0.487982 0.872854i \(-0.337733\pi\)
0.487982 + 0.872854i \(0.337733\pi\)
\(98\) 0 0
\(99\) 0.911603 0.0916196
\(100\) 0 0
\(101\) −11.4010 −1.13445 −0.567223 0.823564i \(-0.691982\pi\)
−0.567223 + 0.823564i \(0.691982\pi\)
\(102\) 0 0
\(103\) −10.9321 −1.07717 −0.538585 0.842572i \(-0.681041\pi\)
−0.538585 + 0.842572i \(0.681041\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 11.0435 1.06761 0.533807 0.845606i \(-0.320761\pi\)
0.533807 + 0.845606i \(0.320761\pi\)
\(108\) 0 0
\(109\) 5.03761 0.482516 0.241258 0.970461i \(-0.422440\pi\)
0.241258 + 0.970461i \(0.422440\pi\)
\(110\) 0 0
\(111\) 5.29948 0.503004
\(112\) 0 0
\(113\) 19.8496 1.86729 0.933645 0.358201i \(-0.116610\pi\)
0.933645 + 0.358201i \(0.116610\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 2.26187 0.209110
\(118\) 0 0
\(119\) 3.47627 0.318669
\(120\) 0 0
\(121\) −10.8496 −0.986323
\(122\) 0 0
\(123\) 3.68735 0.332477
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −11.7685 −1.04428 −0.522141 0.852859i \(-0.674866\pi\)
−0.522141 + 0.852859i \(0.674866\pi\)
\(128\) 0 0
\(129\) 9.27504 0.816622
\(130\) 0 0
\(131\) 15.0884 1.31828 0.659140 0.752021i \(-0.270921\pi\)
0.659140 + 0.752021i \(0.270921\pi\)
\(132\) 0 0
\(133\) 13.6121 1.18032
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −18.5501 −1.58484 −0.792420 0.609976i \(-0.791179\pi\)
−0.792420 + 0.609976i \(0.791179\pi\)
\(138\) 0 0
\(139\) −7.61213 −0.645652 −0.322826 0.946458i \(-0.604633\pi\)
−0.322826 + 0.946458i \(0.604633\pi\)
\(140\) 0 0
\(141\) −3.66291 −0.308473
\(142\) 0 0
\(143\) 0.373285 0.0312156
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −1.89446 −0.156252
\(148\) 0 0
\(149\) 13.6629 1.11931 0.559655 0.828726i \(-0.310934\pi\)
0.559655 + 0.828726i \(0.310934\pi\)
\(150\) 0 0
\(151\) −15.2243 −1.23893 −0.619466 0.785023i \(-0.712651\pi\)
−0.619466 + 0.785023i \(0.712651\pi\)
\(152\) 0 0
\(153\) −3.78892 −0.306316
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 1.42548 0.113766 0.0568830 0.998381i \(-0.481884\pi\)
0.0568830 + 0.998381i \(0.481884\pi\)
\(158\) 0 0
\(159\) 7.22425 0.572921
\(160\) 0 0
\(161\) −13.2750 −1.04622
\(162\) 0 0
\(163\) 8.80606 0.689744 0.344872 0.938650i \(-0.387922\pi\)
0.344872 + 0.938650i \(0.387922\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −10.4690 −0.810114 −0.405057 0.914292i \(-0.632748\pi\)
−0.405057 + 0.914292i \(0.632748\pi\)
\(168\) 0 0
\(169\) −12.0738 −0.928754
\(170\) 0 0
\(171\) −14.8364 −1.13457
\(172\) 0 0
\(173\) 19.9756 1.51871 0.759357 0.650674i \(-0.225514\pi\)
0.759357 + 0.650674i \(0.225514\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −5.08840 −0.382467
\(178\) 0 0
\(179\) −12.2374 −0.914668 −0.457334 0.889295i \(-0.651196\pi\)
−0.457334 + 0.889295i \(0.651196\pi\)
\(180\) 0 0
\(181\) 13.8496 1.02943 0.514715 0.857362i \(-0.327898\pi\)
0.514715 + 0.857362i \(0.327898\pi\)
\(182\) 0 0
\(183\) −0.211080 −0.0156035
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −0.625301 −0.0457265
\(188\) 0 0
\(189\) −9.29948 −0.676437
\(190\) 0 0
\(191\) −3.84955 −0.278544 −0.139272 0.990254i \(-0.544476\pi\)
−0.139272 + 0.990254i \(0.544476\pi\)
\(192\) 0 0
\(193\) 9.61213 0.691896 0.345948 0.938254i \(-0.387557\pi\)
0.345948 + 0.938254i \(0.387557\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −9.58769 −0.683095 −0.341547 0.939865i \(-0.610951\pi\)
−0.341547 + 0.939865i \(0.610951\pi\)
\(198\) 0 0
\(199\) −5.29948 −0.375670 −0.187835 0.982201i \(-0.560147\pi\)
−0.187835 + 0.982201i \(0.560147\pi\)
\(200\) 0 0
\(201\) 7.97556 0.562553
\(202\) 0 0
\(203\) −4.31265 −0.302689
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 14.4690 1.00566
\(208\) 0 0
\(209\) −2.44851 −0.169367
\(210\) 0 0
\(211\) 15.0884 1.03873 0.519364 0.854553i \(-0.326169\pi\)
0.519364 + 0.854553i \(0.326169\pi\)
\(212\) 0 0
\(213\) −8.62530 −0.590996
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 21.4010 1.45280
\(218\) 0 0
\(219\) 10.5501 0.712908
\(220\) 0 0
\(221\) −1.55149 −0.104365
\(222\) 0 0
\(223\) −22.5296 −1.50869 −0.754347 0.656476i \(-0.772046\pi\)
−0.754347 + 0.656476i \(0.772046\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −2.35756 −0.156476 −0.0782382 0.996935i \(-0.524929\pi\)
−0.0782382 + 0.996935i \(0.524929\pi\)
\(228\) 0 0
\(229\) −3.55149 −0.234689 −0.117345 0.993091i \(-0.537438\pi\)
−0.117345 + 0.993091i \(0.537438\pi\)
\(230\) 0 0
\(231\) −0.674176 −0.0443575
\(232\) 0 0
\(233\) 13.0884 0.857449 0.428725 0.903435i \(-0.358963\pi\)
0.428725 + 0.903435i \(0.358963\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −1.55149 −0.100780
\(238\) 0 0
\(239\) 15.3258 0.991345 0.495673 0.868509i \(-0.334922\pi\)
0.495673 + 0.868509i \(0.334922\pi\)
\(240\) 0 0
\(241\) 2.12601 0.136948 0.0684741 0.997653i \(-0.478187\pi\)
0.0684741 + 0.997653i \(0.478187\pi\)
\(242\) 0 0
\(243\) 15.8192 1.01480
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −6.07522 −0.386557
\(248\) 0 0
\(249\) 2.32250 0.147182
\(250\) 0 0
\(251\) −26.6859 −1.68440 −0.842201 0.539164i \(-0.818740\pi\)
−0.842201 + 0.539164i \(0.818740\pi\)
\(252\) 0 0
\(253\) 2.38787 0.150124
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 5.40105 0.336908 0.168454 0.985710i \(-0.446123\pi\)
0.168454 + 0.985710i \(0.446123\pi\)
\(258\) 0 0
\(259\) 14.1768 0.880903
\(260\) 0 0
\(261\) 4.70052 0.290955
\(262\) 0 0
\(263\) 14.4690 0.892195 0.446098 0.894984i \(-0.352813\pi\)
0.446098 + 0.894984i \(0.352813\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 8.56467 0.524149
\(268\) 0 0
\(269\) 28.1114 1.71398 0.856992 0.515330i \(-0.172331\pi\)
0.856992 + 0.515330i \(0.172331\pi\)
\(270\) 0 0
\(271\) 24.8773 1.51119 0.755595 0.655039i \(-0.227348\pi\)
0.755595 + 0.655039i \(0.227348\pi\)
\(272\) 0 0
\(273\) −1.67276 −0.101240
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 19.9756 1.20022 0.600108 0.799919i \(-0.295124\pi\)
0.600108 + 0.799919i \(0.295124\pi\)
\(278\) 0 0
\(279\) −23.3258 −1.39648
\(280\) 0 0
\(281\) −14.4993 −0.864955 −0.432478 0.901645i \(-0.642361\pi\)
−0.432478 + 0.901645i \(0.642361\pi\)
\(282\) 0 0
\(283\) 8.80606 0.523466 0.261733 0.965140i \(-0.415706\pi\)
0.261733 + 0.965140i \(0.415706\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 9.86414 0.582262
\(288\) 0 0
\(289\) −14.4010 −0.847120
\(290\) 0 0
\(291\) 7.74798 0.454195
\(292\) 0 0
\(293\) −3.35026 −0.195724 −0.0978622 0.995200i \(-0.531200\pi\)
−0.0978622 + 0.995200i \(0.531200\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 1.67276 0.0970634
\(298\) 0 0
\(299\) 5.92478 0.342639
\(300\) 0 0
\(301\) 24.8119 1.43014
\(302\) 0 0
\(303\) −9.18997 −0.527950
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −1.95509 −0.111583 −0.0557916 0.998442i \(-0.517768\pi\)
−0.0557916 + 0.998442i \(0.517768\pi\)
\(308\) 0 0
\(309\) −8.81194 −0.501294
\(310\) 0 0
\(311\) −8.77575 −0.497627 −0.248813 0.968551i \(-0.580041\pi\)
−0.248813 + 0.968551i \(0.580041\pi\)
\(312\) 0 0
\(313\) −18.5501 −1.04851 −0.524256 0.851561i \(-0.675657\pi\)
−0.524256 + 0.851561i \(0.675657\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 9.58769 0.538498 0.269249 0.963071i \(-0.413224\pi\)
0.269249 + 0.963071i \(0.413224\pi\)
\(318\) 0 0
\(319\) 0.775746 0.0434335
\(320\) 0 0
\(321\) 8.90175 0.496847
\(322\) 0 0
\(323\) 10.1768 0.566252
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 4.06063 0.224554
\(328\) 0 0
\(329\) −9.79877 −0.540224
\(330\) 0 0
\(331\) −23.0884 −1.26905 −0.634527 0.772901i \(-0.718805\pi\)
−0.634527 + 0.772901i \(0.718805\pi\)
\(332\) 0 0
\(333\) −15.4518 −0.846755
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 4.77575 0.260151 0.130076 0.991504i \(-0.458478\pi\)
0.130076 + 0.991504i \(0.458478\pi\)
\(338\) 0 0
\(339\) 16.0000 0.869001
\(340\) 0 0
\(341\) −3.84955 −0.208465
\(342\) 0 0
\(343\) −20.1622 −1.08866
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.89446 0.101700 0.0508500 0.998706i \(-0.483807\pi\)
0.0508500 + 0.998706i \(0.483807\pi\)
\(348\) 0 0
\(349\) −31.4010 −1.68086 −0.840430 0.541921i \(-0.817697\pi\)
−0.840430 + 0.541921i \(0.817697\pi\)
\(350\) 0 0
\(351\) 4.15045 0.221534
\(352\) 0 0
\(353\) −12.7757 −0.679984 −0.339992 0.940428i \(-0.610424\pi\)
−0.339992 + 0.940428i \(0.610424\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 2.80209 0.148303
\(358\) 0 0
\(359\) −16.4749 −0.869510 −0.434755 0.900549i \(-0.643165\pi\)
−0.434755 + 0.900549i \(0.643165\pi\)
\(360\) 0 0
\(361\) 20.8496 1.09734
\(362\) 0 0
\(363\) −8.74543 −0.459016
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −10.0957 −0.526991 −0.263495 0.964661i \(-0.584875\pi\)
−0.263495 + 0.964661i \(0.584875\pi\)
\(368\) 0 0
\(369\) −10.7513 −0.559691
\(370\) 0 0
\(371\) 19.3258 1.00335
\(372\) 0 0
\(373\) 6.82653 0.353464 0.176732 0.984259i \(-0.443447\pi\)
0.176732 + 0.984259i \(0.443447\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1.92478 0.0991311
\(378\) 0 0
\(379\) −19.4617 −0.999679 −0.499840 0.866118i \(-0.666608\pi\)
−0.499840 + 0.866118i \(0.666608\pi\)
\(380\) 0 0
\(381\) −9.48612 −0.485989
\(382\) 0 0
\(383\) −5.90431 −0.301696 −0.150848 0.988557i \(-0.548200\pi\)
−0.150848 + 0.988557i \(0.548200\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −27.0435 −1.37470
\(388\) 0 0
\(389\) −14.1866 −0.719291 −0.359646 0.933089i \(-0.617102\pi\)
−0.359646 + 0.933089i \(0.617102\pi\)
\(390\) 0 0
\(391\) −9.92478 −0.501918
\(392\) 0 0
\(393\) 12.1622 0.613502
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 28.1866 1.41465 0.707324 0.706890i \(-0.249902\pi\)
0.707324 + 0.706890i \(0.249902\pi\)
\(398\) 0 0
\(399\) 10.9722 0.549299
\(400\) 0 0
\(401\) 6.62530 0.330852 0.165426 0.986222i \(-0.447100\pi\)
0.165426 + 0.986222i \(0.447100\pi\)
\(402\) 0 0
\(403\) −9.55149 −0.475794
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −2.55008 −0.126403
\(408\) 0 0
\(409\) 12.6761 0.626792 0.313396 0.949623i \(-0.398533\pi\)
0.313396 + 0.949623i \(0.398533\pi\)
\(410\) 0 0
\(411\) −14.9525 −0.737554
\(412\) 0 0
\(413\) −13.6121 −0.669809
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −6.13586 −0.300474
\(418\) 0 0
\(419\) −14.8364 −0.724805 −0.362402 0.932022i \(-0.618043\pi\)
−0.362402 + 0.932022i \(0.618043\pi\)
\(420\) 0 0
\(421\) −0.261865 −0.0127625 −0.00638126 0.999980i \(-0.502031\pi\)
−0.00638126 + 0.999980i \(0.502031\pi\)
\(422\) 0 0
\(423\) 10.6801 0.519282
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −0.564666 −0.0273261
\(428\) 0 0
\(429\) 0.300891 0.0145272
\(430\) 0 0
\(431\) 4.52373 0.217900 0.108950 0.994047i \(-0.465251\pi\)
0.108950 + 0.994047i \(0.465251\pi\)
\(432\) 0 0
\(433\) −15.6385 −0.751537 −0.375769 0.926714i \(-0.622621\pi\)
−0.375769 + 0.926714i \(0.622621\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −38.8627 −1.85906
\(438\) 0 0
\(439\) −10.3272 −0.492892 −0.246446 0.969156i \(-0.579263\pi\)
−0.246446 + 0.969156i \(0.579263\pi\)
\(440\) 0 0
\(441\) 5.52373 0.263035
\(442\) 0 0
\(443\) −15.1939 −0.721886 −0.360943 0.932588i \(-0.617545\pi\)
−0.360943 + 0.932588i \(0.617545\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 11.0132 0.520905
\(448\) 0 0
\(449\) 24.6761 1.16454 0.582268 0.812997i \(-0.302165\pi\)
0.582268 + 0.812997i \(0.302165\pi\)
\(450\) 0 0
\(451\) −1.77433 −0.0835500
\(452\) 0 0
\(453\) −12.2717 −0.576575
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 8.37328 0.391686 0.195843 0.980635i \(-0.437256\pi\)
0.195843 + 0.980635i \(0.437256\pi\)
\(458\) 0 0
\(459\) −6.95254 −0.324517
\(460\) 0 0
\(461\) −8.29806 −0.386479 −0.193240 0.981152i \(-0.561899\pi\)
−0.193240 + 0.981152i \(0.561899\pi\)
\(462\) 0 0
\(463\) 39.4676 1.83421 0.917107 0.398642i \(-0.130518\pi\)
0.917107 + 0.398642i \(0.130518\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 2.41819 0.111901 0.0559503 0.998434i \(-0.482181\pi\)
0.0559503 + 0.998434i \(0.482181\pi\)
\(468\) 0 0
\(469\) 21.3357 0.985190
\(470\) 0 0
\(471\) 1.14903 0.0529446
\(472\) 0 0
\(473\) −4.46310 −0.205213
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −21.0640 −0.964452
\(478\) 0 0
\(479\) −6.44851 −0.294640 −0.147320 0.989089i \(-0.547065\pi\)
−0.147320 + 0.989089i \(0.547065\pi\)
\(480\) 0 0
\(481\) −6.32724 −0.288497
\(482\) 0 0
\(483\) −10.7005 −0.486891
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 12.3331 0.558867 0.279433 0.960165i \(-0.409853\pi\)
0.279433 + 0.960165i \(0.409853\pi\)
\(488\) 0 0
\(489\) 7.09825 0.320994
\(490\) 0 0
\(491\) 14.3127 0.645921 0.322960 0.946412i \(-0.395322\pi\)
0.322960 + 0.946412i \(0.395322\pi\)
\(492\) 0 0
\(493\) −3.22425 −0.145213
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −23.0738 −1.03500
\(498\) 0 0
\(499\) 14.0606 0.629440 0.314720 0.949184i \(-0.398089\pi\)
0.314720 + 0.949184i \(0.398089\pi\)
\(500\) 0 0
\(501\) −8.43866 −0.377011
\(502\) 0 0
\(503\) 31.8700 1.42101 0.710507 0.703690i \(-0.248466\pi\)
0.710507 + 0.703690i \(0.248466\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −9.73226 −0.432225
\(508\) 0 0
\(509\) −26.0000 −1.15243 −0.576215 0.817298i \(-0.695471\pi\)
−0.576215 + 0.817298i \(0.695471\pi\)
\(510\) 0 0
\(511\) 28.2228 1.24850
\(512\) 0 0
\(513\) −27.2243 −1.20198
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 1.76257 0.0775178
\(518\) 0 0
\(519\) 16.1016 0.706780
\(520\) 0 0
\(521\) −19.4010 −0.849975 −0.424988 0.905199i \(-0.639722\pi\)
−0.424988 + 0.905199i \(0.639722\pi\)
\(522\) 0 0
\(523\) 7.75860 0.339260 0.169630 0.985508i \(-0.445743\pi\)
0.169630 + 0.985508i \(0.445743\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 16.0000 0.696971
\(528\) 0 0
\(529\) 14.9003 0.647841
\(530\) 0 0
\(531\) 14.8364 0.643844
\(532\) 0 0
\(533\) −4.40246 −0.190692
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −9.86414 −0.425669
\(538\) 0 0
\(539\) 0.911603 0.0392655
\(540\) 0 0
\(541\) −25.8496 −1.11136 −0.555680 0.831397i \(-0.687542\pi\)
−0.555680 + 0.831397i \(0.687542\pi\)
\(542\) 0 0
\(543\) 11.1636 0.479077
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 38.2677 1.63621 0.818105 0.575068i \(-0.195025\pi\)
0.818105 + 0.575068i \(0.195025\pi\)
\(548\) 0 0
\(549\) 0.615452 0.0262668
\(550\) 0 0
\(551\) −12.6253 −0.537856
\(552\) 0 0
\(553\) −4.15045 −0.176495
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −37.5271 −1.59007 −0.795036 0.606562i \(-0.792548\pi\)
−0.795036 + 0.606562i \(0.792548\pi\)
\(558\) 0 0
\(559\) −11.0738 −0.468372
\(560\) 0 0
\(561\) −0.504032 −0.0212802
\(562\) 0 0
\(563\) −43.6688 −1.84042 −0.920210 0.391425i \(-0.871982\pi\)
−0.920210 + 0.391425i \(0.871982\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 7.70782 0.323698
\(568\) 0 0
\(569\) −8.42407 −0.353155 −0.176578 0.984287i \(-0.556503\pi\)
−0.176578 + 0.984287i \(0.556503\pi\)
\(570\) 0 0
\(571\) 24.8627 1.04047 0.520236 0.854022i \(-0.325844\pi\)
0.520236 + 0.854022i \(0.325844\pi\)
\(572\) 0 0
\(573\) −3.10299 −0.129629
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −14.0263 −0.583924 −0.291962 0.956430i \(-0.594308\pi\)
−0.291962 + 0.956430i \(0.594308\pi\)
\(578\) 0 0
\(579\) 7.74798 0.321995
\(580\) 0 0
\(581\) 6.21299 0.257758
\(582\) 0 0
\(583\) −3.47627 −0.143972
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −34.5804 −1.42729 −0.713643 0.700510i \(-0.752956\pi\)
−0.713643 + 0.700510i \(0.752956\pi\)
\(588\) 0 0
\(589\) 62.6516 2.58152
\(590\) 0 0
\(591\) −7.72829 −0.317899
\(592\) 0 0
\(593\) −8.00000 −0.328521 −0.164260 0.986417i \(-0.552524\pi\)
−0.164260 + 0.986417i \(0.552524\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −4.27171 −0.174830
\(598\) 0 0
\(599\) 42.3996 1.73240 0.866201 0.499696i \(-0.166555\pi\)
0.866201 + 0.499696i \(0.166555\pi\)
\(600\) 0 0
\(601\) 2.75131 0.112228 0.0561141 0.998424i \(-0.482129\pi\)
0.0561141 + 0.998424i \(0.482129\pi\)
\(602\) 0 0
\(603\) −23.2546 −0.946999
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −37.7948 −1.53404 −0.767022 0.641621i \(-0.778262\pi\)
−0.767022 + 0.641621i \(0.778262\pi\)
\(608\) 0 0
\(609\) −3.47627 −0.140866
\(610\) 0 0
\(611\) 4.37328 0.176924
\(612\) 0 0
\(613\) −18.7659 −0.757947 −0.378974 0.925407i \(-0.623723\pi\)
−0.378974 + 0.925407i \(0.623723\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −18.6107 −0.749239 −0.374620 0.927179i \(-0.622227\pi\)
−0.374620 + 0.927179i \(0.622227\pi\)
\(618\) 0 0
\(619\) −19.2097 −0.772102 −0.386051 0.922478i \(-0.626161\pi\)
−0.386051 + 0.922478i \(0.626161\pi\)
\(620\) 0 0
\(621\) 26.5501 1.06542
\(622\) 0 0
\(623\) 22.9116 0.917934
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −1.97365 −0.0788201
\(628\) 0 0
\(629\) 10.5990 0.422608
\(630\) 0 0
\(631\) −26.0263 −1.03609 −0.518046 0.855353i \(-0.673341\pi\)
−0.518046 + 0.855353i \(0.673341\pi\)
\(632\) 0 0
\(633\) 12.1622 0.483404
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 2.26187 0.0896184
\(638\) 0 0
\(639\) 25.1490 0.994880
\(640\) 0 0
\(641\) 11.1735 0.441325 0.220663 0.975350i \(-0.429178\pi\)
0.220663 + 0.975350i \(0.429178\pi\)
\(642\) 0 0
\(643\) −35.1451 −1.38599 −0.692993 0.720944i \(-0.743708\pi\)
−0.692993 + 0.720944i \(0.743708\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 6.93207 0.272528 0.136264 0.990673i \(-0.456490\pi\)
0.136264 + 0.990673i \(0.456490\pi\)
\(648\) 0 0
\(649\) 2.44851 0.0961123
\(650\) 0 0
\(651\) 17.2506 0.676104
\(652\) 0 0
\(653\) −29.7381 −1.16374 −0.581872 0.813281i \(-0.697679\pi\)
−0.581872 + 0.813281i \(0.697679\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −30.7612 −1.20011
\(658\) 0 0
\(659\) −24.3879 −0.950017 −0.475008 0.879981i \(-0.657555\pi\)
−0.475008 + 0.879981i \(0.657555\pi\)
\(660\) 0 0
\(661\) −34.1378 −1.32781 −0.663903 0.747819i \(-0.731101\pi\)
−0.663903 + 0.747819i \(0.731101\pi\)
\(662\) 0 0
\(663\) −1.25060 −0.0485693
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 12.3127 0.476748
\(668\) 0 0
\(669\) −18.1603 −0.702118
\(670\) 0 0
\(671\) 0.101570 0.00392108
\(672\) 0 0
\(673\) 23.6385 0.911196 0.455598 0.890186i \(-0.349425\pi\)
0.455598 + 0.890186i \(0.349425\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 2.88717 0.110963 0.0554814 0.998460i \(-0.482331\pi\)
0.0554814 + 0.998460i \(0.482331\pi\)
\(678\) 0 0
\(679\) 20.7269 0.795424
\(680\) 0 0
\(681\) −1.90034 −0.0728212
\(682\) 0 0
\(683\) −13.7440 −0.525900 −0.262950 0.964809i \(-0.584695\pi\)
−0.262950 + 0.964809i \(0.584695\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −2.86273 −0.109220
\(688\) 0 0
\(689\) −8.62530 −0.328598
\(690\) 0 0
\(691\) −31.5633 −1.20072 −0.600361 0.799729i \(-0.704977\pi\)
−0.600361 + 0.799729i \(0.704977\pi\)
\(692\) 0 0
\(693\) 1.96571 0.0746713
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 7.37470 0.279337
\(698\) 0 0
\(699\) 10.5501 0.399041
\(700\) 0 0
\(701\) −23.8397 −0.900413 −0.450207 0.892924i \(-0.648650\pi\)
−0.450207 + 0.892924i \(0.648650\pi\)
\(702\) 0 0
\(703\) 41.5026 1.56530
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −24.5844 −0.924590
\(708\) 0 0
\(709\) −21.8496 −0.820577 −0.410289 0.911956i \(-0.634572\pi\)
−0.410289 + 0.911956i \(0.634572\pi\)
\(710\) 0 0
\(711\) 4.52373 0.169653
\(712\) 0 0
\(713\) −61.1002 −2.28822
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 12.3536 0.461353
\(718\) 0 0
\(719\) −33.9248 −1.26518 −0.632590 0.774487i \(-0.718008\pi\)
−0.632590 + 0.774487i \(0.718008\pi\)
\(720\) 0 0
\(721\) −23.5731 −0.877908
\(722\) 0 0
\(723\) 1.71370 0.0637331
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 2.78163 0.103165 0.0515824 0.998669i \(-0.483574\pi\)
0.0515824 + 0.998669i \(0.483574\pi\)
\(728\) 0 0
\(729\) 2.02776 0.0751023
\(730\) 0 0
\(731\) 18.5501 0.686099
\(732\) 0 0
\(733\) 4.90175 0.181050 0.0905252 0.995894i \(-0.471145\pi\)
0.0905252 + 0.995894i \(0.471145\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −3.83780 −0.141367
\(738\) 0 0
\(739\) 25.9102 0.953122 0.476561 0.879141i \(-0.341883\pi\)
0.476561 + 0.879141i \(0.341883\pi\)
\(740\) 0 0
\(741\) −4.89701 −0.179896
\(742\) 0 0
\(743\) 9.06793 0.332670 0.166335 0.986069i \(-0.446807\pi\)
0.166335 + 0.986069i \(0.446807\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −6.77178 −0.247766
\(748\) 0 0
\(749\) 23.8134 0.870121
\(750\) 0 0
\(751\) −11.8496 −0.432396 −0.216198 0.976349i \(-0.569366\pi\)
−0.216198 + 0.976349i \(0.569366\pi\)
\(752\) 0 0
\(753\) −21.5106 −0.783888
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −2.05079 −0.0745371 −0.0372685 0.999305i \(-0.511866\pi\)
−0.0372685 + 0.999305i \(0.511866\pi\)
\(758\) 0 0
\(759\) 1.92478 0.0698650
\(760\) 0 0
\(761\) 25.0738 0.908925 0.454462 0.890766i \(-0.349831\pi\)
0.454462 + 0.890766i \(0.349831\pi\)
\(762\) 0 0
\(763\) 10.8627 0.393257
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 6.07522 0.219364
\(768\) 0 0
\(769\) −14.7466 −0.531775 −0.265887 0.964004i \(-0.585665\pi\)
−0.265887 + 0.964004i \(0.585665\pi\)
\(770\) 0 0
\(771\) 4.35359 0.156791
\(772\) 0 0
\(773\) −10.8872 −0.391584 −0.195792 0.980645i \(-0.562728\pi\)
−0.195792 + 0.980645i \(0.562728\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 11.4274 0.409955
\(778\) 0 0
\(779\) 28.8773 1.03464
\(780\) 0 0
\(781\) 4.15045 0.148515
\(782\) 0 0
\(783\) 8.62530 0.308243
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 36.8178 1.31241 0.656207 0.754581i \(-0.272160\pi\)
0.656207 + 0.754581i \(0.272160\pi\)
\(788\) 0 0
\(789\) 11.6629 0.415211
\(790\) 0 0
\(791\) 42.8021 1.52187
\(792\) 0 0
\(793\) 0.252016 0.00894935
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 12.8119 0.453822 0.226911 0.973915i \(-0.427137\pi\)
0.226911 + 0.973915i \(0.427137\pi\)
\(798\) 0 0
\(799\) −7.32582 −0.259169
\(800\) 0 0
\(801\) −24.9722 −0.882351
\(802\) 0 0
\(803\) −5.07664 −0.179151
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 22.6596 0.797655
\(808\) 0 0
\(809\) 16.2981 0.573009 0.286505 0.958079i \(-0.407507\pi\)
0.286505 + 0.958079i \(0.407507\pi\)
\(810\) 0 0
\(811\) 2.21108 0.0776415 0.0388208 0.999246i \(-0.487640\pi\)
0.0388208 + 0.999246i \(0.487640\pi\)
\(812\) 0 0
\(813\) 20.0527 0.703279
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 72.6371 2.54125
\(818\) 0 0
\(819\) 4.87732 0.170427
\(820\) 0 0
\(821\) 50.6615 1.76810 0.884049 0.467394i \(-0.154807\pi\)
0.884049 + 0.467394i \(0.154807\pi\)
\(822\) 0 0
\(823\) 0.917483 0.0319814 0.0159907 0.999872i \(-0.494910\pi\)
0.0159907 + 0.999872i \(0.494910\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 10.5198 0.365808 0.182904 0.983131i \(-0.441450\pi\)
0.182904 + 0.983131i \(0.441450\pi\)
\(828\) 0 0
\(829\) −38.6907 −1.34378 −0.671891 0.740650i \(-0.734518\pi\)
−0.671891 + 0.740650i \(0.734518\pi\)
\(830\) 0 0
\(831\) 16.1016 0.558557
\(832\) 0 0
\(833\) −3.78892 −0.131278
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −42.8021 −1.47946
\(838\) 0 0
\(839\) −10.0263 −0.346148 −0.173074 0.984909i \(-0.555370\pi\)
−0.173074 + 0.984909i \(0.555370\pi\)
\(840\) 0 0
\(841\) −25.0000 −0.862069
\(842\) 0 0
\(843\) −11.6873 −0.402534
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −23.3952 −0.803867
\(848\) 0 0
\(849\) 7.09825 0.243611
\(850\) 0 0
\(851\) −40.4749 −1.38746
\(852\) 0 0
\(853\) −49.5388 −1.69618 −0.848088 0.529855i \(-0.822246\pi\)
−0.848088 + 0.529855i \(0.822246\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −43.4763 −1.48512 −0.742561 0.669779i \(-0.766389\pi\)
−0.742561 + 0.669779i \(0.766389\pi\)
\(858\) 0 0
\(859\) −23.5633 −0.803968 −0.401984 0.915647i \(-0.631679\pi\)
−0.401984 + 0.915647i \(0.631679\pi\)
\(860\) 0 0
\(861\) 7.95112 0.270974
\(862\) 0 0
\(863\) −13.3317 −0.453816 −0.226908 0.973916i \(-0.572862\pi\)
−0.226908 + 0.973916i \(0.572862\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −11.6082 −0.394234
\(868\) 0 0
\(869\) 0.746569 0.0253256
\(870\) 0 0
\(871\) −9.52232 −0.322651
\(872\) 0 0
\(873\) −22.5910 −0.764590
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −13.6483 −0.460871 −0.230436 0.973088i \(-0.574015\pi\)
−0.230436 + 0.973088i \(0.574015\pi\)
\(878\) 0 0
\(879\) −2.70052 −0.0910864
\(880\) 0 0
\(881\) 16.3028 0.549255 0.274628 0.961551i \(-0.411445\pi\)
0.274628 + 0.961551i \(0.411445\pi\)
\(882\) 0 0
\(883\) 13.5818 0.457064 0.228532 0.973536i \(-0.426607\pi\)
0.228532 + 0.973536i \(0.426607\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 37.0797 1.24501 0.622507 0.782614i \(-0.286114\pi\)
0.622507 + 0.782614i \(0.286114\pi\)
\(888\) 0 0
\(889\) −25.3766 −0.851104
\(890\) 0 0
\(891\) −1.38646 −0.0464481
\(892\) 0 0
\(893\) −28.6859 −0.959938
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 4.77575 0.159458
\(898\) 0 0
\(899\) −19.8496 −0.662020
\(900\) 0 0
\(901\) 14.4485 0.481350
\(902\) 0 0
\(903\) 20.0000 0.665558
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −35.7294 −1.18638 −0.593188 0.805064i \(-0.702131\pi\)
−0.593188 + 0.805064i \(0.702131\pi\)
\(908\) 0 0
\(909\) 26.7954 0.888749
\(910\) 0 0
\(911\) −20.5237 −0.679982 −0.339991 0.940429i \(-0.610424\pi\)
−0.339991 + 0.940429i \(0.610424\pi\)
\(912\) 0 0
\(913\) −1.11757 −0.0369863
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 32.5355 1.07442
\(918\) 0 0
\(919\) −20.9986 −0.692679 −0.346340 0.938109i \(-0.612576\pi\)
−0.346340 + 0.938109i \(0.612576\pi\)
\(920\) 0 0
\(921\) −1.57593 −0.0519287
\(922\) 0 0
\(923\) 10.2981 0.338965
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 25.6932 0.843876
\(928\) 0 0
\(929\) −31.5271 −1.03437 −0.517185 0.855874i \(-0.673020\pi\)
−0.517185 + 0.855874i \(0.673020\pi\)
\(930\) 0 0
\(931\) −14.8364 −0.486243
\(932\) 0 0
\(933\) −7.07381 −0.231586
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 17.8641 0.583596 0.291798 0.956480i \(-0.405746\pi\)
0.291798 + 0.956480i \(0.405746\pi\)
\(938\) 0 0
\(939\) −14.9525 −0.487958
\(940\) 0 0
\(941\) 45.5487 1.48484 0.742422 0.669933i \(-0.233677\pi\)
0.742422 + 0.669933i \(0.233677\pi\)
\(942\) 0 0
\(943\) −28.1622 −0.917088
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −43.2057 −1.40400 −0.701998 0.712179i \(-0.747709\pi\)
−0.701998 + 0.712179i \(0.747709\pi\)
\(948\) 0 0
\(949\) −12.5961 −0.408887
\(950\) 0 0
\(951\) 7.72829 0.250607
\(952\) 0 0
\(953\) −10.9722 −0.355426 −0.177713 0.984082i \(-0.556870\pi\)
−0.177713 + 0.984082i \(0.556870\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0.625301 0.0202131
\(958\) 0 0
\(959\) −40.0000 −1.29167
\(960\) 0 0
\(961\) 67.5012 2.17746
\(962\) 0 0
\(963\) −25.9551 −0.836391
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −44.1417 −1.41950 −0.709751 0.704452i \(-0.751193\pi\)
−0.709751 + 0.704452i \(0.751193\pi\)
\(968\) 0 0
\(969\) 8.20314 0.263523
\(970\) 0 0
\(971\) −20.1886 −0.647881 −0.323941 0.946077i \(-0.605008\pi\)
−0.323941 + 0.946077i \(0.605008\pi\)
\(972\) 0 0
\(973\) −16.4142 −0.526216
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 1.73340 0.0554562 0.0277281 0.999616i \(-0.491173\pi\)
0.0277281 + 0.999616i \(0.491173\pi\)
\(978\) 0 0
\(979\) −4.12127 −0.131716
\(980\) 0 0
\(981\) −11.8397 −0.378013
\(982\) 0 0
\(983\) −14.0059 −0.446718 −0.223359 0.974736i \(-0.571702\pi\)
−0.223359 + 0.974736i \(0.571702\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −7.89843 −0.251410
\(988\) 0 0
\(989\) −70.8383 −2.25253
\(990\) 0 0
\(991\) −42.8021 −1.35965 −0.679827 0.733373i \(-0.737945\pi\)
−0.679827 + 0.733373i \(0.737945\pi\)
\(992\) 0 0
\(993\) −18.6107 −0.590593
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 42.8872 1.35825 0.679125 0.734023i \(-0.262359\pi\)
0.679125 + 0.734023i \(0.262359\pi\)
\(998\) 0 0
\(999\) −28.3536 −0.897068
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.bs.1.2 3
4.3 odd 2 3200.2.a.br.1.2 3
5.2 odd 4 640.2.c.a.129.3 6
5.3 odd 4 640.2.c.a.129.4 yes 6
5.4 even 2 3200.2.a.bq.1.2 3
8.3 odd 2 3200.2.a.bu.1.2 3
8.5 even 2 3200.2.a.bp.1.2 3
20.3 even 4 640.2.c.b.129.3 yes 6
20.7 even 4 640.2.c.b.129.4 yes 6
20.19 odd 2 3200.2.a.bt.1.2 3
40.3 even 4 640.2.c.c.129.4 yes 6
40.13 odd 4 640.2.c.d.129.3 yes 6
40.19 odd 2 3200.2.a.bo.1.2 3
40.27 even 4 640.2.c.c.129.3 yes 6
40.29 even 2 3200.2.a.bv.1.2 3
40.37 odd 4 640.2.c.d.129.4 yes 6
80.3 even 4 1280.2.f.k.129.3 6
80.13 odd 4 1280.2.f.i.129.3 6
80.27 even 4 1280.2.f.k.129.4 6
80.37 odd 4 1280.2.f.i.129.4 6
80.43 even 4 1280.2.f.j.129.4 6
80.53 odd 4 1280.2.f.l.129.4 6
80.67 even 4 1280.2.f.j.129.3 6
80.77 odd 4 1280.2.f.l.129.3 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
640.2.c.a.129.3 6 5.2 odd 4
640.2.c.a.129.4 yes 6 5.3 odd 4
640.2.c.b.129.3 yes 6 20.3 even 4
640.2.c.b.129.4 yes 6 20.7 even 4
640.2.c.c.129.3 yes 6 40.27 even 4
640.2.c.c.129.4 yes 6 40.3 even 4
640.2.c.d.129.3 yes 6 40.13 odd 4
640.2.c.d.129.4 yes 6 40.37 odd 4
1280.2.f.i.129.3 6 80.13 odd 4
1280.2.f.i.129.4 6 80.37 odd 4
1280.2.f.j.129.3 6 80.67 even 4
1280.2.f.j.129.4 6 80.43 even 4
1280.2.f.k.129.3 6 80.3 even 4
1280.2.f.k.129.4 6 80.27 even 4
1280.2.f.l.129.3 6 80.77 odd 4
1280.2.f.l.129.4 6 80.53 odd 4
3200.2.a.bo.1.2 3 40.19 odd 2
3200.2.a.bp.1.2 3 8.5 even 2
3200.2.a.bq.1.2 3 5.4 even 2
3200.2.a.br.1.2 3 4.3 odd 2
3200.2.a.bs.1.2 3 1.1 even 1 trivial
3200.2.a.bt.1.2 3 20.19 odd 2
3200.2.a.bu.1.2 3 8.3 odd 2
3200.2.a.bv.1.2 3 40.29 even 2