Properties

Label 3200.2.a.bq.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 \(0.311108\) of defining polynomial
Character \(\chi\) \(=\) 3200.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.90321 q^{3} +3.52543 q^{7} +5.42864 q^{9} +O(q^{10})\) \(q-2.90321 q^{3} +3.52543 q^{7} +5.42864 q^{9} +3.80642 q^{11} -2.62222 q^{13} -5.80642 q^{17} -5.05086 q^{19} -10.2351 q^{21} +0.474572 q^{23} -7.05086 q^{27} -2.00000 q^{29} +2.75557 q^{31} -11.0509 q^{33} -7.18421 q^{37} +7.61285 q^{39} +5.18421 q^{41} +1.95407 q^{43} -5.33185 q^{47} +5.42864 q^{49} +16.8573 q^{51} -5.37778 q^{53} +14.6637 q^{57} +5.05086 q^{59} -12.2351 q^{61} +19.1383 q^{63} +7.76049 q^{67} -1.37778 q^{69} +4.85728 q^{71} +6.66370 q^{73} +13.4193 q^{77} +5.24443 q^{79} +4.18421 q^{81} -12.1476 q^{83} +5.80642 q^{87} -12.1017 q^{89} -9.24443 q^{91} -8.00000 q^{93} -13.8064 q^{97} +20.6637 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 2 q^{3} + 4 q^{7} + 3 q^{9}+O(q^{10}) \) 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
\(3\) −2.90321 −1.67617 −0.838085 0.545540i \(-0.816325\pi\)
−0.838085 + 0.545540i \(0.816325\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 3.52543 1.33249 0.666243 0.745735i \(-0.267901\pi\)
0.666243 + 0.745735i \(0.267901\pi\)
\(8\) 0 0
\(9\) 5.42864 1.80955
\(10\) 0 0
\(11\) 3.80642 1.14768 0.573840 0.818967i \(-0.305453\pi\)
0.573840 + 0.818967i \(0.305453\pi\)
\(12\) 0 0
\(13\) −2.62222 −0.727272 −0.363636 0.931541i \(-0.618465\pi\)
−0.363636 + 0.931541i \(0.618465\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −5.80642 −1.40826 −0.704132 0.710069i \(-0.748664\pi\)
−0.704132 + 0.710069i \(0.748664\pi\)
\(18\) 0 0
\(19\) −5.05086 −1.15875 −0.579373 0.815063i \(-0.696702\pi\)
−0.579373 + 0.815063i \(0.696702\pi\)
\(20\) 0 0
\(21\) −10.2351 −2.23347
\(22\) 0 0
\(23\) 0.474572 0.0989552 0.0494776 0.998775i \(-0.484244\pi\)
0.0494776 + 0.998775i \(0.484244\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −7.05086 −1.35694
\(28\) 0 0
\(29\) −2.00000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) 0 0
\(31\) 2.75557 0.494915 0.247457 0.968899i \(-0.420405\pi\)
0.247457 + 0.968899i \(0.420405\pi\)
\(32\) 0 0
\(33\) −11.0509 −1.92371
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −7.18421 −1.18108 −0.590538 0.807010i \(-0.701085\pi\)
−0.590538 + 0.807010i \(0.701085\pi\)
\(38\) 0 0
\(39\) 7.61285 1.21903
\(40\) 0 0
\(41\) 5.18421 0.809637 0.404819 0.914397i \(-0.367335\pi\)
0.404819 + 0.914397i \(0.367335\pi\)
\(42\) 0 0
\(43\) 1.95407 0.297992 0.148996 0.988838i \(-0.452396\pi\)
0.148996 + 0.988838i \(0.452396\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −5.33185 −0.777730 −0.388865 0.921295i \(-0.627133\pi\)
−0.388865 + 0.921295i \(0.627133\pi\)
\(48\) 0 0
\(49\) 5.42864 0.775520
\(50\) 0 0
\(51\) 16.8573 2.36049
\(52\) 0 0
\(53\) −5.37778 −0.738695 −0.369348 0.929291i \(-0.620419\pi\)
−0.369348 + 0.929291i \(0.620419\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 14.6637 1.94225
\(58\) 0 0
\(59\) 5.05086 0.657565 0.328783 0.944406i \(-0.393362\pi\)
0.328783 + 0.944406i \(0.393362\pi\)
\(60\) 0 0
\(61\) −12.2351 −1.56654 −0.783270 0.621682i \(-0.786450\pi\)
−0.783270 + 0.621682i \(0.786450\pi\)
\(62\) 0 0
\(63\) 19.1383 2.41120
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 7.76049 0.948095 0.474047 0.880499i \(-0.342793\pi\)
0.474047 + 0.880499i \(0.342793\pi\)
\(68\) 0 0
\(69\) −1.37778 −0.165866
\(70\) 0 0
\(71\) 4.85728 0.576453 0.288226 0.957562i \(-0.406934\pi\)
0.288226 + 0.957562i \(0.406934\pi\)
\(72\) 0 0
\(73\) 6.66370 0.779927 0.389964 0.920830i \(-0.372488\pi\)
0.389964 + 0.920830i \(0.372488\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 13.4193 1.52927
\(78\) 0 0
\(79\) 5.24443 0.590045 0.295022 0.955490i \(-0.404673\pi\)
0.295022 + 0.955490i \(0.404673\pi\)
\(80\) 0 0
\(81\) 4.18421 0.464912
\(82\) 0 0
\(83\) −12.1476 −1.33338 −0.666689 0.745336i \(-0.732289\pi\)
−0.666689 + 0.745336i \(0.732289\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 5.80642 0.622514
\(88\) 0 0
\(89\) −12.1017 −1.28278 −0.641389 0.767216i \(-0.721642\pi\)
−0.641389 + 0.767216i \(0.721642\pi\)
\(90\) 0 0
\(91\) −9.24443 −0.969080
\(92\) 0 0
\(93\) −8.00000 −0.829561
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −13.8064 −1.40183 −0.700915 0.713245i \(-0.747225\pi\)
−0.700915 + 0.713245i \(0.747225\pi\)
\(98\) 0 0
\(99\) 20.6637 2.07678
\(100\) 0 0
\(101\) 19.7146 1.96167 0.980836 0.194836i \(-0.0624173\pi\)
0.980836 + 0.194836i \(0.0624173\pi\)
\(102\) 0 0
\(103\) −3.13828 −0.309223 −0.154612 0.987975i \(-0.549413\pi\)
−0.154612 + 0.987975i \(0.549413\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 5.39207 0.521272 0.260636 0.965437i \(-0.416068\pi\)
0.260636 + 0.965437i \(0.416068\pi\)
\(108\) 0 0
\(109\) 8.62222 0.825858 0.412929 0.910763i \(-0.364506\pi\)
0.412929 + 0.910763i \(0.364506\pi\)
\(110\) 0 0
\(111\) 20.8573 1.97969
\(112\) 0 0
\(113\) −5.51114 −0.518444 −0.259222 0.965818i \(-0.583466\pi\)
−0.259222 + 0.965818i \(0.583466\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −14.2351 −1.31603
\(118\) 0 0
\(119\) −20.4701 −1.87649
\(120\) 0 0
\(121\) 3.48886 0.317169
\(122\) 0 0
\(123\) −15.0509 −1.35709
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 10.2810 0.912291 0.456145 0.889905i \(-0.349230\pi\)
0.456145 + 0.889905i \(0.349230\pi\)
\(128\) 0 0
\(129\) −5.67307 −0.499486
\(130\) 0 0
\(131\) −4.66370 −0.407470 −0.203735 0.979026i \(-0.565308\pi\)
−0.203735 + 0.979026i \(0.565308\pi\)
\(132\) 0 0
\(133\) −17.8064 −1.54401
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −11.3461 −0.969366 −0.484683 0.874690i \(-0.661065\pi\)
−0.484683 + 0.874690i \(0.661065\pi\)
\(138\) 0 0
\(139\) −11.8064 −1.00141 −0.500704 0.865619i \(-0.666925\pi\)
−0.500704 + 0.865619i \(0.666925\pi\)
\(140\) 0 0
\(141\) 15.4795 1.30361
\(142\) 0 0
\(143\) −9.98126 −0.834675
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −15.7605 −1.29990
\(148\) 0 0
\(149\) −5.47949 −0.448898 −0.224449 0.974486i \(-0.572058\pi\)
−0.224449 + 0.974486i \(0.572058\pi\)
\(150\) 0 0
\(151\) −23.6128 −1.92159 −0.960793 0.277266i \(-0.910572\pi\)
−0.960793 + 0.277266i \(0.910572\pi\)
\(152\) 0 0
\(153\) −31.5210 −2.54832
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −0.815792 −0.0651073 −0.0325536 0.999470i \(-0.510364\pi\)
−0.0325536 + 0.999470i \(0.510364\pi\)
\(158\) 0 0
\(159\) 15.6128 1.23818
\(160\) 0 0
\(161\) 1.67307 0.131856
\(162\) 0 0
\(163\) −10.9032 −0.854005 −0.427003 0.904250i \(-0.640431\pi\)
−0.427003 + 0.904250i \(0.640431\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −6.57628 −0.508888 −0.254444 0.967088i \(-0.581892\pi\)
−0.254444 + 0.967088i \(0.581892\pi\)
\(168\) 0 0
\(169\) −6.12399 −0.471076
\(170\) 0 0
\(171\) −27.4193 −2.09680
\(172\) 0 0
\(173\) 10.5303 0.800608 0.400304 0.916382i \(-0.368905\pi\)
0.400304 + 0.916382i \(0.368905\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −14.6637 −1.10219
\(178\) 0 0
\(179\) 6.29529 0.470532 0.235266 0.971931i \(-0.424404\pi\)
0.235266 + 0.971931i \(0.424404\pi\)
\(180\) 0 0
\(181\) −0.488863 −0.0363369 −0.0181684 0.999835i \(-0.505784\pi\)
−0.0181684 + 0.999835i \(0.505784\pi\)
\(182\) 0 0
\(183\) 35.5210 2.62579
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −22.1017 −1.61624
\(188\) 0 0
\(189\) −24.8573 −1.80810
\(190\) 0 0
\(191\) 10.4889 0.758947 0.379474 0.925203i \(-0.376105\pi\)
0.379474 + 0.925203i \(0.376105\pi\)
\(192\) 0 0
\(193\) −13.8064 −0.993808 −0.496904 0.867805i \(-0.665530\pi\)
−0.496904 + 0.867805i \(0.665530\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −16.7239 −1.19153 −0.595765 0.803159i \(-0.703151\pi\)
−0.595765 + 0.803159i \(0.703151\pi\)
\(198\) 0 0
\(199\) −20.8573 −1.47853 −0.739267 0.673413i \(-0.764828\pi\)
−0.739267 + 0.673413i \(0.764828\pi\)
\(200\) 0 0
\(201\) −22.5303 −1.58917
\(202\) 0 0
\(203\) −7.05086 −0.494873
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 2.57628 0.179064
\(208\) 0 0
\(209\) −19.2257 −1.32987
\(210\) 0 0
\(211\) −4.66370 −0.321063 −0.160531 0.987031i \(-0.551321\pi\)
−0.160531 + 0.987031i \(0.551321\pi\)
\(212\) 0 0
\(213\) −14.1017 −0.966233
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 9.71456 0.659467
\(218\) 0 0
\(219\) −19.3461 −1.30729
\(220\) 0 0
\(221\) 15.2257 1.02419
\(222\) 0 0
\(223\) 26.4558 1.77161 0.885807 0.464054i \(-0.153606\pi\)
0.885807 + 0.464054i \(0.153606\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −12.3225 −0.817872 −0.408936 0.912563i \(-0.634100\pi\)
−0.408936 + 0.912563i \(0.634100\pi\)
\(228\) 0 0
\(229\) 13.2257 0.873979 0.436989 0.899467i \(-0.356045\pi\)
0.436989 + 0.899467i \(0.356045\pi\)
\(230\) 0 0
\(231\) −38.9590 −2.56331
\(232\) 0 0
\(233\) 6.66370 0.436554 0.218277 0.975887i \(-0.429956\pi\)
0.218277 + 0.975887i \(0.429956\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −15.2257 −0.989015
\(238\) 0 0
\(239\) −22.9590 −1.48509 −0.742547 0.669794i \(-0.766382\pi\)
−0.742547 + 0.669794i \(0.766382\pi\)
\(240\) 0 0
\(241\) −14.0415 −0.904492 −0.452246 0.891893i \(-0.649377\pi\)
−0.452246 + 0.891893i \(0.649377\pi\)
\(242\) 0 0
\(243\) 9.00492 0.577666
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 13.2444 0.842723
\(248\) 0 0
\(249\) 35.2672 2.23497
\(250\) 0 0
\(251\) −24.9304 −1.57359 −0.786797 0.617212i \(-0.788262\pi\)
−0.786797 + 0.617212i \(0.788262\pi\)
\(252\) 0 0
\(253\) 1.80642 0.113569
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 25.7146 1.60403 0.802015 0.597304i \(-0.203761\pi\)
0.802015 + 0.597304i \(0.203761\pi\)
\(258\) 0 0
\(259\) −25.3274 −1.57377
\(260\) 0 0
\(261\) −10.8573 −0.672049
\(262\) 0 0
\(263\) 2.57628 0.158860 0.0794302 0.996840i \(-0.474690\pi\)
0.0794302 + 0.996840i \(0.474690\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 35.1338 2.15016
\(268\) 0 0
\(269\) 25.7462 1.56977 0.784887 0.619639i \(-0.212721\pi\)
0.784887 + 0.619639i \(0.212721\pi\)
\(270\) 0 0
\(271\) −30.1847 −1.83359 −0.916795 0.399359i \(-0.869233\pi\)
−0.916795 + 0.399359i \(0.869233\pi\)
\(272\) 0 0
\(273\) 26.8385 1.62434
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 10.5303 0.632707 0.316354 0.948641i \(-0.397541\pi\)
0.316354 + 0.948641i \(0.397541\pi\)
\(278\) 0 0
\(279\) 14.9590 0.895571
\(280\) 0 0
\(281\) −7.93978 −0.473647 −0.236824 0.971553i \(-0.576106\pi\)
−0.236824 + 0.971553i \(0.576106\pi\)
\(282\) 0 0
\(283\) −10.9032 −0.648129 −0.324064 0.946035i \(-0.605049\pi\)
−0.324064 + 0.946035i \(0.605049\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 18.2766 1.07883
\(288\) 0 0
\(289\) 16.7146 0.983209
\(290\) 0 0
\(291\) 40.0830 2.34971
\(292\) 0 0
\(293\) −4.42864 −0.258724 −0.129362 0.991597i \(-0.541293\pi\)
−0.129362 + 0.991597i \(0.541293\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −26.8385 −1.55733
\(298\) 0 0
\(299\) −1.24443 −0.0719673
\(300\) 0 0
\(301\) 6.88892 0.397071
\(302\) 0 0
\(303\) −57.2355 −3.28810
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 5.27163 0.300868 0.150434 0.988620i \(-0.451933\pi\)
0.150434 + 0.988620i \(0.451933\pi\)
\(308\) 0 0
\(309\) 9.11108 0.518311
\(310\) 0 0
\(311\) −0.387152 −0.0219534 −0.0109767 0.999940i \(-0.503494\pi\)
−0.0109767 + 0.999940i \(0.503494\pi\)
\(312\) 0 0
\(313\) −11.3461 −0.641322 −0.320661 0.947194i \(-0.603905\pi\)
−0.320661 + 0.947194i \(0.603905\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 16.7239 0.939309 0.469655 0.882850i \(-0.344378\pi\)
0.469655 + 0.882850i \(0.344378\pi\)
\(318\) 0 0
\(319\) −7.61285 −0.426238
\(320\) 0 0
\(321\) −15.6543 −0.873740
\(322\) 0 0
\(323\) 29.3274 1.63182
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −25.0321 −1.38428
\(328\) 0 0
\(329\) −18.7971 −1.03632
\(330\) 0 0
\(331\) −3.33630 −0.183379 −0.0916897 0.995788i \(-0.529227\pi\)
−0.0916897 + 0.995788i \(0.529227\pi\)
\(332\) 0 0
\(333\) −39.0005 −2.13721
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 3.61285 0.196804 0.0984022 0.995147i \(-0.468627\pi\)
0.0984022 + 0.995147i \(0.468627\pi\)
\(338\) 0 0
\(339\) 16.0000 0.869001
\(340\) 0 0
\(341\) 10.4889 0.568004
\(342\) 0 0
\(343\) −5.53972 −0.299117
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 15.7605 0.846067 0.423034 0.906114i \(-0.360965\pi\)
0.423034 + 0.906114i \(0.360965\pi\)
\(348\) 0 0
\(349\) −0.285442 −0.0152794 −0.00763968 0.999971i \(-0.502432\pi\)
−0.00763968 + 0.999971i \(0.502432\pi\)
\(350\) 0 0
\(351\) 18.4889 0.986862
\(352\) 0 0
\(353\) 4.38715 0.233505 0.116752 0.993161i \(-0.462752\pi\)
0.116752 + 0.993161i \(0.462752\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 59.4291 3.14532
\(358\) 0 0
\(359\) 20.5906 1.08673 0.543364 0.839497i \(-0.317150\pi\)
0.543364 + 0.839497i \(0.317150\pi\)
\(360\) 0 0
\(361\) 6.51114 0.342691
\(362\) 0 0
\(363\) −10.1289 −0.531630
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −16.5575 −0.864297 −0.432148 0.901802i \(-0.642244\pi\)
−0.432148 + 0.901802i \(0.642244\pi\)
\(368\) 0 0
\(369\) 28.1432 1.46508
\(370\) 0 0
\(371\) −18.9590 −0.984302
\(372\) 0 0
\(373\) 24.8988 1.28921 0.644605 0.764516i \(-0.277022\pi\)
0.644605 + 0.764516i \(0.277022\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 5.24443 0.270102
\(378\) 0 0
\(379\) −9.31756 −0.478611 −0.239305 0.970944i \(-0.576920\pi\)
−0.239305 + 0.970944i \(0.576920\pi\)
\(380\) 0 0
\(381\) −29.8479 −1.52915
\(382\) 0 0
\(383\) 32.5575 1.66361 0.831806 0.555066i \(-0.187307\pi\)
0.831806 + 0.555066i \(0.187307\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 10.6079 0.539231
\(388\) 0 0
\(389\) −18.9906 −0.962863 −0.481432 0.876484i \(-0.659883\pi\)
−0.481432 + 0.876484i \(0.659883\pi\)
\(390\) 0 0
\(391\) −2.75557 −0.139355
\(392\) 0 0
\(393\) 13.5397 0.682988
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −32.9906 −1.65575 −0.827876 0.560911i \(-0.810451\pi\)
−0.827876 + 0.560911i \(0.810451\pi\)
\(398\) 0 0
\(399\) 51.6958 2.58803
\(400\) 0 0
\(401\) −16.1017 −0.804081 −0.402041 0.915622i \(-0.631699\pi\)
−0.402041 + 0.915622i \(0.631699\pi\)
\(402\) 0 0
\(403\) −7.22570 −0.359938
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −27.3461 −1.35550
\(408\) 0 0
\(409\) −33.3876 −1.65091 −0.825456 0.564466i \(-0.809082\pi\)
−0.825456 + 0.564466i \(0.809082\pi\)
\(410\) 0 0
\(411\) 32.9403 1.62482
\(412\) 0 0
\(413\) 17.8064 0.876197
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 34.2766 1.67853
\(418\) 0 0
\(419\) −27.4193 −1.33952 −0.669760 0.742578i \(-0.733603\pi\)
−0.669760 + 0.742578i \(0.733603\pi\)
\(420\) 0 0
\(421\) −12.2351 −0.596301 −0.298150 0.954519i \(-0.596370\pi\)
−0.298150 + 0.954519i \(0.596370\pi\)
\(422\) 0 0
\(423\) −28.9447 −1.40734
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −43.1338 −2.08739
\(428\) 0 0
\(429\) 28.9777 1.39906
\(430\) 0 0
\(431\) 28.4701 1.37136 0.685679 0.727904i \(-0.259505\pi\)
0.685679 + 0.727904i \(0.259505\pi\)
\(432\) 0 0
\(433\) −34.0098 −1.63441 −0.817204 0.576348i \(-0.804477\pi\)
−0.817204 + 0.576348i \(0.804477\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −2.39700 −0.114664
\(438\) 0 0
\(439\) 14.8385 0.708205 0.354103 0.935207i \(-0.384786\pi\)
0.354103 + 0.935207i \(0.384786\pi\)
\(440\) 0 0
\(441\) 29.4701 1.40334
\(442\) 0 0
\(443\) 13.0968 0.622247 0.311124 0.950369i \(-0.399295\pi\)
0.311124 + 0.950369i \(0.399295\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 15.9081 0.752429
\(448\) 0 0
\(449\) −21.3876 −1.00934 −0.504672 0.863311i \(-0.668387\pi\)
−0.504672 + 0.863311i \(0.668387\pi\)
\(450\) 0 0
\(451\) 19.7333 0.929205
\(452\) 0 0
\(453\) 68.5531 3.22091
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −17.9813 −0.841128 −0.420564 0.907263i \(-0.638168\pi\)
−0.420564 + 0.907263i \(0.638168\pi\)
\(458\) 0 0
\(459\) 40.9403 1.91093
\(460\) 0 0
\(461\) −10.7368 −0.500064 −0.250032 0.968238i \(-0.580441\pi\)
−0.250032 + 0.968238i \(0.580441\pi\)
\(462\) 0 0
\(463\) −9.30327 −0.432360 −0.216180 0.976354i \(-0.569360\pi\)
−0.216180 + 0.976354i \(0.569360\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −8.70964 −0.403034 −0.201517 0.979485i \(-0.564587\pi\)
−0.201517 + 0.979485i \(0.564587\pi\)
\(468\) 0 0
\(469\) 27.3590 1.26332
\(470\) 0 0
\(471\) 2.36842 0.109131
\(472\) 0 0
\(473\) 7.43801 0.342000
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −29.1941 −1.33670
\(478\) 0 0
\(479\) −23.2257 −1.06121 −0.530605 0.847619i \(-0.678035\pi\)
−0.530605 + 0.847619i \(0.678035\pi\)
\(480\) 0 0
\(481\) 18.8385 0.858964
\(482\) 0 0
\(483\) −4.85728 −0.221014
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 32.8528 1.48870 0.744352 0.667787i \(-0.232759\pi\)
0.744352 + 0.667787i \(0.232759\pi\)
\(488\) 0 0
\(489\) 31.6543 1.43146
\(490\) 0 0
\(491\) 2.94914 0.133093 0.0665465 0.997783i \(-0.478802\pi\)
0.0665465 + 0.997783i \(0.478802\pi\)
\(492\) 0 0
\(493\) 11.6128 0.523016
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 17.1240 0.768116
\(498\) 0 0
\(499\) 35.0321 1.56825 0.784127 0.620601i \(-0.213111\pi\)
0.784127 + 0.620601i \(0.213111\pi\)
\(500\) 0 0
\(501\) 19.0923 0.852983
\(502\) 0 0
\(503\) 16.2908 0.726373 0.363186 0.931717i \(-0.381689\pi\)
0.363186 + 0.931717i \(0.381689\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 17.7792 0.789603
\(508\) 0 0
\(509\) −26.0000 −1.15243 −0.576215 0.817298i \(-0.695471\pi\)
−0.576215 + 0.817298i \(0.695471\pi\)
\(510\) 0 0
\(511\) 23.4924 1.03924
\(512\) 0 0
\(513\) 35.6128 1.57235
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −20.2953 −0.892586
\(518\) 0 0
\(519\) −30.5718 −1.34195
\(520\) 0 0
\(521\) 11.7146 0.513224 0.256612 0.966514i \(-0.417394\pi\)
0.256612 + 0.966514i \(0.417394\pi\)
\(522\) 0 0
\(523\) 38.0370 1.66324 0.831622 0.555342i \(-0.187413\pi\)
0.831622 + 0.555342i \(0.187413\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −16.0000 −0.696971
\(528\) 0 0
\(529\) −22.7748 −0.990208
\(530\) 0 0
\(531\) 27.4193 1.18990
\(532\) 0 0
\(533\) −13.5941 −0.588826
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −18.2766 −0.788691
\(538\) 0 0
\(539\) 20.6637 0.890049
\(540\) 0 0
\(541\) −11.5111 −0.494902 −0.247451 0.968900i \(-0.579593\pi\)
−0.247451 + 0.968900i \(0.579593\pi\)
\(542\) 0 0
\(543\) 1.41927 0.0609068
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −30.2208 −1.29215 −0.646073 0.763275i \(-0.723590\pi\)
−0.646073 + 0.763275i \(0.723590\pi\)
\(548\) 0 0
\(549\) −66.4197 −2.83473
\(550\) 0 0
\(551\) 10.1017 0.430347
\(552\) 0 0
\(553\) 18.4889 0.786226
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −9.75605 −0.413377 −0.206688 0.978407i \(-0.566269\pi\)
−0.206688 + 0.978407i \(0.566269\pi\)
\(558\) 0 0
\(559\) −5.12399 −0.216721
\(560\) 0 0
\(561\) 64.1659 2.70909
\(562\) 0 0
\(563\) 4.50622 0.189914 0.0949572 0.995481i \(-0.469729\pi\)
0.0949572 + 0.995481i \(0.469729\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 14.7511 0.619489
\(568\) 0 0
\(569\) 5.30465 0.222383 0.111191 0.993799i \(-0.464533\pi\)
0.111191 + 0.993799i \(0.464533\pi\)
\(570\) 0 0
\(571\) −16.3970 −0.686193 −0.343096 0.939300i \(-0.611476\pi\)
−0.343096 + 0.939300i \(0.611476\pi\)
\(572\) 0 0
\(573\) −30.4514 −1.27213
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −39.8163 −1.65757 −0.828786 0.559565i \(-0.810968\pi\)
−0.828786 + 0.559565i \(0.810968\pi\)
\(578\) 0 0
\(579\) 40.0830 1.66579
\(580\) 0 0
\(581\) −42.8256 −1.77671
\(582\) 0 0
\(583\) −20.4701 −0.847786
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 15.1699 0.626130 0.313065 0.949732i \(-0.398644\pi\)
0.313065 + 0.949732i \(0.398644\pi\)
\(588\) 0 0
\(589\) −13.9180 −0.573480
\(590\) 0 0
\(591\) 48.5531 1.99721
\(592\) 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
\(597\) 60.5531 2.47827
\(598\) 0 0
\(599\) −1.83500 −0.0749762 −0.0374881 0.999297i \(-0.511936\pi\)
−0.0374881 + 0.999297i \(0.511936\pi\)
\(600\) 0 0
\(601\) −36.1432 −1.47431 −0.737156 0.675723i \(-0.763832\pi\)
−0.737156 + 0.675723i \(0.763832\pi\)
\(602\) 0 0
\(603\) 42.1289 1.71562
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −17.5353 −0.711735 −0.355867 0.934536i \(-0.615815\pi\)
−0.355867 + 0.934536i \(0.615815\pi\)
\(608\) 0 0
\(609\) 20.4701 0.829491
\(610\) 0 0
\(611\) 13.9813 0.565621
\(612\) 0 0
\(613\) −33.9309 −1.37046 −0.685228 0.728329i \(-0.740297\pi\)
−0.685228 + 0.728329i \(0.740297\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 9.68598 0.389943 0.194971 0.980809i \(-0.437539\pi\)
0.194971 + 0.980809i \(0.437539\pi\)
\(618\) 0 0
\(619\) −41.4005 −1.66403 −0.832014 0.554755i \(-0.812812\pi\)
−0.832014 + 0.554755i \(0.812812\pi\)
\(620\) 0 0
\(621\) −3.34614 −0.134276
\(622\) 0 0
\(623\) −42.6637 −1.70929
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 55.8163 2.22909
\(628\) 0 0
\(629\) 41.7146 1.66327
\(630\) 0 0
\(631\) 27.8163 1.10735 0.553674 0.832733i \(-0.313225\pi\)
0.553674 + 0.832733i \(0.313225\pi\)
\(632\) 0 0
\(633\) 13.5397 0.538155
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −14.2351 −0.564014
\(638\) 0 0
\(639\) 26.3684 1.04312
\(640\) 0 0
\(641\) 42.8988 1.69440 0.847200 0.531275i \(-0.178287\pi\)
0.847200 + 0.531275i \(0.178287\pi\)
\(642\) 0 0
\(643\) −27.9639 −1.10279 −0.551395 0.834245i \(-0.685904\pi\)
−0.551395 + 0.834245i \(0.685904\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 7.13828 0.280635 0.140317 0.990107i \(-0.455188\pi\)
0.140317 + 0.990107i \(0.455188\pi\)
\(648\) 0 0
\(649\) 19.2257 0.754675
\(650\) 0 0
\(651\) −28.2034 −1.10538
\(652\) 0 0
\(653\) 17.7649 0.695196 0.347598 0.937644i \(-0.386997\pi\)
0.347598 + 0.937644i \(0.386997\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 36.1748 1.41131
\(658\) 0 0
\(659\) −20.1936 −0.786630 −0.393315 0.919404i \(-0.628672\pi\)
−0.393315 + 0.919404i \(0.628672\pi\)
\(660\) 0 0
\(661\) 22.0701 0.858426 0.429213 0.903203i \(-0.358791\pi\)
0.429213 + 0.903203i \(0.358791\pi\)
\(662\) 0 0
\(663\) −44.2034 −1.71672
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −0.949145 −0.0367510
\(668\) 0 0
\(669\) −76.8069 −2.96953
\(670\) 0 0
\(671\) −46.5718 −1.79789
\(672\) 0 0
\(673\) 26.0098 1.00261 0.501303 0.865272i \(-0.332854\pi\)
0.501303 + 0.865272i \(0.332854\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 7.86665 0.302340 0.151170 0.988508i \(-0.451696\pi\)
0.151170 + 0.988508i \(0.451696\pi\)
\(678\) 0 0
\(679\) −48.6735 −1.86792
\(680\) 0 0
\(681\) 35.7748 1.37089
\(682\) 0 0
\(683\) −18.2494 −0.698292 −0.349146 0.937068i \(-0.613528\pi\)
−0.349146 + 0.937068i \(0.613528\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −38.3970 −1.46494
\(688\) 0 0
\(689\) 14.1017 0.537232
\(690\) 0 0
\(691\) 25.2543 0.960718 0.480359 0.877072i \(-0.340506\pi\)
0.480359 + 0.877072i \(0.340506\pi\)
\(692\) 0 0
\(693\) 72.8484 2.76728
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −30.1017 −1.14018
\(698\) 0 0
\(699\) −19.3461 −0.731738
\(700\) 0 0
\(701\) 34.8069 1.31464 0.657319 0.753612i \(-0.271690\pi\)
0.657319 + 0.753612i \(0.271690\pi\)
\(702\) 0 0
\(703\) 36.2864 1.36857
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 69.5022 2.61390
\(708\) 0 0
\(709\) −7.51114 −0.282087 −0.141043 0.990003i \(-0.545046\pi\)
−0.141043 + 0.990003i \(0.545046\pi\)
\(710\) 0 0
\(711\) 28.4701 1.06771
\(712\) 0 0
\(713\) 1.30772 0.0489744
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 66.6548 2.48927
\(718\) 0 0
\(719\) −26.7556 −0.997814 −0.498907 0.866655i \(-0.666265\pi\)
−0.498907 + 0.866655i \(0.666265\pi\)
\(720\) 0 0
\(721\) −11.0638 −0.412036
\(722\) 0 0
\(723\) 40.7654 1.51608
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 25.6271 0.950458 0.475229 0.879862i \(-0.342365\pi\)
0.475229 + 0.879862i \(0.342365\pi\)
\(728\) 0 0
\(729\) −38.6958 −1.43318
\(730\) 0 0
\(731\) −11.3461 −0.419652
\(732\) 0 0
\(733\) 19.6543 0.725949 0.362975 0.931799i \(-0.381761\pi\)
0.362975 + 0.931799i \(0.381761\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 29.5397 1.08811
\(738\) 0 0
\(739\) 32.5433 1.19712 0.598562 0.801077i \(-0.295739\pi\)
0.598562 + 0.801077i \(0.295739\pi\)
\(740\) 0 0
\(741\) −38.4514 −1.41255
\(742\) 0 0
\(743\) −23.1383 −0.848861 −0.424430 0.905461i \(-0.639526\pi\)
−0.424430 + 0.905461i \(0.639526\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −65.9452 −2.41281
\(748\) 0 0
\(749\) 19.0094 0.694587
\(750\) 0 0
\(751\) 2.48886 0.0908199 0.0454099 0.998968i \(-0.485541\pi\)
0.0454099 + 0.998968i \(0.485541\pi\)
\(752\) 0 0
\(753\) 72.3783 2.63761
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −21.2859 −0.773650 −0.386825 0.922153i \(-0.626428\pi\)
−0.386825 + 0.922153i \(0.626428\pi\)
\(758\) 0 0
\(759\) −5.24443 −0.190361
\(760\) 0 0
\(761\) 19.1240 0.693244 0.346622 0.938005i \(-0.387329\pi\)
0.346622 + 0.938005i \(0.387329\pi\)
\(762\) 0 0
\(763\) 30.3970 1.10045
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −13.2444 −0.478229
\(768\) 0 0
\(769\) −33.9625 −1.22472 −0.612360 0.790579i \(-0.709780\pi\)
−0.612360 + 0.790579i \(0.709780\pi\)
\(770\) 0 0
\(771\) −74.6548 −2.68863
\(772\) 0 0
\(773\) 0.133353 0.00479638 0.00239819 0.999997i \(-0.499237\pi\)
0.00239819 + 0.999997i \(0.499237\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 73.5308 2.63790
\(778\) 0 0
\(779\) −26.1847 −0.938164
\(780\) 0 0
\(781\) 18.4889 0.661584
\(782\) 0 0
\(783\) 14.1017 0.503954
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 1.12537 0.0401150 0.0200575 0.999799i \(-0.493615\pi\)
0.0200575 + 0.999799i \(0.493615\pi\)
\(788\) 0 0
\(789\) −7.47949 −0.266277
\(790\) 0 0
\(791\) −19.4291 −0.690820
\(792\) 0 0
\(793\) 32.0830 1.13930
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 5.11108 0.181044 0.0905218 0.995894i \(-0.471147\pi\)
0.0905218 + 0.995894i \(0.471147\pi\)
\(798\) 0 0
\(799\) 30.9590 1.09525
\(800\) 0 0
\(801\) −65.6958 −2.32125
\(802\) 0 0
\(803\) 25.3649 0.895107
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −74.7467 −2.63121
\(808\) 0 0
\(809\) 18.7368 0.658752 0.329376 0.944199i \(-0.393162\pi\)
0.329376 + 0.944199i \(0.393162\pi\)
\(810\) 0 0
\(811\) 37.5210 1.31754 0.658770 0.752344i \(-0.271077\pi\)
0.658770 + 0.752344i \(0.271077\pi\)
\(812\) 0 0
\(813\) 87.6325 3.07341
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −9.86971 −0.345297
\(818\) 0 0
\(819\) −50.1847 −1.75359
\(820\) 0 0
\(821\) 18.4001 0.642166 0.321083 0.947051i \(-0.395953\pi\)
0.321083 + 0.947051i \(0.395953\pi\)
\(822\) 0 0
\(823\) −0.649413 −0.0226371 −0.0113186 0.999936i \(-0.503603\pi\)
−0.0113186 + 0.999936i \(0.503603\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 29.8622 1.03841 0.519205 0.854650i \(-0.326228\pi\)
0.519205 + 0.854650i \(0.326228\pi\)
\(828\) 0 0
\(829\) 21.1753 0.735449 0.367725 0.929935i \(-0.380137\pi\)
0.367725 + 0.929935i \(0.380137\pi\)
\(830\) 0 0
\(831\) −30.5718 −1.06053
\(832\) 0 0
\(833\) −31.5210 −1.09214
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −19.4291 −0.671568
\(838\) 0 0
\(839\) 43.8163 1.51271 0.756353 0.654164i \(-0.226979\pi\)
0.756353 + 0.654164i \(0.226979\pi\)
\(840\) 0 0
\(841\) −25.0000 −0.862069
\(842\) 0 0
\(843\) 23.0509 0.793914
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 12.2997 0.422624
\(848\) 0 0
\(849\) 31.6543 1.08637
\(850\) 0 0
\(851\) −3.40943 −0.116874
\(852\) 0 0
\(853\) −37.7846 −1.29372 −0.646860 0.762608i \(-0.723918\pi\)
−0.646860 + 0.762608i \(0.723918\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 19.5299 0.667128 0.333564 0.942727i \(-0.391749\pi\)
0.333564 + 0.942727i \(0.391749\pi\)
\(858\) 0 0
\(859\) 33.2543 1.13462 0.567311 0.823504i \(-0.307984\pi\)
0.567311 + 0.823504i \(0.307984\pi\)
\(860\) 0 0
\(861\) −53.0607 −1.80830
\(862\) 0 0
\(863\) −44.9733 −1.53091 −0.765454 0.643490i \(-0.777486\pi\)
−0.765454 + 0.643490i \(0.777486\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −48.5259 −1.64803
\(868\) 0 0
\(869\) 19.9625 0.677182
\(870\) 0 0
\(871\) −20.3497 −0.689523
\(872\) 0 0
\(873\) −74.9501 −2.53668
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 8.30819 0.280548 0.140274 0.990113i \(-0.455202\pi\)
0.140274 + 0.990113i \(0.455202\pi\)
\(878\) 0 0
\(879\) 12.8573 0.433665
\(880\) 0 0
\(881\) −39.3689 −1.32637 −0.663186 0.748455i \(-0.730796\pi\)
−0.663186 + 0.748455i \(0.730796\pi\)
\(882\) 0 0
\(883\) −7.29036 −0.245340 −0.122670 0.992447i \(-0.539146\pi\)
−0.122670 + 0.992447i \(0.539146\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −11.1097 −0.373027 −0.186514 0.982452i \(-0.559719\pi\)
−0.186514 + 0.982452i \(0.559719\pi\)
\(888\) 0 0
\(889\) 36.2449 1.21562
\(890\) 0 0
\(891\) 15.9269 0.533570
\(892\) 0 0
\(893\) 26.9304 0.901192
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 3.61285 0.120629
\(898\) 0 0
\(899\) −5.51114 −0.183807
\(900\) 0 0
\(901\) 31.2257 1.04028
\(902\) 0 0
\(903\) −20.0000 −0.665558
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 17.5383 0.582351 0.291175 0.956670i \(-0.405954\pi\)
0.291175 + 0.956670i \(0.405954\pi\)
\(908\) 0 0
\(909\) 107.023 3.54974
\(910\) 0 0
\(911\) −44.4701 −1.47336 −0.736681 0.676241i \(-0.763608\pi\)
−0.736681 + 0.676241i \(0.763608\pi\)
\(912\) 0 0
\(913\) −46.2391 −1.53029
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −16.4415 −0.542948
\(918\) 0 0
\(919\) −7.87955 −0.259922 −0.129961 0.991519i \(-0.541485\pi\)
−0.129961 + 0.991519i \(0.541485\pi\)
\(920\) 0 0
\(921\) −15.3047 −0.504306
\(922\) 0 0
\(923\) −12.7368 −0.419238
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −17.0366 −0.559554
\(928\) 0 0
\(929\) 15.7560 0.516939 0.258470 0.966019i \(-0.416782\pi\)
0.258470 + 0.966019i \(0.416782\pi\)
\(930\) 0 0
\(931\) −27.4193 −0.898630
\(932\) 0 0
\(933\) 1.12399 0.0367976
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 10.2766 0.335720 0.167860 0.985811i \(-0.446314\pi\)
0.167860 + 0.985811i \(0.446314\pi\)
\(938\) 0 0
\(939\) 32.9403 1.07496
\(940\) 0 0
\(941\) 2.53341 0.0825869 0.0412934 0.999147i \(-0.486852\pi\)
0.0412934 + 0.999147i \(0.486852\pi\)
\(942\) 0 0
\(943\) 2.46028 0.0801178
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 1.06821 0.0347121 0.0173560 0.999849i \(-0.494475\pi\)
0.0173560 + 0.999849i \(0.494475\pi\)
\(948\) 0 0
\(949\) −17.4737 −0.567219
\(950\) 0 0
\(951\) −48.5531 −1.57444
\(952\) 0 0
\(953\) 51.6958 1.67459 0.837296 0.546750i \(-0.184135\pi\)
0.837296 + 0.546750i \(0.184135\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 22.1017 0.714447
\(958\) 0 0
\(959\) −40.0000 −1.29167
\(960\) 0 0
\(961\) −23.4068 −0.755059
\(962\) 0 0
\(963\) 29.2716 0.943265
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 52.2623 1.68064 0.840320 0.542090i \(-0.182367\pi\)
0.840320 + 0.542090i \(0.182367\pi\)
\(968\) 0 0
\(969\) −85.1437 −2.73521
\(970\) 0 0
\(971\) 59.3560 1.90482 0.952412 0.304813i \(-0.0985941\pi\)
0.952412 + 0.304813i \(0.0985941\pi\)
\(972\) 0 0
\(973\) −41.6227 −1.33436
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −47.8707 −1.53152 −0.765759 0.643128i \(-0.777637\pi\)
−0.765759 + 0.643128i \(0.777637\pi\)
\(978\) 0 0
\(979\) −46.0642 −1.47222
\(980\) 0 0
\(981\) 46.8069 1.49443
\(982\) 0 0
\(983\) −6.01429 −0.191826 −0.0959130 0.995390i \(-0.530577\pi\)
−0.0959130 + 0.995390i \(0.530577\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 54.5718 1.73704
\(988\) 0 0
\(989\) 0.927346 0.0294879
\(990\) 0 0
\(991\) 19.4291 0.617186 0.308593 0.951194i \(-0.400142\pi\)
0.308593 + 0.951194i \(0.400142\pi\)
\(992\) 0 0
\(993\) 9.68598 0.307375
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −32.1334 −1.01767 −0.508837 0.860863i \(-0.669924\pi\)
−0.508837 + 0.860863i \(0.669924\pi\)
\(998\) 0 0
\(999\) 50.6548 1.60265
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.bq.1.1 3
4.3 odd 2 3200.2.a.bt.1.3 3
5.2 odd 4 640.2.c.a.129.6 yes 6
5.3 odd 4 640.2.c.a.129.1 6
5.4 even 2 3200.2.a.bs.1.3 3
8.3 odd 2 3200.2.a.bo.1.1 3
8.5 even 2 3200.2.a.bv.1.3 3
20.3 even 4 640.2.c.b.129.6 yes 6
20.7 even 4 640.2.c.b.129.1 yes 6
20.19 odd 2 3200.2.a.br.1.1 3
40.3 even 4 640.2.c.c.129.1 yes 6
40.13 odd 4 640.2.c.d.129.6 yes 6
40.19 odd 2 3200.2.a.bu.1.3 3
40.27 even 4 640.2.c.c.129.6 yes 6
40.29 even 2 3200.2.a.bp.1.1 3
40.37 odd 4 640.2.c.d.129.1 yes 6
80.3 even 4 1280.2.f.j.129.2 6
80.13 odd 4 1280.2.f.l.129.6 6
80.27 even 4 1280.2.f.j.129.1 6
80.37 odd 4 1280.2.f.l.129.5 6
80.43 even 4 1280.2.f.k.129.5 6
80.53 odd 4 1280.2.f.i.129.1 6
80.67 even 4 1280.2.f.k.129.6 6
80.77 odd 4 1280.2.f.i.129.2 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
640.2.c.a.129.1 6 5.3 odd 4
640.2.c.a.129.6 yes 6 5.2 odd 4
640.2.c.b.129.1 yes 6 20.7 even 4
640.2.c.b.129.6 yes 6 20.3 even 4
640.2.c.c.129.1 yes 6 40.3 even 4
640.2.c.c.129.6 yes 6 40.27 even 4
640.2.c.d.129.1 yes 6 40.37 odd 4
640.2.c.d.129.6 yes 6 40.13 odd 4
1280.2.f.i.129.1 6 80.53 odd 4
1280.2.f.i.129.2 6 80.77 odd 4
1280.2.f.j.129.1 6 80.27 even 4
1280.2.f.j.129.2 6 80.3 even 4
1280.2.f.k.129.5 6 80.43 even 4
1280.2.f.k.129.6 6 80.67 even 4
1280.2.f.l.129.5 6 80.37 odd 4
1280.2.f.l.129.6 6 80.13 odd 4
3200.2.a.bo.1.1 3 8.3 odd 2
3200.2.a.bp.1.1 3 40.29 even 2
3200.2.a.bq.1.1 3 1.1 even 1 trivial
3200.2.a.br.1.1 3 20.19 odd 2
3200.2.a.bs.1.3 3 5.4 even 2
3200.2.a.bt.1.3 3 4.3 odd 2
3200.2.a.bu.1.3 3 40.19 odd 2
3200.2.a.bv.1.3 3 8.5 even 2