Properties

Label 280.4.a.a.1.1
Level $280$
Weight $4$
Character 280.1
Self dual yes
Analytic conductor $16.521$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 280.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(16.5205348016\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 280.1

$q$-expansion

\(f(q)\) \(=\) \(q-4.00000 q^{3} +5.00000 q^{5} +7.00000 q^{7} -11.0000 q^{9} +O(q^{10})\) \(q-4.00000 q^{3} +5.00000 q^{5} +7.00000 q^{7} -11.0000 q^{9} +20.0000 q^{11} -10.0000 q^{13} -20.0000 q^{15} -14.0000 q^{17} +12.0000 q^{19} -28.0000 q^{21} +104.000 q^{23} +25.0000 q^{25} +152.000 q^{27} -122.000 q^{29} +224.000 q^{31} -80.0000 q^{33} +35.0000 q^{35} +158.000 q^{37} +40.0000 q^{39} +378.000 q^{41} +404.000 q^{43} -55.0000 q^{45} +112.000 q^{47} +49.0000 q^{49} +56.0000 q^{51} +270.000 q^{53} +100.000 q^{55} -48.0000 q^{57} +324.000 q^{59} -186.000 q^{61} -77.0000 q^{63} -50.0000 q^{65} +156.000 q^{67} -416.000 q^{69} -360.000 q^{71} -102.000 q^{73} -100.000 q^{75} +140.000 q^{77} -912.000 q^{79} -311.000 q^{81} +1068.00 q^{83} -70.0000 q^{85} +488.000 q^{87} -1590.00 q^{89} -70.0000 q^{91} -896.000 q^{93} +60.0000 q^{95} +866.000 q^{97} -220.000 q^{99} +O(q^{100})\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −4.00000 −0.769800 −0.384900 0.922958i \(-0.625764\pi\)
−0.384900 + 0.922958i \(0.625764\pi\)
\(4\) 0 0
\(5\) 5.00000 0.447214
\(6\) 0 0
\(7\) 7.00000 0.377964
\(8\) 0 0
\(9\) −11.0000 −0.407407
\(10\) 0 0
\(11\) 20.0000 0.548202 0.274101 0.961701i \(-0.411620\pi\)
0.274101 + 0.961701i \(0.411620\pi\)
\(12\) 0 0
\(13\) −10.0000 −0.213346 −0.106673 0.994294i \(-0.534020\pi\)
−0.106673 + 0.994294i \(0.534020\pi\)
\(14\) 0 0
\(15\) −20.0000 −0.344265
\(16\) 0 0
\(17\) −14.0000 −0.199735 −0.0998676 0.995001i \(-0.531842\pi\)
−0.0998676 + 0.995001i \(0.531842\pi\)
\(18\) 0 0
\(19\) 12.0000 0.144894 0.0724471 0.997372i \(-0.476919\pi\)
0.0724471 + 0.997372i \(0.476919\pi\)
\(20\) 0 0
\(21\) −28.0000 −0.290957
\(22\) 0 0
\(23\) 104.000 0.942848 0.471424 0.881907i \(-0.343740\pi\)
0.471424 + 0.881907i \(0.343740\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 152.000 1.08342
\(28\) 0 0
\(29\) −122.000 −0.781201 −0.390601 0.920560i \(-0.627733\pi\)
−0.390601 + 0.920560i \(0.627733\pi\)
\(30\) 0 0
\(31\) 224.000 1.29779 0.648897 0.760877i \(-0.275231\pi\)
0.648897 + 0.760877i \(0.275231\pi\)
\(32\) 0 0
\(33\) −80.0000 −0.422006
\(34\) 0 0
\(35\) 35.0000 0.169031
\(36\) 0 0
\(37\) 158.000 0.702028 0.351014 0.936370i \(-0.385837\pi\)
0.351014 + 0.936370i \(0.385837\pi\)
\(38\) 0 0
\(39\) 40.0000 0.164234
\(40\) 0 0
\(41\) 378.000 1.43985 0.719923 0.694054i \(-0.244177\pi\)
0.719923 + 0.694054i \(0.244177\pi\)
\(42\) 0 0
\(43\) 404.000 1.43278 0.716389 0.697701i \(-0.245794\pi\)
0.716389 + 0.697701i \(0.245794\pi\)
\(44\) 0 0
\(45\) −55.0000 −0.182198
\(46\) 0 0
\(47\) 112.000 0.347593 0.173797 0.984782i \(-0.444396\pi\)
0.173797 + 0.984782i \(0.444396\pi\)
\(48\) 0 0
\(49\) 49.0000 0.142857
\(50\) 0 0
\(51\) 56.0000 0.153756
\(52\) 0 0
\(53\) 270.000 0.699761 0.349881 0.936794i \(-0.386222\pi\)
0.349881 + 0.936794i \(0.386222\pi\)
\(54\) 0 0
\(55\) 100.000 0.245164
\(56\) 0 0
\(57\) −48.0000 −0.111540
\(58\) 0 0
\(59\) 324.000 0.714936 0.357468 0.933925i \(-0.383640\pi\)
0.357468 + 0.933925i \(0.383640\pi\)
\(60\) 0 0
\(61\) −186.000 −0.390408 −0.195204 0.980763i \(-0.562537\pi\)
−0.195204 + 0.980763i \(0.562537\pi\)
\(62\) 0 0
\(63\) −77.0000 −0.153986
\(64\) 0 0
\(65\) −50.0000 −0.0954113
\(66\) 0 0
\(67\) 156.000 0.284454 0.142227 0.989834i \(-0.454574\pi\)
0.142227 + 0.989834i \(0.454574\pi\)
\(68\) 0 0
\(69\) −416.000 −0.725805
\(70\) 0 0
\(71\) −360.000 −0.601748 −0.300874 0.953664i \(-0.597278\pi\)
−0.300874 + 0.953664i \(0.597278\pi\)
\(72\) 0 0
\(73\) −102.000 −0.163537 −0.0817685 0.996651i \(-0.526057\pi\)
−0.0817685 + 0.996651i \(0.526057\pi\)
\(74\) 0 0
\(75\) −100.000 −0.153960
\(76\) 0 0
\(77\) 140.000 0.207201
\(78\) 0 0
\(79\) −912.000 −1.29884 −0.649418 0.760432i \(-0.724987\pi\)
−0.649418 + 0.760432i \(0.724987\pi\)
\(80\) 0 0
\(81\) −311.000 −0.426612
\(82\) 0 0
\(83\) 1068.00 1.41239 0.706194 0.708018i \(-0.250411\pi\)
0.706194 + 0.708018i \(0.250411\pi\)
\(84\) 0 0
\(85\) −70.0000 −0.0893243
\(86\) 0 0
\(87\) 488.000 0.601369
\(88\) 0 0
\(89\) −1590.00 −1.89370 −0.946852 0.321669i \(-0.895756\pi\)
−0.946852 + 0.321669i \(0.895756\pi\)
\(90\) 0 0
\(91\) −70.0000 −0.0806373
\(92\) 0 0
\(93\) −896.000 −0.999042
\(94\) 0 0
\(95\) 60.0000 0.0647986
\(96\) 0 0
\(97\) 866.000 0.906484 0.453242 0.891387i \(-0.350267\pi\)
0.453242 + 0.891387i \(0.350267\pi\)
\(98\) 0 0
\(99\) −220.000 −0.223342
\(100\) 0 0
\(101\) 702.000 0.691600 0.345800 0.938308i \(-0.387608\pi\)
0.345800 + 0.938308i \(0.387608\pi\)
\(102\) 0 0
\(103\) −296.000 −0.283163 −0.141581 0.989927i \(-0.545219\pi\)
−0.141581 + 0.989927i \(0.545219\pi\)
\(104\) 0 0
\(105\) −140.000 −0.130120
\(106\) 0 0
\(107\) −44.0000 −0.0397537 −0.0198768 0.999802i \(-0.506327\pi\)
−0.0198768 + 0.999802i \(0.506327\pi\)
\(108\) 0 0
\(109\) −650.000 −0.571181 −0.285590 0.958352i \(-0.592190\pi\)
−0.285590 + 0.958352i \(0.592190\pi\)
\(110\) 0 0
\(111\) −632.000 −0.540421
\(112\) 0 0
\(113\) −942.000 −0.784212 −0.392106 0.919920i \(-0.628253\pi\)
−0.392106 + 0.919920i \(0.628253\pi\)
\(114\) 0 0
\(115\) 520.000 0.421654
\(116\) 0 0
\(117\) 110.000 0.0869188
\(118\) 0 0
\(119\) −98.0000 −0.0754928
\(120\) 0 0
\(121\) −931.000 −0.699474
\(122\) 0 0
\(123\) −1512.00 −1.10839
\(124\) 0 0
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) 736.000 0.514248 0.257124 0.966378i \(-0.417225\pi\)
0.257124 + 0.966378i \(0.417225\pi\)
\(128\) 0 0
\(129\) −1616.00 −1.10295
\(130\) 0 0
\(131\) 924.000 0.616261 0.308131 0.951344i \(-0.400297\pi\)
0.308131 + 0.951344i \(0.400297\pi\)
\(132\) 0 0
\(133\) 84.0000 0.0547648
\(134\) 0 0
\(135\) 760.000 0.484521
\(136\) 0 0
\(137\) 474.000 0.295595 0.147798 0.989018i \(-0.452782\pi\)
0.147798 + 0.989018i \(0.452782\pi\)
\(138\) 0 0
\(139\) 1012.00 0.617530 0.308765 0.951138i \(-0.400084\pi\)
0.308765 + 0.951138i \(0.400084\pi\)
\(140\) 0 0
\(141\) −448.000 −0.267577
\(142\) 0 0
\(143\) −200.000 −0.116957
\(144\) 0 0
\(145\) −610.000 −0.349364
\(146\) 0 0
\(147\) −196.000 −0.109971
\(148\) 0 0
\(149\) 302.000 0.166046 0.0830228 0.996548i \(-0.473543\pi\)
0.0830228 + 0.996548i \(0.473543\pi\)
\(150\) 0 0
\(151\) −2104.00 −1.13391 −0.566957 0.823747i \(-0.691880\pi\)
−0.566957 + 0.823747i \(0.691880\pi\)
\(152\) 0 0
\(153\) 154.000 0.0813736
\(154\) 0 0
\(155\) 1120.00 0.580391
\(156\) 0 0
\(157\) 1190.00 0.604919 0.302460 0.953162i \(-0.402192\pi\)
0.302460 + 0.953162i \(0.402192\pi\)
\(158\) 0 0
\(159\) −1080.00 −0.538677
\(160\) 0 0
\(161\) 728.000 0.356363
\(162\) 0 0
\(163\) −1732.00 −0.832274 −0.416137 0.909302i \(-0.636616\pi\)
−0.416137 + 0.909302i \(0.636616\pi\)
\(164\) 0 0
\(165\) −400.000 −0.188727
\(166\) 0 0
\(167\) 2264.00 1.04906 0.524532 0.851391i \(-0.324240\pi\)
0.524532 + 0.851391i \(0.324240\pi\)
\(168\) 0 0
\(169\) −2097.00 −0.954483
\(170\) 0 0
\(171\) −132.000 −0.0590309
\(172\) 0 0
\(173\) −1066.00 −0.468477 −0.234238 0.972179i \(-0.575260\pi\)
−0.234238 + 0.972179i \(0.575260\pi\)
\(174\) 0 0
\(175\) 175.000 0.0755929
\(176\) 0 0
\(177\) −1296.00 −0.550358
\(178\) 0 0
\(179\) −2356.00 −0.983775 −0.491887 0.870659i \(-0.663693\pi\)
−0.491887 + 0.870659i \(0.663693\pi\)
\(180\) 0 0
\(181\) 2158.00 0.886204 0.443102 0.896471i \(-0.353878\pi\)
0.443102 + 0.896471i \(0.353878\pi\)
\(182\) 0 0
\(183\) 744.000 0.300536
\(184\) 0 0
\(185\) 790.000 0.313957
\(186\) 0 0
\(187\) −280.000 −0.109495
\(188\) 0 0
\(189\) 1064.00 0.409495
\(190\) 0 0
\(191\) −2688.00 −1.01831 −0.509154 0.860675i \(-0.670042\pi\)
−0.509154 + 0.860675i \(0.670042\pi\)
\(192\) 0 0
\(193\) −4414.00 −1.64625 −0.823126 0.567859i \(-0.807772\pi\)
−0.823126 + 0.567859i \(0.807772\pi\)
\(194\) 0 0
\(195\) 200.000 0.0734477
\(196\) 0 0
\(197\) 3774.00 1.36491 0.682453 0.730930i \(-0.260913\pi\)
0.682453 + 0.730930i \(0.260913\pi\)
\(198\) 0 0
\(199\) 664.000 0.236531 0.118266 0.992982i \(-0.462267\pi\)
0.118266 + 0.992982i \(0.462267\pi\)
\(200\) 0 0
\(201\) −624.000 −0.218973
\(202\) 0 0
\(203\) −854.000 −0.295266
\(204\) 0 0
\(205\) 1890.00 0.643919
\(206\) 0 0
\(207\) −1144.00 −0.384123
\(208\) 0 0
\(209\) 240.000 0.0794313
\(210\) 0 0
\(211\) 1260.00 0.411099 0.205550 0.978647i \(-0.434102\pi\)
0.205550 + 0.978647i \(0.434102\pi\)
\(212\) 0 0
\(213\) 1440.00 0.463226
\(214\) 0 0
\(215\) 2020.00 0.640757
\(216\) 0 0
\(217\) 1568.00 0.490520
\(218\) 0 0
\(219\) 408.000 0.125891
\(220\) 0 0
\(221\) 140.000 0.0426128
\(222\) 0 0
\(223\) −1152.00 −0.345936 −0.172968 0.984927i \(-0.555336\pi\)
−0.172968 + 0.984927i \(0.555336\pi\)
\(224\) 0 0
\(225\) −275.000 −0.0814815
\(226\) 0 0
\(227\) 2588.00 0.756703 0.378352 0.925662i \(-0.376491\pi\)
0.378352 + 0.925662i \(0.376491\pi\)
\(228\) 0 0
\(229\) 766.000 0.221042 0.110521 0.993874i \(-0.464748\pi\)
0.110521 + 0.993874i \(0.464748\pi\)
\(230\) 0 0
\(231\) −560.000 −0.159503
\(232\) 0 0
\(233\) 6138.00 1.72581 0.862905 0.505366i \(-0.168643\pi\)
0.862905 + 0.505366i \(0.168643\pi\)
\(234\) 0 0
\(235\) 560.000 0.155448
\(236\) 0 0
\(237\) 3648.00 0.999844
\(238\) 0 0
\(239\) 3856.00 1.04361 0.521807 0.853063i \(-0.325258\pi\)
0.521807 + 0.853063i \(0.325258\pi\)
\(240\) 0 0
\(241\) 2578.00 0.689060 0.344530 0.938775i \(-0.388038\pi\)
0.344530 + 0.938775i \(0.388038\pi\)
\(242\) 0 0
\(243\) −2860.00 −0.755017
\(244\) 0 0
\(245\) 245.000 0.0638877
\(246\) 0 0
\(247\) −120.000 −0.0309126
\(248\) 0 0
\(249\) −4272.00 −1.08726
\(250\) 0 0
\(251\) −1404.00 −0.353067 −0.176533 0.984295i \(-0.556488\pi\)
−0.176533 + 0.984295i \(0.556488\pi\)
\(252\) 0 0
\(253\) 2080.00 0.516871
\(254\) 0 0
\(255\) 280.000 0.0687619
\(256\) 0 0
\(257\) 2946.00 0.715044 0.357522 0.933905i \(-0.383622\pi\)
0.357522 + 0.933905i \(0.383622\pi\)
\(258\) 0 0
\(259\) 1106.00 0.265342
\(260\) 0 0
\(261\) 1342.00 0.318267
\(262\) 0 0
\(263\) −3080.00 −0.722133 −0.361066 0.932540i \(-0.617587\pi\)
−0.361066 + 0.932540i \(0.617587\pi\)
\(264\) 0 0
\(265\) 1350.00 0.312943
\(266\) 0 0
\(267\) 6360.00 1.45777
\(268\) 0 0
\(269\) 2294.00 0.519954 0.259977 0.965615i \(-0.416285\pi\)
0.259977 + 0.965615i \(0.416285\pi\)
\(270\) 0 0
\(271\) −3728.00 −0.835645 −0.417823 0.908529i \(-0.637207\pi\)
−0.417823 + 0.908529i \(0.637207\pi\)
\(272\) 0 0
\(273\) 280.000 0.0620746
\(274\) 0 0
\(275\) 500.000 0.109640
\(276\) 0 0
\(277\) 2734.00 0.593033 0.296516 0.955028i \(-0.404175\pi\)
0.296516 + 0.955028i \(0.404175\pi\)
\(278\) 0 0
\(279\) −2464.00 −0.528731
\(280\) 0 0
\(281\) 1034.00 0.219513 0.109757 0.993958i \(-0.464993\pi\)
0.109757 + 0.993958i \(0.464993\pi\)
\(282\) 0 0
\(283\) −5180.00 −1.08805 −0.544027 0.839068i \(-0.683101\pi\)
−0.544027 + 0.839068i \(0.683101\pi\)
\(284\) 0 0
\(285\) −240.000 −0.0498820
\(286\) 0 0
\(287\) 2646.00 0.544211
\(288\) 0 0
\(289\) −4717.00 −0.960106
\(290\) 0 0
\(291\) −3464.00 −0.697812
\(292\) 0 0
\(293\) 7934.00 1.58194 0.790971 0.611853i \(-0.209576\pi\)
0.790971 + 0.611853i \(0.209576\pi\)
\(294\) 0 0
\(295\) 1620.00 0.319729
\(296\) 0 0
\(297\) 3040.00 0.593935
\(298\) 0 0
\(299\) −1040.00 −0.201153
\(300\) 0 0
\(301\) 2828.00 0.541539
\(302\) 0 0
\(303\) −2808.00 −0.532394
\(304\) 0 0
\(305\) −930.000 −0.174596
\(306\) 0 0
\(307\) −3444.00 −0.640259 −0.320129 0.947374i \(-0.603726\pi\)
−0.320129 + 0.947374i \(0.603726\pi\)
\(308\) 0 0
\(309\) 1184.00 0.217979
\(310\) 0 0
\(311\) 7656.00 1.39592 0.697961 0.716135i \(-0.254091\pi\)
0.697961 + 0.716135i \(0.254091\pi\)
\(312\) 0 0
\(313\) −3798.00 −0.685865 −0.342932 0.939360i \(-0.611420\pi\)
−0.342932 + 0.939360i \(0.611420\pi\)
\(314\) 0 0
\(315\) −385.000 −0.0688644
\(316\) 0 0
\(317\) 6822.00 1.20871 0.604356 0.796714i \(-0.293430\pi\)
0.604356 + 0.796714i \(0.293430\pi\)
\(318\) 0 0
\(319\) −2440.00 −0.428256
\(320\) 0 0
\(321\) 176.000 0.0306024
\(322\) 0 0
\(323\) −168.000 −0.0289405
\(324\) 0 0
\(325\) −250.000 −0.0426692
\(326\) 0 0
\(327\) 2600.00 0.439695
\(328\) 0 0
\(329\) 784.000 0.131378
\(330\) 0 0
\(331\) −6572.00 −1.09133 −0.545664 0.838004i \(-0.683723\pi\)
−0.545664 + 0.838004i \(0.683723\pi\)
\(332\) 0 0
\(333\) −1738.00 −0.286011
\(334\) 0 0
\(335\) 780.000 0.127212
\(336\) 0 0
\(337\) −11022.0 −1.78162 −0.890811 0.454374i \(-0.849863\pi\)
−0.890811 + 0.454374i \(0.849863\pi\)
\(338\) 0 0
\(339\) 3768.00 0.603686
\(340\) 0 0
\(341\) 4480.00 0.711453
\(342\) 0 0
\(343\) 343.000 0.0539949
\(344\) 0 0
\(345\) −2080.00 −0.324590
\(346\) 0 0
\(347\) −10908.0 −1.68753 −0.843764 0.536715i \(-0.819665\pi\)
−0.843764 + 0.536715i \(0.819665\pi\)
\(348\) 0 0
\(349\) −12058.0 −1.84943 −0.924713 0.380664i \(-0.875695\pi\)
−0.924713 + 0.380664i \(0.875695\pi\)
\(350\) 0 0
\(351\) −1520.00 −0.231144
\(352\) 0 0
\(353\) 1570.00 0.236721 0.118361 0.992971i \(-0.462236\pi\)
0.118361 + 0.992971i \(0.462236\pi\)
\(354\) 0 0
\(355\) −1800.00 −0.269110
\(356\) 0 0
\(357\) 392.000 0.0581144
\(358\) 0 0
\(359\) 120.000 0.0176417 0.00882083 0.999961i \(-0.497192\pi\)
0.00882083 + 0.999961i \(0.497192\pi\)
\(360\) 0 0
\(361\) −6715.00 −0.979006
\(362\) 0 0
\(363\) 3724.00 0.538455
\(364\) 0 0
\(365\) −510.000 −0.0731359
\(366\) 0 0
\(367\) 4336.00 0.616723 0.308362 0.951269i \(-0.400219\pi\)
0.308362 + 0.951269i \(0.400219\pi\)
\(368\) 0 0
\(369\) −4158.00 −0.586604
\(370\) 0 0
\(371\) 1890.00 0.264485
\(372\) 0 0
\(373\) 7758.00 1.07693 0.538464 0.842649i \(-0.319005\pi\)
0.538464 + 0.842649i \(0.319005\pi\)
\(374\) 0 0
\(375\) −500.000 −0.0688530
\(376\) 0 0
\(377\) 1220.00 0.166666
\(378\) 0 0
\(379\) 10660.0 1.44477 0.722384 0.691492i \(-0.243046\pi\)
0.722384 + 0.691492i \(0.243046\pi\)
\(380\) 0 0
\(381\) −2944.00 −0.395868
\(382\) 0 0
\(383\) −14304.0 −1.90836 −0.954178 0.299240i \(-0.903267\pi\)
−0.954178 + 0.299240i \(0.903267\pi\)
\(384\) 0 0
\(385\) 700.000 0.0926631
\(386\) 0 0
\(387\) −4444.00 −0.583724
\(388\) 0 0
\(389\) −11970.0 −1.56016 −0.780081 0.625678i \(-0.784822\pi\)
−0.780081 + 0.625678i \(0.784822\pi\)
\(390\) 0 0
\(391\) −1456.00 −0.188320
\(392\) 0 0
\(393\) −3696.00 −0.474398
\(394\) 0 0
\(395\) −4560.00 −0.580857
\(396\) 0 0
\(397\) −4106.00 −0.519079 −0.259539 0.965733i \(-0.583571\pi\)
−0.259539 + 0.965733i \(0.583571\pi\)
\(398\) 0 0
\(399\) −336.000 −0.0421580
\(400\) 0 0
\(401\) −3790.00 −0.471979 −0.235989 0.971756i \(-0.575833\pi\)
−0.235989 + 0.971756i \(0.575833\pi\)
\(402\) 0 0
\(403\) −2240.00 −0.276879
\(404\) 0 0
\(405\) −1555.00 −0.190787
\(406\) 0 0
\(407\) 3160.00 0.384854
\(408\) 0 0
\(409\) −13366.0 −1.61591 −0.807954 0.589246i \(-0.799425\pi\)
−0.807954 + 0.589246i \(0.799425\pi\)
\(410\) 0 0
\(411\) −1896.00 −0.227549
\(412\) 0 0
\(413\) 2268.00 0.270220
\(414\) 0 0
\(415\) 5340.00 0.631639
\(416\) 0 0
\(417\) −4048.00 −0.475375
\(418\) 0 0
\(419\) 6524.00 0.760664 0.380332 0.924850i \(-0.375810\pi\)
0.380332 + 0.924850i \(0.375810\pi\)
\(420\) 0 0
\(421\) −2978.00 −0.344748 −0.172374 0.985032i \(-0.555144\pi\)
−0.172374 + 0.985032i \(0.555144\pi\)
\(422\) 0 0
\(423\) −1232.00 −0.141612
\(424\) 0 0
\(425\) −350.000 −0.0399470
\(426\) 0 0
\(427\) −1302.00 −0.147560
\(428\) 0 0
\(429\) 800.000 0.0900335
\(430\) 0 0
\(431\) 15760.0 1.76133 0.880664 0.473741i \(-0.157097\pi\)
0.880664 + 0.473741i \(0.157097\pi\)
\(432\) 0 0
\(433\) 10322.0 1.14560 0.572799 0.819696i \(-0.305858\pi\)
0.572799 + 0.819696i \(0.305858\pi\)
\(434\) 0 0
\(435\) 2440.00 0.268940
\(436\) 0 0
\(437\) 1248.00 0.136613
\(438\) 0 0
\(439\) −344.000 −0.0373991 −0.0186996 0.999825i \(-0.505953\pi\)
−0.0186996 + 0.999825i \(0.505953\pi\)
\(440\) 0 0
\(441\) −539.000 −0.0582011
\(442\) 0 0
\(443\) −252.000 −0.0270268 −0.0135134 0.999909i \(-0.504302\pi\)
−0.0135134 + 0.999909i \(0.504302\pi\)
\(444\) 0 0
\(445\) −7950.00 −0.846890
\(446\) 0 0
\(447\) −1208.00 −0.127822
\(448\) 0 0
\(449\) −11966.0 −1.25771 −0.628854 0.777524i \(-0.716475\pi\)
−0.628854 + 0.777524i \(0.716475\pi\)
\(450\) 0 0
\(451\) 7560.00 0.789327
\(452\) 0 0
\(453\) 8416.00 0.872888
\(454\) 0 0
\(455\) −350.000 −0.0360621
\(456\) 0 0
\(457\) −15846.0 −1.62198 −0.810990 0.585060i \(-0.801071\pi\)
−0.810990 + 0.585060i \(0.801071\pi\)
\(458\) 0 0
\(459\) −2128.00 −0.216398
\(460\) 0 0
\(461\) 5430.00 0.548591 0.274295 0.961645i \(-0.411555\pi\)
0.274295 + 0.961645i \(0.411555\pi\)
\(462\) 0 0
\(463\) 8912.00 0.894548 0.447274 0.894397i \(-0.352395\pi\)
0.447274 + 0.894397i \(0.352395\pi\)
\(464\) 0 0
\(465\) −4480.00 −0.446785
\(466\) 0 0
\(467\) −11028.0 −1.09275 −0.546376 0.837540i \(-0.683993\pi\)
−0.546376 + 0.837540i \(0.683993\pi\)
\(468\) 0 0
\(469\) 1092.00 0.107514
\(470\) 0 0
\(471\) −4760.00 −0.465667
\(472\) 0 0
\(473\) 8080.00 0.785452
\(474\) 0 0
\(475\) 300.000 0.0289788
\(476\) 0 0
\(477\) −2970.00 −0.285088
\(478\) 0 0
\(479\) 5856.00 0.558596 0.279298 0.960204i \(-0.409898\pi\)
0.279298 + 0.960204i \(0.409898\pi\)
\(480\) 0 0
\(481\) −1580.00 −0.149775
\(482\) 0 0
\(483\) −2912.00 −0.274328
\(484\) 0 0
\(485\) 4330.00 0.405392
\(486\) 0 0
\(487\) 10264.0 0.955044 0.477522 0.878620i \(-0.341535\pi\)
0.477522 + 0.878620i \(0.341535\pi\)
\(488\) 0 0
\(489\) 6928.00 0.640685
\(490\) 0 0
\(491\) 2804.00 0.257725 0.128862 0.991663i \(-0.458867\pi\)
0.128862 + 0.991663i \(0.458867\pi\)
\(492\) 0 0
\(493\) 1708.00 0.156033
\(494\) 0 0
\(495\) −1100.00 −0.0998815
\(496\) 0 0
\(497\) −2520.00 −0.227440
\(498\) 0 0
\(499\) 8716.00 0.781927 0.390964 0.920406i \(-0.372142\pi\)
0.390964 + 0.920406i \(0.372142\pi\)
\(500\) 0 0
\(501\) −9056.00 −0.807569
\(502\) 0 0
\(503\) 2504.00 0.221964 0.110982 0.993822i \(-0.464600\pi\)
0.110982 + 0.993822i \(0.464600\pi\)
\(504\) 0 0
\(505\) 3510.00 0.309293
\(506\) 0 0
\(507\) 8388.00 0.734762
\(508\) 0 0
\(509\) 17094.0 1.48856 0.744281 0.667866i \(-0.232792\pi\)
0.744281 + 0.667866i \(0.232792\pi\)
\(510\) 0 0
\(511\) −714.000 −0.0618112
\(512\) 0 0
\(513\) 1824.00 0.156982
\(514\) 0 0
\(515\) −1480.00 −0.126634
\(516\) 0 0
\(517\) 2240.00 0.190551
\(518\) 0 0
\(519\) 4264.00 0.360634
\(520\) 0 0
\(521\) 9882.00 0.830976 0.415488 0.909599i \(-0.363611\pi\)
0.415488 + 0.909599i \(0.363611\pi\)
\(522\) 0 0
\(523\) −7532.00 −0.629735 −0.314867 0.949136i \(-0.601960\pi\)
−0.314867 + 0.949136i \(0.601960\pi\)
\(524\) 0 0
\(525\) −700.000 −0.0581914
\(526\) 0 0
\(527\) −3136.00 −0.259215
\(528\) 0 0
\(529\) −1351.00 −0.111038
\(530\) 0 0
\(531\) −3564.00 −0.291270
\(532\) 0 0
\(533\) −3780.00 −0.307186
\(534\) 0 0
\(535\) −220.000 −0.0177784
\(536\) 0 0
\(537\) 9424.00 0.757310
\(538\) 0 0
\(539\) 980.000 0.0783146
\(540\) 0 0
\(541\) −17338.0 −1.37785 −0.688927 0.724831i \(-0.741918\pi\)
−0.688927 + 0.724831i \(0.741918\pi\)
\(542\) 0 0
\(543\) −8632.00 −0.682200
\(544\) 0 0
\(545\) −3250.00 −0.255440
\(546\) 0 0
\(547\) 764.000 0.0597190 0.0298595 0.999554i \(-0.490494\pi\)
0.0298595 + 0.999554i \(0.490494\pi\)
\(548\) 0 0
\(549\) 2046.00 0.159055
\(550\) 0 0
\(551\) −1464.00 −0.113191
\(552\) 0 0
\(553\) −6384.00 −0.490914
\(554\) 0 0
\(555\) −3160.00 −0.241684
\(556\) 0 0
\(557\) −2442.00 −0.185765 −0.0928823 0.995677i \(-0.529608\pi\)
−0.0928823 + 0.995677i \(0.529608\pi\)
\(558\) 0 0
\(559\) −4040.00 −0.305678
\(560\) 0 0
\(561\) 1120.00 0.0842895
\(562\) 0 0
\(563\) 8972.00 0.671625 0.335812 0.941929i \(-0.390989\pi\)
0.335812 + 0.941929i \(0.390989\pi\)
\(564\) 0 0
\(565\) −4710.00 −0.350710
\(566\) 0 0
\(567\) −2177.00 −0.161244
\(568\) 0 0
\(569\) 8682.00 0.639663 0.319832 0.947474i \(-0.396374\pi\)
0.319832 + 0.947474i \(0.396374\pi\)
\(570\) 0 0
\(571\) 15524.0 1.13776 0.568878 0.822422i \(-0.307377\pi\)
0.568878 + 0.822422i \(0.307377\pi\)
\(572\) 0 0
\(573\) 10752.0 0.783894
\(574\) 0 0
\(575\) 2600.00 0.188570
\(576\) 0 0
\(577\) −19774.0 −1.42669 −0.713347 0.700811i \(-0.752822\pi\)
−0.713347 + 0.700811i \(0.752822\pi\)
\(578\) 0 0
\(579\) 17656.0 1.26729
\(580\) 0 0
\(581\) 7476.00 0.533833
\(582\) 0 0
\(583\) 5400.00 0.383611
\(584\) 0 0
\(585\) 550.000 0.0388713
\(586\) 0 0
\(587\) −6700.00 −0.471105 −0.235552 0.971862i \(-0.575690\pi\)
−0.235552 + 0.971862i \(0.575690\pi\)
\(588\) 0 0
\(589\) 2688.00 0.188043
\(590\) 0 0
\(591\) −15096.0 −1.05070
\(592\) 0 0
\(593\) −1294.00 −0.0896091 −0.0448046 0.998996i \(-0.514267\pi\)
−0.0448046 + 0.998996i \(0.514267\pi\)
\(594\) 0 0
\(595\) −490.000 −0.0337614
\(596\) 0 0
\(597\) −2656.00 −0.182082
\(598\) 0 0
\(599\) 19720.0 1.34514 0.672569 0.740035i \(-0.265191\pi\)
0.672569 + 0.740035i \(0.265191\pi\)
\(600\) 0 0
\(601\) 21450.0 1.45585 0.727923 0.685659i \(-0.240486\pi\)
0.727923 + 0.685659i \(0.240486\pi\)
\(602\) 0 0
\(603\) −1716.00 −0.115889
\(604\) 0 0
\(605\) −4655.00 −0.312814
\(606\) 0 0
\(607\) −19264.0 −1.28814 −0.644071 0.764966i \(-0.722756\pi\)
−0.644071 + 0.764966i \(0.722756\pi\)
\(608\) 0 0
\(609\) 3416.00 0.227296
\(610\) 0 0
\(611\) −1120.00 −0.0741577
\(612\) 0 0
\(613\) 13150.0 0.866433 0.433217 0.901290i \(-0.357379\pi\)
0.433217 + 0.901290i \(0.357379\pi\)
\(614\) 0 0
\(615\) −7560.00 −0.495689
\(616\) 0 0
\(617\) −15238.0 −0.994261 −0.497130 0.867676i \(-0.665613\pi\)
−0.497130 + 0.867676i \(0.665613\pi\)
\(618\) 0 0
\(619\) 23764.0 1.54306 0.771531 0.636191i \(-0.219491\pi\)
0.771531 + 0.636191i \(0.219491\pi\)
\(620\) 0 0
\(621\) 15808.0 1.02150
\(622\) 0 0
\(623\) −11130.0 −0.715753
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) −960.000 −0.0611463
\(628\) 0 0
\(629\) −2212.00 −0.140220
\(630\) 0 0
\(631\) −2008.00 −0.126683 −0.0633417 0.997992i \(-0.520176\pi\)
−0.0633417 + 0.997992i \(0.520176\pi\)
\(632\) 0 0
\(633\) −5040.00 −0.316464
\(634\) 0 0
\(635\) 3680.00 0.229978
\(636\) 0 0
\(637\) −490.000 −0.0304780
\(638\) 0 0
\(639\) 3960.00 0.245157
\(640\) 0 0
\(641\) 13058.0 0.804618 0.402309 0.915504i \(-0.368208\pi\)
0.402309 + 0.915504i \(0.368208\pi\)
\(642\) 0 0
\(643\) 24188.0 1.48349 0.741743 0.670684i \(-0.233999\pi\)
0.741743 + 0.670684i \(0.233999\pi\)
\(644\) 0 0
\(645\) −8080.00 −0.493255
\(646\) 0 0
\(647\) 6648.00 0.403956 0.201978 0.979390i \(-0.435263\pi\)
0.201978 + 0.979390i \(0.435263\pi\)
\(648\) 0 0
\(649\) 6480.00 0.391930
\(650\) 0 0
\(651\) −6272.00 −0.377602
\(652\) 0 0
\(653\) 9814.00 0.588134 0.294067 0.955785i \(-0.404991\pi\)
0.294067 + 0.955785i \(0.404991\pi\)
\(654\) 0 0
\(655\) 4620.00 0.275601
\(656\) 0 0
\(657\) 1122.00 0.0666262
\(658\) 0 0
\(659\) 26540.0 1.56882 0.784409 0.620243i \(-0.212966\pi\)
0.784409 + 0.620243i \(0.212966\pi\)
\(660\) 0 0
\(661\) −1330.00 −0.0782617 −0.0391309 0.999234i \(-0.512459\pi\)
−0.0391309 + 0.999234i \(0.512459\pi\)
\(662\) 0 0
\(663\) −560.000 −0.0328033
\(664\) 0 0
\(665\) 420.000 0.0244916
\(666\) 0 0
\(667\) −12688.0 −0.736554
\(668\) 0 0
\(669\) 4608.00 0.266301
\(670\) 0 0
\(671\) −3720.00 −0.214022
\(672\) 0 0
\(673\) −17950.0 −1.02812 −0.514058 0.857756i \(-0.671858\pi\)
−0.514058 + 0.857756i \(0.671858\pi\)
\(674\) 0 0
\(675\) 3800.00 0.216685
\(676\) 0 0
\(677\) 23742.0 1.34783 0.673914 0.738810i \(-0.264612\pi\)
0.673914 + 0.738810i \(0.264612\pi\)
\(678\) 0 0
\(679\) 6062.00 0.342619
\(680\) 0 0
\(681\) −10352.0 −0.582510
\(682\) 0 0
\(683\) 6356.00 0.356084 0.178042 0.984023i \(-0.443024\pi\)
0.178042 + 0.984023i \(0.443024\pi\)
\(684\) 0 0
\(685\) 2370.00 0.132194
\(686\) 0 0
\(687\) −3064.00 −0.170159
\(688\) 0 0
\(689\) −2700.00 −0.149291
\(690\) 0 0
\(691\) −3156.00 −0.173748 −0.0868740 0.996219i \(-0.527688\pi\)
−0.0868740 + 0.996219i \(0.527688\pi\)
\(692\) 0 0
\(693\) −1540.00 −0.0844152
\(694\) 0 0
\(695\) 5060.00 0.276168
\(696\) 0 0
\(697\) −5292.00 −0.287588
\(698\) 0 0
\(699\) −24552.0 −1.32853
\(700\) 0 0
\(701\) −18330.0 −0.987610 −0.493805 0.869573i \(-0.664394\pi\)
−0.493805 + 0.869573i \(0.664394\pi\)
\(702\) 0 0
\(703\) 1896.00 0.101720
\(704\) 0 0
\(705\) −2240.00 −0.119664
\(706\) 0 0
\(707\) 4914.00 0.261400
\(708\) 0 0
\(709\) 19070.0 1.01014 0.505070 0.863079i \(-0.331467\pi\)
0.505070 + 0.863079i \(0.331467\pi\)
\(710\) 0 0
\(711\) 10032.0 0.529155
\(712\) 0 0
\(713\) 23296.0 1.22362
\(714\) 0 0
\(715\) −1000.00 −0.0523047
\(716\) 0 0
\(717\) −15424.0 −0.803375
\(718\) 0 0
\(719\) −4176.00 −0.216604 −0.108302 0.994118i \(-0.534541\pi\)
−0.108302 + 0.994118i \(0.534541\pi\)
\(720\) 0 0
\(721\) −2072.00 −0.107025
\(722\) 0 0
\(723\) −10312.0 −0.530439
\(724\) 0 0
\(725\) −3050.00 −0.156240
\(726\) 0 0
\(727\) −10520.0 −0.536678 −0.268339 0.963324i \(-0.586475\pi\)
−0.268339 + 0.963324i \(0.586475\pi\)
\(728\) 0 0
\(729\) 19837.0 1.00782
\(730\) 0 0
\(731\) −5656.00 −0.286176
\(732\) 0 0
\(733\) −6874.00 −0.346381 −0.173190 0.984888i \(-0.555408\pi\)
−0.173190 + 0.984888i \(0.555408\pi\)
\(734\) 0 0
\(735\) −980.000 −0.0491807
\(736\) 0 0
\(737\) 3120.00 0.155939
\(738\) 0 0
\(739\) 11804.0 0.587574 0.293787 0.955871i \(-0.405084\pi\)
0.293787 + 0.955871i \(0.405084\pi\)
\(740\) 0 0
\(741\) 480.000 0.0237965
\(742\) 0 0
\(743\) −20648.0 −1.01952 −0.509759 0.860317i \(-0.670265\pi\)
−0.509759 + 0.860317i \(0.670265\pi\)
\(744\) 0 0
\(745\) 1510.00 0.0742579
\(746\) 0 0
\(747\) −11748.0 −0.575417
\(748\) 0 0
\(749\) −308.000 −0.0150255
\(750\) 0 0
\(751\) 1232.00 0.0598619 0.0299310 0.999552i \(-0.490471\pi\)
0.0299310 + 0.999552i \(0.490471\pi\)
\(752\) 0 0
\(753\) 5616.00 0.271791
\(754\) 0 0
\(755\) −10520.0 −0.507102
\(756\) 0 0
\(757\) −11250.0 −0.540143 −0.270071 0.962840i \(-0.587047\pi\)
−0.270071 + 0.962840i \(0.587047\pi\)
\(758\) 0 0
\(759\) −8320.00 −0.397888
\(760\) 0 0
\(761\) 14698.0 0.700134 0.350067 0.936725i \(-0.386159\pi\)
0.350067 + 0.936725i \(0.386159\pi\)
\(762\) 0 0
\(763\) −4550.00 −0.215886
\(764\) 0 0
\(765\) 770.000 0.0363914
\(766\) 0 0
\(767\) −3240.00 −0.152529
\(768\) 0 0
\(769\) −30014.0 −1.40745 −0.703727 0.710470i \(-0.748482\pi\)
−0.703727 + 0.710470i \(0.748482\pi\)
\(770\) 0 0
\(771\) −11784.0 −0.550441
\(772\) 0 0
\(773\) −34018.0 −1.58285 −0.791425 0.611267i \(-0.790660\pi\)
−0.791425 + 0.611267i \(0.790660\pi\)
\(774\) 0 0
\(775\) 5600.00 0.259559
\(776\) 0 0
\(777\) −4424.00 −0.204260
\(778\) 0 0
\(779\) 4536.00 0.208625
\(780\) 0 0
\(781\) −7200.00 −0.329880
\(782\) 0 0
\(783\) −18544.0 −0.846371
\(784\) 0 0
\(785\) 5950.00 0.270528
\(786\) 0 0
\(787\) −18516.0 −0.838658 −0.419329 0.907834i \(-0.637735\pi\)
−0.419329 + 0.907834i \(0.637735\pi\)
\(788\) 0 0
\(789\) 12320.0 0.555898
\(790\) 0 0
\(791\) −6594.00 −0.296404
\(792\) 0 0
\(793\) 1860.00 0.0832920
\(794\) 0 0
\(795\) −5400.00 −0.240903
\(796\) 0 0
\(797\) −38618.0 −1.71634 −0.858168 0.513369i \(-0.828397\pi\)
−0.858168 + 0.513369i \(0.828397\pi\)
\(798\) 0 0
\(799\) −1568.00 −0.0694266
\(800\) 0 0
\(801\) 17490.0 0.771509
\(802\) 0 0
\(803\) −2040.00 −0.0896514
\(804\) 0 0
\(805\) 3640.00 0.159370
\(806\) 0 0
\(807\) −9176.00 −0.400261
\(808\) 0 0
\(809\) 19514.0 0.848054 0.424027 0.905650i \(-0.360616\pi\)
0.424027 + 0.905650i \(0.360616\pi\)
\(810\) 0 0
\(811\) −31020.0 −1.34311 −0.671553 0.740956i \(-0.734373\pi\)
−0.671553 + 0.740956i \(0.734373\pi\)
\(812\) 0 0
\(813\) 14912.0 0.643280
\(814\) 0 0
\(815\) −8660.00 −0.372204
\(816\) 0 0
\(817\) 4848.00 0.207601
\(818\) 0 0
\(819\) 770.000 0.0328522
\(820\) 0 0
\(821\) 3726.00 0.158390 0.0791951 0.996859i \(-0.474765\pi\)
0.0791951 + 0.996859i \(0.474765\pi\)
\(822\) 0 0
\(823\) 32904.0 1.39363 0.696817 0.717249i \(-0.254599\pi\)
0.696817 + 0.717249i \(0.254599\pi\)
\(824\) 0 0
\(825\) −2000.00 −0.0844013
\(826\) 0 0
\(827\) −39868.0 −1.67636 −0.838178 0.545397i \(-0.816379\pi\)
−0.838178 + 0.545397i \(0.816379\pi\)
\(828\) 0 0
\(829\) −26810.0 −1.12322 −0.561610 0.827402i \(-0.689818\pi\)
−0.561610 + 0.827402i \(0.689818\pi\)
\(830\) 0 0
\(831\) −10936.0 −0.456517
\(832\) 0 0
\(833\) −686.000 −0.0285336
\(834\) 0 0
\(835\) 11320.0 0.469155
\(836\) 0 0
\(837\) 34048.0 1.40606
\(838\) 0 0
\(839\) −37096.0 −1.52646 −0.763228 0.646130i \(-0.776387\pi\)
−0.763228 + 0.646130i \(0.776387\pi\)
\(840\) 0 0
\(841\) −9505.00 −0.389725
\(842\) 0 0
\(843\) −4136.00 −0.168982
\(844\) 0 0
\(845\) −10485.0 −0.426858
\(846\) 0 0
\(847\) −6517.00 −0.264376
\(848\) 0 0
\(849\) 20720.0 0.837584
\(850\) 0 0
\(851\) 16432.0 0.661906
\(852\) 0 0
\(853\) −14386.0 −0.577453 −0.288726 0.957412i \(-0.593232\pi\)
−0.288726 + 0.957412i \(0.593232\pi\)
\(854\) 0 0
\(855\) −660.000 −0.0263994
\(856\) 0 0
\(857\) −118.000 −0.00470339 −0.00235169 0.999997i \(-0.500749\pi\)
−0.00235169 + 0.999997i \(0.500749\pi\)
\(858\) 0 0
\(859\) −25116.0 −0.997610 −0.498805 0.866714i \(-0.666228\pi\)
−0.498805 + 0.866714i \(0.666228\pi\)
\(860\) 0 0
\(861\) −10584.0 −0.418934
\(862\) 0 0
\(863\) −11776.0 −0.464496 −0.232248 0.972657i \(-0.574608\pi\)
−0.232248 + 0.972657i \(0.574608\pi\)
\(864\) 0 0
\(865\) −5330.00 −0.209509
\(866\) 0 0
\(867\) 18868.0 0.739090
\(868\) 0 0
\(869\) −18240.0 −0.712025
\(870\) 0 0
\(871\) −1560.00 −0.0606872
\(872\) 0 0
\(873\) −9526.00 −0.369308
\(874\) 0 0
\(875\) 875.000 0.0338062
\(876\) 0 0
\(877\) 24694.0 0.950806 0.475403 0.879768i \(-0.342302\pi\)
0.475403 + 0.879768i \(0.342302\pi\)
\(878\) 0 0
\(879\) −31736.0 −1.21778
\(880\) 0 0
\(881\) 32850.0 1.25624 0.628118 0.778118i \(-0.283825\pi\)
0.628118 + 0.778118i \(0.283825\pi\)
\(882\) 0 0
\(883\) 47340.0 1.80421 0.902105 0.431516i \(-0.142021\pi\)
0.902105 + 0.431516i \(0.142021\pi\)
\(884\) 0 0
\(885\) −6480.00 −0.246127
\(886\) 0 0
\(887\) 1992.00 0.0754057 0.0377028 0.999289i \(-0.487996\pi\)
0.0377028 + 0.999289i \(0.487996\pi\)
\(888\) 0 0
\(889\) 5152.00 0.194367
\(890\) 0 0
\(891\) −6220.00 −0.233870
\(892\) 0 0
\(893\) 1344.00 0.0503642
\(894\) 0 0
\(895\) −11780.0 −0.439958
\(896\) 0 0
\(897\) 4160.00 0.154848
\(898\) 0 0
\(899\) −27328.0 −1.01384
\(900\) 0 0
\(901\) −3780.00 −0.139767
\(902\) 0 0
\(903\) −11312.0 −0.416877
\(904\) 0 0
\(905\) 10790.0 0.396322
\(906\) 0 0
\(907\) −13516.0 −0.494809 −0.247404 0.968912i \(-0.579578\pi\)
−0.247404 + 0.968912i \(0.579578\pi\)
\(908\) 0 0
\(909\) −7722.00 −0.281763
\(910\) 0 0
\(911\) −3408.00 −0.123943 −0.0619715 0.998078i \(-0.519739\pi\)
−0.0619715 + 0.998078i \(0.519739\pi\)
\(912\) 0 0
\(913\) 21360.0 0.774275
\(914\) 0 0
\(915\) 3720.00 0.134404
\(916\) 0 0
\(917\) 6468.00 0.232925
\(918\) 0 0
\(919\) 39240.0 1.40850 0.704248 0.709954i \(-0.251284\pi\)
0.704248 + 0.709954i \(0.251284\pi\)
\(920\) 0 0
\(921\) 13776.0 0.492871
\(922\) 0 0
\(923\) 3600.00 0.128381
\(924\) 0 0
\(925\) 3950.00 0.140406
\(926\) 0 0
\(927\) 3256.00 0.115363
\(928\) 0 0
\(929\) 21922.0 0.774206 0.387103 0.922036i \(-0.373476\pi\)
0.387103 + 0.922036i \(0.373476\pi\)
\(930\) 0 0
\(931\) 588.000 0.0206992
\(932\) 0 0
\(933\) −30624.0 −1.07458
\(934\) 0 0
\(935\) −1400.00 −0.0489678
\(936\) 0 0
\(937\) 186.000 0.00648490 0.00324245 0.999995i \(-0.498968\pi\)
0.00324245 + 0.999995i \(0.498968\pi\)
\(938\) 0 0
\(939\) 15192.0 0.527979
\(940\) 0 0
\(941\) −18282.0 −0.633343 −0.316672 0.948535i \(-0.602565\pi\)
−0.316672 + 0.948535i \(0.602565\pi\)
\(942\) 0 0
\(943\) 39312.0 1.35756
\(944\) 0 0
\(945\) 5320.00 0.183132
\(946\) 0 0
\(947\) −16980.0 −0.582657 −0.291328 0.956623i \(-0.594097\pi\)
−0.291328 + 0.956623i \(0.594097\pi\)
\(948\) 0 0
\(949\) 1020.00 0.0348900
\(950\) 0 0
\(951\) −27288.0 −0.930467
\(952\) 0 0
\(953\) −44310.0 −1.50613 −0.753065 0.657946i \(-0.771425\pi\)
−0.753065 + 0.657946i \(0.771425\pi\)
\(954\) 0 0
\(955\) −13440.0 −0.455401
\(956\) 0 0
\(957\) 9760.00 0.329672
\(958\) 0 0
\(959\) 3318.00 0.111725
\(960\) 0 0
\(961\) 20385.0 0.684267
\(962\) 0 0
\(963\) 484.000 0.0161959
\(964\) 0 0
\(965\) −22070.0 −0.736226
\(966\) 0 0
\(967\) 51512.0 1.71304 0.856522 0.516110i \(-0.172620\pi\)
0.856522 + 0.516110i \(0.172620\pi\)
\(968\) 0 0
\(969\) 672.000 0.0222784
\(970\) 0 0
\(971\) 1844.00 0.0609442 0.0304721 0.999536i \(-0.490299\pi\)
0.0304721 + 0.999536i \(0.490299\pi\)
\(972\) 0 0
\(973\) 7084.00 0.233405
\(974\) 0 0
\(975\) 1000.00 0.0328468
\(976\) 0 0
\(977\) 34162.0 1.11867 0.559334 0.828942i \(-0.311057\pi\)
0.559334 + 0.828942i \(0.311057\pi\)
\(978\) 0 0
\(979\) −31800.0 −1.03813
\(980\) 0 0
\(981\) 7150.00 0.232703
\(982\) 0 0
\(983\) −216.000 −0.00700847 −0.00350424 0.999994i \(-0.501115\pi\)
−0.00350424 + 0.999994i \(0.501115\pi\)
\(984\) 0 0
\(985\) 18870.0 0.610404
\(986\) 0 0
\(987\) −3136.00 −0.101135
\(988\) 0 0
\(989\) 42016.0 1.35089
\(990\) 0 0
\(991\) 52832.0 1.69351 0.846753 0.531987i \(-0.178554\pi\)
0.846753 + 0.531987i \(0.178554\pi\)
\(992\) 0 0
\(993\) 26288.0 0.840105
\(994\) 0 0
\(995\) 3320.00 0.105780
\(996\) 0 0
\(997\) 5054.00 0.160543 0.0802717 0.996773i \(-0.474421\pi\)
0.0802717 + 0.996773i \(0.474421\pi\)
\(998\) 0 0
\(999\) 24016.0 0.760593
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 280.4.a.a.1.1 1
4.3 odd 2 560.4.a.l.1.1 1
5.2 odd 4 1400.4.g.e.449.2 2
5.3 odd 4 1400.4.g.e.449.1 2
5.4 even 2 1400.4.a.g.1.1 1
7.6 odd 2 1960.4.a.g.1.1 1
8.3 odd 2 2240.4.a.l.1.1 1
8.5 even 2 2240.4.a.z.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
280.4.a.a.1.1 1 1.1 even 1 trivial
560.4.a.l.1.1 1 4.3 odd 2
1400.4.a.g.1.1 1 5.4 even 2
1400.4.g.e.449.1 2 5.3 odd 4
1400.4.g.e.449.2 2 5.2 odd 4
1960.4.a.g.1.1 1 7.6 odd 2
2240.4.a.l.1.1 1 8.3 odd 2
2240.4.a.z.1.1 1 8.5 even 2