Properties

Label 280.4.a.c.1.1
Level $280$
Weight $4$
Character 280.1
Self dual yes
Analytic conductor $16.521$
Analytic rank $1$
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: \(1\)
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

\(f(q)\) \(=\) \(q+5.00000 q^{3} -5.00000 q^{5} -7.00000 q^{7} -2.00000 q^{9} +O(q^{10})\) \(q+5.00000 q^{3} -5.00000 q^{5} -7.00000 q^{7} -2.00000 q^{9} -39.0000 q^{11} -19.0000 q^{13} -25.0000 q^{15} -37.0000 q^{17} -18.0000 q^{19} -35.0000 q^{21} -90.0000 q^{23} +25.0000 q^{25} -145.000 q^{27} +99.0000 q^{29} -32.0000 q^{31} -195.000 q^{33} +35.0000 q^{35} +46.0000 q^{37} -95.0000 q^{39} -248.000 q^{41} +178.000 q^{43} +10.0000 q^{45} +429.000 q^{47} +49.0000 q^{49} -185.000 q^{51} -652.000 q^{53} +195.000 q^{55} -90.0000 q^{57} +40.0000 q^{59} -36.0000 q^{61} +14.0000 q^{63} +95.0000 q^{65} -348.000 q^{67} -450.000 q^{69} +72.0000 q^{71} -1190.00 q^{73} +125.000 q^{75} +273.000 q^{77} +699.000 q^{79} -671.000 q^{81} -116.000 q^{83} +185.000 q^{85} +495.000 q^{87} -704.000 q^{89} +133.000 q^{91} -160.000 q^{93} +90.0000 q^{95} +223.000 q^{97} +78.0000 q^{99} +O(q^{100})\)

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
\(3\) 5.00000 0.962250 0.481125 0.876652i \(-0.340228\pi\)
0.481125 + 0.876652i \(0.340228\pi\)
\(4\) 0 0
\(5\) −5.00000 −0.447214
\(6\) 0 0
\(7\) −7.00000 −0.377964
\(8\) 0 0
\(9\) −2.00000 −0.0740741
\(10\) 0 0
\(11\) −39.0000 −1.06899 −0.534497 0.845170i \(-0.679499\pi\)
−0.534497 + 0.845170i \(0.679499\pi\)
\(12\) 0 0
\(13\) −19.0000 −0.405358 −0.202679 0.979245i \(-0.564965\pi\)
−0.202679 + 0.979245i \(0.564965\pi\)
\(14\) 0 0
\(15\) −25.0000 −0.430331
\(16\) 0 0
\(17\) −37.0000 −0.527872 −0.263936 0.964540i \(-0.585021\pi\)
−0.263936 + 0.964540i \(0.585021\pi\)
\(18\) 0 0
\(19\) −18.0000 −0.217341 −0.108671 0.994078i \(-0.534659\pi\)
−0.108671 + 0.994078i \(0.534659\pi\)
\(20\) 0 0
\(21\) −35.0000 −0.363696
\(22\) 0 0
\(23\) −90.0000 −0.815926 −0.407963 0.912998i \(-0.633761\pi\)
−0.407963 + 0.912998i \(0.633761\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) −145.000 −1.03353
\(28\) 0 0
\(29\) 99.0000 0.633925 0.316963 0.948438i \(-0.397337\pi\)
0.316963 + 0.948438i \(0.397337\pi\)
\(30\) 0 0
\(31\) −32.0000 −0.185399 −0.0926995 0.995694i \(-0.529550\pi\)
−0.0926995 + 0.995694i \(0.529550\pi\)
\(32\) 0 0
\(33\) −195.000 −1.02864
\(34\) 0 0
\(35\) 35.0000 0.169031
\(36\) 0 0
\(37\) 46.0000 0.204388 0.102194 0.994764i \(-0.467414\pi\)
0.102194 + 0.994764i \(0.467414\pi\)
\(38\) 0 0
\(39\) −95.0000 −0.390056
\(40\) 0 0
\(41\) −248.000 −0.944661 −0.472330 0.881422i \(-0.656587\pi\)
−0.472330 + 0.881422i \(0.656587\pi\)
\(42\) 0 0
\(43\) 178.000 0.631273 0.315637 0.948880i \(-0.397782\pi\)
0.315637 + 0.948880i \(0.397782\pi\)
\(44\) 0 0
\(45\) 10.0000 0.0331269
\(46\) 0 0
\(47\) 429.000 1.33141 0.665703 0.746217i \(-0.268132\pi\)
0.665703 + 0.746217i \(0.268132\pi\)
\(48\) 0 0
\(49\) 49.0000 0.142857
\(50\) 0 0
\(51\) −185.000 −0.507945
\(52\) 0 0
\(53\) −652.000 −1.68979 −0.844897 0.534929i \(-0.820338\pi\)
−0.844897 + 0.534929i \(0.820338\pi\)
\(54\) 0 0
\(55\) 195.000 0.478069
\(56\) 0 0
\(57\) −90.0000 −0.209137
\(58\) 0 0
\(59\) 40.0000 0.0882637 0.0441318 0.999026i \(-0.485948\pi\)
0.0441318 + 0.999026i \(0.485948\pi\)
\(60\) 0 0
\(61\) −36.0000 −0.0755627 −0.0377814 0.999286i \(-0.512029\pi\)
−0.0377814 + 0.999286i \(0.512029\pi\)
\(62\) 0 0
\(63\) 14.0000 0.0279974
\(64\) 0 0
\(65\) 95.0000 0.181282
\(66\) 0 0
\(67\) −348.000 −0.634552 −0.317276 0.948333i \(-0.602768\pi\)
−0.317276 + 0.948333i \(0.602768\pi\)
\(68\) 0 0
\(69\) −450.000 −0.785125
\(70\) 0 0
\(71\) 72.0000 0.120350 0.0601748 0.998188i \(-0.480834\pi\)
0.0601748 + 0.998188i \(0.480834\pi\)
\(72\) 0 0
\(73\) −1190.00 −1.90793 −0.953966 0.299916i \(-0.903041\pi\)
−0.953966 + 0.299916i \(0.903041\pi\)
\(74\) 0 0
\(75\) 125.000 0.192450
\(76\) 0 0
\(77\) 273.000 0.404042
\(78\) 0 0
\(79\) 699.000 0.995489 0.497745 0.867324i \(-0.334162\pi\)
0.497745 + 0.867324i \(0.334162\pi\)
\(80\) 0 0
\(81\) −671.000 −0.920439
\(82\) 0 0
\(83\) −116.000 −0.153405 −0.0767027 0.997054i \(-0.524439\pi\)
−0.0767027 + 0.997054i \(0.524439\pi\)
\(84\) 0 0
\(85\) 185.000 0.236071
\(86\) 0 0
\(87\) 495.000 0.609995
\(88\) 0 0
\(89\) −704.000 −0.838470 −0.419235 0.907878i \(-0.637702\pi\)
−0.419235 + 0.907878i \(0.637702\pi\)
\(90\) 0 0
\(91\) 133.000 0.153211
\(92\) 0 0
\(93\) −160.000 −0.178400
\(94\) 0 0
\(95\) 90.0000 0.0971979
\(96\) 0 0
\(97\) 223.000 0.233425 0.116712 0.993166i \(-0.462764\pi\)
0.116712 + 0.993166i \(0.462764\pi\)
\(98\) 0 0
\(99\) 78.0000 0.0791848
\(100\) 0 0
\(101\) 522.000 0.514267 0.257133 0.966376i \(-0.417222\pi\)
0.257133 + 0.966376i \(0.417222\pi\)
\(102\) 0 0
\(103\) 1697.00 1.62340 0.811701 0.584073i \(-0.198542\pi\)
0.811701 + 0.584073i \(0.198542\pi\)
\(104\) 0 0
\(105\) 175.000 0.162650
\(106\) 0 0
\(107\) 246.000 0.222259 0.111130 0.993806i \(-0.464553\pi\)
0.111130 + 0.993806i \(0.464553\pi\)
\(108\) 0 0
\(109\) 345.000 0.303165 0.151583 0.988445i \(-0.451563\pi\)
0.151583 + 0.988445i \(0.451563\pi\)
\(110\) 0 0
\(111\) 230.000 0.196672
\(112\) 0 0
\(113\) 186.000 0.154844 0.0774222 0.996998i \(-0.475331\pi\)
0.0774222 + 0.996998i \(0.475331\pi\)
\(114\) 0 0
\(115\) 450.000 0.364893
\(116\) 0 0
\(117\) 38.0000 0.0300265
\(118\) 0 0
\(119\) 259.000 0.199517
\(120\) 0 0
\(121\) 190.000 0.142750
\(122\) 0 0
\(123\) −1240.00 −0.909000
\(124\) 0 0
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) 2344.00 1.63777 0.818883 0.573960i \(-0.194594\pi\)
0.818883 + 0.573960i \(0.194594\pi\)
\(128\) 0 0
\(129\) 890.000 0.607443
\(130\) 0 0
\(131\) 958.000 0.638938 0.319469 0.947597i \(-0.396496\pi\)
0.319469 + 0.947597i \(0.396496\pi\)
\(132\) 0 0
\(133\) 126.000 0.0821473
\(134\) 0 0
\(135\) 725.000 0.462208
\(136\) 0 0
\(137\) 768.000 0.478939 0.239470 0.970904i \(-0.423026\pi\)
0.239470 + 0.970904i \(0.423026\pi\)
\(138\) 0 0
\(139\) −122.000 −0.0744454 −0.0372227 0.999307i \(-0.511851\pi\)
−0.0372227 + 0.999307i \(0.511851\pi\)
\(140\) 0 0
\(141\) 2145.00 1.28115
\(142\) 0 0
\(143\) 741.000 0.433325
\(144\) 0 0
\(145\) −495.000 −0.283500
\(146\) 0 0
\(147\) 245.000 0.137464
\(148\) 0 0
\(149\) −166.000 −0.0912701 −0.0456351 0.998958i \(-0.514531\pi\)
−0.0456351 + 0.998958i \(0.514531\pi\)
\(150\) 0 0
\(151\) −1725.00 −0.929659 −0.464830 0.885400i \(-0.653884\pi\)
−0.464830 + 0.885400i \(0.653884\pi\)
\(152\) 0 0
\(153\) 74.0000 0.0391016
\(154\) 0 0
\(155\) 160.000 0.0829130
\(156\) 0 0
\(157\) 3686.00 1.87373 0.936863 0.349698i \(-0.113716\pi\)
0.936863 + 0.349698i \(0.113716\pi\)
\(158\) 0 0
\(159\) −3260.00 −1.62601
\(160\) 0 0
\(161\) 630.000 0.308391
\(162\) 0 0
\(163\) 2594.00 1.24649 0.623245 0.782027i \(-0.285814\pi\)
0.623245 + 0.782027i \(0.285814\pi\)
\(164\) 0 0
\(165\) 975.000 0.460022
\(166\) 0 0
\(167\) 1457.00 0.675126 0.337563 0.941303i \(-0.390397\pi\)
0.337563 + 0.941303i \(0.390397\pi\)
\(168\) 0 0
\(169\) −1836.00 −0.835685
\(170\) 0 0
\(171\) 36.0000 0.0160993
\(172\) 0 0
\(173\) −3241.00 −1.42433 −0.712164 0.702013i \(-0.752285\pi\)
−0.712164 + 0.702013i \(0.752285\pi\)
\(174\) 0 0
\(175\) −175.000 −0.0755929
\(176\) 0 0
\(177\) 200.000 0.0849318
\(178\) 0 0
\(179\) −4596.00 −1.91911 −0.959556 0.281517i \(-0.909163\pi\)
−0.959556 + 0.281517i \(0.909163\pi\)
\(180\) 0 0
\(181\) −1140.00 −0.468152 −0.234076 0.972218i \(-0.575206\pi\)
−0.234076 + 0.972218i \(0.575206\pi\)
\(182\) 0 0
\(183\) −180.000 −0.0727103
\(184\) 0 0
\(185\) −230.000 −0.0914051
\(186\) 0 0
\(187\) 1443.00 0.564292
\(188\) 0 0
\(189\) 1015.00 0.390637
\(190\) 0 0
\(191\) −4131.00 −1.56497 −0.782483 0.622671i \(-0.786047\pi\)
−0.782483 + 0.622671i \(0.786047\pi\)
\(192\) 0 0
\(193\) −2792.00 −1.04131 −0.520654 0.853768i \(-0.674312\pi\)
−0.520654 + 0.853768i \(0.674312\pi\)
\(194\) 0 0
\(195\) 475.000 0.174438
\(196\) 0 0
\(197\) 2692.00 0.973589 0.486795 0.873516i \(-0.338166\pi\)
0.486795 + 0.873516i \(0.338166\pi\)
\(198\) 0 0
\(199\) −2640.00 −0.940425 −0.470213 0.882553i \(-0.655823\pi\)
−0.470213 + 0.882553i \(0.655823\pi\)
\(200\) 0 0
\(201\) −1740.00 −0.610598
\(202\) 0 0
\(203\) −693.000 −0.239601
\(204\) 0 0
\(205\) 1240.00 0.422465
\(206\) 0 0
\(207\) 180.000 0.0604390
\(208\) 0 0
\(209\) 702.000 0.232337
\(210\) 0 0
\(211\) 327.000 0.106690 0.0533450 0.998576i \(-0.483012\pi\)
0.0533450 + 0.998576i \(0.483012\pi\)
\(212\) 0 0
\(213\) 360.000 0.115807
\(214\) 0 0
\(215\) −890.000 −0.282314
\(216\) 0 0
\(217\) 224.000 0.0700742
\(218\) 0 0
\(219\) −5950.00 −1.83591
\(220\) 0 0
\(221\) 703.000 0.213977
\(222\) 0 0
\(223\) 4665.00 1.40086 0.700429 0.713722i \(-0.252992\pi\)
0.700429 + 0.713722i \(0.252992\pi\)
\(224\) 0 0
\(225\) −50.0000 −0.0148148
\(226\) 0 0
\(227\) −1071.00 −0.313149 −0.156574 0.987666i \(-0.550045\pi\)
−0.156574 + 0.987666i \(0.550045\pi\)
\(228\) 0 0
\(229\) −3920.00 −1.13118 −0.565591 0.824686i \(-0.691352\pi\)
−0.565591 + 0.824686i \(0.691352\pi\)
\(230\) 0 0
\(231\) 1365.00 0.388790
\(232\) 0 0
\(233\) −2616.00 −0.735536 −0.367768 0.929918i \(-0.619878\pi\)
−0.367768 + 0.929918i \(0.619878\pi\)
\(234\) 0 0
\(235\) −2145.00 −0.595423
\(236\) 0 0
\(237\) 3495.00 0.957910
\(238\) 0 0
\(239\) −6913.00 −1.87098 −0.935491 0.353350i \(-0.885042\pi\)
−0.935491 + 0.353350i \(0.885042\pi\)
\(240\) 0 0
\(241\) 2690.00 0.718996 0.359498 0.933146i \(-0.382948\pi\)
0.359498 + 0.933146i \(0.382948\pi\)
\(242\) 0 0
\(243\) 560.000 0.147835
\(244\) 0 0
\(245\) −245.000 −0.0638877
\(246\) 0 0
\(247\) 342.000 0.0881010
\(248\) 0 0
\(249\) −580.000 −0.147614
\(250\) 0 0
\(251\) 3034.00 0.762966 0.381483 0.924376i \(-0.375414\pi\)
0.381483 + 0.924376i \(0.375414\pi\)
\(252\) 0 0
\(253\) 3510.00 0.872221
\(254\) 0 0
\(255\) 925.000 0.227160
\(256\) 0 0
\(257\) −2266.00 −0.549997 −0.274998 0.961445i \(-0.588677\pi\)
−0.274998 + 0.961445i \(0.588677\pi\)
\(258\) 0 0
\(259\) −322.000 −0.0772514
\(260\) 0 0
\(261\) −198.000 −0.0469574
\(262\) 0 0
\(263\) −7058.00 −1.65481 −0.827405 0.561606i \(-0.810184\pi\)
−0.827405 + 0.561606i \(0.810184\pi\)
\(264\) 0 0
\(265\) 3260.00 0.755699
\(266\) 0 0
\(267\) −3520.00 −0.806818
\(268\) 0 0
\(269\) 3474.00 0.787411 0.393705 0.919237i \(-0.371193\pi\)
0.393705 + 0.919237i \(0.371193\pi\)
\(270\) 0 0
\(271\) −20.0000 −0.00448308 −0.00224154 0.999997i \(-0.500714\pi\)
−0.00224154 + 0.999997i \(0.500714\pi\)
\(272\) 0 0
\(273\) 665.000 0.147427
\(274\) 0 0
\(275\) −975.000 −0.213799
\(276\) 0 0
\(277\) −4186.00 −0.907987 −0.453993 0.891005i \(-0.650001\pi\)
−0.453993 + 0.891005i \(0.650001\pi\)
\(278\) 0 0
\(279\) 64.0000 0.0137333
\(280\) 0 0
\(281\) −7221.00 −1.53298 −0.766492 0.642253i \(-0.778000\pi\)
−0.766492 + 0.642253i \(0.778000\pi\)
\(282\) 0 0
\(283\) 23.0000 0.00483112 0.00241556 0.999997i \(-0.499231\pi\)
0.00241556 + 0.999997i \(0.499231\pi\)
\(284\) 0 0
\(285\) 450.000 0.0935288
\(286\) 0 0
\(287\) 1736.00 0.357048
\(288\) 0 0
\(289\) −3544.00 −0.721352
\(290\) 0 0
\(291\) 1115.00 0.224613
\(292\) 0 0
\(293\) 139.000 0.0277149 0.0138575 0.999904i \(-0.495589\pi\)
0.0138575 + 0.999904i \(0.495589\pi\)
\(294\) 0 0
\(295\) −200.000 −0.0394727
\(296\) 0 0
\(297\) 5655.00 1.10484
\(298\) 0 0
\(299\) 1710.00 0.330742
\(300\) 0 0
\(301\) −1246.00 −0.238599
\(302\) 0 0
\(303\) 2610.00 0.494853
\(304\) 0 0
\(305\) 180.000 0.0337927
\(306\) 0 0
\(307\) 6759.00 1.25654 0.628268 0.777997i \(-0.283764\pi\)
0.628268 + 0.777997i \(0.283764\pi\)
\(308\) 0 0
\(309\) 8485.00 1.56212
\(310\) 0 0
\(311\) 1038.00 0.189259 0.0946295 0.995513i \(-0.469833\pi\)
0.0946295 + 0.995513i \(0.469833\pi\)
\(312\) 0 0
\(313\) −9507.00 −1.71683 −0.858414 0.512957i \(-0.828550\pi\)
−0.858414 + 0.512957i \(0.828550\pi\)
\(314\) 0 0
\(315\) −70.0000 −0.0125208
\(316\) 0 0
\(317\) −1290.00 −0.228560 −0.114280 0.993449i \(-0.536456\pi\)
−0.114280 + 0.993449i \(0.536456\pi\)
\(318\) 0 0
\(319\) −3861.00 −0.677663
\(320\) 0 0
\(321\) 1230.00 0.213869
\(322\) 0 0
\(323\) 666.000 0.114728
\(324\) 0 0
\(325\) −475.000 −0.0810716
\(326\) 0 0
\(327\) 1725.00 0.291721
\(328\) 0 0
\(329\) −3003.00 −0.503224
\(330\) 0 0
\(331\) −5404.00 −0.897374 −0.448687 0.893689i \(-0.648108\pi\)
−0.448687 + 0.893689i \(0.648108\pi\)
\(332\) 0 0
\(333\) −92.0000 −0.0151398
\(334\) 0 0
\(335\) 1740.00 0.283780
\(336\) 0 0
\(337\) 3094.00 0.500121 0.250061 0.968230i \(-0.419549\pi\)
0.250061 + 0.968230i \(0.419549\pi\)
\(338\) 0 0
\(339\) 930.000 0.148999
\(340\) 0 0
\(341\) 1248.00 0.198191
\(342\) 0 0
\(343\) −343.000 −0.0539949
\(344\) 0 0
\(345\) 2250.00 0.351119
\(346\) 0 0
\(347\) −1486.00 −0.229892 −0.114946 0.993372i \(-0.536670\pi\)
−0.114946 + 0.993372i \(0.536670\pi\)
\(348\) 0 0
\(349\) 6630.00 1.01689 0.508447 0.861093i \(-0.330220\pi\)
0.508447 + 0.861093i \(0.330220\pi\)
\(350\) 0 0
\(351\) 2755.00 0.418949
\(352\) 0 0
\(353\) −5417.00 −0.816764 −0.408382 0.912811i \(-0.633907\pi\)
−0.408382 + 0.912811i \(0.633907\pi\)
\(354\) 0 0
\(355\) −360.000 −0.0538220
\(356\) 0 0
\(357\) 1295.00 0.191985
\(358\) 0 0
\(359\) −9200.00 −1.35253 −0.676264 0.736660i \(-0.736402\pi\)
−0.676264 + 0.736660i \(0.736402\pi\)
\(360\) 0 0
\(361\) −6535.00 −0.952763
\(362\) 0 0
\(363\) 950.000 0.137361
\(364\) 0 0
\(365\) 5950.00 0.853253
\(366\) 0 0
\(367\) 4157.00 0.591263 0.295632 0.955302i \(-0.404470\pi\)
0.295632 + 0.955302i \(0.404470\pi\)
\(368\) 0 0
\(369\) 496.000 0.0699749
\(370\) 0 0
\(371\) 4564.00 0.638682
\(372\) 0 0
\(373\) 8592.00 1.19270 0.596350 0.802725i \(-0.296617\pi\)
0.596350 + 0.802725i \(0.296617\pi\)
\(374\) 0 0
\(375\) −625.000 −0.0860663
\(376\) 0 0
\(377\) −1881.00 −0.256967
\(378\) 0 0
\(379\) 2084.00 0.282448 0.141224 0.989978i \(-0.454896\pi\)
0.141224 + 0.989978i \(0.454896\pi\)
\(380\) 0 0
\(381\) 11720.0 1.57594
\(382\) 0 0
\(383\) −9292.00 −1.23968 −0.619842 0.784727i \(-0.712803\pi\)
−0.619842 + 0.784727i \(0.712803\pi\)
\(384\) 0 0
\(385\) −1365.00 −0.180693
\(386\) 0 0
\(387\) −356.000 −0.0467610
\(388\) 0 0
\(389\) −1723.00 −0.224575 −0.112287 0.993676i \(-0.535818\pi\)
−0.112287 + 0.993676i \(0.535818\pi\)
\(390\) 0 0
\(391\) 3330.00 0.430704
\(392\) 0 0
\(393\) 4790.00 0.614818
\(394\) 0 0
\(395\) −3495.00 −0.445196
\(396\) 0 0
\(397\) 3767.00 0.476222 0.238111 0.971238i \(-0.423472\pi\)
0.238111 + 0.971238i \(0.423472\pi\)
\(398\) 0 0
\(399\) 630.000 0.0790462
\(400\) 0 0
\(401\) −14967.0 −1.86388 −0.931941 0.362611i \(-0.881885\pi\)
−0.931941 + 0.362611i \(0.881885\pi\)
\(402\) 0 0
\(403\) 608.000 0.0751529
\(404\) 0 0
\(405\) 3355.00 0.411633
\(406\) 0 0
\(407\) −1794.00 −0.218490
\(408\) 0 0
\(409\) 11374.0 1.37508 0.687540 0.726146i \(-0.258690\pi\)
0.687540 + 0.726146i \(0.258690\pi\)
\(410\) 0 0
\(411\) 3840.00 0.460859
\(412\) 0 0
\(413\) −280.000 −0.0333605
\(414\) 0 0
\(415\) 580.000 0.0686050
\(416\) 0 0
\(417\) −610.000 −0.0716351
\(418\) 0 0
\(419\) 14076.0 1.64119 0.820594 0.571512i \(-0.193643\pi\)
0.820594 + 0.571512i \(0.193643\pi\)
\(420\) 0 0
\(421\) 3769.00 0.436318 0.218159 0.975913i \(-0.429995\pi\)
0.218159 + 0.975913i \(0.429995\pi\)
\(422\) 0 0
\(423\) −858.000 −0.0986227
\(424\) 0 0
\(425\) −925.000 −0.105574
\(426\) 0 0
\(427\) 252.000 0.0285600
\(428\) 0 0
\(429\) 3705.00 0.416968
\(430\) 0 0
\(431\) −7423.00 −0.829590 −0.414795 0.909915i \(-0.636147\pi\)
−0.414795 + 0.909915i \(0.636147\pi\)
\(432\) 0 0
\(433\) −670.000 −0.0743606 −0.0371803 0.999309i \(-0.511838\pi\)
−0.0371803 + 0.999309i \(0.511838\pi\)
\(434\) 0 0
\(435\) −2475.00 −0.272798
\(436\) 0 0
\(437\) 1620.00 0.177334
\(438\) 0 0
\(439\) 6466.00 0.702973 0.351487 0.936193i \(-0.385676\pi\)
0.351487 + 0.936193i \(0.385676\pi\)
\(440\) 0 0
\(441\) −98.0000 −0.0105820
\(442\) 0 0
\(443\) 14618.0 1.56777 0.783885 0.620906i \(-0.213235\pi\)
0.783885 + 0.620906i \(0.213235\pi\)
\(444\) 0 0
\(445\) 3520.00 0.374975
\(446\) 0 0
\(447\) −830.000 −0.0878247
\(448\) 0 0
\(449\) 7551.00 0.793661 0.396830 0.917892i \(-0.370110\pi\)
0.396830 + 0.917892i \(0.370110\pi\)
\(450\) 0 0
\(451\) 9672.00 1.00984
\(452\) 0 0
\(453\) −8625.00 −0.894565
\(454\) 0 0
\(455\) −665.000 −0.0685180
\(456\) 0 0
\(457\) −14076.0 −1.44080 −0.720402 0.693557i \(-0.756043\pi\)
−0.720402 + 0.693557i \(0.756043\pi\)
\(458\) 0 0
\(459\) 5365.00 0.545570
\(460\) 0 0
\(461\) −18360.0 −1.85490 −0.927452 0.373943i \(-0.878006\pi\)
−0.927452 + 0.373943i \(0.878006\pi\)
\(462\) 0 0
\(463\) 2812.00 0.282256 0.141128 0.989991i \(-0.454927\pi\)
0.141128 + 0.989991i \(0.454927\pi\)
\(464\) 0 0
\(465\) 800.000 0.0797830
\(466\) 0 0
\(467\) 2619.00 0.259514 0.129757 0.991546i \(-0.458580\pi\)
0.129757 + 0.991546i \(0.458580\pi\)
\(468\) 0 0
\(469\) 2436.00 0.239838
\(470\) 0 0
\(471\) 18430.0 1.80299
\(472\) 0 0
\(473\) −6942.00 −0.674828
\(474\) 0 0
\(475\) −450.000 −0.0434682
\(476\) 0 0
\(477\) 1304.00 0.125170
\(478\) 0 0
\(479\) −7546.00 −0.719803 −0.359901 0.932990i \(-0.617190\pi\)
−0.359901 + 0.932990i \(0.617190\pi\)
\(480\) 0 0
\(481\) −874.000 −0.0828502
\(482\) 0 0
\(483\) 3150.00 0.296749
\(484\) 0 0
\(485\) −1115.00 −0.104391
\(486\) 0 0
\(487\) 9398.00 0.874464 0.437232 0.899349i \(-0.355959\pi\)
0.437232 + 0.899349i \(0.355959\pi\)
\(488\) 0 0
\(489\) 12970.0 1.19943
\(490\) 0 0
\(491\) −5397.00 −0.496055 −0.248028 0.968753i \(-0.579782\pi\)
−0.248028 + 0.968753i \(0.579782\pi\)
\(492\) 0 0
\(493\) −3663.00 −0.334631
\(494\) 0 0
\(495\) −390.000 −0.0354125
\(496\) 0 0
\(497\) −504.000 −0.0454879
\(498\) 0 0
\(499\) 11669.0 1.04685 0.523423 0.852073i \(-0.324655\pi\)
0.523423 + 0.852073i \(0.324655\pi\)
\(500\) 0 0
\(501\) 7285.00 0.649640
\(502\) 0 0
\(503\) 4055.00 0.359450 0.179725 0.983717i \(-0.442479\pi\)
0.179725 + 0.983717i \(0.442479\pi\)
\(504\) 0 0
\(505\) −2610.00 −0.229987
\(506\) 0 0
\(507\) −9180.00 −0.804138
\(508\) 0 0
\(509\) 12026.0 1.04724 0.523618 0.851953i \(-0.324582\pi\)
0.523618 + 0.851953i \(0.324582\pi\)
\(510\) 0 0
\(511\) 8330.00 0.721130
\(512\) 0 0
\(513\) 2610.00 0.224628
\(514\) 0 0
\(515\) −8485.00 −0.726007
\(516\) 0 0
\(517\) −16731.0 −1.42327
\(518\) 0 0
\(519\) −16205.0 −1.37056
\(520\) 0 0
\(521\) −17622.0 −1.48183 −0.740915 0.671598i \(-0.765608\pi\)
−0.740915 + 0.671598i \(0.765608\pi\)
\(522\) 0 0
\(523\) 14684.0 1.22770 0.613849 0.789423i \(-0.289620\pi\)
0.613849 + 0.789423i \(0.289620\pi\)
\(524\) 0 0
\(525\) −875.000 −0.0727393
\(526\) 0 0
\(527\) 1184.00 0.0978669
\(528\) 0 0
\(529\) −4067.00 −0.334265
\(530\) 0 0
\(531\) −80.0000 −0.00653805
\(532\) 0 0
\(533\) 4712.00 0.382926
\(534\) 0 0
\(535\) −1230.00 −0.0993973
\(536\) 0 0
\(537\) −22980.0 −1.84667
\(538\) 0 0
\(539\) −1911.00 −0.152714
\(540\) 0 0
\(541\) −5741.00 −0.456238 −0.228119 0.973633i \(-0.573258\pi\)
−0.228119 + 0.973633i \(0.573258\pi\)
\(542\) 0 0
\(543\) −5700.00 −0.450480
\(544\) 0 0
\(545\) −1725.00 −0.135580
\(546\) 0 0
\(547\) −9268.00 −0.724444 −0.362222 0.932092i \(-0.617982\pi\)
−0.362222 + 0.932092i \(0.617982\pi\)
\(548\) 0 0
\(549\) 72.0000 0.00559724
\(550\) 0 0
\(551\) −1782.00 −0.137778
\(552\) 0 0
\(553\) −4893.00 −0.376260
\(554\) 0 0
\(555\) −1150.00 −0.0879546
\(556\) 0 0
\(557\) −23112.0 −1.75815 −0.879073 0.476688i \(-0.841837\pi\)
−0.879073 + 0.476688i \(0.841837\pi\)
\(558\) 0 0
\(559\) −3382.00 −0.255892
\(560\) 0 0
\(561\) 7215.00 0.542990
\(562\) 0 0
\(563\) −13284.0 −0.994412 −0.497206 0.867633i \(-0.665641\pi\)
−0.497206 + 0.867633i \(0.665641\pi\)
\(564\) 0 0
\(565\) −930.000 −0.0692485
\(566\) 0 0
\(567\) 4697.00 0.347893
\(568\) 0 0
\(569\) −10446.0 −0.769629 −0.384815 0.922994i \(-0.625735\pi\)
−0.384815 + 0.922994i \(0.625735\pi\)
\(570\) 0 0
\(571\) −2252.00 −0.165050 −0.0825248 0.996589i \(-0.526298\pi\)
−0.0825248 + 0.996589i \(0.526298\pi\)
\(572\) 0 0
\(573\) −20655.0 −1.50589
\(574\) 0 0
\(575\) −2250.00 −0.163185
\(576\) 0 0
\(577\) 4457.00 0.321573 0.160786 0.986989i \(-0.448597\pi\)
0.160786 + 0.986989i \(0.448597\pi\)
\(578\) 0 0
\(579\) −13960.0 −1.00200
\(580\) 0 0
\(581\) 812.000 0.0579818
\(582\) 0 0
\(583\) 25428.0 1.80638
\(584\) 0 0
\(585\) −190.000 −0.0134283
\(586\) 0 0
\(587\) −25048.0 −1.76123 −0.880615 0.473833i \(-0.842870\pi\)
−0.880615 + 0.473833i \(0.842870\pi\)
\(588\) 0 0
\(589\) 576.000 0.0402948
\(590\) 0 0
\(591\) 13460.0 0.936837
\(592\) 0 0
\(593\) 177.000 0.0122572 0.00612860 0.999981i \(-0.498049\pi\)
0.00612860 + 0.999981i \(0.498049\pi\)
\(594\) 0 0
\(595\) −1295.00 −0.0892266
\(596\) 0 0
\(597\) −13200.0 −0.904925
\(598\) 0 0
\(599\) 9009.00 0.614520 0.307260 0.951626i \(-0.400588\pi\)
0.307260 + 0.951626i \(0.400588\pi\)
\(600\) 0 0
\(601\) −25794.0 −1.75068 −0.875340 0.483507i \(-0.839363\pi\)
−0.875340 + 0.483507i \(0.839363\pi\)
\(602\) 0 0
\(603\) 696.000 0.0470038
\(604\) 0 0
\(605\) −950.000 −0.0638397
\(606\) 0 0
\(607\) 4319.00 0.288802 0.144401 0.989519i \(-0.453874\pi\)
0.144401 + 0.989519i \(0.453874\pi\)
\(608\) 0 0
\(609\) −3465.00 −0.230556
\(610\) 0 0
\(611\) −8151.00 −0.539696
\(612\) 0 0
\(613\) −15134.0 −0.997156 −0.498578 0.866845i \(-0.666144\pi\)
−0.498578 + 0.866845i \(0.666144\pi\)
\(614\) 0 0
\(615\) 6200.00 0.406517
\(616\) 0 0
\(617\) 8394.00 0.547698 0.273849 0.961773i \(-0.411703\pi\)
0.273849 + 0.961773i \(0.411703\pi\)
\(618\) 0 0
\(619\) −1658.00 −0.107659 −0.0538293 0.998550i \(-0.517143\pi\)
−0.0538293 + 0.998550i \(0.517143\pi\)
\(620\) 0 0
\(621\) 13050.0 0.843283
\(622\) 0 0
\(623\) 4928.00 0.316912
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 3510.00 0.223566
\(628\) 0 0
\(629\) −1702.00 −0.107891
\(630\) 0 0
\(631\) −8071.00 −0.509194 −0.254597 0.967047i \(-0.581943\pi\)
−0.254597 + 0.967047i \(0.581943\pi\)
\(632\) 0 0
\(633\) 1635.00 0.102663
\(634\) 0 0
\(635\) −11720.0 −0.732432
\(636\) 0 0
\(637\) −931.000 −0.0579083
\(638\) 0 0
\(639\) −144.000 −0.00891479
\(640\) 0 0
\(641\) 28130.0 1.73334 0.866668 0.498886i \(-0.166257\pi\)
0.866668 + 0.498886i \(0.166257\pi\)
\(642\) 0 0
\(643\) 2693.00 0.165166 0.0825829 0.996584i \(-0.473683\pi\)
0.0825829 + 0.996584i \(0.473683\pi\)
\(644\) 0 0
\(645\) −4450.00 −0.271657
\(646\) 0 0
\(647\) 1376.00 0.0836107 0.0418054 0.999126i \(-0.486689\pi\)
0.0418054 + 0.999126i \(0.486689\pi\)
\(648\) 0 0
\(649\) −1560.00 −0.0943534
\(650\) 0 0
\(651\) 1120.00 0.0674290
\(652\) 0 0
\(653\) 30342.0 1.81834 0.909169 0.416428i \(-0.136718\pi\)
0.909169 + 0.416428i \(0.136718\pi\)
\(654\) 0 0
\(655\) −4790.00 −0.285742
\(656\) 0 0
\(657\) 2380.00 0.141328
\(658\) 0 0
\(659\) −15163.0 −0.896307 −0.448154 0.893957i \(-0.647918\pi\)
−0.448154 + 0.893957i \(0.647918\pi\)
\(660\) 0 0
\(661\) −5688.00 −0.334701 −0.167351 0.985897i \(-0.553521\pi\)
−0.167351 + 0.985897i \(0.553521\pi\)
\(662\) 0 0
\(663\) 3515.00 0.205899
\(664\) 0 0
\(665\) −630.000 −0.0367374
\(666\) 0 0
\(667\) −8910.00 −0.517236
\(668\) 0 0
\(669\) 23325.0 1.34798
\(670\) 0 0
\(671\) 1404.00 0.0807762
\(672\) 0 0
\(673\) 21488.0 1.23076 0.615380 0.788231i \(-0.289003\pi\)
0.615380 + 0.788231i \(0.289003\pi\)
\(674\) 0 0
\(675\) −3625.00 −0.206706
\(676\) 0 0
\(677\) 16453.0 0.934033 0.467016 0.884249i \(-0.345329\pi\)
0.467016 + 0.884249i \(0.345329\pi\)
\(678\) 0 0
\(679\) −1561.00 −0.0882263
\(680\) 0 0
\(681\) −5355.00 −0.301328
\(682\) 0 0
\(683\) −3372.00 −0.188911 −0.0944553 0.995529i \(-0.530111\pi\)
−0.0944553 + 0.995529i \(0.530111\pi\)
\(684\) 0 0
\(685\) −3840.00 −0.214188
\(686\) 0 0
\(687\) −19600.0 −1.08848
\(688\) 0 0
\(689\) 12388.0 0.684971
\(690\) 0 0
\(691\) 14172.0 0.780215 0.390107 0.920769i \(-0.372438\pi\)
0.390107 + 0.920769i \(0.372438\pi\)
\(692\) 0 0
\(693\) −546.000 −0.0299290
\(694\) 0 0
\(695\) 610.000 0.0332930
\(696\) 0 0
\(697\) 9176.00 0.498660
\(698\) 0 0
\(699\) −13080.0 −0.707770
\(700\) 0 0
\(701\) 30663.0 1.65210 0.826052 0.563593i \(-0.190581\pi\)
0.826052 + 0.563593i \(0.190581\pi\)
\(702\) 0 0
\(703\) −828.000 −0.0444219
\(704\) 0 0
\(705\) −10725.0 −0.572946
\(706\) 0 0
\(707\) −3654.00 −0.194375
\(708\) 0 0
\(709\) −14485.0 −0.767272 −0.383636 0.923484i \(-0.625328\pi\)
−0.383636 + 0.923484i \(0.625328\pi\)
\(710\) 0 0
\(711\) −1398.00 −0.0737399
\(712\) 0 0
\(713\) 2880.00 0.151272
\(714\) 0 0
\(715\) −3705.00 −0.193789
\(716\) 0 0
\(717\) −34565.0 −1.80035
\(718\) 0 0
\(719\) −8818.00 −0.457380 −0.228690 0.973499i \(-0.573444\pi\)
−0.228690 + 0.973499i \(0.573444\pi\)
\(720\) 0 0
\(721\) −11879.0 −0.613588
\(722\) 0 0
\(723\) 13450.0 0.691855
\(724\) 0 0
\(725\) 2475.00 0.126785
\(726\) 0 0
\(727\) −11408.0 −0.581980 −0.290990 0.956726i \(-0.593985\pi\)
−0.290990 + 0.956726i \(0.593985\pi\)
\(728\) 0 0
\(729\) 20917.0 1.06269
\(730\) 0 0
\(731\) −6586.00 −0.333231
\(732\) 0 0
\(733\) 15233.0 0.767590 0.383795 0.923418i \(-0.374617\pi\)
0.383795 + 0.923418i \(0.374617\pi\)
\(734\) 0 0
\(735\) −1225.00 −0.0614759
\(736\) 0 0
\(737\) 13572.0 0.678332
\(738\) 0 0
\(739\) 32113.0 1.59851 0.799253 0.600995i \(-0.205229\pi\)
0.799253 + 0.600995i \(0.205229\pi\)
\(740\) 0 0
\(741\) 1710.00 0.0847752
\(742\) 0 0
\(743\) 4596.00 0.226933 0.113466 0.993542i \(-0.463805\pi\)
0.113466 + 0.993542i \(0.463805\pi\)
\(744\) 0 0
\(745\) 830.000 0.0408172
\(746\) 0 0
\(747\) 232.000 0.0113634
\(748\) 0 0
\(749\) −1722.00 −0.0840060
\(750\) 0 0
\(751\) −15893.0 −0.772229 −0.386114 0.922451i \(-0.626183\pi\)
−0.386114 + 0.922451i \(0.626183\pi\)
\(752\) 0 0
\(753\) 15170.0 0.734164
\(754\) 0 0
\(755\) 8625.00 0.415756
\(756\) 0 0
\(757\) 15336.0 0.736323 0.368161 0.929762i \(-0.379987\pi\)
0.368161 + 0.929762i \(0.379987\pi\)
\(758\) 0 0
\(759\) 17550.0 0.839295
\(760\) 0 0
\(761\) 33010.0 1.57242 0.786210 0.617959i \(-0.212040\pi\)
0.786210 + 0.617959i \(0.212040\pi\)
\(762\) 0 0
\(763\) −2415.00 −0.114586
\(764\) 0 0
\(765\) −370.000 −0.0174868
\(766\) 0 0
\(767\) −760.000 −0.0357784
\(768\) 0 0
\(769\) 30982.0 1.45285 0.726424 0.687247i \(-0.241181\pi\)
0.726424 + 0.687247i \(0.241181\pi\)
\(770\) 0 0
\(771\) −11330.0 −0.529235
\(772\) 0 0
\(773\) −5915.00 −0.275223 −0.137612 0.990486i \(-0.543943\pi\)
−0.137612 + 0.990486i \(0.543943\pi\)
\(774\) 0 0
\(775\) −800.000 −0.0370798
\(776\) 0 0
\(777\) −1610.00 −0.0743352
\(778\) 0 0
\(779\) 4464.00 0.205314
\(780\) 0 0
\(781\) −2808.00 −0.128653
\(782\) 0 0
\(783\) −14355.0 −0.655180
\(784\) 0 0
\(785\) −18430.0 −0.837955
\(786\) 0 0
\(787\) −24615.0 −1.11490 −0.557452 0.830209i \(-0.688221\pi\)
−0.557452 + 0.830209i \(0.688221\pi\)
\(788\) 0 0
\(789\) −35290.0 −1.59234
\(790\) 0 0
\(791\) −1302.00 −0.0585257
\(792\) 0 0
\(793\) 684.000 0.0306300
\(794\) 0 0
\(795\) 16300.0 0.727172
\(796\) 0 0
\(797\) 6055.00 0.269108 0.134554 0.990906i \(-0.457040\pi\)
0.134554 + 0.990906i \(0.457040\pi\)
\(798\) 0 0
\(799\) −15873.0 −0.702811
\(800\) 0 0
\(801\) 1408.00 0.0621089
\(802\) 0 0
\(803\) 46410.0 2.03957
\(804\) 0 0
\(805\) −3150.00 −0.137917
\(806\) 0 0
\(807\) 17370.0 0.757686
\(808\) 0 0
\(809\) 27809.0 1.20854 0.604272 0.796778i \(-0.293464\pi\)
0.604272 + 0.796778i \(0.293464\pi\)
\(810\) 0 0
\(811\) −18654.0 −0.807683 −0.403841 0.914829i \(-0.632325\pi\)
−0.403841 + 0.914829i \(0.632325\pi\)
\(812\) 0 0
\(813\) −100.000 −0.00431384
\(814\) 0 0
\(815\) −12970.0 −0.557447
\(816\) 0 0
\(817\) −3204.00 −0.137202
\(818\) 0 0
\(819\) −266.000 −0.0113490
\(820\) 0 0
\(821\) 27285.0 1.15987 0.579935 0.814663i \(-0.303078\pi\)
0.579935 + 0.814663i \(0.303078\pi\)
\(822\) 0 0
\(823\) 18592.0 0.787456 0.393728 0.919227i \(-0.371185\pi\)
0.393728 + 0.919227i \(0.371185\pi\)
\(824\) 0 0
\(825\) −4875.00 −0.205728
\(826\) 0 0
\(827\) −37146.0 −1.56190 −0.780951 0.624592i \(-0.785265\pi\)
−0.780951 + 0.624592i \(0.785265\pi\)
\(828\) 0 0
\(829\) 11024.0 0.461857 0.230928 0.972971i \(-0.425824\pi\)
0.230928 + 0.972971i \(0.425824\pi\)
\(830\) 0 0
\(831\) −20930.0 −0.873711
\(832\) 0 0
\(833\) −1813.00 −0.0754102
\(834\) 0 0
\(835\) −7285.00 −0.301926
\(836\) 0 0
\(837\) 4640.00 0.191615
\(838\) 0 0
\(839\) 42858.0 1.76355 0.881777 0.471666i \(-0.156347\pi\)
0.881777 + 0.471666i \(0.156347\pi\)
\(840\) 0 0
\(841\) −14588.0 −0.598139
\(842\) 0 0
\(843\) −36105.0 −1.47512
\(844\) 0 0
\(845\) 9180.00 0.373730
\(846\) 0 0
\(847\) −1330.00 −0.0539544
\(848\) 0 0
\(849\) 115.000 0.00464875
\(850\) 0 0
\(851\) −4140.00 −0.166765
\(852\) 0 0
\(853\) −31522.0 −1.26529 −0.632645 0.774442i \(-0.718031\pi\)
−0.632645 + 0.774442i \(0.718031\pi\)
\(854\) 0 0
\(855\) −180.000 −0.00719985
\(856\) 0 0
\(857\) 37026.0 1.47583 0.737914 0.674895i \(-0.235811\pi\)
0.737914 + 0.674895i \(0.235811\pi\)
\(858\) 0 0
\(859\) 34380.0 1.36558 0.682788 0.730616i \(-0.260767\pi\)
0.682788 + 0.730616i \(0.260767\pi\)
\(860\) 0 0
\(861\) 8680.00 0.343570
\(862\) 0 0
\(863\) −29172.0 −1.15067 −0.575334 0.817919i \(-0.695128\pi\)
−0.575334 + 0.817919i \(0.695128\pi\)
\(864\) 0 0
\(865\) 16205.0 0.636979
\(866\) 0 0
\(867\) −17720.0 −0.694121
\(868\) 0 0
\(869\) −27261.0 −1.06417
\(870\) 0 0
\(871\) 6612.00 0.257221
\(872\) 0 0
\(873\) −446.000 −0.0172907
\(874\) 0 0
\(875\) 875.000 0.0338062
\(876\) 0 0
\(877\) −18178.0 −0.699917 −0.349959 0.936765i \(-0.613804\pi\)
−0.349959 + 0.936765i \(0.613804\pi\)
\(878\) 0 0
\(879\) 695.000 0.0266687
\(880\) 0 0
\(881\) 2608.00 0.0997341 0.0498671 0.998756i \(-0.484120\pi\)
0.0498671 + 0.998756i \(0.484120\pi\)
\(882\) 0 0
\(883\) 26880.0 1.02444 0.512222 0.858853i \(-0.328823\pi\)
0.512222 + 0.858853i \(0.328823\pi\)
\(884\) 0 0
\(885\) −1000.00 −0.0379826
\(886\) 0 0
\(887\) 31208.0 1.18136 0.590678 0.806908i \(-0.298861\pi\)
0.590678 + 0.806908i \(0.298861\pi\)
\(888\) 0 0
\(889\) −16408.0 −0.619018
\(890\) 0 0
\(891\) 26169.0 0.983944
\(892\) 0 0
\(893\) −7722.00 −0.289369
\(894\) 0 0
\(895\) 22980.0 0.858253
\(896\) 0 0
\(897\) 8550.00 0.318257
\(898\) 0 0
\(899\) −3168.00 −0.117529
\(900\) 0 0
\(901\) 24124.0 0.891994
\(902\) 0 0
\(903\) −6230.00 −0.229592
\(904\) 0 0
\(905\) 5700.00 0.209364
\(906\) 0 0
\(907\) 21494.0 0.786876 0.393438 0.919351i \(-0.371286\pi\)
0.393438 + 0.919351i \(0.371286\pi\)
\(908\) 0 0
\(909\) −1044.00 −0.0380938
\(910\) 0 0
\(911\) 3704.00 0.134708 0.0673540 0.997729i \(-0.478544\pi\)
0.0673540 + 0.997729i \(0.478544\pi\)
\(912\) 0 0
\(913\) 4524.00 0.163990
\(914\) 0 0
\(915\) 900.000 0.0325170
\(916\) 0 0
\(917\) −6706.00 −0.241496
\(918\) 0 0
\(919\) −16185.0 −0.580951 −0.290475 0.956882i \(-0.593813\pi\)
−0.290475 + 0.956882i \(0.593813\pi\)
\(920\) 0 0
\(921\) 33795.0 1.20910
\(922\) 0 0
\(923\) −1368.00 −0.0487847
\(924\) 0 0
\(925\) 1150.00 0.0408776
\(926\) 0 0
\(927\) −3394.00 −0.120252
\(928\) 0 0
\(929\) 8500.00 0.300189 0.150095 0.988672i \(-0.452042\pi\)
0.150095 + 0.988672i \(0.452042\pi\)
\(930\) 0 0
\(931\) −882.000 −0.0310487
\(932\) 0 0
\(933\) 5190.00 0.182115
\(934\) 0 0
\(935\) −7215.00 −0.252359
\(936\) 0 0
\(937\) 33415.0 1.16502 0.582508 0.812825i \(-0.302071\pi\)
0.582508 + 0.812825i \(0.302071\pi\)
\(938\) 0 0
\(939\) −47535.0 −1.65202
\(940\) 0 0
\(941\) −25884.0 −0.896700 −0.448350 0.893858i \(-0.647988\pi\)
−0.448350 + 0.893858i \(0.647988\pi\)
\(942\) 0 0
\(943\) 22320.0 0.770773
\(944\) 0 0
\(945\) −5075.00 −0.174698
\(946\) 0 0
\(947\) 26404.0 0.906035 0.453017 0.891502i \(-0.350348\pi\)
0.453017 + 0.891502i \(0.350348\pi\)
\(948\) 0 0
\(949\) 22610.0 0.773395
\(950\) 0 0
\(951\) −6450.00 −0.219932
\(952\) 0 0
\(953\) −21068.0 −0.716117 −0.358058 0.933699i \(-0.616561\pi\)
−0.358058 + 0.933699i \(0.616561\pi\)
\(954\) 0 0
\(955\) 20655.0 0.699874
\(956\) 0 0
\(957\) −19305.0 −0.652082
\(958\) 0 0
\(959\) −5376.00 −0.181022
\(960\) 0 0
\(961\) −28767.0 −0.965627
\(962\) 0 0
\(963\) −492.000 −0.0164636
\(964\) 0 0
\(965\) 13960.0 0.465687
\(966\) 0 0
\(967\) 298.000 0.00991007 0.00495503 0.999988i \(-0.498423\pi\)
0.00495503 + 0.999988i \(0.498423\pi\)
\(968\) 0 0
\(969\) 3330.00 0.110397
\(970\) 0 0
\(971\) −8972.00 −0.296524 −0.148262 0.988948i \(-0.547368\pi\)
−0.148262 + 0.988948i \(0.547368\pi\)
\(972\) 0 0
\(973\) 854.000 0.0281377
\(974\) 0 0
\(975\) −2375.00 −0.0780112
\(976\) 0 0
\(977\) 7874.00 0.257842 0.128921 0.991655i \(-0.458849\pi\)
0.128921 + 0.991655i \(0.458849\pi\)
\(978\) 0 0
\(979\) 27456.0 0.896320
\(980\) 0 0
\(981\) −690.000 −0.0224567
\(982\) 0 0
\(983\) −47585.0 −1.54397 −0.771987 0.635639i \(-0.780737\pi\)
−0.771987 + 0.635639i \(0.780737\pi\)
\(984\) 0 0
\(985\) −13460.0 −0.435402
\(986\) 0 0
\(987\) −15015.0 −0.484228
\(988\) 0 0
\(989\) −16020.0 −0.515072
\(990\) 0 0
\(991\) −42016.0 −1.34680 −0.673402 0.739277i \(-0.735168\pi\)
−0.673402 + 0.739277i \(0.735168\pi\)
\(992\) 0 0
\(993\) −27020.0 −0.863498
\(994\) 0 0
\(995\) 13200.0 0.420571
\(996\) 0 0
\(997\) 1867.00 0.0593064 0.0296532 0.999560i \(-0.490560\pi\)
0.0296532 + 0.999560i \(0.490560\pi\)
\(998\) 0 0
\(999\) −6670.00 −0.211241
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.c.1.1 1
4.3 odd 2 560.4.a.e.1.1 1
5.2 odd 4 1400.4.g.c.449.1 2
5.3 odd 4 1400.4.g.c.449.2 2
5.4 even 2 1400.4.a.d.1.1 1
7.6 odd 2 1960.4.a.d.1.1 1
8.3 odd 2 2240.4.a.be.1.1 1
8.5 even 2 2240.4.a.j.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
280.4.a.c.1.1 1 1.1 even 1 trivial
560.4.a.e.1.1 1 4.3 odd 2
1400.4.a.d.1.1 1 5.4 even 2
1400.4.g.c.449.1 2 5.2 odd 4
1400.4.g.c.449.2 2 5.3 odd 4
1960.4.a.d.1.1 1 7.6 odd 2
2240.4.a.j.1.1 1 8.5 even 2
2240.4.a.be.1.1 1 8.3 odd 2