Properties

Label 588.4.a.i.1.2
Level $588$
Weight $4$
Character 588.1
Self dual yes
Analytic conductor $34.693$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 588.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(34.6931230834\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{193}) \)
Defining polynomial: \(x^{2} - x - 48\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 84)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-6.44622\) of defining polynomial
Character \(\chi\) \(=\) 588.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.00000 q^{3} +12.4462 q^{5} +9.00000 q^{9} +O(q^{10})\) \(q+3.00000 q^{3} +12.4462 q^{5} +9.00000 q^{9} -51.1236 q^{11} +37.2311 q^{13} +37.3387 q^{15} +22.2151 q^{17} +54.3387 q^{19} +176.924 q^{23} +29.9084 q^{25} +27.0000 q^{27} +61.0916 q^{29} +319.924 q^{31} -153.371 q^{33} -315.080 q^{37} +111.693 q^{39} -206.032 q^{41} +339.661 q^{43} +112.016 q^{45} +142.064 q^{47} +66.6453 q^{51} +310.016 q^{53} -636.295 q^{55} +163.016 q^{57} -281.650 q^{59} -543.849 q^{61} +463.387 q^{65} -479.359 q^{67} +530.773 q^{69} +1105.63 q^{71} +239.350 q^{73} +89.7253 q^{75} +1160.67 q^{79} +81.0000 q^{81} -2.93158 q^{83} +276.494 q^{85} +183.275 q^{87} -1278.74 q^{89} +959.773 q^{93} +676.311 q^{95} +79.0596 q^{97} -460.112 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 6 q^{3} + 11 q^{5} + 18 q^{9} + O(q^{10}) \) \( 2 q + 6 q^{3} + 11 q^{5} + 18 q^{9} - 5 q^{11} + 5 q^{13} + 33 q^{15} + 100 q^{17} + 67 q^{19} + 76 q^{23} - 93 q^{25} + 54 q^{27} + 275 q^{29} + 362 q^{31} - 15 q^{33} - 5 q^{37} + 15 q^{39} - 162 q^{41} + 721 q^{43} + 99 q^{45} - 216 q^{47} + 300 q^{51} + 495 q^{53} - 703 q^{55} + 201 q^{57} + 173 q^{59} - 532 q^{61} + 510 q^{65} + 111 q^{67} + 228 q^{69} + 1600 q^{71} + 1215 q^{73} - 279 q^{75} + 1460 q^{79} + 162 q^{81} - 1409 q^{83} + 164 q^{85} + 825 q^{87} - 1974 q^{89} + 1086 q^{93} + 658 q^{95} + 561 q^{97} - 45 q^{99} + O(q^{100}) \)

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
\(3\) 3.00000 0.577350
\(4\) 0 0
\(5\) 12.4462 1.11322 0.556612 0.830773i \(-0.312101\pi\)
0.556612 + 0.830773i \(0.312101\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 9.00000 0.333333
\(10\) 0 0
\(11\) −51.1236 −1.40130 −0.700651 0.713504i \(-0.747107\pi\)
−0.700651 + 0.713504i \(0.747107\pi\)
\(12\) 0 0
\(13\) 37.2311 0.794312 0.397156 0.917751i \(-0.369997\pi\)
0.397156 + 0.917751i \(0.369997\pi\)
\(14\) 0 0
\(15\) 37.3387 0.642720
\(16\) 0 0
\(17\) 22.2151 0.316939 0.158469 0.987364i \(-0.449344\pi\)
0.158469 + 0.987364i \(0.449344\pi\)
\(18\) 0 0
\(19\) 54.3387 0.656113 0.328056 0.944658i \(-0.393606\pi\)
0.328056 + 0.944658i \(0.393606\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 176.924 1.60397 0.801985 0.597345i \(-0.203778\pi\)
0.801985 + 0.597345i \(0.203778\pi\)
\(24\) 0 0
\(25\) 29.9084 0.239268
\(26\) 0 0
\(27\) 27.0000 0.192450
\(28\) 0 0
\(29\) 61.0916 0.391187 0.195593 0.980685i \(-0.437337\pi\)
0.195593 + 0.980685i \(0.437337\pi\)
\(30\) 0 0
\(31\) 319.924 1.85355 0.926776 0.375614i \(-0.122568\pi\)
0.926776 + 0.375614i \(0.122568\pi\)
\(32\) 0 0
\(33\) −153.371 −0.809043
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −315.080 −1.39997 −0.699984 0.714158i \(-0.746810\pi\)
−0.699984 + 0.714158i \(0.746810\pi\)
\(38\) 0 0
\(39\) 111.693 0.458596
\(40\) 0 0
\(41\) −206.032 −0.784800 −0.392400 0.919795i \(-0.628355\pi\)
−0.392400 + 0.919795i \(0.628355\pi\)
\(42\) 0 0
\(43\) 339.661 1.20460 0.602301 0.798269i \(-0.294251\pi\)
0.602301 + 0.798269i \(0.294251\pi\)
\(44\) 0 0
\(45\) 112.016 0.371075
\(46\) 0 0
\(47\) 142.064 0.440897 0.220449 0.975399i \(-0.429248\pi\)
0.220449 + 0.975399i \(0.429248\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 66.6453 0.182985
\(52\) 0 0
\(53\) 310.016 0.803471 0.401736 0.915756i \(-0.368407\pi\)
0.401736 + 0.915756i \(0.368407\pi\)
\(54\) 0 0
\(55\) −636.295 −1.55996
\(56\) 0 0
\(57\) 163.016 0.378807
\(58\) 0 0
\(59\) −281.650 −0.621486 −0.310743 0.950494i \(-0.600578\pi\)
−0.310743 + 0.950494i \(0.600578\pi\)
\(60\) 0 0
\(61\) −543.849 −1.14152 −0.570760 0.821117i \(-0.693351\pi\)
−0.570760 + 0.821117i \(0.693351\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 463.387 0.884247
\(66\) 0 0
\(67\) −479.359 −0.874075 −0.437038 0.899443i \(-0.643972\pi\)
−0.437038 + 0.899443i \(0.643972\pi\)
\(68\) 0 0
\(69\) 530.773 0.926052
\(70\) 0 0
\(71\) 1105.63 1.84809 0.924046 0.382280i \(-0.124861\pi\)
0.924046 + 0.382280i \(0.124861\pi\)
\(72\) 0 0
\(73\) 239.350 0.383751 0.191876 0.981419i \(-0.438543\pi\)
0.191876 + 0.981419i \(0.438543\pi\)
\(74\) 0 0
\(75\) 89.7253 0.138141
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 1160.67 1.65298 0.826488 0.562954i \(-0.190335\pi\)
0.826488 + 0.562954i \(0.190335\pi\)
\(80\) 0 0
\(81\) 81.0000 0.111111
\(82\) 0 0
\(83\) −2.93158 −0.00387690 −0.00193845 0.999998i \(-0.500617\pi\)
−0.00193845 + 0.999998i \(0.500617\pi\)
\(84\) 0 0
\(85\) 276.494 0.352824
\(86\) 0 0
\(87\) 183.275 0.225852
\(88\) 0 0
\(89\) −1278.74 −1.52299 −0.761496 0.648169i \(-0.775535\pi\)
−0.761496 + 0.648169i \(0.775535\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 959.773 1.07015
\(94\) 0 0
\(95\) 676.311 0.730401
\(96\) 0 0
\(97\) 79.0596 0.0827555 0.0413777 0.999144i \(-0.486825\pi\)
0.0413777 + 0.999144i \(0.486825\pi\)
\(98\) 0 0
\(99\) −460.112 −0.467101
\(100\) 0 0
\(101\) 1372.10 1.35178 0.675889 0.737004i \(-0.263760\pi\)
0.675889 + 0.737004i \(0.263760\pi\)
\(102\) 0 0
\(103\) 258.531 0.247318 0.123659 0.992325i \(-0.460537\pi\)
0.123659 + 0.992325i \(0.460537\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1262.37 −1.14054 −0.570270 0.821458i \(-0.693161\pi\)
−0.570270 + 0.821458i \(0.693161\pi\)
\(108\) 0 0
\(109\) 276.833 0.243264 0.121632 0.992575i \(-0.461187\pi\)
0.121632 + 0.992575i \(0.461187\pi\)
\(110\) 0 0
\(111\) −945.240 −0.808272
\(112\) 0 0
\(113\) 52.9156 0.0440520 0.0220260 0.999757i \(-0.492988\pi\)
0.0220260 + 0.999757i \(0.492988\pi\)
\(114\) 0 0
\(115\) 2202.04 1.78558
\(116\) 0 0
\(117\) 335.080 0.264771
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 1282.62 0.963650
\(122\) 0 0
\(123\) −618.096 −0.453104
\(124\) 0 0
\(125\) −1183.53 −0.846866
\(126\) 0 0
\(127\) 443.700 0.310016 0.155008 0.987913i \(-0.450460\pi\)
0.155008 + 0.987913i \(0.450460\pi\)
\(128\) 0 0
\(129\) 1018.98 0.695477
\(130\) 0 0
\(131\) −2153.48 −1.43627 −0.718133 0.695906i \(-0.755003\pi\)
−0.718133 + 0.695906i \(0.755003\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 336.048 0.214240
\(136\) 0 0
\(137\) 263.108 0.164079 0.0820394 0.996629i \(-0.473857\pi\)
0.0820394 + 0.996629i \(0.473857\pi\)
\(138\) 0 0
\(139\) 1165.77 0.711360 0.355680 0.934608i \(-0.384249\pi\)
0.355680 + 0.934608i \(0.384249\pi\)
\(140\) 0 0
\(141\) 426.192 0.254552
\(142\) 0 0
\(143\) −1903.39 −1.11307
\(144\) 0 0
\(145\) 760.359 0.435479
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1765.19 −0.970539 −0.485270 0.874364i \(-0.661279\pi\)
−0.485270 + 0.874364i \(0.661279\pi\)
\(150\) 0 0
\(151\) 2692.31 1.45098 0.725488 0.688235i \(-0.241614\pi\)
0.725488 + 0.688235i \(0.241614\pi\)
\(152\) 0 0
\(153\) 199.936 0.105646
\(154\) 0 0
\(155\) 3981.85 2.06342
\(156\) 0 0
\(157\) −1941.38 −0.986873 −0.493437 0.869782i \(-0.664260\pi\)
−0.493437 + 0.869782i \(0.664260\pi\)
\(158\) 0 0
\(159\) 930.048 0.463884
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 2102.84 1.01047 0.505236 0.862981i \(-0.331405\pi\)
0.505236 + 0.862981i \(0.331405\pi\)
\(164\) 0 0
\(165\) −1908.89 −0.900646
\(166\) 0 0
\(167\) −2344.22 −1.08623 −0.543116 0.839658i \(-0.682756\pi\)
−0.543116 + 0.839658i \(0.682756\pi\)
\(168\) 0 0
\(169\) −810.844 −0.369069
\(170\) 0 0
\(171\) 489.048 0.218704
\(172\) 0 0
\(173\) 3470.65 1.52525 0.762626 0.646840i \(-0.223910\pi\)
0.762626 + 0.646840i \(0.223910\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −844.949 −0.358815
\(178\) 0 0
\(179\) −955.771 −0.399093 −0.199547 0.979888i \(-0.563947\pi\)
−0.199547 + 0.979888i \(0.563947\pi\)
\(180\) 0 0
\(181\) 4220.26 1.73309 0.866546 0.499098i \(-0.166335\pi\)
0.866546 + 0.499098i \(0.166335\pi\)
\(182\) 0 0
\(183\) −1631.55 −0.659057
\(184\) 0 0
\(185\) −3921.56 −1.55848
\(186\) 0 0
\(187\) −1135.72 −0.444127
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −3518.03 −1.33275 −0.666377 0.745615i \(-0.732156\pi\)
−0.666377 + 0.745615i \(0.732156\pi\)
\(192\) 0 0
\(193\) −5017.67 −1.87140 −0.935699 0.352799i \(-0.885230\pi\)
−0.935699 + 0.352799i \(0.885230\pi\)
\(194\) 0 0
\(195\) 1390.16 0.510520
\(196\) 0 0
\(197\) −2838.14 −1.02644 −0.513221 0.858257i \(-0.671548\pi\)
−0.513221 + 0.858257i \(0.671548\pi\)
\(198\) 0 0
\(199\) 354.901 0.126424 0.0632118 0.998000i \(-0.479866\pi\)
0.0632118 + 0.998000i \(0.479866\pi\)
\(200\) 0 0
\(201\) −1438.08 −0.504648
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −2564.32 −0.873658
\(206\) 0 0
\(207\) 1592.32 0.534656
\(208\) 0 0
\(209\) −2777.99 −0.919413
\(210\) 0 0
\(211\) 752.672 0.245574 0.122787 0.992433i \(-0.460817\pi\)
0.122787 + 0.992433i \(0.460817\pi\)
\(212\) 0 0
\(213\) 3316.90 1.06700
\(214\) 0 0
\(215\) 4227.50 1.34099
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 718.051 0.221559
\(220\) 0 0
\(221\) 827.093 0.251748
\(222\) 0 0
\(223\) −3077.75 −0.924221 −0.462111 0.886822i \(-0.652908\pi\)
−0.462111 + 0.886822i \(0.652908\pi\)
\(224\) 0 0
\(225\) 269.176 0.0797558
\(226\) 0 0
\(227\) −6217.43 −1.81791 −0.908955 0.416894i \(-0.863119\pi\)
−0.908955 + 0.416894i \(0.863119\pi\)
\(228\) 0 0
\(229\) 503.254 0.145223 0.0726113 0.997360i \(-0.476867\pi\)
0.0726113 + 0.997360i \(0.476867\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −268.340 −0.0754486 −0.0377243 0.999288i \(-0.512011\pi\)
−0.0377243 + 0.999288i \(0.512011\pi\)
\(234\) 0 0
\(235\) 1768.16 0.490817
\(236\) 0 0
\(237\) 3482.00 0.954346
\(238\) 0 0
\(239\) −5189.77 −1.40459 −0.702297 0.711884i \(-0.747842\pi\)
−0.702297 + 0.711884i \(0.747842\pi\)
\(240\) 0 0
\(241\) 6170.94 1.64940 0.824699 0.565571i \(-0.191344\pi\)
0.824699 + 0.565571i \(0.191344\pi\)
\(242\) 0 0
\(243\) 243.000 0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 2023.09 0.521158
\(248\) 0 0
\(249\) −8.79474 −0.00223833
\(250\) 0 0
\(251\) 1891.91 0.475763 0.237882 0.971294i \(-0.423547\pi\)
0.237882 + 0.971294i \(0.423547\pi\)
\(252\) 0 0
\(253\) −9045.01 −2.24765
\(254\) 0 0
\(255\) 829.483 0.203703
\(256\) 0 0
\(257\) −6539.93 −1.58735 −0.793676 0.608340i \(-0.791836\pi\)
−0.793676 + 0.608340i \(0.791836\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 549.824 0.130396
\(262\) 0 0
\(263\) 5375.90 1.26043 0.630214 0.776422i \(-0.282967\pi\)
0.630214 + 0.776422i \(0.282967\pi\)
\(264\) 0 0
\(265\) 3858.53 0.894443
\(266\) 0 0
\(267\) −3836.22 −0.879300
\(268\) 0 0
\(269\) −3238.88 −0.734119 −0.367060 0.930197i \(-0.619636\pi\)
−0.367060 + 0.930197i \(0.619636\pi\)
\(270\) 0 0
\(271\) 1357.46 0.304279 0.152140 0.988359i \(-0.451384\pi\)
0.152140 + 0.988359i \(0.451384\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1529.03 −0.335286
\(276\) 0 0
\(277\) −2561.63 −0.555645 −0.277823 0.960632i \(-0.589613\pi\)
−0.277823 + 0.960632i \(0.589613\pi\)
\(278\) 0 0
\(279\) 2879.32 0.617851
\(280\) 0 0
\(281\) 1786.17 0.379196 0.189598 0.981862i \(-0.439282\pi\)
0.189598 + 0.981862i \(0.439282\pi\)
\(282\) 0 0
\(283\) −7388.28 −1.55190 −0.775950 0.630794i \(-0.782729\pi\)
−0.775950 + 0.630794i \(0.782729\pi\)
\(284\) 0 0
\(285\) 2028.93 0.421697
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −4419.49 −0.899550
\(290\) 0 0
\(291\) 237.179 0.0477789
\(292\) 0 0
\(293\) 492.981 0.0982945 0.0491472 0.998792i \(-0.484350\pi\)
0.0491472 + 0.998792i \(0.484350\pi\)
\(294\) 0 0
\(295\) −3505.48 −0.691853
\(296\) 0 0
\(297\) −1380.34 −0.269681
\(298\) 0 0
\(299\) 6587.09 1.27405
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 4116.31 0.780449
\(304\) 0 0
\(305\) −6768.86 −1.27077
\(306\) 0 0
\(307\) −988.810 −0.183825 −0.0919126 0.995767i \(-0.529298\pi\)
−0.0919126 + 0.995767i \(0.529298\pi\)
\(308\) 0 0
\(309\) 775.592 0.142789
\(310\) 0 0
\(311\) −9596.57 −1.74975 −0.874874 0.484351i \(-0.839056\pi\)
−0.874874 + 0.484351i \(0.839056\pi\)
\(312\) 0 0
\(313\) 965.713 0.174394 0.0871970 0.996191i \(-0.472209\pi\)
0.0871970 + 0.996191i \(0.472209\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −8985.97 −1.59212 −0.796061 0.605217i \(-0.793086\pi\)
−0.796061 + 0.605217i \(0.793086\pi\)
\(318\) 0 0
\(319\) −3123.22 −0.548171
\(320\) 0 0
\(321\) −3787.10 −0.658491
\(322\) 0 0
\(323\) 1207.14 0.207947
\(324\) 0 0
\(325\) 1113.52 0.190053
\(326\) 0 0
\(327\) 830.499 0.140449
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −3807.30 −0.632230 −0.316115 0.948721i \(-0.602379\pi\)
−0.316115 + 0.948721i \(0.602379\pi\)
\(332\) 0 0
\(333\) −2835.72 −0.466656
\(334\) 0 0
\(335\) −5966.21 −0.973041
\(336\) 0 0
\(337\) −1649.82 −0.266681 −0.133340 0.991070i \(-0.542570\pi\)
−0.133340 + 0.991070i \(0.542570\pi\)
\(338\) 0 0
\(339\) 158.747 0.0254334
\(340\) 0 0
\(341\) −16355.7 −2.59739
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 6606.12 1.03090
\(346\) 0 0
\(347\) 5709.99 0.883368 0.441684 0.897171i \(-0.354381\pi\)
0.441684 + 0.897171i \(0.354381\pi\)
\(348\) 0 0
\(349\) −447.244 −0.0685973 −0.0342986 0.999412i \(-0.510920\pi\)
−0.0342986 + 0.999412i \(0.510920\pi\)
\(350\) 0 0
\(351\) 1005.24 0.152865
\(352\) 0 0
\(353\) −10645.7 −1.60514 −0.802569 0.596560i \(-0.796534\pi\)
−0.802569 + 0.596560i \(0.796534\pi\)
\(354\) 0 0
\(355\) 13761.0 2.05734
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −9097.47 −1.33745 −0.668727 0.743508i \(-0.733161\pi\)
−0.668727 + 0.743508i \(0.733161\pi\)
\(360\) 0 0
\(361\) −3906.31 −0.569516
\(362\) 0 0
\(363\) 3847.85 0.556363
\(364\) 0 0
\(365\) 2979.01 0.427201
\(366\) 0 0
\(367\) 5287.83 0.752104 0.376052 0.926598i \(-0.377281\pi\)
0.376052 + 0.926598i \(0.377281\pi\)
\(368\) 0 0
\(369\) −1854.29 −0.261600
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 5895.01 0.818317 0.409159 0.912463i \(-0.365822\pi\)
0.409159 + 0.912463i \(0.365822\pi\)
\(374\) 0 0
\(375\) −3550.59 −0.488938
\(376\) 0 0
\(377\) 2274.51 0.310724
\(378\) 0 0
\(379\) 3842.41 0.520769 0.260384 0.965505i \(-0.416151\pi\)
0.260384 + 0.965505i \(0.416151\pi\)
\(380\) 0 0
\(381\) 1331.10 0.178988
\(382\) 0 0
\(383\) 5013.74 0.668903 0.334452 0.942413i \(-0.391449\pi\)
0.334452 + 0.942413i \(0.391449\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 3056.95 0.401534
\(388\) 0 0
\(389\) 11182.5 1.45752 0.728758 0.684771i \(-0.240098\pi\)
0.728758 + 0.684771i \(0.240098\pi\)
\(390\) 0 0
\(391\) 3930.40 0.508360
\(392\) 0 0
\(393\) −6460.45 −0.829228
\(394\) 0 0
\(395\) 14445.9 1.84013
\(396\) 0 0
\(397\) −3406.80 −0.430686 −0.215343 0.976539i \(-0.569087\pi\)
−0.215343 + 0.976539i \(0.569087\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 83.0401 0.0103412 0.00517061 0.999987i \(-0.498354\pi\)
0.00517061 + 0.999987i \(0.498354\pi\)
\(402\) 0 0
\(403\) 11911.1 1.47230
\(404\) 0 0
\(405\) 1008.14 0.123692
\(406\) 0 0
\(407\) 16108.0 1.96178
\(408\) 0 0
\(409\) 2456.20 0.296947 0.148473 0.988916i \(-0.452564\pi\)
0.148473 + 0.988916i \(0.452564\pi\)
\(410\) 0 0
\(411\) 789.323 0.0947309
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −36.4871 −0.00431586
\(416\) 0 0
\(417\) 3497.30 0.410704
\(418\) 0 0
\(419\) −3437.96 −0.400848 −0.200424 0.979709i \(-0.564232\pi\)
−0.200424 + 0.979709i \(0.564232\pi\)
\(420\) 0 0
\(421\) −5347.62 −0.619067 −0.309533 0.950889i \(-0.600173\pi\)
−0.309533 + 0.950889i \(0.600173\pi\)
\(422\) 0 0
\(423\) 1278.58 0.146966
\(424\) 0 0
\(425\) 664.419 0.0758331
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −5710.16 −0.642632
\(430\) 0 0
\(431\) 851.643 0.0951791 0.0475895 0.998867i \(-0.484846\pi\)
0.0475895 + 0.998867i \(0.484846\pi\)
\(432\) 0 0
\(433\) −3433.42 −0.381061 −0.190531 0.981681i \(-0.561021\pi\)
−0.190531 + 0.981681i \(0.561021\pi\)
\(434\) 0 0
\(435\) 2281.08 0.251424
\(436\) 0 0
\(437\) 9613.84 1.05238
\(438\) 0 0
\(439\) −9738.39 −1.05874 −0.529371 0.848390i \(-0.677572\pi\)
−0.529371 + 0.848390i \(0.677572\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 9934.96 1.06552 0.532759 0.846267i \(-0.321155\pi\)
0.532759 + 0.846267i \(0.321155\pi\)
\(444\) 0 0
\(445\) −15915.5 −1.69543
\(446\) 0 0
\(447\) −5295.58 −0.560341
\(448\) 0 0
\(449\) −7557.33 −0.794327 −0.397163 0.917748i \(-0.630005\pi\)
−0.397163 + 0.917748i \(0.630005\pi\)
\(450\) 0 0
\(451\) 10533.1 1.09974
\(452\) 0 0
\(453\) 8076.94 0.837721
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 14011.8 1.43424 0.717118 0.696951i \(-0.245461\pi\)
0.717118 + 0.696951i \(0.245461\pi\)
\(458\) 0 0
\(459\) 599.808 0.0609949
\(460\) 0 0
\(461\) −1669.61 −0.168680 −0.0843399 0.996437i \(-0.526878\pi\)
−0.0843399 + 0.996437i \(0.526878\pi\)
\(462\) 0 0
\(463\) 14785.4 1.48409 0.742046 0.670349i \(-0.233856\pi\)
0.742046 + 0.670349i \(0.233856\pi\)
\(464\) 0 0
\(465\) 11945.6 1.19132
\(466\) 0 0
\(467\) 4603.17 0.456122 0.228061 0.973647i \(-0.426761\pi\)
0.228061 + 0.973647i \(0.426761\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −5824.14 −0.569772
\(472\) 0 0
\(473\) −17364.7 −1.68801
\(474\) 0 0
\(475\) 1625.18 0.156987
\(476\) 0 0
\(477\) 2790.14 0.267824
\(478\) 0 0
\(479\) 3477.35 0.331700 0.165850 0.986151i \(-0.446963\pi\)
0.165850 + 0.986151i \(0.446963\pi\)
\(480\) 0 0
\(481\) −11730.8 −1.11201
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 983.993 0.0921254
\(486\) 0 0
\(487\) 4344.17 0.404216 0.202108 0.979363i \(-0.435221\pi\)
0.202108 + 0.979363i \(0.435221\pi\)
\(488\) 0 0
\(489\) 6308.51 0.583396
\(490\) 0 0
\(491\) 4982.89 0.457993 0.228997 0.973427i \(-0.426456\pi\)
0.228997 + 0.973427i \(0.426456\pi\)
\(492\) 0 0
\(493\) 1357.16 0.123982
\(494\) 0 0
\(495\) −5726.66 −0.519988
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 15326.2 1.37494 0.687468 0.726215i \(-0.258722\pi\)
0.687468 + 0.726215i \(0.258722\pi\)
\(500\) 0 0
\(501\) −7032.65 −0.627137
\(502\) 0 0
\(503\) −1516.04 −0.134387 −0.0671936 0.997740i \(-0.521405\pi\)
−0.0671936 + 0.997740i \(0.521405\pi\)
\(504\) 0 0
\(505\) 17077.5 1.50483
\(506\) 0 0
\(507\) −2432.53 −0.213082
\(508\) 0 0
\(509\) 2653.64 0.231081 0.115541 0.993303i \(-0.463140\pi\)
0.115541 + 0.993303i \(0.463140\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 1467.14 0.126269
\(514\) 0 0
\(515\) 3217.73 0.275321
\(516\) 0 0
\(517\) −7262.82 −0.617830
\(518\) 0 0
\(519\) 10411.9 0.880604
\(520\) 0 0
\(521\) −13132.1 −1.10428 −0.552139 0.833752i \(-0.686188\pi\)
−0.552139 + 0.833752i \(0.686188\pi\)
\(522\) 0 0
\(523\) −3086.34 −0.258042 −0.129021 0.991642i \(-0.541184\pi\)
−0.129021 + 0.991642i \(0.541184\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 7107.16 0.587462
\(528\) 0 0
\(529\) 19135.3 1.57272
\(530\) 0 0
\(531\) −2534.85 −0.207162
\(532\) 0 0
\(533\) −7670.80 −0.623376
\(534\) 0 0
\(535\) −15711.7 −1.26968
\(536\) 0 0
\(537\) −2867.31 −0.230416
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 926.095 0.0735969 0.0367985 0.999323i \(-0.488284\pi\)
0.0367985 + 0.999323i \(0.488284\pi\)
\(542\) 0 0
\(543\) 12660.8 1.00060
\(544\) 0 0
\(545\) 3445.52 0.270807
\(546\) 0 0
\(547\) 592.871 0.0463425 0.0231712 0.999732i \(-0.492624\pi\)
0.0231712 + 0.999732i \(0.492624\pi\)
\(548\) 0 0
\(549\) −4894.64 −0.380507
\(550\) 0 0
\(551\) 3319.63 0.256663
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −11764.7 −0.899788
\(556\) 0 0
\(557\) −12245.3 −0.931512 −0.465756 0.884913i \(-0.654217\pi\)
−0.465756 + 0.884913i \(0.654217\pi\)
\(558\) 0 0
\(559\) 12646.0 0.956829
\(560\) 0 0
\(561\) −3407.15 −0.256417
\(562\) 0 0
\(563\) 14594.6 1.09252 0.546261 0.837615i \(-0.316051\pi\)
0.546261 + 0.837615i \(0.316051\pi\)
\(564\) 0 0
\(565\) 658.599 0.0490398
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 22911.2 1.68803 0.844015 0.536320i \(-0.180186\pi\)
0.844015 + 0.536320i \(0.180186\pi\)
\(570\) 0 0
\(571\) 5904.64 0.432752 0.216376 0.976310i \(-0.430576\pi\)
0.216376 + 0.976310i \(0.430576\pi\)
\(572\) 0 0
\(573\) −10554.1 −0.769465
\(574\) 0 0
\(575\) 5291.53 0.383778
\(576\) 0 0
\(577\) 9513.21 0.686378 0.343189 0.939266i \(-0.388493\pi\)
0.343189 + 0.939266i \(0.388493\pi\)
\(578\) 0 0
\(579\) −15053.0 −1.08045
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −15849.1 −1.12591
\(584\) 0 0
\(585\) 4170.48 0.294749
\(586\) 0 0
\(587\) −22790.6 −1.60250 −0.801252 0.598327i \(-0.795833\pi\)
−0.801252 + 0.598327i \(0.795833\pi\)
\(588\) 0 0
\(589\) 17384.3 1.21614
\(590\) 0 0
\(591\) −8514.41 −0.592616
\(592\) 0 0
\(593\) −18262.8 −1.26469 −0.632346 0.774686i \(-0.717908\pi\)
−0.632346 + 0.774686i \(0.717908\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 1064.70 0.0729907
\(598\) 0 0
\(599\) 6958.09 0.474624 0.237312 0.971433i \(-0.423734\pi\)
0.237312 + 0.971433i \(0.423734\pi\)
\(600\) 0 0
\(601\) 2305.39 0.156471 0.0782353 0.996935i \(-0.475071\pi\)
0.0782353 + 0.996935i \(0.475071\pi\)
\(602\) 0 0
\(603\) −4314.23 −0.291358
\(604\) 0 0
\(605\) 15963.7 1.07276
\(606\) 0 0
\(607\) −16179.2 −1.08187 −0.540935 0.841064i \(-0.681929\pi\)
−0.540935 + 0.841064i \(0.681929\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 5289.20 0.350210
\(612\) 0 0
\(613\) 20540.7 1.35340 0.676699 0.736260i \(-0.263410\pi\)
0.676699 + 0.736260i \(0.263410\pi\)
\(614\) 0 0
\(615\) −7692.96 −0.504407
\(616\) 0 0
\(617\) 6918.19 0.451403 0.225702 0.974196i \(-0.427533\pi\)
0.225702 + 0.974196i \(0.427533\pi\)
\(618\) 0 0
\(619\) −8081.62 −0.524762 −0.262381 0.964964i \(-0.584508\pi\)
−0.262381 + 0.964964i \(0.584508\pi\)
\(620\) 0 0
\(621\) 4776.96 0.308684
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −18469.0 −1.18202
\(626\) 0 0
\(627\) −8333.96 −0.530823
\(628\) 0 0
\(629\) −6999.54 −0.443704
\(630\) 0 0
\(631\) −27293.3 −1.72191 −0.860957 0.508677i \(-0.830135\pi\)
−0.860957 + 0.508677i \(0.830135\pi\)
\(632\) 0 0
\(633\) 2258.02 0.141782
\(634\) 0 0
\(635\) 5522.39 0.345117
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 9950.70 0.616031
\(640\) 0 0
\(641\) 19255.6 1.18651 0.593254 0.805015i \(-0.297843\pi\)
0.593254 + 0.805015i \(0.297843\pi\)
\(642\) 0 0
\(643\) −19996.4 −1.22641 −0.613204 0.789925i \(-0.710120\pi\)
−0.613204 + 0.789925i \(0.710120\pi\)
\(644\) 0 0
\(645\) 12682.5 0.774222
\(646\) 0 0
\(647\) 7064.20 0.429246 0.214623 0.976697i \(-0.431148\pi\)
0.214623 + 0.976697i \(0.431148\pi\)
\(648\) 0 0
\(649\) 14398.9 0.870890
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −13821.1 −0.828269 −0.414134 0.910216i \(-0.635916\pi\)
−0.414134 + 0.910216i \(0.635916\pi\)
\(654\) 0 0
\(655\) −26802.7 −1.59889
\(656\) 0 0
\(657\) 2154.15 0.127917
\(658\) 0 0
\(659\) −7802.80 −0.461235 −0.230617 0.973044i \(-0.574075\pi\)
−0.230617 + 0.973044i \(0.574075\pi\)
\(660\) 0 0
\(661\) 15817.3 0.930744 0.465372 0.885115i \(-0.345921\pi\)
0.465372 + 0.885115i \(0.345921\pi\)
\(662\) 0 0
\(663\) 2481.28 0.145347
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 10808.6 0.627452
\(668\) 0 0
\(669\) −9233.25 −0.533599
\(670\) 0 0
\(671\) 27803.5 1.59962
\(672\) 0 0
\(673\) 2943.30 0.168582 0.0842911 0.996441i \(-0.473137\pi\)
0.0842911 + 0.996441i \(0.473137\pi\)
\(674\) 0 0
\(675\) 807.528 0.0460471
\(676\) 0 0
\(677\) −3171.48 −0.180044 −0.0900220 0.995940i \(-0.528694\pi\)
−0.0900220 + 0.995940i \(0.528694\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −18652.3 −1.04957
\(682\) 0 0
\(683\) −24453.2 −1.36995 −0.684975 0.728567i \(-0.740187\pi\)
−0.684975 + 0.728567i \(0.740187\pi\)
\(684\) 0 0
\(685\) 3274.70 0.182656
\(686\) 0 0
\(687\) 1509.76 0.0838443
\(688\) 0 0
\(689\) 11542.2 0.638207
\(690\) 0 0
\(691\) 8595.89 0.473232 0.236616 0.971603i \(-0.423962\pi\)
0.236616 + 0.971603i \(0.423962\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 14509.4 0.791903
\(696\) 0 0
\(697\) −4577.02 −0.248733
\(698\) 0 0
\(699\) −805.019 −0.0435602
\(700\) 0 0
\(701\) −21476.1 −1.15712 −0.578561 0.815639i \(-0.696385\pi\)
−0.578561 + 0.815639i \(0.696385\pi\)
\(702\) 0 0
\(703\) −17121.0 −0.918537
\(704\) 0 0
\(705\) 5304.48 0.283373
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −13538.9 −0.717158 −0.358579 0.933499i \(-0.616739\pi\)
−0.358579 + 0.933499i \(0.616739\pi\)
\(710\) 0 0
\(711\) 10446.0 0.550992
\(712\) 0 0
\(713\) 56602.5 2.97304
\(714\) 0 0
\(715\) −23690.0 −1.23910
\(716\) 0 0
\(717\) −15569.3 −0.810943
\(718\) 0 0
\(719\) 13883.7 0.720131 0.360065 0.932927i \(-0.382754\pi\)
0.360065 + 0.932927i \(0.382754\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 18512.8 0.952281
\(724\) 0 0
\(725\) 1827.15 0.0935983
\(726\) 0 0
\(727\) −18292.9 −0.933215 −0.466607 0.884465i \(-0.654524\pi\)
−0.466607 + 0.884465i \(0.654524\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) 7545.61 0.381785
\(732\) 0 0
\(733\) 14245.8 0.717848 0.358924 0.933367i \(-0.383144\pi\)
0.358924 + 0.933367i \(0.383144\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 24506.5 1.22484
\(738\) 0 0
\(739\) −1363.89 −0.0678913 −0.0339456 0.999424i \(-0.510807\pi\)
−0.0339456 + 0.999424i \(0.510807\pi\)
\(740\) 0 0
\(741\) 6069.27 0.300891
\(742\) 0 0
\(743\) 21789.4 1.07588 0.537938 0.842984i \(-0.319203\pi\)
0.537938 + 0.842984i \(0.319203\pi\)
\(744\) 0 0
\(745\) −21970.0 −1.08043
\(746\) 0 0
\(747\) −26.3842 −0.00129230
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −2119.55 −0.102987 −0.0514937 0.998673i \(-0.516398\pi\)
−0.0514937 + 0.998673i \(0.516398\pi\)
\(752\) 0 0
\(753\) 5675.74 0.274682
\(754\) 0 0
\(755\) 33509.1 1.61526
\(756\) 0 0
\(757\) 28202.4 1.35408 0.677038 0.735948i \(-0.263263\pi\)
0.677038 + 0.735948i \(0.263263\pi\)
\(758\) 0 0
\(759\) −27135.0 −1.29768
\(760\) 0 0
\(761\) 11147.0 0.530985 0.265493 0.964113i \(-0.414465\pi\)
0.265493 + 0.964113i \(0.414465\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 2488.45 0.117608
\(766\) 0 0
\(767\) −10486.1 −0.493654
\(768\) 0 0
\(769\) −4109.29 −0.192698 −0.0963491 0.995348i \(-0.530717\pi\)
−0.0963491 + 0.995348i \(0.530717\pi\)
\(770\) 0 0
\(771\) −19619.8 −0.916459
\(772\) 0 0
\(773\) 13891.4 0.646362 0.323181 0.946337i \(-0.395248\pi\)
0.323181 + 0.946337i \(0.395248\pi\)
\(774\) 0 0
\(775\) 9568.44 0.443495
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −11195.5 −0.514917
\(780\) 0 0
\(781\) −56523.9 −2.58974
\(782\) 0 0
\(783\) 1649.47 0.0752839
\(784\) 0 0
\(785\) −24162.9 −1.09861
\(786\) 0 0
\(787\) −9342.35 −0.423150 −0.211575 0.977362i \(-0.567859\pi\)
−0.211575 + 0.977362i \(0.567859\pi\)
\(788\) 0 0
\(789\) 16127.7 0.727708
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −20248.1 −0.906723
\(794\) 0 0
\(795\) 11575.6 0.516407
\(796\) 0 0
\(797\) −24324.3 −1.08107 −0.540534 0.841322i \(-0.681778\pi\)
−0.540534 + 0.841322i \(0.681778\pi\)
\(798\) 0 0
\(799\) 3155.97 0.139737
\(800\) 0 0
\(801\) −11508.7 −0.507664
\(802\) 0 0
\(803\) −12236.4 −0.537751
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −9716.65 −0.423844
\(808\) 0 0
\(809\) 34454.9 1.49737 0.748684 0.662927i \(-0.230686\pi\)
0.748684 + 0.662927i \(0.230686\pi\)
\(810\) 0 0
\(811\) −8350.13 −0.361545 −0.180772 0.983525i \(-0.557860\pi\)
−0.180772 + 0.983525i \(0.557860\pi\)
\(812\) 0 0
\(813\) 4072.37 0.175676
\(814\) 0 0
\(815\) 26172.4 1.12488
\(816\) 0 0
\(817\) 18456.7 0.790355
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −18834.8 −0.800655 −0.400327 0.916372i \(-0.631104\pi\)
−0.400327 + 0.916372i \(0.631104\pi\)
\(822\) 0 0
\(823\) 9656.76 0.409008 0.204504 0.978866i \(-0.434442\pi\)
0.204504 + 0.978866i \(0.434442\pi\)
\(824\) 0 0
\(825\) −4587.08 −0.193578
\(826\) 0 0
\(827\) −20759.6 −0.872892 −0.436446 0.899731i \(-0.643763\pi\)
−0.436446 + 0.899731i \(0.643763\pi\)
\(828\) 0 0
\(829\) −15616.1 −0.654245 −0.327123 0.944982i \(-0.606079\pi\)
−0.327123 + 0.944982i \(0.606079\pi\)
\(830\) 0 0
\(831\) −7684.90 −0.320802
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −29176.6 −1.20922
\(836\) 0 0
\(837\) 8637.96 0.356716
\(838\) 0 0
\(839\) −417.027 −0.0171601 −0.00858007 0.999963i \(-0.502731\pi\)
−0.00858007 + 0.999963i \(0.502731\pi\)
\(840\) 0 0
\(841\) −20656.8 −0.846973
\(842\) 0 0
\(843\) 5358.52 0.218929
\(844\) 0 0
\(845\) −10092.0 −0.410856
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −22164.8 −0.895990
\(850\) 0 0
\(851\) −55745.4 −2.24551
\(852\) 0 0
\(853\) −24917.4 −1.00018 −0.500092 0.865972i \(-0.666700\pi\)
−0.500092 + 0.865972i \(0.666700\pi\)
\(854\) 0 0
\(855\) 6086.80 0.243467
\(856\) 0 0
\(857\) −44523.8 −1.77468 −0.887342 0.461112i \(-0.847451\pi\)
−0.887342 + 0.461112i \(0.847451\pi\)
\(858\) 0 0
\(859\) −24146.4 −0.959097 −0.479548 0.877515i \(-0.659200\pi\)
−0.479548 + 0.877515i \(0.659200\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −26442.6 −1.04301 −0.521505 0.853248i \(-0.674629\pi\)
−0.521505 + 0.853248i \(0.674629\pi\)
\(864\) 0 0
\(865\) 43196.5 1.69795
\(866\) 0 0
\(867\) −13258.5 −0.519355
\(868\) 0 0
\(869\) −59337.4 −2.31632
\(870\) 0 0
\(871\) −17847.1 −0.694288
\(872\) 0 0
\(873\) 711.536 0.0275852
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −22516.1 −0.866950 −0.433475 0.901166i \(-0.642713\pi\)
−0.433475 + 0.901166i \(0.642713\pi\)
\(878\) 0 0
\(879\) 1478.94 0.0567503
\(880\) 0 0
\(881\) 10120.6 0.387027 0.193514 0.981098i \(-0.438012\pi\)
0.193514 + 0.981098i \(0.438012\pi\)
\(882\) 0 0
\(883\) −20748.5 −0.790761 −0.395380 0.918517i \(-0.629387\pi\)
−0.395380 + 0.918517i \(0.629387\pi\)
\(884\) 0 0
\(885\) −10516.4 −0.399442
\(886\) 0 0
\(887\) 25499.4 0.965259 0.482630 0.875825i \(-0.339682\pi\)
0.482630 + 0.875825i \(0.339682\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −4141.01 −0.155700
\(892\) 0 0
\(893\) 7719.57 0.289278
\(894\) 0 0
\(895\) −11895.7 −0.444280
\(896\) 0 0
\(897\) 19761.3 0.735574
\(898\) 0 0
\(899\) 19544.7 0.725085
\(900\) 0 0
\(901\) 6887.04 0.254651
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 52526.3 1.92932
\(906\) 0 0
\(907\) 37807.0 1.38408 0.692040 0.721859i \(-0.256712\pi\)
0.692040 + 0.721859i \(0.256712\pi\)
\(908\) 0 0
\(909\) 12348.9 0.450593
\(910\) 0 0
\(911\) −3230.08 −0.117472 −0.0587362 0.998274i \(-0.518707\pi\)
−0.0587362 + 0.998274i \(0.518707\pi\)
\(912\) 0 0
\(913\) 149.873 0.00543271
\(914\) 0 0
\(915\) −20306.6 −0.733678
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −35343.1 −1.26862 −0.634310 0.773079i \(-0.718716\pi\)
−0.634310 + 0.773079i \(0.718716\pi\)
\(920\) 0 0
\(921\) −2966.43 −0.106132
\(922\) 0 0
\(923\) 41164.0 1.46796
\(924\) 0 0
\(925\) −9423.55 −0.334967
\(926\) 0 0
\(927\) 2326.78 0.0824394
\(928\) 0 0
\(929\) 33030.2 1.16651 0.583254 0.812289i \(-0.301779\pi\)
0.583254 + 0.812289i \(0.301779\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −28789.7 −1.01022
\(934\) 0 0
\(935\) −14135.4 −0.494413
\(936\) 0 0
\(937\) 54695.9 1.90698 0.953488 0.301430i \(-0.0974640\pi\)
0.953488 + 0.301430i \(0.0974640\pi\)
\(938\) 0 0
\(939\) 2897.14 0.100686
\(940\) 0 0
\(941\) −18255.3 −0.632418 −0.316209 0.948690i \(-0.602410\pi\)
−0.316209 + 0.948690i \(0.602410\pi\)
\(942\) 0 0
\(943\) −36452.1 −1.25879
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 6215.75 0.213289 0.106645 0.994297i \(-0.465989\pi\)
0.106645 + 0.994297i \(0.465989\pi\)
\(948\) 0 0
\(949\) 8911.27 0.304818
\(950\) 0 0
\(951\) −26957.9 −0.919212
\(952\) 0 0
\(953\) 8594.53 0.292135 0.146067 0.989275i \(-0.453338\pi\)
0.146067 + 0.989275i \(0.453338\pi\)
\(954\) 0 0
\(955\) −43786.2 −1.48365
\(956\) 0 0
\(957\) −9369.65 −0.316487
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 72560.6 2.43566
\(962\) 0 0
\(963\) −11361.3 −0.380180
\(964\) 0 0
\(965\) −62451.1 −2.08329
\(966\) 0 0
\(967\) −17168.1 −0.570929 −0.285464 0.958389i \(-0.592148\pi\)
−0.285464 + 0.958389i \(0.592148\pi\)
\(968\) 0 0
\(969\) 3621.42 0.120059
\(970\) 0 0
\(971\) 11926.2 0.394162 0.197081 0.980387i \(-0.436854\pi\)
0.197081 + 0.980387i \(0.436854\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 3340.57 0.109727
\(976\) 0 0
\(977\) 14038.2 0.459696 0.229848 0.973227i \(-0.426177\pi\)
0.229848 + 0.973227i \(0.426177\pi\)
\(978\) 0 0
\(979\) 65373.8 2.13417
\(980\) 0 0
\(981\) 2491.50 0.0810880
\(982\) 0 0
\(983\) 20351.4 0.660334 0.330167 0.943923i \(-0.392895\pi\)
0.330167 + 0.943923i \(0.392895\pi\)
\(984\) 0 0
\(985\) −35324.1 −1.14266
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 60094.4 1.93214
\(990\) 0 0
\(991\) −32505.7 −1.04196 −0.520978 0.853570i \(-0.674433\pi\)
−0.520978 + 0.853570i \(0.674433\pi\)
\(992\) 0 0
\(993\) −11421.9 −0.365018
\(994\) 0 0
\(995\) 4417.18 0.140738
\(996\) 0 0
\(997\) −24847.1 −0.789282 −0.394641 0.918835i \(-0.629131\pi\)
−0.394641 + 0.918835i \(0.629131\pi\)
\(998\) 0 0
\(999\) −8507.16 −0.269424
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 588.4.a.i.1.2 2
3.2 odd 2 1764.4.a.o.1.1 2
4.3 odd 2 2352.4.a.bt.1.2 2
7.2 even 3 84.4.i.a.25.1 4
7.3 odd 6 588.4.i.j.373.2 4
7.4 even 3 84.4.i.a.37.1 yes 4
7.5 odd 6 588.4.i.j.361.2 4
7.6 odd 2 588.4.a.f.1.1 2
21.2 odd 6 252.4.k.f.109.2 4
21.5 even 6 1764.4.k.q.361.1 4
21.11 odd 6 252.4.k.f.37.2 4
21.17 even 6 1764.4.k.q.1549.1 4
21.20 even 2 1764.4.a.y.1.2 2
28.11 odd 6 336.4.q.i.289.1 4
28.23 odd 6 336.4.q.i.193.1 4
28.27 even 2 2352.4.a.bx.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
84.4.i.a.25.1 4 7.2 even 3
84.4.i.a.37.1 yes 4 7.4 even 3
252.4.k.f.37.2 4 21.11 odd 6
252.4.k.f.109.2 4 21.2 odd 6
336.4.q.i.193.1 4 28.23 odd 6
336.4.q.i.289.1 4 28.11 odd 6
588.4.a.f.1.1 2 7.6 odd 2
588.4.a.i.1.2 2 1.1 even 1 trivial
588.4.i.j.361.2 4 7.5 odd 6
588.4.i.j.373.2 4 7.3 odd 6
1764.4.a.o.1.1 2 3.2 odd 2
1764.4.a.y.1.2 2 21.20 even 2
1764.4.k.q.361.1 4 21.5 even 6
1764.4.k.q.1549.1 4 21.17 even 6
2352.4.a.bt.1.2 2 4.3 odd 2
2352.4.a.bx.1.1 2 28.27 even 2