Properties

Label 570.2.a.h.1.1
Level $570$
Weight $2$
Character 570.1
Self dual yes
Analytic conductor $4.551$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(4.55147291521\)
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 \(\chi\) \(=\) 570.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{12} +6.00000 q^{13} -2.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} +8.00000 q^{17} +1.00000 q^{18} +1.00000 q^{19} +1.00000 q^{20} +2.00000 q^{21} -4.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} +6.00000 q^{26} -1.00000 q^{27} -2.00000 q^{28} +2.00000 q^{29} -1.00000 q^{30} -2.00000 q^{31} +1.00000 q^{32} +8.00000 q^{34} -2.00000 q^{35} +1.00000 q^{36} -2.00000 q^{37} +1.00000 q^{38} -6.00000 q^{39} +1.00000 q^{40} -12.0000 q^{41} +2.00000 q^{42} +4.00000 q^{43} +1.00000 q^{45} -4.00000 q^{46} +12.0000 q^{47} -1.00000 q^{48} -3.00000 q^{49} +1.00000 q^{50} -8.00000 q^{51} +6.00000 q^{52} +10.0000 q^{53} -1.00000 q^{54} -2.00000 q^{56} -1.00000 q^{57} +2.00000 q^{58} +6.00000 q^{59} -1.00000 q^{60} -14.0000 q^{61} -2.00000 q^{62} -2.00000 q^{63} +1.00000 q^{64} +6.00000 q^{65} -12.0000 q^{67} +8.00000 q^{68} +4.00000 q^{69} -2.00000 q^{70} -8.00000 q^{71} +1.00000 q^{72} -10.0000 q^{73} -2.00000 q^{74} -1.00000 q^{75} +1.00000 q^{76} -6.00000 q^{78} +14.0000 q^{79} +1.00000 q^{80} +1.00000 q^{81} -12.0000 q^{82} +2.00000 q^{83} +2.00000 q^{84} +8.00000 q^{85} +4.00000 q^{86} -2.00000 q^{87} +1.00000 q^{90} -12.0000 q^{91} -4.00000 q^{92} +2.00000 q^{93} +12.0000 q^{94} +1.00000 q^{95} -1.00000 q^{96} +2.00000 q^{97} -3.00000 q^{98} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) −1.00000 −0.408248
\(7\) −2.00000 −0.755929 −0.377964 0.925820i \(-0.623376\pi\)
−0.377964 + 0.925820i \(0.623376\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 1.00000 0.316228
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) −1.00000 −0.288675
\(13\) 6.00000 1.66410 0.832050 0.554700i \(-0.187167\pi\)
0.832050 + 0.554700i \(0.187167\pi\)
\(14\) −2.00000 −0.534522
\(15\) −1.00000 −0.258199
\(16\) 1.00000 0.250000
\(17\) 8.00000 1.94029 0.970143 0.242536i \(-0.0779791\pi\)
0.970143 + 0.242536i \(0.0779791\pi\)
\(18\) 1.00000 0.235702
\(19\) 1.00000 0.229416
\(20\) 1.00000 0.223607
\(21\) 2.00000 0.436436
\(22\) 0 0
\(23\) −4.00000 −0.834058 −0.417029 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) −1.00000 −0.204124
\(25\) 1.00000 0.200000
\(26\) 6.00000 1.17670
\(27\) −1.00000 −0.192450
\(28\) −2.00000 −0.377964
\(29\) 2.00000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) −1.00000 −0.182574
\(31\) −2.00000 −0.359211 −0.179605 0.983739i \(-0.557482\pi\)
−0.179605 + 0.983739i \(0.557482\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 8.00000 1.37199
\(35\) −2.00000 −0.338062
\(36\) 1.00000 0.166667
\(37\) −2.00000 −0.328798 −0.164399 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) 1.00000 0.162221
\(39\) −6.00000 −0.960769
\(40\) 1.00000 0.158114
\(41\) −12.0000 −1.87409 −0.937043 0.349215i \(-0.886448\pi\)
−0.937043 + 0.349215i \(0.886448\pi\)
\(42\) 2.00000 0.308607
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 0 0
\(45\) 1.00000 0.149071
\(46\) −4.00000 −0.589768
\(47\) 12.0000 1.75038 0.875190 0.483779i \(-0.160736\pi\)
0.875190 + 0.483779i \(0.160736\pi\)
\(48\) −1.00000 −0.144338
\(49\) −3.00000 −0.428571
\(50\) 1.00000 0.141421
\(51\) −8.00000 −1.12022
\(52\) 6.00000 0.832050
\(53\) 10.0000 1.37361 0.686803 0.726844i \(-0.259014\pi\)
0.686803 + 0.726844i \(0.259014\pi\)
\(54\) −1.00000 −0.136083
\(55\) 0 0
\(56\) −2.00000 −0.267261
\(57\) −1.00000 −0.132453
\(58\) 2.00000 0.262613
\(59\) 6.00000 0.781133 0.390567 0.920575i \(-0.372279\pi\)
0.390567 + 0.920575i \(0.372279\pi\)
\(60\) −1.00000 −0.129099
\(61\) −14.0000 −1.79252 −0.896258 0.443533i \(-0.853725\pi\)
−0.896258 + 0.443533i \(0.853725\pi\)
\(62\) −2.00000 −0.254000
\(63\) −2.00000 −0.251976
\(64\) 1.00000 0.125000
\(65\) 6.00000 0.744208
\(66\) 0 0
\(67\) −12.0000 −1.46603 −0.733017 0.680211i \(-0.761888\pi\)
−0.733017 + 0.680211i \(0.761888\pi\)
\(68\) 8.00000 0.970143
\(69\) 4.00000 0.481543
\(70\) −2.00000 −0.239046
\(71\) −8.00000 −0.949425 −0.474713 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) 1.00000 0.117851
\(73\) −10.0000 −1.17041 −0.585206 0.810885i \(-0.698986\pi\)
−0.585206 + 0.810885i \(0.698986\pi\)
\(74\) −2.00000 −0.232495
\(75\) −1.00000 −0.115470
\(76\) 1.00000 0.114708
\(77\) 0 0
\(78\) −6.00000 −0.679366
\(79\) 14.0000 1.57512 0.787562 0.616236i \(-0.211343\pi\)
0.787562 + 0.616236i \(0.211343\pi\)
\(80\) 1.00000 0.111803
\(81\) 1.00000 0.111111
\(82\) −12.0000 −1.32518
\(83\) 2.00000 0.219529 0.109764 0.993958i \(-0.464990\pi\)
0.109764 + 0.993958i \(0.464990\pi\)
\(84\) 2.00000 0.218218
\(85\) 8.00000 0.867722
\(86\) 4.00000 0.431331
\(87\) −2.00000 −0.214423
\(88\) 0 0
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 1.00000 0.105409
\(91\) −12.0000 −1.25794
\(92\) −4.00000 −0.417029
\(93\) 2.00000 0.207390
\(94\) 12.0000 1.23771
\(95\) 1.00000 0.102598
\(96\) −1.00000 −0.102062
\(97\) 2.00000 0.203069 0.101535 0.994832i \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) −3.00000 −0.303046
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) −6.00000 −0.597022 −0.298511 0.954406i \(-0.596490\pi\)
−0.298511 + 0.954406i \(0.596490\pi\)
\(102\) −8.00000 −0.792118
\(103\) −16.0000 −1.57653 −0.788263 0.615338i \(-0.789020\pi\)
−0.788263 + 0.615338i \(0.789020\pi\)
\(104\) 6.00000 0.588348
\(105\) 2.00000 0.195180
\(106\) 10.0000 0.971286
\(107\) −16.0000 −1.54678 −0.773389 0.633932i \(-0.781440\pi\)
−0.773389 + 0.633932i \(0.781440\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −12.0000 −1.14939 −0.574696 0.818367i \(-0.694880\pi\)
−0.574696 + 0.818367i \(0.694880\pi\)
\(110\) 0 0
\(111\) 2.00000 0.189832
\(112\) −2.00000 −0.188982
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) −1.00000 −0.0936586
\(115\) −4.00000 −0.373002
\(116\) 2.00000 0.185695
\(117\) 6.00000 0.554700
\(118\) 6.00000 0.552345
\(119\) −16.0000 −1.46672
\(120\) −1.00000 −0.0912871
\(121\) −11.0000 −1.00000
\(122\) −14.0000 −1.26750
\(123\) 12.0000 1.08200
\(124\) −2.00000 −0.179605
\(125\) 1.00000 0.0894427
\(126\) −2.00000 −0.178174
\(127\) −8.00000 −0.709885 −0.354943 0.934888i \(-0.615500\pi\)
−0.354943 + 0.934888i \(0.615500\pi\)
\(128\) 1.00000 0.0883883
\(129\) −4.00000 −0.352180
\(130\) 6.00000 0.526235
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) −2.00000 −0.173422
\(134\) −12.0000 −1.03664
\(135\) −1.00000 −0.0860663
\(136\) 8.00000 0.685994
\(137\) 12.0000 1.02523 0.512615 0.858619i \(-0.328677\pi\)
0.512615 + 0.858619i \(0.328677\pi\)
\(138\) 4.00000 0.340503
\(139\) −12.0000 −1.01783 −0.508913 0.860818i \(-0.669953\pi\)
−0.508913 + 0.860818i \(0.669953\pi\)
\(140\) −2.00000 −0.169031
\(141\) −12.0000 −1.01058
\(142\) −8.00000 −0.671345
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 2.00000 0.166091
\(146\) −10.0000 −0.827606
\(147\) 3.00000 0.247436
\(148\) −2.00000 −0.164399
\(149\) 10.0000 0.819232 0.409616 0.912258i \(-0.365663\pi\)
0.409616 + 0.912258i \(0.365663\pi\)
\(150\) −1.00000 −0.0816497
\(151\) 18.0000 1.46482 0.732410 0.680864i \(-0.238396\pi\)
0.732410 + 0.680864i \(0.238396\pi\)
\(152\) 1.00000 0.0811107
\(153\) 8.00000 0.646762
\(154\) 0 0
\(155\) −2.00000 −0.160644
\(156\) −6.00000 −0.480384
\(157\) −4.00000 −0.319235 −0.159617 0.987179i \(-0.551026\pi\)
−0.159617 + 0.987179i \(0.551026\pi\)
\(158\) 14.0000 1.11378
\(159\) −10.0000 −0.793052
\(160\) 1.00000 0.0790569
\(161\) 8.00000 0.630488
\(162\) 1.00000 0.0785674
\(163\) 8.00000 0.626608 0.313304 0.949653i \(-0.398564\pi\)
0.313304 + 0.949653i \(0.398564\pi\)
\(164\) −12.0000 −0.937043
\(165\) 0 0
\(166\) 2.00000 0.155230
\(167\) 8.00000 0.619059 0.309529 0.950890i \(-0.399829\pi\)
0.309529 + 0.950890i \(0.399829\pi\)
\(168\) 2.00000 0.154303
\(169\) 23.0000 1.76923
\(170\) 8.00000 0.613572
\(171\) 1.00000 0.0764719
\(172\) 4.00000 0.304997
\(173\) 2.00000 0.152057 0.0760286 0.997106i \(-0.475776\pi\)
0.0760286 + 0.997106i \(0.475776\pi\)
\(174\) −2.00000 −0.151620
\(175\) −2.00000 −0.151186
\(176\) 0 0
\(177\) −6.00000 −0.450988
\(178\) 0 0
\(179\) 10.0000 0.747435 0.373718 0.927543i \(-0.378083\pi\)
0.373718 + 0.927543i \(0.378083\pi\)
\(180\) 1.00000 0.0745356
\(181\) −12.0000 −0.891953 −0.445976 0.895045i \(-0.647144\pi\)
−0.445976 + 0.895045i \(0.647144\pi\)
\(182\) −12.0000 −0.889499
\(183\) 14.0000 1.03491
\(184\) −4.00000 −0.294884
\(185\) −2.00000 −0.147043
\(186\) 2.00000 0.146647
\(187\) 0 0
\(188\) 12.0000 0.875190
\(189\) 2.00000 0.145479
\(190\) 1.00000 0.0725476
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −2.00000 −0.143963 −0.0719816 0.997406i \(-0.522932\pi\)
−0.0719816 + 0.997406i \(0.522932\pi\)
\(194\) 2.00000 0.143592
\(195\) −6.00000 −0.429669
\(196\) −3.00000 −0.214286
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 0 0
\(199\) 4.00000 0.283552 0.141776 0.989899i \(-0.454719\pi\)
0.141776 + 0.989899i \(0.454719\pi\)
\(200\) 1.00000 0.0707107
\(201\) 12.0000 0.846415
\(202\) −6.00000 −0.422159
\(203\) −4.00000 −0.280745
\(204\) −8.00000 −0.560112
\(205\) −12.0000 −0.838116
\(206\) −16.0000 −1.11477
\(207\) −4.00000 −0.278019
\(208\) 6.00000 0.416025
\(209\) 0 0
\(210\) 2.00000 0.138013
\(211\) −16.0000 −1.10149 −0.550743 0.834675i \(-0.685655\pi\)
−0.550743 + 0.834675i \(0.685655\pi\)
\(212\) 10.0000 0.686803
\(213\) 8.00000 0.548151
\(214\) −16.0000 −1.09374
\(215\) 4.00000 0.272798
\(216\) −1.00000 −0.0680414
\(217\) 4.00000 0.271538
\(218\) −12.0000 −0.812743
\(219\) 10.0000 0.675737
\(220\) 0 0
\(221\) 48.0000 3.22883
\(222\) 2.00000 0.134231
\(223\) −4.00000 −0.267860 −0.133930 0.990991i \(-0.542760\pi\)
−0.133930 + 0.990991i \(0.542760\pi\)
\(224\) −2.00000 −0.133631
\(225\) 1.00000 0.0666667
\(226\) 6.00000 0.399114
\(227\) 20.0000 1.32745 0.663723 0.747978i \(-0.268975\pi\)
0.663723 + 0.747978i \(0.268975\pi\)
\(228\) −1.00000 −0.0662266
\(229\) 6.00000 0.396491 0.198246 0.980152i \(-0.436476\pi\)
0.198246 + 0.980152i \(0.436476\pi\)
\(230\) −4.00000 −0.263752
\(231\) 0 0
\(232\) 2.00000 0.131306
\(233\) 24.0000 1.57229 0.786146 0.618041i \(-0.212073\pi\)
0.786146 + 0.618041i \(0.212073\pi\)
\(234\) 6.00000 0.392232
\(235\) 12.0000 0.782794
\(236\) 6.00000 0.390567
\(237\) −14.0000 −0.909398
\(238\) −16.0000 −1.03713
\(239\) −8.00000 −0.517477 −0.258738 0.965947i \(-0.583307\pi\)
−0.258738 + 0.965947i \(0.583307\pi\)
\(240\) −1.00000 −0.0645497
\(241\) −14.0000 −0.901819 −0.450910 0.892570i \(-0.648900\pi\)
−0.450910 + 0.892570i \(0.648900\pi\)
\(242\) −11.0000 −0.707107
\(243\) −1.00000 −0.0641500
\(244\) −14.0000 −0.896258
\(245\) −3.00000 −0.191663
\(246\) 12.0000 0.765092
\(247\) 6.00000 0.381771
\(248\) −2.00000 −0.127000
\(249\) −2.00000 −0.126745
\(250\) 1.00000 0.0632456
\(251\) −12.0000 −0.757433 −0.378717 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) −2.00000 −0.125988
\(253\) 0 0
\(254\) −8.00000 −0.501965
\(255\) −8.00000 −0.500979
\(256\) 1.00000 0.0625000
\(257\) −30.0000 −1.87135 −0.935674 0.352865i \(-0.885208\pi\)
−0.935674 + 0.352865i \(0.885208\pi\)
\(258\) −4.00000 −0.249029
\(259\) 4.00000 0.248548
\(260\) 6.00000 0.372104
\(261\) 2.00000 0.123797
\(262\) 0 0
\(263\) −12.0000 −0.739952 −0.369976 0.929041i \(-0.620634\pi\)
−0.369976 + 0.929041i \(0.620634\pi\)
\(264\) 0 0
\(265\) 10.0000 0.614295
\(266\) −2.00000 −0.122628
\(267\) 0 0
\(268\) −12.0000 −0.733017
\(269\) −30.0000 −1.82913 −0.914566 0.404436i \(-0.867468\pi\)
−0.914566 + 0.404436i \(0.867468\pi\)
\(270\) −1.00000 −0.0608581
\(271\) −4.00000 −0.242983 −0.121491 0.992592i \(-0.538768\pi\)
−0.121491 + 0.992592i \(0.538768\pi\)
\(272\) 8.00000 0.485071
\(273\) 12.0000 0.726273
\(274\) 12.0000 0.724947
\(275\) 0 0
\(276\) 4.00000 0.240772
\(277\) 4.00000 0.240337 0.120168 0.992754i \(-0.461657\pi\)
0.120168 + 0.992754i \(0.461657\pi\)
\(278\) −12.0000 −0.719712
\(279\) −2.00000 −0.119737
\(280\) −2.00000 −0.119523
\(281\) −20.0000 −1.19310 −0.596550 0.802576i \(-0.703462\pi\)
−0.596550 + 0.802576i \(0.703462\pi\)
\(282\) −12.0000 −0.714590
\(283\) 20.0000 1.18888 0.594438 0.804141i \(-0.297374\pi\)
0.594438 + 0.804141i \(0.297374\pi\)
\(284\) −8.00000 −0.474713
\(285\) −1.00000 −0.0592349
\(286\) 0 0
\(287\) 24.0000 1.41668
\(288\) 1.00000 0.0589256
\(289\) 47.0000 2.76471
\(290\) 2.00000 0.117444
\(291\) −2.00000 −0.117242
\(292\) −10.0000 −0.585206
\(293\) −18.0000 −1.05157 −0.525786 0.850617i \(-0.676229\pi\)
−0.525786 + 0.850617i \(0.676229\pi\)
\(294\) 3.00000 0.174964
\(295\) 6.00000 0.349334
\(296\) −2.00000 −0.116248
\(297\) 0 0
\(298\) 10.0000 0.579284
\(299\) −24.0000 −1.38796
\(300\) −1.00000 −0.0577350
\(301\) −8.00000 −0.461112
\(302\) 18.0000 1.03578
\(303\) 6.00000 0.344691
\(304\) 1.00000 0.0573539
\(305\) −14.0000 −0.801638
\(306\) 8.00000 0.457330
\(307\) −28.0000 −1.59804 −0.799022 0.601302i \(-0.794649\pi\)
−0.799022 + 0.601302i \(0.794649\pi\)
\(308\) 0 0
\(309\) 16.0000 0.910208
\(310\) −2.00000 −0.113592
\(311\) 24.0000 1.36092 0.680458 0.732787i \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) −6.00000 −0.339683
\(313\) 6.00000 0.339140 0.169570 0.985518i \(-0.445762\pi\)
0.169570 + 0.985518i \(0.445762\pi\)
\(314\) −4.00000 −0.225733
\(315\) −2.00000 −0.112687
\(316\) 14.0000 0.787562
\(317\) −2.00000 −0.112331 −0.0561656 0.998421i \(-0.517887\pi\)
−0.0561656 + 0.998421i \(0.517887\pi\)
\(318\) −10.0000 −0.560772
\(319\) 0 0
\(320\) 1.00000 0.0559017
\(321\) 16.0000 0.893033
\(322\) 8.00000 0.445823
\(323\) 8.00000 0.445132
\(324\) 1.00000 0.0555556
\(325\) 6.00000 0.332820
\(326\) 8.00000 0.443079
\(327\) 12.0000 0.663602
\(328\) −12.0000 −0.662589
\(329\) −24.0000 −1.32316
\(330\) 0 0
\(331\) 20.0000 1.09930 0.549650 0.835395i \(-0.314761\pi\)
0.549650 + 0.835395i \(0.314761\pi\)
\(332\) 2.00000 0.109764
\(333\) −2.00000 −0.109599
\(334\) 8.00000 0.437741
\(335\) −12.0000 −0.655630
\(336\) 2.00000 0.109109
\(337\) −2.00000 −0.108947 −0.0544735 0.998515i \(-0.517348\pi\)
−0.0544735 + 0.998515i \(0.517348\pi\)
\(338\) 23.0000 1.25104
\(339\) −6.00000 −0.325875
\(340\) 8.00000 0.433861
\(341\) 0 0
\(342\) 1.00000 0.0540738
\(343\) 20.0000 1.07990
\(344\) 4.00000 0.215666
\(345\) 4.00000 0.215353
\(346\) 2.00000 0.107521
\(347\) −10.0000 −0.536828 −0.268414 0.963304i \(-0.586500\pi\)
−0.268414 + 0.963304i \(0.586500\pi\)
\(348\) −2.00000 −0.107211
\(349\) 14.0000 0.749403 0.374701 0.927146i \(-0.377745\pi\)
0.374701 + 0.927146i \(0.377745\pi\)
\(350\) −2.00000 −0.106904
\(351\) −6.00000 −0.320256
\(352\) 0 0
\(353\) 20.0000 1.06449 0.532246 0.846590i \(-0.321348\pi\)
0.532246 + 0.846590i \(0.321348\pi\)
\(354\) −6.00000 −0.318896
\(355\) −8.00000 −0.424596
\(356\) 0 0
\(357\) 16.0000 0.846810
\(358\) 10.0000 0.528516
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 1.00000 0.0527046
\(361\) 1.00000 0.0526316
\(362\) −12.0000 −0.630706
\(363\) 11.0000 0.577350
\(364\) −12.0000 −0.628971
\(365\) −10.0000 −0.523424
\(366\) 14.0000 0.731792
\(367\) 34.0000 1.77479 0.887393 0.461014i \(-0.152514\pi\)
0.887393 + 0.461014i \(0.152514\pi\)
\(368\) −4.00000 −0.208514
\(369\) −12.0000 −0.624695
\(370\) −2.00000 −0.103975
\(371\) −20.0000 −1.03835
\(372\) 2.00000 0.103695
\(373\) −14.0000 −0.724893 −0.362446 0.932005i \(-0.618058\pi\)
−0.362446 + 0.932005i \(0.618058\pi\)
\(374\) 0 0
\(375\) −1.00000 −0.0516398
\(376\) 12.0000 0.618853
\(377\) 12.0000 0.618031
\(378\) 2.00000 0.102869
\(379\) −16.0000 −0.821865 −0.410932 0.911666i \(-0.634797\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(380\) 1.00000 0.0512989
\(381\) 8.00000 0.409852
\(382\) 0 0
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −2.00000 −0.101797
\(387\) 4.00000 0.203331
\(388\) 2.00000 0.101535
\(389\) 18.0000 0.912636 0.456318 0.889817i \(-0.349168\pi\)
0.456318 + 0.889817i \(0.349168\pi\)
\(390\) −6.00000 −0.303822
\(391\) −32.0000 −1.61831
\(392\) −3.00000 −0.151523
\(393\) 0 0
\(394\) 18.0000 0.906827
\(395\) 14.0000 0.704416
\(396\) 0 0
\(397\) 8.00000 0.401508 0.200754 0.979642i \(-0.435661\pi\)
0.200754 + 0.979642i \(0.435661\pi\)
\(398\) 4.00000 0.200502
\(399\) 2.00000 0.100125
\(400\) 1.00000 0.0500000
\(401\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(402\) 12.0000 0.598506
\(403\) −12.0000 −0.597763
\(404\) −6.00000 −0.298511
\(405\) 1.00000 0.0496904
\(406\) −4.00000 −0.198517
\(407\) 0 0
\(408\) −8.00000 −0.396059
\(409\) −6.00000 −0.296681 −0.148340 0.988936i \(-0.547393\pi\)
−0.148340 + 0.988936i \(0.547393\pi\)
\(410\) −12.0000 −0.592638
\(411\) −12.0000 −0.591916
\(412\) −16.0000 −0.788263
\(413\) −12.0000 −0.590481
\(414\) −4.00000 −0.196589
\(415\) 2.00000 0.0981761
\(416\) 6.00000 0.294174
\(417\) 12.0000 0.587643
\(418\) 0 0
\(419\) −28.0000 −1.36789 −0.683945 0.729534i \(-0.739737\pi\)
−0.683945 + 0.729534i \(0.739737\pi\)
\(420\) 2.00000 0.0975900
\(421\) 4.00000 0.194948 0.0974740 0.995238i \(-0.468924\pi\)
0.0974740 + 0.995238i \(0.468924\pi\)
\(422\) −16.0000 −0.778868
\(423\) 12.0000 0.583460
\(424\) 10.0000 0.485643
\(425\) 8.00000 0.388057
\(426\) 8.00000 0.387601
\(427\) 28.0000 1.35501
\(428\) −16.0000 −0.773389
\(429\) 0 0
\(430\) 4.00000 0.192897
\(431\) 24.0000 1.15604 0.578020 0.816023i \(-0.303826\pi\)
0.578020 + 0.816023i \(0.303826\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −34.0000 −1.63394 −0.816968 0.576683i \(-0.804347\pi\)
−0.816968 + 0.576683i \(0.804347\pi\)
\(434\) 4.00000 0.192006
\(435\) −2.00000 −0.0958927
\(436\) −12.0000 −0.574696
\(437\) −4.00000 −0.191346
\(438\) 10.0000 0.477818
\(439\) −10.0000 −0.477274 −0.238637 0.971109i \(-0.576701\pi\)
−0.238637 + 0.971109i \(0.576701\pi\)
\(440\) 0 0
\(441\) −3.00000 −0.142857
\(442\) 48.0000 2.28313
\(443\) −34.0000 −1.61539 −0.807694 0.589601i \(-0.799285\pi\)
−0.807694 + 0.589601i \(0.799285\pi\)
\(444\) 2.00000 0.0949158
\(445\) 0 0
\(446\) −4.00000 −0.189405
\(447\) −10.0000 −0.472984
\(448\) −2.00000 −0.0944911
\(449\) 36.0000 1.69895 0.849473 0.527633i \(-0.176920\pi\)
0.849473 + 0.527633i \(0.176920\pi\)
\(450\) 1.00000 0.0471405
\(451\) 0 0
\(452\) 6.00000 0.282216
\(453\) −18.0000 −0.845714
\(454\) 20.0000 0.938647
\(455\) −12.0000 −0.562569
\(456\) −1.00000 −0.0468293
\(457\) 10.0000 0.467780 0.233890 0.972263i \(-0.424854\pi\)
0.233890 + 0.972263i \(0.424854\pi\)
\(458\) 6.00000 0.280362
\(459\) −8.00000 −0.373408
\(460\) −4.00000 −0.186501
\(461\) −18.0000 −0.838344 −0.419172 0.907907i \(-0.637680\pi\)
−0.419172 + 0.907907i \(0.637680\pi\)
\(462\) 0 0
\(463\) 22.0000 1.02243 0.511213 0.859454i \(-0.329196\pi\)
0.511213 + 0.859454i \(0.329196\pi\)
\(464\) 2.00000 0.0928477
\(465\) 2.00000 0.0927478
\(466\) 24.0000 1.11178
\(467\) −22.0000 −1.01804 −0.509019 0.860755i \(-0.669992\pi\)
−0.509019 + 0.860755i \(0.669992\pi\)
\(468\) 6.00000 0.277350
\(469\) 24.0000 1.10822
\(470\) 12.0000 0.553519
\(471\) 4.00000 0.184310
\(472\) 6.00000 0.276172
\(473\) 0 0
\(474\) −14.0000 −0.643041
\(475\) 1.00000 0.0458831
\(476\) −16.0000 −0.733359
\(477\) 10.0000 0.457869
\(478\) −8.00000 −0.365911
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) −1.00000 −0.0456435
\(481\) −12.0000 −0.547153
\(482\) −14.0000 −0.637683
\(483\) −8.00000 −0.364013
\(484\) −11.0000 −0.500000
\(485\) 2.00000 0.0908153
\(486\) −1.00000 −0.0453609
\(487\) 40.0000 1.81257 0.906287 0.422664i \(-0.138905\pi\)
0.906287 + 0.422664i \(0.138905\pi\)
\(488\) −14.0000 −0.633750
\(489\) −8.00000 −0.361773
\(490\) −3.00000 −0.135526
\(491\) −16.0000 −0.722070 −0.361035 0.932552i \(-0.617576\pi\)
−0.361035 + 0.932552i \(0.617576\pi\)
\(492\) 12.0000 0.541002
\(493\) 16.0000 0.720604
\(494\) 6.00000 0.269953
\(495\) 0 0
\(496\) −2.00000 −0.0898027
\(497\) 16.0000 0.717698
\(498\) −2.00000 −0.0896221
\(499\) 28.0000 1.25345 0.626726 0.779240i \(-0.284395\pi\)
0.626726 + 0.779240i \(0.284395\pi\)
\(500\) 1.00000 0.0447214
\(501\) −8.00000 −0.357414
\(502\) −12.0000 −0.535586
\(503\) −16.0000 −0.713405 −0.356702 0.934218i \(-0.616099\pi\)
−0.356702 + 0.934218i \(0.616099\pi\)
\(504\) −2.00000 −0.0890871
\(505\) −6.00000 −0.266996
\(506\) 0 0
\(507\) −23.0000 −1.02147
\(508\) −8.00000 −0.354943
\(509\) 2.00000 0.0886484 0.0443242 0.999017i \(-0.485887\pi\)
0.0443242 + 0.999017i \(0.485887\pi\)
\(510\) −8.00000 −0.354246
\(511\) 20.0000 0.884748
\(512\) 1.00000 0.0441942
\(513\) −1.00000 −0.0441511
\(514\) −30.0000 −1.32324
\(515\) −16.0000 −0.705044
\(516\) −4.00000 −0.176090
\(517\) 0 0
\(518\) 4.00000 0.175750
\(519\) −2.00000 −0.0877903
\(520\) 6.00000 0.263117
\(521\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(522\) 2.00000 0.0875376
\(523\) −20.0000 −0.874539 −0.437269 0.899331i \(-0.644054\pi\)
−0.437269 + 0.899331i \(0.644054\pi\)
\(524\) 0 0
\(525\) 2.00000 0.0872872
\(526\) −12.0000 −0.523225
\(527\) −16.0000 −0.696971
\(528\) 0 0
\(529\) −7.00000 −0.304348
\(530\) 10.0000 0.434372
\(531\) 6.00000 0.260378
\(532\) −2.00000 −0.0867110
\(533\) −72.0000 −3.11867
\(534\) 0 0
\(535\) −16.0000 −0.691740
\(536\) −12.0000 −0.518321
\(537\) −10.0000 −0.431532
\(538\) −30.0000 −1.29339
\(539\) 0 0
\(540\) −1.00000 −0.0430331
\(541\) −18.0000 −0.773880 −0.386940 0.922105i \(-0.626468\pi\)
−0.386940 + 0.922105i \(0.626468\pi\)
\(542\) −4.00000 −0.171815
\(543\) 12.0000 0.514969
\(544\) 8.00000 0.342997
\(545\) −12.0000 −0.514024
\(546\) 12.0000 0.513553
\(547\) −36.0000 −1.53925 −0.769624 0.638497i \(-0.779557\pi\)
−0.769624 + 0.638497i \(0.779557\pi\)
\(548\) 12.0000 0.512615
\(549\) −14.0000 −0.597505
\(550\) 0 0
\(551\) 2.00000 0.0852029
\(552\) 4.00000 0.170251
\(553\) −28.0000 −1.19068
\(554\) 4.00000 0.169944
\(555\) 2.00000 0.0848953
\(556\) −12.0000 −0.508913
\(557\) −2.00000 −0.0847427 −0.0423714 0.999102i \(-0.513491\pi\)
−0.0423714 + 0.999102i \(0.513491\pi\)
\(558\) −2.00000 −0.0846668
\(559\) 24.0000 1.01509
\(560\) −2.00000 −0.0845154
\(561\) 0 0
\(562\) −20.0000 −0.843649
\(563\) 24.0000 1.01148 0.505740 0.862686i \(-0.331220\pi\)
0.505740 + 0.862686i \(0.331220\pi\)
\(564\) −12.0000 −0.505291
\(565\) 6.00000 0.252422
\(566\) 20.0000 0.840663
\(567\) −2.00000 −0.0839921
\(568\) −8.00000 −0.335673
\(569\) 4.00000 0.167689 0.0838444 0.996479i \(-0.473280\pi\)
0.0838444 + 0.996479i \(0.473280\pi\)
\(570\) −1.00000 −0.0418854
\(571\) 12.0000 0.502184 0.251092 0.967963i \(-0.419210\pi\)
0.251092 + 0.967963i \(0.419210\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 24.0000 1.00174
\(575\) −4.00000 −0.166812
\(576\) 1.00000 0.0416667
\(577\) −30.0000 −1.24892 −0.624458 0.781058i \(-0.714680\pi\)
−0.624458 + 0.781058i \(0.714680\pi\)
\(578\) 47.0000 1.95494
\(579\) 2.00000 0.0831172
\(580\) 2.00000 0.0830455
\(581\) −4.00000 −0.165948
\(582\) −2.00000 −0.0829027
\(583\) 0 0
\(584\) −10.0000 −0.413803
\(585\) 6.00000 0.248069
\(586\) −18.0000 −0.743573
\(587\) −26.0000 −1.07313 −0.536567 0.843857i \(-0.680279\pi\)
−0.536567 + 0.843857i \(0.680279\pi\)
\(588\) 3.00000 0.123718
\(589\) −2.00000 −0.0824086
\(590\) 6.00000 0.247016
\(591\) −18.0000 −0.740421
\(592\) −2.00000 −0.0821995
\(593\) 36.0000 1.47834 0.739171 0.673517i \(-0.235217\pi\)
0.739171 + 0.673517i \(0.235217\pi\)
\(594\) 0 0
\(595\) −16.0000 −0.655936
\(596\) 10.0000 0.409616
\(597\) −4.00000 −0.163709
\(598\) −24.0000 −0.981433
\(599\) −36.0000 −1.47092 −0.735460 0.677568i \(-0.763034\pi\)
−0.735460 + 0.677568i \(0.763034\pi\)
\(600\) −1.00000 −0.0408248
\(601\) −14.0000 −0.571072 −0.285536 0.958368i \(-0.592172\pi\)
−0.285536 + 0.958368i \(0.592172\pi\)
\(602\) −8.00000 −0.326056
\(603\) −12.0000 −0.488678
\(604\) 18.0000 0.732410
\(605\) −11.0000 −0.447214
\(606\) 6.00000 0.243733
\(607\) 24.0000 0.974130 0.487065 0.873366i \(-0.338067\pi\)
0.487065 + 0.873366i \(0.338067\pi\)
\(608\) 1.00000 0.0405554
\(609\) 4.00000 0.162088
\(610\) −14.0000 −0.566843
\(611\) 72.0000 2.91281
\(612\) 8.00000 0.323381
\(613\) −16.0000 −0.646234 −0.323117 0.946359i \(-0.604731\pi\)
−0.323117 + 0.946359i \(0.604731\pi\)
\(614\) −28.0000 −1.12999
\(615\) 12.0000 0.483887
\(616\) 0 0
\(617\) 20.0000 0.805170 0.402585 0.915383i \(-0.368112\pi\)
0.402585 + 0.915383i \(0.368112\pi\)
\(618\) 16.0000 0.643614
\(619\) 4.00000 0.160774 0.0803868 0.996764i \(-0.474384\pi\)
0.0803868 + 0.996764i \(0.474384\pi\)
\(620\) −2.00000 −0.0803219
\(621\) 4.00000 0.160514
\(622\) 24.0000 0.962312
\(623\) 0 0
\(624\) −6.00000 −0.240192
\(625\) 1.00000 0.0400000
\(626\) 6.00000 0.239808
\(627\) 0 0
\(628\) −4.00000 −0.159617
\(629\) −16.0000 −0.637962
\(630\) −2.00000 −0.0796819
\(631\) 16.0000 0.636950 0.318475 0.947931i \(-0.396829\pi\)
0.318475 + 0.947931i \(0.396829\pi\)
\(632\) 14.0000 0.556890
\(633\) 16.0000 0.635943
\(634\) −2.00000 −0.0794301
\(635\) −8.00000 −0.317470
\(636\) −10.0000 −0.396526
\(637\) −18.0000 −0.713186
\(638\) 0 0
\(639\) −8.00000 −0.316475
\(640\) 1.00000 0.0395285
\(641\) −20.0000 −0.789953 −0.394976 0.918691i \(-0.629247\pi\)
−0.394976 + 0.918691i \(0.629247\pi\)
\(642\) 16.0000 0.631470
\(643\) −28.0000 −1.10421 −0.552106 0.833774i \(-0.686176\pi\)
−0.552106 + 0.833774i \(0.686176\pi\)
\(644\) 8.00000 0.315244
\(645\) −4.00000 −0.157500
\(646\) 8.00000 0.314756
\(647\) −16.0000 −0.629025 −0.314512 0.949253i \(-0.601841\pi\)
−0.314512 + 0.949253i \(0.601841\pi\)
\(648\) 1.00000 0.0392837
\(649\) 0 0
\(650\) 6.00000 0.235339
\(651\) −4.00000 −0.156772
\(652\) 8.00000 0.313304
\(653\) −42.0000 −1.64359 −0.821794 0.569785i \(-0.807026\pi\)
−0.821794 + 0.569785i \(0.807026\pi\)
\(654\) 12.0000 0.469237
\(655\) 0 0
\(656\) −12.0000 −0.468521
\(657\) −10.0000 −0.390137
\(658\) −24.0000 −0.935617
\(659\) −6.00000 −0.233727 −0.116863 0.993148i \(-0.537284\pi\)
−0.116863 + 0.993148i \(0.537284\pi\)
\(660\) 0 0
\(661\) −4.00000 −0.155582 −0.0777910 0.996970i \(-0.524787\pi\)
−0.0777910 + 0.996970i \(0.524787\pi\)
\(662\) 20.0000 0.777322
\(663\) −48.0000 −1.86417
\(664\) 2.00000 0.0776151
\(665\) −2.00000 −0.0775567
\(666\) −2.00000 −0.0774984
\(667\) −8.00000 −0.309761
\(668\) 8.00000 0.309529
\(669\) 4.00000 0.154649
\(670\) −12.0000 −0.463600
\(671\) 0 0
\(672\) 2.00000 0.0771517
\(673\) 2.00000 0.0770943 0.0385472 0.999257i \(-0.487727\pi\)
0.0385472 + 0.999257i \(0.487727\pi\)
\(674\) −2.00000 −0.0770371
\(675\) −1.00000 −0.0384900
\(676\) 23.0000 0.884615
\(677\) 6.00000 0.230599 0.115299 0.993331i \(-0.463217\pi\)
0.115299 + 0.993331i \(0.463217\pi\)
\(678\) −6.00000 −0.230429
\(679\) −4.00000 −0.153506
\(680\) 8.00000 0.306786
\(681\) −20.0000 −0.766402
\(682\) 0 0
\(683\) −36.0000 −1.37750 −0.688751 0.724998i \(-0.741841\pi\)
−0.688751 + 0.724998i \(0.741841\pi\)
\(684\) 1.00000 0.0382360
\(685\) 12.0000 0.458496
\(686\) 20.0000 0.763604
\(687\) −6.00000 −0.228914
\(688\) 4.00000 0.152499
\(689\) 60.0000 2.28582
\(690\) 4.00000 0.152277
\(691\) 28.0000 1.06517 0.532585 0.846376i \(-0.321221\pi\)
0.532585 + 0.846376i \(0.321221\pi\)
\(692\) 2.00000 0.0760286
\(693\) 0 0
\(694\) −10.0000 −0.379595
\(695\) −12.0000 −0.455186
\(696\) −2.00000 −0.0758098
\(697\) −96.0000 −3.63626
\(698\) 14.0000 0.529908
\(699\) −24.0000 −0.907763
\(700\) −2.00000 −0.0755929
\(701\) 14.0000 0.528773 0.264386 0.964417i \(-0.414831\pi\)
0.264386 + 0.964417i \(0.414831\pi\)
\(702\) −6.00000 −0.226455
\(703\) −2.00000 −0.0754314
\(704\) 0 0
\(705\) −12.0000 −0.451946
\(706\) 20.0000 0.752710
\(707\) 12.0000 0.451306
\(708\) −6.00000 −0.225494
\(709\) −18.0000 −0.676004 −0.338002 0.941145i \(-0.609751\pi\)
−0.338002 + 0.941145i \(0.609751\pi\)
\(710\) −8.00000 −0.300235
\(711\) 14.0000 0.525041
\(712\) 0 0
\(713\) 8.00000 0.299602
\(714\) 16.0000 0.598785
\(715\) 0 0
\(716\) 10.0000 0.373718
\(717\) 8.00000 0.298765
\(718\) 0 0
\(719\) −8.00000 −0.298350 −0.149175 0.988811i \(-0.547662\pi\)
−0.149175 + 0.988811i \(0.547662\pi\)
\(720\) 1.00000 0.0372678
\(721\) 32.0000 1.19174
\(722\) 1.00000 0.0372161
\(723\) 14.0000 0.520666
\(724\) −12.0000 −0.445976
\(725\) 2.00000 0.0742781
\(726\) 11.0000 0.408248
\(727\) 42.0000 1.55769 0.778847 0.627214i \(-0.215805\pi\)
0.778847 + 0.627214i \(0.215805\pi\)
\(728\) −12.0000 −0.444750
\(729\) 1.00000 0.0370370
\(730\) −10.0000 −0.370117
\(731\) 32.0000 1.18356
\(732\) 14.0000 0.517455
\(733\) 8.00000 0.295487 0.147743 0.989026i \(-0.452799\pi\)
0.147743 + 0.989026i \(0.452799\pi\)
\(734\) 34.0000 1.25496
\(735\) 3.00000 0.110657
\(736\) −4.00000 −0.147442
\(737\) 0 0
\(738\) −12.0000 −0.441726
\(739\) 20.0000 0.735712 0.367856 0.929883i \(-0.380092\pi\)
0.367856 + 0.929883i \(0.380092\pi\)
\(740\) −2.00000 −0.0735215
\(741\) −6.00000 −0.220416
\(742\) −20.0000 −0.734223
\(743\) 40.0000 1.46746 0.733729 0.679442i \(-0.237778\pi\)
0.733729 + 0.679442i \(0.237778\pi\)
\(744\) 2.00000 0.0733236
\(745\) 10.0000 0.366372
\(746\) −14.0000 −0.512576
\(747\) 2.00000 0.0731762
\(748\) 0 0
\(749\) 32.0000 1.16925
\(750\) −1.00000 −0.0365148
\(751\) −2.00000 −0.0729810 −0.0364905 0.999334i \(-0.511618\pi\)
−0.0364905 + 0.999334i \(0.511618\pi\)
\(752\) 12.0000 0.437595
\(753\) 12.0000 0.437304
\(754\) 12.0000 0.437014
\(755\) 18.0000 0.655087
\(756\) 2.00000 0.0727393
\(757\) 40.0000 1.45382 0.726912 0.686730i \(-0.240955\pi\)
0.726912 + 0.686730i \(0.240955\pi\)
\(758\) −16.0000 −0.581146
\(759\) 0 0
\(760\) 1.00000 0.0362738
\(761\) 22.0000 0.797499 0.398750 0.917060i \(-0.369444\pi\)
0.398750 + 0.917060i \(0.369444\pi\)
\(762\) 8.00000 0.289809
\(763\) 24.0000 0.868858
\(764\) 0 0
\(765\) 8.00000 0.289241
\(766\) 0 0
\(767\) 36.0000 1.29988
\(768\) −1.00000 −0.0360844
\(769\) −18.0000 −0.649097 −0.324548 0.945869i \(-0.605212\pi\)
−0.324548 + 0.945869i \(0.605212\pi\)
\(770\) 0 0
\(771\) 30.0000 1.08042
\(772\) −2.00000 −0.0719816
\(773\) 10.0000 0.359675 0.179838 0.983696i \(-0.442443\pi\)
0.179838 + 0.983696i \(0.442443\pi\)
\(774\) 4.00000 0.143777
\(775\) −2.00000 −0.0718421
\(776\) 2.00000 0.0717958
\(777\) −4.00000 −0.143499
\(778\) 18.0000 0.645331
\(779\) −12.0000 −0.429945
\(780\) −6.00000 −0.214834
\(781\) 0 0
\(782\) −32.0000 −1.14432
\(783\) −2.00000 −0.0714742
\(784\) −3.00000 −0.107143
\(785\) −4.00000 −0.142766
\(786\) 0 0
\(787\) −20.0000 −0.712923 −0.356462 0.934310i \(-0.616017\pi\)
−0.356462 + 0.934310i \(0.616017\pi\)
\(788\) 18.0000 0.641223
\(789\) 12.0000 0.427211
\(790\) 14.0000 0.498098
\(791\) −12.0000 −0.426671
\(792\) 0 0
\(793\) −84.0000 −2.98293
\(794\) 8.00000 0.283909
\(795\) −10.0000 −0.354663
\(796\) 4.00000 0.141776
\(797\) −18.0000 −0.637593 −0.318796 0.947823i \(-0.603279\pi\)
−0.318796 + 0.947823i \(0.603279\pi\)
\(798\) 2.00000 0.0707992
\(799\) 96.0000 3.39624
\(800\) 1.00000 0.0353553
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 12.0000 0.423207
\(805\) 8.00000 0.281963
\(806\) −12.0000 −0.422682
\(807\) 30.0000 1.05605
\(808\) −6.00000 −0.211079
\(809\) 38.0000 1.33601 0.668004 0.744157i \(-0.267149\pi\)
0.668004 + 0.744157i \(0.267149\pi\)
\(810\) 1.00000 0.0351364
\(811\) 16.0000 0.561836 0.280918 0.959732i \(-0.409361\pi\)
0.280918 + 0.959732i \(0.409361\pi\)
\(812\) −4.00000 −0.140372
\(813\) 4.00000 0.140286
\(814\) 0 0
\(815\) 8.00000 0.280228
\(816\) −8.00000 −0.280056
\(817\) 4.00000 0.139942
\(818\) −6.00000 −0.209785
\(819\) −12.0000 −0.419314
\(820\) −12.0000 −0.419058
\(821\) −38.0000 −1.32621 −0.663105 0.748527i \(-0.730762\pi\)
−0.663105 + 0.748527i \(0.730762\pi\)
\(822\) −12.0000 −0.418548
\(823\) 14.0000 0.488009 0.244005 0.969774i \(-0.421539\pi\)
0.244005 + 0.969774i \(0.421539\pi\)
\(824\) −16.0000 −0.557386
\(825\) 0 0
\(826\) −12.0000 −0.417533
\(827\) 32.0000 1.11275 0.556375 0.830932i \(-0.312192\pi\)
0.556375 + 0.830932i \(0.312192\pi\)
\(828\) −4.00000 −0.139010
\(829\) 28.0000 0.972480 0.486240 0.873825i \(-0.338368\pi\)
0.486240 + 0.873825i \(0.338368\pi\)
\(830\) 2.00000 0.0694210
\(831\) −4.00000 −0.138758
\(832\) 6.00000 0.208013
\(833\) −24.0000 −0.831551
\(834\) 12.0000 0.415526
\(835\) 8.00000 0.276851
\(836\) 0 0
\(837\) 2.00000 0.0691301
\(838\) −28.0000 −0.967244
\(839\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 2.00000 0.0690066
\(841\) −25.0000 −0.862069
\(842\) 4.00000 0.137849
\(843\) 20.0000 0.688837
\(844\) −16.0000 −0.550743
\(845\) 23.0000 0.791224
\(846\) 12.0000 0.412568
\(847\) 22.0000 0.755929
\(848\) 10.0000 0.343401
\(849\) −20.0000 −0.686398
\(850\) 8.00000 0.274398
\(851\) 8.00000 0.274236
\(852\) 8.00000 0.274075
\(853\) −28.0000 −0.958702 −0.479351 0.877623i \(-0.659128\pi\)
−0.479351 + 0.877623i \(0.659128\pi\)
\(854\) 28.0000 0.958140
\(855\) 1.00000 0.0341993
\(856\) −16.0000 −0.546869
\(857\) 42.0000 1.43469 0.717346 0.696717i \(-0.245357\pi\)
0.717346 + 0.696717i \(0.245357\pi\)
\(858\) 0 0
\(859\) −28.0000 −0.955348 −0.477674 0.878537i \(-0.658520\pi\)
−0.477674 + 0.878537i \(0.658520\pi\)
\(860\) 4.00000 0.136399
\(861\) −24.0000 −0.817918
\(862\) 24.0000 0.817443
\(863\) 8.00000 0.272323 0.136162 0.990687i \(-0.456523\pi\)
0.136162 + 0.990687i \(0.456523\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 2.00000 0.0680020
\(866\) −34.0000 −1.15537
\(867\) −47.0000 −1.59620
\(868\) 4.00000 0.135769
\(869\) 0 0
\(870\) −2.00000 −0.0678064
\(871\) −72.0000 −2.43963
\(872\) −12.0000 −0.406371
\(873\) 2.00000 0.0676897
\(874\) −4.00000 −0.135302
\(875\) −2.00000 −0.0676123
\(876\) 10.0000 0.337869
\(877\) 18.0000 0.607817 0.303908 0.952701i \(-0.401708\pi\)
0.303908 + 0.952701i \(0.401708\pi\)
\(878\) −10.0000 −0.337484
\(879\) 18.0000 0.607125
\(880\) 0 0
\(881\) 42.0000 1.41502 0.707508 0.706705i \(-0.249819\pi\)
0.707508 + 0.706705i \(0.249819\pi\)
\(882\) −3.00000 −0.101015
\(883\) −52.0000 −1.74994 −0.874970 0.484178i \(-0.839119\pi\)
−0.874970 + 0.484178i \(0.839119\pi\)
\(884\) 48.0000 1.61441
\(885\) −6.00000 −0.201688
\(886\) −34.0000 −1.14225
\(887\) 32.0000 1.07445 0.537227 0.843437i \(-0.319472\pi\)
0.537227 + 0.843437i \(0.319472\pi\)
\(888\) 2.00000 0.0671156
\(889\) 16.0000 0.536623
\(890\) 0 0
\(891\) 0 0
\(892\) −4.00000 −0.133930
\(893\) 12.0000 0.401565
\(894\) −10.0000 −0.334450
\(895\) 10.0000 0.334263
\(896\) −2.00000 −0.0668153
\(897\) 24.0000 0.801337
\(898\) 36.0000 1.20134
\(899\) −4.00000 −0.133407
\(900\) 1.00000 0.0333333
\(901\) 80.0000 2.66519
\(902\) 0 0
\(903\) 8.00000 0.266223
\(904\) 6.00000 0.199557
\(905\) −12.0000 −0.398893
\(906\) −18.0000 −0.598010
\(907\) −36.0000 −1.19536 −0.597680 0.801735i \(-0.703911\pi\)
−0.597680 + 0.801735i \(0.703911\pi\)
\(908\) 20.0000 0.663723
\(909\) −6.00000 −0.199007
\(910\) −12.0000 −0.397796
\(911\) 20.0000 0.662630 0.331315 0.943520i \(-0.392508\pi\)
0.331315 + 0.943520i \(0.392508\pi\)
\(912\) −1.00000 −0.0331133
\(913\) 0 0
\(914\) 10.0000 0.330771
\(915\) 14.0000 0.462826
\(916\) 6.00000 0.198246
\(917\) 0 0
\(918\) −8.00000 −0.264039
\(919\) −24.0000 −0.791687 −0.395843 0.918318i \(-0.629548\pi\)
−0.395843 + 0.918318i \(0.629548\pi\)
\(920\) −4.00000 −0.131876
\(921\) 28.0000 0.922631
\(922\) −18.0000 −0.592798
\(923\) −48.0000 −1.57994
\(924\) 0 0
\(925\) −2.00000 −0.0657596
\(926\) 22.0000 0.722965
\(927\) −16.0000 −0.525509
\(928\) 2.00000 0.0656532
\(929\) 34.0000 1.11550 0.557752 0.830008i \(-0.311664\pi\)
0.557752 + 0.830008i \(0.311664\pi\)
\(930\) 2.00000 0.0655826
\(931\) −3.00000 −0.0983210
\(932\) 24.0000 0.786146
\(933\) −24.0000 −0.785725
\(934\) −22.0000 −0.719862
\(935\) 0 0
\(936\) 6.00000 0.196116
\(937\) 2.00000 0.0653372 0.0326686 0.999466i \(-0.489599\pi\)
0.0326686 + 0.999466i \(0.489599\pi\)
\(938\) 24.0000 0.783628
\(939\) −6.00000 −0.195803
\(940\) 12.0000 0.391397
\(941\) 30.0000 0.977972 0.488986 0.872292i \(-0.337367\pi\)
0.488986 + 0.872292i \(0.337367\pi\)
\(942\) 4.00000 0.130327
\(943\) 48.0000 1.56310
\(944\) 6.00000 0.195283
\(945\) 2.00000 0.0650600
\(946\) 0 0
\(947\) 2.00000 0.0649913 0.0324956 0.999472i \(-0.489654\pi\)
0.0324956 + 0.999472i \(0.489654\pi\)
\(948\) −14.0000 −0.454699
\(949\) −60.0000 −1.94768
\(950\) 1.00000 0.0324443
\(951\) 2.00000 0.0648544
\(952\) −16.0000 −0.518563
\(953\) −6.00000 −0.194359 −0.0971795 0.995267i \(-0.530982\pi\)
−0.0971795 + 0.995267i \(0.530982\pi\)
\(954\) 10.0000 0.323762
\(955\) 0 0
\(956\) −8.00000 −0.258738
\(957\) 0 0
\(958\) 0 0
\(959\) −24.0000 −0.775000
\(960\) −1.00000 −0.0322749
\(961\) −27.0000 −0.870968
\(962\) −12.0000 −0.386896
\(963\) −16.0000 −0.515593
\(964\) −14.0000 −0.450910
\(965\) −2.00000 −0.0643823
\(966\) −8.00000 −0.257396
\(967\) −34.0000 −1.09337 −0.546683 0.837340i \(-0.684110\pi\)
−0.546683 + 0.837340i \(0.684110\pi\)
\(968\) −11.0000 −0.353553
\(969\) −8.00000 −0.256997
\(970\) 2.00000 0.0642161
\(971\) −6.00000 −0.192549 −0.0962746 0.995355i \(-0.530693\pi\)
−0.0962746 + 0.995355i \(0.530693\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 24.0000 0.769405
\(974\) 40.0000 1.28168
\(975\) −6.00000 −0.192154
\(976\) −14.0000 −0.448129
\(977\) −30.0000 −0.959785 −0.479893 0.877327i \(-0.659324\pi\)
−0.479893 + 0.877327i \(0.659324\pi\)
\(978\) −8.00000 −0.255812
\(979\) 0 0
\(980\) −3.00000 −0.0958315
\(981\) −12.0000 −0.383131
\(982\) −16.0000 −0.510581
\(983\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) 12.0000 0.382546
\(985\) 18.0000 0.573528
\(986\) 16.0000 0.509544
\(987\) 24.0000 0.763928
\(988\) 6.00000 0.190885
\(989\) −16.0000 −0.508770
\(990\) 0 0
\(991\) 50.0000 1.58830 0.794151 0.607720i \(-0.207916\pi\)
0.794151 + 0.607720i \(0.207916\pi\)
\(992\) −2.00000 −0.0635001
\(993\) −20.0000 −0.634681
\(994\) 16.0000 0.507489
\(995\) 4.00000 0.126809
\(996\) −2.00000 −0.0633724
\(997\) 44.0000 1.39349 0.696747 0.717317i \(-0.254630\pi\)
0.696747 + 0.717317i \(0.254630\pi\)
\(998\) 28.0000 0.886325
\(999\) 2.00000 0.0632772
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 570.2.a.h.1.1 1
3.2 odd 2 1710.2.a.c.1.1 1
4.3 odd 2 4560.2.a.bc.1.1 1
5.2 odd 4 2850.2.d.e.799.2 2
5.3 odd 4 2850.2.d.e.799.1 2
5.4 even 2 2850.2.a.n.1.1 1
15.14 odd 2 8550.2.a.bh.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
570.2.a.h.1.1 1 1.1 even 1 trivial
1710.2.a.c.1.1 1 3.2 odd 2
2850.2.a.n.1.1 1 5.4 even 2
2850.2.d.e.799.1 2 5.3 odd 4
2850.2.d.e.799.2 2 5.2 odd 4
4560.2.a.bc.1.1 1 4.3 odd 2
8550.2.a.bh.1.1 1 15.14 odd 2