Properties

Label 49.4.a.b.1.1
Level $49$
Weight $4$
Character 49.1
Self dual yes
Analytic conductor $2.891$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 49 = 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 49.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(2.89109359028\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 7)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 49.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +2.00000 q^{3} -7.00000 q^{4} -16.0000 q^{5} -2.00000 q^{6} +15.0000 q^{8} -23.0000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +2.00000 q^{3} -7.00000 q^{4} -16.0000 q^{5} -2.00000 q^{6} +15.0000 q^{8} -23.0000 q^{9} +16.0000 q^{10} -8.00000 q^{11} -14.0000 q^{12} -28.0000 q^{13} -32.0000 q^{15} +41.0000 q^{16} -54.0000 q^{17} +23.0000 q^{18} +110.000 q^{19} +112.000 q^{20} +8.00000 q^{22} +48.0000 q^{23} +30.0000 q^{24} +131.000 q^{25} +28.0000 q^{26} -100.000 q^{27} -110.000 q^{29} +32.0000 q^{30} -12.0000 q^{31} -161.000 q^{32} -16.0000 q^{33} +54.0000 q^{34} +161.000 q^{36} -246.000 q^{37} -110.000 q^{38} -56.0000 q^{39} -240.000 q^{40} -182.000 q^{41} +128.000 q^{43} +56.0000 q^{44} +368.000 q^{45} -48.0000 q^{46} -324.000 q^{47} +82.0000 q^{48} -131.000 q^{50} -108.000 q^{51} +196.000 q^{52} -162.000 q^{53} +100.000 q^{54} +128.000 q^{55} +220.000 q^{57} +110.000 q^{58} -810.000 q^{59} +224.000 q^{60} +488.000 q^{61} +12.0000 q^{62} -167.000 q^{64} +448.000 q^{65} +16.0000 q^{66} +244.000 q^{67} +378.000 q^{68} +96.0000 q^{69} -768.000 q^{71} -345.000 q^{72} +702.000 q^{73} +246.000 q^{74} +262.000 q^{75} -770.000 q^{76} +56.0000 q^{78} +440.000 q^{79} -656.000 q^{80} +421.000 q^{81} +182.000 q^{82} +1302.00 q^{83} +864.000 q^{85} -128.000 q^{86} -220.000 q^{87} -120.000 q^{88} -730.000 q^{89} -368.000 q^{90} -336.000 q^{92} -24.0000 q^{93} +324.000 q^{94} -1760.00 q^{95} -322.000 q^{96} -294.000 q^{97} +184.000 q^{99} +O(q^{100})\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.353553 −0.176777 0.984251i \(-0.556567\pi\)
−0.176777 + 0.984251i \(0.556567\pi\)
\(3\) 2.00000 0.384900 0.192450 0.981307i \(-0.438357\pi\)
0.192450 + 0.981307i \(0.438357\pi\)
\(4\) −7.00000 −0.875000
\(5\) −16.0000 −1.43108 −0.715542 0.698570i \(-0.753820\pi\)
−0.715542 + 0.698570i \(0.753820\pi\)
\(6\) −2.00000 −0.136083
\(7\) 0 0
\(8\) 15.0000 0.662913
\(9\) −23.0000 −0.851852
\(10\) 16.0000 0.505964
\(11\) −8.00000 −0.219281 −0.109640 0.993971i \(-0.534970\pi\)
−0.109640 + 0.993971i \(0.534970\pi\)
\(12\) −14.0000 −0.336788
\(13\) −28.0000 −0.597369 −0.298685 0.954352i \(-0.596548\pi\)
−0.298685 + 0.954352i \(0.596548\pi\)
\(14\) 0 0
\(15\) −32.0000 −0.550824
\(16\) 41.0000 0.640625
\(17\) −54.0000 −0.770407 −0.385204 0.922832i \(-0.625869\pi\)
−0.385204 + 0.922832i \(0.625869\pi\)
\(18\) 23.0000 0.301175
\(19\) 110.000 1.32820 0.664098 0.747645i \(-0.268816\pi\)
0.664098 + 0.747645i \(0.268816\pi\)
\(20\) 112.000 1.25220
\(21\) 0 0
\(22\) 8.00000 0.0775275
\(23\) 48.0000 0.435161 0.217580 0.976042i \(-0.430184\pi\)
0.217580 + 0.976042i \(0.430184\pi\)
\(24\) 30.0000 0.255155
\(25\) 131.000 1.04800
\(26\) 28.0000 0.211202
\(27\) −100.000 −0.712778
\(28\) 0 0
\(29\) −110.000 −0.704362 −0.352181 0.935932i \(-0.614560\pi\)
−0.352181 + 0.935932i \(0.614560\pi\)
\(30\) 32.0000 0.194746
\(31\) −12.0000 −0.0695246 −0.0347623 0.999396i \(-0.511067\pi\)
−0.0347623 + 0.999396i \(0.511067\pi\)
\(32\) −161.000 −0.889408
\(33\) −16.0000 −0.0844013
\(34\) 54.0000 0.272380
\(35\) 0 0
\(36\) 161.000 0.745370
\(37\) −246.000 −1.09303 −0.546516 0.837449i \(-0.684046\pi\)
−0.546516 + 0.837449i \(0.684046\pi\)
\(38\) −110.000 −0.469588
\(39\) −56.0000 −0.229928
\(40\) −240.000 −0.948683
\(41\) −182.000 −0.693259 −0.346630 0.938002i \(-0.612674\pi\)
−0.346630 + 0.938002i \(0.612674\pi\)
\(42\) 0 0
\(43\) 128.000 0.453949 0.226975 0.973901i \(-0.427117\pi\)
0.226975 + 0.973901i \(0.427117\pi\)
\(44\) 56.0000 0.191871
\(45\) 368.000 1.21907
\(46\) −48.0000 −0.153852
\(47\) −324.000 −1.00554 −0.502769 0.864421i \(-0.667685\pi\)
−0.502769 + 0.864421i \(0.667685\pi\)
\(48\) 82.0000 0.246577
\(49\) 0 0
\(50\) −131.000 −0.370524
\(51\) −108.000 −0.296530
\(52\) 196.000 0.522698
\(53\) −162.000 −0.419857 −0.209928 0.977717i \(-0.567323\pi\)
−0.209928 + 0.977717i \(0.567323\pi\)
\(54\) 100.000 0.252005
\(55\) 128.000 0.313809
\(56\) 0 0
\(57\) 220.000 0.511223
\(58\) 110.000 0.249029
\(59\) −810.000 −1.78734 −0.893670 0.448725i \(-0.851878\pi\)
−0.893670 + 0.448725i \(0.851878\pi\)
\(60\) 224.000 0.481971
\(61\) 488.000 1.02430 0.512148 0.858898i \(-0.328850\pi\)
0.512148 + 0.858898i \(0.328850\pi\)
\(62\) 12.0000 0.0245807
\(63\) 0 0
\(64\) −167.000 −0.326172
\(65\) 448.000 0.854886
\(66\) 16.0000 0.0298404
\(67\) 244.000 0.444916 0.222458 0.974942i \(-0.428592\pi\)
0.222458 + 0.974942i \(0.428592\pi\)
\(68\) 378.000 0.674106
\(69\) 96.0000 0.167493
\(70\) 0 0
\(71\) −768.000 −1.28373 −0.641865 0.766818i \(-0.721839\pi\)
−0.641865 + 0.766818i \(0.721839\pi\)
\(72\) −345.000 −0.564703
\(73\) 702.000 1.12552 0.562759 0.826621i \(-0.309740\pi\)
0.562759 + 0.826621i \(0.309740\pi\)
\(74\) 246.000 0.386445
\(75\) 262.000 0.403375
\(76\) −770.000 −1.16217
\(77\) 0 0
\(78\) 56.0000 0.0812917
\(79\) 440.000 0.626631 0.313316 0.949649i \(-0.398560\pi\)
0.313316 + 0.949649i \(0.398560\pi\)
\(80\) −656.000 −0.916788
\(81\) 421.000 0.577503
\(82\) 182.000 0.245104
\(83\) 1302.00 1.72184 0.860922 0.508737i \(-0.169887\pi\)
0.860922 + 0.508737i \(0.169887\pi\)
\(84\) 0 0
\(85\) 864.000 1.10252
\(86\) −128.000 −0.160495
\(87\) −220.000 −0.271109
\(88\) −120.000 −0.145364
\(89\) −730.000 −0.869436 −0.434718 0.900567i \(-0.643152\pi\)
−0.434718 + 0.900567i \(0.643152\pi\)
\(90\) −368.000 −0.431007
\(91\) 0 0
\(92\) −336.000 −0.380765
\(93\) −24.0000 −0.0267600
\(94\) 324.000 0.355511
\(95\) −1760.00 −1.90076
\(96\) −322.000 −0.342333
\(97\) −294.000 −0.307744 −0.153872 0.988091i \(-0.549174\pi\)
−0.153872 + 0.988091i \(0.549174\pi\)
\(98\) 0 0
\(99\) 184.000 0.186795
\(100\) −917.000 −0.917000
\(101\) 688.000 0.677808 0.338904 0.940821i \(-0.389944\pi\)
0.338904 + 0.940821i \(0.389944\pi\)
\(102\) 108.000 0.104839
\(103\) −1388.00 −1.32780 −0.663901 0.747820i \(-0.731101\pi\)
−0.663901 + 0.747820i \(0.731101\pi\)
\(104\) −420.000 −0.396004
\(105\) 0 0
\(106\) 162.000 0.148442
\(107\) 244.000 0.220452 0.110226 0.993907i \(-0.464843\pi\)
0.110226 + 0.993907i \(0.464843\pi\)
\(108\) 700.000 0.623681
\(109\) 90.0000 0.0790866 0.0395433 0.999218i \(-0.487410\pi\)
0.0395433 + 0.999218i \(0.487410\pi\)
\(110\) −128.000 −0.110948
\(111\) −492.000 −0.420708
\(112\) 0 0
\(113\) 1318.00 1.09723 0.548615 0.836075i \(-0.315155\pi\)
0.548615 + 0.836075i \(0.315155\pi\)
\(114\) −220.000 −0.180745
\(115\) −768.000 −0.622751
\(116\) 770.000 0.616316
\(117\) 644.000 0.508870
\(118\) 810.000 0.631920
\(119\) 0 0
\(120\) −480.000 −0.365148
\(121\) −1267.00 −0.951916
\(122\) −488.000 −0.362143
\(123\) −364.000 −0.266836
\(124\) 84.0000 0.0608341
\(125\) −96.0000 −0.0686920
\(126\) 0 0
\(127\) −1776.00 −1.24090 −0.620451 0.784245i \(-0.713050\pi\)
−0.620451 + 0.784245i \(0.713050\pi\)
\(128\) 1455.00 1.00473
\(129\) 256.000 0.174725
\(130\) −448.000 −0.302248
\(131\) 1118.00 0.745650 0.372825 0.927902i \(-0.378389\pi\)
0.372825 + 0.927902i \(0.378389\pi\)
\(132\) 112.000 0.0738511
\(133\) 0 0
\(134\) −244.000 −0.157301
\(135\) 1600.00 1.02004
\(136\) −810.000 −0.510713
\(137\) 2274.00 1.41811 0.709054 0.705154i \(-0.249122\pi\)
0.709054 + 0.705154i \(0.249122\pi\)
\(138\) −96.0000 −0.0592178
\(139\) 210.000 0.128144 0.0640718 0.997945i \(-0.479591\pi\)
0.0640718 + 0.997945i \(0.479591\pi\)
\(140\) 0 0
\(141\) −648.000 −0.387032
\(142\) 768.000 0.453867
\(143\) 224.000 0.130992
\(144\) −943.000 −0.545718
\(145\) 1760.00 1.00800
\(146\) −702.000 −0.397931
\(147\) 0 0
\(148\) 1722.00 0.956402
\(149\) −2010.00 −1.10514 −0.552569 0.833467i \(-0.686352\pi\)
−0.552569 + 0.833467i \(0.686352\pi\)
\(150\) −262.000 −0.142615
\(151\) 1112.00 0.599293 0.299647 0.954050i \(-0.403131\pi\)
0.299647 + 0.954050i \(0.403131\pi\)
\(152\) 1650.00 0.880478
\(153\) 1242.00 0.656273
\(154\) 0 0
\(155\) 192.000 0.0994956
\(156\) 392.000 0.201187
\(157\) −124.000 −0.0630336 −0.0315168 0.999503i \(-0.510034\pi\)
−0.0315168 + 0.999503i \(0.510034\pi\)
\(158\) −440.000 −0.221548
\(159\) −324.000 −0.161603
\(160\) 2576.00 1.27282
\(161\) 0 0
\(162\) −421.000 −0.204178
\(163\) 2008.00 0.964900 0.482450 0.875924i \(-0.339747\pi\)
0.482450 + 0.875924i \(0.339747\pi\)
\(164\) 1274.00 0.606602
\(165\) 256.000 0.120785
\(166\) −1302.00 −0.608764
\(167\) −2884.00 −1.33635 −0.668176 0.744004i \(-0.732924\pi\)
−0.668176 + 0.744004i \(0.732924\pi\)
\(168\) 0 0
\(169\) −1413.00 −0.643150
\(170\) −864.000 −0.389799
\(171\) −2530.00 −1.13143
\(172\) −896.000 −0.397206
\(173\) −2228.00 −0.979143 −0.489571 0.871963i \(-0.662847\pi\)
−0.489571 + 0.871963i \(0.662847\pi\)
\(174\) 220.000 0.0958515
\(175\) 0 0
\(176\) −328.000 −0.140477
\(177\) −1620.00 −0.687947
\(178\) 730.000 0.307392
\(179\) −820.000 −0.342400 −0.171200 0.985236i \(-0.554764\pi\)
−0.171200 + 0.985236i \(0.554764\pi\)
\(180\) −2576.00 −1.06669
\(181\) −3892.00 −1.59829 −0.799144 0.601140i \(-0.794713\pi\)
−0.799144 + 0.601140i \(0.794713\pi\)
\(182\) 0 0
\(183\) 976.000 0.394251
\(184\) 720.000 0.288473
\(185\) 3936.00 1.56422
\(186\) 24.0000 0.00946110
\(187\) 432.000 0.168936
\(188\) 2268.00 0.879845
\(189\) 0 0
\(190\) 1760.00 0.672020
\(191\) −5048.00 −1.91236 −0.956179 0.292782i \(-0.905419\pi\)
−0.956179 + 0.292782i \(0.905419\pi\)
\(192\) −334.000 −0.125544
\(193\) −2962.00 −1.10471 −0.552356 0.833608i \(-0.686271\pi\)
−0.552356 + 0.833608i \(0.686271\pi\)
\(194\) 294.000 0.108804
\(195\) 896.000 0.329046
\(196\) 0 0
\(197\) 3334.00 1.20577 0.602887 0.797826i \(-0.294017\pi\)
0.602887 + 0.797826i \(0.294017\pi\)
\(198\) −184.000 −0.0660420
\(199\) −1860.00 −0.662572 −0.331286 0.943530i \(-0.607483\pi\)
−0.331286 + 0.943530i \(0.607483\pi\)
\(200\) 1965.00 0.694732
\(201\) 488.000 0.171248
\(202\) −688.000 −0.239641
\(203\) 0 0
\(204\) 756.000 0.259464
\(205\) 2912.00 0.992112
\(206\) 1388.00 0.469449
\(207\) −1104.00 −0.370692
\(208\) −1148.00 −0.382690
\(209\) −880.000 −0.291248
\(210\) 0 0
\(211\) −4268.00 −1.39252 −0.696259 0.717791i \(-0.745153\pi\)
−0.696259 + 0.717791i \(0.745153\pi\)
\(212\) 1134.00 0.367375
\(213\) −1536.00 −0.494108
\(214\) −244.000 −0.0779416
\(215\) −2048.00 −0.649639
\(216\) −1500.00 −0.472510
\(217\) 0 0
\(218\) −90.0000 −0.0279613
\(219\) 1404.00 0.433212
\(220\) −896.000 −0.274583
\(221\) 1512.00 0.460218
\(222\) 492.000 0.148743
\(223\) 5432.00 1.63118 0.815591 0.578629i \(-0.196412\pi\)
0.815591 + 0.578629i \(0.196412\pi\)
\(224\) 0 0
\(225\) −3013.00 −0.892741
\(226\) −1318.00 −0.387929
\(227\) 2046.00 0.598228 0.299114 0.954217i \(-0.403309\pi\)
0.299114 + 0.954217i \(0.403309\pi\)
\(228\) −1540.00 −0.447320
\(229\) 2980.00 0.859930 0.429965 0.902846i \(-0.358526\pi\)
0.429965 + 0.902846i \(0.358526\pi\)
\(230\) 768.000 0.220176
\(231\) 0 0
\(232\) −1650.00 −0.466930
\(233\) 4458.00 1.25345 0.626724 0.779241i \(-0.284395\pi\)
0.626724 + 0.779241i \(0.284395\pi\)
\(234\) −644.000 −0.179913
\(235\) 5184.00 1.43901
\(236\) 5670.00 1.56392
\(237\) 880.000 0.241190
\(238\) 0 0
\(239\) 4440.00 1.20167 0.600836 0.799372i \(-0.294834\pi\)
0.600836 + 0.799372i \(0.294834\pi\)
\(240\) −1312.00 −0.352872
\(241\) −3302.00 −0.882575 −0.441287 0.897366i \(-0.645478\pi\)
−0.441287 + 0.897366i \(0.645478\pi\)
\(242\) 1267.00 0.336553
\(243\) 3542.00 0.935059
\(244\) −3416.00 −0.896258
\(245\) 0 0
\(246\) 364.000 0.0943406
\(247\) −3080.00 −0.793424
\(248\) −180.000 −0.0460888
\(249\) 2604.00 0.662738
\(250\) 96.0000 0.0242863
\(251\) −1582.00 −0.397829 −0.198914 0.980017i \(-0.563742\pi\)
−0.198914 + 0.980017i \(0.563742\pi\)
\(252\) 0 0
\(253\) −384.000 −0.0954224
\(254\) 1776.00 0.438725
\(255\) 1728.00 0.424359
\(256\) −119.000 −0.0290527
\(257\) −2354.00 −0.571356 −0.285678 0.958326i \(-0.592219\pi\)
−0.285678 + 0.958326i \(0.592219\pi\)
\(258\) −256.000 −0.0617747
\(259\) 0 0
\(260\) −3136.00 −0.748025
\(261\) 2530.00 0.600012
\(262\) −1118.00 −0.263627
\(263\) −3872.00 −0.907824 −0.453912 0.891046i \(-0.649972\pi\)
−0.453912 + 0.891046i \(0.649972\pi\)
\(264\) −240.000 −0.0559507
\(265\) 2592.00 0.600850
\(266\) 0 0
\(267\) −1460.00 −0.334646
\(268\) −1708.00 −0.389301
\(269\) −180.000 −0.0407985 −0.0203992 0.999792i \(-0.506494\pi\)
−0.0203992 + 0.999792i \(0.506494\pi\)
\(270\) −1600.00 −0.360640
\(271\) −2032.00 −0.455480 −0.227740 0.973722i \(-0.573134\pi\)
−0.227740 + 0.973722i \(0.573134\pi\)
\(272\) −2214.00 −0.493542
\(273\) 0 0
\(274\) −2274.00 −0.501377
\(275\) −1048.00 −0.229806
\(276\) −672.000 −0.146557
\(277\) −5426.00 −1.17696 −0.588478 0.808513i \(-0.700273\pi\)
−0.588478 + 0.808513i \(0.700273\pi\)
\(278\) −210.000 −0.0453056
\(279\) 276.000 0.0592247
\(280\) 0 0
\(281\) 842.000 0.178753 0.0893764 0.995998i \(-0.471513\pi\)
0.0893764 + 0.995998i \(0.471513\pi\)
\(282\) 648.000 0.136836
\(283\) 3782.00 0.794405 0.397202 0.917731i \(-0.369981\pi\)
0.397202 + 0.917731i \(0.369981\pi\)
\(284\) 5376.00 1.12326
\(285\) −3520.00 −0.731603
\(286\) −224.000 −0.0463126
\(287\) 0 0
\(288\) 3703.00 0.757644
\(289\) −1997.00 −0.406473
\(290\) −1760.00 −0.356382
\(291\) −588.000 −0.118451
\(292\) −4914.00 −0.984829
\(293\) 4312.00 0.859760 0.429880 0.902886i \(-0.358556\pi\)
0.429880 + 0.902886i \(0.358556\pi\)
\(294\) 0 0
\(295\) 12960.0 2.55783
\(296\) −3690.00 −0.724584
\(297\) 800.000 0.156299
\(298\) 2010.00 0.390725
\(299\) −1344.00 −0.259952
\(300\) −1834.00 −0.352953
\(301\) 0 0
\(302\) −1112.00 −0.211882
\(303\) 1376.00 0.260888
\(304\) 4510.00 0.850876
\(305\) −7808.00 −1.46585
\(306\) −1242.00 −0.232027
\(307\) −2674.00 −0.497112 −0.248556 0.968618i \(-0.579956\pi\)
−0.248556 + 0.968618i \(0.579956\pi\)
\(308\) 0 0
\(309\) −2776.00 −0.511072
\(310\) −192.000 −0.0351770
\(311\) 3768.00 0.687021 0.343511 0.939149i \(-0.388384\pi\)
0.343511 + 0.939149i \(0.388384\pi\)
\(312\) −840.000 −0.152422
\(313\) −2438.00 −0.440268 −0.220134 0.975470i \(-0.570649\pi\)
−0.220134 + 0.975470i \(0.570649\pi\)
\(314\) 124.000 0.0222857
\(315\) 0 0
\(316\) −3080.00 −0.548302
\(317\) −3186.00 −0.564491 −0.282245 0.959342i \(-0.591079\pi\)
−0.282245 + 0.959342i \(0.591079\pi\)
\(318\) 324.000 0.0571353
\(319\) 880.000 0.154453
\(320\) 2672.00 0.466779
\(321\) 488.000 0.0848520
\(322\) 0 0
\(323\) −5940.00 −1.02325
\(324\) −2947.00 −0.505316
\(325\) −3668.00 −0.626043
\(326\) −2008.00 −0.341144
\(327\) 180.000 0.0304404
\(328\) −2730.00 −0.459570
\(329\) 0 0
\(330\) −256.000 −0.0427040
\(331\) 8672.00 1.44005 0.720025 0.693949i \(-0.244131\pi\)
0.720025 + 0.693949i \(0.244131\pi\)
\(332\) −9114.00 −1.50661
\(333\) 5658.00 0.931101
\(334\) 2884.00 0.472471
\(335\) −3904.00 −0.636711
\(336\) 0 0
\(337\) 814.000 0.131577 0.0657884 0.997834i \(-0.479044\pi\)
0.0657884 + 0.997834i \(0.479044\pi\)
\(338\) 1413.00 0.227388
\(339\) 2636.00 0.422324
\(340\) −6048.00 −0.964703
\(341\) 96.0000 0.0152454
\(342\) 2530.00 0.400020
\(343\) 0 0
\(344\) 1920.00 0.300929
\(345\) −1536.00 −0.239697
\(346\) 2228.00 0.346179
\(347\) 9344.00 1.44557 0.722784 0.691074i \(-0.242862\pi\)
0.722784 + 0.691074i \(0.242862\pi\)
\(348\) 1540.00 0.237220
\(349\) 5180.00 0.794496 0.397248 0.917711i \(-0.369965\pi\)
0.397248 + 0.917711i \(0.369965\pi\)
\(350\) 0 0
\(351\) 2800.00 0.425792
\(352\) 1288.00 0.195030
\(353\) −12178.0 −1.83617 −0.918087 0.396379i \(-0.870267\pi\)
−0.918087 + 0.396379i \(0.870267\pi\)
\(354\) 1620.00 0.243226
\(355\) 12288.0 1.83712
\(356\) 5110.00 0.760757
\(357\) 0 0
\(358\) 820.000 0.121057
\(359\) 440.000 0.0646861 0.0323431 0.999477i \(-0.489703\pi\)
0.0323431 + 0.999477i \(0.489703\pi\)
\(360\) 5520.00 0.808138
\(361\) 5241.00 0.764106
\(362\) 3892.00 0.565080
\(363\) −2534.00 −0.366393
\(364\) 0 0
\(365\) −11232.0 −1.61071
\(366\) −976.000 −0.139389
\(367\) 9816.00 1.39616 0.698080 0.716019i \(-0.254038\pi\)
0.698080 + 0.716019i \(0.254038\pi\)
\(368\) 1968.00 0.278775
\(369\) 4186.00 0.590554
\(370\) −3936.00 −0.553035
\(371\) 0 0
\(372\) 168.000 0.0234150
\(373\) −442.000 −0.0613563 −0.0306781 0.999529i \(-0.509767\pi\)
−0.0306781 + 0.999529i \(0.509767\pi\)
\(374\) −432.000 −0.0597278
\(375\) −192.000 −0.0264396
\(376\) −4860.00 −0.666583
\(377\) 3080.00 0.420764
\(378\) 0 0
\(379\) −3960.00 −0.536706 −0.268353 0.963321i \(-0.586479\pi\)
−0.268353 + 0.963321i \(0.586479\pi\)
\(380\) 12320.0 1.66316
\(381\) −3552.00 −0.477623
\(382\) 5048.00 0.676121
\(383\) −6708.00 −0.894942 −0.447471 0.894298i \(-0.647675\pi\)
−0.447471 + 0.894298i \(0.647675\pi\)
\(384\) 2910.00 0.386720
\(385\) 0 0
\(386\) 2962.00 0.390575
\(387\) −2944.00 −0.386697
\(388\) 2058.00 0.269276
\(389\) −13350.0 −1.74003 −0.870015 0.493025i \(-0.835891\pi\)
−0.870015 + 0.493025i \(0.835891\pi\)
\(390\) −896.000 −0.116335
\(391\) −2592.00 −0.335251
\(392\) 0 0
\(393\) 2236.00 0.287001
\(394\) −3334.00 −0.426306
\(395\) −7040.00 −0.896762
\(396\) −1288.00 −0.163446
\(397\) 1356.00 0.171425 0.0857125 0.996320i \(-0.472683\pi\)
0.0857125 + 0.996320i \(0.472683\pi\)
\(398\) 1860.00 0.234255
\(399\) 0 0
\(400\) 5371.00 0.671375
\(401\) 6222.00 0.774843 0.387421 0.921903i \(-0.373366\pi\)
0.387421 + 0.921903i \(0.373366\pi\)
\(402\) −488.000 −0.0605453
\(403\) 336.000 0.0415319
\(404\) −4816.00 −0.593082
\(405\) −6736.00 −0.826456
\(406\) 0 0
\(407\) 1968.00 0.239681
\(408\) −1620.00 −0.196573
\(409\) −5150.00 −0.622619 −0.311309 0.950309i \(-0.600768\pi\)
−0.311309 + 0.950309i \(0.600768\pi\)
\(410\) −2912.00 −0.350764
\(411\) 4548.00 0.545830
\(412\) 9716.00 1.16183
\(413\) 0 0
\(414\) 1104.00 0.131060
\(415\) −20832.0 −2.46410
\(416\) 4508.00 0.531305
\(417\) 420.000 0.0493225
\(418\) 880.000 0.102972
\(419\) −2310.00 −0.269334 −0.134667 0.990891i \(-0.542996\pi\)
−0.134667 + 0.990891i \(0.542996\pi\)
\(420\) 0 0
\(421\) 1262.00 0.146095 0.0730476 0.997328i \(-0.476727\pi\)
0.0730476 + 0.997328i \(0.476727\pi\)
\(422\) 4268.00 0.492329
\(423\) 7452.00 0.856569
\(424\) −2430.00 −0.278328
\(425\) −7074.00 −0.807387
\(426\) 1536.00 0.174694
\(427\) 0 0
\(428\) −1708.00 −0.192896
\(429\) 448.000 0.0504188
\(430\) 2048.00 0.229682
\(431\) −4488.00 −0.501576 −0.250788 0.968042i \(-0.580690\pi\)
−0.250788 + 0.968042i \(0.580690\pi\)
\(432\) −4100.00 −0.456623
\(433\) −17038.0 −1.89098 −0.945490 0.325652i \(-0.894416\pi\)
−0.945490 + 0.325652i \(0.894416\pi\)
\(434\) 0 0
\(435\) 3520.00 0.387979
\(436\) −630.000 −0.0692008
\(437\) 5280.00 0.577979
\(438\) −1404.00 −0.153164
\(439\) −16200.0 −1.76124 −0.880619 0.473824i \(-0.842873\pi\)
−0.880619 + 0.473824i \(0.842873\pi\)
\(440\) 1920.00 0.208028
\(441\) 0 0
\(442\) −1512.00 −0.162712
\(443\) −8772.00 −0.940791 −0.470395 0.882456i \(-0.655889\pi\)
−0.470395 + 0.882456i \(0.655889\pi\)
\(444\) 3444.00 0.368119
\(445\) 11680.0 1.24424
\(446\) −5432.00 −0.576710
\(447\) −4020.00 −0.425368
\(448\) 0 0
\(449\) 2130.00 0.223877 0.111939 0.993715i \(-0.464294\pi\)
0.111939 + 0.993715i \(0.464294\pi\)
\(450\) 3013.00 0.315632
\(451\) 1456.00 0.152019
\(452\) −9226.00 −0.960076
\(453\) 2224.00 0.230668
\(454\) −2046.00 −0.211506
\(455\) 0 0
\(456\) 3300.00 0.338896
\(457\) 10534.0 1.07825 0.539124 0.842226i \(-0.318755\pi\)
0.539124 + 0.842226i \(0.318755\pi\)
\(458\) −2980.00 −0.304031
\(459\) 5400.00 0.549129
\(460\) 5376.00 0.544907
\(461\) 9268.00 0.936342 0.468171 0.883638i \(-0.344913\pi\)
0.468171 + 0.883638i \(0.344913\pi\)
\(462\) 0 0
\(463\) −9392.00 −0.942728 −0.471364 0.881939i \(-0.656238\pi\)
−0.471364 + 0.881939i \(0.656238\pi\)
\(464\) −4510.00 −0.451232
\(465\) 384.000 0.0382959
\(466\) −4458.00 −0.443161
\(467\) 10806.0 1.07075 0.535377 0.844613i \(-0.320170\pi\)
0.535377 + 0.844613i \(0.320170\pi\)
\(468\) −4508.00 −0.445261
\(469\) 0 0
\(470\) −5184.00 −0.508766
\(471\) −248.000 −0.0242616
\(472\) −12150.0 −1.18485
\(473\) −1024.00 −0.0995424
\(474\) −880.000 −0.0852737
\(475\) 14410.0 1.39195
\(476\) 0 0
\(477\) 3726.00 0.357656
\(478\) −4440.00 −0.424855
\(479\) −4940.00 −0.471220 −0.235610 0.971848i \(-0.575709\pi\)
−0.235610 + 0.971848i \(0.575709\pi\)
\(480\) 5152.00 0.489907
\(481\) 6888.00 0.652943
\(482\) 3302.00 0.312037
\(483\) 0 0
\(484\) 8869.00 0.832926
\(485\) 4704.00 0.440407
\(486\) −3542.00 −0.330593
\(487\) −5216.00 −0.485338 −0.242669 0.970109i \(-0.578023\pi\)
−0.242669 + 0.970109i \(0.578023\pi\)
\(488\) 7320.00 0.679018
\(489\) 4016.00 0.371390
\(490\) 0 0
\(491\) 4412.00 0.405521 0.202760 0.979228i \(-0.435009\pi\)
0.202760 + 0.979228i \(0.435009\pi\)
\(492\) 2548.00 0.233481
\(493\) 5940.00 0.542645
\(494\) 3080.00 0.280518
\(495\) −2944.00 −0.267319
\(496\) −492.000 −0.0445392
\(497\) 0 0
\(498\) −2604.00 −0.234313
\(499\) 19060.0 1.70991 0.854953 0.518706i \(-0.173586\pi\)
0.854953 + 0.518706i \(0.173586\pi\)
\(500\) 672.000 0.0601055
\(501\) −5768.00 −0.514362
\(502\) 1582.00 0.140654
\(503\) −12768.0 −1.13180 −0.565902 0.824473i \(-0.691472\pi\)
−0.565902 + 0.824473i \(0.691472\pi\)
\(504\) 0 0
\(505\) −11008.0 −0.969999
\(506\) 384.000 0.0337369
\(507\) −2826.00 −0.247548
\(508\) 12432.0 1.08579
\(509\) 5500.00 0.478945 0.239473 0.970903i \(-0.423025\pi\)
0.239473 + 0.970903i \(0.423025\pi\)
\(510\) −1728.00 −0.150034
\(511\) 0 0
\(512\) −11521.0 −0.994455
\(513\) −11000.0 −0.946709
\(514\) 2354.00 0.202005
\(515\) 22208.0 1.90020
\(516\) −1792.00 −0.152884
\(517\) 2592.00 0.220495
\(518\) 0 0
\(519\) −4456.00 −0.376872
\(520\) 6720.00 0.566714
\(521\) 7338.00 0.617051 0.308526 0.951216i \(-0.400164\pi\)
0.308526 + 0.951216i \(0.400164\pi\)
\(522\) −2530.00 −0.212136
\(523\) 17582.0 1.46999 0.734997 0.678070i \(-0.237183\pi\)
0.734997 + 0.678070i \(0.237183\pi\)
\(524\) −7826.00 −0.652444
\(525\) 0 0
\(526\) 3872.00 0.320964
\(527\) 648.000 0.0535623
\(528\) −656.000 −0.0540696
\(529\) −9863.00 −0.810635
\(530\) −2592.00 −0.212433
\(531\) 18630.0 1.52255
\(532\) 0 0
\(533\) 5096.00 0.414132
\(534\) 1460.00 0.118315
\(535\) −3904.00 −0.315485
\(536\) 3660.00 0.294940
\(537\) −1640.00 −0.131790
\(538\) 180.000 0.0144244
\(539\) 0 0
\(540\) −11200.0 −0.892539
\(541\) −1618.00 −0.128583 −0.0642914 0.997931i \(-0.520479\pi\)
−0.0642914 + 0.997931i \(0.520479\pi\)
\(542\) 2032.00 0.161037
\(543\) −7784.00 −0.615181
\(544\) 8694.00 0.685206
\(545\) −1440.00 −0.113179
\(546\) 0 0
\(547\) 16144.0 1.26192 0.630958 0.775817i \(-0.282662\pi\)
0.630958 + 0.775817i \(0.282662\pi\)
\(548\) −15918.0 −1.24085
\(549\) −11224.0 −0.872548
\(550\) 1048.00 0.0812489
\(551\) −12100.0 −0.935531
\(552\) 1440.00 0.111033
\(553\) 0 0
\(554\) 5426.00 0.416117
\(555\) 7872.00 0.602068
\(556\) −1470.00 −0.112126
\(557\) 4654.00 0.354033 0.177016 0.984208i \(-0.443355\pi\)
0.177016 + 0.984208i \(0.443355\pi\)
\(558\) −276.000 −0.0209391
\(559\) −3584.00 −0.271175
\(560\) 0 0
\(561\) 864.000 0.0650234
\(562\) −842.000 −0.0631986
\(563\) −10078.0 −0.754418 −0.377209 0.926128i \(-0.623116\pi\)
−0.377209 + 0.926128i \(0.623116\pi\)
\(564\) 4536.00 0.338653
\(565\) −21088.0 −1.57023
\(566\) −3782.00 −0.280865
\(567\) 0 0
\(568\) −11520.0 −0.851001
\(569\) −5930.00 −0.436904 −0.218452 0.975848i \(-0.570101\pi\)
−0.218452 + 0.975848i \(0.570101\pi\)
\(570\) 3520.00 0.258661
\(571\) −19048.0 −1.39603 −0.698016 0.716082i \(-0.745933\pi\)
−0.698016 + 0.716082i \(0.745933\pi\)
\(572\) −1568.00 −0.114618
\(573\) −10096.0 −0.736067
\(574\) 0 0
\(575\) 6288.00 0.456048
\(576\) 3841.00 0.277850
\(577\) 14366.0 1.03651 0.518253 0.855227i \(-0.326582\pi\)
0.518253 + 0.855227i \(0.326582\pi\)
\(578\) 1997.00 0.143710
\(579\) −5924.00 −0.425204
\(580\) −12320.0 −0.882000
\(581\) 0 0
\(582\) 588.000 0.0418787
\(583\) 1296.00 0.0920666
\(584\) 10530.0 0.746121
\(585\) −10304.0 −0.728236
\(586\) −4312.00 −0.303971
\(587\) 3626.00 0.254959 0.127480 0.991841i \(-0.459311\pi\)
0.127480 + 0.991841i \(0.459311\pi\)
\(588\) 0 0
\(589\) −1320.00 −0.0923424
\(590\) −12960.0 −0.904330
\(591\) 6668.00 0.464103
\(592\) −10086.0 −0.700223
\(593\) 1062.00 0.0735432 0.0367716 0.999324i \(-0.488293\pi\)
0.0367716 + 0.999324i \(0.488293\pi\)
\(594\) −800.000 −0.0552599
\(595\) 0 0
\(596\) 14070.0 0.966996
\(597\) −3720.00 −0.255024
\(598\) 1344.00 0.0919068
\(599\) −10200.0 −0.695761 −0.347880 0.937539i \(-0.613098\pi\)
−0.347880 + 0.937539i \(0.613098\pi\)
\(600\) 3930.00 0.267403
\(601\) 25158.0 1.70751 0.853757 0.520671i \(-0.174318\pi\)
0.853757 + 0.520671i \(0.174318\pi\)
\(602\) 0 0
\(603\) −5612.00 −0.379002
\(604\) −7784.00 −0.524382
\(605\) 20272.0 1.36227
\(606\) −1376.00 −0.0922379
\(607\) −25664.0 −1.71609 −0.858047 0.513570i \(-0.828323\pi\)
−0.858047 + 0.513570i \(0.828323\pi\)
\(608\) −17710.0 −1.18131
\(609\) 0 0
\(610\) 7808.00 0.518257
\(611\) 9072.00 0.600677
\(612\) −8694.00 −0.574239
\(613\) 19018.0 1.25307 0.626533 0.779395i \(-0.284473\pi\)
0.626533 + 0.779395i \(0.284473\pi\)
\(614\) 2674.00 0.175755
\(615\) 5824.00 0.381864
\(616\) 0 0
\(617\) 17334.0 1.13102 0.565511 0.824741i \(-0.308679\pi\)
0.565511 + 0.824741i \(0.308679\pi\)
\(618\) 2776.00 0.180691
\(619\) −18730.0 −1.21619 −0.608096 0.793864i \(-0.708066\pi\)
−0.608096 + 0.793864i \(0.708066\pi\)
\(620\) −1344.00 −0.0870586
\(621\) −4800.00 −0.310173
\(622\) −3768.00 −0.242899
\(623\) 0 0
\(624\) −2296.00 −0.147297
\(625\) −14839.0 −0.949696
\(626\) 2438.00 0.155658
\(627\) −1760.00 −0.112101
\(628\) 868.000 0.0551544
\(629\) 13284.0 0.842079
\(630\) 0 0
\(631\) −6928.00 −0.437083 −0.218541 0.975828i \(-0.570130\pi\)
−0.218541 + 0.975828i \(0.570130\pi\)
\(632\) 6600.00 0.415402
\(633\) −8536.00 −0.535980
\(634\) 3186.00 0.199578
\(635\) 28416.0 1.77583
\(636\) 2268.00 0.141403
\(637\) 0 0
\(638\) −880.000 −0.0546074
\(639\) 17664.0 1.09355
\(640\) −23280.0 −1.43785
\(641\) 16302.0 1.00451 0.502255 0.864720i \(-0.332504\pi\)
0.502255 + 0.864720i \(0.332504\pi\)
\(642\) −488.000 −0.0299997
\(643\) −4718.00 −0.289362 −0.144681 0.989478i \(-0.546216\pi\)
−0.144681 + 0.989478i \(0.546216\pi\)
\(644\) 0 0
\(645\) −4096.00 −0.250046
\(646\) 5940.00 0.361774
\(647\) 21436.0 1.30253 0.651264 0.758851i \(-0.274239\pi\)
0.651264 + 0.758851i \(0.274239\pi\)
\(648\) 6315.00 0.382834
\(649\) 6480.00 0.391930
\(650\) 3668.00 0.221340
\(651\) 0 0
\(652\) −14056.0 −0.844287
\(653\) 4458.00 0.267159 0.133580 0.991038i \(-0.457353\pi\)
0.133580 + 0.991038i \(0.457353\pi\)
\(654\) −180.000 −0.0107623
\(655\) −17888.0 −1.06709
\(656\) −7462.00 −0.444119
\(657\) −16146.0 −0.958775
\(658\) 0 0
\(659\) −26640.0 −1.57473 −0.787365 0.616487i \(-0.788555\pi\)
−0.787365 + 0.616487i \(0.788555\pi\)
\(660\) −1792.00 −0.105687
\(661\) −7432.00 −0.437324 −0.218662 0.975801i \(-0.570169\pi\)
−0.218662 + 0.975801i \(0.570169\pi\)
\(662\) −8672.00 −0.509134
\(663\) 3024.00 0.177138
\(664\) 19530.0 1.14143
\(665\) 0 0
\(666\) −5658.00 −0.329194
\(667\) −5280.00 −0.306510
\(668\) 20188.0 1.16931
\(669\) 10864.0 0.627842
\(670\) 3904.00 0.225111
\(671\) −3904.00 −0.224608
\(672\) 0 0
\(673\) 58.0000 0.00332204 0.00166102 0.999999i \(-0.499471\pi\)
0.00166102 + 0.999999i \(0.499471\pi\)
\(674\) −814.000 −0.0465194
\(675\) −13100.0 −0.746991
\(676\) 9891.00 0.562756
\(677\) 21516.0 1.22146 0.610729 0.791840i \(-0.290876\pi\)
0.610729 + 0.791840i \(0.290876\pi\)
\(678\) −2636.00 −0.149314
\(679\) 0 0
\(680\) 12960.0 0.730873
\(681\) 4092.00 0.230258
\(682\) −96.0000 −0.00539007
\(683\) 18108.0 1.01447 0.507235 0.861808i \(-0.330668\pi\)
0.507235 + 0.861808i \(0.330668\pi\)
\(684\) 17710.0 0.989998
\(685\) −36384.0 −2.02943
\(686\) 0 0
\(687\) 5960.00 0.330987
\(688\) 5248.00 0.290811
\(689\) 4536.00 0.250810
\(690\) 1536.00 0.0847457
\(691\) 10078.0 0.554827 0.277413 0.960751i \(-0.410523\pi\)
0.277413 + 0.960751i \(0.410523\pi\)
\(692\) 15596.0 0.856750
\(693\) 0 0
\(694\) −9344.00 −0.511086
\(695\) −3360.00 −0.183384
\(696\) −3300.00 −0.179722
\(697\) 9828.00 0.534092
\(698\) −5180.00 −0.280897
\(699\) 8916.00 0.482452
\(700\) 0 0
\(701\) 18762.0 1.01089 0.505443 0.862860i \(-0.331329\pi\)
0.505443 + 0.862860i \(0.331329\pi\)
\(702\) −2800.00 −0.150540
\(703\) −27060.0 −1.45176
\(704\) 1336.00 0.0715233
\(705\) 10368.0 0.553874
\(706\) 12178.0 0.649186
\(707\) 0 0
\(708\) 11340.0 0.601954
\(709\) 6810.00 0.360726 0.180363 0.983600i \(-0.442273\pi\)
0.180363 + 0.983600i \(0.442273\pi\)
\(710\) −12288.0 −0.649522
\(711\) −10120.0 −0.533797
\(712\) −10950.0 −0.576360
\(713\) −576.000 −0.0302544
\(714\) 0 0
\(715\) −3584.00 −0.187460
\(716\) 5740.00 0.299600
\(717\) 8880.00 0.462524
\(718\) −440.000 −0.0228700
\(719\) −4860.00 −0.252083 −0.126041 0.992025i \(-0.540227\pi\)
−0.126041 + 0.992025i \(0.540227\pi\)
\(720\) 15088.0 0.780967
\(721\) 0 0
\(722\) −5241.00 −0.270152
\(723\) −6604.00 −0.339703
\(724\) 27244.0 1.39850
\(725\) −14410.0 −0.738171
\(726\) 2534.00 0.129539
\(727\) 13636.0 0.695641 0.347821 0.937561i \(-0.386922\pi\)
0.347821 + 0.937561i \(0.386922\pi\)
\(728\) 0 0
\(729\) −4283.00 −0.217599
\(730\) 11232.0 0.569473
\(731\) −6912.00 −0.349726
\(732\) −6832.00 −0.344970
\(733\) −2088.00 −0.105214 −0.0526071 0.998615i \(-0.516753\pi\)
−0.0526071 + 0.998615i \(0.516753\pi\)
\(734\) −9816.00 −0.493617
\(735\) 0 0
\(736\) −7728.00 −0.387035
\(737\) −1952.00 −0.0975615
\(738\) −4186.00 −0.208792
\(739\) −5160.00 −0.256852 −0.128426 0.991719i \(-0.540992\pi\)
−0.128426 + 0.991719i \(0.540992\pi\)
\(740\) −27552.0 −1.36869
\(741\) −6160.00 −0.305389
\(742\) 0 0
\(743\) −28152.0 −1.39004 −0.695018 0.718992i \(-0.744604\pi\)
−0.695018 + 0.718992i \(0.744604\pi\)
\(744\) −360.000 −0.0177396
\(745\) 32160.0 1.58155
\(746\) 442.000 0.0216927
\(747\) −29946.0 −1.46676
\(748\) −3024.00 −0.147819
\(749\) 0 0
\(750\) 192.000 0.00934780
\(751\) −16808.0 −0.816688 −0.408344 0.912828i \(-0.633894\pi\)
−0.408344 + 0.912828i \(0.633894\pi\)
\(752\) −13284.0 −0.644172
\(753\) −3164.00 −0.153124
\(754\) −3080.00 −0.148763
\(755\) −17792.0 −0.857639
\(756\) 0 0
\(757\) 21674.0 1.04063 0.520314 0.853975i \(-0.325815\pi\)
0.520314 + 0.853975i \(0.325815\pi\)
\(758\) 3960.00 0.189754
\(759\) −768.000 −0.0367281
\(760\) −26400.0 −1.26004
\(761\) −7422.00 −0.353544 −0.176772 0.984252i \(-0.556566\pi\)
−0.176772 + 0.984252i \(0.556566\pi\)
\(762\) 3552.00 0.168865
\(763\) 0 0
\(764\) 35336.0 1.67331
\(765\) −19872.0 −0.939181
\(766\) 6708.00 0.316410
\(767\) 22680.0 1.06770
\(768\) −238.000 −0.0111824
\(769\) −13790.0 −0.646658 −0.323329 0.946287i \(-0.604802\pi\)
−0.323329 + 0.946287i \(0.604802\pi\)
\(770\) 0 0
\(771\) −4708.00 −0.219915
\(772\) 20734.0 0.966623
\(773\) 6232.00 0.289973 0.144987 0.989434i \(-0.453686\pi\)
0.144987 + 0.989434i \(0.453686\pi\)
\(774\) 2944.00 0.136718
\(775\) −1572.00 −0.0728618
\(776\) −4410.00 −0.204007
\(777\) 0 0
\(778\) 13350.0 0.615194
\(779\) −20020.0 −0.920784
\(780\) −6272.00 −0.287915
\(781\) 6144.00 0.281498
\(782\) 2592.00 0.118529
\(783\) 11000.0 0.502054
\(784\) 0 0
\(785\) 1984.00 0.0902064
\(786\) −2236.00 −0.101470
\(787\) 1766.00 0.0799887 0.0399943 0.999200i \(-0.487266\pi\)
0.0399943 + 0.999200i \(0.487266\pi\)
\(788\) −23338.0 −1.05505
\(789\) −7744.00 −0.349422
\(790\) 7040.00 0.317053
\(791\) 0 0
\(792\) 2760.00 0.123829
\(793\) −13664.0 −0.611883
\(794\) −1356.00 −0.0606079
\(795\) 5184.00 0.231267
\(796\) 13020.0 0.579751
\(797\) −1204.00 −0.0535105 −0.0267552 0.999642i \(-0.508517\pi\)
−0.0267552 + 0.999642i \(0.508517\pi\)
\(798\) 0 0
\(799\) 17496.0 0.774673
\(800\) −21091.0 −0.932099
\(801\) 16790.0 0.740631
\(802\) −6222.00 −0.273948
\(803\) −5616.00 −0.246805
\(804\) −3416.00 −0.149842
\(805\) 0 0
\(806\) −336.000 −0.0146837
\(807\) −360.000 −0.0157033
\(808\) 10320.0 0.449327
\(809\) −7050.00 −0.306384 −0.153192 0.988196i \(-0.548955\pi\)
−0.153192 + 0.988196i \(0.548955\pi\)
\(810\) 6736.00 0.292196
\(811\) −23282.0 −1.00807 −0.504033 0.863684i \(-0.668151\pi\)
−0.504033 + 0.863684i \(0.668151\pi\)
\(812\) 0 0
\(813\) −4064.00 −0.175315
\(814\) −1968.00 −0.0847400
\(815\) −32128.0 −1.38085
\(816\) −4428.00 −0.189964
\(817\) 14080.0 0.602934
\(818\) 5150.00 0.220129
\(819\) 0 0
\(820\) −20384.0 −0.868098
\(821\) 10142.0 0.431131 0.215565 0.976489i \(-0.430841\pi\)
0.215565 + 0.976489i \(0.430841\pi\)
\(822\) −4548.00 −0.192980
\(823\) −9192.00 −0.389323 −0.194662 0.980870i \(-0.562361\pi\)
−0.194662 + 0.980870i \(0.562361\pi\)
\(824\) −20820.0 −0.880217
\(825\) −2096.00 −0.0884525
\(826\) 0 0
\(827\) −46716.0 −1.96430 −0.982149 0.188104i \(-0.939766\pi\)
−0.982149 + 0.188104i \(0.939766\pi\)
\(828\) 7728.00 0.324356
\(829\) −11240.0 −0.470906 −0.235453 0.971886i \(-0.575657\pi\)
−0.235453 + 0.971886i \(0.575657\pi\)
\(830\) 20832.0 0.871192
\(831\) −10852.0 −0.453010
\(832\) 4676.00 0.194845
\(833\) 0 0
\(834\) −420.000 −0.0174381
\(835\) 46144.0 1.91243
\(836\) 6160.00 0.254842
\(837\) 1200.00 0.0495556
\(838\) 2310.00 0.0952239
\(839\) −700.000 −0.0288042 −0.0144021 0.999896i \(-0.504584\pi\)
−0.0144021 + 0.999896i \(0.504584\pi\)
\(840\) 0 0
\(841\) −12289.0 −0.503875
\(842\) −1262.00 −0.0516525
\(843\) 1684.00 0.0688019
\(844\) 29876.0 1.21845
\(845\) 22608.0 0.920401
\(846\) −7452.00 −0.302843
\(847\) 0 0
\(848\) −6642.00 −0.268971
\(849\) 7564.00 0.305767
\(850\) 7074.00 0.285454
\(851\) −11808.0 −0.475644
\(852\) 10752.0 0.432344
\(853\) 37492.0 1.50493 0.752463 0.658635i \(-0.228866\pi\)
0.752463 + 0.658635i \(0.228866\pi\)
\(854\) 0 0
\(855\) 40480.0 1.61917
\(856\) 3660.00 0.146140
\(857\) −28894.0 −1.15169 −0.575846 0.817558i \(-0.695327\pi\)
−0.575846 + 0.817558i \(0.695327\pi\)
\(858\) −448.000 −0.0178257
\(859\) 2770.00 0.110025 0.0550123 0.998486i \(-0.482480\pi\)
0.0550123 + 0.998486i \(0.482480\pi\)
\(860\) 14336.0 0.568434
\(861\) 0 0
\(862\) 4488.00 0.177334
\(863\) 17688.0 0.697690 0.348845 0.937180i \(-0.386574\pi\)
0.348845 + 0.937180i \(0.386574\pi\)
\(864\) 16100.0 0.633950
\(865\) 35648.0 1.40124
\(866\) 17038.0 0.668562
\(867\) −3994.00 −0.156451
\(868\) 0 0
\(869\) −3520.00 −0.137408
\(870\) −3520.00 −0.137171
\(871\) −6832.00 −0.265779
\(872\) 1350.00 0.0524275
\(873\) 6762.00 0.262152
\(874\) −5280.00 −0.204346
\(875\) 0 0
\(876\) −9828.00 −0.379061
\(877\) −33566.0 −1.29241 −0.646205 0.763164i \(-0.723645\pi\)
−0.646205 + 0.763164i \(0.723645\pi\)
\(878\) 16200.0 0.622692
\(879\) 8624.00 0.330922
\(880\) 5248.00 0.201034
\(881\) 16758.0 0.640853 0.320426 0.947273i \(-0.396174\pi\)
0.320426 + 0.947273i \(0.396174\pi\)
\(882\) 0 0
\(883\) 11468.0 0.437066 0.218533 0.975830i \(-0.429873\pi\)
0.218533 + 0.975830i \(0.429873\pi\)
\(884\) −10584.0 −0.402691
\(885\) 25920.0 0.984510
\(886\) 8772.00 0.332620
\(887\) 50356.0 1.90619 0.953094 0.302674i \(-0.0978793\pi\)
0.953094 + 0.302674i \(0.0978793\pi\)
\(888\) −7380.00 −0.278893
\(889\) 0 0
\(890\) −11680.0 −0.439904
\(891\) −3368.00 −0.126636
\(892\) −38024.0 −1.42728
\(893\) −35640.0 −1.33555
\(894\) 4020.00 0.150390
\(895\) 13120.0 0.490004
\(896\) 0 0
\(897\) −2688.00 −0.100055
\(898\) −2130.00 −0.0791526
\(899\) 1320.00 0.0489705
\(900\) 21091.0 0.781148
\(901\) 8748.00 0.323461
\(902\) −1456.00 −0.0537467
\(903\) 0 0
\(904\) 19770.0 0.727368
\(905\) 62272.0 2.28728
\(906\) −2224.00 −0.0815535
\(907\) −8716.00 −0.319085 −0.159542 0.987191i \(-0.551002\pi\)
−0.159542 + 0.987191i \(0.551002\pi\)
\(908\) −14322.0 −0.523450
\(909\) −15824.0 −0.577392
\(910\) 0 0
\(911\) 7632.00 0.277563 0.138781 0.990323i \(-0.455682\pi\)
0.138781 + 0.990323i \(0.455682\pi\)
\(912\) 9020.00 0.327502
\(913\) −10416.0 −0.377568
\(914\) −10534.0 −0.381219
\(915\) −15616.0 −0.564207
\(916\) −20860.0 −0.752439
\(917\) 0 0
\(918\) −5400.00 −0.194147
\(919\) −23080.0 −0.828443 −0.414221 0.910176i \(-0.635946\pi\)
−0.414221 + 0.910176i \(0.635946\pi\)
\(920\) −11520.0 −0.412830
\(921\) −5348.00 −0.191338
\(922\) −9268.00 −0.331047
\(923\) 21504.0 0.766861
\(924\) 0 0
\(925\) −32226.0 −1.14550
\(926\) 9392.00 0.333305
\(927\) 31924.0 1.13109
\(928\) 17710.0 0.626465
\(929\) −45110.0 −1.59312 −0.796561 0.604558i \(-0.793350\pi\)
−0.796561 + 0.604558i \(0.793350\pi\)
\(930\) −384.000 −0.0135396
\(931\) 0 0
\(932\) −31206.0 −1.09677
\(933\) 7536.00 0.264435
\(934\) −10806.0 −0.378569
\(935\) −6912.00 −0.241761
\(936\) 9660.00 0.337337
\(937\) −16674.0 −0.581340 −0.290670 0.956823i \(-0.593878\pi\)
−0.290670 + 0.956823i \(0.593878\pi\)
\(938\) 0 0
\(939\) −4876.00 −0.169459
\(940\) −36288.0 −1.25913
\(941\) −43832.0 −1.51847 −0.759236 0.650815i \(-0.774427\pi\)
−0.759236 + 0.650815i \(0.774427\pi\)
\(942\) 248.000 0.00857779
\(943\) −8736.00 −0.301679
\(944\) −33210.0 −1.14501
\(945\) 0 0
\(946\) 1024.00 0.0351936
\(947\) −736.000 −0.0252553 −0.0126277 0.999920i \(-0.504020\pi\)
−0.0126277 + 0.999920i \(0.504020\pi\)
\(948\) −6160.00 −0.211042
\(949\) −19656.0 −0.672351
\(950\) −14410.0 −0.492129
\(951\) −6372.00 −0.217273
\(952\) 0 0
\(953\) 38138.0 1.29634 0.648169 0.761496i \(-0.275535\pi\)
0.648169 + 0.761496i \(0.275535\pi\)
\(954\) −3726.00 −0.126450
\(955\) 80768.0 2.73674
\(956\) −31080.0 −1.05146
\(957\) 1760.00 0.0594490
\(958\) 4940.00 0.166601
\(959\) 0 0
\(960\) 5344.00 0.179663
\(961\) −29647.0 −0.995166
\(962\) −6888.00 −0.230850
\(963\) −5612.00 −0.187792
\(964\) 23114.0 0.772253
\(965\) 47392.0 1.58094
\(966\) 0 0
\(967\) 26224.0 0.872086 0.436043 0.899926i \(-0.356380\pi\)
0.436043 + 0.899926i \(0.356380\pi\)
\(968\) −19005.0 −0.631037
\(969\) −11880.0 −0.393850
\(970\) −4704.00 −0.155708
\(971\) −18762.0 −0.620084 −0.310042 0.950723i \(-0.600343\pi\)
−0.310042 + 0.950723i \(0.600343\pi\)
\(972\) −24794.0 −0.818177
\(973\) 0 0
\(974\) 5216.00 0.171593
\(975\) −7336.00 −0.240964
\(976\) 20008.0 0.656189
\(977\) 38394.0 1.25725 0.628625 0.777709i \(-0.283618\pi\)
0.628625 + 0.777709i \(0.283618\pi\)
\(978\) −4016.00 −0.131306
\(979\) 5840.00 0.190651
\(980\) 0 0
\(981\) −2070.00 −0.0673700
\(982\) −4412.00 −0.143373
\(983\) −5388.00 −0.174822 −0.0874112 0.996172i \(-0.527859\pi\)
−0.0874112 + 0.996172i \(0.527859\pi\)
\(984\) −5460.00 −0.176889
\(985\) −53344.0 −1.72556
\(986\) −5940.00 −0.191854
\(987\) 0 0
\(988\) 21560.0 0.694246
\(989\) 6144.00 0.197541
\(990\) 2944.00 0.0945116
\(991\) 25472.0 0.816493 0.408247 0.912872i \(-0.366140\pi\)
0.408247 + 0.912872i \(0.366140\pi\)
\(992\) 1932.00 0.0618357
\(993\) 17344.0 0.554275
\(994\) 0 0
\(995\) 29760.0 0.948196
\(996\) −18228.0 −0.579896
\(997\) 17096.0 0.543065 0.271532 0.962429i \(-0.412470\pi\)
0.271532 + 0.962429i \(0.412470\pi\)
\(998\) −19060.0 −0.604543
\(999\) 24600.0 0.779089
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 49.4.a.b.1.1 1
3.2 odd 2 441.4.a.i.1.1 1
4.3 odd 2 784.4.a.g.1.1 1
5.4 even 2 1225.4.a.j.1.1 1
7.2 even 3 49.4.c.b.18.1 2
7.3 odd 6 49.4.c.c.30.1 2
7.4 even 3 49.4.c.b.30.1 2
7.5 odd 6 49.4.c.c.18.1 2
7.6 odd 2 7.4.a.a.1.1 1
21.2 odd 6 441.4.e.e.361.1 2
21.5 even 6 441.4.e.h.361.1 2
21.11 odd 6 441.4.e.e.226.1 2
21.17 even 6 441.4.e.h.226.1 2
21.20 even 2 63.4.a.b.1.1 1
28.27 even 2 112.4.a.f.1.1 1
35.13 even 4 175.4.b.b.99.2 2
35.27 even 4 175.4.b.b.99.1 2
35.34 odd 2 175.4.a.b.1.1 1
56.13 odd 2 448.4.a.i.1.1 1
56.27 even 2 448.4.a.e.1.1 1
77.76 even 2 847.4.a.b.1.1 1
84.83 odd 2 1008.4.a.c.1.1 1
91.90 odd 2 1183.4.a.b.1.1 1
105.104 even 2 1575.4.a.e.1.1 1
119.118 odd 2 2023.4.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7.4.a.a.1.1 1 7.6 odd 2
49.4.a.b.1.1 1 1.1 even 1 trivial
49.4.c.b.18.1 2 7.2 even 3
49.4.c.b.30.1 2 7.4 even 3
49.4.c.c.18.1 2 7.5 odd 6
49.4.c.c.30.1 2 7.3 odd 6
63.4.a.b.1.1 1 21.20 even 2
112.4.a.f.1.1 1 28.27 even 2
175.4.a.b.1.1 1 35.34 odd 2
175.4.b.b.99.1 2 35.27 even 4
175.4.b.b.99.2 2 35.13 even 4
441.4.a.i.1.1 1 3.2 odd 2
441.4.e.e.226.1 2 21.11 odd 6
441.4.e.e.361.1 2 21.2 odd 6
441.4.e.h.226.1 2 21.17 even 6
441.4.e.h.361.1 2 21.5 even 6
448.4.a.e.1.1 1 56.27 even 2
448.4.a.i.1.1 1 56.13 odd 2
784.4.a.g.1.1 1 4.3 odd 2
847.4.a.b.1.1 1 77.76 even 2
1008.4.a.c.1.1 1 84.83 odd 2
1183.4.a.b.1.1 1 91.90 odd 2
1225.4.a.j.1.1 1 5.4 even 2
1575.4.a.e.1.1 1 105.104 even 2
2023.4.a.a.1.1 1 119.118 odd 2