Properties

Label 1225.4.a.d.1.1
Level $1225$
Weight $4$
Character 1225.1
Self dual yes
Analytic conductor $72.277$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 1225 = 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1225.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(72.2773397570\)
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 \(\chi\) \(=\) 1225.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000 q^{2} +7.00000 q^{3} -4.00000 q^{4} -14.0000 q^{6} +24.0000 q^{8} +22.0000 q^{9} +O(q^{10})\) \(q-2.00000 q^{2} +7.00000 q^{3} -4.00000 q^{4} -14.0000 q^{6} +24.0000 q^{8} +22.0000 q^{9} -5.00000 q^{11} -28.0000 q^{12} -14.0000 q^{13} -16.0000 q^{16} -21.0000 q^{17} -44.0000 q^{18} -49.0000 q^{19} +10.0000 q^{22} +159.000 q^{23} +168.000 q^{24} +28.0000 q^{26} -35.0000 q^{27} +58.0000 q^{29} -147.000 q^{31} -160.000 q^{32} -35.0000 q^{33} +42.0000 q^{34} -88.0000 q^{36} -219.000 q^{37} +98.0000 q^{38} -98.0000 q^{39} -350.000 q^{41} +124.000 q^{43} +20.0000 q^{44} -318.000 q^{46} +525.000 q^{47} -112.000 q^{48} -147.000 q^{51} +56.0000 q^{52} -303.000 q^{53} +70.0000 q^{54} -343.000 q^{57} -116.000 q^{58} +105.000 q^{59} +413.000 q^{61} +294.000 q^{62} +448.000 q^{64} +70.0000 q^{66} -415.000 q^{67} +84.0000 q^{68} +1113.00 q^{69} -432.000 q^{71} +528.000 q^{72} -1113.00 q^{73} +438.000 q^{74} +196.000 q^{76} +196.000 q^{78} -103.000 q^{79} -839.000 q^{81} +700.000 q^{82} +1092.00 q^{83} -248.000 q^{86} +406.000 q^{87} -120.000 q^{88} +329.000 q^{89} -636.000 q^{92} -1029.00 q^{93} -1050.00 q^{94} -1120.00 q^{96} -882.000 q^{97} -110.000 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 −0.707107 −0.353553 0.935414i \(-0.615027\pi\)
−0.353553 + 0.935414i \(0.615027\pi\)
\(3\) 7.00000 1.34715 0.673575 0.739119i \(-0.264758\pi\)
0.673575 + 0.739119i \(0.264758\pi\)
\(4\) −4.00000 −0.500000
\(5\) 0 0
\(6\) −14.0000 −0.952579
\(7\) 0 0
\(8\) 24.0000 1.06066
\(9\) 22.0000 0.814815
\(10\) 0 0
\(11\) −5.00000 −0.137051 −0.0685253 0.997649i \(-0.521829\pi\)
−0.0685253 + 0.997649i \(0.521829\pi\)
\(12\) −28.0000 −0.673575
\(13\) −14.0000 −0.298685 −0.149342 0.988786i \(-0.547716\pi\)
−0.149342 + 0.988786i \(0.547716\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −16.0000 −0.250000
\(17\) −21.0000 −0.299603 −0.149801 0.988716i \(-0.547863\pi\)
−0.149801 + 0.988716i \(0.547863\pi\)
\(18\) −44.0000 −0.576161
\(19\) −49.0000 −0.591651 −0.295826 0.955242i \(-0.595595\pi\)
−0.295826 + 0.955242i \(0.595595\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 10.0000 0.0969094
\(23\) 159.000 1.44147 0.720735 0.693211i \(-0.243805\pi\)
0.720735 + 0.693211i \(0.243805\pi\)
\(24\) 168.000 1.42887
\(25\) 0 0
\(26\) 28.0000 0.211202
\(27\) −35.0000 −0.249472
\(28\) 0 0
\(29\) 58.0000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) 0 0
\(31\) −147.000 −0.851677 −0.425838 0.904799i \(-0.640021\pi\)
−0.425838 + 0.904799i \(0.640021\pi\)
\(32\) −160.000 −0.883883
\(33\) −35.0000 −0.184628
\(34\) 42.0000 0.211851
\(35\) 0 0
\(36\) −88.0000 −0.407407
\(37\) −219.000 −0.973064 −0.486532 0.873663i \(-0.661738\pi\)
−0.486532 + 0.873663i \(0.661738\pi\)
\(38\) 98.0000 0.418361
\(39\) −98.0000 −0.402373
\(40\) 0 0
\(41\) −350.000 −1.33319 −0.666595 0.745420i \(-0.732249\pi\)
−0.666595 + 0.745420i \(0.732249\pi\)
\(42\) 0 0
\(43\) 124.000 0.439763 0.219882 0.975527i \(-0.429433\pi\)
0.219882 + 0.975527i \(0.429433\pi\)
\(44\) 20.0000 0.0685253
\(45\) 0 0
\(46\) −318.000 −1.01927
\(47\) 525.000 1.62934 0.814671 0.579923i \(-0.196917\pi\)
0.814671 + 0.579923i \(0.196917\pi\)
\(48\) −112.000 −0.336788
\(49\) 0 0
\(50\) 0 0
\(51\) −147.000 −0.403610
\(52\) 56.0000 0.149342
\(53\) −303.000 −0.785288 −0.392644 0.919691i \(-0.628439\pi\)
−0.392644 + 0.919691i \(0.628439\pi\)
\(54\) 70.0000 0.176404
\(55\) 0 0
\(56\) 0 0
\(57\) −343.000 −0.797043
\(58\) −116.000 −0.262613
\(59\) 105.000 0.231692 0.115846 0.993267i \(-0.463042\pi\)
0.115846 + 0.993267i \(0.463042\pi\)
\(60\) 0 0
\(61\) 413.000 0.866873 0.433436 0.901184i \(-0.357301\pi\)
0.433436 + 0.901184i \(0.357301\pi\)
\(62\) 294.000 0.602226
\(63\) 0 0
\(64\) 448.000 0.875000
\(65\) 0 0
\(66\) 70.0000 0.130552
\(67\) −415.000 −0.756721 −0.378361 0.925658i \(-0.623512\pi\)
−0.378361 + 0.925658i \(0.623512\pi\)
\(68\) 84.0000 0.149801
\(69\) 1113.00 1.94188
\(70\) 0 0
\(71\) −432.000 −0.722098 −0.361049 0.932547i \(-0.617581\pi\)
−0.361049 + 0.932547i \(0.617581\pi\)
\(72\) 528.000 0.864242
\(73\) −1113.00 −1.78448 −0.892238 0.451565i \(-0.850866\pi\)
−0.892238 + 0.451565i \(0.850866\pi\)
\(74\) 438.000 0.688060
\(75\) 0 0
\(76\) 196.000 0.295826
\(77\) 0 0
\(78\) 196.000 0.284521
\(79\) −103.000 −0.146689 −0.0733443 0.997307i \(-0.523367\pi\)
−0.0733443 + 0.997307i \(0.523367\pi\)
\(80\) 0 0
\(81\) −839.000 −1.15089
\(82\) 700.000 0.942708
\(83\) 1092.00 1.44413 0.722064 0.691827i \(-0.243194\pi\)
0.722064 + 0.691827i \(0.243194\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −248.000 −0.310960
\(87\) 406.000 0.500319
\(88\) −120.000 −0.145364
\(89\) 329.000 0.391842 0.195921 0.980620i \(-0.437230\pi\)
0.195921 + 0.980620i \(0.437230\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −636.000 −0.720735
\(93\) −1029.00 −1.14734
\(94\) −1050.00 −1.15212
\(95\) 0 0
\(96\) −1120.00 −1.19072
\(97\) −882.000 −0.923232 −0.461616 0.887080i \(-0.652730\pi\)
−0.461616 + 0.887080i \(0.652730\pi\)
\(98\) 0 0
\(99\) −110.000 −0.111671
\(100\) 0 0
\(101\) −1379.00 −1.35857 −0.679285 0.733874i \(-0.737710\pi\)
−0.679285 + 0.733874i \(0.737710\pi\)
\(102\) 294.000 0.285395
\(103\) −679.000 −0.649552 −0.324776 0.945791i \(-0.605289\pi\)
−0.324776 + 0.945791i \(0.605289\pi\)
\(104\) −336.000 −0.316803
\(105\) 0 0
\(106\) 606.000 0.555282
\(107\) −457.000 −0.412896 −0.206448 0.978458i \(-0.566190\pi\)
−0.206448 + 0.978458i \(0.566190\pi\)
\(108\) 140.000 0.124736
\(109\) −1125.00 −0.988582 −0.494291 0.869296i \(-0.664572\pi\)
−0.494291 + 0.869296i \(0.664572\pi\)
\(110\) 0 0
\(111\) −1533.00 −1.31086
\(112\) 0 0
\(113\) 1538.00 1.28038 0.640190 0.768217i \(-0.278856\pi\)
0.640190 + 0.768217i \(0.278856\pi\)
\(114\) 686.000 0.563595
\(115\) 0 0
\(116\) −232.000 −0.185695
\(117\) −308.000 −0.243373
\(118\) −210.000 −0.163831
\(119\) 0 0
\(120\) 0 0
\(121\) −1306.00 −0.981217
\(122\) −826.000 −0.612972
\(123\) −2450.00 −1.79601
\(124\) 588.000 0.425838
\(125\) 0 0
\(126\) 0 0
\(127\) −72.0000 −0.0503068 −0.0251534 0.999684i \(-0.508007\pi\)
−0.0251534 + 0.999684i \(0.508007\pi\)
\(128\) 384.000 0.265165
\(129\) 868.000 0.592427
\(130\) 0 0
\(131\) −2149.00 −1.43327 −0.716637 0.697446i \(-0.754320\pi\)
−0.716637 + 0.697446i \(0.754320\pi\)
\(132\) 140.000 0.0923139
\(133\) 0 0
\(134\) 830.000 0.535083
\(135\) 0 0
\(136\) −504.000 −0.317777
\(137\) 1125.00 0.701571 0.350786 0.936456i \(-0.385915\pi\)
0.350786 + 0.936456i \(0.385915\pi\)
\(138\) −2226.00 −1.37311
\(139\) −252.000 −0.153772 −0.0768862 0.997040i \(-0.524498\pi\)
−0.0768862 + 0.997040i \(0.524498\pi\)
\(140\) 0 0
\(141\) 3675.00 2.19497
\(142\) 864.000 0.510600
\(143\) 70.0000 0.0409349
\(144\) −352.000 −0.203704
\(145\) 0 0
\(146\) 2226.00 1.26182
\(147\) 0 0
\(148\) 876.000 0.486532
\(149\) −201.000 −0.110514 −0.0552569 0.998472i \(-0.517598\pi\)
−0.0552569 + 0.998472i \(0.517598\pi\)
\(150\) 0 0
\(151\) 1619.00 0.872532 0.436266 0.899818i \(-0.356301\pi\)
0.436266 + 0.899818i \(0.356301\pi\)
\(152\) −1176.00 −0.627541
\(153\) −462.000 −0.244121
\(154\) 0 0
\(155\) 0 0
\(156\) 392.000 0.201187
\(157\) 679.000 0.345160 0.172580 0.984996i \(-0.444790\pi\)
0.172580 + 0.984996i \(0.444790\pi\)
\(158\) 206.000 0.103725
\(159\) −2121.00 −1.05790
\(160\) 0 0
\(161\) 0 0
\(162\) 1678.00 0.813803
\(163\) 467.000 0.224407 0.112203 0.993685i \(-0.464209\pi\)
0.112203 + 0.993685i \(0.464209\pi\)
\(164\) 1400.00 0.666595
\(165\) 0 0
\(166\) −2184.00 −1.02115
\(167\) 1204.00 0.557894 0.278947 0.960306i \(-0.410015\pi\)
0.278947 + 0.960306i \(0.410015\pi\)
\(168\) 0 0
\(169\) −2001.00 −0.910787
\(170\) 0 0
\(171\) −1078.00 −0.482086
\(172\) −496.000 −0.219882
\(173\) −2821.00 −1.23975 −0.619875 0.784701i \(-0.712817\pi\)
−0.619875 + 0.784701i \(0.712817\pi\)
\(174\) −812.000 −0.353779
\(175\) 0 0
\(176\) 80.0000 0.0342627
\(177\) 735.000 0.312124
\(178\) −658.000 −0.277074
\(179\) −3253.00 −1.35833 −0.679164 0.733987i \(-0.737657\pi\)
−0.679164 + 0.733987i \(0.737657\pi\)
\(180\) 0 0
\(181\) −1582.00 −0.649664 −0.324832 0.945772i \(-0.605308\pi\)
−0.324832 + 0.945772i \(0.605308\pi\)
\(182\) 0 0
\(183\) 2891.00 1.16781
\(184\) 3816.00 1.52891
\(185\) 0 0
\(186\) 2058.00 0.811290
\(187\) 105.000 0.0410608
\(188\) −2100.00 −0.814671
\(189\) 0 0
\(190\) 0 0
\(191\) 2557.00 0.968681 0.484340 0.874880i \(-0.339060\pi\)
0.484340 + 0.874880i \(0.339060\pi\)
\(192\) 3136.00 1.17876
\(193\) 397.000 0.148066 0.0740329 0.997256i \(-0.476413\pi\)
0.0740329 + 0.997256i \(0.476413\pi\)
\(194\) 1764.00 0.652824
\(195\) 0 0
\(196\) 0 0
\(197\) −2914.00 −1.05388 −0.526939 0.849903i \(-0.676660\pi\)
−0.526939 + 0.849903i \(0.676660\pi\)
\(198\) 220.000 0.0789632
\(199\) −3339.00 −1.18942 −0.594712 0.803939i \(-0.702734\pi\)
−0.594712 + 0.803939i \(0.702734\pi\)
\(200\) 0 0
\(201\) −2905.00 −1.01942
\(202\) 2758.00 0.960654
\(203\) 0 0
\(204\) 588.000 0.201805
\(205\) 0 0
\(206\) 1358.00 0.459303
\(207\) 3498.00 1.17453
\(208\) 224.000 0.0746712
\(209\) 245.000 0.0810861
\(210\) 0 0
\(211\) 1780.00 0.580759 0.290380 0.956911i \(-0.406218\pi\)
0.290380 + 0.956911i \(0.406218\pi\)
\(212\) 1212.00 0.392644
\(213\) −3024.00 −0.972775
\(214\) 914.000 0.291961
\(215\) 0 0
\(216\) −840.000 −0.264605
\(217\) 0 0
\(218\) 2250.00 0.699033
\(219\) −7791.00 −2.40396
\(220\) 0 0
\(221\) 294.000 0.0894868
\(222\) 3066.00 0.926921
\(223\) −1400.00 −0.420408 −0.210204 0.977658i \(-0.567413\pi\)
−0.210204 + 0.977658i \(0.567413\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −3076.00 −0.905365
\(227\) −2205.00 −0.644718 −0.322359 0.946617i \(-0.604476\pi\)
−0.322359 + 0.946617i \(0.604476\pi\)
\(228\) 1372.00 0.398522
\(229\) −287.000 −0.0828188 −0.0414094 0.999142i \(-0.513185\pi\)
−0.0414094 + 0.999142i \(0.513185\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 1392.00 0.393919
\(233\) −4587.00 −1.28972 −0.644859 0.764301i \(-0.723084\pi\)
−0.644859 + 0.764301i \(0.723084\pi\)
\(234\) 616.000 0.172091
\(235\) 0 0
\(236\) −420.000 −0.115846
\(237\) −721.000 −0.197612
\(238\) 0 0
\(239\) 1668.00 0.451439 0.225720 0.974192i \(-0.427527\pi\)
0.225720 + 0.974192i \(0.427527\pi\)
\(240\) 0 0
\(241\) 3409.00 0.911174 0.455587 0.890191i \(-0.349429\pi\)
0.455587 + 0.890191i \(0.349429\pi\)
\(242\) 2612.00 0.693825
\(243\) −4928.00 −1.30095
\(244\) −1652.00 −0.433436
\(245\) 0 0
\(246\) 4900.00 1.26997
\(247\) 686.000 0.176717
\(248\) −3528.00 −0.903340
\(249\) 7644.00 1.94546
\(250\) 0 0
\(251\) 4760.00 1.19701 0.598503 0.801121i \(-0.295762\pi\)
0.598503 + 0.801121i \(0.295762\pi\)
\(252\) 0 0
\(253\) −795.000 −0.197554
\(254\) 144.000 0.0355723
\(255\) 0 0
\(256\) −4352.00 −1.06250
\(257\) −805.000 −0.195387 −0.0976936 0.995217i \(-0.531147\pi\)
−0.0976936 + 0.995217i \(0.531147\pi\)
\(258\) −1736.00 −0.418909
\(259\) 0 0
\(260\) 0 0
\(261\) 1276.00 0.302615
\(262\) 4298.00 1.01348
\(263\) 257.000 0.0602559 0.0301279 0.999546i \(-0.490409\pi\)
0.0301279 + 0.999546i \(0.490409\pi\)
\(264\) −840.000 −0.195827
\(265\) 0 0
\(266\) 0 0
\(267\) 2303.00 0.527870
\(268\) 1660.00 0.378361
\(269\) −3591.00 −0.813930 −0.406965 0.913444i \(-0.633413\pi\)
−0.406965 + 0.913444i \(0.633413\pi\)
\(270\) 0 0
\(271\) −1393.00 −0.312246 −0.156123 0.987738i \(-0.549900\pi\)
−0.156123 + 0.987738i \(0.549900\pi\)
\(272\) 336.000 0.0749007
\(273\) 0 0
\(274\) −2250.00 −0.496086
\(275\) 0 0
\(276\) −4452.00 −0.970938
\(277\) −415.000 −0.0900178 −0.0450089 0.998987i \(-0.514332\pi\)
−0.0450089 + 0.998987i \(0.514332\pi\)
\(278\) 504.000 0.108733
\(279\) −3234.00 −0.693959
\(280\) 0 0
\(281\) −4954.00 −1.05171 −0.525856 0.850574i \(-0.676255\pi\)
−0.525856 + 0.850574i \(0.676255\pi\)
\(282\) −7350.00 −1.55208
\(283\) −4277.00 −0.898379 −0.449190 0.893437i \(-0.648287\pi\)
−0.449190 + 0.893437i \(0.648287\pi\)
\(284\) 1728.00 0.361049
\(285\) 0 0
\(286\) −140.000 −0.0289454
\(287\) 0 0
\(288\) −3520.00 −0.720201
\(289\) −4472.00 −0.910238
\(290\) 0 0
\(291\) −6174.00 −1.24373
\(292\) 4452.00 0.892238
\(293\) 7742.00 1.54366 0.771830 0.635829i \(-0.219342\pi\)
0.771830 + 0.635829i \(0.219342\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −5256.00 −1.03209
\(297\) 175.000 0.0341903
\(298\) 402.000 0.0781451
\(299\) −2226.00 −0.430545
\(300\) 0 0
\(301\) 0 0
\(302\) −3238.00 −0.616973
\(303\) −9653.00 −1.83020
\(304\) 784.000 0.147913
\(305\) 0 0
\(306\) 924.000 0.172619
\(307\) −7364.00 −1.36901 −0.684504 0.729009i \(-0.739981\pi\)
−0.684504 + 0.729009i \(0.739981\pi\)
\(308\) 0 0
\(309\) −4753.00 −0.875044
\(310\) 0 0
\(311\) −9975.00 −1.81875 −0.909374 0.415980i \(-0.863438\pi\)
−0.909374 + 0.415980i \(0.863438\pi\)
\(312\) −2352.00 −0.426781
\(313\) −4753.00 −0.858324 −0.429162 0.903228i \(-0.641191\pi\)
−0.429162 + 0.903228i \(0.641191\pi\)
\(314\) −1358.00 −0.244065
\(315\) 0 0
\(316\) 412.000 0.0733443
\(317\) 3477.00 0.616050 0.308025 0.951378i \(-0.400332\pi\)
0.308025 + 0.951378i \(0.400332\pi\)
\(318\) 4242.00 0.748049
\(319\) −290.000 −0.0508993
\(320\) 0 0
\(321\) −3199.00 −0.556233
\(322\) 0 0
\(323\) 1029.00 0.177260
\(324\) 3356.00 0.575446
\(325\) 0 0
\(326\) −934.000 −0.158679
\(327\) −7875.00 −1.33177
\(328\) −8400.00 −1.41406
\(329\) 0 0
\(330\) 0 0
\(331\) 3341.00 0.554797 0.277399 0.960755i \(-0.410528\pi\)
0.277399 + 0.960755i \(0.410528\pi\)
\(332\) −4368.00 −0.722064
\(333\) −4818.00 −0.792867
\(334\) −2408.00 −0.394491
\(335\) 0 0
\(336\) 0 0
\(337\) −7366.00 −1.19066 −0.595329 0.803482i \(-0.702978\pi\)
−0.595329 + 0.803482i \(0.702978\pi\)
\(338\) 4002.00 0.644024
\(339\) 10766.0 1.72486
\(340\) 0 0
\(341\) 735.000 0.116723
\(342\) 2156.00 0.340886
\(343\) 0 0
\(344\) 2976.00 0.466439
\(345\) 0 0
\(346\) 5642.00 0.876635
\(347\) −7415.00 −1.14714 −0.573571 0.819156i \(-0.694442\pi\)
−0.573571 + 0.819156i \(0.694442\pi\)
\(348\) −1624.00 −0.250160
\(349\) 3878.00 0.594798 0.297399 0.954753i \(-0.403881\pi\)
0.297399 + 0.954753i \(0.403881\pi\)
\(350\) 0 0
\(351\) 490.000 0.0745136
\(352\) 800.000 0.121137
\(353\) 1267.00 0.191036 0.0955179 0.995428i \(-0.469549\pi\)
0.0955179 + 0.995428i \(0.469549\pi\)
\(354\) −1470.00 −0.220705
\(355\) 0 0
\(356\) −1316.00 −0.195921
\(357\) 0 0
\(358\) 6506.00 0.960483
\(359\) 4685.00 0.688760 0.344380 0.938830i \(-0.388089\pi\)
0.344380 + 0.938830i \(0.388089\pi\)
\(360\) 0 0
\(361\) −4458.00 −0.649949
\(362\) 3164.00 0.459382
\(363\) −9142.00 −1.32185
\(364\) 0 0
\(365\) 0 0
\(366\) −5782.00 −0.825765
\(367\) −4641.00 −0.660104 −0.330052 0.943963i \(-0.607066\pi\)
−0.330052 + 0.943963i \(0.607066\pi\)
\(368\) −2544.00 −0.360367
\(369\) −7700.00 −1.08630
\(370\) 0 0
\(371\) 0 0
\(372\) 4116.00 0.573668
\(373\) 8797.00 1.22116 0.610578 0.791956i \(-0.290937\pi\)
0.610578 + 0.791956i \(0.290937\pi\)
\(374\) −210.000 −0.0290343
\(375\) 0 0
\(376\) 12600.0 1.72818
\(377\) −812.000 −0.110929
\(378\) 0 0
\(379\) 13680.0 1.85407 0.927037 0.374969i \(-0.122347\pi\)
0.927037 + 0.374969i \(0.122347\pi\)
\(380\) 0 0
\(381\) −504.000 −0.0677709
\(382\) −5114.00 −0.684961
\(383\) 9765.00 1.30279 0.651395 0.758739i \(-0.274184\pi\)
0.651395 + 0.758739i \(0.274184\pi\)
\(384\) 2688.00 0.357217
\(385\) 0 0
\(386\) −794.000 −0.104698
\(387\) 2728.00 0.358326
\(388\) 3528.00 0.461616
\(389\) 1731.00 0.225617 0.112809 0.993617i \(-0.464015\pi\)
0.112809 + 0.993617i \(0.464015\pi\)
\(390\) 0 0
\(391\) −3339.00 −0.431868
\(392\) 0 0
\(393\) −15043.0 −1.93084
\(394\) 5828.00 0.745204
\(395\) 0 0
\(396\) 440.000 0.0558354
\(397\) 10983.0 1.38847 0.694233 0.719750i \(-0.255744\pi\)
0.694233 + 0.719750i \(0.255744\pi\)
\(398\) 6678.00 0.841050
\(399\) 0 0
\(400\) 0 0
\(401\) 6603.00 0.822289 0.411145 0.911570i \(-0.365129\pi\)
0.411145 + 0.911570i \(0.365129\pi\)
\(402\) 5810.00 0.720837
\(403\) 2058.00 0.254383
\(404\) 5516.00 0.679285
\(405\) 0 0
\(406\) 0 0
\(407\) 1095.00 0.133359
\(408\) −3528.00 −0.428093
\(409\) −10955.0 −1.32443 −0.662213 0.749316i \(-0.730382\pi\)
−0.662213 + 0.749316i \(0.730382\pi\)
\(410\) 0 0
\(411\) 7875.00 0.945122
\(412\) 2716.00 0.324776
\(413\) 0 0
\(414\) −6996.00 −0.830518
\(415\) 0 0
\(416\) 2240.00 0.264002
\(417\) −1764.00 −0.207155
\(418\) −490.000 −0.0573366
\(419\) −6636.00 −0.773723 −0.386861 0.922138i \(-0.626441\pi\)
−0.386861 + 0.922138i \(0.626441\pi\)
\(420\) 0 0
\(421\) −16630.0 −1.92517 −0.962585 0.270980i \(-0.912652\pi\)
−0.962585 + 0.270980i \(0.912652\pi\)
\(422\) −3560.00 −0.410659
\(423\) 11550.0 1.32761
\(424\) −7272.00 −0.832923
\(425\) 0 0
\(426\) 6048.00 0.687856
\(427\) 0 0
\(428\) 1828.00 0.206448
\(429\) 490.000 0.0551455
\(430\) 0 0
\(431\) 4923.00 0.550192 0.275096 0.961417i \(-0.411290\pi\)
0.275096 + 0.961417i \(0.411290\pi\)
\(432\) 560.000 0.0623681
\(433\) 8974.00 0.995988 0.497994 0.867180i \(-0.334070\pi\)
0.497994 + 0.867180i \(0.334070\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 4500.00 0.494291
\(437\) −7791.00 −0.852847
\(438\) 15582.0 1.69986
\(439\) 4179.00 0.454334 0.227167 0.973856i \(-0.427054\pi\)
0.227167 + 0.973856i \(0.427054\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −588.000 −0.0632767
\(443\) 12927.0 1.38641 0.693206 0.720740i \(-0.256198\pi\)
0.693206 + 0.720740i \(0.256198\pi\)
\(444\) 6132.00 0.655432
\(445\) 0 0
\(446\) 2800.00 0.297273
\(447\) −1407.00 −0.148879
\(448\) 0 0
\(449\) −2826.00 −0.297032 −0.148516 0.988910i \(-0.547450\pi\)
−0.148516 + 0.988910i \(0.547450\pi\)
\(450\) 0 0
\(451\) 1750.00 0.182715
\(452\) −6152.00 −0.640190
\(453\) 11333.0 1.17543
\(454\) 4410.00 0.455884
\(455\) 0 0
\(456\) −8232.00 −0.845392
\(457\) −8479.00 −0.867901 −0.433951 0.900937i \(-0.642881\pi\)
−0.433951 + 0.900937i \(0.642881\pi\)
\(458\) 574.000 0.0585617
\(459\) 735.000 0.0747426
\(460\) 0 0
\(461\) −9338.00 −0.943414 −0.471707 0.881755i \(-0.656362\pi\)
−0.471707 + 0.881755i \(0.656362\pi\)
\(462\) 0 0
\(463\) 4016.00 0.403109 0.201554 0.979477i \(-0.435401\pi\)
0.201554 + 0.979477i \(0.435401\pi\)
\(464\) −928.000 −0.0928477
\(465\) 0 0
\(466\) 9174.00 0.911969
\(467\) −5859.00 −0.580561 −0.290281 0.956942i \(-0.593749\pi\)
−0.290281 + 0.956942i \(0.593749\pi\)
\(468\) 1232.00 0.121686
\(469\) 0 0
\(470\) 0 0
\(471\) 4753.00 0.464982
\(472\) 2520.00 0.245747
\(473\) −620.000 −0.0602698
\(474\) 1442.00 0.139733
\(475\) 0 0
\(476\) 0 0
\(477\) −6666.00 −0.639864
\(478\) −3336.00 −0.319216
\(479\) −6503.00 −0.620312 −0.310156 0.950686i \(-0.600381\pi\)
−0.310156 + 0.950686i \(0.600381\pi\)
\(480\) 0 0
\(481\) 3066.00 0.290639
\(482\) −6818.00 −0.644297
\(483\) 0 0
\(484\) 5224.00 0.490609
\(485\) 0 0
\(486\) 9856.00 0.919912
\(487\) 16049.0 1.49333 0.746663 0.665203i \(-0.231655\pi\)
0.746663 + 0.665203i \(0.231655\pi\)
\(488\) 9912.00 0.919457
\(489\) 3269.00 0.302309
\(490\) 0 0
\(491\) 8864.00 0.814718 0.407359 0.913268i \(-0.366450\pi\)
0.407359 + 0.913268i \(0.366450\pi\)
\(492\) 9800.00 0.898004
\(493\) −1218.00 −0.111270
\(494\) −1372.00 −0.124958
\(495\) 0 0
\(496\) 2352.00 0.212919
\(497\) 0 0
\(498\) −15288.0 −1.37565
\(499\) −10211.0 −0.916046 −0.458023 0.888940i \(-0.651442\pi\)
−0.458023 + 0.888940i \(0.651442\pi\)
\(500\) 0 0
\(501\) 8428.00 0.751567
\(502\) −9520.00 −0.846411
\(503\) −1680.00 −0.148921 −0.0744607 0.997224i \(-0.523724\pi\)
−0.0744607 + 0.997224i \(0.523724\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 1590.00 0.139692
\(507\) −14007.0 −1.22697
\(508\) 288.000 0.0251534
\(509\) 9457.00 0.823525 0.411762 0.911291i \(-0.364913\pi\)
0.411762 + 0.911291i \(0.364913\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 5632.00 0.486136
\(513\) 1715.00 0.147601
\(514\) 1610.00 0.138160
\(515\) 0 0
\(516\) −3472.00 −0.296214
\(517\) −2625.00 −0.223302
\(518\) 0 0
\(519\) −19747.0 −1.67013
\(520\) 0 0
\(521\) 18081.0 1.52043 0.760214 0.649673i \(-0.225094\pi\)
0.760214 + 0.649673i \(0.225094\pi\)
\(522\) −2552.00 −0.213981
\(523\) 20377.0 1.70368 0.851839 0.523803i \(-0.175487\pi\)
0.851839 + 0.523803i \(0.175487\pi\)
\(524\) 8596.00 0.716637
\(525\) 0 0
\(526\) −514.000 −0.0426073
\(527\) 3087.00 0.255165
\(528\) 560.000 0.0461570
\(529\) 13114.0 1.07783
\(530\) 0 0
\(531\) 2310.00 0.188786
\(532\) 0 0
\(533\) 4900.00 0.398204
\(534\) −4606.00 −0.373261
\(535\) 0 0
\(536\) −9960.00 −0.802624
\(537\) −22771.0 −1.82987
\(538\) 7182.00 0.575535
\(539\) 0 0
\(540\) 0 0
\(541\) −6193.00 −0.492159 −0.246079 0.969250i \(-0.579142\pi\)
−0.246079 + 0.969250i \(0.579142\pi\)
\(542\) 2786.00 0.220791
\(543\) −11074.0 −0.875195
\(544\) 3360.00 0.264814
\(545\) 0 0
\(546\) 0 0
\(547\) 18464.0 1.44326 0.721630 0.692279i \(-0.243393\pi\)
0.721630 + 0.692279i \(0.243393\pi\)
\(548\) −4500.00 −0.350786
\(549\) 9086.00 0.706341
\(550\) 0 0
\(551\) −2842.00 −0.219734
\(552\) 26712.0 2.05967
\(553\) 0 0
\(554\) 830.000 0.0636522
\(555\) 0 0
\(556\) 1008.00 0.0768862
\(557\) 9413.00 0.716053 0.358027 0.933711i \(-0.383450\pi\)
0.358027 + 0.933711i \(0.383450\pi\)
\(558\) 6468.00 0.490703
\(559\) −1736.00 −0.131351
\(560\) 0 0
\(561\) 735.000 0.0553150
\(562\) 9908.00 0.743672
\(563\) 3199.00 0.239470 0.119735 0.992806i \(-0.461795\pi\)
0.119735 + 0.992806i \(0.461795\pi\)
\(564\) −14700.0 −1.09749
\(565\) 0 0
\(566\) 8554.00 0.635250
\(567\) 0 0
\(568\) −10368.0 −0.765901
\(569\) 21583.0 1.59017 0.795085 0.606498i \(-0.207426\pi\)
0.795085 + 0.606498i \(0.207426\pi\)
\(570\) 0 0
\(571\) 20267.0 1.48537 0.742686 0.669640i \(-0.233551\pi\)
0.742686 + 0.669640i \(0.233551\pi\)
\(572\) −280.000 −0.0204675
\(573\) 17899.0 1.30496
\(574\) 0 0
\(575\) 0 0
\(576\) 9856.00 0.712963
\(577\) 13951.0 1.00656 0.503282 0.864122i \(-0.332126\pi\)
0.503282 + 0.864122i \(0.332126\pi\)
\(578\) 8944.00 0.643636
\(579\) 2779.00 0.199467
\(580\) 0 0
\(581\) 0 0
\(582\) 12348.0 0.879452
\(583\) 1515.00 0.107624
\(584\) −26712.0 −1.89272
\(585\) 0 0
\(586\) −15484.0 −1.09153
\(587\) −20972.0 −1.47463 −0.737314 0.675550i \(-0.763906\pi\)
−0.737314 + 0.675550i \(0.763906\pi\)
\(588\) 0 0
\(589\) 7203.00 0.503895
\(590\) 0 0
\(591\) −20398.0 −1.41973
\(592\) 3504.00 0.243266
\(593\) −189.000 −0.0130882 −0.00654410 0.999979i \(-0.502083\pi\)
−0.00654410 + 0.999979i \(0.502083\pi\)
\(594\) −350.000 −0.0241762
\(595\) 0 0
\(596\) 804.000 0.0552569
\(597\) −23373.0 −1.60233
\(598\) 4452.00 0.304441
\(599\) −10281.0 −0.701286 −0.350643 0.936509i \(-0.614037\pi\)
−0.350643 + 0.936509i \(0.614037\pi\)
\(600\) 0 0
\(601\) 6090.00 0.413338 0.206669 0.978411i \(-0.433738\pi\)
0.206669 + 0.978411i \(0.433738\pi\)
\(602\) 0 0
\(603\) −9130.00 −0.616588
\(604\) −6476.00 −0.436266
\(605\) 0 0
\(606\) 19306.0 1.29415
\(607\) 4949.00 0.330929 0.165464 0.986216i \(-0.447088\pi\)
0.165464 + 0.986216i \(0.447088\pi\)
\(608\) 7840.00 0.522951
\(609\) 0 0
\(610\) 0 0
\(611\) −7350.00 −0.486660
\(612\) 1848.00 0.122060
\(613\) 15797.0 1.04084 0.520420 0.853910i \(-0.325775\pi\)
0.520420 + 0.853910i \(0.325775\pi\)
\(614\) 14728.0 0.968035
\(615\) 0 0
\(616\) 0 0
\(617\) 9378.00 0.611903 0.305951 0.952047i \(-0.401025\pi\)
0.305951 + 0.952047i \(0.401025\pi\)
\(618\) 9506.00 0.618750
\(619\) 24353.0 1.58131 0.790654 0.612263i \(-0.209741\pi\)
0.790654 + 0.612263i \(0.209741\pi\)
\(620\) 0 0
\(621\) −5565.00 −0.359607
\(622\) 19950.0 1.28605
\(623\) 0 0
\(624\) 1568.00 0.100593
\(625\) 0 0
\(626\) 9506.00 0.606927
\(627\) 1715.00 0.109235
\(628\) −2716.00 −0.172580
\(629\) 4599.00 0.291533
\(630\) 0 0
\(631\) −12640.0 −0.797449 −0.398725 0.917071i \(-0.630547\pi\)
−0.398725 + 0.917071i \(0.630547\pi\)
\(632\) −2472.00 −0.155587
\(633\) 12460.0 0.782371
\(634\) −6954.00 −0.435613
\(635\) 0 0
\(636\) 8484.00 0.528950
\(637\) 0 0
\(638\) 580.000 0.0359913
\(639\) −9504.00 −0.588376
\(640\) 0 0
\(641\) −1041.00 −0.0641451 −0.0320726 0.999486i \(-0.510211\pi\)
−0.0320726 + 0.999486i \(0.510211\pi\)
\(642\) 6398.00 0.393316
\(643\) 9548.00 0.585593 0.292797 0.956175i \(-0.405414\pi\)
0.292797 + 0.956175i \(0.405414\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −2058.00 −0.125342
\(647\) −3241.00 −0.196935 −0.0984674 0.995140i \(-0.531394\pi\)
−0.0984674 + 0.995140i \(0.531394\pi\)
\(648\) −20136.0 −1.22070
\(649\) −525.000 −0.0317535
\(650\) 0 0
\(651\) 0 0
\(652\) −1868.00 −0.112203
\(653\) 8853.00 0.530543 0.265272 0.964174i \(-0.414538\pi\)
0.265272 + 0.964174i \(0.414538\pi\)
\(654\) 15750.0 0.941703
\(655\) 0 0
\(656\) 5600.00 0.333298
\(657\) −24486.0 −1.45402
\(658\) 0 0
\(659\) 7044.00 0.416381 0.208191 0.978088i \(-0.433243\pi\)
0.208191 + 0.978088i \(0.433243\pi\)
\(660\) 0 0
\(661\) 12089.0 0.711358 0.355679 0.934608i \(-0.384250\pi\)
0.355679 + 0.934608i \(0.384250\pi\)
\(662\) −6682.00 −0.392301
\(663\) 2058.00 0.120552
\(664\) 26208.0 1.53173
\(665\) 0 0
\(666\) 9636.00 0.560642
\(667\) 9222.00 0.535348
\(668\) −4816.00 −0.278947
\(669\) −9800.00 −0.566353
\(670\) 0 0
\(671\) −2065.00 −0.118805
\(672\) 0 0
\(673\) −982.000 −0.0562456 −0.0281228 0.999604i \(-0.508953\pi\)
−0.0281228 + 0.999604i \(0.508953\pi\)
\(674\) 14732.0 0.841922
\(675\) 0 0
\(676\) 8004.00 0.455394
\(677\) −30513.0 −1.73222 −0.866108 0.499857i \(-0.833386\pi\)
−0.866108 + 0.499857i \(0.833386\pi\)
\(678\) −21532.0 −1.21966
\(679\) 0 0
\(680\) 0 0
\(681\) −15435.0 −0.868532
\(682\) −1470.00 −0.0825355
\(683\) −11475.0 −0.642868 −0.321434 0.946932i \(-0.604165\pi\)
−0.321434 + 0.946932i \(0.604165\pi\)
\(684\) 4312.00 0.241043
\(685\) 0 0
\(686\) 0 0
\(687\) −2009.00 −0.111569
\(688\) −1984.00 −0.109941
\(689\) 4242.00 0.234553
\(690\) 0 0
\(691\) 28315.0 1.55883 0.779416 0.626506i \(-0.215516\pi\)
0.779416 + 0.626506i \(0.215516\pi\)
\(692\) 11284.0 0.619875
\(693\) 0 0
\(694\) 14830.0 0.811151
\(695\) 0 0
\(696\) 9744.00 0.530669
\(697\) 7350.00 0.399428
\(698\) −7756.00 −0.420586
\(699\) −32109.0 −1.73744
\(700\) 0 0
\(701\) 10614.0 0.571876 0.285938 0.958248i \(-0.407695\pi\)
0.285938 + 0.958248i \(0.407695\pi\)
\(702\) −980.000 −0.0526891
\(703\) 10731.0 0.575715
\(704\) −2240.00 −0.119919
\(705\) 0 0
\(706\) −2534.00 −0.135083
\(707\) 0 0
\(708\) −2940.00 −0.156062
\(709\) 10299.0 0.545539 0.272769 0.962079i \(-0.412060\pi\)
0.272769 + 0.962079i \(0.412060\pi\)
\(710\) 0 0
\(711\) −2266.00 −0.119524
\(712\) 7896.00 0.415611
\(713\) −23373.0 −1.22767
\(714\) 0 0
\(715\) 0 0
\(716\) 13012.0 0.679164
\(717\) 11676.0 0.608156
\(718\) −9370.00 −0.487027
\(719\) −32529.0 −1.68724 −0.843621 0.536939i \(-0.819580\pi\)
−0.843621 + 0.536939i \(0.819580\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 8916.00 0.459583
\(723\) 23863.0 1.22749
\(724\) 6328.00 0.324832
\(725\) 0 0
\(726\) 18284.0 0.934687
\(727\) 29456.0 1.50270 0.751350 0.659904i \(-0.229403\pi\)
0.751350 + 0.659904i \(0.229403\pi\)
\(728\) 0 0
\(729\) −11843.0 −0.601687
\(730\) 0 0
\(731\) −2604.00 −0.131754
\(732\) −11564.0 −0.583904
\(733\) 27867.0 1.40422 0.702109 0.712070i \(-0.252242\pi\)
0.702109 + 0.712070i \(0.252242\pi\)
\(734\) 9282.00 0.466764
\(735\) 0 0
\(736\) −25440.0 −1.27409
\(737\) 2075.00 0.103709
\(738\) 15400.0 0.768133
\(739\) 19539.0 0.972603 0.486302 0.873791i \(-0.338346\pi\)
0.486302 + 0.873791i \(0.338346\pi\)
\(740\) 0 0
\(741\) 4802.00 0.238065
\(742\) 0 0
\(743\) −1248.00 −0.0616214 −0.0308107 0.999525i \(-0.509809\pi\)
−0.0308107 + 0.999525i \(0.509809\pi\)
\(744\) −24696.0 −1.21693
\(745\) 0 0
\(746\) −17594.0 −0.863488
\(747\) 24024.0 1.17670
\(748\) −420.000 −0.0205304
\(749\) 0 0
\(750\) 0 0
\(751\) 28093.0 1.36502 0.682509 0.730877i \(-0.260889\pi\)
0.682509 + 0.730877i \(0.260889\pi\)
\(752\) −8400.00 −0.407336
\(753\) 33320.0 1.61255
\(754\) 1624.00 0.0784385
\(755\) 0 0
\(756\) 0 0
\(757\) −35954.0 −1.72625 −0.863124 0.504991i \(-0.831496\pi\)
−0.863124 + 0.504991i \(0.831496\pi\)
\(758\) −27360.0 −1.31103
\(759\) −5565.00 −0.266135
\(760\) 0 0
\(761\) 861.000 0.0410134 0.0205067 0.999790i \(-0.493472\pi\)
0.0205067 + 0.999790i \(0.493472\pi\)
\(762\) 1008.00 0.0479212
\(763\) 0 0
\(764\) −10228.0 −0.484340
\(765\) 0 0
\(766\) −19530.0 −0.921211
\(767\) −1470.00 −0.0692029
\(768\) −30464.0 −1.43135
\(769\) −24710.0 −1.15873 −0.579366 0.815067i \(-0.696700\pi\)
−0.579366 + 0.815067i \(0.696700\pi\)
\(770\) 0 0
\(771\) −5635.00 −0.263216
\(772\) −1588.00 −0.0740329
\(773\) 16499.0 0.767694 0.383847 0.923397i \(-0.374599\pi\)
0.383847 + 0.923397i \(0.374599\pi\)
\(774\) −5456.00 −0.253375
\(775\) 0 0
\(776\) −21168.0 −0.979236
\(777\) 0 0
\(778\) −3462.00 −0.159536
\(779\) 17150.0 0.788784
\(780\) 0 0
\(781\) 2160.00 0.0989640
\(782\) 6678.00 0.305377
\(783\) −2030.00 −0.0926517
\(784\) 0 0
\(785\) 0 0
\(786\) 30086.0 1.36531
\(787\) 16471.0 0.746033 0.373016 0.927825i \(-0.378324\pi\)
0.373016 + 0.927825i \(0.378324\pi\)
\(788\) 11656.0 0.526939
\(789\) 1799.00 0.0811738
\(790\) 0 0
\(791\) 0 0
\(792\) −2640.00 −0.118445
\(793\) −5782.00 −0.258922
\(794\) −21966.0 −0.981794
\(795\) 0 0
\(796\) 13356.0 0.594712
\(797\) −36470.0 −1.62087 −0.810435 0.585828i \(-0.800769\pi\)
−0.810435 + 0.585828i \(0.800769\pi\)
\(798\) 0 0
\(799\) −11025.0 −0.488156
\(800\) 0 0
\(801\) 7238.00 0.319279
\(802\) −13206.0 −0.581446
\(803\) 5565.00 0.244564
\(804\) 11620.0 0.509709
\(805\) 0 0
\(806\) −4116.00 −0.179876
\(807\) −25137.0 −1.09649
\(808\) −33096.0 −1.44098
\(809\) 35751.0 1.55369 0.776847 0.629690i \(-0.216818\pi\)
0.776847 + 0.629690i \(0.216818\pi\)
\(810\) 0 0
\(811\) 16492.0 0.714072 0.357036 0.934091i \(-0.383787\pi\)
0.357036 + 0.934091i \(0.383787\pi\)
\(812\) 0 0
\(813\) −9751.00 −0.420643
\(814\) −2190.00 −0.0942991
\(815\) 0 0
\(816\) 2352.00 0.100903
\(817\) −6076.00 −0.260186
\(818\) 21910.0 0.936510
\(819\) 0 0
\(820\) 0 0
\(821\) −41473.0 −1.76299 −0.881497 0.472190i \(-0.843464\pi\)
−0.881497 + 0.472190i \(0.843464\pi\)
\(822\) −15750.0 −0.668302
\(823\) 25065.0 1.06162 0.530809 0.847492i \(-0.321888\pi\)
0.530809 + 0.847492i \(0.321888\pi\)
\(824\) −16296.0 −0.688954
\(825\) 0 0
\(826\) 0 0
\(827\) −9732.00 −0.409208 −0.204604 0.978845i \(-0.565591\pi\)
−0.204604 + 0.978845i \(0.565591\pi\)
\(828\) −13992.0 −0.587265
\(829\) −27755.0 −1.16281 −0.581406 0.813614i \(-0.697497\pi\)
−0.581406 + 0.813614i \(0.697497\pi\)
\(830\) 0 0
\(831\) −2905.00 −0.121268
\(832\) −6272.00 −0.261349
\(833\) 0 0
\(834\) 3528.00 0.146480
\(835\) 0 0
\(836\) −980.000 −0.0405431
\(837\) 5145.00 0.212470
\(838\) 13272.0 0.547105
\(839\) −21112.0 −0.868733 −0.434367 0.900736i \(-0.643028\pi\)
−0.434367 + 0.900736i \(0.643028\pi\)
\(840\) 0 0
\(841\) −21025.0 −0.862069
\(842\) 33260.0 1.36130
\(843\) −34678.0 −1.41681
\(844\) −7120.00 −0.290380
\(845\) 0 0
\(846\) −23100.0 −0.938764
\(847\) 0 0
\(848\) 4848.00 0.196322
\(849\) −29939.0 −1.21025
\(850\) 0 0
\(851\) −34821.0 −1.40264
\(852\) 12096.0 0.486387
\(853\) −21238.0 −0.852492 −0.426246 0.904607i \(-0.640164\pi\)
−0.426246 + 0.904607i \(0.640164\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −10968.0 −0.437942
\(857\) −35609.0 −1.41935 −0.709673 0.704531i \(-0.751158\pi\)
−0.709673 + 0.704531i \(0.751158\pi\)
\(858\) −980.000 −0.0389938
\(859\) −2177.00 −0.0864706 −0.0432353 0.999065i \(-0.513767\pi\)
−0.0432353 + 0.999065i \(0.513767\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −9846.00 −0.389044
\(863\) 32247.0 1.27196 0.635980 0.771706i \(-0.280596\pi\)
0.635980 + 0.771706i \(0.280596\pi\)
\(864\) 5600.00 0.220504
\(865\) 0 0
\(866\) −17948.0 −0.704270
\(867\) −31304.0 −1.22623
\(868\) 0 0
\(869\) 515.000 0.0201038
\(870\) 0 0
\(871\) 5810.00 0.226021
\(872\) −27000.0 −1.04855
\(873\) −19404.0 −0.752263
\(874\) 15582.0 0.603054
\(875\) 0 0
\(876\) 31164.0 1.20198
\(877\) −27631.0 −1.06389 −0.531946 0.846779i \(-0.678539\pi\)
−0.531946 + 0.846779i \(0.678539\pi\)
\(878\) −8358.00 −0.321263
\(879\) 54194.0 2.07954
\(880\) 0 0
\(881\) −24402.0 −0.933172 −0.466586 0.884476i \(-0.654516\pi\)
−0.466586 + 0.884476i \(0.654516\pi\)
\(882\) 0 0
\(883\) 19612.0 0.747448 0.373724 0.927540i \(-0.378081\pi\)
0.373724 + 0.927540i \(0.378081\pi\)
\(884\) −1176.00 −0.0447434
\(885\) 0 0
\(886\) −25854.0 −0.980341
\(887\) 2261.00 0.0855884 0.0427942 0.999084i \(-0.486374\pi\)
0.0427942 + 0.999084i \(0.486374\pi\)
\(888\) −36792.0 −1.39038
\(889\) 0 0
\(890\) 0 0
\(891\) 4195.00 0.157730
\(892\) 5600.00 0.210204
\(893\) −25725.0 −0.964003
\(894\) 2814.00 0.105273
\(895\) 0 0
\(896\) 0 0
\(897\) −15582.0 −0.580009
\(898\) 5652.00 0.210033
\(899\) −8526.00 −0.316305
\(900\) 0 0
\(901\) 6363.00 0.235274
\(902\) −3500.00 −0.129199
\(903\) 0 0
\(904\) 36912.0 1.35805
\(905\) 0 0
\(906\) −22666.0 −0.831156
\(907\) 23833.0 0.872505 0.436252 0.899824i \(-0.356305\pi\)
0.436252 + 0.899824i \(0.356305\pi\)
\(908\) 8820.00 0.322359
\(909\) −30338.0 −1.10698
\(910\) 0 0
\(911\) 31824.0 1.15738 0.578692 0.815546i \(-0.303563\pi\)
0.578692 + 0.815546i \(0.303563\pi\)
\(912\) 5488.00 0.199261
\(913\) −5460.00 −0.197919
\(914\) 16958.0 0.613699
\(915\) 0 0
\(916\) 1148.00 0.0414094
\(917\) 0 0
\(918\) −1470.00 −0.0528510
\(919\) −16819.0 −0.603708 −0.301854 0.953354i \(-0.597606\pi\)
−0.301854 + 0.953354i \(0.597606\pi\)
\(920\) 0 0
\(921\) −51548.0 −1.84426
\(922\) 18676.0 0.667095
\(923\) 6048.00 0.215680
\(924\) 0 0
\(925\) 0 0
\(926\) −8032.00 −0.285041
\(927\) −14938.0 −0.529265
\(928\) −9280.00 −0.328266
\(929\) −1799.00 −0.0635342 −0.0317671 0.999495i \(-0.510113\pi\)
−0.0317671 + 0.999495i \(0.510113\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 18348.0 0.644859
\(933\) −69825.0 −2.45013
\(934\) 11718.0 0.410519
\(935\) 0 0
\(936\) −7392.00 −0.258136
\(937\) 14154.0 0.493480 0.246740 0.969082i \(-0.420641\pi\)
0.246740 + 0.969082i \(0.420641\pi\)
\(938\) 0 0
\(939\) −33271.0 −1.15629
\(940\) 0 0
\(941\) −12047.0 −0.417344 −0.208672 0.977986i \(-0.566914\pi\)
−0.208672 + 0.977986i \(0.566914\pi\)
\(942\) −9506.00 −0.328792
\(943\) −55650.0 −1.92175
\(944\) −1680.00 −0.0579230
\(945\) 0 0
\(946\) 1240.00 0.0426172
\(947\) 24379.0 0.836548 0.418274 0.908321i \(-0.362635\pi\)
0.418274 + 0.908321i \(0.362635\pi\)
\(948\) 2884.00 0.0988059
\(949\) 15582.0 0.532996
\(950\) 0 0
\(951\) 24339.0 0.829912
\(952\) 0 0
\(953\) 52330.0 1.77874 0.889368 0.457192i \(-0.151145\pi\)
0.889368 + 0.457192i \(0.151145\pi\)
\(954\) 13332.0 0.452452
\(955\) 0 0
\(956\) −6672.00 −0.225720
\(957\) −2030.00 −0.0685690
\(958\) 13006.0 0.438627
\(959\) 0 0
\(960\) 0 0
\(961\) −8182.00 −0.274647
\(962\) −6132.00 −0.205513
\(963\) −10054.0 −0.336434
\(964\) −13636.0 −0.455587
\(965\) 0 0
\(966\) 0 0
\(967\) 12416.0 0.412897 0.206449 0.978457i \(-0.433809\pi\)
0.206449 + 0.978457i \(0.433809\pi\)
\(968\) −31344.0 −1.04074
\(969\) 7203.00 0.238796
\(970\) 0 0
\(971\) −36813.0 −1.21667 −0.608334 0.793681i \(-0.708162\pi\)
−0.608334 + 0.793681i \(0.708162\pi\)
\(972\) 19712.0 0.650476
\(973\) 0 0
\(974\) −32098.0 −1.05594
\(975\) 0 0
\(976\) −6608.00 −0.216718
\(977\) −34995.0 −1.14595 −0.572973 0.819574i \(-0.694210\pi\)
−0.572973 + 0.819574i \(0.694210\pi\)
\(978\) −6538.00 −0.213765
\(979\) −1645.00 −0.0537022
\(980\) 0 0
\(981\) −24750.0 −0.805511
\(982\) −17728.0 −0.576093
\(983\) −14301.0 −0.464019 −0.232010 0.972713i \(-0.574530\pi\)
−0.232010 + 0.972713i \(0.574530\pi\)
\(984\) −58800.0 −1.90495
\(985\) 0 0
\(986\) 2436.00 0.0786796
\(987\) 0 0
\(988\) −2744.00 −0.0883586
\(989\) 19716.0 0.633905
\(990\) 0 0
\(991\) −2665.00 −0.0854253 −0.0427127 0.999087i \(-0.513600\pi\)
−0.0427127 + 0.999087i \(0.513600\pi\)
\(992\) 23520.0 0.752783
\(993\) 23387.0 0.747396
\(994\) 0 0
\(995\) 0 0
\(996\) −30576.0 −0.972729
\(997\) 24871.0 0.790043 0.395021 0.918672i \(-0.370737\pi\)
0.395021 + 0.918672i \(0.370737\pi\)
\(998\) 20422.0 0.647743
\(999\) 7665.00 0.242753
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 1225.4.a.d.1.1 1
5.4 even 2 49.4.a.c.1.1 1
7.3 odd 6 175.4.e.a.51.1 2
7.5 odd 6 175.4.e.a.151.1 2
7.6 odd 2 1225.4.a.c.1.1 1
15.14 odd 2 441.4.a.e.1.1 1
20.19 odd 2 784.4.a.r.1.1 1
35.3 even 12 175.4.k.a.149.1 4
35.4 even 6 49.4.c.a.30.1 2
35.9 even 6 49.4.c.a.18.1 2
35.12 even 12 175.4.k.a.74.1 4
35.17 even 12 175.4.k.a.149.2 4
35.19 odd 6 7.4.c.a.4.1 yes 2
35.24 odd 6 7.4.c.a.2.1 2
35.33 even 12 175.4.k.a.74.2 4
35.34 odd 2 49.4.a.d.1.1 1
105.44 odd 6 441.4.e.k.361.1 2
105.59 even 6 63.4.e.b.37.1 2
105.74 odd 6 441.4.e.k.226.1 2
105.89 even 6 63.4.e.b.46.1 2
105.104 even 2 441.4.a.d.1.1 1
140.19 even 6 112.4.i.c.81.1 2
140.59 even 6 112.4.i.c.65.1 2
140.139 even 2 784.4.a.b.1.1 1
280.19 even 6 448.4.i.a.193.1 2
280.59 even 6 448.4.i.a.65.1 2
280.229 odd 6 448.4.i.f.193.1 2
280.269 odd 6 448.4.i.f.65.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7.4.c.a.2.1 2 35.24 odd 6
7.4.c.a.4.1 yes 2 35.19 odd 6
49.4.a.c.1.1 1 5.4 even 2
49.4.a.d.1.1 1 35.34 odd 2
49.4.c.a.18.1 2 35.9 even 6
49.4.c.a.30.1 2 35.4 even 6
63.4.e.b.37.1 2 105.59 even 6
63.4.e.b.46.1 2 105.89 even 6
112.4.i.c.65.1 2 140.59 even 6
112.4.i.c.81.1 2 140.19 even 6
175.4.e.a.51.1 2 7.3 odd 6
175.4.e.a.151.1 2 7.5 odd 6
175.4.k.a.74.1 4 35.12 even 12
175.4.k.a.74.2 4 35.33 even 12
175.4.k.a.149.1 4 35.3 even 12
175.4.k.a.149.2 4 35.17 even 12
441.4.a.d.1.1 1 105.104 even 2
441.4.a.e.1.1 1 15.14 odd 2
441.4.e.k.226.1 2 105.74 odd 6
441.4.e.k.361.1 2 105.44 odd 6
448.4.i.a.65.1 2 280.59 even 6
448.4.i.a.193.1 2 280.19 even 6
448.4.i.f.65.1 2 280.269 odd 6
448.4.i.f.193.1 2 280.229 odd 6
784.4.a.b.1.1 1 140.139 even 2
784.4.a.r.1.1 1 20.19 odd 2
1225.4.a.c.1.1 1 7.6 odd 2
1225.4.a.d.1.1 1 1.1 even 1 trivial