Properties

Label 2205.4.a.z.1.2
Level $2205$
Weight $4$
Character 2205.1
Self dual yes
Analytic conductor $130.099$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2205.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(130.099211563\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{65}) \)
Defining polynomial: \( x^{2} - x - 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 105)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-3.53113\) of defining polynomial
Character \(\chi\) \(=\) 2205.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.53113 q^{2} +4.46887 q^{4} +5.00000 q^{5} -12.4689 q^{8} +O(q^{10})\) \(q+3.53113 q^{2} +4.46887 q^{4} +5.00000 q^{5} -12.4689 q^{8} +17.6556 q^{10} +2.93774 q^{11} +19.0623 q^{13} -79.7802 q^{16} +122.498 q^{17} -107.436 q^{19} +22.3444 q^{20} +10.3735 q^{22} -210.623 q^{23} +25.0000 q^{25} +67.3113 q^{26} -95.4942 q^{29} +94.3074 q^{31} -181.963 q^{32} +432.556 q^{34} +97.1206 q^{37} -379.370 q^{38} -62.3444 q^{40} -491.113 q^{41} -43.0039 q^{43} +13.1284 q^{44} -743.735 q^{46} +473.494 q^{47} +88.2782 q^{50} +85.1868 q^{52} +183.677 q^{53} +14.6887 q^{55} -337.202 q^{58} -760.615 q^{59} +198.747 q^{61} +333.012 q^{62} -4.29373 q^{64} +95.3113 q^{65} -309.992 q^{67} +547.428 q^{68} -665.693 q^{71} -621.288 q^{73} +342.945 q^{74} -480.117 q^{76} -24.7626 q^{79} -398.901 q^{80} -1734.18 q^{82} -406.724 q^{83} +612.490 q^{85} -151.852 q^{86} -36.6303 q^{88} +261.751 q^{89} -941.245 q^{92} +1671.97 q^{94} -537.179 q^{95} +1004.77 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} + 17 q^{4} + 10 q^{5} - 33 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} + 17 q^{4} + 10 q^{5} - 33 q^{8} - 5 q^{10} + 22 q^{11} + 22 q^{13} - 87 q^{16} + 116 q^{17} - 102 q^{19} + 85 q^{20} - 76 q^{22} - 260 q^{23} + 50 q^{25} + 54 q^{26} + 196 q^{29} - 150 q^{31} + 15 q^{32} + 462 q^{34} - 96 q^{37} - 404 q^{38} - 165 q^{40} - 176 q^{41} - 344 q^{43} + 252 q^{44} - 520 q^{46} + 560 q^{47} - 25 q^{50} + 122 q^{52} - 326 q^{53} + 110 q^{55} - 1658 q^{58} - 844 q^{59} + 204 q^{61} + 1440 q^{62} - 839 q^{64} + 110 q^{65} - 104 q^{67} + 466 q^{68} - 1670 q^{71} + 386 q^{73} + 1218 q^{74} - 412 q^{76} - 888 q^{79} - 435 q^{80} - 3162 q^{82} + 928 q^{83} + 580 q^{85} + 1212 q^{86} - 428 q^{88} + 588 q^{89} - 1560 q^{92} + 1280 q^{94} - 510 q^{95} - 522 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.53113 1.24844 0.624221 0.781248i \(-0.285416\pi\)
0.624221 + 0.781248i \(0.285416\pi\)
\(3\) 0 0
\(4\) 4.46887 0.558609
\(5\) 5.00000 0.447214
\(6\) 0 0
\(7\) 0 0
\(8\) −12.4689 −0.551051
\(9\) 0 0
\(10\) 17.6556 0.558320
\(11\) 2.93774 0.0805239 0.0402619 0.999189i \(-0.487181\pi\)
0.0402619 + 0.999189i \(0.487181\pi\)
\(12\) 0 0
\(13\) 19.0623 0.406686 0.203343 0.979108i \(-0.434819\pi\)
0.203343 + 0.979108i \(0.434819\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −79.7802 −1.24656
\(17\) 122.498 1.74766 0.873828 0.486236i \(-0.161630\pi\)
0.873828 + 0.486236i \(0.161630\pi\)
\(18\) 0 0
\(19\) −107.436 −1.29723 −0.648617 0.761115i \(-0.724652\pi\)
−0.648617 + 0.761115i \(0.724652\pi\)
\(20\) 22.3444 0.249817
\(21\) 0 0
\(22\) 10.3735 0.100529
\(23\) −210.623 −1.90947 −0.954736 0.297455i \(-0.903862\pi\)
−0.954736 + 0.297455i \(0.903862\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 67.3113 0.507724
\(27\) 0 0
\(28\) 0 0
\(29\) −95.4942 −0.611477 −0.305738 0.952116i \(-0.598903\pi\)
−0.305738 + 0.952116i \(0.598903\pi\)
\(30\) 0 0
\(31\) 94.3074 0.546391 0.273195 0.961959i \(-0.411919\pi\)
0.273195 + 0.961959i \(0.411919\pi\)
\(32\) −181.963 −1.00521
\(33\) 0 0
\(34\) 432.556 2.18185
\(35\) 0 0
\(36\) 0 0
\(37\) 97.1206 0.431528 0.215764 0.976446i \(-0.430776\pi\)
0.215764 + 0.976446i \(0.430776\pi\)
\(38\) −379.370 −1.61952
\(39\) 0 0
\(40\) −62.3444 −0.246438
\(41\) −491.113 −1.87071 −0.935353 0.353716i \(-0.884918\pi\)
−0.935353 + 0.353716i \(0.884918\pi\)
\(42\) 0 0
\(43\) −43.0039 −0.152512 −0.0762562 0.997088i \(-0.524297\pi\)
−0.0762562 + 0.997088i \(0.524297\pi\)
\(44\) 13.1284 0.0449814
\(45\) 0 0
\(46\) −743.735 −2.38387
\(47\) 473.494 1.46949 0.734747 0.678341i \(-0.237301\pi\)
0.734747 + 0.678341i \(0.237301\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 88.2782 0.249689
\(51\) 0 0
\(52\) 85.1868 0.227178
\(53\) 183.677 0.476038 0.238019 0.971261i \(-0.423502\pi\)
0.238019 + 0.971261i \(0.423502\pi\)
\(54\) 0 0
\(55\) 14.6887 0.0360114
\(56\) 0 0
\(57\) 0 0
\(58\) −337.202 −0.763394
\(59\) −760.615 −1.67837 −0.839183 0.543849i \(-0.816966\pi\)
−0.839183 + 0.543849i \(0.816966\pi\)
\(60\) 0 0
\(61\) 198.747 0.417163 0.208582 0.978005i \(-0.433115\pi\)
0.208582 + 0.978005i \(0.433115\pi\)
\(62\) 333.012 0.682137
\(63\) 0 0
\(64\) −4.29373 −0.00838618
\(65\) 95.3113 0.181876
\(66\) 0 0
\(67\) −309.992 −0.565247 −0.282624 0.959231i \(-0.591205\pi\)
−0.282624 + 0.959231i \(0.591205\pi\)
\(68\) 547.428 0.976256
\(69\) 0 0
\(70\) 0 0
\(71\) −665.693 −1.11272 −0.556360 0.830941i \(-0.687803\pi\)
−0.556360 + 0.830941i \(0.687803\pi\)
\(72\) 0 0
\(73\) −621.288 −0.996113 −0.498057 0.867145i \(-0.665953\pi\)
−0.498057 + 0.867145i \(0.665953\pi\)
\(74\) 342.945 0.538738
\(75\) 0 0
\(76\) −480.117 −0.724647
\(77\) 0 0
\(78\) 0 0
\(79\) −24.7626 −0.0352659 −0.0176330 0.999845i \(-0.505613\pi\)
−0.0176330 + 0.999845i \(0.505613\pi\)
\(80\) −398.901 −0.557481
\(81\) 0 0
\(82\) −1734.18 −2.33547
\(83\) −406.724 −0.537876 −0.268938 0.963157i \(-0.586673\pi\)
−0.268938 + 0.963157i \(0.586673\pi\)
\(84\) 0 0
\(85\) 612.490 0.781575
\(86\) −151.852 −0.190403
\(87\) 0 0
\(88\) −36.6303 −0.0443728
\(89\) 261.751 0.311748 0.155874 0.987777i \(-0.450181\pi\)
0.155874 + 0.987777i \(0.450181\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −941.245 −1.06665
\(93\) 0 0
\(94\) 1671.97 1.83458
\(95\) −537.179 −0.580141
\(96\) 0 0
\(97\) 1004.77 1.05175 0.525873 0.850563i \(-0.323739\pi\)
0.525873 + 0.850563i \(0.323739\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 111.722 0.111722
\(101\) −128.872 −0.126962 −0.0634812 0.997983i \(-0.520220\pi\)
−0.0634812 + 0.997983i \(0.520220\pi\)
\(102\) 0 0
\(103\) −806.008 −0.771051 −0.385526 0.922697i \(-0.625980\pi\)
−0.385526 + 0.922697i \(0.625980\pi\)
\(104\) −237.685 −0.224105
\(105\) 0 0
\(106\) 648.587 0.594305
\(107\) 769.712 0.695429 0.347714 0.937600i \(-0.386958\pi\)
0.347714 + 0.937600i \(0.386958\pi\)
\(108\) 0 0
\(109\) −780.856 −0.686169 −0.343085 0.939304i \(-0.611472\pi\)
−0.343085 + 0.939304i \(0.611472\pi\)
\(110\) 51.8677 0.0449581
\(111\) 0 0
\(112\) 0 0
\(113\) 1115.65 0.928771 0.464386 0.885633i \(-0.346275\pi\)
0.464386 + 0.885633i \(0.346275\pi\)
\(114\) 0 0
\(115\) −1053.11 −0.853942
\(116\) −426.751 −0.341576
\(117\) 0 0
\(118\) −2685.83 −2.09534
\(119\) 0 0
\(120\) 0 0
\(121\) −1322.37 −0.993516
\(122\) 701.802 0.520804
\(123\) 0 0
\(124\) 421.448 0.305219
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) −1875.98 −1.31076 −0.655381 0.755299i \(-0.727492\pi\)
−0.655381 + 0.755299i \(0.727492\pi\)
\(128\) 1440.54 0.994744
\(129\) 0 0
\(130\) 336.556 0.227061
\(131\) 364.203 0.242905 0.121452 0.992597i \(-0.461245\pi\)
0.121452 + 0.992597i \(0.461245\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −1094.62 −0.705679
\(135\) 0 0
\(136\) −1527.41 −0.963048
\(137\) −1603.13 −0.999743 −0.499872 0.866099i \(-0.666620\pi\)
−0.499872 + 0.866099i \(0.666620\pi\)
\(138\) 0 0
\(139\) −2431.12 −1.48349 −0.741746 0.670681i \(-0.766002\pi\)
−0.741746 + 0.670681i \(0.766002\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −2350.65 −1.38917
\(143\) 56.0000 0.0327479
\(144\) 0 0
\(145\) −477.471 −0.273461
\(146\) −2193.85 −1.24359
\(147\) 0 0
\(148\) 434.020 0.241055
\(149\) −2341.57 −1.28744 −0.643722 0.765260i \(-0.722611\pi\)
−0.643722 + 0.765260i \(0.722611\pi\)
\(150\) 0 0
\(151\) −2104.07 −1.13395 −0.566976 0.823734i \(-0.691887\pi\)
−0.566976 + 0.823734i \(0.691887\pi\)
\(152\) 1339.60 0.714843
\(153\) 0 0
\(154\) 0 0
\(155\) 471.537 0.244353
\(156\) 0 0
\(157\) 593.467 0.301680 0.150840 0.988558i \(-0.451802\pi\)
0.150840 + 0.988558i \(0.451802\pi\)
\(158\) −87.4399 −0.0440275
\(159\) 0 0
\(160\) −909.815 −0.449545
\(161\) 0 0
\(162\) 0 0
\(163\) 2178.71 1.04693 0.523465 0.852047i \(-0.324639\pi\)
0.523465 + 0.852047i \(0.324639\pi\)
\(164\) −2194.72 −1.04499
\(165\) 0 0
\(166\) −1436.19 −0.671508
\(167\) 799.502 0.370463 0.185231 0.982695i \(-0.440697\pi\)
0.185231 + 0.982695i \(0.440697\pi\)
\(168\) 0 0
\(169\) −1833.63 −0.834606
\(170\) 2162.78 0.975752
\(171\) 0 0
\(172\) −192.179 −0.0851947
\(173\) −1444.36 −0.634754 −0.317377 0.948299i \(-0.602802\pi\)
−0.317377 + 0.948299i \(0.602802\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −234.374 −0.100378
\(177\) 0 0
\(178\) 924.276 0.389199
\(179\) −3343.49 −1.39611 −0.698056 0.716043i \(-0.745952\pi\)
−0.698056 + 0.716043i \(0.745952\pi\)
\(180\) 0 0
\(181\) −2251.81 −0.924729 −0.462365 0.886690i \(-0.652999\pi\)
−0.462365 + 0.886690i \(0.652999\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 2626.23 1.05222
\(185\) 485.603 0.192985
\(186\) 0 0
\(187\) 359.868 0.140728
\(188\) 2115.98 0.820873
\(189\) 0 0
\(190\) −1896.85 −0.724273
\(191\) 1001.93 0.379565 0.189782 0.981826i \(-0.439222\pi\)
0.189782 + 0.981826i \(0.439222\pi\)
\(192\) 0 0
\(193\) −4054.97 −1.51235 −0.756173 0.654372i \(-0.772933\pi\)
−0.756173 + 0.654372i \(0.772933\pi\)
\(194\) 3547.99 1.31304
\(195\) 0 0
\(196\) 0 0
\(197\) 5140.23 1.85902 0.929508 0.368802i \(-0.120232\pi\)
0.929508 + 0.368802i \(0.120232\pi\)
\(198\) 0 0
\(199\) −585.631 −0.208614 −0.104307 0.994545i \(-0.533263\pi\)
−0.104307 + 0.994545i \(0.533263\pi\)
\(200\) −311.722 −0.110210
\(201\) 0 0
\(202\) −455.062 −0.158505
\(203\) 0 0
\(204\) 0 0
\(205\) −2455.56 −0.836605
\(206\) −2846.12 −0.962614
\(207\) 0 0
\(208\) −1520.79 −0.506961
\(209\) −315.619 −0.104458
\(210\) 0 0
\(211\) −1055.16 −0.344266 −0.172133 0.985074i \(-0.555066\pi\)
−0.172133 + 0.985074i \(0.555066\pi\)
\(212\) 820.829 0.265919
\(213\) 0 0
\(214\) 2717.95 0.868203
\(215\) −215.019 −0.0682056
\(216\) 0 0
\(217\) 0 0
\(218\) −2757.30 −0.856643
\(219\) 0 0
\(220\) 65.6420 0.0201163
\(221\) 2335.09 0.710747
\(222\) 0 0
\(223\) −4675.85 −1.40412 −0.702059 0.712119i \(-0.747736\pi\)
−0.702059 + 0.712119i \(0.747736\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 3939.49 1.15952
\(227\) 5443.11 1.59151 0.795754 0.605621i \(-0.207075\pi\)
0.795754 + 0.605621i \(0.207075\pi\)
\(228\) 0 0
\(229\) 536.303 0.154759 0.0773797 0.997002i \(-0.475345\pi\)
0.0773797 + 0.997002i \(0.475345\pi\)
\(230\) −3718.68 −1.06610
\(231\) 0 0
\(232\) 1190.70 0.336955
\(233\) 183.490 0.0515916 0.0257958 0.999667i \(-0.491788\pi\)
0.0257958 + 0.999667i \(0.491788\pi\)
\(234\) 0 0
\(235\) 2367.47 0.657178
\(236\) −3399.09 −0.937550
\(237\) 0 0
\(238\) 0 0
\(239\) −643.218 −0.174085 −0.0870425 0.996205i \(-0.527742\pi\)
−0.0870425 + 0.996205i \(0.527742\pi\)
\(240\) 0 0
\(241\) 5755.61 1.53839 0.769194 0.639015i \(-0.220658\pi\)
0.769194 + 0.639015i \(0.220658\pi\)
\(242\) −4669.46 −1.24035
\(243\) 0 0
\(244\) 888.175 0.233031
\(245\) 0 0
\(246\) 0 0
\(247\) −2047.97 −0.527567
\(248\) −1175.91 −0.301089
\(249\) 0 0
\(250\) 441.391 0.111664
\(251\) −5132.27 −1.29062 −0.645311 0.763920i \(-0.723272\pi\)
−0.645311 + 0.763920i \(0.723272\pi\)
\(252\) 0 0
\(253\) −618.755 −0.153758
\(254\) −6624.34 −1.63641
\(255\) 0 0
\(256\) 5121.09 1.25027
\(257\) 5041.74 1.22372 0.611859 0.790967i \(-0.290422\pi\)
0.611859 + 0.790967i \(0.290422\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 425.934 0.101597
\(261\) 0 0
\(262\) 1286.05 0.303253
\(263\) −7577.00 −1.77649 −0.888246 0.459367i \(-0.848076\pi\)
−0.888246 + 0.459367i \(0.848076\pi\)
\(264\) 0 0
\(265\) 918.385 0.212890
\(266\) 0 0
\(267\) 0 0
\(268\) −1385.32 −0.315752
\(269\) 1023.10 0.231893 0.115947 0.993255i \(-0.463010\pi\)
0.115947 + 0.993255i \(0.463010\pi\)
\(270\) 0 0
\(271\) 2251.98 0.504790 0.252395 0.967624i \(-0.418782\pi\)
0.252395 + 0.967624i \(0.418782\pi\)
\(272\) −9772.91 −2.17857
\(273\) 0 0
\(274\) −5660.87 −1.24812
\(275\) 73.4436 0.0161048
\(276\) 0 0
\(277\) −8630.72 −1.87209 −0.936047 0.351875i \(-0.885544\pi\)
−0.936047 + 0.351875i \(0.885544\pi\)
\(278\) −8584.61 −1.85205
\(279\) 0 0
\(280\) 0 0
\(281\) 7521.62 1.59680 0.798402 0.602124i \(-0.205679\pi\)
0.798402 + 0.602124i \(0.205679\pi\)
\(282\) 0 0
\(283\) −14.8169 −0.00311226 −0.00155613 0.999999i \(-0.500495\pi\)
−0.00155613 + 0.999999i \(0.500495\pi\)
\(284\) −2974.89 −0.621576
\(285\) 0 0
\(286\) 197.743 0.0408839
\(287\) 0 0
\(288\) 0 0
\(289\) 10092.8 2.05430
\(290\) −1686.01 −0.341400
\(291\) 0 0
\(292\) −2776.46 −0.556438
\(293\) 6913.39 1.37844 0.689222 0.724550i \(-0.257952\pi\)
0.689222 + 0.724550i \(0.257952\pi\)
\(294\) 0 0
\(295\) −3803.07 −0.750588
\(296\) −1210.98 −0.237794
\(297\) 0 0
\(298\) −8268.39 −1.60730
\(299\) −4014.94 −0.776555
\(300\) 0 0
\(301\) 0 0
\(302\) −7429.74 −1.41567
\(303\) 0 0
\(304\) 8571.25 1.61709
\(305\) 993.735 0.186561
\(306\) 0 0
\(307\) 7644.12 1.42108 0.710542 0.703655i \(-0.248450\pi\)
0.710542 + 0.703655i \(0.248450\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 1665.06 0.305061
\(311\) 7593.99 1.38462 0.692308 0.721602i \(-0.256594\pi\)
0.692308 + 0.721602i \(0.256594\pi\)
\(312\) 0 0
\(313\) 9127.84 1.64836 0.824179 0.566329i \(-0.191637\pi\)
0.824179 + 0.566329i \(0.191637\pi\)
\(314\) 2095.61 0.376631
\(315\) 0 0
\(316\) −110.661 −0.0196999
\(317\) 4929.81 0.873456 0.436728 0.899593i \(-0.356137\pi\)
0.436728 + 0.899593i \(0.356137\pi\)
\(318\) 0 0
\(319\) −280.537 −0.0492385
\(320\) −21.4686 −0.00375042
\(321\) 0 0
\(322\) 0 0
\(323\) −13160.7 −2.26712
\(324\) 0 0
\(325\) 476.556 0.0813372
\(326\) 7693.30 1.30703
\(327\) 0 0
\(328\) 6123.62 1.03086
\(329\) 0 0
\(330\) 0 0
\(331\) 1221.67 0.202867 0.101433 0.994842i \(-0.467657\pi\)
0.101433 + 0.994842i \(0.467657\pi\)
\(332\) −1817.60 −0.300463
\(333\) 0 0
\(334\) 2823.14 0.462502
\(335\) −1549.96 −0.252786
\(336\) 0 0
\(337\) −8744.83 −1.41354 −0.706768 0.707446i \(-0.749847\pi\)
−0.706768 + 0.707446i \(0.749847\pi\)
\(338\) −6474.79 −1.04196
\(339\) 0 0
\(340\) 2737.14 0.436595
\(341\) 277.051 0.0439975
\(342\) 0 0
\(343\) 0 0
\(344\) 536.210 0.0840421
\(345\) 0 0
\(346\) −5100.21 −0.792454
\(347\) −4589.56 −0.710031 −0.355015 0.934860i \(-0.615524\pi\)
−0.355015 + 0.934860i \(0.615524\pi\)
\(348\) 0 0
\(349\) 3989.89 0.611960 0.305980 0.952038i \(-0.401016\pi\)
0.305980 + 0.952038i \(0.401016\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −534.561 −0.0809437
\(353\) 2416.35 0.364333 0.182166 0.983268i \(-0.441689\pi\)
0.182166 + 0.983268i \(0.441689\pi\)
\(354\) 0 0
\(355\) −3328.46 −0.497624
\(356\) 1169.73 0.174145
\(357\) 0 0
\(358\) −11806.3 −1.74297
\(359\) 2756.24 0.405206 0.202603 0.979261i \(-0.435060\pi\)
0.202603 + 0.979261i \(0.435060\pi\)
\(360\) 0 0
\(361\) 4683.45 0.682818
\(362\) −7951.44 −1.15447
\(363\) 0 0
\(364\) 0 0
\(365\) −3106.44 −0.445475
\(366\) 0 0
\(367\) −11112.8 −1.58061 −0.790307 0.612711i \(-0.790079\pi\)
−0.790307 + 0.612711i \(0.790079\pi\)
\(368\) 16803.5 2.38028
\(369\) 0 0
\(370\) 1714.73 0.240931
\(371\) 0 0
\(372\) 0 0
\(373\) 6091.09 0.845535 0.422768 0.906238i \(-0.361059\pi\)
0.422768 + 0.906238i \(0.361059\pi\)
\(374\) 1270.74 0.175691
\(375\) 0 0
\(376\) −5903.94 −0.809767
\(377\) −1820.33 −0.248679
\(378\) 0 0
\(379\) 3984.29 0.539998 0.269999 0.962861i \(-0.412977\pi\)
0.269999 + 0.962861i \(0.412977\pi\)
\(380\) −2400.58 −0.324072
\(381\) 0 0
\(382\) 3537.93 0.473865
\(383\) 318.475 0.0424890 0.0212445 0.999774i \(-0.493237\pi\)
0.0212445 + 0.999774i \(0.493237\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −14318.6 −1.88808
\(387\) 0 0
\(388\) 4490.21 0.587515
\(389\) −3885.46 −0.506429 −0.253214 0.967410i \(-0.581488\pi\)
−0.253214 + 0.967410i \(0.581488\pi\)
\(390\) 0 0
\(391\) −25800.9 −3.33710
\(392\) 0 0
\(393\) 0 0
\(394\) 18150.8 2.32088
\(395\) −123.813 −0.0157714
\(396\) 0 0
\(397\) −4806.04 −0.607578 −0.303789 0.952739i \(-0.598252\pi\)
−0.303789 + 0.952739i \(0.598252\pi\)
\(398\) −2067.94 −0.260443
\(399\) 0 0
\(400\) −1994.50 −0.249313
\(401\) −3618.59 −0.450633 −0.225316 0.974286i \(-0.572342\pi\)
−0.225316 + 0.974286i \(0.572342\pi\)
\(402\) 0 0
\(403\) 1797.71 0.222209
\(404\) −575.911 −0.0709223
\(405\) 0 0
\(406\) 0 0
\(407\) 285.315 0.0347483
\(408\) 0 0
\(409\) 2109.05 0.254978 0.127489 0.991840i \(-0.459308\pi\)
0.127489 + 0.991840i \(0.459308\pi\)
\(410\) −8670.91 −1.04445
\(411\) 0 0
\(412\) −3601.94 −0.430716
\(413\) 0 0
\(414\) 0 0
\(415\) −2033.62 −0.240546
\(416\) −3468.63 −0.408806
\(417\) 0 0
\(418\) −1114.49 −0.130410
\(419\) −6905.91 −0.805193 −0.402597 0.915377i \(-0.631892\pi\)
−0.402597 + 0.915377i \(0.631892\pi\)
\(420\) 0 0
\(421\) −9647.54 −1.11685 −0.558423 0.829556i \(-0.688593\pi\)
−0.558423 + 0.829556i \(0.688593\pi\)
\(422\) −3725.91 −0.429797
\(423\) 0 0
\(424\) −2290.25 −0.262321
\(425\) 3062.45 0.349531
\(426\) 0 0
\(427\) 0 0
\(428\) 3439.74 0.388473
\(429\) 0 0
\(430\) −759.261 −0.0851508
\(431\) 13002.7 1.45318 0.726589 0.687073i \(-0.241105\pi\)
0.726589 + 0.687073i \(0.241105\pi\)
\(432\) 0 0
\(433\) −7356.07 −0.816420 −0.408210 0.912888i \(-0.633847\pi\)
−0.408210 + 0.912888i \(0.633847\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −3489.55 −0.383300
\(437\) 22628.4 2.47703
\(438\) 0 0
\(439\) −6909.21 −0.751159 −0.375579 0.926790i \(-0.622556\pi\)
−0.375579 + 0.926790i \(0.622556\pi\)
\(440\) −183.152 −0.0198441
\(441\) 0 0
\(442\) 8245.50 0.887327
\(443\) 14812.6 1.58864 0.794318 0.607502i \(-0.207828\pi\)
0.794318 + 0.607502i \(0.207828\pi\)
\(444\) 0 0
\(445\) 1308.75 0.139418
\(446\) −16511.0 −1.75296
\(447\) 0 0
\(448\) 0 0
\(449\) 10654.5 1.11986 0.559932 0.828538i \(-0.310827\pi\)
0.559932 + 0.828538i \(0.310827\pi\)
\(450\) 0 0
\(451\) −1442.76 −0.150636
\(452\) 4985.68 0.518820
\(453\) 0 0
\(454\) 19220.3 1.98691
\(455\) 0 0
\(456\) 0 0
\(457\) −5855.16 −0.599328 −0.299664 0.954045i \(-0.596875\pi\)
−0.299664 + 0.954045i \(0.596875\pi\)
\(458\) 1893.76 0.193208
\(459\) 0 0
\(460\) −4706.23 −0.477019
\(461\) 3204.74 0.323774 0.161887 0.986809i \(-0.448242\pi\)
0.161887 + 0.986809i \(0.448242\pi\)
\(462\) 0 0
\(463\) 371.658 0.0373054 0.0186527 0.999826i \(-0.494062\pi\)
0.0186527 + 0.999826i \(0.494062\pi\)
\(464\) 7618.54 0.762245
\(465\) 0 0
\(466\) 647.927 0.0644091
\(467\) −19752.3 −1.95723 −0.978614 0.205703i \(-0.934052\pi\)
−0.978614 + 0.205703i \(0.934052\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 8359.84 0.820449
\(471\) 0 0
\(472\) 9484.01 0.924866
\(473\) −126.334 −0.0122809
\(474\) 0 0
\(475\) −2685.90 −0.259447
\(476\) 0 0
\(477\) 0 0
\(478\) −2271.28 −0.217335
\(479\) −20762.0 −1.98046 −0.990232 0.139433i \(-0.955472\pi\)
−0.990232 + 0.139433i \(0.955472\pi\)
\(480\) 0 0
\(481\) 1851.34 0.175496
\(482\) 20323.8 1.92059
\(483\) 0 0
\(484\) −5909.50 −0.554987
\(485\) 5023.87 0.470355
\(486\) 0 0
\(487\) 17647.6 1.64207 0.821035 0.570878i \(-0.193397\pi\)
0.821035 + 0.570878i \(0.193397\pi\)
\(488\) −2478.15 −0.229878
\(489\) 0 0
\(490\) 0 0
\(491\) 5637.46 0.518157 0.259078 0.965856i \(-0.416581\pi\)
0.259078 + 0.965856i \(0.416581\pi\)
\(492\) 0 0
\(493\) −11697.9 −1.06865
\(494\) −7231.64 −0.658638
\(495\) 0 0
\(496\) −7523.86 −0.681112
\(497\) 0 0
\(498\) 0 0
\(499\) −17474.1 −1.56764 −0.783818 0.620991i \(-0.786730\pi\)
−0.783818 + 0.620991i \(0.786730\pi\)
\(500\) 558.609 0.0499635
\(501\) 0 0
\(502\) −18122.7 −1.61127
\(503\) 7444.81 0.659936 0.329968 0.943992i \(-0.392962\pi\)
0.329968 + 0.943992i \(0.392962\pi\)
\(504\) 0 0
\(505\) −644.358 −0.0567793
\(506\) −2184.90 −0.191958
\(507\) 0 0
\(508\) −8383.53 −0.732203
\(509\) −3384.48 −0.294724 −0.147362 0.989083i \(-0.547078\pi\)
−0.147362 + 0.989083i \(0.547078\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 6558.89 0.566142
\(513\) 0 0
\(514\) 17803.0 1.52774
\(515\) −4030.04 −0.344825
\(516\) 0 0
\(517\) 1391.00 0.118329
\(518\) 0 0
\(519\) 0 0
\(520\) −1188.42 −0.100223
\(521\) 2973.12 0.250009 0.125005 0.992156i \(-0.460105\pi\)
0.125005 + 0.992156i \(0.460105\pi\)
\(522\) 0 0
\(523\) −2689.02 −0.224823 −0.112412 0.993662i \(-0.535858\pi\)
−0.112412 + 0.993662i \(0.535858\pi\)
\(524\) 1627.57 0.135689
\(525\) 0 0
\(526\) −26755.3 −2.21785
\(527\) 11552.5 0.954903
\(528\) 0 0
\(529\) 32194.9 2.64608
\(530\) 3242.94 0.265781
\(531\) 0 0
\(532\) 0 0
\(533\) −9361.72 −0.760790
\(534\) 0 0
\(535\) 3848.56 0.311005
\(536\) 3865.25 0.311480
\(537\) 0 0
\(538\) 3612.69 0.289506
\(539\) 0 0
\(540\) 0 0
\(541\) −14429.5 −1.14671 −0.573356 0.819306i \(-0.694359\pi\)
−0.573356 + 0.819306i \(0.694359\pi\)
\(542\) 7952.03 0.630201
\(543\) 0 0
\(544\) −22290.1 −1.75677
\(545\) −3904.28 −0.306864
\(546\) 0 0
\(547\) 13811.2 1.07957 0.539784 0.841804i \(-0.318506\pi\)
0.539784 + 0.841804i \(0.318506\pi\)
\(548\) −7164.19 −0.558466
\(549\) 0 0
\(550\) 259.339 0.0201059
\(551\) 10259.5 0.793229
\(552\) 0 0
\(553\) 0 0
\(554\) −30476.2 −2.33720
\(555\) 0 0
\(556\) −10864.4 −0.828692
\(557\) 6033.26 0.458954 0.229477 0.973314i \(-0.426298\pi\)
0.229477 + 0.973314i \(0.426298\pi\)
\(558\) 0 0
\(559\) −819.751 −0.0620246
\(560\) 0 0
\(561\) 0 0
\(562\) 26559.8 1.99352
\(563\) −6958.47 −0.520896 −0.260448 0.965488i \(-0.583870\pi\)
−0.260448 + 0.965488i \(0.583870\pi\)
\(564\) 0 0
\(565\) 5578.23 0.415359
\(566\) −52.3202 −0.00388548
\(567\) 0 0
\(568\) 8300.44 0.613166
\(569\) 13396.4 0.987009 0.493505 0.869743i \(-0.335716\pi\)
0.493505 + 0.869743i \(0.335716\pi\)
\(570\) 0 0
\(571\) −8055.84 −0.590414 −0.295207 0.955433i \(-0.595389\pi\)
−0.295207 + 0.955433i \(0.595389\pi\)
\(572\) 250.257 0.0182933
\(573\) 0 0
\(574\) 0 0
\(575\) −5265.56 −0.381894
\(576\) 0 0
\(577\) 21456.9 1.54812 0.774059 0.633114i \(-0.218223\pi\)
0.774059 + 0.633114i \(0.218223\pi\)
\(578\) 35638.9 2.56468
\(579\) 0 0
\(580\) −2133.76 −0.152758
\(581\) 0 0
\(582\) 0 0
\(583\) 539.596 0.0383324
\(584\) 7746.76 0.548910
\(585\) 0 0
\(586\) 24412.1 1.72091
\(587\) 20156.3 1.41728 0.708638 0.705572i \(-0.249310\pi\)
0.708638 + 0.705572i \(0.249310\pi\)
\(588\) 0 0
\(589\) −10132.0 −0.708797
\(590\) −13429.1 −0.937066
\(591\) 0 0
\(592\) −7748.30 −0.537928
\(593\) 599.307 0.0415018 0.0207509 0.999785i \(-0.493394\pi\)
0.0207509 + 0.999785i \(0.493394\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −10464.2 −0.719177
\(597\) 0 0
\(598\) −14177.3 −0.969485
\(599\) 5493.05 0.374691 0.187346 0.982294i \(-0.440012\pi\)
0.187346 + 0.982294i \(0.440012\pi\)
\(600\) 0 0
\(601\) −24292.8 −1.64879 −0.824396 0.566014i \(-0.808485\pi\)
−0.824396 + 0.566014i \(0.808485\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −9402.82 −0.633436
\(605\) −6611.85 −0.444314
\(606\) 0 0
\(607\) −3029.50 −0.202576 −0.101288 0.994857i \(-0.532296\pi\)
−0.101288 + 0.994857i \(0.532296\pi\)
\(608\) 19549.3 1.30400
\(609\) 0 0
\(610\) 3509.01 0.232911
\(611\) 9025.87 0.597623
\(612\) 0 0
\(613\) −19339.6 −1.27426 −0.637129 0.770757i \(-0.719878\pi\)
−0.637129 + 0.770757i \(0.719878\pi\)
\(614\) 26992.4 1.77414
\(615\) 0 0
\(616\) 0 0
\(617\) 5743.91 0.374783 0.187391 0.982285i \(-0.439997\pi\)
0.187391 + 0.982285i \(0.439997\pi\)
\(618\) 0 0
\(619\) 8243.35 0.535264 0.267632 0.963521i \(-0.413759\pi\)
0.267632 + 0.963521i \(0.413759\pi\)
\(620\) 2107.24 0.136498
\(621\) 0 0
\(622\) 26815.4 1.72861
\(623\) 0 0
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 32231.6 2.05788
\(627\) 0 0
\(628\) 2652.13 0.168521
\(629\) 11897.1 0.754162
\(630\) 0 0
\(631\) −4376.56 −0.276114 −0.138057 0.990424i \(-0.544086\pi\)
−0.138057 + 0.990424i \(0.544086\pi\)
\(632\) 308.762 0.0194334
\(633\) 0 0
\(634\) 17407.8 1.09046
\(635\) −9379.92 −0.586190
\(636\) 0 0
\(637\) 0 0
\(638\) −990.613 −0.0614714
\(639\) 0 0
\(640\) 7202.71 0.444863
\(641\) −11836.6 −0.729357 −0.364678 0.931133i \(-0.618821\pi\)
−0.364678 + 0.931133i \(0.618821\pi\)
\(642\) 0 0
\(643\) −1448.21 −0.0888209 −0.0444104 0.999013i \(-0.514141\pi\)
−0.0444104 + 0.999013i \(0.514141\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −46472.0 −2.83037
\(647\) −8732.95 −0.530646 −0.265323 0.964160i \(-0.585479\pi\)
−0.265323 + 0.964160i \(0.585479\pi\)
\(648\) 0 0
\(649\) −2234.49 −0.135149
\(650\) 1682.78 0.101545
\(651\) 0 0
\(652\) 9736.37 0.584824
\(653\) 21978.4 1.31712 0.658562 0.752527i \(-0.271165\pi\)
0.658562 + 0.752527i \(0.271165\pi\)
\(654\) 0 0
\(655\) 1821.01 0.108630
\(656\) 39181.1 2.33196
\(657\) 0 0
\(658\) 0 0
\(659\) 27761.7 1.64103 0.820516 0.571623i \(-0.193686\pi\)
0.820516 + 0.571623i \(0.193686\pi\)
\(660\) 0 0
\(661\) 8573.72 0.504507 0.252254 0.967661i \(-0.418828\pi\)
0.252254 + 0.967661i \(0.418828\pi\)
\(662\) 4313.86 0.253267
\(663\) 0 0
\(664\) 5071.39 0.296398
\(665\) 0 0
\(666\) 0 0
\(667\) 20113.2 1.16760
\(668\) 3572.87 0.206944
\(669\) 0 0
\(670\) −5473.11 −0.315589
\(671\) 583.868 0.0335916
\(672\) 0 0
\(673\) 27159.2 1.55559 0.777795 0.628518i \(-0.216338\pi\)
0.777795 + 0.628518i \(0.216338\pi\)
\(674\) −30879.1 −1.76472
\(675\) 0 0
\(676\) −8194.26 −0.466219
\(677\) −1392.30 −0.0790404 −0.0395202 0.999219i \(-0.512583\pi\)
−0.0395202 + 0.999219i \(0.512583\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −7637.06 −0.430688
\(681\) 0 0
\(682\) 978.302 0.0549283
\(683\) 8675.09 0.486007 0.243004 0.970025i \(-0.421867\pi\)
0.243004 + 0.970025i \(0.421867\pi\)
\(684\) 0 0
\(685\) −8015.66 −0.447099
\(686\) 0 0
\(687\) 0 0
\(688\) 3430.86 0.190117
\(689\) 3501.30 0.193598
\(690\) 0 0
\(691\) 21426.0 1.17957 0.589785 0.807561i \(-0.299213\pi\)
0.589785 + 0.807561i \(0.299213\pi\)
\(692\) −6454.65 −0.354579
\(693\) 0 0
\(694\) −16206.3 −0.886433
\(695\) −12155.6 −0.663438
\(696\) 0 0
\(697\) −60160.4 −3.26935
\(698\) 14088.8 0.763997
\(699\) 0 0
\(700\) 0 0
\(701\) −24840.5 −1.33839 −0.669197 0.743085i \(-0.733362\pi\)
−0.669197 + 0.743085i \(0.733362\pi\)
\(702\) 0 0
\(703\) −10434.2 −0.559793
\(704\) −12.6139 −0.000675288 0
\(705\) 0 0
\(706\) 8532.45 0.454848
\(707\) 0 0
\(708\) 0 0
\(709\) 12525.0 0.663450 0.331725 0.943376i \(-0.392369\pi\)
0.331725 + 0.943376i \(0.392369\pi\)
\(710\) −11753.2 −0.621255
\(711\) 0 0
\(712\) −3263.74 −0.171789
\(713\) −19863.3 −1.04332
\(714\) 0 0
\(715\) 280.000 0.0146453
\(716\) −14941.6 −0.779881
\(717\) 0 0
\(718\) 9732.66 0.505877
\(719\) 28085.0 1.45674 0.728369 0.685185i \(-0.240279\pi\)
0.728369 + 0.685185i \(0.240279\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 16537.9 0.852460
\(723\) 0 0
\(724\) −10063.1 −0.516562
\(725\) −2387.35 −0.122295
\(726\) 0 0
\(727\) 14326.2 0.730851 0.365426 0.930841i \(-0.380923\pi\)
0.365426 + 0.930841i \(0.380923\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −10969.2 −0.556150
\(731\) −5267.89 −0.266539
\(732\) 0 0
\(733\) −6727.85 −0.339016 −0.169508 0.985529i \(-0.554218\pi\)
−0.169508 + 0.985529i \(0.554218\pi\)
\(734\) −39240.8 −1.97331
\(735\) 0 0
\(736\) 38325.5 1.91943
\(737\) −910.677 −0.0455159
\(738\) 0 0
\(739\) −3418.51 −0.170165 −0.0850826 0.996374i \(-0.527115\pi\)
−0.0850826 + 0.996374i \(0.527115\pi\)
\(740\) 2170.10 0.107803
\(741\) 0 0
\(742\) 0 0
\(743\) −8095.50 −0.399724 −0.199862 0.979824i \(-0.564049\pi\)
−0.199862 + 0.979824i \(0.564049\pi\)
\(744\) 0 0
\(745\) −11707.9 −0.575762
\(746\) 21508.4 1.05560
\(747\) 0 0
\(748\) 1608.20 0.0786119
\(749\) 0 0
\(750\) 0 0
\(751\) 13446.8 0.653371 0.326686 0.945133i \(-0.394068\pi\)
0.326686 + 0.945133i \(0.394068\pi\)
\(752\) −37775.4 −1.83182
\(753\) 0 0
\(754\) −6427.84 −0.310462
\(755\) −10520.4 −0.507119
\(756\) 0 0
\(757\) −2593.24 −0.124508 −0.0622541 0.998060i \(-0.519829\pi\)
−0.0622541 + 0.998060i \(0.519829\pi\)
\(758\) 14069.0 0.674156
\(759\) 0 0
\(760\) 6698.02 0.319688
\(761\) 27079.4 1.28992 0.644959 0.764217i \(-0.276875\pi\)
0.644959 + 0.764217i \(0.276875\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 4477.48 0.212028
\(765\) 0 0
\(766\) 1124.58 0.0530451
\(767\) −14499.0 −0.682568
\(768\) 0 0
\(769\) −2138.72 −0.100292 −0.0501458 0.998742i \(-0.515969\pi\)
−0.0501458 + 0.998742i \(0.515969\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −18121.1 −0.844810
\(773\) 25864.0 1.20345 0.601724 0.798704i \(-0.294481\pi\)
0.601724 + 0.798704i \(0.294481\pi\)
\(774\) 0 0
\(775\) 2357.69 0.109278
\(776\) −12528.4 −0.579566
\(777\) 0 0
\(778\) −13720.1 −0.632247
\(779\) 52763.1 2.42675
\(780\) 0 0
\(781\) −1955.63 −0.0896006
\(782\) −91106.2 −4.16618
\(783\) 0 0
\(784\) 0 0
\(785\) 2967.33 0.134916
\(786\) 0 0
\(787\) 32371.3 1.46621 0.733107 0.680113i \(-0.238069\pi\)
0.733107 + 0.680113i \(0.238069\pi\)
\(788\) 22971.0 1.03846
\(789\) 0 0
\(790\) −437.200 −0.0196897
\(791\) 0 0
\(792\) 0 0
\(793\) 3788.57 0.169654
\(794\) −16970.8 −0.758526
\(795\) 0 0
\(796\) −2617.11 −0.116534
\(797\) 2024.33 0.0899691 0.0449845 0.998988i \(-0.485676\pi\)
0.0449845 + 0.998988i \(0.485676\pi\)
\(798\) 0 0
\(799\) 58002.1 2.56817
\(800\) −4549.08 −0.201043
\(801\) 0 0
\(802\) −12777.7 −0.562589
\(803\) −1825.18 −0.0802109
\(804\) 0 0
\(805\) 0 0
\(806\) 6347.95 0.277416
\(807\) 0 0
\(808\) 1606.88 0.0699628
\(809\) −12391.7 −0.538526 −0.269263 0.963067i \(-0.586780\pi\)
−0.269263 + 0.963067i \(0.586780\pi\)
\(810\) 0 0
\(811\) −14654.5 −0.634511 −0.317256 0.948340i \(-0.602761\pi\)
−0.317256 + 0.948340i \(0.602761\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 1007.49 0.0433813
\(815\) 10893.5 0.468201
\(816\) 0 0
\(817\) 4620.16 0.197844
\(818\) 7447.33 0.318325
\(819\) 0 0
\(820\) −10973.6 −0.467335
\(821\) −23887.9 −1.01546 −0.507731 0.861516i \(-0.669515\pi\)
−0.507731 + 0.861516i \(0.669515\pi\)
\(822\) 0 0
\(823\) −4008.41 −0.169774 −0.0848871 0.996391i \(-0.527053\pi\)
−0.0848871 + 0.996391i \(0.527053\pi\)
\(824\) 10050.0 0.424889
\(825\) 0 0
\(826\) 0 0
\(827\) 45110.4 1.89679 0.948394 0.317096i \(-0.102708\pi\)
0.948394 + 0.317096i \(0.102708\pi\)
\(828\) 0 0
\(829\) −16165.4 −0.677260 −0.338630 0.940920i \(-0.609964\pi\)
−0.338630 + 0.940920i \(0.609964\pi\)
\(830\) −7180.97 −0.300307
\(831\) 0 0
\(832\) −81.8481 −0.00341054
\(833\) 0 0
\(834\) 0 0
\(835\) 3997.51 0.165676
\(836\) −1410.46 −0.0583514
\(837\) 0 0
\(838\) −24385.7 −1.00524
\(839\) −25244.4 −1.03878 −0.519388 0.854538i \(-0.673840\pi\)
−0.519388 + 0.854538i \(0.673840\pi\)
\(840\) 0 0
\(841\) −15269.9 −0.626096
\(842\) −34066.7 −1.39432
\(843\) 0 0
\(844\) −4715.37 −0.192310
\(845\) −9168.15 −0.373247
\(846\) 0 0
\(847\) 0 0
\(848\) −14653.8 −0.593412
\(849\) 0 0
\(850\) 10813.9 0.436370
\(851\) −20455.8 −0.823990
\(852\) 0 0
\(853\) 30168.1 1.21094 0.605472 0.795867i \(-0.292984\pi\)
0.605472 + 0.795867i \(0.292984\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −9597.44 −0.383217
\(857\) −13393.6 −0.533857 −0.266929 0.963716i \(-0.586009\pi\)
−0.266929 + 0.963716i \(0.586009\pi\)
\(858\) 0 0
\(859\) −19060.4 −0.757081 −0.378541 0.925585i \(-0.623574\pi\)
−0.378541 + 0.925585i \(0.623574\pi\)
\(860\) −960.894 −0.0381002
\(861\) 0 0
\(862\) 45914.3 1.81421
\(863\) 9466.86 0.373413 0.186707 0.982416i \(-0.440219\pi\)
0.186707 + 0.982416i \(0.440219\pi\)
\(864\) 0 0
\(865\) −7221.79 −0.283871
\(866\) −25975.2 −1.01925
\(867\) 0 0
\(868\) 0 0
\(869\) −72.7461 −0.00283975
\(870\) 0 0
\(871\) −5909.15 −0.229878
\(872\) 9736.39 0.378115
\(873\) 0 0
\(874\) 79903.8 3.09243
\(875\) 0 0
\(876\) 0 0
\(877\) 37740.6 1.45315 0.726573 0.687090i \(-0.241112\pi\)
0.726573 + 0.687090i \(0.241112\pi\)
\(878\) −24397.3 −0.937778
\(879\) 0 0
\(880\) −1171.87 −0.0448905
\(881\) 25991.5 0.993957 0.496979 0.867763i \(-0.334443\pi\)
0.496979 + 0.867763i \(0.334443\pi\)
\(882\) 0 0
\(883\) 39420.3 1.50238 0.751189 0.660087i \(-0.229481\pi\)
0.751189 + 0.660087i \(0.229481\pi\)
\(884\) 10435.2 0.397030
\(885\) 0 0
\(886\) 52305.0 1.98332
\(887\) 46005.2 1.74149 0.870745 0.491735i \(-0.163637\pi\)
0.870745 + 0.491735i \(0.163637\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 4621.38 0.174055
\(891\) 0 0
\(892\) −20895.8 −0.784353
\(893\) −50870.2 −1.90628
\(894\) 0 0
\(895\) −16717.5 −0.624361
\(896\) 0 0
\(897\) 0 0
\(898\) 37622.6 1.39809
\(899\) −9005.81 −0.334105
\(900\) 0 0
\(901\) 22500.1 0.831950
\(902\) −5094.58 −0.188061
\(903\) 0 0
\(904\) −13910.8 −0.511801
\(905\) −11259.1 −0.413551
\(906\) 0 0
\(907\) −2838.97 −0.103932 −0.0519661 0.998649i \(-0.516549\pi\)
−0.0519661 + 0.998649i \(0.516549\pi\)
\(908\) 24324.6 0.889030
\(909\) 0 0
\(910\) 0 0
\(911\) −39890.9 −1.45076 −0.725382 0.688347i \(-0.758337\pi\)
−0.725382 + 0.688347i \(0.758337\pi\)
\(912\) 0 0
\(913\) −1194.85 −0.0433119
\(914\) −20675.3 −0.748226
\(915\) 0 0
\(916\) 2396.67 0.0864500
\(917\) 0 0
\(918\) 0 0
\(919\) −646.475 −0.0232048 −0.0116024 0.999933i \(-0.503693\pi\)
−0.0116024 + 0.999933i \(0.503693\pi\)
\(920\) 13131.1 0.470566
\(921\) 0 0
\(922\) 11316.3 0.404213
\(923\) −12689.6 −0.452528
\(924\) 0 0
\(925\) 2428.02 0.0863056
\(926\) 1312.37 0.0465737
\(927\) 0 0
\(928\) 17376.4 0.614665
\(929\) 51188.2 1.80778 0.903892 0.427760i \(-0.140697\pi\)
0.903892 + 0.427760i \(0.140697\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 819.993 0.0288195
\(933\) 0 0
\(934\) −69747.8 −2.44349
\(935\) 1799.34 0.0629355
\(936\) 0 0
\(937\) −29786.1 −1.03849 −0.519247 0.854624i \(-0.673788\pi\)
−0.519247 + 0.854624i \(0.673788\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 10579.9 0.367105
\(941\) −44817.4 −1.55261 −0.776304 0.630358i \(-0.782908\pi\)
−0.776304 + 0.630358i \(0.782908\pi\)
\(942\) 0 0
\(943\) 103439. 3.57206
\(944\) 60682.0 2.09219
\(945\) 0 0
\(946\) −446.103 −0.0153320
\(947\) −54697.1 −1.87689 −0.938446 0.345425i \(-0.887735\pi\)
−0.938446 + 0.345425i \(0.887735\pi\)
\(948\) 0 0
\(949\) −11843.2 −0.405105
\(950\) −9484.24 −0.323905
\(951\) 0 0
\(952\) 0 0
\(953\) 7577.51 0.257565 0.128783 0.991673i \(-0.458893\pi\)
0.128783 + 0.991673i \(0.458893\pi\)
\(954\) 0 0
\(955\) 5009.63 0.169746
\(956\) −2874.46 −0.0972454
\(957\) 0 0
\(958\) −73313.4 −2.47249
\(959\) 0 0
\(960\) 0 0
\(961\) −20897.1 −0.701457
\(962\) 6537.32 0.219097
\(963\) 0 0
\(964\) 25721.1 0.859357
\(965\) −20274.8 −0.676342
\(966\) 0 0
\(967\) 50779.0 1.68867 0.844334 0.535817i \(-0.179996\pi\)
0.844334 + 0.535817i \(0.179996\pi\)
\(968\) 16488.5 0.547478
\(969\) 0 0
\(970\) 17739.9 0.587212
\(971\) −15313.2 −0.506102 −0.253051 0.967453i \(-0.581434\pi\)
−0.253051 + 0.967453i \(0.581434\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 62315.9 2.05003
\(975\) 0 0
\(976\) −15856.1 −0.520021
\(977\) −46620.4 −1.52663 −0.763316 0.646025i \(-0.776430\pi\)
−0.763316 + 0.646025i \(0.776430\pi\)
\(978\) 0 0
\(979\) 768.957 0.0251031
\(980\) 0 0
\(981\) 0 0
\(982\) 19906.6 0.646889
\(983\) −2824.37 −0.0916414 −0.0458207 0.998950i \(-0.514590\pi\)
−0.0458207 + 0.998950i \(0.514590\pi\)
\(984\) 0 0
\(985\) 25701.1 0.831377
\(986\) −41306.6 −1.33415
\(987\) 0 0
\(988\) −9152.11 −0.294704
\(989\) 9057.59 0.291218
\(990\) 0 0
\(991\) 16951.4 0.543370 0.271685 0.962386i \(-0.412419\pi\)
0.271685 + 0.962386i \(0.412419\pi\)
\(992\) −17160.5 −0.549239
\(993\) 0 0
\(994\) 0 0
\(995\) −2928.15 −0.0932952
\(996\) 0 0
\(997\) −23847.8 −0.757540 −0.378770 0.925491i \(-0.623653\pi\)
−0.378770 + 0.925491i \(0.623653\pi\)
\(998\) −61703.4 −1.95710
\(999\) 0 0
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 2205.4.a.z.1.2 2
3.2 odd 2 735.4.a.p.1.1 2
7.6 odd 2 315.4.a.i.1.2 2
21.20 even 2 105.4.a.f.1.1 2
35.34 odd 2 1575.4.a.w.1.1 2
84.83 odd 2 1680.4.a.bg.1.1 2
105.62 odd 4 525.4.d.h.274.2 4
105.83 odd 4 525.4.d.h.274.3 4
105.104 even 2 525.4.a.k.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.4.a.f.1.1 2 21.20 even 2
315.4.a.i.1.2 2 7.6 odd 2
525.4.a.k.1.2 2 105.104 even 2
525.4.d.h.274.2 4 105.62 odd 4
525.4.d.h.274.3 4 105.83 odd 4
735.4.a.p.1.1 2 3.2 odd 2
1575.4.a.w.1.1 2 35.34 odd 2
1680.4.a.bg.1.1 2 84.83 odd 2
2205.4.a.z.1.2 2 1.1 even 1 trivial