Properties

Label 4016.2.a.m.1.18
Level 4016
Weight 2
Character 4016.1
Self dual yes
Analytic conductor 32.068
Analytic rank 0
Dimension 23
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4016 = 2^{4} \cdot 251 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4016.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.0679214517\)
Analytic rank: \(0\)
Dimension: \(23\)
Coefficient ring index: multiple of None
Twist minimal: no (minimal twist has level 2008)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 4016.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.13165 q^{3} +0.257423 q^{5} -0.578263 q^{7} +1.54395 q^{9} +O(q^{10})\) \(q+2.13165 q^{3} +0.257423 q^{5} -0.578263 q^{7} +1.54395 q^{9} +1.44278 q^{11} +1.23315 q^{13} +0.548737 q^{15} +3.22998 q^{17} +2.16232 q^{19} -1.23266 q^{21} +3.59035 q^{23} -4.93373 q^{25} -3.10379 q^{27} +1.34015 q^{29} -2.91300 q^{31} +3.07551 q^{33} -0.148858 q^{35} +7.43825 q^{37} +2.62866 q^{39} +9.61132 q^{41} +4.00610 q^{43} +0.397448 q^{45} +7.55848 q^{47} -6.66561 q^{49} +6.88521 q^{51} -5.08800 q^{53} +0.371405 q^{55} +4.60933 q^{57} +4.79877 q^{59} -0.119891 q^{61} -0.892809 q^{63} +0.317442 q^{65} +8.76927 q^{67} +7.65338 q^{69} -14.2487 q^{71} +10.5417 q^{73} -10.5170 q^{75} -0.834306 q^{77} -14.7249 q^{79} -11.2481 q^{81} -9.70080 q^{83} +0.831472 q^{85} +2.85674 q^{87} +15.5478 q^{89} -0.713087 q^{91} -6.20952 q^{93} +0.556632 q^{95} +17.4458 q^{97} +2.22758 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 23q - 2q^{3} + 8q^{5} - 2q^{7} + 45q^{9} + O(q^{10}) \) \( 23q - 2q^{3} + 8q^{5} - 2q^{7} + 45q^{9} - 8q^{11} + 8q^{13} - 7q^{15} + 19q^{17} + 9q^{19} + 9q^{21} - 21q^{23} + 65q^{25} - 5q^{27} + 10q^{29} + 9q^{31} + 34q^{33} - 12q^{35} + 11q^{37} + 9q^{39} + 35q^{41} + 9q^{43} + 29q^{45} - 37q^{47} + 77q^{49} + 17q^{51} + 38q^{53} + 20q^{55} + 51q^{57} - 17q^{59} - 22q^{63} + 41q^{65} - 9q^{67} + 8q^{69} - 13q^{71} + 41q^{73} - 25q^{75} + 36q^{77} + 36q^{79} + 127q^{81} - 29q^{83} + 34q^{85} - 10q^{87} + 36q^{89} + 6q^{91} + 36q^{93} - 25q^{95} + 40q^{97} - 19q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 2.13165 1.23071 0.615356 0.788250i \(-0.289012\pi\)
0.615356 + 0.788250i \(0.289012\pi\)
\(4\) 0 0
\(5\) 0.257423 0.115123 0.0575615 0.998342i \(-0.481667\pi\)
0.0575615 + 0.998342i \(0.481667\pi\)
\(6\) 0 0
\(7\) −0.578263 −0.218563 −0.109281 0.994011i \(-0.534855\pi\)
−0.109281 + 0.994011i \(0.534855\pi\)
\(8\) 0 0
\(9\) 1.54395 0.514650
\(10\) 0 0
\(11\) 1.44278 0.435015 0.217507 0.976059i \(-0.430207\pi\)
0.217507 + 0.976059i \(0.430207\pi\)
\(12\) 0 0
\(13\) 1.23315 0.342015 0.171008 0.985270i \(-0.445298\pi\)
0.171008 + 0.985270i \(0.445298\pi\)
\(14\) 0 0
\(15\) 0.548737 0.141683
\(16\) 0 0
\(17\) 3.22998 0.783386 0.391693 0.920096i \(-0.371890\pi\)
0.391693 + 0.920096i \(0.371890\pi\)
\(18\) 0 0
\(19\) 2.16232 0.496071 0.248036 0.968751i \(-0.420215\pi\)
0.248036 + 0.968751i \(0.420215\pi\)
\(20\) 0 0
\(21\) −1.23266 −0.268988
\(22\) 0 0
\(23\) 3.59035 0.748639 0.374320 0.927300i \(-0.377876\pi\)
0.374320 + 0.927300i \(0.377876\pi\)
\(24\) 0 0
\(25\) −4.93373 −0.986747
\(26\) 0 0
\(27\) −3.10379 −0.597325
\(28\) 0 0
\(29\) 1.34015 0.248860 0.124430 0.992228i \(-0.460290\pi\)
0.124430 + 0.992228i \(0.460290\pi\)
\(30\) 0 0
\(31\) −2.91300 −0.523191 −0.261595 0.965178i \(-0.584249\pi\)
−0.261595 + 0.965178i \(0.584249\pi\)
\(32\) 0 0
\(33\) 3.07551 0.535377
\(34\) 0 0
\(35\) −0.148858 −0.0251616
\(36\) 0 0
\(37\) 7.43825 1.22284 0.611421 0.791306i \(-0.290598\pi\)
0.611421 + 0.791306i \(0.290598\pi\)
\(38\) 0 0
\(39\) 2.62866 0.420922
\(40\) 0 0
\(41\) 9.61132 1.50104 0.750518 0.660850i \(-0.229804\pi\)
0.750518 + 0.660850i \(0.229804\pi\)
\(42\) 0 0
\(43\) 4.00610 0.610925 0.305462 0.952204i \(-0.401189\pi\)
0.305462 + 0.952204i \(0.401189\pi\)
\(44\) 0 0
\(45\) 0.397448 0.0592481
\(46\) 0 0
\(47\) 7.55848 1.10252 0.551259 0.834334i \(-0.314148\pi\)
0.551259 + 0.834334i \(0.314148\pi\)
\(48\) 0 0
\(49\) −6.66561 −0.952230
\(50\) 0 0
\(51\) 6.88521 0.964122
\(52\) 0 0
\(53\) −5.08800 −0.698890 −0.349445 0.936957i \(-0.613630\pi\)
−0.349445 + 0.936957i \(0.613630\pi\)
\(54\) 0 0
\(55\) 0.371405 0.0500802
\(56\) 0 0
\(57\) 4.60933 0.610520
\(58\) 0 0
\(59\) 4.79877 0.624747 0.312374 0.949959i \(-0.398876\pi\)
0.312374 + 0.949959i \(0.398876\pi\)
\(60\) 0 0
\(61\) −0.119891 −0.0153504 −0.00767522 0.999971i \(-0.502443\pi\)
−0.00767522 + 0.999971i \(0.502443\pi\)
\(62\) 0 0
\(63\) −0.892809 −0.112483
\(64\) 0 0
\(65\) 0.317442 0.0393738
\(66\) 0 0
\(67\) 8.76927 1.07134 0.535668 0.844429i \(-0.320060\pi\)
0.535668 + 0.844429i \(0.320060\pi\)
\(68\) 0 0
\(69\) 7.65338 0.921359
\(70\) 0 0
\(71\) −14.2487 −1.69101 −0.845504 0.533969i \(-0.820700\pi\)
−0.845504 + 0.533969i \(0.820700\pi\)
\(72\) 0 0
\(73\) 10.5417 1.23381 0.616905 0.787038i \(-0.288386\pi\)
0.616905 + 0.787038i \(0.288386\pi\)
\(74\) 0 0
\(75\) −10.5170 −1.21440
\(76\) 0 0
\(77\) −0.834306 −0.0950780
\(78\) 0 0
\(79\) −14.7249 −1.65669 −0.828343 0.560222i \(-0.810716\pi\)
−0.828343 + 0.560222i \(0.810716\pi\)
\(80\) 0 0
\(81\) −11.2481 −1.24979
\(82\) 0 0
\(83\) −9.70080 −1.06480 −0.532401 0.846492i \(-0.678710\pi\)
−0.532401 + 0.846492i \(0.678710\pi\)
\(84\) 0 0
\(85\) 0.831472 0.0901858
\(86\) 0 0
\(87\) 2.85674 0.306275
\(88\) 0 0
\(89\) 15.5478 1.64807 0.824034 0.566540i \(-0.191718\pi\)
0.824034 + 0.566540i \(0.191718\pi\)
\(90\) 0 0
\(91\) −0.713087 −0.0747518
\(92\) 0 0
\(93\) −6.20952 −0.643897
\(94\) 0 0
\(95\) 0.556632 0.0571092
\(96\) 0 0
\(97\) 17.4458 1.77135 0.885676 0.464303i \(-0.153695\pi\)
0.885676 + 0.464303i \(0.153695\pi\)
\(98\) 0 0
\(99\) 2.22758 0.223880
\(100\) 0 0
\(101\) 11.4484 1.13916 0.569580 0.821936i \(-0.307106\pi\)
0.569580 + 0.821936i \(0.307106\pi\)
\(102\) 0 0
\(103\) −0.147959 −0.0145789 −0.00728943 0.999973i \(-0.502320\pi\)
−0.00728943 + 0.999973i \(0.502320\pi\)
\(104\) 0 0
\(105\) −0.317314 −0.0309667
\(106\) 0 0
\(107\) 0.777070 0.0751221 0.0375611 0.999294i \(-0.488041\pi\)
0.0375611 + 0.999294i \(0.488041\pi\)
\(108\) 0 0
\(109\) −2.23762 −0.214325 −0.107162 0.994242i \(-0.534176\pi\)
−0.107162 + 0.994242i \(0.534176\pi\)
\(110\) 0 0
\(111\) 15.8558 1.50496
\(112\) 0 0
\(113\) 10.2350 0.962831 0.481416 0.876492i \(-0.340123\pi\)
0.481416 + 0.876492i \(0.340123\pi\)
\(114\) 0 0
\(115\) 0.924238 0.0861857
\(116\) 0 0
\(117\) 1.90393 0.176018
\(118\) 0 0
\(119\) −1.86778 −0.171219
\(120\) 0 0
\(121\) −8.91839 −0.810762
\(122\) 0 0
\(123\) 20.4880 1.84734
\(124\) 0 0
\(125\) −2.55717 −0.228720
\(126\) 0 0
\(127\) −18.6170 −1.65200 −0.825998 0.563674i \(-0.809388\pi\)
−0.825998 + 0.563674i \(0.809388\pi\)
\(128\) 0 0
\(129\) 8.53962 0.751872
\(130\) 0 0
\(131\) 6.50800 0.568607 0.284303 0.958734i \(-0.408238\pi\)
0.284303 + 0.958734i \(0.408238\pi\)
\(132\) 0 0
\(133\) −1.25039 −0.108423
\(134\) 0 0
\(135\) −0.798988 −0.0687659
\(136\) 0 0
\(137\) 18.2925 1.56283 0.781415 0.624012i \(-0.214498\pi\)
0.781415 + 0.624012i \(0.214498\pi\)
\(138\) 0 0
\(139\) 12.7384 1.08046 0.540231 0.841517i \(-0.318337\pi\)
0.540231 + 0.841517i \(0.318337\pi\)
\(140\) 0 0
\(141\) 16.1121 1.35688
\(142\) 0 0
\(143\) 1.77917 0.148782
\(144\) 0 0
\(145\) 0.344986 0.0286495
\(146\) 0 0
\(147\) −14.2088 −1.17192
\(148\) 0 0
\(149\) 3.89636 0.319203 0.159601 0.987182i \(-0.448979\pi\)
0.159601 + 0.987182i \(0.448979\pi\)
\(150\) 0 0
\(151\) −14.6934 −1.19573 −0.597865 0.801597i \(-0.703984\pi\)
−0.597865 + 0.801597i \(0.703984\pi\)
\(152\) 0 0
\(153\) 4.98694 0.403170
\(154\) 0 0
\(155\) −0.749874 −0.0602313
\(156\) 0 0
\(157\) 9.49373 0.757682 0.378841 0.925462i \(-0.376323\pi\)
0.378841 + 0.925462i \(0.376323\pi\)
\(158\) 0 0
\(159\) −10.8458 −0.860132
\(160\) 0 0
\(161\) −2.07617 −0.163625
\(162\) 0 0
\(163\) 16.6323 1.30274 0.651369 0.758761i \(-0.274195\pi\)
0.651369 + 0.758761i \(0.274195\pi\)
\(164\) 0 0
\(165\) 0.791707 0.0616343
\(166\) 0 0
\(167\) −5.05080 −0.390843 −0.195421 0.980719i \(-0.562607\pi\)
−0.195421 + 0.980719i \(0.562607\pi\)
\(168\) 0 0
\(169\) −11.4793 −0.883026
\(170\) 0 0
\(171\) 3.33852 0.255303
\(172\) 0 0
\(173\) 5.19947 0.395308 0.197654 0.980272i \(-0.436668\pi\)
0.197654 + 0.980272i \(0.436668\pi\)
\(174\) 0 0
\(175\) 2.85299 0.215666
\(176\) 0 0
\(177\) 10.2293 0.768883
\(178\) 0 0
\(179\) −4.38408 −0.327681 −0.163841 0.986487i \(-0.552388\pi\)
−0.163841 + 0.986487i \(0.552388\pi\)
\(180\) 0 0
\(181\) 12.9053 0.959241 0.479621 0.877476i \(-0.340774\pi\)
0.479621 + 0.877476i \(0.340774\pi\)
\(182\) 0 0
\(183\) −0.255566 −0.0188920
\(184\) 0 0
\(185\) 1.91478 0.140777
\(186\) 0 0
\(187\) 4.66016 0.340784
\(188\) 0 0
\(189\) 1.79481 0.130553
\(190\) 0 0
\(191\) −14.6014 −1.05652 −0.528261 0.849082i \(-0.677156\pi\)
−0.528261 + 0.849082i \(0.677156\pi\)
\(192\) 0 0
\(193\) 0.612232 0.0440694 0.0220347 0.999757i \(-0.492986\pi\)
0.0220347 + 0.999757i \(0.492986\pi\)
\(194\) 0 0
\(195\) 0.676677 0.0484578
\(196\) 0 0
\(197\) −11.7607 −0.837914 −0.418957 0.908006i \(-0.637604\pi\)
−0.418957 + 0.908006i \(0.637604\pi\)
\(198\) 0 0
\(199\) 5.95001 0.421785 0.210892 0.977509i \(-0.432363\pi\)
0.210892 + 0.977509i \(0.432363\pi\)
\(200\) 0 0
\(201\) 18.6930 1.31851
\(202\) 0 0
\(203\) −0.774961 −0.0543916
\(204\) 0 0
\(205\) 2.47417 0.172804
\(206\) 0 0
\(207\) 5.54332 0.385287
\(208\) 0 0
\(209\) 3.11976 0.215798
\(210\) 0 0
\(211\) −23.4565 −1.61481 −0.807407 0.589995i \(-0.799130\pi\)
−0.807407 + 0.589995i \(0.799130\pi\)
\(212\) 0 0
\(213\) −30.3733 −2.08114
\(214\) 0 0
\(215\) 1.03126 0.0703315
\(216\) 0 0
\(217\) 1.68448 0.114350
\(218\) 0 0
\(219\) 22.4712 1.51846
\(220\) 0 0
\(221\) 3.98306 0.267930
\(222\) 0 0
\(223\) 13.7654 0.921800 0.460900 0.887452i \(-0.347527\pi\)
0.460900 + 0.887452i \(0.347527\pi\)
\(224\) 0 0
\(225\) −7.61744 −0.507829
\(226\) 0 0
\(227\) −25.3420 −1.68201 −0.841005 0.541028i \(-0.818035\pi\)
−0.841005 + 0.541028i \(0.818035\pi\)
\(228\) 0 0
\(229\) −8.16364 −0.539468 −0.269734 0.962935i \(-0.586936\pi\)
−0.269734 + 0.962935i \(0.586936\pi\)
\(230\) 0 0
\(231\) −1.77845 −0.117014
\(232\) 0 0
\(233\) 4.62470 0.302974 0.151487 0.988459i \(-0.451594\pi\)
0.151487 + 0.988459i \(0.451594\pi\)
\(234\) 0 0
\(235\) 1.94573 0.126925
\(236\) 0 0
\(237\) −31.3885 −2.03890
\(238\) 0 0
\(239\) 4.88042 0.315688 0.157844 0.987464i \(-0.449546\pi\)
0.157844 + 0.987464i \(0.449546\pi\)
\(240\) 0 0
\(241\) 0.652332 0.0420204 0.0210102 0.999779i \(-0.493312\pi\)
0.0210102 + 0.999779i \(0.493312\pi\)
\(242\) 0 0
\(243\) −14.6656 −0.940800
\(244\) 0 0
\(245\) −1.71588 −0.109624
\(246\) 0 0
\(247\) 2.66648 0.169664
\(248\) 0 0
\(249\) −20.6788 −1.31046
\(250\) 0 0
\(251\) 1.00000 0.0631194
\(252\) 0 0
\(253\) 5.18008 0.325669
\(254\) 0 0
\(255\) 1.77241 0.110993
\(256\) 0 0
\(257\) −21.6636 −1.35134 −0.675670 0.737205i \(-0.736145\pi\)
−0.675670 + 0.737205i \(0.736145\pi\)
\(258\) 0 0
\(259\) −4.30127 −0.267268
\(260\) 0 0
\(261\) 2.06913 0.128076
\(262\) 0 0
\(263\) −24.1926 −1.49178 −0.745889 0.666070i \(-0.767975\pi\)
−0.745889 + 0.666070i \(0.767975\pi\)
\(264\) 0 0
\(265\) −1.30977 −0.0804584
\(266\) 0 0
\(267\) 33.1426 2.02830
\(268\) 0 0
\(269\) −16.0347 −0.977652 −0.488826 0.872381i \(-0.662575\pi\)
−0.488826 + 0.872381i \(0.662575\pi\)
\(270\) 0 0
\(271\) 28.6525 1.74051 0.870257 0.492598i \(-0.163953\pi\)
0.870257 + 0.492598i \(0.163953\pi\)
\(272\) 0 0
\(273\) −1.52005 −0.0919979
\(274\) 0 0
\(275\) −7.11829 −0.429249
\(276\) 0 0
\(277\) 19.8294 1.19143 0.595717 0.803194i \(-0.296868\pi\)
0.595717 + 0.803194i \(0.296868\pi\)
\(278\) 0 0
\(279\) −4.49753 −0.269260
\(280\) 0 0
\(281\) 7.04601 0.420330 0.210165 0.977666i \(-0.432600\pi\)
0.210165 + 0.977666i \(0.432600\pi\)
\(282\) 0 0
\(283\) −16.2260 −0.964534 −0.482267 0.876024i \(-0.660186\pi\)
−0.482267 + 0.876024i \(0.660186\pi\)
\(284\) 0 0
\(285\) 1.18655 0.0702850
\(286\) 0 0
\(287\) −5.55787 −0.328070
\(288\) 0 0
\(289\) −6.56721 −0.386306
\(290\) 0 0
\(291\) 37.1884 2.18002
\(292\) 0 0
\(293\) 9.06228 0.529424 0.264712 0.964327i \(-0.414723\pi\)
0.264712 + 0.964327i \(0.414723\pi\)
\(294\) 0 0
\(295\) 1.23531 0.0719228
\(296\) 0 0
\(297\) −4.47809 −0.259845
\(298\) 0 0
\(299\) 4.42745 0.256046
\(300\) 0 0
\(301\) −2.31658 −0.133525
\(302\) 0 0
\(303\) 24.4041 1.40198
\(304\) 0 0
\(305\) −0.0308626 −0.00176719
\(306\) 0 0
\(307\) 23.0105 1.31328 0.656638 0.754206i \(-0.271978\pi\)
0.656638 + 0.754206i \(0.271978\pi\)
\(308\) 0 0
\(309\) −0.315398 −0.0179424
\(310\) 0 0
\(311\) 9.22635 0.523179 0.261589 0.965179i \(-0.415753\pi\)
0.261589 + 0.965179i \(0.415753\pi\)
\(312\) 0 0
\(313\) 11.6420 0.658045 0.329022 0.944322i \(-0.393281\pi\)
0.329022 + 0.944322i \(0.393281\pi\)
\(314\) 0 0
\(315\) −0.229830 −0.0129494
\(316\) 0 0
\(317\) −11.7025 −0.657276 −0.328638 0.944456i \(-0.606590\pi\)
−0.328638 + 0.944456i \(0.606590\pi\)
\(318\) 0 0
\(319\) 1.93355 0.108258
\(320\) 0 0
\(321\) 1.65644 0.0924537
\(322\) 0 0
\(323\) 6.98427 0.388615
\(324\) 0 0
\(325\) −6.08405 −0.337482
\(326\) 0 0
\(327\) −4.76983 −0.263772
\(328\) 0 0
\(329\) −4.37079 −0.240969
\(330\) 0 0
\(331\) 2.26578 0.124539 0.0622694 0.998059i \(-0.480166\pi\)
0.0622694 + 0.998059i \(0.480166\pi\)
\(332\) 0 0
\(333\) 11.4843 0.629336
\(334\) 0 0
\(335\) 2.25741 0.123336
\(336\) 0 0
\(337\) −8.58164 −0.467472 −0.233736 0.972300i \(-0.575095\pi\)
−0.233736 + 0.972300i \(0.575095\pi\)
\(338\) 0 0
\(339\) 21.8176 1.18497
\(340\) 0 0
\(341\) −4.20282 −0.227596
\(342\) 0 0
\(343\) 7.90232 0.426685
\(344\) 0 0
\(345\) 1.97016 0.106070
\(346\) 0 0
\(347\) −17.8709 −0.959361 −0.479681 0.877443i \(-0.659248\pi\)
−0.479681 + 0.877443i \(0.659248\pi\)
\(348\) 0 0
\(349\) −22.8884 −1.22519 −0.612594 0.790398i \(-0.709874\pi\)
−0.612594 + 0.790398i \(0.709874\pi\)
\(350\) 0 0
\(351\) −3.82745 −0.204294
\(352\) 0 0
\(353\) −12.4512 −0.662710 −0.331355 0.943506i \(-0.607506\pi\)
−0.331355 + 0.943506i \(0.607506\pi\)
\(354\) 0 0
\(355\) −3.66794 −0.194674
\(356\) 0 0
\(357\) −3.98146 −0.210721
\(358\) 0 0
\(359\) −25.4272 −1.34200 −0.670998 0.741459i \(-0.734134\pi\)
−0.670998 + 0.741459i \(0.734134\pi\)
\(360\) 0 0
\(361\) −14.3244 −0.753913
\(362\) 0 0
\(363\) −19.0109 −0.997814
\(364\) 0 0
\(365\) 2.71367 0.142040
\(366\) 0 0
\(367\) −34.2480 −1.78773 −0.893866 0.448335i \(-0.852017\pi\)
−0.893866 + 0.448335i \(0.852017\pi\)
\(368\) 0 0
\(369\) 14.8394 0.772508
\(370\) 0 0
\(371\) 2.94220 0.152751
\(372\) 0 0
\(373\) 25.8031 1.33603 0.668017 0.744146i \(-0.267143\pi\)
0.668017 + 0.744146i \(0.267143\pi\)
\(374\) 0 0
\(375\) −5.45101 −0.281489
\(376\) 0 0
\(377\) 1.65261 0.0851139
\(378\) 0 0
\(379\) 4.65289 0.239003 0.119502 0.992834i \(-0.461870\pi\)
0.119502 + 0.992834i \(0.461870\pi\)
\(380\) 0 0
\(381\) −39.6851 −2.03313
\(382\) 0 0
\(383\) 10.8385 0.553823 0.276912 0.960895i \(-0.410689\pi\)
0.276912 + 0.960895i \(0.410689\pi\)
\(384\) 0 0
\(385\) −0.214770 −0.0109457
\(386\) 0 0
\(387\) 6.18522 0.314413
\(388\) 0 0
\(389\) −31.2682 −1.58536 −0.792679 0.609639i \(-0.791314\pi\)
−0.792679 + 0.609639i \(0.791314\pi\)
\(390\) 0 0
\(391\) 11.5968 0.586474
\(392\) 0 0
\(393\) 13.8728 0.699791
\(394\) 0 0
\(395\) −3.79054 −0.190723
\(396\) 0 0
\(397\) −18.4742 −0.927195 −0.463597 0.886046i \(-0.653442\pi\)
−0.463597 + 0.886046i \(0.653442\pi\)
\(398\) 0 0
\(399\) −2.66540 −0.133437
\(400\) 0 0
\(401\) 10.3634 0.517525 0.258762 0.965941i \(-0.416685\pi\)
0.258762 + 0.965941i \(0.416685\pi\)
\(402\) 0 0
\(403\) −3.59218 −0.178939
\(404\) 0 0
\(405\) −2.89551 −0.143879
\(406\) 0 0
\(407\) 10.7318 0.531954
\(408\) 0 0
\(409\) −33.5152 −1.65722 −0.828611 0.559825i \(-0.810868\pi\)
−0.828611 + 0.559825i \(0.810868\pi\)
\(410\) 0 0
\(411\) 38.9932 1.92339
\(412\) 0 0
\(413\) −2.77495 −0.136546
\(414\) 0 0
\(415\) −2.49721 −0.122583
\(416\) 0 0
\(417\) 27.1540 1.32974
\(418\) 0 0
\(419\) −8.01559 −0.391587 −0.195794 0.980645i \(-0.562728\pi\)
−0.195794 + 0.980645i \(0.562728\pi\)
\(420\) 0 0
\(421\) −13.1527 −0.641025 −0.320512 0.947244i \(-0.603855\pi\)
−0.320512 + 0.947244i \(0.603855\pi\)
\(422\) 0 0
\(423\) 11.6699 0.567411
\(424\) 0 0
\(425\) −15.9359 −0.773004
\(426\) 0 0
\(427\) 0.0693284 0.00335504
\(428\) 0 0
\(429\) 3.79257 0.183107
\(430\) 0 0
\(431\) −2.41216 −0.116190 −0.0580948 0.998311i \(-0.518503\pi\)
−0.0580948 + 0.998311i \(0.518503\pi\)
\(432\) 0 0
\(433\) −15.1889 −0.729930 −0.364965 0.931021i \(-0.618919\pi\)
−0.364965 + 0.931021i \(0.618919\pi\)
\(434\) 0 0
\(435\) 0.735391 0.0352593
\(436\) 0 0
\(437\) 7.76350 0.371378
\(438\) 0 0
\(439\) 5.98083 0.285449 0.142725 0.989762i \(-0.454414\pi\)
0.142725 + 0.989762i \(0.454414\pi\)
\(440\) 0 0
\(441\) −10.2914 −0.490066
\(442\) 0 0
\(443\) 22.3495 1.06186 0.530928 0.847417i \(-0.321843\pi\)
0.530928 + 0.847417i \(0.321843\pi\)
\(444\) 0 0
\(445\) 4.00237 0.189731
\(446\) 0 0
\(447\) 8.30570 0.392846
\(448\) 0 0
\(449\) −13.5528 −0.639598 −0.319799 0.947485i \(-0.603615\pi\)
−0.319799 + 0.947485i \(0.603615\pi\)
\(450\) 0 0
\(451\) 13.8670 0.652972
\(452\) 0 0
\(453\) −31.3212 −1.47160
\(454\) 0 0
\(455\) −0.183565 −0.00860565
\(456\) 0 0
\(457\) 8.19148 0.383181 0.191591 0.981475i \(-0.438635\pi\)
0.191591 + 0.981475i \(0.438635\pi\)
\(458\) 0 0
\(459\) −10.0252 −0.467936
\(460\) 0 0
\(461\) 13.1494 0.612430 0.306215 0.951962i \(-0.400937\pi\)
0.306215 + 0.951962i \(0.400937\pi\)
\(462\) 0 0
\(463\) −9.03105 −0.419708 −0.209854 0.977733i \(-0.567299\pi\)
−0.209854 + 0.977733i \(0.567299\pi\)
\(464\) 0 0
\(465\) −1.59847 −0.0741274
\(466\) 0 0
\(467\) −11.3433 −0.524908 −0.262454 0.964945i \(-0.584532\pi\)
−0.262454 + 0.964945i \(0.584532\pi\)
\(468\) 0 0
\(469\) −5.07094 −0.234154
\(470\) 0 0
\(471\) 20.2373 0.932488
\(472\) 0 0
\(473\) 5.77992 0.265761
\(474\) 0 0
\(475\) −10.6683 −0.489497
\(476\) 0 0
\(477\) −7.85562 −0.359684
\(478\) 0 0
\(479\) 5.01937 0.229341 0.114670 0.993404i \(-0.463419\pi\)
0.114670 + 0.993404i \(0.463419\pi\)
\(480\) 0 0
\(481\) 9.17251 0.418230
\(482\) 0 0
\(483\) −4.42567 −0.201375
\(484\) 0 0
\(485\) 4.49095 0.203924
\(486\) 0 0
\(487\) 2.51042 0.113758 0.0568789 0.998381i \(-0.481885\pi\)
0.0568789 + 0.998381i \(0.481885\pi\)
\(488\) 0 0
\(489\) 35.4542 1.60330
\(490\) 0 0
\(491\) 2.31426 0.104441 0.0522205 0.998636i \(-0.483370\pi\)
0.0522205 + 0.998636i \(0.483370\pi\)
\(492\) 0 0
\(493\) 4.32867 0.194954
\(494\) 0 0
\(495\) 0.573431 0.0257738
\(496\) 0 0
\(497\) 8.23948 0.369591
\(498\) 0 0
\(499\) 8.76208 0.392244 0.196122 0.980579i \(-0.437165\pi\)
0.196122 + 0.980579i \(0.437165\pi\)
\(500\) 0 0
\(501\) −10.7666 −0.481015
\(502\) 0 0
\(503\) 4.97063 0.221630 0.110815 0.993841i \(-0.464654\pi\)
0.110815 + 0.993841i \(0.464654\pi\)
\(504\) 0 0
\(505\) 2.94709 0.131144
\(506\) 0 0
\(507\) −24.4700 −1.08675
\(508\) 0 0
\(509\) −11.5632 −0.512529 −0.256265 0.966607i \(-0.582492\pi\)
−0.256265 + 0.966607i \(0.582492\pi\)
\(510\) 0 0
\(511\) −6.09586 −0.269665
\(512\) 0 0
\(513\) −6.71141 −0.296316
\(514\) 0 0
\(515\) −0.0380881 −0.00167836
\(516\) 0 0
\(517\) 10.9052 0.479611
\(518\) 0 0
\(519\) 11.0835 0.486511
\(520\) 0 0
\(521\) 22.1108 0.968691 0.484346 0.874877i \(-0.339058\pi\)
0.484346 + 0.874877i \(0.339058\pi\)
\(522\) 0 0
\(523\) −18.6154 −0.813993 −0.406997 0.913430i \(-0.633424\pi\)
−0.406997 + 0.913430i \(0.633424\pi\)
\(524\) 0 0
\(525\) 6.08160 0.265423
\(526\) 0 0
\(527\) −9.40895 −0.409860
\(528\) 0 0
\(529\) −10.1094 −0.439539
\(530\) 0 0
\(531\) 7.40907 0.321526
\(532\) 0 0
\(533\) 11.8522 0.513377
\(534\) 0 0
\(535\) 0.200036 0.00864829
\(536\) 0 0
\(537\) −9.34533 −0.403281
\(538\) 0 0
\(539\) −9.61701 −0.414234
\(540\) 0 0
\(541\) −36.3161 −1.56135 −0.780675 0.624937i \(-0.785124\pi\)
−0.780675 + 0.624937i \(0.785124\pi\)
\(542\) 0 0
\(543\) 27.5096 1.18055
\(544\) 0 0
\(545\) −0.576014 −0.0246737
\(546\) 0 0
\(547\) 2.47047 0.105630 0.0528148 0.998604i \(-0.483181\pi\)
0.0528148 + 0.998604i \(0.483181\pi\)
\(548\) 0 0
\(549\) −0.185105 −0.00790011
\(550\) 0 0
\(551\) 2.89784 0.123452
\(552\) 0 0
\(553\) 8.51489 0.362090
\(554\) 0 0
\(555\) 4.08164 0.173256
\(556\) 0 0
\(557\) −39.3494 −1.66729 −0.833644 0.552302i \(-0.813749\pi\)
−0.833644 + 0.552302i \(0.813749\pi\)
\(558\) 0 0
\(559\) 4.94014 0.208945
\(560\) 0 0
\(561\) 9.93384 0.419407
\(562\) 0 0
\(563\) 12.6798 0.534389 0.267195 0.963643i \(-0.413903\pi\)
0.267195 + 0.963643i \(0.413903\pi\)
\(564\) 0 0
\(565\) 2.63473 0.110844
\(566\) 0 0
\(567\) 6.50434 0.273157
\(568\) 0 0
\(569\) 39.6216 1.66102 0.830512 0.557000i \(-0.188048\pi\)
0.830512 + 0.557000i \(0.188048\pi\)
\(570\) 0 0
\(571\) 10.9909 0.459954 0.229977 0.973196i \(-0.426135\pi\)
0.229977 + 0.973196i \(0.426135\pi\)
\(572\) 0 0
\(573\) −31.1252 −1.30027
\(574\) 0 0
\(575\) −17.7138 −0.738717
\(576\) 0 0
\(577\) 22.5319 0.938017 0.469008 0.883194i \(-0.344611\pi\)
0.469008 + 0.883194i \(0.344611\pi\)
\(578\) 0 0
\(579\) 1.30507 0.0542367
\(580\) 0 0
\(581\) 5.60961 0.232726
\(582\) 0 0
\(583\) −7.34086 −0.304027
\(584\) 0 0
\(585\) 0.490115 0.0202638
\(586\) 0 0
\(587\) −39.4321 −1.62754 −0.813769 0.581189i \(-0.802588\pi\)
−0.813769 + 0.581189i \(0.802588\pi\)
\(588\) 0 0
\(589\) −6.29886 −0.259540
\(590\) 0 0
\(591\) −25.0697 −1.03123
\(592\) 0 0
\(593\) −41.9828 −1.72403 −0.862013 0.506887i \(-0.830796\pi\)
−0.862013 + 0.506887i \(0.830796\pi\)
\(594\) 0 0
\(595\) −0.480809 −0.0197113
\(596\) 0 0
\(597\) 12.6834 0.519096
\(598\) 0 0
\(599\) 15.8875 0.649146 0.324573 0.945861i \(-0.394779\pi\)
0.324573 + 0.945861i \(0.394779\pi\)
\(600\) 0 0
\(601\) 39.4266 1.60825 0.804123 0.594463i \(-0.202635\pi\)
0.804123 + 0.594463i \(0.202635\pi\)
\(602\) 0 0
\(603\) 13.5393 0.551364
\(604\) 0 0
\(605\) −2.29580 −0.0933374
\(606\) 0 0
\(607\) −5.29224 −0.214805 −0.107403 0.994216i \(-0.534253\pi\)
−0.107403 + 0.994216i \(0.534253\pi\)
\(608\) 0 0
\(609\) −1.65195 −0.0669403
\(610\) 0 0
\(611\) 9.32077 0.377078
\(612\) 0 0
\(613\) 34.1195 1.37808 0.689038 0.724725i \(-0.258033\pi\)
0.689038 + 0.724725i \(0.258033\pi\)
\(614\) 0 0
\(615\) 5.27408 0.212672
\(616\) 0 0
\(617\) 29.4738 1.18657 0.593285 0.804992i \(-0.297831\pi\)
0.593285 + 0.804992i \(0.297831\pi\)
\(618\) 0 0
\(619\) 32.8210 1.31919 0.659593 0.751623i \(-0.270729\pi\)
0.659593 + 0.751623i \(0.270729\pi\)
\(620\) 0 0
\(621\) −11.1437 −0.447181
\(622\) 0 0
\(623\) −8.99074 −0.360206
\(624\) 0 0
\(625\) 24.0104 0.960416
\(626\) 0 0
\(627\) 6.65025 0.265585
\(628\) 0 0
\(629\) 24.0254 0.957957
\(630\) 0 0
\(631\) 13.2532 0.527601 0.263801 0.964577i \(-0.415024\pi\)
0.263801 + 0.964577i \(0.415024\pi\)
\(632\) 0 0
\(633\) −50.0012 −1.98737
\(634\) 0 0
\(635\) −4.79245 −0.190183
\(636\) 0 0
\(637\) −8.21972 −0.325677
\(638\) 0 0
\(639\) −21.9993 −0.870278
\(640\) 0 0
\(641\) 1.34546 0.0531426 0.0265713 0.999647i \(-0.491541\pi\)
0.0265713 + 0.999647i \(0.491541\pi\)
\(642\) 0 0
\(643\) 12.2114 0.481569 0.240785 0.970579i \(-0.422595\pi\)
0.240785 + 0.970579i \(0.422595\pi\)
\(644\) 0 0
\(645\) 2.19830 0.0865578
\(646\) 0 0
\(647\) −28.5704 −1.12322 −0.561608 0.827403i \(-0.689817\pi\)
−0.561608 + 0.827403i \(0.689817\pi\)
\(648\) 0 0
\(649\) 6.92358 0.271774
\(650\) 0 0
\(651\) 3.59073 0.140732
\(652\) 0 0
\(653\) 15.3953 0.602463 0.301231 0.953551i \(-0.402602\pi\)
0.301231 + 0.953551i \(0.402602\pi\)
\(654\) 0 0
\(655\) 1.67531 0.0654597
\(656\) 0 0
\(657\) 16.2758 0.634981
\(658\) 0 0
\(659\) −24.7538 −0.964272 −0.482136 0.876096i \(-0.660139\pi\)
−0.482136 + 0.876096i \(0.660139\pi\)
\(660\) 0 0
\(661\) −19.0121 −0.739487 −0.369743 0.929134i \(-0.620554\pi\)
−0.369743 + 0.929134i \(0.620554\pi\)
\(662\) 0 0
\(663\) 8.49052 0.329744
\(664\) 0 0
\(665\) −0.321879 −0.0124820
\(666\) 0 0
\(667\) 4.81162 0.186306
\(668\) 0 0
\(669\) 29.3431 1.13447
\(670\) 0 0
\(671\) −0.172976 −0.00667767
\(672\) 0 0
\(673\) 16.1863 0.623935 0.311967 0.950093i \(-0.399012\pi\)
0.311967 + 0.950093i \(0.399012\pi\)
\(674\) 0 0
\(675\) 15.3133 0.589409
\(676\) 0 0
\(677\) 34.9382 1.34278 0.671392 0.741102i \(-0.265697\pi\)
0.671392 + 0.741102i \(0.265697\pi\)
\(678\) 0 0
\(679\) −10.0883 −0.387152
\(680\) 0 0
\(681\) −54.0204 −2.07007
\(682\) 0 0
\(683\) −39.9757 −1.52963 −0.764813 0.644252i \(-0.777169\pi\)
−0.764813 + 0.644252i \(0.777169\pi\)
\(684\) 0 0
\(685\) 4.70890 0.179918
\(686\) 0 0
\(687\) −17.4021 −0.663930
\(688\) 0 0
\(689\) −6.27428 −0.239031
\(690\) 0 0
\(691\) 3.27679 0.124655 0.0623275 0.998056i \(-0.480148\pi\)
0.0623275 + 0.998056i \(0.480148\pi\)
\(692\) 0 0
\(693\) −1.28813 −0.0489319
\(694\) 0 0
\(695\) 3.27917 0.124386
\(696\) 0 0
\(697\) 31.0444 1.17589
\(698\) 0 0
\(699\) 9.85826 0.372873
\(700\) 0 0
\(701\) −22.9428 −0.866538 −0.433269 0.901265i \(-0.642640\pi\)
−0.433269 + 0.901265i \(0.642640\pi\)
\(702\) 0 0
\(703\) 16.0839 0.606616
\(704\) 0 0
\(705\) 4.14762 0.156208
\(706\) 0 0
\(707\) −6.62020 −0.248978
\(708\) 0 0
\(709\) −51.3035 −1.92674 −0.963371 0.268173i \(-0.913580\pi\)
−0.963371 + 0.268173i \(0.913580\pi\)
\(710\) 0 0
\(711\) −22.7346 −0.852614
\(712\) 0 0
\(713\) −10.4587 −0.391681
\(714\) 0 0
\(715\) 0.457999 0.0171282
\(716\) 0 0
\(717\) 10.4034 0.388521
\(718\) 0 0
\(719\) 4.63057 0.172691 0.0863456 0.996265i \(-0.472481\pi\)
0.0863456 + 0.996265i \(0.472481\pi\)
\(720\) 0 0
\(721\) 0.0855594 0.00318640
\(722\) 0 0
\(723\) 1.39055 0.0517149
\(724\) 0 0
\(725\) −6.61196 −0.245562
\(726\) 0 0
\(727\) 0.697832 0.0258812 0.0129406 0.999916i \(-0.495881\pi\)
0.0129406 + 0.999916i \(0.495881\pi\)
\(728\) 0 0
\(729\) 2.48218 0.0919327
\(730\) 0 0
\(731\) 12.9396 0.478590
\(732\) 0 0
\(733\) −13.5235 −0.499502 −0.249751 0.968310i \(-0.580349\pi\)
−0.249751 + 0.968310i \(0.580349\pi\)
\(734\) 0 0
\(735\) −3.65767 −0.134915
\(736\) 0 0
\(737\) 12.6521 0.466047
\(738\) 0 0
\(739\) −49.4982 −1.82082 −0.910410 0.413708i \(-0.864233\pi\)
−0.910410 + 0.413708i \(0.864233\pi\)
\(740\) 0 0
\(741\) 5.68401 0.208807
\(742\) 0 0
\(743\) −28.6466 −1.05094 −0.525472 0.850811i \(-0.676111\pi\)
−0.525472 + 0.850811i \(0.676111\pi\)
\(744\) 0 0
\(745\) 1.00301 0.0367476
\(746\) 0 0
\(747\) −14.9776 −0.548000
\(748\) 0 0
\(749\) −0.449350 −0.0164189
\(750\) 0 0
\(751\) 12.6351 0.461061 0.230530 0.973065i \(-0.425954\pi\)
0.230530 + 0.973065i \(0.425954\pi\)
\(752\) 0 0
\(753\) 2.13165 0.0776818
\(754\) 0 0
\(755\) −3.78241 −0.137656
\(756\) 0 0
\(757\) 27.6027 1.00324 0.501619 0.865089i \(-0.332738\pi\)
0.501619 + 0.865089i \(0.332738\pi\)
\(758\) 0 0
\(759\) 11.0421 0.400805
\(760\) 0 0
\(761\) 15.9504 0.578201 0.289100 0.957299i \(-0.406644\pi\)
0.289100 + 0.957299i \(0.406644\pi\)
\(762\) 0 0
\(763\) 1.29393 0.0468434
\(764\) 0 0
\(765\) 1.28375 0.0464141
\(766\) 0 0
\(767\) 5.91762 0.213673
\(768\) 0 0
\(769\) 42.2253 1.52268 0.761342 0.648350i \(-0.224541\pi\)
0.761342 + 0.648350i \(0.224541\pi\)
\(770\) 0 0
\(771\) −46.1793 −1.66311
\(772\) 0 0
\(773\) 14.9447 0.537523 0.268761 0.963207i \(-0.413386\pi\)
0.268761 + 0.963207i \(0.413386\pi\)
\(774\) 0 0
\(775\) 14.3720 0.516257
\(776\) 0 0
\(777\) −9.16881 −0.328929
\(778\) 0 0
\(779\) 20.7828 0.744620
\(780\) 0 0
\(781\) −20.5577 −0.735613
\(782\) 0 0
\(783\) −4.15956 −0.148650
\(784\) 0 0
\(785\) 2.44390 0.0872267
\(786\) 0 0
\(787\) 19.8262 0.706727 0.353364 0.935486i \(-0.385038\pi\)
0.353364 + 0.935486i \(0.385038\pi\)
\(788\) 0 0
\(789\) −51.5702 −1.83595
\(790\) 0 0
\(791\) −5.91854 −0.210439
\(792\) 0 0
\(793\) −0.147844 −0.00525008
\(794\) 0 0
\(795\) −2.79197 −0.0990210
\(796\) 0 0
\(797\) 12.3151 0.436224 0.218112 0.975924i \(-0.430010\pi\)
0.218112 + 0.975924i \(0.430010\pi\)
\(798\) 0 0
\(799\) 24.4138 0.863697
\(800\) 0 0
\(801\) 24.0051 0.848179
\(802\) 0 0
\(803\) 15.2093 0.536725
\(804\) 0 0
\(805\) −0.534453 −0.0188370
\(806\) 0 0
\(807\) −34.1804 −1.20321
\(808\) 0 0
\(809\) 1.95284 0.0686581 0.0343291 0.999411i \(-0.489071\pi\)
0.0343291 + 0.999411i \(0.489071\pi\)
\(810\) 0 0
\(811\) 4.28269 0.150386 0.0751928 0.997169i \(-0.476043\pi\)
0.0751928 + 0.997169i \(0.476043\pi\)
\(812\) 0 0
\(813\) 61.0772 2.14207
\(814\) 0 0
\(815\) 4.28153 0.149975
\(816\) 0 0
\(817\) 8.66249 0.303062
\(818\) 0 0
\(819\) −1.10097 −0.0384710
\(820\) 0 0
\(821\) −10.1730 −0.355040 −0.177520 0.984117i \(-0.556808\pi\)
−0.177520 + 0.984117i \(0.556808\pi\)
\(822\) 0 0
\(823\) 9.65644 0.336602 0.168301 0.985736i \(-0.446172\pi\)
0.168301 + 0.985736i \(0.446172\pi\)
\(824\) 0 0
\(825\) −15.1737 −0.528282
\(826\) 0 0
\(827\) −55.4357 −1.92769 −0.963845 0.266464i \(-0.914145\pi\)
−0.963845 + 0.266464i \(0.914145\pi\)
\(828\) 0 0
\(829\) −20.0529 −0.696465 −0.348232 0.937408i \(-0.613218\pi\)
−0.348232 + 0.937408i \(0.613218\pi\)
\(830\) 0 0
\(831\) 42.2695 1.46631
\(832\) 0 0
\(833\) −21.5298 −0.745964
\(834\) 0 0
\(835\) −1.30019 −0.0449950
\(836\) 0 0
\(837\) 9.04136 0.312515
\(838\) 0 0
\(839\) −33.8398 −1.16828 −0.584139 0.811654i \(-0.698568\pi\)
−0.584139 + 0.811654i \(0.698568\pi\)
\(840\) 0 0
\(841\) −27.2040 −0.938069
\(842\) 0 0
\(843\) 15.0197 0.517305
\(844\) 0 0
\(845\) −2.95504 −0.101657
\(846\) 0 0
\(847\) 5.15717 0.177202
\(848\) 0 0
\(849\) −34.5882 −1.18706
\(850\) 0 0
\(851\) 26.7059 0.915467
\(852\) 0 0
\(853\) −43.8531 −1.50150 −0.750751 0.660586i \(-0.770308\pi\)
−0.750751 + 0.660586i \(0.770308\pi\)
\(854\) 0 0
\(855\) 0.859412 0.0293913
\(856\) 0 0
\(857\) −16.7010 −0.570496 −0.285248 0.958454i \(-0.592076\pi\)
−0.285248 + 0.958454i \(0.592076\pi\)
\(858\) 0 0
\(859\) −31.2057 −1.06473 −0.532363 0.846516i \(-0.678696\pi\)
−0.532363 + 0.846516i \(0.678696\pi\)
\(860\) 0 0
\(861\) −11.8475 −0.403760
\(862\) 0 0
\(863\) −28.2924 −0.963083 −0.481542 0.876423i \(-0.659923\pi\)
−0.481542 + 0.876423i \(0.659923\pi\)
\(864\) 0 0
\(865\) 1.33846 0.0455091
\(866\) 0 0
\(867\) −13.9990 −0.475431
\(868\) 0 0
\(869\) −21.2449 −0.720682
\(870\) 0 0
\(871\) 10.8138 0.366413
\(872\) 0 0
\(873\) 26.9355 0.911627
\(874\) 0 0
\(875\) 1.47872 0.0499898
\(876\) 0 0
\(877\) −42.6838 −1.44133 −0.720665 0.693284i \(-0.756163\pi\)
−0.720665 + 0.693284i \(0.756163\pi\)
\(878\) 0 0
\(879\) 19.3177 0.651568
\(880\) 0 0
\(881\) 20.3040 0.684060 0.342030 0.939689i \(-0.388885\pi\)
0.342030 + 0.939689i \(0.388885\pi\)
\(882\) 0 0
\(883\) −47.4337 −1.59627 −0.798135 0.602479i \(-0.794180\pi\)
−0.798135 + 0.602479i \(0.794180\pi\)
\(884\) 0 0
\(885\) 2.63326 0.0885162
\(886\) 0 0
\(887\) −21.3167 −0.715746 −0.357873 0.933770i \(-0.616498\pi\)
−0.357873 + 0.933770i \(0.616498\pi\)
\(888\) 0 0
\(889\) 10.7655 0.361065
\(890\) 0 0
\(891\) −16.2285 −0.543675
\(892\) 0 0
\(893\) 16.3439 0.546927
\(894\) 0 0
\(895\) −1.12856 −0.0377237
\(896\) 0 0
\(897\) 9.43779 0.315119
\(898\) 0 0
\(899\) −3.90387 −0.130201
\(900\) 0 0
\(901\) −16.4341 −0.547501
\(902\) 0 0
\(903\) −4.93815 −0.164331
\(904\) 0 0
\(905\) 3.32211 0.110431
\(906\) 0 0
\(907\) 17.8871 0.593931 0.296966 0.954888i \(-0.404025\pi\)
0.296966 + 0.954888i \(0.404025\pi\)
\(908\) 0 0
\(909\) 17.6758 0.586269
\(910\) 0 0
\(911\) 4.03861 0.133805 0.0669026 0.997760i \(-0.478688\pi\)
0.0669026 + 0.997760i \(0.478688\pi\)
\(912\) 0 0
\(913\) −13.9961 −0.463204
\(914\) 0 0
\(915\) −0.0657885 −0.00217490
\(916\) 0 0
\(917\) −3.76334 −0.124276
\(918\) 0 0
\(919\) −17.2681 −0.569624 −0.284812 0.958583i \(-0.591931\pi\)
−0.284812 + 0.958583i \(0.591931\pi\)
\(920\) 0 0
\(921\) 49.0504 1.61626
\(922\) 0 0
\(923\) −17.5708 −0.578350
\(924\) 0 0
\(925\) −36.6984 −1.20663
\(926\) 0 0
\(927\) −0.228442 −0.00750302
\(928\) 0 0
\(929\) −32.2922 −1.05947 −0.529737 0.848162i \(-0.677709\pi\)
−0.529737 + 0.848162i \(0.677709\pi\)
\(930\) 0 0
\(931\) −14.4132 −0.472374
\(932\) 0 0
\(933\) 19.6674 0.643882
\(934\) 0 0
\(935\) 1.19963 0.0392321
\(936\) 0 0
\(937\) −11.5818 −0.378362 −0.189181 0.981942i \(-0.560583\pi\)
−0.189181 + 0.981942i \(0.560583\pi\)
\(938\) 0 0
\(939\) 24.8167 0.809863
\(940\) 0 0
\(941\) −32.0018 −1.04323 −0.521614 0.853182i \(-0.674670\pi\)
−0.521614 + 0.853182i \(0.674670\pi\)
\(942\) 0 0
\(943\) 34.5080 1.12373
\(944\) 0 0
\(945\) 0.462025 0.0150297
\(946\) 0 0
\(947\) −28.0987 −0.913085 −0.456543 0.889702i \(-0.650912\pi\)
−0.456543 + 0.889702i \(0.650912\pi\)
\(948\) 0 0
\(949\) 12.9995 0.421982
\(950\) 0 0
\(951\) −24.9456 −0.808917
\(952\) 0 0
\(953\) 11.9394 0.386755 0.193377 0.981124i \(-0.438056\pi\)
0.193377 + 0.981124i \(0.438056\pi\)
\(954\) 0 0
\(955\) −3.75874 −0.121630
\(956\) 0 0
\(957\) 4.12165 0.133234
\(958\) 0 0
\(959\) −10.5778 −0.341576
\(960\) 0 0
\(961\) −22.5144 −0.726271
\(962\) 0 0
\(963\) 1.19976 0.0386616
\(964\) 0 0
\(965\) 0.157603 0.00507341
\(966\) 0 0
\(967\) 37.0856 1.19259 0.596296 0.802764i \(-0.296638\pi\)
0.596296 + 0.802764i \(0.296638\pi\)
\(968\) 0 0
\(969\) 14.8881 0.478273
\(970\) 0 0
\(971\) −3.36029 −0.107837 −0.0539184 0.998545i \(-0.517171\pi\)
−0.0539184 + 0.998545i \(0.517171\pi\)
\(972\) 0 0
\(973\) −7.36617 −0.236149
\(974\) 0 0
\(975\) −12.9691 −0.415343
\(976\) 0 0
\(977\) −24.6162 −0.787543 −0.393772 0.919208i \(-0.628830\pi\)
−0.393772 + 0.919208i \(0.628830\pi\)
\(978\) 0 0
\(979\) 22.4321 0.716934
\(980\) 0 0
\(981\) −3.45477 −0.110302
\(982\) 0 0
\(983\) 38.0516 1.21366 0.606829 0.794832i \(-0.292441\pi\)
0.606829 + 0.794832i \(0.292441\pi\)
\(984\) 0 0
\(985\) −3.02747 −0.0964632
\(986\) 0 0
\(987\) −9.31701 −0.296564
\(988\) 0 0
\(989\) 14.3833 0.457362
\(990\) 0 0
\(991\) 41.3513 1.31357 0.656783 0.754080i \(-0.271917\pi\)
0.656783 + 0.754080i \(0.271917\pi\)
\(992\) 0 0
\(993\) 4.82987 0.153271
\(994\) 0 0
\(995\) 1.53167 0.0485572
\(996\) 0 0
\(997\) −5.97938 −0.189369 −0.0946845 0.995507i \(-0.530184\pi\)
−0.0946845 + 0.995507i \(0.530184\pi\)
\(998\) 0 0
\(999\) −23.0868 −0.730434
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 4016.2.a.m.1.18 23
4.3 odd 2 2008.2.a.d.1.6 23
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2008.2.a.d.1.6 23 4.3 odd 2
4016.2.a.m.1.18 23 1.1 even 1 trivial