Properties

Label 4016.2.a.m.1.7
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 1.7
Character \(\chi\) = 4016.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.96174 q^{3} +0.807414 q^{5} -3.34299 q^{7} +0.848432 q^{9} +O(q^{10})\) \(q-1.96174 q^{3} +0.807414 q^{5} -3.34299 q^{7} +0.848432 q^{9} -4.04597 q^{11} -4.44468 q^{13} -1.58394 q^{15} -5.91837 q^{17} -2.98461 q^{19} +6.55809 q^{21} -7.45495 q^{23} -4.34808 q^{25} +4.22082 q^{27} +7.98249 q^{29} -9.58166 q^{31} +7.93716 q^{33} -2.69918 q^{35} +2.67999 q^{37} +8.71932 q^{39} +3.85402 q^{41} -9.57972 q^{43} +0.685036 q^{45} +9.46625 q^{47} +4.17559 q^{49} +11.6103 q^{51} -9.89664 q^{53} -3.26677 q^{55} +5.85503 q^{57} -6.88994 q^{59} -7.56108 q^{61} -2.83630 q^{63} -3.58870 q^{65} +8.97228 q^{67} +14.6247 q^{69} +14.1969 q^{71} +3.51267 q^{73} +8.52982 q^{75} +13.5257 q^{77} +9.64808 q^{79} -10.8255 q^{81} -9.42852 q^{83} -4.77858 q^{85} -15.6596 q^{87} +0.414104 q^{89} +14.8585 q^{91} +18.7967 q^{93} -2.40981 q^{95} +8.39841 q^{97} -3.43274 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 23q - 2q^{3} + 8q^{5} - 2q^{7} + 45q^{9} + O(q^{10}) \) \( 23q - 2q^{3} + 8q^{5} - 2q^{7} + 45q^{9} - 8q^{11} + 8q^{13} - 7q^{15} + 19q^{17} + 9q^{19} + 9q^{21} - 21q^{23} + 65q^{25} - 5q^{27} + 10q^{29} + 9q^{31} + 34q^{33} - 12q^{35} + 11q^{37} + 9q^{39} + 35q^{41} + 9q^{43} + 29q^{45} - 37q^{47} + 77q^{49} + 17q^{51} + 38q^{53} + 20q^{55} + 51q^{57} - 17q^{59} - 22q^{63} + 41q^{65} - 9q^{67} + 8q^{69} - 13q^{71} + 41q^{73} - 25q^{75} + 36q^{77} + 36q^{79} + 127q^{81} - 29q^{83} + 34q^{85} - 10q^{87} + 36q^{89} + 6q^{91} + 36q^{93} - 25q^{95} + 40q^{97} - 19q^{99} + O(q^{100}) \)

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
\(3\) −1.96174 −1.13261 −0.566306 0.824195i \(-0.691628\pi\)
−0.566306 + 0.824195i \(0.691628\pi\)
\(4\) 0 0
\(5\) 0.807414 0.361086 0.180543 0.983567i \(-0.442214\pi\)
0.180543 + 0.983567i \(0.442214\pi\)
\(6\) 0 0
\(7\) −3.34299 −1.26353 −0.631766 0.775159i \(-0.717670\pi\)
−0.631766 + 0.775159i \(0.717670\pi\)
\(8\) 0 0
\(9\) 0.848432 0.282811
\(10\) 0 0
\(11\) −4.04597 −1.21991 −0.609954 0.792437i \(-0.708812\pi\)
−0.609954 + 0.792437i \(0.708812\pi\)
\(12\) 0 0
\(13\) −4.44468 −1.23273 −0.616366 0.787460i \(-0.711396\pi\)
−0.616366 + 0.787460i \(0.711396\pi\)
\(14\) 0 0
\(15\) −1.58394 −0.408971
\(16\) 0 0
\(17\) −5.91837 −1.43542 −0.717708 0.696344i \(-0.754809\pi\)
−0.717708 + 0.696344i \(0.754809\pi\)
\(18\) 0 0
\(19\) −2.98461 −0.684715 −0.342358 0.939570i \(-0.611225\pi\)
−0.342358 + 0.939570i \(0.611225\pi\)
\(20\) 0 0
\(21\) 6.55809 1.43109
\(22\) 0 0
\(23\) −7.45495 −1.55447 −0.777233 0.629213i \(-0.783377\pi\)
−0.777233 + 0.629213i \(0.783377\pi\)
\(24\) 0 0
\(25\) −4.34808 −0.869617
\(26\) 0 0
\(27\) 4.22082 0.812297
\(28\) 0 0
\(29\) 7.98249 1.48231 0.741155 0.671334i \(-0.234278\pi\)
0.741155 + 0.671334i \(0.234278\pi\)
\(30\) 0 0
\(31\) −9.58166 −1.72092 −0.860459 0.509521i \(-0.829823\pi\)
−0.860459 + 0.509521i \(0.829823\pi\)
\(32\) 0 0
\(33\) 7.93716 1.38168
\(34\) 0 0
\(35\) −2.69918 −0.456244
\(36\) 0 0
\(37\) 2.67999 0.440587 0.220294 0.975434i \(-0.429298\pi\)
0.220294 + 0.975434i \(0.429298\pi\)
\(38\) 0 0
\(39\) 8.71932 1.39621
\(40\) 0 0
\(41\) 3.85402 0.601896 0.300948 0.953641i \(-0.402697\pi\)
0.300948 + 0.953641i \(0.402697\pi\)
\(42\) 0 0
\(43\) −9.57972 −1.46089 −0.730447 0.682969i \(-0.760688\pi\)
−0.730447 + 0.682969i \(0.760688\pi\)
\(44\) 0 0
\(45\) 0.685036 0.102119
\(46\) 0 0
\(47\) 9.46625 1.38080 0.690398 0.723430i \(-0.257436\pi\)
0.690398 + 0.723430i \(0.257436\pi\)
\(48\) 0 0
\(49\) 4.17559 0.596512
\(50\) 0 0
\(51\) 11.6103 1.62577
\(52\) 0 0
\(53\) −9.89664 −1.35941 −0.679704 0.733486i \(-0.737892\pi\)
−0.679704 + 0.733486i \(0.737892\pi\)
\(54\) 0 0
\(55\) −3.26677 −0.440492
\(56\) 0 0
\(57\) 5.85503 0.775517
\(58\) 0 0
\(59\) −6.88994 −0.896994 −0.448497 0.893784i \(-0.648041\pi\)
−0.448497 + 0.893784i \(0.648041\pi\)
\(60\) 0 0
\(61\) −7.56108 −0.968097 −0.484048 0.875041i \(-0.660834\pi\)
−0.484048 + 0.875041i \(0.660834\pi\)
\(62\) 0 0
\(63\) −2.83630 −0.357340
\(64\) 0 0
\(65\) −3.58870 −0.445123
\(66\) 0 0
\(67\) 8.97228 1.09614 0.548069 0.836433i \(-0.315363\pi\)
0.548069 + 0.836433i \(0.315363\pi\)
\(68\) 0 0
\(69\) 14.6247 1.76061
\(70\) 0 0
\(71\) 14.1969 1.68486 0.842432 0.538802i \(-0.181123\pi\)
0.842432 + 0.538802i \(0.181123\pi\)
\(72\) 0 0
\(73\) 3.51267 0.411127 0.205563 0.978644i \(-0.434097\pi\)
0.205563 + 0.978644i \(0.434097\pi\)
\(74\) 0 0
\(75\) 8.52982 0.984939
\(76\) 0 0
\(77\) 13.5257 1.54139
\(78\) 0 0
\(79\) 9.64808 1.08549 0.542747 0.839896i \(-0.317384\pi\)
0.542747 + 0.839896i \(0.317384\pi\)
\(80\) 0 0
\(81\) −10.8255 −1.20283
\(82\) 0 0
\(83\) −9.42852 −1.03491 −0.517457 0.855709i \(-0.673121\pi\)
−0.517457 + 0.855709i \(0.673121\pi\)
\(84\) 0 0
\(85\) −4.77858 −0.518309
\(86\) 0 0
\(87\) −15.6596 −1.67888
\(88\) 0 0
\(89\) 0.414104 0.0438949 0.0219474 0.999759i \(-0.493013\pi\)
0.0219474 + 0.999759i \(0.493013\pi\)
\(90\) 0 0
\(91\) 14.8585 1.55760
\(92\) 0 0
\(93\) 18.7967 1.94913
\(94\) 0 0
\(95\) −2.40981 −0.247241
\(96\) 0 0
\(97\) 8.39841 0.852729 0.426365 0.904551i \(-0.359794\pi\)
0.426365 + 0.904551i \(0.359794\pi\)
\(98\) 0 0
\(99\) −3.43274 −0.345003
\(100\) 0 0
\(101\) −8.89308 −0.884894 −0.442447 0.896795i \(-0.645890\pi\)
−0.442447 + 0.896795i \(0.645890\pi\)
\(102\) 0 0
\(103\) −12.4778 −1.22948 −0.614739 0.788730i \(-0.710739\pi\)
−0.614739 + 0.788730i \(0.710739\pi\)
\(104\) 0 0
\(105\) 5.29509 0.516748
\(106\) 0 0
\(107\) −11.1670 −1.07955 −0.539775 0.841809i \(-0.681491\pi\)
−0.539775 + 0.841809i \(0.681491\pi\)
\(108\) 0 0
\(109\) −16.2762 −1.55898 −0.779491 0.626413i \(-0.784522\pi\)
−0.779491 + 0.626413i \(0.784522\pi\)
\(110\) 0 0
\(111\) −5.25744 −0.499015
\(112\) 0 0
\(113\) −3.51526 −0.330687 −0.165344 0.986236i \(-0.552873\pi\)
−0.165344 + 0.986236i \(0.552873\pi\)
\(114\) 0 0
\(115\) −6.01923 −0.561296
\(116\) 0 0
\(117\) −3.77101 −0.348630
\(118\) 0 0
\(119\) 19.7851 1.81369
\(120\) 0 0
\(121\) 5.36991 0.488174
\(122\) 0 0
\(123\) −7.56059 −0.681715
\(124\) 0 0
\(125\) −7.54777 −0.675093
\(126\) 0 0
\(127\) −9.24057 −0.819968 −0.409984 0.912093i \(-0.634466\pi\)
−0.409984 + 0.912093i \(0.634466\pi\)
\(128\) 0 0
\(129\) 18.7929 1.65463
\(130\) 0 0
\(131\) 11.2973 0.987050 0.493525 0.869732i \(-0.335708\pi\)
0.493525 + 0.869732i \(0.335708\pi\)
\(132\) 0 0
\(133\) 9.97751 0.865160
\(134\) 0 0
\(135\) 3.40795 0.293310
\(136\) 0 0
\(137\) 0.354515 0.0302882 0.0151441 0.999885i \(-0.495179\pi\)
0.0151441 + 0.999885i \(0.495179\pi\)
\(138\) 0 0
\(139\) −10.6888 −0.906614 −0.453307 0.891354i \(-0.649756\pi\)
−0.453307 + 0.891354i \(0.649756\pi\)
\(140\) 0 0
\(141\) −18.5704 −1.56391
\(142\) 0 0
\(143\) 17.9831 1.50382
\(144\) 0 0
\(145\) 6.44517 0.535242
\(146\) 0 0
\(147\) −8.19143 −0.675617
\(148\) 0 0
\(149\) 21.5692 1.76702 0.883509 0.468415i \(-0.155175\pi\)
0.883509 + 0.468415i \(0.155175\pi\)
\(150\) 0 0
\(151\) 6.75789 0.549949 0.274975 0.961451i \(-0.411331\pi\)
0.274975 + 0.961451i \(0.411331\pi\)
\(152\) 0 0
\(153\) −5.02134 −0.405951
\(154\) 0 0
\(155\) −7.73636 −0.621400
\(156\) 0 0
\(157\) −4.69940 −0.375053 −0.187526 0.982260i \(-0.560047\pi\)
−0.187526 + 0.982260i \(0.560047\pi\)
\(158\) 0 0
\(159\) 19.4147 1.53968
\(160\) 0 0
\(161\) 24.9218 1.96412
\(162\) 0 0
\(163\) −3.02003 −0.236547 −0.118273 0.992981i \(-0.537736\pi\)
−0.118273 + 0.992981i \(0.537736\pi\)
\(164\) 0 0
\(165\) 6.40857 0.498907
\(166\) 0 0
\(167\) −20.0631 −1.55253 −0.776263 0.630409i \(-0.782887\pi\)
−0.776263 + 0.630409i \(0.782887\pi\)
\(168\) 0 0
\(169\) 6.75519 0.519630
\(170\) 0 0
\(171\) −2.53224 −0.193645
\(172\) 0 0
\(173\) −7.03355 −0.534751 −0.267375 0.963592i \(-0.586156\pi\)
−0.267375 + 0.963592i \(0.586156\pi\)
\(174\) 0 0
\(175\) 14.5356 1.09879
\(176\) 0 0
\(177\) 13.5163 1.01595
\(178\) 0 0
\(179\) −17.3752 −1.29868 −0.649341 0.760497i \(-0.724955\pi\)
−0.649341 + 0.760497i \(0.724955\pi\)
\(180\) 0 0
\(181\) −24.7797 −1.84186 −0.920929 0.389731i \(-0.872568\pi\)
−0.920929 + 0.389731i \(0.872568\pi\)
\(182\) 0 0
\(183\) 14.8329 1.09648
\(184\) 0 0
\(185\) 2.16386 0.159090
\(186\) 0 0
\(187\) 23.9456 1.75107
\(188\) 0 0
\(189\) −14.1102 −1.02636
\(190\) 0 0
\(191\) 1.90787 0.138049 0.0690245 0.997615i \(-0.478011\pi\)
0.0690245 + 0.997615i \(0.478011\pi\)
\(192\) 0 0
\(193\) −3.61802 −0.260431 −0.130215 0.991486i \(-0.541567\pi\)
−0.130215 + 0.991486i \(0.541567\pi\)
\(194\) 0 0
\(195\) 7.04010 0.504152
\(196\) 0 0
\(197\) −2.81406 −0.200494 −0.100247 0.994963i \(-0.531963\pi\)
−0.100247 + 0.994963i \(0.531963\pi\)
\(198\) 0 0
\(199\) 13.7072 0.971680 0.485840 0.874048i \(-0.338514\pi\)
0.485840 + 0.874048i \(0.338514\pi\)
\(200\) 0 0
\(201\) −17.6013 −1.24150
\(202\) 0 0
\(203\) −26.6854 −1.87295
\(204\) 0 0
\(205\) 3.11179 0.217337
\(206\) 0 0
\(207\) −6.32502 −0.439620
\(208\) 0 0
\(209\) 12.0756 0.835289
\(210\) 0 0
\(211\) 23.6771 1.63000 0.814999 0.579463i \(-0.196738\pi\)
0.814999 + 0.579463i \(0.196738\pi\)
\(212\) 0 0
\(213\) −27.8507 −1.90830
\(214\) 0 0
\(215\) −7.73480 −0.527509
\(216\) 0 0
\(217\) 32.0314 2.17443
\(218\) 0 0
\(219\) −6.89095 −0.465647
\(220\) 0 0
\(221\) 26.3053 1.76948
\(222\) 0 0
\(223\) 17.6488 1.18185 0.590927 0.806725i \(-0.298762\pi\)
0.590927 + 0.806725i \(0.298762\pi\)
\(224\) 0 0
\(225\) −3.68905 −0.245937
\(226\) 0 0
\(227\) 24.1655 1.60392 0.801962 0.597375i \(-0.203790\pi\)
0.801962 + 0.597375i \(0.203790\pi\)
\(228\) 0 0
\(229\) −16.2503 −1.07385 −0.536924 0.843630i \(-0.680414\pi\)
−0.536924 + 0.843630i \(0.680414\pi\)
\(230\) 0 0
\(231\) −26.5338 −1.74580
\(232\) 0 0
\(233\) −13.6794 −0.896169 −0.448085 0.893991i \(-0.647894\pi\)
−0.448085 + 0.893991i \(0.647894\pi\)
\(234\) 0 0
\(235\) 7.64318 0.498586
\(236\) 0 0
\(237\) −18.9271 −1.22944
\(238\) 0 0
\(239\) 17.1632 1.11020 0.555099 0.831784i \(-0.312680\pi\)
0.555099 + 0.831784i \(0.312680\pi\)
\(240\) 0 0
\(241\) −12.0334 −0.775139 −0.387570 0.921840i \(-0.626685\pi\)
−0.387570 + 0.921840i \(0.626685\pi\)
\(242\) 0 0
\(243\) 8.57430 0.550041
\(244\) 0 0
\(245\) 3.37143 0.215393
\(246\) 0 0
\(247\) 13.2656 0.844071
\(248\) 0 0
\(249\) 18.4963 1.17216
\(250\) 0 0
\(251\) 1.00000 0.0631194
\(252\) 0 0
\(253\) 30.1626 1.89630
\(254\) 0 0
\(255\) 9.37433 0.587043
\(256\) 0 0
\(257\) 22.2631 1.38873 0.694367 0.719621i \(-0.255685\pi\)
0.694367 + 0.719621i \(0.255685\pi\)
\(258\) 0 0
\(259\) −8.95917 −0.556696
\(260\) 0 0
\(261\) 6.77260 0.419213
\(262\) 0 0
\(263\) −30.0510 −1.85302 −0.926511 0.376268i \(-0.877207\pi\)
−0.926511 + 0.376268i \(0.877207\pi\)
\(264\) 0 0
\(265\) −7.99069 −0.490864
\(266\) 0 0
\(267\) −0.812364 −0.0497159
\(268\) 0 0
\(269\) 13.9225 0.848871 0.424435 0.905458i \(-0.360473\pi\)
0.424435 + 0.905458i \(0.360473\pi\)
\(270\) 0 0
\(271\) 32.0375 1.94614 0.973071 0.230505i \(-0.0740378\pi\)
0.973071 + 0.230505i \(0.0740378\pi\)
\(272\) 0 0
\(273\) −29.1486 −1.76415
\(274\) 0 0
\(275\) 17.5922 1.06085
\(276\) 0 0
\(277\) 27.4178 1.64737 0.823687 0.567044i \(-0.191913\pi\)
0.823687 + 0.567044i \(0.191913\pi\)
\(278\) 0 0
\(279\) −8.12939 −0.486694
\(280\) 0 0
\(281\) −2.36183 −0.140895 −0.0704474 0.997515i \(-0.522443\pi\)
−0.0704474 + 0.997515i \(0.522443\pi\)
\(282\) 0 0
\(283\) 6.40656 0.380831 0.190415 0.981704i \(-0.439017\pi\)
0.190415 + 0.981704i \(0.439017\pi\)
\(284\) 0 0
\(285\) 4.72743 0.280029
\(286\) 0 0
\(287\) −12.8839 −0.760515
\(288\) 0 0
\(289\) 18.0271 1.06042
\(290\) 0 0
\(291\) −16.4755 −0.965812
\(292\) 0 0
\(293\) −2.38006 −0.139045 −0.0695223 0.997580i \(-0.522147\pi\)
−0.0695223 + 0.997580i \(0.522147\pi\)
\(294\) 0 0
\(295\) −5.56303 −0.323892
\(296\) 0 0
\(297\) −17.0773 −0.990927
\(298\) 0 0
\(299\) 33.1349 1.91624
\(300\) 0 0
\(301\) 32.0249 1.84589
\(302\) 0 0
\(303\) 17.4459 1.00224
\(304\) 0 0
\(305\) −6.10492 −0.349566
\(306\) 0 0
\(307\) −11.5792 −0.660861 −0.330430 0.943830i \(-0.607194\pi\)
−0.330430 + 0.943830i \(0.607194\pi\)
\(308\) 0 0
\(309\) 24.4783 1.39252
\(310\) 0 0
\(311\) −18.5945 −1.05440 −0.527198 0.849743i \(-0.676757\pi\)
−0.527198 + 0.849743i \(0.676757\pi\)
\(312\) 0 0
\(313\) −13.4775 −0.761791 −0.380895 0.924618i \(-0.624384\pi\)
−0.380895 + 0.924618i \(0.624384\pi\)
\(314\) 0 0
\(315\) −2.29007 −0.129031
\(316\) 0 0
\(317\) −24.2903 −1.36428 −0.682141 0.731221i \(-0.738951\pi\)
−0.682141 + 0.731221i \(0.738951\pi\)
\(318\) 0 0
\(319\) −32.2969 −1.80828
\(320\) 0 0
\(321\) 21.9067 1.22271
\(322\) 0 0
\(323\) 17.6640 0.982852
\(324\) 0 0
\(325\) 19.3258 1.07200
\(326\) 0 0
\(327\) 31.9298 1.76572
\(328\) 0 0
\(329\) −31.6456 −1.74468
\(330\) 0 0
\(331\) −27.5827 −1.51608 −0.758041 0.652207i \(-0.773843\pi\)
−0.758041 + 0.652207i \(0.773843\pi\)
\(332\) 0 0
\(333\) 2.27379 0.124603
\(334\) 0 0
\(335\) 7.24434 0.395800
\(336\) 0 0
\(337\) −13.0865 −0.712868 −0.356434 0.934320i \(-0.616008\pi\)
−0.356434 + 0.934320i \(0.616008\pi\)
\(338\) 0 0
\(339\) 6.89603 0.374541
\(340\) 0 0
\(341\) 38.7672 2.09936
\(342\) 0 0
\(343\) 9.44199 0.509819
\(344\) 0 0
\(345\) 11.8082 0.635731
\(346\) 0 0
\(347\) −14.0578 −0.754661 −0.377330 0.926079i \(-0.623158\pi\)
−0.377330 + 0.926079i \(0.623158\pi\)
\(348\) 0 0
\(349\) −22.6500 −1.21243 −0.606213 0.795302i \(-0.707312\pi\)
−0.606213 + 0.795302i \(0.707312\pi\)
\(350\) 0 0
\(351\) −18.7602 −1.00135
\(352\) 0 0
\(353\) 14.0640 0.748552 0.374276 0.927317i \(-0.377891\pi\)
0.374276 + 0.927317i \(0.377891\pi\)
\(354\) 0 0
\(355\) 11.4628 0.608382
\(356\) 0 0
\(357\) −38.8132 −2.05421
\(358\) 0 0
\(359\) 5.72191 0.301991 0.150995 0.988534i \(-0.451752\pi\)
0.150995 + 0.988534i \(0.451752\pi\)
\(360\) 0 0
\(361\) −10.0921 −0.531165
\(362\) 0 0
\(363\) −10.5344 −0.552911
\(364\) 0 0
\(365\) 2.83618 0.148452
\(366\) 0 0
\(367\) −35.9154 −1.87477 −0.937385 0.348294i \(-0.886761\pi\)
−0.937385 + 0.348294i \(0.886761\pi\)
\(368\) 0 0
\(369\) 3.26987 0.170223
\(370\) 0 0
\(371\) 33.0844 1.71766
\(372\) 0 0
\(373\) −21.9660 −1.13735 −0.568677 0.822561i \(-0.692545\pi\)
−0.568677 + 0.822561i \(0.692545\pi\)
\(374\) 0 0
\(375\) 14.8068 0.764619
\(376\) 0 0
\(377\) −35.4796 −1.82729
\(378\) 0 0
\(379\) 1.92693 0.0989795 0.0494898 0.998775i \(-0.484240\pi\)
0.0494898 + 0.998775i \(0.484240\pi\)
\(380\) 0 0
\(381\) 18.1276 0.928706
\(382\) 0 0
\(383\) 24.2000 1.23656 0.618280 0.785958i \(-0.287830\pi\)
0.618280 + 0.785958i \(0.287830\pi\)
\(384\) 0 0
\(385\) 10.9208 0.556575
\(386\) 0 0
\(387\) −8.12775 −0.413157
\(388\) 0 0
\(389\) −8.04246 −0.407769 −0.203885 0.978995i \(-0.565357\pi\)
−0.203885 + 0.978995i \(0.565357\pi\)
\(390\) 0 0
\(391\) 44.1212 2.23130
\(392\) 0 0
\(393\) −22.1624 −1.11795
\(394\) 0 0
\(395\) 7.78999 0.391957
\(396\) 0 0
\(397\) −26.3765 −1.32380 −0.661900 0.749592i \(-0.730250\pi\)
−0.661900 + 0.749592i \(0.730250\pi\)
\(398\) 0 0
\(399\) −19.5733 −0.979890
\(400\) 0 0
\(401\) 24.2236 1.20967 0.604835 0.796351i \(-0.293239\pi\)
0.604835 + 0.796351i \(0.293239\pi\)
\(402\) 0 0
\(403\) 42.5874 2.12143
\(404\) 0 0
\(405\) −8.74062 −0.434325
\(406\) 0 0
\(407\) −10.8432 −0.537475
\(408\) 0 0
\(409\) −23.4802 −1.16102 −0.580512 0.814252i \(-0.697147\pi\)
−0.580512 + 0.814252i \(0.697147\pi\)
\(410\) 0 0
\(411\) −0.695466 −0.0343048
\(412\) 0 0
\(413\) 23.0330 1.13338
\(414\) 0 0
\(415\) −7.61271 −0.373693
\(416\) 0 0
\(417\) 20.9687 1.02684
\(418\) 0 0
\(419\) −4.91738 −0.240229 −0.120115 0.992760i \(-0.538326\pi\)
−0.120115 + 0.992760i \(0.538326\pi\)
\(420\) 0 0
\(421\) 9.28392 0.452471 0.226235 0.974073i \(-0.427358\pi\)
0.226235 + 0.974073i \(0.427358\pi\)
\(422\) 0 0
\(423\) 8.03148 0.390504
\(424\) 0 0
\(425\) 25.7336 1.24826
\(426\) 0 0
\(427\) 25.2766 1.22322
\(428\) 0 0
\(429\) −35.2781 −1.70324
\(430\) 0 0
\(431\) 34.4793 1.66081 0.830404 0.557162i \(-0.188110\pi\)
0.830404 + 0.557162i \(0.188110\pi\)
\(432\) 0 0
\(433\) 17.7460 0.852817 0.426408 0.904531i \(-0.359779\pi\)
0.426408 + 0.904531i \(0.359779\pi\)
\(434\) 0 0
\(435\) −12.6438 −0.606222
\(436\) 0 0
\(437\) 22.2501 1.06437
\(438\) 0 0
\(439\) 36.2208 1.72872 0.864362 0.502871i \(-0.167723\pi\)
0.864362 + 0.502871i \(0.167723\pi\)
\(440\) 0 0
\(441\) 3.54270 0.168700
\(442\) 0 0
\(443\) −1.32623 −0.0630109 −0.0315055 0.999504i \(-0.510030\pi\)
−0.0315055 + 0.999504i \(0.510030\pi\)
\(444\) 0 0
\(445\) 0.334353 0.0158498
\(446\) 0 0
\(447\) −42.3132 −2.00135
\(448\) 0 0
\(449\) −9.76016 −0.460611 −0.230305 0.973118i \(-0.573972\pi\)
−0.230305 + 0.973118i \(0.573972\pi\)
\(450\) 0 0
\(451\) −15.5933 −0.734257
\(452\) 0 0
\(453\) −13.2572 −0.622880
\(454\) 0 0
\(455\) 11.9970 0.562427
\(456\) 0 0
\(457\) 34.0108 1.59096 0.795479 0.605981i \(-0.207219\pi\)
0.795479 + 0.605981i \(0.207219\pi\)
\(458\) 0 0
\(459\) −24.9804 −1.16598
\(460\) 0 0
\(461\) −1.06453 −0.0495800 −0.0247900 0.999693i \(-0.507892\pi\)
−0.0247900 + 0.999693i \(0.507892\pi\)
\(462\) 0 0
\(463\) −23.9463 −1.11288 −0.556440 0.830888i \(-0.687833\pi\)
−0.556440 + 0.830888i \(0.687833\pi\)
\(464\) 0 0
\(465\) 15.1768 0.703805
\(466\) 0 0
\(467\) −38.9525 −1.80251 −0.901253 0.433293i \(-0.857351\pi\)
−0.901253 + 0.433293i \(0.857351\pi\)
\(468\) 0 0
\(469\) −29.9942 −1.38500
\(470\) 0 0
\(471\) 9.21901 0.424790
\(472\) 0 0
\(473\) 38.7593 1.78216
\(474\) 0 0
\(475\) 12.9773 0.595440
\(476\) 0 0
\(477\) −8.39663 −0.384455
\(478\) 0 0
\(479\) 0.611331 0.0279324 0.0139662 0.999902i \(-0.495554\pi\)
0.0139662 + 0.999902i \(0.495554\pi\)
\(480\) 0 0
\(481\) −11.9117 −0.543126
\(482\) 0 0
\(483\) −48.8902 −2.22458
\(484\) 0 0
\(485\) 6.78099 0.307909
\(486\) 0 0
\(487\) −19.7281 −0.893965 −0.446983 0.894543i \(-0.647501\pi\)
−0.446983 + 0.894543i \(0.647501\pi\)
\(488\) 0 0
\(489\) 5.92451 0.267916
\(490\) 0 0
\(491\) 19.5698 0.883173 0.441587 0.897219i \(-0.354416\pi\)
0.441587 + 0.897219i \(0.354416\pi\)
\(492\) 0 0
\(493\) −47.2433 −2.12773
\(494\) 0 0
\(495\) −2.77164 −0.124576
\(496\) 0 0
\(497\) −47.4602 −2.12888
\(498\) 0 0
\(499\) −9.20005 −0.411851 −0.205925 0.978568i \(-0.566020\pi\)
−0.205925 + 0.978568i \(0.566020\pi\)
\(500\) 0 0
\(501\) 39.3586 1.75841
\(502\) 0 0
\(503\) −32.5699 −1.45222 −0.726110 0.687578i \(-0.758674\pi\)
−0.726110 + 0.687578i \(0.758674\pi\)
\(504\) 0 0
\(505\) −7.18039 −0.319523
\(506\) 0 0
\(507\) −13.2519 −0.588539
\(508\) 0 0
\(509\) 2.60435 0.115436 0.0577178 0.998333i \(-0.481618\pi\)
0.0577178 + 0.998333i \(0.481618\pi\)
\(510\) 0 0
\(511\) −11.7428 −0.519472
\(512\) 0 0
\(513\) −12.5975 −0.556193
\(514\) 0 0
\(515\) −10.0748 −0.443948
\(516\) 0 0
\(517\) −38.3002 −1.68444
\(518\) 0 0
\(519\) 13.7980 0.605665
\(520\) 0 0
\(521\) −20.2071 −0.885288 −0.442644 0.896697i \(-0.645959\pi\)
−0.442644 + 0.896697i \(0.645959\pi\)
\(522\) 0 0
\(523\) −17.8234 −0.779362 −0.389681 0.920950i \(-0.627415\pi\)
−0.389681 + 0.920950i \(0.627415\pi\)
\(524\) 0 0
\(525\) −28.5151 −1.24450
\(526\) 0 0
\(527\) 56.7078 2.47023
\(528\) 0 0
\(529\) 32.5763 1.41636
\(530\) 0 0
\(531\) −5.84565 −0.253680
\(532\) 0 0
\(533\) −17.1299 −0.741977
\(534\) 0 0
\(535\) −9.01635 −0.389811
\(536\) 0 0
\(537\) 34.0856 1.47090
\(538\) 0 0
\(539\) −16.8943 −0.727690
\(540\) 0 0
\(541\) −3.19983 −0.137571 −0.0687857 0.997631i \(-0.521912\pi\)
−0.0687857 + 0.997631i \(0.521912\pi\)
\(542\) 0 0
\(543\) 48.6113 2.08611
\(544\) 0 0
\(545\) −13.1417 −0.562927
\(546\) 0 0
\(547\) 40.4498 1.72951 0.864753 0.502197i \(-0.167475\pi\)
0.864753 + 0.502197i \(0.167475\pi\)
\(548\) 0 0
\(549\) −6.41506 −0.273788
\(550\) 0 0
\(551\) −23.8246 −1.01496
\(552\) 0 0
\(553\) −32.2535 −1.37156
\(554\) 0 0
\(555\) −4.24493 −0.180187
\(556\) 0 0
\(557\) −21.0135 −0.890369 −0.445184 0.895439i \(-0.646862\pi\)
−0.445184 + 0.895439i \(0.646862\pi\)
\(558\) 0 0
\(559\) 42.5788 1.80089
\(560\) 0 0
\(561\) −46.9751 −1.98329
\(562\) 0 0
\(563\) 26.9398 1.13538 0.567688 0.823244i \(-0.307838\pi\)
0.567688 + 0.823244i \(0.307838\pi\)
\(564\) 0 0
\(565\) −2.83827 −0.119407
\(566\) 0 0
\(567\) 36.1894 1.51981
\(568\) 0 0
\(569\) −10.5424 −0.441959 −0.220979 0.975279i \(-0.570925\pi\)
−0.220979 + 0.975279i \(0.570925\pi\)
\(570\) 0 0
\(571\) 12.2056 0.510788 0.255394 0.966837i \(-0.417795\pi\)
0.255394 + 0.966837i \(0.417795\pi\)
\(572\) 0 0
\(573\) −3.74276 −0.156356
\(574\) 0 0
\(575\) 32.4148 1.35179
\(576\) 0 0
\(577\) 4.42277 0.184122 0.0920612 0.995753i \(-0.470654\pi\)
0.0920612 + 0.995753i \(0.470654\pi\)
\(578\) 0 0
\(579\) 7.09762 0.294967
\(580\) 0 0
\(581\) 31.5194 1.30765
\(582\) 0 0
\(583\) 40.0416 1.65835
\(584\) 0 0
\(585\) −3.04477 −0.125886
\(586\) 0 0
\(587\) −0.600308 −0.0247774 −0.0123887 0.999923i \(-0.503944\pi\)
−0.0123887 + 0.999923i \(0.503944\pi\)
\(588\) 0 0
\(589\) 28.5975 1.17834
\(590\) 0 0
\(591\) 5.52047 0.227082
\(592\) 0 0
\(593\) 14.4881 0.594955 0.297478 0.954729i \(-0.403855\pi\)
0.297478 + 0.954729i \(0.403855\pi\)
\(594\) 0 0
\(595\) 15.9747 0.654900
\(596\) 0 0
\(597\) −26.8900 −1.10054
\(598\) 0 0
\(599\) −29.3814 −1.20049 −0.600245 0.799816i \(-0.704930\pi\)
−0.600245 + 0.799816i \(0.704930\pi\)
\(600\) 0 0
\(601\) −0.578613 −0.0236021 −0.0118011 0.999930i \(-0.503756\pi\)
−0.0118011 + 0.999930i \(0.503756\pi\)
\(602\) 0 0
\(603\) 7.61237 0.310000
\(604\) 0 0
\(605\) 4.33574 0.176273
\(606\) 0 0
\(607\) −5.51793 −0.223966 −0.111983 0.993710i \(-0.535720\pi\)
−0.111983 + 0.993710i \(0.535720\pi\)
\(608\) 0 0
\(609\) 52.3498 2.12132
\(610\) 0 0
\(611\) −42.0745 −1.70215
\(612\) 0 0
\(613\) 9.18481 0.370971 0.185486 0.982647i \(-0.440614\pi\)
0.185486 + 0.982647i \(0.440614\pi\)
\(614\) 0 0
\(615\) −6.10452 −0.246158
\(616\) 0 0
\(617\) 47.0623 1.89466 0.947329 0.320261i \(-0.103771\pi\)
0.947329 + 0.320261i \(0.103771\pi\)
\(618\) 0 0
\(619\) 9.03710 0.363232 0.181616 0.983370i \(-0.441867\pi\)
0.181616 + 0.983370i \(0.441867\pi\)
\(620\) 0 0
\(621\) −31.4660 −1.26269
\(622\) 0 0
\(623\) −1.38434 −0.0554626
\(624\) 0 0
\(625\) 15.6462 0.625850
\(626\) 0 0
\(627\) −23.6893 −0.946059
\(628\) 0 0
\(629\) −15.8612 −0.632426
\(630\) 0 0
\(631\) 35.3376 1.40677 0.703384 0.710810i \(-0.251672\pi\)
0.703384 + 0.710810i \(0.251672\pi\)
\(632\) 0 0
\(633\) −46.4483 −1.84615
\(634\) 0 0
\(635\) −7.46096 −0.296079
\(636\) 0 0
\(637\) −18.5592 −0.735340
\(638\) 0 0
\(639\) 12.0451 0.476498
\(640\) 0 0
\(641\) −38.4145 −1.51728 −0.758640 0.651510i \(-0.774136\pi\)
−0.758640 + 0.651510i \(0.774136\pi\)
\(642\) 0 0
\(643\) 0.214027 0.00844038 0.00422019 0.999991i \(-0.498657\pi\)
0.00422019 + 0.999991i \(0.498657\pi\)
\(644\) 0 0
\(645\) 15.1737 0.597463
\(646\) 0 0
\(647\) −13.2869 −0.522362 −0.261181 0.965290i \(-0.584112\pi\)
−0.261181 + 0.965290i \(0.584112\pi\)
\(648\) 0 0
\(649\) 27.8765 1.09425
\(650\) 0 0
\(651\) −62.8374 −2.46279
\(652\) 0 0
\(653\) −16.6369 −0.651051 −0.325526 0.945533i \(-0.605541\pi\)
−0.325526 + 0.945533i \(0.605541\pi\)
\(654\) 0 0
\(655\) 9.12160 0.356410
\(656\) 0 0
\(657\) 2.98026 0.116271
\(658\) 0 0
\(659\) −34.2857 −1.33558 −0.667790 0.744350i \(-0.732760\pi\)
−0.667790 + 0.744350i \(0.732760\pi\)
\(660\) 0 0
\(661\) −30.9807 −1.20501 −0.602506 0.798115i \(-0.705831\pi\)
−0.602506 + 0.798115i \(0.705831\pi\)
\(662\) 0 0
\(663\) −51.6042 −2.00414
\(664\) 0 0
\(665\) 8.05598 0.312397
\(666\) 0 0
\(667\) −59.5091 −2.30420
\(668\) 0 0
\(669\) −34.6225 −1.33858
\(670\) 0 0
\(671\) 30.5919 1.18099
\(672\) 0 0
\(673\) −15.9279 −0.613977 −0.306989 0.951713i \(-0.599321\pi\)
−0.306989 + 0.951713i \(0.599321\pi\)
\(674\) 0 0
\(675\) −18.3525 −0.706387
\(676\) 0 0
\(677\) −36.9190 −1.41891 −0.709457 0.704749i \(-0.751060\pi\)
−0.709457 + 0.704749i \(0.751060\pi\)
\(678\) 0 0
\(679\) −28.0758 −1.07745
\(680\) 0 0
\(681\) −47.4066 −1.81662
\(682\) 0 0
\(683\) −31.4896 −1.20492 −0.602459 0.798150i \(-0.705812\pi\)
−0.602459 + 0.798150i \(0.705812\pi\)
\(684\) 0 0
\(685\) 0.286240 0.0109367
\(686\) 0 0
\(687\) 31.8789 1.21625
\(688\) 0 0
\(689\) 43.9874 1.67579
\(690\) 0 0
\(691\) 5.15383 0.196061 0.0980305 0.995183i \(-0.468746\pi\)
0.0980305 + 0.995183i \(0.468746\pi\)
\(692\) 0 0
\(693\) 11.4756 0.435922
\(694\) 0 0
\(695\) −8.63030 −0.327366
\(696\) 0 0
\(697\) −22.8095 −0.863972
\(698\) 0 0
\(699\) 26.8355 1.01501
\(700\) 0 0
\(701\) −6.46137 −0.244043 −0.122021 0.992527i \(-0.538938\pi\)
−0.122021 + 0.992527i \(0.538938\pi\)
\(702\) 0 0
\(703\) −7.99870 −0.301677
\(704\) 0 0
\(705\) −14.9940 −0.564705
\(706\) 0 0
\(707\) 29.7295 1.11809
\(708\) 0 0
\(709\) 5.47356 0.205564 0.102782 0.994704i \(-0.467226\pi\)
0.102782 + 0.994704i \(0.467226\pi\)
\(710\) 0 0
\(711\) 8.18575 0.306989
\(712\) 0 0
\(713\) 71.4308 2.67511
\(714\) 0 0
\(715\) 14.5198 0.543009
\(716\) 0 0
\(717\) −33.6699 −1.25742
\(718\) 0 0
\(719\) −42.2216 −1.57460 −0.787300 0.616570i \(-0.788522\pi\)
−0.787300 + 0.616570i \(0.788522\pi\)
\(720\) 0 0
\(721\) 41.7133 1.55349
\(722\) 0 0
\(723\) 23.6064 0.877932
\(724\) 0 0
\(725\) −34.7085 −1.28904
\(726\) 0 0
\(727\) −3.78101 −0.140230 −0.0701149 0.997539i \(-0.522337\pi\)
−0.0701149 + 0.997539i \(0.522337\pi\)
\(728\) 0 0
\(729\) 15.6558 0.579845
\(730\) 0 0
\(731\) 56.6964 2.09699
\(732\) 0 0
\(733\) −3.93004 −0.145159 −0.0725797 0.997363i \(-0.523123\pi\)
−0.0725797 + 0.997363i \(0.523123\pi\)
\(734\) 0 0
\(735\) −6.61387 −0.243956
\(736\) 0 0
\(737\) −36.3016 −1.33719
\(738\) 0 0
\(739\) −13.9677 −0.513810 −0.256905 0.966437i \(-0.582703\pi\)
−0.256905 + 0.966437i \(0.582703\pi\)
\(740\) 0 0
\(741\) −26.0237 −0.956005
\(742\) 0 0
\(743\) −14.9788 −0.549520 −0.274760 0.961513i \(-0.588598\pi\)
−0.274760 + 0.961513i \(0.588598\pi\)
\(744\) 0 0
\(745\) 17.4153 0.638046
\(746\) 0 0
\(747\) −7.99946 −0.292685
\(748\) 0 0
\(749\) 37.3310 1.36405
\(750\) 0 0
\(751\) −38.1760 −1.39306 −0.696530 0.717528i \(-0.745274\pi\)
−0.696530 + 0.717528i \(0.745274\pi\)
\(752\) 0 0
\(753\) −1.96174 −0.0714899
\(754\) 0 0
\(755\) 5.45641 0.198579
\(756\) 0 0
\(757\) −43.6988 −1.58826 −0.794130 0.607748i \(-0.792073\pi\)
−0.794130 + 0.607748i \(0.792073\pi\)
\(758\) 0 0
\(759\) −59.1711 −2.14778
\(760\) 0 0
\(761\) −39.9011 −1.44641 −0.723206 0.690632i \(-0.757332\pi\)
−0.723206 + 0.690632i \(0.757332\pi\)
\(762\) 0 0
\(763\) 54.4114 1.96982
\(764\) 0 0
\(765\) −4.05430 −0.146583
\(766\) 0 0
\(767\) 30.6236 1.10575
\(768\) 0 0
\(769\) −10.3619 −0.373659 −0.186830 0.982392i \(-0.559821\pi\)
−0.186830 + 0.982392i \(0.559821\pi\)
\(770\) 0 0
\(771\) −43.6744 −1.57290
\(772\) 0 0
\(773\) −12.5439 −0.451174 −0.225587 0.974223i \(-0.572430\pi\)
−0.225587 + 0.974223i \(0.572430\pi\)
\(774\) 0 0
\(775\) 41.6619 1.49654
\(776\) 0 0
\(777\) 17.5756 0.630521
\(778\) 0 0
\(779\) −11.5027 −0.412128
\(780\) 0 0
\(781\) −57.4404 −2.05538
\(782\) 0 0
\(783\) 33.6926 1.20408
\(784\) 0 0
\(785\) −3.79436 −0.135426
\(786\) 0 0
\(787\) −11.0440 −0.393677 −0.196838 0.980436i \(-0.563067\pi\)
−0.196838 + 0.980436i \(0.563067\pi\)
\(788\) 0 0
\(789\) 58.9522 2.09876
\(790\) 0 0
\(791\) 11.7515 0.417834
\(792\) 0 0
\(793\) 33.6066 1.19340
\(794\) 0 0
\(795\) 15.6757 0.555959
\(796\) 0 0
\(797\) 18.6839 0.661818 0.330909 0.943663i \(-0.392645\pi\)
0.330909 + 0.943663i \(0.392645\pi\)
\(798\) 0 0
\(799\) −56.0248 −1.98202
\(800\) 0 0
\(801\) 0.351339 0.0124139
\(802\) 0 0
\(803\) −14.2122 −0.501537
\(804\) 0 0
\(805\) 20.1222 0.709216
\(806\) 0 0
\(807\) −27.3124 −0.961441
\(808\) 0 0
\(809\) 47.3125 1.66342 0.831709 0.555211i \(-0.187363\pi\)
0.831709 + 0.555211i \(0.187363\pi\)
\(810\) 0 0
\(811\) 5.37107 0.188604 0.0943019 0.995544i \(-0.469938\pi\)
0.0943019 + 0.995544i \(0.469938\pi\)
\(812\) 0 0
\(813\) −62.8494 −2.20422
\(814\) 0 0
\(815\) −2.43841 −0.0854138
\(816\) 0 0
\(817\) 28.5917 1.00030
\(818\) 0 0
\(819\) 12.6065 0.440505
\(820\) 0 0
\(821\) 3.31427 0.115669 0.0578344 0.998326i \(-0.481580\pi\)
0.0578344 + 0.998326i \(0.481580\pi\)
\(822\) 0 0
\(823\) −3.62186 −0.126250 −0.0631250 0.998006i \(-0.520107\pi\)
−0.0631250 + 0.998006i \(0.520107\pi\)
\(824\) 0 0
\(825\) −34.5114 −1.20153
\(826\) 0 0
\(827\) 32.6087 1.13392 0.566959 0.823746i \(-0.308120\pi\)
0.566959 + 0.823746i \(0.308120\pi\)
\(828\) 0 0
\(829\) −3.90979 −0.135793 −0.0678963 0.997692i \(-0.521629\pi\)
−0.0678963 + 0.997692i \(0.521629\pi\)
\(830\) 0 0
\(831\) −53.7866 −1.86584
\(832\) 0 0
\(833\) −24.7127 −0.856244
\(834\) 0 0
\(835\) −16.1992 −0.560596
\(836\) 0 0
\(837\) −40.4425 −1.39790
\(838\) 0 0
\(839\) −16.9656 −0.585718 −0.292859 0.956156i \(-0.594607\pi\)
−0.292859 + 0.956156i \(0.594607\pi\)
\(840\) 0 0
\(841\) 34.7201 1.19724
\(842\) 0 0
\(843\) 4.63330 0.159579
\(844\) 0 0
\(845\) 5.45423 0.187631
\(846\) 0 0
\(847\) −17.9516 −0.616823
\(848\) 0 0
\(849\) −12.5680 −0.431334
\(850\) 0 0
\(851\) −19.9792 −0.684877
\(852\) 0 0
\(853\) −46.0843 −1.57790 −0.788948 0.614459i \(-0.789374\pi\)
−0.788948 + 0.614459i \(0.789374\pi\)
\(854\) 0 0
\(855\) −2.04456 −0.0699225
\(856\) 0 0
\(857\) −12.5346 −0.428173 −0.214087 0.976815i \(-0.568678\pi\)
−0.214087 + 0.976815i \(0.568678\pi\)
\(858\) 0 0
\(859\) 42.6511 1.45524 0.727618 0.685982i \(-0.240627\pi\)
0.727618 + 0.685982i \(0.240627\pi\)
\(860\) 0 0
\(861\) 25.2750 0.861369
\(862\) 0 0
\(863\) −57.3229 −1.95129 −0.975647 0.219346i \(-0.929608\pi\)
−0.975647 + 0.219346i \(0.929608\pi\)
\(864\) 0 0
\(865\) −5.67898 −0.193091
\(866\) 0 0
\(867\) −35.3646 −1.20104
\(868\) 0 0
\(869\) −39.0359 −1.32420
\(870\) 0 0
\(871\) −39.8789 −1.35125
\(872\) 0 0
\(873\) 7.12548 0.241161
\(874\) 0 0
\(875\) 25.2321 0.853002
\(876\) 0 0
\(877\) 32.6917 1.10392 0.551960 0.833870i \(-0.313880\pi\)
0.551960 + 0.833870i \(0.313880\pi\)
\(878\) 0 0
\(879\) 4.66906 0.157484
\(880\) 0 0
\(881\) −13.4415 −0.452854 −0.226427 0.974028i \(-0.572704\pi\)
−0.226427 + 0.974028i \(0.572704\pi\)
\(882\) 0 0
\(883\) −6.02293 −0.202688 −0.101344 0.994851i \(-0.532314\pi\)
−0.101344 + 0.994851i \(0.532314\pi\)
\(884\) 0 0
\(885\) 10.9132 0.366844
\(886\) 0 0
\(887\) −40.8986 −1.37324 −0.686620 0.727016i \(-0.740906\pi\)
−0.686620 + 0.727016i \(0.740906\pi\)
\(888\) 0 0
\(889\) 30.8911 1.03606
\(890\) 0 0
\(891\) 43.7995 1.46734
\(892\) 0 0
\(893\) −28.2530 −0.945452
\(894\) 0 0
\(895\) −14.0290 −0.468937
\(896\) 0 0
\(897\) −65.0021 −2.17036
\(898\) 0 0
\(899\) −76.4855 −2.55093
\(900\) 0 0
\(901\) 58.5720 1.95132
\(902\) 0 0
\(903\) −62.8247 −2.09067
\(904\) 0 0
\(905\) −20.0074 −0.665070
\(906\) 0 0
\(907\) 15.0074 0.498313 0.249157 0.968463i \(-0.419847\pi\)
0.249157 + 0.968463i \(0.419847\pi\)
\(908\) 0 0
\(909\) −7.54517 −0.250258
\(910\) 0 0
\(911\) −42.5509 −1.40978 −0.704888 0.709319i \(-0.749003\pi\)
−0.704888 + 0.709319i \(0.749003\pi\)
\(912\) 0 0
\(913\) 38.1475 1.26250
\(914\) 0 0
\(915\) 11.9763 0.395923
\(916\) 0 0
\(917\) −37.7668 −1.24717
\(918\) 0 0
\(919\) −3.59673 −0.118645 −0.0593226 0.998239i \(-0.518894\pi\)
−0.0593226 + 0.998239i \(0.518894\pi\)
\(920\) 0 0
\(921\) 22.7154 0.748499
\(922\) 0 0
\(923\) −63.1008 −2.07699
\(924\) 0 0
\(925\) −11.6528 −0.383142
\(926\) 0 0
\(927\) −10.5866 −0.347710
\(928\) 0 0
\(929\) 28.1899 0.924882 0.462441 0.886650i \(-0.346974\pi\)
0.462441 + 0.886650i \(0.346974\pi\)
\(930\) 0 0
\(931\) −12.4625 −0.408441
\(932\) 0 0
\(933\) 36.4776 1.19422
\(934\) 0 0
\(935\) 19.3340 0.632289
\(936\) 0 0
\(937\) 47.0171 1.53598 0.767990 0.640462i \(-0.221257\pi\)
0.767990 + 0.640462i \(0.221257\pi\)
\(938\) 0 0
\(939\) 26.4393 0.862813
\(940\) 0 0
\(941\) −3.16805 −0.103275 −0.0516377 0.998666i \(-0.516444\pi\)
−0.0516377 + 0.998666i \(0.516444\pi\)
\(942\) 0 0
\(943\) −28.7315 −0.935627
\(944\) 0 0
\(945\) −11.3927 −0.370606
\(946\) 0 0
\(947\) 6.73552 0.218875 0.109438 0.993994i \(-0.465095\pi\)
0.109438 + 0.993994i \(0.465095\pi\)
\(948\) 0 0
\(949\) −15.6127 −0.506810
\(950\) 0 0
\(951\) 47.6514 1.54520
\(952\) 0 0
\(953\) 11.4333 0.370362 0.185181 0.982704i \(-0.440713\pi\)
0.185181 + 0.982704i \(0.440713\pi\)
\(954\) 0 0
\(955\) 1.54044 0.0498476
\(956\) 0 0
\(957\) 63.3583 2.04808
\(958\) 0 0
\(959\) −1.18514 −0.0382701
\(960\) 0 0
\(961\) 60.8082 1.96156
\(962\) 0 0
\(963\) −9.47441 −0.305309
\(964\) 0 0
\(965\) −2.92124 −0.0940380
\(966\) 0 0
\(967\) −47.7263 −1.53477 −0.767387 0.641185i \(-0.778443\pi\)
−0.767387 + 0.641185i \(0.778443\pi\)
\(968\) 0 0
\(969\) −34.6522 −1.11319
\(970\) 0 0
\(971\) −25.5475 −0.819860 −0.409930 0.912117i \(-0.634447\pi\)
−0.409930 + 0.912117i \(0.634447\pi\)
\(972\) 0 0
\(973\) 35.7326 1.14554
\(974\) 0 0
\(975\) −37.9123 −1.21417
\(976\) 0 0
\(977\) 18.3454 0.586922 0.293461 0.955971i \(-0.405193\pi\)
0.293461 + 0.955971i \(0.405193\pi\)
\(978\) 0 0
\(979\) −1.67545 −0.0535477
\(980\) 0 0
\(981\) −13.8093 −0.440897
\(982\) 0 0
\(983\) −3.50579 −0.111817 −0.0559087 0.998436i \(-0.517806\pi\)
−0.0559087 + 0.998436i \(0.517806\pi\)
\(984\) 0 0
\(985\) −2.27211 −0.0723955
\(986\) 0 0
\(987\) 62.0805 1.97604
\(988\) 0 0
\(989\) 71.4164 2.27091
\(990\) 0 0
\(991\) −12.4935 −0.396869 −0.198434 0.980114i \(-0.563586\pi\)
−0.198434 + 0.980114i \(0.563586\pi\)
\(992\) 0 0
\(993\) 54.1101 1.71713
\(994\) 0 0
\(995\) 11.0674 0.350860
\(996\) 0 0
\(997\) −62.1074 −1.96696 −0.983480 0.181016i \(-0.942061\pi\)
−0.983480 + 0.181016i \(0.942061\pi\)
\(998\) 0 0
\(999\) 11.3117 0.357888
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.1.7 23
4.3 odd 2 2008.2.a.d.1.17 23
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2008.2.a.d.1.17 23 4.3 odd 2
4016.2.a.m.1.7 23 1.1 even 1 trivial