Properties

Label 4016.2.a.m.1.14
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 1.14
Character \(\chi\) = 4016.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.347951 q^{3} -1.66668 q^{5} -3.92094 q^{7} -2.87893 q^{9} +O(q^{10})\) \(q+0.347951 q^{3} -1.66668 q^{5} -3.92094 q^{7} -2.87893 q^{9} -6.50416 q^{11} -3.17112 q^{13} -0.579924 q^{15} +3.56558 q^{17} -8.45462 q^{19} -1.36430 q^{21} +4.47235 q^{23} -2.22218 q^{25} -2.04558 q^{27} -9.13094 q^{29} +4.27043 q^{31} -2.26313 q^{33} +6.53495 q^{35} +0.328479 q^{37} -1.10340 q^{39} +8.75568 q^{41} +4.27318 q^{43} +4.79826 q^{45} -5.78246 q^{47} +8.37376 q^{49} +1.24065 q^{51} +13.1862 q^{53} +10.8404 q^{55} -2.94180 q^{57} -6.76862 q^{59} -9.71677 q^{61} +11.2881 q^{63} +5.28525 q^{65} -11.0508 q^{67} +1.55616 q^{69} -13.3491 q^{71} +13.0593 q^{73} -0.773209 q^{75} +25.5024 q^{77} -4.45561 q^{79} +7.92503 q^{81} +7.31224 q^{83} -5.94269 q^{85} -3.17712 q^{87} +0.686662 q^{89} +12.4338 q^{91} +1.48590 q^{93} +14.0912 q^{95} -7.21983 q^{97} +18.7250 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 23q - 2q^{3} + 8q^{5} - 2q^{7} + 45q^{9} + O(q^{10}) \) \( 23q - 2q^{3} + 8q^{5} - 2q^{7} + 45q^{9} - 8q^{11} + 8q^{13} - 7q^{15} + 19q^{17} + 9q^{19} + 9q^{21} - 21q^{23} + 65q^{25} - 5q^{27} + 10q^{29} + 9q^{31} + 34q^{33} - 12q^{35} + 11q^{37} + 9q^{39} + 35q^{41} + 9q^{43} + 29q^{45} - 37q^{47} + 77q^{49} + 17q^{51} + 38q^{53} + 20q^{55} + 51q^{57} - 17q^{59} - 22q^{63} + 41q^{65} - 9q^{67} + 8q^{69} - 13q^{71} + 41q^{73} - 25q^{75} + 36q^{77} + 36q^{79} + 127q^{81} - 29q^{83} + 34q^{85} - 10q^{87} + 36q^{89} + 6q^{91} + 36q^{93} - 25q^{95} + 40q^{97} - 19q^{99} + O(q^{100}) \)

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
\(3\) 0.347951 0.200890 0.100445 0.994943i \(-0.467973\pi\)
0.100445 + 0.994943i \(0.467973\pi\)
\(4\) 0 0
\(5\) −1.66668 −0.745362 −0.372681 0.927959i \(-0.621561\pi\)
−0.372681 + 0.927959i \(0.621561\pi\)
\(6\) 0 0
\(7\) −3.92094 −1.48198 −0.740988 0.671518i \(-0.765642\pi\)
−0.740988 + 0.671518i \(0.765642\pi\)
\(8\) 0 0
\(9\) −2.87893 −0.959643
\(10\) 0 0
\(11\) −6.50416 −1.96108 −0.980540 0.196321i \(-0.937100\pi\)
−0.980540 + 0.196321i \(0.937100\pi\)
\(12\) 0 0
\(13\) −3.17112 −0.879511 −0.439756 0.898117i \(-0.644935\pi\)
−0.439756 + 0.898117i \(0.644935\pi\)
\(14\) 0 0
\(15\) −0.579924 −0.149736
\(16\) 0 0
\(17\) 3.56558 0.864781 0.432390 0.901687i \(-0.357670\pi\)
0.432390 + 0.901687i \(0.357670\pi\)
\(18\) 0 0
\(19\) −8.45462 −1.93962 −0.969812 0.243855i \(-0.921588\pi\)
−0.969812 + 0.243855i \(0.921588\pi\)
\(20\) 0 0
\(21\) −1.36430 −0.297714
\(22\) 0 0
\(23\) 4.47235 0.932550 0.466275 0.884640i \(-0.345596\pi\)
0.466275 + 0.884640i \(0.345596\pi\)
\(24\) 0 0
\(25\) −2.22218 −0.444435
\(26\) 0 0
\(27\) −2.04558 −0.393672
\(28\) 0 0
\(29\) −9.13094 −1.69557 −0.847787 0.530337i \(-0.822065\pi\)
−0.847787 + 0.530337i \(0.822065\pi\)
\(30\) 0 0
\(31\) 4.27043 0.766993 0.383496 0.923542i \(-0.374720\pi\)
0.383496 + 0.923542i \(0.374720\pi\)
\(32\) 0 0
\(33\) −2.26313 −0.393961
\(34\) 0 0
\(35\) 6.53495 1.10461
\(36\) 0 0
\(37\) 0.328479 0.0540016 0.0270008 0.999635i \(-0.491404\pi\)
0.0270008 + 0.999635i \(0.491404\pi\)
\(38\) 0 0
\(39\) −1.10340 −0.176685
\(40\) 0 0
\(41\) 8.75568 1.36741 0.683704 0.729760i \(-0.260368\pi\)
0.683704 + 0.729760i \(0.260368\pi\)
\(42\) 0 0
\(43\) 4.27318 0.651653 0.325827 0.945430i \(-0.394357\pi\)
0.325827 + 0.945430i \(0.394357\pi\)
\(44\) 0 0
\(45\) 4.79826 0.715282
\(46\) 0 0
\(47\) −5.78246 −0.843458 −0.421729 0.906722i \(-0.638577\pi\)
−0.421729 + 0.906722i \(0.638577\pi\)
\(48\) 0 0
\(49\) 8.37376 1.19625
\(50\) 0 0
\(51\) 1.24065 0.173726
\(52\) 0 0
\(53\) 13.1862 1.81127 0.905635 0.424058i \(-0.139395\pi\)
0.905635 + 0.424058i \(0.139395\pi\)
\(54\) 0 0
\(55\) 10.8404 1.46171
\(56\) 0 0
\(57\) −2.94180 −0.389650
\(58\) 0 0
\(59\) −6.76862 −0.881199 −0.440599 0.897704i \(-0.645234\pi\)
−0.440599 + 0.897704i \(0.645234\pi\)
\(60\) 0 0
\(61\) −9.71677 −1.24410 −0.622052 0.782976i \(-0.713701\pi\)
−0.622052 + 0.782976i \(0.713701\pi\)
\(62\) 0 0
\(63\) 11.2881 1.42217
\(64\) 0 0
\(65\) 5.28525 0.655554
\(66\) 0 0
\(67\) −11.0508 −1.35007 −0.675035 0.737786i \(-0.735871\pi\)
−0.675035 + 0.737786i \(0.735871\pi\)
\(68\) 0 0
\(69\) 1.55616 0.187340
\(70\) 0 0
\(71\) −13.3491 −1.58425 −0.792126 0.610357i \(-0.791026\pi\)
−0.792126 + 0.610357i \(0.791026\pi\)
\(72\) 0 0
\(73\) 13.0593 1.52847 0.764235 0.644938i \(-0.223117\pi\)
0.764235 + 0.644938i \(0.223117\pi\)
\(74\) 0 0
\(75\) −0.773209 −0.0892825
\(76\) 0 0
\(77\) 25.5024 2.90627
\(78\) 0 0
\(79\) −4.45561 −0.501295 −0.250648 0.968078i \(-0.580644\pi\)
−0.250648 + 0.968078i \(0.580644\pi\)
\(80\) 0 0
\(81\) 7.92503 0.880559
\(82\) 0 0
\(83\) 7.31224 0.802623 0.401312 0.915942i \(-0.368554\pi\)
0.401312 + 0.915942i \(0.368554\pi\)
\(84\) 0 0
\(85\) −5.94269 −0.644575
\(86\) 0 0
\(87\) −3.17712 −0.340623
\(88\) 0 0
\(89\) 0.686662 0.0727860 0.0363930 0.999338i \(-0.488413\pi\)
0.0363930 + 0.999338i \(0.488413\pi\)
\(90\) 0 0
\(91\) 12.4338 1.30341
\(92\) 0 0
\(93\) 1.48590 0.154081
\(94\) 0 0
\(95\) 14.0912 1.44572
\(96\) 0 0
\(97\) −7.21983 −0.733062 −0.366531 0.930406i \(-0.619455\pi\)
−0.366531 + 0.930406i \(0.619455\pi\)
\(98\) 0 0
\(99\) 18.7250 1.88194
\(100\) 0 0
\(101\) −6.30192 −0.627064 −0.313532 0.949578i \(-0.601512\pi\)
−0.313532 + 0.949578i \(0.601512\pi\)
\(102\) 0 0
\(103\) −5.81097 −0.572572 −0.286286 0.958144i \(-0.592421\pi\)
−0.286286 + 0.958144i \(0.592421\pi\)
\(104\) 0 0
\(105\) 2.27385 0.221905
\(106\) 0 0
\(107\) 2.64340 0.255547 0.127773 0.991803i \(-0.459217\pi\)
0.127773 + 0.991803i \(0.459217\pi\)
\(108\) 0 0
\(109\) −11.7569 −1.12611 −0.563054 0.826420i \(-0.690374\pi\)
−0.563054 + 0.826420i \(0.690374\pi\)
\(110\) 0 0
\(111\) 0.114295 0.0108484
\(112\) 0 0
\(113\) −6.65054 −0.625630 −0.312815 0.949814i \(-0.601272\pi\)
−0.312815 + 0.949814i \(0.601272\pi\)
\(114\) 0 0
\(115\) −7.45398 −0.695087
\(116\) 0 0
\(117\) 9.12944 0.844017
\(118\) 0 0
\(119\) −13.9804 −1.28158
\(120\) 0 0
\(121\) 31.3042 2.84583
\(122\) 0 0
\(123\) 3.04655 0.274698
\(124\) 0 0
\(125\) 12.0371 1.07663
\(126\) 0 0
\(127\) −1.19210 −0.105782 −0.0528909 0.998600i \(-0.516844\pi\)
−0.0528909 + 0.998600i \(0.516844\pi\)
\(128\) 0 0
\(129\) 1.48686 0.130910
\(130\) 0 0
\(131\) −10.2112 −0.892155 −0.446078 0.894994i \(-0.647179\pi\)
−0.446078 + 0.894994i \(0.647179\pi\)
\(132\) 0 0
\(133\) 33.1501 2.87447
\(134\) 0 0
\(135\) 3.40933 0.293428
\(136\) 0 0
\(137\) 18.1759 1.55287 0.776436 0.630196i \(-0.217025\pi\)
0.776436 + 0.630196i \(0.217025\pi\)
\(138\) 0 0
\(139\) 14.5710 1.23590 0.617948 0.786219i \(-0.287964\pi\)
0.617948 + 0.786219i \(0.287964\pi\)
\(140\) 0 0
\(141\) −2.01201 −0.169442
\(142\) 0 0
\(143\) 20.6255 1.72479
\(144\) 0 0
\(145\) 15.2184 1.26382
\(146\) 0 0
\(147\) 2.91366 0.240315
\(148\) 0 0
\(149\) −7.11426 −0.582823 −0.291411 0.956598i \(-0.594125\pi\)
−0.291411 + 0.956598i \(0.594125\pi\)
\(150\) 0 0
\(151\) −9.04215 −0.735840 −0.367920 0.929857i \(-0.619930\pi\)
−0.367920 + 0.929857i \(0.619930\pi\)
\(152\) 0 0
\(153\) −10.2651 −0.829881
\(154\) 0 0
\(155\) −7.11745 −0.571687
\(156\) 0 0
\(157\) 10.3571 0.826584 0.413292 0.910599i \(-0.364379\pi\)
0.413292 + 0.910599i \(0.364379\pi\)
\(158\) 0 0
\(159\) 4.58817 0.363866
\(160\) 0 0
\(161\) −17.5358 −1.38202
\(162\) 0 0
\(163\) −2.36738 −0.185427 −0.0927137 0.995693i \(-0.529554\pi\)
−0.0927137 + 0.995693i \(0.529554\pi\)
\(164\) 0 0
\(165\) 3.77192 0.293643
\(166\) 0 0
\(167\) −19.5789 −1.51506 −0.757529 0.652801i \(-0.773594\pi\)
−0.757529 + 0.652801i \(0.773594\pi\)
\(168\) 0 0
\(169\) −2.94398 −0.226460
\(170\) 0 0
\(171\) 24.3403 1.86135
\(172\) 0 0
\(173\) −2.03914 −0.155033 −0.0775166 0.996991i \(-0.524699\pi\)
−0.0775166 + 0.996991i \(0.524699\pi\)
\(174\) 0 0
\(175\) 8.71302 0.658642
\(176\) 0 0
\(177\) −2.35515 −0.177024
\(178\) 0 0
\(179\) −15.6524 −1.16992 −0.584958 0.811063i \(-0.698889\pi\)
−0.584958 + 0.811063i \(0.698889\pi\)
\(180\) 0 0
\(181\) −16.9573 −1.26043 −0.630214 0.776421i \(-0.717033\pi\)
−0.630214 + 0.776421i \(0.717033\pi\)
\(182\) 0 0
\(183\) −3.38096 −0.249928
\(184\) 0 0
\(185\) −0.547470 −0.0402508
\(186\) 0 0
\(187\) −23.1911 −1.69590
\(188\) 0 0
\(189\) 8.02060 0.583413
\(190\) 0 0
\(191\) −14.6370 −1.05910 −0.529550 0.848279i \(-0.677639\pi\)
−0.529550 + 0.848279i \(0.677639\pi\)
\(192\) 0 0
\(193\) −16.2700 −1.17114 −0.585571 0.810621i \(-0.699130\pi\)
−0.585571 + 0.810621i \(0.699130\pi\)
\(194\) 0 0
\(195\) 1.83901 0.131694
\(196\) 0 0
\(197\) −7.90922 −0.563509 −0.281754 0.959487i \(-0.590916\pi\)
−0.281754 + 0.959487i \(0.590916\pi\)
\(198\) 0 0
\(199\) −14.5711 −1.03292 −0.516458 0.856313i \(-0.672750\pi\)
−0.516458 + 0.856313i \(0.672750\pi\)
\(200\) 0 0
\(201\) −3.84514 −0.271215
\(202\) 0 0
\(203\) 35.8019 2.51280
\(204\) 0 0
\(205\) −14.5929 −1.01921
\(206\) 0 0
\(207\) −12.8756 −0.894915
\(208\) 0 0
\(209\) 54.9903 3.80376
\(210\) 0 0
\(211\) 23.8646 1.64291 0.821455 0.570274i \(-0.193163\pi\)
0.821455 + 0.570274i \(0.193163\pi\)
\(212\) 0 0
\(213\) −4.64485 −0.318260
\(214\) 0 0
\(215\) −7.12202 −0.485718
\(216\) 0 0
\(217\) −16.7441 −1.13666
\(218\) 0 0
\(219\) 4.54398 0.307054
\(220\) 0 0
\(221\) −11.3069 −0.760584
\(222\) 0 0
\(223\) −11.7426 −0.786342 −0.393171 0.919465i \(-0.628622\pi\)
−0.393171 + 0.919465i \(0.628622\pi\)
\(224\) 0 0
\(225\) 6.39749 0.426499
\(226\) 0 0
\(227\) 11.6612 0.773980 0.386990 0.922084i \(-0.373515\pi\)
0.386990 + 0.922084i \(0.373515\pi\)
\(228\) 0 0
\(229\) −6.59660 −0.435916 −0.217958 0.975958i \(-0.569940\pi\)
−0.217958 + 0.975958i \(0.569940\pi\)
\(230\) 0 0
\(231\) 8.87360 0.583840
\(232\) 0 0
\(233\) 0.263500 0.0172624 0.00863122 0.999963i \(-0.497253\pi\)
0.00863122 + 0.999963i \(0.497253\pi\)
\(234\) 0 0
\(235\) 9.63751 0.628682
\(236\) 0 0
\(237\) −1.55033 −0.100705
\(238\) 0 0
\(239\) −6.24923 −0.404229 −0.202115 0.979362i \(-0.564781\pi\)
−0.202115 + 0.979362i \(0.564781\pi\)
\(240\) 0 0
\(241\) −8.05529 −0.518887 −0.259443 0.965758i \(-0.583539\pi\)
−0.259443 + 0.965758i \(0.583539\pi\)
\(242\) 0 0
\(243\) 8.89427 0.570567
\(244\) 0 0
\(245\) −13.9564 −0.891641
\(246\) 0 0
\(247\) 26.8106 1.70592
\(248\) 0 0
\(249\) 2.54430 0.161239
\(250\) 0 0
\(251\) 1.00000 0.0631194
\(252\) 0 0
\(253\) −29.0889 −1.82880
\(254\) 0 0
\(255\) −2.06777 −0.129488
\(256\) 0 0
\(257\) 11.1938 0.698247 0.349124 0.937077i \(-0.386479\pi\)
0.349124 + 0.937077i \(0.386479\pi\)
\(258\) 0 0
\(259\) −1.28795 −0.0800291
\(260\) 0 0
\(261\) 26.2873 1.62715
\(262\) 0 0
\(263\) 7.38663 0.455479 0.227740 0.973722i \(-0.426866\pi\)
0.227740 + 0.973722i \(0.426866\pi\)
\(264\) 0 0
\(265\) −21.9773 −1.35005
\(266\) 0 0
\(267\) 0.238925 0.0146220
\(268\) 0 0
\(269\) −19.1530 −1.16778 −0.583890 0.811833i \(-0.698470\pi\)
−0.583890 + 0.811833i \(0.698470\pi\)
\(270\) 0 0
\(271\) −20.7960 −1.26327 −0.631633 0.775268i \(-0.717615\pi\)
−0.631633 + 0.775268i \(0.717615\pi\)
\(272\) 0 0
\(273\) 4.32635 0.261843
\(274\) 0 0
\(275\) 14.4534 0.871573
\(276\) 0 0
\(277\) 17.4617 1.04917 0.524585 0.851358i \(-0.324220\pi\)
0.524585 + 0.851358i \(0.324220\pi\)
\(278\) 0 0
\(279\) −12.2943 −0.736039
\(280\) 0 0
\(281\) −21.1823 −1.26363 −0.631816 0.775118i \(-0.717690\pi\)
−0.631816 + 0.775118i \(0.717690\pi\)
\(282\) 0 0
\(283\) 16.9193 1.00575 0.502873 0.864360i \(-0.332276\pi\)
0.502873 + 0.864360i \(0.332276\pi\)
\(284\) 0 0
\(285\) 4.90304 0.290431
\(286\) 0 0
\(287\) −34.3305 −2.02646
\(288\) 0 0
\(289\) −4.28663 −0.252154
\(290\) 0 0
\(291\) −2.51215 −0.147265
\(292\) 0 0
\(293\) 25.4063 1.48425 0.742126 0.670260i \(-0.233817\pi\)
0.742126 + 0.670260i \(0.233817\pi\)
\(294\) 0 0
\(295\) 11.2811 0.656812
\(296\) 0 0
\(297\) 13.3048 0.772023
\(298\) 0 0
\(299\) −14.1824 −0.820188
\(300\) 0 0
\(301\) −16.7549 −0.965735
\(302\) 0 0
\(303\) −2.19276 −0.125971
\(304\) 0 0
\(305\) 16.1947 0.927308
\(306\) 0 0
\(307\) 10.7326 0.612542 0.306271 0.951944i \(-0.400919\pi\)
0.306271 + 0.951944i \(0.400919\pi\)
\(308\) 0 0
\(309\) −2.02193 −0.115024
\(310\) 0 0
\(311\) 20.4659 1.16052 0.580258 0.814433i \(-0.302952\pi\)
0.580258 + 0.814433i \(0.302952\pi\)
\(312\) 0 0
\(313\) −18.4162 −1.04095 −0.520474 0.853878i \(-0.674245\pi\)
−0.520474 + 0.853878i \(0.674245\pi\)
\(314\) 0 0
\(315\) −18.8137 −1.06003
\(316\) 0 0
\(317\) −18.7775 −1.05465 −0.527324 0.849665i \(-0.676804\pi\)
−0.527324 + 0.849665i \(0.676804\pi\)
\(318\) 0 0
\(319\) 59.3892 3.32515
\(320\) 0 0
\(321\) 0.919774 0.0513368
\(322\) 0 0
\(323\) −30.1457 −1.67735
\(324\) 0 0
\(325\) 7.04679 0.390886
\(326\) 0 0
\(327\) −4.09084 −0.226224
\(328\) 0 0
\(329\) 22.6727 1.24998
\(330\) 0 0
\(331\) 14.4697 0.795325 0.397663 0.917532i \(-0.369821\pi\)
0.397663 + 0.917532i \(0.369821\pi\)
\(332\) 0 0
\(333\) −0.945668 −0.0518223
\(334\) 0 0
\(335\) 18.4181 1.00629
\(336\) 0 0
\(337\) 13.4434 0.732308 0.366154 0.930554i \(-0.380674\pi\)
0.366154 + 0.930554i \(0.380674\pi\)
\(338\) 0 0
\(339\) −2.31406 −0.125683
\(340\) 0 0
\(341\) −27.7756 −1.50413
\(342\) 0 0
\(343\) −5.38644 −0.290841
\(344\) 0 0
\(345\) −2.59362 −0.139636
\(346\) 0 0
\(347\) −23.0973 −1.23993 −0.619965 0.784629i \(-0.712853\pi\)
−0.619965 + 0.784629i \(0.712853\pi\)
\(348\) 0 0
\(349\) −2.67019 −0.142932 −0.0714661 0.997443i \(-0.522768\pi\)
−0.0714661 + 0.997443i \(0.522768\pi\)
\(350\) 0 0
\(351\) 6.48679 0.346239
\(352\) 0 0
\(353\) −1.94957 −0.103765 −0.0518826 0.998653i \(-0.516522\pi\)
−0.0518826 + 0.998653i \(0.516522\pi\)
\(354\) 0 0
\(355\) 22.2488 1.18084
\(356\) 0 0
\(357\) −4.86451 −0.257457
\(358\) 0 0
\(359\) −26.9417 −1.42193 −0.710964 0.703228i \(-0.751741\pi\)
−0.710964 + 0.703228i \(0.751741\pi\)
\(360\) 0 0
\(361\) 52.4806 2.76214
\(362\) 0 0
\(363\) 10.8923 0.571699
\(364\) 0 0
\(365\) −21.7656 −1.13926
\(366\) 0 0
\(367\) 31.6009 1.64956 0.824778 0.565457i \(-0.191300\pi\)
0.824778 + 0.565457i \(0.191300\pi\)
\(368\) 0 0
\(369\) −25.2070 −1.31222
\(370\) 0 0
\(371\) −51.7025 −2.68426
\(372\) 0 0
\(373\) 9.09475 0.470908 0.235454 0.971885i \(-0.424342\pi\)
0.235454 + 0.971885i \(0.424342\pi\)
\(374\) 0 0
\(375\) 4.18831 0.216283
\(376\) 0 0
\(377\) 28.9553 1.49128
\(378\) 0 0
\(379\) 8.83464 0.453805 0.226903 0.973917i \(-0.427140\pi\)
0.226903 + 0.973917i \(0.427140\pi\)
\(380\) 0 0
\(381\) −0.414793 −0.0212505
\(382\) 0 0
\(383\) 20.2103 1.03270 0.516350 0.856378i \(-0.327290\pi\)
0.516350 + 0.856378i \(0.327290\pi\)
\(384\) 0 0
\(385\) −42.5044 −2.16623
\(386\) 0 0
\(387\) −12.3022 −0.625355
\(388\) 0 0
\(389\) −19.0488 −0.965811 −0.482906 0.875672i \(-0.660419\pi\)
−0.482906 + 0.875672i \(0.660419\pi\)
\(390\) 0 0
\(391\) 15.9465 0.806451
\(392\) 0 0
\(393\) −3.55299 −0.179225
\(394\) 0 0
\(395\) 7.42608 0.373646
\(396\) 0 0
\(397\) −3.45788 −0.173546 −0.0867729 0.996228i \(-0.527655\pi\)
−0.0867729 + 0.996228i \(0.527655\pi\)
\(398\) 0 0
\(399\) 11.5346 0.577453
\(400\) 0 0
\(401\) 13.9333 0.695793 0.347897 0.937533i \(-0.386896\pi\)
0.347897 + 0.937533i \(0.386896\pi\)
\(402\) 0 0
\(403\) −13.5421 −0.674579
\(404\) 0 0
\(405\) −13.2085 −0.656335
\(406\) 0 0
\(407\) −2.13648 −0.105901
\(408\) 0 0
\(409\) 16.4690 0.814340 0.407170 0.913352i \(-0.366516\pi\)
0.407170 + 0.913352i \(0.366516\pi\)
\(410\) 0 0
\(411\) 6.32433 0.311956
\(412\) 0 0
\(413\) 26.5393 1.30592
\(414\) 0 0
\(415\) −12.1872 −0.598245
\(416\) 0 0
\(417\) 5.06999 0.248279
\(418\) 0 0
\(419\) −15.8528 −0.774460 −0.387230 0.921983i \(-0.626568\pi\)
−0.387230 + 0.921983i \(0.626568\pi\)
\(420\) 0 0
\(421\) 4.60533 0.224450 0.112225 0.993683i \(-0.464202\pi\)
0.112225 + 0.993683i \(0.464202\pi\)
\(422\) 0 0
\(423\) 16.6473 0.809419
\(424\) 0 0
\(425\) −7.92335 −0.384339
\(426\) 0 0
\(427\) 38.0988 1.84373
\(428\) 0 0
\(429\) 7.17667 0.346493
\(430\) 0 0
\(431\) 14.8906 0.717255 0.358627 0.933481i \(-0.383245\pi\)
0.358627 + 0.933481i \(0.383245\pi\)
\(432\) 0 0
\(433\) 5.48236 0.263466 0.131733 0.991285i \(-0.457946\pi\)
0.131733 + 0.991285i \(0.457946\pi\)
\(434\) 0 0
\(435\) 5.29525 0.253888
\(436\) 0 0
\(437\) −37.8121 −1.80880
\(438\) 0 0
\(439\) 37.5571 1.79250 0.896251 0.443548i \(-0.146280\pi\)
0.896251 + 0.443548i \(0.146280\pi\)
\(440\) 0 0
\(441\) −24.1075 −1.14798
\(442\) 0 0
\(443\) 23.7730 1.12949 0.564744 0.825266i \(-0.308975\pi\)
0.564744 + 0.825266i \(0.308975\pi\)
\(444\) 0 0
\(445\) −1.14445 −0.0542520
\(446\) 0 0
\(447\) −2.47541 −0.117083
\(448\) 0 0
\(449\) 0.102297 0.00482769 0.00241384 0.999997i \(-0.499232\pi\)
0.00241384 + 0.999997i \(0.499232\pi\)
\(450\) 0 0
\(451\) −56.9484 −2.68159
\(452\) 0 0
\(453\) −3.14623 −0.147823
\(454\) 0 0
\(455\) −20.7231 −0.971516
\(456\) 0 0
\(457\) −14.0706 −0.658196 −0.329098 0.944296i \(-0.606745\pi\)
−0.329098 + 0.944296i \(0.606745\pi\)
\(458\) 0 0
\(459\) −7.29369 −0.340440
\(460\) 0 0
\(461\) −36.3917 −1.69493 −0.847466 0.530850i \(-0.821873\pi\)
−0.847466 + 0.530850i \(0.821873\pi\)
\(462\) 0 0
\(463\) −3.66002 −0.170095 −0.0850477 0.996377i \(-0.527104\pi\)
−0.0850477 + 0.996377i \(0.527104\pi\)
\(464\) 0 0
\(465\) −2.47653 −0.114846
\(466\) 0 0
\(467\) −33.6336 −1.55638 −0.778190 0.628029i \(-0.783862\pi\)
−0.778190 + 0.628029i \(0.783862\pi\)
\(468\) 0 0
\(469\) 43.3295 2.00077
\(470\) 0 0
\(471\) 3.60375 0.166052
\(472\) 0 0
\(473\) −27.7934 −1.27794
\(474\) 0 0
\(475\) 18.7877 0.862037
\(476\) 0 0
\(477\) −37.9623 −1.73817
\(478\) 0 0
\(479\) 14.5330 0.664030 0.332015 0.943274i \(-0.392272\pi\)
0.332015 + 0.943274i \(0.392272\pi\)
\(480\) 0 0
\(481\) −1.04165 −0.0474950
\(482\) 0 0
\(483\) −6.10161 −0.277633
\(484\) 0 0
\(485\) 12.0331 0.546397
\(486\) 0 0
\(487\) 7.46156 0.338115 0.169058 0.985606i \(-0.445928\pi\)
0.169058 + 0.985606i \(0.445928\pi\)
\(488\) 0 0
\(489\) −0.823732 −0.0372504
\(490\) 0 0
\(491\) −16.8325 −0.759641 −0.379821 0.925060i \(-0.624014\pi\)
−0.379821 + 0.925060i \(0.624014\pi\)
\(492\) 0 0
\(493\) −32.5571 −1.46630
\(494\) 0 0
\(495\) −31.2086 −1.40272
\(496\) 0 0
\(497\) 52.3412 2.34782
\(498\) 0 0
\(499\) 4.87038 0.218028 0.109014 0.994040i \(-0.465231\pi\)
0.109014 + 0.994040i \(0.465231\pi\)
\(500\) 0 0
\(501\) −6.81249 −0.304360
\(502\) 0 0
\(503\) 21.5924 0.962756 0.481378 0.876513i \(-0.340136\pi\)
0.481378 + 0.876513i \(0.340136\pi\)
\(504\) 0 0
\(505\) 10.5033 0.467390
\(506\) 0 0
\(507\) −1.02436 −0.0454935
\(508\) 0 0
\(509\) 7.12405 0.315768 0.157884 0.987458i \(-0.449533\pi\)
0.157884 + 0.987458i \(0.449533\pi\)
\(510\) 0 0
\(511\) −51.2045 −2.26516
\(512\) 0 0
\(513\) 17.2946 0.763576
\(514\) 0 0
\(515\) 9.68503 0.426773
\(516\) 0 0
\(517\) 37.6101 1.65409
\(518\) 0 0
\(519\) −0.709523 −0.0311446
\(520\) 0 0
\(521\) 2.73427 0.119790 0.0598952 0.998205i \(-0.480923\pi\)
0.0598952 + 0.998205i \(0.480923\pi\)
\(522\) 0 0
\(523\) 27.8346 1.21712 0.608562 0.793506i \(-0.291747\pi\)
0.608562 + 0.793506i \(0.291747\pi\)
\(524\) 0 0
\(525\) 3.03171 0.132314
\(526\) 0 0
\(527\) 15.2266 0.663280
\(528\) 0 0
\(529\) −2.99807 −0.130351
\(530\) 0 0
\(531\) 19.4864 0.845636
\(532\) 0 0
\(533\) −27.7653 −1.20265
\(534\) 0 0
\(535\) −4.40570 −0.190475
\(536\) 0 0
\(537\) −5.44628 −0.235024
\(538\) 0 0
\(539\) −54.4643 −2.34595
\(540\) 0 0
\(541\) −9.64489 −0.414666 −0.207333 0.978270i \(-0.566478\pi\)
−0.207333 + 0.978270i \(0.566478\pi\)
\(542\) 0 0
\(543\) −5.90032 −0.253207
\(544\) 0 0
\(545\) 19.5950 0.839359
\(546\) 0 0
\(547\) −3.28761 −0.140568 −0.0702841 0.997527i \(-0.522391\pi\)
−0.0702841 + 0.997527i \(0.522391\pi\)
\(548\) 0 0
\(549\) 27.9739 1.19390
\(550\) 0 0
\(551\) 77.1987 3.28877
\(552\) 0 0
\(553\) 17.4702 0.742907
\(554\) 0 0
\(555\) −0.190493 −0.00808597
\(556\) 0 0
\(557\) 35.8810 1.52033 0.760163 0.649732i \(-0.225119\pi\)
0.760163 + 0.649732i \(0.225119\pi\)
\(558\) 0 0
\(559\) −13.5508 −0.573137
\(560\) 0 0
\(561\) −8.06938 −0.340690
\(562\) 0 0
\(563\) −20.9369 −0.882386 −0.441193 0.897412i \(-0.645445\pi\)
−0.441193 + 0.897412i \(0.645445\pi\)
\(564\) 0 0
\(565\) 11.0843 0.466321
\(566\) 0 0
\(567\) −31.0735 −1.30497
\(568\) 0 0
\(569\) −8.39753 −0.352043 −0.176021 0.984386i \(-0.556323\pi\)
−0.176021 + 0.984386i \(0.556323\pi\)
\(570\) 0 0
\(571\) 40.4903 1.69446 0.847232 0.531223i \(-0.178267\pi\)
0.847232 + 0.531223i \(0.178267\pi\)
\(572\) 0 0
\(573\) −5.09298 −0.212762
\(574\) 0 0
\(575\) −9.93835 −0.414458
\(576\) 0 0
\(577\) −10.9105 −0.454211 −0.227106 0.973870i \(-0.572926\pi\)
−0.227106 + 0.973870i \(0.572926\pi\)
\(578\) 0 0
\(579\) −5.66118 −0.235271
\(580\) 0 0
\(581\) −28.6709 −1.18947
\(582\) 0 0
\(583\) −85.7655 −3.55204
\(584\) 0 0
\(585\) −15.2159 −0.629098
\(586\) 0 0
\(587\) 27.1630 1.12114 0.560568 0.828108i \(-0.310583\pi\)
0.560568 + 0.828108i \(0.310583\pi\)
\(588\) 0 0
\(589\) −36.1049 −1.48768
\(590\) 0 0
\(591\) −2.75202 −0.113203
\(592\) 0 0
\(593\) 12.1133 0.497433 0.248717 0.968576i \(-0.419991\pi\)
0.248717 + 0.968576i \(0.419991\pi\)
\(594\) 0 0
\(595\) 23.3009 0.955244
\(596\) 0 0
\(597\) −5.07002 −0.207502
\(598\) 0 0
\(599\) −17.8923 −0.731060 −0.365530 0.930800i \(-0.619112\pi\)
−0.365530 + 0.930800i \(0.619112\pi\)
\(600\) 0 0
\(601\) 11.6781 0.476361 0.238181 0.971221i \(-0.423449\pi\)
0.238181 + 0.971221i \(0.423449\pi\)
\(602\) 0 0
\(603\) 31.8145 1.29558
\(604\) 0 0
\(605\) −52.1740 −2.12118
\(606\) 0 0
\(607\) 29.7156 1.20612 0.603060 0.797696i \(-0.293948\pi\)
0.603060 + 0.797696i \(0.293948\pi\)
\(608\) 0 0
\(609\) 12.4573 0.504796
\(610\) 0 0
\(611\) 18.3369 0.741831
\(612\) 0 0
\(613\) 4.87567 0.196926 0.0984632 0.995141i \(-0.468607\pi\)
0.0984632 + 0.995141i \(0.468607\pi\)
\(614\) 0 0
\(615\) −5.07763 −0.204750
\(616\) 0 0
\(617\) −23.4345 −0.943437 −0.471718 0.881749i \(-0.656366\pi\)
−0.471718 + 0.881749i \(0.656366\pi\)
\(618\) 0 0
\(619\) −20.1139 −0.808446 −0.404223 0.914660i \(-0.632458\pi\)
−0.404223 + 0.914660i \(0.632458\pi\)
\(620\) 0 0
\(621\) −9.14856 −0.367119
\(622\) 0 0
\(623\) −2.69236 −0.107867
\(624\) 0 0
\(625\) −8.95105 −0.358042
\(626\) 0 0
\(627\) 19.1339 0.764136
\(628\) 0 0
\(629\) 1.17122 0.0466995
\(630\) 0 0
\(631\) −5.46796 −0.217676 −0.108838 0.994059i \(-0.534713\pi\)
−0.108838 + 0.994059i \(0.534713\pi\)
\(632\) 0 0
\(633\) 8.30373 0.330044
\(634\) 0 0
\(635\) 1.98685 0.0788458
\(636\) 0 0
\(637\) −26.5542 −1.05212
\(638\) 0 0
\(639\) 38.4313 1.52032
\(640\) 0 0
\(641\) −37.9490 −1.49889 −0.749447 0.662065i \(-0.769680\pi\)
−0.749447 + 0.662065i \(0.769680\pi\)
\(642\) 0 0
\(643\) −9.32952 −0.367921 −0.183960 0.982934i \(-0.558892\pi\)
−0.183960 + 0.982934i \(0.558892\pi\)
\(644\) 0 0
\(645\) −2.47812 −0.0975757
\(646\) 0 0
\(647\) −0.0456503 −0.00179470 −0.000897349 1.00000i \(-0.500286\pi\)
−0.000897349 1.00000i \(0.500286\pi\)
\(648\) 0 0
\(649\) 44.0242 1.72810
\(650\) 0 0
\(651\) −5.82613 −0.228344
\(652\) 0 0
\(653\) 28.7896 1.12662 0.563311 0.826245i \(-0.309527\pi\)
0.563311 + 0.826245i \(0.309527\pi\)
\(654\) 0 0
\(655\) 17.0188 0.664979
\(656\) 0 0
\(657\) −37.5967 −1.46679
\(658\) 0 0
\(659\) −37.9516 −1.47838 −0.739192 0.673495i \(-0.764792\pi\)
−0.739192 + 0.673495i \(0.764792\pi\)
\(660\) 0 0
\(661\) −21.0516 −0.818811 −0.409406 0.912353i \(-0.634264\pi\)
−0.409406 + 0.912353i \(0.634264\pi\)
\(662\) 0 0
\(663\) −3.93425 −0.152794
\(664\) 0 0
\(665\) −55.2506 −2.14252
\(666\) 0 0
\(667\) −40.8368 −1.58121
\(668\) 0 0
\(669\) −4.08585 −0.157968
\(670\) 0 0
\(671\) 63.1994 2.43979
\(672\) 0 0
\(673\) −10.9974 −0.423919 −0.211960 0.977278i \(-0.567985\pi\)
−0.211960 + 0.977278i \(0.567985\pi\)
\(674\) 0 0
\(675\) 4.54564 0.174962
\(676\) 0 0
\(677\) −7.64047 −0.293647 −0.146823 0.989163i \(-0.546905\pi\)
−0.146823 + 0.989163i \(0.546905\pi\)
\(678\) 0 0
\(679\) 28.3085 1.08638
\(680\) 0 0
\(681\) 4.05752 0.155485
\(682\) 0 0
\(683\) −10.4797 −0.400994 −0.200497 0.979694i \(-0.564256\pi\)
−0.200497 + 0.979694i \(0.564256\pi\)
\(684\) 0 0
\(685\) −30.2934 −1.15745
\(686\) 0 0
\(687\) −2.29530 −0.0875710
\(688\) 0 0
\(689\) −41.8152 −1.59303
\(690\) 0 0
\(691\) 3.01626 0.114744 0.0573719 0.998353i \(-0.481728\pi\)
0.0573719 + 0.998353i \(0.481728\pi\)
\(692\) 0 0
\(693\) −73.4197 −2.78898
\(694\) 0 0
\(695\) −24.2852 −0.921189
\(696\) 0 0
\(697\) 31.2191 1.18251
\(698\) 0 0
\(699\) 0.0916850 0.00346785
\(700\) 0 0
\(701\) 38.9027 1.46933 0.734667 0.678428i \(-0.237338\pi\)
0.734667 + 0.678428i \(0.237338\pi\)
\(702\) 0 0
\(703\) −2.77717 −0.104743
\(704\) 0 0
\(705\) 3.35338 0.126296
\(706\) 0 0
\(707\) 24.7094 0.929294
\(708\) 0 0
\(709\) −24.5906 −0.923521 −0.461760 0.887005i \(-0.652782\pi\)
−0.461760 + 0.887005i \(0.652782\pi\)
\(710\) 0 0
\(711\) 12.8274 0.481065
\(712\) 0 0
\(713\) 19.0989 0.715259
\(714\) 0 0
\(715\) −34.3761 −1.28559
\(716\) 0 0
\(717\) −2.17443 −0.0812055
\(718\) 0 0
\(719\) 0.156573 0.00583918 0.00291959 0.999996i \(-0.499071\pi\)
0.00291959 + 0.999996i \(0.499071\pi\)
\(720\) 0 0
\(721\) 22.7845 0.848538
\(722\) 0 0
\(723\) −2.80285 −0.104239
\(724\) 0 0
\(725\) 20.2906 0.753573
\(726\) 0 0
\(727\) 11.1047 0.411852 0.205926 0.978568i \(-0.433979\pi\)
0.205926 + 0.978568i \(0.433979\pi\)
\(728\) 0 0
\(729\) −20.6803 −0.765937
\(730\) 0 0
\(731\) 15.2364 0.563537
\(732\) 0 0
\(733\) −7.81269 −0.288568 −0.144284 0.989536i \(-0.546088\pi\)
−0.144284 + 0.989536i \(0.546088\pi\)
\(734\) 0 0
\(735\) −4.85614 −0.179122
\(736\) 0 0
\(737\) 71.8762 2.64759
\(738\) 0 0
\(739\) 29.3982 1.08143 0.540714 0.841206i \(-0.318154\pi\)
0.540714 + 0.841206i \(0.318154\pi\)
\(740\) 0 0
\(741\) 9.32880 0.342702
\(742\) 0 0
\(743\) 7.40008 0.271483 0.135741 0.990744i \(-0.456658\pi\)
0.135741 + 0.990744i \(0.456658\pi\)
\(744\) 0 0
\(745\) 11.8572 0.434414
\(746\) 0 0
\(747\) −21.0514 −0.770232
\(748\) 0 0
\(749\) −10.3646 −0.378714
\(750\) 0 0
\(751\) −25.4408 −0.928348 −0.464174 0.885744i \(-0.653649\pi\)
−0.464174 + 0.885744i \(0.653649\pi\)
\(752\) 0 0
\(753\) 0.347951 0.0126800
\(754\) 0 0
\(755\) 15.0704 0.548467
\(756\) 0 0
\(757\) 29.1043 1.05781 0.528906 0.848680i \(-0.322602\pi\)
0.528906 + 0.848680i \(0.322602\pi\)
\(758\) 0 0
\(759\) −10.1215 −0.367388
\(760\) 0 0
\(761\) −11.7236 −0.424980 −0.212490 0.977163i \(-0.568157\pi\)
−0.212490 + 0.977163i \(0.568157\pi\)
\(762\) 0 0
\(763\) 46.0982 1.66887
\(764\) 0 0
\(765\) 17.1086 0.618562
\(766\) 0 0
\(767\) 21.4641 0.775024
\(768\) 0 0
\(769\) 18.6306 0.671837 0.335918 0.941891i \(-0.390953\pi\)
0.335918 + 0.941891i \(0.390953\pi\)
\(770\) 0 0
\(771\) 3.89488 0.140271
\(772\) 0 0
\(773\) −2.06926 −0.0744261 −0.0372130 0.999307i \(-0.511848\pi\)
−0.0372130 + 0.999307i \(0.511848\pi\)
\(774\) 0 0
\(775\) −9.48965 −0.340878
\(776\) 0 0
\(777\) −0.448142 −0.0160770
\(778\) 0 0
\(779\) −74.0260 −2.65226
\(780\) 0 0
\(781\) 86.8250 3.10684
\(782\) 0 0
\(783\) 18.6781 0.667500
\(784\) 0 0
\(785\) −17.2619 −0.616104
\(786\) 0 0
\(787\) 24.1887 0.862232 0.431116 0.902296i \(-0.358120\pi\)
0.431116 + 0.902296i \(0.358120\pi\)
\(788\) 0 0
\(789\) 2.57019 0.0915011
\(790\) 0 0
\(791\) 26.0764 0.927169
\(792\) 0 0
\(793\) 30.8131 1.09420
\(794\) 0 0
\(795\) −7.64702 −0.271212
\(796\) 0 0
\(797\) −48.7623 −1.72725 −0.863625 0.504135i \(-0.831811\pi\)
−0.863625 + 0.504135i \(0.831811\pi\)
\(798\) 0 0
\(799\) −20.6178 −0.729406
\(800\) 0 0
\(801\) −1.97685 −0.0698486
\(802\) 0 0
\(803\) −84.9395 −2.99745
\(804\) 0 0
\(805\) 29.2266 1.03010
\(806\) 0 0
\(807\) −6.66431 −0.234595
\(808\) 0 0
\(809\) −16.4974 −0.580018 −0.290009 0.957024i \(-0.593658\pi\)
−0.290009 + 0.957024i \(0.593658\pi\)
\(810\) 0 0
\(811\) −25.8204 −0.906678 −0.453339 0.891338i \(-0.649767\pi\)
−0.453339 + 0.891338i \(0.649767\pi\)
\(812\) 0 0
\(813\) −7.23599 −0.253777
\(814\) 0 0
\(815\) 3.94566 0.138211
\(816\) 0 0
\(817\) −36.1281 −1.26396
\(818\) 0 0
\(819\) −35.7960 −1.25081
\(820\) 0 0
\(821\) 36.0442 1.25795 0.628975 0.777425i \(-0.283475\pi\)
0.628975 + 0.777425i \(0.283475\pi\)
\(822\) 0 0
\(823\) −21.4497 −0.747691 −0.373846 0.927491i \(-0.621961\pi\)
−0.373846 + 0.927491i \(0.621961\pi\)
\(824\) 0 0
\(825\) 5.02908 0.175090
\(826\) 0 0
\(827\) 30.7729 1.07008 0.535039 0.844827i \(-0.320297\pi\)
0.535039 + 0.844827i \(0.320297\pi\)
\(828\) 0 0
\(829\) 5.71459 0.198476 0.0992380 0.995064i \(-0.468359\pi\)
0.0992380 + 0.995064i \(0.468359\pi\)
\(830\) 0 0
\(831\) 6.07581 0.210768
\(832\) 0 0
\(833\) 29.8573 1.03450
\(834\) 0 0
\(835\) 32.6317 1.12927
\(836\) 0 0
\(837\) −8.73552 −0.301944
\(838\) 0 0
\(839\) 25.0740 0.865651 0.432825 0.901478i \(-0.357517\pi\)
0.432825 + 0.901478i \(0.357517\pi\)
\(840\) 0 0
\(841\) 54.3741 1.87497
\(842\) 0 0
\(843\) −7.37042 −0.253851
\(844\) 0 0
\(845\) 4.90667 0.168795
\(846\) 0 0
\(847\) −122.742 −4.21745
\(848\) 0 0
\(849\) 5.88708 0.202044
\(850\) 0 0
\(851\) 1.46907 0.0503592
\(852\) 0 0
\(853\) −49.4866 −1.69439 −0.847194 0.531283i \(-0.821710\pi\)
−0.847194 + 0.531283i \(0.821710\pi\)
\(854\) 0 0
\(855\) −40.5674 −1.38738
\(856\) 0 0
\(857\) −10.0799 −0.344323 −0.172162 0.985069i \(-0.555075\pi\)
−0.172162 + 0.985069i \(0.555075\pi\)
\(858\) 0 0
\(859\) −9.05552 −0.308971 −0.154485 0.987995i \(-0.549372\pi\)
−0.154485 + 0.987995i \(0.549372\pi\)
\(860\) 0 0
\(861\) −11.9453 −0.407096
\(862\) 0 0
\(863\) −25.5844 −0.870905 −0.435452 0.900212i \(-0.643412\pi\)
−0.435452 + 0.900212i \(0.643412\pi\)
\(864\) 0 0
\(865\) 3.39860 0.115556
\(866\) 0 0
\(867\) −1.49154 −0.0506552
\(868\) 0 0
\(869\) 28.9800 0.983079
\(870\) 0 0
\(871\) 35.0434 1.18740
\(872\) 0 0
\(873\) 20.7854 0.703478
\(874\) 0 0
\(875\) −47.1966 −1.59554
\(876\) 0 0
\(877\) 0.382964 0.0129318 0.00646589 0.999979i \(-0.497942\pi\)
0.00646589 + 0.999979i \(0.497942\pi\)
\(878\) 0 0
\(879\) 8.84016 0.298171
\(880\) 0 0
\(881\) 31.0150 1.04492 0.522461 0.852663i \(-0.325014\pi\)
0.522461 + 0.852663i \(0.325014\pi\)
\(882\) 0 0
\(883\) 6.08867 0.204900 0.102450 0.994738i \(-0.467332\pi\)
0.102450 + 0.994738i \(0.467332\pi\)
\(884\) 0 0
\(885\) 3.92528 0.131947
\(886\) 0 0
\(887\) 16.8796 0.566761 0.283381 0.959008i \(-0.408544\pi\)
0.283381 + 0.959008i \(0.408544\pi\)
\(888\) 0 0
\(889\) 4.67415 0.156766
\(890\) 0 0
\(891\) −51.5457 −1.72685
\(892\) 0 0
\(893\) 48.8885 1.63599
\(894\) 0 0
\(895\) 26.0876 0.872012
\(896\) 0 0
\(897\) −4.93478 −0.164767
\(898\) 0 0
\(899\) −38.9931 −1.30049
\(900\) 0 0
\(901\) 47.0166 1.56635
\(902\) 0 0
\(903\) −5.82988 −0.194006
\(904\) 0 0
\(905\) 28.2625 0.939476
\(906\) 0 0
\(907\) −40.9172 −1.35863 −0.679316 0.733846i \(-0.737723\pi\)
−0.679316 + 0.733846i \(0.737723\pi\)
\(908\) 0 0
\(909\) 18.1428 0.601758
\(910\) 0 0
\(911\) 17.6427 0.584528 0.292264 0.956338i \(-0.405591\pi\)
0.292264 + 0.956338i \(0.405591\pi\)
\(912\) 0 0
\(913\) −47.5600 −1.57401
\(914\) 0 0
\(915\) 5.63498 0.186287
\(916\) 0 0
\(917\) 40.0374 1.32215
\(918\) 0 0
\(919\) −8.10409 −0.267329 −0.133665 0.991027i \(-0.542675\pi\)
−0.133665 + 0.991027i \(0.542675\pi\)
\(920\) 0 0
\(921\) 3.73443 0.123054
\(922\) 0 0
\(923\) 42.3318 1.39337
\(924\) 0 0
\(925\) −0.729938 −0.0240002
\(926\) 0 0
\(927\) 16.7294 0.549465
\(928\) 0 0
\(929\) 1.87593 0.0615473 0.0307736 0.999526i \(-0.490203\pi\)
0.0307736 + 0.999526i \(0.490203\pi\)
\(930\) 0 0
\(931\) −70.7970 −2.32028
\(932\) 0 0
\(933\) 7.12114 0.233136
\(934\) 0 0
\(935\) 38.6522 1.26406
\(936\) 0 0
\(937\) −43.0032 −1.40485 −0.702427 0.711756i \(-0.747900\pi\)
−0.702427 + 0.711756i \(0.747900\pi\)
\(938\) 0 0
\(939\) −6.40796 −0.209116
\(940\) 0 0
\(941\) −48.6146 −1.58479 −0.792396 0.610007i \(-0.791167\pi\)
−0.792396 + 0.610007i \(0.791167\pi\)
\(942\) 0 0
\(943\) 39.1585 1.27518
\(944\) 0 0
\(945\) −13.3678 −0.434854
\(946\) 0 0
\(947\) −32.0841 −1.04259 −0.521296 0.853376i \(-0.674551\pi\)
−0.521296 + 0.853376i \(0.674551\pi\)
\(948\) 0 0
\(949\) −41.4125 −1.34431
\(950\) 0 0
\(951\) −6.53364 −0.211868
\(952\) 0 0
\(953\) −34.6969 −1.12394 −0.561971 0.827157i \(-0.689957\pi\)
−0.561971 + 0.827157i \(0.689957\pi\)
\(954\) 0 0
\(955\) 24.3953 0.789413
\(956\) 0 0
\(957\) 20.6645 0.667990
\(958\) 0 0
\(959\) −71.2666 −2.30132
\(960\) 0 0
\(961\) −12.7634 −0.411722
\(962\) 0 0
\(963\) −7.61016 −0.245234
\(964\) 0 0
\(965\) 27.1169 0.872925
\(966\) 0 0
\(967\) −4.10488 −0.132004 −0.0660020 0.997819i \(-0.521024\pi\)
−0.0660020 + 0.997819i \(0.521024\pi\)
\(968\) 0 0
\(969\) −10.4892 −0.336962
\(970\) 0 0
\(971\) 30.5760 0.981230 0.490615 0.871377i \(-0.336772\pi\)
0.490615 + 0.871377i \(0.336772\pi\)
\(972\) 0 0
\(973\) −57.1320 −1.83157
\(974\) 0 0
\(975\) 2.45194 0.0785249
\(976\) 0 0
\(977\) −17.3109 −0.553824 −0.276912 0.960895i \(-0.589311\pi\)
−0.276912 + 0.960895i \(0.589311\pi\)
\(978\) 0 0
\(979\) −4.46616 −0.142739
\(980\) 0 0
\(981\) 33.8474 1.08066
\(982\) 0 0
\(983\) −25.9316 −0.827090 −0.413545 0.910484i \(-0.635710\pi\)
−0.413545 + 0.910484i \(0.635710\pi\)
\(984\) 0 0
\(985\) 13.1821 0.420018
\(986\) 0 0
\(987\) 7.88898 0.251109
\(988\) 0 0
\(989\) 19.1112 0.607699
\(990\) 0 0
\(991\) −47.3995 −1.50569 −0.752847 0.658195i \(-0.771320\pi\)
−0.752847 + 0.658195i \(0.771320\pi\)
\(992\) 0 0
\(993\) 5.03474 0.159773
\(994\) 0 0
\(995\) 24.2853 0.769896
\(996\) 0 0
\(997\) 49.4331 1.56556 0.782781 0.622297i \(-0.213800\pi\)
0.782781 + 0.622297i \(0.213800\pi\)
\(998\) 0 0
\(999\) −0.671930 −0.0212589
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.1.14 23
4.3 odd 2 2008.2.a.d.1.10 23
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2008.2.a.d.1.10 23 4.3 odd 2
4016.2.a.m.1.14 23 1.1 even 1 trivial