Properties

Label 6008.2.a.b.1.27
Level 6008
Weight 2
Character 6008.1
Self dual yes
Analytic conductor 47.974
Analytic rank 1
Dimension 44
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6008.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(47.9741215344\)
Analytic rank: \(1\)
Dimension: \(44\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.27
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.278140 q^{3} +1.58670 q^{5} -2.49171 q^{7} -2.92264 q^{9} +O(q^{10})\) \(q+0.278140 q^{3} +1.58670 q^{5} -2.49171 q^{7} -2.92264 q^{9} +5.31839 q^{11} -4.17786 q^{13} +0.441324 q^{15} -3.16226 q^{17} +5.18165 q^{19} -0.693044 q^{21} -2.27106 q^{23} -2.48239 q^{25} -1.64732 q^{27} +4.70849 q^{29} -0.466223 q^{31} +1.47926 q^{33} -3.95359 q^{35} +4.71895 q^{37} -1.16203 q^{39} +4.53789 q^{41} +3.13155 q^{43} -4.63734 q^{45} -1.59850 q^{47} -0.791388 q^{49} -0.879550 q^{51} -3.67829 q^{53} +8.43868 q^{55} +1.44122 q^{57} -3.30428 q^{59} -6.92274 q^{61} +7.28236 q^{63} -6.62900 q^{65} -12.2927 q^{67} -0.631673 q^{69} +12.0893 q^{71} -5.02316 q^{73} -0.690452 q^{75} -13.2519 q^{77} -12.9398 q^{79} +8.30973 q^{81} -12.3149 q^{83} -5.01755 q^{85} +1.30962 q^{87} -15.2492 q^{89} +10.4100 q^{91} -0.129675 q^{93} +8.22171 q^{95} +3.89871 q^{97} -15.5437 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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
\(3\) 0.278140 0.160584 0.0802921 0.996771i \(-0.474415\pi\)
0.0802921 + 0.996771i \(0.474415\pi\)
\(4\) 0 0
\(5\) 1.58670 0.709593 0.354796 0.934944i \(-0.384550\pi\)
0.354796 + 0.934944i \(0.384550\pi\)
\(6\) 0 0
\(7\) −2.49171 −0.941777 −0.470889 0.882193i \(-0.656067\pi\)
−0.470889 + 0.882193i \(0.656067\pi\)
\(8\) 0 0
\(9\) −2.92264 −0.974213
\(10\) 0 0
\(11\) 5.31839 1.60356 0.801778 0.597622i \(-0.203888\pi\)
0.801778 + 0.597622i \(0.203888\pi\)
\(12\) 0 0
\(13\) −4.17786 −1.15873 −0.579365 0.815069i \(-0.696699\pi\)
−0.579365 + 0.815069i \(0.696699\pi\)
\(14\) 0 0
\(15\) 0.441324 0.113949
\(16\) 0 0
\(17\) −3.16226 −0.766960 −0.383480 0.923549i \(-0.625275\pi\)
−0.383480 + 0.923549i \(0.625275\pi\)
\(18\) 0 0
\(19\) 5.18165 1.18875 0.594376 0.804187i \(-0.297399\pi\)
0.594376 + 0.804187i \(0.297399\pi\)
\(20\) 0 0
\(21\) −0.693044 −0.151235
\(22\) 0 0
\(23\) −2.27106 −0.473550 −0.236775 0.971565i \(-0.576090\pi\)
−0.236775 + 0.971565i \(0.576090\pi\)
\(24\) 0 0
\(25\) −2.48239 −0.496478
\(26\) 0 0
\(27\) −1.64732 −0.317027
\(28\) 0 0
\(29\) 4.70849 0.874345 0.437173 0.899378i \(-0.355980\pi\)
0.437173 + 0.899378i \(0.355980\pi\)
\(30\) 0 0
\(31\) −0.466223 −0.0837361 −0.0418680 0.999123i \(-0.513331\pi\)
−0.0418680 + 0.999123i \(0.513331\pi\)
\(32\) 0 0
\(33\) 1.47926 0.257506
\(34\) 0 0
\(35\) −3.95359 −0.668278
\(36\) 0 0
\(37\) 4.71895 0.775791 0.387896 0.921703i \(-0.373202\pi\)
0.387896 + 0.921703i \(0.373202\pi\)
\(38\) 0 0
\(39\) −1.16203 −0.186074
\(40\) 0 0
\(41\) 4.53789 0.708699 0.354349 0.935113i \(-0.384702\pi\)
0.354349 + 0.935113i \(0.384702\pi\)
\(42\) 0 0
\(43\) 3.13155 0.477557 0.238778 0.971074i \(-0.423253\pi\)
0.238778 + 0.971074i \(0.423253\pi\)
\(44\) 0 0
\(45\) −4.63734 −0.691294
\(46\) 0 0
\(47\) −1.59850 −0.233165 −0.116583 0.993181i \(-0.537194\pi\)
−0.116583 + 0.993181i \(0.537194\pi\)
\(48\) 0 0
\(49\) −0.791388 −0.113055
\(50\) 0 0
\(51\) −0.879550 −0.123162
\(52\) 0 0
\(53\) −3.67829 −0.505252 −0.252626 0.967564i \(-0.581294\pi\)
−0.252626 + 0.967564i \(0.581294\pi\)
\(54\) 0 0
\(55\) 8.43868 1.13787
\(56\) 0 0
\(57\) 1.44122 0.190895
\(58\) 0 0
\(59\) −3.30428 −0.430181 −0.215090 0.976594i \(-0.569005\pi\)
−0.215090 + 0.976594i \(0.569005\pi\)
\(60\) 0 0
\(61\) −6.92274 −0.886365 −0.443183 0.896431i \(-0.646151\pi\)
−0.443183 + 0.896431i \(0.646151\pi\)
\(62\) 0 0
\(63\) 7.28236 0.917491
\(64\) 0 0
\(65\) −6.62900 −0.822226
\(66\) 0 0
\(67\) −12.2927 −1.50179 −0.750897 0.660420i \(-0.770378\pi\)
−0.750897 + 0.660420i \(0.770378\pi\)
\(68\) 0 0
\(69\) −0.631673 −0.0760445
\(70\) 0 0
\(71\) 12.0893 1.43474 0.717370 0.696693i \(-0.245346\pi\)
0.717370 + 0.696693i \(0.245346\pi\)
\(72\) 0 0
\(73\) −5.02316 −0.587917 −0.293958 0.955818i \(-0.594973\pi\)
−0.293958 + 0.955818i \(0.594973\pi\)
\(74\) 0 0
\(75\) −0.690452 −0.0797265
\(76\) 0 0
\(77\) −13.2519 −1.51019
\(78\) 0 0
\(79\) −12.9398 −1.45584 −0.727922 0.685660i \(-0.759514\pi\)
−0.727922 + 0.685660i \(0.759514\pi\)
\(80\) 0 0
\(81\) 8.30973 0.923303
\(82\) 0 0
\(83\) −12.3149 −1.35173 −0.675866 0.737024i \(-0.736230\pi\)
−0.675866 + 0.737024i \(0.736230\pi\)
\(84\) 0 0
\(85\) −5.01755 −0.544229
\(86\) 0 0
\(87\) 1.30962 0.140406
\(88\) 0 0
\(89\) −15.2492 −1.61641 −0.808205 0.588902i \(-0.799561\pi\)
−0.808205 + 0.588902i \(0.799561\pi\)
\(90\) 0 0
\(91\) 10.4100 1.09126
\(92\) 0 0
\(93\) −0.129675 −0.0134467
\(94\) 0 0
\(95\) 8.22171 0.843530
\(96\) 0 0
\(97\) 3.89871 0.395854 0.197927 0.980217i \(-0.436579\pi\)
0.197927 + 0.980217i \(0.436579\pi\)
\(98\) 0 0
\(99\) −15.5437 −1.56220
\(100\) 0 0
\(101\) 2.95625 0.294158 0.147079 0.989125i \(-0.453013\pi\)
0.147079 + 0.989125i \(0.453013\pi\)
\(102\) 0 0
\(103\) 2.00210 0.197273 0.0986366 0.995124i \(-0.468552\pi\)
0.0986366 + 0.995124i \(0.468552\pi\)
\(104\) 0 0
\(105\) −1.09965 −0.107315
\(106\) 0 0
\(107\) −16.8999 −1.63378 −0.816889 0.576796i \(-0.804303\pi\)
−0.816889 + 0.576796i \(0.804303\pi\)
\(108\) 0 0
\(109\) 2.73753 0.262208 0.131104 0.991369i \(-0.458148\pi\)
0.131104 + 0.991369i \(0.458148\pi\)
\(110\) 0 0
\(111\) 1.31253 0.124580
\(112\) 0 0
\(113\) 14.8926 1.40098 0.700491 0.713661i \(-0.252964\pi\)
0.700491 + 0.713661i \(0.252964\pi\)
\(114\) 0 0
\(115\) −3.60349 −0.336027
\(116\) 0 0
\(117\) 12.2104 1.12885
\(118\) 0 0
\(119\) 7.87943 0.722306
\(120\) 0 0
\(121\) 17.2853 1.57139
\(122\) 0 0
\(123\) 1.26217 0.113806
\(124\) 0 0
\(125\) −11.8723 −1.06189
\(126\) 0 0
\(127\) 9.64634 0.855974 0.427987 0.903785i \(-0.359223\pi\)
0.427987 + 0.903785i \(0.359223\pi\)
\(128\) 0 0
\(129\) 0.871009 0.0766880
\(130\) 0 0
\(131\) −10.3574 −0.904931 −0.452465 0.891782i \(-0.649455\pi\)
−0.452465 + 0.891782i \(0.649455\pi\)
\(132\) 0 0
\(133\) −12.9112 −1.11954
\(134\) 0 0
\(135\) −2.61380 −0.224960
\(136\) 0 0
\(137\) −20.7335 −1.77138 −0.885692 0.464274i \(-0.846315\pi\)
−0.885692 + 0.464274i \(0.846315\pi\)
\(138\) 0 0
\(139\) −12.3132 −1.04439 −0.522195 0.852826i \(-0.674887\pi\)
−0.522195 + 0.852826i \(0.674887\pi\)
\(140\) 0 0
\(141\) −0.444607 −0.0374426
\(142\) 0 0
\(143\) −22.2195 −1.85809
\(144\) 0 0
\(145\) 7.47095 0.620429
\(146\) 0 0
\(147\) −0.220117 −0.0181549
\(148\) 0 0
\(149\) 0.314134 0.0257349 0.0128674 0.999917i \(-0.495904\pi\)
0.0128674 + 0.999917i \(0.495904\pi\)
\(150\) 0 0
\(151\) −2.56907 −0.209068 −0.104534 0.994521i \(-0.533335\pi\)
−0.104534 + 0.994521i \(0.533335\pi\)
\(152\) 0 0
\(153\) 9.24214 0.747183
\(154\) 0 0
\(155\) −0.739755 −0.0594185
\(156\) 0 0
\(157\) 24.6045 1.96366 0.981828 0.189772i \(-0.0607749\pi\)
0.981828 + 0.189772i \(0.0607749\pi\)
\(158\) 0 0
\(159\) −1.02308 −0.0811355
\(160\) 0 0
\(161\) 5.65883 0.445978
\(162\) 0 0
\(163\) −21.0969 −1.65243 −0.826217 0.563352i \(-0.809511\pi\)
−0.826217 + 0.563352i \(0.809511\pi\)
\(164\) 0 0
\(165\) 2.34713 0.182724
\(166\) 0 0
\(167\) −18.3314 −1.41853 −0.709265 0.704942i \(-0.750973\pi\)
−0.709265 + 0.704942i \(0.750973\pi\)
\(168\) 0 0
\(169\) 4.45449 0.342653
\(170\) 0 0
\(171\) −15.1441 −1.15810
\(172\) 0 0
\(173\) −2.78749 −0.211929 −0.105964 0.994370i \(-0.533793\pi\)
−0.105964 + 0.994370i \(0.533793\pi\)
\(174\) 0 0
\(175\) 6.18540 0.467572
\(176\) 0 0
\(177\) −0.919052 −0.0690802
\(178\) 0 0
\(179\) −5.93477 −0.443585 −0.221793 0.975094i \(-0.571191\pi\)
−0.221793 + 0.975094i \(0.571191\pi\)
\(180\) 0 0
\(181\) 0.676298 0.0502689 0.0251344 0.999684i \(-0.491999\pi\)
0.0251344 + 0.999684i \(0.491999\pi\)
\(182\) 0 0
\(183\) −1.92549 −0.142336
\(184\) 0 0
\(185\) 7.48755 0.550496
\(186\) 0 0
\(187\) −16.8181 −1.22986
\(188\) 0 0
\(189\) 4.10465 0.298569
\(190\) 0 0
\(191\) 4.93976 0.357429 0.178714 0.983901i \(-0.442806\pi\)
0.178714 + 0.983901i \(0.442806\pi\)
\(192\) 0 0
\(193\) 0.427481 0.0307707 0.0153854 0.999882i \(-0.495102\pi\)
0.0153854 + 0.999882i \(0.495102\pi\)
\(194\) 0 0
\(195\) −1.84379 −0.132036
\(196\) 0 0
\(197\) −11.6733 −0.831691 −0.415845 0.909435i \(-0.636514\pi\)
−0.415845 + 0.909435i \(0.636514\pi\)
\(198\) 0 0
\(199\) −21.6843 −1.53716 −0.768579 0.639755i \(-0.779036\pi\)
−0.768579 + 0.639755i \(0.779036\pi\)
\(200\) 0 0
\(201\) −3.41909 −0.241164
\(202\) 0 0
\(203\) −11.7322 −0.823439
\(204\) 0 0
\(205\) 7.20025 0.502887
\(206\) 0 0
\(207\) 6.63750 0.461338
\(208\) 0 0
\(209\) 27.5580 1.90623
\(210\) 0 0
\(211\) −17.7958 −1.22511 −0.612557 0.790427i \(-0.709859\pi\)
−0.612557 + 0.790427i \(0.709859\pi\)
\(212\) 0 0
\(213\) 3.36253 0.230396
\(214\) 0 0
\(215\) 4.96882 0.338871
\(216\) 0 0
\(217\) 1.16169 0.0788608
\(218\) 0 0
\(219\) −1.39714 −0.0944101
\(220\) 0 0
\(221\) 13.2115 0.888699
\(222\) 0 0
\(223\) 6.56036 0.439314 0.219657 0.975577i \(-0.429506\pi\)
0.219657 + 0.975577i \(0.429506\pi\)
\(224\) 0 0
\(225\) 7.25513 0.483675
\(226\) 0 0
\(227\) −6.50792 −0.431946 −0.215973 0.976399i \(-0.569292\pi\)
−0.215973 + 0.976399i \(0.569292\pi\)
\(228\) 0 0
\(229\) 12.9817 0.857853 0.428927 0.903339i \(-0.358892\pi\)
0.428927 + 0.903339i \(0.358892\pi\)
\(230\) 0 0
\(231\) −3.68588 −0.242513
\(232\) 0 0
\(233\) −9.51412 −0.623291 −0.311646 0.950198i \(-0.600880\pi\)
−0.311646 + 0.950198i \(0.600880\pi\)
\(234\) 0 0
\(235\) −2.53634 −0.165452
\(236\) 0 0
\(237\) −3.59908 −0.233785
\(238\) 0 0
\(239\) 21.4019 1.38437 0.692187 0.721718i \(-0.256647\pi\)
0.692187 + 0.721718i \(0.256647\pi\)
\(240\) 0 0
\(241\) −9.72856 −0.626671 −0.313336 0.949642i \(-0.601447\pi\)
−0.313336 + 0.949642i \(0.601447\pi\)
\(242\) 0 0
\(243\) 7.25323 0.465295
\(244\) 0 0
\(245\) −1.25569 −0.0802233
\(246\) 0 0
\(247\) −21.6482 −1.37744
\(248\) 0 0
\(249\) −3.42526 −0.217067
\(250\) 0 0
\(251\) 4.75019 0.299830 0.149915 0.988699i \(-0.452100\pi\)
0.149915 + 0.988699i \(0.452100\pi\)
\(252\) 0 0
\(253\) −12.0784 −0.759363
\(254\) 0 0
\(255\) −1.39558 −0.0873946
\(256\) 0 0
\(257\) −11.8109 −0.736743 −0.368371 0.929679i \(-0.620085\pi\)
−0.368371 + 0.929679i \(0.620085\pi\)
\(258\) 0 0
\(259\) −11.7583 −0.730623
\(260\) 0 0
\(261\) −13.7612 −0.851798
\(262\) 0 0
\(263\) −4.75823 −0.293405 −0.146703 0.989181i \(-0.546866\pi\)
−0.146703 + 0.989181i \(0.546866\pi\)
\(264\) 0 0
\(265\) −5.83634 −0.358523
\(266\) 0 0
\(267\) −4.24140 −0.259570
\(268\) 0 0
\(269\) −10.3181 −0.629103 −0.314551 0.949240i \(-0.601854\pi\)
−0.314551 + 0.949240i \(0.601854\pi\)
\(270\) 0 0
\(271\) 10.9663 0.666153 0.333076 0.942900i \(-0.391913\pi\)
0.333076 + 0.942900i \(0.391913\pi\)
\(272\) 0 0
\(273\) 2.89544 0.175240
\(274\) 0 0
\(275\) −13.2023 −0.796130
\(276\) 0 0
\(277\) 14.3300 0.861007 0.430504 0.902589i \(-0.358336\pi\)
0.430504 + 0.902589i \(0.358336\pi\)
\(278\) 0 0
\(279\) 1.36260 0.0815768
\(280\) 0 0
\(281\) 9.91149 0.591270 0.295635 0.955301i \(-0.404469\pi\)
0.295635 + 0.955301i \(0.404469\pi\)
\(282\) 0 0
\(283\) 1.90578 0.113287 0.0566434 0.998394i \(-0.481960\pi\)
0.0566434 + 0.998394i \(0.481960\pi\)
\(284\) 0 0
\(285\) 2.28679 0.135457
\(286\) 0 0
\(287\) −11.3071 −0.667436
\(288\) 0 0
\(289\) −7.00012 −0.411772
\(290\) 0 0
\(291\) 1.08439 0.0635679
\(292\) 0 0
\(293\) −10.0845 −0.589142 −0.294571 0.955630i \(-0.595177\pi\)
−0.294571 + 0.955630i \(0.595177\pi\)
\(294\) 0 0
\(295\) −5.24289 −0.305253
\(296\) 0 0
\(297\) −8.76110 −0.508371
\(298\) 0 0
\(299\) 9.48818 0.548716
\(300\) 0 0
\(301\) −7.80291 −0.449752
\(302\) 0 0
\(303\) 0.822252 0.0472372
\(304\) 0 0
\(305\) −10.9843 −0.628958
\(306\) 0 0
\(307\) 24.8752 1.41970 0.709850 0.704353i \(-0.248763\pi\)
0.709850 + 0.704353i \(0.248763\pi\)
\(308\) 0 0
\(309\) 0.556865 0.0316789
\(310\) 0 0
\(311\) −24.0379 −1.36306 −0.681531 0.731789i \(-0.738686\pi\)
−0.681531 + 0.731789i \(0.738686\pi\)
\(312\) 0 0
\(313\) 6.12359 0.346126 0.173063 0.984911i \(-0.444634\pi\)
0.173063 + 0.984911i \(0.444634\pi\)
\(314\) 0 0
\(315\) 11.5549 0.651045
\(316\) 0 0
\(317\) 26.9177 1.51185 0.755924 0.654659i \(-0.227188\pi\)
0.755924 + 0.654659i \(0.227188\pi\)
\(318\) 0 0
\(319\) 25.0416 1.40206
\(320\) 0 0
\(321\) −4.70054 −0.262359
\(322\) 0 0
\(323\) −16.3857 −0.911726
\(324\) 0 0
\(325\) 10.3711 0.575284
\(326\) 0 0
\(327\) 0.761417 0.0421064
\(328\) 0 0
\(329\) 3.98300 0.219590
\(330\) 0 0
\(331\) 22.2369 1.22225 0.611125 0.791534i \(-0.290717\pi\)
0.611125 + 0.791534i \(0.290717\pi\)
\(332\) 0 0
\(333\) −13.7918 −0.755786
\(334\) 0 0
\(335\) −19.5048 −1.06566
\(336\) 0 0
\(337\) 34.9032 1.90130 0.950650 0.310265i \(-0.100418\pi\)
0.950650 + 0.310265i \(0.100418\pi\)
\(338\) 0 0
\(339\) 4.14224 0.224976
\(340\) 0 0
\(341\) −2.47956 −0.134275
\(342\) 0 0
\(343\) 19.4139 1.04825
\(344\) 0 0
\(345\) −1.00227 −0.0539606
\(346\) 0 0
\(347\) −19.6429 −1.05449 −0.527243 0.849714i \(-0.676774\pi\)
−0.527243 + 0.849714i \(0.676774\pi\)
\(348\) 0 0
\(349\) −14.5312 −0.777839 −0.388920 0.921272i \(-0.627152\pi\)
−0.388920 + 0.921272i \(0.627152\pi\)
\(350\) 0 0
\(351\) 6.88228 0.367349
\(352\) 0 0
\(353\) −12.8987 −0.686528 −0.343264 0.939239i \(-0.611533\pi\)
−0.343264 + 0.939239i \(0.611533\pi\)
\(354\) 0 0
\(355\) 19.1821 1.01808
\(356\) 0 0
\(357\) 2.19158 0.115991
\(358\) 0 0
\(359\) 15.9031 0.839333 0.419667 0.907678i \(-0.362147\pi\)
0.419667 + 0.907678i \(0.362147\pi\)
\(360\) 0 0
\(361\) 7.84949 0.413131
\(362\) 0 0
\(363\) 4.80773 0.252340
\(364\) 0 0
\(365\) −7.97024 −0.417181
\(366\) 0 0
\(367\) −8.55160 −0.446390 −0.223195 0.974774i \(-0.571649\pi\)
−0.223195 + 0.974774i \(0.571649\pi\)
\(368\) 0 0
\(369\) −13.2626 −0.690423
\(370\) 0 0
\(371\) 9.16523 0.475835
\(372\) 0 0
\(373\) −11.9876 −0.620693 −0.310346 0.950624i \(-0.600445\pi\)
−0.310346 + 0.950624i \(0.600445\pi\)
\(374\) 0 0
\(375\) −3.30216 −0.170523
\(376\) 0 0
\(377\) −19.6714 −1.01313
\(378\) 0 0
\(379\) 3.65175 0.187578 0.0937888 0.995592i \(-0.470102\pi\)
0.0937888 + 0.995592i \(0.470102\pi\)
\(380\) 0 0
\(381\) 2.68303 0.137456
\(382\) 0 0
\(383\) −24.6726 −1.26071 −0.630355 0.776307i \(-0.717090\pi\)
−0.630355 + 0.776307i \(0.717090\pi\)
\(384\) 0 0
\(385\) −21.0267 −1.07162
\(386\) 0 0
\(387\) −9.15239 −0.465242
\(388\) 0 0
\(389\) 30.8541 1.56437 0.782183 0.623049i \(-0.214106\pi\)
0.782183 + 0.623049i \(0.214106\pi\)
\(390\) 0 0
\(391\) 7.18169 0.363194
\(392\) 0 0
\(393\) −2.88081 −0.145318
\(394\) 0 0
\(395\) −20.5316 −1.03306
\(396\) 0 0
\(397\) −6.21276 −0.311809 −0.155905 0.987772i \(-0.549829\pi\)
−0.155905 + 0.987772i \(0.549829\pi\)
\(398\) 0 0
\(399\) −3.59111 −0.179780
\(400\) 0 0
\(401\) −30.7692 −1.53654 −0.768270 0.640126i \(-0.778882\pi\)
−0.768270 + 0.640126i \(0.778882\pi\)
\(402\) 0 0
\(403\) 1.94781 0.0970275
\(404\) 0 0
\(405\) 13.1850 0.655169
\(406\) 0 0
\(407\) 25.0972 1.24402
\(408\) 0 0
\(409\) 34.8667 1.72405 0.862025 0.506866i \(-0.169196\pi\)
0.862025 + 0.506866i \(0.169196\pi\)
\(410\) 0 0
\(411\) −5.76682 −0.284456
\(412\) 0 0
\(413\) 8.23330 0.405134
\(414\) 0 0
\(415\) −19.5400 −0.959180
\(416\) 0 0
\(417\) −3.42479 −0.167713
\(418\) 0 0
\(419\) −3.51925 −0.171926 −0.0859632 0.996298i \(-0.527397\pi\)
−0.0859632 + 0.996298i \(0.527397\pi\)
\(420\) 0 0
\(421\) 6.94511 0.338484 0.169242 0.985575i \(-0.445868\pi\)
0.169242 + 0.985575i \(0.445868\pi\)
\(422\) 0 0
\(423\) 4.67184 0.227153
\(424\) 0 0
\(425\) 7.84996 0.380779
\(426\) 0 0
\(427\) 17.2494 0.834759
\(428\) 0 0
\(429\) −6.18012 −0.298379
\(430\) 0 0
\(431\) 20.4362 0.984376 0.492188 0.870489i \(-0.336197\pi\)
0.492188 + 0.870489i \(0.336197\pi\)
\(432\) 0 0
\(433\) 9.57364 0.460080 0.230040 0.973181i \(-0.426114\pi\)
0.230040 + 0.973181i \(0.426114\pi\)
\(434\) 0 0
\(435\) 2.07797 0.0996310
\(436\) 0 0
\(437\) −11.7679 −0.562933
\(438\) 0 0
\(439\) 12.0237 0.573862 0.286931 0.957951i \(-0.407365\pi\)
0.286931 + 0.957951i \(0.407365\pi\)
\(440\) 0 0
\(441\) 2.31294 0.110140
\(442\) 0 0
\(443\) 15.7043 0.746135 0.373068 0.927804i \(-0.378306\pi\)
0.373068 + 0.927804i \(0.378306\pi\)
\(444\) 0 0
\(445\) −24.1958 −1.14699
\(446\) 0 0
\(447\) 0.0873733 0.00413262
\(448\) 0 0
\(449\) −22.1199 −1.04390 −0.521952 0.852975i \(-0.674796\pi\)
−0.521952 + 0.852975i \(0.674796\pi\)
\(450\) 0 0
\(451\) 24.1343 1.13644
\(452\) 0 0
\(453\) −0.714562 −0.0335731
\(454\) 0 0
\(455\) 16.5175 0.774353
\(456\) 0 0
\(457\) −1.96675 −0.0920009 −0.0460004 0.998941i \(-0.514648\pi\)
−0.0460004 + 0.998941i \(0.514648\pi\)
\(458\) 0 0
\(459\) 5.20926 0.243147
\(460\) 0 0
\(461\) −16.8317 −0.783933 −0.391966 0.919980i \(-0.628205\pi\)
−0.391966 + 0.919980i \(0.628205\pi\)
\(462\) 0 0
\(463\) −12.3927 −0.575936 −0.287968 0.957640i \(-0.592980\pi\)
−0.287968 + 0.957640i \(0.592980\pi\)
\(464\) 0 0
\(465\) −0.205755 −0.00954167
\(466\) 0 0
\(467\) −29.4711 −1.36376 −0.681880 0.731464i \(-0.738837\pi\)
−0.681880 + 0.731464i \(0.738837\pi\)
\(468\) 0 0
\(469\) 30.6298 1.41435
\(470\) 0 0
\(471\) 6.84351 0.315332
\(472\) 0 0
\(473\) 16.6548 0.765789
\(474\) 0 0
\(475\) −12.8629 −0.590190
\(476\) 0 0
\(477\) 10.7503 0.492223
\(478\) 0 0
\(479\) 26.5295 1.21216 0.606082 0.795402i \(-0.292740\pi\)
0.606082 + 0.795402i \(0.292740\pi\)
\(480\) 0 0
\(481\) −19.7151 −0.898932
\(482\) 0 0
\(483\) 1.57395 0.0716170
\(484\) 0 0
\(485\) 6.18608 0.280895
\(486\) 0 0
\(487\) −13.1334 −0.595133 −0.297567 0.954701i \(-0.596175\pi\)
−0.297567 + 0.954701i \(0.596175\pi\)
\(488\) 0 0
\(489\) −5.86788 −0.265355
\(490\) 0 0
\(491\) 5.43276 0.245177 0.122588 0.992458i \(-0.460880\pi\)
0.122588 + 0.992458i \(0.460880\pi\)
\(492\) 0 0
\(493\) −14.8895 −0.670588
\(494\) 0 0
\(495\) −24.6632 −1.10853
\(496\) 0 0
\(497\) −30.1231 −1.35121
\(498\) 0 0
\(499\) −17.9981 −0.805707 −0.402854 0.915264i \(-0.631982\pi\)
−0.402854 + 0.915264i \(0.631982\pi\)
\(500\) 0 0
\(501\) −5.09871 −0.227793
\(502\) 0 0
\(503\) −20.6584 −0.921112 −0.460556 0.887631i \(-0.652350\pi\)
−0.460556 + 0.887631i \(0.652350\pi\)
\(504\) 0 0
\(505\) 4.69068 0.208733
\(506\) 0 0
\(507\) 1.23897 0.0550247
\(508\) 0 0
\(509\) 23.3084 1.03313 0.516564 0.856249i \(-0.327211\pi\)
0.516564 + 0.856249i \(0.327211\pi\)
\(510\) 0 0
\(511\) 12.5163 0.553687
\(512\) 0 0
\(513\) −8.53585 −0.376867
\(514\) 0 0
\(515\) 3.17673 0.139984
\(516\) 0 0
\(517\) −8.50145 −0.373893
\(518\) 0 0
\(519\) −0.775311 −0.0340324
\(520\) 0 0
\(521\) 22.7892 0.998414 0.499207 0.866483i \(-0.333625\pi\)
0.499207 + 0.866483i \(0.333625\pi\)
\(522\) 0 0
\(523\) −15.5606 −0.680416 −0.340208 0.940350i \(-0.610497\pi\)
−0.340208 + 0.940350i \(0.610497\pi\)
\(524\) 0 0
\(525\) 1.72041 0.0750846
\(526\) 0 0
\(527\) 1.47432 0.0642223
\(528\) 0 0
\(529\) −17.8423 −0.775751
\(530\) 0 0
\(531\) 9.65722 0.419088
\(532\) 0 0
\(533\) −18.9586 −0.821190
\(534\) 0 0
\(535\) −26.8151 −1.15932
\(536\) 0 0
\(537\) −1.65070 −0.0712328
\(538\) 0 0
\(539\) −4.20891 −0.181291
\(540\) 0 0
\(541\) −5.00911 −0.215359 −0.107679 0.994186i \(-0.534342\pi\)
−0.107679 + 0.994186i \(0.534342\pi\)
\(542\) 0 0
\(543\) 0.188106 0.00807238
\(544\) 0 0
\(545\) 4.34363 0.186061
\(546\) 0 0
\(547\) 6.38513 0.273008 0.136504 0.990639i \(-0.456413\pi\)
0.136504 + 0.990639i \(0.456413\pi\)
\(548\) 0 0
\(549\) 20.2327 0.863509
\(550\) 0 0
\(551\) 24.3978 1.03938
\(552\) 0 0
\(553\) 32.2423 1.37108
\(554\) 0 0
\(555\) 2.08259 0.0884009
\(556\) 0 0
\(557\) −6.33105 −0.268255 −0.134128 0.990964i \(-0.542823\pi\)
−0.134128 + 0.990964i \(0.542823\pi\)
\(558\) 0 0
\(559\) −13.0832 −0.553359
\(560\) 0 0
\(561\) −4.67779 −0.197497
\(562\) 0 0
\(563\) −19.9729 −0.841759 −0.420880 0.907117i \(-0.638278\pi\)
−0.420880 + 0.907117i \(0.638278\pi\)
\(564\) 0 0
\(565\) 23.6301 0.994127
\(566\) 0 0
\(567\) −20.7054 −0.869546
\(568\) 0 0
\(569\) 11.9790 0.502186 0.251093 0.967963i \(-0.419210\pi\)
0.251093 + 0.967963i \(0.419210\pi\)
\(570\) 0 0
\(571\) −19.5625 −0.818666 −0.409333 0.912385i \(-0.634239\pi\)
−0.409333 + 0.912385i \(0.634239\pi\)
\(572\) 0 0
\(573\) 1.37394 0.0573974
\(574\) 0 0
\(575\) 5.63767 0.235107
\(576\) 0 0
\(577\) −17.9014 −0.745247 −0.372623 0.927983i \(-0.621542\pi\)
−0.372623 + 0.927983i \(0.621542\pi\)
\(578\) 0 0
\(579\) 0.118899 0.00494129
\(580\) 0 0
\(581\) 30.6851 1.27303
\(582\) 0 0
\(583\) −19.5626 −0.810200
\(584\) 0 0
\(585\) 19.3742 0.801023
\(586\) 0 0
\(587\) −28.3919 −1.17186 −0.585930 0.810362i \(-0.699271\pi\)
−0.585930 + 0.810362i \(0.699271\pi\)
\(588\) 0 0
\(589\) −2.41580 −0.0995415
\(590\) 0 0
\(591\) −3.24682 −0.133556
\(592\) 0 0
\(593\) 7.44153 0.305587 0.152794 0.988258i \(-0.451173\pi\)
0.152794 + 0.988258i \(0.451173\pi\)
\(594\) 0 0
\(595\) 12.5023 0.512543
\(596\) 0 0
\(597\) −6.03127 −0.246843
\(598\) 0 0
\(599\) −18.9049 −0.772433 −0.386216 0.922408i \(-0.626218\pi\)
−0.386216 + 0.922408i \(0.626218\pi\)
\(600\) 0 0
\(601\) −24.6229 −1.00439 −0.502194 0.864755i \(-0.667474\pi\)
−0.502194 + 0.864755i \(0.667474\pi\)
\(602\) 0 0
\(603\) 35.9271 1.46307
\(604\) 0 0
\(605\) 27.4265 1.11505
\(606\) 0 0
\(607\) 16.4784 0.668836 0.334418 0.942425i \(-0.391460\pi\)
0.334418 + 0.942425i \(0.391460\pi\)
\(608\) 0 0
\(609\) −3.26319 −0.132231
\(610\) 0 0
\(611\) 6.67831 0.270175
\(612\) 0 0
\(613\) −13.5886 −0.548839 −0.274419 0.961610i \(-0.588486\pi\)
−0.274419 + 0.961610i \(0.588486\pi\)
\(614\) 0 0
\(615\) 2.00268 0.0807557
\(616\) 0 0
\(617\) 6.83640 0.275223 0.137612 0.990486i \(-0.456057\pi\)
0.137612 + 0.990486i \(0.456057\pi\)
\(618\) 0 0
\(619\) 33.8366 1.36001 0.680003 0.733209i \(-0.261978\pi\)
0.680003 + 0.733209i \(0.261978\pi\)
\(620\) 0 0
\(621\) 3.74117 0.150128
\(622\) 0 0
\(623\) 37.9965 1.52230
\(624\) 0 0
\(625\) −6.42578 −0.257031
\(626\) 0 0
\(627\) 7.66499 0.306110
\(628\) 0 0
\(629\) −14.9226 −0.595001
\(630\) 0 0
\(631\) 49.3139 1.96316 0.981578 0.191060i \(-0.0611924\pi\)
0.981578 + 0.191060i \(0.0611924\pi\)
\(632\) 0 0
\(633\) −4.94972 −0.196734
\(634\) 0 0
\(635\) 15.3058 0.607393
\(636\) 0 0
\(637\) 3.30631 0.131001
\(638\) 0 0
\(639\) −35.3327 −1.39774
\(640\) 0 0
\(641\) 17.2970 0.683191 0.341596 0.939847i \(-0.389033\pi\)
0.341596 + 0.939847i \(0.389033\pi\)
\(642\) 0 0
\(643\) 20.3460 0.802366 0.401183 0.915998i \(-0.368599\pi\)
0.401183 + 0.915998i \(0.368599\pi\)
\(644\) 0 0
\(645\) 1.38203 0.0544173
\(646\) 0 0
\(647\) −21.0241 −0.826541 −0.413270 0.910608i \(-0.635614\pi\)
−0.413270 + 0.910608i \(0.635614\pi\)
\(648\) 0 0
\(649\) −17.5735 −0.689819
\(650\) 0 0
\(651\) 0.323113 0.0126638
\(652\) 0 0
\(653\) −24.4175 −0.955530 −0.477765 0.878488i \(-0.658553\pi\)
−0.477765 + 0.878488i \(0.658553\pi\)
\(654\) 0 0
\(655\) −16.4341 −0.642132
\(656\) 0 0
\(657\) 14.6809 0.572756
\(658\) 0 0
\(659\) −26.5985 −1.03613 −0.518064 0.855342i \(-0.673347\pi\)
−0.518064 + 0.855342i \(0.673347\pi\)
\(660\) 0 0
\(661\) −39.9783 −1.55497 −0.777487 0.628899i \(-0.783506\pi\)
−0.777487 + 0.628899i \(0.783506\pi\)
\(662\) 0 0
\(663\) 3.67464 0.142711
\(664\) 0 0
\(665\) −20.4861 −0.794417
\(666\) 0 0
\(667\) −10.6933 −0.414046
\(668\) 0 0
\(669\) 1.82470 0.0705469
\(670\) 0 0
\(671\) −36.8178 −1.42134
\(672\) 0 0
\(673\) 1.23630 0.0476561 0.0238280 0.999716i \(-0.492415\pi\)
0.0238280 + 0.999716i \(0.492415\pi\)
\(674\) 0 0
\(675\) 4.08930 0.157397
\(676\) 0 0
\(677\) 27.8016 1.06850 0.534251 0.845326i \(-0.320594\pi\)
0.534251 + 0.845326i \(0.320594\pi\)
\(678\) 0 0
\(679\) −9.71446 −0.372807
\(680\) 0 0
\(681\) −1.81011 −0.0693637
\(682\) 0 0
\(683\) −0.659163 −0.0252222 −0.0126111 0.999920i \(-0.504014\pi\)
−0.0126111 + 0.999920i \(0.504014\pi\)
\(684\) 0 0
\(685\) −32.8978 −1.25696
\(686\) 0 0
\(687\) 3.61072 0.137758
\(688\) 0 0
\(689\) 15.3674 0.585451
\(690\) 0 0
\(691\) 29.0771 1.10615 0.553073 0.833133i \(-0.313455\pi\)
0.553073 + 0.833133i \(0.313455\pi\)
\(692\) 0 0
\(693\) 38.7305 1.47125
\(694\) 0 0
\(695\) −19.5373 −0.741092
\(696\) 0 0
\(697\) −14.3500 −0.543544
\(698\) 0 0
\(699\) −2.64626 −0.100091
\(700\) 0 0
\(701\) 10.4430 0.394427 0.197213 0.980361i \(-0.436811\pi\)
0.197213 + 0.980361i \(0.436811\pi\)
\(702\) 0 0
\(703\) 24.4520 0.922224
\(704\) 0 0
\(705\) −0.705456 −0.0265690
\(706\) 0 0
\(707\) −7.36613 −0.277032
\(708\) 0 0
\(709\) −46.7017 −1.75392 −0.876960 0.480564i \(-0.840432\pi\)
−0.876960 + 0.480564i \(0.840432\pi\)
\(710\) 0 0
\(711\) 37.8184 1.41830
\(712\) 0 0
\(713\) 1.05882 0.0396532
\(714\) 0 0
\(715\) −35.2556 −1.31848
\(716\) 0 0
\(717\) 5.95272 0.222308
\(718\) 0 0
\(719\) −46.3746 −1.72948 −0.864741 0.502218i \(-0.832517\pi\)
−0.864741 + 0.502218i \(0.832517\pi\)
\(720\) 0 0
\(721\) −4.98866 −0.185787
\(722\) 0 0
\(723\) −2.70590 −0.100634
\(724\) 0 0
\(725\) −11.6883 −0.434093
\(726\) 0 0
\(727\) −0.373294 −0.0138447 −0.00692235 0.999976i \(-0.502203\pi\)
−0.00692235 + 0.999976i \(0.502203\pi\)
\(728\) 0 0
\(729\) −22.9118 −0.848584
\(730\) 0 0
\(731\) −9.90277 −0.366267
\(732\) 0 0
\(733\) −24.0591 −0.888642 −0.444321 0.895868i \(-0.646555\pi\)
−0.444321 + 0.895868i \(0.646555\pi\)
\(734\) 0 0
\(735\) −0.349258 −0.0128826
\(736\) 0 0
\(737\) −65.3774 −2.40821
\(738\) 0 0
\(739\) −3.57096 −0.131360 −0.0656800 0.997841i \(-0.520922\pi\)
−0.0656800 + 0.997841i \(0.520922\pi\)
\(740\) 0 0
\(741\) −6.02123 −0.221195
\(742\) 0 0
\(743\) 5.89842 0.216392 0.108196 0.994130i \(-0.465493\pi\)
0.108196 + 0.994130i \(0.465493\pi\)
\(744\) 0 0
\(745\) 0.498436 0.0182613
\(746\) 0 0
\(747\) 35.9919 1.31688
\(748\) 0 0
\(749\) 42.1097 1.53865
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 1.32122 0.0481479
\(754\) 0 0
\(755\) −4.07634 −0.148353
\(756\) 0 0
\(757\) −8.88934 −0.323089 −0.161544 0.986865i \(-0.551647\pi\)
−0.161544 + 0.986865i \(0.551647\pi\)
\(758\) 0 0
\(759\) −3.35949 −0.121942
\(760\) 0 0
\(761\) 41.0345 1.48750 0.743750 0.668458i \(-0.233045\pi\)
0.743750 + 0.668458i \(0.233045\pi\)
\(762\) 0 0
\(763\) −6.82113 −0.246941
\(764\) 0 0
\(765\) 14.6645 0.530195
\(766\) 0 0
\(767\) 13.8048 0.498463
\(768\) 0 0
\(769\) 20.0124 0.721667 0.360834 0.932630i \(-0.382492\pi\)
0.360834 + 0.932630i \(0.382492\pi\)
\(770\) 0 0
\(771\) −3.28508 −0.118309
\(772\) 0 0
\(773\) 48.4597 1.74297 0.871487 0.490419i \(-0.163156\pi\)
0.871487 + 0.490419i \(0.163156\pi\)
\(774\) 0 0
\(775\) 1.15735 0.0415732
\(776\) 0 0
\(777\) −3.27044 −0.117326
\(778\) 0 0
\(779\) 23.5137 0.842467
\(780\) 0 0
\(781\) 64.2958 2.30068
\(782\) 0 0
\(783\) −7.75640 −0.277191
\(784\) 0 0
\(785\) 39.0400 1.39340
\(786\) 0 0
\(787\) −50.8456 −1.81245 −0.906226 0.422794i \(-0.861049\pi\)
−0.906226 + 0.422794i \(0.861049\pi\)
\(788\) 0 0
\(789\) −1.32345 −0.0471162
\(790\) 0 0
\(791\) −37.1081 −1.31941
\(792\) 0 0
\(793\) 28.9222 1.02706
\(794\) 0 0
\(795\) −1.62332 −0.0575732
\(796\) 0 0
\(797\) −8.19747 −0.290369 −0.145185 0.989405i \(-0.546378\pi\)
−0.145185 + 0.989405i \(0.546378\pi\)
\(798\) 0 0
\(799\) 5.05487 0.178829
\(800\) 0 0
\(801\) 44.5678 1.57473
\(802\) 0 0
\(803\) −26.7151 −0.942757
\(804\) 0 0
\(805\) 8.97885 0.316463
\(806\) 0 0
\(807\) −2.86986 −0.101024
\(808\) 0 0
\(809\) −1.90765 −0.0670693 −0.0335347 0.999438i \(-0.510676\pi\)
−0.0335347 + 0.999438i \(0.510676\pi\)
\(810\) 0 0
\(811\) 16.8725 0.592472 0.296236 0.955115i \(-0.404269\pi\)
0.296236 + 0.955115i \(0.404269\pi\)
\(812\) 0 0
\(813\) 3.05015 0.106974
\(814\) 0 0
\(815\) −33.4743 −1.17255
\(816\) 0 0
\(817\) 16.2266 0.567697
\(818\) 0 0
\(819\) −30.4247 −1.06312
\(820\) 0 0
\(821\) 34.7184 1.21168 0.605841 0.795586i \(-0.292837\pi\)
0.605841 + 0.795586i \(0.292837\pi\)
\(822\) 0 0
\(823\) −20.4354 −0.712332 −0.356166 0.934423i \(-0.615916\pi\)
−0.356166 + 0.934423i \(0.615916\pi\)
\(824\) 0 0
\(825\) −3.67209 −0.127846
\(826\) 0 0
\(827\) 23.3289 0.811225 0.405612 0.914045i \(-0.367058\pi\)
0.405612 + 0.914045i \(0.367058\pi\)
\(828\) 0 0
\(829\) −22.6949 −0.788227 −0.394114 0.919062i \(-0.628948\pi\)
−0.394114 + 0.919062i \(0.628948\pi\)
\(830\) 0 0
\(831\) 3.98575 0.138264
\(832\) 0 0
\(833\) 2.50257 0.0867091
\(834\) 0 0
\(835\) −29.0865 −1.00658
\(836\) 0 0
\(837\) 0.768019 0.0265466
\(838\) 0 0
\(839\) 17.4196 0.601393 0.300696 0.953720i \(-0.402781\pi\)
0.300696 + 0.953720i \(0.402781\pi\)
\(840\) 0 0
\(841\) −6.83009 −0.235520
\(842\) 0 0
\(843\) 2.75678 0.0949485
\(844\) 0 0
\(845\) 7.06793 0.243144
\(846\) 0 0
\(847\) −43.0699 −1.47990
\(848\) 0 0
\(849\) 0.530073 0.0181921
\(850\) 0 0
\(851\) −10.7170 −0.367376
\(852\) 0 0
\(853\) −31.0103 −1.06177 −0.530887 0.847443i \(-0.678141\pi\)
−0.530887 + 0.847443i \(0.678141\pi\)
\(854\) 0 0
\(855\) −24.0291 −0.821777
\(856\) 0 0
\(857\) −25.3182 −0.864855 −0.432427 0.901669i \(-0.642343\pi\)
−0.432427 + 0.901669i \(0.642343\pi\)
\(858\) 0 0
\(859\) −21.4794 −0.732869 −0.366434 0.930444i \(-0.619422\pi\)
−0.366434 + 0.930444i \(0.619422\pi\)
\(860\) 0 0
\(861\) −3.14495 −0.107180
\(862\) 0 0
\(863\) 18.5454 0.631291 0.315646 0.948877i \(-0.397779\pi\)
0.315646 + 0.948877i \(0.397779\pi\)
\(864\) 0 0
\(865\) −4.42290 −0.150383
\(866\) 0 0
\(867\) −1.94701 −0.0661240
\(868\) 0 0
\(869\) −68.8190 −2.33452
\(870\) 0 0
\(871\) 51.3572 1.74017
\(872\) 0 0
\(873\) −11.3945 −0.385646
\(874\) 0 0
\(875\) 29.5823 1.00006
\(876\) 0 0
\(877\) −35.2153 −1.18914 −0.594569 0.804045i \(-0.702677\pi\)
−0.594569 + 0.804045i \(0.702677\pi\)
\(878\) 0 0
\(879\) −2.80490 −0.0946069
\(880\) 0 0
\(881\) 7.75356 0.261224 0.130612 0.991434i \(-0.458306\pi\)
0.130612 + 0.991434i \(0.458306\pi\)
\(882\) 0 0
\(883\) −28.7798 −0.968518 −0.484259 0.874925i \(-0.660911\pi\)
−0.484259 + 0.874925i \(0.660911\pi\)
\(884\) 0 0
\(885\) −1.45826 −0.0490188
\(886\) 0 0
\(887\) −11.5055 −0.386318 −0.193159 0.981167i \(-0.561873\pi\)
−0.193159 + 0.981167i \(0.561873\pi\)
\(888\) 0 0
\(889\) −24.0359 −0.806137
\(890\) 0 0
\(891\) 44.1944 1.48057
\(892\) 0 0
\(893\) −8.28287 −0.277176
\(894\) 0 0
\(895\) −9.41668 −0.314765
\(896\) 0 0
\(897\) 2.63904 0.0881150
\(898\) 0 0
\(899\) −2.19521 −0.0732143
\(900\) 0 0
\(901\) 11.6317 0.387509
\(902\) 0 0
\(903\) −2.17030 −0.0722231
\(904\) 0 0
\(905\) 1.07308 0.0356704
\(906\) 0 0
\(907\) −6.38439 −0.211990 −0.105995 0.994367i \(-0.533803\pi\)
−0.105995 + 0.994367i \(0.533803\pi\)
\(908\) 0 0
\(909\) −8.64006 −0.286573
\(910\) 0 0
\(911\) −23.6633 −0.784001 −0.392001 0.919965i \(-0.628217\pi\)
−0.392001 + 0.919965i \(0.628217\pi\)
\(912\) 0 0
\(913\) −65.4953 −2.16758
\(914\) 0 0
\(915\) −3.05517 −0.101001
\(916\) 0 0
\(917\) 25.8076 0.852243
\(918\) 0 0
\(919\) 36.2900 1.19710 0.598548 0.801087i \(-0.295745\pi\)
0.598548 + 0.801087i \(0.295745\pi\)
\(920\) 0 0
\(921\) 6.91878 0.227981
\(922\) 0 0
\(923\) −50.5075 −1.66247
\(924\) 0 0
\(925\) −11.7143 −0.385164
\(926\) 0 0
\(927\) −5.85143 −0.192186
\(928\) 0 0
\(929\) 36.8539 1.20914 0.604569 0.796553i \(-0.293345\pi\)
0.604569 + 0.796553i \(0.293345\pi\)
\(930\) 0 0
\(931\) −4.10070 −0.134395
\(932\) 0 0
\(933\) −6.68589 −0.218886
\(934\) 0 0
\(935\) −26.6853 −0.872702
\(936\) 0 0
\(937\) 52.5859 1.71791 0.858954 0.512053i \(-0.171115\pi\)
0.858954 + 0.512053i \(0.171115\pi\)
\(938\) 0 0
\(939\) 1.70321 0.0555823
\(940\) 0 0
\(941\) 15.0363 0.490170 0.245085 0.969502i \(-0.421184\pi\)
0.245085 + 0.969502i \(0.421184\pi\)
\(942\) 0 0
\(943\) −10.3058 −0.335604
\(944\) 0 0
\(945\) 6.51283 0.211862
\(946\) 0 0
\(947\) 48.1553 1.56484 0.782418 0.622753i \(-0.213986\pi\)
0.782418 + 0.622753i \(0.213986\pi\)
\(948\) 0 0
\(949\) 20.9861 0.681236
\(950\) 0 0
\(951\) 7.48689 0.242779
\(952\) 0 0
\(953\) 37.1339 1.20288 0.601442 0.798916i \(-0.294593\pi\)
0.601442 + 0.798916i \(0.294593\pi\)
\(954\) 0 0
\(955\) 7.83790 0.253629
\(956\) 0 0
\(957\) 6.96507 0.225149
\(958\) 0 0
\(959\) 51.6619 1.66825
\(960\) 0 0
\(961\) −30.7826 −0.992988
\(962\) 0 0
\(963\) 49.3924 1.59165
\(964\) 0 0
\(965\) 0.678282 0.0218347
\(966\) 0 0
\(967\) −12.7318 −0.409428 −0.204714 0.978822i \(-0.565626\pi\)
−0.204714 + 0.978822i \(0.565626\pi\)
\(968\) 0 0
\(969\) −4.55752 −0.146409
\(970\) 0 0
\(971\) 53.5608 1.71885 0.859423 0.511264i \(-0.170823\pi\)
0.859423 + 0.511264i \(0.170823\pi\)
\(972\) 0 0
\(973\) 30.6809 0.983583
\(974\) 0 0
\(975\) 2.88461 0.0923815
\(976\) 0 0
\(977\) 32.6257 1.04379 0.521895 0.853010i \(-0.325225\pi\)
0.521895 + 0.853010i \(0.325225\pi\)
\(978\) 0 0
\(979\) −81.1011 −2.59200
\(980\) 0 0
\(981\) −8.00081 −0.255446
\(982\) 0 0
\(983\) −29.6145 −0.944556 −0.472278 0.881450i \(-0.656568\pi\)
−0.472278 + 0.881450i \(0.656568\pi\)
\(984\) 0 0
\(985\) −18.5221 −0.590162
\(986\) 0 0
\(987\) 1.10783 0.0352626
\(988\) 0 0
\(989\) −7.11195 −0.226147
\(990\) 0 0
\(991\) 32.7361 1.03990 0.519949 0.854197i \(-0.325951\pi\)
0.519949 + 0.854197i \(0.325951\pi\)
\(992\) 0 0
\(993\) 6.18496 0.196274
\(994\) 0 0
\(995\) −34.4064 −1.09076
\(996\) 0 0
\(997\) 33.1839 1.05094 0.525472 0.850811i \(-0.323889\pi\)
0.525472 + 0.850811i \(0.323889\pi\)
\(998\) 0 0
\(999\) −7.77364 −0.245947
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 6008.2.a.b.1.27 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.27 44 1.1 even 1 trivial