Properties

Label 6008.2.a.b.1.13
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 1.13
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.00709 q^{3} +0.0492234 q^{5} +3.84191 q^{7} +1.02840 q^{9} +O(q^{10})\) \(q-2.00709 q^{3} +0.0492234 q^{5} +3.84191 q^{7} +1.02840 q^{9} -1.21458 q^{11} +1.27285 q^{13} -0.0987957 q^{15} -0.819483 q^{17} -1.24303 q^{19} -7.71105 q^{21} +1.37611 q^{23} -4.99758 q^{25} +3.95718 q^{27} +0.881623 q^{29} -1.56310 q^{31} +2.43776 q^{33} +0.189112 q^{35} +5.05616 q^{37} -2.55473 q^{39} -5.34858 q^{41} -9.30023 q^{43} +0.0506213 q^{45} -3.16855 q^{47} +7.76027 q^{49} +1.64477 q^{51} +3.52915 q^{53} -0.0597856 q^{55} +2.49486 q^{57} +9.34369 q^{59} -5.45413 q^{61} +3.95101 q^{63} +0.0626542 q^{65} -5.39897 q^{67} -2.76196 q^{69} -15.1439 q^{71} -14.3312 q^{73} +10.0306 q^{75} -4.66629 q^{77} -13.4366 q^{79} -11.0276 q^{81} -7.25318 q^{83} -0.0403378 q^{85} -1.76949 q^{87} +1.79541 q^{89} +4.89018 q^{91} +3.13727 q^{93} -0.0611860 q^{95} +15.1851 q^{97} -1.24907 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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
\(3\) −2.00709 −1.15879 −0.579396 0.815046i \(-0.696712\pi\)
−0.579396 + 0.815046i \(0.696712\pi\)
\(4\) 0 0
\(5\) 0.0492234 0.0220134 0.0110067 0.999939i \(-0.496496\pi\)
0.0110067 + 0.999939i \(0.496496\pi\)
\(6\) 0 0
\(7\) 3.84191 1.45211 0.726053 0.687639i \(-0.241353\pi\)
0.726053 + 0.687639i \(0.241353\pi\)
\(8\) 0 0
\(9\) 1.02840 0.342799
\(10\) 0 0
\(11\) −1.21458 −0.366208 −0.183104 0.983094i \(-0.558615\pi\)
−0.183104 + 0.983094i \(0.558615\pi\)
\(12\) 0 0
\(13\) 1.27285 0.353026 0.176513 0.984298i \(-0.443518\pi\)
0.176513 + 0.984298i \(0.443518\pi\)
\(14\) 0 0
\(15\) −0.0987957 −0.0255089
\(16\) 0 0
\(17\) −0.819483 −0.198754 −0.0993770 0.995050i \(-0.531685\pi\)
−0.0993770 + 0.995050i \(0.531685\pi\)
\(18\) 0 0
\(19\) −1.24303 −0.285170 −0.142585 0.989783i \(-0.545541\pi\)
−0.142585 + 0.989783i \(0.545541\pi\)
\(20\) 0 0
\(21\) −7.71105 −1.68269
\(22\) 0 0
\(23\) 1.37611 0.286938 0.143469 0.989655i \(-0.454174\pi\)
0.143469 + 0.989655i \(0.454174\pi\)
\(24\) 0 0
\(25\) −4.99758 −0.999515
\(26\) 0 0
\(27\) 3.95718 0.761559
\(28\) 0 0
\(29\) 0.881623 0.163713 0.0818566 0.996644i \(-0.473915\pi\)
0.0818566 + 0.996644i \(0.473915\pi\)
\(30\) 0 0
\(31\) −1.56310 −0.280741 −0.140370 0.990099i \(-0.544829\pi\)
−0.140370 + 0.990099i \(0.544829\pi\)
\(32\) 0 0
\(33\) 2.43776 0.424359
\(34\) 0 0
\(35\) 0.189112 0.0319658
\(36\) 0 0
\(37\) 5.05616 0.831228 0.415614 0.909541i \(-0.363567\pi\)
0.415614 + 0.909541i \(0.363567\pi\)
\(38\) 0 0
\(39\) −2.55473 −0.409083
\(40\) 0 0
\(41\) −5.34858 −0.835307 −0.417654 0.908606i \(-0.637147\pi\)
−0.417654 + 0.908606i \(0.637147\pi\)
\(42\) 0 0
\(43\) −9.30023 −1.41827 −0.709136 0.705072i \(-0.750915\pi\)
−0.709136 + 0.705072i \(0.750915\pi\)
\(44\) 0 0
\(45\) 0.0506213 0.00754618
\(46\) 0 0
\(47\) −3.16855 −0.462181 −0.231090 0.972932i \(-0.574229\pi\)
−0.231090 + 0.972932i \(0.574229\pi\)
\(48\) 0 0
\(49\) 7.76027 1.10861
\(50\) 0 0
\(51\) 1.64477 0.230314
\(52\) 0 0
\(53\) 3.52915 0.484767 0.242383 0.970181i \(-0.422071\pi\)
0.242383 + 0.970181i \(0.422071\pi\)
\(54\) 0 0
\(55\) −0.0597856 −0.00806149
\(56\) 0 0
\(57\) 2.49486 0.330452
\(58\) 0 0
\(59\) 9.34369 1.21644 0.608222 0.793767i \(-0.291883\pi\)
0.608222 + 0.793767i \(0.291883\pi\)
\(60\) 0 0
\(61\) −5.45413 −0.698329 −0.349165 0.937061i \(-0.613535\pi\)
−0.349165 + 0.937061i \(0.613535\pi\)
\(62\) 0 0
\(63\) 3.95101 0.497781
\(64\) 0 0
\(65\) 0.0626542 0.00777129
\(66\) 0 0
\(67\) −5.39897 −0.659590 −0.329795 0.944053i \(-0.606980\pi\)
−0.329795 + 0.944053i \(0.606980\pi\)
\(68\) 0 0
\(69\) −2.76196 −0.332501
\(70\) 0 0
\(71\) −15.1439 −1.79725 −0.898625 0.438718i \(-0.855433\pi\)
−0.898625 + 0.438718i \(0.855433\pi\)
\(72\) 0 0
\(73\) −14.3312 −1.67733 −0.838667 0.544644i \(-0.816665\pi\)
−0.838667 + 0.544644i \(0.816665\pi\)
\(74\) 0 0
\(75\) 10.0306 1.15823
\(76\) 0 0
\(77\) −4.66629 −0.531773
\(78\) 0 0
\(79\) −13.4366 −1.51174 −0.755868 0.654725i \(-0.772785\pi\)
−0.755868 + 0.654725i \(0.772785\pi\)
\(80\) 0 0
\(81\) −11.0276 −1.22529
\(82\) 0 0
\(83\) −7.25318 −0.796140 −0.398070 0.917355i \(-0.630320\pi\)
−0.398070 + 0.917355i \(0.630320\pi\)
\(84\) 0 0
\(85\) −0.0403378 −0.00437525
\(86\) 0 0
\(87\) −1.76949 −0.189710
\(88\) 0 0
\(89\) 1.79541 0.190313 0.0951565 0.995462i \(-0.469665\pi\)
0.0951565 + 0.995462i \(0.469665\pi\)
\(90\) 0 0
\(91\) 4.89018 0.512630
\(92\) 0 0
\(93\) 3.13727 0.325320
\(94\) 0 0
\(95\) −0.0611860 −0.00627755
\(96\) 0 0
\(97\) 15.1851 1.54181 0.770907 0.636948i \(-0.219803\pi\)
0.770907 + 0.636948i \(0.219803\pi\)
\(98\) 0 0
\(99\) −1.24907 −0.125536
\(100\) 0 0
\(101\) 14.9487 1.48746 0.743728 0.668483i \(-0.233056\pi\)
0.743728 + 0.668483i \(0.233056\pi\)
\(102\) 0 0
\(103\) 17.2962 1.70424 0.852122 0.523343i \(-0.175315\pi\)
0.852122 + 0.523343i \(0.175315\pi\)
\(104\) 0 0
\(105\) −0.379564 −0.0370417
\(106\) 0 0
\(107\) 3.86798 0.373932 0.186966 0.982366i \(-0.440135\pi\)
0.186966 + 0.982366i \(0.440135\pi\)
\(108\) 0 0
\(109\) 9.28036 0.888897 0.444449 0.895804i \(-0.353400\pi\)
0.444449 + 0.895804i \(0.353400\pi\)
\(110\) 0 0
\(111\) −10.1482 −0.963221
\(112\) 0 0
\(113\) 10.0199 0.942594 0.471297 0.881975i \(-0.343786\pi\)
0.471297 + 0.881975i \(0.343786\pi\)
\(114\) 0 0
\(115\) 0.0677367 0.00631648
\(116\) 0 0
\(117\) 1.30900 0.121017
\(118\) 0 0
\(119\) −3.14838 −0.288612
\(120\) 0 0
\(121\) −9.52481 −0.865891
\(122\) 0 0
\(123\) 10.7351 0.967947
\(124\) 0 0
\(125\) −0.492115 −0.0440161
\(126\) 0 0
\(127\) −15.0908 −1.33909 −0.669546 0.742770i \(-0.733511\pi\)
−0.669546 + 0.742770i \(0.733511\pi\)
\(128\) 0 0
\(129\) 18.6664 1.64348
\(130\) 0 0
\(131\) −1.30772 −0.114256 −0.0571281 0.998367i \(-0.518194\pi\)
−0.0571281 + 0.998367i \(0.518194\pi\)
\(132\) 0 0
\(133\) −4.77559 −0.414096
\(134\) 0 0
\(135\) 0.194786 0.0167645
\(136\) 0 0
\(137\) 21.3694 1.82571 0.912855 0.408285i \(-0.133873\pi\)
0.912855 + 0.408285i \(0.133873\pi\)
\(138\) 0 0
\(139\) −6.42998 −0.545383 −0.272692 0.962101i \(-0.587914\pi\)
−0.272692 + 0.962101i \(0.587914\pi\)
\(140\) 0 0
\(141\) 6.35956 0.535571
\(142\) 0 0
\(143\) −1.54598 −0.129281
\(144\) 0 0
\(145\) 0.0433965 0.00360388
\(146\) 0 0
\(147\) −15.5755 −1.28465
\(148\) 0 0
\(149\) 12.3057 1.00812 0.504062 0.863668i \(-0.331838\pi\)
0.504062 + 0.863668i \(0.331838\pi\)
\(150\) 0 0
\(151\) −2.95247 −0.240269 −0.120134 0.992758i \(-0.538333\pi\)
−0.120134 + 0.992758i \(0.538333\pi\)
\(152\) 0 0
\(153\) −0.842755 −0.0681327
\(154\) 0 0
\(155\) −0.0769411 −0.00618005
\(156\) 0 0
\(157\) 10.5631 0.843025 0.421512 0.906823i \(-0.361499\pi\)
0.421512 + 0.906823i \(0.361499\pi\)
\(158\) 0 0
\(159\) −7.08332 −0.561744
\(160\) 0 0
\(161\) 5.28687 0.416664
\(162\) 0 0
\(163\) 19.7136 1.54409 0.772044 0.635570i \(-0.219235\pi\)
0.772044 + 0.635570i \(0.219235\pi\)
\(164\) 0 0
\(165\) 0.119995 0.00934159
\(166\) 0 0
\(167\) −16.9375 −1.31066 −0.655331 0.755342i \(-0.727471\pi\)
−0.655331 + 0.755342i \(0.727471\pi\)
\(168\) 0 0
\(169\) −11.3798 −0.875373
\(170\) 0 0
\(171\) −1.27833 −0.0977560
\(172\) 0 0
\(173\) −23.1723 −1.76175 −0.880877 0.473346i \(-0.843046\pi\)
−0.880877 + 0.473346i \(0.843046\pi\)
\(174\) 0 0
\(175\) −19.2002 −1.45140
\(176\) 0 0
\(177\) −18.7536 −1.40961
\(178\) 0 0
\(179\) 1.05850 0.0791160 0.0395580 0.999217i \(-0.487405\pi\)
0.0395580 + 0.999217i \(0.487405\pi\)
\(180\) 0 0
\(181\) 5.93329 0.441018 0.220509 0.975385i \(-0.429228\pi\)
0.220509 + 0.975385i \(0.429228\pi\)
\(182\) 0 0
\(183\) 10.9469 0.809219
\(184\) 0 0
\(185\) 0.248882 0.0182982
\(186\) 0 0
\(187\) 0.995325 0.0727853
\(188\) 0 0
\(189\) 15.2031 1.10586
\(190\) 0 0
\(191\) −2.85605 −0.206657 −0.103328 0.994647i \(-0.532949\pi\)
−0.103328 + 0.994647i \(0.532949\pi\)
\(192\) 0 0
\(193\) 3.42983 0.246885 0.123442 0.992352i \(-0.460607\pi\)
0.123442 + 0.992352i \(0.460607\pi\)
\(194\) 0 0
\(195\) −0.125752 −0.00900531
\(196\) 0 0
\(197\) 1.67085 0.119043 0.0595216 0.998227i \(-0.481042\pi\)
0.0595216 + 0.998227i \(0.481042\pi\)
\(198\) 0 0
\(199\) −11.0992 −0.786801 −0.393401 0.919367i \(-0.628701\pi\)
−0.393401 + 0.919367i \(0.628701\pi\)
\(200\) 0 0
\(201\) 10.8362 0.764327
\(202\) 0 0
\(203\) 3.38711 0.237729
\(204\) 0 0
\(205\) −0.263275 −0.0183879
\(206\) 0 0
\(207\) 1.41518 0.0983622
\(208\) 0 0
\(209\) 1.50975 0.104432
\(210\) 0 0
\(211\) −24.4236 −1.68139 −0.840697 0.541506i \(-0.817854\pi\)
−0.840697 + 0.541506i \(0.817854\pi\)
\(212\) 0 0
\(213\) 30.3951 2.08264
\(214\) 0 0
\(215\) −0.457789 −0.0312210
\(216\) 0 0
\(217\) −6.00528 −0.407665
\(218\) 0 0
\(219\) 28.7639 1.94368
\(220\) 0 0
\(221\) −1.04308 −0.0701652
\(222\) 0 0
\(223\) −5.66896 −0.379622 −0.189811 0.981821i \(-0.560787\pi\)
−0.189811 + 0.981821i \(0.560787\pi\)
\(224\) 0 0
\(225\) −5.13950 −0.342633
\(226\) 0 0
\(227\) 27.5843 1.83083 0.915416 0.402510i \(-0.131862\pi\)
0.915416 + 0.402510i \(0.131862\pi\)
\(228\) 0 0
\(229\) −21.2397 −1.40356 −0.701781 0.712393i \(-0.747611\pi\)
−0.701781 + 0.712393i \(0.747611\pi\)
\(230\) 0 0
\(231\) 9.36565 0.616214
\(232\) 0 0
\(233\) −21.5364 −1.41089 −0.705447 0.708763i \(-0.749254\pi\)
−0.705447 + 0.708763i \(0.749254\pi\)
\(234\) 0 0
\(235\) −0.155967 −0.0101742
\(236\) 0 0
\(237\) 26.9684 1.75179
\(238\) 0 0
\(239\) 0.920812 0.0595624 0.0297812 0.999556i \(-0.490519\pi\)
0.0297812 + 0.999556i \(0.490519\pi\)
\(240\) 0 0
\(241\) −21.1325 −1.36126 −0.680632 0.732625i \(-0.738295\pi\)
−0.680632 + 0.732625i \(0.738295\pi\)
\(242\) 0 0
\(243\) 10.2618 0.658295
\(244\) 0 0
\(245\) 0.381987 0.0244042
\(246\) 0 0
\(247\) −1.58219 −0.100672
\(248\) 0 0
\(249\) 14.5578 0.922561
\(250\) 0 0
\(251\) −23.7687 −1.50027 −0.750133 0.661287i \(-0.770010\pi\)
−0.750133 + 0.661287i \(0.770010\pi\)
\(252\) 0 0
\(253\) −1.67139 −0.105079
\(254\) 0 0
\(255\) 0.0809614 0.00507000
\(256\) 0 0
\(257\) 6.80865 0.424712 0.212356 0.977192i \(-0.431886\pi\)
0.212356 + 0.977192i \(0.431886\pi\)
\(258\) 0 0
\(259\) 19.4253 1.20703
\(260\) 0 0
\(261\) 0.906659 0.0561208
\(262\) 0 0
\(263\) −10.9060 −0.672491 −0.336246 0.941774i \(-0.609157\pi\)
−0.336246 + 0.941774i \(0.609157\pi\)
\(264\) 0 0
\(265\) 0.173717 0.0106714
\(266\) 0 0
\(267\) −3.60354 −0.220533
\(268\) 0 0
\(269\) −12.3222 −0.751298 −0.375649 0.926762i \(-0.622580\pi\)
−0.375649 + 0.926762i \(0.622580\pi\)
\(270\) 0 0
\(271\) −4.05699 −0.246445 −0.123222 0.992379i \(-0.539323\pi\)
−0.123222 + 0.992379i \(0.539323\pi\)
\(272\) 0 0
\(273\) −9.81502 −0.594032
\(274\) 0 0
\(275\) 6.06994 0.366031
\(276\) 0 0
\(277\) −22.6107 −1.35855 −0.679273 0.733886i \(-0.737705\pi\)
−0.679273 + 0.733886i \(0.737705\pi\)
\(278\) 0 0
\(279\) −1.60749 −0.0962378
\(280\) 0 0
\(281\) 0.573502 0.0342122 0.0171061 0.999854i \(-0.494555\pi\)
0.0171061 + 0.999854i \(0.494555\pi\)
\(282\) 0 0
\(283\) −19.0894 −1.13474 −0.567372 0.823461i \(-0.692040\pi\)
−0.567372 + 0.823461i \(0.692040\pi\)
\(284\) 0 0
\(285\) 0.122806 0.00727438
\(286\) 0 0
\(287\) −20.5487 −1.21295
\(288\) 0 0
\(289\) −16.3284 −0.960497
\(290\) 0 0
\(291\) −30.4778 −1.78664
\(292\) 0 0
\(293\) 19.7114 1.15156 0.575778 0.817606i \(-0.304699\pi\)
0.575778 + 0.817606i \(0.304699\pi\)
\(294\) 0 0
\(295\) 0.459928 0.0267781
\(296\) 0 0
\(297\) −4.80629 −0.278889
\(298\) 0 0
\(299\) 1.75158 0.101296
\(300\) 0 0
\(301\) −35.7307 −2.05948
\(302\) 0 0
\(303\) −30.0034 −1.72365
\(304\) 0 0
\(305\) −0.268471 −0.0153726
\(306\) 0 0
\(307\) −12.9458 −0.738854 −0.369427 0.929260i \(-0.620446\pi\)
−0.369427 + 0.929260i \(0.620446\pi\)
\(308\) 0 0
\(309\) −34.7150 −1.97487
\(310\) 0 0
\(311\) −21.1415 −1.19882 −0.599412 0.800441i \(-0.704599\pi\)
−0.599412 + 0.800441i \(0.704599\pi\)
\(312\) 0 0
\(313\) 0.237249 0.0134101 0.00670504 0.999978i \(-0.497866\pi\)
0.00670504 + 0.999978i \(0.497866\pi\)
\(314\) 0 0
\(315\) 0.194482 0.0109578
\(316\) 0 0
\(317\) −24.5299 −1.37774 −0.688868 0.724887i \(-0.741892\pi\)
−0.688868 + 0.724887i \(0.741892\pi\)
\(318\) 0 0
\(319\) −1.07080 −0.0599532
\(320\) 0 0
\(321\) −7.76338 −0.433309
\(322\) 0 0
\(323\) 1.01864 0.0566786
\(324\) 0 0
\(325\) −6.36118 −0.352855
\(326\) 0 0
\(327\) −18.6265 −1.03005
\(328\) 0 0
\(329\) −12.1733 −0.671135
\(330\) 0 0
\(331\) −16.9064 −0.929258 −0.464629 0.885505i \(-0.653812\pi\)
−0.464629 + 0.885505i \(0.653812\pi\)
\(332\) 0 0
\(333\) 5.19975 0.284945
\(334\) 0 0
\(335\) −0.265756 −0.0145198
\(336\) 0 0
\(337\) 28.4680 1.55075 0.775377 0.631499i \(-0.217560\pi\)
0.775377 + 0.631499i \(0.217560\pi\)
\(338\) 0 0
\(339\) −20.1108 −1.09227
\(340\) 0 0
\(341\) 1.89850 0.102810
\(342\) 0 0
\(343\) 2.92087 0.157712
\(344\) 0 0
\(345\) −0.135953 −0.00731948
\(346\) 0 0
\(347\) 29.2531 1.57039 0.785194 0.619250i \(-0.212563\pi\)
0.785194 + 0.619250i \(0.212563\pi\)
\(348\) 0 0
\(349\) 29.7647 1.59327 0.796633 0.604463i \(-0.206612\pi\)
0.796633 + 0.604463i \(0.206612\pi\)
\(350\) 0 0
\(351\) 5.03690 0.268850
\(352\) 0 0
\(353\) 11.1388 0.592858 0.296429 0.955055i \(-0.404204\pi\)
0.296429 + 0.955055i \(0.404204\pi\)
\(354\) 0 0
\(355\) −0.745434 −0.0395635
\(356\) 0 0
\(357\) 6.31907 0.334441
\(358\) 0 0
\(359\) 11.6789 0.616390 0.308195 0.951323i \(-0.400275\pi\)
0.308195 + 0.951323i \(0.400275\pi\)
\(360\) 0 0
\(361\) −17.4549 −0.918678
\(362\) 0 0
\(363\) 19.1171 1.00339
\(364\) 0 0
\(365\) −0.705428 −0.0369238
\(366\) 0 0
\(367\) −34.3649 −1.79384 −0.896918 0.442197i \(-0.854199\pi\)
−0.896918 + 0.442197i \(0.854199\pi\)
\(368\) 0 0
\(369\) −5.50047 −0.286343
\(370\) 0 0
\(371\) 13.5587 0.703932
\(372\) 0 0
\(373\) 20.2744 1.04977 0.524885 0.851173i \(-0.324108\pi\)
0.524885 + 0.851173i \(0.324108\pi\)
\(374\) 0 0
\(375\) 0.987718 0.0510055
\(376\) 0 0
\(377\) 1.12218 0.0577950
\(378\) 0 0
\(379\) −8.24662 −0.423601 −0.211800 0.977313i \(-0.567933\pi\)
−0.211800 + 0.977313i \(0.567933\pi\)
\(380\) 0 0
\(381\) 30.2886 1.55173
\(382\) 0 0
\(383\) −22.0089 −1.12460 −0.562302 0.826932i \(-0.690084\pi\)
−0.562302 + 0.826932i \(0.690084\pi\)
\(384\) 0 0
\(385\) −0.229691 −0.0117061
\(386\) 0 0
\(387\) −9.56434 −0.486183
\(388\) 0 0
\(389\) −4.20479 −0.213191 −0.106596 0.994302i \(-0.533995\pi\)
−0.106596 + 0.994302i \(0.533995\pi\)
\(390\) 0 0
\(391\) −1.12770 −0.0570300
\(392\) 0 0
\(393\) 2.62471 0.132399
\(394\) 0 0
\(395\) −0.661395 −0.0332784
\(396\) 0 0
\(397\) −19.6563 −0.986523 −0.493261 0.869881i \(-0.664195\pi\)
−0.493261 + 0.869881i \(0.664195\pi\)
\(398\) 0 0
\(399\) 9.58503 0.479852
\(400\) 0 0
\(401\) 9.95152 0.496955 0.248478 0.968638i \(-0.420070\pi\)
0.248478 + 0.968638i \(0.420070\pi\)
\(402\) 0 0
\(403\) −1.98959 −0.0991087
\(404\) 0 0
\(405\) −0.542816 −0.0269727
\(406\) 0 0
\(407\) −6.14109 −0.304403
\(408\) 0 0
\(409\) 19.6345 0.970864 0.485432 0.874274i \(-0.338662\pi\)
0.485432 + 0.874274i \(0.338662\pi\)
\(410\) 0 0
\(411\) −42.8902 −2.11562
\(412\) 0 0
\(413\) 35.8976 1.76641
\(414\) 0 0
\(415\) −0.357027 −0.0175257
\(416\) 0 0
\(417\) 12.9055 0.631986
\(418\) 0 0
\(419\) 8.43531 0.412092 0.206046 0.978542i \(-0.433940\pi\)
0.206046 + 0.978542i \(0.433940\pi\)
\(420\) 0 0
\(421\) 0.170507 0.00831001 0.00415501 0.999991i \(-0.498677\pi\)
0.00415501 + 0.999991i \(0.498677\pi\)
\(422\) 0 0
\(423\) −3.25853 −0.158435
\(424\) 0 0
\(425\) 4.09543 0.198658
\(426\) 0 0
\(427\) −20.9543 −1.01405
\(428\) 0 0
\(429\) 3.10291 0.149810
\(430\) 0 0
\(431\) 2.79223 0.134497 0.0672484 0.997736i \(-0.478578\pi\)
0.0672484 + 0.997736i \(0.478578\pi\)
\(432\) 0 0
\(433\) 7.63595 0.366960 0.183480 0.983023i \(-0.441264\pi\)
0.183480 + 0.983023i \(0.441264\pi\)
\(434\) 0 0
\(435\) −0.0871005 −0.00417615
\(436\) 0 0
\(437\) −1.71054 −0.0818260
\(438\) 0 0
\(439\) −32.3147 −1.54230 −0.771149 0.636655i \(-0.780318\pi\)
−0.771149 + 0.636655i \(0.780318\pi\)
\(440\) 0 0
\(441\) 7.98064 0.380031
\(442\) 0 0
\(443\) −40.5594 −1.92703 −0.963517 0.267646i \(-0.913754\pi\)
−0.963517 + 0.267646i \(0.913754\pi\)
\(444\) 0 0
\(445\) 0.0883762 0.00418943
\(446\) 0 0
\(447\) −24.6986 −1.16821
\(448\) 0 0
\(449\) −13.9801 −0.659760 −0.329880 0.944023i \(-0.607008\pi\)
−0.329880 + 0.944023i \(0.607008\pi\)
\(450\) 0 0
\(451\) 6.49625 0.305896
\(452\) 0 0
\(453\) 5.92587 0.278422
\(454\) 0 0
\(455\) 0.240712 0.0112847
\(456\) 0 0
\(457\) 1.60020 0.0748541 0.0374270 0.999299i \(-0.488084\pi\)
0.0374270 + 0.999299i \(0.488084\pi\)
\(458\) 0 0
\(459\) −3.24284 −0.151363
\(460\) 0 0
\(461\) 14.9778 0.697587 0.348793 0.937200i \(-0.386591\pi\)
0.348793 + 0.937200i \(0.386591\pi\)
\(462\) 0 0
\(463\) 3.03428 0.141015 0.0705075 0.997511i \(-0.477538\pi\)
0.0705075 + 0.997511i \(0.477538\pi\)
\(464\) 0 0
\(465\) 0.154427 0.00716140
\(466\) 0 0
\(467\) 0.611036 0.0282754 0.0141377 0.999900i \(-0.495500\pi\)
0.0141377 + 0.999900i \(0.495500\pi\)
\(468\) 0 0
\(469\) −20.7424 −0.957793
\(470\) 0 0
\(471\) −21.2010 −0.976891
\(472\) 0 0
\(473\) 11.2958 0.519383
\(474\) 0 0
\(475\) 6.21212 0.285031
\(476\) 0 0
\(477\) 3.62937 0.166178
\(478\) 0 0
\(479\) 19.6418 0.897457 0.448728 0.893668i \(-0.351877\pi\)
0.448728 + 0.893668i \(0.351877\pi\)
\(480\) 0 0
\(481\) 6.43575 0.293445
\(482\) 0 0
\(483\) −10.6112 −0.482827
\(484\) 0 0
\(485\) 0.747463 0.0339405
\(486\) 0 0
\(487\) −21.8782 −0.991394 −0.495697 0.868496i \(-0.665087\pi\)
−0.495697 + 0.868496i \(0.665087\pi\)
\(488\) 0 0
\(489\) −39.5669 −1.78928
\(490\) 0 0
\(491\) 26.3666 1.18991 0.594954 0.803759i \(-0.297170\pi\)
0.594954 + 0.803759i \(0.297170\pi\)
\(492\) 0 0
\(493\) −0.722475 −0.0325386
\(494\) 0 0
\(495\) −0.0614834 −0.00276347
\(496\) 0 0
\(497\) −58.1815 −2.60979
\(498\) 0 0
\(499\) −5.58422 −0.249984 −0.124992 0.992158i \(-0.539891\pi\)
−0.124992 + 0.992158i \(0.539891\pi\)
\(500\) 0 0
\(501\) 33.9950 1.51878
\(502\) 0 0
\(503\) −31.0425 −1.38412 −0.692059 0.721841i \(-0.743296\pi\)
−0.692059 + 0.721841i \(0.743296\pi\)
\(504\) 0 0
\(505\) 0.735828 0.0327439
\(506\) 0 0
\(507\) 22.8403 1.01438
\(508\) 0 0
\(509\) −18.4287 −0.816836 −0.408418 0.912795i \(-0.633919\pi\)
−0.408418 + 0.912795i \(0.633919\pi\)
\(510\) 0 0
\(511\) −55.0590 −2.43567
\(512\) 0 0
\(513\) −4.91887 −0.217173
\(514\) 0 0
\(515\) 0.851378 0.0375162
\(516\) 0 0
\(517\) 3.84844 0.169254
\(518\) 0 0
\(519\) 46.5087 2.04151
\(520\) 0 0
\(521\) 28.0249 1.22780 0.613898 0.789386i \(-0.289601\pi\)
0.613898 + 0.789386i \(0.289601\pi\)
\(522\) 0 0
\(523\) −43.0613 −1.88294 −0.941469 0.337100i \(-0.890554\pi\)
−0.941469 + 0.337100i \(0.890554\pi\)
\(524\) 0 0
\(525\) 38.5365 1.68187
\(526\) 0 0
\(527\) 1.28093 0.0557983
\(528\) 0 0
\(529\) −21.1063 −0.917667
\(530\) 0 0
\(531\) 9.60903 0.416996
\(532\) 0 0
\(533\) −6.80795 −0.294885
\(534\) 0 0
\(535\) 0.190395 0.00823151
\(536\) 0 0
\(537\) −2.12450 −0.0916790
\(538\) 0 0
\(539\) −9.42543 −0.405982
\(540\) 0 0
\(541\) 6.99953 0.300933 0.150467 0.988615i \(-0.451922\pi\)
0.150467 + 0.988615i \(0.451922\pi\)
\(542\) 0 0
\(543\) −11.9086 −0.511048
\(544\) 0 0
\(545\) 0.456811 0.0195676
\(546\) 0 0
\(547\) 35.6994 1.52640 0.763199 0.646164i \(-0.223628\pi\)
0.763199 + 0.646164i \(0.223628\pi\)
\(548\) 0 0
\(549\) −5.60901 −0.239387
\(550\) 0 0
\(551\) −1.09588 −0.0466860
\(552\) 0 0
\(553\) −51.6222 −2.19520
\(554\) 0 0
\(555\) −0.499527 −0.0212038
\(556\) 0 0
\(557\) −23.9989 −1.01686 −0.508432 0.861102i \(-0.669775\pi\)
−0.508432 + 0.861102i \(0.669775\pi\)
\(558\) 0 0
\(559\) −11.8378 −0.500687
\(560\) 0 0
\(561\) −1.99770 −0.0843431
\(562\) 0 0
\(563\) 37.5164 1.58113 0.790564 0.612379i \(-0.209788\pi\)
0.790564 + 0.612379i \(0.209788\pi\)
\(564\) 0 0
\(565\) 0.493214 0.0207497
\(566\) 0 0
\(567\) −42.3670 −1.77925
\(568\) 0 0
\(569\) −44.8656 −1.88086 −0.940431 0.339984i \(-0.889578\pi\)
−0.940431 + 0.339984i \(0.889578\pi\)
\(570\) 0 0
\(571\) −10.1072 −0.422973 −0.211486 0.977381i \(-0.567830\pi\)
−0.211486 + 0.977381i \(0.567830\pi\)
\(572\) 0 0
\(573\) 5.73235 0.239472
\(574\) 0 0
\(575\) −6.87720 −0.286799
\(576\) 0 0
\(577\) 29.1503 1.21354 0.606771 0.794877i \(-0.292465\pi\)
0.606771 + 0.794877i \(0.292465\pi\)
\(578\) 0 0
\(579\) −6.88397 −0.286088
\(580\) 0 0
\(581\) −27.8661 −1.15608
\(582\) 0 0
\(583\) −4.28642 −0.177526
\(584\) 0 0
\(585\) 0.0644334 0.00266399
\(586\) 0 0
\(587\) 4.09267 0.168922 0.0844612 0.996427i \(-0.473083\pi\)
0.0844612 + 0.996427i \(0.473083\pi\)
\(588\) 0 0
\(589\) 1.94297 0.0800587
\(590\) 0 0
\(591\) −3.35354 −0.137946
\(592\) 0 0
\(593\) 2.14775 0.0881977 0.0440988 0.999027i \(-0.485958\pi\)
0.0440988 + 0.999027i \(0.485958\pi\)
\(594\) 0 0
\(595\) −0.154974 −0.00635332
\(596\) 0 0
\(597\) 22.2771 0.911739
\(598\) 0 0
\(599\) 4.88974 0.199789 0.0998946 0.994998i \(-0.468149\pi\)
0.0998946 + 0.994998i \(0.468149\pi\)
\(600\) 0 0
\(601\) 45.0994 1.83964 0.919821 0.392337i \(-0.128333\pi\)
0.919821 + 0.392337i \(0.128333\pi\)
\(602\) 0 0
\(603\) −5.55229 −0.226107
\(604\) 0 0
\(605\) −0.468844 −0.0190612
\(606\) 0 0
\(607\) −1.56212 −0.0634043 −0.0317022 0.999497i \(-0.510093\pi\)
−0.0317022 + 0.999497i \(0.510093\pi\)
\(608\) 0 0
\(609\) −6.79823 −0.275478
\(610\) 0 0
\(611\) −4.03310 −0.163162
\(612\) 0 0
\(613\) −18.3643 −0.741727 −0.370864 0.928687i \(-0.620938\pi\)
−0.370864 + 0.928687i \(0.620938\pi\)
\(614\) 0 0
\(615\) 0.528416 0.0213078
\(616\) 0 0
\(617\) 10.3920 0.418368 0.209184 0.977876i \(-0.432919\pi\)
0.209184 + 0.977876i \(0.432919\pi\)
\(618\) 0 0
\(619\) −17.7341 −0.712792 −0.356396 0.934335i \(-0.615995\pi\)
−0.356396 + 0.934335i \(0.615995\pi\)
\(620\) 0 0
\(621\) 5.44549 0.218520
\(622\) 0 0
\(623\) 6.89780 0.276355
\(624\) 0 0
\(625\) 24.9637 0.998546
\(626\) 0 0
\(627\) −3.03020 −0.121014
\(628\) 0 0
\(629\) −4.14344 −0.165210
\(630\) 0 0
\(631\) −11.7614 −0.468214 −0.234107 0.972211i \(-0.575217\pi\)
−0.234107 + 0.972211i \(0.575217\pi\)
\(632\) 0 0
\(633\) 49.0204 1.94839
\(634\) 0 0
\(635\) −0.742821 −0.0294780
\(636\) 0 0
\(637\) 9.87767 0.391368
\(638\) 0 0
\(639\) −15.5739 −0.616096
\(640\) 0 0
\(641\) 18.7298 0.739782 0.369891 0.929075i \(-0.379395\pi\)
0.369891 + 0.929075i \(0.379395\pi\)
\(642\) 0 0
\(643\) −3.33285 −0.131435 −0.0657173 0.997838i \(-0.520934\pi\)
−0.0657173 + 0.997838i \(0.520934\pi\)
\(644\) 0 0
\(645\) 0.918823 0.0361786
\(646\) 0 0
\(647\) −23.5822 −0.927113 −0.463556 0.886067i \(-0.653427\pi\)
−0.463556 + 0.886067i \(0.653427\pi\)
\(648\) 0 0
\(649\) −11.3486 −0.445472
\(650\) 0 0
\(651\) 12.0531 0.472399
\(652\) 0 0
\(653\) 30.5579 1.19582 0.597912 0.801562i \(-0.295997\pi\)
0.597912 + 0.801562i \(0.295997\pi\)
\(654\) 0 0
\(655\) −0.0643706 −0.00251517
\(656\) 0 0
\(657\) −14.7381 −0.574989
\(658\) 0 0
\(659\) 3.20100 0.124693 0.0623467 0.998055i \(-0.480142\pi\)
0.0623467 + 0.998055i \(0.480142\pi\)
\(660\) 0 0
\(661\) −38.9181 −1.51374 −0.756870 0.653566i \(-0.773272\pi\)
−0.756870 + 0.653566i \(0.773272\pi\)
\(662\) 0 0
\(663\) 2.09355 0.0813069
\(664\) 0 0
\(665\) −0.235071 −0.00911566
\(666\) 0 0
\(667\) 1.21321 0.0469755
\(668\) 0 0
\(669\) 11.3781 0.439903
\(670\) 0 0
\(671\) 6.62445 0.255734
\(672\) 0 0
\(673\) −32.1720 −1.24014 −0.620069 0.784547i \(-0.712895\pi\)
−0.620069 + 0.784547i \(0.712895\pi\)
\(674\) 0 0
\(675\) −19.7763 −0.761190
\(676\) 0 0
\(677\) 7.16382 0.275328 0.137664 0.990479i \(-0.456041\pi\)
0.137664 + 0.990479i \(0.456041\pi\)
\(678\) 0 0
\(679\) 58.3398 2.23887
\(680\) 0 0
\(681\) −55.3640 −2.12155
\(682\) 0 0
\(683\) 31.4172 1.20215 0.601073 0.799194i \(-0.294740\pi\)
0.601073 + 0.799194i \(0.294740\pi\)
\(684\) 0 0
\(685\) 1.05187 0.0401900
\(686\) 0 0
\(687\) 42.6300 1.62644
\(688\) 0 0
\(689\) 4.49209 0.171135
\(690\) 0 0
\(691\) −15.3409 −0.583597 −0.291798 0.956480i \(-0.594254\pi\)
−0.291798 + 0.956480i \(0.594254\pi\)
\(692\) 0 0
\(693\) −4.79880 −0.182291
\(694\) 0 0
\(695\) −0.316505 −0.0120057
\(696\) 0 0
\(697\) 4.38307 0.166021
\(698\) 0 0
\(699\) 43.2254 1.63493
\(700\) 0 0
\(701\) −45.8809 −1.73290 −0.866450 0.499265i \(-0.833604\pi\)
−0.866450 + 0.499265i \(0.833604\pi\)
\(702\) 0 0
\(703\) −6.28494 −0.237041
\(704\) 0 0
\(705\) 0.313039 0.0117897
\(706\) 0 0
\(707\) 57.4317 2.15994
\(708\) 0 0
\(709\) 12.2522 0.460141 0.230071 0.973174i \(-0.426104\pi\)
0.230071 + 0.973174i \(0.426104\pi\)
\(710\) 0 0
\(711\) −13.8182 −0.518222
\(712\) 0 0
\(713\) −2.15099 −0.0805552
\(714\) 0 0
\(715\) −0.0760982 −0.00284591
\(716\) 0 0
\(717\) −1.84815 −0.0690204
\(718\) 0 0
\(719\) −25.7323 −0.959653 −0.479826 0.877363i \(-0.659300\pi\)
−0.479826 + 0.877363i \(0.659300\pi\)
\(720\) 0 0
\(721\) 66.4504 2.47474
\(722\) 0 0
\(723\) 42.4148 1.57742
\(724\) 0 0
\(725\) −4.40598 −0.163634
\(726\) 0 0
\(727\) 43.2514 1.60411 0.802053 0.597253i \(-0.203741\pi\)
0.802053 + 0.597253i \(0.203741\pi\)
\(728\) 0 0
\(729\) 12.4864 0.462461
\(730\) 0 0
\(731\) 7.62139 0.281887
\(732\) 0 0
\(733\) −1.44163 −0.0532480 −0.0266240 0.999646i \(-0.508476\pi\)
−0.0266240 + 0.999646i \(0.508476\pi\)
\(734\) 0 0
\(735\) −0.766681 −0.0282795
\(736\) 0 0
\(737\) 6.55746 0.241547
\(738\) 0 0
\(739\) −1.82506 −0.0671360 −0.0335680 0.999436i \(-0.510687\pi\)
−0.0335680 + 0.999436i \(0.510687\pi\)
\(740\) 0 0
\(741\) 3.17559 0.116658
\(742\) 0 0
\(743\) 15.9357 0.584622 0.292311 0.956323i \(-0.405576\pi\)
0.292311 + 0.956323i \(0.405576\pi\)
\(744\) 0 0
\(745\) 0.605729 0.0221922
\(746\) 0 0
\(747\) −7.45916 −0.272916
\(748\) 0 0
\(749\) 14.8604 0.542989
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 47.7058 1.73850
\(754\) 0 0
\(755\) −0.145331 −0.00528913
\(756\) 0 0
\(757\) −51.8492 −1.88449 −0.942246 0.334923i \(-0.891290\pi\)
−0.942246 + 0.334923i \(0.891290\pi\)
\(758\) 0 0
\(759\) 3.35462 0.121765
\(760\) 0 0
\(761\) −39.7590 −1.44126 −0.720631 0.693318i \(-0.756148\pi\)
−0.720631 + 0.693318i \(0.756148\pi\)
\(762\) 0 0
\(763\) 35.6543 1.29077
\(764\) 0 0
\(765\) −0.0414833 −0.00149983
\(766\) 0 0
\(767\) 11.8931 0.429436
\(768\) 0 0
\(769\) −18.2323 −0.657472 −0.328736 0.944422i \(-0.606623\pi\)
−0.328736 + 0.944422i \(0.606623\pi\)
\(770\) 0 0
\(771\) −13.6655 −0.492153
\(772\) 0 0
\(773\) 32.3971 1.16524 0.582621 0.812744i \(-0.302027\pi\)
0.582621 + 0.812744i \(0.302027\pi\)
\(774\) 0 0
\(775\) 7.81170 0.280605
\(776\) 0 0
\(777\) −38.9883 −1.39870
\(778\) 0 0
\(779\) 6.64842 0.238204
\(780\) 0 0
\(781\) 18.3934 0.658168
\(782\) 0 0
\(783\) 3.48874 0.124677
\(784\) 0 0
\(785\) 0.519951 0.0185578
\(786\) 0 0
\(787\) −27.5333 −0.981457 −0.490728 0.871313i \(-0.663269\pi\)
−0.490728 + 0.871313i \(0.663269\pi\)
\(788\) 0 0
\(789\) 21.8892 0.779278
\(790\) 0 0
\(791\) 38.4956 1.36875
\(792\) 0 0
\(793\) −6.94230 −0.246528
\(794\) 0 0
\(795\) −0.348665 −0.0123659
\(796\) 0 0
\(797\) −3.76869 −0.133494 −0.0667469 0.997770i \(-0.521262\pi\)
−0.0667469 + 0.997770i \(0.521262\pi\)
\(798\) 0 0
\(799\) 2.59657 0.0918602
\(800\) 0 0
\(801\) 1.84640 0.0652392
\(802\) 0 0
\(803\) 17.4063 0.614254
\(804\) 0 0
\(805\) 0.260238 0.00917219
\(806\) 0 0
\(807\) 24.7317 0.870598
\(808\) 0 0
\(809\) 35.8165 1.25924 0.629621 0.776902i \(-0.283210\pi\)
0.629621 + 0.776902i \(0.283210\pi\)
\(810\) 0 0
\(811\) −16.1755 −0.567999 −0.284000 0.958824i \(-0.591661\pi\)
−0.284000 + 0.958824i \(0.591661\pi\)
\(812\) 0 0
\(813\) 8.14274 0.285578
\(814\) 0 0
\(815\) 0.970370 0.0339906
\(816\) 0 0
\(817\) 11.5604 0.404448
\(818\) 0 0
\(819\) 5.02906 0.175729
\(820\) 0 0
\(821\) 35.8688 1.25183 0.625914 0.779892i \(-0.284726\pi\)
0.625914 + 0.779892i \(0.284726\pi\)
\(822\) 0 0
\(823\) 13.1572 0.458631 0.229315 0.973352i \(-0.426351\pi\)
0.229315 + 0.973352i \(0.426351\pi\)
\(824\) 0 0
\(825\) −12.1829 −0.424154
\(826\) 0 0
\(827\) 1.90486 0.0662386 0.0331193 0.999451i \(-0.489456\pi\)
0.0331193 + 0.999451i \(0.489456\pi\)
\(828\) 0 0
\(829\) −10.1600 −0.352872 −0.176436 0.984312i \(-0.556457\pi\)
−0.176436 + 0.984312i \(0.556457\pi\)
\(830\) 0 0
\(831\) 45.3816 1.57427
\(832\) 0 0
\(833\) −6.35941 −0.220340
\(834\) 0 0
\(835\) −0.833721 −0.0288521
\(836\) 0 0
\(837\) −6.18546 −0.213801
\(838\) 0 0
\(839\) −20.8208 −0.718813 −0.359406 0.933181i \(-0.617021\pi\)
−0.359406 + 0.933181i \(0.617021\pi\)
\(840\) 0 0
\(841\) −28.2227 −0.973198
\(842\) 0 0
\(843\) −1.15107 −0.0396449
\(844\) 0 0
\(845\) −0.560155 −0.0192699
\(846\) 0 0
\(847\) −36.5934 −1.25737
\(848\) 0 0
\(849\) 38.3140 1.31493
\(850\) 0 0
\(851\) 6.95782 0.238511
\(852\) 0 0
\(853\) −17.7927 −0.609212 −0.304606 0.952478i \(-0.598525\pi\)
−0.304606 + 0.952478i \(0.598525\pi\)
\(854\) 0 0
\(855\) −0.0629236 −0.00215194
\(856\) 0 0
\(857\) −57.9789 −1.98052 −0.990261 0.139221i \(-0.955540\pi\)
−0.990261 + 0.139221i \(0.955540\pi\)
\(858\) 0 0
\(859\) 15.3446 0.523551 0.261775 0.965129i \(-0.415692\pi\)
0.261775 + 0.965129i \(0.415692\pi\)
\(860\) 0 0
\(861\) 41.2431 1.40556
\(862\) 0 0
\(863\) −44.0580 −1.49975 −0.749876 0.661578i \(-0.769887\pi\)
−0.749876 + 0.661578i \(0.769887\pi\)
\(864\) 0 0
\(865\) −1.14062 −0.0387822
\(866\) 0 0
\(867\) 32.7726 1.11302
\(868\) 0 0
\(869\) 16.3198 0.553610
\(870\) 0 0
\(871\) −6.87210 −0.232852
\(872\) 0 0
\(873\) 15.6163 0.528533
\(874\) 0 0
\(875\) −1.89066 −0.0639160
\(876\) 0 0
\(877\) 4.08232 0.137850 0.0689251 0.997622i \(-0.478043\pi\)
0.0689251 + 0.997622i \(0.478043\pi\)
\(878\) 0 0
\(879\) −39.5626 −1.33441
\(880\) 0 0
\(881\) 47.9429 1.61524 0.807619 0.589704i \(-0.200756\pi\)
0.807619 + 0.589704i \(0.200756\pi\)
\(882\) 0 0
\(883\) 37.5593 1.26397 0.631986 0.774980i \(-0.282240\pi\)
0.631986 + 0.774980i \(0.282240\pi\)
\(884\) 0 0
\(885\) −0.923116 −0.0310302
\(886\) 0 0
\(887\) −37.5277 −1.26006 −0.630029 0.776572i \(-0.716957\pi\)
−0.630029 + 0.776572i \(0.716957\pi\)
\(888\) 0 0
\(889\) −57.9775 −1.94450
\(890\) 0 0
\(891\) 13.3938 0.448711
\(892\) 0 0
\(893\) 3.93859 0.131800
\(894\) 0 0
\(895\) 0.0521030 0.00174161
\(896\) 0 0
\(897\) −3.51557 −0.117382
\(898\) 0 0
\(899\) −1.37806 −0.0459610
\(900\) 0 0
\(901\) −2.89208 −0.0963492
\(902\) 0 0
\(903\) 71.7145 2.38651
\(904\) 0 0
\(905\) 0.292057 0.00970830
\(906\) 0 0
\(907\) 12.0360 0.399650 0.199825 0.979832i \(-0.435963\pi\)
0.199825 + 0.979832i \(0.435963\pi\)
\(908\) 0 0
\(909\) 15.3733 0.509899
\(910\) 0 0
\(911\) 59.9162 1.98511 0.992557 0.121784i \(-0.0388614\pi\)
0.992557 + 0.121784i \(0.0388614\pi\)
\(912\) 0 0
\(913\) 8.80954 0.291553
\(914\) 0 0
\(915\) 0.538844 0.0178136
\(916\) 0 0
\(917\) −5.02415 −0.165912
\(918\) 0 0
\(919\) 27.0738 0.893082 0.446541 0.894763i \(-0.352656\pi\)
0.446541 + 0.894763i \(0.352656\pi\)
\(920\) 0 0
\(921\) 25.9833 0.856178
\(922\) 0 0
\(923\) −19.2759 −0.634475
\(924\) 0 0
\(925\) −25.2686 −0.830826
\(926\) 0 0
\(927\) 17.7874 0.584214
\(928\) 0 0
\(929\) 21.5169 0.705947 0.352973 0.935633i \(-0.385171\pi\)
0.352973 + 0.935633i \(0.385171\pi\)
\(930\) 0 0
\(931\) −9.64621 −0.316142
\(932\) 0 0
\(933\) 42.4328 1.38919
\(934\) 0 0
\(935\) 0.0489933 0.00160225
\(936\) 0 0
\(937\) 4.05888 0.132598 0.0662989 0.997800i \(-0.478881\pi\)
0.0662989 + 0.997800i \(0.478881\pi\)
\(938\) 0 0
\(939\) −0.476179 −0.0155395
\(940\) 0 0
\(941\) −33.8277 −1.10275 −0.551376 0.834257i \(-0.685897\pi\)
−0.551376 + 0.834257i \(0.685897\pi\)
\(942\) 0 0
\(943\) −7.36021 −0.239681
\(944\) 0 0
\(945\) 0.748349 0.0243438
\(946\) 0 0
\(947\) 35.9997 1.16983 0.584917 0.811093i \(-0.301127\pi\)
0.584917 + 0.811093i \(0.301127\pi\)
\(948\) 0 0
\(949\) −18.2414 −0.592142
\(950\) 0 0
\(951\) 49.2336 1.59651
\(952\) 0 0
\(953\) 41.3634 1.33989 0.669946 0.742410i \(-0.266317\pi\)
0.669946 + 0.742410i \(0.266317\pi\)
\(954\) 0 0
\(955\) −0.140585 −0.00454922
\(956\) 0 0
\(957\) 2.14918 0.0694733
\(958\) 0 0
\(959\) 82.0992 2.65112
\(960\) 0 0
\(961\) −28.5567 −0.921185
\(962\) 0 0
\(963\) 3.97783 0.128184
\(964\) 0 0
\(965\) 0.168828 0.00543477
\(966\) 0 0
\(967\) 23.9050 0.768735 0.384367 0.923180i \(-0.374420\pi\)
0.384367 + 0.923180i \(0.374420\pi\)
\(968\) 0 0
\(969\) −2.04450 −0.0656787
\(970\) 0 0
\(971\) −49.4606 −1.58727 −0.793633 0.608396i \(-0.791813\pi\)
−0.793633 + 0.608396i \(0.791813\pi\)
\(972\) 0 0
\(973\) −24.7034 −0.791954
\(974\) 0 0
\(975\) 12.7674 0.408885
\(976\) 0 0
\(977\) −33.6360 −1.07611 −0.538056 0.842909i \(-0.680841\pi\)
−0.538056 + 0.842909i \(0.680841\pi\)
\(978\) 0 0
\(979\) −2.18066 −0.0696942
\(980\) 0 0
\(981\) 9.54390 0.304713
\(982\) 0 0
\(983\) −19.1782 −0.611689 −0.305845 0.952081i \(-0.598939\pi\)
−0.305845 + 0.952081i \(0.598939\pi\)
\(984\) 0 0
\(985\) 0.0822450 0.00262054
\(986\) 0 0
\(987\) 24.4328 0.777706
\(988\) 0 0
\(989\) −12.7981 −0.406956
\(990\) 0 0
\(991\) 43.1950 1.37214 0.686068 0.727538i \(-0.259335\pi\)
0.686068 + 0.727538i \(0.259335\pi\)
\(992\) 0 0
\(993\) 33.9325 1.07682
\(994\) 0 0
\(995\) −0.546341 −0.0173202
\(996\) 0 0
\(997\) 3.94299 0.124876 0.0624380 0.998049i \(-0.480112\pi\)
0.0624380 + 0.998049i \(0.480112\pi\)
\(998\) 0 0
\(999\) 20.0081 0.633029
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.1.13 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.13 44 1.1 even 1 trivial