Properties

Label 6008.2.a.b.1.3
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 1.3
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.25538 q^{3} -1.89943 q^{5} -1.94419 q^{7} +7.59748 q^{9} +O(q^{10})\) \(q-3.25538 q^{3} -1.89943 q^{5} -1.94419 q^{7} +7.59748 q^{9} +2.87143 q^{11} -5.69721 q^{13} +6.18336 q^{15} +0.264846 q^{17} +0.150476 q^{19} +6.32908 q^{21} -6.02516 q^{23} -1.39216 q^{25} -14.9665 q^{27} +6.65014 q^{29} -1.66567 q^{31} -9.34760 q^{33} +3.69286 q^{35} +11.9476 q^{37} +18.5466 q^{39} -4.78042 q^{41} -4.59270 q^{43} -14.4309 q^{45} +0.373316 q^{47} -3.22011 q^{49} -0.862175 q^{51} -3.24190 q^{53} -5.45409 q^{55} -0.489856 q^{57} +10.8967 q^{59} +14.2659 q^{61} -14.7710 q^{63} +10.8215 q^{65} +3.11010 q^{67} +19.6142 q^{69} -14.0569 q^{71} +5.06310 q^{73} +4.53201 q^{75} -5.58262 q^{77} +13.8592 q^{79} +25.9293 q^{81} -7.20240 q^{83} -0.503057 q^{85} -21.6487 q^{87} +17.9536 q^{89} +11.0765 q^{91} +5.42238 q^{93} -0.285819 q^{95} -4.67098 q^{97} +21.8157 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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
\(3\) −3.25538 −1.87949 −0.939746 0.341872i \(-0.888939\pi\)
−0.939746 + 0.341872i \(0.888939\pi\)
\(4\) 0 0
\(5\) −1.89943 −0.849451 −0.424726 0.905322i \(-0.639629\pi\)
−0.424726 + 0.905322i \(0.639629\pi\)
\(6\) 0 0
\(7\) −1.94419 −0.734836 −0.367418 0.930056i \(-0.619758\pi\)
−0.367418 + 0.930056i \(0.619758\pi\)
\(8\) 0 0
\(9\) 7.59748 2.53249
\(10\) 0 0
\(11\) 2.87143 0.865770 0.432885 0.901449i \(-0.357496\pi\)
0.432885 + 0.901449i \(0.357496\pi\)
\(12\) 0 0
\(13\) −5.69721 −1.58012 −0.790061 0.613029i \(-0.789951\pi\)
−0.790061 + 0.613029i \(0.789951\pi\)
\(14\) 0 0
\(15\) 6.18336 1.59654
\(16\) 0 0
\(17\) 0.264846 0.0642347 0.0321173 0.999484i \(-0.489775\pi\)
0.0321173 + 0.999484i \(0.489775\pi\)
\(18\) 0 0
\(19\) 0.150476 0.0345215 0.0172608 0.999851i \(-0.494505\pi\)
0.0172608 + 0.999851i \(0.494505\pi\)
\(20\) 0 0
\(21\) 6.32908 1.38112
\(22\) 0 0
\(23\) −6.02516 −1.25633 −0.628167 0.778079i \(-0.716194\pi\)
−0.628167 + 0.778079i \(0.716194\pi\)
\(24\) 0 0
\(25\) −1.39216 −0.278432
\(26\) 0 0
\(27\) −14.9665 −2.88031
\(28\) 0 0
\(29\) 6.65014 1.23490 0.617450 0.786610i \(-0.288166\pi\)
0.617450 + 0.786610i \(0.288166\pi\)
\(30\) 0 0
\(31\) −1.66567 −0.299163 −0.149581 0.988749i \(-0.547793\pi\)
−0.149581 + 0.988749i \(0.547793\pi\)
\(32\) 0 0
\(33\) −9.34760 −1.62721
\(34\) 0 0
\(35\) 3.69286 0.624207
\(36\) 0 0
\(37\) 11.9476 1.96417 0.982086 0.188432i \(-0.0603405\pi\)
0.982086 + 0.188432i \(0.0603405\pi\)
\(38\) 0 0
\(39\) 18.5466 2.96983
\(40\) 0 0
\(41\) −4.78042 −0.746576 −0.373288 0.927716i \(-0.621770\pi\)
−0.373288 + 0.927716i \(0.621770\pi\)
\(42\) 0 0
\(43\) −4.59270 −0.700380 −0.350190 0.936679i \(-0.613883\pi\)
−0.350190 + 0.936679i \(0.613883\pi\)
\(44\) 0 0
\(45\) −14.4309 −2.15123
\(46\) 0 0
\(47\) 0.373316 0.0544538 0.0272269 0.999629i \(-0.491332\pi\)
0.0272269 + 0.999629i \(0.491332\pi\)
\(48\) 0 0
\(49\) −3.22011 −0.460016
\(50\) 0 0
\(51\) −0.862175 −0.120729
\(52\) 0 0
\(53\) −3.24190 −0.445309 −0.222654 0.974897i \(-0.571472\pi\)
−0.222654 + 0.974897i \(0.571472\pi\)
\(54\) 0 0
\(55\) −5.45409 −0.735429
\(56\) 0 0
\(57\) −0.489856 −0.0648830
\(58\) 0 0
\(59\) 10.8967 1.41863 0.709317 0.704889i \(-0.249003\pi\)
0.709317 + 0.704889i \(0.249003\pi\)
\(60\) 0 0
\(61\) 14.2659 1.82656 0.913278 0.407336i \(-0.133542\pi\)
0.913278 + 0.407336i \(0.133542\pi\)
\(62\) 0 0
\(63\) −14.7710 −1.86097
\(64\) 0 0
\(65\) 10.8215 1.34224
\(66\) 0 0
\(67\) 3.11010 0.379959 0.189980 0.981788i \(-0.439158\pi\)
0.189980 + 0.981788i \(0.439158\pi\)
\(68\) 0 0
\(69\) 19.6142 2.36127
\(70\) 0 0
\(71\) −14.0569 −1.66824 −0.834121 0.551582i \(-0.814025\pi\)
−0.834121 + 0.551582i \(0.814025\pi\)
\(72\) 0 0
\(73\) 5.06310 0.592591 0.296295 0.955096i \(-0.404249\pi\)
0.296295 + 0.955096i \(0.404249\pi\)
\(74\) 0 0
\(75\) 4.53201 0.523312
\(76\) 0 0
\(77\) −5.58262 −0.636199
\(78\) 0 0
\(79\) 13.8592 1.55928 0.779639 0.626230i \(-0.215403\pi\)
0.779639 + 0.626230i \(0.215403\pi\)
\(80\) 0 0
\(81\) 25.9293 2.88103
\(82\) 0 0
\(83\) −7.20240 −0.790566 −0.395283 0.918559i \(-0.629353\pi\)
−0.395283 + 0.918559i \(0.629353\pi\)
\(84\) 0 0
\(85\) −0.503057 −0.0545642
\(86\) 0 0
\(87\) −21.6487 −2.32099
\(88\) 0 0
\(89\) 17.9536 1.90308 0.951540 0.307526i \(-0.0995012\pi\)
0.951540 + 0.307526i \(0.0995012\pi\)
\(90\) 0 0
\(91\) 11.0765 1.16113
\(92\) 0 0
\(93\) 5.42238 0.562274
\(94\) 0 0
\(95\) −0.285819 −0.0293244
\(96\) 0 0
\(97\) −4.67098 −0.474267 −0.237133 0.971477i \(-0.576208\pi\)
−0.237133 + 0.971477i \(0.576208\pi\)
\(98\) 0 0
\(99\) 21.8157 2.19256
\(100\) 0 0
\(101\) 1.22719 0.122110 0.0610548 0.998134i \(-0.480554\pi\)
0.0610548 + 0.998134i \(0.480554\pi\)
\(102\) 0 0
\(103\) −10.0786 −0.993072 −0.496536 0.868016i \(-0.665395\pi\)
−0.496536 + 0.868016i \(0.665395\pi\)
\(104\) 0 0
\(105\) −12.0217 −1.17319
\(106\) 0 0
\(107\) 10.8193 1.04595 0.522973 0.852349i \(-0.324823\pi\)
0.522973 + 0.852349i \(0.324823\pi\)
\(108\) 0 0
\(109\) 18.0796 1.73171 0.865856 0.500293i \(-0.166774\pi\)
0.865856 + 0.500293i \(0.166774\pi\)
\(110\) 0 0
\(111\) −38.8939 −3.69165
\(112\) 0 0
\(113\) 4.43265 0.416989 0.208494 0.978024i \(-0.433144\pi\)
0.208494 + 0.978024i \(0.433144\pi\)
\(114\) 0 0
\(115\) 11.4444 1.06719
\(116\) 0 0
\(117\) −43.2844 −4.00165
\(118\) 0 0
\(119\) −0.514912 −0.0472019
\(120\) 0 0
\(121\) −2.75487 −0.250442
\(122\) 0 0
\(123\) 15.5621 1.40318
\(124\) 0 0
\(125\) 12.1415 1.08597
\(126\) 0 0
\(127\) 10.4161 0.924278 0.462139 0.886807i \(-0.347082\pi\)
0.462139 + 0.886807i \(0.347082\pi\)
\(128\) 0 0
\(129\) 14.9510 1.31636
\(130\) 0 0
\(131\) −9.14024 −0.798586 −0.399293 0.916823i \(-0.630744\pi\)
−0.399293 + 0.916823i \(0.630744\pi\)
\(132\) 0 0
\(133\) −0.292554 −0.0253677
\(134\) 0 0
\(135\) 28.4279 2.44668
\(136\) 0 0
\(137\) −14.6319 −1.25008 −0.625042 0.780591i \(-0.714918\pi\)
−0.625042 + 0.780591i \(0.714918\pi\)
\(138\) 0 0
\(139\) −5.80989 −0.492788 −0.246394 0.969170i \(-0.579246\pi\)
−0.246394 + 0.969170i \(0.579246\pi\)
\(140\) 0 0
\(141\) −1.21529 −0.102345
\(142\) 0 0
\(143\) −16.3592 −1.36802
\(144\) 0 0
\(145\) −12.6315 −1.04899
\(146\) 0 0
\(147\) 10.4827 0.864597
\(148\) 0 0
\(149\) −4.15689 −0.340546 −0.170273 0.985397i \(-0.554465\pi\)
−0.170273 + 0.985397i \(0.554465\pi\)
\(150\) 0 0
\(151\) 10.6480 0.866520 0.433260 0.901269i \(-0.357363\pi\)
0.433260 + 0.901269i \(0.357363\pi\)
\(152\) 0 0
\(153\) 2.01216 0.162674
\(154\) 0 0
\(155\) 3.16382 0.254124
\(156\) 0 0
\(157\) 20.5037 1.63637 0.818186 0.574953i \(-0.194980\pi\)
0.818186 + 0.574953i \(0.194980\pi\)
\(158\) 0 0
\(159\) 10.5536 0.836954
\(160\) 0 0
\(161\) 11.7141 0.923199
\(162\) 0 0
\(163\) 8.81524 0.690463 0.345231 0.938518i \(-0.387800\pi\)
0.345231 + 0.938518i \(0.387800\pi\)
\(164\) 0 0
\(165\) 17.7551 1.38223
\(166\) 0 0
\(167\) 6.50201 0.503141 0.251570 0.967839i \(-0.419053\pi\)
0.251570 + 0.967839i \(0.419053\pi\)
\(168\) 0 0
\(169\) 19.4582 1.49678
\(170\) 0 0
\(171\) 1.14324 0.0874256
\(172\) 0 0
\(173\) 10.7128 0.814479 0.407239 0.913321i \(-0.366491\pi\)
0.407239 + 0.913321i \(0.366491\pi\)
\(174\) 0 0
\(175\) 2.70663 0.204602
\(176\) 0 0
\(177\) −35.4730 −2.66631
\(178\) 0 0
\(179\) −12.3476 −0.922903 −0.461451 0.887165i \(-0.652671\pi\)
−0.461451 + 0.887165i \(0.652671\pi\)
\(180\) 0 0
\(181\) −10.5557 −0.784599 −0.392300 0.919838i \(-0.628320\pi\)
−0.392300 + 0.919838i \(0.628320\pi\)
\(182\) 0 0
\(183\) −46.4408 −3.43300
\(184\) 0 0
\(185\) −22.6936 −1.66847
\(186\) 0 0
\(187\) 0.760489 0.0556124
\(188\) 0 0
\(189\) 29.0978 2.11656
\(190\) 0 0
\(191\) 13.7434 0.994440 0.497220 0.867624i \(-0.334354\pi\)
0.497220 + 0.867624i \(0.334354\pi\)
\(192\) 0 0
\(193\) −20.4885 −1.47479 −0.737396 0.675460i \(-0.763945\pi\)
−0.737396 + 0.675460i \(0.763945\pi\)
\(194\) 0 0
\(195\) −35.2279 −2.52272
\(196\) 0 0
\(197\) 17.0890 1.21754 0.608771 0.793346i \(-0.291663\pi\)
0.608771 + 0.793346i \(0.291663\pi\)
\(198\) 0 0
\(199\) −25.6322 −1.81702 −0.908511 0.417861i \(-0.862780\pi\)
−0.908511 + 0.417861i \(0.862780\pi\)
\(200\) 0 0
\(201\) −10.1245 −0.714130
\(202\) 0 0
\(203\) −12.9292 −0.907449
\(204\) 0 0
\(205\) 9.08007 0.634180
\(206\) 0 0
\(207\) −45.7761 −3.18166
\(208\) 0 0
\(209\) 0.432082 0.0298877
\(210\) 0 0
\(211\) −17.7716 −1.22345 −0.611723 0.791072i \(-0.709523\pi\)
−0.611723 + 0.791072i \(0.709523\pi\)
\(212\) 0 0
\(213\) 45.7604 3.13545
\(214\) 0 0
\(215\) 8.72351 0.594939
\(216\) 0 0
\(217\) 3.23838 0.219836
\(218\) 0 0
\(219\) −16.4823 −1.11377
\(220\) 0 0
\(221\) −1.50888 −0.101499
\(222\) 0 0
\(223\) 23.8681 1.59833 0.799163 0.601115i \(-0.205277\pi\)
0.799163 + 0.601115i \(0.205277\pi\)
\(224\) 0 0
\(225\) −10.5769 −0.705128
\(226\) 0 0
\(227\) −19.2514 −1.27776 −0.638880 0.769306i \(-0.720602\pi\)
−0.638880 + 0.769306i \(0.720602\pi\)
\(228\) 0 0
\(229\) 8.36859 0.553012 0.276506 0.961012i \(-0.410823\pi\)
0.276506 + 0.961012i \(0.410823\pi\)
\(230\) 0 0
\(231\) 18.1735 1.19573
\(232\) 0 0
\(233\) 12.3597 0.809708 0.404854 0.914381i \(-0.367322\pi\)
0.404854 + 0.914381i \(0.367322\pi\)
\(234\) 0 0
\(235\) −0.709089 −0.0462558
\(236\) 0 0
\(237\) −45.1168 −2.93065
\(238\) 0 0
\(239\) −17.9362 −1.16020 −0.580099 0.814546i \(-0.696986\pi\)
−0.580099 + 0.814546i \(0.696986\pi\)
\(240\) 0 0
\(241\) −29.7508 −1.91642 −0.958208 0.286071i \(-0.907651\pi\)
−0.958208 + 0.286071i \(0.907651\pi\)
\(242\) 0 0
\(243\) −39.5099 −2.53456
\(244\) 0 0
\(245\) 6.11638 0.390761
\(246\) 0 0
\(247\) −0.857293 −0.0545482
\(248\) 0 0
\(249\) 23.4465 1.48586
\(250\) 0 0
\(251\) −15.0311 −0.948756 −0.474378 0.880321i \(-0.657327\pi\)
−0.474378 + 0.880321i \(0.657327\pi\)
\(252\) 0 0
\(253\) −17.3009 −1.08770
\(254\) 0 0
\(255\) 1.63764 0.102553
\(256\) 0 0
\(257\) −7.01988 −0.437888 −0.218944 0.975737i \(-0.570261\pi\)
−0.218944 + 0.975737i \(0.570261\pi\)
\(258\) 0 0
\(259\) −23.2284 −1.44334
\(260\) 0 0
\(261\) 50.5243 3.12738
\(262\) 0 0
\(263\) −24.8230 −1.53065 −0.765326 0.643643i \(-0.777422\pi\)
−0.765326 + 0.643643i \(0.777422\pi\)
\(264\) 0 0
\(265\) 6.15776 0.378268
\(266\) 0 0
\(267\) −58.4458 −3.57682
\(268\) 0 0
\(269\) −4.48047 −0.273179 −0.136590 0.990628i \(-0.543614\pi\)
−0.136590 + 0.990628i \(0.543614\pi\)
\(270\) 0 0
\(271\) 7.70785 0.468218 0.234109 0.972210i \(-0.424783\pi\)
0.234109 + 0.972210i \(0.424783\pi\)
\(272\) 0 0
\(273\) −36.0581 −2.18234
\(274\) 0 0
\(275\) −3.99750 −0.241058
\(276\) 0 0
\(277\) 28.9263 1.73801 0.869007 0.494799i \(-0.164758\pi\)
0.869007 + 0.494799i \(0.164758\pi\)
\(278\) 0 0
\(279\) −12.6549 −0.757628
\(280\) 0 0
\(281\) 24.8577 1.48288 0.741442 0.671017i \(-0.234142\pi\)
0.741442 + 0.671017i \(0.234142\pi\)
\(282\) 0 0
\(283\) −24.7008 −1.46831 −0.734154 0.678983i \(-0.762421\pi\)
−0.734154 + 0.678983i \(0.762421\pi\)
\(284\) 0 0
\(285\) 0.930447 0.0551149
\(286\) 0 0
\(287\) 9.29405 0.548611
\(288\) 0 0
\(289\) −16.9299 −0.995874
\(290\) 0 0
\(291\) 15.2058 0.891381
\(292\) 0 0
\(293\) −16.3183 −0.953325 −0.476662 0.879086i \(-0.658154\pi\)
−0.476662 + 0.879086i \(0.658154\pi\)
\(294\) 0 0
\(295\) −20.6976 −1.20506
\(296\) 0 0
\(297\) −42.9754 −2.49369
\(298\) 0 0
\(299\) 34.3266 1.98516
\(300\) 0 0
\(301\) 8.92909 0.514664
\(302\) 0 0
\(303\) −3.99496 −0.229504
\(304\) 0 0
\(305\) −27.0970 −1.55157
\(306\) 0 0
\(307\) −16.6020 −0.947525 −0.473762 0.880653i \(-0.657104\pi\)
−0.473762 + 0.880653i \(0.657104\pi\)
\(308\) 0 0
\(309\) 32.8096 1.86647
\(310\) 0 0
\(311\) −13.8524 −0.785495 −0.392747 0.919646i \(-0.628475\pi\)
−0.392747 + 0.919646i \(0.628475\pi\)
\(312\) 0 0
\(313\) −20.6010 −1.16444 −0.582218 0.813033i \(-0.697815\pi\)
−0.582218 + 0.813033i \(0.697815\pi\)
\(314\) 0 0
\(315\) 28.0564 1.58080
\(316\) 0 0
\(317\) 1.68101 0.0944147 0.0472073 0.998885i \(-0.484968\pi\)
0.0472073 + 0.998885i \(0.484968\pi\)
\(318\) 0 0
\(319\) 19.0954 1.06914
\(320\) 0 0
\(321\) −35.2210 −1.96585
\(322\) 0 0
\(323\) 0.0398530 0.00221748
\(324\) 0 0
\(325\) 7.93144 0.439957
\(326\) 0 0
\(327\) −58.8560 −3.25474
\(328\) 0 0
\(329\) −0.725799 −0.0400146
\(330\) 0 0
\(331\) −0.0445026 −0.00244608 −0.00122304 0.999999i \(-0.500389\pi\)
−0.00122304 + 0.999999i \(0.500389\pi\)
\(332\) 0 0
\(333\) 90.7716 4.97425
\(334\) 0 0
\(335\) −5.90742 −0.322757
\(336\) 0 0
\(337\) 24.2964 1.32351 0.661755 0.749720i \(-0.269812\pi\)
0.661755 + 0.749720i \(0.269812\pi\)
\(338\) 0 0
\(339\) −14.4300 −0.783728
\(340\) 0 0
\(341\) −4.78285 −0.259006
\(342\) 0 0
\(343\) 19.8699 1.07287
\(344\) 0 0
\(345\) −37.2558 −2.00578
\(346\) 0 0
\(347\) 9.96838 0.535131 0.267565 0.963540i \(-0.413781\pi\)
0.267565 + 0.963540i \(0.413781\pi\)
\(348\) 0 0
\(349\) −2.59904 −0.139123 −0.0695617 0.997578i \(-0.522160\pi\)
−0.0695617 + 0.997578i \(0.522160\pi\)
\(350\) 0 0
\(351\) 85.2675 4.55124
\(352\) 0 0
\(353\) 9.86509 0.525066 0.262533 0.964923i \(-0.415442\pi\)
0.262533 + 0.964923i \(0.415442\pi\)
\(354\) 0 0
\(355\) 26.7000 1.41709
\(356\) 0 0
\(357\) 1.67623 0.0887157
\(358\) 0 0
\(359\) −16.8267 −0.888077 −0.444038 0.896008i \(-0.646455\pi\)
−0.444038 + 0.896008i \(0.646455\pi\)
\(360\) 0 0
\(361\) −18.9774 −0.998808
\(362\) 0 0
\(363\) 8.96813 0.470705
\(364\) 0 0
\(365\) −9.61700 −0.503377
\(366\) 0 0
\(367\) 3.82197 0.199505 0.0997525 0.995012i \(-0.468195\pi\)
0.0997525 + 0.995012i \(0.468195\pi\)
\(368\) 0 0
\(369\) −36.3191 −1.89070
\(370\) 0 0
\(371\) 6.30287 0.327229
\(372\) 0 0
\(373\) −27.4302 −1.42028 −0.710140 0.704060i \(-0.751368\pi\)
−0.710140 + 0.704060i \(0.751368\pi\)
\(374\) 0 0
\(375\) −39.5251 −2.04107
\(376\) 0 0
\(377\) −37.8872 −1.95129
\(378\) 0 0
\(379\) −4.89613 −0.251497 −0.125749 0.992062i \(-0.540133\pi\)
−0.125749 + 0.992062i \(0.540133\pi\)
\(380\) 0 0
\(381\) −33.9083 −1.73717
\(382\) 0 0
\(383\) 28.4284 1.45262 0.726312 0.687365i \(-0.241233\pi\)
0.726312 + 0.687365i \(0.241233\pi\)
\(384\) 0 0
\(385\) 10.6038 0.540420
\(386\) 0 0
\(387\) −34.8929 −1.77371
\(388\) 0 0
\(389\) −14.6206 −0.741293 −0.370646 0.928774i \(-0.620864\pi\)
−0.370646 + 0.928774i \(0.620864\pi\)
\(390\) 0 0
\(391\) −1.59574 −0.0807002
\(392\) 0 0
\(393\) 29.7549 1.50094
\(394\) 0 0
\(395\) −26.3245 −1.32453
\(396\) 0 0
\(397\) −15.0317 −0.754420 −0.377210 0.926128i \(-0.623116\pi\)
−0.377210 + 0.926128i \(0.623116\pi\)
\(398\) 0 0
\(399\) 0.952374 0.0476784
\(400\) 0 0
\(401\) −8.69181 −0.434048 −0.217024 0.976166i \(-0.569635\pi\)
−0.217024 + 0.976166i \(0.569635\pi\)
\(402\) 0 0
\(403\) 9.48966 0.472713
\(404\) 0 0
\(405\) −49.2509 −2.44729
\(406\) 0 0
\(407\) 34.3067 1.70052
\(408\) 0 0
\(409\) −8.05233 −0.398162 −0.199081 0.979983i \(-0.563796\pi\)
−0.199081 + 0.979983i \(0.563796\pi\)
\(410\) 0 0
\(411\) 47.6322 2.34952
\(412\) 0 0
\(413\) −21.1854 −1.04246
\(414\) 0 0
\(415\) 13.6805 0.671547
\(416\) 0 0
\(417\) 18.9134 0.926192
\(418\) 0 0
\(419\) 11.7729 0.575145 0.287572 0.957759i \(-0.407152\pi\)
0.287572 + 0.957759i \(0.407152\pi\)
\(420\) 0 0
\(421\) −10.2287 −0.498519 −0.249259 0.968437i \(-0.580187\pi\)
−0.249259 + 0.968437i \(0.580187\pi\)
\(422\) 0 0
\(423\) 2.83626 0.137904
\(424\) 0 0
\(425\) −0.368709 −0.0178850
\(426\) 0 0
\(427\) −27.7356 −1.34222
\(428\) 0 0
\(429\) 53.2552 2.57119
\(430\) 0 0
\(431\) 7.93027 0.381988 0.190994 0.981591i \(-0.438829\pi\)
0.190994 + 0.981591i \(0.438829\pi\)
\(432\) 0 0
\(433\) −4.88646 −0.234828 −0.117414 0.993083i \(-0.537460\pi\)
−0.117414 + 0.993083i \(0.537460\pi\)
\(434\) 0 0
\(435\) 41.1202 1.97156
\(436\) 0 0
\(437\) −0.906642 −0.0433706
\(438\) 0 0
\(439\) −29.3402 −1.40033 −0.700167 0.713980i \(-0.746891\pi\)
−0.700167 + 0.713980i \(0.746891\pi\)
\(440\) 0 0
\(441\) −24.4648 −1.16499
\(442\) 0 0
\(443\) −6.18870 −0.294034 −0.147017 0.989134i \(-0.546967\pi\)
−0.147017 + 0.989134i \(0.546967\pi\)
\(444\) 0 0
\(445\) −34.1016 −1.61657
\(446\) 0 0
\(447\) 13.5322 0.640053
\(448\) 0 0
\(449\) 3.70276 0.174744 0.0873720 0.996176i \(-0.472153\pi\)
0.0873720 + 0.996176i \(0.472153\pi\)
\(450\) 0 0
\(451\) −13.7267 −0.646363
\(452\) 0 0
\(453\) −34.6632 −1.62862
\(454\) 0 0
\(455\) −21.0390 −0.986323
\(456\) 0 0
\(457\) 6.34604 0.296855 0.148428 0.988923i \(-0.452579\pi\)
0.148428 + 0.988923i \(0.452579\pi\)
\(458\) 0 0
\(459\) −3.96383 −0.185016
\(460\) 0 0
\(461\) 10.7694 0.501581 0.250790 0.968041i \(-0.419310\pi\)
0.250790 + 0.968041i \(0.419310\pi\)
\(462\) 0 0
\(463\) −10.3467 −0.480853 −0.240427 0.970667i \(-0.577287\pi\)
−0.240427 + 0.970667i \(0.577287\pi\)
\(464\) 0 0
\(465\) −10.2994 −0.477625
\(466\) 0 0
\(467\) −9.90174 −0.458198 −0.229099 0.973403i \(-0.573578\pi\)
−0.229099 + 0.973403i \(0.573578\pi\)
\(468\) 0 0
\(469\) −6.04663 −0.279208
\(470\) 0 0
\(471\) −66.7472 −3.07555
\(472\) 0 0
\(473\) −13.1876 −0.606368
\(474\) 0 0
\(475\) −0.209487 −0.00961192
\(476\) 0 0
\(477\) −24.6302 −1.12774
\(478\) 0 0
\(479\) 34.5995 1.58089 0.790445 0.612533i \(-0.209849\pi\)
0.790445 + 0.612533i \(0.209849\pi\)
\(480\) 0 0
\(481\) −68.0679 −3.10363
\(482\) 0 0
\(483\) −38.1337 −1.73515
\(484\) 0 0
\(485\) 8.87221 0.402866
\(486\) 0 0
\(487\) 16.1438 0.731544 0.365772 0.930704i \(-0.380805\pi\)
0.365772 + 0.930704i \(0.380805\pi\)
\(488\) 0 0
\(489\) −28.6969 −1.29772
\(490\) 0 0
\(491\) 6.43857 0.290569 0.145284 0.989390i \(-0.453590\pi\)
0.145284 + 0.989390i \(0.453590\pi\)
\(492\) 0 0
\(493\) 1.76126 0.0793234
\(494\) 0 0
\(495\) −41.4373 −1.86247
\(496\) 0 0
\(497\) 27.3292 1.22588
\(498\) 0 0
\(499\) 11.1805 0.500508 0.250254 0.968180i \(-0.419486\pi\)
0.250254 + 0.968180i \(0.419486\pi\)
\(500\) 0 0
\(501\) −21.1665 −0.945649
\(502\) 0 0
\(503\) −15.2723 −0.680957 −0.340478 0.940252i \(-0.610589\pi\)
−0.340478 + 0.940252i \(0.610589\pi\)
\(504\) 0 0
\(505\) −2.33096 −0.103726
\(506\) 0 0
\(507\) −63.3438 −2.81319
\(508\) 0 0
\(509\) −25.1006 −1.11256 −0.556282 0.830994i \(-0.687772\pi\)
−0.556282 + 0.830994i \(0.687772\pi\)
\(510\) 0 0
\(511\) −9.84364 −0.435457
\(512\) 0 0
\(513\) −2.25210 −0.0994328
\(514\) 0 0
\(515\) 19.1436 0.843566
\(516\) 0 0
\(517\) 1.07195 0.0471444
\(518\) 0 0
\(519\) −34.8742 −1.53081
\(520\) 0 0
\(521\) −12.8602 −0.563417 −0.281708 0.959500i \(-0.590901\pi\)
−0.281708 + 0.959500i \(0.590901\pi\)
\(522\) 0 0
\(523\) 18.1990 0.795785 0.397892 0.917432i \(-0.369742\pi\)
0.397892 + 0.917432i \(0.369742\pi\)
\(524\) 0 0
\(525\) −8.81111 −0.384548
\(526\) 0 0
\(527\) −0.441146 −0.0192166
\(528\) 0 0
\(529\) 13.3026 0.578374
\(530\) 0 0
\(531\) 82.7878 3.59268
\(532\) 0 0
\(533\) 27.2350 1.17968
\(534\) 0 0
\(535\) −20.5506 −0.888480
\(536\) 0 0
\(537\) 40.1961 1.73459
\(538\) 0 0
\(539\) −9.24634 −0.398268
\(540\) 0 0
\(541\) 21.6770 0.931966 0.465983 0.884794i \(-0.345701\pi\)
0.465983 + 0.884794i \(0.345701\pi\)
\(542\) 0 0
\(543\) 34.3628 1.47465
\(544\) 0 0
\(545\) −34.3410 −1.47101
\(546\) 0 0
\(547\) −30.1348 −1.28847 −0.644235 0.764827i \(-0.722824\pi\)
−0.644235 + 0.764827i \(0.722824\pi\)
\(548\) 0 0
\(549\) 108.385 4.62574
\(550\) 0 0
\(551\) 1.00069 0.0426307
\(552\) 0 0
\(553\) −26.9449 −1.14581
\(554\) 0 0
\(555\) 73.8763 3.13588
\(556\) 0 0
\(557\) 7.90863 0.335099 0.167550 0.985864i \(-0.446415\pi\)
0.167550 + 0.985864i \(0.446415\pi\)
\(558\) 0 0
\(559\) 26.1656 1.10669
\(560\) 0 0
\(561\) −2.47568 −0.104523
\(562\) 0 0
\(563\) −10.1074 −0.425976 −0.212988 0.977055i \(-0.568319\pi\)
−0.212988 + 0.977055i \(0.568319\pi\)
\(564\) 0 0
\(565\) −8.41952 −0.354212
\(566\) 0 0
\(567\) −50.4115 −2.11708
\(568\) 0 0
\(569\) −32.7454 −1.37276 −0.686380 0.727243i \(-0.740801\pi\)
−0.686380 + 0.727243i \(0.740801\pi\)
\(570\) 0 0
\(571\) 10.4423 0.436997 0.218499 0.975837i \(-0.429884\pi\)
0.218499 + 0.975837i \(0.429884\pi\)
\(572\) 0 0
\(573\) −44.7401 −1.86904
\(574\) 0 0
\(575\) 8.38800 0.349804
\(576\) 0 0
\(577\) 16.9248 0.704591 0.352295 0.935889i \(-0.385401\pi\)
0.352295 + 0.935889i \(0.385401\pi\)
\(578\) 0 0
\(579\) 66.6977 2.77186
\(580\) 0 0
\(581\) 14.0028 0.580936
\(582\) 0 0
\(583\) −9.30889 −0.385535
\(584\) 0 0
\(585\) 82.2158 3.39920
\(586\) 0 0
\(587\) 30.4346 1.25617 0.628086 0.778144i \(-0.283839\pi\)
0.628086 + 0.778144i \(0.283839\pi\)
\(588\) 0 0
\(589\) −0.250643 −0.0103276
\(590\) 0 0
\(591\) −55.6312 −2.28836
\(592\) 0 0
\(593\) 15.7745 0.647783 0.323891 0.946094i \(-0.395009\pi\)
0.323891 + 0.946094i \(0.395009\pi\)
\(594\) 0 0
\(595\) 0.978040 0.0400957
\(596\) 0 0
\(597\) 83.4426 3.41508
\(598\) 0 0
\(599\) 27.8825 1.13925 0.569623 0.821906i \(-0.307089\pi\)
0.569623 + 0.821906i \(0.307089\pi\)
\(600\) 0 0
\(601\) −14.9743 −0.610813 −0.305406 0.952222i \(-0.598792\pi\)
−0.305406 + 0.952222i \(0.598792\pi\)
\(602\) 0 0
\(603\) 23.6289 0.962244
\(604\) 0 0
\(605\) 5.23268 0.212739
\(606\) 0 0
\(607\) 33.5976 1.36369 0.681843 0.731498i \(-0.261179\pi\)
0.681843 + 0.731498i \(0.261179\pi\)
\(608\) 0 0
\(609\) 42.0893 1.70554
\(610\) 0 0
\(611\) −2.12686 −0.0860436
\(612\) 0 0
\(613\) 42.7245 1.72563 0.862814 0.505522i \(-0.168700\pi\)
0.862814 + 0.505522i \(0.168700\pi\)
\(614\) 0 0
\(615\) −29.5591 −1.19194
\(616\) 0 0
\(617\) −39.1632 −1.57665 −0.788326 0.615258i \(-0.789052\pi\)
−0.788326 + 0.615258i \(0.789052\pi\)
\(618\) 0 0
\(619\) −32.8180 −1.31907 −0.659534 0.751675i \(-0.729246\pi\)
−0.659534 + 0.751675i \(0.729246\pi\)
\(620\) 0 0
\(621\) 90.1758 3.61863
\(622\) 0 0
\(623\) −34.9053 −1.39845
\(624\) 0 0
\(625\) −16.1011 −0.644043
\(626\) 0 0
\(627\) −1.40659 −0.0561738
\(628\) 0 0
\(629\) 3.16428 0.126168
\(630\) 0 0
\(631\) 23.3532 0.929676 0.464838 0.885396i \(-0.346113\pi\)
0.464838 + 0.885396i \(0.346113\pi\)
\(632\) 0 0
\(633\) 57.8532 2.29946
\(634\) 0 0
\(635\) −19.7846 −0.785129
\(636\) 0 0
\(637\) 18.3457 0.726882
\(638\) 0 0
\(639\) −106.797 −4.22481
\(640\) 0 0
\(641\) 25.4903 1.00680 0.503402 0.864052i \(-0.332081\pi\)
0.503402 + 0.864052i \(0.332081\pi\)
\(642\) 0 0
\(643\) −26.8236 −1.05782 −0.528909 0.848678i \(-0.677399\pi\)
−0.528909 + 0.848678i \(0.677399\pi\)
\(644\) 0 0
\(645\) −28.3983 −1.11818
\(646\) 0 0
\(647\) 23.2640 0.914604 0.457302 0.889311i \(-0.348816\pi\)
0.457302 + 0.889311i \(0.348816\pi\)
\(648\) 0 0
\(649\) 31.2893 1.22821
\(650\) 0 0
\(651\) −10.5421 −0.413179
\(652\) 0 0
\(653\) 15.4286 0.603767 0.301884 0.953345i \(-0.402385\pi\)
0.301884 + 0.953345i \(0.402385\pi\)
\(654\) 0 0
\(655\) 17.3612 0.678360
\(656\) 0 0
\(657\) 38.4668 1.50073
\(658\) 0 0
\(659\) 18.5481 0.722531 0.361265 0.932463i \(-0.382345\pi\)
0.361265 + 0.932463i \(0.382345\pi\)
\(660\) 0 0
\(661\) −32.2144 −1.25300 −0.626498 0.779423i \(-0.715512\pi\)
−0.626498 + 0.779423i \(0.715512\pi\)
\(662\) 0 0
\(663\) 4.91199 0.190766
\(664\) 0 0
\(665\) 0.555687 0.0215486
\(666\) 0 0
\(667\) −40.0682 −1.55145
\(668\) 0 0
\(669\) −77.6996 −3.00404
\(670\) 0 0
\(671\) 40.9635 1.58138
\(672\) 0 0
\(673\) −34.1127 −1.31495 −0.657475 0.753476i \(-0.728375\pi\)
−0.657475 + 0.753476i \(0.728375\pi\)
\(674\) 0 0
\(675\) 20.8358 0.801972
\(676\) 0 0
\(677\) 3.62537 0.139334 0.0696671 0.997570i \(-0.477806\pi\)
0.0696671 + 0.997570i \(0.477806\pi\)
\(678\) 0 0
\(679\) 9.08130 0.348508
\(680\) 0 0
\(681\) 62.6706 2.40154
\(682\) 0 0
\(683\) 43.5808 1.66757 0.833787 0.552087i \(-0.186168\pi\)
0.833787 + 0.552087i \(0.186168\pi\)
\(684\) 0 0
\(685\) 27.7922 1.06189
\(686\) 0 0
\(687\) −27.2429 −1.03938
\(688\) 0 0
\(689\) 18.4698 0.703642
\(690\) 0 0
\(691\) −2.79869 −0.106467 −0.0532337 0.998582i \(-0.516953\pi\)
−0.0532337 + 0.998582i \(0.516953\pi\)
\(692\) 0 0
\(693\) −42.4139 −1.61117
\(694\) 0 0
\(695\) 11.0355 0.418600
\(696\) 0 0
\(697\) −1.26608 −0.0479560
\(698\) 0 0
\(699\) −40.2353 −1.52184
\(700\) 0 0
\(701\) 2.55077 0.0963412 0.0481706 0.998839i \(-0.484661\pi\)
0.0481706 + 0.998839i \(0.484661\pi\)
\(702\) 0 0
\(703\) 1.79783 0.0678063
\(704\) 0 0
\(705\) 2.30835 0.0869375
\(706\) 0 0
\(707\) −2.38589 −0.0897306
\(708\) 0 0
\(709\) 10.9622 0.411693 0.205846 0.978584i \(-0.434005\pi\)
0.205846 + 0.978584i \(0.434005\pi\)
\(710\) 0 0
\(711\) 105.295 3.94886
\(712\) 0 0
\(713\) 10.0359 0.375848
\(714\) 0 0
\(715\) 31.0731 1.16207
\(716\) 0 0
\(717\) 58.3891 2.18058
\(718\) 0 0
\(719\) −45.2556 −1.68775 −0.843875 0.536539i \(-0.819731\pi\)
−0.843875 + 0.536539i \(0.819731\pi\)
\(720\) 0 0
\(721\) 19.5947 0.729745
\(722\) 0 0
\(723\) 96.8500 3.60189
\(724\) 0 0
\(725\) −9.25807 −0.343836
\(726\) 0 0
\(727\) −2.98672 −0.110771 −0.0553856 0.998465i \(-0.517639\pi\)
−0.0553856 + 0.998465i \(0.517639\pi\)
\(728\) 0 0
\(729\) 50.8320 1.88267
\(730\) 0 0
\(731\) −1.21636 −0.0449887
\(732\) 0 0
\(733\) −42.9041 −1.58470 −0.792350 0.610067i \(-0.791142\pi\)
−0.792350 + 0.610067i \(0.791142\pi\)
\(734\) 0 0
\(735\) −19.9111 −0.734433
\(736\) 0 0
\(737\) 8.93044 0.328957
\(738\) 0 0
\(739\) −4.92719 −0.181249 −0.0906247 0.995885i \(-0.528886\pi\)
−0.0906247 + 0.995885i \(0.528886\pi\)
\(740\) 0 0
\(741\) 2.79081 0.102523
\(742\) 0 0
\(743\) 21.8293 0.800841 0.400420 0.916332i \(-0.368864\pi\)
0.400420 + 0.916332i \(0.368864\pi\)
\(744\) 0 0
\(745\) 7.89572 0.289277
\(746\) 0 0
\(747\) −54.7201 −2.00210
\(748\) 0 0
\(749\) −21.0349 −0.768598
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 48.9319 1.78318
\(754\) 0 0
\(755\) −20.2251 −0.736067
\(756\) 0 0
\(757\) −37.4801 −1.36224 −0.681118 0.732173i \(-0.738506\pi\)
−0.681118 + 0.732173i \(0.738506\pi\)
\(758\) 0 0
\(759\) 56.3208 2.04432
\(760\) 0 0
\(761\) 7.99404 0.289784 0.144892 0.989448i \(-0.453717\pi\)
0.144892 + 0.989448i \(0.453717\pi\)
\(762\) 0 0
\(763\) −35.1503 −1.27252
\(764\) 0 0
\(765\) −3.82197 −0.138184
\(766\) 0 0
\(767\) −62.0810 −2.24162
\(768\) 0 0
\(769\) −4.56017 −0.164444 −0.0822220 0.996614i \(-0.526202\pi\)
−0.0822220 + 0.996614i \(0.526202\pi\)
\(770\) 0 0
\(771\) 22.8523 0.823007
\(772\) 0 0
\(773\) −21.0761 −0.758053 −0.379027 0.925386i \(-0.623741\pi\)
−0.379027 + 0.925386i \(0.623741\pi\)
\(774\) 0 0
\(775\) 2.31888 0.0832966
\(776\) 0 0
\(777\) 75.6173 2.71276
\(778\) 0 0
\(779\) −0.719338 −0.0257730
\(780\) 0 0
\(781\) −40.3633 −1.44431
\(782\) 0 0
\(783\) −99.5295 −3.55690
\(784\) 0 0
\(785\) −38.9453 −1.39002
\(786\) 0 0
\(787\) −25.3383 −0.903211 −0.451606 0.892218i \(-0.649149\pi\)
−0.451606 + 0.892218i \(0.649149\pi\)
\(788\) 0 0
\(789\) 80.8082 2.87685
\(790\) 0 0
\(791\) −8.61793 −0.306418
\(792\) 0 0
\(793\) −81.2756 −2.88618
\(794\) 0 0
\(795\) −20.0458 −0.710952
\(796\) 0 0
\(797\) 41.5673 1.47239 0.736194 0.676771i \(-0.236621\pi\)
0.736194 + 0.676771i \(0.236621\pi\)
\(798\) 0 0
\(799\) 0.0988714 0.00349782
\(800\) 0 0
\(801\) 136.402 4.81954
\(802\) 0 0
\(803\) 14.5383 0.513047
\(804\) 0 0
\(805\) −22.2501 −0.784212
\(806\) 0 0
\(807\) 14.5856 0.513438
\(808\) 0 0
\(809\) −39.4663 −1.38756 −0.693781 0.720186i \(-0.744056\pi\)
−0.693781 + 0.720186i \(0.744056\pi\)
\(810\) 0 0
\(811\) −26.1658 −0.918806 −0.459403 0.888228i \(-0.651937\pi\)
−0.459403 + 0.888228i \(0.651937\pi\)
\(812\) 0 0
\(813\) −25.0920 −0.880013
\(814\) 0 0
\(815\) −16.7439 −0.586515
\(816\) 0 0
\(817\) −0.691091 −0.0241782
\(818\) 0 0
\(819\) 84.1533 2.94055
\(820\) 0 0
\(821\) −44.3337 −1.54726 −0.773629 0.633639i \(-0.781560\pi\)
−0.773629 + 0.633639i \(0.781560\pi\)
\(822\) 0 0
\(823\) −17.1910 −0.599242 −0.299621 0.954058i \(-0.596860\pi\)
−0.299621 + 0.954058i \(0.596860\pi\)
\(824\) 0 0
\(825\) 13.0134 0.453068
\(826\) 0 0
\(827\) −34.8054 −1.21030 −0.605152 0.796110i \(-0.706887\pi\)
−0.605152 + 0.796110i \(0.706887\pi\)
\(828\) 0 0
\(829\) 11.4690 0.398335 0.199168 0.979965i \(-0.436176\pi\)
0.199168 + 0.979965i \(0.436176\pi\)
\(830\) 0 0
\(831\) −94.1661 −3.26659
\(832\) 0 0
\(833\) −0.852835 −0.0295490
\(834\) 0 0
\(835\) −12.3501 −0.427393
\(836\) 0 0
\(837\) 24.9293 0.861682
\(838\) 0 0
\(839\) 40.4858 1.39773 0.698863 0.715255i \(-0.253690\pi\)
0.698863 + 0.715255i \(0.253690\pi\)
\(840\) 0 0
\(841\) 15.2244 0.524978
\(842\) 0 0
\(843\) −80.9210 −2.78707
\(844\) 0 0
\(845\) −36.9595 −1.27145
\(846\) 0 0
\(847\) 5.35599 0.184034
\(848\) 0 0
\(849\) 80.4103 2.75967
\(850\) 0 0
\(851\) −71.9862 −2.46766
\(852\) 0 0
\(853\) −42.9963 −1.47216 −0.736082 0.676893i \(-0.763326\pi\)
−0.736082 + 0.676893i \(0.763326\pi\)
\(854\) 0 0
\(855\) −2.17150 −0.0742638
\(856\) 0 0
\(857\) −37.6398 −1.28575 −0.642875 0.765971i \(-0.722259\pi\)
−0.642875 + 0.765971i \(0.722259\pi\)
\(858\) 0 0
\(859\) 10.1473 0.346220 0.173110 0.984902i \(-0.444618\pi\)
0.173110 + 0.984902i \(0.444618\pi\)
\(860\) 0 0
\(861\) −30.2557 −1.03111
\(862\) 0 0
\(863\) −8.98553 −0.305871 −0.152935 0.988236i \(-0.548873\pi\)
−0.152935 + 0.988236i \(0.548873\pi\)
\(864\) 0 0
\(865\) −20.3482 −0.691860
\(866\) 0 0
\(867\) 55.1131 1.87174
\(868\) 0 0
\(869\) 39.7957 1.34998
\(870\) 0 0
\(871\) −17.7189 −0.600381
\(872\) 0 0
\(873\) −35.4877 −1.20108
\(874\) 0 0
\(875\) −23.6054 −0.798007
\(876\) 0 0
\(877\) −40.0623 −1.35281 −0.676404 0.736531i \(-0.736463\pi\)
−0.676404 + 0.736531i \(0.736463\pi\)
\(878\) 0 0
\(879\) 53.1222 1.79177
\(880\) 0 0
\(881\) 16.1564 0.544322 0.272161 0.962252i \(-0.412262\pi\)
0.272161 + 0.962252i \(0.412262\pi\)
\(882\) 0 0
\(883\) 8.24155 0.277350 0.138675 0.990338i \(-0.455716\pi\)
0.138675 + 0.990338i \(0.455716\pi\)
\(884\) 0 0
\(885\) 67.3785 2.26490
\(886\) 0 0
\(887\) −13.0485 −0.438127 −0.219063 0.975711i \(-0.570300\pi\)
−0.219063 + 0.975711i \(0.570300\pi\)
\(888\) 0 0
\(889\) −20.2509 −0.679193
\(890\) 0 0
\(891\) 74.4542 2.49431
\(892\) 0 0
\(893\) 0.0561751 0.00187983
\(894\) 0 0
\(895\) 23.4534 0.783961
\(896\) 0 0
\(897\) −111.746 −3.73109
\(898\) 0 0
\(899\) −11.0769 −0.369436
\(900\) 0 0
\(901\) −0.858604 −0.0286042
\(902\) 0 0
\(903\) −29.0676 −0.967308
\(904\) 0 0
\(905\) 20.0498 0.666479
\(906\) 0 0
\(907\) 43.5156 1.44491 0.722456 0.691417i \(-0.243013\pi\)
0.722456 + 0.691417i \(0.243013\pi\)
\(908\) 0 0
\(909\) 9.32353 0.309242
\(910\) 0 0
\(911\) 40.1001 1.32858 0.664288 0.747477i \(-0.268735\pi\)
0.664288 + 0.747477i \(0.268735\pi\)
\(912\) 0 0
\(913\) −20.6812 −0.684448
\(914\) 0 0
\(915\) 88.2110 2.91617
\(916\) 0 0
\(917\) 17.7704 0.586830
\(918\) 0 0
\(919\) 25.2636 0.833368 0.416684 0.909051i \(-0.363192\pi\)
0.416684 + 0.909051i \(0.363192\pi\)
\(920\) 0 0
\(921\) 54.0457 1.78087
\(922\) 0 0
\(923\) 80.0849 2.63602
\(924\) 0 0
\(925\) −16.6330 −0.546889
\(926\) 0 0
\(927\) −76.5718 −2.51495
\(928\) 0 0
\(929\) −2.98452 −0.0979189 −0.0489595 0.998801i \(-0.515591\pi\)
−0.0489595 + 0.998801i \(0.515591\pi\)
\(930\) 0 0
\(931\) −0.484550 −0.0158805
\(932\) 0 0
\(933\) 45.0946 1.47633
\(934\) 0 0
\(935\) −1.44450 −0.0472401
\(936\) 0 0
\(937\) 30.6853 1.00244 0.501222 0.865319i \(-0.332884\pi\)
0.501222 + 0.865319i \(0.332884\pi\)
\(938\) 0 0
\(939\) 67.0639 2.18855
\(940\) 0 0
\(941\) −17.8260 −0.581112 −0.290556 0.956858i \(-0.593840\pi\)
−0.290556 + 0.956858i \(0.593840\pi\)
\(942\) 0 0
\(943\) 28.8028 0.937948
\(944\) 0 0
\(945\) −55.2693 −1.79791
\(946\) 0 0
\(947\) −50.5741 −1.64344 −0.821719 0.569892i \(-0.806985\pi\)
−0.821719 + 0.569892i \(0.806985\pi\)
\(948\) 0 0
\(949\) −28.8455 −0.936365
\(950\) 0 0
\(951\) −5.47231 −0.177452
\(952\) 0 0
\(953\) 3.94969 0.127943 0.0639715 0.997952i \(-0.479623\pi\)
0.0639715 + 0.997952i \(0.479623\pi\)
\(954\) 0 0
\(955\) −26.1047 −0.844729
\(956\) 0 0
\(957\) −62.1629 −2.00944
\(958\) 0 0
\(959\) 28.4471 0.918606
\(960\) 0 0
\(961\) −28.2256 −0.910502
\(962\) 0 0
\(963\) 82.1997 2.64885
\(964\) 0 0
\(965\) 38.9164 1.25276
\(966\) 0 0
\(967\) 20.5721 0.661553 0.330777 0.943709i \(-0.392689\pi\)
0.330777 + 0.943709i \(0.392689\pi\)
\(968\) 0 0
\(969\) −0.129737 −0.00416774
\(970\) 0 0
\(971\) 31.1573 0.999885 0.499942 0.866059i \(-0.333355\pi\)
0.499942 + 0.866059i \(0.333355\pi\)
\(972\) 0 0
\(973\) 11.2955 0.362118
\(974\) 0 0
\(975\) −25.8198 −0.826896
\(976\) 0 0
\(977\) 33.8762 1.08380 0.541898 0.840444i \(-0.317706\pi\)
0.541898 + 0.840444i \(0.317706\pi\)
\(978\) 0 0
\(979\) 51.5526 1.64763
\(980\) 0 0
\(981\) 137.359 4.38555
\(982\) 0 0
\(983\) −50.3897 −1.60718 −0.803592 0.595181i \(-0.797080\pi\)
−0.803592 + 0.595181i \(0.797080\pi\)
\(984\) 0 0
\(985\) −32.4594 −1.03424
\(986\) 0 0
\(987\) 2.36275 0.0752071
\(988\) 0 0
\(989\) 27.6718 0.879911
\(990\) 0 0
\(991\) 10.6068 0.336937 0.168469 0.985707i \(-0.446118\pi\)
0.168469 + 0.985707i \(0.446118\pi\)
\(992\) 0 0
\(993\) 0.144873 0.00459740
\(994\) 0 0
\(995\) 48.6867 1.54347
\(996\) 0 0
\(997\) −49.8630 −1.57918 −0.789588 0.613637i \(-0.789706\pi\)
−0.789588 + 0.613637i \(0.789706\pi\)
\(998\) 0 0
\(999\) −178.814 −5.65743
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.1.3 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.3 44 1.1 even 1 trivial