Properties

Label 6008.2.a.b.1.25
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 1.25
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.107352 q^{3} +0.451859 q^{5} +2.31721 q^{7} -2.98848 q^{9} +O(q^{10})\) \(q-0.107352 q^{3} +0.451859 q^{5} +2.31721 q^{7} -2.98848 q^{9} +2.84297 q^{11} +2.31366 q^{13} -0.0485078 q^{15} +0.174832 q^{17} -2.11240 q^{19} -0.248756 q^{21} +0.730513 q^{23} -4.79582 q^{25} +0.642873 q^{27} -7.10282 q^{29} -10.1070 q^{31} -0.305197 q^{33} +1.04705 q^{35} -2.63181 q^{37} -0.248376 q^{39} -7.51725 q^{41} -0.351209 q^{43} -1.35037 q^{45} -6.18043 q^{47} -1.63054 q^{49} -0.0187686 q^{51} -0.440982 q^{53} +1.28462 q^{55} +0.226770 q^{57} -1.57828 q^{59} -4.03536 q^{61} -6.92493 q^{63} +1.04545 q^{65} -4.68956 q^{67} -0.0784218 q^{69} +14.4991 q^{71} +3.78102 q^{73} +0.514840 q^{75} +6.58775 q^{77} +16.4620 q^{79} +8.89641 q^{81} -7.15521 q^{83} +0.0789996 q^{85} +0.762500 q^{87} +3.87479 q^{89} +5.36124 q^{91} +1.08500 q^{93} -0.954508 q^{95} +11.6388 q^{97} -8.49614 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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
\(3\) −0.107352 −0.0619795 −0.0309898 0.999520i \(-0.509866\pi\)
−0.0309898 + 0.999520i \(0.509866\pi\)
\(4\) 0 0
\(5\) 0.451859 0.202077 0.101039 0.994882i \(-0.467783\pi\)
0.101039 + 0.994882i \(0.467783\pi\)
\(6\) 0 0
\(7\) 2.31721 0.875823 0.437912 0.899018i \(-0.355718\pi\)
0.437912 + 0.899018i \(0.355718\pi\)
\(8\) 0 0
\(9\) −2.98848 −0.996159
\(10\) 0 0
\(11\) 2.84297 0.857187 0.428593 0.903498i \(-0.359009\pi\)
0.428593 + 0.903498i \(0.359009\pi\)
\(12\) 0 0
\(13\) 2.31366 0.641695 0.320847 0.947131i \(-0.396032\pi\)
0.320847 + 0.947131i \(0.396032\pi\)
\(14\) 0 0
\(15\) −0.0485078 −0.0125247
\(16\) 0 0
\(17\) 0.174832 0.0424031 0.0212016 0.999775i \(-0.493251\pi\)
0.0212016 + 0.999775i \(0.493251\pi\)
\(18\) 0 0
\(19\) −2.11240 −0.484619 −0.242309 0.970199i \(-0.577905\pi\)
−0.242309 + 0.970199i \(0.577905\pi\)
\(20\) 0 0
\(21\) −0.248756 −0.0542831
\(22\) 0 0
\(23\) 0.730513 0.152323 0.0761613 0.997096i \(-0.475734\pi\)
0.0761613 + 0.997096i \(0.475734\pi\)
\(24\) 0 0
\(25\) −4.79582 −0.959165
\(26\) 0 0
\(27\) 0.642873 0.123721
\(28\) 0 0
\(29\) −7.10282 −1.31896 −0.659480 0.751722i \(-0.729224\pi\)
−0.659480 + 0.751722i \(0.729224\pi\)
\(30\) 0 0
\(31\) −10.1070 −1.81526 −0.907632 0.419767i \(-0.862112\pi\)
−0.907632 + 0.419767i \(0.862112\pi\)
\(32\) 0 0
\(33\) −0.305197 −0.0531280
\(34\) 0 0
\(35\) 1.04705 0.176984
\(36\) 0 0
\(37\) −2.63181 −0.432667 −0.216333 0.976320i \(-0.569410\pi\)
−0.216333 + 0.976320i \(0.569410\pi\)
\(38\) 0 0
\(39\) −0.248376 −0.0397719
\(40\) 0 0
\(41\) −7.51725 −1.17400 −0.586998 0.809588i \(-0.699691\pi\)
−0.586998 + 0.809588i \(0.699691\pi\)
\(42\) 0 0
\(43\) −0.351209 −0.0535589 −0.0267795 0.999641i \(-0.508525\pi\)
−0.0267795 + 0.999641i \(0.508525\pi\)
\(44\) 0 0
\(45\) −1.35037 −0.201301
\(46\) 0 0
\(47\) −6.18043 −0.901508 −0.450754 0.892648i \(-0.648845\pi\)
−0.450754 + 0.892648i \(0.648845\pi\)
\(48\) 0 0
\(49\) −1.63054 −0.232934
\(50\) 0 0
\(51\) −0.0187686 −0.00262812
\(52\) 0 0
\(53\) −0.440982 −0.0605735 −0.0302867 0.999541i \(-0.509642\pi\)
−0.0302867 + 0.999541i \(0.509642\pi\)
\(54\) 0 0
\(55\) 1.28462 0.173218
\(56\) 0 0
\(57\) 0.226770 0.0300364
\(58\) 0 0
\(59\) −1.57828 −0.205474 −0.102737 0.994709i \(-0.532760\pi\)
−0.102737 + 0.994709i \(0.532760\pi\)
\(60\) 0 0
\(61\) −4.03536 −0.516674 −0.258337 0.966055i \(-0.583175\pi\)
−0.258337 + 0.966055i \(0.583175\pi\)
\(62\) 0 0
\(63\) −6.92493 −0.872459
\(64\) 0 0
\(65\) 1.04545 0.129672
\(66\) 0 0
\(67\) −4.68956 −0.572921 −0.286461 0.958092i \(-0.592479\pi\)
−0.286461 + 0.958092i \(0.592479\pi\)
\(68\) 0 0
\(69\) −0.0784218 −0.00944088
\(70\) 0 0
\(71\) 14.4991 1.72073 0.860363 0.509682i \(-0.170237\pi\)
0.860363 + 0.509682i \(0.170237\pi\)
\(72\) 0 0
\(73\) 3.78102 0.442535 0.221268 0.975213i \(-0.428981\pi\)
0.221268 + 0.975213i \(0.428981\pi\)
\(74\) 0 0
\(75\) 0.514840 0.0594486
\(76\) 0 0
\(77\) 6.58775 0.750744
\(78\) 0 0
\(79\) 16.4620 1.85211 0.926057 0.377383i \(-0.123176\pi\)
0.926057 + 0.377383i \(0.123176\pi\)
\(80\) 0 0
\(81\) 8.89641 0.988490
\(82\) 0 0
\(83\) −7.15521 −0.785386 −0.392693 0.919670i \(-0.628457\pi\)
−0.392693 + 0.919670i \(0.628457\pi\)
\(84\) 0 0
\(85\) 0.0789996 0.00856871
\(86\) 0 0
\(87\) 0.762500 0.0817486
\(88\) 0 0
\(89\) 3.87479 0.410726 0.205363 0.978686i \(-0.434162\pi\)
0.205363 + 0.978686i \(0.434162\pi\)
\(90\) 0 0
\(91\) 5.36124 0.562011
\(92\) 0 0
\(93\) 1.08500 0.112509
\(94\) 0 0
\(95\) −0.954508 −0.0979305
\(96\) 0 0
\(97\) 11.6388 1.18174 0.590872 0.806765i \(-0.298784\pi\)
0.590872 + 0.806765i \(0.298784\pi\)
\(98\) 0 0
\(99\) −8.49614 −0.853894
\(100\) 0 0
\(101\) −10.0335 −0.998371 −0.499186 0.866495i \(-0.666367\pi\)
−0.499186 + 0.866495i \(0.666367\pi\)
\(102\) 0 0
\(103\) −7.62007 −0.750828 −0.375414 0.926857i \(-0.622499\pi\)
−0.375414 + 0.926857i \(0.622499\pi\)
\(104\) 0 0
\(105\) −0.112403 −0.0109694
\(106\) 0 0
\(107\) −14.7831 −1.42914 −0.714568 0.699566i \(-0.753377\pi\)
−0.714568 + 0.699566i \(0.753377\pi\)
\(108\) 0 0
\(109\) −11.2344 −1.07606 −0.538029 0.842926i \(-0.680831\pi\)
−0.538029 + 0.842926i \(0.680831\pi\)
\(110\) 0 0
\(111\) 0.282529 0.0268165
\(112\) 0 0
\(113\) 1.39916 0.131622 0.0658112 0.997832i \(-0.479037\pi\)
0.0658112 + 0.997832i \(0.479037\pi\)
\(114\) 0 0
\(115\) 0.330089 0.0307809
\(116\) 0 0
\(117\) −6.91432 −0.639230
\(118\) 0 0
\(119\) 0.405124 0.0371376
\(120\) 0 0
\(121\) −2.91754 −0.265231
\(122\) 0 0
\(123\) 0.806989 0.0727638
\(124\) 0 0
\(125\) −4.42633 −0.395903
\(126\) 0 0
\(127\) 12.6770 1.12491 0.562453 0.826829i \(-0.309858\pi\)
0.562453 + 0.826829i \(0.309858\pi\)
\(128\) 0 0
\(129\) 0.0377029 0.00331956
\(130\) 0 0
\(131\) −15.5557 −1.35911 −0.679553 0.733627i \(-0.737826\pi\)
−0.679553 + 0.733627i \(0.737826\pi\)
\(132\) 0 0
\(133\) −4.89488 −0.424440
\(134\) 0 0
\(135\) 0.290488 0.0250012
\(136\) 0 0
\(137\) 4.15472 0.354962 0.177481 0.984124i \(-0.443205\pi\)
0.177481 + 0.984124i \(0.443205\pi\)
\(138\) 0 0
\(139\) 10.8863 0.923362 0.461681 0.887046i \(-0.347246\pi\)
0.461681 + 0.887046i \(0.347246\pi\)
\(140\) 0 0
\(141\) 0.663479 0.0558750
\(142\) 0 0
\(143\) 6.57767 0.550052
\(144\) 0 0
\(145\) −3.20947 −0.266532
\(146\) 0 0
\(147\) 0.175041 0.0144371
\(148\) 0 0
\(149\) 11.5547 0.946599 0.473300 0.880901i \(-0.343063\pi\)
0.473300 + 0.880901i \(0.343063\pi\)
\(150\) 0 0
\(151\) −0.593480 −0.0482967 −0.0241484 0.999708i \(-0.507687\pi\)
−0.0241484 + 0.999708i \(0.507687\pi\)
\(152\) 0 0
\(153\) −0.522483 −0.0422402
\(154\) 0 0
\(155\) −4.56692 −0.366824
\(156\) 0 0
\(157\) −6.89377 −0.550183 −0.275091 0.961418i \(-0.588708\pi\)
−0.275091 + 0.961418i \(0.588708\pi\)
\(158\) 0 0
\(159\) 0.0473401 0.00375432
\(160\) 0 0
\(161\) 1.69275 0.133408
\(162\) 0 0
\(163\) 12.7980 1.00242 0.501208 0.865327i \(-0.332889\pi\)
0.501208 + 0.865327i \(0.332889\pi\)
\(164\) 0 0
\(165\) −0.137906 −0.0107360
\(166\) 0 0
\(167\) −12.3617 −0.956576 −0.478288 0.878203i \(-0.658742\pi\)
−0.478288 + 0.878203i \(0.658742\pi\)
\(168\) 0 0
\(169\) −7.64697 −0.588228
\(170\) 0 0
\(171\) 6.31287 0.482757
\(172\) 0 0
\(173\) 17.9487 1.36462 0.682308 0.731065i \(-0.260976\pi\)
0.682308 + 0.731065i \(0.260976\pi\)
\(174\) 0 0
\(175\) −11.1129 −0.840059
\(176\) 0 0
\(177\) 0.169431 0.0127352
\(178\) 0 0
\(179\) −15.5568 −1.16277 −0.581386 0.813628i \(-0.697489\pi\)
−0.581386 + 0.813628i \(0.697489\pi\)
\(180\) 0 0
\(181\) −7.18764 −0.534253 −0.267127 0.963661i \(-0.586074\pi\)
−0.267127 + 0.963661i \(0.586074\pi\)
\(182\) 0 0
\(183\) 0.433202 0.0320232
\(184\) 0 0
\(185\) −1.18921 −0.0874322
\(186\) 0 0
\(187\) 0.497043 0.0363474
\(188\) 0 0
\(189\) 1.48967 0.108358
\(190\) 0 0
\(191\) −10.6830 −0.772993 −0.386496 0.922291i \(-0.626315\pi\)
−0.386496 + 0.922291i \(0.626315\pi\)
\(192\) 0 0
\(193\) 23.2083 1.67057 0.835284 0.549818i \(-0.185303\pi\)
0.835284 + 0.549818i \(0.185303\pi\)
\(194\) 0 0
\(195\) −0.112231 −0.00803701
\(196\) 0 0
\(197\) 6.22567 0.443561 0.221780 0.975097i \(-0.428813\pi\)
0.221780 + 0.975097i \(0.428813\pi\)
\(198\) 0 0
\(199\) −20.4044 −1.44643 −0.723216 0.690622i \(-0.757337\pi\)
−0.723216 + 0.690622i \(0.757337\pi\)
\(200\) 0 0
\(201\) 0.503433 0.0355094
\(202\) 0 0
\(203\) −16.4587 −1.15518
\(204\) 0 0
\(205\) −3.39673 −0.237238
\(206\) 0 0
\(207\) −2.18312 −0.151737
\(208\) 0 0
\(209\) −6.00549 −0.415409
\(210\) 0 0
\(211\) −1.20727 −0.0831119 −0.0415559 0.999136i \(-0.513231\pi\)
−0.0415559 + 0.999136i \(0.513231\pi\)
\(212\) 0 0
\(213\) −1.55650 −0.106650
\(214\) 0 0
\(215\) −0.158697 −0.0108230
\(216\) 0 0
\(217\) −23.4200 −1.58985
\(218\) 0 0
\(219\) −0.405899 −0.0274281
\(220\) 0 0
\(221\) 0.404503 0.0272098
\(222\) 0 0
\(223\) −27.0513 −1.81149 −0.905746 0.423821i \(-0.860688\pi\)
−0.905746 + 0.423821i \(0.860688\pi\)
\(224\) 0 0
\(225\) 14.3322 0.955480
\(226\) 0 0
\(227\) 15.3831 1.02101 0.510505 0.859875i \(-0.329458\pi\)
0.510505 + 0.859875i \(0.329458\pi\)
\(228\) 0 0
\(229\) −26.6244 −1.75939 −0.879696 0.475536i \(-0.842254\pi\)
−0.879696 + 0.475536i \(0.842254\pi\)
\(230\) 0 0
\(231\) −0.707206 −0.0465308
\(232\) 0 0
\(233\) −11.2611 −0.737738 −0.368869 0.929481i \(-0.620255\pi\)
−0.368869 + 0.929481i \(0.620255\pi\)
\(234\) 0 0
\(235\) −2.79268 −0.182174
\(236\) 0 0
\(237\) −1.76722 −0.114793
\(238\) 0 0
\(239\) −19.5825 −1.26669 −0.633344 0.773870i \(-0.718318\pi\)
−0.633344 + 0.773870i \(0.718318\pi\)
\(240\) 0 0
\(241\) −12.9928 −0.836940 −0.418470 0.908231i \(-0.637434\pi\)
−0.418470 + 0.908231i \(0.637434\pi\)
\(242\) 0 0
\(243\) −2.88366 −0.184987
\(244\) 0 0
\(245\) −0.736772 −0.0470706
\(246\) 0 0
\(247\) −4.88739 −0.310977
\(248\) 0 0
\(249\) 0.768124 0.0486779
\(250\) 0 0
\(251\) 24.9178 1.57280 0.786398 0.617720i \(-0.211943\pi\)
0.786398 + 0.617720i \(0.211943\pi\)
\(252\) 0 0
\(253\) 2.07682 0.130569
\(254\) 0 0
\(255\) −0.00848074 −0.000531084 0
\(256\) 0 0
\(257\) 8.45169 0.527202 0.263601 0.964632i \(-0.415090\pi\)
0.263601 + 0.964632i \(0.415090\pi\)
\(258\) 0 0
\(259\) −6.09846 −0.378940
\(260\) 0 0
\(261\) 21.2266 1.31389
\(262\) 0 0
\(263\) 5.45332 0.336266 0.168133 0.985764i \(-0.446226\pi\)
0.168133 + 0.985764i \(0.446226\pi\)
\(264\) 0 0
\(265\) −0.199261 −0.0122405
\(266\) 0 0
\(267\) −0.415965 −0.0254566
\(268\) 0 0
\(269\) 17.1104 1.04324 0.521620 0.853178i \(-0.325328\pi\)
0.521620 + 0.853178i \(0.325328\pi\)
\(270\) 0 0
\(271\) −19.8965 −1.20863 −0.604314 0.796747i \(-0.706553\pi\)
−0.604314 + 0.796747i \(0.706553\pi\)
\(272\) 0 0
\(273\) −0.575539 −0.0348332
\(274\) 0 0
\(275\) −13.6344 −0.822183
\(276\) 0 0
\(277\) 16.4773 0.990027 0.495013 0.868885i \(-0.335163\pi\)
0.495013 + 0.868885i \(0.335163\pi\)
\(278\) 0 0
\(279\) 30.2044 1.80829
\(280\) 0 0
\(281\) 14.4031 0.859216 0.429608 0.903016i \(-0.358652\pi\)
0.429608 + 0.903016i \(0.358652\pi\)
\(282\) 0 0
\(283\) 24.5725 1.46068 0.730342 0.683081i \(-0.239361\pi\)
0.730342 + 0.683081i \(0.239361\pi\)
\(284\) 0 0
\(285\) 0.102468 0.00606968
\(286\) 0 0
\(287\) −17.4190 −1.02821
\(288\) 0 0
\(289\) −16.9694 −0.998202
\(290\) 0 0
\(291\) −1.24945 −0.0732439
\(292\) 0 0
\(293\) −5.42243 −0.316782 −0.158391 0.987377i \(-0.550631\pi\)
−0.158391 + 0.987377i \(0.550631\pi\)
\(294\) 0 0
\(295\) −0.713159 −0.0415217
\(296\) 0 0
\(297\) 1.82767 0.106052
\(298\) 0 0
\(299\) 1.69016 0.0977445
\(300\) 0 0
\(301\) −0.813826 −0.0469082
\(302\) 0 0
\(303\) 1.07711 0.0618786
\(304\) 0 0
\(305\) −1.82341 −0.104408
\(306\) 0 0
\(307\) −23.9641 −1.36771 −0.683853 0.729620i \(-0.739697\pi\)
−0.683853 + 0.729620i \(0.739697\pi\)
\(308\) 0 0
\(309\) 0.818027 0.0465360
\(310\) 0 0
\(311\) −14.0880 −0.798857 −0.399429 0.916764i \(-0.630791\pi\)
−0.399429 + 0.916764i \(0.630791\pi\)
\(312\) 0 0
\(313\) 25.6192 1.44808 0.724042 0.689755i \(-0.242282\pi\)
0.724042 + 0.689755i \(0.242282\pi\)
\(314\) 0 0
\(315\) −3.12909 −0.176304
\(316\) 0 0
\(317\) 23.5791 1.32433 0.662166 0.749357i \(-0.269637\pi\)
0.662166 + 0.749357i \(0.269637\pi\)
\(318\) 0 0
\(319\) −20.1931 −1.13060
\(320\) 0 0
\(321\) 1.58699 0.0885771
\(322\) 0 0
\(323\) −0.369317 −0.0205493
\(324\) 0 0
\(325\) −11.0959 −0.615491
\(326\) 0 0
\(327\) 1.20603 0.0666936
\(328\) 0 0
\(329\) −14.3213 −0.789562
\(330\) 0 0
\(331\) −6.32751 −0.347791 −0.173896 0.984764i \(-0.555636\pi\)
−0.173896 + 0.984764i \(0.555636\pi\)
\(332\) 0 0
\(333\) 7.86510 0.431005
\(334\) 0 0
\(335\) −2.11902 −0.115774
\(336\) 0 0
\(337\) 28.7099 1.56393 0.781965 0.623322i \(-0.214217\pi\)
0.781965 + 0.623322i \(0.214217\pi\)
\(338\) 0 0
\(339\) −0.150203 −0.00815789
\(340\) 0 0
\(341\) −28.7338 −1.55602
\(342\) 0 0
\(343\) −19.9988 −1.07983
\(344\) 0 0
\(345\) −0.0354356 −0.00190779
\(346\) 0 0
\(347\) −5.17786 −0.277962 −0.138981 0.990295i \(-0.544383\pi\)
−0.138981 + 0.990295i \(0.544383\pi\)
\(348\) 0 0
\(349\) 7.66160 0.410116 0.205058 0.978750i \(-0.434262\pi\)
0.205058 + 0.978750i \(0.434262\pi\)
\(350\) 0 0
\(351\) 1.48739 0.0793911
\(352\) 0 0
\(353\) 17.0257 0.906187 0.453093 0.891463i \(-0.350320\pi\)
0.453093 + 0.891463i \(0.350320\pi\)
\(354\) 0 0
\(355\) 6.55154 0.347720
\(356\) 0 0
\(357\) −0.0434907 −0.00230177
\(358\) 0 0
\(359\) −36.1540 −1.90813 −0.954067 0.299593i \(-0.903149\pi\)
−0.954067 + 0.299593i \(0.903149\pi\)
\(360\) 0 0
\(361\) −14.5378 −0.765145
\(362\) 0 0
\(363\) 0.313203 0.0164389
\(364\) 0 0
\(365\) 1.70849 0.0894263
\(366\) 0 0
\(367\) 21.8084 1.13839 0.569193 0.822204i \(-0.307256\pi\)
0.569193 + 0.822204i \(0.307256\pi\)
\(368\) 0 0
\(369\) 22.4651 1.16949
\(370\) 0 0
\(371\) −1.02185 −0.0530517
\(372\) 0 0
\(373\) 20.6769 1.07061 0.535305 0.844659i \(-0.320197\pi\)
0.535305 + 0.844659i \(0.320197\pi\)
\(374\) 0 0
\(375\) 0.475174 0.0245379
\(376\) 0 0
\(377\) −16.4335 −0.846370
\(378\) 0 0
\(379\) −26.0304 −1.33709 −0.668546 0.743671i \(-0.733083\pi\)
−0.668546 + 0.743671i \(0.733083\pi\)
\(380\) 0 0
\(381\) −1.36090 −0.0697211
\(382\) 0 0
\(383\) −11.7677 −0.601300 −0.300650 0.953734i \(-0.597204\pi\)
−0.300650 + 0.953734i \(0.597204\pi\)
\(384\) 0 0
\(385\) 2.97673 0.151708
\(386\) 0 0
\(387\) 1.04958 0.0533532
\(388\) 0 0
\(389\) −27.5703 −1.39787 −0.698936 0.715184i \(-0.746343\pi\)
−0.698936 + 0.715184i \(0.746343\pi\)
\(390\) 0 0
\(391\) 0.127717 0.00645895
\(392\) 0 0
\(393\) 1.66993 0.0842367
\(394\) 0 0
\(395\) 7.43848 0.374270
\(396\) 0 0
\(397\) 1.42649 0.0715933 0.0357967 0.999359i \(-0.488603\pi\)
0.0357967 + 0.999359i \(0.488603\pi\)
\(398\) 0 0
\(399\) 0.525474 0.0263066
\(400\) 0 0
\(401\) 13.9135 0.694806 0.347403 0.937716i \(-0.387064\pi\)
0.347403 + 0.937716i \(0.387064\pi\)
\(402\) 0 0
\(403\) −23.3841 −1.16484
\(404\) 0 0
\(405\) 4.01992 0.199752
\(406\) 0 0
\(407\) −7.48215 −0.370876
\(408\) 0 0
\(409\) −31.0654 −1.53608 −0.768042 0.640400i \(-0.778769\pi\)
−0.768042 + 0.640400i \(0.778769\pi\)
\(410\) 0 0
\(411\) −0.446017 −0.0220004
\(412\) 0 0
\(413\) −3.65720 −0.179959
\(414\) 0 0
\(415\) −3.23314 −0.158709
\(416\) 0 0
\(417\) −1.16866 −0.0572296
\(418\) 0 0
\(419\) 21.8128 1.06562 0.532812 0.846233i \(-0.321135\pi\)
0.532812 + 0.846233i \(0.321135\pi\)
\(420\) 0 0
\(421\) 18.1058 0.882421 0.441210 0.897404i \(-0.354549\pi\)
0.441210 + 0.897404i \(0.354549\pi\)
\(422\) 0 0
\(423\) 18.4701 0.898045
\(424\) 0 0
\(425\) −0.838466 −0.0406716
\(426\) 0 0
\(427\) −9.35077 −0.452515
\(428\) 0 0
\(429\) −0.706124 −0.0340920
\(430\) 0 0
\(431\) 11.1394 0.536567 0.268283 0.963340i \(-0.413544\pi\)
0.268283 + 0.963340i \(0.413544\pi\)
\(432\) 0 0
\(433\) −1.34326 −0.0645531 −0.0322766 0.999479i \(-0.510276\pi\)
−0.0322766 + 0.999479i \(0.510276\pi\)
\(434\) 0 0
\(435\) 0.344542 0.0165195
\(436\) 0 0
\(437\) −1.54314 −0.0738183
\(438\) 0 0
\(439\) −24.9691 −1.19171 −0.595855 0.803092i \(-0.703187\pi\)
−0.595855 + 0.803092i \(0.703187\pi\)
\(440\) 0 0
\(441\) 4.87282 0.232039
\(442\) 0 0
\(443\) −0.639008 −0.0303602 −0.0151801 0.999885i \(-0.504832\pi\)
−0.0151801 + 0.999885i \(0.504832\pi\)
\(444\) 0 0
\(445\) 1.75086 0.0829985
\(446\) 0 0
\(447\) −1.24042 −0.0586698
\(448\) 0 0
\(449\) 27.6952 1.30702 0.653508 0.756920i \(-0.273297\pi\)
0.653508 + 0.756920i \(0.273297\pi\)
\(450\) 0 0
\(451\) −21.3713 −1.00633
\(452\) 0 0
\(453\) 0.0637111 0.00299341
\(454\) 0 0
\(455\) 2.42252 0.113570
\(456\) 0 0
\(457\) −20.8213 −0.973979 −0.486989 0.873408i \(-0.661905\pi\)
−0.486989 + 0.873408i \(0.661905\pi\)
\(458\) 0 0
\(459\) 0.112395 0.00524615
\(460\) 0 0
\(461\) 29.6918 1.38289 0.691443 0.722431i \(-0.256975\pi\)
0.691443 + 0.722431i \(0.256975\pi\)
\(462\) 0 0
\(463\) −17.3241 −0.805118 −0.402559 0.915394i \(-0.631879\pi\)
−0.402559 + 0.915394i \(0.631879\pi\)
\(464\) 0 0
\(465\) 0.490266 0.0227356
\(466\) 0 0
\(467\) 14.0705 0.651104 0.325552 0.945524i \(-0.394450\pi\)
0.325552 + 0.945524i \(0.394450\pi\)
\(468\) 0 0
\(469\) −10.8667 −0.501778
\(470\) 0 0
\(471\) 0.740058 0.0341001
\(472\) 0 0
\(473\) −0.998477 −0.0459100
\(474\) 0 0
\(475\) 10.1307 0.464829
\(476\) 0 0
\(477\) 1.31786 0.0603408
\(478\) 0 0
\(479\) −9.28506 −0.424245 −0.212123 0.977243i \(-0.568038\pi\)
−0.212123 + 0.977243i \(0.568038\pi\)
\(480\) 0 0
\(481\) −6.08912 −0.277640
\(482\) 0 0
\(483\) −0.181720 −0.00826854
\(484\) 0 0
\(485\) 5.25910 0.238804
\(486\) 0 0
\(487\) 25.0038 1.13303 0.566516 0.824051i \(-0.308291\pi\)
0.566516 + 0.824051i \(0.308291\pi\)
\(488\) 0 0
\(489\) −1.37389 −0.0621292
\(490\) 0 0
\(491\) −12.4337 −0.561124 −0.280562 0.959836i \(-0.590521\pi\)
−0.280562 + 0.959836i \(0.590521\pi\)
\(492\) 0 0
\(493\) −1.24180 −0.0559280
\(494\) 0 0
\(495\) −3.83905 −0.172553
\(496\) 0 0
\(497\) 33.5974 1.50705
\(498\) 0 0
\(499\) −20.1592 −0.902451 −0.451226 0.892410i \(-0.649013\pi\)
−0.451226 + 0.892410i \(0.649013\pi\)
\(500\) 0 0
\(501\) 1.32705 0.0592881
\(502\) 0 0
\(503\) −16.6026 −0.740275 −0.370137 0.928977i \(-0.620689\pi\)
−0.370137 + 0.928977i \(0.620689\pi\)
\(504\) 0 0
\(505\) −4.53373 −0.201748
\(506\) 0 0
\(507\) 0.820915 0.0364581
\(508\) 0 0
\(509\) −29.9133 −1.32588 −0.662941 0.748672i \(-0.730692\pi\)
−0.662941 + 0.748672i \(0.730692\pi\)
\(510\) 0 0
\(511\) 8.76142 0.387583
\(512\) 0 0
\(513\) −1.35801 −0.0599575
\(514\) 0 0
\(515\) −3.44320 −0.151725
\(516\) 0 0
\(517\) −17.5707 −0.772761
\(518\) 0 0
\(519\) −1.92682 −0.0845782
\(520\) 0 0
\(521\) −1.12510 −0.0492913 −0.0246457 0.999696i \(-0.507846\pi\)
−0.0246457 + 0.999696i \(0.507846\pi\)
\(522\) 0 0
\(523\) 30.1807 1.31971 0.659855 0.751393i \(-0.270618\pi\)
0.659855 + 0.751393i \(0.270618\pi\)
\(524\) 0 0
\(525\) 1.19299 0.0520664
\(526\) 0 0
\(527\) −1.76702 −0.0769728
\(528\) 0 0
\(529\) −22.4664 −0.976798
\(530\) 0 0
\(531\) 4.71665 0.204685
\(532\) 0 0
\(533\) −17.3924 −0.753347
\(534\) 0 0
\(535\) −6.67987 −0.288796
\(536\) 0 0
\(537\) 1.67005 0.0720680
\(538\) 0 0
\(539\) −4.63556 −0.199668
\(540\) 0 0
\(541\) −6.11773 −0.263022 −0.131511 0.991315i \(-0.541983\pi\)
−0.131511 + 0.991315i \(0.541983\pi\)
\(542\) 0 0
\(543\) 0.771605 0.0331128
\(544\) 0 0
\(545\) −5.07635 −0.217447
\(546\) 0 0
\(547\) −27.0335 −1.15587 −0.577935 0.816083i \(-0.696141\pi\)
−0.577935 + 0.816083i \(0.696141\pi\)
\(548\) 0 0
\(549\) 12.0596 0.514690
\(550\) 0 0
\(551\) 15.0040 0.639193
\(552\) 0 0
\(553\) 38.1458 1.62212
\(554\) 0 0
\(555\) 0.127663 0.00541901
\(556\) 0 0
\(557\) −5.99360 −0.253957 −0.126979 0.991905i \(-0.540528\pi\)
−0.126979 + 0.991905i \(0.540528\pi\)
\(558\) 0 0
\(559\) −0.812580 −0.0343685
\(560\) 0 0
\(561\) −0.0533584 −0.00225279
\(562\) 0 0
\(563\) 1.04268 0.0439436 0.0219718 0.999759i \(-0.493006\pi\)
0.0219718 + 0.999759i \(0.493006\pi\)
\(564\) 0 0
\(565\) 0.632225 0.0265979
\(566\) 0 0
\(567\) 20.6149 0.865743
\(568\) 0 0
\(569\) 11.2345 0.470974 0.235487 0.971877i \(-0.424331\pi\)
0.235487 + 0.971877i \(0.424331\pi\)
\(570\) 0 0
\(571\) −18.8623 −0.789361 −0.394681 0.918818i \(-0.629145\pi\)
−0.394681 + 0.918818i \(0.629145\pi\)
\(572\) 0 0
\(573\) 1.14683 0.0479097
\(574\) 0 0
\(575\) −3.50341 −0.146102
\(576\) 0 0
\(577\) −44.6470 −1.85868 −0.929339 0.369227i \(-0.879622\pi\)
−0.929339 + 0.369227i \(0.879622\pi\)
\(578\) 0 0
\(579\) −2.49145 −0.103541
\(580\) 0 0
\(581\) −16.5801 −0.687860
\(582\) 0 0
\(583\) −1.25370 −0.0519228
\(584\) 0 0
\(585\) −3.12430 −0.129174
\(586\) 0 0
\(587\) −8.91920 −0.368135 −0.184067 0.982914i \(-0.558926\pi\)
−0.184067 + 0.982914i \(0.558926\pi\)
\(588\) 0 0
\(589\) 21.3500 0.879711
\(590\) 0 0
\(591\) −0.668336 −0.0274917
\(592\) 0 0
\(593\) 4.02432 0.165259 0.0826294 0.996580i \(-0.473668\pi\)
0.0826294 + 0.996580i \(0.473668\pi\)
\(594\) 0 0
\(595\) 0.183059 0.00750467
\(596\) 0 0
\(597\) 2.19045 0.0896491
\(598\) 0 0
\(599\) −1.32840 −0.0542769 −0.0271385 0.999632i \(-0.508640\pi\)
−0.0271385 + 0.999632i \(0.508640\pi\)
\(600\) 0 0
\(601\) −14.2283 −0.580383 −0.290191 0.956969i \(-0.593719\pi\)
−0.290191 + 0.956969i \(0.593719\pi\)
\(602\) 0 0
\(603\) 14.0146 0.570721
\(604\) 0 0
\(605\) −1.31832 −0.0535972
\(606\) 0 0
\(607\) 0.892481 0.0362247 0.0181123 0.999836i \(-0.494234\pi\)
0.0181123 + 0.999836i \(0.494234\pi\)
\(608\) 0 0
\(609\) 1.76687 0.0715973
\(610\) 0 0
\(611\) −14.2994 −0.578493
\(612\) 0 0
\(613\) 46.4577 1.87641 0.938204 0.346082i \(-0.112488\pi\)
0.938204 + 0.346082i \(0.112488\pi\)
\(614\) 0 0
\(615\) 0.364645 0.0147039
\(616\) 0 0
\(617\) 3.60787 0.145247 0.0726236 0.997359i \(-0.476863\pi\)
0.0726236 + 0.997359i \(0.476863\pi\)
\(618\) 0 0
\(619\) −6.47639 −0.260308 −0.130154 0.991494i \(-0.541547\pi\)
−0.130154 + 0.991494i \(0.541547\pi\)
\(620\) 0 0
\(621\) 0.469627 0.0188455
\(622\) 0 0
\(623\) 8.97869 0.359724
\(624\) 0 0
\(625\) 21.9790 0.879162
\(626\) 0 0
\(627\) 0.644700 0.0257468
\(628\) 0 0
\(629\) −0.460126 −0.0183464
\(630\) 0 0
\(631\) 28.0230 1.11558 0.557789 0.829983i \(-0.311650\pi\)
0.557789 + 0.829983i \(0.311650\pi\)
\(632\) 0 0
\(633\) 0.129602 0.00515123
\(634\) 0 0
\(635\) 5.72823 0.227318
\(636\) 0 0
\(637\) −3.77251 −0.149472
\(638\) 0 0
\(639\) −43.3302 −1.71412
\(640\) 0 0
\(641\) −46.6522 −1.84265 −0.921325 0.388793i \(-0.872892\pi\)
−0.921325 + 0.388793i \(0.872892\pi\)
\(642\) 0 0
\(643\) −42.5101 −1.67643 −0.838217 0.545337i \(-0.816402\pi\)
−0.838217 + 0.545337i \(0.816402\pi\)
\(644\) 0 0
\(645\) 0.0170364 0.000670807 0
\(646\) 0 0
\(647\) 6.42299 0.252514 0.126257 0.991998i \(-0.459704\pi\)
0.126257 + 0.991998i \(0.459704\pi\)
\(648\) 0 0
\(649\) −4.48699 −0.176130
\(650\) 0 0
\(651\) 2.51417 0.0985382
\(652\) 0 0
\(653\) 23.8518 0.933394 0.466697 0.884417i \(-0.345444\pi\)
0.466697 + 0.884417i \(0.345444\pi\)
\(654\) 0 0
\(655\) −7.02896 −0.274644
\(656\) 0 0
\(657\) −11.2995 −0.440835
\(658\) 0 0
\(659\) 27.9511 1.08882 0.544411 0.838819i \(-0.316753\pi\)
0.544411 + 0.838819i \(0.316753\pi\)
\(660\) 0 0
\(661\) 39.1041 1.52097 0.760486 0.649354i \(-0.224961\pi\)
0.760486 + 0.649354i \(0.224961\pi\)
\(662\) 0 0
\(663\) −0.0434241 −0.00168645
\(664\) 0 0
\(665\) −2.21180 −0.0857698
\(666\) 0 0
\(667\) −5.18870 −0.200907
\(668\) 0 0
\(669\) 2.90401 0.112275
\(670\) 0 0
\(671\) −11.4724 −0.442886
\(672\) 0 0
\(673\) −46.0585 −1.77542 −0.887712 0.460398i \(-0.847707\pi\)
−0.887712 + 0.460398i \(0.847707\pi\)
\(674\) 0 0
\(675\) −3.08311 −0.118669
\(676\) 0 0
\(677\) 32.9725 1.26723 0.633617 0.773647i \(-0.281569\pi\)
0.633617 + 0.773647i \(0.281569\pi\)
\(678\) 0 0
\(679\) 26.9696 1.03500
\(680\) 0 0
\(681\) −1.65140 −0.0632817
\(682\) 0 0
\(683\) 37.4858 1.43435 0.717176 0.696892i \(-0.245434\pi\)
0.717176 + 0.696892i \(0.245434\pi\)
\(684\) 0 0
\(685\) 1.87735 0.0717298
\(686\) 0 0
\(687\) 2.85818 0.109046
\(688\) 0 0
\(689\) −1.02028 −0.0388697
\(690\) 0 0
\(691\) 24.7575 0.941819 0.470910 0.882181i \(-0.343926\pi\)
0.470910 + 0.882181i \(0.343926\pi\)
\(692\) 0 0
\(693\) −19.6873 −0.747860
\(694\) 0 0
\(695\) 4.91906 0.186591
\(696\) 0 0
\(697\) −1.31426 −0.0497811
\(698\) 0 0
\(699\) 1.20890 0.0457247
\(700\) 0 0
\(701\) 15.2572 0.576255 0.288127 0.957592i \(-0.406967\pi\)
0.288127 + 0.957592i \(0.406967\pi\)
\(702\) 0 0
\(703\) 5.55945 0.209679
\(704\) 0 0
\(705\) 0.299799 0.0112911
\(706\) 0 0
\(707\) −23.2498 −0.874397
\(708\) 0 0
\(709\) 4.80936 0.180619 0.0903097 0.995914i \(-0.471214\pi\)
0.0903097 + 0.995914i \(0.471214\pi\)
\(710\) 0 0
\(711\) −49.1961 −1.84500
\(712\) 0 0
\(713\) −7.38327 −0.276506
\(714\) 0 0
\(715\) 2.97218 0.111153
\(716\) 0 0
\(717\) 2.10222 0.0785087
\(718\) 0 0
\(719\) 40.7242 1.51876 0.759378 0.650649i \(-0.225503\pi\)
0.759378 + 0.650649i \(0.225503\pi\)
\(720\) 0 0
\(721\) −17.6573 −0.657592
\(722\) 0 0
\(723\) 1.39480 0.0518732
\(724\) 0 0
\(725\) 34.0639 1.26510
\(726\) 0 0
\(727\) 22.3452 0.828738 0.414369 0.910109i \(-0.364002\pi\)
0.414369 + 0.910109i \(0.364002\pi\)
\(728\) 0 0
\(729\) −26.3797 −0.977025
\(730\) 0 0
\(731\) −0.0614028 −0.00227106
\(732\) 0 0
\(733\) −42.7743 −1.57990 −0.789952 0.613169i \(-0.789895\pi\)
−0.789952 + 0.613169i \(0.789895\pi\)
\(734\) 0 0
\(735\) 0.0790937 0.00291741
\(736\) 0 0
\(737\) −13.3323 −0.491101
\(738\) 0 0
\(739\) −38.8243 −1.42818 −0.714088 0.700056i \(-0.753158\pi\)
−0.714088 + 0.700056i \(0.753158\pi\)
\(740\) 0 0
\(741\) 0.524670 0.0192742
\(742\) 0 0
\(743\) 44.1174 1.61851 0.809254 0.587458i \(-0.199871\pi\)
0.809254 + 0.587458i \(0.199871\pi\)
\(744\) 0 0
\(745\) 5.22110 0.191286
\(746\) 0 0
\(747\) 21.3832 0.782369
\(748\) 0 0
\(749\) −34.2555 −1.25167
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −2.67497 −0.0974812
\(754\) 0 0
\(755\) −0.268169 −0.00975968
\(756\) 0 0
\(757\) −42.2316 −1.53493 −0.767467 0.641089i \(-0.778483\pi\)
−0.767467 + 0.641089i \(0.778483\pi\)
\(758\) 0 0
\(759\) −0.222951 −0.00809260
\(760\) 0 0
\(761\) 1.89838 0.0688161 0.0344080 0.999408i \(-0.489045\pi\)
0.0344080 + 0.999408i \(0.489045\pi\)
\(762\) 0 0
\(763\) −26.0324 −0.942437
\(764\) 0 0
\(765\) −0.236088 −0.00853579
\(766\) 0 0
\(767\) −3.65160 −0.131852
\(768\) 0 0
\(769\) −18.4764 −0.666276 −0.333138 0.942878i \(-0.608108\pi\)
−0.333138 + 0.942878i \(0.608108\pi\)
\(770\) 0 0
\(771\) −0.907304 −0.0326757
\(772\) 0 0
\(773\) 49.9195 1.79548 0.897740 0.440525i \(-0.145208\pi\)
0.897740 + 0.440525i \(0.145208\pi\)
\(774\) 0 0
\(775\) 48.4712 1.74114
\(776\) 0 0
\(777\) 0.654680 0.0234865
\(778\) 0 0
\(779\) 15.8795 0.568941
\(780\) 0 0
\(781\) 41.2204 1.47498
\(782\) 0 0
\(783\) −4.56621 −0.163183
\(784\) 0 0
\(785\) −3.11501 −0.111179
\(786\) 0 0
\(787\) 18.2768 0.651498 0.325749 0.945456i \(-0.394384\pi\)
0.325749 + 0.945456i \(0.394384\pi\)
\(788\) 0 0
\(789\) −0.585423 −0.0208416
\(790\) 0 0
\(791\) 3.24216 0.115278
\(792\) 0 0
\(793\) −9.33645 −0.331547
\(794\) 0 0
\(795\) 0.0213910 0.000758662 0
\(796\) 0 0
\(797\) −42.3265 −1.49928 −0.749640 0.661846i \(-0.769773\pi\)
−0.749640 + 0.661846i \(0.769773\pi\)
\(798\) 0 0
\(799\) −1.08054 −0.0382267
\(800\) 0 0
\(801\) −11.5797 −0.409149
\(802\) 0 0
\(803\) 10.7493 0.379335
\(804\) 0 0
\(805\) 0.764885 0.0269587
\(806\) 0 0
\(807\) −1.83683 −0.0646595
\(808\) 0 0
\(809\) 19.5609 0.687726 0.343863 0.939020i \(-0.388264\pi\)
0.343863 + 0.939020i \(0.388264\pi\)
\(810\) 0 0
\(811\) 3.47091 0.121880 0.0609400 0.998141i \(-0.480590\pi\)
0.0609400 + 0.998141i \(0.480590\pi\)
\(812\) 0 0
\(813\) 2.13592 0.0749101
\(814\) 0 0
\(815\) 5.78288 0.202565
\(816\) 0 0
\(817\) 0.741896 0.0259557
\(818\) 0 0
\(819\) −16.0219 −0.559852
\(820\) 0 0
\(821\) 25.3122 0.883403 0.441702 0.897162i \(-0.354375\pi\)
0.441702 + 0.897162i \(0.354375\pi\)
\(822\) 0 0
\(823\) −29.0117 −1.01128 −0.505642 0.862743i \(-0.668744\pi\)
−0.505642 + 0.862743i \(0.668744\pi\)
\(824\) 0 0
\(825\) 1.46367 0.0509585
\(826\) 0 0
\(827\) 5.79862 0.201638 0.100819 0.994905i \(-0.467854\pi\)
0.100819 + 0.994905i \(0.467854\pi\)
\(828\) 0 0
\(829\) −39.7053 −1.37902 −0.689511 0.724275i \(-0.742175\pi\)
−0.689511 + 0.724275i \(0.742175\pi\)
\(830\) 0 0
\(831\) −1.76887 −0.0613614
\(832\) 0 0
\(833\) −0.285071 −0.00987711
\(834\) 0 0
\(835\) −5.58573 −0.193302
\(836\) 0 0
\(837\) −6.49749 −0.224586
\(838\) 0 0
\(839\) −32.9306 −1.13689 −0.568446 0.822721i \(-0.692455\pi\)
−0.568446 + 0.822721i \(0.692455\pi\)
\(840\) 0 0
\(841\) 21.4501 0.739657
\(842\) 0 0
\(843\) −1.54619 −0.0532538
\(844\) 0 0
\(845\) −3.45535 −0.118868
\(846\) 0 0
\(847\) −6.76056 −0.232295
\(848\) 0 0
\(849\) −2.63790 −0.0905325
\(850\) 0 0
\(851\) −1.92257 −0.0659049
\(852\) 0 0
\(853\) 37.7219 1.29157 0.645786 0.763518i \(-0.276530\pi\)
0.645786 + 0.763518i \(0.276530\pi\)
\(854\) 0 0
\(855\) 2.85252 0.0975543
\(856\) 0 0
\(857\) −39.5648 −1.35151 −0.675754 0.737128i \(-0.736182\pi\)
−0.675754 + 0.737128i \(0.736182\pi\)
\(858\) 0 0
\(859\) 5.06855 0.172937 0.0864683 0.996255i \(-0.472442\pi\)
0.0864683 + 0.996255i \(0.472442\pi\)
\(860\) 0 0
\(861\) 1.86996 0.0637282
\(862\) 0 0
\(863\) −20.1956 −0.687467 −0.343734 0.939067i \(-0.611692\pi\)
−0.343734 + 0.939067i \(0.611692\pi\)
\(864\) 0 0
\(865\) 8.11028 0.275758
\(866\) 0 0
\(867\) 1.82170 0.0618681
\(868\) 0 0
\(869\) 46.8008 1.58761
\(870\) 0 0
\(871\) −10.8501 −0.367641
\(872\) 0 0
\(873\) −34.7823 −1.17720
\(874\) 0 0
\(875\) −10.2567 −0.346741
\(876\) 0 0
\(877\) −29.7360 −1.00411 −0.502057 0.864835i \(-0.667423\pi\)
−0.502057 + 0.864835i \(0.667423\pi\)
\(878\) 0 0
\(879\) 0.582107 0.0196340
\(880\) 0 0
\(881\) 49.4222 1.66508 0.832538 0.553968i \(-0.186887\pi\)
0.832538 + 0.553968i \(0.186887\pi\)
\(882\) 0 0
\(883\) 26.7724 0.900964 0.450482 0.892786i \(-0.351252\pi\)
0.450482 + 0.892786i \(0.351252\pi\)
\(884\) 0 0
\(885\) 0.0765588 0.00257350
\(886\) 0 0
\(887\) −38.5906 −1.29575 −0.647873 0.761748i \(-0.724341\pi\)
−0.647873 + 0.761748i \(0.724341\pi\)
\(888\) 0 0
\(889\) 29.3754 0.985218
\(890\) 0 0
\(891\) 25.2922 0.847321
\(892\) 0 0
\(893\) 13.0556 0.436888
\(894\) 0 0
\(895\) −7.02948 −0.234970
\(896\) 0 0
\(897\) −0.181442 −0.00605816
\(898\) 0 0
\(899\) 71.7879 2.39426
\(900\) 0 0
\(901\) −0.0770979 −0.00256850
\(902\) 0 0
\(903\) 0.0873656 0.00290735
\(904\) 0 0
\(905\) −3.24780 −0.107960
\(906\) 0 0
\(907\) −55.5012 −1.84289 −0.921444 0.388512i \(-0.872989\pi\)
−0.921444 + 0.388512i \(0.872989\pi\)
\(908\) 0 0
\(909\) 29.9849 0.994536
\(910\) 0 0
\(911\) 6.73076 0.223000 0.111500 0.993764i \(-0.464435\pi\)
0.111500 + 0.993764i \(0.464435\pi\)
\(912\) 0 0
\(913\) −20.3420 −0.673223
\(914\) 0 0
\(915\) 0.195746 0.00647117
\(916\) 0 0
\(917\) −36.0458 −1.19034
\(918\) 0 0
\(919\) 44.2852 1.46084 0.730418 0.683001i \(-0.239326\pi\)
0.730418 + 0.683001i \(0.239326\pi\)
\(920\) 0 0
\(921\) 2.57259 0.0847698
\(922\) 0 0
\(923\) 33.5460 1.10418
\(924\) 0 0
\(925\) 12.6217 0.414999
\(926\) 0 0
\(927\) 22.7724 0.747944
\(928\) 0 0
\(929\) 4.03372 0.132342 0.0661710 0.997808i \(-0.478922\pi\)
0.0661710 + 0.997808i \(0.478922\pi\)
\(930\) 0 0
\(931\) 3.44435 0.112884
\(932\) 0 0
\(933\) 1.51237 0.0495128
\(934\) 0 0
\(935\) 0.224593 0.00734498
\(936\) 0 0
\(937\) −14.2626 −0.465939 −0.232969 0.972484i \(-0.574844\pi\)
−0.232969 + 0.972484i \(0.574844\pi\)
\(938\) 0 0
\(939\) −2.75027 −0.0897516
\(940\) 0 0
\(941\) 30.6788 1.00010 0.500050 0.865997i \(-0.333315\pi\)
0.500050 + 0.865997i \(0.333315\pi\)
\(942\) 0 0
\(943\) −5.49145 −0.178826
\(944\) 0 0
\(945\) 0.673121 0.0218966
\(946\) 0 0
\(947\) −29.0991 −0.945594 −0.472797 0.881171i \(-0.656756\pi\)
−0.472797 + 0.881171i \(0.656756\pi\)
\(948\) 0 0
\(949\) 8.74801 0.283972
\(950\) 0 0
\(951\) −2.53125 −0.0820815
\(952\) 0 0
\(953\) 13.7057 0.443972 0.221986 0.975050i \(-0.428746\pi\)
0.221986 + 0.975050i \(0.428746\pi\)
\(954\) 0 0
\(955\) −4.82719 −0.156204
\(956\) 0 0
\(957\) 2.16776 0.0700738
\(958\) 0 0
\(959\) 9.62737 0.310884
\(960\) 0 0
\(961\) 71.1506 2.29518
\(962\) 0 0
\(963\) 44.1789 1.42365
\(964\) 0 0
\(965\) 10.4869 0.337584
\(966\) 0 0
\(967\) 19.8636 0.638770 0.319385 0.947625i \(-0.396524\pi\)
0.319385 + 0.947625i \(0.396524\pi\)
\(968\) 0 0
\(969\) 0.0396468 0.00127364
\(970\) 0 0
\(971\) 5.00233 0.160533 0.0802663 0.996773i \(-0.474423\pi\)
0.0802663 + 0.996773i \(0.474423\pi\)
\(972\) 0 0
\(973\) 25.2258 0.808702
\(974\) 0 0
\(975\) 1.19117 0.0381478
\(976\) 0 0
\(977\) −36.1794 −1.15748 −0.578741 0.815512i \(-0.696456\pi\)
−0.578741 + 0.815512i \(0.696456\pi\)
\(978\) 0 0
\(979\) 11.0159 0.352069
\(980\) 0 0
\(981\) 33.5737 1.07192
\(982\) 0 0
\(983\) 35.3163 1.12641 0.563207 0.826316i \(-0.309567\pi\)
0.563207 + 0.826316i \(0.309567\pi\)
\(984\) 0 0
\(985\) 2.81312 0.0896336
\(986\) 0 0
\(987\) 1.53742 0.0489366
\(988\) 0 0
\(989\) −0.256563 −0.00815823
\(990\) 0 0
\(991\) 38.3902 1.21950 0.609752 0.792592i \(-0.291269\pi\)
0.609752 + 0.792592i \(0.291269\pi\)
\(992\) 0 0
\(993\) 0.679269 0.0215559
\(994\) 0 0
\(995\) −9.21992 −0.292291
\(996\) 0 0
\(997\) 24.3654 0.771661 0.385830 0.922570i \(-0.373915\pi\)
0.385830 + 0.922570i \(0.373915\pi\)
\(998\) 0 0
\(999\) −1.69192 −0.0535300
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.1.25 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.25 44 1.1 even 1 trivial