Properties

Label 6008.2.a.b.1.15
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 1.15
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.61777 q^{3} -2.18000 q^{5} -2.82839 q^{7} -0.382806 q^{9} +O(q^{10})\) \(q-1.61777 q^{3} -2.18000 q^{5} -2.82839 q^{7} -0.382806 q^{9} -0.331382 q^{11} +1.18515 q^{13} +3.52675 q^{15} -0.850397 q^{17} -2.54729 q^{19} +4.57569 q^{21} -2.89409 q^{23} -0.247601 q^{25} +5.47262 q^{27} +3.27328 q^{29} +9.17864 q^{31} +0.536102 q^{33} +6.16588 q^{35} +4.19824 q^{37} -1.91730 q^{39} +10.8726 q^{41} +5.52475 q^{43} +0.834518 q^{45} -3.07403 q^{47} +0.999768 q^{49} +1.37575 q^{51} -7.07359 q^{53} +0.722413 q^{55} +4.12095 q^{57} -5.25476 q^{59} +5.14026 q^{61} +1.08272 q^{63} -2.58362 q^{65} -12.7145 q^{67} +4.68198 q^{69} +6.59360 q^{71} +8.22764 q^{73} +0.400563 q^{75} +0.937277 q^{77} -7.17156 q^{79} -7.70504 q^{81} +5.27522 q^{83} +1.85387 q^{85} -5.29544 q^{87} +15.0525 q^{89} -3.35205 q^{91} -14.8490 q^{93} +5.55310 q^{95} -11.5270 q^{97} +0.126855 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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
\(3\) −1.61777 −0.934022 −0.467011 0.884251i \(-0.654669\pi\)
−0.467011 + 0.884251i \(0.654669\pi\)
\(4\) 0 0
\(5\) −2.18000 −0.974926 −0.487463 0.873144i \(-0.662078\pi\)
−0.487463 + 0.873144i \(0.662078\pi\)
\(6\) 0 0
\(7\) −2.82839 −1.06903 −0.534515 0.845159i \(-0.679506\pi\)
−0.534515 + 0.845159i \(0.679506\pi\)
\(8\) 0 0
\(9\) −0.382806 −0.127602
\(10\) 0 0
\(11\) −0.331382 −0.0999155 −0.0499578 0.998751i \(-0.515909\pi\)
−0.0499578 + 0.998751i \(0.515909\pi\)
\(12\) 0 0
\(13\) 1.18515 0.328700 0.164350 0.986402i \(-0.447447\pi\)
0.164350 + 0.986402i \(0.447447\pi\)
\(14\) 0 0
\(15\) 3.52675 0.910602
\(16\) 0 0
\(17\) −0.850397 −0.206252 −0.103126 0.994668i \(-0.532884\pi\)
−0.103126 + 0.994668i \(0.532884\pi\)
\(18\) 0 0
\(19\) −2.54729 −0.584389 −0.292195 0.956359i \(-0.594386\pi\)
−0.292195 + 0.956359i \(0.594386\pi\)
\(20\) 0 0
\(21\) 4.57569 0.998498
\(22\) 0 0
\(23\) −2.89409 −0.603459 −0.301730 0.953394i \(-0.597564\pi\)
−0.301730 + 0.953394i \(0.597564\pi\)
\(24\) 0 0
\(25\) −0.247601 −0.0495202
\(26\) 0 0
\(27\) 5.47262 1.05321
\(28\) 0 0
\(29\) 3.27328 0.607834 0.303917 0.952699i \(-0.401706\pi\)
0.303917 + 0.952699i \(0.401706\pi\)
\(30\) 0 0
\(31\) 9.17864 1.64853 0.824266 0.566202i \(-0.191588\pi\)
0.824266 + 0.566202i \(0.191588\pi\)
\(32\) 0 0
\(33\) 0.536102 0.0933234
\(34\) 0 0
\(35\) 6.16588 1.04222
\(36\) 0 0
\(37\) 4.19824 0.690186 0.345093 0.938569i \(-0.387847\pi\)
0.345093 + 0.938569i \(0.387847\pi\)
\(38\) 0 0
\(39\) −1.91730 −0.307014
\(40\) 0 0
\(41\) 10.8726 1.69801 0.849007 0.528382i \(-0.177201\pi\)
0.849007 + 0.528382i \(0.177201\pi\)
\(42\) 0 0
\(43\) 5.52475 0.842516 0.421258 0.906941i \(-0.361589\pi\)
0.421258 + 0.906941i \(0.361589\pi\)
\(44\) 0 0
\(45\) 0.834518 0.124403
\(46\) 0 0
\(47\) −3.07403 −0.448393 −0.224196 0.974544i \(-0.571976\pi\)
−0.224196 + 0.974544i \(0.571976\pi\)
\(48\) 0 0
\(49\) 0.999768 0.142824
\(50\) 0 0
\(51\) 1.37575 0.192644
\(52\) 0 0
\(53\) −7.07359 −0.971632 −0.485816 0.874061i \(-0.661478\pi\)
−0.485816 + 0.874061i \(0.661478\pi\)
\(54\) 0 0
\(55\) 0.722413 0.0974102
\(56\) 0 0
\(57\) 4.12095 0.545833
\(58\) 0 0
\(59\) −5.25476 −0.684111 −0.342056 0.939680i \(-0.611123\pi\)
−0.342056 + 0.939680i \(0.611123\pi\)
\(60\) 0 0
\(61\) 5.14026 0.658143 0.329072 0.944305i \(-0.393264\pi\)
0.329072 + 0.944305i \(0.393264\pi\)
\(62\) 0 0
\(63\) 1.08272 0.136410
\(64\) 0 0
\(65\) −2.58362 −0.320459
\(66\) 0 0
\(67\) −12.7145 −1.55332 −0.776660 0.629920i \(-0.783088\pi\)
−0.776660 + 0.629920i \(0.783088\pi\)
\(68\) 0 0
\(69\) 4.68198 0.563644
\(70\) 0 0
\(71\) 6.59360 0.782516 0.391258 0.920281i \(-0.372040\pi\)
0.391258 + 0.920281i \(0.372040\pi\)
\(72\) 0 0
\(73\) 8.22764 0.962973 0.481486 0.876454i \(-0.340097\pi\)
0.481486 + 0.876454i \(0.340097\pi\)
\(74\) 0 0
\(75\) 0.400563 0.0462530
\(76\) 0 0
\(77\) 0.937277 0.106813
\(78\) 0 0
\(79\) −7.17156 −0.806864 −0.403432 0.915010i \(-0.632183\pi\)
−0.403432 + 0.915010i \(0.632183\pi\)
\(80\) 0 0
\(81\) −7.70504 −0.856116
\(82\) 0 0
\(83\) 5.27522 0.579030 0.289515 0.957173i \(-0.406506\pi\)
0.289515 + 0.957173i \(0.406506\pi\)
\(84\) 0 0
\(85\) 1.85387 0.201080
\(86\) 0 0
\(87\) −5.29544 −0.567730
\(88\) 0 0
\(89\) 15.0525 1.59556 0.797781 0.602947i \(-0.206007\pi\)
0.797781 + 0.602947i \(0.206007\pi\)
\(90\) 0 0
\(91\) −3.35205 −0.351391
\(92\) 0 0
\(93\) −14.8490 −1.53977
\(94\) 0 0
\(95\) 5.55310 0.569736
\(96\) 0 0
\(97\) −11.5270 −1.17039 −0.585194 0.810894i \(-0.698982\pi\)
−0.585194 + 0.810894i \(0.698982\pi\)
\(98\) 0 0
\(99\) 0.126855 0.0127494
\(100\) 0 0
\(101\) 5.19217 0.516641 0.258320 0.966059i \(-0.416831\pi\)
0.258320 + 0.966059i \(0.416831\pi\)
\(102\) 0 0
\(103\) −5.44827 −0.536834 −0.268417 0.963303i \(-0.586500\pi\)
−0.268417 + 0.963303i \(0.586500\pi\)
\(104\) 0 0
\(105\) −9.97500 −0.973461
\(106\) 0 0
\(107\) −11.5635 −1.11788 −0.558942 0.829207i \(-0.688793\pi\)
−0.558942 + 0.829207i \(0.688793\pi\)
\(108\) 0 0
\(109\) 2.31632 0.221864 0.110932 0.993828i \(-0.464616\pi\)
0.110932 + 0.993828i \(0.464616\pi\)
\(110\) 0 0
\(111\) −6.79180 −0.644649
\(112\) 0 0
\(113\) 9.68156 0.910765 0.455382 0.890296i \(-0.349503\pi\)
0.455382 + 0.890296i \(0.349503\pi\)
\(114\) 0 0
\(115\) 6.30911 0.588328
\(116\) 0 0
\(117\) −0.453682 −0.0419429
\(118\) 0 0
\(119\) 2.40525 0.220489
\(120\) 0 0
\(121\) −10.8902 −0.990017
\(122\) 0 0
\(123\) −17.5894 −1.58598
\(124\) 0 0
\(125\) 11.4398 1.02320
\(126\) 0 0
\(127\) −7.05321 −0.625871 −0.312935 0.949774i \(-0.601312\pi\)
−0.312935 + 0.949774i \(0.601312\pi\)
\(128\) 0 0
\(129\) −8.93779 −0.786929
\(130\) 0 0
\(131\) 7.97466 0.696749 0.348374 0.937355i \(-0.386734\pi\)
0.348374 + 0.937355i \(0.386734\pi\)
\(132\) 0 0
\(133\) 7.20473 0.624729
\(134\) 0 0
\(135\) −11.9303 −1.02680
\(136\) 0 0
\(137\) 11.9659 1.02232 0.511160 0.859486i \(-0.329216\pi\)
0.511160 + 0.859486i \(0.329216\pi\)
\(138\) 0 0
\(139\) 5.48764 0.465456 0.232728 0.972542i \(-0.425235\pi\)
0.232728 + 0.972542i \(0.425235\pi\)
\(140\) 0 0
\(141\) 4.97308 0.418809
\(142\) 0 0
\(143\) −0.392737 −0.0328423
\(144\) 0 0
\(145\) −7.13576 −0.592593
\(146\) 0 0
\(147\) −1.61740 −0.133401
\(148\) 0 0
\(149\) 6.73467 0.551726 0.275863 0.961197i \(-0.411036\pi\)
0.275863 + 0.961197i \(0.411036\pi\)
\(150\) 0 0
\(151\) −3.35880 −0.273335 −0.136668 0.990617i \(-0.543639\pi\)
−0.136668 + 0.990617i \(0.543639\pi\)
\(152\) 0 0
\(153\) 0.325538 0.0263182
\(154\) 0 0
\(155\) −20.0094 −1.60720
\(156\) 0 0
\(157\) −2.51309 −0.200567 −0.100283 0.994959i \(-0.531975\pi\)
−0.100283 + 0.994959i \(0.531975\pi\)
\(158\) 0 0
\(159\) 11.4435 0.907526
\(160\) 0 0
\(161\) 8.18560 0.645116
\(162\) 0 0
\(163\) 17.4645 1.36793 0.683963 0.729517i \(-0.260255\pi\)
0.683963 + 0.729517i \(0.260255\pi\)
\(164\) 0 0
\(165\) −1.16870 −0.0909833
\(166\) 0 0
\(167\) 7.00372 0.541964 0.270982 0.962584i \(-0.412652\pi\)
0.270982 + 0.962584i \(0.412652\pi\)
\(168\) 0 0
\(169\) −11.5954 −0.891956
\(170\) 0 0
\(171\) 0.975120 0.0745693
\(172\) 0 0
\(173\) −20.4743 −1.55663 −0.778317 0.627871i \(-0.783926\pi\)
−0.778317 + 0.627871i \(0.783926\pi\)
\(174\) 0 0
\(175\) 0.700312 0.0529386
\(176\) 0 0
\(177\) 8.50101 0.638975
\(178\) 0 0
\(179\) −5.71742 −0.427340 −0.213670 0.976906i \(-0.568542\pi\)
−0.213670 + 0.976906i \(0.568542\pi\)
\(180\) 0 0
\(181\) 0.109937 0.00817157 0.00408578 0.999992i \(-0.498699\pi\)
0.00408578 + 0.999992i \(0.498699\pi\)
\(182\) 0 0
\(183\) −8.31578 −0.614720
\(184\) 0 0
\(185\) −9.15215 −0.672880
\(186\) 0 0
\(187\) 0.281807 0.0206077
\(188\) 0 0
\(189\) −15.4787 −1.12591
\(190\) 0 0
\(191\) 4.31899 0.312511 0.156256 0.987717i \(-0.450058\pi\)
0.156256 + 0.987717i \(0.450058\pi\)
\(192\) 0 0
\(193\) 22.6709 1.63189 0.815944 0.578131i \(-0.196218\pi\)
0.815944 + 0.578131i \(0.196218\pi\)
\(194\) 0 0
\(195\) 4.17971 0.299315
\(196\) 0 0
\(197\) −2.32993 −0.166000 −0.0830002 0.996550i \(-0.526450\pi\)
−0.0830002 + 0.996550i \(0.526450\pi\)
\(198\) 0 0
\(199\) −18.2582 −1.29429 −0.647145 0.762367i \(-0.724037\pi\)
−0.647145 + 0.762367i \(0.724037\pi\)
\(200\) 0 0
\(201\) 20.5691 1.45084
\(202\) 0 0
\(203\) −9.25811 −0.649792
\(204\) 0 0
\(205\) −23.7022 −1.65544
\(206\) 0 0
\(207\) 1.10788 0.0770027
\(208\) 0 0
\(209\) 0.844128 0.0583896
\(210\) 0 0
\(211\) −0.0484845 −0.00333781 −0.00166890 0.999999i \(-0.500531\pi\)
−0.00166890 + 0.999999i \(0.500531\pi\)
\(212\) 0 0
\(213\) −10.6670 −0.730888
\(214\) 0 0
\(215\) −12.0439 −0.821390
\(216\) 0 0
\(217\) −25.9607 −1.76233
\(218\) 0 0
\(219\) −13.3105 −0.899438
\(220\) 0 0
\(221\) −1.00785 −0.0677950
\(222\) 0 0
\(223\) −4.76174 −0.318869 −0.159435 0.987208i \(-0.550967\pi\)
−0.159435 + 0.987208i \(0.550967\pi\)
\(224\) 0 0
\(225\) 0.0947833 0.00631889
\(226\) 0 0
\(227\) −15.2257 −1.01057 −0.505284 0.862953i \(-0.668612\pi\)
−0.505284 + 0.862953i \(0.668612\pi\)
\(228\) 0 0
\(229\) 9.93794 0.656718 0.328359 0.944553i \(-0.393505\pi\)
0.328359 + 0.944553i \(0.393505\pi\)
\(230\) 0 0
\(231\) −1.51630 −0.0997654
\(232\) 0 0
\(233\) −27.6931 −1.81423 −0.907117 0.420878i \(-0.861722\pi\)
−0.907117 + 0.420878i \(0.861722\pi\)
\(234\) 0 0
\(235\) 6.70138 0.437150
\(236\) 0 0
\(237\) 11.6020 0.753629
\(238\) 0 0
\(239\) −16.8636 −1.09082 −0.545409 0.838170i \(-0.683626\pi\)
−0.545409 + 0.838170i \(0.683626\pi\)
\(240\) 0 0
\(241\) 2.81397 0.181264 0.0906319 0.995884i \(-0.471111\pi\)
0.0906319 + 0.995884i \(0.471111\pi\)
\(242\) 0 0
\(243\) −3.95284 −0.253575
\(244\) 0 0
\(245\) −2.17949 −0.139243
\(246\) 0 0
\(247\) −3.01892 −0.192089
\(248\) 0 0
\(249\) −8.53411 −0.540827
\(250\) 0 0
\(251\) 3.23936 0.204467 0.102233 0.994760i \(-0.467401\pi\)
0.102233 + 0.994760i \(0.467401\pi\)
\(252\) 0 0
\(253\) 0.959050 0.0602949
\(254\) 0 0
\(255\) −2.99914 −0.187813
\(256\) 0 0
\(257\) −19.4266 −1.21180 −0.605900 0.795541i \(-0.707187\pi\)
−0.605900 + 0.795541i \(0.707187\pi\)
\(258\) 0 0
\(259\) −11.8742 −0.737829
\(260\) 0 0
\(261\) −1.25303 −0.0775609
\(262\) 0 0
\(263\) −8.47044 −0.522310 −0.261155 0.965297i \(-0.584103\pi\)
−0.261155 + 0.965297i \(0.584103\pi\)
\(264\) 0 0
\(265\) 15.4204 0.947269
\(266\) 0 0
\(267\) −24.3516 −1.49029
\(268\) 0 0
\(269\) −21.8233 −1.33059 −0.665294 0.746582i \(-0.731694\pi\)
−0.665294 + 0.746582i \(0.731694\pi\)
\(270\) 0 0
\(271\) −19.7397 −1.19910 −0.599550 0.800337i \(-0.704654\pi\)
−0.599550 + 0.800337i \(0.704654\pi\)
\(272\) 0 0
\(273\) 5.42286 0.328207
\(274\) 0 0
\(275\) 0.0820506 0.00494784
\(276\) 0 0
\(277\) 20.7197 1.24492 0.622462 0.782650i \(-0.286133\pi\)
0.622462 + 0.782650i \(0.286133\pi\)
\(278\) 0 0
\(279\) −3.51364 −0.210356
\(280\) 0 0
\(281\) 18.8087 1.12203 0.561017 0.827804i \(-0.310410\pi\)
0.561017 + 0.827804i \(0.310410\pi\)
\(282\) 0 0
\(283\) 3.11774 0.185330 0.0926652 0.995697i \(-0.470461\pi\)
0.0926652 + 0.995697i \(0.470461\pi\)
\(284\) 0 0
\(285\) −8.98366 −0.532146
\(286\) 0 0
\(287\) −30.7519 −1.81523
\(288\) 0 0
\(289\) −16.2768 −0.957460
\(290\) 0 0
\(291\) 18.6480 1.09317
\(292\) 0 0
\(293\) 28.3597 1.65679 0.828396 0.560143i \(-0.189254\pi\)
0.828396 + 0.560143i \(0.189254\pi\)
\(294\) 0 0
\(295\) 11.4554 0.666957
\(296\) 0 0
\(297\) −1.81353 −0.105232
\(298\) 0 0
\(299\) −3.42992 −0.198357
\(300\) 0 0
\(301\) −15.6261 −0.900674
\(302\) 0 0
\(303\) −8.39977 −0.482554
\(304\) 0 0
\(305\) −11.2058 −0.641641
\(306\) 0 0
\(307\) −14.6160 −0.834180 −0.417090 0.908865i \(-0.636950\pi\)
−0.417090 + 0.908865i \(0.636950\pi\)
\(308\) 0 0
\(309\) 8.81406 0.501415
\(310\) 0 0
\(311\) −23.4725 −1.33100 −0.665501 0.746397i \(-0.731782\pi\)
−0.665501 + 0.746397i \(0.731782\pi\)
\(312\) 0 0
\(313\) 1.09616 0.0619588 0.0309794 0.999520i \(-0.490137\pi\)
0.0309794 + 0.999520i \(0.490137\pi\)
\(314\) 0 0
\(315\) −2.36034 −0.132990
\(316\) 0 0
\(317\) 15.8084 0.887886 0.443943 0.896055i \(-0.353579\pi\)
0.443943 + 0.896055i \(0.353579\pi\)
\(318\) 0 0
\(319\) −1.08471 −0.0607320
\(320\) 0 0
\(321\) 18.7071 1.04413
\(322\) 0 0
\(323\) 2.16621 0.120531
\(324\) 0 0
\(325\) −0.293444 −0.0162773
\(326\) 0 0
\(327\) −3.74729 −0.207226
\(328\) 0 0
\(329\) 8.69453 0.479345
\(330\) 0 0
\(331\) −12.5388 −0.689193 −0.344597 0.938751i \(-0.611984\pi\)
−0.344597 + 0.938751i \(0.611984\pi\)
\(332\) 0 0
\(333\) −1.60711 −0.0880692
\(334\) 0 0
\(335\) 27.7175 1.51437
\(336\) 0 0
\(337\) −33.0821 −1.80210 −0.901049 0.433718i \(-0.857201\pi\)
−0.901049 + 0.433718i \(0.857201\pi\)
\(338\) 0 0
\(339\) −15.6626 −0.850675
\(340\) 0 0
\(341\) −3.04164 −0.164714
\(342\) 0 0
\(343\) 16.9710 0.916346
\(344\) 0 0
\(345\) −10.2067 −0.549511
\(346\) 0 0
\(347\) 3.10816 0.166855 0.0834275 0.996514i \(-0.473413\pi\)
0.0834275 + 0.996514i \(0.473413\pi\)
\(348\) 0 0
\(349\) 32.5026 1.73983 0.869913 0.493205i \(-0.164175\pi\)
0.869913 + 0.493205i \(0.164175\pi\)
\(350\) 0 0
\(351\) 6.48585 0.346189
\(352\) 0 0
\(353\) −20.5439 −1.09344 −0.546721 0.837315i \(-0.684124\pi\)
−0.546721 + 0.837315i \(0.684124\pi\)
\(354\) 0 0
\(355\) −14.3740 −0.762895
\(356\) 0 0
\(357\) −3.89115 −0.205942
\(358\) 0 0
\(359\) 1.61257 0.0851081 0.0425540 0.999094i \(-0.486451\pi\)
0.0425540 + 0.999094i \(0.486451\pi\)
\(360\) 0 0
\(361\) −12.5113 −0.658489
\(362\) 0 0
\(363\) 17.6179 0.924698
\(364\) 0 0
\(365\) −17.9363 −0.938827
\(366\) 0 0
\(367\) −9.27677 −0.484244 −0.242122 0.970246i \(-0.577843\pi\)
−0.242122 + 0.970246i \(0.577843\pi\)
\(368\) 0 0
\(369\) −4.16210 −0.216670
\(370\) 0 0
\(371\) 20.0068 1.03870
\(372\) 0 0
\(373\) 20.5507 1.06407 0.532037 0.846721i \(-0.321427\pi\)
0.532037 + 0.846721i \(0.321427\pi\)
\(374\) 0 0
\(375\) −18.5070 −0.955696
\(376\) 0 0
\(377\) 3.87932 0.199795
\(378\) 0 0
\(379\) 6.56327 0.337132 0.168566 0.985690i \(-0.446086\pi\)
0.168566 + 0.985690i \(0.446086\pi\)
\(380\) 0 0
\(381\) 11.4105 0.584577
\(382\) 0 0
\(383\) −9.58685 −0.489865 −0.244932 0.969540i \(-0.578766\pi\)
−0.244932 + 0.969540i \(0.578766\pi\)
\(384\) 0 0
\(385\) −2.04326 −0.104134
\(386\) 0 0
\(387\) −2.11491 −0.107507
\(388\) 0 0
\(389\) 18.5963 0.942869 0.471434 0.881901i \(-0.343736\pi\)
0.471434 + 0.881901i \(0.343736\pi\)
\(390\) 0 0
\(391\) 2.46113 0.124464
\(392\) 0 0
\(393\) −12.9012 −0.650779
\(394\) 0 0
\(395\) 15.6340 0.786632
\(396\) 0 0
\(397\) −0.780429 −0.0391686 −0.0195843 0.999808i \(-0.506234\pi\)
−0.0195843 + 0.999808i \(0.506234\pi\)
\(398\) 0 0
\(399\) −11.6556 −0.583511
\(400\) 0 0
\(401\) 17.0706 0.852463 0.426231 0.904614i \(-0.359841\pi\)
0.426231 + 0.904614i \(0.359841\pi\)
\(402\) 0 0
\(403\) 10.8780 0.541874
\(404\) 0 0
\(405\) 16.7970 0.834649
\(406\) 0 0
\(407\) −1.39122 −0.0689603
\(408\) 0 0
\(409\) −23.8796 −1.18077 −0.590385 0.807122i \(-0.701024\pi\)
−0.590385 + 0.807122i \(0.701024\pi\)
\(410\) 0 0
\(411\) −19.3582 −0.954869
\(412\) 0 0
\(413\) 14.8625 0.731335
\(414\) 0 0
\(415\) −11.5000 −0.564511
\(416\) 0 0
\(417\) −8.87776 −0.434746
\(418\) 0 0
\(419\) −4.69668 −0.229448 −0.114724 0.993397i \(-0.536598\pi\)
−0.114724 + 0.993397i \(0.536598\pi\)
\(420\) 0 0
\(421\) 34.5652 1.68461 0.842303 0.539005i \(-0.181200\pi\)
0.842303 + 0.539005i \(0.181200\pi\)
\(422\) 0 0
\(423\) 1.17676 0.0572159
\(424\) 0 0
\(425\) 0.210559 0.0102136
\(426\) 0 0
\(427\) −14.5386 −0.703574
\(428\) 0 0
\(429\) 0.635359 0.0306754
\(430\) 0 0
\(431\) −14.3310 −0.690301 −0.345150 0.938547i \(-0.612172\pi\)
−0.345150 + 0.938547i \(0.612172\pi\)
\(432\) 0 0
\(433\) −11.0660 −0.531799 −0.265900 0.964001i \(-0.585669\pi\)
−0.265900 + 0.964001i \(0.585669\pi\)
\(434\) 0 0
\(435\) 11.5440 0.553495
\(436\) 0 0
\(437\) 7.37209 0.352655
\(438\) 0 0
\(439\) −19.0090 −0.907248 −0.453624 0.891193i \(-0.649869\pi\)
−0.453624 + 0.891193i \(0.649869\pi\)
\(440\) 0 0
\(441\) −0.382718 −0.0182247
\(442\) 0 0
\(443\) 11.2504 0.534525 0.267262 0.963624i \(-0.413881\pi\)
0.267262 + 0.963624i \(0.413881\pi\)
\(444\) 0 0
\(445\) −32.8145 −1.55555
\(446\) 0 0
\(447\) −10.8952 −0.515324
\(448\) 0 0
\(449\) 7.28506 0.343803 0.171902 0.985114i \(-0.445009\pi\)
0.171902 + 0.985114i \(0.445009\pi\)
\(450\) 0 0
\(451\) −3.60298 −0.169658
\(452\) 0 0
\(453\) 5.43378 0.255301
\(454\) 0 0
\(455\) 7.30747 0.342580
\(456\) 0 0
\(457\) −1.07677 −0.0503690 −0.0251845 0.999683i \(-0.508017\pi\)
−0.0251845 + 0.999683i \(0.508017\pi\)
\(458\) 0 0
\(459\) −4.65390 −0.217225
\(460\) 0 0
\(461\) −11.3033 −0.526448 −0.263224 0.964735i \(-0.584786\pi\)
−0.263224 + 0.964735i \(0.584786\pi\)
\(462\) 0 0
\(463\) 40.2496 1.87056 0.935278 0.353914i \(-0.115149\pi\)
0.935278 + 0.353914i \(0.115149\pi\)
\(464\) 0 0
\(465\) 32.3708 1.50116
\(466\) 0 0
\(467\) −3.99138 −0.184699 −0.0923494 0.995727i \(-0.529438\pi\)
−0.0923494 + 0.995727i \(0.529438\pi\)
\(468\) 0 0
\(469\) 35.9614 1.66054
\(470\) 0 0
\(471\) 4.06562 0.187334
\(472\) 0 0
\(473\) −1.83080 −0.0841804
\(474\) 0 0
\(475\) 0.630713 0.0289391
\(476\) 0 0
\(477\) 2.70782 0.123982
\(478\) 0 0
\(479\) −28.6774 −1.31030 −0.655152 0.755497i \(-0.727396\pi\)
−0.655152 + 0.755497i \(0.727396\pi\)
\(480\) 0 0
\(481\) 4.97552 0.226864
\(482\) 0 0
\(483\) −13.2425 −0.602552
\(484\) 0 0
\(485\) 25.1288 1.14104
\(486\) 0 0
\(487\) 7.42705 0.336552 0.168276 0.985740i \(-0.446180\pi\)
0.168276 + 0.985740i \(0.446180\pi\)
\(488\) 0 0
\(489\) −28.2536 −1.27767
\(490\) 0 0
\(491\) 10.2390 0.462077 0.231039 0.972945i \(-0.425788\pi\)
0.231039 + 0.972945i \(0.425788\pi\)
\(492\) 0 0
\(493\) −2.78359 −0.125367
\(494\) 0 0
\(495\) −0.276545 −0.0124298
\(496\) 0 0
\(497\) −18.6492 −0.836533
\(498\) 0 0
\(499\) −20.9983 −0.940014 −0.470007 0.882663i \(-0.655749\pi\)
−0.470007 + 0.882663i \(0.655749\pi\)
\(500\) 0 0
\(501\) −11.3304 −0.506207
\(502\) 0 0
\(503\) −0.586864 −0.0261670 −0.0130835 0.999914i \(-0.504165\pi\)
−0.0130835 + 0.999914i \(0.504165\pi\)
\(504\) 0 0
\(505\) −11.3189 −0.503686
\(506\) 0 0
\(507\) 18.7588 0.833107
\(508\) 0 0
\(509\) 14.8536 0.658372 0.329186 0.944265i \(-0.393226\pi\)
0.329186 + 0.944265i \(0.393226\pi\)
\(510\) 0 0
\(511\) −23.2710 −1.02945
\(512\) 0 0
\(513\) −13.9404 −0.615482
\(514\) 0 0
\(515\) 11.8772 0.523373
\(516\) 0 0
\(517\) 1.01868 0.0448014
\(518\) 0 0
\(519\) 33.1228 1.45393
\(520\) 0 0
\(521\) 17.0182 0.745583 0.372791 0.927915i \(-0.378401\pi\)
0.372791 + 0.927915i \(0.378401\pi\)
\(522\) 0 0
\(523\) −19.6229 −0.858052 −0.429026 0.903292i \(-0.641143\pi\)
−0.429026 + 0.903292i \(0.641143\pi\)
\(524\) 0 0
\(525\) −1.13295 −0.0494458
\(526\) 0 0
\(527\) −7.80549 −0.340013
\(528\) 0 0
\(529\) −14.6243 −0.635837
\(530\) 0 0
\(531\) 2.01155 0.0872940
\(532\) 0 0
\(533\) 12.8856 0.558138
\(534\) 0 0
\(535\) 25.2084 1.08985
\(536\) 0 0
\(537\) 9.24949 0.399145
\(538\) 0 0
\(539\) −0.331306 −0.0142703
\(540\) 0 0
\(541\) −13.4535 −0.578409 −0.289205 0.957267i \(-0.593391\pi\)
−0.289205 + 0.957267i \(0.593391\pi\)
\(542\) 0 0
\(543\) −0.177854 −0.00763243
\(544\) 0 0
\(545\) −5.04958 −0.216300
\(546\) 0 0
\(547\) −4.68961 −0.200513 −0.100257 0.994962i \(-0.531966\pi\)
−0.100257 + 0.994962i \(0.531966\pi\)
\(548\) 0 0
\(549\) −1.96773 −0.0839805
\(550\) 0 0
\(551\) −8.33802 −0.355211
\(552\) 0 0
\(553\) 20.2839 0.862561
\(554\) 0 0
\(555\) 14.8061 0.628485
\(556\) 0 0
\(557\) −3.91801 −0.166011 −0.0830057 0.996549i \(-0.526452\pi\)
−0.0830057 + 0.996549i \(0.526452\pi\)
\(558\) 0 0
\(559\) 6.54763 0.276935
\(560\) 0 0
\(561\) −0.455900 −0.0192481
\(562\) 0 0
\(563\) −27.9203 −1.17670 −0.588350 0.808607i \(-0.700222\pi\)
−0.588350 + 0.808607i \(0.700222\pi\)
\(564\) 0 0
\(565\) −21.1058 −0.887928
\(566\) 0 0
\(567\) 21.7928 0.915213
\(568\) 0 0
\(569\) 31.8580 1.33556 0.667779 0.744360i \(-0.267245\pi\)
0.667779 + 0.744360i \(0.267245\pi\)
\(570\) 0 0
\(571\) −36.4804 −1.52666 −0.763329 0.646010i \(-0.776437\pi\)
−0.763329 + 0.646010i \(0.776437\pi\)
\(572\) 0 0
\(573\) −6.98715 −0.291893
\(574\) 0 0
\(575\) 0.716579 0.0298834
\(576\) 0 0
\(577\) −40.3484 −1.67972 −0.839862 0.542799i \(-0.817364\pi\)
−0.839862 + 0.542799i \(0.817364\pi\)
\(578\) 0 0
\(579\) −36.6764 −1.52422
\(580\) 0 0
\(581\) −14.9204 −0.619000
\(582\) 0 0
\(583\) 2.34406 0.0970812
\(584\) 0 0
\(585\) 0.989026 0.0408912
\(586\) 0 0
\(587\) 25.3099 1.04465 0.522325 0.852746i \(-0.325065\pi\)
0.522325 + 0.852746i \(0.325065\pi\)
\(588\) 0 0
\(589\) −23.3807 −0.963385
\(590\) 0 0
\(591\) 3.76929 0.155048
\(592\) 0 0
\(593\) −5.64223 −0.231698 −0.115849 0.993267i \(-0.536959\pi\)
−0.115849 + 0.993267i \(0.536959\pi\)
\(594\) 0 0
\(595\) −5.24345 −0.214960
\(596\) 0 0
\(597\) 29.5376 1.20890
\(598\) 0 0
\(599\) 3.94680 0.161262 0.0806309 0.996744i \(-0.474306\pi\)
0.0806309 + 0.996744i \(0.474306\pi\)
\(600\) 0 0
\(601\) −13.5665 −0.553391 −0.276695 0.960958i \(-0.589239\pi\)
−0.276695 + 0.960958i \(0.589239\pi\)
\(602\) 0 0
\(603\) 4.86718 0.198207
\(604\) 0 0
\(605\) 23.7406 0.965193
\(606\) 0 0
\(607\) 8.36799 0.339646 0.169823 0.985475i \(-0.445680\pi\)
0.169823 + 0.985475i \(0.445680\pi\)
\(608\) 0 0
\(609\) 14.9775 0.606920
\(610\) 0 0
\(611\) −3.64317 −0.147387
\(612\) 0 0
\(613\) 0.277150 0.0111940 0.00559698 0.999984i \(-0.498218\pi\)
0.00559698 + 0.999984i \(0.498218\pi\)
\(614\) 0 0
\(615\) 38.3449 1.54621
\(616\) 0 0
\(617\) 27.1309 1.09225 0.546124 0.837704i \(-0.316103\pi\)
0.546124 + 0.837704i \(0.316103\pi\)
\(618\) 0 0
\(619\) 37.2491 1.49717 0.748583 0.663041i \(-0.230734\pi\)
0.748583 + 0.663041i \(0.230734\pi\)
\(620\) 0 0
\(621\) −15.8382 −0.635567
\(622\) 0 0
\(623\) −42.5743 −1.70570
\(624\) 0 0
\(625\) −23.7007 −0.948028
\(626\) 0 0
\(627\) −1.36561 −0.0545372
\(628\) 0 0
\(629\) −3.57017 −0.142352
\(630\) 0 0
\(631\) 17.2921 0.688388 0.344194 0.938899i \(-0.388152\pi\)
0.344194 + 0.938899i \(0.388152\pi\)
\(632\) 0 0
\(633\) 0.0784370 0.00311759
\(634\) 0 0
\(635\) 15.3760 0.610178
\(636\) 0 0
\(637\) 1.18487 0.0469463
\(638\) 0 0
\(639\) −2.52407 −0.0998507
\(640\) 0 0
\(641\) −5.71059 −0.225555 −0.112777 0.993620i \(-0.535975\pi\)
−0.112777 + 0.993620i \(0.535975\pi\)
\(642\) 0 0
\(643\) −39.8738 −1.57247 −0.786234 0.617929i \(-0.787972\pi\)
−0.786234 + 0.617929i \(0.787972\pi\)
\(644\) 0 0
\(645\) 19.4844 0.767197
\(646\) 0 0
\(647\) −35.5414 −1.39728 −0.698639 0.715474i \(-0.746211\pi\)
−0.698639 + 0.715474i \(0.746211\pi\)
\(648\) 0 0
\(649\) 1.74133 0.0683533
\(650\) 0 0
\(651\) 41.9986 1.64606
\(652\) 0 0
\(653\) 46.0880 1.80356 0.901782 0.432191i \(-0.142259\pi\)
0.901782 + 0.432191i \(0.142259\pi\)
\(654\) 0 0
\(655\) −17.3847 −0.679278
\(656\) 0 0
\(657\) −3.14959 −0.122877
\(658\) 0 0
\(659\) −1.34339 −0.0523311 −0.0261656 0.999658i \(-0.508330\pi\)
−0.0261656 + 0.999658i \(0.508330\pi\)
\(660\) 0 0
\(661\) −0.189408 −0.00736712 −0.00368356 0.999993i \(-0.501173\pi\)
−0.00368356 + 0.999993i \(0.501173\pi\)
\(662\) 0 0
\(663\) 1.63047 0.0633221
\(664\) 0 0
\(665\) −15.7063 −0.609065
\(666\) 0 0
\(667\) −9.47317 −0.366803
\(668\) 0 0
\(669\) 7.70342 0.297831
\(670\) 0 0
\(671\) −1.70339 −0.0657587
\(672\) 0 0
\(673\) −30.8302 −1.18842 −0.594208 0.804311i \(-0.702534\pi\)
−0.594208 + 0.804311i \(0.702534\pi\)
\(674\) 0 0
\(675\) −1.35503 −0.0521550
\(676\) 0 0
\(677\) −26.6069 −1.02259 −0.511294 0.859406i \(-0.670834\pi\)
−0.511294 + 0.859406i \(0.670834\pi\)
\(678\) 0 0
\(679\) 32.6027 1.25118
\(680\) 0 0
\(681\) 24.6318 0.943893
\(682\) 0 0
\(683\) −47.5141 −1.81808 −0.909038 0.416712i \(-0.863182\pi\)
−0.909038 + 0.416712i \(0.863182\pi\)
\(684\) 0 0
\(685\) −26.0858 −0.996685
\(686\) 0 0
\(687\) −16.0773 −0.613389
\(688\) 0 0
\(689\) −8.38324 −0.319376
\(690\) 0 0
\(691\) −24.2081 −0.920920 −0.460460 0.887680i \(-0.652316\pi\)
−0.460460 + 0.887680i \(0.652316\pi\)
\(692\) 0 0
\(693\) −0.358796 −0.0136295
\(694\) 0 0
\(695\) −11.9631 −0.453785
\(696\) 0 0
\(697\) −9.24602 −0.350218
\(698\) 0 0
\(699\) 44.8012 1.69454
\(700\) 0 0
\(701\) 8.80260 0.332470 0.166235 0.986086i \(-0.446839\pi\)
0.166235 + 0.986086i \(0.446839\pi\)
\(702\) 0 0
\(703\) −10.6941 −0.403337
\(704\) 0 0
\(705\) −10.8413 −0.408307
\(706\) 0 0
\(707\) −14.6855 −0.552304
\(708\) 0 0
\(709\) 23.5395 0.884045 0.442022 0.897004i \(-0.354261\pi\)
0.442022 + 0.897004i \(0.354261\pi\)
\(710\) 0 0
\(711\) 2.74532 0.102958
\(712\) 0 0
\(713\) −26.5638 −0.994822
\(714\) 0 0
\(715\) 0.856166 0.0320188
\(716\) 0 0
\(717\) 27.2815 1.01885
\(718\) 0 0
\(719\) 51.9497 1.93740 0.968698 0.248244i \(-0.0798534\pi\)
0.968698 + 0.248244i \(0.0798534\pi\)
\(720\) 0 0
\(721\) 15.4098 0.573891
\(722\) 0 0
\(723\) −4.55237 −0.169304
\(724\) 0 0
\(725\) −0.810469 −0.0301001
\(726\) 0 0
\(727\) 19.7904 0.733986 0.366993 0.930224i \(-0.380387\pi\)
0.366993 + 0.930224i \(0.380387\pi\)
\(728\) 0 0
\(729\) 29.5099 1.09296
\(730\) 0 0
\(731\) −4.69823 −0.173770
\(732\) 0 0
\(733\) −17.3444 −0.640630 −0.320315 0.947311i \(-0.603789\pi\)
−0.320315 + 0.947311i \(0.603789\pi\)
\(734\) 0 0
\(735\) 3.52593 0.130056
\(736\) 0 0
\(737\) 4.21335 0.155201
\(738\) 0 0
\(739\) 25.6769 0.944539 0.472270 0.881454i \(-0.343435\pi\)
0.472270 + 0.881454i \(0.343435\pi\)
\(740\) 0 0
\(741\) 4.88392 0.179415
\(742\) 0 0
\(743\) −43.4030 −1.59230 −0.796151 0.605098i \(-0.793134\pi\)
−0.796151 + 0.605098i \(0.793134\pi\)
\(744\) 0 0
\(745\) −14.6816 −0.537891
\(746\) 0 0
\(747\) −2.01939 −0.0738855
\(748\) 0 0
\(749\) 32.7060 1.19505
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −5.24055 −0.190976
\(754\) 0 0
\(755\) 7.32219 0.266482
\(756\) 0 0
\(757\) 32.2539 1.17229 0.586145 0.810206i \(-0.300645\pi\)
0.586145 + 0.810206i \(0.300645\pi\)
\(758\) 0 0
\(759\) −1.55153 −0.0563168
\(760\) 0 0
\(761\) −9.03410 −0.327486 −0.163743 0.986503i \(-0.552357\pi\)
−0.163743 + 0.986503i \(0.552357\pi\)
\(762\) 0 0
\(763\) −6.55146 −0.237179
\(764\) 0 0
\(765\) −0.709672 −0.0256582
\(766\) 0 0
\(767\) −6.22766 −0.224868
\(768\) 0 0
\(769\) −52.7801 −1.90330 −0.951649 0.307186i \(-0.900613\pi\)
−0.951649 + 0.307186i \(0.900613\pi\)
\(770\) 0 0
\(771\) 31.4279 1.13185
\(772\) 0 0
\(773\) 40.9954 1.47450 0.737251 0.675619i \(-0.236124\pi\)
0.737251 + 0.675619i \(0.236124\pi\)
\(774\) 0 0
\(775\) −2.27264 −0.0816357
\(776\) 0 0
\(777\) 19.2098 0.689149
\(778\) 0 0
\(779\) −27.6957 −0.992301
\(780\) 0 0
\(781\) −2.18500 −0.0781855
\(782\) 0 0
\(783\) 17.9134 0.640174
\(784\) 0 0
\(785\) 5.47854 0.195538
\(786\) 0 0
\(787\) 19.7088 0.702544 0.351272 0.936273i \(-0.385749\pi\)
0.351272 + 0.936273i \(0.385749\pi\)
\(788\) 0 0
\(789\) 13.7033 0.487849
\(790\) 0 0
\(791\) −27.3832 −0.973634
\(792\) 0 0
\(793\) 6.09196 0.216332
\(794\) 0 0
\(795\) −24.9468 −0.884771
\(796\) 0 0
\(797\) 9.73666 0.344890 0.172445 0.985019i \(-0.444833\pi\)
0.172445 + 0.985019i \(0.444833\pi\)
\(798\) 0 0
\(799\) 2.61414 0.0924817
\(800\) 0 0
\(801\) −5.76220 −0.203597
\(802\) 0 0
\(803\) −2.72650 −0.0962160
\(804\) 0 0
\(805\) −17.8446 −0.628940
\(806\) 0 0
\(807\) 35.3051 1.24280
\(808\) 0 0
\(809\) 27.3284 0.960814 0.480407 0.877046i \(-0.340489\pi\)
0.480407 + 0.877046i \(0.340489\pi\)
\(810\) 0 0
\(811\) 8.14626 0.286054 0.143027 0.989719i \(-0.454316\pi\)
0.143027 + 0.989719i \(0.454316\pi\)
\(812\) 0 0
\(813\) 31.9343 1.11999
\(814\) 0 0
\(815\) −38.0726 −1.33363
\(816\) 0 0
\(817\) −14.0732 −0.492357
\(818\) 0 0
\(819\) 1.28319 0.0448382
\(820\) 0 0
\(821\) 28.8107 1.00550 0.502750 0.864432i \(-0.332322\pi\)
0.502750 + 0.864432i \(0.332322\pi\)
\(822\) 0 0
\(823\) 19.1723 0.668305 0.334152 0.942519i \(-0.391550\pi\)
0.334152 + 0.942519i \(0.391550\pi\)
\(824\) 0 0
\(825\) −0.132739 −0.00462139
\(826\) 0 0
\(827\) −23.1729 −0.805800 −0.402900 0.915244i \(-0.631998\pi\)
−0.402900 + 0.915244i \(0.631998\pi\)
\(828\) 0 0
\(829\) −21.9673 −0.762955 −0.381478 0.924378i \(-0.624585\pi\)
−0.381478 + 0.924378i \(0.624585\pi\)
\(830\) 0 0
\(831\) −33.5197 −1.16279
\(832\) 0 0
\(833\) −0.850200 −0.0294577
\(834\) 0 0
\(835\) −15.2681 −0.528375
\(836\) 0 0
\(837\) 50.2312 1.73624
\(838\) 0 0
\(839\) −40.4409 −1.39618 −0.698088 0.716012i \(-0.745965\pi\)
−0.698088 + 0.716012i \(0.745965\pi\)
\(840\) 0 0
\(841\) −18.2856 −0.630538
\(842\) 0 0
\(843\) −30.4282 −1.04800
\(844\) 0 0
\(845\) 25.2780 0.869591
\(846\) 0 0
\(847\) 30.8017 1.05836
\(848\) 0 0
\(849\) −5.04380 −0.173103
\(850\) 0 0
\(851\) −12.1501 −0.416499
\(852\) 0 0
\(853\) 13.3680 0.457710 0.228855 0.973460i \(-0.426502\pi\)
0.228855 + 0.973460i \(0.426502\pi\)
\(854\) 0 0
\(855\) −2.12576 −0.0726995
\(856\) 0 0
\(857\) 40.4263 1.38094 0.690469 0.723362i \(-0.257404\pi\)
0.690469 + 0.723362i \(0.257404\pi\)
\(858\) 0 0
\(859\) 0.796162 0.0271647 0.0135823 0.999908i \(-0.495676\pi\)
0.0135823 + 0.999908i \(0.495676\pi\)
\(860\) 0 0
\(861\) 49.7496 1.69546
\(862\) 0 0
\(863\) 24.4938 0.833778 0.416889 0.908958i \(-0.363120\pi\)
0.416889 + 0.908958i \(0.363120\pi\)
\(864\) 0 0
\(865\) 44.6340 1.51760
\(866\) 0 0
\(867\) 26.3322 0.894289
\(868\) 0 0
\(869\) 2.37653 0.0806182
\(870\) 0 0
\(871\) −15.0685 −0.510577
\(872\) 0 0
\(873\) 4.41260 0.149344
\(874\) 0 0
\(875\) −32.3561 −1.09384
\(876\) 0 0
\(877\) −42.8172 −1.44584 −0.722918 0.690934i \(-0.757199\pi\)
−0.722918 + 0.690934i \(0.757199\pi\)
\(878\) 0 0
\(879\) −45.8796 −1.54748
\(880\) 0 0
\(881\) 4.70084 0.158375 0.0791876 0.996860i \(-0.474767\pi\)
0.0791876 + 0.996860i \(0.474767\pi\)
\(882\) 0 0
\(883\) −8.87909 −0.298805 −0.149403 0.988776i \(-0.547735\pi\)
−0.149403 + 0.988776i \(0.547735\pi\)
\(884\) 0 0
\(885\) −18.5322 −0.622953
\(886\) 0 0
\(887\) 49.1295 1.64961 0.824803 0.565421i \(-0.191286\pi\)
0.824803 + 0.565421i \(0.191286\pi\)
\(888\) 0 0
\(889\) 19.9492 0.669074
\(890\) 0 0
\(891\) 2.55331 0.0855393
\(892\) 0 0
\(893\) 7.83045 0.262036
\(894\) 0 0
\(895\) 12.4640 0.416624
\(896\) 0 0
\(897\) 5.54883 0.185270
\(898\) 0 0
\(899\) 30.0443 1.00203
\(900\) 0 0
\(901\) 6.01536 0.200401
\(902\) 0 0
\(903\) 25.2795 0.841250
\(904\) 0 0
\(905\) −0.239663 −0.00796667
\(906\) 0 0
\(907\) 59.2812 1.96840 0.984200 0.177060i \(-0.0566585\pi\)
0.984200 + 0.177060i \(0.0566585\pi\)
\(908\) 0 0
\(909\) −1.98760 −0.0659245
\(910\) 0 0
\(911\) 5.71519 0.189353 0.0946763 0.995508i \(-0.469818\pi\)
0.0946763 + 0.995508i \(0.469818\pi\)
\(912\) 0 0
\(913\) −1.74811 −0.0578541
\(914\) 0 0
\(915\) 18.1284 0.599307
\(916\) 0 0
\(917\) −22.5554 −0.744845
\(918\) 0 0
\(919\) 20.3009 0.669663 0.334832 0.942278i \(-0.391321\pi\)
0.334832 + 0.942278i \(0.391321\pi\)
\(920\) 0 0
\(921\) 23.6454 0.779143
\(922\) 0 0
\(923\) 7.81438 0.257213
\(924\) 0 0
\(925\) −1.03949 −0.0341781
\(926\) 0 0
\(927\) 2.08563 0.0685011
\(928\) 0 0
\(929\) −24.1868 −0.793543 −0.396771 0.917918i \(-0.629869\pi\)
−0.396771 + 0.917918i \(0.629869\pi\)
\(930\) 0 0
\(931\) −2.54670 −0.0834648
\(932\) 0 0
\(933\) 37.9732 1.24319
\(934\) 0 0
\(935\) −0.614338 −0.0200910
\(936\) 0 0
\(937\) −48.8114 −1.59460 −0.797300 0.603584i \(-0.793739\pi\)
−0.797300 + 0.603584i \(0.793739\pi\)
\(938\) 0 0
\(939\) −1.77334 −0.0578709
\(940\) 0 0
\(941\) 22.5023 0.733555 0.366777 0.930309i \(-0.380461\pi\)
0.366777 + 0.930309i \(0.380461\pi\)
\(942\) 0 0
\(943\) −31.4662 −1.02468
\(944\) 0 0
\(945\) 33.7435 1.09768
\(946\) 0 0
\(947\) −2.60674 −0.0847075 −0.0423538 0.999103i \(-0.513486\pi\)
−0.0423538 + 0.999103i \(0.513486\pi\)
\(948\) 0 0
\(949\) 9.75096 0.316530
\(950\) 0 0
\(951\) −25.5744 −0.829306
\(952\) 0 0
\(953\) −29.1285 −0.943565 −0.471783 0.881715i \(-0.656389\pi\)
−0.471783 + 0.881715i \(0.656389\pi\)
\(954\) 0 0
\(955\) −9.41540 −0.304675
\(956\) 0 0
\(957\) 1.75481 0.0567251
\(958\) 0 0
\(959\) −33.8443 −1.09289
\(960\) 0 0
\(961\) 53.2475 1.71766
\(962\) 0 0
\(963\) 4.42657 0.142644
\(964\) 0 0
\(965\) −49.4226 −1.59097
\(966\) 0 0
\(967\) −44.1094 −1.41846 −0.709231 0.704976i \(-0.750958\pi\)
−0.709231 + 0.704976i \(0.750958\pi\)
\(968\) 0 0
\(969\) −3.50444 −0.112579
\(970\) 0 0
\(971\) −16.3250 −0.523896 −0.261948 0.965082i \(-0.584365\pi\)
−0.261948 + 0.965082i \(0.584365\pi\)
\(972\) 0 0
\(973\) −15.5212 −0.497586
\(974\) 0 0
\(975\) 0.474725 0.0152034
\(976\) 0 0
\(977\) 19.5231 0.624601 0.312300 0.949983i \(-0.398900\pi\)
0.312300 + 0.949983i \(0.398900\pi\)
\(978\) 0 0
\(979\) −4.98814 −0.159422
\(980\) 0 0
\(981\) −0.886703 −0.0283103
\(982\) 0 0
\(983\) −37.9408 −1.21012 −0.605062 0.796179i \(-0.706852\pi\)
−0.605062 + 0.796179i \(0.706852\pi\)
\(984\) 0 0
\(985\) 5.07924 0.161838
\(986\) 0 0
\(987\) −14.0658 −0.447719
\(988\) 0 0
\(989\) −15.9891 −0.508424
\(990\) 0 0
\(991\) 30.6236 0.972792 0.486396 0.873739i \(-0.338311\pi\)
0.486396 + 0.873739i \(0.338311\pi\)
\(992\) 0 0
\(993\) 20.2849 0.643722
\(994\) 0 0
\(995\) 39.8029 1.26184
\(996\) 0 0
\(997\) −41.5890 −1.31714 −0.658569 0.752520i \(-0.728838\pi\)
−0.658569 + 0.752520i \(0.728838\pi\)
\(998\) 0 0
\(999\) 22.9753 0.726907
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.1.15 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.15 44 1.1 even 1 trivial