Properties

Label 6008.2.a.b.1.33
Level 6008
Weight 2
Character 6008.1
Self dual yes
Analytic conductor 47.974
Analytic rank 1
Dimension 44
CM no
Inner twists 1

Related objects

Downloads

Learn more about

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 1.33
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.63164 q^{3} -0.519900 q^{5} -1.27819 q^{7} -0.337735 q^{9} +O(q^{10})\) \(q+1.63164 q^{3} -0.519900 q^{5} -1.27819 q^{7} -0.337735 q^{9} +0.383001 q^{11} -3.76097 q^{13} -0.848293 q^{15} -2.19611 q^{17} +8.06921 q^{19} -2.08556 q^{21} +8.44221 q^{23} -4.72970 q^{25} -5.44600 q^{27} +1.75121 q^{29} +2.47392 q^{31} +0.624921 q^{33} +0.664532 q^{35} -5.22407 q^{37} -6.13656 q^{39} -8.06867 q^{41} -2.28300 q^{43} +0.175589 q^{45} +6.12174 q^{47} -5.36623 q^{49} -3.58327 q^{51} -7.72001 q^{53} -0.199122 q^{55} +13.1661 q^{57} -7.93756 q^{59} -1.43166 q^{61} +0.431691 q^{63} +1.95533 q^{65} +10.2817 q^{67} +13.7747 q^{69} -3.82462 q^{71} +4.88864 q^{73} -7.71720 q^{75} -0.489548 q^{77} -4.92386 q^{79} -7.87273 q^{81} +6.10004 q^{83} +1.14176 q^{85} +2.85735 q^{87} -0.946343 q^{89} +4.80724 q^{91} +4.03656 q^{93} -4.19518 q^{95} -5.40244 q^{97} -0.129353 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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
\(3\) 1.63164 0.942031 0.471015 0.882125i \(-0.343888\pi\)
0.471015 + 0.882125i \(0.343888\pi\)
\(4\) 0 0
\(5\) −0.519900 −0.232507 −0.116253 0.993220i \(-0.537088\pi\)
−0.116253 + 0.993220i \(0.537088\pi\)
\(6\) 0 0
\(7\) −1.27819 −0.483111 −0.241556 0.970387i \(-0.577658\pi\)
−0.241556 + 0.970387i \(0.577658\pi\)
\(8\) 0 0
\(9\) −0.337735 −0.112578
\(10\) 0 0
\(11\) 0.383001 0.115479 0.0577395 0.998332i \(-0.481611\pi\)
0.0577395 + 0.998332i \(0.481611\pi\)
\(12\) 0 0
\(13\) −3.76097 −1.04310 −0.521552 0.853219i \(-0.674647\pi\)
−0.521552 + 0.853219i \(0.674647\pi\)
\(14\) 0 0
\(15\) −0.848293 −0.219028
\(16\) 0 0
\(17\) −2.19611 −0.532635 −0.266318 0.963885i \(-0.585807\pi\)
−0.266318 + 0.963885i \(0.585807\pi\)
\(18\) 0 0
\(19\) 8.06921 1.85120 0.925601 0.378500i \(-0.123560\pi\)
0.925601 + 0.378500i \(0.123560\pi\)
\(20\) 0 0
\(21\) −2.08556 −0.455105
\(22\) 0 0
\(23\) 8.44221 1.76032 0.880161 0.474675i \(-0.157435\pi\)
0.880161 + 0.474675i \(0.157435\pi\)
\(24\) 0 0
\(25\) −4.72970 −0.945941
\(26\) 0 0
\(27\) −5.44600 −1.04808
\(28\) 0 0
\(29\) 1.75121 0.325191 0.162595 0.986693i \(-0.448013\pi\)
0.162595 + 0.986693i \(0.448013\pi\)
\(30\) 0 0
\(31\) 2.47392 0.444329 0.222164 0.975009i \(-0.428688\pi\)
0.222164 + 0.975009i \(0.428688\pi\)
\(32\) 0 0
\(33\) 0.624921 0.108785
\(34\) 0 0
\(35\) 0.664532 0.112326
\(36\) 0 0
\(37\) −5.22407 −0.858832 −0.429416 0.903107i \(-0.641281\pi\)
−0.429416 + 0.903107i \(0.641281\pi\)
\(38\) 0 0
\(39\) −6.13656 −0.982636
\(40\) 0 0
\(41\) −8.06867 −1.26011 −0.630057 0.776549i \(-0.716969\pi\)
−0.630057 + 0.776549i \(0.716969\pi\)
\(42\) 0 0
\(43\) −2.28300 −0.348154 −0.174077 0.984732i \(-0.555694\pi\)
−0.174077 + 0.984732i \(0.555694\pi\)
\(44\) 0 0
\(45\) 0.175589 0.0261752
\(46\) 0 0
\(47\) 6.12174 0.892947 0.446474 0.894797i \(-0.352680\pi\)
0.446474 + 0.894797i \(0.352680\pi\)
\(48\) 0 0
\(49\) −5.36623 −0.766604
\(50\) 0 0
\(51\) −3.58327 −0.501759
\(52\) 0 0
\(53\) −7.72001 −1.06043 −0.530213 0.847865i \(-0.677888\pi\)
−0.530213 + 0.847865i \(0.677888\pi\)
\(54\) 0 0
\(55\) −0.199122 −0.0268496
\(56\) 0 0
\(57\) 13.1661 1.74389
\(58\) 0 0
\(59\) −7.93756 −1.03338 −0.516691 0.856172i \(-0.672836\pi\)
−0.516691 + 0.856172i \(0.672836\pi\)
\(60\) 0 0
\(61\) −1.43166 −0.183306 −0.0916529 0.995791i \(-0.529215\pi\)
−0.0916529 + 0.995791i \(0.529215\pi\)
\(62\) 0 0
\(63\) 0.431691 0.0543879
\(64\) 0 0
\(65\) 1.95533 0.242529
\(66\) 0 0
\(67\) 10.2817 1.25611 0.628056 0.778169i \(-0.283851\pi\)
0.628056 + 0.778169i \(0.283851\pi\)
\(68\) 0 0
\(69\) 13.7747 1.65828
\(70\) 0 0
\(71\) −3.82462 −0.453899 −0.226949 0.973907i \(-0.572875\pi\)
−0.226949 + 0.973907i \(0.572875\pi\)
\(72\) 0 0
\(73\) 4.88864 0.572172 0.286086 0.958204i \(-0.407646\pi\)
0.286086 + 0.958204i \(0.407646\pi\)
\(74\) 0 0
\(75\) −7.71720 −0.891105
\(76\) 0 0
\(77\) −0.489548 −0.0557892
\(78\) 0 0
\(79\) −4.92386 −0.553978 −0.276989 0.960873i \(-0.589337\pi\)
−0.276989 + 0.960873i \(0.589337\pi\)
\(80\) 0 0
\(81\) −7.87273 −0.874748
\(82\) 0 0
\(83\) 6.10004 0.669566 0.334783 0.942295i \(-0.391337\pi\)
0.334783 + 0.942295i \(0.391337\pi\)
\(84\) 0 0
\(85\) 1.14176 0.123841
\(86\) 0 0
\(87\) 2.85735 0.306340
\(88\) 0 0
\(89\) −0.946343 −0.100312 −0.0501561 0.998741i \(-0.515972\pi\)
−0.0501561 + 0.998741i \(0.515972\pi\)
\(90\) 0 0
\(91\) 4.80724 0.503935
\(92\) 0 0
\(93\) 4.03656 0.418571
\(94\) 0 0
\(95\) −4.19518 −0.430417
\(96\) 0 0
\(97\) −5.40244 −0.548534 −0.274267 0.961654i \(-0.588435\pi\)
−0.274267 + 0.961654i \(0.588435\pi\)
\(98\) 0 0
\(99\) −0.129353 −0.0130005
\(100\) 0 0
\(101\) −12.5860 −1.25236 −0.626179 0.779679i \(-0.715382\pi\)
−0.626179 + 0.779679i \(0.715382\pi\)
\(102\) 0 0
\(103\) −15.9759 −1.57415 −0.787077 0.616855i \(-0.788406\pi\)
−0.787077 + 0.616855i \(0.788406\pi\)
\(104\) 0 0
\(105\) 1.08428 0.105815
\(106\) 0 0
\(107\) −10.8671 −1.05056 −0.525279 0.850930i \(-0.676039\pi\)
−0.525279 + 0.850930i \(0.676039\pi\)
\(108\) 0 0
\(109\) 15.8708 1.52015 0.760074 0.649836i \(-0.225162\pi\)
0.760074 + 0.649836i \(0.225162\pi\)
\(110\) 0 0
\(111\) −8.52383 −0.809046
\(112\) 0 0
\(113\) −17.7683 −1.67150 −0.835751 0.549109i \(-0.814967\pi\)
−0.835751 + 0.549109i \(0.814967\pi\)
\(114\) 0 0
\(115\) −4.38911 −0.409286
\(116\) 0 0
\(117\) 1.27021 0.117431
\(118\) 0 0
\(119\) 2.80705 0.257322
\(120\) 0 0
\(121\) −10.8533 −0.986665
\(122\) 0 0
\(123\) −13.1652 −1.18707
\(124\) 0 0
\(125\) 5.05848 0.452444
\(126\) 0 0
\(127\) −12.1961 −1.08223 −0.541114 0.840949i \(-0.681997\pi\)
−0.541114 + 0.840949i \(0.681997\pi\)
\(128\) 0 0
\(129\) −3.72504 −0.327972
\(130\) 0 0
\(131\) −22.1634 −1.93643 −0.968213 0.250126i \(-0.919528\pi\)
−0.968213 + 0.250126i \(0.919528\pi\)
\(132\) 0 0
\(133\) −10.3140 −0.894337
\(134\) 0 0
\(135\) 2.83138 0.243686
\(136\) 0 0
\(137\) 17.5640 1.50059 0.750296 0.661102i \(-0.229911\pi\)
0.750296 + 0.661102i \(0.229911\pi\)
\(138\) 0 0
\(139\) 3.33869 0.283184 0.141592 0.989925i \(-0.454778\pi\)
0.141592 + 0.989925i \(0.454778\pi\)
\(140\) 0 0
\(141\) 9.98850 0.841184
\(142\) 0 0
\(143\) −1.44045 −0.120457
\(144\) 0 0
\(145\) −0.910453 −0.0756090
\(146\) 0 0
\(147\) −8.75577 −0.722164
\(148\) 0 0
\(149\) −20.8219 −1.70580 −0.852898 0.522078i \(-0.825157\pi\)
−0.852898 + 0.522078i \(0.825157\pi\)
\(150\) 0 0
\(151\) −3.90638 −0.317897 −0.158948 0.987287i \(-0.550810\pi\)
−0.158948 + 0.987287i \(0.550810\pi\)
\(152\) 0 0
\(153\) 0.741704 0.0599632
\(154\) 0 0
\(155\) −1.28619 −0.103309
\(156\) 0 0
\(157\) −10.7533 −0.858206 −0.429103 0.903256i \(-0.641170\pi\)
−0.429103 + 0.903256i \(0.641170\pi\)
\(158\) 0 0
\(159\) −12.5963 −0.998953
\(160\) 0 0
\(161\) −10.7908 −0.850431
\(162\) 0 0
\(163\) 10.5041 0.822745 0.411373 0.911467i \(-0.365050\pi\)
0.411373 + 0.911467i \(0.365050\pi\)
\(164\) 0 0
\(165\) −0.324897 −0.0252932
\(166\) 0 0
\(167\) 8.18037 0.633016 0.316508 0.948590i \(-0.397490\pi\)
0.316508 + 0.948590i \(0.397490\pi\)
\(168\) 0 0
\(169\) 1.14487 0.0880666
\(170\) 0 0
\(171\) −2.72526 −0.208406
\(172\) 0 0
\(173\) −1.14699 −0.0872044 −0.0436022 0.999049i \(-0.513883\pi\)
−0.0436022 + 0.999049i \(0.513883\pi\)
\(174\) 0 0
\(175\) 6.04547 0.456994
\(176\) 0 0
\(177\) −12.9513 −0.973477
\(178\) 0 0
\(179\) −23.4530 −1.75296 −0.876481 0.481436i \(-0.840115\pi\)
−0.876481 + 0.481436i \(0.840115\pi\)
\(180\) 0 0
\(181\) 13.9417 1.03628 0.518140 0.855296i \(-0.326625\pi\)
0.518140 + 0.855296i \(0.326625\pi\)
\(182\) 0 0
\(183\) −2.33597 −0.172680
\(184\) 0 0
\(185\) 2.71600 0.199684
\(186\) 0 0
\(187\) −0.841112 −0.0615082
\(188\) 0 0
\(189\) 6.96103 0.506340
\(190\) 0 0
\(191\) 15.8513 1.14696 0.573481 0.819219i \(-0.305593\pi\)
0.573481 + 0.819219i \(0.305593\pi\)
\(192\) 0 0
\(193\) −2.28410 −0.164413 −0.0822067 0.996615i \(-0.526197\pi\)
−0.0822067 + 0.996615i \(0.526197\pi\)
\(194\) 0 0
\(195\) 3.19040 0.228469
\(196\) 0 0
\(197\) −1.21403 −0.0864960 −0.0432480 0.999064i \(-0.513771\pi\)
−0.0432480 + 0.999064i \(0.513771\pi\)
\(198\) 0 0
\(199\) 9.53278 0.675761 0.337880 0.941189i \(-0.390290\pi\)
0.337880 + 0.941189i \(0.390290\pi\)
\(200\) 0 0
\(201\) 16.7761 1.18330
\(202\) 0 0
\(203\) −2.23838 −0.157103
\(204\) 0 0
\(205\) 4.19490 0.292985
\(206\) 0 0
\(207\) −2.85123 −0.198174
\(208\) 0 0
\(209\) 3.09051 0.213775
\(210\) 0 0
\(211\) −18.8770 −1.29955 −0.649773 0.760128i \(-0.725136\pi\)
−0.649773 + 0.760128i \(0.725136\pi\)
\(212\) 0 0
\(213\) −6.24042 −0.427586
\(214\) 0 0
\(215\) 1.18693 0.0809481
\(216\) 0 0
\(217\) −3.16214 −0.214660
\(218\) 0 0
\(219\) 7.97652 0.539003
\(220\) 0 0
\(221\) 8.25950 0.555594
\(222\) 0 0
\(223\) 2.63077 0.176169 0.0880845 0.996113i \(-0.471925\pi\)
0.0880845 + 0.996113i \(0.471925\pi\)
\(224\) 0 0
\(225\) 1.59739 0.106493
\(226\) 0 0
\(227\) 5.40495 0.358739 0.179369 0.983782i \(-0.442594\pi\)
0.179369 + 0.983782i \(0.442594\pi\)
\(228\) 0 0
\(229\) −24.9130 −1.64629 −0.823147 0.567828i \(-0.807784\pi\)
−0.823147 + 0.567828i \(0.807784\pi\)
\(230\) 0 0
\(231\) −0.798769 −0.0525551
\(232\) 0 0
\(233\) −25.7780 −1.68877 −0.844386 0.535735i \(-0.820035\pi\)
−0.844386 + 0.535735i \(0.820035\pi\)
\(234\) 0 0
\(235\) −3.18269 −0.207616
\(236\) 0 0
\(237\) −8.03399 −0.521864
\(238\) 0 0
\(239\) 16.2855 1.05342 0.526712 0.850044i \(-0.323425\pi\)
0.526712 + 0.850044i \(0.323425\pi\)
\(240\) 0 0
\(241\) −8.30023 −0.534665 −0.267332 0.963604i \(-0.586142\pi\)
−0.267332 + 0.963604i \(0.586142\pi\)
\(242\) 0 0
\(243\) 3.49250 0.224044
\(244\) 0 0
\(245\) 2.78990 0.178240
\(246\) 0 0
\(247\) −30.3480 −1.93100
\(248\) 0 0
\(249\) 9.95310 0.630752
\(250\) 0 0
\(251\) −9.43018 −0.595228 −0.297614 0.954686i \(-0.596191\pi\)
−0.297614 + 0.954686i \(0.596191\pi\)
\(252\) 0 0
\(253\) 3.23337 0.203280
\(254\) 0 0
\(255\) 1.86294 0.116662
\(256\) 0 0
\(257\) 26.5912 1.65871 0.829357 0.558719i \(-0.188707\pi\)
0.829357 + 0.558719i \(0.188707\pi\)
\(258\) 0 0
\(259\) 6.67736 0.414911
\(260\) 0 0
\(261\) −0.591444 −0.0366095
\(262\) 0 0
\(263\) 22.3272 1.37675 0.688377 0.725353i \(-0.258323\pi\)
0.688377 + 0.725353i \(0.258323\pi\)
\(264\) 0 0
\(265\) 4.01364 0.246556
\(266\) 0 0
\(267\) −1.54410 −0.0944971
\(268\) 0 0
\(269\) −0.776865 −0.0473663 −0.0236831 0.999720i \(-0.507539\pi\)
−0.0236831 + 0.999720i \(0.507539\pi\)
\(270\) 0 0
\(271\) 12.0735 0.733415 0.366707 0.930336i \(-0.380485\pi\)
0.366707 + 0.930336i \(0.380485\pi\)
\(272\) 0 0
\(273\) 7.84370 0.474722
\(274\) 0 0
\(275\) −1.81148 −0.109236
\(276\) 0 0
\(277\) 27.3898 1.64569 0.822846 0.568264i \(-0.192385\pi\)
0.822846 + 0.568264i \(0.192385\pi\)
\(278\) 0 0
\(279\) −0.835530 −0.0500219
\(280\) 0 0
\(281\) 5.34335 0.318758 0.159379 0.987218i \(-0.449051\pi\)
0.159379 + 0.987218i \(0.449051\pi\)
\(282\) 0 0
\(283\) 1.87101 0.111220 0.0556101 0.998453i \(-0.482290\pi\)
0.0556101 + 0.998453i \(0.482290\pi\)
\(284\) 0 0
\(285\) −6.84505 −0.405466
\(286\) 0 0
\(287\) 10.3133 0.608775
\(288\) 0 0
\(289\) −12.1771 −0.716300
\(290\) 0 0
\(291\) −8.81486 −0.516736
\(292\) 0 0
\(293\) −3.16992 −0.185189 −0.0925944 0.995704i \(-0.529516\pi\)
−0.0925944 + 0.995704i \(0.529516\pi\)
\(294\) 0 0
\(295\) 4.12674 0.240268
\(296\) 0 0
\(297\) −2.08582 −0.121032
\(298\) 0 0
\(299\) −31.7509 −1.83620
\(300\) 0 0
\(301\) 2.91811 0.168197
\(302\) 0 0
\(303\) −20.5359 −1.17976
\(304\) 0 0
\(305\) 0.744323 0.0426198
\(306\) 0 0
\(307\) −29.1125 −1.66154 −0.830769 0.556617i \(-0.812099\pi\)
−0.830769 + 0.556617i \(0.812099\pi\)
\(308\) 0 0
\(309\) −26.0670 −1.48290
\(310\) 0 0
\(311\) 6.42040 0.364067 0.182034 0.983292i \(-0.441732\pi\)
0.182034 + 0.983292i \(0.441732\pi\)
\(312\) 0 0
\(313\) −7.25399 −0.410020 −0.205010 0.978760i \(-0.565723\pi\)
−0.205010 + 0.978760i \(0.565723\pi\)
\(314\) 0 0
\(315\) −0.224436 −0.0126455
\(316\) 0 0
\(317\) 24.6434 1.38411 0.692055 0.721844i \(-0.256705\pi\)
0.692055 + 0.721844i \(0.256705\pi\)
\(318\) 0 0
\(319\) 0.670713 0.0375527
\(320\) 0 0
\(321\) −17.7312 −0.989657
\(322\) 0 0
\(323\) −17.7209 −0.986015
\(324\) 0 0
\(325\) 17.7883 0.986715
\(326\) 0 0
\(327\) 25.8955 1.43203
\(328\) 0 0
\(329\) −7.82476 −0.431393
\(330\) 0 0
\(331\) 24.5919 1.35169 0.675847 0.737042i \(-0.263778\pi\)
0.675847 + 0.737042i \(0.263778\pi\)
\(332\) 0 0
\(333\) 1.76435 0.0966860
\(334\) 0 0
\(335\) −5.34547 −0.292054
\(336\) 0 0
\(337\) −36.1661 −1.97009 −0.985046 0.172292i \(-0.944883\pi\)
−0.985046 + 0.172292i \(0.944883\pi\)
\(338\) 0 0
\(339\) −28.9916 −1.57461
\(340\) 0 0
\(341\) 0.947513 0.0513107
\(342\) 0 0
\(343\) 15.8064 0.853466
\(344\) 0 0
\(345\) −7.16146 −0.385560
\(346\) 0 0
\(347\) 28.0991 1.50844 0.754218 0.656624i \(-0.228016\pi\)
0.754218 + 0.656624i \(0.228016\pi\)
\(348\) 0 0
\(349\) 25.8008 1.38109 0.690543 0.723291i \(-0.257371\pi\)
0.690543 + 0.723291i \(0.257371\pi\)
\(350\) 0 0
\(351\) 20.4822 1.09326
\(352\) 0 0
\(353\) −32.7293 −1.74200 −0.871002 0.491279i \(-0.836529\pi\)
−0.871002 + 0.491279i \(0.836529\pi\)
\(354\) 0 0
\(355\) 1.98842 0.105534
\(356\) 0 0
\(357\) 4.58011 0.242405
\(358\) 0 0
\(359\) 16.8878 0.891304 0.445652 0.895206i \(-0.352972\pi\)
0.445652 + 0.895206i \(0.352972\pi\)
\(360\) 0 0
\(361\) 46.1121 2.42695
\(362\) 0 0
\(363\) −17.7087 −0.929468
\(364\) 0 0
\(365\) −2.54160 −0.133034
\(366\) 0 0
\(367\) 3.03169 0.158253 0.0791264 0.996865i \(-0.474787\pi\)
0.0791264 + 0.996865i \(0.474787\pi\)
\(368\) 0 0
\(369\) 2.72508 0.141862
\(370\) 0 0
\(371\) 9.86766 0.512303
\(372\) 0 0
\(373\) −4.21939 −0.218472 −0.109236 0.994016i \(-0.534840\pi\)
−0.109236 + 0.994016i \(0.534840\pi\)
\(374\) 0 0
\(375\) 8.25364 0.426216
\(376\) 0 0
\(377\) −6.58623 −0.339208
\(378\) 0 0
\(379\) 8.78811 0.451415 0.225708 0.974195i \(-0.427531\pi\)
0.225708 + 0.974195i \(0.427531\pi\)
\(380\) 0 0
\(381\) −19.8997 −1.01949
\(382\) 0 0
\(383\) 12.6473 0.646247 0.323123 0.946357i \(-0.395267\pi\)
0.323123 + 0.946357i \(0.395267\pi\)
\(384\) 0 0
\(385\) 0.254516 0.0129714
\(386\) 0 0
\(387\) 0.771050 0.0391947
\(388\) 0 0
\(389\) −11.9113 −0.603925 −0.301963 0.953320i \(-0.597642\pi\)
−0.301963 + 0.953320i \(0.597642\pi\)
\(390\) 0 0
\(391\) −18.5400 −0.937609
\(392\) 0 0
\(393\) −36.1628 −1.82417
\(394\) 0 0
\(395\) 2.55992 0.128803
\(396\) 0 0
\(397\) −17.8188 −0.894302 −0.447151 0.894458i \(-0.647561\pi\)
−0.447151 + 0.894458i \(0.647561\pi\)
\(398\) 0 0
\(399\) −16.8288 −0.842492
\(400\) 0 0
\(401\) −0.610489 −0.0304864 −0.0152432 0.999884i \(-0.504852\pi\)
−0.0152432 + 0.999884i \(0.504852\pi\)
\(402\) 0 0
\(403\) −9.30433 −0.463481
\(404\) 0 0
\(405\) 4.09303 0.203385
\(406\) 0 0
\(407\) −2.00082 −0.0991771
\(408\) 0 0
\(409\) 20.7557 1.02631 0.513153 0.858297i \(-0.328477\pi\)
0.513153 + 0.858297i \(0.328477\pi\)
\(410\) 0 0
\(411\) 28.6582 1.41360
\(412\) 0 0
\(413\) 10.1457 0.499238
\(414\) 0 0
\(415\) −3.17141 −0.155678
\(416\) 0 0
\(417\) 5.44756 0.266768
\(418\) 0 0
\(419\) 11.4840 0.561028 0.280514 0.959850i \(-0.409495\pi\)
0.280514 + 0.959850i \(0.409495\pi\)
\(420\) 0 0
\(421\) −32.7955 −1.59836 −0.799178 0.601094i \(-0.794732\pi\)
−0.799178 + 0.601094i \(0.794732\pi\)
\(422\) 0 0
\(423\) −2.06753 −0.100527
\(424\) 0 0
\(425\) 10.3870 0.503841
\(426\) 0 0
\(427\) 1.82994 0.0885571
\(428\) 0 0
\(429\) −2.35031 −0.113474
\(430\) 0 0
\(431\) −1.90266 −0.0916477 −0.0458239 0.998950i \(-0.514591\pi\)
−0.0458239 + 0.998950i \(0.514591\pi\)
\(432\) 0 0
\(433\) −21.3370 −1.02539 −0.512695 0.858571i \(-0.671353\pi\)
−0.512695 + 0.858571i \(0.671353\pi\)
\(434\) 0 0
\(435\) −1.48554 −0.0712260
\(436\) 0 0
\(437\) 68.1219 3.25871
\(438\) 0 0
\(439\) 7.14565 0.341043 0.170522 0.985354i \(-0.445455\pi\)
0.170522 + 0.985354i \(0.445455\pi\)
\(440\) 0 0
\(441\) 1.81236 0.0863031
\(442\) 0 0
\(443\) −28.6484 −1.36113 −0.680564 0.732688i \(-0.738265\pi\)
−0.680564 + 0.732688i \(0.738265\pi\)
\(444\) 0 0
\(445\) 0.492004 0.0233232
\(446\) 0 0
\(447\) −33.9739 −1.60691
\(448\) 0 0
\(449\) −5.18915 −0.244891 −0.122446 0.992475i \(-0.539074\pi\)
−0.122446 + 0.992475i \(0.539074\pi\)
\(450\) 0 0
\(451\) −3.09031 −0.145517
\(452\) 0 0
\(453\) −6.37382 −0.299468
\(454\) 0 0
\(455\) −2.49928 −0.117168
\(456\) 0 0
\(457\) −23.1887 −1.08472 −0.542360 0.840146i \(-0.682469\pi\)
−0.542360 + 0.840146i \(0.682469\pi\)
\(458\) 0 0
\(459\) 11.9600 0.558246
\(460\) 0 0
\(461\) 40.1289 1.86899 0.934495 0.355977i \(-0.115852\pi\)
0.934495 + 0.355977i \(0.115852\pi\)
\(462\) 0 0
\(463\) −4.21569 −0.195920 −0.0979600 0.995190i \(-0.531232\pi\)
−0.0979600 + 0.995190i \(0.531232\pi\)
\(464\) 0 0
\(465\) −2.09861 −0.0973206
\(466\) 0 0
\(467\) 5.38825 0.249338 0.124669 0.992198i \(-0.460213\pi\)
0.124669 + 0.992198i \(0.460213\pi\)
\(468\) 0 0
\(469\) −13.1420 −0.606841
\(470\) 0 0
\(471\) −17.5456 −0.808456
\(472\) 0 0
\(473\) −0.874390 −0.0402045
\(474\) 0 0
\(475\) −38.1649 −1.75113
\(476\) 0 0
\(477\) 2.60732 0.119381
\(478\) 0 0
\(479\) −27.6881 −1.26510 −0.632552 0.774518i \(-0.717992\pi\)
−0.632552 + 0.774518i \(0.717992\pi\)
\(480\) 0 0
\(481\) 19.6475 0.895851
\(482\) 0 0
\(483\) −17.6067 −0.801132
\(484\) 0 0
\(485\) 2.80873 0.127538
\(486\) 0 0
\(487\) 6.35708 0.288067 0.144033 0.989573i \(-0.453993\pi\)
0.144033 + 0.989573i \(0.453993\pi\)
\(488\) 0 0
\(489\) 17.1390 0.775051
\(490\) 0 0
\(491\) 37.7915 1.70551 0.852754 0.522313i \(-0.174931\pi\)
0.852754 + 0.522313i \(0.174931\pi\)
\(492\) 0 0
\(493\) −3.84584 −0.173208
\(494\) 0 0
\(495\) 0.0672506 0.00302269
\(496\) 0 0
\(497\) 4.88859 0.219283
\(498\) 0 0
\(499\) −15.0710 −0.674672 −0.337336 0.941384i \(-0.609526\pi\)
−0.337336 + 0.941384i \(0.609526\pi\)
\(500\) 0 0
\(501\) 13.3475 0.596320
\(502\) 0 0
\(503\) −7.39872 −0.329893 −0.164946 0.986303i \(-0.552745\pi\)
−0.164946 + 0.986303i \(0.552745\pi\)
\(504\) 0 0
\(505\) 6.54349 0.291181
\(506\) 0 0
\(507\) 1.86802 0.0829615
\(508\) 0 0
\(509\) 18.5571 0.822530 0.411265 0.911516i \(-0.365087\pi\)
0.411265 + 0.911516i \(0.365087\pi\)
\(510\) 0 0
\(511\) −6.24862 −0.276423
\(512\) 0 0
\(513\) −43.9449 −1.94021
\(514\) 0 0
\(515\) 8.30588 0.366001
\(516\) 0 0
\(517\) 2.34463 0.103117
\(518\) 0 0
\(519\) −1.87149 −0.0821492
\(520\) 0 0
\(521\) 5.69083 0.249320 0.124660 0.992200i \(-0.460216\pi\)
0.124660 + 0.992200i \(0.460216\pi\)
\(522\) 0 0
\(523\) −21.9303 −0.958947 −0.479474 0.877556i \(-0.659172\pi\)
−0.479474 + 0.877556i \(0.659172\pi\)
\(524\) 0 0
\(525\) 9.86406 0.430503
\(526\) 0 0
\(527\) −5.43300 −0.236665
\(528\) 0 0
\(529\) 48.2709 2.09873
\(530\) 0 0
\(531\) 2.68079 0.116337
\(532\) 0 0
\(533\) 30.3460 1.31443
\(534\) 0 0
\(535\) 5.64978 0.244261
\(536\) 0 0
\(537\) −38.2670 −1.65134
\(538\) 0 0
\(539\) −2.05527 −0.0885267
\(540\) 0 0
\(541\) 14.4062 0.619372 0.309686 0.950839i \(-0.399776\pi\)
0.309686 + 0.950839i \(0.399776\pi\)
\(542\) 0 0
\(543\) 22.7479 0.976207
\(544\) 0 0
\(545\) −8.25124 −0.353444
\(546\) 0 0
\(547\) −36.1731 −1.54665 −0.773325 0.634010i \(-0.781408\pi\)
−0.773325 + 0.634010i \(0.781408\pi\)
\(548\) 0 0
\(549\) 0.483524 0.0206363
\(550\) 0 0
\(551\) 14.1308 0.601994
\(552\) 0 0
\(553\) 6.29364 0.267633
\(554\) 0 0
\(555\) 4.43154 0.188108
\(556\) 0 0
\(557\) −8.03899 −0.340623 −0.170311 0.985390i \(-0.554477\pi\)
−0.170311 + 0.985390i \(0.554477\pi\)
\(558\) 0 0
\(559\) 8.58628 0.363161
\(560\) 0 0
\(561\) −1.37240 −0.0579426
\(562\) 0 0
\(563\) −33.3931 −1.40735 −0.703675 0.710522i \(-0.748459\pi\)
−0.703675 + 0.710522i \(0.748459\pi\)
\(564\) 0 0
\(565\) 9.23775 0.388635
\(566\) 0 0
\(567\) 10.0629 0.422600
\(568\) 0 0
\(569\) 30.2062 1.26631 0.633154 0.774026i \(-0.281760\pi\)
0.633154 + 0.774026i \(0.281760\pi\)
\(570\) 0 0
\(571\) 40.9251 1.71266 0.856331 0.516427i \(-0.172738\pi\)
0.856331 + 0.516427i \(0.172738\pi\)
\(572\) 0 0
\(573\) 25.8637 1.08047
\(574\) 0 0
\(575\) −39.9291 −1.66516
\(576\) 0 0
\(577\) 16.0167 0.666784 0.333392 0.942788i \(-0.391807\pi\)
0.333392 + 0.942788i \(0.391807\pi\)
\(578\) 0 0
\(579\) −3.72684 −0.154882
\(580\) 0 0
\(581\) −7.79702 −0.323475
\(582\) 0 0
\(583\) −2.95677 −0.122457
\(584\) 0 0
\(585\) −0.660383 −0.0273035
\(586\) 0 0
\(587\) −22.7927 −0.940755 −0.470377 0.882465i \(-0.655882\pi\)
−0.470377 + 0.882465i \(0.655882\pi\)
\(588\) 0 0
\(589\) 19.9626 0.822543
\(590\) 0 0
\(591\) −1.98086 −0.0814819
\(592\) 0 0
\(593\) 39.3825 1.61724 0.808622 0.588329i \(-0.200214\pi\)
0.808622 + 0.588329i \(0.200214\pi\)
\(594\) 0 0
\(595\) −1.45939 −0.0598290
\(596\) 0 0
\(597\) 15.5541 0.636587
\(598\) 0 0
\(599\) 4.13150 0.168808 0.0844042 0.996432i \(-0.473101\pi\)
0.0844042 + 0.996432i \(0.473101\pi\)
\(600\) 0 0
\(601\) −0.283139 −0.0115495 −0.00577474 0.999983i \(-0.501838\pi\)
−0.00577474 + 0.999983i \(0.501838\pi\)
\(602\) 0 0
\(603\) −3.47250 −0.141411
\(604\) 0 0
\(605\) 5.64264 0.229406
\(606\) 0 0
\(607\) 23.8306 0.967255 0.483628 0.875274i \(-0.339319\pi\)
0.483628 + 0.875274i \(0.339319\pi\)
\(608\) 0 0
\(609\) −3.65224 −0.147996
\(610\) 0 0
\(611\) −23.0237 −0.931437
\(612\) 0 0
\(613\) 7.32587 0.295889 0.147944 0.988996i \(-0.452734\pi\)
0.147944 + 0.988996i \(0.452734\pi\)
\(614\) 0 0
\(615\) 6.84459 0.276001
\(616\) 0 0
\(617\) −14.4726 −0.582644 −0.291322 0.956625i \(-0.594095\pi\)
−0.291322 + 0.956625i \(0.594095\pi\)
\(618\) 0 0
\(619\) −9.33303 −0.375126 −0.187563 0.982253i \(-0.560059\pi\)
−0.187563 + 0.982253i \(0.560059\pi\)
\(620\) 0 0
\(621\) −45.9762 −1.84496
\(622\) 0 0
\(623\) 1.20961 0.0484619
\(624\) 0 0
\(625\) 21.0186 0.840745
\(626\) 0 0
\(627\) 5.04262 0.201383
\(628\) 0 0
\(629\) 11.4726 0.457444
\(630\) 0 0
\(631\) −46.2937 −1.84292 −0.921461 0.388470i \(-0.873004\pi\)
−0.921461 + 0.388470i \(0.873004\pi\)
\(632\) 0 0
\(633\) −30.8006 −1.22421
\(634\) 0 0
\(635\) 6.34076 0.251625
\(636\) 0 0
\(637\) 20.1822 0.799648
\(638\) 0 0
\(639\) 1.29171 0.0510992
\(640\) 0 0
\(641\) 18.4108 0.727183 0.363591 0.931559i \(-0.381550\pi\)
0.363591 + 0.931559i \(0.381550\pi\)
\(642\) 0 0
\(643\) 17.2184 0.679028 0.339514 0.940601i \(-0.389737\pi\)
0.339514 + 0.940601i \(0.389737\pi\)
\(644\) 0 0
\(645\) 1.93665 0.0762556
\(646\) 0 0
\(647\) −33.0169 −1.29803 −0.649014 0.760776i \(-0.724819\pi\)
−0.649014 + 0.760776i \(0.724819\pi\)
\(648\) 0 0
\(649\) −3.04009 −0.119334
\(650\) 0 0
\(651\) −5.15949 −0.202217
\(652\) 0 0
\(653\) 40.3689 1.57976 0.789878 0.613264i \(-0.210144\pi\)
0.789878 + 0.613264i \(0.210144\pi\)
\(654\) 0 0
\(655\) 11.5228 0.450232
\(656\) 0 0
\(657\) −1.65107 −0.0644142
\(658\) 0 0
\(659\) −1.04165 −0.0405767 −0.0202884 0.999794i \(-0.506458\pi\)
−0.0202884 + 0.999794i \(0.506458\pi\)
\(660\) 0 0
\(661\) 28.3410 1.10234 0.551168 0.834394i \(-0.314182\pi\)
0.551168 + 0.834394i \(0.314182\pi\)
\(662\) 0 0
\(663\) 13.4766 0.523386
\(664\) 0 0
\(665\) 5.36225 0.207939
\(666\) 0 0
\(667\) 14.7840 0.572440
\(668\) 0 0
\(669\) 4.29247 0.165957
\(670\) 0 0
\(671\) −0.548328 −0.0211680
\(672\) 0 0
\(673\) 1.74126 0.0671207 0.0335603 0.999437i \(-0.489315\pi\)
0.0335603 + 0.999437i \(0.489315\pi\)
\(674\) 0 0
\(675\) 25.7580 0.991424
\(676\) 0 0
\(677\) −14.4763 −0.556369 −0.278185 0.960528i \(-0.589733\pi\)
−0.278185 + 0.960528i \(0.589733\pi\)
\(678\) 0 0
\(679\) 6.90535 0.265003
\(680\) 0 0
\(681\) 8.81895 0.337943
\(682\) 0 0
\(683\) 5.72391 0.219019 0.109510 0.993986i \(-0.465072\pi\)
0.109510 + 0.993986i \(0.465072\pi\)
\(684\) 0 0
\(685\) −9.13152 −0.348898
\(686\) 0 0
\(687\) −40.6491 −1.55086
\(688\) 0 0
\(689\) 29.0347 1.10613
\(690\) 0 0
\(691\) 36.2033 1.37724 0.688618 0.725124i \(-0.258218\pi\)
0.688618 + 0.725124i \(0.258218\pi\)
\(692\) 0 0
\(693\) 0.165338 0.00628066
\(694\) 0 0
\(695\) −1.73579 −0.0658422
\(696\) 0 0
\(697\) 17.7197 0.671181
\(698\) 0 0
\(699\) −42.0605 −1.59087
\(700\) 0 0
\(701\) −14.6725 −0.554174 −0.277087 0.960845i \(-0.589369\pi\)
−0.277087 + 0.960845i \(0.589369\pi\)
\(702\) 0 0
\(703\) −42.1541 −1.58987
\(704\) 0 0
\(705\) −5.19303 −0.195581
\(706\) 0 0
\(707\) 16.0874 0.605028
\(708\) 0 0
\(709\) −47.9570 −1.80106 −0.900531 0.434793i \(-0.856822\pi\)
−0.900531 + 0.434793i \(0.856822\pi\)
\(710\) 0 0
\(711\) 1.66296 0.0623660
\(712\) 0 0
\(713\) 20.8853 0.782162
\(714\) 0 0
\(715\) 0.748892 0.0280070
\(716\) 0 0
\(717\) 26.5722 0.992358
\(718\) 0 0
\(719\) 32.5548 1.21409 0.607044 0.794668i \(-0.292355\pi\)
0.607044 + 0.794668i \(0.292355\pi\)
\(720\) 0 0
\(721\) 20.4203 0.760491
\(722\) 0 0
\(723\) −13.5430 −0.503670
\(724\) 0 0
\(725\) −8.28268 −0.307611
\(726\) 0 0
\(727\) 38.9803 1.44570 0.722850 0.691005i \(-0.242832\pi\)
0.722850 + 0.691005i \(0.242832\pi\)
\(728\) 0 0
\(729\) 29.3167 1.08580
\(730\) 0 0
\(731\) 5.01372 0.185439
\(732\) 0 0
\(733\) −44.9398 −1.65989 −0.829945 0.557845i \(-0.811628\pi\)
−0.829945 + 0.557845i \(0.811628\pi\)
\(734\) 0 0
\(735\) 4.55213 0.167908
\(736\) 0 0
\(737\) 3.93790 0.145055
\(738\) 0 0
\(739\) −20.1255 −0.740330 −0.370165 0.928966i \(-0.620699\pi\)
−0.370165 + 0.928966i \(0.620699\pi\)
\(740\) 0 0
\(741\) −49.5172 −1.81906
\(742\) 0 0
\(743\) 13.8225 0.507099 0.253550 0.967322i \(-0.418402\pi\)
0.253550 + 0.967322i \(0.418402\pi\)
\(744\) 0 0
\(745\) 10.8253 0.396608
\(746\) 0 0
\(747\) −2.06020 −0.0753787
\(748\) 0 0
\(749\) 13.8902 0.507536
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −15.3867 −0.560723
\(754\) 0 0
\(755\) 2.03093 0.0739130
\(756\) 0 0
\(757\) 10.6862 0.388397 0.194199 0.980962i \(-0.437789\pi\)
0.194199 + 0.980962i \(0.437789\pi\)
\(758\) 0 0
\(759\) 5.27571 0.191496
\(760\) 0 0
\(761\) −34.8972 −1.26502 −0.632511 0.774551i \(-0.717976\pi\)
−0.632511 + 0.774551i \(0.717976\pi\)
\(762\) 0 0
\(763\) −20.2860 −0.734401
\(764\) 0 0
\(765\) −0.385612 −0.0139418
\(766\) 0 0
\(767\) 29.8529 1.07793
\(768\) 0 0
\(769\) 17.6260 0.635609 0.317804 0.948156i \(-0.397055\pi\)
0.317804 + 0.948156i \(0.397055\pi\)
\(770\) 0 0
\(771\) 43.3874 1.56256
\(772\) 0 0
\(773\) −22.2447 −0.800085 −0.400042 0.916497i \(-0.631005\pi\)
−0.400042 + 0.916497i \(0.631005\pi\)
\(774\) 0 0
\(775\) −11.7009 −0.420309
\(776\) 0 0
\(777\) 10.8951 0.390859
\(778\) 0 0
\(779\) −65.1078 −2.33273
\(780\) 0 0
\(781\) −1.46483 −0.0524158
\(782\) 0 0
\(783\) −9.53706 −0.340827
\(784\) 0 0
\(785\) 5.59064 0.199538
\(786\) 0 0
\(787\) 54.8518 1.95526 0.977628 0.210341i \(-0.0674576\pi\)
0.977628 + 0.210341i \(0.0674576\pi\)
\(788\) 0 0
\(789\) 36.4301 1.29694
\(790\) 0 0
\(791\) 22.7113 0.807521
\(792\) 0 0
\(793\) 5.38444 0.191207
\(794\) 0 0
\(795\) 6.54883 0.232263
\(796\) 0 0
\(797\) 6.92472 0.245286 0.122643 0.992451i \(-0.460863\pi\)
0.122643 + 0.992451i \(0.460863\pi\)
\(798\) 0 0
\(799\) −13.4440 −0.475615
\(800\) 0 0
\(801\) 0.319613 0.0112930
\(802\) 0 0
\(803\) 1.87235 0.0660739
\(804\) 0 0
\(805\) 5.61012 0.197731
\(806\) 0 0
\(807\) −1.26757 −0.0446205
\(808\) 0 0
\(809\) 33.7643 1.18709 0.593545 0.804801i \(-0.297728\pi\)
0.593545 + 0.804801i \(0.297728\pi\)
\(810\) 0 0
\(811\) 8.27492 0.290572 0.145286 0.989390i \(-0.453590\pi\)
0.145286 + 0.989390i \(0.453590\pi\)
\(812\) 0 0
\(813\) 19.6997 0.690899
\(814\) 0 0
\(815\) −5.46109 −0.191294
\(816\) 0 0
\(817\) −18.4220 −0.644504
\(818\) 0 0
\(819\) −1.62357 −0.0567323
\(820\) 0 0
\(821\) 0.982535 0.0342907 0.0171454 0.999853i \(-0.494542\pi\)
0.0171454 + 0.999853i \(0.494542\pi\)
\(822\) 0 0
\(823\) −45.2269 −1.57651 −0.788255 0.615349i \(-0.789015\pi\)
−0.788255 + 0.615349i \(0.789015\pi\)
\(824\) 0 0
\(825\) −2.95569 −0.102904
\(826\) 0 0
\(827\) −18.2375 −0.634181 −0.317091 0.948395i \(-0.602706\pi\)
−0.317091 + 0.948395i \(0.602706\pi\)
\(828\) 0 0
\(829\) 19.5986 0.680688 0.340344 0.940301i \(-0.389456\pi\)
0.340344 + 0.940301i \(0.389456\pi\)
\(830\) 0 0
\(831\) 44.6904 1.55029
\(832\) 0 0
\(833\) 11.7848 0.408320
\(834\) 0 0
\(835\) −4.25298 −0.147180
\(836\) 0 0
\(837\) −13.4730 −0.465694
\(838\) 0 0
\(839\) −10.6993 −0.369383 −0.184691 0.982797i \(-0.559129\pi\)
−0.184691 + 0.982797i \(0.559129\pi\)
\(840\) 0 0
\(841\) −25.9333 −0.894251
\(842\) 0 0
\(843\) 8.71845 0.300279
\(844\) 0 0
\(845\) −0.595216 −0.0204761
\(846\) 0 0
\(847\) 13.8726 0.476669
\(848\) 0 0
\(849\) 3.05283 0.104773
\(850\) 0 0
\(851\) −44.1027 −1.51182
\(852\) 0 0
\(853\) −53.6259 −1.83612 −0.918058 0.396446i \(-0.870243\pi\)
−0.918058 + 0.396446i \(0.870243\pi\)
\(854\) 0 0
\(855\) 1.41686 0.0484556
\(856\) 0 0
\(857\) −39.4616 −1.34798 −0.673991 0.738740i \(-0.735421\pi\)
−0.673991 + 0.738740i \(0.735421\pi\)
\(858\) 0 0
\(859\) 16.2957 0.556001 0.278001 0.960581i \(-0.410328\pi\)
0.278001 + 0.960581i \(0.410328\pi\)
\(860\) 0 0
\(861\) 16.8277 0.573485
\(862\) 0 0
\(863\) 1.46043 0.0497136 0.0248568 0.999691i \(-0.492087\pi\)
0.0248568 + 0.999691i \(0.492087\pi\)
\(864\) 0 0
\(865\) 0.596323 0.0202756
\(866\) 0 0
\(867\) −19.8687 −0.674776
\(868\) 0 0
\(869\) −1.88584 −0.0639728
\(870\) 0 0
\(871\) −38.6692 −1.31025
\(872\) 0 0
\(873\) 1.82459 0.0617532
\(874\) 0 0
\(875\) −6.46570 −0.218581
\(876\) 0 0
\(877\) −17.2373 −0.582063 −0.291031 0.956713i \(-0.593998\pi\)
−0.291031 + 0.956713i \(0.593998\pi\)
\(878\) 0 0
\(879\) −5.17219 −0.174454
\(880\) 0 0
\(881\) 35.4211 1.19337 0.596684 0.802476i \(-0.296484\pi\)
0.596684 + 0.802476i \(0.296484\pi\)
\(882\) 0 0
\(883\) −45.0915 −1.51745 −0.758725 0.651411i \(-0.774178\pi\)
−0.758725 + 0.651411i \(0.774178\pi\)
\(884\) 0 0
\(885\) 6.73337 0.226340
\(886\) 0 0
\(887\) −49.4841 −1.66151 −0.830757 0.556636i \(-0.812092\pi\)
−0.830757 + 0.556636i \(0.812092\pi\)
\(888\) 0 0
\(889\) 15.5890 0.522837
\(890\) 0 0
\(891\) −3.01526 −0.101015
\(892\) 0 0
\(893\) 49.3976 1.65303
\(894\) 0 0
\(895\) 12.1932 0.407575
\(896\) 0 0
\(897\) −51.8061 −1.72976
\(898\) 0 0
\(899\) 4.33234 0.144492
\(900\) 0 0
\(901\) 16.9540 0.564820
\(902\) 0 0
\(903\) 4.76132 0.158447
\(904\) 0 0
\(905\) −7.24830 −0.240942
\(906\) 0 0
\(907\) 6.17856 0.205156 0.102578 0.994725i \(-0.467291\pi\)
0.102578 + 0.994725i \(0.467291\pi\)
\(908\) 0 0
\(909\) 4.25075 0.140989
\(910\) 0 0
\(911\) 4.49634 0.148970 0.0744852 0.997222i \(-0.476269\pi\)
0.0744852 + 0.997222i \(0.476269\pi\)
\(912\) 0 0
\(913\) 2.33632 0.0773209
\(914\) 0 0
\(915\) 1.21447 0.0401491
\(916\) 0 0
\(917\) 28.3291 0.935509
\(918\) 0 0
\(919\) −17.2810 −0.570047 −0.285023 0.958521i \(-0.592001\pi\)
−0.285023 + 0.958521i \(0.592001\pi\)
\(920\) 0 0
\(921\) −47.5013 −1.56522
\(922\) 0 0
\(923\) 14.3843 0.473464
\(924\) 0 0
\(925\) 24.7083 0.812404
\(926\) 0 0
\(927\) 5.39563 0.177216
\(928\) 0 0
\(929\) −27.4154 −0.899469 −0.449734 0.893162i \(-0.648481\pi\)
−0.449734 + 0.893162i \(0.648481\pi\)
\(930\) 0 0
\(931\) −43.3012 −1.41914
\(932\) 0 0
\(933\) 10.4758 0.342963
\(934\) 0 0
\(935\) 0.437294 0.0143011
\(936\) 0 0
\(937\) −44.3272 −1.44811 −0.724054 0.689744i \(-0.757723\pi\)
−0.724054 + 0.689744i \(0.757723\pi\)
\(938\) 0 0
\(939\) −11.8359 −0.386251
\(940\) 0 0
\(941\) −47.6965 −1.55486 −0.777430 0.628969i \(-0.783477\pi\)
−0.777430 + 0.628969i \(0.783477\pi\)
\(942\) 0 0
\(943\) −68.1174 −2.21821
\(944\) 0 0
\(945\) −3.61904 −0.117727
\(946\) 0 0
\(947\) 0.0523762 0.00170200 0.000850998 1.00000i \(-0.499729\pi\)
0.000850998 1.00000i \(0.499729\pi\)
\(948\) 0 0
\(949\) −18.3860 −0.596835
\(950\) 0 0
\(951\) 40.2093 1.30387
\(952\) 0 0
\(953\) −9.41868 −0.305101 −0.152551 0.988296i \(-0.548749\pi\)
−0.152551 + 0.988296i \(0.548749\pi\)
\(954\) 0 0
\(955\) −8.24111 −0.266676
\(956\) 0 0
\(957\) 1.09437 0.0353758
\(958\) 0 0
\(959\) −22.4501 −0.724953
\(960\) 0 0
\(961\) −24.8797 −0.802572
\(962\) 0 0
\(963\) 3.67019 0.118270
\(964\) 0 0
\(965\) 1.18751 0.0382272
\(966\) 0 0
\(967\) 7.94883 0.255617 0.127809 0.991799i \(-0.459206\pi\)
0.127809 + 0.991799i \(0.459206\pi\)
\(968\) 0 0
\(969\) −28.9142 −0.928857
\(970\) 0 0
\(971\) −49.4669 −1.58747 −0.793735 0.608264i \(-0.791866\pi\)
−0.793735 + 0.608264i \(0.791866\pi\)
\(972\) 0 0
\(973\) −4.26749 −0.136809
\(974\) 0 0
\(975\) 29.0241 0.929516
\(976\) 0 0
\(977\) −21.0335 −0.672921 −0.336460 0.941698i \(-0.609230\pi\)
−0.336460 + 0.941698i \(0.609230\pi\)
\(978\) 0 0
\(979\) −0.362450 −0.0115839
\(980\) 0 0
\(981\) −5.36014 −0.171136
\(982\) 0 0
\(983\) 2.56718 0.0818804 0.0409402 0.999162i \(-0.486965\pi\)
0.0409402 + 0.999162i \(0.486965\pi\)
\(984\) 0 0
\(985\) 0.631174 0.0201109
\(986\) 0 0
\(987\) −12.7672 −0.406385
\(988\) 0 0
\(989\) −19.2735 −0.612863
\(990\) 0 0
\(991\) 15.4055 0.489372 0.244686 0.969602i \(-0.421315\pi\)
0.244686 + 0.969602i \(0.421315\pi\)
\(992\) 0 0
\(993\) 40.1253 1.27334
\(994\) 0 0
\(995\) −4.95609 −0.157119
\(996\) 0 0
\(997\) −18.6797 −0.591593 −0.295797 0.955251i \(-0.595585\pi\)
−0.295797 + 0.955251i \(0.595585\pi\)
\(998\) 0 0
\(999\) 28.4503 0.900127
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.1.33 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.33 44 1.1 even 1 trivial