Properties

Label 4034.2.a.d.1.14
Level 4034
Weight 2
Character 4034.1
Self dual yes
Analytic conductor 32.212
Analytic rank 0
Dimension 52
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4034 = 2 \cdot 2017 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4034.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.2116521754\)
Analytic rank: \(0\)
Dimension: \(52\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 4034.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.45785 q^{3} +1.00000 q^{4} +0.272726 q^{5} -1.45785 q^{6} +4.58744 q^{7} +1.00000 q^{8} -0.874665 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.45785 q^{3} +1.00000 q^{4} +0.272726 q^{5} -1.45785 q^{6} +4.58744 q^{7} +1.00000 q^{8} -0.874665 q^{9} +0.272726 q^{10} -1.88209 q^{11} -1.45785 q^{12} -4.55484 q^{13} +4.58744 q^{14} -0.397594 q^{15} +1.00000 q^{16} -4.81630 q^{17} -0.874665 q^{18} +3.57600 q^{19} +0.272726 q^{20} -6.68782 q^{21} -1.88209 q^{22} +2.91478 q^{23} -1.45785 q^{24} -4.92562 q^{25} -4.55484 q^{26} +5.64869 q^{27} +4.58744 q^{28} +6.32421 q^{29} -0.397594 q^{30} +4.00085 q^{31} +1.00000 q^{32} +2.74381 q^{33} -4.81630 q^{34} +1.25111 q^{35} -0.874665 q^{36} +6.09247 q^{37} +3.57600 q^{38} +6.64029 q^{39} +0.272726 q^{40} +3.62123 q^{41} -6.68782 q^{42} +3.58714 q^{43} -1.88209 q^{44} -0.238544 q^{45} +2.91478 q^{46} +3.64602 q^{47} -1.45785 q^{48} +14.0446 q^{49} -4.92562 q^{50} +7.02146 q^{51} -4.55484 q^{52} -0.684641 q^{53} +5.64869 q^{54} -0.513295 q^{55} +4.58744 q^{56} -5.21328 q^{57} +6.32421 q^{58} +12.0566 q^{59} -0.397594 q^{60} -11.4376 q^{61} +4.00085 q^{62} -4.01248 q^{63} +1.00000 q^{64} -1.24222 q^{65} +2.74381 q^{66} +0.692854 q^{67} -4.81630 q^{68} -4.24932 q^{69} +1.25111 q^{70} -2.37181 q^{71} -0.874665 q^{72} +7.13870 q^{73} +6.09247 q^{74} +7.18083 q^{75} +3.57600 q^{76} -8.63398 q^{77} +6.64029 q^{78} +8.92250 q^{79} +0.272726 q^{80} -5.61097 q^{81} +3.62123 q^{82} +6.97015 q^{83} -6.68782 q^{84} -1.31353 q^{85} +3.58714 q^{86} -9.21976 q^{87} -1.88209 q^{88} -5.64258 q^{89} -0.238544 q^{90} -20.8951 q^{91} +2.91478 q^{92} -5.83265 q^{93} +3.64602 q^{94} +0.975267 q^{95} -1.45785 q^{96} +6.48014 q^{97} +14.0446 q^{98} +1.64620 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q + 52q^{2} + 16q^{3} + 52q^{4} + 24q^{5} + 16q^{6} + 12q^{7} + 52q^{8} + 70q^{9} + O(q^{10}) \) \( 52q + 52q^{2} + 16q^{3} + 52q^{4} + 24q^{5} + 16q^{6} + 12q^{7} + 52q^{8} + 70q^{9} + 24q^{10} + 19q^{11} + 16q^{12} + 27q^{13} + 12q^{14} + 5q^{15} + 52q^{16} + 43q^{17} + 70q^{18} + 35q^{19} + 24q^{20} + 29q^{21} + 19q^{22} + 2q^{23} + 16q^{24} + 88q^{25} + 27q^{26} + 49q^{27} + 12q^{28} + 31q^{29} + 5q^{30} + 59q^{31} + 52q^{32} + 45q^{33} + 43q^{34} + 18q^{35} + 70q^{36} + 60q^{37} + 35q^{38} + 6q^{39} + 24q^{40} + 56q^{41} + 29q^{42} + 34q^{43} + 19q^{44} + 61q^{45} + 2q^{46} - 4q^{47} + 16q^{48} + 102q^{49} + 88q^{50} + 23q^{51} + 27q^{52} + 30q^{53} + 49q^{54} + 24q^{55} + 12q^{56} + 32q^{57} + 31q^{58} + 27q^{59} + 5q^{60} + 107q^{61} + 59q^{62} - 4q^{63} + 52q^{64} + 46q^{65} + 45q^{66} + 22q^{67} + 43q^{68} + 36q^{69} + 18q^{70} + 8q^{71} + 70q^{72} + 66q^{73} + 60q^{74} + 53q^{75} + 35q^{76} + 26q^{77} + 6q^{78} + 50q^{79} + 24q^{80} + 108q^{81} + 56q^{82} + 52q^{83} + 29q^{84} + 19q^{85} + 34q^{86} - 32q^{87} + 19q^{88} + 62q^{89} + 61q^{90} + 69q^{91} + 2q^{92} + 21q^{93} - 4q^{94} - 44q^{95} + 16q^{96} + 82q^{97} + 102q^{98} + 16q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.45785 −0.841692 −0.420846 0.907132i \(-0.638267\pi\)
−0.420846 + 0.907132i \(0.638267\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.272726 0.121967 0.0609834 0.998139i \(-0.480576\pi\)
0.0609834 + 0.998139i \(0.480576\pi\)
\(6\) −1.45785 −0.595166
\(7\) 4.58744 1.73389 0.866945 0.498403i \(-0.166080\pi\)
0.866945 + 0.498403i \(0.166080\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.874665 −0.291555
\(10\) 0.272726 0.0862435
\(11\) −1.88209 −0.567472 −0.283736 0.958902i \(-0.591574\pi\)
−0.283736 + 0.958902i \(0.591574\pi\)
\(12\) −1.45785 −0.420846
\(13\) −4.55484 −1.26329 −0.631643 0.775260i \(-0.717619\pi\)
−0.631643 + 0.775260i \(0.717619\pi\)
\(14\) 4.58744 1.22605
\(15\) −0.397594 −0.102658
\(16\) 1.00000 0.250000
\(17\) −4.81630 −1.16812 −0.584062 0.811709i \(-0.698538\pi\)
−0.584062 + 0.811709i \(0.698538\pi\)
\(18\) −0.874665 −0.206161
\(19\) 3.57600 0.820390 0.410195 0.911998i \(-0.365461\pi\)
0.410195 + 0.911998i \(0.365461\pi\)
\(20\) 0.272726 0.0609834
\(21\) −6.68782 −1.45940
\(22\) −1.88209 −0.401263
\(23\) 2.91478 0.607774 0.303887 0.952708i \(-0.401715\pi\)
0.303887 + 0.952708i \(0.401715\pi\)
\(24\) −1.45785 −0.297583
\(25\) −4.92562 −0.985124
\(26\) −4.55484 −0.893278
\(27\) 5.64869 1.08709
\(28\) 4.58744 0.866945
\(29\) 6.32421 1.17438 0.587188 0.809451i \(-0.300235\pi\)
0.587188 + 0.809451i \(0.300235\pi\)
\(30\) −0.397594 −0.0725904
\(31\) 4.00085 0.718573 0.359287 0.933227i \(-0.383020\pi\)
0.359287 + 0.933227i \(0.383020\pi\)
\(32\) 1.00000 0.176777
\(33\) 2.74381 0.477636
\(34\) −4.81630 −0.825989
\(35\) 1.25111 0.211477
\(36\) −0.874665 −0.145778
\(37\) 6.09247 1.00160 0.500798 0.865564i \(-0.333040\pi\)
0.500798 + 0.865564i \(0.333040\pi\)
\(38\) 3.57600 0.580103
\(39\) 6.64029 1.06330
\(40\) 0.272726 0.0431217
\(41\) 3.62123 0.565542 0.282771 0.959187i \(-0.408746\pi\)
0.282771 + 0.959187i \(0.408746\pi\)
\(42\) −6.68782 −1.03195
\(43\) 3.58714 0.547033 0.273517 0.961867i \(-0.411813\pi\)
0.273517 + 0.961867i \(0.411813\pi\)
\(44\) −1.88209 −0.283736
\(45\) −0.238544 −0.0355600
\(46\) 2.91478 0.429761
\(47\) 3.64602 0.531826 0.265913 0.963997i \(-0.414327\pi\)
0.265913 + 0.963997i \(0.414327\pi\)
\(48\) −1.45785 −0.210423
\(49\) 14.0446 2.00638
\(50\) −4.92562 −0.696588
\(51\) 7.02146 0.983201
\(52\) −4.55484 −0.631643
\(53\) −0.684641 −0.0940427 −0.0470214 0.998894i \(-0.514973\pi\)
−0.0470214 + 0.998894i \(0.514973\pi\)
\(54\) 5.64869 0.768690
\(55\) −0.513295 −0.0692126
\(56\) 4.58744 0.613023
\(57\) −5.21328 −0.690515
\(58\) 6.32421 0.830409
\(59\) 12.0566 1.56963 0.784815 0.619730i \(-0.212758\pi\)
0.784815 + 0.619730i \(0.212758\pi\)
\(60\) −0.397594 −0.0513292
\(61\) −11.4376 −1.46443 −0.732214 0.681075i \(-0.761513\pi\)
−0.732214 + 0.681075i \(0.761513\pi\)
\(62\) 4.00085 0.508108
\(63\) −4.01248 −0.505524
\(64\) 1.00000 0.125000
\(65\) −1.24222 −0.154079
\(66\) 2.74381 0.337740
\(67\) 0.692854 0.0846456 0.0423228 0.999104i \(-0.486524\pi\)
0.0423228 + 0.999104i \(0.486524\pi\)
\(68\) −4.81630 −0.584062
\(69\) −4.24932 −0.511558
\(70\) 1.25111 0.149537
\(71\) −2.37181 −0.281481 −0.140741 0.990046i \(-0.544948\pi\)
−0.140741 + 0.990046i \(0.544948\pi\)
\(72\) −0.874665 −0.103080
\(73\) 7.13870 0.835522 0.417761 0.908557i \(-0.362815\pi\)
0.417761 + 0.908557i \(0.362815\pi\)
\(74\) 6.09247 0.708235
\(75\) 7.18083 0.829171
\(76\) 3.57600 0.410195
\(77\) −8.63398 −0.983934
\(78\) 6.64029 0.751865
\(79\) 8.92250 1.00386 0.501930 0.864908i \(-0.332623\pi\)
0.501930 + 0.864908i \(0.332623\pi\)
\(80\) 0.272726 0.0304917
\(81\) −5.61097 −0.623441
\(82\) 3.62123 0.399898
\(83\) 6.97015 0.765074 0.382537 0.923940i \(-0.375051\pi\)
0.382537 + 0.923940i \(0.375051\pi\)
\(84\) −6.68782 −0.729701
\(85\) −1.31353 −0.142472
\(86\) 3.58714 0.386811
\(87\) −9.21976 −0.988462
\(88\) −1.88209 −0.200632
\(89\) −5.64258 −0.598113 −0.299056 0.954235i \(-0.596672\pi\)
−0.299056 + 0.954235i \(0.596672\pi\)
\(90\) −0.238544 −0.0251447
\(91\) −20.8951 −2.19040
\(92\) 2.91478 0.303887
\(93\) −5.83265 −0.604817
\(94\) 3.64602 0.376058
\(95\) 0.975267 0.100060
\(96\) −1.45785 −0.148791
\(97\) 6.48014 0.657959 0.328979 0.944337i \(-0.393295\pi\)
0.328979 + 0.944337i \(0.393295\pi\)
\(98\) 14.0446 1.41872
\(99\) 1.64620 0.165449
\(100\) −4.92562 −0.492562
\(101\) 8.58012 0.853754 0.426877 0.904310i \(-0.359614\pi\)
0.426877 + 0.904310i \(0.359614\pi\)
\(102\) 7.02146 0.695228
\(103\) −3.22241 −0.317514 −0.158757 0.987318i \(-0.550749\pi\)
−0.158757 + 0.987318i \(0.550749\pi\)
\(104\) −4.55484 −0.446639
\(105\) −1.82394 −0.177998
\(106\) −0.684641 −0.0664982
\(107\) −2.60671 −0.252000 −0.126000 0.992030i \(-0.540214\pi\)
−0.126000 + 0.992030i \(0.540214\pi\)
\(108\) 5.64869 0.543546
\(109\) −5.81982 −0.557438 −0.278719 0.960373i \(-0.589910\pi\)
−0.278719 + 0.960373i \(0.589910\pi\)
\(110\) −0.513295 −0.0489407
\(111\) −8.88192 −0.843035
\(112\) 4.58744 0.433473
\(113\) −8.17856 −0.769375 −0.384687 0.923047i \(-0.625691\pi\)
−0.384687 + 0.923047i \(0.625691\pi\)
\(114\) −5.21328 −0.488268
\(115\) 0.794936 0.0741282
\(116\) 6.32421 0.587188
\(117\) 3.98396 0.368317
\(118\) 12.0566 1.10990
\(119\) −22.0945 −2.02540
\(120\) −0.397594 −0.0362952
\(121\) −7.45774 −0.677976
\(122\) −11.4376 −1.03551
\(123\) −5.27923 −0.476012
\(124\) 4.00085 0.359287
\(125\) −2.70697 −0.242119
\(126\) −4.01248 −0.357460
\(127\) 10.5022 0.931917 0.465958 0.884807i \(-0.345710\pi\)
0.465958 + 0.884807i \(0.345710\pi\)
\(128\) 1.00000 0.0883883
\(129\) −5.22952 −0.460434
\(130\) −1.24222 −0.108950
\(131\) 14.3205 1.25119 0.625595 0.780148i \(-0.284856\pi\)
0.625595 + 0.780148i \(0.284856\pi\)
\(132\) 2.74381 0.238818
\(133\) 16.4047 1.42247
\(134\) 0.692854 0.0598535
\(135\) 1.54054 0.132589
\(136\) −4.81630 −0.412995
\(137\) −8.86989 −0.757806 −0.378903 0.925436i \(-0.623699\pi\)
−0.378903 + 0.925436i \(0.623699\pi\)
\(138\) −4.24932 −0.361726
\(139\) 18.8865 1.60193 0.800964 0.598712i \(-0.204321\pi\)
0.800964 + 0.598712i \(0.204321\pi\)
\(140\) 1.25111 0.105738
\(141\) −5.31536 −0.447634
\(142\) −2.37181 −0.199037
\(143\) 8.57262 0.716879
\(144\) −0.874665 −0.0728888
\(145\) 1.72477 0.143235
\(146\) 7.13870 0.590803
\(147\) −20.4750 −1.68875
\(148\) 6.09247 0.500798
\(149\) −11.0950 −0.908936 −0.454468 0.890763i \(-0.650171\pi\)
−0.454468 + 0.890763i \(0.650171\pi\)
\(150\) 7.18083 0.586312
\(151\) 17.8872 1.45564 0.727821 0.685767i \(-0.240533\pi\)
0.727821 + 0.685767i \(0.240533\pi\)
\(152\) 3.57600 0.290052
\(153\) 4.21265 0.340573
\(154\) −8.63398 −0.695746
\(155\) 1.09113 0.0876420
\(156\) 6.64029 0.531649
\(157\) −13.4535 −1.07371 −0.536854 0.843675i \(-0.680388\pi\)
−0.536854 + 0.843675i \(0.680388\pi\)
\(158\) 8.92250 0.709836
\(159\) 0.998106 0.0791550
\(160\) 0.272726 0.0215609
\(161\) 13.3714 1.05381
\(162\) −5.61097 −0.440839
\(163\) 12.6837 0.993467 0.496733 0.867903i \(-0.334533\pi\)
0.496733 + 0.867903i \(0.334533\pi\)
\(164\) 3.62123 0.282771
\(165\) 0.748308 0.0582557
\(166\) 6.97015 0.540989
\(167\) −15.5279 −1.20159 −0.600793 0.799405i \(-0.705148\pi\)
−0.600793 + 0.799405i \(0.705148\pi\)
\(168\) −6.68782 −0.515976
\(169\) 7.74658 0.595891
\(170\) −1.31353 −0.100743
\(171\) −3.12780 −0.239189
\(172\) 3.58714 0.273517
\(173\) 19.7193 1.49923 0.749614 0.661876i \(-0.230239\pi\)
0.749614 + 0.661876i \(0.230239\pi\)
\(174\) −9.21976 −0.698949
\(175\) −22.5960 −1.70810
\(176\) −1.88209 −0.141868
\(177\) −17.5767 −1.32114
\(178\) −5.64258 −0.422930
\(179\) −6.74100 −0.503846 −0.251923 0.967747i \(-0.581063\pi\)
−0.251923 + 0.967747i \(0.581063\pi\)
\(180\) −0.238544 −0.0177800
\(181\) 7.20245 0.535354 0.267677 0.963509i \(-0.413744\pi\)
0.267677 + 0.963509i \(0.413744\pi\)
\(182\) −20.8951 −1.54885
\(183\) 16.6743 1.23260
\(184\) 2.91478 0.214881
\(185\) 1.66157 0.122161
\(186\) −5.83265 −0.427670
\(187\) 9.06472 0.662878
\(188\) 3.64602 0.265913
\(189\) 25.9131 1.88490
\(190\) 0.975267 0.0707533
\(191\) −7.02014 −0.507959 −0.253980 0.967210i \(-0.581740\pi\)
−0.253980 + 0.967210i \(0.581740\pi\)
\(192\) −1.45785 −0.105211
\(193\) −10.5912 −0.762370 −0.381185 0.924499i \(-0.624484\pi\)
−0.381185 + 0.924499i \(0.624484\pi\)
\(194\) 6.48014 0.465247
\(195\) 1.81098 0.129687
\(196\) 14.0446 1.00319
\(197\) 7.58015 0.540063 0.270032 0.962851i \(-0.412966\pi\)
0.270032 + 0.962851i \(0.412966\pi\)
\(198\) 1.64620 0.116990
\(199\) 18.3153 1.29834 0.649168 0.760645i \(-0.275117\pi\)
0.649168 + 0.760645i \(0.275117\pi\)
\(200\) −4.92562 −0.348294
\(201\) −1.01008 −0.0712455
\(202\) 8.58012 0.603695
\(203\) 29.0119 2.03624
\(204\) 7.02146 0.491601
\(205\) 0.987604 0.0689773
\(206\) −3.22241 −0.224516
\(207\) −2.54946 −0.177200
\(208\) −4.55484 −0.315821
\(209\) −6.73035 −0.465548
\(210\) −1.82394 −0.125864
\(211\) −3.91259 −0.269354 −0.134677 0.990890i \(-0.543000\pi\)
−0.134677 + 0.990890i \(0.543000\pi\)
\(212\) −0.684641 −0.0470214
\(213\) 3.45774 0.236921
\(214\) −2.60671 −0.178191
\(215\) 0.978305 0.0667199
\(216\) 5.64869 0.384345
\(217\) 18.3537 1.24593
\(218\) −5.81982 −0.394168
\(219\) −10.4072 −0.703252
\(220\) −0.513295 −0.0346063
\(221\) 21.9375 1.47568
\(222\) −8.88192 −0.596116
\(223\) −12.7908 −0.856536 −0.428268 0.903652i \(-0.640876\pi\)
−0.428268 + 0.903652i \(0.640876\pi\)
\(224\) 4.58744 0.306511
\(225\) 4.30827 0.287218
\(226\) −8.17856 −0.544030
\(227\) −24.4022 −1.61963 −0.809815 0.586686i \(-0.800432\pi\)
−0.809815 + 0.586686i \(0.800432\pi\)
\(228\) −5.21328 −0.345258
\(229\) 16.9084 1.11734 0.558668 0.829391i \(-0.311313\pi\)
0.558668 + 0.829391i \(0.311313\pi\)
\(230\) 0.794936 0.0524165
\(231\) 12.5871 0.828169
\(232\) 6.32421 0.415205
\(233\) 6.29988 0.412719 0.206360 0.978476i \(-0.433838\pi\)
0.206360 + 0.978476i \(0.433838\pi\)
\(234\) 3.98396 0.260440
\(235\) 0.994363 0.0648651
\(236\) 12.0566 0.784815
\(237\) −13.0077 −0.844941
\(238\) −22.0945 −1.43217
\(239\) 26.9213 1.74139 0.870696 0.491821i \(-0.163669\pi\)
0.870696 + 0.491821i \(0.163669\pi\)
\(240\) −0.397594 −0.0256646
\(241\) −1.72834 −0.111332 −0.0556661 0.998449i \(-0.517728\pi\)
−0.0556661 + 0.998449i \(0.517728\pi\)
\(242\) −7.45774 −0.479401
\(243\) −8.76611 −0.562346
\(244\) −11.4376 −0.732214
\(245\) 3.83034 0.244711
\(246\) −5.27923 −0.336591
\(247\) −16.2881 −1.03639
\(248\) 4.00085 0.254054
\(249\) −10.1615 −0.643956
\(250\) −2.70697 −0.171204
\(251\) 6.10643 0.385434 0.192717 0.981254i \(-0.438270\pi\)
0.192717 + 0.981254i \(0.438270\pi\)
\(252\) −4.01248 −0.252762
\(253\) −5.48588 −0.344894
\(254\) 10.5022 0.658965
\(255\) 1.91493 0.119918
\(256\) 1.00000 0.0625000
\(257\) 0.844669 0.0526890 0.0263445 0.999653i \(-0.491613\pi\)
0.0263445 + 0.999653i \(0.491613\pi\)
\(258\) −5.22952 −0.325576
\(259\) 27.9488 1.73666
\(260\) −1.24222 −0.0770394
\(261\) −5.53156 −0.342395
\(262\) 14.3205 0.884725
\(263\) −8.09836 −0.499366 −0.249683 0.968328i \(-0.580326\pi\)
−0.249683 + 0.968328i \(0.580326\pi\)
\(264\) 2.74381 0.168870
\(265\) −0.186719 −0.0114701
\(266\) 16.4047 1.00584
\(267\) 8.22606 0.503427
\(268\) 0.692854 0.0423228
\(269\) −10.5581 −0.643738 −0.321869 0.946784i \(-0.604311\pi\)
−0.321869 + 0.946784i \(0.604311\pi\)
\(270\) 1.54054 0.0937545
\(271\) −5.24362 −0.318527 −0.159264 0.987236i \(-0.550912\pi\)
−0.159264 + 0.987236i \(0.550912\pi\)
\(272\) −4.81630 −0.292031
\(273\) 30.4619 1.84364
\(274\) −8.86989 −0.535850
\(275\) 9.27046 0.559030
\(276\) −4.24932 −0.255779
\(277\) 15.5586 0.934828 0.467414 0.884039i \(-0.345186\pi\)
0.467414 + 0.884039i \(0.345186\pi\)
\(278\) 18.8865 1.13273
\(279\) −3.49940 −0.209504
\(280\) 1.25111 0.0747684
\(281\) −3.50481 −0.209079 −0.104540 0.994521i \(-0.533337\pi\)
−0.104540 + 0.994521i \(0.533337\pi\)
\(282\) −5.31536 −0.316525
\(283\) −8.93733 −0.531269 −0.265635 0.964074i \(-0.585581\pi\)
−0.265635 + 0.964074i \(0.585581\pi\)
\(284\) −2.37181 −0.140741
\(285\) −1.42180 −0.0842199
\(286\) 8.57262 0.506910
\(287\) 16.6122 0.980588
\(288\) −0.874665 −0.0515401
\(289\) 6.19677 0.364516
\(290\) 1.72477 0.101282
\(291\) −9.44709 −0.553798
\(292\) 7.13870 0.417761
\(293\) −2.23322 −0.130466 −0.0652330 0.997870i \(-0.520779\pi\)
−0.0652330 + 0.997870i \(0.520779\pi\)
\(294\) −20.4750 −1.19413
\(295\) 3.28813 0.191443
\(296\) 6.09247 0.354117
\(297\) −10.6313 −0.616893
\(298\) −11.0950 −0.642715
\(299\) −13.2764 −0.767792
\(300\) 7.18083 0.414585
\(301\) 16.4558 0.948496
\(302\) 17.8872 1.02929
\(303\) −12.5086 −0.718597
\(304\) 3.57600 0.205097
\(305\) −3.11932 −0.178611
\(306\) 4.21265 0.240821
\(307\) 19.8899 1.13518 0.567589 0.823312i \(-0.307876\pi\)
0.567589 + 0.823312i \(0.307876\pi\)
\(308\) −8.63398 −0.491967
\(309\) 4.69780 0.267249
\(310\) 1.09113 0.0619723
\(311\) −23.9249 −1.35665 −0.678327 0.734760i \(-0.737295\pi\)
−0.678327 + 0.734760i \(0.737295\pi\)
\(312\) 6.64029 0.375932
\(313\) −5.72885 −0.323814 −0.161907 0.986806i \(-0.551764\pi\)
−0.161907 + 0.986806i \(0.551764\pi\)
\(314\) −13.4535 −0.759227
\(315\) −1.09431 −0.0616572
\(316\) 8.92250 0.501930
\(317\) −34.0783 −1.91403 −0.957013 0.290044i \(-0.906330\pi\)
−0.957013 + 0.290044i \(0.906330\pi\)
\(318\) 0.998106 0.0559710
\(319\) −11.9027 −0.666425
\(320\) 0.272726 0.0152458
\(321\) 3.80020 0.212106
\(322\) 13.3714 0.745159
\(323\) −17.2231 −0.958318
\(324\) −5.61097 −0.311720
\(325\) 22.4354 1.24449
\(326\) 12.6837 0.702487
\(327\) 8.48444 0.469191
\(328\) 3.62123 0.199949
\(329\) 16.7259 0.922128
\(330\) 0.748308 0.0411930
\(331\) −20.6223 −1.13350 −0.566752 0.823889i \(-0.691800\pi\)
−0.566752 + 0.823889i \(0.691800\pi\)
\(332\) 6.97015 0.382537
\(333\) −5.32887 −0.292020
\(334\) −15.5279 −0.849650
\(335\) 0.188959 0.0103239
\(336\) −6.68782 −0.364850
\(337\) 21.3936 1.16538 0.582692 0.812693i \(-0.301999\pi\)
0.582692 + 0.812693i \(0.301999\pi\)
\(338\) 7.74658 0.421358
\(339\) 11.9231 0.647576
\(340\) −1.31353 −0.0712362
\(341\) −7.52996 −0.407770
\(342\) −3.12780 −0.169132
\(343\) 32.3169 1.74495
\(344\) 3.58714 0.193406
\(345\) −1.15890 −0.0623931
\(346\) 19.7193 1.06011
\(347\) −22.2924 −1.19672 −0.598359 0.801228i \(-0.704180\pi\)
−0.598359 + 0.801228i \(0.704180\pi\)
\(348\) −9.21976 −0.494231
\(349\) 29.7073 1.59019 0.795097 0.606482i \(-0.207420\pi\)
0.795097 + 0.606482i \(0.207420\pi\)
\(350\) −22.5960 −1.20781
\(351\) −25.7289 −1.37331
\(352\) −1.88209 −0.100316
\(353\) −13.8095 −0.735005 −0.367502 0.930023i \(-0.619787\pi\)
−0.367502 + 0.930023i \(0.619787\pi\)
\(354\) −17.5767 −0.934190
\(355\) −0.646853 −0.0343314
\(356\) −5.64258 −0.299056
\(357\) 32.2106 1.70476
\(358\) −6.74100 −0.356273
\(359\) 13.4255 0.708570 0.354285 0.935138i \(-0.384724\pi\)
0.354285 + 0.935138i \(0.384724\pi\)
\(360\) −0.238544 −0.0125724
\(361\) −6.21225 −0.326961
\(362\) 7.20245 0.378552
\(363\) 10.8723 0.570647
\(364\) −20.8951 −1.09520
\(365\) 1.94691 0.101906
\(366\) 16.6743 0.871578
\(367\) 33.6156 1.75472 0.877359 0.479834i \(-0.159303\pi\)
0.877359 + 0.479834i \(0.159303\pi\)
\(368\) 2.91478 0.151943
\(369\) −3.16737 −0.164887
\(370\) 1.66157 0.0863811
\(371\) −3.14075 −0.163060
\(372\) −5.83265 −0.302409
\(373\) 14.4484 0.748110 0.374055 0.927407i \(-0.377967\pi\)
0.374055 + 0.927407i \(0.377967\pi\)
\(374\) 9.06472 0.468725
\(375\) 3.94637 0.203790
\(376\) 3.64602 0.188029
\(377\) −28.8058 −1.48357
\(378\) 25.9131 1.33282
\(379\) 3.81403 0.195914 0.0979568 0.995191i \(-0.468769\pi\)
0.0979568 + 0.995191i \(0.468769\pi\)
\(380\) 0.975267 0.0500301
\(381\) −15.3106 −0.784387
\(382\) −7.02014 −0.359181
\(383\) 13.4704 0.688304 0.344152 0.938914i \(-0.388166\pi\)
0.344152 + 0.938914i \(0.388166\pi\)
\(384\) −1.45785 −0.0743957
\(385\) −2.35471 −0.120007
\(386\) −10.5912 −0.539077
\(387\) −3.13754 −0.159490
\(388\) 6.48014 0.328979
\(389\) 22.6974 1.15080 0.575401 0.817871i \(-0.304846\pi\)
0.575401 + 0.817871i \(0.304846\pi\)
\(390\) 1.81098 0.0917024
\(391\) −14.0385 −0.709956
\(392\) 14.0446 0.709361
\(393\) −20.8772 −1.05312
\(394\) 7.58015 0.381882
\(395\) 2.43340 0.122438
\(396\) 1.64620 0.0827246
\(397\) 35.3314 1.77323 0.886616 0.462506i \(-0.153050\pi\)
0.886616 + 0.462506i \(0.153050\pi\)
\(398\) 18.3153 0.918062
\(399\) −23.9156 −1.19728
\(400\) −4.92562 −0.246281
\(401\) 24.4662 1.22178 0.610892 0.791714i \(-0.290811\pi\)
0.610892 + 0.791714i \(0.290811\pi\)
\(402\) −1.01008 −0.0503782
\(403\) −18.2232 −0.907763
\(404\) 8.58012 0.426877
\(405\) −1.53026 −0.0760390
\(406\) 29.0119 1.43984
\(407\) −11.4666 −0.568377
\(408\) 7.02146 0.347614
\(409\) 2.13462 0.105550 0.0527752 0.998606i \(-0.483193\pi\)
0.0527752 + 0.998606i \(0.483193\pi\)
\(410\) 0.987604 0.0487743
\(411\) 12.9310 0.637839
\(412\) −3.22241 −0.158757
\(413\) 55.3088 2.72157
\(414\) −2.54946 −0.125299
\(415\) 1.90094 0.0933135
\(416\) −4.55484 −0.223319
\(417\) −27.5337 −1.34833
\(418\) −6.73035 −0.329192
\(419\) −13.2991 −0.649704 −0.324852 0.945765i \(-0.605314\pi\)
−0.324852 + 0.945765i \(0.605314\pi\)
\(420\) −1.82394 −0.0889992
\(421\) −16.4472 −0.801586 −0.400793 0.916169i \(-0.631265\pi\)
−0.400793 + 0.916169i \(0.631265\pi\)
\(422\) −3.91259 −0.190462
\(423\) −3.18904 −0.155057
\(424\) −0.684641 −0.0332491
\(425\) 23.7233 1.15075
\(426\) 3.45774 0.167528
\(427\) −52.4691 −2.53916
\(428\) −2.60671 −0.126000
\(429\) −12.4976 −0.603391
\(430\) 0.978305 0.0471781
\(431\) −38.1987 −1.83997 −0.919984 0.391957i \(-0.871798\pi\)
−0.919984 + 0.391957i \(0.871798\pi\)
\(432\) 5.64869 0.271773
\(433\) 33.8447 1.62647 0.813236 0.581934i \(-0.197704\pi\)
0.813236 + 0.581934i \(0.197704\pi\)
\(434\) 18.3537 0.881004
\(435\) −2.51447 −0.120560
\(436\) −5.81982 −0.278719
\(437\) 10.4232 0.498612
\(438\) −10.4072 −0.497274
\(439\) −8.27917 −0.395143 −0.197572 0.980288i \(-0.563305\pi\)
−0.197572 + 0.980288i \(0.563305\pi\)
\(440\) −0.513295 −0.0244704
\(441\) −12.2844 −0.584969
\(442\) 21.9375 1.04346
\(443\) −9.44031 −0.448523 −0.224261 0.974529i \(-0.571997\pi\)
−0.224261 + 0.974529i \(0.571997\pi\)
\(444\) −8.88192 −0.421517
\(445\) −1.53888 −0.0729498
\(446\) −12.7908 −0.605662
\(447\) 16.1748 0.765044
\(448\) 4.58744 0.216736
\(449\) −23.8641 −1.12622 −0.563109 0.826383i \(-0.690395\pi\)
−0.563109 + 0.826383i \(0.690395\pi\)
\(450\) 4.30827 0.203094
\(451\) −6.81549 −0.320929
\(452\) −8.17856 −0.384687
\(453\) −26.0770 −1.22520
\(454\) −24.4022 −1.14525
\(455\) −5.69863 −0.267156
\(456\) −5.21328 −0.244134
\(457\) 15.8047 0.739314 0.369657 0.929168i \(-0.379475\pi\)
0.369657 + 0.929168i \(0.379475\pi\)
\(458\) 16.9084 0.790076
\(459\) −27.2058 −1.26986
\(460\) 0.794936 0.0370641
\(461\) 31.9144 1.48640 0.743202 0.669067i \(-0.233306\pi\)
0.743202 + 0.669067i \(0.233306\pi\)
\(462\) 12.5871 0.585604
\(463\) 5.12251 0.238063 0.119032 0.992890i \(-0.462021\pi\)
0.119032 + 0.992890i \(0.462021\pi\)
\(464\) 6.32421 0.293594
\(465\) −1.59071 −0.0737676
\(466\) 6.29988 0.291836
\(467\) −27.3516 −1.26568 −0.632841 0.774282i \(-0.718111\pi\)
−0.632841 + 0.774282i \(0.718111\pi\)
\(468\) 3.98396 0.184159
\(469\) 3.17843 0.146766
\(470\) 0.994363 0.0458665
\(471\) 19.6133 0.903732
\(472\) 12.0566 0.554948
\(473\) −6.75132 −0.310426
\(474\) −13.0077 −0.597463
\(475\) −17.6140 −0.808186
\(476\) −22.0945 −1.01270
\(477\) 0.598832 0.0274186
\(478\) 26.9213 1.23135
\(479\) −38.1374 −1.74254 −0.871271 0.490802i \(-0.836704\pi\)
−0.871271 + 0.490802i \(0.836704\pi\)
\(480\) −0.397594 −0.0181476
\(481\) −27.7502 −1.26530
\(482\) −1.72834 −0.0787237
\(483\) −19.4935 −0.886986
\(484\) −7.45774 −0.338988
\(485\) 1.76730 0.0802490
\(486\) −8.76611 −0.397639
\(487\) −32.6262 −1.47843 −0.739217 0.673468i \(-0.764804\pi\)
−0.739217 + 0.673468i \(0.764804\pi\)
\(488\) −11.4376 −0.517754
\(489\) −18.4910 −0.836193
\(490\) 3.83034 0.173037
\(491\) 5.95061 0.268547 0.134274 0.990944i \(-0.457130\pi\)
0.134274 + 0.990944i \(0.457130\pi\)
\(492\) −5.27923 −0.238006
\(493\) −30.4593 −1.37182
\(494\) −16.2881 −0.732836
\(495\) 0.448961 0.0201793
\(496\) 4.00085 0.179643
\(497\) −10.8805 −0.488058
\(498\) −10.1615 −0.455346
\(499\) −40.3308 −1.80545 −0.902727 0.430213i \(-0.858438\pi\)
−0.902727 + 0.430213i \(0.858438\pi\)
\(500\) −2.70697 −0.121060
\(501\) 22.6374 1.01137
\(502\) 6.10643 0.272543
\(503\) −12.0073 −0.535377 −0.267689 0.963505i \(-0.586260\pi\)
−0.267689 + 0.963505i \(0.586260\pi\)
\(504\) −4.01248 −0.178730
\(505\) 2.34002 0.104130
\(506\) −5.48588 −0.243877
\(507\) −11.2934 −0.501556
\(508\) 10.5022 0.465958
\(509\) −39.2735 −1.74077 −0.870384 0.492374i \(-0.836129\pi\)
−0.870384 + 0.492374i \(0.836129\pi\)
\(510\) 1.91493 0.0847947
\(511\) 32.7484 1.44870
\(512\) 1.00000 0.0441942
\(513\) 20.1997 0.891839
\(514\) 0.844669 0.0372568
\(515\) −0.878835 −0.0387261
\(516\) −5.22952 −0.230217
\(517\) −6.86213 −0.301796
\(518\) 27.9488 1.22800
\(519\) −28.7478 −1.26189
\(520\) −1.24222 −0.0544751
\(521\) 4.30490 0.188601 0.0943005 0.995544i \(-0.469939\pi\)
0.0943005 + 0.995544i \(0.469939\pi\)
\(522\) −5.53156 −0.242110
\(523\) 1.68521 0.0736892 0.0368446 0.999321i \(-0.488269\pi\)
0.0368446 + 0.999321i \(0.488269\pi\)
\(524\) 14.3205 0.625595
\(525\) 32.9417 1.43769
\(526\) −8.09836 −0.353105
\(527\) −19.2693 −0.839384
\(528\) 2.74381 0.119409
\(529\) −14.5040 −0.630611
\(530\) −0.186719 −0.00811057
\(531\) −10.5454 −0.457633
\(532\) 16.4047 0.711233
\(533\) −16.4941 −0.714441
\(534\) 8.22606 0.355976
\(535\) −0.710917 −0.0307356
\(536\) 0.692854 0.0299267
\(537\) 9.82738 0.424083
\(538\) −10.5581 −0.455191
\(539\) −26.4333 −1.13856
\(540\) 1.54054 0.0662945
\(541\) 9.92954 0.426904 0.213452 0.976954i \(-0.431529\pi\)
0.213452 + 0.976954i \(0.431529\pi\)
\(542\) −5.24362 −0.225233
\(543\) −10.5001 −0.450603
\(544\) −4.81630 −0.206497
\(545\) −1.58722 −0.0679889
\(546\) 30.4619 1.30365
\(547\) −42.8561 −1.83239 −0.916197 0.400729i \(-0.868757\pi\)
−0.916197 + 0.400729i \(0.868757\pi\)
\(548\) −8.86989 −0.378903
\(549\) 10.0040 0.426961
\(550\) 9.27046 0.395294
\(551\) 22.6153 0.963446
\(552\) −4.24932 −0.180863
\(553\) 40.9315 1.74058
\(554\) 15.5586 0.661023
\(555\) −2.42233 −0.102822
\(556\) 18.8865 0.800964
\(557\) 2.54870 0.107992 0.0539960 0.998541i \(-0.482804\pi\)
0.0539960 + 0.998541i \(0.482804\pi\)
\(558\) −3.49940 −0.148141
\(559\) −16.3388 −0.691060
\(560\) 1.25111 0.0528692
\(561\) −13.2150 −0.557939
\(562\) −3.50481 −0.147841
\(563\) 21.4520 0.904093 0.452047 0.891994i \(-0.350694\pi\)
0.452047 + 0.891994i \(0.350694\pi\)
\(564\) −5.31536 −0.223817
\(565\) −2.23051 −0.0938381
\(566\) −8.93733 −0.375664
\(567\) −25.7400 −1.08098
\(568\) −2.37181 −0.0995187
\(569\) −26.9069 −1.12800 −0.563998 0.825776i \(-0.690738\pi\)
−0.563998 + 0.825776i \(0.690738\pi\)
\(570\) −1.42180 −0.0595524
\(571\) 18.6844 0.781917 0.390958 0.920408i \(-0.372144\pi\)
0.390958 + 0.920408i \(0.372144\pi\)
\(572\) 8.57262 0.358439
\(573\) 10.2343 0.427545
\(574\) 16.6122 0.693380
\(575\) −14.3571 −0.598733
\(576\) −0.874665 −0.0364444
\(577\) −12.0482 −0.501574 −0.250787 0.968042i \(-0.580689\pi\)
−0.250787 + 0.968042i \(0.580689\pi\)
\(578\) 6.19677 0.257752
\(579\) 15.4404 0.641681
\(580\) 1.72477 0.0716174
\(581\) 31.9752 1.32655
\(582\) −9.44709 −0.391594
\(583\) 1.28856 0.0533666
\(584\) 7.13870 0.295402
\(585\) 1.08653 0.0449224
\(586\) −2.23322 −0.0922534
\(587\) 31.6915 1.30805 0.654025 0.756473i \(-0.273079\pi\)
0.654025 + 0.756473i \(0.273079\pi\)
\(588\) −20.4750 −0.844375
\(589\) 14.3070 0.589510
\(590\) 3.28813 0.135370
\(591\) −11.0507 −0.454567
\(592\) 6.09247 0.250399
\(593\) −41.6109 −1.70876 −0.854378 0.519652i \(-0.826062\pi\)
−0.854378 + 0.519652i \(0.826062\pi\)
\(594\) −10.6313 −0.436209
\(595\) −6.02575 −0.247031
\(596\) −11.0950 −0.454468
\(597\) −26.7010 −1.09280
\(598\) −13.2764 −0.542911
\(599\) −39.8614 −1.62869 −0.814347 0.580378i \(-0.802905\pi\)
−0.814347 + 0.580378i \(0.802905\pi\)
\(600\) 7.18083 0.293156
\(601\) −16.5908 −0.676751 −0.338375 0.941011i \(-0.609877\pi\)
−0.338375 + 0.941011i \(0.609877\pi\)
\(602\) 16.4558 0.670688
\(603\) −0.606015 −0.0246789
\(604\) 17.8872 0.727821
\(605\) −2.03392 −0.0826905
\(606\) −12.5086 −0.508125
\(607\) −3.52190 −0.142949 −0.0714747 0.997442i \(-0.522771\pi\)
−0.0714747 + 0.997442i \(0.522771\pi\)
\(608\) 3.57600 0.145026
\(609\) −42.2951 −1.71389
\(610\) −3.11932 −0.126297
\(611\) −16.6070 −0.671848
\(612\) 4.21265 0.170286
\(613\) −19.5830 −0.790952 −0.395476 0.918476i \(-0.629420\pi\)
−0.395476 + 0.918476i \(0.629420\pi\)
\(614\) 19.8899 0.802692
\(615\) −1.43978 −0.0580576
\(616\) −8.63398 −0.347873
\(617\) −10.7978 −0.434703 −0.217352 0.976093i \(-0.569742\pi\)
−0.217352 + 0.976093i \(0.569742\pi\)
\(618\) 4.69780 0.188973
\(619\) −41.5303 −1.66924 −0.834621 0.550824i \(-0.814313\pi\)
−0.834621 + 0.550824i \(0.814313\pi\)
\(620\) 1.09113 0.0438210
\(621\) 16.4647 0.660706
\(622\) −23.9249 −0.959299
\(623\) −25.8850 −1.03706
\(624\) 6.64029 0.265824
\(625\) 23.8898 0.955594
\(626\) −5.72885 −0.228971
\(627\) 9.81186 0.391848
\(628\) −13.4535 −0.536854
\(629\) −29.3432 −1.16999
\(630\) −1.09431 −0.0435982
\(631\) 10.6832 0.425292 0.212646 0.977129i \(-0.431792\pi\)
0.212646 + 0.977129i \(0.431792\pi\)
\(632\) 8.92250 0.354918
\(633\) 5.70398 0.226713
\(634\) −34.0783 −1.35342
\(635\) 2.86421 0.113663
\(636\) 0.998106 0.0395775
\(637\) −63.9711 −2.53463
\(638\) −11.9027 −0.471234
\(639\) 2.07453 0.0820673
\(640\) 0.272726 0.0107804
\(641\) −36.0857 −1.42530 −0.712650 0.701520i \(-0.752505\pi\)
−0.712650 + 0.701520i \(0.752505\pi\)
\(642\) 3.80020 0.149982
\(643\) 40.2987 1.58923 0.794613 0.607116i \(-0.207674\pi\)
0.794613 + 0.607116i \(0.207674\pi\)
\(644\) 13.3714 0.526907
\(645\) −1.42623 −0.0561576
\(646\) −17.2231 −0.677633
\(647\) 21.3984 0.841257 0.420629 0.907233i \(-0.361810\pi\)
0.420629 + 0.907233i \(0.361810\pi\)
\(648\) −5.61097 −0.220420
\(649\) −22.6915 −0.890720
\(650\) 22.4354 0.879990
\(651\) −26.7569 −1.04869
\(652\) 12.6837 0.496733
\(653\) −10.2723 −0.401986 −0.200993 0.979593i \(-0.564417\pi\)
−0.200993 + 0.979593i \(0.564417\pi\)
\(654\) 8.48444 0.331768
\(655\) 3.90558 0.152604
\(656\) 3.62123 0.141385
\(657\) −6.24397 −0.243601
\(658\) 16.7259 0.652043
\(659\) 18.9604 0.738592 0.369296 0.929312i \(-0.379599\pi\)
0.369296 + 0.929312i \(0.379599\pi\)
\(660\) 0.748308 0.0291279
\(661\) 28.9784 1.12713 0.563564 0.826072i \(-0.309430\pi\)
0.563564 + 0.826072i \(0.309430\pi\)
\(662\) −20.6223 −0.801508
\(663\) −31.9816 −1.24206
\(664\) 6.97015 0.270494
\(665\) 4.47398 0.173494
\(666\) −5.32887 −0.206489
\(667\) 18.4337 0.713755
\(668\) −15.5279 −0.600793
\(669\) 18.6471 0.720939
\(670\) 0.188959 0.00730013
\(671\) 21.5265 0.831021
\(672\) −6.68782 −0.257988
\(673\) 4.61859 0.178034 0.0890168 0.996030i \(-0.471628\pi\)
0.0890168 + 0.996030i \(0.471628\pi\)
\(674\) 21.3936 0.824051
\(675\) −27.8233 −1.07092
\(676\) 7.74658 0.297945
\(677\) 31.4416 1.20840 0.604200 0.796833i \(-0.293493\pi\)
0.604200 + 0.796833i \(0.293493\pi\)
\(678\) 11.9231 0.457906
\(679\) 29.7273 1.14083
\(680\) −1.31353 −0.0503716
\(681\) 35.5748 1.36323
\(682\) −7.52996 −0.288337
\(683\) 38.7254 1.48179 0.740893 0.671623i \(-0.234402\pi\)
0.740893 + 0.671623i \(0.234402\pi\)
\(684\) −3.12780 −0.119594
\(685\) −2.41905 −0.0924271
\(686\) 32.3169 1.23386
\(687\) −24.6499 −0.940453
\(688\) 3.58714 0.136758
\(689\) 3.11843 0.118803
\(690\) −1.15890 −0.0441186
\(691\) 30.0841 1.14445 0.572227 0.820095i \(-0.306080\pi\)
0.572227 + 0.820095i \(0.306080\pi\)
\(692\) 19.7193 0.749614
\(693\) 7.55184 0.286871
\(694\) −22.2924 −0.846207
\(695\) 5.15082 0.195382
\(696\) −9.21976 −0.349474
\(697\) −17.4410 −0.660624
\(698\) 29.7073 1.12444
\(699\) −9.18430 −0.347382
\(700\) −22.5960 −0.854049
\(701\) −25.0157 −0.944831 −0.472415 0.881376i \(-0.656618\pi\)
−0.472415 + 0.881376i \(0.656618\pi\)
\(702\) −25.7289 −0.971074
\(703\) 21.7866 0.821699
\(704\) −1.88209 −0.0709339
\(705\) −1.44963 −0.0545964
\(706\) −13.8095 −0.519727
\(707\) 39.3608 1.48032
\(708\) −17.5767 −0.660572
\(709\) 8.28621 0.311195 0.155598 0.987821i \(-0.450270\pi\)
0.155598 + 0.987821i \(0.450270\pi\)
\(710\) −0.646853 −0.0242759
\(711\) −7.80420 −0.292680
\(712\) −5.64258 −0.211465
\(713\) 11.6616 0.436730
\(714\) 32.2106 1.20545
\(715\) 2.33798 0.0874353
\(716\) −6.74100 −0.251923
\(717\) −39.2473 −1.46572
\(718\) 13.4255 0.501035
\(719\) 45.2588 1.68787 0.843933 0.536448i \(-0.180234\pi\)
0.843933 + 0.536448i \(0.180234\pi\)
\(720\) −0.238544 −0.00889000
\(721\) −14.7826 −0.550534
\(722\) −6.21225 −0.231196
\(723\) 2.51967 0.0937074
\(724\) 7.20245 0.267677
\(725\) −31.1506 −1.15691
\(726\) 10.8723 0.403508
\(727\) −47.8798 −1.77576 −0.887882 0.460072i \(-0.847824\pi\)
−0.887882 + 0.460072i \(0.847824\pi\)
\(728\) −20.8951 −0.774423
\(729\) 29.6126 1.09676
\(730\) 1.94691 0.0720583
\(731\) −17.2767 −0.639003
\(732\) 16.6743 0.616299
\(733\) 16.6669 0.615605 0.307803 0.951450i \(-0.400406\pi\)
0.307803 + 0.951450i \(0.400406\pi\)
\(734\) 33.6156 1.24077
\(735\) −5.58407 −0.205971
\(736\) 2.91478 0.107440
\(737\) −1.30401 −0.0480340
\(738\) −3.16737 −0.116592
\(739\) 20.2131 0.743552 0.371776 0.928323i \(-0.378749\pi\)
0.371776 + 0.928323i \(0.378749\pi\)
\(740\) 1.66157 0.0610807
\(741\) 23.7456 0.872318
\(742\) −3.14075 −0.115301
\(743\) 16.8568 0.618416 0.309208 0.950994i \(-0.399936\pi\)
0.309208 + 0.950994i \(0.399936\pi\)
\(744\) −5.83265 −0.213835
\(745\) −3.02589 −0.110860
\(746\) 14.4484 0.528993
\(747\) −6.09655 −0.223061
\(748\) 9.06472 0.331439
\(749\) −11.9581 −0.436941
\(750\) 3.94637 0.144101
\(751\) 11.6969 0.426824 0.213412 0.976962i \(-0.431542\pi\)
0.213412 + 0.976962i \(0.431542\pi\)
\(752\) 3.64602 0.132957
\(753\) −8.90227 −0.324417
\(754\) −28.8058 −1.04904
\(755\) 4.87831 0.177540
\(756\) 25.9131 0.942449
\(757\) 54.2544 1.97191 0.985954 0.167016i \(-0.0534133\pi\)
0.985954 + 0.167016i \(0.0534133\pi\)
\(758\) 3.81403 0.138532
\(759\) 7.99761 0.290295
\(760\) 0.975267 0.0353766
\(761\) −20.5485 −0.744884 −0.372442 0.928056i \(-0.621479\pi\)
−0.372442 + 0.928056i \(0.621479\pi\)
\(762\) −15.3106 −0.554645
\(763\) −26.6981 −0.966536
\(764\) −7.02014 −0.253980
\(765\) 1.14890 0.0415385
\(766\) 13.4704 0.486704
\(767\) −54.9157 −1.98289
\(768\) −1.45785 −0.0526057
\(769\) −13.9108 −0.501635 −0.250818 0.968034i \(-0.580699\pi\)
−0.250818 + 0.968034i \(0.580699\pi\)
\(770\) −2.35471 −0.0848579
\(771\) −1.23140 −0.0443479
\(772\) −10.5912 −0.381185
\(773\) −20.7907 −0.747790 −0.373895 0.927471i \(-0.621978\pi\)
−0.373895 + 0.927471i \(0.621978\pi\)
\(774\) −3.13754 −0.112777
\(775\) −19.7067 −0.707884
\(776\) 6.48014 0.232623
\(777\) −40.7453 −1.46173
\(778\) 22.6974 0.813740
\(779\) 12.9495 0.463965
\(780\) 1.81098 0.0648434
\(781\) 4.46395 0.159733
\(782\) −14.0385 −0.502015
\(783\) 35.7235 1.27665
\(784\) 14.0446 0.501594
\(785\) −3.66913 −0.130957
\(786\) −20.8772 −0.744666
\(787\) −33.3231 −1.18784 −0.593920 0.804524i \(-0.702421\pi\)
−0.593920 + 0.804524i \(0.702421\pi\)
\(788\) 7.58015 0.270032
\(789\) 11.8062 0.420312
\(790\) 2.43340 0.0865764
\(791\) −37.5187 −1.33401
\(792\) 1.64620 0.0584951
\(793\) 52.0962 1.84999
\(794\) 35.3314 1.25386
\(795\) 0.272209 0.00965427
\(796\) 18.3153 0.649168
\(797\) −36.4468 −1.29101 −0.645507 0.763755i \(-0.723354\pi\)
−0.645507 + 0.763755i \(0.723354\pi\)
\(798\) −23.9156 −0.846603
\(799\) −17.5603 −0.621239
\(800\) −4.92562 −0.174147
\(801\) 4.93537 0.174383
\(802\) 24.4662 0.863932
\(803\) −13.4357 −0.474135
\(804\) −1.01008 −0.0356228
\(805\) 3.64673 0.128530
\(806\) −18.2232 −0.641886
\(807\) 15.3921 0.541829
\(808\) 8.58012 0.301848
\(809\) −8.85480 −0.311318 −0.155659 0.987811i \(-0.549750\pi\)
−0.155659 + 0.987811i \(0.549750\pi\)
\(810\) −1.53026 −0.0537677
\(811\) 3.57581 0.125564 0.0627818 0.998027i \(-0.480003\pi\)
0.0627818 + 0.998027i \(0.480003\pi\)
\(812\) 29.0119 1.01812
\(813\) 7.64443 0.268102
\(814\) −11.4666 −0.401903
\(815\) 3.45918 0.121170
\(816\) 7.02146 0.245800
\(817\) 12.8276 0.448781
\(818\) 2.13462 0.0746354
\(819\) 18.2762 0.638622
\(820\) 0.987604 0.0344886
\(821\) 15.5800 0.543745 0.271873 0.962333i \(-0.412357\pi\)
0.271873 + 0.962333i \(0.412357\pi\)
\(822\) 12.9310 0.451020
\(823\) −21.7041 −0.756559 −0.378279 0.925691i \(-0.623484\pi\)
−0.378279 + 0.925691i \(0.623484\pi\)
\(824\) −3.22241 −0.112258
\(825\) −13.5150 −0.470531
\(826\) 55.3088 1.92444
\(827\) 20.2410 0.703848 0.351924 0.936029i \(-0.385528\pi\)
0.351924 + 0.936029i \(0.385528\pi\)
\(828\) −2.54946 −0.0885998
\(829\) 18.6382 0.647331 0.323666 0.946172i \(-0.395085\pi\)
0.323666 + 0.946172i \(0.395085\pi\)
\(830\) 1.90094 0.0659826
\(831\) −22.6822 −0.786837
\(832\) −4.55484 −0.157911
\(833\) −67.6432 −2.34370
\(834\) −27.5337 −0.953413
\(835\) −4.23486 −0.146554
\(836\) −6.73035 −0.232774
\(837\) 22.5996 0.781155
\(838\) −13.2991 −0.459410
\(839\) −22.1060 −0.763183 −0.381591 0.924331i \(-0.624624\pi\)
−0.381591 + 0.924331i \(0.624624\pi\)
\(840\) −1.82394 −0.0629319
\(841\) 10.9956 0.379159
\(842\) −16.4472 −0.566807
\(843\) 5.10949 0.175980
\(844\) −3.91259 −0.134677
\(845\) 2.11269 0.0726788
\(846\) −3.18904 −0.109642
\(847\) −34.2119 −1.17554
\(848\) −0.684641 −0.0235107
\(849\) 13.0293 0.447165
\(850\) 23.7233 0.813702
\(851\) 17.7582 0.608744
\(852\) 3.45774 0.118460
\(853\) −26.6607 −0.912844 −0.456422 0.889764i \(-0.650869\pi\)
−0.456422 + 0.889764i \(0.650869\pi\)
\(854\) −52.4691 −1.79546
\(855\) −0.853032 −0.0291731
\(856\) −2.60671 −0.0890955
\(857\) −22.2750 −0.760898 −0.380449 0.924802i \(-0.624231\pi\)
−0.380449 + 0.924802i \(0.624231\pi\)
\(858\) −12.4976 −0.426662
\(859\) −33.6768 −1.14904 −0.574519 0.818491i \(-0.694811\pi\)
−0.574519 + 0.818491i \(0.694811\pi\)
\(860\) 0.978305 0.0333599
\(861\) −24.2182 −0.825353
\(862\) −38.1987 −1.30105
\(863\) 21.4571 0.730408 0.365204 0.930928i \(-0.380999\pi\)
0.365204 + 0.930928i \(0.380999\pi\)
\(864\) 5.64869 0.192172
\(865\) 5.37795 0.182856
\(866\) 33.8447 1.15009
\(867\) −9.03398 −0.306810
\(868\) 18.3537 0.622964
\(869\) −16.7930 −0.569662
\(870\) −2.51447 −0.0852484
\(871\) −3.15584 −0.106932
\(872\) −5.81982 −0.197084
\(873\) −5.66795 −0.191831
\(874\) 10.4232 0.352572
\(875\) −12.4181 −0.419808
\(876\) −10.4072 −0.351626
\(877\) 32.9314 1.11201 0.556007 0.831177i \(-0.312333\pi\)
0.556007 + 0.831177i \(0.312333\pi\)
\(878\) −8.27917 −0.279408
\(879\) 3.25570 0.109812
\(880\) −0.513295 −0.0173032
\(881\) −16.8413 −0.567397 −0.283698 0.958914i \(-0.591561\pi\)
−0.283698 + 0.958914i \(0.591561\pi\)
\(882\) −12.2844 −0.413636
\(883\) 5.55649 0.186991 0.0934953 0.995620i \(-0.470196\pi\)
0.0934953 + 0.995620i \(0.470196\pi\)
\(884\) 21.9375 0.737838
\(885\) −4.79362 −0.161136
\(886\) −9.44031 −0.317153
\(887\) −8.27433 −0.277825 −0.138912 0.990305i \(-0.544361\pi\)
−0.138912 + 0.990305i \(0.544361\pi\)
\(888\) −8.88192 −0.298058
\(889\) 48.1781 1.61584
\(890\) −1.53888 −0.0515833
\(891\) 10.5603 0.353785
\(892\) −12.7908 −0.428268
\(893\) 13.0381 0.436305
\(894\) 16.1748 0.540968
\(895\) −1.83844 −0.0614524
\(896\) 4.58744 0.153256
\(897\) 19.3550 0.646244
\(898\) −23.8641 −0.796356
\(899\) 25.3022 0.843875
\(900\) 4.30827 0.143609
\(901\) 3.29744 0.109854
\(902\) −6.81549 −0.226931
\(903\) −23.9901 −0.798341
\(904\) −8.17856 −0.272015
\(905\) 1.96429 0.0652953
\(906\) −26.0770 −0.866349
\(907\) −0.489746 −0.0162617 −0.00813087 0.999967i \(-0.502588\pi\)
−0.00813087 + 0.999967i \(0.502588\pi\)
\(908\) −24.4022 −0.809815
\(909\) −7.50473 −0.248916
\(910\) −5.69863 −0.188908
\(911\) 8.68182 0.287642 0.143821 0.989604i \(-0.454061\pi\)
0.143821 + 0.989604i \(0.454061\pi\)
\(912\) −5.21328 −0.172629
\(913\) −13.1185 −0.434157
\(914\) 15.8047 0.522774
\(915\) 4.54750 0.150336
\(916\) 16.9084 0.558668
\(917\) 65.6946 2.16943
\(918\) −27.2058 −0.897925
\(919\) −22.5601 −0.744187 −0.372094 0.928195i \(-0.621360\pi\)
−0.372094 + 0.928195i \(0.621360\pi\)
\(920\) 0.794936 0.0262083
\(921\) −28.9966 −0.955470
\(922\) 31.9144 1.05105
\(923\) 10.8032 0.355592
\(924\) 12.5871 0.414084
\(925\) −30.0092 −0.986696
\(926\) 5.12251 0.168336
\(927\) 2.81853 0.0925727
\(928\) 6.32421 0.207602
\(929\) −24.9243 −0.817738 −0.408869 0.912593i \(-0.634077\pi\)
−0.408869 + 0.912593i \(0.634077\pi\)
\(930\) −1.59071 −0.0521616
\(931\) 50.2236 1.64601
\(932\) 6.29988 0.206360
\(933\) 34.8789 1.14188
\(934\) −27.3516 −0.894972
\(935\) 2.47218 0.0808490
\(936\) 3.98396 0.130220
\(937\) 1.56449 0.0511097 0.0255548 0.999673i \(-0.491865\pi\)
0.0255548 + 0.999673i \(0.491865\pi\)
\(938\) 3.17843 0.103779
\(939\) 8.35183 0.272552
\(940\) 0.994363 0.0324325
\(941\) 50.4348 1.64413 0.822065 0.569394i \(-0.192822\pi\)
0.822065 + 0.569394i \(0.192822\pi\)
\(942\) 19.6133 0.639035
\(943\) 10.5551 0.343722
\(944\) 12.0566 0.392407
\(945\) 7.06716 0.229895
\(946\) −6.75132 −0.219504
\(947\) 15.3263 0.498037 0.249018 0.968499i \(-0.419892\pi\)
0.249018 + 0.968499i \(0.419892\pi\)
\(948\) −13.0077 −0.422470
\(949\) −32.5157 −1.05550
\(950\) −17.6140 −0.571474
\(951\) 49.6811 1.61102
\(952\) −22.0945 −0.716087
\(953\) −32.2732 −1.04543 −0.522715 0.852507i \(-0.675081\pi\)
−0.522715 + 0.852507i \(0.675081\pi\)
\(954\) 0.598832 0.0193879
\(955\) −1.91457 −0.0619541
\(956\) 26.9213 0.870696
\(957\) 17.3524 0.560924
\(958\) −38.1374 −1.23216
\(959\) −40.6901 −1.31395
\(960\) −0.397594 −0.0128323
\(961\) −14.9932 −0.483652
\(962\) −27.7502 −0.894703
\(963\) 2.28000 0.0734719
\(964\) −1.72834 −0.0556661
\(965\) −2.88849 −0.0929838
\(966\) −19.4935 −0.627194
\(967\) −30.7470 −0.988756 −0.494378 0.869247i \(-0.664604\pi\)
−0.494378 + 0.869247i \(0.664604\pi\)
\(968\) −7.45774 −0.239701
\(969\) 25.1087 0.806608
\(970\) 1.76730 0.0567446
\(971\) −1.62463 −0.0521368 −0.0260684 0.999660i \(-0.508299\pi\)
−0.0260684 + 0.999660i \(0.508299\pi\)
\(972\) −8.76611 −0.281173
\(973\) 86.6405 2.77757
\(974\) −32.6262 −1.04541
\(975\) −32.7075 −1.04748
\(976\) −11.4376 −0.366107
\(977\) −20.0462 −0.641334 −0.320667 0.947192i \(-0.603907\pi\)
−0.320667 + 0.947192i \(0.603907\pi\)
\(978\) −18.4910 −0.591278
\(979\) 10.6199 0.339412
\(980\) 3.83034 0.122356
\(981\) 5.09039 0.162524
\(982\) 5.95061 0.189892
\(983\) 11.1380 0.355247 0.177624 0.984098i \(-0.443159\pi\)
0.177624 + 0.984098i \(0.443159\pi\)
\(984\) −5.27923 −0.168296
\(985\) 2.06730 0.0658697
\(986\) −30.4593 −0.970022
\(987\) −24.3839 −0.776148
\(988\) −16.2881 −0.518193
\(989\) 10.4557 0.332473
\(990\) 0.448961 0.0142689
\(991\) 45.3052 1.43917 0.719584 0.694406i \(-0.244333\pi\)
0.719584 + 0.694406i \(0.244333\pi\)
\(992\) 4.00085 0.127027
\(993\) 30.0642 0.954060
\(994\) −10.8805 −0.345109
\(995\) 4.99505 0.158354
\(996\) −10.1615 −0.321978
\(997\) 38.0287 1.20438 0.602190 0.798352i \(-0.294295\pi\)
0.602190 + 0.798352i \(0.294295\pi\)
\(998\) −40.3308 −1.27665
\(999\) 34.4145 1.08883
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 4034.2.a.d.1.14 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4034.2.a.d.1.14 52 1.1 even 1 trivial