Properties

Label 8007.2.a.f.1.25
Level 8007
Weight 2
Character 8007.1
Self dual yes
Analytic conductor 63.936
Analytic rank 1
Dimension 48
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(48\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.25
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.0687697 q^{2} -1.00000 q^{3} -1.99527 q^{4} +0.966871 q^{5} -0.0687697 q^{6} +0.824977 q^{7} -0.274754 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.0687697 q^{2} -1.00000 q^{3} -1.99527 q^{4} +0.966871 q^{5} -0.0687697 q^{6} +0.824977 q^{7} -0.274754 q^{8} +1.00000 q^{9} +0.0664914 q^{10} +2.54836 q^{11} +1.99527 q^{12} -0.576726 q^{13} +0.0567334 q^{14} -0.966871 q^{15} +3.97165 q^{16} -1.00000 q^{17} +0.0687697 q^{18} +3.08913 q^{19} -1.92917 q^{20} -0.824977 q^{21} +0.175250 q^{22} -2.04623 q^{23} +0.274754 q^{24} -4.06516 q^{25} -0.0396613 q^{26} -1.00000 q^{27} -1.64605 q^{28} +2.52229 q^{29} -0.0664914 q^{30} -6.07647 q^{31} +0.822636 q^{32} -2.54836 q^{33} -0.0687697 q^{34} +0.797646 q^{35} -1.99527 q^{36} -5.31637 q^{37} +0.212438 q^{38} +0.576726 q^{39} -0.265651 q^{40} +3.31387 q^{41} -0.0567334 q^{42} +4.06976 q^{43} -5.08466 q^{44} +0.966871 q^{45} -0.140718 q^{46} -6.63993 q^{47} -3.97165 q^{48} -6.31941 q^{49} -0.279560 q^{50} +1.00000 q^{51} +1.15073 q^{52} -10.1015 q^{53} -0.0687697 q^{54} +2.46393 q^{55} -0.226665 q^{56} -3.08913 q^{57} +0.173457 q^{58} -10.1129 q^{59} +1.92917 q^{60} +3.84193 q^{61} -0.417877 q^{62} +0.824977 q^{63} -7.88672 q^{64} -0.557620 q^{65} -0.175250 q^{66} +12.8564 q^{67} +1.99527 q^{68} +2.04623 q^{69} +0.0548539 q^{70} +6.40860 q^{71} -0.274754 q^{72} +10.2174 q^{73} -0.365605 q^{74} +4.06516 q^{75} -6.16365 q^{76} +2.10234 q^{77} +0.0396613 q^{78} -2.90388 q^{79} +3.84007 q^{80} +1.00000 q^{81} +0.227894 q^{82} -3.83473 q^{83} +1.64605 q^{84} -0.966871 q^{85} +0.279876 q^{86} -2.52229 q^{87} -0.700170 q^{88} +16.7151 q^{89} +0.0664914 q^{90} -0.475786 q^{91} +4.08278 q^{92} +6.07647 q^{93} -0.456626 q^{94} +2.98679 q^{95} -0.822636 q^{96} -4.28099 q^{97} -0.434584 q^{98} +2.54836 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0687697 0.0486275 0.0243138 0.999704i \(-0.492260\pi\)
0.0243138 + 0.999704i \(0.492260\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.99527 −0.997635
\(5\) 0.966871 0.432398 0.216199 0.976349i \(-0.430634\pi\)
0.216199 + 0.976349i \(0.430634\pi\)
\(6\) −0.0687697 −0.0280751
\(7\) 0.824977 0.311812 0.155906 0.987772i \(-0.450170\pi\)
0.155906 + 0.987772i \(0.450170\pi\)
\(8\) −0.274754 −0.0971400
\(9\) 1.00000 0.333333
\(10\) 0.0664914 0.0210264
\(11\) 2.54836 0.768359 0.384179 0.923259i \(-0.374484\pi\)
0.384179 + 0.923259i \(0.374484\pi\)
\(12\) 1.99527 0.575985
\(13\) −0.576726 −0.159955 −0.0799775 0.996797i \(-0.525485\pi\)
−0.0799775 + 0.996797i \(0.525485\pi\)
\(14\) 0.0567334 0.0151626
\(15\) −0.966871 −0.249645
\(16\) 3.97165 0.992912
\(17\) −1.00000 −0.242536
\(18\) 0.0687697 0.0162092
\(19\) 3.08913 0.708695 0.354347 0.935114i \(-0.384703\pi\)
0.354347 + 0.935114i \(0.384703\pi\)
\(20\) −1.92917 −0.431375
\(21\) −0.824977 −0.180025
\(22\) 0.175250 0.0373634
\(23\) −2.04623 −0.426668 −0.213334 0.976979i \(-0.568432\pi\)
−0.213334 + 0.976979i \(0.568432\pi\)
\(24\) 0.274754 0.0560838
\(25\) −4.06516 −0.813032
\(26\) −0.0396613 −0.00777822
\(27\) −1.00000 −0.192450
\(28\) −1.64605 −0.311075
\(29\) 2.52229 0.468377 0.234189 0.972191i \(-0.424757\pi\)
0.234189 + 0.972191i \(0.424757\pi\)
\(30\) −0.0664914 −0.0121396
\(31\) −6.07647 −1.09137 −0.545683 0.837992i \(-0.683730\pi\)
−0.545683 + 0.837992i \(0.683730\pi\)
\(32\) 0.822636 0.145423
\(33\) −2.54836 −0.443612
\(34\) −0.0687697 −0.0117939
\(35\) 0.797646 0.134827
\(36\) −1.99527 −0.332545
\(37\) −5.31637 −0.874005 −0.437003 0.899460i \(-0.643960\pi\)
−0.437003 + 0.899460i \(0.643960\pi\)
\(38\) 0.212438 0.0344621
\(39\) 0.576726 0.0923501
\(40\) −0.265651 −0.0420031
\(41\) 3.31387 0.517540 0.258770 0.965939i \(-0.416683\pi\)
0.258770 + 0.965939i \(0.416683\pi\)
\(42\) −0.0567334 −0.00875416
\(43\) 4.06976 0.620632 0.310316 0.950633i \(-0.399565\pi\)
0.310316 + 0.950633i \(0.399565\pi\)
\(44\) −5.08466 −0.766542
\(45\) 0.966871 0.144133
\(46\) −0.140718 −0.0207478
\(47\) −6.63993 −0.968533 −0.484266 0.874921i \(-0.660913\pi\)
−0.484266 + 0.874921i \(0.660913\pi\)
\(48\) −3.97165 −0.573258
\(49\) −6.31941 −0.902773
\(50\) −0.279560 −0.0395357
\(51\) 1.00000 0.140028
\(52\) 1.15073 0.159577
\(53\) −10.1015 −1.38755 −0.693777 0.720190i \(-0.744055\pi\)
−0.693777 + 0.720190i \(0.744055\pi\)
\(54\) −0.0687697 −0.00935837
\(55\) 2.46393 0.332236
\(56\) −0.226665 −0.0302894
\(57\) −3.08913 −0.409165
\(58\) 0.173457 0.0227760
\(59\) −10.1129 −1.31659 −0.658295 0.752760i \(-0.728722\pi\)
−0.658295 + 0.752760i \(0.728722\pi\)
\(60\) 1.92917 0.249055
\(61\) 3.84193 0.491909 0.245955 0.969281i \(-0.420899\pi\)
0.245955 + 0.969281i \(0.420899\pi\)
\(62\) −0.417877 −0.0530704
\(63\) 0.824977 0.103937
\(64\) −7.88672 −0.985840
\(65\) −0.557620 −0.0691642
\(66\) −0.175250 −0.0215717
\(67\) 12.8564 1.57066 0.785328 0.619080i \(-0.212494\pi\)
0.785328 + 0.619080i \(0.212494\pi\)
\(68\) 1.99527 0.241962
\(69\) 2.04623 0.246337
\(70\) 0.0548539 0.00655629
\(71\) 6.40860 0.760560 0.380280 0.924871i \(-0.375828\pi\)
0.380280 + 0.924871i \(0.375828\pi\)
\(72\) −0.274754 −0.0323800
\(73\) 10.2174 1.19586 0.597929 0.801549i \(-0.295991\pi\)
0.597929 + 0.801549i \(0.295991\pi\)
\(74\) −0.365605 −0.0425007
\(75\) 4.06516 0.469404
\(76\) −6.16365 −0.707019
\(77\) 2.10234 0.239583
\(78\) 0.0396613 0.00449076
\(79\) −2.90388 −0.326712 −0.163356 0.986567i \(-0.552232\pi\)
−0.163356 + 0.986567i \(0.552232\pi\)
\(80\) 3.84007 0.429333
\(81\) 1.00000 0.111111
\(82\) 0.227894 0.0251667
\(83\) −3.83473 −0.420916 −0.210458 0.977603i \(-0.567495\pi\)
−0.210458 + 0.977603i \(0.567495\pi\)
\(84\) 1.64605 0.179599
\(85\) −0.966871 −0.104872
\(86\) 0.279876 0.0301798
\(87\) −2.52229 −0.270418
\(88\) −0.700170 −0.0746384
\(89\) 16.7151 1.77180 0.885901 0.463874i \(-0.153541\pi\)
0.885901 + 0.463874i \(0.153541\pi\)
\(90\) 0.0664914 0.00700881
\(91\) −0.475786 −0.0498759
\(92\) 4.08278 0.425659
\(93\) 6.07647 0.630100
\(94\) −0.456626 −0.0470973
\(95\) 2.98679 0.306438
\(96\) −0.822636 −0.0839599
\(97\) −4.28099 −0.434669 −0.217334 0.976097i \(-0.569736\pi\)
−0.217334 + 0.976097i \(0.569736\pi\)
\(98\) −0.434584 −0.0438996
\(99\) 2.54836 0.256120
\(100\) 8.11110 0.811110
\(101\) 9.43930 0.939245 0.469623 0.882867i \(-0.344390\pi\)
0.469623 + 0.882867i \(0.344390\pi\)
\(102\) 0.0687697 0.00680921
\(103\) −12.0973 −1.19198 −0.595990 0.802992i \(-0.703240\pi\)
−0.595990 + 0.802992i \(0.703240\pi\)
\(104\) 0.158458 0.0155380
\(105\) −0.797646 −0.0778423
\(106\) −0.694680 −0.0674733
\(107\) 4.73549 0.457797 0.228899 0.973450i \(-0.426488\pi\)
0.228899 + 0.973450i \(0.426488\pi\)
\(108\) 1.99527 0.191995
\(109\) −0.611447 −0.0585660 −0.0292830 0.999571i \(-0.509322\pi\)
−0.0292830 + 0.999571i \(0.509322\pi\)
\(110\) 0.169444 0.0161558
\(111\) 5.31637 0.504607
\(112\) 3.27652 0.309602
\(113\) −3.91752 −0.368530 −0.184265 0.982877i \(-0.558990\pi\)
−0.184265 + 0.982877i \(0.558990\pi\)
\(114\) −0.212438 −0.0198967
\(115\) −1.97844 −0.184490
\(116\) −5.03265 −0.467270
\(117\) −0.576726 −0.0533184
\(118\) −0.695463 −0.0640225
\(119\) −0.824977 −0.0756255
\(120\) 0.265651 0.0242505
\(121\) −4.50588 −0.409625
\(122\) 0.264209 0.0239203
\(123\) −3.31387 −0.298802
\(124\) 12.1242 1.08878
\(125\) −8.76484 −0.783951
\(126\) 0.0567334 0.00505421
\(127\) 7.91384 0.702240 0.351120 0.936330i \(-0.385801\pi\)
0.351120 + 0.936330i \(0.385801\pi\)
\(128\) −2.18764 −0.193362
\(129\) −4.06976 −0.358322
\(130\) −0.0383473 −0.00336328
\(131\) −21.4229 −1.87173 −0.935865 0.352358i \(-0.885380\pi\)
−0.935865 + 0.352358i \(0.885380\pi\)
\(132\) 5.08466 0.442563
\(133\) 2.54846 0.220980
\(134\) 0.884129 0.0763771
\(135\) −0.966871 −0.0832150
\(136\) 0.274754 0.0235599
\(137\) 11.9255 1.01887 0.509434 0.860510i \(-0.329855\pi\)
0.509434 + 0.860510i \(0.329855\pi\)
\(138\) 0.140718 0.0119787
\(139\) 21.8098 1.84989 0.924944 0.380104i \(-0.124112\pi\)
0.924944 + 0.380104i \(0.124112\pi\)
\(140\) −1.59152 −0.134508
\(141\) 6.63993 0.559183
\(142\) 0.440717 0.0369842
\(143\) −1.46970 −0.122903
\(144\) 3.97165 0.330971
\(145\) 2.43873 0.202525
\(146\) 0.702648 0.0581516
\(147\) 6.31941 0.521216
\(148\) 10.6076 0.871939
\(149\) −8.52523 −0.698414 −0.349207 0.937046i \(-0.613549\pi\)
−0.349207 + 0.937046i \(0.613549\pi\)
\(150\) 0.279560 0.0228260
\(151\) −13.9347 −1.13399 −0.566994 0.823722i \(-0.691894\pi\)
−0.566994 + 0.823722i \(0.691894\pi\)
\(152\) −0.848749 −0.0688426
\(153\) −1.00000 −0.0808452
\(154\) 0.144577 0.0116503
\(155\) −5.87516 −0.471904
\(156\) −1.15073 −0.0921317
\(157\) −1.00000 −0.0798087
\(158\) −0.199699 −0.0158872
\(159\) 10.1015 0.801105
\(160\) 0.795382 0.0628805
\(161\) −1.68809 −0.133040
\(162\) 0.0687697 0.00540306
\(163\) −9.69336 −0.759243 −0.379621 0.925142i \(-0.623946\pi\)
−0.379621 + 0.925142i \(0.623946\pi\)
\(164\) −6.61207 −0.516316
\(165\) −2.46393 −0.191817
\(166\) −0.263713 −0.0204681
\(167\) −9.75695 −0.755015 −0.377508 0.926006i \(-0.623219\pi\)
−0.377508 + 0.926006i \(0.623219\pi\)
\(168\) 0.226665 0.0174876
\(169\) −12.6674 −0.974414
\(170\) −0.0664914 −0.00509966
\(171\) 3.08913 0.236232
\(172\) −8.12026 −0.619164
\(173\) 0.531310 0.0403948 0.0201974 0.999796i \(-0.493571\pi\)
0.0201974 + 0.999796i \(0.493571\pi\)
\(174\) −0.173457 −0.0131497
\(175\) −3.35367 −0.253513
\(176\) 10.1212 0.762912
\(177\) 10.1129 0.760134
\(178\) 1.14950 0.0861583
\(179\) −9.59285 −0.717003 −0.358502 0.933529i \(-0.616712\pi\)
−0.358502 + 0.933529i \(0.616712\pi\)
\(180\) −1.92917 −0.143792
\(181\) −9.73938 −0.723922 −0.361961 0.932193i \(-0.617893\pi\)
−0.361961 + 0.932193i \(0.617893\pi\)
\(182\) −0.0327197 −0.00242534
\(183\) −3.84193 −0.284004
\(184\) 0.562208 0.0414465
\(185\) −5.14024 −0.377918
\(186\) 0.417877 0.0306402
\(187\) −2.54836 −0.186354
\(188\) 13.2484 0.966242
\(189\) −0.824977 −0.0600083
\(190\) 0.205400 0.0149013
\(191\) 6.94877 0.502795 0.251398 0.967884i \(-0.419110\pi\)
0.251398 + 0.967884i \(0.419110\pi\)
\(192\) 7.88672 0.569175
\(193\) 3.53567 0.254503 0.127251 0.991870i \(-0.459384\pi\)
0.127251 + 0.991870i \(0.459384\pi\)
\(194\) −0.294402 −0.0211369
\(195\) 0.557620 0.0399320
\(196\) 12.6089 0.900639
\(197\) 5.99851 0.427376 0.213688 0.976902i \(-0.431452\pi\)
0.213688 + 0.976902i \(0.431452\pi\)
\(198\) 0.175250 0.0124545
\(199\) 13.5931 0.963591 0.481796 0.876284i \(-0.339985\pi\)
0.481796 + 0.876284i \(0.339985\pi\)
\(200\) 1.11692 0.0789780
\(201\) −12.8564 −0.906819
\(202\) 0.649138 0.0456732
\(203\) 2.08083 0.146046
\(204\) −1.99527 −0.139697
\(205\) 3.20408 0.223783
\(206\) −0.831926 −0.0579630
\(207\) −2.04623 −0.142223
\(208\) −2.29055 −0.158821
\(209\) 7.87220 0.544532
\(210\) −0.0548539 −0.00378528
\(211\) −14.8816 −1.02449 −0.512247 0.858838i \(-0.671187\pi\)
−0.512247 + 0.858838i \(0.671187\pi\)
\(212\) 20.1553 1.38427
\(213\) −6.40860 −0.439110
\(214\) 0.325658 0.0222615
\(215\) 3.93493 0.268360
\(216\) 0.274754 0.0186946
\(217\) −5.01295 −0.340301
\(218\) −0.0420490 −0.00284792
\(219\) −10.2174 −0.690429
\(220\) −4.91621 −0.331451
\(221\) 0.576726 0.0387948
\(222\) 0.365605 0.0245378
\(223\) −4.95072 −0.331525 −0.165762 0.986166i \(-0.553008\pi\)
−0.165762 + 0.986166i \(0.553008\pi\)
\(224\) 0.678656 0.0453446
\(225\) −4.06516 −0.271011
\(226\) −0.269407 −0.0179207
\(227\) −11.0409 −0.732809 −0.366405 0.930456i \(-0.619411\pi\)
−0.366405 + 0.930456i \(0.619411\pi\)
\(228\) 6.16365 0.408198
\(229\) 9.24283 0.610783 0.305392 0.952227i \(-0.401213\pi\)
0.305392 + 0.952227i \(0.401213\pi\)
\(230\) −0.136056 −0.00897130
\(231\) −2.10234 −0.138324
\(232\) −0.693007 −0.0454982
\(233\) 2.08683 0.136713 0.0683565 0.997661i \(-0.478224\pi\)
0.0683565 + 0.997661i \(0.478224\pi\)
\(234\) −0.0396613 −0.00259274
\(235\) −6.41995 −0.418791
\(236\) 20.1780 1.31348
\(237\) 2.90388 0.188627
\(238\) −0.0567334 −0.00367748
\(239\) 0.540533 0.0349642 0.0174821 0.999847i \(-0.494435\pi\)
0.0174821 + 0.999847i \(0.494435\pi\)
\(240\) −3.84007 −0.247875
\(241\) 9.24566 0.595565 0.297783 0.954634i \(-0.403753\pi\)
0.297783 + 0.954634i \(0.403753\pi\)
\(242\) −0.309868 −0.0199191
\(243\) −1.00000 −0.0641500
\(244\) −7.66570 −0.490746
\(245\) −6.11005 −0.390357
\(246\) −0.227894 −0.0145300
\(247\) −1.78158 −0.113359
\(248\) 1.66953 0.106015
\(249\) 3.83473 0.243016
\(250\) −0.602755 −0.0381216
\(251\) −17.7905 −1.12293 −0.561463 0.827502i \(-0.689761\pi\)
−0.561463 + 0.827502i \(0.689761\pi\)
\(252\) −1.64605 −0.103692
\(253\) −5.21452 −0.327834
\(254\) 0.544232 0.0341482
\(255\) 0.966871 0.0605478
\(256\) 15.6230 0.976437
\(257\) −2.87289 −0.179206 −0.0896029 0.995978i \(-0.528560\pi\)
−0.0896029 + 0.995978i \(0.528560\pi\)
\(258\) −0.279876 −0.0174243
\(259\) −4.38588 −0.272525
\(260\) 1.11260 0.0690007
\(261\) 2.52229 0.156126
\(262\) −1.47325 −0.0910176
\(263\) 18.6756 1.15159 0.575794 0.817595i \(-0.304693\pi\)
0.575794 + 0.817595i \(0.304693\pi\)
\(264\) 0.700170 0.0430925
\(265\) −9.76689 −0.599975
\(266\) 0.175257 0.0107457
\(267\) −16.7151 −1.02295
\(268\) −25.6519 −1.56694
\(269\) 14.3871 0.877195 0.438597 0.898684i \(-0.355475\pi\)
0.438597 + 0.898684i \(0.355475\pi\)
\(270\) −0.0664914 −0.00404654
\(271\) 21.8858 1.32947 0.664734 0.747080i \(-0.268545\pi\)
0.664734 + 0.747080i \(0.268545\pi\)
\(272\) −3.97165 −0.240816
\(273\) 0.475786 0.0287959
\(274\) 0.820116 0.0495450
\(275\) −10.3595 −0.624700
\(276\) −4.08278 −0.245754
\(277\) −26.1129 −1.56897 −0.784485 0.620147i \(-0.787073\pi\)
−0.784485 + 0.620147i \(0.787073\pi\)
\(278\) 1.49986 0.0899554
\(279\) −6.07647 −0.363789
\(280\) −0.219156 −0.0130971
\(281\) −11.3572 −0.677516 −0.338758 0.940874i \(-0.610007\pi\)
−0.338758 + 0.940874i \(0.610007\pi\)
\(282\) 0.456626 0.0271917
\(283\) −11.2005 −0.665803 −0.332901 0.942962i \(-0.608028\pi\)
−0.332901 + 0.942962i \(0.608028\pi\)
\(284\) −12.7869 −0.758762
\(285\) −2.98679 −0.176922
\(286\) −0.101071 −0.00597646
\(287\) 2.73387 0.161375
\(288\) 0.822636 0.0484743
\(289\) 1.00000 0.0588235
\(290\) 0.167710 0.00984829
\(291\) 4.28099 0.250956
\(292\) −20.3865 −1.19303
\(293\) −30.9160 −1.80613 −0.903066 0.429503i \(-0.858689\pi\)
−0.903066 + 0.429503i \(0.858689\pi\)
\(294\) 0.434584 0.0253455
\(295\) −9.77789 −0.569291
\(296\) 1.46069 0.0849009
\(297\) −2.54836 −0.147871
\(298\) −0.586278 −0.0339621
\(299\) 1.18011 0.0682477
\(300\) −8.11110 −0.468294
\(301\) 3.35746 0.193521
\(302\) −0.958283 −0.0551430
\(303\) −9.43930 −0.542274
\(304\) 12.2689 0.703671
\(305\) 3.71465 0.212700
\(306\) −0.0687697 −0.00393130
\(307\) 1.62405 0.0926896 0.0463448 0.998926i \(-0.485243\pi\)
0.0463448 + 0.998926i \(0.485243\pi\)
\(308\) −4.19473 −0.239017
\(309\) 12.0973 0.688190
\(310\) −0.404033 −0.0229475
\(311\) −11.2601 −0.638504 −0.319252 0.947670i \(-0.603432\pi\)
−0.319252 + 0.947670i \(0.603432\pi\)
\(312\) −0.158458 −0.00897089
\(313\) −22.5098 −1.27233 −0.636164 0.771554i \(-0.719480\pi\)
−0.636164 + 0.771554i \(0.719480\pi\)
\(314\) −0.0687697 −0.00388090
\(315\) 0.797646 0.0449423
\(316\) 5.79403 0.325940
\(317\) −2.96039 −0.166272 −0.0831360 0.996538i \(-0.526494\pi\)
−0.0831360 + 0.996538i \(0.526494\pi\)
\(318\) 0.694680 0.0389557
\(319\) 6.42769 0.359882
\(320\) −7.62544 −0.426275
\(321\) −4.73549 −0.264309
\(322\) −0.116089 −0.00646941
\(323\) −3.08913 −0.171884
\(324\) −1.99527 −0.110848
\(325\) 2.34449 0.130049
\(326\) −0.666609 −0.0369201
\(327\) 0.611447 0.0338131
\(328\) −0.910498 −0.0502738
\(329\) −5.47779 −0.302000
\(330\) −0.169444 −0.00932757
\(331\) 4.04784 0.222490 0.111245 0.993793i \(-0.464516\pi\)
0.111245 + 0.993793i \(0.464516\pi\)
\(332\) 7.65132 0.419921
\(333\) −5.31637 −0.291335
\(334\) −0.670982 −0.0367145
\(335\) 12.4304 0.679148
\(336\) −3.27652 −0.178749
\(337\) 0.477945 0.0260353 0.0130177 0.999915i \(-0.495856\pi\)
0.0130177 + 0.999915i \(0.495856\pi\)
\(338\) −0.871132 −0.0473833
\(339\) 3.91752 0.212771
\(340\) 1.92917 0.104624
\(341\) −15.4850 −0.838560
\(342\) 0.212438 0.0114874
\(343\) −10.9882 −0.593308
\(344\) −1.11818 −0.0602882
\(345\) 1.97844 0.106515
\(346\) 0.0365380 0.00196430
\(347\) −25.3343 −1.36002 −0.680009 0.733204i \(-0.738024\pi\)
−0.680009 + 0.733204i \(0.738024\pi\)
\(348\) 5.03265 0.269778
\(349\) 15.8302 0.847372 0.423686 0.905809i \(-0.360736\pi\)
0.423686 + 0.905809i \(0.360736\pi\)
\(350\) −0.230631 −0.0123277
\(351\) 0.576726 0.0307834
\(352\) 2.09637 0.111737
\(353\) −24.6173 −1.31024 −0.655122 0.755523i \(-0.727383\pi\)
−0.655122 + 0.755523i \(0.727383\pi\)
\(354\) 0.695463 0.0369634
\(355\) 6.19628 0.328865
\(356\) −33.3512 −1.76761
\(357\) 0.824977 0.0436624
\(358\) −0.659697 −0.0348661
\(359\) −7.01481 −0.370228 −0.185114 0.982717i \(-0.559265\pi\)
−0.185114 + 0.982717i \(0.559265\pi\)
\(360\) −0.265651 −0.0140010
\(361\) −9.45729 −0.497752
\(362\) −0.669774 −0.0352025
\(363\) 4.50588 0.236497
\(364\) 0.949322 0.0497580
\(365\) 9.87892 0.517086
\(366\) −0.264209 −0.0138104
\(367\) 3.84028 0.200461 0.100231 0.994964i \(-0.468042\pi\)
0.100231 + 0.994964i \(0.468042\pi\)
\(368\) −8.12689 −0.423643
\(369\) 3.31387 0.172513
\(370\) −0.353493 −0.0183772
\(371\) −8.33355 −0.432656
\(372\) −12.1242 −0.628610
\(373\) 24.4529 1.26612 0.633062 0.774101i \(-0.281798\pi\)
0.633062 + 0.774101i \(0.281798\pi\)
\(374\) −0.175250 −0.00906195
\(375\) 8.76484 0.452614
\(376\) 1.82434 0.0940833
\(377\) −1.45467 −0.0749193
\(378\) −0.0567334 −0.00291805
\(379\) 13.3686 0.686697 0.343349 0.939208i \(-0.388439\pi\)
0.343349 + 0.939208i \(0.388439\pi\)
\(380\) −5.95945 −0.305713
\(381\) −7.91384 −0.405438
\(382\) 0.477864 0.0244497
\(383\) −32.9298 −1.68264 −0.841318 0.540541i \(-0.818220\pi\)
−0.841318 + 0.540541i \(0.818220\pi\)
\(384\) 2.18764 0.111637
\(385\) 2.03269 0.103595
\(386\) 0.243147 0.0123758
\(387\) 4.06976 0.206877
\(388\) 8.54173 0.433641
\(389\) −0.409278 −0.0207512 −0.0103756 0.999946i \(-0.503303\pi\)
−0.0103756 + 0.999946i \(0.503303\pi\)
\(390\) 0.0383473 0.00194179
\(391\) 2.04623 0.103482
\(392\) 1.73628 0.0876954
\(393\) 21.4229 1.08064
\(394\) 0.412516 0.0207822
\(395\) −2.80768 −0.141270
\(396\) −5.08466 −0.255514
\(397\) 7.91068 0.397026 0.198513 0.980098i \(-0.436389\pi\)
0.198513 + 0.980098i \(0.436389\pi\)
\(398\) 0.934795 0.0468570
\(399\) −2.54846 −0.127583
\(400\) −16.1454 −0.807269
\(401\) 32.2072 1.60835 0.804175 0.594393i \(-0.202608\pi\)
0.804175 + 0.594393i \(0.202608\pi\)
\(402\) −0.884129 −0.0440963
\(403\) 3.50446 0.174569
\(404\) −18.8340 −0.937024
\(405\) 0.966871 0.0480442
\(406\) 0.143098 0.00710184
\(407\) −13.5480 −0.671549
\(408\) −0.274754 −0.0136023
\(409\) −5.31972 −0.263043 −0.131522 0.991313i \(-0.541986\pi\)
−0.131522 + 0.991313i \(0.541986\pi\)
\(410\) 0.220344 0.0108820
\(411\) −11.9255 −0.588244
\(412\) 24.1373 1.18916
\(413\) −8.34293 −0.410529
\(414\) −0.140718 −0.00691593
\(415\) −3.70768 −0.182003
\(416\) −0.474436 −0.0232611
\(417\) −21.8098 −1.06803
\(418\) 0.541369 0.0264792
\(419\) −30.2684 −1.47871 −0.739353 0.673318i \(-0.764869\pi\)
−0.739353 + 0.673318i \(0.764869\pi\)
\(420\) 1.59152 0.0776582
\(421\) −4.19061 −0.204238 −0.102119 0.994772i \(-0.532562\pi\)
−0.102119 + 0.994772i \(0.532562\pi\)
\(422\) −1.02341 −0.0498186
\(423\) −6.63993 −0.322844
\(424\) 2.77544 0.134787
\(425\) 4.06516 0.197189
\(426\) −0.440717 −0.0213528
\(427\) 3.16951 0.153383
\(428\) −9.44859 −0.456715
\(429\) 1.46970 0.0709580
\(430\) 0.270604 0.0130497
\(431\) 0.408370 0.0196705 0.00983525 0.999952i \(-0.496869\pi\)
0.00983525 + 0.999952i \(0.496869\pi\)
\(432\) −3.97165 −0.191086
\(433\) −33.2431 −1.59756 −0.798781 0.601622i \(-0.794521\pi\)
−0.798781 + 0.601622i \(0.794521\pi\)
\(434\) −0.344739 −0.0165480
\(435\) −2.43873 −0.116928
\(436\) 1.22000 0.0584275
\(437\) −6.32106 −0.302377
\(438\) −0.702648 −0.0335738
\(439\) 19.7194 0.941155 0.470577 0.882359i \(-0.344046\pi\)
0.470577 + 0.882359i \(0.344046\pi\)
\(440\) −0.676974 −0.0322735
\(441\) −6.31941 −0.300924
\(442\) 0.0396613 0.00188649
\(443\) −7.83890 −0.372438 −0.186219 0.982508i \(-0.559623\pi\)
−0.186219 + 0.982508i \(0.559623\pi\)
\(444\) −10.6076 −0.503414
\(445\) 16.1614 0.766123
\(446\) −0.340460 −0.0161212
\(447\) 8.52523 0.403230
\(448\) −6.50637 −0.307397
\(449\) −1.68732 −0.0796294 −0.0398147 0.999207i \(-0.512677\pi\)
−0.0398147 + 0.999207i \(0.512677\pi\)
\(450\) −0.279560 −0.0131786
\(451\) 8.44493 0.397656
\(452\) 7.81652 0.367658
\(453\) 13.9347 0.654708
\(454\) −0.759278 −0.0356347
\(455\) −0.460024 −0.0215662
\(456\) 0.848749 0.0397463
\(457\) −35.9817 −1.68315 −0.841577 0.540137i \(-0.818373\pi\)
−0.841577 + 0.540137i \(0.818373\pi\)
\(458\) 0.635626 0.0297009
\(459\) 1.00000 0.0466760
\(460\) 3.94752 0.184054
\(461\) −30.0935 −1.40159 −0.700796 0.713361i \(-0.747172\pi\)
−0.700796 + 0.713361i \(0.747172\pi\)
\(462\) −0.144577 −0.00672633
\(463\) −10.7252 −0.498443 −0.249221 0.968447i \(-0.580175\pi\)
−0.249221 + 0.968447i \(0.580175\pi\)
\(464\) 10.0176 0.465057
\(465\) 5.87516 0.272454
\(466\) 0.143511 0.00664801
\(467\) 17.6134 0.815050 0.407525 0.913194i \(-0.366392\pi\)
0.407525 + 0.913194i \(0.366392\pi\)
\(468\) 1.15073 0.0531923
\(469\) 10.6062 0.489749
\(470\) −0.441498 −0.0203648
\(471\) 1.00000 0.0460776
\(472\) 2.77856 0.127894
\(473\) 10.3712 0.476868
\(474\) 0.199699 0.00917248
\(475\) −12.5578 −0.576192
\(476\) 1.64605 0.0754467
\(477\) −10.1015 −0.462518
\(478\) 0.0371723 0.00170022
\(479\) 29.8068 1.36191 0.680955 0.732325i \(-0.261565\pi\)
0.680955 + 0.732325i \(0.261565\pi\)
\(480\) −0.795382 −0.0363041
\(481\) 3.06609 0.139802
\(482\) 0.635821 0.0289609
\(483\) 1.68809 0.0768108
\(484\) 8.99044 0.408657
\(485\) −4.13916 −0.187950
\(486\) −0.0687697 −0.00311946
\(487\) 14.5380 0.658782 0.329391 0.944194i \(-0.393157\pi\)
0.329391 + 0.944194i \(0.393157\pi\)
\(488\) −1.05558 −0.0477841
\(489\) 9.69336 0.438349
\(490\) −0.420186 −0.0189821
\(491\) 18.0350 0.813907 0.406954 0.913449i \(-0.366591\pi\)
0.406954 + 0.913449i \(0.366591\pi\)
\(492\) 6.61207 0.298095
\(493\) −2.52229 −0.113598
\(494\) −0.122519 −0.00551238
\(495\) 2.46393 0.110745
\(496\) −24.1336 −1.08363
\(497\) 5.28695 0.237152
\(498\) 0.263713 0.0118173
\(499\) −17.6642 −0.790759 −0.395380 0.918518i \(-0.629387\pi\)
−0.395380 + 0.918518i \(0.629387\pi\)
\(500\) 17.4882 0.782097
\(501\) 9.75695 0.435908
\(502\) −1.22345 −0.0546051
\(503\) 10.6248 0.473738 0.236869 0.971542i \(-0.423879\pi\)
0.236869 + 0.971542i \(0.423879\pi\)
\(504\) −0.226665 −0.0100965
\(505\) 9.12658 0.406127
\(506\) −0.358601 −0.0159417
\(507\) 12.6674 0.562578
\(508\) −15.7903 −0.700579
\(509\) 3.24495 0.143830 0.0719148 0.997411i \(-0.477089\pi\)
0.0719148 + 0.997411i \(0.477089\pi\)
\(510\) 0.0664914 0.00294429
\(511\) 8.42913 0.372883
\(512\) 5.44967 0.240844
\(513\) −3.08913 −0.136388
\(514\) −0.197568 −0.00871433
\(515\) −11.6965 −0.515409
\(516\) 8.12026 0.357475
\(517\) −16.9209 −0.744180
\(518\) −0.301616 −0.0132522
\(519\) −0.531310 −0.0233219
\(520\) 0.153208 0.00671861
\(521\) −10.2212 −0.447799 −0.223900 0.974612i \(-0.571879\pi\)
−0.223900 + 0.974612i \(0.571879\pi\)
\(522\) 0.173457 0.00759200
\(523\) 10.4413 0.456565 0.228283 0.973595i \(-0.426689\pi\)
0.228283 + 0.973595i \(0.426689\pi\)
\(524\) 42.7446 1.86730
\(525\) 3.35367 0.146366
\(526\) 1.28432 0.0559989
\(527\) 6.07647 0.264695
\(528\) −10.1212 −0.440468
\(529\) −18.8130 −0.817955
\(530\) −0.671666 −0.0291753
\(531\) −10.1129 −0.438864
\(532\) −5.08487 −0.220457
\(533\) −1.91120 −0.0827831
\(534\) −1.14950 −0.0497435
\(535\) 4.57861 0.197951
\(536\) −3.53233 −0.152574
\(537\) 9.59285 0.413962
\(538\) 0.989394 0.0426558
\(539\) −16.1041 −0.693654
\(540\) 1.92917 0.0830182
\(541\) −32.5297 −1.39856 −0.699280 0.714848i \(-0.746496\pi\)
−0.699280 + 0.714848i \(0.746496\pi\)
\(542\) 1.50508 0.0646487
\(543\) 9.73938 0.417957
\(544\) −0.822636 −0.0352702
\(545\) −0.591190 −0.0253238
\(546\) 0.0327197 0.00140027
\(547\) −39.2313 −1.67741 −0.838705 0.544586i \(-0.816687\pi\)
−0.838705 + 0.544586i \(0.816687\pi\)
\(548\) −23.7947 −1.01646
\(549\) 3.84193 0.163970
\(550\) −0.712418 −0.0303776
\(551\) 7.79167 0.331936
\(552\) −0.562208 −0.0239292
\(553\) −2.39564 −0.101873
\(554\) −1.79577 −0.0762951
\(555\) 5.14024 0.218191
\(556\) −43.5166 −1.84551
\(557\) −10.5474 −0.446908 −0.223454 0.974714i \(-0.571733\pi\)
−0.223454 + 0.974714i \(0.571733\pi\)
\(558\) −0.417877 −0.0176901
\(559\) −2.34714 −0.0992732
\(560\) 3.16797 0.133871
\(561\) 2.54836 0.107592
\(562\) −0.781033 −0.0329459
\(563\) 6.89047 0.290399 0.145199 0.989402i \(-0.453618\pi\)
0.145199 + 0.989402i \(0.453618\pi\)
\(564\) −13.2484 −0.557860
\(565\) −3.78774 −0.159351
\(566\) −0.770257 −0.0323763
\(567\) 0.824977 0.0346458
\(568\) −1.76078 −0.0738809
\(569\) −27.2018 −1.14036 −0.570179 0.821521i \(-0.693126\pi\)
−0.570179 + 0.821521i \(0.693126\pi\)
\(570\) −0.205400 −0.00860328
\(571\) −25.2597 −1.05709 −0.528543 0.848906i \(-0.677262\pi\)
−0.528543 + 0.848906i \(0.677262\pi\)
\(572\) 2.93246 0.122612
\(573\) −6.94877 −0.290289
\(574\) 0.188007 0.00784727
\(575\) 8.31824 0.346895
\(576\) −7.88672 −0.328613
\(577\) −37.0556 −1.54265 −0.771323 0.636444i \(-0.780405\pi\)
−0.771323 + 0.636444i \(0.780405\pi\)
\(578\) 0.0687697 0.00286044
\(579\) −3.53567 −0.146937
\(580\) −4.86592 −0.202046
\(581\) −3.16356 −0.131247
\(582\) 0.294402 0.0122034
\(583\) −25.7424 −1.06614
\(584\) −2.80727 −0.116166
\(585\) −0.557620 −0.0230547
\(586\) −2.12608 −0.0878277
\(587\) 17.3541 0.716282 0.358141 0.933668i \(-0.383411\pi\)
0.358141 + 0.933668i \(0.383411\pi\)
\(588\) −12.6089 −0.519984
\(589\) −18.7710 −0.773445
\(590\) −0.672423 −0.0276832
\(591\) −5.99851 −0.246746
\(592\) −21.1147 −0.867810
\(593\) 29.6823 1.21890 0.609452 0.792823i \(-0.291389\pi\)
0.609452 + 0.792823i \(0.291389\pi\)
\(594\) −0.175250 −0.00719058
\(595\) −0.797646 −0.0327003
\(596\) 17.0101 0.696763
\(597\) −13.5931 −0.556330
\(598\) 0.0811560 0.00331871
\(599\) −41.6829 −1.70312 −0.851558 0.524260i \(-0.824342\pi\)
−0.851558 + 0.524260i \(0.824342\pi\)
\(600\) −1.11692 −0.0455980
\(601\) 19.5374 0.796947 0.398474 0.917180i \(-0.369540\pi\)
0.398474 + 0.917180i \(0.369540\pi\)
\(602\) 0.230891 0.00941042
\(603\) 12.8564 0.523552
\(604\) 27.8035 1.13131
\(605\) −4.35660 −0.177121
\(606\) −0.649138 −0.0263694
\(607\) −17.4722 −0.709175 −0.354587 0.935023i \(-0.615379\pi\)
−0.354587 + 0.935023i \(0.615379\pi\)
\(608\) 2.54123 0.103060
\(609\) −2.08083 −0.0843195
\(610\) 0.255455 0.0103431
\(611\) 3.82942 0.154922
\(612\) 1.99527 0.0806540
\(613\) −28.1104 −1.13537 −0.567684 0.823246i \(-0.692161\pi\)
−0.567684 + 0.823246i \(0.692161\pi\)
\(614\) 0.111686 0.00450726
\(615\) −3.20408 −0.129201
\(616\) −0.577624 −0.0232731
\(617\) −0.102618 −0.00413123 −0.00206562 0.999998i \(-0.500658\pi\)
−0.00206562 + 0.999998i \(0.500658\pi\)
\(618\) 0.831926 0.0334650
\(619\) −22.8024 −0.916504 −0.458252 0.888822i \(-0.651524\pi\)
−0.458252 + 0.888822i \(0.651524\pi\)
\(620\) 11.7225 0.470788
\(621\) 2.04623 0.0821122
\(622\) −0.774356 −0.0310489
\(623\) 13.7896 0.552469
\(624\) 2.29055 0.0916955
\(625\) 11.8513 0.474054
\(626\) −1.54799 −0.0618702
\(627\) −7.87220 −0.314385
\(628\) 1.99527 0.0796200
\(629\) 5.31637 0.211977
\(630\) 0.0548539 0.00218543
\(631\) 41.4338 1.64945 0.824727 0.565531i \(-0.191329\pi\)
0.824727 + 0.565531i \(0.191329\pi\)
\(632\) 0.797851 0.0317368
\(633\) 14.8816 0.591492
\(634\) −0.203585 −0.00808539
\(635\) 7.65166 0.303647
\(636\) −20.1553 −0.799211
\(637\) 3.64457 0.144403
\(638\) 0.442030 0.0175001
\(639\) 6.40860 0.253520
\(640\) −2.11516 −0.0836092
\(641\) 4.64518 0.183474 0.0917368 0.995783i \(-0.470758\pi\)
0.0917368 + 0.995783i \(0.470758\pi\)
\(642\) −0.325658 −0.0128527
\(643\) −15.1821 −0.598726 −0.299363 0.954139i \(-0.596774\pi\)
−0.299363 + 0.954139i \(0.596774\pi\)
\(644\) 3.36820 0.132726
\(645\) −3.93493 −0.154938
\(646\) −0.212438 −0.00835828
\(647\) 17.5083 0.688324 0.344162 0.938910i \(-0.388163\pi\)
0.344162 + 0.938910i \(0.388163\pi\)
\(648\) −0.274754 −0.0107933
\(649\) −25.7713 −1.01161
\(650\) 0.161230 0.00632394
\(651\) 5.01295 0.196473
\(652\) 19.3409 0.757447
\(653\) −3.82453 −0.149665 −0.0748327 0.997196i \(-0.523842\pi\)
−0.0748327 + 0.997196i \(0.523842\pi\)
\(654\) 0.0420490 0.00164425
\(655\) −20.7132 −0.809332
\(656\) 13.1615 0.513871
\(657\) 10.2174 0.398619
\(658\) −0.376706 −0.0146855
\(659\) −38.8396 −1.51297 −0.756487 0.654008i \(-0.773086\pi\)
−0.756487 + 0.654008i \(0.773086\pi\)
\(660\) 4.91621 0.191363
\(661\) 9.57670 0.372490 0.186245 0.982503i \(-0.440368\pi\)
0.186245 + 0.982503i \(0.440368\pi\)
\(662\) 0.278369 0.0108191
\(663\) −0.576726 −0.0223982
\(664\) 1.05360 0.0408878
\(665\) 2.46403 0.0955510
\(666\) −0.365605 −0.0141669
\(667\) −5.16117 −0.199841
\(668\) 19.4678 0.753230
\(669\) 4.95072 0.191406
\(670\) 0.854838 0.0330253
\(671\) 9.79062 0.377963
\(672\) −0.678656 −0.0261797
\(673\) −39.4313 −1.51996 −0.759982 0.649944i \(-0.774792\pi\)
−0.759982 + 0.649944i \(0.774792\pi\)
\(674\) 0.0328681 0.00126603
\(675\) 4.06516 0.156468
\(676\) 25.2749 0.972110
\(677\) −0.00774676 −0.000297732 0 −0.000148866 1.00000i \(-0.500047\pi\)
−0.000148866 1.00000i \(0.500047\pi\)
\(678\) 0.269407 0.0103465
\(679\) −3.53172 −0.135535
\(680\) 0.265651 0.0101873
\(681\) 11.0409 0.423087
\(682\) −1.06490 −0.0407771
\(683\) 27.0165 1.03376 0.516879 0.856058i \(-0.327094\pi\)
0.516879 + 0.856058i \(0.327094\pi\)
\(684\) −6.16365 −0.235673
\(685\) 11.5305 0.440556
\(686\) −0.755656 −0.0288511
\(687\) −9.24283 −0.352636
\(688\) 16.1636 0.616233
\(689\) 5.82583 0.221946
\(690\) 0.136056 0.00517958
\(691\) −9.29832 −0.353725 −0.176862 0.984236i \(-0.556595\pi\)
−0.176862 + 0.984236i \(0.556595\pi\)
\(692\) −1.06011 −0.0402993
\(693\) 2.10234 0.0798612
\(694\) −1.74223 −0.0661343
\(695\) 21.0873 0.799887
\(696\) 0.693007 0.0262684
\(697\) −3.31387 −0.125522
\(698\) 1.08864 0.0412056
\(699\) −2.08683 −0.0789313
\(700\) 6.69147 0.252914
\(701\) 5.52829 0.208800 0.104400 0.994535i \(-0.466708\pi\)
0.104400 + 0.994535i \(0.466708\pi\)
\(702\) 0.0396613 0.00149692
\(703\) −16.4229 −0.619403
\(704\) −20.0982 −0.757479
\(705\) 6.41995 0.241789
\(706\) −1.69292 −0.0637139
\(707\) 7.78721 0.292868
\(708\) −20.1780 −0.758337
\(709\) −28.3740 −1.06561 −0.532805 0.846238i \(-0.678862\pi\)
−0.532805 + 0.846238i \(0.678862\pi\)
\(710\) 0.426116 0.0159919
\(711\) −2.90388 −0.108904
\(712\) −4.59255 −0.172113
\(713\) 12.4338 0.465651
\(714\) 0.0567334 0.00212319
\(715\) −1.42101 −0.0531429
\(716\) 19.1403 0.715308
\(717\) −0.540533 −0.0201866
\(718\) −0.482406 −0.0180032
\(719\) 23.2060 0.865436 0.432718 0.901529i \(-0.357555\pi\)
0.432718 + 0.901529i \(0.357555\pi\)
\(720\) 3.84007 0.143111
\(721\) −9.97998 −0.371674
\(722\) −0.650375 −0.0242044
\(723\) −9.24566 −0.343850
\(724\) 19.4327 0.722211
\(725\) −10.2535 −0.380806
\(726\) 0.309868 0.0115003
\(727\) 26.9755 1.00047 0.500233 0.865891i \(-0.333248\pi\)
0.500233 + 0.865891i \(0.333248\pi\)
\(728\) 0.130724 0.00484495
\(729\) 1.00000 0.0370370
\(730\) 0.679370 0.0251446
\(731\) −4.06976 −0.150525
\(732\) 7.66570 0.283332
\(733\) −29.4234 −1.08678 −0.543389 0.839481i \(-0.682859\pi\)
−0.543389 + 0.839481i \(0.682859\pi\)
\(734\) 0.264095 0.00974792
\(735\) 6.11005 0.225373
\(736\) −1.68330 −0.0620472
\(737\) 32.7626 1.20683
\(738\) 0.227894 0.00838889
\(739\) −21.4206 −0.787971 −0.393986 0.919117i \(-0.628904\pi\)
−0.393986 + 0.919117i \(0.628904\pi\)
\(740\) 10.2562 0.377024
\(741\) 1.78158 0.0654480
\(742\) −0.573095 −0.0210390
\(743\) 11.6596 0.427748 0.213874 0.976861i \(-0.431392\pi\)
0.213874 + 0.976861i \(0.431392\pi\)
\(744\) −1.66953 −0.0612080
\(745\) −8.24280 −0.301993
\(746\) 1.68162 0.0615684
\(747\) −3.83473 −0.140305
\(748\) 5.08466 0.185914
\(749\) 3.90667 0.142747
\(750\) 0.602755 0.0220095
\(751\) 51.9532 1.89580 0.947899 0.318570i \(-0.103203\pi\)
0.947899 + 0.318570i \(0.103203\pi\)
\(752\) −26.3714 −0.961667
\(753\) 17.7905 0.648322
\(754\) −0.100037 −0.00364314
\(755\) −13.4730 −0.490334
\(756\) 1.64605 0.0598664
\(757\) 36.6772 1.33306 0.666528 0.745480i \(-0.267780\pi\)
0.666528 + 0.745480i \(0.267780\pi\)
\(758\) 0.919352 0.0333924
\(759\) 5.21452 0.189275
\(760\) −0.820630 −0.0297674
\(761\) −20.0013 −0.725048 −0.362524 0.931974i \(-0.618085\pi\)
−0.362524 + 0.931974i \(0.618085\pi\)
\(762\) −0.544232 −0.0197155
\(763\) −0.504430 −0.0182616
\(764\) −13.8647 −0.501606
\(765\) −0.966871 −0.0349573
\(766\) −2.26457 −0.0818224
\(767\) 5.83239 0.210595
\(768\) −15.6230 −0.563746
\(769\) −32.7710 −1.18175 −0.590876 0.806762i \(-0.701218\pi\)
−0.590876 + 0.806762i \(0.701218\pi\)
\(770\) 0.139787 0.00503758
\(771\) 2.87289 0.103465
\(772\) −7.05461 −0.253901
\(773\) −2.69412 −0.0969008 −0.0484504 0.998826i \(-0.515428\pi\)
−0.0484504 + 0.998826i \(0.515428\pi\)
\(774\) 0.279876 0.0100599
\(775\) 24.7018 0.887315
\(776\) 1.17622 0.0422237
\(777\) 4.38588 0.157343
\(778\) −0.0281459 −0.00100908
\(779\) 10.2370 0.366778
\(780\) −1.11260 −0.0398375
\(781\) 16.3314 0.584383
\(782\) 0.140718 0.00503208
\(783\) −2.52229 −0.0901392
\(784\) −25.0985 −0.896374
\(785\) −0.966871 −0.0345091
\(786\) 1.47325 0.0525490
\(787\) −12.8933 −0.459597 −0.229799 0.973238i \(-0.573807\pi\)
−0.229799 + 0.973238i \(0.573807\pi\)
\(788\) −11.9687 −0.426366
\(789\) −18.6756 −0.664870
\(790\) −0.193083 −0.00686959
\(791\) −3.23187 −0.114912
\(792\) −0.700170 −0.0248795
\(793\) −2.21574 −0.0786834
\(794\) 0.544015 0.0193064
\(795\) 9.76689 0.346396
\(796\) −27.1220 −0.961313
\(797\) 7.58947 0.268833 0.134416 0.990925i \(-0.457084\pi\)
0.134416 + 0.990925i \(0.457084\pi\)
\(798\) −0.175257 −0.00620402
\(799\) 6.63993 0.234904
\(800\) −3.34415 −0.118233
\(801\) 16.7151 0.590601
\(802\) 2.21488 0.0782100
\(803\) 26.0376 0.918847
\(804\) 25.6519 0.904674
\(805\) −1.63216 −0.0575263
\(806\) 0.241000 0.00848888
\(807\) −14.3871 −0.506449
\(808\) −2.59348 −0.0912383
\(809\) −19.7295 −0.693652 −0.346826 0.937930i \(-0.612741\pi\)
−0.346826 + 0.937930i \(0.612741\pi\)
\(810\) 0.0664914 0.00233627
\(811\) −14.5012 −0.509206 −0.254603 0.967046i \(-0.581945\pi\)
−0.254603 + 0.967046i \(0.581945\pi\)
\(812\) −4.15182 −0.145700
\(813\) −21.8858 −0.767569
\(814\) −0.931692 −0.0326558
\(815\) −9.37222 −0.328295
\(816\) 3.97165 0.139035
\(817\) 12.5720 0.439839
\(818\) −0.365835 −0.0127911
\(819\) −0.475786 −0.0166253
\(820\) −6.39302 −0.223254
\(821\) 21.5499 0.752096 0.376048 0.926600i \(-0.377283\pi\)
0.376048 + 0.926600i \(0.377283\pi\)
\(822\) −0.820116 −0.0286048
\(823\) −40.1187 −1.39845 −0.699226 0.714901i \(-0.746472\pi\)
−0.699226 + 0.714901i \(0.746472\pi\)
\(824\) 3.32377 0.115789
\(825\) 10.3595 0.360671
\(826\) −0.573741 −0.0199630
\(827\) 29.5649 1.02807 0.514037 0.857768i \(-0.328150\pi\)
0.514037 + 0.857768i \(0.328150\pi\)
\(828\) 4.08278 0.141886
\(829\) 13.1440 0.456510 0.228255 0.973601i \(-0.426698\pi\)
0.228255 + 0.973601i \(0.426698\pi\)
\(830\) −0.254976 −0.00885035
\(831\) 26.1129 0.905846
\(832\) 4.54848 0.157690
\(833\) 6.31941 0.218955
\(834\) −1.49986 −0.0519358
\(835\) −9.43371 −0.326467
\(836\) −15.7072 −0.543244
\(837\) 6.07647 0.210033
\(838\) −2.08155 −0.0719058
\(839\) 11.9853 0.413780 0.206890 0.978364i \(-0.433666\pi\)
0.206890 + 0.978364i \(0.433666\pi\)
\(840\) 0.219156 0.00756160
\(841\) −22.6381 −0.780623
\(842\) −0.288187 −0.00993157
\(843\) 11.3572 0.391164
\(844\) 29.6929 1.02207
\(845\) −12.2477 −0.421335
\(846\) −0.456626 −0.0156991
\(847\) −3.71725 −0.127726
\(848\) −40.1198 −1.37772
\(849\) 11.2005 0.384401
\(850\) 0.279560 0.00958882
\(851\) 10.8785 0.372910
\(852\) 12.7869 0.438071
\(853\) −40.7194 −1.39421 −0.697103 0.716971i \(-0.745528\pi\)
−0.697103 + 0.716971i \(0.745528\pi\)
\(854\) 0.217966 0.00745864
\(855\) 2.98679 0.102146
\(856\) −1.30109 −0.0444705
\(857\) 44.0574 1.50497 0.752486 0.658608i \(-0.228854\pi\)
0.752486 + 0.658608i \(0.228854\pi\)
\(858\) 0.101071 0.00345051
\(859\) −11.1755 −0.381305 −0.190652 0.981658i \(-0.561060\pi\)
−0.190652 + 0.981658i \(0.561060\pi\)
\(860\) −7.85124 −0.267725
\(861\) −2.73387 −0.0931700
\(862\) 0.0280835 0.000956527 0
\(863\) 19.0744 0.649299 0.324650 0.945834i \(-0.394754\pi\)
0.324650 + 0.945834i \(0.394754\pi\)
\(864\) −0.822636 −0.0279866
\(865\) 0.513708 0.0174666
\(866\) −2.28612 −0.0776855
\(867\) −1.00000 −0.0339618
\(868\) 10.0022 0.339496
\(869\) −7.40012 −0.251032
\(870\) −0.167710 −0.00568592
\(871\) −7.41461 −0.251234
\(872\) 0.167997 0.00568910
\(873\) −4.28099 −0.144890
\(874\) −0.434697 −0.0147038
\(875\) −7.23079 −0.244445
\(876\) 20.3865 0.688796
\(877\) −28.8006 −0.972526 −0.486263 0.873812i \(-0.661640\pi\)
−0.486263 + 0.873812i \(0.661640\pi\)
\(878\) 1.35610 0.0457660
\(879\) 30.9160 1.04277
\(880\) 9.78586 0.329881
\(881\) 8.52856 0.287335 0.143667 0.989626i \(-0.454110\pi\)
0.143667 + 0.989626i \(0.454110\pi\)
\(882\) −0.434584 −0.0146332
\(883\) −18.6902 −0.628975 −0.314488 0.949262i \(-0.601833\pi\)
−0.314488 + 0.949262i \(0.601833\pi\)
\(884\) −1.15073 −0.0387031
\(885\) 9.77789 0.328680
\(886\) −0.539079 −0.0181107
\(887\) 21.3802 0.717876 0.358938 0.933361i \(-0.383139\pi\)
0.358938 + 0.933361i \(0.383139\pi\)
\(888\) −1.46069 −0.0490176
\(889\) 6.52874 0.218967
\(890\) 1.11141 0.0372547
\(891\) 2.54836 0.0853732
\(892\) 9.87803 0.330741
\(893\) −20.5116 −0.686394
\(894\) 0.586278 0.0196081
\(895\) −9.27504 −0.310030
\(896\) −1.80475 −0.0602925
\(897\) −1.18011 −0.0394028
\(898\) −0.116036 −0.00387218
\(899\) −15.3266 −0.511171
\(900\) 8.11110 0.270370
\(901\) 10.1015 0.336531
\(902\) 0.580755 0.0193370
\(903\) −3.35746 −0.111729
\(904\) 1.07635 0.0357990
\(905\) −9.41672 −0.313022
\(906\) 0.958283 0.0318368
\(907\) 34.0469 1.13051 0.565254 0.824917i \(-0.308778\pi\)
0.565254 + 0.824917i \(0.308778\pi\)
\(908\) 22.0295 0.731076
\(909\) 9.43930 0.313082
\(910\) −0.0316357 −0.00104871
\(911\) 4.73100 0.156745 0.0783725 0.996924i \(-0.475028\pi\)
0.0783725 + 0.996924i \(0.475028\pi\)
\(912\) −12.2689 −0.406265
\(913\) −9.77225 −0.323414
\(914\) −2.47445 −0.0818476
\(915\) −3.71465 −0.122803
\(916\) −18.4419 −0.609339
\(917\) −17.6734 −0.583628
\(918\) 0.0687697 0.00226974
\(919\) −8.05465 −0.265698 −0.132849 0.991136i \(-0.542413\pi\)
−0.132849 + 0.991136i \(0.542413\pi\)
\(920\) 0.543582 0.0179214
\(921\) −1.62405 −0.0535143
\(922\) −2.06952 −0.0681560
\(923\) −3.69601 −0.121656
\(924\) 4.19473 0.137996
\(925\) 21.6119 0.710595
\(926\) −0.737569 −0.0242380
\(927\) −12.0973 −0.397327
\(928\) 2.07492 0.0681127
\(929\) 17.9894 0.590215 0.295107 0.955464i \(-0.404645\pi\)
0.295107 + 0.955464i \(0.404645\pi\)
\(930\) 0.404033 0.0132488
\(931\) −19.5215 −0.639791
\(932\) −4.16380 −0.136390
\(933\) 11.2601 0.368640
\(934\) 1.21127 0.0396339
\(935\) −2.46393 −0.0805792
\(936\) 0.158458 0.00517935
\(937\) −37.1453 −1.21348 −0.606742 0.794899i \(-0.707524\pi\)
−0.606742 + 0.794899i \(0.707524\pi\)
\(938\) 0.729386 0.0238153
\(939\) 22.5098 0.734579
\(940\) 12.8095 0.417801
\(941\) −9.88039 −0.322092 −0.161046 0.986947i \(-0.551487\pi\)
−0.161046 + 0.986947i \(0.551487\pi\)
\(942\) 0.0687697 0.00224064
\(943\) −6.78093 −0.220818
\(944\) −40.1650 −1.30726
\(945\) −0.797646 −0.0259474
\(946\) 0.713223 0.0231889
\(947\) 48.1681 1.56525 0.782626 0.622492i \(-0.213880\pi\)
0.782626 + 0.622492i \(0.213880\pi\)
\(948\) −5.79403 −0.188181
\(949\) −5.89265 −0.191284
\(950\) −0.863596 −0.0280188
\(951\) 2.96039 0.0959972
\(952\) 0.226665 0.00734627
\(953\) 0.832859 0.0269789 0.0134895 0.999909i \(-0.495706\pi\)
0.0134895 + 0.999909i \(0.495706\pi\)
\(954\) −0.694680 −0.0224911
\(955\) 6.71856 0.217407
\(956\) −1.07851 −0.0348815
\(957\) −6.42769 −0.207778
\(958\) 2.04981 0.0662263
\(959\) 9.83830 0.317695
\(960\) 7.62544 0.246110
\(961\) 5.92345 0.191079
\(962\) 0.210854 0.00679820
\(963\) 4.73549 0.152599
\(964\) −18.4476 −0.594157
\(965\) 3.41853 0.110046
\(966\) 0.116089 0.00373512
\(967\) −45.0988 −1.45028 −0.725139 0.688602i \(-0.758225\pi\)
−0.725139 + 0.688602i \(0.758225\pi\)
\(968\) 1.23801 0.0397910
\(969\) 3.08913 0.0992371
\(970\) −0.284649 −0.00913953
\(971\) 13.6771 0.438919 0.219460 0.975622i \(-0.429571\pi\)
0.219460 + 0.975622i \(0.429571\pi\)
\(972\) 1.99527 0.0639983
\(973\) 17.9926 0.576817
\(974\) 0.999777 0.0320349
\(975\) −2.34449 −0.0750836
\(976\) 15.2588 0.488422
\(977\) −12.5137 −0.400350 −0.200175 0.979760i \(-0.564151\pi\)
−0.200175 + 0.979760i \(0.564151\pi\)
\(978\) 0.666609 0.0213158
\(979\) 42.5962 1.36138
\(980\) 12.1912 0.389434
\(981\) −0.611447 −0.0195220
\(982\) 1.24026 0.0395783
\(983\) 8.65602 0.276084 0.138042 0.990426i \(-0.455919\pi\)
0.138042 + 0.990426i \(0.455919\pi\)
\(984\) 0.910498 0.0290256
\(985\) 5.79978 0.184796
\(986\) −0.173457 −0.00552399
\(987\) 5.47779 0.174360
\(988\) 3.55474 0.113091
\(989\) −8.32764 −0.264804
\(990\) 0.169444 0.00538528
\(991\) 22.1611 0.703971 0.351986 0.936005i \(-0.385507\pi\)
0.351986 + 0.936005i \(0.385507\pi\)
\(992\) −4.99872 −0.158710
\(993\) −4.04784 −0.128454
\(994\) 0.363582 0.0115321
\(995\) 13.1428 0.416655
\(996\) −7.65132 −0.242441
\(997\) −4.89419 −0.155001 −0.0775003 0.996992i \(-0.524694\pi\)
−0.0775003 + 0.996992i \(0.524694\pi\)
\(998\) −1.21476 −0.0384527
\(999\) 5.31637 0.168202
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 8007.2.a.f.1.25 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.f.1.25 48 1.1 even 1 trivial