Properties

Label 6026.2.a.i.1.5
Level 6026
Weight 2
Character 6026.1
Self dual Yes
Analytic conductor 48.118
Analytic rank 1
Dimension 25
CM No

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Newspace parameters

Level: \( N \) = \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.117852258\)
Analytic rank: \(1\)
Dimension: \(25\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.37203 q^{3} +1.00000 q^{4} +3.53118 q^{5} +2.37203 q^{6} -2.86520 q^{7} -1.00000 q^{8} +2.62654 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.37203 q^{3} +1.00000 q^{4} +3.53118 q^{5} +2.37203 q^{6} -2.86520 q^{7} -1.00000 q^{8} +2.62654 q^{9} -3.53118 q^{10} -4.60247 q^{11} -2.37203 q^{12} +2.65812 q^{13} +2.86520 q^{14} -8.37608 q^{15} +1.00000 q^{16} -6.58468 q^{17} -2.62654 q^{18} +1.84283 q^{19} +3.53118 q^{20} +6.79636 q^{21} +4.60247 q^{22} +1.00000 q^{23} +2.37203 q^{24} +7.46926 q^{25} -2.65812 q^{26} +0.885865 q^{27} -2.86520 q^{28} +2.39794 q^{29} +8.37608 q^{30} -6.52436 q^{31} -1.00000 q^{32} +10.9172 q^{33} +6.58468 q^{34} -10.1176 q^{35} +2.62654 q^{36} +3.71765 q^{37} -1.84283 q^{38} -6.30514 q^{39} -3.53118 q^{40} +0.349877 q^{41} -6.79636 q^{42} +5.24396 q^{43} -4.60247 q^{44} +9.27479 q^{45} -1.00000 q^{46} +13.5458 q^{47} -2.37203 q^{48} +1.20940 q^{49} -7.46926 q^{50} +15.6191 q^{51} +2.65812 q^{52} +12.3827 q^{53} -0.885865 q^{54} -16.2522 q^{55} +2.86520 q^{56} -4.37125 q^{57} -2.39794 q^{58} -2.43257 q^{59} -8.37608 q^{60} +8.63341 q^{61} +6.52436 q^{62} -7.52557 q^{63} +1.00000 q^{64} +9.38629 q^{65} -10.9172 q^{66} -7.42685 q^{67} -6.58468 q^{68} -2.37203 q^{69} +10.1176 q^{70} -1.64634 q^{71} -2.62654 q^{72} -4.60406 q^{73} -3.71765 q^{74} -17.7173 q^{75} +1.84283 q^{76} +13.1870 q^{77} +6.30514 q^{78} +7.32188 q^{79} +3.53118 q^{80} -9.98091 q^{81} -0.349877 q^{82} -7.98777 q^{83} +6.79636 q^{84} -23.2517 q^{85} -5.24396 q^{86} -5.68799 q^{87} +4.60247 q^{88} +5.19792 q^{89} -9.27479 q^{90} -7.61604 q^{91} +1.00000 q^{92} +15.4760 q^{93} -13.5458 q^{94} +6.50736 q^{95} +2.37203 q^{96} -4.38352 q^{97} -1.20940 q^{98} -12.0886 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25q - 25q^{2} - 4q^{3} + 25q^{4} - 3q^{5} + 4q^{6} - 11q^{7} - 25q^{8} + 19q^{9} + O(q^{10}) \) \( 25q - 25q^{2} - 4q^{3} + 25q^{4} - 3q^{5} + 4q^{6} - 11q^{7} - 25q^{8} + 19q^{9} + 3q^{10} - 12q^{11} - 4q^{12} - 6q^{13} + 11q^{14} + 25q^{16} + 8q^{17} - 19q^{18} - 23q^{19} - 3q^{20} - 16q^{21} + 12q^{22} + 25q^{23} + 4q^{24} + 4q^{25} + 6q^{26} - 13q^{27} - 11q^{28} - 7q^{29} - 7q^{31} - 25q^{32} + 3q^{33} - 8q^{34} - 18q^{35} + 19q^{36} - 7q^{37} + 23q^{38} - 2q^{39} + 3q^{40} - 10q^{41} + 16q^{42} - 26q^{43} - 12q^{44} + 20q^{45} - 25q^{46} - 2q^{47} - 4q^{48} + 2q^{49} - 4q^{50} - 28q^{51} - 6q^{52} + 47q^{53} + 13q^{54} - 38q^{55} + 11q^{56} - 4q^{57} + 7q^{58} - 19q^{59} - 26q^{61} + 7q^{62} - 15q^{63} + 25q^{64} + 13q^{65} - 3q^{66} - 34q^{67} + 8q^{68} - 4q^{69} + 18q^{70} - 10q^{71} - 19q^{72} - 22q^{73} + 7q^{74} - 8q^{75} - 23q^{76} + 28q^{77} + 2q^{78} - 21q^{79} - 3q^{80} - 27q^{81} + 10q^{82} - 16q^{83} - 16q^{84} - 42q^{85} + 26q^{86} - 17q^{87} + 12q^{88} + 27q^{89} - 20q^{90} - 26q^{91} + 25q^{92} - 27q^{93} + 2q^{94} + 4q^{96} + 4q^{97} - 2q^{98} - 2q^{99} + O(q^{100}) \)

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
\(3\) −2.37203 −1.36949 −0.684747 0.728781i \(-0.740087\pi\)
−0.684747 + 0.728781i \(0.740087\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.53118 1.57919 0.789597 0.613626i \(-0.210290\pi\)
0.789597 + 0.613626i \(0.210290\pi\)
\(6\) 2.37203 0.968378
\(7\) −2.86520 −1.08295 −0.541473 0.840718i \(-0.682133\pi\)
−0.541473 + 0.840718i \(0.682133\pi\)
\(8\) −1.00000 −0.353553
\(9\) 2.62654 0.875513
\(10\) −3.53118 −1.11666
\(11\) −4.60247 −1.38770 −0.693849 0.720121i \(-0.744086\pi\)
−0.693849 + 0.720121i \(0.744086\pi\)
\(12\) −2.37203 −0.684747
\(13\) 2.65812 0.737229 0.368614 0.929582i \(-0.379832\pi\)
0.368614 + 0.929582i \(0.379832\pi\)
\(14\) 2.86520 0.765758
\(15\) −8.37608 −2.16269
\(16\) 1.00000 0.250000
\(17\) −6.58468 −1.59702 −0.798510 0.601982i \(-0.794378\pi\)
−0.798510 + 0.601982i \(0.794378\pi\)
\(18\) −2.62654 −0.619081
\(19\) 1.84283 0.422774 0.211387 0.977402i \(-0.432202\pi\)
0.211387 + 0.977402i \(0.432202\pi\)
\(20\) 3.53118 0.789597
\(21\) 6.79636 1.48309
\(22\) 4.60247 0.981250
\(23\) 1.00000 0.208514
\(24\) 2.37203 0.484189
\(25\) 7.46926 1.49385
\(26\) −2.65812 −0.521299
\(27\) 0.885865 0.170485
\(28\) −2.86520 −0.541473
\(29\) 2.39794 0.445286 0.222643 0.974900i \(-0.428532\pi\)
0.222643 + 0.974900i \(0.428532\pi\)
\(30\) 8.37608 1.52926
\(31\) −6.52436 −1.17181 −0.585905 0.810380i \(-0.699261\pi\)
−0.585905 + 0.810380i \(0.699261\pi\)
\(32\) −1.00000 −0.176777
\(33\) 10.9172 1.90044
\(34\) 6.58468 1.12926
\(35\) −10.1176 −1.71018
\(36\) 2.62654 0.437756
\(37\) 3.71765 0.611179 0.305589 0.952163i \(-0.401147\pi\)
0.305589 + 0.952163i \(0.401147\pi\)
\(38\) −1.84283 −0.298946
\(39\) −6.30514 −1.00963
\(40\) −3.53118 −0.558329
\(41\) 0.349877 0.0546416 0.0273208 0.999627i \(-0.491302\pi\)
0.0273208 + 0.999627i \(0.491302\pi\)
\(42\) −6.79636 −1.04870
\(43\) 5.24396 0.799697 0.399848 0.916581i \(-0.369063\pi\)
0.399848 + 0.916581i \(0.369063\pi\)
\(44\) −4.60247 −0.693849
\(45\) 9.27479 1.38260
\(46\) −1.00000 −0.147442
\(47\) 13.5458 1.97586 0.987929 0.154906i \(-0.0495075\pi\)
0.987929 + 0.154906i \(0.0495075\pi\)
\(48\) −2.37203 −0.342373
\(49\) 1.20940 0.172771
\(50\) −7.46926 −1.05631
\(51\) 15.6191 2.18711
\(52\) 2.65812 0.368614
\(53\) 12.3827 1.70089 0.850446 0.526063i \(-0.176332\pi\)
0.850446 + 0.526063i \(0.176332\pi\)
\(54\) −0.885865 −0.120551
\(55\) −16.2522 −2.19144
\(56\) 2.86520 0.382879
\(57\) −4.37125 −0.578986
\(58\) −2.39794 −0.314865
\(59\) −2.43257 −0.316693 −0.158347 0.987384i \(-0.550616\pi\)
−0.158347 + 0.987384i \(0.550616\pi\)
\(60\) −8.37608 −1.08135
\(61\) 8.63341 1.10540 0.552698 0.833382i \(-0.313598\pi\)
0.552698 + 0.833382i \(0.313598\pi\)
\(62\) 6.52436 0.828594
\(63\) −7.52557 −0.948132
\(64\) 1.00000 0.125000
\(65\) 9.38629 1.16423
\(66\) −10.9172 −1.34382
\(67\) −7.42685 −0.907334 −0.453667 0.891171i \(-0.649884\pi\)
−0.453667 + 0.891171i \(0.649884\pi\)
\(68\) −6.58468 −0.798510
\(69\) −2.37203 −0.285559
\(70\) 10.1176 1.20928
\(71\) −1.64634 −0.195384 −0.0976921 0.995217i \(-0.531146\pi\)
−0.0976921 + 0.995217i \(0.531146\pi\)
\(72\) −2.62654 −0.309540
\(73\) −4.60406 −0.538865 −0.269432 0.963019i \(-0.586836\pi\)
−0.269432 + 0.963019i \(0.586836\pi\)
\(74\) −3.71765 −0.432169
\(75\) −17.7173 −2.04582
\(76\) 1.84283 0.211387
\(77\) 13.1870 1.50280
\(78\) 6.30514 0.713916
\(79\) 7.32188 0.823776 0.411888 0.911235i \(-0.364870\pi\)
0.411888 + 0.911235i \(0.364870\pi\)
\(80\) 3.53118 0.394798
\(81\) −9.98091 −1.10899
\(82\) −0.349877 −0.0386375
\(83\) −7.98777 −0.876772 −0.438386 0.898787i \(-0.644450\pi\)
−0.438386 + 0.898787i \(0.644450\pi\)
\(84\) 6.79636 0.741543
\(85\) −23.2517 −2.52200
\(86\) −5.24396 −0.565471
\(87\) −5.68799 −0.609816
\(88\) 4.60247 0.490625
\(89\) 5.19792 0.550978 0.275489 0.961304i \(-0.411160\pi\)
0.275489 + 0.961304i \(0.411160\pi\)
\(90\) −9.27479 −0.977648
\(91\) −7.61604 −0.798378
\(92\) 1.00000 0.104257
\(93\) 15.4760 1.60479
\(94\) −13.5458 −1.39714
\(95\) 6.50736 0.667641
\(96\) 2.37203 0.242095
\(97\) −4.38352 −0.445079 −0.222539 0.974924i \(-0.571435\pi\)
−0.222539 + 0.974924i \(0.571435\pi\)
\(98\) −1.20940 −0.122168
\(99\) −12.0886 −1.21495
\(100\) 7.46926 0.746926
\(101\) −6.86910 −0.683501 −0.341750 0.939791i \(-0.611020\pi\)
−0.341750 + 0.939791i \(0.611020\pi\)
\(102\) −15.6191 −1.54652
\(103\) −9.31126 −0.917466 −0.458733 0.888574i \(-0.651697\pi\)
−0.458733 + 0.888574i \(0.651697\pi\)
\(104\) −2.65812 −0.260650
\(105\) 23.9992 2.34208
\(106\) −12.3827 −1.20271
\(107\) 0.856111 0.0827634 0.0413817 0.999143i \(-0.486824\pi\)
0.0413817 + 0.999143i \(0.486824\pi\)
\(108\) 0.885865 0.0852424
\(109\) −10.8634 −1.04052 −0.520262 0.854006i \(-0.674166\pi\)
−0.520262 + 0.854006i \(0.674166\pi\)
\(110\) 16.2522 1.54958
\(111\) −8.81840 −0.837005
\(112\) −2.86520 −0.270736
\(113\) 1.39476 0.131208 0.0656039 0.997846i \(-0.479103\pi\)
0.0656039 + 0.997846i \(0.479103\pi\)
\(114\) 4.37125 0.409405
\(115\) 3.53118 0.329285
\(116\) 2.39794 0.222643
\(117\) 6.98164 0.645453
\(118\) 2.43257 0.223936
\(119\) 18.8665 1.72948
\(120\) 8.37608 0.764628
\(121\) 10.1828 0.925705
\(122\) −8.63341 −0.781633
\(123\) −0.829920 −0.0748314
\(124\) −6.52436 −0.585905
\(125\) 8.71940 0.779887
\(126\) 7.52557 0.670431
\(127\) −19.2048 −1.70415 −0.852074 0.523421i \(-0.824656\pi\)
−0.852074 + 0.523421i \(0.824656\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −12.4389 −1.09518
\(130\) −9.38629 −0.823232
\(131\) 1.00000 0.0873704
\(132\) 10.9172 0.950221
\(133\) −5.28008 −0.457841
\(134\) 7.42685 0.641582
\(135\) 3.12815 0.269228
\(136\) 6.58468 0.564632
\(137\) −13.4176 −1.14634 −0.573171 0.819435i \(-0.694287\pi\)
−0.573171 + 0.819435i \(0.694287\pi\)
\(138\) 2.37203 0.201921
\(139\) −0.128035 −0.0108598 −0.00542988 0.999985i \(-0.501728\pi\)
−0.00542988 + 0.999985i \(0.501728\pi\)
\(140\) −10.1176 −0.855090
\(141\) −32.1311 −2.70593
\(142\) 1.64634 0.138157
\(143\) −12.2339 −1.02305
\(144\) 2.62654 0.218878
\(145\) 8.46756 0.703193
\(146\) 4.60406 0.381035
\(147\) −2.86873 −0.236609
\(148\) 3.71765 0.305589
\(149\) 10.8685 0.890385 0.445192 0.895435i \(-0.353135\pi\)
0.445192 + 0.895435i \(0.353135\pi\)
\(150\) 17.7173 1.44661
\(151\) −20.2227 −1.64570 −0.822850 0.568258i \(-0.807618\pi\)
−0.822850 + 0.568258i \(0.807618\pi\)
\(152\) −1.84283 −0.149473
\(153\) −17.2949 −1.39821
\(154\) −13.1870 −1.06264
\(155\) −23.0387 −1.85051
\(156\) −6.30514 −0.504815
\(157\) 10.8903 0.869138 0.434569 0.900639i \(-0.356901\pi\)
0.434569 + 0.900639i \(0.356901\pi\)
\(158\) −7.32188 −0.582497
\(159\) −29.3721 −2.32936
\(160\) −3.53118 −0.279165
\(161\) −2.86520 −0.225810
\(162\) 9.98091 0.784175
\(163\) −1.48802 −0.116550 −0.0582752 0.998301i \(-0.518560\pi\)
−0.0582752 + 0.998301i \(0.518560\pi\)
\(164\) 0.349877 0.0273208
\(165\) 38.5507 3.00117
\(166\) 7.98777 0.619971
\(167\) −1.28328 −0.0993032 −0.0496516 0.998767i \(-0.515811\pi\)
−0.0496516 + 0.998767i \(0.515811\pi\)
\(168\) −6.79636 −0.524350
\(169\) −5.93442 −0.456494
\(170\) 23.2517 1.78332
\(171\) 4.84026 0.370144
\(172\) 5.24396 0.399848
\(173\) 15.6009 1.18612 0.593058 0.805160i \(-0.297920\pi\)
0.593058 + 0.805160i \(0.297920\pi\)
\(174\) 5.68799 0.431205
\(175\) −21.4009 −1.61776
\(176\) −4.60247 −0.346924
\(177\) 5.77013 0.433710
\(178\) −5.19792 −0.389601
\(179\) 2.30979 0.172642 0.0863208 0.996267i \(-0.472489\pi\)
0.0863208 + 0.996267i \(0.472489\pi\)
\(180\) 9.27479 0.691302
\(181\) −1.65690 −0.123156 −0.0615782 0.998102i \(-0.519613\pi\)
−0.0615782 + 0.998102i \(0.519613\pi\)
\(182\) 7.61604 0.564539
\(183\) −20.4787 −1.51383
\(184\) −1.00000 −0.0737210
\(185\) 13.1277 0.965169
\(186\) −15.4760 −1.13475
\(187\) 30.3058 2.21618
\(188\) 13.5458 0.987929
\(189\) −2.53818 −0.184626
\(190\) −6.50736 −0.472094
\(191\) −15.3327 −1.10943 −0.554717 0.832039i \(-0.687173\pi\)
−0.554717 + 0.832039i \(0.687173\pi\)
\(192\) −2.37203 −0.171187
\(193\) 18.0487 1.29917 0.649587 0.760287i \(-0.274942\pi\)
0.649587 + 0.760287i \(0.274942\pi\)
\(194\) 4.38352 0.314718
\(195\) −22.2646 −1.59440
\(196\) 1.20940 0.0863855
\(197\) 12.4726 0.888636 0.444318 0.895869i \(-0.353446\pi\)
0.444318 + 0.895869i \(0.353446\pi\)
\(198\) 12.0886 0.859097
\(199\) 14.9259 1.05807 0.529035 0.848600i \(-0.322554\pi\)
0.529035 + 0.848600i \(0.322554\pi\)
\(200\) −7.46926 −0.528156
\(201\) 17.6167 1.24259
\(202\) 6.86910 0.483308
\(203\) −6.87058 −0.482221
\(204\) 15.6191 1.09355
\(205\) 1.23548 0.0862897
\(206\) 9.31126 0.648746
\(207\) 2.62654 0.182557
\(208\) 2.65812 0.184307
\(209\) −8.48156 −0.586682
\(210\) −23.9992 −1.65610
\(211\) 17.6352 1.21405 0.607027 0.794681i \(-0.292362\pi\)
0.607027 + 0.794681i \(0.292362\pi\)
\(212\) 12.3827 0.850446
\(213\) 3.90516 0.267577
\(214\) −0.856111 −0.0585225
\(215\) 18.5174 1.26288
\(216\) −0.885865 −0.0602755
\(217\) 18.6936 1.26901
\(218\) 10.8634 0.735762
\(219\) 10.9210 0.737972
\(220\) −16.2522 −1.09572
\(221\) −17.5028 −1.17737
\(222\) 8.81840 0.591852
\(223\) 15.1656 1.01557 0.507783 0.861485i \(-0.330465\pi\)
0.507783 + 0.861485i \(0.330465\pi\)
\(224\) 2.86520 0.191440
\(225\) 19.6183 1.30789
\(226\) −1.39476 −0.0927780
\(227\) 1.68550 0.111870 0.0559352 0.998434i \(-0.482186\pi\)
0.0559352 + 0.998434i \(0.482186\pi\)
\(228\) −4.37125 −0.289493
\(229\) 0.649134 0.0428960 0.0214480 0.999770i \(-0.493172\pi\)
0.0214480 + 0.999770i \(0.493172\pi\)
\(230\) −3.53118 −0.232839
\(231\) −31.2800 −2.05808
\(232\) −2.39794 −0.157432
\(233\) 2.37661 0.155697 0.0778484 0.996965i \(-0.475195\pi\)
0.0778484 + 0.996965i \(0.475195\pi\)
\(234\) −6.98164 −0.456404
\(235\) 47.8327 3.12026
\(236\) −2.43257 −0.158347
\(237\) −17.3677 −1.12816
\(238\) −18.8665 −1.22293
\(239\) −17.5990 −1.13838 −0.569192 0.822204i \(-0.692744\pi\)
−0.569192 + 0.822204i \(0.692744\pi\)
\(240\) −8.37608 −0.540674
\(241\) −22.2621 −1.43403 −0.717013 0.697060i \(-0.754491\pi\)
−0.717013 + 0.697060i \(0.754491\pi\)
\(242\) −10.1828 −0.654572
\(243\) 21.0175 1.34827
\(244\) 8.63341 0.552698
\(245\) 4.27060 0.272839
\(246\) 0.829920 0.0529138
\(247\) 4.89845 0.311681
\(248\) 6.52436 0.414297
\(249\) 18.9472 1.20073
\(250\) −8.71940 −0.551463
\(251\) 25.2953 1.59662 0.798311 0.602245i \(-0.205727\pi\)
0.798311 + 0.602245i \(0.205727\pi\)
\(252\) −7.52557 −0.474066
\(253\) −4.60247 −0.289355
\(254\) 19.2048 1.20502
\(255\) 55.1538 3.45387
\(256\) 1.00000 0.0625000
\(257\) −21.9256 −1.36768 −0.683839 0.729633i \(-0.739691\pi\)
−0.683839 + 0.729633i \(0.739691\pi\)
\(258\) 12.4389 0.774409
\(259\) −10.6518 −0.661873
\(260\) 9.38629 0.582113
\(261\) 6.29828 0.389854
\(262\) −1.00000 −0.0617802
\(263\) −5.77093 −0.355851 −0.177925 0.984044i \(-0.556939\pi\)
−0.177925 + 0.984044i \(0.556939\pi\)
\(264\) −10.9172 −0.671908
\(265\) 43.7255 2.68604
\(266\) 5.28008 0.323742
\(267\) −12.3296 −0.754561
\(268\) −7.42685 −0.453667
\(269\) −5.91183 −0.360450 −0.180225 0.983625i \(-0.557683\pi\)
−0.180225 + 0.983625i \(0.557683\pi\)
\(270\) −3.12815 −0.190373
\(271\) −25.4696 −1.54717 −0.773584 0.633693i \(-0.781538\pi\)
−0.773584 + 0.633693i \(0.781538\pi\)
\(272\) −6.58468 −0.399255
\(273\) 18.0655 1.09337
\(274\) 13.4176 0.810587
\(275\) −34.3770 −2.07301
\(276\) −2.37203 −0.142780
\(277\) 12.3341 0.741086 0.370543 0.928815i \(-0.379172\pi\)
0.370543 + 0.928815i \(0.379172\pi\)
\(278\) 0.128035 0.00767900
\(279\) −17.1365 −1.02593
\(280\) 10.1176 0.604640
\(281\) −27.6165 −1.64746 −0.823732 0.566979i \(-0.808112\pi\)
−0.823732 + 0.566979i \(0.808112\pi\)
\(282\) 32.1311 1.91338
\(283\) −8.49092 −0.504733 −0.252366 0.967632i \(-0.581209\pi\)
−0.252366 + 0.967632i \(0.581209\pi\)
\(284\) −1.64634 −0.0976921
\(285\) −15.4357 −0.914330
\(286\) 12.2339 0.723406
\(287\) −1.00247 −0.0591739
\(288\) −2.62654 −0.154770
\(289\) 26.3580 1.55047
\(290\) −8.46756 −0.497232
\(291\) 10.3978 0.609532
\(292\) −4.60406 −0.269432
\(293\) −9.55457 −0.558184 −0.279092 0.960264i \(-0.590033\pi\)
−0.279092 + 0.960264i \(0.590033\pi\)
\(294\) 2.86873 0.167308
\(295\) −8.58985 −0.500120
\(296\) −3.71765 −0.216084
\(297\) −4.07717 −0.236581
\(298\) −10.8685 −0.629597
\(299\) 2.65812 0.153723
\(300\) −17.7173 −1.02291
\(301\) −15.0250 −0.866028
\(302\) 20.2227 1.16369
\(303\) 16.2937 0.936050
\(304\) 1.84283 0.105693
\(305\) 30.4862 1.74563
\(306\) 17.2949 0.988684
\(307\) 18.8150 1.07383 0.536913 0.843637i \(-0.319590\pi\)
0.536913 + 0.843637i \(0.319590\pi\)
\(308\) 13.1870 0.751400
\(309\) 22.0866 1.25646
\(310\) 23.0387 1.30851
\(311\) 1.17689 0.0667352 0.0333676 0.999443i \(-0.489377\pi\)
0.0333676 + 0.999443i \(0.489377\pi\)
\(312\) 6.30514 0.356958
\(313\) −13.7512 −0.777265 −0.388633 0.921393i \(-0.627052\pi\)
−0.388633 + 0.921393i \(0.627052\pi\)
\(314\) −10.8903 −0.614573
\(315\) −26.5742 −1.49728
\(316\) 7.32188 0.411888
\(317\) 4.27224 0.239953 0.119976 0.992777i \(-0.461718\pi\)
0.119976 + 0.992777i \(0.461718\pi\)
\(318\) 29.3721 1.64711
\(319\) −11.0364 −0.617922
\(320\) 3.53118 0.197399
\(321\) −2.03072 −0.113344
\(322\) 2.86520 0.159672
\(323\) −12.1344 −0.675178
\(324\) −9.98091 −0.554495
\(325\) 19.8541 1.10131
\(326\) 1.48802 0.0824136
\(327\) 25.7683 1.42499
\(328\) −0.349877 −0.0193187
\(329\) −38.8115 −2.13975
\(330\) −38.5507 −2.12215
\(331\) −31.3277 −1.72193 −0.860963 0.508668i \(-0.830138\pi\)
−0.860963 + 0.508668i \(0.830138\pi\)
\(332\) −7.98777 −0.438386
\(333\) 9.76456 0.535095
\(334\) 1.28328 0.0702180
\(335\) −26.2256 −1.43286
\(336\) 6.79636 0.370772
\(337\) −32.6826 −1.78033 −0.890167 0.455634i \(-0.849412\pi\)
−0.890167 + 0.455634i \(0.849412\pi\)
\(338\) 5.93442 0.322790
\(339\) −3.30841 −0.179688
\(340\) −23.2517 −1.26100
\(341\) 30.0282 1.62612
\(342\) −4.84026 −0.261731
\(343\) 16.5913 0.895844
\(344\) −5.24396 −0.282736
\(345\) −8.37608 −0.450953
\(346\) −15.6009 −0.838711
\(347\) −19.5655 −1.05033 −0.525165 0.851000i \(-0.675997\pi\)
−0.525165 + 0.851000i \(0.675997\pi\)
\(348\) −5.68799 −0.304908
\(349\) −13.9082 −0.744489 −0.372244 0.928135i \(-0.621412\pi\)
−0.372244 + 0.928135i \(0.621412\pi\)
\(350\) 21.4009 1.14393
\(351\) 2.35473 0.125686
\(352\) 4.60247 0.245313
\(353\) −21.3628 −1.13703 −0.568514 0.822673i \(-0.692482\pi\)
−0.568514 + 0.822673i \(0.692482\pi\)
\(354\) −5.77013 −0.306679
\(355\) −5.81351 −0.308549
\(356\) 5.19792 0.275489
\(357\) −44.7518 −2.36852
\(358\) −2.30979 −0.122076
\(359\) −6.05902 −0.319783 −0.159891 0.987135i \(-0.551114\pi\)
−0.159891 + 0.987135i \(0.551114\pi\)
\(360\) −9.27479 −0.488824
\(361\) −15.6040 −0.821262
\(362\) 1.65690 0.0870848
\(363\) −24.1538 −1.26775
\(364\) −7.61604 −0.399189
\(365\) −16.2578 −0.850971
\(366\) 20.4787 1.07044
\(367\) −26.9114 −1.40477 −0.702383 0.711799i \(-0.747881\pi\)
−0.702383 + 0.711799i \(0.747881\pi\)
\(368\) 1.00000 0.0521286
\(369\) 0.918966 0.0478394
\(370\) −13.1277 −0.682478
\(371\) −35.4789 −1.84197
\(372\) 15.4760 0.802393
\(373\) 18.0155 0.932806 0.466403 0.884572i \(-0.345550\pi\)
0.466403 + 0.884572i \(0.345550\pi\)
\(374\) −30.3058 −1.56708
\(375\) −20.6827 −1.06805
\(376\) −13.5458 −0.698571
\(377\) 6.37400 0.328278
\(378\) 2.53818 0.130550
\(379\) −12.2255 −0.627981 −0.313991 0.949426i \(-0.601666\pi\)
−0.313991 + 0.949426i \(0.601666\pi\)
\(380\) 6.50736 0.333821
\(381\) 45.5544 2.33382
\(382\) 15.3327 0.784488
\(383\) −10.9076 −0.557354 −0.278677 0.960385i \(-0.589896\pi\)
−0.278677 + 0.960385i \(0.589896\pi\)
\(384\) 2.37203 0.121047
\(385\) 46.5658 2.37321
\(386\) −18.0487 −0.918655
\(387\) 13.7735 0.700145
\(388\) −4.38352 −0.222539
\(389\) 19.6342 0.995494 0.497747 0.867322i \(-0.334161\pi\)
0.497747 + 0.867322i \(0.334161\pi\)
\(390\) 22.2646 1.12741
\(391\) −6.58468 −0.333002
\(392\) −1.20940 −0.0610838
\(393\) −2.37203 −0.119653
\(394\) −12.4726 −0.628361
\(395\) 25.8549 1.30090
\(396\) −12.0886 −0.607473
\(397\) −22.9879 −1.15373 −0.576864 0.816840i \(-0.695724\pi\)
−0.576864 + 0.816840i \(0.695724\pi\)
\(398\) −14.9259 −0.748168
\(399\) 12.5245 0.627010
\(400\) 7.46926 0.373463
\(401\) −36.6215 −1.82879 −0.914396 0.404820i \(-0.867334\pi\)
−0.914396 + 0.404820i \(0.867334\pi\)
\(402\) −17.6167 −0.878642
\(403\) −17.3425 −0.863891
\(404\) −6.86910 −0.341750
\(405\) −35.2444 −1.75131
\(406\) 6.87058 0.340981
\(407\) −17.1104 −0.848131
\(408\) −15.6191 −0.773259
\(409\) −2.15209 −0.106414 −0.0532069 0.998584i \(-0.516944\pi\)
−0.0532069 + 0.998584i \(0.516944\pi\)
\(410\) −1.23548 −0.0610160
\(411\) 31.8270 1.56991
\(412\) −9.31126 −0.458733
\(413\) 6.96981 0.342962
\(414\) −2.62654 −0.129087
\(415\) −28.2063 −1.38459
\(416\) −2.65812 −0.130325
\(417\) 0.303702 0.0148724
\(418\) 8.48156 0.414847
\(419\) −17.0774 −0.834284 −0.417142 0.908841i \(-0.636968\pi\)
−0.417142 + 0.908841i \(0.636968\pi\)
\(420\) 23.9992 1.17104
\(421\) 0.0841046 0.00409901 0.00204950 0.999998i \(-0.499348\pi\)
0.00204950 + 0.999998i \(0.499348\pi\)
\(422\) −17.6352 −0.858466
\(423\) 35.5786 1.72989
\(424\) −12.3827 −0.601356
\(425\) −49.1827 −2.38571
\(426\) −3.90516 −0.189206
\(427\) −24.7365 −1.19708
\(428\) 0.856111 0.0413817
\(429\) 29.0192 1.40106
\(430\) −18.5174 −0.892988
\(431\) −12.7222 −0.612809 −0.306404 0.951901i \(-0.599126\pi\)
−0.306404 + 0.951901i \(0.599126\pi\)
\(432\) 0.885865 0.0426212
\(433\) 38.6024 1.85511 0.927557 0.373681i \(-0.121905\pi\)
0.927557 + 0.373681i \(0.121905\pi\)
\(434\) −18.6936 −0.897322
\(435\) −20.0853 −0.963018
\(436\) −10.8634 −0.520262
\(437\) 1.84283 0.0881544
\(438\) −10.9210 −0.521825
\(439\) −25.2085 −1.20314 −0.601569 0.798821i \(-0.705457\pi\)
−0.601569 + 0.798821i \(0.705457\pi\)
\(440\) 16.2522 0.774792
\(441\) 3.17653 0.151263
\(442\) 17.5028 0.832525
\(443\) 37.5340 1.78330 0.891648 0.452730i \(-0.149550\pi\)
0.891648 + 0.452730i \(0.149550\pi\)
\(444\) −8.81840 −0.418503
\(445\) 18.3548 0.870101
\(446\) −15.1656 −0.718113
\(447\) −25.7805 −1.21938
\(448\) −2.86520 −0.135368
\(449\) 33.5043 1.58117 0.790584 0.612354i \(-0.209777\pi\)
0.790584 + 0.612354i \(0.209777\pi\)
\(450\) −19.6183 −0.924815
\(451\) −1.61030 −0.0758261
\(452\) 1.39476 0.0656039
\(453\) 47.9689 2.25378
\(454\) −1.68550 −0.0791043
\(455\) −26.8936 −1.26079
\(456\) 4.37125 0.204702
\(457\) −24.4964 −1.14589 −0.572947 0.819592i \(-0.694200\pi\)
−0.572947 + 0.819592i \(0.694200\pi\)
\(458\) −0.649134 −0.0303320
\(459\) −5.83314 −0.272267
\(460\) 3.53118 0.164642
\(461\) 1.63657 0.0762225 0.0381112 0.999274i \(-0.487866\pi\)
0.0381112 + 0.999274i \(0.487866\pi\)
\(462\) 31.2800 1.45528
\(463\) 35.5683 1.65300 0.826499 0.562938i \(-0.190329\pi\)
0.826499 + 0.562938i \(0.190329\pi\)
\(464\) 2.39794 0.111322
\(465\) 54.6486 2.53427
\(466\) −2.37661 −0.110094
\(467\) 1.65707 0.0766801 0.0383401 0.999265i \(-0.487793\pi\)
0.0383401 + 0.999265i \(0.487793\pi\)
\(468\) 6.98164 0.322726
\(469\) 21.2794 0.982593
\(470\) −47.8327 −2.20636
\(471\) −25.8321 −1.19028
\(472\) 2.43257 0.111968
\(473\) −24.1352 −1.10974
\(474\) 17.3677 0.797727
\(475\) 13.7646 0.631561
\(476\) 18.8665 0.864742
\(477\) 32.5236 1.48915
\(478\) 17.5990 0.804960
\(479\) 15.7331 0.718866 0.359433 0.933171i \(-0.382970\pi\)
0.359433 + 0.933171i \(0.382970\pi\)
\(480\) 8.37608 0.382314
\(481\) 9.88195 0.450578
\(482\) 22.2621 1.01401
\(483\) 6.79636 0.309245
\(484\) 10.1828 0.462852
\(485\) −15.4790 −0.702865
\(486\) −21.0175 −0.953371
\(487\) −8.28468 −0.375415 −0.187707 0.982225i \(-0.560106\pi\)
−0.187707 + 0.982225i \(0.560106\pi\)
\(488\) −8.63341 −0.390816
\(489\) 3.52962 0.159615
\(490\) −4.27060 −0.192926
\(491\) −39.5767 −1.78607 −0.893037 0.449984i \(-0.851430\pi\)
−0.893037 + 0.449984i \(0.851430\pi\)
\(492\) −0.829920 −0.0374157
\(493\) −15.7897 −0.711130
\(494\) −4.89845 −0.220392
\(495\) −42.6869 −1.91864
\(496\) −6.52436 −0.292952
\(497\) 4.71709 0.211590
\(498\) −18.9472 −0.849046
\(499\) 9.09192 0.407010 0.203505 0.979074i \(-0.434767\pi\)
0.203505 + 0.979074i \(0.434767\pi\)
\(500\) 8.71940 0.389943
\(501\) 3.04398 0.135995
\(502\) −25.2953 −1.12898
\(503\) 8.35263 0.372425 0.186213 0.982509i \(-0.440379\pi\)
0.186213 + 0.982509i \(0.440379\pi\)
\(504\) 7.52557 0.335215
\(505\) −24.2560 −1.07938
\(506\) 4.60247 0.204605
\(507\) 14.0766 0.625166
\(508\) −19.2048 −0.852074
\(509\) −16.9820 −0.752714 −0.376357 0.926475i \(-0.622823\pi\)
−0.376357 + 0.926475i \(0.622823\pi\)
\(510\) −55.1538 −2.44225
\(511\) 13.1916 0.583561
\(512\) −1.00000 −0.0441942
\(513\) 1.63250 0.0720765
\(514\) 21.9256 0.967095
\(515\) −32.8798 −1.44886
\(516\) −12.4389 −0.547590
\(517\) −62.3442 −2.74189
\(518\) 10.6518 0.468015
\(519\) −37.0059 −1.62438
\(520\) −9.38629 −0.411616
\(521\) −22.3861 −0.980751 −0.490376 0.871511i \(-0.663140\pi\)
−0.490376 + 0.871511i \(0.663140\pi\)
\(522\) −6.29828 −0.275668
\(523\) −4.29538 −0.187824 −0.0939119 0.995581i \(-0.529937\pi\)
−0.0939119 + 0.995581i \(0.529937\pi\)
\(524\) 1.00000 0.0436852
\(525\) 50.7637 2.21551
\(526\) 5.77093 0.251624
\(527\) 42.9608 1.87140
\(528\) 10.9172 0.475111
\(529\) 1.00000 0.0434783
\(530\) −43.7255 −1.89931
\(531\) −6.38923 −0.277269
\(532\) −5.28008 −0.228920
\(533\) 0.930014 0.0402834
\(534\) 12.3296 0.533555
\(535\) 3.02308 0.130699
\(536\) 7.42685 0.320791
\(537\) −5.47889 −0.236431
\(538\) 5.91183 0.254877
\(539\) −5.56622 −0.239754
\(540\) 3.12815 0.134614
\(541\) −30.6922 −1.31956 −0.659780 0.751459i \(-0.729351\pi\)
−0.659780 + 0.751459i \(0.729351\pi\)
\(542\) 25.4696 1.09401
\(543\) 3.93022 0.168662
\(544\) 6.58468 0.282316
\(545\) −38.3607 −1.64319
\(546\) −18.0655 −0.773132
\(547\) 19.1282 0.817864 0.408932 0.912565i \(-0.365901\pi\)
0.408932 + 0.912565i \(0.365901\pi\)
\(548\) −13.4176 −0.573171
\(549\) 22.6760 0.967788
\(550\) 34.3770 1.46584
\(551\) 4.41899 0.188255
\(552\) 2.37203 0.100960
\(553\) −20.9787 −0.892104
\(554\) −12.3341 −0.524027
\(555\) −31.1394 −1.32179
\(556\) −0.128035 −0.00542988
\(557\) 40.4673 1.71465 0.857327 0.514772i \(-0.172123\pi\)
0.857327 + 0.514772i \(0.172123\pi\)
\(558\) 17.1365 0.725445
\(559\) 13.9391 0.589559
\(560\) −10.1176 −0.427545
\(561\) −71.8863 −3.03504
\(562\) 27.6165 1.16493
\(563\) 23.7118 0.999334 0.499667 0.866218i \(-0.333456\pi\)
0.499667 + 0.866218i \(0.333456\pi\)
\(564\) −32.1311 −1.35296
\(565\) 4.92515 0.207203
\(566\) 8.49092 0.356900
\(567\) 28.5974 1.20098
\(568\) 1.64634 0.0690787
\(569\) −0.740963 −0.0310628 −0.0155314 0.999879i \(-0.504944\pi\)
−0.0155314 + 0.999879i \(0.504944\pi\)
\(570\) 15.4357 0.646529
\(571\) −7.78316 −0.325715 −0.162858 0.986650i \(-0.552071\pi\)
−0.162858 + 0.986650i \(0.552071\pi\)
\(572\) −12.2339 −0.511525
\(573\) 36.3696 1.51936
\(574\) 1.00247 0.0418423
\(575\) 7.46926 0.311490
\(576\) 2.62654 0.109439
\(577\) −15.1287 −0.629818 −0.314909 0.949122i \(-0.601974\pi\)
−0.314909 + 0.949122i \(0.601974\pi\)
\(578\) −26.3580 −1.09635
\(579\) −42.8121 −1.77921
\(580\) 8.46756 0.351596
\(581\) 22.8866 0.949496
\(582\) −10.3978 −0.431004
\(583\) −56.9909 −2.36032
\(584\) 4.60406 0.190517
\(585\) 24.6535 1.01929
\(586\) 9.55457 0.394696
\(587\) 4.55083 0.187833 0.0939163 0.995580i \(-0.470061\pi\)
0.0939163 + 0.995580i \(0.470061\pi\)
\(588\) −2.86873 −0.118304
\(589\) −12.0233 −0.495410
\(590\) 8.58985 0.353638
\(591\) −29.5854 −1.21698
\(592\) 3.71765 0.152795
\(593\) 3.57161 0.146668 0.0733341 0.997307i \(-0.476636\pi\)
0.0733341 + 0.997307i \(0.476636\pi\)
\(594\) 4.07717 0.167288
\(595\) 66.6209 2.73119
\(596\) 10.8685 0.445192
\(597\) −35.4047 −1.44902
\(598\) −2.65812 −0.108698
\(599\) −19.7144 −0.805507 −0.402753 0.915309i \(-0.631947\pi\)
−0.402753 + 0.915309i \(0.631947\pi\)
\(600\) 17.7173 0.723307
\(601\) −33.0536 −1.34828 −0.674142 0.738602i \(-0.735487\pi\)
−0.674142 + 0.738602i \(0.735487\pi\)
\(602\) 15.0250 0.612374
\(603\) −19.5069 −0.794382
\(604\) −20.2227 −0.822850
\(605\) 35.9572 1.46187
\(606\) −16.2937 −0.661887
\(607\) 43.9075 1.78215 0.891075 0.453856i \(-0.149952\pi\)
0.891075 + 0.453856i \(0.149952\pi\)
\(608\) −1.84283 −0.0747365
\(609\) 16.2972 0.660398
\(610\) −30.4862 −1.23435
\(611\) 36.0063 1.45666
\(612\) −17.2949 −0.699105
\(613\) −29.5240 −1.19246 −0.596232 0.802812i \(-0.703336\pi\)
−0.596232 + 0.802812i \(0.703336\pi\)
\(614\) −18.8150 −0.759310
\(615\) −2.93060 −0.118173
\(616\) −13.1870 −0.531320
\(617\) 29.9401 1.20534 0.602672 0.797989i \(-0.294103\pi\)
0.602672 + 0.797989i \(0.294103\pi\)
\(618\) −22.0866 −0.888454
\(619\) 4.22964 0.170004 0.0850018 0.996381i \(-0.472910\pi\)
0.0850018 + 0.996381i \(0.472910\pi\)
\(620\) −23.0387 −0.925257
\(621\) 0.885865 0.0355485
\(622\) −1.17689 −0.0471889
\(623\) −14.8931 −0.596680
\(624\) −6.30514 −0.252407
\(625\) −6.55649 −0.262259
\(626\) 13.7512 0.549610
\(627\) 20.1185 0.803457
\(628\) 10.8903 0.434569
\(629\) −24.4796 −0.976064
\(630\) 26.5742 1.05874
\(631\) −46.6851 −1.85850 −0.929252 0.369446i \(-0.879548\pi\)
−0.929252 + 0.369446i \(0.879548\pi\)
\(632\) −7.32188 −0.291249
\(633\) −41.8312 −1.66264
\(634\) −4.27224 −0.169672
\(635\) −67.8156 −2.69118
\(636\) −29.3721 −1.16468
\(637\) 3.21472 0.127372
\(638\) 11.0364 0.436937
\(639\) −4.32416 −0.171061
\(640\) −3.53118 −0.139582
\(641\) 39.5775 1.56322 0.781609 0.623768i \(-0.214399\pi\)
0.781609 + 0.623768i \(0.214399\pi\)
\(642\) 2.03072 0.0801462
\(643\) 17.9126 0.706404 0.353202 0.935547i \(-0.385093\pi\)
0.353202 + 0.935547i \(0.385093\pi\)
\(644\) −2.86520 −0.112905
\(645\) −43.9239 −1.72950
\(646\) 12.1344 0.477423
\(647\) −23.0255 −0.905224 −0.452612 0.891707i \(-0.649508\pi\)
−0.452612 + 0.891707i \(0.649508\pi\)
\(648\) 9.98091 0.392087
\(649\) 11.1958 0.439475
\(650\) −19.8541 −0.778744
\(651\) −44.3419 −1.73789
\(652\) −1.48802 −0.0582752
\(653\) 20.5208 0.803040 0.401520 0.915850i \(-0.368482\pi\)
0.401520 + 0.915850i \(0.368482\pi\)
\(654\) −25.7683 −1.00762
\(655\) 3.53118 0.137975
\(656\) 0.349877 0.0136604
\(657\) −12.0927 −0.471783
\(658\) 38.8115 1.51303
\(659\) 12.3967 0.482908 0.241454 0.970412i \(-0.422376\pi\)
0.241454 + 0.970412i \(0.422376\pi\)
\(660\) 38.5507 1.50058
\(661\) −5.06913 −0.197166 −0.0985831 0.995129i \(-0.531431\pi\)
−0.0985831 + 0.995129i \(0.531431\pi\)
\(662\) 31.3277 1.21759
\(663\) 41.5173 1.61240
\(664\) 7.98777 0.309986
\(665\) −18.6449 −0.723019
\(666\) −9.76456 −0.378369
\(667\) 2.39794 0.0928486
\(668\) −1.28328 −0.0496516
\(669\) −35.9734 −1.39081
\(670\) 26.2256 1.01318
\(671\) −39.7351 −1.53395
\(672\) −6.79636 −0.262175
\(673\) 6.79725 0.262015 0.131007 0.991381i \(-0.458179\pi\)
0.131007 + 0.991381i \(0.458179\pi\)
\(674\) 32.6826 1.25889
\(675\) 6.61675 0.254679
\(676\) −5.93442 −0.228247
\(677\) −36.2236 −1.39218 −0.696092 0.717952i \(-0.745080\pi\)
−0.696092 + 0.717952i \(0.745080\pi\)
\(678\) 3.30841 0.127059
\(679\) 12.5597 0.481996
\(680\) 23.2517 0.891662
\(681\) −3.99805 −0.153206
\(682\) −30.0282 −1.14984
\(683\) −13.3243 −0.509842 −0.254921 0.966962i \(-0.582049\pi\)
−0.254921 + 0.966962i \(0.582049\pi\)
\(684\) 4.84026 0.185072
\(685\) −47.3800 −1.81030
\(686\) −16.5913 −0.633457
\(687\) −1.53977 −0.0587458
\(688\) 5.24396 0.199924
\(689\) 32.9146 1.25395
\(690\) 8.37608 0.318872
\(691\) 20.6876 0.786993 0.393497 0.919326i \(-0.371265\pi\)
0.393497 + 0.919326i \(0.371265\pi\)
\(692\) 15.6009 0.593058
\(693\) 34.6362 1.31572
\(694\) 19.5655 0.742696
\(695\) −0.452114 −0.0171496
\(696\) 5.68799 0.215603
\(697\) −2.30383 −0.0872638
\(698\) 13.9082 0.526433
\(699\) −5.63739 −0.213226
\(700\) −21.4009 −0.808880
\(701\) 14.8534 0.561004 0.280502 0.959853i \(-0.409499\pi\)
0.280502 + 0.959853i \(0.409499\pi\)
\(702\) −2.35473 −0.0888736
\(703\) 6.85100 0.258390
\(704\) −4.60247 −0.173462
\(705\) −113.461 −4.27318
\(706\) 21.3628 0.804001
\(707\) 19.6814 0.740194
\(708\) 5.77013 0.216855
\(709\) −3.73424 −0.140242 −0.0701211 0.997538i \(-0.522339\pi\)
−0.0701211 + 0.997538i \(0.522339\pi\)
\(710\) 5.81351 0.218177
\(711\) 19.2312 0.721226
\(712\) −5.19792 −0.194800
\(713\) −6.52436 −0.244339
\(714\) 44.7518 1.67480
\(715\) −43.2002 −1.61559
\(716\) 2.30979 0.0863208
\(717\) 41.7454 1.55901
\(718\) 6.05902 0.226120
\(719\) −48.2345 −1.79884 −0.899422 0.437082i \(-0.856012\pi\)
−0.899422 + 0.437082i \(0.856012\pi\)
\(720\) 9.27479 0.345651
\(721\) 26.6787 0.993565
\(722\) 15.6040 0.580720
\(723\) 52.8063 1.96389
\(724\) −1.65690 −0.0615782
\(725\) 17.9108 0.665191
\(726\) 24.1538 0.896432
\(727\) 27.0226 1.00221 0.501107 0.865385i \(-0.332926\pi\)
0.501107 + 0.865385i \(0.332926\pi\)
\(728\) 7.61604 0.282269
\(729\) −19.9113 −0.737457
\(730\) 16.2578 0.601728
\(731\) −34.5298 −1.27713
\(732\) −20.4787 −0.756916
\(733\) −15.2136 −0.561928 −0.280964 0.959718i \(-0.590654\pi\)
−0.280964 + 0.959718i \(0.590654\pi\)
\(734\) 26.9114 0.993319
\(735\) −10.1300 −0.373651
\(736\) −1.00000 −0.0368605
\(737\) 34.1819 1.25910
\(738\) −0.918966 −0.0338276
\(739\) 1.87499 0.0689727 0.0344863 0.999405i \(-0.489020\pi\)
0.0344863 + 0.999405i \(0.489020\pi\)
\(740\) 13.1277 0.482585
\(741\) −11.6193 −0.426845
\(742\) 35.4789 1.30247
\(743\) −49.8667 −1.82943 −0.914717 0.404096i \(-0.867586\pi\)
−0.914717 + 0.404096i \(0.867586\pi\)
\(744\) −15.4760 −0.567377
\(745\) 38.3788 1.40609
\(746\) −18.0155 −0.659594
\(747\) −20.9802 −0.767625
\(748\) 30.3058 1.10809
\(749\) −2.45293 −0.0896282
\(750\) 20.6827 0.755225
\(751\) −19.9923 −0.729530 −0.364765 0.931100i \(-0.618851\pi\)
−0.364765 + 0.931100i \(0.618851\pi\)
\(752\) 13.5458 0.493965
\(753\) −60.0012 −2.18656
\(754\) −6.37400 −0.232127
\(755\) −71.4101 −2.59888
\(756\) −2.53818 −0.0923129
\(757\) 22.8026 0.828776 0.414388 0.910100i \(-0.363996\pi\)
0.414388 + 0.910100i \(0.363996\pi\)
\(758\) 12.2255 0.444050
\(759\) 10.9172 0.396270
\(760\) −6.50736 −0.236047
\(761\) −22.5876 −0.818799 −0.409399 0.912355i \(-0.634262\pi\)
−0.409399 + 0.912355i \(0.634262\pi\)
\(762\) −45.5544 −1.65026
\(763\) 31.1259 1.12683
\(764\) −15.3327 −0.554717
\(765\) −61.0715 −2.20804
\(766\) 10.9076 0.394109
\(767\) −6.46605 −0.233475
\(768\) −2.37203 −0.0855933
\(769\) −7.91301 −0.285350 −0.142675 0.989770i \(-0.545570\pi\)
−0.142675 + 0.989770i \(0.545570\pi\)
\(770\) −46.5658 −1.67812
\(771\) 52.0081 1.87303
\(772\) 18.0487 0.649587
\(773\) 19.8640 0.714460 0.357230 0.934016i \(-0.383721\pi\)
0.357230 + 0.934016i \(0.383721\pi\)
\(774\) −13.7735 −0.495077
\(775\) −48.7321 −1.75051
\(776\) 4.38352 0.157359
\(777\) 25.2665 0.906431
\(778\) −19.6342 −0.703920
\(779\) 0.644763 0.0231010
\(780\) −22.2646 −0.797200
\(781\) 7.57721 0.271134
\(782\) 6.58468 0.235468
\(783\) 2.12425 0.0759145
\(784\) 1.20940 0.0431927
\(785\) 38.4555 1.37254
\(786\) 2.37203 0.0846076
\(787\) −44.3764 −1.58185 −0.790924 0.611914i \(-0.790400\pi\)
−0.790924 + 0.611914i \(0.790400\pi\)
\(788\) 12.4726 0.444318
\(789\) 13.6888 0.487335
\(790\) −25.8549 −0.919876
\(791\) −3.99627 −0.142091
\(792\) 12.0886 0.429548
\(793\) 22.9486 0.814929
\(794\) 22.9879 0.815809
\(795\) −103.718 −3.67851
\(796\) 14.9259 0.529035
\(797\) 46.7683 1.65662 0.828309 0.560272i \(-0.189303\pi\)
0.828309 + 0.560272i \(0.189303\pi\)
\(798\) −12.5245 −0.443363
\(799\) −89.1948 −3.15548
\(800\) −7.46926 −0.264078
\(801\) 13.6525 0.482388
\(802\) 36.6215 1.29315
\(803\) 21.1901 0.747781
\(804\) 17.6167 0.621294
\(805\) −10.1176 −0.356597
\(806\) 17.3425 0.610863
\(807\) 14.0230 0.493635
\(808\) 6.86910 0.241654
\(809\) 37.5122 1.31886 0.659430 0.751766i \(-0.270798\pi\)
0.659430 + 0.751766i \(0.270798\pi\)
\(810\) 35.2444 1.23836
\(811\) −31.7522 −1.11497 −0.557484 0.830187i \(-0.688233\pi\)
−0.557484 + 0.830187i \(0.688233\pi\)
\(812\) −6.87058 −0.241110
\(813\) 60.4147 2.11884
\(814\) 17.1104 0.599719
\(815\) −5.25446 −0.184056
\(816\) 15.6191 0.546777
\(817\) 9.66372 0.338091
\(818\) 2.15209 0.0752459
\(819\) −20.0038 −0.698990
\(820\) 1.23548 0.0431449
\(821\) −8.28674 −0.289209 −0.144605 0.989490i \(-0.546191\pi\)
−0.144605 + 0.989490i \(0.546191\pi\)
\(822\) −31.8270 −1.11009
\(823\) −25.8356 −0.900574 −0.450287 0.892884i \(-0.648678\pi\)
−0.450287 + 0.892884i \(0.648678\pi\)
\(824\) 9.31126 0.324373
\(825\) 81.5435 2.83898
\(826\) −6.96981 −0.242511
\(827\) 39.0464 1.35778 0.678888 0.734242i \(-0.262462\pi\)
0.678888 + 0.734242i \(0.262462\pi\)
\(828\) 2.62654 0.0912785
\(829\) −32.1720 −1.11738 −0.558691 0.829376i \(-0.688696\pi\)
−0.558691 + 0.829376i \(0.688696\pi\)
\(830\) 28.2063 0.979054
\(831\) −29.2570 −1.01491
\(832\) 2.65812 0.0921536
\(833\) −7.96349 −0.275919
\(834\) −0.303702 −0.0105163
\(835\) −4.53150 −0.156819
\(836\) −8.48156 −0.293341
\(837\) −5.77970 −0.199776
\(838\) 17.0774 0.589928
\(839\) −39.8153 −1.37458 −0.687289 0.726385i \(-0.741199\pi\)
−0.687289 + 0.726385i \(0.741199\pi\)
\(840\) −23.9992 −0.828051
\(841\) −23.2499 −0.801720
\(842\) −0.0841046 −0.00289843
\(843\) 65.5073 2.25619
\(844\) 17.6352 0.607027
\(845\) −20.9555 −0.720892
\(846\) −35.5786 −1.22322
\(847\) −29.1757 −1.00249
\(848\) 12.3827 0.425223
\(849\) 20.1407 0.691228
\(850\) 49.1827 1.68695
\(851\) 3.71765 0.127440
\(852\) 3.90516 0.133789
\(853\) −12.6996 −0.434826 −0.217413 0.976080i \(-0.569762\pi\)
−0.217413 + 0.976080i \(0.569762\pi\)
\(854\) 24.7365 0.846466
\(855\) 17.0918 0.584528
\(856\) −0.856111 −0.0292613
\(857\) −36.0254 −1.23061 −0.615303 0.788291i \(-0.710966\pi\)
−0.615303 + 0.788291i \(0.710966\pi\)
\(858\) −29.0192 −0.990700
\(859\) 40.0603 1.36684 0.683420 0.730026i \(-0.260492\pi\)
0.683420 + 0.730026i \(0.260492\pi\)
\(860\) 18.5174 0.631438
\(861\) 2.37789 0.0810383
\(862\) 12.7222 0.433321
\(863\) 19.4249 0.661232 0.330616 0.943765i \(-0.392744\pi\)
0.330616 + 0.943765i \(0.392744\pi\)
\(864\) −0.885865 −0.0301377
\(865\) 55.0897 1.87311
\(866\) −38.6024 −1.31176
\(867\) −62.5220 −2.12336
\(868\) 18.6936 0.634503
\(869\) −33.6987 −1.14315
\(870\) 20.0853 0.680956
\(871\) −19.7414 −0.668912
\(872\) 10.8634 0.367881
\(873\) −11.5135 −0.389672
\(874\) −1.84283 −0.0623346
\(875\) −24.9829 −0.844575
\(876\) 10.9210 0.368986
\(877\) −40.3489 −1.36248 −0.681242 0.732058i \(-0.738560\pi\)
−0.681242 + 0.732058i \(0.738560\pi\)
\(878\) 25.2085 0.850747
\(879\) 22.6637 0.764429
\(880\) −16.2522 −0.547861
\(881\) 21.7726 0.733539 0.366769 0.930312i \(-0.380464\pi\)
0.366769 + 0.930312i \(0.380464\pi\)
\(882\) −3.17653 −0.106959
\(883\) −26.7765 −0.901102 −0.450551 0.892751i \(-0.648772\pi\)
−0.450551 + 0.892751i \(0.648772\pi\)
\(884\) −17.5028 −0.588684
\(885\) 20.3754 0.684911
\(886\) −37.5340 −1.26098
\(887\) −25.4827 −0.855626 −0.427813 0.903867i \(-0.640716\pi\)
−0.427813 + 0.903867i \(0.640716\pi\)
\(888\) 8.81840 0.295926
\(889\) 55.0256 1.84550
\(890\) −18.3548 −0.615255
\(891\) 45.9369 1.53894
\(892\) 15.1656 0.507783
\(893\) 24.9626 0.835341
\(894\) 25.7805 0.862229
\(895\) 8.15628 0.272634
\(896\) 2.86520 0.0957198
\(897\) −6.30514 −0.210522
\(898\) −33.5043 −1.11805
\(899\) −15.6450 −0.521790
\(900\) 19.6183 0.653943
\(901\) −81.5360 −2.71636
\(902\) 1.61030 0.0536171
\(903\) 35.6399 1.18602
\(904\) −1.39476 −0.0463890
\(905\) −5.85082 −0.194488
\(906\) −47.9689 −1.59366
\(907\) −28.5005 −0.946342 −0.473171 0.880971i \(-0.656891\pi\)
−0.473171 + 0.880971i \(0.656891\pi\)
\(908\) 1.68550 0.0559352
\(909\) −18.0419 −0.598413
\(910\) 26.8936 0.891516
\(911\) 60.1730 1.99362 0.996810 0.0798139i \(-0.0254326\pi\)
0.996810 + 0.0798139i \(0.0254326\pi\)
\(912\) −4.37125 −0.144746
\(913\) 36.7635 1.21669
\(914\) 24.4964 0.810269
\(915\) −72.3142 −2.39063
\(916\) 0.649134 0.0214480
\(917\) −2.86520 −0.0946174
\(918\) 5.83314 0.192522
\(919\) 23.7586 0.783725 0.391862 0.920024i \(-0.371831\pi\)
0.391862 + 0.920024i \(0.371831\pi\)
\(920\) −3.53118 −0.116420
\(921\) −44.6297 −1.47060
\(922\) −1.63657 −0.0538974
\(923\) −4.37615 −0.144043
\(924\) −31.2800 −1.02904
\(925\) 27.7681 0.913010
\(926\) −35.5683 −1.16885
\(927\) −24.4564 −0.803253
\(928\) −2.39794 −0.0787162
\(929\) 8.42074 0.276276 0.138138 0.990413i \(-0.455888\pi\)
0.138138 + 0.990413i \(0.455888\pi\)
\(930\) −54.6486 −1.79200
\(931\) 2.22871 0.0730430
\(932\) 2.37661 0.0778484
\(933\) −2.79162 −0.0913934
\(934\) −1.65707 −0.0542210
\(935\) 107.015 3.49978
\(936\) −6.98164 −0.228202
\(937\) 9.88632 0.322972 0.161486 0.986875i \(-0.448371\pi\)
0.161486 + 0.986875i \(0.448371\pi\)
\(938\) −21.2794 −0.694798
\(939\) 32.6184 1.06446
\(940\) 47.8327 1.56013
\(941\) −32.6253 −1.06355 −0.531777 0.846885i \(-0.678475\pi\)
−0.531777 + 0.846885i \(0.678475\pi\)
\(942\) 25.8321 0.841654
\(943\) 0.349877 0.0113936
\(944\) −2.43257 −0.0791734
\(945\) −8.96279 −0.291560
\(946\) 24.1352 0.784703
\(947\) 24.1008 0.783172 0.391586 0.920141i \(-0.371926\pi\)
0.391586 + 0.920141i \(0.371926\pi\)
\(948\) −17.3677 −0.564078
\(949\) −12.2381 −0.397266
\(950\) −13.7646 −0.446581
\(951\) −10.1339 −0.328614
\(952\) −18.8665 −0.611465
\(953\) −0.345883 −0.0112043 −0.00560213 0.999984i \(-0.501783\pi\)
−0.00560213 + 0.999984i \(0.501783\pi\)
\(954\) −32.5236 −1.05299
\(955\) −54.1425 −1.75201
\(956\) −17.5990 −0.569192
\(957\) 26.1788 0.846241
\(958\) −15.7331 −0.508315
\(959\) 38.4442 1.24143
\(960\) −8.37608 −0.270337
\(961\) 11.5672 0.373137
\(962\) −9.88195 −0.318607
\(963\) 2.24861 0.0724604
\(964\) −22.2621 −0.717013
\(965\) 63.7333 2.05165
\(966\) −6.79636 −0.218669
\(967\) 21.8543 0.702787 0.351393 0.936228i \(-0.385708\pi\)
0.351393 + 0.936228i \(0.385708\pi\)
\(968\) −10.1828 −0.327286
\(969\) 28.7833 0.924651
\(970\) 15.4790 0.497001
\(971\) −15.1720 −0.486892 −0.243446 0.969914i \(-0.578278\pi\)
−0.243446 + 0.969914i \(0.578278\pi\)
\(972\) 21.0175 0.674135
\(973\) 0.366845 0.0117605
\(974\) 8.28468 0.265458
\(975\) −47.0947 −1.50824
\(976\) 8.63341 0.276349
\(977\) −44.0516 −1.40934 −0.704668 0.709537i \(-0.748904\pi\)
−0.704668 + 0.709537i \(0.748904\pi\)
\(978\) −3.52962 −0.112865
\(979\) −23.9233 −0.764591
\(980\) 4.27060 0.136419
\(981\) −28.5331 −0.910993
\(982\) 39.5767 1.26294
\(983\) 37.5443 1.19748 0.598739 0.800944i \(-0.295669\pi\)
0.598739 + 0.800944i \(0.295669\pi\)
\(984\) 0.829920 0.0264569
\(985\) 44.0431 1.40333
\(986\) 15.7897 0.502845
\(987\) 92.0621 2.93037
\(988\) 4.89845 0.155840
\(989\) 5.24396 0.166748
\(990\) 42.6869 1.35668
\(991\) −18.8640 −0.599233 −0.299617 0.954060i \(-0.596859\pi\)
−0.299617 + 0.954060i \(0.596859\pi\)
\(992\) 6.52436 0.207149
\(993\) 74.3103 2.35817
\(994\) −4.71709 −0.149617
\(995\) 52.7061 1.67090
\(996\) 18.9472 0.600367
\(997\) −20.6152 −0.652889 −0.326445 0.945216i \(-0.605851\pi\)
−0.326445 + 0.945216i \(0.605851\pi\)
\(998\) −9.09192 −0.287800
\(999\) 3.29334 0.104197
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 \(a_p\))