Properties

Label 8047.2.a.b.1.9
Level 8047
Weight 2
Character 8047.1
Self dual Yes
Analytic conductor 64.256
Analytic rank 1
Dimension 142
CM No

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Newspace parameters

Level: \( N \) = \( 8047 = 13 \cdot 619 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8047.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2556185065\)
Analytic rank: \(1\)
Dimension: \(142\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 8047.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.55403 q^{2} +1.62979 q^{3} +4.52309 q^{4} +1.02400 q^{5} -4.16254 q^{6} -2.90866 q^{7} -6.44404 q^{8} -0.343777 q^{9} +O(q^{10})\) \(q-2.55403 q^{2} +1.62979 q^{3} +4.52309 q^{4} +1.02400 q^{5} -4.16254 q^{6} -2.90866 q^{7} -6.44404 q^{8} -0.343777 q^{9} -2.61533 q^{10} +3.97579 q^{11} +7.37169 q^{12} +1.00000 q^{13} +7.42882 q^{14} +1.66891 q^{15} +7.41213 q^{16} +1.98444 q^{17} +0.878017 q^{18} -4.42735 q^{19} +4.63164 q^{20} -4.74052 q^{21} -10.1543 q^{22} +0.308540 q^{23} -10.5025 q^{24} -3.95142 q^{25} -2.55403 q^{26} -5.44966 q^{27} -13.1561 q^{28} +8.91343 q^{29} -4.26245 q^{30} +6.21590 q^{31} -6.04274 q^{32} +6.47971 q^{33} -5.06833 q^{34} -2.97847 q^{35} -1.55493 q^{36} +3.18018 q^{37} +11.3076 q^{38} +1.62979 q^{39} -6.59870 q^{40} -0.0267494 q^{41} +12.1074 q^{42} -9.51525 q^{43} +17.9828 q^{44} -0.352027 q^{45} -0.788021 q^{46} -4.23608 q^{47} +12.0802 q^{48} +1.46032 q^{49} +10.0921 q^{50} +3.23423 q^{51} +4.52309 q^{52} -14.1988 q^{53} +13.9186 q^{54} +4.07121 q^{55} +18.7435 q^{56} -7.21565 q^{57} -22.7652 q^{58} -6.82188 q^{59} +7.54861 q^{60} -5.60653 q^{61} -15.8756 q^{62} +0.999930 q^{63} +0.609101 q^{64} +1.02400 q^{65} -16.5494 q^{66} +2.47014 q^{67} +8.97580 q^{68} +0.502856 q^{69} +7.60711 q^{70} -2.65237 q^{71} +2.21531 q^{72} +2.32901 q^{73} -8.12229 q^{74} -6.44000 q^{75} -20.0253 q^{76} -11.5642 q^{77} -4.16254 q^{78} -12.0907 q^{79} +7.59003 q^{80} -7.85049 q^{81} +0.0683188 q^{82} +10.0470 q^{83} -21.4418 q^{84} +2.03207 q^{85} +24.3023 q^{86} +14.5270 q^{87} -25.6202 q^{88} +15.5551 q^{89} +0.899090 q^{90} -2.90866 q^{91} +1.39555 q^{92} +10.1306 q^{93} +10.8191 q^{94} -4.53360 q^{95} -9.84842 q^{96} -2.41387 q^{97} -3.72969 q^{98} -1.36678 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} + O(q^{10}) \) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} - 25q^{10} - 25q^{11} - 62q^{12} + 142q^{13} - 57q^{14} - 14q^{15} + 111q^{16} - 141q^{17} - 29q^{18} - 3q^{19} - 87q^{20} - 19q^{21} - 24q^{22} - 69q^{23} - 40q^{24} + 87q^{25} - 13q^{26} - 95q^{27} - 34q^{28} - 147q^{29} - 2q^{30} - 21q^{31} - 66q^{32} - 62q^{33} - 6q^{34} - 59q^{35} + 74q^{36} - 37q^{37} - 76q^{38} - 26q^{39} - 61q^{40} - 97q^{41} - 29q^{42} - 33q^{43} - 57q^{44} - 86q^{45} - q^{46} - 102q^{47} - 141q^{48} + 70q^{49} - 28q^{50} - 13q^{51} + 129q^{52} - 137q^{53} - 29q^{54} - 24q^{55} - 130q^{56} - 65q^{57} - 15q^{58} - 56q^{59} + 11q^{60} - 77q^{61} - 150q^{62} - 32q^{63} + 73q^{64} - 37q^{65} - 32q^{66} - 9q^{67} - 226q^{68} - 113q^{69} + 6q^{70} - 18q^{71} - 82q^{72} - 117q^{73} - 70q^{74} - 83q^{75} + 40q^{76} - 214q^{77} - 15q^{78} - 52q^{79} - 161q^{80} - 10q^{81} - 36q^{82} - 74q^{83} + 53q^{84} + 2q^{85} + 17q^{86} - 49q^{87} - 29q^{88} - 171q^{89} - 57q^{90} - 14q^{91} - 187q^{92} - 39q^{93} + 13q^{94} - 150q^{95} - 47q^{96} - 126q^{97} - 85q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.55403 −1.80597 −0.902987 0.429668i \(-0.858631\pi\)
−0.902987 + 0.429668i \(0.858631\pi\)
\(3\) 1.62979 0.940961 0.470481 0.882410i \(-0.344081\pi\)
0.470481 + 0.882410i \(0.344081\pi\)
\(4\) 4.52309 2.26154
\(5\) 1.02400 0.457947 0.228973 0.973433i \(-0.426463\pi\)
0.228973 + 0.973433i \(0.426463\pi\)
\(6\) −4.16254 −1.69935
\(7\) −2.90866 −1.09937 −0.549685 0.835372i \(-0.685252\pi\)
−0.549685 + 0.835372i \(0.685252\pi\)
\(8\) −6.44404 −2.27831
\(9\) −0.343777 −0.114592
\(10\) −2.61533 −0.827040
\(11\) 3.97579 1.19875 0.599373 0.800470i \(-0.295417\pi\)
0.599373 + 0.800470i \(0.295417\pi\)
\(12\) 7.37169 2.12802
\(13\) 1.00000 0.277350
\(14\) 7.42882 1.98544
\(15\) 1.66891 0.430910
\(16\) 7.41213 1.85303
\(17\) 1.98444 0.481298 0.240649 0.970612i \(-0.422640\pi\)
0.240649 + 0.970612i \(0.422640\pi\)
\(18\) 0.878017 0.206951
\(19\) −4.42735 −1.01570 −0.507851 0.861445i \(-0.669560\pi\)
−0.507851 + 0.861445i \(0.669560\pi\)
\(20\) 4.63164 1.03567
\(21\) −4.74052 −1.03447
\(22\) −10.1543 −2.16490
\(23\) 0.308540 0.0643350 0.0321675 0.999482i \(-0.489759\pi\)
0.0321675 + 0.999482i \(0.489759\pi\)
\(24\) −10.5025 −2.14380
\(25\) −3.95142 −0.790285
\(26\) −2.55403 −0.500887
\(27\) −5.44966 −1.04879
\(28\) −13.1561 −2.48627
\(29\) 8.91343 1.65518 0.827591 0.561331i \(-0.189710\pi\)
0.827591 + 0.561331i \(0.189710\pi\)
\(30\) −4.26245 −0.778213
\(31\) 6.21590 1.11641 0.558204 0.829704i \(-0.311491\pi\)
0.558204 + 0.829704i \(0.311491\pi\)
\(32\) −6.04274 −1.06822
\(33\) 6.47971 1.12797
\(34\) −5.06833 −0.869211
\(35\) −2.97847 −0.503453
\(36\) −1.55493 −0.259155
\(37\) 3.18018 0.522819 0.261409 0.965228i \(-0.415813\pi\)
0.261409 + 0.965228i \(0.415813\pi\)
\(38\) 11.3076 1.83433
\(39\) 1.62979 0.260976
\(40\) −6.59870 −1.04335
\(41\) −0.0267494 −0.00417755 −0.00208878 0.999998i \(-0.500665\pi\)
−0.00208878 + 0.999998i \(0.500665\pi\)
\(42\) 12.1074 1.86822
\(43\) −9.51525 −1.45106 −0.725531 0.688190i \(-0.758406\pi\)
−0.725531 + 0.688190i \(0.758406\pi\)
\(44\) 17.9828 2.71101
\(45\) −0.352027 −0.0524771
\(46\) −0.788021 −0.116187
\(47\) −4.23608 −0.617896 −0.308948 0.951079i \(-0.599977\pi\)
−0.308948 + 0.951079i \(0.599977\pi\)
\(48\) 12.0802 1.74363
\(49\) 1.46032 0.208616
\(50\) 10.0921 1.42723
\(51\) 3.23423 0.452882
\(52\) 4.52309 0.627239
\(53\) −14.1988 −1.95036 −0.975180 0.221415i \(-0.928932\pi\)
−0.975180 + 0.221415i \(0.928932\pi\)
\(54\) 13.9186 1.89408
\(55\) 4.07121 0.548962
\(56\) 18.7435 2.50471
\(57\) −7.21565 −0.955737
\(58\) −22.7652 −2.98922
\(59\) −6.82188 −0.888133 −0.444067 0.895994i \(-0.646465\pi\)
−0.444067 + 0.895994i \(0.646465\pi\)
\(60\) 7.54861 0.974522
\(61\) −5.60653 −0.717842 −0.358921 0.933368i \(-0.616855\pi\)
−0.358921 + 0.933368i \(0.616855\pi\)
\(62\) −15.8756 −2.01620
\(63\) 0.999930 0.125979
\(64\) 0.609101 0.0761376
\(65\) 1.02400 0.127012
\(66\) −16.5494 −2.03709
\(67\) 2.47014 0.301776 0.150888 0.988551i \(-0.451787\pi\)
0.150888 + 0.988551i \(0.451787\pi\)
\(68\) 8.97580 1.08848
\(69\) 0.502856 0.0605367
\(70\) 7.60711 0.909224
\(71\) −2.65237 −0.314779 −0.157389 0.987537i \(-0.550308\pi\)
−0.157389 + 0.987537i \(0.550308\pi\)
\(72\) 2.21531 0.261077
\(73\) 2.32901 0.272590 0.136295 0.990668i \(-0.456481\pi\)
0.136295 + 0.990668i \(0.456481\pi\)
\(74\) −8.12229 −0.944198
\(75\) −6.44000 −0.743627
\(76\) −20.0253 −2.29706
\(77\) −11.5642 −1.31787
\(78\) −4.16254 −0.471315
\(79\) −12.0907 −1.36031 −0.680157 0.733067i \(-0.738088\pi\)
−0.680157 + 0.733067i \(0.738088\pi\)
\(80\) 7.59003 0.848591
\(81\) −7.85049 −0.872276
\(82\) 0.0683188 0.00754455
\(83\) 10.0470 1.10280 0.551399 0.834242i \(-0.314094\pi\)
0.551399 + 0.834242i \(0.314094\pi\)
\(84\) −21.4418 −2.33949
\(85\) 2.03207 0.220409
\(86\) 24.3023 2.62058
\(87\) 14.5270 1.55746
\(88\) −25.6202 −2.73112
\(89\) 15.5551 1.64884 0.824418 0.565981i \(-0.191503\pi\)
0.824418 + 0.565981i \(0.191503\pi\)
\(90\) 0.899090 0.0947724
\(91\) −2.90866 −0.304911
\(92\) 1.39555 0.145496
\(93\) 10.1306 1.05050
\(94\) 10.8191 1.11590
\(95\) −4.53360 −0.465138
\(96\) −9.84842 −1.00515
\(97\) −2.41387 −0.245092 −0.122546 0.992463i \(-0.539106\pi\)
−0.122546 + 0.992463i \(0.539106\pi\)
\(98\) −3.72969 −0.376756
\(99\) −1.36678 −0.137367
\(100\) −17.8726 −1.78726
\(101\) −10.6593 −1.06064 −0.530318 0.847799i \(-0.677927\pi\)
−0.530318 + 0.847799i \(0.677927\pi\)
\(102\) −8.26033 −0.817894
\(103\) −6.09693 −0.600748 −0.300374 0.953821i \(-0.597112\pi\)
−0.300374 + 0.953821i \(0.597112\pi\)
\(104\) −6.44404 −0.631891
\(105\) −4.85429 −0.473730
\(106\) 36.2643 3.52230
\(107\) −7.31454 −0.707123 −0.353562 0.935411i \(-0.615030\pi\)
−0.353562 + 0.935411i \(0.615030\pi\)
\(108\) −24.6493 −2.37188
\(109\) −6.67058 −0.638926 −0.319463 0.947599i \(-0.603503\pi\)
−0.319463 + 0.947599i \(0.603503\pi\)
\(110\) −10.3980 −0.991411
\(111\) 5.18304 0.491952
\(112\) −21.5594 −2.03717
\(113\) −2.69215 −0.253256 −0.126628 0.991950i \(-0.540415\pi\)
−0.126628 + 0.991950i \(0.540415\pi\)
\(114\) 18.4290 1.72604
\(115\) 0.315945 0.0294620
\(116\) 40.3162 3.74327
\(117\) −0.343777 −0.0317822
\(118\) 17.4233 1.60395
\(119\) −5.77207 −0.529125
\(120\) −10.7545 −0.981749
\(121\) 4.80690 0.436991
\(122\) 14.3193 1.29640
\(123\) −0.0435959 −0.00393091
\(124\) 28.1150 2.52480
\(125\) −9.16626 −0.819855
\(126\) −2.55385 −0.227515
\(127\) 19.6413 1.74288 0.871441 0.490501i \(-0.163186\pi\)
0.871441 + 0.490501i \(0.163186\pi\)
\(128\) 10.5298 0.930713
\(129\) −15.5079 −1.36539
\(130\) −2.61533 −0.229380
\(131\) 7.20969 0.629914 0.314957 0.949106i \(-0.398010\pi\)
0.314957 + 0.949106i \(0.398010\pi\)
\(132\) 29.3083 2.55096
\(133\) 12.8777 1.11663
\(134\) −6.30882 −0.544999
\(135\) −5.58046 −0.480289
\(136\) −12.7878 −1.09655
\(137\) 6.56121 0.560562 0.280281 0.959918i \(-0.409572\pi\)
0.280281 + 0.959918i \(0.409572\pi\)
\(138\) −1.28431 −0.109328
\(139\) 17.1211 1.45219 0.726096 0.687594i \(-0.241333\pi\)
0.726096 + 0.687594i \(0.241333\pi\)
\(140\) −13.4719 −1.13858
\(141\) −6.90394 −0.581416
\(142\) 6.77425 0.568482
\(143\) 3.97579 0.332472
\(144\) −2.54812 −0.212343
\(145\) 9.12736 0.757986
\(146\) −5.94836 −0.492290
\(147\) 2.38001 0.196300
\(148\) 14.3842 1.18238
\(149\) 11.7777 0.964864 0.482432 0.875933i \(-0.339754\pi\)
0.482432 + 0.875933i \(0.339754\pi\)
\(150\) 16.4480 1.34297
\(151\) 6.67775 0.543428 0.271714 0.962378i \(-0.412410\pi\)
0.271714 + 0.962378i \(0.412410\pi\)
\(152\) 28.5300 2.31409
\(153\) −0.682205 −0.0551530
\(154\) 29.5354 2.38003
\(155\) 6.36508 0.511255
\(156\) 7.37169 0.590208
\(157\) −21.3365 −1.70284 −0.851421 0.524484i \(-0.824258\pi\)
−0.851421 + 0.524484i \(0.824258\pi\)
\(158\) 30.8801 2.45669
\(159\) −23.1411 −1.83521
\(160\) −6.18777 −0.489186
\(161\) −0.897438 −0.0707280
\(162\) 20.0504 1.57531
\(163\) 3.18815 0.249715 0.124857 0.992175i \(-0.460153\pi\)
0.124857 + 0.992175i \(0.460153\pi\)
\(164\) −0.120990 −0.00944771
\(165\) 6.63523 0.516552
\(166\) −25.6603 −1.99162
\(167\) 3.88570 0.300685 0.150342 0.988634i \(-0.451962\pi\)
0.150342 + 0.988634i \(0.451962\pi\)
\(168\) 30.5481 2.35684
\(169\) 1.00000 0.0769231
\(170\) −5.18997 −0.398053
\(171\) 1.52202 0.116392
\(172\) −43.0383 −3.28164
\(173\) −16.1138 −1.22511 −0.612553 0.790429i \(-0.709857\pi\)
−0.612553 + 0.790429i \(0.709857\pi\)
\(174\) −37.1026 −2.81274
\(175\) 11.4934 0.868816
\(176\) 29.4691 2.22132
\(177\) −11.1182 −0.835699
\(178\) −39.7282 −2.97776
\(179\) −14.3389 −1.07174 −0.535868 0.844302i \(-0.680016\pi\)
−0.535868 + 0.844302i \(0.680016\pi\)
\(180\) −1.59225 −0.118679
\(181\) 15.1000 1.12237 0.561187 0.827689i \(-0.310345\pi\)
0.561187 + 0.827689i \(0.310345\pi\)
\(182\) 7.42882 0.550661
\(183\) −9.13748 −0.675462
\(184\) −1.98824 −0.146575
\(185\) 3.25651 0.239423
\(186\) −25.8739 −1.89717
\(187\) 7.88972 0.576954
\(188\) −19.1602 −1.39740
\(189\) 15.8512 1.15301
\(190\) 11.5790 0.840027
\(191\) 1.14122 0.0825754 0.0412877 0.999147i \(-0.486854\pi\)
0.0412877 + 0.999147i \(0.486854\pi\)
\(192\) 0.992708 0.0716426
\(193\) −2.92073 −0.210239 −0.105119 0.994460i \(-0.533523\pi\)
−0.105119 + 0.994460i \(0.533523\pi\)
\(194\) 6.16511 0.442629
\(195\) 1.66891 0.119513
\(196\) 6.60513 0.471795
\(197\) −7.08505 −0.504789 −0.252394 0.967624i \(-0.581218\pi\)
−0.252394 + 0.967624i \(0.581218\pi\)
\(198\) 3.49081 0.248081
\(199\) −0.196138 −0.0139038 −0.00695191 0.999976i \(-0.502213\pi\)
−0.00695191 + 0.999976i \(0.502213\pi\)
\(200\) 25.4631 1.80052
\(201\) 4.02582 0.283959
\(202\) 27.2241 1.91548
\(203\) −25.9262 −1.81966
\(204\) 14.6287 1.02421
\(205\) −0.0273914 −0.00191310
\(206\) 15.5718 1.08494
\(207\) −0.106069 −0.00737229
\(208\) 7.41213 0.513939
\(209\) −17.6022 −1.21757
\(210\) 12.3980 0.855544
\(211\) 23.3760 1.60927 0.804634 0.593770i \(-0.202361\pi\)
0.804634 + 0.593770i \(0.202361\pi\)
\(212\) −64.2225 −4.41082
\(213\) −4.32282 −0.296195
\(214\) 18.6816 1.27705
\(215\) −9.74361 −0.664509
\(216\) 35.1179 2.38947
\(217\) −18.0799 −1.22735
\(218\) 17.0369 1.15388
\(219\) 3.79580 0.256496
\(220\) 18.4144 1.24150
\(221\) 1.98444 0.133488
\(222\) −13.2377 −0.888453
\(223\) −26.1888 −1.75373 −0.876866 0.480735i \(-0.840370\pi\)
−0.876866 + 0.480735i \(0.840370\pi\)
\(224\) 17.5763 1.17437
\(225\) 1.35841 0.0905605
\(226\) 6.87584 0.457374
\(227\) −6.63089 −0.440108 −0.220054 0.975488i \(-0.570623\pi\)
−0.220054 + 0.975488i \(0.570623\pi\)
\(228\) −32.6370 −2.16144
\(229\) 0.611183 0.0403881 0.0201941 0.999796i \(-0.493572\pi\)
0.0201941 + 0.999796i \(0.493572\pi\)
\(230\) −0.806933 −0.0532076
\(231\) −18.8473 −1.24006
\(232\) −57.4386 −3.77103
\(233\) −5.30818 −0.347750 −0.173875 0.984768i \(-0.555629\pi\)
−0.173875 + 0.984768i \(0.555629\pi\)
\(234\) 0.878017 0.0573978
\(235\) −4.33775 −0.282964
\(236\) −30.8559 −2.00855
\(237\) −19.7054 −1.28000
\(238\) 14.7421 0.955586
\(239\) −8.62869 −0.558144 −0.279072 0.960270i \(-0.590027\pi\)
−0.279072 + 0.960270i \(0.590027\pi\)
\(240\) 12.3702 0.798491
\(241\) −18.2713 −1.17696 −0.588480 0.808512i \(-0.700273\pi\)
−0.588480 + 0.808512i \(0.700273\pi\)
\(242\) −12.2770 −0.789195
\(243\) 3.55432 0.228010
\(244\) −25.3588 −1.62343
\(245\) 1.49536 0.0955352
\(246\) 0.111345 0.00709913
\(247\) −4.42735 −0.281705
\(248\) −40.0555 −2.54353
\(249\) 16.3745 1.03769
\(250\) 23.4109 1.48064
\(251\) −5.12680 −0.323601 −0.161801 0.986823i \(-0.551730\pi\)
−0.161801 + 0.986823i \(0.551730\pi\)
\(252\) 4.52277 0.284908
\(253\) 1.22669 0.0771213
\(254\) −50.1645 −3.14760
\(255\) 3.31185 0.207396
\(256\) −28.1117 −1.75698
\(257\) −2.73524 −0.170620 −0.0853098 0.996354i \(-0.527188\pi\)
−0.0853098 + 0.996354i \(0.527188\pi\)
\(258\) 39.6076 2.46586
\(259\) −9.25008 −0.574772
\(260\) 4.63164 0.287242
\(261\) −3.06423 −0.189671
\(262\) −18.4138 −1.13761
\(263\) 12.1182 0.747241 0.373621 0.927582i \(-0.378116\pi\)
0.373621 + 0.927582i \(0.378116\pi\)
\(264\) −41.7555 −2.56988
\(265\) −14.5396 −0.893161
\(266\) −32.8900 −2.01661
\(267\) 25.3516 1.55149
\(268\) 11.1727 0.682479
\(269\) 6.00156 0.365922 0.182961 0.983120i \(-0.441432\pi\)
0.182961 + 0.983120i \(0.441432\pi\)
\(270\) 14.2527 0.867390
\(271\) −4.34502 −0.263941 −0.131971 0.991254i \(-0.542130\pi\)
−0.131971 + 0.991254i \(0.542130\pi\)
\(272\) 14.7089 0.891861
\(273\) −4.74052 −0.286909
\(274\) −16.7575 −1.01236
\(275\) −15.7100 −0.947350
\(276\) 2.27446 0.136906
\(277\) 0.625737 0.0375969 0.0187984 0.999823i \(-0.494016\pi\)
0.0187984 + 0.999823i \(0.494016\pi\)
\(278\) −43.7278 −2.62262
\(279\) −2.13688 −0.127932
\(280\) 19.1934 1.14702
\(281\) −4.69727 −0.280216 −0.140108 0.990136i \(-0.544745\pi\)
−0.140108 + 0.990136i \(0.544745\pi\)
\(282\) 17.6329 1.05002
\(283\) −2.01970 −0.120059 −0.0600293 0.998197i \(-0.519119\pi\)
−0.0600293 + 0.998197i \(0.519119\pi\)
\(284\) −11.9969 −0.711886
\(285\) −7.38883 −0.437677
\(286\) −10.1543 −0.600436
\(287\) 0.0778049 0.00459268
\(288\) 2.07735 0.122409
\(289\) −13.0620 −0.768352
\(290\) −23.3116 −1.36890
\(291\) −3.93411 −0.230622
\(292\) 10.5343 0.616473
\(293\) −30.0046 −1.75289 −0.876445 0.481502i \(-0.840091\pi\)
−0.876445 + 0.481502i \(0.840091\pi\)
\(294\) −6.07863 −0.354513
\(295\) −6.98561 −0.406718
\(296\) −20.4932 −1.19115
\(297\) −21.6667 −1.25723
\(298\) −30.0805 −1.74252
\(299\) 0.308540 0.0178433
\(300\) −29.1287 −1.68174
\(301\) 27.6766 1.59525
\(302\) −17.0552 −0.981417
\(303\) −17.3724 −0.998017
\(304\) −32.8161 −1.88213
\(305\) −5.74109 −0.328734
\(306\) 1.74237 0.0996048
\(307\) −1.51115 −0.0862457 −0.0431228 0.999070i \(-0.513731\pi\)
−0.0431228 + 0.999070i \(0.513731\pi\)
\(308\) −52.3060 −2.98041
\(309\) −9.93673 −0.565281
\(310\) −16.2566 −0.923314
\(311\) −21.5447 −1.22169 −0.610845 0.791750i \(-0.709170\pi\)
−0.610845 + 0.791750i \(0.709170\pi\)
\(312\) −10.5025 −0.594584
\(313\) −14.5264 −0.821083 −0.410542 0.911842i \(-0.634660\pi\)
−0.410542 + 0.911842i \(0.634660\pi\)
\(314\) 54.4942 3.07529
\(315\) 1.02393 0.0576918
\(316\) −54.6874 −3.07641
\(317\) −14.5019 −0.814508 −0.407254 0.913315i \(-0.633514\pi\)
−0.407254 + 0.913315i \(0.633514\pi\)
\(318\) 59.1033 3.31435
\(319\) 35.4379 1.98414
\(320\) 0.623720 0.0348670
\(321\) −11.9212 −0.665376
\(322\) 2.29209 0.127733
\(323\) −8.78581 −0.488855
\(324\) −35.5084 −1.97269
\(325\) −3.95142 −0.219186
\(326\) −8.14263 −0.450979
\(327\) −10.8717 −0.601205
\(328\) 0.172374 0.00951777
\(329\) 12.3213 0.679297
\(330\) −16.9466 −0.932879
\(331\) 26.7247 1.46892 0.734461 0.678651i \(-0.237435\pi\)
0.734461 + 0.678651i \(0.237435\pi\)
\(332\) 45.4433 2.49402
\(333\) −1.09327 −0.0599110
\(334\) −9.92421 −0.543029
\(335\) 2.52942 0.138197
\(336\) −35.1373 −1.91690
\(337\) −16.4810 −0.897776 −0.448888 0.893588i \(-0.648180\pi\)
−0.448888 + 0.893588i \(0.648180\pi\)
\(338\) −2.55403 −0.138921
\(339\) −4.38765 −0.238304
\(340\) 9.19122 0.498464
\(341\) 24.7131 1.33829
\(342\) −3.88728 −0.210200
\(343\) 16.1131 0.870024
\(344\) 61.3167 3.30597
\(345\) 0.514924 0.0277226
\(346\) 41.1551 2.21251
\(347\) −0.946071 −0.0507877 −0.0253939 0.999678i \(-0.508084\pi\)
−0.0253939 + 0.999678i \(0.508084\pi\)
\(348\) 65.7071 3.52227
\(349\) 25.3789 1.35850 0.679250 0.733907i \(-0.262305\pi\)
0.679250 + 0.733907i \(0.262305\pi\)
\(350\) −29.3544 −1.56906
\(351\) −5.44966 −0.290881
\(352\) −24.0247 −1.28052
\(353\) −11.7032 −0.622897 −0.311449 0.950263i \(-0.600814\pi\)
−0.311449 + 0.950263i \(0.600814\pi\)
\(354\) 28.3964 1.50925
\(355\) −2.71603 −0.144152
\(356\) 70.3570 3.72891
\(357\) −9.40728 −0.497886
\(358\) 36.6219 1.93553
\(359\) −4.76066 −0.251258 −0.125629 0.992077i \(-0.540095\pi\)
−0.125629 + 0.992077i \(0.540095\pi\)
\(360\) 2.26848 0.119559
\(361\) 0.601391 0.0316521
\(362\) −38.5659 −2.02698
\(363\) 7.83425 0.411192
\(364\) −13.1561 −0.689568
\(365\) 2.38490 0.124832
\(366\) 23.3374 1.21987
\(367\) 10.6744 0.557199 0.278600 0.960407i \(-0.410130\pi\)
0.278600 + 0.960407i \(0.410130\pi\)
\(368\) 2.28694 0.119215
\(369\) 0.00919581 0.000478715 0
\(370\) −8.31723 −0.432392
\(371\) 41.2996 2.14417
\(372\) 45.8217 2.37574
\(373\) 17.7186 0.917434 0.458717 0.888582i \(-0.348309\pi\)
0.458717 + 0.888582i \(0.348309\pi\)
\(374\) −20.1506 −1.04196
\(375\) −14.9391 −0.771452
\(376\) 27.2975 1.40776
\(377\) 8.91343 0.459065
\(378\) −40.4846 −2.08230
\(379\) −22.9984 −1.18135 −0.590674 0.806910i \(-0.701138\pi\)
−0.590674 + 0.806910i \(0.701138\pi\)
\(380\) −20.5059 −1.05193
\(381\) 32.0112 1.63998
\(382\) −2.91470 −0.149129
\(383\) −0.696736 −0.0356015 −0.0178008 0.999842i \(-0.505666\pi\)
−0.0178008 + 0.999842i \(0.505666\pi\)
\(384\) 17.1614 0.875765
\(385\) −11.8418 −0.603513
\(386\) 7.45965 0.379686
\(387\) 3.27112 0.166280
\(388\) −10.9182 −0.554285
\(389\) 2.43948 0.123686 0.0618432 0.998086i \(-0.480302\pi\)
0.0618432 + 0.998086i \(0.480302\pi\)
\(390\) −4.26245 −0.215837
\(391\) 0.612279 0.0309643
\(392\) −9.41033 −0.475294
\(393\) 11.7503 0.592724
\(394\) 18.0954 0.911636
\(395\) −12.3809 −0.622951
\(396\) −6.18208 −0.310661
\(397\) −34.0916 −1.71101 −0.855504 0.517797i \(-0.826752\pi\)
−0.855504 + 0.517797i \(0.826752\pi\)
\(398\) 0.500942 0.0251100
\(399\) 20.9879 1.05071
\(400\) −29.2885 −1.46442
\(401\) −30.2271 −1.50947 −0.754735 0.656030i \(-0.772234\pi\)
−0.754735 + 0.656030i \(0.772234\pi\)
\(402\) −10.2821 −0.512823
\(403\) 6.21590 0.309636
\(404\) −48.2127 −2.39867
\(405\) −8.03890 −0.399456
\(406\) 66.2163 3.28626
\(407\) 12.6437 0.626727
\(408\) −20.8415 −1.03181
\(409\) −9.89835 −0.489442 −0.244721 0.969594i \(-0.578696\pi\)
−0.244721 + 0.969594i \(0.578696\pi\)
\(410\) 0.0699585 0.00345500
\(411\) 10.6934 0.527467
\(412\) −27.5769 −1.35862
\(413\) 19.8425 0.976388
\(414\) 0.270903 0.0133142
\(415\) 10.2881 0.505022
\(416\) −6.04274 −0.296270
\(417\) 27.9038 1.36646
\(418\) 44.9566 2.19890
\(419\) −11.0171 −0.538221 −0.269111 0.963109i \(-0.586730\pi\)
−0.269111 + 0.963109i \(0.586730\pi\)
\(420\) −21.9564 −1.07136
\(421\) 34.5975 1.68618 0.843089 0.537774i \(-0.180735\pi\)
0.843089 + 0.537774i \(0.180735\pi\)
\(422\) −59.7030 −2.90630
\(423\) 1.45627 0.0708061
\(424\) 91.4979 4.44353
\(425\) −7.84137 −0.380362
\(426\) 11.0406 0.534920
\(427\) 16.3075 0.789175
\(428\) −33.0843 −1.59919
\(429\) 6.47971 0.312843
\(430\) 24.8855 1.20009
\(431\) −19.9265 −0.959825 −0.479913 0.877316i \(-0.659332\pi\)
−0.479913 + 0.877316i \(0.659332\pi\)
\(432\) −40.3936 −1.94344
\(433\) −4.63653 −0.222817 −0.111409 0.993775i \(-0.535536\pi\)
−0.111409 + 0.993775i \(0.535536\pi\)
\(434\) 46.1768 2.21656
\(435\) 14.8757 0.713235
\(436\) −30.1716 −1.44496
\(437\) −1.36601 −0.0653452
\(438\) −9.69459 −0.463226
\(439\) 14.5172 0.692868 0.346434 0.938074i \(-0.387392\pi\)
0.346434 + 0.938074i \(0.387392\pi\)
\(440\) −26.2351 −1.25071
\(441\) −0.502022 −0.0239058
\(442\) −5.06833 −0.241076
\(443\) −9.38896 −0.446083 −0.223041 0.974809i \(-0.571599\pi\)
−0.223041 + 0.974809i \(0.571599\pi\)
\(444\) 23.4433 1.11257
\(445\) 15.9284 0.755079
\(446\) 66.8871 3.16719
\(447\) 19.1952 0.907899
\(448\) −1.77167 −0.0837035
\(449\) −31.0801 −1.46676 −0.733379 0.679820i \(-0.762058\pi\)
−0.733379 + 0.679820i \(0.762058\pi\)
\(450\) −3.46942 −0.163550
\(451\) −0.106350 −0.00500782
\(452\) −12.1768 −0.572750
\(453\) 10.8834 0.511344
\(454\) 16.9355 0.794823
\(455\) −2.97847 −0.139633
\(456\) 46.4980 2.17747
\(457\) 14.0870 0.658963 0.329482 0.944162i \(-0.393126\pi\)
0.329482 + 0.944162i \(0.393126\pi\)
\(458\) −1.56098 −0.0729399
\(459\) −10.8145 −0.504779
\(460\) 1.42905 0.0666296
\(461\) 37.0414 1.72519 0.862594 0.505897i \(-0.168838\pi\)
0.862594 + 0.505897i \(0.168838\pi\)
\(462\) 48.1366 2.23952
\(463\) 22.0189 1.02330 0.511652 0.859193i \(-0.329034\pi\)
0.511652 + 0.859193i \(0.329034\pi\)
\(464\) 66.0675 3.06711
\(465\) 10.3738 0.481071
\(466\) 13.5573 0.628028
\(467\) 8.09255 0.374478 0.187239 0.982314i \(-0.440046\pi\)
0.187239 + 0.982314i \(0.440046\pi\)
\(468\) −1.55493 −0.0718767
\(469\) −7.18480 −0.331763
\(470\) 11.0788 0.511025
\(471\) −34.7741 −1.60231
\(472\) 43.9605 2.02345
\(473\) −37.8306 −1.73945
\(474\) 50.3282 2.31165
\(475\) 17.4943 0.802694
\(476\) −26.1076 −1.19664
\(477\) 4.88123 0.223496
\(478\) 22.0380 1.00799
\(479\) 16.1781 0.739196 0.369598 0.929192i \(-0.379495\pi\)
0.369598 + 0.929192i \(0.379495\pi\)
\(480\) −10.0848 −0.460305
\(481\) 3.18018 0.145004
\(482\) 46.6656 2.12556
\(483\) −1.46264 −0.0665523
\(484\) 21.7420 0.988274
\(485\) −2.47181 −0.112239
\(486\) −9.07785 −0.411780
\(487\) −19.6696 −0.891316 −0.445658 0.895203i \(-0.647030\pi\)
−0.445658 + 0.895203i \(0.647030\pi\)
\(488\) 36.1287 1.63547
\(489\) 5.19602 0.234972
\(490\) −3.81921 −0.172534
\(491\) −28.7346 −1.29678 −0.648388 0.761310i \(-0.724557\pi\)
−0.648388 + 0.761310i \(0.724557\pi\)
\(492\) −0.197188 −0.00888993
\(493\) 17.6882 0.796636
\(494\) 11.3076 0.508752
\(495\) −1.39959 −0.0629067
\(496\) 46.0730 2.06874
\(497\) 7.71486 0.346059
\(498\) −41.8209 −1.87404
\(499\) 10.9592 0.490601 0.245301 0.969447i \(-0.421113\pi\)
0.245301 + 0.969447i \(0.421113\pi\)
\(500\) −41.4598 −1.85414
\(501\) 6.33289 0.282933
\(502\) 13.0940 0.584415
\(503\) 0.948787 0.0423043 0.0211522 0.999776i \(-0.493267\pi\)
0.0211522 + 0.999776i \(0.493267\pi\)
\(504\) −6.44359 −0.287020
\(505\) −10.9151 −0.485715
\(506\) −3.13300 −0.139279
\(507\) 1.62979 0.0723816
\(508\) 88.8392 3.94160
\(509\) −31.3466 −1.38941 −0.694707 0.719293i \(-0.744466\pi\)
−0.694707 + 0.719293i \(0.744466\pi\)
\(510\) −8.45858 −0.374552
\(511\) −6.77429 −0.299677
\(512\) 50.7386 2.24235
\(513\) 24.1275 1.06526
\(514\) 6.98590 0.308135
\(515\) −6.24326 −0.275111
\(516\) −70.1434 −3.08789
\(517\) −16.8418 −0.740700
\(518\) 23.6250 1.03802
\(519\) −26.2621 −1.15278
\(520\) −6.59870 −0.289372
\(521\) 2.83178 0.124063 0.0620313 0.998074i \(-0.480242\pi\)
0.0620313 + 0.998074i \(0.480242\pi\)
\(522\) 7.82614 0.342541
\(523\) −33.6100 −1.46966 −0.734831 0.678250i \(-0.762739\pi\)
−0.734831 + 0.678250i \(0.762739\pi\)
\(524\) 32.6101 1.42458
\(525\) 18.7318 0.817522
\(526\) −30.9503 −1.34950
\(527\) 12.3351 0.537325
\(528\) 48.0285 2.09017
\(529\) −22.9048 −0.995861
\(530\) 37.1346 1.61303
\(531\) 2.34520 0.101773
\(532\) 58.2467 2.52532
\(533\) −0.0267494 −0.00115864
\(534\) −64.7487 −2.80195
\(535\) −7.49009 −0.323825
\(536\) −15.9177 −0.687540
\(537\) −23.3694 −1.00846
\(538\) −15.3282 −0.660845
\(539\) 5.80591 0.250078
\(540\) −25.2409 −1.08619
\(541\) −35.9301 −1.54475 −0.772377 0.635164i \(-0.780932\pi\)
−0.772377 + 0.635164i \(0.780932\pi\)
\(542\) 11.0973 0.476671
\(543\) 24.6099 1.05611
\(544\) −11.9915 −0.514130
\(545\) −6.83068 −0.292594
\(546\) 12.1074 0.518150
\(547\) 0.307514 0.0131483 0.00657417 0.999978i \(-0.497907\pi\)
0.00657417 + 0.999978i \(0.497907\pi\)
\(548\) 29.6769 1.26773
\(549\) 1.92739 0.0822592
\(550\) 40.1239 1.71089
\(551\) −39.4628 −1.68117
\(552\) −3.24042 −0.137922
\(553\) 35.1678 1.49549
\(554\) −1.59815 −0.0678990
\(555\) 5.30743 0.225288
\(556\) 77.4401 3.28419
\(557\) −26.3182 −1.11514 −0.557570 0.830130i \(-0.688266\pi\)
−0.557570 + 0.830130i \(0.688266\pi\)
\(558\) 5.45766 0.231041
\(559\) −9.51525 −0.402452
\(560\) −22.0768 −0.932916
\(561\) 12.8586 0.542891
\(562\) 11.9970 0.506062
\(563\) 6.77145 0.285383 0.142691 0.989767i \(-0.454424\pi\)
0.142691 + 0.989767i \(0.454424\pi\)
\(564\) −31.2271 −1.31490
\(565\) −2.75676 −0.115978
\(566\) 5.15838 0.216823
\(567\) 22.8344 0.958955
\(568\) 17.0920 0.717165
\(569\) 41.5018 1.73984 0.869922 0.493189i \(-0.164169\pi\)
0.869922 + 0.493189i \(0.164169\pi\)
\(570\) 18.8713 0.790433
\(571\) 3.86062 0.161562 0.0807810 0.996732i \(-0.474259\pi\)
0.0807810 + 0.996732i \(0.474259\pi\)
\(572\) 17.9828 0.751900
\(573\) 1.85994 0.0777003
\(574\) −0.198716 −0.00829426
\(575\) −1.21917 −0.0508430
\(576\) −0.209395 −0.00872478
\(577\) 24.5035 1.02009 0.510047 0.860147i \(-0.329628\pi\)
0.510047 + 0.860147i \(0.329628\pi\)
\(578\) 33.3608 1.38762
\(579\) −4.76019 −0.197827
\(580\) 41.2838 1.71422
\(581\) −29.2232 −1.21238
\(582\) 10.0479 0.416497
\(583\) −56.4516 −2.33798
\(584\) −15.0082 −0.621045
\(585\) −0.352027 −0.0145545
\(586\) 76.6328 3.16567
\(587\) 18.7607 0.774336 0.387168 0.922009i \(-0.373453\pi\)
0.387168 + 0.922009i \(0.373453\pi\)
\(588\) 10.7650 0.443941
\(589\) −27.5199 −1.13394
\(590\) 17.8415 0.734522
\(591\) −11.5472 −0.474987
\(592\) 23.5719 0.968801
\(593\) 33.0962 1.35910 0.679550 0.733629i \(-0.262175\pi\)
0.679550 + 0.733629i \(0.262175\pi\)
\(594\) 55.3375 2.27052
\(595\) −5.91060 −0.242311
\(596\) 53.2714 2.18208
\(597\) −0.319664 −0.0130830
\(598\) −0.788021 −0.0322246
\(599\) −29.2262 −1.19415 −0.597075 0.802185i \(-0.703671\pi\)
−0.597075 + 0.802185i \(0.703671\pi\)
\(600\) 41.4996 1.69422
\(601\) −0.652714 −0.0266248 −0.0133124 0.999911i \(-0.504238\pi\)
−0.0133124 + 0.999911i \(0.504238\pi\)
\(602\) −70.6870 −2.88099
\(603\) −0.849177 −0.0345811
\(604\) 30.2041 1.22899
\(605\) 4.92227 0.200119
\(606\) 44.3696 1.80239
\(607\) −10.4935 −0.425918 −0.212959 0.977061i \(-0.568310\pi\)
−0.212959 + 0.977061i \(0.568310\pi\)
\(608\) 26.7533 1.08499
\(609\) −42.2543 −1.71223
\(610\) 14.6629 0.593685
\(611\) −4.23608 −0.171374
\(612\) −3.08567 −0.124731
\(613\) −10.5606 −0.426539 −0.213270 0.976993i \(-0.568411\pi\)
−0.213270 + 0.976993i \(0.568411\pi\)
\(614\) 3.85952 0.155757
\(615\) −0.0446423 −0.00180015
\(616\) 74.5204 3.00251
\(617\) −18.6433 −0.750551 −0.375276 0.926913i \(-0.622452\pi\)
−0.375276 + 0.926913i \(0.622452\pi\)
\(618\) 25.3787 1.02088
\(619\) 1.00000 0.0401934
\(620\) 28.7898 1.15623
\(621\) −1.68144 −0.0674738
\(622\) 55.0260 2.20634
\(623\) −45.2445 −1.81268
\(624\) 12.0802 0.483596
\(625\) 10.3709 0.414835
\(626\) 37.1010 1.48286
\(627\) −28.6879 −1.14569
\(628\) −96.5070 −3.85105
\(629\) 6.31089 0.251632
\(630\) −2.61515 −0.104190
\(631\) −25.0624 −0.997719 −0.498859 0.866683i \(-0.666248\pi\)
−0.498859 + 0.866683i \(0.666248\pi\)
\(632\) 77.9132 3.09922
\(633\) 38.0980 1.51426
\(634\) 37.0383 1.47098
\(635\) 20.1127 0.798147
\(636\) −104.669 −4.15041
\(637\) 1.46032 0.0578598
\(638\) −90.5097 −3.58331
\(639\) 0.911824 0.0360712
\(640\) 10.7825 0.426217
\(641\) 6.74162 0.266278 0.133139 0.991097i \(-0.457494\pi\)
0.133139 + 0.991097i \(0.457494\pi\)
\(642\) 30.4471 1.20165
\(643\) −19.3974 −0.764960 −0.382480 0.923964i \(-0.624930\pi\)
−0.382480 + 0.923964i \(0.624930\pi\)
\(644\) −4.05919 −0.159954
\(645\) −15.8801 −0.625277
\(646\) 22.4392 0.882860
\(647\) −24.4001 −0.959267 −0.479634 0.877469i \(-0.659230\pi\)
−0.479634 + 0.877469i \(0.659230\pi\)
\(648\) 50.5889 1.98732
\(649\) −27.1224 −1.06465
\(650\) 10.0921 0.395843
\(651\) −29.4665 −1.15489
\(652\) 14.4203 0.564741
\(653\) −21.8357 −0.854499 −0.427249 0.904134i \(-0.640517\pi\)
−0.427249 + 0.904134i \(0.640517\pi\)
\(654\) 27.7666 1.08576
\(655\) 7.38273 0.288467
\(656\) −0.198270 −0.00774114
\(657\) −0.800658 −0.0312366
\(658\) −31.4691 −1.22679
\(659\) −1.10163 −0.0429135 −0.0214568 0.999770i \(-0.506830\pi\)
−0.0214568 + 0.999770i \(0.506830\pi\)
\(660\) 30.0117 1.16820
\(661\) 10.5964 0.412152 0.206076 0.978536i \(-0.433931\pi\)
0.206076 + 0.978536i \(0.433931\pi\)
\(662\) −68.2557 −2.65283
\(663\) 3.23423 0.125607
\(664\) −64.7431 −2.51252
\(665\) 13.1867 0.511359
\(666\) 2.79225 0.108198
\(667\) 2.75015 0.106486
\(668\) 17.5754 0.680011
\(669\) −42.6823 −1.65019
\(670\) −6.46024 −0.249581
\(671\) −22.2904 −0.860511
\(672\) 28.6457 1.10503
\(673\) −39.9817 −1.54118 −0.770591 0.637330i \(-0.780039\pi\)
−0.770591 + 0.637330i \(0.780039\pi\)
\(674\) 42.0930 1.62136
\(675\) 21.5339 0.828841
\(676\) 4.52309 0.173965
\(677\) −32.2859 −1.24085 −0.620424 0.784266i \(-0.713040\pi\)
−0.620424 + 0.784266i \(0.713040\pi\)
\(678\) 11.2062 0.430371
\(679\) 7.02114 0.269447
\(680\) −13.0947 −0.502160
\(681\) −10.8070 −0.414124
\(682\) −63.1181 −2.41692
\(683\) 35.2089 1.34723 0.673616 0.739082i \(-0.264740\pi\)
0.673616 + 0.739082i \(0.264740\pi\)
\(684\) 6.88422 0.263225
\(685\) 6.71868 0.256708
\(686\) −41.1533 −1.57124
\(687\) 0.996101 0.0380036
\(688\) −70.5283 −2.68886
\(689\) −14.1988 −0.540932
\(690\) −1.31513 −0.0500663
\(691\) 32.7784 1.24695 0.623475 0.781843i \(-0.285720\pi\)
0.623475 + 0.781843i \(0.285720\pi\)
\(692\) −72.8839 −2.77063
\(693\) 3.97551 0.151017
\(694\) 2.41630 0.0917213
\(695\) 17.5320 0.665026
\(696\) −93.6129 −3.54839
\(697\) −0.0530826 −0.00201065
\(698\) −64.8185 −2.45342
\(699\) −8.65123 −0.327220
\(700\) 51.9854 1.96486
\(701\) 18.6055 0.702721 0.351361 0.936240i \(-0.385719\pi\)
0.351361 + 0.936240i \(0.385719\pi\)
\(702\) 13.9186 0.525324
\(703\) −14.0798 −0.531029
\(704\) 2.42166 0.0912697
\(705\) −7.06963 −0.266258
\(706\) 29.8903 1.12494
\(707\) 31.0042 1.16603
\(708\) −50.2888 −1.88997
\(709\) 6.90762 0.259421 0.129711 0.991552i \(-0.458595\pi\)
0.129711 + 0.991552i \(0.458595\pi\)
\(710\) 6.93683 0.260335
\(711\) 4.15651 0.155881
\(712\) −100.238 −3.75657
\(713\) 1.91785 0.0718241
\(714\) 24.0265 0.899169
\(715\) 4.07121 0.152255
\(716\) −64.8559 −2.42378
\(717\) −14.0630 −0.525192
\(718\) 12.1589 0.453766
\(719\) −3.87798 −0.144624 −0.0723122 0.997382i \(-0.523038\pi\)
−0.0723122 + 0.997382i \(0.523038\pi\)
\(720\) −2.60927 −0.0972419
\(721\) 17.7339 0.660445
\(722\) −1.53597 −0.0571629
\(723\) −29.7785 −1.10747
\(724\) 68.2986 2.53830
\(725\) −35.2207 −1.30807
\(726\) −20.0089 −0.742601
\(727\) 32.5422 1.20692 0.603462 0.797392i \(-0.293788\pi\)
0.603462 + 0.797392i \(0.293788\pi\)
\(728\) 18.7435 0.694682
\(729\) 29.3443 1.08682
\(730\) −6.09112 −0.225443
\(731\) −18.8824 −0.698393
\(732\) −41.3296 −1.52759
\(733\) 11.9408 0.441043 0.220521 0.975382i \(-0.429224\pi\)
0.220521 + 0.975382i \(0.429224\pi\)
\(734\) −27.2628 −1.00629
\(735\) 2.43713 0.0898949
\(736\) −1.86443 −0.0687237
\(737\) 9.82076 0.361752
\(738\) −0.0234864 −0.000864547 0
\(739\) −41.1678 −1.51438 −0.757191 0.653193i \(-0.773429\pi\)
−0.757191 + 0.653193i \(0.773429\pi\)
\(740\) 14.7295 0.541466
\(741\) −7.21565 −0.265074
\(742\) −105.481 −3.87231
\(743\) −9.84809 −0.361291 −0.180646 0.983548i \(-0.557819\pi\)
−0.180646 + 0.983548i \(0.557819\pi\)
\(744\) −65.2822 −2.39336
\(745\) 12.0603 0.441856
\(746\) −45.2539 −1.65686
\(747\) −3.45391 −0.126372
\(748\) 35.6859 1.30481
\(749\) 21.2755 0.777391
\(750\) 38.1550 1.39322
\(751\) −5.66009 −0.206540 −0.103270 0.994653i \(-0.532931\pi\)
−0.103270 + 0.994653i \(0.532931\pi\)
\(752\) −31.3984 −1.14498
\(753\) −8.35563 −0.304496
\(754\) −22.7652 −0.829060
\(755\) 6.83802 0.248861
\(756\) 71.6964 2.60757
\(757\) 45.5787 1.65659 0.828293 0.560295i \(-0.189312\pi\)
0.828293 + 0.560295i \(0.189312\pi\)
\(758\) 58.7386 2.13348
\(759\) 1.99925 0.0725681
\(760\) 29.2147 1.05973
\(761\) −18.5609 −0.672832 −0.336416 0.941714i \(-0.609215\pi\)
−0.336416 + 0.941714i \(0.609215\pi\)
\(762\) −81.7577 −2.96177
\(763\) 19.4025 0.702417
\(764\) 5.16181 0.186748
\(765\) −0.698578 −0.0252571
\(766\) 1.77949 0.0642955
\(767\) −6.82188 −0.246324
\(768\) −45.8163 −1.65325
\(769\) −18.2706 −0.658854 −0.329427 0.944181i \(-0.606855\pi\)
−0.329427 + 0.944181i \(0.606855\pi\)
\(770\) 30.2443 1.08993
\(771\) −4.45787 −0.160546
\(772\) −13.2107 −0.475464
\(773\) −39.8456 −1.43315 −0.716574 0.697511i \(-0.754291\pi\)
−0.716574 + 0.697511i \(0.754291\pi\)
\(774\) −8.35455 −0.300298
\(775\) −24.5616 −0.882280
\(776\) 15.5551 0.558396
\(777\) −15.0757 −0.540838
\(778\) −6.23050 −0.223374
\(779\) 0.118429 0.00424315
\(780\) 7.54861 0.270284
\(781\) −10.5453 −0.377340
\(782\) −1.56378 −0.0559207
\(783\) −48.5752 −1.73594
\(784\) 10.8240 0.386573
\(785\) −21.8486 −0.779811
\(786\) −30.0107 −1.07044
\(787\) 5.40363 0.192619 0.0963093 0.995351i \(-0.469296\pi\)
0.0963093 + 0.995351i \(0.469296\pi\)
\(788\) −32.0463 −1.14160
\(789\) 19.7502 0.703125
\(790\) 31.6213 1.12503
\(791\) 7.83056 0.278422
\(792\) 8.80761 0.312965
\(793\) −5.60653 −0.199094
\(794\) 87.0710 3.09003
\(795\) −23.6965 −0.840430
\(796\) −0.887147 −0.0314441
\(797\) −19.3230 −0.684455 −0.342228 0.939617i \(-0.611181\pi\)
−0.342228 + 0.939617i \(0.611181\pi\)
\(798\) −53.6038 −1.89755
\(799\) −8.40626 −0.297392
\(800\) 23.8774 0.844195
\(801\) −5.34748 −0.188944
\(802\) 77.2010 2.72606
\(803\) 9.25964 0.326766
\(804\) 18.2091 0.642186
\(805\) −0.918977 −0.0323897
\(806\) −15.8756 −0.559194
\(807\) 9.78131 0.344318
\(808\) 68.6887 2.41646
\(809\) 14.8754 0.522991 0.261495 0.965205i \(-0.415784\pi\)
0.261495 + 0.965205i \(0.415784\pi\)
\(810\) 20.5316 0.721408
\(811\) 47.0386 1.65175 0.825875 0.563853i \(-0.190682\pi\)
0.825875 + 0.563853i \(0.190682\pi\)
\(812\) −117.266 −4.11524
\(813\) −7.08148 −0.248358
\(814\) −32.2925 −1.13185
\(815\) 3.26466 0.114356
\(816\) 23.9725 0.839206
\(817\) 42.1273 1.47385
\(818\) 25.2807 0.883920
\(819\) 0.999930 0.0349404
\(820\) −0.123894 −0.00432655
\(821\) −28.9893 −1.01173 −0.505867 0.862612i \(-0.668827\pi\)
−0.505867 + 0.862612i \(0.668827\pi\)
\(822\) −27.3113 −0.952592
\(823\) −1.09719 −0.0382455 −0.0191228 0.999817i \(-0.506087\pi\)
−0.0191228 + 0.999817i \(0.506087\pi\)
\(824\) 39.2889 1.36869
\(825\) −25.6041 −0.891420
\(826\) −50.6785 −1.76333
\(827\) 15.4497 0.537239 0.268620 0.963246i \(-0.413433\pi\)
0.268620 + 0.963246i \(0.413433\pi\)
\(828\) −0.479758 −0.0166727
\(829\) 18.4367 0.640332 0.320166 0.947361i \(-0.396261\pi\)
0.320166 + 0.947361i \(0.396261\pi\)
\(830\) −26.2761 −0.912058
\(831\) 1.01982 0.0353772
\(832\) 0.609101 0.0211168
\(833\) 2.89791 0.100407
\(834\) −71.2673 −2.46778
\(835\) 3.97896 0.137698
\(836\) −79.6162 −2.75359
\(837\) −33.8745 −1.17088
\(838\) 28.1381 0.972013
\(839\) −10.7781 −0.372102 −0.186051 0.982540i \(-0.559569\pi\)
−0.186051 + 0.982540i \(0.559569\pi\)
\(840\) 31.2813 1.07931
\(841\) 50.4493 1.73963
\(842\) −88.3631 −3.04519
\(843\) −7.65558 −0.263672
\(844\) 105.732 3.63943
\(845\) 1.02400 0.0352267
\(846\) −3.71935 −0.127874
\(847\) −13.9817 −0.480415
\(848\) −105.244 −3.61408
\(849\) −3.29169 −0.112971
\(850\) 20.0271 0.686924
\(851\) 0.981213 0.0336356
\(852\) −19.5525 −0.669857
\(853\) 53.0279 1.81564 0.907820 0.419361i \(-0.137746\pi\)
0.907820 + 0.419361i \(0.137746\pi\)
\(854\) −41.6499 −1.42523
\(855\) 1.55855 0.0533012
\(856\) 47.1352 1.61105
\(857\) −46.8574 −1.60062 −0.800309 0.599587i \(-0.795331\pi\)
−0.800309 + 0.599587i \(0.795331\pi\)
\(858\) −16.5494 −0.564987
\(859\) −48.4914 −1.65450 −0.827252 0.561831i \(-0.810097\pi\)
−0.827252 + 0.561831i \(0.810097\pi\)
\(860\) −44.0712 −1.50282
\(861\) 0.126806 0.00432153
\(862\) 50.8929 1.73342
\(863\) −28.7922 −0.980098 −0.490049 0.871695i \(-0.663021\pi\)
−0.490049 + 0.871695i \(0.663021\pi\)
\(864\) 32.9309 1.12033
\(865\) −16.5005 −0.561034
\(866\) 11.8418 0.402402
\(867\) −21.2883 −0.722990
\(868\) −81.7771 −2.77570
\(869\) −48.0702 −1.63067
\(870\) −37.9930 −1.28808
\(871\) 2.47014 0.0836975
\(872\) 42.9855 1.45567
\(873\) 0.829833 0.0280856
\(874\) 3.48884 0.118012
\(875\) 26.6616 0.901325
\(876\) 17.1687 0.580077
\(877\) 7.73754 0.261278 0.130639 0.991430i \(-0.458297\pi\)
0.130639 + 0.991430i \(0.458297\pi\)
\(878\) −37.0774 −1.25130
\(879\) −48.9013 −1.64940
\(880\) 30.1763 1.01724
\(881\) −5.25275 −0.176970 −0.0884849 0.996078i \(-0.528203\pi\)
−0.0884849 + 0.996078i \(0.528203\pi\)
\(882\) 1.28218 0.0431733
\(883\) −50.0178 −1.68323 −0.841616 0.540077i \(-0.818395\pi\)
−0.841616 + 0.540077i \(0.818395\pi\)
\(884\) 8.97580 0.301889
\(885\) −11.3851 −0.382706
\(886\) 23.9797 0.805614
\(887\) 17.6175 0.591539 0.295770 0.955259i \(-0.404424\pi\)
0.295770 + 0.955259i \(0.404424\pi\)
\(888\) −33.3997 −1.12082
\(889\) −57.1298 −1.91607
\(890\) −40.6817 −1.36365
\(891\) −31.2119 −1.04564
\(892\) −118.454 −3.96614
\(893\) 18.7546 0.627599
\(894\) −49.0251 −1.63964
\(895\) −14.6830 −0.490798
\(896\) −30.6277 −1.02320
\(897\) 0.502856 0.0167899
\(898\) 79.3795 2.64893
\(899\) 55.4050 1.84786
\(900\) 6.14419 0.204806
\(901\) −28.1767 −0.938704
\(902\) 0.271621 0.00904400
\(903\) 45.1072 1.50107
\(904\) 17.3483 0.576997
\(905\) 15.4624 0.513988
\(906\) −27.7964 −0.923475
\(907\) 9.67109 0.321123 0.160562 0.987026i \(-0.448669\pi\)
0.160562 + 0.987026i \(0.448669\pi\)
\(908\) −29.9921 −0.995322
\(909\) 3.66440 0.121541
\(910\) 7.60711 0.252173
\(911\) 14.7174 0.487608 0.243804 0.969825i \(-0.421605\pi\)
0.243804 + 0.969825i \(0.421605\pi\)
\(912\) −53.4834 −1.77101
\(913\) 39.9446 1.32197
\(914\) −35.9787 −1.19007
\(915\) −9.35678 −0.309326
\(916\) 2.76443 0.0913394
\(917\) −20.9706 −0.692509
\(918\) 27.6207 0.911618
\(919\) −13.7418 −0.453302 −0.226651 0.973976i \(-0.572778\pi\)
−0.226651 + 0.973976i \(0.572778\pi\)
\(920\) −2.03596 −0.0671237
\(921\) −2.46285 −0.0811538
\(922\) −94.6049 −3.11565
\(923\) −2.65237 −0.0873039
\(924\) −85.2479 −2.80445
\(925\) −12.5663 −0.413176
\(926\) −56.2370 −1.84806
\(927\) 2.09598 0.0688411
\(928\) −53.8616 −1.76809
\(929\) −25.3935 −0.833133 −0.416567 0.909105i \(-0.636767\pi\)
−0.416567 + 0.909105i \(0.636767\pi\)
\(930\) −26.4949 −0.868803
\(931\) −6.46532 −0.211892
\(932\) −24.0094 −0.786453
\(933\) −35.1135 −1.14956
\(934\) −20.6686 −0.676298
\(935\) 8.07908 0.264214
\(936\) 2.21531 0.0724097
\(937\) 40.5030 1.32317 0.661587 0.749868i \(-0.269883\pi\)
0.661587 + 0.749868i \(0.269883\pi\)
\(938\) 18.3502 0.599156
\(939\) −23.6751 −0.772607
\(940\) −19.6200 −0.639934
\(941\) 18.2501 0.594935 0.297468 0.954732i \(-0.403858\pi\)
0.297468 + 0.954732i \(0.403858\pi\)
\(942\) 88.8143 2.89373
\(943\) −0.00825325 −0.000268763 0
\(944\) −50.5647 −1.64574
\(945\) 16.2317 0.528016
\(946\) 96.6206 3.14141
\(947\) −32.2871 −1.04919 −0.524594 0.851352i \(-0.675783\pi\)
−0.524594 + 0.851352i \(0.675783\pi\)
\(948\) −89.1291 −2.89478
\(949\) 2.32901 0.0756028
\(950\) −44.6811 −1.44965
\(951\) −23.6351 −0.766420
\(952\) 37.1955 1.20551
\(953\) 9.14062 0.296094 0.148047 0.988980i \(-0.452701\pi\)
0.148047 + 0.988980i \(0.452701\pi\)
\(954\) −12.4668 −0.403628
\(955\) 1.16860 0.0378152
\(956\) −39.0283 −1.26227
\(957\) 57.7565 1.86700
\(958\) −41.3194 −1.33497
\(959\) −19.0843 −0.616266
\(960\) 1.01653 0.0328085
\(961\) 7.63736 0.246366
\(962\) −8.12229 −0.261873
\(963\) 2.51457 0.0810308
\(964\) −82.6428 −2.66174
\(965\) −2.99083 −0.0962783
\(966\) 3.73562 0.120192
\(967\) 57.2053 1.83960 0.919800 0.392387i \(-0.128351\pi\)
0.919800 + 0.392387i \(0.128351\pi\)
\(968\) −30.9759 −0.995603
\(969\) −14.3190 −0.459994
\(970\) 6.31308 0.202701
\(971\) −5.65710 −0.181545 −0.0907725 0.995872i \(-0.528934\pi\)
−0.0907725 + 0.995872i \(0.528934\pi\)
\(972\) 16.0765 0.515654
\(973\) −49.7994 −1.59650
\(974\) 50.2369 1.60969
\(975\) −6.44000 −0.206245
\(976\) −41.5563 −1.33019
\(977\) 21.4501 0.686248 0.343124 0.939290i \(-0.388515\pi\)
0.343124 + 0.939290i \(0.388515\pi\)
\(978\) −13.2708 −0.424354
\(979\) 61.8438 1.97653
\(980\) 6.76365 0.216057
\(981\) 2.29319 0.0732160
\(982\) 73.3892 2.34194
\(983\) 34.6664 1.10569 0.552843 0.833285i \(-0.313543\pi\)
0.552843 + 0.833285i \(0.313543\pi\)
\(984\) 0.280934 0.00895586
\(985\) −7.25509 −0.231166
\(986\) −45.1762 −1.43870
\(987\) 20.0812 0.639192
\(988\) −20.0253 −0.637089
\(989\) −2.93583 −0.0933540
\(990\) 3.57459 0.113608
\(991\) 10.4081 0.330626 0.165313 0.986241i \(-0.447137\pi\)
0.165313 + 0.986241i \(0.447137\pi\)
\(992\) −37.5611 −1.19256
\(993\) 43.5557 1.38220
\(994\) −19.7040 −0.624973
\(995\) −0.200845 −0.00636721
\(996\) 74.0631 2.34678
\(997\) −3.70648 −0.117385 −0.0586927 0.998276i \(-0.518693\pi\)
−0.0586927 + 0.998276i \(0.518693\pi\)
\(998\) −27.9902 −0.886013
\(999\) −17.3309 −0.548326
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 \(a_p\))