Properties

Label 8007.2.a.e.1.44
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 1
Dimension 46
CM No

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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: \(46\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.44
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.33434 q^{2} +1.00000 q^{3} +3.44916 q^{4} -3.01300 q^{5} +2.33434 q^{6} +0.805971 q^{7} +3.38285 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.33434 q^{2} +1.00000 q^{3} +3.44916 q^{4} -3.01300 q^{5} +2.33434 q^{6} +0.805971 q^{7} +3.38285 q^{8} +1.00000 q^{9} -7.03338 q^{10} +0.210193 q^{11} +3.44916 q^{12} -2.50157 q^{13} +1.88141 q^{14} -3.01300 q^{15} +0.998405 q^{16} -1.00000 q^{17} +2.33434 q^{18} +1.78533 q^{19} -10.3923 q^{20} +0.805971 q^{21} +0.490663 q^{22} -1.54799 q^{23} +3.38285 q^{24} +4.07816 q^{25} -5.83952 q^{26} +1.00000 q^{27} +2.77993 q^{28} -7.23400 q^{29} -7.03338 q^{30} -7.38077 q^{31} -4.43508 q^{32} +0.210193 q^{33} -2.33434 q^{34} -2.42839 q^{35} +3.44916 q^{36} -10.0586 q^{37} +4.16757 q^{38} -2.50157 q^{39} -10.1925 q^{40} -8.23202 q^{41} +1.88141 q^{42} +10.4057 q^{43} +0.724991 q^{44} -3.01300 q^{45} -3.61354 q^{46} +11.1683 q^{47} +0.998405 q^{48} -6.35041 q^{49} +9.51984 q^{50} -1.00000 q^{51} -8.62831 q^{52} +10.4577 q^{53} +2.33434 q^{54} -0.633312 q^{55} +2.72648 q^{56} +1.78533 q^{57} -16.8867 q^{58} -7.17161 q^{59} -10.3923 q^{60} +5.34097 q^{61} -17.2293 q^{62} +0.805971 q^{63} -12.3498 q^{64} +7.53722 q^{65} +0.490663 q^{66} -12.4841 q^{67} -3.44916 q^{68} -1.54799 q^{69} -5.66870 q^{70} -11.5697 q^{71} +3.38285 q^{72} +1.18077 q^{73} -23.4802 q^{74} +4.07816 q^{75} +6.15788 q^{76} +0.169410 q^{77} -5.83952 q^{78} +10.8894 q^{79} -3.00819 q^{80} +1.00000 q^{81} -19.2164 q^{82} +8.24034 q^{83} +2.77993 q^{84} +3.01300 q^{85} +24.2905 q^{86} -7.23400 q^{87} +0.711051 q^{88} -9.83273 q^{89} -7.03338 q^{90} -2.01619 q^{91} -5.33928 q^{92} -7.38077 q^{93} +26.0707 q^{94} -5.37919 q^{95} -4.43508 q^{96} +10.5645 q^{97} -14.8240 q^{98} +0.210193 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 46q - 5q^{2} + 46q^{3} + 43q^{4} - 19q^{5} - 5q^{6} + q^{7} - 18q^{8} + 46q^{9} + O(q^{10}) \) \( 46q - 5q^{2} + 46q^{3} + 43q^{4} - 19q^{5} - 5q^{6} + q^{7} - 18q^{8} + 46q^{9} - 10q^{10} - 25q^{11} + 43q^{12} - 8q^{13} - 28q^{14} - 19q^{15} + 33q^{16} - 46q^{17} - 5q^{18} - 2q^{19} - 56q^{20} + q^{21} - 19q^{22} - 64q^{23} - 18q^{24} + 11q^{25} - 13q^{26} + 46q^{27} - 38q^{28} - 51q^{29} - 10q^{30} - 19q^{31} - 61q^{32} - 25q^{33} + 5q^{34} - 39q^{35} + 43q^{36} - 46q^{37} - 48q^{38} - 8q^{39} - 10q^{40} - 53q^{41} - 28q^{42} - 33q^{43} - 62q^{44} - 19q^{45} + 2q^{46} - 45q^{47} + 33q^{48} + 21q^{49} - 60q^{50} - 46q^{51} - 63q^{52} - 47q^{53} - 5q^{54} + 5q^{55} - 82q^{56} - 2q^{57} - 21q^{58} - 65q^{59} - 56q^{60} - 37q^{61} - 46q^{62} + q^{63} + 74q^{64} - 85q^{65} - 19q^{66} - 52q^{67} - 43q^{68} - 64q^{69} - 20q^{70} - 48q^{71} - 18q^{72} - 39q^{73} - 16q^{74} + 11q^{75} + 42q^{76} - 78q^{77} - 13q^{78} - 26q^{79} - 78q^{80} + 46q^{81} + 3q^{82} - 47q^{83} - 38q^{84} + 19q^{85} - 6q^{86} - 51q^{87} - 58q^{88} - 58q^{89} - 10q^{90} - 43q^{91} - 68q^{92} - 19q^{93} - 78q^{95} - 61q^{96} - 44q^{97} - 4q^{98} - 25q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.33434 1.65063 0.825315 0.564672i \(-0.190997\pi\)
0.825315 + 0.564672i \(0.190997\pi\)
\(3\) 1.00000 0.577350
\(4\) 3.44916 1.72458
\(5\) −3.01300 −1.34745 −0.673727 0.738980i \(-0.735308\pi\)
−0.673727 + 0.738980i \(0.735308\pi\)
\(6\) 2.33434 0.952992
\(7\) 0.805971 0.304629 0.152314 0.988332i \(-0.451327\pi\)
0.152314 + 0.988332i \(0.451327\pi\)
\(8\) 3.38285 1.19602
\(9\) 1.00000 0.333333
\(10\) −7.03338 −2.22415
\(11\) 0.210193 0.0633756 0.0316878 0.999498i \(-0.489912\pi\)
0.0316878 + 0.999498i \(0.489912\pi\)
\(12\) 3.44916 0.995688
\(13\) −2.50157 −0.693810 −0.346905 0.937900i \(-0.612767\pi\)
−0.346905 + 0.937900i \(0.612767\pi\)
\(14\) 1.88141 0.502829
\(15\) −3.01300 −0.777953
\(16\) 0.998405 0.249601
\(17\) −1.00000 −0.242536
\(18\) 2.33434 0.550210
\(19\) 1.78533 0.409582 0.204791 0.978806i \(-0.434349\pi\)
0.204791 + 0.978806i \(0.434349\pi\)
\(20\) −10.3923 −2.32380
\(21\) 0.805971 0.175877
\(22\) 0.490663 0.104610
\(23\) −1.54799 −0.322778 −0.161389 0.986891i \(-0.551597\pi\)
−0.161389 + 0.986891i \(0.551597\pi\)
\(24\) 3.38285 0.690521
\(25\) 4.07816 0.815633
\(26\) −5.83952 −1.14522
\(27\) 1.00000 0.192450
\(28\) 2.77993 0.525357
\(29\) −7.23400 −1.34332 −0.671660 0.740859i \(-0.734419\pi\)
−0.671660 + 0.740859i \(0.734419\pi\)
\(30\) −7.03338 −1.28411
\(31\) −7.38077 −1.32563 −0.662813 0.748785i \(-0.730638\pi\)
−0.662813 + 0.748785i \(0.730638\pi\)
\(32\) −4.43508 −0.784018
\(33\) 0.210193 0.0365899
\(34\) −2.33434 −0.400337
\(35\) −2.42839 −0.410473
\(36\) 3.44916 0.574861
\(37\) −10.0586 −1.65362 −0.826811 0.562480i \(-0.809847\pi\)
−0.826811 + 0.562480i \(0.809847\pi\)
\(38\) 4.16757 0.676068
\(39\) −2.50157 −0.400571
\(40\) −10.1925 −1.61158
\(41\) −8.23202 −1.28563 −0.642813 0.766023i \(-0.722233\pi\)
−0.642813 + 0.766023i \(0.722233\pi\)
\(42\) 1.88141 0.290309
\(43\) 10.4057 1.58686 0.793429 0.608663i \(-0.208294\pi\)
0.793429 + 0.608663i \(0.208294\pi\)
\(44\) 0.724991 0.109296
\(45\) −3.01300 −0.449151
\(46\) −3.61354 −0.532788
\(47\) 11.1683 1.62907 0.814533 0.580118i \(-0.196993\pi\)
0.814533 + 0.580118i \(0.196993\pi\)
\(48\) 0.998405 0.144107
\(49\) −6.35041 −0.907201
\(50\) 9.51984 1.34631
\(51\) −1.00000 −0.140028
\(52\) −8.62831 −1.19653
\(53\) 10.4577 1.43648 0.718238 0.695798i \(-0.244949\pi\)
0.718238 + 0.695798i \(0.244949\pi\)
\(54\) 2.33434 0.317664
\(55\) −0.633312 −0.0853957
\(56\) 2.72648 0.364341
\(57\) 1.78533 0.236472
\(58\) −16.8867 −2.21733
\(59\) −7.17161 −0.933663 −0.466832 0.884346i \(-0.654605\pi\)
−0.466832 + 0.884346i \(0.654605\pi\)
\(60\) −10.3923 −1.34164
\(61\) 5.34097 0.683841 0.341921 0.939729i \(-0.388923\pi\)
0.341921 + 0.939729i \(0.388923\pi\)
\(62\) −17.2293 −2.18812
\(63\) 0.805971 0.101543
\(64\) −12.3498 −1.54373
\(65\) 7.53722 0.934877
\(66\) 0.490663 0.0603965
\(67\) −12.4841 −1.52518 −0.762588 0.646885i \(-0.776071\pi\)
−0.762588 + 0.646885i \(0.776071\pi\)
\(68\) −3.44916 −0.418273
\(69\) −1.54799 −0.186356
\(70\) −5.66870 −0.677539
\(71\) −11.5697 −1.37307 −0.686533 0.727098i \(-0.740868\pi\)
−0.686533 + 0.727098i \(0.740868\pi\)
\(72\) 3.38285 0.398672
\(73\) 1.18077 0.138199 0.0690993 0.997610i \(-0.477987\pi\)
0.0690993 + 0.997610i \(0.477987\pi\)
\(74\) −23.4802 −2.72952
\(75\) 4.07816 0.470906
\(76\) 6.15788 0.706358
\(77\) 0.169410 0.0193060
\(78\) −5.83952 −0.661195
\(79\) 10.8894 1.22516 0.612579 0.790409i \(-0.290132\pi\)
0.612579 + 0.790409i \(0.290132\pi\)
\(80\) −3.00819 −0.336326
\(81\) 1.00000 0.111111
\(82\) −19.2164 −2.12209
\(83\) 8.24034 0.904495 0.452247 0.891893i \(-0.350622\pi\)
0.452247 + 0.891893i \(0.350622\pi\)
\(84\) 2.77993 0.303315
\(85\) 3.01300 0.326806
\(86\) 24.2905 2.61932
\(87\) −7.23400 −0.775567
\(88\) 0.711051 0.0757983
\(89\) −9.83273 −1.04227 −0.521134 0.853475i \(-0.674491\pi\)
−0.521134 + 0.853475i \(0.674491\pi\)
\(90\) −7.03338 −0.741383
\(91\) −2.01619 −0.211354
\(92\) −5.33928 −0.556658
\(93\) −7.38077 −0.765350
\(94\) 26.0707 2.68899
\(95\) −5.37919 −0.551893
\(96\) −4.43508 −0.452653
\(97\) 10.5645 1.07266 0.536332 0.844007i \(-0.319809\pi\)
0.536332 + 0.844007i \(0.319809\pi\)
\(98\) −14.8240 −1.49745
\(99\) 0.210193 0.0211252
\(100\) 14.0663 1.40663
\(101\) −12.9343 −1.28701 −0.643506 0.765441i \(-0.722521\pi\)
−0.643506 + 0.765441i \(0.722521\pi\)
\(102\) −2.33434 −0.231135
\(103\) 1.18927 0.117182 0.0585909 0.998282i \(-0.481339\pi\)
0.0585909 + 0.998282i \(0.481339\pi\)
\(104\) −8.46242 −0.829808
\(105\) −2.42839 −0.236987
\(106\) 24.4119 2.37109
\(107\) −0.460731 −0.0445406 −0.0222703 0.999752i \(-0.507089\pi\)
−0.0222703 + 0.999752i \(0.507089\pi\)
\(108\) 3.44916 0.331896
\(109\) 8.68386 0.831763 0.415882 0.909419i \(-0.363473\pi\)
0.415882 + 0.909419i \(0.363473\pi\)
\(110\) −1.47837 −0.140957
\(111\) −10.0586 −0.954719
\(112\) 0.804686 0.0760357
\(113\) −14.0081 −1.31778 −0.658888 0.752241i \(-0.728973\pi\)
−0.658888 + 0.752241i \(0.728973\pi\)
\(114\) 4.16757 0.390328
\(115\) 4.66410 0.434929
\(116\) −24.9513 −2.31667
\(117\) −2.50157 −0.231270
\(118\) −16.7410 −1.54113
\(119\) −0.805971 −0.0738833
\(120\) −10.1925 −0.930445
\(121\) −10.9558 −0.995984
\(122\) 12.4677 1.12877
\(123\) −8.23202 −0.742256
\(124\) −25.4575 −2.28615
\(125\) 2.77749 0.248427
\(126\) 1.88141 0.167610
\(127\) 2.09797 0.186164 0.0930822 0.995658i \(-0.470328\pi\)
0.0930822 + 0.995658i \(0.470328\pi\)
\(128\) −19.9585 −1.76410
\(129\) 10.4057 0.916173
\(130\) 17.5945 1.54314
\(131\) −13.7280 −1.19942 −0.599708 0.800219i \(-0.704717\pi\)
−0.599708 + 0.800219i \(0.704717\pi\)
\(132\) 0.724991 0.0631023
\(133\) 1.43892 0.124770
\(134\) −29.1422 −2.51750
\(135\) −3.01300 −0.259318
\(136\) −3.38285 −0.290077
\(137\) 14.6945 1.25543 0.627717 0.778442i \(-0.283990\pi\)
0.627717 + 0.778442i \(0.283990\pi\)
\(138\) −3.61354 −0.307605
\(139\) 11.5687 0.981243 0.490622 0.871373i \(-0.336770\pi\)
0.490622 + 0.871373i \(0.336770\pi\)
\(140\) −8.37592 −0.707894
\(141\) 11.1683 0.940541
\(142\) −27.0076 −2.26643
\(143\) −0.525812 −0.0439706
\(144\) 0.998405 0.0832004
\(145\) 21.7960 1.81006
\(146\) 2.75632 0.228115
\(147\) −6.35041 −0.523773
\(148\) −34.6937 −2.85181
\(149\) 2.16182 0.177103 0.0885515 0.996072i \(-0.471776\pi\)
0.0885515 + 0.996072i \(0.471776\pi\)
\(150\) 9.51984 0.777291
\(151\) −13.9815 −1.13780 −0.568901 0.822406i \(-0.692631\pi\)
−0.568901 + 0.822406i \(0.692631\pi\)
\(152\) 6.03949 0.489867
\(153\) −1.00000 −0.0808452
\(154\) 0.395460 0.0318671
\(155\) 22.2383 1.78622
\(156\) −8.62831 −0.690818
\(157\) 1.00000 0.0798087
\(158\) 25.4197 2.02228
\(159\) 10.4577 0.829349
\(160\) 13.3629 1.05643
\(161\) −1.24764 −0.0983275
\(162\) 2.33434 0.183403
\(163\) −20.4399 −1.60098 −0.800490 0.599346i \(-0.795427\pi\)
−0.800490 + 0.599346i \(0.795427\pi\)
\(164\) −28.3936 −2.21717
\(165\) −0.633312 −0.0493032
\(166\) 19.2358 1.49299
\(167\) −7.74487 −0.599316 −0.299658 0.954047i \(-0.596873\pi\)
−0.299658 + 0.954047i \(0.596873\pi\)
\(168\) 2.72648 0.210352
\(169\) −6.74217 −0.518628
\(170\) 7.03338 0.539435
\(171\) 1.78533 0.136527
\(172\) 35.8911 2.73667
\(173\) 23.6620 1.79899 0.899493 0.436936i \(-0.143936\pi\)
0.899493 + 0.436936i \(0.143936\pi\)
\(174\) −16.8867 −1.28017
\(175\) 3.28688 0.248465
\(176\) 0.209858 0.0158186
\(177\) −7.17161 −0.539051
\(178\) −22.9530 −1.72040
\(179\) 7.66328 0.572781 0.286390 0.958113i \(-0.407545\pi\)
0.286390 + 0.958113i \(0.407545\pi\)
\(180\) −10.3923 −0.774598
\(181\) −6.29563 −0.467950 −0.233975 0.972243i \(-0.575173\pi\)
−0.233975 + 0.972243i \(0.575173\pi\)
\(182\) −4.70648 −0.348868
\(183\) 5.34097 0.394816
\(184\) −5.23662 −0.386049
\(185\) 30.3065 2.22818
\(186\) −17.2293 −1.26331
\(187\) −0.210193 −0.0153708
\(188\) 38.5213 2.80946
\(189\) 0.805971 0.0586258
\(190\) −12.5569 −0.910971
\(191\) −9.23979 −0.668567 −0.334284 0.942472i \(-0.608494\pi\)
−0.334284 + 0.942472i \(0.608494\pi\)
\(192\) −12.3498 −0.891270
\(193\) 7.42968 0.534800 0.267400 0.963586i \(-0.413835\pi\)
0.267400 + 0.963586i \(0.413835\pi\)
\(194\) 24.6612 1.77057
\(195\) 7.53722 0.539751
\(196\) −21.9036 −1.56454
\(197\) −15.7636 −1.12311 −0.561554 0.827440i \(-0.689796\pi\)
−0.561554 + 0.827440i \(0.689796\pi\)
\(198\) 0.490663 0.0348699
\(199\) 4.79962 0.340236 0.170118 0.985424i \(-0.445585\pi\)
0.170118 + 0.985424i \(0.445585\pi\)
\(200\) 13.7958 0.975511
\(201\) −12.4841 −0.880560
\(202\) −30.1932 −2.12438
\(203\) −5.83040 −0.409214
\(204\) −3.44916 −0.241490
\(205\) 24.8031 1.73232
\(206\) 2.77615 0.193424
\(207\) −1.54799 −0.107593
\(208\) −2.49758 −0.173176
\(209\) 0.375263 0.0259575
\(210\) −5.66870 −0.391177
\(211\) −8.65142 −0.595589 −0.297794 0.954630i \(-0.596251\pi\)
−0.297794 + 0.954630i \(0.596251\pi\)
\(212\) 36.0703 2.47732
\(213\) −11.5697 −0.792740
\(214\) −1.07551 −0.0735200
\(215\) −31.3524 −2.13822
\(216\) 3.38285 0.230174
\(217\) −5.94869 −0.403823
\(218\) 20.2711 1.37293
\(219\) 1.18077 0.0797889
\(220\) −2.18440 −0.147272
\(221\) 2.50157 0.168274
\(222\) −23.4802 −1.57589
\(223\) 13.6820 0.916213 0.458107 0.888897i \(-0.348528\pi\)
0.458107 + 0.888897i \(0.348528\pi\)
\(224\) −3.57454 −0.238834
\(225\) 4.07816 0.271878
\(226\) −32.6998 −2.17516
\(227\) −21.3227 −1.41524 −0.707619 0.706594i \(-0.750231\pi\)
−0.707619 + 0.706594i \(0.750231\pi\)
\(228\) 6.15788 0.407816
\(229\) 1.64624 0.108787 0.0543933 0.998520i \(-0.482678\pi\)
0.0543933 + 0.998520i \(0.482678\pi\)
\(230\) 10.8876 0.717908
\(231\) 0.169410 0.0111463
\(232\) −24.4715 −1.60663
\(233\) −4.81556 −0.315478 −0.157739 0.987481i \(-0.550420\pi\)
−0.157739 + 0.987481i \(0.550420\pi\)
\(234\) −5.83952 −0.381741
\(235\) −33.6501 −2.19509
\(236\) −24.7360 −1.61018
\(237\) 10.8894 0.707346
\(238\) −1.88141 −0.121954
\(239\) 12.7659 0.825758 0.412879 0.910786i \(-0.364523\pi\)
0.412879 + 0.910786i \(0.364523\pi\)
\(240\) −3.00819 −0.194178
\(241\) −12.1817 −0.784690 −0.392345 0.919818i \(-0.628336\pi\)
−0.392345 + 0.919818i \(0.628336\pi\)
\(242\) −25.5747 −1.64400
\(243\) 1.00000 0.0641500
\(244\) 18.4219 1.17934
\(245\) 19.1338 1.22241
\(246\) −19.2164 −1.22519
\(247\) −4.46611 −0.284172
\(248\) −24.9680 −1.58547
\(249\) 8.24034 0.522210
\(250\) 6.48363 0.410061
\(251\) −29.7706 −1.87910 −0.939551 0.342409i \(-0.888757\pi\)
−0.939551 + 0.342409i \(0.888757\pi\)
\(252\) 2.77993 0.175119
\(253\) −0.325377 −0.0204563
\(254\) 4.89738 0.307289
\(255\) 3.01300 0.188681
\(256\) −21.8905 −1.36816
\(257\) 6.89417 0.430046 0.215023 0.976609i \(-0.431017\pi\)
0.215023 + 0.976609i \(0.431017\pi\)
\(258\) 24.2905 1.51226
\(259\) −8.10693 −0.503740
\(260\) 25.9971 1.61227
\(261\) −7.23400 −0.447774
\(262\) −32.0458 −1.97979
\(263\) 6.05378 0.373292 0.186646 0.982427i \(-0.440238\pi\)
0.186646 + 0.982427i \(0.440238\pi\)
\(264\) 0.711051 0.0437622
\(265\) −31.5090 −1.93558
\(266\) 3.35894 0.205950
\(267\) −9.83273 −0.601754
\(268\) −43.0597 −2.63029
\(269\) 4.60492 0.280767 0.140384 0.990097i \(-0.455166\pi\)
0.140384 + 0.990097i \(0.455166\pi\)
\(270\) −7.03338 −0.428038
\(271\) 21.2581 1.29134 0.645668 0.763618i \(-0.276579\pi\)
0.645668 + 0.763618i \(0.276579\pi\)
\(272\) −0.998405 −0.0605372
\(273\) −2.01619 −0.122025
\(274\) 34.3020 2.07226
\(275\) 0.857202 0.0516912
\(276\) −5.33928 −0.321387
\(277\) 1.12974 0.0678794 0.0339397 0.999424i \(-0.489195\pi\)
0.0339397 + 0.999424i \(0.489195\pi\)
\(278\) 27.0053 1.61967
\(279\) −7.38077 −0.441875
\(280\) −8.21488 −0.490933
\(281\) −29.5848 −1.76488 −0.882441 0.470423i \(-0.844101\pi\)
−0.882441 + 0.470423i \(0.844101\pi\)
\(282\) 26.0707 1.55249
\(283\) −17.6514 −1.04926 −0.524632 0.851329i \(-0.675797\pi\)
−0.524632 + 0.851329i \(0.675797\pi\)
\(284\) −39.9057 −2.36797
\(285\) −5.37919 −0.318635
\(286\) −1.22743 −0.0725792
\(287\) −6.63477 −0.391638
\(288\) −4.43508 −0.261339
\(289\) 1.00000 0.0588235
\(290\) 50.8795 2.98775
\(291\) 10.5645 0.619303
\(292\) 4.07266 0.238335
\(293\) 8.64625 0.505119 0.252560 0.967581i \(-0.418728\pi\)
0.252560 + 0.967581i \(0.418728\pi\)
\(294\) −14.8240 −0.864556
\(295\) 21.6080 1.25807
\(296\) −34.0267 −1.97776
\(297\) 0.210193 0.0121966
\(298\) 5.04643 0.292332
\(299\) 3.87240 0.223947
\(300\) 14.0663 0.812115
\(301\) 8.38672 0.483402
\(302\) −32.6377 −1.87809
\(303\) −12.9343 −0.743057
\(304\) 1.78248 0.102232
\(305\) −16.0923 −0.921445
\(306\) −2.33434 −0.133446
\(307\) 16.6426 0.949844 0.474922 0.880028i \(-0.342476\pi\)
0.474922 + 0.880028i \(0.342476\pi\)
\(308\) 0.584322 0.0332948
\(309\) 1.18927 0.0676549
\(310\) 51.9118 2.94839
\(311\) 14.2059 0.805544 0.402772 0.915300i \(-0.368047\pi\)
0.402772 + 0.915300i \(0.368047\pi\)
\(312\) −8.46242 −0.479090
\(313\) −9.53976 −0.539219 −0.269609 0.962970i \(-0.586895\pi\)
−0.269609 + 0.962970i \(0.586895\pi\)
\(314\) 2.33434 0.131735
\(315\) −2.42839 −0.136824
\(316\) 37.5595 2.11289
\(317\) 4.23111 0.237643 0.118822 0.992916i \(-0.462088\pi\)
0.118822 + 0.992916i \(0.462088\pi\)
\(318\) 24.4119 1.36895
\(319\) −1.52054 −0.0851338
\(320\) 37.2099 2.08010
\(321\) −0.460731 −0.0257155
\(322\) −2.91241 −0.162302
\(323\) −1.78533 −0.0993382
\(324\) 3.44916 0.191620
\(325\) −10.2018 −0.565894
\(326\) −47.7139 −2.64263
\(327\) 8.68386 0.480219
\(328\) −27.8477 −1.53763
\(329\) 9.00134 0.496260
\(330\) −1.47837 −0.0813815
\(331\) 9.99683 0.549476 0.274738 0.961519i \(-0.411409\pi\)
0.274738 + 0.961519i \(0.411409\pi\)
\(332\) 28.4223 1.55988
\(333\) −10.0586 −0.551207
\(334\) −18.0792 −0.989249
\(335\) 37.6146 2.05510
\(336\) 0.804686 0.0438992
\(337\) 35.1802 1.91639 0.958195 0.286117i \(-0.0923645\pi\)
0.958195 + 0.286117i \(0.0923645\pi\)
\(338\) −15.7385 −0.856064
\(339\) −14.0081 −0.760818
\(340\) 10.3923 0.563603
\(341\) −1.55139 −0.0840123
\(342\) 4.16757 0.225356
\(343\) −10.7600 −0.580988
\(344\) 35.2010 1.89791
\(345\) 4.66410 0.251106
\(346\) 55.2352 2.96946
\(347\) 12.5869 0.675699 0.337850 0.941200i \(-0.390300\pi\)
0.337850 + 0.941200i \(0.390300\pi\)
\(348\) −24.9513 −1.33753
\(349\) 21.8636 1.17033 0.585166 0.810914i \(-0.301029\pi\)
0.585166 + 0.810914i \(0.301029\pi\)
\(350\) 7.67271 0.410124
\(351\) −2.50157 −0.133524
\(352\) −0.932222 −0.0496876
\(353\) −19.0946 −1.01630 −0.508151 0.861268i \(-0.669671\pi\)
−0.508151 + 0.861268i \(0.669671\pi\)
\(354\) −16.7410 −0.889774
\(355\) 34.8594 1.85014
\(356\) −33.9147 −1.79748
\(357\) −0.805971 −0.0426565
\(358\) 17.8887 0.945449
\(359\) −21.0810 −1.11261 −0.556307 0.830977i \(-0.687782\pi\)
−0.556307 + 0.830977i \(0.687782\pi\)
\(360\) −10.1925 −0.537193
\(361\) −15.8126 −0.832243
\(362\) −14.6962 −0.772413
\(363\) −10.9558 −0.575031
\(364\) −6.95417 −0.364498
\(365\) −3.55765 −0.186216
\(366\) 12.4677 0.651695
\(367\) 22.4163 1.17012 0.585060 0.810990i \(-0.301071\pi\)
0.585060 + 0.810990i \(0.301071\pi\)
\(368\) −1.54552 −0.0805659
\(369\) −8.23202 −0.428542
\(370\) 70.7459 3.67790
\(371\) 8.42860 0.437591
\(372\) −25.4575 −1.31991
\(373\) 22.3743 1.15849 0.579247 0.815152i \(-0.303347\pi\)
0.579247 + 0.815152i \(0.303347\pi\)
\(374\) −0.490663 −0.0253716
\(375\) 2.77749 0.143429
\(376\) 37.7807 1.94839
\(377\) 18.0963 0.932009
\(378\) 1.88141 0.0967695
\(379\) −4.61512 −0.237063 −0.118531 0.992950i \(-0.537819\pi\)
−0.118531 + 0.992950i \(0.537819\pi\)
\(380\) −18.5537 −0.951784
\(381\) 2.09797 0.107482
\(382\) −21.5688 −1.10356
\(383\) 28.6156 1.46219 0.731095 0.682276i \(-0.239010\pi\)
0.731095 + 0.682276i \(0.239010\pi\)
\(384\) −19.9585 −1.01851
\(385\) −0.510431 −0.0260140
\(386\) 17.3434 0.882757
\(387\) 10.4057 0.528953
\(388\) 36.4388 1.84990
\(389\) −11.1433 −0.564988 −0.282494 0.959269i \(-0.591162\pi\)
−0.282494 + 0.959269i \(0.591162\pi\)
\(390\) 17.5945 0.890930
\(391\) 1.54799 0.0782853
\(392\) −21.4825 −1.08503
\(393\) −13.7280 −0.692484
\(394\) −36.7976 −1.85384
\(395\) −32.8099 −1.65085
\(396\) 0.724991 0.0364321
\(397\) 15.8714 0.796560 0.398280 0.917264i \(-0.369607\pi\)
0.398280 + 0.917264i \(0.369607\pi\)
\(398\) 11.2040 0.561604
\(399\) 1.43892 0.0720362
\(400\) 4.07166 0.203583
\(401\) 12.3380 0.616129 0.308065 0.951365i \(-0.400319\pi\)
0.308065 + 0.951365i \(0.400319\pi\)
\(402\) −29.1422 −1.45348
\(403\) 18.4635 0.919732
\(404\) −44.6126 −2.21956
\(405\) −3.01300 −0.149717
\(406\) −13.6102 −0.675461
\(407\) −2.11425 −0.104799
\(408\) −3.38285 −0.167476
\(409\) −19.0994 −0.944403 −0.472201 0.881491i \(-0.656540\pi\)
−0.472201 + 0.881491i \(0.656540\pi\)
\(410\) 57.8989 2.85942
\(411\) 14.6945 0.724825
\(412\) 4.10197 0.202090
\(413\) −5.78011 −0.284420
\(414\) −3.61354 −0.177596
\(415\) −24.8281 −1.21877
\(416\) 11.0946 0.543959
\(417\) 11.5687 0.566521
\(418\) 0.875994 0.0428463
\(419\) −39.2009 −1.91509 −0.957545 0.288283i \(-0.906916\pi\)
−0.957545 + 0.288283i \(0.906916\pi\)
\(420\) −8.37592 −0.408703
\(421\) 0.356212 0.0173607 0.00868036 0.999962i \(-0.497237\pi\)
0.00868036 + 0.999962i \(0.497237\pi\)
\(422\) −20.1954 −0.983097
\(423\) 11.1683 0.543022
\(424\) 35.3768 1.71805
\(425\) −4.07816 −0.197820
\(426\) −27.0076 −1.30852
\(427\) 4.30467 0.208318
\(428\) −1.58914 −0.0768139
\(429\) −0.525812 −0.0253864
\(430\) −73.1874 −3.52941
\(431\) 23.0133 1.10851 0.554256 0.832346i \(-0.313003\pi\)
0.554256 + 0.832346i \(0.313003\pi\)
\(432\) 0.998405 0.0480358
\(433\) 36.9862 1.77744 0.888722 0.458447i \(-0.151594\pi\)
0.888722 + 0.458447i \(0.151594\pi\)
\(434\) −13.8863 −0.666563
\(435\) 21.7960 1.04504
\(436\) 29.9521 1.43444
\(437\) −2.76367 −0.132204
\(438\) 2.75632 0.131702
\(439\) 12.5687 0.599871 0.299935 0.953960i \(-0.403035\pi\)
0.299935 + 0.953960i \(0.403035\pi\)
\(440\) −2.14240 −0.102135
\(441\) −6.35041 −0.302400
\(442\) 5.83952 0.277757
\(443\) 12.1228 0.575973 0.287986 0.957635i \(-0.407014\pi\)
0.287986 + 0.957635i \(0.407014\pi\)
\(444\) −34.6937 −1.64649
\(445\) 29.6260 1.40441
\(446\) 31.9385 1.51233
\(447\) 2.16182 0.102251
\(448\) −9.95359 −0.470263
\(449\) −12.7054 −0.599603 −0.299802 0.954002i \(-0.596921\pi\)
−0.299802 + 0.954002i \(0.596921\pi\)
\(450\) 9.51984 0.448769
\(451\) −1.73031 −0.0814773
\(452\) −48.3164 −2.27261
\(453\) −13.9815 −0.656910
\(454\) −49.7746 −2.33604
\(455\) 6.07478 0.284790
\(456\) 6.03949 0.282825
\(457\) 4.74661 0.222037 0.111019 0.993818i \(-0.464589\pi\)
0.111019 + 0.993818i \(0.464589\pi\)
\(458\) 3.84289 0.179567
\(459\) −1.00000 −0.0466760
\(460\) 16.0872 0.750071
\(461\) 13.2043 0.614983 0.307492 0.951551i \(-0.400510\pi\)
0.307492 + 0.951551i \(0.400510\pi\)
\(462\) 0.395460 0.0183985
\(463\) 28.9153 1.34381 0.671904 0.740639i \(-0.265477\pi\)
0.671904 + 0.740639i \(0.265477\pi\)
\(464\) −7.22246 −0.335295
\(465\) 22.2383 1.03127
\(466\) −11.2412 −0.520738
\(467\) −13.9397 −0.645054 −0.322527 0.946560i \(-0.604532\pi\)
−0.322527 + 0.946560i \(0.604532\pi\)
\(468\) −8.62831 −0.398844
\(469\) −10.0618 −0.464612
\(470\) −78.5509 −3.62328
\(471\) 1.00000 0.0460776
\(472\) −24.2605 −1.11668
\(473\) 2.18721 0.100568
\(474\) 25.4197 1.16757
\(475\) 7.28085 0.334068
\(476\) −2.77993 −0.127418
\(477\) 10.4577 0.478825
\(478\) 29.8000 1.36302
\(479\) 35.8323 1.63722 0.818609 0.574351i \(-0.194746\pi\)
0.818609 + 0.574351i \(0.194746\pi\)
\(480\) 13.3629 0.609929
\(481\) 25.1622 1.14730
\(482\) −28.4362 −1.29523
\(483\) −1.24764 −0.0567694
\(484\) −37.7884 −1.71766
\(485\) −31.8309 −1.44537
\(486\) 2.33434 0.105888
\(487\) −1.20338 −0.0545305 −0.0272652 0.999628i \(-0.508680\pi\)
−0.0272652 + 0.999628i \(0.508680\pi\)
\(488\) 18.0677 0.817886
\(489\) −20.4399 −0.924326
\(490\) 44.6648 2.01775
\(491\) −27.1922 −1.22717 −0.613584 0.789630i \(-0.710273\pi\)
−0.613584 + 0.789630i \(0.710273\pi\)
\(492\) −28.3936 −1.28008
\(493\) 7.23400 0.325803
\(494\) −10.4254 −0.469063
\(495\) −0.633312 −0.0284652
\(496\) −7.36900 −0.330878
\(497\) −9.32482 −0.418275
\(498\) 19.2358 0.861976
\(499\) −37.2496 −1.66752 −0.833762 0.552125i \(-0.813817\pi\)
−0.833762 + 0.552125i \(0.813817\pi\)
\(500\) 9.58003 0.428432
\(501\) −7.74487 −0.346015
\(502\) −69.4948 −3.10170
\(503\) −27.7338 −1.23659 −0.618295 0.785946i \(-0.712176\pi\)
−0.618295 + 0.785946i \(0.712176\pi\)
\(504\) 2.72648 0.121447
\(505\) 38.9711 1.73419
\(506\) −0.759542 −0.0337658
\(507\) −6.74217 −0.299430
\(508\) 7.23623 0.321056
\(509\) 34.7406 1.53985 0.769925 0.638135i \(-0.220294\pi\)
0.769925 + 0.638135i \(0.220294\pi\)
\(510\) 7.03338 0.311443
\(511\) 0.951666 0.0420992
\(512\) −11.1829 −0.494219
\(513\) 1.78533 0.0788241
\(514\) 16.0934 0.709848
\(515\) −3.58325 −0.157897
\(516\) 35.8911 1.58002
\(517\) 2.34750 0.103243
\(518\) −18.9244 −0.831489
\(519\) 23.6620 1.03864
\(520\) 25.4973 1.11813
\(521\) 32.3325 1.41651 0.708256 0.705956i \(-0.249482\pi\)
0.708256 + 0.705956i \(0.249482\pi\)
\(522\) −16.8867 −0.739109
\(523\) 11.4691 0.501510 0.250755 0.968051i \(-0.419321\pi\)
0.250755 + 0.968051i \(0.419321\pi\)
\(524\) −47.3500 −2.06849
\(525\) 3.28688 0.143451
\(526\) 14.1316 0.616167
\(527\) 7.38077 0.321511
\(528\) 0.209858 0.00913289
\(529\) −20.6037 −0.895814
\(530\) −73.5529 −3.19494
\(531\) −7.17161 −0.311221
\(532\) 4.96308 0.215177
\(533\) 20.5929 0.891980
\(534\) −22.9530 −0.993273
\(535\) 1.38818 0.0600164
\(536\) −42.2318 −1.82414
\(537\) 7.66328 0.330695
\(538\) 10.7495 0.463443
\(539\) −1.33481 −0.0574944
\(540\) −10.3923 −0.447215
\(541\) −23.0579 −0.991337 −0.495669 0.868512i \(-0.665077\pi\)
−0.495669 + 0.868512i \(0.665077\pi\)
\(542\) 49.6237 2.13152
\(543\) −6.29563 −0.270171
\(544\) 4.43508 0.190152
\(545\) −26.1645 −1.12076
\(546\) −4.70648 −0.201419
\(547\) 37.0974 1.58617 0.793086 0.609110i \(-0.208473\pi\)
0.793086 + 0.609110i \(0.208473\pi\)
\(548\) 50.6837 2.16510
\(549\) 5.34097 0.227947
\(550\) 2.00100 0.0853231
\(551\) −12.9151 −0.550200
\(552\) −5.23662 −0.222885
\(553\) 8.77658 0.373218
\(554\) 2.63720 0.112044
\(555\) 30.3065 1.28644
\(556\) 39.9023 1.69223
\(557\) 7.00635 0.296868 0.148434 0.988922i \(-0.452577\pi\)
0.148434 + 0.988922i \(0.452577\pi\)
\(558\) −17.2293 −0.729373
\(559\) −26.0306 −1.10098
\(560\) −2.42452 −0.102455
\(561\) −0.210193 −0.00887436
\(562\) −69.0611 −2.91317
\(563\) −29.9681 −1.26300 −0.631502 0.775375i \(-0.717561\pi\)
−0.631502 + 0.775375i \(0.717561\pi\)
\(564\) 38.5213 1.62204
\(565\) 42.2065 1.77564
\(566\) −41.2043 −1.73195
\(567\) 0.805971 0.0338476
\(568\) −39.1384 −1.64221
\(569\) −22.8734 −0.958901 −0.479450 0.877569i \(-0.659164\pi\)
−0.479450 + 0.877569i \(0.659164\pi\)
\(570\) −12.5569 −0.525949
\(571\) −17.6045 −0.736727 −0.368364 0.929682i \(-0.620082\pi\)
−0.368364 + 0.929682i \(0.620082\pi\)
\(572\) −1.81361 −0.0758309
\(573\) −9.23979 −0.385998
\(574\) −15.4878 −0.646450
\(575\) −6.31296 −0.263269
\(576\) −12.3498 −0.514575
\(577\) 8.44725 0.351663 0.175832 0.984420i \(-0.443739\pi\)
0.175832 + 0.984420i \(0.443739\pi\)
\(578\) 2.33434 0.0970959
\(579\) 7.42968 0.308767
\(580\) 75.1781 3.12160
\(581\) 6.64148 0.275535
\(582\) 24.6612 1.02224
\(583\) 2.19814 0.0910375
\(584\) 3.99436 0.165288
\(585\) 7.53722 0.311626
\(586\) 20.1833 0.833766
\(587\) 23.7706 0.981116 0.490558 0.871408i \(-0.336793\pi\)
0.490558 + 0.871408i \(0.336793\pi\)
\(588\) −21.9036 −0.903290
\(589\) −13.1771 −0.542952
\(590\) 50.4406 2.07661
\(591\) −15.7636 −0.648427
\(592\) −10.0425 −0.412746
\(593\) 45.7958 1.88061 0.940304 0.340336i \(-0.110541\pi\)
0.940304 + 0.340336i \(0.110541\pi\)
\(594\) 0.490663 0.0201322
\(595\) 2.42839 0.0995543
\(596\) 7.45647 0.305429
\(597\) 4.79962 0.196436
\(598\) 9.03952 0.369653
\(599\) −40.4504 −1.65276 −0.826380 0.563113i \(-0.809604\pi\)
−0.826380 + 0.563113i \(0.809604\pi\)
\(600\) 13.7958 0.563211
\(601\) −30.7754 −1.25535 −0.627677 0.778474i \(-0.715994\pi\)
−0.627677 + 0.778474i \(0.715994\pi\)
\(602\) 19.5775 0.797919
\(603\) −12.4841 −0.508392
\(604\) −48.2246 −1.96223
\(605\) 33.0099 1.34204
\(606\) −30.1932 −1.22651
\(607\) 2.40352 0.0975560 0.0487780 0.998810i \(-0.484467\pi\)
0.0487780 + 0.998810i \(0.484467\pi\)
\(608\) −7.91806 −0.321120
\(609\) −5.83040 −0.236260
\(610\) −37.5651 −1.52097
\(611\) −27.9383 −1.13026
\(612\) −3.44916 −0.139424
\(613\) 38.7499 1.56509 0.782547 0.622591i \(-0.213920\pi\)
0.782547 + 0.622591i \(0.213920\pi\)
\(614\) 38.8496 1.56784
\(615\) 24.8031 1.00016
\(616\) 0.573087 0.0230903
\(617\) −8.25971 −0.332523 −0.166262 0.986082i \(-0.553170\pi\)
−0.166262 + 0.986082i \(0.553170\pi\)
\(618\) 2.77615 0.111673
\(619\) 38.1020 1.53145 0.765724 0.643169i \(-0.222381\pi\)
0.765724 + 0.643169i \(0.222381\pi\)
\(620\) 76.7034 3.08048
\(621\) −1.54799 −0.0621187
\(622\) 33.1615 1.32966
\(623\) −7.92490 −0.317504
\(624\) −2.49758 −0.0999831
\(625\) −28.7594 −1.15038
\(626\) −22.2691 −0.890051
\(627\) 0.375263 0.0149866
\(628\) 3.44916 0.137637
\(629\) 10.0586 0.401062
\(630\) −5.66870 −0.225846
\(631\) 29.5729 1.17728 0.588639 0.808396i \(-0.299664\pi\)
0.588639 + 0.808396i \(0.299664\pi\)
\(632\) 36.8374 1.46531
\(633\) −8.65142 −0.343863
\(634\) 9.87688 0.392261
\(635\) −6.32117 −0.250848
\(636\) 36.0703 1.43028
\(637\) 15.8860 0.629425
\(638\) −3.54946 −0.140524
\(639\) −11.5697 −0.457689
\(640\) 60.1351 2.37705
\(641\) −2.70994 −0.107036 −0.0535180 0.998567i \(-0.517043\pi\)
−0.0535180 + 0.998567i \(0.517043\pi\)
\(642\) −1.07551 −0.0424468
\(643\) 37.4984 1.47879 0.739396 0.673271i \(-0.235111\pi\)
0.739396 + 0.673271i \(0.235111\pi\)
\(644\) −4.30330 −0.169574
\(645\) −31.3524 −1.23450
\(646\) −4.16757 −0.163971
\(647\) −24.2480 −0.953286 −0.476643 0.879097i \(-0.658147\pi\)
−0.476643 + 0.879097i \(0.658147\pi\)
\(648\) 3.38285 0.132891
\(649\) −1.50742 −0.0591715
\(650\) −23.8145 −0.934082
\(651\) −5.94869 −0.233148
\(652\) −70.5007 −2.76102
\(653\) −37.9146 −1.48371 −0.741856 0.670559i \(-0.766054\pi\)
−0.741856 + 0.670559i \(0.766054\pi\)
\(654\) 20.2711 0.792664
\(655\) 41.3623 1.61616
\(656\) −8.21889 −0.320894
\(657\) 1.18077 0.0460662
\(658\) 21.0122 0.819142
\(659\) −51.0527 −1.98873 −0.994366 0.106003i \(-0.966195\pi\)
−0.994366 + 0.106003i \(0.966195\pi\)
\(660\) −2.18440 −0.0850275
\(661\) 46.3119 1.80132 0.900662 0.434521i \(-0.143082\pi\)
0.900662 + 0.434521i \(0.143082\pi\)
\(662\) 23.3360 0.906981
\(663\) 2.50157 0.0971528
\(664\) 27.8758 1.08179
\(665\) −4.33547 −0.168122
\(666\) −23.4802 −0.909840
\(667\) 11.1982 0.433595
\(668\) −26.7133 −1.03357
\(669\) 13.6820 0.528976
\(670\) 87.8054 3.39222
\(671\) 1.12264 0.0433389
\(672\) −3.57454 −0.137891
\(673\) −16.0357 −0.618133 −0.309066 0.951040i \(-0.600017\pi\)
−0.309066 + 0.951040i \(0.600017\pi\)
\(674\) 82.1228 3.16325
\(675\) 4.07816 0.156969
\(676\) −23.2548 −0.894417
\(677\) −0.442477 −0.0170058 −0.00850289 0.999964i \(-0.502707\pi\)
−0.00850289 + 0.999964i \(0.502707\pi\)
\(678\) −32.6998 −1.25583
\(679\) 8.51470 0.326764
\(680\) 10.1925 0.390865
\(681\) −21.3227 −0.817089
\(682\) −3.62147 −0.138673
\(683\) 35.3839 1.35393 0.676963 0.736017i \(-0.263296\pi\)
0.676963 + 0.736017i \(0.263296\pi\)
\(684\) 6.15788 0.235453
\(685\) −44.2744 −1.69164
\(686\) −25.1177 −0.958997
\(687\) 1.64624 0.0628080
\(688\) 10.3891 0.396082
\(689\) −26.1606 −0.996640
\(690\) 10.8876 0.414484
\(691\) −19.4329 −0.739263 −0.369632 0.929178i \(-0.620516\pi\)
−0.369632 + 0.929178i \(0.620516\pi\)
\(692\) 81.6140 3.10250
\(693\) 0.169410 0.00643534
\(694\) 29.3821 1.11533
\(695\) −34.8564 −1.32218
\(696\) −24.4715 −0.927591
\(697\) 8.23202 0.311810
\(698\) 51.0372 1.93179
\(699\) −4.81556 −0.182141
\(700\) 11.3370 0.428498
\(701\) −9.59954 −0.362570 −0.181285 0.983431i \(-0.558026\pi\)
−0.181285 + 0.983431i \(0.558026\pi\)
\(702\) −5.83952 −0.220398
\(703\) −17.9579 −0.677294
\(704\) −2.59584 −0.0978345
\(705\) −33.6501 −1.26734
\(706\) −44.5734 −1.67754
\(707\) −10.4247 −0.392061
\(708\) −24.7360 −0.929637
\(709\) 41.9921 1.57705 0.788524 0.615004i \(-0.210846\pi\)
0.788524 + 0.615004i \(0.210846\pi\)
\(710\) 81.3738 3.05391
\(711\) 10.8894 0.408386
\(712\) −33.2626 −1.24657
\(713\) 11.4254 0.427884
\(714\) −1.88141 −0.0704102
\(715\) 1.58427 0.0592484
\(716\) 26.4319 0.987807
\(717\) 12.7659 0.476752
\(718\) −49.2103 −1.83651
\(719\) −34.8735 −1.30056 −0.650282 0.759693i \(-0.725349\pi\)
−0.650282 + 0.759693i \(0.725349\pi\)
\(720\) −3.00819 −0.112109
\(721\) 0.958513 0.0356969
\(722\) −36.9121 −1.37373
\(723\) −12.1817 −0.453041
\(724\) −21.7146 −0.807018
\(725\) −29.5014 −1.09566
\(726\) −25.5747 −0.949164
\(727\) −16.1988 −0.600779 −0.300389 0.953817i \(-0.597117\pi\)
−0.300389 + 0.953817i \(0.597117\pi\)
\(728\) −6.82047 −0.252783
\(729\) 1.00000 0.0370370
\(730\) −8.30479 −0.307374
\(731\) −10.4057 −0.384870
\(732\) 18.4219 0.680893
\(733\) −21.7530 −0.803464 −0.401732 0.915757i \(-0.631592\pi\)
−0.401732 + 0.915757i \(0.631592\pi\)
\(734\) 52.3273 1.93144
\(735\) 19.1338 0.705760
\(736\) 6.86546 0.253064
\(737\) −2.62407 −0.0966589
\(738\) −19.2164 −0.707365
\(739\) −8.99049 −0.330720 −0.165360 0.986233i \(-0.552879\pi\)
−0.165360 + 0.986233i \(0.552879\pi\)
\(740\) 104.532 3.84268
\(741\) −4.46611 −0.164067
\(742\) 19.6753 0.722302
\(743\) −35.9387 −1.31846 −0.659232 0.751940i \(-0.729118\pi\)
−0.659232 + 0.751940i \(0.729118\pi\)
\(744\) −24.9680 −0.915373
\(745\) −6.51356 −0.238638
\(746\) 52.2292 1.91225
\(747\) 8.24034 0.301498
\(748\) −0.724991 −0.0265083
\(749\) −0.371336 −0.0135683
\(750\) 6.48363 0.236749
\(751\) 31.1926 1.13823 0.569116 0.822257i \(-0.307285\pi\)
0.569116 + 0.822257i \(0.307285\pi\)
\(752\) 11.1505 0.406617
\(753\) −29.7706 −1.08490
\(754\) 42.2431 1.53840
\(755\) 42.1264 1.53314
\(756\) 2.77993 0.101105
\(757\) 44.5491 1.61917 0.809583 0.587005i \(-0.199693\pi\)
0.809583 + 0.587005i \(0.199693\pi\)
\(758\) −10.7733 −0.391303
\(759\) −0.325377 −0.0118104
\(760\) −18.1970 −0.660073
\(761\) 4.11217 0.149066 0.0745330 0.997219i \(-0.476253\pi\)
0.0745330 + 0.997219i \(0.476253\pi\)
\(762\) 4.89738 0.177413
\(763\) 6.99894 0.253379
\(764\) −31.8695 −1.15300
\(765\) 3.01300 0.108935
\(766\) 66.7987 2.41354
\(767\) 17.9402 0.647785
\(768\) −21.8905 −0.789906
\(769\) −9.10726 −0.328416 −0.164208 0.986426i \(-0.552507\pi\)
−0.164208 + 0.986426i \(0.552507\pi\)
\(770\) −1.19152 −0.0429395
\(771\) 6.89417 0.248287
\(772\) 25.6262 0.922307
\(773\) −41.9843 −1.51007 −0.755035 0.655684i \(-0.772380\pi\)
−0.755035 + 0.655684i \(0.772380\pi\)
\(774\) 24.2905 0.873106
\(775\) −30.1000 −1.08122
\(776\) 35.7382 1.28293
\(777\) −8.10693 −0.290835
\(778\) −26.0123 −0.932586
\(779\) −14.6968 −0.526569
\(780\) 25.9971 0.930845
\(781\) −2.43186 −0.0870189
\(782\) 3.61354 0.129220
\(783\) −7.23400 −0.258522
\(784\) −6.34028 −0.226439
\(785\) −3.01300 −0.107539
\(786\) −32.0458 −1.14303
\(787\) −32.2848 −1.15083 −0.575414 0.817862i \(-0.695159\pi\)
−0.575414 + 0.817862i \(0.695159\pi\)
\(788\) −54.3712 −1.93689
\(789\) 6.05378 0.215520
\(790\) −76.5896 −2.72494
\(791\) −11.2902 −0.401432
\(792\) 0.711051 0.0252661
\(793\) −13.3608 −0.474456
\(794\) 37.0492 1.31483
\(795\) −31.5090 −1.11751
\(796\) 16.5547 0.586765
\(797\) −4.73632 −0.167769 −0.0838845 0.996475i \(-0.526733\pi\)
−0.0838845 + 0.996475i \(0.526733\pi\)
\(798\) 3.35894 0.118905
\(799\) −11.1683 −0.395106
\(800\) −18.0870 −0.639471
\(801\) −9.83273 −0.347423
\(802\) 28.8011 1.01700
\(803\) 0.248189 0.00875842
\(804\) −43.0597 −1.51860
\(805\) 3.75913 0.132492
\(806\) 43.1001 1.51814
\(807\) 4.60492 0.162101
\(808\) −43.7548 −1.53929
\(809\) −17.7046 −0.622460 −0.311230 0.950335i \(-0.600741\pi\)
−0.311230 + 0.950335i \(0.600741\pi\)
\(810\) −7.03338 −0.247128
\(811\) −11.8186 −0.415008 −0.207504 0.978234i \(-0.566534\pi\)
−0.207504 + 0.978234i \(0.566534\pi\)
\(812\) −20.1100 −0.705723
\(813\) 21.2581 0.745553
\(814\) −4.93538 −0.172985
\(815\) 61.5855 2.15725
\(816\) −0.998405 −0.0349512
\(817\) 18.5776 0.649948
\(818\) −44.5845 −1.55886
\(819\) −2.01619 −0.0704514
\(820\) 85.5499 2.98753
\(821\) 18.5887 0.648751 0.324376 0.945928i \(-0.394846\pi\)
0.324376 + 0.945928i \(0.394846\pi\)
\(822\) 34.3020 1.19642
\(823\) −43.8139 −1.52726 −0.763629 0.645655i \(-0.776584\pi\)
−0.763629 + 0.645655i \(0.776584\pi\)
\(824\) 4.02310 0.140151
\(825\) 0.857202 0.0298439
\(826\) −13.4928 −0.469473
\(827\) 42.9585 1.49381 0.746907 0.664929i \(-0.231538\pi\)
0.746907 + 0.664929i \(0.231538\pi\)
\(828\) −5.33928 −0.185553
\(829\) −11.7202 −0.407059 −0.203529 0.979069i \(-0.565241\pi\)
−0.203529 + 0.979069i \(0.565241\pi\)
\(830\) −57.9574 −2.01173
\(831\) 1.12974 0.0391902
\(832\) 30.8938 1.07105
\(833\) 6.35041 0.220029
\(834\) 27.0053 0.935117
\(835\) 23.3353 0.807550
\(836\) 1.29434 0.0447658
\(837\) −7.38077 −0.255117
\(838\) −91.5085 −3.16111
\(839\) 38.1403 1.31675 0.658375 0.752690i \(-0.271244\pi\)
0.658375 + 0.752690i \(0.271244\pi\)
\(840\) −8.21488 −0.283440
\(841\) 23.3308 0.804510
\(842\) 0.831522 0.0286562
\(843\) −29.5848 −1.01895
\(844\) −29.8402 −1.02714
\(845\) 20.3141 0.698828
\(846\) 26.0707 0.896328
\(847\) −8.83008 −0.303405
\(848\) 10.4410 0.358546
\(849\) −17.6514 −0.605793
\(850\) −9.51984 −0.326528
\(851\) 15.5706 0.533754
\(852\) −39.9057 −1.36715
\(853\) −17.7907 −0.609141 −0.304570 0.952490i \(-0.598513\pi\)
−0.304570 + 0.952490i \(0.598513\pi\)
\(854\) 10.0486 0.343855
\(855\) −5.37919 −0.183964
\(856\) −1.55858 −0.0532713
\(857\) 23.0846 0.788555 0.394278 0.918991i \(-0.370995\pi\)
0.394278 + 0.918991i \(0.370995\pi\)
\(858\) −1.22743 −0.0419036
\(859\) −43.0125 −1.46757 −0.733784 0.679383i \(-0.762247\pi\)
−0.733784 + 0.679383i \(0.762247\pi\)
\(860\) −108.140 −3.68753
\(861\) −6.63477 −0.226112
\(862\) 53.7210 1.82974
\(863\) 23.2619 0.791844 0.395922 0.918284i \(-0.370425\pi\)
0.395922 + 0.918284i \(0.370425\pi\)
\(864\) −4.43508 −0.150884
\(865\) −71.2935 −2.42405
\(866\) 86.3385 2.93390
\(867\) 1.00000 0.0339618
\(868\) −20.5180 −0.696427
\(869\) 2.28889 0.0776452
\(870\) 50.8795 1.72498
\(871\) 31.2298 1.05818
\(872\) 29.3762 0.994803
\(873\) 10.5645 0.357555
\(874\) −6.45136 −0.218220
\(875\) 2.23858 0.0756778
\(876\) 4.07266 0.137603
\(877\) 48.7521 1.64624 0.823121 0.567866i \(-0.192231\pi\)
0.823121 + 0.567866i \(0.192231\pi\)
\(878\) 29.3396 0.990165
\(879\) 8.64625 0.291631
\(880\) −0.632302 −0.0213149
\(881\) −47.7849 −1.60991 −0.804957 0.593334i \(-0.797811\pi\)
−0.804957 + 0.593334i \(0.797811\pi\)
\(882\) −14.8240 −0.499152
\(883\) 38.5348 1.29680 0.648400 0.761300i \(-0.275438\pi\)
0.648400 + 0.761300i \(0.275438\pi\)
\(884\) 8.62831 0.290202
\(885\) 21.6080 0.726346
\(886\) 28.2988 0.950718
\(887\) −45.6170 −1.53167 −0.765835 0.643037i \(-0.777674\pi\)
−0.765835 + 0.643037i \(0.777674\pi\)
\(888\) −34.0267 −1.14186
\(889\) 1.69090 0.0567110
\(890\) 69.1573 2.31816
\(891\) 0.210193 0.00704173
\(892\) 47.1914 1.58008
\(893\) 19.9391 0.667236
\(894\) 5.04643 0.168778
\(895\) −23.0895 −0.771795
\(896\) −16.0860 −0.537396
\(897\) 3.87240 0.129296
\(898\) −29.6587 −0.989724
\(899\) 53.3925 1.78074
\(900\) 14.0663 0.468875
\(901\) −10.4577 −0.348396
\(902\) −4.03915 −0.134489
\(903\) 8.38672 0.279092
\(904\) −47.3874 −1.57608
\(905\) 18.9687 0.630541
\(906\) −32.6377 −1.08432
\(907\) −34.7499 −1.15385 −0.576927 0.816796i \(-0.695748\pi\)
−0.576927 + 0.816796i \(0.695748\pi\)
\(908\) −73.5456 −2.44070
\(909\) −12.9343 −0.429004
\(910\) 14.1806 0.470083
\(911\) 50.9296 1.68737 0.843687 0.536836i \(-0.180381\pi\)
0.843687 + 0.536836i \(0.180381\pi\)
\(912\) 1.78248 0.0590238
\(913\) 1.73206 0.0573229
\(914\) 11.0802 0.366501
\(915\) −16.0923 −0.531996
\(916\) 5.67815 0.187611
\(917\) −11.0643 −0.365377
\(918\) −2.33434 −0.0770448
\(919\) −24.1295 −0.795957 −0.397979 0.917395i \(-0.630288\pi\)
−0.397979 + 0.917395i \(0.630288\pi\)
\(920\) 15.7779 0.520183
\(921\) 16.6426 0.548393
\(922\) 30.8233 1.01511
\(923\) 28.9423 0.952647
\(924\) 0.584322 0.0192228
\(925\) −41.0206 −1.34875
\(926\) 67.4982 2.21813
\(927\) 1.18927 0.0390606
\(928\) 32.0833 1.05319
\(929\) 35.5707 1.16704 0.583518 0.812100i \(-0.301676\pi\)
0.583518 + 0.812100i \(0.301676\pi\)
\(930\) 51.9118 1.70225
\(931\) −11.3376 −0.371573
\(932\) −16.6097 −0.544068
\(933\) 14.2059 0.465081
\(934\) −32.5402 −1.06475
\(935\) 0.633312 0.0207115
\(936\) −8.46242 −0.276603
\(937\) 8.00653 0.261562 0.130781 0.991411i \(-0.458252\pi\)
0.130781 + 0.991411i \(0.458252\pi\)
\(938\) −23.4878 −0.766903
\(939\) −9.53976 −0.311318
\(940\) −116.065 −3.78561
\(941\) 24.5049 0.798838 0.399419 0.916768i \(-0.369212\pi\)
0.399419 + 0.916768i \(0.369212\pi\)
\(942\) 2.33434 0.0760571
\(943\) 12.7431 0.414972
\(944\) −7.16017 −0.233044
\(945\) −2.42839 −0.0789956
\(946\) 5.10571 0.166001
\(947\) −18.7833 −0.610375 −0.305188 0.952292i \(-0.598719\pi\)
−0.305188 + 0.952292i \(0.598719\pi\)
\(948\) 37.5595 1.21988
\(949\) −2.95377 −0.0958834
\(950\) 16.9960 0.551423
\(951\) 4.23111 0.137203
\(952\) −2.72648 −0.0883657
\(953\) −9.02456 −0.292334 −0.146167 0.989260i \(-0.546694\pi\)
−0.146167 + 0.989260i \(0.546694\pi\)
\(954\) 24.4119 0.790363
\(955\) 27.8395 0.900864
\(956\) 44.0317 1.42409
\(957\) −1.52054 −0.0491520
\(958\) 83.6448 2.70244
\(959\) 11.8433 0.382441
\(960\) 37.2099 1.20095
\(961\) 23.4758 0.757284
\(962\) 58.7373 1.89377
\(963\) −0.460731 −0.0148469
\(964\) −42.0165 −1.35326
\(965\) −22.3856 −0.720618
\(966\) −2.91241 −0.0937054
\(967\) 5.02954 0.161739 0.0808696 0.996725i \(-0.474230\pi\)
0.0808696 + 0.996725i \(0.474230\pi\)
\(968\) −37.0619 −1.19121
\(969\) −1.78533 −0.0573529
\(970\) −74.3043 −2.38577
\(971\) 44.4677 1.42704 0.713518 0.700637i \(-0.247101\pi\)
0.713518 + 0.700637i \(0.247101\pi\)
\(972\) 3.44916 0.110632
\(973\) 9.32403 0.298915
\(974\) −2.80911 −0.0900097
\(975\) −10.2018 −0.326719
\(976\) 5.33245 0.170688
\(977\) 5.87955 0.188103 0.0940517 0.995567i \(-0.470018\pi\)
0.0940517 + 0.995567i \(0.470018\pi\)
\(978\) −47.7139 −1.52572
\(979\) −2.06677 −0.0660544
\(980\) 65.9955 2.10815
\(981\) 8.68386 0.277254
\(982\) −63.4760 −2.02560
\(983\) 42.6059 1.35892 0.679459 0.733714i \(-0.262215\pi\)
0.679459 + 0.733714i \(0.262215\pi\)
\(984\) −27.8477 −0.887752
\(985\) 47.4957 1.51334
\(986\) 16.8867 0.537781
\(987\) 9.00134 0.286516
\(988\) −15.4043 −0.490078
\(989\) −16.1080 −0.512204
\(990\) −1.47837 −0.0469856
\(991\) −34.1905 −1.08610 −0.543049 0.839701i \(-0.682730\pi\)
−0.543049 + 0.839701i \(0.682730\pi\)
\(992\) 32.7343 1.03931
\(993\) 9.99683 0.317240
\(994\) −21.7673 −0.690418
\(995\) −14.4613 −0.458453
\(996\) 28.4223 0.900594
\(997\) −42.0504 −1.33175 −0.665875 0.746063i \(-0.731942\pi\)
−0.665875 + 0.746063i \(0.731942\pi\)
\(998\) −86.9535 −2.75246
\(999\) −10.0586 −0.318240
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 \(a_p\))