Properties

Label 8047.2.a.b.1.19
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 1.19
Character \(\chi\) = 8047.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.23735 q^{2} -0.938044 q^{3} +3.00574 q^{4} +3.28954 q^{5} +2.09873 q^{6} +1.35040 q^{7} -2.25019 q^{8} -2.12007 q^{9} +O(q^{10})\) \(q-2.23735 q^{2} -0.938044 q^{3} +3.00574 q^{4} +3.28954 q^{5} +2.09873 q^{6} +1.35040 q^{7} -2.25019 q^{8} -2.12007 q^{9} -7.35985 q^{10} -0.595247 q^{11} -2.81952 q^{12} +1.00000 q^{13} -3.02131 q^{14} -3.08573 q^{15} -0.977008 q^{16} +5.30619 q^{17} +4.74335 q^{18} -1.67376 q^{19} +9.88749 q^{20} -1.26673 q^{21} +1.33178 q^{22} -8.87996 q^{23} +2.11078 q^{24} +5.82105 q^{25} -2.23735 q^{26} +4.80285 q^{27} +4.05894 q^{28} -1.53783 q^{29} +6.90386 q^{30} -2.30591 q^{31} +6.68630 q^{32} +0.558368 q^{33} -11.8718 q^{34} +4.44218 q^{35} -6.37239 q^{36} -4.70751 q^{37} +3.74480 q^{38} -0.938044 q^{39} -7.40209 q^{40} -4.26242 q^{41} +2.83412 q^{42} -2.71574 q^{43} -1.78916 q^{44} -6.97406 q^{45} +19.8676 q^{46} +5.75978 q^{47} +0.916476 q^{48} -5.17643 q^{49} -13.0237 q^{50} -4.97744 q^{51} +3.00574 q^{52} +6.39058 q^{53} -10.7457 q^{54} -1.95809 q^{55} -3.03866 q^{56} +1.57006 q^{57} +3.44066 q^{58} +2.32958 q^{59} -9.27490 q^{60} +0.743528 q^{61} +5.15913 q^{62} -2.86294 q^{63} -13.0056 q^{64} +3.28954 q^{65} -1.24926 q^{66} +4.96940 q^{67} +15.9490 q^{68} +8.32980 q^{69} -9.93872 q^{70} -0.701613 q^{71} +4.77057 q^{72} +7.63942 q^{73} +10.5324 q^{74} -5.46040 q^{75} -5.03090 q^{76} -0.803820 q^{77} +2.09873 q^{78} +3.41878 q^{79} -3.21390 q^{80} +1.85493 q^{81} +9.53653 q^{82} +3.79747 q^{83} -3.80747 q^{84} +17.4549 q^{85} +6.07606 q^{86} +1.44255 q^{87} +1.33942 q^{88} -3.35078 q^{89} +15.6034 q^{90} +1.35040 q^{91} -26.6909 q^{92} +2.16305 q^{93} -12.8866 q^{94} -5.50591 q^{95} -6.27204 q^{96} -9.76960 q^{97} +11.5815 q^{98} +1.26197 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} + O(q^{10}) \) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} - 25q^{10} - 25q^{11} - 62q^{12} + 142q^{13} - 57q^{14} - 14q^{15} + 111q^{16} - 141q^{17} - 29q^{18} - 3q^{19} - 87q^{20} - 19q^{21} - 24q^{22} - 69q^{23} - 40q^{24} + 87q^{25} - 13q^{26} - 95q^{27} - 34q^{28} - 147q^{29} - 2q^{30} - 21q^{31} - 66q^{32} - 62q^{33} - 6q^{34} - 59q^{35} + 74q^{36} - 37q^{37} - 76q^{38} - 26q^{39} - 61q^{40} - 97q^{41} - 29q^{42} - 33q^{43} - 57q^{44} - 86q^{45} - q^{46} - 102q^{47} - 141q^{48} + 70q^{49} - 28q^{50} - 13q^{51} + 129q^{52} - 137q^{53} - 29q^{54} - 24q^{55} - 130q^{56} - 65q^{57} - 15q^{58} - 56q^{59} + 11q^{60} - 77q^{61} - 150q^{62} - 32q^{63} + 73q^{64} - 37q^{65} - 32q^{66} - 9q^{67} - 226q^{68} - 113q^{69} + 6q^{70} - 18q^{71} - 82q^{72} - 117q^{73} - 70q^{74} - 83q^{75} + 40q^{76} - 214q^{77} - 15q^{78} - 52q^{79} - 161q^{80} - 10q^{81} - 36q^{82} - 74q^{83} + 53q^{84} + 2q^{85} + 17q^{86} - 49q^{87} - 29q^{88} - 171q^{89} - 57q^{90} - 14q^{91} - 187q^{92} - 39q^{93} + 13q^{94} - 150q^{95} - 47q^{96} - 126q^{97} - 85q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.23735 −1.58205 −0.791023 0.611786i \(-0.790451\pi\)
−0.791023 + 0.611786i \(0.790451\pi\)
\(3\) −0.938044 −0.541580 −0.270790 0.962638i \(-0.587285\pi\)
−0.270790 + 0.962638i \(0.587285\pi\)
\(4\) 3.00574 1.50287
\(5\) 3.28954 1.47113 0.735563 0.677457i \(-0.236918\pi\)
0.735563 + 0.677457i \(0.236918\pi\)
\(6\) 2.09873 0.856804
\(7\) 1.35040 0.510402 0.255201 0.966888i \(-0.417858\pi\)
0.255201 + 0.966888i \(0.417858\pi\)
\(8\) −2.25019 −0.795563
\(9\) −2.12007 −0.706691
\(10\) −7.35985 −2.32739
\(11\) −0.595247 −0.179474 −0.0897368 0.995966i \(-0.528603\pi\)
−0.0897368 + 0.995966i \(0.528603\pi\)
\(12\) −2.81952 −0.813924
\(13\) 1.00000 0.277350
\(14\) −3.02131 −0.807480
\(15\) −3.08573 −0.796732
\(16\) −0.977008 −0.244252
\(17\) 5.30619 1.28694 0.643470 0.765471i \(-0.277494\pi\)
0.643470 + 0.765471i \(0.277494\pi\)
\(18\) 4.74335 1.11802
\(19\) −1.67376 −0.383988 −0.191994 0.981396i \(-0.561495\pi\)
−0.191994 + 0.981396i \(0.561495\pi\)
\(20\) 9.88749 2.21091
\(21\) −1.26673 −0.276424
\(22\) 1.33178 0.283936
\(23\) −8.87996 −1.85160 −0.925800 0.378013i \(-0.876607\pi\)
−0.925800 + 0.378013i \(0.876607\pi\)
\(24\) 2.11078 0.430861
\(25\) 5.82105 1.16421
\(26\) −2.23735 −0.438781
\(27\) 4.80285 0.924310
\(28\) 4.05894 0.767068
\(29\) −1.53783 −0.285568 −0.142784 0.989754i \(-0.545605\pi\)
−0.142784 + 0.989754i \(0.545605\pi\)
\(30\) 6.90386 1.26047
\(31\) −2.30591 −0.414154 −0.207077 0.978325i \(-0.566395\pi\)
−0.207077 + 0.978325i \(0.566395\pi\)
\(32\) 6.68630 1.18198
\(33\) 0.558368 0.0971993
\(34\) −11.8718 −2.03600
\(35\) 4.44218 0.750866
\(36\) −6.37239 −1.06207
\(37\) −4.70751 −0.773910 −0.386955 0.922099i \(-0.626473\pi\)
−0.386955 + 0.922099i \(0.626473\pi\)
\(38\) 3.74480 0.607486
\(39\) −0.938044 −0.150207
\(40\) −7.40209 −1.17037
\(41\) −4.26242 −0.665678 −0.332839 0.942984i \(-0.608007\pi\)
−0.332839 + 0.942984i \(0.608007\pi\)
\(42\) 2.83412 0.437315
\(43\) −2.71574 −0.414146 −0.207073 0.978325i \(-0.566394\pi\)
−0.207073 + 0.978325i \(0.566394\pi\)
\(44\) −1.78916 −0.269726
\(45\) −6.97406 −1.03963
\(46\) 19.8676 2.92932
\(47\) 5.75978 0.840150 0.420075 0.907489i \(-0.362004\pi\)
0.420075 + 0.907489i \(0.362004\pi\)
\(48\) 0.916476 0.132282
\(49\) −5.17643 −0.739489
\(50\) −13.0237 −1.84183
\(51\) −4.97744 −0.696981
\(52\) 3.00574 0.416821
\(53\) 6.39058 0.877813 0.438907 0.898533i \(-0.355366\pi\)
0.438907 + 0.898533i \(0.355366\pi\)
\(54\) −10.7457 −1.46230
\(55\) −1.95809 −0.264028
\(56\) −3.03866 −0.406057
\(57\) 1.57006 0.207960
\(58\) 3.44066 0.451781
\(59\) 2.32958 0.303285 0.151642 0.988435i \(-0.451544\pi\)
0.151642 + 0.988435i \(0.451544\pi\)
\(60\) −9.27490 −1.19738
\(61\) 0.743528 0.0951990 0.0475995 0.998867i \(-0.484843\pi\)
0.0475995 + 0.998867i \(0.484843\pi\)
\(62\) 5.15913 0.655210
\(63\) −2.86294 −0.360697
\(64\) −13.0056 −1.62570
\(65\) 3.28954 0.408017
\(66\) −1.24926 −0.153774
\(67\) 4.96940 0.607109 0.303554 0.952814i \(-0.401827\pi\)
0.303554 + 0.952814i \(0.401827\pi\)
\(68\) 15.9490 1.93410
\(69\) 8.32980 1.00279
\(70\) −9.93872 −1.18790
\(71\) −0.701613 −0.0832662 −0.0416331 0.999133i \(-0.513256\pi\)
−0.0416331 + 0.999133i \(0.513256\pi\)
\(72\) 4.77057 0.562218
\(73\) 7.63942 0.894126 0.447063 0.894502i \(-0.352470\pi\)
0.447063 + 0.894502i \(0.352470\pi\)
\(74\) 10.5324 1.22436
\(75\) −5.46040 −0.630513
\(76\) −5.03090 −0.577083
\(77\) −0.803820 −0.0916038
\(78\) 2.09873 0.237635
\(79\) 3.41878 0.384643 0.192321 0.981332i \(-0.438398\pi\)
0.192321 + 0.981332i \(0.438398\pi\)
\(80\) −3.21390 −0.359325
\(81\) 1.85493 0.206104
\(82\) 9.53653 1.05313
\(83\) 3.79747 0.416826 0.208413 0.978041i \(-0.433170\pi\)
0.208413 + 0.978041i \(0.433170\pi\)
\(84\) −3.80747 −0.415429
\(85\) 17.4549 1.89325
\(86\) 6.07606 0.655199
\(87\) 1.44255 0.154658
\(88\) 1.33942 0.142783
\(89\) −3.35078 −0.355182 −0.177591 0.984104i \(-0.556830\pi\)
−0.177591 + 0.984104i \(0.556830\pi\)
\(90\) 15.6034 1.64475
\(91\) 1.35040 0.141560
\(92\) −26.6909 −2.78271
\(93\) 2.16305 0.224297
\(94\) −12.8866 −1.32916
\(95\) −5.50591 −0.564894
\(96\) −6.27204 −0.640137
\(97\) −9.76960 −0.991953 −0.495976 0.868336i \(-0.665190\pi\)
−0.495976 + 0.868336i \(0.665190\pi\)
\(98\) 11.5815 1.16991
\(99\) 1.26197 0.126832
\(100\) 17.4966 1.74966
\(101\) −15.0646 −1.49899 −0.749494 0.662012i \(-0.769703\pi\)
−0.749494 + 0.662012i \(0.769703\pi\)
\(102\) 11.1363 1.10266
\(103\) 6.28849 0.619623 0.309812 0.950798i \(-0.399734\pi\)
0.309812 + 0.950798i \(0.399734\pi\)
\(104\) −2.25019 −0.220650
\(105\) −4.16696 −0.406654
\(106\) −14.2980 −1.38874
\(107\) 7.91911 0.765569 0.382785 0.923838i \(-0.374965\pi\)
0.382785 + 0.923838i \(0.374965\pi\)
\(108\) 14.4361 1.38912
\(109\) −15.1891 −1.45485 −0.727427 0.686185i \(-0.759284\pi\)
−0.727427 + 0.686185i \(0.759284\pi\)
\(110\) 4.38093 0.417705
\(111\) 4.41585 0.419134
\(112\) −1.31935 −0.124667
\(113\) −9.19746 −0.865224 −0.432612 0.901580i \(-0.642408\pi\)
−0.432612 + 0.901580i \(0.642408\pi\)
\(114\) −3.51278 −0.329002
\(115\) −29.2110 −2.72394
\(116\) −4.62231 −0.429171
\(117\) −2.12007 −0.196001
\(118\) −5.21208 −0.479811
\(119\) 7.16547 0.656857
\(120\) 6.94349 0.633851
\(121\) −10.6457 −0.967789
\(122\) −1.66353 −0.150609
\(123\) 3.99834 0.360518
\(124\) −6.93097 −0.622419
\(125\) 2.70088 0.241574
\(126\) 6.40541 0.570639
\(127\) −3.83285 −0.340111 −0.170055 0.985435i \(-0.554395\pi\)
−0.170055 + 0.985435i \(0.554395\pi\)
\(128\) 15.7254 1.38995
\(129\) 2.54748 0.224293
\(130\) −7.35985 −0.645501
\(131\) −7.00487 −0.612018 −0.306009 0.952029i \(-0.598994\pi\)
−0.306009 + 0.952029i \(0.598994\pi\)
\(132\) 1.67831 0.146078
\(133\) −2.26025 −0.195988
\(134\) −11.1183 −0.960474
\(135\) 15.7992 1.35978
\(136\) −11.9400 −1.02384
\(137\) 3.84846 0.328796 0.164398 0.986394i \(-0.447432\pi\)
0.164398 + 0.986394i \(0.447432\pi\)
\(138\) −18.6367 −1.58646
\(139\) 15.6625 1.32848 0.664240 0.747520i \(-0.268755\pi\)
0.664240 + 0.747520i \(0.268755\pi\)
\(140\) 13.3520 1.12845
\(141\) −5.40292 −0.455008
\(142\) 1.56975 0.131731
\(143\) −0.595247 −0.0497770
\(144\) 2.07133 0.172611
\(145\) −5.05874 −0.420106
\(146\) −17.0921 −1.41455
\(147\) 4.85571 0.400493
\(148\) −14.1496 −1.16309
\(149\) −9.71773 −0.796107 −0.398054 0.917362i \(-0.630314\pi\)
−0.398054 + 0.917362i \(0.630314\pi\)
\(150\) 12.2168 0.997500
\(151\) 1.20241 0.0978505 0.0489252 0.998802i \(-0.484420\pi\)
0.0489252 + 0.998802i \(0.484420\pi\)
\(152\) 3.76629 0.305486
\(153\) −11.2495 −0.909470
\(154\) 1.79843 0.144921
\(155\) −7.58538 −0.609272
\(156\) −2.81952 −0.225742
\(157\) −4.20621 −0.335692 −0.167846 0.985813i \(-0.553681\pi\)
−0.167846 + 0.985813i \(0.553681\pi\)
\(158\) −7.64901 −0.608523
\(159\) −5.99464 −0.475406
\(160\) 21.9948 1.73884
\(161\) −11.9915 −0.945061
\(162\) −4.15014 −0.326066
\(163\) −4.84787 −0.379714 −0.189857 0.981812i \(-0.560803\pi\)
−0.189857 + 0.981812i \(0.560803\pi\)
\(164\) −12.8117 −1.00043
\(165\) 1.83677 0.142992
\(166\) −8.49627 −0.659439
\(167\) −19.0540 −1.47444 −0.737220 0.675653i \(-0.763862\pi\)
−0.737220 + 0.675653i \(0.763862\pi\)
\(168\) 2.85039 0.219912
\(169\) 1.00000 0.0769231
\(170\) −39.0528 −2.99521
\(171\) 3.54850 0.271361
\(172\) −8.16281 −0.622408
\(173\) −23.7562 −1.80615 −0.903074 0.429486i \(-0.858695\pi\)
−0.903074 + 0.429486i \(0.858695\pi\)
\(174\) −3.22749 −0.244676
\(175\) 7.86073 0.594216
\(176\) 0.581561 0.0438368
\(177\) −2.18524 −0.164253
\(178\) 7.49688 0.561915
\(179\) 14.7178 1.10006 0.550031 0.835144i \(-0.314616\pi\)
0.550031 + 0.835144i \(0.314616\pi\)
\(180\) −20.9622 −1.56243
\(181\) −12.3414 −0.917327 −0.458664 0.888610i \(-0.651672\pi\)
−0.458664 + 0.888610i \(0.651672\pi\)
\(182\) −3.02131 −0.223955
\(183\) −0.697462 −0.0515579
\(184\) 19.9816 1.47307
\(185\) −15.4855 −1.13852
\(186\) −4.83949 −0.354849
\(187\) −3.15849 −0.230972
\(188\) 17.3124 1.26264
\(189\) 6.48576 0.471770
\(190\) 12.3186 0.893688
\(191\) −21.5503 −1.55933 −0.779663 0.626199i \(-0.784610\pi\)
−0.779663 + 0.626199i \(0.784610\pi\)
\(192\) 12.1998 0.880445
\(193\) −20.6610 −1.48721 −0.743604 0.668620i \(-0.766885\pi\)
−0.743604 + 0.668620i \(0.766885\pi\)
\(194\) 21.8580 1.56931
\(195\) −3.08573 −0.220974
\(196\) −15.5590 −1.11136
\(197\) −18.6708 −1.33024 −0.665120 0.746737i \(-0.731620\pi\)
−0.665120 + 0.746737i \(0.731620\pi\)
\(198\) −2.82346 −0.200655
\(199\) 19.1014 1.35406 0.677030 0.735955i \(-0.263267\pi\)
0.677030 + 0.735955i \(0.263267\pi\)
\(200\) −13.0985 −0.926203
\(201\) −4.66152 −0.328798
\(202\) 33.7049 2.37147
\(203\) −2.07668 −0.145754
\(204\) −14.9609 −1.04747
\(205\) −14.0214 −0.979296
\(206\) −14.0696 −0.980272
\(207\) 18.8262 1.30851
\(208\) −0.977008 −0.0677433
\(209\) 0.996302 0.0689157
\(210\) 9.32296 0.643345
\(211\) 21.9462 1.51084 0.755418 0.655243i \(-0.227434\pi\)
0.755418 + 0.655243i \(0.227434\pi\)
\(212\) 19.2084 1.31924
\(213\) 0.658144 0.0450953
\(214\) −17.7178 −1.21117
\(215\) −8.93353 −0.609261
\(216\) −10.8073 −0.735347
\(217\) −3.11390 −0.211385
\(218\) 33.9834 2.30165
\(219\) −7.16611 −0.484241
\(220\) −5.88550 −0.396800
\(221\) 5.30619 0.356933
\(222\) −9.87981 −0.663090
\(223\) 20.6274 1.38131 0.690657 0.723182i \(-0.257321\pi\)
0.690657 + 0.723182i \(0.257321\pi\)
\(224\) 9.02916 0.603286
\(225\) −12.3411 −0.822737
\(226\) 20.5779 1.36882
\(227\) −8.61570 −0.571844 −0.285922 0.958253i \(-0.592300\pi\)
−0.285922 + 0.958253i \(0.592300\pi\)
\(228\) 4.71920 0.312537
\(229\) −13.0813 −0.864435 −0.432217 0.901769i \(-0.642269\pi\)
−0.432217 + 0.901769i \(0.642269\pi\)
\(230\) 65.3552 4.30939
\(231\) 0.754018 0.0496108
\(232\) 3.46041 0.227187
\(233\) 16.6865 1.09317 0.546585 0.837403i \(-0.315927\pi\)
0.546585 + 0.837403i \(0.315927\pi\)
\(234\) 4.74335 0.310082
\(235\) 18.9470 1.23597
\(236\) 7.00210 0.455798
\(237\) −3.20697 −0.208315
\(238\) −16.0317 −1.03918
\(239\) 5.04296 0.326202 0.163101 0.986609i \(-0.447850\pi\)
0.163101 + 0.986609i \(0.447850\pi\)
\(240\) 3.01478 0.194603
\(241\) −21.5179 −1.38609 −0.693043 0.720896i \(-0.743731\pi\)
−0.693043 + 0.720896i \(0.743731\pi\)
\(242\) 23.8181 1.53109
\(243\) −16.1486 −1.03593
\(244\) 2.23485 0.143072
\(245\) −17.0280 −1.08788
\(246\) −8.94569 −0.570356
\(247\) −1.67376 −0.106499
\(248\) 5.18874 0.329486
\(249\) −3.56219 −0.225745
\(250\) −6.04281 −0.382181
\(251\) 4.45999 0.281512 0.140756 0.990044i \(-0.455047\pi\)
0.140756 + 0.990044i \(0.455047\pi\)
\(252\) −8.60526 −0.542080
\(253\) 5.28577 0.332314
\(254\) 8.57544 0.538071
\(255\) −16.3735 −1.02535
\(256\) −9.17219 −0.573262
\(257\) 17.6052 1.09818 0.549090 0.835763i \(-0.314974\pi\)
0.549090 + 0.835763i \(0.314974\pi\)
\(258\) −5.69961 −0.354842
\(259\) −6.35701 −0.395006
\(260\) 9.88749 0.613196
\(261\) 3.26031 0.201808
\(262\) 15.6724 0.968241
\(263\) 14.8660 0.916674 0.458337 0.888779i \(-0.348445\pi\)
0.458337 + 0.888779i \(0.348445\pi\)
\(264\) −1.25643 −0.0773282
\(265\) 21.0220 1.29137
\(266\) 5.05696 0.310062
\(267\) 3.14318 0.192360
\(268\) 14.9367 0.912406
\(269\) 19.2844 1.17579 0.587895 0.808937i \(-0.299957\pi\)
0.587895 + 0.808937i \(0.299957\pi\)
\(270\) −35.3483 −2.15123
\(271\) −0.735617 −0.0446856 −0.0223428 0.999750i \(-0.507113\pi\)
−0.0223428 + 0.999750i \(0.507113\pi\)
\(272\) −5.18419 −0.314338
\(273\) −1.26673 −0.0766661
\(274\) −8.61036 −0.520171
\(275\) −3.46496 −0.208945
\(276\) 25.0372 1.50706
\(277\) 6.74014 0.404975 0.202488 0.979285i \(-0.435097\pi\)
0.202488 + 0.979285i \(0.435097\pi\)
\(278\) −35.0426 −2.10172
\(279\) 4.88870 0.292679
\(280\) −9.99577 −0.597361
\(281\) −0.568633 −0.0339218 −0.0169609 0.999856i \(-0.505399\pi\)
−0.0169609 + 0.999856i \(0.505399\pi\)
\(282\) 12.0882 0.719844
\(283\) −12.3845 −0.736180 −0.368090 0.929790i \(-0.619988\pi\)
−0.368090 + 0.929790i \(0.619988\pi\)
\(284\) −2.10887 −0.125138
\(285\) 5.16478 0.305935
\(286\) 1.33178 0.0787496
\(287\) −5.75596 −0.339764
\(288\) −14.1754 −0.835296
\(289\) 11.1557 0.656216
\(290\) 11.3182 0.664627
\(291\) 9.16431 0.537221
\(292\) 22.9621 1.34376
\(293\) −14.4702 −0.845358 −0.422679 0.906280i \(-0.638910\pi\)
−0.422679 + 0.906280i \(0.638910\pi\)
\(294\) −10.8639 −0.633598
\(295\) 7.66323 0.446170
\(296\) 10.5928 0.615695
\(297\) −2.85888 −0.165889
\(298\) 21.7420 1.25948
\(299\) −8.87996 −0.513542
\(300\) −16.4125 −0.947579
\(301\) −3.66733 −0.211381
\(302\) −2.69021 −0.154804
\(303\) 14.1313 0.811821
\(304\) 1.63528 0.0937898
\(305\) 2.44586 0.140050
\(306\) 25.1691 1.43882
\(307\) 27.1793 1.55120 0.775601 0.631223i \(-0.217447\pi\)
0.775601 + 0.631223i \(0.217447\pi\)
\(308\) −2.41607 −0.137669
\(309\) −5.89888 −0.335575
\(310\) 16.9712 0.963897
\(311\) −19.2253 −1.09017 −0.545083 0.838382i \(-0.683502\pi\)
−0.545083 + 0.838382i \(0.683502\pi\)
\(312\) 2.11078 0.119499
\(313\) −27.4501 −1.55157 −0.775784 0.630998i \(-0.782646\pi\)
−0.775784 + 0.630998i \(0.782646\pi\)
\(314\) 9.41077 0.531081
\(315\) −9.41775 −0.530630
\(316\) 10.2760 0.578068
\(317\) −4.04735 −0.227322 −0.113661 0.993520i \(-0.536258\pi\)
−0.113661 + 0.993520i \(0.536258\pi\)
\(318\) 13.4121 0.752114
\(319\) 0.915388 0.0512519
\(320\) −42.7823 −2.39160
\(321\) −7.42847 −0.414617
\(322\) 26.8292 1.49513
\(323\) −8.88131 −0.494169
\(324\) 5.57545 0.309747
\(325\) 5.82105 0.322894
\(326\) 10.8464 0.600726
\(327\) 14.2481 0.787919
\(328\) 9.59127 0.529589
\(329\) 7.77799 0.428814
\(330\) −4.10950 −0.226221
\(331\) −6.23182 −0.342532 −0.171266 0.985225i \(-0.554786\pi\)
−0.171266 + 0.985225i \(0.554786\pi\)
\(332\) 11.4142 0.626436
\(333\) 9.98027 0.546916
\(334\) 42.6304 2.33263
\(335\) 16.3470 0.893133
\(336\) 1.23761 0.0675170
\(337\) −10.6648 −0.580951 −0.290475 0.956883i \(-0.593813\pi\)
−0.290475 + 0.956883i \(0.593813\pi\)
\(338\) −2.23735 −0.121696
\(339\) 8.62762 0.468588
\(340\) 52.4649 2.84531
\(341\) 1.37259 0.0743297
\(342\) −7.93924 −0.429305
\(343\) −16.4430 −0.887839
\(344\) 6.11094 0.329480
\(345\) 27.4012 1.47523
\(346\) 53.1509 2.85741
\(347\) −24.5443 −1.31761 −0.658803 0.752316i \(-0.728937\pi\)
−0.658803 + 0.752316i \(0.728937\pi\)
\(348\) 4.33593 0.232430
\(349\) −8.65982 −0.463549 −0.231775 0.972770i \(-0.574453\pi\)
−0.231775 + 0.972770i \(0.574453\pi\)
\(350\) −17.5872 −0.940076
\(351\) 4.80285 0.256357
\(352\) −3.98000 −0.212135
\(353\) 8.89387 0.473373 0.236687 0.971586i \(-0.423939\pi\)
0.236687 + 0.971586i \(0.423939\pi\)
\(354\) 4.88916 0.259856
\(355\) −2.30798 −0.122495
\(356\) −10.0716 −0.533793
\(357\) −6.72152 −0.355741
\(358\) −32.9289 −1.74035
\(359\) −32.7781 −1.72996 −0.864981 0.501804i \(-0.832670\pi\)
−0.864981 + 0.501804i \(0.832670\pi\)
\(360\) 15.6930 0.827093
\(361\) −16.1985 −0.852554
\(362\) 27.6120 1.45125
\(363\) 9.98612 0.524135
\(364\) 4.05894 0.212746
\(365\) 25.1301 1.31537
\(366\) 1.56047 0.0815669
\(367\) 16.6653 0.869921 0.434960 0.900450i \(-0.356762\pi\)
0.434960 + 0.900450i \(0.356762\pi\)
\(368\) 8.67580 0.452257
\(369\) 9.03665 0.470429
\(370\) 34.6466 1.80119
\(371\) 8.62982 0.448038
\(372\) 6.50155 0.337090
\(373\) 10.8470 0.561636 0.280818 0.959761i \(-0.409394\pi\)
0.280818 + 0.959761i \(0.409394\pi\)
\(374\) 7.06666 0.365408
\(375\) −2.53354 −0.130831
\(376\) −12.9606 −0.668392
\(377\) −1.53783 −0.0792022
\(378\) −14.5109 −0.746362
\(379\) −31.8530 −1.63618 −0.818090 0.575090i \(-0.804967\pi\)
−0.818090 + 0.575090i \(0.804967\pi\)
\(380\) −16.5493 −0.848962
\(381\) 3.59538 0.184197
\(382\) 48.2156 2.46693
\(383\) 7.71012 0.393969 0.196984 0.980407i \(-0.436885\pi\)
0.196984 + 0.980407i \(0.436885\pi\)
\(384\) −14.7512 −0.752767
\(385\) −2.64420 −0.134761
\(386\) 46.2258 2.35283
\(387\) 5.75757 0.292674
\(388\) −29.3649 −1.49078
\(389\) 32.9206 1.66914 0.834571 0.550900i \(-0.185715\pi\)
0.834571 + 0.550900i \(0.185715\pi\)
\(390\) 6.90386 0.349591
\(391\) −47.1188 −2.38290
\(392\) 11.6480 0.588311
\(393\) 6.57088 0.331457
\(394\) 41.7731 2.10450
\(395\) 11.2462 0.565858
\(396\) 3.79315 0.190613
\(397\) 20.9505 1.05147 0.525737 0.850647i \(-0.323790\pi\)
0.525737 + 0.850647i \(0.323790\pi\)
\(398\) −42.7365 −2.14219
\(399\) 2.12021 0.106143
\(400\) −5.68721 −0.284361
\(401\) 12.4828 0.623360 0.311680 0.950187i \(-0.399108\pi\)
0.311680 + 0.950187i \(0.399108\pi\)
\(402\) 10.4294 0.520173
\(403\) −2.30591 −0.114866
\(404\) −45.2804 −2.25278
\(405\) 6.10187 0.303205
\(406\) 4.64626 0.230590
\(407\) 2.80213 0.138897
\(408\) 11.2002 0.554492
\(409\) 14.5083 0.717391 0.358696 0.933455i \(-0.383222\pi\)
0.358696 + 0.933455i \(0.383222\pi\)
\(410\) 31.3708 1.54929
\(411\) −3.61003 −0.178069
\(412\) 18.9016 0.931213
\(413\) 3.14585 0.154797
\(414\) −42.1208 −2.07012
\(415\) 12.4919 0.613204
\(416\) 6.68630 0.327823
\(417\) −14.6921 −0.719477
\(418\) −2.22908 −0.109028
\(419\) 21.9543 1.07254 0.536269 0.844047i \(-0.319833\pi\)
0.536269 + 0.844047i \(0.319833\pi\)
\(420\) −12.5248 −0.611148
\(421\) 12.8925 0.628344 0.314172 0.949366i \(-0.398273\pi\)
0.314172 + 0.949366i \(0.398273\pi\)
\(422\) −49.1013 −2.39021
\(423\) −12.2112 −0.593726
\(424\) −14.3800 −0.698356
\(425\) 30.8876 1.49827
\(426\) −1.47250 −0.0713428
\(427\) 1.00406 0.0485898
\(428\) 23.8028 1.15055
\(429\) 0.558368 0.0269582
\(430\) 19.9874 0.963880
\(431\) 11.2294 0.540901 0.270450 0.962734i \(-0.412827\pi\)
0.270450 + 0.962734i \(0.412827\pi\)
\(432\) −4.69243 −0.225764
\(433\) 9.86622 0.474140 0.237070 0.971493i \(-0.423813\pi\)
0.237070 + 0.971493i \(0.423813\pi\)
\(434\) 6.96688 0.334421
\(435\) 4.74532 0.227521
\(436\) −45.6545 −2.18646
\(437\) 14.8630 0.710992
\(438\) 16.0331 0.766091
\(439\) 16.1928 0.772839 0.386419 0.922323i \(-0.373712\pi\)
0.386419 + 0.922323i \(0.373712\pi\)
\(440\) 4.40607 0.210051
\(441\) 10.9744 0.522591
\(442\) −11.8718 −0.564685
\(443\) 8.90015 0.422859 0.211429 0.977393i \(-0.432188\pi\)
0.211429 + 0.977393i \(0.432188\pi\)
\(444\) 13.2729 0.629904
\(445\) −11.0225 −0.522518
\(446\) −46.1508 −2.18530
\(447\) 9.11566 0.431156
\(448\) −17.5627 −0.829759
\(449\) −22.0449 −1.04036 −0.520181 0.854056i \(-0.674136\pi\)
−0.520181 + 0.854056i \(0.674136\pi\)
\(450\) 27.6113 1.30161
\(451\) 2.53719 0.119472
\(452\) −27.6452 −1.30032
\(453\) −1.12791 −0.0529939
\(454\) 19.2763 0.904683
\(455\) 4.44218 0.208253
\(456\) −3.53294 −0.165445
\(457\) −13.6202 −0.637126 −0.318563 0.947902i \(-0.603200\pi\)
−0.318563 + 0.947902i \(0.603200\pi\)
\(458\) 29.2674 1.36758
\(459\) 25.4849 1.18953
\(460\) −87.8006 −4.09372
\(461\) −3.62235 −0.168710 −0.0843549 0.996436i \(-0.526883\pi\)
−0.0843549 + 0.996436i \(0.526883\pi\)
\(462\) −1.68700 −0.0784865
\(463\) 3.56388 0.165627 0.0828137 0.996565i \(-0.473609\pi\)
0.0828137 + 0.996565i \(0.473609\pi\)
\(464\) 1.50247 0.0697505
\(465\) 7.11542 0.329970
\(466\) −37.3336 −1.72945
\(467\) 19.6261 0.908186 0.454093 0.890954i \(-0.349963\pi\)
0.454093 + 0.890954i \(0.349963\pi\)
\(468\) −6.37239 −0.294564
\(469\) 6.71067 0.309870
\(470\) −42.3911 −1.95535
\(471\) 3.94561 0.181804
\(472\) −5.24200 −0.241282
\(473\) 1.61654 0.0743284
\(474\) 7.17511 0.329564
\(475\) −9.74306 −0.447042
\(476\) 21.5375 0.987171
\(477\) −13.5485 −0.620343
\(478\) −11.2829 −0.516067
\(479\) 40.7996 1.86418 0.932091 0.362224i \(-0.117983\pi\)
0.932091 + 0.362224i \(0.117983\pi\)
\(480\) −20.6321 −0.941722
\(481\) −4.70751 −0.214644
\(482\) 48.1430 2.19285
\(483\) 11.2485 0.511826
\(484\) −31.9981 −1.45446
\(485\) −32.1375 −1.45929
\(486\) 36.1300 1.63889
\(487\) 20.2029 0.915482 0.457741 0.889086i \(-0.348659\pi\)
0.457741 + 0.889086i \(0.348659\pi\)
\(488\) −1.67308 −0.0757369
\(489\) 4.54751 0.205646
\(490\) 38.0977 1.72108
\(491\) 5.75387 0.259668 0.129834 0.991536i \(-0.458555\pi\)
0.129834 + 0.991536i \(0.458555\pi\)
\(492\) 12.0180 0.541812
\(493\) −8.16001 −0.367509
\(494\) 3.74480 0.168486
\(495\) 4.15129 0.186586
\(496\) 2.25289 0.101158
\(497\) −0.947457 −0.0424992
\(498\) 7.96988 0.357139
\(499\) −12.4284 −0.556371 −0.278185 0.960527i \(-0.589733\pi\)
−0.278185 + 0.960527i \(0.589733\pi\)
\(500\) 8.11813 0.363054
\(501\) 17.8735 0.798527
\(502\) −9.97855 −0.445365
\(503\) −15.5509 −0.693378 −0.346689 0.937980i \(-0.612694\pi\)
−0.346689 + 0.937980i \(0.612694\pi\)
\(504\) 6.44217 0.286957
\(505\) −49.5557 −2.20520
\(506\) −11.8261 −0.525735
\(507\) −0.938044 −0.0416600
\(508\) −11.5206 −0.511142
\(509\) −22.7199 −1.00704 −0.503521 0.863983i \(-0.667962\pi\)
−0.503521 + 0.863983i \(0.667962\pi\)
\(510\) 36.6332 1.62215
\(511\) 10.3163 0.456364
\(512\) −10.9295 −0.483019
\(513\) −8.03884 −0.354923
\(514\) −39.3890 −1.73737
\(515\) 20.6862 0.911543
\(516\) 7.65707 0.337084
\(517\) −3.42849 −0.150785
\(518\) 14.2229 0.624917
\(519\) 22.2843 0.978173
\(520\) −7.40209 −0.324603
\(521\) −28.6442 −1.25492 −0.627462 0.778647i \(-0.715906\pi\)
−0.627462 + 0.778647i \(0.715906\pi\)
\(522\) −7.29446 −0.319270
\(523\) −41.2631 −1.80431 −0.902154 0.431413i \(-0.858015\pi\)
−0.902154 + 0.431413i \(0.858015\pi\)
\(524\) −21.0548 −0.919784
\(525\) −7.37371 −0.321815
\(526\) −33.2604 −1.45022
\(527\) −12.2356 −0.532991
\(528\) −0.545530 −0.0237411
\(529\) 55.8538 2.42842
\(530\) −47.0337 −2.04301
\(531\) −4.93887 −0.214329
\(532\) −6.79371 −0.294545
\(533\) −4.26242 −0.184626
\(534\) −7.03240 −0.304322
\(535\) 26.0502 1.12625
\(536\) −11.1821 −0.482994
\(537\) −13.8060 −0.595771
\(538\) −43.1459 −1.86015
\(539\) 3.08125 0.132719
\(540\) 47.4882 2.04357
\(541\) 16.6868 0.717420 0.358710 0.933449i \(-0.383217\pi\)
0.358710 + 0.933449i \(0.383217\pi\)
\(542\) 1.64583 0.0706946
\(543\) 11.5768 0.496806
\(544\) 35.4788 1.52114
\(545\) −49.9652 −2.14027
\(546\) 2.83412 0.121289
\(547\) −32.6697 −1.39685 −0.698427 0.715681i \(-0.746117\pi\)
−0.698427 + 0.715681i \(0.746117\pi\)
\(548\) 11.5675 0.494138
\(549\) −1.57633 −0.0672763
\(550\) 7.75234 0.330561
\(551\) 2.57396 0.109654
\(552\) −18.7436 −0.797783
\(553\) 4.61671 0.196323
\(554\) −15.0800 −0.640690
\(555\) 14.5261 0.616599
\(556\) 47.0775 1.99653
\(557\) −37.5986 −1.59310 −0.796552 0.604570i \(-0.793345\pi\)
−0.796552 + 0.604570i \(0.793345\pi\)
\(558\) −10.9377 −0.463031
\(559\) −2.71574 −0.114864
\(560\) −4.34005 −0.183401
\(561\) 2.96281 0.125090
\(562\) 1.27223 0.0536658
\(563\) −25.7144 −1.08373 −0.541867 0.840465i \(-0.682282\pi\)
−0.541867 + 0.840465i \(0.682282\pi\)
\(564\) −16.2398 −0.683818
\(565\) −30.2554 −1.27285
\(566\) 27.7084 1.16467
\(567\) 2.50490 0.105196
\(568\) 1.57876 0.0662435
\(569\) −5.38096 −0.225582 −0.112791 0.993619i \(-0.535979\pi\)
−0.112791 + 0.993619i \(0.535979\pi\)
\(570\) −11.5554 −0.484004
\(571\) 29.3783 1.22945 0.614723 0.788743i \(-0.289268\pi\)
0.614723 + 0.788743i \(0.289268\pi\)
\(572\) −1.78916 −0.0748084
\(573\) 20.2151 0.844500
\(574\) 12.8781 0.537522
\(575\) −51.6907 −2.15565
\(576\) 27.5728 1.14887
\(577\) 13.2299 0.550770 0.275385 0.961334i \(-0.411195\pi\)
0.275385 + 0.961334i \(0.411195\pi\)
\(578\) −24.9591 −1.03816
\(579\) 19.3809 0.805442
\(580\) −15.2053 −0.631364
\(581\) 5.12809 0.212749
\(582\) −20.5038 −0.849909
\(583\) −3.80397 −0.157544
\(584\) −17.1902 −0.711334
\(585\) −6.97406 −0.288342
\(586\) 32.3749 1.33739
\(587\) −36.9201 −1.52385 −0.761927 0.647663i \(-0.775747\pi\)
−0.761927 + 0.647663i \(0.775747\pi\)
\(588\) 14.5950 0.601888
\(589\) 3.85955 0.159030
\(590\) −17.1453 −0.705862
\(591\) 17.5140 0.720431
\(592\) 4.59928 0.189029
\(593\) −26.5640 −1.09085 −0.545427 0.838159i \(-0.683632\pi\)
−0.545427 + 0.838159i \(0.683632\pi\)
\(594\) 6.39633 0.262444
\(595\) 23.5711 0.966320
\(596\) −29.2090 −1.19645
\(597\) −17.9179 −0.733332
\(598\) 19.8676 0.812447
\(599\) −30.4030 −1.24223 −0.621115 0.783719i \(-0.713320\pi\)
−0.621115 + 0.783719i \(0.713320\pi\)
\(600\) 12.2870 0.501613
\(601\) 8.78391 0.358303 0.179152 0.983821i \(-0.442665\pi\)
0.179152 + 0.983821i \(0.442665\pi\)
\(602\) 8.20510 0.334415
\(603\) −10.5355 −0.429039
\(604\) 3.61412 0.147057
\(605\) −35.0194 −1.42374
\(606\) −31.6166 −1.28434
\(607\) 5.39318 0.218902 0.109451 0.993992i \(-0.465091\pi\)
0.109451 + 0.993992i \(0.465091\pi\)
\(608\) −11.1913 −0.453866
\(609\) 1.94802 0.0789376
\(610\) −5.47225 −0.221565
\(611\) 5.75978 0.233016
\(612\) −33.8131 −1.36681
\(613\) 13.8341 0.558755 0.279378 0.960181i \(-0.409872\pi\)
0.279378 + 0.960181i \(0.409872\pi\)
\(614\) −60.8095 −2.45407
\(615\) 13.1527 0.530367
\(616\) 1.80875 0.0728766
\(617\) −9.71227 −0.391001 −0.195501 0.980704i \(-0.562633\pi\)
−0.195501 + 0.980704i \(0.562633\pi\)
\(618\) 13.1979 0.530896
\(619\) 1.00000 0.0401934
\(620\) −22.7997 −0.915657
\(621\) −42.6492 −1.71145
\(622\) 43.0138 1.72469
\(623\) −4.52489 −0.181286
\(624\) 0.916476 0.0366884
\(625\) −20.2206 −0.808825
\(626\) 61.4154 2.45465
\(627\) −0.934575 −0.0373233
\(628\) −12.6428 −0.504502
\(629\) −24.9790 −0.995976
\(630\) 21.0708 0.839482
\(631\) 38.4510 1.53071 0.765354 0.643609i \(-0.222564\pi\)
0.765354 + 0.643609i \(0.222564\pi\)
\(632\) −7.69292 −0.306008
\(633\) −20.5865 −0.818238
\(634\) 9.05533 0.359633
\(635\) −12.6083 −0.500346
\(636\) −18.0183 −0.714473
\(637\) −5.17643 −0.205097
\(638\) −2.04804 −0.0810828
\(639\) 1.48747 0.0588435
\(640\) 51.7294 2.04479
\(641\) −14.3631 −0.567306 −0.283653 0.958927i \(-0.591546\pi\)
−0.283653 + 0.958927i \(0.591546\pi\)
\(642\) 16.6201 0.655943
\(643\) −34.6299 −1.36567 −0.682835 0.730573i \(-0.739253\pi\)
−0.682835 + 0.730573i \(0.739253\pi\)
\(644\) −36.0433 −1.42030
\(645\) 8.38004 0.329964
\(646\) 19.8706 0.781798
\(647\) −17.7831 −0.699127 −0.349563 0.936913i \(-0.613670\pi\)
−0.349563 + 0.936913i \(0.613670\pi\)
\(648\) −4.17396 −0.163969
\(649\) −1.38667 −0.0544317
\(650\) −13.0237 −0.510833
\(651\) 2.92097 0.114482
\(652\) −14.5714 −0.570661
\(653\) 3.40673 0.133315 0.0666577 0.997776i \(-0.478766\pi\)
0.0666577 + 0.997776i \(0.478766\pi\)
\(654\) −31.8779 −1.24652
\(655\) −23.0428 −0.900356
\(656\) 4.16442 0.162593
\(657\) −16.1961 −0.631871
\(658\) −17.4021 −0.678404
\(659\) −30.1384 −1.17403 −0.587013 0.809577i \(-0.699696\pi\)
−0.587013 + 0.809577i \(0.699696\pi\)
\(660\) 5.52085 0.214899
\(661\) 43.3354 1.68555 0.842775 0.538266i \(-0.180920\pi\)
0.842775 + 0.538266i \(0.180920\pi\)
\(662\) 13.9428 0.541901
\(663\) −4.97744 −0.193308
\(664\) −8.54504 −0.331612
\(665\) −7.43516 −0.288323
\(666\) −22.3294 −0.865246
\(667\) 13.6559 0.528757
\(668\) −57.2713 −2.21589
\(669\) −19.3494 −0.748092
\(670\) −36.5740 −1.41298
\(671\) −0.442583 −0.0170857
\(672\) −8.46975 −0.326728
\(673\) 27.0013 1.04082 0.520412 0.853915i \(-0.325778\pi\)
0.520412 + 0.853915i \(0.325778\pi\)
\(674\) 23.8610 0.919091
\(675\) 27.9577 1.07609
\(676\) 3.00574 0.115605
\(677\) 25.6036 0.984027 0.492013 0.870588i \(-0.336261\pi\)
0.492013 + 0.870588i \(0.336261\pi\)
\(678\) −19.3030 −0.741328
\(679\) −13.1928 −0.506295
\(680\) −39.2769 −1.50620
\(681\) 8.08190 0.309699
\(682\) −3.07096 −0.117593
\(683\) 11.1505 0.426662 0.213331 0.976980i \(-0.431569\pi\)
0.213331 + 0.976980i \(0.431569\pi\)
\(684\) 10.6659 0.407820
\(685\) 12.6597 0.483701
\(686\) 36.7888 1.40460
\(687\) 12.2708 0.468160
\(688\) 2.65330 0.101156
\(689\) 6.39058 0.243462
\(690\) −61.3060 −2.33388
\(691\) −12.2393 −0.465606 −0.232803 0.972524i \(-0.574790\pi\)
−0.232803 + 0.972524i \(0.574790\pi\)
\(692\) −71.4048 −2.71440
\(693\) 1.70416 0.0647356
\(694\) 54.9141 2.08451
\(695\) 51.5225 1.95436
\(696\) −3.24602 −0.123040
\(697\) −22.6172 −0.856688
\(698\) 19.3750 0.733356
\(699\) −15.6527 −0.592039
\(700\) 23.6273 0.893029
\(701\) −29.5498 −1.11608 −0.558041 0.829814i \(-0.688447\pi\)
−0.558041 + 0.829814i \(0.688447\pi\)
\(702\) −10.7457 −0.405569
\(703\) 7.87926 0.297172
\(704\) 7.74153 0.291770
\(705\) −17.7731 −0.669374
\(706\) −19.8987 −0.748898
\(707\) −20.3432 −0.765087
\(708\) −6.56828 −0.246851
\(709\) −20.9036 −0.785052 −0.392526 0.919741i \(-0.628399\pi\)
−0.392526 + 0.919741i \(0.628399\pi\)
\(710\) 5.16377 0.193793
\(711\) −7.24807 −0.271824
\(712\) 7.53991 0.282570
\(713\) 20.4764 0.766847
\(714\) 15.0384 0.562798
\(715\) −1.95809 −0.0732283
\(716\) 44.2379 1.65325
\(717\) −4.73052 −0.176664
\(718\) 73.3361 2.73688
\(719\) −29.7210 −1.10841 −0.554203 0.832381i \(-0.686977\pi\)
−0.554203 + 0.832381i \(0.686977\pi\)
\(720\) 6.81371 0.253932
\(721\) 8.49196 0.316257
\(722\) 36.2418 1.34878
\(723\) 20.1847 0.750677
\(724\) −37.0950 −1.37862
\(725\) −8.95178 −0.332461
\(726\) −22.3424 −0.829206
\(727\) 33.5118 1.24288 0.621442 0.783460i \(-0.286547\pi\)
0.621442 + 0.783460i \(0.286547\pi\)
\(728\) −3.03866 −0.112620
\(729\) 9.58326 0.354936
\(730\) −56.2250 −2.08098
\(731\) −14.4102 −0.532982
\(732\) −2.09639 −0.0774848
\(733\) −25.4936 −0.941626 −0.470813 0.882233i \(-0.656039\pi\)
−0.470813 + 0.882233i \(0.656039\pi\)
\(734\) −37.2861 −1.37625
\(735\) 15.9731 0.589175
\(736\) −59.3741 −2.18856
\(737\) −2.95802 −0.108960
\(738\) −20.2182 −0.744241
\(739\) −10.7694 −0.396160 −0.198080 0.980186i \(-0.563471\pi\)
−0.198080 + 0.980186i \(0.563471\pi\)
\(740\) −46.5455 −1.71105
\(741\) 1.57006 0.0576777
\(742\) −19.3079 −0.708817
\(743\) −5.60021 −0.205452 −0.102726 0.994710i \(-0.532756\pi\)
−0.102726 + 0.994710i \(0.532756\pi\)
\(744\) −4.86727 −0.178443
\(745\) −31.9668 −1.17117
\(746\) −24.2685 −0.888534
\(747\) −8.05092 −0.294568
\(748\) −9.49361 −0.347121
\(749\) 10.6939 0.390748
\(750\) 5.66842 0.206981
\(751\) −25.8931 −0.944851 −0.472426 0.881370i \(-0.656622\pi\)
−0.472426 + 0.881370i \(0.656622\pi\)
\(752\) −5.62735 −0.205208
\(753\) −4.18366 −0.152461
\(754\) 3.44066 0.125302
\(755\) 3.95536 0.143950
\(756\) 19.4945 0.709009
\(757\) −43.2747 −1.57284 −0.786422 0.617689i \(-0.788069\pi\)
−0.786422 + 0.617689i \(0.788069\pi\)
\(758\) 71.2664 2.58851
\(759\) −4.95828 −0.179974
\(760\) 12.3893 0.449409
\(761\) −1.11120 −0.0402811 −0.0201405 0.999797i \(-0.506411\pi\)
−0.0201405 + 0.999797i \(0.506411\pi\)
\(762\) −8.04414 −0.291408
\(763\) −20.5114 −0.742561
\(764\) −64.7747 −2.34346
\(765\) −37.0057 −1.33794
\(766\) −17.2502 −0.623277
\(767\) 2.32958 0.0841161
\(768\) 8.60392 0.310467
\(769\) 43.0096 1.55096 0.775482 0.631369i \(-0.217507\pi\)
0.775482 + 0.631369i \(0.217507\pi\)
\(770\) 5.91599 0.213198
\(771\) −16.5144 −0.594753
\(772\) −62.1015 −2.23508
\(773\) 2.04564 0.0735767 0.0367884 0.999323i \(-0.488287\pi\)
0.0367884 + 0.999323i \(0.488287\pi\)
\(774\) −12.8817 −0.463023
\(775\) −13.4228 −0.482162
\(776\) 21.9835 0.789161
\(777\) 5.96316 0.213927
\(778\) −73.6550 −2.64066
\(779\) 7.13428 0.255612
\(780\) −9.27490 −0.332095
\(781\) 0.417633 0.0149441
\(782\) 105.421 3.76986
\(783\) −7.38597 −0.263953
\(784\) 5.05741 0.180622
\(785\) −13.8365 −0.493846
\(786\) −14.7014 −0.524380
\(787\) −26.9848 −0.961906 −0.480953 0.876746i \(-0.659709\pi\)
−0.480953 + 0.876746i \(0.659709\pi\)
\(788\) −56.1196 −1.99918
\(789\) −13.9449 −0.496452
\(790\) −25.1617 −0.895214
\(791\) −12.4202 −0.441613
\(792\) −2.83967 −0.100903
\(793\) 0.743528 0.0264035
\(794\) −46.8736 −1.66348
\(795\) −19.7196 −0.699382
\(796\) 57.4137 2.03498
\(797\) −14.5305 −0.514698 −0.257349 0.966318i \(-0.582849\pi\)
−0.257349 + 0.966318i \(0.582849\pi\)
\(798\) −4.74365 −0.167924
\(799\) 30.5625 1.08122
\(800\) 38.9213 1.37607
\(801\) 7.10391 0.251004
\(802\) −27.9283 −0.986183
\(803\) −4.54734 −0.160472
\(804\) −14.0113 −0.494140
\(805\) −39.4464 −1.39030
\(806\) 5.15913 0.181723
\(807\) −18.0896 −0.636784
\(808\) 33.8983 1.19254
\(809\) −40.5481 −1.42560 −0.712798 0.701369i \(-0.752572\pi\)
−0.712798 + 0.701369i \(0.752572\pi\)
\(810\) −13.6520 −0.479684
\(811\) 22.3376 0.784380 0.392190 0.919884i \(-0.371718\pi\)
0.392190 + 0.919884i \(0.371718\pi\)
\(812\) −6.24196 −0.219050
\(813\) 0.690041 0.0242008
\(814\) −6.26935 −0.219741
\(815\) −15.9472 −0.558608
\(816\) 4.86300 0.170239
\(817\) 4.54551 0.159027
\(818\) −32.4602 −1.13495
\(819\) −2.86294 −0.100039
\(820\) −42.1447 −1.47176
\(821\) 25.1200 0.876693 0.438346 0.898806i \(-0.355564\pi\)
0.438346 + 0.898806i \(0.355564\pi\)
\(822\) 8.07689 0.281714
\(823\) −29.9364 −1.04352 −0.521759 0.853093i \(-0.674724\pi\)
−0.521759 + 0.853093i \(0.674724\pi\)
\(824\) −14.1503 −0.492949
\(825\) 3.25029 0.113160
\(826\) −7.03838 −0.244897
\(827\) −18.6835 −0.649689 −0.324845 0.945767i \(-0.605312\pi\)
−0.324845 + 0.945767i \(0.605312\pi\)
\(828\) 56.5866 1.96652
\(829\) 14.1711 0.492184 0.246092 0.969246i \(-0.420853\pi\)
0.246092 + 0.969246i \(0.420853\pi\)
\(830\) −27.9488 −0.970117
\(831\) −6.32254 −0.219327
\(832\) −13.0056 −0.450887
\(833\) −27.4671 −0.951679
\(834\) 32.8715 1.13825
\(835\) −62.6787 −2.16909
\(836\) 2.99463 0.103571
\(837\) −11.0750 −0.382806
\(838\) −49.1195 −1.69680
\(839\) 19.5107 0.673584 0.336792 0.941579i \(-0.390658\pi\)
0.336792 + 0.941579i \(0.390658\pi\)
\(840\) 9.37647 0.323519
\(841\) −26.6351 −0.918451
\(842\) −28.8451 −0.994069
\(843\) 0.533403 0.0183714
\(844\) 65.9644 2.27059
\(845\) 3.28954 0.113163
\(846\) 27.3206 0.939303
\(847\) −14.3759 −0.493962
\(848\) −6.24365 −0.214408
\(849\) 11.6172 0.398700
\(850\) −69.1064 −2.37033
\(851\) 41.8025 1.43297
\(852\) 1.97821 0.0677723
\(853\) 21.8949 0.749668 0.374834 0.927092i \(-0.377700\pi\)
0.374834 + 0.927092i \(0.377700\pi\)
\(854\) −2.24643 −0.0768713
\(855\) 11.6729 0.399206
\(856\) −17.8195 −0.609059
\(857\) −19.0692 −0.651393 −0.325696 0.945474i \(-0.605599\pi\)
−0.325696 + 0.945474i \(0.605599\pi\)
\(858\) −1.24926 −0.0426492
\(859\) 55.5376 1.89492 0.947459 0.319878i \(-0.103642\pi\)
0.947459 + 0.319878i \(0.103642\pi\)
\(860\) −26.8519 −0.915641
\(861\) 5.39935 0.184009
\(862\) −25.1241 −0.855730
\(863\) −6.96072 −0.236946 −0.118473 0.992957i \(-0.537800\pi\)
−0.118473 + 0.992957i \(0.537800\pi\)
\(864\) 32.1133 1.09252
\(865\) −78.1467 −2.65707
\(866\) −22.0742 −0.750111
\(867\) −10.4645 −0.355393
\(868\) −9.35956 −0.317684
\(869\) −2.03502 −0.0690333
\(870\) −10.6170 −0.359948
\(871\) 4.96940 0.168382
\(872\) 34.1784 1.15743
\(873\) 20.7123 0.701004
\(874\) −33.2537 −1.12482
\(875\) 3.64726 0.123300
\(876\) −21.5395 −0.727751
\(877\) 13.3839 0.451941 0.225971 0.974134i \(-0.427445\pi\)
0.225971 + 0.974134i \(0.427445\pi\)
\(878\) −36.2289 −1.22267
\(879\) 13.5737 0.457829
\(880\) 1.91307 0.0644895
\(881\) −24.3616 −0.820762 −0.410381 0.911914i \(-0.634604\pi\)
−0.410381 + 0.911914i \(0.634604\pi\)
\(882\) −24.5536 −0.826763
\(883\) 19.5899 0.659252 0.329626 0.944112i \(-0.393077\pi\)
0.329626 + 0.944112i \(0.393077\pi\)
\(884\) 15.9490 0.536424
\(885\) −7.18844 −0.241637
\(886\) −19.9128 −0.668982
\(887\) 4.86503 0.163352 0.0816758 0.996659i \(-0.473973\pi\)
0.0816758 + 0.996659i \(0.473973\pi\)
\(888\) −9.93652 −0.333448
\(889\) −5.17588 −0.173593
\(890\) 24.6613 0.826647
\(891\) −1.10414 −0.0369902
\(892\) 62.0006 2.07594
\(893\) −9.64050 −0.322607
\(894\) −20.3949 −0.682108
\(895\) 48.4148 1.61833
\(896\) 21.2356 0.709432
\(897\) 8.32980 0.278124
\(898\) 49.3222 1.64590
\(899\) 3.54610 0.118269
\(900\) −37.0940 −1.23647
\(901\) 33.9096 1.12969
\(902\) −5.67659 −0.189010
\(903\) 3.44012 0.114480
\(904\) 20.6961 0.688341
\(905\) −40.5974 −1.34950
\(906\) 2.52353 0.0838387
\(907\) −9.91371 −0.329179 −0.164590 0.986362i \(-0.552630\pi\)
−0.164590 + 0.986362i \(0.552630\pi\)
\(908\) −25.8965 −0.859407
\(909\) 31.9381 1.05932
\(910\) −9.93872 −0.329465
\(911\) −33.4496 −1.10824 −0.554118 0.832438i \(-0.686944\pi\)
−0.554118 + 0.832438i \(0.686944\pi\)
\(912\) −1.53396 −0.0507946
\(913\) −2.26043 −0.0748094
\(914\) 30.4732 1.00796
\(915\) −2.29433 −0.0758481
\(916\) −39.3189 −1.29913
\(917\) −9.45936 −0.312376
\(918\) −57.0186 −1.88189
\(919\) −4.45521 −0.146964 −0.0734819 0.997297i \(-0.523411\pi\)
−0.0734819 + 0.997297i \(0.523411\pi\)
\(920\) 65.7303 2.16706
\(921\) −25.4953 −0.840100
\(922\) 8.10448 0.266907
\(923\) −0.701613 −0.0230939
\(924\) 2.26638 0.0745585
\(925\) −27.4027 −0.900994
\(926\) −7.97364 −0.262030
\(927\) −13.3321 −0.437882
\(928\) −10.2824 −0.337536
\(929\) 53.5178 1.75586 0.877931 0.478788i \(-0.158924\pi\)
0.877931 + 0.478788i \(0.158924\pi\)
\(930\) −15.9197 −0.522027
\(931\) 8.66411 0.283955
\(932\) 50.1554 1.64289
\(933\) 18.0342 0.590412
\(934\) −43.9104 −1.43679
\(935\) −10.3900 −0.339789
\(936\) 4.77057 0.155931
\(937\) 58.8849 1.92368 0.961842 0.273604i \(-0.0882158\pi\)
0.961842 + 0.273604i \(0.0882158\pi\)
\(938\) −15.0141 −0.490228
\(939\) 25.7493 0.840298
\(940\) 56.9497 1.85750
\(941\) 0.646434 0.0210732 0.0105366 0.999944i \(-0.496646\pi\)
0.0105366 + 0.999944i \(0.496646\pi\)
\(942\) −8.82772 −0.287623
\(943\) 37.8502 1.23257
\(944\) −2.27601 −0.0740780
\(945\) 21.3352 0.694033
\(946\) −3.61676 −0.117591
\(947\) −28.6486 −0.930955 −0.465478 0.885060i \(-0.654117\pi\)
−0.465478 + 0.885060i \(0.654117\pi\)
\(948\) −9.63931 −0.313070
\(949\) 7.63942 0.247986
\(950\) 21.7986 0.707241
\(951\) 3.79659 0.123113
\(952\) −16.1237 −0.522572
\(953\) −14.7327 −0.477239 −0.238619 0.971113i \(-0.576695\pi\)
−0.238619 + 0.971113i \(0.576695\pi\)
\(954\) 30.3127 0.981411
\(955\) −70.8906 −2.29396
\(956\) 15.1578 0.490239
\(957\) −0.858674 −0.0277570
\(958\) −91.2831 −2.94922
\(959\) 5.19695 0.167818
\(960\) 40.1317 1.29524
\(961\) −25.6828 −0.828477
\(962\) 10.5324 0.339577
\(963\) −16.7891 −0.541021
\(964\) −64.6771 −2.08311
\(965\) −67.9650 −2.18787
\(966\) −25.1669 −0.809733
\(967\) 20.4639 0.658073 0.329037 0.944317i \(-0.393276\pi\)
0.329037 + 0.944317i \(0.393276\pi\)
\(968\) 23.9548 0.769938
\(969\) 8.33106 0.267632
\(970\) 71.9028 2.30866
\(971\) 0.468217 0.0150258 0.00751290 0.999972i \(-0.497609\pi\)
0.00751290 + 0.999972i \(0.497609\pi\)
\(972\) −48.5384 −1.55687
\(973\) 21.1507 0.678059
\(974\) −45.2010 −1.44833
\(975\) −5.46040 −0.174873
\(976\) −0.726433 −0.0232526
\(977\) −10.7379 −0.343537 −0.171768 0.985137i \(-0.554948\pi\)
−0.171768 + 0.985137i \(0.554948\pi\)
\(978\) −10.1744 −0.325341
\(979\) 1.99454 0.0637459
\(980\) −51.1819 −1.63494
\(981\) 32.2021 1.02813
\(982\) −12.8734 −0.410807
\(983\) 36.5648 1.16624 0.583119 0.812387i \(-0.301832\pi\)
0.583119 + 0.812387i \(0.301832\pi\)
\(984\) −8.99703 −0.286815
\(985\) −61.4183 −1.95695
\(986\) 18.2568 0.581415
\(987\) −7.29609 −0.232237
\(988\) −5.03090 −0.160054
\(989\) 24.1157 0.766834
\(990\) −9.28789 −0.295188
\(991\) 34.7234 1.10303 0.551513 0.834167i \(-0.314051\pi\)
0.551513 + 0.834167i \(0.314051\pi\)
\(992\) −15.4180 −0.489522
\(993\) 5.84572 0.185508
\(994\) 2.11979 0.0672358
\(995\) 62.8346 1.99199
\(996\) −10.7070 −0.339265
\(997\) −0.516300 −0.0163514 −0.00817569 0.999967i \(-0.502602\pi\)
−0.00817569 + 0.999967i \(0.502602\pi\)
\(998\) 27.8066 0.880204
\(999\) −22.6095 −0.715333
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 \(a_p\))