Properties

Label 8047.2.a.b.1.10
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 1.10
Character \(\chi\) = 8047.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.52587 q^{2} -3.25300 q^{3} +4.38004 q^{4} -2.46689 q^{5} +8.21667 q^{6} -3.38874 q^{7} -6.01169 q^{8} +7.58202 q^{9} +O(q^{10})\) \(q-2.52587 q^{2} -3.25300 q^{3} +4.38004 q^{4} -2.46689 q^{5} +8.21667 q^{6} -3.38874 q^{7} -6.01169 q^{8} +7.58202 q^{9} +6.23106 q^{10} +4.40988 q^{11} -14.2483 q^{12} +1.00000 q^{13} +8.55953 q^{14} +8.02480 q^{15} +6.42469 q^{16} +1.63656 q^{17} -19.1512 q^{18} +4.16852 q^{19} -10.8051 q^{20} +11.0236 q^{21} -11.1388 q^{22} +1.46454 q^{23} +19.5560 q^{24} +1.08555 q^{25} -2.52587 q^{26} -14.9053 q^{27} -14.8428 q^{28} +2.21107 q^{29} -20.2696 q^{30} +0.120759 q^{31} -4.20458 q^{32} -14.3453 q^{33} -4.13376 q^{34} +8.35965 q^{35} +33.2096 q^{36} +9.09197 q^{37} -10.5292 q^{38} -3.25300 q^{39} +14.8302 q^{40} +2.20916 q^{41} -27.8442 q^{42} -2.05769 q^{43} +19.3154 q^{44} -18.7040 q^{45} -3.69923 q^{46} +2.03892 q^{47} -20.8995 q^{48} +4.48356 q^{49} -2.74197 q^{50} -5.32375 q^{51} +4.38004 q^{52} -9.70810 q^{53} +37.6490 q^{54} -10.8787 q^{55} +20.3720 q^{56} -13.5602 q^{57} -5.58490 q^{58} -4.84207 q^{59} +35.1490 q^{60} -5.70646 q^{61} -0.305022 q^{62} -25.6935 q^{63} -2.22914 q^{64} -2.46689 q^{65} +36.2345 q^{66} +5.60774 q^{67} +7.16822 q^{68} -4.76414 q^{69} -21.1154 q^{70} -8.23489 q^{71} -45.5808 q^{72} -11.0604 q^{73} -22.9652 q^{74} -3.53130 q^{75} +18.2583 q^{76} -14.9439 q^{77} +8.21667 q^{78} +7.65557 q^{79} -15.8490 q^{80} +25.7410 q^{81} -5.58006 q^{82} +1.67921 q^{83} +48.2837 q^{84} -4.03723 q^{85} +5.19746 q^{86} -7.19263 q^{87} -26.5108 q^{88} -16.1435 q^{89} +47.2440 q^{90} -3.38874 q^{91} +6.41473 q^{92} -0.392829 q^{93} -5.15005 q^{94} -10.2833 q^{95} +13.6775 q^{96} +8.90888 q^{97} -11.3249 q^{98} +33.4358 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} + O(q^{10}) \) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} - 25q^{10} - 25q^{11} - 62q^{12} + 142q^{13} - 57q^{14} - 14q^{15} + 111q^{16} - 141q^{17} - 29q^{18} - 3q^{19} - 87q^{20} - 19q^{21} - 24q^{22} - 69q^{23} - 40q^{24} + 87q^{25} - 13q^{26} - 95q^{27} - 34q^{28} - 147q^{29} - 2q^{30} - 21q^{31} - 66q^{32} - 62q^{33} - 6q^{34} - 59q^{35} + 74q^{36} - 37q^{37} - 76q^{38} - 26q^{39} - 61q^{40} - 97q^{41} - 29q^{42} - 33q^{43} - 57q^{44} - 86q^{45} - q^{46} - 102q^{47} - 141q^{48} + 70q^{49} - 28q^{50} - 13q^{51} + 129q^{52} - 137q^{53} - 29q^{54} - 24q^{55} - 130q^{56} - 65q^{57} - 15q^{58} - 56q^{59} + 11q^{60} - 77q^{61} - 150q^{62} - 32q^{63} + 73q^{64} - 37q^{65} - 32q^{66} - 9q^{67} - 226q^{68} - 113q^{69} + 6q^{70} - 18q^{71} - 82q^{72} - 117q^{73} - 70q^{74} - 83q^{75} + 40q^{76} - 214q^{77} - 15q^{78} - 52q^{79} - 161q^{80} - 10q^{81} - 36q^{82} - 74q^{83} + 53q^{84} + 2q^{85} + 17q^{86} - 49q^{87} - 29q^{88} - 171q^{89} - 57q^{90} - 14q^{91} - 187q^{92} - 39q^{93} + 13q^{94} - 150q^{95} - 47q^{96} - 126q^{97} - 85q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.52587 −1.78606 −0.893032 0.449994i \(-0.851426\pi\)
−0.893032 + 0.449994i \(0.851426\pi\)
\(3\) −3.25300 −1.87812 −0.939061 0.343751i \(-0.888302\pi\)
−0.939061 + 0.343751i \(0.888302\pi\)
\(4\) 4.38004 2.19002
\(5\) −2.46689 −1.10323 −0.551614 0.834100i \(-0.685988\pi\)
−0.551614 + 0.834100i \(0.685988\pi\)
\(6\) 8.21667 3.35444
\(7\) −3.38874 −1.28082 −0.640412 0.768032i \(-0.721236\pi\)
−0.640412 + 0.768032i \(0.721236\pi\)
\(8\) −6.01169 −2.12545
\(9\) 7.58202 2.52734
\(10\) 6.23106 1.97043
\(11\) 4.40988 1.32963 0.664814 0.747009i \(-0.268511\pi\)
0.664814 + 0.747009i \(0.268511\pi\)
\(12\) −14.2483 −4.11313
\(13\) 1.00000 0.277350
\(14\) 8.55953 2.28763
\(15\) 8.02480 2.07199
\(16\) 6.42469 1.60617
\(17\) 1.63656 0.396925 0.198463 0.980108i \(-0.436405\pi\)
0.198463 + 0.980108i \(0.436405\pi\)
\(18\) −19.1512 −4.51399
\(19\) 4.16852 0.956325 0.478162 0.878271i \(-0.341303\pi\)
0.478162 + 0.878271i \(0.341303\pi\)
\(20\) −10.8051 −2.41609
\(21\) 11.0236 2.40554
\(22\) −11.1388 −2.37480
\(23\) 1.46454 0.305377 0.152688 0.988274i \(-0.451207\pi\)
0.152688 + 0.988274i \(0.451207\pi\)
\(24\) 19.5560 3.99186
\(25\) 1.08555 0.217110
\(26\) −2.52587 −0.495365
\(27\) −14.9053 −2.86853
\(28\) −14.8428 −2.80503
\(29\) 2.21107 0.410586 0.205293 0.978701i \(-0.434185\pi\)
0.205293 + 0.978701i \(0.434185\pi\)
\(30\) −20.2696 −3.70071
\(31\) 0.120759 0.0216889 0.0108445 0.999941i \(-0.496548\pi\)
0.0108445 + 0.999941i \(0.496548\pi\)
\(32\) −4.20458 −0.743271
\(33\) −14.3453 −2.49720
\(34\) −4.13376 −0.708933
\(35\) 8.35965 1.41304
\(36\) 33.2096 5.53493
\(37\) 9.09197 1.49471 0.747356 0.664424i \(-0.231323\pi\)
0.747356 + 0.664424i \(0.231323\pi\)
\(38\) −10.5292 −1.70806
\(39\) −3.25300 −0.520897
\(40\) 14.8302 2.34486
\(41\) 2.20916 0.345013 0.172506 0.985008i \(-0.444813\pi\)
0.172506 + 0.985008i \(0.444813\pi\)
\(42\) −27.8442 −4.29645
\(43\) −2.05769 −0.313794 −0.156897 0.987615i \(-0.550149\pi\)
−0.156897 + 0.987615i \(0.550149\pi\)
\(44\) 19.3154 2.91191
\(45\) −18.7040 −2.78823
\(46\) −3.69923 −0.545422
\(47\) 2.03892 0.297407 0.148703 0.988882i \(-0.452490\pi\)
0.148703 + 0.988882i \(0.452490\pi\)
\(48\) −20.8995 −3.01659
\(49\) 4.48356 0.640508
\(50\) −2.74197 −0.387773
\(51\) −5.32375 −0.745474
\(52\) 4.38004 0.607403
\(53\) −9.70810 −1.33351 −0.666755 0.745277i \(-0.732317\pi\)
−0.666755 + 0.745277i \(0.732317\pi\)
\(54\) 37.6490 5.12338
\(55\) −10.8787 −1.46688
\(56\) 20.3720 2.72233
\(57\) −13.5602 −1.79609
\(58\) −5.58490 −0.733333
\(59\) −4.84207 −0.630384 −0.315192 0.949028i \(-0.602069\pi\)
−0.315192 + 0.949028i \(0.602069\pi\)
\(60\) 35.1490 4.53771
\(61\) −5.70646 −0.730638 −0.365319 0.930882i \(-0.619040\pi\)
−0.365319 + 0.930882i \(0.619040\pi\)
\(62\) −0.305022 −0.0387378
\(63\) −25.6935 −3.23708
\(64\) −2.22914 −0.278643
\(65\) −2.46689 −0.305980
\(66\) 36.2345 4.46016
\(67\) 5.60774 0.685095 0.342547 0.939501i \(-0.388710\pi\)
0.342547 + 0.939501i \(0.388710\pi\)
\(68\) 7.16822 0.869275
\(69\) −4.76414 −0.573535
\(70\) −21.1154 −2.52378
\(71\) −8.23489 −0.977301 −0.488651 0.872479i \(-0.662511\pi\)
−0.488651 + 0.872479i \(0.662511\pi\)
\(72\) −45.5808 −5.37174
\(73\) −11.0604 −1.29452 −0.647261 0.762269i \(-0.724086\pi\)
−0.647261 + 0.762269i \(0.724086\pi\)
\(74\) −22.9652 −2.66965
\(75\) −3.53130 −0.407760
\(76\) 18.2583 2.09437
\(77\) −14.9439 −1.70302
\(78\) 8.21667 0.930355
\(79\) 7.65557 0.861319 0.430660 0.902514i \(-0.358281\pi\)
0.430660 + 0.902514i \(0.358281\pi\)
\(80\) −15.8490 −1.77197
\(81\) 25.7410 2.86011
\(82\) −5.58006 −0.616215
\(83\) 1.67921 0.184317 0.0921586 0.995744i \(-0.470623\pi\)
0.0921586 + 0.995744i \(0.470623\pi\)
\(84\) 48.2837 5.26819
\(85\) −4.03723 −0.437899
\(86\) 5.19746 0.560456
\(87\) −7.19263 −0.771131
\(88\) −26.5108 −2.82606
\(89\) −16.1435 −1.71121 −0.855605 0.517629i \(-0.826815\pi\)
−0.855605 + 0.517629i \(0.826815\pi\)
\(90\) 47.2440 4.97996
\(91\) −3.38874 −0.355236
\(92\) 6.41473 0.668782
\(93\) −0.392829 −0.0407344
\(94\) −5.15005 −0.531187
\(95\) −10.2833 −1.05504
\(96\) 13.6775 1.39595
\(97\) 8.90888 0.904559 0.452280 0.891876i \(-0.350611\pi\)
0.452280 + 0.891876i \(0.350611\pi\)
\(98\) −11.3249 −1.14399
\(99\) 33.4358 3.36042
\(100\) 4.75477 0.475477
\(101\) 5.66423 0.563612 0.281806 0.959471i \(-0.409067\pi\)
0.281806 + 0.959471i \(0.409067\pi\)
\(102\) 13.4471 1.33146
\(103\) 3.22548 0.317816 0.158908 0.987293i \(-0.449203\pi\)
0.158908 + 0.987293i \(0.449203\pi\)
\(104\) −6.01169 −0.589495
\(105\) −27.1940 −2.65386
\(106\) 24.5215 2.38173
\(107\) −8.48853 −0.820617 −0.410309 0.911947i \(-0.634579\pi\)
−0.410309 + 0.911947i \(0.634579\pi\)
\(108\) −65.2860 −6.28214
\(109\) −1.83986 −0.176226 −0.0881131 0.996110i \(-0.528084\pi\)
−0.0881131 + 0.996110i \(0.528084\pi\)
\(110\) 27.4782 2.61994
\(111\) −29.5762 −2.80725
\(112\) −21.7716 −2.05722
\(113\) −1.91102 −0.179774 −0.0898868 0.995952i \(-0.528651\pi\)
−0.0898868 + 0.995952i \(0.528651\pi\)
\(114\) 34.2514 3.20794
\(115\) −3.61285 −0.336900
\(116\) 9.68460 0.899192
\(117\) 7.58202 0.700958
\(118\) 12.2305 1.12591
\(119\) −5.54589 −0.508391
\(120\) −48.2426 −4.40393
\(121\) 8.44700 0.767909
\(122\) 14.4138 1.30497
\(123\) −7.18640 −0.647976
\(124\) 0.528929 0.0474992
\(125\) 9.65652 0.863705
\(126\) 64.8985 5.78162
\(127\) 16.1250 1.43087 0.715433 0.698681i \(-0.246229\pi\)
0.715433 + 0.698681i \(0.246229\pi\)
\(128\) 14.0397 1.24094
\(129\) 6.69366 0.589343
\(130\) 6.23106 0.546500
\(131\) −13.2142 −1.15453 −0.577265 0.816557i \(-0.695880\pi\)
−0.577265 + 0.816557i \(0.695880\pi\)
\(132\) −62.8332 −5.46893
\(133\) −14.1260 −1.22488
\(134\) −14.1644 −1.22362
\(135\) 36.7698 3.16464
\(136\) −9.83852 −0.843646
\(137\) 10.5547 0.901745 0.450872 0.892588i \(-0.351113\pi\)
0.450872 + 0.892588i \(0.351113\pi\)
\(138\) 12.0336 1.02437
\(139\) 13.8873 1.17791 0.588954 0.808166i \(-0.299540\pi\)
0.588954 + 0.808166i \(0.299540\pi\)
\(140\) 36.6156 3.09459
\(141\) −6.63260 −0.558566
\(142\) 20.8003 1.74552
\(143\) 4.40988 0.368772
\(144\) 48.7121 4.05934
\(145\) −5.45448 −0.452970
\(146\) 27.9372 2.31210
\(147\) −14.5850 −1.20295
\(148\) 39.8232 3.27345
\(149\) −13.1052 −1.07362 −0.536811 0.843703i \(-0.680371\pi\)
−0.536811 + 0.843703i \(0.680371\pi\)
\(150\) 8.91963 0.728285
\(151\) −4.58018 −0.372730 −0.186365 0.982481i \(-0.559671\pi\)
−0.186365 + 0.982481i \(0.559671\pi\)
\(152\) −25.0599 −2.03262
\(153\) 12.4085 1.00317
\(154\) 37.7465 3.04170
\(155\) −0.297899 −0.0239278
\(156\) −14.2483 −1.14078
\(157\) −14.3771 −1.14741 −0.573707 0.819060i \(-0.694495\pi\)
−0.573707 + 0.819060i \(0.694495\pi\)
\(158\) −19.3370 −1.53837
\(159\) 31.5805 2.50450
\(160\) 10.3722 0.819997
\(161\) −4.96293 −0.391134
\(162\) −65.0185 −5.10834
\(163\) −14.2884 −1.11916 −0.559578 0.828778i \(-0.689037\pi\)
−0.559578 + 0.828778i \(0.689037\pi\)
\(164\) 9.67622 0.755586
\(165\) 35.3884 2.75498
\(166\) −4.24147 −0.329202
\(167\) 3.15708 0.244302 0.122151 0.992512i \(-0.461021\pi\)
0.122151 + 0.992512i \(0.461021\pi\)
\(168\) −66.2703 −5.11287
\(169\) 1.00000 0.0769231
\(170\) 10.1975 0.782115
\(171\) 31.6058 2.41696
\(172\) −9.01275 −0.687216
\(173\) −18.3857 −1.39784 −0.698918 0.715201i \(-0.746335\pi\)
−0.698918 + 0.715201i \(0.746335\pi\)
\(174\) 18.1677 1.37729
\(175\) −3.67865 −0.278080
\(176\) 28.3321 2.13561
\(177\) 15.7513 1.18394
\(178\) 40.7765 3.05633
\(179\) 15.6377 1.16882 0.584409 0.811459i \(-0.301326\pi\)
0.584409 + 0.811459i \(0.301326\pi\)
\(180\) −81.9244 −6.10629
\(181\) −16.2267 −1.20612 −0.603061 0.797695i \(-0.706053\pi\)
−0.603061 + 0.797695i \(0.706053\pi\)
\(182\) 8.55953 0.634475
\(183\) 18.5631 1.37223
\(184\) −8.80433 −0.649064
\(185\) −22.4289 −1.64901
\(186\) 0.992236 0.0727543
\(187\) 7.21705 0.527763
\(188\) 8.93054 0.651327
\(189\) 50.5103 3.67408
\(190\) 25.9743 1.88437
\(191\) 13.1338 0.950332 0.475166 0.879896i \(-0.342388\pi\)
0.475166 + 0.879896i \(0.342388\pi\)
\(192\) 7.25140 0.523325
\(193\) −5.92724 −0.426652 −0.213326 0.976981i \(-0.568430\pi\)
−0.213326 + 0.976981i \(0.568430\pi\)
\(194\) −22.5027 −1.61560
\(195\) 8.02480 0.574668
\(196\) 19.6382 1.40273
\(197\) −15.4973 −1.10413 −0.552067 0.833800i \(-0.686161\pi\)
−0.552067 + 0.833800i \(0.686161\pi\)
\(198\) −84.4546 −6.00192
\(199\) 16.7125 1.18472 0.592359 0.805674i \(-0.298197\pi\)
0.592359 + 0.805674i \(0.298197\pi\)
\(200\) −6.52600 −0.461458
\(201\) −18.2420 −1.28669
\(202\) −14.3071 −1.00665
\(203\) −7.49275 −0.525888
\(204\) −23.3182 −1.63260
\(205\) −5.44976 −0.380628
\(206\) −8.14716 −0.567640
\(207\) 11.1041 0.771791
\(208\) 6.42469 0.445472
\(209\) 18.3827 1.27156
\(210\) 68.6885 4.73996
\(211\) −5.56321 −0.382988 −0.191494 0.981494i \(-0.561333\pi\)
−0.191494 + 0.981494i \(0.561333\pi\)
\(212\) −42.5219 −2.92042
\(213\) 26.7881 1.83549
\(214\) 21.4410 1.46567
\(215\) 5.07609 0.346186
\(216\) 89.6062 6.09693
\(217\) −0.409220 −0.0277797
\(218\) 4.64724 0.314751
\(219\) 35.9795 2.43127
\(220\) −47.6491 −3.21250
\(221\) 1.63656 0.110087
\(222\) 74.7058 5.01392
\(223\) −21.8320 −1.46198 −0.730989 0.682389i \(-0.760941\pi\)
−0.730989 + 0.682389i \(0.760941\pi\)
\(224\) 14.2482 0.951999
\(225\) 8.23068 0.548712
\(226\) 4.82700 0.321087
\(227\) 1.71020 0.113510 0.0567551 0.998388i \(-0.481925\pi\)
0.0567551 + 0.998388i \(0.481925\pi\)
\(228\) −59.3943 −3.93348
\(229\) 20.9060 1.38151 0.690755 0.723089i \(-0.257279\pi\)
0.690755 + 0.723089i \(0.257279\pi\)
\(230\) 9.12560 0.601725
\(231\) 48.6126 3.19847
\(232\) −13.2923 −0.872682
\(233\) −21.9669 −1.43910 −0.719549 0.694442i \(-0.755651\pi\)
−0.719549 + 0.694442i \(0.755651\pi\)
\(234\) −19.1512 −1.25196
\(235\) −5.02979 −0.328107
\(236\) −21.2085 −1.38055
\(237\) −24.9036 −1.61766
\(238\) 14.0082 0.908018
\(239\) 0.839606 0.0543096 0.0271548 0.999631i \(-0.491355\pi\)
0.0271548 + 0.999631i \(0.491355\pi\)
\(240\) 51.5568 3.32798
\(241\) 19.0933 1.22991 0.614953 0.788563i \(-0.289175\pi\)
0.614953 + 0.788563i \(0.289175\pi\)
\(242\) −21.3361 −1.37153
\(243\) −39.0195 −2.50310
\(244\) −24.9946 −1.60011
\(245\) −11.0604 −0.706626
\(246\) 18.1520 1.15733
\(247\) 4.16852 0.265237
\(248\) −0.725965 −0.0460988
\(249\) −5.46247 −0.346170
\(250\) −24.3911 −1.54263
\(251\) −7.66731 −0.483956 −0.241978 0.970282i \(-0.577796\pi\)
−0.241978 + 0.970282i \(0.577796\pi\)
\(252\) −112.539 −7.08927
\(253\) 6.45842 0.406037
\(254\) −40.7298 −2.55562
\(255\) 13.1331 0.822427
\(256\) −31.0042 −1.93776
\(257\) −14.0903 −0.878926 −0.439463 0.898261i \(-0.644831\pi\)
−0.439463 + 0.898261i \(0.644831\pi\)
\(258\) −16.9073 −1.05260
\(259\) −30.8103 −1.91446
\(260\) −10.8051 −0.670103
\(261\) 16.7644 1.03769
\(262\) 33.3774 2.06206
\(263\) −2.01515 −0.124260 −0.0621299 0.998068i \(-0.519789\pi\)
−0.0621299 + 0.998068i \(0.519789\pi\)
\(264\) 86.2397 5.30769
\(265\) 23.9488 1.47117
\(266\) 35.6806 2.18772
\(267\) 52.5149 3.21386
\(268\) 24.5621 1.50037
\(269\) −4.15091 −0.253085 −0.126543 0.991961i \(-0.540388\pi\)
−0.126543 + 0.991961i \(0.540388\pi\)
\(270\) −92.8759 −5.65225
\(271\) 18.1385 1.10183 0.550916 0.834560i \(-0.314278\pi\)
0.550916 + 0.834560i \(0.314278\pi\)
\(272\) 10.5144 0.637530
\(273\) 11.0236 0.667177
\(274\) −26.6597 −1.61057
\(275\) 4.78715 0.288676
\(276\) −20.8671 −1.25605
\(277\) −0.0231764 −0.00139254 −0.000696269 1.00000i \(-0.500222\pi\)
−0.000696269 1.00000i \(0.500222\pi\)
\(278\) −35.0777 −2.10382
\(279\) 0.915596 0.0548153
\(280\) −50.2556 −3.00335
\(281\) −0.321557 −0.0191825 −0.00959126 0.999954i \(-0.503053\pi\)
−0.00959126 + 0.999954i \(0.503053\pi\)
\(282\) 16.7531 0.997634
\(283\) 14.7800 0.878580 0.439290 0.898345i \(-0.355230\pi\)
0.439290 + 0.898345i \(0.355230\pi\)
\(284\) −36.0692 −2.14031
\(285\) 33.4516 1.98150
\(286\) −11.1388 −0.658651
\(287\) −7.48627 −0.441900
\(288\) −31.8792 −1.87850
\(289\) −14.3217 −0.842450
\(290\) 13.7773 0.809033
\(291\) −28.9806 −1.69887
\(292\) −48.4450 −2.83503
\(293\) −6.33053 −0.369833 −0.184917 0.982754i \(-0.559202\pi\)
−0.184917 + 0.982754i \(0.559202\pi\)
\(294\) 36.8399 2.14855
\(295\) 11.9449 0.695457
\(296\) −54.6581 −3.17694
\(297\) −65.7306 −3.81408
\(298\) 33.1021 1.91756
\(299\) 1.46454 0.0846963
\(300\) −15.4673 −0.893003
\(301\) 6.97296 0.401915
\(302\) 11.5690 0.665719
\(303\) −18.4258 −1.05853
\(304\) 26.7815 1.53602
\(305\) 14.0772 0.806060
\(306\) −31.3422 −1.79172
\(307\) 9.48140 0.541132 0.270566 0.962701i \(-0.412789\pi\)
0.270566 + 0.962701i \(0.412789\pi\)
\(308\) −65.4550 −3.72965
\(309\) −10.4925 −0.596897
\(310\) 0.752455 0.0427366
\(311\) 21.7050 1.23078 0.615390 0.788223i \(-0.288999\pi\)
0.615390 + 0.788223i \(0.288999\pi\)
\(312\) 19.5560 1.10714
\(313\) 33.7685 1.90871 0.954355 0.298674i \(-0.0965444\pi\)
0.954355 + 0.298674i \(0.0965444\pi\)
\(314\) 36.3147 2.04935
\(315\) 63.3831 3.57123
\(316\) 33.5317 1.88631
\(317\) 15.7820 0.886406 0.443203 0.896421i \(-0.353842\pi\)
0.443203 + 0.896421i \(0.353842\pi\)
\(318\) −79.7683 −4.47319
\(319\) 9.75056 0.545927
\(320\) 5.49905 0.307406
\(321\) 27.6132 1.54122
\(322\) 12.5357 0.698589
\(323\) 6.82206 0.379589
\(324\) 112.747 6.26370
\(325\) 1.08555 0.0602156
\(326\) 36.0908 1.99888
\(327\) 5.98505 0.330974
\(328\) −13.2808 −0.733309
\(329\) −6.90936 −0.380925
\(330\) −89.3866 −4.92057
\(331\) 23.7160 1.30355 0.651774 0.758414i \(-0.274025\pi\)
0.651774 + 0.758414i \(0.274025\pi\)
\(332\) 7.35501 0.403659
\(333\) 68.9355 3.77764
\(334\) −7.97439 −0.436339
\(335\) −13.8337 −0.755815
\(336\) 70.8230 3.86371
\(337\) 27.2889 1.48652 0.743260 0.669003i \(-0.233279\pi\)
0.743260 + 0.669003i \(0.233279\pi\)
\(338\) −2.52587 −0.137389
\(339\) 6.21655 0.337637
\(340\) −17.6832 −0.959008
\(341\) 0.532531 0.0288382
\(342\) −79.8324 −4.31684
\(343\) 8.52757 0.460446
\(344\) 12.3702 0.666955
\(345\) 11.7526 0.632739
\(346\) 46.4399 2.49662
\(347\) −18.3794 −0.986657 −0.493329 0.869843i \(-0.664220\pi\)
−0.493329 + 0.869843i \(0.664220\pi\)
\(348\) −31.5040 −1.68879
\(349\) −6.34447 −0.339612 −0.169806 0.985478i \(-0.554314\pi\)
−0.169806 + 0.985478i \(0.554314\pi\)
\(350\) 9.29182 0.496669
\(351\) −14.9053 −0.795587
\(352\) −18.5417 −0.988274
\(353\) −13.6413 −0.726053 −0.363027 0.931779i \(-0.618257\pi\)
−0.363027 + 0.931779i \(0.618257\pi\)
\(354\) −39.7857 −2.11459
\(355\) 20.3146 1.07819
\(356\) −70.7093 −3.74759
\(357\) 18.0408 0.954820
\(358\) −39.4989 −2.08758
\(359\) 22.4081 1.18265 0.591327 0.806432i \(-0.298604\pi\)
0.591327 + 0.806432i \(0.298604\pi\)
\(360\) 112.443 5.92625
\(361\) −1.62342 −0.0854430
\(362\) 40.9867 2.15421
\(363\) −27.4781 −1.44223
\(364\) −14.8428 −0.777975
\(365\) 27.2848 1.42815
\(366\) −46.8882 −2.45088
\(367\) −31.9021 −1.66528 −0.832638 0.553818i \(-0.813170\pi\)
−0.832638 + 0.553818i \(0.813170\pi\)
\(368\) 9.40918 0.490488
\(369\) 16.7499 0.871965
\(370\) 56.6526 2.94523
\(371\) 32.8982 1.70799
\(372\) −1.72061 −0.0892093
\(373\) 31.8156 1.64735 0.823674 0.567063i \(-0.191920\pi\)
0.823674 + 0.567063i \(0.191920\pi\)
\(374\) −18.2294 −0.942617
\(375\) −31.4127 −1.62214
\(376\) −12.2573 −0.632124
\(377\) 2.21107 0.113876
\(378\) −127.583 −6.56214
\(379\) 12.0375 0.618327 0.309163 0.951009i \(-0.399951\pi\)
0.309163 + 0.951009i \(0.399951\pi\)
\(380\) −45.0413 −2.31057
\(381\) −52.4548 −2.68734
\(382\) −33.1744 −1.69735
\(383\) −1.29214 −0.0660252 −0.0330126 0.999455i \(-0.510510\pi\)
−0.0330126 + 0.999455i \(0.510510\pi\)
\(384\) −45.6711 −2.33064
\(385\) 36.8650 1.87882
\(386\) 14.9715 0.762027
\(387\) −15.6014 −0.793065
\(388\) 39.0213 1.98100
\(389\) 10.9433 0.554845 0.277423 0.960748i \(-0.410520\pi\)
0.277423 + 0.960748i \(0.410520\pi\)
\(390\) −20.2696 −1.02639
\(391\) 2.39681 0.121212
\(392\) −26.9537 −1.36137
\(393\) 42.9858 2.16835
\(394\) 39.1441 1.97205
\(395\) −18.8855 −0.950231
\(396\) 146.450 7.35939
\(397\) 37.9222 1.90326 0.951631 0.307243i \(-0.0994064\pi\)
0.951631 + 0.307243i \(0.0994064\pi\)
\(398\) −42.2137 −2.11598
\(399\) 45.9520 2.30048
\(400\) 6.97433 0.348717
\(401\) −29.8711 −1.49169 −0.745846 0.666118i \(-0.767955\pi\)
−0.745846 + 0.666118i \(0.767955\pi\)
\(402\) 46.0770 2.29811
\(403\) 0.120759 0.00601543
\(404\) 24.8096 1.23432
\(405\) −63.5002 −3.15535
\(406\) 18.9258 0.939270
\(407\) 40.0945 1.98741
\(408\) 32.0047 1.58447
\(409\) −4.53690 −0.224335 −0.112168 0.993689i \(-0.535779\pi\)
−0.112168 + 0.993689i \(0.535779\pi\)
\(410\) 13.7654 0.679825
\(411\) −34.3343 −1.69359
\(412\) 14.1277 0.696024
\(413\) 16.4085 0.807410
\(414\) −28.0477 −1.37847
\(415\) −4.14243 −0.203344
\(416\) −4.20458 −0.206146
\(417\) −45.1755 −2.21226
\(418\) −46.4323 −2.27108
\(419\) −34.8034 −1.70026 −0.850128 0.526577i \(-0.823475\pi\)
−0.850128 + 0.526577i \(0.823475\pi\)
\(420\) −119.111 −5.81201
\(421\) 8.40464 0.409617 0.204808 0.978802i \(-0.434343\pi\)
0.204808 + 0.978802i \(0.434343\pi\)
\(422\) 14.0520 0.684040
\(423\) 15.4591 0.751648
\(424\) 58.3621 2.83431
\(425\) 1.77658 0.0861766
\(426\) −67.6634 −3.27830
\(427\) 19.3377 0.935818
\(428\) −37.1801 −1.79717
\(429\) −14.3453 −0.692599
\(430\) −12.8216 −0.618310
\(431\) −0.953929 −0.0459491 −0.0229746 0.999736i \(-0.507314\pi\)
−0.0229746 + 0.999736i \(0.507314\pi\)
\(432\) −95.7621 −4.60735
\(433\) −17.7329 −0.852189 −0.426094 0.904679i \(-0.640111\pi\)
−0.426094 + 0.904679i \(0.640111\pi\)
\(434\) 1.03364 0.0496163
\(435\) 17.7434 0.850732
\(436\) −8.05865 −0.385939
\(437\) 6.10495 0.292039
\(438\) −90.8797 −4.34240
\(439\) −34.5804 −1.65043 −0.825216 0.564817i \(-0.808947\pi\)
−0.825216 + 0.564817i \(0.808947\pi\)
\(440\) 65.3993 3.11779
\(441\) 33.9944 1.61878
\(442\) −4.13376 −0.196623
\(443\) −5.88598 −0.279651 −0.139826 0.990176i \(-0.544654\pi\)
−0.139826 + 0.990176i \(0.544654\pi\)
\(444\) −129.545 −6.14794
\(445\) 39.8243 1.88785
\(446\) 55.1449 2.61119
\(447\) 42.6313 2.01639
\(448\) 7.55398 0.356892
\(449\) 31.1042 1.46790 0.733949 0.679205i \(-0.237675\pi\)
0.733949 + 0.679205i \(0.237675\pi\)
\(450\) −20.7897 −0.980034
\(451\) 9.74212 0.458739
\(452\) −8.37035 −0.393708
\(453\) 14.8993 0.700032
\(454\) −4.31976 −0.202736
\(455\) 8.35965 0.391907
\(456\) 81.5198 3.81751
\(457\) −36.5753 −1.71092 −0.855461 0.517867i \(-0.826726\pi\)
−0.855461 + 0.517867i \(0.826726\pi\)
\(458\) −52.8060 −2.46746
\(459\) −24.3935 −1.13859
\(460\) −15.8244 −0.737818
\(461\) −10.5570 −0.491686 −0.245843 0.969310i \(-0.579065\pi\)
−0.245843 + 0.969310i \(0.579065\pi\)
\(462\) −122.789 −5.71268
\(463\) 2.59293 0.120504 0.0602519 0.998183i \(-0.480810\pi\)
0.0602519 + 0.998183i \(0.480810\pi\)
\(464\) 14.2055 0.659472
\(465\) 0.969066 0.0449393
\(466\) 55.4856 2.57032
\(467\) −7.75694 −0.358948 −0.179474 0.983763i \(-0.557440\pi\)
−0.179474 + 0.983763i \(0.557440\pi\)
\(468\) 33.2096 1.53511
\(469\) −19.0032 −0.877485
\(470\) 12.7046 0.586020
\(471\) 46.7686 2.15498
\(472\) 29.1090 1.33985
\(473\) −9.07414 −0.417229
\(474\) 62.9034 2.88925
\(475\) 4.52515 0.207628
\(476\) −24.2912 −1.11339
\(477\) −73.6071 −3.37024
\(478\) −2.12074 −0.0970003
\(479\) −9.12367 −0.416871 −0.208436 0.978036i \(-0.566837\pi\)
−0.208436 + 0.978036i \(0.566837\pi\)
\(480\) −33.7409 −1.54005
\(481\) 9.09197 0.414558
\(482\) −48.2273 −2.19669
\(483\) 16.1444 0.734596
\(484\) 36.9982 1.68174
\(485\) −21.9772 −0.997934
\(486\) 98.5584 4.47070
\(487\) 28.5242 1.29256 0.646279 0.763102i \(-0.276324\pi\)
0.646279 + 0.763102i \(0.276324\pi\)
\(488\) 34.3055 1.55294
\(489\) 46.4803 2.10191
\(490\) 27.9373 1.26208
\(491\) 12.0146 0.542211 0.271106 0.962550i \(-0.412611\pi\)
0.271106 + 0.962550i \(0.412611\pi\)
\(492\) −31.4767 −1.41908
\(493\) 3.61857 0.162972
\(494\) −10.5292 −0.473730
\(495\) −82.4824 −3.70731
\(496\) 0.775838 0.0348361
\(497\) 27.9059 1.25175
\(498\) 13.7975 0.618282
\(499\) 18.5350 0.829739 0.414869 0.909881i \(-0.363827\pi\)
0.414869 + 0.909881i \(0.363827\pi\)
\(500\) 42.2960 1.89153
\(501\) −10.2700 −0.458829
\(502\) 19.3667 0.864376
\(503\) −33.2696 −1.48342 −0.741708 0.670723i \(-0.765984\pi\)
−0.741708 + 0.670723i \(0.765984\pi\)
\(504\) 154.461 6.88025
\(505\) −13.9730 −0.621792
\(506\) −16.3132 −0.725208
\(507\) −3.25300 −0.144471
\(508\) 70.6284 3.13363
\(509\) 2.99173 0.132606 0.0663029 0.997800i \(-0.478880\pi\)
0.0663029 + 0.997800i \(0.478880\pi\)
\(510\) −33.1726 −1.46891
\(511\) 37.4808 1.65805
\(512\) 50.2334 2.22002
\(513\) −62.1332 −2.74325
\(514\) 35.5902 1.56982
\(515\) −7.95691 −0.350623
\(516\) 29.3185 1.29067
\(517\) 8.99137 0.395440
\(518\) 77.8230 3.41935
\(519\) 59.8086 2.62531
\(520\) 14.8302 0.650347
\(521\) −39.1306 −1.71434 −0.857171 0.515032i \(-0.827780\pi\)
−0.857171 + 0.515032i \(0.827780\pi\)
\(522\) −42.3448 −1.85338
\(523\) 22.2910 0.974718 0.487359 0.873202i \(-0.337960\pi\)
0.487359 + 0.873202i \(0.337960\pi\)
\(524\) −57.8788 −2.52845
\(525\) 11.9667 0.522268
\(526\) 5.09003 0.221936
\(527\) 0.197630 0.00860888
\(528\) −92.1643 −4.01094
\(529\) −20.8551 −0.906745
\(530\) −60.4918 −2.62759
\(531\) −36.7127 −1.59319
\(532\) −61.8726 −2.68252
\(533\) 2.20916 0.0956894
\(534\) −132.646 −5.74016
\(535\) 20.9403 0.905327
\(536\) −33.7120 −1.45614
\(537\) −50.8695 −2.19518
\(538\) 10.4847 0.452026
\(539\) 19.7719 0.851637
\(540\) 161.053 6.93063
\(541\) 2.82447 0.121433 0.0607167 0.998155i \(-0.480661\pi\)
0.0607167 + 0.998155i \(0.480661\pi\)
\(542\) −45.8155 −1.96794
\(543\) 52.7856 2.26525
\(544\) −6.88106 −0.295023
\(545\) 4.53872 0.194418
\(546\) −27.8442 −1.19162
\(547\) −45.5705 −1.94846 −0.974228 0.225567i \(-0.927577\pi\)
−0.974228 + 0.225567i \(0.927577\pi\)
\(548\) 46.2298 1.97484
\(549\) −43.2665 −1.84657
\(550\) −12.0917 −0.515594
\(551\) 9.21691 0.392654
\(552\) 28.6405 1.21902
\(553\) −25.9427 −1.10320
\(554\) 0.0585408 0.00248716
\(555\) 72.9613 3.09703
\(556\) 60.8271 2.57965
\(557\) 45.1243 1.91198 0.955989 0.293404i \(-0.0947880\pi\)
0.955989 + 0.293404i \(0.0947880\pi\)
\(558\) −2.31268 −0.0979036
\(559\) −2.05769 −0.0870308
\(560\) 53.7081 2.26958
\(561\) −23.4771 −0.991203
\(562\) 0.812214 0.0342612
\(563\) 34.7076 1.46275 0.731376 0.681975i \(-0.238879\pi\)
0.731376 + 0.681975i \(0.238879\pi\)
\(564\) −29.0511 −1.22327
\(565\) 4.71428 0.198331
\(566\) −37.3324 −1.56920
\(567\) −87.2295 −3.66329
\(568\) 49.5056 2.07721
\(569\) −31.9039 −1.33748 −0.668741 0.743495i \(-0.733166\pi\)
−0.668741 + 0.743495i \(0.733166\pi\)
\(570\) −84.4945 −3.53908
\(571\) −23.3277 −0.976235 −0.488118 0.872778i \(-0.662316\pi\)
−0.488118 + 0.872778i \(0.662316\pi\)
\(572\) 19.3154 0.807619
\(573\) −42.7244 −1.78484
\(574\) 18.9094 0.789262
\(575\) 1.58983 0.0663005
\(576\) −16.9014 −0.704225
\(577\) 42.3485 1.76299 0.881495 0.472193i \(-0.156537\pi\)
0.881495 + 0.472193i \(0.156537\pi\)
\(578\) 36.1747 1.50467
\(579\) 19.2813 0.801304
\(580\) −23.8909 −0.992014
\(581\) −5.69040 −0.236078
\(582\) 73.2013 3.03429
\(583\) −42.8115 −1.77307
\(584\) 66.4917 2.75145
\(585\) −18.7040 −0.773316
\(586\) 15.9901 0.660546
\(587\) −42.5550 −1.75643 −0.878217 0.478262i \(-0.841267\pi\)
−0.878217 + 0.478262i \(0.841267\pi\)
\(588\) −63.8830 −2.63449
\(589\) 0.503386 0.0207417
\(590\) −30.1712 −1.24213
\(591\) 50.4126 2.07370
\(592\) 58.4131 2.40076
\(593\) −43.6727 −1.79342 −0.896711 0.442617i \(-0.854050\pi\)
−0.896711 + 0.442617i \(0.854050\pi\)
\(594\) 166.027 6.81218
\(595\) 13.6811 0.560871
\(596\) −57.4014 −2.35125
\(597\) −54.3658 −2.22504
\(598\) −3.69923 −0.151273
\(599\) −17.4443 −0.712755 −0.356377 0.934342i \(-0.615988\pi\)
−0.356377 + 0.934342i \(0.615988\pi\)
\(600\) 21.2291 0.866674
\(601\) −34.3766 −1.40225 −0.701125 0.713039i \(-0.747318\pi\)
−0.701125 + 0.713039i \(0.747318\pi\)
\(602\) −17.6128 −0.717845
\(603\) 42.5180 1.73147
\(604\) −20.0614 −0.816286
\(605\) −20.8378 −0.847179
\(606\) 46.5412 1.89061
\(607\) −39.9912 −1.62319 −0.811596 0.584220i \(-0.801401\pi\)
−0.811596 + 0.584220i \(0.801401\pi\)
\(608\) −17.5269 −0.710809
\(609\) 24.3739 0.987682
\(610\) −35.5573 −1.43967
\(611\) 2.03892 0.0824857
\(612\) 54.3496 2.19695
\(613\) 33.3161 1.34563 0.672813 0.739813i \(-0.265086\pi\)
0.672813 + 0.739813i \(0.265086\pi\)
\(614\) −23.9488 −0.966496
\(615\) 17.7281 0.714865
\(616\) 89.8382 3.61968
\(617\) −5.20072 −0.209373 −0.104687 0.994505i \(-0.533384\pi\)
−0.104687 + 0.994505i \(0.533384\pi\)
\(618\) 26.5027 1.06610
\(619\) 1.00000 0.0401934
\(620\) −1.30481 −0.0524024
\(621\) −21.8294 −0.875983
\(622\) −54.8242 −2.19825
\(623\) 54.7062 2.19176
\(624\) −20.8995 −0.836650
\(625\) −29.2493 −1.16997
\(626\) −85.2951 −3.40908
\(627\) −59.7989 −2.38814
\(628\) −62.9721 −2.51286
\(629\) 14.8796 0.593289
\(630\) −160.098 −6.37844
\(631\) −3.51758 −0.140033 −0.0700163 0.997546i \(-0.522305\pi\)
−0.0700163 + 0.997546i \(0.522305\pi\)
\(632\) −46.0229 −1.83069
\(633\) 18.0971 0.719297
\(634\) −39.8634 −1.58318
\(635\) −39.7787 −1.57857
\(636\) 138.324 5.48490
\(637\) 4.48356 0.177645
\(638\) −24.6287 −0.975059
\(639\) −62.4371 −2.46997
\(640\) −34.6344 −1.36904
\(641\) −9.75926 −0.385468 −0.192734 0.981251i \(-0.561735\pi\)
−0.192734 + 0.981251i \(0.561735\pi\)
\(642\) −69.7475 −2.75271
\(643\) −44.7857 −1.76618 −0.883088 0.469208i \(-0.844540\pi\)
−0.883088 + 0.469208i \(0.844540\pi\)
\(644\) −21.7378 −0.856591
\(645\) −16.5125 −0.650180
\(646\) −17.2317 −0.677971
\(647\) 34.1283 1.34172 0.670860 0.741584i \(-0.265925\pi\)
0.670860 + 0.741584i \(0.265925\pi\)
\(648\) −154.747 −6.07903
\(649\) −21.3529 −0.838176
\(650\) −2.74197 −0.107549
\(651\) 1.33119 0.0521736
\(652\) −62.5839 −2.45098
\(653\) −15.2619 −0.597244 −0.298622 0.954371i \(-0.596527\pi\)
−0.298622 + 0.954371i \(0.596527\pi\)
\(654\) −15.1175 −0.591141
\(655\) 32.5980 1.27371
\(656\) 14.1932 0.554150
\(657\) −83.8602 −3.27170
\(658\) 17.4522 0.680356
\(659\) −23.6298 −0.920487 −0.460243 0.887793i \(-0.652238\pi\)
−0.460243 + 0.887793i \(0.652238\pi\)
\(660\) 155.003 6.03347
\(661\) 3.33121 0.129569 0.0647845 0.997899i \(-0.479364\pi\)
0.0647845 + 0.997899i \(0.479364\pi\)
\(662\) −59.9035 −2.32822
\(663\) −5.32375 −0.206757
\(664\) −10.0949 −0.391757
\(665\) 34.8474 1.35132
\(666\) −174.123 −6.74711
\(667\) 3.23820 0.125383
\(668\) 13.8281 0.535027
\(669\) 71.0195 2.74577
\(670\) 34.9422 1.34993
\(671\) −25.1648 −0.971476
\(672\) −46.3495 −1.78797
\(673\) 22.2686 0.858392 0.429196 0.903211i \(-0.358797\pi\)
0.429196 + 0.903211i \(0.358797\pi\)
\(674\) −68.9283 −2.65502
\(675\) −16.1805 −0.622788
\(676\) 4.38004 0.168463
\(677\) 12.3002 0.472734 0.236367 0.971664i \(-0.424043\pi\)
0.236367 + 0.971664i \(0.424043\pi\)
\(678\) −15.7022 −0.603041
\(679\) −30.1899 −1.15858
\(680\) 24.2706 0.930733
\(681\) −5.56329 −0.213186
\(682\) −1.34511 −0.0515068
\(683\) 19.3669 0.741053 0.370526 0.928822i \(-0.379177\pi\)
0.370526 + 0.928822i \(0.379177\pi\)
\(684\) 138.435 5.29319
\(685\) −26.0372 −0.994829
\(686\) −21.5396 −0.822385
\(687\) −68.0073 −2.59464
\(688\) −13.2200 −0.504007
\(689\) −9.70810 −0.369849
\(690\) −29.6856 −1.13011
\(691\) −20.5961 −0.783513 −0.391756 0.920069i \(-0.628132\pi\)
−0.391756 + 0.920069i \(0.628132\pi\)
\(692\) −80.5300 −3.06129
\(693\) −113.305 −4.30411
\(694\) 46.4240 1.76223
\(695\) −34.2586 −1.29950
\(696\) 43.2398 1.63900
\(697\) 3.61543 0.136944
\(698\) 16.0253 0.606568
\(699\) 71.4583 2.70280
\(700\) −16.1127 −0.609001
\(701\) −34.5345 −1.30435 −0.652175 0.758069i \(-0.726143\pi\)
−0.652175 + 0.758069i \(0.726143\pi\)
\(702\) 37.6490 1.42097
\(703\) 37.9001 1.42943
\(704\) −9.83023 −0.370491
\(705\) 16.3619 0.616225
\(706\) 34.4562 1.29678
\(707\) −19.1946 −0.721887
\(708\) 68.9912 2.59285
\(709\) 12.6790 0.476168 0.238084 0.971245i \(-0.423481\pi\)
0.238084 + 0.971245i \(0.423481\pi\)
\(710\) −51.3121 −1.92571
\(711\) 58.0447 2.17685
\(712\) 97.0499 3.63710
\(713\) 0.176856 0.00662329
\(714\) −45.5688 −1.70537
\(715\) −10.8787 −0.406840
\(716\) 68.4939 2.55974
\(717\) −2.73124 −0.102000
\(718\) −56.6000 −2.11229
\(719\) −39.4697 −1.47197 −0.735986 0.676997i \(-0.763281\pi\)
−0.735986 + 0.676997i \(0.763281\pi\)
\(720\) −120.167 −4.47838
\(721\) −10.9303 −0.407066
\(722\) 4.10055 0.152607
\(723\) −62.1105 −2.30991
\(724\) −71.0737 −2.64143
\(725\) 2.40024 0.0891426
\(726\) 69.4063 2.57591
\(727\) 1.45149 0.0538327 0.0269164 0.999638i \(-0.491431\pi\)
0.0269164 + 0.999638i \(0.491431\pi\)
\(728\) 20.3720 0.755038
\(729\) 49.7076 1.84102
\(730\) −68.9180 −2.55077
\(731\) −3.36754 −0.124553
\(732\) 81.3073 3.00521
\(733\) 1.84156 0.0680196 0.0340098 0.999421i \(-0.489172\pi\)
0.0340098 + 0.999421i \(0.489172\pi\)
\(734\) 80.5807 2.97429
\(735\) 35.9796 1.32713
\(736\) −6.15775 −0.226978
\(737\) 24.7294 0.910921
\(738\) −42.3081 −1.55738
\(739\) 15.1247 0.556371 0.278186 0.960527i \(-0.410267\pi\)
0.278186 + 0.960527i \(0.410267\pi\)
\(740\) −98.2396 −3.61136
\(741\) −13.5602 −0.498147
\(742\) −83.0968 −3.05058
\(743\) 18.6613 0.684617 0.342309 0.939588i \(-0.388791\pi\)
0.342309 + 0.939588i \(0.388791\pi\)
\(744\) 2.36156 0.0865791
\(745\) 32.3291 1.18445
\(746\) −80.3622 −2.94227
\(747\) 12.7318 0.465832
\(748\) 31.6110 1.15581
\(749\) 28.7654 1.05107
\(750\) 79.3445 2.89725
\(751\) 27.9338 1.01932 0.509659 0.860377i \(-0.329772\pi\)
0.509659 + 0.860377i \(0.329772\pi\)
\(752\) 13.0994 0.477686
\(753\) 24.9418 0.908929
\(754\) −5.58490 −0.203390
\(755\) 11.2988 0.411206
\(756\) 221.237 8.04632
\(757\) −20.7823 −0.755346 −0.377673 0.925939i \(-0.623276\pi\)
−0.377673 + 0.925939i \(0.623276\pi\)
\(758\) −30.4053 −1.10437
\(759\) −21.0092 −0.762587
\(760\) 61.8200 2.24245
\(761\) 33.1746 1.20258 0.601290 0.799031i \(-0.294654\pi\)
0.601290 + 0.799031i \(0.294654\pi\)
\(762\) 132.494 4.79976
\(763\) 6.23479 0.225715
\(764\) 57.5268 2.08125
\(765\) −30.6103 −1.10672
\(766\) 3.26378 0.117925
\(767\) −4.84207 −0.174837
\(768\) 100.857 3.63935
\(769\) 11.9381 0.430497 0.215249 0.976559i \(-0.430944\pi\)
0.215249 + 0.976559i \(0.430944\pi\)
\(770\) −93.1164 −3.35568
\(771\) 45.8356 1.65073
\(772\) −25.9615 −0.934377
\(773\) 36.8151 1.32415 0.662074 0.749438i \(-0.269676\pi\)
0.662074 + 0.749438i \(0.269676\pi\)
\(774\) 39.4072 1.41646
\(775\) 0.131090 0.00470889
\(776\) −53.5574 −1.92260
\(777\) 100.226 3.59559
\(778\) −27.6413 −0.990989
\(779\) 9.20894 0.329944
\(780\) 35.1490 1.25854
\(781\) −36.3148 −1.29945
\(782\) −6.05403 −0.216492
\(783\) −32.9568 −1.17778
\(784\) 28.8054 1.02877
\(785\) 35.4666 1.26586
\(786\) −108.577 −3.87281
\(787\) −49.7745 −1.77427 −0.887135 0.461510i \(-0.847308\pi\)
−0.887135 + 0.461510i \(0.847308\pi\)
\(788\) −67.8786 −2.41808
\(789\) 6.55530 0.233375
\(790\) 47.7023 1.69717
\(791\) 6.47595 0.230258
\(792\) −201.005 −7.14242
\(793\) −5.70646 −0.202643
\(794\) −95.7868 −3.39935
\(795\) −77.9056 −2.76303
\(796\) 73.2015 2.59456
\(797\) −1.29914 −0.0460177 −0.0230089 0.999735i \(-0.507325\pi\)
−0.0230089 + 0.999735i \(0.507325\pi\)
\(798\) −116.069 −4.10880
\(799\) 3.33682 0.118048
\(800\) −4.56429 −0.161372
\(801\) −122.401 −4.32481
\(802\) 75.4507 2.66426
\(803\) −48.7750 −1.72123
\(804\) −79.9007 −2.81788
\(805\) 12.2430 0.431509
\(806\) −0.305022 −0.0107439
\(807\) 13.5029 0.475325
\(808\) −34.0516 −1.19793
\(809\) −16.1240 −0.566888 −0.283444 0.958989i \(-0.591477\pi\)
−0.283444 + 0.958989i \(0.591477\pi\)
\(810\) 160.394 5.63566
\(811\) 28.6228 1.00508 0.502541 0.864553i \(-0.332399\pi\)
0.502541 + 0.864553i \(0.332399\pi\)
\(812\) −32.8186 −1.15171
\(813\) −59.0044 −2.06938
\(814\) −101.274 −3.54964
\(815\) 35.2480 1.23468
\(816\) −34.2034 −1.19736
\(817\) −8.57751 −0.300089
\(818\) 11.4596 0.400677
\(819\) −25.6935 −0.897803
\(820\) −23.8702 −0.833583
\(821\) 5.53525 0.193182 0.0965908 0.995324i \(-0.469206\pi\)
0.0965908 + 0.995324i \(0.469206\pi\)
\(822\) 86.7241 3.02485
\(823\) 37.7630 1.31634 0.658168 0.752871i \(-0.271331\pi\)
0.658168 + 0.752871i \(0.271331\pi\)
\(824\) −19.3906 −0.675503
\(825\) −15.5726 −0.542169
\(826\) −41.4458 −1.44209
\(827\) 50.2629 1.74781 0.873906 0.486095i \(-0.161579\pi\)
0.873906 + 0.486095i \(0.161579\pi\)
\(828\) 48.6366 1.69024
\(829\) −8.09939 −0.281303 −0.140652 0.990059i \(-0.544920\pi\)
−0.140652 + 0.990059i \(0.544920\pi\)
\(830\) 10.4633 0.363185
\(831\) 0.0753930 0.00261535
\(832\) −2.22914 −0.0772816
\(833\) 7.33763 0.254234
\(834\) 114.108 3.95123
\(835\) −7.78817 −0.269521
\(836\) 80.5169 2.78473
\(837\) −1.79995 −0.0622154
\(838\) 87.9089 3.03676
\(839\) 14.5271 0.501530 0.250765 0.968048i \(-0.419318\pi\)
0.250765 + 0.968048i \(0.419318\pi\)
\(840\) 163.482 5.64065
\(841\) −24.1112 −0.831419
\(842\) −21.2291 −0.731602
\(843\) 1.04603 0.0360271
\(844\) −24.3671 −0.838751
\(845\) −2.46689 −0.0848636
\(846\) −39.0478 −1.34249
\(847\) −28.6247 −0.983556
\(848\) −62.3715 −2.14185
\(849\) −48.0794 −1.65008
\(850\) −4.48741 −0.153917
\(851\) 13.3155 0.456450
\(852\) 117.333 4.01976
\(853\) 1.67049 0.0571966 0.0285983 0.999591i \(-0.490896\pi\)
0.0285983 + 0.999591i \(0.490896\pi\)
\(854\) −48.8447 −1.67143
\(855\) −77.9681 −2.66645
\(856\) 51.0304 1.74418
\(857\) −17.6379 −0.602500 −0.301250 0.953545i \(-0.597404\pi\)
−0.301250 + 0.953545i \(0.597404\pi\)
\(858\) 36.2345 1.23703
\(859\) −17.0412 −0.581437 −0.290719 0.956809i \(-0.593894\pi\)
−0.290719 + 0.956809i \(0.593894\pi\)
\(860\) 22.2335 0.758155
\(861\) 24.3528 0.829943
\(862\) 2.40950 0.0820681
\(863\) 49.6007 1.68843 0.844214 0.536006i \(-0.180068\pi\)
0.844214 + 0.536006i \(0.180068\pi\)
\(864\) 62.6706 2.13210
\(865\) 45.3555 1.54213
\(866\) 44.7911 1.52206
\(867\) 46.5884 1.58222
\(868\) −1.79240 −0.0608381
\(869\) 33.7601 1.14523
\(870\) −44.8177 −1.51946
\(871\) 5.60774 0.190011
\(872\) 11.0606 0.374561
\(873\) 67.5473 2.28613
\(874\) −15.4203 −0.521601
\(875\) −32.7234 −1.10625
\(876\) 157.592 5.32453
\(877\) −18.3764 −0.620527 −0.310264 0.950651i \(-0.600417\pi\)
−0.310264 + 0.950651i \(0.600417\pi\)
\(878\) 87.3457 2.94778
\(879\) 20.5932 0.694592
\(880\) −69.8921 −2.35606
\(881\) −44.8623 −1.51145 −0.755724 0.654890i \(-0.772715\pi\)
−0.755724 + 0.654890i \(0.772715\pi\)
\(882\) −85.8656 −2.89125
\(883\) 50.0351 1.68382 0.841908 0.539621i \(-0.181432\pi\)
0.841908 + 0.539621i \(0.181432\pi\)
\(884\) 7.16822 0.241093
\(885\) −38.8566 −1.30615
\(886\) 14.8673 0.499475
\(887\) 48.8566 1.64044 0.820221 0.572046i \(-0.193850\pi\)
0.820221 + 0.572046i \(0.193850\pi\)
\(888\) 177.803 5.96668
\(889\) −54.6436 −1.83269
\(890\) −100.591 −3.37183
\(891\) 113.515 3.80288
\(892\) −95.6250 −3.20176
\(893\) 8.49927 0.284417
\(894\) −107.681 −3.60140
\(895\) −38.5765 −1.28947
\(896\) −47.5768 −1.58943
\(897\) −4.76414 −0.159070
\(898\) −78.5653 −2.62176
\(899\) 0.267007 0.00890517
\(900\) 36.0507 1.20169
\(901\) −15.8879 −0.529304
\(902\) −24.6074 −0.819336
\(903\) −22.6831 −0.754845
\(904\) 11.4885 0.382100
\(905\) 40.0296 1.33063
\(906\) −37.6338 −1.25030
\(907\) 38.7907 1.28802 0.644012 0.765016i \(-0.277269\pi\)
0.644012 + 0.765016i \(0.277269\pi\)
\(908\) 7.49076 0.248590
\(909\) 42.9463 1.42444
\(910\) −21.1154 −0.699970
\(911\) −12.7878 −0.423680 −0.211840 0.977304i \(-0.567946\pi\)
−0.211840 + 0.977304i \(0.567946\pi\)
\(912\) −87.1201 −2.88484
\(913\) 7.40510 0.245073
\(914\) 92.3847 3.05581
\(915\) −45.7932 −1.51388
\(916\) 91.5693 3.02553
\(917\) 44.7795 1.47875
\(918\) 61.6150 2.03360
\(919\) −13.1655 −0.434290 −0.217145 0.976139i \(-0.569674\pi\)
−0.217145 + 0.976139i \(0.569674\pi\)
\(920\) 21.7193 0.716065
\(921\) −30.8430 −1.01631
\(922\) 26.6655 0.878183
\(923\) −8.23489 −0.271055
\(924\) 212.925 7.00473
\(925\) 9.86981 0.324517
\(926\) −6.54943 −0.215228
\(927\) 24.4557 0.803229
\(928\) −9.29663 −0.305177
\(929\) −31.3068 −1.02714 −0.513571 0.858047i \(-0.671678\pi\)
−0.513571 + 0.858047i \(0.671678\pi\)
\(930\) −2.44774 −0.0802645
\(931\) 18.6898 0.612534
\(932\) −96.2158 −3.15165
\(933\) −70.6065 −2.31155
\(934\) 19.5931 0.641105
\(935\) −17.8037 −0.582242
\(936\) −45.5808 −1.48985
\(937\) −1.79387 −0.0586031 −0.0293015 0.999571i \(-0.509328\pi\)
−0.0293015 + 0.999571i \(0.509328\pi\)
\(938\) 47.9996 1.56724
\(939\) −109.849 −3.58479
\(940\) −22.0307 −0.718561
\(941\) −38.5341 −1.25617 −0.628087 0.778143i \(-0.716162\pi\)
−0.628087 + 0.778143i \(0.716162\pi\)
\(942\) −118.132 −3.84894
\(943\) 3.23539 0.105359
\(944\) −31.1088 −1.01250
\(945\) −124.603 −4.05335
\(946\) 22.9201 0.745198
\(947\) 44.8393 1.45708 0.728541 0.685002i \(-0.240199\pi\)
0.728541 + 0.685002i \(0.240199\pi\)
\(948\) −109.079 −3.54272
\(949\) −11.0604 −0.359036
\(950\) −11.4300 −0.370837
\(951\) −51.3389 −1.66478
\(952\) 33.3402 1.08056
\(953\) −17.1480 −0.555480 −0.277740 0.960656i \(-0.589585\pi\)
−0.277740 + 0.960656i \(0.589585\pi\)
\(954\) 185.922 6.01945
\(955\) −32.3998 −1.04843
\(956\) 3.67751 0.118939
\(957\) −31.7186 −1.02532
\(958\) 23.0453 0.744558
\(959\) −35.7670 −1.15498
\(960\) −17.8884 −0.577346
\(961\) −30.9854 −0.999530
\(962\) −22.9652 −0.740427
\(963\) −64.3602 −2.07398
\(964\) 83.6294 2.69352
\(965\) 14.6218 0.470694
\(966\) −40.7788 −1.31204
\(967\) −1.81842 −0.0584764 −0.0292382 0.999572i \(-0.509308\pi\)
−0.0292382 + 0.999572i \(0.509308\pi\)
\(968\) −50.7808 −1.63216
\(969\) −22.1922 −0.712915
\(970\) 55.5117 1.78237
\(971\) 52.4539 1.68333 0.841664 0.540002i \(-0.181577\pi\)
0.841664 + 0.540002i \(0.181577\pi\)
\(972\) −170.907 −5.48185
\(973\) −47.0606 −1.50869
\(974\) −72.0487 −2.30859
\(975\) −3.53130 −0.113092
\(976\) −36.6623 −1.17353
\(977\) −42.3402 −1.35458 −0.677292 0.735714i \(-0.736847\pi\)
−0.677292 + 0.735714i \(0.736847\pi\)
\(978\) −117.403 −3.75415
\(979\) −71.1910 −2.27527
\(980\) −48.4452 −1.54753
\(981\) −13.9498 −0.445384
\(982\) −30.3474 −0.968424
\(983\) 45.4109 1.44838 0.724192 0.689598i \(-0.242213\pi\)
0.724192 + 0.689598i \(0.242213\pi\)
\(984\) 43.2024 1.37724
\(985\) 38.2300 1.21811
\(986\) −9.14004 −0.291078
\(987\) 22.4762 0.715424
\(988\) 18.2583 0.580874
\(989\) −3.01355 −0.0958254
\(990\) 208.340 6.62149
\(991\) 29.8715 0.948900 0.474450 0.880283i \(-0.342647\pi\)
0.474450 + 0.880283i \(0.342647\pi\)
\(992\) −0.507740 −0.0161208
\(993\) −77.1481 −2.44822
\(994\) −70.4868 −2.23571
\(995\) −41.2279 −1.30701
\(996\) −23.9259 −0.758120
\(997\) −38.9231 −1.23271 −0.616353 0.787470i \(-0.711390\pi\)
−0.616353 + 0.787470i \(0.711390\pi\)
\(998\) −46.8170 −1.48197
\(999\) −135.519 −4.28763
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 \(a_p\))