Properties

Label 8047.2.a.b.1.6
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 1.6
Character \(\chi\) = 8047.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.65986 q^{2} -2.58294 q^{3} +5.07483 q^{4} +0.599360 q^{5} +6.87024 q^{6} -3.90786 q^{7} -8.17861 q^{8} +3.67156 q^{9} +O(q^{10})\) \(q-2.65986 q^{2} -2.58294 q^{3} +5.07483 q^{4} +0.599360 q^{5} +6.87024 q^{6} -3.90786 q^{7} -8.17861 q^{8} +3.67156 q^{9} -1.59421 q^{10} -2.24374 q^{11} -13.1080 q^{12} +1.00000 q^{13} +10.3944 q^{14} -1.54811 q^{15} +11.6043 q^{16} -5.38716 q^{17} -9.76583 q^{18} -1.97118 q^{19} +3.04165 q^{20} +10.0938 q^{21} +5.96803 q^{22} +6.80240 q^{23} +21.1248 q^{24} -4.64077 q^{25} -2.65986 q^{26} -1.73460 q^{27} -19.8317 q^{28} -10.4559 q^{29} +4.11774 q^{30} +1.00433 q^{31} -14.5084 q^{32} +5.79545 q^{33} +14.3291 q^{34} -2.34222 q^{35} +18.6326 q^{36} -0.135048 q^{37} +5.24305 q^{38} -2.58294 q^{39} -4.90193 q^{40} +10.9084 q^{41} -26.8479 q^{42} -2.44326 q^{43} -11.3866 q^{44} +2.20059 q^{45} -18.0934 q^{46} -7.37674 q^{47} -29.9731 q^{48} +8.27139 q^{49} +12.3438 q^{50} +13.9147 q^{51} +5.07483 q^{52} -13.0609 q^{53} +4.61379 q^{54} -1.34481 q^{55} +31.9609 q^{56} +5.09143 q^{57} +27.8112 q^{58} +5.66496 q^{59} -7.85639 q^{60} +14.3580 q^{61} -2.67138 q^{62} -14.3480 q^{63} +15.3818 q^{64} +0.599360 q^{65} -15.4151 q^{66} -8.28360 q^{67} -27.3390 q^{68} -17.5702 q^{69} +6.22995 q^{70} +5.77090 q^{71} -30.0283 q^{72} +11.5264 q^{73} +0.359209 q^{74} +11.9868 q^{75} -10.0034 q^{76} +8.76824 q^{77} +6.87024 q^{78} +2.74018 q^{79} +6.95512 q^{80} -6.53432 q^{81} -29.0147 q^{82} +9.98586 q^{83} +51.2241 q^{84} -3.22885 q^{85} +6.49872 q^{86} +27.0069 q^{87} +18.3507 q^{88} +0.0258145 q^{89} -5.85324 q^{90} -3.90786 q^{91} +34.5210 q^{92} -2.59413 q^{93} +19.6211 q^{94} -1.18144 q^{95} +37.4744 q^{96} -8.17149 q^{97} -22.0007 q^{98} -8.23805 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} + O(q^{10}) \) \( 142q - 13q^{2} - 26q^{3} + 129q^{4} - 37q^{5} - 15q^{6} - 14q^{7} - 39q^{8} + 98q^{9} - 25q^{10} - 25q^{11} - 62q^{12} + 142q^{13} - 57q^{14} - 14q^{15} + 111q^{16} - 141q^{17} - 29q^{18} - 3q^{19} - 87q^{20} - 19q^{21} - 24q^{22} - 69q^{23} - 40q^{24} + 87q^{25} - 13q^{26} - 95q^{27} - 34q^{28} - 147q^{29} - 2q^{30} - 21q^{31} - 66q^{32} - 62q^{33} - 6q^{34} - 59q^{35} + 74q^{36} - 37q^{37} - 76q^{38} - 26q^{39} - 61q^{40} - 97q^{41} - 29q^{42} - 33q^{43} - 57q^{44} - 86q^{45} - q^{46} - 102q^{47} - 141q^{48} + 70q^{49} - 28q^{50} - 13q^{51} + 129q^{52} - 137q^{53} - 29q^{54} - 24q^{55} - 130q^{56} - 65q^{57} - 15q^{58} - 56q^{59} + 11q^{60} - 77q^{61} - 150q^{62} - 32q^{63} + 73q^{64} - 37q^{65} - 32q^{66} - 9q^{67} - 226q^{68} - 113q^{69} + 6q^{70} - 18q^{71} - 82q^{72} - 117q^{73} - 70q^{74} - 83q^{75} + 40q^{76} - 214q^{77} - 15q^{78} - 52q^{79} - 161q^{80} - 10q^{81} - 36q^{82} - 74q^{83} + 53q^{84} + 2q^{85} + 17q^{86} - 49q^{87} - 29q^{88} - 171q^{89} - 57q^{90} - 14q^{91} - 187q^{92} - 39q^{93} + 13q^{94} - 150q^{95} - 47q^{96} - 126q^{97} - 85q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.65986 −1.88080 −0.940401 0.340068i \(-0.889550\pi\)
−0.940401 + 0.340068i \(0.889550\pi\)
\(3\) −2.58294 −1.49126 −0.745630 0.666361i \(-0.767851\pi\)
−0.745630 + 0.666361i \(0.767851\pi\)
\(4\) 5.07483 2.53742
\(5\) 0.599360 0.268042 0.134021 0.990979i \(-0.457211\pi\)
0.134021 + 0.990979i \(0.457211\pi\)
\(6\) 6.87024 2.80476
\(7\) −3.90786 −1.47703 −0.738517 0.674235i \(-0.764473\pi\)
−0.738517 + 0.674235i \(0.764473\pi\)
\(8\) −8.17861 −2.89158
\(9\) 3.67156 1.22385
\(10\) −1.59421 −0.504134
\(11\) −2.24374 −0.676514 −0.338257 0.941054i \(-0.609837\pi\)
−0.338257 + 0.941054i \(0.609837\pi\)
\(12\) −13.1080 −3.78395
\(13\) 1.00000 0.277350
\(14\) 10.3944 2.77801
\(15\) −1.54811 −0.399720
\(16\) 11.6043 2.90106
\(17\) −5.38716 −1.30658 −0.653290 0.757108i \(-0.726612\pi\)
−0.653290 + 0.757108i \(0.726612\pi\)
\(18\) −9.76583 −2.30183
\(19\) −1.97118 −0.452219 −0.226110 0.974102i \(-0.572601\pi\)
−0.226110 + 0.974102i \(0.572601\pi\)
\(20\) 3.04165 0.680134
\(21\) 10.0938 2.20264
\(22\) 5.96803 1.27239
\(23\) 6.80240 1.41840 0.709199 0.705008i \(-0.249057\pi\)
0.709199 + 0.705008i \(0.249057\pi\)
\(24\) 21.1248 4.31209
\(25\) −4.64077 −0.928154
\(26\) −2.65986 −0.521641
\(27\) −1.73460 −0.333825
\(28\) −19.8317 −3.74785
\(29\) −10.4559 −1.94161 −0.970807 0.239863i \(-0.922897\pi\)
−0.970807 + 0.239863i \(0.922897\pi\)
\(30\) 4.11774 0.751794
\(31\) 1.00433 0.180383 0.0901917 0.995924i \(-0.471252\pi\)
0.0901917 + 0.995924i \(0.471252\pi\)
\(32\) −14.5084 −2.56475
\(33\) 5.79545 1.00886
\(34\) 14.3291 2.45742
\(35\) −2.34222 −0.395907
\(36\) 18.6326 3.10543
\(37\) −0.135048 −0.0222018 −0.0111009 0.999938i \(-0.503534\pi\)
−0.0111009 + 0.999938i \(0.503534\pi\)
\(38\) 5.24305 0.850535
\(39\) −2.58294 −0.413601
\(40\) −4.90193 −0.775063
\(41\) 10.9084 1.70360 0.851802 0.523863i \(-0.175510\pi\)
0.851802 + 0.523863i \(0.175510\pi\)
\(42\) −26.8479 −4.14273
\(43\) −2.44326 −0.372594 −0.186297 0.982493i \(-0.559649\pi\)
−0.186297 + 0.982493i \(0.559649\pi\)
\(44\) −11.3866 −1.71660
\(45\) 2.20059 0.328044
\(46\) −18.0934 −2.66773
\(47\) −7.37674 −1.07601 −0.538004 0.842942i \(-0.680821\pi\)
−0.538004 + 0.842942i \(0.680821\pi\)
\(48\) −29.9731 −4.32624
\(49\) 8.27139 1.18163
\(50\) 12.3438 1.74567
\(51\) 13.9147 1.94845
\(52\) 5.07483 0.703753
\(53\) −13.0609 −1.79405 −0.897027 0.441976i \(-0.854278\pi\)
−0.897027 + 0.441976i \(0.854278\pi\)
\(54\) 4.61379 0.627858
\(55\) −1.34481 −0.181334
\(56\) 31.9609 4.27095
\(57\) 5.09143 0.674376
\(58\) 27.8112 3.65179
\(59\) 5.66496 0.737514 0.368757 0.929526i \(-0.379783\pi\)
0.368757 + 0.929526i \(0.379783\pi\)
\(60\) −7.85639 −1.01426
\(61\) 14.3580 1.83836 0.919178 0.393843i \(-0.128855\pi\)
0.919178 + 0.393843i \(0.128855\pi\)
\(62\) −2.67138 −0.339265
\(63\) −14.3480 −1.80767
\(64\) 15.3818 1.92273
\(65\) 0.599360 0.0743414
\(66\) −15.4151 −1.89746
\(67\) −8.28360 −1.01200 −0.506001 0.862533i \(-0.668877\pi\)
−0.506001 + 0.862533i \(0.668877\pi\)
\(68\) −27.3390 −3.31533
\(69\) −17.5702 −2.11520
\(70\) 6.22995 0.744622
\(71\) 5.77090 0.684880 0.342440 0.939540i \(-0.388747\pi\)
0.342440 + 0.939540i \(0.388747\pi\)
\(72\) −30.0283 −3.53887
\(73\) 11.5264 1.34906 0.674532 0.738246i \(-0.264345\pi\)
0.674532 + 0.738246i \(0.264345\pi\)
\(74\) 0.359209 0.0417572
\(75\) 11.9868 1.38412
\(76\) −10.0034 −1.14747
\(77\) 8.76824 0.999234
\(78\) 6.87024 0.777901
\(79\) 2.74018 0.308295 0.154147 0.988048i \(-0.450737\pi\)
0.154147 + 0.988048i \(0.450737\pi\)
\(80\) 6.95512 0.777607
\(81\) −6.53432 −0.726035
\(82\) −29.0147 −3.20414
\(83\) 9.98586 1.09609 0.548045 0.836449i \(-0.315372\pi\)
0.548045 + 0.836449i \(0.315372\pi\)
\(84\) 51.2241 5.58901
\(85\) −3.22885 −0.350218
\(86\) 6.49872 0.700775
\(87\) 27.0069 2.89545
\(88\) 18.3507 1.95619
\(89\) 0.0258145 0.00273633 0.00136817 0.999999i \(-0.499564\pi\)
0.00136817 + 0.999999i \(0.499564\pi\)
\(90\) −5.85324 −0.616986
\(91\) −3.90786 −0.409655
\(92\) 34.5210 3.59907
\(93\) −2.59413 −0.268998
\(94\) 19.6211 2.02376
\(95\) −1.18144 −0.121214
\(96\) 37.4744 3.82471
\(97\) −8.17149 −0.829689 −0.414844 0.909892i \(-0.636164\pi\)
−0.414844 + 0.909892i \(0.636164\pi\)
\(98\) −22.0007 −2.22241
\(99\) −8.23805 −0.827955
\(100\) −23.5511 −2.35511
\(101\) −7.92682 −0.788748 −0.394374 0.918950i \(-0.629039\pi\)
−0.394374 + 0.918950i \(0.629039\pi\)
\(102\) −37.0111 −3.66465
\(103\) 11.7750 1.16023 0.580115 0.814535i \(-0.303008\pi\)
0.580115 + 0.814535i \(0.303008\pi\)
\(104\) −8.17861 −0.801979
\(105\) 6.04979 0.590399
\(106\) 34.7401 3.37426
\(107\) 16.4407 1.58938 0.794691 0.607014i \(-0.207633\pi\)
0.794691 + 0.607014i \(0.207633\pi\)
\(108\) −8.80282 −0.847052
\(109\) 5.97978 0.572759 0.286380 0.958116i \(-0.407548\pi\)
0.286380 + 0.958116i \(0.407548\pi\)
\(110\) 3.57700 0.341054
\(111\) 0.348821 0.0331087
\(112\) −45.3478 −4.28497
\(113\) −5.83160 −0.548591 −0.274295 0.961645i \(-0.588445\pi\)
−0.274295 + 0.961645i \(0.588445\pi\)
\(114\) −13.5425 −1.26837
\(115\) 4.07708 0.380190
\(116\) −53.0620 −4.92668
\(117\) 3.67156 0.339436
\(118\) −15.0680 −1.38712
\(119\) 21.0523 1.92986
\(120\) 12.6614 1.15582
\(121\) −5.96561 −0.542329
\(122\) −38.1903 −3.45758
\(123\) −28.1757 −2.54052
\(124\) 5.09682 0.457708
\(125\) −5.77829 −0.516826
\(126\) 38.1635 3.39988
\(127\) −16.6031 −1.47329 −0.736645 0.676280i \(-0.763591\pi\)
−0.736645 + 0.676280i \(0.763591\pi\)
\(128\) −11.8966 −1.05152
\(129\) 6.31079 0.555634
\(130\) −1.59421 −0.139821
\(131\) 16.7024 1.45930 0.729649 0.683822i \(-0.239684\pi\)
0.729649 + 0.683822i \(0.239684\pi\)
\(132\) 29.4109 2.55989
\(133\) 7.70309 0.667943
\(134\) 22.0332 1.90338
\(135\) −1.03965 −0.0894789
\(136\) 44.0595 3.77807
\(137\) −16.7026 −1.42700 −0.713501 0.700654i \(-0.752892\pi\)
−0.713501 + 0.700654i \(0.752892\pi\)
\(138\) 46.7341 3.97827
\(139\) 9.09521 0.771446 0.385723 0.922615i \(-0.373952\pi\)
0.385723 + 0.922615i \(0.373952\pi\)
\(140\) −11.8863 −1.00458
\(141\) 19.0536 1.60461
\(142\) −15.3498 −1.28812
\(143\) −2.24374 −0.187631
\(144\) 42.6058 3.55048
\(145\) −6.26685 −0.520434
\(146\) −30.6586 −2.53732
\(147\) −21.3645 −1.76211
\(148\) −0.685348 −0.0563352
\(149\) −1.73566 −0.142191 −0.0710954 0.997470i \(-0.522649\pi\)
−0.0710954 + 0.997470i \(0.522649\pi\)
\(150\) −31.8832 −2.60325
\(151\) 23.5930 1.91997 0.959985 0.280051i \(-0.0903514\pi\)
0.959985 + 0.280051i \(0.0903514\pi\)
\(152\) 16.1215 1.30763
\(153\) −19.7793 −1.59906
\(154\) −23.3223 −1.87936
\(155\) 0.601956 0.0483503
\(156\) −13.1080 −1.04948
\(157\) −6.78825 −0.541761 −0.270881 0.962613i \(-0.587315\pi\)
−0.270881 + 0.962613i \(0.587315\pi\)
\(158\) −7.28849 −0.579841
\(159\) 33.7355 2.67540
\(160\) −8.69577 −0.687461
\(161\) −26.5828 −2.09502
\(162\) 17.3803 1.36553
\(163\) 13.1082 1.02671 0.513357 0.858175i \(-0.328402\pi\)
0.513357 + 0.858175i \(0.328402\pi\)
\(164\) 55.3583 4.32275
\(165\) 3.47356 0.270416
\(166\) −26.5609 −2.06153
\(167\) −24.3678 −1.88564 −0.942818 0.333309i \(-0.891835\pi\)
−0.942818 + 0.333309i \(0.891835\pi\)
\(168\) −82.5529 −6.36910
\(169\) 1.00000 0.0769231
\(170\) 8.58827 0.658690
\(171\) −7.23730 −0.553451
\(172\) −12.3991 −0.945425
\(173\) −10.4507 −0.794550 −0.397275 0.917700i \(-0.630044\pi\)
−0.397275 + 0.917700i \(0.630044\pi\)
\(174\) −71.8346 −5.44577
\(175\) 18.1355 1.37091
\(176\) −26.0370 −1.96261
\(177\) −14.6322 −1.09983
\(178\) −0.0686629 −0.00514650
\(179\) −17.1583 −1.28247 −0.641234 0.767345i \(-0.721577\pi\)
−0.641234 + 0.767345i \(0.721577\pi\)
\(180\) 11.1676 0.832384
\(181\) −1.00854 −0.0749641 −0.0374820 0.999297i \(-0.511934\pi\)
−0.0374820 + 0.999297i \(0.511934\pi\)
\(182\) 10.3944 0.770481
\(183\) −37.0858 −2.74146
\(184\) −55.6342 −4.10140
\(185\) −0.0809425 −0.00595101
\(186\) 6.90000 0.505933
\(187\) 12.0874 0.883919
\(188\) −37.4357 −2.73028
\(189\) 6.77859 0.493070
\(190\) 3.14247 0.227979
\(191\) −5.66617 −0.409990 −0.204995 0.978763i \(-0.565718\pi\)
−0.204995 + 0.978763i \(0.565718\pi\)
\(192\) −39.7303 −2.86729
\(193\) 14.9952 1.07938 0.539689 0.841864i \(-0.318542\pi\)
0.539689 + 0.841864i \(0.318542\pi\)
\(194\) 21.7350 1.56048
\(195\) −1.54811 −0.110862
\(196\) 41.9759 2.99828
\(197\) 0.365077 0.0260107 0.0130053 0.999915i \(-0.495860\pi\)
0.0130053 + 0.999915i \(0.495860\pi\)
\(198\) 21.9120 1.55722
\(199\) 5.47512 0.388121 0.194061 0.980990i \(-0.437834\pi\)
0.194061 + 0.980990i \(0.437834\pi\)
\(200\) 37.9550 2.68383
\(201\) 21.3960 1.50916
\(202\) 21.0842 1.48348
\(203\) 40.8602 2.86783
\(204\) 70.6148 4.94402
\(205\) 6.53805 0.456637
\(206\) −31.3199 −2.18216
\(207\) 24.9754 1.73591
\(208\) 11.6043 0.804611
\(209\) 4.42282 0.305933
\(210\) −16.0916 −1.11042
\(211\) 2.26944 0.156235 0.0781174 0.996944i \(-0.475109\pi\)
0.0781174 + 0.996944i \(0.475109\pi\)
\(212\) −66.2819 −4.55226
\(213\) −14.9059 −1.02133
\(214\) −43.7299 −2.98931
\(215\) −1.46439 −0.0998707
\(216\) 14.1866 0.965279
\(217\) −3.92479 −0.266432
\(218\) −15.9054 −1.07725
\(219\) −29.7720 −2.01180
\(220\) −6.82468 −0.460120
\(221\) −5.38716 −0.362380
\(222\) −0.927814 −0.0622708
\(223\) 17.1933 1.15135 0.575674 0.817679i \(-0.304740\pi\)
0.575674 + 0.817679i \(0.304740\pi\)
\(224\) 56.6970 3.78822
\(225\) −17.0389 −1.13592
\(226\) 15.5112 1.03179
\(227\) 20.2222 1.34219 0.671097 0.741370i \(-0.265824\pi\)
0.671097 + 0.741370i \(0.265824\pi\)
\(228\) 25.8382 1.71117
\(229\) 2.22853 0.147265 0.0736327 0.997285i \(-0.476541\pi\)
0.0736327 + 0.997285i \(0.476541\pi\)
\(230\) −10.8445 −0.715062
\(231\) −22.6478 −1.49012
\(232\) 85.5148 5.61432
\(233\) 5.14335 0.336952 0.168476 0.985706i \(-0.446115\pi\)
0.168476 + 0.985706i \(0.446115\pi\)
\(234\) −9.76583 −0.638412
\(235\) −4.42132 −0.288415
\(236\) 28.7487 1.87138
\(237\) −7.07772 −0.459747
\(238\) −55.9961 −3.62969
\(239\) 3.19761 0.206836 0.103418 0.994638i \(-0.467022\pi\)
0.103418 + 0.994638i \(0.467022\pi\)
\(240\) −17.9646 −1.15961
\(241\) −23.7720 −1.53129 −0.765644 0.643265i \(-0.777579\pi\)
−0.765644 + 0.643265i \(0.777579\pi\)
\(242\) 15.8677 1.02001
\(243\) 22.0815 1.41653
\(244\) 72.8645 4.66467
\(245\) 4.95754 0.316725
\(246\) 74.9433 4.77821
\(247\) −1.97118 −0.125423
\(248\) −8.21404 −0.521592
\(249\) −25.7928 −1.63456
\(250\) 15.3694 0.972047
\(251\) 10.7050 0.675694 0.337847 0.941201i \(-0.390301\pi\)
0.337847 + 0.941201i \(0.390301\pi\)
\(252\) −72.8135 −4.58682
\(253\) −15.2628 −0.959566
\(254\) 44.1619 2.77097
\(255\) 8.33991 0.522266
\(256\) 0.879483 0.0549677
\(257\) −26.2906 −1.63996 −0.819981 0.572390i \(-0.806016\pi\)
−0.819981 + 0.572390i \(0.806016\pi\)
\(258\) −16.7858 −1.04504
\(259\) 0.527750 0.0327928
\(260\) 3.04165 0.188635
\(261\) −38.3895 −2.37625
\(262\) −44.4260 −2.74465
\(263\) −21.2644 −1.31122 −0.655609 0.755101i \(-0.727588\pi\)
−0.655609 + 0.755101i \(0.727588\pi\)
\(264\) −47.3987 −2.91719
\(265\) −7.82818 −0.480881
\(266\) −20.4891 −1.25627
\(267\) −0.0666773 −0.00408058
\(268\) −42.0379 −2.56787
\(269\) 13.8465 0.844236 0.422118 0.906541i \(-0.361287\pi\)
0.422118 + 0.906541i \(0.361287\pi\)
\(270\) 2.76532 0.168292
\(271\) 3.69372 0.224377 0.112189 0.993687i \(-0.464214\pi\)
0.112189 + 0.993687i \(0.464214\pi\)
\(272\) −62.5140 −3.79047
\(273\) 10.0938 0.610902
\(274\) 44.4266 2.68391
\(275\) 10.4127 0.627909
\(276\) −89.1656 −5.36714
\(277\) 14.7473 0.886080 0.443040 0.896502i \(-0.353900\pi\)
0.443040 + 0.896502i \(0.353900\pi\)
\(278\) −24.1919 −1.45094
\(279\) 3.68747 0.220763
\(280\) 19.1561 1.14479
\(281\) 23.3895 1.39530 0.697651 0.716438i \(-0.254229\pi\)
0.697651 + 0.716438i \(0.254229\pi\)
\(282\) −50.6799 −3.01795
\(283\) −6.22626 −0.370113 −0.185056 0.982728i \(-0.559247\pi\)
−0.185056 + 0.982728i \(0.559247\pi\)
\(284\) 29.2864 1.73783
\(285\) 3.05160 0.180761
\(286\) 5.96803 0.352897
\(287\) −42.6285 −2.51628
\(288\) −53.2686 −3.13888
\(289\) 12.0215 0.707149
\(290\) 16.6689 0.978832
\(291\) 21.1064 1.23728
\(292\) 58.4946 3.42314
\(293\) 6.32713 0.369635 0.184818 0.982773i \(-0.440831\pi\)
0.184818 + 0.982773i \(0.440831\pi\)
\(294\) 56.8264 3.31418
\(295\) 3.39535 0.197685
\(296\) 1.10451 0.0641982
\(297\) 3.89201 0.225837
\(298\) 4.61661 0.267433
\(299\) 6.80240 0.393393
\(300\) 60.8311 3.51208
\(301\) 9.54793 0.550333
\(302\) −62.7539 −3.61108
\(303\) 20.4745 1.17623
\(304\) −22.8741 −1.31192
\(305\) 8.60562 0.492756
\(306\) 52.6101 3.00752
\(307\) 29.7130 1.69581 0.847906 0.530147i \(-0.177863\pi\)
0.847906 + 0.530147i \(0.177863\pi\)
\(308\) 44.4974 2.53547
\(309\) −30.4142 −1.73020
\(310\) −1.60112 −0.0909373
\(311\) 30.0465 1.70378 0.851891 0.523719i \(-0.175456\pi\)
0.851891 + 0.523719i \(0.175456\pi\)
\(312\) 21.1248 1.19596
\(313\) 23.2483 1.31407 0.657037 0.753858i \(-0.271809\pi\)
0.657037 + 0.753858i \(0.271809\pi\)
\(314\) 18.0558 1.01895
\(315\) −8.59959 −0.484532
\(316\) 13.9060 0.782272
\(317\) 14.6310 0.821761 0.410880 0.911689i \(-0.365221\pi\)
0.410880 + 0.911689i \(0.365221\pi\)
\(318\) −89.7316 −5.03190
\(319\) 23.4604 1.31353
\(320\) 9.21924 0.515371
\(321\) −42.4653 −2.37018
\(322\) 70.7065 3.94032
\(323\) 10.6191 0.590860
\(324\) −33.1606 −1.84225
\(325\) −4.64077 −0.257423
\(326\) −34.8659 −1.93105
\(327\) −15.4454 −0.854133
\(328\) −89.2155 −4.92610
\(329\) 28.8273 1.58930
\(330\) −9.23916 −0.508599
\(331\) −12.1120 −0.665734 −0.332867 0.942974i \(-0.608016\pi\)
−0.332867 + 0.942974i \(0.608016\pi\)
\(332\) 50.6766 2.78124
\(333\) −0.495838 −0.0271718
\(334\) 64.8148 3.54651
\(335\) −4.96486 −0.271259
\(336\) 117.131 6.39000
\(337\) 17.8256 0.971021 0.485511 0.874231i \(-0.338634\pi\)
0.485511 + 0.874231i \(0.338634\pi\)
\(338\) −2.65986 −0.144677
\(339\) 15.0627 0.818091
\(340\) −16.3859 −0.888648
\(341\) −2.25346 −0.122032
\(342\) 19.2502 1.04093
\(343\) −4.96841 −0.268269
\(344\) 19.9825 1.07738
\(345\) −10.5308 −0.566962
\(346\) 27.7973 1.49439
\(347\) −18.2641 −0.980467 −0.490234 0.871591i \(-0.663089\pi\)
−0.490234 + 0.871591i \(0.663089\pi\)
\(348\) 137.056 7.34696
\(349\) 20.9162 1.11962 0.559810 0.828621i \(-0.310874\pi\)
0.559810 + 0.828621i \(0.310874\pi\)
\(350\) −48.2378 −2.57842
\(351\) −1.73460 −0.0925863
\(352\) 32.5532 1.73509
\(353\) 19.4957 1.03765 0.518825 0.854881i \(-0.326370\pi\)
0.518825 + 0.854881i \(0.326370\pi\)
\(354\) 38.9196 2.06855
\(355\) 3.45885 0.183576
\(356\) 0.131004 0.00694322
\(357\) −54.3767 −2.87792
\(358\) 45.6385 2.41207
\(359\) 14.4743 0.763923 0.381961 0.924178i \(-0.375249\pi\)
0.381961 + 0.924178i \(0.375249\pi\)
\(360\) −17.9977 −0.948564
\(361\) −15.1145 −0.795498
\(362\) 2.68257 0.140993
\(363\) 15.4088 0.808752
\(364\) −19.8317 −1.03947
\(365\) 6.90847 0.361606
\(366\) 98.6430 5.15615
\(367\) 14.8002 0.772565 0.386282 0.922381i \(-0.373759\pi\)
0.386282 + 0.922381i \(0.373759\pi\)
\(368\) 78.9368 4.11486
\(369\) 40.0508 2.08496
\(370\) 0.215295 0.0111927
\(371\) 51.0402 2.64988
\(372\) −13.1648 −0.682561
\(373\) 27.0044 1.39823 0.699117 0.715008i \(-0.253577\pi\)
0.699117 + 0.715008i \(0.253577\pi\)
\(374\) −32.1508 −1.66248
\(375\) 14.9250 0.770721
\(376\) 60.3314 3.11136
\(377\) −10.4559 −0.538507
\(378\) −18.0301 −0.927367
\(379\) −12.6254 −0.648524 −0.324262 0.945967i \(-0.605116\pi\)
−0.324262 + 0.945967i \(0.605116\pi\)
\(380\) −5.99563 −0.307570
\(381\) 42.8848 2.19706
\(382\) 15.0712 0.771109
\(383\) 11.9853 0.612420 0.306210 0.951964i \(-0.400939\pi\)
0.306210 + 0.951964i \(0.400939\pi\)
\(384\) 30.7281 1.56808
\(385\) 5.25533 0.267836
\(386\) −39.8851 −2.03010
\(387\) −8.97058 −0.456000
\(388\) −41.4689 −2.10527
\(389\) −30.9272 −1.56807 −0.784036 0.620716i \(-0.786842\pi\)
−0.784036 + 0.620716i \(0.786842\pi\)
\(390\) 4.11774 0.208510
\(391\) −36.6456 −1.85325
\(392\) −67.6485 −3.41676
\(393\) −43.1413 −2.17619
\(394\) −0.971053 −0.0489209
\(395\) 1.64236 0.0826359
\(396\) −41.8067 −2.10087
\(397\) 13.0082 0.652864 0.326432 0.945221i \(-0.394154\pi\)
0.326432 + 0.945221i \(0.394154\pi\)
\(398\) −14.5630 −0.729979
\(399\) −19.8966 −0.996076
\(400\) −53.8527 −2.69263
\(401\) 33.5218 1.67400 0.836999 0.547205i \(-0.184308\pi\)
0.836999 + 0.547205i \(0.184308\pi\)
\(402\) −56.9103 −2.83843
\(403\) 1.00433 0.0500293
\(404\) −40.2273 −2.00138
\(405\) −3.91641 −0.194608
\(406\) −108.682 −5.39382
\(407\) 0.303014 0.0150198
\(408\) −113.803 −5.63408
\(409\) −6.59118 −0.325913 −0.162956 0.986633i \(-0.552103\pi\)
−0.162956 + 0.986633i \(0.552103\pi\)
\(410\) −17.3903 −0.858844
\(411\) 43.1419 2.12803
\(412\) 59.7564 2.94399
\(413\) −22.1379 −1.08933
\(414\) −66.4310 −3.26491
\(415\) 5.98512 0.293798
\(416\) −14.5084 −0.711334
\(417\) −23.4923 −1.15043
\(418\) −11.7641 −0.575399
\(419\) −33.5443 −1.63875 −0.819373 0.573261i \(-0.805678\pi\)
−0.819373 + 0.573261i \(0.805678\pi\)
\(420\) 30.7017 1.49809
\(421\) 16.4992 0.804123 0.402062 0.915613i \(-0.368294\pi\)
0.402062 + 0.915613i \(0.368294\pi\)
\(422\) −6.03639 −0.293847
\(423\) −27.0841 −1.31688
\(424\) 106.820 5.18764
\(425\) 25.0006 1.21271
\(426\) 39.6475 1.92093
\(427\) −56.1092 −2.71531
\(428\) 83.4338 4.03292
\(429\) 5.79545 0.279807
\(430\) 3.89507 0.187837
\(431\) −2.79993 −0.134868 −0.0674340 0.997724i \(-0.521481\pi\)
−0.0674340 + 0.997724i \(0.521481\pi\)
\(432\) −20.1288 −0.968447
\(433\) −32.2715 −1.55087 −0.775434 0.631429i \(-0.782469\pi\)
−0.775434 + 0.631429i \(0.782469\pi\)
\(434\) 10.4394 0.501106
\(435\) 16.1869 0.776101
\(436\) 30.3464 1.45333
\(437\) −13.4087 −0.641427
\(438\) 79.1892 3.78381
\(439\) 34.1561 1.63018 0.815091 0.579333i \(-0.196687\pi\)
0.815091 + 0.579333i \(0.196687\pi\)
\(440\) 10.9987 0.524341
\(441\) 30.3689 1.44614
\(442\) 14.3291 0.681565
\(443\) −6.70246 −0.318443 −0.159222 0.987243i \(-0.550898\pi\)
−0.159222 + 0.987243i \(0.550898\pi\)
\(444\) 1.77021 0.0840104
\(445\) 0.0154722 0.000733452 0
\(446\) −45.7317 −2.16546
\(447\) 4.48310 0.212043
\(448\) −60.1100 −2.83993
\(449\) −36.1352 −1.70533 −0.852663 0.522462i \(-0.825014\pi\)
−0.852663 + 0.522462i \(0.825014\pi\)
\(450\) 45.3209 2.13645
\(451\) −24.4756 −1.15251
\(452\) −29.5944 −1.39200
\(453\) −60.9392 −2.86317
\(454\) −53.7881 −2.52440
\(455\) −2.34222 −0.109805
\(456\) −41.6408 −1.95001
\(457\) −34.9102 −1.63303 −0.816516 0.577323i \(-0.804097\pi\)
−0.816516 + 0.577323i \(0.804097\pi\)
\(458\) −5.92757 −0.276977
\(459\) 9.34459 0.436168
\(460\) 20.6905 0.964700
\(461\) 3.16348 0.147338 0.0736689 0.997283i \(-0.476529\pi\)
0.0736689 + 0.997283i \(0.476529\pi\)
\(462\) 60.2399 2.80261
\(463\) 6.63613 0.308407 0.154204 0.988039i \(-0.450719\pi\)
0.154204 + 0.988039i \(0.450719\pi\)
\(464\) −121.333 −5.63275
\(465\) −1.55481 −0.0721028
\(466\) −13.6806 −0.633740
\(467\) 38.9260 1.80128 0.900640 0.434566i \(-0.143098\pi\)
0.900640 + 0.434566i \(0.143098\pi\)
\(468\) 18.6326 0.861291
\(469\) 32.3712 1.49476
\(470\) 11.7601 0.542451
\(471\) 17.5336 0.807907
\(472\) −46.3315 −2.13258
\(473\) 5.48205 0.252065
\(474\) 18.8257 0.864694
\(475\) 9.14778 0.419729
\(476\) 106.837 4.89686
\(477\) −47.9539 −2.19566
\(478\) −8.50518 −0.389018
\(479\) 2.57323 0.117574 0.0587869 0.998271i \(-0.481277\pi\)
0.0587869 + 0.998271i \(0.481277\pi\)
\(480\) 22.4606 1.02518
\(481\) −0.135048 −0.00615767
\(482\) 63.2300 2.88005
\(483\) 68.6618 3.12422
\(484\) −30.2745 −1.37611
\(485\) −4.89766 −0.222391
\(486\) −58.7337 −2.66421
\(487\) 27.1382 1.22975 0.614875 0.788624i \(-0.289206\pi\)
0.614875 + 0.788624i \(0.289206\pi\)
\(488\) −117.429 −5.31574
\(489\) −33.8577 −1.53110
\(490\) −13.1863 −0.595698
\(491\) −8.56114 −0.386359 −0.193179 0.981163i \(-0.561880\pi\)
−0.193179 + 0.981163i \(0.561880\pi\)
\(492\) −142.987 −6.44635
\(493\) 56.3277 2.53687
\(494\) 5.24305 0.235896
\(495\) −4.93755 −0.221926
\(496\) 11.6545 0.523304
\(497\) −22.5519 −1.01159
\(498\) 68.6052 3.07427
\(499\) −16.5623 −0.741430 −0.370715 0.928747i \(-0.620887\pi\)
−0.370715 + 0.928747i \(0.620887\pi\)
\(500\) −29.3238 −1.31140
\(501\) 62.9404 2.81197
\(502\) −28.4738 −1.27085
\(503\) 9.73394 0.434015 0.217007 0.976170i \(-0.430370\pi\)
0.217007 + 0.976170i \(0.430370\pi\)
\(504\) 117.346 5.22702
\(505\) −4.75102 −0.211417
\(506\) 40.5969 1.80475
\(507\) −2.58294 −0.114712
\(508\) −84.2581 −3.73835
\(509\) −1.08851 −0.0482473 −0.0241237 0.999709i \(-0.507680\pi\)
−0.0241237 + 0.999709i \(0.507680\pi\)
\(510\) −22.1830 −0.982278
\(511\) −45.0436 −1.99261
\(512\) 21.4538 0.948134
\(513\) 3.41921 0.150962
\(514\) 69.9292 3.08444
\(515\) 7.05749 0.310990
\(516\) 32.0262 1.40987
\(517\) 16.5515 0.727934
\(518\) −1.40374 −0.0616768
\(519\) 26.9934 1.18488
\(520\) −4.90193 −0.214964
\(521\) −21.7020 −0.950780 −0.475390 0.879775i \(-0.657693\pi\)
−0.475390 + 0.879775i \(0.657693\pi\)
\(522\) 102.111 4.46926
\(523\) −23.9664 −1.04798 −0.523988 0.851725i \(-0.675556\pi\)
−0.523988 + 0.851725i \(0.675556\pi\)
\(524\) 84.7620 3.70284
\(525\) −46.8428 −2.04439
\(526\) 56.5602 2.46614
\(527\) −5.41050 −0.235685
\(528\) 67.2519 2.92676
\(529\) 23.2726 1.01185
\(530\) 20.8218 0.904443
\(531\) 20.7992 0.902610
\(532\) 39.0919 1.69485
\(533\) 10.9084 0.472495
\(534\) 0.177352 0.00767477
\(535\) 9.85389 0.426021
\(536\) 67.7483 2.92628
\(537\) 44.3187 1.91249
\(538\) −36.8297 −1.58784
\(539\) −18.5589 −0.799387
\(540\) −5.27606 −0.227045
\(541\) −14.2889 −0.614330 −0.307165 0.951656i \(-0.599380\pi\)
−0.307165 + 0.951656i \(0.599380\pi\)
\(542\) −9.82475 −0.422009
\(543\) 2.60499 0.111791
\(544\) 78.1593 3.35105
\(545\) 3.58404 0.153523
\(546\) −26.8479 −1.14899
\(547\) 1.35973 0.0581377 0.0290689 0.999577i \(-0.490746\pi\)
0.0290689 + 0.999577i \(0.490746\pi\)
\(548\) −84.7631 −3.62090
\(549\) 52.7164 2.24988
\(550\) −27.6963 −1.18097
\(551\) 20.6105 0.878035
\(552\) 143.700 6.11626
\(553\) −10.7083 −0.455362
\(554\) −39.2257 −1.66654
\(555\) 0.209069 0.00887450
\(556\) 46.1567 1.95748
\(557\) 15.3855 0.651907 0.325953 0.945386i \(-0.394315\pi\)
0.325953 + 0.945386i \(0.394315\pi\)
\(558\) −9.80813 −0.415211
\(559\) −2.44326 −0.103339
\(560\) −27.1797 −1.14855
\(561\) −31.2210 −1.31815
\(562\) −62.2127 −2.62429
\(563\) 4.88977 0.206079 0.103040 0.994677i \(-0.467143\pi\)
0.103040 + 0.994677i \(0.467143\pi\)
\(564\) 96.6940 4.07155
\(565\) −3.49523 −0.147045
\(566\) 16.5610 0.696109
\(567\) 25.5352 1.07238
\(568\) −47.1980 −1.98038
\(569\) −14.4521 −0.605862 −0.302931 0.953012i \(-0.597965\pi\)
−0.302931 + 0.953012i \(0.597965\pi\)
\(570\) −8.11681 −0.339976
\(571\) −0.483688 −0.0202417 −0.0101209 0.999949i \(-0.503222\pi\)
−0.0101209 + 0.999949i \(0.503222\pi\)
\(572\) −11.3866 −0.476099
\(573\) 14.6354 0.611401
\(574\) 113.386 4.73263
\(575\) −31.5683 −1.31649
\(576\) 56.4753 2.35314
\(577\) −10.1132 −0.421017 −0.210508 0.977592i \(-0.567512\pi\)
−0.210508 + 0.977592i \(0.567512\pi\)
\(578\) −31.9755 −1.33001
\(579\) −38.7316 −1.60963
\(580\) −31.8032 −1.32056
\(581\) −39.0234 −1.61896
\(582\) −56.1401 −2.32708
\(583\) 29.3053 1.21370
\(584\) −94.2700 −3.90092
\(585\) 2.20059 0.0909831
\(586\) −16.8293 −0.695210
\(587\) −29.4474 −1.21542 −0.607711 0.794158i \(-0.707912\pi\)
−0.607711 + 0.794158i \(0.707912\pi\)
\(588\) −108.421 −4.47121
\(589\) −1.97972 −0.0815728
\(590\) −9.03113 −0.371806
\(591\) −0.942972 −0.0387887
\(592\) −1.56714 −0.0644089
\(593\) 31.1972 1.28112 0.640559 0.767909i \(-0.278703\pi\)
0.640559 + 0.767909i \(0.278703\pi\)
\(594\) −10.3522 −0.424755
\(595\) 12.6179 0.517283
\(596\) −8.80819 −0.360797
\(597\) −14.1419 −0.578789
\(598\) −18.0934 −0.739894
\(599\) −18.6954 −0.763872 −0.381936 0.924189i \(-0.624742\pi\)
−0.381936 + 0.924189i \(0.624742\pi\)
\(600\) −98.0355 −4.00228
\(601\) 20.8606 0.850920 0.425460 0.904977i \(-0.360112\pi\)
0.425460 + 0.904977i \(0.360112\pi\)
\(602\) −25.3961 −1.03507
\(603\) −30.4138 −1.23854
\(604\) 119.730 4.87176
\(605\) −3.57555 −0.145367
\(606\) −54.4591 −2.21225
\(607\) −39.1901 −1.59068 −0.795339 0.606165i \(-0.792707\pi\)
−0.795339 + 0.606165i \(0.792707\pi\)
\(608\) 28.5987 1.15983
\(609\) −105.539 −4.27667
\(610\) −22.8897 −0.926777
\(611\) −7.37674 −0.298431
\(612\) −100.377 −4.05749
\(613\) −16.5368 −0.667916 −0.333958 0.942588i \(-0.608384\pi\)
−0.333958 + 0.942588i \(0.608384\pi\)
\(614\) −79.0323 −3.18948
\(615\) −16.8874 −0.680964
\(616\) −71.7120 −2.88936
\(617\) −39.8494 −1.60428 −0.802138 0.597139i \(-0.796304\pi\)
−0.802138 + 0.597139i \(0.796304\pi\)
\(618\) 80.8974 3.25417
\(619\) 1.00000 0.0401934
\(620\) 3.05483 0.122685
\(621\) −11.7995 −0.473496
\(622\) −79.9194 −3.20448
\(623\) −0.100880 −0.00404165
\(624\) −29.9731 −1.19988
\(625\) 19.7406 0.789623
\(626\) −61.8372 −2.47151
\(627\) −11.4239 −0.456225
\(628\) −34.4492 −1.37467
\(629\) 0.727528 0.0290084
\(630\) 22.8737 0.911309
\(631\) 27.2691 1.08557 0.542784 0.839873i \(-0.317370\pi\)
0.542784 + 0.839873i \(0.317370\pi\)
\(632\) −22.4109 −0.891457
\(633\) −5.86183 −0.232987
\(634\) −38.9164 −1.54557
\(635\) −9.95125 −0.394903
\(636\) 171.202 6.78860
\(637\) 8.27139 0.327724
\(638\) −62.4012 −2.47049
\(639\) 21.1882 0.838193
\(640\) −7.13032 −0.281850
\(641\) 45.4628 1.79567 0.897836 0.440331i \(-0.145139\pi\)
0.897836 + 0.440331i \(0.145139\pi\)
\(642\) 112.952 4.45784
\(643\) 15.6912 0.618802 0.309401 0.950932i \(-0.399872\pi\)
0.309401 + 0.950932i \(0.399872\pi\)
\(644\) −134.903 −5.31594
\(645\) 3.78243 0.148933
\(646\) −28.2452 −1.11129
\(647\) 14.0326 0.551680 0.275840 0.961204i \(-0.411044\pi\)
0.275840 + 0.961204i \(0.411044\pi\)
\(648\) 53.4416 2.09939
\(649\) −12.7107 −0.498939
\(650\) 12.3438 0.484163
\(651\) 10.1375 0.397319
\(652\) 66.5219 2.60520
\(653\) 2.57443 0.100745 0.0503725 0.998730i \(-0.483959\pi\)
0.0503725 + 0.998730i \(0.483959\pi\)
\(654\) 41.0825 1.60645
\(655\) 10.0108 0.391153
\(656\) 126.584 4.94227
\(657\) 42.3199 1.65106
\(658\) −76.6764 −2.98916
\(659\) 7.70514 0.300150 0.150075 0.988675i \(-0.452049\pi\)
0.150075 + 0.988675i \(0.452049\pi\)
\(660\) 17.6277 0.686158
\(661\) 30.0611 1.16924 0.584621 0.811306i \(-0.301243\pi\)
0.584621 + 0.811306i \(0.301243\pi\)
\(662\) 32.2161 1.25211
\(663\) 13.9147 0.540402
\(664\) −81.6705 −3.16943
\(665\) 4.61692 0.179037
\(666\) 1.31886 0.0511047
\(667\) −71.1252 −2.75398
\(668\) −123.662 −4.78464
\(669\) −44.4092 −1.71696
\(670\) 13.2058 0.510185
\(671\) −32.2157 −1.24367
\(672\) −146.445 −5.64923
\(673\) 36.4508 1.40507 0.702537 0.711647i \(-0.252051\pi\)
0.702537 + 0.711647i \(0.252051\pi\)
\(674\) −47.4135 −1.82630
\(675\) 8.04989 0.309840
\(676\) 5.07483 0.195186
\(677\) −47.0194 −1.80710 −0.903551 0.428480i \(-0.859049\pi\)
−0.903551 + 0.428480i \(0.859049\pi\)
\(678\) −40.0645 −1.53867
\(679\) 31.9331 1.22548
\(680\) 26.4075 1.01268
\(681\) −52.2326 −2.00156
\(682\) 5.99389 0.229518
\(683\) 22.2040 0.849614 0.424807 0.905284i \(-0.360342\pi\)
0.424807 + 0.905284i \(0.360342\pi\)
\(684\) −36.7281 −1.40433
\(685\) −10.0109 −0.382496
\(686\) 13.2153 0.504561
\(687\) −5.75615 −0.219611
\(688\) −28.3522 −1.08092
\(689\) −13.0609 −0.497581
\(690\) 28.0105 1.06634
\(691\) −12.2979 −0.467836 −0.233918 0.972256i \(-0.575155\pi\)
−0.233918 + 0.972256i \(0.575155\pi\)
\(692\) −53.0354 −2.01610
\(693\) 32.1931 1.22292
\(694\) 48.5798 1.84406
\(695\) 5.45130 0.206780
\(696\) −220.879 −8.37241
\(697\) −58.7653 −2.22589
\(698\) −55.6341 −2.10578
\(699\) −13.2849 −0.502482
\(700\) 92.0345 3.47858
\(701\) −18.0585 −0.682060 −0.341030 0.940052i \(-0.610776\pi\)
−0.341030 + 0.940052i \(0.610776\pi\)
\(702\) 4.61379 0.174136
\(703\) 0.266204 0.0100401
\(704\) −34.5129 −1.30075
\(705\) 11.4200 0.430101
\(706\) −51.8556 −1.95161
\(707\) 30.9769 1.16501
\(708\) −74.2561 −2.79071
\(709\) 29.0464 1.09086 0.545430 0.838156i \(-0.316366\pi\)
0.545430 + 0.838156i \(0.316366\pi\)
\(710\) −9.20003 −0.345271
\(711\) 10.0608 0.377308
\(712\) −0.211127 −0.00791231
\(713\) 6.83187 0.255855
\(714\) 144.634 5.41280
\(715\) −1.34481 −0.0502930
\(716\) −87.0752 −3.25415
\(717\) −8.25922 −0.308446
\(718\) −38.4995 −1.43679
\(719\) −32.5691 −1.21462 −0.607312 0.794464i \(-0.707752\pi\)
−0.607312 + 0.794464i \(0.707752\pi\)
\(720\) 25.5362 0.951677
\(721\) −46.0153 −1.71370
\(722\) 40.2023 1.49617
\(723\) 61.4015 2.28355
\(724\) −5.11816 −0.190215
\(725\) 48.5234 1.80212
\(726\) −40.9852 −1.52110
\(727\) −26.1060 −0.968217 −0.484108 0.875008i \(-0.660856\pi\)
−0.484108 + 0.875008i \(0.660856\pi\)
\(728\) 31.9609 1.18455
\(729\) −37.4323 −1.38638
\(730\) −18.3755 −0.680109
\(731\) 13.1622 0.486823
\(732\) −188.204 −6.95624
\(733\) 4.64473 0.171557 0.0857785 0.996314i \(-0.472662\pi\)
0.0857785 + 0.996314i \(0.472662\pi\)
\(734\) −39.3664 −1.45304
\(735\) −12.8050 −0.472320
\(736\) −98.6921 −3.63784
\(737\) 18.5863 0.684634
\(738\) −106.529 −3.92140
\(739\) −19.5355 −0.718623 −0.359312 0.933218i \(-0.616988\pi\)
−0.359312 + 0.933218i \(0.616988\pi\)
\(740\) −0.410770 −0.0151002
\(741\) 5.09143 0.187038
\(742\) −135.760 −4.98389
\(743\) −52.2786 −1.91792 −0.958958 0.283549i \(-0.908488\pi\)
−0.958958 + 0.283549i \(0.908488\pi\)
\(744\) 21.2163 0.777829
\(745\) −1.04028 −0.0381131
\(746\) −71.8277 −2.62980
\(747\) 36.6637 1.34145
\(748\) 61.3416 2.24287
\(749\) −64.2480 −2.34757
\(750\) −39.6982 −1.44957
\(751\) −28.9954 −1.05806 −0.529029 0.848604i \(-0.677444\pi\)
−0.529029 + 0.848604i \(0.677444\pi\)
\(752\) −85.6015 −3.12157
\(753\) −27.6504 −1.00764
\(754\) 27.8112 1.01282
\(755\) 14.1407 0.514632
\(756\) 34.4002 1.25112
\(757\) 45.4148 1.65063 0.825314 0.564675i \(-0.190998\pi\)
0.825314 + 0.564675i \(0.190998\pi\)
\(758\) 33.5818 1.21975
\(759\) 39.4229 1.43096
\(760\) 9.66258 0.350499
\(761\) −14.7985 −0.536446 −0.268223 0.963357i \(-0.586436\pi\)
−0.268223 + 0.963357i \(0.586436\pi\)
\(762\) −114.067 −4.13223
\(763\) −23.3682 −0.845985
\(764\) −28.7549 −1.04031
\(765\) −11.8549 −0.428616
\(766\) −31.8792 −1.15184
\(767\) 5.66496 0.204550
\(768\) −2.27165 −0.0819711
\(769\) −36.0435 −1.29976 −0.649881 0.760036i \(-0.725181\pi\)
−0.649881 + 0.760036i \(0.725181\pi\)
\(770\) −13.9784 −0.503747
\(771\) 67.9069 2.44561
\(772\) 76.0981 2.73883
\(773\) −19.8286 −0.713186 −0.356593 0.934260i \(-0.616062\pi\)
−0.356593 + 0.934260i \(0.616062\pi\)
\(774\) 23.8605 0.857647
\(775\) −4.66087 −0.167423
\(776\) 66.8314 2.39911
\(777\) −1.36315 −0.0489026
\(778\) 82.2619 2.94923
\(779\) −21.5024 −0.770403
\(780\) −7.85639 −0.281304
\(781\) −12.9484 −0.463331
\(782\) 97.4721 3.48559
\(783\) 18.1369 0.648158
\(784\) 95.9833 3.42798
\(785\) −4.06860 −0.145215
\(786\) 114.750 4.09298
\(787\) −9.95588 −0.354889 −0.177444 0.984131i \(-0.556783\pi\)
−0.177444 + 0.984131i \(0.556783\pi\)
\(788\) 1.85271 0.0659999
\(789\) 54.9246 1.95537
\(790\) −4.36843 −0.155422
\(791\) 22.7891 0.810287
\(792\) 67.3758 2.39409
\(793\) 14.3580 0.509868
\(794\) −34.6000 −1.22791
\(795\) 20.2197 0.717119
\(796\) 27.7853 0.984825
\(797\) 0.0542137 0.00192035 0.000960175 1.00000i \(-0.499694\pi\)
0.000960175 1.00000i \(0.499694\pi\)
\(798\) 52.9221 1.87342
\(799\) 39.7397 1.40589
\(800\) 67.3303 2.38048
\(801\) 0.0947796 0.00334887
\(802\) −89.1631 −3.14846
\(803\) −25.8623 −0.912661
\(804\) 108.581 3.82936
\(805\) −15.9327 −0.561553
\(806\) −2.67138 −0.0940953
\(807\) −35.7646 −1.25897
\(808\) 64.8304 2.28072
\(809\) −53.3467 −1.87557 −0.937784 0.347218i \(-0.887126\pi\)
−0.937784 + 0.347218i \(0.887126\pi\)
\(810\) 10.4171 0.366019
\(811\) 20.8040 0.730526 0.365263 0.930904i \(-0.380979\pi\)
0.365263 + 0.930904i \(0.380979\pi\)
\(812\) 207.359 7.27687
\(813\) −9.54064 −0.334605
\(814\) −0.805973 −0.0282493
\(815\) 7.85653 0.275202
\(816\) 161.470 5.65257
\(817\) 4.81610 0.168494
\(818\) 17.5316 0.612977
\(819\) −14.3480 −0.501358
\(820\) 33.1795 1.15868
\(821\) −33.7272 −1.17709 −0.588544 0.808465i \(-0.700299\pi\)
−0.588544 + 0.808465i \(0.700299\pi\)
\(822\) −114.751 −4.00241
\(823\) −39.1297 −1.36397 −0.681987 0.731364i \(-0.738884\pi\)
−0.681987 + 0.731364i \(0.738884\pi\)
\(824\) −96.3035 −3.35489
\(825\) −26.8953 −0.936375
\(826\) 58.8835 2.04882
\(827\) 21.9711 0.764010 0.382005 0.924160i \(-0.375234\pi\)
0.382005 + 0.924160i \(0.375234\pi\)
\(828\) 126.746 4.40473
\(829\) 29.7441 1.03306 0.516528 0.856270i \(-0.327224\pi\)
0.516528 + 0.856270i \(0.327224\pi\)
\(830\) −15.9196 −0.552576
\(831\) −38.0914 −1.32138
\(832\) 15.3818 0.533269
\(833\) −44.5593 −1.54389
\(834\) 62.4863 2.16372
\(835\) −14.6051 −0.505429
\(836\) 22.4451 0.776279
\(837\) −1.74212 −0.0602164
\(838\) 89.2230 3.08216
\(839\) −32.1524 −1.11002 −0.555011 0.831843i \(-0.687286\pi\)
−0.555011 + 0.831843i \(0.687286\pi\)
\(840\) −49.4789 −1.70718
\(841\) 80.3260 2.76986
\(842\) −43.8856 −1.51240
\(843\) −60.4136 −2.08076
\(844\) 11.5170 0.396433
\(845\) 0.599360 0.0206186
\(846\) 72.0399 2.47678
\(847\) 23.3128 0.801037
\(848\) −151.562 −5.20467
\(849\) 16.0820 0.551934
\(850\) −66.4979 −2.28086
\(851\) −0.918653 −0.0314910
\(852\) −75.6448 −2.59155
\(853\) −11.2807 −0.386245 −0.193122 0.981175i \(-0.561861\pi\)
−0.193122 + 0.981175i \(0.561861\pi\)
\(854\) 149.242 5.10696
\(855\) −4.33775 −0.148348
\(856\) −134.462 −4.59582
\(857\) −8.06981 −0.275659 −0.137830 0.990456i \(-0.544013\pi\)
−0.137830 + 0.990456i \(0.544013\pi\)
\(858\) −15.4151 −0.526261
\(859\) −12.3178 −0.420277 −0.210138 0.977672i \(-0.567391\pi\)
−0.210138 + 0.977672i \(0.567391\pi\)
\(860\) −7.43154 −0.253414
\(861\) 110.107 3.75243
\(862\) 7.44742 0.253660
\(863\) −3.32543 −0.113199 −0.0565995 0.998397i \(-0.518026\pi\)
−0.0565995 + 0.998397i \(0.518026\pi\)
\(864\) 25.1664 0.856177
\(865\) −6.26371 −0.212973
\(866\) 85.8374 2.91687
\(867\) −31.0509 −1.05454
\(868\) −19.9177 −0.676049
\(869\) −6.14827 −0.208566
\(870\) −43.0548 −1.45969
\(871\) −8.28360 −0.280679
\(872\) −48.9063 −1.65618
\(873\) −30.0021 −1.01542
\(874\) 35.6653 1.20640
\(875\) 22.5808 0.763369
\(876\) −151.088 −5.10479
\(877\) 28.5152 0.962892 0.481446 0.876476i \(-0.340112\pi\)
0.481446 + 0.876476i \(0.340112\pi\)
\(878\) −90.8503 −3.06605
\(879\) −16.3426 −0.551222
\(880\) −15.6055 −0.526062
\(881\) −3.36251 −0.113286 −0.0566429 0.998395i \(-0.518040\pi\)
−0.0566429 + 0.998395i \(0.518040\pi\)
\(882\) −80.7769 −2.71990
\(883\) −32.4508 −1.09206 −0.546029 0.837766i \(-0.683861\pi\)
−0.546029 + 0.837766i \(0.683861\pi\)
\(884\) −27.3390 −0.919508
\(885\) −8.76996 −0.294799
\(886\) 17.8276 0.598929
\(887\) −7.75431 −0.260364 −0.130182 0.991490i \(-0.541556\pi\)
−0.130182 + 0.991490i \(0.541556\pi\)
\(888\) −2.85287 −0.0957362
\(889\) 64.8827 2.17610
\(890\) −0.0411538 −0.00137948
\(891\) 14.6613 0.491173
\(892\) 87.2531 2.92145
\(893\) 14.5409 0.486591
\(894\) −11.9244 −0.398812
\(895\) −10.2840 −0.343755
\(896\) 46.4901 1.55313
\(897\) −17.5702 −0.586651
\(898\) 96.1144 3.20738
\(899\) −10.5012 −0.350235
\(900\) −86.4694 −2.88231
\(901\) 70.3612 2.34407
\(902\) 65.1017 2.16765
\(903\) −24.6617 −0.820690
\(904\) 47.6944 1.58629
\(905\) −0.604477 −0.0200935
\(906\) 162.089 5.38506
\(907\) 17.4546 0.579571 0.289786 0.957092i \(-0.406416\pi\)
0.289786 + 0.957092i \(0.406416\pi\)
\(908\) 102.624 3.40570
\(909\) −29.1038 −0.965312
\(910\) 6.22995 0.206521
\(911\) −10.0043 −0.331456 −0.165728 0.986171i \(-0.552997\pi\)
−0.165728 + 0.986171i \(0.552997\pi\)
\(912\) 59.0823 1.95641
\(913\) −22.4057 −0.741521
\(914\) 92.8562 3.07141
\(915\) −22.2278 −0.734827
\(916\) 11.3094 0.373674
\(917\) −65.2708 −2.15543
\(918\) −24.8553 −0.820346
\(919\) 32.5243 1.07288 0.536439 0.843939i \(-0.319769\pi\)
0.536439 + 0.843939i \(0.319769\pi\)
\(920\) −33.3449 −1.09935
\(921\) −76.7468 −2.52889
\(922\) −8.41439 −0.277113
\(923\) 5.77090 0.189952
\(924\) −114.934 −3.78105
\(925\) 0.626728 0.0206067
\(926\) −17.6511 −0.580053
\(927\) 43.2328 1.41995
\(928\) 151.699 4.97976
\(929\) −29.1706 −0.957057 −0.478529 0.878072i \(-0.658830\pi\)
−0.478529 + 0.878072i \(0.658830\pi\)
\(930\) 4.13558 0.135611
\(931\) −16.3044 −0.534355
\(932\) 26.1016 0.854987
\(933\) −77.6083 −2.54078
\(934\) −103.538 −3.38785
\(935\) 7.24471 0.236927
\(936\) −30.0283 −0.981505
\(937\) 48.3898 1.58083 0.790413 0.612574i \(-0.209866\pi\)
0.790413 + 0.612574i \(0.209866\pi\)
\(938\) −86.1026 −2.81135
\(939\) −60.0490 −1.95963
\(940\) −22.4374 −0.731829
\(941\) −40.9168 −1.33385 −0.666925 0.745125i \(-0.732390\pi\)
−0.666925 + 0.745125i \(0.732390\pi\)
\(942\) −46.6369 −1.51951
\(943\) 74.2032 2.41639
\(944\) 65.7376 2.13958
\(945\) 4.06281 0.132163
\(946\) −14.5815 −0.474084
\(947\) −2.95800 −0.0961221 −0.0480611 0.998844i \(-0.515304\pi\)
−0.0480611 + 0.998844i \(0.515304\pi\)
\(948\) −35.9182 −1.16657
\(949\) 11.5264 0.374163
\(950\) −24.3318 −0.789427
\(951\) −37.7910 −1.22546
\(952\) −172.179 −5.58034
\(953\) −21.5717 −0.698777 −0.349389 0.936978i \(-0.613611\pi\)
−0.349389 + 0.936978i \(0.613611\pi\)
\(954\) 127.551 4.12960
\(955\) −3.39607 −0.109894
\(956\) 16.2273 0.524829
\(957\) −60.5967 −1.95881
\(958\) −6.84442 −0.221133
\(959\) 65.2716 2.10773
\(960\) −23.8127 −0.768552
\(961\) −29.9913 −0.967462
\(962\) 0.359209 0.0115814
\(963\) 60.3631 1.94517
\(964\) −120.639 −3.88551
\(965\) 8.98752 0.289318
\(966\) −182.630 −5.87604
\(967\) −3.61422 −0.116226 −0.0581128 0.998310i \(-0.518508\pi\)
−0.0581128 + 0.998310i \(0.518508\pi\)
\(968\) 48.7904 1.56818
\(969\) −27.4284 −0.881126
\(970\) 13.0271 0.418274
\(971\) −15.9826 −0.512905 −0.256453 0.966557i \(-0.582554\pi\)
−0.256453 + 0.966557i \(0.582554\pi\)
\(972\) 112.060 3.59433
\(973\) −35.5428 −1.13945
\(974\) −72.1838 −2.31292
\(975\) 11.9868 0.383885
\(976\) 166.614 5.33319
\(977\) 9.87777 0.316018 0.158009 0.987438i \(-0.449493\pi\)
0.158009 + 0.987438i \(0.449493\pi\)
\(978\) 90.0565 2.87969
\(979\) −0.0579212 −0.00185117
\(980\) 25.1587 0.803664
\(981\) 21.9552 0.700974
\(982\) 22.7714 0.726664
\(983\) −11.8157 −0.376861 −0.188431 0.982087i \(-0.560340\pi\)
−0.188431 + 0.982087i \(0.560340\pi\)
\(984\) 230.438 7.34609
\(985\) 0.218813 0.00697195
\(986\) −149.824 −4.77135
\(987\) −74.4590 −2.37006
\(988\) −10.0034 −0.318251
\(989\) −16.6200 −0.528486
\(990\) 13.1332 0.417400
\(991\) 26.3314 0.836446 0.418223 0.908344i \(-0.362653\pi\)
0.418223 + 0.908344i \(0.362653\pi\)
\(992\) −14.5713 −0.462639
\(993\) 31.2845 0.992782
\(994\) 59.9848 1.90260
\(995\) 3.28157 0.104033
\(996\) −130.894 −4.14755
\(997\) −0.944094 −0.0298997 −0.0149499 0.999888i \(-0.504759\pi\)
−0.0149499 + 0.999888i \(0.504759\pi\)
\(998\) 44.0533 1.39448
\(999\) 0.234255 0.00741151
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 \(a_p\))