Properties

Label 8007.2.a.e.1.10
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 1
Dimension 46
CM No

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(46\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.83962 q^{2} +1.00000 q^{3} +1.38420 q^{4} +0.446319 q^{5} -1.83962 q^{6} +3.21050 q^{7} +1.13283 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.83962 q^{2} +1.00000 q^{3} +1.38420 q^{4} +0.446319 q^{5} -1.83962 q^{6} +3.21050 q^{7} +1.13283 q^{8} +1.00000 q^{9} -0.821058 q^{10} +0.755063 q^{11} +1.38420 q^{12} -6.00546 q^{13} -5.90609 q^{14} +0.446319 q^{15} -4.85239 q^{16} -1.00000 q^{17} -1.83962 q^{18} -3.47410 q^{19} +0.617796 q^{20} +3.21050 q^{21} -1.38903 q^{22} -1.33575 q^{23} +1.13283 q^{24} -4.80080 q^{25} +11.0478 q^{26} +1.00000 q^{27} +4.44398 q^{28} -5.99876 q^{29} -0.821058 q^{30} +0.937935 q^{31} +6.66089 q^{32} +0.755063 q^{33} +1.83962 q^{34} +1.43291 q^{35} +1.38420 q^{36} +7.61442 q^{37} +6.39102 q^{38} -6.00546 q^{39} +0.505605 q^{40} +4.83292 q^{41} -5.90609 q^{42} +11.5470 q^{43} +1.04516 q^{44} +0.446319 q^{45} +2.45728 q^{46} +4.65967 q^{47} -4.85239 q^{48} +3.30728 q^{49} +8.83165 q^{50} -1.00000 q^{51} -8.31277 q^{52} -0.522651 q^{53} -1.83962 q^{54} +0.336999 q^{55} +3.63695 q^{56} -3.47410 q^{57} +11.0354 q^{58} -3.59680 q^{59} +0.617796 q^{60} -3.89238 q^{61} -1.72544 q^{62} +3.21050 q^{63} -2.54873 q^{64} -2.68035 q^{65} -1.38903 q^{66} -4.41034 q^{67} -1.38420 q^{68} -1.33575 q^{69} -2.63600 q^{70} -10.1666 q^{71} +1.13283 q^{72} +15.6550 q^{73} -14.0076 q^{74} -4.80080 q^{75} -4.80885 q^{76} +2.42413 q^{77} +11.0478 q^{78} -15.3608 q^{79} -2.16571 q^{80} +1.00000 q^{81} -8.89074 q^{82} +3.70090 q^{83} +4.44398 q^{84} -0.446319 q^{85} -21.2422 q^{86} -5.99876 q^{87} +0.855361 q^{88} +1.35034 q^{89} -0.821058 q^{90} -19.2805 q^{91} -1.84895 q^{92} +0.937935 q^{93} -8.57202 q^{94} -1.55056 q^{95} +6.66089 q^{96} -12.1618 q^{97} -6.08414 q^{98} +0.755063 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 46q - 5q^{2} + 46q^{3} + 43q^{4} - 19q^{5} - 5q^{6} + q^{7} - 18q^{8} + 46q^{9} + O(q^{10}) \) \( 46q - 5q^{2} + 46q^{3} + 43q^{4} - 19q^{5} - 5q^{6} + q^{7} - 18q^{8} + 46q^{9} - 10q^{10} - 25q^{11} + 43q^{12} - 8q^{13} - 28q^{14} - 19q^{15} + 33q^{16} - 46q^{17} - 5q^{18} - 2q^{19} - 56q^{20} + q^{21} - 19q^{22} - 64q^{23} - 18q^{24} + 11q^{25} - 13q^{26} + 46q^{27} - 38q^{28} - 51q^{29} - 10q^{30} - 19q^{31} - 61q^{32} - 25q^{33} + 5q^{34} - 39q^{35} + 43q^{36} - 46q^{37} - 48q^{38} - 8q^{39} - 10q^{40} - 53q^{41} - 28q^{42} - 33q^{43} - 62q^{44} - 19q^{45} + 2q^{46} - 45q^{47} + 33q^{48} + 21q^{49} - 60q^{50} - 46q^{51} - 63q^{52} - 47q^{53} - 5q^{54} + 5q^{55} - 82q^{56} - 2q^{57} - 21q^{58} - 65q^{59} - 56q^{60} - 37q^{61} - 46q^{62} + q^{63} + 74q^{64} - 85q^{65} - 19q^{66} - 52q^{67} - 43q^{68} - 64q^{69} - 20q^{70} - 48q^{71} - 18q^{72} - 39q^{73} - 16q^{74} + 11q^{75} + 42q^{76} - 78q^{77} - 13q^{78} - 26q^{79} - 78q^{80} + 46q^{81} + 3q^{82} - 47q^{83} - 38q^{84} + 19q^{85} - 6q^{86} - 51q^{87} - 58q^{88} - 58q^{89} - 10q^{90} - 43q^{91} - 68q^{92} - 19q^{93} - 78q^{95} - 61q^{96} - 44q^{97} - 4q^{98} - 25q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.83962 −1.30081 −0.650404 0.759588i \(-0.725400\pi\)
−0.650404 + 0.759588i \(0.725400\pi\)
\(3\) 1.00000 0.577350
\(4\) 1.38420 0.692102
\(5\) 0.446319 0.199600 0.0998000 0.995008i \(-0.468180\pi\)
0.0998000 + 0.995008i \(0.468180\pi\)
\(6\) −1.83962 −0.751022
\(7\) 3.21050 1.21345 0.606727 0.794911i \(-0.292482\pi\)
0.606727 + 0.794911i \(0.292482\pi\)
\(8\) 1.13283 0.400517
\(9\) 1.00000 0.333333
\(10\) −0.821058 −0.259641
\(11\) 0.755063 0.227660 0.113830 0.993500i \(-0.463688\pi\)
0.113830 + 0.993500i \(0.463688\pi\)
\(12\) 1.38420 0.399585
\(13\) −6.00546 −1.66561 −0.832807 0.553563i \(-0.813268\pi\)
−0.832807 + 0.553563i \(0.813268\pi\)
\(14\) −5.90609 −1.57847
\(15\) 0.446319 0.115239
\(16\) −4.85239 −1.21310
\(17\) −1.00000 −0.242536
\(18\) −1.83962 −0.433603
\(19\) −3.47410 −0.797012 −0.398506 0.917166i \(-0.630471\pi\)
−0.398506 + 0.917166i \(0.630471\pi\)
\(20\) 0.617796 0.138143
\(21\) 3.21050 0.700588
\(22\) −1.38903 −0.296142
\(23\) −1.33575 −0.278524 −0.139262 0.990256i \(-0.544473\pi\)
−0.139262 + 0.990256i \(0.544473\pi\)
\(24\) 1.13283 0.231238
\(25\) −4.80080 −0.960160
\(26\) 11.0478 2.16664
\(27\) 1.00000 0.192450
\(28\) 4.44398 0.839833
\(29\) −5.99876 −1.11394 −0.556971 0.830532i \(-0.688037\pi\)
−0.556971 + 0.830532i \(0.688037\pi\)
\(30\) −0.821058 −0.149904
\(31\) 0.937935 0.168458 0.0842290 0.996446i \(-0.473157\pi\)
0.0842290 + 0.996446i \(0.473157\pi\)
\(32\) 6.66089 1.17749
\(33\) 0.755063 0.131440
\(34\) 1.83962 0.315492
\(35\) 1.43291 0.242205
\(36\) 1.38420 0.230701
\(37\) 7.61442 1.25180 0.625901 0.779902i \(-0.284731\pi\)
0.625901 + 0.779902i \(0.284731\pi\)
\(38\) 6.39102 1.03676
\(39\) −6.00546 −0.961643
\(40\) 0.505605 0.0799432
\(41\) 4.83292 0.754776 0.377388 0.926055i \(-0.376822\pi\)
0.377388 + 0.926055i \(0.376822\pi\)
\(42\) −5.90609 −0.911330
\(43\) 11.5470 1.76091 0.880454 0.474131i \(-0.157238\pi\)
0.880454 + 0.474131i \(0.157238\pi\)
\(44\) 1.04516 0.157564
\(45\) 0.446319 0.0665333
\(46\) 2.45728 0.362306
\(47\) 4.65967 0.679682 0.339841 0.940483i \(-0.389627\pi\)
0.339841 + 0.940483i \(0.389627\pi\)
\(48\) −4.85239 −0.700382
\(49\) 3.30728 0.472469
\(50\) 8.83165 1.24898
\(51\) −1.00000 −0.140028
\(52\) −8.31277 −1.15277
\(53\) −0.522651 −0.0717917 −0.0358958 0.999356i \(-0.511428\pi\)
−0.0358958 + 0.999356i \(0.511428\pi\)
\(54\) −1.83962 −0.250341
\(55\) 0.336999 0.0454410
\(56\) 3.63695 0.486008
\(57\) −3.47410 −0.460155
\(58\) 11.0354 1.44902
\(59\) −3.59680 −0.468264 −0.234132 0.972205i \(-0.575225\pi\)
−0.234132 + 0.972205i \(0.575225\pi\)
\(60\) 0.617796 0.0797572
\(61\) −3.89238 −0.498369 −0.249184 0.968456i \(-0.580163\pi\)
−0.249184 + 0.968456i \(0.580163\pi\)
\(62\) −1.72544 −0.219132
\(63\) 3.21050 0.404484
\(64\) −2.54873 −0.318591
\(65\) −2.68035 −0.332457
\(66\) −1.38903 −0.170978
\(67\) −4.41034 −0.538809 −0.269404 0.963027i \(-0.586827\pi\)
−0.269404 + 0.963027i \(0.586827\pi\)
\(68\) −1.38420 −0.167859
\(69\) −1.33575 −0.160806
\(70\) −2.63600 −0.315063
\(71\) −10.1666 −1.20655 −0.603275 0.797533i \(-0.706138\pi\)
−0.603275 + 0.797533i \(0.706138\pi\)
\(72\) 1.13283 0.133506
\(73\) 15.6550 1.83228 0.916142 0.400854i \(-0.131287\pi\)
0.916142 + 0.400854i \(0.131287\pi\)
\(74\) −14.0076 −1.62836
\(75\) −4.80080 −0.554349
\(76\) −4.80885 −0.551613
\(77\) 2.42413 0.276255
\(78\) 11.0478 1.25091
\(79\) −15.3608 −1.72822 −0.864112 0.503300i \(-0.832119\pi\)
−0.864112 + 0.503300i \(0.832119\pi\)
\(80\) −2.16571 −0.242134
\(81\) 1.00000 0.111111
\(82\) −8.89074 −0.981818
\(83\) 3.70090 0.406226 0.203113 0.979155i \(-0.434894\pi\)
0.203113 + 0.979155i \(0.434894\pi\)
\(84\) 4.44398 0.484878
\(85\) −0.446319 −0.0484101
\(86\) −21.2422 −2.29060
\(87\) −5.99876 −0.643135
\(88\) 0.855361 0.0911817
\(89\) 1.35034 0.143135 0.0715677 0.997436i \(-0.477200\pi\)
0.0715677 + 0.997436i \(0.477200\pi\)
\(90\) −0.821058 −0.0865471
\(91\) −19.2805 −2.02114
\(92\) −1.84895 −0.192767
\(93\) 0.937935 0.0972593
\(94\) −8.57202 −0.884136
\(95\) −1.55056 −0.159084
\(96\) 6.66089 0.679824
\(97\) −12.1618 −1.23484 −0.617421 0.786633i \(-0.711823\pi\)
−0.617421 + 0.786633i \(0.711823\pi\)
\(98\) −6.08414 −0.614591
\(99\) 0.755063 0.0758867
\(100\) −6.64528 −0.664528
\(101\) −9.20932 −0.916362 −0.458181 0.888859i \(-0.651499\pi\)
−0.458181 + 0.888859i \(0.651499\pi\)
\(102\) 1.83962 0.182150
\(103\) 12.9331 1.27434 0.637170 0.770724i \(-0.280105\pi\)
0.637170 + 0.770724i \(0.280105\pi\)
\(104\) −6.80318 −0.667106
\(105\) 1.43291 0.139837
\(106\) 0.961480 0.0933872
\(107\) 2.40569 0.232567 0.116284 0.993216i \(-0.462902\pi\)
0.116284 + 0.993216i \(0.462902\pi\)
\(108\) 1.38420 0.133195
\(109\) −4.36744 −0.418325 −0.209163 0.977881i \(-0.567074\pi\)
−0.209163 + 0.977881i \(0.567074\pi\)
\(110\) −0.619951 −0.0591100
\(111\) 7.61442 0.722729
\(112\) −15.5786 −1.47204
\(113\) −3.50544 −0.329764 −0.164882 0.986313i \(-0.552724\pi\)
−0.164882 + 0.986313i \(0.552724\pi\)
\(114\) 6.39102 0.598574
\(115\) −0.596173 −0.0555934
\(116\) −8.30350 −0.770961
\(117\) −6.00546 −0.555205
\(118\) 6.61675 0.609122
\(119\) −3.21050 −0.294306
\(120\) 0.505605 0.0461552
\(121\) −10.4299 −0.948171
\(122\) 7.16051 0.648282
\(123\) 4.83292 0.435770
\(124\) 1.29829 0.116590
\(125\) −4.37428 −0.391248
\(126\) −5.90609 −0.526157
\(127\) 8.25531 0.732541 0.366270 0.930508i \(-0.380635\pi\)
0.366270 + 0.930508i \(0.380635\pi\)
\(128\) −8.63308 −0.763064
\(129\) 11.5470 1.01666
\(130\) 4.93083 0.432462
\(131\) −22.4186 −1.95872 −0.979360 0.202122i \(-0.935216\pi\)
−0.979360 + 0.202122i \(0.935216\pi\)
\(132\) 1.04516 0.0909696
\(133\) −11.1536 −0.967137
\(134\) 8.11335 0.700887
\(135\) 0.446319 0.0384130
\(136\) −1.13283 −0.0971396
\(137\) −18.1655 −1.55198 −0.775992 0.630743i \(-0.782750\pi\)
−0.775992 + 0.630743i \(0.782750\pi\)
\(138\) 2.45728 0.209178
\(139\) 3.44808 0.292462 0.146231 0.989250i \(-0.453286\pi\)
0.146231 + 0.989250i \(0.453286\pi\)
\(140\) 1.98343 0.167631
\(141\) 4.65967 0.392415
\(142\) 18.7026 1.56949
\(143\) −4.53450 −0.379194
\(144\) −4.85239 −0.404366
\(145\) −2.67736 −0.222343
\(146\) −28.7993 −2.38345
\(147\) 3.30728 0.272780
\(148\) 10.5399 0.866375
\(149\) −8.39683 −0.687895 −0.343947 0.938989i \(-0.611764\pi\)
−0.343947 + 0.938989i \(0.611764\pi\)
\(150\) 8.83165 0.721101
\(151\) 4.71303 0.383541 0.191771 0.981440i \(-0.438577\pi\)
0.191771 + 0.981440i \(0.438577\pi\)
\(152\) −3.93557 −0.319217
\(153\) −1.00000 −0.0808452
\(154\) −4.45947 −0.359355
\(155\) 0.418618 0.0336242
\(156\) −8.31277 −0.665554
\(157\) 1.00000 0.0798087
\(158\) 28.2580 2.24809
\(159\) −0.522651 −0.0414489
\(160\) 2.97288 0.235027
\(161\) −4.28843 −0.337976
\(162\) −1.83962 −0.144534
\(163\) −2.89363 −0.226646 −0.113323 0.993558i \(-0.536150\pi\)
−0.113323 + 0.993558i \(0.536150\pi\)
\(164\) 6.68975 0.522381
\(165\) 0.336999 0.0262354
\(166\) −6.80824 −0.528422
\(167\) −19.4708 −1.50670 −0.753349 0.657621i \(-0.771563\pi\)
−0.753349 + 0.657621i \(0.771563\pi\)
\(168\) 3.63695 0.280597
\(169\) 23.0655 1.77427
\(170\) 0.821058 0.0629723
\(171\) −3.47410 −0.265671
\(172\) 15.9835 1.21873
\(173\) 7.43832 0.565525 0.282763 0.959190i \(-0.408749\pi\)
0.282763 + 0.959190i \(0.408749\pi\)
\(174\) 11.0354 0.836595
\(175\) −15.4129 −1.16511
\(176\) −3.66386 −0.276174
\(177\) −3.59680 −0.270352
\(178\) −2.48411 −0.186192
\(179\) 17.2445 1.28892 0.644458 0.764639i \(-0.277083\pi\)
0.644458 + 0.764639i \(0.277083\pi\)
\(180\) 0.617796 0.0460478
\(181\) 1.93638 0.143930 0.0719649 0.997407i \(-0.477073\pi\)
0.0719649 + 0.997407i \(0.477073\pi\)
\(182\) 35.4688 2.62912
\(183\) −3.89238 −0.287733
\(184\) −1.51319 −0.111554
\(185\) 3.39846 0.249860
\(186\) −1.72544 −0.126516
\(187\) −0.755063 −0.0552157
\(188\) 6.44992 0.470409
\(189\) 3.21050 0.233529
\(190\) 2.85243 0.206937
\(191\) −17.5547 −1.27022 −0.635108 0.772423i \(-0.719045\pi\)
−0.635108 + 0.772423i \(0.719045\pi\)
\(192\) −2.54873 −0.183938
\(193\) −17.4943 −1.25926 −0.629632 0.776894i \(-0.716794\pi\)
−0.629632 + 0.776894i \(0.716794\pi\)
\(194\) 22.3731 1.60629
\(195\) −2.68035 −0.191944
\(196\) 4.57795 0.326996
\(197\) 0.781602 0.0556868 0.0278434 0.999612i \(-0.491136\pi\)
0.0278434 + 0.999612i \(0.491136\pi\)
\(198\) −1.38903 −0.0987141
\(199\) 3.72043 0.263734 0.131867 0.991267i \(-0.457903\pi\)
0.131867 + 0.991267i \(0.457903\pi\)
\(200\) −5.43850 −0.384560
\(201\) −4.41034 −0.311081
\(202\) 16.9417 1.19201
\(203\) −19.2590 −1.35172
\(204\) −1.38420 −0.0969136
\(205\) 2.15703 0.150653
\(206\) −23.7921 −1.65767
\(207\) −1.33575 −0.0928413
\(208\) 29.1408 2.02055
\(209\) −2.62316 −0.181448
\(210\) −2.63600 −0.181901
\(211\) −2.95112 −0.203164 −0.101582 0.994827i \(-0.532390\pi\)
−0.101582 + 0.994827i \(0.532390\pi\)
\(212\) −0.723455 −0.0496871
\(213\) −10.1666 −0.696602
\(214\) −4.42556 −0.302525
\(215\) 5.15367 0.351477
\(216\) 1.13283 0.0770795
\(217\) 3.01123 0.204416
\(218\) 8.03444 0.544161
\(219\) 15.6550 1.05787
\(220\) 0.466475 0.0314498
\(221\) 6.00546 0.403971
\(222\) −14.0076 −0.940131
\(223\) 5.81311 0.389275 0.194637 0.980875i \(-0.437647\pi\)
0.194637 + 0.980875i \(0.437647\pi\)
\(224\) 21.3847 1.42883
\(225\) −4.80080 −0.320053
\(226\) 6.44867 0.428959
\(227\) −2.81084 −0.186562 −0.0932812 0.995640i \(-0.529736\pi\)
−0.0932812 + 0.995640i \(0.529736\pi\)
\(228\) −4.80885 −0.318474
\(229\) 19.7529 1.30531 0.652655 0.757655i \(-0.273655\pi\)
0.652655 + 0.757655i \(0.273655\pi\)
\(230\) 1.09673 0.0723163
\(231\) 2.42413 0.159496
\(232\) −6.79559 −0.446153
\(233\) −8.79173 −0.575965 −0.287983 0.957636i \(-0.592985\pi\)
−0.287983 + 0.957636i \(0.592985\pi\)
\(234\) 11.0478 0.722215
\(235\) 2.07970 0.135665
\(236\) −4.97871 −0.324086
\(237\) −15.3608 −0.997790
\(238\) 5.90609 0.382835
\(239\) −11.7069 −0.757258 −0.378629 0.925549i \(-0.623604\pi\)
−0.378629 + 0.925549i \(0.623604\pi\)
\(240\) −2.16571 −0.139796
\(241\) 21.6664 1.39565 0.697826 0.716267i \(-0.254151\pi\)
0.697826 + 0.716267i \(0.254151\pi\)
\(242\) 19.1870 1.23339
\(243\) 1.00000 0.0641500
\(244\) −5.38785 −0.344922
\(245\) 1.47610 0.0943048
\(246\) −8.89074 −0.566853
\(247\) 20.8635 1.32752
\(248\) 1.06252 0.0674703
\(249\) 3.70090 0.234535
\(250\) 8.04702 0.508938
\(251\) −16.4457 −1.03804 −0.519022 0.854761i \(-0.673704\pi\)
−0.519022 + 0.854761i \(0.673704\pi\)
\(252\) 4.44398 0.279944
\(253\) −1.00858 −0.0634088
\(254\) −15.1866 −0.952895
\(255\) −0.446319 −0.0279496
\(256\) 20.9791 1.31119
\(257\) −2.86778 −0.178887 −0.0894437 0.995992i \(-0.528509\pi\)
−0.0894437 + 0.995992i \(0.528509\pi\)
\(258\) −21.2422 −1.32248
\(259\) 24.4461 1.51900
\(260\) −3.71015 −0.230094
\(261\) −5.99876 −0.371314
\(262\) 41.2417 2.54792
\(263\) 12.7348 0.785263 0.392631 0.919696i \(-0.371565\pi\)
0.392631 + 0.919696i \(0.371565\pi\)
\(264\) 0.855361 0.0526438
\(265\) −0.233269 −0.0143296
\(266\) 20.5183 1.25806
\(267\) 1.35034 0.0826392
\(268\) −6.10481 −0.372910
\(269\) −22.2195 −1.35475 −0.677373 0.735640i \(-0.736882\pi\)
−0.677373 + 0.735640i \(0.736882\pi\)
\(270\) −0.821058 −0.0499680
\(271\) 6.43735 0.391041 0.195520 0.980700i \(-0.437360\pi\)
0.195520 + 0.980700i \(0.437360\pi\)
\(272\) 4.85239 0.294219
\(273\) −19.2805 −1.16691
\(274\) 33.4176 2.01883
\(275\) −3.62491 −0.218590
\(276\) −1.84895 −0.111294
\(277\) 12.7060 0.763430 0.381715 0.924280i \(-0.375334\pi\)
0.381715 + 0.924280i \(0.375334\pi\)
\(278\) −6.34315 −0.380437
\(279\) 0.937935 0.0561527
\(280\) 1.62324 0.0970073
\(281\) −20.0757 −1.19761 −0.598807 0.800893i \(-0.704358\pi\)
−0.598807 + 0.800893i \(0.704358\pi\)
\(282\) −8.57202 −0.510456
\(283\) −17.1401 −1.01887 −0.509437 0.860508i \(-0.670146\pi\)
−0.509437 + 0.860508i \(0.670146\pi\)
\(284\) −14.0726 −0.835056
\(285\) −1.55056 −0.0918470
\(286\) 8.34176 0.493259
\(287\) 15.5161 0.915885
\(288\) 6.66089 0.392496
\(289\) 1.00000 0.0588235
\(290\) 4.92533 0.289225
\(291\) −12.1618 −0.712937
\(292\) 21.6698 1.26813
\(293\) 14.7028 0.858945 0.429473 0.903080i \(-0.358699\pi\)
0.429473 + 0.903080i \(0.358699\pi\)
\(294\) −6.08414 −0.354834
\(295\) −1.60532 −0.0934655
\(296\) 8.62586 0.501368
\(297\) 0.755063 0.0438132
\(298\) 15.4470 0.894819
\(299\) 8.02181 0.463913
\(300\) −6.64528 −0.383665
\(301\) 37.0717 2.13678
\(302\) −8.67019 −0.498913
\(303\) −9.20932 −0.529062
\(304\) 16.8577 0.966853
\(305\) −1.73725 −0.0994744
\(306\) 1.83962 0.105164
\(307\) −12.8210 −0.731736 −0.365868 0.930667i \(-0.619228\pi\)
−0.365868 + 0.930667i \(0.619228\pi\)
\(308\) 3.35549 0.191197
\(309\) 12.9331 0.735740
\(310\) −0.770098 −0.0437387
\(311\) −10.9232 −0.619399 −0.309699 0.950834i \(-0.600228\pi\)
−0.309699 + 0.950834i \(0.600228\pi\)
\(312\) −6.80318 −0.385154
\(313\) −19.8697 −1.12310 −0.561552 0.827442i \(-0.689795\pi\)
−0.561552 + 0.827442i \(0.689795\pi\)
\(314\) −1.83962 −0.103816
\(315\) 1.43291 0.0807351
\(316\) −21.2624 −1.19611
\(317\) 8.79359 0.493897 0.246948 0.969029i \(-0.420572\pi\)
0.246948 + 0.969029i \(0.420572\pi\)
\(318\) 0.961480 0.0539171
\(319\) −4.52945 −0.253600
\(320\) −1.13755 −0.0635907
\(321\) 2.40569 0.134273
\(322\) 7.88909 0.439642
\(323\) 3.47410 0.193304
\(324\) 1.38420 0.0769002
\(325\) 28.8310 1.59926
\(326\) 5.32318 0.294824
\(327\) −4.36744 −0.241520
\(328\) 5.47489 0.302300
\(329\) 14.9598 0.824762
\(330\) −0.619951 −0.0341272
\(331\) −18.6818 −1.02684 −0.513422 0.858136i \(-0.671622\pi\)
−0.513422 + 0.858136i \(0.671622\pi\)
\(332\) 5.12279 0.281150
\(333\) 7.61442 0.417268
\(334\) 35.8189 1.95992
\(335\) −1.96842 −0.107546
\(336\) −15.5786 −0.849881
\(337\) −10.3404 −0.563276 −0.281638 0.959521i \(-0.590878\pi\)
−0.281638 + 0.959521i \(0.590878\pi\)
\(338\) −42.4318 −2.30799
\(339\) −3.50544 −0.190389
\(340\) −0.617796 −0.0335047
\(341\) 0.708200 0.0383512
\(342\) 6.39102 0.345587
\(343\) −11.8555 −0.640135
\(344\) 13.0809 0.705273
\(345\) −0.596173 −0.0320969
\(346\) −13.6837 −0.735640
\(347\) −11.9471 −0.641356 −0.320678 0.947188i \(-0.603911\pi\)
−0.320678 + 0.947188i \(0.603911\pi\)
\(348\) −8.30350 −0.445114
\(349\) −24.1205 −1.29114 −0.645571 0.763700i \(-0.723380\pi\)
−0.645571 + 0.763700i \(0.723380\pi\)
\(350\) 28.3540 1.51558
\(351\) −6.00546 −0.320548
\(352\) 5.02939 0.268067
\(353\) −30.4099 −1.61855 −0.809277 0.587427i \(-0.800141\pi\)
−0.809277 + 0.587427i \(0.800141\pi\)
\(354\) 6.61675 0.351677
\(355\) −4.53754 −0.240828
\(356\) 1.86914 0.0990642
\(357\) −3.21050 −0.169917
\(358\) −31.7234 −1.67663
\(359\) −1.91066 −0.100841 −0.0504204 0.998728i \(-0.516056\pi\)
−0.0504204 + 0.998728i \(0.516056\pi\)
\(360\) 0.505605 0.0266477
\(361\) −6.93065 −0.364771
\(362\) −3.56220 −0.187225
\(363\) −10.4299 −0.547427
\(364\) −26.6881 −1.39884
\(365\) 6.98714 0.365724
\(366\) 7.16051 0.374286
\(367\) −18.2460 −0.952436 −0.476218 0.879327i \(-0.657993\pi\)
−0.476218 + 0.879327i \(0.657993\pi\)
\(368\) 6.48160 0.337877
\(369\) 4.83292 0.251592
\(370\) −6.25188 −0.325020
\(371\) −1.67797 −0.0871158
\(372\) 1.29829 0.0673133
\(373\) 23.9197 1.23851 0.619257 0.785189i \(-0.287434\pi\)
0.619257 + 0.785189i \(0.287434\pi\)
\(374\) 1.38903 0.0718250
\(375\) −4.37428 −0.225887
\(376\) 5.27862 0.272224
\(377\) 36.0253 1.85540
\(378\) −5.90609 −0.303777
\(379\) −27.7164 −1.42370 −0.711848 0.702333i \(-0.752142\pi\)
−0.711848 + 0.702333i \(0.752142\pi\)
\(380\) −2.14628 −0.110102
\(381\) 8.25531 0.422933
\(382\) 32.2941 1.65231
\(383\) −22.7856 −1.16429 −0.582146 0.813084i \(-0.697787\pi\)
−0.582146 + 0.813084i \(0.697787\pi\)
\(384\) −8.63308 −0.440555
\(385\) 1.08193 0.0551405
\(386\) 32.1828 1.63806
\(387\) 11.5470 0.586970
\(388\) −16.8344 −0.854636
\(389\) −8.42203 −0.427014 −0.213507 0.976942i \(-0.568489\pi\)
−0.213507 + 0.976942i \(0.568489\pi\)
\(390\) 4.93083 0.249682
\(391\) 1.33575 0.0675520
\(392\) 3.74660 0.189232
\(393\) −22.4186 −1.13087
\(394\) −1.43785 −0.0724379
\(395\) −6.85581 −0.344953
\(396\) 1.04516 0.0525213
\(397\) 23.1340 1.16106 0.580532 0.814237i \(-0.302845\pi\)
0.580532 + 0.814237i \(0.302845\pi\)
\(398\) −6.84418 −0.343068
\(399\) −11.1536 −0.558377
\(400\) 23.2953 1.16477
\(401\) 7.12378 0.355745 0.177872 0.984054i \(-0.443079\pi\)
0.177872 + 0.984054i \(0.443079\pi\)
\(402\) 8.11335 0.404657
\(403\) −5.63273 −0.280586
\(404\) −12.7476 −0.634215
\(405\) 0.446319 0.0221778
\(406\) 35.4292 1.75832
\(407\) 5.74937 0.284986
\(408\) −1.13283 −0.0560836
\(409\) −4.09474 −0.202472 −0.101236 0.994862i \(-0.532280\pi\)
−0.101236 + 0.994862i \(0.532280\pi\)
\(410\) −3.96811 −0.195971
\(411\) −18.1655 −0.896038
\(412\) 17.9021 0.881972
\(413\) −11.5475 −0.568217
\(414\) 2.45728 0.120769
\(415\) 1.65178 0.0810827
\(416\) −40.0017 −1.96124
\(417\) 3.44808 0.168853
\(418\) 4.82562 0.236029
\(419\) −4.09700 −0.200152 −0.100076 0.994980i \(-0.531909\pi\)
−0.100076 + 0.994980i \(0.531909\pi\)
\(420\) 1.98343 0.0967816
\(421\) 16.7932 0.818453 0.409226 0.912433i \(-0.365799\pi\)
0.409226 + 0.912433i \(0.365799\pi\)
\(422\) 5.42895 0.264277
\(423\) 4.65967 0.226561
\(424\) −0.592076 −0.0287538
\(425\) 4.80080 0.232873
\(426\) 18.7026 0.906146
\(427\) −12.4965 −0.604747
\(428\) 3.32997 0.160960
\(429\) −4.53450 −0.218928
\(430\) −9.48080 −0.457205
\(431\) −38.3833 −1.84886 −0.924430 0.381351i \(-0.875459\pi\)
−0.924430 + 0.381351i \(0.875459\pi\)
\(432\) −4.85239 −0.233461
\(433\) 21.1848 1.01808 0.509038 0.860744i \(-0.330001\pi\)
0.509038 + 0.860744i \(0.330001\pi\)
\(434\) −5.53953 −0.265906
\(435\) −2.67736 −0.128370
\(436\) −6.04543 −0.289524
\(437\) 4.64054 0.221987
\(438\) −28.7993 −1.37609
\(439\) −5.09873 −0.243349 −0.121675 0.992570i \(-0.538826\pi\)
−0.121675 + 0.992570i \(0.538826\pi\)
\(440\) 0.381764 0.0181999
\(441\) 3.30728 0.157490
\(442\) −11.0478 −0.525488
\(443\) 9.28038 0.440924 0.220462 0.975396i \(-0.429243\pi\)
0.220462 + 0.975396i \(0.429243\pi\)
\(444\) 10.5399 0.500202
\(445\) 0.602681 0.0285698
\(446\) −10.6939 −0.506372
\(447\) −8.39683 −0.397156
\(448\) −8.18267 −0.386595
\(449\) 26.1201 1.23269 0.616343 0.787478i \(-0.288614\pi\)
0.616343 + 0.787478i \(0.288614\pi\)
\(450\) 8.83165 0.416328
\(451\) 3.64916 0.171832
\(452\) −4.85224 −0.228230
\(453\) 4.71303 0.221438
\(454\) 5.17089 0.242682
\(455\) −8.60525 −0.403421
\(456\) −3.93557 −0.184300
\(457\) −31.8956 −1.49201 −0.746006 0.665940i \(-0.768031\pi\)
−0.746006 + 0.665940i \(0.768031\pi\)
\(458\) −36.3379 −1.69796
\(459\) −1.00000 −0.0466760
\(460\) −0.825224 −0.0384763
\(461\) −17.8924 −0.833334 −0.416667 0.909059i \(-0.636802\pi\)
−0.416667 + 0.909059i \(0.636802\pi\)
\(462\) −4.45947 −0.207474
\(463\) −15.5257 −0.721538 −0.360769 0.932655i \(-0.617486\pi\)
−0.360769 + 0.932655i \(0.617486\pi\)
\(464\) 29.1083 1.35132
\(465\) 0.418618 0.0194130
\(466\) 16.1734 0.749220
\(467\) −28.7219 −1.32909 −0.664545 0.747248i \(-0.731375\pi\)
−0.664545 + 0.747248i \(0.731375\pi\)
\(468\) −8.31277 −0.384258
\(469\) −14.1594 −0.653819
\(470\) −3.82586 −0.176474
\(471\) 1.00000 0.0460776
\(472\) −4.07458 −0.187548
\(473\) 8.71876 0.400889
\(474\) 28.2580 1.29793
\(475\) 16.6784 0.765259
\(476\) −4.44398 −0.203689
\(477\) −0.522651 −0.0239306
\(478\) 21.5363 0.985047
\(479\) 4.37172 0.199749 0.0998744 0.995000i \(-0.468156\pi\)
0.0998744 + 0.995000i \(0.468156\pi\)
\(480\) 2.97288 0.135693
\(481\) −45.7281 −2.08502
\(482\) −39.8579 −1.81548
\(483\) −4.28843 −0.195130
\(484\) −14.4371 −0.656230
\(485\) −5.42804 −0.246475
\(486\) −1.83962 −0.0834469
\(487\) −13.5242 −0.612839 −0.306419 0.951897i \(-0.599131\pi\)
−0.306419 + 0.951897i \(0.599131\pi\)
\(488\) −4.40942 −0.199605
\(489\) −2.89363 −0.130854
\(490\) −2.71547 −0.122672
\(491\) 33.9148 1.53055 0.765276 0.643702i \(-0.222602\pi\)
0.765276 + 0.643702i \(0.222602\pi\)
\(492\) 6.68975 0.301597
\(493\) 5.99876 0.270171
\(494\) −38.3810 −1.72684
\(495\) 0.336999 0.0151470
\(496\) −4.55122 −0.204356
\(497\) −32.6398 −1.46409
\(498\) −6.80824 −0.305085
\(499\) 13.9621 0.625030 0.312515 0.949913i \(-0.398829\pi\)
0.312515 + 0.949913i \(0.398829\pi\)
\(500\) −6.05490 −0.270783
\(501\) −19.4708 −0.869892
\(502\) 30.2539 1.35030
\(503\) −1.05698 −0.0471283 −0.0235642 0.999722i \(-0.507501\pi\)
−0.0235642 + 0.999722i \(0.507501\pi\)
\(504\) 3.63695 0.162003
\(505\) −4.11030 −0.182906
\(506\) 1.85540 0.0824827
\(507\) 23.0655 1.02438
\(508\) 11.4270 0.506993
\(509\) 11.0058 0.487823 0.243911 0.969798i \(-0.421569\pi\)
0.243911 + 0.969798i \(0.421569\pi\)
\(510\) 0.821058 0.0363571
\(511\) 50.2604 2.22339
\(512\) −21.3273 −0.942543
\(513\) −3.47410 −0.153385
\(514\) 5.27563 0.232698
\(515\) 5.77230 0.254358
\(516\) 15.9835 0.703633
\(517\) 3.51834 0.154737
\(518\) −44.9715 −1.97593
\(519\) 7.43832 0.326506
\(520\) −3.03639 −0.133154
\(521\) −17.9608 −0.786876 −0.393438 0.919351i \(-0.628714\pi\)
−0.393438 + 0.919351i \(0.628714\pi\)
\(522\) 11.0354 0.483008
\(523\) −0.352744 −0.0154244 −0.00771220 0.999970i \(-0.502455\pi\)
−0.00771220 + 0.999970i \(0.502455\pi\)
\(524\) −31.0319 −1.35563
\(525\) −15.4129 −0.672676
\(526\) −23.4272 −1.02148
\(527\) −0.937935 −0.0408571
\(528\) −3.66386 −0.159449
\(529\) −21.2158 −0.922424
\(530\) 0.429127 0.0186401
\(531\) −3.59680 −0.156088
\(532\) −15.4388 −0.669357
\(533\) −29.0239 −1.25717
\(534\) −2.48411 −0.107498
\(535\) 1.07371 0.0464204
\(536\) −4.99618 −0.215802
\(537\) 17.2445 0.744156
\(538\) 40.8754 1.76226
\(539\) 2.49721 0.107562
\(540\) 0.617796 0.0265857
\(541\) −0.711043 −0.0305701 −0.0152851 0.999883i \(-0.504866\pi\)
−0.0152851 + 0.999883i \(0.504866\pi\)
\(542\) −11.8423 −0.508669
\(543\) 1.93638 0.0830979
\(544\) −6.66089 −0.285583
\(545\) −1.94927 −0.0834977
\(546\) 35.4688 1.51792
\(547\) −19.5158 −0.834436 −0.417218 0.908807i \(-0.636995\pi\)
−0.417218 + 0.908807i \(0.636995\pi\)
\(548\) −25.1447 −1.07413
\(549\) −3.89238 −0.166123
\(550\) 6.66845 0.284344
\(551\) 20.8403 0.887826
\(552\) −1.51319 −0.0644055
\(553\) −49.3157 −2.09712
\(554\) −23.3742 −0.993076
\(555\) 3.39846 0.144257
\(556\) 4.77284 0.202413
\(557\) −7.48203 −0.317024 −0.158512 0.987357i \(-0.550670\pi\)
−0.158512 + 0.987357i \(0.550670\pi\)
\(558\) −1.72544 −0.0730438
\(559\) −69.3453 −2.93299
\(560\) −6.95301 −0.293818
\(561\) −0.755063 −0.0318788
\(562\) 36.9316 1.55787
\(563\) 13.2808 0.559721 0.279860 0.960041i \(-0.409712\pi\)
0.279860 + 0.960041i \(0.409712\pi\)
\(564\) 6.44992 0.271591
\(565\) −1.56454 −0.0658208
\(566\) 31.5313 1.32536
\(567\) 3.21050 0.134828
\(568\) −11.5170 −0.483244
\(569\) 34.2610 1.43630 0.718148 0.695891i \(-0.244990\pi\)
0.718148 + 0.695891i \(0.244990\pi\)
\(570\) 2.85243 0.119475
\(571\) 26.5105 1.10943 0.554714 0.832041i \(-0.312828\pi\)
0.554714 + 0.832041i \(0.312828\pi\)
\(572\) −6.27667 −0.262441
\(573\) −17.5547 −0.733360
\(574\) −28.5437 −1.19139
\(575\) 6.41269 0.267428
\(576\) −2.54873 −0.106197
\(577\) 27.5838 1.14833 0.574165 0.818740i \(-0.305327\pi\)
0.574165 + 0.818740i \(0.305327\pi\)
\(578\) −1.83962 −0.0765181
\(579\) −17.4943 −0.727036
\(580\) −3.70601 −0.153884
\(581\) 11.8817 0.492936
\(582\) 22.3731 0.927394
\(583\) −0.394635 −0.0163441
\(584\) 17.7345 0.733860
\(585\) −2.68035 −0.110819
\(586\) −27.0475 −1.11732
\(587\) −40.4654 −1.67019 −0.835093 0.550109i \(-0.814586\pi\)
−0.835093 + 0.550109i \(0.814586\pi\)
\(588\) 4.57795 0.188791
\(589\) −3.25847 −0.134263
\(590\) 2.95318 0.121581
\(591\) 0.781602 0.0321508
\(592\) −36.9481 −1.51856
\(593\) 24.0408 0.987239 0.493620 0.869678i \(-0.335674\pi\)
0.493620 + 0.869678i \(0.335674\pi\)
\(594\) −1.38903 −0.0569926
\(595\) −1.43291 −0.0587434
\(596\) −11.6229 −0.476093
\(597\) 3.72043 0.152267
\(598\) −14.7571 −0.603462
\(599\) 22.8014 0.931639 0.465819 0.884880i \(-0.345760\pi\)
0.465819 + 0.884880i \(0.345760\pi\)
\(600\) −5.43850 −0.222026
\(601\) −11.5020 −0.469175 −0.234587 0.972095i \(-0.575374\pi\)
−0.234587 + 0.972095i \(0.575374\pi\)
\(602\) −68.1979 −2.77954
\(603\) −4.41034 −0.179603
\(604\) 6.52379 0.265449
\(605\) −4.65505 −0.189255
\(606\) 16.9417 0.688208
\(607\) 26.0331 1.05665 0.528326 0.849042i \(-0.322820\pi\)
0.528326 + 0.849042i \(0.322820\pi\)
\(608\) −23.1406 −0.938474
\(609\) −19.2590 −0.780414
\(610\) 3.19587 0.129397
\(611\) −27.9834 −1.13209
\(612\) −1.38420 −0.0559531
\(613\) 42.7072 1.72493 0.862464 0.506119i \(-0.168920\pi\)
0.862464 + 0.506119i \(0.168920\pi\)
\(614\) 23.5859 0.951848
\(615\) 2.15703 0.0869797
\(616\) 2.74613 0.110645
\(617\) 12.5604 0.505663 0.252831 0.967510i \(-0.418638\pi\)
0.252831 + 0.967510i \(0.418638\pi\)
\(618\) −23.7921 −0.957057
\(619\) 2.29891 0.0924010 0.0462005 0.998932i \(-0.485289\pi\)
0.0462005 + 0.998932i \(0.485289\pi\)
\(620\) 0.579453 0.0232714
\(621\) −1.33575 −0.0536020
\(622\) 20.0946 0.805719
\(623\) 4.33525 0.173688
\(624\) 29.1408 1.16657
\(625\) 22.0517 0.882067
\(626\) 36.5527 1.46094
\(627\) −2.62316 −0.104759
\(628\) 1.38420 0.0552357
\(629\) −7.61442 −0.303607
\(630\) −2.63600 −0.105021
\(631\) 7.25565 0.288843 0.144421 0.989516i \(-0.453868\pi\)
0.144421 + 0.989516i \(0.453868\pi\)
\(632\) −17.4012 −0.692183
\(633\) −2.95112 −0.117297
\(634\) −16.1769 −0.642465
\(635\) 3.68451 0.146215
\(636\) −0.723455 −0.0286869
\(637\) −19.8617 −0.786951
\(638\) 8.33246 0.329885
\(639\) −10.1666 −0.402184
\(640\) −3.85311 −0.152308
\(641\) 22.8705 0.903332 0.451666 0.892187i \(-0.350830\pi\)
0.451666 + 0.892187i \(0.350830\pi\)
\(642\) −4.42556 −0.174663
\(643\) 27.5324 1.08577 0.542887 0.839806i \(-0.317331\pi\)
0.542887 + 0.839806i \(0.317331\pi\)
\(644\) −5.93606 −0.233914
\(645\) 5.15367 0.202926
\(646\) −6.39102 −0.251451
\(647\) −13.7759 −0.541586 −0.270793 0.962638i \(-0.587286\pi\)
−0.270793 + 0.962638i \(0.587286\pi\)
\(648\) 1.13283 0.0445019
\(649\) −2.71582 −0.106605
\(650\) −53.0381 −2.08032
\(651\) 3.01123 0.118020
\(652\) −4.00537 −0.156862
\(653\) 31.2456 1.22273 0.611367 0.791347i \(-0.290620\pi\)
0.611367 + 0.791347i \(0.290620\pi\)
\(654\) 8.03444 0.314171
\(655\) −10.0058 −0.390961
\(656\) −23.4512 −0.915616
\(657\) 15.6550 0.610761
\(658\) −27.5204 −1.07286
\(659\) −23.7045 −0.923396 −0.461698 0.887037i \(-0.652760\pi\)
−0.461698 + 0.887037i \(0.652760\pi\)
\(660\) 0.466475 0.0181575
\(661\) −19.8230 −0.771026 −0.385513 0.922702i \(-0.625976\pi\)
−0.385513 + 0.922702i \(0.625976\pi\)
\(662\) 34.3674 1.33573
\(663\) 6.00546 0.233233
\(664\) 4.19250 0.162700
\(665\) −4.97805 −0.193041
\(666\) −14.0076 −0.542785
\(667\) 8.01287 0.310260
\(668\) −26.9516 −1.04279
\(669\) 5.81311 0.224748
\(670\) 3.62114 0.139897
\(671\) −2.93900 −0.113459
\(672\) 21.3847 0.824934
\(673\) 41.4024 1.59594 0.797972 0.602694i \(-0.205906\pi\)
0.797972 + 0.602694i \(0.205906\pi\)
\(674\) 19.0224 0.732714
\(675\) −4.80080 −0.184783
\(676\) 31.9274 1.22798
\(677\) 40.4080 1.55301 0.776503 0.630114i \(-0.216992\pi\)
0.776503 + 0.630114i \(0.216992\pi\)
\(678\) 6.44867 0.247660
\(679\) −39.0454 −1.49842
\(680\) −0.505605 −0.0193891
\(681\) −2.81084 −0.107712
\(682\) −1.30282 −0.0498875
\(683\) −45.2385 −1.73100 −0.865501 0.500907i \(-0.833000\pi\)
−0.865501 + 0.500907i \(0.833000\pi\)
\(684\) −4.80885 −0.183871
\(685\) −8.10761 −0.309776
\(686\) 21.8095 0.832692
\(687\) 19.7529 0.753621
\(688\) −56.0308 −2.13615
\(689\) 3.13876 0.119577
\(690\) 1.09673 0.0417518
\(691\) −46.2740 −1.76034 −0.880172 0.474655i \(-0.842573\pi\)
−0.880172 + 0.474655i \(0.842573\pi\)
\(692\) 10.2962 0.391401
\(693\) 2.42413 0.0920850
\(694\) 21.9782 0.834280
\(695\) 1.53894 0.0583754
\(696\) −6.79559 −0.257586
\(697\) −4.83292 −0.183060
\(698\) 44.3726 1.67953
\(699\) −8.79173 −0.332534
\(700\) −21.3346 −0.806374
\(701\) 8.49922 0.321011 0.160505 0.987035i \(-0.448688\pi\)
0.160505 + 0.987035i \(0.448688\pi\)
\(702\) 11.0478 0.416971
\(703\) −26.4532 −0.997702
\(704\) −1.92445 −0.0725304
\(705\) 2.07970 0.0783260
\(706\) 55.9426 2.10543
\(707\) −29.5665 −1.11196
\(708\) −4.97871 −0.187111
\(709\) −12.5160 −0.470048 −0.235024 0.971990i \(-0.575517\pi\)
−0.235024 + 0.971990i \(0.575517\pi\)
\(710\) 8.34735 0.313270
\(711\) −15.3608 −0.576075
\(712\) 1.52970 0.0573281
\(713\) −1.25285 −0.0469196
\(714\) 5.90609 0.221030
\(715\) −2.02383 −0.0756871
\(716\) 23.8699 0.892061
\(717\) −11.7069 −0.437203
\(718\) 3.51489 0.131175
\(719\) 13.9248 0.519306 0.259653 0.965702i \(-0.416392\pi\)
0.259653 + 0.965702i \(0.416392\pi\)
\(720\) −2.16571 −0.0807114
\(721\) 41.5218 1.54635
\(722\) 12.7498 0.474497
\(723\) 21.6664 0.805780
\(724\) 2.68034 0.0996140
\(725\) 28.7988 1.06956
\(726\) 19.1870 0.712097
\(727\) 20.0022 0.741839 0.370919 0.928665i \(-0.379043\pi\)
0.370919 + 0.928665i \(0.379043\pi\)
\(728\) −21.8416 −0.809503
\(729\) 1.00000 0.0370370
\(730\) −12.8537 −0.475736
\(731\) −11.5470 −0.427083
\(732\) −5.38785 −0.199141
\(733\) −34.0639 −1.25818 −0.629090 0.777332i \(-0.716572\pi\)
−0.629090 + 0.777332i \(0.716572\pi\)
\(734\) 33.5658 1.23894
\(735\) 1.47610 0.0544469
\(736\) −8.89731 −0.327959
\(737\) −3.33009 −0.122665
\(738\) −8.89074 −0.327273
\(739\) −23.0416 −0.847600 −0.423800 0.905756i \(-0.639304\pi\)
−0.423800 + 0.905756i \(0.639304\pi\)
\(740\) 4.70416 0.172928
\(741\) 20.8635 0.766441
\(742\) 3.08683 0.113321
\(743\) 33.6432 1.23425 0.617126 0.786865i \(-0.288297\pi\)
0.617126 + 0.786865i \(0.288297\pi\)
\(744\) 1.06252 0.0389540
\(745\) −3.74766 −0.137304
\(746\) −44.0031 −1.61107
\(747\) 3.70090 0.135409
\(748\) −1.04516 −0.0382149
\(749\) 7.72347 0.282209
\(750\) 8.04702 0.293836
\(751\) −8.22992 −0.300314 −0.150157 0.988662i \(-0.547978\pi\)
−0.150157 + 0.988662i \(0.547978\pi\)
\(752\) −22.6105 −0.824520
\(753\) −16.4457 −0.599315
\(754\) −66.2729 −2.41352
\(755\) 2.10352 0.0765548
\(756\) 4.44398 0.161626
\(757\) 36.0285 1.30948 0.654738 0.755856i \(-0.272779\pi\)
0.654738 + 0.755856i \(0.272779\pi\)
\(758\) 50.9877 1.85196
\(759\) −1.00858 −0.0366091
\(760\) −1.75652 −0.0637157
\(761\) −9.75040 −0.353452 −0.176726 0.984260i \(-0.556551\pi\)
−0.176726 + 0.984260i \(0.556551\pi\)
\(762\) −15.1866 −0.550154
\(763\) −14.0217 −0.507618
\(764\) −24.2993 −0.879119
\(765\) −0.446319 −0.0161367
\(766\) 41.9169 1.51452
\(767\) 21.6005 0.779947
\(768\) 20.9791 0.757016
\(769\) 9.07378 0.327209 0.163604 0.986526i \(-0.447688\pi\)
0.163604 + 0.986526i \(0.447688\pi\)
\(770\) −1.99035 −0.0717272
\(771\) −2.86778 −0.103281
\(772\) −24.2156 −0.871538
\(773\) −10.3566 −0.372499 −0.186250 0.982502i \(-0.559633\pi\)
−0.186250 + 0.982502i \(0.559633\pi\)
\(774\) −21.2422 −0.763535
\(775\) −4.50284 −0.161747
\(776\) −13.7773 −0.494575
\(777\) 24.4461 0.876997
\(778\) 15.4933 0.555463
\(779\) −16.7900 −0.601566
\(780\) −3.71015 −0.132845
\(781\) −7.67641 −0.274684
\(782\) −2.45728 −0.0878722
\(783\) −5.99876 −0.214378
\(784\) −16.0482 −0.573150
\(785\) 0.446319 0.0159298
\(786\) 41.2417 1.47104
\(787\) 47.6846 1.69977 0.849886 0.526967i \(-0.176671\pi\)
0.849886 + 0.526967i \(0.176671\pi\)
\(788\) 1.08190 0.0385409
\(789\) 12.7348 0.453372
\(790\) 12.6121 0.448718
\(791\) −11.2542 −0.400153
\(792\) 0.855361 0.0303939
\(793\) 23.3755 0.830090
\(794\) −42.5579 −1.51032
\(795\) −0.233269 −0.00827321
\(796\) 5.14983 0.182531
\(797\) −43.3536 −1.53566 −0.767831 0.640652i \(-0.778664\pi\)
−0.767831 + 0.640652i \(0.778664\pi\)
\(798\) 20.5183 0.726341
\(799\) −4.65967 −0.164847
\(800\) −31.9776 −1.13058
\(801\) 1.35034 0.0477118
\(802\) −13.1051 −0.462755
\(803\) 11.8205 0.417138
\(804\) −6.10481 −0.215300
\(805\) −1.91401 −0.0674600
\(806\) 10.3621 0.364989
\(807\) −22.2195 −0.782163
\(808\) −10.4326 −0.367018
\(809\) 27.1159 0.953345 0.476672 0.879081i \(-0.341843\pi\)
0.476672 + 0.879081i \(0.341843\pi\)
\(810\) −0.821058 −0.0288490
\(811\) 46.4477 1.63100 0.815500 0.578758i \(-0.196462\pi\)
0.815500 + 0.578758i \(0.196462\pi\)
\(812\) −26.6584 −0.935525
\(813\) 6.43735 0.225768
\(814\) −10.5767 −0.370712
\(815\) −1.29148 −0.0452386
\(816\) 4.85239 0.169868
\(817\) −40.1156 −1.40347
\(818\) 7.53277 0.263377
\(819\) −19.2805 −0.673715
\(820\) 2.98576 0.104267
\(821\) −34.2620 −1.19575 −0.597876 0.801589i \(-0.703988\pi\)
−0.597876 + 0.801589i \(0.703988\pi\)
\(822\) 33.4176 1.16557
\(823\) −21.4199 −0.746651 −0.373326 0.927700i \(-0.621783\pi\)
−0.373326 + 0.927700i \(0.621783\pi\)
\(824\) 14.6511 0.510394
\(825\) −3.62491 −0.126203
\(826\) 21.2431 0.739141
\(827\) 24.3985 0.848419 0.424210 0.905564i \(-0.360552\pi\)
0.424210 + 0.905564i \(0.360552\pi\)
\(828\) −1.84895 −0.0642556
\(829\) 55.4033 1.92424 0.962119 0.272631i \(-0.0878937\pi\)
0.962119 + 0.272631i \(0.0878937\pi\)
\(830\) −3.03865 −0.105473
\(831\) 12.7060 0.440767
\(832\) 15.3063 0.530649
\(833\) −3.30728 −0.114590
\(834\) −6.34315 −0.219645
\(835\) −8.69020 −0.300737
\(836\) −3.63099 −0.125580
\(837\) 0.937935 0.0324198
\(838\) 7.53692 0.260359
\(839\) −35.7078 −1.23277 −0.616384 0.787445i \(-0.711403\pi\)
−0.616384 + 0.787445i \(0.711403\pi\)
\(840\) 1.62324 0.0560072
\(841\) 6.98513 0.240867
\(842\) −30.8932 −1.06465
\(843\) −20.0757 −0.691443
\(844\) −4.08495 −0.140610
\(845\) 10.2946 0.354144
\(846\) −8.57202 −0.294712
\(847\) −33.4851 −1.15056
\(848\) 2.53611 0.0870903
\(849\) −17.1401 −0.588247
\(850\) −8.83165 −0.302923
\(851\) −10.1710 −0.348657
\(852\) −14.0726 −0.482120
\(853\) −38.9845 −1.33480 −0.667402 0.744697i \(-0.732594\pi\)
−0.667402 + 0.744697i \(0.732594\pi\)
\(854\) 22.9888 0.786660
\(855\) −1.55056 −0.0530279
\(856\) 2.72525 0.0931471
\(857\) −7.36037 −0.251425 −0.125713 0.992067i \(-0.540122\pi\)
−0.125713 + 0.992067i \(0.540122\pi\)
\(858\) 8.34176 0.284783
\(859\) 7.23709 0.246926 0.123463 0.992349i \(-0.460600\pi\)
0.123463 + 0.992349i \(0.460600\pi\)
\(860\) 7.13372 0.243258
\(861\) 15.5161 0.528786
\(862\) 70.6108 2.40501
\(863\) 44.5640 1.51697 0.758487 0.651688i \(-0.225939\pi\)
0.758487 + 0.651688i \(0.225939\pi\)
\(864\) 6.66089 0.226608
\(865\) 3.31987 0.112879
\(866\) −38.9720 −1.32432
\(867\) 1.00000 0.0339618
\(868\) 4.16816 0.141477
\(869\) −11.5984 −0.393448
\(870\) 4.92533 0.166984
\(871\) 26.4861 0.897448
\(872\) −4.94758 −0.167546
\(873\) −12.1618 −0.411614
\(874\) −8.53683 −0.288763
\(875\) −14.0436 −0.474761
\(876\) 21.6698 0.732153
\(877\) 58.5585 1.97738 0.988690 0.149974i \(-0.0479190\pi\)
0.988690 + 0.149974i \(0.0479190\pi\)
\(878\) 9.37973 0.316551
\(879\) 14.7028 0.495912
\(880\) −1.63525 −0.0551243
\(881\) −14.2452 −0.479932 −0.239966 0.970781i \(-0.577136\pi\)
−0.239966 + 0.970781i \(0.577136\pi\)
\(882\) −6.08414 −0.204864
\(883\) 36.4077 1.22522 0.612609 0.790386i \(-0.290120\pi\)
0.612609 + 0.790386i \(0.290120\pi\)
\(884\) 8.31277 0.279589
\(885\) −1.60532 −0.0539623
\(886\) −17.0724 −0.573558
\(887\) 1.35943 0.0456453 0.0228226 0.999740i \(-0.492735\pi\)
0.0228226 + 0.999740i \(0.492735\pi\)
\(888\) 8.62586 0.289465
\(889\) 26.5036 0.888904
\(890\) −1.10870 −0.0371638
\(891\) 0.755063 0.0252956
\(892\) 8.04653 0.269418
\(893\) −16.1881 −0.541715
\(894\) 15.4470 0.516624
\(895\) 7.69656 0.257268
\(896\) −27.7165 −0.925943
\(897\) 8.02181 0.267841
\(898\) −48.0511 −1.60349
\(899\) −5.62645 −0.187652
\(900\) −6.64528 −0.221509
\(901\) 0.522651 0.0174120
\(902\) −6.71308 −0.223521
\(903\) 37.0717 1.23367
\(904\) −3.97107 −0.132076
\(905\) 0.864242 0.0287284
\(906\) −8.67019 −0.288048
\(907\) 17.4641 0.579887 0.289943 0.957044i \(-0.406364\pi\)
0.289943 + 0.957044i \(0.406364\pi\)
\(908\) −3.89078 −0.129120
\(909\) −9.20932 −0.305454
\(910\) 15.8304 0.524773
\(911\) 32.8539 1.08850 0.544249 0.838923i \(-0.316815\pi\)
0.544249 + 0.838923i \(0.316815\pi\)
\(912\) 16.8577 0.558213
\(913\) 2.79441 0.0924815
\(914\) 58.6757 1.94082
\(915\) −1.73725 −0.0574316
\(916\) 27.3421 0.903407
\(917\) −71.9748 −2.37682
\(918\) 1.83962 0.0607165
\(919\) −22.6488 −0.747114 −0.373557 0.927607i \(-0.621862\pi\)
−0.373557 + 0.927607i \(0.621862\pi\)
\(920\) −0.675364 −0.0222661
\(921\) −12.8210 −0.422468
\(922\) 32.9153 1.08401
\(923\) 61.0549 2.00965
\(924\) 3.35549 0.110387
\(925\) −36.5553 −1.20193
\(926\) 28.5613 0.938583
\(927\) 12.9331 0.424780
\(928\) −39.9571 −1.31165
\(929\) −4.60508 −0.151088 −0.0755438 0.997142i \(-0.524069\pi\)
−0.0755438 + 0.997142i \(0.524069\pi\)
\(930\) −0.770098 −0.0252525
\(931\) −11.4898 −0.376563
\(932\) −12.1695 −0.398626
\(933\) −10.9232 −0.357610
\(934\) 52.8374 1.72889
\(935\) −0.336999 −0.0110211
\(936\) −6.80318 −0.222369
\(937\) −37.9397 −1.23943 −0.619717 0.784825i \(-0.712753\pi\)
−0.619717 + 0.784825i \(0.712753\pi\)
\(938\) 26.0479 0.850493
\(939\) −19.8697 −0.648424
\(940\) 2.87872 0.0938936
\(941\) −39.5174 −1.28823 −0.644116 0.764928i \(-0.722774\pi\)
−0.644116 + 0.764928i \(0.722774\pi\)
\(942\) −1.83962 −0.0599381
\(943\) −6.45560 −0.210223
\(944\) 17.4531 0.568050
\(945\) 1.43291 0.0466124
\(946\) −16.0392 −0.521479
\(947\) 46.1968 1.50119 0.750597 0.660760i \(-0.229766\pi\)
0.750597 + 0.660760i \(0.229766\pi\)
\(948\) −21.2624 −0.690572
\(949\) −94.0157 −3.05188
\(950\) −30.6820 −0.995455
\(951\) 8.79359 0.285152
\(952\) −3.63695 −0.117874
\(953\) −29.7051 −0.962242 −0.481121 0.876654i \(-0.659770\pi\)
−0.481121 + 0.876654i \(0.659770\pi\)
\(954\) 0.961480 0.0311291
\(955\) −7.83502 −0.253535
\(956\) −16.2048 −0.524099
\(957\) −4.52945 −0.146416
\(958\) −8.04230 −0.259835
\(959\) −58.3203 −1.88326
\(960\) −1.13755 −0.0367141
\(961\) −30.1203 −0.971622
\(962\) 84.1223 2.71221
\(963\) 2.40569 0.0775224
\(964\) 29.9906 0.965933
\(965\) −7.80802 −0.251349
\(966\) 7.88909 0.253827
\(967\) −9.07931 −0.291971 −0.145986 0.989287i \(-0.546635\pi\)
−0.145986 + 0.989287i \(0.546635\pi\)
\(968\) −11.8153 −0.379758
\(969\) 3.47410 0.111604
\(970\) 9.98553 0.320616
\(971\) 13.8983 0.446018 0.223009 0.974816i \(-0.428412\pi\)
0.223009 + 0.974816i \(0.428412\pi\)
\(972\) 1.38420 0.0443983
\(973\) 11.0700 0.354889
\(974\) 24.8793 0.797185
\(975\) 28.8310 0.923331
\(976\) 18.8874 0.604570
\(977\) −23.1988 −0.742196 −0.371098 0.928594i \(-0.621019\pi\)
−0.371098 + 0.928594i \(0.621019\pi\)
\(978\) 5.32318 0.170216
\(979\) 1.01959 0.0325862
\(980\) 2.04323 0.0652685
\(981\) −4.36744 −0.139442
\(982\) −62.3903 −1.99095
\(983\) −4.95426 −0.158016 −0.0790082 0.996874i \(-0.525175\pi\)
−0.0790082 + 0.996874i \(0.525175\pi\)
\(984\) 5.47489 0.174533
\(985\) 0.348844 0.0111151
\(986\) −11.0354 −0.351440
\(987\) 14.9598 0.476177
\(988\) 28.8794 0.918775
\(989\) −15.4240 −0.490455
\(990\) −0.619951 −0.0197033
\(991\) −30.3631 −0.964516 −0.482258 0.876029i \(-0.660183\pi\)
−0.482258 + 0.876029i \(0.660183\pi\)
\(992\) 6.24748 0.198358
\(993\) −18.6818 −0.592848
\(994\) 60.0448 1.90450
\(995\) 1.66050 0.0526414
\(996\) 5.12279 0.162322
\(997\) −33.7430 −1.06865 −0.534326 0.845278i \(-0.679435\pi\)
−0.534326 + 0.845278i \(0.679435\pi\)
\(998\) −25.6850 −0.813044
\(999\) 7.61442 0.240910
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 \(a_p\))