Properties

Label 8043.2.a.t.1.7
Level 8043
Weight 2
Character 8043.1
Self dual Yes
Analytic conductor 64.224
Analytic rank 0
Dimension 52
CM No

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Newspace parameters

Level: \( N \) = \( 8043 = 3 \cdot 7 \cdot 383 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8043.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2236783457\)
Analytic rank: \(0\)
Dimension: \(52\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 8043.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.28128 q^{2} -1.00000 q^{3} +3.20426 q^{4} +2.19375 q^{5} +2.28128 q^{6} +1.00000 q^{7} -2.74725 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.28128 q^{2} -1.00000 q^{3} +3.20426 q^{4} +2.19375 q^{5} +2.28128 q^{6} +1.00000 q^{7} -2.74725 q^{8} +1.00000 q^{9} -5.00457 q^{10} -5.46288 q^{11} -3.20426 q^{12} -1.92610 q^{13} -2.28128 q^{14} -2.19375 q^{15} -0.141251 q^{16} -3.39222 q^{17} -2.28128 q^{18} +4.43083 q^{19} +7.02934 q^{20} -1.00000 q^{21} +12.4624 q^{22} -5.61925 q^{23} +2.74725 q^{24} -0.187455 q^{25} +4.39397 q^{26} -1.00000 q^{27} +3.20426 q^{28} -4.28623 q^{29} +5.00457 q^{30} +3.43056 q^{31} +5.81674 q^{32} +5.46288 q^{33} +7.73862 q^{34} +2.19375 q^{35} +3.20426 q^{36} -8.18210 q^{37} -10.1080 q^{38} +1.92610 q^{39} -6.02679 q^{40} -6.81620 q^{41} +2.28128 q^{42} +1.40342 q^{43} -17.5045 q^{44} +2.19375 q^{45} +12.8191 q^{46} -7.83905 q^{47} +0.141251 q^{48} +1.00000 q^{49} +0.427638 q^{50} +3.39222 q^{51} -6.17171 q^{52} +3.13136 q^{53} +2.28128 q^{54} -11.9842 q^{55} -2.74725 q^{56} -4.43083 q^{57} +9.77810 q^{58} -1.91066 q^{59} -7.02934 q^{60} -5.52236 q^{61} -7.82609 q^{62} +1.00000 q^{63} -12.9871 q^{64} -4.22538 q^{65} -12.4624 q^{66} -4.20815 q^{67} -10.8695 q^{68} +5.61925 q^{69} -5.00457 q^{70} -7.79993 q^{71} -2.74725 q^{72} +12.9587 q^{73} +18.6657 q^{74} +0.187455 q^{75} +14.1975 q^{76} -5.46288 q^{77} -4.39397 q^{78} -14.7769 q^{79} -0.309871 q^{80} +1.00000 q^{81} +15.5497 q^{82} +11.1649 q^{83} -3.20426 q^{84} -7.44169 q^{85} -3.20161 q^{86} +4.28623 q^{87} +15.0079 q^{88} +2.89981 q^{89} -5.00457 q^{90} -1.92610 q^{91} -18.0055 q^{92} -3.43056 q^{93} +17.8831 q^{94} +9.72014 q^{95} -5.81674 q^{96} +0.436297 q^{97} -2.28128 q^{98} -5.46288 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q + 3q^{2} - 52q^{3} + 61q^{4} - 7q^{5} - 3q^{6} + 52q^{7} + 24q^{8} + 52q^{9} + O(q^{10}) \) \( 52q + 3q^{2} - 52q^{3} + 61q^{4} - 7q^{5} - 3q^{6} + 52q^{7} + 24q^{8} + 52q^{9} - 2q^{10} + 9q^{11} - 61q^{12} + 44q^{13} + 3q^{14} + 7q^{15} + 95q^{16} - 6q^{17} + 3q^{18} + 7q^{19} - 21q^{20} - 52q^{21} + 19q^{22} - 4q^{23} - 24q^{24} + 83q^{25} - 5q^{26} - 52q^{27} + 61q^{28} + 31q^{29} + 2q^{30} + 11q^{31} + 71q^{32} - 9q^{33} + 17q^{34} - 7q^{35} + 61q^{36} + 71q^{37} - 8q^{38} - 44q^{39} + 20q^{40} - 25q^{41} - 3q^{42} + 75q^{43} + 14q^{44} - 7q^{45} + 36q^{46} - 20q^{47} - 95q^{48} + 52q^{49} + 26q^{50} + 6q^{51} + 88q^{52} + 70q^{53} - 3q^{54} + 12q^{55} + 24q^{56} - 7q^{57} + 48q^{58} - 27q^{59} + 21q^{60} + 59q^{61} - 23q^{62} + 52q^{63} + 138q^{64} + 44q^{65} - 19q^{66} + 65q^{67} - 8q^{68} + 4q^{69} - 2q^{70} - 11q^{71} + 24q^{72} + 34q^{73} + 38q^{74} - 83q^{75} + 31q^{76} + 9q^{77} + 5q^{78} + 74q^{79} - 5q^{80} + 52q^{81} + 51q^{82} - 30q^{83} - 61q^{84} + 70q^{85} + 29q^{86} - 31q^{87} + 90q^{88} - q^{89} - 2q^{90} + 44q^{91} + 34q^{92} - 11q^{93} + 27q^{94} + 9q^{95} - 71q^{96} + 73q^{97} + 3q^{98} + 9q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.28128 −1.61311 −0.806556 0.591158i \(-0.798671\pi\)
−0.806556 + 0.591158i \(0.798671\pi\)
\(3\) −1.00000 −0.577350
\(4\) 3.20426 1.60213
\(5\) 2.19375 0.981075 0.490538 0.871420i \(-0.336800\pi\)
0.490538 + 0.871420i \(0.336800\pi\)
\(6\) 2.28128 0.931330
\(7\) 1.00000 0.377964
\(8\) −2.74725 −0.971300
\(9\) 1.00000 0.333333
\(10\) −5.00457 −1.58258
\(11\) −5.46288 −1.64712 −0.823560 0.567228i \(-0.808016\pi\)
−0.823560 + 0.567228i \(0.808016\pi\)
\(12\) −3.20426 −0.924989
\(13\) −1.92610 −0.534203 −0.267102 0.963668i \(-0.586066\pi\)
−0.267102 + 0.963668i \(0.586066\pi\)
\(14\) −2.28128 −0.609699
\(15\) −2.19375 −0.566424
\(16\) −0.141251 −0.0353129
\(17\) −3.39222 −0.822734 −0.411367 0.911470i \(-0.634949\pi\)
−0.411367 + 0.911470i \(0.634949\pi\)
\(18\) −2.28128 −0.537704
\(19\) 4.43083 1.01650 0.508251 0.861209i \(-0.330292\pi\)
0.508251 + 0.861209i \(0.330292\pi\)
\(20\) 7.02934 1.57181
\(21\) −1.00000 −0.218218
\(22\) 12.4624 2.65699
\(23\) −5.61925 −1.17169 −0.585847 0.810422i \(-0.699238\pi\)
−0.585847 + 0.810422i \(0.699238\pi\)
\(24\) 2.74725 0.560780
\(25\) −0.187455 −0.0374909
\(26\) 4.39397 0.861729
\(27\) −1.00000 −0.192450
\(28\) 3.20426 0.605548
\(29\) −4.28623 −0.795932 −0.397966 0.917400i \(-0.630284\pi\)
−0.397966 + 0.917400i \(0.630284\pi\)
\(30\) 5.00457 0.913705
\(31\) 3.43056 0.616148 0.308074 0.951362i \(-0.400316\pi\)
0.308074 + 0.951362i \(0.400316\pi\)
\(32\) 5.81674 1.02826
\(33\) 5.46288 0.950966
\(34\) 7.73862 1.32716
\(35\) 2.19375 0.370812
\(36\) 3.20426 0.534043
\(37\) −8.18210 −1.34513 −0.672565 0.740038i \(-0.734807\pi\)
−0.672565 + 0.740038i \(0.734807\pi\)
\(38\) −10.1080 −1.63973
\(39\) 1.92610 0.308422
\(40\) −6.02679 −0.952919
\(41\) −6.81620 −1.06451 −0.532256 0.846584i \(-0.678655\pi\)
−0.532256 + 0.846584i \(0.678655\pi\)
\(42\) 2.28128 0.352010
\(43\) 1.40342 0.214020 0.107010 0.994258i \(-0.465872\pi\)
0.107010 + 0.994258i \(0.465872\pi\)
\(44\) −17.5045 −2.63890
\(45\) 2.19375 0.327025
\(46\) 12.8191 1.89007
\(47\) −7.83905 −1.14344 −0.571721 0.820448i \(-0.693724\pi\)
−0.571721 + 0.820448i \(0.693724\pi\)
\(48\) 0.141251 0.0203879
\(49\) 1.00000 0.142857
\(50\) 0.427638 0.0604771
\(51\) 3.39222 0.475006
\(52\) −6.17171 −0.855862
\(53\) 3.13136 0.430126 0.215063 0.976600i \(-0.431004\pi\)
0.215063 + 0.976600i \(0.431004\pi\)
\(54\) 2.28128 0.310443
\(55\) −11.9842 −1.61595
\(56\) −2.74725 −0.367117
\(57\) −4.43083 −0.586878
\(58\) 9.77810 1.28393
\(59\) −1.91066 −0.248746 −0.124373 0.992236i \(-0.539692\pi\)
−0.124373 + 0.992236i \(0.539692\pi\)
\(60\) −7.02934 −0.907484
\(61\) −5.52236 −0.707065 −0.353533 0.935422i \(-0.615020\pi\)
−0.353533 + 0.935422i \(0.615020\pi\)
\(62\) −7.82609 −0.993915
\(63\) 1.00000 0.125988
\(64\) −12.9871 −1.62339
\(65\) −4.22538 −0.524094
\(66\) −12.4624 −1.53401
\(67\) −4.20815 −0.514107 −0.257054 0.966397i \(-0.582752\pi\)
−0.257054 + 0.966397i \(0.582752\pi\)
\(68\) −10.8695 −1.31813
\(69\) 5.61925 0.676478
\(70\) −5.00457 −0.598161
\(71\) −7.79993 −0.925682 −0.462841 0.886441i \(-0.653170\pi\)
−0.462841 + 0.886441i \(0.653170\pi\)
\(72\) −2.74725 −0.323767
\(73\) 12.9587 1.51670 0.758351 0.651847i \(-0.226005\pi\)
0.758351 + 0.651847i \(0.226005\pi\)
\(74\) 18.6657 2.16984
\(75\) 0.187455 0.0216454
\(76\) 14.1975 1.62857
\(77\) −5.46288 −0.622553
\(78\) −4.39397 −0.497520
\(79\) −14.7769 −1.66253 −0.831265 0.555876i \(-0.812383\pi\)
−0.831265 + 0.555876i \(0.812383\pi\)
\(80\) −0.309871 −0.0346446
\(81\) 1.00000 0.111111
\(82\) 15.5497 1.71718
\(83\) 11.1649 1.22551 0.612753 0.790275i \(-0.290062\pi\)
0.612753 + 0.790275i \(0.290062\pi\)
\(84\) −3.20426 −0.349613
\(85\) −7.44169 −0.807164
\(86\) −3.20161 −0.345238
\(87\) 4.28623 0.459532
\(88\) 15.0079 1.59985
\(89\) 2.89981 0.307380 0.153690 0.988119i \(-0.450884\pi\)
0.153690 + 0.988119i \(0.450884\pi\)
\(90\) −5.00457 −0.527528
\(91\) −1.92610 −0.201910
\(92\) −18.0055 −1.87720
\(93\) −3.43056 −0.355733
\(94\) 17.8831 1.84450
\(95\) 9.72014 0.997265
\(96\) −5.81674 −0.593668
\(97\) 0.436297 0.0442993 0.0221496 0.999755i \(-0.492949\pi\)
0.0221496 + 0.999755i \(0.492949\pi\)
\(98\) −2.28128 −0.230444
\(99\) −5.46288 −0.549040
\(100\) −0.600653 −0.0600653
\(101\) 14.3744 1.43030 0.715152 0.698969i \(-0.246358\pi\)
0.715152 + 0.698969i \(0.246358\pi\)
\(102\) −7.73862 −0.766237
\(103\) 8.82271 0.869328 0.434664 0.900593i \(-0.356867\pi\)
0.434664 + 0.900593i \(0.356867\pi\)
\(104\) 5.29147 0.518872
\(105\) −2.19375 −0.214088
\(106\) −7.14352 −0.693840
\(107\) 6.13689 0.593275 0.296638 0.954990i \(-0.404135\pi\)
0.296638 + 0.954990i \(0.404135\pi\)
\(108\) −3.20426 −0.308330
\(109\) −9.50038 −0.909972 −0.454986 0.890499i \(-0.650356\pi\)
−0.454986 + 0.890499i \(0.650356\pi\)
\(110\) 27.3394 2.60671
\(111\) 8.18210 0.776611
\(112\) −0.141251 −0.0133470
\(113\) 5.69556 0.535793 0.267896 0.963448i \(-0.413672\pi\)
0.267896 + 0.963448i \(0.413672\pi\)
\(114\) 10.1080 0.946699
\(115\) −12.3272 −1.14952
\(116\) −13.7342 −1.27519
\(117\) −1.92610 −0.178068
\(118\) 4.35875 0.401256
\(119\) −3.39222 −0.310964
\(120\) 6.02679 0.550168
\(121\) 18.8431 1.71301
\(122\) 12.5981 1.14058
\(123\) 6.81620 0.614596
\(124\) 10.9924 0.987148
\(125\) −11.3800 −1.01786
\(126\) −2.28128 −0.203233
\(127\) 8.28600 0.735263 0.367632 0.929971i \(-0.380169\pi\)
0.367632 + 0.929971i \(0.380169\pi\)
\(128\) 17.9939 1.59045
\(129\) −1.40342 −0.123565
\(130\) 9.63929 0.845422
\(131\) 1.05531 0.0922027 0.0461014 0.998937i \(-0.485320\pi\)
0.0461014 + 0.998937i \(0.485320\pi\)
\(132\) 17.5045 1.52357
\(133\) 4.43083 0.384202
\(134\) 9.59998 0.829312
\(135\) −2.19375 −0.188808
\(136\) 9.31928 0.799122
\(137\) 17.6510 1.50803 0.754015 0.656857i \(-0.228115\pi\)
0.754015 + 0.656857i \(0.228115\pi\)
\(138\) −12.8191 −1.09123
\(139\) 6.79197 0.576087 0.288044 0.957617i \(-0.406995\pi\)
0.288044 + 0.957617i \(0.406995\pi\)
\(140\) 7.02934 0.594088
\(141\) 7.83905 0.660167
\(142\) 17.7939 1.49323
\(143\) 10.5220 0.879897
\(144\) −0.141251 −0.0117710
\(145\) −9.40292 −0.780870
\(146\) −29.5625 −2.44661
\(147\) −1.00000 −0.0824786
\(148\) −26.2176 −2.15507
\(149\) −3.84397 −0.314910 −0.157455 0.987526i \(-0.550329\pi\)
−0.157455 + 0.987526i \(0.550329\pi\)
\(150\) −0.427638 −0.0349165
\(151\) 16.4355 1.33750 0.668752 0.743485i \(-0.266829\pi\)
0.668752 + 0.743485i \(0.266829\pi\)
\(152\) −12.1726 −0.987329
\(153\) −3.39222 −0.274245
\(154\) 12.4624 1.00425
\(155\) 7.52581 0.604487
\(156\) 6.17171 0.494132
\(157\) 10.7735 0.859819 0.429909 0.902872i \(-0.358545\pi\)
0.429909 + 0.902872i \(0.358545\pi\)
\(158\) 33.7103 2.68185
\(159\) −3.13136 −0.248333
\(160\) 12.7605 1.00880
\(161\) −5.61925 −0.442859
\(162\) −2.28128 −0.179235
\(163\) 3.40427 0.266643 0.133322 0.991073i \(-0.457436\pi\)
0.133322 + 0.991073i \(0.457436\pi\)
\(164\) −21.8408 −1.70548
\(165\) 11.9842 0.932969
\(166\) −25.4703 −1.97688
\(167\) −0.0615062 −0.00475949 −0.00237975 0.999997i \(-0.500757\pi\)
−0.00237975 + 0.999997i \(0.500757\pi\)
\(168\) 2.74725 0.211955
\(169\) −9.29015 −0.714627
\(170\) 16.9766 1.30205
\(171\) 4.43083 0.338834
\(172\) 4.49693 0.342888
\(173\) 7.48230 0.568869 0.284435 0.958695i \(-0.408194\pi\)
0.284435 + 0.958695i \(0.408194\pi\)
\(174\) −9.77810 −0.741276
\(175\) −0.187455 −0.0141702
\(176\) 0.771640 0.0581646
\(177\) 1.91066 0.143614
\(178\) −6.61530 −0.495837
\(179\) 13.8749 1.03706 0.518529 0.855060i \(-0.326480\pi\)
0.518529 + 0.855060i \(0.326480\pi\)
\(180\) 7.02934 0.523936
\(181\) 18.1717 1.35069 0.675346 0.737501i \(-0.263994\pi\)
0.675346 + 0.737501i \(0.263994\pi\)
\(182\) 4.39397 0.325703
\(183\) 5.52236 0.408224
\(184\) 15.4375 1.13807
\(185\) −17.9495 −1.31967
\(186\) 7.82609 0.573837
\(187\) 18.5313 1.35514
\(188\) −25.1183 −1.83194
\(189\) −1.00000 −0.0727393
\(190\) −22.1744 −1.60870
\(191\) −12.1055 −0.875926 −0.437963 0.898993i \(-0.644300\pi\)
−0.437963 + 0.898993i \(0.644300\pi\)
\(192\) 12.9871 0.937265
\(193\) 17.8606 1.28564 0.642819 0.766018i \(-0.277765\pi\)
0.642819 + 0.766018i \(0.277765\pi\)
\(194\) −0.995318 −0.0714597
\(195\) 4.22538 0.302586
\(196\) 3.20426 0.228875
\(197\) 0.905420 0.0645085 0.0322542 0.999480i \(-0.489731\pi\)
0.0322542 + 0.999480i \(0.489731\pi\)
\(198\) 12.4624 0.885663
\(199\) 28.0185 1.98618 0.993089 0.117368i \(-0.0374456\pi\)
0.993089 + 0.117368i \(0.0374456\pi\)
\(200\) 0.514985 0.0364150
\(201\) 4.20815 0.296820
\(202\) −32.7920 −2.30724
\(203\) −4.28623 −0.300834
\(204\) 10.8695 0.761020
\(205\) −14.9530 −1.04437
\(206\) −20.1271 −1.40232
\(207\) −5.61925 −0.390565
\(208\) 0.272064 0.0188642
\(209\) −24.2051 −1.67430
\(210\) 5.00457 0.345348
\(211\) 1.39710 0.0961806 0.0480903 0.998843i \(-0.484686\pi\)
0.0480903 + 0.998843i \(0.484686\pi\)
\(212\) 10.0337 0.689116
\(213\) 7.79993 0.534442
\(214\) −14.0000 −0.957019
\(215\) 3.07876 0.209970
\(216\) 2.74725 0.186927
\(217\) 3.43056 0.232882
\(218\) 21.6731 1.46789
\(219\) −12.9587 −0.875668
\(220\) −38.4005 −2.58896
\(221\) 6.53374 0.439507
\(222\) −18.6657 −1.25276
\(223\) −2.97094 −0.198949 −0.0994744 0.995040i \(-0.531716\pi\)
−0.0994744 + 0.995040i \(0.531716\pi\)
\(224\) 5.81674 0.388647
\(225\) −0.187455 −0.0124970
\(226\) −12.9932 −0.864293
\(227\) −20.5827 −1.36612 −0.683062 0.730360i \(-0.739352\pi\)
−0.683062 + 0.730360i \(0.739352\pi\)
\(228\) −14.1975 −0.940254
\(229\) 29.7267 1.96439 0.982196 0.187857i \(-0.0601542\pi\)
0.982196 + 0.187857i \(0.0601542\pi\)
\(230\) 28.1219 1.85430
\(231\) 5.46288 0.359431
\(232\) 11.7753 0.773089
\(233\) −20.3326 −1.33203 −0.666017 0.745937i \(-0.732002\pi\)
−0.666017 + 0.745937i \(0.732002\pi\)
\(234\) 4.39397 0.287243
\(235\) −17.1969 −1.12180
\(236\) −6.12224 −0.398524
\(237\) 14.7769 0.959862
\(238\) 7.73862 0.501620
\(239\) −12.7437 −0.824324 −0.412162 0.911111i \(-0.635226\pi\)
−0.412162 + 0.911111i \(0.635226\pi\)
\(240\) 0.309871 0.0200021
\(241\) 13.5865 0.875183 0.437592 0.899174i \(-0.355832\pi\)
0.437592 + 0.899174i \(0.355832\pi\)
\(242\) −42.9864 −2.76327
\(243\) −1.00000 −0.0641500
\(244\) −17.6951 −1.13281
\(245\) 2.19375 0.140154
\(246\) −15.5497 −0.991412
\(247\) −8.53421 −0.543019
\(248\) −9.42463 −0.598464
\(249\) −11.1649 −0.707546
\(250\) 25.9610 1.64192
\(251\) −28.3298 −1.78816 −0.894080 0.447907i \(-0.852169\pi\)
−0.894080 + 0.447907i \(0.852169\pi\)
\(252\) 3.20426 0.201849
\(253\) 30.6973 1.92992
\(254\) −18.9027 −1.18606
\(255\) 7.44169 0.466016
\(256\) −15.0748 −0.942177
\(257\) 28.0780 1.75146 0.875730 0.482801i \(-0.160380\pi\)
0.875730 + 0.482801i \(0.160380\pi\)
\(258\) 3.20161 0.199323
\(259\) −8.18210 −0.508411
\(260\) −13.5392 −0.839665
\(261\) −4.28623 −0.265311
\(262\) −2.40746 −0.148733
\(263\) −18.0835 −1.11508 −0.557540 0.830150i \(-0.688255\pi\)
−0.557540 + 0.830150i \(0.688255\pi\)
\(264\) −15.0079 −0.923673
\(265\) 6.86943 0.421986
\(266\) −10.1080 −0.619760
\(267\) −2.89981 −0.177466
\(268\) −13.4840 −0.823666
\(269\) 16.8302 1.02616 0.513078 0.858342i \(-0.328505\pi\)
0.513078 + 0.858342i \(0.328505\pi\)
\(270\) 5.00457 0.304568
\(271\) 11.4478 0.695405 0.347702 0.937605i \(-0.386962\pi\)
0.347702 + 0.937605i \(0.386962\pi\)
\(272\) 0.479156 0.0290531
\(273\) 1.92610 0.116573
\(274\) −40.2670 −2.43262
\(275\) 1.02404 0.0617521
\(276\) 18.0055 1.08380
\(277\) −4.25874 −0.255883 −0.127941 0.991782i \(-0.540837\pi\)
−0.127941 + 0.991782i \(0.540837\pi\)
\(278\) −15.4944 −0.929293
\(279\) 3.43056 0.205383
\(280\) −6.02679 −0.360169
\(281\) 5.79790 0.345874 0.172937 0.984933i \(-0.444674\pi\)
0.172937 + 0.984933i \(0.444674\pi\)
\(282\) −17.8831 −1.06492
\(283\) −28.1059 −1.67072 −0.835360 0.549704i \(-0.814741\pi\)
−0.835360 + 0.549704i \(0.814741\pi\)
\(284\) −24.9930 −1.48306
\(285\) −9.72014 −0.575771
\(286\) −24.0038 −1.41937
\(287\) −6.81620 −0.402347
\(288\) 5.81674 0.342755
\(289\) −5.49285 −0.323109
\(290\) 21.4507 1.25963
\(291\) −0.436297 −0.0255762
\(292\) 41.5230 2.42995
\(293\) 16.5857 0.968946 0.484473 0.874806i \(-0.339011\pi\)
0.484473 + 0.874806i \(0.339011\pi\)
\(294\) 2.28128 0.133047
\(295\) −4.19151 −0.244039
\(296\) 22.4783 1.30652
\(297\) 5.46288 0.316989
\(298\) 8.76919 0.507985
\(299\) 10.8232 0.625923
\(300\) 0.600653 0.0346787
\(301\) 1.40342 0.0808920
\(302\) −37.4941 −2.15754
\(303\) −14.3744 −0.825786
\(304\) −0.625861 −0.0358956
\(305\) −12.1147 −0.693685
\(306\) 7.73862 0.442387
\(307\) 21.2542 1.21304 0.606519 0.795069i \(-0.292565\pi\)
0.606519 + 0.795069i \(0.292565\pi\)
\(308\) −17.5045 −0.997410
\(309\) −8.82271 −0.501907
\(310\) −17.1685 −0.975105
\(311\) 2.45714 0.139332 0.0696659 0.997570i \(-0.477807\pi\)
0.0696659 + 0.997570i \(0.477807\pi\)
\(312\) −5.29147 −0.299571
\(313\) 8.75490 0.494856 0.247428 0.968906i \(-0.420415\pi\)
0.247428 + 0.968906i \(0.420415\pi\)
\(314\) −24.5774 −1.38698
\(315\) 2.19375 0.123604
\(316\) −47.3489 −2.66359
\(317\) −4.77605 −0.268250 −0.134125 0.990964i \(-0.542822\pi\)
−0.134125 + 0.990964i \(0.542822\pi\)
\(318\) 7.14352 0.400589
\(319\) 23.4152 1.31100
\(320\) −28.4905 −1.59267
\(321\) −6.13689 −0.342528
\(322\) 12.8191 0.714380
\(323\) −15.0303 −0.836311
\(324\) 3.20426 0.178014
\(325\) 0.361056 0.0200278
\(326\) −7.76611 −0.430125
\(327\) 9.50038 0.525372
\(328\) 18.7258 1.03396
\(329\) −7.83905 −0.432181
\(330\) −27.3394 −1.50498
\(331\) 8.21512 0.451544 0.225772 0.974180i \(-0.427510\pi\)
0.225772 + 0.974180i \(0.427510\pi\)
\(332\) 35.7752 1.96342
\(333\) −8.18210 −0.448377
\(334\) 0.140313 0.00767759
\(335\) −9.23163 −0.504378
\(336\) 0.141251 0.00770590
\(337\) 10.0724 0.548681 0.274341 0.961633i \(-0.411540\pi\)
0.274341 + 0.961633i \(0.411540\pi\)
\(338\) 21.1935 1.15277
\(339\) −5.69556 −0.309340
\(340\) −23.8451 −1.29318
\(341\) −18.7408 −1.01487
\(342\) −10.1080 −0.546577
\(343\) 1.00000 0.0539949
\(344\) −3.85556 −0.207878
\(345\) 12.3272 0.663676
\(346\) −17.0693 −0.917649
\(347\) 10.9984 0.590425 0.295212 0.955432i \(-0.404610\pi\)
0.295212 + 0.955432i \(0.404610\pi\)
\(348\) 13.7342 0.736229
\(349\) 11.3989 0.610167 0.305084 0.952326i \(-0.401316\pi\)
0.305084 + 0.952326i \(0.401316\pi\)
\(350\) 0.427638 0.0228582
\(351\) 1.92610 0.102807
\(352\) −31.7762 −1.69367
\(353\) −18.4733 −0.983235 −0.491618 0.870811i \(-0.663594\pi\)
−0.491618 + 0.870811i \(0.663594\pi\)
\(354\) −4.35875 −0.231665
\(355\) −17.1111 −0.908163
\(356\) 9.29174 0.492461
\(357\) 3.39222 0.179535
\(358\) −31.6526 −1.67289
\(359\) −29.9687 −1.58169 −0.790844 0.612018i \(-0.790358\pi\)
−0.790844 + 0.612018i \(0.790358\pi\)
\(360\) −6.02679 −0.317640
\(361\) 0.632252 0.0332764
\(362\) −41.4548 −2.17882
\(363\) −18.8431 −0.989005
\(364\) −6.17171 −0.323486
\(365\) 28.4282 1.48800
\(366\) −12.5981 −0.658511
\(367\) 25.6218 1.33745 0.668725 0.743510i \(-0.266840\pi\)
0.668725 + 0.743510i \(0.266840\pi\)
\(368\) 0.793727 0.0413759
\(369\) −6.81620 −0.354837
\(370\) 40.9479 2.12878
\(371\) 3.13136 0.162572
\(372\) −10.9924 −0.569930
\(373\) −26.6011 −1.37735 −0.688675 0.725070i \(-0.741807\pi\)
−0.688675 + 0.725070i \(0.741807\pi\)
\(374\) −42.2751 −2.18600
\(375\) 11.3800 0.587660
\(376\) 21.5358 1.11063
\(377\) 8.25569 0.425190
\(378\) 2.28128 0.117337
\(379\) −25.3810 −1.30374 −0.651868 0.758332i \(-0.726014\pi\)
−0.651868 + 0.758332i \(0.726014\pi\)
\(380\) 31.1458 1.59775
\(381\) −8.28600 −0.424505
\(382\) 27.6162 1.41297
\(383\) −1.00000 −0.0510976
\(384\) −17.9939 −0.918245
\(385\) −11.9842 −0.610772
\(386\) −40.7452 −2.07388
\(387\) 1.40342 0.0713400
\(388\) 1.39801 0.0709732
\(389\) −10.3706 −0.525811 −0.262906 0.964822i \(-0.584681\pi\)
−0.262906 + 0.964822i \(0.584681\pi\)
\(390\) −9.63929 −0.488104
\(391\) 19.0617 0.963992
\(392\) −2.74725 −0.138757
\(393\) −1.05531 −0.0532333
\(394\) −2.06552 −0.104059
\(395\) −32.4168 −1.63107
\(396\) −17.5045 −0.879633
\(397\) −24.1372 −1.21141 −0.605705 0.795689i \(-0.707109\pi\)
−0.605705 + 0.795689i \(0.707109\pi\)
\(398\) −63.9181 −3.20392
\(399\) −4.43083 −0.221819
\(400\) 0.0264783 0.00132391
\(401\) −29.8872 −1.49250 −0.746249 0.665667i \(-0.768147\pi\)
−0.746249 + 0.665667i \(0.768147\pi\)
\(402\) −9.59998 −0.478804
\(403\) −6.60760 −0.329148
\(404\) 46.0592 2.29153
\(405\) 2.19375 0.109008
\(406\) 9.77810 0.485279
\(407\) 44.6979 2.21559
\(408\) −9.31928 −0.461373
\(409\) −11.5768 −0.572437 −0.286219 0.958164i \(-0.592398\pi\)
−0.286219 + 0.958164i \(0.592398\pi\)
\(410\) 34.1121 1.68468
\(411\) −17.6510 −0.870662
\(412\) 28.2702 1.39277
\(413\) −1.91066 −0.0940173
\(414\) 12.8191 0.630024
\(415\) 24.4930 1.20231
\(416\) −11.2036 −0.549302
\(417\) −6.79197 −0.332604
\(418\) 55.2187 2.70084
\(419\) −16.0627 −0.784716 −0.392358 0.919813i \(-0.628340\pi\)
−0.392358 + 0.919813i \(0.628340\pi\)
\(420\) −7.02934 −0.342997
\(421\) −10.5434 −0.513854 −0.256927 0.966431i \(-0.582710\pi\)
−0.256927 + 0.966431i \(0.582710\pi\)
\(422\) −3.18719 −0.155150
\(423\) −7.83905 −0.381148
\(424\) −8.60264 −0.417781
\(425\) 0.635888 0.0308451
\(426\) −17.7939 −0.862115
\(427\) −5.52236 −0.267246
\(428\) 19.6642 0.950503
\(429\) −10.5220 −0.508009
\(430\) −7.02353 −0.338705
\(431\) 22.8062 1.09853 0.549267 0.835647i \(-0.314907\pi\)
0.549267 + 0.835647i \(0.314907\pi\)
\(432\) 0.141251 0.00679596
\(433\) −8.04282 −0.386513 −0.193257 0.981148i \(-0.561905\pi\)
−0.193257 + 0.981148i \(0.561905\pi\)
\(434\) −7.82609 −0.375664
\(435\) 9.40292 0.450835
\(436\) −30.4417 −1.45789
\(437\) −24.8979 −1.19103
\(438\) 29.5625 1.41255
\(439\) 15.0166 0.716701 0.358351 0.933587i \(-0.383339\pi\)
0.358351 + 0.933587i \(0.383339\pi\)
\(440\) 32.9236 1.56957
\(441\) 1.00000 0.0476190
\(442\) −14.9053 −0.708974
\(443\) 7.00952 0.333032 0.166516 0.986039i \(-0.446748\pi\)
0.166516 + 0.986039i \(0.446748\pi\)
\(444\) 26.2176 1.24423
\(445\) 6.36147 0.301562
\(446\) 6.77755 0.320927
\(447\) 3.84397 0.181814
\(448\) −12.9871 −0.613584
\(449\) 30.5637 1.44239 0.721195 0.692732i \(-0.243593\pi\)
0.721195 + 0.692732i \(0.243593\pi\)
\(450\) 0.427638 0.0201590
\(451\) 37.2361 1.75338
\(452\) 18.2500 0.858409
\(453\) −16.4355 −0.772209
\(454\) 46.9551 2.20371
\(455\) −4.22538 −0.198089
\(456\) 12.1726 0.570035
\(457\) 18.3199 0.856970 0.428485 0.903549i \(-0.359048\pi\)
0.428485 + 0.903549i \(0.359048\pi\)
\(458\) −67.8149 −3.16878
\(459\) 3.39222 0.158335
\(460\) −39.4996 −1.84168
\(461\) 25.4410 1.18490 0.592452 0.805605i \(-0.298160\pi\)
0.592452 + 0.805605i \(0.298160\pi\)
\(462\) −12.4624 −0.579803
\(463\) 9.08976 0.422437 0.211219 0.977439i \(-0.432257\pi\)
0.211219 + 0.977439i \(0.432257\pi\)
\(464\) 0.605436 0.0281066
\(465\) −7.52581 −0.349001
\(466\) 46.3845 2.14872
\(467\) 14.9405 0.691365 0.345683 0.938351i \(-0.387647\pi\)
0.345683 + 0.938351i \(0.387647\pi\)
\(468\) −6.17171 −0.285287
\(469\) −4.20815 −0.194314
\(470\) 39.2311 1.80959
\(471\) −10.7735 −0.496417
\(472\) 5.24906 0.241607
\(473\) −7.66674 −0.352517
\(474\) −33.7103 −1.54836
\(475\) −0.830580 −0.0381096
\(476\) −10.8695 −0.498205
\(477\) 3.13136 0.143375
\(478\) 29.0721 1.32973
\(479\) 6.43845 0.294180 0.147090 0.989123i \(-0.453009\pi\)
0.147090 + 0.989123i \(0.453009\pi\)
\(480\) −12.7605 −0.582434
\(481\) 15.7595 0.718573
\(482\) −30.9947 −1.41177
\(483\) 5.61925 0.255685
\(484\) 60.3781 2.74446
\(485\) 0.957128 0.0434609
\(486\) 2.28128 0.103481
\(487\) −20.3815 −0.923575 −0.461788 0.886991i \(-0.652792\pi\)
−0.461788 + 0.886991i \(0.652792\pi\)
\(488\) 15.1713 0.686773
\(489\) −3.40427 −0.153946
\(490\) −5.00457 −0.226083
\(491\) 38.1855 1.72329 0.861644 0.507514i \(-0.169435\pi\)
0.861644 + 0.507514i \(0.169435\pi\)
\(492\) 21.8408 0.984662
\(493\) 14.5398 0.654841
\(494\) 19.4690 0.875950
\(495\) −11.9842 −0.538650
\(496\) −0.484572 −0.0217579
\(497\) −7.79993 −0.349875
\(498\) 25.4703 1.14135
\(499\) −13.1560 −0.588944 −0.294472 0.955660i \(-0.595144\pi\)
−0.294472 + 0.955660i \(0.595144\pi\)
\(500\) −36.4644 −1.63074
\(501\) 0.0615062 0.00274790
\(502\) 64.6283 2.88450
\(503\) 33.6597 1.50081 0.750406 0.660977i \(-0.229858\pi\)
0.750406 + 0.660977i \(0.229858\pi\)
\(504\) −2.74725 −0.122372
\(505\) 31.5338 1.40324
\(506\) −70.0292 −3.11318
\(507\) 9.29015 0.412590
\(508\) 26.5505 1.17799
\(509\) 2.55359 0.113186 0.0565930 0.998397i \(-0.481976\pi\)
0.0565930 + 0.998397i \(0.481976\pi\)
\(510\) −16.9766 −0.751736
\(511\) 12.9587 0.573259
\(512\) −1.59773 −0.0706103
\(513\) −4.43083 −0.195626
\(514\) −64.0540 −2.82530
\(515\) 19.3548 0.852876
\(516\) −4.49693 −0.197966
\(517\) 42.8238 1.88339
\(518\) 18.6657 0.820124
\(519\) −7.48230 −0.328437
\(520\) 11.6082 0.509052
\(521\) −9.53258 −0.417630 −0.208815 0.977955i \(-0.566961\pi\)
−0.208815 + 0.977955i \(0.566961\pi\)
\(522\) 9.77810 0.427976
\(523\) −16.2112 −0.708868 −0.354434 0.935081i \(-0.615326\pi\)
−0.354434 + 0.935081i \(0.615326\pi\)
\(524\) 3.38148 0.147721
\(525\) 0.187455 0.00818120
\(526\) 41.2537 1.79875
\(527\) −11.6372 −0.506926
\(528\) −0.771640 −0.0335813
\(529\) 8.57592 0.372866
\(530\) −15.6711 −0.680710
\(531\) −1.91066 −0.0829155
\(532\) 14.1975 0.615540
\(533\) 13.1287 0.568665
\(534\) 6.61530 0.286272
\(535\) 13.4628 0.582048
\(536\) 11.5608 0.499353
\(537\) −13.8749 −0.598746
\(538\) −38.3945 −1.65530
\(539\) −5.46288 −0.235303
\(540\) −7.02934 −0.302495
\(541\) 0.345102 0.0148371 0.00741855 0.999972i \(-0.497639\pi\)
0.00741855 + 0.999972i \(0.497639\pi\)
\(542\) −26.1157 −1.12177
\(543\) −18.1717 −0.779823
\(544\) −19.7317 −0.845988
\(545\) −20.8415 −0.892751
\(546\) −4.39397 −0.188045
\(547\) −9.76904 −0.417694 −0.208847 0.977948i \(-0.566971\pi\)
−0.208847 + 0.977948i \(0.566971\pi\)
\(548\) 56.5585 2.41606
\(549\) −5.52236 −0.235688
\(550\) −2.33613 −0.0996131
\(551\) −18.9915 −0.809067
\(552\) −15.4375 −0.657063
\(553\) −14.7769 −0.628377
\(554\) 9.71539 0.412767
\(555\) 17.9495 0.761914
\(556\) 21.7632 0.922966
\(557\) 13.4070 0.568071 0.284036 0.958814i \(-0.408327\pi\)
0.284036 + 0.958814i \(0.408327\pi\)
\(558\) −7.82609 −0.331305
\(559\) −2.70313 −0.114330
\(560\) −0.309871 −0.0130944
\(561\) −18.5313 −0.782392
\(562\) −13.2267 −0.557933
\(563\) 13.4824 0.568217 0.284109 0.958792i \(-0.408302\pi\)
0.284109 + 0.958792i \(0.408302\pi\)
\(564\) 25.1183 1.05767
\(565\) 12.4946 0.525653
\(566\) 64.1174 2.69506
\(567\) 1.00000 0.0419961
\(568\) 21.4284 0.899115
\(569\) −39.0815 −1.63838 −0.819191 0.573521i \(-0.805577\pi\)
−0.819191 + 0.573521i \(0.805577\pi\)
\(570\) 22.1744 0.928783
\(571\) −20.1576 −0.843570 −0.421785 0.906696i \(-0.638596\pi\)
−0.421785 + 0.906696i \(0.638596\pi\)
\(572\) 33.7153 1.40971
\(573\) 12.1055 0.505716
\(574\) 15.5497 0.649031
\(575\) 1.05335 0.0439279
\(576\) −12.9871 −0.541130
\(577\) 20.6831 0.861048 0.430524 0.902579i \(-0.358329\pi\)
0.430524 + 0.902579i \(0.358329\pi\)
\(578\) 12.5307 0.521210
\(579\) −17.8606 −0.742263
\(580\) −30.1294 −1.25105
\(581\) 11.1649 0.463197
\(582\) 0.995318 0.0412573
\(583\) −17.1063 −0.708469
\(584\) −35.6008 −1.47317
\(585\) −4.22538 −0.174698
\(586\) −37.8367 −1.56302
\(587\) 9.31754 0.384576 0.192288 0.981339i \(-0.438409\pi\)
0.192288 + 0.981339i \(0.438409\pi\)
\(588\) −3.20426 −0.132141
\(589\) 15.2002 0.626315
\(590\) 9.56202 0.393662
\(591\) −0.905420 −0.0372440
\(592\) 1.15573 0.0475004
\(593\) −25.8868 −1.06305 −0.531523 0.847044i \(-0.678380\pi\)
−0.531523 + 0.847044i \(0.678380\pi\)
\(594\) −12.4624 −0.511338
\(595\) −7.44169 −0.305079
\(596\) −12.3171 −0.504527
\(597\) −28.0185 −1.14672
\(598\) −24.6908 −1.00968
\(599\) −18.3707 −0.750606 −0.375303 0.926902i \(-0.622461\pi\)
−0.375303 + 0.926902i \(0.622461\pi\)
\(600\) −0.514985 −0.0210242
\(601\) 10.5435 0.430076 0.215038 0.976606i \(-0.431012\pi\)
0.215038 + 0.976606i \(0.431012\pi\)
\(602\) −3.20161 −0.130488
\(603\) −4.20815 −0.171369
\(604\) 52.6637 2.14285
\(605\) 41.3370 1.68059
\(606\) 32.7920 1.33208
\(607\) 13.6682 0.554777 0.277388 0.960758i \(-0.410531\pi\)
0.277388 + 0.960758i \(0.410531\pi\)
\(608\) 25.7730 1.04523
\(609\) 4.28623 0.173687
\(610\) 27.6370 1.11899
\(611\) 15.0988 0.610831
\(612\) −10.8695 −0.439375
\(613\) 40.9081 1.65226 0.826131 0.563478i \(-0.190537\pi\)
0.826131 + 0.563478i \(0.190537\pi\)
\(614\) −48.4868 −1.95677
\(615\) 14.9530 0.602965
\(616\) 15.0079 0.604686
\(617\) 38.7478 1.55993 0.779964 0.625824i \(-0.215237\pi\)
0.779964 + 0.625824i \(0.215237\pi\)
\(618\) 20.1271 0.809631
\(619\) −38.9712 −1.56638 −0.783192 0.621780i \(-0.786410\pi\)
−0.783192 + 0.621780i \(0.786410\pi\)
\(620\) 24.1146 0.968466
\(621\) 5.61925 0.225493
\(622\) −5.60544 −0.224758
\(623\) 2.89981 0.116179
\(624\) −0.272064 −0.0108913
\(625\) −24.0276 −0.961103
\(626\) −19.9724 −0.798258
\(627\) 24.2051 0.966659
\(628\) 34.5211 1.37754
\(629\) 27.7555 1.10668
\(630\) −5.00457 −0.199387
\(631\) −32.0129 −1.27441 −0.637206 0.770693i \(-0.719910\pi\)
−0.637206 + 0.770693i \(0.719910\pi\)
\(632\) 40.5958 1.61482
\(633\) −1.39710 −0.0555299
\(634\) 10.8955 0.432716
\(635\) 18.1774 0.721349
\(636\) −10.0337 −0.397861
\(637\) −1.92610 −0.0763147
\(638\) −53.4166 −2.11478
\(639\) −7.79993 −0.308561
\(640\) 39.4740 1.56035
\(641\) 10.6974 0.422522 0.211261 0.977430i \(-0.432243\pi\)
0.211261 + 0.977430i \(0.432243\pi\)
\(642\) 14.0000 0.552535
\(643\) −30.3063 −1.19516 −0.597581 0.801809i \(-0.703871\pi\)
−0.597581 + 0.801809i \(0.703871\pi\)
\(644\) −18.0055 −0.709516
\(645\) −3.07876 −0.121226
\(646\) 34.2885 1.34906
\(647\) 10.7901 0.424205 0.212102 0.977247i \(-0.431969\pi\)
0.212102 + 0.977247i \(0.431969\pi\)
\(648\) −2.74725 −0.107922
\(649\) 10.4377 0.409715
\(650\) −0.823671 −0.0323071
\(651\) −3.43056 −0.134454
\(652\) 10.9082 0.427196
\(653\) −27.2266 −1.06546 −0.532730 0.846285i \(-0.678834\pi\)
−0.532730 + 0.846285i \(0.678834\pi\)
\(654\) −21.6731 −0.847484
\(655\) 2.31508 0.0904579
\(656\) 0.962798 0.0375909
\(657\) 12.9587 0.505567
\(658\) 17.8831 0.697156
\(659\) −37.1884 −1.44865 −0.724326 0.689457i \(-0.757849\pi\)
−0.724326 + 0.689457i \(0.757849\pi\)
\(660\) 38.4005 1.49474
\(661\) 46.0608 1.79156 0.895779 0.444500i \(-0.146619\pi\)
0.895779 + 0.444500i \(0.146619\pi\)
\(662\) −18.7410 −0.728391
\(663\) −6.53374 −0.253750
\(664\) −30.6728 −1.19033
\(665\) 9.72014 0.376931
\(666\) 18.6657 0.723281
\(667\) 24.0854 0.932589
\(668\) −0.197082 −0.00762532
\(669\) 2.97094 0.114863
\(670\) 21.0600 0.813618
\(671\) 30.1680 1.16462
\(672\) −5.81674 −0.224386
\(673\) 0.419999 0.0161898 0.00809488 0.999967i \(-0.497423\pi\)
0.00809488 + 0.999967i \(0.497423\pi\)
\(674\) −22.9781 −0.885084
\(675\) 0.187455 0.00721514
\(676\) −29.7680 −1.14492
\(677\) −36.8349 −1.41568 −0.707840 0.706373i \(-0.750330\pi\)
−0.707840 + 0.706373i \(0.750330\pi\)
\(678\) 12.9932 0.499000
\(679\) 0.436297 0.0167436
\(680\) 20.4442 0.783999
\(681\) 20.5827 0.788733
\(682\) 42.7530 1.63710
\(683\) 10.5538 0.403830 0.201915 0.979403i \(-0.435284\pi\)
0.201915 + 0.979403i \(0.435284\pi\)
\(684\) 14.1975 0.542856
\(685\) 38.7220 1.47949
\(686\) −2.28128 −0.0870998
\(687\) −29.7267 −1.13414
\(688\) −0.198236 −0.00755766
\(689\) −6.03131 −0.229774
\(690\) −28.1219 −1.07058
\(691\) −19.4193 −0.738744 −0.369372 0.929282i \(-0.620427\pi\)
−0.369372 + 0.929282i \(0.620427\pi\)
\(692\) 23.9752 0.911401
\(693\) −5.46288 −0.207518
\(694\) −25.0905 −0.952421
\(695\) 14.8999 0.565185
\(696\) −11.7753 −0.446343
\(697\) 23.1220 0.875810
\(698\) −26.0040 −0.984268
\(699\) 20.3326 0.769050
\(700\) −0.600653 −0.0227026
\(701\) −20.9067 −0.789633 −0.394817 0.918760i \(-0.629192\pi\)
−0.394817 + 0.918760i \(0.629192\pi\)
\(702\) −4.39397 −0.165840
\(703\) −36.2535 −1.36733
\(704\) 70.9472 2.67392
\(705\) 17.1969 0.647674
\(706\) 42.1429 1.58607
\(707\) 14.3744 0.540604
\(708\) 6.12224 0.230088
\(709\) 36.8601 1.38431 0.692155 0.721749i \(-0.256661\pi\)
0.692155 + 0.721749i \(0.256661\pi\)
\(710\) 39.0353 1.46497
\(711\) −14.7769 −0.554177
\(712\) −7.96652 −0.298558
\(713\) −19.2772 −0.721936
\(714\) −7.73862 −0.289610
\(715\) 23.0827 0.863246
\(716\) 44.4587 1.66150
\(717\) 12.7437 0.475923
\(718\) 68.3672 2.55144
\(719\) 2.04824 0.0763864 0.0381932 0.999270i \(-0.487840\pi\)
0.0381932 + 0.999270i \(0.487840\pi\)
\(720\) −0.309871 −0.0115482
\(721\) 8.82271 0.328575
\(722\) −1.44235 −0.0536786
\(723\) −13.5865 −0.505287
\(724\) 58.2268 2.16398
\(725\) 0.803474 0.0298403
\(726\) 42.9864 1.59538
\(727\) −4.22436 −0.156673 −0.0783365 0.996927i \(-0.524961\pi\)
−0.0783365 + 0.996927i \(0.524961\pi\)
\(728\) 5.29147 0.196115
\(729\) 1.00000 0.0370370
\(730\) −64.8528 −2.40031
\(731\) −4.76072 −0.176082
\(732\) 17.6951 0.654028
\(733\) 16.1955 0.598196 0.299098 0.954222i \(-0.403314\pi\)
0.299098 + 0.954222i \(0.403314\pi\)
\(734\) −58.4507 −2.15745
\(735\) −2.19375 −0.0809177
\(736\) −32.6857 −1.20481
\(737\) 22.9886 0.846797
\(738\) 15.5497 0.572392
\(739\) −8.26782 −0.304137 −0.152068 0.988370i \(-0.548593\pi\)
−0.152068 + 0.988370i \(0.548593\pi\)
\(740\) −57.5148 −2.11429
\(741\) 8.53421 0.313512
\(742\) −7.14352 −0.262247
\(743\) 26.3038 0.964994 0.482497 0.875898i \(-0.339730\pi\)
0.482497 + 0.875898i \(0.339730\pi\)
\(744\) 9.42463 0.345524
\(745\) −8.43272 −0.308951
\(746\) 60.6846 2.22182
\(747\) 11.1649 0.408502
\(748\) 59.3790 2.17111
\(749\) 6.13689 0.224237
\(750\) −25.9610 −0.947961
\(751\) −5.73891 −0.209416 −0.104708 0.994503i \(-0.533391\pi\)
−0.104708 + 0.994503i \(0.533391\pi\)
\(752\) 1.10728 0.0403782
\(753\) 28.3298 1.03239
\(754\) −18.8336 −0.685878
\(755\) 36.0555 1.31219
\(756\) −3.20426 −0.116538
\(757\) 2.40581 0.0874407 0.0437204 0.999044i \(-0.486079\pi\)
0.0437204 + 0.999044i \(0.486079\pi\)
\(758\) 57.9013 2.10307
\(759\) −30.6973 −1.11424
\(760\) −26.7037 −0.968644
\(761\) 11.6920 0.423836 0.211918 0.977287i \(-0.432029\pi\)
0.211918 + 0.977287i \(0.432029\pi\)
\(762\) 18.9027 0.684773
\(763\) −9.50038 −0.343937
\(764\) −38.7893 −1.40335
\(765\) −7.44169 −0.269055
\(766\) 2.28128 0.0824261
\(767\) 3.68011 0.132881
\(768\) 15.0748 0.543966
\(769\) 16.8320 0.606978 0.303489 0.952835i \(-0.401848\pi\)
0.303489 + 0.952835i \(0.401848\pi\)
\(770\) 27.3394 0.985243
\(771\) −28.0780 −1.01121
\(772\) 57.2301 2.05976
\(773\) 2.75083 0.0989406 0.0494703 0.998776i \(-0.484247\pi\)
0.0494703 + 0.998776i \(0.484247\pi\)
\(774\) −3.20161 −0.115079
\(775\) −0.643076 −0.0231000
\(776\) −1.19862 −0.0430279
\(777\) 8.18210 0.293531
\(778\) 23.6583 0.848192
\(779\) −30.2014 −1.08208
\(780\) 13.5392 0.484781
\(781\) 42.6101 1.52471
\(782\) −43.4852 −1.55503
\(783\) 4.28623 0.153177
\(784\) −0.141251 −0.00504469
\(785\) 23.6344 0.843547
\(786\) 2.40746 0.0858712
\(787\) 17.5721 0.626379 0.313190 0.949691i \(-0.398602\pi\)
0.313190 + 0.949691i \(0.398602\pi\)
\(788\) 2.90120 0.103351
\(789\) 18.0835 0.643791
\(790\) 73.9520 2.63109
\(791\) 5.69556 0.202511
\(792\) 15.0079 0.533283
\(793\) 10.6366 0.377717
\(794\) 55.0638 1.95414
\(795\) −6.86943 −0.243633
\(796\) 89.7784 3.18211
\(797\) 27.6712 0.980163 0.490082 0.871676i \(-0.336967\pi\)
0.490082 + 0.871676i \(0.336967\pi\)
\(798\) 10.1080 0.357819
\(799\) 26.5918 0.940749
\(800\) −1.09038 −0.0385506
\(801\) 2.89981 0.102460
\(802\) 68.1813 2.40757
\(803\) −70.7919 −2.49819
\(804\) 13.4840 0.475544
\(805\) −12.3272 −0.434478
\(806\) 15.0738 0.530952
\(807\) −16.8302 −0.592451
\(808\) −39.4900 −1.38925
\(809\) −30.9280 −1.08737 −0.543685 0.839290i \(-0.682971\pi\)
−0.543685 + 0.839290i \(0.682971\pi\)
\(810\) −5.00457 −0.175843
\(811\) −42.6182 −1.49653 −0.748263 0.663402i \(-0.769112\pi\)
−0.748263 + 0.663402i \(0.769112\pi\)
\(812\) −13.7342 −0.481975
\(813\) −11.4478 −0.401492
\(814\) −101.969 −3.57400
\(815\) 7.46812 0.261597
\(816\) −0.479156 −0.0167738
\(817\) 6.21833 0.217552
\(818\) 26.4100 0.923405
\(819\) −1.92610 −0.0673033
\(820\) −47.9134 −1.67321
\(821\) 35.4160 1.23603 0.618013 0.786168i \(-0.287938\pi\)
0.618013 + 0.786168i \(0.287938\pi\)
\(822\) 40.2670 1.40447
\(823\) 10.8636 0.378682 0.189341 0.981911i \(-0.439365\pi\)
0.189341 + 0.981911i \(0.439365\pi\)
\(824\) −24.2382 −0.844378
\(825\) −1.02404 −0.0356526
\(826\) 4.35875 0.151660
\(827\) −1.05651 −0.0367383 −0.0183692 0.999831i \(-0.505847\pi\)
−0.0183692 + 0.999831i \(0.505847\pi\)
\(828\) −18.0055 −0.625735
\(829\) −1.48088 −0.0514331 −0.0257165 0.999669i \(-0.508187\pi\)
−0.0257165 + 0.999669i \(0.508187\pi\)
\(830\) −55.8755 −1.93947
\(831\) 4.25874 0.147734
\(832\) 25.0145 0.867221
\(833\) −3.39222 −0.117533
\(834\) 15.4944 0.536527
\(835\) −0.134929 −0.00466942
\(836\) −77.5594 −2.68245
\(837\) −3.43056 −0.118578
\(838\) 36.6436 1.26583
\(839\) −45.4542 −1.56925 −0.784627 0.619968i \(-0.787146\pi\)
−0.784627 + 0.619968i \(0.787146\pi\)
\(840\) 6.02679 0.207944
\(841\) −10.6283 −0.366492
\(842\) 24.0525 0.828904
\(843\) −5.79790 −0.199690
\(844\) 4.47668 0.154094
\(845\) −20.3803 −0.701103
\(846\) 17.8831 0.614833
\(847\) 18.8431 0.647456
\(848\) −0.442309 −0.0151890
\(849\) 28.1059 0.964590
\(850\) −1.45064 −0.0497566
\(851\) 45.9773 1.57608
\(852\) 24.9930 0.856246
\(853\) 38.1836 1.30738 0.653690 0.756762i \(-0.273220\pi\)
0.653690 + 0.756762i \(0.273220\pi\)
\(854\) 12.5981 0.431097
\(855\) 9.72014 0.332422
\(856\) −16.8596 −0.576249
\(857\) 0.761898 0.0260259 0.0130130 0.999915i \(-0.495858\pi\)
0.0130130 + 0.999915i \(0.495858\pi\)
\(858\) 24.0038 0.819475
\(859\) 31.9384 1.08972 0.544862 0.838526i \(-0.316582\pi\)
0.544862 + 0.838526i \(0.316582\pi\)
\(860\) 9.86515 0.336399
\(861\) 6.81620 0.232295
\(862\) −52.0273 −1.77206
\(863\) −43.8945 −1.49419 −0.747094 0.664719i \(-0.768551\pi\)
−0.747094 + 0.664719i \(0.768551\pi\)
\(864\) −5.81674 −0.197889
\(865\) 16.4143 0.558103
\(866\) 18.3480 0.623489
\(867\) 5.49285 0.186547
\(868\) 10.9924 0.373107
\(869\) 80.7244 2.73839
\(870\) −21.4507 −0.727248
\(871\) 8.10530 0.274638
\(872\) 26.0999 0.883856
\(873\) 0.436297 0.0147664
\(874\) 56.7992 1.92126
\(875\) −11.3800 −0.384714
\(876\) −41.5230 −1.40293
\(877\) 29.7703 1.00527 0.502636 0.864498i \(-0.332364\pi\)
0.502636 + 0.864498i \(0.332364\pi\)
\(878\) −34.2570 −1.15612
\(879\) −16.5857 −0.559421
\(880\) 1.69279 0.0570638
\(881\) 19.9190 0.671087 0.335544 0.942025i \(-0.391080\pi\)
0.335544 + 0.942025i \(0.391080\pi\)
\(882\) −2.28128 −0.0768148
\(883\) 26.5329 0.892902 0.446451 0.894808i \(-0.352688\pi\)
0.446451 + 0.894808i \(0.352688\pi\)
\(884\) 20.9358 0.704147
\(885\) 4.19151 0.140896
\(886\) −15.9907 −0.537218
\(887\) −38.0119 −1.27632 −0.638158 0.769905i \(-0.720303\pi\)
−0.638158 + 0.769905i \(0.720303\pi\)
\(888\) −22.4783 −0.754322
\(889\) 8.28600 0.277903
\(890\) −14.5123 −0.486454
\(891\) −5.46288 −0.183013
\(892\) −9.51965 −0.318741
\(893\) −34.7335 −1.16231
\(894\) −8.76919 −0.293286
\(895\) 30.4381 1.01743
\(896\) 17.9939 0.601133
\(897\) −10.8232 −0.361377
\(898\) −69.7245 −2.32674
\(899\) −14.7042 −0.490412
\(900\) −0.600653 −0.0200218
\(901\) −10.6223 −0.353879
\(902\) −84.9461 −2.82840
\(903\) −1.40342 −0.0467030
\(904\) −15.6471 −0.520416
\(905\) 39.8642 1.32513
\(906\) 37.4941 1.24566
\(907\) −29.2416 −0.970951 −0.485476 0.874250i \(-0.661354\pi\)
−0.485476 + 0.874250i \(0.661354\pi\)
\(908\) −65.9524 −2.18871
\(909\) 14.3744 0.476768
\(910\) 9.63929 0.319539
\(911\) −23.2938 −0.771758 −0.385879 0.922549i \(-0.626102\pi\)
−0.385879 + 0.922549i \(0.626102\pi\)
\(912\) 0.625861 0.0207243
\(913\) −60.9925 −2.01856
\(914\) −41.7929 −1.38239
\(915\) 12.1147 0.400499
\(916\) 95.2518 3.14721
\(917\) 1.05531 0.0348494
\(918\) −7.73862 −0.255412
\(919\) −46.0969 −1.52060 −0.760298 0.649574i \(-0.774947\pi\)
−0.760298 + 0.649574i \(0.774947\pi\)
\(920\) 33.8660 1.11653
\(921\) −21.2542 −0.700348
\(922\) −58.0381 −1.91138
\(923\) 15.0234 0.494502
\(924\) 17.5045 0.575855
\(925\) 1.53377 0.0504302
\(926\) −20.7363 −0.681438
\(927\) 8.82271 0.289776
\(928\) −24.9319 −0.818429
\(929\) −1.32804 −0.0435716 −0.0217858 0.999763i \(-0.506935\pi\)
−0.0217858 + 0.999763i \(0.506935\pi\)
\(930\) 17.1685 0.562977
\(931\) 4.43083 0.145215
\(932\) −65.1509 −2.13409
\(933\) −2.45714 −0.0804432
\(934\) −34.0836 −1.11525
\(935\) 40.6531 1.32950
\(936\) 5.29147 0.172957
\(937\) 18.4171 0.601660 0.300830 0.953678i \(-0.402736\pi\)
0.300830 + 0.953678i \(0.402736\pi\)
\(938\) 9.59998 0.313451
\(939\) −8.75490 −0.285705
\(940\) −55.1034 −1.79727
\(941\) −17.0217 −0.554891 −0.277445 0.960741i \(-0.589488\pi\)
−0.277445 + 0.960741i \(0.589488\pi\)
\(942\) 24.5774 0.800775
\(943\) 38.3019 1.24728
\(944\) 0.269883 0.00878395
\(945\) −2.19375 −0.0713627
\(946\) 17.4900 0.568649
\(947\) 20.4681 0.665125 0.332563 0.943081i \(-0.392087\pi\)
0.332563 + 0.943081i \(0.392087\pi\)
\(948\) 47.3489 1.53782
\(949\) −24.9597 −0.810227
\(950\) 1.89479 0.0614751
\(951\) 4.77605 0.154874
\(952\) 9.31928 0.302040
\(953\) −32.1294 −1.04077 −0.520387 0.853930i \(-0.674212\pi\)
−0.520387 + 0.853930i \(0.674212\pi\)
\(954\) −7.14352 −0.231280
\(955\) −26.5566 −0.859350
\(956\) −40.8342 −1.32067
\(957\) −23.4152 −0.756904
\(958\) −14.6879 −0.474546
\(959\) 17.6510 0.569982
\(960\) 28.4905 0.919528
\(961\) −19.2312 −0.620362
\(962\) −35.9520 −1.15914
\(963\) 6.13689 0.197758
\(964\) 43.5346 1.40216
\(965\) 39.1818 1.26131
\(966\) −12.8191 −0.412448
\(967\) 18.5651 0.597014 0.298507 0.954407i \(-0.403511\pi\)
0.298507 + 0.954407i \(0.403511\pi\)
\(968\) −51.7667 −1.66384
\(969\) 15.0303 0.482844
\(970\) −2.18348 −0.0701073
\(971\) −3.32985 −0.106860 −0.0534300 0.998572i \(-0.517015\pi\)
−0.0534300 + 0.998572i \(0.517015\pi\)
\(972\) −3.20426 −0.102777
\(973\) 6.79197 0.217740
\(974\) 46.4961 1.48983
\(975\) −0.361056 −0.0115630
\(976\) 0.780041 0.0249685
\(977\) 51.1646 1.63690 0.818449 0.574578i \(-0.194834\pi\)
0.818449 + 0.574578i \(0.194834\pi\)
\(978\) 7.76611 0.248333
\(979\) −15.8413 −0.506291
\(980\) 7.02934 0.224544
\(981\) −9.50038 −0.303324
\(982\) −87.1120 −2.77985
\(983\) −37.1740 −1.18567 −0.592834 0.805325i \(-0.701991\pi\)
−0.592834 + 0.805325i \(0.701991\pi\)
\(984\) −18.7258 −0.596957
\(985\) 1.98627 0.0632877
\(986\) −33.1695 −1.05633
\(987\) 7.83905 0.249520
\(988\) −27.3458 −0.869986
\(989\) −7.88618 −0.250766
\(990\) 27.3394 0.868902
\(991\) 7.79804 0.247713 0.123856 0.992300i \(-0.460474\pi\)
0.123856 + 0.992300i \(0.460474\pi\)
\(992\) 19.9547 0.633562
\(993\) −8.21512 −0.260699
\(994\) 17.7939 0.564387
\(995\) 61.4656 1.94859
\(996\) −35.7752 −1.13358
\(997\) −54.1840 −1.71602 −0.858011 0.513631i \(-0.828300\pi\)
−0.858011 + 0.513631i \(0.828300\pi\)
\(998\) 30.0126 0.950032
\(999\) 8.18210 0.258870
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 \(a_p\))