Properties

Label 8041.2.a.i.1.12
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 0
Dimension 78
CM No

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Newspace parameters

Level: \( N \) = \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(0\)
Dimension: \(78\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.05622 q^{2} -3.10600 q^{3} +2.22804 q^{4} -2.37865 q^{5} +6.38662 q^{6} -3.40012 q^{7} -0.468901 q^{8} +6.64724 q^{9} +O(q^{10})\) \(q-2.05622 q^{2} -3.10600 q^{3} +2.22804 q^{4} -2.37865 q^{5} +6.38662 q^{6} -3.40012 q^{7} -0.468901 q^{8} +6.64724 q^{9} +4.89103 q^{10} +1.00000 q^{11} -6.92029 q^{12} -5.45676 q^{13} +6.99140 q^{14} +7.38809 q^{15} -3.49192 q^{16} -1.00000 q^{17} -13.6682 q^{18} +1.95391 q^{19} -5.29973 q^{20} +10.5608 q^{21} -2.05622 q^{22} -4.50873 q^{23} +1.45641 q^{24} +0.657984 q^{25} +11.2203 q^{26} -11.3283 q^{27} -7.57561 q^{28} +5.46615 q^{29} -15.1915 q^{30} +6.68356 q^{31} +8.11795 q^{32} -3.10600 q^{33} +2.05622 q^{34} +8.08770 q^{35} +14.8103 q^{36} +1.68237 q^{37} -4.01767 q^{38} +16.9487 q^{39} +1.11535 q^{40} -8.75055 q^{41} -21.7153 q^{42} -1.00000 q^{43} +2.22804 q^{44} -15.8115 q^{45} +9.27094 q^{46} -3.32091 q^{47} +10.8459 q^{48} +4.56082 q^{49} -1.35296 q^{50} +3.10600 q^{51} -12.1579 q^{52} -3.01462 q^{53} +23.2935 q^{54} -2.37865 q^{55} +1.59432 q^{56} -6.06884 q^{57} -11.2396 q^{58} +0.487630 q^{59} +16.4610 q^{60} +6.07482 q^{61} -13.7429 q^{62} -22.6014 q^{63} -9.70846 q^{64} +12.9797 q^{65} +6.38662 q^{66} -0.331210 q^{67} -2.22804 q^{68} +14.0041 q^{69} -16.6301 q^{70} -0.741187 q^{71} -3.11689 q^{72} +11.8136 q^{73} -3.45933 q^{74} -2.04370 q^{75} +4.35339 q^{76} -3.40012 q^{77} -34.8502 q^{78} +14.0142 q^{79} +8.30606 q^{80} +15.2441 q^{81} +17.9931 q^{82} +2.19179 q^{83} +23.5298 q^{84} +2.37865 q^{85} +2.05622 q^{86} -16.9779 q^{87} -0.468901 q^{88} -4.14803 q^{89} +32.5119 q^{90} +18.5536 q^{91} -10.0456 q^{92} -20.7591 q^{93} +6.82852 q^{94} -4.64767 q^{95} -25.2144 q^{96} -1.97190 q^{97} -9.37805 q^{98} +6.64724 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + O(q^{10}) \) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + 3q^{10} + 78q^{11} + 31q^{12} - 16q^{13} + 31q^{14} + 38q^{15} + 121q^{16} - 78q^{17} + 11q^{18} + 51q^{20} + 6q^{21} + 7q^{22} + 48q^{23} + 11q^{24} + 101q^{25} + 18q^{26} + 46q^{27} + 27q^{28} + 22q^{29} + 14q^{30} + 56q^{31} + 83q^{32} + 10q^{33} - 7q^{34} + 24q^{35} + 139q^{36} + 53q^{37} + 10q^{38} + 79q^{39} - q^{40} + 23q^{41} + 17q^{42} - 78q^{43} + 91q^{44} + 76q^{45} + 21q^{46} + 57q^{47} + 78q^{48} + 115q^{49} + 58q^{50} - 10q^{51} - 63q^{52} + 22q^{53} - 18q^{54} + 17q^{55} + 111q^{56} - 11q^{57} + 36q^{58} + 71q^{59} + 36q^{60} + 4q^{61} - 5q^{62} + 71q^{63} + 183q^{64} + 47q^{65} + 12q^{66} + 11q^{67} - 91q^{68} + 31q^{69} + 33q^{70} + 159q^{71} + 59q^{72} + 2q^{73} - 4q^{74} + 83q^{75} - 44q^{76} + 11q^{77} + 101q^{78} + 35q^{79} + 85q^{80} + 170q^{81} + 98q^{82} - 32q^{83} + 44q^{84} - 17q^{85} - 7q^{86} - 6q^{87} + 33q^{88} + 50q^{89} - 5q^{90} + 86q^{91} + 106q^{92} + 68q^{93} - q^{94} + 109q^{95} - 50q^{96} + 40q^{97} + 106q^{98} + 102q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.05622 −1.45397 −0.726984 0.686655i \(-0.759078\pi\)
−0.726984 + 0.686655i \(0.759078\pi\)
\(3\) −3.10600 −1.79325 −0.896625 0.442790i \(-0.853989\pi\)
−0.896625 + 0.442790i \(0.853989\pi\)
\(4\) 2.22804 1.11402
\(5\) −2.37865 −1.06377 −0.531883 0.846818i \(-0.678515\pi\)
−0.531883 + 0.846818i \(0.678515\pi\)
\(6\) 6.38662 2.60733
\(7\) −3.40012 −1.28512 −0.642562 0.766233i \(-0.722129\pi\)
−0.642562 + 0.766233i \(0.722129\pi\)
\(8\) −0.468901 −0.165781
\(9\) 6.64724 2.21575
\(10\) 4.89103 1.54668
\(11\) 1.00000 0.301511
\(12\) −6.92029 −1.99772
\(13\) −5.45676 −1.51343 −0.756716 0.653743i \(-0.773198\pi\)
−0.756716 + 0.653743i \(0.773198\pi\)
\(14\) 6.99140 1.86853
\(15\) 7.38809 1.90760
\(16\) −3.49192 −0.872979
\(17\) −1.00000 −0.242536
\(18\) −13.6682 −3.22162
\(19\) 1.95391 0.448257 0.224129 0.974560i \(-0.428046\pi\)
0.224129 + 0.974560i \(0.428046\pi\)
\(20\) −5.29973 −1.18506
\(21\) 10.5608 2.30455
\(22\) −2.05622 −0.438388
\(23\) −4.50873 −0.940135 −0.470068 0.882630i \(-0.655770\pi\)
−0.470068 + 0.882630i \(0.655770\pi\)
\(24\) 1.45641 0.297288
\(25\) 0.657984 0.131597
\(26\) 11.2203 2.20048
\(27\) −11.3283 −2.18014
\(28\) −7.57561 −1.43165
\(29\) 5.46615 1.01504 0.507520 0.861640i \(-0.330563\pi\)
0.507520 + 0.861640i \(0.330563\pi\)
\(30\) −15.1915 −2.77358
\(31\) 6.68356 1.20040 0.600201 0.799849i \(-0.295087\pi\)
0.600201 + 0.799849i \(0.295087\pi\)
\(32\) 8.11795 1.43506
\(33\) −3.10600 −0.540685
\(34\) 2.05622 0.352639
\(35\) 8.08770 1.36707
\(36\) 14.8103 2.46839
\(37\) 1.68237 0.276580 0.138290 0.990392i \(-0.455839\pi\)
0.138290 + 0.990392i \(0.455839\pi\)
\(38\) −4.01767 −0.651751
\(39\) 16.9487 2.71396
\(40\) 1.11535 0.176353
\(41\) −8.75055 −1.36661 −0.683303 0.730135i \(-0.739457\pi\)
−0.683303 + 0.730135i \(0.739457\pi\)
\(42\) −21.7153 −3.35074
\(43\) −1.00000 −0.152499
\(44\) 2.22804 0.335890
\(45\) −15.8115 −2.35703
\(46\) 9.27094 1.36693
\(47\) −3.32091 −0.484404 −0.242202 0.970226i \(-0.577870\pi\)
−0.242202 + 0.970226i \(0.577870\pi\)
\(48\) 10.8459 1.56547
\(49\) 4.56082 0.651546
\(50\) −1.35296 −0.191337
\(51\) 3.10600 0.434927
\(52\) −12.1579 −1.68599
\(53\) −3.01462 −0.414090 −0.207045 0.978331i \(-0.566385\pi\)
−0.207045 + 0.978331i \(0.566385\pi\)
\(54\) 23.2935 3.16985
\(55\) −2.37865 −0.320737
\(56\) 1.59432 0.213050
\(57\) −6.06884 −0.803838
\(58\) −11.2396 −1.47583
\(59\) 0.487630 0.0634840 0.0317420 0.999496i \(-0.489895\pi\)
0.0317420 + 0.999496i \(0.489895\pi\)
\(60\) 16.4610 2.12510
\(61\) 6.07482 0.777801 0.388900 0.921280i \(-0.372855\pi\)
0.388900 + 0.921280i \(0.372855\pi\)
\(62\) −13.7429 −1.74535
\(63\) −22.6014 −2.84751
\(64\) −9.70846 −1.21356
\(65\) 12.9797 1.60994
\(66\) 6.38662 0.786139
\(67\) −0.331210 −0.0404638 −0.0202319 0.999795i \(-0.506440\pi\)
−0.0202319 + 0.999795i \(0.506440\pi\)
\(68\) −2.22804 −0.270190
\(69\) 14.0041 1.68590
\(70\) −16.6301 −1.98768
\(71\) −0.741187 −0.0879627 −0.0439813 0.999032i \(-0.514004\pi\)
−0.0439813 + 0.999032i \(0.514004\pi\)
\(72\) −3.11689 −0.367330
\(73\) 11.8136 1.38268 0.691340 0.722530i \(-0.257021\pi\)
0.691340 + 0.722530i \(0.257021\pi\)
\(74\) −3.45933 −0.402139
\(75\) −2.04370 −0.235986
\(76\) 4.35339 0.499368
\(77\) −3.40012 −0.387480
\(78\) −34.8502 −3.94601
\(79\) 14.0142 1.57672 0.788362 0.615212i \(-0.210929\pi\)
0.788362 + 0.615212i \(0.210929\pi\)
\(80\) 8.30606 0.928645
\(81\) 15.2441 1.69379
\(82\) 17.9931 1.98700
\(83\) 2.19179 0.240580 0.120290 0.992739i \(-0.461618\pi\)
0.120290 + 0.992739i \(0.461618\pi\)
\(84\) 23.5298 2.56732
\(85\) 2.37865 0.258001
\(86\) 2.05622 0.221728
\(87\) −16.9779 −1.82022
\(88\) −0.468901 −0.0499850
\(89\) −4.14803 −0.439691 −0.219845 0.975535i \(-0.570555\pi\)
−0.219845 + 0.975535i \(0.570555\pi\)
\(90\) 32.5119 3.42705
\(91\) 18.5536 1.94495
\(92\) −10.0456 −1.04733
\(93\) −20.7591 −2.15262
\(94\) 6.82852 0.704308
\(95\) −4.64767 −0.476841
\(96\) −25.2144 −2.57343
\(97\) −1.97190 −0.200216 −0.100108 0.994977i \(-0.531919\pi\)
−0.100108 + 0.994977i \(0.531919\pi\)
\(98\) −9.37805 −0.947326
\(99\) 6.64724 0.668073
\(100\) 1.46601 0.146601
\(101\) −13.2539 −1.31881 −0.659407 0.751786i \(-0.729193\pi\)
−0.659407 + 0.751786i \(0.729193\pi\)
\(102\) −6.38662 −0.632370
\(103\) −17.7757 −1.75149 −0.875744 0.482776i \(-0.839629\pi\)
−0.875744 + 0.482776i \(0.839629\pi\)
\(104\) 2.55868 0.250899
\(105\) −25.1204 −2.45150
\(106\) 6.19873 0.602074
\(107\) 11.8902 1.14947 0.574737 0.818338i \(-0.305104\pi\)
0.574737 + 0.818338i \(0.305104\pi\)
\(108\) −25.2400 −2.42872
\(109\) −10.3027 −0.986816 −0.493408 0.869798i \(-0.664249\pi\)
−0.493408 + 0.869798i \(0.664249\pi\)
\(110\) 4.89103 0.466342
\(111\) −5.22545 −0.495978
\(112\) 11.8729 1.12189
\(113\) 19.5391 1.83808 0.919040 0.394164i \(-0.128966\pi\)
0.919040 + 0.394164i \(0.128966\pi\)
\(114\) 12.4789 1.16875
\(115\) 10.7247 1.00008
\(116\) 12.1788 1.13077
\(117\) −36.2724 −3.35338
\(118\) −1.00267 −0.0923037
\(119\) 3.40012 0.311689
\(120\) −3.46428 −0.316244
\(121\) 1.00000 0.0909091
\(122\) −12.4912 −1.13090
\(123\) 27.1792 2.45067
\(124\) 14.8912 1.33727
\(125\) 10.3281 0.923777
\(126\) 46.4735 4.14019
\(127\) 2.33243 0.206970 0.103485 0.994631i \(-0.467001\pi\)
0.103485 + 0.994631i \(0.467001\pi\)
\(128\) 3.72682 0.329408
\(129\) 3.10600 0.273468
\(130\) −26.6892 −2.34080
\(131\) −11.7720 −1.02852 −0.514260 0.857634i \(-0.671933\pi\)
−0.514260 + 0.857634i \(0.671933\pi\)
\(132\) −6.92029 −0.602334
\(133\) −6.64353 −0.576067
\(134\) 0.681042 0.0588330
\(135\) 26.9461 2.31916
\(136\) 0.468901 0.0402079
\(137\) −0.629780 −0.0538057 −0.0269029 0.999638i \(-0.508564\pi\)
−0.0269029 + 0.999638i \(0.508564\pi\)
\(138\) −28.7955 −2.45124
\(139\) −2.08107 −0.176514 −0.0882569 0.996098i \(-0.528130\pi\)
−0.0882569 + 0.996098i \(0.528130\pi\)
\(140\) 18.0197 1.52294
\(141\) 10.3147 0.868658
\(142\) 1.52404 0.127895
\(143\) −5.45676 −0.456317
\(144\) −23.2116 −1.93430
\(145\) −13.0021 −1.07976
\(146\) −24.2914 −2.01037
\(147\) −14.1659 −1.16838
\(148\) 3.74839 0.308116
\(149\) 8.29557 0.679600 0.339800 0.940498i \(-0.389641\pi\)
0.339800 + 0.940498i \(0.389641\pi\)
\(150\) 4.20229 0.343116
\(151\) −5.92641 −0.482285 −0.241142 0.970490i \(-0.577522\pi\)
−0.241142 + 0.970490i \(0.577522\pi\)
\(152\) −0.916189 −0.0743127
\(153\) −6.64724 −0.537397
\(154\) 6.99140 0.563383
\(155\) −15.8979 −1.27695
\(156\) 37.7624 3.02341
\(157\) 4.63271 0.369731 0.184865 0.982764i \(-0.440815\pi\)
0.184865 + 0.982764i \(0.440815\pi\)
\(158\) −28.8163 −2.29250
\(159\) 9.36342 0.742568
\(160\) −19.3098 −1.52657
\(161\) 15.3302 1.20819
\(162\) −31.3452 −2.46271
\(163\) −15.7248 −1.23166 −0.615829 0.787880i \(-0.711179\pi\)
−0.615829 + 0.787880i \(0.711179\pi\)
\(164\) −19.4966 −1.52243
\(165\) 7.38809 0.575162
\(166\) −4.50680 −0.349796
\(167\) 5.67202 0.438914 0.219457 0.975622i \(-0.429571\pi\)
0.219457 + 0.975622i \(0.429571\pi\)
\(168\) −4.95195 −0.382052
\(169\) 16.7762 1.29048
\(170\) −4.89103 −0.375125
\(171\) 12.9881 0.993225
\(172\) −2.22804 −0.169886
\(173\) −18.9204 −1.43849 −0.719244 0.694757i \(-0.755512\pi\)
−0.719244 + 0.694757i \(0.755512\pi\)
\(174\) 34.9102 2.64654
\(175\) −2.23723 −0.169118
\(176\) −3.49192 −0.263213
\(177\) −1.51458 −0.113843
\(178\) 8.52927 0.639296
\(179\) −14.9099 −1.11442 −0.557210 0.830371i \(-0.688128\pi\)
−0.557210 + 0.830371i \(0.688128\pi\)
\(180\) −35.2286 −2.62578
\(181\) 1.19021 0.0884672 0.0442336 0.999021i \(-0.485915\pi\)
0.0442336 + 0.999021i \(0.485915\pi\)
\(182\) −38.1504 −2.82789
\(183\) −18.8684 −1.39479
\(184\) 2.11415 0.155857
\(185\) −4.00178 −0.294217
\(186\) 42.6853 3.12984
\(187\) −1.00000 −0.0731272
\(188\) −7.39912 −0.539636
\(189\) 38.5177 2.80175
\(190\) 9.55663 0.693311
\(191\) −11.6775 −0.844955 −0.422477 0.906374i \(-0.638839\pi\)
−0.422477 + 0.906374i \(0.638839\pi\)
\(192\) 30.1545 2.17621
\(193\) −16.3980 −1.18035 −0.590176 0.807274i \(-0.700942\pi\)
−0.590176 + 0.807274i \(0.700942\pi\)
\(194\) 4.05465 0.291107
\(195\) −40.3150 −2.88702
\(196\) 10.1617 0.725835
\(197\) −6.90365 −0.491864 −0.245932 0.969287i \(-0.579094\pi\)
−0.245932 + 0.969287i \(0.579094\pi\)
\(198\) −13.6682 −0.971356
\(199\) −24.5560 −1.74073 −0.870363 0.492411i \(-0.836116\pi\)
−0.870363 + 0.492411i \(0.836116\pi\)
\(200\) −0.308529 −0.0218163
\(201\) 1.02874 0.0725617
\(202\) 27.2530 1.91751
\(203\) −18.5856 −1.30445
\(204\) 6.92029 0.484517
\(205\) 20.8145 1.45375
\(206\) 36.5507 2.54661
\(207\) −29.9706 −2.08310
\(208\) 19.0546 1.32120
\(209\) 1.95391 0.135155
\(210\) 51.6531 3.56440
\(211\) −26.0649 −1.79438 −0.897191 0.441642i \(-0.854396\pi\)
−0.897191 + 0.441642i \(0.854396\pi\)
\(212\) −6.71670 −0.461305
\(213\) 2.30213 0.157739
\(214\) −24.4490 −1.67130
\(215\) 2.37865 0.162223
\(216\) 5.31186 0.361426
\(217\) −22.7249 −1.54267
\(218\) 21.1845 1.43480
\(219\) −36.6931 −2.47949
\(220\) −5.29973 −0.357308
\(221\) 5.45676 0.367061
\(222\) 10.7447 0.721135
\(223\) −11.1035 −0.743543 −0.371771 0.928324i \(-0.621250\pi\)
−0.371771 + 0.928324i \(0.621250\pi\)
\(224\) −27.6020 −1.84424
\(225\) 4.37378 0.291585
\(226\) −40.1766 −2.67251
\(227\) −0.650589 −0.0431811 −0.0215906 0.999767i \(-0.506873\pi\)
−0.0215906 + 0.999767i \(0.506873\pi\)
\(228\) −13.5216 −0.895491
\(229\) −8.72696 −0.576694 −0.288347 0.957526i \(-0.593106\pi\)
−0.288347 + 0.957526i \(0.593106\pi\)
\(230\) −22.0523 −1.45409
\(231\) 10.5608 0.694848
\(232\) −2.56308 −0.168275
\(233\) −11.4269 −0.748600 −0.374300 0.927308i \(-0.622117\pi\)
−0.374300 + 0.927308i \(0.622117\pi\)
\(234\) 74.5840 4.87571
\(235\) 7.89929 0.515293
\(236\) 1.08646 0.0707225
\(237\) −43.5282 −2.82746
\(238\) −6.99140 −0.453185
\(239\) −6.82199 −0.441278 −0.220639 0.975356i \(-0.570814\pi\)
−0.220639 + 0.975356i \(0.570814\pi\)
\(240\) −25.7986 −1.66529
\(241\) −19.5256 −1.25775 −0.628876 0.777505i \(-0.716485\pi\)
−0.628876 + 0.777505i \(0.716485\pi\)
\(242\) −2.05622 −0.132179
\(243\) −13.3631 −0.857245
\(244\) 13.5349 0.866486
\(245\) −10.8486 −0.693092
\(246\) −55.8865 −3.56319
\(247\) −10.6620 −0.678407
\(248\) −3.13392 −0.199004
\(249\) −6.80770 −0.431421
\(250\) −21.2369 −1.34314
\(251\) 12.0823 0.762626 0.381313 0.924446i \(-0.375472\pi\)
0.381313 + 0.924446i \(0.375472\pi\)
\(252\) −50.3569 −3.17218
\(253\) −4.50873 −0.283461
\(254\) −4.79599 −0.300927
\(255\) −7.38809 −0.462660
\(256\) 11.7538 0.734610
\(257\) 2.53783 0.158306 0.0791528 0.996862i \(-0.474779\pi\)
0.0791528 + 0.996862i \(0.474779\pi\)
\(258\) −6.38662 −0.397614
\(259\) −5.72027 −0.355440
\(260\) 28.9194 1.79350
\(261\) 36.3348 2.24907
\(262\) 24.2057 1.49544
\(263\) 15.5504 0.958880 0.479440 0.877575i \(-0.340840\pi\)
0.479440 + 0.877575i \(0.340840\pi\)
\(264\) 1.45641 0.0896356
\(265\) 7.17074 0.440495
\(266\) 13.6605 0.837582
\(267\) 12.8838 0.788476
\(268\) −0.737950 −0.0450775
\(269\) 18.2485 1.11263 0.556314 0.830972i \(-0.312215\pi\)
0.556314 + 0.830972i \(0.312215\pi\)
\(270\) −55.4072 −3.37198
\(271\) −0.581663 −0.0353335 −0.0176668 0.999844i \(-0.505624\pi\)
−0.0176668 + 0.999844i \(0.505624\pi\)
\(272\) 3.49192 0.211729
\(273\) −57.6276 −3.48778
\(274\) 1.29497 0.0782317
\(275\) 0.657984 0.0396779
\(276\) 31.2017 1.87812
\(277\) −16.8074 −1.00986 −0.504929 0.863161i \(-0.668481\pi\)
−0.504929 + 0.863161i \(0.668481\pi\)
\(278\) 4.27913 0.256645
\(279\) 44.4272 2.65979
\(280\) −3.79233 −0.226635
\(281\) −14.3817 −0.857939 −0.428969 0.903319i \(-0.641123\pi\)
−0.428969 + 0.903319i \(0.641123\pi\)
\(282\) −21.2094 −1.26300
\(283\) −22.6885 −1.34869 −0.674346 0.738416i \(-0.735574\pi\)
−0.674346 + 0.738416i \(0.735574\pi\)
\(284\) −1.65139 −0.0979922
\(285\) 14.4357 0.855095
\(286\) 11.2203 0.663470
\(287\) 29.7529 1.75626
\(288\) 53.9620 3.17974
\(289\) 1.00000 0.0588235
\(290\) 26.7351 1.56994
\(291\) 6.12471 0.359037
\(292\) 26.3212 1.54033
\(293\) −18.1415 −1.05984 −0.529919 0.848048i \(-0.677778\pi\)
−0.529919 + 0.848048i \(0.677778\pi\)
\(294\) 29.1282 1.69879
\(295\) −1.15990 −0.0675321
\(296\) −0.788865 −0.0458519
\(297\) −11.3283 −0.657336
\(298\) −17.0575 −0.988116
\(299\) 24.6030 1.42283
\(300\) −4.55344 −0.262893
\(301\) 3.40012 0.195980
\(302\) 12.1860 0.701226
\(303\) 41.1667 2.36496
\(304\) −6.82289 −0.391319
\(305\) −14.4499 −0.827397
\(306\) 13.6682 0.781358
\(307\) −10.1942 −0.581811 −0.290906 0.956752i \(-0.593957\pi\)
−0.290906 + 0.956752i \(0.593957\pi\)
\(308\) −7.57561 −0.431660
\(309\) 55.2112 3.14086
\(310\) 32.6895 1.85664
\(311\) 7.16815 0.406469 0.203234 0.979130i \(-0.434855\pi\)
0.203234 + 0.979130i \(0.434855\pi\)
\(312\) −7.94725 −0.449925
\(313\) −16.8453 −0.952155 −0.476078 0.879403i \(-0.657942\pi\)
−0.476078 + 0.879403i \(0.657942\pi\)
\(314\) −9.52588 −0.537576
\(315\) 53.7609 3.02908
\(316\) 31.2243 1.75650
\(317\) −26.9650 −1.51450 −0.757252 0.653123i \(-0.773459\pi\)
−0.757252 + 0.653123i \(0.773459\pi\)
\(318\) −19.2533 −1.07967
\(319\) 5.46615 0.306046
\(320\) 23.0930 1.29094
\(321\) −36.9311 −2.06129
\(322\) −31.5223 −1.75667
\(323\) −1.95391 −0.108718
\(324\) 33.9644 1.88691
\(325\) −3.59046 −0.199163
\(326\) 32.3336 1.79079
\(327\) 32.0001 1.76961
\(328\) 4.10314 0.226558
\(329\) 11.2915 0.622520
\(330\) −15.1915 −0.836267
\(331\) −9.23332 −0.507509 −0.253755 0.967269i \(-0.581666\pi\)
−0.253755 + 0.967269i \(0.581666\pi\)
\(332\) 4.88340 0.268011
\(333\) 11.1831 0.612832
\(334\) −11.6629 −0.638167
\(335\) 0.787834 0.0430440
\(336\) −36.8774 −2.01182
\(337\) −17.0333 −0.927862 −0.463931 0.885871i \(-0.653561\pi\)
−0.463931 + 0.885871i \(0.653561\pi\)
\(338\) −34.4956 −1.87631
\(339\) −60.6883 −3.29614
\(340\) 5.29973 0.287418
\(341\) 6.68356 0.361935
\(342\) −26.7064 −1.44412
\(343\) 8.29351 0.447807
\(344\) 0.468901 0.0252814
\(345\) −33.3109 −1.79340
\(346\) 38.9044 2.09152
\(347\) 30.0576 1.61358 0.806788 0.590840i \(-0.201204\pi\)
0.806788 + 0.590840i \(0.201204\pi\)
\(348\) −37.8274 −2.02776
\(349\) −19.3592 −1.03627 −0.518136 0.855298i \(-0.673374\pi\)
−0.518136 + 0.855298i \(0.673374\pi\)
\(350\) 4.60023 0.245892
\(351\) 61.8160 3.29949
\(352\) 8.11795 0.432688
\(353\) 3.49404 0.185969 0.0929846 0.995668i \(-0.470359\pi\)
0.0929846 + 0.995668i \(0.470359\pi\)
\(354\) 3.11431 0.165524
\(355\) 1.76303 0.0935717
\(356\) −9.24199 −0.489824
\(357\) −10.5608 −0.558936
\(358\) 30.6581 1.62033
\(359\) 1.53087 0.0807963 0.0403982 0.999184i \(-0.487137\pi\)
0.0403982 + 0.999184i \(0.487137\pi\)
\(360\) 7.41401 0.390752
\(361\) −15.1822 −0.799065
\(362\) −2.44732 −0.128628
\(363\) −3.10600 −0.163023
\(364\) 41.3383 2.16671
\(365\) −28.1005 −1.47085
\(366\) 38.7976 2.02798
\(367\) 33.8086 1.76479 0.882397 0.470505i \(-0.155928\pi\)
0.882397 + 0.470505i \(0.155928\pi\)
\(368\) 15.7441 0.820719
\(369\) −58.1670 −3.02805
\(370\) 8.22854 0.427781
\(371\) 10.2501 0.532158
\(372\) −46.2522 −2.39806
\(373\) 11.7615 0.608988 0.304494 0.952514i \(-0.401513\pi\)
0.304494 + 0.952514i \(0.401513\pi\)
\(374\) 2.05622 0.106325
\(375\) −32.0792 −1.65656
\(376\) 1.55718 0.0803053
\(377\) −29.8275 −1.53619
\(378\) −79.2008 −4.07365
\(379\) 22.2130 1.14101 0.570504 0.821295i \(-0.306748\pi\)
0.570504 + 0.821295i \(0.306748\pi\)
\(380\) −10.3552 −0.531210
\(381\) −7.24452 −0.371148
\(382\) 24.0115 1.22854
\(383\) 25.4421 1.30003 0.650014 0.759922i \(-0.274763\pi\)
0.650014 + 0.759922i \(0.274763\pi\)
\(384\) −11.5755 −0.590710
\(385\) 8.08770 0.412188
\(386\) 33.7179 1.71619
\(387\) −6.64724 −0.337898
\(388\) −4.39347 −0.223044
\(389\) 31.7725 1.61093 0.805464 0.592645i \(-0.201916\pi\)
0.805464 + 0.592645i \(0.201916\pi\)
\(390\) 82.8966 4.19763
\(391\) 4.50873 0.228016
\(392\) −2.13857 −0.108014
\(393\) 36.5637 1.84439
\(394\) 14.1954 0.715155
\(395\) −33.3350 −1.67726
\(396\) 14.8103 0.744246
\(397\) −15.0628 −0.755981 −0.377991 0.925809i \(-0.623385\pi\)
−0.377991 + 0.925809i \(0.623385\pi\)
\(398\) 50.4924 2.53096
\(399\) 20.6348 1.03303
\(400\) −2.29763 −0.114881
\(401\) −1.42657 −0.0712393 −0.0356196 0.999365i \(-0.511340\pi\)
−0.0356196 + 0.999365i \(0.511340\pi\)
\(402\) −2.11532 −0.105502
\(403\) −36.4706 −1.81673
\(404\) −29.5303 −1.46918
\(405\) −36.2603 −1.80179
\(406\) 38.2160 1.89663
\(407\) 1.68237 0.0833921
\(408\) −1.45641 −0.0721028
\(409\) −38.6806 −1.91263 −0.956316 0.292334i \(-0.905568\pi\)
−0.956316 + 0.292334i \(0.905568\pi\)
\(410\) −42.7992 −2.11370
\(411\) 1.95610 0.0964871
\(412\) −39.6049 −1.95119
\(413\) −1.65800 −0.0815849
\(414\) 61.6262 3.02876
\(415\) −5.21351 −0.255921
\(416\) −44.2977 −2.17187
\(417\) 6.46379 0.316533
\(418\) −4.01767 −0.196510
\(419\) −6.55337 −0.320153 −0.160076 0.987105i \(-0.551174\pi\)
−0.160076 + 0.987105i \(0.551174\pi\)
\(420\) −55.9693 −2.73102
\(421\) −8.75754 −0.426817 −0.213408 0.976963i \(-0.568456\pi\)
−0.213408 + 0.976963i \(0.568456\pi\)
\(422\) 53.5952 2.60897
\(423\) −22.0749 −1.07332
\(424\) 1.41356 0.0686485
\(425\) −0.657984 −0.0319169
\(426\) −4.73368 −0.229347
\(427\) −20.6551 −0.999571
\(428\) 26.4919 1.28054
\(429\) 16.9487 0.818291
\(430\) −4.89103 −0.235866
\(431\) 41.0193 1.97583 0.987915 0.154997i \(-0.0495368\pi\)
0.987915 + 0.154997i \(0.0495368\pi\)
\(432\) 39.5576 1.90322
\(433\) −23.2297 −1.11635 −0.558175 0.829724i \(-0.688498\pi\)
−0.558175 + 0.829724i \(0.688498\pi\)
\(434\) 46.7274 2.24299
\(435\) 40.3844 1.93629
\(436\) −22.9547 −1.09933
\(437\) −8.80965 −0.421423
\(438\) 75.4491 3.60510
\(439\) −5.15671 −0.246116 −0.123058 0.992399i \(-0.539270\pi\)
−0.123058 + 0.992399i \(0.539270\pi\)
\(440\) 1.11535 0.0531723
\(441\) 30.3169 1.44366
\(442\) −11.2203 −0.533695
\(443\) −39.4287 −1.87331 −0.936657 0.350247i \(-0.886098\pi\)
−0.936657 + 0.350247i \(0.886098\pi\)
\(444\) −11.6425 −0.552529
\(445\) 9.86673 0.467728
\(446\) 22.8312 1.08109
\(447\) −25.7661 −1.21869
\(448\) 33.0099 1.55957
\(449\) −17.5279 −0.827193 −0.413597 0.910460i \(-0.635728\pi\)
−0.413597 + 0.910460i \(0.635728\pi\)
\(450\) −8.99345 −0.423955
\(451\) −8.75055 −0.412047
\(452\) 43.5338 2.04766
\(453\) 18.4074 0.864857
\(454\) 1.33775 0.0627839
\(455\) −44.1326 −2.06897
\(456\) 2.84568 0.133261
\(457\) 9.57992 0.448130 0.224065 0.974574i \(-0.428067\pi\)
0.224065 + 0.974574i \(0.428067\pi\)
\(458\) 17.9446 0.838494
\(459\) 11.3283 0.528761
\(460\) 23.8951 1.11411
\(461\) −6.04114 −0.281364 −0.140682 0.990055i \(-0.544929\pi\)
−0.140682 + 0.990055i \(0.544929\pi\)
\(462\) −21.7153 −1.01029
\(463\) 33.8178 1.57165 0.785823 0.618452i \(-0.212240\pi\)
0.785823 + 0.618452i \(0.212240\pi\)
\(464\) −19.0874 −0.886108
\(465\) 49.3788 2.28988
\(466\) 23.4962 1.08844
\(467\) −1.06940 −0.0494858 −0.0247429 0.999694i \(-0.507877\pi\)
−0.0247429 + 0.999694i \(0.507877\pi\)
\(468\) −80.8163 −3.73574
\(469\) 1.12616 0.0520010
\(470\) −16.2427 −0.749219
\(471\) −14.3892 −0.663020
\(472\) −0.228650 −0.0105245
\(473\) −1.00000 −0.0459800
\(474\) 89.5036 4.11103
\(475\) 1.28564 0.0589892
\(476\) 7.57561 0.347227
\(477\) −20.0389 −0.917519
\(478\) 14.0275 0.641603
\(479\) −7.61412 −0.347898 −0.173949 0.984755i \(-0.555653\pi\)
−0.173949 + 0.984755i \(0.555653\pi\)
\(480\) 59.9762 2.73753
\(481\) −9.18030 −0.418586
\(482\) 40.1489 1.82873
\(483\) −47.6157 −2.16659
\(484\) 2.22804 0.101275
\(485\) 4.69046 0.212983
\(486\) 27.4775 1.24641
\(487\) 15.5730 0.705681 0.352841 0.935683i \(-0.385216\pi\)
0.352841 + 0.935683i \(0.385216\pi\)
\(488\) −2.84849 −0.128945
\(489\) 48.8411 2.20867
\(490\) 22.3071 1.00773
\(491\) 26.4059 1.19168 0.595840 0.803103i \(-0.296819\pi\)
0.595840 + 0.803103i \(0.296819\pi\)
\(492\) 60.5564 2.73009
\(493\) −5.46615 −0.246183
\(494\) 21.9234 0.986382
\(495\) −15.8115 −0.710673
\(496\) −23.3384 −1.04793
\(497\) 2.52012 0.113043
\(498\) 13.9981 0.627271
\(499\) 11.0078 0.492778 0.246389 0.969171i \(-0.420756\pi\)
0.246389 + 0.969171i \(0.420756\pi\)
\(500\) 23.0115 1.02911
\(501\) −17.6173 −0.787083
\(502\) −24.8438 −1.10883
\(503\) 36.9931 1.64944 0.824720 0.565541i \(-0.191333\pi\)
0.824720 + 0.565541i \(0.191333\pi\)
\(504\) 10.5978 0.472064
\(505\) 31.5264 1.40291
\(506\) 9.27094 0.412144
\(507\) −52.1069 −2.31415
\(508\) 5.19674 0.230568
\(509\) −30.1261 −1.33532 −0.667658 0.744468i \(-0.732703\pi\)
−0.667658 + 0.744468i \(0.732703\pi\)
\(510\) 15.1915 0.672693
\(511\) −40.1677 −1.77692
\(512\) −31.6219 −1.39751
\(513\) −22.1345 −0.977263
\(514\) −5.21834 −0.230171
\(515\) 42.2821 1.86317
\(516\) 6.92029 0.304649
\(517\) −3.32091 −0.146053
\(518\) 11.7621 0.516798
\(519\) 58.7667 2.57957
\(520\) −6.08620 −0.266898
\(521\) 0.373711 0.0163726 0.00818628 0.999966i \(-0.497394\pi\)
0.00818628 + 0.999966i \(0.497394\pi\)
\(522\) −74.7124 −3.27007
\(523\) 0.530468 0.0231957 0.0115979 0.999933i \(-0.496308\pi\)
0.0115979 + 0.999933i \(0.496308\pi\)
\(524\) −26.2284 −1.14579
\(525\) 6.94882 0.303271
\(526\) −31.9751 −1.39418
\(527\) −6.68356 −0.291140
\(528\) 10.8459 0.472007
\(529\) −2.67136 −0.116146
\(530\) −14.7446 −0.640465
\(531\) 3.24139 0.140664
\(532\) −14.8020 −0.641750
\(533\) 47.7497 2.06827
\(534\) −26.4919 −1.14642
\(535\) −28.2828 −1.22277
\(536\) 0.155305 0.00670815
\(537\) 46.3103 1.99843
\(538\) −37.5228 −1.61772
\(539\) 4.56082 0.196448
\(540\) 60.0371 2.58359
\(541\) −44.6332 −1.91893 −0.959466 0.281825i \(-0.909060\pi\)
−0.959466 + 0.281825i \(0.909060\pi\)
\(542\) 1.19603 0.0513738
\(543\) −3.69678 −0.158644
\(544\) −8.11795 −0.348054
\(545\) 24.5064 1.04974
\(546\) 118.495 5.07112
\(547\) −15.6384 −0.668652 −0.334326 0.942458i \(-0.608509\pi\)
−0.334326 + 0.942458i \(0.608509\pi\)
\(548\) −1.40317 −0.0599406
\(549\) 40.3808 1.72341
\(550\) −1.35296 −0.0576904
\(551\) 10.6804 0.454999
\(552\) −6.56654 −0.279490
\(553\) −47.6501 −2.02629
\(554\) 34.5597 1.46830
\(555\) 12.4295 0.527604
\(556\) −4.63670 −0.196640
\(557\) 7.85876 0.332986 0.166493 0.986043i \(-0.446756\pi\)
0.166493 + 0.986043i \(0.446756\pi\)
\(558\) −91.3521 −3.86724
\(559\) 5.45676 0.230796
\(560\) −28.2416 −1.19343
\(561\) 3.10600 0.131135
\(562\) 29.5719 1.24741
\(563\) −29.1530 −1.22865 −0.614326 0.789053i \(-0.710572\pi\)
−0.614326 + 0.789053i \(0.710572\pi\)
\(564\) 22.9817 0.967703
\(565\) −46.4766 −1.95529
\(566\) 46.6526 1.96095
\(567\) −51.8317 −2.17673
\(568\) 0.347543 0.0145826
\(569\) 5.28132 0.221404 0.110702 0.993854i \(-0.464690\pi\)
0.110702 + 0.993854i \(0.464690\pi\)
\(570\) −29.6829 −1.24328
\(571\) −30.1706 −1.26260 −0.631301 0.775538i \(-0.717479\pi\)
−0.631301 + 0.775538i \(0.717479\pi\)
\(572\) −12.1579 −0.508346
\(573\) 36.2703 1.51521
\(574\) −61.1786 −2.55354
\(575\) −2.96667 −0.123719
\(576\) −64.5344 −2.68894
\(577\) 2.27433 0.0946816 0.0473408 0.998879i \(-0.484925\pi\)
0.0473408 + 0.998879i \(0.484925\pi\)
\(578\) −2.05622 −0.0855275
\(579\) 50.9322 2.11667
\(580\) −28.9691 −1.20288
\(581\) −7.45235 −0.309176
\(582\) −12.5938 −0.522028
\(583\) −3.01462 −0.124853
\(584\) −5.53941 −0.229222
\(585\) 86.2794 3.56721
\(586\) 37.3029 1.54097
\(587\) −40.2557 −1.66153 −0.830765 0.556623i \(-0.812097\pi\)
−0.830765 + 0.556623i \(0.812097\pi\)
\(588\) −31.5622 −1.30160
\(589\) 13.0591 0.538089
\(590\) 2.38501 0.0981894
\(591\) 21.4427 0.882036
\(592\) −5.87471 −0.241449
\(593\) 19.9104 0.817621 0.408811 0.912619i \(-0.365944\pi\)
0.408811 + 0.912619i \(0.365944\pi\)
\(594\) 23.2935 0.955745
\(595\) −8.08770 −0.331563
\(596\) 18.4829 0.757088
\(597\) 76.2708 3.12156
\(598\) −50.5893 −2.06875
\(599\) −1.50958 −0.0616800 −0.0308400 0.999524i \(-0.509818\pi\)
−0.0308400 + 0.999524i \(0.509818\pi\)
\(600\) 0.958292 0.0391221
\(601\) −38.6248 −1.57554 −0.787770 0.615970i \(-0.788764\pi\)
−0.787770 + 0.615970i \(0.788764\pi\)
\(602\) −6.99140 −0.284948
\(603\) −2.20164 −0.0896575
\(604\) −13.2043 −0.537275
\(605\) −2.37865 −0.0967059
\(606\) −84.6477 −3.43858
\(607\) 24.9818 1.01398 0.506989 0.861952i \(-0.330758\pi\)
0.506989 + 0.861952i \(0.330758\pi\)
\(608\) 15.8617 0.643278
\(609\) 57.7268 2.33921
\(610\) 29.7121 1.20301
\(611\) 18.1214 0.733114
\(612\) −14.8103 −0.598672
\(613\) 26.3188 1.06300 0.531502 0.847057i \(-0.321628\pi\)
0.531502 + 0.847057i \(0.321628\pi\)
\(614\) 20.9614 0.845934
\(615\) −64.6499 −2.60694
\(616\) 1.59432 0.0642369
\(617\) −14.0481 −0.565557 −0.282778 0.959185i \(-0.591256\pi\)
−0.282778 + 0.959185i \(0.591256\pi\)
\(618\) −113.526 −4.56670
\(619\) 33.6935 1.35426 0.677128 0.735865i \(-0.263224\pi\)
0.677128 + 0.735865i \(0.263224\pi\)
\(620\) −35.4211 −1.42254
\(621\) 51.0764 2.04962
\(622\) −14.7393 −0.590992
\(623\) 14.1038 0.565058
\(624\) −59.1835 −2.36923
\(625\) −27.8570 −1.11428
\(626\) 34.6377 1.38440
\(627\) −6.06884 −0.242366
\(628\) 10.3219 0.411888
\(629\) −1.68237 −0.0670806
\(630\) −110.544 −4.40419
\(631\) 40.9122 1.62869 0.814344 0.580383i \(-0.197097\pi\)
0.814344 + 0.580383i \(0.197097\pi\)
\(632\) −6.57128 −0.261392
\(633\) 80.9576 3.21778
\(634\) 55.4459 2.20204
\(635\) −5.54803 −0.220167
\(636\) 20.8621 0.827235
\(637\) −24.8873 −0.986071
\(638\) −11.2396 −0.444980
\(639\) −4.92685 −0.194903
\(640\) −8.86481 −0.350412
\(641\) 1.50910 0.0596058 0.0298029 0.999556i \(-0.490512\pi\)
0.0298029 + 0.999556i \(0.490512\pi\)
\(642\) 75.9385 2.99705
\(643\) −7.99676 −0.315361 −0.157681 0.987490i \(-0.550402\pi\)
−0.157681 + 0.987490i \(0.550402\pi\)
\(644\) 34.1564 1.34595
\(645\) −7.38809 −0.290906
\(646\) 4.01767 0.158073
\(647\) −7.66951 −0.301520 −0.150760 0.988570i \(-0.548172\pi\)
−0.150760 + 0.988570i \(0.548172\pi\)
\(648\) −7.14796 −0.280798
\(649\) 0.487630 0.0191412
\(650\) 7.38278 0.289576
\(651\) 70.5836 2.76639
\(652\) −35.0354 −1.37209
\(653\) 18.5430 0.725642 0.362821 0.931859i \(-0.381814\pi\)
0.362821 + 0.931859i \(0.381814\pi\)
\(654\) −65.7992 −2.57295
\(655\) 28.0014 1.09410
\(656\) 30.5562 1.19302
\(657\) 78.5279 3.06367
\(658\) −23.2178 −0.905124
\(659\) −17.0114 −0.662668 −0.331334 0.943513i \(-0.607499\pi\)
−0.331334 + 0.943513i \(0.607499\pi\)
\(660\) 16.4610 0.640742
\(661\) −35.7015 −1.38863 −0.694313 0.719673i \(-0.744292\pi\)
−0.694313 + 0.719673i \(0.744292\pi\)
\(662\) 18.9857 0.737902
\(663\) −16.9487 −0.658233
\(664\) −1.02773 −0.0398837
\(665\) 15.8026 0.612800
\(666\) −22.9950 −0.891037
\(667\) −24.6454 −0.954274
\(668\) 12.6375 0.488959
\(669\) 34.4874 1.33336
\(670\) −1.61996 −0.0625845
\(671\) 6.07482 0.234516
\(672\) 85.7319 3.30718
\(673\) 18.6793 0.720036 0.360018 0.932945i \(-0.382771\pi\)
0.360018 + 0.932945i \(0.382771\pi\)
\(674\) 35.0242 1.34908
\(675\) −7.45386 −0.286899
\(676\) 37.3781 1.43762
\(677\) 32.3805 1.24448 0.622242 0.782825i \(-0.286222\pi\)
0.622242 + 0.782825i \(0.286222\pi\)
\(678\) 124.789 4.79248
\(679\) 6.70469 0.257302
\(680\) −1.11535 −0.0427718
\(681\) 2.02073 0.0774345
\(682\) −13.7429 −0.526241
\(683\) 30.7170 1.17535 0.587676 0.809096i \(-0.300043\pi\)
0.587676 + 0.809096i \(0.300043\pi\)
\(684\) 28.9380 1.10647
\(685\) 1.49803 0.0572366
\(686\) −17.0533 −0.651097
\(687\) 27.1060 1.03416
\(688\) 3.49192 0.133128
\(689\) 16.4501 0.626698
\(690\) 68.4946 2.60754
\(691\) −8.95350 −0.340607 −0.170304 0.985392i \(-0.554475\pi\)
−0.170304 + 0.985392i \(0.554475\pi\)
\(692\) −42.1553 −1.60251
\(693\) −22.6014 −0.858557
\(694\) −61.8050 −2.34609
\(695\) 4.95013 0.187769
\(696\) 7.96093 0.301758
\(697\) 8.75055 0.331451
\(698\) 39.8067 1.50671
\(699\) 35.4919 1.34243
\(700\) −4.98463 −0.188401
\(701\) −31.5969 −1.19340 −0.596699 0.802465i \(-0.703521\pi\)
−0.596699 + 0.802465i \(0.703521\pi\)
\(702\) −127.107 −4.79735
\(703\) 3.28720 0.123979
\(704\) −9.70846 −0.365901
\(705\) −24.5352 −0.924049
\(706\) −7.18452 −0.270393
\(707\) 45.0649 1.69484
\(708\) −3.37454 −0.126823
\(709\) 1.13802 0.0427391 0.0213695 0.999772i \(-0.493197\pi\)
0.0213695 + 0.999772i \(0.493197\pi\)
\(710\) −3.62517 −0.136050
\(711\) 93.1559 3.49362
\(712\) 1.94502 0.0728926
\(713\) −30.1344 −1.12854
\(714\) 21.7153 0.812674
\(715\) 12.9797 0.485414
\(716\) −33.2199 −1.24149
\(717\) 21.1891 0.791321
\(718\) −3.14781 −0.117475
\(719\) 6.65675 0.248255 0.124127 0.992266i \(-0.460387\pi\)
0.124127 + 0.992266i \(0.460387\pi\)
\(720\) 55.2123 2.05764
\(721\) 60.4394 2.25088
\(722\) 31.2180 1.16181
\(723\) 60.6464 2.25547
\(724\) 2.65182 0.0985543
\(725\) 3.59664 0.133576
\(726\) 6.38662 0.237030
\(727\) −20.6180 −0.764680 −0.382340 0.924022i \(-0.624882\pi\)
−0.382340 + 0.924022i \(0.624882\pi\)
\(728\) −8.69981 −0.322437
\(729\) −4.22636 −0.156532
\(730\) 57.7808 2.13856
\(731\) 1.00000 0.0369863
\(732\) −42.0395 −1.55383
\(733\) 10.2608 0.378990 0.189495 0.981882i \(-0.439315\pi\)
0.189495 + 0.981882i \(0.439315\pi\)
\(734\) −69.5179 −2.56595
\(735\) 33.6958 1.24289
\(736\) −36.6016 −1.34915
\(737\) −0.331210 −0.0122003
\(738\) 119.604 4.40269
\(739\) −23.9256 −0.880119 −0.440059 0.897969i \(-0.645043\pi\)
−0.440059 + 0.897969i \(0.645043\pi\)
\(740\) −8.91612 −0.327763
\(741\) 33.1162 1.21655
\(742\) −21.0764 −0.773740
\(743\) 9.96762 0.365676 0.182838 0.983143i \(-0.441472\pi\)
0.182838 + 0.983143i \(0.441472\pi\)
\(744\) 9.73397 0.356865
\(745\) −19.7323 −0.722935
\(746\) −24.1842 −0.885448
\(747\) 14.5694 0.533065
\(748\) −2.22804 −0.0814652
\(749\) −40.4283 −1.47722
\(750\) 65.9619 2.40859
\(751\) 1.75348 0.0639855 0.0319927 0.999488i \(-0.489815\pi\)
0.0319927 + 0.999488i \(0.489815\pi\)
\(752\) 11.5963 0.422875
\(753\) −37.5275 −1.36758
\(754\) 61.3318 2.23357
\(755\) 14.0969 0.513038
\(756\) 85.8189 3.12120
\(757\) −18.2790 −0.664363 −0.332181 0.943216i \(-0.607785\pi\)
−0.332181 + 0.943216i \(0.607785\pi\)
\(758\) −45.6749 −1.65899
\(759\) 14.0041 0.508317
\(760\) 2.17929 0.0790513
\(761\) 2.52033 0.0913620 0.0456810 0.998956i \(-0.485454\pi\)
0.0456810 + 0.998956i \(0.485454\pi\)
\(762\) 14.8963 0.539637
\(763\) 35.0303 1.26818
\(764\) −26.0179 −0.941296
\(765\) 15.8115 0.571665
\(766\) −52.3145 −1.89020
\(767\) −2.66088 −0.0960788
\(768\) −36.5072 −1.31734
\(769\) −19.2276 −0.693365 −0.346683 0.937982i \(-0.612692\pi\)
−0.346683 + 0.937982i \(0.612692\pi\)
\(770\) −16.6301 −0.599307
\(771\) −7.88251 −0.283881
\(772\) −36.5354 −1.31494
\(773\) 23.8924 0.859349 0.429674 0.902984i \(-0.358628\pi\)
0.429674 + 0.902984i \(0.358628\pi\)
\(774\) 13.6682 0.491293
\(775\) 4.39767 0.157969
\(776\) 0.924624 0.0331921
\(777\) 17.7672 0.637393
\(778\) −65.3311 −2.34224
\(779\) −17.0978 −0.612592
\(780\) −89.8235 −3.21620
\(781\) −0.741187 −0.0265218
\(782\) −9.27094 −0.331528
\(783\) −61.9224 −2.21292
\(784\) −15.9260 −0.568786
\(785\) −11.0196 −0.393307
\(786\) −75.1830 −2.68169
\(787\) 5.71799 0.203824 0.101912 0.994793i \(-0.467504\pi\)
0.101912 + 0.994793i \(0.467504\pi\)
\(788\) −15.3816 −0.547947
\(789\) −48.2996 −1.71951
\(790\) 68.5440 2.43869
\(791\) −66.4352 −2.36216
\(792\) −3.11689 −0.110754
\(793\) −33.1488 −1.17715
\(794\) 30.9725 1.09917
\(795\) −22.2723 −0.789918
\(796\) −54.7116 −1.93920
\(797\) −31.3544 −1.11063 −0.555315 0.831640i \(-0.687402\pi\)
−0.555315 + 0.831640i \(0.687402\pi\)
\(798\) −42.4297 −1.50199
\(799\) 3.32091 0.117485
\(800\) 5.34148 0.188850
\(801\) −27.5730 −0.974243
\(802\) 2.93333 0.103580
\(803\) 11.8136 0.416893
\(804\) 2.29207 0.0808352
\(805\) −36.4653 −1.28523
\(806\) 74.9915 2.64146
\(807\) −56.6797 −1.99522
\(808\) 6.21477 0.218635
\(809\) 24.5251 0.862258 0.431129 0.902290i \(-0.358115\pi\)
0.431129 + 0.902290i \(0.358115\pi\)
\(810\) 74.5592 2.61974
\(811\) −3.83856 −0.134790 −0.0673950 0.997726i \(-0.521469\pi\)
−0.0673950 + 0.997726i \(0.521469\pi\)
\(812\) −41.4094 −1.45319
\(813\) 1.80665 0.0633618
\(814\) −3.45933 −0.121249
\(815\) 37.4037 1.31020
\(816\) −10.8459 −0.379682
\(817\) −1.95391 −0.0683586
\(818\) 79.5358 2.78090
\(819\) 123.330 4.30952
\(820\) 46.3756 1.61951
\(821\) −22.8585 −0.797765 −0.398883 0.917002i \(-0.630602\pi\)
−0.398883 + 0.917002i \(0.630602\pi\)
\(822\) −4.02216 −0.140289
\(823\) 5.16310 0.179974 0.0899872 0.995943i \(-0.471317\pi\)
0.0899872 + 0.995943i \(0.471317\pi\)
\(824\) 8.33502 0.290364
\(825\) −2.04370 −0.0711525
\(826\) 3.40921 0.118622
\(827\) −7.46910 −0.259726 −0.129863 0.991532i \(-0.541454\pi\)
−0.129863 + 0.991532i \(0.541454\pi\)
\(828\) −66.7757 −2.32062
\(829\) 14.9944 0.520777 0.260389 0.965504i \(-0.416149\pi\)
0.260389 + 0.965504i \(0.416149\pi\)
\(830\) 10.7201 0.372101
\(831\) 52.2037 1.81093
\(832\) 52.9767 1.83664
\(833\) −4.56082 −0.158023
\(834\) −13.2910 −0.460229
\(835\) −13.4918 −0.466902
\(836\) 4.35339 0.150565
\(837\) −75.7135 −2.61704
\(838\) 13.4752 0.465492
\(839\) −13.2047 −0.455878 −0.227939 0.973675i \(-0.573199\pi\)
−0.227939 + 0.973675i \(0.573199\pi\)
\(840\) 11.7790 0.406413
\(841\) 0.878821 0.0303042
\(842\) 18.0074 0.620577
\(843\) 44.6695 1.53850
\(844\) −58.0737 −1.99898
\(845\) −39.9048 −1.37277
\(846\) 45.3908 1.56057
\(847\) −3.40012 −0.116830
\(848\) 10.5268 0.361492
\(849\) 70.4705 2.41854
\(850\) 1.35296 0.0464061
\(851\) −7.58536 −0.260023
\(852\) 5.12923 0.175725
\(853\) −21.4738 −0.735249 −0.367625 0.929974i \(-0.619829\pi\)
−0.367625 + 0.929974i \(0.619829\pi\)
\(854\) 42.4715 1.45334
\(855\) −30.8942 −1.05656
\(856\) −5.57534 −0.190561
\(857\) −1.23096 −0.0420488 −0.0210244 0.999779i \(-0.506693\pi\)
−0.0210244 + 0.999779i \(0.506693\pi\)
\(858\) −34.8502 −1.18977
\(859\) −46.7517 −1.59515 −0.797574 0.603221i \(-0.793884\pi\)
−0.797574 + 0.603221i \(0.793884\pi\)
\(860\) 5.29973 0.180719
\(861\) −92.4126 −3.14941
\(862\) −84.3447 −2.87279
\(863\) −31.2387 −1.06338 −0.531688 0.846940i \(-0.678442\pi\)
−0.531688 + 0.846940i \(0.678442\pi\)
\(864\) −91.9628 −3.12864
\(865\) 45.0050 1.53021
\(866\) 47.7654 1.62313
\(867\) −3.10600 −0.105485
\(868\) −50.6320 −1.71856
\(869\) 14.0142 0.475400
\(870\) −83.0393 −2.81530
\(871\) 1.80734 0.0612392
\(872\) 4.83092 0.163596
\(873\) −13.1077 −0.443628
\(874\) 18.1146 0.612734
\(875\) −35.1169 −1.18717
\(876\) −81.7537 −2.76220
\(877\) 31.7235 1.07123 0.535613 0.844463i \(-0.320080\pi\)
0.535613 + 0.844463i \(0.320080\pi\)
\(878\) 10.6033 0.357845
\(879\) 56.3475 1.90055
\(880\) 8.30606 0.279997
\(881\) −10.8547 −0.365706 −0.182853 0.983140i \(-0.558533\pi\)
−0.182853 + 0.983140i \(0.558533\pi\)
\(882\) −62.3381 −2.09903
\(883\) 24.7126 0.831646 0.415823 0.909445i \(-0.363493\pi\)
0.415823 + 0.909445i \(0.363493\pi\)
\(884\) 12.1579 0.408914
\(885\) 3.60266 0.121102
\(886\) 81.0741 2.72374
\(887\) 36.3601 1.22085 0.610426 0.792073i \(-0.290998\pi\)
0.610426 + 0.792073i \(0.290998\pi\)
\(888\) 2.45022 0.0822239
\(889\) −7.93054 −0.265982
\(890\) −20.2882 −0.680061
\(891\) 15.2441 0.510696
\(892\) −24.7390 −0.828322
\(893\) −6.48875 −0.217138
\(894\) 52.9807 1.77194
\(895\) 35.4655 1.18548
\(896\) −12.6716 −0.423330
\(897\) −76.4171 −2.55149
\(898\) 36.0412 1.20271
\(899\) 36.5333 1.21846
\(900\) 9.74495 0.324832
\(901\) 3.01462 0.100432
\(902\) 17.9931 0.599103
\(903\) −10.5608 −0.351441
\(904\) −9.16188 −0.304719
\(905\) −2.83108 −0.0941084
\(906\) −37.8497 −1.25747
\(907\) 42.7889 1.42078 0.710391 0.703808i \(-0.248518\pi\)
0.710391 + 0.703808i \(0.248518\pi\)
\(908\) −1.44954 −0.0481046
\(909\) −88.1019 −2.92216
\(910\) 90.7464 3.00821
\(911\) 9.40165 0.311491 0.155745 0.987797i \(-0.450222\pi\)
0.155745 + 0.987797i \(0.450222\pi\)
\(912\) 21.1919 0.701734
\(913\) 2.19179 0.0725377
\(914\) −19.6984 −0.651566
\(915\) 44.8813 1.48373
\(916\) −19.4440 −0.642449
\(917\) 40.0261 1.32178
\(918\) −23.2935 −0.768801
\(919\) 24.0228 0.792437 0.396219 0.918156i \(-0.370322\pi\)
0.396219 + 0.918156i \(0.370322\pi\)
\(920\) −5.02882 −0.165795
\(921\) 31.6631 1.04333
\(922\) 12.4219 0.409094
\(923\) 4.04448 0.133126
\(924\) 23.5298 0.774075
\(925\) 1.10697 0.0363971
\(926\) −69.5368 −2.28512
\(927\) −118.159 −3.88085
\(928\) 44.3740 1.45665
\(929\) 53.0682 1.74111 0.870556 0.492069i \(-0.163759\pi\)
0.870556 + 0.492069i \(0.163759\pi\)
\(930\) −101.534 −3.32942
\(931\) 8.91143 0.292060
\(932\) −25.4596 −0.833956
\(933\) −22.2643 −0.728900
\(934\) 2.19891 0.0719507
\(935\) 2.37865 0.0777902
\(936\) 17.0081 0.555929
\(937\) 17.1710 0.560953 0.280476 0.959861i \(-0.409508\pi\)
0.280476 + 0.959861i \(0.409508\pi\)
\(938\) −2.31562 −0.0756078
\(939\) 52.3216 1.70745
\(940\) 17.5999 0.574046
\(941\) 15.8365 0.516255 0.258127 0.966111i \(-0.416895\pi\)
0.258127 + 0.966111i \(0.416895\pi\)
\(942\) 29.5874 0.964009
\(943\) 39.4539 1.28480
\(944\) −1.70276 −0.0554202
\(945\) −91.6202 −2.98040
\(946\) 2.05622 0.0668535
\(947\) 47.4657 1.54243 0.771213 0.636577i \(-0.219650\pi\)
0.771213 + 0.636577i \(0.219650\pi\)
\(948\) −96.9826 −3.14985
\(949\) −64.4640 −2.09259
\(950\) −2.64356 −0.0857684
\(951\) 83.7532 2.71588
\(952\) −1.59432 −0.0516722
\(953\) −32.9572 −1.06759 −0.533795 0.845614i \(-0.679234\pi\)
−0.533795 + 0.845614i \(0.679234\pi\)
\(954\) 41.2044 1.33404
\(955\) 27.7767 0.898833
\(956\) −15.1997 −0.491592
\(957\) −16.9779 −0.548817
\(958\) 15.6563 0.505832
\(959\) 2.14133 0.0691470
\(960\) −71.7270 −2.31498
\(961\) 13.6699 0.440966
\(962\) 18.8767 0.608610
\(963\) 79.0373 2.54694
\(964\) −43.5038 −1.40116
\(965\) 39.0051 1.25562
\(966\) 97.9083 3.15015
\(967\) −13.3301 −0.428666 −0.214333 0.976761i \(-0.568758\pi\)
−0.214333 + 0.976761i \(0.568758\pi\)
\(968\) −0.468901 −0.0150710
\(969\) 6.06884 0.194959
\(970\) −9.64461 −0.309670
\(971\) 6.35365 0.203898 0.101949 0.994790i \(-0.467492\pi\)
0.101949 + 0.994790i \(0.467492\pi\)
\(972\) −29.7736 −0.954988
\(973\) 7.07588 0.226842
\(974\) −32.0216 −1.02604
\(975\) 11.1520 0.357149
\(976\) −21.2128 −0.679004
\(977\) −22.9043 −0.732772 −0.366386 0.930463i \(-0.619405\pi\)
−0.366386 + 0.930463i \(0.619405\pi\)
\(978\) −100.428 −3.21134
\(979\) −4.14803 −0.132572
\(980\) −24.1711 −0.772118
\(981\) −68.4843 −2.18653
\(982\) −54.2963 −1.73266
\(983\) 44.8318 1.42991 0.714956 0.699170i \(-0.246447\pi\)
0.714956 + 0.699170i \(0.246447\pi\)
\(984\) −12.7444 −0.406275
\(985\) 16.4214 0.523228
\(986\) 11.2396 0.357942
\(987\) −35.0714 −1.11633
\(988\) −23.7554 −0.755759
\(989\) 4.50873 0.143369
\(990\) 32.5119 1.03329
\(991\) 15.1643 0.481710 0.240855 0.970561i \(-0.422572\pi\)
0.240855 + 0.970561i \(0.422572\pi\)
\(992\) 54.2568 1.72266
\(993\) 28.6787 0.910091
\(994\) −5.18193 −0.164361
\(995\) 58.4101 1.85172
\(996\) −15.1678 −0.480611
\(997\) 58.2846 1.84589 0.922946 0.384930i \(-0.125774\pi\)
0.922946 + 0.384930i \(0.125774\pi\)
\(998\) −22.6345 −0.716483
\(999\) −19.0585 −0.602983
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 \(a_p\))