Properties

Label 8041.2.a.i.1.2
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 0
Dimension 78
CM No

Related objects

Downloads

Learn more about

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 1.2
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.68205 q^{2} +1.14586 q^{3} +5.19341 q^{4} +0.981432 q^{5} -3.07326 q^{6} -5.03314 q^{7} -8.56488 q^{8} -1.68700 q^{9} +O(q^{10})\) \(q-2.68205 q^{2} +1.14586 q^{3} +5.19341 q^{4} +0.981432 q^{5} -3.07326 q^{6} -5.03314 q^{7} -8.56488 q^{8} -1.68700 q^{9} -2.63225 q^{10} +1.00000 q^{11} +5.95092 q^{12} -2.90244 q^{13} +13.4991 q^{14} +1.12458 q^{15} +12.5847 q^{16} -1.00000 q^{17} +4.52463 q^{18} -0.273183 q^{19} +5.09697 q^{20} -5.76728 q^{21} -2.68205 q^{22} -0.344383 q^{23} -9.81417 q^{24} -4.03679 q^{25} +7.78451 q^{26} -5.37065 q^{27} -26.1391 q^{28} -5.98996 q^{29} -3.01620 q^{30} +0.228383 q^{31} -16.6229 q^{32} +1.14586 q^{33} +2.68205 q^{34} -4.93968 q^{35} -8.76128 q^{36} +0.957214 q^{37} +0.732692 q^{38} -3.32580 q^{39} -8.40585 q^{40} -8.93139 q^{41} +15.4681 q^{42} -1.00000 q^{43} +5.19341 q^{44} -1.65568 q^{45} +0.923654 q^{46} -5.63631 q^{47} +14.4203 q^{48} +18.3325 q^{49} +10.8269 q^{50} -1.14586 q^{51} -15.0736 q^{52} +0.243489 q^{53} +14.4044 q^{54} +0.981432 q^{55} +43.1082 q^{56} -0.313030 q^{57} +16.0654 q^{58} +6.15588 q^{59} +5.84043 q^{60} +3.10856 q^{61} -0.612535 q^{62} +8.49091 q^{63} +19.4143 q^{64} -2.84855 q^{65} -3.07326 q^{66} -9.16623 q^{67} -5.19341 q^{68} -0.394615 q^{69} +13.2485 q^{70} -0.195261 q^{71} +14.4490 q^{72} +0.0243280 q^{73} -2.56730 q^{74} -4.62560 q^{75} -1.41875 q^{76} -5.03314 q^{77} +8.91997 q^{78} +0.00321078 q^{79} +12.3510 q^{80} -1.09302 q^{81} +23.9545 q^{82} -10.2623 q^{83} -29.9518 q^{84} -0.981432 q^{85} +2.68205 q^{86} -6.86366 q^{87} -8.56488 q^{88} -1.74790 q^{89} +4.44061 q^{90} +14.6084 q^{91} -1.78852 q^{92} +0.261695 q^{93} +15.1169 q^{94} -0.268111 q^{95} -19.0476 q^{96} +16.2141 q^{97} -49.1686 q^{98} -1.68700 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + O(q^{10}) \) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + 3q^{10} + 78q^{11} + 31q^{12} - 16q^{13} + 31q^{14} + 38q^{15} + 121q^{16} - 78q^{17} + 11q^{18} + 51q^{20} + 6q^{21} + 7q^{22} + 48q^{23} + 11q^{24} + 101q^{25} + 18q^{26} + 46q^{27} + 27q^{28} + 22q^{29} + 14q^{30} + 56q^{31} + 83q^{32} + 10q^{33} - 7q^{34} + 24q^{35} + 139q^{36} + 53q^{37} + 10q^{38} + 79q^{39} - q^{40} + 23q^{41} + 17q^{42} - 78q^{43} + 91q^{44} + 76q^{45} + 21q^{46} + 57q^{47} + 78q^{48} + 115q^{49} + 58q^{50} - 10q^{51} - 63q^{52} + 22q^{53} - 18q^{54} + 17q^{55} + 111q^{56} - 11q^{57} + 36q^{58} + 71q^{59} + 36q^{60} + 4q^{61} - 5q^{62} + 71q^{63} + 183q^{64} + 47q^{65} + 12q^{66} + 11q^{67} - 91q^{68} + 31q^{69} + 33q^{70} + 159q^{71} + 59q^{72} + 2q^{73} - 4q^{74} + 83q^{75} - 44q^{76} + 11q^{77} + 101q^{78} + 35q^{79} + 85q^{80} + 170q^{81} + 98q^{82} - 32q^{83} + 44q^{84} - 17q^{85} - 7q^{86} - 6q^{87} + 33q^{88} + 50q^{89} - 5q^{90} + 86q^{91} + 106q^{92} + 68q^{93} - q^{94} + 109q^{95} - 50q^{96} + 40q^{97} + 106q^{98} + 102q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.68205 −1.89650 −0.948249 0.317528i \(-0.897147\pi\)
−0.948249 + 0.317528i \(0.897147\pi\)
\(3\) 1.14586 0.661564 0.330782 0.943707i \(-0.392688\pi\)
0.330782 + 0.943707i \(0.392688\pi\)
\(4\) 5.19341 2.59670
\(5\) 0.981432 0.438910 0.219455 0.975623i \(-0.429572\pi\)
0.219455 + 0.975623i \(0.429572\pi\)
\(6\) −3.07326 −1.25465
\(7\) −5.03314 −1.90235 −0.951173 0.308657i \(-0.900120\pi\)
−0.951173 + 0.308657i \(0.900120\pi\)
\(8\) −8.56488 −3.02814
\(9\) −1.68700 −0.562334
\(10\) −2.63225 −0.832391
\(11\) 1.00000 0.301511
\(12\) 5.95092 1.71788
\(13\) −2.90244 −0.804993 −0.402497 0.915422i \(-0.631857\pi\)
−0.402497 + 0.915422i \(0.631857\pi\)
\(14\) 13.4991 3.60780
\(15\) 1.12458 0.290367
\(16\) 12.5847 3.14616
\(17\) −1.00000 −0.242536
\(18\) 4.52463 1.06646
\(19\) −0.273183 −0.0626725 −0.0313363 0.999509i \(-0.509976\pi\)
−0.0313363 + 0.999509i \(0.509976\pi\)
\(20\) 5.09697 1.13972
\(21\) −5.76728 −1.25852
\(22\) −2.68205 −0.571816
\(23\) −0.344383 −0.0718089 −0.0359044 0.999355i \(-0.511431\pi\)
−0.0359044 + 0.999355i \(0.511431\pi\)
\(24\) −9.81417 −2.00331
\(25\) −4.03679 −0.807358
\(26\) 7.78451 1.52667
\(27\) −5.37065 −1.03358
\(28\) −26.1391 −4.93983
\(29\) −5.98996 −1.11231 −0.556153 0.831080i \(-0.687723\pi\)
−0.556153 + 0.831080i \(0.687723\pi\)
\(30\) −3.01620 −0.550679
\(31\) 0.228383 0.0410188 0.0205094 0.999790i \(-0.493471\pi\)
0.0205094 + 0.999790i \(0.493471\pi\)
\(32\) −16.6229 −2.93855
\(33\) 1.14586 0.199469
\(34\) 2.68205 0.459968
\(35\) −4.93968 −0.834958
\(36\) −8.76128 −1.46021
\(37\) 0.957214 0.157365 0.0786825 0.996900i \(-0.474929\pi\)
0.0786825 + 0.996900i \(0.474929\pi\)
\(38\) 0.732692 0.118858
\(39\) −3.32580 −0.532554
\(40\) −8.40585 −1.32908
\(41\) −8.93139 −1.39485 −0.697425 0.716658i \(-0.745671\pi\)
−0.697425 + 0.716658i \(0.745671\pi\)
\(42\) 15.4681 2.38679
\(43\) −1.00000 −0.152499
\(44\) 5.19341 0.782935
\(45\) −1.65568 −0.246814
\(46\) 0.923654 0.136185
\(47\) −5.63631 −0.822140 −0.411070 0.911604i \(-0.634845\pi\)
−0.411070 + 0.911604i \(0.634845\pi\)
\(48\) 14.4203 2.08139
\(49\) 18.3325 2.61892
\(50\) 10.8269 1.53115
\(51\) −1.14586 −0.160453
\(52\) −15.0736 −2.09033
\(53\) 0.243489 0.0334458 0.0167229 0.999860i \(-0.494677\pi\)
0.0167229 + 0.999860i \(0.494677\pi\)
\(54\) 14.4044 1.96019
\(55\) 0.981432 0.132336
\(56\) 43.1082 5.76058
\(57\) −0.313030 −0.0414619
\(58\) 16.0654 2.10949
\(59\) 6.15588 0.801427 0.400713 0.916203i \(-0.368762\pi\)
0.400713 + 0.916203i \(0.368762\pi\)
\(60\) 5.84043 0.753996
\(61\) 3.10856 0.398010 0.199005 0.979998i \(-0.436229\pi\)
0.199005 + 0.979998i \(0.436229\pi\)
\(62\) −0.612535 −0.0777920
\(63\) 8.49091 1.06975
\(64\) 19.4143 2.42679
\(65\) −2.84855 −0.353319
\(66\) −3.07326 −0.378292
\(67\) −9.16623 −1.11983 −0.559917 0.828549i \(-0.689167\pi\)
−0.559917 + 0.828549i \(0.689167\pi\)
\(68\) −5.19341 −0.629793
\(69\) −0.394615 −0.0475061
\(70\) 13.2485 1.58350
\(71\) −0.195261 −0.0231732 −0.0115866 0.999933i \(-0.503688\pi\)
−0.0115866 + 0.999933i \(0.503688\pi\)
\(72\) 14.4490 1.70283
\(73\) 0.0243280 0.00284738 0.00142369 0.999999i \(-0.499547\pi\)
0.00142369 + 0.999999i \(0.499547\pi\)
\(74\) −2.56730 −0.298442
\(75\) −4.62560 −0.534119
\(76\) −1.41875 −0.162742
\(77\) −5.03314 −0.573579
\(78\) 8.91997 1.00999
\(79\) 0.00321078 0.000361241 0 0.000180621 1.00000i \(-0.499943\pi\)
0.000180621 1.00000i \(0.499943\pi\)
\(80\) 12.3510 1.38088
\(81\) −1.09302 −0.121447
\(82\) 23.9545 2.64533
\(83\) −10.2623 −1.12643 −0.563217 0.826309i \(-0.690437\pi\)
−0.563217 + 0.826309i \(0.690437\pi\)
\(84\) −29.9518 −3.26801
\(85\) −0.981432 −0.106451
\(86\) 2.68205 0.289213
\(87\) −6.86366 −0.735862
\(88\) −8.56488 −0.913020
\(89\) −1.74790 −0.185278 −0.0926388 0.995700i \(-0.529530\pi\)
−0.0926388 + 0.995700i \(0.529530\pi\)
\(90\) 4.44061 0.468081
\(91\) 14.6084 1.53138
\(92\) −1.78852 −0.186466
\(93\) 0.261695 0.0271365
\(94\) 15.1169 1.55919
\(95\) −0.268111 −0.0275076
\(96\) −19.0476 −1.94404
\(97\) 16.2141 1.64629 0.823145 0.567832i \(-0.192218\pi\)
0.823145 + 0.567832i \(0.192218\pi\)
\(98\) −49.1686 −4.96678
\(99\) −1.68700 −0.169550
\(100\) −20.9647 −2.09647
\(101\) 1.13915 0.113350 0.0566748 0.998393i \(-0.481950\pi\)
0.0566748 + 0.998393i \(0.481950\pi\)
\(102\) 3.07326 0.304298
\(103\) −0.788327 −0.0776762 −0.0388381 0.999246i \(-0.512366\pi\)
−0.0388381 + 0.999246i \(0.512366\pi\)
\(104\) 24.8591 2.43763
\(105\) −5.66019 −0.552378
\(106\) −0.653051 −0.0634299
\(107\) 2.16497 0.209295 0.104648 0.994509i \(-0.466629\pi\)
0.104648 + 0.994509i \(0.466629\pi\)
\(108\) −27.8920 −2.68391
\(109\) 0.912693 0.0874201 0.0437101 0.999044i \(-0.486082\pi\)
0.0437101 + 0.999044i \(0.486082\pi\)
\(110\) −2.63225 −0.250975
\(111\) 1.09683 0.104107
\(112\) −63.3403 −5.98509
\(113\) −17.3980 −1.63667 −0.818334 0.574743i \(-0.805102\pi\)
−0.818334 + 0.574743i \(0.805102\pi\)
\(114\) 0.839564 0.0786323
\(115\) −0.337989 −0.0315176
\(116\) −31.1083 −2.88833
\(117\) 4.89643 0.452675
\(118\) −16.5104 −1.51990
\(119\) 5.03314 0.461387
\(120\) −9.63194 −0.879272
\(121\) 1.00000 0.0909091
\(122\) −8.33731 −0.754825
\(123\) −10.2341 −0.922781
\(124\) 1.18609 0.106514
\(125\) −8.86899 −0.793267
\(126\) −22.7731 −2.02879
\(127\) −16.4896 −1.46321 −0.731606 0.681728i \(-0.761229\pi\)
−0.731606 + 0.681728i \(0.761229\pi\)
\(128\) −18.8243 −1.66385
\(129\) −1.14586 −0.100887
\(130\) 7.63996 0.670069
\(131\) 7.12350 0.622383 0.311191 0.950347i \(-0.399272\pi\)
0.311191 + 0.950347i \(0.399272\pi\)
\(132\) 5.95092 0.517962
\(133\) 1.37497 0.119225
\(134\) 24.5843 2.12376
\(135\) −5.27093 −0.453649
\(136\) 8.56488 0.734433
\(137\) −12.6086 −1.07723 −0.538614 0.842553i \(-0.681052\pi\)
−0.538614 + 0.842553i \(0.681052\pi\)
\(138\) 1.05838 0.0900952
\(139\) −19.9661 −1.69350 −0.846752 0.531987i \(-0.821445\pi\)
−0.846752 + 0.531987i \(0.821445\pi\)
\(140\) −25.6538 −2.16814
\(141\) −6.45843 −0.543898
\(142\) 0.523699 0.0439479
\(143\) −2.90244 −0.242715
\(144\) −21.2303 −1.76919
\(145\) −5.87873 −0.488202
\(146\) −0.0652490 −0.00540005
\(147\) 21.0065 1.73258
\(148\) 4.97120 0.408630
\(149\) 23.1013 1.89254 0.946268 0.323384i \(-0.104821\pi\)
0.946268 + 0.323384i \(0.104821\pi\)
\(150\) 12.4061 1.01296
\(151\) 23.6025 1.92074 0.960370 0.278728i \(-0.0899126\pi\)
0.960370 + 0.278728i \(0.0899126\pi\)
\(152\) 2.33978 0.189781
\(153\) 1.68700 0.136386
\(154\) 13.4991 1.08779
\(155\) 0.224142 0.0180035
\(156\) −17.2722 −1.38288
\(157\) −8.05506 −0.642864 −0.321432 0.946933i \(-0.604164\pi\)
−0.321432 + 0.946933i \(0.604164\pi\)
\(158\) −0.00861148 −0.000685093 0
\(159\) 0.279005 0.0221265
\(160\) −16.3143 −1.28976
\(161\) 1.73333 0.136605
\(162\) 2.93155 0.230324
\(163\) 5.59141 0.437953 0.218976 0.975730i \(-0.429728\pi\)
0.218976 + 0.975730i \(0.429728\pi\)
\(164\) −46.3844 −3.62201
\(165\) 1.12458 0.0875488
\(166\) 27.5241 2.13628
\(167\) 14.9658 1.15809 0.579044 0.815296i \(-0.303426\pi\)
0.579044 + 0.815296i \(0.303426\pi\)
\(168\) 49.3961 3.81099
\(169\) −4.57582 −0.351986
\(170\) 2.63225 0.201884
\(171\) 0.460861 0.0352429
\(172\) −5.19341 −0.395994
\(173\) −8.18974 −0.622655 −0.311327 0.950303i \(-0.600774\pi\)
−0.311327 + 0.950303i \(0.600774\pi\)
\(174\) 18.4087 1.39556
\(175\) 20.3177 1.53588
\(176\) 12.5847 0.948604
\(177\) 7.05378 0.530195
\(178\) 4.68797 0.351378
\(179\) 3.99655 0.298716 0.149358 0.988783i \(-0.452279\pi\)
0.149358 + 0.988783i \(0.452279\pi\)
\(180\) −8.59860 −0.640902
\(181\) −16.1486 −1.20032 −0.600158 0.799881i \(-0.704896\pi\)
−0.600158 + 0.799881i \(0.704896\pi\)
\(182\) −39.1805 −2.90425
\(183\) 3.56198 0.263309
\(184\) 2.94960 0.217448
\(185\) 0.939440 0.0690690
\(186\) −0.701880 −0.0514644
\(187\) −1.00000 −0.0731272
\(188\) −29.2716 −2.13485
\(189\) 27.0312 1.96623
\(190\) 0.719087 0.0521681
\(191\) 15.2302 1.10202 0.551009 0.834500i \(-0.314243\pi\)
0.551009 + 0.834500i \(0.314243\pi\)
\(192\) 22.2461 1.60547
\(193\) 9.01455 0.648882 0.324441 0.945906i \(-0.394824\pi\)
0.324441 + 0.945906i \(0.394824\pi\)
\(194\) −43.4870 −3.12218
\(195\) −3.26404 −0.233743
\(196\) 95.2079 6.80056
\(197\) 6.50400 0.463391 0.231695 0.972788i \(-0.425573\pi\)
0.231695 + 0.972788i \(0.425573\pi\)
\(198\) 4.52463 0.321551
\(199\) −4.19871 −0.297639 −0.148819 0.988864i \(-0.547547\pi\)
−0.148819 + 0.988864i \(0.547547\pi\)
\(200\) 34.5747 2.44480
\(201\) −10.5032 −0.740841
\(202\) −3.05526 −0.214967
\(203\) 30.1483 2.11599
\(204\) −5.95092 −0.416648
\(205\) −8.76555 −0.612213
\(206\) 2.11434 0.147313
\(207\) 0.580975 0.0403805
\(208\) −36.5263 −2.53264
\(209\) −0.273183 −0.0188965
\(210\) 15.1809 1.04758
\(211\) −22.6661 −1.56040 −0.780198 0.625532i \(-0.784882\pi\)
−0.780198 + 0.625532i \(0.784882\pi\)
\(212\) 1.26454 0.0868489
\(213\) −0.223742 −0.0153305
\(214\) −5.80656 −0.396928
\(215\) −0.981432 −0.0669331
\(216\) 45.9990 3.12984
\(217\) −1.14948 −0.0780319
\(218\) −2.44789 −0.165792
\(219\) 0.0278765 0.00188372
\(220\) 5.09697 0.343638
\(221\) 2.90244 0.195240
\(222\) −2.94177 −0.197439
\(223\) −22.3465 −1.49644 −0.748218 0.663453i \(-0.769090\pi\)
−0.748218 + 0.663453i \(0.769090\pi\)
\(224\) 83.6655 5.59014
\(225\) 6.81007 0.454005
\(226\) 46.6624 3.10394
\(227\) 19.2243 1.27596 0.637981 0.770052i \(-0.279770\pi\)
0.637981 + 0.770052i \(0.279770\pi\)
\(228\) −1.62569 −0.107664
\(229\) 18.0906 1.19546 0.597729 0.801698i \(-0.296070\pi\)
0.597729 + 0.801698i \(0.296070\pi\)
\(230\) 0.906503 0.0597730
\(231\) −5.76728 −0.379459
\(232\) 51.3033 3.36822
\(233\) 22.0896 1.44714 0.723569 0.690252i \(-0.242500\pi\)
0.723569 + 0.690252i \(0.242500\pi\)
\(234\) −13.1325 −0.858497
\(235\) −5.53165 −0.360845
\(236\) 31.9700 2.08107
\(237\) 0.00367911 0.000238984 0
\(238\) −13.4991 −0.875019
\(239\) −14.5934 −0.943968 −0.471984 0.881607i \(-0.656462\pi\)
−0.471984 + 0.881607i \(0.656462\pi\)
\(240\) 14.1525 0.913541
\(241\) −5.77517 −0.372012 −0.186006 0.982549i \(-0.559554\pi\)
−0.186006 + 0.982549i \(0.559554\pi\)
\(242\) −2.68205 −0.172409
\(243\) 14.8595 0.953238
\(244\) 16.1440 1.03351
\(245\) 17.9921 1.14947
\(246\) 27.4485 1.75005
\(247\) 0.792899 0.0504510
\(248\) −1.95607 −0.124211
\(249\) −11.7592 −0.745208
\(250\) 23.7871 1.50443
\(251\) 11.9139 0.751999 0.375999 0.926620i \(-0.377299\pi\)
0.375999 + 0.926620i \(0.377299\pi\)
\(252\) 44.0967 2.77783
\(253\) −0.344383 −0.0216512
\(254\) 44.2259 2.77498
\(255\) −1.12458 −0.0704242
\(256\) 11.6591 0.728693
\(257\) 23.4005 1.45968 0.729841 0.683617i \(-0.239594\pi\)
0.729841 + 0.683617i \(0.239594\pi\)
\(258\) 3.07326 0.191333
\(259\) −4.81779 −0.299363
\(260\) −14.7937 −0.917465
\(261\) 10.1051 0.625488
\(262\) −19.1056 −1.18035
\(263\) 18.0538 1.11325 0.556623 0.830765i \(-0.312097\pi\)
0.556623 + 0.830765i \(0.312097\pi\)
\(264\) −9.81417 −0.604020
\(265\) 0.238968 0.0146797
\(266\) −3.68774 −0.226110
\(267\) −2.00286 −0.122573
\(268\) −47.6040 −2.90788
\(269\) −12.6976 −0.774188 −0.387094 0.922040i \(-0.626521\pi\)
−0.387094 + 0.922040i \(0.626521\pi\)
\(270\) 14.1369 0.860345
\(271\) −13.5090 −0.820615 −0.410308 0.911947i \(-0.634579\pi\)
−0.410308 + 0.911947i \(0.634579\pi\)
\(272\) −12.5847 −0.763057
\(273\) 16.7392 1.01310
\(274\) 33.8170 2.04296
\(275\) −4.03679 −0.243428
\(276\) −2.04940 −0.123359
\(277\) 2.26865 0.136310 0.0681550 0.997675i \(-0.478289\pi\)
0.0681550 + 0.997675i \(0.478289\pi\)
\(278\) 53.5502 3.21173
\(279\) −0.385282 −0.0230662
\(280\) 42.3078 2.52837
\(281\) 18.5367 1.10581 0.552903 0.833245i \(-0.313520\pi\)
0.552903 + 0.833245i \(0.313520\pi\)
\(282\) 17.3218 1.03150
\(283\) 1.92296 0.114308 0.0571541 0.998365i \(-0.481797\pi\)
0.0571541 + 0.998365i \(0.481797\pi\)
\(284\) −1.01407 −0.0601739
\(285\) −0.307218 −0.0181980
\(286\) 7.78451 0.460308
\(287\) 44.9529 2.65349
\(288\) 28.0429 1.65244
\(289\) 1.00000 0.0588235
\(290\) 15.7671 0.925874
\(291\) 18.5791 1.08912
\(292\) 0.126345 0.00739380
\(293\) 4.95214 0.289307 0.144653 0.989482i \(-0.453793\pi\)
0.144653 + 0.989482i \(0.453793\pi\)
\(294\) −56.3404 −3.28584
\(295\) 6.04157 0.351754
\(296\) −8.19842 −0.476524
\(297\) −5.37065 −0.311637
\(298\) −61.9590 −3.58919
\(299\) 0.999553 0.0578056
\(300\) −24.0226 −1.38695
\(301\) 5.03314 0.290105
\(302\) −63.3030 −3.64268
\(303\) 1.30531 0.0749879
\(304\) −3.43792 −0.197178
\(305\) 3.05084 0.174690
\(306\) −4.52463 −0.258656
\(307\) −22.0202 −1.25676 −0.628379 0.777907i \(-0.716281\pi\)
−0.628379 + 0.777907i \(0.716281\pi\)
\(308\) −26.1391 −1.48941
\(309\) −0.903314 −0.0513878
\(310\) −0.601161 −0.0341437
\(311\) 18.4222 1.04463 0.522314 0.852753i \(-0.325069\pi\)
0.522314 + 0.852753i \(0.325069\pi\)
\(312\) 28.4851 1.61265
\(313\) −7.01710 −0.396630 −0.198315 0.980138i \(-0.563547\pi\)
−0.198315 + 0.980138i \(0.563547\pi\)
\(314\) 21.6041 1.21919
\(315\) 8.33324 0.469525
\(316\) 0.0166749 0.000938036 0
\(317\) 4.68555 0.263167 0.131583 0.991305i \(-0.457994\pi\)
0.131583 + 0.991305i \(0.457994\pi\)
\(318\) −0.748306 −0.0419629
\(319\) −5.98996 −0.335373
\(320\) 19.0538 1.06514
\(321\) 2.48075 0.138462
\(322\) −4.64887 −0.259072
\(323\) 0.273183 0.0152003
\(324\) −5.67652 −0.315362
\(325\) 11.7166 0.649918
\(326\) −14.9964 −0.830576
\(327\) 1.04582 0.0578340
\(328\) 76.4963 4.22380
\(329\) 28.3683 1.56399
\(330\) −3.01620 −0.166036
\(331\) −14.7801 −0.812389 −0.406195 0.913787i \(-0.633145\pi\)
−0.406195 + 0.913787i \(0.633145\pi\)
\(332\) −53.2963 −2.92502
\(333\) −1.61482 −0.0884916
\(334\) −40.1391 −2.19631
\(335\) −8.99603 −0.491506
\(336\) −72.5792 −3.95952
\(337\) −3.99398 −0.217566 −0.108783 0.994066i \(-0.534695\pi\)
−0.108783 + 0.994066i \(0.534695\pi\)
\(338\) 12.2726 0.667541
\(339\) −19.9357 −1.08276
\(340\) −5.09697 −0.276422
\(341\) 0.228383 0.0123676
\(342\) −1.23605 −0.0668380
\(343\) −57.0378 −3.07975
\(344\) 8.56488 0.461788
\(345\) −0.387288 −0.0208509
\(346\) 21.9653 1.18086
\(347\) 28.7142 1.54146 0.770729 0.637163i \(-0.219892\pi\)
0.770729 + 0.637163i \(0.219892\pi\)
\(348\) −35.6458 −1.91081
\(349\) −28.5594 −1.52875 −0.764375 0.644772i \(-0.776952\pi\)
−0.764375 + 0.644772i \(0.776952\pi\)
\(350\) −54.4932 −2.91278
\(351\) 15.5880 0.832027
\(352\) −16.6229 −0.886006
\(353\) −6.44851 −0.343220 −0.171610 0.985165i \(-0.554897\pi\)
−0.171610 + 0.985165i \(0.554897\pi\)
\(354\) −18.9186 −1.00551
\(355\) −0.191635 −0.0101709
\(356\) −9.07758 −0.481111
\(357\) 5.76728 0.305237
\(358\) −10.7189 −0.566514
\(359\) −1.78918 −0.0944293 −0.0472147 0.998885i \(-0.515034\pi\)
−0.0472147 + 0.998885i \(0.515034\pi\)
\(360\) 14.1807 0.747387
\(361\) −18.9254 −0.996072
\(362\) 43.3114 2.27640
\(363\) 1.14586 0.0601421
\(364\) 75.8673 3.97653
\(365\) 0.0238763 0.00124974
\(366\) −9.55341 −0.499365
\(367\) −12.9632 −0.676675 −0.338338 0.941025i \(-0.609865\pi\)
−0.338338 + 0.941025i \(0.609865\pi\)
\(368\) −4.33394 −0.225922
\(369\) 15.0673 0.784371
\(370\) −2.51963 −0.130989
\(371\) −1.22551 −0.0636255
\(372\) 1.35909 0.0704655
\(373\) 4.98892 0.258317 0.129158 0.991624i \(-0.458772\pi\)
0.129158 + 0.991624i \(0.458772\pi\)
\(374\) 2.68205 0.138686
\(375\) −10.1626 −0.524796
\(376\) 48.2743 2.48956
\(377\) 17.3855 0.895399
\(378\) −72.4992 −3.72896
\(379\) 30.6359 1.57366 0.786830 0.617170i \(-0.211721\pi\)
0.786830 + 0.617170i \(0.211721\pi\)
\(380\) −1.39241 −0.0714290
\(381\) −18.8947 −0.968007
\(382\) −40.8481 −2.08997
\(383\) 22.8370 1.16692 0.583458 0.812144i \(-0.301699\pi\)
0.583458 + 0.812144i \(0.301699\pi\)
\(384\) −21.5700 −1.10074
\(385\) −4.93968 −0.251749
\(386\) −24.1775 −1.23060
\(387\) 1.68700 0.0857551
\(388\) 84.2062 4.27492
\(389\) 7.90735 0.400918 0.200459 0.979702i \(-0.435757\pi\)
0.200459 + 0.979702i \(0.435757\pi\)
\(390\) 8.75434 0.443293
\(391\) 0.344383 0.0174162
\(392\) −157.015 −7.93047
\(393\) 8.16254 0.411746
\(394\) −17.4441 −0.878819
\(395\) 0.00315116 0.000158552 0
\(396\) −8.76128 −0.440271
\(397\) −23.4770 −1.17828 −0.589139 0.808031i \(-0.700533\pi\)
−0.589139 + 0.808031i \(0.700533\pi\)
\(398\) 11.2612 0.564471
\(399\) 1.57552 0.0788748
\(400\) −50.8016 −2.54008
\(401\) −3.80819 −0.190172 −0.0950859 0.995469i \(-0.530313\pi\)
−0.0950859 + 0.995469i \(0.530313\pi\)
\(402\) 28.1702 1.40500
\(403\) −0.662868 −0.0330198
\(404\) 5.91606 0.294335
\(405\) −1.07273 −0.0533043
\(406\) −80.8592 −4.01298
\(407\) 0.957214 0.0474473
\(408\) 9.81417 0.485874
\(409\) 38.4371 1.90059 0.950296 0.311347i \(-0.100780\pi\)
0.950296 + 0.311347i \(0.100780\pi\)
\(410\) 23.5097 1.16106
\(411\) −14.4477 −0.712654
\(412\) −4.09410 −0.201702
\(413\) −30.9834 −1.52459
\(414\) −1.55820 −0.0765816
\(415\) −10.0718 −0.494403
\(416\) 48.2472 2.36551
\(417\) −22.8784 −1.12036
\(418\) 0.732692 0.0358371
\(419\) −12.2719 −0.599524 −0.299762 0.954014i \(-0.596907\pi\)
−0.299762 + 0.954014i \(0.596907\pi\)
\(420\) −29.3957 −1.43436
\(421\) 7.64573 0.372630 0.186315 0.982490i \(-0.440345\pi\)
0.186315 + 0.982490i \(0.440345\pi\)
\(422\) 60.7916 2.95929
\(423\) 9.50846 0.462317
\(424\) −2.08546 −0.101279
\(425\) 4.03679 0.195813
\(426\) 0.600087 0.0290743
\(427\) −15.6458 −0.757153
\(428\) 11.2436 0.543478
\(429\) −3.32580 −0.160571
\(430\) 2.63225 0.126938
\(431\) −4.49698 −0.216612 −0.108306 0.994118i \(-0.534543\pi\)
−0.108306 + 0.994118i \(0.534543\pi\)
\(432\) −67.5878 −3.25182
\(433\) 31.0069 1.49010 0.745048 0.667011i \(-0.232427\pi\)
0.745048 + 0.667011i \(0.232427\pi\)
\(434\) 3.08297 0.147987
\(435\) −6.73621 −0.322977
\(436\) 4.73999 0.227004
\(437\) 0.0940797 0.00450044
\(438\) −0.0747663 −0.00357247
\(439\) 38.9290 1.85798 0.928989 0.370106i \(-0.120679\pi\)
0.928989 + 0.370106i \(0.120679\pi\)
\(440\) −8.40585 −0.400733
\(441\) −30.9269 −1.47271
\(442\) −7.78451 −0.370271
\(443\) −36.9343 −1.75480 −0.877401 0.479758i \(-0.840725\pi\)
−0.877401 + 0.479758i \(0.840725\pi\)
\(444\) 5.69631 0.270335
\(445\) −1.71545 −0.0813201
\(446\) 59.9346 2.83799
\(447\) 26.4709 1.25203
\(448\) −97.7148 −4.61659
\(449\) 4.58261 0.216267 0.108133 0.994136i \(-0.465513\pi\)
0.108133 + 0.994136i \(0.465513\pi\)
\(450\) −18.2650 −0.861019
\(451\) −8.93139 −0.420563
\(452\) −90.3550 −4.24994
\(453\) 27.0451 1.27069
\(454\) −51.5606 −2.41986
\(455\) 14.3371 0.672136
\(456\) 2.68107 0.125552
\(457\) 15.0410 0.703590 0.351795 0.936077i \(-0.385571\pi\)
0.351795 + 0.936077i \(0.385571\pi\)
\(458\) −48.5198 −2.26718
\(459\) 5.37065 0.250681
\(460\) −1.75531 −0.0818418
\(461\) 18.7453 0.873057 0.436529 0.899690i \(-0.356208\pi\)
0.436529 + 0.899690i \(0.356208\pi\)
\(462\) 15.4681 0.719643
\(463\) −21.0570 −0.978602 −0.489301 0.872115i \(-0.662748\pi\)
−0.489301 + 0.872115i \(0.662748\pi\)
\(464\) −75.3815 −3.49950
\(465\) 0.256836 0.0119105
\(466\) −59.2455 −2.74449
\(467\) 21.1238 0.977495 0.488747 0.872425i \(-0.337454\pi\)
0.488747 + 0.872425i \(0.337454\pi\)
\(468\) 25.4291 1.17546
\(469\) 46.1349 2.13031
\(470\) 14.8362 0.684342
\(471\) −9.22998 −0.425295
\(472\) −52.7244 −2.42684
\(473\) −1.00000 −0.0459800
\(474\) −0.00986757 −0.000453232 0
\(475\) 1.10278 0.0505992
\(476\) 26.1391 1.19808
\(477\) −0.410767 −0.0188077
\(478\) 39.1403 1.79023
\(479\) 29.4813 1.34703 0.673517 0.739172i \(-0.264783\pi\)
0.673517 + 0.739172i \(0.264783\pi\)
\(480\) −18.6939 −0.853256
\(481\) −2.77826 −0.126678
\(482\) 15.4893 0.705519
\(483\) 1.98615 0.0903731
\(484\) 5.19341 0.236064
\(485\) 15.9130 0.722572
\(486\) −39.8540 −1.80781
\(487\) 21.0030 0.951738 0.475869 0.879516i \(-0.342134\pi\)
0.475869 + 0.879516i \(0.342134\pi\)
\(488\) −26.6244 −1.20523
\(489\) 6.40698 0.289734
\(490\) −48.2556 −2.17997
\(491\) −26.1681 −1.18095 −0.590476 0.807055i \(-0.701060\pi\)
−0.590476 + 0.807055i \(0.701060\pi\)
\(492\) −53.1501 −2.39619
\(493\) 5.98996 0.269774
\(494\) −2.12660 −0.0956801
\(495\) −1.65568 −0.0744171
\(496\) 2.87412 0.129052
\(497\) 0.982774 0.0440834
\(498\) 31.5388 1.41329
\(499\) 25.2566 1.13064 0.565321 0.824871i \(-0.308752\pi\)
0.565321 + 0.824871i \(0.308752\pi\)
\(500\) −46.0603 −2.05988
\(501\) 17.1487 0.766149
\(502\) −31.9537 −1.42616
\(503\) −28.2099 −1.25782 −0.628909 0.777479i \(-0.716498\pi\)
−0.628909 + 0.777479i \(0.716498\pi\)
\(504\) −72.7236 −3.23937
\(505\) 1.11800 0.0497502
\(506\) 0.923654 0.0410614
\(507\) −5.24326 −0.232861
\(508\) −85.6370 −3.79953
\(509\) 5.62121 0.249156 0.124578 0.992210i \(-0.460242\pi\)
0.124578 + 0.992210i \(0.460242\pi\)
\(510\) 3.01620 0.133559
\(511\) −0.122446 −0.00541670
\(512\) 6.37823 0.281881
\(513\) 1.46717 0.0647773
\(514\) −62.7613 −2.76828
\(515\) −0.773690 −0.0340928
\(516\) −5.95092 −0.261975
\(517\) −5.63631 −0.247884
\(518\) 12.9216 0.567741
\(519\) −9.38431 −0.411926
\(520\) 24.3975 1.06990
\(521\) 0.0571298 0.00250290 0.00125145 0.999999i \(-0.499602\pi\)
0.00125145 + 0.999999i \(0.499602\pi\)
\(522\) −27.1023 −1.18624
\(523\) −27.4976 −1.20238 −0.601192 0.799104i \(-0.705307\pi\)
−0.601192 + 0.799104i \(0.705307\pi\)
\(524\) 36.9952 1.61614
\(525\) 23.2813 1.01608
\(526\) −48.4213 −2.11127
\(527\) −0.228383 −0.00994851
\(528\) 14.4203 0.627562
\(529\) −22.8814 −0.994843
\(530\) −0.640925 −0.0278400
\(531\) −10.3850 −0.450669
\(532\) 7.14077 0.309592
\(533\) 25.9229 1.12284
\(534\) 5.37177 0.232459
\(535\) 2.12477 0.0918617
\(536\) 78.5077 3.39102
\(537\) 4.57949 0.197620
\(538\) 34.0557 1.46825
\(539\) 18.3325 0.789635
\(540\) −27.3741 −1.17799
\(541\) 1.81798 0.0781610 0.0390805 0.999236i \(-0.487557\pi\)
0.0390805 + 0.999236i \(0.487557\pi\)
\(542\) 36.2319 1.55629
\(543\) −18.5041 −0.794085
\(544\) 16.6229 0.712703
\(545\) 0.895746 0.0383695
\(546\) −44.8954 −1.92135
\(547\) −11.3395 −0.484842 −0.242421 0.970171i \(-0.577941\pi\)
−0.242421 + 0.970171i \(0.577941\pi\)
\(548\) −65.4817 −2.79724
\(549\) −5.24414 −0.223814
\(550\) 10.8269 0.461660
\(551\) 1.63636 0.0697111
\(552\) 3.37984 0.143855
\(553\) −0.0161603 −0.000687206 0
\(554\) −6.08464 −0.258512
\(555\) 1.07647 0.0456935
\(556\) −103.692 −4.39753
\(557\) −2.94061 −0.124598 −0.0622988 0.998058i \(-0.519843\pi\)
−0.0622988 + 0.998058i \(0.519843\pi\)
\(558\) 1.03335 0.0437451
\(559\) 2.90244 0.122760
\(560\) −62.1642 −2.62692
\(561\) −1.14586 −0.0483783
\(562\) −49.7164 −2.09716
\(563\) −37.1914 −1.56743 −0.783715 0.621121i \(-0.786678\pi\)
−0.783715 + 0.621121i \(0.786678\pi\)
\(564\) −33.5412 −1.41234
\(565\) −17.0750 −0.718349
\(566\) −5.15749 −0.216785
\(567\) 5.50134 0.231034
\(568\) 1.67239 0.0701717
\(569\) 0.857071 0.0359303 0.0179652 0.999839i \(-0.494281\pi\)
0.0179652 + 0.999839i \(0.494281\pi\)
\(570\) 0.823974 0.0345125
\(571\) 11.4881 0.480762 0.240381 0.970679i \(-0.422728\pi\)
0.240381 + 0.970679i \(0.422728\pi\)
\(572\) −15.0736 −0.630258
\(573\) 17.4517 0.729054
\(574\) −120.566 −5.03233
\(575\) 1.39020 0.0579755
\(576\) −32.7519 −1.36466
\(577\) 28.7769 1.19800 0.598998 0.800751i \(-0.295566\pi\)
0.598998 + 0.800751i \(0.295566\pi\)
\(578\) −2.68205 −0.111559
\(579\) 10.3294 0.429277
\(580\) −30.5306 −1.26772
\(581\) 51.6516 2.14287
\(582\) −49.8301 −2.06552
\(583\) 0.243489 0.0100843
\(584\) −0.208367 −0.00862227
\(585\) 4.80551 0.198683
\(586\) −13.2819 −0.548670
\(587\) 1.69810 0.0700880 0.0350440 0.999386i \(-0.488843\pi\)
0.0350440 + 0.999386i \(0.488843\pi\)
\(588\) 109.095 4.49900
\(589\) −0.0623904 −0.00257075
\(590\) −16.2038 −0.667100
\(591\) 7.45268 0.306562
\(592\) 12.0462 0.495096
\(593\) −38.6960 −1.58905 −0.794527 0.607228i \(-0.792281\pi\)
−0.794527 + 0.607228i \(0.792281\pi\)
\(594\) 14.4044 0.591019
\(595\) 4.93968 0.202507
\(596\) 119.975 4.91435
\(597\) −4.81114 −0.196907
\(598\) −2.68085 −0.109628
\(599\) 32.5578 1.33028 0.665139 0.746720i \(-0.268372\pi\)
0.665139 + 0.746720i \(0.268372\pi\)
\(600\) 39.6178 1.61739
\(601\) −12.4198 −0.506615 −0.253307 0.967386i \(-0.581518\pi\)
−0.253307 + 0.967386i \(0.581518\pi\)
\(602\) −13.4991 −0.550184
\(603\) 15.4634 0.629720
\(604\) 122.577 4.98759
\(605\) 0.981432 0.0399009
\(606\) −3.50090 −0.142214
\(607\) 8.29832 0.336818 0.168409 0.985717i \(-0.446137\pi\)
0.168409 + 0.985717i \(0.446137\pi\)
\(608\) 4.54111 0.184166
\(609\) 34.5457 1.39986
\(610\) −8.18250 −0.331300
\(611\) 16.3591 0.661817
\(612\) 8.76128 0.354154
\(613\) −19.1583 −0.773795 −0.386898 0.922123i \(-0.626453\pi\)
−0.386898 + 0.922123i \(0.626453\pi\)
\(614\) 59.0593 2.38344
\(615\) −10.0441 −0.405018
\(616\) 43.1082 1.73688
\(617\) 8.08259 0.325393 0.162696 0.986676i \(-0.447981\pi\)
0.162696 + 0.986676i \(0.447981\pi\)
\(618\) 2.42274 0.0974567
\(619\) 27.3218 1.09815 0.549077 0.835771i \(-0.314979\pi\)
0.549077 + 0.835771i \(0.314979\pi\)
\(620\) 1.16406 0.0467498
\(621\) 1.84956 0.0742204
\(622\) −49.4094 −1.98113
\(623\) 8.79744 0.352462
\(624\) −41.8540 −1.67550
\(625\) 11.4796 0.459186
\(626\) 18.8202 0.752207
\(627\) −0.313030 −0.0125012
\(628\) −41.8332 −1.66933
\(629\) −0.957214 −0.0381666
\(630\) −22.3502 −0.890453
\(631\) −22.7858 −0.907089 −0.453544 0.891234i \(-0.649841\pi\)
−0.453544 + 0.891234i \(0.649841\pi\)
\(632\) −0.0275000 −0.00109389
\(633\) −25.9722 −1.03230
\(634\) −12.5669 −0.499095
\(635\) −16.1834 −0.642217
\(636\) 1.44899 0.0574560
\(637\) −53.2089 −2.10821
\(638\) 16.0654 0.636034
\(639\) 0.329405 0.0130311
\(640\) −18.4747 −0.730278
\(641\) −29.9983 −1.18486 −0.592431 0.805622i \(-0.701832\pi\)
−0.592431 + 0.805622i \(0.701832\pi\)
\(642\) −6.65351 −0.262593
\(643\) −10.9536 −0.431967 −0.215983 0.976397i \(-0.569296\pi\)
−0.215983 + 0.976397i \(0.569296\pi\)
\(644\) 9.00187 0.354723
\(645\) −1.12458 −0.0442805
\(646\) −0.732692 −0.0288274
\(647\) 10.3836 0.408223 0.204111 0.978948i \(-0.434570\pi\)
0.204111 + 0.978948i \(0.434570\pi\)
\(648\) 9.36162 0.367759
\(649\) 6.15588 0.241639
\(650\) −31.4244 −1.23257
\(651\) −1.31715 −0.0516231
\(652\) 29.0384 1.13723
\(653\) −12.8307 −0.502106 −0.251053 0.967973i \(-0.580777\pi\)
−0.251053 + 0.967973i \(0.580777\pi\)
\(654\) −2.80494 −0.109682
\(655\) 6.99123 0.273170
\(656\) −112.399 −4.38842
\(657\) −0.0410414 −0.00160118
\(658\) −76.0853 −2.96611
\(659\) 45.1519 1.75887 0.879434 0.476020i \(-0.157921\pi\)
0.879434 + 0.476020i \(0.157921\pi\)
\(660\) 5.84043 0.227338
\(661\) 20.0011 0.777953 0.388976 0.921248i \(-0.372829\pi\)
0.388976 + 0.921248i \(0.372829\pi\)
\(662\) 39.6411 1.54069
\(663\) 3.32580 0.129163
\(664\) 87.8955 3.41101
\(665\) 1.34944 0.0523290
\(666\) 4.33103 0.167824
\(667\) 2.06284 0.0798735
\(668\) 77.7235 3.00721
\(669\) −25.6061 −0.989987
\(670\) 24.1278 0.932139
\(671\) 3.10856 0.120005
\(672\) 95.8691 3.69823
\(673\) −14.1438 −0.545205 −0.272602 0.962127i \(-0.587884\pi\)
−0.272602 + 0.962127i \(0.587884\pi\)
\(674\) 10.7121 0.412613
\(675\) 21.6802 0.834472
\(676\) −23.7641 −0.914003
\(677\) −47.0578 −1.80858 −0.904289 0.426920i \(-0.859599\pi\)
−0.904289 + 0.426920i \(0.859599\pi\)
\(678\) 53.4687 2.05345
\(679\) −81.6076 −3.13181
\(680\) 8.40585 0.322350
\(681\) 22.0284 0.844130
\(682\) −0.612535 −0.0234552
\(683\) −46.1301 −1.76512 −0.882560 0.470201i \(-0.844182\pi\)
−0.882560 + 0.470201i \(0.844182\pi\)
\(684\) 2.39344 0.0915153
\(685\) −12.3745 −0.472805
\(686\) 152.978 5.84074
\(687\) 20.7293 0.790871
\(688\) −12.5847 −0.479785
\(689\) −0.706714 −0.0269237
\(690\) 1.03873 0.0395437
\(691\) 11.5960 0.441131 0.220566 0.975372i \(-0.429210\pi\)
0.220566 + 0.975372i \(0.429210\pi\)
\(692\) −42.5327 −1.61685
\(693\) 8.49091 0.322543
\(694\) −77.0129 −2.92337
\(695\) −19.5954 −0.743295
\(696\) 58.7865 2.22829
\(697\) 8.93139 0.338301
\(698\) 76.5978 2.89927
\(699\) 25.3116 0.957374
\(700\) 105.518 3.98821
\(701\) 16.5468 0.624963 0.312481 0.949924i \(-0.398840\pi\)
0.312481 + 0.949924i \(0.398840\pi\)
\(702\) −41.8079 −1.57794
\(703\) −0.261495 −0.00986246
\(704\) 19.4143 0.731704
\(705\) −6.33851 −0.238722
\(706\) 17.2953 0.650916
\(707\) −5.73349 −0.215630
\(708\) 36.6332 1.37676
\(709\) −34.2212 −1.28520 −0.642602 0.766200i \(-0.722145\pi\)
−0.642602 + 0.766200i \(0.722145\pi\)
\(710\) 0.513975 0.0192891
\(711\) −0.00541659 −0.000203138 0
\(712\) 14.9706 0.561047
\(713\) −0.0786512 −0.00294551
\(714\) −15.4681 −0.578881
\(715\) −2.84855 −0.106530
\(716\) 20.7557 0.775676
\(717\) −16.7220 −0.624495
\(718\) 4.79868 0.179085
\(719\) 23.2293 0.866306 0.433153 0.901320i \(-0.357401\pi\)
0.433153 + 0.901320i \(0.357401\pi\)
\(720\) −20.8361 −0.776516
\(721\) 3.96776 0.147767
\(722\) 50.7588 1.88905
\(723\) −6.61755 −0.246109
\(724\) −83.8662 −3.11686
\(725\) 24.1802 0.898030
\(726\) −3.07326 −0.114059
\(727\) 31.2635 1.15950 0.579749 0.814795i \(-0.303151\pi\)
0.579749 + 0.814795i \(0.303151\pi\)
\(728\) −125.119 −4.63723
\(729\) 20.3060 0.752075
\(730\) −0.0640374 −0.00237013
\(731\) 1.00000 0.0369863
\(732\) 18.4988 0.683735
\(733\) 14.6776 0.542130 0.271065 0.962561i \(-0.412624\pi\)
0.271065 + 0.962561i \(0.412624\pi\)
\(734\) 34.7681 1.28331
\(735\) 20.6164 0.760447
\(736\) 5.72466 0.211014
\(737\) −9.16623 −0.337643
\(738\) −40.4112 −1.48756
\(739\) −19.4465 −0.715352 −0.357676 0.933846i \(-0.616431\pi\)
−0.357676 + 0.933846i \(0.616431\pi\)
\(740\) 4.87889 0.179352
\(741\) 0.908553 0.0333765
\(742\) 3.28689 0.120666
\(743\) 27.8622 1.02217 0.511083 0.859531i \(-0.329245\pi\)
0.511083 + 0.859531i \(0.329245\pi\)
\(744\) −2.24139 −0.0821733
\(745\) 22.6724 0.830652
\(746\) −13.3806 −0.489897
\(747\) 17.3125 0.633432
\(748\) −5.19341 −0.189890
\(749\) −10.8966 −0.398152
\(750\) 27.2567 0.995275
\(751\) 37.2067 1.35769 0.678845 0.734282i \(-0.262481\pi\)
0.678845 + 0.734282i \(0.262481\pi\)
\(752\) −70.9310 −2.58659
\(753\) 13.6517 0.497495
\(754\) −46.6289 −1.69812
\(755\) 23.1642 0.843031
\(756\) 140.384 5.10572
\(757\) 44.1438 1.60443 0.802216 0.597033i \(-0.203654\pi\)
0.802216 + 0.597033i \(0.203654\pi\)
\(758\) −82.1671 −2.98444
\(759\) −0.394615 −0.0143236
\(760\) 2.29634 0.0832969
\(761\) 11.7585 0.426247 0.213123 0.977025i \(-0.431636\pi\)
0.213123 + 0.977025i \(0.431636\pi\)
\(762\) 50.6767 1.83582
\(763\) −4.59371 −0.166303
\(764\) 79.0965 2.86161
\(765\) 1.65568 0.0598611
\(766\) −61.2500 −2.21305
\(767\) −17.8671 −0.645143
\(768\) 13.3597 0.482077
\(769\) −3.97356 −0.143290 −0.0716451 0.997430i \(-0.522825\pi\)
−0.0716451 + 0.997430i \(0.522825\pi\)
\(770\) 13.2485 0.477442
\(771\) 26.8137 0.965672
\(772\) 46.8162 1.68495
\(773\) −24.4234 −0.878447 −0.439223 0.898378i \(-0.644746\pi\)
−0.439223 + 0.898378i \(0.644746\pi\)
\(774\) −4.52463 −0.162634
\(775\) −0.921934 −0.0331169
\(776\) −138.872 −4.98520
\(777\) −5.52052 −0.198047
\(778\) −21.2079 −0.760341
\(779\) 2.43991 0.0874188
\(780\) −16.9515 −0.606961
\(781\) −0.195261 −0.00698698
\(782\) −0.923654 −0.0330298
\(783\) 32.1700 1.14966
\(784\) 230.708 8.23956
\(785\) −7.90549 −0.282159
\(786\) −21.8924 −0.780875
\(787\) 33.5515 1.19598 0.597991 0.801503i \(-0.295966\pi\)
0.597991 + 0.801503i \(0.295966\pi\)
\(788\) 33.7779 1.20329
\(789\) 20.6872 0.736483
\(790\) −0.00845158 −0.000300694 0
\(791\) 87.5666 3.11351
\(792\) 14.4490 0.513422
\(793\) −9.02241 −0.320395
\(794\) 62.9667 2.23460
\(795\) 0.273824 0.00971155
\(796\) −21.8056 −0.772879
\(797\) −12.0487 −0.426786 −0.213393 0.976966i \(-0.568451\pi\)
−0.213393 + 0.976966i \(0.568451\pi\)
\(798\) −4.22564 −0.149586
\(799\) 5.63631 0.199398
\(800\) 67.1034 2.37246
\(801\) 2.94872 0.104188
\(802\) 10.2138 0.360660
\(803\) 0.0243280 0.000858517 0
\(804\) −54.5476 −1.92374
\(805\) 1.70114 0.0599574
\(806\) 1.77785 0.0626220
\(807\) −14.5497 −0.512174
\(808\) −9.75668 −0.343239
\(809\) −3.70740 −0.130345 −0.0651726 0.997874i \(-0.520760\pi\)
−0.0651726 + 0.997874i \(0.520760\pi\)
\(810\) 2.87711 0.101091
\(811\) −20.2513 −0.711121 −0.355560 0.934653i \(-0.615710\pi\)
−0.355560 + 0.934653i \(0.615710\pi\)
\(812\) 156.572 5.49461
\(813\) −15.4795 −0.542889
\(814\) −2.56730 −0.0899837
\(815\) 5.48758 0.192222
\(816\) −14.4203 −0.504811
\(817\) 0.273183 0.00955747
\(818\) −103.090 −3.60447
\(819\) −24.6444 −0.861144
\(820\) −45.5231 −1.58973
\(821\) −2.72666 −0.0951612 −0.0475806 0.998867i \(-0.515151\pi\)
−0.0475806 + 0.998867i \(0.515151\pi\)
\(822\) 38.7496 1.35155
\(823\) −1.30669 −0.0455485 −0.0227742 0.999741i \(-0.507250\pi\)
−0.0227742 + 0.999741i \(0.507250\pi\)
\(824\) 6.75193 0.235215
\(825\) −4.62560 −0.161043
\(826\) 83.0990 2.89138
\(827\) 8.93328 0.310641 0.155320 0.987864i \(-0.450359\pi\)
0.155320 + 0.987864i \(0.450359\pi\)
\(828\) 3.01724 0.104856
\(829\) 10.0858 0.350293 0.175147 0.984542i \(-0.443960\pi\)
0.175147 + 0.984542i \(0.443960\pi\)
\(830\) 27.0130 0.937634
\(831\) 2.59956 0.0901777
\(832\) −56.3489 −1.95355
\(833\) −18.3325 −0.635182
\(834\) 61.3611 2.12476
\(835\) 14.6879 0.508296
\(836\) −1.41875 −0.0490686
\(837\) −1.22657 −0.0423963
\(838\) 32.9140 1.13700
\(839\) −6.52371 −0.225223 −0.112612 0.993639i \(-0.535922\pi\)
−0.112612 + 0.993639i \(0.535922\pi\)
\(840\) 48.4789 1.67268
\(841\) 6.87957 0.237227
\(842\) −20.5062 −0.706692
\(843\) 21.2405 0.731561
\(844\) −117.714 −4.05189
\(845\) −4.49085 −0.154490
\(846\) −25.5022 −0.876783
\(847\) −5.03314 −0.172941
\(848\) 3.06423 0.105226
\(849\) 2.20345 0.0756222
\(850\) −10.8269 −0.371359
\(851\) −0.329648 −0.0113002
\(852\) −1.16198 −0.0398088
\(853\) 5.04085 0.172595 0.0862977 0.996269i \(-0.472496\pi\)
0.0862977 + 0.996269i \(0.472496\pi\)
\(854\) 41.9628 1.43594
\(855\) 0.452303 0.0154684
\(856\) −18.5427 −0.633776
\(857\) −13.1579 −0.449465 −0.224732 0.974421i \(-0.572151\pi\)
−0.224732 + 0.974421i \(0.572151\pi\)
\(858\) 8.91997 0.304523
\(859\) −46.3631 −1.58189 −0.790945 0.611888i \(-0.790411\pi\)
−0.790945 + 0.611888i \(0.790411\pi\)
\(860\) −5.09697 −0.173805
\(861\) 51.5098 1.75545
\(862\) 12.0611 0.410804
\(863\) 39.6295 1.34900 0.674501 0.738274i \(-0.264359\pi\)
0.674501 + 0.738274i \(0.264359\pi\)
\(864\) 89.2761 3.03723
\(865\) −8.03767 −0.273289
\(866\) −83.1621 −2.82596
\(867\) 1.14586 0.0389155
\(868\) −5.96973 −0.202626
\(869\) 0.00321078 0.000108918 0
\(870\) 18.0669 0.612525
\(871\) 26.6045 0.901458
\(872\) −7.81711 −0.264721
\(873\) −27.3531 −0.925764
\(874\) −0.252327 −0.00853508
\(875\) 44.6389 1.50907
\(876\) 0.144774 0.00489147
\(877\) 9.70909 0.327853 0.163926 0.986473i \(-0.447584\pi\)
0.163926 + 0.986473i \(0.447584\pi\)
\(878\) −104.410 −3.52365
\(879\) 5.67447 0.191395
\(880\) 12.3510 0.416351
\(881\) 9.22782 0.310893 0.155447 0.987844i \(-0.450318\pi\)
0.155447 + 0.987844i \(0.450318\pi\)
\(882\) 82.9475 2.79299
\(883\) −18.2323 −0.613565 −0.306783 0.951780i \(-0.599252\pi\)
−0.306783 + 0.951780i \(0.599252\pi\)
\(884\) 15.0736 0.506979
\(885\) 6.92281 0.232708
\(886\) 99.0598 3.32798
\(887\) 21.9751 0.737852 0.368926 0.929459i \(-0.379726\pi\)
0.368926 + 0.929459i \(0.379726\pi\)
\(888\) −9.39426 −0.315251
\(889\) 82.9942 2.78353
\(890\) 4.60092 0.154223
\(891\) −1.09302 −0.0366177
\(892\) −116.055 −3.88580
\(893\) 1.53974 0.0515256
\(894\) −70.9964 −2.37448
\(895\) 3.92234 0.131109
\(896\) 94.7451 3.16521
\(897\) 1.14535 0.0382421
\(898\) −12.2908 −0.410149
\(899\) −1.36800 −0.0456255
\(900\) 35.3675 1.17892
\(901\) −0.243489 −0.00811180
\(902\) 23.9545 0.797597
\(903\) 5.76728 0.191923
\(904\) 149.012 4.95607
\(905\) −15.8487 −0.526830
\(906\) −72.5365 −2.40986
\(907\) 14.0340 0.465990 0.232995 0.972478i \(-0.425147\pi\)
0.232995 + 0.972478i \(0.425147\pi\)
\(908\) 99.8397 3.31330
\(909\) −1.92175 −0.0637403
\(910\) −38.4530 −1.27470
\(911\) 9.68789 0.320974 0.160487 0.987038i \(-0.448694\pi\)
0.160487 + 0.987038i \(0.448694\pi\)
\(912\) −3.93938 −0.130446
\(913\) −10.2623 −0.339633
\(914\) −40.3408 −1.33436
\(915\) 3.49584 0.115569
\(916\) 93.9516 3.10425
\(917\) −35.8535 −1.18399
\(918\) −14.4044 −0.475415
\(919\) −0.446725 −0.0147361 −0.00736804 0.999973i \(-0.502345\pi\)
−0.00736804 + 0.999973i \(0.502345\pi\)
\(920\) 2.89483 0.0954398
\(921\) −25.2321 −0.831425
\(922\) −50.2760 −1.65575
\(923\) 0.566733 0.0186543
\(924\) −29.9518 −0.985342
\(925\) −3.86407 −0.127050
\(926\) 56.4760 1.85592
\(927\) 1.32991 0.0436800
\(928\) 99.5707 3.26857
\(929\) 23.3522 0.766160 0.383080 0.923715i \(-0.374863\pi\)
0.383080 + 0.923715i \(0.374863\pi\)
\(930\) −0.688847 −0.0225882
\(931\) −5.00812 −0.164135
\(932\) 114.720 3.75779
\(933\) 21.1093 0.691088
\(934\) −56.6552 −1.85382
\(935\) −0.981432 −0.0320962
\(936\) −41.9373 −1.37076
\(937\) 10.9116 0.356468 0.178234 0.983988i \(-0.442962\pi\)
0.178234 + 0.983988i \(0.442962\pi\)
\(938\) −123.736 −4.04013
\(939\) −8.04062 −0.262396
\(940\) −28.7281 −0.937007
\(941\) 15.2914 0.498484 0.249242 0.968441i \(-0.419819\pi\)
0.249242 + 0.968441i \(0.419819\pi\)
\(942\) 24.7553 0.806571
\(943\) 3.07582 0.100163
\(944\) 77.4696 2.52142
\(945\) 26.5293 0.862999
\(946\) 2.68205 0.0872011
\(947\) −10.5487 −0.342787 −0.171393 0.985203i \(-0.554827\pi\)
−0.171393 + 0.985203i \(0.554827\pi\)
\(948\) 0.0191071 0.000620570 0
\(949\) −0.0706107 −0.00229212
\(950\) −2.95773 −0.0959613
\(951\) 5.36899 0.174101
\(952\) −43.1082 −1.39715
\(953\) 6.98516 0.226271 0.113136 0.993580i \(-0.463911\pi\)
0.113136 + 0.993580i \(0.463911\pi\)
\(954\) 1.10170 0.0356688
\(955\) 14.9474 0.483686
\(956\) −75.7894 −2.45121
\(957\) −6.86366 −0.221871
\(958\) −79.0704 −2.55465
\(959\) 63.4609 2.04926
\(960\) 21.8330 0.704658
\(961\) −30.9478 −0.998317
\(962\) 7.45144 0.240244
\(963\) −3.65230 −0.117694
\(964\) −29.9928 −0.966004
\(965\) 8.84717 0.284800
\(966\) −5.32697 −0.171392
\(967\) 6.54757 0.210556 0.105278 0.994443i \(-0.466427\pi\)
0.105278 + 0.994443i \(0.466427\pi\)
\(968\) −8.56488 −0.275286
\(969\) 0.313030 0.0100560
\(970\) −42.6795 −1.37036
\(971\) −51.9599 −1.66747 −0.833737 0.552162i \(-0.813803\pi\)
−0.833737 + 0.552162i \(0.813803\pi\)
\(972\) 77.1715 2.47528
\(973\) 100.492 3.22163
\(974\) −56.3312 −1.80497
\(975\) 13.4256 0.429962
\(976\) 39.1201 1.25220
\(977\) −21.7013 −0.694287 −0.347143 0.937812i \(-0.612848\pi\)
−0.347143 + 0.937812i \(0.612848\pi\)
\(978\) −17.1839 −0.549479
\(979\) −1.74790 −0.0558633
\(980\) 93.4400 2.98483
\(981\) −1.53971 −0.0491593
\(982\) 70.1844 2.23967
\(983\) 52.3229 1.66884 0.834421 0.551128i \(-0.185802\pi\)
0.834421 + 0.551128i \(0.185802\pi\)
\(984\) 87.6542 2.79431
\(985\) 6.38323 0.203387
\(986\) −16.0654 −0.511626
\(987\) 32.5061 1.03468
\(988\) 4.11785 0.131006
\(989\) 0.344383 0.0109507
\(990\) 4.44061 0.141132
\(991\) 5.07432 0.161191 0.0805956 0.996747i \(-0.474318\pi\)
0.0805956 + 0.996747i \(0.474318\pi\)
\(992\) −3.79640 −0.120536
\(993\) −16.9360 −0.537447
\(994\) −2.63585 −0.0836041
\(995\) −4.12075 −0.130636
\(996\) −61.0702 −1.93508
\(997\) 32.1989 1.01975 0.509874 0.860249i \(-0.329692\pi\)
0.509874 + 0.860249i \(0.329692\pi\)
\(998\) −67.7397 −2.14426
\(999\) −5.14086 −0.162650
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 \(a_p\))