Properties

Label 8015.2.a.l.1.20
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.21148 q^{2} +1.67937 q^{3} -0.532324 q^{4} -1.00000 q^{5} -2.03452 q^{6} -1.00000 q^{7} +3.06785 q^{8} -0.179714 q^{9} +O(q^{10})\) \(q-1.21148 q^{2} +1.67937 q^{3} -0.532324 q^{4} -1.00000 q^{5} -2.03452 q^{6} -1.00000 q^{7} +3.06785 q^{8} -0.179714 q^{9} +1.21148 q^{10} -5.20420 q^{11} -0.893970 q^{12} +4.41019 q^{13} +1.21148 q^{14} -1.67937 q^{15} -2.65198 q^{16} -0.830757 q^{17} +0.217720 q^{18} -7.19999 q^{19} +0.532324 q^{20} -1.67937 q^{21} +6.30476 q^{22} -1.03249 q^{23} +5.15206 q^{24} +1.00000 q^{25} -5.34284 q^{26} -5.33992 q^{27} +0.532324 q^{28} -6.71927 q^{29} +2.03452 q^{30} +0.399125 q^{31} -2.92289 q^{32} -8.73977 q^{33} +1.00644 q^{34} +1.00000 q^{35} +0.0956662 q^{36} +6.46999 q^{37} +8.72262 q^{38} +7.40634 q^{39} -3.06785 q^{40} +6.34004 q^{41} +2.03452 q^{42} -1.63582 q^{43} +2.77032 q^{44} +0.179714 q^{45} +1.25084 q^{46} -5.69334 q^{47} -4.45366 q^{48} +1.00000 q^{49} -1.21148 q^{50} -1.39515 q^{51} -2.34765 q^{52} -10.3766 q^{53} +6.46919 q^{54} +5.20420 q^{55} -3.06785 q^{56} -12.0915 q^{57} +8.14024 q^{58} -14.5415 q^{59} +0.893970 q^{60} +8.62838 q^{61} -0.483530 q^{62} +0.179714 q^{63} +8.84498 q^{64} -4.41019 q^{65} +10.5880 q^{66} -2.55982 q^{67} +0.442232 q^{68} -1.73393 q^{69} -1.21148 q^{70} +15.5322 q^{71} -0.551337 q^{72} +6.22453 q^{73} -7.83824 q^{74} +1.67937 q^{75} +3.83273 q^{76} +5.20420 q^{77} -8.97261 q^{78} +8.09991 q^{79} +2.65198 q^{80} -8.42856 q^{81} -7.68081 q^{82} +11.9391 q^{83} +0.893970 q^{84} +0.830757 q^{85} +1.98176 q^{86} -11.2841 q^{87} -15.9657 q^{88} -5.80329 q^{89} -0.217720 q^{90} -4.41019 q^{91} +0.549619 q^{92} +0.670278 q^{93} +6.89735 q^{94} +7.19999 q^{95} -4.90861 q^{96} -8.15777 q^{97} -1.21148 q^{98} +0.935268 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.21148 −0.856643 −0.428322 0.903626i \(-0.640895\pi\)
−0.428322 + 0.903626i \(0.640895\pi\)
\(3\) 1.67937 0.969585 0.484793 0.874629i \(-0.338895\pi\)
0.484793 + 0.874629i \(0.338895\pi\)
\(4\) −0.532324 −0.266162
\(5\) −1.00000 −0.447214
\(6\) −2.03452 −0.830589
\(7\) −1.00000 −0.377964
\(8\) 3.06785 1.08465
\(9\) −0.179714 −0.0599047
\(10\) 1.21148 0.383103
\(11\) −5.20420 −1.56912 −0.784562 0.620050i \(-0.787112\pi\)
−0.784562 + 0.620050i \(0.787112\pi\)
\(12\) −0.893970 −0.258067
\(13\) 4.41019 1.22317 0.611583 0.791180i \(-0.290533\pi\)
0.611583 + 0.791180i \(0.290533\pi\)
\(14\) 1.21148 0.323781
\(15\) −1.67937 −0.433612
\(16\) −2.65198 −0.662996
\(17\) −0.830757 −0.201488 −0.100744 0.994912i \(-0.532122\pi\)
−0.100744 + 0.994912i \(0.532122\pi\)
\(18\) 0.217720 0.0513170
\(19\) −7.19999 −1.65179 −0.825896 0.563823i \(-0.809330\pi\)
−0.825896 + 0.563823i \(0.809330\pi\)
\(20\) 0.532324 0.119031
\(21\) −1.67937 −0.366469
\(22\) 6.30476 1.34418
\(23\) −1.03249 −0.215289 −0.107644 0.994189i \(-0.534331\pi\)
−0.107644 + 0.994189i \(0.534331\pi\)
\(24\) 5.15206 1.05166
\(25\) 1.00000 0.200000
\(26\) −5.34284 −1.04782
\(27\) −5.33992 −1.02767
\(28\) 0.532324 0.100600
\(29\) −6.71927 −1.24774 −0.623868 0.781529i \(-0.714440\pi\)
−0.623868 + 0.781529i \(0.714440\pi\)
\(30\) 2.03452 0.371451
\(31\) 0.399125 0.0716849 0.0358424 0.999357i \(-0.488589\pi\)
0.0358424 + 0.999357i \(0.488589\pi\)
\(32\) −2.92289 −0.516699
\(33\) −8.73977 −1.52140
\(34\) 1.00644 0.172604
\(35\) 1.00000 0.169031
\(36\) 0.0956662 0.0159444
\(37\) 6.46999 1.06366 0.531830 0.846851i \(-0.321505\pi\)
0.531830 + 0.846851i \(0.321505\pi\)
\(38\) 8.72262 1.41500
\(39\) 7.40634 1.18596
\(40\) −3.06785 −0.485070
\(41\) 6.34004 0.990148 0.495074 0.868851i \(-0.335141\pi\)
0.495074 + 0.868851i \(0.335141\pi\)
\(42\) 2.03452 0.313933
\(43\) −1.63582 −0.249461 −0.124730 0.992191i \(-0.539807\pi\)
−0.124730 + 0.992191i \(0.539807\pi\)
\(44\) 2.77032 0.417641
\(45\) 0.179714 0.0267902
\(46\) 1.25084 0.184426
\(47\) −5.69334 −0.830459 −0.415229 0.909717i \(-0.636299\pi\)
−0.415229 + 0.909717i \(0.636299\pi\)
\(48\) −4.45366 −0.642831
\(49\) 1.00000 0.142857
\(50\) −1.21148 −0.171329
\(51\) −1.39515 −0.195360
\(52\) −2.34765 −0.325561
\(53\) −10.3766 −1.42533 −0.712665 0.701504i \(-0.752512\pi\)
−0.712665 + 0.701504i \(0.752512\pi\)
\(54\) 6.46919 0.880345
\(55\) 5.20420 0.701734
\(56\) −3.06785 −0.409959
\(57\) −12.0915 −1.60155
\(58\) 8.14024 1.06887
\(59\) −14.5415 −1.89315 −0.946574 0.322487i \(-0.895481\pi\)
−0.946574 + 0.322487i \(0.895481\pi\)
\(60\) 0.893970 0.115411
\(61\) 8.62838 1.10475 0.552375 0.833596i \(-0.313722\pi\)
0.552375 + 0.833596i \(0.313722\pi\)
\(62\) −0.483530 −0.0614084
\(63\) 0.179714 0.0226419
\(64\) 8.84498 1.10562
\(65\) −4.41019 −0.547017
\(66\) 10.5880 1.30330
\(67\) −2.55982 −0.312732 −0.156366 0.987699i \(-0.549978\pi\)
−0.156366 + 0.987699i \(0.549978\pi\)
\(68\) 0.442232 0.0536285
\(69\) −1.73393 −0.208741
\(70\) −1.21148 −0.144799
\(71\) 15.5322 1.84334 0.921668 0.387981i \(-0.126827\pi\)
0.921668 + 0.387981i \(0.126827\pi\)
\(72\) −0.551337 −0.0649756
\(73\) 6.22453 0.728527 0.364263 0.931296i \(-0.381321\pi\)
0.364263 + 0.931296i \(0.381321\pi\)
\(74\) −7.83824 −0.911177
\(75\) 1.67937 0.193917
\(76\) 3.83273 0.439644
\(77\) 5.20420 0.593073
\(78\) −8.97261 −1.01595
\(79\) 8.09991 0.911311 0.455655 0.890156i \(-0.349405\pi\)
0.455655 + 0.890156i \(0.349405\pi\)
\(80\) 2.65198 0.296501
\(81\) −8.42856 −0.936507
\(82\) −7.68081 −0.848204
\(83\) 11.9391 1.31048 0.655242 0.755419i \(-0.272567\pi\)
0.655242 + 0.755419i \(0.272567\pi\)
\(84\) 0.893970 0.0975401
\(85\) 0.830757 0.0901083
\(86\) 1.98176 0.213699
\(87\) −11.2841 −1.20979
\(88\) −15.9657 −1.70195
\(89\) −5.80329 −0.615147 −0.307574 0.951524i \(-0.599517\pi\)
−0.307574 + 0.951524i \(0.599517\pi\)
\(90\) −0.217720 −0.0229497
\(91\) −4.41019 −0.462313
\(92\) 0.549619 0.0573017
\(93\) 0.670278 0.0695046
\(94\) 6.89735 0.711407
\(95\) 7.19999 0.738703
\(96\) −4.90861 −0.500983
\(97\) −8.15777 −0.828296 −0.414148 0.910210i \(-0.635920\pi\)
−0.414148 + 0.910210i \(0.635920\pi\)
\(98\) −1.21148 −0.122378
\(99\) 0.935268 0.0939980
\(100\) −0.532324 −0.0532324
\(101\) 9.42696 0.938017 0.469009 0.883194i \(-0.344611\pi\)
0.469009 + 0.883194i \(0.344611\pi\)
\(102\) 1.69019 0.167354
\(103\) −0.699690 −0.0689425 −0.0344713 0.999406i \(-0.510975\pi\)
−0.0344713 + 0.999406i \(0.510975\pi\)
\(104\) 13.5298 1.32671
\(105\) 1.67937 0.163890
\(106\) 12.5710 1.22100
\(107\) −7.12220 −0.688529 −0.344264 0.938873i \(-0.611872\pi\)
−0.344264 + 0.938873i \(0.611872\pi\)
\(108\) 2.84257 0.273526
\(109\) −5.44814 −0.521837 −0.260919 0.965361i \(-0.584025\pi\)
−0.260919 + 0.965361i \(0.584025\pi\)
\(110\) −6.30476 −0.601136
\(111\) 10.8655 1.03131
\(112\) 2.65198 0.250589
\(113\) −1.58231 −0.148851 −0.0744255 0.997227i \(-0.523712\pi\)
−0.0744255 + 0.997227i \(0.523712\pi\)
\(114\) 14.6485 1.37196
\(115\) 1.03249 0.0962801
\(116\) 3.57683 0.332100
\(117\) −0.792574 −0.0732735
\(118\) 17.6167 1.62175
\(119\) 0.830757 0.0761554
\(120\) −5.15206 −0.470317
\(121\) 16.0837 1.46215
\(122\) −10.4531 −0.946377
\(123\) 10.6473 0.960033
\(124\) −0.212464 −0.0190798
\(125\) −1.00000 −0.0894427
\(126\) −0.217720 −0.0193960
\(127\) −5.30748 −0.470963 −0.235482 0.971879i \(-0.575667\pi\)
−0.235482 + 0.971879i \(0.575667\pi\)
\(128\) −4.86970 −0.430425
\(129\) −2.74715 −0.241873
\(130\) 5.34284 0.468598
\(131\) 9.34518 0.816492 0.408246 0.912872i \(-0.366141\pi\)
0.408246 + 0.912872i \(0.366141\pi\)
\(132\) 4.65239 0.404939
\(133\) 7.19999 0.624318
\(134\) 3.10117 0.267900
\(135\) 5.33992 0.459587
\(136\) −2.54864 −0.218544
\(137\) −12.7964 −1.09327 −0.546637 0.837370i \(-0.684092\pi\)
−0.546637 + 0.837370i \(0.684092\pi\)
\(138\) 2.10062 0.178816
\(139\) 1.58170 0.134158 0.0670790 0.997748i \(-0.478632\pi\)
0.0670790 + 0.997748i \(0.478632\pi\)
\(140\) −0.532324 −0.0449896
\(141\) −9.56122 −0.805200
\(142\) −18.8169 −1.57908
\(143\) −22.9515 −1.91930
\(144\) 0.476599 0.0397166
\(145\) 6.71927 0.558005
\(146\) −7.54088 −0.624087
\(147\) 1.67937 0.138512
\(148\) −3.44413 −0.283106
\(149\) 1.46551 0.120059 0.0600296 0.998197i \(-0.480880\pi\)
0.0600296 + 0.998197i \(0.480880\pi\)
\(150\) −2.03452 −0.166118
\(151\) 10.8842 0.885748 0.442874 0.896584i \(-0.353959\pi\)
0.442874 + 0.896584i \(0.353959\pi\)
\(152\) −22.0885 −1.79161
\(153\) 0.149299 0.0120701
\(154\) −6.30476 −0.508052
\(155\) −0.399125 −0.0320585
\(156\) −3.94258 −0.315659
\(157\) −3.90830 −0.311917 −0.155958 0.987764i \(-0.549847\pi\)
−0.155958 + 0.987764i \(0.549847\pi\)
\(158\) −9.81285 −0.780668
\(159\) −17.4261 −1.38198
\(160\) 2.92289 0.231075
\(161\) 1.03249 0.0813715
\(162\) 10.2110 0.802252
\(163\) 8.96770 0.702405 0.351202 0.936300i \(-0.385773\pi\)
0.351202 + 0.936300i \(0.385773\pi\)
\(164\) −3.37496 −0.263540
\(165\) 8.73977 0.680391
\(166\) −14.4639 −1.12262
\(167\) 3.62653 0.280630 0.140315 0.990107i \(-0.455189\pi\)
0.140315 + 0.990107i \(0.455189\pi\)
\(168\) −5.15206 −0.397490
\(169\) 6.44977 0.496136
\(170\) −1.00644 −0.0771906
\(171\) 1.29394 0.0989501
\(172\) 0.870788 0.0663970
\(173\) 7.05442 0.536338 0.268169 0.963372i \(-0.413581\pi\)
0.268169 + 0.963372i \(0.413581\pi\)
\(174\) 13.6705 1.03636
\(175\) −1.00000 −0.0755929
\(176\) 13.8014 1.04032
\(177\) −24.4206 −1.83557
\(178\) 7.03055 0.526962
\(179\) 3.13166 0.234071 0.117036 0.993128i \(-0.462661\pi\)
0.117036 + 0.993128i \(0.462661\pi\)
\(180\) −0.0956662 −0.00713054
\(181\) 22.4452 1.66834 0.834168 0.551510i \(-0.185948\pi\)
0.834168 + 0.551510i \(0.185948\pi\)
\(182\) 5.34284 0.396038
\(183\) 14.4902 1.07115
\(184\) −3.16752 −0.233513
\(185\) −6.46999 −0.475683
\(186\) −0.812026 −0.0595407
\(187\) 4.32342 0.316160
\(188\) 3.03070 0.221037
\(189\) 5.33992 0.388422
\(190\) −8.72262 −0.632805
\(191\) −25.4447 −1.84112 −0.920558 0.390606i \(-0.872266\pi\)
−0.920558 + 0.390606i \(0.872266\pi\)
\(192\) 14.8540 1.07199
\(193\) −16.0136 −1.15268 −0.576341 0.817210i \(-0.695520\pi\)
−0.576341 + 0.817210i \(0.695520\pi\)
\(194\) 9.88295 0.709554
\(195\) −7.40634 −0.530379
\(196\) −0.532324 −0.0380232
\(197\) 24.7300 1.76194 0.880971 0.473170i \(-0.156890\pi\)
0.880971 + 0.473170i \(0.156890\pi\)
\(198\) −1.13306 −0.0805228
\(199\) −1.74351 −0.123594 −0.0617972 0.998089i \(-0.519683\pi\)
−0.0617972 + 0.998089i \(0.519683\pi\)
\(200\) 3.06785 0.216930
\(201\) −4.29889 −0.303221
\(202\) −11.4205 −0.803546
\(203\) 6.71927 0.471600
\(204\) 0.742672 0.0519974
\(205\) −6.34004 −0.442808
\(206\) 0.847658 0.0590592
\(207\) 0.185553 0.0128968
\(208\) −11.6957 −0.810954
\(209\) 37.4702 2.59187
\(210\) −2.03452 −0.140395
\(211\) −10.5180 −0.724088 −0.362044 0.932161i \(-0.617921\pi\)
−0.362044 + 0.932161i \(0.617921\pi\)
\(212\) 5.52370 0.379369
\(213\) 26.0843 1.78727
\(214\) 8.62838 0.589824
\(215\) 1.63582 0.111562
\(216\) −16.3821 −1.11466
\(217\) −0.399125 −0.0270943
\(218\) 6.60029 0.447028
\(219\) 10.4533 0.706368
\(220\) −2.77032 −0.186775
\(221\) −3.66380 −0.246454
\(222\) −13.1633 −0.883464
\(223\) 4.06215 0.272021 0.136011 0.990707i \(-0.456572\pi\)
0.136011 + 0.990707i \(0.456572\pi\)
\(224\) 2.92289 0.195294
\(225\) −0.179714 −0.0119809
\(226\) 1.91693 0.127512
\(227\) −13.3462 −0.885820 −0.442910 0.896566i \(-0.646054\pi\)
−0.442910 + 0.896566i \(0.646054\pi\)
\(228\) 6.43657 0.426273
\(229\) 1.00000 0.0660819
\(230\) −1.25084 −0.0824777
\(231\) 8.73977 0.575035
\(232\) −20.6137 −1.35336
\(233\) 15.2104 0.996465 0.498232 0.867044i \(-0.333983\pi\)
0.498232 + 0.867044i \(0.333983\pi\)
\(234\) 0.960185 0.0627692
\(235\) 5.69334 0.371392
\(236\) 7.74082 0.503884
\(237\) 13.6027 0.883593
\(238\) −1.00644 −0.0652380
\(239\) −12.8861 −0.833536 −0.416768 0.909013i \(-0.636837\pi\)
−0.416768 + 0.909013i \(0.636837\pi\)
\(240\) 4.45366 0.287483
\(241\) 6.39447 0.411904 0.205952 0.978562i \(-0.433971\pi\)
0.205952 + 0.978562i \(0.433971\pi\)
\(242\) −19.4850 −1.25254
\(243\) 1.86508 0.119645
\(244\) −4.59310 −0.294043
\(245\) −1.00000 −0.0638877
\(246\) −12.8989 −0.822406
\(247\) −31.7533 −2.02042
\(248\) 1.22446 0.0777530
\(249\) 20.0501 1.27062
\(250\) 1.21148 0.0766205
\(251\) −9.03909 −0.570542 −0.285271 0.958447i \(-0.592084\pi\)
−0.285271 + 0.958447i \(0.592084\pi\)
\(252\) −0.0956662 −0.00602641
\(253\) 5.37327 0.337815
\(254\) 6.42989 0.403447
\(255\) 1.39515 0.0873676
\(256\) −11.7904 −0.736901
\(257\) −17.6408 −1.10040 −0.550200 0.835033i \(-0.685449\pi\)
−0.550200 + 0.835033i \(0.685449\pi\)
\(258\) 3.32811 0.207199
\(259\) −6.46999 −0.402026
\(260\) 2.34765 0.145595
\(261\) 1.20755 0.0747453
\(262\) −11.3215 −0.699442
\(263\) 18.1765 1.12081 0.560405 0.828219i \(-0.310646\pi\)
0.560405 + 0.828219i \(0.310646\pi\)
\(264\) −26.8123 −1.65019
\(265\) 10.3766 0.637427
\(266\) −8.72262 −0.534818
\(267\) −9.74587 −0.596438
\(268\) 1.36266 0.0832375
\(269\) −5.15450 −0.314276 −0.157138 0.987577i \(-0.550227\pi\)
−0.157138 + 0.987577i \(0.550227\pi\)
\(270\) −6.46919 −0.393702
\(271\) 16.4518 0.999374 0.499687 0.866206i \(-0.333448\pi\)
0.499687 + 0.866206i \(0.333448\pi\)
\(272\) 2.20315 0.133586
\(273\) −7.40634 −0.448252
\(274\) 15.5026 0.936546
\(275\) −5.20420 −0.313825
\(276\) 0.923014 0.0555589
\(277\) 29.5923 1.77803 0.889015 0.457877i \(-0.151390\pi\)
0.889015 + 0.457877i \(0.151390\pi\)
\(278\) −1.91619 −0.114926
\(279\) −0.0717284 −0.00429427
\(280\) 3.06785 0.183339
\(281\) 6.48794 0.387038 0.193519 0.981097i \(-0.438010\pi\)
0.193519 + 0.981097i \(0.438010\pi\)
\(282\) 11.5832 0.689770
\(283\) −20.9612 −1.24601 −0.623007 0.782217i \(-0.714089\pi\)
−0.623007 + 0.782217i \(0.714089\pi\)
\(284\) −8.26818 −0.490626
\(285\) 12.0915 0.716236
\(286\) 27.8052 1.64416
\(287\) −6.34004 −0.374241
\(288\) 0.525285 0.0309527
\(289\) −16.3098 −0.959403
\(290\) −8.14024 −0.478011
\(291\) −13.6999 −0.803104
\(292\) −3.31347 −0.193906
\(293\) −9.48074 −0.553871 −0.276935 0.960889i \(-0.589319\pi\)
−0.276935 + 0.960889i \(0.589319\pi\)
\(294\) −2.03452 −0.118656
\(295\) 14.5415 0.846641
\(296\) 19.8490 1.15370
\(297\) 27.7900 1.61254
\(298\) −1.77543 −0.102848
\(299\) −4.55347 −0.263334
\(300\) −0.893970 −0.0516134
\(301\) 1.63582 0.0942872
\(302\) −13.1860 −0.758770
\(303\) 15.8314 0.909487
\(304\) 19.0942 1.09513
\(305\) −8.62838 −0.494059
\(306\) −0.180872 −0.0103398
\(307\) −14.2468 −0.813109 −0.406554 0.913627i \(-0.633270\pi\)
−0.406554 + 0.913627i \(0.633270\pi\)
\(308\) −2.77032 −0.157854
\(309\) −1.17504 −0.0668457
\(310\) 0.483530 0.0274627
\(311\) 3.14087 0.178102 0.0890512 0.996027i \(-0.471617\pi\)
0.0890512 + 0.996027i \(0.471617\pi\)
\(312\) 22.7216 1.28636
\(313\) 29.6973 1.67859 0.839295 0.543677i \(-0.182968\pi\)
0.839295 + 0.543677i \(0.182968\pi\)
\(314\) 4.73482 0.267201
\(315\) −0.179714 −0.0101257
\(316\) −4.31178 −0.242556
\(317\) 26.3993 1.48273 0.741367 0.671100i \(-0.234178\pi\)
0.741367 + 0.671100i \(0.234178\pi\)
\(318\) 21.1113 1.18386
\(319\) 34.9684 1.95785
\(320\) −8.84498 −0.494449
\(321\) −11.9608 −0.667587
\(322\) −1.25084 −0.0697064
\(323\) 5.98144 0.332816
\(324\) 4.48673 0.249263
\(325\) 4.41019 0.244633
\(326\) −10.8642 −0.601710
\(327\) −9.14944 −0.505965
\(328\) 19.4503 1.07396
\(329\) 5.69334 0.313884
\(330\) −10.5880 −0.582852
\(331\) 17.4298 0.958029 0.479015 0.877807i \(-0.340994\pi\)
0.479015 + 0.877807i \(0.340994\pi\)
\(332\) −6.35546 −0.348801
\(333\) −1.16275 −0.0637183
\(334\) −4.39346 −0.240399
\(335\) 2.55982 0.139858
\(336\) 4.45366 0.242967
\(337\) 16.5637 0.902282 0.451141 0.892453i \(-0.351017\pi\)
0.451141 + 0.892453i \(0.351017\pi\)
\(338\) −7.81375 −0.425012
\(339\) −2.65728 −0.144324
\(340\) −0.442232 −0.0239834
\(341\) −2.07712 −0.112483
\(342\) −1.56758 −0.0847650
\(343\) −1.00000 −0.0539949
\(344\) −5.01846 −0.270577
\(345\) 1.73393 0.0933517
\(346\) −8.54627 −0.459450
\(347\) 23.3487 1.25342 0.626712 0.779251i \(-0.284400\pi\)
0.626712 + 0.779251i \(0.284400\pi\)
\(348\) 6.00682 0.321999
\(349\) 24.2150 1.29620 0.648101 0.761555i \(-0.275564\pi\)
0.648101 + 0.761555i \(0.275564\pi\)
\(350\) 1.21148 0.0647562
\(351\) −23.5501 −1.25701
\(352\) 15.2113 0.810764
\(353\) 6.44993 0.343295 0.171647 0.985158i \(-0.445091\pi\)
0.171647 + 0.985158i \(0.445091\pi\)
\(354\) 29.5850 1.57243
\(355\) −15.5322 −0.824365
\(356\) 3.08923 0.163729
\(357\) 1.39515 0.0738391
\(358\) −3.79394 −0.200516
\(359\) 32.5794 1.71948 0.859739 0.510734i \(-0.170626\pi\)
0.859739 + 0.510734i \(0.170626\pi\)
\(360\) 0.551337 0.0290580
\(361\) 32.8399 1.72841
\(362\) −27.1918 −1.42917
\(363\) 27.0104 1.41768
\(364\) 2.34765 0.123050
\(365\) −6.22453 −0.325807
\(366\) −17.5546 −0.917593
\(367\) −3.67511 −0.191839 −0.0959197 0.995389i \(-0.530579\pi\)
−0.0959197 + 0.995389i \(0.530579\pi\)
\(368\) 2.73814 0.142736
\(369\) −1.13940 −0.0593146
\(370\) 7.83824 0.407491
\(371\) 10.3766 0.538724
\(372\) −0.356805 −0.0184995
\(373\) 0.818134 0.0423614 0.0211807 0.999776i \(-0.493257\pi\)
0.0211807 + 0.999776i \(0.493257\pi\)
\(374\) −5.23773 −0.270836
\(375\) −1.67937 −0.0867223
\(376\) −17.4663 −0.900757
\(377\) −29.6332 −1.52619
\(378\) −6.46919 −0.332739
\(379\) 7.86409 0.403951 0.201976 0.979391i \(-0.435264\pi\)
0.201976 + 0.979391i \(0.435264\pi\)
\(380\) −3.83273 −0.196615
\(381\) −8.91323 −0.456639
\(382\) 30.8257 1.57718
\(383\) −16.6110 −0.848784 −0.424392 0.905479i \(-0.639512\pi\)
−0.424392 + 0.905479i \(0.639512\pi\)
\(384\) −8.17804 −0.417334
\(385\) −5.20420 −0.265230
\(386\) 19.4001 0.987437
\(387\) 0.293981 0.0149439
\(388\) 4.34258 0.220461
\(389\) 16.1772 0.820219 0.410110 0.912036i \(-0.365490\pi\)
0.410110 + 0.912036i \(0.365490\pi\)
\(390\) 8.97261 0.454346
\(391\) 0.857747 0.0433781
\(392\) 3.06785 0.154950
\(393\) 15.6940 0.791658
\(394\) −29.9599 −1.50936
\(395\) −8.09991 −0.407551
\(396\) −0.497866 −0.0250187
\(397\) 1.58954 0.0797767 0.0398884 0.999204i \(-0.487300\pi\)
0.0398884 + 0.999204i \(0.487300\pi\)
\(398\) 2.11223 0.105876
\(399\) 12.0915 0.605330
\(400\) −2.65198 −0.132599
\(401\) 0.780173 0.0389600 0.0194800 0.999810i \(-0.493799\pi\)
0.0194800 + 0.999810i \(0.493799\pi\)
\(402\) 5.20801 0.259752
\(403\) 1.76022 0.0876826
\(404\) −5.01820 −0.249665
\(405\) 8.42856 0.418819
\(406\) −8.14024 −0.403993
\(407\) −33.6711 −1.66901
\(408\) −4.28011 −0.211897
\(409\) −31.1049 −1.53804 −0.769018 0.639227i \(-0.779254\pi\)
−0.769018 + 0.639227i \(0.779254\pi\)
\(410\) 7.68081 0.379328
\(411\) −21.4900 −1.06002
\(412\) 0.372462 0.0183499
\(413\) 14.5415 0.715543
\(414\) −0.224793 −0.0110480
\(415\) −11.9391 −0.586066
\(416\) −12.8905 −0.632008
\(417\) 2.65626 0.130078
\(418\) −45.3942 −2.22030
\(419\) −11.7006 −0.571611 −0.285806 0.958288i \(-0.592261\pi\)
−0.285806 + 0.958288i \(0.592261\pi\)
\(420\) −0.893970 −0.0436213
\(421\) −31.0490 −1.51323 −0.756617 0.653858i \(-0.773149\pi\)
−0.756617 + 0.653858i \(0.773149\pi\)
\(422\) 12.7423 0.620285
\(423\) 1.02317 0.0497484
\(424\) −31.8338 −1.54598
\(425\) −0.830757 −0.0402976
\(426\) −31.6006 −1.53105
\(427\) −8.62838 −0.417556
\(428\) 3.79132 0.183260
\(429\) −38.5441 −1.86092
\(430\) −1.98176 −0.0955690
\(431\) 7.44759 0.358738 0.179369 0.983782i \(-0.442594\pi\)
0.179369 + 0.983782i \(0.442594\pi\)
\(432\) 14.1614 0.681339
\(433\) 18.3812 0.883344 0.441672 0.897177i \(-0.354385\pi\)
0.441672 + 0.897177i \(0.354385\pi\)
\(434\) 0.483530 0.0232102
\(435\) 11.2841 0.541033
\(436\) 2.90018 0.138893
\(437\) 7.43391 0.355612
\(438\) −12.6639 −0.605106
\(439\) 9.57580 0.457028 0.228514 0.973541i \(-0.426613\pi\)
0.228514 + 0.973541i \(0.426613\pi\)
\(440\) 15.9657 0.761135
\(441\) −0.179714 −0.00855782
\(442\) 4.43860 0.211123
\(443\) −10.9484 −0.520174 −0.260087 0.965585i \(-0.583751\pi\)
−0.260087 + 0.965585i \(0.583751\pi\)
\(444\) −5.78397 −0.274495
\(445\) 5.80329 0.275102
\(446\) −4.92119 −0.233025
\(447\) 2.46113 0.116408
\(448\) −8.84498 −0.417886
\(449\) 27.2355 1.28532 0.642661 0.766150i \(-0.277830\pi\)
0.642661 + 0.766150i \(0.277830\pi\)
\(450\) 0.217720 0.0102634
\(451\) −32.9948 −1.55367
\(452\) 0.842301 0.0396185
\(453\) 18.2787 0.858808
\(454\) 16.1686 0.758832
\(455\) 4.41019 0.206753
\(456\) −37.0948 −1.73712
\(457\) −0.651536 −0.0304776 −0.0152388 0.999884i \(-0.504851\pi\)
−0.0152388 + 0.999884i \(0.504851\pi\)
\(458\) −1.21148 −0.0566086
\(459\) 4.43618 0.207063
\(460\) −0.549619 −0.0256261
\(461\) 14.3290 0.667369 0.333684 0.942685i \(-0.391708\pi\)
0.333684 + 0.942685i \(0.391708\pi\)
\(462\) −10.5880 −0.492600
\(463\) −8.87000 −0.412224 −0.206112 0.978528i \(-0.566081\pi\)
−0.206112 + 0.978528i \(0.566081\pi\)
\(464\) 17.8194 0.827244
\(465\) −0.670278 −0.0310834
\(466\) −18.4270 −0.853615
\(467\) 14.8062 0.685150 0.342575 0.939491i \(-0.388701\pi\)
0.342575 + 0.939491i \(0.388701\pi\)
\(468\) 0.421906 0.0195026
\(469\) 2.55982 0.118202
\(470\) −6.89735 −0.318151
\(471\) −6.56349 −0.302430
\(472\) −44.6113 −2.05340
\(473\) 8.51314 0.391435
\(474\) −16.4794 −0.756924
\(475\) −7.19999 −0.330358
\(476\) −0.442232 −0.0202697
\(477\) 1.86482 0.0853841
\(478\) 15.6113 0.714043
\(479\) 21.2236 0.969730 0.484865 0.874589i \(-0.338869\pi\)
0.484865 + 0.874589i \(0.338869\pi\)
\(480\) 4.90861 0.224047
\(481\) 28.5339 1.30103
\(482\) −7.74675 −0.352855
\(483\) 1.73393 0.0788966
\(484\) −8.56172 −0.389169
\(485\) 8.15777 0.370425
\(486\) −2.25950 −0.102493
\(487\) 31.8562 1.44354 0.721770 0.692132i \(-0.243329\pi\)
0.721770 + 0.692132i \(0.243329\pi\)
\(488\) 26.4706 1.19827
\(489\) 15.0601 0.681041
\(490\) 1.21148 0.0547289
\(491\) −18.6585 −0.842046 −0.421023 0.907050i \(-0.638329\pi\)
−0.421023 + 0.907050i \(0.638329\pi\)
\(492\) −5.66781 −0.255524
\(493\) 5.58208 0.251404
\(494\) 38.4684 1.73078
\(495\) −0.935268 −0.0420372
\(496\) −1.05847 −0.0475268
\(497\) −15.5322 −0.696715
\(498\) −24.2903 −1.08847
\(499\) −12.6494 −0.566264 −0.283132 0.959081i \(-0.591373\pi\)
−0.283132 + 0.959081i \(0.591373\pi\)
\(500\) 0.532324 0.0238063
\(501\) 6.09029 0.272094
\(502\) 10.9506 0.488751
\(503\) 29.5547 1.31778 0.658889 0.752240i \(-0.271027\pi\)
0.658889 + 0.752240i \(0.271027\pi\)
\(504\) 0.551337 0.0245585
\(505\) −9.42696 −0.419494
\(506\) −6.50960 −0.289387
\(507\) 10.8316 0.481046
\(508\) 2.82530 0.125353
\(509\) −16.4136 −0.727520 −0.363760 0.931493i \(-0.618507\pi\)
−0.363760 + 0.931493i \(0.618507\pi\)
\(510\) −1.69019 −0.0748429
\(511\) −6.22453 −0.275357
\(512\) 24.0232 1.06169
\(513\) 38.4474 1.69749
\(514\) 21.3714 0.942651
\(515\) 0.699690 0.0308320
\(516\) 1.46238 0.0643775
\(517\) 29.6292 1.30309
\(518\) 7.83824 0.344392
\(519\) 11.8470 0.520025
\(520\) −13.5298 −0.593321
\(521\) −12.0011 −0.525776 −0.262888 0.964826i \(-0.584675\pi\)
−0.262888 + 0.964826i \(0.584675\pi\)
\(522\) −1.46292 −0.0640301
\(523\) −37.2948 −1.63079 −0.815393 0.578907i \(-0.803479\pi\)
−0.815393 + 0.578907i \(0.803479\pi\)
\(524\) −4.97466 −0.217319
\(525\) −1.67937 −0.0732937
\(526\) −22.0204 −0.960134
\(527\) −0.331576 −0.0144437
\(528\) 23.1777 1.00868
\(529\) −21.9340 −0.953651
\(530\) −12.5710 −0.546048
\(531\) 2.61332 0.113409
\(532\) −3.83273 −0.166170
\(533\) 27.9608 1.21112
\(534\) 11.8069 0.510934
\(535\) 7.12220 0.307919
\(536\) −7.85316 −0.339205
\(537\) 5.25922 0.226952
\(538\) 6.24456 0.269222
\(539\) −5.20420 −0.224161
\(540\) −2.84257 −0.122325
\(541\) 16.4106 0.705549 0.352774 0.935708i \(-0.385238\pi\)
0.352774 + 0.935708i \(0.385238\pi\)
\(542\) −19.9309 −0.856107
\(543\) 37.6938 1.61759
\(544\) 2.42821 0.104109
\(545\) 5.44814 0.233373
\(546\) 8.97261 0.383992
\(547\) −3.72065 −0.159084 −0.0795418 0.996832i \(-0.525346\pi\)
−0.0795418 + 0.996832i \(0.525346\pi\)
\(548\) 6.81186 0.290988
\(549\) −1.55064 −0.0661798
\(550\) 6.30476 0.268836
\(551\) 48.3787 2.06100
\(552\) −5.31944 −0.226411
\(553\) −8.09991 −0.344443
\(554\) −35.8504 −1.52314
\(555\) −10.8655 −0.461215
\(556\) −0.841977 −0.0357078
\(557\) −18.5330 −0.785268 −0.392634 0.919695i \(-0.628436\pi\)
−0.392634 + 0.919695i \(0.628436\pi\)
\(558\) 0.0868972 0.00367865
\(559\) −7.21429 −0.305132
\(560\) −2.65198 −0.112067
\(561\) 7.26063 0.306544
\(562\) −7.85999 −0.331554
\(563\) −22.1107 −0.931857 −0.465928 0.884822i \(-0.654280\pi\)
−0.465928 + 0.884822i \(0.654280\pi\)
\(564\) 5.08967 0.214314
\(565\) 1.58231 0.0665682
\(566\) 25.3940 1.06739
\(567\) 8.42856 0.353966
\(568\) 47.6505 1.99937
\(569\) 0.831052 0.0348395 0.0174198 0.999848i \(-0.494455\pi\)
0.0174198 + 0.999848i \(0.494455\pi\)
\(570\) −14.6485 −0.613559
\(571\) 23.5897 0.987200 0.493600 0.869689i \(-0.335681\pi\)
0.493600 + 0.869689i \(0.335681\pi\)
\(572\) 12.2176 0.510845
\(573\) −42.7311 −1.78512
\(574\) 7.68081 0.320591
\(575\) −1.03249 −0.0430578
\(576\) −1.58957 −0.0662320
\(577\) 46.7857 1.94771 0.973857 0.227163i \(-0.0729450\pi\)
0.973857 + 0.227163i \(0.0729450\pi\)
\(578\) 19.7590 0.821866
\(579\) −26.8927 −1.11762
\(580\) −3.57683 −0.148520
\(581\) −11.9391 −0.495316
\(582\) 16.5971 0.687973
\(583\) 54.0017 2.23652
\(584\) 19.0959 0.790196
\(585\) 0.792574 0.0327689
\(586\) 11.4857 0.474469
\(587\) −22.4244 −0.925552 −0.462776 0.886475i \(-0.653147\pi\)
−0.462776 + 0.886475i \(0.653147\pi\)
\(588\) −0.893970 −0.0368667
\(589\) −2.87369 −0.118408
\(590\) −17.6167 −0.725270
\(591\) 41.5309 1.70835
\(592\) −17.1583 −0.705202
\(593\) 18.9139 0.776700 0.388350 0.921512i \(-0.373045\pi\)
0.388350 + 0.921512i \(0.373045\pi\)
\(594\) −33.6669 −1.38137
\(595\) −0.830757 −0.0340577
\(596\) −0.780126 −0.0319552
\(597\) −2.92801 −0.119835
\(598\) 5.51642 0.225583
\(599\) 27.9809 1.14327 0.571635 0.820508i \(-0.306309\pi\)
0.571635 + 0.820508i \(0.306309\pi\)
\(600\) 5.15206 0.210332
\(601\) −23.5211 −0.959444 −0.479722 0.877420i \(-0.659263\pi\)
−0.479722 + 0.877420i \(0.659263\pi\)
\(602\) −1.98176 −0.0807705
\(603\) 0.460037 0.0187341
\(604\) −5.79395 −0.235752
\(605\) −16.0837 −0.653894
\(606\) −19.1793 −0.779106
\(607\) 24.4743 0.993383 0.496691 0.867927i \(-0.334548\pi\)
0.496691 + 0.867927i \(0.334548\pi\)
\(608\) 21.0448 0.853478
\(609\) 11.2841 0.457256
\(610\) 10.4531 0.423233
\(611\) −25.1087 −1.01579
\(612\) −0.0794754 −0.00321260
\(613\) −28.3221 −1.14392 −0.571959 0.820283i \(-0.693816\pi\)
−0.571959 + 0.820283i \(0.693816\pi\)
\(614\) 17.2597 0.696544
\(615\) −10.6473 −0.429340
\(616\) 15.9657 0.643277
\(617\) 4.95914 0.199647 0.0998237 0.995005i \(-0.468172\pi\)
0.0998237 + 0.995005i \(0.468172\pi\)
\(618\) 1.42353 0.0572629
\(619\) −18.2756 −0.734557 −0.367278 0.930111i \(-0.619710\pi\)
−0.367278 + 0.930111i \(0.619710\pi\)
\(620\) 0.212464 0.00853275
\(621\) 5.51341 0.221245
\(622\) −3.80509 −0.152570
\(623\) 5.80329 0.232504
\(624\) −19.6415 −0.786289
\(625\) 1.00000 0.0400000
\(626\) −35.9776 −1.43795
\(627\) 62.9263 2.51303
\(628\) 2.08048 0.0830204
\(629\) −5.37499 −0.214315
\(630\) 0.217720 0.00867416
\(631\) 37.5771 1.49592 0.747960 0.663744i \(-0.231034\pi\)
0.747960 + 0.663744i \(0.231034\pi\)
\(632\) 24.8493 0.988453
\(633\) −17.6636 −0.702065
\(634\) −31.9822 −1.27017
\(635\) 5.30748 0.210621
\(636\) 9.27633 0.367831
\(637\) 4.41019 0.174738
\(638\) −42.3634 −1.67718
\(639\) −2.79136 −0.110425
\(640\) 4.86970 0.192492
\(641\) 39.1973 1.54820 0.774100 0.633063i \(-0.218203\pi\)
0.774100 + 0.633063i \(0.218203\pi\)
\(642\) 14.4902 0.571884
\(643\) 11.1838 0.441044 0.220522 0.975382i \(-0.429224\pi\)
0.220522 + 0.975382i \(0.429224\pi\)
\(644\) −0.549619 −0.0216580
\(645\) 2.74715 0.108169
\(646\) −7.24638 −0.285105
\(647\) 8.01306 0.315026 0.157513 0.987517i \(-0.449652\pi\)
0.157513 + 0.987517i \(0.449652\pi\)
\(648\) −25.8576 −1.01578
\(649\) 75.6770 2.97058
\(650\) −5.34284 −0.209563
\(651\) −0.670278 −0.0262703
\(652\) −4.77373 −0.186954
\(653\) −31.1546 −1.21917 −0.609586 0.792720i \(-0.708664\pi\)
−0.609586 + 0.792720i \(0.708664\pi\)
\(654\) 11.0843 0.433432
\(655\) −9.34518 −0.365146
\(656\) −16.8137 −0.656464
\(657\) −1.11864 −0.0436422
\(658\) −6.89735 −0.268887
\(659\) −5.48445 −0.213644 −0.106822 0.994278i \(-0.534067\pi\)
−0.106822 + 0.994278i \(0.534067\pi\)
\(660\) −4.65239 −0.181094
\(661\) 40.0157 1.55643 0.778215 0.627998i \(-0.216125\pi\)
0.778215 + 0.627998i \(0.216125\pi\)
\(662\) −21.1158 −0.820690
\(663\) −6.15287 −0.238958
\(664\) 36.6273 1.42141
\(665\) −7.19999 −0.279204
\(666\) 1.40864 0.0545838
\(667\) 6.93757 0.268624
\(668\) −1.93049 −0.0746930
\(669\) 6.82185 0.263748
\(670\) −3.10117 −0.119809
\(671\) −44.9038 −1.73349
\(672\) 4.90861 0.189354
\(673\) −30.4785 −1.17486 −0.587431 0.809274i \(-0.699861\pi\)
−0.587431 + 0.809274i \(0.699861\pi\)
\(674\) −20.0665 −0.772933
\(675\) −5.33992 −0.205534
\(676\) −3.43337 −0.132053
\(677\) 14.6811 0.564241 0.282121 0.959379i \(-0.408962\pi\)
0.282121 + 0.959379i \(0.408962\pi\)
\(678\) 3.21923 0.123634
\(679\) 8.15777 0.313067
\(680\) 2.54864 0.0977359
\(681\) −22.4133 −0.858878
\(682\) 2.51639 0.0963574
\(683\) 13.7959 0.527886 0.263943 0.964538i \(-0.414977\pi\)
0.263943 + 0.964538i \(0.414977\pi\)
\(684\) −0.688796 −0.0263368
\(685\) 12.7964 0.488927
\(686\) 1.21148 0.0462544
\(687\) 1.67937 0.0640720
\(688\) 4.33817 0.165391
\(689\) −45.7626 −1.74342
\(690\) −2.10062 −0.0799691
\(691\) 33.3779 1.26975 0.634877 0.772614i \(-0.281051\pi\)
0.634877 + 0.772614i \(0.281051\pi\)
\(692\) −3.75524 −0.142753
\(693\) −0.935268 −0.0355279
\(694\) −28.2864 −1.07374
\(695\) −1.58170 −0.0599973
\(696\) −34.6181 −1.31219
\(697\) −5.26703 −0.199503
\(698\) −29.3360 −1.11038
\(699\) 25.5439 0.966157
\(700\) 0.532324 0.0201200
\(701\) −5.55442 −0.209787 −0.104894 0.994483i \(-0.533450\pi\)
−0.104894 + 0.994483i \(0.533450\pi\)
\(702\) 28.5303 1.07681
\(703\) −46.5839 −1.75694
\(704\) −46.0310 −1.73486
\(705\) 9.56122 0.360097
\(706\) −7.81393 −0.294081
\(707\) −9.42696 −0.354537
\(708\) 12.9997 0.488559
\(709\) 31.4048 1.17943 0.589717 0.807610i \(-0.299239\pi\)
0.589717 + 0.807610i \(0.299239\pi\)
\(710\) 18.8169 0.706186
\(711\) −1.45567 −0.0545918
\(712\) −17.8036 −0.667219
\(713\) −0.412092 −0.0154330
\(714\) −1.69019 −0.0632538
\(715\) 22.9515 0.858337
\(716\) −1.66706 −0.0623010
\(717\) −21.6406 −0.808184
\(718\) −39.4692 −1.47298
\(719\) −36.5380 −1.36264 −0.681318 0.731987i \(-0.738593\pi\)
−0.681318 + 0.731987i \(0.738593\pi\)
\(720\) −0.476599 −0.0177618
\(721\) 0.699690 0.0260578
\(722\) −39.7847 −1.48063
\(723\) 10.7387 0.399376
\(724\) −11.9481 −0.444048
\(725\) −6.71927 −0.249547
\(726\) −32.7225 −1.21445
\(727\) 31.0389 1.15117 0.575585 0.817742i \(-0.304774\pi\)
0.575585 + 0.817742i \(0.304774\pi\)
\(728\) −13.5298 −0.501448
\(729\) 28.4178 1.05251
\(730\) 7.54088 0.279100
\(731\) 1.35897 0.0502634
\(732\) −7.71351 −0.285099
\(733\) 1.66939 0.0616602 0.0308301 0.999525i \(-0.490185\pi\)
0.0308301 + 0.999525i \(0.490185\pi\)
\(734\) 4.45231 0.164338
\(735\) −1.67937 −0.0619445
\(736\) 3.01785 0.111239
\(737\) 13.3218 0.490716
\(738\) 1.38035 0.0508114
\(739\) −40.7099 −1.49754 −0.748769 0.662831i \(-0.769355\pi\)
−0.748769 + 0.662831i \(0.769355\pi\)
\(740\) 3.44413 0.126609
\(741\) −53.3256 −1.95896
\(742\) −12.5710 −0.461495
\(743\) 2.42226 0.0888639 0.0444320 0.999012i \(-0.485852\pi\)
0.0444320 + 0.999012i \(0.485852\pi\)
\(744\) 2.05631 0.0753881
\(745\) −1.46551 −0.0536921
\(746\) −0.991150 −0.0362886
\(747\) −2.14562 −0.0785042
\(748\) −2.30146 −0.0841498
\(749\) 7.12220 0.260239
\(750\) 2.03452 0.0742901
\(751\) −28.5100 −1.04034 −0.520172 0.854061i \(-0.674132\pi\)
−0.520172 + 0.854061i \(0.674132\pi\)
\(752\) 15.0986 0.550590
\(753\) −15.1800 −0.553189
\(754\) 35.9000 1.30740
\(755\) −10.8842 −0.396118
\(756\) −2.84257 −0.103383
\(757\) 26.2780 0.955089 0.477544 0.878608i \(-0.341527\pi\)
0.477544 + 0.878608i \(0.341527\pi\)
\(758\) −9.52717 −0.346042
\(759\) 9.02372 0.327540
\(760\) 22.0885 0.801234
\(761\) −44.1265 −1.59958 −0.799792 0.600277i \(-0.795057\pi\)
−0.799792 + 0.600277i \(0.795057\pi\)
\(762\) 10.7982 0.391177
\(763\) 5.44814 0.197236
\(764\) 13.5448 0.490035
\(765\) −0.149299 −0.00539791
\(766\) 20.1239 0.727105
\(767\) −64.1310 −2.31563
\(768\) −19.8005 −0.714488
\(769\) 50.7840 1.83132 0.915659 0.401956i \(-0.131670\pi\)
0.915659 + 0.401956i \(0.131670\pi\)
\(770\) 6.30476 0.227208
\(771\) −29.6254 −1.06693
\(772\) 8.52441 0.306800
\(773\) −33.1988 −1.19408 −0.597038 0.802213i \(-0.703656\pi\)
−0.597038 + 0.802213i \(0.703656\pi\)
\(774\) −0.356151 −0.0128016
\(775\) 0.399125 0.0143370
\(776\) −25.0268 −0.898411
\(777\) −10.8655 −0.389798
\(778\) −19.5984 −0.702635
\(779\) −45.6482 −1.63552
\(780\) 3.94258 0.141167
\(781\) −80.8327 −2.89242
\(782\) −1.03914 −0.0371596
\(783\) 35.8803 1.28226
\(784\) −2.65198 −0.0947137
\(785\) 3.90830 0.139493
\(786\) −19.0129 −0.678169
\(787\) −45.7887 −1.63219 −0.816096 0.577916i \(-0.803866\pi\)
−0.816096 + 0.577916i \(0.803866\pi\)
\(788\) −13.1644 −0.468962
\(789\) 30.5250 1.08672
\(790\) 9.81285 0.349126
\(791\) 1.58231 0.0562604
\(792\) 2.86926 0.101955
\(793\) 38.0528 1.35129
\(794\) −1.92569 −0.0683402
\(795\) 17.4261 0.618040
\(796\) 0.928115 0.0328962
\(797\) 19.1935 0.679868 0.339934 0.940449i \(-0.389595\pi\)
0.339934 + 0.940449i \(0.389595\pi\)
\(798\) −14.6485 −0.518552
\(799\) 4.72978 0.167328
\(800\) −2.92289 −0.103340
\(801\) 1.04293 0.0368503
\(802\) −0.945161 −0.0333748
\(803\) −32.3937 −1.14315
\(804\) 2.28840 0.0807058
\(805\) −1.03249 −0.0363905
\(806\) −2.13246 −0.0751127
\(807\) −8.65632 −0.304717
\(808\) 28.9205 1.01742
\(809\) −3.73090 −0.131171 −0.0655857 0.997847i \(-0.520892\pi\)
−0.0655857 + 0.997847i \(0.520892\pi\)
\(810\) −10.2110 −0.358778
\(811\) −50.0738 −1.75833 −0.879165 0.476518i \(-0.841899\pi\)
−0.879165 + 0.476518i \(0.841899\pi\)
\(812\) −3.57683 −0.125522
\(813\) 27.6286 0.968978
\(814\) 40.7917 1.42975
\(815\) −8.96770 −0.314125
\(816\) 3.69991 0.129523
\(817\) 11.7779 0.412057
\(818\) 37.6828 1.31755
\(819\) 0.792574 0.0276948
\(820\) 3.37496 0.117859
\(821\) 41.5748 1.45097 0.725485 0.688238i \(-0.241615\pi\)
0.725485 + 0.688238i \(0.241615\pi\)
\(822\) 26.0346 0.908061
\(823\) −32.8745 −1.14593 −0.572967 0.819578i \(-0.694208\pi\)
−0.572967 + 0.819578i \(0.694208\pi\)
\(824\) −2.14655 −0.0747785
\(825\) −8.73977 −0.304280
\(826\) −17.6167 −0.612965
\(827\) 15.5065 0.539214 0.269607 0.962970i \(-0.413106\pi\)
0.269607 + 0.962970i \(0.413106\pi\)
\(828\) −0.0987743 −0.00343265
\(829\) 43.5863 1.51382 0.756908 0.653522i \(-0.226709\pi\)
0.756908 + 0.653522i \(0.226709\pi\)
\(830\) 14.4639 0.502049
\(831\) 49.6965 1.72395
\(832\) 39.0080 1.35236
\(833\) −0.830757 −0.0287840
\(834\) −3.21800 −0.111430
\(835\) −3.62653 −0.125501
\(836\) −19.9463 −0.689857
\(837\) −2.13129 −0.0736683
\(838\) 14.1750 0.489667
\(839\) −8.93743 −0.308554 −0.154277 0.988028i \(-0.549305\pi\)
−0.154277 + 0.988028i \(0.549305\pi\)
\(840\) 5.15206 0.177763
\(841\) 16.1486 0.556847
\(842\) 37.6151 1.29630
\(843\) 10.8957 0.375267
\(844\) 5.59898 0.192725
\(845\) −6.44977 −0.221879
\(846\) −1.23955 −0.0426167
\(847\) −16.0837 −0.552641
\(848\) 27.5185 0.944988
\(849\) −35.2016 −1.20812
\(850\) 1.00644 0.0345207
\(851\) −6.68019 −0.228994
\(852\) −13.8853 −0.475704
\(853\) −20.3463 −0.696646 −0.348323 0.937375i \(-0.613249\pi\)
−0.348323 + 0.937375i \(0.613249\pi\)
\(854\) 10.4531 0.357697
\(855\) −1.29394 −0.0442518
\(856\) −21.8498 −0.746812
\(857\) −24.2576 −0.828622 −0.414311 0.910135i \(-0.635977\pi\)
−0.414311 + 0.910135i \(0.635977\pi\)
\(858\) 46.6952 1.59415
\(859\) −58.1446 −1.98387 −0.991933 0.126761i \(-0.959542\pi\)
−0.991933 + 0.126761i \(0.959542\pi\)
\(860\) −0.870788 −0.0296936
\(861\) −10.6473 −0.362858
\(862\) −9.02258 −0.307310
\(863\) −12.4828 −0.424920 −0.212460 0.977170i \(-0.568148\pi\)
−0.212460 + 0.977170i \(0.568148\pi\)
\(864\) 15.6080 0.530995
\(865\) −7.05442 −0.239858
\(866\) −22.2684 −0.756711
\(867\) −27.3903 −0.930222
\(868\) 0.212464 0.00721149
\(869\) −42.1535 −1.42996
\(870\) −13.6705 −0.463472
\(871\) −11.2893 −0.382524
\(872\) −16.7141 −0.566010
\(873\) 1.46607 0.0496189
\(874\) −9.00601 −0.304633
\(875\) 1.00000 0.0338062
\(876\) −5.56454 −0.188009
\(877\) 28.4690 0.961330 0.480665 0.876904i \(-0.340395\pi\)
0.480665 + 0.876904i \(0.340395\pi\)
\(878\) −11.6009 −0.391510
\(879\) −15.9217 −0.537025
\(880\) −13.8014 −0.465246
\(881\) 19.1957 0.646719 0.323360 0.946276i \(-0.395188\pi\)
0.323360 + 0.946276i \(0.395188\pi\)
\(882\) 0.217720 0.00733100
\(883\) 2.63445 0.0886561 0.0443281 0.999017i \(-0.485885\pi\)
0.0443281 + 0.999017i \(0.485885\pi\)
\(884\) 1.95033 0.0655966
\(885\) 24.4206 0.820891
\(886\) 13.2637 0.445603
\(887\) −21.7274 −0.729533 −0.364767 0.931099i \(-0.618851\pi\)
−0.364767 + 0.931099i \(0.618851\pi\)
\(888\) 33.3338 1.11861
\(889\) 5.30748 0.178007
\(890\) −7.03055 −0.235665
\(891\) 43.8639 1.46950
\(892\) −2.16238 −0.0724018
\(893\) 40.9920 1.37174
\(894\) −2.98161 −0.0997198
\(895\) −3.13166 −0.104680
\(896\) 4.86970 0.162685
\(897\) −7.64697 −0.255325
\(898\) −32.9952 −1.10106
\(899\) −2.68182 −0.0894439
\(900\) 0.0956662 0.00318887
\(901\) 8.62040 0.287187
\(902\) 39.9725 1.33094
\(903\) 2.74715 0.0914195
\(904\) −4.85428 −0.161451
\(905\) −22.4452 −0.746103
\(906\) −22.1442 −0.735692
\(907\) −24.4192 −0.810826 −0.405413 0.914134i \(-0.632872\pi\)
−0.405413 + 0.914134i \(0.632872\pi\)
\(908\) 7.10452 0.235772
\(909\) −1.69416 −0.0561917
\(910\) −5.34284 −0.177113
\(911\) 33.0116 1.09372 0.546862 0.837223i \(-0.315822\pi\)
0.546862 + 0.837223i \(0.315822\pi\)
\(912\) 32.0663 1.06182
\(913\) −62.1333 −2.05631
\(914\) 0.789321 0.0261084
\(915\) −14.4902 −0.479033
\(916\) −0.532324 −0.0175885
\(917\) −9.34518 −0.308605
\(918\) −5.37432 −0.177379
\(919\) 42.2800 1.39469 0.697344 0.716736i \(-0.254365\pi\)
0.697344 + 0.716736i \(0.254365\pi\)
\(920\) 3.16752 0.104430
\(921\) −23.9257 −0.788378
\(922\) −17.3593 −0.571697
\(923\) 68.5000 2.25471
\(924\) −4.65239 −0.153053
\(925\) 6.46999 0.212732
\(926\) 10.7458 0.353129
\(927\) 0.125744 0.00412998
\(928\) 19.6397 0.644704
\(929\) 7.20203 0.236291 0.118145 0.992996i \(-0.462305\pi\)
0.118145 + 0.992996i \(0.462305\pi\)
\(930\) 0.812026 0.0266274
\(931\) −7.19999 −0.235970
\(932\) −8.09685 −0.265221
\(933\) 5.27469 0.172685
\(934\) −17.9374 −0.586929
\(935\) −4.32342 −0.141391
\(936\) −2.43150 −0.0794760
\(937\) 41.1492 1.34428 0.672142 0.740422i \(-0.265374\pi\)
0.672142 + 0.740422i \(0.265374\pi\)
\(938\) −3.10117 −0.101257
\(939\) 49.8727 1.62754
\(940\) −3.03070 −0.0988506
\(941\) −26.8462 −0.875161 −0.437580 0.899179i \(-0.644164\pi\)
−0.437580 + 0.899179i \(0.644164\pi\)
\(942\) 7.95151 0.259074
\(943\) −6.54602 −0.213168
\(944\) 38.5639 1.25515
\(945\) −5.33992 −0.173708
\(946\) −10.3135 −0.335320
\(947\) −40.7037 −1.32269 −0.661347 0.750080i \(-0.730015\pi\)
−0.661347 + 0.750080i \(0.730015\pi\)
\(948\) −7.24107 −0.235179
\(949\) 27.4514 0.891109
\(950\) 8.72262 0.282999
\(951\) 44.3342 1.43764
\(952\) 2.54864 0.0826019
\(953\) −40.7762 −1.32087 −0.660435 0.750883i \(-0.729628\pi\)
−0.660435 + 0.750883i \(0.729628\pi\)
\(954\) −2.25918 −0.0731437
\(955\) 25.4447 0.823372
\(956\) 6.85961 0.221856
\(957\) 58.7249 1.89831
\(958\) −25.7119 −0.830713
\(959\) 12.7964 0.413219
\(960\) −14.8540 −0.479411
\(961\) −30.8407 −0.994861
\(962\) −34.5681 −1.11452
\(963\) 1.27996 0.0412461
\(964\) −3.40393 −0.109633
\(965\) 16.0136 0.515495
\(966\) −2.10062 −0.0675863
\(967\) 25.7602 0.828393 0.414197 0.910187i \(-0.364063\pi\)
0.414197 + 0.910187i \(0.364063\pi\)
\(968\) 49.3423 1.58592
\(969\) 10.0451 0.322694
\(970\) −9.88295 −0.317322
\(971\) 3.89442 0.124978 0.0624890 0.998046i \(-0.480096\pi\)
0.0624890 + 0.998046i \(0.480096\pi\)
\(972\) −0.992827 −0.0318449
\(973\) −1.58170 −0.0507069
\(974\) −38.5930 −1.23660
\(975\) 7.40634 0.237193
\(976\) −22.8823 −0.732445
\(977\) −41.5162 −1.32822 −0.664111 0.747634i \(-0.731190\pi\)
−0.664111 + 0.747634i \(0.731190\pi\)
\(978\) −18.2450 −0.583409
\(979\) 30.2015 0.965243
\(980\) 0.532324 0.0170045
\(981\) 0.979108 0.0312605
\(982\) 22.6043 0.721333
\(983\) −53.0915 −1.69336 −0.846679 0.532105i \(-0.821401\pi\)
−0.846679 + 0.532105i \(0.821401\pi\)
\(984\) 32.6643 1.04130
\(985\) −24.7300 −0.787965
\(986\) −6.76256 −0.215364
\(987\) 9.56122 0.304337
\(988\) 16.9031 0.537758
\(989\) 1.68897 0.0537061
\(990\) 1.13306 0.0360109
\(991\) −6.81162 −0.216378 −0.108189 0.994130i \(-0.534505\pi\)
−0.108189 + 0.994130i \(0.534505\pi\)
\(992\) −1.16660 −0.0370395
\(993\) 29.2711 0.928891
\(994\) 18.8169 0.596836
\(995\) 1.74351 0.0552731
\(996\) −10.6732 −0.338192
\(997\) 41.2097 1.30512 0.652561 0.757736i \(-0.273694\pi\)
0.652561 + 0.757736i \(0.273694\pi\)
\(998\) 15.3244 0.485086
\(999\) −34.5492 −1.09309
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 \(a_p\))