Properties

Label 8015.2.a.l.1.34
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 1.34
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.179639 q^{2} +1.24714 q^{3} -1.96773 q^{4} -1.00000 q^{5} +0.224036 q^{6} -1.00000 q^{7} -0.712759 q^{8} -1.44463 q^{9} +O(q^{10})\) \(q+0.179639 q^{2} +1.24714 q^{3} -1.96773 q^{4} -1.00000 q^{5} +0.224036 q^{6} -1.00000 q^{7} -0.712759 q^{8} -1.44463 q^{9} -0.179639 q^{10} -4.52267 q^{11} -2.45404 q^{12} -6.55095 q^{13} -0.179639 q^{14} -1.24714 q^{15} +3.80742 q^{16} -4.38185 q^{17} -0.259512 q^{18} -1.34868 q^{19} +1.96773 q^{20} -1.24714 q^{21} -0.812448 q^{22} -2.35145 q^{23} -0.888913 q^{24} +1.00000 q^{25} -1.17681 q^{26} -5.54310 q^{27} +1.96773 q^{28} +1.86073 q^{29} -0.224036 q^{30} -6.41599 q^{31} +2.10948 q^{32} -5.64042 q^{33} -0.787152 q^{34} +1.00000 q^{35} +2.84265 q^{36} +10.5656 q^{37} -0.242276 q^{38} -8.16997 q^{39} +0.712759 q^{40} -0.929475 q^{41} -0.224036 q^{42} -6.66311 q^{43} +8.89939 q^{44} +1.44463 q^{45} -0.422412 q^{46} -12.1671 q^{47} +4.74840 q^{48} +1.00000 q^{49} +0.179639 q^{50} -5.46480 q^{51} +12.8905 q^{52} -8.21751 q^{53} -0.995756 q^{54} +4.52267 q^{55} +0.712759 q^{56} -1.68200 q^{57} +0.334259 q^{58} +4.77445 q^{59} +2.45404 q^{60} -2.51566 q^{61} -1.15256 q^{62} +1.44463 q^{63} -7.23590 q^{64} +6.55095 q^{65} -1.01324 q^{66} -5.21661 q^{67} +8.62230 q^{68} -2.93259 q^{69} +0.179639 q^{70} -11.2022 q^{71} +1.02968 q^{72} +13.1656 q^{73} +1.89799 q^{74} +1.24714 q^{75} +2.65384 q^{76} +4.52267 q^{77} -1.46765 q^{78} -13.0044 q^{79} -3.80742 q^{80} -2.57914 q^{81} -0.166970 q^{82} -1.40063 q^{83} +2.45404 q^{84} +4.38185 q^{85} -1.19695 q^{86} +2.32059 q^{87} +3.22357 q^{88} -14.6845 q^{89} +0.259512 q^{90} +6.55095 q^{91} +4.62701 q^{92} -8.00166 q^{93} -2.18569 q^{94} +1.34868 q^{95} +2.63082 q^{96} +9.91511 q^{97} +0.179639 q^{98} +6.53360 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.179639 0.127024 0.0635120 0.997981i \(-0.479770\pi\)
0.0635120 + 0.997981i \(0.479770\pi\)
\(3\) 1.24714 0.720039 0.360019 0.932945i \(-0.382770\pi\)
0.360019 + 0.932945i \(0.382770\pi\)
\(4\) −1.96773 −0.983865
\(5\) −1.00000 −0.447214
\(6\) 0.224036 0.0914622
\(7\) −1.00000 −0.377964
\(8\) −0.712759 −0.251998
\(9\) −1.44463 −0.481544
\(10\) −0.179639 −0.0568069
\(11\) −4.52267 −1.36364 −0.681818 0.731522i \(-0.738810\pi\)
−0.681818 + 0.731522i \(0.738810\pi\)
\(12\) −2.45404 −0.708421
\(13\) −6.55095 −1.81691 −0.908453 0.417987i \(-0.862736\pi\)
−0.908453 + 0.417987i \(0.862736\pi\)
\(14\) −0.179639 −0.0480106
\(15\) −1.24714 −0.322011
\(16\) 3.80742 0.951855
\(17\) −4.38185 −1.06276 −0.531378 0.847135i \(-0.678326\pi\)
−0.531378 + 0.847135i \(0.678326\pi\)
\(18\) −0.259512 −0.0611677
\(19\) −1.34868 −0.309409 −0.154704 0.987961i \(-0.549442\pi\)
−0.154704 + 0.987961i \(0.549442\pi\)
\(20\) 1.96773 0.439998
\(21\) −1.24714 −0.272149
\(22\) −0.812448 −0.173214
\(23\) −2.35145 −0.490311 −0.245155 0.969484i \(-0.578839\pi\)
−0.245155 + 0.969484i \(0.578839\pi\)
\(24\) −0.888913 −0.181449
\(25\) 1.00000 0.200000
\(26\) −1.17681 −0.230791
\(27\) −5.54310 −1.06677
\(28\) 1.96773 0.371866
\(29\) 1.86073 0.345528 0.172764 0.984963i \(-0.444730\pi\)
0.172764 + 0.984963i \(0.444730\pi\)
\(30\) −0.224036 −0.0409031
\(31\) −6.41599 −1.15235 −0.576173 0.817328i \(-0.695454\pi\)
−0.576173 + 0.817328i \(0.695454\pi\)
\(32\) 2.10948 0.372907
\(33\) −5.64042 −0.981870
\(34\) −0.787152 −0.134995
\(35\) 1.00000 0.169031
\(36\) 2.84265 0.473775
\(37\) 10.5656 1.73697 0.868485 0.495715i \(-0.165094\pi\)
0.868485 + 0.495715i \(0.165094\pi\)
\(38\) −0.242276 −0.0393023
\(39\) −8.16997 −1.30824
\(40\) 0.712759 0.112697
\(41\) −0.929475 −0.145160 −0.0725798 0.997363i \(-0.523123\pi\)
−0.0725798 + 0.997363i \(0.523123\pi\)
\(42\) −0.224036 −0.0345695
\(43\) −6.66311 −1.01611 −0.508057 0.861323i \(-0.669636\pi\)
−0.508057 + 0.861323i \(0.669636\pi\)
\(44\) 8.89939 1.34163
\(45\) 1.44463 0.215353
\(46\) −0.422412 −0.0622812
\(47\) −12.1671 −1.77476 −0.887379 0.461040i \(-0.847476\pi\)
−0.887379 + 0.461040i \(0.847476\pi\)
\(48\) 4.74840 0.685372
\(49\) 1.00000 0.142857
\(50\) 0.179639 0.0254048
\(51\) −5.46480 −0.765225
\(52\) 12.8905 1.78759
\(53\) −8.21751 −1.12876 −0.564381 0.825514i \(-0.690885\pi\)
−0.564381 + 0.825514i \(0.690885\pi\)
\(54\) −0.995756 −0.135505
\(55\) 4.52267 0.609836
\(56\) 0.712759 0.0952465
\(57\) −1.68200 −0.222786
\(58\) 0.334259 0.0438904
\(59\) 4.77445 0.621580 0.310790 0.950479i \(-0.399406\pi\)
0.310790 + 0.950479i \(0.399406\pi\)
\(60\) 2.45404 0.316815
\(61\) −2.51566 −0.322097 −0.161049 0.986946i \(-0.551488\pi\)
−0.161049 + 0.986946i \(0.551488\pi\)
\(62\) −1.15256 −0.146375
\(63\) 1.44463 0.182007
\(64\) −7.23590 −0.904487
\(65\) 6.55095 0.812545
\(66\) −1.01324 −0.124721
\(67\) −5.21661 −0.637310 −0.318655 0.947871i \(-0.603231\pi\)
−0.318655 + 0.947871i \(0.603231\pi\)
\(68\) 8.62230 1.04561
\(69\) −2.93259 −0.353043
\(70\) 0.179639 0.0214710
\(71\) −11.2022 −1.32946 −0.664731 0.747083i \(-0.731454\pi\)
−0.664731 + 0.747083i \(0.731454\pi\)
\(72\) 1.02968 0.121348
\(73\) 13.1656 1.54092 0.770461 0.637487i \(-0.220026\pi\)
0.770461 + 0.637487i \(0.220026\pi\)
\(74\) 1.89799 0.220637
\(75\) 1.24714 0.144008
\(76\) 2.65384 0.304416
\(77\) 4.52267 0.515406
\(78\) −1.46765 −0.166178
\(79\) −13.0044 −1.46311 −0.731553 0.681784i \(-0.761204\pi\)
−0.731553 + 0.681784i \(0.761204\pi\)
\(80\) −3.80742 −0.425683
\(81\) −2.57914 −0.286571
\(82\) −0.166970 −0.0184388
\(83\) −1.40063 −0.153739 −0.0768696 0.997041i \(-0.524493\pi\)
−0.0768696 + 0.997041i \(0.524493\pi\)
\(84\) 2.45404 0.267758
\(85\) 4.38185 0.475279
\(86\) −1.19695 −0.129071
\(87\) 2.32059 0.248794
\(88\) 3.22357 0.343634
\(89\) −14.6845 −1.55655 −0.778277 0.627921i \(-0.783906\pi\)
−0.778277 + 0.627921i \(0.783906\pi\)
\(90\) 0.259512 0.0273550
\(91\) 6.55095 0.686726
\(92\) 4.62701 0.482400
\(93\) −8.00166 −0.829733
\(94\) −2.18569 −0.225437
\(95\) 1.34868 0.138372
\(96\) 2.63082 0.268507
\(97\) 9.91511 1.00673 0.503364 0.864075i \(-0.332096\pi\)
0.503364 + 0.864075i \(0.332096\pi\)
\(98\) 0.179639 0.0181463
\(99\) 6.53360 0.656651
\(100\) −1.96773 −0.196773
\(101\) 13.0207 1.29561 0.647803 0.761808i \(-0.275688\pi\)
0.647803 + 0.761808i \(0.275688\pi\)
\(102\) −0.981692 −0.0972019
\(103\) 10.9863 1.08251 0.541255 0.840858i \(-0.317949\pi\)
0.541255 + 0.840858i \(0.317949\pi\)
\(104\) 4.66925 0.457858
\(105\) 1.24714 0.121709
\(106\) −1.47619 −0.143380
\(107\) 2.31493 0.223793 0.111896 0.993720i \(-0.464308\pi\)
0.111896 + 0.993720i \(0.464308\pi\)
\(108\) 10.9073 1.04956
\(109\) 16.4402 1.57469 0.787344 0.616515i \(-0.211456\pi\)
0.787344 + 0.616515i \(0.211456\pi\)
\(110\) 0.812448 0.0774639
\(111\) 13.1768 1.25069
\(112\) −3.80742 −0.359767
\(113\) −4.32759 −0.407105 −0.203553 0.979064i \(-0.565249\pi\)
−0.203553 + 0.979064i \(0.565249\pi\)
\(114\) −0.302153 −0.0282992
\(115\) 2.35145 0.219274
\(116\) −3.66141 −0.339953
\(117\) 9.46372 0.874921
\(118\) 0.857677 0.0789555
\(119\) 4.38185 0.401684
\(120\) 0.888913 0.0811463
\(121\) 9.45453 0.859502
\(122\) −0.451910 −0.0409140
\(123\) −1.15919 −0.104521
\(124\) 12.6249 1.13375
\(125\) −1.00000 −0.0894427
\(126\) 0.259512 0.0231192
\(127\) −13.6204 −1.20862 −0.604308 0.796751i \(-0.706550\pi\)
−0.604308 + 0.796751i \(0.706550\pi\)
\(128\) −5.51881 −0.487798
\(129\) −8.30985 −0.731642
\(130\) 1.17681 0.103213
\(131\) 6.73229 0.588203 0.294102 0.955774i \(-0.404980\pi\)
0.294102 + 0.955774i \(0.404980\pi\)
\(132\) 11.0988 0.966028
\(133\) 1.34868 0.116945
\(134\) −0.937107 −0.0809537
\(135\) 5.54310 0.477074
\(136\) 3.12321 0.267813
\(137\) −2.22633 −0.190208 −0.0951041 0.995467i \(-0.530318\pi\)
−0.0951041 + 0.995467i \(0.530318\pi\)
\(138\) −0.526808 −0.0448449
\(139\) −5.23703 −0.444199 −0.222100 0.975024i \(-0.571291\pi\)
−0.222100 + 0.975024i \(0.571291\pi\)
\(140\) −1.96773 −0.166304
\(141\) −15.1742 −1.27789
\(142\) −2.01236 −0.168874
\(143\) 29.6278 2.47760
\(144\) −5.50032 −0.458360
\(145\) −1.86073 −0.154525
\(146\) 2.36506 0.195734
\(147\) 1.24714 0.102863
\(148\) −20.7902 −1.70894
\(149\) 1.88046 0.154053 0.0770266 0.997029i \(-0.475457\pi\)
0.0770266 + 0.997029i \(0.475457\pi\)
\(150\) 0.224036 0.0182924
\(151\) −22.0938 −1.79797 −0.898986 0.437978i \(-0.855695\pi\)
−0.898986 + 0.437978i \(0.855695\pi\)
\(152\) 0.961285 0.0779705
\(153\) 6.33017 0.511764
\(154\) 0.812448 0.0654689
\(155\) 6.41599 0.515344
\(156\) 16.0763 1.28713
\(157\) 11.4740 0.915725 0.457862 0.889023i \(-0.348615\pi\)
0.457862 + 0.889023i \(0.348615\pi\)
\(158\) −2.33609 −0.185850
\(159\) −10.2484 −0.812752
\(160\) −2.10948 −0.166769
\(161\) 2.35145 0.185320
\(162\) −0.463314 −0.0364014
\(163\) −7.46119 −0.584406 −0.292203 0.956356i \(-0.594388\pi\)
−0.292203 + 0.956356i \(0.594388\pi\)
\(164\) 1.82896 0.142817
\(165\) 5.64042 0.439106
\(166\) −0.251608 −0.0195286
\(167\) −8.88878 −0.687834 −0.343917 0.939000i \(-0.611754\pi\)
−0.343917 + 0.939000i \(0.611754\pi\)
\(168\) 0.888913 0.0685811
\(169\) 29.9149 2.30115
\(170\) 0.787152 0.0603718
\(171\) 1.94835 0.148994
\(172\) 13.1112 0.999720
\(173\) 12.0386 0.915279 0.457640 0.889138i \(-0.348695\pi\)
0.457640 + 0.889138i \(0.348695\pi\)
\(174\) 0.416869 0.0316028
\(175\) −1.00000 −0.0755929
\(176\) −17.2197 −1.29798
\(177\) 5.95442 0.447561
\(178\) −2.63791 −0.197720
\(179\) 0.847211 0.0633235 0.0316618 0.999499i \(-0.489920\pi\)
0.0316618 + 0.999499i \(0.489920\pi\)
\(180\) −2.84265 −0.211878
\(181\) −21.0682 −1.56599 −0.782995 0.622029i \(-0.786309\pi\)
−0.782995 + 0.622029i \(0.786309\pi\)
\(182\) 1.17681 0.0872307
\(183\) −3.13739 −0.231922
\(184\) 1.67602 0.123558
\(185\) −10.5656 −0.776797
\(186\) −1.43741 −0.105396
\(187\) 19.8177 1.44921
\(188\) 23.9416 1.74612
\(189\) 5.54310 0.403201
\(190\) 0.242276 0.0175765
\(191\) −19.2876 −1.39560 −0.697801 0.716291i \(-0.745838\pi\)
−0.697801 + 0.716291i \(0.745838\pi\)
\(192\) −9.02420 −0.651266
\(193\) 20.3865 1.46745 0.733725 0.679446i \(-0.237780\pi\)
0.733725 + 0.679446i \(0.237780\pi\)
\(194\) 1.78114 0.127878
\(195\) 8.16997 0.585064
\(196\) −1.96773 −0.140552
\(197\) 14.7013 1.04743 0.523714 0.851894i \(-0.324546\pi\)
0.523714 + 0.851894i \(0.324546\pi\)
\(198\) 1.17369 0.0834104
\(199\) 25.3833 1.79937 0.899686 0.436538i \(-0.143796\pi\)
0.899686 + 0.436538i \(0.143796\pi\)
\(200\) −0.712759 −0.0503997
\(201\) −6.50586 −0.458888
\(202\) 2.33902 0.164573
\(203\) −1.86073 −0.130597
\(204\) 10.7533 0.752878
\(205\) 0.929475 0.0649174
\(206\) 1.97356 0.137505
\(207\) 3.39698 0.236106
\(208\) −24.9422 −1.72943
\(209\) 6.09964 0.421921
\(210\) 0.224036 0.0154599
\(211\) −18.6649 −1.28494 −0.642471 0.766310i \(-0.722091\pi\)
−0.642471 + 0.766310i \(0.722091\pi\)
\(212\) 16.1698 1.11055
\(213\) −13.9708 −0.957264
\(214\) 0.415852 0.0284270
\(215\) 6.66311 0.454420
\(216\) 3.95089 0.268824
\(217\) 6.41599 0.435546
\(218\) 2.95330 0.200023
\(219\) 16.4194 1.10952
\(220\) −8.89939 −0.599997
\(221\) 28.7053 1.93093
\(222\) 2.36707 0.158867
\(223\) −0.601140 −0.0402553 −0.0201277 0.999797i \(-0.506407\pi\)
−0.0201277 + 0.999797i \(0.506407\pi\)
\(224\) −2.10948 −0.140946
\(225\) −1.44463 −0.0963089
\(226\) −0.777403 −0.0517121
\(227\) −16.2970 −1.08167 −0.540836 0.841128i \(-0.681892\pi\)
−0.540836 + 0.841128i \(0.681892\pi\)
\(228\) 3.30972 0.219192
\(229\) 1.00000 0.0660819
\(230\) 0.422412 0.0278530
\(231\) 5.64042 0.371112
\(232\) −1.32625 −0.0870726
\(233\) 10.7761 0.705963 0.352982 0.935630i \(-0.385168\pi\)
0.352982 + 0.935630i \(0.385168\pi\)
\(234\) 1.70005 0.111136
\(235\) 12.1671 0.793696
\(236\) −9.39482 −0.611551
\(237\) −16.2183 −1.05349
\(238\) 0.787152 0.0510235
\(239\) 20.9865 1.35750 0.678751 0.734369i \(-0.262522\pi\)
0.678751 + 0.734369i \(0.262522\pi\)
\(240\) −4.74840 −0.306508
\(241\) 5.50538 0.354633 0.177316 0.984154i \(-0.443258\pi\)
0.177316 + 0.984154i \(0.443258\pi\)
\(242\) 1.69840 0.109177
\(243\) 13.4127 0.860427
\(244\) 4.95014 0.316900
\(245\) −1.00000 −0.0638877
\(246\) −0.208236 −0.0132766
\(247\) 8.83514 0.562167
\(248\) 4.57305 0.290389
\(249\) −1.74679 −0.110698
\(250\) −0.179639 −0.0113614
\(251\) 25.2007 1.59066 0.795328 0.606180i \(-0.207299\pi\)
0.795328 + 0.606180i \(0.207299\pi\)
\(252\) −2.84265 −0.179070
\(253\) 10.6348 0.668605
\(254\) −2.44676 −0.153523
\(255\) 5.46480 0.342219
\(256\) 13.4804 0.842525
\(257\) −4.84465 −0.302201 −0.151100 0.988518i \(-0.548282\pi\)
−0.151100 + 0.988518i \(0.548282\pi\)
\(258\) −1.49277 −0.0929361
\(259\) −10.5656 −0.656513
\(260\) −12.8905 −0.799435
\(261\) −2.68807 −0.166387
\(262\) 1.20938 0.0747159
\(263\) −8.46459 −0.521949 −0.260974 0.965346i \(-0.584044\pi\)
−0.260974 + 0.965346i \(0.584044\pi\)
\(264\) 4.02026 0.247430
\(265\) 8.21751 0.504798
\(266\) 0.242276 0.0148549
\(267\) −18.3137 −1.12078
\(268\) 10.2649 0.627027
\(269\) −25.5176 −1.55584 −0.777918 0.628366i \(-0.783724\pi\)
−0.777918 + 0.628366i \(0.783724\pi\)
\(270\) 0.995756 0.0605998
\(271\) −30.6200 −1.86003 −0.930017 0.367515i \(-0.880209\pi\)
−0.930017 + 0.367515i \(0.880209\pi\)
\(272\) −16.6836 −1.01159
\(273\) 8.16997 0.494469
\(274\) −0.399936 −0.0241610
\(275\) −4.52267 −0.272727
\(276\) 5.77055 0.347346
\(277\) 1.56193 0.0938476 0.0469238 0.998898i \(-0.485058\pi\)
0.0469238 + 0.998898i \(0.485058\pi\)
\(278\) −0.940775 −0.0564239
\(279\) 9.26875 0.554905
\(280\) −0.712759 −0.0425955
\(281\) −21.3378 −1.27290 −0.636452 0.771316i \(-0.719599\pi\)
−0.636452 + 0.771316i \(0.719599\pi\)
\(282\) −2.72587 −0.162323
\(283\) −15.3388 −0.911796 −0.455898 0.890032i \(-0.650682\pi\)
−0.455898 + 0.890032i \(0.650682\pi\)
\(284\) 22.0430 1.30801
\(285\) 1.68200 0.0996330
\(286\) 5.32230 0.314714
\(287\) 0.929475 0.0548652
\(288\) −3.04742 −0.179571
\(289\) 2.20064 0.129450
\(290\) −0.334259 −0.0196284
\(291\) 12.3656 0.724882
\(292\) −25.9064 −1.51606
\(293\) −12.3702 −0.722675 −0.361338 0.932435i \(-0.617680\pi\)
−0.361338 + 0.932435i \(0.617680\pi\)
\(294\) 0.224036 0.0130660
\(295\) −4.77445 −0.277979
\(296\) −7.53071 −0.437714
\(297\) 25.0696 1.45468
\(298\) 0.337804 0.0195685
\(299\) 15.4042 0.890849
\(300\) −2.45404 −0.141684
\(301\) 6.66311 0.384055
\(302\) −3.96892 −0.228385
\(303\) 16.2387 0.932886
\(304\) −5.13500 −0.294512
\(305\) 2.51566 0.144046
\(306\) 1.13715 0.0650063
\(307\) −20.7965 −1.18692 −0.593458 0.804865i \(-0.702238\pi\)
−0.593458 + 0.804865i \(0.702238\pi\)
\(308\) −8.89939 −0.507090
\(309\) 13.7015 0.779449
\(310\) 1.15256 0.0654611
\(311\) −15.9982 −0.907175 −0.453588 0.891212i \(-0.649856\pi\)
−0.453588 + 0.891212i \(0.649856\pi\)
\(312\) 5.82322 0.329675
\(313\) −26.3238 −1.48791 −0.743955 0.668230i \(-0.767052\pi\)
−0.743955 + 0.668230i \(0.767052\pi\)
\(314\) 2.06118 0.116319
\(315\) −1.44463 −0.0813958
\(316\) 25.5891 1.43950
\(317\) −23.2142 −1.30384 −0.651920 0.758288i \(-0.726036\pi\)
−0.651920 + 0.758288i \(0.726036\pi\)
\(318\) −1.84102 −0.103239
\(319\) −8.41545 −0.471175
\(320\) 7.23590 0.404499
\(321\) 2.88705 0.161139
\(322\) 0.422412 0.0235401
\(323\) 5.90972 0.328826
\(324\) 5.07504 0.281947
\(325\) −6.55095 −0.363381
\(326\) −1.34032 −0.0742336
\(327\) 20.5033 1.13384
\(328\) 0.662492 0.0365800
\(329\) 12.1671 0.670796
\(330\) 1.01324 0.0557770
\(331\) −24.9895 −1.37355 −0.686773 0.726872i \(-0.740973\pi\)
−0.686773 + 0.726872i \(0.740973\pi\)
\(332\) 2.75606 0.151259
\(333\) −15.2634 −0.836428
\(334\) −1.59677 −0.0873715
\(335\) 5.21661 0.285014
\(336\) −4.74840 −0.259046
\(337\) 16.8202 0.916254 0.458127 0.888887i \(-0.348520\pi\)
0.458127 + 0.888887i \(0.348520\pi\)
\(338\) 5.37389 0.292301
\(339\) −5.39712 −0.293131
\(340\) −8.62230 −0.467610
\(341\) 29.0174 1.57138
\(342\) 0.350000 0.0189258
\(343\) −1.00000 −0.0539949
\(344\) 4.74919 0.256059
\(345\) 2.93259 0.157886
\(346\) 2.16261 0.116262
\(347\) −1.98583 −0.106605 −0.0533025 0.998578i \(-0.516975\pi\)
−0.0533025 + 0.998578i \(0.516975\pi\)
\(348\) −4.56630 −0.244779
\(349\) 32.1604 1.72151 0.860753 0.509023i \(-0.169993\pi\)
0.860753 + 0.509023i \(0.169993\pi\)
\(350\) −0.179639 −0.00960211
\(351\) 36.3125 1.93822
\(352\) −9.54048 −0.508509
\(353\) −26.4549 −1.40805 −0.704026 0.710174i \(-0.748616\pi\)
−0.704026 + 0.710174i \(0.748616\pi\)
\(354\) 1.06965 0.0568510
\(355\) 11.2022 0.594554
\(356\) 28.8951 1.53144
\(357\) 5.46480 0.289228
\(358\) 0.152192 0.00804361
\(359\) −13.4400 −0.709335 −0.354668 0.934992i \(-0.615406\pi\)
−0.354668 + 0.934992i \(0.615406\pi\)
\(360\) −1.02968 −0.0542687
\(361\) −17.1811 −0.904266
\(362\) −3.78468 −0.198918
\(363\) 11.7912 0.618875
\(364\) −12.8905 −0.675646
\(365\) −13.1656 −0.689121
\(366\) −0.563597 −0.0294597
\(367\) 26.2727 1.37143 0.685713 0.727872i \(-0.259491\pi\)
0.685713 + 0.727872i \(0.259491\pi\)
\(368\) −8.95295 −0.466705
\(369\) 1.34275 0.0699008
\(370\) −1.89799 −0.0986718
\(371\) 8.21751 0.426632
\(372\) 15.7451 0.816345
\(373\) 25.2499 1.30739 0.653695 0.756758i \(-0.273218\pi\)
0.653695 + 0.756758i \(0.273218\pi\)
\(374\) 3.56003 0.184085
\(375\) −1.24714 −0.0644022
\(376\) 8.67223 0.447236
\(377\) −12.1895 −0.627793
\(378\) 0.995756 0.0512162
\(379\) −5.54649 −0.284904 −0.142452 0.989802i \(-0.545499\pi\)
−0.142452 + 0.989802i \(0.545499\pi\)
\(380\) −2.65384 −0.136139
\(381\) −16.9866 −0.870250
\(382\) −3.46481 −0.177275
\(383\) −28.6395 −1.46341 −0.731706 0.681620i \(-0.761276\pi\)
−0.731706 + 0.681620i \(0.761276\pi\)
\(384\) −6.88275 −0.351234
\(385\) −4.52267 −0.230497
\(386\) 3.66221 0.186401
\(387\) 9.62575 0.489304
\(388\) −19.5103 −0.990483
\(389\) −18.9748 −0.962061 −0.481031 0.876704i \(-0.659737\pi\)
−0.481031 + 0.876704i \(0.659737\pi\)
\(390\) 1.46765 0.0743172
\(391\) 10.3037 0.521081
\(392\) −0.712759 −0.0359998
\(393\) 8.39614 0.423529
\(394\) 2.64094 0.133048
\(395\) 13.0044 0.654321
\(396\) −12.8564 −0.646056
\(397\) 6.32624 0.317505 0.158753 0.987318i \(-0.449253\pi\)
0.158753 + 0.987318i \(0.449253\pi\)
\(398\) 4.55982 0.228563
\(399\) 1.68200 0.0842053
\(400\) 3.80742 0.190371
\(401\) 23.6958 1.18331 0.591655 0.806191i \(-0.298475\pi\)
0.591655 + 0.806191i \(0.298475\pi\)
\(402\) −1.16871 −0.0582898
\(403\) 42.0308 2.09370
\(404\) −25.6212 −1.27470
\(405\) 2.57914 0.128158
\(406\) −0.334259 −0.0165890
\(407\) −47.7846 −2.36859
\(408\) 3.89509 0.192836
\(409\) 10.5100 0.519684 0.259842 0.965651i \(-0.416329\pi\)
0.259842 + 0.965651i \(0.416329\pi\)
\(410\) 0.166970 0.00824606
\(411\) −2.77655 −0.136957
\(412\) −21.6180 −1.06504
\(413\) −4.77445 −0.234935
\(414\) 0.610230 0.0299912
\(415\) 1.40063 0.0687543
\(416\) −13.8191 −0.677537
\(417\) −6.53133 −0.319841
\(418\) 1.09573 0.0535940
\(419\) 38.2278 1.86755 0.933774 0.357863i \(-0.116495\pi\)
0.933774 + 0.357863i \(0.116495\pi\)
\(420\) −2.45404 −0.119745
\(421\) −4.05223 −0.197494 −0.0987468 0.995113i \(-0.531483\pi\)
−0.0987468 + 0.995113i \(0.531483\pi\)
\(422\) −3.35294 −0.163219
\(423\) 17.5770 0.854625
\(424\) 5.85711 0.284446
\(425\) −4.38185 −0.212551
\(426\) −2.50970 −0.121596
\(427\) 2.51566 0.121741
\(428\) −4.55515 −0.220182
\(429\) 36.9501 1.78397
\(430\) 1.19695 0.0577223
\(431\) −7.34112 −0.353609 −0.176805 0.984246i \(-0.556576\pi\)
−0.176805 + 0.984246i \(0.556576\pi\)
\(432\) −21.1049 −1.01541
\(433\) −25.1686 −1.20953 −0.604763 0.796405i \(-0.706732\pi\)
−0.604763 + 0.796405i \(0.706732\pi\)
\(434\) 1.15256 0.0553247
\(435\) −2.32059 −0.111264
\(436\) −32.3499 −1.54928
\(437\) 3.17135 0.151706
\(438\) 2.94957 0.140936
\(439\) −4.54952 −0.217137 −0.108568 0.994089i \(-0.534627\pi\)
−0.108568 + 0.994089i \(0.534627\pi\)
\(440\) −3.22357 −0.153678
\(441\) −1.44463 −0.0687920
\(442\) 5.15659 0.245274
\(443\) 3.54927 0.168631 0.0843154 0.996439i \(-0.473130\pi\)
0.0843154 + 0.996439i \(0.473130\pi\)
\(444\) −25.9284 −1.23051
\(445\) 14.6845 0.696112
\(446\) −0.107988 −0.00511339
\(447\) 2.34520 0.110924
\(448\) 7.23590 0.341864
\(449\) −3.27848 −0.154721 −0.0773605 0.997003i \(-0.524649\pi\)
−0.0773605 + 0.997003i \(0.524649\pi\)
\(450\) −0.259512 −0.0122335
\(451\) 4.20371 0.197945
\(452\) 8.51552 0.400536
\(453\) −27.5542 −1.29461
\(454\) −2.92758 −0.137398
\(455\) −6.55095 −0.307113
\(456\) 1.19886 0.0561418
\(457\) 14.6993 0.687604 0.343802 0.939042i \(-0.388285\pi\)
0.343802 + 0.939042i \(0.388285\pi\)
\(458\) 0.179639 0.00839398
\(459\) 24.2890 1.13372
\(460\) −4.62701 −0.215736
\(461\) 24.8659 1.15812 0.579061 0.815284i \(-0.303419\pi\)
0.579061 + 0.815284i \(0.303419\pi\)
\(462\) 1.01324 0.0471401
\(463\) −7.62940 −0.354568 −0.177284 0.984160i \(-0.556731\pi\)
−0.177284 + 0.984160i \(0.556731\pi\)
\(464\) 7.08457 0.328893
\(465\) 8.00166 0.371068
\(466\) 1.93580 0.0896743
\(467\) −19.5235 −0.903441 −0.451720 0.892160i \(-0.649190\pi\)
−0.451720 + 0.892160i \(0.649190\pi\)
\(468\) −18.6220 −0.860804
\(469\) 5.21661 0.240881
\(470\) 2.18569 0.100818
\(471\) 14.3097 0.659357
\(472\) −3.40303 −0.156637
\(473\) 30.1350 1.38561
\(474\) −2.91344 −0.133819
\(475\) −1.34868 −0.0618817
\(476\) −8.62230 −0.395203
\(477\) 11.8713 0.543549
\(478\) 3.76999 0.172435
\(479\) −3.87223 −0.176927 −0.0884635 0.996079i \(-0.528196\pi\)
−0.0884635 + 0.996079i \(0.528196\pi\)
\(480\) −2.63082 −0.120080
\(481\) −69.2146 −3.15591
\(482\) 0.988982 0.0450469
\(483\) 2.93259 0.133438
\(484\) −18.6040 −0.845634
\(485\) −9.91511 −0.450222
\(486\) 2.40945 0.109295
\(487\) −4.29980 −0.194843 −0.0974213 0.995243i \(-0.531059\pi\)
−0.0974213 + 0.995243i \(0.531059\pi\)
\(488\) 1.79306 0.0811679
\(489\) −9.30518 −0.420795
\(490\) −0.179639 −0.00811526
\(491\) −10.4678 −0.472404 −0.236202 0.971704i \(-0.575903\pi\)
−0.236202 + 0.971704i \(0.575903\pi\)
\(492\) 2.28097 0.102834
\(493\) −8.15343 −0.367212
\(494\) 1.58714 0.0714086
\(495\) −6.53360 −0.293663
\(496\) −24.4284 −1.09687
\(497\) 11.2022 0.502490
\(498\) −0.313791 −0.0140613
\(499\) 21.3619 0.956289 0.478144 0.878281i \(-0.341310\pi\)
0.478144 + 0.878281i \(0.341310\pi\)
\(500\) 1.96773 0.0879996
\(501\) −11.0856 −0.495267
\(502\) 4.52703 0.202051
\(503\) 21.6048 0.963310 0.481655 0.876361i \(-0.340036\pi\)
0.481655 + 0.876361i \(0.340036\pi\)
\(504\) −1.02968 −0.0458654
\(505\) −13.0207 −0.579413
\(506\) 1.91043 0.0849289
\(507\) 37.3082 1.65692
\(508\) 26.8013 1.18911
\(509\) 21.1871 0.939103 0.469551 0.882905i \(-0.344416\pi\)
0.469551 + 0.882905i \(0.344416\pi\)
\(510\) 0.981692 0.0434700
\(511\) −13.1656 −0.582414
\(512\) 13.4592 0.594819
\(513\) 7.47587 0.330068
\(514\) −0.870288 −0.0383867
\(515\) −10.9863 −0.484113
\(516\) 16.3515 0.719837
\(517\) 55.0279 2.42012
\(518\) −1.89799 −0.0833929
\(519\) 15.0139 0.659036
\(520\) −4.66925 −0.204760
\(521\) 6.02350 0.263894 0.131947 0.991257i \(-0.457877\pi\)
0.131947 + 0.991257i \(0.457877\pi\)
\(522\) −0.482882 −0.0211352
\(523\) −8.36604 −0.365821 −0.182911 0.983130i \(-0.558552\pi\)
−0.182911 + 0.983130i \(0.558552\pi\)
\(524\) −13.2473 −0.578712
\(525\) −1.24714 −0.0544298
\(526\) −1.52057 −0.0663000
\(527\) 28.1139 1.22466
\(528\) −21.4754 −0.934598
\(529\) −17.4707 −0.759595
\(530\) 1.47619 0.0641214
\(531\) −6.89732 −0.299318
\(532\) −2.65384 −0.115059
\(533\) 6.08895 0.263741
\(534\) −3.28985 −0.142366
\(535\) −2.31493 −0.100083
\(536\) 3.71819 0.160601
\(537\) 1.05659 0.0455954
\(538\) −4.58396 −0.197628
\(539\) −4.52267 −0.194805
\(540\) −10.9073 −0.469376
\(541\) 9.68052 0.416198 0.208099 0.978108i \(-0.433272\pi\)
0.208099 + 0.978108i \(0.433272\pi\)
\(542\) −5.50055 −0.236269
\(543\) −26.2751 −1.12757
\(544\) −9.24343 −0.396309
\(545\) −16.4402 −0.704221
\(546\) 1.46765 0.0628095
\(547\) 8.40350 0.359308 0.179654 0.983730i \(-0.442502\pi\)
0.179654 + 0.983730i \(0.442502\pi\)
\(548\) 4.38081 0.187139
\(549\) 3.63420 0.155104
\(550\) −0.812448 −0.0346429
\(551\) −2.50953 −0.106909
\(552\) 2.09023 0.0889662
\(553\) 13.0044 0.553002
\(554\) 0.280584 0.0119209
\(555\) −13.1768 −0.559324
\(556\) 10.3051 0.437032
\(557\) 6.36153 0.269547 0.134773 0.990876i \(-0.456969\pi\)
0.134773 + 0.990876i \(0.456969\pi\)
\(558\) 1.66503 0.0704863
\(559\) 43.6497 1.84619
\(560\) 3.80742 0.160893
\(561\) 24.7155 1.04349
\(562\) −3.83309 −0.161689
\(563\) 4.37192 0.184255 0.0921273 0.995747i \(-0.470633\pi\)
0.0921273 + 0.995747i \(0.470633\pi\)
\(564\) 29.8586 1.25728
\(565\) 4.32759 0.182063
\(566\) −2.75544 −0.115820
\(567\) 2.57914 0.108314
\(568\) 7.98451 0.335022
\(569\) −5.74704 −0.240928 −0.120464 0.992718i \(-0.538438\pi\)
−0.120464 + 0.992718i \(0.538438\pi\)
\(570\) 0.302153 0.0126558
\(571\) −17.2480 −0.721806 −0.360903 0.932603i \(-0.617532\pi\)
−0.360903 + 0.932603i \(0.617532\pi\)
\(572\) −58.2994 −2.43762
\(573\) −24.0544 −1.00489
\(574\) 0.166970 0.00696920
\(575\) −2.35145 −0.0980622
\(576\) 10.4532 0.435551
\(577\) −9.18311 −0.382298 −0.191149 0.981561i \(-0.561221\pi\)
−0.191149 + 0.981561i \(0.561221\pi\)
\(578\) 0.395321 0.0164432
\(579\) 25.4249 1.05662
\(580\) 3.66141 0.152032
\(581\) 1.40063 0.0581080
\(582\) 2.22134 0.0920774
\(583\) 37.1651 1.53922
\(584\) −9.38393 −0.388310
\(585\) −9.46372 −0.391277
\(586\) −2.22217 −0.0917971
\(587\) 2.68149 0.110677 0.0553385 0.998468i \(-0.482376\pi\)
0.0553385 + 0.998468i \(0.482376\pi\)
\(588\) −2.45404 −0.101203
\(589\) 8.65312 0.356546
\(590\) −0.857677 −0.0353100
\(591\) 18.3347 0.754188
\(592\) 40.2276 1.65334
\(593\) −22.1550 −0.909798 −0.454899 0.890543i \(-0.650325\pi\)
−0.454899 + 0.890543i \(0.650325\pi\)
\(594\) 4.50348 0.184780
\(595\) −4.38185 −0.179638
\(596\) −3.70024 −0.151568
\(597\) 31.6566 1.29562
\(598\) 2.76720 0.113159
\(599\) −19.1492 −0.782414 −0.391207 0.920303i \(-0.627942\pi\)
−0.391207 + 0.920303i \(0.627942\pi\)
\(600\) −0.888913 −0.0362897
\(601\) 40.7852 1.66366 0.831832 0.555028i \(-0.187292\pi\)
0.831832 + 0.555028i \(0.187292\pi\)
\(602\) 1.19695 0.0487842
\(603\) 7.53608 0.306893
\(604\) 43.4747 1.76896
\(605\) −9.45453 −0.384381
\(606\) 2.91710 0.118499
\(607\) 7.53532 0.305849 0.152925 0.988238i \(-0.451131\pi\)
0.152925 + 0.988238i \(0.451131\pi\)
\(608\) −2.84502 −0.115381
\(609\) −2.32059 −0.0940352
\(610\) 0.451910 0.0182973
\(611\) 79.7063 3.22457
\(612\) −12.4561 −0.503507
\(613\) −35.7511 −1.44397 −0.721987 0.691906i \(-0.756771\pi\)
−0.721987 + 0.691906i \(0.756771\pi\)
\(614\) −3.73586 −0.150767
\(615\) 1.15919 0.0467430
\(616\) −3.22357 −0.129881
\(617\) 4.24593 0.170935 0.0854673 0.996341i \(-0.472762\pi\)
0.0854673 + 0.996341i \(0.472762\pi\)
\(618\) 2.46132 0.0990087
\(619\) 16.4678 0.661895 0.330948 0.943649i \(-0.392632\pi\)
0.330948 + 0.943649i \(0.392632\pi\)
\(620\) −12.6249 −0.507029
\(621\) 13.0343 0.523048
\(622\) −2.87390 −0.115233
\(623\) 14.6845 0.588322
\(624\) −31.1065 −1.24526
\(625\) 1.00000 0.0400000
\(626\) −4.72878 −0.189000
\(627\) 7.60712 0.303799
\(628\) −22.5777 −0.900950
\(629\) −46.2968 −1.84598
\(630\) −0.259512 −0.0103392
\(631\) −7.61028 −0.302961 −0.151480 0.988460i \(-0.548404\pi\)
−0.151480 + 0.988460i \(0.548404\pi\)
\(632\) 9.26899 0.368701
\(633\) −23.2778 −0.925209
\(634\) −4.17018 −0.165619
\(635\) 13.6204 0.540509
\(636\) 20.1661 0.799638
\(637\) −6.55095 −0.259558
\(638\) −1.51174 −0.0598505
\(639\) 16.1831 0.640195
\(640\) 5.51881 0.218150
\(641\) −44.4887 −1.75720 −0.878600 0.477559i \(-0.841522\pi\)
−0.878600 + 0.477559i \(0.841522\pi\)
\(642\) 0.518627 0.0204686
\(643\) −25.5345 −1.00698 −0.503490 0.864001i \(-0.667951\pi\)
−0.503490 + 0.864001i \(0.667951\pi\)
\(644\) −4.62701 −0.182330
\(645\) 8.30985 0.327200
\(646\) 1.06162 0.0417688
\(647\) 22.5789 0.887667 0.443833 0.896109i \(-0.353618\pi\)
0.443833 + 0.896109i \(0.353618\pi\)
\(648\) 1.83830 0.0722154
\(649\) −21.5932 −0.847608
\(650\) −1.17681 −0.0461581
\(651\) 8.00166 0.313610
\(652\) 14.6816 0.574976
\(653\) −23.5308 −0.920833 −0.460417 0.887703i \(-0.652300\pi\)
−0.460417 + 0.887703i \(0.652300\pi\)
\(654\) 3.68319 0.144024
\(655\) −6.73229 −0.263052
\(656\) −3.53890 −0.138171
\(657\) −19.0195 −0.742022
\(658\) 2.18569 0.0852071
\(659\) 37.1088 1.44555 0.722777 0.691082i \(-0.242866\pi\)
0.722777 + 0.691082i \(0.242866\pi\)
\(660\) −11.0988 −0.432021
\(661\) 36.0491 1.40215 0.701074 0.713089i \(-0.252704\pi\)
0.701074 + 0.713089i \(0.252704\pi\)
\(662\) −4.48909 −0.174473
\(663\) 35.7996 1.39034
\(664\) 0.998312 0.0387420
\(665\) −1.34868 −0.0522996
\(666\) −2.74190 −0.106246
\(667\) −4.37540 −0.169416
\(668\) 17.4907 0.676736
\(669\) −0.749708 −0.0289854
\(670\) 0.937107 0.0362036
\(671\) 11.3775 0.439223
\(672\) −2.63082 −0.101486
\(673\) 2.29189 0.0883460 0.0441730 0.999024i \(-0.485935\pi\)
0.0441730 + 0.999024i \(0.485935\pi\)
\(674\) 3.02156 0.116386
\(675\) −5.54310 −0.213354
\(676\) −58.8645 −2.26402
\(677\) −44.4561 −1.70859 −0.854293 0.519791i \(-0.826010\pi\)
−0.854293 + 0.519791i \(0.826010\pi\)
\(678\) −0.969534 −0.0372347
\(679\) −9.91511 −0.380507
\(680\) −3.12321 −0.119770
\(681\) −20.3247 −0.778845
\(682\) 5.21265 0.199603
\(683\) 44.2546 1.69336 0.846678 0.532105i \(-0.178599\pi\)
0.846678 + 0.532105i \(0.178599\pi\)
\(684\) −3.83382 −0.146590
\(685\) 2.22633 0.0850637
\(686\) −0.179639 −0.00685865
\(687\) 1.24714 0.0475815
\(688\) −25.3693 −0.967194
\(689\) 53.8325 2.05085
\(690\) 0.526808 0.0200552
\(691\) 3.73101 0.141934 0.0709671 0.997479i \(-0.477391\pi\)
0.0709671 + 0.997479i \(0.477391\pi\)
\(692\) −23.6887 −0.900511
\(693\) −6.53360 −0.248191
\(694\) −0.356733 −0.0135414
\(695\) 5.23703 0.198652
\(696\) −1.65402 −0.0626956
\(697\) 4.07283 0.154269
\(698\) 5.77726 0.218672
\(699\) 13.4393 0.508321
\(700\) 1.96773 0.0743732
\(701\) −18.5140 −0.699264 −0.349632 0.936887i \(-0.613693\pi\)
−0.349632 + 0.936887i \(0.613693\pi\)
\(702\) 6.52315 0.246200
\(703\) −14.2496 −0.537434
\(704\) 32.7256 1.23339
\(705\) 15.1742 0.571492
\(706\) −4.75233 −0.178856
\(707\) −13.0207 −0.489693
\(708\) −11.7167 −0.440340
\(709\) −30.3271 −1.13896 −0.569478 0.822006i \(-0.692855\pi\)
−0.569478 + 0.822006i \(0.692855\pi\)
\(710\) 2.01236 0.0755226
\(711\) 18.7865 0.704551
\(712\) 10.4665 0.392249
\(713\) 15.0869 0.565007
\(714\) 0.981692 0.0367389
\(715\) −29.6278 −1.10802
\(716\) −1.66708 −0.0623018
\(717\) 26.1731 0.977454
\(718\) −2.41435 −0.0901026
\(719\) −20.6934 −0.771732 −0.385866 0.922555i \(-0.626097\pi\)
−0.385866 + 0.922555i \(0.626097\pi\)
\(720\) 5.50032 0.204985
\(721\) −10.9863 −0.409150
\(722\) −3.08639 −0.114864
\(723\) 6.86600 0.255349
\(724\) 41.4566 1.54072
\(725\) 1.86073 0.0691057
\(726\) 2.11815 0.0786120
\(727\) −26.4036 −0.979255 −0.489627 0.871932i \(-0.662867\pi\)
−0.489627 + 0.871932i \(0.662867\pi\)
\(728\) −4.66925 −0.173054
\(729\) 24.4650 0.906112
\(730\) −2.36506 −0.0875349
\(731\) 29.1968 1.07988
\(732\) 6.17353 0.228180
\(733\) −1.88817 −0.0697410 −0.0348705 0.999392i \(-0.511102\pi\)
−0.0348705 + 0.999392i \(0.511102\pi\)
\(734\) 4.71961 0.174204
\(735\) −1.24714 −0.0460016
\(736\) −4.96033 −0.182840
\(737\) 23.5930 0.869059
\(738\) 0.241210 0.00887908
\(739\) 9.63772 0.354529 0.177265 0.984163i \(-0.443275\pi\)
0.177265 + 0.984163i \(0.443275\pi\)
\(740\) 20.7902 0.764263
\(741\) 11.0187 0.404782
\(742\) 1.47619 0.0541925
\(743\) 31.9723 1.17295 0.586474 0.809968i \(-0.300516\pi\)
0.586474 + 0.809968i \(0.300516\pi\)
\(744\) 5.70325 0.209091
\(745\) −1.88046 −0.0688947
\(746\) 4.53587 0.166070
\(747\) 2.02340 0.0740322
\(748\) −38.9958 −1.42583
\(749\) −2.31493 −0.0845857
\(750\) −0.224036 −0.00818063
\(751\) −40.6806 −1.48446 −0.742228 0.670148i \(-0.766231\pi\)
−0.742228 + 0.670148i \(0.766231\pi\)
\(752\) −46.3254 −1.68931
\(753\) 31.4289 1.14533
\(754\) −2.18971 −0.0797447
\(755\) 22.0938 0.804077
\(756\) −10.9073 −0.396695
\(757\) −32.2777 −1.17315 −0.586577 0.809894i \(-0.699525\pi\)
−0.586577 + 0.809894i \(0.699525\pi\)
\(758\) −0.996366 −0.0361896
\(759\) 13.2631 0.481422
\(760\) −0.961285 −0.0348695
\(761\) −34.0183 −1.23316 −0.616581 0.787291i \(-0.711483\pi\)
−0.616581 + 0.787291i \(0.711483\pi\)
\(762\) −3.05146 −0.110543
\(763\) −16.4402 −0.595176
\(764\) 37.9528 1.37308
\(765\) −6.33017 −0.228868
\(766\) −5.14478 −0.185888
\(767\) −31.2771 −1.12935
\(768\) 16.8120 0.606650
\(769\) 36.9315 1.33178 0.665892 0.746048i \(-0.268051\pi\)
0.665892 + 0.746048i \(0.268051\pi\)
\(770\) −0.812448 −0.0292786
\(771\) −6.04197 −0.217596
\(772\) −40.1151 −1.44377
\(773\) 41.9884 1.51022 0.755109 0.655600i \(-0.227584\pi\)
0.755109 + 0.655600i \(0.227584\pi\)
\(774\) 1.72916 0.0621534
\(775\) −6.41599 −0.230469
\(776\) −7.06709 −0.253694
\(777\) −13.1768 −0.472715
\(778\) −3.40862 −0.122205
\(779\) 1.25357 0.0449137
\(780\) −16.0763 −0.575624
\(781\) 50.6641 1.81290
\(782\) 1.85095 0.0661897
\(783\) −10.3142 −0.368599
\(784\) 3.80742 0.135979
\(785\) −11.4740 −0.409525
\(786\) 1.50827 0.0537983
\(787\) −39.2919 −1.40060 −0.700302 0.713846i \(-0.746951\pi\)
−0.700302 + 0.713846i \(0.746951\pi\)
\(788\) −28.9283 −1.03053
\(789\) −10.5566 −0.375823
\(790\) 2.33609 0.0831145
\(791\) 4.32759 0.153871
\(792\) −4.65688 −0.165475
\(793\) 16.4799 0.585220
\(794\) 1.13644 0.0403307
\(795\) 10.2484 0.363474
\(796\) −49.9474 −1.77034
\(797\) 51.0039 1.80665 0.903325 0.428957i \(-0.141119\pi\)
0.903325 + 0.428957i \(0.141119\pi\)
\(798\) 0.302153 0.0106961
\(799\) 53.3146 1.88613
\(800\) 2.10948 0.0745814
\(801\) 21.2137 0.749550
\(802\) 4.25669 0.150309
\(803\) −59.5438 −2.10126
\(804\) 12.8018 0.451484
\(805\) −2.35145 −0.0828776
\(806\) 7.55037 0.265951
\(807\) −31.8241 −1.12026
\(808\) −9.28061 −0.326491
\(809\) 0.241469 0.00848959 0.00424480 0.999991i \(-0.498649\pi\)
0.00424480 + 0.999991i \(0.498649\pi\)
\(810\) 0.463314 0.0162792
\(811\) −7.66521 −0.269162 −0.134581 0.990903i \(-0.542969\pi\)
−0.134581 + 0.990903i \(0.542969\pi\)
\(812\) 3.66141 0.128490
\(813\) −38.1876 −1.33930
\(814\) −8.58398 −0.300868
\(815\) 7.46119 0.261354
\(816\) −20.8068 −0.728383
\(817\) 8.98641 0.314395
\(818\) 1.88800 0.0660124
\(819\) −9.46372 −0.330689
\(820\) −1.82896 −0.0638699
\(821\) −40.6216 −1.41770 −0.708851 0.705358i \(-0.750786\pi\)
−0.708851 + 0.705358i \(0.750786\pi\)
\(822\) −0.498777 −0.0173969
\(823\) 34.0765 1.18783 0.593917 0.804526i \(-0.297581\pi\)
0.593917 + 0.804526i \(0.297581\pi\)
\(824\) −7.83057 −0.272791
\(825\) −5.64042 −0.196374
\(826\) −0.857677 −0.0298424
\(827\) −10.9977 −0.382427 −0.191214 0.981548i \(-0.561242\pi\)
−0.191214 + 0.981548i \(0.561242\pi\)
\(828\) −6.68434 −0.232297
\(829\) −17.6792 −0.614024 −0.307012 0.951706i \(-0.599329\pi\)
−0.307012 + 0.951706i \(0.599329\pi\)
\(830\) 0.251608 0.00873344
\(831\) 1.94796 0.0675739
\(832\) 47.4020 1.64337
\(833\) −4.38185 −0.151822
\(834\) −1.17328 −0.0406274
\(835\) 8.88878 0.307609
\(836\) −12.0024 −0.415113
\(837\) 35.5644 1.22929
\(838\) 6.86720 0.237223
\(839\) 35.6846 1.23197 0.615984 0.787759i \(-0.288759\pi\)
0.615984 + 0.787759i \(0.288759\pi\)
\(840\) −0.888913 −0.0306704
\(841\) −25.5377 −0.880610
\(842\) −0.727939 −0.0250864
\(843\) −26.6112 −0.916540
\(844\) 36.7274 1.26421
\(845\) −29.9149 −1.02910
\(846\) 3.15752 0.108558
\(847\) −9.45453 −0.324861
\(848\) −31.2875 −1.07442
\(849\) −19.1297 −0.656528
\(850\) −0.787152 −0.0269991
\(851\) −24.8444 −0.851655
\(852\) 27.4908 0.941819
\(853\) 12.7514 0.436599 0.218300 0.975882i \(-0.429949\pi\)
0.218300 + 0.975882i \(0.429949\pi\)
\(854\) 0.451910 0.0154641
\(855\) −1.94835 −0.0666321
\(856\) −1.64999 −0.0563954
\(857\) −38.9379 −1.33009 −0.665047 0.746802i \(-0.731588\pi\)
−0.665047 + 0.746802i \(0.731588\pi\)
\(858\) 6.63768 0.226607
\(859\) 21.9545 0.749078 0.374539 0.927211i \(-0.377801\pi\)
0.374539 + 0.927211i \(0.377801\pi\)
\(860\) −13.1112 −0.447088
\(861\) 1.15919 0.0395051
\(862\) −1.31875 −0.0449169
\(863\) −25.2930 −0.860983 −0.430491 0.902595i \(-0.641660\pi\)
−0.430491 + 0.902595i \(0.641660\pi\)
\(864\) −11.6930 −0.397806
\(865\) −12.0386 −0.409325
\(866\) −4.52127 −0.153639
\(867\) 2.74452 0.0932087
\(868\) −12.6249 −0.428518
\(869\) 58.8145 1.99514
\(870\) −0.416869 −0.0141332
\(871\) 34.1737 1.15793
\(872\) −11.7179 −0.396819
\(873\) −14.3237 −0.484784
\(874\) 0.569699 0.0192704
\(875\) 1.00000 0.0338062
\(876\) −32.3090 −1.09162
\(877\) −47.9156 −1.61800 −0.808998 0.587811i \(-0.799990\pi\)
−0.808998 + 0.587811i \(0.799990\pi\)
\(878\) −0.817272 −0.0275816
\(879\) −15.4274 −0.520354
\(880\) 17.2197 0.580476
\(881\) −19.9498 −0.672127 −0.336064 0.941839i \(-0.609096\pi\)
−0.336064 + 0.941839i \(0.609096\pi\)
\(882\) −0.259512 −0.00873824
\(883\) −18.8386 −0.633968 −0.316984 0.948431i \(-0.602670\pi\)
−0.316984 + 0.948431i \(0.602670\pi\)
\(884\) −56.4843 −1.89977
\(885\) −5.95442 −0.200156
\(886\) 0.637587 0.0214201
\(887\) 30.2434 1.01547 0.507737 0.861512i \(-0.330482\pi\)
0.507737 + 0.861512i \(0.330482\pi\)
\(888\) −9.39188 −0.315171
\(889\) 13.6204 0.456814
\(890\) 2.63791 0.0884229
\(891\) 11.6646 0.390778
\(892\) 1.18288 0.0396058
\(893\) 16.4096 0.549126
\(894\) 0.421290 0.0140900
\(895\) −0.847211 −0.0283192
\(896\) 5.51881 0.184370
\(897\) 19.2113 0.641446
\(898\) −0.588943 −0.0196533
\(899\) −11.9384 −0.398168
\(900\) 2.84265 0.0947549
\(901\) 36.0079 1.19960
\(902\) 0.755150 0.0251437
\(903\) 8.30985 0.276535
\(904\) 3.08453 0.102590
\(905\) 21.0682 0.700332
\(906\) −4.94981 −0.164446
\(907\) 27.6646 0.918589 0.459294 0.888284i \(-0.348102\pi\)
0.459294 + 0.888284i \(0.348102\pi\)
\(908\) 32.0681 1.06422
\(909\) −18.8101 −0.623892
\(910\) −1.17681 −0.0390107
\(911\) −9.01315 −0.298619 −0.149309 0.988791i \(-0.547705\pi\)
−0.149309 + 0.988791i \(0.547705\pi\)
\(912\) −6.40408 −0.212060
\(913\) 6.33459 0.209644
\(914\) 2.64057 0.0873422
\(915\) 3.13739 0.103719
\(916\) −1.96773 −0.0650156
\(917\) −6.73229 −0.222320
\(918\) 4.36326 0.144009
\(919\) −21.1166 −0.696571 −0.348286 0.937388i \(-0.613236\pi\)
−0.348286 + 0.937388i \(0.613236\pi\)
\(920\) −1.67602 −0.0552566
\(921\) −25.9362 −0.854626
\(922\) 4.46690 0.147109
\(923\) 73.3854 2.41551
\(924\) −11.0988 −0.365124
\(925\) 10.5656 0.347394
\(926\) −1.37054 −0.0450387
\(927\) −15.8711 −0.521277
\(928\) 3.92517 0.128850
\(929\) −26.8667 −0.881468 −0.440734 0.897638i \(-0.645282\pi\)
−0.440734 + 0.897638i \(0.645282\pi\)
\(930\) 1.43741 0.0471345
\(931\) −1.34868 −0.0442012
\(932\) −21.2044 −0.694572
\(933\) −19.9521 −0.653201
\(934\) −3.50719 −0.114759
\(935\) −19.8177 −0.648107
\(936\) −6.74535 −0.220479
\(937\) 50.3232 1.64399 0.821994 0.569496i \(-0.192862\pi\)
0.821994 + 0.569496i \(0.192862\pi\)
\(938\) 0.937107 0.0305976
\(939\) −32.8296 −1.07135
\(940\) −23.9416 −0.780890
\(941\) −41.2944 −1.34616 −0.673080 0.739570i \(-0.735029\pi\)
−0.673080 + 0.739570i \(0.735029\pi\)
\(942\) 2.57059 0.0837542
\(943\) 2.18561 0.0711733
\(944\) 18.1783 0.591654
\(945\) −5.54310 −0.180317
\(946\) 5.41343 0.176006
\(947\) −38.2608 −1.24331 −0.621655 0.783291i \(-0.713539\pi\)
−0.621655 + 0.783291i \(0.713539\pi\)
\(948\) 31.9133 1.03650
\(949\) −86.2475 −2.79971
\(950\) −0.242276 −0.00786046
\(951\) −28.9515 −0.938815
\(952\) −3.12321 −0.101224
\(953\) 16.0526 0.519995 0.259998 0.965609i \(-0.416278\pi\)
0.259998 + 0.965609i \(0.416278\pi\)
\(954\) 2.13255 0.0690438
\(955\) 19.2876 0.624133
\(956\) −41.2957 −1.33560
\(957\) −10.4953 −0.339264
\(958\) −0.695605 −0.0224740
\(959\) 2.22633 0.0718919
\(960\) 9.02420 0.291255
\(961\) 10.1649 0.327900
\(962\) −12.4336 −0.400877
\(963\) −3.34422 −0.107766
\(964\) −10.8331 −0.348911
\(965\) −20.3865 −0.656264
\(966\) 0.526808 0.0169498
\(967\) −57.3282 −1.84355 −0.921775 0.387725i \(-0.873261\pi\)
−0.921775 + 0.387725i \(0.873261\pi\)
\(968\) −6.73880 −0.216593
\(969\) 7.37027 0.236767
\(970\) −1.78114 −0.0571890
\(971\) −57.3914 −1.84178 −0.920888 0.389827i \(-0.872535\pi\)
−0.920888 + 0.389827i \(0.872535\pi\)
\(972\) −26.3926 −0.846544
\(973\) 5.23703 0.167891
\(974\) −0.772412 −0.0247497
\(975\) −8.16997 −0.261649
\(976\) −9.57817 −0.306590
\(977\) −13.9642 −0.446753 −0.223376 0.974732i \(-0.571708\pi\)
−0.223376 + 0.974732i \(0.571708\pi\)
\(978\) −1.67157 −0.0534510
\(979\) 66.4131 2.12257
\(980\) 1.96773 0.0628568
\(981\) −23.7501 −0.758282
\(982\) −1.88042 −0.0600066
\(983\) 59.7734 1.90648 0.953238 0.302221i \(-0.0977280\pi\)
0.953238 + 0.302221i \(0.0977280\pi\)
\(984\) 0.826223 0.0263390
\(985\) −14.7013 −0.468424
\(986\) −1.46467 −0.0466448
\(987\) 15.1742 0.482999
\(988\) −17.3852 −0.553096
\(989\) 15.6680 0.498212
\(990\) −1.17369 −0.0373023
\(991\) 24.9969 0.794054 0.397027 0.917807i \(-0.370042\pi\)
0.397027 + 0.917807i \(0.370042\pi\)
\(992\) −13.5344 −0.429717
\(993\) −31.1655 −0.989007
\(994\) 2.01236 0.0638282
\(995\) −25.3833 −0.804703
\(996\) 3.43721 0.108912
\(997\) −40.1126 −1.27038 −0.635190 0.772356i \(-0.719078\pi\)
−0.635190 + 0.772356i \(0.719078\pi\)
\(998\) 3.83743 0.121472
\(999\) −58.5660 −1.85295
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 \(a_p\))