Properties

Label 8015.2.a.l.1.30
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 1.30
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.214735 q^{2} -3.36877 q^{3} -1.95389 q^{4} -1.00000 q^{5} +0.723394 q^{6} -1.00000 q^{7} +0.849039 q^{8} +8.34862 q^{9} +O(q^{10})\) \(q-0.214735 q^{2} -3.36877 q^{3} -1.95389 q^{4} -1.00000 q^{5} +0.723394 q^{6} -1.00000 q^{7} +0.849039 q^{8} +8.34862 q^{9} +0.214735 q^{10} -5.90573 q^{11} +6.58220 q^{12} -2.24878 q^{13} +0.214735 q^{14} +3.36877 q^{15} +3.72546 q^{16} +7.21459 q^{17} -1.79274 q^{18} +0.212612 q^{19} +1.95389 q^{20} +3.36877 q^{21} +1.26817 q^{22} +5.27505 q^{23} -2.86022 q^{24} +1.00000 q^{25} +0.482893 q^{26} -18.0183 q^{27} +1.95389 q^{28} -2.08268 q^{29} -0.723394 q^{30} +5.05725 q^{31} -2.49807 q^{32} +19.8951 q^{33} -1.54923 q^{34} +1.00000 q^{35} -16.3123 q^{36} +8.04630 q^{37} -0.0456552 q^{38} +7.57563 q^{39} -0.849039 q^{40} +11.1283 q^{41} -0.723394 q^{42} -10.3449 q^{43} +11.5391 q^{44} -8.34862 q^{45} -1.13274 q^{46} +0.0414681 q^{47} -12.5502 q^{48} +1.00000 q^{49} -0.214735 q^{50} -24.3043 q^{51} +4.39387 q^{52} +5.38853 q^{53} +3.86916 q^{54} +5.90573 q^{55} -0.849039 q^{56} -0.716240 q^{57} +0.447226 q^{58} -9.03869 q^{59} -6.58220 q^{60} +11.8257 q^{61} -1.08597 q^{62} -8.34862 q^{63} -6.91449 q^{64} +2.24878 q^{65} -4.27217 q^{66} -3.53434 q^{67} -14.0965 q^{68} -17.7705 q^{69} -0.214735 q^{70} +13.2611 q^{71} +7.08831 q^{72} -6.55806 q^{73} -1.72782 q^{74} -3.36877 q^{75} -0.415420 q^{76} +5.90573 q^{77} -1.62675 q^{78} -8.07443 q^{79} -3.72546 q^{80} +35.6536 q^{81} -2.38963 q^{82} +13.9985 q^{83} -6.58220 q^{84} -7.21459 q^{85} +2.22141 q^{86} +7.01609 q^{87} -5.01420 q^{88} -14.8472 q^{89} +1.79274 q^{90} +2.24878 q^{91} -10.3069 q^{92} -17.0367 q^{93} -0.00890467 q^{94} -0.212612 q^{95} +8.41541 q^{96} -3.46927 q^{97} -0.214735 q^{98} -49.3047 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.214735 −0.151841 −0.0759204 0.997114i \(-0.524189\pi\)
−0.0759204 + 0.997114i \(0.524189\pi\)
\(3\) −3.36877 −1.94496 −0.972481 0.232984i \(-0.925151\pi\)
−0.972481 + 0.232984i \(0.925151\pi\)
\(4\) −1.95389 −0.976944
\(5\) −1.00000 −0.447214
\(6\) 0.723394 0.295324
\(7\) −1.00000 −0.377964
\(8\) 0.849039 0.300181
\(9\) 8.34862 2.78287
\(10\) 0.214735 0.0679053
\(11\) −5.90573 −1.78064 −0.890322 0.455331i \(-0.849521\pi\)
−0.890322 + 0.455331i \(0.849521\pi\)
\(12\) 6.58220 1.90012
\(13\) −2.24878 −0.623700 −0.311850 0.950131i \(-0.600949\pi\)
−0.311850 + 0.950131i \(0.600949\pi\)
\(14\) 0.214735 0.0573904
\(15\) 3.36877 0.869813
\(16\) 3.72546 0.931365
\(17\) 7.21459 1.74980 0.874898 0.484308i \(-0.160929\pi\)
0.874898 + 0.484308i \(0.160929\pi\)
\(18\) −1.79274 −0.422554
\(19\) 0.212612 0.0487765 0.0243882 0.999703i \(-0.492236\pi\)
0.0243882 + 0.999703i \(0.492236\pi\)
\(20\) 1.95389 0.436903
\(21\) 3.36877 0.735126
\(22\) 1.26817 0.270374
\(23\) 5.27505 1.09992 0.549962 0.835189i \(-0.314642\pi\)
0.549962 + 0.835189i \(0.314642\pi\)
\(24\) −2.86022 −0.583840
\(25\) 1.00000 0.200000
\(26\) 0.482893 0.0947030
\(27\) −18.0183 −3.46762
\(28\) 1.95389 0.369250
\(29\) −2.08268 −0.386745 −0.193372 0.981125i \(-0.561943\pi\)
−0.193372 + 0.981125i \(0.561943\pi\)
\(30\) −0.723394 −0.132073
\(31\) 5.05725 0.908309 0.454155 0.890923i \(-0.349941\pi\)
0.454155 + 0.890923i \(0.349941\pi\)
\(32\) −2.49807 −0.441600
\(33\) 19.8951 3.46328
\(34\) −1.54923 −0.265690
\(35\) 1.00000 0.169031
\(36\) −16.3123 −2.71871
\(37\) 8.04630 1.32280 0.661402 0.750032i \(-0.269962\pi\)
0.661402 + 0.750032i \(0.269962\pi\)
\(38\) −0.0456552 −0.00740626
\(39\) 7.57563 1.21307
\(40\) −0.849039 −0.134245
\(41\) 11.1283 1.73795 0.868973 0.494860i \(-0.164781\pi\)
0.868973 + 0.494860i \(0.164781\pi\)
\(42\) −0.723394 −0.111622
\(43\) −10.3449 −1.57758 −0.788788 0.614665i \(-0.789291\pi\)
−0.788788 + 0.614665i \(0.789291\pi\)
\(44\) 11.5391 1.73959
\(45\) −8.34862 −1.24454
\(46\) −1.13274 −0.167013
\(47\) 0.0414681 0.00604875 0.00302437 0.999995i \(-0.499037\pi\)
0.00302437 + 0.999995i \(0.499037\pi\)
\(48\) −12.5502 −1.81147
\(49\) 1.00000 0.142857
\(50\) −0.214735 −0.0303682
\(51\) −24.3043 −3.40328
\(52\) 4.39387 0.609320
\(53\) 5.38853 0.740171 0.370086 0.928998i \(-0.379328\pi\)
0.370086 + 0.928998i \(0.379328\pi\)
\(54\) 3.86916 0.526526
\(55\) 5.90573 0.796328
\(56\) −0.849039 −0.113458
\(57\) −0.716240 −0.0948683
\(58\) 0.447226 0.0587236
\(59\) −9.03869 −1.17674 −0.588368 0.808593i \(-0.700230\pi\)
−0.588368 + 0.808593i \(0.700230\pi\)
\(60\) −6.58220 −0.849759
\(61\) 11.8257 1.51412 0.757060 0.653345i \(-0.226635\pi\)
0.757060 + 0.653345i \(0.226635\pi\)
\(62\) −1.08597 −0.137918
\(63\) −8.34862 −1.05183
\(64\) −6.91449 −0.864312
\(65\) 2.24878 0.278927
\(66\) −4.27217 −0.525868
\(67\) −3.53434 −0.431788 −0.215894 0.976417i \(-0.569267\pi\)
−0.215894 + 0.976417i \(0.569267\pi\)
\(68\) −14.0965 −1.70945
\(69\) −17.7705 −2.13931
\(70\) −0.214735 −0.0256658
\(71\) 13.2611 1.57381 0.786904 0.617076i \(-0.211683\pi\)
0.786904 + 0.617076i \(0.211683\pi\)
\(72\) 7.08831 0.835365
\(73\) −6.55806 −0.767563 −0.383781 0.923424i \(-0.625378\pi\)
−0.383781 + 0.923424i \(0.625378\pi\)
\(74\) −1.72782 −0.200855
\(75\) −3.36877 −0.388992
\(76\) −0.415420 −0.0476519
\(77\) 5.90573 0.673020
\(78\) −1.62675 −0.184194
\(79\) −8.07443 −0.908445 −0.454222 0.890888i \(-0.650083\pi\)
−0.454222 + 0.890888i \(0.650083\pi\)
\(80\) −3.72546 −0.416519
\(81\) 35.6536 3.96151
\(82\) −2.38963 −0.263891
\(83\) 13.9985 1.53654 0.768268 0.640129i \(-0.221119\pi\)
0.768268 + 0.640129i \(0.221119\pi\)
\(84\) −6.58220 −0.718177
\(85\) −7.21459 −0.782532
\(86\) 2.22141 0.239540
\(87\) 7.01609 0.752203
\(88\) −5.01420 −0.534515
\(89\) −14.8472 −1.57379 −0.786897 0.617084i \(-0.788314\pi\)
−0.786897 + 0.617084i \(0.788314\pi\)
\(90\) 1.79274 0.188972
\(91\) 2.24878 0.235736
\(92\) −10.3069 −1.07457
\(93\) −17.0367 −1.76663
\(94\) −0.00890467 −0.000918447 0
\(95\) −0.212612 −0.0218135
\(96\) 8.41541 0.858895
\(97\) −3.46927 −0.352251 −0.176125 0.984368i \(-0.556356\pi\)
−0.176125 + 0.984368i \(0.556356\pi\)
\(98\) −0.214735 −0.0216915
\(99\) −49.3047 −4.95531
\(100\) −1.95389 −0.195389
\(101\) −16.5026 −1.64207 −0.821036 0.570877i \(-0.806603\pi\)
−0.821036 + 0.570877i \(0.806603\pi\)
\(102\) 5.21899 0.516757
\(103\) 6.61010 0.651312 0.325656 0.945488i \(-0.394415\pi\)
0.325656 + 0.945488i \(0.394415\pi\)
\(104\) −1.90930 −0.187223
\(105\) −3.36877 −0.328758
\(106\) −1.15711 −0.112388
\(107\) 9.59029 0.927128 0.463564 0.886063i \(-0.346570\pi\)
0.463564 + 0.886063i \(0.346570\pi\)
\(108\) 35.2057 3.38767
\(109\) 18.7119 1.79227 0.896135 0.443781i \(-0.146363\pi\)
0.896135 + 0.443781i \(0.146363\pi\)
\(110\) −1.26817 −0.120915
\(111\) −27.1061 −2.57280
\(112\) −3.72546 −0.352023
\(113\) 2.15784 0.202993 0.101496 0.994836i \(-0.467637\pi\)
0.101496 + 0.994836i \(0.467637\pi\)
\(114\) 0.153802 0.0144049
\(115\) −5.27505 −0.491901
\(116\) 4.06933 0.377828
\(117\) −18.7742 −1.73568
\(118\) 1.94092 0.178677
\(119\) −7.21459 −0.661360
\(120\) 2.86022 0.261101
\(121\) 23.8776 2.17070
\(122\) −2.53939 −0.229905
\(123\) −37.4886 −3.38024
\(124\) −9.88131 −0.887368
\(125\) −1.00000 −0.0894427
\(126\) 1.79274 0.159710
\(127\) −5.65578 −0.501870 −0.250935 0.968004i \(-0.580738\pi\)
−0.250935 + 0.968004i \(0.580738\pi\)
\(128\) 6.48092 0.572838
\(129\) 34.8495 3.06832
\(130\) −0.482893 −0.0423525
\(131\) −3.01657 −0.263559 −0.131779 0.991279i \(-0.542069\pi\)
−0.131779 + 0.991279i \(0.542069\pi\)
\(132\) −38.8727 −3.38344
\(133\) −0.212612 −0.0184358
\(134\) 0.758947 0.0655631
\(135\) 18.0183 1.55077
\(136\) 6.12547 0.525255
\(137\) −6.57150 −0.561441 −0.280721 0.959790i \(-0.590573\pi\)
−0.280721 + 0.959790i \(0.590573\pi\)
\(138\) 3.81594 0.324835
\(139\) −21.6124 −1.83314 −0.916569 0.399876i \(-0.869053\pi\)
−0.916569 + 0.399876i \(0.869053\pi\)
\(140\) −1.95389 −0.165134
\(141\) −0.139697 −0.0117646
\(142\) −2.84763 −0.238968
\(143\) 13.2807 1.11059
\(144\) 31.1024 2.59187
\(145\) 2.08268 0.172957
\(146\) 1.40825 0.116547
\(147\) −3.36877 −0.277852
\(148\) −15.7216 −1.29231
\(149\) −8.29212 −0.679317 −0.339659 0.940549i \(-0.610312\pi\)
−0.339659 + 0.940549i \(0.610312\pi\)
\(150\) 0.723394 0.0590649
\(151\) −15.8865 −1.29282 −0.646411 0.762989i \(-0.723731\pi\)
−0.646411 + 0.762989i \(0.723731\pi\)
\(152\) 0.180516 0.0146418
\(153\) 60.2319 4.86946
\(154\) −1.26817 −0.102192
\(155\) −5.05725 −0.406208
\(156\) −14.8019 −1.18510
\(157\) 13.1304 1.04792 0.523959 0.851744i \(-0.324455\pi\)
0.523959 + 0.851744i \(0.324455\pi\)
\(158\) 1.73387 0.137939
\(159\) −18.1527 −1.43960
\(160\) 2.49807 0.197489
\(161\) −5.27505 −0.415732
\(162\) −7.65609 −0.601519
\(163\) −9.76544 −0.764888 −0.382444 0.923979i \(-0.624918\pi\)
−0.382444 + 0.923979i \(0.624918\pi\)
\(164\) −21.7434 −1.69788
\(165\) −19.8951 −1.54883
\(166\) −3.00597 −0.233309
\(167\) −4.12300 −0.319047 −0.159524 0.987194i \(-0.550996\pi\)
−0.159524 + 0.987194i \(0.550996\pi\)
\(168\) 2.86022 0.220671
\(169\) −7.94298 −0.610999
\(170\) 1.54923 0.118820
\(171\) 1.77501 0.135739
\(172\) 20.2127 1.54120
\(173\) 3.65042 0.277537 0.138768 0.990325i \(-0.455686\pi\)
0.138768 + 0.990325i \(0.455686\pi\)
\(174\) −1.50660 −0.114215
\(175\) −1.00000 −0.0755929
\(176\) −22.0016 −1.65843
\(177\) 30.4493 2.28871
\(178\) 3.18821 0.238966
\(179\) −2.01838 −0.150861 −0.0754304 0.997151i \(-0.524033\pi\)
−0.0754304 + 0.997151i \(0.524033\pi\)
\(180\) 16.3123 1.21585
\(181\) −9.63014 −0.715802 −0.357901 0.933759i \(-0.616508\pi\)
−0.357901 + 0.933759i \(0.616508\pi\)
\(182\) −0.482893 −0.0357944
\(183\) −39.8379 −2.94491
\(184\) 4.47873 0.330176
\(185\) −8.04630 −0.591576
\(186\) 3.65839 0.268246
\(187\) −42.6074 −3.11576
\(188\) −0.0810241 −0.00590929
\(189\) 18.0183 1.31064
\(190\) 0.0456552 0.00331218
\(191\) 13.7663 0.996097 0.498049 0.867149i \(-0.334050\pi\)
0.498049 + 0.867149i \(0.334050\pi\)
\(192\) 23.2934 1.68105
\(193\) −5.92065 −0.426178 −0.213089 0.977033i \(-0.568352\pi\)
−0.213089 + 0.977033i \(0.568352\pi\)
\(194\) 0.744974 0.0534860
\(195\) −7.57563 −0.542502
\(196\) −1.95389 −0.139563
\(197\) −14.0239 −0.999159 −0.499579 0.866268i \(-0.666512\pi\)
−0.499579 + 0.866268i \(0.666512\pi\)
\(198\) 10.5875 0.752418
\(199\) 7.10809 0.503879 0.251940 0.967743i \(-0.418932\pi\)
0.251940 + 0.967743i \(0.418932\pi\)
\(200\) 0.849039 0.0600361
\(201\) 11.9064 0.839812
\(202\) 3.54369 0.249333
\(203\) 2.08268 0.146176
\(204\) 47.4879 3.32482
\(205\) −11.1283 −0.777233
\(206\) −1.41942 −0.0988958
\(207\) 44.0394 3.06095
\(208\) −8.37774 −0.580892
\(209\) −1.25563 −0.0868535
\(210\) 0.723394 0.0499189
\(211\) −12.6434 −0.870405 −0.435202 0.900333i \(-0.643323\pi\)
−0.435202 + 0.900333i \(0.643323\pi\)
\(212\) −10.5286 −0.723106
\(213\) −44.6737 −3.06099
\(214\) −2.05937 −0.140776
\(215\) 10.3449 0.705514
\(216\) −15.2982 −1.04091
\(217\) −5.05725 −0.343309
\(218\) −4.01810 −0.272140
\(219\) 22.0926 1.49288
\(220\) −11.5391 −0.777969
\(221\) −16.2240 −1.09135
\(222\) 5.82064 0.390656
\(223\) 6.29390 0.421470 0.210735 0.977543i \(-0.432414\pi\)
0.210735 + 0.977543i \(0.432414\pi\)
\(224\) 2.49807 0.166909
\(225\) 8.34862 0.556575
\(226\) −0.463365 −0.0308226
\(227\) 23.8554 1.58334 0.791668 0.610951i \(-0.209213\pi\)
0.791668 + 0.610951i \(0.209213\pi\)
\(228\) 1.39945 0.0926811
\(229\) 1.00000 0.0660819
\(230\) 1.13274 0.0746907
\(231\) −19.8951 −1.30900
\(232\) −1.76828 −0.116093
\(233\) −10.0348 −0.657404 −0.328702 0.944434i \(-0.606611\pi\)
−0.328702 + 0.944434i \(0.606611\pi\)
\(234\) 4.03149 0.263547
\(235\) −0.0414681 −0.00270508
\(236\) 17.6606 1.14961
\(237\) 27.2009 1.76689
\(238\) 1.54923 0.100421
\(239\) −13.2097 −0.854467 −0.427234 0.904141i \(-0.640512\pi\)
−0.427234 + 0.904141i \(0.640512\pi\)
\(240\) 12.5502 0.810113
\(241\) −0.767351 −0.0494294 −0.0247147 0.999695i \(-0.507868\pi\)
−0.0247147 + 0.999695i \(0.507868\pi\)
\(242\) −5.12737 −0.329600
\(243\) −66.0541 −4.23737
\(244\) −23.1060 −1.47921
\(245\) −1.00000 −0.0638877
\(246\) 8.05013 0.513258
\(247\) −0.478117 −0.0304219
\(248\) 4.29381 0.272657
\(249\) −47.1578 −2.98850
\(250\) 0.214735 0.0135811
\(251\) 26.4762 1.67116 0.835581 0.549367i \(-0.185131\pi\)
0.835581 + 0.549367i \(0.185131\pi\)
\(252\) 16.3123 1.02758
\(253\) −31.1530 −1.95858
\(254\) 1.21450 0.0762043
\(255\) 24.3043 1.52199
\(256\) 12.4373 0.777332
\(257\) 3.52176 0.219681 0.109841 0.993949i \(-0.464966\pi\)
0.109841 + 0.993949i \(0.464966\pi\)
\(258\) −7.48341 −0.465897
\(259\) −8.04630 −0.499973
\(260\) −4.39387 −0.272496
\(261\) −17.3875 −1.07626
\(262\) 0.647764 0.0400190
\(263\) −14.4363 −0.890183 −0.445091 0.895485i \(-0.646829\pi\)
−0.445091 + 0.895485i \(0.646829\pi\)
\(264\) 16.8917 1.03961
\(265\) −5.38853 −0.331015
\(266\) 0.0456552 0.00279930
\(267\) 50.0167 3.06097
\(268\) 6.90571 0.421833
\(269\) −4.41729 −0.269327 −0.134664 0.990891i \(-0.542995\pi\)
−0.134664 + 0.990891i \(0.542995\pi\)
\(270\) −3.86916 −0.235470
\(271\) 15.0281 0.912889 0.456445 0.889752i \(-0.349123\pi\)
0.456445 + 0.889752i \(0.349123\pi\)
\(272\) 26.8777 1.62970
\(273\) −7.57563 −0.458498
\(274\) 1.41113 0.0852497
\(275\) −5.90573 −0.356129
\(276\) 34.7215 2.08999
\(277\) 26.7200 1.60545 0.802725 0.596349i \(-0.203383\pi\)
0.802725 + 0.596349i \(0.203383\pi\)
\(278\) 4.64094 0.278345
\(279\) 42.2211 2.52771
\(280\) 0.849039 0.0507398
\(281\) −17.4509 −1.04104 −0.520518 0.853851i \(-0.674261\pi\)
−0.520518 + 0.853851i \(0.674261\pi\)
\(282\) 0.0299978 0.00178634
\(283\) 17.6667 1.05018 0.525088 0.851048i \(-0.324032\pi\)
0.525088 + 0.851048i \(0.324032\pi\)
\(284\) −25.9108 −1.53752
\(285\) 0.716240 0.0424264
\(286\) −2.85183 −0.168632
\(287\) −11.1283 −0.656882
\(288\) −20.8554 −1.22892
\(289\) 35.0503 2.06178
\(290\) −0.447226 −0.0262620
\(291\) 11.6872 0.685114
\(292\) 12.8137 0.749866
\(293\) 29.6384 1.73150 0.865748 0.500480i \(-0.166843\pi\)
0.865748 + 0.500480i \(0.166843\pi\)
\(294\) 0.723394 0.0421892
\(295\) 9.03869 0.526253
\(296\) 6.83162 0.397080
\(297\) 106.411 6.17460
\(298\) 1.78061 0.103148
\(299\) −11.8624 −0.686023
\(300\) 6.58220 0.380024
\(301\) 10.3449 0.596268
\(302\) 3.41139 0.196303
\(303\) 55.5935 3.19377
\(304\) 0.792076 0.0454287
\(305\) −11.8257 −0.677135
\(306\) −12.9339 −0.739383
\(307\) 31.8488 1.81771 0.908854 0.417115i \(-0.136959\pi\)
0.908854 + 0.417115i \(0.136959\pi\)
\(308\) −11.5391 −0.657504
\(309\) −22.2679 −1.26678
\(310\) 1.08597 0.0616790
\(311\) 2.35266 0.133407 0.0667037 0.997773i \(-0.478752\pi\)
0.0667037 + 0.997773i \(0.478752\pi\)
\(312\) 6.43201 0.364141
\(313\) −7.46303 −0.421835 −0.210918 0.977504i \(-0.567645\pi\)
−0.210918 + 0.977504i \(0.567645\pi\)
\(314\) −2.81955 −0.159117
\(315\) 8.34862 0.470392
\(316\) 15.7765 0.887500
\(317\) 21.1525 1.18804 0.594022 0.804449i \(-0.297539\pi\)
0.594022 + 0.804449i \(0.297539\pi\)
\(318\) 3.89803 0.218591
\(319\) 12.2998 0.688655
\(320\) 6.91449 0.386532
\(321\) −32.3075 −1.80323
\(322\) 1.13274 0.0631251
\(323\) 1.53391 0.0853488
\(324\) −69.6632 −3.87018
\(325\) −2.24878 −0.124740
\(326\) 2.09698 0.116141
\(327\) −63.0360 −3.48590
\(328\) 9.44835 0.521698
\(329\) −0.0414681 −0.00228621
\(330\) 4.27217 0.235175
\(331\) −26.7487 −1.47024 −0.735120 0.677937i \(-0.762874\pi\)
−0.735120 + 0.677937i \(0.762874\pi\)
\(332\) −27.3515 −1.50111
\(333\) 67.1755 3.68120
\(334\) 0.885354 0.0484444
\(335\) 3.53434 0.193102
\(336\) 12.5502 0.684671
\(337\) −4.21474 −0.229591 −0.114796 0.993389i \(-0.536621\pi\)
−0.114796 + 0.993389i \(0.536621\pi\)
\(338\) 1.70564 0.0927745
\(339\) −7.26929 −0.394813
\(340\) 14.0965 0.764490
\(341\) −29.8668 −1.61738
\(342\) −0.381158 −0.0206107
\(343\) −1.00000 −0.0539949
\(344\) −8.78319 −0.473558
\(345\) 17.7705 0.956729
\(346\) −0.783875 −0.0421414
\(347\) −4.57978 −0.245855 −0.122928 0.992416i \(-0.539228\pi\)
−0.122928 + 0.992416i \(0.539228\pi\)
\(348\) −13.7087 −0.734861
\(349\) −4.92462 −0.263609 −0.131804 0.991276i \(-0.542077\pi\)
−0.131804 + 0.991276i \(0.542077\pi\)
\(350\) 0.214735 0.0114781
\(351\) 40.5192 2.16275
\(352\) 14.7529 0.786332
\(353\) 6.98527 0.371788 0.185894 0.982570i \(-0.440482\pi\)
0.185894 + 0.982570i \(0.440482\pi\)
\(354\) −6.53853 −0.347519
\(355\) −13.2611 −0.703828
\(356\) 29.0097 1.53751
\(357\) 24.3043 1.28632
\(358\) 0.433417 0.0229068
\(359\) −29.4696 −1.55534 −0.777672 0.628670i \(-0.783600\pi\)
−0.777672 + 0.628670i \(0.783600\pi\)
\(360\) −7.08831 −0.373587
\(361\) −18.9548 −0.997621
\(362\) 2.06793 0.108688
\(363\) −80.4383 −4.22192
\(364\) −4.39387 −0.230301
\(365\) 6.55806 0.343264
\(366\) 8.55461 0.447157
\(367\) 30.8786 1.61185 0.805926 0.592016i \(-0.201668\pi\)
0.805926 + 0.592016i \(0.201668\pi\)
\(368\) 19.6520 1.02443
\(369\) 92.9058 4.83648
\(370\) 1.72782 0.0898253
\(371\) −5.38853 −0.279758
\(372\) 33.2879 1.72590
\(373\) −5.29925 −0.274385 −0.137192 0.990544i \(-0.543808\pi\)
−0.137192 + 0.990544i \(0.543808\pi\)
\(374\) 9.14932 0.473100
\(375\) 3.36877 0.173963
\(376\) 0.0352081 0.00181572
\(377\) 4.68350 0.241212
\(378\) −3.86916 −0.199008
\(379\) 17.5667 0.902339 0.451170 0.892438i \(-0.351007\pi\)
0.451170 + 0.892438i \(0.351007\pi\)
\(380\) 0.415420 0.0213106
\(381\) 19.0530 0.976117
\(382\) −2.95612 −0.151248
\(383\) 8.16215 0.417066 0.208533 0.978015i \(-0.433131\pi\)
0.208533 + 0.978015i \(0.433131\pi\)
\(384\) −21.8327 −1.11415
\(385\) −5.90573 −0.300984
\(386\) 1.27137 0.0647112
\(387\) −86.3653 −4.39020
\(388\) 6.77856 0.344129
\(389\) −30.8453 −1.56392 −0.781960 0.623328i \(-0.785780\pi\)
−0.781960 + 0.623328i \(0.785780\pi\)
\(390\) 1.62675 0.0823739
\(391\) 38.0574 1.92464
\(392\) 0.849039 0.0428830
\(393\) 10.1621 0.512612
\(394\) 3.01142 0.151713
\(395\) 8.07443 0.406269
\(396\) 96.3359 4.84106
\(397\) −1.14908 −0.0576707 −0.0288354 0.999584i \(-0.509180\pi\)
−0.0288354 + 0.999584i \(0.509180\pi\)
\(398\) −1.52636 −0.0765094
\(399\) 0.716240 0.0358569
\(400\) 3.72546 0.186273
\(401\) −28.8654 −1.44147 −0.720734 0.693212i \(-0.756195\pi\)
−0.720734 + 0.693212i \(0.756195\pi\)
\(402\) −2.55672 −0.127518
\(403\) −11.3727 −0.566512
\(404\) 32.2443 1.60421
\(405\) −35.6536 −1.77164
\(406\) −0.447226 −0.0221954
\(407\) −47.5193 −2.35544
\(408\) −20.6353 −1.02160
\(409\) 21.7493 1.07543 0.537717 0.843126i \(-0.319287\pi\)
0.537717 + 0.843126i \(0.319287\pi\)
\(410\) 2.38963 0.118016
\(411\) 22.1379 1.09198
\(412\) −12.9154 −0.636296
\(413\) 9.03869 0.444765
\(414\) −9.45682 −0.464777
\(415\) −13.9985 −0.687160
\(416\) 5.61760 0.275426
\(417\) 72.8072 3.56538
\(418\) 0.269627 0.0131879
\(419\) 24.7149 1.20740 0.603700 0.797211i \(-0.293692\pi\)
0.603700 + 0.797211i \(0.293692\pi\)
\(420\) 6.58220 0.321179
\(421\) 0.861250 0.0419747 0.0209874 0.999780i \(-0.493319\pi\)
0.0209874 + 0.999780i \(0.493319\pi\)
\(422\) 2.71498 0.132163
\(423\) 0.346202 0.0168329
\(424\) 4.57507 0.222185
\(425\) 7.21459 0.349959
\(426\) 9.59303 0.464784
\(427\) −11.8257 −0.572284
\(428\) −18.7384 −0.905752
\(429\) −44.7396 −2.16005
\(430\) −2.22141 −0.107126
\(431\) 10.4696 0.504305 0.252152 0.967688i \(-0.418862\pi\)
0.252152 + 0.967688i \(0.418862\pi\)
\(432\) −67.1264 −3.22962
\(433\) 9.07031 0.435891 0.217946 0.975961i \(-0.430064\pi\)
0.217946 + 0.975961i \(0.430064\pi\)
\(434\) 1.08597 0.0521282
\(435\) −7.01609 −0.336396
\(436\) −36.5609 −1.75095
\(437\) 1.12154 0.0536504
\(438\) −4.74406 −0.226680
\(439\) −14.7510 −0.704026 −0.352013 0.935995i \(-0.614503\pi\)
−0.352013 + 0.935995i \(0.614503\pi\)
\(440\) 5.01420 0.239042
\(441\) 8.34862 0.397553
\(442\) 3.48387 0.165711
\(443\) −27.5647 −1.30964 −0.654819 0.755786i \(-0.727255\pi\)
−0.654819 + 0.755786i \(0.727255\pi\)
\(444\) 52.9624 2.51348
\(445\) 14.8472 0.703822
\(446\) −1.35152 −0.0639964
\(447\) 27.9343 1.32125
\(448\) 6.91449 0.326679
\(449\) 4.21130 0.198744 0.0993719 0.995050i \(-0.468317\pi\)
0.0993719 + 0.995050i \(0.468317\pi\)
\(450\) −1.79274 −0.0845107
\(451\) −65.7206 −3.09466
\(452\) −4.21619 −0.198313
\(453\) 53.5179 2.51449
\(454\) −5.12259 −0.240415
\(455\) −2.24878 −0.105424
\(456\) −0.608116 −0.0284776
\(457\) −4.61480 −0.215871 −0.107936 0.994158i \(-0.534424\pi\)
−0.107936 + 0.994158i \(0.534424\pi\)
\(458\) −0.214735 −0.0100339
\(459\) −129.995 −6.06763
\(460\) 10.3069 0.480560
\(461\) −5.87390 −0.273575 −0.136787 0.990600i \(-0.543678\pi\)
−0.136787 + 0.990600i \(0.543678\pi\)
\(462\) 4.27217 0.198759
\(463\) 39.6134 1.84099 0.920495 0.390754i \(-0.127786\pi\)
0.920495 + 0.390754i \(0.127786\pi\)
\(464\) −7.75895 −0.360200
\(465\) 17.0367 0.790059
\(466\) 2.15483 0.0998207
\(467\) 19.6211 0.907955 0.453977 0.891013i \(-0.350005\pi\)
0.453977 + 0.891013i \(0.350005\pi\)
\(468\) 36.6827 1.69566
\(469\) 3.53434 0.163201
\(470\) 0.00890467 0.000410742 0
\(471\) −44.2332 −2.03816
\(472\) −7.67420 −0.353234
\(473\) 61.0939 2.80910
\(474\) −5.84100 −0.268286
\(475\) 0.212612 0.00975529
\(476\) 14.0965 0.646112
\(477\) 44.9868 2.05980
\(478\) 2.83660 0.129743
\(479\) 1.81031 0.0827151 0.0413575 0.999144i \(-0.486832\pi\)
0.0413575 + 0.999144i \(0.486832\pi\)
\(480\) −8.41541 −0.384109
\(481\) −18.0944 −0.825032
\(482\) 0.164777 0.00750540
\(483\) 17.7705 0.808584
\(484\) −46.6543 −2.12065
\(485\) 3.46927 0.157531
\(486\) 14.1841 0.643405
\(487\) −12.9102 −0.585018 −0.292509 0.956263i \(-0.594490\pi\)
−0.292509 + 0.956263i \(0.594490\pi\)
\(488\) 10.0405 0.454510
\(489\) 32.8975 1.48768
\(490\) 0.214735 0.00970075
\(491\) 30.5302 1.37781 0.688903 0.724853i \(-0.258092\pi\)
0.688903 + 0.724853i \(0.258092\pi\)
\(492\) 73.2486 3.30230
\(493\) −15.0257 −0.676724
\(494\) 0.102669 0.00461928
\(495\) 49.3047 2.21608
\(496\) 18.8406 0.845967
\(497\) −13.2611 −0.594843
\(498\) 10.1264 0.453776
\(499\) −33.8841 −1.51686 −0.758431 0.651754i \(-0.774034\pi\)
−0.758431 + 0.651754i \(0.774034\pi\)
\(500\) 1.95389 0.0873806
\(501\) 13.8895 0.620535
\(502\) −5.68537 −0.253751
\(503\) 0.190938 0.00851352 0.00425676 0.999991i \(-0.498645\pi\)
0.00425676 + 0.999991i \(0.498645\pi\)
\(504\) −7.08831 −0.315738
\(505\) 16.5026 0.734357
\(506\) 6.68966 0.297392
\(507\) 26.7581 1.18837
\(508\) 11.0508 0.490299
\(509\) −25.2523 −1.11929 −0.559644 0.828733i \(-0.689062\pi\)
−0.559644 + 0.828733i \(0.689062\pi\)
\(510\) −5.21899 −0.231101
\(511\) 6.55806 0.290111
\(512\) −15.6326 −0.690868
\(513\) −3.83090 −0.169138
\(514\) −0.756246 −0.0333566
\(515\) −6.61010 −0.291276
\(516\) −68.0920 −2.99758
\(517\) −0.244900 −0.0107707
\(518\) 1.72782 0.0759162
\(519\) −12.2974 −0.539798
\(520\) 1.90930 0.0837285
\(521\) −25.2292 −1.10531 −0.552655 0.833410i \(-0.686385\pi\)
−0.552655 + 0.833410i \(0.686385\pi\)
\(522\) 3.73372 0.163420
\(523\) 31.4204 1.37392 0.686959 0.726697i \(-0.258945\pi\)
0.686959 + 0.726697i \(0.258945\pi\)
\(524\) 5.89404 0.257482
\(525\) 3.36877 0.147025
\(526\) 3.09999 0.135166
\(527\) 36.4860 1.58936
\(528\) 74.1182 3.22558
\(529\) 4.82619 0.209834
\(530\) 1.15711 0.0502615
\(531\) −75.4606 −3.27471
\(532\) 0.415420 0.0180107
\(533\) −25.0251 −1.08396
\(534\) −10.7403 −0.464780
\(535\) −9.59029 −0.414624
\(536\) −3.00079 −0.129615
\(537\) 6.79946 0.293418
\(538\) 0.948549 0.0408948
\(539\) −5.90573 −0.254378
\(540\) −35.2057 −1.51501
\(541\) 21.4603 0.922651 0.461326 0.887231i \(-0.347374\pi\)
0.461326 + 0.887231i \(0.347374\pi\)
\(542\) −3.22705 −0.138614
\(543\) 32.4417 1.39221
\(544\) −18.0225 −0.772709
\(545\) −18.7119 −0.801528
\(546\) 1.62675 0.0696187
\(547\) −17.9077 −0.765676 −0.382838 0.923815i \(-0.625053\pi\)
−0.382838 + 0.923815i \(0.625053\pi\)
\(548\) 12.8400 0.548497
\(549\) 98.7280 4.21361
\(550\) 1.26817 0.0540749
\(551\) −0.442803 −0.0188640
\(552\) −15.0878 −0.642180
\(553\) 8.07443 0.343360
\(554\) −5.73773 −0.243773
\(555\) 27.1061 1.15059
\(556\) 42.2282 1.79087
\(557\) 38.5013 1.63135 0.815676 0.578509i \(-0.196365\pi\)
0.815676 + 0.578509i \(0.196365\pi\)
\(558\) −9.06636 −0.383809
\(559\) 23.2633 0.983934
\(560\) 3.72546 0.157429
\(561\) 143.535 6.06004
\(562\) 3.74733 0.158072
\(563\) 17.4376 0.734906 0.367453 0.930042i \(-0.380230\pi\)
0.367453 + 0.930042i \(0.380230\pi\)
\(564\) 0.272952 0.0114933
\(565\) −2.15784 −0.0907812
\(566\) −3.79366 −0.159459
\(567\) −35.6536 −1.49731
\(568\) 11.2592 0.472427
\(569\) 1.80984 0.0758723 0.0379361 0.999280i \(-0.487922\pi\)
0.0379361 + 0.999280i \(0.487922\pi\)
\(570\) −0.153802 −0.00644206
\(571\) −22.3497 −0.935307 −0.467653 0.883912i \(-0.654900\pi\)
−0.467653 + 0.883912i \(0.654900\pi\)
\(572\) −25.9490 −1.08498
\(573\) −46.3757 −1.93737
\(574\) 2.38963 0.0997414
\(575\) 5.27505 0.219985
\(576\) −57.7265 −2.40527
\(577\) 20.0123 0.833124 0.416562 0.909107i \(-0.363235\pi\)
0.416562 + 0.909107i \(0.363235\pi\)
\(578\) −7.52654 −0.313063
\(579\) 19.9453 0.828899
\(580\) −4.06933 −0.168970
\(581\) −13.9985 −0.580756
\(582\) −2.50965 −0.104028
\(583\) −31.8232 −1.31798
\(584\) −5.56805 −0.230408
\(585\) 18.7742 0.776219
\(586\) −6.36442 −0.262912
\(587\) 46.1266 1.90385 0.951924 0.306333i \(-0.0991021\pi\)
0.951924 + 0.306333i \(0.0991021\pi\)
\(588\) 6.58220 0.271446
\(589\) 1.07523 0.0443041
\(590\) −1.94092 −0.0799066
\(591\) 47.2432 1.94333
\(592\) 29.9762 1.23201
\(593\) 12.5822 0.516689 0.258344 0.966053i \(-0.416823\pi\)
0.258344 + 0.966053i \(0.416823\pi\)
\(594\) −22.8502 −0.937556
\(595\) 7.21459 0.295769
\(596\) 16.2019 0.663655
\(597\) −23.9455 −0.980026
\(598\) 2.54728 0.104166
\(599\) 21.7020 0.886720 0.443360 0.896344i \(-0.353786\pi\)
0.443360 + 0.896344i \(0.353786\pi\)
\(600\) −2.86022 −0.116768
\(601\) −16.0622 −0.655190 −0.327595 0.944818i \(-0.606238\pi\)
−0.327595 + 0.944818i \(0.606238\pi\)
\(602\) −2.22141 −0.0905378
\(603\) −29.5069 −1.20161
\(604\) 31.0404 1.26302
\(605\) −23.8776 −0.970764
\(606\) −11.9379 −0.484944
\(607\) −5.94493 −0.241297 −0.120649 0.992695i \(-0.538497\pi\)
−0.120649 + 0.992695i \(0.538497\pi\)
\(608\) −0.531118 −0.0215397
\(609\) −7.01609 −0.284306
\(610\) 2.53939 0.102817
\(611\) −0.0932528 −0.00377260
\(612\) −117.686 −4.75719
\(613\) 32.4329 1.30995 0.654977 0.755649i \(-0.272678\pi\)
0.654977 + 0.755649i \(0.272678\pi\)
\(614\) −6.83906 −0.276002
\(615\) 37.4886 1.51169
\(616\) 5.01420 0.202028
\(617\) −0.977694 −0.0393605 −0.0196802 0.999806i \(-0.506265\pi\)
−0.0196802 + 0.999806i \(0.506265\pi\)
\(618\) 4.78171 0.192348
\(619\) −0.688141 −0.0276587 −0.0138294 0.999904i \(-0.504402\pi\)
−0.0138294 + 0.999904i \(0.504402\pi\)
\(620\) 9.88131 0.396843
\(621\) −95.0474 −3.81412
\(622\) −0.505200 −0.0202567
\(623\) 14.8472 0.594839
\(624\) 28.2227 1.12981
\(625\) 1.00000 0.0400000
\(626\) 1.60258 0.0640518
\(627\) 4.22992 0.168927
\(628\) −25.6553 −1.02376
\(629\) 58.0508 2.31464
\(630\) −1.79274 −0.0714246
\(631\) 38.6787 1.53977 0.769887 0.638180i \(-0.220312\pi\)
0.769887 + 0.638180i \(0.220312\pi\)
\(632\) −6.85551 −0.272698
\(633\) 42.5926 1.69290
\(634\) −4.54219 −0.180394
\(635\) 5.65578 0.224443
\(636\) 35.4684 1.40641
\(637\) −2.24878 −0.0891000
\(638\) −2.64119 −0.104566
\(639\) 110.712 4.37971
\(640\) −6.48092 −0.256181
\(641\) −2.62399 −0.103641 −0.0518207 0.998656i \(-0.516502\pi\)
−0.0518207 + 0.998656i \(0.516502\pi\)
\(642\) 6.93756 0.273803
\(643\) −38.7090 −1.52653 −0.763267 0.646083i \(-0.776406\pi\)
−0.763267 + 0.646083i \(0.776406\pi\)
\(644\) 10.3069 0.406148
\(645\) −34.8495 −1.37220
\(646\) −0.329384 −0.0129594
\(647\) −8.02974 −0.315682 −0.157841 0.987465i \(-0.550453\pi\)
−0.157841 + 0.987465i \(0.550453\pi\)
\(648\) 30.2713 1.18917
\(649\) 53.3800 2.09535
\(650\) 0.482893 0.0189406
\(651\) 17.0367 0.667722
\(652\) 19.0806 0.747253
\(653\) 3.28284 0.128468 0.0642338 0.997935i \(-0.479540\pi\)
0.0642338 + 0.997935i \(0.479540\pi\)
\(654\) 13.5360 0.529301
\(655\) 3.01657 0.117867
\(656\) 41.4579 1.61866
\(657\) −54.7508 −2.13603
\(658\) 0.00890467 0.000347140 0
\(659\) −8.97821 −0.349742 −0.174871 0.984591i \(-0.555951\pi\)
−0.174871 + 0.984591i \(0.555951\pi\)
\(660\) 38.8727 1.51312
\(661\) −27.2798 −1.06106 −0.530531 0.847666i \(-0.678007\pi\)
−0.530531 + 0.847666i \(0.678007\pi\)
\(662\) 5.74388 0.223242
\(663\) 54.6551 2.12263
\(664\) 11.8853 0.461238
\(665\) 0.212612 0.00824473
\(666\) −14.4250 −0.558955
\(667\) −10.9863 −0.425390
\(668\) 8.05589 0.311692
\(669\) −21.2027 −0.819744
\(670\) −0.758947 −0.0293207
\(671\) −69.8392 −2.69611
\(672\) −8.41541 −0.324632
\(673\) −29.8943 −1.15234 −0.576170 0.817330i \(-0.695453\pi\)
−0.576170 + 0.817330i \(0.695453\pi\)
\(674\) 0.905053 0.0348613
\(675\) −18.0183 −0.693524
\(676\) 15.5197 0.596912
\(677\) −30.4545 −1.17046 −0.585230 0.810867i \(-0.698996\pi\)
−0.585230 + 0.810867i \(0.698996\pi\)
\(678\) 1.56097 0.0599488
\(679\) 3.46927 0.133138
\(680\) −6.12547 −0.234901
\(681\) −80.3633 −3.07953
\(682\) 6.41345 0.245584
\(683\) −26.7470 −1.02345 −0.511723 0.859151i \(-0.670993\pi\)
−0.511723 + 0.859151i \(0.670993\pi\)
\(684\) −3.46818 −0.132609
\(685\) 6.57150 0.251084
\(686\) 0.214735 0.00819863
\(687\) −3.36877 −0.128527
\(688\) −38.5393 −1.46930
\(689\) −12.1176 −0.461644
\(690\) −3.81594 −0.145270
\(691\) 18.6827 0.710724 0.355362 0.934729i \(-0.384358\pi\)
0.355362 + 0.934729i \(0.384358\pi\)
\(692\) −7.13252 −0.271138
\(693\) 49.3047 1.87293
\(694\) 0.983440 0.0373309
\(695\) 21.6124 0.819804
\(696\) 5.95693 0.225797
\(697\) 80.2860 3.04105
\(698\) 1.05749 0.0400265
\(699\) 33.8051 1.27862
\(700\) 1.95389 0.0738501
\(701\) 3.81048 0.143920 0.0719599 0.997408i \(-0.477075\pi\)
0.0719599 + 0.997408i \(0.477075\pi\)
\(702\) −8.70090 −0.328394
\(703\) 1.71074 0.0645217
\(704\) 40.8351 1.53903
\(705\) 0.139697 0.00526128
\(706\) −1.49998 −0.0564526
\(707\) 16.5026 0.620645
\(708\) −59.4945 −2.23594
\(709\) 36.2561 1.36163 0.680813 0.732457i \(-0.261627\pi\)
0.680813 + 0.732457i \(0.261627\pi\)
\(710\) 2.84763 0.106870
\(711\) −67.4104 −2.52809
\(712\) −12.6058 −0.472423
\(713\) 26.6773 0.999072
\(714\) −5.21899 −0.195316
\(715\) −13.2807 −0.496670
\(716\) 3.94369 0.147383
\(717\) 44.5006 1.66191
\(718\) 6.32816 0.236165
\(719\) 10.6407 0.396832 0.198416 0.980118i \(-0.436420\pi\)
0.198416 + 0.980118i \(0.436420\pi\)
\(720\) −31.1024 −1.15912
\(721\) −6.61010 −0.246173
\(722\) 4.07026 0.151480
\(723\) 2.58503 0.0961383
\(724\) 18.8162 0.699299
\(725\) −2.08268 −0.0773489
\(726\) 17.2729 0.641059
\(727\) 26.0857 0.967463 0.483732 0.875216i \(-0.339281\pi\)
0.483732 + 0.875216i \(0.339281\pi\)
\(728\) 1.90930 0.0707635
\(729\) 115.560 4.28001
\(730\) −1.40825 −0.0521215
\(731\) −74.6339 −2.76044
\(732\) 77.8389 2.87701
\(733\) 22.6223 0.835575 0.417788 0.908545i \(-0.362806\pi\)
0.417788 + 0.908545i \(0.362806\pi\)
\(734\) −6.63073 −0.244745
\(735\) 3.36877 0.124259
\(736\) −13.1774 −0.485727
\(737\) 20.8729 0.768862
\(738\) −19.9502 −0.734375
\(739\) 21.8936 0.805370 0.402685 0.915339i \(-0.368077\pi\)
0.402685 + 0.915339i \(0.368077\pi\)
\(740\) 15.7216 0.577937
\(741\) 1.61067 0.0591693
\(742\) 1.15711 0.0424787
\(743\) 15.1105 0.554351 0.277176 0.960819i \(-0.410602\pi\)
0.277176 + 0.960819i \(0.410602\pi\)
\(744\) −14.4649 −0.530307
\(745\) 8.29212 0.303800
\(746\) 1.13794 0.0416628
\(747\) 116.868 4.27598
\(748\) 83.2502 3.04393
\(749\) −9.59029 −0.350421
\(750\) −0.723394 −0.0264146
\(751\) 41.5660 1.51677 0.758383 0.651809i \(-0.225990\pi\)
0.758383 + 0.651809i \(0.225990\pi\)
\(752\) 0.154488 0.00563359
\(753\) −89.1923 −3.25035
\(754\) −1.00571 −0.0366259
\(755\) 15.8865 0.578168
\(756\) −35.2057 −1.28042
\(757\) 15.0214 0.545961 0.272981 0.962020i \(-0.411991\pi\)
0.272981 + 0.962020i \(0.411991\pi\)
\(758\) −3.77218 −0.137012
\(759\) 104.947 3.80935
\(760\) −0.180516 −0.00654799
\(761\) 22.6050 0.819432 0.409716 0.912213i \(-0.365628\pi\)
0.409716 + 0.912213i \(0.365628\pi\)
\(762\) −4.09136 −0.148214
\(763\) −18.7119 −0.677415
\(764\) −26.8979 −0.973132
\(765\) −60.2319 −2.17769
\(766\) −1.75270 −0.0633277
\(767\) 20.3260 0.733930
\(768\) −41.8984 −1.51188
\(769\) −49.2171 −1.77482 −0.887408 0.460986i \(-0.847496\pi\)
−0.887408 + 0.460986i \(0.847496\pi\)
\(770\) 1.26817 0.0457016
\(771\) −11.8640 −0.427272
\(772\) 11.5683 0.416352
\(773\) −30.7727 −1.10682 −0.553409 0.832910i \(-0.686673\pi\)
−0.553409 + 0.832910i \(0.686673\pi\)
\(774\) 18.5457 0.666611
\(775\) 5.05725 0.181662
\(776\) −2.94554 −0.105739
\(777\) 27.1061 0.972427
\(778\) 6.62358 0.237467
\(779\) 2.36600 0.0847708
\(780\) 14.8019 0.529994
\(781\) −78.3167 −2.80239
\(782\) −8.17226 −0.292239
\(783\) 37.5264 1.34108
\(784\) 3.72546 0.133052
\(785\) −13.1304 −0.468643
\(786\) −2.18217 −0.0778354
\(787\) −36.7557 −1.31020 −0.655100 0.755542i \(-0.727373\pi\)
−0.655100 + 0.755542i \(0.727373\pi\)
\(788\) 27.4011 0.976123
\(789\) 48.6327 1.73137
\(790\) −1.73387 −0.0616882
\(791\) −2.15784 −0.0767241
\(792\) −41.8616 −1.48749
\(793\) −26.5933 −0.944357
\(794\) 0.246748 0.00875677
\(795\) 18.1527 0.643810
\(796\) −13.8884 −0.492262
\(797\) 16.8828 0.598019 0.299010 0.954250i \(-0.403344\pi\)
0.299010 + 0.954250i \(0.403344\pi\)
\(798\) −0.153802 −0.00544453
\(799\) 0.299176 0.0105841
\(800\) −2.49807 −0.0883200
\(801\) −123.953 −4.37967
\(802\) 6.19841 0.218874
\(803\) 38.7301 1.36676
\(804\) −23.2637 −0.820449
\(805\) 5.27505 0.185921
\(806\) 2.44211 0.0860196
\(807\) 14.8809 0.523831
\(808\) −14.0114 −0.492918
\(809\) −46.4383 −1.63268 −0.816342 0.577568i \(-0.804002\pi\)
−0.816342 + 0.577568i \(0.804002\pi\)
\(810\) 7.65609 0.269008
\(811\) −44.7473 −1.57129 −0.785646 0.618677i \(-0.787669\pi\)
−0.785646 + 0.618677i \(0.787669\pi\)
\(812\) −4.06933 −0.142806
\(813\) −50.6261 −1.77553
\(814\) 10.2041 0.357652
\(815\) 9.76544 0.342068
\(816\) −90.5447 −3.16970
\(817\) −2.19944 −0.0769486
\(818\) −4.67034 −0.163295
\(819\) 18.7742 0.656024
\(820\) 21.7434 0.759313
\(821\) 7.10233 0.247873 0.123937 0.992290i \(-0.460448\pi\)
0.123937 + 0.992290i \(0.460448\pi\)
\(822\) −4.75379 −0.165807
\(823\) −17.8533 −0.622325 −0.311163 0.950357i \(-0.600718\pi\)
−0.311163 + 0.950357i \(0.600718\pi\)
\(824\) 5.61223 0.195511
\(825\) 19.8951 0.692657
\(826\) −1.94092 −0.0675334
\(827\) −45.9424 −1.59757 −0.798786 0.601615i \(-0.794524\pi\)
−0.798786 + 0.601615i \(0.794524\pi\)
\(828\) −86.0481 −2.99038
\(829\) 47.0502 1.63412 0.817061 0.576552i \(-0.195602\pi\)
0.817061 + 0.576552i \(0.195602\pi\)
\(830\) 3.00597 0.104339
\(831\) −90.0136 −3.12254
\(832\) 15.5492 0.539071
\(833\) 7.21459 0.249971
\(834\) −15.6343 −0.541370
\(835\) 4.12300 0.142682
\(836\) 2.45336 0.0848511
\(837\) −91.1230 −3.14967
\(838\) −5.30715 −0.183333
\(839\) −24.4294 −0.843398 −0.421699 0.906736i \(-0.638566\pi\)
−0.421699 + 0.906736i \(0.638566\pi\)
\(840\) −2.86022 −0.0986870
\(841\) −24.6624 −0.850429
\(842\) −0.184941 −0.00637348
\(843\) 58.7883 2.02478
\(844\) 24.7037 0.850337
\(845\) 7.94298 0.273247
\(846\) −0.0743417 −0.00255592
\(847\) −23.8776 −0.820446
\(848\) 20.0747 0.689369
\(849\) −59.5150 −2.04255
\(850\) −1.54923 −0.0531381
\(851\) 42.4447 1.45498
\(852\) 87.2875 2.99042
\(853\) −26.8172 −0.918204 −0.459102 0.888384i \(-0.651829\pi\)
−0.459102 + 0.888384i \(0.651829\pi\)
\(854\) 2.53939 0.0868960
\(855\) −1.77501 −0.0607042
\(856\) 8.14253 0.278306
\(857\) −43.4612 −1.48460 −0.742302 0.670065i \(-0.766266\pi\)
−0.742302 + 0.670065i \(0.766266\pi\)
\(858\) 9.60718 0.327984
\(859\) −20.5241 −0.700272 −0.350136 0.936699i \(-0.613865\pi\)
−0.350136 + 0.936699i \(0.613865\pi\)
\(860\) −20.2127 −0.689247
\(861\) 37.4886 1.27761
\(862\) −2.24820 −0.0765740
\(863\) 9.26840 0.315500 0.157750 0.987479i \(-0.449576\pi\)
0.157750 + 0.987479i \(0.449576\pi\)
\(864\) 45.0109 1.53130
\(865\) −3.65042 −0.124118
\(866\) −1.94771 −0.0661860
\(867\) −118.077 −4.01009
\(868\) 9.88131 0.335393
\(869\) 47.6854 1.61762
\(870\) 1.50660 0.0510786
\(871\) 7.94796 0.269306
\(872\) 15.8871 0.538005
\(873\) −28.9636 −0.980269
\(874\) −0.240834 −0.00814632
\(875\) 1.00000 0.0338062
\(876\) −43.1665 −1.45846
\(877\) −9.63559 −0.325371 −0.162685 0.986678i \(-0.552016\pi\)
−0.162685 + 0.986678i \(0.552016\pi\)
\(878\) 3.16756 0.106900
\(879\) −99.8452 −3.36769
\(880\) 22.0016 0.741672
\(881\) −17.3349 −0.584029 −0.292014 0.956414i \(-0.594326\pi\)
−0.292014 + 0.956414i \(0.594326\pi\)
\(882\) −1.79274 −0.0603648
\(883\) 20.6680 0.695534 0.347767 0.937581i \(-0.386940\pi\)
0.347767 + 0.937581i \(0.386940\pi\)
\(884\) 31.7000 1.06619
\(885\) −30.4493 −1.02354
\(886\) 5.91911 0.198856
\(887\) 0.301726 0.0101310 0.00506549 0.999987i \(-0.498388\pi\)
0.00506549 + 0.999987i \(0.498388\pi\)
\(888\) −23.0142 −0.772305
\(889\) 5.65578 0.189689
\(890\) −3.18821 −0.106869
\(891\) −210.561 −7.05405
\(892\) −12.2976 −0.411753
\(893\) 0.00881661 0.000295037 0
\(894\) −5.99847 −0.200619
\(895\) 2.01838 0.0674670
\(896\) −6.48092 −0.216512
\(897\) 39.9619 1.33429
\(898\) −0.904316 −0.0301774
\(899\) −10.5327 −0.351284
\(900\) −16.3123 −0.543743
\(901\) 38.8760 1.29515
\(902\) 14.1125 0.469896
\(903\) −34.8495 −1.15972
\(904\) 1.83209 0.0609346
\(905\) 9.63014 0.320117
\(906\) −11.4922 −0.381802
\(907\) −21.8085 −0.724141 −0.362070 0.932151i \(-0.617930\pi\)
−0.362070 + 0.932151i \(0.617930\pi\)
\(908\) −46.6107 −1.54683
\(909\) −137.774 −4.56968
\(910\) 0.482893 0.0160077
\(911\) 8.41717 0.278873 0.139437 0.990231i \(-0.455471\pi\)
0.139437 + 0.990231i \(0.455471\pi\)
\(912\) −2.66832 −0.0883570
\(913\) −82.6714 −2.73602
\(914\) 0.990959 0.0327780
\(915\) 39.8379 1.31700
\(916\) −1.95389 −0.0645583
\(917\) 3.01657 0.0996159
\(918\) 27.9144 0.921313
\(919\) 20.6215 0.680242 0.340121 0.940382i \(-0.389532\pi\)
0.340121 + 0.940382i \(0.389532\pi\)
\(920\) −4.47873 −0.147659
\(921\) −107.291 −3.53537
\(922\) 1.26133 0.0415398
\(923\) −29.8214 −0.981583
\(924\) 38.8727 1.27882
\(925\) 8.04630 0.264561
\(926\) −8.50639 −0.279537
\(927\) 55.1852 1.81252
\(928\) 5.20268 0.170786
\(929\) 40.0576 1.31425 0.657124 0.753782i \(-0.271773\pi\)
0.657124 + 0.753782i \(0.271773\pi\)
\(930\) −3.65839 −0.119963
\(931\) 0.212612 0.00696807
\(932\) 19.6069 0.642247
\(933\) −7.92559 −0.259472
\(934\) −4.21334 −0.137865
\(935\) 42.6074 1.39341
\(936\) −15.9401 −0.521017
\(937\) −47.6732 −1.55742 −0.778708 0.627386i \(-0.784125\pi\)
−0.778708 + 0.627386i \(0.784125\pi\)
\(938\) −0.758947 −0.0247805
\(939\) 25.1412 0.820454
\(940\) 0.0810241 0.00264272
\(941\) −14.7938 −0.482265 −0.241132 0.970492i \(-0.577519\pi\)
−0.241132 + 0.970492i \(0.577519\pi\)
\(942\) 9.49843 0.309476
\(943\) 58.7023 1.91161
\(944\) −33.6733 −1.09597
\(945\) −18.0183 −0.586135
\(946\) −13.1190 −0.426536
\(947\) −35.9742 −1.16900 −0.584502 0.811392i \(-0.698710\pi\)
−0.584502 + 0.811392i \(0.698710\pi\)
\(948\) −53.1476 −1.72615
\(949\) 14.7476 0.478729
\(950\) −0.0456552 −0.00148125
\(951\) −71.2580 −2.31070
\(952\) −6.12547 −0.198528
\(953\) 9.32512 0.302070 0.151035 0.988528i \(-0.451739\pi\)
0.151035 + 0.988528i \(0.451739\pi\)
\(954\) −9.66025 −0.312762
\(955\) −13.7663 −0.445468
\(956\) 25.8104 0.834767
\(957\) −41.4351 −1.33941
\(958\) −0.388737 −0.0125595
\(959\) 6.57150 0.212205
\(960\) −23.2934 −0.751790
\(961\) −5.42420 −0.174974
\(962\) 3.88550 0.125273
\(963\) 80.0657 2.58008
\(964\) 1.49932 0.0482898
\(965\) 5.92065 0.190593
\(966\) −3.81594 −0.122776
\(967\) −60.9891 −1.96128 −0.980639 0.195822i \(-0.937262\pi\)
−0.980639 + 0.195822i \(0.937262\pi\)
\(968\) 20.2731 0.651601
\(969\) −5.16738 −0.166000
\(970\) −0.744974 −0.0239197
\(971\) −4.43121 −0.142204 −0.0711021 0.997469i \(-0.522652\pi\)
−0.0711021 + 0.997469i \(0.522652\pi\)
\(972\) 129.062 4.13967
\(973\) 21.6124 0.692861
\(974\) 2.77228 0.0888296
\(975\) 7.57563 0.242614
\(976\) 44.0560 1.41020
\(977\) −24.6038 −0.787147 −0.393573 0.919293i \(-0.628761\pi\)
−0.393573 + 0.919293i \(0.628761\pi\)
\(978\) −7.06426 −0.225890
\(979\) 87.6833 2.80237
\(980\) 1.95389 0.0624147
\(981\) 156.218 4.98766
\(982\) −6.55590 −0.209207
\(983\) 7.99230 0.254915 0.127457 0.991844i \(-0.459318\pi\)
0.127457 + 0.991844i \(0.459318\pi\)
\(984\) −31.8293 −1.01468
\(985\) 14.0239 0.446837
\(986\) 3.22655 0.102754
\(987\) 0.139697 0.00444659
\(988\) 0.934188 0.0297205
\(989\) −54.5697 −1.73522
\(990\) −10.5875 −0.336492
\(991\) −51.7569 −1.64411 −0.822056 0.569406i \(-0.807173\pi\)
−0.822056 + 0.569406i \(0.807173\pi\)
\(992\) −12.6333 −0.401109
\(993\) 90.1102 2.85956
\(994\) 2.84763 0.0903215
\(995\) −7.10809 −0.225342
\(996\) 92.1410 2.91960
\(997\) 36.7264 1.16314 0.581568 0.813498i \(-0.302439\pi\)
0.581568 + 0.813498i \(0.302439\pi\)
\(998\) 7.27611 0.230321
\(999\) −144.981 −4.58698
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 \(a_p\))