Properties

Label 8023.2.a.c.1.19
Level 8023
Weight 2
Character 8023.1
Self dual Yes
Analytic conductor 64.064
Analytic rank 1
Dimension 158
CM No

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Newspace parameters

Level: \( N \) = \( 8023 = 71 \cdot 113 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8023.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0639775417\)
Analytic rank: \(1\)
Dimension: \(158\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 8023.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.36796 q^{2}\) \(+1.87225 q^{3}\) \(+3.60725 q^{4}\) \(+0.382969 q^{5}\) \(-4.43341 q^{6}\) \(+2.54225 q^{7}\) \(-3.80591 q^{8}\) \(+0.505313 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.36796 q^{2}\) \(+1.87225 q^{3}\) \(+3.60725 q^{4}\) \(+0.382969 q^{5}\) \(-4.43341 q^{6}\) \(+2.54225 q^{7}\) \(-3.80591 q^{8}\) \(+0.505313 q^{9}\) \(-0.906856 q^{10}\) \(-4.20676 q^{11}\) \(+6.75366 q^{12}\) \(+4.28238 q^{13}\) \(-6.01995 q^{14}\) \(+0.717013 q^{15}\) \(+1.79775 q^{16}\) \(-3.63669 q^{17}\) \(-1.19656 q^{18}\) \(+0.776850 q^{19}\) \(+1.38146 q^{20}\) \(+4.75972 q^{21}\) \(+9.96145 q^{22}\) \(-4.01328 q^{23}\) \(-7.12560 q^{24}\) \(-4.85333 q^{25}\) \(-10.1405 q^{26}\) \(-4.67067 q^{27}\) \(+9.17053 q^{28}\) \(+4.95761 q^{29}\) \(-1.69786 q^{30}\) \(-9.26957 q^{31}\) \(+3.35481 q^{32}\) \(-7.87610 q^{33}\) \(+8.61156 q^{34}\) \(+0.973603 q^{35}\) \(+1.82279 q^{36}\) \(+10.1191 q^{37}\) \(-1.83955 q^{38}\) \(+8.01768 q^{39}\) \(-1.45754 q^{40}\) \(+3.97685 q^{41}\) \(-11.2708 q^{42}\) \(+0.574947 q^{43}\) \(-15.1748 q^{44}\) \(+0.193519 q^{45}\) \(+9.50330 q^{46}\) \(-1.41817 q^{47}\) \(+3.36583 q^{48}\) \(-0.536969 q^{49}\) \(+11.4925 q^{50}\) \(-6.80879 q^{51}\) \(+15.4476 q^{52}\) \(+0.542074 q^{53}\) \(+11.0600 q^{54}\) \(-1.61106 q^{55}\) \(-9.67556 q^{56}\) \(+1.45446 q^{57}\) \(-11.7394 q^{58}\) \(-8.80321 q^{59}\) \(+2.58644 q^{60}\) \(+5.60772 q^{61}\) \(+21.9500 q^{62}\) \(+1.28463 q^{63}\) \(-11.5396 q^{64}\) \(+1.64002 q^{65}\) \(+18.6503 q^{66}\) \(+0.897999 q^{67}\) \(-13.1185 q^{68}\) \(-7.51386 q^{69}\) \(-2.30546 q^{70}\) \(-1.00000 q^{71}\) \(-1.92317 q^{72}\) \(+8.25075 q^{73}\) \(-23.9617 q^{74}\) \(-9.08665 q^{75}\) \(+2.80229 q^{76}\) \(-10.6946 q^{77}\) \(-18.9856 q^{78}\) \(-8.24501 q^{79}\) \(+0.688481 q^{80}\) \(-10.2606 q^{81}\) \(-9.41703 q^{82}\) \(+11.2534 q^{83}\) \(+17.1695 q^{84}\) \(-1.39274 q^{85}\) \(-1.36145 q^{86}\) \(+9.28188 q^{87}\) \(+16.0105 q^{88}\) \(-4.33152 q^{89}\) \(-0.458246 q^{90}\) \(+10.8869 q^{91}\) \(-14.4769 q^{92}\) \(-17.3549 q^{93}\) \(+3.35817 q^{94}\) \(+0.297510 q^{95}\) \(+6.28104 q^{96}\) \(-16.7245 q^{97}\) \(+1.27152 q^{98}\) \(-2.12573 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(158q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 158q^{4} \) \(\mathstrut -\mathstrut 31q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(158q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 158q^{4} \) \(\mathstrut -\mathstrut 31q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 10q^{11} \) \(\mathstrut -\mathstrut 46q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 27q^{14} \) \(\mathstrut -\mathstrut 41q^{15} \) \(\mathstrut +\mathstrut 150q^{16} \) \(\mathstrut -\mathstrut 137q^{17} \) \(\mathstrut -\mathstrut 67q^{18} \) \(\mathstrut -\mathstrut 42q^{19} \) \(\mathstrut -\mathstrut 66q^{20} \) \(\mathstrut -\mathstrut 46q^{21} \) \(\mathstrut -\mathstrut 8q^{22} \) \(\mathstrut -\mathstrut 26q^{23} \) \(\mathstrut -\mathstrut 48q^{24} \) \(\mathstrut +\mathstrut 129q^{25} \) \(\mathstrut -\mathstrut 67q^{26} \) \(\mathstrut -\mathstrut 89q^{27} \) \(\mathstrut -\mathstrut 21q^{28} \) \(\mathstrut -\mathstrut 79q^{29} \) \(\mathstrut -\mathstrut 11q^{30} \) \(\mathstrut +\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 147q^{32} \) \(\mathstrut -\mathstrut 112q^{33} \) \(\mathstrut -\mathstrut 28q^{34} \) \(\mathstrut -\mathstrut 53q^{35} \) \(\mathstrut +\mathstrut 141q^{36} \) \(\mathstrut -\mathstrut 60q^{37} \) \(\mathstrut -\mathstrut 53q^{38} \) \(\mathstrut -\mathstrut 3q^{39} \) \(\mathstrut -\mathstrut 48q^{40} \) \(\mathstrut -\mathstrut 128q^{41} \) \(\mathstrut +\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 63q^{43} \) \(\mathstrut -\mathstrut 88q^{45} \) \(\mathstrut -\mathstrut 2q^{46} \) \(\mathstrut -\mathstrut 92q^{47} \) \(\mathstrut -\mathstrut 131q^{48} \) \(\mathstrut +\mathstrut 122q^{49} \) \(\mathstrut -\mathstrut 116q^{50} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 89q^{52} \) \(\mathstrut -\mathstrut 94q^{53} \) \(\mathstrut -\mathstrut 71q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 104q^{56} \) \(\mathstrut -\mathstrut 93q^{57} \) \(\mathstrut -\mathstrut 65q^{58} \) \(\mathstrut -\mathstrut 54q^{59} \) \(\mathstrut -\mathstrut 12q^{60} \) \(\mathstrut +\mathstrut 17q^{61} \) \(\mathstrut -\mathstrut 97q^{62} \) \(\mathstrut -\mathstrut 28q^{63} \) \(\mathstrut +\mathstrut 163q^{64} \) \(\mathstrut -\mathstrut 163q^{65} \) \(\mathstrut -\mathstrut 65q^{66} \) \(\mathstrut -\mathstrut 35q^{67} \) \(\mathstrut -\mathstrut 217q^{68} \) \(\mathstrut -\mathstrut 46q^{69} \) \(\mathstrut -\mathstrut 79q^{70} \) \(\mathstrut -\mathstrut 158q^{71} \) \(\mathstrut -\mathstrut 99q^{72} \) \(\mathstrut -\mathstrut 165q^{73} \) \(\mathstrut -\mathstrut 94q^{75} \) \(\mathstrut -\mathstrut 93q^{76} \) \(\mathstrut -\mathstrut 140q^{77} \) \(\mathstrut +\mathstrut 25q^{78} \) \(\mathstrut -\mathstrut 61q^{79} \) \(\mathstrut -\mathstrut 134q^{80} \) \(\mathstrut +\mathstrut 114q^{81} \) \(\mathstrut +\mathstrut 10q^{82} \) \(\mathstrut -\mathstrut 158q^{83} \) \(\mathstrut -\mathstrut 160q^{84} \) \(\mathstrut +\mathstrut 23q^{85} \) \(\mathstrut -\mathstrut 122q^{86} \) \(\mathstrut -\mathstrut 71q^{87} \) \(\mathstrut -\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 251q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut -\mathstrut 57q^{91} \) \(\mathstrut -\mathstrut 58q^{92} \) \(\mathstrut -\mathstrut 52q^{93} \) \(\mathstrut -\mathstrut 64q^{94} \) \(\mathstrut -\mathstrut 84q^{95} \) \(\mathstrut -\mathstrut 98q^{96} \) \(\mathstrut -\mathstrut 48q^{97} \) \(\mathstrut -\mathstrut 84q^{98} \) \(\mathstrut +\mathstrut 85q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.36796 −1.67440 −0.837201 0.546895i \(-0.815810\pi\)
−0.837201 + 0.546895i \(0.815810\pi\)
\(3\) 1.87225 1.08094 0.540471 0.841362i \(-0.318246\pi\)
0.540471 + 0.841362i \(0.318246\pi\)
\(4\) 3.60725 1.80362
\(5\) 0.382969 0.171269 0.0856345 0.996327i \(-0.472708\pi\)
0.0856345 + 0.996327i \(0.472708\pi\)
\(6\) −4.43341 −1.80993
\(7\) 2.54225 0.960880 0.480440 0.877028i \(-0.340477\pi\)
0.480440 + 0.877028i \(0.340477\pi\)
\(8\) −3.80591 −1.34559
\(9\) 0.505313 0.168438
\(10\) −0.906856 −0.286773
\(11\) −4.20676 −1.26839 −0.634193 0.773175i \(-0.718668\pi\)
−0.634193 + 0.773175i \(0.718668\pi\)
\(12\) 6.75366 1.94962
\(13\) 4.28238 1.18772 0.593860 0.804569i \(-0.297603\pi\)
0.593860 + 0.804569i \(0.297603\pi\)
\(14\) −6.01995 −1.60890
\(15\) 0.717013 0.185132
\(16\) 1.79775 0.449437
\(17\) −3.63669 −0.882028 −0.441014 0.897500i \(-0.645381\pi\)
−0.441014 + 0.897500i \(0.645381\pi\)
\(18\) −1.19656 −0.282032
\(19\) 0.776850 0.178222 0.0891109 0.996022i \(-0.471597\pi\)
0.0891109 + 0.996022i \(0.471597\pi\)
\(20\) 1.38146 0.308905
\(21\) 4.75972 1.03866
\(22\) 9.96145 2.12379
\(23\) −4.01328 −0.836827 −0.418413 0.908257i \(-0.637414\pi\)
−0.418413 + 0.908257i \(0.637414\pi\)
\(24\) −7.12560 −1.45451
\(25\) −4.85333 −0.970667
\(26\) −10.1405 −1.98872
\(27\) −4.67067 −0.898872
\(28\) 9.17053 1.73307
\(29\) 4.95761 0.920606 0.460303 0.887762i \(-0.347741\pi\)
0.460303 + 0.887762i \(0.347741\pi\)
\(30\) −1.69786 −0.309985
\(31\) −9.26957 −1.66486 −0.832432 0.554128i \(-0.813052\pi\)
−0.832432 + 0.554128i \(0.813052\pi\)
\(32\) 3.35481 0.593053
\(33\) −7.87610 −1.37105
\(34\) 8.61156 1.47687
\(35\) 0.973603 0.164569
\(36\) 1.82279 0.303798
\(37\) 10.1191 1.66358 0.831788 0.555093i \(-0.187317\pi\)
0.831788 + 0.555093i \(0.187317\pi\)
\(38\) −1.83955 −0.298415
\(39\) 8.01768 1.28386
\(40\) −1.45754 −0.230458
\(41\) 3.97685 0.621079 0.310540 0.950560i \(-0.399490\pi\)
0.310540 + 0.950560i \(0.399490\pi\)
\(42\) −11.2708 −1.73913
\(43\) 0.574947 0.0876786 0.0438393 0.999039i \(-0.486041\pi\)
0.0438393 + 0.999039i \(0.486041\pi\)
\(44\) −15.1748 −2.28769
\(45\) 0.193519 0.0288481
\(46\) 9.50330 1.40118
\(47\) −1.41817 −0.206861 −0.103431 0.994637i \(-0.532982\pi\)
−0.103431 + 0.994637i \(0.532982\pi\)
\(48\) 3.36583 0.485815
\(49\) −0.536969 −0.0767099
\(50\) 11.4925 1.62529
\(51\) −6.80879 −0.953422
\(52\) 15.4476 2.14220
\(53\) 0.542074 0.0744596 0.0372298 0.999307i \(-0.488147\pi\)
0.0372298 + 0.999307i \(0.488147\pi\)
\(54\) 11.0600 1.50507
\(55\) −1.61106 −0.217235
\(56\) −9.67556 −1.29295
\(57\) 1.45446 0.192647
\(58\) −11.7394 −1.54146
\(59\) −8.80321 −1.14608 −0.573040 0.819527i \(-0.694236\pi\)
−0.573040 + 0.819527i \(0.694236\pi\)
\(60\) 2.58644 0.333909
\(61\) 5.60772 0.717995 0.358997 0.933339i \(-0.383119\pi\)
0.358997 + 0.933339i \(0.383119\pi\)
\(62\) 21.9500 2.78765
\(63\) 1.28463 0.161848
\(64\) −11.5396 −1.44245
\(65\) 1.64002 0.203419
\(66\) 18.6503 2.29569
\(67\) 0.897999 0.109708 0.0548540 0.998494i \(-0.482531\pi\)
0.0548540 + 0.998494i \(0.482531\pi\)
\(68\) −13.1185 −1.59085
\(69\) −7.51386 −0.904562
\(70\) −2.30546 −0.275555
\(71\) −1.00000 −0.118678
\(72\) −1.92317 −0.226648
\(73\) 8.25075 0.965677 0.482839 0.875709i \(-0.339606\pi\)
0.482839 + 0.875709i \(0.339606\pi\)
\(74\) −23.9617 −2.78550
\(75\) −9.08665 −1.04924
\(76\) 2.80229 0.321445
\(77\) −10.6946 −1.21877
\(78\) −18.9856 −2.14969
\(79\) −8.24501 −0.927636 −0.463818 0.885931i \(-0.653521\pi\)
−0.463818 + 0.885931i \(0.653521\pi\)
\(80\) 0.688481 0.0769745
\(81\) −10.2606 −1.14007
\(82\) −9.41703 −1.03994
\(83\) 11.2534 1.23522 0.617610 0.786484i \(-0.288101\pi\)
0.617610 + 0.786484i \(0.288101\pi\)
\(84\) 17.1695 1.87335
\(85\) −1.39274 −0.151064
\(86\) −1.36145 −0.146809
\(87\) 9.28188 0.995122
\(88\) 16.0105 1.70673
\(89\) −4.33152 −0.459140 −0.229570 0.973292i \(-0.573732\pi\)
−0.229570 + 0.973292i \(0.573732\pi\)
\(90\) −0.458246 −0.0483034
\(91\) 10.8869 1.14126
\(92\) −14.4769 −1.50932
\(93\) −17.3549 −1.79962
\(94\) 3.35817 0.346369
\(95\) 0.297510 0.0305238
\(96\) 6.28104 0.641056
\(97\) −16.7245 −1.69812 −0.849058 0.528300i \(-0.822830\pi\)
−0.849058 + 0.528300i \(0.822830\pi\)
\(98\) 1.27152 0.128443
\(99\) −2.12573 −0.213644
\(100\) −17.5072 −1.75072
\(101\) −6.73956 −0.670611 −0.335305 0.942109i \(-0.608840\pi\)
−0.335305 + 0.942109i \(0.608840\pi\)
\(102\) 16.1230 1.59641
\(103\) 14.3076 1.40977 0.704886 0.709320i \(-0.250998\pi\)
0.704886 + 0.709320i \(0.250998\pi\)
\(104\) −16.2983 −1.59818
\(105\) 1.82283 0.177890
\(106\) −1.28361 −0.124675
\(107\) −10.6256 −1.02721 −0.513606 0.858026i \(-0.671691\pi\)
−0.513606 + 0.858026i \(0.671691\pi\)
\(108\) −16.8483 −1.62123
\(109\) 3.36276 0.322094 0.161047 0.986947i \(-0.448513\pi\)
0.161047 + 0.986947i \(0.448513\pi\)
\(110\) 3.81493 0.363739
\(111\) 18.9455 1.79823
\(112\) 4.57032 0.431855
\(113\) −1.00000 −0.0940721
\(114\) −3.44410 −0.322569
\(115\) −1.53696 −0.143322
\(116\) 17.8833 1.66043
\(117\) 2.16394 0.200057
\(118\) 20.8457 1.91900
\(119\) −9.24538 −0.847523
\(120\) −2.72888 −0.249112
\(121\) 6.69683 0.608803
\(122\) −13.2789 −1.20221
\(123\) 7.44565 0.671351
\(124\) −33.4376 −3.00279
\(125\) −3.77352 −0.337514
\(126\) −3.04196 −0.270999
\(127\) 16.1851 1.43620 0.718099 0.695941i \(-0.245012\pi\)
0.718099 + 0.695941i \(0.245012\pi\)
\(128\) 20.6156 1.82218
\(129\) 1.07644 0.0947755
\(130\) −3.88351 −0.340606
\(131\) 4.51588 0.394554 0.197277 0.980348i \(-0.436790\pi\)
0.197277 + 0.980348i \(0.436790\pi\)
\(132\) −28.4110 −2.47286
\(133\) 1.97495 0.171250
\(134\) −2.12643 −0.183695
\(135\) −1.78872 −0.153949
\(136\) 13.8409 1.18685
\(137\) −11.0970 −0.948078 −0.474039 0.880504i \(-0.657205\pi\)
−0.474039 + 0.880504i \(0.657205\pi\)
\(138\) 17.7925 1.51460
\(139\) 10.0748 0.854537 0.427268 0.904125i \(-0.359476\pi\)
0.427268 + 0.904125i \(0.359476\pi\)
\(140\) 3.51203 0.296820
\(141\) −2.65517 −0.223605
\(142\) 2.36796 0.198715
\(143\) −18.0150 −1.50649
\(144\) 0.908424 0.0757020
\(145\) 1.89861 0.157671
\(146\) −19.5375 −1.61693
\(147\) −1.00534 −0.0829190
\(148\) 36.5023 3.00047
\(149\) −14.0421 −1.15037 −0.575186 0.818023i \(-0.695070\pi\)
−0.575186 + 0.818023i \(0.695070\pi\)
\(150\) 21.5168 1.75684
\(151\) −16.5753 −1.34887 −0.674437 0.738332i \(-0.735614\pi\)
−0.674437 + 0.738332i \(0.735614\pi\)
\(152\) −2.95662 −0.239814
\(153\) −1.83767 −0.148567
\(154\) 25.3245 2.04071
\(155\) −3.54996 −0.285139
\(156\) 28.9218 2.31560
\(157\) −0.0325466 −0.00259750 −0.00129875 0.999999i \(-0.500413\pi\)
−0.00129875 + 0.999999i \(0.500413\pi\)
\(158\) 19.5239 1.55324
\(159\) 1.01490 0.0804866
\(160\) 1.28479 0.101572
\(161\) −10.2028 −0.804090
\(162\) 24.2967 1.90893
\(163\) −17.8994 −1.40199 −0.700996 0.713166i \(-0.747261\pi\)
−0.700996 + 0.713166i \(0.747261\pi\)
\(164\) 14.3455 1.12019
\(165\) −3.01630 −0.234819
\(166\) −26.6476 −2.06826
\(167\) −0.886279 −0.0685823 −0.0342912 0.999412i \(-0.510917\pi\)
−0.0342912 + 0.999412i \(0.510917\pi\)
\(168\) −18.1151 −1.39761
\(169\) 5.33880 0.410677
\(170\) 3.29796 0.252942
\(171\) 0.392552 0.0300192
\(172\) 2.07398 0.158139
\(173\) −17.2769 −1.31354 −0.656770 0.754091i \(-0.728078\pi\)
−0.656770 + 0.754091i \(0.728078\pi\)
\(174\) −21.9792 −1.66624
\(175\) −12.3384 −0.932694
\(176\) −7.56269 −0.570059
\(177\) −16.4818 −1.23885
\(178\) 10.2569 0.768786
\(179\) −13.0727 −0.977099 −0.488550 0.872536i \(-0.662474\pi\)
−0.488550 + 0.872536i \(0.662474\pi\)
\(180\) 0.698072 0.0520312
\(181\) 5.27337 0.391967 0.195983 0.980607i \(-0.437210\pi\)
0.195983 + 0.980607i \(0.437210\pi\)
\(182\) −25.7797 −1.91092
\(183\) 10.4990 0.776111
\(184\) 15.2742 1.12603
\(185\) 3.87532 0.284919
\(186\) 41.0958 3.01329
\(187\) 15.2987 1.11875
\(188\) −5.11569 −0.373100
\(189\) −11.8740 −0.863708
\(190\) −0.704492 −0.0511092
\(191\) −24.1124 −1.74471 −0.872356 0.488871i \(-0.837409\pi\)
−0.872356 + 0.488871i \(0.837409\pi\)
\(192\) −21.6049 −1.55920
\(193\) 21.4365 1.54303 0.771516 0.636209i \(-0.219499\pi\)
0.771516 + 0.636209i \(0.219499\pi\)
\(194\) 39.6030 2.84333
\(195\) 3.07052 0.219885
\(196\) −1.93698 −0.138356
\(197\) −25.5483 −1.82024 −0.910119 0.414348i \(-0.864010\pi\)
−0.910119 + 0.414348i \(0.864010\pi\)
\(198\) 5.03365 0.357726
\(199\) −4.20266 −0.297919 −0.148960 0.988843i \(-0.547592\pi\)
−0.148960 + 0.988843i \(0.547592\pi\)
\(200\) 18.4713 1.30612
\(201\) 1.68128 0.118588
\(202\) 15.9590 1.12287
\(203\) 12.6035 0.884592
\(204\) −24.5610 −1.71961
\(205\) 1.52301 0.106372
\(206\) −33.8799 −2.36053
\(207\) −2.02796 −0.140953
\(208\) 7.69864 0.533805
\(209\) −3.26802 −0.226054
\(210\) −4.31638 −0.297859
\(211\) −19.8670 −1.36770 −0.683850 0.729622i \(-0.739696\pi\)
−0.683850 + 0.729622i \(0.739696\pi\)
\(212\) 1.95540 0.134297
\(213\) −1.87225 −0.128284
\(214\) 25.1610 1.71997
\(215\) 0.220187 0.0150166
\(216\) 17.7761 1.20951
\(217\) −23.5655 −1.59973
\(218\) −7.96290 −0.539316
\(219\) 15.4475 1.04384
\(220\) −5.81149 −0.391811
\(221\) −15.5737 −1.04760
\(222\) −44.8623 −3.01096
\(223\) 19.6582 1.31641 0.658205 0.752839i \(-0.271316\pi\)
0.658205 + 0.752839i \(0.271316\pi\)
\(224\) 8.52877 0.569853
\(225\) −2.45245 −0.163497
\(226\) 2.36796 0.157515
\(227\) 23.9419 1.58908 0.794541 0.607210i \(-0.207711\pi\)
0.794541 + 0.607210i \(0.207711\pi\)
\(228\) 5.24659 0.347464
\(229\) −27.2214 −1.79884 −0.899420 0.437086i \(-0.856011\pi\)
−0.899420 + 0.437086i \(0.856011\pi\)
\(230\) 3.63947 0.239979
\(231\) −20.0230 −1.31742
\(232\) −18.8682 −1.23876
\(233\) −15.7125 −1.02936 −0.514680 0.857382i \(-0.672089\pi\)
−0.514680 + 0.857382i \(0.672089\pi\)
\(234\) −5.12414 −0.334975
\(235\) −0.543115 −0.0354289
\(236\) −31.7554 −2.06710
\(237\) −15.4367 −1.00272
\(238\) 21.8927 1.41909
\(239\) 8.67855 0.561369 0.280684 0.959800i \(-0.409439\pi\)
0.280684 + 0.959800i \(0.409439\pi\)
\(240\) 1.28901 0.0832051
\(241\) −12.1075 −0.779912 −0.389956 0.920834i \(-0.627510\pi\)
−0.389956 + 0.920834i \(0.627510\pi\)
\(242\) −15.8579 −1.01938
\(243\) −5.19836 −0.333475
\(244\) 20.2284 1.29499
\(245\) −0.205643 −0.0131380
\(246\) −17.6310 −1.12411
\(247\) 3.32677 0.211677
\(248\) 35.2791 2.24022
\(249\) 21.0691 1.33520
\(250\) 8.93556 0.565134
\(251\) 1.12180 0.0708077 0.0354038 0.999373i \(-0.488728\pi\)
0.0354038 + 0.999373i \(0.488728\pi\)
\(252\) 4.63398 0.291914
\(253\) 16.8829 1.06142
\(254\) −38.3258 −2.40478
\(255\) −2.60756 −0.163292
\(256\) −25.7379 −1.60862
\(257\) −31.6507 −1.97431 −0.987157 0.159752i \(-0.948931\pi\)
−0.987157 + 0.159752i \(0.948931\pi\)
\(258\) −2.54898 −0.158692
\(259\) 25.7254 1.59850
\(260\) 5.91596 0.366892
\(261\) 2.50515 0.155065
\(262\) −10.6934 −0.660643
\(263\) 29.9446 1.84646 0.923231 0.384245i \(-0.125538\pi\)
0.923231 + 0.384245i \(0.125538\pi\)
\(264\) 29.9757 1.84488
\(265\) 0.207598 0.0127526
\(266\) −4.67660 −0.286741
\(267\) −8.10968 −0.496305
\(268\) 3.23931 0.197872
\(269\) −30.5929 −1.86528 −0.932641 0.360806i \(-0.882501\pi\)
−0.932641 + 0.360806i \(0.882501\pi\)
\(270\) 4.23563 0.257772
\(271\) −19.2200 −1.16753 −0.583766 0.811922i \(-0.698421\pi\)
−0.583766 + 0.811922i \(0.698421\pi\)
\(272\) −6.53785 −0.396416
\(273\) 20.3829 1.23363
\(274\) 26.2772 1.58747
\(275\) 20.4168 1.23118
\(276\) −27.1043 −1.63149
\(277\) −18.5752 −1.11608 −0.558038 0.829816i \(-0.688446\pi\)
−0.558038 + 0.829816i \(0.688446\pi\)
\(278\) −23.8568 −1.43084
\(279\) −4.68403 −0.280425
\(280\) −3.70544 −0.221442
\(281\) 3.17225 0.189241 0.0946204 0.995513i \(-0.469836\pi\)
0.0946204 + 0.995513i \(0.469836\pi\)
\(282\) 6.28734 0.374405
\(283\) 14.0610 0.835838 0.417919 0.908484i \(-0.362760\pi\)
0.417919 + 0.908484i \(0.362760\pi\)
\(284\) −3.60725 −0.214051
\(285\) 0.557012 0.0329945
\(286\) 42.6588 2.52246
\(287\) 10.1101 0.596783
\(288\) 1.69523 0.0998924
\(289\) −3.77446 −0.222027
\(290\) −4.49584 −0.264005
\(291\) −31.3124 −1.83557
\(292\) 29.7625 1.74172
\(293\) −9.24420 −0.540052 −0.270026 0.962853i \(-0.587032\pi\)
−0.270026 + 0.962853i \(0.587032\pi\)
\(294\) 2.38061 0.138840
\(295\) −3.37136 −0.196288
\(296\) −38.5125 −2.23849
\(297\) 19.6484 1.14012
\(298\) 33.2511 1.92619
\(299\) −17.1864 −0.993915
\(300\) −32.7778 −1.89243
\(301\) 1.46166 0.0842486
\(302\) 39.2496 2.25856
\(303\) −12.6181 −0.724892
\(304\) 1.39658 0.0800994
\(305\) 2.14758 0.122970
\(306\) 4.35153 0.248760
\(307\) 17.8048 1.01618 0.508088 0.861305i \(-0.330352\pi\)
0.508088 + 0.861305i \(0.330352\pi\)
\(308\) −38.5782 −2.19820
\(309\) 26.7874 1.52388
\(310\) 8.40617 0.477438
\(311\) −6.69804 −0.379811 −0.189906 0.981802i \(-0.560818\pi\)
−0.189906 + 0.981802i \(0.560818\pi\)
\(312\) −30.5145 −1.72755
\(313\) −2.86602 −0.161997 −0.0809985 0.996714i \(-0.525811\pi\)
−0.0809985 + 0.996714i \(0.525811\pi\)
\(314\) 0.0770691 0.00434926
\(315\) 0.491974 0.0277196
\(316\) −29.7418 −1.67311
\(317\) 6.36404 0.357440 0.178720 0.983900i \(-0.442804\pi\)
0.178720 + 0.983900i \(0.442804\pi\)
\(318\) −2.40324 −0.134767
\(319\) −20.8555 −1.16768
\(320\) −4.41930 −0.247046
\(321\) −19.8937 −1.11036
\(322\) 24.1598 1.34637
\(323\) −2.82517 −0.157197
\(324\) −37.0125 −2.05625
\(325\) −20.7838 −1.15288
\(326\) 42.3852 2.34750
\(327\) 6.29593 0.348166
\(328\) −15.1355 −0.835719
\(329\) −3.60534 −0.198769
\(330\) 7.14249 0.393181
\(331\) 20.7825 1.14231 0.571156 0.820842i \(-0.306495\pi\)
0.571156 + 0.820842i \(0.306495\pi\)
\(332\) 40.5938 2.22787
\(333\) 5.11333 0.280209
\(334\) 2.09868 0.114834
\(335\) 0.343906 0.0187896
\(336\) 8.55677 0.466810
\(337\) 2.93539 0.159901 0.0799505 0.996799i \(-0.474524\pi\)
0.0799505 + 0.996799i \(0.474524\pi\)
\(338\) −12.6421 −0.687639
\(339\) −1.87225 −0.101687
\(340\) −5.02396 −0.272463
\(341\) 38.9948 2.11169
\(342\) −0.929550 −0.0502643
\(343\) −19.1609 −1.03459
\(344\) −2.18819 −0.117979
\(345\) −2.87757 −0.154923
\(346\) 40.9111 2.19939
\(347\) −31.8702 −1.71088 −0.855442 0.517899i \(-0.826714\pi\)
−0.855442 + 0.517899i \(0.826714\pi\)
\(348\) 33.4821 1.79483
\(349\) 24.3320 1.30246 0.651230 0.758881i \(-0.274253\pi\)
0.651230 + 0.758881i \(0.274253\pi\)
\(350\) 29.2168 1.56171
\(351\) −20.0016 −1.06761
\(352\) −14.1129 −0.752220
\(353\) 24.2652 1.29150 0.645752 0.763547i \(-0.276544\pi\)
0.645752 + 0.763547i \(0.276544\pi\)
\(354\) 39.0283 2.07433
\(355\) −0.382969 −0.0203259
\(356\) −15.6249 −0.828117
\(357\) −17.3096 −0.916124
\(358\) 30.9557 1.63606
\(359\) 9.08424 0.479448 0.239724 0.970841i \(-0.422943\pi\)
0.239724 + 0.970841i \(0.422943\pi\)
\(360\) −0.736516 −0.0388178
\(361\) −18.3965 −0.968237
\(362\) −12.4872 −0.656310
\(363\) 12.5381 0.658081
\(364\) 39.2717 2.05840
\(365\) 3.15978 0.165391
\(366\) −24.8613 −1.29952
\(367\) 5.89639 0.307789 0.153894 0.988087i \(-0.450818\pi\)
0.153894 + 0.988087i \(0.450818\pi\)
\(368\) −7.21486 −0.376101
\(369\) 2.00955 0.104613
\(370\) −9.17661 −0.477069
\(371\) 1.37809 0.0715467
\(372\) −62.6035 −3.24584
\(373\) −9.50582 −0.492192 −0.246096 0.969245i \(-0.579148\pi\)
−0.246096 + 0.969245i \(0.579148\pi\)
\(374\) −36.2268 −1.87324
\(375\) −7.06497 −0.364833
\(376\) 5.39742 0.278351
\(377\) 21.2304 1.09342
\(378\) 28.1172 1.44619
\(379\) −4.33740 −0.222797 −0.111399 0.993776i \(-0.535533\pi\)
−0.111399 + 0.993776i \(0.535533\pi\)
\(380\) 1.07319 0.0550536
\(381\) 30.3026 1.55245
\(382\) 57.0973 2.92135
\(383\) 20.4611 1.04551 0.522756 0.852483i \(-0.324904\pi\)
0.522756 + 0.852483i \(0.324904\pi\)
\(384\) 38.5976 1.96968
\(385\) −4.09571 −0.208737
\(386\) −50.7608 −2.58366
\(387\) 0.290528 0.0147684
\(388\) −60.3294 −3.06276
\(389\) −31.2315 −1.58350 −0.791751 0.610844i \(-0.790830\pi\)
−0.791751 + 0.610844i \(0.790830\pi\)
\(390\) −7.27089 −0.368176
\(391\) 14.5951 0.738105
\(392\) 2.04365 0.103220
\(393\) 8.45485 0.426491
\(394\) 60.4973 3.04781
\(395\) −3.15758 −0.158875
\(396\) −7.66804 −0.385333
\(397\) −8.85079 −0.444208 −0.222104 0.975023i \(-0.571292\pi\)
−0.222104 + 0.975023i \(0.571292\pi\)
\(398\) 9.95175 0.498836
\(399\) 3.69759 0.185111
\(400\) −8.72507 −0.436253
\(401\) −29.9470 −1.49548 −0.747741 0.663990i \(-0.768862\pi\)
−0.747741 + 0.663990i \(0.768862\pi\)
\(402\) −3.98120 −0.198564
\(403\) −39.6958 −1.97739
\(404\) −24.3113 −1.20953
\(405\) −3.92949 −0.195258
\(406\) −29.8446 −1.48116
\(407\) −42.5688 −2.11006
\(408\) 25.9136 1.28292
\(409\) −30.0722 −1.48697 −0.743487 0.668750i \(-0.766830\pi\)
−0.743487 + 0.668750i \(0.766830\pi\)
\(410\) −3.60643 −0.178109
\(411\) −20.7763 −1.02482
\(412\) 51.6112 2.54270
\(413\) −22.3800 −1.10125
\(414\) 4.80214 0.236012
\(415\) 4.30970 0.211555
\(416\) 14.3666 0.704380
\(417\) 18.8626 0.923705
\(418\) 7.73856 0.378505
\(419\) −15.2639 −0.745688 −0.372844 0.927894i \(-0.621617\pi\)
−0.372844 + 0.927894i \(0.621617\pi\)
\(420\) 6.57539 0.320846
\(421\) −8.34912 −0.406911 −0.203455 0.979084i \(-0.565217\pi\)
−0.203455 + 0.979084i \(0.565217\pi\)
\(422\) 47.0443 2.29008
\(423\) −0.716619 −0.0348432
\(424\) −2.06308 −0.100192
\(425\) 17.6501 0.856155
\(426\) 4.43341 0.214800
\(427\) 14.2562 0.689907
\(428\) −38.3291 −1.85271
\(429\) −33.7285 −1.62843
\(430\) −0.521394 −0.0251439
\(431\) −1.93351 −0.0931341 −0.0465670 0.998915i \(-0.514828\pi\)
−0.0465670 + 0.998915i \(0.514828\pi\)
\(432\) −8.39669 −0.403986
\(433\) 1.61567 0.0776443 0.0388221 0.999246i \(-0.487639\pi\)
0.0388221 + 0.999246i \(0.487639\pi\)
\(434\) 55.8023 2.67860
\(435\) 3.55467 0.170434
\(436\) 12.1303 0.580937
\(437\) −3.11772 −0.149141
\(438\) −36.5790 −1.74781
\(439\) 13.7342 0.655495 0.327748 0.944765i \(-0.393710\pi\)
0.327748 + 0.944765i \(0.393710\pi\)
\(440\) 6.13154 0.292310
\(441\) −0.271337 −0.0129208
\(442\) 36.8780 1.75411
\(443\) −10.2199 −0.485564 −0.242782 0.970081i \(-0.578060\pi\)
−0.242782 + 0.970081i \(0.578060\pi\)
\(444\) 68.3413 3.24333
\(445\) −1.65884 −0.0786365
\(446\) −46.5499 −2.20420
\(447\) −26.2903 −1.24349
\(448\) −29.3365 −1.38602
\(449\) 37.5400 1.77162 0.885812 0.464044i \(-0.153602\pi\)
0.885812 + 0.464044i \(0.153602\pi\)
\(450\) 5.80732 0.273759
\(451\) −16.7296 −0.787768
\(452\) −3.60725 −0.169671
\(453\) −31.0330 −1.45806
\(454\) −56.6936 −2.66076
\(455\) 4.16934 0.195462
\(456\) −5.53553 −0.259225
\(457\) 35.6097 1.66575 0.832876 0.553459i \(-0.186693\pi\)
0.832876 + 0.553459i \(0.186693\pi\)
\(458\) 64.4592 3.01198
\(459\) 16.9858 0.792830
\(460\) −5.54420 −0.258500
\(461\) −8.33587 −0.388240 −0.194120 0.980978i \(-0.562185\pi\)
−0.194120 + 0.980978i \(0.562185\pi\)
\(462\) 47.4137 2.20589
\(463\) −15.1864 −0.705771 −0.352885 0.935667i \(-0.614799\pi\)
−0.352885 + 0.935667i \(0.614799\pi\)
\(464\) 8.91253 0.413754
\(465\) −6.64640 −0.308219
\(466\) 37.2067 1.72356
\(467\) 34.6760 1.60462 0.802308 0.596911i \(-0.203605\pi\)
0.802308 + 0.596911i \(0.203605\pi\)
\(468\) 7.80588 0.360827
\(469\) 2.28294 0.105416
\(470\) 1.28608 0.0593223
\(471\) −0.0609353 −0.00280775
\(472\) 33.5042 1.54216
\(473\) −2.41866 −0.111210
\(474\) 36.5535 1.67896
\(475\) −3.77032 −0.172994
\(476\) −33.3504 −1.52861
\(477\) 0.273917 0.0125418
\(478\) −20.5505 −0.939957
\(479\) −6.04205 −0.276068 −0.138034 0.990427i \(-0.544078\pi\)
−0.138034 + 0.990427i \(0.544078\pi\)
\(480\) 2.40545 0.109793
\(481\) 43.3340 1.97586
\(482\) 28.6701 1.30589
\(483\) −19.1021 −0.869175
\(484\) 24.1571 1.09805
\(485\) −6.40497 −0.290834
\(486\) 12.3095 0.558372
\(487\) 15.7574 0.714038 0.357019 0.934097i \(-0.383793\pi\)
0.357019 + 0.934097i \(0.383793\pi\)
\(488\) −21.3424 −0.966127
\(489\) −33.5122 −1.51547
\(490\) 0.486954 0.0219983
\(491\) 39.4706 1.78128 0.890642 0.454705i \(-0.150255\pi\)
0.890642 + 0.454705i \(0.150255\pi\)
\(492\) 26.8583 1.21087
\(493\) −18.0293 −0.812000
\(494\) −7.87767 −0.354433
\(495\) −0.814089 −0.0365906
\(496\) −16.6643 −0.748250
\(497\) −2.54225 −0.114035
\(498\) −49.8909 −2.23567
\(499\) −16.7550 −0.750057 −0.375028 0.927013i \(-0.622367\pi\)
−0.375028 + 0.927013i \(0.622367\pi\)
\(500\) −13.6120 −0.608749
\(501\) −1.65933 −0.0741336
\(502\) −2.65639 −0.118561
\(503\) 35.4947 1.58263 0.791315 0.611409i \(-0.209397\pi\)
0.791315 + 0.611409i \(0.209397\pi\)
\(504\) −4.88918 −0.217782
\(505\) −2.58104 −0.114855
\(506\) −39.9781 −1.77724
\(507\) 9.99556 0.443918
\(508\) 58.3838 2.59036
\(509\) 19.3050 0.855678 0.427839 0.903855i \(-0.359275\pi\)
0.427839 + 0.903855i \(0.359275\pi\)
\(510\) 6.17460 0.273416
\(511\) 20.9755 0.927900
\(512\) 19.7152 0.871298
\(513\) −3.62841 −0.160198
\(514\) 74.9476 3.30580
\(515\) 5.47938 0.241450
\(516\) 3.88300 0.170939
\(517\) 5.96590 0.262380
\(518\) −60.9167 −2.67653
\(519\) −32.3467 −1.41986
\(520\) −6.24176 −0.273719
\(521\) 9.52590 0.417337 0.208669 0.977986i \(-0.433087\pi\)
0.208669 + 0.977986i \(0.433087\pi\)
\(522\) −5.93209 −0.259641
\(523\) 22.7372 0.994229 0.497115 0.867685i \(-0.334393\pi\)
0.497115 + 0.867685i \(0.334393\pi\)
\(524\) 16.2899 0.711628
\(525\) −23.1005 −1.00819
\(526\) −70.9077 −3.09172
\(527\) 33.7106 1.46846
\(528\) −14.1592 −0.616201
\(529\) −6.89358 −0.299721
\(530\) −0.491583 −0.0213530
\(531\) −4.44838 −0.193043
\(532\) 7.12413 0.308870
\(533\) 17.0304 0.737668
\(534\) 19.2034 0.831014
\(535\) −4.06926 −0.175930
\(536\) −3.41770 −0.147622
\(537\) −24.4753 −1.05619
\(538\) 72.4428 3.12323
\(539\) 2.25890 0.0972977
\(540\) −6.45237 −0.277666
\(541\) −16.1885 −0.695997 −0.347999 0.937495i \(-0.613139\pi\)
−0.347999 + 0.937495i \(0.613139\pi\)
\(542\) 45.5122 1.95492
\(543\) 9.87307 0.423694
\(544\) −12.2004 −0.523089
\(545\) 1.28783 0.0551648
\(546\) −48.2661 −2.06560
\(547\) 14.2216 0.608070 0.304035 0.952661i \(-0.401666\pi\)
0.304035 + 0.952661i \(0.401666\pi\)
\(548\) −40.0295 −1.70998
\(549\) 2.83365 0.120937
\(550\) −48.3463 −2.06149
\(551\) 3.85132 0.164072
\(552\) 28.5970 1.21717
\(553\) −20.9609 −0.891346
\(554\) 43.9854 1.86876
\(555\) 7.25555 0.307981
\(556\) 36.3425 1.54126
\(557\) −0.235644 −0.00998454 −0.00499227 0.999988i \(-0.501589\pi\)
−0.00499227 + 0.999988i \(0.501589\pi\)
\(558\) 11.0916 0.469545
\(559\) 2.46214 0.104138
\(560\) 1.75029 0.0739633
\(561\) 28.6430 1.20931
\(562\) −7.51178 −0.316865
\(563\) 39.9289 1.68280 0.841401 0.540411i \(-0.181731\pi\)
0.841401 + 0.540411i \(0.181731\pi\)
\(564\) −9.57785 −0.403300
\(565\) −0.382969 −0.0161116
\(566\) −33.2959 −1.39953
\(567\) −26.0850 −1.09547
\(568\) 3.80591 0.159692
\(569\) 8.01365 0.335950 0.167975 0.985791i \(-0.446277\pi\)
0.167975 + 0.985791i \(0.446277\pi\)
\(570\) −1.31898 −0.0552461
\(571\) −7.01647 −0.293630 −0.146815 0.989164i \(-0.546902\pi\)
−0.146815 + 0.989164i \(0.546902\pi\)
\(572\) −64.9844 −2.71714
\(573\) −45.1444 −1.88593
\(574\) −23.9404 −0.999255
\(575\) 19.4778 0.812280
\(576\) −5.83109 −0.242962
\(577\) 5.03346 0.209546 0.104773 0.994496i \(-0.466588\pi\)
0.104773 + 0.994496i \(0.466588\pi\)
\(578\) 8.93777 0.371762
\(579\) 40.1344 1.66793
\(580\) 6.84877 0.284380
\(581\) 28.6089 1.18690
\(582\) 74.1466 3.07348
\(583\) −2.28038 −0.0944435
\(584\) −31.4016 −1.29941
\(585\) 0.828723 0.0342635
\(586\) 21.8899 0.904265
\(587\) −40.8609 −1.68651 −0.843255 0.537514i \(-0.819363\pi\)
−0.843255 + 0.537514i \(0.819363\pi\)
\(588\) −3.62651 −0.149555
\(589\) −7.20107 −0.296715
\(590\) 7.98325 0.328665
\(591\) −47.8327 −1.96757
\(592\) 18.1916 0.747672
\(593\) 4.27503 0.175554 0.0877772 0.996140i \(-0.472024\pi\)
0.0877772 + 0.996140i \(0.472024\pi\)
\(594\) −46.5267 −1.90901
\(595\) −3.54070 −0.145154
\(596\) −50.6533 −2.07484
\(597\) −7.86843 −0.322033
\(598\) 40.6968 1.66421
\(599\) 48.8280 1.99506 0.997529 0.0702594i \(-0.0223827\pi\)
0.997529 + 0.0702594i \(0.0223827\pi\)
\(600\) 34.5829 1.41184
\(601\) 11.9507 0.487479 0.243740 0.969841i \(-0.421626\pi\)
0.243740 + 0.969841i \(0.421626\pi\)
\(602\) −3.46115 −0.141066
\(603\) 0.453770 0.0184790
\(604\) −59.7911 −2.43286
\(605\) 2.56468 0.104269
\(606\) 29.8792 1.21376
\(607\) 18.7993 0.763039 0.381519 0.924361i \(-0.375401\pi\)
0.381519 + 0.924361i \(0.375401\pi\)
\(608\) 2.60619 0.105695
\(609\) 23.5969 0.956193
\(610\) −5.08540 −0.205902
\(611\) −6.07315 −0.245693
\(612\) −6.62893 −0.267958
\(613\) 31.6030 1.27643 0.638216 0.769857i \(-0.279673\pi\)
0.638216 + 0.769857i \(0.279673\pi\)
\(614\) −42.1612 −1.70149
\(615\) 2.85145 0.114982
\(616\) 40.7028 1.63996
\(617\) −35.3749 −1.42414 −0.712070 0.702109i \(-0.752242\pi\)
−0.712070 + 0.702109i \(0.752242\pi\)
\(618\) −63.4316 −2.55159
\(619\) 25.3752 1.01992 0.509958 0.860199i \(-0.329661\pi\)
0.509958 + 0.860199i \(0.329661\pi\)
\(620\) −12.8056 −0.514284
\(621\) 18.7447 0.752200
\(622\) 15.8607 0.635957
\(623\) −11.0118 −0.441179
\(624\) 14.4138 0.577012
\(625\) 22.8215 0.912861
\(626\) 6.78663 0.271248
\(627\) −6.11855 −0.244351
\(628\) −0.117404 −0.00468492
\(629\) −36.8002 −1.46732
\(630\) −1.16498 −0.0464137
\(631\) −30.1080 −1.19858 −0.599291 0.800532i \(-0.704551\pi\)
−0.599291 + 0.800532i \(0.704551\pi\)
\(632\) 31.3797 1.24822
\(633\) −37.1959 −1.47841
\(634\) −15.0698 −0.598498
\(635\) 6.19841 0.245976
\(636\) 3.66099 0.145168
\(637\) −2.29951 −0.0911098
\(638\) 49.3850 1.95517
\(639\) −0.505313 −0.0199899
\(640\) 7.89515 0.312083
\(641\) 11.0015 0.434533 0.217267 0.976112i \(-0.430286\pi\)
0.217267 + 0.976112i \(0.430286\pi\)
\(642\) 47.1075 1.85919
\(643\) −21.6101 −0.852219 −0.426110 0.904672i \(-0.640116\pi\)
−0.426110 + 0.904672i \(0.640116\pi\)
\(644\) −36.8039 −1.45028
\(645\) 0.412244 0.0162321
\(646\) 6.68989 0.263210
\(647\) −38.6812 −1.52071 −0.760357 0.649505i \(-0.774976\pi\)
−0.760357 + 0.649505i \(0.774976\pi\)
\(648\) 39.0509 1.53406
\(649\) 37.0330 1.45367
\(650\) 49.2154 1.93039
\(651\) −44.1205 −1.72922
\(652\) −64.5677 −2.52867
\(653\) 36.9556 1.44619 0.723093 0.690751i \(-0.242720\pi\)
0.723093 + 0.690751i \(0.242720\pi\)
\(654\) −14.9085 −0.582969
\(655\) 1.72944 0.0675749
\(656\) 7.14937 0.279136
\(657\) 4.16921 0.162656
\(658\) 8.53732 0.332819
\(659\) −37.7321 −1.46983 −0.734916 0.678158i \(-0.762779\pi\)
−0.734916 + 0.678158i \(0.762779\pi\)
\(660\) −10.8806 −0.423525
\(661\) 8.62632 0.335525 0.167762 0.985827i \(-0.446346\pi\)
0.167762 + 0.985827i \(0.446346\pi\)
\(662\) −49.2123 −1.91269
\(663\) −29.1579 −1.13240
\(664\) −42.8293 −1.66210
\(665\) 0.756344 0.0293297
\(666\) −12.1082 −0.469182
\(667\) −19.8963 −0.770387
\(668\) −3.19703 −0.123697
\(669\) 36.8050 1.42296
\(670\) −0.814356 −0.0314613
\(671\) −23.5903 −0.910694
\(672\) 15.9680 0.615978
\(673\) 24.1834 0.932203 0.466102 0.884731i \(-0.345658\pi\)
0.466102 + 0.884731i \(0.345658\pi\)
\(674\) −6.95090 −0.267739
\(675\) 22.6683 0.872505
\(676\) 19.2584 0.740707
\(677\) −14.4312 −0.554636 −0.277318 0.960778i \(-0.589446\pi\)
−0.277318 + 0.960778i \(0.589446\pi\)
\(678\) 4.43341 0.170264
\(679\) −42.5178 −1.63169
\(680\) 5.30064 0.203270
\(681\) 44.8253 1.71771
\(682\) −92.3383 −3.53582
\(683\) 50.1150 1.91760 0.958798 0.284087i \(-0.0916905\pi\)
0.958798 + 0.284087i \(0.0916905\pi\)
\(684\) 1.41603 0.0541434
\(685\) −4.24980 −0.162376
\(686\) 45.3722 1.73232
\(687\) −50.9652 −1.94444
\(688\) 1.03361 0.0394060
\(689\) 2.32137 0.0884371
\(690\) 6.81399 0.259404
\(691\) −1.04136 −0.0396153 −0.0198076 0.999804i \(-0.506305\pi\)
−0.0198076 + 0.999804i \(0.506305\pi\)
\(692\) −62.3221 −2.36913
\(693\) −5.40413 −0.205286
\(694\) 75.4675 2.86471
\(695\) 3.85835 0.146356
\(696\) −35.3260 −1.33903
\(697\) −14.4626 −0.547809
\(698\) −57.6172 −2.18084
\(699\) −29.4177 −1.11268
\(700\) −44.5076 −1.68223
\(701\) −44.5857 −1.68398 −0.841989 0.539495i \(-0.818615\pi\)
−0.841989 + 0.539495i \(0.818615\pi\)
\(702\) 47.3631 1.78760
\(703\) 7.86106 0.296485
\(704\) 48.5442 1.82958
\(705\) −1.01685 −0.0382966
\(706\) −57.4590 −2.16250
\(707\) −17.1336 −0.644376
\(708\) −59.4540 −2.23442
\(709\) 0.213503 0.00801829 0.00400914 0.999992i \(-0.498724\pi\)
0.00400914 + 0.999992i \(0.498724\pi\)
\(710\) 0.906856 0.0340337
\(711\) −4.16631 −0.156249
\(712\) 16.4854 0.617815
\(713\) 37.2014 1.39320
\(714\) 40.9886 1.53396
\(715\) −6.89917 −0.258014
\(716\) −47.1565 −1.76232
\(717\) 16.2484 0.606807
\(718\) −21.5111 −0.802789
\(719\) −8.27870 −0.308743 −0.154372 0.988013i \(-0.549335\pi\)
−0.154372 + 0.988013i \(0.549335\pi\)
\(720\) 0.347898 0.0129654
\(721\) 36.3736 1.35462
\(722\) 43.5622 1.62122
\(723\) −22.6682 −0.843040
\(724\) 19.0224 0.706961
\(725\) −24.0610 −0.893602
\(726\) −29.6898 −1.10189
\(727\) −50.7048 −1.88054 −0.940269 0.340433i \(-0.889426\pi\)
−0.940269 + 0.340433i \(0.889426\pi\)
\(728\) −41.4345 −1.53566
\(729\) 21.0492 0.779599
\(730\) −7.48225 −0.276930
\(731\) −2.09091 −0.0773349
\(732\) 37.8726 1.39981
\(733\) −38.0462 −1.40527 −0.702635 0.711550i \(-0.747993\pi\)
−0.702635 + 0.711550i \(0.747993\pi\)
\(734\) −13.9624 −0.515363
\(735\) −0.385014 −0.0142014
\(736\) −13.4638 −0.496283
\(737\) −3.77767 −0.139152
\(738\) −4.75855 −0.175164
\(739\) 29.4993 1.08515 0.542574 0.840008i \(-0.317450\pi\)
0.542574 + 0.840008i \(0.317450\pi\)
\(740\) 13.9792 0.513887
\(741\) 6.22854 0.228811
\(742\) −3.26326 −0.119798
\(743\) −19.8973 −0.729963 −0.364981 0.931015i \(-0.618925\pi\)
−0.364981 + 0.931015i \(0.618925\pi\)
\(744\) 66.0512 2.42155
\(745\) −5.37768 −0.197023
\(746\) 22.5094 0.824128
\(747\) 5.68648 0.208057
\(748\) 55.1862 2.01781
\(749\) −27.0128 −0.987028
\(750\) 16.7296 0.610878
\(751\) −50.6187 −1.84710 −0.923552 0.383474i \(-0.874728\pi\)
−0.923552 + 0.383474i \(0.874728\pi\)
\(752\) −2.54951 −0.0929711
\(753\) 2.10030 0.0765391
\(754\) −50.2728 −1.83083
\(755\) −6.34781 −0.231020
\(756\) −42.8325 −1.55780
\(757\) −22.9645 −0.834660 −0.417330 0.908755i \(-0.637034\pi\)
−0.417330 + 0.908755i \(0.637034\pi\)
\(758\) 10.2708 0.373052
\(759\) 31.6090 1.14733
\(760\) −1.13229 −0.0410726
\(761\) 46.7157 1.69344 0.846721 0.532037i \(-0.178573\pi\)
0.846721 + 0.532037i \(0.178573\pi\)
\(762\) −71.7554 −2.59942
\(763\) 8.54898 0.309494
\(764\) −86.9794 −3.14681
\(765\) −0.703770 −0.0254449
\(766\) −48.4510 −1.75061
\(767\) −37.6987 −1.36122
\(768\) −48.1878 −1.73883
\(769\) −30.0135 −1.08231 −0.541156 0.840922i \(-0.682013\pi\)
−0.541156 + 0.840922i \(0.682013\pi\)
\(770\) 9.69850 0.349510
\(771\) −59.2579 −2.13412
\(772\) 77.3268 2.78305
\(773\) −1.85225 −0.0666209 −0.0333104 0.999445i \(-0.510605\pi\)
−0.0333104 + 0.999445i \(0.510605\pi\)
\(774\) −0.687959 −0.0247282
\(775\) 44.9883 1.61603
\(776\) 63.6519 2.28497
\(777\) 48.1643 1.72788
\(778\) 73.9551 2.65142
\(779\) 3.08942 0.110690
\(780\) 11.0761 0.396590
\(781\) 4.20676 0.150530
\(782\) −34.5606 −1.23588
\(783\) −23.1554 −0.827506
\(784\) −0.965334 −0.0344762
\(785\) −0.0124643 −0.000444871 0
\(786\) −20.0208 −0.714117
\(787\) 42.4685 1.51384 0.756920 0.653508i \(-0.226703\pi\)
0.756920 + 0.653508i \(0.226703\pi\)
\(788\) −92.1589 −3.28302
\(789\) 56.0637 1.99592
\(790\) 7.47704 0.266021
\(791\) −2.54225 −0.0903920
\(792\) 8.09033 0.287477
\(793\) 24.0144 0.852776
\(794\) 20.9583 0.743784
\(795\) 0.388674 0.0137849
\(796\) −15.1601 −0.537334
\(797\) 43.4242 1.53817 0.769083 0.639149i \(-0.220713\pi\)
0.769083 + 0.639149i \(0.220713\pi\)
\(798\) −8.75576 −0.309951
\(799\) 5.15745 0.182457
\(800\) −16.2820 −0.575657
\(801\) −2.18877 −0.0773365
\(802\) 70.9134 2.50404
\(803\) −34.7089 −1.22485
\(804\) 6.06478 0.213888
\(805\) −3.90734 −0.137716
\(806\) 93.9982 3.31095
\(807\) −57.2775 −2.01626
\(808\) 25.6501 0.902368
\(809\) 20.8543 0.733198 0.366599 0.930379i \(-0.380522\pi\)
0.366599 + 0.930379i \(0.380522\pi\)
\(810\) 9.30489 0.326940
\(811\) −0.0621278 −0.00218160 −0.00109080 0.999999i \(-0.500347\pi\)
−0.00109080 + 0.999999i \(0.500347\pi\)
\(812\) 45.4639 1.59547
\(813\) −35.9846 −1.26203
\(814\) 100.801 3.53308
\(815\) −6.85493 −0.240118
\(816\) −12.2405 −0.428503
\(817\) 0.446648 0.0156262
\(818\) 71.2098 2.48979
\(819\) 5.50128 0.192230
\(820\) 5.49388 0.191854
\(821\) −6.22126 −0.217123 −0.108562 0.994090i \(-0.534625\pi\)
−0.108562 + 0.994090i \(0.534625\pi\)
\(822\) 49.1975 1.71596
\(823\) 22.0097 0.767211 0.383606 0.923497i \(-0.374682\pi\)
0.383606 + 0.923497i \(0.374682\pi\)
\(824\) −54.4535 −1.89698
\(825\) 38.2253 1.33084
\(826\) 52.9949 1.84393
\(827\) 41.7274 1.45100 0.725502 0.688220i \(-0.241608\pi\)
0.725502 + 0.688220i \(0.241608\pi\)
\(828\) −7.31536 −0.254226
\(829\) −29.2948 −1.01745 −0.508725 0.860929i \(-0.669883\pi\)
−0.508725 + 0.860929i \(0.669883\pi\)
\(830\) −10.2052 −0.354228
\(831\) −34.7774 −1.20641
\(832\) −49.4169 −1.71322
\(833\) 1.95279 0.0676602
\(834\) −44.6659 −1.54665
\(835\) −0.339417 −0.0117460
\(836\) −11.7886 −0.407716
\(837\) 43.2951 1.49650
\(838\) 36.1442 1.24858
\(839\) 43.8771 1.51481 0.757403 0.652948i \(-0.226468\pi\)
0.757403 + 0.652948i \(0.226468\pi\)
\(840\) −6.93750 −0.239367
\(841\) −4.42207 −0.152485
\(842\) 19.7704 0.681333
\(843\) 5.93925 0.204559
\(844\) −71.6652 −2.46682
\(845\) 2.04460 0.0703362
\(846\) 1.69693 0.0583416
\(847\) 17.0250 0.584986
\(848\) 0.974512 0.0334649
\(849\) 26.3256 0.903494
\(850\) −41.7948 −1.43355
\(851\) −40.6109 −1.39213
\(852\) −6.75366 −0.231377
\(853\) −22.7824 −0.780054 −0.390027 0.920803i \(-0.627534\pi\)
−0.390027 + 0.920803i \(0.627534\pi\)
\(854\) −33.7582 −1.15518
\(855\) 0.150335 0.00514136
\(856\) 40.4399 1.38221
\(857\) −37.9647 −1.29685 −0.648425 0.761278i \(-0.724572\pi\)
−0.648425 + 0.761278i \(0.724572\pi\)
\(858\) 79.8678 2.72664
\(859\) 10.5546 0.360118 0.180059 0.983656i \(-0.442371\pi\)
0.180059 + 0.983656i \(0.442371\pi\)
\(860\) 0.794269 0.0270843
\(861\) 18.9287 0.645088
\(862\) 4.57849 0.155944
\(863\) 20.3171 0.691602 0.345801 0.938308i \(-0.387607\pi\)
0.345801 + 0.938308i \(0.387607\pi\)
\(864\) −15.6692 −0.533078
\(865\) −6.61652 −0.224968
\(866\) −3.82585 −0.130008
\(867\) −7.06672 −0.239998
\(868\) −85.0068 −2.88532
\(869\) 34.6848 1.17660
\(870\) −8.41734 −0.285374
\(871\) 3.84557 0.130302
\(872\) −12.7984 −0.433407
\(873\) −8.45110 −0.286026
\(874\) 7.38264 0.249722
\(875\) −9.59323 −0.324310
\(876\) 55.7228 1.88270
\(877\) −42.0790 −1.42091 −0.710454 0.703743i \(-0.751510\pi\)
−0.710454 + 0.703743i \(0.751510\pi\)
\(878\) −32.5220 −1.09756
\(879\) −17.3074 −0.583766
\(880\) −2.89628 −0.0976334
\(881\) −38.4119 −1.29413 −0.647065 0.762435i \(-0.724004\pi\)
−0.647065 + 0.762435i \(0.724004\pi\)
\(882\) 0.642517 0.0216347
\(883\) 16.0584 0.540409 0.270205 0.962803i \(-0.412909\pi\)
0.270205 + 0.962803i \(0.412909\pi\)
\(884\) −56.1783 −1.88948
\(885\) −6.31202 −0.212176
\(886\) 24.2004 0.813029
\(887\) 27.6120 0.927121 0.463561 0.886065i \(-0.346572\pi\)
0.463561 + 0.886065i \(0.346572\pi\)
\(888\) −72.1049 −2.41968
\(889\) 41.1467 1.38001
\(890\) 3.92807 0.131669
\(891\) 43.1639 1.44604
\(892\) 70.9120 2.37431
\(893\) −1.10171 −0.0368672
\(894\) 62.2544 2.08210
\(895\) −5.00644 −0.167347
\(896\) 52.4101 1.75090
\(897\) −32.1772 −1.07437
\(898\) −88.8934 −2.96641
\(899\) −45.9549 −1.53268
\(900\) −8.84660 −0.294887
\(901\) −1.97136 −0.0656755
\(902\) 39.6152 1.31904
\(903\) 2.73659 0.0910679
\(904\) 3.80591 0.126583
\(905\) 2.01954 0.0671318
\(906\) 73.4850 2.44137
\(907\) −48.9541 −1.62549 −0.812747 0.582617i \(-0.802029\pi\)
−0.812747 + 0.582617i \(0.802029\pi\)
\(908\) 86.3646 2.86611
\(909\) −3.40558 −0.112956
\(910\) −9.87284 −0.327281
\(911\) −49.3858 −1.63622 −0.818111 0.575060i \(-0.804979\pi\)
−0.818111 + 0.575060i \(0.804979\pi\)
\(912\) 2.61474 0.0865828
\(913\) −47.3403 −1.56674
\(914\) −84.3225 −2.78914
\(915\) 4.02081 0.132924
\(916\) −98.1943 −3.24443
\(917\) 11.4805 0.379119
\(918\) −40.2218 −1.32752
\(919\) −20.7861 −0.685670 −0.342835 0.939396i \(-0.611387\pi\)
−0.342835 + 0.939396i \(0.611387\pi\)
\(920\) 5.84953 0.192853
\(921\) 33.3351 1.09843
\(922\) 19.7390 0.650071
\(923\) −4.28238 −0.140956
\(924\) −72.2280 −2.37613
\(925\) −49.1116 −1.61478
\(926\) 35.9608 1.18174
\(927\) 7.22983 0.237459
\(928\) 16.6319 0.545968
\(929\) 5.41506 0.177662 0.0888312 0.996047i \(-0.471687\pi\)
0.0888312 + 0.996047i \(0.471687\pi\)
\(930\) 15.7384 0.516083
\(931\) −0.417145 −0.0136714
\(932\) −56.6789 −1.85658
\(933\) −12.5404 −0.410554
\(934\) −82.1116 −2.68677
\(935\) 5.85893 0.191607
\(936\) −8.23576 −0.269194
\(937\) 9.39056 0.306776 0.153388 0.988166i \(-0.450982\pi\)
0.153388 + 0.988166i \(0.450982\pi\)
\(938\) −5.40591 −0.176509
\(939\) −5.36590 −0.175110
\(940\) −1.95915 −0.0639005
\(941\) −58.7116 −1.91394 −0.956972 0.290180i \(-0.906285\pi\)
−0.956972 + 0.290180i \(0.906285\pi\)
\(942\) 0.144293 0.00470131
\(943\) −15.9602 −0.519736
\(944\) −15.8259 −0.515091
\(945\) −4.54738 −0.147926
\(946\) 5.72730 0.186211
\(947\) −45.6167 −1.48234 −0.741172 0.671315i \(-0.765730\pi\)
−0.741172 + 0.671315i \(0.765730\pi\)
\(948\) −55.6840 −1.80853
\(949\) 35.3329 1.14695
\(950\) 8.92797 0.289661
\(951\) 11.9151 0.386372
\(952\) 35.1871 1.14042
\(953\) 2.82658 0.0915619 0.0457809 0.998952i \(-0.485422\pi\)
0.0457809 + 0.998952i \(0.485422\pi\)
\(954\) −0.648625 −0.0210000
\(955\) −9.23430 −0.298815
\(956\) 31.3057 1.01250
\(957\) −39.0467 −1.26220
\(958\) 14.3073 0.462249
\(959\) −28.2113 −0.910989
\(960\) −8.27402 −0.267043
\(961\) 54.9248 1.77177
\(962\) −102.613 −3.30839
\(963\) −5.36923 −0.173021
\(964\) −43.6747 −1.40667
\(965\) 8.20951 0.264274
\(966\) 45.2331 1.45535
\(967\) 38.5321 1.23911 0.619555 0.784953i \(-0.287313\pi\)
0.619555 + 0.784953i \(0.287313\pi\)
\(968\) −25.4875 −0.819200
\(969\) −5.28941 −0.169920
\(970\) 15.1667 0.486974
\(971\) −8.94066 −0.286920 −0.143460 0.989656i \(-0.545823\pi\)
−0.143460 + 0.989656i \(0.545823\pi\)
\(972\) −18.7518 −0.601464
\(973\) 25.6128 0.821107
\(974\) −37.3130 −1.19559
\(975\) −38.9125 −1.24620
\(976\) 10.0813 0.322693
\(977\) 41.3714 1.32359 0.661794 0.749686i \(-0.269795\pi\)
0.661794 + 0.749686i \(0.269795\pi\)
\(978\) 79.3556 2.53751
\(979\) 18.2217 0.582367
\(980\) −0.741804 −0.0236961
\(981\) 1.69925 0.0542528
\(982\) −93.4650 −2.98259
\(983\) 40.9891 1.30735 0.653675 0.756776i \(-0.273226\pi\)
0.653675 + 0.756776i \(0.273226\pi\)
\(984\) −28.3374 −0.903364
\(985\) −9.78419 −0.311750
\(986\) 42.6928 1.35961
\(987\) −6.75009 −0.214858
\(988\) 12.0005 0.381786
\(989\) −2.30742 −0.0733718
\(990\) 1.92773 0.0612673
\(991\) 29.3543 0.932471 0.466235 0.884661i \(-0.345610\pi\)
0.466235 + 0.884661i \(0.345610\pi\)
\(992\) −31.0977 −0.987352
\(993\) 38.9101 1.23477
\(994\) 6.01995 0.190941
\(995\) −1.60949 −0.0510243
\(996\) 76.0016 2.40820
\(997\) 6.32836 0.200421 0.100211 0.994966i \(-0.468048\pi\)
0.100211 + 0.994966i \(0.468048\pi\)
\(998\) 39.6752 1.25590
\(999\) −47.2632 −1.49534
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 \(a_p\))