Properties

Label 4015.2.a.h.1.12
Level 4015
Weight 2
Character 4015.1
Self dual Yes
Analytic conductor 32.060
Analytic rank 0
Dimension 37
CM No

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Newspace parameters

Level: \( N \) = \( 4015 = 5 \cdot 11 \cdot 73 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0599364115\)
Analytic rank: \(0\)
Dimension: \(37\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 4015.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.11064 q^{2}\) \(+3.24263 q^{3}\) \(-0.766474 q^{4}\) \(+1.00000 q^{5}\) \(-3.60140 q^{6}\) \(+2.31774 q^{7}\) \(+3.07256 q^{8}\) \(+7.51466 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.11064 q^{2}\) \(+3.24263 q^{3}\) \(-0.766474 q^{4}\) \(+1.00000 q^{5}\) \(-3.60140 q^{6}\) \(+2.31774 q^{7}\) \(+3.07256 q^{8}\) \(+7.51466 q^{9}\) \(-1.11064 q^{10}\) \(+1.00000 q^{11}\) \(-2.48539 q^{12}\) \(-0.104355 q^{13}\) \(-2.57417 q^{14}\) \(+3.24263 q^{15}\) \(-1.87957 q^{16}\) \(+3.59955 q^{17}\) \(-8.34610 q^{18}\) \(+3.68931 q^{19}\) \(-0.766474 q^{20}\) \(+7.51556 q^{21}\) \(-1.11064 q^{22}\) \(+7.11088 q^{23}\) \(+9.96319 q^{24}\) \(+1.00000 q^{25}\) \(+0.115901 q^{26}\) \(+14.6394 q^{27}\) \(-1.77648 q^{28}\) \(+4.35072 q^{29}\) \(-3.60140 q^{30}\) \(+0.187969 q^{31}\) \(-4.05760 q^{32}\) \(+3.24263 q^{33}\) \(-3.99781 q^{34}\) \(+2.31774 q^{35}\) \(-5.75979 q^{36}\) \(-2.99014 q^{37}\) \(-4.09750 q^{38}\) \(-0.338386 q^{39}\) \(+3.07256 q^{40}\) \(-9.01977 q^{41}\) \(-8.34710 q^{42}\) \(-5.30348 q^{43}\) \(-0.766474 q^{44}\) \(+7.51466 q^{45}\) \(-7.89764 q^{46}\) \(-12.0184 q^{47}\) \(-6.09475 q^{48}\) \(-1.62810 q^{49}\) \(-1.11064 q^{50}\) \(+11.6720 q^{51}\) \(+0.0799857 q^{52}\) \(-12.2860 q^{53}\) \(-16.2591 q^{54}\) \(+1.00000 q^{55}\) \(+7.12139 q^{56}\) \(+11.9631 q^{57}\) \(-4.83209 q^{58}\) \(-4.26462 q^{59}\) \(-2.48539 q^{60}\) \(-0.802852 q^{61}\) \(-0.208766 q^{62}\) \(+17.4170 q^{63}\) \(+8.26568 q^{64}\) \(-0.104355 q^{65}\) \(-3.60140 q^{66}\) \(+6.84360 q^{67}\) \(-2.75896 q^{68}\) \(+23.0580 q^{69}\) \(-2.57417 q^{70}\) \(-8.85756 q^{71}\) \(+23.0893 q^{72}\) \(+1.00000 q^{73}\) \(+3.32098 q^{74}\) \(+3.24263 q^{75}\) \(-2.82776 q^{76}\) \(+2.31774 q^{77}\) \(+0.375826 q^{78}\) \(-4.89807 q^{79}\) \(-1.87957 q^{80}\) \(+24.9261 q^{81}\) \(+10.0177 q^{82}\) \(+8.39151 q^{83}\) \(-5.76048 q^{84}\) \(+3.59955 q^{85}\) \(+5.89027 q^{86}\) \(+14.1078 q^{87}\) \(+3.07256 q^{88}\) \(+2.19724 q^{89}\) \(-8.34610 q^{90}\) \(-0.241868 q^{91}\) \(-5.45030 q^{92}\) \(+0.609514 q^{93}\) \(+13.3481 q^{94}\) \(+3.68931 q^{95}\) \(-13.1573 q^{96}\) \(-0.769097 q^{97}\) \(+1.80824 q^{98}\) \(+7.51466 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut 5q^{10} \) \(\mathstrut +\mathstrut 37q^{11} \) \(\mathstrut +\mathstrut 6q^{12} \) \(\mathstrut +\mathstrut 11q^{13} \) \(\mathstrut +\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 43q^{16} \) \(\mathstrut +\mathstrut 38q^{17} \) \(\mathstrut +\mathstrut 11q^{18} \) \(\mathstrut +\mathstrut 34q^{19} \) \(\mathstrut +\mathstrut 43q^{20} \) \(\mathstrut +\mathstrut 39q^{21} \) \(\mathstrut +\mathstrut 5q^{22} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 37q^{25} \) \(\mathstrut -\mathstrut 9q^{26} \) \(\mathstrut +\mathstrut 3q^{27} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut +\mathstrut 9q^{30} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut +\mathstrut 14q^{32} \) \(\mathstrut +\mathstrut 3q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 6q^{35} \) \(\mathstrut +\mathstrut 20q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 15q^{38} \) \(\mathstrut +\mathstrut 14q^{39} \) \(\mathstrut +\mathstrut 12q^{40} \) \(\mathstrut +\mathstrut 62q^{41} \) \(\mathstrut -\mathstrut 13q^{42} \) \(\mathstrut +\mathstrut 30q^{43} \) \(\mathstrut +\mathstrut 43q^{44} \) \(\mathstrut +\mathstrut 50q^{45} \) \(\mathstrut +\mathstrut 31q^{46} \) \(\mathstrut +\mathstrut 5q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 59q^{49} \) \(\mathstrut +\mathstrut 5q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 13q^{54} \) \(\mathstrut +\mathstrut 37q^{55} \) \(\mathstrut +\mathstrut 22q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 40q^{58} \) \(\mathstrut +\mathstrut 15q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut +\mathstrut 57q^{61} \) \(\mathstrut +\mathstrut 20q^{62} \) \(\mathstrut -\mathstrut 29q^{63} \) \(\mathstrut +\mathstrut 10q^{64} \) \(\mathstrut +\mathstrut 11q^{65} \) \(\mathstrut +\mathstrut 9q^{66} \) \(\mathstrut -\mathstrut 14q^{67} \) \(\mathstrut +\mathstrut 53q^{68} \) \(\mathstrut +\mathstrut 24q^{69} \) \(\mathstrut +\mathstrut 11q^{70} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 15q^{72} \) \(\mathstrut +\mathstrut 37q^{73} \) \(\mathstrut +\mathstrut 7q^{74} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut +\mathstrut 59q^{76} \) \(\mathstrut +\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut q^{78} \) \(\mathstrut +\mathstrut 42q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 61q^{81} \) \(\mathstrut -\mathstrut 22q^{82} \) \(\mathstrut +\mathstrut 44q^{83} \) \(\mathstrut +\mathstrut 66q^{84} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut -\mathstrut q^{86} \) \(\mathstrut -\mathstrut 26q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 69q^{89} \) \(\mathstrut +\mathstrut 11q^{90} \) \(\mathstrut -\mathstrut 10q^{91} \) \(\mathstrut -\mathstrut 21q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut +\mathstrut 29q^{94} \) \(\mathstrut +\mathstrut 34q^{95} \) \(\mathstrut -\mathstrut 9q^{96} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut -\mathstrut 15q^{98} \) \(\mathstrut +\mathstrut 50q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.11064 −0.785343 −0.392671 0.919679i \(-0.628449\pi\)
−0.392671 + 0.919679i \(0.628449\pi\)
\(3\) 3.24263 1.87213 0.936067 0.351821i \(-0.114438\pi\)
0.936067 + 0.351821i \(0.114438\pi\)
\(4\) −0.766474 −0.383237
\(5\) 1.00000 0.447214
\(6\) −3.60140 −1.47027
\(7\) 2.31774 0.876021 0.438011 0.898970i \(-0.355683\pi\)
0.438011 + 0.898970i \(0.355683\pi\)
\(8\) 3.07256 1.08631
\(9\) 7.51466 2.50489
\(10\) −1.11064 −0.351216
\(11\) 1.00000 0.301511
\(12\) −2.48539 −0.717471
\(13\) −0.104355 −0.0289430 −0.0144715 0.999895i \(-0.504607\pi\)
−0.0144715 + 0.999895i \(0.504607\pi\)
\(14\) −2.57417 −0.687977
\(15\) 3.24263 0.837244
\(16\) −1.87957 −0.469892
\(17\) 3.59955 0.873019 0.436509 0.899700i \(-0.356215\pi\)
0.436509 + 0.899700i \(0.356215\pi\)
\(18\) −8.34610 −1.96719
\(19\) 3.68931 0.846386 0.423193 0.906040i \(-0.360909\pi\)
0.423193 + 0.906040i \(0.360909\pi\)
\(20\) −0.766474 −0.171389
\(21\) 7.51556 1.64003
\(22\) −1.11064 −0.236790
\(23\) 7.11088 1.48272 0.741360 0.671107i \(-0.234181\pi\)
0.741360 + 0.671107i \(0.234181\pi\)
\(24\) 9.96319 2.03373
\(25\) 1.00000 0.200000
\(26\) 0.115901 0.0227301
\(27\) 14.6394 2.81735
\(28\) −1.77648 −0.335724
\(29\) 4.35072 0.807908 0.403954 0.914779i \(-0.367636\pi\)
0.403954 + 0.914779i \(0.367636\pi\)
\(30\) −3.60140 −0.657523
\(31\) 0.187969 0.0337602 0.0168801 0.999858i \(-0.494627\pi\)
0.0168801 + 0.999858i \(0.494627\pi\)
\(32\) −4.05760 −0.717289
\(33\) 3.24263 0.564470
\(34\) −3.99781 −0.685619
\(35\) 2.31774 0.391769
\(36\) −5.75979 −0.959966
\(37\) −2.99014 −0.491576 −0.245788 0.969324i \(-0.579047\pi\)
−0.245788 + 0.969324i \(0.579047\pi\)
\(38\) −4.09750 −0.664703
\(39\) −0.338386 −0.0541851
\(40\) 3.07256 0.485815
\(41\) −9.01977 −1.40865 −0.704325 0.709877i \(-0.748750\pi\)
−0.704325 + 0.709877i \(0.748750\pi\)
\(42\) −8.34710 −1.28799
\(43\) −5.30348 −0.808773 −0.404387 0.914588i \(-0.632515\pi\)
−0.404387 + 0.914588i \(0.632515\pi\)
\(44\) −0.766474 −0.115550
\(45\) 7.51466 1.12022
\(46\) −7.89764 −1.16444
\(47\) −12.0184 −1.75306 −0.876532 0.481344i \(-0.840149\pi\)
−0.876532 + 0.481344i \(0.840149\pi\)
\(48\) −6.09475 −0.879701
\(49\) −1.62810 −0.232586
\(50\) −1.11064 −0.157069
\(51\) 11.6720 1.63441
\(52\) 0.0799857 0.0110920
\(53\) −12.2860 −1.68762 −0.843808 0.536646i \(-0.819691\pi\)
−0.843808 + 0.536646i \(0.819691\pi\)
\(54\) −16.2591 −2.21258
\(55\) 1.00000 0.134840
\(56\) 7.12139 0.951635
\(57\) 11.9631 1.58455
\(58\) −4.83209 −0.634484
\(59\) −4.26462 −0.555206 −0.277603 0.960696i \(-0.589540\pi\)
−0.277603 + 0.960696i \(0.589540\pi\)
\(60\) −2.48539 −0.320863
\(61\) −0.802852 −0.102795 −0.0513973 0.998678i \(-0.516367\pi\)
−0.0513973 + 0.998678i \(0.516367\pi\)
\(62\) −0.208766 −0.0265133
\(63\) 17.4170 2.19433
\(64\) 8.26568 1.03321
\(65\) −0.104355 −0.0129437
\(66\) −3.60140 −0.443302
\(67\) 6.84360 0.836079 0.418039 0.908429i \(-0.362717\pi\)
0.418039 + 0.908429i \(0.362717\pi\)
\(68\) −2.75896 −0.334573
\(69\) 23.0580 2.77585
\(70\) −2.57417 −0.307673
\(71\) −8.85756 −1.05120 −0.525600 0.850732i \(-0.676159\pi\)
−0.525600 + 0.850732i \(0.676159\pi\)
\(72\) 23.0893 2.72110
\(73\) 1.00000 0.117041
\(74\) 3.32098 0.386056
\(75\) 3.24263 0.374427
\(76\) −2.82776 −0.324366
\(77\) 2.31774 0.264130
\(78\) 0.375826 0.0425539
\(79\) −4.89807 −0.551076 −0.275538 0.961290i \(-0.588856\pi\)
−0.275538 + 0.961290i \(0.588856\pi\)
\(80\) −1.87957 −0.210142
\(81\) 24.9261 2.76957
\(82\) 10.0177 1.10627
\(83\) 8.39151 0.921088 0.460544 0.887637i \(-0.347654\pi\)
0.460544 + 0.887637i \(0.347654\pi\)
\(84\) −5.76048 −0.628520
\(85\) 3.59955 0.390426
\(86\) 5.89027 0.635164
\(87\) 14.1078 1.51251
\(88\) 3.07256 0.327536
\(89\) 2.19724 0.232907 0.116454 0.993196i \(-0.462847\pi\)
0.116454 + 0.993196i \(0.462847\pi\)
\(90\) −8.34610 −0.879756
\(91\) −0.241868 −0.0253547
\(92\) −5.45030 −0.568233
\(93\) 0.609514 0.0632037
\(94\) 13.3481 1.37676
\(95\) 3.68931 0.378515
\(96\) −13.1573 −1.34286
\(97\) −0.769097 −0.0780900 −0.0390450 0.999237i \(-0.512432\pi\)
−0.0390450 + 0.999237i \(0.512432\pi\)
\(98\) 1.80824 0.182660
\(99\) 7.51466 0.755252
\(100\) −0.766474 −0.0766474
\(101\) −12.0828 −1.20229 −0.601143 0.799141i \(-0.705288\pi\)
−0.601143 + 0.799141i \(0.705288\pi\)
\(102\) −12.9634 −1.28357
\(103\) −2.23624 −0.220344 −0.110172 0.993913i \(-0.535140\pi\)
−0.110172 + 0.993913i \(0.535140\pi\)
\(104\) −0.320638 −0.0314412
\(105\) 7.51556 0.733444
\(106\) 13.6454 1.32536
\(107\) 11.7229 1.13330 0.566649 0.823959i \(-0.308239\pi\)
0.566649 + 0.823959i \(0.308239\pi\)
\(108\) −11.2207 −1.07971
\(109\) −6.69712 −0.641468 −0.320734 0.947169i \(-0.603930\pi\)
−0.320734 + 0.947169i \(0.603930\pi\)
\(110\) −1.11064 −0.105896
\(111\) −9.69593 −0.920297
\(112\) −4.35634 −0.411636
\(113\) −10.6623 −1.00302 −0.501511 0.865151i \(-0.667222\pi\)
−0.501511 + 0.865151i \(0.667222\pi\)
\(114\) −13.2867 −1.24441
\(115\) 7.11088 0.663093
\(116\) −3.33471 −0.309620
\(117\) −0.784195 −0.0724989
\(118\) 4.73647 0.436027
\(119\) 8.34280 0.764783
\(120\) 9.96319 0.909511
\(121\) 1.00000 0.0909091
\(122\) 0.891681 0.0807290
\(123\) −29.2478 −2.63718
\(124\) −0.144073 −0.0129382
\(125\) 1.00000 0.0894427
\(126\) −19.3440 −1.72330
\(127\) −8.78544 −0.779582 −0.389791 0.920903i \(-0.627453\pi\)
−0.389791 + 0.920903i \(0.627453\pi\)
\(128\) −1.06501 −0.0941347
\(129\) −17.1972 −1.51413
\(130\) 0.115901 0.0101652
\(131\) 1.42501 0.124504 0.0622519 0.998060i \(-0.480172\pi\)
0.0622519 + 0.998060i \(0.480172\pi\)
\(132\) −2.48539 −0.216326
\(133\) 8.55084 0.741452
\(134\) −7.60079 −0.656608
\(135\) 14.6394 1.25996
\(136\) 11.0598 0.948373
\(137\) 1.06013 0.0905734 0.0452867 0.998974i \(-0.485580\pi\)
0.0452867 + 0.998974i \(0.485580\pi\)
\(138\) −25.6091 −2.17999
\(139\) 3.28018 0.278221 0.139111 0.990277i \(-0.455576\pi\)
0.139111 + 0.990277i \(0.455576\pi\)
\(140\) −1.77648 −0.150140
\(141\) −38.9712 −3.28197
\(142\) 9.83758 0.825551
\(143\) −0.104355 −0.00872663
\(144\) −14.1243 −1.17703
\(145\) 4.35072 0.361307
\(146\) −1.11064 −0.0919174
\(147\) −5.27934 −0.435433
\(148\) 2.29187 0.188390
\(149\) 1.07627 0.0881711 0.0440856 0.999028i \(-0.485963\pi\)
0.0440856 + 0.999028i \(0.485963\pi\)
\(150\) −3.60140 −0.294053
\(151\) 12.7304 1.03599 0.517994 0.855384i \(-0.326679\pi\)
0.517994 + 0.855384i \(0.326679\pi\)
\(152\) 11.3356 0.919442
\(153\) 27.0494 2.18681
\(154\) −2.57417 −0.207433
\(155\) 0.187969 0.0150980
\(156\) 0.259364 0.0207657
\(157\) 16.1169 1.28627 0.643136 0.765752i \(-0.277633\pi\)
0.643136 + 0.765752i \(0.277633\pi\)
\(158\) 5.44000 0.432783
\(159\) −39.8391 −3.15944
\(160\) −4.05760 −0.320781
\(161\) 16.4811 1.29889
\(162\) −27.6840 −2.17506
\(163\) −5.22058 −0.408907 −0.204454 0.978876i \(-0.565542\pi\)
−0.204454 + 0.978876i \(0.565542\pi\)
\(164\) 6.91342 0.539847
\(165\) 3.24263 0.252439
\(166\) −9.31997 −0.723370
\(167\) 1.12152 0.0867855 0.0433928 0.999058i \(-0.486183\pi\)
0.0433928 + 0.999058i \(0.486183\pi\)
\(168\) 23.0920 1.78159
\(169\) −12.9891 −0.999162
\(170\) −3.99781 −0.306618
\(171\) 27.7239 2.12010
\(172\) 4.06498 0.309952
\(173\) −11.1407 −0.847010 −0.423505 0.905894i \(-0.639200\pi\)
−0.423505 + 0.905894i \(0.639200\pi\)
\(174\) −15.6687 −1.18784
\(175\) 2.31774 0.175204
\(176\) −1.87957 −0.141678
\(177\) −13.8286 −1.03942
\(178\) −2.44035 −0.182912
\(179\) 5.42469 0.405460 0.202730 0.979235i \(-0.435019\pi\)
0.202730 + 0.979235i \(0.435019\pi\)
\(180\) −5.75979 −0.429310
\(181\) −24.4907 −1.82038 −0.910190 0.414191i \(-0.864065\pi\)
−0.910190 + 0.414191i \(0.864065\pi\)
\(182\) 0.268629 0.0199121
\(183\) −2.60335 −0.192445
\(184\) 21.8486 1.61070
\(185\) −2.99014 −0.219840
\(186\) −0.676952 −0.0496365
\(187\) 3.59955 0.263225
\(188\) 9.21179 0.671839
\(189\) 33.9302 2.46806
\(190\) −4.09750 −0.297264
\(191\) −5.73400 −0.414898 −0.207449 0.978246i \(-0.566516\pi\)
−0.207449 + 0.978246i \(0.566516\pi\)
\(192\) 26.8025 1.93431
\(193\) −6.13432 −0.441558 −0.220779 0.975324i \(-0.570860\pi\)
−0.220779 + 0.975324i \(0.570860\pi\)
\(194\) 0.854192 0.0613274
\(195\) −0.338386 −0.0242323
\(196\) 1.24790 0.0891357
\(197\) 21.1772 1.50881 0.754406 0.656408i \(-0.227925\pi\)
0.754406 + 0.656408i \(0.227925\pi\)
\(198\) −8.34610 −0.593131
\(199\) −15.3514 −1.08823 −0.544114 0.839011i \(-0.683134\pi\)
−0.544114 + 0.839011i \(0.683134\pi\)
\(200\) 3.07256 0.217263
\(201\) 22.1913 1.56525
\(202\) 13.4197 0.944207
\(203\) 10.0838 0.707745
\(204\) −8.94630 −0.626366
\(205\) −9.01977 −0.629968
\(206\) 2.48367 0.173045
\(207\) 53.4358 3.71405
\(208\) 0.196143 0.0136001
\(209\) 3.68931 0.255195
\(210\) −8.34710 −0.576004
\(211\) −5.00689 −0.344688 −0.172344 0.985037i \(-0.555134\pi\)
−0.172344 + 0.985037i \(0.555134\pi\)
\(212\) 9.41692 0.646757
\(213\) −28.7218 −1.96799
\(214\) −13.0200 −0.890028
\(215\) −5.30348 −0.361694
\(216\) 44.9804 3.06053
\(217\) 0.435662 0.0295747
\(218\) 7.43810 0.503772
\(219\) 3.24263 0.219117
\(220\) −0.766474 −0.0516757
\(221\) −0.375632 −0.0252678
\(222\) 10.7687 0.722748
\(223\) 1.46903 0.0983736 0.0491868 0.998790i \(-0.484337\pi\)
0.0491868 + 0.998790i \(0.484337\pi\)
\(224\) −9.40444 −0.628360
\(225\) 7.51466 0.500977
\(226\) 11.8420 0.787716
\(227\) 14.8681 0.986829 0.493414 0.869794i \(-0.335749\pi\)
0.493414 + 0.869794i \(0.335749\pi\)
\(228\) −9.16939 −0.607258
\(229\) −7.39386 −0.488600 −0.244300 0.969700i \(-0.578558\pi\)
−0.244300 + 0.969700i \(0.578558\pi\)
\(230\) −7.89764 −0.520755
\(231\) 7.51556 0.494488
\(232\) 13.3678 0.877642
\(233\) −9.19061 −0.602097 −0.301048 0.953609i \(-0.597337\pi\)
−0.301048 + 0.953609i \(0.597337\pi\)
\(234\) 0.870960 0.0569364
\(235\) −12.0184 −0.783994
\(236\) 3.26872 0.212776
\(237\) −15.8826 −1.03169
\(238\) −9.26586 −0.600617
\(239\) −17.5535 −1.13544 −0.567720 0.823222i \(-0.692174\pi\)
−0.567720 + 0.823222i \(0.692174\pi\)
\(240\) −6.09475 −0.393414
\(241\) 13.9738 0.900133 0.450066 0.892995i \(-0.351400\pi\)
0.450066 + 0.892995i \(0.351400\pi\)
\(242\) −1.11064 −0.0713948
\(243\) 36.9081 2.36766
\(244\) 0.615366 0.0393947
\(245\) −1.62810 −0.104016
\(246\) 32.4838 2.07109
\(247\) −0.384999 −0.0244969
\(248\) 0.577546 0.0366742
\(249\) 27.2106 1.72440
\(250\) −1.11064 −0.0702432
\(251\) −15.8761 −1.00209 −0.501044 0.865422i \(-0.667050\pi\)
−0.501044 + 0.865422i \(0.667050\pi\)
\(252\) −13.3497 −0.840950
\(253\) 7.11088 0.447057
\(254\) 9.75748 0.612239
\(255\) 11.6720 0.730930
\(256\) −15.3485 −0.959281
\(257\) −10.8144 −0.674583 −0.337291 0.941400i \(-0.609511\pi\)
−0.337291 + 0.941400i \(0.609511\pi\)
\(258\) 19.1000 1.18911
\(259\) −6.93035 −0.430631
\(260\) 0.0799857 0.00496050
\(261\) 32.6942 2.02372
\(262\) −1.58268 −0.0977782
\(263\) 9.71885 0.599290 0.299645 0.954051i \(-0.403132\pi\)
0.299645 + 0.954051i \(0.403132\pi\)
\(264\) 9.96319 0.613192
\(265\) −12.2860 −0.754725
\(266\) −9.49693 −0.582294
\(267\) 7.12485 0.436034
\(268\) −5.24544 −0.320416
\(269\) 14.9942 0.914212 0.457106 0.889412i \(-0.348886\pi\)
0.457106 + 0.889412i \(0.348886\pi\)
\(270\) −16.2591 −0.989498
\(271\) 17.1807 1.04365 0.521827 0.853052i \(-0.325251\pi\)
0.521827 + 0.853052i \(0.325251\pi\)
\(272\) −6.76560 −0.410225
\(273\) −0.784289 −0.0474673
\(274\) −1.17743 −0.0711312
\(275\) 1.00000 0.0603023
\(276\) −17.6733 −1.06381
\(277\) 21.3363 1.28198 0.640988 0.767551i \(-0.278525\pi\)
0.640988 + 0.767551i \(0.278525\pi\)
\(278\) −3.64310 −0.218499
\(279\) 1.41252 0.0845655
\(280\) 7.12139 0.425584
\(281\) 5.93349 0.353962 0.176981 0.984214i \(-0.443367\pi\)
0.176981 + 0.984214i \(0.443367\pi\)
\(282\) 43.2831 2.57747
\(283\) 10.5608 0.627775 0.313888 0.949460i \(-0.398368\pi\)
0.313888 + 0.949460i \(0.398368\pi\)
\(284\) 6.78909 0.402858
\(285\) 11.9631 0.708631
\(286\) 0.115901 0.00685340
\(287\) −20.9054 −1.23401
\(288\) −30.4915 −1.79673
\(289\) −4.04325 −0.237838
\(290\) −4.83209 −0.283750
\(291\) −2.49390 −0.146195
\(292\) −0.766474 −0.0448545
\(293\) 17.5725 1.02660 0.513298 0.858211i \(-0.328424\pi\)
0.513298 + 0.858211i \(0.328424\pi\)
\(294\) 5.86346 0.341964
\(295\) −4.26462 −0.248296
\(296\) −9.18740 −0.534006
\(297\) 14.6394 0.849463
\(298\) −1.19535 −0.0692445
\(299\) −0.742058 −0.0429143
\(300\) −2.48539 −0.143494
\(301\) −12.2921 −0.708503
\(302\) −14.1390 −0.813605
\(303\) −39.1802 −2.25084
\(304\) −6.93431 −0.397710
\(305\) −0.802852 −0.0459712
\(306\) −30.0422 −1.71740
\(307\) 28.5979 1.63217 0.816083 0.577935i \(-0.196141\pi\)
0.816083 + 0.577935i \(0.196141\pi\)
\(308\) −1.77648 −0.101225
\(309\) −7.25132 −0.412513
\(310\) −0.208766 −0.0118571
\(311\) −7.86587 −0.446033 −0.223016 0.974815i \(-0.571590\pi\)
−0.223016 + 0.974815i \(0.571590\pi\)
\(312\) −1.03971 −0.0588621
\(313\) −34.7967 −1.96683 −0.983414 0.181375i \(-0.941945\pi\)
−0.983414 + 0.181375i \(0.941945\pi\)
\(314\) −17.9002 −1.01016
\(315\) 17.4170 0.981336
\(316\) 3.75425 0.211193
\(317\) 13.8673 0.778867 0.389434 0.921055i \(-0.372671\pi\)
0.389434 + 0.921055i \(0.372671\pi\)
\(318\) 44.2469 2.48124
\(319\) 4.35072 0.243593
\(320\) 8.26568 0.462065
\(321\) 38.0132 2.12169
\(322\) −18.3046 −1.02008
\(323\) 13.2799 0.738911
\(324\) −19.1052 −1.06140
\(325\) −0.104355 −0.00578859
\(326\) 5.79819 0.321132
\(327\) −21.7163 −1.20091
\(328\) −27.7138 −1.53024
\(329\) −27.8555 −1.53572
\(330\) −3.60140 −0.198251
\(331\) −0.832550 −0.0457611 −0.0228806 0.999738i \(-0.507284\pi\)
−0.0228806 + 0.999738i \(0.507284\pi\)
\(332\) −6.43188 −0.352995
\(333\) −22.4699 −1.23134
\(334\) −1.24560 −0.0681563
\(335\) 6.84360 0.373906
\(336\) −14.1260 −0.770637
\(337\) −6.98939 −0.380736 −0.190368 0.981713i \(-0.560968\pi\)
−0.190368 + 0.981713i \(0.560968\pi\)
\(338\) 14.4263 0.784685
\(339\) −34.5738 −1.87779
\(340\) −2.75896 −0.149626
\(341\) 0.187969 0.0101791
\(342\) −30.7913 −1.66501
\(343\) −19.9977 −1.07977
\(344\) −16.2953 −0.878582
\(345\) 23.0580 1.24140
\(346\) 12.3733 0.665193
\(347\) 17.4871 0.938755 0.469378 0.882998i \(-0.344478\pi\)
0.469378 + 0.882998i \(0.344478\pi\)
\(348\) −10.8132 −0.579651
\(349\) 19.0408 1.01923 0.509616 0.860402i \(-0.329788\pi\)
0.509616 + 0.860402i \(0.329788\pi\)
\(350\) −2.57417 −0.137595
\(351\) −1.52770 −0.0815425
\(352\) −4.05760 −0.216271
\(353\) 3.33126 0.177305 0.0886524 0.996063i \(-0.471744\pi\)
0.0886524 + 0.996063i \(0.471744\pi\)
\(354\) 15.3586 0.816301
\(355\) −8.85756 −0.470111
\(356\) −1.68413 −0.0892587
\(357\) 27.0526 1.43178
\(358\) −6.02489 −0.318425
\(359\) 35.6412 1.88107 0.940535 0.339696i \(-0.110324\pi\)
0.940535 + 0.339696i \(0.110324\pi\)
\(360\) 23.0893 1.21691
\(361\) −5.38899 −0.283631
\(362\) 27.2004 1.42962
\(363\) 3.24263 0.170194
\(364\) 0.185386 0.00971685
\(365\) 1.00000 0.0523424
\(366\) 2.89139 0.151136
\(367\) 31.4974 1.64415 0.822075 0.569379i \(-0.192816\pi\)
0.822075 + 0.569379i \(0.192816\pi\)
\(368\) −13.3654 −0.696719
\(369\) −67.7805 −3.52851
\(370\) 3.32098 0.172649
\(371\) −28.4757 −1.47839
\(372\) −0.467177 −0.0242220
\(373\) −18.3239 −0.948775 −0.474388 0.880316i \(-0.657331\pi\)
−0.474388 + 0.880316i \(0.657331\pi\)
\(374\) −3.99781 −0.206722
\(375\) 3.24263 0.167449
\(376\) −36.9273 −1.90438
\(377\) −0.454021 −0.0233832
\(378\) −37.6843 −1.93827
\(379\) −26.1585 −1.34367 −0.671835 0.740701i \(-0.734494\pi\)
−0.671835 + 0.740701i \(0.734494\pi\)
\(380\) −2.82776 −0.145061
\(381\) −28.4879 −1.45948
\(382\) 6.36843 0.325837
\(383\) 21.8437 1.11616 0.558082 0.829786i \(-0.311538\pi\)
0.558082 + 0.829786i \(0.311538\pi\)
\(384\) −3.45344 −0.176233
\(385\) 2.31774 0.118123
\(386\) 6.81304 0.346775
\(387\) −39.8538 −2.02588
\(388\) 0.589493 0.0299270
\(389\) 21.6212 1.09624 0.548119 0.836401i \(-0.315344\pi\)
0.548119 + 0.836401i \(0.315344\pi\)
\(390\) 0.375826 0.0190307
\(391\) 25.5959 1.29444
\(392\) −5.00245 −0.252662
\(393\) 4.62079 0.233088
\(394\) −23.5203 −1.18493
\(395\) −4.89807 −0.246449
\(396\) −5.75979 −0.289441
\(397\) −23.7727 −1.19312 −0.596560 0.802569i \(-0.703466\pi\)
−0.596560 + 0.802569i \(0.703466\pi\)
\(398\) 17.0499 0.854632
\(399\) 27.7272 1.38810
\(400\) −1.87957 −0.0939784
\(401\) 12.7742 0.637911 0.318955 0.947770i \(-0.396668\pi\)
0.318955 + 0.947770i \(0.396668\pi\)
\(402\) −24.6466 −1.22926
\(403\) −0.0196156 −0.000977121 0
\(404\) 9.26118 0.460761
\(405\) 24.9261 1.23859
\(406\) −11.1995 −0.555822
\(407\) −2.99014 −0.148216
\(408\) 35.8630 1.77548
\(409\) −19.0333 −0.941136 −0.470568 0.882364i \(-0.655951\pi\)
−0.470568 + 0.882364i \(0.655951\pi\)
\(410\) 10.0177 0.494741
\(411\) 3.43763 0.169566
\(412\) 1.71402 0.0844439
\(413\) −9.88426 −0.486373
\(414\) −59.3481 −2.91680
\(415\) 8.39151 0.411923
\(416\) 0.423432 0.0207605
\(417\) 10.6364 0.520867
\(418\) −4.09750 −0.200415
\(419\) −27.3911 −1.33814 −0.669072 0.743198i \(-0.733308\pi\)
−0.669072 + 0.743198i \(0.733308\pi\)
\(420\) −5.76048 −0.281083
\(421\) 15.2897 0.745176 0.372588 0.927997i \(-0.378471\pi\)
0.372588 + 0.927997i \(0.378471\pi\)
\(422\) 5.56086 0.270699
\(423\) −90.3142 −4.39123
\(424\) −37.7496 −1.83328
\(425\) 3.59955 0.174604
\(426\) 31.8996 1.54554
\(427\) −1.86080 −0.0900504
\(428\) −8.98533 −0.434322
\(429\) −0.338386 −0.0163374
\(430\) 5.89027 0.284054
\(431\) −21.5046 −1.03584 −0.517919 0.855430i \(-0.673293\pi\)
−0.517919 + 0.855430i \(0.673293\pi\)
\(432\) −27.5157 −1.32385
\(433\) 34.0633 1.63698 0.818489 0.574522i \(-0.194812\pi\)
0.818489 + 0.574522i \(0.194812\pi\)
\(434\) −0.483865 −0.0232263
\(435\) 14.1078 0.676416
\(436\) 5.13317 0.245834
\(437\) 26.2342 1.25495
\(438\) −3.60140 −0.172082
\(439\) −22.3758 −1.06794 −0.533968 0.845504i \(-0.679300\pi\)
−0.533968 + 0.845504i \(0.679300\pi\)
\(440\) 3.07256 0.146479
\(441\) −12.2347 −0.582602
\(442\) 0.417193 0.0198438
\(443\) 10.8216 0.514147 0.257074 0.966392i \(-0.417242\pi\)
0.257074 + 0.966392i \(0.417242\pi\)
\(444\) 7.43168 0.352692
\(445\) 2.19724 0.104159
\(446\) −1.63157 −0.0772569
\(447\) 3.48993 0.165068
\(448\) 19.1576 0.905114
\(449\) 34.7691 1.64085 0.820427 0.571751i \(-0.193736\pi\)
0.820427 + 0.571751i \(0.193736\pi\)
\(450\) −8.34610 −0.393439
\(451\) −9.01977 −0.424724
\(452\) 8.17236 0.384395
\(453\) 41.2801 1.93951
\(454\) −16.5131 −0.774998
\(455\) −0.241868 −0.0113389
\(456\) 36.7573 1.72132
\(457\) −19.5949 −0.916612 −0.458306 0.888795i \(-0.651544\pi\)
−0.458306 + 0.888795i \(0.651544\pi\)
\(458\) 8.21193 0.383718
\(459\) 52.6952 2.45960
\(460\) −5.45030 −0.254122
\(461\) −8.50366 −0.396055 −0.198027 0.980196i \(-0.563454\pi\)
−0.198027 + 0.980196i \(0.563454\pi\)
\(462\) −8.34710 −0.388342
\(463\) −1.52409 −0.0708303 −0.0354152 0.999373i \(-0.511275\pi\)
−0.0354152 + 0.999373i \(0.511275\pi\)
\(464\) −8.17747 −0.379630
\(465\) 0.609514 0.0282655
\(466\) 10.2075 0.472852
\(467\) −8.67250 −0.401315 −0.200658 0.979661i \(-0.564308\pi\)
−0.200658 + 0.979661i \(0.564308\pi\)
\(468\) 0.601065 0.0277843
\(469\) 15.8617 0.732423
\(470\) 13.3481 0.615704
\(471\) 52.2613 2.40807
\(472\) −13.1033 −0.603129
\(473\) −5.30348 −0.243854
\(474\) 17.6399 0.810229
\(475\) 3.68931 0.169277
\(476\) −6.39454 −0.293093
\(477\) −92.3253 −4.22729
\(478\) 19.4956 0.891709
\(479\) −30.7065 −1.40301 −0.701507 0.712662i \(-0.747489\pi\)
−0.701507 + 0.712662i \(0.747489\pi\)
\(480\) −13.1573 −0.600546
\(481\) 0.312037 0.0142277
\(482\) −15.5199 −0.706912
\(483\) 53.4422 2.43171
\(484\) −0.766474 −0.0348397
\(485\) −0.769097 −0.0349229
\(486\) −40.9917 −1.85942
\(487\) −5.66639 −0.256768 −0.128384 0.991725i \(-0.540979\pi\)
−0.128384 + 0.991725i \(0.540979\pi\)
\(488\) −2.46681 −0.111667
\(489\) −16.9284 −0.765529
\(490\) 1.80824 0.0816880
\(491\) 27.3569 1.23460 0.617300 0.786728i \(-0.288227\pi\)
0.617300 + 0.786728i \(0.288227\pi\)
\(492\) 22.4177 1.01067
\(493\) 15.6606 0.705319
\(494\) 0.427596 0.0192385
\(495\) 7.51466 0.337759
\(496\) −0.353301 −0.0158637
\(497\) −20.5295 −0.920873
\(498\) −30.2212 −1.35425
\(499\) 2.61647 0.117129 0.0585647 0.998284i \(-0.481348\pi\)
0.0585647 + 0.998284i \(0.481348\pi\)
\(500\) −0.766474 −0.0342778
\(501\) 3.63666 0.162474
\(502\) 17.6326 0.786982
\(503\) 14.7349 0.656996 0.328498 0.944505i \(-0.393458\pi\)
0.328498 + 0.944505i \(0.393458\pi\)
\(504\) 53.5148 2.38374
\(505\) −12.0828 −0.537679
\(506\) −7.89764 −0.351093
\(507\) −42.1189 −1.87057
\(508\) 6.73381 0.298765
\(509\) 24.3139 1.07769 0.538847 0.842404i \(-0.318860\pi\)
0.538847 + 0.842404i \(0.318860\pi\)
\(510\) −12.9634 −0.574030
\(511\) 2.31774 0.102531
\(512\) 19.1767 0.847499
\(513\) 54.0092 2.38457
\(514\) 12.0109 0.529778
\(515\) −2.23624 −0.0985407
\(516\) 13.1812 0.580272
\(517\) −12.0184 −0.528568
\(518\) 7.69714 0.338193
\(519\) −36.1251 −1.58572
\(520\) −0.320638 −0.0140609
\(521\) 18.4182 0.806917 0.403459 0.914998i \(-0.367808\pi\)
0.403459 + 0.914998i \(0.367808\pi\)
\(522\) −36.3115 −1.58931
\(523\) 9.39261 0.410710 0.205355 0.978688i \(-0.434165\pi\)
0.205355 + 0.978688i \(0.434165\pi\)
\(524\) −1.09223 −0.0477145
\(525\) 7.51556 0.328006
\(526\) −10.7942 −0.470648
\(527\) 0.676603 0.0294733
\(528\) −6.09475 −0.265240
\(529\) 27.5646 1.19846
\(530\) 13.6454 0.592717
\(531\) −32.0472 −1.39073
\(532\) −6.55400 −0.284152
\(533\) 0.941261 0.0407705
\(534\) −7.91316 −0.342436
\(535\) 11.7229 0.506827
\(536\) 21.0274 0.908245
\(537\) 17.5903 0.759076
\(538\) −16.6532 −0.717969
\(539\) −1.62810 −0.0701274
\(540\) −11.2207 −0.482862
\(541\) 26.4794 1.13844 0.569220 0.822185i \(-0.307245\pi\)
0.569220 + 0.822185i \(0.307245\pi\)
\(542\) −19.0816 −0.819625
\(543\) −79.4144 −3.40800
\(544\) −14.6055 −0.626206
\(545\) −6.69712 −0.286873
\(546\) 0.871064 0.0372781
\(547\) 23.5934 1.00878 0.504391 0.863475i \(-0.331717\pi\)
0.504391 + 0.863475i \(0.331717\pi\)
\(548\) −0.812566 −0.0347111
\(549\) −6.03316 −0.257489
\(550\) −1.11064 −0.0473579
\(551\) 16.0511 0.683802
\(552\) 70.8470 3.01545
\(553\) −11.3524 −0.482754
\(554\) −23.6970 −1.00679
\(555\) −9.69593 −0.411569
\(556\) −2.51417 −0.106625
\(557\) −27.7533 −1.17595 −0.587973 0.808881i \(-0.700074\pi\)
−0.587973 + 0.808881i \(0.700074\pi\)
\(558\) −1.56881 −0.0664129
\(559\) 0.553447 0.0234083
\(560\) −4.35634 −0.184089
\(561\) 11.6720 0.492793
\(562\) −6.58998 −0.277982
\(563\) −22.3231 −0.940808 −0.470404 0.882451i \(-0.655892\pi\)
−0.470404 + 0.882451i \(0.655892\pi\)
\(564\) 29.8704 1.25777
\(565\) −10.6623 −0.448565
\(566\) −11.7293 −0.493019
\(567\) 57.7722 2.42620
\(568\) −27.2154 −1.14193
\(569\) 4.78450 0.200577 0.100288 0.994958i \(-0.468023\pi\)
0.100288 + 0.994958i \(0.468023\pi\)
\(570\) −13.2867 −0.556518
\(571\) 17.6031 0.736668 0.368334 0.929693i \(-0.379928\pi\)
0.368334 + 0.929693i \(0.379928\pi\)
\(572\) 0.0799857 0.00334437
\(573\) −18.5933 −0.776745
\(574\) 23.2184 0.969119
\(575\) 7.11088 0.296544
\(576\) 62.1137 2.58807
\(577\) −19.6879 −0.819616 −0.409808 0.912172i \(-0.634404\pi\)
−0.409808 + 0.912172i \(0.634404\pi\)
\(578\) 4.49060 0.186784
\(579\) −19.8914 −0.826656
\(580\) −3.33471 −0.138466
\(581\) 19.4493 0.806893
\(582\) 2.76983 0.114813
\(583\) −12.2860 −0.508835
\(584\) 3.07256 0.127144
\(585\) −0.784195 −0.0324225
\(586\) −19.5167 −0.806229
\(587\) −16.7400 −0.690934 −0.345467 0.938431i \(-0.612279\pi\)
−0.345467 + 0.938431i \(0.612279\pi\)
\(588\) 4.04648 0.166874
\(589\) 0.693476 0.0285742
\(590\) 4.73647 0.194997
\(591\) 68.6698 2.82470
\(592\) 5.62018 0.230988
\(593\) −34.5839 −1.42019 −0.710096 0.704105i \(-0.751348\pi\)
−0.710096 + 0.704105i \(0.751348\pi\)
\(594\) −16.2591 −0.667119
\(595\) 8.34280 0.342021
\(596\) −0.824930 −0.0337905
\(597\) −49.7788 −2.03731
\(598\) 0.824161 0.0337024
\(599\) 1.02128 0.0417283 0.0208642 0.999782i \(-0.493358\pi\)
0.0208642 + 0.999782i \(0.493358\pi\)
\(600\) 9.96319 0.406745
\(601\) 36.9998 1.50925 0.754626 0.656156i \(-0.227818\pi\)
0.754626 + 0.656156i \(0.227818\pi\)
\(602\) 13.6521 0.556417
\(603\) 51.4273 2.09428
\(604\) −9.75755 −0.397029
\(605\) 1.00000 0.0406558
\(606\) 43.5151 1.76768
\(607\) −38.3325 −1.55587 −0.777934 0.628346i \(-0.783732\pi\)
−0.777934 + 0.628346i \(0.783732\pi\)
\(608\) −14.9697 −0.607103
\(609\) 32.6981 1.32499
\(610\) 0.891681 0.0361031
\(611\) 1.25418 0.0507389
\(612\) −20.7327 −0.838068
\(613\) −7.99889 −0.323072 −0.161536 0.986867i \(-0.551645\pi\)
−0.161536 + 0.986867i \(0.551645\pi\)
\(614\) −31.7620 −1.28181
\(615\) −29.2478 −1.17938
\(616\) 7.12139 0.286929
\(617\) 8.32067 0.334978 0.167489 0.985874i \(-0.446434\pi\)
0.167489 + 0.985874i \(0.446434\pi\)
\(618\) 8.05362 0.323964
\(619\) −3.23706 −0.130108 −0.0650541 0.997882i \(-0.520722\pi\)
−0.0650541 + 0.997882i \(0.520722\pi\)
\(620\) −0.144073 −0.00578613
\(621\) 104.099 4.17734
\(622\) 8.73616 0.350288
\(623\) 5.09263 0.204032
\(624\) 0.636020 0.0254612
\(625\) 1.00000 0.0400000
\(626\) 38.6467 1.54463
\(627\) 11.9631 0.477759
\(628\) −12.3532 −0.492947
\(629\) −10.7632 −0.429155
\(630\) −19.3440 −0.770685
\(631\) −45.7667 −1.82194 −0.910972 0.412469i \(-0.864667\pi\)
−0.910972 + 0.412469i \(0.864667\pi\)
\(632\) −15.0496 −0.598642
\(633\) −16.2355 −0.645303
\(634\) −15.4016 −0.611677
\(635\) −8.78544 −0.348640
\(636\) 30.5356 1.21082
\(637\) 0.169901 0.00673174
\(638\) −4.83209 −0.191304
\(639\) −66.5616 −2.63313
\(640\) −1.06501 −0.0420983
\(641\) −19.4579 −0.768542 −0.384271 0.923220i \(-0.625547\pi\)
−0.384271 + 0.923220i \(0.625547\pi\)
\(642\) −42.2190 −1.66625
\(643\) −22.2063 −0.875732 −0.437866 0.899040i \(-0.644266\pi\)
−0.437866 + 0.899040i \(0.644266\pi\)
\(644\) −12.6324 −0.497785
\(645\) −17.1972 −0.677140
\(646\) −14.7492 −0.580298
\(647\) 41.1684 1.61850 0.809249 0.587466i \(-0.199874\pi\)
0.809249 + 0.587466i \(0.199874\pi\)
\(648\) 76.5871 3.00863
\(649\) −4.26462 −0.167401
\(650\) 0.115901 0.00454603
\(651\) 1.41269 0.0553678
\(652\) 4.00144 0.156708
\(653\) −27.1831 −1.06376 −0.531879 0.846820i \(-0.678514\pi\)
−0.531879 + 0.846820i \(0.678514\pi\)
\(654\) 24.1190 0.943129
\(655\) 1.42501 0.0556798
\(656\) 16.9533 0.661914
\(657\) 7.51466 0.293175
\(658\) 30.9374 1.20607
\(659\) −4.05460 −0.157945 −0.0789723 0.996877i \(-0.525164\pi\)
−0.0789723 + 0.996877i \(0.525164\pi\)
\(660\) −2.48539 −0.0967438
\(661\) 25.5990 0.995686 0.497843 0.867267i \(-0.334126\pi\)
0.497843 + 0.867267i \(0.334126\pi\)
\(662\) 0.924665 0.0359381
\(663\) −1.21804 −0.0473046
\(664\) 25.7835 1.00059
\(665\) 8.55084 0.331588
\(666\) 24.9560 0.967026
\(667\) 30.9374 1.19790
\(668\) −0.859613 −0.0332594
\(669\) 4.76353 0.184169
\(670\) −7.60079 −0.293644
\(671\) −0.802852 −0.0309938
\(672\) −30.4951 −1.17637
\(673\) 5.15543 0.198727 0.0993637 0.995051i \(-0.468319\pi\)
0.0993637 + 0.995051i \(0.468319\pi\)
\(674\) 7.76271 0.299009
\(675\) 14.6394 0.563470
\(676\) 9.95582 0.382916
\(677\) 30.3026 1.16462 0.582312 0.812965i \(-0.302148\pi\)
0.582312 + 0.812965i \(0.302148\pi\)
\(678\) 38.3991 1.47471
\(679\) −1.78256 −0.0684085
\(680\) 11.0598 0.424125
\(681\) 48.2117 1.84748
\(682\) −0.208766 −0.00799407
\(683\) 35.3348 1.35205 0.676024 0.736879i \(-0.263701\pi\)
0.676024 + 0.736879i \(0.263701\pi\)
\(684\) −21.2497 −0.812501
\(685\) 1.06013 0.0405057
\(686\) 22.2102 0.847991
\(687\) −23.9756 −0.914725
\(688\) 9.96825 0.380036
\(689\) 1.28211 0.0488446
\(690\) −25.6091 −0.974923
\(691\) 28.4840 1.08358 0.541791 0.840513i \(-0.317746\pi\)
0.541791 + 0.840513i \(0.317746\pi\)
\(692\) 8.53905 0.324606
\(693\) 17.4170 0.661617
\(694\) −19.4219 −0.737244
\(695\) 3.28018 0.124424
\(696\) 43.3470 1.64306
\(697\) −32.4671 −1.22978
\(698\) −21.1475 −0.800445
\(699\) −29.8018 −1.12721
\(700\) −1.77648 −0.0671448
\(701\) −25.7728 −0.973424 −0.486712 0.873562i \(-0.661804\pi\)
−0.486712 + 0.873562i \(0.661804\pi\)
\(702\) 1.69673 0.0640388
\(703\) −11.0316 −0.416063
\(704\) 8.26568 0.311524
\(705\) −38.9712 −1.46774
\(706\) −3.69983 −0.139245
\(707\) −28.0048 −1.05323
\(708\) 10.5993 0.398345
\(709\) 37.6115 1.41253 0.706265 0.707948i \(-0.250379\pi\)
0.706265 + 0.707948i \(0.250379\pi\)
\(710\) 9.83758 0.369198
\(711\) −36.8073 −1.38038
\(712\) 6.75117 0.253011
\(713\) 1.33662 0.0500570
\(714\) −30.0458 −1.12444
\(715\) −0.104355 −0.00390267
\(716\) −4.15789 −0.155387
\(717\) −56.9194 −2.12570
\(718\) −39.5846 −1.47728
\(719\) 16.3335 0.609137 0.304568 0.952490i \(-0.401488\pi\)
0.304568 + 0.952490i \(0.401488\pi\)
\(720\) −14.1243 −0.526382
\(721\) −5.18302 −0.193026
\(722\) 5.98524 0.222747
\(723\) 45.3119 1.68517
\(724\) 18.7715 0.697637
\(725\) 4.35072 0.161582
\(726\) −3.60140 −0.133661
\(727\) −23.3093 −0.864492 −0.432246 0.901756i \(-0.642279\pi\)
−0.432246 + 0.901756i \(0.642279\pi\)
\(728\) −0.743155 −0.0275431
\(729\) 44.9011 1.66300
\(730\) −1.11064 −0.0411067
\(731\) −19.0901 −0.706074
\(732\) 1.99540 0.0737522
\(733\) −50.1884 −1.85375 −0.926875 0.375371i \(-0.877515\pi\)
−0.926875 + 0.375371i \(0.877515\pi\)
\(734\) −34.9823 −1.29122
\(735\) −5.27934 −0.194732
\(736\) −28.8531 −1.06354
\(737\) 6.84360 0.252087
\(738\) 75.2799 2.77109
\(739\) 39.1895 1.44161 0.720805 0.693138i \(-0.243772\pi\)
0.720805 + 0.693138i \(0.243772\pi\)
\(740\) 2.29187 0.0842507
\(741\) −1.24841 −0.0458615
\(742\) 31.6264 1.16104
\(743\) 35.4247 1.29961 0.649803 0.760102i \(-0.274851\pi\)
0.649803 + 0.760102i \(0.274851\pi\)
\(744\) 1.87277 0.0686591
\(745\) 1.07627 0.0394313
\(746\) 20.3513 0.745114
\(747\) 63.0594 2.30722
\(748\) −2.75896 −0.100878
\(749\) 27.1707 0.992794
\(750\) −3.60140 −0.131505
\(751\) 18.1970 0.664019 0.332010 0.943276i \(-0.392273\pi\)
0.332010 + 0.943276i \(0.392273\pi\)
\(752\) 22.5894 0.823751
\(753\) −51.4802 −1.87604
\(754\) 0.504254 0.0183639
\(755\) 12.7304 0.463308
\(756\) −26.0066 −0.945852
\(757\) 8.91458 0.324006 0.162003 0.986790i \(-0.448205\pi\)
0.162003 + 0.986790i \(0.448205\pi\)
\(758\) 29.0527 1.05524
\(759\) 23.0580 0.836951
\(760\) 11.3356 0.411187
\(761\) 20.5297 0.744201 0.372100 0.928192i \(-0.378638\pi\)
0.372100 + 0.928192i \(0.378638\pi\)
\(762\) 31.6399 1.14619
\(763\) −15.5222 −0.561940
\(764\) 4.39497 0.159004
\(765\) 27.0494 0.977973
\(766\) −24.2606 −0.876570
\(767\) 0.445036 0.0160693
\(768\) −49.7695 −1.79590
\(769\) 37.1119 1.33829 0.669145 0.743132i \(-0.266660\pi\)
0.669145 + 0.743132i \(0.266660\pi\)
\(770\) −2.57417 −0.0927668
\(771\) −35.0671 −1.26291
\(772\) 4.70180 0.169222
\(773\) −46.0364 −1.65581 −0.827907 0.560866i \(-0.810468\pi\)
−0.827907 + 0.560866i \(0.810468\pi\)
\(774\) 44.2634 1.59101
\(775\) 0.187969 0.00675204
\(776\) −2.36310 −0.0848303
\(777\) −22.4726 −0.806200
\(778\) −24.0134 −0.860922
\(779\) −33.2767 −1.19226
\(780\) 0.259364 0.00928673
\(781\) −8.85756 −0.316948
\(782\) −28.4279 −1.01658
\(783\) 63.6918 2.27616
\(784\) 3.06013 0.109291
\(785\) 16.1169 0.575238
\(786\) −5.13204 −0.183054
\(787\) −45.1949 −1.61102 −0.805512 0.592580i \(-0.798110\pi\)
−0.805512 + 0.592580i \(0.798110\pi\)
\(788\) −16.2318 −0.578233
\(789\) 31.5146 1.12195
\(790\) 5.44000 0.193547
\(791\) −24.7123 −0.878669
\(792\) 23.0893 0.820441
\(793\) 0.0837819 0.00297518
\(794\) 26.4030 0.937007
\(795\) −39.8391 −1.41295
\(796\) 11.7664 0.417050
\(797\) −46.4228 −1.64438 −0.822191 0.569212i \(-0.807248\pi\)
−0.822191 + 0.569212i \(0.807248\pi\)
\(798\) −30.7950 −1.09013
\(799\) −43.2608 −1.53046
\(800\) −4.05760 −0.143458
\(801\) 16.5115 0.583406
\(802\) −14.1875 −0.500979
\(803\) 1.00000 0.0352892
\(804\) −17.0090 −0.599863
\(805\) 16.4811 0.580883
\(806\) 0.0217859 0.000767375 0
\(807\) 48.6206 1.71153
\(808\) −37.1252 −1.30606
\(809\) 22.3728 0.786584 0.393292 0.919414i \(-0.371336\pi\)
0.393292 + 0.919414i \(0.371336\pi\)
\(810\) −27.6840 −0.972717
\(811\) 49.9496 1.75397 0.876984 0.480520i \(-0.159552\pi\)
0.876984 + 0.480520i \(0.159552\pi\)
\(812\) −7.72898 −0.271234
\(813\) 55.7107 1.95386
\(814\) 3.32098 0.116400
\(815\) −5.22058 −0.182869
\(816\) −21.9383 −0.767996
\(817\) −19.5662 −0.684534
\(818\) 21.1392 0.739114
\(819\) −1.81756 −0.0635106
\(820\) 6.91342 0.241427
\(821\) 12.9215 0.450963 0.225482 0.974247i \(-0.427604\pi\)
0.225482 + 0.974247i \(0.427604\pi\)
\(822\) −3.81797 −0.133167
\(823\) −30.8889 −1.07672 −0.538359 0.842715i \(-0.680956\pi\)
−0.538359 + 0.842715i \(0.680956\pi\)
\(824\) −6.87100 −0.239363
\(825\) 3.24263 0.112894
\(826\) 10.9779 0.381969
\(827\) 22.0987 0.768446 0.384223 0.923240i \(-0.374469\pi\)
0.384223 + 0.923240i \(0.374469\pi\)
\(828\) −40.9572 −1.42336
\(829\) −23.1793 −0.805049 −0.402525 0.915409i \(-0.631867\pi\)
−0.402525 + 0.915409i \(0.631867\pi\)
\(830\) −9.31997 −0.323501
\(831\) 69.1859 2.40003
\(832\) −0.862567 −0.0299041
\(833\) −5.86044 −0.203052
\(834\) −11.8132 −0.409059
\(835\) 1.12152 0.0388117
\(836\) −2.82776 −0.0978002
\(837\) 2.75175 0.0951143
\(838\) 30.4217 1.05090
\(839\) 54.6105 1.88537 0.942683 0.333690i \(-0.108294\pi\)
0.942683 + 0.333690i \(0.108294\pi\)
\(840\) 23.0920 0.796751
\(841\) −10.0713 −0.347285
\(842\) −16.9814 −0.585218
\(843\) 19.2401 0.662665
\(844\) 3.83765 0.132097
\(845\) −12.9891 −0.446839
\(846\) 100.307 3.44862
\(847\) 2.31774 0.0796383
\(848\) 23.0924 0.792997
\(849\) 34.2448 1.17528
\(850\) −3.99781 −0.137124
\(851\) −21.2625 −0.728870
\(852\) 22.0145 0.754205
\(853\) −44.7750 −1.53307 −0.766534 0.642204i \(-0.778020\pi\)
−0.766534 + 0.642204i \(0.778020\pi\)
\(854\) 2.06668 0.0707204
\(855\) 27.7239 0.948138
\(856\) 36.0194 1.23112
\(857\) 53.9241 1.84201 0.921006 0.389549i \(-0.127369\pi\)
0.921006 + 0.389549i \(0.127369\pi\)
\(858\) 0.375826 0.0128305
\(859\) 14.6892 0.501190 0.250595 0.968092i \(-0.419374\pi\)
0.250595 + 0.968092i \(0.419374\pi\)
\(860\) 4.06498 0.138615
\(861\) −67.7886 −2.31023
\(862\) 23.8839 0.813488
\(863\) −13.7763 −0.468952 −0.234476 0.972122i \(-0.575337\pi\)
−0.234476 + 0.972122i \(0.575337\pi\)
\(864\) −59.4007 −2.02085
\(865\) −11.1407 −0.378795
\(866\) −37.8321 −1.28559
\(867\) −13.1108 −0.445265
\(868\) −0.333924 −0.0113341
\(869\) −4.89807 −0.166156
\(870\) −15.6687 −0.531218
\(871\) −0.714166 −0.0241986
\(872\) −20.5773 −0.696836
\(873\) −5.77951 −0.195607
\(874\) −29.1368 −0.985568
\(875\) 2.31774 0.0783537
\(876\) −2.48539 −0.0839737
\(877\) −12.2557 −0.413844 −0.206922 0.978357i \(-0.566345\pi\)
−0.206922 + 0.978357i \(0.566345\pi\)
\(878\) 24.8515 0.838696
\(879\) 56.9811 1.92192
\(880\) −1.87957 −0.0633602
\(881\) −37.9263 −1.27777 −0.638885 0.769302i \(-0.720604\pi\)
−0.638885 + 0.769302i \(0.720604\pi\)
\(882\) 13.5883 0.457542
\(883\) 26.3489 0.886710 0.443355 0.896346i \(-0.353788\pi\)
0.443355 + 0.896346i \(0.353788\pi\)
\(884\) 0.287912 0.00968354
\(885\) −13.8286 −0.464843
\(886\) −12.0189 −0.403782
\(887\) 5.07689 0.170465 0.0852327 0.996361i \(-0.472837\pi\)
0.0852327 + 0.996361i \(0.472837\pi\)
\(888\) −29.7913 −0.999732
\(889\) −20.3623 −0.682930
\(890\) −2.44035 −0.0818007
\(891\) 24.9261 0.835057
\(892\) −1.12597 −0.0377004
\(893\) −44.3396 −1.48377
\(894\) −3.87607 −0.129635
\(895\) 5.42469 0.181327
\(896\) −2.46842 −0.0824640
\(897\) −2.40622 −0.0803414
\(898\) −38.6160 −1.28863
\(899\) 0.817800 0.0272751
\(900\) −5.75979 −0.191993
\(901\) −44.2241 −1.47332
\(902\) 10.0177 0.333554
\(903\) −39.8586 −1.32641
\(904\) −32.7605 −1.08960
\(905\) −24.4907 −0.814099
\(906\) −45.8474 −1.52318
\(907\) −38.5702 −1.28070 −0.640351 0.768082i \(-0.721211\pi\)
−0.640351 + 0.768082i \(0.721211\pi\)
\(908\) −11.3960 −0.378189
\(909\) −90.7984 −3.01159
\(910\) 0.268629 0.00890496
\(911\) 48.1779 1.59621 0.798103 0.602521i \(-0.205837\pi\)
0.798103 + 0.602521i \(0.205837\pi\)
\(912\) −22.4854 −0.744567
\(913\) 8.39151 0.277719
\(914\) 21.7629 0.719854
\(915\) −2.60335 −0.0860642
\(916\) 5.66720 0.187250
\(917\) 3.30280 0.109068
\(918\) −58.5255 −1.93163
\(919\) 18.8156 0.620671 0.310335 0.950627i \(-0.399559\pi\)
0.310335 + 0.950627i \(0.399559\pi\)
\(920\) 21.8486 0.720327
\(921\) 92.7323 3.05563
\(922\) 9.44452 0.311039
\(923\) 0.924334 0.0304248
\(924\) −5.76048 −0.189506
\(925\) −2.99014 −0.0983152
\(926\) 1.69272 0.0556261
\(927\) −16.8046 −0.551936
\(928\) −17.6535 −0.579503
\(929\) −55.5219 −1.82162 −0.910808 0.412830i \(-0.864540\pi\)
−0.910808 + 0.412830i \(0.864540\pi\)
\(930\) −0.676952 −0.0221981
\(931\) −6.00658 −0.196858
\(932\) 7.04437 0.230746
\(933\) −25.5061 −0.835033
\(934\) 9.63204 0.315170
\(935\) 3.59955 0.117718
\(936\) −2.40949 −0.0787566
\(937\) 2.30247 0.0752184 0.0376092 0.999293i \(-0.488026\pi\)
0.0376092 + 0.999293i \(0.488026\pi\)
\(938\) −17.6166 −0.575203
\(939\) −112.833 −3.68217
\(940\) 9.21179 0.300456
\(941\) −53.8253 −1.75465 −0.877327 0.479893i \(-0.840676\pi\)
−0.877327 + 0.479893i \(0.840676\pi\)
\(942\) −58.0436 −1.89116
\(943\) −64.1384 −2.08864
\(944\) 8.01565 0.260887
\(945\) 33.9302 1.10375
\(946\) 5.89027 0.191509
\(947\) 5.47100 0.177784 0.0888918 0.996041i \(-0.471667\pi\)
0.0888918 + 0.996041i \(0.471667\pi\)
\(948\) 12.1736 0.395381
\(949\) −0.104355 −0.00338752
\(950\) −4.09750 −0.132941
\(951\) 44.9667 1.45814
\(952\) 25.6338 0.830795
\(953\) −14.2194 −0.460613 −0.230307 0.973118i \(-0.573973\pi\)
−0.230307 + 0.973118i \(0.573973\pi\)
\(954\) 102.540 3.31987
\(955\) −5.73400 −0.185548
\(956\) 13.4543 0.435143
\(957\) 14.1078 0.456039
\(958\) 34.1039 1.10185
\(959\) 2.45711 0.0793443
\(960\) 26.8025 0.865048
\(961\) −30.9647 −0.998860
\(962\) −0.346562 −0.0111736
\(963\) 88.0939 2.83879
\(964\) −10.7106 −0.344964
\(965\) −6.13432 −0.197471
\(966\) −59.3552 −1.90972
\(967\) −27.1002 −0.871484 −0.435742 0.900072i \(-0.643514\pi\)
−0.435742 + 0.900072i \(0.643514\pi\)
\(968\) 3.07256 0.0987559
\(969\) 43.0617 1.38334
\(970\) 0.854192 0.0274264
\(971\) −28.0582 −0.900431 −0.450215 0.892920i \(-0.648653\pi\)
−0.450215 + 0.892920i \(0.648653\pi\)
\(972\) −28.2891 −0.907375
\(973\) 7.60258 0.243728
\(974\) 6.29333 0.201651
\(975\) −0.338386 −0.0108370
\(976\) 1.50902 0.0483024
\(977\) −17.0216 −0.544569 −0.272285 0.962217i \(-0.587779\pi\)
−0.272285 + 0.962217i \(0.587779\pi\)
\(978\) 18.8014 0.601203
\(979\) 2.19724 0.0702242
\(980\) 1.24790 0.0398627
\(981\) −50.3266 −1.60680
\(982\) −30.3837 −0.969584
\(983\) 33.1812 1.05832 0.529158 0.848523i \(-0.322508\pi\)
0.529158 + 0.848523i \(0.322508\pi\)
\(984\) −89.8656 −2.86481
\(985\) 21.1772 0.674761
\(986\) −17.3933 −0.553917
\(987\) −90.3250 −2.87508
\(988\) 0.295092 0.00938813
\(989\) −37.7124 −1.19918
\(990\) −8.34610 −0.265256
\(991\) −59.5509 −1.89170 −0.945848 0.324610i \(-0.894767\pi\)
−0.945848 + 0.324610i \(0.894767\pi\)
\(992\) −0.762702 −0.0242158
\(993\) −2.69965 −0.0856709
\(994\) 22.8009 0.723201
\(995\) −15.3514 −0.486671
\(996\) −20.8562 −0.660854
\(997\) 11.7572 0.372355 0.186177 0.982516i \(-0.440390\pi\)
0.186177 + 0.982516i \(0.440390\pi\)
\(998\) −2.90596 −0.0919866
\(999\) −43.7738 −1.38494
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 \(a_p\))