Properties

Label 8042.2.a.c.1.13
Level 8042
Weight 2
Character 8042.1
Self dual Yes
Analytic conductor 64.216
Analytic rank 0
Dimension 86
CM No

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Newspace parameters

Level: \( N \) = \( 8042 = 2 \cdot 4021 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8042.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2156933055\)
Analytic rank: \(0\)
Dimension: \(86\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-2.19026 q^{3}\) \(+1.00000 q^{4}\) \(-2.77068 q^{5}\) \(+2.19026 q^{6}\) \(+3.06919 q^{7}\) \(-1.00000 q^{8}\) \(+1.79726 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-2.19026 q^{3}\) \(+1.00000 q^{4}\) \(-2.77068 q^{5}\) \(+2.19026 q^{6}\) \(+3.06919 q^{7}\) \(-1.00000 q^{8}\) \(+1.79726 q^{9}\) \(+2.77068 q^{10}\) \(-4.27619 q^{11}\) \(-2.19026 q^{12}\) \(+6.31398 q^{13}\) \(-3.06919 q^{14}\) \(+6.06852 q^{15}\) \(+1.00000 q^{16}\) \(-5.67143 q^{17}\) \(-1.79726 q^{18}\) \(+3.05034 q^{19}\) \(-2.77068 q^{20}\) \(-6.72234 q^{21}\) \(+4.27619 q^{22}\) \(-3.16331 q^{23}\) \(+2.19026 q^{24}\) \(+2.67665 q^{25}\) \(-6.31398 q^{26}\) \(+2.63432 q^{27}\) \(+3.06919 q^{28}\) \(-5.56146 q^{29}\) \(-6.06852 q^{30}\) \(+1.42455 q^{31}\) \(-1.00000 q^{32}\) \(+9.36599 q^{33}\) \(+5.67143 q^{34}\) \(-8.50374 q^{35}\) \(+1.79726 q^{36}\) \(+0.630865 q^{37}\) \(-3.05034 q^{38}\) \(-13.8293 q^{39}\) \(+2.77068 q^{40}\) \(+8.42078 q^{41}\) \(+6.72234 q^{42}\) \(-9.98240 q^{43}\) \(-4.27619 q^{44}\) \(-4.97963 q^{45}\) \(+3.16331 q^{46}\) \(+4.60486 q^{47}\) \(-2.19026 q^{48}\) \(+2.41992 q^{49}\) \(-2.67665 q^{50}\) \(+12.4219 q^{51}\) \(+6.31398 q^{52}\) \(+6.71274 q^{53}\) \(-2.63432 q^{54}\) \(+11.8479 q^{55}\) \(-3.06919 q^{56}\) \(-6.68106 q^{57}\) \(+5.56146 q^{58}\) \(+10.9137 q^{59}\) \(+6.06852 q^{60}\) \(+3.67051 q^{61}\) \(-1.42455 q^{62}\) \(+5.51613 q^{63}\) \(+1.00000 q^{64}\) \(-17.4940 q^{65}\) \(-9.36599 q^{66}\) \(-5.77000 q^{67}\) \(-5.67143 q^{68}\) \(+6.92848 q^{69}\) \(+8.50374 q^{70}\) \(+4.19250 q^{71}\) \(-1.79726 q^{72}\) \(-6.91203 q^{73}\) \(-0.630865 q^{74}\) \(-5.86258 q^{75}\) \(+3.05034 q^{76}\) \(-13.1244 q^{77}\) \(+13.8293 q^{78}\) \(-17.2341 q^{79}\) \(-2.77068 q^{80}\) \(-11.1616 q^{81}\) \(-8.42078 q^{82}\) \(+4.21083 q^{83}\) \(-6.72234 q^{84}\) \(+15.7137 q^{85}\) \(+9.98240 q^{86}\) \(+12.1811 q^{87}\) \(+4.27619 q^{88}\) \(-5.49270 q^{89}\) \(+4.97963 q^{90}\) \(+19.3788 q^{91}\) \(-3.16331 q^{92}\) \(-3.12014 q^{93}\) \(-4.60486 q^{94}\) \(-8.45152 q^{95}\) \(+2.19026 q^{96}\) \(+5.15491 q^{97}\) \(-2.41992 q^{98}\) \(-7.68542 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(86q \) \(\mathstrut -\mathstrut 86q^{2} \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 86q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 35q^{7} \) \(\mathstrut -\mathstrut 86q^{8} \) \(\mathstrut +\mathstrut 72q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(86q \) \(\mathstrut -\mathstrut 86q^{2} \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 86q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 35q^{7} \) \(\mathstrut -\mathstrut 86q^{8} \) \(\mathstrut +\mathstrut 72q^{9} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 13q^{11} \) \(\mathstrut +\mathstrut 12q^{12} \) \(\mathstrut +\mathstrut 45q^{13} \) \(\mathstrut -\mathstrut 35q^{14} \) \(\mathstrut +\mathstrut 17q^{15} \) \(\mathstrut +\mathstrut 86q^{16} \) \(\mathstrut +\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 72q^{18} \) \(\mathstrut +\mathstrut 47q^{19} \) \(\mathstrut -\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 15q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut +\mathstrut 6q^{23} \) \(\mathstrut -\mathstrut 12q^{24} \) \(\mathstrut +\mathstrut 112q^{25} \) \(\mathstrut -\mathstrut 45q^{26} \) \(\mathstrut +\mathstrut 51q^{27} \) \(\mathstrut +\mathstrut 35q^{28} \) \(\mathstrut -\mathstrut 14q^{29} \) \(\mathstrut -\mathstrut 17q^{30} \) \(\mathstrut +\mathstrut 24q^{31} \) \(\mathstrut -\mathstrut 86q^{32} \) \(\mathstrut +\mathstrut 43q^{33} \) \(\mathstrut -\mathstrut 5q^{34} \) \(\mathstrut +\mathstrut 42q^{35} \) \(\mathstrut +\mathstrut 72q^{36} \) \(\mathstrut +\mathstrut 61q^{37} \) \(\mathstrut -\mathstrut 47q^{38} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 4q^{40} \) \(\mathstrut -\mathstrut 16q^{41} \) \(\mathstrut -\mathstrut 15q^{42} \) \(\mathstrut +\mathstrut 72q^{43} \) \(\mathstrut +\mathstrut 13q^{44} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut +\mathstrut 11q^{47} \) \(\mathstrut +\mathstrut 12q^{48} \) \(\mathstrut +\mathstrut 89q^{49} \) \(\mathstrut -\mathstrut 112q^{50} \) \(\mathstrut +\mathstrut 56q^{51} \) \(\mathstrut +\mathstrut 45q^{52} \) \(\mathstrut -\mathstrut 7q^{53} \) \(\mathstrut -\mathstrut 51q^{54} \) \(\mathstrut +\mathstrut 48q^{55} \) \(\mathstrut -\mathstrut 35q^{56} \) \(\mathstrut +\mathstrut 65q^{57} \) \(\mathstrut +\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 17q^{60} \) \(\mathstrut +\mathstrut 31q^{61} \) \(\mathstrut -\mathstrut 24q^{62} \) \(\mathstrut +\mathstrut 98q^{63} \) \(\mathstrut +\mathstrut 86q^{64} \) \(\mathstrut -\mathstrut 9q^{65} \) \(\mathstrut -\mathstrut 43q^{66} \) \(\mathstrut +\mathstrut 157q^{67} \) \(\mathstrut +\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut q^{69} \) \(\mathstrut -\mathstrut 42q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut -\mathstrut 72q^{72} \) \(\mathstrut +\mathstrut 74q^{73} \) \(\mathstrut -\mathstrut 61q^{74} \) \(\mathstrut +\mathstrut 76q^{75} \) \(\mathstrut +\mathstrut 47q^{76} \) \(\mathstrut -\mathstrut 13q^{77} \) \(\mathstrut -\mathstrut 20q^{78} \) \(\mathstrut +\mathstrut 57q^{79} \) \(\mathstrut -\mathstrut 4q^{80} \) \(\mathstrut +\mathstrut 34q^{81} \) \(\mathstrut +\mathstrut 16q^{82} \) \(\mathstrut +\mathstrut 65q^{83} \) \(\mathstrut +\mathstrut 15q^{84} \) \(\mathstrut +\mathstrut 102q^{85} \) \(\mathstrut -\mathstrut 72q^{86} \) \(\mathstrut +\mathstrut 49q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut -\mathstrut 34q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 91q^{91} \) \(\mathstrut +\mathstrut 6q^{92} \) \(\mathstrut +\mathstrut 57q^{93} \) \(\mathstrut -\mathstrut 11q^{94} \) \(\mathstrut -\mathstrut 13q^{95} \) \(\mathstrut -\mathstrut 12q^{96} \) \(\mathstrut +\mathstrut 64q^{97} \) \(\mathstrut -\mathstrut 89q^{98} \) \(\mathstrut +\mathstrut 56q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −2.19026 −1.26455 −0.632275 0.774744i \(-0.717879\pi\)
−0.632275 + 0.774744i \(0.717879\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.77068 −1.23908 −0.619542 0.784963i \(-0.712682\pi\)
−0.619542 + 0.784963i \(0.712682\pi\)
\(6\) 2.19026 0.894172
\(7\) 3.06919 1.16004 0.580022 0.814601i \(-0.303044\pi\)
0.580022 + 0.814601i \(0.303044\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.79726 0.599086
\(10\) 2.77068 0.876165
\(11\) −4.27619 −1.28932 −0.644660 0.764469i \(-0.723001\pi\)
−0.644660 + 0.764469i \(0.723001\pi\)
\(12\) −2.19026 −0.632275
\(13\) 6.31398 1.75118 0.875592 0.483051i \(-0.160472\pi\)
0.875592 + 0.483051i \(0.160472\pi\)
\(14\) −3.06919 −0.820275
\(15\) 6.06852 1.56688
\(16\) 1.00000 0.250000
\(17\) −5.67143 −1.37552 −0.687762 0.725936i \(-0.741407\pi\)
−0.687762 + 0.725936i \(0.741407\pi\)
\(18\) −1.79726 −0.423618
\(19\) 3.05034 0.699797 0.349898 0.936788i \(-0.386216\pi\)
0.349898 + 0.936788i \(0.386216\pi\)
\(20\) −2.77068 −0.619542
\(21\) −6.72234 −1.46693
\(22\) 4.27619 0.911687
\(23\) −3.16331 −0.659595 −0.329797 0.944052i \(-0.606980\pi\)
−0.329797 + 0.944052i \(0.606980\pi\)
\(24\) 2.19026 0.447086
\(25\) 2.67665 0.535331
\(26\) −6.31398 −1.23827
\(27\) 2.63432 0.506975
\(28\) 3.06919 0.580022
\(29\) −5.56146 −1.03274 −0.516368 0.856367i \(-0.672716\pi\)
−0.516368 + 0.856367i \(0.672716\pi\)
\(30\) −6.06852 −1.10795
\(31\) 1.42455 0.255857 0.127928 0.991783i \(-0.459167\pi\)
0.127928 + 0.991783i \(0.459167\pi\)
\(32\) −1.00000 −0.176777
\(33\) 9.36599 1.63041
\(34\) 5.67143 0.972642
\(35\) −8.50374 −1.43739
\(36\) 1.79726 0.299543
\(37\) 0.630865 0.103714 0.0518568 0.998655i \(-0.483486\pi\)
0.0518568 + 0.998655i \(0.483486\pi\)
\(38\) −3.05034 −0.494831
\(39\) −13.8293 −2.21446
\(40\) 2.77068 0.438083
\(41\) 8.42078 1.31510 0.657552 0.753409i \(-0.271592\pi\)
0.657552 + 0.753409i \(0.271592\pi\)
\(42\) 6.72234 1.03728
\(43\) −9.98240 −1.52230 −0.761151 0.648575i \(-0.775365\pi\)
−0.761151 + 0.648575i \(0.775365\pi\)
\(44\) −4.27619 −0.644660
\(45\) −4.97963 −0.742319
\(46\) 3.16331 0.466404
\(47\) 4.60486 0.671688 0.335844 0.941918i \(-0.390978\pi\)
0.335844 + 0.941918i \(0.390978\pi\)
\(48\) −2.19026 −0.316137
\(49\) 2.41992 0.345704
\(50\) −2.67665 −0.378536
\(51\) 12.4219 1.73942
\(52\) 6.31398 0.875592
\(53\) 6.71274 0.922066 0.461033 0.887383i \(-0.347479\pi\)
0.461033 + 0.887383i \(0.347479\pi\)
\(54\) −2.63432 −0.358486
\(55\) 11.8479 1.59758
\(56\) −3.06919 −0.410138
\(57\) −6.68106 −0.884928
\(58\) 5.56146 0.730255
\(59\) 10.9137 1.42084 0.710422 0.703776i \(-0.248504\pi\)
0.710422 + 0.703776i \(0.248504\pi\)
\(60\) 6.06852 0.783442
\(61\) 3.67051 0.469961 0.234981 0.972000i \(-0.424497\pi\)
0.234981 + 0.972000i \(0.424497\pi\)
\(62\) −1.42455 −0.180918
\(63\) 5.51613 0.694967
\(64\) 1.00000 0.125000
\(65\) −17.4940 −2.16987
\(66\) −9.36599 −1.15287
\(67\) −5.77000 −0.704918 −0.352459 0.935827i \(-0.614654\pi\)
−0.352459 + 0.935827i \(0.614654\pi\)
\(68\) −5.67143 −0.687762
\(69\) 6.92848 0.834091
\(70\) 8.50374 1.01639
\(71\) 4.19250 0.497558 0.248779 0.968560i \(-0.419971\pi\)
0.248779 + 0.968560i \(0.419971\pi\)
\(72\) −1.79726 −0.211809
\(73\) −6.91203 −0.808992 −0.404496 0.914540i \(-0.632553\pi\)
−0.404496 + 0.914540i \(0.632553\pi\)
\(74\) −0.630865 −0.0733365
\(75\) −5.86258 −0.676953
\(76\) 3.05034 0.349898
\(77\) −13.1244 −1.49567
\(78\) 13.8293 1.56586
\(79\) −17.2341 −1.93899 −0.969496 0.245107i \(-0.921177\pi\)
−0.969496 + 0.245107i \(0.921177\pi\)
\(80\) −2.77068 −0.309771
\(81\) −11.1616 −1.24018
\(82\) −8.42078 −0.929920
\(83\) 4.21083 0.462199 0.231099 0.972930i \(-0.425768\pi\)
0.231099 + 0.972930i \(0.425768\pi\)
\(84\) −6.72234 −0.733467
\(85\) 15.7137 1.70439
\(86\) 9.98240 1.07643
\(87\) 12.1811 1.30595
\(88\) 4.27619 0.455844
\(89\) −5.49270 −0.582225 −0.291112 0.956689i \(-0.594025\pi\)
−0.291112 + 0.956689i \(0.594025\pi\)
\(90\) 4.97963 0.524899
\(91\) 19.3788 2.03145
\(92\) −3.16331 −0.329797
\(93\) −3.12014 −0.323543
\(94\) −4.60486 −0.474955
\(95\) −8.45152 −0.867107
\(96\) 2.19026 0.223543
\(97\) 5.15491 0.523402 0.261701 0.965149i \(-0.415717\pi\)
0.261701 + 0.965149i \(0.415717\pi\)
\(98\) −2.41992 −0.244449
\(99\) −7.68542 −0.772414
\(100\) 2.67665 0.267665
\(101\) 0.0775340 0.00771492 0.00385746 0.999993i \(-0.498772\pi\)
0.00385746 + 0.999993i \(0.498772\pi\)
\(102\) −12.4219 −1.22995
\(103\) 14.7092 1.44934 0.724670 0.689096i \(-0.241992\pi\)
0.724670 + 0.689096i \(0.241992\pi\)
\(104\) −6.31398 −0.619137
\(105\) 18.6254 1.81766
\(106\) −6.71274 −0.651999
\(107\) 9.78969 0.946405 0.473202 0.880954i \(-0.343098\pi\)
0.473202 + 0.880954i \(0.343098\pi\)
\(108\) 2.63432 0.253488
\(109\) 4.28813 0.410728 0.205364 0.978686i \(-0.434162\pi\)
0.205364 + 0.978686i \(0.434162\pi\)
\(110\) −11.8479 −1.12966
\(111\) −1.38176 −0.131151
\(112\) 3.06919 0.290011
\(113\) −10.1591 −0.955688 −0.477844 0.878445i \(-0.658581\pi\)
−0.477844 + 0.878445i \(0.658581\pi\)
\(114\) 6.68106 0.625738
\(115\) 8.76450 0.817294
\(116\) −5.56146 −0.516368
\(117\) 11.3479 1.04911
\(118\) −10.9137 −1.00469
\(119\) −17.4067 −1.59567
\(120\) −6.06852 −0.553977
\(121\) 7.28581 0.662347
\(122\) −3.67051 −0.332313
\(123\) −18.4437 −1.66302
\(124\) 1.42455 0.127928
\(125\) 6.43724 0.575764
\(126\) −5.51613 −0.491416
\(127\) −17.1035 −1.51769 −0.758845 0.651271i \(-0.774236\pi\)
−0.758845 + 0.651271i \(0.774236\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 21.8641 1.92503
\(130\) 17.4940 1.53433
\(131\) −1.46655 −0.128133 −0.0640667 0.997946i \(-0.520407\pi\)
−0.0640667 + 0.997946i \(0.520407\pi\)
\(132\) 9.36599 0.815205
\(133\) 9.36208 0.811795
\(134\) 5.77000 0.498452
\(135\) −7.29886 −0.628185
\(136\) 5.67143 0.486321
\(137\) −9.74768 −0.832801 −0.416400 0.909181i \(-0.636709\pi\)
−0.416400 + 0.909181i \(0.636709\pi\)
\(138\) −6.92848 −0.589791
\(139\) −22.3524 −1.89591 −0.947954 0.318407i \(-0.896852\pi\)
−0.947954 + 0.318407i \(0.896852\pi\)
\(140\) −8.50374 −0.718697
\(141\) −10.0859 −0.849383
\(142\) −4.19250 −0.351827
\(143\) −26.9998 −2.25784
\(144\) 1.79726 0.149772
\(145\) 15.4090 1.27965
\(146\) 6.91203 0.572044
\(147\) −5.30027 −0.437159
\(148\) 0.630865 0.0518568
\(149\) −13.6798 −1.12069 −0.560346 0.828259i \(-0.689332\pi\)
−0.560346 + 0.828259i \(0.689332\pi\)
\(150\) 5.86258 0.478678
\(151\) −10.9167 −0.888390 −0.444195 0.895930i \(-0.646510\pi\)
−0.444195 + 0.895930i \(0.646510\pi\)
\(152\) −3.05034 −0.247415
\(153\) −10.1930 −0.824058
\(154\) 13.1244 1.05760
\(155\) −3.94697 −0.317028
\(156\) −13.8293 −1.10723
\(157\) −0.191486 −0.0152823 −0.00764113 0.999971i \(-0.502432\pi\)
−0.00764113 + 0.999971i \(0.502432\pi\)
\(158\) 17.2341 1.37107
\(159\) −14.7027 −1.16600
\(160\) 2.77068 0.219041
\(161\) −9.70879 −0.765160
\(162\) 11.1616 0.876941
\(163\) −12.3496 −0.967294 −0.483647 0.875263i \(-0.660688\pi\)
−0.483647 + 0.875263i \(0.660688\pi\)
\(164\) 8.42078 0.657552
\(165\) −25.9501 −2.02022
\(166\) −4.21083 −0.326824
\(167\) −2.57759 −0.199460 −0.0997298 0.995015i \(-0.531798\pi\)
−0.0997298 + 0.995015i \(0.531798\pi\)
\(168\) 6.72234 0.518640
\(169\) 26.8664 2.06665
\(170\) −15.7137 −1.20519
\(171\) 5.48225 0.419238
\(172\) −9.98240 −0.761151
\(173\) 7.80926 0.593727 0.296863 0.954920i \(-0.404059\pi\)
0.296863 + 0.954920i \(0.404059\pi\)
\(174\) −12.1811 −0.923444
\(175\) 8.21516 0.621008
\(176\) −4.27619 −0.322330
\(177\) −23.9039 −1.79673
\(178\) 5.49270 0.411695
\(179\) −13.1978 −0.986451 −0.493226 0.869901i \(-0.664182\pi\)
−0.493226 + 0.869901i \(0.664182\pi\)
\(180\) −4.97963 −0.371159
\(181\) 10.7292 0.797499 0.398749 0.917060i \(-0.369444\pi\)
0.398749 + 0.917060i \(0.369444\pi\)
\(182\) −19.3788 −1.43645
\(183\) −8.03940 −0.594289
\(184\) 3.16331 0.233202
\(185\) −1.74792 −0.128510
\(186\) 3.12014 0.228780
\(187\) 24.2521 1.77349
\(188\) 4.60486 0.335844
\(189\) 8.08523 0.588114
\(190\) 8.45152 0.613137
\(191\) 19.3721 1.40172 0.700858 0.713301i \(-0.252801\pi\)
0.700858 + 0.713301i \(0.252801\pi\)
\(192\) −2.19026 −0.158069
\(193\) −22.3466 −1.60855 −0.804273 0.594260i \(-0.797445\pi\)
−0.804273 + 0.594260i \(0.797445\pi\)
\(194\) −5.15491 −0.370101
\(195\) 38.3165 2.74390
\(196\) 2.41992 0.172852
\(197\) −17.1642 −1.22290 −0.611448 0.791285i \(-0.709413\pi\)
−0.611448 + 0.791285i \(0.709413\pi\)
\(198\) 7.68542 0.546179
\(199\) 12.8124 0.908246 0.454123 0.890939i \(-0.349953\pi\)
0.454123 + 0.890939i \(0.349953\pi\)
\(200\) −2.67665 −0.189268
\(201\) 12.6378 0.891404
\(202\) −0.0775340 −0.00545527
\(203\) −17.0692 −1.19802
\(204\) 12.4219 0.869709
\(205\) −23.3313 −1.62953
\(206\) −14.7092 −1.02484
\(207\) −5.68528 −0.395154
\(208\) 6.31398 0.437796
\(209\) −13.0438 −0.902262
\(210\) −18.6254 −1.28528
\(211\) 22.8910 1.57588 0.787939 0.615753i \(-0.211148\pi\)
0.787939 + 0.615753i \(0.211148\pi\)
\(212\) 6.71274 0.461033
\(213\) −9.18269 −0.629187
\(214\) −9.78969 −0.669209
\(215\) 27.6580 1.88626
\(216\) −2.63432 −0.179243
\(217\) 4.37221 0.296805
\(218\) −4.28813 −0.290429
\(219\) 15.1392 1.02301
\(220\) 11.8479 0.798789
\(221\) −35.8093 −2.40880
\(222\) 1.38176 0.0927377
\(223\) 6.58421 0.440911 0.220456 0.975397i \(-0.429246\pi\)
0.220456 + 0.975397i \(0.429246\pi\)
\(224\) −3.06919 −0.205069
\(225\) 4.81064 0.320709
\(226\) 10.1591 0.675773
\(227\) −5.96504 −0.395914 −0.197957 0.980211i \(-0.563431\pi\)
−0.197957 + 0.980211i \(0.563431\pi\)
\(228\) −6.68106 −0.442464
\(229\) −5.79620 −0.383024 −0.191512 0.981490i \(-0.561339\pi\)
−0.191512 + 0.981490i \(0.561339\pi\)
\(230\) −8.76450 −0.577914
\(231\) 28.7460 1.89135
\(232\) 5.56146 0.365128
\(233\) 7.47164 0.489483 0.244742 0.969588i \(-0.421297\pi\)
0.244742 + 0.969588i \(0.421297\pi\)
\(234\) −11.3479 −0.741833
\(235\) −12.7586 −0.832278
\(236\) 10.9137 0.710422
\(237\) 37.7473 2.45195
\(238\) 17.4067 1.12831
\(239\) −0.953242 −0.0616601 −0.0308301 0.999525i \(-0.509815\pi\)
−0.0308301 + 0.999525i \(0.509815\pi\)
\(240\) 6.06852 0.391721
\(241\) 8.63373 0.556147 0.278074 0.960560i \(-0.410304\pi\)
0.278074 + 0.960560i \(0.410304\pi\)
\(242\) −7.28581 −0.468350
\(243\) 16.5440 1.06130
\(244\) 3.67051 0.234981
\(245\) −6.70483 −0.428356
\(246\) 18.4437 1.17593
\(247\) 19.2598 1.22547
\(248\) −1.42455 −0.0904590
\(249\) −9.22283 −0.584473
\(250\) −6.43724 −0.407127
\(251\) −11.3676 −0.717519 −0.358760 0.933430i \(-0.616800\pi\)
−0.358760 + 0.933430i \(0.616800\pi\)
\(252\) 5.51613 0.347483
\(253\) 13.5269 0.850429
\(254\) 17.1035 1.07317
\(255\) −34.4172 −2.15529
\(256\) 1.00000 0.0625000
\(257\) −13.3223 −0.831025 −0.415512 0.909587i \(-0.636398\pi\)
−0.415512 + 0.909587i \(0.636398\pi\)
\(258\) −21.8641 −1.36120
\(259\) 1.93624 0.120312
\(260\) −17.4940 −1.08493
\(261\) −9.99538 −0.618698
\(262\) 1.46655 0.0906040
\(263\) 7.66856 0.472864 0.236432 0.971648i \(-0.424022\pi\)
0.236432 + 0.971648i \(0.424022\pi\)
\(264\) −9.36599 −0.576437
\(265\) −18.5989 −1.14252
\(266\) −9.36208 −0.574026
\(267\) 12.0305 0.736252
\(268\) −5.77000 −0.352459
\(269\) −3.02964 −0.184720 −0.0923601 0.995726i \(-0.529441\pi\)
−0.0923601 + 0.995726i \(0.529441\pi\)
\(270\) 7.29886 0.444194
\(271\) 13.0886 0.795076 0.397538 0.917586i \(-0.369865\pi\)
0.397538 + 0.917586i \(0.369865\pi\)
\(272\) −5.67143 −0.343881
\(273\) −42.4447 −2.56887
\(274\) 9.74768 0.588879
\(275\) −11.4459 −0.690213
\(276\) 6.92848 0.417045
\(277\) −0.588778 −0.0353762 −0.0176881 0.999844i \(-0.505631\pi\)
−0.0176881 + 0.999844i \(0.505631\pi\)
\(278\) 22.3524 1.34061
\(279\) 2.56028 0.153280
\(280\) 8.50374 0.508195
\(281\) 10.0168 0.597554 0.298777 0.954323i \(-0.403421\pi\)
0.298777 + 0.954323i \(0.403421\pi\)
\(282\) 10.0859 0.600605
\(283\) 21.7789 1.29462 0.647309 0.762227i \(-0.275894\pi\)
0.647309 + 0.762227i \(0.275894\pi\)
\(284\) 4.19250 0.248779
\(285\) 18.5111 1.09650
\(286\) 26.9998 1.59653
\(287\) 25.8450 1.52558
\(288\) −1.79726 −0.105904
\(289\) 15.1651 0.892066
\(290\) −15.4090 −0.904848
\(291\) −11.2906 −0.661868
\(292\) −6.91203 −0.404496
\(293\) −12.2822 −0.717532 −0.358766 0.933427i \(-0.616802\pi\)
−0.358766 + 0.933427i \(0.616802\pi\)
\(294\) 5.30027 0.309118
\(295\) −30.2384 −1.76055
\(296\) −0.630865 −0.0366683
\(297\) −11.2649 −0.653654
\(298\) 13.6798 0.792448
\(299\) −19.9731 −1.15507
\(300\) −5.86258 −0.338476
\(301\) −30.6379 −1.76594
\(302\) 10.9167 0.628187
\(303\) −0.169820 −0.00975591
\(304\) 3.05034 0.174949
\(305\) −10.1698 −0.582322
\(306\) 10.1930 0.582697
\(307\) −7.09108 −0.404709 −0.202355 0.979312i \(-0.564859\pi\)
−0.202355 + 0.979312i \(0.564859\pi\)
\(308\) −13.1244 −0.747835
\(309\) −32.2170 −1.83276
\(310\) 3.94697 0.224173
\(311\) −20.4211 −1.15798 −0.578988 0.815336i \(-0.696552\pi\)
−0.578988 + 0.815336i \(0.696552\pi\)
\(312\) 13.8293 0.782930
\(313\) 31.4280 1.77642 0.888209 0.459440i \(-0.151950\pi\)
0.888209 + 0.459440i \(0.151950\pi\)
\(314\) 0.191486 0.0108062
\(315\) −15.2834 −0.861123
\(316\) −17.2341 −0.969496
\(317\) 7.66928 0.430750 0.215375 0.976531i \(-0.430903\pi\)
0.215375 + 0.976531i \(0.430903\pi\)
\(318\) 14.7027 0.824486
\(319\) 23.7819 1.33153
\(320\) −2.77068 −0.154886
\(321\) −21.4420 −1.19678
\(322\) 9.70879 0.541050
\(323\) −17.2998 −0.962587
\(324\) −11.1616 −0.620091
\(325\) 16.9004 0.937463
\(326\) 12.3496 0.683980
\(327\) −9.39213 −0.519386
\(328\) −8.42078 −0.464960
\(329\) 14.1332 0.779188
\(330\) 25.9501 1.42851
\(331\) −22.4770 −1.23545 −0.617724 0.786395i \(-0.711945\pi\)
−0.617724 + 0.786395i \(0.711945\pi\)
\(332\) 4.21083 0.231099
\(333\) 1.13383 0.0621333
\(334\) 2.57759 0.141039
\(335\) 15.9868 0.873453
\(336\) −6.72234 −0.366734
\(337\) −32.4632 −1.76838 −0.884191 0.467126i \(-0.845289\pi\)
−0.884191 + 0.467126i \(0.845289\pi\)
\(338\) −26.8664 −1.46134
\(339\) 22.2511 1.20851
\(340\) 15.7137 0.852195
\(341\) −6.09164 −0.329881
\(342\) −5.48225 −0.296446
\(343\) −14.0571 −0.759013
\(344\) 9.98240 0.538215
\(345\) −19.1966 −1.03351
\(346\) −7.80926 −0.419828
\(347\) 3.93027 0.210988 0.105494 0.994420i \(-0.466358\pi\)
0.105494 + 0.994420i \(0.466358\pi\)
\(348\) 12.1811 0.652973
\(349\) 35.1030 1.87902 0.939509 0.342523i \(-0.111281\pi\)
0.939509 + 0.342523i \(0.111281\pi\)
\(350\) −8.21516 −0.439119
\(351\) 16.6331 0.887807
\(352\) 4.27619 0.227922
\(353\) −6.16529 −0.328145 −0.164073 0.986448i \(-0.552463\pi\)
−0.164073 + 0.986448i \(0.552463\pi\)
\(354\) 23.9039 1.27048
\(355\) −11.6161 −0.616517
\(356\) −5.49270 −0.291112
\(357\) 38.1253 2.01780
\(358\) 13.1978 0.697527
\(359\) 8.39889 0.443277 0.221638 0.975129i \(-0.428860\pi\)
0.221638 + 0.975129i \(0.428860\pi\)
\(360\) 4.97963 0.262449
\(361\) −9.69541 −0.510285
\(362\) −10.7292 −0.563917
\(363\) −15.9579 −0.837570
\(364\) 19.3788 1.01573
\(365\) 19.1510 1.00241
\(366\) 8.03940 0.420226
\(367\) −17.7449 −0.926277 −0.463139 0.886286i \(-0.653277\pi\)
−0.463139 + 0.886286i \(0.653277\pi\)
\(368\) −3.16331 −0.164899
\(369\) 15.1343 0.787861
\(370\) 1.74792 0.0908702
\(371\) 20.6027 1.06964
\(372\) −3.12014 −0.161772
\(373\) 9.17792 0.475215 0.237607 0.971361i \(-0.423637\pi\)
0.237607 + 0.971361i \(0.423637\pi\)
\(374\) −24.2521 −1.25405
\(375\) −14.0993 −0.728083
\(376\) −4.60486 −0.237478
\(377\) −35.1149 −1.80851
\(378\) −8.08523 −0.415859
\(379\) −15.6763 −0.805239 −0.402619 0.915367i \(-0.631900\pi\)
−0.402619 + 0.915367i \(0.631900\pi\)
\(380\) −8.45152 −0.433554
\(381\) 37.4612 1.91919
\(382\) −19.3721 −0.991163
\(383\) −24.9315 −1.27394 −0.636971 0.770888i \(-0.719813\pi\)
−0.636971 + 0.770888i \(0.719813\pi\)
\(384\) 2.19026 0.111771
\(385\) 36.3636 1.85326
\(386\) 22.3466 1.13741
\(387\) −17.9410 −0.911990
\(388\) 5.15491 0.261701
\(389\) 5.71843 0.289936 0.144968 0.989436i \(-0.453692\pi\)
0.144968 + 0.989436i \(0.453692\pi\)
\(390\) −38.3165 −1.94023
\(391\) 17.9405 0.907289
\(392\) −2.41992 −0.122225
\(393\) 3.21214 0.162031
\(394\) 17.1642 0.864718
\(395\) 47.7502 2.40258
\(396\) −7.68542 −0.386207
\(397\) 24.0531 1.20719 0.603596 0.797290i \(-0.293734\pi\)
0.603596 + 0.797290i \(0.293734\pi\)
\(398\) −12.8124 −0.642227
\(399\) −20.5054 −1.02656
\(400\) 2.67665 0.133833
\(401\) −26.0036 −1.29856 −0.649278 0.760551i \(-0.724929\pi\)
−0.649278 + 0.760551i \(0.724929\pi\)
\(402\) −12.6378 −0.630318
\(403\) 8.99458 0.448052
\(404\) 0.0775340 0.00385746
\(405\) 30.9253 1.53669
\(406\) 17.0692 0.847128
\(407\) −2.69770 −0.133720
\(408\) −12.4219 −0.614977
\(409\) −6.36860 −0.314907 −0.157454 0.987526i \(-0.550328\pi\)
−0.157454 + 0.987526i \(0.550328\pi\)
\(410\) 23.3313 1.15225
\(411\) 21.3500 1.05312
\(412\) 14.7092 0.724670
\(413\) 33.4963 1.64824
\(414\) 5.68528 0.279416
\(415\) −11.6669 −0.572703
\(416\) −6.31398 −0.309569
\(417\) 48.9577 2.39747
\(418\) 13.0438 0.637995
\(419\) 12.7030 0.620582 0.310291 0.950642i \(-0.399574\pi\)
0.310291 + 0.950642i \(0.399574\pi\)
\(420\) 18.6254 0.908828
\(421\) −10.1853 −0.496400 −0.248200 0.968709i \(-0.579839\pi\)
−0.248200 + 0.968709i \(0.579839\pi\)
\(422\) −22.8910 −1.11431
\(423\) 8.27613 0.402399
\(424\) −6.71274 −0.326000
\(425\) −15.1805 −0.736361
\(426\) 9.18269 0.444903
\(427\) 11.2655 0.545176
\(428\) 9.78969 0.473202
\(429\) 59.1367 2.85515
\(430\) −27.6580 −1.33379
\(431\) 26.0235 1.25351 0.626754 0.779217i \(-0.284383\pi\)
0.626754 + 0.779217i \(0.284383\pi\)
\(432\) 2.63432 0.126744
\(433\) 19.3961 0.932119 0.466059 0.884753i \(-0.345673\pi\)
0.466059 + 0.884753i \(0.345673\pi\)
\(434\) −4.37221 −0.209873
\(435\) −33.7498 −1.61818
\(436\) 4.28813 0.205364
\(437\) −9.64917 −0.461582
\(438\) −15.1392 −0.723378
\(439\) 32.7508 1.56311 0.781556 0.623835i \(-0.214426\pi\)
0.781556 + 0.623835i \(0.214426\pi\)
\(440\) −11.8479 −0.564829
\(441\) 4.34923 0.207106
\(442\) 35.8093 1.70328
\(443\) 26.6685 1.26706 0.633529 0.773719i \(-0.281606\pi\)
0.633529 + 0.773719i \(0.281606\pi\)
\(444\) −1.38176 −0.0655754
\(445\) 15.2185 0.721426
\(446\) −6.58421 −0.311771
\(447\) 29.9623 1.41717
\(448\) 3.06919 0.145006
\(449\) 34.5933 1.63256 0.816279 0.577657i \(-0.196033\pi\)
0.816279 + 0.577657i \(0.196033\pi\)
\(450\) −4.81064 −0.226776
\(451\) −36.0089 −1.69559
\(452\) −10.1591 −0.477844
\(453\) 23.9105 1.12341
\(454\) 5.96504 0.279953
\(455\) −53.6924 −2.51714
\(456\) 6.68106 0.312869
\(457\) 4.18826 0.195919 0.0979594 0.995190i \(-0.468768\pi\)
0.0979594 + 0.995190i \(0.468768\pi\)
\(458\) 5.79620 0.270839
\(459\) −14.9404 −0.697357
\(460\) 8.76450 0.408647
\(461\) 1.84749 0.0860461 0.0430230 0.999074i \(-0.486301\pi\)
0.0430230 + 0.999074i \(0.486301\pi\)
\(462\) −28.7460 −1.33739
\(463\) 3.11585 0.144806 0.0724030 0.997375i \(-0.476933\pi\)
0.0724030 + 0.997375i \(0.476933\pi\)
\(464\) −5.56146 −0.258184
\(465\) 8.64490 0.400898
\(466\) −7.47164 −0.346117
\(467\) 36.8552 1.70546 0.852729 0.522354i \(-0.174946\pi\)
0.852729 + 0.522354i \(0.174946\pi\)
\(468\) 11.3479 0.524555
\(469\) −17.7092 −0.817737
\(470\) 12.7586 0.588510
\(471\) 0.419405 0.0193252
\(472\) −10.9137 −0.502344
\(473\) 42.6867 1.96273
\(474\) −37.7473 −1.73379
\(475\) 8.16471 0.374623
\(476\) −17.4067 −0.797835
\(477\) 12.0645 0.552397
\(478\) 0.953242 0.0436003
\(479\) −15.7315 −0.718791 −0.359396 0.933185i \(-0.617017\pi\)
−0.359396 + 0.933185i \(0.617017\pi\)
\(480\) −6.06852 −0.276989
\(481\) 3.98327 0.181621
\(482\) −8.63373 −0.393256
\(483\) 21.2648 0.967582
\(484\) 7.28581 0.331173
\(485\) −14.2826 −0.648539
\(486\) −16.5440 −0.750450
\(487\) 30.6542 1.38907 0.694537 0.719457i \(-0.255609\pi\)
0.694537 + 0.719457i \(0.255609\pi\)
\(488\) −3.67051 −0.166156
\(489\) 27.0489 1.22319
\(490\) 6.70483 0.302893
\(491\) 23.6703 1.06822 0.534112 0.845414i \(-0.320646\pi\)
0.534112 + 0.845414i \(0.320646\pi\)
\(492\) −18.4437 −0.831508
\(493\) 31.5414 1.42055
\(494\) −19.2598 −0.866540
\(495\) 21.2938 0.957087
\(496\) 1.42455 0.0639641
\(497\) 12.8676 0.577190
\(498\) 9.22283 0.413285
\(499\) 6.01488 0.269263 0.134631 0.990896i \(-0.457015\pi\)
0.134631 + 0.990896i \(0.457015\pi\)
\(500\) 6.43724 0.287882
\(501\) 5.64559 0.252227
\(502\) 11.3676 0.507363
\(503\) 1.13420 0.0505715 0.0252857 0.999680i \(-0.491950\pi\)
0.0252857 + 0.999680i \(0.491950\pi\)
\(504\) −5.51613 −0.245708
\(505\) −0.214822 −0.00955944
\(506\) −13.5269 −0.601344
\(507\) −58.8445 −2.61338
\(508\) −17.1035 −0.758845
\(509\) 26.0814 1.15604 0.578019 0.816023i \(-0.303826\pi\)
0.578019 + 0.816023i \(0.303826\pi\)
\(510\) 34.4172 1.52402
\(511\) −21.2143 −0.938467
\(512\) −1.00000 −0.0441942
\(513\) 8.03558 0.354780
\(514\) 13.3223 0.587623
\(515\) −40.7545 −1.79586
\(516\) 21.8641 0.962513
\(517\) −19.6913 −0.866021
\(518\) −1.93624 −0.0850736
\(519\) −17.1043 −0.750797
\(520\) 17.4940 0.767163
\(521\) −40.7469 −1.78515 −0.892577 0.450896i \(-0.851105\pi\)
−0.892577 + 0.450896i \(0.851105\pi\)
\(522\) 9.99538 0.437486
\(523\) −0.222001 −0.00970744 −0.00485372 0.999988i \(-0.501545\pi\)
−0.00485372 + 0.999988i \(0.501545\pi\)
\(524\) −1.46655 −0.0640667
\(525\) −17.9934 −0.785295
\(526\) −7.66856 −0.334365
\(527\) −8.07923 −0.351937
\(528\) 9.36599 0.407602
\(529\) −12.9935 −0.564935
\(530\) 18.5989 0.807882
\(531\) 19.6148 0.851208
\(532\) 9.36208 0.405898
\(533\) 53.1687 2.30299
\(534\) −12.0305 −0.520609
\(535\) −27.1241 −1.17268
\(536\) 5.77000 0.249226
\(537\) 28.9067 1.24742
\(538\) 3.02964 0.130617
\(539\) −10.3481 −0.445723
\(540\) −7.29886 −0.314093
\(541\) 22.0086 0.946224 0.473112 0.881002i \(-0.343131\pi\)
0.473112 + 0.881002i \(0.343131\pi\)
\(542\) −13.0886 −0.562203
\(543\) −23.4999 −1.00848
\(544\) 5.67143 0.243161
\(545\) −11.8810 −0.508927
\(546\) 42.4447 1.81647
\(547\) 43.2481 1.84916 0.924578 0.380992i \(-0.124418\pi\)
0.924578 + 0.380992i \(0.124418\pi\)
\(548\) −9.74768 −0.416400
\(549\) 6.59686 0.281547
\(550\) 11.4459 0.488054
\(551\) −16.9643 −0.722705
\(552\) −6.92848 −0.294896
\(553\) −52.8948 −2.24932
\(554\) 0.588778 0.0250148
\(555\) 3.82841 0.162507
\(556\) −22.3524 −0.947954
\(557\) 20.2941 0.859889 0.429945 0.902855i \(-0.358533\pi\)
0.429945 + 0.902855i \(0.358533\pi\)
\(558\) −2.56028 −0.108385
\(559\) −63.0287 −2.66583
\(560\) −8.50374 −0.359348
\(561\) −53.1186 −2.24267
\(562\) −10.0168 −0.422534
\(563\) −15.9327 −0.671483 −0.335741 0.941954i \(-0.608987\pi\)
−0.335741 + 0.941954i \(0.608987\pi\)
\(564\) −10.0859 −0.424692
\(565\) 28.1476 1.18418
\(566\) −21.7789 −0.915434
\(567\) −34.2572 −1.43867
\(568\) −4.19250 −0.175913
\(569\) 14.1002 0.591109 0.295555 0.955326i \(-0.404496\pi\)
0.295555 + 0.955326i \(0.404496\pi\)
\(570\) −18.5111 −0.775343
\(571\) −12.6378 −0.528874 −0.264437 0.964403i \(-0.585186\pi\)
−0.264437 + 0.964403i \(0.585186\pi\)
\(572\) −26.9998 −1.12892
\(573\) −42.4300 −1.77254
\(574\) −25.8450 −1.07875
\(575\) −8.46708 −0.353102
\(576\) 1.79726 0.0748858
\(577\) −20.7629 −0.864369 −0.432184 0.901785i \(-0.642257\pi\)
−0.432184 + 0.901785i \(0.642257\pi\)
\(578\) −15.1651 −0.630786
\(579\) 48.9451 2.03409
\(580\) 15.4090 0.639824
\(581\) 12.9238 0.536171
\(582\) 11.2906 0.468011
\(583\) −28.7050 −1.18884
\(584\) 6.91203 0.286022
\(585\) −31.4413 −1.29994
\(586\) 12.2822 0.507372
\(587\) 24.5443 1.01305 0.506527 0.862224i \(-0.330929\pi\)
0.506527 + 0.862224i \(0.330929\pi\)
\(588\) −5.30027 −0.218580
\(589\) 4.34536 0.179048
\(590\) 30.2384 1.24489
\(591\) 37.5940 1.54641
\(592\) 0.630865 0.0259284
\(593\) 21.9320 0.900638 0.450319 0.892868i \(-0.351310\pi\)
0.450319 + 0.892868i \(0.351310\pi\)
\(594\) 11.2649 0.462203
\(595\) 48.2283 1.97717
\(596\) −13.6798 −0.560346
\(597\) −28.0625 −1.14852
\(598\) 19.9731 0.816759
\(599\) 37.3098 1.52444 0.762219 0.647320i \(-0.224110\pi\)
0.762219 + 0.647320i \(0.224110\pi\)
\(600\) 5.86258 0.239339
\(601\) 10.0699 0.410758 0.205379 0.978683i \(-0.434157\pi\)
0.205379 + 0.978683i \(0.434157\pi\)
\(602\) 30.6379 1.24871
\(603\) −10.3702 −0.422307
\(604\) −10.9167 −0.444195
\(605\) −20.1866 −0.820704
\(606\) 0.169820 0.00689847
\(607\) −1.02591 −0.0416404 −0.0208202 0.999783i \(-0.506628\pi\)
−0.0208202 + 0.999783i \(0.506628\pi\)
\(608\) −3.05034 −0.123708
\(609\) 37.3860 1.51496
\(610\) 10.1698 0.411764
\(611\) 29.0750 1.17625
\(612\) −10.1930 −0.412029
\(613\) 6.06510 0.244967 0.122484 0.992471i \(-0.460914\pi\)
0.122484 + 0.992471i \(0.460914\pi\)
\(614\) 7.09108 0.286173
\(615\) 51.1016 2.06062
\(616\) 13.1244 0.528799
\(617\) 24.0196 0.966993 0.483496 0.875346i \(-0.339367\pi\)
0.483496 + 0.875346i \(0.339367\pi\)
\(618\) 32.2170 1.29596
\(619\) 34.9878 1.40628 0.703138 0.711053i \(-0.251781\pi\)
0.703138 + 0.711053i \(0.251781\pi\)
\(620\) −3.94697 −0.158514
\(621\) −8.33316 −0.334398
\(622\) 20.4211 0.818813
\(623\) −16.8581 −0.675407
\(624\) −13.8293 −0.553615
\(625\) −31.2188 −1.24875
\(626\) −31.4280 −1.25612
\(627\) 28.5695 1.14096
\(628\) −0.191486 −0.00764113
\(629\) −3.57790 −0.142660
\(630\) 15.2834 0.608906
\(631\) 1.11155 0.0442501 0.0221250 0.999755i \(-0.492957\pi\)
0.0221250 + 0.999755i \(0.492957\pi\)
\(632\) 17.2341 0.685537
\(633\) −50.1372 −1.99278
\(634\) −7.66928 −0.304586
\(635\) 47.3883 1.88055
\(636\) −14.7027 −0.582999
\(637\) 15.2794 0.605390
\(638\) −23.7819 −0.941533
\(639\) 7.53501 0.298080
\(640\) 2.77068 0.109521
\(641\) −22.7019 −0.896671 −0.448335 0.893865i \(-0.647983\pi\)
−0.448335 + 0.893865i \(0.647983\pi\)
\(642\) 21.4420 0.846249
\(643\) 15.2835 0.602724 0.301362 0.953510i \(-0.402559\pi\)
0.301362 + 0.953510i \(0.402559\pi\)
\(644\) −9.70879 −0.382580
\(645\) −60.5784 −2.38527
\(646\) 17.2998 0.680652
\(647\) 1.68254 0.0661476 0.0330738 0.999453i \(-0.489470\pi\)
0.0330738 + 0.999453i \(0.489470\pi\)
\(648\) 11.1616 0.438471
\(649\) −46.6691 −1.83192
\(650\) −16.9004 −0.662886
\(651\) −9.57630 −0.375325
\(652\) −12.3496 −0.483647
\(653\) 34.4669 1.34879 0.674397 0.738369i \(-0.264404\pi\)
0.674397 + 0.738369i \(0.264404\pi\)
\(654\) 9.39213 0.367261
\(655\) 4.06335 0.158768
\(656\) 8.42078 0.328776
\(657\) −12.4227 −0.484656
\(658\) −14.1332 −0.550969
\(659\) 41.5462 1.61841 0.809205 0.587526i \(-0.199898\pi\)
0.809205 + 0.587526i \(0.199898\pi\)
\(660\) −25.9501 −1.01011
\(661\) −12.0867 −0.470120 −0.235060 0.971981i \(-0.575529\pi\)
−0.235060 + 0.971981i \(0.575529\pi\)
\(662\) 22.4770 0.873593
\(663\) 78.4319 3.04604
\(664\) −4.21083 −0.163412
\(665\) −25.9393 −1.00588
\(666\) −1.13383 −0.0439349
\(667\) 17.5926 0.681188
\(668\) −2.57759 −0.0997298
\(669\) −14.4212 −0.557555
\(670\) −15.9868 −0.617625
\(671\) −15.6958 −0.605930
\(672\) 6.72234 0.259320
\(673\) 20.7127 0.798416 0.399208 0.916860i \(-0.369285\pi\)
0.399208 + 0.916860i \(0.369285\pi\)
\(674\) 32.4632 1.25043
\(675\) 7.05117 0.271400
\(676\) 26.8664 1.03332
\(677\) −30.2979 −1.16444 −0.582222 0.813030i \(-0.697816\pi\)
−0.582222 + 0.813030i \(0.697816\pi\)
\(678\) −22.2511 −0.854549
\(679\) 15.8214 0.607169
\(680\) −15.7137 −0.602593
\(681\) 13.0650 0.500653
\(682\) 6.09164 0.233261
\(683\) −15.7487 −0.602608 −0.301304 0.953528i \(-0.597422\pi\)
−0.301304 + 0.953528i \(0.597422\pi\)
\(684\) 5.48225 0.209619
\(685\) 27.0077 1.03191
\(686\) 14.0571 0.536703
\(687\) 12.6952 0.484353
\(688\) −9.98240 −0.380575
\(689\) 42.3842 1.61471
\(690\) 19.1966 0.730801
\(691\) −33.6615 −1.28054 −0.640272 0.768148i \(-0.721179\pi\)
−0.640272 + 0.768148i \(0.721179\pi\)
\(692\) 7.80926 0.296863
\(693\) −23.5880 −0.896035
\(694\) −3.93027 −0.149191
\(695\) 61.9314 2.34919
\(696\) −12.1811 −0.461722
\(697\) −47.7579 −1.80896
\(698\) −35.1030 −1.32867
\(699\) −16.3649 −0.618976
\(700\) 8.21516 0.310504
\(701\) 33.6404 1.27058 0.635290 0.772273i \(-0.280880\pi\)
0.635290 + 0.772273i \(0.280880\pi\)
\(702\) −16.6331 −0.627774
\(703\) 1.92435 0.0725783
\(704\) −4.27619 −0.161165
\(705\) 27.9447 1.05246
\(706\) 6.16529 0.232034
\(707\) 0.237967 0.00894966
\(708\) −23.9039 −0.898364
\(709\) 4.46979 0.167867 0.0839333 0.996471i \(-0.473252\pi\)
0.0839333 + 0.996471i \(0.473252\pi\)
\(710\) 11.6161 0.435943
\(711\) −30.9742 −1.16162
\(712\) 5.49270 0.205848
\(713\) −4.50628 −0.168762
\(714\) −38.1253 −1.42680
\(715\) 74.8078 2.79765
\(716\) −13.1978 −0.493226
\(717\) 2.08785 0.0779723
\(718\) −8.39889 −0.313444
\(719\) 6.61299 0.246623 0.123311 0.992368i \(-0.460649\pi\)
0.123311 + 0.992368i \(0.460649\pi\)
\(720\) −4.97963 −0.185580
\(721\) 45.1453 1.68130
\(722\) 9.69541 0.360826
\(723\) −18.9102 −0.703276
\(724\) 10.7292 0.398749
\(725\) −14.8861 −0.552856
\(726\) 15.9579 0.592252
\(727\) −12.3702 −0.458785 −0.229392 0.973334i \(-0.573674\pi\)
−0.229392 + 0.973334i \(0.573674\pi\)
\(728\) −19.3788 −0.718227
\(729\) −2.75077 −0.101880
\(730\) −19.1510 −0.708811
\(731\) 56.6145 2.09396
\(732\) −8.03940 −0.297145
\(733\) −8.53985 −0.315427 −0.157713 0.987485i \(-0.550412\pi\)
−0.157713 + 0.987485i \(0.550412\pi\)
\(734\) 17.7449 0.654977
\(735\) 14.6854 0.541677
\(736\) 3.16331 0.116601
\(737\) 24.6736 0.908865
\(738\) −15.1343 −0.557102
\(739\) 6.19418 0.227857 0.113928 0.993489i \(-0.463657\pi\)
0.113928 + 0.993489i \(0.463657\pi\)
\(740\) −1.74792 −0.0642549
\(741\) −42.1841 −1.54967
\(742\) −20.6027 −0.756348
\(743\) 22.0148 0.807646 0.403823 0.914837i \(-0.367681\pi\)
0.403823 + 0.914837i \(0.367681\pi\)
\(744\) 3.12014 0.114390
\(745\) 37.9023 1.38863
\(746\) −9.17792 −0.336028
\(747\) 7.56795 0.276897
\(748\) 24.2521 0.886746
\(749\) 30.0464 1.09787
\(750\) 14.0993 0.514832
\(751\) −30.8343 −1.12516 −0.562580 0.826743i \(-0.690191\pi\)
−0.562580 + 0.826743i \(0.690191\pi\)
\(752\) 4.60486 0.167922
\(753\) 24.8981 0.907339
\(754\) 35.1149 1.27881
\(755\) 30.2467 1.10079
\(756\) 8.08523 0.294057
\(757\) 29.3128 1.06539 0.532696 0.846307i \(-0.321179\pi\)
0.532696 + 0.846307i \(0.321179\pi\)
\(758\) 15.6763 0.569390
\(759\) −29.6275 −1.07541
\(760\) 8.45152 0.306569
\(761\) −45.8413 −1.66175 −0.830873 0.556462i \(-0.812159\pi\)
−0.830873 + 0.556462i \(0.812159\pi\)
\(762\) −37.4612 −1.35708
\(763\) 13.1611 0.476463
\(764\) 19.3721 0.700858
\(765\) 28.2416 1.02108
\(766\) 24.9315 0.900813
\(767\) 68.9090 2.48816
\(768\) −2.19026 −0.0790344
\(769\) −45.9403 −1.65665 −0.828324 0.560249i \(-0.810705\pi\)
−0.828324 + 0.560249i \(0.810705\pi\)
\(770\) −36.3636 −1.31045
\(771\) 29.1795 1.05087
\(772\) −22.3466 −0.804273
\(773\) 34.4048 1.23745 0.618727 0.785606i \(-0.287649\pi\)
0.618727 + 0.785606i \(0.287649\pi\)
\(774\) 17.9410 0.644874
\(775\) 3.81303 0.136968
\(776\) −5.15491 −0.185050
\(777\) −4.24088 −0.152141
\(778\) −5.71843 −0.205016
\(779\) 25.6863 0.920306
\(780\) 38.3165 1.37195
\(781\) −17.9279 −0.641512
\(782\) −17.9405 −0.641550
\(783\) −14.6507 −0.523572
\(784\) 2.41992 0.0864259
\(785\) 0.530547 0.0189360
\(786\) −3.21214 −0.114573
\(787\) 5.47953 0.195324 0.0976621 0.995220i \(-0.468864\pi\)
0.0976621 + 0.995220i \(0.468864\pi\)
\(788\) −17.1642 −0.611448
\(789\) −16.7962 −0.597960
\(790\) −47.7502 −1.69888
\(791\) −31.1802 −1.10864
\(792\) 7.68542 0.273090
\(793\) 23.1756 0.822988
\(794\) −24.0531 −0.853614
\(795\) 40.7364 1.44477
\(796\) 12.8124 0.454123
\(797\) 14.9007 0.527811 0.263905 0.964549i \(-0.414989\pi\)
0.263905 + 0.964549i \(0.414989\pi\)
\(798\) 20.5054 0.725884
\(799\) −26.1162 −0.923923
\(800\) −2.67665 −0.0946340
\(801\) −9.87180 −0.348803
\(802\) 26.0036 0.918218
\(803\) 29.5572 1.04305
\(804\) 12.6378 0.445702
\(805\) 26.8999 0.948098
\(806\) −8.99458 −0.316821
\(807\) 6.63571 0.233588
\(808\) −0.0775340 −0.00272764
\(809\) −14.5812 −0.512646 −0.256323 0.966591i \(-0.582511\pi\)
−0.256323 + 0.966591i \(0.582511\pi\)
\(810\) −30.9253 −1.08660
\(811\) 14.0382 0.492947 0.246473 0.969150i \(-0.420728\pi\)
0.246473 + 0.969150i \(0.420728\pi\)
\(812\) −17.0692 −0.599010
\(813\) −28.6675 −1.00541
\(814\) 2.69770 0.0945543
\(815\) 34.2167 1.19856
\(816\) 12.4219 0.434855
\(817\) −30.4497 −1.06530
\(818\) 6.36860 0.222673
\(819\) 34.8287 1.21701
\(820\) −23.3313 −0.814763
\(821\) −50.2071 −1.75224 −0.876119 0.482094i \(-0.839876\pi\)
−0.876119 + 0.482094i \(0.839876\pi\)
\(822\) −21.3500 −0.744667
\(823\) −12.2022 −0.425342 −0.212671 0.977124i \(-0.568216\pi\)
−0.212671 + 0.977124i \(0.568216\pi\)
\(824\) −14.7092 −0.512419
\(825\) 25.0695 0.872809
\(826\) −33.4963 −1.16548
\(827\) −4.40461 −0.153163 −0.0765816 0.997063i \(-0.524401\pi\)
−0.0765816 + 0.997063i \(0.524401\pi\)
\(828\) −5.68528 −0.197577
\(829\) 2.50953 0.0871596 0.0435798 0.999050i \(-0.486124\pi\)
0.0435798 + 0.999050i \(0.486124\pi\)
\(830\) 11.6669 0.404962
\(831\) 1.28958 0.0447350
\(832\) 6.31398 0.218898
\(833\) −13.7244 −0.475523
\(834\) −48.9577 −1.69527
\(835\) 7.14166 0.247147
\(836\) −13.0438 −0.451131
\(837\) 3.75272 0.129713
\(838\) −12.7030 −0.438817
\(839\) 12.8516 0.443686 0.221843 0.975082i \(-0.428793\pi\)
0.221843 + 0.975082i \(0.428793\pi\)
\(840\) −18.6254 −0.642638
\(841\) 1.92980 0.0665449
\(842\) 10.1853 0.351008
\(843\) −21.9395 −0.755637
\(844\) 22.8910 0.787939
\(845\) −74.4381 −2.56075
\(846\) −8.27613 −0.284539
\(847\) 22.3615 0.768352
\(848\) 6.71274 0.230517
\(849\) −47.7015 −1.63711
\(850\) 15.1805 0.520686
\(851\) −1.99562 −0.0684089
\(852\) −9.18269 −0.314594
\(853\) 29.2685 1.00213 0.501067 0.865409i \(-0.332941\pi\)
0.501067 + 0.865409i \(0.332941\pi\)
\(854\) −11.2655 −0.385498
\(855\) −15.1896 −0.519472
\(856\) −9.78969 −0.334605
\(857\) 23.1817 0.791870 0.395935 0.918279i \(-0.370421\pi\)
0.395935 + 0.918279i \(0.370421\pi\)
\(858\) −59.1367 −2.01889
\(859\) 11.0145 0.375810 0.187905 0.982187i \(-0.439830\pi\)
0.187905 + 0.982187i \(0.439830\pi\)
\(860\) 27.6580 0.943130
\(861\) −56.6073 −1.92917
\(862\) −26.0235 −0.886365
\(863\) 1.22035 0.0415411 0.0207705 0.999784i \(-0.493388\pi\)
0.0207705 + 0.999784i \(0.493388\pi\)
\(864\) −2.63432 −0.0896214
\(865\) −21.6369 −0.735678
\(866\) −19.3961 −0.659107
\(867\) −33.2156 −1.12806
\(868\) 4.37221 0.148403
\(869\) 73.6965 2.49998
\(870\) 33.7498 1.14423
\(871\) −36.4317 −1.23444
\(872\) −4.28813 −0.145214
\(873\) 9.26471 0.313563
\(874\) 9.64917 0.326388
\(875\) 19.7571 0.667912
\(876\) 15.1392 0.511505
\(877\) 18.1457 0.612736 0.306368 0.951913i \(-0.400886\pi\)
0.306368 + 0.951913i \(0.400886\pi\)
\(878\) −32.7508 −1.10529
\(879\) 26.9012 0.907355
\(880\) 11.8479 0.399394
\(881\) −23.0693 −0.777225 −0.388613 0.921401i \(-0.627046\pi\)
−0.388613 + 0.921401i \(0.627046\pi\)
\(882\) −4.34923 −0.146446
\(883\) 52.9051 1.78040 0.890199 0.455572i \(-0.150565\pi\)
0.890199 + 0.455572i \(0.150565\pi\)
\(884\) −35.8093 −1.20440
\(885\) 66.2301 2.22630
\(886\) −26.6685 −0.895945
\(887\) 22.7817 0.764935 0.382467 0.923969i \(-0.375074\pi\)
0.382467 + 0.923969i \(0.375074\pi\)
\(888\) 1.38176 0.0463688
\(889\) −52.4939 −1.76059
\(890\) −15.2185 −0.510125
\(891\) 47.7293 1.59899
\(892\) 6.58421 0.220456
\(893\) 14.0464 0.470045
\(894\) −29.9623 −1.00209
\(895\) 36.5669 1.22230
\(896\) −3.06919 −0.102534
\(897\) 43.7463 1.46065
\(898\) −34.5933 −1.15439
\(899\) −7.92257 −0.264232
\(900\) 4.81064 0.160355
\(901\) −38.0709 −1.26832
\(902\) 36.0089 1.19896
\(903\) 67.1051 2.23312
\(904\) 10.1591 0.337887
\(905\) −29.7273 −0.988168
\(906\) −23.9105 −0.794373
\(907\) 27.6388 0.917731 0.458866 0.888506i \(-0.348256\pi\)
0.458866 + 0.888506i \(0.348256\pi\)
\(908\) −5.96504 −0.197957
\(909\) 0.139349 0.00462190
\(910\) 53.6924 1.77989
\(911\) 1.81558 0.0601530 0.0300765 0.999548i \(-0.490425\pi\)
0.0300765 + 0.999548i \(0.490425\pi\)
\(912\) −6.68106 −0.221232
\(913\) −18.0063 −0.595922
\(914\) −4.18826 −0.138535
\(915\) 22.2746 0.736375
\(916\) −5.79620 −0.191512
\(917\) −4.50113 −0.148640
\(918\) 14.9404 0.493106
\(919\) 22.5149 0.742699 0.371350 0.928493i \(-0.378895\pi\)
0.371350 + 0.928493i \(0.378895\pi\)
\(920\) −8.76450 −0.288957
\(921\) 15.5313 0.511775
\(922\) −1.84749 −0.0608438
\(923\) 26.4714 0.871316
\(924\) 28.7460 0.945674
\(925\) 1.68861 0.0555210
\(926\) −3.11585 −0.102393
\(927\) 26.4362 0.868280
\(928\) 5.56146 0.182564
\(929\) −0.836070 −0.0274306 −0.0137153 0.999906i \(-0.504366\pi\)
−0.0137153 + 0.999906i \(0.504366\pi\)
\(930\) −8.64490 −0.283477
\(931\) 7.38160 0.241922
\(932\) 7.47164 0.244742
\(933\) 44.7277 1.46432
\(934\) −36.8552 −1.20594
\(935\) −67.1948 −2.19751
\(936\) −11.3479 −0.370917
\(937\) 39.1560 1.27917 0.639585 0.768721i \(-0.279106\pi\)
0.639585 + 0.768721i \(0.279106\pi\)
\(938\) 17.7092 0.578227
\(939\) −68.8357 −2.24637
\(940\) −12.7586 −0.416139
\(941\) 27.3600 0.891910 0.445955 0.895055i \(-0.352864\pi\)
0.445955 + 0.895055i \(0.352864\pi\)
\(942\) −0.419405 −0.0136650
\(943\) −26.6375 −0.867437
\(944\) 10.9137 0.355211
\(945\) −22.4016 −0.728723
\(946\) −42.6867 −1.38786
\(947\) −10.7260 −0.348547 −0.174273 0.984697i \(-0.555758\pi\)
−0.174273 + 0.984697i \(0.555758\pi\)
\(948\) 37.7473 1.22598
\(949\) −43.6424 −1.41669
\(950\) −8.16471 −0.264898
\(951\) −16.7978 −0.544704
\(952\) 17.4067 0.564154
\(953\) 8.95474 0.290072 0.145036 0.989426i \(-0.453670\pi\)
0.145036 + 0.989426i \(0.453670\pi\)
\(954\) −12.0645 −0.390604
\(955\) −53.6738 −1.73684
\(956\) −0.953242 −0.0308301
\(957\) −52.0886 −1.68378
\(958\) 15.7315 0.508262
\(959\) −29.9175 −0.966086
\(960\) 6.06852 0.195861
\(961\) −28.9707 −0.934537
\(962\) −3.98327 −0.128426
\(963\) 17.5946 0.566978
\(964\) 8.63373 0.278074
\(965\) 61.9153 1.99313
\(966\) −21.2648 −0.684184
\(967\) 44.6121 1.43463 0.717313 0.696751i \(-0.245372\pi\)
0.717313 + 0.696751i \(0.245372\pi\)
\(968\) −7.28581 −0.234175
\(969\) 37.8912 1.21724
\(970\) 14.2826 0.458586
\(971\) 34.1411 1.09564 0.547820 0.836596i \(-0.315458\pi\)
0.547820 + 0.836596i \(0.315458\pi\)
\(972\) 16.5440 0.530648
\(973\) −68.6038 −2.19934
\(974\) −30.6542 −0.982224
\(975\) −37.0162 −1.18547
\(976\) 3.67051 0.117490
\(977\) −47.4945 −1.51948 −0.759742 0.650225i \(-0.774675\pi\)
−0.759742 + 0.650225i \(0.774675\pi\)
\(978\) −27.0489 −0.864927
\(979\) 23.4878 0.750674
\(980\) −6.70483 −0.214178
\(981\) 7.70687 0.246062
\(982\) −23.6703 −0.755348
\(983\) 6.64117 0.211820 0.105910 0.994376i \(-0.466224\pi\)
0.105910 + 0.994376i \(0.466224\pi\)
\(984\) 18.4437 0.587965
\(985\) 47.5564 1.51527
\(986\) −31.5414 −1.00448
\(987\) −30.9554 −0.985322
\(988\) 19.2598 0.612736
\(989\) 31.5774 1.00410
\(990\) −21.2938 −0.676762
\(991\) 3.10904 0.0987620 0.0493810 0.998780i \(-0.484275\pi\)
0.0493810 + 0.998780i \(0.484275\pi\)
\(992\) −1.42455 −0.0452295
\(993\) 49.2306 1.56229
\(994\) −12.8676 −0.408135
\(995\) −35.4990 −1.12539
\(996\) −9.22283 −0.292237
\(997\) −10.3976 −0.329296 −0.164648 0.986352i \(-0.552649\pi\)
−0.164648 + 0.986352i \(0.552649\pi\)
\(998\) −6.01488 −0.190398
\(999\) 1.66190 0.0525802
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 \(a_p\))