Properties

Label 8007.2.a.j.1.20
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 0
Dimension 64
CM No

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(0\)
Dimension: \(64\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.28460 q^{2}\) \(-1.00000 q^{3}\) \(-0.349799 q^{4}\) \(-0.580730 q^{5}\) \(+1.28460 q^{6}\) \(-1.93204 q^{7}\) \(+3.01856 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.28460 q^{2}\) \(-1.00000 q^{3}\) \(-0.349799 q^{4}\) \(-0.580730 q^{5}\) \(+1.28460 q^{6}\) \(-1.93204 q^{7}\) \(+3.01856 q^{8}\) \(+1.00000 q^{9}\) \(+0.746007 q^{10}\) \(+1.58316 q^{11}\) \(+0.349799 q^{12}\) \(-0.419632 q^{13}\) \(+2.48191 q^{14}\) \(+0.580730 q^{15}\) \(-3.17804 q^{16}\) \(+1.00000 q^{17}\) \(-1.28460 q^{18}\) \(-2.91658 q^{19}\) \(+0.203139 q^{20}\) \(+1.93204 q^{21}\) \(-2.03372 q^{22}\) \(+8.95631 q^{23}\) \(-3.01856 q^{24}\) \(-4.66275 q^{25}\) \(+0.539060 q^{26}\) \(-1.00000 q^{27}\) \(+0.675827 q^{28}\) \(+4.63895 q^{29}\) \(-0.746007 q^{30}\) \(+1.94626 q^{31}\) \(-1.95459 q^{32}\) \(-1.58316 q^{33}\) \(-1.28460 q^{34}\) \(+1.12200 q^{35}\) \(-0.349799 q^{36}\) \(+8.65463 q^{37}\) \(+3.74664 q^{38}\) \(+0.419632 q^{39}\) \(-1.75297 q^{40}\) \(+10.2986 q^{41}\) \(-2.48191 q^{42}\) \(-1.03555 q^{43}\) \(-0.553786 q^{44}\) \(-0.580730 q^{45}\) \(-11.5053 q^{46}\) \(+7.92894 q^{47}\) \(+3.17804 q^{48}\) \(-3.26721 q^{49}\) \(+5.98978 q^{50}\) \(-1.00000 q^{51}\) \(+0.146787 q^{52}\) \(-10.1848 q^{53}\) \(+1.28460 q^{54}\) \(-0.919386 q^{55}\) \(-5.83198 q^{56}\) \(+2.91658 q^{57}\) \(-5.95921 q^{58}\) \(-11.7856 q^{59}\) \(-0.203139 q^{60}\) \(-3.15724 q^{61}\) \(-2.50016 q^{62}\) \(-1.93204 q^{63}\) \(+8.86696 q^{64}\) \(+0.243693 q^{65}\) \(+2.03372 q^{66}\) \(-5.25076 q^{67}\) \(-0.349799 q^{68}\) \(-8.95631 q^{69}\) \(-1.44132 q^{70}\) \(+10.2391 q^{71}\) \(+3.01856 q^{72}\) \(-0.696030 q^{73}\) \(-11.1177 q^{74}\) \(+4.66275 q^{75}\) \(+1.02022 q^{76}\) \(-3.05873 q^{77}\) \(-0.539060 q^{78}\) \(-4.38503 q^{79}\) \(+1.84559 q^{80}\) \(+1.00000 q^{81}\) \(-13.2296 q^{82}\) \(-0.402925 q^{83}\) \(-0.675827 q^{84}\) \(-0.580730 q^{85}\) \(+1.33027 q^{86}\) \(-4.63895 q^{87}\) \(+4.77884 q^{88}\) \(+3.07805 q^{89}\) \(+0.746007 q^{90}\) \(+0.810747 q^{91}\) \(-3.13291 q^{92}\) \(-1.94626 q^{93}\) \(-10.1855 q^{94}\) \(+1.69375 q^{95}\) \(+1.95459 q^{96}\) \(+18.6258 q^{97}\) \(+4.19706 q^{98}\) \(+1.58316 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(64q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 64q^{3} \) \(\mathstrut +\mathstrut 77q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 64q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(64q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 64q^{3} \) \(\mathstrut +\mathstrut 77q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 64q^{9} \) \(\mathstrut +\mathstrut 12q^{10} \) \(\mathstrut -\mathstrut 7q^{11} \) \(\mathstrut -\mathstrut 77q^{12} \) \(\mathstrut +\mathstrut 24q^{13} \) \(\mathstrut -\mathstrut 14q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 103q^{16} \) \(\mathstrut +\mathstrut 64q^{17} \) \(\mathstrut +\mathstrut 5q^{18} \) \(\mathstrut +\mathstrut 26q^{19} \) \(\mathstrut -\mathstrut 24q^{20} \) \(\mathstrut -\mathstrut 5q^{21} \) \(\mathstrut +\mathstrut 25q^{22} \) \(\mathstrut +\mathstrut 20q^{23} \) \(\mathstrut -\mathstrut 18q^{24} \) \(\mathstrut +\mathstrut 141q^{25} \) \(\mathstrut +\mathstrut 9q^{26} \) \(\mathstrut -\mathstrut 64q^{27} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut +\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 31q^{32} \) \(\mathstrut +\mathstrut 7q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 3q^{35} \) \(\mathstrut +\mathstrut 77q^{36} \) \(\mathstrut +\mathstrut 50q^{37} \) \(\mathstrut +\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut +\mathstrut 28q^{40} \) \(\mathstrut -\mathstrut 9q^{41} \) \(\mathstrut +\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 59q^{43} \) \(\mathstrut -\mathstrut 6q^{44} \) \(\mathstrut -\mathstrut 3q^{45} \) \(\mathstrut +\mathstrut 11q^{47} \) \(\mathstrut -\mathstrut 103q^{48} \) \(\mathstrut +\mathstrut 163q^{49} \) \(\mathstrut +\mathstrut 20q^{50} \) \(\mathstrut -\mathstrut 64q^{51} \) \(\mathstrut +\mathstrut 65q^{52} \) \(\mathstrut +\mathstrut 39q^{53} \) \(\mathstrut -\mathstrut 5q^{54} \) \(\mathstrut +\mathstrut 35q^{55} \) \(\mathstrut -\mathstrut 34q^{56} \) \(\mathstrut -\mathstrut 26q^{57} \) \(\mathstrut -\mathstrut 27q^{58} \) \(\mathstrut -\mathstrut 65q^{59} \) \(\mathstrut +\mathstrut 24q^{60} \) \(\mathstrut +\mathstrut 15q^{61} \) \(\mathstrut +\mathstrut 18q^{62} \) \(\mathstrut +\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 152q^{64} \) \(\mathstrut +\mathstrut 49q^{65} \) \(\mathstrut -\mathstrut 25q^{66} \) \(\mathstrut +\mathstrut 56q^{67} \) \(\mathstrut +\mathstrut 77q^{68} \) \(\mathstrut -\mathstrut 20q^{69} \) \(\mathstrut +\mathstrut 28q^{70} \) \(\mathstrut -\mathstrut 18q^{71} \) \(\mathstrut +\mathstrut 18q^{72} \) \(\mathstrut +\mathstrut 37q^{73} \) \(\mathstrut -\mathstrut 76q^{74} \) \(\mathstrut -\mathstrut 141q^{75} \) \(\mathstrut +\mathstrut 30q^{76} \) \(\mathstrut +\mathstrut 80q^{77} \) \(\mathstrut -\mathstrut 9q^{78} \) \(\mathstrut +\mathstrut 20q^{79} \) \(\mathstrut -\mathstrut 144q^{80} \) \(\mathstrut +\mathstrut 64q^{81} \) \(\mathstrut +\mathstrut 27q^{82} \) \(\mathstrut +\mathstrut 3q^{83} \) \(\mathstrut -\mathstrut 14q^{84} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 12q^{86} \) \(\mathstrut -\mathstrut 5q^{87} \) \(\mathstrut +\mathstrut 108q^{88} \) \(\mathstrut +\mathstrut 42q^{89} \) \(\mathstrut +\mathstrut 12q^{90} \) \(\mathstrut +\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 18q^{92} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 60q^{94} \) \(\mathstrut +\mathstrut 42q^{95} \) \(\mathstrut -\mathstrut 31q^{96} \) \(\mathstrut +\mathstrut 72q^{97} \) \(\mathstrut +\mathstrut 18q^{98} \) \(\mathstrut -\mathstrut 7q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.28460 −0.908350 −0.454175 0.890912i \(-0.650066\pi\)
−0.454175 + 0.890912i \(0.650066\pi\)
\(3\) −1.00000 −0.577350
\(4\) −0.349799 −0.174899
\(5\) −0.580730 −0.259710 −0.129855 0.991533i \(-0.541451\pi\)
−0.129855 + 0.991533i \(0.541451\pi\)
\(6\) 1.28460 0.524436
\(7\) −1.93204 −0.730244 −0.365122 0.930960i \(-0.618973\pi\)
−0.365122 + 0.930960i \(0.618973\pi\)
\(8\) 3.01856 1.06722
\(9\) 1.00000 0.333333
\(10\) 0.746007 0.235908
\(11\) 1.58316 0.477340 0.238670 0.971101i \(-0.423289\pi\)
0.238670 + 0.971101i \(0.423289\pi\)
\(12\) 0.349799 0.100978
\(13\) −0.419632 −0.116385 −0.0581925 0.998305i \(-0.518534\pi\)
−0.0581925 + 0.998305i \(0.518534\pi\)
\(14\) 2.48191 0.663317
\(15\) 0.580730 0.149944
\(16\) −3.17804 −0.794511
\(17\) 1.00000 0.242536
\(18\) −1.28460 −0.302783
\(19\) −2.91658 −0.669109 −0.334555 0.942376i \(-0.608586\pi\)
−0.334555 + 0.942376i \(0.608586\pi\)
\(20\) 0.203139 0.0454232
\(21\) 1.93204 0.421607
\(22\) −2.03372 −0.433592
\(23\) 8.95631 1.86752 0.933760 0.357901i \(-0.116507\pi\)
0.933760 + 0.357901i \(0.116507\pi\)
\(24\) −3.01856 −0.616160
\(25\) −4.66275 −0.932551
\(26\) 0.539060 0.105718
\(27\) −1.00000 −0.192450
\(28\) 0.675827 0.127719
\(29\) 4.63895 0.861432 0.430716 0.902488i \(-0.358261\pi\)
0.430716 + 0.902488i \(0.358261\pi\)
\(30\) −0.746007 −0.136202
\(31\) 1.94626 0.349558 0.174779 0.984608i \(-0.444079\pi\)
0.174779 + 0.984608i \(0.444079\pi\)
\(32\) −1.95459 −0.345526
\(33\) −1.58316 −0.275592
\(34\) −1.28460 −0.220307
\(35\) 1.12200 0.189652
\(36\) −0.349799 −0.0582998
\(37\) 8.65463 1.42281 0.711406 0.702781i \(-0.248059\pi\)
0.711406 + 0.702781i \(0.248059\pi\)
\(38\) 3.74664 0.607786
\(39\) 0.419632 0.0671949
\(40\) −1.75297 −0.277168
\(41\) 10.2986 1.60837 0.804187 0.594376i \(-0.202601\pi\)
0.804187 + 0.594376i \(0.202601\pi\)
\(42\) −2.48191 −0.382967
\(43\) −1.03555 −0.157920 −0.0789602 0.996878i \(-0.525160\pi\)
−0.0789602 + 0.996878i \(0.525160\pi\)
\(44\) −0.553786 −0.0834864
\(45\) −0.580730 −0.0865701
\(46\) −11.5053 −1.69636
\(47\) 7.92894 1.15656 0.578278 0.815840i \(-0.303725\pi\)
0.578278 + 0.815840i \(0.303725\pi\)
\(48\) 3.17804 0.458711
\(49\) −3.26721 −0.466744
\(50\) 5.98978 0.847083
\(51\) −1.00000 −0.140028
\(52\) 0.146787 0.0203557
\(53\) −10.1848 −1.39898 −0.699492 0.714641i \(-0.746590\pi\)
−0.699492 + 0.714641i \(0.746590\pi\)
\(54\) 1.28460 0.174812
\(55\) −0.919386 −0.123970
\(56\) −5.83198 −0.779331
\(57\) 2.91658 0.386310
\(58\) −5.95921 −0.782482
\(59\) −11.7856 −1.53436 −0.767179 0.641433i \(-0.778340\pi\)
−0.767179 + 0.641433i \(0.778340\pi\)
\(60\) −0.203139 −0.0262251
\(61\) −3.15724 −0.404243 −0.202121 0.979360i \(-0.564784\pi\)
−0.202121 + 0.979360i \(0.564784\pi\)
\(62\) −2.50016 −0.317521
\(63\) −1.93204 −0.243415
\(64\) 8.86696 1.10837
\(65\) 0.243693 0.0302264
\(66\) 2.03372 0.250334
\(67\) −5.25076 −0.641482 −0.320741 0.947167i \(-0.603932\pi\)
−0.320741 + 0.947167i \(0.603932\pi\)
\(68\) −0.349799 −0.0424193
\(69\) −8.95631 −1.07821
\(70\) −1.44132 −0.172270
\(71\) 10.2391 1.21515 0.607577 0.794260i \(-0.292141\pi\)
0.607577 + 0.794260i \(0.292141\pi\)
\(72\) 3.01856 0.355740
\(73\) −0.696030 −0.0814641 −0.0407321 0.999170i \(-0.512969\pi\)
−0.0407321 + 0.999170i \(0.512969\pi\)
\(74\) −11.1177 −1.29241
\(75\) 4.66275 0.538408
\(76\) 1.02022 0.117027
\(77\) −3.05873 −0.348574
\(78\) −0.539060 −0.0610365
\(79\) −4.38503 −0.493354 −0.246677 0.969098i \(-0.579339\pi\)
−0.246677 + 0.969098i \(0.579339\pi\)
\(80\) 1.84559 0.206343
\(81\) 1.00000 0.111111
\(82\) −13.2296 −1.46097
\(83\) −0.402925 −0.0442268 −0.0221134 0.999755i \(-0.507039\pi\)
−0.0221134 + 0.999755i \(0.507039\pi\)
\(84\) −0.675827 −0.0737387
\(85\) −0.580730 −0.0629890
\(86\) 1.33027 0.143447
\(87\) −4.63895 −0.497348
\(88\) 4.77884 0.509426
\(89\) 3.07805 0.326273 0.163137 0.986603i \(-0.447839\pi\)
0.163137 + 0.986603i \(0.447839\pi\)
\(90\) 0.746007 0.0786360
\(91\) 0.810747 0.0849894
\(92\) −3.13291 −0.326628
\(93\) −1.94626 −0.201817
\(94\) −10.1855 −1.05056
\(95\) 1.69375 0.173775
\(96\) 1.95459 0.199490
\(97\) 18.6258 1.89117 0.945583 0.325382i \(-0.105493\pi\)
0.945583 + 0.325382i \(0.105493\pi\)
\(98\) 4.19706 0.423967
\(99\) 1.58316 0.159113
\(100\) 1.63103 0.163103
\(101\) 17.5565 1.74694 0.873469 0.486880i \(-0.161865\pi\)
0.873469 + 0.486880i \(0.161865\pi\)
\(102\) 1.28460 0.127195
\(103\) −4.39526 −0.433078 −0.216539 0.976274i \(-0.569477\pi\)
−0.216539 + 0.976274i \(0.569477\pi\)
\(104\) −1.26668 −0.124208
\(105\) −1.12200 −0.109496
\(106\) 13.0833 1.27077
\(107\) 2.56618 0.248082 0.124041 0.992277i \(-0.460415\pi\)
0.124041 + 0.992277i \(0.460415\pi\)
\(108\) 0.349799 0.0336594
\(109\) 5.05854 0.484520 0.242260 0.970211i \(-0.422111\pi\)
0.242260 + 0.970211i \(0.422111\pi\)
\(110\) 1.18105 0.112608
\(111\) −8.65463 −0.821461
\(112\) 6.14012 0.580187
\(113\) 0.902607 0.0849102 0.0424551 0.999098i \(-0.486482\pi\)
0.0424551 + 0.999098i \(0.486482\pi\)
\(114\) −3.74664 −0.350905
\(115\) −5.20120 −0.485014
\(116\) −1.62270 −0.150664
\(117\) −0.419632 −0.0387950
\(118\) 15.1398 1.39374
\(119\) −1.93204 −0.177110
\(120\) 1.75297 0.160023
\(121\) −8.49362 −0.772147
\(122\) 4.05579 0.367194
\(123\) −10.2986 −0.928596
\(124\) −0.680798 −0.0611375
\(125\) 5.61145 0.501903
\(126\) 2.48191 0.221106
\(127\) −8.31090 −0.737473 −0.368736 0.929534i \(-0.620210\pi\)
−0.368736 + 0.929534i \(0.620210\pi\)
\(128\) −7.48132 −0.661262
\(129\) 1.03555 0.0911754
\(130\) −0.313048 −0.0274561
\(131\) −0.701360 −0.0612781 −0.0306391 0.999531i \(-0.509754\pi\)
−0.0306391 + 0.999531i \(0.509754\pi\)
\(132\) 0.553786 0.0482009
\(133\) 5.63496 0.488613
\(134\) 6.74513 0.582690
\(135\) 0.580730 0.0499813
\(136\) 3.01856 0.258839
\(137\) −17.9637 −1.53474 −0.767370 0.641205i \(-0.778435\pi\)
−0.767370 + 0.641205i \(0.778435\pi\)
\(138\) 11.5053 0.979395
\(139\) −6.77443 −0.574600 −0.287300 0.957841i \(-0.592758\pi\)
−0.287300 + 0.957841i \(0.592758\pi\)
\(140\) −0.392473 −0.0331700
\(141\) −7.92894 −0.667738
\(142\) −13.1531 −1.10379
\(143\) −0.664343 −0.0555551
\(144\) −3.17804 −0.264837
\(145\) −2.69398 −0.223723
\(146\) 0.894121 0.0739980
\(147\) 3.26721 0.269475
\(148\) −3.02738 −0.248849
\(149\) 12.3459 1.01141 0.505707 0.862706i \(-0.331232\pi\)
0.505707 + 0.862706i \(0.331232\pi\)
\(150\) −5.98978 −0.489063
\(151\) 19.9042 1.61978 0.809890 0.586582i \(-0.199527\pi\)
0.809890 + 0.586582i \(0.199527\pi\)
\(152\) −8.80386 −0.714087
\(153\) 1.00000 0.0808452
\(154\) 3.92925 0.316628
\(155\) −1.13025 −0.0907838
\(156\) −0.146787 −0.0117523
\(157\) −1.00000 −0.0798087
\(158\) 5.63301 0.448138
\(159\) 10.1848 0.807703
\(160\) 1.13509 0.0897367
\(161\) −17.3040 −1.36374
\(162\) −1.28460 −0.100928
\(163\) −22.4318 −1.75699 −0.878496 0.477749i \(-0.841453\pi\)
−0.878496 + 0.477749i \(0.841453\pi\)
\(164\) −3.60245 −0.281304
\(165\) 0.919386 0.0715741
\(166\) 0.517598 0.0401734
\(167\) 3.34538 0.258873 0.129436 0.991588i \(-0.458683\pi\)
0.129436 + 0.991588i \(0.458683\pi\)
\(168\) 5.83198 0.449947
\(169\) −12.8239 −0.986455
\(170\) 0.746007 0.0572161
\(171\) −2.91658 −0.223036
\(172\) 0.362235 0.0276202
\(173\) −14.7573 −1.12197 −0.560987 0.827824i \(-0.689578\pi\)
−0.560987 + 0.827824i \(0.689578\pi\)
\(174\) 5.95921 0.451766
\(175\) 9.00864 0.680989
\(176\) −5.03134 −0.379251
\(177\) 11.7856 0.885862
\(178\) −3.95407 −0.296370
\(179\) −16.7116 −1.24909 −0.624543 0.780991i \(-0.714715\pi\)
−0.624543 + 0.780991i \(0.714715\pi\)
\(180\) 0.203139 0.0151411
\(181\) −0.391152 −0.0290741 −0.0145371 0.999894i \(-0.504627\pi\)
−0.0145371 + 0.999894i \(0.504627\pi\)
\(182\) −1.04149 −0.0772002
\(183\) 3.15724 0.233390
\(184\) 27.0351 1.99305
\(185\) −5.02600 −0.369519
\(186\) 2.50016 0.183321
\(187\) 1.58316 0.115772
\(188\) −2.77354 −0.202281
\(189\) 1.93204 0.140536
\(190\) −2.17579 −0.157848
\(191\) −23.7512 −1.71857 −0.859287 0.511495i \(-0.829092\pi\)
−0.859287 + 0.511495i \(0.829092\pi\)
\(192\) −8.86696 −0.639918
\(193\) −15.1485 −1.09041 −0.545206 0.838302i \(-0.683548\pi\)
−0.545206 + 0.838302i \(0.683548\pi\)
\(194\) −23.9268 −1.71784
\(195\) −0.243693 −0.0174512
\(196\) 1.14286 0.0816332
\(197\) −10.6745 −0.760528 −0.380264 0.924878i \(-0.624167\pi\)
−0.380264 + 0.924878i \(0.624167\pi\)
\(198\) −2.03372 −0.144531
\(199\) 9.56418 0.677987 0.338993 0.940789i \(-0.389914\pi\)
0.338993 + 0.940789i \(0.389914\pi\)
\(200\) −14.0748 −0.995237
\(201\) 5.25076 0.370360
\(202\) −22.5531 −1.58683
\(203\) −8.96266 −0.629055
\(204\) 0.349799 0.0244908
\(205\) −5.98072 −0.417712
\(206\) 5.64616 0.393387
\(207\) 8.95631 0.622506
\(208\) 1.33361 0.0924691
\(209\) −4.61740 −0.319392
\(210\) 1.44132 0.0994604
\(211\) 21.5889 1.48624 0.743122 0.669156i \(-0.233344\pi\)
0.743122 + 0.669156i \(0.233344\pi\)
\(212\) 3.56261 0.244681
\(213\) −10.2391 −0.701570
\(214\) −3.29652 −0.225346
\(215\) 0.601377 0.0410136
\(216\) −3.01856 −0.205387
\(217\) −3.76025 −0.255262
\(218\) −6.49821 −0.440114
\(219\) 0.696030 0.0470333
\(220\) 0.321600 0.0216823
\(221\) −0.419632 −0.0282275
\(222\) 11.1177 0.746175
\(223\) 29.2522 1.95887 0.979436 0.201757i \(-0.0646653\pi\)
0.979436 + 0.201757i \(0.0646653\pi\)
\(224\) 3.77636 0.252318
\(225\) −4.66275 −0.310850
\(226\) −1.15949 −0.0771282
\(227\) −18.6000 −1.23452 −0.617262 0.786758i \(-0.711758\pi\)
−0.617262 + 0.786758i \(0.711758\pi\)
\(228\) −1.02022 −0.0675655
\(229\) −17.4519 −1.15326 −0.576628 0.817007i \(-0.695632\pi\)
−0.576628 + 0.817007i \(0.695632\pi\)
\(230\) 6.68147 0.440563
\(231\) 3.05873 0.201249
\(232\) 14.0029 0.919338
\(233\) 16.3122 1.06865 0.534325 0.845279i \(-0.320566\pi\)
0.534325 + 0.845279i \(0.320566\pi\)
\(234\) 0.539060 0.0352394
\(235\) −4.60458 −0.300369
\(236\) 4.12260 0.268358
\(237\) 4.38503 0.284838
\(238\) 2.48191 0.160878
\(239\) −10.4899 −0.678534 −0.339267 0.940690i \(-0.610179\pi\)
−0.339267 + 0.940690i \(0.610179\pi\)
\(240\) −1.84559 −0.119132
\(241\) 3.20071 0.206176 0.103088 0.994672i \(-0.467128\pi\)
0.103088 + 0.994672i \(0.467128\pi\)
\(242\) 10.9109 0.701380
\(243\) −1.00000 −0.0641500
\(244\) 1.10440 0.0707018
\(245\) 1.89737 0.121218
\(246\) 13.2296 0.843490
\(247\) 1.22389 0.0778742
\(248\) 5.87488 0.373055
\(249\) 0.402925 0.0255343
\(250\) −7.20848 −0.455904
\(251\) −9.17030 −0.578824 −0.289412 0.957205i \(-0.593460\pi\)
−0.289412 + 0.957205i \(0.593460\pi\)
\(252\) 0.675827 0.0425731
\(253\) 14.1792 0.891441
\(254\) 10.6762 0.669884
\(255\) 0.580730 0.0363667
\(256\) −8.12339 −0.507712
\(257\) 17.5100 1.09224 0.546122 0.837706i \(-0.316104\pi\)
0.546122 + 0.837706i \(0.316104\pi\)
\(258\) −1.33027 −0.0828192
\(259\) −16.7211 −1.03900
\(260\) −0.0852435 −0.00528658
\(261\) 4.63895 0.287144
\(262\) 0.900969 0.0556620
\(263\) 14.3398 0.884228 0.442114 0.896959i \(-0.354229\pi\)
0.442114 + 0.896959i \(0.354229\pi\)
\(264\) −4.77884 −0.294118
\(265\) 5.91459 0.363331
\(266\) −7.23868 −0.443832
\(267\) −3.07805 −0.188374
\(268\) 1.83671 0.112195
\(269\) 5.81592 0.354603 0.177301 0.984157i \(-0.443263\pi\)
0.177301 + 0.984157i \(0.443263\pi\)
\(270\) −0.746007 −0.0454005
\(271\) 4.72990 0.287321 0.143661 0.989627i \(-0.454113\pi\)
0.143661 + 0.989627i \(0.454113\pi\)
\(272\) −3.17804 −0.192697
\(273\) −0.810747 −0.0490687
\(274\) 23.0762 1.39408
\(275\) −7.38186 −0.445143
\(276\) 3.13291 0.188579
\(277\) −9.62977 −0.578597 −0.289298 0.957239i \(-0.593422\pi\)
−0.289298 + 0.957239i \(0.593422\pi\)
\(278\) 8.70245 0.521938
\(279\) 1.94626 0.116519
\(280\) 3.38681 0.202400
\(281\) −23.3377 −1.39221 −0.696105 0.717940i \(-0.745085\pi\)
−0.696105 + 0.717940i \(0.745085\pi\)
\(282\) 10.1855 0.606540
\(283\) 10.3845 0.617292 0.308646 0.951177i \(-0.400124\pi\)
0.308646 + 0.951177i \(0.400124\pi\)
\(284\) −3.58162 −0.212530
\(285\) −1.69375 −0.100329
\(286\) 0.853416 0.0504635
\(287\) −19.8974 −1.17451
\(288\) −1.95459 −0.115175
\(289\) 1.00000 0.0588235
\(290\) 3.46069 0.203219
\(291\) −18.6258 −1.09186
\(292\) 0.243470 0.0142480
\(293\) 6.43263 0.375798 0.187899 0.982188i \(-0.439832\pi\)
0.187899 + 0.982188i \(0.439832\pi\)
\(294\) −4.19706 −0.244777
\(295\) 6.84427 0.398489
\(296\) 26.1245 1.51845
\(297\) −1.58316 −0.0918640
\(298\) −15.8595 −0.918718
\(299\) −3.75835 −0.217351
\(300\) −1.63103 −0.0941673
\(301\) 2.00074 0.115320
\(302\) −25.5690 −1.47133
\(303\) −17.5565 −1.00859
\(304\) 9.26902 0.531615
\(305\) 1.83350 0.104986
\(306\) −1.28460 −0.0734358
\(307\) 18.5904 1.06101 0.530504 0.847682i \(-0.322003\pi\)
0.530504 + 0.847682i \(0.322003\pi\)
\(308\) 1.06994 0.0609654
\(309\) 4.39526 0.250038
\(310\) 1.45192 0.0824635
\(311\) −10.0164 −0.567979 −0.283989 0.958827i \(-0.591658\pi\)
−0.283989 + 0.958827i \(0.591658\pi\)
\(312\) 1.26668 0.0717118
\(313\) −30.8487 −1.74367 −0.871835 0.489799i \(-0.837070\pi\)
−0.871835 + 0.489799i \(0.837070\pi\)
\(314\) 1.28460 0.0724943
\(315\) 1.12200 0.0632173
\(316\) 1.53388 0.0862873
\(317\) 30.7099 1.72484 0.862421 0.506192i \(-0.168947\pi\)
0.862421 + 0.506192i \(0.168947\pi\)
\(318\) −13.0833 −0.733678
\(319\) 7.34419 0.411195
\(320\) −5.14931 −0.287855
\(321\) −2.56618 −0.143230
\(322\) 22.2287 1.23876
\(323\) −2.91658 −0.162283
\(324\) −0.349799 −0.0194333
\(325\) 1.95664 0.108535
\(326\) 28.8159 1.59597
\(327\) −5.05854 −0.279738
\(328\) 31.0870 1.71649
\(329\) −15.3191 −0.844568
\(330\) −1.18105 −0.0650144
\(331\) 7.37770 0.405515 0.202758 0.979229i \(-0.435010\pi\)
0.202758 + 0.979229i \(0.435010\pi\)
\(332\) 0.140943 0.00773524
\(333\) 8.65463 0.474271
\(334\) −4.29748 −0.235147
\(335\) 3.04927 0.166600
\(336\) −6.14012 −0.334971
\(337\) 23.5861 1.28482 0.642408 0.766363i \(-0.277936\pi\)
0.642408 + 0.766363i \(0.277936\pi\)
\(338\) 16.4736 0.896046
\(339\) −0.902607 −0.0490229
\(340\) 0.203139 0.0110167
\(341\) 3.08123 0.166858
\(342\) 3.74664 0.202595
\(343\) 19.8367 1.07108
\(344\) −3.12588 −0.168536
\(345\) 5.20120 0.280023
\(346\) 18.9572 1.01915
\(347\) −7.99274 −0.429073 −0.214536 0.976716i \(-0.568824\pi\)
−0.214536 + 0.976716i \(0.568824\pi\)
\(348\) 1.62270 0.0869859
\(349\) 2.28026 0.122060 0.0610298 0.998136i \(-0.480562\pi\)
0.0610298 + 0.998136i \(0.480562\pi\)
\(350\) −11.5725 −0.618577
\(351\) 0.419632 0.0223983
\(352\) −3.09442 −0.164933
\(353\) 15.6438 0.832633 0.416317 0.909220i \(-0.363321\pi\)
0.416317 + 0.909220i \(0.363321\pi\)
\(354\) −15.1398 −0.804673
\(355\) −5.94614 −0.315588
\(356\) −1.07670 −0.0570650
\(357\) 1.93204 0.102255
\(358\) 21.4678 1.13461
\(359\) 37.0267 1.95420 0.977098 0.212791i \(-0.0682554\pi\)
0.977098 + 0.212791i \(0.0682554\pi\)
\(360\) −1.75297 −0.0923894
\(361\) −10.4936 −0.552293
\(362\) 0.502475 0.0264095
\(363\) 8.49362 0.445799
\(364\) −0.283598 −0.0148646
\(365\) 0.404205 0.0211571
\(366\) −4.05579 −0.212000
\(367\) 6.04369 0.315478 0.157739 0.987481i \(-0.449580\pi\)
0.157739 + 0.987481i \(0.449580\pi\)
\(368\) −28.4635 −1.48376
\(369\) 10.2986 0.536125
\(370\) 6.45641 0.335653
\(371\) 19.6774 1.02160
\(372\) 0.680798 0.0352977
\(373\) −33.3692 −1.72779 −0.863896 0.503670i \(-0.831983\pi\)
−0.863896 + 0.503670i \(0.831983\pi\)
\(374\) −2.03372 −0.105161
\(375\) −5.61145 −0.289774
\(376\) 23.9340 1.23430
\(377\) −1.94665 −0.100258
\(378\) −2.48191 −0.127656
\(379\) 4.49054 0.230663 0.115332 0.993327i \(-0.463207\pi\)
0.115332 + 0.993327i \(0.463207\pi\)
\(380\) −0.592470 −0.0303931
\(381\) 8.31090 0.425780
\(382\) 30.5108 1.56107
\(383\) −31.6450 −1.61698 −0.808492 0.588507i \(-0.799716\pi\)
−0.808492 + 0.588507i \(0.799716\pi\)
\(384\) 7.48132 0.381780
\(385\) 1.77629 0.0905284
\(386\) 19.4598 0.990476
\(387\) −1.03555 −0.0526402
\(388\) −6.51529 −0.330764
\(389\) −21.8230 −1.10647 −0.553234 0.833026i \(-0.686606\pi\)
−0.553234 + 0.833026i \(0.686606\pi\)
\(390\) 0.313048 0.0158518
\(391\) 8.95631 0.452940
\(392\) −9.86224 −0.498118
\(393\) 0.701360 0.0353789
\(394\) 13.7125 0.690826
\(395\) 2.54652 0.128129
\(396\) −0.553786 −0.0278288
\(397\) 3.00144 0.150638 0.0753191 0.997159i \(-0.476002\pi\)
0.0753191 + 0.997159i \(0.476002\pi\)
\(398\) −12.2862 −0.615849
\(399\) −5.63496 −0.282101
\(400\) 14.8184 0.740921
\(401\) 8.96913 0.447897 0.223949 0.974601i \(-0.428105\pi\)
0.223949 + 0.974601i \(0.428105\pi\)
\(402\) −6.74513 −0.336416
\(403\) −0.816711 −0.0406833
\(404\) −6.14125 −0.305538
\(405\) −0.580730 −0.0288567
\(406\) 11.5134 0.571403
\(407\) 13.7016 0.679164
\(408\) −3.01856 −0.149441
\(409\) −5.88355 −0.290923 −0.145461 0.989364i \(-0.546467\pi\)
−0.145461 + 0.989364i \(0.546467\pi\)
\(410\) 7.68284 0.379429
\(411\) 17.9637 0.886082
\(412\) 1.53746 0.0757451
\(413\) 22.7704 1.12046
\(414\) −11.5053 −0.565454
\(415\) 0.233991 0.0114862
\(416\) 0.820209 0.0402140
\(417\) 6.77443 0.331745
\(418\) 5.93152 0.290120
\(419\) 15.5704 0.760663 0.380332 0.924850i \(-0.375810\pi\)
0.380332 + 0.924850i \(0.375810\pi\)
\(420\) 0.392473 0.0191507
\(421\) 7.58791 0.369812 0.184906 0.982756i \(-0.440802\pi\)
0.184906 + 0.982756i \(0.440802\pi\)
\(422\) −27.7332 −1.35003
\(423\) 7.92894 0.385518
\(424\) −30.7432 −1.49302
\(425\) −4.66275 −0.226177
\(426\) 13.1531 0.637271
\(427\) 6.09992 0.295196
\(428\) −0.897647 −0.0433894
\(429\) 0.664343 0.0320748
\(430\) −0.772530 −0.0372547
\(431\) 17.4846 0.842204 0.421102 0.907013i \(-0.361643\pi\)
0.421102 + 0.907013i \(0.361643\pi\)
\(432\) 3.17804 0.152904
\(433\) 7.59170 0.364834 0.182417 0.983221i \(-0.441608\pi\)
0.182417 + 0.983221i \(0.441608\pi\)
\(434\) 4.83042 0.231868
\(435\) 2.69398 0.129166
\(436\) −1.76947 −0.0847423
\(437\) −26.1218 −1.24957
\(438\) −0.894121 −0.0427227
\(439\) 8.08953 0.386092 0.193046 0.981190i \(-0.438163\pi\)
0.193046 + 0.981190i \(0.438163\pi\)
\(440\) −2.77522 −0.132303
\(441\) −3.26721 −0.155581
\(442\) 0.539060 0.0256405
\(443\) −15.9530 −0.757951 −0.378975 0.925407i \(-0.623723\pi\)
−0.378975 + 0.925407i \(0.623723\pi\)
\(444\) 3.02738 0.143673
\(445\) −1.78752 −0.0847365
\(446\) −37.5774 −1.77934
\(447\) −12.3459 −0.583940
\(448\) −17.1314 −0.809380
\(449\) 38.0474 1.79557 0.897784 0.440435i \(-0.145176\pi\)
0.897784 + 0.440435i \(0.145176\pi\)
\(450\) 5.98978 0.282361
\(451\) 16.3043 0.767741
\(452\) −0.315731 −0.0148507
\(453\) −19.9042 −0.935180
\(454\) 23.8936 1.12138
\(455\) −0.470825 −0.0220726
\(456\) 8.80386 0.412278
\(457\) 23.3400 1.09180 0.545899 0.837851i \(-0.316188\pi\)
0.545899 + 0.837851i \(0.316188\pi\)
\(458\) 22.4188 1.04756
\(459\) −1.00000 −0.0466760
\(460\) 1.81937 0.0848287
\(461\) −19.1263 −0.890800 −0.445400 0.895332i \(-0.646939\pi\)
−0.445400 + 0.895332i \(0.646939\pi\)
\(462\) −3.92925 −0.182805
\(463\) −19.7251 −0.916703 −0.458351 0.888771i \(-0.651560\pi\)
−0.458351 + 0.888771i \(0.651560\pi\)
\(464\) −14.7428 −0.684417
\(465\) 1.13025 0.0524141
\(466\) −20.9547 −0.970708
\(467\) 22.4299 1.03793 0.518966 0.854795i \(-0.326317\pi\)
0.518966 + 0.854795i \(0.326317\pi\)
\(468\) 0.146787 0.00678522
\(469\) 10.1447 0.468438
\(470\) 5.91505 0.272841
\(471\) 1.00000 0.0460776
\(472\) −35.5756 −1.63750
\(473\) −1.63944 −0.0753817
\(474\) −5.63301 −0.258733
\(475\) 13.5993 0.623978
\(476\) 0.675827 0.0309765
\(477\) −10.1848 −0.466328
\(478\) 13.4753 0.616347
\(479\) 0.871785 0.0398329 0.0199164 0.999802i \(-0.493660\pi\)
0.0199164 + 0.999802i \(0.493660\pi\)
\(480\) −1.13509 −0.0518095
\(481\) −3.63176 −0.165594
\(482\) −4.11164 −0.187280
\(483\) 17.3040 0.787358
\(484\) 2.97106 0.135048
\(485\) −10.8166 −0.491155
\(486\) 1.28460 0.0582707
\(487\) 14.2150 0.644144 0.322072 0.946715i \(-0.395621\pi\)
0.322072 + 0.946715i \(0.395621\pi\)
\(488\) −9.53029 −0.431416
\(489\) 22.4318 1.01440
\(490\) −2.43736 −0.110109
\(491\) 1.41434 0.0638284 0.0319142 0.999491i \(-0.489840\pi\)
0.0319142 + 0.999491i \(0.489840\pi\)
\(492\) 3.60245 0.162411
\(493\) 4.63895 0.208928
\(494\) −1.57221 −0.0707371
\(495\) −0.919386 −0.0413233
\(496\) −6.18528 −0.277727
\(497\) −19.7823 −0.887359
\(498\) −0.517598 −0.0231941
\(499\) −11.3148 −0.506519 −0.253259 0.967398i \(-0.581503\pi\)
−0.253259 + 0.967398i \(0.581503\pi\)
\(500\) −1.96288 −0.0877826
\(501\) −3.34538 −0.149460
\(502\) 11.7802 0.525775
\(503\) 7.36129 0.328224 0.164112 0.986442i \(-0.447524\pi\)
0.164112 + 0.986442i \(0.447524\pi\)
\(504\) −5.83198 −0.259777
\(505\) −10.1956 −0.453698
\(506\) −18.2147 −0.809741
\(507\) 12.8239 0.569530
\(508\) 2.90714 0.128984
\(509\) 39.5981 1.75515 0.877577 0.479436i \(-0.159159\pi\)
0.877577 + 0.479436i \(0.159159\pi\)
\(510\) −0.746007 −0.0330337
\(511\) 1.34476 0.0594887
\(512\) 25.3980 1.12244
\(513\) 2.91658 0.128770
\(514\) −22.4934 −0.992140
\(515\) 2.55246 0.112475
\(516\) −0.362235 −0.0159465
\(517\) 12.5528 0.552070
\(518\) 21.4800 0.943776
\(519\) 14.7573 0.647772
\(520\) 0.735600 0.0322582
\(521\) 36.4594 1.59732 0.798658 0.601785i \(-0.205543\pi\)
0.798658 + 0.601785i \(0.205543\pi\)
\(522\) −5.95921 −0.260827
\(523\) −0.196520 −0.00859323 −0.00429661 0.999991i \(-0.501368\pi\)
−0.00429661 + 0.999991i \(0.501368\pi\)
\(524\) 0.245335 0.0107175
\(525\) −9.00864 −0.393169
\(526\) −18.4209 −0.803189
\(527\) 1.94626 0.0847802
\(528\) 5.03134 0.218961
\(529\) 57.2154 2.48763
\(530\) −7.59790 −0.330031
\(531\) −11.7856 −0.511453
\(532\) −1.97110 −0.0854581
\(533\) −4.32163 −0.187191
\(534\) 3.95407 0.171110
\(535\) −1.49026 −0.0644295
\(536\) −15.8497 −0.684603
\(537\) 16.7116 0.721160
\(538\) −7.47113 −0.322103
\(539\) −5.17250 −0.222795
\(540\) −0.203139 −0.00874170
\(541\) 21.9594 0.944110 0.472055 0.881569i \(-0.343512\pi\)
0.472055 + 0.881569i \(0.343512\pi\)
\(542\) −6.07604 −0.260988
\(543\) 0.391152 0.0167859
\(544\) −1.95459 −0.0838024
\(545\) −2.93765 −0.125835
\(546\) 1.04149 0.0445715
\(547\) 42.7422 1.82753 0.913763 0.406248i \(-0.133163\pi\)
0.913763 + 0.406248i \(0.133163\pi\)
\(548\) 6.28367 0.268425
\(549\) −3.15724 −0.134748
\(550\) 9.48276 0.404346
\(551\) −13.5299 −0.576392
\(552\) −27.0351 −1.15069
\(553\) 8.47206 0.360269
\(554\) 12.3704 0.525569
\(555\) 5.02600 0.213342
\(556\) 2.36969 0.100497
\(557\) 30.0082 1.27149 0.635745 0.771900i \(-0.280693\pi\)
0.635745 + 0.771900i \(0.280693\pi\)
\(558\) −2.50016 −0.105840
\(559\) 0.434551 0.0183796
\(560\) −3.56575 −0.150681
\(561\) −1.58316 −0.0668409
\(562\) 29.9797 1.26462
\(563\) −46.6016 −1.96402 −0.982012 0.188819i \(-0.939534\pi\)
−0.982012 + 0.188819i \(0.939534\pi\)
\(564\) 2.77354 0.116787
\(565\) −0.524171 −0.0220521
\(566\) −13.3399 −0.560717
\(567\) −1.93204 −0.0811382
\(568\) 30.9072 1.29684
\(569\) 28.5846 1.19833 0.599164 0.800626i \(-0.295500\pi\)
0.599164 + 0.800626i \(0.295500\pi\)
\(570\) 2.17579 0.0911337
\(571\) −27.9481 −1.16959 −0.584797 0.811180i \(-0.698826\pi\)
−0.584797 + 0.811180i \(0.698826\pi\)
\(572\) 0.232386 0.00971656
\(573\) 23.7512 0.992219
\(574\) 25.5602 1.06686
\(575\) −41.7610 −1.74156
\(576\) 8.86696 0.369457
\(577\) 32.3210 1.34554 0.672770 0.739852i \(-0.265104\pi\)
0.672770 + 0.739852i \(0.265104\pi\)
\(578\) −1.28460 −0.0534324
\(579\) 15.1485 0.629549
\(580\) 0.942351 0.0391290
\(581\) 0.778469 0.0322963
\(582\) 23.9268 0.991796
\(583\) −16.1241 −0.667790
\(584\) −2.10100 −0.0869402
\(585\) 0.243693 0.0100755
\(586\) −8.26336 −0.341356
\(587\) 11.0951 0.457945 0.228972 0.973433i \(-0.426463\pi\)
0.228972 + 0.973433i \(0.426463\pi\)
\(588\) −1.14286 −0.0471310
\(589\) −5.67641 −0.233892
\(590\) −8.79216 −0.361968
\(591\) 10.6745 0.439091
\(592\) −27.5048 −1.13044
\(593\) −18.8893 −0.775692 −0.387846 0.921724i \(-0.626781\pi\)
−0.387846 + 0.921724i \(0.626781\pi\)
\(594\) 2.03372 0.0834447
\(595\) 1.12200 0.0459974
\(596\) −4.31857 −0.176896
\(597\) −9.56418 −0.391436
\(598\) 4.82798 0.197431
\(599\) −36.1983 −1.47902 −0.739510 0.673145i \(-0.764943\pi\)
−0.739510 + 0.673145i \(0.764943\pi\)
\(600\) 14.0748 0.574600
\(601\) −0.160125 −0.00653163 −0.00326582 0.999995i \(-0.501040\pi\)
−0.00326582 + 0.999995i \(0.501040\pi\)
\(602\) −2.57015 −0.104751
\(603\) −5.25076 −0.213827
\(604\) −6.96246 −0.283299
\(605\) 4.93250 0.200535
\(606\) 22.5531 0.916158
\(607\) 43.5689 1.76841 0.884204 0.467102i \(-0.154702\pi\)
0.884204 + 0.467102i \(0.154702\pi\)
\(608\) 5.70072 0.231195
\(609\) 8.96266 0.363185
\(610\) −2.35532 −0.0953641
\(611\) −3.32724 −0.134606
\(612\) −0.349799 −0.0141398
\(613\) 39.9136 1.61209 0.806047 0.591851i \(-0.201603\pi\)
0.806047 + 0.591851i \(0.201603\pi\)
\(614\) −23.8812 −0.963768
\(615\) 5.98072 0.241166
\(616\) −9.23294 −0.372006
\(617\) 22.0134 0.886224 0.443112 0.896466i \(-0.353874\pi\)
0.443112 + 0.896466i \(0.353874\pi\)
\(618\) −5.64616 −0.227122
\(619\) 0.629398 0.0252976 0.0126488 0.999920i \(-0.495974\pi\)
0.0126488 + 0.999920i \(0.495974\pi\)
\(620\) 0.395360 0.0158780
\(621\) −8.95631 −0.359404
\(622\) 12.8671 0.515924
\(623\) −5.94694 −0.238259
\(624\) −1.33361 −0.0533871
\(625\) 20.0550 0.802201
\(626\) 39.6283 1.58386
\(627\) 4.61740 0.184401
\(628\) 0.349799 0.0139585
\(629\) 8.65463 0.345083
\(630\) −1.44132 −0.0574235
\(631\) 30.9936 1.23384 0.616919 0.787027i \(-0.288381\pi\)
0.616919 + 0.787027i \(0.288381\pi\)
\(632\) −13.2364 −0.526517
\(633\) −21.5889 −0.858083
\(634\) −39.4500 −1.56676
\(635\) 4.82639 0.191529
\(636\) −3.56261 −0.141267
\(637\) 1.37102 0.0543219
\(638\) −9.43435 −0.373510
\(639\) 10.2391 0.405052
\(640\) 4.34463 0.171737
\(641\) −1.27589 −0.0503946 −0.0251973 0.999682i \(-0.508021\pi\)
−0.0251973 + 0.999682i \(0.508021\pi\)
\(642\) 3.29652 0.130103
\(643\) −17.5334 −0.691451 −0.345725 0.938336i \(-0.612367\pi\)
−0.345725 + 0.938336i \(0.612367\pi\)
\(644\) 6.05291 0.238518
\(645\) −0.601377 −0.0236792
\(646\) 3.74664 0.147410
\(647\) 40.3844 1.58767 0.793837 0.608131i \(-0.208080\pi\)
0.793837 + 0.608131i \(0.208080\pi\)
\(648\) 3.01856 0.118580
\(649\) −18.6585 −0.732410
\(650\) −2.51350 −0.0985877
\(651\) 3.76025 0.147376
\(652\) 7.84661 0.307297
\(653\) −2.29700 −0.0898887 −0.0449444 0.998989i \(-0.514311\pi\)
−0.0449444 + 0.998989i \(0.514311\pi\)
\(654\) 6.49821 0.254100
\(655\) 0.407301 0.0159146
\(656\) −32.7295 −1.27787
\(657\) −0.696030 −0.0271547
\(658\) 19.6789 0.767163
\(659\) −10.5022 −0.409108 −0.204554 0.978855i \(-0.565574\pi\)
−0.204554 + 0.978855i \(0.565574\pi\)
\(660\) −0.321600 −0.0125183
\(661\) −22.8718 −0.889611 −0.444805 0.895627i \(-0.646727\pi\)
−0.444805 + 0.895627i \(0.646727\pi\)
\(662\) −9.47741 −0.368350
\(663\) 0.419632 0.0162972
\(664\) −1.21625 −0.0471997
\(665\) −3.27239 −0.126898
\(666\) −11.1177 −0.430804
\(667\) 41.5479 1.60874
\(668\) −1.17021 −0.0452767
\(669\) −29.2522 −1.13095
\(670\) −3.91710 −0.151331
\(671\) −4.99840 −0.192961
\(672\) −3.77636 −0.145676
\(673\) 21.1862 0.816667 0.408333 0.912833i \(-0.366110\pi\)
0.408333 + 0.912833i \(0.366110\pi\)
\(674\) −30.2987 −1.16706
\(675\) 4.66275 0.179469
\(676\) 4.48579 0.172530
\(677\) 32.2338 1.23885 0.619423 0.785057i \(-0.287367\pi\)
0.619423 + 0.785057i \(0.287367\pi\)
\(678\) 1.15949 0.0445300
\(679\) −35.9859 −1.38101
\(680\) −1.75297 −0.0672232
\(681\) 18.6000 0.712753
\(682\) −3.95815 −0.151565
\(683\) −1.30901 −0.0500878 −0.0250439 0.999686i \(-0.507973\pi\)
−0.0250439 + 0.999686i \(0.507973\pi\)
\(684\) 1.02022 0.0390089
\(685\) 10.4320 0.398588
\(686\) −25.4822 −0.972917
\(687\) 17.4519 0.665832
\(688\) 3.29103 0.125470
\(689\) 4.27385 0.162821
\(690\) −6.68147 −0.254359
\(691\) −16.2990 −0.620044 −0.310022 0.950729i \(-0.600336\pi\)
−0.310022 + 0.950729i \(0.600336\pi\)
\(692\) 5.16208 0.196233
\(693\) −3.05873 −0.116191
\(694\) 10.2675 0.389748
\(695\) 3.93412 0.149230
\(696\) −14.0029 −0.530780
\(697\) 10.2986 0.390088
\(698\) −2.92923 −0.110873
\(699\) −16.3122 −0.616985
\(700\) −3.15121 −0.119105
\(701\) −27.0494 −1.02164 −0.510822 0.859687i \(-0.670659\pi\)
−0.510822 + 0.859687i \(0.670659\pi\)
\(702\) −0.539060 −0.0203455
\(703\) −25.2419 −0.952017
\(704\) 14.0378 0.529069
\(705\) 4.60458 0.173418
\(706\) −20.0960 −0.756323
\(707\) −33.9199 −1.27569
\(708\) −4.12260 −0.154937
\(709\) 35.3361 1.32708 0.663538 0.748143i \(-0.269054\pi\)
0.663538 + 0.748143i \(0.269054\pi\)
\(710\) 7.63842 0.286665
\(711\) −4.38503 −0.164451
\(712\) 9.29128 0.348205
\(713\) 17.4313 0.652806
\(714\) −2.48191 −0.0928830
\(715\) 0.385804 0.0144282
\(716\) 5.84571 0.218464
\(717\) 10.4899 0.391752
\(718\) −47.5646 −1.77509
\(719\) −12.0611 −0.449802 −0.224901 0.974382i \(-0.572206\pi\)
−0.224901 + 0.974382i \(0.572206\pi\)
\(720\) 1.84559 0.0687809
\(721\) 8.49184 0.316253
\(722\) 13.4800 0.501675
\(723\) −3.20071 −0.119036
\(724\) 0.136825 0.00508505
\(725\) −21.6303 −0.803329
\(726\) −10.9109 −0.404942
\(727\) −30.9749 −1.14880 −0.574399 0.818576i \(-0.694764\pi\)
−0.574399 + 0.818576i \(0.694764\pi\)
\(728\) 2.44729 0.0907024
\(729\) 1.00000 0.0370370
\(730\) −0.519243 −0.0192180
\(731\) −1.03555 −0.0383013
\(732\) −1.10440 −0.0408197
\(733\) −11.5014 −0.424814 −0.212407 0.977181i \(-0.568130\pi\)
−0.212407 + 0.977181i \(0.568130\pi\)
\(734\) −7.76373 −0.286565
\(735\) −1.89737 −0.0699854
\(736\) −17.5059 −0.645277
\(737\) −8.31277 −0.306205
\(738\) −13.2296 −0.486989
\(739\) −44.0418 −1.62010 −0.810052 0.586358i \(-0.800561\pi\)
−0.810052 + 0.586358i \(0.800561\pi\)
\(740\) 1.75809 0.0646287
\(741\) −1.22389 −0.0449607
\(742\) −25.2776 −0.927970
\(743\) 42.9094 1.57419 0.787096 0.616830i \(-0.211583\pi\)
0.787096 + 0.616830i \(0.211583\pi\)
\(744\) −5.87488 −0.215384
\(745\) −7.16962 −0.262675
\(746\) 42.8661 1.56944
\(747\) −0.402925 −0.0147423
\(748\) −0.553786 −0.0202484
\(749\) −4.95798 −0.181160
\(750\) 7.20848 0.263216
\(751\) −2.33818 −0.0853215 −0.0426607 0.999090i \(-0.513583\pi\)
−0.0426607 + 0.999090i \(0.513583\pi\)
\(752\) −25.1985 −0.918896
\(753\) 9.17030 0.334184
\(754\) 2.50067 0.0910691
\(755\) −11.5590 −0.420674
\(756\) −0.675827 −0.0245796
\(757\) 31.0994 1.13033 0.565164 0.824979i \(-0.308813\pi\)
0.565164 + 0.824979i \(0.308813\pi\)
\(758\) −5.76855 −0.209523
\(759\) −14.1792 −0.514673
\(760\) 5.11267 0.185456
\(761\) −3.11941 −0.113079 −0.0565393 0.998400i \(-0.518007\pi\)
−0.0565393 + 0.998400i \(0.518007\pi\)
\(762\) −10.6762 −0.386758
\(763\) −9.77332 −0.353818
\(764\) 8.30812 0.300577
\(765\) −0.580730 −0.0209963
\(766\) 40.6512 1.46879
\(767\) 4.94563 0.178576
\(768\) 8.12339 0.293128
\(769\) −3.95661 −0.142679 −0.0713396 0.997452i \(-0.522727\pi\)
−0.0713396 + 0.997452i \(0.522727\pi\)
\(770\) −2.28183 −0.0822315
\(771\) −17.5100 −0.630607
\(772\) 5.29892 0.190712
\(773\) 11.8318 0.425560 0.212780 0.977100i \(-0.431748\pi\)
0.212780 + 0.977100i \(0.431748\pi\)
\(774\) 1.33027 0.0478157
\(775\) −9.07491 −0.325980
\(776\) 56.2231 2.01829
\(777\) 16.7211 0.599867
\(778\) 28.0338 1.00506
\(779\) −30.0368 −1.07618
\(780\) 0.0852435 0.00305221
\(781\) 16.2101 0.580041
\(782\) −11.5053 −0.411428
\(783\) −4.63895 −0.165783
\(784\) 10.3833 0.370833
\(785\) 0.580730 0.0207271
\(786\) −0.900969 −0.0321365
\(787\) 31.3642 1.11801 0.559007 0.829163i \(-0.311183\pi\)
0.559007 + 0.829163i \(0.311183\pi\)
\(788\) 3.73393 0.133016
\(789\) −14.3398 −0.510509
\(790\) −3.27126 −0.116386
\(791\) −1.74388 −0.0620051
\(792\) 4.77884 0.169809
\(793\) 1.32488 0.0470478
\(794\) −3.85566 −0.136832
\(795\) −5.91459 −0.209769
\(796\) −3.34554 −0.118579
\(797\) 24.4835 0.867250 0.433625 0.901093i \(-0.357234\pi\)
0.433625 + 0.901093i \(0.357234\pi\)
\(798\) 7.23868 0.256246
\(799\) 7.92894 0.280506
\(800\) 9.11378 0.322221
\(801\) 3.07805 0.108758
\(802\) −11.5218 −0.406848
\(803\) −1.10192 −0.0388860
\(804\) −1.83671 −0.0647757
\(805\) 10.0489 0.354179
\(806\) 1.04915 0.0369547
\(807\) −5.81592 −0.204730
\(808\) 52.9953 1.86437
\(809\) −18.3096 −0.643731 −0.321866 0.946785i \(-0.604310\pi\)
−0.321866 + 0.946785i \(0.604310\pi\)
\(810\) 0.746007 0.0262120
\(811\) −38.1005 −1.33789 −0.668945 0.743312i \(-0.733254\pi\)
−0.668945 + 0.743312i \(0.733254\pi\)
\(812\) 3.13513 0.110021
\(813\) −4.72990 −0.165885
\(814\) −17.6011 −0.616919
\(815\) 13.0268 0.456309
\(816\) 3.17804 0.111254
\(817\) 3.02027 0.105666
\(818\) 7.55801 0.264260
\(819\) 0.810747 0.0283298
\(820\) 2.09205 0.0730575
\(821\) 16.7676 0.585195 0.292597 0.956236i \(-0.405480\pi\)
0.292597 + 0.956236i \(0.405480\pi\)
\(822\) −23.0762 −0.804873
\(823\) −2.29394 −0.0799617 −0.0399809 0.999200i \(-0.512730\pi\)
−0.0399809 + 0.999200i \(0.512730\pi\)
\(824\) −13.2673 −0.462190
\(825\) 7.38186 0.257004
\(826\) −29.2508 −1.01777
\(827\) 20.3470 0.707534 0.353767 0.935334i \(-0.384901\pi\)
0.353767 + 0.935334i \(0.384901\pi\)
\(828\) −3.13291 −0.108876
\(829\) 11.8751 0.412439 0.206220 0.978506i \(-0.433884\pi\)
0.206220 + 0.978506i \(0.433884\pi\)
\(830\) −0.300585 −0.0104335
\(831\) 9.62977 0.334053
\(832\) −3.72086 −0.128998
\(833\) −3.26721 −0.113202
\(834\) −8.70245 −0.301341
\(835\) −1.94276 −0.0672320
\(836\) 1.61516 0.0558615
\(837\) −1.94626 −0.0672724
\(838\) −20.0017 −0.690949
\(839\) −35.7098 −1.23284 −0.616420 0.787418i \(-0.711417\pi\)
−0.616420 + 0.787418i \(0.711417\pi\)
\(840\) −3.38681 −0.116856
\(841\) −7.48012 −0.257935
\(842\) −9.74744 −0.335919
\(843\) 23.3377 0.803793
\(844\) −7.55178 −0.259943
\(845\) 7.44723 0.256193
\(846\) −10.1855 −0.350186
\(847\) 16.4100 0.563856
\(848\) 32.3676 1.11151
\(849\) −10.3845 −0.356393
\(850\) 5.98978 0.205448
\(851\) 77.5135 2.65713
\(852\) 3.58162 0.122704
\(853\) 1.39229 0.0476712 0.0238356 0.999716i \(-0.492412\pi\)
0.0238356 + 0.999716i \(0.492412\pi\)
\(854\) −7.83597 −0.268141
\(855\) 1.69375 0.0579249
\(856\) 7.74616 0.264758
\(857\) −36.6477 −1.25186 −0.625932 0.779878i \(-0.715281\pi\)
−0.625932 + 0.779878i \(0.715281\pi\)
\(858\) −0.853416 −0.0291351
\(859\) −2.53062 −0.0863436 −0.0431718 0.999068i \(-0.513746\pi\)
−0.0431718 + 0.999068i \(0.513746\pi\)
\(860\) −0.210361 −0.00717325
\(861\) 19.8974 0.678101
\(862\) −22.4607 −0.765016
\(863\) 1.06128 0.0361264 0.0180632 0.999837i \(-0.494250\pi\)
0.0180632 + 0.999837i \(0.494250\pi\)
\(864\) 1.95459 0.0664965
\(865\) 8.56999 0.291389
\(866\) −9.75231 −0.331397
\(867\) −1.00000 −0.0339618
\(868\) 1.31533 0.0446453
\(869\) −6.94218 −0.235497
\(870\) −3.46069 −0.117328
\(871\) 2.20338 0.0746588
\(872\) 15.2695 0.517090
\(873\) 18.6258 0.630388
\(874\) 33.5561 1.13505
\(875\) −10.8416 −0.366512
\(876\) −0.243470 −0.00822610
\(877\) 25.1578 0.849517 0.424759 0.905307i \(-0.360359\pi\)
0.424759 + 0.905307i \(0.360359\pi\)
\(878\) −10.3918 −0.350707
\(879\) −6.43263 −0.216967
\(880\) 2.92185 0.0984955
\(881\) −15.5299 −0.523216 −0.261608 0.965174i \(-0.584253\pi\)
−0.261608 + 0.965174i \(0.584253\pi\)
\(882\) 4.19706 0.141322
\(883\) −22.0705 −0.742730 −0.371365 0.928487i \(-0.621110\pi\)
−0.371365 + 0.928487i \(0.621110\pi\)
\(884\) 0.146787 0.00493697
\(885\) −6.84427 −0.230068
\(886\) 20.4933 0.688485
\(887\) −35.8404 −1.20340 −0.601701 0.798721i \(-0.705510\pi\)
−0.601701 + 0.798721i \(0.705510\pi\)
\(888\) −26.1245 −0.876680
\(889\) 16.0570 0.538535
\(890\) 2.29625 0.0769705
\(891\) 1.58316 0.0530377
\(892\) −10.2324 −0.342605
\(893\) −23.1254 −0.773862
\(894\) 15.8595 0.530422
\(895\) 9.70494 0.324400
\(896\) 14.4542 0.482883
\(897\) 3.75835 0.125488
\(898\) −48.8758 −1.63101
\(899\) 9.02859 0.301120
\(900\) 1.63103 0.0543675
\(901\) −10.1848 −0.339303
\(902\) −20.9446 −0.697378
\(903\) −2.00074 −0.0665803
\(904\) 2.72457 0.0906179
\(905\) 0.227154 0.00755085
\(906\) 25.5690 0.849472
\(907\) 48.3005 1.60379 0.801896 0.597464i \(-0.203825\pi\)
0.801896 + 0.597464i \(0.203825\pi\)
\(908\) 6.50625 0.215917
\(909\) 17.5565 0.582313
\(910\) 0.604823 0.0200497
\(911\) 16.5488 0.548287 0.274144 0.961689i \(-0.411606\pi\)
0.274144 + 0.961689i \(0.411606\pi\)
\(912\) −9.26902 −0.306928
\(913\) −0.637893 −0.0211112
\(914\) −29.9826 −0.991736
\(915\) −1.83350 −0.0606137
\(916\) 6.10466 0.201704
\(917\) 1.35506 0.0447480
\(918\) 1.28460 0.0423982
\(919\) −18.0335 −0.594870 −0.297435 0.954742i \(-0.596131\pi\)
−0.297435 + 0.954742i \(0.596131\pi\)
\(920\) −15.7001 −0.517617
\(921\) −18.5904 −0.612574
\(922\) 24.5697 0.809159
\(923\) −4.29664 −0.141426
\(924\) −1.06994 −0.0351984
\(925\) −40.3544 −1.32684
\(926\) 25.3389 0.832688
\(927\) −4.39526 −0.144359
\(928\) −9.06726 −0.297647
\(929\) −51.8467 −1.70104 −0.850518 0.525946i \(-0.823711\pi\)
−0.850518 + 0.525946i \(0.823711\pi\)
\(930\) −1.45192 −0.0476103
\(931\) 9.52907 0.312303
\(932\) −5.70600 −0.186906
\(933\) 10.0164 0.327923
\(934\) −28.8135 −0.942807
\(935\) −0.919386 −0.0300672
\(936\) −1.26668 −0.0414028
\(937\) −11.6436 −0.380381 −0.190190 0.981747i \(-0.560911\pi\)
−0.190190 + 0.981747i \(0.560911\pi\)
\(938\) −13.0319 −0.425506
\(939\) 30.8487 1.00671
\(940\) 1.61068 0.0525344
\(941\) −12.3134 −0.401406 −0.200703 0.979652i \(-0.564323\pi\)
−0.200703 + 0.979652i \(0.564323\pi\)
\(942\) −1.28460 −0.0418546
\(943\) 92.2376 3.00367
\(944\) 37.4552 1.21906
\(945\) −1.12200 −0.0364985
\(946\) 2.10603 0.0684730
\(947\) 20.8079 0.676166 0.338083 0.941116i \(-0.390222\pi\)
0.338083 + 0.941116i \(0.390222\pi\)
\(948\) −1.53388 −0.0498180
\(949\) 0.292076 0.00948120
\(950\) −17.4697 −0.566791
\(951\) −30.7099 −0.995838
\(952\) −5.83198 −0.189016
\(953\) −12.1442 −0.393389 −0.196694 0.980465i \(-0.563021\pi\)
−0.196694 + 0.980465i \(0.563021\pi\)
\(954\) 13.0833 0.423589
\(955\) 13.7930 0.446331
\(956\) 3.66935 0.118675
\(957\) −7.34419 −0.237404
\(958\) −1.11990 −0.0361822
\(959\) 34.7066 1.12073
\(960\) 5.14931 0.166193
\(961\) −27.2121 −0.877809
\(962\) 4.66536 0.150417
\(963\) 2.56618 0.0826940
\(964\) −1.11960 −0.0360600
\(965\) 8.79718 0.283191
\(966\) −22.2287 −0.715197
\(967\) 44.4464 1.42930 0.714649 0.699483i \(-0.246586\pi\)
0.714649 + 0.699483i \(0.246586\pi\)
\(968\) −25.6385 −0.824051
\(969\) 2.91658 0.0936940
\(970\) 13.8950 0.446141
\(971\) −26.0163 −0.834904 −0.417452 0.908699i \(-0.637077\pi\)
−0.417452 + 0.908699i \(0.637077\pi\)
\(972\) 0.349799 0.0112198
\(973\) 13.0885 0.419598
\(974\) −18.2606 −0.585109
\(975\) −1.95664 −0.0626626
\(976\) 10.0338 0.321175
\(977\) −1.97570 −0.0632084 −0.0316042 0.999500i \(-0.510062\pi\)
−0.0316042 + 0.999500i \(0.510062\pi\)
\(978\) −28.8159 −0.921431
\(979\) 4.87304 0.155743
\(980\) −0.663696 −0.0212010
\(981\) 5.05854 0.161507
\(982\) −1.81687 −0.0579785
\(983\) −12.8906 −0.411148 −0.205574 0.978642i \(-0.565906\pi\)
−0.205574 + 0.978642i \(0.565906\pi\)
\(984\) −31.0870 −0.991016
\(985\) 6.19902 0.197517
\(986\) −5.95921 −0.189780
\(987\) 15.3191 0.487611
\(988\) −0.428115 −0.0136202
\(989\) −9.27474 −0.294919
\(990\) 1.18105 0.0375361
\(991\) 12.7498 0.405011 0.202506 0.979281i \(-0.435092\pi\)
0.202506 + 0.979281i \(0.435092\pi\)
\(992\) −3.80413 −0.120781
\(993\) −7.37770 −0.234124
\(994\) 25.4124 0.806033
\(995\) −5.55421 −0.176080
\(996\) −0.140943 −0.00446594
\(997\) 33.3101 1.05494 0.527470 0.849573i \(-0.323141\pi\)
0.527470 + 0.849573i \(0.323141\pi\)
\(998\) 14.5350 0.460097
\(999\) −8.65463 −0.273820
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 \(a_p\))