Properties

Label 8041.2.a.j.1.16
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 0
Dimension 82
CM No

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Newspace parameters

Level: \( N \) = \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(0\)
Dimension: \(82\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.88314 q^{2}\) \(-1.39410 q^{3}\) \(+1.54622 q^{4}\) \(-3.71860 q^{5}\) \(+2.62529 q^{6}\) \(+0.268017 q^{7}\) \(+0.854526 q^{8}\) \(-1.05649 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.88314 q^{2}\) \(-1.39410 q^{3}\) \(+1.54622 q^{4}\) \(-3.71860 q^{5}\) \(+2.62529 q^{6}\) \(+0.268017 q^{7}\) \(+0.854526 q^{8}\) \(-1.05649 q^{9}\) \(+7.00266 q^{10}\) \(+1.00000 q^{11}\) \(-2.15559 q^{12}\) \(+4.11678 q^{13}\) \(-0.504714 q^{14}\) \(+5.18410 q^{15}\) \(-4.70164 q^{16}\) \(+1.00000 q^{17}\) \(+1.98952 q^{18}\) \(-7.20890 q^{19}\) \(-5.74979 q^{20}\) \(-0.373642 q^{21}\) \(-1.88314 q^{22}\) \(+5.54871 q^{23}\) \(-1.19129 q^{24}\) \(+8.82800 q^{25}\) \(-7.75249 q^{26}\) \(+5.65515 q^{27}\) \(+0.414414 q^{28}\) \(+4.02113 q^{29}\) \(-9.76239 q^{30}\) \(+9.00678 q^{31}\) \(+7.14480 q^{32}\) \(-1.39410 q^{33}\) \(-1.88314 q^{34}\) \(-0.996648 q^{35}\) \(-1.63357 q^{36}\) \(+11.9900 q^{37}\) \(+13.5754 q^{38}\) \(-5.73920 q^{39}\) \(-3.17764 q^{40}\) \(-2.01260 q^{41}\) \(+0.703620 q^{42}\) \(+1.00000 q^{43}\) \(+1.54622 q^{44}\) \(+3.92866 q^{45}\) \(-10.4490 q^{46}\) \(-2.88297 q^{47}\) \(+6.55455 q^{48}\) \(-6.92817 q^{49}\) \(-16.6244 q^{50}\) \(-1.39410 q^{51}\) \(+6.36547 q^{52}\) \(+8.83666 q^{53}\) \(-10.6494 q^{54}\) \(-3.71860 q^{55}\) \(+0.229027 q^{56}\) \(+10.0499 q^{57}\) \(-7.57236 q^{58}\) \(+6.16726 q^{59}\) \(+8.01577 q^{60}\) \(+4.31404 q^{61}\) \(-16.9610 q^{62}\) \(-0.283157 q^{63}\) \(-4.05140 q^{64}\) \(-15.3087 q^{65}\) \(+2.62529 q^{66}\) \(-7.87681 q^{67}\) \(+1.54622 q^{68}\) \(-7.73545 q^{69}\) \(+1.87683 q^{70}\) \(+10.3270 q^{71}\) \(-0.902798 q^{72}\) \(+1.50125 q^{73}\) \(-22.5788 q^{74}\) \(-12.3071 q^{75}\) \(-11.1466 q^{76}\) \(+0.268017 q^{77}\) \(+10.8077 q^{78}\) \(-7.38185 q^{79}\) \(+17.4835 q^{80}\) \(-4.71436 q^{81}\) \(+3.79001 q^{82}\) \(+15.0476 q^{83}\) \(-0.577733 q^{84}\) \(-3.71860 q^{85}\) \(-1.88314 q^{86}\) \(-5.60585 q^{87}\) \(+0.854526 q^{88}\) \(-18.5244 q^{89}\) \(-7.39823 q^{90}\) \(+1.10337 q^{91}\) \(+8.57954 q^{92}\) \(-12.5563 q^{93}\) \(+5.42905 q^{94}\) \(+26.8070 q^{95}\) \(-9.96056 q^{96}\) \(+11.0659 q^{97}\) \(+13.0467 q^{98}\) \(-1.05649 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(82q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(82q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut +\mathstrut 82q^{11} \) \(\mathstrut +\mathstrut 3q^{12} \) \(\mathstrut +\mathstrut 26q^{13} \) \(\mathstrut +\mathstrut 17q^{14} \) \(\mathstrut +\mathstrut 66q^{15} \) \(\mathstrut +\mathstrut 122q^{16} \) \(\mathstrut +\mathstrut 82q^{17} \) \(\mathstrut +\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 9q^{20} \) \(\mathstrut +\mathstrut 22q^{21} \) \(\mathstrut +\mathstrut 8q^{22} \) \(\mathstrut +\mathstrut 50q^{23} \) \(\mathstrut +\mathstrut 15q^{24} \) \(\mathstrut +\mathstrut 117q^{25} \) \(\mathstrut +\mathstrut 36q^{26} \) \(\mathstrut +\mathstrut 30q^{27} \) \(\mathstrut +\mathstrut 11q^{28} \) \(\mathstrut +\mathstrut 33q^{29} \) \(\mathstrut -\mathstrut 26q^{30} \) \(\mathstrut +\mathstrut 40q^{31} \) \(\mathstrut +\mathstrut 58q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 16q^{35} \) \(\mathstrut +\mathstrut 160q^{36} \) \(\mathstrut +\mathstrut 31q^{37} \) \(\mathstrut +\mathstrut 18q^{38} \) \(\mathstrut +\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 29q^{40} \) \(\mathstrut +\mathstrut 42q^{41} \) \(\mathstrut -\mathstrut 51q^{42} \) \(\mathstrut +\mathstrut 82q^{43} \) \(\mathstrut +\mathstrut 98q^{44} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 19q^{46} \) \(\mathstrut +\mathstrut 84q^{47} \) \(\mathstrut -\mathstrut 46q^{48} \) \(\mathstrut +\mathstrut 136q^{49} \) \(\mathstrut +\mathstrut 59q^{50} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 45q^{52} \) \(\mathstrut +\mathstrut 83q^{53} \) \(\mathstrut +\mathstrut 24q^{54} \) \(\mathstrut +\mathstrut 11q^{55} \) \(\mathstrut +\mathstrut 21q^{56} \) \(\mathstrut +\mathstrut 23q^{57} \) \(\mathstrut +\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 96q^{59} \) \(\mathstrut +\mathstrut 184q^{60} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut -\mathstrut 23q^{62} \) \(\mathstrut +\mathstrut 8q^{63} \) \(\mathstrut +\mathstrut 148q^{64} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut +\mathstrut 10q^{66} \) \(\mathstrut +\mathstrut 78q^{67} \) \(\mathstrut +\mathstrut 98q^{68} \) \(\mathstrut +\mathstrut 61q^{69} \) \(\mathstrut -\mathstrut 3q^{70} \) \(\mathstrut +\mathstrut 155q^{71} \) \(\mathstrut +\mathstrut 50q^{72} \) \(\mathstrut -\mathstrut 23q^{73} \) \(\mathstrut +\mathstrut 10q^{74} \) \(\mathstrut -\mathstrut 19q^{75} \) \(\mathstrut +\mathstrut 44q^{76} \) \(\mathstrut +\mathstrut 8q^{77} \) \(\mathstrut -\mathstrut 27q^{78} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut +\mathstrut 19q^{80} \) \(\mathstrut +\mathstrut 150q^{81} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 54q^{83} \) \(\mathstrut +\mathstrut 8q^{84} \) \(\mathstrut +\mathstrut 11q^{85} \) \(\mathstrut +\mathstrut 8q^{86} \) \(\mathstrut +\mathstrut 20q^{87} \) \(\mathstrut +\mathstrut 30q^{88} \) \(\mathstrut +\mathstrut 25q^{89} \) \(\mathstrut -\mathstrut 81q^{90} \) \(\mathstrut -\mathstrut 14q^{91} \) \(\mathstrut +\mathstrut 60q^{92} \) \(\mathstrut +\mathstrut 36q^{93} \) \(\mathstrut +\mathstrut 19q^{94} \) \(\mathstrut +\mathstrut 111q^{95} \) \(\mathstrut -\mathstrut 6q^{96} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 5q^{98} \) \(\mathstrut +\mathstrut 108q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.88314 −1.33158 −0.665791 0.746138i \(-0.731906\pi\)
−0.665791 + 0.746138i \(0.731906\pi\)
\(3\) −1.39410 −0.804883 −0.402442 0.915446i \(-0.631838\pi\)
−0.402442 + 0.915446i \(0.631838\pi\)
\(4\) 1.54622 0.773112
\(5\) −3.71860 −1.66301 −0.831505 0.555518i \(-0.812520\pi\)
−0.831505 + 0.555518i \(0.812520\pi\)
\(6\) 2.62529 1.07177
\(7\) 0.268017 0.101301 0.0506504 0.998716i \(-0.483871\pi\)
0.0506504 + 0.998716i \(0.483871\pi\)
\(8\) 0.854526 0.302121
\(9\) −1.05649 −0.352163
\(10\) 7.00266 2.21443
\(11\) 1.00000 0.301511
\(12\) −2.15559 −0.622264
\(13\) 4.11678 1.14179 0.570895 0.821023i \(-0.306596\pi\)
0.570895 + 0.821023i \(0.306596\pi\)
\(14\) −0.504714 −0.134890
\(15\) 5.18410 1.33853
\(16\) −4.70164 −1.17541
\(17\) 1.00000 0.242536
\(18\) 1.98952 0.468934
\(19\) −7.20890 −1.65384 −0.826918 0.562323i \(-0.809908\pi\)
−0.826918 + 0.562323i \(0.809908\pi\)
\(20\) −5.74979 −1.28569
\(21\) −0.373642 −0.0815353
\(22\) −1.88314 −0.401487
\(23\) 5.54871 1.15699 0.578493 0.815687i \(-0.303641\pi\)
0.578493 + 0.815687i \(0.303641\pi\)
\(24\) −1.19129 −0.243172
\(25\) 8.82800 1.76560
\(26\) −7.75249 −1.52039
\(27\) 5.65515 1.08833
\(28\) 0.414414 0.0783168
\(29\) 4.02113 0.746705 0.373353 0.927689i \(-0.378208\pi\)
0.373353 + 0.927689i \(0.378208\pi\)
\(30\) −9.76239 −1.78236
\(31\) 9.00678 1.61766 0.808832 0.588039i \(-0.200100\pi\)
0.808832 + 0.588039i \(0.200100\pi\)
\(32\) 7.14480 1.26303
\(33\) −1.39410 −0.242681
\(34\) −1.88314 −0.322956
\(35\) −0.996648 −0.168464
\(36\) −1.63357 −0.272261
\(37\) 11.9900 1.97114 0.985568 0.169279i \(-0.0541438\pi\)
0.985568 + 0.169279i \(0.0541438\pi\)
\(38\) 13.5754 2.20222
\(39\) −5.73920 −0.919008
\(40\) −3.17764 −0.502430
\(41\) −2.01260 −0.314315 −0.157158 0.987574i \(-0.550233\pi\)
−0.157158 + 0.987574i \(0.550233\pi\)
\(42\) 0.703620 0.108571
\(43\) 1.00000 0.152499
\(44\) 1.54622 0.233102
\(45\) 3.92866 0.585650
\(46\) −10.4490 −1.54062
\(47\) −2.88297 −0.420525 −0.210263 0.977645i \(-0.567432\pi\)
−0.210263 + 0.977645i \(0.567432\pi\)
\(48\) 6.55455 0.946068
\(49\) −6.92817 −0.989738
\(50\) −16.6244 −2.35104
\(51\) −1.39410 −0.195213
\(52\) 6.36547 0.882731
\(53\) 8.83666 1.21381 0.606904 0.794775i \(-0.292411\pi\)
0.606904 + 0.794775i \(0.292411\pi\)
\(54\) −10.6494 −1.44921
\(55\) −3.71860 −0.501416
\(56\) 0.229027 0.0306051
\(57\) 10.0499 1.33114
\(58\) −7.57236 −0.994300
\(59\) 6.16726 0.802909 0.401454 0.915879i \(-0.368505\pi\)
0.401454 + 0.915879i \(0.368505\pi\)
\(60\) 8.01577 1.03483
\(61\) 4.31404 0.552357 0.276178 0.961106i \(-0.410932\pi\)
0.276178 + 0.961106i \(0.410932\pi\)
\(62\) −16.9610 −2.15405
\(63\) −0.283157 −0.0356744
\(64\) −4.05140 −0.506425
\(65\) −15.3087 −1.89881
\(66\) 2.62529 0.323150
\(67\) −7.87681 −0.962305 −0.481153 0.876637i \(-0.659782\pi\)
−0.481153 + 0.876637i \(0.659782\pi\)
\(68\) 1.54622 0.187507
\(69\) −7.73545 −0.931239
\(70\) 1.87683 0.224324
\(71\) 10.3270 1.22559 0.612794 0.790243i \(-0.290045\pi\)
0.612794 + 0.790243i \(0.290045\pi\)
\(72\) −0.902798 −0.106396
\(73\) 1.50125 0.175708 0.0878541 0.996133i \(-0.471999\pi\)
0.0878541 + 0.996133i \(0.471999\pi\)
\(74\) −22.5788 −2.62473
\(75\) −12.3071 −1.42110
\(76\) −11.1466 −1.27860
\(77\) 0.268017 0.0305433
\(78\) 10.8077 1.22373
\(79\) −7.38185 −0.830523 −0.415262 0.909702i \(-0.636310\pi\)
−0.415262 + 0.909702i \(0.636310\pi\)
\(80\) 17.4835 1.95472
\(81\) −4.71436 −0.523818
\(82\) 3.79001 0.418536
\(83\) 15.0476 1.65169 0.825843 0.563899i \(-0.190699\pi\)
0.825843 + 0.563899i \(0.190699\pi\)
\(84\) −0.577733 −0.0630359
\(85\) −3.71860 −0.403339
\(86\) −1.88314 −0.203064
\(87\) −5.60585 −0.601011
\(88\) 0.854526 0.0910928
\(89\) −18.5244 −1.96359 −0.981793 0.189956i \(-0.939165\pi\)
−0.981793 + 0.189956i \(0.939165\pi\)
\(90\) −7.39823 −0.779842
\(91\) 1.10337 0.115664
\(92\) 8.57954 0.894479
\(93\) −12.5563 −1.30203
\(94\) 5.42905 0.559964
\(95\) 26.8070 2.75034
\(96\) −9.96056 −1.01660
\(97\) 11.0659 1.12357 0.561786 0.827282i \(-0.310114\pi\)
0.561786 + 0.827282i \(0.310114\pi\)
\(98\) 13.0467 1.31792
\(99\) −1.05649 −0.106181
\(100\) 13.6501 1.36501
\(101\) 10.5670 1.05145 0.525727 0.850654i \(-0.323794\pi\)
0.525727 + 0.850654i \(0.323794\pi\)
\(102\) 2.62529 0.259942
\(103\) 11.5580 1.13885 0.569424 0.822044i \(-0.307166\pi\)
0.569424 + 0.822044i \(0.307166\pi\)
\(104\) 3.51790 0.344958
\(105\) 1.38942 0.135594
\(106\) −16.6407 −1.61629
\(107\) 17.6236 1.70374 0.851870 0.523754i \(-0.175469\pi\)
0.851870 + 0.523754i \(0.175469\pi\)
\(108\) 8.74412 0.841403
\(109\) −13.9390 −1.33511 −0.667555 0.744561i \(-0.732659\pi\)
−0.667555 + 0.744561i \(0.732659\pi\)
\(110\) 7.00266 0.667677
\(111\) −16.7152 −1.58653
\(112\) −1.26012 −0.119070
\(113\) 18.6373 1.75325 0.876625 0.481175i \(-0.159790\pi\)
0.876625 + 0.481175i \(0.159790\pi\)
\(114\) −18.9254 −1.77253
\(115\) −20.6334 −1.92408
\(116\) 6.21757 0.577286
\(117\) −4.34934 −0.402096
\(118\) −11.6138 −1.06914
\(119\) 0.268017 0.0245691
\(120\) 4.42995 0.404397
\(121\) 1.00000 0.0909091
\(122\) −8.12396 −0.735508
\(123\) 2.80576 0.252987
\(124\) 13.9265 1.25064
\(125\) −14.2348 −1.27320
\(126\) 0.533224 0.0475034
\(127\) −16.8633 −1.49638 −0.748189 0.663485i \(-0.769076\pi\)
−0.748189 + 0.663485i \(0.769076\pi\)
\(128\) −6.66025 −0.588689
\(129\) −1.39410 −0.122744
\(130\) 28.8284 2.52842
\(131\) 3.99445 0.348997 0.174498 0.984657i \(-0.444170\pi\)
0.174498 + 0.984657i \(0.444170\pi\)
\(132\) −2.15559 −0.187620
\(133\) −1.93211 −0.167535
\(134\) 14.8331 1.28139
\(135\) −21.0292 −1.80991
\(136\) 0.854526 0.0732750
\(137\) 22.0551 1.88429 0.942146 0.335203i \(-0.108805\pi\)
0.942146 + 0.335203i \(0.108805\pi\)
\(138\) 14.5669 1.24002
\(139\) 5.19228 0.440404 0.220202 0.975454i \(-0.429328\pi\)
0.220202 + 0.975454i \(0.429328\pi\)
\(140\) −1.54104 −0.130242
\(141\) 4.01915 0.338474
\(142\) −19.4472 −1.63197
\(143\) 4.11678 0.344263
\(144\) 4.96723 0.413936
\(145\) −14.9530 −1.24178
\(146\) −2.82707 −0.233970
\(147\) 9.65855 0.796624
\(148\) 18.5391 1.52391
\(149\) −12.8961 −1.05649 −0.528245 0.849092i \(-0.677150\pi\)
−0.528245 + 0.849092i \(0.677150\pi\)
\(150\) 23.1760 1.89231
\(151\) −3.84674 −0.313043 −0.156522 0.987675i \(-0.550028\pi\)
−0.156522 + 0.987675i \(0.550028\pi\)
\(152\) −6.16020 −0.499658
\(153\) −1.05649 −0.0854121
\(154\) −0.504714 −0.0406710
\(155\) −33.4926 −2.69019
\(156\) −8.87409 −0.710496
\(157\) −20.6773 −1.65023 −0.825115 0.564964i \(-0.808890\pi\)
−0.825115 + 0.564964i \(0.808890\pi\)
\(158\) 13.9011 1.10591
\(159\) −12.3192 −0.976974
\(160\) −26.5687 −2.10044
\(161\) 1.48715 0.117204
\(162\) 8.87781 0.697507
\(163\) −2.62710 −0.205770 −0.102885 0.994693i \(-0.532807\pi\)
−0.102885 + 0.994693i \(0.532807\pi\)
\(164\) −3.11193 −0.243001
\(165\) 5.18410 0.403581
\(166\) −28.3367 −2.19936
\(167\) 0.863007 0.0667815 0.0333907 0.999442i \(-0.489369\pi\)
0.0333907 + 0.999442i \(0.489369\pi\)
\(168\) −0.319287 −0.0246335
\(169\) 3.94791 0.303685
\(170\) 7.00266 0.537079
\(171\) 7.61613 0.582420
\(172\) 1.54622 0.117898
\(173\) −12.9176 −0.982109 −0.491055 0.871129i \(-0.663388\pi\)
−0.491055 + 0.871129i \(0.663388\pi\)
\(174\) 10.5566 0.800295
\(175\) 2.36605 0.178857
\(176\) −4.70164 −0.354399
\(177\) −8.59776 −0.646248
\(178\) 34.8841 2.61468
\(179\) 14.3762 1.07453 0.537264 0.843414i \(-0.319458\pi\)
0.537264 + 0.843414i \(0.319458\pi\)
\(180\) 6.07459 0.452773
\(181\) 5.21715 0.387788 0.193894 0.981022i \(-0.437888\pi\)
0.193894 + 0.981022i \(0.437888\pi\)
\(182\) −2.07780 −0.154017
\(183\) −6.01420 −0.444583
\(184\) 4.74152 0.349549
\(185\) −44.5859 −3.27802
\(186\) 23.6454 1.73376
\(187\) 1.00000 0.0731272
\(188\) −4.45772 −0.325113
\(189\) 1.51567 0.110249
\(190\) −50.4814 −3.66231
\(191\) −26.9109 −1.94720 −0.973601 0.228258i \(-0.926697\pi\)
−0.973601 + 0.228258i \(0.926697\pi\)
\(192\) 5.64805 0.407613
\(193\) 9.10495 0.655389 0.327694 0.944784i \(-0.393728\pi\)
0.327694 + 0.944784i \(0.393728\pi\)
\(194\) −20.8387 −1.49613
\(195\) 21.3418 1.52832
\(196\) −10.7125 −0.765178
\(197\) −14.0809 −1.00322 −0.501612 0.865093i \(-0.667259\pi\)
−0.501612 + 0.865093i \(0.667259\pi\)
\(198\) 1.98952 0.141389
\(199\) −20.9912 −1.48803 −0.744015 0.668163i \(-0.767081\pi\)
−0.744015 + 0.668163i \(0.767081\pi\)
\(200\) 7.54376 0.533424
\(201\) 10.9810 0.774543
\(202\) −19.8991 −1.40010
\(203\) 1.07773 0.0756418
\(204\) −2.15559 −0.150921
\(205\) 7.48405 0.522709
\(206\) −21.7654 −1.51647
\(207\) −5.86215 −0.407448
\(208\) −19.3556 −1.34207
\(209\) −7.20890 −0.498650
\(210\) −2.61648 −0.180555
\(211\) −13.3331 −0.917888 −0.458944 0.888465i \(-0.651772\pi\)
−0.458944 + 0.888465i \(0.651772\pi\)
\(212\) 13.6634 0.938409
\(213\) −14.3968 −0.986455
\(214\) −33.1878 −2.26867
\(215\) −3.71860 −0.253607
\(216\) 4.83247 0.328808
\(217\) 2.41397 0.163871
\(218\) 26.2490 1.77781
\(219\) −2.09289 −0.141425
\(220\) −5.74979 −0.387651
\(221\) 4.11678 0.276925
\(222\) 31.4771 2.11260
\(223\) 27.0556 1.81178 0.905890 0.423514i \(-0.139203\pi\)
0.905890 + 0.423514i \(0.139203\pi\)
\(224\) 1.91493 0.127946
\(225\) −9.32669 −0.621779
\(226\) −35.0967 −2.33460
\(227\) −22.8165 −1.51438 −0.757192 0.653192i \(-0.773429\pi\)
−0.757192 + 0.653192i \(0.773429\pi\)
\(228\) 15.5394 1.02912
\(229\) −7.73835 −0.511365 −0.255682 0.966761i \(-0.582300\pi\)
−0.255682 + 0.966761i \(0.582300\pi\)
\(230\) 38.8557 2.56207
\(231\) −0.373642 −0.0245838
\(232\) 3.43616 0.225595
\(233\) −20.7681 −1.36056 −0.680281 0.732951i \(-0.738142\pi\)
−0.680281 + 0.732951i \(0.738142\pi\)
\(234\) 8.19042 0.535424
\(235\) 10.7206 0.699337
\(236\) 9.53596 0.620738
\(237\) 10.2910 0.668474
\(238\) −0.504714 −0.0327157
\(239\) 6.03261 0.390217 0.195109 0.980782i \(-0.437494\pi\)
0.195109 + 0.980782i \(0.437494\pi\)
\(240\) −24.3738 −1.57332
\(241\) 5.25130 0.338266 0.169133 0.985593i \(-0.445903\pi\)
0.169133 + 0.985593i \(0.445903\pi\)
\(242\) −1.88314 −0.121053
\(243\) −10.3932 −0.666721
\(244\) 6.67047 0.427033
\(245\) 25.7631 1.64594
\(246\) −5.28364 −0.336873
\(247\) −29.6775 −1.88833
\(248\) 7.69653 0.488730
\(249\) −20.9778 −1.32942
\(250\) 26.8062 1.69537
\(251\) 29.7444 1.87745 0.938725 0.344668i \(-0.112009\pi\)
0.938725 + 0.344668i \(0.112009\pi\)
\(252\) −0.437824 −0.0275803
\(253\) 5.54871 0.348844
\(254\) 31.7560 1.99255
\(255\) 5.18410 0.324641
\(256\) 20.6450 1.29031
\(257\) 1.51638 0.0945889 0.0472944 0.998881i \(-0.484940\pi\)
0.0472944 + 0.998881i \(0.484940\pi\)
\(258\) 2.62529 0.163443
\(259\) 3.21351 0.199678
\(260\) −23.6706 −1.46799
\(261\) −4.24828 −0.262962
\(262\) −7.52212 −0.464718
\(263\) 11.3156 0.697753 0.348876 0.937169i \(-0.386563\pi\)
0.348876 + 0.937169i \(0.386563\pi\)
\(264\) −1.19129 −0.0733191
\(265\) −32.8600 −2.01858
\(266\) 3.63843 0.223086
\(267\) 25.8249 1.58046
\(268\) −12.1793 −0.743969
\(269\) 0.830705 0.0506490 0.0253245 0.999679i \(-0.491938\pi\)
0.0253245 + 0.999679i \(0.491938\pi\)
\(270\) 39.6010 2.41004
\(271\) 4.87000 0.295831 0.147916 0.989000i \(-0.452744\pi\)
0.147916 + 0.989000i \(0.452744\pi\)
\(272\) −4.70164 −0.285079
\(273\) −1.53820 −0.0930962
\(274\) −41.5328 −2.50909
\(275\) 8.82800 0.532349
\(276\) −11.9607 −0.719951
\(277\) 31.0685 1.86673 0.933363 0.358935i \(-0.116860\pi\)
0.933363 + 0.358935i \(0.116860\pi\)
\(278\) −9.77780 −0.586434
\(279\) −9.51556 −0.569682
\(280\) −0.851662 −0.0508965
\(281\) 0.817245 0.0487527 0.0243764 0.999703i \(-0.492240\pi\)
0.0243764 + 0.999703i \(0.492240\pi\)
\(282\) −7.56863 −0.450705
\(283\) −27.1985 −1.61678 −0.808391 0.588646i \(-0.799661\pi\)
−0.808391 + 0.588646i \(0.799661\pi\)
\(284\) 15.9678 0.947516
\(285\) −37.3716 −2.21371
\(286\) −7.75249 −0.458414
\(287\) −0.539410 −0.0318404
\(288\) −7.54841 −0.444794
\(289\) 1.00000 0.0588235
\(290\) 28.1586 1.65353
\(291\) −15.4270 −0.904345
\(292\) 2.32127 0.135842
\(293\) 5.76773 0.336954 0.168477 0.985706i \(-0.446115\pi\)
0.168477 + 0.985706i \(0.446115\pi\)
\(294\) −18.1884 −1.06077
\(295\) −22.9336 −1.33524
\(296\) 10.2457 0.595521
\(297\) 5.65515 0.328145
\(298\) 24.2852 1.40680
\(299\) 22.8428 1.32104
\(300\) −19.0295 −1.09867
\(301\) 0.268017 0.0154482
\(302\) 7.24395 0.416843
\(303\) −14.7314 −0.846297
\(304\) 33.8937 1.94393
\(305\) −16.0422 −0.918574
\(306\) 1.98952 0.113733
\(307\) −1.08423 −0.0618801 −0.0309401 0.999521i \(-0.509850\pi\)
−0.0309401 + 0.999521i \(0.509850\pi\)
\(308\) 0.414414 0.0236134
\(309\) −16.1131 −0.916640
\(310\) 63.0713 3.58221
\(311\) −23.4481 −1.32962 −0.664811 0.747012i \(-0.731488\pi\)
−0.664811 + 0.747012i \(0.731488\pi\)
\(312\) −4.90430 −0.277651
\(313\) −21.2373 −1.20041 −0.600203 0.799848i \(-0.704914\pi\)
−0.600203 + 0.799848i \(0.704914\pi\)
\(314\) 38.9383 2.19742
\(315\) 1.05295 0.0593269
\(316\) −11.4140 −0.642087
\(317\) −1.68927 −0.0948790 −0.0474395 0.998874i \(-0.515106\pi\)
−0.0474395 + 0.998874i \(0.515106\pi\)
\(318\) 23.1988 1.30092
\(319\) 4.02113 0.225140
\(320\) 15.0655 0.842189
\(321\) −24.5691 −1.37131
\(322\) −2.80051 −0.156066
\(323\) −7.20890 −0.401114
\(324\) −7.28946 −0.404970
\(325\) 36.3430 2.01595
\(326\) 4.94720 0.274000
\(327\) 19.4323 1.07461
\(328\) −1.71982 −0.0949611
\(329\) −0.772685 −0.0425995
\(330\) −9.76239 −0.537402
\(331\) −14.6981 −0.807882 −0.403941 0.914785i \(-0.632360\pi\)
−0.403941 + 0.914785i \(0.632360\pi\)
\(332\) 23.2669 1.27694
\(333\) −12.6673 −0.694161
\(334\) −1.62516 −0.0889250
\(335\) 29.2907 1.60032
\(336\) 1.75673 0.0958374
\(337\) 33.7847 1.84037 0.920186 0.391481i \(-0.128037\pi\)
0.920186 + 0.391481i \(0.128037\pi\)
\(338\) −7.43447 −0.404382
\(339\) −25.9822 −1.41116
\(340\) −5.74979 −0.311826
\(341\) 9.00678 0.487744
\(342\) −14.3422 −0.775540
\(343\) −3.73298 −0.201562
\(344\) 0.854526 0.0460730
\(345\) 28.7651 1.54866
\(346\) 24.3257 1.30776
\(347\) −7.43894 −0.399343 −0.199672 0.979863i \(-0.563988\pi\)
−0.199672 + 0.979863i \(0.563988\pi\)
\(348\) −8.66790 −0.464648
\(349\) 8.44151 0.451864 0.225932 0.974143i \(-0.427457\pi\)
0.225932 + 0.974143i \(0.427457\pi\)
\(350\) −4.45561 −0.238162
\(351\) 23.2810 1.24265
\(352\) 7.14480 0.380819
\(353\) −16.6812 −0.887851 −0.443926 0.896064i \(-0.646415\pi\)
−0.443926 + 0.896064i \(0.646415\pi\)
\(354\) 16.1908 0.860532
\(355\) −38.4020 −2.03816
\(356\) −28.6429 −1.51807
\(357\) −0.373642 −0.0197752
\(358\) −27.0724 −1.43082
\(359\) 33.6262 1.77472 0.887361 0.461075i \(-0.152536\pi\)
0.887361 + 0.461075i \(0.152536\pi\)
\(360\) 3.35715 0.176937
\(361\) 32.9682 1.73517
\(362\) −9.82464 −0.516372
\(363\) −1.39410 −0.0731712
\(364\) 1.70605 0.0894214
\(365\) −5.58256 −0.292204
\(366\) 11.3256 0.591998
\(367\) −23.9805 −1.25177 −0.625887 0.779914i \(-0.715263\pi\)
−0.625887 + 0.779914i \(0.715263\pi\)
\(368\) −26.0880 −1.35993
\(369\) 2.12629 0.110690
\(370\) 83.9615 4.36495
\(371\) 2.36837 0.122960
\(372\) −19.4149 −1.00662
\(373\) −7.31294 −0.378650 −0.189325 0.981915i \(-0.560630\pi\)
−0.189325 + 0.981915i \(0.560630\pi\)
\(374\) −1.88314 −0.0973749
\(375\) 19.8447 1.02478
\(376\) −2.46358 −0.127049
\(377\) 16.5541 0.852581
\(378\) −2.85423 −0.146806
\(379\) 27.0147 1.38765 0.693825 0.720144i \(-0.255924\pi\)
0.693825 + 0.720144i \(0.255924\pi\)
\(380\) 41.4497 2.12632
\(381\) 23.5091 1.20441
\(382\) 50.6770 2.59286
\(383\) 10.5477 0.538960 0.269480 0.963006i \(-0.413148\pi\)
0.269480 + 0.963006i \(0.413148\pi\)
\(384\) 9.28505 0.473826
\(385\) −0.996648 −0.0507939
\(386\) −17.1459 −0.872704
\(387\) −1.05649 −0.0537044
\(388\) 17.1104 0.868647
\(389\) −21.3522 −1.08260 −0.541299 0.840830i \(-0.682067\pi\)
−0.541299 + 0.840830i \(0.682067\pi\)
\(390\) −40.1897 −2.03508
\(391\) 5.54871 0.280610
\(392\) −5.92030 −0.299020
\(393\) −5.56866 −0.280902
\(394\) 26.5164 1.33588
\(395\) 27.4502 1.38117
\(396\) −1.63357 −0.0820899
\(397\) −17.5852 −0.882578 −0.441289 0.897365i \(-0.645479\pi\)
−0.441289 + 0.897365i \(0.645479\pi\)
\(398\) 39.5295 1.98143
\(399\) 2.69355 0.134846
\(400\) −41.5061 −2.07530
\(401\) 10.3884 0.518774 0.259387 0.965773i \(-0.416479\pi\)
0.259387 + 0.965773i \(0.416479\pi\)
\(402\) −20.6789 −1.03137
\(403\) 37.0789 1.84703
\(404\) 16.3389 0.812891
\(405\) 17.5308 0.871115
\(406\) −2.02952 −0.100723
\(407\) 11.9900 0.594320
\(408\) −1.19129 −0.0589778
\(409\) −7.00777 −0.346512 −0.173256 0.984877i \(-0.555429\pi\)
−0.173256 + 0.984877i \(0.555429\pi\)
\(410\) −14.0935 −0.696030
\(411\) −30.7469 −1.51663
\(412\) 17.8713 0.880457
\(413\) 1.65293 0.0813353
\(414\) 11.0393 0.542550
\(415\) −55.9560 −2.74677
\(416\) 29.4136 1.44212
\(417\) −7.23855 −0.354473
\(418\) 13.5754 0.663994
\(419\) −23.8967 −1.16743 −0.583714 0.811959i \(-0.698401\pi\)
−0.583714 + 0.811959i \(0.698401\pi\)
\(420\) 2.14836 0.104829
\(421\) −36.4372 −1.77584 −0.887921 0.459996i \(-0.847851\pi\)
−0.887921 + 0.459996i \(0.847851\pi\)
\(422\) 25.1081 1.22224
\(423\) 3.04583 0.148093
\(424\) 7.55116 0.366717
\(425\) 8.82800 0.428221
\(426\) 27.1113 1.31355
\(427\) 1.15624 0.0559542
\(428\) 27.2500 1.31718
\(429\) −5.73920 −0.277091
\(430\) 7.00266 0.337698
\(431\) 22.9405 1.10501 0.552503 0.833511i \(-0.313673\pi\)
0.552503 + 0.833511i \(0.313673\pi\)
\(432\) −26.5885 −1.27924
\(433\) 10.4123 0.500382 0.250191 0.968196i \(-0.419507\pi\)
0.250191 + 0.968196i \(0.419507\pi\)
\(434\) −4.54584 −0.218207
\(435\) 20.8459 0.999486
\(436\) −21.5527 −1.03219
\(437\) −40.0001 −1.91346
\(438\) 3.94121 0.188319
\(439\) 33.9784 1.62170 0.810850 0.585254i \(-0.199005\pi\)
0.810850 + 0.585254i \(0.199005\pi\)
\(440\) −3.17764 −0.151488
\(441\) 7.31953 0.348549
\(442\) −7.75249 −0.368748
\(443\) 31.6269 1.50264 0.751320 0.659938i \(-0.229418\pi\)
0.751320 + 0.659938i \(0.229418\pi\)
\(444\) −25.8454 −1.22657
\(445\) 68.8850 3.26546
\(446\) −50.9496 −2.41253
\(447\) 17.9784 0.850351
\(448\) −1.08584 −0.0513012
\(449\) −4.48583 −0.211699 −0.105850 0.994382i \(-0.533756\pi\)
−0.105850 + 0.994382i \(0.533756\pi\)
\(450\) 17.5635 0.827950
\(451\) −2.01260 −0.0947696
\(452\) 28.8174 1.35546
\(453\) 5.36273 0.251963
\(454\) 42.9667 2.01653
\(455\) −4.10298 −0.192351
\(456\) 8.58792 0.402166
\(457\) 30.2004 1.41271 0.706357 0.707856i \(-0.250337\pi\)
0.706357 + 0.707856i \(0.250337\pi\)
\(458\) 14.5724 0.680924
\(459\) 5.65515 0.263960
\(460\) −31.9039 −1.48753
\(461\) 1.89178 0.0881091 0.0440546 0.999029i \(-0.485972\pi\)
0.0440546 + 0.999029i \(0.485972\pi\)
\(462\) 0.703620 0.0327354
\(463\) 19.4766 0.905153 0.452577 0.891725i \(-0.350505\pi\)
0.452577 + 0.891725i \(0.350505\pi\)
\(464\) −18.9059 −0.877685
\(465\) 46.6920 2.16529
\(466\) 39.1092 1.81170
\(467\) 10.1469 0.469540 0.234770 0.972051i \(-0.424566\pi\)
0.234770 + 0.972051i \(0.424566\pi\)
\(468\) −6.72505 −0.310865
\(469\) −2.11112 −0.0974823
\(470\) −20.1885 −0.931225
\(471\) 28.8262 1.32824
\(472\) 5.27008 0.242575
\(473\) 1.00000 0.0459800
\(474\) −19.3795 −0.890128
\(475\) −63.6402 −2.92001
\(476\) 0.414414 0.0189946
\(477\) −9.33584 −0.427459
\(478\) −11.3603 −0.519607
\(479\) 10.7061 0.489175 0.244588 0.969627i \(-0.421347\pi\)
0.244588 + 0.969627i \(0.421347\pi\)
\(480\) 37.0394 1.69061
\(481\) 49.3601 2.25062
\(482\) −9.88895 −0.450429
\(483\) −2.07323 −0.0943352
\(484\) 1.54622 0.0702829
\(485\) −41.1497 −1.86851
\(486\) 19.5718 0.887794
\(487\) 8.86535 0.401728 0.200864 0.979619i \(-0.435625\pi\)
0.200864 + 0.979619i \(0.435625\pi\)
\(488\) 3.68646 0.166878
\(489\) 3.66243 0.165621
\(490\) −48.5156 −2.19171
\(491\) 7.03978 0.317701 0.158850 0.987303i \(-0.449221\pi\)
0.158850 + 0.987303i \(0.449221\pi\)
\(492\) 4.33833 0.195587
\(493\) 4.02113 0.181103
\(494\) 55.8869 2.51447
\(495\) 3.92866 0.176580
\(496\) −42.3466 −1.90142
\(497\) 2.76781 0.124153
\(498\) 39.5042 1.77023
\(499\) −2.28533 −0.102305 −0.0511526 0.998691i \(-0.516290\pi\)
−0.0511526 + 0.998691i \(0.516290\pi\)
\(500\) −22.0102 −0.984326
\(501\) −1.20312 −0.0537513
\(502\) −56.0129 −2.49998
\(503\) −3.51163 −0.156576 −0.0782880 0.996931i \(-0.524945\pi\)
−0.0782880 + 0.996931i \(0.524945\pi\)
\(504\) −0.241965 −0.0107780
\(505\) −39.2944 −1.74858
\(506\) −10.4490 −0.464515
\(507\) −5.50377 −0.244431
\(508\) −26.0745 −1.15687
\(509\) 18.9113 0.838229 0.419115 0.907933i \(-0.362341\pi\)
0.419115 + 0.907933i \(0.362341\pi\)
\(510\) −9.76239 −0.432286
\(511\) 0.402361 0.0177994
\(512\) −25.5569 −1.12947
\(513\) −40.7674 −1.79992
\(514\) −2.85555 −0.125953
\(515\) −42.9798 −1.89392
\(516\) −2.15559 −0.0948944
\(517\) −2.88297 −0.126793
\(518\) −6.05149 −0.265887
\(519\) 18.0084 0.790483
\(520\) −13.0817 −0.573669
\(521\) 4.88973 0.214223 0.107111 0.994247i \(-0.465840\pi\)
0.107111 + 0.994247i \(0.465840\pi\)
\(522\) 8.00012 0.350156
\(523\) −32.9050 −1.43884 −0.719418 0.694578i \(-0.755591\pi\)
−0.719418 + 0.694578i \(0.755591\pi\)
\(524\) 6.17631 0.269814
\(525\) −3.29851 −0.143959
\(526\) −21.3090 −0.929115
\(527\) 9.00678 0.392341
\(528\) 6.55455 0.285250
\(529\) 7.78819 0.338617
\(530\) 61.8801 2.68790
\(531\) −6.51564 −0.282755
\(532\) −2.98747 −0.129523
\(533\) −8.28543 −0.358882
\(534\) −48.6319 −2.10451
\(535\) −65.5352 −2.83333
\(536\) −6.73094 −0.290732
\(537\) −20.0418 −0.864869
\(538\) −1.56434 −0.0674433
\(539\) −6.92817 −0.298417
\(540\) −32.5159 −1.39926
\(541\) −5.16862 −0.222216 −0.111108 0.993808i \(-0.535440\pi\)
−0.111108 + 0.993808i \(0.535440\pi\)
\(542\) −9.17090 −0.393924
\(543\) −7.27323 −0.312124
\(544\) 7.14480 0.306331
\(545\) 51.8334 2.22030
\(546\) 2.89665 0.123965
\(547\) 4.50332 0.192548 0.0962740 0.995355i \(-0.469307\pi\)
0.0962740 + 0.995355i \(0.469307\pi\)
\(548\) 34.1021 1.45677
\(549\) −4.55774 −0.194520
\(550\) −16.6244 −0.708866
\(551\) −28.9879 −1.23493
\(552\) −6.61015 −0.281346
\(553\) −1.97846 −0.0841327
\(554\) −58.5064 −2.48570
\(555\) 62.1571 2.63842
\(556\) 8.02843 0.340481
\(557\) 19.9158 0.843860 0.421930 0.906628i \(-0.361353\pi\)
0.421930 + 0.906628i \(0.361353\pi\)
\(558\) 17.9191 0.758578
\(559\) 4.11678 0.174121
\(560\) 4.68588 0.198015
\(561\) −1.39410 −0.0588589
\(562\) −1.53899 −0.0649183
\(563\) 8.60556 0.362681 0.181340 0.983420i \(-0.441956\pi\)
0.181340 + 0.983420i \(0.441956\pi\)
\(564\) 6.21450 0.261678
\(565\) −69.3047 −2.91567
\(566\) 51.2186 2.15288
\(567\) −1.26353 −0.0530632
\(568\) 8.82468 0.370276
\(569\) 20.3262 0.852117 0.426059 0.904696i \(-0.359902\pi\)
0.426059 + 0.904696i \(0.359902\pi\)
\(570\) 70.3761 2.94773
\(571\) 14.6511 0.613128 0.306564 0.951850i \(-0.400821\pi\)
0.306564 + 0.951850i \(0.400821\pi\)
\(572\) 6.36547 0.266154
\(573\) 37.5164 1.56727
\(574\) 1.01579 0.0423981
\(575\) 48.9840 2.04278
\(576\) 4.28026 0.178344
\(577\) 22.5456 0.938586 0.469293 0.883043i \(-0.344509\pi\)
0.469293 + 0.883043i \(0.344509\pi\)
\(578\) −1.88314 −0.0783284
\(579\) −12.6932 −0.527511
\(580\) −23.1207 −0.960033
\(581\) 4.03300 0.167317
\(582\) 29.0512 1.20421
\(583\) 8.83666 0.365977
\(584\) 1.28286 0.0530851
\(585\) 16.1735 0.668690
\(586\) −10.8615 −0.448683
\(587\) −6.20168 −0.255971 −0.127985 0.991776i \(-0.540851\pi\)
−0.127985 + 0.991776i \(0.540851\pi\)
\(588\) 14.9343 0.615879
\(589\) −64.9289 −2.67535
\(590\) 43.1872 1.77799
\(591\) 19.6302 0.807478
\(592\) −56.3725 −2.31689
\(593\) 34.7628 1.42754 0.713768 0.700383i \(-0.246987\pi\)
0.713768 + 0.700383i \(0.246987\pi\)
\(594\) −10.6494 −0.436952
\(595\) −0.996648 −0.0408586
\(596\) −19.9403 −0.816784
\(597\) 29.2639 1.19769
\(598\) −43.0163 −1.75907
\(599\) −18.6792 −0.763213 −0.381606 0.924325i \(-0.624629\pi\)
−0.381606 + 0.924325i \(0.624629\pi\)
\(600\) −10.5167 −0.429344
\(601\) −4.77135 −0.194627 −0.0973136 0.995254i \(-0.531025\pi\)
−0.0973136 + 0.995254i \(0.531025\pi\)
\(602\) −0.504714 −0.0205706
\(603\) 8.32176 0.338888
\(604\) −5.94792 −0.242017
\(605\) −3.71860 −0.151183
\(606\) 27.7413 1.12691
\(607\) −12.1515 −0.493214 −0.246607 0.969116i \(-0.579316\pi\)
−0.246607 + 0.969116i \(0.579316\pi\)
\(608\) −51.5062 −2.08885
\(609\) −1.50246 −0.0608829
\(610\) 30.2098 1.22316
\(611\) −11.8686 −0.480151
\(612\) −1.63357 −0.0660331
\(613\) −30.3364 −1.22528 −0.612639 0.790363i \(-0.709892\pi\)
−0.612639 + 0.790363i \(0.709892\pi\)
\(614\) 2.04175 0.0823985
\(615\) −10.4335 −0.420720
\(616\) 0.229027 0.00922777
\(617\) 31.0987 1.25199 0.625993 0.779828i \(-0.284694\pi\)
0.625993 + 0.779828i \(0.284694\pi\)
\(618\) 30.3432 1.22058
\(619\) 6.61058 0.265701 0.132851 0.991136i \(-0.457587\pi\)
0.132851 + 0.991136i \(0.457587\pi\)
\(620\) −51.7871 −2.07982
\(621\) 31.3788 1.25919
\(622\) 44.1561 1.77050
\(623\) −4.96486 −0.198913
\(624\) 26.9837 1.08021
\(625\) 8.79361 0.351744
\(626\) 39.9929 1.59844
\(627\) 10.0499 0.401355
\(628\) −31.9718 −1.27581
\(629\) 11.9900 0.478071
\(630\) −1.98285 −0.0789986
\(631\) −12.7104 −0.505992 −0.252996 0.967467i \(-0.581416\pi\)
−0.252996 + 0.967467i \(0.581416\pi\)
\(632\) −6.30799 −0.250918
\(633\) 18.5877 0.738793
\(634\) 3.18114 0.126339
\(635\) 62.7080 2.48849
\(636\) −19.0482 −0.755310
\(637\) −28.5218 −1.13007
\(638\) −7.57236 −0.299793
\(639\) −10.9104 −0.431607
\(640\) 24.7668 0.978995
\(641\) 23.8135 0.940577 0.470289 0.882513i \(-0.344150\pi\)
0.470289 + 0.882513i \(0.344150\pi\)
\(642\) 46.2670 1.82601
\(643\) 12.3271 0.486133 0.243066 0.970010i \(-0.421847\pi\)
0.243066 + 0.970010i \(0.421847\pi\)
\(644\) 2.29946 0.0906115
\(645\) 5.18410 0.204124
\(646\) 13.5754 0.534116
\(647\) 17.4223 0.684942 0.342471 0.939528i \(-0.388736\pi\)
0.342471 + 0.939528i \(0.388736\pi\)
\(648\) −4.02855 −0.158256
\(649\) 6.16726 0.242086
\(650\) −68.4390 −2.68440
\(651\) −3.36531 −0.131897
\(652\) −4.06208 −0.159083
\(653\) 3.00249 0.117497 0.0587483 0.998273i \(-0.481289\pi\)
0.0587483 + 0.998273i \(0.481289\pi\)
\(654\) −36.5937 −1.43093
\(655\) −14.8538 −0.580385
\(656\) 9.46251 0.369449
\(657\) −1.58606 −0.0618780
\(658\) 1.45508 0.0567248
\(659\) −20.2166 −0.787528 −0.393764 0.919211i \(-0.628827\pi\)
−0.393764 + 0.919211i \(0.628827\pi\)
\(660\) 8.01577 0.312013
\(661\) 41.7230 1.62284 0.811419 0.584466i \(-0.198696\pi\)
0.811419 + 0.584466i \(0.198696\pi\)
\(662\) 27.6787 1.07576
\(663\) −5.73920 −0.222892
\(664\) 12.8586 0.499009
\(665\) 7.18473 0.278612
\(666\) 23.8542 0.924333
\(667\) 22.3121 0.863928
\(668\) 1.33440 0.0516295
\(669\) −37.7182 −1.45827
\(670\) −55.1586 −2.13096
\(671\) 4.31404 0.166542
\(672\) −2.66960 −0.102982
\(673\) 19.5486 0.753545 0.376772 0.926306i \(-0.377034\pi\)
0.376772 + 0.926306i \(0.377034\pi\)
\(674\) −63.6215 −2.45061
\(675\) 49.9236 1.92156
\(676\) 6.10435 0.234783
\(677\) −28.8002 −1.10688 −0.553440 0.832889i \(-0.686685\pi\)
−0.553440 + 0.832889i \(0.686685\pi\)
\(678\) 48.9282 1.87908
\(679\) 2.96585 0.113819
\(680\) −3.17764 −0.121857
\(681\) 31.8084 1.21890
\(682\) −16.9610 −0.649472
\(683\) −5.70887 −0.218444 −0.109222 0.994017i \(-0.534836\pi\)
−0.109222 + 0.994017i \(0.534836\pi\)
\(684\) 11.7762 0.450275
\(685\) −82.0140 −3.13360
\(686\) 7.02973 0.268396
\(687\) 10.7880 0.411589
\(688\) −4.70164 −0.179248
\(689\) 36.3786 1.38591
\(690\) −54.1687 −2.06217
\(691\) 14.1861 0.539664 0.269832 0.962907i \(-0.413032\pi\)
0.269832 + 0.962907i \(0.413032\pi\)
\(692\) −19.9735 −0.759280
\(693\) −0.283157 −0.0107562
\(694\) 14.0086 0.531758
\(695\) −19.3080 −0.732395
\(696\) −4.79035 −0.181578
\(697\) −2.01260 −0.0762326
\(698\) −15.8966 −0.601694
\(699\) 28.9528 1.09509
\(700\) 3.65844 0.138276
\(701\) −2.46376 −0.0930549 −0.0465275 0.998917i \(-0.514815\pi\)
−0.0465275 + 0.998917i \(0.514815\pi\)
\(702\) −43.8414 −1.65469
\(703\) −86.4344 −3.25993
\(704\) −4.05140 −0.152693
\(705\) −14.9456 −0.562885
\(706\) 31.4131 1.18225
\(707\) 2.83213 0.106513
\(708\) −13.2941 −0.499621
\(709\) −1.06179 −0.0398763 −0.0199382 0.999801i \(-0.506347\pi\)
−0.0199382 + 0.999801i \(0.506347\pi\)
\(710\) 72.3164 2.71398
\(711\) 7.79885 0.292480
\(712\) −15.8296 −0.593240
\(713\) 49.9760 1.87162
\(714\) 0.703620 0.0263323
\(715\) −15.3087 −0.572512
\(716\) 22.2288 0.830729
\(717\) −8.41006 −0.314079
\(718\) −63.3229 −2.36319
\(719\) −25.4788 −0.950199 −0.475099 0.879932i \(-0.657588\pi\)
−0.475099 + 0.879932i \(0.657588\pi\)
\(720\) −18.4712 −0.688379
\(721\) 3.09775 0.115366
\(722\) −62.0839 −2.31052
\(723\) −7.32084 −0.272265
\(724\) 8.06688 0.299803
\(725\) 35.4986 1.31838
\(726\) 2.62529 0.0974335
\(727\) 13.6911 0.507775 0.253888 0.967234i \(-0.418291\pi\)
0.253888 + 0.967234i \(0.418291\pi\)
\(728\) 0.942856 0.0349446
\(729\) 28.6322 1.06045
\(730\) 10.5128 0.389094
\(731\) 1.00000 0.0369863
\(732\) −9.29930 −0.343712
\(733\) 3.07724 0.113660 0.0568302 0.998384i \(-0.481901\pi\)
0.0568302 + 0.998384i \(0.481901\pi\)
\(734\) 45.1588 1.66684
\(735\) −35.9163 −1.32479
\(736\) 39.6444 1.46131
\(737\) −7.87681 −0.290146
\(738\) −4.00410 −0.147393
\(739\) −33.8930 −1.24677 −0.623387 0.781913i \(-0.714244\pi\)
−0.623387 + 0.781913i \(0.714244\pi\)
\(740\) −68.9397 −2.53427
\(741\) 41.3733 1.51989
\(742\) −4.45998 −0.163731
\(743\) 10.6012 0.388922 0.194461 0.980910i \(-0.437704\pi\)
0.194461 + 0.980910i \(0.437704\pi\)
\(744\) −10.7297 −0.393370
\(745\) 47.9555 1.75695
\(746\) 13.7713 0.504203
\(747\) −15.8976 −0.581663
\(748\) 1.54622 0.0565355
\(749\) 4.72342 0.172590
\(750\) −37.3705 −1.36458
\(751\) −22.6133 −0.825171 −0.412586 0.910919i \(-0.635374\pi\)
−0.412586 + 0.910919i \(0.635374\pi\)
\(752\) 13.5547 0.494289
\(753\) −41.4666 −1.51113
\(754\) −31.1738 −1.13528
\(755\) 14.3045 0.520594
\(756\) 2.34357 0.0852348
\(757\) 0.941456 0.0342178 0.0171089 0.999854i \(-0.494554\pi\)
0.0171089 + 0.999854i \(0.494554\pi\)
\(758\) −50.8725 −1.84777
\(759\) −7.73545 −0.280779
\(760\) 22.9073 0.830936
\(761\) 25.7853 0.934715 0.467358 0.884068i \(-0.345206\pi\)
0.467358 + 0.884068i \(0.345206\pi\)
\(762\) −44.2710 −1.60377
\(763\) −3.73587 −0.135248
\(764\) −41.6102 −1.50540
\(765\) 3.92866 0.142041
\(766\) −19.8627 −0.717670
\(767\) 25.3893 0.916753
\(768\) −28.7812 −1.03855
\(769\) −2.02442 −0.0730025 −0.0365013 0.999334i \(-0.511621\pi\)
−0.0365013 + 0.999334i \(0.511621\pi\)
\(770\) 1.87683 0.0676362
\(771\) −2.11398 −0.0761330
\(772\) 14.0783 0.506689
\(773\) −7.69676 −0.276833 −0.138417 0.990374i \(-0.544201\pi\)
−0.138417 + 0.990374i \(0.544201\pi\)
\(774\) 1.98952 0.0715118
\(775\) 79.5118 2.85615
\(776\) 9.45611 0.339455
\(777\) −4.47995 −0.160717
\(778\) 40.2092 1.44157
\(779\) 14.5086 0.519825
\(780\) 32.9992 1.18156
\(781\) 10.3270 0.369529
\(782\) −10.4490 −0.373656
\(783\) 22.7401 0.812664
\(784\) 32.5737 1.16335
\(785\) 76.8908 2.74435
\(786\) 10.4866 0.374044
\(787\) −3.51186 −0.125184 −0.0625922 0.998039i \(-0.519937\pi\)
−0.0625922 + 0.998039i \(0.519937\pi\)
\(788\) −21.7722 −0.775604
\(789\) −15.7751 −0.561609
\(790\) −51.6926 −1.83914
\(791\) 4.99511 0.177606
\(792\) −0.902798 −0.0320795
\(793\) 17.7600 0.630675
\(794\) 33.1155 1.17523
\(795\) 45.8101 1.62472
\(796\) −32.4572 −1.15041
\(797\) 35.6789 1.26381 0.631906 0.775045i \(-0.282273\pi\)
0.631906 + 0.775045i \(0.282273\pi\)
\(798\) −5.07233 −0.179559
\(799\) −2.88297 −0.101992
\(800\) 63.0743 2.23001
\(801\) 19.5709 0.691502
\(802\) −19.5629 −0.690791
\(803\) 1.50125 0.0529780
\(804\) 16.9791 0.598808
\(805\) −5.53011 −0.194911
\(806\) −69.8249 −2.45948
\(807\) −1.15809 −0.0407665
\(808\) 9.02976 0.317666
\(809\) −26.5986 −0.935158 −0.467579 0.883951i \(-0.654874\pi\)
−0.467579 + 0.883951i \(0.654874\pi\)
\(810\) −33.0131 −1.15996
\(811\) −34.7318 −1.21960 −0.609799 0.792556i \(-0.708750\pi\)
−0.609799 + 0.792556i \(0.708750\pi\)
\(812\) 1.66641 0.0584796
\(813\) −6.78926 −0.238110
\(814\) −22.5788 −0.791386
\(815\) 9.76913 0.342198
\(816\) 6.55455 0.229455
\(817\) −7.20890 −0.252208
\(818\) 13.1966 0.461409
\(819\) −1.16570 −0.0407327
\(820\) 11.5720 0.404112
\(821\) 41.3194 1.44206 0.721028 0.692906i \(-0.243670\pi\)
0.721028 + 0.692906i \(0.243670\pi\)
\(822\) 57.9009 2.01952
\(823\) 1.32929 0.0463361 0.0231681 0.999732i \(-0.492625\pi\)
0.0231681 + 0.999732i \(0.492625\pi\)
\(824\) 9.87665 0.344070
\(825\) −12.3071 −0.428478
\(826\) −3.11270 −0.108305
\(827\) 15.7232 0.546748 0.273374 0.961908i \(-0.411860\pi\)
0.273374 + 0.961908i \(0.411860\pi\)
\(828\) −9.06420 −0.315003
\(829\) 11.0233 0.382854 0.191427 0.981507i \(-0.438688\pi\)
0.191427 + 0.981507i \(0.438688\pi\)
\(830\) 105.373 3.65755
\(831\) −43.3125 −1.50250
\(832\) −16.6787 −0.578231
\(833\) −6.92817 −0.240047
\(834\) 13.6312 0.472011
\(835\) −3.20918 −0.111058
\(836\) −11.1466 −0.385512
\(837\) 50.9346 1.76056
\(838\) 45.0008 1.55453
\(839\) 11.4887 0.396636 0.198318 0.980138i \(-0.436452\pi\)
0.198318 + 0.980138i \(0.436452\pi\)
\(840\) 1.18730 0.0409657
\(841\) −12.8305 −0.442431
\(842\) 68.6165 2.36468
\(843\) −1.13932 −0.0392402
\(844\) −20.6159 −0.709630
\(845\) −14.6807 −0.505031
\(846\) −5.73573 −0.197199
\(847\) 0.268017 0.00920916
\(848\) −41.5468 −1.42672
\(849\) 37.9174 1.30132
\(850\) −16.6244 −0.570212
\(851\) 66.5288 2.28058
\(852\) −22.2607 −0.762640
\(853\) −4.38160 −0.150023 −0.0750115 0.997183i \(-0.523899\pi\)
−0.0750115 + 0.997183i \(0.523899\pi\)
\(854\) −2.17736 −0.0745076
\(855\) −28.3213 −0.968569
\(856\) 15.0598 0.514735
\(857\) 6.88626 0.235230 0.117615 0.993059i \(-0.462475\pi\)
0.117615 + 0.993059i \(0.462475\pi\)
\(858\) 10.8077 0.368970
\(859\) 28.1249 0.959609 0.479804 0.877376i \(-0.340708\pi\)
0.479804 + 0.877376i \(0.340708\pi\)
\(860\) −5.74979 −0.196066
\(861\) 0.751991 0.0256278
\(862\) −43.2003 −1.47141
\(863\) 18.9152 0.643880 0.321940 0.946760i \(-0.395665\pi\)
0.321940 + 0.946760i \(0.395665\pi\)
\(864\) 40.4049 1.37460
\(865\) 48.0355 1.63326
\(866\) −19.6078 −0.666300
\(867\) −1.39410 −0.0473461
\(868\) 3.73253 0.126690
\(869\) −7.38185 −0.250412
\(870\) −39.2559 −1.33090
\(871\) −32.4271 −1.09875
\(872\) −11.9112 −0.403364
\(873\) −11.6910 −0.395681
\(874\) 75.3259 2.54794
\(875\) −3.81517 −0.128976
\(876\) −3.23608 −0.109337
\(877\) −37.6775 −1.27228 −0.636139 0.771574i \(-0.719470\pi\)
−0.636139 + 0.771574i \(0.719470\pi\)
\(878\) −63.9861 −2.15943
\(879\) −8.04078 −0.271209
\(880\) 17.4835 0.589370
\(881\) 26.2568 0.884615 0.442308 0.896863i \(-0.354160\pi\)
0.442308 + 0.896863i \(0.354160\pi\)
\(882\) −13.7837 −0.464122
\(883\) −3.58650 −0.120695 −0.0603477 0.998177i \(-0.519221\pi\)
−0.0603477 + 0.998177i \(0.519221\pi\)
\(884\) 6.36547 0.214094
\(885\) 31.9717 1.07472
\(886\) −59.5579 −2.00089
\(887\) 2.73119 0.0917043 0.0458522 0.998948i \(-0.485400\pi\)
0.0458522 + 0.998948i \(0.485400\pi\)
\(888\) −14.2836 −0.479325
\(889\) −4.51965 −0.151584
\(890\) −129.720 −4.34823
\(891\) −4.71436 −0.157937
\(892\) 41.8341 1.40071
\(893\) 20.7831 0.695479
\(894\) −33.8559 −1.13231
\(895\) −53.4593 −1.78695
\(896\) −1.78506 −0.0596346
\(897\) −31.8452 −1.06328
\(898\) 8.44745 0.281895
\(899\) 36.2174 1.20792
\(900\) −14.4211 −0.480705
\(901\) 8.83666 0.294392
\(902\) 3.79001 0.126193
\(903\) −0.373642 −0.0124340
\(904\) 15.9261 0.529693
\(905\) −19.4005 −0.644895
\(906\) −10.0988 −0.335510
\(907\) 10.7295 0.356268 0.178134 0.984006i \(-0.442994\pi\)
0.178134 + 0.984006i \(0.442994\pi\)
\(908\) −35.2794 −1.17079
\(909\) −11.1639 −0.370283
\(910\) 7.72650 0.256131
\(911\) −48.0816 −1.59301 −0.796507 0.604629i \(-0.793321\pi\)
−0.796507 + 0.604629i \(0.793321\pi\)
\(912\) −47.2511 −1.56464
\(913\) 15.0476 0.498002
\(914\) −56.8716 −1.88114
\(915\) 22.3644 0.739345
\(916\) −11.9652 −0.395342
\(917\) 1.07058 0.0353537
\(918\) −10.6494 −0.351484
\(919\) −17.5073 −0.577512 −0.288756 0.957403i \(-0.593242\pi\)
−0.288756 + 0.957403i \(0.593242\pi\)
\(920\) −17.6318 −0.581304
\(921\) 1.51152 0.0498063
\(922\) −3.56250 −0.117325
\(923\) 42.5140 1.39936
\(924\) −0.577733 −0.0190060
\(925\) 105.847 3.48024
\(926\) −36.6772 −1.20529
\(927\) −12.2110 −0.401060
\(928\) 28.7302 0.943115
\(929\) 30.2025 0.990911 0.495455 0.868633i \(-0.335001\pi\)
0.495455 + 0.868633i \(0.335001\pi\)
\(930\) −87.9277 −2.88326
\(931\) 49.9445 1.63686
\(932\) −32.1121 −1.05187
\(933\) 32.6890 1.07019
\(934\) −19.1080 −0.625232
\(935\) −3.71860 −0.121611
\(936\) −3.71662 −0.121482
\(937\) −39.6641 −1.29577 −0.647886 0.761738i \(-0.724346\pi\)
−0.647886 + 0.761738i \(0.724346\pi\)
\(938\) 3.97553 0.129806
\(939\) 29.6070 0.966187
\(940\) 16.5765 0.540666
\(941\) −16.2573 −0.529973 −0.264986 0.964252i \(-0.585367\pi\)
−0.264986 + 0.964252i \(0.585367\pi\)
\(942\) −54.2839 −1.76866
\(943\) −11.1673 −0.363658
\(944\) −28.9962 −0.943747
\(945\) −5.63619 −0.183345
\(946\) −1.88314 −0.0612262
\(947\) −6.11803 −0.198809 −0.0994047 0.995047i \(-0.531694\pi\)
−0.0994047 + 0.995047i \(0.531694\pi\)
\(948\) 15.9122 0.516805
\(949\) 6.18033 0.200622
\(950\) 119.843 3.88824
\(951\) 2.35501 0.0763665
\(952\) 0.229027 0.00742282
\(953\) 6.05132 0.196022 0.0980108 0.995185i \(-0.468752\pi\)
0.0980108 + 0.995185i \(0.468752\pi\)
\(954\) 17.5807 0.569196
\(955\) 100.071 3.23821
\(956\) 9.32777 0.301682
\(957\) −5.60585 −0.181212
\(958\) −20.1611 −0.651377
\(959\) 5.91113 0.190880
\(960\) −21.0028 −0.677864
\(961\) 50.1220 1.61684
\(962\) −92.9520 −2.99689
\(963\) −18.6192 −0.599994
\(964\) 8.11969 0.261518
\(965\) −33.8577 −1.08992
\(966\) 3.90419 0.125615
\(967\) −5.35053 −0.172062 −0.0860308 0.996292i \(-0.527418\pi\)
−0.0860308 + 0.996292i \(0.527418\pi\)
\(968\) 0.854526 0.0274655
\(969\) 10.0499 0.322850
\(970\) 77.4907 2.48808
\(971\) 10.6797 0.342729 0.171365 0.985208i \(-0.445182\pi\)
0.171365 + 0.985208i \(0.445182\pi\)
\(972\) −16.0701 −0.515450
\(973\) 1.39162 0.0446132
\(974\) −16.6947 −0.534933
\(975\) −50.6657 −1.62260
\(976\) −20.2831 −0.649246
\(977\) 21.9043 0.700781 0.350390 0.936604i \(-0.386049\pi\)
0.350390 + 0.936604i \(0.386049\pi\)
\(978\) −6.89688 −0.220538
\(979\) −18.5244 −0.592043
\(980\) 39.8355 1.27250
\(981\) 14.7264 0.470176
\(982\) −13.2569 −0.423045
\(983\) −5.85558 −0.186764 −0.0933820 0.995630i \(-0.529768\pi\)
−0.0933820 + 0.995630i \(0.529768\pi\)
\(984\) 2.39760 0.0764326
\(985\) 52.3613 1.66837
\(986\) −7.57236 −0.241153
\(987\) 1.07720 0.0342876
\(988\) −45.8880 −1.45989
\(989\) 5.54871 0.176439
\(990\) −7.39823 −0.235131
\(991\) 43.2988 1.37543 0.687716 0.725980i \(-0.258613\pi\)
0.687716 + 0.725980i \(0.258613\pi\)
\(992\) 64.3516 2.04317
\(993\) 20.4906 0.650251
\(994\) −5.21217 −0.165320
\(995\) 78.0581 2.47461
\(996\) −32.4364 −1.02779
\(997\) 62.0036 1.96368 0.981838 0.189723i \(-0.0607591\pi\)
0.981838 + 0.189723i \(0.0607591\pi\)
\(998\) 4.30359 0.136228
\(999\) 67.8049 2.14525
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 \(a_p\))