Properties

Label 8041.2.a.j.1.19
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 1.19
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.64446 q^{2}\) \(-1.94286 q^{3}\) \(+0.704260 q^{4}\) \(-2.95674 q^{5}\) \(+3.19496 q^{6}\) \(+4.77511 q^{7}\) \(+2.13080 q^{8}\) \(+0.774694 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.64446 q^{2}\) \(-1.94286 q^{3}\) \(+0.704260 q^{4}\) \(-2.95674 q^{5}\) \(+3.19496 q^{6}\) \(+4.77511 q^{7}\) \(+2.13080 q^{8}\) \(+0.774694 q^{9}\) \(+4.86225 q^{10}\) \(+1.00000 q^{11}\) \(-1.36828 q^{12}\) \(-2.28957 q^{13}\) \(-7.85249 q^{14}\) \(+5.74452 q^{15}\) \(-4.91254 q^{16}\) \(+1.00000 q^{17}\) \(-1.27396 q^{18}\) \(-5.82001 q^{19}\) \(-2.08231 q^{20}\) \(-9.27736 q^{21}\) \(-1.64446 q^{22}\) \(-3.60225 q^{23}\) \(-4.13983 q^{24}\) \(+3.74230 q^{25}\) \(+3.76512 q^{26}\) \(+4.32345 q^{27}\) \(+3.36292 q^{28}\) \(-5.58285 q^{29}\) \(-9.44665 q^{30}\) \(-8.37229 q^{31}\) \(+3.81689 q^{32}\) \(-1.94286 q^{33}\) \(-1.64446 q^{34}\) \(-14.1188 q^{35}\) \(+0.545586 q^{36}\) \(-7.78932 q^{37}\) \(+9.57079 q^{38}\) \(+4.44831 q^{39}\) \(-6.30021 q^{40}\) \(-9.62588 q^{41}\) \(+15.2563 q^{42}\) \(+1.00000 q^{43}\) \(+0.704260 q^{44}\) \(-2.29057 q^{45}\) \(+5.92376 q^{46}\) \(+6.14277 q^{47}\) \(+9.54436 q^{48}\) \(+15.8017 q^{49}\) \(-6.15408 q^{50}\) \(-1.94286 q^{51}\) \(-1.61245 q^{52}\) \(+9.24846 q^{53}\) \(-7.10976 q^{54}\) \(-2.95674 q^{55}\) \(+10.1748 q^{56}\) \(+11.3074 q^{57}\) \(+9.18079 q^{58}\) \(+9.16404 q^{59}\) \(+4.04564 q^{60}\) \(-2.77872 q^{61}\) \(+13.7679 q^{62}\) \(+3.69925 q^{63}\) \(+3.54833 q^{64}\) \(+6.76967 q^{65}\) \(+3.19496 q^{66}\) \(+6.69264 q^{67}\) \(+0.704260 q^{68}\) \(+6.99865 q^{69}\) \(+23.2178 q^{70}\) \(-5.95574 q^{71}\) \(+1.65072 q^{72}\) \(+2.32040 q^{73}\) \(+12.8093 q^{74}\) \(-7.27076 q^{75}\) \(-4.09880 q^{76}\) \(+4.77511 q^{77}\) \(-7.31509 q^{78}\) \(-4.03573 q^{79}\) \(+14.5251 q^{80}\) \(-10.7239 q^{81}\) \(+15.8294 q^{82}\) \(-3.03874 q^{83}\) \(-6.53367 q^{84}\) \(-2.95674 q^{85}\) \(-1.64446 q^{86}\) \(+10.8467 q^{87}\) \(+2.13080 q^{88}\) \(-3.24843 q^{89}\) \(+3.76675 q^{90}\) \(-10.9330 q^{91}\) \(-2.53692 q^{92}\) \(+16.2662 q^{93}\) \(-10.1016 q^{94}\) \(+17.2082 q^{95}\) \(-7.41568 q^{96}\) \(-12.4311 q^{97}\) \(-25.9853 q^{98}\) \(+0.774694 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(82q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(82q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut +\mathstrut 82q^{11} \) \(\mathstrut +\mathstrut 3q^{12} \) \(\mathstrut +\mathstrut 26q^{13} \) \(\mathstrut +\mathstrut 17q^{14} \) \(\mathstrut +\mathstrut 66q^{15} \) \(\mathstrut +\mathstrut 122q^{16} \) \(\mathstrut +\mathstrut 82q^{17} \) \(\mathstrut +\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 9q^{20} \) \(\mathstrut +\mathstrut 22q^{21} \) \(\mathstrut +\mathstrut 8q^{22} \) \(\mathstrut +\mathstrut 50q^{23} \) \(\mathstrut +\mathstrut 15q^{24} \) \(\mathstrut +\mathstrut 117q^{25} \) \(\mathstrut +\mathstrut 36q^{26} \) \(\mathstrut +\mathstrut 30q^{27} \) \(\mathstrut +\mathstrut 11q^{28} \) \(\mathstrut +\mathstrut 33q^{29} \) \(\mathstrut -\mathstrut 26q^{30} \) \(\mathstrut +\mathstrut 40q^{31} \) \(\mathstrut +\mathstrut 58q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 16q^{35} \) \(\mathstrut +\mathstrut 160q^{36} \) \(\mathstrut +\mathstrut 31q^{37} \) \(\mathstrut +\mathstrut 18q^{38} \) \(\mathstrut +\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 29q^{40} \) \(\mathstrut +\mathstrut 42q^{41} \) \(\mathstrut -\mathstrut 51q^{42} \) \(\mathstrut +\mathstrut 82q^{43} \) \(\mathstrut +\mathstrut 98q^{44} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 19q^{46} \) \(\mathstrut +\mathstrut 84q^{47} \) \(\mathstrut -\mathstrut 46q^{48} \) \(\mathstrut +\mathstrut 136q^{49} \) \(\mathstrut +\mathstrut 59q^{50} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 45q^{52} \) \(\mathstrut +\mathstrut 83q^{53} \) \(\mathstrut +\mathstrut 24q^{54} \) \(\mathstrut +\mathstrut 11q^{55} \) \(\mathstrut +\mathstrut 21q^{56} \) \(\mathstrut +\mathstrut 23q^{57} \) \(\mathstrut +\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 96q^{59} \) \(\mathstrut +\mathstrut 184q^{60} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut -\mathstrut 23q^{62} \) \(\mathstrut +\mathstrut 8q^{63} \) \(\mathstrut +\mathstrut 148q^{64} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut +\mathstrut 10q^{66} \) \(\mathstrut +\mathstrut 78q^{67} \) \(\mathstrut +\mathstrut 98q^{68} \) \(\mathstrut +\mathstrut 61q^{69} \) \(\mathstrut -\mathstrut 3q^{70} \) \(\mathstrut +\mathstrut 155q^{71} \) \(\mathstrut +\mathstrut 50q^{72} \) \(\mathstrut -\mathstrut 23q^{73} \) \(\mathstrut +\mathstrut 10q^{74} \) \(\mathstrut -\mathstrut 19q^{75} \) \(\mathstrut +\mathstrut 44q^{76} \) \(\mathstrut +\mathstrut 8q^{77} \) \(\mathstrut -\mathstrut 27q^{78} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut +\mathstrut 19q^{80} \) \(\mathstrut +\mathstrut 150q^{81} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 54q^{83} \) \(\mathstrut +\mathstrut 8q^{84} \) \(\mathstrut +\mathstrut 11q^{85} \) \(\mathstrut +\mathstrut 8q^{86} \) \(\mathstrut +\mathstrut 20q^{87} \) \(\mathstrut +\mathstrut 30q^{88} \) \(\mathstrut +\mathstrut 25q^{89} \) \(\mathstrut -\mathstrut 81q^{90} \) \(\mathstrut -\mathstrut 14q^{91} \) \(\mathstrut +\mathstrut 60q^{92} \) \(\mathstrut +\mathstrut 36q^{93} \) \(\mathstrut +\mathstrut 19q^{94} \) \(\mathstrut +\mathstrut 111q^{95} \) \(\mathstrut -\mathstrut 6q^{96} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 5q^{98} \) \(\mathstrut +\mathstrut 108q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.64446 −1.16281 −0.581406 0.813614i \(-0.697497\pi\)
−0.581406 + 0.813614i \(0.697497\pi\)
\(3\) −1.94286 −1.12171 −0.560855 0.827914i \(-0.689527\pi\)
−0.560855 + 0.827914i \(0.689527\pi\)
\(4\) 0.704260 0.352130
\(5\) −2.95674 −1.32229 −0.661147 0.750257i \(-0.729930\pi\)
−0.661147 + 0.750257i \(0.729930\pi\)
\(6\) 3.19496 1.30434
\(7\) 4.77511 1.80482 0.902411 0.430876i \(-0.141795\pi\)
0.902411 + 0.430876i \(0.141795\pi\)
\(8\) 2.13080 0.753351
\(9\) 0.774694 0.258231
\(10\) 4.86225 1.53758
\(11\) 1.00000 0.301511
\(12\) −1.36828 −0.394987
\(13\) −2.28957 −0.635013 −0.317507 0.948256i \(-0.602846\pi\)
−0.317507 + 0.948256i \(0.602846\pi\)
\(14\) −7.85249 −2.09867
\(15\) 5.74452 1.48323
\(16\) −4.91254 −1.22813
\(17\) 1.00000 0.242536
\(18\) −1.27396 −0.300274
\(19\) −5.82001 −1.33520 −0.667601 0.744519i \(-0.732679\pi\)
−0.667601 + 0.744519i \(0.732679\pi\)
\(20\) −2.08231 −0.465619
\(21\) −9.27736 −2.02449
\(22\) −1.64446 −0.350601
\(23\) −3.60225 −0.751121 −0.375560 0.926798i \(-0.622550\pi\)
−0.375560 + 0.926798i \(0.622550\pi\)
\(24\) −4.13983 −0.845040
\(25\) 3.74230 0.748460
\(26\) 3.76512 0.738400
\(27\) 4.32345 0.832049
\(28\) 3.36292 0.635532
\(29\) −5.58285 −1.03671 −0.518354 0.855166i \(-0.673455\pi\)
−0.518354 + 0.855166i \(0.673455\pi\)
\(30\) −9.44665 −1.72472
\(31\) −8.37229 −1.50371 −0.751854 0.659329i \(-0.770840\pi\)
−0.751854 + 0.659329i \(0.770840\pi\)
\(32\) 3.81689 0.674738
\(33\) −1.94286 −0.338208
\(34\) −1.64446 −0.282023
\(35\) −14.1188 −2.38650
\(36\) 0.545586 0.0909310
\(37\) −7.78932 −1.28056 −0.640278 0.768143i \(-0.721181\pi\)
−0.640278 + 0.768143i \(0.721181\pi\)
\(38\) 9.57079 1.55259
\(39\) 4.44831 0.712300
\(40\) −6.30021 −0.996151
\(41\) −9.62588 −1.50331 −0.751655 0.659557i \(-0.770744\pi\)
−0.751655 + 0.659557i \(0.770744\pi\)
\(42\) 15.2563 2.35409
\(43\) 1.00000 0.152499
\(44\) 0.704260 0.106171
\(45\) −2.29057 −0.341458
\(46\) 5.92376 0.873411
\(47\) 6.14277 0.896015 0.448007 0.894030i \(-0.352134\pi\)
0.448007 + 0.894030i \(0.352134\pi\)
\(48\) 9.54436 1.37761
\(49\) 15.8017 2.25738
\(50\) −6.15408 −0.870318
\(51\) −1.94286 −0.272054
\(52\) −1.61245 −0.223607
\(53\) 9.24846 1.27037 0.635187 0.772358i \(-0.280923\pi\)
0.635187 + 0.772358i \(0.280923\pi\)
\(54\) −7.10976 −0.967516
\(55\) −2.95674 −0.398687
\(56\) 10.1748 1.35966
\(57\) 11.3074 1.49771
\(58\) 9.18079 1.20550
\(59\) 9.16404 1.19306 0.596528 0.802592i \(-0.296546\pi\)
0.596528 + 0.802592i \(0.296546\pi\)
\(60\) 4.04564 0.522289
\(61\) −2.77872 −0.355779 −0.177889 0.984050i \(-0.556927\pi\)
−0.177889 + 0.984050i \(0.556927\pi\)
\(62\) 13.7679 1.74853
\(63\) 3.69925 0.466062
\(64\) 3.54833 0.443541
\(65\) 6.76967 0.839674
\(66\) 3.19496 0.393272
\(67\) 6.69264 0.817637 0.408818 0.912616i \(-0.365941\pi\)
0.408818 + 0.912616i \(0.365941\pi\)
\(68\) 0.704260 0.0854041
\(69\) 6.99865 0.842539
\(70\) 23.2178 2.77505
\(71\) −5.95574 −0.706816 −0.353408 0.935469i \(-0.614977\pi\)
−0.353408 + 0.935469i \(0.614977\pi\)
\(72\) 1.65072 0.194539
\(73\) 2.32040 0.271582 0.135791 0.990738i \(-0.456642\pi\)
0.135791 + 0.990738i \(0.456642\pi\)
\(74\) 12.8093 1.48905
\(75\) −7.27076 −0.839555
\(76\) −4.09880 −0.470165
\(77\) 4.77511 0.544174
\(78\) −7.31509 −0.828270
\(79\) −4.03573 −0.454055 −0.227028 0.973888i \(-0.572901\pi\)
−0.227028 + 0.973888i \(0.572901\pi\)
\(80\) 14.5251 1.62395
\(81\) −10.7239 −1.19155
\(82\) 15.8294 1.74807
\(83\) −3.03874 −0.333545 −0.166772 0.985995i \(-0.553335\pi\)
−0.166772 + 0.985995i \(0.553335\pi\)
\(84\) −6.53367 −0.712882
\(85\) −2.95674 −0.320703
\(86\) −1.64446 −0.177327
\(87\) 10.8467 1.16289
\(88\) 2.13080 0.227144
\(89\) −3.24843 −0.344333 −0.172166 0.985068i \(-0.555077\pi\)
−0.172166 + 0.985068i \(0.555077\pi\)
\(90\) 3.76675 0.397051
\(91\) −10.9330 −1.14609
\(92\) −2.53692 −0.264492
\(93\) 16.2662 1.68672
\(94\) −10.1016 −1.04190
\(95\) 17.2082 1.76553
\(96\) −7.41568 −0.756860
\(97\) −12.4311 −1.26219 −0.631096 0.775705i \(-0.717394\pi\)
−0.631096 + 0.775705i \(0.717394\pi\)
\(98\) −25.9853 −2.62491
\(99\) 0.774694 0.0778597
\(100\) 2.63555 0.263555
\(101\) −7.23369 −0.719779 −0.359889 0.932995i \(-0.617186\pi\)
−0.359889 + 0.932995i \(0.617186\pi\)
\(102\) 3.19496 0.316348
\(103\) −7.89260 −0.777681 −0.388840 0.921305i \(-0.627124\pi\)
−0.388840 + 0.921305i \(0.627124\pi\)
\(104\) −4.87861 −0.478387
\(105\) 27.4307 2.67696
\(106\) −15.2088 −1.47720
\(107\) −18.1335 −1.75303 −0.876517 0.481370i \(-0.840139\pi\)
−0.876517 + 0.481370i \(0.840139\pi\)
\(108\) 3.04483 0.292989
\(109\) −17.5717 −1.68306 −0.841530 0.540210i \(-0.818345\pi\)
−0.841530 + 0.540210i \(0.818345\pi\)
\(110\) 4.86225 0.463597
\(111\) 15.1335 1.43641
\(112\) −23.4579 −2.21656
\(113\) 17.4238 1.63909 0.819545 0.573015i \(-0.194226\pi\)
0.819545 + 0.573015i \(0.194226\pi\)
\(114\) −18.5947 −1.74155
\(115\) 10.6509 0.993202
\(116\) −3.93178 −0.365056
\(117\) −1.77372 −0.163980
\(118\) −15.0699 −1.38730
\(119\) 4.77511 0.437734
\(120\) 12.2404 1.11739
\(121\) 1.00000 0.0909091
\(122\) 4.56951 0.413704
\(123\) 18.7017 1.68628
\(124\) −5.89627 −0.529501
\(125\) 3.71869 0.332609
\(126\) −6.08328 −0.541942
\(127\) 11.3492 1.00708 0.503540 0.863972i \(-0.332031\pi\)
0.503540 + 0.863972i \(0.332031\pi\)
\(128\) −13.4689 −1.19049
\(129\) −1.94286 −0.171059
\(130\) −11.1325 −0.976382
\(131\) −8.95903 −0.782754 −0.391377 0.920230i \(-0.628001\pi\)
−0.391377 + 0.920230i \(0.628001\pi\)
\(132\) −1.36828 −0.119093
\(133\) −27.7912 −2.40980
\(134\) −11.0058 −0.950757
\(135\) −12.7833 −1.10021
\(136\) 2.13080 0.182714
\(137\) 10.6613 0.910854 0.455427 0.890273i \(-0.349487\pi\)
0.455427 + 0.890273i \(0.349487\pi\)
\(138\) −11.5090 −0.979714
\(139\) −0.136853 −0.0116077 −0.00580387 0.999983i \(-0.501847\pi\)
−0.00580387 + 0.999983i \(0.501847\pi\)
\(140\) −9.94327 −0.840360
\(141\) −11.9345 −1.00507
\(142\) 9.79400 0.821894
\(143\) −2.28957 −0.191464
\(144\) −3.80571 −0.317143
\(145\) 16.5070 1.37083
\(146\) −3.81581 −0.315798
\(147\) −30.7004 −2.53213
\(148\) −5.48571 −0.450923
\(149\) −8.76063 −0.717699 −0.358849 0.933395i \(-0.616831\pi\)
−0.358849 + 0.933395i \(0.616831\pi\)
\(150\) 11.9565 0.976244
\(151\) −12.3579 −1.00567 −0.502834 0.864383i \(-0.667709\pi\)
−0.502834 + 0.864383i \(0.667709\pi\)
\(152\) −12.4013 −1.00588
\(153\) 0.774694 0.0626303
\(154\) −7.85249 −0.632772
\(155\) 24.7547 1.98834
\(156\) 3.13277 0.250822
\(157\) 4.56302 0.364168 0.182084 0.983283i \(-0.441716\pi\)
0.182084 + 0.983283i \(0.441716\pi\)
\(158\) 6.63661 0.527981
\(159\) −17.9684 −1.42499
\(160\) −11.2856 −0.892202
\(161\) −17.2011 −1.35564
\(162\) 17.6351 1.38555
\(163\) −16.9655 −1.32884 −0.664421 0.747358i \(-0.731322\pi\)
−0.664421 + 0.747358i \(0.731322\pi\)
\(164\) −6.77912 −0.529360
\(165\) 5.74452 0.447210
\(166\) 4.99709 0.387850
\(167\) 22.7932 1.76379 0.881894 0.471447i \(-0.156268\pi\)
0.881894 + 0.471447i \(0.156268\pi\)
\(168\) −19.7682 −1.52515
\(169\) −7.75786 −0.596758
\(170\) 4.86225 0.372917
\(171\) −4.50873 −0.344791
\(172\) 0.704260 0.0536993
\(173\) −8.59668 −0.653593 −0.326797 0.945095i \(-0.605969\pi\)
−0.326797 + 0.945095i \(0.605969\pi\)
\(174\) −17.8370 −1.35222
\(175\) 17.8699 1.35084
\(176\) −4.91254 −0.370296
\(177\) −17.8044 −1.33826
\(178\) 5.34192 0.400394
\(179\) −16.0783 −1.20175 −0.600873 0.799345i \(-0.705180\pi\)
−0.600873 + 0.799345i \(0.705180\pi\)
\(180\) −1.61315 −0.120237
\(181\) 4.42219 0.328699 0.164349 0.986402i \(-0.447448\pi\)
0.164349 + 0.986402i \(0.447448\pi\)
\(182\) 17.9789 1.33268
\(183\) 5.39866 0.399080
\(184\) −7.67566 −0.565857
\(185\) 23.0310 1.69327
\(186\) −26.7491 −1.96134
\(187\) 1.00000 0.0731272
\(188\) 4.32611 0.315514
\(189\) 20.6450 1.50170
\(190\) −28.2983 −2.05298
\(191\) 1.86036 0.134611 0.0673054 0.997732i \(-0.478560\pi\)
0.0673054 + 0.997732i \(0.478560\pi\)
\(192\) −6.89390 −0.497524
\(193\) 8.14579 0.586347 0.293173 0.956059i \(-0.405289\pi\)
0.293173 + 0.956059i \(0.405289\pi\)
\(194\) 20.4426 1.46769
\(195\) −13.1525 −0.941870
\(196\) 11.1285 0.794892
\(197\) −4.01311 −0.285922 −0.142961 0.989728i \(-0.545662\pi\)
−0.142961 + 0.989728i \(0.545662\pi\)
\(198\) −1.27396 −0.0905361
\(199\) 24.6152 1.74493 0.872463 0.488680i \(-0.162521\pi\)
0.872463 + 0.488680i \(0.162521\pi\)
\(200\) 7.97408 0.563853
\(201\) −13.0029 −0.917150
\(202\) 11.8955 0.836967
\(203\) −26.6587 −1.87107
\(204\) −1.36828 −0.0957985
\(205\) 28.4612 1.98782
\(206\) 12.9791 0.904296
\(207\) −2.79064 −0.193963
\(208\) 11.2476 0.779881
\(209\) −5.82001 −0.402579
\(210\) −45.1088 −3.11280
\(211\) −8.14028 −0.560400 −0.280200 0.959942i \(-0.590401\pi\)
−0.280200 + 0.959942i \(0.590401\pi\)
\(212\) 6.51332 0.447337
\(213\) 11.5712 0.792842
\(214\) 29.8199 2.03845
\(215\) −2.95674 −0.201648
\(216\) 9.21240 0.626824
\(217\) −39.9786 −2.71393
\(218\) 28.8960 1.95708
\(219\) −4.50820 −0.304636
\(220\) −2.08231 −0.140389
\(221\) −2.28957 −0.154013
\(222\) −24.8866 −1.67028
\(223\) 2.66724 0.178611 0.0893056 0.996004i \(-0.471535\pi\)
0.0893056 + 0.996004i \(0.471535\pi\)
\(224\) 18.2261 1.21778
\(225\) 2.89914 0.193276
\(226\) −28.6527 −1.90595
\(227\) 29.3656 1.94906 0.974532 0.224250i \(-0.0719932\pi\)
0.974532 + 0.224250i \(0.0719932\pi\)
\(228\) 7.96338 0.527388
\(229\) 4.07694 0.269412 0.134706 0.990886i \(-0.456991\pi\)
0.134706 + 0.990886i \(0.456991\pi\)
\(230\) −17.5150 −1.15491
\(231\) −9.27736 −0.610405
\(232\) −11.8959 −0.781005
\(233\) 27.1664 1.77973 0.889866 0.456223i \(-0.150798\pi\)
0.889866 + 0.456223i \(0.150798\pi\)
\(234\) 2.91681 0.190678
\(235\) −18.1626 −1.18479
\(236\) 6.45387 0.420111
\(237\) 7.84085 0.509318
\(238\) −7.85249 −0.509002
\(239\) −16.3415 −1.05704 −0.528520 0.848921i \(-0.677253\pi\)
−0.528520 + 0.848921i \(0.677253\pi\)
\(240\) −28.2202 −1.82160
\(241\) −15.1841 −0.978093 −0.489047 0.872258i \(-0.662655\pi\)
−0.489047 + 0.872258i \(0.662655\pi\)
\(242\) −1.64446 −0.105710
\(243\) 7.86471 0.504521
\(244\) −1.95694 −0.125280
\(245\) −46.7214 −2.98492
\(246\) −30.7543 −1.96082
\(247\) 13.3253 0.847871
\(248\) −17.8397 −1.13282
\(249\) 5.90383 0.374140
\(250\) −6.11524 −0.386762
\(251\) −6.33278 −0.399721 −0.199861 0.979824i \(-0.564049\pi\)
−0.199861 + 0.979824i \(0.564049\pi\)
\(252\) 2.60523 0.164114
\(253\) −3.60225 −0.226471
\(254\) −18.6634 −1.17104
\(255\) 5.74452 0.359736
\(256\) 15.0524 0.940777
\(257\) 25.2212 1.57326 0.786629 0.617426i \(-0.211825\pi\)
0.786629 + 0.617426i \(0.211825\pi\)
\(258\) 3.19496 0.198909
\(259\) −37.1949 −2.31118
\(260\) 4.76761 0.295674
\(261\) −4.32500 −0.267711
\(262\) 14.7328 0.910195
\(263\) −3.92188 −0.241833 −0.120917 0.992663i \(-0.538583\pi\)
−0.120917 + 0.992663i \(0.538583\pi\)
\(264\) −4.13983 −0.254789
\(265\) −27.3453 −1.67981
\(266\) 45.7016 2.80214
\(267\) 6.31123 0.386241
\(268\) 4.71336 0.287914
\(269\) 21.8430 1.33179 0.665895 0.746046i \(-0.268050\pi\)
0.665895 + 0.746046i \(0.268050\pi\)
\(270\) 21.0217 1.27934
\(271\) −10.5045 −0.638105 −0.319052 0.947737i \(-0.603365\pi\)
−0.319052 + 0.947737i \(0.603365\pi\)
\(272\) −4.91254 −0.297866
\(273\) 21.2412 1.28557
\(274\) −17.5321 −1.05915
\(275\) 3.74230 0.225669
\(276\) 4.92887 0.296683
\(277\) −27.5546 −1.65560 −0.827799 0.561025i \(-0.810407\pi\)
−0.827799 + 0.561025i \(0.810407\pi\)
\(278\) 0.225050 0.0134976
\(279\) −6.48597 −0.388305
\(280\) −30.0842 −1.79787
\(281\) 3.63868 0.217066 0.108533 0.994093i \(-0.465385\pi\)
0.108533 + 0.994093i \(0.465385\pi\)
\(282\) 19.6259 1.16870
\(283\) 2.45733 0.146073 0.0730364 0.997329i \(-0.476731\pi\)
0.0730364 + 0.997329i \(0.476731\pi\)
\(284\) −4.19439 −0.248891
\(285\) −33.4332 −1.98041
\(286\) 3.76512 0.222636
\(287\) −45.9646 −2.71321
\(288\) 2.95693 0.174238
\(289\) 1.00000 0.0588235
\(290\) −27.1452 −1.59402
\(291\) 24.1519 1.41581
\(292\) 1.63416 0.0956321
\(293\) −5.87484 −0.343212 −0.171606 0.985166i \(-0.554896\pi\)
−0.171606 + 0.985166i \(0.554896\pi\)
\(294\) 50.4857 2.94439
\(295\) −27.0957 −1.57757
\(296\) −16.5975 −0.964708
\(297\) 4.32345 0.250872
\(298\) 14.4065 0.834548
\(299\) 8.24761 0.476971
\(300\) −5.12050 −0.295632
\(301\) 4.77511 0.275233
\(302\) 20.3220 1.16940
\(303\) 14.0540 0.807382
\(304\) 28.5910 1.63981
\(305\) 8.21595 0.470444
\(306\) −1.27396 −0.0728272
\(307\) −15.4638 −0.882567 −0.441284 0.897368i \(-0.645477\pi\)
−0.441284 + 0.897368i \(0.645477\pi\)
\(308\) 3.36292 0.191620
\(309\) 15.3342 0.872331
\(310\) −40.7082 −2.31207
\(311\) −29.4004 −1.66714 −0.833571 0.552412i \(-0.813707\pi\)
−0.833571 + 0.552412i \(0.813707\pi\)
\(312\) 9.47845 0.536612
\(313\) −21.9524 −1.24082 −0.620411 0.784277i \(-0.713034\pi\)
−0.620411 + 0.784277i \(0.713034\pi\)
\(314\) −7.50371 −0.423459
\(315\) −10.9377 −0.616270
\(316\) −2.84220 −0.159887
\(317\) −3.21794 −0.180737 −0.0903687 0.995908i \(-0.528805\pi\)
−0.0903687 + 0.995908i \(0.528805\pi\)
\(318\) 29.5484 1.65699
\(319\) −5.58285 −0.312579
\(320\) −10.4915 −0.586492
\(321\) 35.2309 1.96640
\(322\) 28.2866 1.57635
\(323\) −5.82001 −0.323834
\(324\) −7.55244 −0.419580
\(325\) −8.56827 −0.475282
\(326\) 27.8992 1.54519
\(327\) 34.1392 1.88790
\(328\) −20.5108 −1.13252
\(329\) 29.3324 1.61715
\(330\) −9.44665 −0.520021
\(331\) −16.6539 −0.915380 −0.457690 0.889112i \(-0.651323\pi\)
−0.457690 + 0.889112i \(0.651323\pi\)
\(332\) −2.14006 −0.117451
\(333\) −6.03434 −0.330680
\(334\) −37.4825 −2.05095
\(335\) −19.7884 −1.08116
\(336\) 45.5754 2.48634
\(337\) 32.3995 1.76492 0.882458 0.470391i \(-0.155887\pi\)
0.882458 + 0.470391i \(0.155887\pi\)
\(338\) 12.7575 0.693917
\(339\) −33.8519 −1.83858
\(340\) −2.08231 −0.112929
\(341\) −8.37229 −0.453385
\(342\) 7.41444 0.400927
\(343\) 42.0290 2.26935
\(344\) 2.13080 0.114885
\(345\) −20.6932 −1.11408
\(346\) 14.1369 0.760006
\(347\) −1.74904 −0.0938931 −0.0469466 0.998897i \(-0.514949\pi\)
−0.0469466 + 0.998897i \(0.514949\pi\)
\(348\) 7.63888 0.409487
\(349\) −16.8556 −0.902261 −0.451131 0.892458i \(-0.648979\pi\)
−0.451131 + 0.892458i \(0.648979\pi\)
\(350\) −29.3864 −1.57077
\(351\) −9.89886 −0.528362
\(352\) 3.81689 0.203441
\(353\) −9.68542 −0.515503 −0.257751 0.966211i \(-0.582982\pi\)
−0.257751 + 0.966211i \(0.582982\pi\)
\(354\) 29.2787 1.55615
\(355\) 17.6096 0.934619
\(356\) −2.28774 −0.121250
\(357\) −9.27736 −0.491010
\(358\) 26.4401 1.39740
\(359\) 25.5976 1.35099 0.675494 0.737365i \(-0.263930\pi\)
0.675494 + 0.737365i \(0.263930\pi\)
\(360\) −4.88073 −0.257237
\(361\) 14.8725 0.782764
\(362\) −7.27213 −0.382215
\(363\) −1.94286 −0.101974
\(364\) −7.69965 −0.403571
\(365\) −6.86080 −0.359111
\(366\) −8.87790 −0.464055
\(367\) −9.80014 −0.511563 −0.255782 0.966735i \(-0.582333\pi\)
−0.255782 + 0.966735i \(0.582333\pi\)
\(368\) 17.6962 0.922477
\(369\) −7.45711 −0.388202
\(370\) −37.8736 −1.96896
\(371\) 44.1624 2.29280
\(372\) 11.4556 0.593946
\(373\) 21.5707 1.11689 0.558443 0.829543i \(-0.311399\pi\)
0.558443 + 0.829543i \(0.311399\pi\)
\(374\) −1.64446 −0.0850332
\(375\) −7.22488 −0.373091
\(376\) 13.0890 0.675013
\(377\) 12.7823 0.658324
\(378\) −33.9499 −1.74619
\(379\) −23.1734 −1.19034 −0.595168 0.803601i \(-0.702915\pi\)
−0.595168 + 0.803601i \(0.702915\pi\)
\(380\) 12.1191 0.621696
\(381\) −22.0499 −1.12965
\(382\) −3.05929 −0.156527
\(383\) 34.5842 1.76717 0.883586 0.468269i \(-0.155122\pi\)
0.883586 + 0.468269i \(0.155122\pi\)
\(384\) 26.1681 1.33539
\(385\) −14.1188 −0.719558
\(386\) −13.3955 −0.681811
\(387\) 0.774694 0.0393799
\(388\) −8.75476 −0.444455
\(389\) −33.6067 −1.70393 −0.851963 0.523601i \(-0.824588\pi\)
−0.851963 + 0.523601i \(0.824588\pi\)
\(390\) 21.6288 1.09522
\(391\) −3.60225 −0.182173
\(392\) 33.6702 1.70060
\(393\) 17.4061 0.878022
\(394\) 6.59941 0.332473
\(395\) 11.9326 0.600394
\(396\) 0.545586 0.0274167
\(397\) −9.00556 −0.451976 −0.225988 0.974130i \(-0.572561\pi\)
−0.225988 + 0.974130i \(0.572561\pi\)
\(398\) −40.4788 −2.02902
\(399\) 53.9943 2.70310
\(400\) −18.3842 −0.919210
\(401\) 8.56851 0.427891 0.213945 0.976846i \(-0.431369\pi\)
0.213945 + 0.976846i \(0.431369\pi\)
\(402\) 21.3827 1.06647
\(403\) 19.1690 0.954875
\(404\) −5.09440 −0.253456
\(405\) 31.7079 1.57558
\(406\) 43.8393 2.17571
\(407\) −7.78932 −0.386102
\(408\) −4.13983 −0.204952
\(409\) 10.1428 0.501530 0.250765 0.968048i \(-0.419318\pi\)
0.250765 + 0.968048i \(0.419318\pi\)
\(410\) −46.8034 −2.31146
\(411\) −20.7133 −1.02171
\(412\) −5.55844 −0.273845
\(413\) 43.7593 2.15325
\(414\) 4.58910 0.225542
\(415\) 8.98475 0.441044
\(416\) −8.73906 −0.428468
\(417\) 0.265886 0.0130205
\(418\) 9.57079 0.468123
\(419\) −20.5572 −1.00428 −0.502142 0.864785i \(-0.667455\pi\)
−0.502142 + 0.864785i \(0.667455\pi\)
\(420\) 19.3184 0.942639
\(421\) 35.6523 1.73759 0.868793 0.495175i \(-0.164896\pi\)
0.868793 + 0.495175i \(0.164896\pi\)
\(422\) 13.3864 0.651639
\(423\) 4.75876 0.231379
\(424\) 19.7066 0.957037
\(425\) 3.74230 0.181528
\(426\) −19.0283 −0.921926
\(427\) −13.2687 −0.642117
\(428\) −12.7707 −0.617296
\(429\) 4.44831 0.214767
\(430\) 4.86225 0.234478
\(431\) 7.85944 0.378576 0.189288 0.981922i \(-0.439382\pi\)
0.189288 + 0.981922i \(0.439382\pi\)
\(432\) −21.2391 −1.02187
\(433\) 22.3319 1.07320 0.536600 0.843837i \(-0.319708\pi\)
0.536600 + 0.843837i \(0.319708\pi\)
\(434\) 65.7434 3.15578
\(435\) −32.0708 −1.53768
\(436\) −12.3750 −0.592656
\(437\) 20.9651 1.00290
\(438\) 7.41357 0.354234
\(439\) −28.7777 −1.37348 −0.686742 0.726901i \(-0.740960\pi\)
−0.686742 + 0.726901i \(0.740960\pi\)
\(440\) −6.30021 −0.300351
\(441\) 12.2415 0.582927
\(442\) 3.76512 0.179088
\(443\) 5.48444 0.260574 0.130287 0.991476i \(-0.458410\pi\)
0.130287 + 0.991476i \(0.458410\pi\)
\(444\) 10.6580 0.505804
\(445\) 9.60475 0.455309
\(446\) −4.38617 −0.207691
\(447\) 17.0207 0.805049
\(448\) 16.9437 0.800513
\(449\) 9.92615 0.468444 0.234222 0.972183i \(-0.424746\pi\)
0.234222 + 0.972183i \(0.424746\pi\)
\(450\) −4.76753 −0.224743
\(451\) −9.62588 −0.453265
\(452\) 12.2709 0.577173
\(453\) 24.0096 1.12807
\(454\) −48.2907 −2.26639
\(455\) 32.3259 1.51546
\(456\) 24.0939 1.12830
\(457\) −22.4088 −1.04824 −0.524121 0.851644i \(-0.675606\pi\)
−0.524121 + 0.851644i \(0.675606\pi\)
\(458\) −6.70438 −0.313275
\(459\) 4.32345 0.201801
\(460\) 7.50101 0.349736
\(461\) −10.5041 −0.489224 −0.244612 0.969621i \(-0.578661\pi\)
−0.244612 + 0.969621i \(0.578661\pi\)
\(462\) 15.2563 0.709786
\(463\) 12.0208 0.558652 0.279326 0.960196i \(-0.409889\pi\)
0.279326 + 0.960196i \(0.409889\pi\)
\(464\) 27.4259 1.27322
\(465\) −48.0948 −2.23034
\(466\) −44.6742 −2.06949
\(467\) −35.0169 −1.62039 −0.810194 0.586162i \(-0.800638\pi\)
−0.810194 + 0.586162i \(0.800638\pi\)
\(468\) −1.24916 −0.0577424
\(469\) 31.9581 1.47569
\(470\) 29.8677 1.37769
\(471\) −8.86529 −0.408491
\(472\) 19.5267 0.898790
\(473\) 1.00000 0.0459800
\(474\) −12.8940 −0.592241
\(475\) −21.7802 −0.999346
\(476\) 3.36292 0.154139
\(477\) 7.16473 0.328050
\(478\) 26.8729 1.22914
\(479\) 1.88956 0.0863361 0.0431680 0.999068i \(-0.486255\pi\)
0.0431680 + 0.999068i \(0.486255\pi\)
\(480\) 21.9262 1.00079
\(481\) 17.8342 0.813170
\(482\) 24.9697 1.13734
\(483\) 33.4193 1.52063
\(484\) 0.704260 0.0320118
\(485\) 36.7556 1.66899
\(486\) −12.9332 −0.586663
\(487\) −5.29052 −0.239737 −0.119868 0.992790i \(-0.538247\pi\)
−0.119868 + 0.992790i \(0.538247\pi\)
\(488\) −5.92089 −0.268026
\(489\) 32.9616 1.49057
\(490\) 76.8317 3.47090
\(491\) 9.06938 0.409295 0.204648 0.978836i \(-0.434395\pi\)
0.204648 + 0.978836i \(0.434395\pi\)
\(492\) 13.1709 0.593788
\(493\) −5.58285 −0.251439
\(494\) −21.9130 −0.985914
\(495\) −2.29057 −0.102953
\(496\) 41.1292 1.84676
\(497\) −28.4393 −1.27568
\(498\) −9.70864 −0.435055
\(499\) −20.3970 −0.913094 −0.456547 0.889699i \(-0.650914\pi\)
−0.456547 + 0.889699i \(0.650914\pi\)
\(500\) 2.61892 0.117122
\(501\) −44.2839 −1.97846
\(502\) 10.4140 0.464801
\(503\) −43.6014 −1.94409 −0.972046 0.234791i \(-0.924559\pi\)
−0.972046 + 0.234791i \(0.924559\pi\)
\(504\) 7.88235 0.351108
\(505\) 21.3881 0.951759
\(506\) 5.92376 0.263343
\(507\) 15.0724 0.669389
\(508\) 7.99279 0.354623
\(509\) 38.8502 1.72201 0.861003 0.508599i \(-0.169836\pi\)
0.861003 + 0.508599i \(0.169836\pi\)
\(510\) −9.44665 −0.418305
\(511\) 11.0801 0.490157
\(512\) 2.18460 0.0965466
\(513\) −25.1625 −1.11095
\(514\) −41.4754 −1.82940
\(515\) 23.3363 1.02832
\(516\) −1.36828 −0.0602350
\(517\) 6.14277 0.270159
\(518\) 61.1656 2.68746
\(519\) 16.7021 0.733141
\(520\) 14.4248 0.632569
\(521\) 31.2427 1.36877 0.684384 0.729122i \(-0.260071\pi\)
0.684384 + 0.729122i \(0.260071\pi\)
\(522\) 7.11230 0.311297
\(523\) −14.7705 −0.645867 −0.322934 0.946422i \(-0.604669\pi\)
−0.322934 + 0.946422i \(0.604669\pi\)
\(524\) −6.30949 −0.275631
\(525\) −34.7187 −1.51525
\(526\) 6.44938 0.281206
\(527\) −8.37229 −0.364703
\(528\) 9.54436 0.415365
\(529\) −10.0238 −0.435818
\(530\) 44.9683 1.95330
\(531\) 7.09933 0.308085
\(532\) −19.5722 −0.848564
\(533\) 22.0391 0.954621
\(534\) −10.3786 −0.449125
\(535\) 53.6161 2.31803
\(536\) 14.2607 0.615967
\(537\) 31.2378 1.34801
\(538\) −35.9200 −1.54862
\(539\) 15.8017 0.680626
\(540\) −9.00278 −0.387418
\(541\) 37.1509 1.59724 0.798621 0.601835i \(-0.205563\pi\)
0.798621 + 0.601835i \(0.205563\pi\)
\(542\) 17.2743 0.741995
\(543\) −8.59169 −0.368705
\(544\) 3.81689 0.163648
\(545\) 51.9548 2.22550
\(546\) −34.9303 −1.49488
\(547\) 7.30496 0.312337 0.156169 0.987730i \(-0.450086\pi\)
0.156169 + 0.987730i \(0.450086\pi\)
\(548\) 7.50831 0.320739
\(549\) −2.15266 −0.0918732
\(550\) −6.15408 −0.262411
\(551\) 32.4922 1.38422
\(552\) 14.9127 0.634727
\(553\) −19.2711 −0.819489
\(554\) 45.3126 1.92515
\(555\) −44.7459 −1.89936
\(556\) −0.0963802 −0.00408743
\(557\) 22.3229 0.945852 0.472926 0.881102i \(-0.343198\pi\)
0.472926 + 0.881102i \(0.343198\pi\)
\(558\) 10.6659 0.451525
\(559\) −2.28957 −0.0968386
\(560\) 69.3589 2.93095
\(561\) −1.94286 −0.0820275
\(562\) −5.98368 −0.252406
\(563\) −17.0300 −0.717728 −0.358864 0.933390i \(-0.616836\pi\)
−0.358864 + 0.933390i \(0.616836\pi\)
\(564\) −8.40501 −0.353915
\(565\) −51.5175 −2.16736
\(566\) −4.04098 −0.169855
\(567\) −51.2080 −2.15053
\(568\) −12.6905 −0.532481
\(569\) 15.7258 0.659262 0.329631 0.944110i \(-0.393076\pi\)
0.329631 + 0.944110i \(0.393076\pi\)
\(570\) 54.9796 2.30284
\(571\) −26.0892 −1.09180 −0.545900 0.837850i \(-0.683812\pi\)
−0.545900 + 0.837850i \(0.683812\pi\)
\(572\) −1.61245 −0.0674201
\(573\) −3.61441 −0.150994
\(574\) 75.5871 3.15495
\(575\) −13.4807 −0.562184
\(576\) 2.74887 0.114536
\(577\) −25.7780 −1.07315 −0.536577 0.843851i \(-0.680283\pi\)
−0.536577 + 0.843851i \(0.680283\pi\)
\(578\) −1.64446 −0.0684007
\(579\) −15.8261 −0.657710
\(580\) 11.6252 0.482712
\(581\) −14.5103 −0.601989
\(582\) −39.7170 −1.64632
\(583\) 9.24846 0.383032
\(584\) 4.94429 0.204596
\(585\) 5.24442 0.216830
\(586\) 9.66096 0.399090
\(587\) −20.6768 −0.853421 −0.426711 0.904388i \(-0.640328\pi\)
−0.426711 + 0.904388i \(0.640328\pi\)
\(588\) −21.6211 −0.891638
\(589\) 48.7268 2.00775
\(590\) 44.5578 1.83442
\(591\) 7.79689 0.320721
\(592\) 38.2653 1.57270
\(593\) −27.5109 −1.12974 −0.564869 0.825181i \(-0.691073\pi\)
−0.564869 + 0.825181i \(0.691073\pi\)
\(594\) −7.10976 −0.291717
\(595\) −14.1188 −0.578812
\(596\) −6.16976 −0.252723
\(597\) −47.8238 −1.95730
\(598\) −13.5629 −0.554628
\(599\) 34.9211 1.42684 0.713418 0.700739i \(-0.247146\pi\)
0.713418 + 0.700739i \(0.247146\pi\)
\(600\) −15.4925 −0.632479
\(601\) −43.6928 −1.78227 −0.891133 0.453742i \(-0.850089\pi\)
−0.891133 + 0.453742i \(0.850089\pi\)
\(602\) −7.85249 −0.320044
\(603\) 5.18475 0.211139
\(604\) −8.70315 −0.354126
\(605\) −2.95674 −0.120209
\(606\) −23.1113 −0.938833
\(607\) −21.9130 −0.889423 −0.444711 0.895674i \(-0.646694\pi\)
−0.444711 + 0.895674i \(0.646694\pi\)
\(608\) −22.2144 −0.900912
\(609\) 51.7941 2.09880
\(610\) −13.5108 −0.547038
\(611\) −14.0643 −0.568981
\(612\) 0.545586 0.0220540
\(613\) 44.1446 1.78298 0.891491 0.453038i \(-0.149660\pi\)
0.891491 + 0.453038i \(0.149660\pi\)
\(614\) 25.4297 1.02626
\(615\) −55.2960 −2.22975
\(616\) 10.1748 0.409954
\(617\) 19.4359 0.782461 0.391230 0.920293i \(-0.372050\pi\)
0.391230 + 0.920293i \(0.372050\pi\)
\(618\) −25.2165 −1.01436
\(619\) −12.9647 −0.521096 −0.260548 0.965461i \(-0.583903\pi\)
−0.260548 + 0.965461i \(0.583903\pi\)
\(620\) 17.4337 0.700156
\(621\) −15.5741 −0.624969
\(622\) 48.3478 1.93857
\(623\) −15.5116 −0.621459
\(624\) −21.8525 −0.874800
\(625\) −29.7067 −1.18827
\(626\) 36.0999 1.44284
\(627\) 11.3074 0.451576
\(628\) 3.21355 0.128235
\(629\) −7.78932 −0.310581
\(630\) 17.9867 0.716606
\(631\) 33.6831 1.34090 0.670452 0.741953i \(-0.266100\pi\)
0.670452 + 0.741953i \(0.266100\pi\)
\(632\) −8.59933 −0.342063
\(633\) 15.8154 0.628606
\(634\) 5.29178 0.210163
\(635\) −33.5566 −1.33165
\(636\) −12.6545 −0.501782
\(637\) −36.1791 −1.43347
\(638\) 9.18079 0.363471
\(639\) −4.61388 −0.182522
\(640\) 39.8240 1.57418
\(641\) −13.1907 −0.521002 −0.260501 0.965474i \(-0.583888\pi\)
−0.260501 + 0.965474i \(0.583888\pi\)
\(642\) −57.9359 −2.28655
\(643\) −29.5366 −1.16481 −0.582404 0.812899i \(-0.697888\pi\)
−0.582404 + 0.812899i \(0.697888\pi\)
\(644\) −12.1141 −0.477361
\(645\) 5.74452 0.226190
\(646\) 9.57079 0.376558
\(647\) 0.481803 0.0189416 0.00947081 0.999955i \(-0.496985\pi\)
0.00947081 + 0.999955i \(0.496985\pi\)
\(648\) −22.8505 −0.897653
\(649\) 9.16404 0.359720
\(650\) 14.0902 0.552663
\(651\) 77.6728 3.04424
\(652\) −11.9481 −0.467925
\(653\) 47.2058 1.84731 0.923653 0.383229i \(-0.125188\pi\)
0.923653 + 0.383229i \(0.125188\pi\)
\(654\) −56.1407 −2.19528
\(655\) 26.4895 1.03503
\(656\) 47.2875 1.84627
\(657\) 1.79760 0.0701309
\(658\) −48.2360 −1.88044
\(659\) 40.1909 1.56562 0.782808 0.622263i \(-0.213787\pi\)
0.782808 + 0.622263i \(0.213787\pi\)
\(660\) 4.04564 0.157476
\(661\) −19.0399 −0.740568 −0.370284 0.928919i \(-0.620740\pi\)
−0.370284 + 0.928919i \(0.620740\pi\)
\(662\) 27.3867 1.06441
\(663\) 4.44831 0.172758
\(664\) −6.47493 −0.251276
\(665\) 82.1713 3.18647
\(666\) 9.92325 0.384518
\(667\) 20.1108 0.778693
\(668\) 16.0523 0.621083
\(669\) −5.18206 −0.200350
\(670\) 32.5413 1.25718
\(671\) −2.77872 −0.107271
\(672\) −35.4107 −1.36600
\(673\) 5.94965 0.229342 0.114671 0.993404i \(-0.463419\pi\)
0.114671 + 0.993404i \(0.463419\pi\)
\(674\) −53.2799 −2.05226
\(675\) 16.1797 0.622755
\(676\) −5.46355 −0.210137
\(677\) 29.4847 1.13319 0.566594 0.823997i \(-0.308261\pi\)
0.566594 + 0.823997i \(0.308261\pi\)
\(678\) 55.6682 2.13792
\(679\) −59.3601 −2.27803
\(680\) −6.30021 −0.241602
\(681\) −57.0532 −2.18628
\(682\) 13.7679 0.527201
\(683\) 40.9665 1.56754 0.783771 0.621050i \(-0.213294\pi\)
0.783771 + 0.621050i \(0.213294\pi\)
\(684\) −3.17532 −0.121411
\(685\) −31.5226 −1.20442
\(686\) −69.1151 −2.63883
\(687\) −7.92091 −0.302202
\(688\) −4.91254 −0.187289
\(689\) −21.1750 −0.806704
\(690\) 34.0292 1.29547
\(691\) −20.5544 −0.781927 −0.390963 0.920406i \(-0.627858\pi\)
−0.390963 + 0.920406i \(0.627858\pi\)
\(692\) −6.05430 −0.230150
\(693\) 3.69925 0.140523
\(694\) 2.87622 0.109180
\(695\) 0.404639 0.0153488
\(696\) 23.1121 0.876060
\(697\) −9.62588 −0.364606
\(698\) 27.7185 1.04916
\(699\) −52.7805 −1.99634
\(700\) 12.5851 0.475670
\(701\) −44.2235 −1.67030 −0.835148 0.550025i \(-0.814618\pi\)
−0.835148 + 0.550025i \(0.814618\pi\)
\(702\) 16.2783 0.614385
\(703\) 45.3339 1.70980
\(704\) 3.54833 0.133733
\(705\) 35.2873 1.32899
\(706\) 15.9273 0.599432
\(707\) −34.5417 −1.29907
\(708\) −12.5389 −0.471242
\(709\) 28.1386 1.05677 0.528383 0.849006i \(-0.322798\pi\)
0.528383 + 0.849006i \(0.322798\pi\)
\(710\) −28.9583 −1.08679
\(711\) −3.12646 −0.117251
\(712\) −6.92174 −0.259403
\(713\) 30.1591 1.12947
\(714\) 15.2563 0.570952
\(715\) 6.76967 0.253171
\(716\) −11.3233 −0.423171
\(717\) 31.7491 1.18569
\(718\) −42.0943 −1.57094
\(719\) −13.1666 −0.491032 −0.245516 0.969392i \(-0.578957\pi\)
−0.245516 + 0.969392i \(0.578957\pi\)
\(720\) 11.2525 0.419356
\(721\) −37.6880 −1.40357
\(722\) −24.4573 −0.910207
\(723\) 29.5005 1.09714
\(724\) 3.11437 0.115745
\(725\) −20.8927 −0.775935
\(726\) 3.19496 0.118576
\(727\) −25.3974 −0.941939 −0.470969 0.882150i \(-0.656096\pi\)
−0.470969 + 0.882150i \(0.656096\pi\)
\(728\) −23.2959 −0.863404
\(729\) 16.8918 0.625622
\(730\) 11.2823 0.417578
\(731\) 1.00000 0.0369863
\(732\) 3.80206 0.140528
\(733\) −15.7470 −0.581628 −0.290814 0.956780i \(-0.593926\pi\)
−0.290814 + 0.956780i \(0.593926\pi\)
\(734\) 16.1160 0.594852
\(735\) 90.7731 3.34821
\(736\) −13.7494 −0.506810
\(737\) 6.69264 0.246527
\(738\) 12.2629 0.451405
\(739\) 33.1785 1.22049 0.610245 0.792213i \(-0.291071\pi\)
0.610245 + 0.792213i \(0.291071\pi\)
\(740\) 16.2198 0.596252
\(741\) −25.8892 −0.951064
\(742\) −72.6235 −2.66609
\(743\) −7.68842 −0.282061 −0.141030 0.990005i \(-0.545042\pi\)
−0.141030 + 0.990005i \(0.545042\pi\)
\(744\) 34.6599 1.27069
\(745\) 25.9029 0.949009
\(746\) −35.4722 −1.29873
\(747\) −2.35409 −0.0861317
\(748\) 0.704260 0.0257503
\(749\) −86.5896 −3.16392
\(750\) 11.8810 0.433834
\(751\) 1.82447 0.0665760 0.0332880 0.999446i \(-0.489402\pi\)
0.0332880 + 0.999446i \(0.489402\pi\)
\(752\) −30.1766 −1.10043
\(753\) 12.3037 0.448371
\(754\) −21.0201 −0.765506
\(755\) 36.5390 1.32979
\(756\) 14.5394 0.528794
\(757\) −22.6835 −0.824445 −0.412222 0.911083i \(-0.635247\pi\)
−0.412222 + 0.911083i \(0.635247\pi\)
\(758\) 38.1078 1.38414
\(759\) 6.99865 0.254035
\(760\) 36.6673 1.33006
\(761\) −20.8028 −0.754100 −0.377050 0.926193i \(-0.623062\pi\)
−0.377050 + 0.926193i \(0.623062\pi\)
\(762\) 36.2602 1.31357
\(763\) −83.9067 −3.03763
\(764\) 1.31018 0.0474005
\(765\) −2.29057 −0.0828156
\(766\) −56.8725 −2.05489
\(767\) −20.9817 −0.757606
\(768\) −29.2447 −1.05528
\(769\) 7.17586 0.258768 0.129384 0.991595i \(-0.458700\pi\)
0.129384 + 0.991595i \(0.458700\pi\)
\(770\) 23.2178 0.836710
\(771\) −49.0013 −1.76474
\(772\) 5.73675 0.206470
\(773\) 19.0414 0.684872 0.342436 0.939541i \(-0.388748\pi\)
0.342436 + 0.939541i \(0.388748\pi\)
\(774\) −1.27396 −0.0457914
\(775\) −31.3316 −1.12547
\(776\) −26.4882 −0.950872
\(777\) 72.2643 2.59247
\(778\) 55.2650 1.98135
\(779\) 56.0227 2.00722
\(780\) −9.26278 −0.331661
\(781\) −5.95574 −0.213113
\(782\) 5.92376 0.211833
\(783\) −24.1372 −0.862592
\(784\) −77.6263 −2.77237
\(785\) −13.4916 −0.481537
\(786\) −28.6237 −1.02097
\(787\) −38.7395 −1.38091 −0.690456 0.723374i \(-0.742590\pi\)
−0.690456 + 0.723374i \(0.742590\pi\)
\(788\) −2.82627 −0.100682
\(789\) 7.61965 0.271267
\(790\) −19.6227 −0.698145
\(791\) 83.2004 2.95827
\(792\) 1.65072 0.0586556
\(793\) 6.36208 0.225924
\(794\) 14.8093 0.525563
\(795\) 53.1280 1.88425
\(796\) 17.3355 0.614441
\(797\) −14.5289 −0.514639 −0.257320 0.966326i \(-0.582839\pi\)
−0.257320 + 0.966326i \(0.582839\pi\)
\(798\) −88.7917 −3.14319
\(799\) 6.14277 0.217315
\(800\) 14.2840 0.505015
\(801\) −2.51654 −0.0889175
\(802\) −14.0906 −0.497556
\(803\) 2.32040 0.0818850
\(804\) −9.15739 −0.322956
\(805\) 50.8592 1.79255
\(806\) −31.5227 −1.11034
\(807\) −42.4378 −1.49388
\(808\) −15.4135 −0.542246
\(809\) 22.4885 0.790654 0.395327 0.918540i \(-0.370631\pi\)
0.395327 + 0.918540i \(0.370631\pi\)
\(810\) −52.1424 −1.83210
\(811\) 30.5584 1.07305 0.536525 0.843884i \(-0.319737\pi\)
0.536525 + 0.843884i \(0.319737\pi\)
\(812\) −18.7747 −0.658862
\(813\) 20.4088 0.715768
\(814\) 12.8093 0.448964
\(815\) 50.1626 1.75712
\(816\) 9.54436 0.334119
\(817\) −5.82001 −0.203616
\(818\) −16.6795 −0.583185
\(819\) −8.46970 −0.295955
\(820\) 20.0441 0.699970
\(821\) −27.7881 −0.969810 −0.484905 0.874567i \(-0.661146\pi\)
−0.484905 + 0.874567i \(0.661146\pi\)
\(822\) 34.0623 1.18806
\(823\) 4.67070 0.162810 0.0814051 0.996681i \(-0.474059\pi\)
0.0814051 + 0.996681i \(0.474059\pi\)
\(824\) −16.8175 −0.585866
\(825\) −7.27076 −0.253135
\(826\) −71.9606 −2.50383
\(827\) 28.3357 0.985330 0.492665 0.870219i \(-0.336023\pi\)
0.492665 + 0.870219i \(0.336023\pi\)
\(828\) −1.96534 −0.0683001
\(829\) 21.9316 0.761716 0.380858 0.924634i \(-0.375629\pi\)
0.380858 + 0.924634i \(0.375629\pi\)
\(830\) −14.7751 −0.512851
\(831\) 53.5347 1.85710
\(832\) −8.12416 −0.281655
\(833\) 15.8017 0.547496
\(834\) −0.437240 −0.0151404
\(835\) −67.3934 −2.33225
\(836\) −4.09880 −0.141760
\(837\) −36.1972 −1.25116
\(838\) 33.8055 1.16779
\(839\) 26.6214 0.919072 0.459536 0.888159i \(-0.348016\pi\)
0.459536 + 0.888159i \(0.348016\pi\)
\(840\) 58.4493 2.01669
\(841\) 2.16818 0.0747648
\(842\) −58.6289 −2.02048
\(843\) −7.06944 −0.243484
\(844\) −5.73287 −0.197334
\(845\) 22.9380 0.789090
\(846\) −7.82561 −0.269050
\(847\) 4.77511 0.164075
\(848\) −45.4334 −1.56019
\(849\) −4.77423 −0.163851
\(850\) −6.15408 −0.211083
\(851\) 28.0591 0.961853
\(852\) 8.14910 0.279184
\(853\) 33.2826 1.13957 0.569787 0.821792i \(-0.307026\pi\)
0.569787 + 0.821792i \(0.307026\pi\)
\(854\) 21.8199 0.746661
\(855\) 13.3311 0.455915
\(856\) −38.6389 −1.32065
\(857\) −39.8814 −1.36232 −0.681162 0.732133i \(-0.738525\pi\)
−0.681162 + 0.732133i \(0.738525\pi\)
\(858\) −7.31509 −0.249733
\(859\) 29.0384 0.990777 0.495388 0.868672i \(-0.335026\pi\)
0.495388 + 0.868672i \(0.335026\pi\)
\(860\) −2.08231 −0.0710063
\(861\) 89.3027 3.04343
\(862\) −12.9246 −0.440212
\(863\) 25.1673 0.856704 0.428352 0.903612i \(-0.359094\pi\)
0.428352 + 0.903612i \(0.359094\pi\)
\(864\) 16.5022 0.561415
\(865\) 25.4181 0.864242
\(866\) −36.7239 −1.24793
\(867\) −1.94286 −0.0659829
\(868\) −28.1554 −0.955655
\(869\) −4.03573 −0.136903
\(870\) 52.7392 1.78803
\(871\) −15.3233 −0.519210
\(872\) −37.4417 −1.26793
\(873\) −9.63033 −0.325937
\(874\) −34.4764 −1.16618
\(875\) 17.7571 0.600301
\(876\) −3.17494 −0.107271
\(877\) 25.6479 0.866067 0.433033 0.901378i \(-0.357443\pi\)
0.433033 + 0.901378i \(0.357443\pi\)
\(878\) 47.3238 1.59710
\(879\) 11.4140 0.384984
\(880\) 14.5251 0.489641
\(881\) 39.6620 1.33625 0.668124 0.744050i \(-0.267098\pi\)
0.668124 + 0.744050i \(0.267098\pi\)
\(882\) −20.1306 −0.677834
\(883\) 11.4480 0.385257 0.192629 0.981272i \(-0.438299\pi\)
0.192629 + 0.981272i \(0.438299\pi\)
\(884\) −1.61245 −0.0542327
\(885\) 52.6430 1.76958
\(886\) −9.01896 −0.302998
\(887\) −25.5448 −0.857709 −0.428855 0.903374i \(-0.641083\pi\)
−0.428855 + 0.903374i \(0.641083\pi\)
\(888\) 32.2465 1.08212
\(889\) 54.1937 1.81760
\(890\) −15.7947 −0.529438
\(891\) −10.7239 −0.359265
\(892\) 1.87843 0.0628944
\(893\) −35.7510 −1.19636
\(894\) −27.9898 −0.936120
\(895\) 47.5392 1.58906
\(896\) −64.3154 −2.14863
\(897\) −16.0239 −0.535023
\(898\) −16.3232 −0.544712
\(899\) 46.7412 1.55891
\(900\) 2.04175 0.0680582
\(901\) 9.24846 0.308111
\(902\) 15.8294 0.527061
\(903\) −9.27736 −0.308731
\(904\) 37.1265 1.23481
\(905\) −13.0753 −0.434636
\(906\) −39.4828 −1.31173
\(907\) 23.7587 0.788895 0.394448 0.918918i \(-0.370936\pi\)
0.394448 + 0.918918i \(0.370936\pi\)
\(908\) 20.6810 0.686324
\(909\) −5.60389 −0.185869
\(910\) −53.1588 −1.76220
\(911\) 27.0870 0.897431 0.448716 0.893675i \(-0.351882\pi\)
0.448716 + 0.893675i \(0.351882\pi\)
\(912\) −55.5483 −1.83939
\(913\) −3.03874 −0.100568
\(914\) 36.8505 1.21891
\(915\) −15.9624 −0.527701
\(916\) 2.87123 0.0948679
\(917\) −42.7803 −1.41273
\(918\) −7.10976 −0.234657
\(919\) −6.51543 −0.214924 −0.107462 0.994209i \(-0.534272\pi\)
−0.107462 + 0.994209i \(0.534272\pi\)
\(920\) 22.6949 0.748229
\(921\) 30.0440 0.989984
\(922\) 17.2736 0.568875
\(923\) 13.6361 0.448838
\(924\) −6.53367 −0.214942
\(925\) −29.1500 −0.958446
\(926\) −19.7677 −0.649607
\(927\) −6.11435 −0.200821
\(928\) −21.3091 −0.699507
\(929\) 19.0451 0.624849 0.312425 0.949943i \(-0.398859\pi\)
0.312425 + 0.949943i \(0.398859\pi\)
\(930\) 79.0902 2.59347
\(931\) −91.9659 −3.01406
\(932\) 19.1322 0.626697
\(933\) 57.1207 1.87005
\(934\) 57.5840 1.88421
\(935\) −2.95674 −0.0966957
\(936\) −3.77943 −0.123535
\(937\) −2.95270 −0.0964606 −0.0482303 0.998836i \(-0.515358\pi\)
−0.0482303 + 0.998836i \(0.515358\pi\)
\(938\) −52.5539 −1.71595
\(939\) 42.6503 1.39184
\(940\) −12.7912 −0.417202
\(941\) 54.7847 1.78593 0.892966 0.450125i \(-0.148621\pi\)
0.892966 + 0.450125i \(0.148621\pi\)
\(942\) 14.5786 0.474998
\(943\) 34.6748 1.12917
\(944\) −45.0187 −1.46523
\(945\) −61.0417 −1.98569
\(946\) −1.64446 −0.0534661
\(947\) 9.55200 0.310398 0.155199 0.987883i \(-0.450398\pi\)
0.155199 + 0.987883i \(0.450398\pi\)
\(948\) 5.52200 0.179346
\(949\) −5.31271 −0.172458
\(950\) 35.8168 1.16205
\(951\) 6.25199 0.202735
\(952\) 10.1748 0.329767
\(953\) 55.6199 1.80170 0.900852 0.434125i \(-0.142943\pi\)
0.900852 + 0.434125i \(0.142943\pi\)
\(954\) −11.7821 −0.381461
\(955\) −5.50059 −0.177995
\(956\) −11.5086 −0.372216
\(957\) 10.8467 0.350623
\(958\) −3.10731 −0.100393
\(959\) 50.9087 1.64393
\(960\) 20.3835 0.657873
\(961\) 39.0953 1.26114
\(962\) −29.3277 −0.945564
\(963\) −14.0479 −0.452688
\(964\) −10.6935 −0.344416
\(965\) −24.0850 −0.775323
\(966\) −54.9569 −1.76821
\(967\) 52.7756 1.69715 0.848575 0.529075i \(-0.177461\pi\)
0.848575 + 0.529075i \(0.177461\pi\)
\(968\) 2.13080 0.0684864
\(969\) 11.3074 0.363248
\(970\) −60.4433 −1.94072
\(971\) 35.3771 1.13531 0.567653 0.823268i \(-0.307851\pi\)
0.567653 + 0.823268i \(0.307851\pi\)
\(972\) 5.53880 0.177657
\(973\) −0.653489 −0.0209499
\(974\) 8.70007 0.278768
\(975\) 16.6469 0.533128
\(976\) 13.6506 0.436944
\(977\) 5.57192 0.178262 0.0891308 0.996020i \(-0.471591\pi\)
0.0891308 + 0.996020i \(0.471591\pi\)
\(978\) −54.2041 −1.73326
\(979\) −3.24843 −0.103820
\(980\) −32.9040 −1.05108
\(981\) −13.6127 −0.434619
\(982\) −14.9143 −0.475933
\(983\) 17.5270 0.559023 0.279511 0.960142i \(-0.409827\pi\)
0.279511 + 0.960142i \(0.409827\pi\)
\(984\) 39.8495 1.27036
\(985\) 11.8657 0.378073
\(986\) 9.18079 0.292376
\(987\) −56.9886 −1.81397
\(988\) 9.38450 0.298561
\(989\) −3.60225 −0.114545
\(990\) 3.76675 0.119715
\(991\) −16.4255 −0.521774 −0.260887 0.965369i \(-0.584015\pi\)
−0.260887 + 0.965369i \(0.584015\pi\)
\(992\) −31.9562 −1.01461
\(993\) 32.3561 1.02679
\(994\) 46.7674 1.48337
\(995\) −72.7807 −2.30730
\(996\) 4.15783 0.131746
\(997\) 9.17777 0.290663 0.145331 0.989383i \(-0.453575\pi\)
0.145331 + 0.989383i \(0.453575\pi\)
\(998\) 33.5421 1.06176
\(999\) −33.6768 −1.06549
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 \(a_p\))