Properties

Label 8021.2.a.a.1.14
Level 8021
Weight 2
Character 8021.1
Self dual Yes
Analytic conductor 64.048
Analytic rank 1
Dimension 134
CM No

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Newspace parameters

Level: \( N \) = \( 8021 = 13 \cdot 617 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8021.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0480074613\)
Analytic rank: \(1\)
Dimension: \(134\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 8021.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.34085 q^{2}\) \(+2.34194 q^{3}\) \(+3.47957 q^{4}\) \(-2.42598 q^{5}\) \(-5.48214 q^{6}\) \(+1.51832 q^{7}\) \(-3.46345 q^{8}\) \(+2.48470 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.34085 q^{2}\) \(+2.34194 q^{3}\) \(+3.47957 q^{4}\) \(-2.42598 q^{5}\) \(-5.48214 q^{6}\) \(+1.51832 q^{7}\) \(-3.46345 q^{8}\) \(+2.48470 q^{9}\) \(+5.67886 q^{10}\) \(+2.65943 q^{11}\) \(+8.14896 q^{12}\) \(+1.00000 q^{13}\) \(-3.55415 q^{14}\) \(-5.68152 q^{15}\) \(+1.14827 q^{16}\) \(+3.00913 q^{17}\) \(-5.81631 q^{18}\) \(+2.11531 q^{19}\) \(-8.44138 q^{20}\) \(+3.55581 q^{21}\) \(-6.22532 q^{22}\) \(-7.19317 q^{23}\) \(-8.11121 q^{24}\) \(+0.885393 q^{25}\) \(-2.34085 q^{26}\) \(-1.20680 q^{27}\) \(+5.28309 q^{28}\) \(+3.00331 q^{29}\) \(+13.2996 q^{30}\) \(-2.77304 q^{31}\) \(+4.23897 q^{32}\) \(+6.22823 q^{33}\) \(-7.04393 q^{34}\) \(-3.68341 q^{35}\) \(+8.64570 q^{36}\) \(-4.23653 q^{37}\) \(-4.95162 q^{38}\) \(+2.34194 q^{39}\) \(+8.40228 q^{40}\) \(-7.07473 q^{41}\) \(-8.32362 q^{42}\) \(-9.17119 q^{43}\) \(+9.25367 q^{44}\) \(-6.02784 q^{45}\) \(+16.8381 q^{46}\) \(+8.86754 q^{47}\) \(+2.68919 q^{48}\) \(-4.69471 q^{49}\) \(-2.07257 q^{50}\) \(+7.04722 q^{51}\) \(+3.47957 q^{52}\) \(+1.43807 q^{53}\) \(+2.82493 q^{54}\) \(-6.45173 q^{55}\) \(-5.25862 q^{56}\) \(+4.95394 q^{57}\) \(-7.03030 q^{58}\) \(+8.99201 q^{59}\) \(-19.7692 q^{60}\) \(-0.583142 q^{61}\) \(+6.49126 q^{62}\) \(+3.77257 q^{63}\) \(-12.2193 q^{64}\) \(-2.42598 q^{65}\) \(-14.5793 q^{66}\) \(+0.703364 q^{67}\) \(+10.4705 q^{68}\) \(-16.8460 q^{69}\) \(+8.62231 q^{70}\) \(-7.84594 q^{71}\) \(-8.60565 q^{72}\) \(-6.82349 q^{73}\) \(+9.91707 q^{74}\) \(+2.07354 q^{75}\) \(+7.36037 q^{76}\) \(+4.03785 q^{77}\) \(-5.48214 q^{78}\) \(-15.3853 q^{79}\) \(-2.78569 q^{80}\) \(-10.2804 q^{81}\) \(+16.5609 q^{82}\) \(-4.23397 q^{83}\) \(+12.3727 q^{84}\) \(-7.30011 q^{85}\) \(+21.4684 q^{86}\) \(+7.03359 q^{87}\) \(-9.21080 q^{88}\) \(+9.26227 q^{89}\) \(+14.1103 q^{90}\) \(+1.51832 q^{91}\) \(-25.0292 q^{92}\) \(-6.49430 q^{93}\) \(-20.7576 q^{94}\) \(-5.13170 q^{95}\) \(+9.92743 q^{96}\) \(-9.77363 q^{97}\) \(+10.9896 q^{98}\) \(+6.60789 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(134q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 33q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 101q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(134q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 33q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 101q^{9} \) \(\mathstrut -\mathstrut 33q^{10} \) \(\mathstrut -\mathstrut 47q^{11} \) \(\mathstrut -\mathstrut 53q^{12} \) \(\mathstrut +\mathstrut 134q^{13} \) \(\mathstrut -\mathstrut 28q^{14} \) \(\mathstrut -\mathstrut 30q^{15} \) \(\mathstrut +\mathstrut 30q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut -\mathstrut 14q^{18} \) \(\mathstrut -\mathstrut 87q^{19} \) \(\mathstrut -\mathstrut 12q^{20} \) \(\mathstrut -\mathstrut 24q^{21} \) \(\mathstrut -\mathstrut 52q^{22} \) \(\mathstrut -\mathstrut 44q^{23} \) \(\mathstrut -\mathstrut 36q^{24} \) \(\mathstrut +\mathstrut 58q^{25} \) \(\mathstrut -\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 117q^{27} \) \(\mathstrut -\mathstrut 71q^{28} \) \(\mathstrut -\mathstrut 42q^{29} \) \(\mathstrut -\mathstrut 21q^{30} \) \(\mathstrut -\mathstrut 82q^{31} \) \(\mathstrut -\mathstrut 31q^{32} \) \(\mathstrut +\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 30q^{34} \) \(\mathstrut -\mathstrut 54q^{35} \) \(\mathstrut +\mathstrut 32q^{36} \) \(\mathstrut -\mathstrut 55q^{37} \) \(\mathstrut -\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut 33q^{39} \) \(\mathstrut -\mathstrut 86q^{40} \) \(\mathstrut -\mathstrut 16q^{41} \) \(\mathstrut +\mathstrut 6q^{42} \) \(\mathstrut -\mathstrut 148q^{43} \) \(\mathstrut -\mathstrut 54q^{44} \) \(\mathstrut -\mathstrut 24q^{45} \) \(\mathstrut -\mathstrut 57q^{46} \) \(\mathstrut -\mathstrut 21q^{47} \) \(\mathstrut -\mathstrut 82q^{48} \) \(\mathstrut +\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 17q^{50} \) \(\mathstrut -\mathstrut 123q^{51} \) \(\mathstrut +\mathstrut 98q^{52} \) \(\mathstrut -\mathstrut 17q^{53} \) \(\mathstrut -\mathstrut 10q^{54} \) \(\mathstrut -\mathstrut 148q^{55} \) \(\mathstrut -\mathstrut 47q^{56} \) \(\mathstrut -\mathstrut q^{57} \) \(\mathstrut -\mathstrut 58q^{58} \) \(\mathstrut -\mathstrut 64q^{59} \) \(\mathstrut -\mathstrut 16q^{60} \) \(\mathstrut -\mathstrut 112q^{61} \) \(\mathstrut -\mathstrut 15q^{62} \) \(\mathstrut -\mathstrut 58q^{63} \) \(\mathstrut -\mathstrut 65q^{64} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 20q^{66} \) \(\mathstrut -\mathstrut 110q^{67} \) \(\mathstrut -\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 57q^{69} \) \(\mathstrut -\mathstrut 40q^{70} \) \(\mathstrut -\mathstrut 78q^{71} \) \(\mathstrut -\mathstrut 28q^{72} \) \(\mathstrut -\mathstrut 43q^{73} \) \(\mathstrut -\mathstrut 52q^{74} \) \(\mathstrut -\mathstrut 150q^{75} \) \(\mathstrut -\mathstrut 96q^{76} \) \(\mathstrut -\mathstrut 24q^{77} \) \(\mathstrut -\mathstrut 16q^{78} \) \(\mathstrut -\mathstrut 228q^{79} \) \(\mathstrut +\mathstrut 20q^{80} \) \(\mathstrut +\mathstrut 54q^{81} \) \(\mathstrut -\mathstrut 89q^{82} \) \(\mathstrut -\mathstrut 12q^{83} \) \(\mathstrut +\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 77q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut -\mathstrut 77q^{87} \) \(\mathstrut -\mathstrut 95q^{88} \) \(\mathstrut -\mathstrut 32q^{89} \) \(\mathstrut -\mathstrut 46q^{90} \) \(\mathstrut -\mathstrut 32q^{91} \) \(\mathstrut -\mathstrut 62q^{92} \) \(\mathstrut -\mathstrut 9q^{93} \) \(\mathstrut -\mathstrut 87q^{94} \) \(\mathstrut -\mathstrut 61q^{95} \) \(\mathstrut -\mathstrut 54q^{96} \) \(\mathstrut -\mathstrut 38q^{97} \) \(\mathstrut +\mathstrut 6q^{98} \) \(\mathstrut -\mathstrut 193q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.34085 −1.65523 −0.827615 0.561296i \(-0.810303\pi\)
−0.827615 + 0.561296i \(0.810303\pi\)
\(3\) 2.34194 1.35212 0.676061 0.736846i \(-0.263686\pi\)
0.676061 + 0.736846i \(0.263686\pi\)
\(4\) 3.47957 1.73979
\(5\) −2.42598 −1.08493 −0.542466 0.840078i \(-0.682509\pi\)
−0.542466 + 0.840078i \(0.682509\pi\)
\(6\) −5.48214 −2.23807
\(7\) 1.51832 0.573870 0.286935 0.957950i \(-0.407364\pi\)
0.286935 + 0.957950i \(0.407364\pi\)
\(8\) −3.46345 −1.22452
\(9\) 2.48470 0.828234
\(10\) 5.67886 1.79581
\(11\) 2.65943 0.801848 0.400924 0.916111i \(-0.368689\pi\)
0.400924 + 0.916111i \(0.368689\pi\)
\(12\) 8.14896 2.35240
\(13\) 1.00000 0.277350
\(14\) −3.55415 −0.949886
\(15\) −5.68152 −1.46696
\(16\) 1.14827 0.287069
\(17\) 3.00913 0.729822 0.364911 0.931042i \(-0.381099\pi\)
0.364911 + 0.931042i \(0.381099\pi\)
\(18\) −5.81631 −1.37092
\(19\) 2.11531 0.485285 0.242643 0.970116i \(-0.421986\pi\)
0.242643 + 0.970116i \(0.421986\pi\)
\(20\) −8.44138 −1.88755
\(21\) 3.55581 0.775942
\(22\) −6.22532 −1.32724
\(23\) −7.19317 −1.49988 −0.749940 0.661506i \(-0.769918\pi\)
−0.749940 + 0.661506i \(0.769918\pi\)
\(24\) −8.11121 −1.65569
\(25\) 0.885393 0.177079
\(26\) −2.34085 −0.459078
\(27\) −1.20680 −0.232249
\(28\) 5.28309 0.998411
\(29\) 3.00331 0.557701 0.278851 0.960334i \(-0.410047\pi\)
0.278851 + 0.960334i \(0.410047\pi\)
\(30\) 13.2996 2.42816
\(31\) −2.77304 −0.498052 −0.249026 0.968497i \(-0.580111\pi\)
−0.249026 + 0.968497i \(0.580111\pi\)
\(32\) 4.23897 0.749351
\(33\) 6.22823 1.08420
\(34\) −7.04393 −1.20802
\(35\) −3.68341 −0.622610
\(36\) 8.64570 1.44095
\(37\) −4.23653 −0.696481 −0.348241 0.937405i \(-0.613221\pi\)
−0.348241 + 0.937405i \(0.613221\pi\)
\(38\) −4.95162 −0.803259
\(39\) 2.34194 0.375011
\(40\) 8.40228 1.32852
\(41\) −7.07473 −1.10489 −0.552444 0.833550i \(-0.686305\pi\)
−0.552444 + 0.833550i \(0.686305\pi\)
\(42\) −8.32362 −1.28436
\(43\) −9.17119 −1.39859 −0.699297 0.714831i \(-0.746503\pi\)
−0.699297 + 0.714831i \(0.746503\pi\)
\(44\) 9.25367 1.39504
\(45\) −6.02784 −0.898578
\(46\) 16.8381 2.48265
\(47\) 8.86754 1.29346 0.646732 0.762718i \(-0.276135\pi\)
0.646732 + 0.762718i \(0.276135\pi\)
\(48\) 2.68919 0.388152
\(49\) −4.69471 −0.670673
\(50\) −2.07257 −0.293106
\(51\) 7.04722 0.986809
\(52\) 3.47957 0.482530
\(53\) 1.43807 0.197534 0.0987671 0.995111i \(-0.468510\pi\)
0.0987671 + 0.995111i \(0.468510\pi\)
\(54\) 2.82493 0.384425
\(55\) −6.45173 −0.869951
\(56\) −5.25862 −0.702712
\(57\) 4.95394 0.656165
\(58\) −7.03030 −0.923124
\(59\) 8.99201 1.17066 0.585330 0.810795i \(-0.300965\pi\)
0.585330 + 0.810795i \(0.300965\pi\)
\(60\) −19.7692 −2.55220
\(61\) −0.583142 −0.0746636 −0.0373318 0.999303i \(-0.511886\pi\)
−0.0373318 + 0.999303i \(0.511886\pi\)
\(62\) 6.49126 0.824391
\(63\) 3.77257 0.475299
\(64\) −12.2193 −1.52742
\(65\) −2.42598 −0.300906
\(66\) −14.5793 −1.79459
\(67\) 0.703364 0.0859296 0.0429648 0.999077i \(-0.486320\pi\)
0.0429648 + 0.999077i \(0.486320\pi\)
\(68\) 10.4705 1.26973
\(69\) −16.8460 −2.02802
\(70\) 8.62231 1.03056
\(71\) −7.84594 −0.931142 −0.465571 0.885011i \(-0.654151\pi\)
−0.465571 + 0.885011i \(0.654151\pi\)
\(72\) −8.60565 −1.01419
\(73\) −6.82349 −0.798630 −0.399315 0.916814i \(-0.630752\pi\)
−0.399315 + 0.916814i \(0.630752\pi\)
\(74\) 9.91707 1.15284
\(75\) 2.07354 0.239432
\(76\) 7.36037 0.844292
\(77\) 4.03785 0.460156
\(78\) −5.48214 −0.620730
\(79\) −15.3853 −1.73098 −0.865489 0.500929i \(-0.832992\pi\)
−0.865489 + 0.500929i \(0.832992\pi\)
\(80\) −2.78569 −0.311450
\(81\) −10.2804 −1.14226
\(82\) 16.5609 1.82884
\(83\) −4.23397 −0.464738 −0.232369 0.972628i \(-0.574648\pi\)
−0.232369 + 0.972628i \(0.574648\pi\)
\(84\) 12.3727 1.34997
\(85\) −7.30011 −0.791808
\(86\) 21.4684 2.31499
\(87\) 7.03359 0.754080
\(88\) −9.21080 −0.981875
\(89\) 9.26227 0.981799 0.490899 0.871216i \(-0.336668\pi\)
0.490899 + 0.871216i \(0.336668\pi\)
\(90\) 14.1103 1.48735
\(91\) 1.51832 0.159163
\(92\) −25.0292 −2.60947
\(93\) −6.49430 −0.673427
\(94\) −20.7576 −2.14098
\(95\) −5.13170 −0.526502
\(96\) 9.92743 1.01321
\(97\) −9.77363 −0.992362 −0.496181 0.868219i \(-0.665265\pi\)
−0.496181 + 0.868219i \(0.665265\pi\)
\(98\) 10.9896 1.11012
\(99\) 6.60789 0.664118
\(100\) 3.08079 0.308079
\(101\) 10.0104 0.996074 0.498037 0.867156i \(-0.334054\pi\)
0.498037 + 0.867156i \(0.334054\pi\)
\(102\) −16.4965 −1.63340
\(103\) −16.1135 −1.58771 −0.793853 0.608110i \(-0.791928\pi\)
−0.793853 + 0.608110i \(0.791928\pi\)
\(104\) −3.46345 −0.339619
\(105\) −8.62634 −0.841845
\(106\) −3.36631 −0.326965
\(107\) −0.293953 −0.0284175 −0.0142088 0.999899i \(-0.504523\pi\)
−0.0142088 + 0.999899i \(0.504523\pi\)
\(108\) −4.19914 −0.404063
\(109\) −8.12687 −0.778413 −0.389206 0.921151i \(-0.627251\pi\)
−0.389206 + 0.921151i \(0.627251\pi\)
\(110\) 15.1025 1.43997
\(111\) −9.92171 −0.941727
\(112\) 1.74344 0.164740
\(113\) 2.41575 0.227255 0.113627 0.993523i \(-0.463753\pi\)
0.113627 + 0.993523i \(0.463753\pi\)
\(114\) −11.5964 −1.08610
\(115\) 17.4505 1.62727
\(116\) 10.4502 0.970281
\(117\) 2.48470 0.229711
\(118\) −21.0489 −1.93771
\(119\) 4.56882 0.418823
\(120\) 19.6777 1.79632
\(121\) −3.92744 −0.357040
\(122\) 1.36505 0.123585
\(123\) −16.5686 −1.49394
\(124\) −9.64898 −0.866504
\(125\) 9.98197 0.892814
\(126\) −8.83100 −0.786728
\(127\) 4.61124 0.409182 0.204591 0.978848i \(-0.434414\pi\)
0.204591 + 0.978848i \(0.434414\pi\)
\(128\) 20.1257 1.77887
\(129\) −21.4784 −1.89107
\(130\) 5.67886 0.498069
\(131\) −18.9509 −1.65575 −0.827876 0.560912i \(-0.810451\pi\)
−0.827876 + 0.560912i \(0.810451\pi\)
\(132\) 21.6716 1.88627
\(133\) 3.21171 0.278491
\(134\) −1.64647 −0.142233
\(135\) 2.92767 0.251974
\(136\) −10.4220 −0.893678
\(137\) −9.61518 −0.821480 −0.410740 0.911753i \(-0.634730\pi\)
−0.410740 + 0.911753i \(0.634730\pi\)
\(138\) 39.4339 3.35684
\(139\) −4.57728 −0.388240 −0.194120 0.980978i \(-0.562185\pi\)
−0.194120 + 0.980978i \(0.562185\pi\)
\(140\) −12.8167 −1.08321
\(141\) 20.7673 1.74892
\(142\) 18.3662 1.54125
\(143\) 2.65943 0.222393
\(144\) 2.85312 0.237760
\(145\) −7.28599 −0.605068
\(146\) 15.9728 1.32192
\(147\) −10.9948 −0.906832
\(148\) −14.7413 −1.21173
\(149\) 5.26476 0.431306 0.215653 0.976470i \(-0.430812\pi\)
0.215653 + 0.976470i \(0.430812\pi\)
\(150\) −4.85384 −0.396315
\(151\) −15.1616 −1.23383 −0.616916 0.787029i \(-0.711618\pi\)
−0.616916 + 0.787029i \(0.711618\pi\)
\(152\) −7.32627 −0.594239
\(153\) 7.47680 0.604464
\(154\) −9.45201 −0.761664
\(155\) 6.72734 0.540353
\(156\) 8.14896 0.652439
\(157\) 18.8624 1.50539 0.752693 0.658372i \(-0.228754\pi\)
0.752693 + 0.658372i \(0.228754\pi\)
\(158\) 36.0146 2.86516
\(159\) 3.36788 0.267090
\(160\) −10.2837 −0.812995
\(161\) −10.9215 −0.860736
\(162\) 24.0648 1.89071
\(163\) 17.8985 1.40192 0.700961 0.713200i \(-0.252755\pi\)
0.700961 + 0.713200i \(0.252755\pi\)
\(164\) −24.6170 −1.92227
\(165\) −15.1096 −1.17628
\(166\) 9.91108 0.769249
\(167\) 3.38343 0.261818 0.130909 0.991394i \(-0.458210\pi\)
0.130909 + 0.991394i \(0.458210\pi\)
\(168\) −12.3154 −0.950153
\(169\) 1.00000 0.0769231
\(170\) 17.0884 1.31062
\(171\) 5.25591 0.401930
\(172\) −31.9118 −2.43325
\(173\) −0.702172 −0.0533851 −0.0266926 0.999644i \(-0.508498\pi\)
−0.0266926 + 0.999644i \(0.508498\pi\)
\(174\) −16.4646 −1.24818
\(175\) 1.34431 0.101620
\(176\) 3.05375 0.230185
\(177\) 21.0588 1.58287
\(178\) −21.6816 −1.62510
\(179\) −4.47110 −0.334186 −0.167093 0.985941i \(-0.553438\pi\)
−0.167093 + 0.985941i \(0.553438\pi\)
\(180\) −20.9743 −1.56333
\(181\) 7.32982 0.544822 0.272411 0.962181i \(-0.412179\pi\)
0.272411 + 0.962181i \(0.412179\pi\)
\(182\) −3.55415 −0.263451
\(183\) −1.36569 −0.100954
\(184\) 24.9132 1.83663
\(185\) 10.2777 0.755635
\(186\) 15.2022 1.11468
\(187\) 8.00258 0.585206
\(188\) 30.8552 2.25035
\(189\) −1.83230 −0.133280
\(190\) 12.0125 0.871481
\(191\) 21.2241 1.53572 0.767859 0.640619i \(-0.221322\pi\)
0.767859 + 0.640619i \(0.221322\pi\)
\(192\) −28.6170 −2.06525
\(193\) −4.84981 −0.349097 −0.174548 0.984649i \(-0.555847\pi\)
−0.174548 + 0.984649i \(0.555847\pi\)
\(194\) 22.8786 1.64259
\(195\) −5.68152 −0.406862
\(196\) −16.3356 −1.16683
\(197\) 1.52871 0.108916 0.0544581 0.998516i \(-0.482657\pi\)
0.0544581 + 0.998516i \(0.482657\pi\)
\(198\) −15.4681 −1.09927
\(199\) 13.4566 0.953915 0.476957 0.878926i \(-0.341740\pi\)
0.476957 + 0.878926i \(0.341740\pi\)
\(200\) −3.06652 −0.216835
\(201\) 1.64724 0.116187
\(202\) −23.4329 −1.64873
\(203\) 4.55998 0.320048
\(204\) 24.5213 1.71684
\(205\) 17.1632 1.19873
\(206\) 37.7191 2.62802
\(207\) −17.8729 −1.24225
\(208\) 1.14827 0.0796185
\(209\) 5.62551 0.389125
\(210\) 20.1930 1.39345
\(211\) −12.3636 −0.851146 −0.425573 0.904924i \(-0.639927\pi\)
−0.425573 + 0.904924i \(0.639927\pi\)
\(212\) 5.00387 0.343667
\(213\) −18.3748 −1.25902
\(214\) 0.688100 0.0470376
\(215\) 22.2492 1.51738
\(216\) 4.17969 0.284392
\(217\) −4.21035 −0.285817
\(218\) 19.0238 1.28845
\(219\) −15.9802 −1.07984
\(220\) −22.4492 −1.51353
\(221\) 3.00913 0.202416
\(222\) 23.2252 1.55878
\(223\) −8.39067 −0.561881 −0.280940 0.959725i \(-0.590646\pi\)
−0.280940 + 0.959725i \(0.590646\pi\)
\(224\) 6.43610 0.430030
\(225\) 2.19994 0.146662
\(226\) −5.65491 −0.376159
\(227\) 10.0524 0.667200 0.333600 0.942715i \(-0.391737\pi\)
0.333600 + 0.942715i \(0.391737\pi\)
\(228\) 17.2376 1.14159
\(229\) 19.8995 1.31500 0.657498 0.753457i \(-0.271615\pi\)
0.657498 + 0.753457i \(0.271615\pi\)
\(230\) −40.8490 −2.69350
\(231\) 9.45643 0.622187
\(232\) −10.4018 −0.682914
\(233\) −5.78501 −0.378989 −0.189494 0.981882i \(-0.560685\pi\)
−0.189494 + 0.981882i \(0.560685\pi\)
\(234\) −5.81631 −0.380224
\(235\) −21.5125 −1.40332
\(236\) 31.2883 2.03670
\(237\) −36.0314 −2.34049
\(238\) −10.6949 −0.693248
\(239\) −11.1143 −0.718924 −0.359462 0.933160i \(-0.617040\pi\)
−0.359462 + 0.933160i \(0.617040\pi\)
\(240\) −6.52394 −0.421118
\(241\) 25.3488 1.63286 0.816430 0.577444i \(-0.195950\pi\)
0.816430 + 0.577444i \(0.195950\pi\)
\(242\) 9.19354 0.590983
\(243\) −20.4556 −1.31223
\(244\) −2.02908 −0.129899
\(245\) 11.3893 0.727635
\(246\) 38.7846 2.47282
\(247\) 2.11531 0.134594
\(248\) 9.60428 0.609873
\(249\) −9.91572 −0.628383
\(250\) −23.3663 −1.47781
\(251\) −14.0264 −0.885336 −0.442668 0.896686i \(-0.645968\pi\)
−0.442668 + 0.896686i \(0.645968\pi\)
\(252\) 13.1269 0.826918
\(253\) −19.1297 −1.20268
\(254\) −10.7942 −0.677290
\(255\) −17.0964 −1.07062
\(256\) −22.6725 −1.41703
\(257\) −20.2110 −1.26073 −0.630365 0.776299i \(-0.717095\pi\)
−0.630365 + 0.776299i \(0.717095\pi\)
\(258\) 50.2777 3.13015
\(259\) −6.43239 −0.399689
\(260\) −8.44138 −0.523512
\(261\) 7.46234 0.461907
\(262\) 44.3613 2.74065
\(263\) 5.69799 0.351353 0.175677 0.984448i \(-0.443789\pi\)
0.175677 + 0.984448i \(0.443789\pi\)
\(264\) −21.5712 −1.32761
\(265\) −3.48874 −0.214311
\(266\) −7.51813 −0.460966
\(267\) 21.6917 1.32751
\(268\) 2.44741 0.149499
\(269\) −1.06652 −0.0650270 −0.0325135 0.999471i \(-0.510351\pi\)
−0.0325135 + 0.999471i \(0.510351\pi\)
\(270\) −6.85324 −0.417075
\(271\) −16.0574 −0.975420 −0.487710 0.873006i \(-0.662168\pi\)
−0.487710 + 0.873006i \(0.662168\pi\)
\(272\) 3.45531 0.209509
\(273\) 3.55581 0.215208
\(274\) 22.5077 1.35974
\(275\) 2.35464 0.141990
\(276\) −58.6169 −3.52832
\(277\) 14.2038 0.853427 0.426713 0.904387i \(-0.359671\pi\)
0.426713 + 0.904387i \(0.359671\pi\)
\(278\) 10.7147 0.642627
\(279\) −6.89017 −0.412504
\(280\) 12.7573 0.762396
\(281\) −11.3902 −0.679481 −0.339740 0.940519i \(-0.610339\pi\)
−0.339740 + 0.940519i \(0.610339\pi\)
\(282\) −48.6130 −2.89486
\(283\) −25.9812 −1.54442 −0.772212 0.635365i \(-0.780850\pi\)
−0.772212 + 0.635365i \(0.780850\pi\)
\(284\) −27.3005 −1.61999
\(285\) −12.0182 −0.711895
\(286\) −6.22532 −0.368111
\(287\) −10.7417 −0.634061
\(288\) 10.5326 0.620638
\(289\) −7.94511 −0.467360
\(290\) 17.0554 1.00153
\(291\) −22.8893 −1.34179
\(292\) −23.7428 −1.38944
\(293\) 16.5274 0.965544 0.482772 0.875746i \(-0.339630\pi\)
0.482772 + 0.875746i \(0.339630\pi\)
\(294\) 25.7371 1.50102
\(295\) −21.8145 −1.27009
\(296\) 14.6730 0.852852
\(297\) −3.20940 −0.186228
\(298\) −12.3240 −0.713911
\(299\) −7.19317 −0.415992
\(300\) 7.21503 0.416560
\(301\) −13.9248 −0.802611
\(302\) 35.4910 2.04228
\(303\) 23.4438 1.34681
\(304\) 2.42895 0.139310
\(305\) 1.41469 0.0810050
\(306\) −17.5021 −1.00053
\(307\) −5.62180 −0.320853 −0.160427 0.987048i \(-0.551287\pi\)
−0.160427 + 0.987048i \(0.551287\pi\)
\(308\) 14.0500 0.800573
\(309\) −37.7368 −2.14677
\(310\) −15.7477 −0.894409
\(311\) −11.3999 −0.646426 −0.323213 0.946326i \(-0.604763\pi\)
−0.323213 + 0.946326i \(0.604763\pi\)
\(312\) −8.11121 −0.459207
\(313\) −9.01461 −0.509536 −0.254768 0.967002i \(-0.581999\pi\)
−0.254768 + 0.967002i \(0.581999\pi\)
\(314\) −44.1541 −2.49176
\(315\) −9.15218 −0.515667
\(316\) −53.5341 −3.01153
\(317\) 22.4985 1.26364 0.631821 0.775114i \(-0.282308\pi\)
0.631821 + 0.775114i \(0.282308\pi\)
\(318\) −7.88370 −0.442096
\(319\) 7.98710 0.447192
\(320\) 29.6439 1.65714
\(321\) −0.688422 −0.0384240
\(322\) 25.5656 1.42472
\(323\) 6.36525 0.354172
\(324\) −35.7713 −1.98729
\(325\) 0.885393 0.0491128
\(326\) −41.8978 −2.32050
\(327\) −19.0327 −1.05251
\(328\) 24.5030 1.35295
\(329\) 13.4637 0.742280
\(330\) 35.3692 1.94701
\(331\) 19.0781 1.04863 0.524314 0.851525i \(-0.324322\pi\)
0.524314 + 0.851525i \(0.324322\pi\)
\(332\) −14.7324 −0.808545
\(333\) −10.5265 −0.576849
\(334\) −7.92010 −0.433369
\(335\) −1.70635 −0.0932278
\(336\) 4.08305 0.222749
\(337\) −11.3084 −0.616008 −0.308004 0.951385i \(-0.599661\pi\)
−0.308004 + 0.951385i \(0.599661\pi\)
\(338\) −2.34085 −0.127325
\(339\) 5.65755 0.307276
\(340\) −25.4012 −1.37758
\(341\) −7.37470 −0.399362
\(342\) −12.3033 −0.665286
\(343\) −17.7563 −0.958749
\(344\) 31.7640 1.71260
\(345\) 40.8681 2.20027
\(346\) 1.64368 0.0883646
\(347\) −10.7513 −0.577162 −0.288581 0.957455i \(-0.593184\pi\)
−0.288581 + 0.957455i \(0.593184\pi\)
\(348\) 24.4739 1.31194
\(349\) 5.87035 0.314233 0.157116 0.987580i \(-0.449780\pi\)
0.157116 + 0.987580i \(0.449780\pi\)
\(350\) −3.14682 −0.168205
\(351\) −1.20680 −0.0644142
\(352\) 11.2732 0.600865
\(353\) 5.72281 0.304594 0.152297 0.988335i \(-0.451333\pi\)
0.152297 + 0.988335i \(0.451333\pi\)
\(354\) −49.2954 −2.62002
\(355\) 19.0341 1.01023
\(356\) 32.2287 1.70812
\(357\) 10.6999 0.566300
\(358\) 10.4662 0.553155
\(359\) −15.6724 −0.827157 −0.413578 0.910468i \(-0.635721\pi\)
−0.413578 + 0.910468i \(0.635721\pi\)
\(360\) 20.8772 1.10032
\(361\) −14.5255 −0.764498
\(362\) −17.1580 −0.901805
\(363\) −9.19785 −0.482762
\(364\) 5.28309 0.276909
\(365\) 16.5537 0.866459
\(366\) 3.19686 0.167103
\(367\) −15.9089 −0.830437 −0.415219 0.909722i \(-0.636295\pi\)
−0.415219 + 0.909722i \(0.636295\pi\)
\(368\) −8.25973 −0.430568
\(369\) −17.5786 −0.915105
\(370\) −24.0586 −1.25075
\(371\) 2.18345 0.113359
\(372\) −22.5974 −1.17162
\(373\) 29.1928 1.51154 0.755772 0.654835i \(-0.227262\pi\)
0.755772 + 0.654835i \(0.227262\pi\)
\(374\) −18.7328 −0.968651
\(375\) 23.3772 1.20719
\(376\) −30.7123 −1.58387
\(377\) 3.00331 0.154679
\(378\) 4.28914 0.220610
\(379\) 31.0348 1.59415 0.797076 0.603880i \(-0.206379\pi\)
0.797076 + 0.603880i \(0.206379\pi\)
\(380\) −17.8561 −0.916000
\(381\) 10.7993 0.553264
\(382\) −49.6823 −2.54197
\(383\) −12.3422 −0.630658 −0.315329 0.948982i \(-0.602115\pi\)
−0.315329 + 0.948982i \(0.602115\pi\)
\(384\) 47.1332 2.40526
\(385\) −9.79577 −0.499238
\(386\) 11.3527 0.577835
\(387\) −22.7877 −1.15836
\(388\) −34.0080 −1.72650
\(389\) −9.55393 −0.484404 −0.242202 0.970226i \(-0.577870\pi\)
−0.242202 + 0.970226i \(0.577870\pi\)
\(390\) 13.2996 0.673450
\(391\) −21.6452 −1.09465
\(392\) 16.2599 0.821250
\(393\) −44.3820 −2.23878
\(394\) −3.57848 −0.180281
\(395\) 37.3244 1.87799
\(396\) 22.9926 1.15542
\(397\) 30.3129 1.52136 0.760680 0.649127i \(-0.224866\pi\)
0.760680 + 0.649127i \(0.224866\pi\)
\(398\) −31.4999 −1.57895
\(399\) 7.52165 0.376553
\(400\) 1.01667 0.0508337
\(401\) −6.72509 −0.335835 −0.167917 0.985801i \(-0.553704\pi\)
−0.167917 + 0.985801i \(0.553704\pi\)
\(402\) −3.85594 −0.192317
\(403\) −2.77304 −0.138135
\(404\) 34.8320 1.73295
\(405\) 24.9400 1.23928
\(406\) −10.6742 −0.529753
\(407\) −11.2667 −0.558472
\(408\) −24.4077 −1.20836
\(409\) −27.4481 −1.35722 −0.678612 0.734497i \(-0.737418\pi\)
−0.678612 + 0.734497i \(0.737418\pi\)
\(410\) −40.1764 −1.98417
\(411\) −22.5182 −1.11074
\(412\) −56.0679 −2.76227
\(413\) 13.6527 0.671806
\(414\) 41.8377 2.05621
\(415\) 10.2715 0.504210
\(416\) 4.23897 0.207833
\(417\) −10.7197 −0.524948
\(418\) −13.1685 −0.644091
\(419\) −31.6035 −1.54393 −0.771967 0.635663i \(-0.780727\pi\)
−0.771967 + 0.635663i \(0.780727\pi\)
\(420\) −30.0160 −1.46463
\(421\) 6.50887 0.317223 0.158611 0.987341i \(-0.449298\pi\)
0.158611 + 0.987341i \(0.449298\pi\)
\(422\) 28.9413 1.40884
\(423\) 22.0332 1.07129
\(424\) −4.98069 −0.241884
\(425\) 2.66427 0.129236
\(426\) 43.0125 2.08396
\(427\) −0.885394 −0.0428472
\(428\) −1.02283 −0.0494404
\(429\) 6.22823 0.300702
\(430\) −52.0819 −2.51161
\(431\) 2.78910 0.134346 0.0671730 0.997741i \(-0.478602\pi\)
0.0671730 + 0.997741i \(0.478602\pi\)
\(432\) −1.38574 −0.0666712
\(433\) 2.78467 0.133823 0.0669115 0.997759i \(-0.478685\pi\)
0.0669115 + 0.997759i \(0.478685\pi\)
\(434\) 9.85579 0.473093
\(435\) −17.0634 −0.818126
\(436\) −28.2780 −1.35427
\(437\) −15.2158 −0.727870
\(438\) 37.4073 1.78739
\(439\) −2.45492 −0.117167 −0.0585836 0.998283i \(-0.518658\pi\)
−0.0585836 + 0.998283i \(0.518658\pi\)
\(440\) 22.3452 1.06527
\(441\) −11.6650 −0.555475
\(442\) −7.04393 −0.335045
\(443\) −36.8345 −1.75006 −0.875029 0.484070i \(-0.839158\pi\)
−0.875029 + 0.484070i \(0.839158\pi\)
\(444\) −34.5233 −1.63840
\(445\) −22.4701 −1.06519
\(446\) 19.6413 0.930042
\(447\) 12.3298 0.583179
\(448\) −18.5528 −0.876538
\(449\) 21.9722 1.03693 0.518466 0.855098i \(-0.326503\pi\)
0.518466 + 0.855098i \(0.326503\pi\)
\(450\) −5.14972 −0.242760
\(451\) −18.8147 −0.885951
\(452\) 8.40578 0.395375
\(453\) −35.5076 −1.66829
\(454\) −23.5311 −1.10437
\(455\) −3.68341 −0.172681
\(456\) −17.1577 −0.803484
\(457\) 7.10682 0.332443 0.166221 0.986088i \(-0.446843\pi\)
0.166221 + 0.986088i \(0.446843\pi\)
\(458\) −46.5817 −2.17662
\(459\) −3.63142 −0.169500
\(460\) 60.7203 2.83110
\(461\) −17.4123 −0.810973 −0.405487 0.914101i \(-0.632898\pi\)
−0.405487 + 0.914101i \(0.632898\pi\)
\(462\) −22.1361 −1.02986
\(463\) 20.3428 0.945408 0.472704 0.881221i \(-0.343278\pi\)
0.472704 + 0.881221i \(0.343278\pi\)
\(464\) 3.44863 0.160098
\(465\) 15.7551 0.730623
\(466\) 13.5418 0.627314
\(467\) −14.3974 −0.666233 −0.333117 0.942886i \(-0.608100\pi\)
−0.333117 + 0.942886i \(0.608100\pi\)
\(468\) 8.64570 0.399648
\(469\) 1.06793 0.0493124
\(470\) 50.3575 2.32282
\(471\) 44.1748 2.03547
\(472\) −31.1434 −1.43349
\(473\) −24.3901 −1.12146
\(474\) 84.3441 3.87405
\(475\) 1.87288 0.0859336
\(476\) 15.8975 0.728662
\(477\) 3.57318 0.163605
\(478\) 26.0169 1.18998
\(479\) −37.5170 −1.71420 −0.857098 0.515154i \(-0.827735\pi\)
−0.857098 + 0.515154i \(0.827735\pi\)
\(480\) −24.0838 −1.09927
\(481\) −4.23653 −0.193169
\(482\) −59.3377 −2.70276
\(483\) −25.5776 −1.16382
\(484\) −13.6658 −0.621173
\(485\) 23.7107 1.07665
\(486\) 47.8835 2.17204
\(487\) −9.16211 −0.415175 −0.207587 0.978216i \(-0.566561\pi\)
−0.207587 + 0.978216i \(0.566561\pi\)
\(488\) 2.01968 0.0914268
\(489\) 41.9174 1.89557
\(490\) −26.6606 −1.20440
\(491\) 35.6702 1.60977 0.804886 0.593429i \(-0.202226\pi\)
0.804886 + 0.593429i \(0.202226\pi\)
\(492\) −57.6517 −2.59914
\(493\) 9.03737 0.407023
\(494\) −4.95162 −0.222784
\(495\) −16.0306 −0.720523
\(496\) −3.18421 −0.142975
\(497\) −11.9126 −0.534354
\(498\) 23.2112 1.04012
\(499\) 9.28553 0.415677 0.207839 0.978163i \(-0.433357\pi\)
0.207839 + 0.978163i \(0.433357\pi\)
\(500\) 34.7330 1.55331
\(501\) 7.92381 0.354010
\(502\) 32.8336 1.46543
\(503\) −2.39025 −0.106576 −0.0532881 0.998579i \(-0.516970\pi\)
−0.0532881 + 0.998579i \(0.516970\pi\)
\(504\) −13.0661 −0.582010
\(505\) −24.2851 −1.08067
\(506\) 44.7798 1.99070
\(507\) 2.34194 0.104009
\(508\) 16.0452 0.711889
\(509\) −24.3716 −1.08025 −0.540126 0.841584i \(-0.681623\pi\)
−0.540126 + 0.841584i \(0.681623\pi\)
\(510\) 40.0202 1.77212
\(511\) −10.3602 −0.458309
\(512\) 12.8215 0.566635
\(513\) −2.55275 −0.112707
\(514\) 47.3109 2.08680
\(515\) 39.0910 1.72255
\(516\) −74.7357 −3.29006
\(517\) 23.5826 1.03716
\(518\) 15.0573 0.661578
\(519\) −1.64445 −0.0721832
\(520\) 8.40228 0.368464
\(521\) −23.9596 −1.04969 −0.524845 0.851198i \(-0.675877\pi\)
−0.524845 + 0.851198i \(0.675877\pi\)
\(522\) −17.4682 −0.764563
\(523\) −24.5867 −1.07510 −0.537550 0.843232i \(-0.680650\pi\)
−0.537550 + 0.843232i \(0.680650\pi\)
\(524\) −65.9411 −2.88065
\(525\) 3.14829 0.137403
\(526\) −13.3381 −0.581571
\(527\) −8.34444 −0.363490
\(528\) 7.15172 0.311239
\(529\) 28.7417 1.24964
\(530\) 8.16660 0.354734
\(531\) 22.3425 0.969580
\(532\) 11.1754 0.484514
\(533\) −7.07473 −0.306441
\(534\) −50.7770 −2.19734
\(535\) 0.713126 0.0308311
\(536\) −2.43607 −0.105222
\(537\) −10.4711 −0.451860
\(538\) 2.49657 0.107635
\(539\) −12.4853 −0.537778
\(540\) 10.1870 0.438381
\(541\) 40.1382 1.72567 0.862837 0.505482i \(-0.168685\pi\)
0.862837 + 0.505482i \(0.168685\pi\)
\(542\) 37.5880 1.61454
\(543\) 17.1660 0.736665
\(544\) 12.7556 0.546893
\(545\) 19.7156 0.844525
\(546\) −8.32362 −0.356218
\(547\) 21.3075 0.911042 0.455521 0.890225i \(-0.349453\pi\)
0.455521 + 0.890225i \(0.349453\pi\)
\(548\) −33.4567 −1.42920
\(549\) −1.44893 −0.0618390
\(550\) −5.51185 −0.235026
\(551\) 6.35294 0.270644
\(552\) 58.3453 2.48334
\(553\) −23.3597 −0.993356
\(554\) −33.2491 −1.41262
\(555\) 24.0699 1.02171
\(556\) −15.9270 −0.675455
\(557\) −35.8138 −1.51748 −0.758739 0.651395i \(-0.774184\pi\)
−0.758739 + 0.651395i \(0.774184\pi\)
\(558\) 16.1289 0.682789
\(559\) −9.17119 −0.387900
\(560\) −4.22956 −0.178732
\(561\) 18.7416 0.791270
\(562\) 26.6627 1.12470
\(563\) −7.92162 −0.333856 −0.166928 0.985969i \(-0.553385\pi\)
−0.166928 + 0.985969i \(0.553385\pi\)
\(564\) 72.2612 3.04275
\(565\) −5.86057 −0.246556
\(566\) 60.8182 2.55638
\(567\) −15.6088 −0.655510
\(568\) 27.1740 1.14020
\(569\) 19.8059 0.830305 0.415153 0.909752i \(-0.363728\pi\)
0.415153 + 0.909752i \(0.363728\pi\)
\(570\) 28.1327 1.17835
\(571\) 31.1658 1.30425 0.652125 0.758111i \(-0.273878\pi\)
0.652125 + 0.758111i \(0.273878\pi\)
\(572\) 9.25367 0.386915
\(573\) 49.7055 2.07648
\(574\) 25.1446 1.04952
\(575\) −6.36878 −0.265597
\(576\) −30.3614 −1.26506
\(577\) −3.99736 −0.166412 −0.0832062 0.996532i \(-0.526516\pi\)
−0.0832062 + 0.996532i \(0.526516\pi\)
\(578\) 18.5983 0.773588
\(579\) −11.3580 −0.472021
\(580\) −25.3521 −1.05269
\(581\) −6.42851 −0.266699
\(582\) 53.5804 2.22098
\(583\) 3.82445 0.158392
\(584\) 23.6328 0.977934
\(585\) −6.02784 −0.249221
\(586\) −38.6882 −1.59820
\(587\) −1.50438 −0.0620924 −0.0310462 0.999518i \(-0.509884\pi\)
−0.0310462 + 0.999518i \(0.509884\pi\)
\(588\) −38.2570 −1.57769
\(589\) −5.86583 −0.241697
\(590\) 51.0643 2.10229
\(591\) 3.58016 0.147268
\(592\) −4.86470 −0.199938
\(593\) 29.9659 1.23055 0.615275 0.788312i \(-0.289045\pi\)
0.615275 + 0.788312i \(0.289045\pi\)
\(594\) 7.51271 0.308250
\(595\) −11.0839 −0.454395
\(596\) 18.3191 0.750380
\(597\) 31.5147 1.28981
\(598\) 16.8381 0.688562
\(599\) 5.89108 0.240703 0.120351 0.992731i \(-0.461598\pi\)
0.120351 + 0.992731i \(0.461598\pi\)
\(600\) −7.18161 −0.293188
\(601\) −18.3146 −0.747070 −0.373535 0.927616i \(-0.621854\pi\)
−0.373535 + 0.927616i \(0.621854\pi\)
\(602\) 32.5958 1.32851
\(603\) 1.74765 0.0711698
\(604\) −52.7558 −2.14660
\(605\) 9.52790 0.387364
\(606\) −54.8785 −2.22929
\(607\) 44.5759 1.80928 0.904639 0.426178i \(-0.140140\pi\)
0.904639 + 0.426178i \(0.140140\pi\)
\(608\) 8.96673 0.363649
\(609\) 10.6792 0.432744
\(610\) −3.31158 −0.134082
\(611\) 8.86754 0.358742
\(612\) 26.0161 1.05164
\(613\) 30.8263 1.24506 0.622532 0.782595i \(-0.286104\pi\)
0.622532 + 0.782595i \(0.286104\pi\)
\(614\) 13.1598 0.531086
\(615\) 40.1952 1.62083
\(616\) −13.9849 −0.563468
\(617\) 1.00000 0.0402585
\(618\) 88.3361 3.55340
\(619\) 3.46319 0.139197 0.0695987 0.997575i \(-0.477828\pi\)
0.0695987 + 0.997575i \(0.477828\pi\)
\(620\) 23.4083 0.940099
\(621\) 8.68071 0.348345
\(622\) 26.6853 1.06998
\(623\) 14.0631 0.563425
\(624\) 2.68919 0.107654
\(625\) −28.6430 −1.14572
\(626\) 21.1018 0.843399
\(627\) 13.1746 0.526144
\(628\) 65.6332 2.61905
\(629\) −12.7483 −0.508307
\(630\) 21.4239 0.853547
\(631\) −30.5186 −1.21493 −0.607463 0.794348i \(-0.707813\pi\)
−0.607463 + 0.794348i \(0.707813\pi\)
\(632\) 53.2861 2.11961
\(633\) −28.9549 −1.15085
\(634\) −52.6656 −2.09162
\(635\) −11.1868 −0.443935
\(636\) 11.7188 0.464680
\(637\) −4.69471 −0.186011
\(638\) −18.6966 −0.740205
\(639\) −19.4948 −0.771204
\(640\) −48.8245 −1.92996
\(641\) 1.89749 0.0749462 0.0374731 0.999298i \(-0.488069\pi\)
0.0374731 + 0.999298i \(0.488069\pi\)
\(642\) 1.61149 0.0636005
\(643\) −41.8612 −1.65084 −0.825422 0.564516i \(-0.809063\pi\)
−0.825422 + 0.564516i \(0.809063\pi\)
\(644\) −38.0022 −1.49750
\(645\) 52.1063 2.05168
\(646\) −14.9001 −0.586236
\(647\) 34.7683 1.36688 0.683441 0.730005i \(-0.260482\pi\)
0.683441 + 0.730005i \(0.260482\pi\)
\(648\) 35.6055 1.39872
\(649\) 23.9136 0.938691
\(650\) −2.07257 −0.0812929
\(651\) −9.86040 −0.386460
\(652\) 62.2792 2.43904
\(653\) 31.4487 1.23068 0.615341 0.788261i \(-0.289018\pi\)
0.615341 + 0.788261i \(0.289018\pi\)
\(654\) 44.5526 1.74214
\(655\) 45.9746 1.79638
\(656\) −8.12373 −0.317178
\(657\) −16.9544 −0.661452
\(658\) −31.5166 −1.22864
\(659\) −18.3207 −0.713673 −0.356836 0.934167i \(-0.616145\pi\)
−0.356836 + 0.934167i \(0.616145\pi\)
\(660\) −52.5749 −2.04647
\(661\) −29.3618 −1.14204 −0.571020 0.820936i \(-0.693452\pi\)
−0.571020 + 0.820936i \(0.693452\pi\)
\(662\) −44.6590 −1.73572
\(663\) 7.04722 0.273691
\(664\) 14.6641 0.569079
\(665\) −7.79155 −0.302143
\(666\) 24.6410 0.954818
\(667\) −21.6034 −0.836485
\(668\) 11.7729 0.455507
\(669\) −19.6505 −0.759731
\(670\) 3.99431 0.154313
\(671\) −1.55082 −0.0598689
\(672\) 15.0730 0.581453
\(673\) 32.5036 1.25292 0.626461 0.779453i \(-0.284503\pi\)
0.626461 + 0.779453i \(0.284503\pi\)
\(674\) 26.4713 1.01964
\(675\) −1.06849 −0.0411262
\(676\) 3.47957 0.133830
\(677\) −18.2837 −0.702700 −0.351350 0.936244i \(-0.614277\pi\)
−0.351350 + 0.936244i \(0.614277\pi\)
\(678\) −13.2435 −0.508613
\(679\) −14.8395 −0.569486
\(680\) 25.2836 0.969581
\(681\) 23.5421 0.902135
\(682\) 17.2630 0.661036
\(683\) −6.70576 −0.256589 −0.128294 0.991736i \(-0.540950\pi\)
−0.128294 + 0.991736i \(0.540950\pi\)
\(684\) 18.2883 0.699272
\(685\) 23.3263 0.891250
\(686\) 41.5648 1.58695
\(687\) 46.6035 1.77803
\(688\) −10.5310 −0.401492
\(689\) 1.43807 0.0547861
\(690\) −95.6661 −3.64195
\(691\) 1.06364 0.0404629 0.0202315 0.999795i \(-0.493560\pi\)
0.0202315 + 0.999795i \(0.493560\pi\)
\(692\) −2.44326 −0.0928787
\(693\) 10.0329 0.381117
\(694\) 25.1673 0.955336
\(695\) 11.1044 0.421214
\(696\) −24.3605 −0.923383
\(697\) −21.2888 −0.806371
\(698\) −13.7416 −0.520127
\(699\) −13.5482 −0.512439
\(700\) 4.67761 0.176797
\(701\) 44.2099 1.66979 0.834893 0.550412i \(-0.185529\pi\)
0.834893 + 0.550412i \(0.185529\pi\)
\(702\) 2.82493 0.106620
\(703\) −8.96157 −0.337992
\(704\) −32.4964 −1.22476
\(705\) −50.3811 −1.89746
\(706\) −13.3962 −0.504174
\(707\) 15.1990 0.571617
\(708\) 73.2755 2.75386
\(709\) −35.2676 −1.32450 −0.662252 0.749281i \(-0.730399\pi\)
−0.662252 + 0.749281i \(0.730399\pi\)
\(710\) −44.5560 −1.67216
\(711\) −38.2278 −1.43365
\(712\) −32.0794 −1.20223
\(713\) 19.9469 0.747019
\(714\) −25.0469 −0.937356
\(715\) −6.45173 −0.241281
\(716\) −15.5575 −0.581412
\(717\) −26.0290 −0.972072
\(718\) 36.6867 1.36913
\(719\) 41.9764 1.56546 0.782728 0.622364i \(-0.213827\pi\)
0.782728 + 0.622364i \(0.213827\pi\)
\(720\) −6.92162 −0.257953
\(721\) −24.4653 −0.911136
\(722\) 34.0019 1.26542
\(723\) 59.3655 2.20783
\(724\) 25.5046 0.947873
\(725\) 2.65911 0.0987569
\(726\) 21.5308 0.799082
\(727\) −31.3884 −1.16413 −0.582065 0.813142i \(-0.697755\pi\)
−0.582065 + 0.813142i \(0.697755\pi\)
\(728\) −5.25862 −0.194897
\(729\) −17.0649 −0.632032
\(730\) −38.7497 −1.43419
\(731\) −27.5973 −1.02072
\(732\) −4.75200 −0.175639
\(733\) −38.4279 −1.41937 −0.709683 0.704521i \(-0.751162\pi\)
−0.709683 + 0.704521i \(0.751162\pi\)
\(734\) 37.2403 1.37456
\(735\) 26.6731 0.983852
\(736\) −30.4916 −1.12394
\(737\) 1.87055 0.0689025
\(738\) 41.1488 1.51471
\(739\) −32.1871 −1.18402 −0.592011 0.805930i \(-0.701666\pi\)
−0.592011 + 0.805930i \(0.701666\pi\)
\(740\) 35.7622 1.31464
\(741\) 4.95394 0.181987
\(742\) −5.11112 −0.187635
\(743\) −6.46620 −0.237222 −0.118611 0.992941i \(-0.537844\pi\)
−0.118611 + 0.992941i \(0.537844\pi\)
\(744\) 22.4927 0.824622
\(745\) −12.7722 −0.467938
\(746\) −68.3358 −2.50195
\(747\) −10.5201 −0.384912
\(748\) 27.8455 1.01813
\(749\) −0.446314 −0.0163080
\(750\) −54.7225 −1.99818
\(751\) −16.2957 −0.594640 −0.297320 0.954778i \(-0.596093\pi\)
−0.297320 + 0.954778i \(0.596093\pi\)
\(752\) 10.1824 0.371313
\(753\) −32.8490 −1.19708
\(754\) −7.03030 −0.256029
\(755\) 36.7817 1.33862
\(756\) −6.37563 −0.231879
\(757\) −41.2802 −1.50035 −0.750177 0.661237i \(-0.770032\pi\)
−0.750177 + 0.661237i \(0.770032\pi\)
\(758\) −72.6478 −2.63869
\(759\) −44.8007 −1.62616
\(760\) 17.7734 0.644709
\(761\) 0.140877 0.00510678 0.00255339 0.999997i \(-0.499187\pi\)
0.00255339 + 0.999997i \(0.499187\pi\)
\(762\) −25.2795 −0.915779
\(763\) −12.3392 −0.446708
\(764\) 73.8506 2.67182
\(765\) −18.1386 −0.655802
\(766\) 28.8913 1.04388
\(767\) 8.99201 0.324683
\(768\) −53.0977 −1.91600
\(769\) −31.7753 −1.14585 −0.572923 0.819609i \(-0.694190\pi\)
−0.572923 + 0.819609i \(0.694190\pi\)
\(770\) 22.9304 0.826354
\(771\) −47.3331 −1.70466
\(772\) −16.8752 −0.607353
\(773\) 39.4266 1.41808 0.709038 0.705171i \(-0.249130\pi\)
0.709038 + 0.705171i \(0.249130\pi\)
\(774\) 53.3425 1.91736
\(775\) −2.45523 −0.0881944
\(776\) 33.8505 1.21516
\(777\) −15.0643 −0.540429
\(778\) 22.3643 0.801799
\(779\) −14.9652 −0.536185
\(780\) −19.7692 −0.707852
\(781\) −20.8657 −0.746634
\(782\) 50.6682 1.81189
\(783\) −3.62440 −0.129525
\(784\) −5.39082 −0.192529
\(785\) −45.7599 −1.63324
\(786\) 103.892 3.70569
\(787\) 15.4489 0.550695 0.275347 0.961345i \(-0.411207\pi\)
0.275347 + 0.961345i \(0.411207\pi\)
\(788\) 5.31926 0.189491
\(789\) 13.3444 0.475073
\(790\) −87.3707 −3.10851
\(791\) 3.66788 0.130415
\(792\) −22.8861 −0.813222
\(793\) −0.583142 −0.0207080
\(794\) −70.9578 −2.51820
\(795\) −8.17042 −0.289775
\(796\) 46.8233 1.65961
\(797\) −55.4933 −1.96567 −0.982837 0.184477i \(-0.940941\pi\)
−0.982837 + 0.184477i \(0.940941\pi\)
\(798\) −17.6070 −0.623282
\(799\) 26.6836 0.943998
\(800\) 3.75315 0.132694
\(801\) 23.0140 0.813159
\(802\) 15.7424 0.555884
\(803\) −18.1466 −0.640379
\(804\) 5.73169 0.202141
\(805\) 26.4954 0.933840
\(806\) 6.49126 0.228645
\(807\) −2.49774 −0.0879244
\(808\) −34.6706 −1.21971
\(809\) 34.8125 1.22394 0.611971 0.790880i \(-0.290377\pi\)
0.611971 + 0.790880i \(0.290377\pi\)
\(810\) −58.3807 −2.05129
\(811\) 29.6716 1.04191 0.520955 0.853584i \(-0.325576\pi\)
0.520955 + 0.853584i \(0.325576\pi\)
\(812\) 15.8668 0.556815
\(813\) −37.6056 −1.31889
\(814\) 26.3737 0.924399
\(815\) −43.4215 −1.52099
\(816\) 8.09214 0.283282
\(817\) −19.3999 −0.678717
\(818\) 64.2519 2.24652
\(819\) 3.77257 0.131824
\(820\) 59.7205 2.08553
\(821\) −12.1450 −0.423865 −0.211933 0.977284i \(-0.567976\pi\)
−0.211933 + 0.977284i \(0.567976\pi\)
\(822\) 52.7117 1.83853
\(823\) 16.1021 0.561285 0.280642 0.959812i \(-0.409453\pi\)
0.280642 + 0.959812i \(0.409453\pi\)
\(824\) 55.8082 1.94417
\(825\) 5.51443 0.191988
\(826\) −31.9589 −1.11199
\(827\) −32.1114 −1.11662 −0.558312 0.829631i \(-0.688551\pi\)
−0.558312 + 0.829631i \(0.688551\pi\)
\(828\) −62.1900 −2.16125
\(829\) 25.0136 0.868759 0.434380 0.900730i \(-0.356968\pi\)
0.434380 + 0.900730i \(0.356968\pi\)
\(830\) −24.0441 −0.834583
\(831\) 33.2646 1.15394
\(832\) −12.2193 −0.423629
\(833\) −14.1270 −0.489472
\(834\) 25.0933 0.868910
\(835\) −8.20815 −0.284055
\(836\) 19.5744 0.676994
\(837\) 3.34650 0.115672
\(838\) 73.9791 2.55557
\(839\) 21.5695 0.744663 0.372332 0.928100i \(-0.378558\pi\)
0.372332 + 0.928100i \(0.378558\pi\)
\(840\) 29.8769 1.03085
\(841\) −19.9801 −0.688969
\(842\) −15.2363 −0.525077
\(843\) −26.6751 −0.918741
\(844\) −43.0201 −1.48081
\(845\) −2.42598 −0.0834563
\(846\) −51.5764 −1.77323
\(847\) −5.96310 −0.204895
\(848\) 1.65130 0.0567059
\(849\) −60.8466 −2.08825
\(850\) −6.23664 −0.213915
\(851\) 30.4741 1.04464
\(852\) −63.9363 −2.19042
\(853\) −36.7256 −1.25746 −0.628730 0.777623i \(-0.716425\pi\)
−0.628730 + 0.777623i \(0.716425\pi\)
\(854\) 2.07257 0.0709220
\(855\) −12.7508 −0.436067
\(856\) 1.01809 0.0347977
\(857\) −55.9330 −1.91064 −0.955318 0.295581i \(-0.904487\pi\)
−0.955318 + 0.295581i \(0.904487\pi\)
\(858\) −14.5793 −0.497731
\(859\) −10.5106 −0.358616 −0.179308 0.983793i \(-0.557386\pi\)
−0.179308 + 0.983793i \(0.557386\pi\)
\(860\) 77.4175 2.63992
\(861\) −25.1564 −0.857328
\(862\) −6.52885 −0.222374
\(863\) −53.9838 −1.83763 −0.918815 0.394689i \(-0.870852\pi\)
−0.918815 + 0.394689i \(0.870852\pi\)
\(864\) −5.11558 −0.174036
\(865\) 1.70346 0.0579192
\(866\) −6.51850 −0.221508
\(867\) −18.6070 −0.631927
\(868\) −14.6502 −0.497261
\(869\) −40.9160 −1.38798
\(870\) 39.9428 1.35419
\(871\) 0.703364 0.0238326
\(872\) 28.1470 0.953179
\(873\) −24.2846 −0.821908
\(874\) 35.6178 1.20479
\(875\) 15.1558 0.512359
\(876\) −55.6044 −1.87870
\(877\) −19.7264 −0.666114 −0.333057 0.942907i \(-0.608080\pi\)
−0.333057 + 0.942907i \(0.608080\pi\)
\(878\) 5.74661 0.193939
\(879\) 38.7064 1.30553
\(880\) −7.40835 −0.249735
\(881\) −52.3514 −1.76376 −0.881881 0.471472i \(-0.843723\pi\)
−0.881881 + 0.471472i \(0.843723\pi\)
\(882\) 27.3059 0.919438
\(883\) −18.8832 −0.635469 −0.317734 0.948180i \(-0.602922\pi\)
−0.317734 + 0.948180i \(0.602922\pi\)
\(884\) 10.4705 0.352161
\(885\) −51.0882 −1.71731
\(886\) 86.2239 2.89675
\(887\) 18.4114 0.618193 0.309096 0.951031i \(-0.399973\pi\)
0.309096 + 0.951031i \(0.399973\pi\)
\(888\) 34.3634 1.15316
\(889\) 7.00133 0.234817
\(890\) 52.5991 1.76313
\(891\) −27.3399 −0.915921
\(892\) −29.1959 −0.977552
\(893\) 18.7576 0.627699
\(894\) −28.8621 −0.965295
\(895\) 10.8468 0.362569
\(896\) 30.5571 1.02084
\(897\) −16.8460 −0.562472
\(898\) −51.4336 −1.71636
\(899\) −8.32830 −0.277764
\(900\) 7.65484 0.255161
\(901\) 4.32735 0.144165
\(902\) 44.0424 1.46645
\(903\) −32.6110 −1.08523
\(904\) −8.36684 −0.278277
\(905\) −17.7820 −0.591095
\(906\) 83.1179 2.76141
\(907\) −11.0164 −0.365793 −0.182896 0.983132i \(-0.558547\pi\)
−0.182896 + 0.983132i \(0.558547\pi\)
\(908\) 34.9780 1.16078
\(909\) 24.8729 0.824982
\(910\) 8.62231 0.285827
\(911\) 47.9069 1.58723 0.793613 0.608423i \(-0.208198\pi\)
0.793613 + 0.608423i \(0.208198\pi\)
\(912\) 5.68848 0.188364
\(913\) −11.2599 −0.372649
\(914\) −16.6360 −0.550269
\(915\) 3.31313 0.109529
\(916\) 69.2417 2.28781
\(917\) −28.7735 −0.950186
\(918\) 8.50060 0.280562
\(919\) −29.7835 −0.982468 −0.491234 0.871028i \(-0.663454\pi\)
−0.491234 + 0.871028i \(0.663454\pi\)
\(920\) −60.4390 −1.99262
\(921\) −13.1660 −0.433833
\(922\) 40.7596 1.34235
\(923\) −7.84594 −0.258252
\(924\) 32.9043 1.08247
\(925\) −3.75099 −0.123332
\(926\) −47.6193 −1.56487
\(927\) −40.0371 −1.31499
\(928\) 12.7310 0.417914
\(929\) 12.7826 0.419384 0.209692 0.977767i \(-0.432754\pi\)
0.209692 + 0.977767i \(0.432754\pi\)
\(930\) −36.8802 −1.20935
\(931\) −9.93077 −0.325468
\(932\) −20.1294 −0.659359
\(933\) −26.6978 −0.874047
\(934\) 33.7022 1.10277
\(935\) −19.4141 −0.634909
\(936\) −8.60565 −0.281284
\(937\) −32.9838 −1.07753 −0.538767 0.842455i \(-0.681110\pi\)
−0.538767 + 0.842455i \(0.681110\pi\)
\(938\) −2.49986 −0.0816234
\(939\) −21.1117 −0.688955
\(940\) −74.8543 −2.44148
\(941\) 14.9952 0.488830 0.244415 0.969671i \(-0.421404\pi\)
0.244415 + 0.969671i \(0.421404\pi\)
\(942\) −103.406 −3.36916
\(943\) 50.8897 1.65720
\(944\) 10.3253 0.336059
\(945\) 4.44514 0.144600
\(946\) 57.0936 1.85627
\(947\) −3.17110 −0.103047 −0.0515235 0.998672i \(-0.516408\pi\)
−0.0515235 + 0.998672i \(0.516408\pi\)
\(948\) −125.374 −4.07195
\(949\) −6.82349 −0.221500
\(950\) −4.38413 −0.142240
\(951\) 52.6903 1.70860
\(952\) −15.8239 −0.512855
\(953\) 31.0428 1.00558 0.502788 0.864410i \(-0.332308\pi\)
0.502788 + 0.864410i \(0.332308\pi\)
\(954\) −8.36427 −0.270803
\(955\) −51.4892 −1.66615
\(956\) −38.6730 −1.25077
\(957\) 18.7053 0.604658
\(958\) 87.8216 2.83739
\(959\) −14.5989 −0.471423
\(960\) 69.4243 2.24066
\(961\) −23.3103 −0.751944
\(962\) 9.91707 0.319739
\(963\) −0.730387 −0.0235364
\(964\) 88.2030 2.84083
\(965\) 11.7655 0.378746
\(966\) 59.8732 1.92639
\(967\) 10.0169 0.322120 0.161060 0.986945i \(-0.448509\pi\)
0.161060 + 0.986945i \(0.448509\pi\)
\(968\) 13.6025 0.437201
\(969\) 14.9071 0.478884
\(970\) −55.5031 −1.78210
\(971\) 25.8998 0.831163 0.415581 0.909556i \(-0.363578\pi\)
0.415581 + 0.909556i \(0.363578\pi\)
\(972\) −71.1768 −2.28300
\(973\) −6.94977 −0.222799
\(974\) 21.4471 0.687210
\(975\) 2.07354 0.0664064
\(976\) −0.669606 −0.0214336
\(977\) 19.2731 0.616601 0.308300 0.951289i \(-0.400240\pi\)
0.308300 + 0.951289i \(0.400240\pi\)
\(978\) −98.1222 −3.13760
\(979\) 24.6323 0.787253
\(980\) 39.6299 1.26593
\(981\) −20.1928 −0.644708
\(982\) −83.4985 −2.66454
\(983\) 7.67243 0.244713 0.122356 0.992486i \(-0.460955\pi\)
0.122356 + 0.992486i \(0.460955\pi\)
\(984\) 57.3846 1.82935
\(985\) −3.70863 −0.118167
\(986\) −21.1551 −0.673716
\(987\) 31.5313 1.00365
\(988\) 7.36037 0.234165
\(989\) 65.9700 2.09772
\(990\) 37.5253 1.19263
\(991\) −33.5673 −1.06630 −0.533149 0.846021i \(-0.678992\pi\)
−0.533149 + 0.846021i \(0.678992\pi\)
\(992\) −11.7548 −0.373216
\(993\) 44.6799 1.41787
\(994\) 27.8857 0.884479
\(995\) −32.6455 −1.03493
\(996\) −34.5024 −1.09325
\(997\) −42.2270 −1.33734 −0.668672 0.743558i \(-0.733137\pi\)
−0.668672 + 0.743558i \(0.733137\pi\)
\(998\) −21.7360 −0.688042
\(999\) 5.11264 0.161757
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 \(a_p\))