Properties

Label 4031.2.a.c.1.8
Level 4031
Weight 2
Character 4031.1
Self dual Yes
Analytic conductor 32.188
Analytic rank 1
Dimension 61
CM No

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Newspace parameters

Level: \( N \) = \( 4031 = 29 \cdot 139 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4031.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1876970548\)
Analytic rank: \(1\)
Dimension: \(61\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 4031.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.23009 q^{2}\) \(+1.62667 q^{3}\) \(+2.97329 q^{4}\) \(+2.06861 q^{5}\) \(-3.62762 q^{6}\) \(+3.32810 q^{7}\) \(-2.17052 q^{8}\) \(-0.353941 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.23009 q^{2}\) \(+1.62667 q^{3}\) \(+2.97329 q^{4}\) \(+2.06861 q^{5}\) \(-3.62762 q^{6}\) \(+3.32810 q^{7}\) \(-2.17052 q^{8}\) \(-0.353941 q^{9}\) \(-4.61317 q^{10}\) \(-2.00414 q^{11}\) \(+4.83656 q^{12}\) \(-4.84916 q^{13}\) \(-7.42196 q^{14}\) \(+3.36494 q^{15}\) \(-1.10613 q^{16}\) \(-1.62307 q^{17}\) \(+0.789318 q^{18}\) \(-7.82976 q^{19}\) \(+6.15056 q^{20}\) \(+5.41373 q^{21}\) \(+4.46940 q^{22}\) \(+1.63989 q^{23}\) \(-3.53072 q^{24}\) \(-0.720871 q^{25}\) \(+10.8140 q^{26}\) \(-5.45576 q^{27}\) \(+9.89541 q^{28}\) \(-1.00000 q^{29}\) \(-7.50411 q^{30}\) \(+6.32579 q^{31}\) \(+6.80781 q^{32}\) \(-3.26007 q^{33}\) \(+3.61959 q^{34}\) \(+6.88453 q^{35}\) \(-1.05237 q^{36}\) \(+5.26453 q^{37}\) \(+17.4610 q^{38}\) \(-7.88798 q^{39}\) \(-4.48995 q^{40}\) \(-10.6234 q^{41}\) \(-12.0731 q^{42}\) \(+2.54793 q^{43}\) \(-5.95888 q^{44}\) \(-0.732163 q^{45}\) \(-3.65711 q^{46}\) \(-0.424949 q^{47}\) \(-1.79931 q^{48}\) \(+4.07626 q^{49}\) \(+1.60761 q^{50}\) \(-2.64020 q^{51}\) \(-14.4179 q^{52}\) \(-6.57658 q^{53}\) \(+12.1668 q^{54}\) \(-4.14577 q^{55}\) \(-7.22371 q^{56}\) \(-12.7364 q^{57}\) \(+2.23009 q^{58}\) \(+11.3340 q^{59}\) \(+10.0049 q^{60}\) \(+8.32864 q^{61}\) \(-14.1071 q^{62}\) \(-1.17795 q^{63}\) \(-12.9697 q^{64}\) \(-10.0310 q^{65}\) \(+7.27025 q^{66}\) \(-5.61260 q^{67}\) \(-4.82586 q^{68}\) \(+2.66757 q^{69}\) \(-15.3531 q^{70}\) \(-12.4573 q^{71}\) \(+0.768235 q^{72}\) \(-13.5411 q^{73}\) \(-11.7404 q^{74}\) \(-1.17262 q^{75}\) \(-23.2801 q^{76}\) \(-6.66997 q^{77}\) \(+17.5909 q^{78}\) \(-1.51687 q^{79}\) \(-2.28815 q^{80}\) \(-7.81290 q^{81}\) \(+23.6911 q^{82}\) \(-8.94568 q^{83}\) \(+16.0966 q^{84}\) \(-3.35749 q^{85}\) \(-5.68210 q^{86}\) \(-1.62667 q^{87}\) \(+4.35002 q^{88}\) \(+9.67158 q^{89}\) \(+1.63279 q^{90}\) \(-16.1385 q^{91}\) \(+4.87588 q^{92}\) \(+10.2900 q^{93}\) \(+0.947674 q^{94}\) \(-16.1967 q^{95}\) \(+11.0741 q^{96}\) \(+15.2303 q^{97}\) \(-9.09041 q^{98}\) \(+0.709345 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut -\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 18q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 14q^{14} \) \(\mathstrut -\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 11q^{16} \) \(\mathstrut -\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 17q^{18} \) \(\mathstrut -\mathstrut 36q^{19} \) \(\mathstrut -\mathstrut 16q^{20} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 42q^{22} \) \(\mathstrut -\mathstrut 15q^{23} \) \(\mathstrut -\mathstrut 28q^{24} \) \(\mathstrut -\mathstrut 16q^{25} \) \(\mathstrut -\mathstrut 13q^{26} \) \(\mathstrut -\mathstrut 10q^{27} \) \(\mathstrut -\mathstrut 25q^{28} \) \(\mathstrut -\mathstrut 61q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut -\mathstrut 18q^{31} \) \(\mathstrut -\mathstrut 3q^{32} \) \(\mathstrut -\mathstrut 42q^{33} \) \(\mathstrut -\mathstrut 22q^{34} \) \(\mathstrut -\mathstrut 29q^{35} \) \(\mathstrut -\mathstrut 38q^{36} \) \(\mathstrut -\mathstrut 30q^{37} \) \(\mathstrut -\mathstrut 27q^{38} \) \(\mathstrut -\mathstrut 31q^{39} \) \(\mathstrut -\mathstrut 22q^{40} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 9q^{42} \) \(\mathstrut -\mathstrut 58q^{43} \) \(\mathstrut -\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut 31q^{45} \) \(\mathstrut -\mathstrut 40q^{46} \) \(\mathstrut -\mathstrut 6q^{47} \) \(\mathstrut -\mathstrut 37q^{48} \) \(\mathstrut -\mathstrut 37q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut -\mathstrut 44q^{51} \) \(\mathstrut -\mathstrut 43q^{52} \) \(\mathstrut -\mathstrut 27q^{53} \) \(\mathstrut -\mathstrut 18q^{54} \) \(\mathstrut -\mathstrut 38q^{55} \) \(\mathstrut -\mathstrut 22q^{56} \) \(\mathstrut -\mathstrut 50q^{57} \) \(\mathstrut +\mathstrut q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 76q^{61} \) \(\mathstrut -\mathstrut 17q^{62} \) \(\mathstrut -\mathstrut 6q^{63} \) \(\mathstrut -\mathstrut 60q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut -\mathstrut 7q^{66} \) \(\mathstrut -\mathstrut 45q^{67} \) \(\mathstrut -\mathstrut 31q^{68} \) \(\mathstrut -\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 48q^{70} \) \(\mathstrut -\mathstrut 28q^{71} \) \(\mathstrut -\mathstrut 40q^{72} \) \(\mathstrut -\mathstrut 50q^{73} \) \(\mathstrut -\mathstrut 17q^{74} \) \(\mathstrut -\mathstrut 35q^{75} \) \(\mathstrut -\mathstrut 100q^{76} \) \(\mathstrut +\mathstrut q^{77} \) \(\mathstrut -\mathstrut 6q^{78} \) \(\mathstrut -\mathstrut 66q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut -\mathstrut 63q^{81} \) \(\mathstrut -\mathstrut 5q^{82} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 24q^{84} \) \(\mathstrut -\mathstrut 77q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut -\mathstrut 62q^{88} \) \(\mathstrut -\mathstrut 30q^{89} \) \(\mathstrut +\mathstrut 50q^{90} \) \(\mathstrut -\mathstrut 52q^{91} \) \(\mathstrut -\mathstrut 53q^{92} \) \(\mathstrut -\mathstrut 42q^{93} \) \(\mathstrut -\mathstrut 92q^{94} \) \(\mathstrut -\mathstrut 20q^{95} \) \(\mathstrut -\mathstrut 47q^{96} \) \(\mathstrut -\mathstrut 34q^{97} \) \(\mathstrut +\mathstrut 36q^{98} \) \(\mathstrut -\mathstrut 29q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.23009 −1.57691 −0.788455 0.615093i \(-0.789119\pi\)
−0.788455 + 0.615093i \(0.789119\pi\)
\(3\) 1.62667 0.939159 0.469580 0.882890i \(-0.344406\pi\)
0.469580 + 0.882890i \(0.344406\pi\)
\(4\) 2.97329 1.48664
\(5\) 2.06861 0.925109 0.462554 0.886591i \(-0.346933\pi\)
0.462554 + 0.886591i \(0.346933\pi\)
\(6\) −3.62762 −1.48097
\(7\) 3.32810 1.25790 0.628952 0.777444i \(-0.283484\pi\)
0.628952 + 0.777444i \(0.283484\pi\)
\(8\) −2.17052 −0.767394
\(9\) −0.353941 −0.117980
\(10\) −4.61317 −1.45881
\(11\) −2.00414 −0.604270 −0.302135 0.953265i \(-0.597699\pi\)
−0.302135 + 0.953265i \(0.597699\pi\)
\(12\) 4.83656 1.39620
\(13\) −4.84916 −1.34491 −0.672457 0.740136i \(-0.734761\pi\)
−0.672457 + 0.740136i \(0.734761\pi\)
\(14\) −7.42196 −1.98360
\(15\) 3.36494 0.868824
\(16\) −1.10613 −0.276533
\(17\) −1.62307 −0.393652 −0.196826 0.980438i \(-0.563063\pi\)
−0.196826 + 0.980438i \(0.563063\pi\)
\(18\) 0.789318 0.186044
\(19\) −7.82976 −1.79627 −0.898135 0.439720i \(-0.855078\pi\)
−0.898135 + 0.439720i \(0.855078\pi\)
\(20\) 6.15056 1.37531
\(21\) 5.41373 1.18137
\(22\) 4.46940 0.952879
\(23\) 1.63989 0.341942 0.170971 0.985276i \(-0.445310\pi\)
0.170971 + 0.985276i \(0.445310\pi\)
\(24\) −3.53072 −0.720706
\(25\) −0.720871 −0.144174
\(26\) 10.8140 2.12081
\(27\) −5.45576 −1.04996
\(28\) 9.89541 1.87006
\(29\) −1.00000 −0.185695
\(30\) −7.50411 −1.37006
\(31\) 6.32579 1.13615 0.568073 0.822978i \(-0.307689\pi\)
0.568073 + 0.822978i \(0.307689\pi\)
\(32\) 6.80781 1.20346
\(33\) −3.26007 −0.567506
\(34\) 3.61959 0.620754
\(35\) 6.88453 1.16370
\(36\) −1.05237 −0.175395
\(37\) 5.26453 0.865483 0.432742 0.901518i \(-0.357546\pi\)
0.432742 + 0.901518i \(0.357546\pi\)
\(38\) 17.4610 2.83256
\(39\) −7.88798 −1.26309
\(40\) −4.48995 −0.709923
\(41\) −10.6234 −1.65910 −0.829548 0.558436i \(-0.811402\pi\)
−0.829548 + 0.558436i \(0.811402\pi\)
\(42\) −12.0731 −1.86292
\(43\) 2.54793 0.388556 0.194278 0.980947i \(-0.437764\pi\)
0.194278 + 0.980947i \(0.437764\pi\)
\(44\) −5.95888 −0.898335
\(45\) −0.732163 −0.109144
\(46\) −3.65711 −0.539211
\(47\) −0.424949 −0.0619852 −0.0309926 0.999520i \(-0.509867\pi\)
−0.0309926 + 0.999520i \(0.509867\pi\)
\(48\) −1.79931 −0.259708
\(49\) 4.07626 0.582323
\(50\) 1.60761 0.227350
\(51\) −2.64020 −0.369702
\(52\) −14.4179 −1.99941
\(53\) −6.57658 −0.903363 −0.451682 0.892179i \(-0.649176\pi\)
−0.451682 + 0.892179i \(0.649176\pi\)
\(54\) 12.1668 1.65569
\(55\) −4.14577 −0.559015
\(56\) −7.22371 −0.965309
\(57\) −12.7364 −1.68698
\(58\) 2.23009 0.292825
\(59\) 11.3340 1.47556 0.737778 0.675043i \(-0.235875\pi\)
0.737778 + 0.675043i \(0.235875\pi\)
\(60\) 10.0049 1.29163
\(61\) 8.32864 1.06637 0.533186 0.845998i \(-0.320994\pi\)
0.533186 + 0.845998i \(0.320994\pi\)
\(62\) −14.1071 −1.79160
\(63\) −1.17795 −0.148408
\(64\) −12.9697 −1.62122
\(65\) −10.0310 −1.24419
\(66\) 7.27025 0.894905
\(67\) −5.61260 −0.685689 −0.342844 0.939392i \(-0.611390\pi\)
−0.342844 + 0.939392i \(0.611390\pi\)
\(68\) −4.82586 −0.585221
\(69\) 2.66757 0.321138
\(70\) −15.3531 −1.83505
\(71\) −12.4573 −1.47841 −0.739206 0.673480i \(-0.764799\pi\)
−0.739206 + 0.673480i \(0.764799\pi\)
\(72\) 0.768235 0.0905373
\(73\) −13.5411 −1.58487 −0.792433 0.609959i \(-0.791186\pi\)
−0.792433 + 0.609959i \(0.791186\pi\)
\(74\) −11.7404 −1.36479
\(75\) −1.17262 −0.135403
\(76\) −23.2801 −2.67041
\(77\) −6.66997 −0.760114
\(78\) 17.5909 1.99178
\(79\) −1.51687 −0.170661 −0.0853306 0.996353i \(-0.527195\pi\)
−0.0853306 + 0.996353i \(0.527195\pi\)
\(80\) −2.28815 −0.255823
\(81\) −7.81290 −0.868100
\(82\) 23.6911 2.61624
\(83\) −8.94568 −0.981916 −0.490958 0.871183i \(-0.663353\pi\)
−0.490958 + 0.871183i \(0.663353\pi\)
\(84\) 16.0966 1.75628
\(85\) −3.35749 −0.364171
\(86\) −5.68210 −0.612717
\(87\) −1.62667 −0.174397
\(88\) 4.35002 0.463714
\(89\) 9.67158 1.02519 0.512593 0.858632i \(-0.328685\pi\)
0.512593 + 0.858632i \(0.328685\pi\)
\(90\) 1.63279 0.172111
\(91\) −16.1385 −1.69177
\(92\) 4.87588 0.508346
\(93\) 10.2900 1.06702
\(94\) 0.947674 0.0977451
\(95\) −16.1967 −1.66174
\(96\) 11.0741 1.13024
\(97\) 15.2303 1.54640 0.773202 0.634160i \(-0.218654\pi\)
0.773202 + 0.634160i \(0.218654\pi\)
\(98\) −9.09041 −0.918270
\(99\) 0.709345 0.0712919
\(100\) −2.14336 −0.214336
\(101\) 4.31572 0.429430 0.214715 0.976677i \(-0.431118\pi\)
0.214715 + 0.976677i \(0.431118\pi\)
\(102\) 5.88788 0.582987
\(103\) −9.10379 −0.897023 −0.448511 0.893777i \(-0.648046\pi\)
−0.448511 + 0.893777i \(0.648046\pi\)
\(104\) 10.5252 1.03208
\(105\) 11.1989 1.09290
\(106\) 14.6664 1.42452
\(107\) −5.45640 −0.527490 −0.263745 0.964592i \(-0.584958\pi\)
−0.263745 + 0.964592i \(0.584958\pi\)
\(108\) −16.2215 −1.56092
\(109\) −3.83694 −0.367512 −0.183756 0.982972i \(-0.558826\pi\)
−0.183756 + 0.982972i \(0.558826\pi\)
\(110\) 9.24543 0.881517
\(111\) 8.56366 0.812827
\(112\) −3.68131 −0.347852
\(113\) −0.301048 −0.0283202 −0.0141601 0.999900i \(-0.504507\pi\)
−0.0141601 + 0.999900i \(0.504507\pi\)
\(114\) 28.4034 2.66022
\(115\) 3.39230 0.316333
\(116\) −2.97329 −0.276063
\(117\) 1.71631 0.158673
\(118\) −25.2757 −2.32682
\(119\) −5.40174 −0.495177
\(120\) −7.30367 −0.666731
\(121\) −6.98343 −0.634858
\(122\) −18.5736 −1.68157
\(123\) −17.2808 −1.55815
\(124\) 18.8084 1.68904
\(125\) −11.8342 −1.05849
\(126\) 2.62693 0.234026
\(127\) −15.6010 −1.38436 −0.692181 0.721724i \(-0.743350\pi\)
−0.692181 + 0.721724i \(0.743350\pi\)
\(128\) 15.3080 1.35305
\(129\) 4.14464 0.364915
\(130\) 22.3700 1.96198
\(131\) −2.18610 −0.191000 −0.0955002 0.995429i \(-0.530445\pi\)
−0.0955002 + 0.995429i \(0.530445\pi\)
\(132\) −9.69314 −0.843679
\(133\) −26.0582 −2.25953
\(134\) 12.5166 1.08127
\(135\) −11.2858 −0.971328
\(136\) 3.52291 0.302087
\(137\) 6.34961 0.542484 0.271242 0.962511i \(-0.412566\pi\)
0.271242 + 0.962511i \(0.412566\pi\)
\(138\) −5.94891 −0.506405
\(139\) −1.00000 −0.0848189
\(140\) 20.4697 1.73000
\(141\) −0.691253 −0.0582140
\(142\) 27.7809 2.33132
\(143\) 9.71837 0.812691
\(144\) 0.391504 0.0326254
\(145\) −2.06861 −0.171788
\(146\) 30.1978 2.49919
\(147\) 6.63073 0.546894
\(148\) 15.6530 1.28667
\(149\) 10.8391 0.887976 0.443988 0.896033i \(-0.353563\pi\)
0.443988 + 0.896033i \(0.353563\pi\)
\(150\) 2.61505 0.213518
\(151\) −11.3195 −0.921169 −0.460585 0.887616i \(-0.652360\pi\)
−0.460585 + 0.887616i \(0.652360\pi\)
\(152\) 16.9946 1.37845
\(153\) 0.574471 0.0464432
\(154\) 14.8746 1.19863
\(155\) 13.0856 1.05106
\(156\) −23.4533 −1.87776
\(157\) 3.51999 0.280926 0.140463 0.990086i \(-0.455141\pi\)
0.140463 + 0.990086i \(0.455141\pi\)
\(158\) 3.38275 0.269117
\(159\) −10.6979 −0.848402
\(160\) 14.0827 1.11333
\(161\) 5.45774 0.430130
\(162\) 17.4235 1.36892
\(163\) −20.4997 −1.60566 −0.802830 0.596208i \(-0.796673\pi\)
−0.802830 + 0.596208i \(0.796673\pi\)
\(164\) −31.5864 −2.46649
\(165\) −6.74380 −0.525004
\(166\) 19.9497 1.54839
\(167\) 3.20714 0.248176 0.124088 0.992271i \(-0.460400\pi\)
0.124088 + 0.992271i \(0.460400\pi\)
\(168\) −11.7506 −0.906578
\(169\) 10.5143 0.808794
\(170\) 7.48750 0.574265
\(171\) 2.77127 0.211924
\(172\) 7.57573 0.577644
\(173\) −9.90703 −0.753217 −0.376609 0.926372i \(-0.622910\pi\)
−0.376609 + 0.926372i \(0.622910\pi\)
\(174\) 3.62762 0.275009
\(175\) −2.39913 −0.181357
\(176\) 2.21684 0.167100
\(177\) 18.4366 1.38578
\(178\) −21.5685 −1.61662
\(179\) 21.6756 1.62011 0.810056 0.586352i \(-0.199436\pi\)
0.810056 + 0.586352i \(0.199436\pi\)
\(180\) −2.17693 −0.162259
\(181\) −11.3952 −0.846999 −0.423499 0.905896i \(-0.639198\pi\)
−0.423499 + 0.905896i \(0.639198\pi\)
\(182\) 35.9902 2.66777
\(183\) 13.5480 1.00149
\(184\) −3.55942 −0.262404
\(185\) 10.8902 0.800666
\(186\) −22.9476 −1.68260
\(187\) 3.25286 0.237872
\(188\) −1.26350 −0.0921500
\(189\) −18.1573 −1.32075
\(190\) 36.1200 2.62042
\(191\) 22.3658 1.61833 0.809166 0.587580i \(-0.199919\pi\)
0.809166 + 0.587580i \(0.199919\pi\)
\(192\) −21.0975 −1.52258
\(193\) 0.808022 0.0581627 0.0290814 0.999577i \(-0.490742\pi\)
0.0290814 + 0.999577i \(0.490742\pi\)
\(194\) −33.9649 −2.43854
\(195\) −16.3171 −1.16849
\(196\) 12.1199 0.865707
\(197\) 0.534542 0.0380845 0.0190423 0.999819i \(-0.493938\pi\)
0.0190423 + 0.999819i \(0.493938\pi\)
\(198\) −1.58190 −0.112421
\(199\) −15.5310 −1.10096 −0.550482 0.834847i \(-0.685556\pi\)
−0.550482 + 0.834847i \(0.685556\pi\)
\(200\) 1.56466 0.110638
\(201\) −9.12986 −0.643971
\(202\) −9.62443 −0.677173
\(203\) −3.32810 −0.233587
\(204\) −7.85008 −0.549616
\(205\) −21.9756 −1.53484
\(206\) 20.3022 1.41452
\(207\) −0.580425 −0.0403423
\(208\) 5.36380 0.371913
\(209\) 15.6919 1.08543
\(210\) −24.9744 −1.72340
\(211\) 12.2123 0.840727 0.420364 0.907356i \(-0.361902\pi\)
0.420364 + 0.907356i \(0.361902\pi\)
\(212\) −19.5541 −1.34298
\(213\) −20.2640 −1.38846
\(214\) 12.1683 0.831805
\(215\) 5.27066 0.359456
\(216\) 11.8418 0.805734
\(217\) 21.0529 1.42916
\(218\) 8.55670 0.579533
\(219\) −22.0269 −1.48844
\(220\) −12.3266 −0.831057
\(221\) 7.87052 0.529429
\(222\) −19.0977 −1.28175
\(223\) −22.0995 −1.47989 −0.739945 0.672667i \(-0.765149\pi\)
−0.739945 + 0.672667i \(0.765149\pi\)
\(224\) 22.6571 1.51384
\(225\) 0.255145 0.0170097
\(226\) 0.671362 0.0446583
\(227\) −20.8932 −1.38673 −0.693365 0.720586i \(-0.743873\pi\)
−0.693365 + 0.720586i \(0.743873\pi\)
\(228\) −37.8691 −2.50794
\(229\) −15.1793 −1.00307 −0.501537 0.865136i \(-0.667232\pi\)
−0.501537 + 0.865136i \(0.667232\pi\)
\(230\) −7.56511 −0.498829
\(231\) −10.8499 −0.713868
\(232\) 2.17052 0.142502
\(233\) 16.1529 1.05821 0.529106 0.848556i \(-0.322527\pi\)
0.529106 + 0.848556i \(0.322527\pi\)
\(234\) −3.82753 −0.250213
\(235\) −0.879053 −0.0573431
\(236\) 33.6991 2.19363
\(237\) −2.46745 −0.160278
\(238\) 12.0464 0.780849
\(239\) 8.09766 0.523794 0.261897 0.965096i \(-0.415652\pi\)
0.261897 + 0.965096i \(0.415652\pi\)
\(240\) −3.72206 −0.240258
\(241\) −25.6664 −1.65332 −0.826660 0.562702i \(-0.809762\pi\)
−0.826660 + 0.562702i \(0.809762\pi\)
\(242\) 15.5737 1.00111
\(243\) 3.65825 0.234677
\(244\) 24.7634 1.58532
\(245\) 8.43217 0.538712
\(246\) 38.5376 2.45707
\(247\) 37.9677 2.41583
\(248\) −13.7302 −0.871872
\(249\) −14.5517 −0.922176
\(250\) 26.3914 1.66914
\(251\) −11.8184 −0.745971 −0.372985 0.927837i \(-0.621666\pi\)
−0.372985 + 0.927837i \(0.621666\pi\)
\(252\) −3.50239 −0.220630
\(253\) −3.28657 −0.206625
\(254\) 34.7915 2.18301
\(255\) −5.46154 −0.342015
\(256\) −8.19878 −0.512424
\(257\) 7.95527 0.496236 0.248118 0.968730i \(-0.420188\pi\)
0.248118 + 0.968730i \(0.420188\pi\)
\(258\) −9.24292 −0.575439
\(259\) 17.5209 1.08869
\(260\) −29.8250 −1.84967
\(261\) 0.353941 0.0219084
\(262\) 4.87519 0.301190
\(263\) 19.0798 1.17651 0.588254 0.808676i \(-0.299815\pi\)
0.588254 + 0.808676i \(0.299815\pi\)
\(264\) 7.07605 0.435501
\(265\) −13.6044 −0.835709
\(266\) 58.1121 3.56308
\(267\) 15.7325 0.962812
\(268\) −16.6879 −1.01938
\(269\) 20.3650 1.24168 0.620839 0.783938i \(-0.286792\pi\)
0.620839 + 0.783938i \(0.286792\pi\)
\(270\) 25.1683 1.53170
\(271\) −12.0740 −0.733442 −0.366721 0.930331i \(-0.619520\pi\)
−0.366721 + 0.930331i \(0.619520\pi\)
\(272\) 1.79533 0.108858
\(273\) −26.2520 −1.58884
\(274\) −14.1602 −0.855448
\(275\) 1.44472 0.0871202
\(276\) 7.93146 0.477418
\(277\) −30.9603 −1.86022 −0.930111 0.367279i \(-0.880289\pi\)
−0.930111 + 0.367279i \(0.880289\pi\)
\(278\) 2.23009 0.133752
\(279\) −2.23895 −0.134043
\(280\) −14.9430 −0.893015
\(281\) 17.0485 1.01703 0.508513 0.861054i \(-0.330195\pi\)
0.508513 + 0.861054i \(0.330195\pi\)
\(282\) 1.54155 0.0917982
\(283\) 11.4998 0.683595 0.341798 0.939774i \(-0.388964\pi\)
0.341798 + 0.939774i \(0.388964\pi\)
\(284\) −37.0392 −2.19787
\(285\) −26.3467 −1.56064
\(286\) −21.6728 −1.28154
\(287\) −35.3557 −2.08698
\(288\) −2.40956 −0.141985
\(289\) −14.3656 −0.845038
\(290\) 4.61317 0.270895
\(291\) 24.7747 1.45232
\(292\) −40.2616 −2.35613
\(293\) 23.1786 1.35411 0.677055 0.735933i \(-0.263256\pi\)
0.677055 + 0.735933i \(0.263256\pi\)
\(294\) −14.7871 −0.862402
\(295\) 23.4455 1.36505
\(296\) −11.4268 −0.664167
\(297\) 10.9341 0.634460
\(298\) −24.1722 −1.40026
\(299\) −7.95211 −0.459882
\(300\) −3.48654 −0.201295
\(301\) 8.47977 0.488766
\(302\) 25.2435 1.45260
\(303\) 7.02026 0.403303
\(304\) 8.66073 0.496727
\(305\) 17.2287 0.986511
\(306\) −1.28112 −0.0732367
\(307\) 18.6235 1.06290 0.531451 0.847089i \(-0.321647\pi\)
0.531451 + 0.847089i \(0.321647\pi\)
\(308\) −19.8318 −1.13002
\(309\) −14.8089 −0.842447
\(310\) −29.1819 −1.65742
\(311\) −10.2082 −0.578854 −0.289427 0.957200i \(-0.593465\pi\)
−0.289427 + 0.957200i \(0.593465\pi\)
\(312\) 17.1210 0.969287
\(313\) 27.0218 1.52736 0.763682 0.645593i \(-0.223390\pi\)
0.763682 + 0.645593i \(0.223390\pi\)
\(314\) −7.84989 −0.442995
\(315\) −2.43671 −0.137293
\(316\) −4.51009 −0.253713
\(317\) −0.589377 −0.0331027 −0.0165514 0.999863i \(-0.505269\pi\)
−0.0165514 + 0.999863i \(0.505269\pi\)
\(318\) 23.8573 1.33785
\(319\) 2.00414 0.112210
\(320\) −26.8293 −1.49980
\(321\) −8.87577 −0.495397
\(322\) −12.1712 −0.678276
\(323\) 12.7083 0.707106
\(324\) −23.2300 −1.29056
\(325\) 3.49562 0.193902
\(326\) 45.7161 2.53198
\(327\) −6.24143 −0.345152
\(328\) 23.0583 1.27318
\(329\) −1.41427 −0.0779715
\(330\) 15.0393 0.827885
\(331\) 3.15968 0.173672 0.0868359 0.996223i \(-0.472324\pi\)
0.0868359 + 0.996223i \(0.472324\pi\)
\(332\) −26.5981 −1.45976
\(333\) −1.86333 −0.102110
\(334\) −7.15220 −0.391351
\(335\) −11.6103 −0.634336
\(336\) −5.98829 −0.326688
\(337\) −23.3601 −1.27251 −0.636253 0.771480i \(-0.719517\pi\)
−0.636253 + 0.771480i \(0.719517\pi\)
\(338\) −23.4479 −1.27540
\(339\) −0.489705 −0.0265971
\(340\) −9.98280 −0.541393
\(341\) −12.6777 −0.686539
\(342\) −6.18017 −0.334185
\(343\) −9.73051 −0.525398
\(344\) −5.53033 −0.298175
\(345\) 5.51815 0.297087
\(346\) 22.0935 1.18776
\(347\) 19.1623 1.02869 0.514343 0.857585i \(-0.328036\pi\)
0.514343 + 0.857585i \(0.328036\pi\)
\(348\) −4.83656 −0.259267
\(349\) −3.23030 −0.172914 −0.0864569 0.996256i \(-0.527554\pi\)
−0.0864569 + 0.996256i \(0.527554\pi\)
\(350\) 5.35027 0.285984
\(351\) 26.4558 1.41211
\(352\) −13.6438 −0.727216
\(353\) −2.26308 −0.120452 −0.0602259 0.998185i \(-0.519182\pi\)
−0.0602259 + 0.998185i \(0.519182\pi\)
\(354\) −41.1153 −2.18525
\(355\) −25.7693 −1.36769
\(356\) 28.7564 1.52409
\(357\) −8.78686 −0.465050
\(358\) −48.3385 −2.55477
\(359\) −2.32848 −0.122893 −0.0614463 0.998110i \(-0.519571\pi\)
−0.0614463 + 0.998110i \(0.519571\pi\)
\(360\) 1.58917 0.0837569
\(361\) 42.3051 2.22658
\(362\) 25.4123 1.33564
\(363\) −11.3598 −0.596232
\(364\) −47.9844 −2.51506
\(365\) −28.0112 −1.46617
\(366\) −30.2131 −1.57927
\(367\) 28.0257 1.46293 0.731465 0.681879i \(-0.238837\pi\)
0.731465 + 0.681879i \(0.238837\pi\)
\(368\) −1.81394 −0.0945580
\(369\) 3.76005 0.195740
\(370\) −24.2862 −1.26258
\(371\) −21.8875 −1.13634
\(372\) 30.5951 1.58628
\(373\) 14.2166 0.736110 0.368055 0.929804i \(-0.380024\pi\)
0.368055 + 0.929804i \(0.380024\pi\)
\(374\) −7.25415 −0.375103
\(375\) −19.2504 −0.994086
\(376\) 0.922361 0.0475671
\(377\) 4.84916 0.249744
\(378\) 40.4924 2.08270
\(379\) 7.51950 0.386251 0.193125 0.981174i \(-0.438138\pi\)
0.193125 + 0.981174i \(0.438138\pi\)
\(380\) −48.1574 −2.47042
\(381\) −25.3776 −1.30014
\(382\) −49.8777 −2.55196
\(383\) 16.9232 0.864733 0.432367 0.901698i \(-0.357679\pi\)
0.432367 + 0.901698i \(0.357679\pi\)
\(384\) 24.9011 1.27073
\(385\) −13.7975 −0.703188
\(386\) −1.80196 −0.0917174
\(387\) −0.901815 −0.0458419
\(388\) 45.2841 2.29895
\(389\) −25.4599 −1.29087 −0.645433 0.763817i \(-0.723323\pi\)
−0.645433 + 0.763817i \(0.723323\pi\)
\(390\) 36.3886 1.84261
\(391\) −2.66166 −0.134606
\(392\) −8.84760 −0.446871
\(393\) −3.55607 −0.179380
\(394\) −1.19207 −0.0600559
\(395\) −3.13781 −0.157880
\(396\) 2.10909 0.105986
\(397\) −31.1844 −1.56510 −0.782549 0.622588i \(-0.786081\pi\)
−0.782549 + 0.622588i \(0.786081\pi\)
\(398\) 34.6355 1.73612
\(399\) −42.3882 −2.12206
\(400\) 0.797377 0.0398689
\(401\) 16.1080 0.804397 0.402199 0.915552i \(-0.368246\pi\)
0.402199 + 0.915552i \(0.368246\pi\)
\(402\) 20.3604 1.01548
\(403\) −30.6747 −1.52802
\(404\) 12.8319 0.638410
\(405\) −16.1618 −0.803087
\(406\) 7.42196 0.368345
\(407\) −10.5508 −0.522986
\(408\) 5.73061 0.283708
\(409\) 13.3481 0.660023 0.330011 0.943977i \(-0.392947\pi\)
0.330011 + 0.943977i \(0.392947\pi\)
\(410\) 49.0075 2.42031
\(411\) 10.3287 0.509479
\(412\) −27.0682 −1.33355
\(413\) 37.7206 1.85611
\(414\) 1.29440 0.0636162
\(415\) −18.5051 −0.908379
\(416\) −33.0121 −1.61855
\(417\) −1.62667 −0.0796584
\(418\) −34.9943 −1.71163
\(419\) 11.9738 0.584960 0.292480 0.956272i \(-0.405520\pi\)
0.292480 + 0.956272i \(0.405520\pi\)
\(420\) 33.2975 1.62475
\(421\) 9.39326 0.457799 0.228900 0.973450i \(-0.426487\pi\)
0.228900 + 0.973450i \(0.426487\pi\)
\(422\) −27.2344 −1.32575
\(423\) 0.150407 0.00731303
\(424\) 14.2746 0.693236
\(425\) 1.17002 0.0567545
\(426\) 45.1904 2.18948
\(427\) 27.7186 1.34139
\(428\) −16.2235 −0.784191
\(429\) 15.8086 0.763246
\(430\) −11.7540 −0.566830
\(431\) −17.4723 −0.841613 −0.420806 0.907150i \(-0.638253\pi\)
−0.420806 + 0.907150i \(0.638253\pi\)
\(432\) 6.03478 0.290349
\(433\) −17.6263 −0.847065 −0.423533 0.905881i \(-0.639210\pi\)
−0.423533 + 0.905881i \(0.639210\pi\)
\(434\) −46.9497 −2.25366
\(435\) −3.36494 −0.161337
\(436\) −11.4083 −0.546360
\(437\) −12.8400 −0.614219
\(438\) 49.1220 2.34714
\(439\) 23.7987 1.13585 0.567925 0.823080i \(-0.307746\pi\)
0.567925 + 0.823080i \(0.307746\pi\)
\(440\) 8.99847 0.428985
\(441\) −1.44275 −0.0687025
\(442\) −17.5520 −0.834861
\(443\) −3.55883 −0.169085 −0.0845426 0.996420i \(-0.526943\pi\)
−0.0845426 + 0.996420i \(0.526943\pi\)
\(444\) 25.4622 1.20838
\(445\) 20.0067 0.948407
\(446\) 49.2838 2.33365
\(447\) 17.6317 0.833951
\(448\) −43.1646 −2.03934
\(449\) 21.7192 1.02499 0.512496 0.858689i \(-0.328721\pi\)
0.512496 + 0.858689i \(0.328721\pi\)
\(450\) −0.568997 −0.0268228
\(451\) 21.2907 1.00254
\(452\) −0.895101 −0.0421020
\(453\) −18.4131 −0.865125
\(454\) 46.5937 2.18675
\(455\) −33.3842 −1.56507
\(456\) 27.6447 1.29458
\(457\) −29.8607 −1.39683 −0.698413 0.715695i \(-0.746110\pi\)
−0.698413 + 0.715695i \(0.746110\pi\)
\(458\) 33.8511 1.58176
\(459\) 8.85508 0.413320
\(460\) 10.0863 0.470275
\(461\) −36.6909 −1.70886 −0.854432 0.519562i \(-0.826095\pi\)
−0.854432 + 0.519562i \(0.826095\pi\)
\(462\) 24.1961 1.12571
\(463\) −6.64217 −0.308688 −0.154344 0.988017i \(-0.549326\pi\)
−0.154344 + 0.988017i \(0.549326\pi\)
\(464\) 1.10613 0.0513508
\(465\) 21.2859 0.987110
\(466\) −36.0224 −1.66870
\(467\) −25.5035 −1.18016 −0.590079 0.807345i \(-0.700904\pi\)
−0.590079 + 0.807345i \(0.700904\pi\)
\(468\) 5.10310 0.235891
\(469\) −18.6793 −0.862531
\(470\) 1.96036 0.0904248
\(471\) 5.72587 0.263834
\(472\) −24.6006 −1.13233
\(473\) −5.10640 −0.234792
\(474\) 5.50263 0.252744
\(475\) 5.64425 0.258976
\(476\) −16.0609 −0.736152
\(477\) 2.32772 0.106579
\(478\) −18.0585 −0.825976
\(479\) 2.85060 0.130247 0.0651236 0.997877i \(-0.479256\pi\)
0.0651236 + 0.997877i \(0.479256\pi\)
\(480\) 22.9079 1.04560
\(481\) −25.5285 −1.16400
\(482\) 57.2384 2.60714
\(483\) 8.87794 0.403960
\(484\) −20.7638 −0.943808
\(485\) 31.5055 1.43059
\(486\) −8.15821 −0.370064
\(487\) −13.9850 −0.633720 −0.316860 0.948472i \(-0.602629\pi\)
−0.316860 + 0.948472i \(0.602629\pi\)
\(488\) −18.0775 −0.818329
\(489\) −33.3463 −1.50797
\(490\) −18.8045 −0.849500
\(491\) −10.1823 −0.459520 −0.229760 0.973247i \(-0.573794\pi\)
−0.229760 + 0.973247i \(0.573794\pi\)
\(492\) −51.3807 −2.31642
\(493\) 1.62307 0.0730994
\(494\) −84.6713 −3.80954
\(495\) 1.46736 0.0659527
\(496\) −6.99715 −0.314181
\(497\) −41.4592 −1.85970
\(498\) 32.4515 1.45419
\(499\) 25.7520 1.15282 0.576409 0.817161i \(-0.304453\pi\)
0.576409 + 0.817161i \(0.304453\pi\)
\(500\) −35.1866 −1.57359
\(501\) 5.21696 0.233077
\(502\) 26.3561 1.17633
\(503\) −39.8631 −1.77741 −0.888703 0.458484i \(-0.848393\pi\)
−0.888703 + 0.458484i \(0.848393\pi\)
\(504\) 2.55676 0.113887
\(505\) 8.92752 0.397270
\(506\) 7.32935 0.325829
\(507\) 17.1033 0.759586
\(508\) −46.3862 −2.05805
\(509\) −23.0811 −1.02305 −0.511526 0.859268i \(-0.670920\pi\)
−0.511526 + 0.859268i \(0.670920\pi\)
\(510\) 12.1797 0.539326
\(511\) −45.0662 −1.99361
\(512\) −12.3321 −0.545006
\(513\) 42.7173 1.88601
\(514\) −17.7410 −0.782520
\(515\) −18.8321 −0.829843
\(516\) 12.3232 0.542500
\(517\) 0.851657 0.0374558
\(518\) −39.0731 −1.71677
\(519\) −16.1155 −0.707391
\(520\) 21.7725 0.954786
\(521\) 6.04798 0.264967 0.132483 0.991185i \(-0.457705\pi\)
0.132483 + 0.991185i \(0.457705\pi\)
\(522\) −0.789318 −0.0345475
\(523\) 12.7479 0.557429 0.278714 0.960374i \(-0.410092\pi\)
0.278714 + 0.960374i \(0.410092\pi\)
\(524\) −6.49991 −0.283950
\(525\) −3.90260 −0.170323
\(526\) −42.5495 −1.85525
\(527\) −10.2672 −0.447246
\(528\) 3.60607 0.156934
\(529\) −20.3107 −0.883076
\(530\) 30.3389 1.31784
\(531\) −4.01155 −0.174086
\(532\) −77.4786 −3.35912
\(533\) 51.5145 2.23134
\(534\) −35.0848 −1.51827
\(535\) −11.2871 −0.487986
\(536\) 12.1823 0.526194
\(537\) 35.2591 1.52154
\(538\) −45.4158 −1.95801
\(539\) −8.16938 −0.351880
\(540\) −33.5560 −1.44402
\(541\) 17.3732 0.746934 0.373467 0.927643i \(-0.378169\pi\)
0.373467 + 0.927643i \(0.378169\pi\)
\(542\) 26.9260 1.15657
\(543\) −18.5362 −0.795466
\(544\) −11.0496 −0.473746
\(545\) −7.93711 −0.339988
\(546\) 58.5443 2.50546
\(547\) −16.9118 −0.723094 −0.361547 0.932354i \(-0.617751\pi\)
−0.361547 + 0.932354i \(0.617751\pi\)
\(548\) 18.8792 0.806481
\(549\) −2.94784 −0.125811
\(550\) −3.22186 −0.137381
\(551\) 7.82976 0.333559
\(552\) −5.79001 −0.246439
\(553\) −5.04830 −0.214675
\(554\) 69.0441 2.93340
\(555\) 17.7148 0.751953
\(556\) −2.97329 −0.126096
\(557\) 34.1912 1.44873 0.724363 0.689419i \(-0.242134\pi\)
0.724363 + 0.689419i \(0.242134\pi\)
\(558\) 4.99306 0.211373
\(559\) −12.3553 −0.522574
\(560\) −7.61519 −0.321800
\(561\) 5.29133 0.223400
\(562\) −38.0195 −1.60376
\(563\) 5.85329 0.246687 0.123343 0.992364i \(-0.460638\pi\)
0.123343 + 0.992364i \(0.460638\pi\)
\(564\) −2.05529 −0.0865435
\(565\) −0.622749 −0.0261992
\(566\) −25.6457 −1.07797
\(567\) −26.0021 −1.09199
\(568\) 27.0388 1.13452
\(569\) −14.2454 −0.597200 −0.298600 0.954378i \(-0.596520\pi\)
−0.298600 + 0.954378i \(0.596520\pi\)
\(570\) 58.7554 2.46099
\(571\) −28.8133 −1.20580 −0.602900 0.797816i \(-0.705988\pi\)
−0.602900 + 0.797816i \(0.705988\pi\)
\(572\) 28.8955 1.20818
\(573\) 36.3818 1.51987
\(574\) 78.8464 3.29098
\(575\) −1.18215 −0.0492992
\(576\) 4.59052 0.191272
\(577\) 9.18311 0.382298 0.191149 0.981561i \(-0.438779\pi\)
0.191149 + 0.981561i \(0.438779\pi\)
\(578\) 32.0366 1.33255
\(579\) 1.31439 0.0546241
\(580\) −6.15056 −0.255388
\(581\) −29.7721 −1.23516
\(582\) −55.2497 −2.29018
\(583\) 13.1804 0.545875
\(584\) 29.3912 1.21622
\(585\) 3.55038 0.146790
\(586\) −51.6903 −2.13531
\(587\) 13.7807 0.568789 0.284394 0.958707i \(-0.408208\pi\)
0.284394 + 0.958707i \(0.408208\pi\)
\(588\) 19.7151 0.813036
\(589\) −49.5294 −2.04082
\(590\) −52.2855 −2.15256
\(591\) 0.869524 0.0357674
\(592\) −5.82326 −0.239334
\(593\) 40.9084 1.67991 0.839953 0.542659i \(-0.182582\pi\)
0.839953 + 0.542659i \(0.182582\pi\)
\(594\) −24.3840 −1.00049
\(595\) −11.1741 −0.458092
\(596\) 32.2279 1.32011
\(597\) −25.2639 −1.03398
\(598\) 17.7339 0.725193
\(599\) 2.14220 0.0875280 0.0437640 0.999042i \(-0.486065\pi\)
0.0437640 + 0.999042i \(0.486065\pi\)
\(600\) 2.54519 0.103907
\(601\) 31.7908 1.29678 0.648388 0.761310i \(-0.275444\pi\)
0.648388 + 0.761310i \(0.275444\pi\)
\(602\) −18.9106 −0.770739
\(603\) 1.98653 0.0808977
\(604\) −33.6562 −1.36945
\(605\) −14.4460 −0.587312
\(606\) −15.6558 −0.635973
\(607\) −22.6788 −0.920506 −0.460253 0.887788i \(-0.652241\pi\)
−0.460253 + 0.887788i \(0.652241\pi\)
\(608\) −53.3035 −2.16174
\(609\) −5.41373 −0.219375
\(610\) −38.4214 −1.55564
\(611\) 2.06065 0.0833648
\(612\) 1.70807 0.0690445
\(613\) 41.9692 1.69512 0.847559 0.530701i \(-0.178071\pi\)
0.847559 + 0.530701i \(0.178071\pi\)
\(614\) −41.5321 −1.67610
\(615\) −35.7471 −1.44146
\(616\) 14.4773 0.583307
\(617\) 0.831162 0.0334613 0.0167307 0.999860i \(-0.494674\pi\)
0.0167307 + 0.999860i \(0.494674\pi\)
\(618\) 33.0251 1.32846
\(619\) 40.0922 1.61144 0.805720 0.592296i \(-0.201778\pi\)
0.805720 + 0.592296i \(0.201778\pi\)
\(620\) 38.9072 1.56255
\(621\) −8.94687 −0.359026
\(622\) 22.7652 0.912800
\(623\) 32.1880 1.28958
\(624\) 8.72514 0.349285
\(625\) −20.8760 −0.835040
\(626\) −60.2610 −2.40852
\(627\) 25.5256 1.01939
\(628\) 10.4660 0.417637
\(629\) −8.54470 −0.340700
\(630\) 5.43408 0.216499
\(631\) −30.6732 −1.22108 −0.610540 0.791985i \(-0.709048\pi\)
−0.610540 + 0.791985i \(0.709048\pi\)
\(632\) 3.29240 0.130964
\(633\) 19.8653 0.789577
\(634\) 1.31436 0.0522000
\(635\) −32.2722 −1.28068
\(636\) −31.8081 −1.26127
\(637\) −19.7664 −0.783174
\(638\) −4.46940 −0.176945
\(639\) 4.40915 0.174423
\(640\) 31.6663 1.25172
\(641\) 2.81583 0.111219 0.0556093 0.998453i \(-0.482290\pi\)
0.0556093 + 0.998453i \(0.482290\pi\)
\(642\) 19.7938 0.781197
\(643\) 13.6795 0.539467 0.269734 0.962935i \(-0.413064\pi\)
0.269734 + 0.962935i \(0.413064\pi\)
\(644\) 16.2274 0.639450
\(645\) 8.57363 0.337586
\(646\) −28.3405 −1.11504
\(647\) 13.8958 0.546301 0.273151 0.961971i \(-0.411934\pi\)
0.273151 + 0.961971i \(0.411934\pi\)
\(648\) 16.9581 0.666176
\(649\) −22.7148 −0.891634
\(650\) −7.79553 −0.305766
\(651\) 34.2461 1.34221
\(652\) −60.9515 −2.38704
\(653\) 7.37217 0.288495 0.144248 0.989542i \(-0.453924\pi\)
0.144248 + 0.989542i \(0.453924\pi\)
\(654\) 13.9189 0.544274
\(655\) −4.52218 −0.176696
\(656\) 11.7509 0.458794
\(657\) 4.79275 0.186983
\(658\) 3.15396 0.122954
\(659\) −33.1597 −1.29172 −0.645859 0.763456i \(-0.723501\pi\)
−0.645859 + 0.763456i \(0.723501\pi\)
\(660\) −20.0513 −0.780495
\(661\) 25.8127 1.00400 0.502000 0.864868i \(-0.332598\pi\)
0.502000 + 0.864868i \(0.332598\pi\)
\(662\) −7.04636 −0.273865
\(663\) 12.8028 0.497218
\(664\) 19.4168 0.753517
\(665\) −53.9042 −2.09031
\(666\) 4.15539 0.161018
\(667\) −1.63989 −0.0634970
\(668\) 9.53575 0.368949
\(669\) −35.9486 −1.38985
\(670\) 25.8919 1.00029
\(671\) −16.6917 −0.644377
\(672\) 36.8556 1.42174
\(673\) 12.9902 0.500736 0.250368 0.968151i \(-0.419448\pi\)
0.250368 + 0.968151i \(0.419448\pi\)
\(674\) 52.0951 2.00663
\(675\) 3.93290 0.151377
\(676\) 31.2621 1.20239
\(677\) 12.7421 0.489718 0.244859 0.969559i \(-0.421258\pi\)
0.244859 + 0.969559i \(0.421258\pi\)
\(678\) 1.09209 0.0419413
\(679\) 50.6880 1.94523
\(680\) 7.28750 0.279463
\(681\) −33.9864 −1.30236
\(682\) 28.2725 1.08261
\(683\) −35.9900 −1.37712 −0.688559 0.725181i \(-0.741756\pi\)
−0.688559 + 0.725181i \(0.741756\pi\)
\(684\) 8.23978 0.315056
\(685\) 13.1348 0.501856
\(686\) 21.6999 0.828506
\(687\) −24.6917 −0.942047
\(688\) −2.81834 −0.107448
\(689\) 31.8909 1.21495
\(690\) −12.3060 −0.468480
\(691\) −46.8937 −1.78392 −0.891960 0.452115i \(-0.850670\pi\)
−0.891960 + 0.452115i \(0.850670\pi\)
\(692\) −29.4565 −1.11977
\(693\) 2.36077 0.0896784
\(694\) −42.7336 −1.62214
\(695\) −2.06861 −0.0784667
\(696\) 3.53072 0.133832
\(697\) 17.2425 0.653107
\(698\) 7.20384 0.272670
\(699\) 26.2755 0.993829
\(700\) −7.13331 −0.269614
\(701\) 27.2766 1.03022 0.515112 0.857123i \(-0.327750\pi\)
0.515112 + 0.857123i \(0.327750\pi\)
\(702\) −58.9988 −2.22677
\(703\) −41.2200 −1.55464
\(704\) 25.9931 0.979653
\(705\) −1.42993 −0.0538543
\(706\) 5.04687 0.189941
\(707\) 14.3632 0.540182
\(708\) 54.8174 2.06017
\(709\) 30.7105 1.15336 0.576678 0.816971i \(-0.304349\pi\)
0.576678 + 0.816971i \(0.304349\pi\)
\(710\) 57.4677 2.15673
\(711\) 0.536882 0.0201346
\(712\) −20.9923 −0.786721
\(713\) 10.3736 0.388495
\(714\) 19.5955 0.733342
\(715\) 20.1035 0.751828
\(716\) 64.4479 2.40853
\(717\) 13.1722 0.491926
\(718\) 5.19272 0.193791
\(719\) 7.48553 0.279163 0.139582 0.990211i \(-0.455424\pi\)
0.139582 + 0.990211i \(0.455424\pi\)
\(720\) 0.809868 0.0301820
\(721\) −30.2983 −1.12837
\(722\) −94.3441 −3.51112
\(723\) −41.7508 −1.55273
\(724\) −33.8812 −1.25919
\(725\) 0.720871 0.0267725
\(726\) 25.3332 0.940205
\(727\) −22.8517 −0.847522 −0.423761 0.905774i \(-0.639290\pi\)
−0.423761 + 0.905774i \(0.639290\pi\)
\(728\) 35.0289 1.29826
\(729\) 29.3895 1.08850
\(730\) 62.4674 2.31202
\(731\) −4.13547 −0.152956
\(732\) 40.2820 1.48887
\(733\) 27.2790 1.00757 0.503787 0.863828i \(-0.331940\pi\)
0.503787 + 0.863828i \(0.331940\pi\)
\(734\) −62.4998 −2.30691
\(735\) 13.7164 0.505936
\(736\) 11.1641 0.411514
\(737\) 11.2484 0.414341
\(738\) −8.38524 −0.308665
\(739\) −44.8365 −1.64934 −0.824668 0.565617i \(-0.808638\pi\)
−0.824668 + 0.565617i \(0.808638\pi\)
\(740\) 32.3798 1.19031
\(741\) 61.7610 2.26885
\(742\) 48.8111 1.79191
\(743\) −25.3567 −0.930246 −0.465123 0.885246i \(-0.653990\pi\)
−0.465123 + 0.885246i \(0.653990\pi\)
\(744\) −22.3346 −0.818826
\(745\) 22.4219 0.821474
\(746\) −31.7043 −1.16078
\(747\) 3.16624 0.115847
\(748\) 9.67168 0.353632
\(749\) −18.1595 −0.663532
\(750\) 42.9301 1.56758
\(751\) 42.1518 1.53814 0.769071 0.639163i \(-0.220719\pi\)
0.769071 + 0.639163i \(0.220719\pi\)
\(752\) 0.470049 0.0171409
\(753\) −19.2247 −0.700585
\(754\) −10.8140 −0.393824
\(755\) −23.4156 −0.852182
\(756\) −53.9870 −1.96349
\(757\) −11.0969 −0.403323 −0.201662 0.979455i \(-0.564634\pi\)
−0.201662 + 0.979455i \(0.564634\pi\)
\(758\) −16.7691 −0.609083
\(759\) −5.34618 −0.194054
\(760\) 35.1552 1.27521
\(761\) −47.0563 −1.70579 −0.852895 0.522082i \(-0.825156\pi\)
−0.852895 + 0.522082i \(0.825156\pi\)
\(762\) 56.5943 2.05020
\(763\) −12.7697 −0.462295
\(764\) 66.4999 2.40588
\(765\) 1.18835 0.0429650
\(766\) −37.7401 −1.36361
\(767\) −54.9602 −1.98450
\(768\) −13.3367 −0.481248
\(769\) −31.5357 −1.13721 −0.568603 0.822612i \(-0.692516\pi\)
−0.568603 + 0.822612i \(0.692516\pi\)
\(770\) 30.7697 1.10886
\(771\) 12.9406 0.466045
\(772\) 2.40248 0.0864673
\(773\) 30.7894 1.10742 0.553710 0.832710i \(-0.313212\pi\)
0.553710 + 0.832710i \(0.313212\pi\)
\(774\) 2.01113 0.0722885
\(775\) −4.56008 −0.163803
\(776\) −33.0577 −1.18670
\(777\) 28.5007 1.02246
\(778\) 56.7777 2.03558
\(779\) 83.1786 2.98018
\(780\) −48.5155 −1.73713
\(781\) 24.9662 0.893360
\(782\) 5.93575 0.212262
\(783\) 5.45576 0.194973
\(784\) −4.50887 −0.161031
\(785\) 7.28148 0.259887
\(786\) 7.93034 0.282866
\(787\) 26.6385 0.949559 0.474780 0.880105i \(-0.342528\pi\)
0.474780 + 0.880105i \(0.342528\pi\)
\(788\) 1.58935 0.0566182
\(789\) 31.0365 1.10493
\(790\) 6.99758 0.248963
\(791\) −1.00192 −0.0356241
\(792\) −1.53965 −0.0547090
\(793\) −40.3869 −1.43418
\(794\) 69.5439 2.46802
\(795\) −22.1298 −0.784864
\(796\) −46.1782 −1.63674
\(797\) 25.1024 0.889171 0.444586 0.895736i \(-0.353351\pi\)
0.444586 + 0.895736i \(0.353351\pi\)
\(798\) 94.5293 3.34630
\(799\) 0.689723 0.0244006
\(800\) −4.90755 −0.173508
\(801\) −3.42316 −0.120952
\(802\) −35.9224 −1.26846
\(803\) 27.1382 0.957687
\(804\) −27.1457 −0.957356
\(805\) 11.2899 0.397917
\(806\) 68.4074 2.40955
\(807\) 33.1272 1.16613
\(808\) −9.36736 −0.329542
\(809\) 2.94582 0.103570 0.0517848 0.998658i \(-0.483509\pi\)
0.0517848 + 0.998658i \(0.483509\pi\)
\(810\) 36.0423 1.26640
\(811\) 33.7456 1.18497 0.592485 0.805582i \(-0.298147\pi\)
0.592485 + 0.805582i \(0.298147\pi\)
\(812\) −9.89541 −0.347261
\(813\) −19.6404 −0.688818
\(814\) 23.5293 0.824701
\(815\) −42.4058 −1.48541
\(816\) 2.92041 0.102235
\(817\) −19.9497 −0.697951
\(818\) −29.7675 −1.04080
\(819\) 5.71206 0.199596
\(820\) −65.3398 −2.28177
\(821\) −40.4922 −1.41319 −0.706594 0.707619i \(-0.749769\pi\)
−0.706594 + 0.707619i \(0.749769\pi\)
\(822\) −23.0340 −0.803402
\(823\) −30.9083 −1.07739 −0.538697 0.842500i \(-0.681083\pi\)
−0.538697 + 0.842500i \(0.681083\pi\)
\(824\) 19.7599 0.688370
\(825\) 2.35009 0.0818197
\(826\) −84.1202 −2.92691
\(827\) 47.7083 1.65898 0.829489 0.558522i \(-0.188632\pi\)
0.829489 + 0.558522i \(0.188632\pi\)
\(828\) −1.72577 −0.0599747
\(829\) 12.1639 0.422469 0.211234 0.977435i \(-0.432252\pi\)
0.211234 + 0.977435i \(0.432252\pi\)
\(830\) 41.2680 1.43243
\(831\) −50.3622 −1.74704
\(832\) 62.8923 2.18040
\(833\) −6.61605 −0.229233
\(834\) 3.62762 0.125614
\(835\) 6.63431 0.229590
\(836\) 46.6566 1.61365
\(837\) −34.5120 −1.19291
\(838\) −26.7027 −0.922428
\(839\) 33.8683 1.16926 0.584632 0.811299i \(-0.301239\pi\)
0.584632 + 0.811299i \(0.301239\pi\)
\(840\) −24.3074 −0.838683
\(841\) 1.00000 0.0344828
\(842\) −20.9478 −0.721908
\(843\) 27.7322 0.955149
\(844\) 36.3106 1.24986
\(845\) 21.7500 0.748222
\(846\) −0.335420 −0.0115320
\(847\) −23.2416 −0.798590
\(848\) 7.27456 0.249809
\(849\) 18.7065 0.642005
\(850\) −2.60926 −0.0894968
\(851\) 8.63327 0.295945
\(852\) −60.2506 −2.06415
\(853\) 45.8445 1.56969 0.784843 0.619695i \(-0.212744\pi\)
0.784843 + 0.619695i \(0.212744\pi\)
\(854\) −61.8148 −2.11526
\(855\) 5.73266 0.196053
\(856\) 11.8432 0.404793
\(857\) −22.8100 −0.779173 −0.389587 0.920990i \(-0.627382\pi\)
−0.389587 + 0.920990i \(0.627382\pi\)
\(858\) −35.2546 −1.20357
\(859\) 39.6239 1.35195 0.675974 0.736925i \(-0.263723\pi\)
0.675974 + 0.736925i \(0.263723\pi\)
\(860\) 15.6712 0.534383
\(861\) −57.5122 −1.96001
\(862\) 38.9648 1.32715
\(863\) −3.44833 −0.117382 −0.0586912 0.998276i \(-0.518693\pi\)
−0.0586912 + 0.998276i \(0.518693\pi\)
\(864\) −37.1417 −1.26359
\(865\) −20.4937 −0.696808
\(866\) 39.3081 1.33575
\(867\) −23.3682 −0.793625
\(868\) 62.5963 2.12466
\(869\) 3.04002 0.103125
\(870\) 7.50411 0.254413
\(871\) 27.2164 0.922192
\(872\) 8.32815 0.282027
\(873\) −5.39062 −0.182445
\(874\) 28.6343 0.968569
\(875\) −39.3855 −1.33147
\(876\) −65.4924 −2.21278
\(877\) −44.8728 −1.51525 −0.757624 0.652692i \(-0.773640\pi\)
−0.757624 + 0.652692i \(0.773640\pi\)
\(878\) −53.0732 −1.79113
\(879\) 37.7040 1.27172
\(880\) 4.58576 0.154586
\(881\) −38.1710 −1.28601 −0.643007 0.765861i \(-0.722313\pi\)
−0.643007 + 0.765861i \(0.722313\pi\)
\(882\) 3.21746 0.108338
\(883\) 12.1408 0.408571 0.204286 0.978911i \(-0.434513\pi\)
0.204286 + 0.978911i \(0.434513\pi\)
\(884\) 23.4013 0.787072
\(885\) 38.1381 1.28200
\(886\) 7.93651 0.266632
\(887\) −27.0924 −0.909674 −0.454837 0.890575i \(-0.650302\pi\)
−0.454837 + 0.890575i \(0.650302\pi\)
\(888\) −18.5876 −0.623759
\(889\) −51.9216 −1.74139
\(890\) −44.6166 −1.49555
\(891\) 15.6581 0.524567
\(892\) −65.7081 −2.20007
\(893\) 3.32725 0.111342
\(894\) −39.3202 −1.31507
\(895\) 44.8383 1.49878
\(896\) 50.9467 1.70201
\(897\) −12.9355 −0.431903
\(898\) −48.4357 −1.61632
\(899\) −6.32579 −0.210977
\(900\) 0.758621 0.0252874
\(901\) 10.6743 0.355611
\(902\) −47.4802 −1.58092
\(903\) 13.7938 0.459029
\(904\) 0.653429 0.0217327
\(905\) −23.5722 −0.783566
\(906\) 41.0629 1.36422
\(907\) 1.50185 0.0498680 0.0249340 0.999689i \(-0.492062\pi\)
0.0249340 + 0.999689i \(0.492062\pi\)
\(908\) −62.1215 −2.06158
\(909\) −1.52751 −0.0506643
\(910\) 74.4496 2.46798
\(911\) 51.8367 1.71743 0.858714 0.512456i \(-0.171264\pi\)
0.858714 + 0.512456i \(0.171264\pi\)
\(912\) 14.0882 0.466506
\(913\) 17.9284 0.593343
\(914\) 66.5920 2.20267
\(915\) 28.0254 0.926490
\(916\) −45.1324 −1.49122
\(917\) −7.27556 −0.240260
\(918\) −19.7476 −0.651768
\(919\) 51.5656 1.70099 0.850496 0.525981i \(-0.176302\pi\)
0.850496 + 0.525981i \(0.176302\pi\)
\(920\) −7.36304 −0.242752
\(921\) 30.2944 0.998234
\(922\) 81.8239 2.69473
\(923\) 60.4075 1.98834
\(924\) −32.2597 −1.06127
\(925\) −3.79505 −0.124780
\(926\) 14.8126 0.486773
\(927\) 3.22220 0.105831
\(928\) −6.80781 −0.223477
\(929\) 29.9546 0.982777 0.491389 0.870940i \(-0.336489\pi\)
0.491389 + 0.870940i \(0.336489\pi\)
\(930\) −47.4694 −1.55658
\(931\) −31.9161 −1.04601
\(932\) 48.0272 1.57318
\(933\) −16.6054 −0.543636
\(934\) 56.8749 1.86100
\(935\) 6.72888 0.220058
\(936\) −3.72529 −0.121765
\(937\) 23.0102 0.751711 0.375855 0.926678i \(-0.377349\pi\)
0.375855 + 0.926678i \(0.377349\pi\)
\(938\) 41.6565 1.36013
\(939\) 43.9556 1.43444
\(940\) −2.61368 −0.0852488
\(941\) −17.5020 −0.570550 −0.285275 0.958446i \(-0.592085\pi\)
−0.285275 + 0.958446i \(0.592085\pi\)
\(942\) −12.7692 −0.416043
\(943\) −17.4212 −0.567314
\(944\) −12.5368 −0.408039
\(945\) −37.5603 −1.22184
\(946\) 11.3877 0.370247
\(947\) 36.8926 1.19885 0.599424 0.800432i \(-0.295396\pi\)
0.599424 + 0.800432i \(0.295396\pi\)
\(948\) −7.33644 −0.238276
\(949\) 65.6629 2.13151
\(950\) −12.5872 −0.408381
\(951\) −0.958723 −0.0310887
\(952\) 11.7246 0.379996
\(953\) 33.8136 1.09533 0.547666 0.836697i \(-0.315517\pi\)
0.547666 + 0.836697i \(0.315517\pi\)
\(954\) −5.19102 −0.168065
\(955\) 46.2660 1.49713
\(956\) 24.0767 0.778696
\(957\) 3.26007 0.105383
\(958\) −6.35709 −0.205388
\(959\) 21.1321 0.682393
\(960\) −43.6424 −1.40855
\(961\) 9.01561 0.290826
\(962\) 56.9308 1.83552
\(963\) 1.93124 0.0622334
\(964\) −76.3137 −2.45790
\(965\) 1.67148 0.0538068
\(966\) −19.7986 −0.637009
\(967\) −9.92616 −0.319204 −0.159602 0.987181i \(-0.551021\pi\)
−0.159602 + 0.987181i \(0.551021\pi\)
\(968\) 15.1577 0.487186
\(969\) 20.6721 0.664085
\(970\) −70.2600 −2.25591
\(971\) 5.11391 0.164113 0.0820566 0.996628i \(-0.473851\pi\)
0.0820566 + 0.996628i \(0.473851\pi\)
\(972\) 10.8770 0.348881
\(973\) −3.32810 −0.106694
\(974\) 31.1877 0.999320
\(975\) 5.68622 0.182105
\(976\) −9.21256 −0.294887
\(977\) −44.3943 −1.42030 −0.710150 0.704051i \(-0.751373\pi\)
−0.710150 + 0.704051i \(0.751373\pi\)
\(978\) 74.3651 2.37793
\(979\) −19.3832 −0.619489
\(980\) 25.0713 0.800873
\(981\) 1.35805 0.0433591
\(982\) 22.7074 0.724622
\(983\) 11.0923 0.353790 0.176895 0.984230i \(-0.443395\pi\)
0.176895 + 0.984230i \(0.443395\pi\)
\(984\) 37.5082 1.19572
\(985\) 1.10576 0.0352323
\(986\) −3.61959 −0.115271
\(987\) −2.30056 −0.0732276
\(988\) 112.889 3.59148
\(989\) 4.17834 0.132863
\(990\) −3.27233 −0.104002
\(991\) −38.6015 −1.22622 −0.613108 0.789999i \(-0.710081\pi\)
−0.613108 + 0.789999i \(0.710081\pi\)
\(992\) 43.0647 1.36731
\(993\) 5.13976 0.163105
\(994\) 92.4577 2.93258
\(995\) −32.1275 −1.01851
\(996\) −43.2664 −1.37095
\(997\) 25.3592 0.803135 0.401568 0.915829i \(-0.368465\pi\)
0.401568 + 0.915829i \(0.368465\pi\)
\(998\) −57.4293 −1.81789
\(999\) −28.7220 −0.908724
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 \(a_p\))