Properties

Label 4015.2.a.h.1.8
Level 4015
Weight 2
Character 4015.1
Self dual Yes
Analytic conductor 32.060
Analytic rank 0
Dimension 37
CM No

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Newspace parameters

Level: \( N \) = \( 4015 = 5 \cdot 11 \cdot 73 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0599364115\)
Analytic rank: \(0\)
Dimension: \(37\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 4015.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.86942 q^{2}\) \(-2.63227 q^{3}\) \(+1.49473 q^{4}\) \(+1.00000 q^{5}\) \(+4.92082 q^{6}\) \(-2.31866 q^{7}\) \(+0.944554 q^{8}\) \(+3.92884 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.86942 q^{2}\) \(-2.63227 q^{3}\) \(+1.49473 q^{4}\) \(+1.00000 q^{5}\) \(+4.92082 q^{6}\) \(-2.31866 q^{7}\) \(+0.944554 q^{8}\) \(+3.92884 q^{9}\) \(-1.86942 q^{10}\) \(+1.00000 q^{11}\) \(-3.93454 q^{12}\) \(-2.05468 q^{13}\) \(+4.33454 q^{14}\) \(-2.63227 q^{15}\) \(-4.75524 q^{16}\) \(-5.64494 q^{17}\) \(-7.34466 q^{18}\) \(-4.69534 q^{19}\) \(+1.49473 q^{20}\) \(+6.10333 q^{21}\) \(-1.86942 q^{22}\) \(-7.33488 q^{23}\) \(-2.48632 q^{24}\) \(+1.00000 q^{25}\) \(+3.84106 q^{26}\) \(-2.44496 q^{27}\) \(-3.46577 q^{28}\) \(-5.39768 q^{29}\) \(+4.92082 q^{30}\) \(+2.07630 q^{31}\) \(+7.00043 q^{32}\) \(-2.63227 q^{33}\) \(+10.5528 q^{34}\) \(-2.31866 q^{35}\) \(+5.87257 q^{36}\) \(+2.42502 q^{37}\) \(+8.77757 q^{38}\) \(+5.40846 q^{39}\) \(+0.944554 q^{40}\) \(+10.2948 q^{41}\) \(-11.4097 q^{42}\) \(+0.817099 q^{43}\) \(+1.49473 q^{44}\) \(+3.92884 q^{45}\) \(+13.7120 q^{46}\) \(-2.17927 q^{47}\) \(+12.5171 q^{48}\) \(-1.62384 q^{49}\) \(-1.86942 q^{50}\) \(+14.8590 q^{51}\) \(-3.07120 q^{52}\) \(-8.22789 q^{53}\) \(+4.57066 q^{54}\) \(+1.00000 q^{55}\) \(-2.19010 q^{56}\) \(+12.3594 q^{57}\) \(+10.0905 q^{58}\) \(-0.531662 q^{59}\) \(-3.93454 q^{60}\) \(-6.90212 q^{61}\) \(-3.88148 q^{62}\) \(-9.10963 q^{63}\) \(-3.57628 q^{64}\) \(-2.05468 q^{65}\) \(+4.92082 q^{66}\) \(-6.19999 q^{67}\) \(-8.43768 q^{68}\) \(+19.3074 q^{69}\) \(+4.33454 q^{70}\) \(-8.72428 q^{71}\) \(+3.71100 q^{72}\) \(+1.00000 q^{73}\) \(-4.53339 q^{74}\) \(-2.63227 q^{75}\) \(-7.01829 q^{76}\) \(-2.31866 q^{77}\) \(-10.1107 q^{78}\) \(+2.92720 q^{79}\) \(-4.75524 q^{80}\) \(-5.35073 q^{81}\) \(-19.2453 q^{82}\) \(-7.28519 q^{83}\) \(+9.12285 q^{84}\) \(-5.64494 q^{85}\) \(-1.52750 q^{86}\) \(+14.2082 q^{87}\) \(+0.944554 q^{88}\) \(-2.65720 q^{89}\) \(-7.34466 q^{90}\) \(+4.76409 q^{91}\) \(-10.9637 q^{92}\) \(-5.46538 q^{93}\) \(+4.07397 q^{94}\) \(-4.69534 q^{95}\) \(-18.4270 q^{96}\) \(-15.5081 q^{97}\) \(+3.03563 q^{98}\) \(+3.92884 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut 5q^{10} \) \(\mathstrut +\mathstrut 37q^{11} \) \(\mathstrut +\mathstrut 6q^{12} \) \(\mathstrut +\mathstrut 11q^{13} \) \(\mathstrut +\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 43q^{16} \) \(\mathstrut +\mathstrut 38q^{17} \) \(\mathstrut +\mathstrut 11q^{18} \) \(\mathstrut +\mathstrut 34q^{19} \) \(\mathstrut +\mathstrut 43q^{20} \) \(\mathstrut +\mathstrut 39q^{21} \) \(\mathstrut +\mathstrut 5q^{22} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 37q^{25} \) \(\mathstrut -\mathstrut 9q^{26} \) \(\mathstrut +\mathstrut 3q^{27} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut +\mathstrut 9q^{30} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut +\mathstrut 14q^{32} \) \(\mathstrut +\mathstrut 3q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 6q^{35} \) \(\mathstrut +\mathstrut 20q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 15q^{38} \) \(\mathstrut +\mathstrut 14q^{39} \) \(\mathstrut +\mathstrut 12q^{40} \) \(\mathstrut +\mathstrut 62q^{41} \) \(\mathstrut -\mathstrut 13q^{42} \) \(\mathstrut +\mathstrut 30q^{43} \) \(\mathstrut +\mathstrut 43q^{44} \) \(\mathstrut +\mathstrut 50q^{45} \) \(\mathstrut +\mathstrut 31q^{46} \) \(\mathstrut +\mathstrut 5q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 59q^{49} \) \(\mathstrut +\mathstrut 5q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 13q^{54} \) \(\mathstrut +\mathstrut 37q^{55} \) \(\mathstrut +\mathstrut 22q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 40q^{58} \) \(\mathstrut +\mathstrut 15q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut +\mathstrut 57q^{61} \) \(\mathstrut +\mathstrut 20q^{62} \) \(\mathstrut -\mathstrut 29q^{63} \) \(\mathstrut +\mathstrut 10q^{64} \) \(\mathstrut +\mathstrut 11q^{65} \) \(\mathstrut +\mathstrut 9q^{66} \) \(\mathstrut -\mathstrut 14q^{67} \) \(\mathstrut +\mathstrut 53q^{68} \) \(\mathstrut +\mathstrut 24q^{69} \) \(\mathstrut +\mathstrut 11q^{70} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 15q^{72} \) \(\mathstrut +\mathstrut 37q^{73} \) \(\mathstrut +\mathstrut 7q^{74} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut +\mathstrut 59q^{76} \) \(\mathstrut +\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut q^{78} \) \(\mathstrut +\mathstrut 42q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 61q^{81} \) \(\mathstrut -\mathstrut 22q^{82} \) \(\mathstrut +\mathstrut 44q^{83} \) \(\mathstrut +\mathstrut 66q^{84} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut -\mathstrut q^{86} \) \(\mathstrut -\mathstrut 26q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 69q^{89} \) \(\mathstrut +\mathstrut 11q^{90} \) \(\mathstrut -\mathstrut 10q^{91} \) \(\mathstrut -\mathstrut 21q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut +\mathstrut 29q^{94} \) \(\mathstrut +\mathstrut 34q^{95} \) \(\mathstrut -\mathstrut 9q^{96} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut -\mathstrut 15q^{98} \) \(\mathstrut +\mathstrut 50q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.86942 −1.32188 −0.660940 0.750439i \(-0.729842\pi\)
−0.660940 + 0.750439i \(0.729842\pi\)
\(3\) −2.63227 −1.51974 −0.759871 0.650074i \(-0.774738\pi\)
−0.759871 + 0.650074i \(0.774738\pi\)
\(4\) 1.49473 0.747367
\(5\) 1.00000 0.447214
\(6\) 4.92082 2.00892
\(7\) −2.31866 −0.876369 −0.438185 0.898885i \(-0.644378\pi\)
−0.438185 + 0.898885i \(0.644378\pi\)
\(8\) 0.944554 0.333950
\(9\) 3.92884 1.30961
\(10\) −1.86942 −0.591163
\(11\) 1.00000 0.301511
\(12\) −3.93454 −1.13580
\(13\) −2.05468 −0.569865 −0.284932 0.958548i \(-0.591971\pi\)
−0.284932 + 0.958548i \(0.591971\pi\)
\(14\) 4.33454 1.15846
\(15\) −2.63227 −0.679649
\(16\) −4.75524 −1.18881
\(17\) −5.64494 −1.36910 −0.684549 0.728967i \(-0.740001\pi\)
−0.684549 + 0.728967i \(0.740001\pi\)
\(18\) −7.34466 −1.73115
\(19\) −4.69534 −1.07719 −0.538593 0.842566i \(-0.681044\pi\)
−0.538593 + 0.842566i \(0.681044\pi\)
\(20\) 1.49473 0.334233
\(21\) 6.10333 1.33185
\(22\) −1.86942 −0.398562
\(23\) −7.33488 −1.52943 −0.764715 0.644369i \(-0.777120\pi\)
−0.764715 + 0.644369i \(0.777120\pi\)
\(24\) −2.48632 −0.507518
\(25\) 1.00000 0.200000
\(26\) 3.84106 0.753293
\(27\) −2.44496 −0.470533
\(28\) −3.46577 −0.654970
\(29\) −5.39768 −1.00232 −0.501162 0.865353i \(-0.667094\pi\)
−0.501162 + 0.865353i \(0.667094\pi\)
\(30\) 4.92082 0.898415
\(31\) 2.07630 0.372915 0.186457 0.982463i \(-0.440299\pi\)
0.186457 + 0.982463i \(0.440299\pi\)
\(32\) 7.00043 1.23751
\(33\) −2.63227 −0.458219
\(34\) 10.5528 1.80978
\(35\) −2.31866 −0.391924
\(36\) 5.87257 0.978762
\(37\) 2.42502 0.398671 0.199336 0.979931i \(-0.436122\pi\)
0.199336 + 0.979931i \(0.436122\pi\)
\(38\) 8.77757 1.42391
\(39\) 5.40846 0.866047
\(40\) 0.944554 0.149347
\(41\) 10.2948 1.60778 0.803890 0.594778i \(-0.202760\pi\)
0.803890 + 0.594778i \(0.202760\pi\)
\(42\) −11.4097 −1.76055
\(43\) 0.817099 0.124606 0.0623032 0.998057i \(-0.480155\pi\)
0.0623032 + 0.998057i \(0.480155\pi\)
\(44\) 1.49473 0.225340
\(45\) 3.92884 0.585677
\(46\) 13.7120 2.02172
\(47\) −2.17927 −0.317879 −0.158940 0.987288i \(-0.550808\pi\)
−0.158940 + 0.987288i \(0.550808\pi\)
\(48\) 12.5171 1.80668
\(49\) −1.62384 −0.231977
\(50\) −1.86942 −0.264376
\(51\) 14.8590 2.08068
\(52\) −3.07120 −0.425898
\(53\) −8.22789 −1.13019 −0.565094 0.825026i \(-0.691160\pi\)
−0.565094 + 0.825026i \(0.691160\pi\)
\(54\) 4.57066 0.621988
\(55\) 1.00000 0.134840
\(56\) −2.19010 −0.292664
\(57\) 12.3594 1.63704
\(58\) 10.0905 1.32495
\(59\) −0.531662 −0.0692164 −0.0346082 0.999401i \(-0.511018\pi\)
−0.0346082 + 0.999401i \(0.511018\pi\)
\(60\) −3.93454 −0.507947
\(61\) −6.90212 −0.883726 −0.441863 0.897082i \(-0.645682\pi\)
−0.441863 + 0.897082i \(0.645682\pi\)
\(62\) −3.88148 −0.492948
\(63\) −9.10963 −1.14771
\(64\) −3.57628 −0.447035
\(65\) −2.05468 −0.254851
\(66\) 4.92082 0.605711
\(67\) −6.19999 −0.757449 −0.378725 0.925509i \(-0.623637\pi\)
−0.378725 + 0.925509i \(0.623637\pi\)
\(68\) −8.43768 −1.02322
\(69\) 19.3074 2.32434
\(70\) 4.33454 0.518077
\(71\) −8.72428 −1.03538 −0.517691 0.855568i \(-0.673208\pi\)
−0.517691 + 0.855568i \(0.673208\pi\)
\(72\) 3.71100 0.437346
\(73\) 1.00000 0.117041
\(74\) −4.53339 −0.526996
\(75\) −2.63227 −0.303948
\(76\) −7.01829 −0.805053
\(77\) −2.31866 −0.264235
\(78\) −10.1107 −1.14481
\(79\) 2.92720 0.329335 0.164668 0.986349i \(-0.447345\pi\)
0.164668 + 0.986349i \(0.447345\pi\)
\(80\) −4.75524 −0.531652
\(81\) −5.35073 −0.594526
\(82\) −19.2453 −2.12529
\(83\) −7.28519 −0.799654 −0.399827 0.916591i \(-0.630930\pi\)
−0.399827 + 0.916591i \(0.630930\pi\)
\(84\) 9.12285 0.995385
\(85\) −5.64494 −0.612279
\(86\) −1.52750 −0.164715
\(87\) 14.2082 1.52327
\(88\) 0.944554 0.100690
\(89\) −2.65720 −0.281662 −0.140831 0.990034i \(-0.544977\pi\)
−0.140831 + 0.990034i \(0.544977\pi\)
\(90\) −7.34466 −0.774195
\(91\) 4.76409 0.499412
\(92\) −10.9637 −1.14305
\(93\) −5.46538 −0.566734
\(94\) 4.07397 0.420198
\(95\) −4.69534 −0.481732
\(96\) −18.4270 −1.88070
\(97\) −15.5081 −1.57461 −0.787307 0.616561i \(-0.788525\pi\)
−0.787307 + 0.616561i \(0.788525\pi\)
\(98\) 3.03563 0.306645
\(99\) 3.92884 0.394863
\(100\) 1.49473 0.149473
\(101\) 19.9313 1.98323 0.991617 0.129210i \(-0.0412442\pi\)
0.991617 + 0.129210i \(0.0412442\pi\)
\(102\) −27.7777 −2.75040
\(103\) −8.67756 −0.855026 −0.427513 0.904009i \(-0.640610\pi\)
−0.427513 + 0.904009i \(0.640610\pi\)
\(104\) −1.94075 −0.190306
\(105\) 6.10333 0.595624
\(106\) 15.3814 1.49397
\(107\) −15.3399 −1.48296 −0.741480 0.670975i \(-0.765876\pi\)
−0.741480 + 0.670975i \(0.765876\pi\)
\(108\) −3.65457 −0.351661
\(109\) 3.80535 0.364487 0.182243 0.983253i \(-0.441664\pi\)
0.182243 + 0.983253i \(0.441664\pi\)
\(110\) −1.86942 −0.178242
\(111\) −6.38331 −0.605877
\(112\) 11.0258 1.04184
\(113\) −7.99314 −0.751931 −0.375966 0.926634i \(-0.622689\pi\)
−0.375966 + 0.926634i \(0.622689\pi\)
\(114\) −23.1049 −2.16398
\(115\) −7.33488 −0.683982
\(116\) −8.06810 −0.749104
\(117\) −8.07250 −0.746303
\(118\) 0.993899 0.0914958
\(119\) 13.0887 1.19984
\(120\) −2.48632 −0.226969
\(121\) 1.00000 0.0909091
\(122\) 12.9030 1.16818
\(123\) −27.0987 −2.44341
\(124\) 3.10352 0.278704
\(125\) 1.00000 0.0894427
\(126\) 17.0297 1.51713
\(127\) 17.1056 1.51787 0.758937 0.651164i \(-0.225719\pi\)
0.758937 + 0.651164i \(0.225719\pi\)
\(128\) −7.31529 −0.646587
\(129\) −2.15082 −0.189370
\(130\) 3.84106 0.336883
\(131\) −5.97264 −0.521832 −0.260916 0.965362i \(-0.584024\pi\)
−0.260916 + 0.965362i \(0.584024\pi\)
\(132\) −3.93454 −0.342458
\(133\) 10.8869 0.944013
\(134\) 11.5904 1.00126
\(135\) −2.44496 −0.210429
\(136\) −5.33195 −0.457211
\(137\) 1.16619 0.0996345 0.0498173 0.998758i \(-0.484136\pi\)
0.0498173 + 0.998758i \(0.484136\pi\)
\(138\) −36.0936 −3.07249
\(139\) −2.46233 −0.208852 −0.104426 0.994533i \(-0.533301\pi\)
−0.104426 + 0.994533i \(0.533301\pi\)
\(140\) −3.46577 −0.292911
\(141\) 5.73642 0.483094
\(142\) 16.3093 1.36865
\(143\) −2.05468 −0.171821
\(144\) −18.6826 −1.55688
\(145\) −5.39768 −0.448253
\(146\) −1.86942 −0.154714
\(147\) 4.27437 0.352544
\(148\) 3.62477 0.297954
\(149\) 13.9210 1.14045 0.570225 0.821489i \(-0.306856\pi\)
0.570225 + 0.821489i \(0.306856\pi\)
\(150\) 4.92082 0.401783
\(151\) −22.0184 −1.79183 −0.895915 0.444226i \(-0.853479\pi\)
−0.895915 + 0.444226i \(0.853479\pi\)
\(152\) −4.43501 −0.359726
\(153\) −22.1781 −1.79299
\(154\) 4.33454 0.349287
\(155\) 2.07630 0.166772
\(156\) 8.08421 0.647255
\(157\) 4.30608 0.343663 0.171831 0.985126i \(-0.445032\pi\)
0.171831 + 0.985126i \(0.445032\pi\)
\(158\) −5.47216 −0.435342
\(159\) 21.6580 1.71759
\(160\) 7.00043 0.553433
\(161\) 17.0071 1.34034
\(162\) 10.0028 0.785892
\(163\) 5.31470 0.416279 0.208140 0.978099i \(-0.433259\pi\)
0.208140 + 0.978099i \(0.433259\pi\)
\(164\) 15.3880 1.20160
\(165\) −2.63227 −0.204922
\(166\) 13.6191 1.05705
\(167\) 5.28842 0.409230 0.204615 0.978843i \(-0.434406\pi\)
0.204615 + 0.978843i \(0.434406\pi\)
\(168\) 5.76492 0.444773
\(169\) −8.77830 −0.675254
\(170\) 10.5528 0.809360
\(171\) −18.4473 −1.41070
\(172\) 1.22135 0.0931267
\(173\) −22.8886 −1.74018 −0.870092 0.492889i \(-0.835941\pi\)
−0.870092 + 0.492889i \(0.835941\pi\)
\(174\) −26.5610 −2.01359
\(175\) −2.31866 −0.175274
\(176\) −4.75524 −0.358440
\(177\) 1.39948 0.105191
\(178\) 4.96742 0.372324
\(179\) −20.5054 −1.53264 −0.766321 0.642458i \(-0.777915\pi\)
−0.766321 + 0.642458i \(0.777915\pi\)
\(180\) 5.87257 0.437716
\(181\) 13.7138 1.01934 0.509671 0.860369i \(-0.329767\pi\)
0.509671 + 0.860369i \(0.329767\pi\)
\(182\) −8.90608 −0.660163
\(183\) 18.1682 1.34304
\(184\) −6.92819 −0.510753
\(185\) 2.42502 0.178291
\(186\) 10.2171 0.749154
\(187\) −5.64494 −0.412799
\(188\) −3.25743 −0.237572
\(189\) 5.66902 0.412360
\(190\) 8.77757 0.636792
\(191\) −23.6805 −1.71346 −0.856730 0.515765i \(-0.827508\pi\)
−0.856730 + 0.515765i \(0.827508\pi\)
\(192\) 9.41373 0.679378
\(193\) 22.3771 1.61074 0.805370 0.592772i \(-0.201966\pi\)
0.805370 + 0.592772i \(0.201966\pi\)
\(194\) 28.9913 2.08145
\(195\) 5.40846 0.387308
\(196\) −2.42720 −0.173372
\(197\) 12.2767 0.874680 0.437340 0.899296i \(-0.355921\pi\)
0.437340 + 0.899296i \(0.355921\pi\)
\(198\) −7.34466 −0.521962
\(199\) −10.9920 −0.779203 −0.389602 0.920984i \(-0.627387\pi\)
−0.389602 + 0.920984i \(0.627387\pi\)
\(200\) 0.944554 0.0667901
\(201\) 16.3200 1.15113
\(202\) −37.2599 −2.62160
\(203\) 12.5154 0.878406
\(204\) 22.2102 1.55503
\(205\) 10.2948 0.719021
\(206\) 16.2220 1.13024
\(207\) −28.8176 −2.00296
\(208\) 9.77048 0.677461
\(209\) −4.69534 −0.324784
\(210\) −11.4097 −0.787343
\(211\) −5.05261 −0.347836 −0.173918 0.984760i \(-0.555643\pi\)
−0.173918 + 0.984760i \(0.555643\pi\)
\(212\) −12.2985 −0.844666
\(213\) 22.9646 1.57351
\(214\) 28.6766 1.96029
\(215\) 0.817099 0.0557257
\(216\) −2.30940 −0.157135
\(217\) −4.81423 −0.326811
\(218\) −7.11381 −0.481808
\(219\) −2.63227 −0.177872
\(220\) 1.49473 0.100775
\(221\) 11.5985 0.780201
\(222\) 11.9331 0.800897
\(223\) −24.7199 −1.65537 −0.827684 0.561194i \(-0.810342\pi\)
−0.827684 + 0.561194i \(0.810342\pi\)
\(224\) −16.2316 −1.08452
\(225\) 3.92884 0.261923
\(226\) 14.9425 0.993963
\(227\) −3.44484 −0.228642 −0.114321 0.993444i \(-0.536469\pi\)
−0.114321 + 0.993444i \(0.536469\pi\)
\(228\) 18.4740 1.22347
\(229\) −12.1093 −0.800206 −0.400103 0.916470i \(-0.631026\pi\)
−0.400103 + 0.916470i \(0.631026\pi\)
\(230\) 13.7120 0.904142
\(231\) 6.10333 0.401569
\(232\) −5.09840 −0.334726
\(233\) 2.23168 0.146202 0.0731011 0.997325i \(-0.476710\pi\)
0.0731011 + 0.997325i \(0.476710\pi\)
\(234\) 15.0909 0.986523
\(235\) −2.17927 −0.142160
\(236\) −0.794693 −0.0517301
\(237\) −7.70517 −0.500504
\(238\) −24.4682 −1.58604
\(239\) −4.32984 −0.280074 −0.140037 0.990146i \(-0.544722\pi\)
−0.140037 + 0.990146i \(0.544722\pi\)
\(240\) 12.5171 0.807973
\(241\) 10.1902 0.656410 0.328205 0.944607i \(-0.393556\pi\)
0.328205 + 0.944607i \(0.393556\pi\)
\(242\) −1.86942 −0.120171
\(243\) 21.4194 1.37406
\(244\) −10.3168 −0.660468
\(245\) −1.62384 −0.103743
\(246\) 50.6589 3.22989
\(247\) 9.64741 0.613850
\(248\) 1.96118 0.124535
\(249\) 19.1766 1.21527
\(250\) −1.86942 −0.118233
\(251\) 20.3922 1.28714 0.643572 0.765386i \(-0.277452\pi\)
0.643572 + 0.765386i \(0.277452\pi\)
\(252\) −13.6165 −0.857757
\(253\) −7.33488 −0.461140
\(254\) −31.9775 −2.00645
\(255\) 14.8590 0.930506
\(256\) 20.8279 1.30175
\(257\) 8.69505 0.542382 0.271191 0.962526i \(-0.412582\pi\)
0.271191 + 0.962526i \(0.412582\pi\)
\(258\) 4.02080 0.250324
\(259\) −5.62279 −0.349383
\(260\) −3.07120 −0.190467
\(261\) −21.2066 −1.31266
\(262\) 11.1654 0.689799
\(263\) 22.1826 1.36784 0.683918 0.729559i \(-0.260275\pi\)
0.683918 + 0.729559i \(0.260275\pi\)
\(264\) −2.48632 −0.153022
\(265\) −8.22789 −0.505436
\(266\) −20.3522 −1.24787
\(267\) 6.99446 0.428054
\(268\) −9.26734 −0.566093
\(269\) −10.3880 −0.633370 −0.316685 0.948531i \(-0.602570\pi\)
−0.316685 + 0.948531i \(0.602570\pi\)
\(270\) 4.57066 0.278161
\(271\) −3.19327 −0.193977 −0.0969886 0.995285i \(-0.530921\pi\)
−0.0969886 + 0.995285i \(0.530921\pi\)
\(272\) 26.8430 1.62760
\(273\) −12.5404 −0.758977
\(274\) −2.18010 −0.131705
\(275\) 1.00000 0.0603023
\(276\) 28.8594 1.73713
\(277\) 25.1949 1.51381 0.756907 0.653522i \(-0.226709\pi\)
0.756907 + 0.653522i \(0.226709\pi\)
\(278\) 4.60314 0.276078
\(279\) 8.15745 0.488374
\(280\) −2.19010 −0.130883
\(281\) −6.41999 −0.382985 −0.191492 0.981494i \(-0.561333\pi\)
−0.191492 + 0.981494i \(0.561333\pi\)
\(282\) −10.7238 −0.638593
\(283\) −22.1267 −1.31529 −0.657647 0.753326i \(-0.728448\pi\)
−0.657647 + 0.753326i \(0.728448\pi\)
\(284\) −13.0405 −0.773810
\(285\) 12.3594 0.732108
\(286\) 3.84106 0.227126
\(287\) −23.8701 −1.40901
\(288\) 27.5036 1.62066
\(289\) 14.8653 0.874430
\(290\) 10.0905 0.592537
\(291\) 40.8216 2.39301
\(292\) 1.49473 0.0874727
\(293\) −10.6042 −0.619504 −0.309752 0.950817i \(-0.600246\pi\)
−0.309752 + 0.950817i \(0.600246\pi\)
\(294\) −7.99060 −0.466021
\(295\) −0.531662 −0.0309545
\(296\) 2.29057 0.133136
\(297\) −2.44496 −0.141871
\(298\) −26.0241 −1.50754
\(299\) 15.0708 0.871568
\(300\) −3.93454 −0.227161
\(301\) −1.89457 −0.109201
\(302\) 41.1616 2.36858
\(303\) −52.4644 −3.01400
\(304\) 22.3275 1.28057
\(305\) −6.90212 −0.395214
\(306\) 41.4601 2.37012
\(307\) −15.5305 −0.886370 −0.443185 0.896430i \(-0.646151\pi\)
−0.443185 + 0.896430i \(0.646151\pi\)
\(308\) −3.46577 −0.197481
\(309\) 22.8417 1.29942
\(310\) −3.88148 −0.220453
\(311\) 26.0257 1.47578 0.737891 0.674920i \(-0.235822\pi\)
0.737891 + 0.674920i \(0.235822\pi\)
\(312\) 5.10858 0.289217
\(313\) 8.77516 0.496002 0.248001 0.968760i \(-0.420226\pi\)
0.248001 + 0.968760i \(0.420226\pi\)
\(314\) −8.04988 −0.454281
\(315\) −9.10963 −0.513269
\(316\) 4.37538 0.246134
\(317\) 14.8784 0.835654 0.417827 0.908527i \(-0.362792\pi\)
0.417827 + 0.908527i \(0.362792\pi\)
\(318\) −40.4880 −2.27045
\(319\) −5.39768 −0.302212
\(320\) −3.57628 −0.199920
\(321\) 40.3786 2.25371
\(322\) −31.7934 −1.77178
\(323\) 26.5049 1.47477
\(324\) −7.99792 −0.444329
\(325\) −2.05468 −0.113973
\(326\) −9.93540 −0.550271
\(327\) −10.0167 −0.553926
\(328\) 9.72401 0.536918
\(329\) 5.05298 0.278580
\(330\) 4.92082 0.270882
\(331\) −15.9860 −0.878673 −0.439336 0.898323i \(-0.644786\pi\)
−0.439336 + 0.898323i \(0.644786\pi\)
\(332\) −10.8894 −0.597635
\(333\) 9.52753 0.522105
\(334\) −9.88627 −0.540953
\(335\) −6.19999 −0.338742
\(336\) −29.0228 −1.58332
\(337\) 10.6872 0.582166 0.291083 0.956698i \(-0.405984\pi\)
0.291083 + 0.956698i \(0.405984\pi\)
\(338\) 16.4103 0.892605
\(339\) 21.0401 1.14274
\(340\) −8.43768 −0.457597
\(341\) 2.07630 0.112438
\(342\) 34.4857 1.86477
\(343\) 19.9957 1.07967
\(344\) 0.771794 0.0416123
\(345\) 19.3074 1.03947
\(346\) 42.7883 2.30032
\(347\) −12.8687 −0.690827 −0.345413 0.938451i \(-0.612261\pi\)
−0.345413 + 0.938451i \(0.612261\pi\)
\(348\) 21.2374 1.13844
\(349\) −23.7664 −1.27219 −0.636093 0.771612i \(-0.719451\pi\)
−0.636093 + 0.771612i \(0.719451\pi\)
\(350\) 4.33454 0.231691
\(351\) 5.02360 0.268140
\(352\) 7.00043 0.373124
\(353\) 34.5154 1.83707 0.918535 0.395339i \(-0.129373\pi\)
0.918535 + 0.395339i \(0.129373\pi\)
\(354\) −2.61621 −0.139050
\(355\) −8.72428 −0.463037
\(356\) −3.97181 −0.210505
\(357\) −34.4529 −1.82344
\(358\) 38.3331 2.02597
\(359\) 17.0673 0.900780 0.450390 0.892832i \(-0.351285\pi\)
0.450390 + 0.892832i \(0.351285\pi\)
\(360\) 3.71100 0.195587
\(361\) 3.04625 0.160329
\(362\) −25.6369 −1.34745
\(363\) −2.63227 −0.138158
\(364\) 7.12105 0.373244
\(365\) 1.00000 0.0523424
\(366\) −33.9641 −1.77533
\(367\) −36.0794 −1.88333 −0.941666 0.336550i \(-0.890740\pi\)
−0.941666 + 0.336550i \(0.890740\pi\)
\(368\) 34.8791 1.81820
\(369\) 40.4467 2.10557
\(370\) −4.53339 −0.235680
\(371\) 19.0777 0.990462
\(372\) −8.16929 −0.423558
\(373\) −17.8517 −0.924328 −0.462164 0.886794i \(-0.652927\pi\)
−0.462164 + 0.886794i \(0.652927\pi\)
\(374\) 10.5528 0.545670
\(375\) −2.63227 −0.135930
\(376\) −2.05844 −0.106156
\(377\) 11.0905 0.571189
\(378\) −10.5978 −0.545091
\(379\) −9.76239 −0.501460 −0.250730 0.968057i \(-0.580671\pi\)
−0.250730 + 0.968057i \(0.580671\pi\)
\(380\) −7.01829 −0.360031
\(381\) −45.0265 −2.30678
\(382\) 44.2688 2.26499
\(383\) 32.6905 1.67041 0.835203 0.549942i \(-0.185350\pi\)
0.835203 + 0.549942i \(0.185350\pi\)
\(384\) 19.2558 0.982645
\(385\) −2.31866 −0.118170
\(386\) −41.8323 −2.12921
\(387\) 3.21025 0.163186
\(388\) −23.1806 −1.17681
\(389\) 15.3291 0.777214 0.388607 0.921404i \(-0.372956\pi\)
0.388607 + 0.921404i \(0.372956\pi\)
\(390\) −10.1107 −0.511975
\(391\) 41.4050 2.09394
\(392\) −1.53380 −0.0774686
\(393\) 15.7216 0.793049
\(394\) −22.9504 −1.15622
\(395\) 2.92720 0.147283
\(396\) 5.87257 0.295108
\(397\) −1.20870 −0.0606629 −0.0303315 0.999540i \(-0.509656\pi\)
−0.0303315 + 0.999540i \(0.509656\pi\)
\(398\) 20.5487 1.03001
\(399\) −28.6572 −1.43466
\(400\) −4.75524 −0.237762
\(401\) −19.0629 −0.951956 −0.475978 0.879457i \(-0.657906\pi\)
−0.475978 + 0.879457i \(0.657906\pi\)
\(402\) −30.5090 −1.52165
\(403\) −4.26613 −0.212511
\(404\) 29.7919 1.48220
\(405\) −5.35073 −0.265880
\(406\) −23.3965 −1.16115
\(407\) 2.42502 0.120204
\(408\) 14.0351 0.694842
\(409\) −4.81050 −0.237864 −0.118932 0.992902i \(-0.537947\pi\)
−0.118932 + 0.992902i \(0.537947\pi\)
\(410\) −19.2453 −0.950459
\(411\) −3.06973 −0.151419
\(412\) −12.9707 −0.639018
\(413\) 1.23274 0.0606592
\(414\) 53.8722 2.64767
\(415\) −7.28519 −0.357616
\(416\) −14.3836 −0.705215
\(417\) 6.48152 0.317401
\(418\) 8.77757 0.429325
\(419\) −5.31371 −0.259592 −0.129796 0.991541i \(-0.541432\pi\)
−0.129796 + 0.991541i \(0.541432\pi\)
\(420\) 9.12285 0.445150
\(421\) 37.0089 1.80371 0.901853 0.432044i \(-0.142207\pi\)
0.901853 + 0.432044i \(0.142207\pi\)
\(422\) 9.44546 0.459798
\(423\) −8.56200 −0.416299
\(424\) −7.77169 −0.377427
\(425\) −5.64494 −0.273820
\(426\) −42.9306 −2.07999
\(427\) 16.0036 0.774471
\(428\) −22.9290 −1.10832
\(429\) 5.40846 0.261123
\(430\) −1.52750 −0.0736627
\(431\) 27.7183 1.33514 0.667572 0.744545i \(-0.267334\pi\)
0.667572 + 0.744545i \(0.267334\pi\)
\(432\) 11.6264 0.559374
\(433\) 5.52240 0.265390 0.132695 0.991157i \(-0.457637\pi\)
0.132695 + 0.991157i \(0.457637\pi\)
\(434\) 8.99981 0.432005
\(435\) 14.2082 0.681229
\(436\) 5.68799 0.272406
\(437\) 34.4398 1.64748
\(438\) 4.92082 0.235126
\(439\) −29.8825 −1.42621 −0.713106 0.701056i \(-0.752712\pi\)
−0.713106 + 0.701056i \(0.752712\pi\)
\(440\) 0.944554 0.0450298
\(441\) −6.37979 −0.303800
\(442\) −21.6825 −1.03133
\(443\) 1.22325 0.0581185 0.0290592 0.999578i \(-0.490749\pi\)
0.0290592 + 0.999578i \(0.490749\pi\)
\(444\) −9.54136 −0.452813
\(445\) −2.65720 −0.125963
\(446\) 46.2119 2.18820
\(447\) −36.6437 −1.73319
\(448\) 8.29216 0.391768
\(449\) 2.24760 0.106071 0.0530354 0.998593i \(-0.483110\pi\)
0.0530354 + 0.998593i \(0.483110\pi\)
\(450\) −7.34466 −0.346230
\(451\) 10.2948 0.484764
\(452\) −11.9476 −0.561969
\(453\) 57.9583 2.72312
\(454\) 6.43986 0.302238
\(455\) 4.76409 0.223344
\(456\) 11.6741 0.546691
\(457\) 16.8453 0.787988 0.393994 0.919113i \(-0.371093\pi\)
0.393994 + 0.919113i \(0.371093\pi\)
\(458\) 22.6374 1.05778
\(459\) 13.8016 0.644205
\(460\) −10.9637 −0.511185
\(461\) 17.3722 0.809103 0.404552 0.914515i \(-0.367428\pi\)
0.404552 + 0.914515i \(0.367428\pi\)
\(462\) −11.4097 −0.530827
\(463\) 14.1392 0.657103 0.328552 0.944486i \(-0.393439\pi\)
0.328552 + 0.944486i \(0.393439\pi\)
\(464\) 25.6673 1.19157
\(465\) −5.46538 −0.253451
\(466\) −4.17195 −0.193262
\(467\) −0.111111 −0.00514160 −0.00257080 0.999997i \(-0.500818\pi\)
−0.00257080 + 0.999997i \(0.500818\pi\)
\(468\) −12.0662 −0.557762
\(469\) 14.3756 0.663806
\(470\) 4.07397 0.187918
\(471\) −11.3348 −0.522278
\(472\) −0.502183 −0.0231148
\(473\) 0.817099 0.0375702
\(474\) 14.4042 0.661607
\(475\) −4.69534 −0.215437
\(476\) 19.5641 0.896718
\(477\) −32.3261 −1.48011
\(478\) 8.09429 0.370224
\(479\) 0.0129715 0.000592681 0 0.000296341 1.00000i \(-0.499906\pi\)
0.000296341 1.00000i \(0.499906\pi\)
\(480\) −18.4270 −0.841075
\(481\) −4.98264 −0.227189
\(482\) −19.0498 −0.867695
\(483\) −44.7672 −2.03698
\(484\) 1.49473 0.0679425
\(485\) −15.5081 −0.704189
\(486\) −40.0420 −1.81634
\(487\) −36.8567 −1.67014 −0.835069 0.550145i \(-0.814572\pi\)
−0.835069 + 0.550145i \(0.814572\pi\)
\(488\) −6.51943 −0.295121
\(489\) −13.9897 −0.632637
\(490\) 3.03563 0.137136
\(491\) 41.3508 1.86614 0.933068 0.359701i \(-0.117121\pi\)
0.933068 + 0.359701i \(0.117121\pi\)
\(492\) −40.5054 −1.82612
\(493\) 30.4696 1.37228
\(494\) −18.0351 −0.811436
\(495\) 3.92884 0.176588
\(496\) −9.87330 −0.443324
\(497\) 20.2286 0.907377
\(498\) −35.8491 −1.60644
\(499\) −29.2254 −1.30831 −0.654153 0.756362i \(-0.726975\pi\)
−0.654153 + 0.756362i \(0.726975\pi\)
\(500\) 1.49473 0.0668466
\(501\) −13.9205 −0.621924
\(502\) −38.1216 −1.70145
\(503\) −10.5576 −0.470738 −0.235369 0.971906i \(-0.575630\pi\)
−0.235369 + 0.971906i \(0.575630\pi\)
\(504\) −8.60454 −0.383277
\(505\) 19.9313 0.886929
\(506\) 13.7120 0.609572
\(507\) 23.1069 1.02621
\(508\) 25.5683 1.13441
\(509\) 19.5917 0.868389 0.434194 0.900819i \(-0.357033\pi\)
0.434194 + 0.900819i \(0.357033\pi\)
\(510\) −27.7777 −1.23002
\(511\) −2.31866 −0.102571
\(512\) −24.3056 −1.07416
\(513\) 11.4799 0.506851
\(514\) −16.2547 −0.716964
\(515\) −8.67756 −0.382379
\(516\) −3.21491 −0.141529
\(517\) −2.17927 −0.0958442
\(518\) 10.5114 0.461843
\(519\) 60.2488 2.64463
\(520\) −1.94075 −0.0851076
\(521\) 26.7569 1.17224 0.586120 0.810224i \(-0.300655\pi\)
0.586120 + 0.810224i \(0.300655\pi\)
\(522\) 39.6441 1.73518
\(523\) 33.2544 1.45412 0.727058 0.686576i \(-0.240887\pi\)
0.727058 + 0.686576i \(0.240887\pi\)
\(524\) −8.92750 −0.390000
\(525\) 6.10333 0.266371
\(526\) −41.4685 −1.80811
\(527\) −11.7206 −0.510557
\(528\) 12.5171 0.544735
\(529\) 30.8005 1.33915
\(530\) 15.3814 0.668125
\(531\) −2.08881 −0.0906468
\(532\) 16.2730 0.705524
\(533\) −21.1525 −0.916217
\(534\) −13.0756 −0.565836
\(535\) −15.3399 −0.663200
\(536\) −5.85623 −0.252950
\(537\) 53.9756 2.32922
\(538\) 19.4196 0.837240
\(539\) −1.62384 −0.0699436
\(540\) −3.65457 −0.157267
\(541\) −23.7282 −1.02015 −0.510077 0.860129i \(-0.670383\pi\)
−0.510077 + 0.860129i \(0.670383\pi\)
\(542\) 5.96956 0.256415
\(543\) −36.0985 −1.54914
\(544\) −39.5170 −1.69428
\(545\) 3.80535 0.163003
\(546\) 23.4432 1.00328
\(547\) 23.2207 0.992844 0.496422 0.868081i \(-0.334647\pi\)
0.496422 + 0.868081i \(0.334647\pi\)
\(548\) 1.74315 0.0744636
\(549\) −27.1173 −1.15734
\(550\) −1.86942 −0.0797124
\(551\) 25.3440 1.07969
\(552\) 18.2369 0.776213
\(553\) −6.78716 −0.288619
\(554\) −47.0999 −2.00108
\(555\) −6.38331 −0.270957
\(556\) −3.68053 −0.156089
\(557\) 6.21306 0.263256 0.131628 0.991299i \(-0.457980\pi\)
0.131628 + 0.991299i \(0.457980\pi\)
\(558\) −15.2497 −0.645572
\(559\) −1.67887 −0.0710088
\(560\) 11.0258 0.465923
\(561\) 14.8590 0.627347
\(562\) 12.0017 0.506260
\(563\) 43.4457 1.83102 0.915509 0.402297i \(-0.131788\pi\)
0.915509 + 0.402297i \(0.131788\pi\)
\(564\) 8.57443 0.361049
\(565\) −7.99314 −0.336274
\(566\) 41.3641 1.73866
\(567\) 12.4065 0.521024
\(568\) −8.24055 −0.345766
\(569\) 16.6658 0.698666 0.349333 0.936999i \(-0.386408\pi\)
0.349333 + 0.936999i \(0.386408\pi\)
\(570\) −23.1049 −0.967759
\(571\) 33.6730 1.40917 0.704585 0.709619i \(-0.251133\pi\)
0.704585 + 0.709619i \(0.251133\pi\)
\(572\) −3.07120 −0.128413
\(573\) 62.3334 2.60402
\(574\) 44.6233 1.86254
\(575\) −7.33488 −0.305886
\(576\) −14.0506 −0.585443
\(577\) 19.8551 0.826580 0.413290 0.910599i \(-0.364380\pi\)
0.413290 + 0.910599i \(0.364380\pi\)
\(578\) −27.7895 −1.15589
\(579\) −58.9026 −2.44791
\(580\) −8.06810 −0.335010
\(581\) 16.8919 0.700792
\(582\) −76.3128 −3.16327
\(583\) −8.22789 −0.340765
\(584\) 0.944554 0.0390859
\(585\) −8.07250 −0.333757
\(586\) 19.8237 0.818911
\(587\) 29.4398 1.21511 0.607556 0.794277i \(-0.292150\pi\)
0.607556 + 0.794277i \(0.292150\pi\)
\(588\) 6.38905 0.263480
\(589\) −9.74894 −0.401698
\(590\) 0.993899 0.0409182
\(591\) −32.3156 −1.32929
\(592\) −11.5316 −0.473944
\(593\) −27.4004 −1.12520 −0.562600 0.826729i \(-0.690199\pi\)
−0.562600 + 0.826729i \(0.690199\pi\)
\(594\) 4.57066 0.187536
\(595\) 13.0887 0.536583
\(596\) 20.8081 0.852335
\(597\) 28.9339 1.18419
\(598\) −28.1737 −1.15211
\(599\) 34.7195 1.41860 0.709299 0.704907i \(-0.249012\pi\)
0.709299 + 0.704907i \(0.249012\pi\)
\(600\) −2.48632 −0.101504
\(601\) −3.41657 −0.139365 −0.0696825 0.997569i \(-0.522199\pi\)
−0.0696825 + 0.997569i \(0.522199\pi\)
\(602\) 3.54175 0.144351
\(603\) −24.3588 −0.991966
\(604\) −32.9116 −1.33915
\(605\) 1.00000 0.0406558
\(606\) 98.0781 3.98415
\(607\) 39.0259 1.58401 0.792006 0.610513i \(-0.209037\pi\)
0.792006 + 0.610513i \(0.209037\pi\)
\(608\) −32.8694 −1.33303
\(609\) −32.9438 −1.33495
\(610\) 12.9030 0.522426
\(611\) 4.47769 0.181148
\(612\) −33.1503 −1.34002
\(613\) −29.4630 −1.19000 −0.594999 0.803726i \(-0.702848\pi\)
−0.594999 + 0.803726i \(0.702848\pi\)
\(614\) 29.0330 1.17167
\(615\) −27.0987 −1.09273
\(616\) −2.19010 −0.0882415
\(617\) −36.0242 −1.45028 −0.725139 0.688603i \(-0.758224\pi\)
−0.725139 + 0.688603i \(0.758224\pi\)
\(618\) −42.7007 −1.71767
\(619\) −35.9962 −1.44681 −0.723405 0.690424i \(-0.757424\pi\)
−0.723405 + 0.690424i \(0.757424\pi\)
\(620\) 3.10352 0.124640
\(621\) 17.9335 0.719646
\(622\) −48.6530 −1.95081
\(623\) 6.16113 0.246840
\(624\) −25.7185 −1.02956
\(625\) 1.00000 0.0400000
\(626\) −16.4045 −0.655655
\(627\) 12.3594 0.493587
\(628\) 6.43645 0.256842
\(629\) −13.6891 −0.545820
\(630\) 17.0297 0.678481
\(631\) −31.6079 −1.25829 −0.629146 0.777288i \(-0.716595\pi\)
−0.629146 + 0.777288i \(0.716595\pi\)
\(632\) 2.76489 0.109982
\(633\) 13.2998 0.528621
\(634\) −27.8140 −1.10463
\(635\) 17.1056 0.678814
\(636\) 32.3730 1.28367
\(637\) 3.33646 0.132195
\(638\) 10.0905 0.399488
\(639\) −34.2763 −1.35595
\(640\) −7.31529 −0.289162
\(641\) 20.5015 0.809761 0.404881 0.914370i \(-0.367313\pi\)
0.404881 + 0.914370i \(0.367313\pi\)
\(642\) −75.4846 −2.97914
\(643\) −27.5515 −1.08652 −0.543262 0.839563i \(-0.682811\pi\)
−0.543262 + 0.839563i \(0.682811\pi\)
\(644\) 25.4211 1.00173
\(645\) −2.15082 −0.0846886
\(646\) −49.5488 −1.94947
\(647\) −16.6039 −0.652765 −0.326382 0.945238i \(-0.605830\pi\)
−0.326382 + 0.945238i \(0.605830\pi\)
\(648\) −5.05405 −0.198542
\(649\) −0.531662 −0.0208695
\(650\) 3.84106 0.150659
\(651\) 12.6723 0.496668
\(652\) 7.94406 0.311113
\(653\) −7.21202 −0.282228 −0.141114 0.989993i \(-0.545068\pi\)
−0.141114 + 0.989993i \(0.545068\pi\)
\(654\) 18.7255 0.732223
\(655\) −5.97264 −0.233370
\(656\) −48.9543 −1.91134
\(657\) 3.92884 0.153279
\(658\) −9.44614 −0.368249
\(659\) −27.2223 −1.06043 −0.530214 0.847864i \(-0.677889\pi\)
−0.530214 + 0.847864i \(0.677889\pi\)
\(660\) −3.93454 −0.153152
\(661\) 5.53570 0.215314 0.107657 0.994188i \(-0.465665\pi\)
0.107657 + 0.994188i \(0.465665\pi\)
\(662\) 29.8847 1.16150
\(663\) −30.5304 −1.18570
\(664\) −6.88126 −0.267045
\(665\) 10.8869 0.422175
\(666\) −17.8110 −0.690161
\(667\) 39.5914 1.53298
\(668\) 7.90478 0.305845
\(669\) 65.0695 2.51573
\(670\) 11.5904 0.447776
\(671\) −6.90212 −0.266454
\(672\) 42.7259 1.64819
\(673\) −17.7571 −0.684487 −0.342243 0.939611i \(-0.611187\pi\)
−0.342243 + 0.939611i \(0.611187\pi\)
\(674\) −19.9788 −0.769554
\(675\) −2.44496 −0.0941065
\(676\) −13.1212 −0.504663
\(677\) −31.9759 −1.22893 −0.614467 0.788942i \(-0.710629\pi\)
−0.614467 + 0.788942i \(0.710629\pi\)
\(678\) −39.3328 −1.51057
\(679\) 35.9581 1.37994
\(680\) −5.33195 −0.204471
\(681\) 9.06775 0.347477
\(682\) −3.88148 −0.148630
\(683\) −9.38423 −0.359077 −0.179539 0.983751i \(-0.557461\pi\)
−0.179539 + 0.983751i \(0.557461\pi\)
\(684\) −27.5738 −1.05431
\(685\) 1.16619 0.0445579
\(686\) −37.3804 −1.42719
\(687\) 31.8750 1.21611
\(688\) −3.88550 −0.148133
\(689\) 16.9057 0.644054
\(690\) −36.0936 −1.37406
\(691\) 20.1558 0.766765 0.383382 0.923590i \(-0.374759\pi\)
0.383382 + 0.923590i \(0.374759\pi\)
\(692\) −34.2123 −1.30056
\(693\) −9.10963 −0.346046
\(694\) 24.0570 0.913190
\(695\) −2.46233 −0.0934016
\(696\) 13.4204 0.508698
\(697\) −58.1136 −2.20121
\(698\) 44.4294 1.68168
\(699\) −5.87438 −0.222189
\(700\) −3.46577 −0.130994
\(701\) −4.28717 −0.161924 −0.0809621 0.996717i \(-0.525799\pi\)
−0.0809621 + 0.996717i \(0.525799\pi\)
\(702\) −9.39122 −0.354449
\(703\) −11.3863 −0.429443
\(704\) −3.57628 −0.134786
\(705\) 5.73642 0.216046
\(706\) −64.5238 −2.42839
\(707\) −46.2137 −1.73805
\(708\) 2.09185 0.0786164
\(709\) −39.7722 −1.49367 −0.746837 0.665007i \(-0.768429\pi\)
−0.746837 + 0.665007i \(0.768429\pi\)
\(710\) 16.3093 0.612079
\(711\) 11.5005 0.431302
\(712\) −2.50987 −0.0940612
\(713\) −15.2294 −0.570346
\(714\) 64.4069 2.41037
\(715\) −2.05468 −0.0768405
\(716\) −30.6501 −1.14545
\(717\) 11.3973 0.425640
\(718\) −31.9061 −1.19072
\(719\) −11.1836 −0.417076 −0.208538 0.978014i \(-0.566871\pi\)
−0.208538 + 0.978014i \(0.566871\pi\)
\(720\) −18.6826 −0.696258
\(721\) 20.1203 0.749318
\(722\) −5.69473 −0.211936
\(723\) −26.8234 −0.997573
\(724\) 20.4986 0.761823
\(725\) −5.39768 −0.200465
\(726\) 4.92082 0.182629
\(727\) 5.24603 0.194565 0.0972823 0.995257i \(-0.468985\pi\)
0.0972823 + 0.995257i \(0.468985\pi\)
\(728\) 4.49994 0.166779
\(729\) −40.3295 −1.49369
\(730\) −1.86942 −0.0691904
\(731\) −4.61247 −0.170598
\(732\) 27.1567 1.00374
\(733\) −47.8133 −1.76602 −0.883012 0.469351i \(-0.844488\pi\)
−0.883012 + 0.469351i \(0.844488\pi\)
\(734\) 67.4476 2.48954
\(735\) 4.27437 0.157663
\(736\) −51.3474 −1.89269
\(737\) −6.19999 −0.228380
\(738\) −75.6119 −2.78331
\(739\) −16.5685 −0.609483 −0.304742 0.952435i \(-0.598570\pi\)
−0.304742 + 0.952435i \(0.598570\pi\)
\(740\) 3.62477 0.133249
\(741\) −25.3946 −0.932893
\(742\) −35.6642 −1.30927
\(743\) 0.360507 0.0132257 0.00661285 0.999978i \(-0.497895\pi\)
0.00661285 + 0.999978i \(0.497895\pi\)
\(744\) −5.16235 −0.189261
\(745\) 13.9210 0.510025
\(746\) 33.3724 1.22185
\(747\) −28.6224 −1.04724
\(748\) −8.43768 −0.308512
\(749\) 35.5678 1.29962
\(750\) 4.92082 0.179683
\(751\) −8.54101 −0.311666 −0.155833 0.987783i \(-0.549806\pi\)
−0.155833 + 0.987783i \(0.549806\pi\)
\(752\) 10.3629 0.377898
\(753\) −53.6777 −1.95613
\(754\) −20.7328 −0.755044
\(755\) −22.0184 −0.801331
\(756\) 8.47368 0.308185
\(757\) 4.95859 0.180223 0.0901115 0.995932i \(-0.471278\pi\)
0.0901115 + 0.995932i \(0.471278\pi\)
\(758\) 18.2500 0.662871
\(759\) 19.3074 0.700814
\(760\) −4.43501 −0.160875
\(761\) 27.9433 1.01294 0.506471 0.862257i \(-0.330950\pi\)
0.506471 + 0.862257i \(0.330950\pi\)
\(762\) 84.1734 3.04928
\(763\) −8.82331 −0.319425
\(764\) −35.3961 −1.28058
\(765\) −22.1781 −0.801849
\(766\) −61.1123 −2.20808
\(767\) 1.09239 0.0394440
\(768\) −54.8247 −1.97832
\(769\) −37.1776 −1.34066 −0.670330 0.742064i \(-0.733847\pi\)
−0.670330 + 0.742064i \(0.733847\pi\)
\(770\) 4.33454 0.156206
\(771\) −22.8877 −0.824281
\(772\) 33.4479 1.20381
\(773\) 31.5644 1.13529 0.567645 0.823273i \(-0.307854\pi\)
0.567645 + 0.823273i \(0.307854\pi\)
\(774\) −6.00131 −0.215713
\(775\) 2.07630 0.0745829
\(776\) −14.6483 −0.525843
\(777\) 14.8007 0.530972
\(778\) −28.6565 −1.02738
\(779\) −48.3377 −1.73188
\(780\) 8.08421 0.289461
\(781\) −8.72428 −0.312179
\(782\) −77.4033 −2.76794
\(783\) 13.1971 0.471626
\(784\) 7.72173 0.275776
\(785\) 4.30608 0.153691
\(786\) −29.3903 −1.04832
\(787\) 14.1531 0.504503 0.252251 0.967662i \(-0.418829\pi\)
0.252251 + 0.967662i \(0.418829\pi\)
\(788\) 18.3504 0.653707
\(789\) −58.3905 −2.07876
\(790\) −5.47216 −0.194691
\(791\) 18.5333 0.658970
\(792\) 3.71100 0.131865
\(793\) 14.1816 0.503604
\(794\) 2.25957 0.0801891
\(795\) 21.6580 0.768131
\(796\) −16.4301 −0.582351
\(797\) 21.1224 0.748194 0.374097 0.927389i \(-0.377953\pi\)
0.374097 + 0.927389i \(0.377953\pi\)
\(798\) 53.5724 1.89644
\(799\) 12.3018 0.435208
\(800\) 7.00043 0.247503
\(801\) −10.4397 −0.368869
\(802\) 35.6366 1.25837
\(803\) 1.00000 0.0352892
\(804\) 24.3941 0.860315
\(805\) 17.0071 0.599420
\(806\) 7.97518 0.280914
\(807\) 27.3441 0.962559
\(808\) 18.8262 0.662302
\(809\) −13.9789 −0.491473 −0.245736 0.969337i \(-0.579030\pi\)
−0.245736 + 0.969337i \(0.579030\pi\)
\(810\) 10.0028 0.351461
\(811\) 47.0796 1.65319 0.826593 0.562800i \(-0.190276\pi\)
0.826593 + 0.562800i \(0.190276\pi\)
\(812\) 18.7071 0.656492
\(813\) 8.40554 0.294795
\(814\) −4.53339 −0.158895
\(815\) 5.31470 0.186166
\(816\) −70.6580 −2.47353
\(817\) −3.83656 −0.134224
\(818\) 8.99284 0.314427
\(819\) 18.7173 0.654037
\(820\) 15.3880 0.537373
\(821\) 5.52178 0.192711 0.0963557 0.995347i \(-0.469281\pi\)
0.0963557 + 0.995347i \(0.469281\pi\)
\(822\) 5.73862 0.200157
\(823\) 16.2460 0.566301 0.283150 0.959076i \(-0.408620\pi\)
0.283150 + 0.959076i \(0.408620\pi\)
\(824\) −8.19643 −0.285536
\(825\) −2.63227 −0.0916438
\(826\) −2.30451 −0.0801842
\(827\) 28.5272 0.991989 0.495995 0.868326i \(-0.334804\pi\)
0.495995 + 0.868326i \(0.334804\pi\)
\(828\) −43.0747 −1.49695
\(829\) 14.1575 0.491711 0.245855 0.969307i \(-0.420931\pi\)
0.245855 + 0.969307i \(0.420931\pi\)
\(830\) 13.6191 0.472726
\(831\) −66.3198 −2.30061
\(832\) 7.34810 0.254749
\(833\) 9.16645 0.317599
\(834\) −12.1167 −0.419567
\(835\) 5.28842 0.183013
\(836\) −7.01829 −0.242733
\(837\) −5.07647 −0.175468
\(838\) 9.93356 0.343149
\(839\) 12.0464 0.415887 0.207943 0.978141i \(-0.433323\pi\)
0.207943 + 0.978141i \(0.433323\pi\)
\(840\) 5.76492 0.198909
\(841\) 0.134966 0.00465399
\(842\) −69.1853 −2.38428
\(843\) 16.8991 0.582037
\(844\) −7.55232 −0.259961
\(845\) −8.77830 −0.301983
\(846\) 16.0060 0.550297
\(847\) −2.31866 −0.0796699
\(848\) 39.1256 1.34358
\(849\) 58.2434 1.99891
\(850\) 10.5528 0.361957
\(851\) −17.7873 −0.609740
\(852\) 34.3261 1.17599
\(853\) 11.8617 0.406136 0.203068 0.979165i \(-0.434909\pi\)
0.203068 + 0.979165i \(0.434909\pi\)
\(854\) −29.9176 −1.02376
\(855\) −18.4473 −0.630883
\(856\) −14.4893 −0.495235
\(857\) 51.0560 1.74404 0.872020 0.489470i \(-0.162810\pi\)
0.872020 + 0.489470i \(0.162810\pi\)
\(858\) −10.1107 −0.345173
\(859\) −25.0448 −0.854518 −0.427259 0.904129i \(-0.640521\pi\)
−0.427259 + 0.904129i \(0.640521\pi\)
\(860\) 1.22135 0.0416475
\(861\) 62.8326 2.14133
\(862\) −51.8172 −1.76490
\(863\) −11.2661 −0.383503 −0.191751 0.981444i \(-0.561417\pi\)
−0.191751 + 0.981444i \(0.561417\pi\)
\(864\) −17.1158 −0.582290
\(865\) −22.8886 −0.778234
\(866\) −10.3237 −0.350813
\(867\) −39.1295 −1.32891
\(868\) −7.19599 −0.244248
\(869\) 2.92720 0.0992983
\(870\) −26.5610 −0.900503
\(871\) 12.7390 0.431644
\(872\) 3.59436 0.121720
\(873\) −60.9290 −2.06214
\(874\) −64.3825 −2.17777
\(875\) −2.31866 −0.0783849
\(876\) −3.93454 −0.132936
\(877\) 17.7317 0.598756 0.299378 0.954135i \(-0.403221\pi\)
0.299378 + 0.954135i \(0.403221\pi\)
\(878\) 55.8629 1.88528
\(879\) 27.9131 0.941486
\(880\) −4.75524 −0.160299
\(881\) 27.1891 0.916024 0.458012 0.888946i \(-0.348562\pi\)
0.458012 + 0.888946i \(0.348562\pi\)
\(882\) 11.9265 0.401587
\(883\) 20.0274 0.673974 0.336987 0.941509i \(-0.390592\pi\)
0.336987 + 0.941509i \(0.390592\pi\)
\(884\) 17.3367 0.583096
\(885\) 1.39948 0.0470429
\(886\) −2.28677 −0.0768257
\(887\) −1.46978 −0.0493504 −0.0246752 0.999696i \(-0.507855\pi\)
−0.0246752 + 0.999696i \(0.507855\pi\)
\(888\) −6.02938 −0.202333
\(889\) −39.6619 −1.33022
\(890\) 4.96742 0.166508
\(891\) −5.35073 −0.179256
\(892\) −36.9497 −1.23717
\(893\) 10.2324 0.342415
\(894\) 68.5026 2.29107
\(895\) −20.5054 −0.685419
\(896\) 16.9616 0.566649
\(897\) −39.6704 −1.32456
\(898\) −4.20171 −0.140213
\(899\) −11.2072 −0.373781
\(900\) 5.87257 0.195752
\(901\) 46.4459 1.54734
\(902\) −19.2453 −0.640800
\(903\) 4.98702 0.165958
\(904\) −7.54995 −0.251108
\(905\) 13.7138 0.455864
\(906\) −108.348 −3.59964
\(907\) 7.40490 0.245876 0.122938 0.992414i \(-0.460768\pi\)
0.122938 + 0.992414i \(0.460768\pi\)
\(908\) −5.14913 −0.170880
\(909\) 78.3068 2.59727
\(910\) −8.90608 −0.295234
\(911\) −10.3475 −0.342828 −0.171414 0.985199i \(-0.554834\pi\)
−0.171414 + 0.985199i \(0.554834\pi\)
\(912\) −58.7719 −1.94613
\(913\) −7.28519 −0.241105
\(914\) −31.4909 −1.04163
\(915\) 18.1682 0.600624
\(916\) −18.1002 −0.598048
\(917\) 13.8485 0.457317
\(918\) −25.8011 −0.851562
\(919\) 20.6624 0.681588 0.340794 0.940138i \(-0.389304\pi\)
0.340794 + 0.940138i \(0.389304\pi\)
\(920\) −6.92819 −0.228416
\(921\) 40.8803 1.34705
\(922\) −32.4759 −1.06954
\(923\) 17.9256 0.590027
\(924\) 9.12285 0.300120
\(925\) 2.42502 0.0797343
\(926\) −26.4321 −0.868612
\(927\) −34.0928 −1.11975
\(928\) −37.7861 −1.24039
\(929\) −2.16663 −0.0710848 −0.0355424 0.999368i \(-0.511316\pi\)
−0.0355424 + 0.999368i \(0.511316\pi\)
\(930\) 10.2171 0.335032
\(931\) 7.62447 0.249882
\(932\) 3.33577 0.109267
\(933\) −68.5067 −2.24281
\(934\) 0.207713 0.00679657
\(935\) −5.64494 −0.184609
\(936\) −7.62491 −0.249228
\(937\) −1.18997 −0.0388745 −0.0194373 0.999811i \(-0.506187\pi\)
−0.0194373 + 0.999811i \(0.506187\pi\)
\(938\) −26.8741 −0.877471
\(939\) −23.0986 −0.753794
\(940\) −3.25743 −0.106246
\(941\) 17.5590 0.572406 0.286203 0.958169i \(-0.407607\pi\)
0.286203 + 0.958169i \(0.407607\pi\)
\(942\) 21.1894 0.690390
\(943\) −75.5113 −2.45899
\(944\) 2.52818 0.0822852
\(945\) 5.66902 0.184413
\(946\) −1.52750 −0.0496634
\(947\) 44.0792 1.43238 0.716191 0.697904i \(-0.245884\pi\)
0.716191 + 0.697904i \(0.245884\pi\)
\(948\) −11.5172 −0.374061
\(949\) −2.05468 −0.0666976
\(950\) 8.77757 0.284782
\(951\) −39.1640 −1.26998
\(952\) 12.3629 0.400685
\(953\) −6.83843 −0.221519 −0.110759 0.993847i \(-0.535328\pi\)
−0.110759 + 0.993847i \(0.535328\pi\)
\(954\) 60.4311 1.95653
\(955\) −23.6805 −0.766283
\(956\) −6.47196 −0.209318
\(957\) 14.2082 0.459284
\(958\) −0.0242491 −0.000783454 0
\(959\) −2.70400 −0.0873167
\(960\) 9.41373 0.303827
\(961\) −26.6890 −0.860935
\(962\) 9.31465 0.300316
\(963\) −60.2678 −1.94210
\(964\) 15.2317 0.490579
\(965\) 22.3771 0.720345
\(966\) 83.6887 2.69264
\(967\) 51.7397 1.66384 0.831918 0.554899i \(-0.187243\pi\)
0.831918 + 0.554899i \(0.187243\pi\)
\(968\) 0.944554 0.0303591
\(969\) −69.7681 −2.24127
\(970\) 28.9913 0.930853
\(971\) 12.1075 0.388547 0.194274 0.980947i \(-0.437765\pi\)
0.194274 + 0.980947i \(0.437765\pi\)
\(972\) 32.0164 1.02693
\(973\) 5.70930 0.183032
\(974\) 68.9008 2.20772
\(975\) 5.40846 0.173209
\(976\) 32.8212 1.05058
\(977\) 13.2742 0.424679 0.212339 0.977196i \(-0.431892\pi\)
0.212339 + 0.977196i \(0.431892\pi\)
\(978\) 26.1527 0.836270
\(979\) −2.65720 −0.0849244
\(980\) −2.42720 −0.0775342
\(981\) 14.9506 0.477337
\(982\) −77.3020 −2.46681
\(983\) 41.2776 1.31655 0.658275 0.752777i \(-0.271286\pi\)
0.658275 + 0.752777i \(0.271286\pi\)
\(984\) −25.5962 −0.815977
\(985\) 12.2767 0.391169
\(986\) −56.9604 −1.81399
\(987\) −13.3008 −0.423369
\(988\) 14.4203 0.458771
\(989\) −5.99333 −0.190577
\(990\) −7.34466 −0.233429
\(991\) −38.0590 −1.20899 −0.604493 0.796611i \(-0.706624\pi\)
−0.604493 + 0.796611i \(0.706624\pi\)
\(992\) 14.5350 0.461487
\(993\) 42.0796 1.33536
\(994\) −37.8158 −1.19944
\(995\) −10.9920 −0.348470
\(996\) 28.6639 0.908251
\(997\) 7.56988 0.239741 0.119870 0.992790i \(-0.461752\pi\)
0.119870 + 0.992790i \(0.461752\pi\)
\(998\) 54.6345 1.72942
\(999\) −5.92908 −0.187588
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 \(a_p\))