Properties

Label 4015.2.a.h.1.10
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 1.10
Character \(\chi\) = 4015.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.58931 q^{2}\) \(-0.358295 q^{3}\) \(+0.525917 q^{4}\) \(+1.00000 q^{5}\) \(+0.569443 q^{6}\) \(+2.77249 q^{7}\) \(+2.34278 q^{8}\) \(-2.87162 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.58931 q^{2}\) \(-0.358295 q^{3}\) \(+0.525917 q^{4}\) \(+1.00000 q^{5}\) \(+0.569443 q^{6}\) \(+2.77249 q^{7}\) \(+2.34278 q^{8}\) \(-2.87162 q^{9}\) \(-1.58931 q^{10}\) \(+1.00000 q^{11}\) \(-0.188433 q^{12}\) \(+1.54440 q^{13}\) \(-4.40635 q^{14}\) \(-0.358295 q^{15}\) \(-4.77525 q^{16}\) \(+3.82023 q^{17}\) \(+4.56391 q^{18}\) \(+5.21934 q^{19}\) \(+0.525917 q^{20}\) \(-0.993369 q^{21}\) \(-1.58931 q^{22}\) \(+4.87751 q^{23}\) \(-0.839406 q^{24}\) \(+1.00000 q^{25}\) \(-2.45454 q^{26}\) \(+2.10377 q^{27}\) \(+1.45810 q^{28}\) \(-6.06529 q^{29}\) \(+0.569443 q^{30}\) \(+2.13802 q^{31}\) \(+2.90380 q^{32}\) \(-0.358295 q^{33}\) \(-6.07154 q^{34}\) \(+2.77249 q^{35}\) \(-1.51024 q^{36}\) \(+2.69997 q^{37}\) \(-8.29517 q^{38}\) \(-0.553352 q^{39}\) \(+2.34278 q^{40}\) \(-2.64072 q^{41}\) \(+1.57877 q^{42}\) \(+2.93477 q^{43}\) \(+0.525917 q^{44}\) \(-2.87162 q^{45}\) \(-7.75189 q^{46}\) \(+13.5437 q^{47}\) \(+1.71095 q^{48}\) \(+0.686693 q^{49}\) \(-1.58931 q^{50}\) \(-1.36877 q^{51}\) \(+0.812228 q^{52}\) \(-0.687193 q^{53}\) \(-3.34355 q^{54}\) \(+1.00000 q^{55}\) \(+6.49533 q^{56}\) \(-1.87006 q^{57}\) \(+9.63964 q^{58}\) \(-2.29624 q^{59}\) \(-0.188433 q^{60}\) \(-11.0870 q^{61}\) \(-3.39798 q^{62}\) \(-7.96155 q^{63}\) \(+4.93544 q^{64}\) \(+1.54440 q^{65}\) \(+0.569443 q^{66}\) \(-6.87347 q^{67}\) \(+2.00912 q^{68}\) \(-1.74759 q^{69}\) \(-4.40635 q^{70}\) \(+15.4683 q^{71}\) \(-6.72759 q^{72}\) \(+1.00000 q^{73}\) \(-4.29109 q^{74}\) \(-0.358295 q^{75}\) \(+2.74494 q^{76}\) \(+2.77249 q^{77}\) \(+0.879450 q^{78}\) \(+12.3392 q^{79}\) \(-4.77525 q^{80}\) \(+7.86110 q^{81}\) \(+4.19693 q^{82}\) \(-3.83901 q^{83}\) \(-0.522429 q^{84}\) \(+3.82023 q^{85}\) \(-4.66427 q^{86}\) \(+2.17316 q^{87}\) \(+2.34278 q^{88}\) \(-1.55274 q^{89}\) \(+4.56391 q^{90}\) \(+4.28184 q^{91}\) \(+2.56516 q^{92}\) \(-0.766041 q^{93}\) \(-21.5252 q^{94}\) \(+5.21934 q^{95}\) \(-1.04042 q^{96}\) \(+6.46974 q^{97}\) \(-1.09137 q^{98}\) \(-2.87162 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut 5q^{10} \) \(\mathstrut +\mathstrut 37q^{11} \) \(\mathstrut +\mathstrut 6q^{12} \) \(\mathstrut +\mathstrut 11q^{13} \) \(\mathstrut +\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 43q^{16} \) \(\mathstrut +\mathstrut 38q^{17} \) \(\mathstrut +\mathstrut 11q^{18} \) \(\mathstrut +\mathstrut 34q^{19} \) \(\mathstrut +\mathstrut 43q^{20} \) \(\mathstrut +\mathstrut 39q^{21} \) \(\mathstrut +\mathstrut 5q^{22} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 37q^{25} \) \(\mathstrut -\mathstrut 9q^{26} \) \(\mathstrut +\mathstrut 3q^{27} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut +\mathstrut 9q^{30} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut +\mathstrut 14q^{32} \) \(\mathstrut +\mathstrut 3q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 6q^{35} \) \(\mathstrut +\mathstrut 20q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 15q^{38} \) \(\mathstrut +\mathstrut 14q^{39} \) \(\mathstrut +\mathstrut 12q^{40} \) \(\mathstrut +\mathstrut 62q^{41} \) \(\mathstrut -\mathstrut 13q^{42} \) \(\mathstrut +\mathstrut 30q^{43} \) \(\mathstrut +\mathstrut 43q^{44} \) \(\mathstrut +\mathstrut 50q^{45} \) \(\mathstrut +\mathstrut 31q^{46} \) \(\mathstrut +\mathstrut 5q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 59q^{49} \) \(\mathstrut +\mathstrut 5q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 13q^{54} \) \(\mathstrut +\mathstrut 37q^{55} \) \(\mathstrut +\mathstrut 22q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 40q^{58} \) \(\mathstrut +\mathstrut 15q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut +\mathstrut 57q^{61} \) \(\mathstrut +\mathstrut 20q^{62} \) \(\mathstrut -\mathstrut 29q^{63} \) \(\mathstrut +\mathstrut 10q^{64} \) \(\mathstrut +\mathstrut 11q^{65} \) \(\mathstrut +\mathstrut 9q^{66} \) \(\mathstrut -\mathstrut 14q^{67} \) \(\mathstrut +\mathstrut 53q^{68} \) \(\mathstrut +\mathstrut 24q^{69} \) \(\mathstrut +\mathstrut 11q^{70} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 15q^{72} \) \(\mathstrut +\mathstrut 37q^{73} \) \(\mathstrut +\mathstrut 7q^{74} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut +\mathstrut 59q^{76} \) \(\mathstrut +\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut q^{78} \) \(\mathstrut +\mathstrut 42q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 61q^{81} \) \(\mathstrut -\mathstrut 22q^{82} \) \(\mathstrut +\mathstrut 44q^{83} \) \(\mathstrut +\mathstrut 66q^{84} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut -\mathstrut q^{86} \) \(\mathstrut -\mathstrut 26q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 69q^{89} \) \(\mathstrut +\mathstrut 11q^{90} \) \(\mathstrut -\mathstrut 10q^{91} \) \(\mathstrut -\mathstrut 21q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut +\mathstrut 29q^{94} \) \(\mathstrut +\mathstrut 34q^{95} \) \(\mathstrut -\mathstrut 9q^{96} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut -\mathstrut 15q^{98} \) \(\mathstrut +\mathstrut 50q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.58931 −1.12381 −0.561907 0.827200i \(-0.689932\pi\)
−0.561907 + 0.827200i \(0.689932\pi\)
\(3\) −0.358295 −0.206862 −0.103431 0.994637i \(-0.532982\pi\)
−0.103431 + 0.994637i \(0.532982\pi\)
\(4\) 0.525917 0.262958
\(5\) 1.00000 0.447214
\(6\) 0.569443 0.232474
\(7\) 2.77249 1.04790 0.523951 0.851748i \(-0.324457\pi\)
0.523951 + 0.851748i \(0.324457\pi\)
\(8\) 2.34278 0.828298
\(9\) −2.87162 −0.957208
\(10\) −1.58931 −0.502585
\(11\) 1.00000 0.301511
\(12\) −0.188433 −0.0543960
\(13\) 1.54440 0.428341 0.214170 0.976796i \(-0.431295\pi\)
0.214170 + 0.976796i \(0.431295\pi\)
\(14\) −4.40635 −1.17765
\(15\) −0.358295 −0.0925114
\(16\) −4.77525 −1.19381
\(17\) 3.82023 0.926542 0.463271 0.886217i \(-0.346676\pi\)
0.463271 + 0.886217i \(0.346676\pi\)
\(18\) 4.56391 1.07572
\(19\) 5.21934 1.19740 0.598700 0.800974i \(-0.295684\pi\)
0.598700 + 0.800974i \(0.295684\pi\)
\(20\) 0.525917 0.117599
\(21\) −0.993369 −0.216771
\(22\) −1.58931 −0.338843
\(23\) 4.87751 1.01703 0.508516 0.861053i \(-0.330194\pi\)
0.508516 + 0.861053i \(0.330194\pi\)
\(24\) −0.839406 −0.171343
\(25\) 1.00000 0.200000
\(26\) −2.45454 −0.481375
\(27\) 2.10377 0.404871
\(28\) 1.45810 0.275555
\(29\) −6.06529 −1.12630 −0.563148 0.826356i \(-0.690410\pi\)
−0.563148 + 0.826356i \(0.690410\pi\)
\(30\) 0.569443 0.103966
\(31\) 2.13802 0.383999 0.192000 0.981395i \(-0.438503\pi\)
0.192000 + 0.981395i \(0.438503\pi\)
\(32\) 2.90380 0.513324
\(33\) −0.358295 −0.0623711
\(34\) −6.07154 −1.04126
\(35\) 2.77249 0.468636
\(36\) −1.51024 −0.251706
\(37\) 2.69997 0.443872 0.221936 0.975061i \(-0.428762\pi\)
0.221936 + 0.975061i \(0.428762\pi\)
\(38\) −8.29517 −1.34565
\(39\) −0.553352 −0.0886073
\(40\) 2.34278 0.370426
\(41\) −2.64072 −0.412411 −0.206205 0.978509i \(-0.566111\pi\)
−0.206205 + 0.978509i \(0.566111\pi\)
\(42\) 1.57877 0.243610
\(43\) 2.93477 0.447548 0.223774 0.974641i \(-0.428162\pi\)
0.223774 + 0.974641i \(0.428162\pi\)
\(44\) 0.525917 0.0792849
\(45\) −2.87162 −0.428077
\(46\) −7.75189 −1.14295
\(47\) 13.5437 1.97555 0.987775 0.155888i \(-0.0498238\pi\)
0.987775 + 0.155888i \(0.0498238\pi\)
\(48\) 1.71095 0.246954
\(49\) 0.686693 0.0980990
\(50\) −1.58931 −0.224763
\(51\) −1.36877 −0.191666
\(52\) 0.812228 0.112636
\(53\) −0.687193 −0.0943932 −0.0471966 0.998886i \(-0.515029\pi\)
−0.0471966 + 0.998886i \(0.515029\pi\)
\(54\) −3.34355 −0.455000
\(55\) 1.00000 0.134840
\(56\) 6.49533 0.867975
\(57\) −1.87006 −0.247696
\(58\) 9.63964 1.26575
\(59\) −2.29624 −0.298944 −0.149472 0.988766i \(-0.547757\pi\)
−0.149472 + 0.988766i \(0.547757\pi\)
\(60\) −0.188433 −0.0243266
\(61\) −11.0870 −1.41954 −0.709770 0.704434i \(-0.751201\pi\)
−0.709770 + 0.704434i \(0.751201\pi\)
\(62\) −3.39798 −0.431544
\(63\) −7.96155 −1.00306
\(64\) 4.93544 0.616930
\(65\) 1.54440 0.191560
\(66\) 0.569443 0.0700936
\(67\) −6.87347 −0.839728 −0.419864 0.907587i \(-0.637922\pi\)
−0.419864 + 0.907587i \(0.637922\pi\)
\(68\) 2.00912 0.243642
\(69\) −1.74759 −0.210385
\(70\) −4.40635 −0.526660
\(71\) 15.4683 1.83576 0.917878 0.396864i \(-0.129901\pi\)
0.917878 + 0.396864i \(0.129901\pi\)
\(72\) −6.72759 −0.792854
\(73\) 1.00000 0.117041
\(74\) −4.29109 −0.498830
\(75\) −0.358295 −0.0413723
\(76\) 2.74494 0.314866
\(77\) 2.77249 0.315954
\(78\) 0.879450 0.0995781
\(79\) 12.3392 1.38827 0.694133 0.719847i \(-0.255788\pi\)
0.694133 + 0.719847i \(0.255788\pi\)
\(80\) −4.77525 −0.533889
\(81\) 7.86110 0.873456
\(82\) 4.19693 0.463473
\(83\) −3.83901 −0.421386 −0.210693 0.977552i \(-0.567572\pi\)
−0.210693 + 0.977552i \(0.567572\pi\)
\(84\) −0.522429 −0.0570017
\(85\) 3.82023 0.414362
\(86\) −4.66427 −0.502961
\(87\) 2.17316 0.232987
\(88\) 2.34278 0.249741
\(89\) −1.55274 −0.164590 −0.0822952 0.996608i \(-0.526225\pi\)
−0.0822952 + 0.996608i \(0.526225\pi\)
\(90\) 4.56391 0.481079
\(91\) 4.28184 0.448859
\(92\) 2.56516 0.267437
\(93\) −0.766041 −0.0794347
\(94\) −21.5252 −2.22015
\(95\) 5.21934 0.535493
\(96\) −1.04042 −0.106187
\(97\) 6.46974 0.656902 0.328451 0.944521i \(-0.393473\pi\)
0.328451 + 0.944521i \(0.393473\pi\)
\(98\) −1.09137 −0.110245
\(99\) −2.87162 −0.288609
\(100\) 0.525917 0.0525917
\(101\) 10.7012 1.06481 0.532405 0.846490i \(-0.321288\pi\)
0.532405 + 0.846490i \(0.321288\pi\)
\(102\) 2.17540 0.215397
\(103\) 0.663135 0.0653407 0.0326703 0.999466i \(-0.489599\pi\)
0.0326703 + 0.999466i \(0.489599\pi\)
\(104\) 3.61820 0.354794
\(105\) −0.993369 −0.0969428
\(106\) 1.09216 0.106080
\(107\) −5.14402 −0.497291 −0.248646 0.968595i \(-0.579985\pi\)
−0.248646 + 0.968595i \(0.579985\pi\)
\(108\) 1.10641 0.106464
\(109\) −19.0573 −1.82536 −0.912680 0.408675i \(-0.865991\pi\)
−0.912680 + 0.408675i \(0.865991\pi\)
\(110\) −1.58931 −0.151535
\(111\) −0.967385 −0.0918201
\(112\) −13.2393 −1.25100
\(113\) −17.0646 −1.60530 −0.802651 0.596449i \(-0.796578\pi\)
−0.802651 + 0.596449i \(0.796578\pi\)
\(114\) 2.97212 0.278364
\(115\) 4.87751 0.454830
\(116\) −3.18984 −0.296169
\(117\) −4.43495 −0.410011
\(118\) 3.64944 0.335958
\(119\) 10.5915 0.970926
\(120\) −0.839406 −0.0766270
\(121\) 1.00000 0.0909091
\(122\) 17.6206 1.59530
\(123\) 0.946155 0.0853120
\(124\) 1.12442 0.100976
\(125\) 1.00000 0.0894427
\(126\) 12.6534 1.12725
\(127\) −9.78783 −0.868529 −0.434265 0.900785i \(-0.642992\pi\)
−0.434265 + 0.900785i \(0.642992\pi\)
\(128\) −13.6516 −1.20664
\(129\) −1.05151 −0.0925805
\(130\) −2.45454 −0.215278
\(131\) −8.33503 −0.728235 −0.364117 0.931353i \(-0.618629\pi\)
−0.364117 + 0.931353i \(0.618629\pi\)
\(132\) −0.188433 −0.0164010
\(133\) 14.4706 1.25476
\(134\) 10.9241 0.943698
\(135\) 2.10377 0.181064
\(136\) 8.94996 0.767453
\(137\) 7.43070 0.634848 0.317424 0.948284i \(-0.397182\pi\)
0.317424 + 0.948284i \(0.397182\pi\)
\(138\) 2.77746 0.236433
\(139\) −6.67957 −0.566553 −0.283277 0.959038i \(-0.591421\pi\)
−0.283277 + 0.959038i \(0.591421\pi\)
\(140\) 1.45810 0.123232
\(141\) −4.85263 −0.408665
\(142\) −24.5841 −2.06305
\(143\) 1.54440 0.129150
\(144\) 13.7127 1.14273
\(145\) −6.06529 −0.503695
\(146\) −1.58931 −0.131533
\(147\) −0.246039 −0.0202929
\(148\) 1.41996 0.116720
\(149\) −8.40880 −0.688876 −0.344438 0.938809i \(-0.611930\pi\)
−0.344438 + 0.938809i \(0.611930\pi\)
\(150\) 0.569443 0.0464948
\(151\) 19.4962 1.58658 0.793288 0.608846i \(-0.208367\pi\)
0.793288 + 0.608846i \(0.208367\pi\)
\(152\) 12.2278 0.991803
\(153\) −10.9703 −0.886894
\(154\) −4.40635 −0.355074
\(155\) 2.13802 0.171730
\(156\) −0.291017 −0.0233000
\(157\) −2.51905 −0.201042 −0.100521 0.994935i \(-0.532051\pi\)
−0.100521 + 0.994935i \(0.532051\pi\)
\(158\) −19.6108 −1.56015
\(159\) 0.246218 0.0195263
\(160\) 2.90380 0.229566
\(161\) 13.5228 1.06575
\(162\) −12.4938 −0.981602
\(163\) −18.1926 −1.42496 −0.712478 0.701694i \(-0.752427\pi\)
−0.712478 + 0.701694i \(0.752427\pi\)
\(164\) −1.38880 −0.108447
\(165\) −0.358295 −0.0278932
\(166\) 6.10139 0.473559
\(167\) 6.56752 0.508210 0.254105 0.967177i \(-0.418219\pi\)
0.254105 + 0.967177i \(0.418219\pi\)
\(168\) −2.32724 −0.179551
\(169\) −10.6148 −0.816524
\(170\) −6.07154 −0.465666
\(171\) −14.9880 −1.14616
\(172\) 1.54344 0.117687
\(173\) −11.7823 −0.895791 −0.447896 0.894086i \(-0.647826\pi\)
−0.447896 + 0.894086i \(0.647826\pi\)
\(174\) −3.45383 −0.261834
\(175\) 2.77249 0.209580
\(176\) −4.77525 −0.359948
\(177\) 0.822730 0.0618402
\(178\) 2.46780 0.184969
\(179\) 0.760265 0.0568249 0.0284124 0.999596i \(-0.490955\pi\)
0.0284124 + 0.999596i \(0.490955\pi\)
\(180\) −1.51024 −0.112566
\(181\) −1.51659 −0.112727 −0.0563635 0.998410i \(-0.517951\pi\)
−0.0563635 + 0.998410i \(0.517951\pi\)
\(182\) −6.80519 −0.504434
\(183\) 3.97240 0.293648
\(184\) 11.4269 0.842405
\(185\) 2.69997 0.198506
\(186\) 1.21748 0.0892699
\(187\) 3.82023 0.279363
\(188\) 7.12285 0.519487
\(189\) 5.83269 0.424266
\(190\) −8.29517 −0.601795
\(191\) −20.5084 −1.48393 −0.741967 0.670436i \(-0.766107\pi\)
−0.741967 + 0.670436i \(0.766107\pi\)
\(192\) −1.76834 −0.127619
\(193\) 18.9736 1.36575 0.682875 0.730535i \(-0.260729\pi\)
0.682875 + 0.730535i \(0.260729\pi\)
\(194\) −10.2824 −0.738236
\(195\) −0.553352 −0.0396264
\(196\) 0.361143 0.0257960
\(197\) −18.7332 −1.33468 −0.667341 0.744752i \(-0.732568\pi\)
−0.667341 + 0.744752i \(0.732568\pi\)
\(198\) 4.56391 0.324343
\(199\) −8.45384 −0.599277 −0.299639 0.954053i \(-0.596866\pi\)
−0.299639 + 0.954053i \(0.596866\pi\)
\(200\) 2.34278 0.165660
\(201\) 2.46273 0.173708
\(202\) −17.0076 −1.19665
\(203\) −16.8159 −1.18025
\(204\) −0.719859 −0.0504002
\(205\) −2.64072 −0.184436
\(206\) −1.05393 −0.0734308
\(207\) −14.0064 −0.973511
\(208\) −7.37491 −0.511358
\(209\) 5.21934 0.361029
\(210\) 1.57877 0.108946
\(211\) 23.0640 1.58779 0.793895 0.608054i \(-0.208050\pi\)
0.793895 + 0.608054i \(0.208050\pi\)
\(212\) −0.361406 −0.0248215
\(213\) −5.54223 −0.379747
\(214\) 8.17546 0.558863
\(215\) 2.93477 0.200150
\(216\) 4.92868 0.335354
\(217\) 5.92763 0.402394
\(218\) 30.2881 2.05137
\(219\) −0.358295 −0.0242113
\(220\) 0.525917 0.0354573
\(221\) 5.89998 0.396876
\(222\) 1.53748 0.103189
\(223\) −1.18111 −0.0790930 −0.0395465 0.999218i \(-0.512591\pi\)
−0.0395465 + 0.999218i \(0.512591\pi\)
\(224\) 8.05075 0.537914
\(225\) −2.87162 −0.191442
\(226\) 27.1210 1.80406
\(227\) 22.7929 1.51282 0.756410 0.654098i \(-0.226952\pi\)
0.756410 + 0.654098i \(0.226952\pi\)
\(228\) −0.983498 −0.0651337
\(229\) 5.05456 0.334014 0.167007 0.985956i \(-0.446590\pi\)
0.167007 + 0.985956i \(0.446590\pi\)
\(230\) −7.75189 −0.511145
\(231\) −0.993369 −0.0653589
\(232\) −14.2096 −0.932908
\(233\) 17.1854 1.12586 0.562928 0.826506i \(-0.309675\pi\)
0.562928 + 0.826506i \(0.309675\pi\)
\(234\) 7.04852 0.460776
\(235\) 13.5437 0.883493
\(236\) −1.20763 −0.0786100
\(237\) −4.42106 −0.287179
\(238\) −16.8333 −1.09114
\(239\) 30.0725 1.94523 0.972614 0.232427i \(-0.0746667\pi\)
0.972614 + 0.232427i \(0.0746667\pi\)
\(240\) 1.71095 0.110441
\(241\) −22.8889 −1.47441 −0.737203 0.675672i \(-0.763854\pi\)
−0.737203 + 0.675672i \(0.763854\pi\)
\(242\) −1.58931 −0.102165
\(243\) −9.12791 −0.585556
\(244\) −5.83082 −0.373280
\(245\) 0.686693 0.0438712
\(246\) −1.50374 −0.0958748
\(247\) 8.06077 0.512895
\(248\) 5.00890 0.318066
\(249\) 1.37550 0.0871686
\(250\) −1.58931 −0.100517
\(251\) 7.07469 0.446551 0.223275 0.974755i \(-0.428325\pi\)
0.223275 + 0.974755i \(0.428325\pi\)
\(252\) −4.18711 −0.263763
\(253\) 4.87751 0.306646
\(254\) 15.5559 0.976066
\(255\) −1.36877 −0.0857157
\(256\) 11.8257 0.739108
\(257\) 9.48611 0.591728 0.295864 0.955230i \(-0.404393\pi\)
0.295864 + 0.955230i \(0.404393\pi\)
\(258\) 1.67118 0.104043
\(259\) 7.48563 0.465134
\(260\) 0.812228 0.0503722
\(261\) 17.4172 1.07810
\(262\) 13.2470 0.818401
\(263\) 12.2124 0.753048 0.376524 0.926407i \(-0.377119\pi\)
0.376524 + 0.926407i \(0.377119\pi\)
\(264\) −0.839406 −0.0516619
\(265\) −0.687193 −0.0422139
\(266\) −22.9983 −1.41011
\(267\) 0.556340 0.0340475
\(268\) −3.61487 −0.220814
\(269\) 8.12364 0.495307 0.247654 0.968849i \(-0.420341\pi\)
0.247654 + 0.968849i \(0.420341\pi\)
\(270\) −3.34355 −0.203482
\(271\) 13.2137 0.802677 0.401339 0.915930i \(-0.368545\pi\)
0.401339 + 0.915930i \(0.368545\pi\)
\(272\) −18.2425 −1.10612
\(273\) −1.53416 −0.0928517
\(274\) −11.8097 −0.713451
\(275\) 1.00000 0.0603023
\(276\) −0.919085 −0.0553224
\(277\) 16.6660 1.00137 0.500683 0.865631i \(-0.333082\pi\)
0.500683 + 0.865631i \(0.333082\pi\)
\(278\) 10.6159 0.636701
\(279\) −6.13958 −0.367567
\(280\) 6.49533 0.388170
\(281\) 15.0661 0.898766 0.449383 0.893339i \(-0.351644\pi\)
0.449383 + 0.893339i \(0.351644\pi\)
\(282\) 7.71236 0.459264
\(283\) −5.64685 −0.335671 −0.167835 0.985815i \(-0.553678\pi\)
−0.167835 + 0.985815i \(0.553678\pi\)
\(284\) 8.13506 0.482727
\(285\) −1.87006 −0.110773
\(286\) −2.45454 −0.145140
\(287\) −7.32136 −0.432166
\(288\) −8.33862 −0.491358
\(289\) −2.40583 −0.141520
\(290\) 9.63964 0.566059
\(291\) −2.31807 −0.135888
\(292\) 0.525917 0.0307769
\(293\) 21.0863 1.23187 0.615936 0.787796i \(-0.288778\pi\)
0.615936 + 0.787796i \(0.288778\pi\)
\(294\) 0.391032 0.0228055
\(295\) −2.29624 −0.133692
\(296\) 6.32543 0.367658
\(297\) 2.10377 0.122073
\(298\) 13.3642 0.774168
\(299\) 7.53285 0.435636
\(300\) −0.188433 −0.0108792
\(301\) 8.13661 0.468987
\(302\) −30.9855 −1.78302
\(303\) −3.83419 −0.220268
\(304\) −24.9236 −1.42947
\(305\) −11.0870 −0.634837
\(306\) 17.4352 0.996704
\(307\) 4.68925 0.267630 0.133815 0.991006i \(-0.457277\pi\)
0.133815 + 0.991006i \(0.457277\pi\)
\(308\) 1.45810 0.0830829
\(309\) −0.237598 −0.0135165
\(310\) −3.39798 −0.192992
\(311\) 18.5820 1.05369 0.526845 0.849961i \(-0.323375\pi\)
0.526845 + 0.849961i \(0.323375\pi\)
\(312\) −1.29638 −0.0733932
\(313\) 22.0184 1.24456 0.622278 0.782796i \(-0.286207\pi\)
0.622278 + 0.782796i \(0.286207\pi\)
\(314\) 4.00357 0.225934
\(315\) −7.96155 −0.448582
\(316\) 6.48938 0.365056
\(317\) 25.1735 1.41389 0.706943 0.707270i \(-0.250074\pi\)
0.706943 + 0.707270i \(0.250074\pi\)
\(318\) −0.391317 −0.0219440
\(319\) −6.06529 −0.339591
\(320\) 4.93544 0.275900
\(321\) 1.84308 0.102871
\(322\) −21.4920 −1.19770
\(323\) 19.9391 1.10944
\(324\) 4.13429 0.229683
\(325\) 1.54440 0.0856681
\(326\) 28.9138 1.60139
\(327\) 6.82814 0.377597
\(328\) −6.18662 −0.341599
\(329\) 37.5497 2.07018
\(330\) 0.569443 0.0313468
\(331\) −3.08347 −0.169483 −0.0847413 0.996403i \(-0.527006\pi\)
−0.0847413 + 0.996403i \(0.527006\pi\)
\(332\) −2.01900 −0.110807
\(333\) −7.75329 −0.424878
\(334\) −10.4378 −0.571134
\(335\) −6.87347 −0.375538
\(336\) 4.74358 0.258783
\(337\) −6.37803 −0.347433 −0.173717 0.984796i \(-0.555578\pi\)
−0.173717 + 0.984796i \(0.555578\pi\)
\(338\) 16.8703 0.917622
\(339\) 6.11416 0.332076
\(340\) 2.00912 0.108960
\(341\) 2.13802 0.115780
\(342\) 23.8206 1.28807
\(343\) −17.5036 −0.945104
\(344\) 6.87552 0.370703
\(345\) −1.74759 −0.0940869
\(346\) 18.7258 1.00670
\(347\) −27.1949 −1.45990 −0.729948 0.683503i \(-0.760456\pi\)
−0.729948 + 0.683503i \(0.760456\pi\)
\(348\) 1.14290 0.0612660
\(349\) 4.95780 0.265385 0.132692 0.991157i \(-0.457638\pi\)
0.132692 + 0.991157i \(0.457638\pi\)
\(350\) −4.40635 −0.235529
\(351\) 3.24908 0.173423
\(352\) 2.90380 0.154773
\(353\) 2.14290 0.114055 0.0570274 0.998373i \(-0.481838\pi\)
0.0570274 + 0.998373i \(0.481838\pi\)
\(354\) −1.30758 −0.0694968
\(355\) 15.4683 0.820975
\(356\) −0.816614 −0.0432804
\(357\) −3.79490 −0.200847
\(358\) −1.20830 −0.0638606
\(359\) −23.9840 −1.26582 −0.632912 0.774223i \(-0.718141\pi\)
−0.632912 + 0.774223i \(0.718141\pi\)
\(360\) −6.72759 −0.354575
\(361\) 8.24154 0.433765
\(362\) 2.41033 0.126684
\(363\) −0.358295 −0.0188056
\(364\) 2.25189 0.118031
\(365\) 1.00000 0.0523424
\(366\) −6.31339 −0.330006
\(367\) 8.11237 0.423462 0.211731 0.977328i \(-0.432090\pi\)
0.211731 + 0.977328i \(0.432090\pi\)
\(368\) −23.2913 −1.21414
\(369\) 7.58315 0.394763
\(370\) −4.29109 −0.223083
\(371\) −1.90523 −0.0989148
\(372\) −0.402874 −0.0208880
\(373\) −34.6277 −1.79296 −0.896478 0.443089i \(-0.853883\pi\)
−0.896478 + 0.443089i \(0.853883\pi\)
\(374\) −6.07154 −0.313952
\(375\) −0.358295 −0.0185023
\(376\) 31.7299 1.63634
\(377\) −9.36725 −0.482438
\(378\) −9.26997 −0.476796
\(379\) 11.8174 0.607021 0.303510 0.952828i \(-0.401841\pi\)
0.303510 + 0.952828i \(0.401841\pi\)
\(380\) 2.74494 0.140812
\(381\) 3.50693 0.179665
\(382\) 32.5942 1.66767
\(383\) 25.3422 1.29492 0.647462 0.762098i \(-0.275830\pi\)
0.647462 + 0.762098i \(0.275830\pi\)
\(384\) 4.89129 0.249607
\(385\) 2.77249 0.141299
\(386\) −30.1550 −1.53485
\(387\) −8.42756 −0.428397
\(388\) 3.40254 0.172738
\(389\) 12.6873 0.643273 0.321637 0.946863i \(-0.395767\pi\)
0.321637 + 0.946863i \(0.395767\pi\)
\(390\) 0.879450 0.0445327
\(391\) 18.6332 0.942322
\(392\) 1.60877 0.0812552
\(393\) 2.98640 0.150644
\(394\) 29.7729 1.49994
\(395\) 12.3392 0.620851
\(396\) −1.51024 −0.0758922
\(397\) −3.57925 −0.179637 −0.0898186 0.995958i \(-0.528629\pi\)
−0.0898186 + 0.995958i \(0.528629\pi\)
\(398\) 13.4358 0.673476
\(399\) −5.18473 −0.259561
\(400\) −4.77525 −0.238762
\(401\) −12.4739 −0.622917 −0.311459 0.950260i \(-0.600818\pi\)
−0.311459 + 0.950260i \(0.600818\pi\)
\(402\) −3.91405 −0.195215
\(403\) 3.30196 0.164482
\(404\) 5.62795 0.280001
\(405\) 7.86110 0.390621
\(406\) 26.7258 1.32638
\(407\) 2.69997 0.133832
\(408\) −3.20673 −0.158757
\(409\) −3.57165 −0.176607 −0.0883035 0.996094i \(-0.528145\pi\)
−0.0883035 + 0.996094i \(0.528145\pi\)
\(410\) 4.19693 0.207271
\(411\) −2.66238 −0.131326
\(412\) 0.348754 0.0171819
\(413\) −6.36629 −0.313265
\(414\) 22.2605 1.09405
\(415\) −3.83901 −0.188449
\(416\) 4.48464 0.219878
\(417\) 2.39325 0.117198
\(418\) −8.29517 −0.405730
\(419\) 7.44269 0.363599 0.181799 0.983336i \(-0.441808\pi\)
0.181799 + 0.983336i \(0.441808\pi\)
\(420\) −0.522429 −0.0254919
\(421\) 31.0592 1.51373 0.756867 0.653568i \(-0.226729\pi\)
0.756867 + 0.653568i \(0.226729\pi\)
\(422\) −36.6559 −1.78438
\(423\) −38.8924 −1.89101
\(424\) −1.60994 −0.0781857
\(425\) 3.82023 0.185308
\(426\) 8.80834 0.426766
\(427\) −30.7385 −1.48754
\(428\) −2.70533 −0.130767
\(429\) −0.553352 −0.0267161
\(430\) −4.66427 −0.224931
\(431\) 18.5244 0.892290 0.446145 0.894961i \(-0.352797\pi\)
0.446145 + 0.894961i \(0.352797\pi\)
\(432\) −10.0460 −0.483340
\(433\) −35.8455 −1.72262 −0.861312 0.508077i \(-0.830357\pi\)
−0.861312 + 0.508077i \(0.830357\pi\)
\(434\) −9.42086 −0.452216
\(435\) 2.17316 0.104195
\(436\) −10.0226 −0.479994
\(437\) 25.4574 1.21779
\(438\) 0.569443 0.0272090
\(439\) 33.7428 1.61046 0.805228 0.592965i \(-0.202043\pi\)
0.805228 + 0.592965i \(0.202043\pi\)
\(440\) 2.34278 0.111688
\(441\) −1.97192 −0.0939012
\(442\) −9.37692 −0.446015
\(443\) −27.4936 −1.30626 −0.653131 0.757245i \(-0.726545\pi\)
−0.653131 + 0.757245i \(0.726545\pi\)
\(444\) −0.508764 −0.0241449
\(445\) −1.55274 −0.0736071
\(446\) 1.87715 0.0888858
\(447\) 3.01283 0.142502
\(448\) 13.6835 0.646483
\(449\) −13.0328 −0.615057 −0.307528 0.951539i \(-0.599502\pi\)
−0.307528 + 0.951539i \(0.599502\pi\)
\(450\) 4.56391 0.215145
\(451\) −2.64072 −0.124346
\(452\) −8.97456 −0.422128
\(453\) −6.98538 −0.328202
\(454\) −36.2251 −1.70013
\(455\) 4.28184 0.200736
\(456\) −4.38115 −0.205166
\(457\) 0.283972 0.0132836 0.00664182 0.999978i \(-0.497886\pi\)
0.00664182 + 0.999978i \(0.497886\pi\)
\(458\) −8.03327 −0.375370
\(459\) 8.03690 0.375130
\(460\) 2.56516 0.119601
\(461\) 27.9712 1.30275 0.651374 0.758757i \(-0.274193\pi\)
0.651374 + 0.758757i \(0.274193\pi\)
\(462\) 1.57877 0.0734512
\(463\) −24.2650 −1.12769 −0.563845 0.825880i \(-0.690679\pi\)
−0.563845 + 0.825880i \(0.690679\pi\)
\(464\) 28.9632 1.34458
\(465\) −0.766041 −0.0355243
\(466\) −27.3130 −1.26525
\(467\) 41.3041 1.91133 0.955663 0.294463i \(-0.0951408\pi\)
0.955663 + 0.294463i \(0.0951408\pi\)
\(468\) −2.33241 −0.107816
\(469\) −19.0566 −0.879953
\(470\) −21.5252 −0.992882
\(471\) 0.902564 0.0415880
\(472\) −5.37958 −0.247615
\(473\) 2.93477 0.134941
\(474\) 7.02646 0.322736
\(475\) 5.21934 0.239480
\(476\) 5.57027 0.255313
\(477\) 1.97336 0.0903539
\(478\) −47.7946 −2.18607
\(479\) −27.1543 −1.24071 −0.620357 0.784320i \(-0.713012\pi\)
−0.620357 + 0.784320i \(0.713012\pi\)
\(480\) −1.04042 −0.0474883
\(481\) 4.16984 0.190128
\(482\) 36.3777 1.65696
\(483\) −4.84517 −0.220463
\(484\) 0.525917 0.0239053
\(485\) 6.46974 0.293776
\(486\) 14.5071 0.658056
\(487\) −4.87307 −0.220820 −0.110410 0.993886i \(-0.535216\pi\)
−0.110410 + 0.993886i \(0.535216\pi\)
\(488\) −25.9743 −1.17580
\(489\) 6.51833 0.294769
\(490\) −1.09137 −0.0493031
\(491\) 31.3247 1.41366 0.706831 0.707382i \(-0.250124\pi\)
0.706831 + 0.707382i \(0.250124\pi\)
\(492\) 0.497599 0.0224335
\(493\) −23.1708 −1.04356
\(494\) −12.8111 −0.576398
\(495\) −2.87162 −0.129070
\(496\) −10.2096 −0.458423
\(497\) 42.8858 1.92369
\(498\) −2.18610 −0.0979613
\(499\) 27.7778 1.24351 0.621754 0.783213i \(-0.286421\pi\)
0.621754 + 0.783213i \(0.286421\pi\)
\(500\) 0.525917 0.0235197
\(501\) −2.35311 −0.105129
\(502\) −11.2439 −0.501840
\(503\) −16.2552 −0.724782 −0.362391 0.932026i \(-0.618039\pi\)
−0.362391 + 0.932026i \(0.618039\pi\)
\(504\) −18.6522 −0.830833
\(505\) 10.7012 0.476198
\(506\) −7.75189 −0.344614
\(507\) 3.80323 0.168908
\(508\) −5.14758 −0.228387
\(509\) −2.33732 −0.103600 −0.0517999 0.998657i \(-0.516496\pi\)
−0.0517999 + 0.998657i \(0.516496\pi\)
\(510\) 2.17540 0.0963285
\(511\) 2.77249 0.122648
\(512\) 8.50834 0.376019
\(513\) 10.9803 0.484793
\(514\) −15.0764 −0.664992
\(515\) 0.663135 0.0292212
\(516\) −0.553008 −0.0243448
\(517\) 13.5437 0.595651
\(518\) −11.8970 −0.522725
\(519\) 4.22154 0.185305
\(520\) 3.61820 0.158669
\(521\) 7.13712 0.312683 0.156341 0.987703i \(-0.450030\pi\)
0.156341 + 0.987703i \(0.450030\pi\)
\(522\) −27.6814 −1.21158
\(523\) −35.5719 −1.55545 −0.777726 0.628603i \(-0.783627\pi\)
−0.777726 + 0.628603i \(0.783627\pi\)
\(524\) −4.38353 −0.191495
\(525\) −0.993369 −0.0433542
\(526\) −19.4093 −0.846286
\(527\) 8.16772 0.355791
\(528\) 1.71095 0.0744594
\(529\) 0.790109 0.0343526
\(530\) 1.09216 0.0474406
\(531\) 6.59393 0.286152
\(532\) 7.61031 0.329949
\(533\) −4.07833 −0.176652
\(534\) −0.884198 −0.0382630
\(535\) −5.14402 −0.222395
\(536\) −16.1030 −0.695545
\(537\) −0.272399 −0.0117549
\(538\) −12.9110 −0.556633
\(539\) 0.686693 0.0295780
\(540\) 1.10641 0.0476123
\(541\) 14.9080 0.640946 0.320473 0.947258i \(-0.396158\pi\)
0.320473 + 0.947258i \(0.396158\pi\)
\(542\) −21.0008 −0.902060
\(543\) 0.543386 0.0233189
\(544\) 11.0932 0.475617
\(545\) −19.0573 −0.816326
\(546\) 2.43826 0.104348
\(547\) 12.7017 0.543085 0.271542 0.962427i \(-0.412466\pi\)
0.271542 + 0.962427i \(0.412466\pi\)
\(548\) 3.90793 0.166939
\(549\) 31.8376 1.35879
\(550\) −1.58931 −0.0677685
\(551\) −31.6568 −1.34863
\(552\) −4.09421 −0.174261
\(553\) 34.2102 1.45477
\(554\) −26.4876 −1.12535
\(555\) −0.967385 −0.0410632
\(556\) −3.51290 −0.148980
\(557\) 30.5291 1.29356 0.646779 0.762677i \(-0.276116\pi\)
0.646779 + 0.762677i \(0.276116\pi\)
\(558\) 9.75772 0.413077
\(559\) 4.53247 0.191703
\(560\) −13.2393 −0.559463
\(561\) −1.36877 −0.0577895
\(562\) −23.9447 −1.01005
\(563\) 13.9172 0.586540 0.293270 0.956030i \(-0.405256\pi\)
0.293270 + 0.956030i \(0.405256\pi\)
\(564\) −2.55208 −0.107462
\(565\) −17.0646 −0.717913
\(566\) 8.97462 0.377231
\(567\) 21.7948 0.915296
\(568\) 36.2389 1.52055
\(569\) 22.8833 0.959319 0.479659 0.877455i \(-0.340760\pi\)
0.479659 + 0.877455i \(0.340760\pi\)
\(570\) 2.97212 0.124488
\(571\) −12.9138 −0.540425 −0.270212 0.962801i \(-0.587094\pi\)
−0.270212 + 0.962801i \(0.587094\pi\)
\(572\) 0.812228 0.0339610
\(573\) 7.34805 0.306969
\(574\) 11.6359 0.485674
\(575\) 4.87751 0.203406
\(576\) −14.1727 −0.590531
\(577\) −29.6690 −1.23514 −0.617569 0.786516i \(-0.711882\pi\)
−0.617569 + 0.786516i \(0.711882\pi\)
\(578\) 3.82362 0.159042
\(579\) −6.79815 −0.282521
\(580\) −3.18984 −0.132451
\(581\) −10.6436 −0.441571
\(582\) 3.68415 0.152713
\(583\) −0.687193 −0.0284606
\(584\) 2.34278 0.0969449
\(585\) −4.43495 −0.183363
\(586\) −33.5127 −1.38440
\(587\) 9.91066 0.409057 0.204528 0.978861i \(-0.434434\pi\)
0.204528 + 0.978861i \(0.434434\pi\)
\(588\) −0.129396 −0.00533619
\(589\) 11.1590 0.459800
\(590\) 3.64944 0.150245
\(591\) 6.71200 0.276095
\(592\) −12.8930 −0.529899
\(593\) 18.3040 0.751656 0.375828 0.926689i \(-0.377358\pi\)
0.375828 + 0.926689i \(0.377358\pi\)
\(594\) −3.34355 −0.137188
\(595\) 10.5915 0.434211
\(596\) −4.42233 −0.181146
\(597\) 3.02897 0.123967
\(598\) −11.9721 −0.489574
\(599\) 13.3164 0.544095 0.272047 0.962284i \(-0.412299\pi\)
0.272047 + 0.962284i \(0.412299\pi\)
\(600\) −0.839406 −0.0342686
\(601\) 32.7419 1.33557 0.667785 0.744354i \(-0.267243\pi\)
0.667785 + 0.744354i \(0.267243\pi\)
\(602\) −12.9316 −0.527054
\(603\) 19.7380 0.803795
\(604\) 10.2534 0.417204
\(605\) 1.00000 0.0406558
\(606\) 6.09373 0.247541
\(607\) 8.71880 0.353885 0.176943 0.984221i \(-0.443379\pi\)
0.176943 + 0.984221i \(0.443379\pi\)
\(608\) 15.1559 0.614654
\(609\) 6.02507 0.244148
\(610\) 17.6206 0.713439
\(611\) 20.9169 0.846208
\(612\) −5.76945 −0.233216
\(613\) −15.2287 −0.615083 −0.307541 0.951535i \(-0.599506\pi\)
−0.307541 + 0.951535i \(0.599506\pi\)
\(614\) −7.45269 −0.300766
\(615\) 0.946155 0.0381527
\(616\) 6.49533 0.261704
\(617\) 7.25939 0.292252 0.146126 0.989266i \(-0.453319\pi\)
0.146126 + 0.989266i \(0.453319\pi\)
\(618\) 0.377618 0.0151900
\(619\) −33.0601 −1.32880 −0.664399 0.747378i \(-0.731313\pi\)
−0.664399 + 0.747378i \(0.731313\pi\)
\(620\) 1.12442 0.0451578
\(621\) 10.2612 0.411767
\(622\) −29.5327 −1.18415
\(623\) −4.30496 −0.172475
\(624\) 2.64239 0.105780
\(625\) 1.00000 0.0400000
\(626\) −34.9942 −1.39865
\(627\) −1.87006 −0.0746832
\(628\) −1.32481 −0.0528658
\(629\) 10.3145 0.411266
\(630\) 12.6534 0.504123
\(631\) 2.09192 0.0832779 0.0416389 0.999133i \(-0.486742\pi\)
0.0416389 + 0.999133i \(0.486742\pi\)
\(632\) 28.9080 1.14990
\(633\) −8.26371 −0.328453
\(634\) −40.0086 −1.58895
\(635\) −9.78783 −0.388418
\(636\) 0.129490 0.00513461
\(637\) 1.06053 0.0420198
\(638\) 9.63964 0.381637
\(639\) −44.4193 −1.75720
\(640\) −13.6516 −0.539625
\(641\) 25.9614 1.02542 0.512708 0.858563i \(-0.328643\pi\)
0.512708 + 0.858563i \(0.328643\pi\)
\(642\) −2.92923 −0.115607
\(643\) −37.4967 −1.47873 −0.739364 0.673306i \(-0.764874\pi\)
−0.739364 + 0.673306i \(0.764874\pi\)
\(644\) 7.11189 0.280248
\(645\) −1.05151 −0.0414033
\(646\) −31.6895 −1.24681
\(647\) −41.2807 −1.62291 −0.811456 0.584413i \(-0.801325\pi\)
−0.811456 + 0.584413i \(0.801325\pi\)
\(648\) 18.4168 0.723482
\(649\) −2.29624 −0.0901352
\(650\) −2.45454 −0.0962751
\(651\) −2.12384 −0.0832398
\(652\) −9.56781 −0.374704
\(653\) −34.0475 −1.33238 −0.666190 0.745782i \(-0.732076\pi\)
−0.666190 + 0.745782i \(0.732076\pi\)
\(654\) −10.8521 −0.424349
\(655\) −8.33503 −0.325677
\(656\) 12.6101 0.492341
\(657\) −2.87162 −0.112033
\(658\) −59.6783 −2.32650
\(659\) 35.1215 1.36814 0.684071 0.729416i \(-0.260208\pi\)
0.684071 + 0.729416i \(0.260208\pi\)
\(660\) −0.188433 −0.00733476
\(661\) −38.9130 −1.51354 −0.756769 0.653682i \(-0.773223\pi\)
−0.756769 + 0.653682i \(0.773223\pi\)
\(662\) 4.90059 0.190467
\(663\) −2.11393 −0.0820984
\(664\) −8.99395 −0.349033
\(665\) 14.4706 0.561145
\(666\) 12.3224 0.477484
\(667\) −29.5835 −1.14548
\(668\) 3.45397 0.133638
\(669\) 0.423186 0.0163613
\(670\) 10.9241 0.422035
\(671\) −11.0870 −0.428007
\(672\) −2.88454 −0.111274
\(673\) 11.2565 0.433904 0.216952 0.976182i \(-0.430388\pi\)
0.216952 + 0.976182i \(0.430388\pi\)
\(674\) 10.1367 0.390450
\(675\) 2.10377 0.0809743
\(676\) −5.58251 −0.214712
\(677\) 21.3808 0.821731 0.410865 0.911696i \(-0.365227\pi\)
0.410865 + 0.911696i \(0.365227\pi\)
\(678\) −9.71731 −0.373191
\(679\) 17.9373 0.688369
\(680\) 8.94996 0.343215
\(681\) −8.16659 −0.312944
\(682\) −3.39798 −0.130115
\(683\) 42.2983 1.61850 0.809249 0.587466i \(-0.199874\pi\)
0.809249 + 0.587466i \(0.199874\pi\)
\(684\) −7.88244 −0.301393
\(685\) 7.43070 0.283912
\(686\) 27.8187 1.06212
\(687\) −1.81102 −0.0690948
\(688\) −14.0142 −0.534288
\(689\) −1.06130 −0.0404324
\(690\) 2.77746 0.105736
\(691\) 42.3738 1.61197 0.805987 0.591933i \(-0.201635\pi\)
0.805987 + 0.591933i \(0.201635\pi\)
\(692\) −6.19651 −0.235556
\(693\) −7.96155 −0.302434
\(694\) 43.2211 1.64065
\(695\) −6.67957 −0.253370
\(696\) 5.09124 0.192983
\(697\) −10.0881 −0.382116
\(698\) −7.87949 −0.298243
\(699\) −6.15745 −0.232896
\(700\) 1.45810 0.0551109
\(701\) 17.5189 0.661681 0.330841 0.943687i \(-0.392668\pi\)
0.330841 + 0.943687i \(0.392668\pi\)
\(702\) −5.16380 −0.194895
\(703\) 14.0921 0.531492
\(704\) 4.93544 0.186011
\(705\) −4.85263 −0.182761
\(706\) −3.40573 −0.128176
\(707\) 29.6690 1.11582
\(708\) 0.432687 0.0162614
\(709\) −30.4570 −1.14384 −0.571918 0.820311i \(-0.693800\pi\)
−0.571918 + 0.820311i \(0.693800\pi\)
\(710\) −24.5841 −0.922623
\(711\) −35.4335 −1.32886
\(712\) −3.63774 −0.136330
\(713\) 10.4282 0.390539
\(714\) 6.03128 0.225715
\(715\) 1.54440 0.0577574
\(716\) 0.399836 0.0149426
\(717\) −10.7748 −0.402393
\(718\) 38.1180 1.42255
\(719\) −11.3820 −0.424475 −0.212238 0.977218i \(-0.568075\pi\)
−0.212238 + 0.977218i \(0.568075\pi\)
\(720\) 13.7127 0.511043
\(721\) 1.83854 0.0684706
\(722\) −13.0984 −0.487472
\(723\) 8.20098 0.304998
\(724\) −0.797599 −0.0296425
\(725\) −6.06529 −0.225259
\(726\) 0.569443 0.0211340
\(727\) 17.1104 0.634589 0.317294 0.948327i \(-0.397226\pi\)
0.317294 + 0.948327i \(0.397226\pi\)
\(728\) 10.0314 0.371789
\(729\) −20.3128 −0.752327
\(730\) −1.58931 −0.0588231
\(731\) 11.2115 0.414672
\(732\) 2.08915 0.0772173
\(733\) −26.9184 −0.994254 −0.497127 0.867678i \(-0.665612\pi\)
−0.497127 + 0.867678i \(0.665612\pi\)
\(734\) −12.8931 −0.475893
\(735\) −0.246039 −0.00907527
\(736\) 14.1633 0.522067
\(737\) −6.87347 −0.253188
\(738\) −12.0520 −0.443640
\(739\) −45.6317 −1.67859 −0.839294 0.543677i \(-0.817032\pi\)
−0.839294 + 0.543677i \(0.817032\pi\)
\(740\) 1.41996 0.0521987
\(741\) −2.88813 −0.106098
\(742\) 3.02801 0.111162
\(743\) 53.7454 1.97173 0.985863 0.167554i \(-0.0535867\pi\)
0.985863 + 0.167554i \(0.0535867\pi\)
\(744\) −1.79466 −0.0657956
\(745\) −8.40880 −0.308075
\(746\) 55.0343 2.01495
\(747\) 11.0242 0.403354
\(748\) 2.00912 0.0734608
\(749\) −14.2617 −0.521113
\(750\) 0.569443 0.0207931
\(751\) 2.61297 0.0953486 0.0476743 0.998863i \(-0.484819\pi\)
0.0476743 + 0.998863i \(0.484819\pi\)
\(752\) −64.6744 −2.35843
\(753\) −2.53483 −0.0923742
\(754\) 14.8875 0.542171
\(755\) 19.4962 0.709538
\(756\) 3.06751 0.111564
\(757\) 28.3526 1.03049 0.515246 0.857042i \(-0.327701\pi\)
0.515246 + 0.857042i \(0.327701\pi\)
\(758\) −18.7816 −0.682178
\(759\) −1.74759 −0.0634334
\(760\) 12.2278 0.443548
\(761\) −49.4215 −1.79153 −0.895763 0.444531i \(-0.853370\pi\)
−0.895763 + 0.444531i \(0.853370\pi\)
\(762\) −5.57361 −0.201911
\(763\) −52.8362 −1.91280
\(764\) −10.7857 −0.390213
\(765\) −10.9703 −0.396631
\(766\) −40.2766 −1.45525
\(767\) −3.54632 −0.128050
\(768\) −4.23710 −0.152893
\(769\) −5.00599 −0.180521 −0.0902603 0.995918i \(-0.528770\pi\)
−0.0902603 + 0.995918i \(0.528770\pi\)
\(770\) −4.40635 −0.158794
\(771\) −3.39883 −0.122406
\(772\) 9.97854 0.359135
\(773\) −47.5925 −1.71178 −0.855892 0.517155i \(-0.826991\pi\)
−0.855892 + 0.517155i \(0.826991\pi\)
\(774\) 13.3940 0.481438
\(775\) 2.13802 0.0767998
\(776\) 15.1572 0.544111
\(777\) −2.68206 −0.0962185
\(778\) −20.1642 −0.722920
\(779\) −13.7828 −0.493820
\(780\) −0.291017 −0.0104201
\(781\) 15.4683 0.553501
\(782\) −29.6140 −1.05900
\(783\) −12.7600 −0.456005
\(784\) −3.27913 −0.117112
\(785\) −2.51905 −0.0899089
\(786\) −4.74632 −0.169296
\(787\) −46.7784 −1.66747 −0.833735 0.552164i \(-0.813802\pi\)
−0.833735 + 0.552164i \(0.813802\pi\)
\(788\) −9.85209 −0.350966
\(789\) −4.37563 −0.155777
\(790\) −19.6108 −0.697722
\(791\) −47.3114 −1.68220
\(792\) −6.72759 −0.239054
\(793\) −17.1227 −0.608046
\(794\) 5.68854 0.201879
\(795\) 0.246218 0.00873244
\(796\) −4.44602 −0.157585
\(797\) 10.6258 0.376386 0.188193 0.982132i \(-0.439737\pi\)
0.188193 + 0.982132i \(0.439737\pi\)
\(798\) 8.24016 0.291699
\(799\) 51.7400 1.83043
\(800\) 2.90380 0.102665
\(801\) 4.45890 0.157547
\(802\) 19.8250 0.700043
\(803\) 1.00000 0.0352892
\(804\) 1.29519 0.0456779
\(805\) 13.5228 0.476618
\(806\) −5.24785 −0.184848
\(807\) −2.91066 −0.102460
\(808\) 25.0706 0.881980
\(809\) −28.0198 −0.985124 −0.492562 0.870277i \(-0.663940\pi\)
−0.492562 + 0.870277i \(0.663940\pi\)
\(810\) −12.4938 −0.438986
\(811\) −39.8403 −1.39898 −0.699491 0.714641i \(-0.746590\pi\)
−0.699491 + 0.714641i \(0.746590\pi\)
\(812\) −8.84378 −0.310356
\(813\) −4.73441 −0.166043
\(814\) −4.29109 −0.150403
\(815\) −18.1926 −0.637260
\(816\) 6.53621 0.228813
\(817\) 15.3176 0.535894
\(818\) 5.67648 0.198473
\(819\) −12.2958 −0.429652
\(820\) −1.38880 −0.0484989
\(821\) 2.87142 0.100213 0.0501067 0.998744i \(-0.484044\pi\)
0.0501067 + 0.998744i \(0.484044\pi\)
\(822\) 4.23136 0.147586
\(823\) 10.1523 0.353886 0.176943 0.984221i \(-0.443379\pi\)
0.176943 + 0.984221i \(0.443379\pi\)
\(824\) 1.55358 0.0541215
\(825\) −0.358295 −0.0124742
\(826\) 10.1180 0.352051
\(827\) 8.78411 0.305453 0.152727 0.988268i \(-0.451195\pi\)
0.152727 + 0.988268i \(0.451195\pi\)
\(828\) −7.36619 −0.255993
\(829\) −10.1027 −0.350881 −0.175440 0.984490i \(-0.556135\pi\)
−0.175440 + 0.984490i \(0.556135\pi\)
\(830\) 6.10139 0.211782
\(831\) −5.97136 −0.207144
\(832\) 7.62232 0.264256
\(833\) 2.62333 0.0908929
\(834\) −3.80363 −0.131709
\(835\) 6.56752 0.227278
\(836\) 2.74494 0.0949357
\(837\) 4.49790 0.155470
\(838\) −11.8288 −0.408618
\(839\) −29.0683 −1.00355 −0.501774 0.864999i \(-0.667319\pi\)
−0.501774 + 0.864999i \(0.667319\pi\)
\(840\) −2.32724 −0.0802976
\(841\) 7.78770 0.268541
\(842\) −49.3629 −1.70116
\(843\) −5.39810 −0.185920
\(844\) 12.1297 0.417523
\(845\) −10.6148 −0.365161
\(846\) 61.8122 2.12515
\(847\) 2.77249 0.0952638
\(848\) 3.28151 0.112688
\(849\) 2.02324 0.0694374
\(850\) −6.07154 −0.208252
\(851\) 13.1691 0.451432
\(852\) −2.91475 −0.0998578
\(853\) −6.58834 −0.225580 −0.112790 0.993619i \(-0.535979\pi\)
−0.112790 + 0.993619i \(0.535979\pi\)
\(854\) 48.8530 1.67172
\(855\) −14.9880 −0.512579
\(856\) −12.0513 −0.411905
\(857\) −22.5970 −0.771900 −0.385950 0.922520i \(-0.626126\pi\)
−0.385950 + 0.922520i \(0.626126\pi\)
\(858\) 0.879450 0.0300239
\(859\) 23.5812 0.804579 0.402290 0.915512i \(-0.368214\pi\)
0.402290 + 0.915512i \(0.368214\pi\)
\(860\) 1.54344 0.0526310
\(861\) 2.62321 0.0893986
\(862\) −29.4411 −1.00277
\(863\) −13.0857 −0.445443 −0.222721 0.974882i \(-0.571494\pi\)
−0.222721 + 0.974882i \(0.571494\pi\)
\(864\) 6.10894 0.207830
\(865\) −11.7823 −0.400610
\(866\) 56.9697 1.93591
\(867\) 0.861998 0.0292750
\(868\) 3.11744 0.105813
\(869\) 12.3392 0.418578
\(870\) −3.45383 −0.117096
\(871\) −10.6154 −0.359690
\(872\) −44.6471 −1.51194
\(873\) −18.5787 −0.628792
\(874\) −40.4598 −1.36857
\(875\) 2.77249 0.0937272
\(876\) −0.188433 −0.00636657
\(877\) −5.04783 −0.170453 −0.0852266 0.996362i \(-0.527161\pi\)
−0.0852266 + 0.996362i \(0.527161\pi\)
\(878\) −53.6279 −1.80985
\(879\) −7.55510 −0.254827
\(880\) −4.77525 −0.160973
\(881\) 18.0015 0.606485 0.303242 0.952913i \(-0.401931\pi\)
0.303242 + 0.952913i \(0.401931\pi\)
\(882\) 3.13401 0.105527
\(883\) 6.77061 0.227849 0.113925 0.993489i \(-0.463658\pi\)
0.113925 + 0.993489i \(0.463658\pi\)
\(884\) 3.10290 0.104362
\(885\) 0.822730 0.0276558
\(886\) 43.6960 1.46800
\(887\) −38.4285 −1.29030 −0.645152 0.764054i \(-0.723206\pi\)
−0.645152 + 0.764054i \(0.723206\pi\)
\(888\) −2.26637 −0.0760544
\(889\) −27.1366 −0.910134
\(890\) 2.46780 0.0827207
\(891\) 7.86110 0.263357
\(892\) −0.621165 −0.0207982
\(893\) 70.6891 2.36552
\(894\) −4.78833 −0.160146
\(895\) 0.760265 0.0254129
\(896\) −37.8488 −1.26444
\(897\) −2.69898 −0.0901164
\(898\) 20.7132 0.691210
\(899\) −12.9677 −0.432497
\(900\) −1.51024 −0.0503412
\(901\) −2.62524 −0.0874593
\(902\) 4.19693 0.139742
\(903\) −2.91531 −0.0970154
\(904\) −39.9786 −1.32967
\(905\) −1.51659 −0.0504131
\(906\) 11.1020 0.368838
\(907\) 10.3893 0.344971 0.172486 0.985012i \(-0.444820\pi\)
0.172486 + 0.985012i \(0.444820\pi\)
\(908\) 11.9872 0.397808
\(909\) −30.7299 −1.01925
\(910\) −6.80519 −0.225590
\(911\) 54.2046 1.79588 0.897939 0.440120i \(-0.145064\pi\)
0.897939 + 0.440120i \(0.145064\pi\)
\(912\) 8.93001 0.295702
\(913\) −3.83901 −0.127053
\(914\) −0.451320 −0.0149283
\(915\) 3.97240 0.131324
\(916\) 2.65828 0.0878319
\(917\) −23.1088 −0.763119
\(918\) −12.7732 −0.421577
\(919\) 20.4846 0.675724 0.337862 0.941196i \(-0.390296\pi\)
0.337862 + 0.941196i \(0.390296\pi\)
\(920\) 11.4269 0.376735
\(921\) −1.68014 −0.0553623
\(922\) −44.4550 −1.46405
\(923\) 23.8894 0.786329
\(924\) −0.522429 −0.0171867
\(925\) 2.69997 0.0887744
\(926\) 38.5647 1.26731
\(927\) −1.90428 −0.0625446
\(928\) −17.6124 −0.578155
\(929\) −18.6103 −0.610584 −0.305292 0.952259i \(-0.598754\pi\)
−0.305292 + 0.952259i \(0.598754\pi\)
\(930\) 1.21748 0.0399227
\(931\) 3.58409 0.117464
\(932\) 9.03811 0.296053
\(933\) −6.65785 −0.217968
\(934\) −65.6452 −2.14797
\(935\) 3.82023 0.124935
\(936\) −10.3901 −0.339611
\(937\) 17.3476 0.566723 0.283361 0.959013i \(-0.408550\pi\)
0.283361 + 0.959013i \(0.408550\pi\)
\(938\) 30.2869 0.988904
\(939\) −7.88910 −0.257451
\(940\) 7.12285 0.232322
\(941\) 27.9871 0.912352 0.456176 0.889890i \(-0.349219\pi\)
0.456176 + 0.889890i \(0.349219\pi\)
\(942\) −1.43446 −0.0467371
\(943\) −12.8801 −0.419435
\(944\) 10.9651 0.356883
\(945\) 5.83269 0.189737
\(946\) −4.66427 −0.151648
\(947\) 27.3964 0.890263 0.445132 0.895465i \(-0.353157\pi\)
0.445132 + 0.895465i \(0.353157\pi\)
\(948\) −2.32511 −0.0755161
\(949\) 1.54440 0.0501335
\(950\) −8.29517 −0.269131
\(951\) −9.01955 −0.292479
\(952\) 24.8137 0.804216
\(953\) 26.4846 0.857919 0.428959 0.903324i \(-0.358880\pi\)
0.428959 + 0.903324i \(0.358880\pi\)
\(954\) −3.13629 −0.101541
\(955\) −20.5084 −0.663636
\(956\) 15.8156 0.511514
\(957\) 2.17316 0.0702483
\(958\) 43.1567 1.39433
\(959\) 20.6015 0.665258
\(960\) −1.76834 −0.0570730
\(961\) −26.4289 −0.852545
\(962\) −6.62718 −0.213669
\(963\) 14.7717 0.476011
\(964\) −12.0377 −0.387707
\(965\) 18.9736 0.610782
\(966\) 7.70049 0.247759
\(967\) 1.40806 0.0452801 0.0226401 0.999744i \(-0.492793\pi\)
0.0226401 + 0.999744i \(0.492793\pi\)
\(968\) 2.34278 0.0752998
\(969\) −7.14408 −0.229501
\(970\) −10.2824 −0.330149
\(971\) −53.4940 −1.71670 −0.858352 0.513061i \(-0.828512\pi\)
−0.858352 + 0.513061i \(0.828512\pi\)
\(972\) −4.80052 −0.153977
\(973\) −18.5190 −0.593693
\(974\) 7.74484 0.248161
\(975\) −0.553352 −0.0177215
\(976\) 52.9429 1.69466
\(977\) −31.4776 −1.00706 −0.503529 0.863978i \(-0.667965\pi\)
−0.503529 + 0.863978i \(0.667965\pi\)
\(978\) −10.3597 −0.331265
\(979\) −1.55274 −0.0496259
\(980\) 0.361143 0.0115363
\(981\) 54.7255 1.74725
\(982\) −49.7847 −1.58869
\(983\) −14.8466 −0.473532 −0.236766 0.971567i \(-0.576087\pi\)
−0.236766 + 0.971567i \(0.576087\pi\)
\(984\) 2.21663 0.0706637
\(985\) −18.7332 −0.596888
\(986\) 36.8257 1.17277
\(987\) −13.4539 −0.428241
\(988\) 4.23930 0.134870
\(989\) 14.3144 0.455170
\(990\) 4.56391 0.145051
\(991\) −8.68902 −0.276016 −0.138008 0.990431i \(-0.544070\pi\)
−0.138008 + 0.990431i \(0.544070\pi\)
\(992\) 6.20838 0.197116
\(993\) 1.10479 0.0350595
\(994\) −68.1590 −2.16187
\(995\) −8.45384 −0.268005
\(996\) 0.723397 0.0229217
\(997\) −12.9670 −0.410669 −0.205335 0.978692i \(-0.565828\pi\)
−0.205335 + 0.978692i \(0.565828\pi\)
\(998\) −44.1477 −1.39747
\(999\) 5.68012 0.179711
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 \(a_p\))