Properties

Label 6041.2.a.f.1.2
Level 6041
Weight 2
Character 6041.1
Self dual Yes
Analytic conductor 48.238
Analytic rank 0
Dimension 132
CM No

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Newspace parameters

Level: \( N \) = \( 6041 = 7 \cdot 863 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2376278611\)
Analytic rank: \(0\)
Dimension: \(132\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 6041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.78355 q^{2}\) \(+3.33951 q^{3}\) \(+5.74813 q^{4}\) \(+2.68755 q^{5}\) \(-9.29568 q^{6}\) \(+1.00000 q^{7}\) \(-10.4331 q^{8}\) \(+8.15233 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.78355 q^{2}\) \(+3.33951 q^{3}\) \(+5.74813 q^{4}\) \(+2.68755 q^{5}\) \(-9.29568 q^{6}\) \(+1.00000 q^{7}\) \(-10.4331 q^{8}\) \(+8.15233 q^{9}\) \(-7.48091 q^{10}\) \(-2.52684 q^{11}\) \(+19.1959 q^{12}\) \(-4.90685 q^{13}\) \(-2.78355 q^{14}\) \(+8.97509 q^{15}\) \(+17.5447 q^{16}\) \(-0.898319 q^{17}\) \(-22.6924 q^{18}\) \(+1.96499 q^{19}\) \(+15.4484 q^{20}\) \(+3.33951 q^{21}\) \(+7.03359 q^{22}\) \(-7.40366 q^{23}\) \(-34.8414 q^{24}\) \(+2.22291 q^{25}\) \(+13.6585 q^{26}\) \(+17.2063 q^{27}\) \(+5.74813 q^{28}\) \(+3.52400 q^{29}\) \(-24.9826 q^{30}\) \(+5.35439 q^{31}\) \(-27.9703 q^{32}\) \(-8.43842 q^{33}\) \(+2.50051 q^{34}\) \(+2.68755 q^{35}\) \(+46.8606 q^{36}\) \(+10.1575 q^{37}\) \(-5.46964 q^{38}\) \(-16.3865 q^{39}\) \(-28.0394 q^{40}\) \(+3.52367 q^{41}\) \(-9.29568 q^{42}\) \(+2.64184 q^{43}\) \(-14.5246 q^{44}\) \(+21.9098 q^{45}\) \(+20.6084 q^{46}\) \(+4.92135 q^{47}\) \(+58.5907 q^{48}\) \(+1.00000 q^{49}\) \(-6.18756 q^{50}\) \(-2.99995 q^{51}\) \(-28.2052 q^{52}\) \(+10.7700 q^{53}\) \(-47.8944 q^{54}\) \(-6.79101 q^{55}\) \(-10.4331 q^{56}\) \(+6.56211 q^{57}\) \(-9.80922 q^{58}\) \(-3.69514 q^{59}\) \(+51.5900 q^{60}\) \(+4.74191 q^{61}\) \(-14.9042 q^{62}\) \(+8.15233 q^{63}\) \(+42.7673 q^{64}\) \(-13.1874 q^{65}\) \(+23.4887 q^{66}\) \(+15.0912 q^{67}\) \(-5.16365 q^{68}\) \(-24.7246 q^{69}\) \(-7.48091 q^{70}\) \(-4.59300 q^{71}\) \(-85.0539 q^{72}\) \(+0.997451 q^{73}\) \(-28.2740 q^{74}\) \(+7.42342 q^{75}\) \(+11.2950 q^{76}\) \(-2.52684 q^{77}\) \(+45.6126 q^{78}\) \(-2.20739 q^{79}\) \(+47.1522 q^{80}\) \(+33.0035 q^{81}\) \(-9.80830 q^{82}\) \(+6.11616 q^{83}\) \(+19.1959 q^{84}\) \(-2.41427 q^{85}\) \(-7.35367 q^{86}\) \(+11.7684 q^{87}\) \(+26.3628 q^{88}\) \(-0.258006 q^{89}\) \(-60.9869 q^{90}\) \(-4.90685 q^{91}\) \(-42.5571 q^{92}\) \(+17.8810 q^{93}\) \(-13.6988 q^{94}\) \(+5.28100 q^{95}\) \(-93.4072 q^{96}\) \(-12.8683 q^{97}\) \(-2.78355 q^{98}\) \(-20.5997 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut 22q^{10} \) \(\mathstrut +\mathstrut 32q^{11} \) \(\mathstrut +\mathstrut 30q^{12} \) \(\mathstrut +\mathstrut 16q^{13} \) \(\mathstrut +\mathstrut 8q^{14} \) \(\mathstrut +\mathstrut 59q^{15} \) \(\mathstrut +\mathstrut 254q^{16} \) \(\mathstrut +\mathstrut 11q^{17} \) \(\mathstrut +\mathstrut 33q^{18} \) \(\mathstrut +\mathstrut 40q^{19} \) \(\mathstrut +\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 10q^{21} \) \(\mathstrut +\mathstrut 66q^{22} \) \(\mathstrut +\mathstrut 62q^{23} \) \(\mathstrut +\mathstrut 36q^{24} \) \(\mathstrut +\mathstrut 235q^{25} \) \(\mathstrut +\mathstrut 25q^{26} \) \(\mathstrut +\mathstrut 37q^{27} \) \(\mathstrut +\mathstrut 174q^{28} \) \(\mathstrut +\mathstrut 28q^{29} \) \(\mathstrut +\mathstrut 45q^{30} \) \(\mathstrut +\mathstrut 121q^{31} \) \(\mathstrut +\mathstrut 53q^{32} \) \(\mathstrut -\mathstrut 13q^{33} \) \(\mathstrut +\mathstrut 44q^{34} \) \(\mathstrut +\mathstrut 11q^{35} \) \(\mathstrut +\mathstrut 274q^{36} \) \(\mathstrut +\mathstrut 61q^{37} \) \(\mathstrut -\mathstrut 28q^{38} \) \(\mathstrut +\mathstrut 114q^{39} \) \(\mathstrut +\mathstrut 32q^{40} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut +\mathstrut 105q^{43} \) \(\mathstrut +\mathstrut 54q^{44} \) \(\mathstrut +\mathstrut 29q^{45} \) \(\mathstrut +\mathstrut 104q^{46} \) \(\mathstrut +\mathstrut 33q^{47} \) \(\mathstrut +\mathstrut 16q^{48} \) \(\mathstrut +\mathstrut 132q^{49} \) \(\mathstrut -\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 53q^{51} \) \(\mathstrut -\mathstrut 11q^{52} \) \(\mathstrut +\mathstrut 48q^{53} \) \(\mathstrut +\mathstrut 11q^{54} \) \(\mathstrut +\mathstrut 118q^{55} \) \(\mathstrut +\mathstrut 30q^{56} \) \(\mathstrut +\mathstrut 93q^{57} \) \(\mathstrut +\mathstrut 87q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut +\mathstrut 41q^{60} \) \(\mathstrut +\mathstrut 54q^{61} \) \(\mathstrut -\mathstrut 28q^{62} \) \(\mathstrut +\mathstrut 178q^{63} \) \(\mathstrut +\mathstrut 376q^{64} \) \(\mathstrut +\mathstrut 22q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 123q^{67} \) \(\mathstrut -\mathstrut 47q^{68} \) \(\mathstrut +\mathstrut 58q^{69} \) \(\mathstrut +\mathstrut 22q^{70} \) \(\mathstrut +\mathstrut 108q^{71} \) \(\mathstrut +\mathstrut 97q^{72} \) \(\mathstrut +\mathstrut q^{73} \) \(\mathstrut -\mathstrut 10q^{74} \) \(\mathstrut +\mathstrut 23q^{75} \) \(\mathstrut +\mathstrut 71q^{76} \) \(\mathstrut +\mathstrut 32q^{77} \) \(\mathstrut +\mathstrut 5q^{78} \) \(\mathstrut +\mathstrut 204q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut +\mathstrut 296q^{81} \) \(\mathstrut +\mathstrut 80q^{82} \) \(\mathstrut -\mathstrut 10q^{83} \) \(\mathstrut +\mathstrut 30q^{84} \) \(\mathstrut +\mathstrut 94q^{85} \) \(\mathstrut +\mathstrut 48q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut +\mathstrut 155q^{88} \) \(\mathstrut +\mathstrut q^{89} \) \(\mathstrut -\mathstrut 66q^{90} \) \(\mathstrut +\mathstrut 16q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 90q^{93} \) \(\mathstrut +\mathstrut 79q^{94} \) \(\mathstrut +\mathstrut 100q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut +\mathstrut 18q^{97} \) \(\mathstrut +\mathstrut 8q^{98} \) \(\mathstrut +\mathstrut 96q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.78355 −1.96826 −0.984132 0.177438i \(-0.943219\pi\)
−0.984132 + 0.177438i \(0.943219\pi\)
\(3\) 3.33951 1.92807 0.964034 0.265780i \(-0.0856294\pi\)
0.964034 + 0.265780i \(0.0856294\pi\)
\(4\) 5.74813 2.87406
\(5\) 2.68755 1.20191 0.600954 0.799284i \(-0.294788\pi\)
0.600954 + 0.799284i \(0.294788\pi\)
\(6\) −9.29568 −3.79495
\(7\) 1.00000 0.377964
\(8\) −10.4331 −3.68865
\(9\) 8.15233 2.71744
\(10\) −7.48091 −2.36567
\(11\) −2.52684 −0.761872 −0.380936 0.924601i \(-0.624398\pi\)
−0.380936 + 0.924601i \(0.624398\pi\)
\(12\) 19.1959 5.54139
\(13\) −4.90685 −1.36092 −0.680458 0.732787i \(-0.738219\pi\)
−0.680458 + 0.732787i \(0.738219\pi\)
\(14\) −2.78355 −0.743934
\(15\) 8.97509 2.31736
\(16\) 17.5447 4.38618
\(17\) −0.898319 −0.217874 −0.108937 0.994049i \(-0.534745\pi\)
−0.108937 + 0.994049i \(0.534745\pi\)
\(18\) −22.6924 −5.34865
\(19\) 1.96499 0.450800 0.225400 0.974266i \(-0.427631\pi\)
0.225400 + 0.974266i \(0.427631\pi\)
\(20\) 15.4484 3.45436
\(21\) 3.33951 0.728741
\(22\) 7.03359 1.49957
\(23\) −7.40366 −1.54377 −0.771884 0.635763i \(-0.780686\pi\)
−0.771884 + 0.635763i \(0.780686\pi\)
\(24\) −34.8414 −7.11197
\(25\) 2.22291 0.444581
\(26\) 13.6585 2.67864
\(27\) 17.2063 3.31135
\(28\) 5.74813 1.08629
\(29\) 3.52400 0.654391 0.327195 0.944957i \(-0.393896\pi\)
0.327195 + 0.944957i \(0.393896\pi\)
\(30\) −24.9826 −4.56117
\(31\) 5.35439 0.961677 0.480838 0.876809i \(-0.340332\pi\)
0.480838 + 0.876809i \(0.340332\pi\)
\(32\) −27.9703 −4.94450
\(33\) −8.43842 −1.46894
\(34\) 2.50051 0.428834
\(35\) 2.68755 0.454278
\(36\) 46.8606 7.81011
\(37\) 10.1575 1.66989 0.834945 0.550333i \(-0.185499\pi\)
0.834945 + 0.550333i \(0.185499\pi\)
\(38\) −5.46964 −0.887293
\(39\) −16.3865 −2.62394
\(40\) −28.0394 −4.43342
\(41\) 3.52367 0.550305 0.275153 0.961401i \(-0.411272\pi\)
0.275153 + 0.961401i \(0.411272\pi\)
\(42\) −9.29568 −1.43435
\(43\) 2.64184 0.402876 0.201438 0.979501i \(-0.435439\pi\)
0.201438 + 0.979501i \(0.435439\pi\)
\(44\) −14.5246 −2.18967
\(45\) 21.9098 3.26612
\(46\) 20.6084 3.03854
\(47\) 4.92135 0.717852 0.358926 0.933366i \(-0.383143\pi\)
0.358926 + 0.933366i \(0.383143\pi\)
\(48\) 58.5907 8.45684
\(49\) 1.00000 0.142857
\(50\) −6.18756 −0.875053
\(51\) −2.99995 −0.420077
\(52\) −28.2052 −3.91136
\(53\) 10.7700 1.47938 0.739689 0.672949i \(-0.234973\pi\)
0.739689 + 0.672949i \(0.234973\pi\)
\(54\) −47.8944 −6.51761
\(55\) −6.79101 −0.915700
\(56\) −10.4331 −1.39418
\(57\) 6.56211 0.869172
\(58\) −9.80922 −1.28801
\(59\) −3.69514 −0.481067 −0.240533 0.970641i \(-0.577322\pi\)
−0.240533 + 0.970641i \(0.577322\pi\)
\(60\) 51.5900 6.66023
\(61\) 4.74191 0.607139 0.303570 0.952809i \(-0.401821\pi\)
0.303570 + 0.952809i \(0.401821\pi\)
\(62\) −14.9042 −1.89283
\(63\) 8.15233 1.02710
\(64\) 42.7673 5.34591
\(65\) −13.1874 −1.63570
\(66\) 23.4887 2.89126
\(67\) 15.0912 1.84368 0.921840 0.387570i \(-0.126685\pi\)
0.921840 + 0.387570i \(0.126685\pi\)
\(68\) −5.16365 −0.626185
\(69\) −24.7246 −2.97649
\(70\) −7.48091 −0.894140
\(71\) −4.59300 −0.545089 −0.272545 0.962143i \(-0.587865\pi\)
−0.272545 + 0.962143i \(0.587865\pi\)
\(72\) −85.0539 −10.0237
\(73\) 0.997451 0.116743 0.0583714 0.998295i \(-0.481409\pi\)
0.0583714 + 0.998295i \(0.481409\pi\)
\(74\) −28.2740 −3.28679
\(75\) 7.42342 0.857182
\(76\) 11.2950 1.29563
\(77\) −2.52684 −0.287961
\(78\) 45.6126 5.16461
\(79\) −2.20739 −0.248351 −0.124175 0.992260i \(-0.539629\pi\)
−0.124175 + 0.992260i \(0.539629\pi\)
\(80\) 47.1522 5.27178
\(81\) 33.0035 3.66706
\(82\) −9.80830 −1.08315
\(83\) 6.11616 0.671336 0.335668 0.941980i \(-0.391038\pi\)
0.335668 + 0.941980i \(0.391038\pi\)
\(84\) 19.1959 2.09445
\(85\) −2.41427 −0.261865
\(86\) −7.35367 −0.792967
\(87\) 11.7684 1.26171
\(88\) 26.3628 2.81028
\(89\) −0.258006 −0.0273486 −0.0136743 0.999907i \(-0.504353\pi\)
−0.0136743 + 0.999907i \(0.504353\pi\)
\(90\) −60.9869 −6.42858
\(91\) −4.90685 −0.514378
\(92\) −42.5571 −4.43689
\(93\) 17.8810 1.85418
\(94\) −13.6988 −1.41292
\(95\) 5.28100 0.541820
\(96\) −93.4072 −9.53333
\(97\) −12.8683 −1.30658 −0.653289 0.757109i \(-0.726611\pi\)
−0.653289 + 0.757109i \(0.726611\pi\)
\(98\) −2.78355 −0.281181
\(99\) −20.5997 −2.07035
\(100\) 12.7775 1.27775
\(101\) 8.24089 0.820000 0.410000 0.912086i \(-0.365529\pi\)
0.410000 + 0.912086i \(0.365529\pi\)
\(102\) 8.35049 0.826822
\(103\) −15.5304 −1.53025 −0.765126 0.643881i \(-0.777323\pi\)
−0.765126 + 0.643881i \(0.777323\pi\)
\(104\) 51.1936 5.01995
\(105\) 8.97509 0.875879
\(106\) −29.9789 −2.91181
\(107\) −9.87896 −0.955035 −0.477518 0.878622i \(-0.658463\pi\)
−0.477518 + 0.878622i \(0.658463\pi\)
\(108\) 98.9038 9.51703
\(109\) −13.9776 −1.33881 −0.669407 0.742895i \(-0.733452\pi\)
−0.669407 + 0.742895i \(0.733452\pi\)
\(110\) 18.9031 1.80234
\(111\) 33.9212 3.21966
\(112\) 17.5447 1.65782
\(113\) 6.40810 0.602824 0.301412 0.953494i \(-0.402542\pi\)
0.301412 + 0.953494i \(0.402542\pi\)
\(114\) −18.2659 −1.71076
\(115\) −19.8977 −1.85547
\(116\) 20.2564 1.88076
\(117\) −40.0023 −3.69822
\(118\) 10.2856 0.946866
\(119\) −0.898319 −0.0823488
\(120\) −93.6378 −8.54793
\(121\) −4.61506 −0.419551
\(122\) −13.1993 −1.19501
\(123\) 11.7673 1.06103
\(124\) 30.7777 2.76392
\(125\) −7.46357 −0.667562
\(126\) −22.6924 −2.02160
\(127\) 14.9068 1.32277 0.661383 0.750048i \(-0.269970\pi\)
0.661383 + 0.750048i \(0.269970\pi\)
\(128\) −63.1040 −5.57765
\(129\) 8.82244 0.776772
\(130\) 36.7077 3.21948
\(131\) 15.7376 1.37500 0.687499 0.726185i \(-0.258708\pi\)
0.687499 + 0.726185i \(0.258708\pi\)
\(132\) −48.5051 −4.22183
\(133\) 1.96499 0.170386
\(134\) −42.0070 −3.62885
\(135\) 46.2427 3.97993
\(136\) 9.37224 0.803663
\(137\) −13.4824 −1.15188 −0.575938 0.817493i \(-0.695363\pi\)
−0.575938 + 0.817493i \(0.695363\pi\)
\(138\) 68.8220 5.85852
\(139\) 19.3976 1.64528 0.822641 0.568560i \(-0.192499\pi\)
0.822641 + 0.568560i \(0.192499\pi\)
\(140\) 15.4484 1.30562
\(141\) 16.4349 1.38407
\(142\) 12.7848 1.07288
\(143\) 12.3989 1.03684
\(144\) 143.030 11.9192
\(145\) 9.47092 0.786517
\(146\) −2.77645 −0.229781
\(147\) 3.33951 0.275438
\(148\) 58.3869 4.79937
\(149\) −15.4967 −1.26954 −0.634771 0.772700i \(-0.718906\pi\)
−0.634771 + 0.772700i \(0.718906\pi\)
\(150\) −20.6634 −1.68716
\(151\) 6.75090 0.549380 0.274690 0.961533i \(-0.411425\pi\)
0.274690 + 0.961533i \(0.411425\pi\)
\(152\) −20.5009 −1.66284
\(153\) −7.32340 −0.592062
\(154\) 7.03359 0.566782
\(155\) 14.3902 1.15585
\(156\) −94.1916 −7.54137
\(157\) 16.2790 1.29920 0.649602 0.760275i \(-0.274936\pi\)
0.649602 + 0.760275i \(0.274936\pi\)
\(158\) 6.14437 0.488820
\(159\) 35.9666 2.85234
\(160\) −75.1715 −5.94283
\(161\) −7.40366 −0.583490
\(162\) −91.8669 −7.21774
\(163\) −19.5637 −1.53235 −0.766174 0.642633i \(-0.777842\pi\)
−0.766174 + 0.642633i \(0.777842\pi\)
\(164\) 20.2545 1.58161
\(165\) −22.6787 −1.76553
\(166\) −17.0246 −1.32137
\(167\) −17.3096 −1.33946 −0.669730 0.742604i \(-0.733590\pi\)
−0.669730 + 0.742604i \(0.733590\pi\)
\(168\) −34.8414 −2.68807
\(169\) 11.0772 0.852094
\(170\) 6.72024 0.515419
\(171\) 16.0193 1.22502
\(172\) 15.1856 1.15789
\(173\) 0.548365 0.0416915 0.0208457 0.999783i \(-0.493364\pi\)
0.0208457 + 0.999783i \(0.493364\pi\)
\(174\) −32.7580 −2.48338
\(175\) 2.22291 0.168036
\(176\) −44.3327 −3.34170
\(177\) −12.3400 −0.927529
\(178\) 0.718172 0.0538292
\(179\) −0.833334 −0.0622863 −0.0311432 0.999515i \(-0.509915\pi\)
−0.0311432 + 0.999515i \(0.509915\pi\)
\(180\) 125.940 9.38702
\(181\) 4.58760 0.340994 0.170497 0.985358i \(-0.445463\pi\)
0.170497 + 0.985358i \(0.445463\pi\)
\(182\) 13.6585 1.01243
\(183\) 15.8357 1.17061
\(184\) 77.2429 5.69442
\(185\) 27.2989 2.00705
\(186\) −49.7727 −3.64951
\(187\) 2.26991 0.165992
\(188\) 28.2885 2.06315
\(189\) 17.2063 1.25157
\(190\) −14.6999 −1.06644
\(191\) 8.06570 0.583614 0.291807 0.956477i \(-0.405744\pi\)
0.291807 + 0.956477i \(0.405744\pi\)
\(192\) 142.822 10.3073
\(193\) −17.8443 −1.28446 −0.642230 0.766512i \(-0.721990\pi\)
−0.642230 + 0.766512i \(0.721990\pi\)
\(194\) 35.8195 2.57169
\(195\) −44.0395 −3.15373
\(196\) 5.74813 0.410580
\(197\) 18.2105 1.29744 0.648721 0.761026i \(-0.275304\pi\)
0.648721 + 0.761026i \(0.275304\pi\)
\(198\) 57.3401 4.07499
\(199\) 7.39789 0.524422 0.262211 0.965011i \(-0.415548\pi\)
0.262211 + 0.965011i \(0.415548\pi\)
\(200\) −23.1918 −1.63990
\(201\) 50.3971 3.55474
\(202\) −22.9389 −1.61398
\(203\) 3.52400 0.247336
\(204\) −17.2441 −1.20733
\(205\) 9.47003 0.661416
\(206\) 43.2295 3.01194
\(207\) −60.3571 −4.19511
\(208\) −86.0893 −5.96922
\(209\) −4.96522 −0.343452
\(210\) −24.9826 −1.72396
\(211\) 15.7152 1.08188 0.540940 0.841061i \(-0.318069\pi\)
0.540940 + 0.841061i \(0.318069\pi\)
\(212\) 61.9075 4.25182
\(213\) −15.3384 −1.05097
\(214\) 27.4985 1.87976
\(215\) 7.10005 0.484220
\(216\) −179.514 −12.2144
\(217\) 5.35439 0.363480
\(218\) 38.9074 2.63514
\(219\) 3.33100 0.225088
\(220\) −39.0356 −2.63178
\(221\) 4.40792 0.296509
\(222\) −94.4213 −6.33714
\(223\) 18.1665 1.21652 0.608260 0.793738i \(-0.291868\pi\)
0.608260 + 0.793738i \(0.291868\pi\)
\(224\) −27.9703 −1.86885
\(225\) 18.1219 1.20812
\(226\) −17.8372 −1.18652
\(227\) −16.9383 −1.12423 −0.562116 0.827058i \(-0.690013\pi\)
−0.562116 + 0.827058i \(0.690013\pi\)
\(228\) 37.7198 2.49806
\(229\) 7.58780 0.501416 0.250708 0.968063i \(-0.419337\pi\)
0.250708 + 0.968063i \(0.419337\pi\)
\(230\) 55.3861 3.65205
\(231\) −8.43842 −0.555207
\(232\) −36.7662 −2.41382
\(233\) 1.43260 0.0938528 0.0469264 0.998898i \(-0.485057\pi\)
0.0469264 + 0.998898i \(0.485057\pi\)
\(234\) 111.348 7.27906
\(235\) 13.2263 0.862792
\(236\) −21.2401 −1.38262
\(237\) −7.37160 −0.478837
\(238\) 2.50051 0.162084
\(239\) 19.8979 1.28709 0.643545 0.765409i \(-0.277463\pi\)
0.643545 + 0.765409i \(0.277463\pi\)
\(240\) 157.465 10.1643
\(241\) 9.23048 0.594587 0.297294 0.954786i \(-0.403916\pi\)
0.297294 + 0.954786i \(0.403916\pi\)
\(242\) 12.8462 0.825787
\(243\) 58.5969 3.75899
\(244\) 27.2571 1.74496
\(245\) 2.68755 0.171701
\(246\) −32.7549 −2.08838
\(247\) −9.64192 −0.613501
\(248\) −55.8628 −3.54729
\(249\) 20.4250 1.29438
\(250\) 20.7752 1.31394
\(251\) −16.1184 −1.01739 −0.508694 0.860948i \(-0.669871\pi\)
−0.508694 + 0.860948i \(0.669871\pi\)
\(252\) 46.8606 2.95194
\(253\) 18.7079 1.17615
\(254\) −41.4938 −2.60355
\(255\) −8.06250 −0.504893
\(256\) 90.1182 5.63239
\(257\) 11.4760 0.715856 0.357928 0.933749i \(-0.383483\pi\)
0.357928 + 0.933749i \(0.383483\pi\)
\(258\) −24.5577 −1.52889
\(259\) 10.1575 0.631159
\(260\) −75.8028 −4.70109
\(261\) 28.7288 1.77827
\(262\) −43.8063 −2.70636
\(263\) −20.6072 −1.27070 −0.635348 0.772226i \(-0.719143\pi\)
−0.635348 + 0.772226i \(0.719143\pi\)
\(264\) 88.0387 5.41841
\(265\) 28.9450 1.77807
\(266\) −5.46964 −0.335365
\(267\) −0.861614 −0.0527299
\(268\) 86.7460 5.29885
\(269\) −21.2595 −1.29621 −0.648107 0.761550i \(-0.724439\pi\)
−0.648107 + 0.761550i \(0.724439\pi\)
\(270\) −128.719 −7.83356
\(271\) 3.13508 0.190443 0.0952213 0.995456i \(-0.469644\pi\)
0.0952213 + 0.995456i \(0.469644\pi\)
\(272\) −15.7607 −0.955636
\(273\) −16.3865 −0.991756
\(274\) 37.5288 2.26720
\(275\) −5.61694 −0.338714
\(276\) −142.120 −8.55462
\(277\) 1.68902 0.101483 0.0507416 0.998712i \(-0.483842\pi\)
0.0507416 + 0.998712i \(0.483842\pi\)
\(278\) −53.9941 −3.23835
\(279\) 43.6508 2.61330
\(280\) −28.0394 −1.67567
\(281\) 30.7213 1.83268 0.916340 0.400401i \(-0.131129\pi\)
0.916340 + 0.400401i \(0.131129\pi\)
\(282\) −45.7473 −2.72421
\(283\) 7.82297 0.465027 0.232514 0.972593i \(-0.425305\pi\)
0.232514 + 0.972593i \(0.425305\pi\)
\(284\) −26.4012 −1.56662
\(285\) 17.6360 1.04466
\(286\) −34.5128 −2.04078
\(287\) 3.52367 0.207996
\(288\) −228.023 −13.4364
\(289\) −16.1930 −0.952531
\(290\) −26.3627 −1.54807
\(291\) −42.9738 −2.51917
\(292\) 5.73347 0.335526
\(293\) −14.1345 −0.825746 −0.412873 0.910789i \(-0.635475\pi\)
−0.412873 + 0.910789i \(0.635475\pi\)
\(294\) −9.29568 −0.542135
\(295\) −9.93087 −0.578197
\(296\) −105.975 −6.15964
\(297\) −43.4776 −2.52282
\(298\) 43.1359 2.49879
\(299\) 36.3287 2.10094
\(300\) 42.6707 2.46360
\(301\) 2.64184 0.152273
\(302\) −18.7914 −1.08133
\(303\) 27.5206 1.58101
\(304\) 34.4752 1.97729
\(305\) 12.7441 0.729725
\(306\) 20.3850 1.16533
\(307\) −12.1644 −0.694259 −0.347130 0.937817i \(-0.612844\pi\)
−0.347130 + 0.937817i \(0.612844\pi\)
\(308\) −14.5246 −0.827617
\(309\) −51.8638 −2.95043
\(310\) −40.0557 −2.27501
\(311\) 12.5605 0.712240 0.356120 0.934440i \(-0.384099\pi\)
0.356120 + 0.934440i \(0.384099\pi\)
\(312\) 170.962 9.67880
\(313\) −26.9599 −1.52386 −0.761932 0.647657i \(-0.775749\pi\)
−0.761932 + 0.647657i \(0.775749\pi\)
\(314\) −45.3133 −2.55717
\(315\) 21.9098 1.23448
\(316\) −12.6883 −0.713775
\(317\) 0.212403 0.0119297 0.00596486 0.999982i \(-0.498101\pi\)
0.00596486 + 0.999982i \(0.498101\pi\)
\(318\) −100.115 −5.61416
\(319\) −8.90460 −0.498562
\(320\) 114.939 6.42528
\(321\) −32.9909 −1.84137
\(322\) 20.6084 1.14846
\(323\) −1.76519 −0.0982178
\(324\) 189.709 10.5394
\(325\) −10.9075 −0.605038
\(326\) 54.4565 3.01607
\(327\) −46.6785 −2.58133
\(328\) −36.7628 −2.02988
\(329\) 4.92135 0.271323
\(330\) 63.1271 3.47503
\(331\) 32.4629 1.78432 0.892161 0.451717i \(-0.149188\pi\)
0.892161 + 0.451717i \(0.149188\pi\)
\(332\) 35.1564 1.92946
\(333\) 82.8077 4.53784
\(334\) 48.1822 2.63641
\(335\) 40.5582 2.21593
\(336\) 58.5907 3.19639
\(337\) −18.4264 −1.00375 −0.501875 0.864940i \(-0.667356\pi\)
−0.501875 + 0.864940i \(0.667356\pi\)
\(338\) −30.8340 −1.67715
\(339\) 21.3999 1.16228
\(340\) −13.8776 −0.752616
\(341\) −13.5297 −0.732675
\(342\) −44.5903 −2.41117
\(343\) 1.00000 0.0539949
\(344\) −27.5625 −1.48607
\(345\) −66.4485 −3.57747
\(346\) −1.52640 −0.0820598
\(347\) −4.83747 −0.259689 −0.129845 0.991534i \(-0.541448\pi\)
−0.129845 + 0.991534i \(0.541448\pi\)
\(348\) 67.6465 3.62623
\(349\) −27.2657 −1.45950 −0.729749 0.683715i \(-0.760363\pi\)
−0.729749 + 0.683715i \(0.760363\pi\)
\(350\) −6.18756 −0.330739
\(351\) −84.4287 −4.50647
\(352\) 70.6766 3.76708
\(353\) −28.4196 −1.51262 −0.756311 0.654212i \(-0.773000\pi\)
−0.756311 + 0.654212i \(0.773000\pi\)
\(354\) 34.3489 1.82562
\(355\) −12.3439 −0.655147
\(356\) −1.48305 −0.0786016
\(357\) −2.99995 −0.158774
\(358\) 2.31962 0.122596
\(359\) −11.5307 −0.608566 −0.304283 0.952582i \(-0.598417\pi\)
−0.304283 + 0.952582i \(0.598417\pi\)
\(360\) −228.586 −12.0476
\(361\) −15.1388 −0.796780
\(362\) −12.7698 −0.671166
\(363\) −15.4120 −0.808922
\(364\) −28.2052 −1.47836
\(365\) 2.68070 0.140314
\(366\) −44.0793 −2.30406
\(367\) −27.2059 −1.42014 −0.710069 0.704133i \(-0.751336\pi\)
−0.710069 + 0.704133i \(0.751336\pi\)
\(368\) −129.895 −6.77124
\(369\) 28.7262 1.49542
\(370\) −75.9877 −3.95041
\(371\) 10.7700 0.559152
\(372\) 102.782 5.32902
\(373\) 23.8295 1.23384 0.616922 0.787025i \(-0.288380\pi\)
0.616922 + 0.787025i \(0.288380\pi\)
\(374\) −6.31841 −0.326717
\(375\) −24.9247 −1.28710
\(376\) −51.3448 −2.64791
\(377\) −17.2918 −0.890571
\(378\) −47.8944 −2.46342
\(379\) −10.2577 −0.526902 −0.263451 0.964673i \(-0.584861\pi\)
−0.263451 + 0.964673i \(0.584861\pi\)
\(380\) 30.3559 1.55722
\(381\) 49.7815 2.55038
\(382\) −22.4512 −1.14871
\(383\) −34.2465 −1.74991 −0.874957 0.484200i \(-0.839111\pi\)
−0.874957 + 0.484200i \(0.839111\pi\)
\(384\) −210.736 −10.7541
\(385\) −6.79101 −0.346102
\(386\) 49.6704 2.52815
\(387\) 21.5371 1.09479
\(388\) −73.9686 −3.75519
\(389\) 11.2757 0.571701 0.285850 0.958274i \(-0.407724\pi\)
0.285850 + 0.958274i \(0.407724\pi\)
\(390\) 122.586 6.20738
\(391\) 6.65085 0.336348
\(392\) −10.4331 −0.526950
\(393\) 52.5558 2.65109
\(394\) −50.6897 −2.55371
\(395\) −5.93246 −0.298494
\(396\) −118.410 −5.95030
\(397\) 3.68603 0.184996 0.0924982 0.995713i \(-0.470515\pi\)
0.0924982 + 0.995713i \(0.470515\pi\)
\(398\) −20.5924 −1.03220
\(399\) 6.56211 0.328516
\(400\) 39.0002 1.95001
\(401\) −15.1300 −0.755555 −0.377777 0.925896i \(-0.623312\pi\)
−0.377777 + 0.925896i \(0.623312\pi\)
\(402\) −140.283 −6.99667
\(403\) −26.2732 −1.30876
\(404\) 47.3697 2.35673
\(405\) 88.6985 4.40747
\(406\) −9.80922 −0.486824
\(407\) −25.6665 −1.27224
\(408\) 31.2987 1.54952
\(409\) 11.7652 0.581751 0.290876 0.956761i \(-0.406053\pi\)
0.290876 + 0.956761i \(0.406053\pi\)
\(410\) −26.3603 −1.30184
\(411\) −45.0245 −2.22090
\(412\) −89.2705 −4.39804
\(413\) −3.69514 −0.181826
\(414\) 168.007 8.25708
\(415\) 16.4375 0.806883
\(416\) 137.246 6.72905
\(417\) 64.7785 3.17222
\(418\) 13.8209 0.676004
\(419\) −4.40570 −0.215233 −0.107616 0.994193i \(-0.534322\pi\)
−0.107616 + 0.994193i \(0.534322\pi\)
\(420\) 51.5900 2.51733
\(421\) 2.54369 0.123972 0.0619860 0.998077i \(-0.480257\pi\)
0.0619860 + 0.998077i \(0.480257\pi\)
\(422\) −43.7440 −2.12943
\(423\) 40.1204 1.95072
\(424\) −112.365 −5.45691
\(425\) −1.99688 −0.0968629
\(426\) 42.6951 2.06858
\(427\) 4.74191 0.229477
\(428\) −56.7855 −2.74483
\(429\) 41.4061 1.99911
\(430\) −19.7633 −0.953072
\(431\) −34.5764 −1.66548 −0.832742 0.553661i \(-0.813230\pi\)
−0.832742 + 0.553661i \(0.813230\pi\)
\(432\) 301.879 14.5242
\(433\) 1.26053 0.0605774 0.0302887 0.999541i \(-0.490357\pi\)
0.0302887 + 0.999541i \(0.490357\pi\)
\(434\) −14.9042 −0.715424
\(435\) 31.6282 1.51646
\(436\) −80.3452 −3.84784
\(437\) −14.5481 −0.695931
\(438\) −9.27199 −0.443033
\(439\) 38.1478 1.82070 0.910348 0.413844i \(-0.135814\pi\)
0.910348 + 0.413844i \(0.135814\pi\)
\(440\) 70.8512 3.37770
\(441\) 8.15233 0.388206
\(442\) −12.2697 −0.583608
\(443\) 5.85895 0.278367 0.139184 0.990267i \(-0.455552\pi\)
0.139184 + 0.990267i \(0.455552\pi\)
\(444\) 194.984 9.25351
\(445\) −0.693403 −0.0328705
\(446\) −50.5674 −2.39443
\(447\) −51.7515 −2.44776
\(448\) 42.7673 2.02056
\(449\) 8.75706 0.413271 0.206636 0.978418i \(-0.433749\pi\)
0.206636 + 0.978418i \(0.433749\pi\)
\(450\) −50.4430 −2.37791
\(451\) −8.90377 −0.419262
\(452\) 36.8346 1.73255
\(453\) 22.5447 1.05924
\(454\) 47.1484 2.21279
\(455\) −13.1874 −0.618235
\(456\) −68.4630 −3.20607
\(457\) 24.3779 1.14035 0.570174 0.821524i \(-0.306876\pi\)
0.570174 + 0.821524i \(0.306876\pi\)
\(458\) −21.1210 −0.986920
\(459\) −15.4567 −0.721458
\(460\) −114.374 −5.33273
\(461\) 5.55811 0.258867 0.129433 0.991588i \(-0.458684\pi\)
0.129433 + 0.991588i \(0.458684\pi\)
\(462\) 23.4887 1.09279
\(463\) −36.1419 −1.67966 −0.839828 0.542852i \(-0.817344\pi\)
−0.839828 + 0.542852i \(0.817344\pi\)
\(464\) 61.8276 2.87027
\(465\) 48.0561 2.22855
\(466\) −3.98771 −0.184727
\(467\) 25.8200 1.19481 0.597403 0.801941i \(-0.296199\pi\)
0.597403 + 0.801941i \(0.296199\pi\)
\(468\) −229.938 −10.6289
\(469\) 15.0912 0.696846
\(470\) −36.8161 −1.69820
\(471\) 54.3638 2.50495
\(472\) 38.5517 1.77449
\(473\) −6.67551 −0.306940
\(474\) 20.5192 0.942477
\(475\) 4.36799 0.200417
\(476\) −5.16365 −0.236676
\(477\) 87.8009 4.02013
\(478\) −55.3868 −2.53333
\(479\) −22.7515 −1.03954 −0.519771 0.854306i \(-0.673983\pi\)
−0.519771 + 0.854306i \(0.673983\pi\)
\(480\) −251.036 −11.4582
\(481\) −49.8416 −2.27258
\(482\) −25.6935 −1.17030
\(483\) −24.7246 −1.12501
\(484\) −26.5279 −1.20582
\(485\) −34.5841 −1.57039
\(486\) −163.107 −7.39869
\(487\) 19.5000 0.883631 0.441815 0.897106i \(-0.354335\pi\)
0.441815 + 0.897106i \(0.354335\pi\)
\(488\) −49.4727 −2.23953
\(489\) −65.3333 −2.95447
\(490\) −7.48091 −0.337953
\(491\) 0.825638 0.0372605 0.0186303 0.999826i \(-0.494069\pi\)
0.0186303 + 0.999826i \(0.494069\pi\)
\(492\) 67.6402 3.04945
\(493\) −3.16568 −0.142575
\(494\) 26.8387 1.20753
\(495\) −55.3626 −2.48836
\(496\) 93.9412 4.21808
\(497\) −4.59300 −0.206024
\(498\) −56.8539 −2.54768
\(499\) −6.39391 −0.286231 −0.143115 0.989706i \(-0.545712\pi\)
−0.143115 + 0.989706i \(0.545712\pi\)
\(500\) −42.9015 −1.91862
\(501\) −57.8058 −2.58257
\(502\) 44.8664 2.00249
\(503\) −1.65864 −0.0739551 −0.0369776 0.999316i \(-0.511773\pi\)
−0.0369776 + 0.999316i \(0.511773\pi\)
\(504\) −85.0539 −3.78860
\(505\) 22.1478 0.985563
\(506\) −52.0742 −2.31498
\(507\) 36.9925 1.64290
\(508\) 85.6863 3.80172
\(509\) −32.8921 −1.45792 −0.728959 0.684557i \(-0.759996\pi\)
−0.728959 + 0.684557i \(0.759996\pi\)
\(510\) 22.4423 0.993763
\(511\) 0.997451 0.0441246
\(512\) −124.640 −5.50838
\(513\) 33.8102 1.49276
\(514\) −31.9441 −1.40899
\(515\) −41.7386 −1.83922
\(516\) 50.7125 2.23249
\(517\) −12.4355 −0.546911
\(518\) −28.2740 −1.24229
\(519\) 1.83127 0.0803839
\(520\) 137.585 6.03351
\(521\) −25.7490 −1.12809 −0.564043 0.825746i \(-0.690755\pi\)
−0.564043 + 0.825746i \(0.690755\pi\)
\(522\) −79.9680 −3.50011
\(523\) 8.38881 0.366817 0.183408 0.983037i \(-0.441287\pi\)
0.183408 + 0.983037i \(0.441287\pi\)
\(524\) 90.4616 3.95183
\(525\) 7.42342 0.323985
\(526\) 57.3611 2.50106
\(527\) −4.80995 −0.209525
\(528\) −148.050 −6.44303
\(529\) 31.8141 1.38322
\(530\) −80.5696 −3.49972
\(531\) −30.1240 −1.30727
\(532\) 11.2950 0.489701
\(533\) −17.2902 −0.748920
\(534\) 2.39834 0.103786
\(535\) −26.5502 −1.14786
\(536\) −157.447 −6.80069
\(537\) −2.78293 −0.120092
\(538\) 59.1767 2.55129
\(539\) −2.52684 −0.108839
\(540\) 265.809 11.4386
\(541\) −15.9640 −0.686347 −0.343173 0.939272i \(-0.611502\pi\)
−0.343173 + 0.939272i \(0.611502\pi\)
\(542\) −8.72664 −0.374841
\(543\) 15.3203 0.657459
\(544\) 25.1263 1.07728
\(545\) −37.5655 −1.60913
\(546\) 45.6126 1.95204
\(547\) −12.7862 −0.546697 −0.273349 0.961915i \(-0.588131\pi\)
−0.273349 + 0.961915i \(0.588131\pi\)
\(548\) −77.4984 −3.31057
\(549\) 38.6576 1.64987
\(550\) 15.6350 0.666679
\(551\) 6.92463 0.294999
\(552\) 257.954 10.9792
\(553\) −2.20739 −0.0938677
\(554\) −4.70146 −0.199746
\(555\) 91.1649 3.86974
\(556\) 111.500 4.72865
\(557\) 32.8370 1.39135 0.695675 0.718357i \(-0.255106\pi\)
0.695675 + 0.718357i \(0.255106\pi\)
\(558\) −121.504 −5.14367
\(559\) −12.9631 −0.548281
\(560\) 47.1522 1.99254
\(561\) 7.58040 0.320045
\(562\) −85.5142 −3.60720
\(563\) −4.79678 −0.202160 −0.101080 0.994878i \(-0.532230\pi\)
−0.101080 + 0.994878i \(0.532230\pi\)
\(564\) 94.4698 3.97790
\(565\) 17.2221 0.724538
\(566\) −21.7756 −0.915296
\(567\) 33.0035 1.38602
\(568\) 47.9192 2.01064
\(569\) −28.2119 −1.18270 −0.591352 0.806413i \(-0.701406\pi\)
−0.591352 + 0.806413i \(0.701406\pi\)
\(570\) −49.0905 −2.05618
\(571\) 12.8718 0.538666 0.269333 0.963047i \(-0.413197\pi\)
0.269333 + 0.963047i \(0.413197\pi\)
\(572\) 71.2702 2.97996
\(573\) 26.9355 1.12525
\(574\) −9.80830 −0.409391
\(575\) −16.4576 −0.686331
\(576\) 348.653 14.5272
\(577\) −5.28478 −0.220008 −0.110004 0.993931i \(-0.535086\pi\)
−0.110004 + 0.993931i \(0.535086\pi\)
\(578\) 45.0740 1.87483
\(579\) −59.5912 −2.47652
\(580\) 54.4400 2.26050
\(581\) 6.11616 0.253741
\(582\) 119.620 4.95839
\(583\) −27.2142 −1.12710
\(584\) −10.4065 −0.430623
\(585\) −107.508 −4.44491
\(586\) 39.3440 1.62529
\(587\) −5.85564 −0.241688 −0.120844 0.992672i \(-0.538560\pi\)
−0.120844 + 0.992672i \(0.538560\pi\)
\(588\) 19.1959 0.791627
\(589\) 10.5213 0.433524
\(590\) 27.6430 1.13805
\(591\) 60.8141 2.50156
\(592\) 178.211 7.32443
\(593\) −39.8727 −1.63737 −0.818687 0.574240i \(-0.805297\pi\)
−0.818687 + 0.574240i \(0.805297\pi\)
\(594\) 121.022 4.96558
\(595\) −2.41427 −0.0989756
\(596\) −89.0772 −3.64874
\(597\) 24.7053 1.01112
\(598\) −101.122 −4.13521
\(599\) 21.6257 0.883602 0.441801 0.897113i \(-0.354340\pi\)
0.441801 + 0.897113i \(0.354340\pi\)
\(600\) −77.4491 −3.16185
\(601\) 6.15561 0.251092 0.125546 0.992088i \(-0.459932\pi\)
0.125546 + 0.992088i \(0.459932\pi\)
\(602\) −7.35367 −0.299713
\(603\) 123.028 5.01010
\(604\) 38.8050 1.57895
\(605\) −12.4032 −0.504261
\(606\) −76.6047 −3.11185
\(607\) −32.1224 −1.30381 −0.651904 0.758301i \(-0.726030\pi\)
−0.651904 + 0.758301i \(0.726030\pi\)
\(608\) −54.9614 −2.22898
\(609\) 11.7684 0.476881
\(610\) −35.4738 −1.43629
\(611\) −24.1483 −0.976937
\(612\) −42.0958 −1.70162
\(613\) 24.4930 0.989263 0.494632 0.869103i \(-0.335303\pi\)
0.494632 + 0.869103i \(0.335303\pi\)
\(614\) 33.8602 1.36649
\(615\) 31.6253 1.27525
\(616\) 26.3628 1.06219
\(617\) −11.9827 −0.482407 −0.241203 0.970475i \(-0.577542\pi\)
−0.241203 + 0.970475i \(0.577542\pi\)
\(618\) 144.365 5.80722
\(619\) 10.5974 0.425944 0.212972 0.977058i \(-0.431686\pi\)
0.212972 + 0.977058i \(0.431686\pi\)
\(620\) 82.7165 3.32198
\(621\) −127.389 −5.11196
\(622\) −34.9627 −1.40188
\(623\) −0.258006 −0.0103368
\(624\) −287.496 −11.5091
\(625\) −31.1732 −1.24693
\(626\) 75.0441 2.99937
\(627\) −16.5814 −0.662198
\(628\) 93.5736 3.73399
\(629\) −9.12472 −0.363826
\(630\) −60.9869 −2.42977
\(631\) −19.8811 −0.791454 −0.395727 0.918368i \(-0.629507\pi\)
−0.395727 + 0.918368i \(0.629507\pi\)
\(632\) 23.0299 0.916079
\(633\) 52.4811 2.08594
\(634\) −0.591232 −0.0234808
\(635\) 40.0628 1.58984
\(636\) 206.741 8.19780
\(637\) −4.90685 −0.194417
\(638\) 24.7864 0.981302
\(639\) −37.4437 −1.48125
\(640\) −169.595 −6.70382
\(641\) −25.1021 −0.991474 −0.495737 0.868473i \(-0.665102\pi\)
−0.495737 + 0.868473i \(0.665102\pi\)
\(642\) 91.8317 3.62431
\(643\) 26.5726 1.04792 0.523961 0.851742i \(-0.324454\pi\)
0.523961 + 0.851742i \(0.324454\pi\)
\(644\) −42.5571 −1.67699
\(645\) 23.7107 0.933608
\(646\) 4.91348 0.193318
\(647\) 20.7820 0.817024 0.408512 0.912753i \(-0.366048\pi\)
0.408512 + 0.912753i \(0.366048\pi\)
\(648\) −344.329 −13.5265
\(649\) 9.33705 0.366511
\(650\) 30.3615 1.19087
\(651\) 17.8810 0.700813
\(652\) −112.455 −4.40407
\(653\) −12.8734 −0.503775 −0.251887 0.967757i \(-0.581051\pi\)
−0.251887 + 0.967757i \(0.581051\pi\)
\(654\) 129.932 5.08073
\(655\) 42.2955 1.65262
\(656\) 61.8218 2.41374
\(657\) 8.13155 0.317242
\(658\) −13.6988 −0.534034
\(659\) −22.9558 −0.894231 −0.447116 0.894476i \(-0.647549\pi\)
−0.447116 + 0.894476i \(0.647549\pi\)
\(660\) −130.360 −5.07425
\(661\) 32.9435 1.28135 0.640677 0.767811i \(-0.278654\pi\)
0.640677 + 0.767811i \(0.278654\pi\)
\(662\) −90.3620 −3.51202
\(663\) 14.7203 0.571689
\(664\) −63.8104 −2.47632
\(665\) 5.28100 0.204789
\(666\) −230.499 −8.93166
\(667\) −26.0905 −1.01023
\(668\) −99.4981 −3.84970
\(669\) 60.6673 2.34553
\(670\) −112.896 −4.36154
\(671\) −11.9821 −0.462563
\(672\) −93.4072 −3.60326
\(673\) −23.0069 −0.886852 −0.443426 0.896311i \(-0.646237\pi\)
−0.443426 + 0.896311i \(0.646237\pi\)
\(674\) 51.2907 1.97565
\(675\) 38.2479 1.47216
\(676\) 63.6733 2.44897
\(677\) 0.672321 0.0258394 0.0129197 0.999917i \(-0.495887\pi\)
0.0129197 + 0.999917i \(0.495887\pi\)
\(678\) −59.5677 −2.28768
\(679\) −12.8683 −0.493840
\(680\) 25.1883 0.965928
\(681\) −56.5655 −2.16760
\(682\) 37.6606 1.44210
\(683\) −13.2574 −0.507282 −0.253641 0.967298i \(-0.581628\pi\)
−0.253641 + 0.967298i \(0.581628\pi\)
\(684\) 92.0807 3.52079
\(685\) −36.2345 −1.38445
\(686\) −2.78355 −0.106276
\(687\) 25.3396 0.966764
\(688\) 46.3502 1.76709
\(689\) −52.8470 −2.01331
\(690\) 184.962 7.04140
\(691\) 48.8133 1.85695 0.928473 0.371400i \(-0.121122\pi\)
0.928473 + 0.371400i \(0.121122\pi\)
\(692\) 3.15207 0.119824
\(693\) −20.5997 −0.782517
\(694\) 13.4653 0.511137
\(695\) 52.1319 1.97748
\(696\) −122.781 −4.65401
\(697\) −3.16538 −0.119897
\(698\) 75.8952 2.87268
\(699\) 4.78419 0.180955
\(700\) 12.7775 0.482946
\(701\) 34.6479 1.30863 0.654316 0.756221i \(-0.272957\pi\)
0.654316 + 0.756221i \(0.272957\pi\)
\(702\) 235.011 8.86992
\(703\) 19.9595 0.752786
\(704\) −108.066 −4.07290
\(705\) 44.1695 1.66352
\(706\) 79.1072 2.97724
\(707\) 8.24089 0.309931
\(708\) −70.9317 −2.66578
\(709\) −33.1037 −1.24323 −0.621617 0.783321i \(-0.713524\pi\)
−0.621617 + 0.783321i \(0.713524\pi\)
\(710\) 34.3598 1.28950
\(711\) −17.9954 −0.674879
\(712\) 2.69180 0.100879
\(713\) −39.6421 −1.48461
\(714\) 8.35049 0.312509
\(715\) 33.3225 1.24619
\(716\) −4.79011 −0.179015
\(717\) 66.4493 2.48160
\(718\) 32.0962 1.19782
\(719\) −14.6559 −0.546573 −0.273287 0.961933i \(-0.588111\pi\)
−0.273287 + 0.961933i \(0.588111\pi\)
\(720\) 384.400 14.3258
\(721\) −15.5304 −0.578381
\(722\) 42.1396 1.56827
\(723\) 30.8253 1.14640
\(724\) 26.3701 0.980037
\(725\) 7.83353 0.290930
\(726\) 42.9001 1.59217
\(727\) 27.5681 1.02244 0.511222 0.859449i \(-0.329193\pi\)
0.511222 + 0.859449i \(0.329193\pi\)
\(728\) 51.1936 1.89736
\(729\) 96.6743 3.58053
\(730\) −7.46184 −0.276175
\(731\) −2.37321 −0.0877764
\(732\) 91.0254 3.36439
\(733\) 31.0660 1.14745 0.573724 0.819049i \(-0.305498\pi\)
0.573724 + 0.819049i \(0.305498\pi\)
\(734\) 75.7289 2.79520
\(735\) 8.97509 0.331051
\(736\) 207.083 7.63317
\(737\) −38.1330 −1.40465
\(738\) −79.9606 −2.94339
\(739\) 52.1990 1.92017 0.960087 0.279703i \(-0.0902361\pi\)
0.960087 + 0.279703i \(0.0902361\pi\)
\(740\) 156.917 5.76840
\(741\) −32.1993 −1.18287
\(742\) −29.9789 −1.10056
\(743\) 0.203467 0.00746447 0.00373224 0.999993i \(-0.498812\pi\)
0.00373224 + 0.999993i \(0.498812\pi\)
\(744\) −186.554 −6.83941
\(745\) −41.6482 −1.52587
\(746\) −66.3304 −2.42853
\(747\) 49.8610 1.82432
\(748\) 13.0477 0.477073
\(749\) −9.87896 −0.360969
\(750\) 69.3790 2.53336
\(751\) −34.0461 −1.24236 −0.621181 0.783667i \(-0.713347\pi\)
−0.621181 + 0.783667i \(0.713347\pi\)
\(752\) 86.3435 3.14862
\(753\) −53.8277 −1.96159
\(754\) 48.1324 1.75288
\(755\) 18.1434 0.660304
\(756\) 98.9038 3.59710
\(757\) −34.4288 −1.25134 −0.625668 0.780090i \(-0.715173\pi\)
−0.625668 + 0.780090i \(0.715173\pi\)
\(758\) 28.5527 1.03708
\(759\) 62.4752 2.26771
\(760\) −55.0971 −1.99858
\(761\) −19.1195 −0.693082 −0.346541 0.938035i \(-0.612644\pi\)
−0.346541 + 0.938035i \(0.612644\pi\)
\(762\) −138.569 −5.01983
\(763\) −13.9776 −0.506024
\(764\) 46.3627 1.67734
\(765\) −19.6820 −0.711603
\(766\) 95.3267 3.44429
\(767\) 18.1315 0.654692
\(768\) 300.951 10.8596
\(769\) −38.5267 −1.38931 −0.694654 0.719344i \(-0.744442\pi\)
−0.694654 + 0.719344i \(0.744442\pi\)
\(770\) 18.9031 0.681220
\(771\) 38.3244 1.38022
\(772\) −102.571 −3.69162
\(773\) −4.05449 −0.145830 −0.0729149 0.997338i \(-0.523230\pi\)
−0.0729149 + 0.997338i \(0.523230\pi\)
\(774\) −59.9496 −2.15484
\(775\) 11.9023 0.427543
\(776\) 134.256 4.81951
\(777\) 33.9212 1.21692
\(778\) −31.3864 −1.12526
\(779\) 6.92398 0.248077
\(780\) −253.144 −9.06402
\(781\) 11.6058 0.415288
\(782\) −18.5129 −0.662021
\(783\) 60.6350 2.16692
\(784\) 17.5447 0.626597
\(785\) 43.7505 1.56152
\(786\) −146.292 −5.21805
\(787\) −50.4683 −1.79900 −0.899501 0.436920i \(-0.856069\pi\)
−0.899501 + 0.436920i \(0.856069\pi\)
\(788\) 104.676 3.72893
\(789\) −68.8180 −2.44999
\(790\) 16.5133 0.587516
\(791\) 6.40810 0.227846
\(792\) 214.918 7.63678
\(793\) −23.2679 −0.826266
\(794\) −10.2602 −0.364122
\(795\) 96.6620 3.42825
\(796\) 42.5240 1.50722
\(797\) 52.0598 1.84405 0.922026 0.387129i \(-0.126533\pi\)
0.922026 + 0.387129i \(0.126533\pi\)
\(798\) −18.2659 −0.646607
\(799\) −4.42094 −0.156402
\(800\) −62.1754 −2.19823
\(801\) −2.10335 −0.0743183
\(802\) 42.1150 1.48713
\(803\) −2.52040 −0.0889431
\(804\) 289.689 10.2165
\(805\) −19.8977 −0.701301
\(806\) 73.1327 2.57599
\(807\) −70.9963 −2.49919
\(808\) −85.9779 −3.02469
\(809\) 27.0305 0.950343 0.475171 0.879893i \(-0.342386\pi\)
0.475171 + 0.879893i \(0.342386\pi\)
\(810\) −246.896 −8.67506
\(811\) −45.0723 −1.58270 −0.791352 0.611361i \(-0.790622\pi\)
−0.791352 + 0.611361i \(0.790622\pi\)
\(812\) 20.2564 0.710861
\(813\) 10.4696 0.367186
\(814\) 71.4440 2.50411
\(815\) −52.5784 −1.84174
\(816\) −52.6332 −1.84253
\(817\) 5.19118 0.181616
\(818\) −32.7489 −1.14504
\(819\) −40.0023 −1.39779
\(820\) 54.4349 1.90095
\(821\) 34.1637 1.19232 0.596160 0.802866i \(-0.296692\pi\)
0.596160 + 0.802866i \(0.296692\pi\)
\(822\) 125.328 4.37131
\(823\) 19.7111 0.687086 0.343543 0.939137i \(-0.388373\pi\)
0.343543 + 0.939137i \(0.388373\pi\)
\(824\) 162.029 5.64456
\(825\) −18.7578 −0.653063
\(826\) 10.2856 0.357882
\(827\) −16.1912 −0.563022 −0.281511 0.959558i \(-0.590836\pi\)
−0.281511 + 0.959558i \(0.590836\pi\)
\(828\) −346.940 −12.0570
\(829\) 18.5905 0.645673 0.322837 0.946455i \(-0.395364\pi\)
0.322837 + 0.946455i \(0.395364\pi\)
\(830\) −45.7544 −1.58816
\(831\) 5.64049 0.195667
\(832\) −209.853 −7.27533
\(833\) −0.898319 −0.0311249
\(834\) −180.314 −6.24376
\(835\) −46.5205 −1.60991
\(836\) −28.5407 −0.987102
\(837\) 92.1291 3.18445
\(838\) 12.2635 0.423635
\(839\) −37.2509 −1.28604 −0.643022 0.765848i \(-0.722320\pi\)
−0.643022 + 0.765848i \(0.722320\pi\)
\(840\) −93.6378 −3.23081
\(841\) −16.5814 −0.571773
\(842\) −7.08048 −0.244010
\(843\) 102.594 3.53353
\(844\) 90.3330 3.10939
\(845\) 29.7706 1.02414
\(846\) −111.677 −3.83954
\(847\) −4.61506 −0.158575
\(848\) 188.957 6.48881
\(849\) 26.1249 0.896604
\(850\) 5.55840 0.190652
\(851\) −75.2030 −2.57793
\(852\) −88.1670 −3.02055
\(853\) −15.3883 −0.526887 −0.263444 0.964675i \(-0.584858\pi\)
−0.263444 + 0.964675i \(0.584858\pi\)
\(854\) −13.1993 −0.451672
\(855\) 43.0525 1.47236
\(856\) 103.068 3.52279
\(857\) −26.6079 −0.908907 −0.454454 0.890770i \(-0.650165\pi\)
−0.454454 + 0.890770i \(0.650165\pi\)
\(858\) −115.256 −3.93477
\(859\) 17.4030 0.593781 0.296891 0.954911i \(-0.404050\pi\)
0.296891 + 0.954911i \(0.404050\pi\)
\(860\) 40.8120 1.39168
\(861\) 11.7673 0.401030
\(862\) 96.2449 3.27811
\(863\) −1.00000 −0.0340404
\(864\) −481.265 −16.3730
\(865\) 1.47376 0.0501093
\(866\) −3.50876 −0.119232
\(867\) −54.0768 −1.83654
\(868\) 30.7777 1.04466
\(869\) 5.57773 0.189211
\(870\) −88.0387 −2.98479
\(871\) −74.0502 −2.50910
\(872\) 145.830 4.93842
\(873\) −104.907 −3.55055
\(874\) 40.4953 1.36978
\(875\) −7.46357 −0.252315
\(876\) 19.1470 0.646917
\(877\) 24.6938 0.833851 0.416925 0.908941i \(-0.363108\pi\)
0.416925 + 0.908941i \(0.363108\pi\)
\(878\) −106.186 −3.58361
\(879\) −47.2023 −1.59209
\(880\) −119.146 −4.01642
\(881\) −30.7811 −1.03704 −0.518521 0.855065i \(-0.673517\pi\)
−0.518521 + 0.855065i \(0.673517\pi\)
\(882\) −22.6924 −0.764093
\(883\) 42.6404 1.43496 0.717482 0.696578i \(-0.245295\pi\)
0.717482 + 0.696578i \(0.245295\pi\)
\(884\) 25.3373 0.852185
\(885\) −33.1642 −1.11480
\(886\) −16.3086 −0.547900
\(887\) 57.5076 1.93092 0.965458 0.260560i \(-0.0839071\pi\)
0.965458 + 0.260560i \(0.0839071\pi\)
\(888\) −353.903 −11.8762
\(889\) 14.9068 0.499959
\(890\) 1.93012 0.0646978
\(891\) −83.3948 −2.79383
\(892\) 104.423 3.49636
\(893\) 9.67040 0.323608
\(894\) 144.053 4.81784
\(895\) −2.23962 −0.0748624
\(896\) −63.1040 −2.10816
\(897\) 121.320 4.05076
\(898\) −24.3757 −0.813427
\(899\) 18.8689 0.629312
\(900\) 104.167 3.47223
\(901\) −9.67493 −0.322319
\(902\) 24.7841 0.825219
\(903\) 8.82244 0.293592
\(904\) −66.8563 −2.22361
\(905\) 12.3294 0.409843
\(906\) −62.7542 −2.08487
\(907\) −31.2796 −1.03862 −0.519312 0.854585i \(-0.673812\pi\)
−0.519312 + 0.854585i \(0.673812\pi\)
\(908\) −97.3633 −3.23111
\(909\) 67.1825 2.22830
\(910\) 36.7077 1.21685
\(911\) 51.8378 1.71746 0.858731 0.512427i \(-0.171253\pi\)
0.858731 + 0.512427i \(0.171253\pi\)
\(912\) 115.130 3.81234
\(913\) −15.4546 −0.511472
\(914\) −67.8569 −2.24451
\(915\) 42.5591 1.40696
\(916\) 43.6157 1.44110
\(917\) 15.7376 0.519701
\(918\) 43.0245 1.42002
\(919\) 17.4053 0.574149 0.287075 0.957908i \(-0.407317\pi\)
0.287075 + 0.957908i \(0.407317\pi\)
\(920\) 207.594 6.84417
\(921\) −40.6232 −1.33858
\(922\) −15.4713 −0.509519
\(923\) 22.5372 0.741821
\(924\) −48.5051 −1.59570
\(925\) 22.5793 0.742402
\(926\) 100.603 3.30601
\(927\) −126.609 −4.15837
\(928\) −98.5675 −3.23564
\(929\) −6.59507 −0.216377 −0.108189 0.994130i \(-0.534505\pi\)
−0.108189 + 0.994130i \(0.534505\pi\)
\(930\) −133.766 −4.38637
\(931\) 1.96499 0.0644000
\(932\) 8.23477 0.269739
\(933\) 41.9459 1.37325
\(934\) −71.8711 −2.35169
\(935\) 6.10050 0.199508
\(936\) 417.347 13.6414
\(937\) −18.8613 −0.616170 −0.308085 0.951359i \(-0.599688\pi\)
−0.308085 + 0.951359i \(0.599688\pi\)
\(938\) −42.0070 −1.37158
\(939\) −90.0329 −2.93811
\(940\) 76.0267 2.47972
\(941\) 17.9991 0.586755 0.293378 0.955997i \(-0.405221\pi\)
0.293378 + 0.955997i \(0.405221\pi\)
\(942\) −151.324 −4.93041
\(943\) −26.0881 −0.849544
\(944\) −64.8302 −2.11004
\(945\) 46.2427 1.50427
\(946\) 18.5816 0.604139
\(947\) 12.9401 0.420496 0.210248 0.977648i \(-0.432573\pi\)
0.210248 + 0.977648i \(0.432573\pi\)
\(948\) −42.3729 −1.37621
\(949\) −4.89435 −0.158877
\(950\) −12.1585 −0.394474
\(951\) 0.709321 0.0230013
\(952\) 9.37224 0.303756
\(953\) −21.0421 −0.681620 −0.340810 0.940132i \(-0.610701\pi\)
−0.340810 + 0.940132i \(0.610701\pi\)
\(954\) −244.398 −7.91267
\(955\) 21.6769 0.701450
\(956\) 114.376 3.69918
\(957\) −29.7370 −0.961261
\(958\) 63.3298 2.04609
\(959\) −13.4824 −0.435368
\(960\) 383.840 12.3884
\(961\) −2.33051 −0.0751778
\(962\) 138.736 4.47304
\(963\) −80.5366 −2.59526
\(964\) 53.0580 1.70888
\(965\) −47.9573 −1.54380
\(966\) 68.8220 2.21431
\(967\) −29.3495 −0.943816 −0.471908 0.881648i \(-0.656435\pi\)
−0.471908 + 0.881648i \(0.656435\pi\)
\(968\) 48.1493 1.54758
\(969\) −5.89487 −0.189370
\(970\) 96.2665 3.09093
\(971\) 47.3344 1.51903 0.759517 0.650488i \(-0.225435\pi\)
0.759517 + 0.650488i \(0.225435\pi\)
\(972\) 336.822 10.8036
\(973\) 19.3976 0.621858
\(974\) −54.2792 −1.73922
\(975\) −36.4256 −1.16655
\(976\) 83.1954 2.66302
\(977\) −24.5942 −0.786840 −0.393420 0.919359i \(-0.628708\pi\)
−0.393420 + 0.919359i \(0.628708\pi\)
\(978\) 181.858 5.81518
\(979\) 0.651941 0.0208361
\(980\) 15.4484 0.493480
\(981\) −113.950 −3.63816
\(982\) −2.29820 −0.0733386
\(983\) −39.8918 −1.27235 −0.636175 0.771545i \(-0.719484\pi\)
−0.636175 + 0.771545i \(0.719484\pi\)
\(984\) −122.770 −3.91375
\(985\) 48.9415 1.55941
\(986\) 8.81181 0.280625
\(987\) 16.4349 0.523128
\(988\) −55.4230 −1.76324
\(989\) −19.5592 −0.621948
\(990\) 154.104 4.89776
\(991\) 50.0976 1.59140 0.795701 0.605690i \(-0.207103\pi\)
0.795701 + 0.605690i \(0.207103\pi\)
\(992\) −149.764 −4.75501
\(993\) 108.410 3.44029
\(994\) 12.7848 0.405510
\(995\) 19.8822 0.630307
\(996\) 117.405 3.72013
\(997\) 13.3312 0.422203 0.211101 0.977464i \(-0.432295\pi\)
0.211101 + 0.977464i \(0.432295\pi\)
\(998\) 17.7977 0.563377
\(999\) 174.774 5.52959
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 \(a_p\))