Properties

Label 6026.2.a.h.1.18
Level 6026
Weight 2
Character 6026.1
Self dual Yes
Analytic conductor 48.118
Analytic rank 1
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.117852258\)
Analytic rank: \(1\)
Dimension: \(24\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+1.66164 q^{3}\) \(+1.00000 q^{4}\) \(+0.0681057 q^{5}\) \(-1.66164 q^{6}\) \(+0.103168 q^{7}\) \(-1.00000 q^{8}\) \(-0.238964 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+1.66164 q^{3}\) \(+1.00000 q^{4}\) \(+0.0681057 q^{5}\) \(-1.66164 q^{6}\) \(+0.103168 q^{7}\) \(-1.00000 q^{8}\) \(-0.238964 q^{9}\) \(-0.0681057 q^{10}\) \(-0.129315 q^{11}\) \(+1.66164 q^{12}\) \(-1.57480 q^{13}\) \(-0.103168 q^{14}\) \(+0.113167 q^{15}\) \(+1.00000 q^{16}\) \(+4.28009 q^{17}\) \(+0.238964 q^{18}\) \(+4.77084 q^{19}\) \(+0.0681057 q^{20}\) \(+0.171428 q^{21}\) \(+0.129315 q^{22}\) \(-1.00000 q^{23}\) \(-1.66164 q^{24}\) \(-4.99536 q^{25}\) \(+1.57480 q^{26}\) \(-5.38198 q^{27}\) \(+0.103168 q^{28}\) \(-5.98015 q^{29}\) \(-0.113167 q^{30}\) \(+3.37662 q^{31}\) \(-1.00000 q^{32}\) \(-0.214874 q^{33}\) \(-4.28009 q^{34}\) \(+0.00702635 q^{35}\) \(-0.238964 q^{36}\) \(-6.98679 q^{37}\) \(-4.77084 q^{38}\) \(-2.61675 q^{39}\) \(-0.0681057 q^{40}\) \(-0.948349 q^{41}\) \(-0.171428 q^{42}\) \(-13.0487 q^{43}\) \(-0.129315 q^{44}\) \(-0.0162748 q^{45}\) \(+1.00000 q^{46}\) \(-0.273217 q^{47}\) \(+1.66164 q^{48}\) \(-6.98936 q^{49}\) \(+4.99536 q^{50}\) \(+7.11195 q^{51}\) \(-1.57480 q^{52}\) \(-3.18399 q^{53}\) \(+5.38198 q^{54}\) \(-0.00880707 q^{55}\) \(-0.103168 q^{56}\) \(+7.92741 q^{57}\) \(+5.98015 q^{58}\) \(-9.41679 q^{59}\) \(+0.113167 q^{60}\) \(-4.95302 q^{61}\) \(-3.37662 q^{62}\) \(-0.0246535 q^{63}\) \(+1.00000 q^{64}\) \(-0.107253 q^{65}\) \(+0.214874 q^{66}\) \(+13.4210 q^{67}\) \(+4.28009 q^{68}\) \(-1.66164 q^{69}\) \(-0.00702635 q^{70}\) \(+3.25184 q^{71}\) \(+0.238964 q^{72}\) \(+2.62561 q^{73}\) \(+6.98679 q^{74}\) \(-8.30048 q^{75}\) \(+4.77084 q^{76}\) \(-0.0133412 q^{77}\) \(+2.61675 q^{78}\) \(+2.17954 q^{79}\) \(+0.0681057 q^{80}\) \(-8.22600 q^{81}\) \(+0.948349 q^{82}\) \(-2.80733 q^{83}\) \(+0.171428 q^{84}\) \(+0.291499 q^{85}\) \(+13.0487 q^{86}\) \(-9.93683 q^{87}\) \(+0.129315 q^{88}\) \(+8.53563 q^{89}\) \(+0.0162748 q^{90}\) \(-0.162470 q^{91}\) \(-1.00000 q^{92}\) \(+5.61072 q^{93}\) \(+0.273217 q^{94}\) \(+0.324922 q^{95}\) \(-1.66164 q^{96}\) \(+10.8859 q^{97}\) \(+6.98936 q^{98}\) \(+0.0309015 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 27q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 27q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut q^{12} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut 7q^{14} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 24q^{16} \) \(\mathstrut +\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 27q^{18} \) \(\mathstrut -\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut q^{20} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut q^{24} \) \(\mathstrut +\mathstrut q^{25} \) \(\mathstrut +\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut q^{27} \) \(\mathstrut -\mathstrut 7q^{28} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 6q^{30} \) \(\mathstrut -\mathstrut 23q^{31} \) \(\mathstrut -\mathstrut 24q^{32} \) \(\mathstrut -\mathstrut 6q^{33} \) \(\mathstrut -\mathstrut 5q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 27q^{36} \) \(\mathstrut -\mathstrut 6q^{37} \) \(\mathstrut +\mathstrut 20q^{38} \) \(\mathstrut -\mathstrut 39q^{39} \) \(\mathstrut +\mathstrut q^{40} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut -\mathstrut 44q^{43} \) \(\mathstrut -\mathstrut 4q^{44} \) \(\mathstrut -\mathstrut 13q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 32q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut -\mathstrut 13q^{49} \) \(\mathstrut -\mathstrut q^{50} \) \(\mathstrut -\mathstrut 44q^{51} \) \(\mathstrut -\mathstrut 5q^{52} \) \(\mathstrut +\mathstrut 21q^{53} \) \(\mathstrut +\mathstrut q^{54} \) \(\mathstrut -\mathstrut 13q^{55} \) \(\mathstrut +\mathstrut 7q^{56} \) \(\mathstrut +\mathstrut 10q^{57} \) \(\mathstrut +\mathstrut 6q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut -\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 40q^{61} \) \(\mathstrut +\mathstrut 23q^{62} \) \(\mathstrut -\mathstrut 54q^{63} \) \(\mathstrut +\mathstrut 24q^{64} \) \(\mathstrut -\mathstrut 29q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut -\mathstrut 17q^{67} \) \(\mathstrut +\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut q^{69} \) \(\mathstrut -\mathstrut 5q^{70} \) \(\mathstrut +\mathstrut 4q^{71} \) \(\mathstrut -\mathstrut 27q^{72} \) \(\mathstrut -\mathstrut 16q^{73} \) \(\mathstrut +\mathstrut 6q^{74} \) \(\mathstrut -\mathstrut 36q^{75} \) \(\mathstrut -\mathstrut 20q^{76} \) \(\mathstrut +\mathstrut 24q^{77} \) \(\mathstrut +\mathstrut 39q^{78} \) \(\mathstrut -\mathstrut 53q^{79} \) \(\mathstrut -\mathstrut q^{80} \) \(\mathstrut +\mathstrut 24q^{81} \) \(\mathstrut +\mathstrut q^{82} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 37q^{85} \) \(\mathstrut +\mathstrut 44q^{86} \) \(\mathstrut +\mathstrut 7q^{87} \) \(\mathstrut +\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 46q^{89} \) \(\mathstrut +\mathstrut 13q^{90} \) \(\mathstrut -\mathstrut 44q^{91} \) \(\mathstrut -\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 23q^{93} \) \(\mathstrut -\mathstrut 32q^{94} \) \(\mathstrut +\mathstrut 28q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut -\mathstrut 20q^{97} \) \(\mathstrut +\mathstrut 13q^{98} \) \(\mathstrut -\mathstrut 78q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 1.66164 0.959346 0.479673 0.877447i \(-0.340755\pi\)
0.479673 + 0.877447i \(0.340755\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.0681057 0.0304578 0.0152289 0.999884i \(-0.495152\pi\)
0.0152289 + 0.999884i \(0.495152\pi\)
\(6\) −1.66164 −0.678360
\(7\) 0.103168 0.0389939 0.0194970 0.999810i \(-0.493794\pi\)
0.0194970 + 0.999810i \(0.493794\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.238964 −0.0796546
\(10\) −0.0681057 −0.0215369
\(11\) −0.129315 −0.0389898 −0.0194949 0.999810i \(-0.506206\pi\)
−0.0194949 + 0.999810i \(0.506206\pi\)
\(12\) 1.66164 0.479673
\(13\) −1.57480 −0.436772 −0.218386 0.975863i \(-0.570079\pi\)
−0.218386 + 0.975863i \(0.570079\pi\)
\(14\) −0.103168 −0.0275729
\(15\) 0.113167 0.0292196
\(16\) 1.00000 0.250000
\(17\) 4.28009 1.03807 0.519037 0.854752i \(-0.326291\pi\)
0.519037 + 0.854752i \(0.326291\pi\)
\(18\) 0.238964 0.0563243
\(19\) 4.77084 1.09451 0.547253 0.836967i \(-0.315674\pi\)
0.547253 + 0.836967i \(0.315674\pi\)
\(20\) 0.0681057 0.0152289
\(21\) 0.171428 0.0374087
\(22\) 0.129315 0.0275700
\(23\) −1.00000 −0.208514
\(24\) −1.66164 −0.339180
\(25\) −4.99536 −0.999072
\(26\) 1.57480 0.308844
\(27\) −5.38198 −1.03576
\(28\) 0.103168 0.0194970
\(29\) −5.98015 −1.11049 −0.555243 0.831688i \(-0.687375\pi\)
−0.555243 + 0.831688i \(0.687375\pi\)
\(30\) −0.113167 −0.0206614
\(31\) 3.37662 0.606459 0.303230 0.952917i \(-0.401935\pi\)
0.303230 + 0.952917i \(0.401935\pi\)
\(32\) −1.00000 −0.176777
\(33\) −0.214874 −0.0374048
\(34\) −4.28009 −0.734029
\(35\) 0.00702635 0.00118767
\(36\) −0.238964 −0.0398273
\(37\) −6.98679 −1.14862 −0.574311 0.818637i \(-0.694730\pi\)
−0.574311 + 0.818637i \(0.694730\pi\)
\(38\) −4.77084 −0.773933
\(39\) −2.61675 −0.419015
\(40\) −0.0681057 −0.0107685
\(41\) −0.948349 −0.148107 −0.0740536 0.997254i \(-0.523594\pi\)
−0.0740536 + 0.997254i \(0.523594\pi\)
\(42\) −0.171428 −0.0264519
\(43\) −13.0487 −1.98991 −0.994956 0.100315i \(-0.968015\pi\)
−0.994956 + 0.100315i \(0.968015\pi\)
\(44\) −0.129315 −0.0194949
\(45\) −0.0162748 −0.00242611
\(46\) 1.00000 0.147442
\(47\) −0.273217 −0.0398528 −0.0199264 0.999801i \(-0.506343\pi\)
−0.0199264 + 0.999801i \(0.506343\pi\)
\(48\) 1.66164 0.239837
\(49\) −6.98936 −0.998479
\(50\) 4.99536 0.706451
\(51\) 7.11195 0.995873
\(52\) −1.57480 −0.218386
\(53\) −3.18399 −0.437354 −0.218677 0.975797i \(-0.570174\pi\)
−0.218677 + 0.975797i \(0.570174\pi\)
\(54\) 5.38198 0.732395
\(55\) −0.00880707 −0.00118755
\(56\) −0.103168 −0.0137864
\(57\) 7.92741 1.05001
\(58\) 5.98015 0.785232
\(59\) −9.41679 −1.22596 −0.612981 0.790098i \(-0.710030\pi\)
−0.612981 + 0.790098i \(0.710030\pi\)
\(60\) 0.113167 0.0146098
\(61\) −4.95302 −0.634169 −0.317084 0.948397i \(-0.602704\pi\)
−0.317084 + 0.948397i \(0.602704\pi\)
\(62\) −3.37662 −0.428832
\(63\) −0.0246535 −0.00310605
\(64\) 1.00000 0.125000
\(65\) −0.107253 −0.0133031
\(66\) 0.214874 0.0264492
\(67\) 13.4210 1.63963 0.819816 0.572626i \(-0.194075\pi\)
0.819816 + 0.572626i \(0.194075\pi\)
\(68\) 4.28009 0.519037
\(69\) −1.66164 −0.200038
\(70\) −0.00702635 −0.000839809 0
\(71\) 3.25184 0.385922 0.192961 0.981206i \(-0.438191\pi\)
0.192961 + 0.981206i \(0.438191\pi\)
\(72\) 0.238964 0.0281622
\(73\) 2.62561 0.307304 0.153652 0.988125i \(-0.450896\pi\)
0.153652 + 0.988125i \(0.450896\pi\)
\(74\) 6.98679 0.812198
\(75\) −8.30048 −0.958456
\(76\) 4.77084 0.547253
\(77\) −0.0133412 −0.00152037
\(78\) 2.61675 0.296289
\(79\) 2.17954 0.245218 0.122609 0.992455i \(-0.460874\pi\)
0.122609 + 0.992455i \(0.460874\pi\)
\(80\) 0.0681057 0.00761445
\(81\) −8.22600 −0.914001
\(82\) 0.948349 0.104728
\(83\) −2.80733 −0.308144 −0.154072 0.988060i \(-0.549239\pi\)
−0.154072 + 0.988060i \(0.549239\pi\)
\(84\) 0.171428 0.0187043
\(85\) 0.291499 0.0316175
\(86\) 13.0487 1.40708
\(87\) −9.93683 −1.06534
\(88\) 0.129315 0.0137850
\(89\) 8.53563 0.904775 0.452388 0.891821i \(-0.350572\pi\)
0.452388 + 0.891821i \(0.350572\pi\)
\(90\) 0.0162748 0.00171552
\(91\) −0.162470 −0.0170314
\(92\) −1.00000 −0.104257
\(93\) 5.61072 0.581805
\(94\) 0.273217 0.0281802
\(95\) 0.324922 0.0333363
\(96\) −1.66164 −0.169590
\(97\) 10.8859 1.10529 0.552646 0.833416i \(-0.313618\pi\)
0.552646 + 0.833416i \(0.313618\pi\)
\(98\) 6.98936 0.706032
\(99\) 0.0309015 0.00310572
\(100\) −4.99536 −0.499536
\(101\) 1.91639 0.190688 0.0953442 0.995444i \(-0.469605\pi\)
0.0953442 + 0.995444i \(0.469605\pi\)
\(102\) −7.11195 −0.704188
\(103\) 6.22040 0.612915 0.306457 0.951884i \(-0.400856\pi\)
0.306457 + 0.951884i \(0.400856\pi\)
\(104\) 1.57480 0.154422
\(105\) 0.0116752 0.00113939
\(106\) 3.18399 0.309256
\(107\) 6.76105 0.653616 0.326808 0.945091i \(-0.394027\pi\)
0.326808 + 0.945091i \(0.394027\pi\)
\(108\) −5.38198 −0.517881
\(109\) −5.02739 −0.481537 −0.240768 0.970583i \(-0.577399\pi\)
−0.240768 + 0.970583i \(0.577399\pi\)
\(110\) 0.00880707 0.000839721 0
\(111\) −11.6095 −1.10193
\(112\) 0.103168 0.00974848
\(113\) −19.2653 −1.81233 −0.906164 0.422926i \(-0.861003\pi\)
−0.906164 + 0.422926i \(0.861003\pi\)
\(114\) −7.92741 −0.742470
\(115\) −0.0681057 −0.00635089
\(116\) −5.98015 −0.555243
\(117\) 0.376321 0.0347909
\(118\) 9.41679 0.866886
\(119\) 0.441569 0.0404786
\(120\) −0.113167 −0.0103307
\(121\) −10.9833 −0.998480
\(122\) 4.95302 0.448425
\(123\) −1.57581 −0.142086
\(124\) 3.37662 0.303230
\(125\) −0.680742 −0.0608874
\(126\) 0.0246535 0.00219631
\(127\) 3.87668 0.344000 0.172000 0.985097i \(-0.444977\pi\)
0.172000 + 0.985097i \(0.444977\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −21.6822 −1.90901
\(130\) 0.107253 0.00940672
\(131\) −1.00000 −0.0873704
\(132\) −0.214874 −0.0187024
\(133\) 0.492199 0.0426791
\(134\) −13.4210 −1.15940
\(135\) −0.366544 −0.0315471
\(136\) −4.28009 −0.367015
\(137\) −6.06546 −0.518207 −0.259104 0.965850i \(-0.583427\pi\)
−0.259104 + 0.965850i \(0.583427\pi\)
\(138\) 1.66164 0.141448
\(139\) 3.01603 0.255817 0.127908 0.991786i \(-0.459174\pi\)
0.127908 + 0.991786i \(0.459174\pi\)
\(140\) 0.00702635 0.000593835 0
\(141\) −0.453988 −0.0382327
\(142\) −3.25184 −0.272888
\(143\) 0.203645 0.0170297
\(144\) −0.238964 −0.0199137
\(145\) −0.407282 −0.0338230
\(146\) −2.62561 −0.217297
\(147\) −11.6138 −0.957888
\(148\) −6.98679 −0.574311
\(149\) 22.4253 1.83715 0.918576 0.395245i \(-0.129340\pi\)
0.918576 + 0.395245i \(0.129340\pi\)
\(150\) 8.30048 0.677731
\(151\) −0.552905 −0.0449948 −0.0224974 0.999747i \(-0.507162\pi\)
−0.0224974 + 0.999747i \(0.507162\pi\)
\(152\) −4.77084 −0.386966
\(153\) −1.02279 −0.0826874
\(154\) 0.0133412 0.00107506
\(155\) 0.229967 0.0184714
\(156\) −2.61675 −0.209508
\(157\) −1.07714 −0.0859655 −0.0429828 0.999076i \(-0.513686\pi\)
−0.0429828 + 0.999076i \(0.513686\pi\)
\(158\) −2.17954 −0.173395
\(159\) −5.29063 −0.419574
\(160\) −0.0681057 −0.00538423
\(161\) −0.103168 −0.00813079
\(162\) 8.22600 0.646296
\(163\) 1.63737 0.128249 0.0641245 0.997942i \(-0.479575\pi\)
0.0641245 + 0.997942i \(0.479575\pi\)
\(164\) −0.948349 −0.0740536
\(165\) −0.0146342 −0.00113927
\(166\) 2.80733 0.217891
\(167\) 8.65968 0.670106 0.335053 0.942199i \(-0.391246\pi\)
0.335053 + 0.942199i \(0.391246\pi\)
\(168\) −0.171428 −0.0132260
\(169\) −10.5200 −0.809230
\(170\) −0.291499 −0.0223569
\(171\) −1.14006 −0.0871825
\(172\) −13.0487 −0.994956
\(173\) −19.0933 −1.45163 −0.725817 0.687888i \(-0.758538\pi\)
−0.725817 + 0.687888i \(0.758538\pi\)
\(174\) 9.93683 0.753309
\(175\) −0.515363 −0.0389577
\(176\) −0.129315 −0.00974746
\(177\) −15.6473 −1.17612
\(178\) −8.53563 −0.639773
\(179\) −19.5982 −1.46484 −0.732419 0.680854i \(-0.761609\pi\)
−0.732419 + 0.680854i \(0.761609\pi\)
\(180\) −0.0162748 −0.00121305
\(181\) −16.7947 −1.24834 −0.624172 0.781287i \(-0.714563\pi\)
−0.624172 + 0.781287i \(0.714563\pi\)
\(182\) 0.162470 0.0120430
\(183\) −8.23011 −0.608387
\(184\) 1.00000 0.0737210
\(185\) −0.475841 −0.0349845
\(186\) −5.61072 −0.411398
\(187\) −0.553478 −0.0404743
\(188\) −0.273217 −0.0199264
\(189\) −0.555249 −0.0403884
\(190\) −0.324922 −0.0235723
\(191\) 22.5027 1.62824 0.814118 0.580700i \(-0.197221\pi\)
0.814118 + 0.580700i \(0.197221\pi\)
\(192\) 1.66164 0.119918
\(193\) 1.78146 0.128232 0.0641161 0.997942i \(-0.479577\pi\)
0.0641161 + 0.997942i \(0.479577\pi\)
\(194\) −10.8859 −0.781560
\(195\) −0.178216 −0.0127623
\(196\) −6.98936 −0.499240
\(197\) −6.52172 −0.464653 −0.232327 0.972638i \(-0.574634\pi\)
−0.232327 + 0.972638i \(0.574634\pi\)
\(198\) −0.0309015 −0.00219608
\(199\) −15.2926 −1.08406 −0.542031 0.840358i \(-0.682345\pi\)
−0.542031 + 0.840358i \(0.682345\pi\)
\(200\) 4.99536 0.353225
\(201\) 22.3008 1.57298
\(202\) −1.91639 −0.134837
\(203\) −0.616961 −0.0433022
\(204\) 7.11195 0.497936
\(205\) −0.0645880 −0.00451102
\(206\) −6.22040 −0.433396
\(207\) 0.238964 0.0166091
\(208\) −1.57480 −0.109193
\(209\) −0.616940 −0.0426746
\(210\) −0.0116752 −0.000805668 0
\(211\) −22.3879 −1.54124 −0.770622 0.637292i \(-0.780054\pi\)
−0.770622 + 0.637292i \(0.780054\pi\)
\(212\) −3.18399 −0.218677
\(213\) 5.40337 0.370233
\(214\) −6.76105 −0.462176
\(215\) −0.888693 −0.0606084
\(216\) 5.38198 0.366197
\(217\) 0.348360 0.0236482
\(218\) 5.02739 0.340498
\(219\) 4.36281 0.294811
\(220\) −0.00880707 −0.000593773 0
\(221\) −6.74030 −0.453401
\(222\) 11.6095 0.779179
\(223\) −24.0032 −1.60737 −0.803687 0.595052i \(-0.797131\pi\)
−0.803687 + 0.595052i \(0.797131\pi\)
\(224\) −0.103168 −0.00689322
\(225\) 1.19371 0.0795807
\(226\) 19.2653 1.28151
\(227\) 15.5676 1.03326 0.516629 0.856209i \(-0.327186\pi\)
0.516629 + 0.856209i \(0.327186\pi\)
\(228\) 7.92741 0.525005
\(229\) −11.0634 −0.731088 −0.365544 0.930794i \(-0.619117\pi\)
−0.365544 + 0.930794i \(0.619117\pi\)
\(230\) 0.0681057 0.00449076
\(231\) −0.0221682 −0.00145856
\(232\) 5.98015 0.392616
\(233\) −15.7481 −1.03169 −0.515846 0.856681i \(-0.672522\pi\)
−0.515846 + 0.856681i \(0.672522\pi\)
\(234\) −0.376321 −0.0246009
\(235\) −0.0186077 −0.00121383
\(236\) −9.41679 −0.612981
\(237\) 3.62161 0.235249
\(238\) −0.441569 −0.0286227
\(239\) 19.4788 1.25998 0.629989 0.776604i \(-0.283059\pi\)
0.629989 + 0.776604i \(0.283059\pi\)
\(240\) 0.113167 0.00730490
\(241\) 25.5974 1.64887 0.824435 0.565956i \(-0.191493\pi\)
0.824435 + 0.565956i \(0.191493\pi\)
\(242\) 10.9833 0.706032
\(243\) 2.47731 0.158920
\(244\) −4.95302 −0.317084
\(245\) −0.476015 −0.0304115
\(246\) 1.57581 0.100470
\(247\) −7.51313 −0.478049
\(248\) −3.37662 −0.214416
\(249\) −4.66476 −0.295617
\(250\) 0.680742 0.0430539
\(251\) −27.2530 −1.72020 −0.860098 0.510129i \(-0.829598\pi\)
−0.860098 + 0.510129i \(0.829598\pi\)
\(252\) −0.0246535 −0.00155302
\(253\) 0.129315 0.00812994
\(254\) −3.87668 −0.243245
\(255\) 0.484365 0.0303321
\(256\) 1.00000 0.0625000
\(257\) 26.7783 1.67038 0.835192 0.549958i \(-0.185356\pi\)
0.835192 + 0.549958i \(0.185356\pi\)
\(258\) 21.6822 1.34988
\(259\) −0.720815 −0.0447893
\(260\) −0.107253 −0.00665156
\(261\) 1.42904 0.0884553
\(262\) 1.00000 0.0617802
\(263\) 19.4072 1.19670 0.598350 0.801235i \(-0.295823\pi\)
0.598350 + 0.801235i \(0.295823\pi\)
\(264\) 0.214874 0.0132246
\(265\) −0.216848 −0.0133209
\(266\) −0.492199 −0.0301787
\(267\) 14.1831 0.867993
\(268\) 13.4210 0.819816
\(269\) −13.5901 −0.828602 −0.414301 0.910140i \(-0.635974\pi\)
−0.414301 + 0.910140i \(0.635974\pi\)
\(270\) 0.366544 0.0223071
\(271\) −6.73699 −0.409243 −0.204621 0.978841i \(-0.565596\pi\)
−0.204621 + 0.978841i \(0.565596\pi\)
\(272\) 4.28009 0.259519
\(273\) −0.269965 −0.0163391
\(274\) 6.06546 0.366428
\(275\) 0.645973 0.0389537
\(276\) −1.66164 −0.100019
\(277\) −13.9821 −0.840100 −0.420050 0.907501i \(-0.637987\pi\)
−0.420050 + 0.907501i \(0.637987\pi\)
\(278\) −3.01603 −0.180890
\(279\) −0.806891 −0.0483073
\(280\) −0.00702635 −0.000419905 0
\(281\) −20.2562 −1.20838 −0.604191 0.796840i \(-0.706503\pi\)
−0.604191 + 0.796840i \(0.706503\pi\)
\(282\) 0.453988 0.0270346
\(283\) −29.7323 −1.76740 −0.883700 0.468054i \(-0.844955\pi\)
−0.883700 + 0.468054i \(0.844955\pi\)
\(284\) 3.25184 0.192961
\(285\) 0.539902 0.0319810
\(286\) −0.203645 −0.0120418
\(287\) −0.0978395 −0.00577528
\(288\) 0.238964 0.0140811
\(289\) 1.31917 0.0775981
\(290\) 0.407282 0.0239164
\(291\) 18.0884 1.06036
\(292\) 2.62561 0.153652
\(293\) −11.4793 −0.670630 −0.335315 0.942106i \(-0.608843\pi\)
−0.335315 + 0.942106i \(0.608843\pi\)
\(294\) 11.6138 0.677329
\(295\) −0.641337 −0.0373401
\(296\) 6.98679 0.406099
\(297\) 0.695969 0.0403842
\(298\) −22.4253 −1.29906
\(299\) 1.57480 0.0910732
\(300\) −8.30048 −0.479228
\(301\) −1.34621 −0.0775944
\(302\) 0.552905 0.0318161
\(303\) 3.18435 0.182936
\(304\) 4.77084 0.273627
\(305\) −0.337329 −0.0193154
\(306\) 1.02279 0.0584688
\(307\) −31.7828 −1.81394 −0.906969 0.421197i \(-0.861610\pi\)
−0.906969 + 0.421197i \(0.861610\pi\)
\(308\) −0.0133412 −0.000760183 0
\(309\) 10.3361 0.587997
\(310\) −0.229967 −0.0130613
\(311\) 15.1847 0.861045 0.430522 0.902580i \(-0.358329\pi\)
0.430522 + 0.902580i \(0.358329\pi\)
\(312\) 2.61675 0.148144
\(313\) 15.3439 0.867289 0.433644 0.901084i \(-0.357227\pi\)
0.433644 + 0.901084i \(0.357227\pi\)
\(314\) 1.07714 0.0607868
\(315\) −0.00167904 −9.46034e−5 0
\(316\) 2.17954 0.122609
\(317\) −4.79810 −0.269488 −0.134744 0.990880i \(-0.543021\pi\)
−0.134744 + 0.990880i \(0.543021\pi\)
\(318\) 5.29063 0.296684
\(319\) 0.773321 0.0432976
\(320\) 0.0681057 0.00380723
\(321\) 11.2344 0.627044
\(322\) 0.103168 0.00574934
\(323\) 20.4196 1.13618
\(324\) −8.22600 −0.457000
\(325\) 7.86671 0.436367
\(326\) −1.63737 −0.0906858
\(327\) −8.35370 −0.461960
\(328\) 0.948349 0.0523638
\(329\) −0.0281873 −0.00155402
\(330\) 0.0146342 0.000805583 0
\(331\) −22.3587 −1.22895 −0.614474 0.788937i \(-0.710632\pi\)
−0.614474 + 0.788937i \(0.710632\pi\)
\(332\) −2.80733 −0.154072
\(333\) 1.66959 0.0914930
\(334\) −8.65968 −0.473837
\(335\) 0.914046 0.0499396
\(336\) 0.171428 0.00935217
\(337\) 1.67063 0.0910050 0.0455025 0.998964i \(-0.485511\pi\)
0.0455025 + 0.998964i \(0.485511\pi\)
\(338\) 10.5200 0.572212
\(339\) −32.0120 −1.73865
\(340\) 0.291499 0.0158087
\(341\) −0.436647 −0.0236458
\(342\) 1.14006 0.0616473
\(343\) −1.44326 −0.0779286
\(344\) 13.0487 0.703540
\(345\) −0.113167 −0.00609271
\(346\) 19.0933 1.02646
\(347\) 17.1821 0.922381 0.461191 0.887301i \(-0.347422\pi\)
0.461191 + 0.887301i \(0.347422\pi\)
\(348\) −9.93683 −0.532670
\(349\) −8.12701 −0.435029 −0.217514 0.976057i \(-0.569795\pi\)
−0.217514 + 0.976057i \(0.569795\pi\)
\(350\) 0.515363 0.0275473
\(351\) 8.47556 0.452392
\(352\) 0.129315 0.00689249
\(353\) −5.53155 −0.294415 −0.147207 0.989106i \(-0.547029\pi\)
−0.147207 + 0.989106i \(0.547029\pi\)
\(354\) 15.6473 0.831644
\(355\) 0.221469 0.0117544
\(356\) 8.53563 0.452388
\(357\) 0.733728 0.0388330
\(358\) 19.5982 1.03580
\(359\) −18.6210 −0.982781 −0.491390 0.870939i \(-0.663511\pi\)
−0.491390 + 0.870939i \(0.663511\pi\)
\(360\) 0.0162748 0.000857758 0
\(361\) 3.76093 0.197944
\(362\) 16.7947 0.882712
\(363\) −18.2502 −0.957888
\(364\) −0.162470 −0.00851572
\(365\) 0.178819 0.00935982
\(366\) 8.23011 0.430195
\(367\) −0.636508 −0.0332254 −0.0166127 0.999862i \(-0.505288\pi\)
−0.0166127 + 0.999862i \(0.505288\pi\)
\(368\) −1.00000 −0.0521286
\(369\) 0.226621 0.0117974
\(370\) 0.475841 0.0247378
\(371\) −0.328486 −0.0170542
\(372\) 5.61072 0.290902
\(373\) 33.1785 1.71792 0.858960 0.512043i \(-0.171111\pi\)
0.858960 + 0.512043i \(0.171111\pi\)
\(374\) 0.553478 0.0286197
\(375\) −1.13115 −0.0584121
\(376\) 0.273217 0.0140901
\(377\) 9.41755 0.485029
\(378\) 0.555249 0.0285589
\(379\) −9.59012 −0.492611 −0.246306 0.969192i \(-0.579217\pi\)
−0.246306 + 0.969192i \(0.579217\pi\)
\(380\) 0.324922 0.0166681
\(381\) 6.44164 0.330015
\(382\) −22.5027 −1.15134
\(383\) 35.3604 1.80683 0.903415 0.428768i \(-0.141052\pi\)
0.903415 + 0.428768i \(0.141052\pi\)
\(384\) −1.66164 −0.0847950
\(385\) −0.000908610 0 −4.63070e−5 0
\(386\) −1.78146 −0.0906739
\(387\) 3.11817 0.158506
\(388\) 10.8859 0.552646
\(389\) 2.45355 0.124400 0.0621998 0.998064i \(-0.480188\pi\)
0.0621998 + 0.998064i \(0.480188\pi\)
\(390\) 0.178216 0.00902430
\(391\) −4.28009 −0.216453
\(392\) 6.98936 0.353016
\(393\) −1.66164 −0.0838185
\(394\) 6.52172 0.328559
\(395\) 0.148439 0.00746880
\(396\) 0.0309015 0.00155286
\(397\) −11.0341 −0.553784 −0.276892 0.960901i \(-0.589304\pi\)
−0.276892 + 0.960901i \(0.589304\pi\)
\(398\) 15.2926 0.766548
\(399\) 0.817856 0.0409440
\(400\) −4.99536 −0.249768
\(401\) −37.7797 −1.88663 −0.943314 0.331902i \(-0.892310\pi\)
−0.943314 + 0.331902i \(0.892310\pi\)
\(402\) −22.3008 −1.11226
\(403\) −5.31752 −0.264884
\(404\) 1.91639 0.0953442
\(405\) −0.560238 −0.0278385
\(406\) 0.616961 0.0306193
\(407\) 0.903494 0.0447846
\(408\) −7.11195 −0.352094
\(409\) −13.9430 −0.689436 −0.344718 0.938706i \(-0.612025\pi\)
−0.344718 + 0.938706i \(0.612025\pi\)
\(410\) 0.0645880 0.00318977
\(411\) −10.0786 −0.497140
\(412\) 6.22040 0.306457
\(413\) −0.971513 −0.0478050
\(414\) −0.238964 −0.0117444
\(415\) −0.191195 −0.00938540
\(416\) 1.57480 0.0772111
\(417\) 5.01155 0.245417
\(418\) 0.616940 0.0301755
\(419\) 11.1923 0.546782 0.273391 0.961903i \(-0.411855\pi\)
0.273391 + 0.961903i \(0.411855\pi\)
\(420\) 0.0116752 0.000569693 0
\(421\) 29.4705 1.43630 0.718152 0.695887i \(-0.244988\pi\)
0.718152 + 0.695887i \(0.244988\pi\)
\(422\) 22.3879 1.08982
\(423\) 0.0652891 0.00317446
\(424\) 3.18399 0.154628
\(425\) −21.3806 −1.03711
\(426\) −5.40337 −0.261794
\(427\) −0.510994 −0.0247287
\(428\) 6.76105 0.326808
\(429\) 0.338384 0.0163373
\(430\) 0.888693 0.0428566
\(431\) −21.7821 −1.04921 −0.524605 0.851346i \(-0.675787\pi\)
−0.524605 + 0.851346i \(0.675787\pi\)
\(432\) −5.38198 −0.258941
\(433\) −3.14831 −0.151298 −0.0756491 0.997134i \(-0.524103\pi\)
−0.0756491 + 0.997134i \(0.524103\pi\)
\(434\) −0.348360 −0.0167218
\(435\) −0.676755 −0.0324479
\(436\) −5.02739 −0.240768
\(437\) −4.77084 −0.228220
\(438\) −4.36281 −0.208463
\(439\) 9.32482 0.445049 0.222525 0.974927i \(-0.428570\pi\)
0.222525 + 0.974927i \(0.428570\pi\)
\(440\) 0.00880707 0.000419861 0
\(441\) 1.67020 0.0795335
\(442\) 6.74030 0.320603
\(443\) −37.2152 −1.76815 −0.884074 0.467347i \(-0.845210\pi\)
−0.884074 + 0.467347i \(0.845210\pi\)
\(444\) −11.6095 −0.550963
\(445\) 0.581326 0.0275575
\(446\) 24.0032 1.13659
\(447\) 37.2627 1.76246
\(448\) 0.103168 0.00487424
\(449\) 16.4776 0.777624 0.388812 0.921317i \(-0.372886\pi\)
0.388812 + 0.921317i \(0.372886\pi\)
\(450\) −1.19371 −0.0562721
\(451\) 0.122635 0.00577468
\(452\) −19.2653 −0.906164
\(453\) −0.918728 −0.0431656
\(454\) −15.5676 −0.730624
\(455\) −0.0110651 −0.000518741 0
\(456\) −7.92741 −0.371235
\(457\) −12.2407 −0.572596 −0.286298 0.958141i \(-0.592425\pi\)
−0.286298 + 0.958141i \(0.592425\pi\)
\(458\) 11.0634 0.516957
\(459\) −23.0354 −1.07520
\(460\) −0.0681057 −0.00317545
\(461\) −6.20618 −0.289051 −0.144525 0.989501i \(-0.546166\pi\)
−0.144525 + 0.989501i \(0.546166\pi\)
\(462\) 0.0221682 0.00103136
\(463\) 36.9146 1.71557 0.857785 0.514009i \(-0.171840\pi\)
0.857785 + 0.514009i \(0.171840\pi\)
\(464\) −5.98015 −0.277621
\(465\) 0.382122 0.0177205
\(466\) 15.7481 0.729517
\(467\) −0.590865 −0.0273420 −0.0136710 0.999907i \(-0.504352\pi\)
−0.0136710 + 0.999907i \(0.504352\pi\)
\(468\) 0.376321 0.0173954
\(469\) 1.38462 0.0639357
\(470\) 0.0186077 0.000858308 0
\(471\) −1.78982 −0.0824707
\(472\) 9.41679 0.433443
\(473\) 1.68739 0.0775863
\(474\) −3.62161 −0.166346
\(475\) −23.8321 −1.09349
\(476\) 0.441569 0.0202393
\(477\) 0.760858 0.0348373
\(478\) −19.4788 −0.890939
\(479\) 43.2955 1.97822 0.989111 0.147172i \(-0.0470172\pi\)
0.989111 + 0.147172i \(0.0470172\pi\)
\(480\) −0.113167 −0.00516534
\(481\) 11.0028 0.501685
\(482\) −25.5974 −1.16593
\(483\) −0.171428 −0.00780025
\(484\) −10.9833 −0.499240
\(485\) 0.741390 0.0336648
\(486\) −2.47731 −0.112373
\(487\) −12.0357 −0.545391 −0.272695 0.962100i \(-0.587915\pi\)
−0.272695 + 0.962100i \(0.587915\pi\)
\(488\) 4.95302 0.224212
\(489\) 2.72072 0.123035
\(490\) 0.476015 0.0215042
\(491\) 18.9412 0.854803 0.427402 0.904062i \(-0.359429\pi\)
0.427402 + 0.904062i \(0.359429\pi\)
\(492\) −1.57581 −0.0710431
\(493\) −25.5956 −1.15277
\(494\) 7.51313 0.338032
\(495\) 0.00210457 9.45935e−5 0
\(496\) 3.37662 0.151615
\(497\) 0.335486 0.0150486
\(498\) 4.66476 0.209033
\(499\) −0.580220 −0.0259742 −0.0129871 0.999916i \(-0.504134\pi\)
−0.0129871 + 0.999916i \(0.504134\pi\)
\(500\) −0.680742 −0.0304437
\(501\) 14.3892 0.642864
\(502\) 27.2530 1.21636
\(503\) 7.21164 0.321551 0.160775 0.986991i \(-0.448601\pi\)
0.160775 + 0.986991i \(0.448601\pi\)
\(504\) 0.0246535 0.00109815
\(505\) 0.130517 0.00580795
\(506\) −0.129315 −0.00574874
\(507\) −17.4804 −0.776332
\(508\) 3.87668 0.172000
\(509\) 37.1143 1.64506 0.822531 0.568720i \(-0.192561\pi\)
0.822531 + 0.568720i \(0.192561\pi\)
\(510\) −0.484365 −0.0214480
\(511\) 0.270879 0.0119830
\(512\) −1.00000 −0.0441942
\(513\) −25.6766 −1.13365
\(514\) −26.7783 −1.18114
\(515\) 0.423645 0.0186680
\(516\) −21.6822 −0.954507
\(517\) 0.0353310 0.00155386
\(518\) 0.720815 0.0316708
\(519\) −31.7261 −1.39262
\(520\) 0.107253 0.00470336
\(521\) −13.1708 −0.577023 −0.288511 0.957476i \(-0.593160\pi\)
−0.288511 + 0.957476i \(0.593160\pi\)
\(522\) −1.42904 −0.0625474
\(523\) 7.06875 0.309095 0.154547 0.987985i \(-0.450608\pi\)
0.154547 + 0.987985i \(0.450608\pi\)
\(524\) −1.00000 −0.0436852
\(525\) −0.856345 −0.0373740
\(526\) −19.4072 −0.846195
\(527\) 14.4523 0.629550
\(528\) −0.214874 −0.00935119
\(529\) 1.00000 0.0434783
\(530\) 0.216848 0.00941927
\(531\) 2.25027 0.0976535
\(532\) 0.492199 0.0213395
\(533\) 1.49346 0.0646890
\(534\) −14.1831 −0.613764
\(535\) 0.460467 0.0199077
\(536\) −13.4210 −0.579698
\(537\) −32.5651 −1.40529
\(538\) 13.5901 0.585910
\(539\) 0.903826 0.0389305
\(540\) −0.366544 −0.0157735
\(541\) −35.2227 −1.51434 −0.757171 0.653216i \(-0.773419\pi\)
−0.757171 + 0.653216i \(0.773419\pi\)
\(542\) 6.73699 0.289378
\(543\) −27.9068 −1.19759
\(544\) −4.28009 −0.183507
\(545\) −0.342394 −0.0146666
\(546\) 0.269965 0.0115535
\(547\) 28.8398 1.23310 0.616550 0.787316i \(-0.288530\pi\)
0.616550 + 0.787316i \(0.288530\pi\)
\(548\) −6.06546 −0.259104
\(549\) 1.18359 0.0505145
\(550\) −0.645973 −0.0275444
\(551\) −28.5303 −1.21543
\(552\) 1.66164 0.0707239
\(553\) 0.224860 0.00956200
\(554\) 13.9821 0.594040
\(555\) −0.790674 −0.0335622
\(556\) 3.01603 0.127908
\(557\) −35.4117 −1.50044 −0.750221 0.661188i \(-0.770053\pi\)
−0.750221 + 0.661188i \(0.770053\pi\)
\(558\) 0.806891 0.0341584
\(559\) 20.5492 0.869137
\(560\) 0.00702635 0.000296917 0
\(561\) −0.919680 −0.0388289
\(562\) 20.2562 0.854454
\(563\) −1.28144 −0.0540063 −0.0270032 0.999635i \(-0.508596\pi\)
−0.0270032 + 0.999635i \(0.508596\pi\)
\(564\) −0.453988 −0.0191163
\(565\) −1.31208 −0.0551996
\(566\) 29.7323 1.24974
\(567\) −0.848662 −0.0356405
\(568\) −3.25184 −0.136444
\(569\) −10.2066 −0.427885 −0.213942 0.976846i \(-0.568631\pi\)
−0.213942 + 0.976846i \(0.568631\pi\)
\(570\) −0.539902 −0.0226140
\(571\) −10.3662 −0.433811 −0.216905 0.976193i \(-0.569596\pi\)
−0.216905 + 0.976193i \(0.569596\pi\)
\(572\) 0.203645 0.00851483
\(573\) 37.3912 1.56204
\(574\) 0.0978395 0.00408374
\(575\) 4.99536 0.208321
\(576\) −0.238964 −0.00995683
\(577\) −1.27987 −0.0532816 −0.0266408 0.999645i \(-0.508481\pi\)
−0.0266408 + 0.999645i \(0.508481\pi\)
\(578\) −1.31917 −0.0548701
\(579\) 2.96014 0.123019
\(580\) −0.407282 −0.0169115
\(581\) −0.289627 −0.0120157
\(582\) −18.0884 −0.749787
\(583\) 0.411736 0.0170524
\(584\) −2.62561 −0.108648
\(585\) 0.0256296 0.00105965
\(586\) 11.4793 0.474207
\(587\) 6.05942 0.250099 0.125050 0.992150i \(-0.460091\pi\)
0.125050 + 0.992150i \(0.460091\pi\)
\(588\) −11.6138 −0.478944
\(589\) 16.1093 0.663774
\(590\) 0.641337 0.0264034
\(591\) −10.8367 −0.445763
\(592\) −6.98679 −0.287155
\(593\) 23.2391 0.954317 0.477159 0.878817i \(-0.341667\pi\)
0.477159 + 0.878817i \(0.341667\pi\)
\(594\) −0.695969 −0.0285560
\(595\) 0.0300734 0.00123289
\(596\) 22.4253 0.918576
\(597\) −25.4107 −1.03999
\(598\) −1.57480 −0.0643985
\(599\) 3.34062 0.136494 0.0682470 0.997668i \(-0.478259\pi\)
0.0682470 + 0.997668i \(0.478259\pi\)
\(600\) 8.30048 0.338865
\(601\) −7.25587 −0.295973 −0.147987 0.988989i \(-0.547279\pi\)
−0.147987 + 0.988989i \(0.547279\pi\)
\(602\) 1.34621 0.0548676
\(603\) −3.20713 −0.130604
\(604\) −0.552905 −0.0224974
\(605\) −0.748024 −0.0304115
\(606\) −3.18435 −0.129355
\(607\) −19.8661 −0.806341 −0.403171 0.915125i \(-0.632092\pi\)
−0.403171 + 0.915125i \(0.632092\pi\)
\(608\) −4.77084 −0.193483
\(609\) −1.02517 −0.0415418
\(610\) 0.337329 0.0136580
\(611\) 0.430263 0.0174066
\(612\) −1.02279 −0.0413437
\(613\) −36.8621 −1.48885 −0.744423 0.667708i \(-0.767275\pi\)
−0.744423 + 0.667708i \(0.767275\pi\)
\(614\) 31.7828 1.28265
\(615\) −0.107322 −0.00432763
\(616\) 0.0133412 0.000537531 0
\(617\) 14.6106 0.588199 0.294099 0.955775i \(-0.404980\pi\)
0.294099 + 0.955775i \(0.404980\pi\)
\(618\) −10.3361 −0.415777
\(619\) 45.0525 1.81081 0.905406 0.424548i \(-0.139567\pi\)
0.905406 + 0.424548i \(0.139567\pi\)
\(620\) 0.229967 0.00923571
\(621\) 5.38198 0.215971
\(622\) −15.1847 −0.608850
\(623\) 0.880606 0.0352807
\(624\) −2.61675 −0.104754
\(625\) 24.9304 0.997218
\(626\) −15.3439 −0.613266
\(627\) −1.02513 −0.0409397
\(628\) −1.07714 −0.0429828
\(629\) −29.9041 −1.19235
\(630\) 0.00167904 6.68947e−5 0
\(631\) −32.0164 −1.27455 −0.637277 0.770635i \(-0.719939\pi\)
−0.637277 + 0.770635i \(0.719939\pi\)
\(632\) −2.17954 −0.0866976
\(633\) −37.2005 −1.47859
\(634\) 4.79810 0.190557
\(635\) 0.264024 0.0104775
\(636\) −5.29063 −0.209787
\(637\) 11.0069 0.436108
\(638\) −0.773321 −0.0306161
\(639\) −0.777072 −0.0307405
\(640\) −0.0681057 −0.00269212
\(641\) 27.6756 1.09312 0.546560 0.837420i \(-0.315937\pi\)
0.546560 + 0.837420i \(0.315937\pi\)
\(642\) −11.2344 −0.443387
\(643\) −27.7603 −1.09476 −0.547380 0.836884i \(-0.684375\pi\)
−0.547380 + 0.836884i \(0.684375\pi\)
\(644\) −0.103168 −0.00406540
\(645\) −1.47668 −0.0581444
\(646\) −20.4196 −0.803400
\(647\) −42.4703 −1.66968 −0.834839 0.550494i \(-0.814439\pi\)
−0.834839 + 0.550494i \(0.814439\pi\)
\(648\) 8.22600 0.323148
\(649\) 1.21773 0.0478000
\(650\) −7.86671 −0.308558
\(651\) 0.578848 0.0226868
\(652\) 1.63737 0.0641245
\(653\) 28.3733 1.11033 0.555167 0.831739i \(-0.312654\pi\)
0.555167 + 0.831739i \(0.312654\pi\)
\(654\) 8.35370 0.326655
\(655\) −0.0681057 −0.00266111
\(656\) −0.948349 −0.0370268
\(657\) −0.627426 −0.0244782
\(658\) 0.0281873 0.00109886
\(659\) 35.1529 1.36936 0.684682 0.728842i \(-0.259941\pi\)
0.684682 + 0.728842i \(0.259941\pi\)
\(660\) −0.0146342 −0.000569634 0
\(661\) −38.5901 −1.50098 −0.750490 0.660882i \(-0.770182\pi\)
−0.750490 + 0.660882i \(0.770182\pi\)
\(662\) 22.3587 0.868997
\(663\) −11.1999 −0.434969
\(664\) 2.80733 0.108945
\(665\) 0.0335216 0.00129991
\(666\) −1.66959 −0.0646953
\(667\) 5.98015 0.231552
\(668\) 8.65968 0.335053
\(669\) −39.8846 −1.54203
\(670\) −0.914046 −0.0353127
\(671\) 0.640497 0.0247261
\(672\) −0.171428 −0.00661298
\(673\) 3.22933 0.124482 0.0622409 0.998061i \(-0.480175\pi\)
0.0622409 + 0.998061i \(0.480175\pi\)
\(674\) −1.67063 −0.0643502
\(675\) 26.8849 1.03480
\(676\) −10.5200 −0.404615
\(677\) 35.9550 1.38186 0.690932 0.722920i \(-0.257201\pi\)
0.690932 + 0.722920i \(0.257201\pi\)
\(678\) 32.0120 1.22941
\(679\) 1.12308 0.0430997
\(680\) −0.291499 −0.0111785
\(681\) 25.8677 0.991253
\(682\) 0.436647 0.0167201
\(683\) 37.3860 1.43053 0.715267 0.698851i \(-0.246305\pi\)
0.715267 + 0.698851i \(0.246305\pi\)
\(684\) −1.14006 −0.0435912
\(685\) −0.413093 −0.0157835
\(686\) 1.44326 0.0551038
\(687\) −18.3833 −0.701366
\(688\) −13.0487 −0.497478
\(689\) 5.01415 0.191024
\(690\) 0.113167 0.00430819
\(691\) 19.8892 0.756622 0.378311 0.925679i \(-0.376505\pi\)
0.378311 + 0.925679i \(0.376505\pi\)
\(692\) −19.0933 −0.725817
\(693\) 0.00318806 0.000121104 0
\(694\) −17.1821 −0.652222
\(695\) 0.205409 0.00779161
\(696\) 9.93683 0.376655
\(697\) −4.05902 −0.153746
\(698\) 8.12701 0.307612
\(699\) −26.1676 −0.989750
\(700\) −0.515363 −0.0194789
\(701\) −2.15357 −0.0813393 −0.0406696 0.999173i \(-0.512949\pi\)
−0.0406696 + 0.999173i \(0.512949\pi\)
\(702\) −8.47556 −0.319889
\(703\) −33.3329 −1.25717
\(704\) −0.129315 −0.00487373
\(705\) −0.0309192 −0.00116448
\(706\) 5.53155 0.208183
\(707\) 0.197711 0.00743569
\(708\) −15.6473 −0.588061
\(709\) 40.9246 1.53696 0.768478 0.639876i \(-0.221014\pi\)
0.768478 + 0.639876i \(0.221014\pi\)
\(710\) −0.221469 −0.00831158
\(711\) −0.520832 −0.0195327
\(712\) −8.53563 −0.319886
\(713\) −3.37662 −0.126456
\(714\) −0.733728 −0.0274591
\(715\) 0.0138694 0.000518686 0
\(716\) −19.5982 −0.732419
\(717\) 32.3667 1.20876
\(718\) 18.6210 0.694931
\(719\) −23.6341 −0.881403 −0.440701 0.897654i \(-0.645270\pi\)
−0.440701 + 0.897654i \(0.645270\pi\)
\(720\) −0.0162748 −0.000606527 0
\(721\) 0.641748 0.0238999
\(722\) −3.76093 −0.139967
\(723\) 42.5335 1.58184
\(724\) −16.7947 −0.624172
\(725\) 29.8730 1.10946
\(726\) 18.2502 0.677329
\(727\) 3.72667 0.138215 0.0691073 0.997609i \(-0.477985\pi\)
0.0691073 + 0.997609i \(0.477985\pi\)
\(728\) 0.162470 0.00602152
\(729\) 28.7944 1.06646
\(730\) −0.178819 −0.00661839
\(731\) −55.8497 −2.06568
\(732\) −8.23011 −0.304194
\(733\) 38.1577 1.40939 0.704693 0.709513i \(-0.251085\pi\)
0.704693 + 0.709513i \(0.251085\pi\)
\(734\) 0.636508 0.0234939
\(735\) −0.790964 −0.0291752
\(736\) 1.00000 0.0368605
\(737\) −1.73553 −0.0639290
\(738\) −0.226621 −0.00834204
\(739\) 49.8362 1.83325 0.916626 0.399745i \(-0.130901\pi\)
0.916626 + 0.399745i \(0.130901\pi\)
\(740\) −0.475841 −0.0174922
\(741\) −12.4841 −0.458615
\(742\) 0.328486 0.0120591
\(743\) 42.5633 1.56150 0.780748 0.624847i \(-0.214838\pi\)
0.780748 + 0.624847i \(0.214838\pi\)
\(744\) −5.61072 −0.205699
\(745\) 1.52729 0.0559556
\(746\) −33.1785 −1.21475
\(747\) 0.670850 0.0245451
\(748\) −0.553478 −0.0202372
\(749\) 0.697526 0.0254870
\(750\) 1.13115 0.0413036
\(751\) 41.8799 1.52822 0.764110 0.645086i \(-0.223179\pi\)
0.764110 + 0.645086i \(0.223179\pi\)
\(752\) −0.273217 −0.00996321
\(753\) −45.2846 −1.65026
\(754\) −9.41755 −0.342967
\(755\) −0.0376560 −0.00137044
\(756\) −0.555249 −0.0201942
\(757\) 11.9595 0.434676 0.217338 0.976096i \(-0.430263\pi\)
0.217338 + 0.976096i \(0.430263\pi\)
\(758\) 9.59012 0.348329
\(759\) 0.214874 0.00779943
\(760\) −0.324922 −0.0117862
\(761\) 26.5509 0.962468 0.481234 0.876592i \(-0.340189\pi\)
0.481234 + 0.876592i \(0.340189\pi\)
\(762\) −6.44164 −0.233356
\(763\) −0.518667 −0.0187770
\(764\) 22.5027 0.814118
\(765\) −0.0696577 −0.00251848
\(766\) −35.3604 −1.27762
\(767\) 14.8296 0.535465
\(768\) 1.66164 0.0599591
\(769\) 33.0702 1.19254 0.596271 0.802783i \(-0.296648\pi\)
0.596271 + 0.802783i \(0.296648\pi\)
\(770\) 0.000908610 0 3.27440e−5 0
\(771\) 44.4958 1.60248
\(772\) 1.78146 0.0641161
\(773\) −12.6664 −0.455580 −0.227790 0.973710i \(-0.573150\pi\)
−0.227790 + 0.973710i \(0.573150\pi\)
\(774\) −3.11817 −0.112080
\(775\) −16.8675 −0.605897
\(776\) −10.8859 −0.390780
\(777\) −1.19773 −0.0429684
\(778\) −2.45355 −0.0879639
\(779\) −4.52442 −0.162104
\(780\) −0.178216 −0.00638115
\(781\) −0.420510 −0.0150470
\(782\) 4.28009 0.153056
\(783\) 32.1850 1.15020
\(784\) −6.98936 −0.249620
\(785\) −0.0733598 −0.00261832
\(786\) 1.66164 0.0592686
\(787\) −27.5283 −0.981277 −0.490638 0.871363i \(-0.663236\pi\)
−0.490638 + 0.871363i \(0.663236\pi\)
\(788\) −6.52172 −0.232327
\(789\) 32.2477 1.14805
\(790\) −0.148439 −0.00528124
\(791\) −1.98757 −0.0706698
\(792\) −0.0309015 −0.00109804
\(793\) 7.80002 0.276987
\(794\) 11.0341 0.391584
\(795\) −0.360322 −0.0127793
\(796\) −15.2926 −0.542031
\(797\) −19.3932 −0.686943 −0.343471 0.939163i \(-0.611603\pi\)
−0.343471 + 0.939163i \(0.611603\pi\)
\(798\) −0.817856 −0.0289518
\(799\) −1.16939 −0.0413702
\(800\) 4.99536 0.176613
\(801\) −2.03971 −0.0720695
\(802\) 37.7797 1.33405
\(803\) −0.339530 −0.0119817
\(804\) 22.3008 0.786488
\(805\) −0.00702635 −0.000247646 0
\(806\) 5.31752 0.187301
\(807\) −22.5818 −0.794917
\(808\) −1.91639 −0.0674185
\(809\) 25.2514 0.887793 0.443897 0.896078i \(-0.353596\pi\)
0.443897 + 0.896078i \(0.353596\pi\)
\(810\) 0.560238 0.0196848
\(811\) −13.1333 −0.461171 −0.230585 0.973052i \(-0.574064\pi\)
−0.230585 + 0.973052i \(0.574064\pi\)
\(812\) −0.616961 −0.0216511
\(813\) −11.1944 −0.392605
\(814\) −0.903494 −0.0316675
\(815\) 0.111515 0.00390619
\(816\) 7.11195 0.248968
\(817\) −62.2534 −2.17797
\(818\) 13.9430 0.487505
\(819\) 0.0388244 0.00135663
\(820\) −0.0645880 −0.00225551
\(821\) 29.2836 1.02200 0.511002 0.859580i \(-0.329275\pi\)
0.511002 + 0.859580i \(0.329275\pi\)
\(822\) 10.0786 0.351531
\(823\) 5.77425 0.201278 0.100639 0.994923i \(-0.467911\pi\)
0.100639 + 0.994923i \(0.467911\pi\)
\(824\) −6.22040 −0.216698
\(825\) 1.07337 0.0373701
\(826\) 0.971513 0.0338033
\(827\) −33.2577 −1.15649 −0.578243 0.815865i \(-0.696261\pi\)
−0.578243 + 0.815865i \(0.696261\pi\)
\(828\) 0.238964 0.00830457
\(829\) −1.22601 −0.0425810 −0.0212905 0.999773i \(-0.506777\pi\)
−0.0212905 + 0.999773i \(0.506777\pi\)
\(830\) 0.191195 0.00663648
\(831\) −23.2331 −0.805947
\(832\) −1.57480 −0.0545965
\(833\) −29.9151 −1.03650
\(834\) −5.01155 −0.173536
\(835\) 0.589774 0.0204100
\(836\) −0.616940 −0.0213373
\(837\) −18.1729 −0.628148
\(838\) −11.1923 −0.386633
\(839\) 4.38282 0.151312 0.0756558 0.997134i \(-0.475895\pi\)
0.0756558 + 0.997134i \(0.475895\pi\)
\(840\) −0.0116752 −0.000402834 0
\(841\) 6.76216 0.233178
\(842\) −29.4705 −1.01562
\(843\) −33.6584 −1.15926
\(844\) −22.3879 −0.770622
\(845\) −0.716472 −0.0246474
\(846\) −0.0652891 −0.00224468
\(847\) −1.13313 −0.0389346
\(848\) −3.18399 −0.109339
\(849\) −49.4042 −1.69555
\(850\) 21.3806 0.733348
\(851\) 6.98679 0.239504
\(852\) 5.40337 0.185117
\(853\) −52.5689 −1.79993 −0.899963 0.435967i \(-0.856407\pi\)
−0.899963 + 0.435967i \(0.856407\pi\)
\(854\) 0.510994 0.0174858
\(855\) −0.0776446 −0.00265539
\(856\) −6.76105 −0.231088
\(857\) −45.6787 −1.56035 −0.780177 0.625559i \(-0.784871\pi\)
−0.780177 + 0.625559i \(0.784871\pi\)
\(858\) −0.338384 −0.0115522
\(859\) −48.5674 −1.65710 −0.828548 0.559917i \(-0.810833\pi\)
−0.828548 + 0.559917i \(0.810833\pi\)
\(860\) −0.888693 −0.0303042
\(861\) −0.162574 −0.00554050
\(862\) 21.7821 0.741903
\(863\) −22.1014 −0.752340 −0.376170 0.926551i \(-0.622759\pi\)
−0.376170 + 0.926551i \(0.622759\pi\)
\(864\) 5.38198 0.183099
\(865\) −1.30036 −0.0442136
\(866\) 3.14831 0.106984
\(867\) 2.19198 0.0744434
\(868\) 0.348360 0.0118241
\(869\) −0.281847 −0.00956100
\(870\) 0.676755 0.0229442
\(871\) −21.1354 −0.716145
\(872\) 5.02739 0.170249
\(873\) −2.60133 −0.0880417
\(874\) 4.77084 0.161376
\(875\) −0.0702309 −0.00237424
\(876\) 4.36281 0.147406
\(877\) −7.44859 −0.251521 −0.125760 0.992061i \(-0.540137\pi\)
−0.125760 + 0.992061i \(0.540137\pi\)
\(878\) −9.32482 −0.314697
\(879\) −19.0745 −0.643366
\(880\) −0.00880707 −0.000296886 0
\(881\) −16.1167 −0.542984 −0.271492 0.962441i \(-0.587517\pi\)
−0.271492 + 0.962441i \(0.587517\pi\)
\(882\) −1.67020 −0.0562387
\(883\) 44.4679 1.49646 0.748232 0.663437i \(-0.230903\pi\)
0.748232 + 0.663437i \(0.230903\pi\)
\(884\) −6.74030 −0.226701
\(885\) −1.06567 −0.0358221
\(886\) 37.2152 1.25027
\(887\) −47.7750 −1.60413 −0.802063 0.597239i \(-0.796264\pi\)
−0.802063 + 0.597239i \(0.796264\pi\)
\(888\) 11.6095 0.389590
\(889\) 0.399950 0.0134139
\(890\) −0.581326 −0.0194861
\(891\) 1.06374 0.0356367
\(892\) −24.0032 −0.803687
\(893\) −1.30348 −0.0436192
\(894\) −37.2627 −1.24625
\(895\) −1.33475 −0.0446158
\(896\) −0.103168 −0.00344661
\(897\) 2.61675 0.0873707
\(898\) −16.4776 −0.549863
\(899\) −20.1927 −0.673464
\(900\) 1.19371 0.0397904
\(901\) −13.6277 −0.454006
\(902\) −0.122635 −0.00408331
\(903\) −2.23692 −0.0744399
\(904\) 19.2653 0.640755
\(905\) −1.14382 −0.0380218
\(906\) 0.918728 0.0305227
\(907\) 7.52431 0.249840 0.124920 0.992167i \(-0.460133\pi\)
0.124920 + 0.992167i \(0.460133\pi\)
\(908\) 15.5676 0.516629
\(909\) −0.457949 −0.0151892
\(910\) 0.0110651 0.000366805 0
\(911\) −6.23744 −0.206656 −0.103328 0.994647i \(-0.532949\pi\)
−0.103328 + 0.994647i \(0.532949\pi\)
\(912\) 7.92741 0.262503
\(913\) 0.363028 0.0120145
\(914\) 12.2407 0.404886
\(915\) −0.560518 −0.0185301
\(916\) −11.0634 −0.365544
\(917\) −0.103168 −0.00340691
\(918\) 23.0354 0.760280
\(919\) −0.685114 −0.0225998 −0.0112999 0.999936i \(-0.503597\pi\)
−0.0112999 + 0.999936i \(0.503597\pi\)
\(920\) 0.0681057 0.00224538
\(921\) −52.8114 −1.74019
\(922\) 6.20618 0.204390
\(923\) −5.12101 −0.168560
\(924\) −0.0221682 −0.000729279 0
\(925\) 34.9015 1.14756
\(926\) −36.9146 −1.21309
\(927\) −1.48645 −0.0488215
\(928\) 5.98015 0.196308
\(929\) −34.1747 −1.12124 −0.560618 0.828075i \(-0.689436\pi\)
−0.560618 + 0.828075i \(0.689436\pi\)
\(930\) −0.382122 −0.0125303
\(931\) −33.3451 −1.09284
\(932\) −15.7481 −0.515846
\(933\) 25.2314 0.826040
\(934\) 0.590865 0.0193337
\(935\) −0.0376951 −0.00123276
\(936\) −0.376321 −0.0123004
\(937\) 5.66657 0.185119 0.0925593 0.995707i \(-0.470495\pi\)
0.0925593 + 0.995707i \(0.470495\pi\)
\(938\) −1.38462 −0.0452094
\(939\) 25.4960 0.832030
\(940\) −0.0186077 −0.000606915 0
\(941\) 38.6785 1.26088 0.630441 0.776237i \(-0.282874\pi\)
0.630441 + 0.776237i \(0.282874\pi\)
\(942\) 1.78982 0.0583156
\(943\) 0.948349 0.0308825
\(944\) −9.41679 −0.306490
\(945\) −0.0378157 −0.00123014
\(946\) −1.68739 −0.0548618
\(947\) 39.6055 1.28700 0.643502 0.765444i \(-0.277481\pi\)
0.643502 + 0.765444i \(0.277481\pi\)
\(948\) 3.62161 0.117624
\(949\) −4.13482 −0.134222
\(950\) 23.8321 0.773215
\(951\) −7.97269 −0.258532
\(952\) −0.441569 −0.0143113
\(953\) 0.252656 0.00818434 0.00409217 0.999992i \(-0.498697\pi\)
0.00409217 + 0.999992i \(0.498697\pi\)
\(954\) −0.760858 −0.0246337
\(955\) 1.53256 0.0495925
\(956\) 19.4788 0.629989
\(957\) 1.28498 0.0415374
\(958\) −43.2955 −1.39881
\(959\) −0.625763 −0.0202069
\(960\) 0.113167 0.00365245
\(961\) −19.5984 −0.632207
\(962\) −11.0028 −0.354745
\(963\) −1.61565 −0.0520635
\(964\) 25.5974 0.824435
\(965\) 0.121328 0.00390567
\(966\) 0.171428 0.00551561
\(967\) −29.7690 −0.957307 −0.478654 0.878004i \(-0.658875\pi\)
−0.478654 + 0.878004i \(0.658875\pi\)
\(968\) 10.9833 0.353016
\(969\) 33.9300 1.08999
\(970\) −0.741390 −0.0238046
\(971\) −29.7422 −0.954473 −0.477237 0.878775i \(-0.658362\pi\)
−0.477237 + 0.878775i \(0.658362\pi\)
\(972\) 2.47731 0.0794598
\(973\) 0.311159 0.00997529
\(974\) 12.0357 0.385649
\(975\) 13.0716 0.418627
\(976\) −4.95302 −0.158542
\(977\) 29.8376 0.954589 0.477295 0.878743i \(-0.341617\pi\)
0.477295 + 0.878743i \(0.341617\pi\)
\(978\) −2.72072 −0.0869991
\(979\) −1.10378 −0.0352770
\(980\) −0.476015 −0.0152058
\(981\) 1.20136 0.0383566
\(982\) −18.9412 −0.604437
\(983\) 50.5612 1.61265 0.806325 0.591472i \(-0.201453\pi\)
0.806325 + 0.591472i \(0.201453\pi\)
\(984\) 1.57581 0.0502350
\(985\) −0.444166 −0.0141523
\(986\) 25.5956 0.815129
\(987\) −0.0468371 −0.00149084
\(988\) −7.51313 −0.239025
\(989\) 13.0487 0.414925
\(990\) −0.00210457 −6.68877e−5 0
\(991\) 35.9668 1.14252 0.571261 0.820768i \(-0.306454\pi\)
0.571261 + 0.820768i \(0.306454\pi\)
\(992\) −3.37662 −0.107208
\(993\) −37.1521 −1.17899
\(994\) −0.335486 −0.0106410
\(995\) −1.04151 −0.0330182
\(996\) −4.66476 −0.147808
\(997\) −14.8725 −0.471017 −0.235509 0.971872i \(-0.575676\pi\)
−0.235509 + 0.971872i \(0.575676\pi\)
\(998\) 0.580220 0.0183665
\(999\) 37.6028 1.18970
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 \(a_p\))