Properties

Label 6026.2.a.h.1.7
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 1.7
Character \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-1.71989 q^{3}\) \(+1.00000 q^{4}\) \(-2.14325 q^{5}\) \(+1.71989 q^{6}\) \(-1.30637 q^{7}\) \(-1.00000 q^{8}\) \(-0.0419677 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-1.71989 q^{3}\) \(+1.00000 q^{4}\) \(-2.14325 q^{5}\) \(+1.71989 q^{6}\) \(-1.30637 q^{7}\) \(-1.00000 q^{8}\) \(-0.0419677 q^{9}\) \(+2.14325 q^{10}\) \(+4.74810 q^{11}\) \(-1.71989 q^{12}\) \(+1.19392 q^{13}\) \(+1.30637 q^{14}\) \(+3.68616 q^{15}\) \(+1.00000 q^{16}\) \(-1.31027 q^{17}\) \(+0.0419677 q^{18}\) \(+0.113276 q^{19}\) \(-2.14325 q^{20}\) \(+2.24681 q^{21}\) \(-4.74810 q^{22}\) \(-1.00000 q^{23}\) \(+1.71989 q^{24}\) \(-0.406485 q^{25}\) \(-1.19392 q^{26}\) \(+5.23186 q^{27}\) \(-1.30637 q^{28}\) \(-8.62398 q^{29}\) \(-3.68616 q^{30}\) \(-1.19203 q^{31}\) \(-1.00000 q^{32}\) \(-8.16623 q^{33}\) \(+1.31027 q^{34}\) \(+2.79987 q^{35}\) \(-0.0419677 q^{36}\) \(-7.65635 q^{37}\) \(-0.113276 q^{38}\) \(-2.05342 q^{39}\) \(+2.14325 q^{40}\) \(+4.88513 q^{41}\) \(-2.24681 q^{42}\) \(+6.12492 q^{43}\) \(+4.74810 q^{44}\) \(+0.0899473 q^{45}\) \(+1.00000 q^{46}\) \(+7.88063 q^{47}\) \(-1.71989 q^{48}\) \(-5.29341 q^{49}\) \(+0.406485 q^{50}\) \(+2.25353 q^{51}\) \(+1.19392 q^{52}\) \(+4.06464 q^{53}\) \(-5.23186 q^{54}\) \(-10.1764 q^{55}\) \(+1.30637 q^{56}\) \(-0.194822 q^{57}\) \(+8.62398 q^{58}\) \(-9.74386 q^{59}\) \(+3.68616 q^{60}\) \(+0.336312 q^{61}\) \(+1.19203 q^{62}\) \(+0.0548252 q^{63}\) \(+1.00000 q^{64}\) \(-2.55887 q^{65}\) \(+8.16623 q^{66}\) \(+8.95728 q^{67}\) \(-1.31027 q^{68}\) \(+1.71989 q^{69}\) \(-2.79987 q^{70}\) \(-1.24515 q^{71}\) \(+0.0419677 q^{72}\) \(-9.56377 q^{73}\) \(+7.65635 q^{74}\) \(+0.699111 q^{75}\) \(+0.113276 q^{76}\) \(-6.20276 q^{77}\) \(+2.05342 q^{78}\) \(+12.8401 q^{79}\) \(-2.14325 q^{80}\) \(-8.87234 q^{81}\) \(-4.88513 q^{82}\) \(+11.4351 q^{83}\) \(+2.24681 q^{84}\) \(+2.80824 q^{85}\) \(-6.12492 q^{86}\) \(+14.8323 q^{87}\) \(-4.74810 q^{88}\) \(+5.53195 q^{89}\) \(-0.0899473 q^{90}\) \(-1.55970 q^{91}\) \(-1.00000 q^{92}\) \(+2.05016 q^{93}\) \(-7.88063 q^{94}\) \(-0.242778 q^{95}\) \(+1.71989 q^{96}\) \(+8.36663 q^{97}\) \(+5.29341 q^{98}\) \(-0.199267 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 27q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 27q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut q^{12} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut 7q^{14} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 24q^{16} \) \(\mathstrut +\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 27q^{18} \) \(\mathstrut -\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut q^{20} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut q^{24} \) \(\mathstrut +\mathstrut q^{25} \) \(\mathstrut +\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut q^{27} \) \(\mathstrut -\mathstrut 7q^{28} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 6q^{30} \) \(\mathstrut -\mathstrut 23q^{31} \) \(\mathstrut -\mathstrut 24q^{32} \) \(\mathstrut -\mathstrut 6q^{33} \) \(\mathstrut -\mathstrut 5q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 27q^{36} \) \(\mathstrut -\mathstrut 6q^{37} \) \(\mathstrut +\mathstrut 20q^{38} \) \(\mathstrut -\mathstrut 39q^{39} \) \(\mathstrut +\mathstrut q^{40} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut -\mathstrut 44q^{43} \) \(\mathstrut -\mathstrut 4q^{44} \) \(\mathstrut -\mathstrut 13q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 32q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut -\mathstrut 13q^{49} \) \(\mathstrut -\mathstrut q^{50} \) \(\mathstrut -\mathstrut 44q^{51} \) \(\mathstrut -\mathstrut 5q^{52} \) \(\mathstrut +\mathstrut 21q^{53} \) \(\mathstrut +\mathstrut q^{54} \) \(\mathstrut -\mathstrut 13q^{55} \) \(\mathstrut +\mathstrut 7q^{56} \) \(\mathstrut +\mathstrut 10q^{57} \) \(\mathstrut +\mathstrut 6q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut -\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 40q^{61} \) \(\mathstrut +\mathstrut 23q^{62} \) \(\mathstrut -\mathstrut 54q^{63} \) \(\mathstrut +\mathstrut 24q^{64} \) \(\mathstrut -\mathstrut 29q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut -\mathstrut 17q^{67} \) \(\mathstrut +\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut q^{69} \) \(\mathstrut -\mathstrut 5q^{70} \) \(\mathstrut +\mathstrut 4q^{71} \) \(\mathstrut -\mathstrut 27q^{72} \) \(\mathstrut -\mathstrut 16q^{73} \) \(\mathstrut +\mathstrut 6q^{74} \) \(\mathstrut -\mathstrut 36q^{75} \) \(\mathstrut -\mathstrut 20q^{76} \) \(\mathstrut +\mathstrut 24q^{77} \) \(\mathstrut +\mathstrut 39q^{78} \) \(\mathstrut -\mathstrut 53q^{79} \) \(\mathstrut -\mathstrut q^{80} \) \(\mathstrut +\mathstrut 24q^{81} \) \(\mathstrut +\mathstrut q^{82} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 37q^{85} \) \(\mathstrut +\mathstrut 44q^{86} \) \(\mathstrut +\mathstrut 7q^{87} \) \(\mathstrut +\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 46q^{89} \) \(\mathstrut +\mathstrut 13q^{90} \) \(\mathstrut -\mathstrut 44q^{91} \) \(\mathstrut -\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 23q^{93} \) \(\mathstrut -\mathstrut 32q^{94} \) \(\mathstrut +\mathstrut 28q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut -\mathstrut 20q^{97} \) \(\mathstrut +\mathstrut 13q^{98} \) \(\mathstrut -\mathstrut 78q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.71989 −0.992981 −0.496490 0.868042i \(-0.665378\pi\)
−0.496490 + 0.868042i \(0.665378\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.14325 −0.958490 −0.479245 0.877681i \(-0.659089\pi\)
−0.479245 + 0.877681i \(0.659089\pi\)
\(6\) 1.71989 0.702143
\(7\) −1.30637 −0.493760 −0.246880 0.969046i \(-0.579405\pi\)
−0.246880 + 0.969046i \(0.579405\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.0419677 −0.0139892
\(10\) 2.14325 0.677755
\(11\) 4.74810 1.43161 0.715803 0.698302i \(-0.246061\pi\)
0.715803 + 0.698302i \(0.246061\pi\)
\(12\) −1.71989 −0.496490
\(13\) 1.19392 0.331135 0.165567 0.986198i \(-0.447054\pi\)
0.165567 + 0.986198i \(0.447054\pi\)
\(14\) 1.30637 0.349141
\(15\) 3.68616 0.951762
\(16\) 1.00000 0.250000
\(17\) −1.31027 −0.317788 −0.158894 0.987296i \(-0.550793\pi\)
−0.158894 + 0.987296i \(0.550793\pi\)
\(18\) 0.0419677 0.00989189
\(19\) 0.113276 0.0259873 0.0129936 0.999916i \(-0.495864\pi\)
0.0129936 + 0.999916i \(0.495864\pi\)
\(20\) −2.14325 −0.479245
\(21\) 2.24681 0.490294
\(22\) −4.74810 −1.01230
\(23\) −1.00000 −0.208514
\(24\) 1.71989 0.351072
\(25\) −0.406485 −0.0812971
\(26\) −1.19392 −0.234148
\(27\) 5.23186 1.00687
\(28\) −1.30637 −0.246880
\(29\) −8.62398 −1.60143 −0.800717 0.599043i \(-0.795548\pi\)
−0.800717 + 0.599043i \(0.795548\pi\)
\(30\) −3.68616 −0.672997
\(31\) −1.19203 −0.214095 −0.107047 0.994254i \(-0.534140\pi\)
−0.107047 + 0.994254i \(0.534140\pi\)
\(32\) −1.00000 −0.176777
\(33\) −8.16623 −1.42156
\(34\) 1.31027 0.224710
\(35\) 2.79987 0.473264
\(36\) −0.0419677 −0.00699462
\(37\) −7.65635 −1.25870 −0.629348 0.777123i \(-0.716678\pi\)
−0.629348 + 0.777123i \(0.716678\pi\)
\(38\) −0.113276 −0.0183758
\(39\) −2.05342 −0.328810
\(40\) 2.14325 0.338877
\(41\) 4.88513 0.762929 0.381464 0.924384i \(-0.375420\pi\)
0.381464 + 0.924384i \(0.375420\pi\)
\(42\) −2.24681 −0.346690
\(43\) 6.12492 0.934042 0.467021 0.884246i \(-0.345327\pi\)
0.467021 + 0.884246i \(0.345327\pi\)
\(44\) 4.74810 0.715803
\(45\) 0.0899473 0.0134086
\(46\) 1.00000 0.147442
\(47\) 7.88063 1.14951 0.574754 0.818326i \(-0.305098\pi\)
0.574754 + 0.818326i \(0.305098\pi\)
\(48\) −1.71989 −0.248245
\(49\) −5.29341 −0.756201
\(50\) 0.406485 0.0574857
\(51\) 2.25353 0.315557
\(52\) 1.19392 0.165567
\(53\) 4.06464 0.558321 0.279160 0.960244i \(-0.409944\pi\)
0.279160 + 0.960244i \(0.409944\pi\)
\(54\) −5.23186 −0.711966
\(55\) −10.1764 −1.37218
\(56\) 1.30637 0.174570
\(57\) −0.194822 −0.0258049
\(58\) 8.62398 1.13238
\(59\) −9.74386 −1.26854 −0.634271 0.773111i \(-0.718700\pi\)
−0.634271 + 0.773111i \(0.718700\pi\)
\(60\) 3.68616 0.475881
\(61\) 0.336312 0.0430604 0.0215302 0.999768i \(-0.493146\pi\)
0.0215302 + 0.999768i \(0.493146\pi\)
\(62\) 1.19203 0.151388
\(63\) 0.0548252 0.00690733
\(64\) 1.00000 0.125000
\(65\) −2.55887 −0.317389
\(66\) 8.16623 1.00519
\(67\) 8.95728 1.09431 0.547153 0.837033i \(-0.315712\pi\)
0.547153 + 0.837033i \(0.315712\pi\)
\(68\) −1.31027 −0.158894
\(69\) 1.71989 0.207051
\(70\) −2.79987 −0.334648
\(71\) −1.24515 −0.147772 −0.0738861 0.997267i \(-0.523540\pi\)
−0.0738861 + 0.997267i \(0.523540\pi\)
\(72\) 0.0419677 0.00494595
\(73\) −9.56377 −1.11935 −0.559677 0.828711i \(-0.689075\pi\)
−0.559677 + 0.828711i \(0.689075\pi\)
\(74\) 7.65635 0.890033
\(75\) 0.699111 0.0807264
\(76\) 0.113276 0.0129936
\(77\) −6.20276 −0.706870
\(78\) 2.05342 0.232504
\(79\) 12.8401 1.44462 0.722310 0.691569i \(-0.243080\pi\)
0.722310 + 0.691569i \(0.243080\pi\)
\(80\) −2.14325 −0.239622
\(81\) −8.87234 −0.985815
\(82\) −4.88513 −0.539472
\(83\) 11.4351 1.25517 0.627585 0.778548i \(-0.284043\pi\)
0.627585 + 0.778548i \(0.284043\pi\)
\(84\) 2.24681 0.245147
\(85\) 2.80824 0.304597
\(86\) −6.12492 −0.660467
\(87\) 14.8323 1.59019
\(88\) −4.74810 −0.506149
\(89\) 5.53195 0.586386 0.293193 0.956053i \(-0.405282\pi\)
0.293193 + 0.956053i \(0.405282\pi\)
\(90\) −0.0899473 −0.00948128
\(91\) −1.55970 −0.163501
\(92\) −1.00000 −0.104257
\(93\) 2.05016 0.212592
\(94\) −7.88063 −0.812825
\(95\) −0.242778 −0.0249085
\(96\) 1.71989 0.175536
\(97\) 8.36663 0.849503 0.424751 0.905310i \(-0.360361\pi\)
0.424751 + 0.905310i \(0.360361\pi\)
\(98\) 5.29341 0.534715
\(99\) −0.199267 −0.0200271
\(100\) −0.406485 −0.0406485
\(101\) 2.32659 0.231504 0.115752 0.993278i \(-0.463072\pi\)
0.115752 + 0.993278i \(0.463072\pi\)
\(102\) −2.25353 −0.223133
\(103\) 4.35870 0.429475 0.214738 0.976672i \(-0.431110\pi\)
0.214738 + 0.976672i \(0.431110\pi\)
\(104\) −1.19392 −0.117074
\(105\) −4.81547 −0.469942
\(106\) −4.06464 −0.394793
\(107\) 10.8528 1.04918 0.524588 0.851356i \(-0.324219\pi\)
0.524588 + 0.851356i \(0.324219\pi\)
\(108\) 5.23186 0.503436
\(109\) 17.1537 1.64302 0.821512 0.570191i \(-0.193131\pi\)
0.821512 + 0.570191i \(0.193131\pi\)
\(110\) 10.1764 0.970278
\(111\) 13.1681 1.24986
\(112\) −1.30637 −0.123440
\(113\) −4.20293 −0.395378 −0.197689 0.980265i \(-0.563344\pi\)
−0.197689 + 0.980265i \(0.563344\pi\)
\(114\) 0.194822 0.0182468
\(115\) 2.14325 0.199859
\(116\) −8.62398 −0.800717
\(117\) −0.0501063 −0.00463233
\(118\) 9.74386 0.896995
\(119\) 1.71170 0.156911
\(120\) −3.68616 −0.336499
\(121\) 11.5445 1.04950
\(122\) −0.336312 −0.0304483
\(123\) −8.40190 −0.757573
\(124\) −1.19203 −0.107047
\(125\) 11.5874 1.03641
\(126\) −0.0548252 −0.00488422
\(127\) 13.1941 1.17079 0.585394 0.810749i \(-0.300940\pi\)
0.585394 + 0.810749i \(0.300940\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −10.5342 −0.927485
\(130\) 2.55887 0.224428
\(131\) −1.00000 −0.0873704
\(132\) −8.16623 −0.710779
\(133\) −0.147980 −0.0128315
\(134\) −8.95728 −0.773791
\(135\) −11.2132 −0.965076
\(136\) 1.31027 0.112355
\(137\) 15.1515 1.29448 0.647241 0.762286i \(-0.275923\pi\)
0.647241 + 0.762286i \(0.275923\pi\)
\(138\) −1.71989 −0.146407
\(139\) −11.8906 −1.00854 −0.504272 0.863545i \(-0.668239\pi\)
−0.504272 + 0.863545i \(0.668239\pi\)
\(140\) 2.79987 0.236632
\(141\) −13.5538 −1.14144
\(142\) 1.24515 0.104491
\(143\) 5.66887 0.474055
\(144\) −0.0419677 −0.00349731
\(145\) 18.4833 1.53496
\(146\) 9.56377 0.791503
\(147\) 9.10410 0.750893
\(148\) −7.65635 −0.629348
\(149\) 6.76725 0.554395 0.277197 0.960813i \(-0.410594\pi\)
0.277197 + 0.960813i \(0.410594\pi\)
\(150\) −0.699111 −0.0570822
\(151\) −14.6117 −1.18908 −0.594541 0.804065i \(-0.702666\pi\)
−0.594541 + 0.804065i \(0.702666\pi\)
\(152\) −0.113276 −0.00918789
\(153\) 0.0549892 0.00444562
\(154\) 6.20276 0.499833
\(155\) 2.55481 0.205208
\(156\) −2.05342 −0.164405
\(157\) −5.16105 −0.411896 −0.205948 0.978563i \(-0.566028\pi\)
−0.205948 + 0.978563i \(0.566028\pi\)
\(158\) −12.8401 −1.02150
\(159\) −6.99074 −0.554402
\(160\) 2.14325 0.169439
\(161\) 1.30637 0.102956
\(162\) 8.87234 0.697077
\(163\) −17.9401 −1.40517 −0.702587 0.711598i \(-0.747972\pi\)
−0.702587 + 0.711598i \(0.747972\pi\)
\(164\) 4.88513 0.381464
\(165\) 17.5023 1.36255
\(166\) −11.4351 −0.887539
\(167\) −15.7089 −1.21559 −0.607795 0.794094i \(-0.707946\pi\)
−0.607795 + 0.794094i \(0.707946\pi\)
\(168\) −2.24681 −0.173345
\(169\) −11.5745 −0.890350
\(170\) −2.80824 −0.215382
\(171\) −0.00475394 −0.000363543 0
\(172\) 6.12492 0.467021
\(173\) −7.13838 −0.542721 −0.271360 0.962478i \(-0.587474\pi\)
−0.271360 + 0.962478i \(0.587474\pi\)
\(174\) −14.8323 −1.12444
\(175\) 0.531018 0.0401412
\(176\) 4.74810 0.357902
\(177\) 16.7584 1.25964
\(178\) −5.53195 −0.414637
\(179\) −22.6654 −1.69409 −0.847046 0.531519i \(-0.821621\pi\)
−0.847046 + 0.531519i \(0.821621\pi\)
\(180\) 0.0899473 0.00670428
\(181\) −4.59296 −0.341392 −0.170696 0.985324i \(-0.554602\pi\)
−0.170696 + 0.985324i \(0.554602\pi\)
\(182\) 1.55970 0.115613
\(183\) −0.578421 −0.0427581
\(184\) 1.00000 0.0737210
\(185\) 16.4095 1.20645
\(186\) −2.05016 −0.150325
\(187\) −6.22131 −0.454948
\(188\) 7.88063 0.574754
\(189\) −6.83472 −0.497153
\(190\) 0.242778 0.0176130
\(191\) −21.9018 −1.58476 −0.792381 0.610027i \(-0.791159\pi\)
−0.792381 + 0.610027i \(0.791159\pi\)
\(192\) −1.71989 −0.124123
\(193\) −16.9676 −1.22136 −0.610678 0.791879i \(-0.709103\pi\)
−0.610678 + 0.791879i \(0.709103\pi\)
\(194\) −8.36663 −0.600689
\(195\) 4.40099 0.315161
\(196\) −5.29341 −0.378101
\(197\) 14.5728 1.03827 0.519133 0.854693i \(-0.326255\pi\)
0.519133 + 0.854693i \(0.326255\pi\)
\(198\) 0.199267 0.0141613
\(199\) 14.0456 0.995666 0.497833 0.867273i \(-0.334129\pi\)
0.497833 + 0.867273i \(0.334129\pi\)
\(200\) 0.406485 0.0287429
\(201\) −15.4056 −1.08662
\(202\) −2.32659 −0.163698
\(203\) 11.2661 0.790724
\(204\) 2.25353 0.157779
\(205\) −10.4700 −0.731259
\(206\) −4.35870 −0.303685
\(207\) 0.0419677 0.00291696
\(208\) 1.19392 0.0827837
\(209\) 0.537846 0.0372036
\(210\) 4.81547 0.332299
\(211\) −7.95729 −0.547803 −0.273901 0.961758i \(-0.588314\pi\)
−0.273901 + 0.961758i \(0.588314\pi\)
\(212\) 4.06464 0.279160
\(213\) 2.14153 0.146735
\(214\) −10.8528 −0.741880
\(215\) −13.1272 −0.895269
\(216\) −5.23186 −0.355983
\(217\) 1.55723 0.105711
\(218\) −17.1537 −1.16179
\(219\) 16.4487 1.11150
\(220\) −10.1764 −0.686090
\(221\) −1.56437 −0.105231
\(222\) −13.1681 −0.883786
\(223\) −9.02798 −0.604558 −0.302279 0.953219i \(-0.597747\pi\)
−0.302279 + 0.953219i \(0.597747\pi\)
\(224\) 1.30637 0.0872852
\(225\) 0.0170593 0.00113728
\(226\) 4.20293 0.279575
\(227\) 19.7457 1.31057 0.655283 0.755383i \(-0.272549\pi\)
0.655283 + 0.755383i \(0.272549\pi\)
\(228\) −0.194822 −0.0129024
\(229\) −7.72671 −0.510595 −0.255298 0.966863i \(-0.582173\pi\)
−0.255298 + 0.966863i \(0.582173\pi\)
\(230\) −2.14325 −0.141322
\(231\) 10.6681 0.701908
\(232\) 8.62398 0.566192
\(233\) −5.21127 −0.341402 −0.170701 0.985323i \(-0.554603\pi\)
−0.170701 + 0.985323i \(0.554603\pi\)
\(234\) 0.0501063 0.00327555
\(235\) −16.8902 −1.10179
\(236\) −9.74386 −0.634271
\(237\) −22.0835 −1.43448
\(238\) −1.71170 −0.110953
\(239\) 11.9227 0.771213 0.385606 0.922663i \(-0.373992\pi\)
0.385606 + 0.922663i \(0.373992\pi\)
\(240\) 3.68616 0.237941
\(241\) 0.950549 0.0612303 0.0306151 0.999531i \(-0.490253\pi\)
0.0306151 + 0.999531i \(0.490253\pi\)
\(242\) −11.5445 −0.742107
\(243\) −0.436109 −0.0279764
\(244\) 0.336312 0.0215302
\(245\) 11.3451 0.724811
\(246\) 8.40190 0.535685
\(247\) 0.135243 0.00860529
\(248\) 1.19203 0.0756939
\(249\) −19.6672 −1.24636
\(250\) −11.5874 −0.732854
\(251\) −4.37103 −0.275897 −0.137949 0.990439i \(-0.544051\pi\)
−0.137949 + 0.990439i \(0.544051\pi\)
\(252\) 0.0548252 0.00345366
\(253\) −4.74810 −0.298511
\(254\) −13.1941 −0.827872
\(255\) −4.82988 −0.302459
\(256\) 1.00000 0.0625000
\(257\) 1.17486 0.0732858 0.0366429 0.999328i \(-0.488334\pi\)
0.0366429 + 0.999328i \(0.488334\pi\)
\(258\) 10.5342 0.655831
\(259\) 10.0020 0.621494
\(260\) −2.55887 −0.158695
\(261\) 0.361929 0.0224029
\(262\) 1.00000 0.0617802
\(263\) 19.5813 1.20743 0.603717 0.797199i \(-0.293686\pi\)
0.603717 + 0.797199i \(0.293686\pi\)
\(264\) 8.16623 0.502597
\(265\) −8.71153 −0.535145
\(266\) 0.147980 0.00907322
\(267\) −9.51437 −0.582270
\(268\) 8.95728 0.547153
\(269\) 0.279423 0.0170367 0.00851836 0.999964i \(-0.497288\pi\)
0.00851836 + 0.999964i \(0.497288\pi\)
\(270\) 11.2132 0.682412
\(271\) −26.6202 −1.61706 −0.808531 0.588454i \(-0.799737\pi\)
−0.808531 + 0.588454i \(0.799737\pi\)
\(272\) −1.31027 −0.0794470
\(273\) 2.68252 0.162353
\(274\) −15.1515 −0.915336
\(275\) −1.93003 −0.116385
\(276\) 1.71989 0.103525
\(277\) 30.0658 1.80648 0.903241 0.429134i \(-0.141181\pi\)
0.903241 + 0.429134i \(0.141181\pi\)
\(278\) 11.8906 0.713148
\(279\) 0.0500268 0.00299502
\(280\) −2.79987 −0.167324
\(281\) −20.7955 −1.24055 −0.620277 0.784383i \(-0.712980\pi\)
−0.620277 + 0.784383i \(0.712980\pi\)
\(282\) 13.5538 0.807120
\(283\) −30.4313 −1.80895 −0.904477 0.426522i \(-0.859739\pi\)
−0.904477 + 0.426522i \(0.859739\pi\)
\(284\) −1.24515 −0.0738861
\(285\) 0.417553 0.0247337
\(286\) −5.66887 −0.335207
\(287\) −6.38176 −0.376703
\(288\) 0.0419677 0.00247297
\(289\) −15.2832 −0.899011
\(290\) −18.4833 −1.08538
\(291\) −14.3897 −0.843540
\(292\) −9.56377 −0.559677
\(293\) 11.6987 0.683444 0.341722 0.939801i \(-0.388990\pi\)
0.341722 + 0.939801i \(0.388990\pi\)
\(294\) −9.10410 −0.530962
\(295\) 20.8835 1.21588
\(296\) 7.65635 0.445016
\(297\) 24.8414 1.44144
\(298\) −6.76725 −0.392016
\(299\) −1.19392 −0.0690463
\(300\) 0.699111 0.0403632
\(301\) −8.00138 −0.461192
\(302\) 14.6117 0.840808
\(303\) −4.00148 −0.229879
\(304\) 0.113276 0.00649682
\(305\) −0.720801 −0.0412729
\(306\) −0.0549892 −0.00314353
\(307\) 30.5843 1.74554 0.872769 0.488134i \(-0.162322\pi\)
0.872769 + 0.488134i \(0.162322\pi\)
\(308\) −6.20276 −0.353435
\(309\) −7.49649 −0.426460
\(310\) −2.55481 −0.145104
\(311\) 31.6222 1.79313 0.896566 0.442910i \(-0.146054\pi\)
0.896566 + 0.442910i \(0.146054\pi\)
\(312\) 2.05342 0.116252
\(313\) −14.5106 −0.820185 −0.410092 0.912044i \(-0.634504\pi\)
−0.410092 + 0.912044i \(0.634504\pi\)
\(314\) 5.16105 0.291255
\(315\) −0.117504 −0.00662060
\(316\) 12.8401 0.722310
\(317\) 13.2217 0.742604 0.371302 0.928512i \(-0.378912\pi\)
0.371302 + 0.928512i \(0.378912\pi\)
\(318\) 6.99074 0.392021
\(319\) −40.9476 −2.29262
\(320\) −2.14325 −0.119811
\(321\) −18.6656 −1.04181
\(322\) −1.30637 −0.0728009
\(323\) −0.148422 −0.00825845
\(324\) −8.87234 −0.492908
\(325\) −0.485312 −0.0269203
\(326\) 17.9401 0.993608
\(327\) −29.5025 −1.63149
\(328\) −4.88513 −0.269736
\(329\) −10.2950 −0.567581
\(330\) −17.5023 −0.963468
\(331\) 8.20755 0.451128 0.225564 0.974228i \(-0.427578\pi\)
0.225564 + 0.974228i \(0.427578\pi\)
\(332\) 11.4351 0.627585
\(333\) 0.321320 0.0176082
\(334\) 15.7089 0.859552
\(335\) −19.1977 −1.04888
\(336\) 2.24681 0.122573
\(337\) −16.0731 −0.875557 −0.437779 0.899083i \(-0.644235\pi\)
−0.437779 + 0.899083i \(0.644235\pi\)
\(338\) 11.5745 0.629572
\(339\) 7.22859 0.392603
\(340\) 2.80824 0.152298
\(341\) −5.65987 −0.306499
\(342\) 0.00475394 0.000257063 0
\(343\) 16.0597 0.867142
\(344\) −6.12492 −0.330234
\(345\) −3.68616 −0.198456
\(346\) 7.13838 0.383762
\(347\) −1.50632 −0.0808634 −0.0404317 0.999182i \(-0.512873\pi\)
−0.0404317 + 0.999182i \(0.512873\pi\)
\(348\) 14.8323 0.795096
\(349\) 32.2290 1.72518 0.862591 0.505902i \(-0.168840\pi\)
0.862591 + 0.505902i \(0.168840\pi\)
\(350\) −0.531018 −0.0283841
\(351\) 6.24644 0.333410
\(352\) −4.74810 −0.253075
\(353\) −18.4442 −0.981688 −0.490844 0.871248i \(-0.663311\pi\)
−0.490844 + 0.871248i \(0.663311\pi\)
\(354\) −16.7584 −0.890699
\(355\) 2.66867 0.141638
\(356\) 5.53195 0.293193
\(357\) −2.94393 −0.155810
\(358\) 22.6654 1.19790
\(359\) 25.0310 1.32108 0.660542 0.750789i \(-0.270327\pi\)
0.660542 + 0.750789i \(0.270327\pi\)
\(360\) −0.0899473 −0.00474064
\(361\) −18.9872 −0.999325
\(362\) 4.59296 0.241401
\(363\) −19.8553 −1.04213
\(364\) −1.55970 −0.0817505
\(365\) 20.4975 1.07289
\(366\) 0.578421 0.0302346
\(367\) 0.325219 0.0169763 0.00848814 0.999964i \(-0.497298\pi\)
0.00848814 + 0.999964i \(0.497298\pi\)
\(368\) −1.00000 −0.0521286
\(369\) −0.205018 −0.0106728
\(370\) −16.4095 −0.853088
\(371\) −5.30990 −0.275676
\(372\) 2.05016 0.106296
\(373\) −11.1171 −0.575623 −0.287811 0.957687i \(-0.592928\pi\)
−0.287811 + 0.957687i \(0.592928\pi\)
\(374\) 6.22131 0.321696
\(375\) −19.9292 −1.02914
\(376\) −7.88063 −0.406413
\(377\) −10.2964 −0.530290
\(378\) 6.83472 0.351540
\(379\) −21.1963 −1.08878 −0.544391 0.838832i \(-0.683239\pi\)
−0.544391 + 0.838832i \(0.683239\pi\)
\(380\) −0.242778 −0.0124543
\(381\) −22.6925 −1.16257
\(382\) 21.9018 1.12060
\(383\) −27.9138 −1.42633 −0.713164 0.700998i \(-0.752738\pi\)
−0.713164 + 0.700998i \(0.752738\pi\)
\(384\) 1.71989 0.0877679
\(385\) 13.2941 0.677528
\(386\) 16.9676 0.863629
\(387\) −0.257049 −0.0130665
\(388\) 8.36663 0.424751
\(389\) −16.7983 −0.851708 −0.425854 0.904792i \(-0.640026\pi\)
−0.425854 + 0.904792i \(0.640026\pi\)
\(390\) −4.40099 −0.222853
\(391\) 1.31027 0.0662634
\(392\) 5.29341 0.267358
\(393\) 1.71989 0.0867571
\(394\) −14.5728 −0.734166
\(395\) −27.5195 −1.38465
\(396\) −0.199267 −0.0100136
\(397\) 7.41739 0.372268 0.186134 0.982524i \(-0.440404\pi\)
0.186134 + 0.982524i \(0.440404\pi\)
\(398\) −14.0456 −0.704042
\(399\) 0.254509 0.0127414
\(400\) −0.406485 −0.0203243
\(401\) 8.45159 0.422052 0.211026 0.977480i \(-0.432319\pi\)
0.211026 + 0.977480i \(0.432319\pi\)
\(402\) 15.4056 0.768360
\(403\) −1.42319 −0.0708942
\(404\) 2.32659 0.115752
\(405\) 19.0156 0.944894
\(406\) −11.2661 −0.559126
\(407\) −36.3531 −1.80196
\(408\) −2.25353 −0.111566
\(409\) −19.1937 −0.949065 −0.474533 0.880238i \(-0.657383\pi\)
−0.474533 + 0.880238i \(0.657383\pi\)
\(410\) 10.4700 0.517078
\(411\) −26.0590 −1.28539
\(412\) 4.35870 0.214738
\(413\) 12.7290 0.626355
\(414\) −0.0419677 −0.00206260
\(415\) −24.5084 −1.20307
\(416\) −1.19392 −0.0585369
\(417\) 20.4505 1.00146
\(418\) −0.537846 −0.0263069
\(419\) 20.3707 0.995172 0.497586 0.867415i \(-0.334220\pi\)
0.497586 + 0.867415i \(0.334220\pi\)
\(420\) −4.81547 −0.234971
\(421\) −37.4866 −1.82699 −0.913493 0.406853i \(-0.866626\pi\)
−0.913493 + 0.406853i \(0.866626\pi\)
\(422\) 7.95729 0.387355
\(423\) −0.330732 −0.0160808
\(424\) −4.06464 −0.197396
\(425\) 0.532607 0.0258352
\(426\) −2.14153 −0.103757
\(427\) −0.439347 −0.0212615
\(428\) 10.8528 0.524588
\(429\) −9.74985 −0.470727
\(430\) 13.1272 0.633051
\(431\) −18.6956 −0.900536 −0.450268 0.892893i \(-0.648672\pi\)
−0.450268 + 0.892893i \(0.648672\pi\)
\(432\) 5.23186 0.251718
\(433\) −7.80537 −0.375102 −0.187551 0.982255i \(-0.560055\pi\)
−0.187551 + 0.982255i \(0.560055\pi\)
\(434\) −1.55723 −0.0747492
\(435\) −31.7894 −1.52418
\(436\) 17.1537 0.821512
\(437\) −0.113276 −0.00541872
\(438\) −16.4487 −0.785948
\(439\) −4.02590 −0.192146 −0.0960729 0.995374i \(-0.530628\pi\)
−0.0960729 + 0.995374i \(0.530628\pi\)
\(440\) 10.1764 0.485139
\(441\) 0.222152 0.0105787
\(442\) 1.56437 0.0744093
\(443\) −11.7695 −0.559187 −0.279593 0.960119i \(-0.590200\pi\)
−0.279593 + 0.960119i \(0.590200\pi\)
\(444\) 13.1681 0.624931
\(445\) −11.8564 −0.562045
\(446\) 9.02798 0.427487
\(447\) −11.6389 −0.550503
\(448\) −1.30637 −0.0617200
\(449\) 24.8386 1.17220 0.586102 0.810237i \(-0.300662\pi\)
0.586102 + 0.810237i \(0.300662\pi\)
\(450\) −0.0170593 −0.000804182 0
\(451\) 23.1951 1.09221
\(452\) −4.20293 −0.197689
\(453\) 25.1305 1.18074
\(454\) −19.7457 −0.926711
\(455\) 3.34282 0.156714
\(456\) 0.194822 0.00912340
\(457\) −8.47035 −0.396226 −0.198113 0.980179i \(-0.563481\pi\)
−0.198113 + 0.980179i \(0.563481\pi\)
\(458\) 7.72671 0.361045
\(459\) −6.85517 −0.319972
\(460\) 2.14325 0.0999295
\(461\) 5.75911 0.268228 0.134114 0.990966i \(-0.457181\pi\)
0.134114 + 0.990966i \(0.457181\pi\)
\(462\) −10.6681 −0.496324
\(463\) −7.74262 −0.359830 −0.179915 0.983682i \(-0.557582\pi\)
−0.179915 + 0.983682i \(0.557582\pi\)
\(464\) −8.62398 −0.400358
\(465\) −4.39401 −0.203767
\(466\) 5.21127 0.241407
\(467\) −25.4019 −1.17546 −0.587729 0.809058i \(-0.699978\pi\)
−0.587729 + 0.809058i \(0.699978\pi\)
\(468\) −0.0501063 −0.00231616
\(469\) −11.7015 −0.540324
\(470\) 16.8902 0.779085
\(471\) 8.87645 0.409005
\(472\) 9.74386 0.448497
\(473\) 29.0818 1.33718
\(474\) 22.0835 1.01433
\(475\) −0.0460450 −0.00211269
\(476\) 1.71170 0.0784555
\(477\) −0.170584 −0.00781049
\(478\) −11.9227 −0.545330
\(479\) −35.9072 −1.64064 −0.820322 0.571902i \(-0.806206\pi\)
−0.820322 + 0.571902i \(0.806206\pi\)
\(480\) −3.68616 −0.168249
\(481\) −9.14109 −0.416798
\(482\) −0.950549 −0.0432963
\(483\) −2.24681 −0.102233
\(484\) 11.5445 0.524749
\(485\) −17.9318 −0.814240
\(486\) 0.436109 0.0197823
\(487\) 29.9563 1.35745 0.678725 0.734392i \(-0.262533\pi\)
0.678725 + 0.734392i \(0.262533\pi\)
\(488\) −0.336312 −0.0152241
\(489\) 30.8550 1.39531
\(490\) −11.3451 −0.512519
\(491\) −0.427788 −0.0193058 −0.00965290 0.999953i \(-0.503073\pi\)
−0.00965290 + 0.999953i \(0.503073\pi\)
\(492\) −8.40190 −0.378787
\(493\) 11.2998 0.508916
\(494\) −0.135243 −0.00608486
\(495\) 0.427079 0.0191958
\(496\) −1.19203 −0.0535237
\(497\) 1.62662 0.0729640
\(498\) 19.6672 0.881309
\(499\) −32.9391 −1.47456 −0.737279 0.675589i \(-0.763890\pi\)
−0.737279 + 0.675589i \(0.763890\pi\)
\(500\) 11.5874 0.518206
\(501\) 27.0176 1.20706
\(502\) 4.37103 0.195089
\(503\) 35.6081 1.58769 0.793844 0.608122i \(-0.208077\pi\)
0.793844 + 0.608122i \(0.208077\pi\)
\(504\) −0.0548252 −0.00244211
\(505\) −4.98646 −0.221894
\(506\) 4.74810 0.211079
\(507\) 19.9070 0.884100
\(508\) 13.1941 0.585394
\(509\) −13.4443 −0.595907 −0.297954 0.954580i \(-0.596304\pi\)
−0.297954 + 0.954580i \(0.596304\pi\)
\(510\) 4.82988 0.213871
\(511\) 12.4938 0.552692
\(512\) −1.00000 −0.0441942
\(513\) 0.592644 0.0261659
\(514\) −1.17486 −0.0518209
\(515\) −9.34177 −0.411648
\(516\) −10.5342 −0.463743
\(517\) 37.4181 1.64564
\(518\) −10.0020 −0.439462
\(519\) 12.2773 0.538911
\(520\) 2.55887 0.112214
\(521\) 15.2942 0.670051 0.335025 0.942209i \(-0.391255\pi\)
0.335025 + 0.942209i \(0.391255\pi\)
\(522\) −0.361929 −0.0158412
\(523\) −35.3348 −1.54508 −0.772542 0.634963i \(-0.781015\pi\)
−0.772542 + 0.634963i \(0.781015\pi\)
\(524\) −1.00000 −0.0436852
\(525\) −0.913295 −0.0398595
\(526\) −19.5813 −0.853784
\(527\) 1.56188 0.0680367
\(528\) −8.16623 −0.355390
\(529\) 1.00000 0.0434783
\(530\) 8.71153 0.378405
\(531\) 0.408928 0.0177460
\(532\) −0.147980 −0.00641574
\(533\) 5.83247 0.252632
\(534\) 9.51437 0.411727
\(535\) −23.2602 −1.00562
\(536\) −8.95728 −0.386896
\(537\) 38.9821 1.68220
\(538\) −0.279423 −0.0120468
\(539\) −25.1337 −1.08258
\(540\) −11.2132 −0.482538
\(541\) −2.67913 −0.115185 −0.0575924 0.998340i \(-0.518342\pi\)
−0.0575924 + 0.998340i \(0.518342\pi\)
\(542\) 26.6202 1.14343
\(543\) 7.89940 0.338996
\(544\) 1.31027 0.0561775
\(545\) −36.7646 −1.57482
\(546\) −2.68252 −0.114801
\(547\) −26.4471 −1.13080 −0.565399 0.824818i \(-0.691278\pi\)
−0.565399 + 0.824818i \(0.691278\pi\)
\(548\) 15.1515 0.647241
\(549\) −0.0141143 −0.000602382 0
\(550\) 1.93003 0.0822969
\(551\) −0.976890 −0.0416169
\(552\) −1.71989 −0.0732035
\(553\) −16.7738 −0.713296
\(554\) −30.0658 −1.27738
\(555\) −28.2225 −1.19798
\(556\) −11.8906 −0.504272
\(557\) −7.98297 −0.338250 −0.169125 0.985595i \(-0.554094\pi\)
−0.169125 + 0.985595i \(0.554094\pi\)
\(558\) −0.0500268 −0.00211780
\(559\) 7.31268 0.309294
\(560\) 2.79987 0.118316
\(561\) 10.7000 0.451754
\(562\) 20.7955 0.877204
\(563\) −32.5769 −1.37295 −0.686475 0.727153i \(-0.740843\pi\)
−0.686475 + 0.727153i \(0.740843\pi\)
\(564\) −13.5538 −0.570720
\(565\) 9.00792 0.378966
\(566\) 30.4313 1.27912
\(567\) 11.5905 0.486756
\(568\) 1.24515 0.0522454
\(569\) −37.2092 −1.55989 −0.779946 0.625847i \(-0.784754\pi\)
−0.779946 + 0.625847i \(0.784754\pi\)
\(570\) −0.417553 −0.0174894
\(571\) −14.1233 −0.591041 −0.295520 0.955336i \(-0.595493\pi\)
−0.295520 + 0.955336i \(0.595493\pi\)
\(572\) 5.66887 0.237027
\(573\) 37.6688 1.57364
\(574\) 6.38176 0.266370
\(575\) 0.406485 0.0169516
\(576\) −0.0419677 −0.00174866
\(577\) 27.9249 1.16253 0.581265 0.813714i \(-0.302558\pi\)
0.581265 + 0.813714i \(0.302558\pi\)
\(578\) 15.2832 0.635697
\(579\) 29.1825 1.21278
\(580\) 18.4833 0.767479
\(581\) −14.9385 −0.619752
\(582\) 14.3897 0.596473
\(583\) 19.2993 0.799296
\(584\) 9.56377 0.395752
\(585\) 0.107390 0.00444004
\(586\) −11.6987 −0.483268
\(587\) 21.4175 0.883995 0.441998 0.897016i \(-0.354270\pi\)
0.441998 + 0.897016i \(0.354270\pi\)
\(588\) 9.10410 0.375447
\(589\) −0.135028 −0.00556374
\(590\) −20.8835 −0.859760
\(591\) −25.0636 −1.03098
\(592\) −7.65635 −0.314674
\(593\) 5.12394 0.210415 0.105207 0.994450i \(-0.466449\pi\)
0.105207 + 0.994450i \(0.466449\pi\)
\(594\) −24.8414 −1.01926
\(595\) −3.66859 −0.150398
\(596\) 6.76725 0.277197
\(597\) −24.1569 −0.988678
\(598\) 1.19392 0.0488231
\(599\) 45.0047 1.83884 0.919422 0.393272i \(-0.128657\pi\)
0.919422 + 0.393272i \(0.128657\pi\)
\(600\) −0.699111 −0.0285411
\(601\) −15.6494 −0.638353 −0.319176 0.947695i \(-0.603406\pi\)
−0.319176 + 0.947695i \(0.603406\pi\)
\(602\) 8.00138 0.326112
\(603\) −0.375917 −0.0153085
\(604\) −14.6117 −0.594541
\(605\) −24.7427 −1.00593
\(606\) 4.00148 0.162549
\(607\) 8.53550 0.346445 0.173223 0.984883i \(-0.444582\pi\)
0.173223 + 0.984883i \(0.444582\pi\)
\(608\) −0.113276 −0.00459395
\(609\) −19.3764 −0.785173
\(610\) 0.720801 0.0291844
\(611\) 9.40887 0.380642
\(612\) 0.0549892 0.00222281
\(613\) 24.2113 0.977886 0.488943 0.872316i \(-0.337383\pi\)
0.488943 + 0.872316i \(0.337383\pi\)
\(614\) −30.5843 −1.23428
\(615\) 18.0074 0.726127
\(616\) 6.20276 0.249916
\(617\) 10.0339 0.403951 0.201975 0.979391i \(-0.435264\pi\)
0.201975 + 0.979391i \(0.435264\pi\)
\(618\) 7.49649 0.301553
\(619\) −17.4888 −0.702934 −0.351467 0.936200i \(-0.614317\pi\)
−0.351467 + 0.936200i \(0.614317\pi\)
\(620\) 2.55481 0.102604
\(621\) −5.23186 −0.209947
\(622\) −31.6222 −1.26794
\(623\) −7.22675 −0.289534
\(624\) −2.05342 −0.0822026
\(625\) −22.8023 −0.912094
\(626\) 14.5106 0.579958
\(627\) −0.925037 −0.0369424
\(628\) −5.16105 −0.205948
\(629\) 10.0319 0.399999
\(630\) 0.117504 0.00468147
\(631\) −28.4408 −1.13221 −0.566105 0.824333i \(-0.691550\pi\)
−0.566105 + 0.824333i \(0.691550\pi\)
\(632\) −12.8401 −0.510751
\(633\) 13.6857 0.543957
\(634\) −13.2217 −0.525100
\(635\) −28.2783 −1.12219
\(636\) −6.99074 −0.277201
\(637\) −6.31992 −0.250404
\(638\) 40.9476 1.62113
\(639\) 0.0522562 0.00206722
\(640\) 2.14325 0.0847193
\(641\) 4.69292 0.185359 0.0926796 0.995696i \(-0.470457\pi\)
0.0926796 + 0.995696i \(0.470457\pi\)
\(642\) 18.6656 0.736672
\(643\) 25.2909 0.997376 0.498688 0.866782i \(-0.333815\pi\)
0.498688 + 0.866782i \(0.333815\pi\)
\(644\) 1.30637 0.0514780
\(645\) 22.5774 0.888985
\(646\) 0.148422 0.00583960
\(647\) −38.3839 −1.50903 −0.754514 0.656284i \(-0.772127\pi\)
−0.754514 + 0.656284i \(0.772127\pi\)
\(648\) 8.87234 0.348538
\(649\) −46.2648 −1.81605
\(650\) 0.485312 0.0190355
\(651\) −2.67826 −0.104969
\(652\) −17.9401 −0.702587
\(653\) −44.8498 −1.75511 −0.877554 0.479478i \(-0.840826\pi\)
−0.877554 + 0.479478i \(0.840826\pi\)
\(654\) 29.5025 1.15364
\(655\) 2.14325 0.0837437
\(656\) 4.88513 0.190732
\(657\) 0.401370 0.0156589
\(658\) 10.2950 0.401340
\(659\) 18.6965 0.728311 0.364156 0.931338i \(-0.381358\pi\)
0.364156 + 0.931338i \(0.381358\pi\)
\(660\) 17.5023 0.681275
\(661\) 21.0524 0.818844 0.409422 0.912345i \(-0.365730\pi\)
0.409422 + 0.912345i \(0.365730\pi\)
\(662\) −8.20755 −0.318995
\(663\) 2.69054 0.104492
\(664\) −11.4351 −0.443770
\(665\) 0.317157 0.0122988
\(666\) −0.321320 −0.0124509
\(667\) 8.62398 0.333922
\(668\) −15.7089 −0.607795
\(669\) 15.5272 0.600315
\(670\) 19.1977 0.741671
\(671\) 1.59684 0.0616455
\(672\) −2.24681 −0.0866725
\(673\) −18.4051 −0.709463 −0.354732 0.934968i \(-0.615428\pi\)
−0.354732 + 0.934968i \(0.615428\pi\)
\(674\) 16.0731 0.619112
\(675\) −2.12667 −0.0818557
\(676\) −11.5745 −0.445175
\(677\) 11.3329 0.435560 0.217780 0.975998i \(-0.430118\pi\)
0.217780 + 0.975998i \(0.430118\pi\)
\(678\) −7.22859 −0.277612
\(679\) −10.9299 −0.419450
\(680\) −2.80824 −0.107691
\(681\) −33.9605 −1.30137
\(682\) 5.65987 0.216728
\(683\) −36.7981 −1.40804 −0.704021 0.710179i \(-0.748614\pi\)
−0.704021 + 0.710179i \(0.748614\pi\)
\(684\) −0.00475394 −0.000181771 0
\(685\) −32.4735 −1.24075
\(686\) −16.0597 −0.613162
\(687\) 13.2891 0.507011
\(688\) 6.12492 0.233510
\(689\) 4.85286 0.184879
\(690\) 3.68616 0.140330
\(691\) −34.4811 −1.31172 −0.655862 0.754881i \(-0.727695\pi\)
−0.655862 + 0.754881i \(0.727695\pi\)
\(692\) −7.13838 −0.271360
\(693\) 0.260316 0.00988858
\(694\) 1.50632 0.0571790
\(695\) 25.4844 0.966679
\(696\) −14.8323 −0.562218
\(697\) −6.40085 −0.242450
\(698\) −32.2290 −1.21989
\(699\) 8.96283 0.339005
\(700\) 0.531018 0.0200706
\(701\) −42.8496 −1.61841 −0.809203 0.587529i \(-0.800101\pi\)
−0.809203 + 0.587529i \(0.800101\pi\)
\(702\) −6.24644 −0.235757
\(703\) −0.867280 −0.0327101
\(704\) 4.74810 0.178951
\(705\) 29.0493 1.09406
\(706\) 18.4442 0.694158
\(707\) −3.03937 −0.114307
\(708\) 16.7584 0.629819
\(709\) −47.9555 −1.80101 −0.900503 0.434850i \(-0.856801\pi\)
−0.900503 + 0.434850i \(0.856801\pi\)
\(710\) −2.66867 −0.100153
\(711\) −0.538869 −0.0202092
\(712\) −5.53195 −0.207319
\(713\) 1.19203 0.0446418
\(714\) 2.94393 0.110174
\(715\) −12.1498 −0.454377
\(716\) −22.6654 −0.847046
\(717\) −20.5057 −0.765800
\(718\) −25.0310 −0.934147
\(719\) 39.9379 1.48943 0.744716 0.667382i \(-0.232585\pi\)
0.744716 + 0.667382i \(0.232585\pi\)
\(720\) 0.0899473 0.00335214
\(721\) −5.69405 −0.212058
\(722\) 18.9872 0.706629
\(723\) −1.63484 −0.0608005
\(724\) −4.59296 −0.170696
\(725\) 3.50552 0.130192
\(726\) 19.8553 0.736898
\(727\) −9.20926 −0.341553 −0.170776 0.985310i \(-0.554628\pi\)
−0.170776 + 0.985310i \(0.554628\pi\)
\(728\) 1.55970 0.0578063
\(729\) 27.3671 1.01360
\(730\) −20.4975 −0.758648
\(731\) −8.02532 −0.296827
\(732\) −0.578421 −0.0213791
\(733\) −6.05931 −0.223806 −0.111903 0.993719i \(-0.535695\pi\)
−0.111903 + 0.993719i \(0.535695\pi\)
\(734\) −0.325219 −0.0120040
\(735\) −19.5123 −0.719724
\(736\) 1.00000 0.0368605
\(737\) 42.5301 1.56662
\(738\) 0.205018 0.00754681
\(739\) −42.3001 −1.55604 −0.778018 0.628242i \(-0.783775\pi\)
−0.778018 + 0.628242i \(0.783775\pi\)
\(740\) 16.4095 0.603224
\(741\) −0.232603 −0.00854489
\(742\) 5.30990 0.194933
\(743\) −49.9222 −1.83147 −0.915734 0.401785i \(-0.868390\pi\)
−0.915734 + 0.401785i \(0.868390\pi\)
\(744\) −2.05016 −0.0751626
\(745\) −14.5039 −0.531382
\(746\) 11.1171 0.407027
\(747\) −0.479907 −0.0175589
\(748\) −6.22131 −0.227474
\(749\) −14.1777 −0.518041
\(750\) 19.9292 0.727710
\(751\) 30.7250 1.12117 0.560586 0.828096i \(-0.310576\pi\)
0.560586 + 0.828096i \(0.310576\pi\)
\(752\) 7.88063 0.287377
\(753\) 7.51771 0.273961
\(754\) 10.2964 0.374972
\(755\) 31.3165 1.13972
\(756\) −6.83472 −0.248576
\(757\) −48.1973 −1.75176 −0.875881 0.482527i \(-0.839719\pi\)
−0.875881 + 0.482527i \(0.839719\pi\)
\(758\) 21.1963 0.769885
\(759\) 8.16623 0.296415
\(760\) 0.242778 0.00880650
\(761\) −50.9334 −1.84633 −0.923167 0.384399i \(-0.874409\pi\)
−0.923167 + 0.384399i \(0.874409\pi\)
\(762\) 22.6925 0.822061
\(763\) −22.4090 −0.811260
\(764\) −21.9018 −0.792381
\(765\) −0.117856 −0.00426108
\(766\) 27.9138 1.00857
\(767\) −11.6334 −0.420058
\(768\) −1.71989 −0.0620613
\(769\) −30.3248 −1.09354 −0.546771 0.837282i \(-0.684143\pi\)
−0.546771 + 0.837282i \(0.684143\pi\)
\(770\) −13.2941 −0.479084
\(771\) −2.02064 −0.0727714
\(772\) −16.9676 −0.610678
\(773\) 40.8243 1.46835 0.734175 0.678961i \(-0.237569\pi\)
0.734175 + 0.678961i \(0.237569\pi\)
\(774\) 0.257049 0.00923944
\(775\) 0.484542 0.0174053
\(776\) −8.36663 −0.300345
\(777\) −17.2024 −0.617131
\(778\) 16.7983 0.602249
\(779\) 0.553367 0.0198264
\(780\) 4.40099 0.157581
\(781\) −5.91210 −0.211552
\(782\) −1.31027 −0.0468553
\(783\) −45.1195 −1.61244
\(784\) −5.29341 −0.189050
\(785\) 11.0614 0.394799
\(786\) −1.71989 −0.0613466
\(787\) 33.1044 1.18004 0.590022 0.807387i \(-0.299119\pi\)
0.590022 + 0.807387i \(0.299119\pi\)
\(788\) 14.5728 0.519133
\(789\) −33.6777 −1.19896
\(790\) 27.5195 0.979099
\(791\) 5.49056 0.195222
\(792\) 0.199267 0.00708065
\(793\) 0.401531 0.0142588
\(794\) −7.41739 −0.263233
\(795\) 14.9829 0.531389
\(796\) 14.0456 0.497833
\(797\) 17.6413 0.624887 0.312443 0.949936i \(-0.398853\pi\)
0.312443 + 0.949936i \(0.398853\pi\)
\(798\) −0.254509 −0.00900954
\(799\) −10.3258 −0.365300
\(800\) 0.406485 0.0143714
\(801\) −0.232164 −0.00820310
\(802\) −8.45159 −0.298436
\(803\) −45.4098 −1.60248
\(804\) −15.4056 −0.543312
\(805\) −2.79987 −0.0986823
\(806\) 1.42319 0.0501297
\(807\) −0.480578 −0.0169171
\(808\) −2.32659 −0.0818491
\(809\) 27.5207 0.967577 0.483788 0.875185i \(-0.339260\pi\)
0.483788 + 0.875185i \(0.339260\pi\)
\(810\) −19.0156 −0.668141
\(811\) 34.8704 1.22447 0.612233 0.790677i \(-0.290271\pi\)
0.612233 + 0.790677i \(0.290271\pi\)
\(812\) 11.2661 0.395362
\(813\) 45.7839 1.60571
\(814\) 36.3531 1.27418
\(815\) 38.4500 1.34685
\(816\) 2.25353 0.0788893
\(817\) 0.693806 0.0242732
\(818\) 19.1937 0.671091
\(819\) 0.0654571 0.00228726
\(820\) −10.4700 −0.365630
\(821\) 15.5996 0.544431 0.272215 0.962236i \(-0.412244\pi\)
0.272215 + 0.962236i \(0.412244\pi\)
\(822\) 26.0590 0.908911
\(823\) 40.6348 1.41644 0.708219 0.705992i \(-0.249499\pi\)
0.708219 + 0.705992i \(0.249499\pi\)
\(824\) −4.35870 −0.151842
\(825\) 3.31945 0.115569
\(826\) −12.7290 −0.442900
\(827\) 16.4536 0.572148 0.286074 0.958208i \(-0.407650\pi\)
0.286074 + 0.958208i \(0.407650\pi\)
\(828\) 0.0419677 0.00145848
\(829\) 19.2688 0.669233 0.334616 0.942354i \(-0.391393\pi\)
0.334616 + 0.942354i \(0.391393\pi\)
\(830\) 24.5084 0.850697
\(831\) −51.7100 −1.79380
\(832\) 1.19392 0.0413918
\(833\) 6.93581 0.240312
\(834\) −20.4505 −0.708142
\(835\) 33.6681 1.16513
\(836\) 0.537846 0.0186018
\(837\) −6.23653 −0.215566
\(838\) −20.3707 −0.703693
\(839\) −17.3927 −0.600462 −0.300231 0.953867i \(-0.597064\pi\)
−0.300231 + 0.953867i \(0.597064\pi\)
\(840\) 4.81547 0.166150
\(841\) 45.3731 1.56459
\(842\) 37.4866 1.29187
\(843\) 35.7660 1.23185
\(844\) −7.95729 −0.273901
\(845\) 24.8071 0.853391
\(846\) 0.330732 0.0113708
\(847\) −15.0813 −0.518200
\(848\) 4.06464 0.139580
\(849\) 52.3386 1.79626
\(850\) −0.532607 −0.0182683
\(851\) 7.65635 0.262456
\(852\) 2.14153 0.0733675
\(853\) 38.0571 1.30305 0.651525 0.758627i \(-0.274130\pi\)
0.651525 + 0.758627i \(0.274130\pi\)
\(854\) 0.439347 0.0150341
\(855\) 0.0101889 0.000348452 0
\(856\) −10.8528 −0.370940
\(857\) −55.3565 −1.89094 −0.945470 0.325708i \(-0.894397\pi\)
−0.945470 + 0.325708i \(0.894397\pi\)
\(858\) 9.74985 0.332854
\(859\) −41.6508 −1.42111 −0.710553 0.703643i \(-0.751555\pi\)
−0.710553 + 0.703643i \(0.751555\pi\)
\(860\) −13.1272 −0.447635
\(861\) 10.9759 0.374059
\(862\) 18.6956 0.636775
\(863\) −49.3177 −1.67879 −0.839397 0.543518i \(-0.817092\pi\)
−0.839397 + 0.543518i \(0.817092\pi\)
\(864\) −5.23186 −0.177991
\(865\) 15.2993 0.520193
\(866\) 7.80537 0.265237
\(867\) 26.2854 0.892700
\(868\) 1.55723 0.0528557
\(869\) 60.9660 2.06813
\(870\) 31.7894 1.07776
\(871\) 10.6943 0.362363
\(872\) −17.1537 −0.580897
\(873\) −0.351129 −0.0118839
\(874\) 0.113276 0.00383162
\(875\) −15.1374 −0.511739
\(876\) 16.4487 0.555749
\(877\) −39.9427 −1.34877 −0.674384 0.738381i \(-0.735591\pi\)
−0.674384 + 0.738381i \(0.735591\pi\)
\(878\) 4.02590 0.135868
\(879\) −20.1205 −0.678647
\(880\) −10.1764 −0.343045
\(881\) −45.8060 −1.54324 −0.771622 0.636081i \(-0.780554\pi\)
−0.771622 + 0.636081i \(0.780554\pi\)
\(882\) −0.222152 −0.00748026
\(883\) −33.5871 −1.13030 −0.565148 0.824990i \(-0.691181\pi\)
−0.565148 + 0.824990i \(0.691181\pi\)
\(884\) −1.56437 −0.0526153
\(885\) −35.9174 −1.20735
\(886\) 11.7695 0.395405
\(887\) 50.5726 1.69806 0.849030 0.528344i \(-0.177187\pi\)
0.849030 + 0.528344i \(0.177187\pi\)
\(888\) −13.1681 −0.441893
\(889\) −17.2363 −0.578088
\(890\) 11.8564 0.397426
\(891\) −42.1268 −1.41130
\(892\) −9.02798 −0.302279
\(893\) 0.892686 0.0298726
\(894\) 11.6389 0.389265
\(895\) 48.5776 1.62377
\(896\) 1.30637 0.0436426
\(897\) 2.05342 0.0685617
\(898\) −24.8386 −0.828874
\(899\) 10.2800 0.342858
\(900\) 0.0170593 0.000568642 0
\(901\) −5.32579 −0.177428
\(902\) −23.1951 −0.772312
\(903\) 13.7615 0.457955
\(904\) 4.20293 0.139787
\(905\) 9.84386 0.327221
\(906\) −25.1305 −0.834906
\(907\) −26.5438 −0.881373 −0.440686 0.897661i \(-0.645265\pi\)
−0.440686 + 0.897661i \(0.645265\pi\)
\(908\) 19.7457 0.655283
\(909\) −0.0976416 −0.00323857
\(910\) −3.34282 −0.110814
\(911\) 33.1352 1.09782 0.548909 0.835882i \(-0.315043\pi\)
0.548909 + 0.835882i \(0.315043\pi\)
\(912\) −0.194822 −0.00645122
\(913\) 54.2952 1.79691
\(914\) 8.47035 0.280174
\(915\) 1.23970 0.0409832
\(916\) −7.72671 −0.255298
\(917\) 1.30637 0.0431400
\(918\) 6.85517 0.226254
\(919\) −21.3143 −0.703094 −0.351547 0.936170i \(-0.614344\pi\)
−0.351547 + 0.936170i \(0.614344\pi\)
\(920\) −2.14325 −0.0706608
\(921\) −52.6017 −1.73329
\(922\) −5.75911 −0.189666
\(923\) −1.48661 −0.0489325
\(924\) 10.6681 0.350954
\(925\) 3.11220 0.102328
\(926\) 7.74262 0.254438
\(927\) −0.182925 −0.00600803
\(928\) 8.62398 0.283096
\(929\) 46.9705 1.54105 0.770526 0.637408i \(-0.219993\pi\)
0.770526 + 0.637408i \(0.219993\pi\)
\(930\) 4.39401 0.144085
\(931\) −0.599616 −0.0196516
\(932\) −5.21127 −0.170701
\(933\) −54.3868 −1.78055
\(934\) 25.4019 0.831175
\(935\) 13.3338 0.436063
\(936\) 0.0501063 0.00163777
\(937\) 38.7754 1.26674 0.633369 0.773850i \(-0.281672\pi\)
0.633369 + 0.773850i \(0.281672\pi\)
\(938\) 11.7015 0.382067
\(939\) 24.9566 0.814428
\(940\) −16.8902 −0.550896
\(941\) −15.6269 −0.509422 −0.254711 0.967017i \(-0.581980\pi\)
−0.254711 + 0.967017i \(0.581980\pi\)
\(942\) −8.87645 −0.289210
\(943\) −4.88513 −0.159082
\(944\) −9.74386 −0.317136
\(945\) 14.6485 0.476516
\(946\) −29.0818 −0.945529
\(947\) −15.6082 −0.507198 −0.253599 0.967309i \(-0.581614\pi\)
−0.253599 + 0.967309i \(0.581614\pi\)
\(948\) −22.0835 −0.717240
\(949\) −11.4184 −0.370657
\(950\) 0.0460450 0.00149390
\(951\) −22.7399 −0.737391
\(952\) −1.71170 −0.0554764
\(953\) 46.8772 1.51850 0.759250 0.650799i \(-0.225566\pi\)
0.759250 + 0.650799i \(0.225566\pi\)
\(954\) 0.170584 0.00552285
\(955\) 46.9411 1.51898
\(956\) 11.9227 0.385606
\(957\) 70.4254 2.27653
\(958\) 35.9072 1.16011
\(959\) −19.7934 −0.639163
\(960\) 3.68616 0.118970
\(961\) −29.5791 −0.954163
\(962\) 9.14109 0.294721
\(963\) −0.455466 −0.0146772
\(964\) 0.950549 0.0306151
\(965\) 36.3658 1.17066
\(966\) 2.24681 0.0722899
\(967\) 21.3384 0.686195 0.343098 0.939300i \(-0.388524\pi\)
0.343098 + 0.939300i \(0.388524\pi\)
\(968\) −11.5445 −0.371054
\(969\) 0.255271 0.00820048
\(970\) 17.9318 0.575755
\(971\) −35.3159 −1.13334 −0.566671 0.823944i \(-0.691769\pi\)
−0.566671 + 0.823944i \(0.691769\pi\)
\(972\) −0.436109 −0.0139882
\(973\) 15.5334 0.497978
\(974\) −29.9563 −0.959862
\(975\) 0.834685 0.0267313
\(976\) 0.336312 0.0107651
\(977\) 47.3796 1.51581 0.757903 0.652367i \(-0.226224\pi\)
0.757903 + 0.652367i \(0.226224\pi\)
\(978\) −30.8550 −0.986634
\(979\) 26.2663 0.839474
\(980\) 11.3451 0.362406
\(981\) −0.719901 −0.0229847
\(982\) 0.427788 0.0136513
\(983\) −6.18402 −0.197240 −0.0986198 0.995125i \(-0.531443\pi\)
−0.0986198 + 0.995125i \(0.531443\pi\)
\(984\) 8.40190 0.267843
\(985\) −31.2331 −0.995168
\(986\) −11.2998 −0.359858
\(987\) 17.7063 0.563597
\(988\) 0.135243 0.00430264
\(989\) −6.12492 −0.194761
\(990\) −0.427079 −0.0135735
\(991\) 17.4429 0.554093 0.277046 0.960857i \(-0.410644\pi\)
0.277046 + 0.960857i \(0.410644\pi\)
\(992\) 1.19203 0.0378469
\(993\) −14.1161 −0.447961
\(994\) −1.62662 −0.0515933
\(995\) −30.1032 −0.954336
\(996\) −19.6672 −0.623180
\(997\) −11.7778 −0.373008 −0.186504 0.982454i \(-0.559716\pi\)
−0.186504 + 0.982454i \(0.559716\pi\)
\(998\) 32.9391 1.04267
\(999\) −40.0570 −1.26735
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 \(a_p\))