Properties

Label 8041.2.a.j.1.15
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 0
Dimension 82
CM No

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Newspace parameters

Level: \( N \) = \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(0\)
Dimension: \(82\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.99568 q^{2}\) \(+2.01372 q^{3}\) \(+1.98276 q^{4}\) \(+2.98897 q^{5}\) \(-4.01875 q^{6}\) \(-3.65858 q^{7}\) \(+0.0344145 q^{8}\) \(+1.05506 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.99568 q^{2}\) \(+2.01372 q^{3}\) \(+1.98276 q^{4}\) \(+2.98897 q^{5}\) \(-4.01875 q^{6}\) \(-3.65858 q^{7}\) \(+0.0344145 q^{8}\) \(+1.05506 q^{9}\) \(-5.96504 q^{10}\) \(+1.00000 q^{11}\) \(+3.99271 q^{12}\) \(-6.84703 q^{13}\) \(+7.30137 q^{14}\) \(+6.01894 q^{15}\) \(-4.03419 q^{16}\) \(+1.00000 q^{17}\) \(-2.10557 q^{18}\) \(-3.07074 q^{19}\) \(+5.92640 q^{20}\) \(-7.36735 q^{21}\) \(-1.99568 q^{22}\) \(-5.38280 q^{23}\) \(+0.0693010 q^{24}\) \(+3.93394 q^{25}\) \(+13.6645 q^{26}\) \(-3.91656 q^{27}\) \(-7.25407 q^{28}\) \(+1.49706 q^{29}\) \(-12.0119 q^{30}\) \(+6.38953 q^{31}\) \(+7.98214 q^{32}\) \(+2.01372 q^{33}\) \(-1.99568 q^{34}\) \(-10.9354 q^{35}\) \(+2.09193 q^{36}\) \(-0.850029 q^{37}\) \(+6.12823 q^{38}\) \(-13.7880 q^{39}\) \(+0.102864 q^{40}\) \(-2.35309 q^{41}\) \(+14.7029 q^{42}\) \(+1.00000 q^{43}\) \(+1.98276 q^{44}\) \(+3.15355 q^{45}\) \(+10.7424 q^{46}\) \(+2.66712 q^{47}\) \(-8.12373 q^{48}\) \(+6.38520 q^{49}\) \(-7.85090 q^{50}\) \(+2.01372 q^{51}\) \(-13.5760 q^{52}\) \(+0.780277 q^{53}\) \(+7.81621 q^{54}\) \(+2.98897 q^{55}\) \(-0.125908 q^{56}\) \(-6.18361 q^{57}\) \(-2.98765 q^{58}\) \(+8.77764 q^{59}\) \(+11.9341 q^{60}\) \(+6.61552 q^{61}\) \(-12.7515 q^{62}\) \(-3.86003 q^{63}\) \(-7.86145 q^{64}\) \(-20.4656 q^{65}\) \(-4.01875 q^{66}\) \(+5.23002 q^{67}\) \(+1.98276 q^{68}\) \(-10.8395 q^{69}\) \(+21.8236 q^{70}\) \(-0.390257 q^{71}\) \(+0.0363094 q^{72}\) \(+4.83248 q^{73}\) \(+1.69639 q^{74}\) \(+7.92184 q^{75}\) \(-6.08853 q^{76}\) \(-3.65858 q^{77}\) \(+27.5165 q^{78}\) \(+11.9195 q^{79}\) \(-12.0581 q^{80}\) \(-11.0520 q^{81}\) \(+4.69602 q^{82}\) \(-1.62949 q^{83}\) \(-14.6076 q^{84}\) \(+2.98897 q^{85}\) \(-1.99568 q^{86}\) \(+3.01465 q^{87}\) \(+0.0344145 q^{88}\) \(+5.39227 q^{89}\) \(-6.29349 q^{90}\) \(+25.0504 q^{91}\) \(-10.6728 q^{92}\) \(+12.8667 q^{93}\) \(-5.32273 q^{94}\) \(-9.17835 q^{95}\) \(+16.0738 q^{96}\) \(+1.69533 q^{97}\) \(-12.7428 q^{98}\) \(+1.05506 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(82q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(82q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut +\mathstrut 82q^{11} \) \(\mathstrut +\mathstrut 3q^{12} \) \(\mathstrut +\mathstrut 26q^{13} \) \(\mathstrut +\mathstrut 17q^{14} \) \(\mathstrut +\mathstrut 66q^{15} \) \(\mathstrut +\mathstrut 122q^{16} \) \(\mathstrut +\mathstrut 82q^{17} \) \(\mathstrut +\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 9q^{20} \) \(\mathstrut +\mathstrut 22q^{21} \) \(\mathstrut +\mathstrut 8q^{22} \) \(\mathstrut +\mathstrut 50q^{23} \) \(\mathstrut +\mathstrut 15q^{24} \) \(\mathstrut +\mathstrut 117q^{25} \) \(\mathstrut +\mathstrut 36q^{26} \) \(\mathstrut +\mathstrut 30q^{27} \) \(\mathstrut +\mathstrut 11q^{28} \) \(\mathstrut +\mathstrut 33q^{29} \) \(\mathstrut -\mathstrut 26q^{30} \) \(\mathstrut +\mathstrut 40q^{31} \) \(\mathstrut +\mathstrut 58q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 16q^{35} \) \(\mathstrut +\mathstrut 160q^{36} \) \(\mathstrut +\mathstrut 31q^{37} \) \(\mathstrut +\mathstrut 18q^{38} \) \(\mathstrut +\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 29q^{40} \) \(\mathstrut +\mathstrut 42q^{41} \) \(\mathstrut -\mathstrut 51q^{42} \) \(\mathstrut +\mathstrut 82q^{43} \) \(\mathstrut +\mathstrut 98q^{44} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 19q^{46} \) \(\mathstrut +\mathstrut 84q^{47} \) \(\mathstrut -\mathstrut 46q^{48} \) \(\mathstrut +\mathstrut 136q^{49} \) \(\mathstrut +\mathstrut 59q^{50} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 45q^{52} \) \(\mathstrut +\mathstrut 83q^{53} \) \(\mathstrut +\mathstrut 24q^{54} \) \(\mathstrut +\mathstrut 11q^{55} \) \(\mathstrut +\mathstrut 21q^{56} \) \(\mathstrut +\mathstrut 23q^{57} \) \(\mathstrut +\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 96q^{59} \) \(\mathstrut +\mathstrut 184q^{60} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut -\mathstrut 23q^{62} \) \(\mathstrut +\mathstrut 8q^{63} \) \(\mathstrut +\mathstrut 148q^{64} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut +\mathstrut 10q^{66} \) \(\mathstrut +\mathstrut 78q^{67} \) \(\mathstrut +\mathstrut 98q^{68} \) \(\mathstrut +\mathstrut 61q^{69} \) \(\mathstrut -\mathstrut 3q^{70} \) \(\mathstrut +\mathstrut 155q^{71} \) \(\mathstrut +\mathstrut 50q^{72} \) \(\mathstrut -\mathstrut 23q^{73} \) \(\mathstrut +\mathstrut 10q^{74} \) \(\mathstrut -\mathstrut 19q^{75} \) \(\mathstrut +\mathstrut 44q^{76} \) \(\mathstrut +\mathstrut 8q^{77} \) \(\mathstrut -\mathstrut 27q^{78} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut +\mathstrut 19q^{80} \) \(\mathstrut +\mathstrut 150q^{81} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 54q^{83} \) \(\mathstrut +\mathstrut 8q^{84} \) \(\mathstrut +\mathstrut 11q^{85} \) \(\mathstrut +\mathstrut 8q^{86} \) \(\mathstrut +\mathstrut 20q^{87} \) \(\mathstrut +\mathstrut 30q^{88} \) \(\mathstrut +\mathstrut 25q^{89} \) \(\mathstrut -\mathstrut 81q^{90} \) \(\mathstrut -\mathstrut 14q^{91} \) \(\mathstrut +\mathstrut 60q^{92} \) \(\mathstrut +\mathstrut 36q^{93} \) \(\mathstrut +\mathstrut 19q^{94} \) \(\mathstrut +\mathstrut 111q^{95} \) \(\mathstrut -\mathstrut 6q^{96} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 5q^{98} \) \(\mathstrut +\mathstrut 108q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.99568 −1.41116 −0.705581 0.708629i \(-0.749314\pi\)
−0.705581 + 0.708629i \(0.749314\pi\)
\(3\) 2.01372 1.16262 0.581311 0.813682i \(-0.302540\pi\)
0.581311 + 0.813682i \(0.302540\pi\)
\(4\) 1.98276 0.991378
\(5\) 2.98897 1.33671 0.668354 0.743843i \(-0.266999\pi\)
0.668354 + 0.743843i \(0.266999\pi\)
\(6\) −4.01875 −1.64065
\(7\) −3.65858 −1.38281 −0.691406 0.722466i \(-0.743009\pi\)
−0.691406 + 0.722466i \(0.743009\pi\)
\(8\) 0.0344145 0.0121674
\(9\) 1.05506 0.351688
\(10\) −5.96504 −1.88631
\(11\) 1.00000 0.301511
\(12\) 3.99271 1.15260
\(13\) −6.84703 −1.89902 −0.949512 0.313729i \(-0.898422\pi\)
−0.949512 + 0.313729i \(0.898422\pi\)
\(14\) 7.30137 1.95137
\(15\) 6.01894 1.55408
\(16\) −4.03419 −1.00855
\(17\) 1.00000 0.242536
\(18\) −2.10557 −0.496288
\(19\) −3.07074 −0.704477 −0.352238 0.935910i \(-0.614579\pi\)
−0.352238 + 0.935910i \(0.614579\pi\)
\(20\) 5.92640 1.32518
\(21\) −7.36735 −1.60769
\(22\) −1.99568 −0.425481
\(23\) −5.38280 −1.12239 −0.561196 0.827683i \(-0.689659\pi\)
−0.561196 + 0.827683i \(0.689659\pi\)
\(24\) 0.0693010 0.0141460
\(25\) 3.93394 0.786788
\(26\) 13.6645 2.67983
\(27\) −3.91656 −0.753742
\(28\) −7.25407 −1.37089
\(29\) 1.49706 0.277997 0.138998 0.990293i \(-0.455612\pi\)
0.138998 + 0.990293i \(0.455612\pi\)
\(30\) −12.0119 −2.19306
\(31\) 6.38953 1.14759 0.573797 0.818998i \(-0.305470\pi\)
0.573797 + 0.818998i \(0.305470\pi\)
\(32\) 7.98214 1.41106
\(33\) 2.01372 0.350543
\(34\) −1.99568 −0.342257
\(35\) −10.9354 −1.84842
\(36\) 2.09193 0.348655
\(37\) −0.850029 −0.139744 −0.0698720 0.997556i \(-0.522259\pi\)
−0.0698720 + 0.997556i \(0.522259\pi\)
\(38\) 6.12823 0.994130
\(39\) −13.7880 −2.20785
\(40\) 0.102864 0.0162642
\(41\) −2.35309 −0.367490 −0.183745 0.982974i \(-0.558822\pi\)
−0.183745 + 0.982974i \(0.558822\pi\)
\(42\) 14.7029 2.26871
\(43\) 1.00000 0.152499
\(44\) 1.98276 0.298912
\(45\) 3.15355 0.470104
\(46\) 10.7424 1.58388
\(47\) 2.66712 0.389039 0.194520 0.980899i \(-0.437685\pi\)
0.194520 + 0.980899i \(0.437685\pi\)
\(48\) −8.12373 −1.17256
\(49\) 6.38520 0.912171
\(50\) −7.85090 −1.11028
\(51\) 2.01372 0.281977
\(52\) −13.5760 −1.88265
\(53\) 0.780277 0.107179 0.0535896 0.998563i \(-0.482934\pi\)
0.0535896 + 0.998563i \(0.482934\pi\)
\(54\) 7.81621 1.06365
\(55\) 2.98897 0.403033
\(56\) −0.125908 −0.0168252
\(57\) −6.18361 −0.819039
\(58\) −2.98765 −0.392298
\(59\) 8.77764 1.14275 0.571376 0.820689i \(-0.306410\pi\)
0.571376 + 0.820689i \(0.306410\pi\)
\(60\) 11.9341 1.54068
\(61\) 6.61552 0.847031 0.423515 0.905889i \(-0.360796\pi\)
0.423515 + 0.905889i \(0.360796\pi\)
\(62\) −12.7515 −1.61944
\(63\) −3.86003 −0.486318
\(64\) −7.86145 −0.982682
\(65\) −20.4656 −2.53844
\(66\) −4.01875 −0.494674
\(67\) 5.23002 0.638948 0.319474 0.947595i \(-0.396494\pi\)
0.319474 + 0.947595i \(0.396494\pi\)
\(68\) 1.98276 0.240444
\(69\) −10.8395 −1.30492
\(70\) 21.8236 2.60841
\(71\) −0.390257 −0.0463150 −0.0231575 0.999732i \(-0.507372\pi\)
−0.0231575 + 0.999732i \(0.507372\pi\)
\(72\) 0.0363094 0.00427911
\(73\) 4.83248 0.565599 0.282799 0.959179i \(-0.408737\pi\)
0.282799 + 0.959179i \(0.408737\pi\)
\(74\) 1.69639 0.197201
\(75\) 7.92184 0.914736
\(76\) −6.08853 −0.698402
\(77\) −3.65858 −0.416934
\(78\) 27.5165 3.11563
\(79\) 11.9195 1.34104 0.670522 0.741890i \(-0.266070\pi\)
0.670522 + 0.741890i \(0.266070\pi\)
\(80\) −12.0581 −1.34813
\(81\) −11.0520 −1.22800
\(82\) 4.69602 0.518588
\(83\) −1.62949 −0.178860 −0.0894300 0.995993i \(-0.528505\pi\)
−0.0894300 + 0.995993i \(0.528505\pi\)
\(84\) −14.6076 −1.59383
\(85\) 2.98897 0.324199
\(86\) −1.99568 −0.215200
\(87\) 3.01465 0.323205
\(88\) 0.0344145 0.00366859
\(89\) 5.39227 0.571579 0.285790 0.958292i \(-0.407744\pi\)
0.285790 + 0.958292i \(0.407744\pi\)
\(90\) −6.29349 −0.663392
\(91\) 25.0504 2.62600
\(92\) −10.6728 −1.11271
\(93\) 12.8667 1.33422
\(94\) −5.32273 −0.548997
\(95\) −9.17835 −0.941679
\(96\) 16.0738 1.64052
\(97\) 1.69533 0.172134 0.0860671 0.996289i \(-0.472570\pi\)
0.0860671 + 0.996289i \(0.472570\pi\)
\(98\) −12.7428 −1.28722
\(99\) 1.05506 0.106038
\(100\) 7.80004 0.780004
\(101\) 12.2693 1.22084 0.610418 0.792079i \(-0.291001\pi\)
0.610418 + 0.792079i \(0.291001\pi\)
\(102\) −4.01875 −0.397915
\(103\) 12.0081 1.18319 0.591597 0.806234i \(-0.298498\pi\)
0.591597 + 0.806234i \(0.298498\pi\)
\(104\) −0.235637 −0.0231061
\(105\) −22.0208 −2.14901
\(106\) −1.55719 −0.151247
\(107\) −14.7131 −1.42237 −0.711183 0.703007i \(-0.751840\pi\)
−0.711183 + 0.703007i \(0.751840\pi\)
\(108\) −7.76557 −0.747243
\(109\) 2.41804 0.231606 0.115803 0.993272i \(-0.463056\pi\)
0.115803 + 0.993272i \(0.463056\pi\)
\(110\) −5.96504 −0.568744
\(111\) −1.71172 −0.162469
\(112\) 14.7594 1.39463
\(113\) 17.9932 1.69265 0.846327 0.532663i \(-0.178809\pi\)
0.846327 + 0.532663i \(0.178809\pi\)
\(114\) 12.3405 1.15580
\(115\) −16.0890 −1.50031
\(116\) 2.96830 0.275600
\(117\) −7.22405 −0.667864
\(118\) −17.5174 −1.61261
\(119\) −3.65858 −0.335381
\(120\) 0.207139 0.0189091
\(121\) 1.00000 0.0909091
\(122\) −13.2025 −1.19530
\(123\) −4.73845 −0.427252
\(124\) 12.6689 1.13770
\(125\) −3.18643 −0.285003
\(126\) 7.70340 0.686273
\(127\) 8.43518 0.748501 0.374251 0.927328i \(-0.377900\pi\)
0.374251 + 0.927328i \(0.377900\pi\)
\(128\) −0.275305 −0.0243338
\(129\) 2.01372 0.177298
\(130\) 40.8428 3.58215
\(131\) −0.202841 −0.0177223 −0.00886117 0.999961i \(-0.502821\pi\)
−0.00886117 + 0.999961i \(0.502821\pi\)
\(132\) 3.99271 0.347521
\(133\) 11.2346 0.974159
\(134\) −10.4375 −0.901659
\(135\) −11.7065 −1.00753
\(136\) 0.0344145 0.00295102
\(137\) 4.28062 0.365718 0.182859 0.983139i \(-0.441465\pi\)
0.182859 + 0.983139i \(0.441465\pi\)
\(138\) 21.6321 1.84145
\(139\) 0.0540394 0.00458356 0.00229178 0.999997i \(-0.499271\pi\)
0.00229178 + 0.999997i \(0.499271\pi\)
\(140\) −21.6822 −1.83248
\(141\) 5.37083 0.452305
\(142\) 0.778831 0.0653580
\(143\) −6.84703 −0.572578
\(144\) −4.25633 −0.354694
\(145\) 4.47466 0.371600
\(146\) −9.64410 −0.798151
\(147\) 12.8580 1.06051
\(148\) −1.68540 −0.138539
\(149\) −1.26485 −0.103620 −0.0518101 0.998657i \(-0.516499\pi\)
−0.0518101 + 0.998657i \(0.516499\pi\)
\(150\) −15.8095 −1.29084
\(151\) −6.21522 −0.505787 −0.252894 0.967494i \(-0.581382\pi\)
−0.252894 + 0.967494i \(0.581382\pi\)
\(152\) −0.105678 −0.00857161
\(153\) 1.05506 0.0852968
\(154\) 7.30137 0.588361
\(155\) 19.0981 1.53400
\(156\) −27.3382 −2.18881
\(157\) −3.37072 −0.269013 −0.134507 0.990913i \(-0.542945\pi\)
−0.134507 + 0.990913i \(0.542945\pi\)
\(158\) −23.7875 −1.89243
\(159\) 1.57126 0.124609
\(160\) 23.8584 1.88617
\(161\) 19.6934 1.55206
\(162\) 22.0564 1.73291
\(163\) 3.40983 0.267079 0.133539 0.991044i \(-0.457366\pi\)
0.133539 + 0.991044i \(0.457366\pi\)
\(164\) −4.66559 −0.364322
\(165\) 6.01894 0.468574
\(166\) 3.25195 0.252400
\(167\) 9.66139 0.747621 0.373810 0.927505i \(-0.378051\pi\)
0.373810 + 0.927505i \(0.378051\pi\)
\(168\) −0.253543 −0.0195613
\(169\) 33.8818 2.60630
\(170\) −5.96504 −0.457498
\(171\) −3.23983 −0.247756
\(172\) 1.98276 0.151184
\(173\) −16.1204 −1.22561 −0.612807 0.790233i \(-0.709960\pi\)
−0.612807 + 0.790233i \(0.709960\pi\)
\(174\) −6.01629 −0.456094
\(175\) −14.3926 −1.08798
\(176\) −4.03419 −0.304089
\(177\) 17.6757 1.32859
\(178\) −10.7613 −0.806591
\(179\) 24.4422 1.82690 0.913450 0.406952i \(-0.133408\pi\)
0.913450 + 0.406952i \(0.133408\pi\)
\(180\) 6.25272 0.466050
\(181\) 19.2481 1.43070 0.715351 0.698765i \(-0.246267\pi\)
0.715351 + 0.698765i \(0.246267\pi\)
\(182\) −49.9927 −3.70570
\(183\) 13.3218 0.984776
\(184\) −0.185246 −0.0136565
\(185\) −2.54071 −0.186797
\(186\) −25.6779 −1.88279
\(187\) 1.00000 0.0731272
\(188\) 5.28824 0.385685
\(189\) 14.3290 1.04228
\(190\) 18.3171 1.32886
\(191\) −5.69075 −0.411768 −0.205884 0.978576i \(-0.566007\pi\)
−0.205884 + 0.978576i \(0.566007\pi\)
\(192\) −15.8308 −1.14249
\(193\) −21.2835 −1.53202 −0.766011 0.642828i \(-0.777761\pi\)
−0.766011 + 0.642828i \(0.777761\pi\)
\(194\) −3.38334 −0.242909
\(195\) −41.2119 −2.95125
\(196\) 12.6603 0.904306
\(197\) 19.3181 1.37636 0.688180 0.725540i \(-0.258410\pi\)
0.688180 + 0.725540i \(0.258410\pi\)
\(198\) −2.10557 −0.149636
\(199\) 2.36371 0.167559 0.0837795 0.996484i \(-0.473301\pi\)
0.0837795 + 0.996484i \(0.473301\pi\)
\(200\) 0.135384 0.00957312
\(201\) 10.5318 0.742855
\(202\) −24.4855 −1.72280
\(203\) −5.47710 −0.384417
\(204\) 3.99271 0.279546
\(205\) −7.03330 −0.491227
\(206\) −23.9644 −1.66968
\(207\) −5.67920 −0.394731
\(208\) 27.6222 1.91526
\(209\) −3.07074 −0.212408
\(210\) 43.9465 3.03260
\(211\) 21.7421 1.49679 0.748394 0.663254i \(-0.230825\pi\)
0.748394 + 0.663254i \(0.230825\pi\)
\(212\) 1.54710 0.106255
\(213\) −0.785869 −0.0538468
\(214\) 29.3627 2.00719
\(215\) 2.98897 0.203846
\(216\) −0.134786 −0.00917104
\(217\) −23.3766 −1.58691
\(218\) −4.82564 −0.326834
\(219\) 9.73125 0.657577
\(220\) 5.92640 0.399558
\(221\) −6.84703 −0.460581
\(222\) 3.41605 0.229270
\(223\) 17.2298 1.15379 0.576896 0.816818i \(-0.304264\pi\)
0.576896 + 0.816818i \(0.304264\pi\)
\(224\) −29.2033 −1.95123
\(225\) 4.15055 0.276703
\(226\) −35.9087 −2.38861
\(227\) −20.7921 −1.38002 −0.690009 0.723800i \(-0.742394\pi\)
−0.690009 + 0.723800i \(0.742394\pi\)
\(228\) −12.2606 −0.811977
\(229\) 18.1741 1.20098 0.600491 0.799632i \(-0.294972\pi\)
0.600491 + 0.799632i \(0.294972\pi\)
\(230\) 32.1086 2.11718
\(231\) −7.36735 −0.484736
\(232\) 0.0515204 0.00338248
\(233\) 4.54643 0.297847 0.148923 0.988849i \(-0.452419\pi\)
0.148923 + 0.988849i \(0.452419\pi\)
\(234\) 14.4169 0.942463
\(235\) 7.97194 0.520032
\(236\) 17.4039 1.13290
\(237\) 24.0024 1.55913
\(238\) 7.30137 0.473277
\(239\) −6.12210 −0.396006 −0.198003 0.980201i \(-0.563446\pi\)
−0.198003 + 0.980201i \(0.563446\pi\)
\(240\) −24.2816 −1.56737
\(241\) −29.8222 −1.92102 −0.960509 0.278249i \(-0.910246\pi\)
−0.960509 + 0.278249i \(0.910246\pi\)
\(242\) −1.99568 −0.128287
\(243\) −10.5060 −0.673961
\(244\) 13.1170 0.839727
\(245\) 19.0852 1.21931
\(246\) 9.45646 0.602922
\(247\) 21.0255 1.33782
\(248\) 0.219892 0.0139632
\(249\) −3.28134 −0.207946
\(250\) 6.35910 0.402185
\(251\) 15.4748 0.976759 0.488380 0.872631i \(-0.337588\pi\)
0.488380 + 0.872631i \(0.337588\pi\)
\(252\) −7.65350 −0.482125
\(253\) −5.38280 −0.338414
\(254\) −16.8340 −1.05626
\(255\) 6.01894 0.376921
\(256\) 16.2723 1.01702
\(257\) 0.895769 0.0558766 0.0279383 0.999610i \(-0.491106\pi\)
0.0279383 + 0.999610i \(0.491106\pi\)
\(258\) −4.01875 −0.250196
\(259\) 3.10990 0.193240
\(260\) −40.5782 −2.51655
\(261\) 1.57949 0.0977680
\(262\) 0.404807 0.0250091
\(263\) 16.3127 1.00589 0.502944 0.864319i \(-0.332250\pi\)
0.502944 + 0.864319i \(0.332250\pi\)
\(264\) 0.0693010 0.00426518
\(265\) 2.33222 0.143267
\(266\) −22.4206 −1.37470
\(267\) 10.8585 0.664530
\(268\) 10.3698 0.633439
\(269\) −2.44411 −0.149020 −0.0745101 0.997220i \(-0.523739\pi\)
−0.0745101 + 0.997220i \(0.523739\pi\)
\(270\) 23.3624 1.42179
\(271\) −6.60008 −0.400926 −0.200463 0.979701i \(-0.564245\pi\)
−0.200463 + 0.979701i \(0.564245\pi\)
\(272\) −4.03419 −0.244609
\(273\) 50.4445 3.05304
\(274\) −8.54277 −0.516088
\(275\) 3.93394 0.237225
\(276\) −21.4920 −1.29367
\(277\) 14.3396 0.861582 0.430791 0.902452i \(-0.358235\pi\)
0.430791 + 0.902452i \(0.358235\pi\)
\(278\) −0.107846 −0.00646815
\(279\) 6.74135 0.403594
\(280\) −0.376335 −0.0224903
\(281\) 5.10183 0.304350 0.152175 0.988354i \(-0.451372\pi\)
0.152175 + 0.988354i \(0.451372\pi\)
\(282\) −10.7185 −0.638276
\(283\) 8.14402 0.484112 0.242056 0.970262i \(-0.422178\pi\)
0.242056 + 0.970262i \(0.422178\pi\)
\(284\) −0.773785 −0.0459157
\(285\) −18.4826 −1.09482
\(286\) 13.6645 0.808000
\(287\) 8.60895 0.508170
\(288\) 8.42166 0.496251
\(289\) 1.00000 0.0588235
\(290\) −8.93001 −0.524388
\(291\) 3.41391 0.200127
\(292\) 9.58162 0.560722
\(293\) −5.66645 −0.331037 −0.165519 0.986207i \(-0.552930\pi\)
−0.165519 + 0.986207i \(0.552930\pi\)
\(294\) −25.6605 −1.49655
\(295\) 26.2361 1.52752
\(296\) −0.0292533 −0.00170031
\(297\) −3.91656 −0.227262
\(298\) 2.52423 0.146225
\(299\) 36.8562 2.13145
\(300\) 15.7071 0.906849
\(301\) −3.65858 −0.210877
\(302\) 12.4036 0.713748
\(303\) 24.7068 1.41937
\(304\) 12.3880 0.710498
\(305\) 19.7736 1.13223
\(306\) −2.10557 −0.120368
\(307\) 18.1046 1.03329 0.516643 0.856201i \(-0.327182\pi\)
0.516643 + 0.856201i \(0.327182\pi\)
\(308\) −7.25407 −0.413339
\(309\) 24.1810 1.37561
\(310\) −38.1138 −2.16472
\(311\) −26.3232 −1.49265 −0.746326 0.665580i \(-0.768184\pi\)
−0.746326 + 0.665580i \(0.768184\pi\)
\(312\) −0.474506 −0.0268636
\(313\) −8.08672 −0.457088 −0.228544 0.973534i \(-0.573397\pi\)
−0.228544 + 0.973534i \(0.573397\pi\)
\(314\) 6.72690 0.379621
\(315\) −11.5375 −0.650065
\(316\) 23.6334 1.32948
\(317\) 19.6879 1.10578 0.552890 0.833254i \(-0.313525\pi\)
0.552890 + 0.833254i \(0.313525\pi\)
\(318\) −3.13573 −0.175843
\(319\) 1.49706 0.0838191
\(320\) −23.4976 −1.31356
\(321\) −29.6280 −1.65367
\(322\) −39.3018 −2.19020
\(323\) −3.07074 −0.170861
\(324\) −21.9135 −1.21742
\(325\) −26.9358 −1.49413
\(326\) −6.80495 −0.376891
\(327\) 4.86925 0.269270
\(328\) −0.0809802 −0.00447138
\(329\) −9.75786 −0.537968
\(330\) −12.0119 −0.661234
\(331\) 31.8317 1.74963 0.874813 0.484460i \(-0.160984\pi\)
0.874813 + 0.484460i \(0.160984\pi\)
\(332\) −3.23088 −0.177318
\(333\) −0.896834 −0.0491462
\(334\) −19.2811 −1.05501
\(335\) 15.6324 0.854087
\(336\) 29.7213 1.62143
\(337\) −10.4485 −0.569165 −0.284583 0.958652i \(-0.591855\pi\)
−0.284583 + 0.958652i \(0.591855\pi\)
\(338\) −67.6175 −3.67790
\(339\) 36.2332 1.96792
\(340\) 5.92640 0.321404
\(341\) 6.38953 0.346012
\(342\) 6.46567 0.349623
\(343\) 2.24931 0.121451
\(344\) 0.0344145 0.00185550
\(345\) −32.3988 −1.74429
\(346\) 32.1713 1.72954
\(347\) −9.04774 −0.485708 −0.242854 0.970063i \(-0.578084\pi\)
−0.242854 + 0.970063i \(0.578084\pi\)
\(348\) 5.97732 0.320418
\(349\) 14.9812 0.801925 0.400962 0.916095i \(-0.368676\pi\)
0.400962 + 0.916095i \(0.368676\pi\)
\(350\) 28.7231 1.53532
\(351\) 26.8168 1.43137
\(352\) 7.98214 0.425450
\(353\) −1.94042 −0.103278 −0.0516391 0.998666i \(-0.516445\pi\)
−0.0516391 + 0.998666i \(0.516445\pi\)
\(354\) −35.2751 −1.87485
\(355\) −1.16647 −0.0619097
\(356\) 10.6916 0.566651
\(357\) −7.36735 −0.389921
\(358\) −48.7790 −2.57805
\(359\) 0.545541 0.0287926 0.0143963 0.999896i \(-0.495417\pi\)
0.0143963 + 0.999896i \(0.495417\pi\)
\(360\) 0.108528 0.00571991
\(361\) −9.57054 −0.503713
\(362\) −38.4132 −2.01895
\(363\) 2.01372 0.105693
\(364\) 49.6688 2.60335
\(365\) 14.4441 0.756040
\(366\) −26.5861 −1.38968
\(367\) −10.0219 −0.523138 −0.261569 0.965185i \(-0.584240\pi\)
−0.261569 + 0.965185i \(0.584240\pi\)
\(368\) 21.7153 1.13199
\(369\) −2.48265 −0.129242
\(370\) 5.07046 0.263601
\(371\) −2.85470 −0.148209
\(372\) 25.5115 1.32271
\(373\) −28.9043 −1.49661 −0.748303 0.663357i \(-0.769131\pi\)
−0.748303 + 0.663357i \(0.769131\pi\)
\(374\) −1.99568 −0.103194
\(375\) −6.41657 −0.331350
\(376\) 0.0917875 0.00473358
\(377\) −10.2504 −0.527922
\(378\) −28.5962 −1.47083
\(379\) −30.3828 −1.56066 −0.780330 0.625367i \(-0.784949\pi\)
−0.780330 + 0.625367i \(0.784949\pi\)
\(380\) −18.1984 −0.933560
\(381\) 16.9861 0.870223
\(382\) 11.3569 0.581072
\(383\) −11.9180 −0.608984 −0.304492 0.952515i \(-0.598487\pi\)
−0.304492 + 0.952515i \(0.598487\pi\)
\(384\) −0.554388 −0.0282910
\(385\) −10.9354 −0.557318
\(386\) 42.4752 2.16193
\(387\) 1.05506 0.0536319
\(388\) 3.36142 0.170650
\(389\) −14.1172 −0.715771 −0.357885 0.933766i \(-0.616502\pi\)
−0.357885 + 0.933766i \(0.616502\pi\)
\(390\) 82.2459 4.16468
\(391\) −5.38280 −0.272220
\(392\) 0.219743 0.0110987
\(393\) −0.408466 −0.0206044
\(394\) −38.5529 −1.94227
\(395\) 35.6269 1.79258
\(396\) 2.09193 0.105124
\(397\) −9.14910 −0.459180 −0.229590 0.973287i \(-0.573739\pi\)
−0.229590 + 0.973287i \(0.573739\pi\)
\(398\) −4.71722 −0.236453
\(399\) 22.6232 1.13258
\(400\) −15.8703 −0.793513
\(401\) 7.86101 0.392560 0.196280 0.980548i \(-0.437114\pi\)
0.196280 + 0.980548i \(0.437114\pi\)
\(402\) −21.0181 −1.04829
\(403\) −43.7493 −2.17931
\(404\) 24.3269 1.21031
\(405\) −33.0342 −1.64148
\(406\) 10.9306 0.542475
\(407\) −0.850029 −0.0421344
\(408\) 0.0693010 0.00343091
\(409\) 25.1811 1.24512 0.622562 0.782570i \(-0.286092\pi\)
0.622562 + 0.782570i \(0.286092\pi\)
\(410\) 14.0363 0.693201
\(411\) 8.61997 0.425192
\(412\) 23.8092 1.17299
\(413\) −32.1137 −1.58021
\(414\) 11.3339 0.557030
\(415\) −4.87050 −0.239084
\(416\) −54.6540 −2.67963
\(417\) 0.108820 0.00532895
\(418\) 6.12823 0.299742
\(419\) −13.6261 −0.665676 −0.332838 0.942984i \(-0.608006\pi\)
−0.332838 + 0.942984i \(0.608006\pi\)
\(420\) −43.6618 −2.13048
\(421\) −15.0241 −0.732228 −0.366114 0.930570i \(-0.619312\pi\)
−0.366114 + 0.930570i \(0.619312\pi\)
\(422\) −43.3904 −2.11221
\(423\) 2.81398 0.136820
\(424\) 0.0268528 0.00130409
\(425\) 3.93394 0.190824
\(426\) 1.56835 0.0759866
\(427\) −24.2034 −1.17128
\(428\) −29.1724 −1.41010
\(429\) −13.7880 −0.665691
\(430\) −5.96504 −0.287660
\(431\) −16.1547 −0.778145 −0.389072 0.921207i \(-0.627204\pi\)
−0.389072 + 0.921207i \(0.627204\pi\)
\(432\) 15.8001 0.760185
\(433\) −14.0979 −0.677503 −0.338752 0.940876i \(-0.610005\pi\)
−0.338752 + 0.940876i \(0.610005\pi\)
\(434\) 46.6523 2.23938
\(435\) 9.01070 0.432030
\(436\) 4.79438 0.229609
\(437\) 16.5292 0.790699
\(438\) −19.4205 −0.927948
\(439\) −13.9030 −0.663556 −0.331778 0.943357i \(-0.607649\pi\)
−0.331778 + 0.943357i \(0.607649\pi\)
\(440\) 0.102864 0.00490384
\(441\) 6.73678 0.320799
\(442\) 13.6645 0.649955
\(443\) −24.4830 −1.16322 −0.581611 0.813467i \(-0.697577\pi\)
−0.581611 + 0.813467i \(0.697577\pi\)
\(444\) −3.39392 −0.161068
\(445\) 16.1173 0.764035
\(446\) −34.3852 −1.62819
\(447\) −2.54704 −0.120471
\(448\) 28.7617 1.35886
\(449\) −25.4448 −1.20082 −0.600408 0.799694i \(-0.704995\pi\)
−0.600408 + 0.799694i \(0.704995\pi\)
\(450\) −8.28319 −0.390473
\(451\) −2.35309 −0.110802
\(452\) 35.6761 1.67806
\(453\) −12.5157 −0.588039
\(454\) 41.4944 1.94743
\(455\) 74.8749 3.51019
\(456\) −0.212806 −0.00996554
\(457\) −22.7696 −1.06512 −0.532558 0.846394i \(-0.678769\pi\)
−0.532558 + 0.846394i \(0.678769\pi\)
\(458\) −36.2699 −1.69478
\(459\) −3.91656 −0.182809
\(460\) −31.9006 −1.48737
\(461\) 31.7509 1.47879 0.739393 0.673274i \(-0.235112\pi\)
0.739393 + 0.673274i \(0.235112\pi\)
\(462\) 14.7029 0.684041
\(463\) 0.103811 0.00482449 0.00241224 0.999997i \(-0.499232\pi\)
0.00241224 + 0.999997i \(0.499232\pi\)
\(464\) −6.03942 −0.280373
\(465\) 38.4582 1.78346
\(466\) −9.07324 −0.420310
\(467\) −34.7660 −1.60878 −0.804388 0.594104i \(-0.797507\pi\)
−0.804388 + 0.594104i \(0.797507\pi\)
\(468\) −14.3235 −0.662105
\(469\) −19.1344 −0.883546
\(470\) −15.9095 −0.733849
\(471\) −6.78769 −0.312760
\(472\) 0.302078 0.0139043
\(473\) 1.00000 0.0459800
\(474\) −47.9013 −2.20018
\(475\) −12.0801 −0.554273
\(476\) −7.25407 −0.332490
\(477\) 0.823241 0.0376936
\(478\) 12.2178 0.558828
\(479\) 43.0851 1.96861 0.984305 0.176476i \(-0.0564697\pi\)
0.984305 + 0.176476i \(0.0564697\pi\)
\(480\) 48.0441 2.19290
\(481\) 5.82018 0.265377
\(482\) 59.5157 2.71087
\(483\) 39.6570 1.80446
\(484\) 1.98276 0.0901253
\(485\) 5.06728 0.230093
\(486\) 20.9667 0.951068
\(487\) −8.71484 −0.394907 −0.197453 0.980312i \(-0.563267\pi\)
−0.197453 + 0.980312i \(0.563267\pi\)
\(488\) 0.227670 0.0103061
\(489\) 6.86645 0.310511
\(490\) −38.0879 −1.72064
\(491\) 31.0375 1.40070 0.700352 0.713797i \(-0.253026\pi\)
0.700352 + 0.713797i \(0.253026\pi\)
\(492\) −9.39519 −0.423568
\(493\) 1.49706 0.0674241
\(494\) −41.9602 −1.88788
\(495\) 3.15355 0.141742
\(496\) −25.7766 −1.15740
\(497\) 1.42779 0.0640450
\(498\) 6.54851 0.293446
\(499\) −10.2855 −0.460440 −0.230220 0.973139i \(-0.573945\pi\)
−0.230220 + 0.973139i \(0.573945\pi\)
\(500\) −6.31791 −0.282545
\(501\) 19.4553 0.869199
\(502\) −30.8828 −1.37837
\(503\) 5.63461 0.251235 0.125617 0.992079i \(-0.459909\pi\)
0.125617 + 0.992079i \(0.459909\pi\)
\(504\) −0.132841 −0.00591720
\(505\) 36.6724 1.63190
\(506\) 10.7424 0.477557
\(507\) 68.2285 3.03013
\(508\) 16.7249 0.742048
\(509\) −40.8634 −1.81124 −0.905620 0.424090i \(-0.860594\pi\)
−0.905620 + 0.424090i \(0.860594\pi\)
\(510\) −12.0119 −0.531896
\(511\) −17.6800 −0.782117
\(512\) −31.9238 −1.41085
\(513\) 12.0267 0.530993
\(514\) −1.78767 −0.0788509
\(515\) 35.8919 1.58159
\(516\) 3.99271 0.175769
\(517\) 2.66712 0.117300
\(518\) −6.20638 −0.272693
\(519\) −32.4620 −1.42492
\(520\) −0.704312 −0.0308861
\(521\) −26.8073 −1.17445 −0.587225 0.809424i \(-0.699780\pi\)
−0.587225 + 0.809424i \(0.699780\pi\)
\(522\) −3.15216 −0.137966
\(523\) −29.3492 −1.28335 −0.641675 0.766976i \(-0.721760\pi\)
−0.641675 + 0.766976i \(0.721760\pi\)
\(524\) −0.402185 −0.0175695
\(525\) −28.9827 −1.26491
\(526\) −32.5551 −1.41947
\(527\) 6.38953 0.278332
\(528\) −8.12373 −0.353540
\(529\) 5.97457 0.259764
\(530\) −4.65438 −0.202173
\(531\) 9.26096 0.401892
\(532\) 22.2754 0.965760
\(533\) 16.1117 0.697873
\(534\) −21.6702 −0.937760
\(535\) −43.9769 −1.90129
\(536\) 0.179988 0.00777431
\(537\) 49.2198 2.12399
\(538\) 4.87768 0.210292
\(539\) 6.38520 0.275030
\(540\) −23.2111 −0.998845
\(541\) −30.7335 −1.32133 −0.660667 0.750679i \(-0.729727\pi\)
−0.660667 + 0.750679i \(0.729727\pi\)
\(542\) 13.1717 0.565772
\(543\) 38.7603 1.66336
\(544\) 7.98214 0.342232
\(545\) 7.22745 0.309590
\(546\) −100.671 −4.30833
\(547\) 35.4321 1.51497 0.757483 0.652855i \(-0.226429\pi\)
0.757483 + 0.652855i \(0.226429\pi\)
\(548\) 8.48743 0.362565
\(549\) 6.97979 0.297890
\(550\) −7.85090 −0.334763
\(551\) −4.59708 −0.195842
\(552\) −0.373034 −0.0158774
\(553\) −43.6083 −1.85441
\(554\) −28.6173 −1.21583
\(555\) −5.11628 −0.217174
\(556\) 0.107147 0.00454404
\(557\) −30.6062 −1.29683 −0.648414 0.761288i \(-0.724567\pi\)
−0.648414 + 0.761288i \(0.724567\pi\)
\(558\) −13.4536 −0.569537
\(559\) −6.84703 −0.289599
\(560\) 44.1154 1.86422
\(561\) 2.01372 0.0850193
\(562\) −10.1816 −0.429487
\(563\) −24.1511 −1.01785 −0.508925 0.860811i \(-0.669957\pi\)
−0.508925 + 0.860811i \(0.669957\pi\)
\(564\) 10.6490 0.448405
\(565\) 53.7810 2.26258
\(566\) −16.2529 −0.683160
\(567\) 40.4347 1.69810
\(568\) −0.0134305 −0.000563531 0
\(569\) 43.2255 1.81211 0.906054 0.423162i \(-0.139080\pi\)
0.906054 + 0.423162i \(0.139080\pi\)
\(570\) 36.8855 1.54496
\(571\) −15.6365 −0.654366 −0.327183 0.944961i \(-0.606099\pi\)
−0.327183 + 0.944961i \(0.606099\pi\)
\(572\) −13.5760 −0.567641
\(573\) −11.4596 −0.478731
\(574\) −17.1807 −0.717110
\(575\) −21.1756 −0.883084
\(576\) −8.29433 −0.345597
\(577\) 18.1121 0.754018 0.377009 0.926210i \(-0.376953\pi\)
0.377009 + 0.926210i \(0.376953\pi\)
\(578\) −1.99568 −0.0830095
\(579\) −42.8590 −1.78116
\(580\) 8.87215 0.368396
\(581\) 5.96162 0.247330
\(582\) −6.81309 −0.282412
\(583\) 0.780277 0.0323158
\(584\) 0.166307 0.00688184
\(585\) −21.5925 −0.892738
\(586\) 11.3084 0.467147
\(587\) −13.8227 −0.570526 −0.285263 0.958449i \(-0.592081\pi\)
−0.285263 + 0.958449i \(0.592081\pi\)
\(588\) 25.4942 1.05136
\(589\) −19.6206 −0.808453
\(590\) −52.3590 −2.15558
\(591\) 38.9013 1.60018
\(592\) 3.42918 0.140938
\(593\) −1.32481 −0.0544034 −0.0272017 0.999630i \(-0.508660\pi\)
−0.0272017 + 0.999630i \(0.508660\pi\)
\(594\) 7.81621 0.320703
\(595\) −10.9354 −0.448307
\(596\) −2.50788 −0.102727
\(597\) 4.75985 0.194808
\(598\) −73.5534 −3.00782
\(599\) 10.0144 0.409179 0.204589 0.978848i \(-0.434414\pi\)
0.204589 + 0.978848i \(0.434414\pi\)
\(600\) 0.272626 0.0111299
\(601\) 21.0792 0.859839 0.429919 0.902867i \(-0.358542\pi\)
0.429919 + 0.902867i \(0.358542\pi\)
\(602\) 7.30137 0.297582
\(603\) 5.51800 0.224710
\(604\) −12.3233 −0.501426
\(605\) 2.98897 0.121519
\(606\) −49.3070 −2.00296
\(607\) 21.0044 0.852541 0.426270 0.904596i \(-0.359827\pi\)
0.426270 + 0.904596i \(0.359827\pi\)
\(608\) −24.5111 −0.994057
\(609\) −11.0293 −0.446932
\(610\) −39.4618 −1.59776
\(611\) −18.2618 −0.738795
\(612\) 2.09193 0.0845613
\(613\) −19.2691 −0.778272 −0.389136 0.921180i \(-0.627226\pi\)
−0.389136 + 0.921180i \(0.627226\pi\)
\(614\) −36.1311 −1.45813
\(615\) −14.1631 −0.571111
\(616\) −0.125908 −0.00507298
\(617\) 18.3306 0.737964 0.368982 0.929437i \(-0.379706\pi\)
0.368982 + 0.929437i \(0.379706\pi\)
\(618\) −48.2576 −1.94120
\(619\) −14.5335 −0.584152 −0.292076 0.956395i \(-0.594346\pi\)
−0.292076 + 0.956395i \(0.594346\pi\)
\(620\) 37.8669 1.52077
\(621\) 21.0821 0.845994
\(622\) 52.5328 2.10637
\(623\) −19.7280 −0.790387
\(624\) 55.6234 2.22672
\(625\) −29.1938 −1.16775
\(626\) 16.1385 0.645025
\(627\) −6.18361 −0.246950
\(628\) −6.68332 −0.266694
\(629\) −0.850029 −0.0338929
\(630\) 23.0252 0.917347
\(631\) 17.5475 0.698557 0.349278 0.937019i \(-0.386427\pi\)
0.349278 + 0.937019i \(0.386427\pi\)
\(632\) 0.410202 0.0163169
\(633\) 43.7825 1.74020
\(634\) −39.2907 −1.56043
\(635\) 25.2125 1.00053
\(636\) 3.11542 0.123534
\(637\) −43.7196 −1.73223
\(638\) −2.98765 −0.118282
\(639\) −0.411746 −0.0162884
\(640\) −0.822880 −0.0325272
\(641\) 6.52429 0.257694 0.128847 0.991664i \(-0.458872\pi\)
0.128847 + 0.991664i \(0.458872\pi\)
\(642\) 59.1281 2.33360
\(643\) −19.1891 −0.756743 −0.378371 0.925654i \(-0.623516\pi\)
−0.378371 + 0.925654i \(0.623516\pi\)
\(644\) 39.0472 1.53868
\(645\) 6.01894 0.236996
\(646\) 6.12823 0.241112
\(647\) 40.3419 1.58600 0.793002 0.609219i \(-0.208517\pi\)
0.793002 + 0.609219i \(0.208517\pi\)
\(648\) −0.380350 −0.0149415
\(649\) 8.77764 0.344553
\(650\) 53.7553 2.10846
\(651\) −47.0739 −1.84497
\(652\) 6.76087 0.264776
\(653\) 25.4098 0.994361 0.497180 0.867647i \(-0.334369\pi\)
0.497180 + 0.867647i \(0.334369\pi\)
\(654\) −9.71749 −0.379984
\(655\) −0.606287 −0.0236896
\(656\) 9.49280 0.370632
\(657\) 5.09857 0.198914
\(658\) 19.4736 0.759160
\(659\) −7.05669 −0.274890 −0.137445 0.990509i \(-0.543889\pi\)
−0.137445 + 0.990509i \(0.543889\pi\)
\(660\) 11.9341 0.464534
\(661\) −35.1252 −1.36621 −0.683105 0.730320i \(-0.739371\pi\)
−0.683105 + 0.730320i \(0.739371\pi\)
\(662\) −63.5260 −2.46901
\(663\) −13.7880 −0.535481
\(664\) −0.0560781 −0.00217625
\(665\) 33.5797 1.30217
\(666\) 1.78980 0.0693533
\(667\) −8.05837 −0.312021
\(668\) 19.1562 0.741175
\(669\) 34.6959 1.34142
\(670\) −31.1973 −1.20526
\(671\) 6.61552 0.255389
\(672\) −58.8072 −2.26854
\(673\) 5.37573 0.207219 0.103609 0.994618i \(-0.466961\pi\)
0.103609 + 0.994618i \(0.466961\pi\)
\(674\) 20.8519 0.803184
\(675\) −15.4075 −0.593035
\(676\) 67.1794 2.58382
\(677\) 35.6241 1.36915 0.684573 0.728944i \(-0.259989\pi\)
0.684573 + 0.728944i \(0.259989\pi\)
\(678\) −72.3100 −2.77705
\(679\) −6.20248 −0.238029
\(680\) 0.102864 0.00394465
\(681\) −41.8694 −1.60444
\(682\) −12.7515 −0.488280
\(683\) −46.5915 −1.78278 −0.891388 0.453242i \(-0.850267\pi\)
−0.891388 + 0.453242i \(0.850267\pi\)
\(684\) −6.42378 −0.245619
\(685\) 12.7947 0.488858
\(686\) −4.48891 −0.171388
\(687\) 36.5976 1.39629
\(688\) −4.03419 −0.153802
\(689\) −5.34258 −0.203536
\(690\) 64.6577 2.46148
\(691\) 11.8262 0.449890 0.224945 0.974371i \(-0.427780\pi\)
0.224945 + 0.974371i \(0.427780\pi\)
\(692\) −31.9629 −1.21505
\(693\) −3.86003 −0.146630
\(694\) 18.0564 0.685413
\(695\) 0.161522 0.00612689
\(696\) 0.103748 0.00393254
\(697\) −2.35309 −0.0891295
\(698\) −29.8977 −1.13165
\(699\) 9.15523 0.346283
\(700\) −28.5370 −1.07860
\(701\) 22.6647 0.856034 0.428017 0.903771i \(-0.359212\pi\)
0.428017 + 0.903771i \(0.359212\pi\)
\(702\) −53.5178 −2.01990
\(703\) 2.61022 0.0984464
\(704\) −7.86145 −0.296290
\(705\) 16.0532 0.604600
\(706\) 3.87247 0.145742
\(707\) −44.8880 −1.68819
\(708\) 35.0466 1.31713
\(709\) −13.2822 −0.498822 −0.249411 0.968398i \(-0.580237\pi\)
−0.249411 + 0.968398i \(0.580237\pi\)
\(710\) 2.32790 0.0873646
\(711\) 12.5758 0.471628
\(712\) 0.185572 0.00695461
\(713\) −34.3936 −1.28805
\(714\) 14.7029 0.550242
\(715\) −20.4656 −0.765369
\(716\) 48.4630 1.81115
\(717\) −12.3282 −0.460405
\(718\) −1.08873 −0.0406309
\(719\) 13.6866 0.510424 0.255212 0.966885i \(-0.417855\pi\)
0.255212 + 0.966885i \(0.417855\pi\)
\(720\) −12.7220 −0.474122
\(721\) −43.9326 −1.63614
\(722\) 19.0998 0.710820
\(723\) −60.0536 −2.23342
\(724\) 38.1643 1.41837
\(725\) 5.88933 0.218724
\(726\) −4.01875 −0.149150
\(727\) 1.26731 0.0470018 0.0235009 0.999724i \(-0.492519\pi\)
0.0235009 + 0.999724i \(0.492519\pi\)
\(728\) 0.862096 0.0319514
\(729\) 11.9999 0.444442
\(730\) −28.8259 −1.06690
\(731\) 1.00000 0.0369863
\(732\) 26.4139 0.976285
\(733\) −3.58895 −0.132561 −0.0662805 0.997801i \(-0.521113\pi\)
−0.0662805 + 0.997801i \(0.521113\pi\)
\(734\) 20.0005 0.738233
\(735\) 38.4321 1.41759
\(736\) −42.9663 −1.58376
\(737\) 5.23002 0.192650
\(738\) 4.95459 0.182381
\(739\) −9.47879 −0.348683 −0.174342 0.984685i \(-0.555780\pi\)
−0.174342 + 0.984685i \(0.555780\pi\)
\(740\) −5.03761 −0.185186
\(741\) 42.3394 1.55538
\(742\) 5.69709 0.209147
\(743\) −45.6023 −1.67299 −0.836493 0.547978i \(-0.815398\pi\)
−0.836493 + 0.547978i \(0.815398\pi\)
\(744\) 0.442801 0.0162339
\(745\) −3.78058 −0.138510
\(746\) 57.6838 2.11195
\(747\) −1.71922 −0.0629028
\(748\) 1.98276 0.0724967
\(749\) 53.8289 1.96687
\(750\) 12.8054 0.467589
\(751\) −11.0599 −0.403581 −0.201791 0.979429i \(-0.564676\pi\)
−0.201791 + 0.979429i \(0.564676\pi\)
\(752\) −10.7597 −0.392365
\(753\) 31.1618 1.13560
\(754\) 20.4566 0.744984
\(755\) −18.5771 −0.676090
\(756\) 28.4110 1.03330
\(757\) 19.9278 0.724288 0.362144 0.932122i \(-0.382045\pi\)
0.362144 + 0.932122i \(0.382045\pi\)
\(758\) 60.6345 2.20235
\(759\) −10.8395 −0.393447
\(760\) −0.315868 −0.0114577
\(761\) 7.74149 0.280629 0.140314 0.990107i \(-0.455189\pi\)
0.140314 + 0.990107i \(0.455189\pi\)
\(762\) −33.8989 −1.22803
\(763\) −8.84659 −0.320268
\(764\) −11.2834 −0.408218
\(765\) 3.15355 0.114017
\(766\) 23.7847 0.859375
\(767\) −60.1008 −2.17011
\(768\) 32.7679 1.18241
\(769\) −13.1274 −0.473388 −0.236694 0.971584i \(-0.576064\pi\)
−0.236694 + 0.971584i \(0.576064\pi\)
\(770\) 21.8236 0.786467
\(771\) 1.80383 0.0649633
\(772\) −42.2000 −1.51881
\(773\) −24.3671 −0.876423 −0.438211 0.898872i \(-0.644388\pi\)
−0.438211 + 0.898872i \(0.644388\pi\)
\(774\) −2.10557 −0.0756832
\(775\) 25.1360 0.902912
\(776\) 0.0583437 0.00209442
\(777\) 6.26246 0.224665
\(778\) 28.1735 1.01007
\(779\) 7.22572 0.258888
\(780\) −81.7131 −2.92580
\(781\) −0.390257 −0.0139645
\(782\) 10.7424 0.384147
\(783\) −5.86331 −0.209538
\(784\) −25.7591 −0.919968
\(785\) −10.0750 −0.359592
\(786\) 0.815168 0.0290761
\(787\) 41.9572 1.49561 0.747807 0.663916i \(-0.231107\pi\)
0.747807 + 0.663916i \(0.231107\pi\)
\(788\) 38.3031 1.36449
\(789\) 32.8493 1.16947
\(790\) −71.1000 −2.52963
\(791\) −65.8294 −2.34062
\(792\) 0.0363094 0.00129020
\(793\) −45.2967 −1.60853
\(794\) 18.2587 0.647978
\(795\) 4.69644 0.166566
\(796\) 4.68666 0.166114
\(797\) −22.7238 −0.804917 −0.402458 0.915438i \(-0.631844\pi\)
−0.402458 + 0.915438i \(0.631844\pi\)
\(798\) −45.1488 −1.59825
\(799\) 2.66712 0.0943559
\(800\) 31.4013 1.11020
\(801\) 5.68918 0.201017
\(802\) −15.6881 −0.553966
\(803\) 4.83248 0.170534
\(804\) 20.8819 0.736450
\(805\) 58.8630 2.07465
\(806\) 87.3098 3.07536
\(807\) −4.92176 −0.173254
\(808\) 0.422240 0.0148543
\(809\) 8.80446 0.309548 0.154774 0.987950i \(-0.450535\pi\)
0.154774 + 0.987950i \(0.450535\pi\)
\(810\) 65.9258 2.31640
\(811\) 44.9326 1.57780 0.788898 0.614524i \(-0.210652\pi\)
0.788898 + 0.614524i \(0.210652\pi\)
\(812\) −10.8598 −0.381103
\(813\) −13.2907 −0.466125
\(814\) 1.69639 0.0594585
\(815\) 10.1919 0.357006
\(816\) −8.12373 −0.284387
\(817\) −3.07074 −0.107432
\(818\) −50.2535 −1.75707
\(819\) 26.4297 0.923530
\(820\) −13.9453 −0.486992
\(821\) 48.4134 1.68964 0.844820 0.535051i \(-0.179708\pi\)
0.844820 + 0.535051i \(0.179708\pi\)
\(822\) −17.2027 −0.600014
\(823\) −42.2303 −1.47206 −0.736028 0.676951i \(-0.763301\pi\)
−0.736028 + 0.676951i \(0.763301\pi\)
\(824\) 0.413253 0.0143963
\(825\) 7.92184 0.275803
\(826\) 64.0888 2.22993
\(827\) 36.6138 1.27319 0.636594 0.771199i \(-0.280343\pi\)
0.636594 + 0.771199i \(0.280343\pi\)
\(828\) −11.2605 −0.391328
\(829\) 26.5336 0.921549 0.460774 0.887517i \(-0.347572\pi\)
0.460774 + 0.887517i \(0.347572\pi\)
\(830\) 9.71998 0.337386
\(831\) 28.8759 1.00169
\(832\) 53.8276 1.86614
\(833\) 6.38520 0.221234
\(834\) −0.217171 −0.00752001
\(835\) 28.8776 0.999350
\(836\) −6.08853 −0.210576
\(837\) −25.0250 −0.864989
\(838\) 27.1933 0.939377
\(839\) 5.64083 0.194743 0.0973715 0.995248i \(-0.468956\pi\)
0.0973715 + 0.995248i \(0.468956\pi\)
\(840\) −0.757833 −0.0261477
\(841\) −26.7588 −0.922718
\(842\) 29.9833 1.03329
\(843\) 10.2737 0.353844
\(844\) 43.1093 1.48388
\(845\) 101.272 3.48386
\(846\) −5.61581 −0.193076
\(847\) −3.65858 −0.125710
\(848\) −3.14779 −0.108095
\(849\) 16.3998 0.562839
\(850\) −7.85090 −0.269284
\(851\) 4.57554 0.156848
\(852\) −1.55819 −0.0533826
\(853\) 11.6787 0.399871 0.199935 0.979809i \(-0.435927\pi\)
0.199935 + 0.979809i \(0.435927\pi\)
\(854\) 48.3023 1.65287
\(855\) −9.68374 −0.331177
\(856\) −0.506343 −0.0173064
\(857\) −34.2962 −1.17154 −0.585768 0.810479i \(-0.699207\pi\)
−0.585768 + 0.810479i \(0.699207\pi\)
\(858\) 27.5165 0.939397
\(859\) 54.2497 1.85098 0.925488 0.378778i \(-0.123656\pi\)
0.925488 + 0.378778i \(0.123656\pi\)
\(860\) 5.92640 0.202088
\(861\) 17.3360 0.590809
\(862\) 32.2397 1.09809
\(863\) 56.3274 1.91741 0.958704 0.284406i \(-0.0917963\pi\)
0.958704 + 0.284406i \(0.0917963\pi\)
\(864\) −31.2625 −1.06357
\(865\) −48.1835 −1.63829
\(866\) 28.1350 0.956067
\(867\) 2.01372 0.0683895
\(868\) −46.3501 −1.57322
\(869\) 11.9195 0.404340
\(870\) −17.9825 −0.609665
\(871\) −35.8101 −1.21338
\(872\) 0.0832155 0.00281803
\(873\) 1.78868 0.0605375
\(874\) −32.9871 −1.11580
\(875\) 11.6578 0.394105
\(876\) 19.2947 0.651907
\(877\) −34.3979 −1.16153 −0.580767 0.814070i \(-0.697247\pi\)
−0.580767 + 0.814070i \(0.697247\pi\)
\(878\) 27.7461 0.936385
\(879\) −11.4106 −0.384871
\(880\) −12.0581 −0.406478
\(881\) 6.57047 0.221365 0.110682 0.993856i \(-0.464696\pi\)
0.110682 + 0.993856i \(0.464696\pi\)
\(882\) −13.4445 −0.452700
\(883\) 26.4466 0.889999 0.444999 0.895531i \(-0.353204\pi\)
0.444999 + 0.895531i \(0.353204\pi\)
\(884\) −13.5760 −0.456610
\(885\) 52.8321 1.77593
\(886\) 48.8603 1.64149
\(887\) 16.9262 0.568326 0.284163 0.958776i \(-0.408284\pi\)
0.284163 + 0.958776i \(0.408284\pi\)
\(888\) −0.0589079 −0.00197682
\(889\) −30.8608 −1.03504
\(890\) −32.1651 −1.07818
\(891\) −11.0520 −0.370257
\(892\) 34.1625 1.14384
\(893\) −8.19003 −0.274069
\(894\) 5.08309 0.170004
\(895\) 73.0571 2.44203
\(896\) 1.00723 0.0336491
\(897\) 74.2181 2.47807
\(898\) 50.7799 1.69455
\(899\) 9.56549 0.319027
\(900\) 8.22953 0.274318
\(901\) 0.780277 0.0259948
\(902\) 4.69602 0.156360
\(903\) −7.36735 −0.245170
\(904\) 0.619225 0.0205951
\(905\) 57.5321 1.91243
\(906\) 24.9774 0.829818
\(907\) 21.7189 0.721163 0.360581 0.932728i \(-0.382578\pi\)
0.360581 + 0.932728i \(0.382578\pi\)
\(908\) −41.2256 −1.36812
\(909\) 12.9448 0.429353
\(910\) −149.427 −4.95344
\(911\) −7.92085 −0.262430 −0.131215 0.991354i \(-0.541888\pi\)
−0.131215 + 0.991354i \(0.541888\pi\)
\(912\) 24.9459 0.826040
\(913\) −1.62949 −0.0539283
\(914\) 45.4408 1.50305
\(915\) 39.8184 1.31636
\(916\) 36.0349 1.19063
\(917\) 0.742111 0.0245067
\(918\) 7.81621 0.257973
\(919\) 14.8547 0.490011 0.245005 0.969522i \(-0.421210\pi\)
0.245005 + 0.969522i \(0.421210\pi\)
\(920\) −0.553695 −0.0182548
\(921\) 36.4576 1.20132
\(922\) −63.3648 −2.08681
\(923\) 2.67210 0.0879534
\(924\) −14.6076 −0.480556
\(925\) −3.34396 −0.109949
\(926\) −0.207173 −0.00680813
\(927\) 12.6693 0.416115
\(928\) 11.9497 0.392269
\(929\) −35.7661 −1.17345 −0.586724 0.809787i \(-0.699583\pi\)
−0.586724 + 0.809787i \(0.699583\pi\)
\(930\) −76.7505 −2.51675
\(931\) −19.6073 −0.642603
\(932\) 9.01446 0.295278
\(933\) −53.0075 −1.73539
\(934\) 69.3819 2.27024
\(935\) 2.98897 0.0977497
\(936\) −0.248612 −0.00812613
\(937\) 49.5046 1.61725 0.808623 0.588328i \(-0.200213\pi\)
0.808623 + 0.588328i \(0.200213\pi\)
\(938\) 38.1863 1.24683
\(939\) −16.2844 −0.531420
\(940\) 15.8064 0.515548
\(941\) −21.8253 −0.711483 −0.355742 0.934584i \(-0.615772\pi\)
−0.355742 + 0.934584i \(0.615772\pi\)
\(942\) 13.5461 0.441355
\(943\) 12.6662 0.412468
\(944\) −35.4107 −1.15252
\(945\) 42.8290 1.39323
\(946\) −1.99568 −0.0648853
\(947\) 42.9854 1.39684 0.698420 0.715688i \(-0.253887\pi\)
0.698420 + 0.715688i \(0.253887\pi\)
\(948\) 47.5910 1.54568
\(949\) −33.0881 −1.07409
\(950\) 24.1081 0.782169
\(951\) 39.6458 1.28560
\(952\) −0.125908 −0.00408070
\(953\) 18.3008 0.592821 0.296410 0.955061i \(-0.404210\pi\)
0.296410 + 0.955061i \(0.404210\pi\)
\(954\) −1.64293 −0.0531918
\(955\) −17.0095 −0.550414
\(956\) −12.1386 −0.392591
\(957\) 3.01465 0.0974499
\(958\) −85.9843 −2.77803
\(959\) −15.6610 −0.505720
\(960\) −47.3177 −1.52717
\(961\) 9.82608 0.316970
\(962\) −11.6152 −0.374490
\(963\) −15.5232 −0.500229
\(964\) −59.1302 −1.90445
\(965\) −63.6158 −2.04786
\(966\) −79.1428 −2.54638
\(967\) 18.5193 0.595539 0.297770 0.954638i \(-0.403757\pi\)
0.297770 + 0.954638i \(0.403757\pi\)
\(968\) 0.0344145 0.00110612
\(969\) −6.18361 −0.198646
\(970\) −10.1127 −0.324699
\(971\) −12.4524 −0.399618 −0.199809 0.979835i \(-0.564032\pi\)
−0.199809 + 0.979835i \(0.564032\pi\)
\(972\) −20.8309 −0.668150
\(973\) −0.197707 −0.00633821
\(974\) 17.3921 0.557278
\(975\) −54.2411 −1.73711
\(976\) −26.6883 −0.854271
\(977\) 40.4508 1.29414 0.647069 0.762432i \(-0.275995\pi\)
0.647069 + 0.762432i \(0.275995\pi\)
\(978\) −13.7033 −0.438182
\(979\) 5.39227 0.172338
\(980\) 37.8412 1.20879
\(981\) 2.55118 0.0814530
\(982\) −61.9411 −1.97662
\(983\) −8.73218 −0.278513 −0.139257 0.990256i \(-0.544471\pi\)
−0.139257 + 0.990256i \(0.544471\pi\)
\(984\) −0.163071 −0.00519852
\(985\) 57.7413 1.83979
\(986\) −2.98765 −0.0951463
\(987\) −19.6496 −0.625453
\(988\) 41.6884 1.32628
\(989\) −5.38280 −0.171163
\(990\) −6.29349 −0.200020
\(991\) 2.56381 0.0814422 0.0407211 0.999171i \(-0.487034\pi\)
0.0407211 + 0.999171i \(0.487034\pi\)
\(992\) 51.0021 1.61932
\(993\) 64.1000 2.03415
\(994\) −2.84941 −0.0903779
\(995\) 7.06506 0.223977
\(996\) −6.50609 −0.206153
\(997\) 4.72770 0.149728 0.0748640 0.997194i \(-0.476148\pi\)
0.0748640 + 0.997194i \(0.476148\pi\)
\(998\) 20.5265 0.649756
\(999\) 3.32919 0.105331
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 \(a_p\))