Properties

Label 4015.2.a.h.1.28
Level 4015
Weight 2
Character 4015.1
Self dual Yes
Analytic conductor 32.060
Analytic rank 0
Dimension 37
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4015 = 5 \cdot 11 \cdot 73 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0599364115\)
Analytic rank: \(0\)
Dimension: \(37\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.28
Character \(\chi\) = 4015.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.91950 q^{2}\) \(-0.260789 q^{3}\) \(+1.68450 q^{4}\) \(+1.00000 q^{5}\) \(-0.500585 q^{6}\) \(-5.05939 q^{7}\) \(-0.605613 q^{8}\) \(-2.93199 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.91950 q^{2}\) \(-0.260789 q^{3}\) \(+1.68450 q^{4}\) \(+1.00000 q^{5}\) \(-0.500585 q^{6}\) \(-5.05939 q^{7}\) \(-0.605613 q^{8}\) \(-2.93199 q^{9}\) \(+1.91950 q^{10}\) \(+1.00000 q^{11}\) \(-0.439297 q^{12}\) \(-1.62207 q^{13}\) \(-9.71152 q^{14}\) \(-0.260789 q^{15}\) \(-4.53147 q^{16}\) \(+8.05028 q^{17}\) \(-5.62796 q^{18}\) \(+2.76332 q^{19}\) \(+1.68450 q^{20}\) \(+1.31943 q^{21}\) \(+1.91950 q^{22}\) \(+6.01036 q^{23}\) \(+0.157937 q^{24}\) \(+1.00000 q^{25}\) \(-3.11357 q^{26}\) \(+1.54700 q^{27}\) \(-8.52252 q^{28}\) \(+9.05396 q^{29}\) \(-0.500585 q^{30}\) \(+3.49816 q^{31}\) \(-7.48694 q^{32}\) \(-0.260789 q^{33}\) \(+15.4526 q^{34}\) \(-5.05939 q^{35}\) \(-4.93892 q^{36}\) \(-2.75291 q^{37}\) \(+5.30419 q^{38}\) \(+0.423017 q^{39}\) \(-0.605613 q^{40}\) \(-2.96672 q^{41}\) \(+2.53265 q^{42}\) \(-8.50985 q^{43}\) \(+1.68450 q^{44}\) \(-2.93199 q^{45}\) \(+11.5369 q^{46}\) \(-1.94959 q^{47}\) \(+1.18175 q^{48}\) \(+18.5974 q^{49}\) \(+1.91950 q^{50}\) \(-2.09942 q^{51}\) \(-2.73237 q^{52}\) \(+8.90378 q^{53}\) \(+2.96946 q^{54}\) \(+1.00000 q^{55}\) \(+3.06403 q^{56}\) \(-0.720641 q^{57}\) \(+17.3791 q^{58}\) \(-8.85846 q^{59}\) \(-0.439297 q^{60}\) \(+8.65733 q^{61}\) \(+6.71474 q^{62}\) \(+14.8341 q^{63}\) \(-5.30828 q^{64}\) \(-1.62207 q^{65}\) \(-0.500585 q^{66}\) \(-4.09260 q^{67}\) \(+13.5607 q^{68}\) \(-1.56743 q^{69}\) \(-9.71152 q^{70}\) \(+0.239302 q^{71}\) \(+1.77565 q^{72}\) \(+1.00000 q^{73}\) \(-5.28422 q^{74}\) \(-0.260789 q^{75}\) \(+4.65479 q^{76}\) \(-5.05939 q^{77}\) \(+0.811983 q^{78}\) \(+0.231708 q^{79}\) \(-4.53147 q^{80}\) \(+8.39253 q^{81}\) \(-5.69463 q^{82}\) \(+16.6802 q^{83}\) \(+2.22258 q^{84}\) \(+8.05028 q^{85}\) \(-16.3347 q^{86}\) \(-2.36117 q^{87}\) \(-0.605613 q^{88}\) \(+16.9646 q^{89}\) \(-5.62796 q^{90}\) \(+8.20668 q^{91}\) \(+10.1244 q^{92}\) \(-0.912281 q^{93}\) \(-3.74225 q^{94}\) \(+2.76332 q^{95}\) \(+1.95251 q^{96}\) \(-2.05323 q^{97}\) \(+35.6978 q^{98}\) \(-2.93199 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut 5q^{10} \) \(\mathstrut +\mathstrut 37q^{11} \) \(\mathstrut +\mathstrut 6q^{12} \) \(\mathstrut +\mathstrut 11q^{13} \) \(\mathstrut +\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 43q^{16} \) \(\mathstrut +\mathstrut 38q^{17} \) \(\mathstrut +\mathstrut 11q^{18} \) \(\mathstrut +\mathstrut 34q^{19} \) \(\mathstrut +\mathstrut 43q^{20} \) \(\mathstrut +\mathstrut 39q^{21} \) \(\mathstrut +\mathstrut 5q^{22} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 37q^{25} \) \(\mathstrut -\mathstrut 9q^{26} \) \(\mathstrut +\mathstrut 3q^{27} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut +\mathstrut 9q^{30} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut +\mathstrut 14q^{32} \) \(\mathstrut +\mathstrut 3q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 6q^{35} \) \(\mathstrut +\mathstrut 20q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 15q^{38} \) \(\mathstrut +\mathstrut 14q^{39} \) \(\mathstrut +\mathstrut 12q^{40} \) \(\mathstrut +\mathstrut 62q^{41} \) \(\mathstrut -\mathstrut 13q^{42} \) \(\mathstrut +\mathstrut 30q^{43} \) \(\mathstrut +\mathstrut 43q^{44} \) \(\mathstrut +\mathstrut 50q^{45} \) \(\mathstrut +\mathstrut 31q^{46} \) \(\mathstrut +\mathstrut 5q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 59q^{49} \) \(\mathstrut +\mathstrut 5q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 13q^{54} \) \(\mathstrut +\mathstrut 37q^{55} \) \(\mathstrut +\mathstrut 22q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 40q^{58} \) \(\mathstrut +\mathstrut 15q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut +\mathstrut 57q^{61} \) \(\mathstrut +\mathstrut 20q^{62} \) \(\mathstrut -\mathstrut 29q^{63} \) \(\mathstrut +\mathstrut 10q^{64} \) \(\mathstrut +\mathstrut 11q^{65} \) \(\mathstrut +\mathstrut 9q^{66} \) \(\mathstrut -\mathstrut 14q^{67} \) \(\mathstrut +\mathstrut 53q^{68} \) \(\mathstrut +\mathstrut 24q^{69} \) \(\mathstrut +\mathstrut 11q^{70} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 15q^{72} \) \(\mathstrut +\mathstrut 37q^{73} \) \(\mathstrut +\mathstrut 7q^{74} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut +\mathstrut 59q^{76} \) \(\mathstrut +\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut q^{78} \) \(\mathstrut +\mathstrut 42q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 61q^{81} \) \(\mathstrut -\mathstrut 22q^{82} \) \(\mathstrut +\mathstrut 44q^{83} \) \(\mathstrut +\mathstrut 66q^{84} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut -\mathstrut q^{86} \) \(\mathstrut -\mathstrut 26q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 69q^{89} \) \(\mathstrut +\mathstrut 11q^{90} \) \(\mathstrut -\mathstrut 10q^{91} \) \(\mathstrut -\mathstrut 21q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut +\mathstrut 29q^{94} \) \(\mathstrut +\mathstrut 34q^{95} \) \(\mathstrut -\mathstrut 9q^{96} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut -\mathstrut 15q^{98} \) \(\mathstrut +\mathstrut 50q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.91950 1.35729 0.678647 0.734464i \(-0.262567\pi\)
0.678647 + 0.734464i \(0.262567\pi\)
\(3\) −0.260789 −0.150566 −0.0752832 0.997162i \(-0.523986\pi\)
−0.0752832 + 0.997162i \(0.523986\pi\)
\(4\) 1.68450 0.842248
\(5\) 1.00000 0.447214
\(6\) −0.500585 −0.204363
\(7\) −5.05939 −1.91227 −0.956135 0.292927i \(-0.905371\pi\)
−0.956135 + 0.292927i \(0.905371\pi\)
\(8\) −0.605613 −0.214116
\(9\) −2.93199 −0.977330
\(10\) 1.91950 0.607000
\(11\) 1.00000 0.301511
\(12\) −0.439297 −0.126814
\(13\) −1.62207 −0.449881 −0.224941 0.974372i \(-0.572219\pi\)
−0.224941 + 0.974372i \(0.572219\pi\)
\(14\) −9.71152 −2.59551
\(15\) −0.260789 −0.0673353
\(16\) −4.53147 −1.13287
\(17\) 8.05028 1.95248 0.976240 0.216691i \(-0.0695264\pi\)
0.976240 + 0.216691i \(0.0695264\pi\)
\(18\) −5.62796 −1.32652
\(19\) 2.76332 0.633948 0.316974 0.948434i \(-0.397333\pi\)
0.316974 + 0.948434i \(0.397333\pi\)
\(20\) 1.68450 0.376665
\(21\) 1.31943 0.287923
\(22\) 1.91950 0.409240
\(23\) 6.01036 1.25325 0.626624 0.779322i \(-0.284436\pi\)
0.626624 + 0.779322i \(0.284436\pi\)
\(24\) 0.157937 0.0322387
\(25\) 1.00000 0.200000
\(26\) −3.11357 −0.610621
\(27\) 1.54700 0.297719
\(28\) −8.52252 −1.61060
\(29\) 9.05396 1.68128 0.840639 0.541596i \(-0.182180\pi\)
0.840639 + 0.541596i \(0.182180\pi\)
\(30\) −0.500585 −0.0913938
\(31\) 3.49816 0.628289 0.314144 0.949375i \(-0.398282\pi\)
0.314144 + 0.949375i \(0.398282\pi\)
\(32\) −7.48694 −1.32352
\(33\) −0.260789 −0.0453975
\(34\) 15.4526 2.65009
\(35\) −5.05939 −0.855193
\(36\) −4.93892 −0.823154
\(37\) −2.75291 −0.452576 −0.226288 0.974060i \(-0.572659\pi\)
−0.226288 + 0.974060i \(0.572659\pi\)
\(38\) 5.30419 0.860454
\(39\) 0.423017 0.0677370
\(40\) −0.605613 −0.0957558
\(41\) −2.96672 −0.463324 −0.231662 0.972796i \(-0.574416\pi\)
−0.231662 + 0.972796i \(0.574416\pi\)
\(42\) 2.53265 0.390797
\(43\) −8.50985 −1.29774 −0.648870 0.760899i \(-0.724758\pi\)
−0.648870 + 0.760899i \(0.724758\pi\)
\(44\) 1.68450 0.253947
\(45\) −2.93199 −0.437075
\(46\) 11.5369 1.70102
\(47\) −1.94959 −0.284377 −0.142189 0.989840i \(-0.545414\pi\)
−0.142189 + 0.989840i \(0.545414\pi\)
\(48\) 1.18175 0.170572
\(49\) 18.5974 2.65678
\(50\) 1.91950 0.271459
\(51\) −2.09942 −0.293978
\(52\) −2.73237 −0.378911
\(53\) 8.90378 1.22303 0.611514 0.791234i \(-0.290561\pi\)
0.611514 + 0.791234i \(0.290561\pi\)
\(54\) 2.96946 0.404093
\(55\) 1.00000 0.134840
\(56\) 3.06403 0.409448
\(57\) −0.720641 −0.0954512
\(58\) 17.3791 2.28199
\(59\) −8.85846 −1.15327 −0.576637 0.817001i \(-0.695635\pi\)
−0.576637 + 0.817001i \(0.695635\pi\)
\(60\) −0.439297 −0.0567130
\(61\) 8.65733 1.10846 0.554229 0.832364i \(-0.313013\pi\)
0.554229 + 0.832364i \(0.313013\pi\)
\(62\) 6.71474 0.852773
\(63\) 14.8341 1.86892
\(64\) −5.30828 −0.663535
\(65\) −1.62207 −0.201193
\(66\) −0.500585 −0.0616177
\(67\) −4.09260 −0.499991 −0.249996 0.968247i \(-0.580429\pi\)
−0.249996 + 0.968247i \(0.580429\pi\)
\(68\) 13.5607 1.64447
\(69\) −1.56743 −0.188697
\(70\) −9.71152 −1.16075
\(71\) 0.239302 0.0283999 0.0141999 0.999899i \(-0.495480\pi\)
0.0141999 + 0.999899i \(0.495480\pi\)
\(72\) 1.77565 0.209262
\(73\) 1.00000 0.117041
\(74\) −5.28422 −0.614279
\(75\) −0.260789 −0.0301133
\(76\) 4.65479 0.533941
\(77\) −5.05939 −0.576571
\(78\) 0.811983 0.0919390
\(79\) 0.231708 0.0260692 0.0130346 0.999915i \(-0.495851\pi\)
0.0130346 + 0.999915i \(0.495851\pi\)
\(80\) −4.53147 −0.506633
\(81\) 8.39253 0.932503
\(82\) −5.69463 −0.628867
\(83\) 16.6802 1.83089 0.915443 0.402447i \(-0.131840\pi\)
0.915443 + 0.402447i \(0.131840\pi\)
\(84\) 2.22258 0.242503
\(85\) 8.05028 0.873176
\(86\) −16.3347 −1.76142
\(87\) −2.36117 −0.253144
\(88\) −0.605613 −0.0645585
\(89\) 16.9646 1.79825 0.899124 0.437694i \(-0.144205\pi\)
0.899124 + 0.437694i \(0.144205\pi\)
\(90\) −5.62796 −0.593240
\(91\) 8.20668 0.860294
\(92\) 10.1244 1.05554
\(93\) −0.912281 −0.0945991
\(94\) −3.74225 −0.385984
\(95\) 2.76332 0.283510
\(96\) 1.95251 0.199277
\(97\) −2.05323 −0.208474 −0.104237 0.994552i \(-0.533240\pi\)
−0.104237 + 0.994552i \(0.533240\pi\)
\(98\) 35.6978 3.60603
\(99\) −2.93199 −0.294676
\(100\) 1.68450 0.168450
\(101\) 2.37103 0.235927 0.117963 0.993018i \(-0.462363\pi\)
0.117963 + 0.993018i \(0.462363\pi\)
\(102\) −4.02985 −0.399014
\(103\) −3.30328 −0.325482 −0.162741 0.986669i \(-0.552033\pi\)
−0.162741 + 0.986669i \(0.552033\pi\)
\(104\) 0.982346 0.0963269
\(105\) 1.31943 0.128763
\(106\) 17.0908 1.66001
\(107\) −0.293542 −0.0283778 −0.0141889 0.999899i \(-0.504517\pi\)
−0.0141889 + 0.999899i \(0.504517\pi\)
\(108\) 2.60591 0.250753
\(109\) 14.8598 1.42331 0.711655 0.702529i \(-0.247946\pi\)
0.711655 + 0.702529i \(0.247946\pi\)
\(110\) 1.91950 0.183018
\(111\) 0.717928 0.0681427
\(112\) 22.9265 2.16635
\(113\) 7.21829 0.679039 0.339520 0.940599i \(-0.389735\pi\)
0.339520 + 0.940599i \(0.389735\pi\)
\(114\) −1.38327 −0.129555
\(115\) 6.01036 0.560469
\(116\) 15.2513 1.41605
\(117\) 4.75589 0.439682
\(118\) −17.0038 −1.56533
\(119\) −40.7295 −3.73367
\(120\) 0.157937 0.0144176
\(121\) 1.00000 0.0909091
\(122\) 16.6178 1.50450
\(123\) 0.773687 0.0697610
\(124\) 5.89264 0.529175
\(125\) 1.00000 0.0894427
\(126\) 28.4741 2.53667
\(127\) 14.1325 1.25405 0.627026 0.778998i \(-0.284272\pi\)
0.627026 + 0.778998i \(0.284272\pi\)
\(128\) 4.78462 0.422904
\(129\) 2.21927 0.195396
\(130\) −3.11357 −0.273078
\(131\) −22.2478 −1.94380 −0.971899 0.235396i \(-0.924361\pi\)
−0.971899 + 0.235396i \(0.924361\pi\)
\(132\) −0.439297 −0.0382359
\(133\) −13.9807 −1.21228
\(134\) −7.85577 −0.678635
\(135\) 1.54700 0.133144
\(136\) −4.87535 −0.418058
\(137\) −3.39120 −0.289729 −0.144865 0.989451i \(-0.546275\pi\)
−0.144865 + 0.989451i \(0.546275\pi\)
\(138\) −3.00870 −0.256117
\(139\) −13.3808 −1.13494 −0.567472 0.823393i \(-0.692079\pi\)
−0.567472 + 0.823393i \(0.692079\pi\)
\(140\) −8.52252 −0.720284
\(141\) 0.508432 0.0428177
\(142\) 0.459341 0.0385470
\(143\) −1.62207 −0.135644
\(144\) 13.2862 1.10718
\(145\) 9.05396 0.751890
\(146\) 1.91950 0.158859
\(147\) −4.85000 −0.400021
\(148\) −4.63727 −0.381181
\(149\) −12.3339 −1.01043 −0.505214 0.862994i \(-0.668587\pi\)
−0.505214 + 0.862994i \(0.668587\pi\)
\(150\) −0.500585 −0.0408726
\(151\) 13.3710 1.08811 0.544056 0.839049i \(-0.316888\pi\)
0.544056 + 0.839049i \(0.316888\pi\)
\(152\) −1.67350 −0.135739
\(153\) −23.6033 −1.90822
\(154\) −9.71152 −0.782576
\(155\) 3.49816 0.280979
\(156\) 0.712570 0.0570513
\(157\) −19.5703 −1.56188 −0.780938 0.624608i \(-0.785259\pi\)
−0.780938 + 0.624608i \(0.785259\pi\)
\(158\) 0.444765 0.0353836
\(159\) −2.32200 −0.184147
\(160\) −7.48694 −0.591895
\(161\) −30.4088 −2.39655
\(162\) 16.1095 1.26568
\(163\) 5.77977 0.452706 0.226353 0.974045i \(-0.427320\pi\)
0.226353 + 0.974045i \(0.427320\pi\)
\(164\) −4.99743 −0.390233
\(165\) −0.260789 −0.0203024
\(166\) 32.0177 2.48505
\(167\) 9.08740 0.703204 0.351602 0.936150i \(-0.385637\pi\)
0.351602 + 0.936150i \(0.385637\pi\)
\(168\) −0.799064 −0.0616491
\(169\) −10.3689 −0.797607
\(170\) 15.4526 1.18516
\(171\) −8.10201 −0.619576
\(172\) −14.3348 −1.09302
\(173\) −22.1123 −1.68116 −0.840582 0.541685i \(-0.817787\pi\)
−0.840582 + 0.541685i \(0.817787\pi\)
\(174\) −4.53227 −0.343591
\(175\) −5.05939 −0.382454
\(176\) −4.53147 −0.341572
\(177\) 2.31018 0.173644
\(178\) 32.5637 2.44075
\(179\) 18.4166 1.37652 0.688262 0.725462i \(-0.258374\pi\)
0.688262 + 0.725462i \(0.258374\pi\)
\(180\) −4.93892 −0.368126
\(181\) −5.15509 −0.383175 −0.191588 0.981476i \(-0.561364\pi\)
−0.191588 + 0.981476i \(0.561364\pi\)
\(182\) 15.7528 1.16767
\(183\) −2.25773 −0.166896
\(184\) −3.63995 −0.268341
\(185\) −2.75291 −0.202398
\(186\) −1.75113 −0.128399
\(187\) 8.05028 0.588695
\(188\) −3.28408 −0.239516
\(189\) −7.82685 −0.569320
\(190\) 5.30419 0.384807
\(191\) 3.36000 0.243121 0.121561 0.992584i \(-0.461210\pi\)
0.121561 + 0.992584i \(0.461210\pi\)
\(192\) 1.38434 0.0999061
\(193\) 20.2514 1.45773 0.728863 0.684660i \(-0.240049\pi\)
0.728863 + 0.684660i \(0.240049\pi\)
\(194\) −3.94118 −0.282960
\(195\) 0.423017 0.0302929
\(196\) 31.3273 2.23766
\(197\) −14.3042 −1.01913 −0.509565 0.860432i \(-0.670194\pi\)
−0.509565 + 0.860432i \(0.670194\pi\)
\(198\) −5.62796 −0.399962
\(199\) −10.2846 −0.729058 −0.364529 0.931192i \(-0.618770\pi\)
−0.364529 + 0.931192i \(0.618770\pi\)
\(200\) −0.605613 −0.0428233
\(201\) 1.06730 0.0752818
\(202\) 4.55121 0.320222
\(203\) −45.8075 −3.21506
\(204\) −3.53647 −0.247602
\(205\) −2.96672 −0.207205
\(206\) −6.34066 −0.441774
\(207\) −17.6223 −1.22484
\(208\) 7.35035 0.509655
\(209\) 2.76332 0.191142
\(210\) 2.53265 0.174770
\(211\) 2.08830 0.143764 0.0718822 0.997413i \(-0.477099\pi\)
0.0718822 + 0.997413i \(0.477099\pi\)
\(212\) 14.9984 1.03009
\(213\) −0.0624071 −0.00427607
\(214\) −0.563455 −0.0385170
\(215\) −8.50985 −0.580367
\(216\) −0.936880 −0.0637466
\(217\) −17.6986 −1.20146
\(218\) 28.5234 1.93185
\(219\) −0.260789 −0.0176225
\(220\) 1.68450 0.113569
\(221\) −13.0581 −0.878384
\(222\) 1.37807 0.0924897
\(223\) 26.4461 1.77096 0.885482 0.464674i \(-0.153829\pi\)
0.885482 + 0.464674i \(0.153829\pi\)
\(224\) 37.8794 2.53092
\(225\) −2.93199 −0.195466
\(226\) 13.8555 0.921656
\(227\) −11.0178 −0.731276 −0.365638 0.930757i \(-0.619149\pi\)
−0.365638 + 0.930757i \(0.619149\pi\)
\(228\) −1.21392 −0.0803936
\(229\) 12.8889 0.851719 0.425860 0.904789i \(-0.359972\pi\)
0.425860 + 0.904789i \(0.359972\pi\)
\(230\) 11.5369 0.760721
\(231\) 1.31943 0.0868122
\(232\) −5.48319 −0.359989
\(233\) 1.64458 0.107740 0.0538700 0.998548i \(-0.482844\pi\)
0.0538700 + 0.998548i \(0.482844\pi\)
\(234\) 9.12895 0.596778
\(235\) −1.94959 −0.127177
\(236\) −14.9220 −0.971342
\(237\) −0.0604269 −0.00392515
\(238\) −78.1805 −5.06769
\(239\) 11.8217 0.764685 0.382343 0.924021i \(-0.375117\pi\)
0.382343 + 0.924021i \(0.375117\pi\)
\(240\) 1.18175 0.0762819
\(241\) 21.1752 1.36401 0.682007 0.731345i \(-0.261107\pi\)
0.682007 + 0.731345i \(0.261107\pi\)
\(242\) 1.91950 0.123390
\(243\) −6.82966 −0.438123
\(244\) 14.5832 0.933595
\(245\) 18.5974 1.18815
\(246\) 1.48510 0.0946862
\(247\) −4.48229 −0.285201
\(248\) −2.11853 −0.134527
\(249\) −4.35000 −0.275670
\(250\) 1.91950 0.121400
\(251\) 16.6286 1.04959 0.524794 0.851229i \(-0.324142\pi\)
0.524794 + 0.851229i \(0.324142\pi\)
\(252\) 24.9879 1.57409
\(253\) 6.01036 0.377868
\(254\) 27.1273 1.70212
\(255\) −2.09942 −0.131471
\(256\) 19.8007 1.23754
\(257\) −29.6351 −1.84859 −0.924294 0.381682i \(-0.875345\pi\)
−0.924294 + 0.381682i \(0.875345\pi\)
\(258\) 4.25990 0.265210
\(259\) 13.9281 0.865447
\(260\) −2.73237 −0.169454
\(261\) −26.5461 −1.64316
\(262\) −42.7047 −2.63831
\(263\) −9.47055 −0.583979 −0.291990 0.956421i \(-0.594317\pi\)
−0.291990 + 0.956421i \(0.594317\pi\)
\(264\) 0.157937 0.00972034
\(265\) 8.90378 0.546955
\(266\) −26.8360 −1.64542
\(267\) −4.42418 −0.270756
\(268\) −6.89397 −0.421116
\(269\) 14.7519 0.899439 0.449719 0.893170i \(-0.351524\pi\)
0.449719 + 0.893170i \(0.351524\pi\)
\(270\) 2.96946 0.180716
\(271\) −0.504336 −0.0306362 −0.0153181 0.999883i \(-0.504876\pi\)
−0.0153181 + 0.999883i \(0.504876\pi\)
\(272\) −36.4796 −2.21190
\(273\) −2.14021 −0.129531
\(274\) −6.50941 −0.393248
\(275\) 1.00000 0.0603023
\(276\) −2.64033 −0.158929
\(277\) 3.17052 0.190498 0.0952489 0.995453i \(-0.469635\pi\)
0.0952489 + 0.995453i \(0.469635\pi\)
\(278\) −25.6845 −1.54045
\(279\) −10.2566 −0.614045
\(280\) 3.06403 0.183111
\(281\) −18.6576 −1.11302 −0.556508 0.830842i \(-0.687859\pi\)
−0.556508 + 0.830842i \(0.687859\pi\)
\(282\) 0.975936 0.0581162
\(283\) −2.36183 −0.140396 −0.0701980 0.997533i \(-0.522363\pi\)
−0.0701980 + 0.997533i \(0.522363\pi\)
\(284\) 0.403103 0.0239197
\(285\) −0.720641 −0.0426871
\(286\) −3.11357 −0.184109
\(287\) 15.0098 0.886000
\(288\) 21.9516 1.29351
\(289\) 47.8071 2.81218
\(290\) 17.3791 1.02054
\(291\) 0.535459 0.0313891
\(292\) 1.68450 0.0985776
\(293\) −1.04737 −0.0611879 −0.0305940 0.999532i \(-0.509740\pi\)
−0.0305940 + 0.999532i \(0.509740\pi\)
\(294\) −9.30959 −0.542946
\(295\) −8.85846 −0.515759
\(296\) 1.66720 0.0969039
\(297\) 1.54700 0.0897658
\(298\) −23.6749 −1.37145
\(299\) −9.74922 −0.563812
\(300\) −0.439297 −0.0253628
\(301\) 43.0547 2.48163
\(302\) 25.6656 1.47689
\(303\) −0.618338 −0.0355226
\(304\) −12.5219 −0.718178
\(305\) 8.65733 0.495717
\(306\) −45.3067 −2.59001
\(307\) 17.6897 1.00960 0.504802 0.863235i \(-0.331565\pi\)
0.504802 + 0.863235i \(0.331565\pi\)
\(308\) −8.52252 −0.485616
\(309\) 0.861457 0.0490066
\(310\) 6.71474 0.381372
\(311\) 12.6987 0.720077 0.360039 0.932937i \(-0.382763\pi\)
0.360039 + 0.932937i \(0.382763\pi\)
\(312\) −0.256184 −0.0145036
\(313\) −6.00541 −0.339446 −0.169723 0.985492i \(-0.554287\pi\)
−0.169723 + 0.985492i \(0.554287\pi\)
\(314\) −37.5652 −2.11993
\(315\) 14.8341 0.835806
\(316\) 0.390312 0.0219568
\(317\) 6.17630 0.346895 0.173448 0.984843i \(-0.444509\pi\)
0.173448 + 0.984843i \(0.444509\pi\)
\(318\) −4.45709 −0.249941
\(319\) 9.05396 0.506924
\(320\) −5.30828 −0.296742
\(321\) 0.0765524 0.00427274
\(322\) −58.3697 −3.25282
\(323\) 22.2455 1.23777
\(324\) 14.1372 0.785399
\(325\) −1.62207 −0.0899762
\(326\) 11.0943 0.614456
\(327\) −3.87526 −0.214303
\(328\) 1.79668 0.0992052
\(329\) 9.86375 0.543806
\(330\) −0.500585 −0.0275563
\(331\) −28.4197 −1.56209 −0.781045 0.624475i \(-0.785313\pi\)
−0.781045 + 0.624475i \(0.785313\pi\)
\(332\) 28.0977 1.54206
\(333\) 8.07151 0.442316
\(334\) 17.4433 0.954455
\(335\) −4.09260 −0.223603
\(336\) −5.97896 −0.326179
\(337\) 7.52437 0.409879 0.204939 0.978775i \(-0.434300\pi\)
0.204939 + 0.978775i \(0.434300\pi\)
\(338\) −19.9031 −1.08259
\(339\) −1.88245 −0.102240
\(340\) 13.5607 0.735430
\(341\) 3.49816 0.189436
\(342\) −15.5518 −0.840947
\(343\) −58.6759 −3.16820
\(344\) 5.15367 0.277867
\(345\) −1.56743 −0.0843878
\(346\) −42.4446 −2.28183
\(347\) −14.9875 −0.804572 −0.402286 0.915514i \(-0.631784\pi\)
−0.402286 + 0.915514i \(0.631784\pi\)
\(348\) −3.97738 −0.213210
\(349\) 2.33812 0.125157 0.0625784 0.998040i \(-0.480068\pi\)
0.0625784 + 0.998040i \(0.480068\pi\)
\(350\) −9.71152 −0.519103
\(351\) −2.50933 −0.133938
\(352\) −7.48694 −0.399055
\(353\) 23.8996 1.27205 0.636024 0.771669i \(-0.280578\pi\)
0.636024 + 0.771669i \(0.280578\pi\)
\(354\) 4.43441 0.235686
\(355\) 0.239302 0.0127008
\(356\) 28.5769 1.51457
\(357\) 10.6218 0.562165
\(358\) 35.3508 1.86835
\(359\) 28.4313 1.50055 0.750273 0.661128i \(-0.229922\pi\)
0.750273 + 0.661128i \(0.229922\pi\)
\(360\) 1.77565 0.0935850
\(361\) −11.3641 −0.598110
\(362\) −9.89522 −0.520081
\(363\) −0.260789 −0.0136879
\(364\) 13.8241 0.724580
\(365\) 1.00000 0.0523424
\(366\) −4.33373 −0.226527
\(367\) 10.7479 0.561037 0.280519 0.959849i \(-0.409494\pi\)
0.280519 + 0.959849i \(0.409494\pi\)
\(368\) −27.2358 −1.41976
\(369\) 8.69839 0.452820
\(370\) −5.28422 −0.274714
\(371\) −45.0477 −2.33876
\(372\) −1.53673 −0.0796759
\(373\) −1.85363 −0.0959771 −0.0479885 0.998848i \(-0.515281\pi\)
−0.0479885 + 0.998848i \(0.515281\pi\)
\(374\) 15.4526 0.799032
\(375\) −0.260789 −0.0134671
\(376\) 1.18070 0.0608898
\(377\) −14.6861 −0.756375
\(378\) −15.0237 −0.772734
\(379\) −18.2285 −0.936335 −0.468167 0.883640i \(-0.655086\pi\)
−0.468167 + 0.883640i \(0.655086\pi\)
\(380\) 4.65479 0.238786
\(381\) −3.68558 −0.188818
\(382\) 6.44953 0.329987
\(383\) −15.9244 −0.813699 −0.406849 0.913495i \(-0.633373\pi\)
−0.406849 + 0.913495i \(0.633373\pi\)
\(384\) −1.24777 −0.0636752
\(385\) −5.05939 −0.257850
\(386\) 38.8726 1.97856
\(387\) 24.9508 1.26832
\(388\) −3.45865 −0.175587
\(389\) −0.186606 −0.00946132 −0.00473066 0.999989i \(-0.501506\pi\)
−0.00473066 + 0.999989i \(0.501506\pi\)
\(390\) 0.811983 0.0411164
\(391\) 48.3851 2.44694
\(392\) −11.2628 −0.568859
\(393\) 5.80197 0.292671
\(394\) −27.4569 −1.38326
\(395\) 0.231708 0.0116585
\(396\) −4.93892 −0.248190
\(397\) −29.9531 −1.50330 −0.751652 0.659560i \(-0.770742\pi\)
−0.751652 + 0.659560i \(0.770742\pi\)
\(398\) −19.7414 −0.989546
\(399\) 3.64600 0.182529
\(400\) −4.53147 −0.226573
\(401\) 0.923651 0.0461249 0.0230625 0.999734i \(-0.492658\pi\)
0.0230625 + 0.999734i \(0.492658\pi\)
\(402\) 2.04869 0.102180
\(403\) −5.67426 −0.282655
\(404\) 3.99399 0.198709
\(405\) 8.39253 0.417028
\(406\) −87.9277 −4.36378
\(407\) −2.75291 −0.136457
\(408\) 1.27144 0.0629455
\(409\) 17.1161 0.846335 0.423167 0.906052i \(-0.360918\pi\)
0.423167 + 0.906052i \(0.360918\pi\)
\(410\) −5.69463 −0.281238
\(411\) 0.884385 0.0436235
\(412\) −5.56436 −0.274136
\(413\) 44.8184 2.20537
\(414\) −33.8261 −1.66246
\(415\) 16.6802 0.818797
\(416\) 12.1443 0.595425
\(417\) 3.48956 0.170884
\(418\) 5.30419 0.259437
\(419\) 26.1991 1.27991 0.639954 0.768413i \(-0.278953\pi\)
0.639954 + 0.768413i \(0.278953\pi\)
\(420\) 2.22258 0.108451
\(421\) −10.0051 −0.487621 −0.243810 0.969823i \(-0.578397\pi\)
−0.243810 + 0.969823i \(0.578397\pi\)
\(422\) 4.00850 0.195131
\(423\) 5.71619 0.277930
\(424\) −5.39224 −0.261870
\(425\) 8.05028 0.390496
\(426\) −0.119791 −0.00580388
\(427\) −43.8008 −2.11967
\(428\) −0.494470 −0.0239011
\(429\) 0.423017 0.0204235
\(430\) −16.3347 −0.787729
\(431\) −21.3432 −1.02806 −0.514032 0.857771i \(-0.671849\pi\)
−0.514032 + 0.857771i \(0.671849\pi\)
\(432\) −7.01016 −0.337276
\(433\) −21.9708 −1.05585 −0.527925 0.849291i \(-0.677030\pi\)
−0.527925 + 0.849291i \(0.677030\pi\)
\(434\) −33.9725 −1.63073
\(435\) −2.36117 −0.113209
\(436\) 25.0312 1.19878
\(437\) 16.6085 0.794493
\(438\) −0.500585 −0.0239189
\(439\) 11.0330 0.526575 0.263287 0.964717i \(-0.415193\pi\)
0.263287 + 0.964717i \(0.415193\pi\)
\(440\) −0.605613 −0.0288714
\(441\) −54.5275 −2.59655
\(442\) −25.0651 −1.19223
\(443\) −12.1571 −0.577599 −0.288800 0.957390i \(-0.593256\pi\)
−0.288800 + 0.957390i \(0.593256\pi\)
\(444\) 1.20935 0.0573930
\(445\) 16.9646 0.804201
\(446\) 50.7634 2.40372
\(447\) 3.21653 0.152137
\(448\) 26.8567 1.26886
\(449\) −10.5329 −0.497077 −0.248538 0.968622i \(-0.579950\pi\)
−0.248538 + 0.968622i \(0.579950\pi\)
\(450\) −5.62796 −0.265305
\(451\) −2.96672 −0.139697
\(452\) 12.1592 0.571919
\(453\) −3.48699 −0.163833
\(454\) −21.1487 −0.992557
\(455\) 8.20668 0.384735
\(456\) 0.436429 0.0204377
\(457\) −4.23915 −0.198299 −0.0991496 0.995073i \(-0.531612\pi\)
−0.0991496 + 0.995073i \(0.531612\pi\)
\(458\) 24.7402 1.15603
\(459\) 12.4537 0.581291
\(460\) 10.1244 0.472054
\(461\) −4.53169 −0.211062 −0.105531 0.994416i \(-0.533654\pi\)
−0.105531 + 0.994416i \(0.533654\pi\)
\(462\) 2.53265 0.117830
\(463\) 35.5819 1.65363 0.826815 0.562473i \(-0.190150\pi\)
0.826815 + 0.562473i \(0.190150\pi\)
\(464\) −41.0277 −1.90466
\(465\) −0.912281 −0.0423060
\(466\) 3.15678 0.146235
\(467\) −35.5349 −1.64436 −0.822180 0.569228i \(-0.807242\pi\)
−0.822180 + 0.569228i \(0.807242\pi\)
\(468\) 8.01127 0.370321
\(469\) 20.7061 0.956118
\(470\) −3.74225 −0.172617
\(471\) 5.10370 0.235166
\(472\) 5.36479 0.246935
\(473\) −8.50985 −0.391283
\(474\) −0.115990 −0.00532758
\(475\) 2.76332 0.126790
\(476\) −68.6087 −3.14467
\(477\) −26.1058 −1.19530
\(478\) 22.6919 1.03790
\(479\) −26.0127 −1.18855 −0.594274 0.804262i \(-0.702561\pi\)
−0.594274 + 0.804262i \(0.702561\pi\)
\(480\) 1.95251 0.0891194
\(481\) 4.46541 0.203605
\(482\) 40.6459 1.85137
\(483\) 7.93026 0.360839
\(484\) 1.68450 0.0765680
\(485\) −2.05323 −0.0932323
\(486\) −13.1096 −0.594662
\(487\) −40.5386 −1.83698 −0.918490 0.395443i \(-0.870591\pi\)
−0.918490 + 0.395443i \(0.870591\pi\)
\(488\) −5.24299 −0.237339
\(489\) −1.50730 −0.0681624
\(490\) 35.6978 1.61266
\(491\) 12.5485 0.566307 0.283153 0.959075i \(-0.408619\pi\)
0.283153 + 0.959075i \(0.408619\pi\)
\(492\) 1.30327 0.0587560
\(493\) 72.8869 3.28266
\(494\) −8.60377 −0.387102
\(495\) −2.93199 −0.131783
\(496\) −15.8518 −0.711767
\(497\) −1.21072 −0.0543082
\(498\) −8.34984 −0.374165
\(499\) 14.2569 0.638228 0.319114 0.947716i \(-0.396615\pi\)
0.319114 + 0.947716i \(0.396615\pi\)
\(500\) 1.68450 0.0753329
\(501\) −2.36989 −0.105879
\(502\) 31.9187 1.42460
\(503\) 9.76277 0.435300 0.217650 0.976027i \(-0.430161\pi\)
0.217650 + 0.976027i \(0.430161\pi\)
\(504\) −8.98370 −0.400166
\(505\) 2.37103 0.105510
\(506\) 11.5369 0.512878
\(507\) 2.70409 0.120093
\(508\) 23.8060 1.05622
\(509\) −31.2400 −1.38469 −0.692344 0.721567i \(-0.743422\pi\)
−0.692344 + 0.721567i \(0.743422\pi\)
\(510\) −4.02985 −0.178445
\(511\) −5.05939 −0.223814
\(512\) 28.4382 1.25680
\(513\) 4.27483 0.188739
\(514\) −56.8847 −2.50908
\(515\) −3.30328 −0.145560
\(516\) 3.73835 0.164572
\(517\) −1.94959 −0.0857430
\(518\) 26.7350 1.17467
\(519\) 5.76662 0.253127
\(520\) 0.982346 0.0430787
\(521\) 40.3474 1.76765 0.883826 0.467817i \(-0.154959\pi\)
0.883826 + 0.467817i \(0.154959\pi\)
\(522\) −50.9554 −2.23026
\(523\) 36.5074 1.59636 0.798178 0.602421i \(-0.205797\pi\)
0.798178 + 0.602421i \(0.205797\pi\)
\(524\) −37.4763 −1.63716
\(525\) 1.31943 0.0575847
\(526\) −18.1788 −0.792632
\(527\) 28.1612 1.22672
\(528\) 1.18175 0.0514293
\(529\) 13.1244 0.570628
\(530\) 17.0908 0.742378
\(531\) 25.9729 1.12713
\(532\) −23.5504 −1.02104
\(533\) 4.81223 0.208441
\(534\) −8.49224 −0.367495
\(535\) −0.293542 −0.0126909
\(536\) 2.47853 0.107056
\(537\) −4.80285 −0.207258
\(538\) 28.3163 1.22080
\(539\) 18.5974 0.801048
\(540\) 2.60591 0.112140
\(541\) 33.3113 1.43216 0.716082 0.698016i \(-0.245934\pi\)
0.716082 + 0.698016i \(0.245934\pi\)
\(542\) −0.968075 −0.0415824
\(543\) 1.34439 0.0576933
\(544\) −60.2720 −2.58414
\(545\) 14.8598 0.636523
\(546\) −4.10814 −0.175812
\(547\) 12.0433 0.514935 0.257468 0.966287i \(-0.417112\pi\)
0.257468 + 0.966287i \(0.417112\pi\)
\(548\) −5.71245 −0.244024
\(549\) −25.3832 −1.08333
\(550\) 1.91950 0.0818479
\(551\) 25.0189 1.06584
\(552\) 0.949258 0.0404031
\(553\) −1.17230 −0.0498514
\(554\) 6.08582 0.258562
\(555\) 0.717928 0.0304743
\(556\) −22.5399 −0.955904
\(557\) −7.13074 −0.302139 −0.151070 0.988523i \(-0.548272\pi\)
−0.151070 + 0.988523i \(0.548272\pi\)
\(558\) −19.6875 −0.833440
\(559\) 13.8036 0.583829
\(560\) 22.9265 0.968820
\(561\) −2.09942 −0.0886377
\(562\) −35.8132 −1.51069
\(563\) 6.82712 0.287729 0.143864 0.989597i \(-0.454047\pi\)
0.143864 + 0.989597i \(0.454047\pi\)
\(564\) 0.856451 0.0360631
\(565\) 7.21829 0.303676
\(566\) −4.53353 −0.190559
\(567\) −42.4611 −1.78320
\(568\) −0.144924 −0.00608088
\(569\) 34.9467 1.46504 0.732520 0.680745i \(-0.238344\pi\)
0.732520 + 0.680745i \(0.238344\pi\)
\(570\) −1.38327 −0.0579389
\(571\) −28.3733 −1.18739 −0.593694 0.804691i \(-0.702331\pi\)
−0.593694 + 0.804691i \(0.702331\pi\)
\(572\) −2.73237 −0.114246
\(573\) −0.876250 −0.0366059
\(574\) 28.8114 1.20256
\(575\) 6.01036 0.250649
\(576\) 15.5638 0.648493
\(577\) 25.9918 1.08205 0.541027 0.841005i \(-0.318036\pi\)
0.541027 + 0.841005i \(0.318036\pi\)
\(578\) 91.7658 3.81696
\(579\) −5.28132 −0.219484
\(580\) 15.2513 0.633278
\(581\) −84.3915 −3.50115
\(582\) 1.02781 0.0426043
\(583\) 8.90378 0.368757
\(584\) −0.605613 −0.0250604
\(585\) 4.75589 0.196632
\(586\) −2.01043 −0.0830500
\(587\) 16.3037 0.672924 0.336462 0.941697i \(-0.390770\pi\)
0.336462 + 0.941697i \(0.390770\pi\)
\(588\) −8.16980 −0.336917
\(589\) 9.66653 0.398302
\(590\) −17.0038 −0.700037
\(591\) 3.73037 0.153447
\(592\) 12.4747 0.512708
\(593\) 29.7094 1.22002 0.610009 0.792394i \(-0.291166\pi\)
0.610009 + 0.792394i \(0.291166\pi\)
\(594\) 2.96946 0.121839
\(595\) −40.7295 −1.66975
\(596\) −20.7763 −0.851031
\(597\) 2.68211 0.109772
\(598\) −18.7137 −0.765259
\(599\) 29.5739 1.20836 0.604179 0.796848i \(-0.293501\pi\)
0.604179 + 0.796848i \(0.293501\pi\)
\(600\) 0.157937 0.00644774
\(601\) 33.3005 1.35835 0.679177 0.733975i \(-0.262337\pi\)
0.679177 + 0.733975i \(0.262337\pi\)
\(602\) 82.6436 3.36830
\(603\) 11.9995 0.488656
\(604\) 22.5233 0.916460
\(605\) 1.00000 0.0406558
\(606\) −1.18690 −0.0482146
\(607\) −43.5409 −1.76727 −0.883635 0.468176i \(-0.844911\pi\)
−0.883635 + 0.468176i \(0.844911\pi\)
\(608\) −20.6888 −0.839041
\(609\) 11.9461 0.484079
\(610\) 16.6178 0.672834
\(611\) 3.16237 0.127936
\(612\) −39.7597 −1.60719
\(613\) 43.0817 1.74005 0.870026 0.493006i \(-0.164102\pi\)
0.870026 + 0.493006i \(0.164102\pi\)
\(614\) 33.9554 1.37033
\(615\) 0.773687 0.0311981
\(616\) 3.06403 0.123453
\(617\) 5.40838 0.217733 0.108867 0.994056i \(-0.465278\pi\)
0.108867 + 0.994056i \(0.465278\pi\)
\(618\) 1.65357 0.0665164
\(619\) 24.5407 0.986373 0.493186 0.869924i \(-0.335832\pi\)
0.493186 + 0.869924i \(0.335832\pi\)
\(620\) 5.89264 0.236654
\(621\) 9.29800 0.373116
\(622\) 24.3752 0.977357
\(623\) −85.8307 −3.43874
\(624\) −1.91689 −0.0767369
\(625\) 1.00000 0.0400000
\(626\) −11.5274 −0.460728
\(627\) −0.720641 −0.0287796
\(628\) −32.9660 −1.31549
\(629\) −22.1617 −0.883646
\(630\) 28.4741 1.13443
\(631\) 5.18828 0.206542 0.103271 0.994653i \(-0.467069\pi\)
0.103271 + 0.994653i \(0.467069\pi\)
\(632\) −0.140326 −0.00558185
\(633\) −0.544605 −0.0216461
\(634\) 11.8554 0.470839
\(635\) 14.1325 0.560829
\(636\) −3.91140 −0.155097
\(637\) −30.1663 −1.19523
\(638\) 17.3791 0.688045
\(639\) −0.701630 −0.0277561
\(640\) 4.78462 0.189129
\(641\) 6.78306 0.267915 0.133957 0.990987i \(-0.457231\pi\)
0.133957 + 0.990987i \(0.457231\pi\)
\(642\) 0.146943 0.00579936
\(643\) 44.0325 1.73647 0.868236 0.496151i \(-0.165254\pi\)
0.868236 + 0.496151i \(0.165254\pi\)
\(644\) −51.2234 −2.01849
\(645\) 2.21927 0.0873838
\(646\) 42.7003 1.68002
\(647\) −35.2216 −1.38470 −0.692352 0.721560i \(-0.743425\pi\)
−0.692352 + 0.721560i \(0.743425\pi\)
\(648\) −5.08262 −0.199664
\(649\) −8.85846 −0.347725
\(650\) −3.11357 −0.122124
\(651\) 4.61559 0.180899
\(652\) 9.73599 0.381291
\(653\) −12.0554 −0.471765 −0.235882 0.971782i \(-0.575798\pi\)
−0.235882 + 0.971782i \(0.575798\pi\)
\(654\) −7.43858 −0.290872
\(655\) −22.2478 −0.869293
\(656\) 13.4436 0.524884
\(657\) −2.93199 −0.114388
\(658\) 18.9335 0.738105
\(659\) −6.40438 −0.249479 −0.124740 0.992190i \(-0.539810\pi\)
−0.124740 + 0.992190i \(0.539810\pi\)
\(660\) −0.439297 −0.0170996
\(661\) −32.3306 −1.25751 −0.628757 0.777602i \(-0.716436\pi\)
−0.628757 + 0.777602i \(0.716436\pi\)
\(662\) −54.5518 −2.12021
\(663\) 3.40541 0.132255
\(664\) −10.1017 −0.392023
\(665\) −13.9807 −0.542148
\(666\) 15.4933 0.600353
\(667\) 54.4176 2.10706
\(668\) 15.3077 0.592272
\(669\) −6.89685 −0.266647
\(670\) −7.85577 −0.303495
\(671\) 8.65733 0.334212
\(672\) −9.87850 −0.381072
\(673\) −14.0369 −0.541082 −0.270541 0.962708i \(-0.587203\pi\)
−0.270541 + 0.962708i \(0.587203\pi\)
\(674\) 14.4431 0.556326
\(675\) 1.54700 0.0595439
\(676\) −17.4663 −0.671783
\(677\) 19.9621 0.767208 0.383604 0.923498i \(-0.374683\pi\)
0.383604 + 0.923498i \(0.374683\pi\)
\(678\) −3.61336 −0.138770
\(679\) 10.3881 0.398658
\(680\) −4.87535 −0.186961
\(681\) 2.87331 0.110106
\(682\) 6.71474 0.257121
\(683\) −6.63806 −0.253998 −0.126999 0.991903i \(-0.540535\pi\)
−0.126999 + 0.991903i \(0.540535\pi\)
\(684\) −13.6478 −0.521837
\(685\) −3.39120 −0.129571
\(686\) −112.629 −4.30018
\(687\) −3.36127 −0.128240
\(688\) 38.5621 1.47017
\(689\) −14.4425 −0.550217
\(690\) −3.00870 −0.114539
\(691\) 6.91495 0.263057 0.131529 0.991312i \(-0.458011\pi\)
0.131529 + 0.991312i \(0.458011\pi\)
\(692\) −37.2480 −1.41596
\(693\) 14.8341 0.563500
\(694\) −28.7686 −1.09204
\(695\) −13.3808 −0.507563
\(696\) 1.42995 0.0542022
\(697\) −23.8829 −0.904631
\(698\) 4.48804 0.169875
\(699\) −0.428888 −0.0162220
\(700\) −8.52252 −0.322121
\(701\) 26.8781 1.01517 0.507585 0.861602i \(-0.330538\pi\)
0.507585 + 0.861602i \(0.330538\pi\)
\(702\) −4.81667 −0.181794
\(703\) −7.60716 −0.286910
\(704\) −5.30828 −0.200063
\(705\) 0.508432 0.0191486
\(706\) 45.8754 1.72654
\(707\) −11.9960 −0.451155
\(708\) 3.89150 0.146251
\(709\) 3.08730 0.115946 0.0579729 0.998318i \(-0.481536\pi\)
0.0579729 + 0.998318i \(0.481536\pi\)
\(710\) 0.459341 0.0172387
\(711\) −0.679367 −0.0254782
\(712\) −10.2740 −0.385034
\(713\) 21.0252 0.787401
\(714\) 20.3886 0.763023
\(715\) −1.62207 −0.0606619
\(716\) 31.0227 1.15937
\(717\) −3.08298 −0.115136
\(718\) 54.5740 2.03668
\(719\) −5.54758 −0.206890 −0.103445 0.994635i \(-0.532987\pi\)
−0.103445 + 0.994635i \(0.532987\pi\)
\(720\) 13.2862 0.495148
\(721\) 16.7126 0.622409
\(722\) −21.8134 −0.811811
\(723\) −5.52225 −0.205375
\(724\) −8.68373 −0.322728
\(725\) 9.05396 0.336256
\(726\) −0.500585 −0.0185784
\(727\) −2.51174 −0.0931553 −0.0465777 0.998915i \(-0.514831\pi\)
−0.0465777 + 0.998915i \(0.514831\pi\)
\(728\) −4.97007 −0.184203
\(729\) −23.3965 −0.866537
\(730\) 1.91950 0.0710440
\(731\) −68.5067 −2.53381
\(732\) −3.80314 −0.140568
\(733\) 34.6386 1.27941 0.639704 0.768622i \(-0.279057\pi\)
0.639704 + 0.768622i \(0.279057\pi\)
\(734\) 20.6307 0.761493
\(735\) −4.85000 −0.178895
\(736\) −44.9992 −1.65869
\(737\) −4.09260 −0.150753
\(738\) 16.6966 0.614610
\(739\) −24.1154 −0.887098 −0.443549 0.896250i \(-0.646281\pi\)
−0.443549 + 0.896250i \(0.646281\pi\)
\(740\) −4.63727 −0.170469
\(741\) 1.16893 0.0429417
\(742\) −86.4692 −3.17438
\(743\) −34.9553 −1.28239 −0.641193 0.767380i \(-0.721560\pi\)
−0.641193 + 0.767380i \(0.721560\pi\)
\(744\) 0.552489 0.0202552
\(745\) −12.3339 −0.451877
\(746\) −3.55804 −0.130269
\(747\) −48.9061 −1.78938
\(748\) 13.5607 0.495827
\(749\) 1.48514 0.0542659
\(750\) −0.500585 −0.0182788
\(751\) −11.1374 −0.406408 −0.203204 0.979136i \(-0.565135\pi\)
−0.203204 + 0.979136i \(0.565135\pi\)
\(752\) 8.83451 0.322162
\(753\) −4.33655 −0.158033
\(754\) −28.1901 −1.02662
\(755\) 13.3710 0.486619
\(756\) −13.1843 −0.479508
\(757\) −7.09223 −0.257771 −0.128886 0.991659i \(-0.541140\pi\)
−0.128886 + 0.991659i \(0.541140\pi\)
\(758\) −34.9897 −1.27088
\(759\) −1.56743 −0.0568942
\(760\) −1.67350 −0.0607042
\(761\) 8.13384 0.294852 0.147426 0.989073i \(-0.452901\pi\)
0.147426 + 0.989073i \(0.452901\pi\)
\(762\) −7.07449 −0.256282
\(763\) −75.1815 −2.72175
\(764\) 5.65990 0.204768
\(765\) −23.6033 −0.853381
\(766\) −30.5669 −1.10443
\(767\) 14.3690 0.518836
\(768\) −5.16378 −0.186332
\(769\) 1.31148 0.0472932 0.0236466 0.999720i \(-0.492472\pi\)
0.0236466 + 0.999720i \(0.492472\pi\)
\(770\) −9.71152 −0.349979
\(771\) 7.72850 0.278335
\(772\) 34.1133 1.22777
\(773\) −12.7660 −0.459162 −0.229581 0.973290i \(-0.573736\pi\)
−0.229581 + 0.973290i \(0.573736\pi\)
\(774\) 47.8932 1.72148
\(775\) 3.49816 0.125658
\(776\) 1.24346 0.0446377
\(777\) −3.63228 −0.130307
\(778\) −0.358192 −0.0128418
\(779\) −8.19798 −0.293723
\(780\) 0.712570 0.0255141
\(781\) 0.239302 0.00856289
\(782\) 92.8754 3.32122
\(783\) 14.0064 0.500549
\(784\) −84.2736 −3.00977
\(785\) −19.5703 −0.698493
\(786\) 11.1369 0.397240
\(787\) −40.5526 −1.44554 −0.722771 0.691087i \(-0.757132\pi\)
−0.722771 + 0.691087i \(0.757132\pi\)
\(788\) −24.0953 −0.858361
\(789\) 2.46981 0.0879276
\(790\) 0.444765 0.0158240
\(791\) −36.5201 −1.29851
\(792\) 1.77565 0.0630950
\(793\) −14.0428 −0.498674
\(794\) −57.4951 −2.04042
\(795\) −2.32200 −0.0823530
\(796\) −17.3244 −0.614047
\(797\) −23.8325 −0.844191 −0.422096 0.906551i \(-0.638705\pi\)
−0.422096 + 0.906551i \(0.638705\pi\)
\(798\) 6.99852 0.247745
\(799\) −15.6948 −0.555241
\(800\) −7.48694 −0.264703
\(801\) −49.7401 −1.75748
\(802\) 1.77295 0.0626051
\(803\) 1.00000 0.0352892
\(804\) 1.79787 0.0634060
\(805\) −30.4088 −1.07177
\(806\) −10.8918 −0.383646
\(807\) −3.84713 −0.135425
\(808\) −1.43593 −0.0505157
\(809\) 16.0244 0.563390 0.281695 0.959504i \(-0.409103\pi\)
0.281695 + 0.959504i \(0.409103\pi\)
\(810\) 16.1095 0.566030
\(811\) 47.9010 1.68203 0.841015 0.541012i \(-0.181959\pi\)
0.841015 + 0.541012i \(0.181959\pi\)
\(812\) −77.1625 −2.70787
\(813\) 0.131525 0.00461279
\(814\) −5.28422 −0.185212
\(815\) 5.77977 0.202457
\(816\) 9.51346 0.333038
\(817\) −23.5154 −0.822700
\(818\) 32.8543 1.14873
\(819\) −24.0619 −0.840791
\(820\) −4.99743 −0.174518
\(821\) 11.4420 0.399327 0.199664 0.979865i \(-0.436015\pi\)
0.199664 + 0.979865i \(0.436015\pi\)
\(822\) 1.69758 0.0592099
\(823\) −20.1196 −0.701325 −0.350662 0.936502i \(-0.614044\pi\)
−0.350662 + 0.936502i \(0.614044\pi\)
\(824\) 2.00051 0.0696910
\(825\) −0.260789 −0.00907949
\(826\) 86.0291 2.99333
\(827\) −16.5886 −0.576843 −0.288422 0.957503i \(-0.593130\pi\)
−0.288422 + 0.957503i \(0.593130\pi\)
\(828\) −29.6847 −1.03161
\(829\) 42.7293 1.48405 0.742025 0.670372i \(-0.233865\pi\)
0.742025 + 0.670372i \(0.233865\pi\)
\(830\) 32.0177 1.11135
\(831\) −0.826834 −0.0286826
\(832\) 8.61040 0.298512
\(833\) 149.715 5.18730
\(834\) 6.69822 0.231940
\(835\) 9.08740 0.314482
\(836\) 4.65479 0.160989
\(837\) 5.41164 0.187054
\(838\) 50.2892 1.73721
\(839\) −28.0798 −0.969422 −0.484711 0.874674i \(-0.661075\pi\)
−0.484711 + 0.874674i \(0.661075\pi\)
\(840\) −0.799064 −0.0275703
\(841\) 52.9742 1.82669
\(842\) −19.2049 −0.661845
\(843\) 4.86568 0.167583
\(844\) 3.51773 0.121085
\(845\) −10.3689 −0.356701
\(846\) 10.9722 0.377233
\(847\) −5.05939 −0.173843
\(848\) −40.3472 −1.38553
\(849\) 0.615937 0.0211389
\(850\) 15.4526 0.530018
\(851\) −16.5460 −0.567189
\(852\) −0.105125 −0.00360151
\(853\) 31.9888 1.09528 0.547638 0.836715i \(-0.315527\pi\)
0.547638 + 0.836715i \(0.315527\pi\)
\(854\) −84.0758 −2.87701
\(855\) −8.10201 −0.277083
\(856\) 0.177773 0.00607615
\(857\) 36.5653 1.24905 0.624524 0.781006i \(-0.285293\pi\)
0.624524 + 0.781006i \(0.285293\pi\)
\(858\) 0.811983 0.0277206
\(859\) −9.29029 −0.316981 −0.158490 0.987361i \(-0.550663\pi\)
−0.158490 + 0.987361i \(0.550663\pi\)
\(860\) −14.3348 −0.488813
\(861\) −3.91438 −0.133402
\(862\) −40.9683 −1.39539
\(863\) −11.2880 −0.384248 −0.192124 0.981371i \(-0.561538\pi\)
−0.192124 + 0.981371i \(0.561538\pi\)
\(864\) −11.5823 −0.394037
\(865\) −22.1123 −0.751839
\(866\) −42.1731 −1.43310
\(867\) −12.4675 −0.423420
\(868\) −29.8132 −1.01192
\(869\) 0.231708 0.00786017
\(870\) −4.53227 −0.153658
\(871\) 6.63849 0.224937
\(872\) −8.99928 −0.304754
\(873\) 6.02004 0.203748
\(874\) 31.8801 1.07836
\(875\) −5.05939 −0.171039
\(876\) −0.439297 −0.0148425
\(877\) −2.78097 −0.0939067 −0.0469534 0.998897i \(-0.514951\pi\)
−0.0469534 + 0.998897i \(0.514951\pi\)
\(878\) 21.1778 0.714717
\(879\) 0.273142 0.00921284
\(880\) −4.53147 −0.152756
\(881\) −7.67817 −0.258684 −0.129342 0.991600i \(-0.541287\pi\)
−0.129342 + 0.991600i \(0.541287\pi\)
\(882\) −104.666 −3.52428
\(883\) −8.38796 −0.282277 −0.141139 0.989990i \(-0.545076\pi\)
−0.141139 + 0.989990i \(0.545076\pi\)
\(884\) −21.9963 −0.739817
\(885\) 2.31018 0.0776560
\(886\) −23.3355 −0.783972
\(887\) 0.678209 0.0227720 0.0113860 0.999935i \(-0.496376\pi\)
0.0113860 + 0.999935i \(0.496376\pi\)
\(888\) −0.434786 −0.0145905
\(889\) −71.5016 −2.39809
\(890\) 32.5637 1.09154
\(891\) 8.39253 0.281160
\(892\) 44.5484 1.49159
\(893\) −5.38734 −0.180280
\(894\) 6.17414 0.206494
\(895\) 18.4166 0.615600
\(896\) −24.2072 −0.808707
\(897\) 2.54249 0.0848911
\(898\) −20.2179 −0.674679
\(899\) 31.6722 1.05633
\(900\) −4.93892 −0.164631
\(901\) 71.6779 2.38794
\(902\) −5.69463 −0.189611
\(903\) −11.2282 −0.373650
\(904\) −4.37149 −0.145393
\(905\) −5.15509 −0.171361
\(906\) −6.69329 −0.222370
\(907\) −31.6705 −1.05160 −0.525801 0.850608i \(-0.676234\pi\)
−0.525801 + 0.850608i \(0.676234\pi\)
\(908\) −18.5594 −0.615916
\(909\) −6.95184 −0.230578
\(910\) 15.7528 0.522199
\(911\) −22.6435 −0.750213 −0.375107 0.926982i \(-0.622394\pi\)
−0.375107 + 0.926982i \(0.622394\pi\)
\(912\) 3.26556 0.108134
\(913\) 16.6802 0.552033
\(914\) −8.13707 −0.269150
\(915\) −2.25773 −0.0746383
\(916\) 21.7112 0.717359
\(917\) 112.560 3.71707
\(918\) 23.9050 0.788983
\(919\) −20.7185 −0.683439 −0.341720 0.939802i \(-0.611009\pi\)
−0.341720 + 0.939802i \(0.611009\pi\)
\(920\) −3.63995 −0.120006
\(921\) −4.61327 −0.152012
\(922\) −8.69860 −0.286473
\(923\) −0.388164 −0.0127766
\(924\) 2.22258 0.0731174
\(925\) −2.75291 −0.0905152
\(926\) 68.2996 2.24446
\(927\) 9.68518 0.318103
\(928\) −67.7865 −2.22520
\(929\) 7.04258 0.231059 0.115530 0.993304i \(-0.463143\pi\)
0.115530 + 0.993304i \(0.463143\pi\)
\(930\) −1.75113 −0.0574217
\(931\) 51.3905 1.68426
\(932\) 2.77029 0.0907438
\(933\) −3.31168 −0.108419
\(934\) −68.2094 −2.23188
\(935\) 8.05028 0.263272
\(936\) −2.88023 −0.0941432
\(937\) 30.7631 1.00499 0.502493 0.864581i \(-0.332416\pi\)
0.502493 + 0.864581i \(0.332416\pi\)
\(938\) 39.7454 1.29773
\(939\) 1.56614 0.0511091
\(940\) −3.28408 −0.107115
\(941\) −19.5241 −0.636469 −0.318235 0.948012i \(-0.603090\pi\)
−0.318235 + 0.948012i \(0.603090\pi\)
\(942\) 9.79657 0.319190
\(943\) −17.8311 −0.580659
\(944\) 40.1418 1.30650
\(945\) −7.82685 −0.254607
\(946\) −16.3347 −0.531087
\(947\) 44.0813 1.43245 0.716226 0.697869i \(-0.245868\pi\)
0.716226 + 0.697869i \(0.245868\pi\)
\(948\) −0.101789 −0.00330595
\(949\) −1.62207 −0.0526546
\(950\) 5.30419 0.172091
\(951\) −1.61071 −0.0522308
\(952\) 24.6663 0.799440
\(953\) 34.2161 1.10837 0.554185 0.832394i \(-0.313030\pi\)
0.554185 + 0.832394i \(0.313030\pi\)
\(954\) −50.1101 −1.62238
\(955\) 3.36000 0.108727
\(956\) 19.9137 0.644054
\(957\) −2.36117 −0.0763257
\(958\) −49.9314 −1.61321
\(959\) 17.1574 0.554041
\(960\) 1.38434 0.0446794
\(961\) −18.7629 −0.605253
\(962\) 8.57138 0.276352
\(963\) 0.860662 0.0277344
\(964\) 35.6695 1.14884
\(965\) 20.2514 0.651915
\(966\) 15.2222 0.489765
\(967\) −29.8521 −0.959978 −0.479989 0.877274i \(-0.659359\pi\)
−0.479989 + 0.877274i \(0.659359\pi\)
\(968\) −0.605613 −0.0194651
\(969\) −5.80136 −0.186367
\(970\) −3.94118 −0.126544
\(971\) −35.3502 −1.13444 −0.567221 0.823565i \(-0.691982\pi\)
−0.567221 + 0.823565i \(0.691982\pi\)
\(972\) −11.5045 −0.369008
\(973\) 67.6987 2.17032
\(974\) −77.8141 −2.49332
\(975\) 0.423017 0.0135474
\(976\) −39.2304 −1.25573
\(977\) −40.1721 −1.28522 −0.642610 0.766193i \(-0.722148\pi\)
−0.642610 + 0.766193i \(0.722148\pi\)
\(978\) −2.89326 −0.0925164
\(979\) 16.9646 0.542192
\(980\) 31.3273 1.00071
\(981\) −43.5687 −1.39104
\(982\) 24.0869 0.768645
\(983\) −15.6324 −0.498597 −0.249298 0.968427i \(-0.580200\pi\)
−0.249298 + 0.968427i \(0.580200\pi\)
\(984\) −0.468555 −0.0149370
\(985\) −14.3042 −0.455769
\(986\) 139.907 4.45554
\(987\) −2.57235 −0.0818789
\(988\) −7.55039 −0.240210
\(989\) −51.1473 −1.62639
\(990\) −5.62796 −0.178868
\(991\) −2.27823 −0.0723703 −0.0361852 0.999345i \(-0.511521\pi\)
−0.0361852 + 0.999345i \(0.511521\pi\)
\(992\) −26.1905 −0.831551
\(993\) 7.41154 0.235198
\(994\) −2.32398 −0.0737123
\(995\) −10.2846 −0.326044
\(996\) −7.32755 −0.232182
\(997\) −12.1301 −0.384163 −0.192082 0.981379i \(-0.561524\pi\)
−0.192082 + 0.981379i \(0.561524\pi\)
\(998\) 27.3662 0.866263
\(999\) −4.25874 −0.134741
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 \(a_p\))