Properties

Label 6041.2.a.b.1.2
Level 6041
Weight 2
Character 6041.1
Self dual Yes
Analytic conductor 48.238
Analytic rank 1
Dimension 2
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

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

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2376278611\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(1.61803\)
Character \(\chi\) = 6041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+2.61803 q^{3}\) \(-1.00000 q^{4}\) \(-0.618034 q^{5}\) \(-2.61803 q^{6}\) \(-1.00000 q^{7}\) \(+3.00000 q^{8}\) \(+3.85410 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+2.61803 q^{3}\) \(-1.00000 q^{4}\) \(-0.618034 q^{5}\) \(-2.61803 q^{6}\) \(-1.00000 q^{7}\) \(+3.00000 q^{8}\) \(+3.85410 q^{9}\) \(+0.618034 q^{10}\) \(-2.61803 q^{11}\) \(-2.61803 q^{12}\) \(+5.61803 q^{13}\) \(+1.00000 q^{14}\) \(-1.61803 q^{15}\) \(-1.00000 q^{16}\) \(-3.23607 q^{17}\) \(-3.85410 q^{18}\) \(-4.09017 q^{19}\) \(+0.618034 q^{20}\) \(-2.61803 q^{21}\) \(+2.61803 q^{22}\) \(+5.09017 q^{23}\) \(+7.85410 q^{24}\) \(-4.61803 q^{25}\) \(-5.61803 q^{26}\) \(+2.23607 q^{27}\) \(+1.00000 q^{28}\) \(-4.47214 q^{29}\) \(+1.61803 q^{30}\) \(+2.47214 q^{31}\) \(-5.00000 q^{32}\) \(-6.85410 q^{33}\) \(+3.23607 q^{34}\) \(+0.618034 q^{35}\) \(-3.85410 q^{36}\) \(-2.14590 q^{37}\) \(+4.09017 q^{38}\) \(+14.7082 q^{39}\) \(-1.85410 q^{40}\) \(+8.94427 q^{41}\) \(+2.61803 q^{42}\) \(-5.70820 q^{43}\) \(+2.61803 q^{44}\) \(-2.38197 q^{45}\) \(-5.09017 q^{46}\) \(+1.23607 q^{47}\) \(-2.61803 q^{48}\) \(+1.00000 q^{49}\) \(+4.61803 q^{50}\) \(-8.47214 q^{51}\) \(-5.61803 q^{52}\) \(-4.32624 q^{53}\) \(-2.23607 q^{54}\) \(+1.61803 q^{55}\) \(-3.00000 q^{56}\) \(-10.7082 q^{57}\) \(+4.47214 q^{58}\) \(-10.6180 q^{59}\) \(+1.61803 q^{60}\) \(+13.7082 q^{61}\) \(-2.47214 q^{62}\) \(-3.85410 q^{63}\) \(+7.00000 q^{64}\) \(-3.47214 q^{65}\) \(+6.85410 q^{66}\) \(-7.14590 q^{67}\) \(+3.23607 q^{68}\) \(+13.3262 q^{69}\) \(-0.618034 q^{70}\) \(-2.47214 q^{71}\) \(+11.5623 q^{72}\) \(-1.85410 q^{73}\) \(+2.14590 q^{74}\) \(-12.0902 q^{75}\) \(+4.09017 q^{76}\) \(+2.61803 q^{77}\) \(-14.7082 q^{78}\) \(-13.6180 q^{79}\) \(+0.618034 q^{80}\) \(-5.70820 q^{81}\) \(-8.94427 q^{82}\) \(+8.76393 q^{83}\) \(+2.61803 q^{84}\) \(+2.00000 q^{85}\) \(+5.70820 q^{86}\) \(-11.7082 q^{87}\) \(-7.85410 q^{88}\) \(-6.94427 q^{89}\) \(+2.38197 q^{90}\) \(-5.61803 q^{91}\) \(-5.09017 q^{92}\) \(+6.47214 q^{93}\) \(-1.23607 q^{94}\) \(+2.52786 q^{95}\) \(-13.0902 q^{96}\) \(-4.85410 q^{97}\) \(-1.00000 q^{98}\) \(-10.0902 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(2q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut -\mathstrut q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 3q^{12} \) \(\mathstrut +\mathstrut 9q^{13} \) \(\mathstrut +\mathstrut 2q^{14} \) \(\mathstrut -\mathstrut q^{15} \) \(\mathstrut -\mathstrut 2q^{16} \) \(\mathstrut -\mathstrut 2q^{17} \) \(\mathstrut -\mathstrut q^{18} \) \(\mathstrut +\mathstrut 3q^{19} \) \(\mathstrut -\mathstrut q^{20} \) \(\mathstrut -\mathstrut 3q^{21} \) \(\mathstrut +\mathstrut 3q^{22} \) \(\mathstrut -\mathstrut q^{23} \) \(\mathstrut +\mathstrut 9q^{24} \) \(\mathstrut -\mathstrut 7q^{25} \) \(\mathstrut -\mathstrut 9q^{26} \) \(\mathstrut +\mathstrut 2q^{28} \) \(\mathstrut +\mathstrut q^{30} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut -\mathstrut 10q^{32} \) \(\mathstrut -\mathstrut 7q^{33} \) \(\mathstrut +\mathstrut 2q^{34} \) \(\mathstrut -\mathstrut q^{35} \) \(\mathstrut -\mathstrut q^{36} \) \(\mathstrut -\mathstrut 11q^{37} \) \(\mathstrut -\mathstrut 3q^{38} \) \(\mathstrut +\mathstrut 16q^{39} \) \(\mathstrut +\mathstrut 3q^{40} \) \(\mathstrut +\mathstrut 3q^{42} \) \(\mathstrut +\mathstrut 2q^{43} \) \(\mathstrut +\mathstrut 3q^{44} \) \(\mathstrut -\mathstrut 7q^{45} \) \(\mathstrut +\mathstrut q^{46} \) \(\mathstrut -\mathstrut 2q^{47} \) \(\mathstrut -\mathstrut 3q^{48} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut +\mathstrut 7q^{50} \) \(\mathstrut -\mathstrut 8q^{51} \) \(\mathstrut -\mathstrut 9q^{52} \) \(\mathstrut +\mathstrut 7q^{53} \) \(\mathstrut +\mathstrut q^{55} \) \(\mathstrut -\mathstrut 6q^{56} \) \(\mathstrut -\mathstrut 8q^{57} \) \(\mathstrut -\mathstrut 19q^{59} \) \(\mathstrut +\mathstrut q^{60} \) \(\mathstrut +\mathstrut 14q^{61} \) \(\mathstrut +\mathstrut 4q^{62} \) \(\mathstrut -\mathstrut q^{63} \) \(\mathstrut +\mathstrut 14q^{64} \) \(\mathstrut +\mathstrut 2q^{65} \) \(\mathstrut +\mathstrut 7q^{66} \) \(\mathstrut -\mathstrut 21q^{67} \) \(\mathstrut +\mathstrut 2q^{68} \) \(\mathstrut +\mathstrut 11q^{69} \) \(\mathstrut +\mathstrut q^{70} \) \(\mathstrut +\mathstrut 4q^{71} \) \(\mathstrut +\mathstrut 3q^{72} \) \(\mathstrut +\mathstrut 3q^{73} \) \(\mathstrut +\mathstrut 11q^{74} \) \(\mathstrut -\mathstrut 13q^{75} \) \(\mathstrut -\mathstrut 3q^{76} \) \(\mathstrut +\mathstrut 3q^{77} \) \(\mathstrut -\mathstrut 16q^{78} \) \(\mathstrut -\mathstrut 25q^{79} \) \(\mathstrut -\mathstrut q^{80} \) \(\mathstrut +\mathstrut 2q^{81} \) \(\mathstrut +\mathstrut 22q^{83} \) \(\mathstrut +\mathstrut 3q^{84} \) \(\mathstrut +\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 2q^{86} \) \(\mathstrut -\mathstrut 10q^{87} \) \(\mathstrut -\mathstrut 9q^{88} \) \(\mathstrut +\mathstrut 4q^{89} \) \(\mathstrut +\mathstrut 7q^{90} \) \(\mathstrut -\mathstrut 9q^{91} \) \(\mathstrut +\mathstrut q^{92} \) \(\mathstrut +\mathstrut 4q^{93} \) \(\mathstrut +\mathstrut 2q^{94} \) \(\mathstrut +\mathstrut 14q^{95} \) \(\mathstrut -\mathstrut 15q^{96} \) \(\mathstrut -\mathstrut 3q^{97} \) \(\mathstrut -\mathstrut 2q^{98} \) \(\mathstrut -\mathstrut 9q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −0.353553 0.935414i \(-0.615027\pi\)
−0.353553 + 0.935414i \(0.615027\pi\)
\(3\) 2.61803 1.51152 0.755761 0.654847i \(-0.227267\pi\)
0.755761 + 0.654847i \(0.227267\pi\)
\(4\) −1.00000 −0.500000
\(5\) −0.618034 −0.276393 −0.138197 0.990405i \(-0.544131\pi\)
−0.138197 + 0.990405i \(0.544131\pi\)
\(6\) −2.61803 −1.06881
\(7\) −1.00000 −0.377964
\(8\) 3.00000 1.06066
\(9\) 3.85410 1.28470
\(10\) 0.618034 0.195440
\(11\) −2.61803 −0.789367 −0.394683 0.918817i \(-0.629146\pi\)
−0.394683 + 0.918817i \(0.629146\pi\)
\(12\) −2.61803 −0.755761
\(13\) 5.61803 1.55816 0.779081 0.626923i \(-0.215686\pi\)
0.779081 + 0.626923i \(0.215686\pi\)
\(14\) 1.00000 0.267261
\(15\) −1.61803 −0.417775
\(16\) −1.00000 −0.250000
\(17\) −3.23607 −0.784862 −0.392431 0.919781i \(-0.628366\pi\)
−0.392431 + 0.919781i \(0.628366\pi\)
\(18\) −3.85410 −0.908421
\(19\) −4.09017 −0.938349 −0.469175 0.883105i \(-0.655449\pi\)
−0.469175 + 0.883105i \(0.655449\pi\)
\(20\) 0.618034 0.138197
\(21\) −2.61803 −0.571302
\(22\) 2.61803 0.558167
\(23\) 5.09017 1.06137 0.530687 0.847568i \(-0.321934\pi\)
0.530687 + 0.847568i \(0.321934\pi\)
\(24\) 7.85410 1.60321
\(25\) −4.61803 −0.923607
\(26\) −5.61803 −1.10179
\(27\) 2.23607 0.430331
\(28\) 1.00000 0.188982
\(29\) −4.47214 −0.830455 −0.415227 0.909718i \(-0.636298\pi\)
−0.415227 + 0.909718i \(0.636298\pi\)
\(30\) 1.61803 0.295411
\(31\) 2.47214 0.444009 0.222004 0.975046i \(-0.428740\pi\)
0.222004 + 0.975046i \(0.428740\pi\)
\(32\) −5.00000 −0.883883
\(33\) −6.85410 −1.19315
\(34\) 3.23607 0.554981
\(35\) 0.618034 0.104467
\(36\) −3.85410 −0.642350
\(37\) −2.14590 −0.352783 −0.176392 0.984320i \(-0.556443\pi\)
−0.176392 + 0.984320i \(0.556443\pi\)
\(38\) 4.09017 0.663513
\(39\) 14.7082 2.35520
\(40\) −1.85410 −0.293159
\(41\) 8.94427 1.39686 0.698430 0.715678i \(-0.253882\pi\)
0.698430 + 0.715678i \(0.253882\pi\)
\(42\) 2.61803 0.403971
\(43\) −5.70820 −0.870493 −0.435246 0.900311i \(-0.643339\pi\)
−0.435246 + 0.900311i \(0.643339\pi\)
\(44\) 2.61803 0.394683
\(45\) −2.38197 −0.355083
\(46\) −5.09017 −0.750505
\(47\) 1.23607 0.180299 0.0901495 0.995928i \(-0.471266\pi\)
0.0901495 + 0.995928i \(0.471266\pi\)
\(48\) −2.61803 −0.377881
\(49\) 1.00000 0.142857
\(50\) 4.61803 0.653089
\(51\) −8.47214 −1.18634
\(52\) −5.61803 −0.779081
\(53\) −4.32624 −0.594254 −0.297127 0.954838i \(-0.596029\pi\)
−0.297127 + 0.954838i \(0.596029\pi\)
\(54\) −2.23607 −0.304290
\(55\) 1.61803 0.218176
\(56\) −3.00000 −0.400892
\(57\) −10.7082 −1.41834
\(58\) 4.47214 0.587220
\(59\) −10.6180 −1.38235 −0.691175 0.722687i \(-0.742907\pi\)
−0.691175 + 0.722687i \(0.742907\pi\)
\(60\) 1.61803 0.208887
\(61\) 13.7082 1.75516 0.877578 0.479434i \(-0.159158\pi\)
0.877578 + 0.479434i \(0.159158\pi\)
\(62\) −2.47214 −0.313962
\(63\) −3.85410 −0.485571
\(64\) 7.00000 0.875000
\(65\) −3.47214 −0.430665
\(66\) 6.85410 0.843682
\(67\) −7.14590 −0.873010 −0.436505 0.899702i \(-0.643784\pi\)
−0.436505 + 0.899702i \(0.643784\pi\)
\(68\) 3.23607 0.392431
\(69\) 13.3262 1.60429
\(70\) −0.618034 −0.0738692
\(71\) −2.47214 −0.293389 −0.146694 0.989182i \(-0.546863\pi\)
−0.146694 + 0.989182i \(0.546863\pi\)
\(72\) 11.5623 1.36263
\(73\) −1.85410 −0.217006 −0.108503 0.994096i \(-0.534606\pi\)
−0.108503 + 0.994096i \(0.534606\pi\)
\(74\) 2.14590 0.249456
\(75\) −12.0902 −1.39605
\(76\) 4.09017 0.469175
\(77\) 2.61803 0.298353
\(78\) −14.7082 −1.66538
\(79\) −13.6180 −1.53215 −0.766074 0.642752i \(-0.777793\pi\)
−0.766074 + 0.642752i \(0.777793\pi\)
\(80\) 0.618034 0.0690983
\(81\) −5.70820 −0.634245
\(82\) −8.94427 −0.987730
\(83\) 8.76393 0.961967 0.480983 0.876730i \(-0.340280\pi\)
0.480983 + 0.876730i \(0.340280\pi\)
\(84\) 2.61803 0.285651
\(85\) 2.00000 0.216930
\(86\) 5.70820 0.615531
\(87\) −11.7082 −1.25525
\(88\) −7.85410 −0.837250
\(89\) −6.94427 −0.736091 −0.368046 0.929808i \(-0.619973\pi\)
−0.368046 + 0.929808i \(0.619973\pi\)
\(90\) 2.38197 0.251081
\(91\) −5.61803 −0.588930
\(92\) −5.09017 −0.530687
\(93\) 6.47214 0.671129
\(94\) −1.23607 −0.127491
\(95\) 2.52786 0.259353
\(96\) −13.0902 −1.33601
\(97\) −4.85410 −0.492859 −0.246430 0.969161i \(-0.579257\pi\)
−0.246430 + 0.969161i \(0.579257\pi\)
\(98\) −1.00000 −0.101015
\(99\) −10.0902 −1.01410
\(100\) 4.61803 0.461803
\(101\) −4.47214 −0.444994 −0.222497 0.974933i \(-0.571421\pi\)
−0.222497 + 0.974933i \(0.571421\pi\)
\(102\) 8.47214 0.838866
\(103\) 17.0902 1.68394 0.841972 0.539521i \(-0.181395\pi\)
0.841972 + 0.539521i \(0.181395\pi\)
\(104\) 16.8541 1.65268
\(105\) 1.61803 0.157904
\(106\) 4.32624 0.420201
\(107\) 6.00000 0.580042 0.290021 0.957020i \(-0.406338\pi\)
0.290021 + 0.957020i \(0.406338\pi\)
\(108\) −2.23607 −0.215166
\(109\) −9.85410 −0.943852 −0.471926 0.881638i \(-0.656441\pi\)
−0.471926 + 0.881638i \(0.656441\pi\)
\(110\) −1.61803 −0.154273
\(111\) −5.61803 −0.533240
\(112\) 1.00000 0.0944911
\(113\) −14.3820 −1.35294 −0.676471 0.736469i \(-0.736491\pi\)
−0.676471 + 0.736469i \(0.736491\pi\)
\(114\) 10.7082 1.00292
\(115\) −3.14590 −0.293357
\(116\) 4.47214 0.415227
\(117\) 21.6525 2.00177
\(118\) 10.6180 0.977469
\(119\) 3.23607 0.296650
\(120\) −4.85410 −0.443117
\(121\) −4.14590 −0.376900
\(122\) −13.7082 −1.24108
\(123\) 23.4164 2.11139
\(124\) −2.47214 −0.222004
\(125\) 5.94427 0.531672
\(126\) 3.85410 0.343351
\(127\) −4.00000 −0.354943 −0.177471 0.984126i \(-0.556792\pi\)
−0.177471 + 0.984126i \(0.556792\pi\)
\(128\) 3.00000 0.265165
\(129\) −14.9443 −1.31577
\(130\) 3.47214 0.304526
\(131\) −6.29180 −0.549717 −0.274858 0.961485i \(-0.588631\pi\)
−0.274858 + 0.961485i \(0.588631\pi\)
\(132\) 6.85410 0.596573
\(133\) 4.09017 0.354663
\(134\) 7.14590 0.617312
\(135\) −1.38197 −0.118941
\(136\) −9.70820 −0.832472
\(137\) 12.4721 1.06557 0.532783 0.846252i \(-0.321146\pi\)
0.532783 + 0.846252i \(0.321146\pi\)
\(138\) −13.3262 −1.13440
\(139\) −11.4164 −0.968327 −0.484164 0.874978i \(-0.660876\pi\)
−0.484164 + 0.874978i \(0.660876\pi\)
\(140\) −0.618034 −0.0522334
\(141\) 3.23607 0.272526
\(142\) 2.47214 0.207457
\(143\) −14.7082 −1.22996
\(144\) −3.85410 −0.321175
\(145\) 2.76393 0.229532
\(146\) 1.85410 0.153447
\(147\) 2.61803 0.215932
\(148\) 2.14590 0.176392
\(149\) −5.41641 −0.443729 −0.221865 0.975077i \(-0.571214\pi\)
−0.221865 + 0.975077i \(0.571214\pi\)
\(150\) 12.0902 0.987158
\(151\) −6.76393 −0.550441 −0.275220 0.961381i \(-0.588751\pi\)
−0.275220 + 0.961381i \(0.588751\pi\)
\(152\) −12.2705 −0.995270
\(153\) −12.4721 −1.00831
\(154\) −2.61803 −0.210967
\(155\) −1.52786 −0.122721
\(156\) −14.7082 −1.17760
\(157\) 3.14590 0.251070 0.125535 0.992089i \(-0.459935\pi\)
0.125535 + 0.992089i \(0.459935\pi\)
\(158\) 13.6180 1.08339
\(159\) −11.3262 −0.898229
\(160\) 3.09017 0.244299
\(161\) −5.09017 −0.401162
\(162\) 5.70820 0.448479
\(163\) −6.47214 −0.506937 −0.253468 0.967344i \(-0.581571\pi\)
−0.253468 + 0.967344i \(0.581571\pi\)
\(164\) −8.94427 −0.698430
\(165\) 4.23607 0.329777
\(166\) −8.76393 −0.680213
\(167\) 12.1803 0.942543 0.471271 0.881988i \(-0.343795\pi\)
0.471271 + 0.881988i \(0.343795\pi\)
\(168\) −7.85410 −0.605957
\(169\) 18.5623 1.42787
\(170\) −2.00000 −0.153393
\(171\) −15.7639 −1.20550
\(172\) 5.70820 0.435246
\(173\) 1.56231 0.118780 0.0593900 0.998235i \(-0.481084\pi\)
0.0593900 + 0.998235i \(0.481084\pi\)
\(174\) 11.7082 0.887597
\(175\) 4.61803 0.349091
\(176\) 2.61803 0.197342
\(177\) −27.7984 −2.08945
\(178\) 6.94427 0.520495
\(179\) 3.32624 0.248615 0.124307 0.992244i \(-0.460329\pi\)
0.124307 + 0.992244i \(0.460329\pi\)
\(180\) 2.38197 0.177541
\(181\) −2.94427 −0.218846 −0.109423 0.993995i \(-0.534900\pi\)
−0.109423 + 0.993995i \(0.534900\pi\)
\(182\) 5.61803 0.416436
\(183\) 35.8885 2.65296
\(184\) 15.2705 1.12576
\(185\) 1.32624 0.0975070
\(186\) −6.47214 −0.474560
\(187\) 8.47214 0.619544
\(188\) −1.23607 −0.0901495
\(189\) −2.23607 −0.162650
\(190\) −2.52786 −0.183391
\(191\) 17.8885 1.29437 0.647185 0.762333i \(-0.275946\pi\)
0.647185 + 0.762333i \(0.275946\pi\)
\(192\) 18.3262 1.32258
\(193\) −18.7639 −1.35066 −0.675329 0.737517i \(-0.735998\pi\)
−0.675329 + 0.737517i \(0.735998\pi\)
\(194\) 4.85410 0.348504
\(195\) −9.09017 −0.650961
\(196\) −1.00000 −0.0714286
\(197\) −3.05573 −0.217712 −0.108856 0.994058i \(-0.534719\pi\)
−0.108856 + 0.994058i \(0.534719\pi\)
\(198\) 10.0902 0.717077
\(199\) 0.854102 0.0605457 0.0302728 0.999542i \(-0.490362\pi\)
0.0302728 + 0.999542i \(0.490362\pi\)
\(200\) −13.8541 −0.979633
\(201\) −18.7082 −1.31957
\(202\) 4.47214 0.314658
\(203\) 4.47214 0.313882
\(204\) 8.47214 0.593168
\(205\) −5.52786 −0.386083
\(206\) −17.0902 −1.19073
\(207\) 19.6180 1.36355
\(208\) −5.61803 −0.389541
\(209\) 10.7082 0.740702
\(210\) −1.61803 −0.111655
\(211\) −26.5623 −1.82862 −0.914312 0.405010i \(-0.867268\pi\)
−0.914312 + 0.405010i \(0.867268\pi\)
\(212\) 4.32624 0.297127
\(213\) −6.47214 −0.443463
\(214\) −6.00000 −0.410152
\(215\) 3.52786 0.240598
\(216\) 6.70820 0.456435
\(217\) −2.47214 −0.167820
\(218\) 9.85410 0.667404
\(219\) −4.85410 −0.328010
\(220\) −1.61803 −0.109088
\(221\) −18.1803 −1.22294
\(222\) 5.61803 0.377058
\(223\) 0.437694 0.0293102 0.0146551 0.999893i \(-0.495335\pi\)
0.0146551 + 0.999893i \(0.495335\pi\)
\(224\) 5.00000 0.334077
\(225\) −17.7984 −1.18656
\(226\) 14.3820 0.956674
\(227\) 18.9443 1.25738 0.628688 0.777658i \(-0.283592\pi\)
0.628688 + 0.777658i \(0.283592\pi\)
\(228\) 10.7082 0.709168
\(229\) 22.1803 1.46572 0.732859 0.680380i \(-0.238185\pi\)
0.732859 + 0.680380i \(0.238185\pi\)
\(230\) 3.14590 0.207434
\(231\) 6.85410 0.450967
\(232\) −13.4164 −0.880830
\(233\) −1.81966 −0.119210 −0.0596049 0.998222i \(-0.518984\pi\)
−0.0596049 + 0.998222i \(0.518984\pi\)
\(234\) −21.6525 −1.41547
\(235\) −0.763932 −0.0498334
\(236\) 10.6180 0.691175
\(237\) −35.6525 −2.31588
\(238\) −3.23607 −0.209763
\(239\) −24.7639 −1.60185 −0.800923 0.598768i \(-0.795657\pi\)
−0.800923 + 0.598768i \(0.795657\pi\)
\(240\) 1.61803 0.104444
\(241\) 10.3820 0.668761 0.334381 0.942438i \(-0.391473\pi\)
0.334381 + 0.942438i \(0.391473\pi\)
\(242\) 4.14590 0.266508
\(243\) −21.6525 −1.38901
\(244\) −13.7082 −0.877578
\(245\) −0.618034 −0.0394847
\(246\) −23.4164 −1.49298
\(247\) −22.9787 −1.46210
\(248\) 7.41641 0.470942
\(249\) 22.9443 1.45403
\(250\) −5.94427 −0.375949
\(251\) −10.6525 −0.672378 −0.336189 0.941794i \(-0.609138\pi\)
−0.336189 + 0.941794i \(0.609138\pi\)
\(252\) 3.85410 0.242786
\(253\) −13.3262 −0.837813
\(254\) 4.00000 0.250982
\(255\) 5.23607 0.327895
\(256\) −17.0000 −1.06250
\(257\) −16.9443 −1.05695 −0.528477 0.848947i \(-0.677237\pi\)
−0.528477 + 0.848947i \(0.677237\pi\)
\(258\) 14.9443 0.930390
\(259\) 2.14590 0.133340
\(260\) 3.47214 0.215333
\(261\) −17.2361 −1.06689
\(262\) 6.29180 0.388708
\(263\) 22.7426 1.40237 0.701186 0.712979i \(-0.252654\pi\)
0.701186 + 0.712979i \(0.252654\pi\)
\(264\) −20.5623 −1.26552
\(265\) 2.67376 0.164248
\(266\) −4.09017 −0.250784
\(267\) −18.1803 −1.11262
\(268\) 7.14590 0.436505
\(269\) −7.70820 −0.469977 −0.234989 0.971998i \(-0.575505\pi\)
−0.234989 + 0.971998i \(0.575505\pi\)
\(270\) 1.38197 0.0841038
\(271\) −25.1246 −1.52621 −0.763106 0.646274i \(-0.776326\pi\)
−0.763106 + 0.646274i \(0.776326\pi\)
\(272\) 3.23607 0.196215
\(273\) −14.7082 −0.890181
\(274\) −12.4721 −0.753469
\(275\) 12.0902 0.729065
\(276\) −13.3262 −0.802145
\(277\) −5.52786 −0.332137 −0.166069 0.986114i \(-0.553107\pi\)
−0.166069 + 0.986114i \(0.553107\pi\)
\(278\) 11.4164 0.684711
\(279\) 9.52786 0.570418
\(280\) 1.85410 0.110804
\(281\) −25.2705 −1.50751 −0.753756 0.657154i \(-0.771760\pi\)
−0.753756 + 0.657154i \(0.771760\pi\)
\(282\) −3.23607 −0.192705
\(283\) 0.673762 0.0400510 0.0200255 0.999799i \(-0.493625\pi\)
0.0200255 + 0.999799i \(0.493625\pi\)
\(284\) 2.47214 0.146694
\(285\) 6.61803 0.392019
\(286\) 14.7082 0.869714
\(287\) −8.94427 −0.527964
\(288\) −19.2705 −1.13553
\(289\) −6.52786 −0.383992
\(290\) −2.76393 −0.162304
\(291\) −12.7082 −0.744968
\(292\) 1.85410 0.108503
\(293\) −16.4721 −0.962312 −0.481156 0.876635i \(-0.659783\pi\)
−0.481156 + 0.876635i \(0.659783\pi\)
\(294\) −2.61803 −0.152687
\(295\) 6.56231 0.382072
\(296\) −6.43769 −0.374183
\(297\) −5.85410 −0.339689
\(298\) 5.41641 0.313764
\(299\) 28.5967 1.65379
\(300\) 12.0902 0.698026
\(301\) 5.70820 0.329015
\(302\) 6.76393 0.389221
\(303\) −11.7082 −0.672619
\(304\) 4.09017 0.234587
\(305\) −8.47214 −0.485113
\(306\) 12.4721 0.712985
\(307\) −29.7984 −1.70068 −0.850342 0.526231i \(-0.823605\pi\)
−0.850342 + 0.526231i \(0.823605\pi\)
\(308\) −2.61803 −0.149176
\(309\) 44.7426 2.54532
\(310\) 1.52786 0.0867768
\(311\) 8.94427 0.507183 0.253592 0.967311i \(-0.418388\pi\)
0.253592 + 0.967311i \(0.418388\pi\)
\(312\) 44.1246 2.49806
\(313\) 22.1803 1.25371 0.626853 0.779137i \(-0.284342\pi\)
0.626853 + 0.779137i \(0.284342\pi\)
\(314\) −3.14590 −0.177533
\(315\) 2.38197 0.134209
\(316\) 13.6180 0.766074
\(317\) −28.6525 −1.60928 −0.804642 0.593761i \(-0.797643\pi\)
−0.804642 + 0.593761i \(0.797643\pi\)
\(318\) 11.3262 0.635144
\(319\) 11.7082 0.655534
\(320\) −4.32624 −0.241844
\(321\) 15.7082 0.876746
\(322\) 5.09017 0.283664
\(323\) 13.2361 0.736475
\(324\) 5.70820 0.317122
\(325\) −25.9443 −1.43913
\(326\) 6.47214 0.358458
\(327\) −25.7984 −1.42665
\(328\) 26.8328 1.48159
\(329\) −1.23607 −0.0681466
\(330\) −4.23607 −0.233188
\(331\) −22.4721 −1.23518 −0.617590 0.786500i \(-0.711891\pi\)
−0.617590 + 0.786500i \(0.711891\pi\)
\(332\) −8.76393 −0.480983
\(333\) −8.27051 −0.453221
\(334\) −12.1803 −0.666479
\(335\) 4.41641 0.241294
\(336\) 2.61803 0.142825
\(337\) 16.0902 0.876487 0.438244 0.898856i \(-0.355601\pi\)
0.438244 + 0.898856i \(0.355601\pi\)
\(338\) −18.5623 −1.00966
\(339\) −37.6525 −2.04500
\(340\) −2.00000 −0.108465
\(341\) −6.47214 −0.350486
\(342\) 15.7639 0.852416
\(343\) −1.00000 −0.0539949
\(344\) −17.1246 −0.923297
\(345\) −8.23607 −0.443415
\(346\) −1.56231 −0.0839901
\(347\) −32.4508 −1.74205 −0.871026 0.491236i \(-0.836545\pi\)
−0.871026 + 0.491236i \(0.836545\pi\)
\(348\) 11.7082 0.627626
\(349\) 31.8885 1.70695 0.853477 0.521130i \(-0.174489\pi\)
0.853477 + 0.521130i \(0.174489\pi\)
\(350\) −4.61803 −0.246844
\(351\) 12.5623 0.670526
\(352\) 13.0902 0.697708
\(353\) −13.7082 −0.729614 −0.364807 0.931083i \(-0.618865\pi\)
−0.364807 + 0.931083i \(0.618865\pi\)
\(354\) 27.7984 1.47747
\(355\) 1.52786 0.0810906
\(356\) 6.94427 0.368046
\(357\) 8.47214 0.448393
\(358\) −3.32624 −0.175797
\(359\) 32.1803 1.69841 0.849207 0.528061i \(-0.177081\pi\)
0.849207 + 0.528061i \(0.177081\pi\)
\(360\) −7.14590 −0.376622
\(361\) −2.27051 −0.119501
\(362\) 2.94427 0.154747
\(363\) −10.8541 −0.569693
\(364\) 5.61803 0.294465
\(365\) 1.14590 0.0599790
\(366\) −35.8885 −1.87592
\(367\) −30.0000 −1.56599 −0.782994 0.622030i \(-0.786308\pi\)
−0.782994 + 0.622030i \(0.786308\pi\)
\(368\) −5.09017 −0.265343
\(369\) 34.4721 1.79455
\(370\) −1.32624 −0.0689478
\(371\) 4.32624 0.224607
\(372\) −6.47214 −0.335565
\(373\) −19.3262 −1.00067 −0.500337 0.865831i \(-0.666791\pi\)
−0.500337 + 0.865831i \(0.666791\pi\)
\(374\) −8.47214 −0.438084
\(375\) 15.5623 0.803634
\(376\) 3.70820 0.191236
\(377\) −25.1246 −1.29398
\(378\) 2.23607 0.115011
\(379\) 13.0344 0.669534 0.334767 0.942301i \(-0.391342\pi\)
0.334767 + 0.942301i \(0.391342\pi\)
\(380\) −2.52786 −0.129677
\(381\) −10.4721 −0.536504
\(382\) −17.8885 −0.915258
\(383\) −12.8541 −0.656814 −0.328407 0.944536i \(-0.606512\pi\)
−0.328407 + 0.944536i \(0.606512\pi\)
\(384\) 7.85410 0.400803
\(385\) −1.61803 −0.0824626
\(386\) 18.7639 0.955059
\(387\) −22.0000 −1.11832
\(388\) 4.85410 0.246430
\(389\) 21.9787 1.11437 0.557183 0.830390i \(-0.311882\pi\)
0.557183 + 0.830390i \(0.311882\pi\)
\(390\) 9.09017 0.460299
\(391\) −16.4721 −0.833032
\(392\) 3.00000 0.151523
\(393\) −16.4721 −0.830909
\(394\) 3.05573 0.153945
\(395\) 8.41641 0.423475
\(396\) 10.0902 0.507050
\(397\) 7.88854 0.395915 0.197957 0.980211i \(-0.436569\pi\)
0.197957 + 0.980211i \(0.436569\pi\)
\(398\) −0.854102 −0.0428123
\(399\) 10.7082 0.536081
\(400\) 4.61803 0.230902
\(401\) −1.05573 −0.0527205 −0.0263603 0.999653i \(-0.508392\pi\)
−0.0263603 + 0.999653i \(0.508392\pi\)
\(402\) 18.7082 0.933080
\(403\) 13.8885 0.691838
\(404\) 4.47214 0.222497
\(405\) 3.52786 0.175301
\(406\) −4.47214 −0.221948
\(407\) 5.61803 0.278476
\(408\) −25.4164 −1.25830
\(409\) −20.6525 −1.02120 −0.510600 0.859819i \(-0.670577\pi\)
−0.510600 + 0.859819i \(0.670577\pi\)
\(410\) 5.52786 0.273002
\(411\) 32.6525 1.61063
\(412\) −17.0902 −0.841972
\(413\) 10.6180 0.522479
\(414\) −19.6180 −0.964174
\(415\) −5.41641 −0.265881
\(416\) −28.0902 −1.37723
\(417\) −29.8885 −1.46365
\(418\) −10.7082 −0.523755
\(419\) −20.0000 −0.977064 −0.488532 0.872546i \(-0.662467\pi\)
−0.488532 + 0.872546i \(0.662467\pi\)
\(420\) −1.61803 −0.0789520
\(421\) 2.20163 0.107301 0.0536503 0.998560i \(-0.482914\pi\)
0.0536503 + 0.998560i \(0.482914\pi\)
\(422\) 26.5623 1.29303
\(423\) 4.76393 0.231630
\(424\) −12.9787 −0.630302
\(425\) 14.9443 0.724904
\(426\) 6.47214 0.313576
\(427\) −13.7082 −0.663386
\(428\) −6.00000 −0.290021
\(429\) −38.5066 −1.85912
\(430\) −3.52786 −0.170129
\(431\) −36.9443 −1.77954 −0.889771 0.456406i \(-0.849136\pi\)
−0.889771 + 0.456406i \(0.849136\pi\)
\(432\) −2.23607 −0.107583
\(433\) −18.3607 −0.882358 −0.441179 0.897419i \(-0.645440\pi\)
−0.441179 + 0.897419i \(0.645440\pi\)
\(434\) 2.47214 0.118666
\(435\) 7.23607 0.346943
\(436\) 9.85410 0.471926
\(437\) −20.8197 −0.995939
\(438\) 4.85410 0.231938
\(439\) 17.1246 0.817313 0.408657 0.912688i \(-0.365997\pi\)
0.408657 + 0.912688i \(0.365997\pi\)
\(440\) 4.85410 0.231410
\(441\) 3.85410 0.183529
\(442\) 18.1803 0.864751
\(443\) −13.7984 −0.655581 −0.327790 0.944751i \(-0.606304\pi\)
−0.327790 + 0.944751i \(0.606304\pi\)
\(444\) 5.61803 0.266620
\(445\) 4.29180 0.203451
\(446\) −0.437694 −0.0207254
\(447\) −14.1803 −0.670707
\(448\) −7.00000 −0.330719
\(449\) 39.6869 1.87294 0.936471 0.350746i \(-0.114072\pi\)
0.936471 + 0.350746i \(0.114072\pi\)
\(450\) 17.7984 0.839023
\(451\) −23.4164 −1.10264
\(452\) 14.3820 0.676471
\(453\) −17.7082 −0.832004
\(454\) −18.9443 −0.889099
\(455\) 3.47214 0.162776
\(456\) −32.1246 −1.50437
\(457\) 20.6869 0.967693 0.483847 0.875153i \(-0.339239\pi\)
0.483847 + 0.875153i \(0.339239\pi\)
\(458\) −22.1803 −1.03642
\(459\) −7.23607 −0.337751
\(460\) 3.14590 0.146678
\(461\) 27.5967 1.28531 0.642654 0.766156i \(-0.277833\pi\)
0.642654 + 0.766156i \(0.277833\pi\)
\(462\) −6.85410 −0.318882
\(463\) −8.00000 −0.371792 −0.185896 0.982569i \(-0.559519\pi\)
−0.185896 + 0.982569i \(0.559519\pi\)
\(464\) 4.47214 0.207614
\(465\) −4.00000 −0.185496
\(466\) 1.81966 0.0842941
\(467\) −21.0344 −0.973358 −0.486679 0.873581i \(-0.661792\pi\)
−0.486679 + 0.873581i \(0.661792\pi\)
\(468\) −21.6525 −1.00089
\(469\) 7.14590 0.329967
\(470\) 0.763932 0.0352376
\(471\) 8.23607 0.379498
\(472\) −31.8541 −1.46620
\(473\) 14.9443 0.687138
\(474\) 35.6525 1.63757
\(475\) 18.8885 0.866666
\(476\) −3.23607 −0.148325
\(477\) −16.6738 −0.763439
\(478\) 24.7639 1.13268
\(479\) −6.65248 −0.303959 −0.151980 0.988384i \(-0.548565\pi\)
−0.151980 + 0.988384i \(0.548565\pi\)
\(480\) 8.09017 0.369264
\(481\) −12.0557 −0.549694
\(482\) −10.3820 −0.472886
\(483\) −13.3262 −0.606365
\(484\) 4.14590 0.188450
\(485\) 3.00000 0.136223
\(486\) 21.6525 0.982176
\(487\) −25.4164 −1.15173 −0.575864 0.817546i \(-0.695334\pi\)
−0.575864 + 0.817546i \(0.695334\pi\)
\(488\) 41.1246 1.86162
\(489\) −16.9443 −0.766246
\(490\) 0.618034 0.0279199
\(491\) 21.7426 0.981232 0.490616 0.871376i \(-0.336772\pi\)
0.490616 + 0.871376i \(0.336772\pi\)
\(492\) −23.4164 −1.05569
\(493\) 14.4721 0.651792
\(494\) 22.9787 1.03386
\(495\) 6.23607 0.280290
\(496\) −2.47214 −0.111002
\(497\) 2.47214 0.110890
\(498\) −22.9443 −1.02816
\(499\) 21.8885 0.979866 0.489933 0.871760i \(-0.337021\pi\)
0.489933 + 0.871760i \(0.337021\pi\)
\(500\) −5.94427 −0.265836
\(501\) 31.8885 1.42468
\(502\) 10.6525 0.475443
\(503\) −28.0902 −1.25248 −0.626239 0.779631i \(-0.715407\pi\)
−0.626239 + 0.779631i \(0.715407\pi\)
\(504\) −11.5623 −0.515026
\(505\) 2.76393 0.122993
\(506\) 13.3262 0.592424
\(507\) 48.5967 2.15826
\(508\) 4.00000 0.177471
\(509\) 32.8541 1.45623 0.728116 0.685454i \(-0.240396\pi\)
0.728116 + 0.685454i \(0.240396\pi\)
\(510\) −5.23607 −0.231857
\(511\) 1.85410 0.0820206
\(512\) 11.0000 0.486136
\(513\) −9.14590 −0.403801
\(514\) 16.9443 0.747380
\(515\) −10.5623 −0.465431
\(516\) 14.9443 0.657885
\(517\) −3.23607 −0.142322
\(518\) −2.14590 −0.0942853
\(519\) 4.09017 0.179539
\(520\) −10.4164 −0.456790
\(521\) 4.90983 0.215104 0.107552 0.994199i \(-0.465699\pi\)
0.107552 + 0.994199i \(0.465699\pi\)
\(522\) 17.2361 0.754402
\(523\) 30.7426 1.34428 0.672141 0.740423i \(-0.265375\pi\)
0.672141 + 0.740423i \(0.265375\pi\)
\(524\) 6.29180 0.274858
\(525\) 12.0902 0.527658
\(526\) −22.7426 −0.991626
\(527\) −8.00000 −0.348485
\(528\) 6.85410 0.298287
\(529\) 2.90983 0.126514
\(530\) −2.67376 −0.116141
\(531\) −40.9230 −1.77591
\(532\) −4.09017 −0.177331
\(533\) 50.2492 2.17654
\(534\) 18.1803 0.786740
\(535\) −3.70820 −0.160320
\(536\) −21.4377 −0.925967
\(537\) 8.70820 0.375787
\(538\) 7.70820 0.332324
\(539\) −2.61803 −0.112767
\(540\) 1.38197 0.0594703
\(541\) 38.5410 1.65701 0.828504 0.559983i \(-0.189192\pi\)
0.828504 + 0.559983i \(0.189192\pi\)
\(542\) 25.1246 1.07919
\(543\) −7.70820 −0.330791
\(544\) 16.1803 0.693726
\(545\) 6.09017 0.260874
\(546\) 14.7082 0.629453
\(547\) −44.0689 −1.88425 −0.942125 0.335263i \(-0.891175\pi\)
−0.942125 + 0.335263i \(0.891175\pi\)
\(548\) −12.4721 −0.532783
\(549\) 52.8328 2.25485
\(550\) −12.0902 −0.515527
\(551\) 18.2918 0.779257
\(552\) 39.9787 1.70161
\(553\) 13.6180 0.579098
\(554\) 5.52786 0.234856
\(555\) 3.47214 0.147384
\(556\) 11.4164 0.484164
\(557\) −7.12461 −0.301879 −0.150940 0.988543i \(-0.548230\pi\)
−0.150940 + 0.988543i \(0.548230\pi\)
\(558\) −9.52786 −0.403347
\(559\) −32.0689 −1.35637
\(560\) −0.618034 −0.0261167
\(561\) 22.1803 0.936455
\(562\) 25.2705 1.06597
\(563\) 30.0689 1.26725 0.633626 0.773639i \(-0.281566\pi\)
0.633626 + 0.773639i \(0.281566\pi\)
\(564\) −3.23607 −0.136263
\(565\) 8.88854 0.373944
\(566\) −0.673762 −0.0283203
\(567\) 5.70820 0.239722
\(568\) −7.41641 −0.311186
\(569\) 26.0000 1.08998 0.544988 0.838444i \(-0.316534\pi\)
0.544988 + 0.838444i \(0.316534\pi\)
\(570\) −6.61803 −0.277199
\(571\) 22.0689 0.923554 0.461777 0.886996i \(-0.347212\pi\)
0.461777 + 0.886996i \(0.347212\pi\)
\(572\) 14.7082 0.614981
\(573\) 46.8328 1.95647
\(574\) 8.94427 0.373327
\(575\) −23.5066 −0.980292
\(576\) 26.9787 1.12411
\(577\) −17.4377 −0.725941 −0.362970 0.931801i \(-0.618237\pi\)
−0.362970 + 0.931801i \(0.618237\pi\)
\(578\) 6.52786 0.271523
\(579\) −49.1246 −2.04155
\(580\) −2.76393 −0.114766
\(581\) −8.76393 −0.363589
\(582\) 12.7082 0.526772
\(583\) 11.3262 0.469085
\(584\) −5.56231 −0.230170
\(585\) −13.3820 −0.553276
\(586\) 16.4721 0.680458
\(587\) 4.00000 0.165098 0.0825488 0.996587i \(-0.473694\pi\)
0.0825488 + 0.996587i \(0.473694\pi\)
\(588\) −2.61803 −0.107966
\(589\) −10.1115 −0.416635
\(590\) −6.56231 −0.270166
\(591\) −8.00000 −0.329076
\(592\) 2.14590 0.0881959
\(593\) 24.2918 0.997545 0.498772 0.866733i \(-0.333784\pi\)
0.498772 + 0.866733i \(0.333784\pi\)
\(594\) 5.85410 0.240197
\(595\) −2.00000 −0.0819920
\(596\) 5.41641 0.221865
\(597\) 2.23607 0.0915162
\(598\) −28.5967 −1.16941
\(599\) 12.6525 0.516966 0.258483 0.966016i \(-0.416777\pi\)
0.258483 + 0.966016i \(0.416777\pi\)
\(600\) −36.2705 −1.48074
\(601\) −1.34752 −0.0549667 −0.0274833 0.999622i \(-0.508749\pi\)
−0.0274833 + 0.999622i \(0.508749\pi\)
\(602\) −5.70820 −0.232649
\(603\) −27.5410 −1.12156
\(604\) 6.76393 0.275220
\(605\) 2.56231 0.104173
\(606\) 11.7082 0.475613
\(607\) 32.9443 1.33717 0.668583 0.743637i \(-0.266901\pi\)
0.668583 + 0.743637i \(0.266901\pi\)
\(608\) 20.4508 0.829391
\(609\) 11.7082 0.474440
\(610\) 8.47214 0.343027
\(611\) 6.94427 0.280935
\(612\) 12.4721 0.504156
\(613\) 23.4508 0.947171 0.473585 0.880748i \(-0.342960\pi\)
0.473585 + 0.880748i \(0.342960\pi\)
\(614\) 29.7984 1.20256
\(615\) −14.4721 −0.583573
\(616\) 7.85410 0.316451
\(617\) −10.3607 −0.417105 −0.208553 0.978011i \(-0.566875\pi\)
−0.208553 + 0.978011i \(0.566875\pi\)
\(618\) −44.7426 −1.79981
\(619\) 5.70820 0.229432 0.114716 0.993398i \(-0.463404\pi\)
0.114716 + 0.993398i \(0.463404\pi\)
\(620\) 1.52786 0.0613605
\(621\) 11.3820 0.456743
\(622\) −8.94427 −0.358633
\(623\) 6.94427 0.278216
\(624\) −14.7082 −0.588799
\(625\) 19.4164 0.776656
\(626\) −22.1803 −0.886505
\(627\) 28.0344 1.11959
\(628\) −3.14590 −0.125535
\(629\) 6.94427 0.276886
\(630\) −2.38197 −0.0948998
\(631\) −37.7426 −1.50251 −0.751256 0.660011i \(-0.770551\pi\)
−0.751256 + 0.660011i \(0.770551\pi\)
\(632\) −40.8541 −1.62509
\(633\) −69.5410 −2.76401
\(634\) 28.6525 1.13794
\(635\) 2.47214 0.0981037
\(636\) 11.3262 0.449115
\(637\) 5.61803 0.222595
\(638\) −11.7082 −0.463532
\(639\) −9.52786 −0.376916
\(640\) −1.85410 −0.0732898
\(641\) −35.0132 −1.38294 −0.691468 0.722407i \(-0.743036\pi\)
−0.691468 + 0.722407i \(0.743036\pi\)
\(642\) −15.7082 −0.619953
\(643\) 46.3607 1.82829 0.914143 0.405391i \(-0.132865\pi\)
0.914143 + 0.405391i \(0.132865\pi\)
\(644\) 5.09017 0.200581
\(645\) 9.23607 0.363670
\(646\) −13.2361 −0.520766
\(647\) −3.70820 −0.145785 −0.0728923 0.997340i \(-0.523223\pi\)
−0.0728923 + 0.997340i \(0.523223\pi\)
\(648\) −17.1246 −0.672718
\(649\) 27.7984 1.09118
\(650\) 25.9443 1.01762
\(651\) −6.47214 −0.253663
\(652\) 6.47214 0.253468
\(653\) 15.0557 0.589176 0.294588 0.955624i \(-0.404818\pi\)
0.294588 + 0.955624i \(0.404818\pi\)
\(654\) 25.7984 1.00880
\(655\) 3.88854 0.151938
\(656\) −8.94427 −0.349215
\(657\) −7.14590 −0.278788
\(658\) 1.23607 0.0481869
\(659\) 9.03444 0.351932 0.175966 0.984396i \(-0.443695\pi\)
0.175966 + 0.984396i \(0.443695\pi\)
\(660\) −4.23607 −0.164889
\(661\) −17.2361 −0.670405 −0.335203 0.942146i \(-0.608805\pi\)
−0.335203 + 0.942146i \(0.608805\pi\)
\(662\) 22.4721 0.873404
\(663\) −47.5967 −1.84850
\(664\) 26.2918 1.02032
\(665\) −2.52786 −0.0980264
\(666\) 8.27051 0.320476
\(667\) −22.7639 −0.881423
\(668\) −12.1803 −0.471271
\(669\) 1.14590 0.0443030
\(670\) −4.41641 −0.170621
\(671\) −35.8885 −1.38546
\(672\) 13.0902 0.504964
\(673\) −43.5066 −1.67706 −0.838528 0.544859i \(-0.816583\pi\)
−0.838528 + 0.544859i \(0.816583\pi\)
\(674\) −16.0902 −0.619770
\(675\) −10.3262 −0.397457
\(676\) −18.5623 −0.713935
\(677\) −22.1459 −0.851136 −0.425568 0.904926i \(-0.639926\pi\)
−0.425568 + 0.904926i \(0.639926\pi\)
\(678\) 37.6525 1.44603
\(679\) 4.85410 0.186283
\(680\) 6.00000 0.230089
\(681\) 49.5967 1.90055
\(682\) 6.47214 0.247831
\(683\) −11.5279 −0.441101 −0.220551 0.975376i \(-0.570785\pi\)
−0.220551 + 0.975376i \(0.570785\pi\)
\(684\) 15.7639 0.602749
\(685\) −7.70820 −0.294515
\(686\) 1.00000 0.0381802
\(687\) 58.0689 2.21547
\(688\) 5.70820 0.217623
\(689\) −24.3050 −0.925945
\(690\) 8.23607 0.313542
\(691\) 33.7082 1.28232 0.641160 0.767407i \(-0.278453\pi\)
0.641160 + 0.767407i \(0.278453\pi\)
\(692\) −1.56231 −0.0593900
\(693\) 10.0902 0.383294
\(694\) 32.4508 1.23182
\(695\) 7.05573 0.267639
\(696\) −35.1246 −1.33139
\(697\) −28.9443 −1.09634
\(698\) −31.8885 −1.20700
\(699\) −4.76393 −0.180188
\(700\) −4.61803 −0.174545
\(701\) 2.11146 0.0797486 0.0398743 0.999205i \(-0.487304\pi\)
0.0398743 + 0.999205i \(0.487304\pi\)
\(702\) −12.5623 −0.474134
\(703\) 8.77709 0.331034
\(704\) −18.3262 −0.690696
\(705\) −2.00000 −0.0753244
\(706\) 13.7082 0.515915
\(707\) 4.47214 0.168192
\(708\) 27.7984 1.04473
\(709\) −18.0000 −0.676004 −0.338002 0.941145i \(-0.609751\pi\)
−0.338002 + 0.941145i \(0.609751\pi\)
\(710\) −1.52786 −0.0573397
\(711\) −52.4853 −1.96835
\(712\) −20.8328 −0.780743
\(713\) 12.5836 0.471259
\(714\) −8.47214 −0.317062
\(715\) 9.09017 0.339953
\(716\) −3.32624 −0.124307
\(717\) −64.8328 −2.42123
\(718\) −32.1803 −1.20096
\(719\) −10.3607 −0.386388 −0.193194 0.981161i \(-0.561885\pi\)
−0.193194 + 0.981161i \(0.561885\pi\)
\(720\) 2.38197 0.0887706
\(721\) −17.0902 −0.636471
\(722\) 2.27051 0.0844996
\(723\) 27.1803 1.01085
\(724\) 2.94427 0.109423
\(725\) 20.6525 0.767014
\(726\) 10.8541 0.402834
\(727\) 30.5410 1.13270 0.566352 0.824164i \(-0.308354\pi\)
0.566352 + 0.824164i \(0.308354\pi\)
\(728\) −16.8541 −0.624655
\(729\) −39.5623 −1.46527
\(730\) −1.14590 −0.0424116
\(731\) 18.4721 0.683217
\(732\) −35.8885 −1.32648
\(733\) −24.6738 −0.911346 −0.455673 0.890147i \(-0.650601\pi\)
−0.455673 + 0.890147i \(0.650601\pi\)
\(734\) 30.0000 1.10732
\(735\) −1.61803 −0.0596821
\(736\) −25.4508 −0.938131
\(737\) 18.7082 0.689126
\(738\) −34.4721 −1.26894
\(739\) 22.4721 0.826651 0.413325 0.910583i \(-0.364367\pi\)
0.413325 + 0.910583i \(0.364367\pi\)
\(740\) −1.32624 −0.0487535
\(741\) −60.1591 −2.21000
\(742\) −4.32624 −0.158821
\(743\) −15.7082 −0.576278 −0.288139 0.957589i \(-0.593037\pi\)
−0.288139 + 0.957589i \(0.593037\pi\)
\(744\) 19.4164 0.711840
\(745\) 3.34752 0.122644
\(746\) 19.3262 0.707584
\(747\) 33.7771 1.23584
\(748\) −8.47214 −0.309772
\(749\) −6.00000 −0.219235
\(750\) −15.5623 −0.568255
\(751\) −18.2918 −0.667477 −0.333739 0.942666i \(-0.608310\pi\)
−0.333739 + 0.942666i \(0.608310\pi\)
\(752\) −1.23607 −0.0450748
\(753\) −27.8885 −1.01632
\(754\) 25.1246 0.914984
\(755\) 4.18034 0.152138
\(756\) 2.23607 0.0813250
\(757\) −18.2918 −0.664827 −0.332413 0.943134i \(-0.607863\pi\)
−0.332413 + 0.943134i \(0.607863\pi\)
\(758\) −13.0344 −0.473432
\(759\) −34.8885 −1.26637
\(760\) 7.58359 0.275086
\(761\) 24.3262 0.881825 0.440913 0.897550i \(-0.354655\pi\)
0.440913 + 0.897550i \(0.354655\pi\)
\(762\) 10.4721 0.379365
\(763\) 9.85410 0.356742
\(764\) −17.8885 −0.647185
\(765\) 7.70820 0.278691
\(766\) 12.8541 0.464438
\(767\) −59.6525 −2.15393
\(768\) −44.5066 −1.60599
\(769\) 3.63932 0.131237 0.0656186 0.997845i \(-0.479098\pi\)
0.0656186 + 0.997845i \(0.479098\pi\)
\(770\) 1.61803 0.0583099
\(771\) −44.3607 −1.59761
\(772\) 18.7639 0.675329
\(773\) 1.88854 0.0679262 0.0339631 0.999423i \(-0.489187\pi\)
0.0339631 + 0.999423i \(0.489187\pi\)
\(774\) 22.0000 0.790774
\(775\) −11.4164 −0.410089
\(776\) −14.5623 −0.522756
\(777\) 5.61803 0.201546
\(778\) −21.9787 −0.787975
\(779\) −36.5836 −1.31074
\(780\) 9.09017 0.325480
\(781\) 6.47214 0.231591
\(782\) 16.4721 0.589042
\(783\) −10.0000 −0.357371
\(784\) −1.00000 −0.0357143
\(785\) −1.94427 −0.0693940
\(786\) 16.4721 0.587542
\(787\) −27.7082 −0.987691 −0.493845 0.869550i \(-0.664409\pi\)
−0.493845 + 0.869550i \(0.664409\pi\)
\(788\) 3.05573 0.108856
\(789\) 59.5410 2.11972
\(790\) −8.41641 −0.299442
\(791\) 14.3820 0.511364
\(792\) −30.2705 −1.07562
\(793\) 77.0132 2.73482
\(794\) −7.88854 −0.279954
\(795\) 7.00000 0.248264
\(796\) −0.854102 −0.0302728
\(797\) 53.4164 1.89211 0.946053 0.324012i \(-0.105032\pi\)
0.946053 + 0.324012i \(0.105032\pi\)
\(798\) −10.7082 −0.379066
\(799\) −4.00000 −0.141510
\(800\) 23.0902 0.816361
\(801\) −26.7639 −0.945657
\(802\) 1.05573 0.0372791
\(803\) 4.85410 0.171298
\(804\) 18.7082 0.659787
\(805\) 3.14590 0.110878
\(806\) −13.8885 −0.489203
\(807\) −20.1803 −0.710382
\(808\) −13.4164 −0.471988
\(809\) 23.8885 0.839876 0.419938 0.907553i \(-0.362052\pi\)
0.419938 + 0.907553i \(0.362052\pi\)
\(810\) −3.52786 −0.123957
\(811\) 36.1459 1.26925 0.634627 0.772819i \(-0.281154\pi\)
0.634627 + 0.772819i \(0.281154\pi\)
\(812\) −4.47214 −0.156941
\(813\) −65.7771 −2.30690
\(814\) −5.61803 −0.196912
\(815\) 4.00000 0.140114
\(816\) 8.47214 0.296584
\(817\) 23.3475 0.816826
\(818\) 20.6525 0.722097
\(819\) −21.6525 −0.756599
\(820\) 5.52786 0.193041
\(821\) 19.6738 0.686619 0.343310 0.939222i \(-0.388452\pi\)
0.343310 + 0.939222i \(0.388452\pi\)
\(822\) −32.6525 −1.13889
\(823\) −49.8885 −1.73901 −0.869503 0.493928i \(-0.835561\pi\)
−0.869503 + 0.493928i \(0.835561\pi\)
\(824\) 51.2705 1.78609
\(825\) 31.6525 1.10200
\(826\) −10.6180 −0.369449
\(827\) 15.6869 0.545488 0.272744 0.962087i \(-0.412069\pi\)
0.272744 + 0.962087i \(0.412069\pi\)
\(828\) −19.6180 −0.681774
\(829\) 48.8541 1.69677 0.848387 0.529377i \(-0.177574\pi\)
0.848387 + 0.529377i \(0.177574\pi\)
\(830\) 5.41641 0.188006
\(831\) −14.4721 −0.502033
\(832\) 39.3262 1.36339
\(833\) −3.23607 −0.112123
\(834\) 29.8885 1.03496
\(835\) −7.52786 −0.260512
\(836\) −10.7082 −0.370351
\(837\) 5.52786 0.191071
\(838\) 20.0000 0.690889
\(839\) −26.7639 −0.923994 −0.461997 0.886882i \(-0.652867\pi\)
−0.461997 + 0.886882i \(0.652867\pi\)
\(840\) 4.85410 0.167482
\(841\) −9.00000 −0.310345
\(842\) −2.20163 −0.0758730
\(843\) −66.1591 −2.27864
\(844\) 26.5623 0.914312
\(845\) −11.4721 −0.394653
\(846\) −4.76393 −0.163787
\(847\) 4.14590 0.142455
\(848\) 4.32624 0.148564
\(849\) 1.76393 0.0605380
\(850\) −14.9443 −0.512584
\(851\) −10.9230 −0.374435
\(852\) 6.47214 0.221732
\(853\) −4.18034 −0.143132 −0.0715661 0.997436i \(-0.522800\pi\)
−0.0715661 + 0.997436i \(0.522800\pi\)
\(854\) 13.7082 0.469085
\(855\) 9.74265 0.333191
\(856\) 18.0000 0.615227
\(857\) 7.52786 0.257147 0.128573 0.991700i \(-0.458960\pi\)
0.128573 + 0.991700i \(0.458960\pi\)
\(858\) 38.5066 1.31459
\(859\) −26.4721 −0.903218 −0.451609 0.892216i \(-0.649150\pi\)
−0.451609 + 0.892216i \(0.649150\pi\)
\(860\) −3.52786 −0.120299
\(861\) −23.4164 −0.798029
\(862\) 36.9443 1.25833
\(863\) −1.00000 −0.0340404
\(864\) −11.1803 −0.380363
\(865\) −0.965558 −0.0328300
\(866\) 18.3607 0.623921
\(867\) −17.0902 −0.580413
\(868\) 2.47214 0.0839098
\(869\) 35.6525 1.20943
\(870\) −7.23607 −0.245326
\(871\) −40.1459 −1.36029
\(872\) −29.5623 −1.00111
\(873\) −18.7082 −0.633177
\(874\) 20.8197 0.704236
\(875\) −5.94427 −0.200953
\(876\) 4.85410 0.164005
\(877\) −22.9443 −0.774773 −0.387387 0.921917i \(-0.626622\pi\)
−0.387387 + 0.921917i \(0.626622\pi\)
\(878\) −17.1246 −0.577928
\(879\) −43.1246 −1.45456
\(880\) −1.61803 −0.0545439
\(881\) 10.7639 0.362646 0.181323 0.983424i \(-0.441962\pi\)
0.181323 + 0.983424i \(0.441962\pi\)
\(882\) −3.85410 −0.129774
\(883\) −35.0557 −1.17972 −0.589860 0.807506i \(-0.700817\pi\)
−0.589860 + 0.807506i \(0.700817\pi\)
\(884\) 18.1803 0.611471
\(885\) 17.1803 0.577511
\(886\) 13.7984 0.463565
\(887\) −47.1935 −1.58460 −0.792301 0.610130i \(-0.791117\pi\)
−0.792301 + 0.610130i \(0.791117\pi\)
\(888\) −16.8541 −0.565587
\(889\) 4.00000 0.134156
\(890\) −4.29180 −0.143861
\(891\) 14.9443 0.500652
\(892\) −0.437694 −0.0146551
\(893\) −5.05573 −0.169183
\(894\) 14.1803 0.474262
\(895\) −2.05573 −0.0687154
\(896\) −3.00000 −0.100223
\(897\) 74.8673 2.49974
\(898\) −39.6869 −1.32437
\(899\) −11.0557 −0.368729
\(900\) 17.7984 0.593279
\(901\) 14.0000 0.466408
\(902\) 23.4164 0.779681
\(903\) 14.9443 0.497314
\(904\) −43.1459 −1.43501
\(905\) 1.81966 0.0604875
\(906\) 17.7082 0.588316
\(907\) −6.74265 −0.223886 −0.111943 0.993715i \(-0.535707\pi\)
−0.111943 + 0.993715i \(0.535707\pi\)
\(908\) −18.9443 −0.628688
\(909\) −17.2361 −0.571684
\(910\) −3.47214 −0.115100
\(911\) −14.8328 −0.491433 −0.245717 0.969342i \(-0.579023\pi\)
−0.245717 + 0.969342i \(0.579023\pi\)
\(912\) 10.7082 0.354584
\(913\) −22.9443 −0.759345
\(914\) −20.6869 −0.684262
\(915\) −22.1803 −0.733259
\(916\) −22.1803 −0.732859
\(917\) 6.29180 0.207773
\(918\) 7.23607 0.238826
\(919\) −29.6180 −0.977009 −0.488504 0.872561i \(-0.662457\pi\)
−0.488504 + 0.872561i \(0.662457\pi\)
\(920\) −9.43769 −0.311152
\(921\) −78.0132 −2.57062
\(922\) −27.5967 −0.908850
\(923\) −13.8885 −0.457147
\(924\) −6.85410 −0.225483
\(925\) 9.90983 0.325833
\(926\) 8.00000 0.262896
\(927\) 65.8673 2.16336
\(928\) 22.3607 0.734025
\(929\) −7.45085 −0.244454 −0.122227 0.992502i \(-0.539004\pi\)
−0.122227 + 0.992502i \(0.539004\pi\)
\(930\) 4.00000 0.131165
\(931\) −4.09017 −0.134050
\(932\) 1.81966 0.0596049
\(933\) 23.4164 0.766619
\(934\) 21.0344 0.688268
\(935\) −5.23607 −0.171238
\(936\) 64.9574 2.12320
\(937\) 22.6525 0.740024 0.370012 0.929027i \(-0.379354\pi\)
0.370012 + 0.929027i \(0.379354\pi\)
\(938\) −7.14590 −0.233322
\(939\) 58.0689 1.89501
\(940\) 0.763932 0.0249167
\(941\) 10.9443 0.356773 0.178387 0.983960i \(-0.442912\pi\)
0.178387 + 0.983960i \(0.442912\pi\)
\(942\) −8.23607 −0.268346
\(943\) 45.5279 1.48259
\(944\) 10.6180 0.345588
\(945\) 1.38197 0.0449554
\(946\) −14.9443 −0.485880
\(947\) 42.9787 1.39662 0.698310 0.715795i \(-0.253936\pi\)
0.698310 + 0.715795i \(0.253936\pi\)
\(948\) 35.6525 1.15794
\(949\) −10.4164 −0.338131
\(950\) −18.8885 −0.612825
\(951\) −75.0132 −2.43247
\(952\) 9.70820 0.314645
\(953\) 17.8885 0.579467 0.289733 0.957107i \(-0.406433\pi\)
0.289733 + 0.957107i \(0.406433\pi\)
\(954\) 16.6738 0.539833
\(955\) −11.0557 −0.357755
\(956\) 24.7639 0.800923
\(957\) 30.6525 0.990854
\(958\) 6.65248 0.214932
\(959\) −12.4721 −0.402746
\(960\) −11.3262 −0.365553
\(961\) −24.8885 −0.802856
\(962\) 12.0557 0.388692
\(963\) 23.1246 0.745180
\(964\) −10.3820 −0.334381
\(965\) 11.5967 0.373313
\(966\) 13.3262 0.428765
\(967\) 14.0213 0.450894 0.225447 0.974255i \(-0.427616\pi\)
0.225447 + 0.974255i \(0.427616\pi\)
\(968\) −12.4377 −0.399763
\(969\) 34.6525 1.11320
\(970\) −3.00000 −0.0963242
\(971\) 40.7214 1.30681 0.653405 0.757008i \(-0.273340\pi\)
0.653405 + 0.757008i \(0.273340\pi\)
\(972\) 21.6525 0.694503
\(973\) 11.4164 0.365993
\(974\) 25.4164 0.814394
\(975\) −67.9230 −2.17528
\(976\) −13.7082 −0.438789
\(977\) −1.41641 −0.0453149 −0.0226575 0.999743i \(-0.507213\pi\)
−0.0226575 + 0.999743i \(0.507213\pi\)
\(978\) 16.9443 0.541818
\(979\) 18.1803 0.581046
\(980\) 0.618034 0.0197424
\(981\) −37.9787 −1.21257
\(982\) −21.7426 −0.693836
\(983\) 16.0000 0.510321 0.255160 0.966899i \(-0.417872\pi\)
0.255160 + 0.966899i \(0.417872\pi\)
\(984\) 70.2492 2.23946
\(985\) 1.88854 0.0601740
\(986\) −14.4721 −0.460887
\(987\) −3.23607 −0.103005
\(988\) 22.9787 0.731050
\(989\) −29.0557 −0.923918
\(990\) −6.23607 −0.198195
\(991\) 32.0000 1.01651 0.508257 0.861206i \(-0.330290\pi\)
0.508257 + 0.861206i \(0.330290\pi\)
\(992\) −12.3607 −0.392452
\(993\) −58.8328 −1.86700
\(994\) −2.47214 −0.0784114
\(995\) −0.527864 −0.0167344
\(996\) −22.9443 −0.727017
\(997\) 29.9787 0.949435 0.474718 0.880138i \(-0.342550\pi\)
0.474718 + 0.880138i \(0.342550\pi\)
\(998\) −21.8885 −0.692870
\(999\) −4.79837 −0.151814
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 \(a_p\))