Properties

Label 6017.2.a.c.1.15
Level 6017
Weight 2
Character 6017.1
Self dual Yes
Analytic conductor 48.046
Analytic rank 1
Dimension 106
CM No

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Newspace parameters

Level: \( N \) = \( 6017 = 11 \cdot 547 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6017.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0459868962\)
Analytic rank: \(1\)
Dimension: \(106\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 6017.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.32398 q^{2}\) \(-3.12042 q^{3}\) \(+3.40089 q^{4}\) \(+3.91464 q^{5}\) \(+7.25180 q^{6}\) \(-0.989043 q^{7}\) \(-3.25564 q^{8}\) \(+6.73703 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.32398 q^{2}\) \(-3.12042 q^{3}\) \(+3.40089 q^{4}\) \(+3.91464 q^{5}\) \(+7.25180 q^{6}\) \(-0.989043 q^{7}\) \(-3.25564 q^{8}\) \(+6.73703 q^{9}\) \(-9.09756 q^{10}\) \(+1.00000 q^{11}\) \(-10.6122 q^{12}\) \(-5.46513 q^{13}\) \(+2.29852 q^{14}\) \(-12.2153 q^{15}\) \(+0.764273 q^{16}\) \(+2.88434 q^{17}\) \(-15.6567 q^{18}\) \(-4.30630 q^{19}\) \(+13.3133 q^{20}\) \(+3.08623 q^{21}\) \(-2.32398 q^{22}\) \(-7.74043 q^{23}\) \(+10.1590 q^{24}\) \(+10.3244 q^{25}\) \(+12.7009 q^{26}\) \(-11.6611 q^{27}\) \(-3.36363 q^{28}\) \(+0.271701 q^{29}\) \(+28.3882 q^{30}\) \(+10.4398 q^{31}\) \(+4.73513 q^{32}\) \(-3.12042 q^{33}\) \(-6.70315 q^{34}\) \(-3.87175 q^{35}\) \(+22.9119 q^{36}\) \(+7.72811 q^{37}\) \(+10.0078 q^{38}\) \(+17.0535 q^{39}\) \(-12.7447 q^{40}\) \(-0.0770176 q^{41}\) \(-7.17235 q^{42}\) \(-0.563563 q^{43}\) \(+3.40089 q^{44}\) \(+26.3731 q^{45}\) \(+17.9886 q^{46}\) \(-8.68749 q^{47}\) \(-2.38486 q^{48}\) \(-6.02179 q^{49}\) \(-23.9938 q^{50}\) \(-9.00035 q^{51}\) \(-18.5863 q^{52}\) \(+1.79037 q^{53}\) \(+27.1002 q^{54}\) \(+3.91464 q^{55}\) \(+3.21997 q^{56}\) \(+13.4375 q^{57}\) \(-0.631429 q^{58}\) \(+1.90517 q^{59}\) \(-41.5430 q^{60}\) \(-2.52628 q^{61}\) \(-24.2620 q^{62}\) \(-6.66322 q^{63}\) \(-12.5329 q^{64}\) \(-21.3940 q^{65}\) \(+7.25180 q^{66}\) \(+13.7996 q^{67}\) \(+9.80932 q^{68}\) \(+24.1534 q^{69}\) \(+8.99788 q^{70}\) \(-4.88488 q^{71}\) \(-21.9334 q^{72}\) \(+2.95790 q^{73}\) \(-17.9600 q^{74}\) \(-32.2166 q^{75}\) \(-14.6452 q^{76}\) \(-0.989043 q^{77}\) \(-39.6320 q^{78}\) \(+4.88730 q^{79}\) \(+2.99186 q^{80}\) \(+16.1765 q^{81}\) \(+0.178987 q^{82}\) \(-10.2679 q^{83}\) \(+10.4959 q^{84}\) \(+11.2912 q^{85}\) \(+1.30971 q^{86}\) \(-0.847823 q^{87}\) \(-3.25564 q^{88}\) \(+3.31687 q^{89}\) \(-61.2905 q^{90}\) \(+5.40525 q^{91}\) \(-26.3244 q^{92}\) \(-32.5767 q^{93}\) \(+20.1896 q^{94}\) \(-16.8576 q^{95}\) \(-14.7756 q^{96}\) \(-7.85906 q^{97}\) \(+13.9945 q^{98}\) \(+6.73703 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(106q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 66q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(106q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 66q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut -\mathstrut 30q^{10} \) \(\mathstrut +\mathstrut 106q^{11} \) \(\mathstrut -\mathstrut 26q^{12} \) \(\mathstrut -\mathstrut 72q^{13} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut -\mathstrut 46q^{15} \) \(\mathstrut +\mathstrut 75q^{16} \) \(\mathstrut -\mathstrut 65q^{17} \) \(\mathstrut -\mathstrut 37q^{18} \) \(\mathstrut -\mathstrut 63q^{19} \) \(\mathstrut -\mathstrut 25q^{20} \) \(\mathstrut -\mathstrut 27q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut -\mathstrut 23q^{23} \) \(\mathstrut -\mathstrut 56q^{24} \) \(\mathstrut +\mathstrut 74q^{25} \) \(\mathstrut +\mathstrut 2q^{26} \) \(\mathstrut -\mathstrut 54q^{27} \) \(\mathstrut -\mathstrut 115q^{28} \) \(\mathstrut -\mathstrut 45q^{29} \) \(\mathstrut -\mathstrut 14q^{30} \) \(\mathstrut -\mathstrut 89q^{31} \) \(\mathstrut -\mathstrut 96q^{32} \) \(\mathstrut -\mathstrut 15q^{33} \) \(\mathstrut -\mathstrut 26q^{34} \) \(\mathstrut -\mathstrut 52q^{35} \) \(\mathstrut +\mathstrut 91q^{36} \) \(\mathstrut -\mathstrut 35q^{37} \) \(\mathstrut +\mathstrut 7q^{38} \) \(\mathstrut -\mathstrut 34q^{39} \) \(\mathstrut -\mathstrut 74q^{40} \) \(\mathstrut -\mathstrut 32q^{41} \) \(\mathstrut -\mathstrut 94q^{43} \) \(\mathstrut +\mathstrut 93q^{44} \) \(\mathstrut -\mathstrut 46q^{45} \) \(\mathstrut -\mathstrut 20q^{46} \) \(\mathstrut -\mathstrut 105q^{47} \) \(\mathstrut -\mathstrut 57q^{48} \) \(\mathstrut +\mathstrut 80q^{49} \) \(\mathstrut -\mathstrut 60q^{50} \) \(\mathstrut -\mathstrut 36q^{51} \) \(\mathstrut -\mathstrut 137q^{52} \) \(\mathstrut -\mathstrut 61q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 32q^{56} \) \(\mathstrut -\mathstrut 71q^{57} \) \(\mathstrut -\mathstrut 28q^{58} \) \(\mathstrut -\mathstrut 15q^{59} \) \(\mathstrut -\mathstrut 21q^{60} \) \(\mathstrut -\mathstrut 80q^{61} \) \(\mathstrut -\mathstrut 84q^{62} \) \(\mathstrut -\mathstrut 182q^{63} \) \(\mathstrut +\mathstrut 55q^{64} \) \(\mathstrut -\mathstrut 73q^{65} \) \(\mathstrut -\mathstrut 22q^{66} \) \(\mathstrut -\mathstrut 58q^{67} \) \(\mathstrut -\mathstrut 145q^{68} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 39q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut -\mathstrut 100q^{72} \) \(\mathstrut -\mathstrut 155q^{73} \) \(\mathstrut -\mathstrut 15q^{74} \) \(\mathstrut -\mathstrut 15q^{75} \) \(\mathstrut -\mathstrut 132q^{76} \) \(\mathstrut -\mathstrut 66q^{77} \) \(\mathstrut -\mathstrut 45q^{78} \) \(\mathstrut -\mathstrut 50q^{79} \) \(\mathstrut -\mathstrut 28q^{80} \) \(\mathstrut +\mathstrut 114q^{81} \) \(\mathstrut -\mathstrut 57q^{82} \) \(\mathstrut -\mathstrut 96q^{83} \) \(\mathstrut -\mathstrut 27q^{84} \) \(\mathstrut -\mathstrut 74q^{85} \) \(\mathstrut +\mathstrut 54q^{86} \) \(\mathstrut -\mathstrut 182q^{87} \) \(\mathstrut -\mathstrut 39q^{88} \) \(\mathstrut +\mathstrut 9q^{89} \) \(\mathstrut -\mathstrut 53q^{90} \) \(\mathstrut +\mathstrut 6q^{91} \) \(\mathstrut -\mathstrut 18q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut -\mathstrut 33q^{94} \) \(\mathstrut -\mathstrut 49q^{95} \) \(\mathstrut -\mathstrut 56q^{96} \) \(\mathstrut -\mathstrut 102q^{97} \) \(\mathstrut -\mathstrut 76q^{98} \) \(\mathstrut +\mathstrut 97q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.32398 −1.64330 −0.821652 0.569990i \(-0.806947\pi\)
−0.821652 + 0.569990i \(0.806947\pi\)
\(3\) −3.12042 −1.80158 −0.900788 0.434259i \(-0.857010\pi\)
−0.900788 + 0.434259i \(0.857010\pi\)
\(4\) 3.40089 1.70045
\(5\) 3.91464 1.75068 0.875341 0.483507i \(-0.160637\pi\)
0.875341 + 0.483507i \(0.160637\pi\)
\(6\) 7.25180 2.96054
\(7\) −0.989043 −0.373823 −0.186912 0.982377i \(-0.559848\pi\)
−0.186912 + 0.982377i \(0.559848\pi\)
\(8\) −3.25564 −1.15104
\(9\) 6.73703 2.24568
\(10\) −9.09756 −2.87690
\(11\) 1.00000 0.301511
\(12\) −10.6122 −3.06348
\(13\) −5.46513 −1.51575 −0.757877 0.652397i \(-0.773763\pi\)
−0.757877 + 0.652397i \(0.773763\pi\)
\(14\) 2.29852 0.614305
\(15\) −12.2153 −3.15399
\(16\) 0.764273 0.191068
\(17\) 2.88434 0.699555 0.349777 0.936833i \(-0.386257\pi\)
0.349777 + 0.936833i \(0.386257\pi\)
\(18\) −15.6567 −3.69033
\(19\) −4.30630 −0.987932 −0.493966 0.869481i \(-0.664453\pi\)
−0.493966 + 0.869481i \(0.664453\pi\)
\(20\) 13.3133 2.97694
\(21\) 3.08623 0.673471
\(22\) −2.32398 −0.495475
\(23\) −7.74043 −1.61399 −0.806996 0.590557i \(-0.798908\pi\)
−0.806996 + 0.590557i \(0.798908\pi\)
\(24\) 10.1590 2.07369
\(25\) 10.3244 2.06489
\(26\) 12.7009 2.49084
\(27\) −11.6611 −2.24418
\(28\) −3.36363 −0.635666
\(29\) 0.271701 0.0504537 0.0252268 0.999682i \(-0.491969\pi\)
0.0252268 + 0.999682i \(0.491969\pi\)
\(30\) 28.3882 5.18295
\(31\) 10.4398 1.87505 0.937525 0.347918i \(-0.113111\pi\)
0.937525 + 0.347918i \(0.113111\pi\)
\(32\) 4.73513 0.837060
\(33\) −3.12042 −0.543196
\(34\) −6.70315 −1.14958
\(35\) −3.87175 −0.654445
\(36\) 22.9119 3.81865
\(37\) 7.72811 1.27049 0.635247 0.772309i \(-0.280898\pi\)
0.635247 + 0.772309i \(0.280898\pi\)
\(38\) 10.0078 1.62347
\(39\) 17.0535 2.73075
\(40\) −12.7447 −2.01511
\(41\) −0.0770176 −0.0120281 −0.00601406 0.999982i \(-0.501914\pi\)
−0.00601406 + 0.999982i \(0.501914\pi\)
\(42\) −7.17235 −1.10672
\(43\) −0.563563 −0.0859425 −0.0429712 0.999076i \(-0.513682\pi\)
−0.0429712 + 0.999076i \(0.513682\pi\)
\(44\) 3.40089 0.512703
\(45\) 26.3731 3.93147
\(46\) 17.9886 2.65228
\(47\) −8.68749 −1.26720 −0.633601 0.773660i \(-0.718424\pi\)
−0.633601 + 0.773660i \(0.718424\pi\)
\(48\) −2.38486 −0.344224
\(49\) −6.02179 −0.860256
\(50\) −23.9938 −3.39323
\(51\) −9.00035 −1.26030
\(52\) −18.5863 −2.57746
\(53\) 1.79037 0.245926 0.122963 0.992411i \(-0.460760\pi\)
0.122963 + 0.992411i \(0.460760\pi\)
\(54\) 27.1002 3.68787
\(55\) 3.91464 0.527850
\(56\) 3.21997 0.430287
\(57\) 13.4375 1.77984
\(58\) −0.631429 −0.0829107
\(59\) 1.90517 0.248032 0.124016 0.992280i \(-0.460423\pi\)
0.124016 + 0.992280i \(0.460423\pi\)
\(60\) −41.5430 −5.36318
\(61\) −2.52628 −0.323458 −0.161729 0.986835i \(-0.551707\pi\)
−0.161729 + 0.986835i \(0.551707\pi\)
\(62\) −24.2620 −3.08128
\(63\) −6.66322 −0.839486
\(64\) −12.5329 −1.56661
\(65\) −21.3940 −2.65360
\(66\) 7.25180 0.892635
\(67\) 13.7996 1.68589 0.842945 0.538000i \(-0.180820\pi\)
0.842945 + 0.538000i \(0.180820\pi\)
\(68\) 9.80932 1.18955
\(69\) 24.1534 2.90773
\(70\) 8.99788 1.07545
\(71\) −4.88488 −0.579729 −0.289864 0.957068i \(-0.593610\pi\)
−0.289864 + 0.957068i \(0.593610\pi\)
\(72\) −21.9334 −2.58487
\(73\) 2.95790 0.346196 0.173098 0.984905i \(-0.444622\pi\)
0.173098 + 0.984905i \(0.444622\pi\)
\(74\) −17.9600 −2.08781
\(75\) −32.2166 −3.72005
\(76\) −14.6452 −1.67992
\(77\) −0.989043 −0.112712
\(78\) −39.6320 −4.48744
\(79\) 4.88730 0.549864 0.274932 0.961464i \(-0.411345\pi\)
0.274932 + 0.961464i \(0.411345\pi\)
\(80\) 2.99186 0.334500
\(81\) 16.1765 1.79739
\(82\) 0.178987 0.0197659
\(83\) −10.2679 −1.12705 −0.563525 0.826099i \(-0.690555\pi\)
−0.563525 + 0.826099i \(0.690555\pi\)
\(84\) 10.4959 1.14520
\(85\) 11.2912 1.22470
\(86\) 1.30971 0.141230
\(87\) −0.847823 −0.0908962
\(88\) −3.25564 −0.347053
\(89\) 3.31687 0.351587 0.175794 0.984427i \(-0.443751\pi\)
0.175794 + 0.984427i \(0.443751\pi\)
\(90\) −61.2905 −6.46059
\(91\) 5.40525 0.566624
\(92\) −26.3244 −2.74450
\(93\) −32.5767 −3.37805
\(94\) 20.1896 2.08240
\(95\) −16.8576 −1.72955
\(96\) −14.7756 −1.50803
\(97\) −7.85906 −0.797966 −0.398983 0.916958i \(-0.630637\pi\)
−0.398983 + 0.916958i \(0.630637\pi\)
\(98\) 13.9945 1.41366
\(99\) 6.73703 0.677097
\(100\) 35.1122 3.51122
\(101\) −9.28820 −0.924210 −0.462105 0.886825i \(-0.652906\pi\)
−0.462105 + 0.886825i \(0.652906\pi\)
\(102\) 20.9167 2.07106
\(103\) −13.3614 −1.31654 −0.658270 0.752782i \(-0.728711\pi\)
−0.658270 + 0.752782i \(0.728711\pi\)
\(104\) 17.7925 1.74470
\(105\) 12.0815 1.17903
\(106\) −4.16078 −0.404130
\(107\) −5.85554 −0.566076 −0.283038 0.959109i \(-0.591342\pi\)
−0.283038 + 0.959109i \(0.591342\pi\)
\(108\) −39.6582 −3.81611
\(109\) 18.7078 1.79189 0.895943 0.444168i \(-0.146501\pi\)
0.895943 + 0.444168i \(0.146501\pi\)
\(110\) −9.09756 −0.867418
\(111\) −24.1150 −2.28889
\(112\) −0.755899 −0.0714258
\(113\) 18.5240 1.74259 0.871295 0.490759i \(-0.163281\pi\)
0.871295 + 0.490759i \(0.163281\pi\)
\(114\) −31.2284 −2.92481
\(115\) −30.3010 −2.82559
\(116\) 0.924027 0.0857937
\(117\) −36.8187 −3.40389
\(118\) −4.42759 −0.407592
\(119\) −2.85274 −0.261510
\(120\) 39.7688 3.63038
\(121\) 1.00000 0.0909091
\(122\) 5.87104 0.531539
\(123\) 0.240327 0.0216696
\(124\) 35.5047 3.18842
\(125\) 20.8432 1.86427
\(126\) 15.4852 1.37953
\(127\) −12.5205 −1.11101 −0.555506 0.831512i \(-0.687476\pi\)
−0.555506 + 0.831512i \(0.687476\pi\)
\(128\) 19.6560 1.73736
\(129\) 1.75855 0.154832
\(130\) 49.7193 4.36067
\(131\) 16.4051 1.43332 0.716661 0.697422i \(-0.245669\pi\)
0.716661 + 0.697422i \(0.245669\pi\)
\(132\) −10.6122 −0.923674
\(133\) 4.25911 0.369312
\(134\) −32.0700 −2.77043
\(135\) −45.6491 −3.92885
\(136\) −9.39037 −0.805218
\(137\) 6.54882 0.559503 0.279752 0.960072i \(-0.409748\pi\)
0.279752 + 0.960072i \(0.409748\pi\)
\(138\) −56.1321 −4.77828
\(139\) −14.7493 −1.25102 −0.625509 0.780217i \(-0.715109\pi\)
−0.625509 + 0.780217i \(0.715109\pi\)
\(140\) −13.1674 −1.11285
\(141\) 27.1086 2.28296
\(142\) 11.3524 0.952670
\(143\) −5.46513 −0.457017
\(144\) 5.14893 0.429078
\(145\) 1.06361 0.0883283
\(146\) −6.87411 −0.568905
\(147\) 18.7905 1.54982
\(148\) 26.2825 2.16040
\(149\) −20.8605 −1.70896 −0.854478 0.519487i \(-0.826123\pi\)
−0.854478 + 0.519487i \(0.826123\pi\)
\(150\) 74.8707 6.11317
\(151\) 8.79515 0.715739 0.357870 0.933772i \(-0.383503\pi\)
0.357870 + 0.933772i \(0.383503\pi\)
\(152\) 14.0198 1.13715
\(153\) 19.4319 1.57097
\(154\) 2.29852 0.185220
\(155\) 40.8682 3.28261
\(156\) 57.9971 4.64348
\(157\) 0.853945 0.0681522 0.0340761 0.999419i \(-0.489151\pi\)
0.0340761 + 0.999419i \(0.489151\pi\)
\(158\) −11.3580 −0.903594
\(159\) −5.58669 −0.443054
\(160\) 18.5363 1.46543
\(161\) 7.65562 0.603348
\(162\) −37.5939 −2.95365
\(163\) −16.8640 −1.32089 −0.660445 0.750875i \(-0.729632\pi\)
−0.660445 + 0.750875i \(0.729632\pi\)
\(164\) −0.261928 −0.0204532
\(165\) −12.2153 −0.950963
\(166\) 23.8624 1.85208
\(167\) −5.35048 −0.414032 −0.207016 0.978338i \(-0.566375\pi\)
−0.207016 + 0.978338i \(0.566375\pi\)
\(168\) −10.0477 −0.775195
\(169\) 16.8676 1.29751
\(170\) −26.2404 −2.01255
\(171\) −29.0117 −2.21858
\(172\) −1.91661 −0.146140
\(173\) −17.5815 −1.33670 −0.668350 0.743847i \(-0.732999\pi\)
−0.668350 + 0.743847i \(0.732999\pi\)
\(174\) 1.97033 0.149370
\(175\) −10.2113 −0.771902
\(176\) 0.764273 0.0576093
\(177\) −5.94494 −0.446849
\(178\) −7.70834 −0.577764
\(179\) 8.33719 0.623151 0.311576 0.950221i \(-0.399143\pi\)
0.311576 + 0.950221i \(0.399143\pi\)
\(180\) 89.6919 6.68524
\(181\) −10.0813 −0.749340 −0.374670 0.927158i \(-0.622244\pi\)
−0.374670 + 0.927158i \(0.622244\pi\)
\(182\) −12.5617 −0.931135
\(183\) 7.88307 0.582734
\(184\) 25.2001 1.85777
\(185\) 30.2528 2.22423
\(186\) 75.7076 5.55115
\(187\) 2.88434 0.210924
\(188\) −29.5452 −2.15481
\(189\) 11.5333 0.838928
\(190\) 39.1768 2.84218
\(191\) 3.91318 0.283148 0.141574 0.989928i \(-0.454784\pi\)
0.141574 + 0.989928i \(0.454784\pi\)
\(192\) 39.1079 2.82237
\(193\) −13.2973 −0.957162 −0.478581 0.878043i \(-0.658849\pi\)
−0.478581 + 0.878043i \(0.658849\pi\)
\(194\) 18.2643 1.31130
\(195\) 66.7584 4.78067
\(196\) −20.4795 −1.46282
\(197\) −8.35699 −0.595411 −0.297705 0.954658i \(-0.596221\pi\)
−0.297705 + 0.954658i \(0.596221\pi\)
\(198\) −15.6567 −1.11268
\(199\) 18.0808 1.28171 0.640855 0.767662i \(-0.278580\pi\)
0.640855 + 0.767662i \(0.278580\pi\)
\(200\) −33.6126 −2.37677
\(201\) −43.0606 −3.03726
\(202\) 21.5856 1.51876
\(203\) −0.268725 −0.0188608
\(204\) −30.6092 −2.14307
\(205\) −0.301496 −0.0210574
\(206\) 31.0517 2.16347
\(207\) −52.1475 −3.62450
\(208\) −4.17685 −0.289613
\(209\) −4.30630 −0.297873
\(210\) −28.0772 −1.93751
\(211\) 4.83386 0.332776 0.166388 0.986060i \(-0.446790\pi\)
0.166388 + 0.986060i \(0.446790\pi\)
\(212\) 6.08884 0.418183
\(213\) 15.2429 1.04443
\(214\) 13.6082 0.930235
\(215\) −2.20615 −0.150458
\(216\) 37.9644 2.58315
\(217\) −10.3255 −0.700937
\(218\) −43.4767 −2.94461
\(219\) −9.22990 −0.623699
\(220\) 13.3133 0.897580
\(221\) −15.7633 −1.06035
\(222\) 56.0427 3.76134
\(223\) −3.64940 −0.244382 −0.122191 0.992507i \(-0.538992\pi\)
−0.122191 + 0.992507i \(0.538992\pi\)
\(224\) −4.68325 −0.312913
\(225\) 69.5560 4.63707
\(226\) −43.0494 −2.86360
\(227\) 11.3474 0.753156 0.376578 0.926385i \(-0.377101\pi\)
0.376578 + 0.926385i \(0.377101\pi\)
\(228\) 45.6993 3.02651
\(229\) 10.0950 0.667095 0.333548 0.942733i \(-0.391754\pi\)
0.333548 + 0.942733i \(0.391754\pi\)
\(230\) 70.4190 4.64329
\(231\) 3.08623 0.203059
\(232\) −0.884563 −0.0580744
\(233\) 3.27832 0.214770 0.107385 0.994218i \(-0.465752\pi\)
0.107385 + 0.994218i \(0.465752\pi\)
\(234\) 85.5661 5.59363
\(235\) −34.0084 −2.21847
\(236\) 6.47928 0.421765
\(237\) −15.2504 −0.990623
\(238\) 6.62971 0.429740
\(239\) 30.5312 1.97490 0.987449 0.157940i \(-0.0504852\pi\)
0.987449 + 0.157940i \(0.0504852\pi\)
\(240\) −9.33585 −0.602627
\(241\) −0.511349 −0.0329389 −0.0164694 0.999864i \(-0.505243\pi\)
−0.0164694 + 0.999864i \(0.505243\pi\)
\(242\) −2.32398 −0.149391
\(243\) −15.4942 −0.993951
\(244\) −8.59162 −0.550022
\(245\) −23.5732 −1.50603
\(246\) −0.558516 −0.0356097
\(247\) 23.5345 1.49746
\(248\) −33.9884 −2.15826
\(249\) 32.0402 2.03047
\(250\) −48.4393 −3.06357
\(251\) −7.72835 −0.487809 −0.243905 0.969799i \(-0.578428\pi\)
−0.243905 + 0.969799i \(0.578428\pi\)
\(252\) −22.6609 −1.42750
\(253\) −7.74043 −0.486637
\(254\) 29.0974 1.82573
\(255\) −35.2332 −2.20639
\(256\) −20.6143 −1.28839
\(257\) −0.877666 −0.0547473 −0.0273737 0.999625i \(-0.508714\pi\)
−0.0273737 + 0.999625i \(0.508714\pi\)
\(258\) −4.08684 −0.254436
\(259\) −7.64344 −0.474940
\(260\) −72.7587 −4.51231
\(261\) 1.83046 0.113303
\(262\) −38.1252 −2.35538
\(263\) 0.120138 0.00740801 0.00370400 0.999993i \(-0.498821\pi\)
0.00370400 + 0.999993i \(0.498821\pi\)
\(264\) 10.1590 0.625242
\(265\) 7.00864 0.430537
\(266\) −9.89810 −0.606892
\(267\) −10.3500 −0.633411
\(268\) 46.9309 2.86676
\(269\) 10.7429 0.655005 0.327503 0.944850i \(-0.393793\pi\)
0.327503 + 0.944850i \(0.393793\pi\)
\(270\) 106.088 6.45629
\(271\) −21.3912 −1.29942 −0.649711 0.760182i \(-0.725110\pi\)
−0.649711 + 0.760182i \(0.725110\pi\)
\(272\) 2.20442 0.133663
\(273\) −16.8667 −1.02082
\(274\) −15.2193 −0.919434
\(275\) 10.3244 0.622586
\(276\) 82.1431 4.94443
\(277\) 31.0245 1.86408 0.932042 0.362351i \(-0.118026\pi\)
0.932042 + 0.362351i \(0.118026\pi\)
\(278\) 34.2771 2.05580
\(279\) 70.3335 4.21076
\(280\) 12.6050 0.753295
\(281\) −7.99646 −0.477029 −0.238514 0.971139i \(-0.576660\pi\)
−0.238514 + 0.971139i \(0.576660\pi\)
\(282\) −63.0000 −3.75159
\(283\) −22.0007 −1.30781 −0.653903 0.756578i \(-0.726870\pi\)
−0.653903 + 0.756578i \(0.726870\pi\)
\(284\) −16.6129 −0.985797
\(285\) 52.6029 3.11592
\(286\) 12.7009 0.751018
\(287\) 0.0761737 0.00449639
\(288\) 31.9007 1.87977
\(289\) −8.68059 −0.510623
\(290\) −2.47182 −0.145150
\(291\) 24.5236 1.43760
\(292\) 10.0595 0.588688
\(293\) −21.7929 −1.27315 −0.636577 0.771214i \(-0.719650\pi\)
−0.636577 + 0.771214i \(0.719650\pi\)
\(294\) −43.6689 −2.54682
\(295\) 7.45807 0.434226
\(296\) −25.1600 −1.46239
\(297\) −11.6611 −0.676646
\(298\) 48.4794 2.80833
\(299\) 42.3025 2.44641
\(300\) −109.565 −6.32574
\(301\) 0.557388 0.0321273
\(302\) −20.4398 −1.17618
\(303\) 28.9831 1.66504
\(304\) −3.29119 −0.188763
\(305\) −9.88950 −0.566271
\(306\) −45.1593 −2.58159
\(307\) 12.4051 0.707998 0.353999 0.935246i \(-0.384822\pi\)
0.353999 + 0.935246i \(0.384822\pi\)
\(308\) −3.36363 −0.191660
\(309\) 41.6933 2.37185
\(310\) −94.9770 −5.39433
\(311\) −24.0234 −1.36224 −0.681121 0.732171i \(-0.738507\pi\)
−0.681121 + 0.732171i \(0.738507\pi\)
\(312\) −55.5201 −3.14321
\(313\) −34.6386 −1.95789 −0.978944 0.204129i \(-0.934564\pi\)
−0.978944 + 0.204129i \(0.934564\pi\)
\(314\) −1.98455 −0.111995
\(315\) −26.0841 −1.46967
\(316\) 16.6212 0.935014
\(317\) 26.3736 1.48129 0.740645 0.671897i \(-0.234520\pi\)
0.740645 + 0.671897i \(0.234520\pi\)
\(318\) 12.9834 0.728071
\(319\) 0.271701 0.0152124
\(320\) −49.0618 −2.74264
\(321\) 18.2718 1.01983
\(322\) −17.7915 −0.991483
\(323\) −12.4208 −0.691113
\(324\) 55.0145 3.05636
\(325\) −56.4243 −3.12986
\(326\) 39.1916 2.17062
\(327\) −58.3764 −3.22822
\(328\) 0.250742 0.0138449
\(329\) 8.59231 0.473709
\(330\) 28.3882 1.56272
\(331\) 2.15727 0.118574 0.0592872 0.998241i \(-0.481117\pi\)
0.0592872 + 0.998241i \(0.481117\pi\)
\(332\) −34.9200 −1.91649
\(333\) 52.0645 2.85312
\(334\) 12.4344 0.680381
\(335\) 54.0205 2.95146
\(336\) 2.35873 0.128679
\(337\) −30.3746 −1.65461 −0.827304 0.561755i \(-0.810126\pi\)
−0.827304 + 0.561755i \(0.810126\pi\)
\(338\) −39.2001 −2.13220
\(339\) −57.8027 −3.13941
\(340\) 38.4000 2.08253
\(341\) 10.4398 0.565349
\(342\) 67.4225 3.64579
\(343\) 12.8791 0.695407
\(344\) 1.83476 0.0989236
\(345\) 94.5520 5.09051
\(346\) 40.8592 2.19660
\(347\) −13.2719 −0.712472 −0.356236 0.934396i \(-0.615940\pi\)
−0.356236 + 0.934396i \(0.615940\pi\)
\(348\) −2.88335 −0.154564
\(349\) 25.8817 1.38542 0.692708 0.721218i \(-0.256417\pi\)
0.692708 + 0.721218i \(0.256417\pi\)
\(350\) 23.7309 1.26847
\(351\) 63.7295 3.40163
\(352\) 4.73513 0.252383
\(353\) −7.14649 −0.380369 −0.190185 0.981748i \(-0.560909\pi\)
−0.190185 + 0.981748i \(0.560909\pi\)
\(354\) 13.8159 0.734309
\(355\) −19.1226 −1.01492
\(356\) 11.2803 0.597855
\(357\) 8.90174 0.471130
\(358\) −19.3755 −1.02403
\(359\) −22.8912 −1.20815 −0.604075 0.796928i \(-0.706457\pi\)
−0.604075 + 0.796928i \(0.706457\pi\)
\(360\) −85.8613 −4.52529
\(361\) −0.455812 −0.0239901
\(362\) 23.4289 1.23139
\(363\) −3.12042 −0.163780
\(364\) 18.3827 0.963513
\(365\) 11.5791 0.606079
\(366\) −18.3201 −0.957608
\(367\) −31.5802 −1.64847 −0.824236 0.566246i \(-0.808395\pi\)
−0.824236 + 0.566246i \(0.808395\pi\)
\(368\) −5.91581 −0.308383
\(369\) −0.518870 −0.0270113
\(370\) −70.3069 −3.65508
\(371\) −1.77075 −0.0919327
\(372\) −110.790 −5.74418
\(373\) 8.13353 0.421138 0.210569 0.977579i \(-0.432468\pi\)
0.210569 + 0.977579i \(0.432468\pi\)
\(374\) −6.70315 −0.346612
\(375\) −65.0396 −3.35863
\(376\) 28.2834 1.45860
\(377\) −1.48488 −0.0764754
\(378\) −26.8033 −1.37861
\(379\) 9.60766 0.493512 0.246756 0.969078i \(-0.420635\pi\)
0.246756 + 0.969078i \(0.420635\pi\)
\(380\) −57.3309 −2.94101
\(381\) 39.0692 2.00157
\(382\) −9.09416 −0.465298
\(383\) 26.9494 1.37705 0.688525 0.725212i \(-0.258258\pi\)
0.688525 + 0.725212i \(0.258258\pi\)
\(384\) −61.3349 −3.12998
\(385\) −3.87175 −0.197323
\(386\) 30.9027 1.57291
\(387\) −3.79674 −0.192999
\(388\) −26.7278 −1.35690
\(389\) 1.85321 0.0939616 0.0469808 0.998896i \(-0.485040\pi\)
0.0469808 + 0.998896i \(0.485040\pi\)
\(390\) −155.145 −7.85609
\(391\) −22.3260 −1.12908
\(392\) 19.6048 0.990192
\(393\) −51.1909 −2.58224
\(394\) 19.4215 0.978441
\(395\) 19.1320 0.962637
\(396\) 22.9119 1.15137
\(397\) 29.8357 1.49741 0.748706 0.662902i \(-0.230675\pi\)
0.748706 + 0.662902i \(0.230675\pi\)
\(398\) −42.0193 −2.10624
\(399\) −13.2902 −0.665344
\(400\) 7.89068 0.394534
\(401\) 7.20686 0.359894 0.179947 0.983676i \(-0.442407\pi\)
0.179947 + 0.983676i \(0.442407\pi\)
\(402\) 100.072 4.99114
\(403\) −57.0551 −2.84211
\(404\) −31.5881 −1.57157
\(405\) 63.3252 3.14666
\(406\) 0.624511 0.0309940
\(407\) 7.72811 0.383068
\(408\) 29.3019 1.45066
\(409\) −29.8441 −1.47569 −0.737847 0.674968i \(-0.764157\pi\)
−0.737847 + 0.674968i \(0.764157\pi\)
\(410\) 0.700672 0.0346037
\(411\) −20.4351 −1.00799
\(412\) −45.4407 −2.23870
\(413\) −1.88430 −0.0927203
\(414\) 121.190 5.95616
\(415\) −40.1952 −1.97311
\(416\) −25.8781 −1.26878
\(417\) 46.0240 2.25380
\(418\) 10.0078 0.489495
\(419\) −27.4342 −1.34025 −0.670125 0.742248i \(-0.733760\pi\)
−0.670125 + 0.742248i \(0.733760\pi\)
\(420\) 41.0878 2.00488
\(421\) −19.1594 −0.933770 −0.466885 0.884318i \(-0.654624\pi\)
−0.466885 + 0.884318i \(0.654624\pi\)
\(422\) −11.2338 −0.546853
\(423\) −58.5279 −2.84572
\(424\) −5.82879 −0.283071
\(425\) 29.7791 1.44450
\(426\) −35.4242 −1.71631
\(427\) 2.49861 0.120916
\(428\) −19.9140 −0.962582
\(429\) 17.0535 0.823351
\(430\) 5.12704 0.247248
\(431\) 5.18554 0.249779 0.124889 0.992171i \(-0.460142\pi\)
0.124889 + 0.992171i \(0.460142\pi\)
\(432\) −8.91228 −0.428792
\(433\) −9.97758 −0.479492 −0.239746 0.970836i \(-0.577064\pi\)
−0.239746 + 0.970836i \(0.577064\pi\)
\(434\) 23.9962 1.15185
\(435\) −3.31892 −0.159130
\(436\) 63.6233 3.04700
\(437\) 33.3326 1.59451
\(438\) 21.4501 1.02493
\(439\) −6.52581 −0.311460 −0.155730 0.987800i \(-0.549773\pi\)
−0.155730 + 0.987800i \(0.549773\pi\)
\(440\) −12.7447 −0.607579
\(441\) −40.5690 −1.93186
\(442\) 36.6336 1.74248
\(443\) 2.91342 0.138421 0.0692104 0.997602i \(-0.477952\pi\)
0.0692104 + 0.997602i \(0.477952\pi\)
\(444\) −82.0123 −3.89213
\(445\) 12.9843 0.615517
\(446\) 8.48113 0.401593
\(447\) 65.0935 3.07882
\(448\) 12.3956 0.585636
\(449\) 39.0106 1.84102 0.920512 0.390715i \(-0.127772\pi\)
0.920512 + 0.390715i \(0.127772\pi\)
\(450\) −161.647 −7.62010
\(451\) −0.0770176 −0.00362662
\(452\) 62.9981 2.96318
\(453\) −27.4446 −1.28946
\(454\) −26.3712 −1.23766
\(455\) 21.1596 0.991978
\(456\) −43.7476 −2.04867
\(457\) −12.5891 −0.588891 −0.294446 0.955668i \(-0.595135\pi\)
−0.294446 + 0.955668i \(0.595135\pi\)
\(458\) −23.4606 −1.09624
\(459\) −33.6346 −1.56993
\(460\) −103.050 −4.80475
\(461\) 6.64598 0.309534 0.154767 0.987951i \(-0.450537\pi\)
0.154767 + 0.987951i \(0.450537\pi\)
\(462\) −7.17235 −0.333688
\(463\) −13.7760 −0.640225 −0.320113 0.947379i \(-0.603721\pi\)
−0.320113 + 0.947379i \(0.603721\pi\)
\(464\) 0.207654 0.00964010
\(465\) −127.526 −5.91388
\(466\) −7.61876 −0.352932
\(467\) 29.5667 1.36818 0.684092 0.729396i \(-0.260199\pi\)
0.684092 + 0.729396i \(0.260199\pi\)
\(468\) −125.217 −5.78814
\(469\) −13.6484 −0.630225
\(470\) 79.0350 3.64561
\(471\) −2.66467 −0.122781
\(472\) −6.20256 −0.285496
\(473\) −0.563563 −0.0259126
\(474\) 35.4417 1.62789
\(475\) −44.4600 −2.03997
\(476\) −9.70184 −0.444683
\(477\) 12.0617 0.552269
\(478\) −70.9539 −3.24536
\(479\) −17.0721 −0.780046 −0.390023 0.920805i \(-0.627533\pi\)
−0.390023 + 0.920805i \(0.627533\pi\)
\(480\) −57.8412 −2.64008
\(481\) −42.2351 −1.92576
\(482\) 1.18836 0.0541285
\(483\) −23.8888 −1.08698
\(484\) 3.40089 0.154586
\(485\) −30.7654 −1.39698
\(486\) 36.0081 1.63336
\(487\) 31.4032 1.42301 0.711507 0.702679i \(-0.248013\pi\)
0.711507 + 0.702679i \(0.248013\pi\)
\(488\) 8.22468 0.372314
\(489\) 52.6227 2.37968
\(490\) 54.7836 2.47487
\(491\) −27.5209 −1.24200 −0.621000 0.783810i \(-0.713273\pi\)
−0.621000 + 0.783810i \(0.713273\pi\)
\(492\) 0.817327 0.0368479
\(493\) 0.783679 0.0352951
\(494\) −54.6937 −2.46078
\(495\) 26.3731 1.18538
\(496\) 7.97889 0.358263
\(497\) 4.83136 0.216716
\(498\) −74.4609 −3.33667
\(499\) 5.11144 0.228819 0.114410 0.993434i \(-0.463502\pi\)
0.114410 + 0.993434i \(0.463502\pi\)
\(500\) 70.8855 3.17010
\(501\) 16.6957 0.745911
\(502\) 17.9606 0.801619
\(503\) −4.40334 −0.196335 −0.0981676 0.995170i \(-0.531298\pi\)
−0.0981676 + 0.995170i \(0.531298\pi\)
\(504\) 21.6931 0.966285
\(505\) −36.3600 −1.61800
\(506\) 17.9886 0.799692
\(507\) −52.6341 −2.33756
\(508\) −42.5808 −1.88922
\(509\) −5.18003 −0.229601 −0.114800 0.993389i \(-0.536623\pi\)
−0.114800 + 0.993389i \(0.536623\pi\)
\(510\) 81.8812 3.62576
\(511\) −2.92549 −0.129416
\(512\) 8.59533 0.379864
\(513\) 50.2162 2.21710
\(514\) 2.03968 0.0899665
\(515\) −52.3052 −2.30484
\(516\) 5.98065 0.263283
\(517\) −8.68749 −0.382076
\(518\) 17.7632 0.780471
\(519\) 54.8618 2.40817
\(520\) 69.6513 3.05441
\(521\) 37.4812 1.64208 0.821041 0.570869i \(-0.193394\pi\)
0.821041 + 0.570869i \(0.193394\pi\)
\(522\) −4.25396 −0.186191
\(523\) 15.4728 0.676578 0.338289 0.941042i \(-0.390152\pi\)
0.338289 + 0.941042i \(0.390152\pi\)
\(524\) 55.7920 2.43729
\(525\) 31.8636 1.39064
\(526\) −0.279198 −0.0121736
\(527\) 30.1120 1.31170
\(528\) −2.38486 −0.103787
\(529\) 36.9143 1.60497
\(530\) −16.2879 −0.707503
\(531\) 12.8352 0.557001
\(532\) 14.4848 0.627995
\(533\) 0.420911 0.0182317
\(534\) 24.0533 1.04089
\(535\) −22.9223 −0.991019
\(536\) −44.9266 −1.94053
\(537\) −26.0156 −1.12265
\(538\) −24.9663 −1.07637
\(539\) −6.02179 −0.259377
\(540\) −155.248 −6.68079
\(541\) −33.1585 −1.42560 −0.712799 0.701369i \(-0.752573\pi\)
−0.712799 + 0.701369i \(0.752573\pi\)
\(542\) 49.7127 2.13534
\(543\) 31.4580 1.34999
\(544\) 13.6577 0.585570
\(545\) 73.2345 3.13702
\(546\) 39.1978 1.67751
\(547\) 1.00000 0.0427569
\(548\) 22.2718 0.951405
\(549\) −17.0197 −0.726381
\(550\) −23.9938 −1.02310
\(551\) −1.17003 −0.0498448
\(552\) −78.6349 −3.34692
\(553\) −4.83375 −0.205552
\(554\) −72.1004 −3.06325
\(555\) −94.4015 −4.00712
\(556\) −50.1607 −2.12729
\(557\) 10.1001 0.427954 0.213977 0.976839i \(-0.431358\pi\)
0.213977 + 0.976839i \(0.431358\pi\)
\(558\) −163.454 −6.91955
\(559\) 3.07994 0.130268
\(560\) −2.95908 −0.125044
\(561\) −9.00035 −0.379995
\(562\) 18.5836 0.783903
\(563\) 13.2203 0.557168 0.278584 0.960412i \(-0.410135\pi\)
0.278584 + 0.960412i \(0.410135\pi\)
\(564\) 92.1935 3.88205
\(565\) 72.5148 3.05072
\(566\) 51.1293 2.14912
\(567\) −15.9993 −0.671906
\(568\) 15.9034 0.667293
\(569\) −33.1591 −1.39010 −0.695050 0.718961i \(-0.744618\pi\)
−0.695050 + 0.718961i \(0.744618\pi\)
\(570\) −122.248 −5.12041
\(571\) −4.12183 −0.172493 −0.0862466 0.996274i \(-0.527487\pi\)
−0.0862466 + 0.996274i \(0.527487\pi\)
\(572\) −18.5863 −0.777132
\(573\) −12.2108 −0.510112
\(574\) −0.177026 −0.00738894
\(575\) −79.9155 −3.33271
\(576\) −84.4345 −3.51811
\(577\) 12.9288 0.538232 0.269116 0.963108i \(-0.413268\pi\)
0.269116 + 0.963108i \(0.413268\pi\)
\(578\) 20.1735 0.839109
\(579\) 41.4932 1.72440
\(580\) 3.61723 0.150197
\(581\) 10.1554 0.421317
\(582\) −56.9923 −2.36241
\(583\) 1.79037 0.0741493
\(584\) −9.62987 −0.398487
\(585\) −144.132 −5.95913
\(586\) 50.6462 2.09218
\(587\) 2.70196 0.111522 0.0557609 0.998444i \(-0.482242\pi\)
0.0557609 + 0.998444i \(0.482242\pi\)
\(588\) 63.9045 2.63538
\(589\) −44.9570 −1.85242
\(590\) −17.3324 −0.713564
\(591\) 26.0773 1.07268
\(592\) 5.90639 0.242751
\(593\) 2.24776 0.0923043 0.0461521 0.998934i \(-0.485304\pi\)
0.0461521 + 0.998934i \(0.485304\pi\)
\(594\) 27.1002 1.11194
\(595\) −11.1674 −0.457820
\(596\) −70.9442 −2.90599
\(597\) −56.4196 −2.30910
\(598\) −98.3101 −4.02020
\(599\) −39.3969 −1.60971 −0.804856 0.593470i \(-0.797758\pi\)
−0.804856 + 0.593470i \(0.797758\pi\)
\(600\) 104.886 4.28194
\(601\) −46.1784 −1.88366 −0.941828 0.336095i \(-0.890894\pi\)
−0.941828 + 0.336095i \(0.890894\pi\)
\(602\) −1.29536 −0.0527949
\(603\) 92.9684 3.78596
\(604\) 29.9113 1.21708
\(605\) 3.91464 0.159153
\(606\) −67.3562 −2.73616
\(607\) −35.5472 −1.44282 −0.721408 0.692510i \(-0.756505\pi\)
−0.721408 + 0.692510i \(0.756505\pi\)
\(608\) −20.3909 −0.826959
\(609\) 0.838534 0.0339791
\(610\) 22.9830 0.930555
\(611\) 47.4783 1.92077
\(612\) 66.0857 2.67136
\(613\) 29.3972 1.18734 0.593672 0.804707i \(-0.297678\pi\)
0.593672 + 0.804707i \(0.297678\pi\)
\(614\) −28.8293 −1.16346
\(615\) 0.940796 0.0379365
\(616\) 3.21997 0.129736
\(617\) −26.7220 −1.07579 −0.537894 0.843012i \(-0.680780\pi\)
−0.537894 + 0.843012i \(0.680780\pi\)
\(618\) −96.8944 −3.89766
\(619\) −37.3098 −1.49961 −0.749803 0.661661i \(-0.769852\pi\)
−0.749803 + 0.661661i \(0.769852\pi\)
\(620\) 138.988 5.58191
\(621\) 90.2621 3.62209
\(622\) 55.8300 2.23858
\(623\) −3.28052 −0.131431
\(624\) 13.0335 0.521759
\(625\) 29.9716 1.19887
\(626\) 80.4994 3.21740
\(627\) 13.4375 0.536640
\(628\) 2.90417 0.115889
\(629\) 22.2905 0.888780
\(630\) 60.6190 2.41512
\(631\) 17.8482 0.710526 0.355263 0.934766i \(-0.384391\pi\)
0.355263 + 0.934766i \(0.384391\pi\)
\(632\) −15.9113 −0.632918
\(633\) −15.0837 −0.599522
\(634\) −61.2918 −2.43421
\(635\) −49.0132 −1.94503
\(636\) −18.9997 −0.753388
\(637\) 32.9099 1.30394
\(638\) −0.631429 −0.0249985
\(639\) −32.9096 −1.30188
\(640\) 76.9461 3.04156
\(641\) −1.39722 −0.0551867 −0.0275934 0.999619i \(-0.508784\pi\)
−0.0275934 + 0.999619i \(0.508784\pi\)
\(642\) −42.4632 −1.67589
\(643\) 20.7995 0.820251 0.410126 0.912029i \(-0.365485\pi\)
0.410126 + 0.912029i \(0.365485\pi\)
\(644\) 26.0359 1.02596
\(645\) 6.88411 0.271061
\(646\) 28.8657 1.13571
\(647\) −22.4543 −0.882770 −0.441385 0.897318i \(-0.645513\pi\)
−0.441385 + 0.897318i \(0.645513\pi\)
\(648\) −52.6649 −2.06887
\(649\) 1.90517 0.0747846
\(650\) 131.129 5.14331
\(651\) 32.2198 1.26279
\(652\) −57.3526 −2.24610
\(653\) 16.1770 0.633056 0.316528 0.948583i \(-0.397483\pi\)
0.316528 + 0.948583i \(0.397483\pi\)
\(654\) 135.666 5.30494
\(655\) 64.2202 2.50929
\(656\) −0.0588625 −0.00229819
\(657\) 19.9275 0.777445
\(658\) −19.9684 −0.778448
\(659\) −18.0432 −0.702862 −0.351431 0.936214i \(-0.614305\pi\)
−0.351431 + 0.936214i \(0.614305\pi\)
\(660\) −41.5430 −1.61706
\(661\) −24.3431 −0.946839 −0.473419 0.880837i \(-0.656980\pi\)
−0.473419 + 0.880837i \(0.656980\pi\)
\(662\) −5.01346 −0.194854
\(663\) 49.1881 1.91031
\(664\) 33.4287 1.29728
\(665\) 16.6729 0.646548
\(666\) −120.997 −4.68854
\(667\) −2.10309 −0.0814318
\(668\) −18.1964 −0.704039
\(669\) 11.3877 0.440272
\(670\) −125.543 −4.85014
\(671\) −2.52628 −0.0975261
\(672\) 14.6137 0.563736
\(673\) −23.5376 −0.907307 −0.453653 0.891178i \(-0.649880\pi\)
−0.453653 + 0.891178i \(0.649880\pi\)
\(674\) 70.5899 2.71902
\(675\) −120.394 −4.63398
\(676\) 57.3650 2.20635
\(677\) 23.1229 0.888687 0.444343 0.895857i \(-0.353437\pi\)
0.444343 + 0.895857i \(0.353437\pi\)
\(678\) 134.332 5.15900
\(679\) 7.77295 0.298298
\(680\) −36.7600 −1.40968
\(681\) −35.4088 −1.35687
\(682\) −24.2620 −0.929039
\(683\) −20.5893 −0.787828 −0.393914 0.919147i \(-0.628879\pi\)
−0.393914 + 0.919147i \(0.628879\pi\)
\(684\) −98.6654 −3.77257
\(685\) 25.6363 0.979512
\(686\) −29.9308 −1.14276
\(687\) −31.5006 −1.20182
\(688\) −0.430716 −0.0164209
\(689\) −9.78458 −0.372763
\(690\) −219.737 −8.36525
\(691\) 18.2539 0.694412 0.347206 0.937789i \(-0.387130\pi\)
0.347206 + 0.937789i \(0.387130\pi\)
\(692\) −59.7929 −2.27299
\(693\) −6.66322 −0.253115
\(694\) 30.8436 1.17081
\(695\) −57.7382 −2.19013
\(696\) 2.76021 0.104625
\(697\) −0.222145 −0.00841433
\(698\) −60.1486 −2.27666
\(699\) −10.2298 −0.386925
\(700\) −34.7275 −1.31258
\(701\) 10.1841 0.384650 0.192325 0.981331i \(-0.438397\pi\)
0.192325 + 0.981331i \(0.438397\pi\)
\(702\) −148.106 −5.58991
\(703\) −33.2795 −1.25516
\(704\) −12.5329 −0.472351
\(705\) 106.121 3.99673
\(706\) 16.6083 0.625062
\(707\) 9.18643 0.345491
\(708\) −20.2181 −0.759843
\(709\) −36.9445 −1.38748 −0.693739 0.720226i \(-0.744038\pi\)
−0.693739 + 0.720226i \(0.744038\pi\)
\(710\) 44.4405 1.66782
\(711\) 32.9259 1.23482
\(712\) −10.7985 −0.404692
\(713\) −80.8089 −3.02632
\(714\) −20.6875 −0.774209
\(715\) −21.3940 −0.800091
\(716\) 28.3539 1.05963
\(717\) −95.2701 −3.55793
\(718\) 53.1986 1.98536
\(719\) −13.1988 −0.492232 −0.246116 0.969240i \(-0.579154\pi\)
−0.246116 + 0.969240i \(0.579154\pi\)
\(720\) 20.1562 0.751178
\(721\) 13.2150 0.492153
\(722\) 1.05930 0.0394230
\(723\) 1.59562 0.0593419
\(724\) −34.2855 −1.27421
\(725\) 2.80516 0.104181
\(726\) 7.25180 0.269140
\(727\) −3.14236 −0.116544 −0.0582718 0.998301i \(-0.518559\pi\)
−0.0582718 + 0.998301i \(0.518559\pi\)
\(728\) −17.5976 −0.652209
\(729\) −0.181194 −0.00671090
\(730\) −26.9097 −0.995972
\(731\) −1.62551 −0.0601215
\(732\) 26.8095 0.990906
\(733\) −9.07674 −0.335257 −0.167628 0.985850i \(-0.553611\pi\)
−0.167628 + 0.985850i \(0.553611\pi\)
\(734\) 73.3918 2.70894
\(735\) 73.5582 2.71324
\(736\) −36.6519 −1.35101
\(737\) 13.7996 0.508315
\(738\) 1.20584 0.0443877
\(739\) 35.5021 1.30597 0.652983 0.757373i \(-0.273517\pi\)
0.652983 + 0.757373i \(0.273517\pi\)
\(740\) 102.886 3.78218
\(741\) −73.4375 −2.69779
\(742\) 4.11519 0.151073
\(743\) −25.9303 −0.951290 −0.475645 0.879637i \(-0.657785\pi\)
−0.475645 + 0.879637i \(0.657785\pi\)
\(744\) 106.058 3.88828
\(745\) −81.6613 −2.99184
\(746\) −18.9022 −0.692058
\(747\) −69.1753 −2.53099
\(748\) 9.80932 0.358664
\(749\) 5.79138 0.211613
\(750\) 151.151 5.51925
\(751\) −0.803820 −0.0293318 −0.0146659 0.999892i \(-0.504668\pi\)
−0.0146659 + 0.999892i \(0.504668\pi\)
\(752\) −6.63962 −0.242122
\(753\) 24.1157 0.878826
\(754\) 3.45084 0.125672
\(755\) 34.4299 1.25303
\(756\) 39.2237 1.42655
\(757\) −20.6466 −0.750414 −0.375207 0.926941i \(-0.622428\pi\)
−0.375207 + 0.926941i \(0.622428\pi\)
\(758\) −22.3280 −0.810990
\(759\) 24.1534 0.876713
\(760\) 54.8824 1.99079
\(761\) 50.6273 1.83524 0.917618 0.397462i \(-0.130109\pi\)
0.917618 + 0.397462i \(0.130109\pi\)
\(762\) −90.7960 −3.28919
\(763\) −18.5029 −0.669849
\(764\) 13.3083 0.481477
\(765\) 76.0689 2.75028
\(766\) −62.6299 −2.26291
\(767\) −10.4120 −0.375956
\(768\) 64.3253 2.32114
\(769\) 18.1721 0.655303 0.327651 0.944799i \(-0.393743\pi\)
0.327651 + 0.944799i \(0.393743\pi\)
\(770\) 8.99788 0.324261
\(771\) 2.73869 0.0986315
\(772\) −45.2227 −1.62760
\(773\) 34.1281 1.22750 0.613750 0.789500i \(-0.289660\pi\)
0.613750 + 0.789500i \(0.289660\pi\)
\(774\) 8.82355 0.317156
\(775\) 107.785 3.87176
\(776\) 25.5863 0.918494
\(777\) 23.8507 0.855641
\(778\) −4.30683 −0.154407
\(779\) 0.331661 0.0118830
\(780\) 227.038 8.12926
\(781\) −4.88488 −0.174795
\(782\) 51.8853 1.85541
\(783\) −3.16834 −0.113227
\(784\) −4.60230 −0.164368
\(785\) 3.34289 0.119313
\(786\) 118.967 4.24340
\(787\) 36.8236 1.31262 0.656309 0.754492i \(-0.272117\pi\)
0.656309 + 0.754492i \(0.272117\pi\)
\(788\) −28.4212 −1.01246
\(789\) −0.374880 −0.0133461
\(790\) −44.4625 −1.58191
\(791\) −18.3210 −0.651421
\(792\) −21.9334 −0.779368
\(793\) 13.8065 0.490282
\(794\) −69.3377 −2.46070
\(795\) −21.8699 −0.775646
\(796\) 61.4906 2.17948
\(797\) −45.3960 −1.60801 −0.804005 0.594622i \(-0.797302\pi\)
−0.804005 + 0.594622i \(0.797302\pi\)
\(798\) 30.8863 1.09336
\(799\) −25.0577 −0.886477
\(800\) 48.8875 1.72843
\(801\) 22.3458 0.789551
\(802\) −16.7486 −0.591414
\(803\) 2.95790 0.104382
\(804\) −146.444 −5.16469
\(805\) 29.9690 1.05627
\(806\) 132.595 4.67046
\(807\) −33.5223 −1.18004
\(808\) 30.2391 1.06381
\(809\) −34.4760 −1.21211 −0.606055 0.795423i \(-0.707249\pi\)
−0.606055 + 0.795423i \(0.707249\pi\)
\(810\) −147.167 −5.17091
\(811\) 19.1727 0.673246 0.336623 0.941640i \(-0.390715\pi\)
0.336623 + 0.941640i \(0.390715\pi\)
\(812\) −0.913903 −0.0320717
\(813\) 66.7495 2.34101
\(814\) −17.9600 −0.629497
\(815\) −66.0165 −2.31246
\(816\) −6.87873 −0.240804
\(817\) 2.42687 0.0849054
\(818\) 69.3571 2.42501
\(819\) 36.4153 1.27245
\(820\) −1.02536 −0.0358070
\(821\) −35.3962 −1.23534 −0.617668 0.786439i \(-0.711922\pi\)
−0.617668 + 0.786439i \(0.711922\pi\)
\(822\) 47.4907 1.65643
\(823\) 14.9994 0.522846 0.261423 0.965224i \(-0.415808\pi\)
0.261423 + 0.965224i \(0.415808\pi\)
\(824\) 43.5000 1.51539
\(825\) −32.2166 −1.12164
\(826\) 4.37907 0.152367
\(827\) 17.1114 0.595023 0.297511 0.954718i \(-0.403843\pi\)
0.297511 + 0.954718i \(0.403843\pi\)
\(828\) −177.348 −6.16327
\(829\) −32.2151 −1.11888 −0.559438 0.828872i \(-0.688983\pi\)
−0.559438 + 0.828872i \(0.688983\pi\)
\(830\) 93.4129 3.24241
\(831\) −96.8096 −3.35829
\(832\) 68.4939 2.37460
\(833\) −17.3689 −0.601796
\(834\) −106.959 −3.70368
\(835\) −20.9452 −0.724839
\(836\) −14.6452 −0.506516
\(837\) −121.740 −4.20795
\(838\) 63.7567 2.20244
\(839\) −57.2147 −1.97527 −0.987635 0.156773i \(-0.949891\pi\)
−0.987635 + 0.156773i \(0.949891\pi\)
\(840\) −39.3330 −1.35712
\(841\) −28.9262 −0.997454
\(842\) 44.5260 1.53447
\(843\) 24.9523 0.859404
\(844\) 16.4394 0.565868
\(845\) 66.0308 2.27153
\(846\) 136.018 4.67639
\(847\) −0.989043 −0.0339839
\(848\) 1.36833 0.0469886
\(849\) 68.6515 2.35611
\(850\) −69.2062 −2.37375
\(851\) −59.8189 −2.05057
\(852\) 51.8394 1.77599
\(853\) 26.3255 0.901370 0.450685 0.892683i \(-0.351180\pi\)
0.450685 + 0.892683i \(0.351180\pi\)
\(854\) −5.80671 −0.198702
\(855\) −113.570 −3.88402
\(856\) 19.0635 0.651579
\(857\) −9.70733 −0.331596 −0.165798 0.986160i \(-0.553020\pi\)
−0.165798 + 0.986160i \(0.553020\pi\)
\(858\) −39.6320 −1.35302
\(859\) −22.4855 −0.767197 −0.383598 0.923500i \(-0.625315\pi\)
−0.383598 + 0.923500i \(0.625315\pi\)
\(860\) −7.50286 −0.255845
\(861\) −0.237694 −0.00810060
\(862\) −12.0511 −0.410462
\(863\) −40.7277 −1.38639 −0.693193 0.720752i \(-0.743797\pi\)
−0.693193 + 0.720752i \(0.743797\pi\)
\(864\) −55.2169 −1.87852
\(865\) −68.8255 −2.34014
\(866\) 23.1877 0.787951
\(867\) 27.0871 0.919927
\(868\) −35.1157 −1.19191
\(869\) 4.88730 0.165790
\(870\) 7.71312 0.261499
\(871\) −75.4166 −2.55539
\(872\) −60.9061 −2.06254
\(873\) −52.9467 −1.79197
\(874\) −77.4643 −2.62027
\(875\) −20.6149 −0.696909
\(876\) −31.3899 −1.06057
\(877\) −34.6196 −1.16902 −0.584510 0.811387i \(-0.698713\pi\)
−0.584510 + 0.811387i \(0.698713\pi\)
\(878\) 15.1659 0.511823
\(879\) 68.0029 2.29368
\(880\) 2.99186 0.100855
\(881\) 4.22540 0.142357 0.0711787 0.997464i \(-0.477324\pi\)
0.0711787 + 0.997464i \(0.477324\pi\)
\(882\) 94.2816 3.17463
\(883\) 12.4434 0.418755 0.209378 0.977835i \(-0.432856\pi\)
0.209378 + 0.977835i \(0.432856\pi\)
\(884\) −53.6092 −1.80307
\(885\) −23.2723 −0.782291
\(886\) −6.77074 −0.227467
\(887\) 48.0810 1.61440 0.807201 0.590276i \(-0.200981\pi\)
0.807201 + 0.590276i \(0.200981\pi\)
\(888\) 78.5097 2.63461
\(889\) 12.3833 0.415322
\(890\) −30.1754 −1.01148
\(891\) 16.1765 0.541933
\(892\) −12.4112 −0.415558
\(893\) 37.4109 1.25191
\(894\) −151.276 −5.05943
\(895\) 32.6371 1.09094
\(896\) −19.4406 −0.649465
\(897\) −132.002 −4.40740
\(898\) −90.6599 −3.02536
\(899\) 2.83652 0.0946032
\(900\) 236.552 7.88507
\(901\) 5.16402 0.172038
\(902\) 0.178987 0.00595963
\(903\) −1.73929 −0.0578798
\(904\) −60.3075 −2.00580
\(905\) −39.4648 −1.31186
\(906\) 63.7807 2.11897
\(907\) −29.8929 −0.992578 −0.496289 0.868157i \(-0.665304\pi\)
−0.496289 + 0.868157i \(0.665304\pi\)
\(908\) 38.5914 1.28070
\(909\) −62.5749 −2.07548
\(910\) −49.1746 −1.63012
\(911\) 22.9212 0.759413 0.379707 0.925107i \(-0.376025\pi\)
0.379707 + 0.925107i \(0.376025\pi\)
\(912\) 10.2699 0.340070
\(913\) −10.2679 −0.339818
\(914\) 29.2567 0.967727
\(915\) 30.8594 1.02018
\(916\) 34.3319 1.13436
\(917\) −16.2254 −0.535809
\(918\) 78.1662 2.57987
\(919\) 51.0750 1.68481 0.842404 0.538847i \(-0.181140\pi\)
0.842404 + 0.538847i \(0.181140\pi\)
\(920\) 98.6493 3.25237
\(921\) −38.7092 −1.27551
\(922\) −15.4451 −0.508659
\(923\) 26.6965 0.878726
\(924\) 10.4959 0.345291
\(925\) 79.7883 2.62342
\(926\) 32.0152 1.05208
\(927\) −90.0163 −2.95652
\(928\) 1.28654 0.0422328
\(929\) 47.8929 1.57132 0.785658 0.618661i \(-0.212325\pi\)
0.785658 + 0.618661i \(0.212325\pi\)
\(930\) 296.368 9.71830
\(931\) 25.9316 0.849875
\(932\) 11.1492 0.365205
\(933\) 74.9632 2.45418
\(934\) −68.7124 −2.24834
\(935\) 11.2912 0.369260
\(936\) 119.869 3.91803
\(937\) 32.8592 1.07346 0.536731 0.843754i \(-0.319659\pi\)
0.536731 + 0.843754i \(0.319659\pi\)
\(938\) 31.7187 1.03565
\(939\) 108.087 3.52728
\(940\) −115.659 −3.77238
\(941\) −32.8230 −1.07000 −0.535000 0.844852i \(-0.679689\pi\)
−0.535000 + 0.844852i \(0.679689\pi\)
\(942\) 6.19264 0.201767
\(943\) 0.596149 0.0194133
\(944\) 1.45607 0.0473911
\(945\) 45.1489 1.46869
\(946\) 1.30971 0.0425823
\(947\) −4.42335 −0.143740 −0.0718698 0.997414i \(-0.522897\pi\)
−0.0718698 + 0.997414i \(0.522897\pi\)
\(948\) −51.8651 −1.68450
\(949\) −16.1653 −0.524748
\(950\) 103.324 3.35228
\(951\) −82.2968 −2.66866
\(952\) 9.28749 0.301009
\(953\) −32.7593 −1.06118 −0.530589 0.847629i \(-0.678029\pi\)
−0.530589 + 0.847629i \(0.678029\pi\)
\(954\) −28.0313 −0.907546
\(955\) 15.3187 0.495702
\(956\) 103.833 3.35820
\(957\) −0.847823 −0.0274062
\(958\) 39.6753 1.28185
\(959\) −6.47707 −0.209155
\(960\) 153.094 4.94107
\(961\) 77.9902 2.51581
\(962\) 98.1536 3.16460
\(963\) −39.4490 −1.27123
\(964\) −1.73904 −0.0560107
\(965\) −52.0542 −1.67569
\(966\) 55.5171 1.78623
\(967\) 34.9707 1.12458 0.562290 0.826940i \(-0.309920\pi\)
0.562290 + 0.826940i \(0.309920\pi\)
\(968\) −3.25564 −0.104640
\(969\) 38.7582 1.24509
\(970\) 71.4982 2.29567
\(971\) 27.1071 0.869908 0.434954 0.900453i \(-0.356765\pi\)
0.434954 + 0.900453i \(0.356765\pi\)
\(972\) −52.6939 −1.69016
\(973\) 14.5877 0.467660
\(974\) −72.9804 −2.33844
\(975\) 176.068 5.63868
\(976\) −1.93077 −0.0618025
\(977\) 55.0874 1.76240 0.881200 0.472743i \(-0.156736\pi\)
0.881200 + 0.472743i \(0.156736\pi\)
\(978\) −122.294 −3.91054
\(979\) 3.31687 0.106008
\(980\) −80.1697 −2.56093
\(981\) 126.035 4.02400
\(982\) 63.9580 2.04098
\(983\) 10.5168 0.335433 0.167716 0.985835i \(-0.446361\pi\)
0.167716 + 0.985835i \(0.446361\pi\)
\(984\) −0.782420 −0.0249426
\(985\) −32.7146 −1.04237
\(986\) −1.82126 −0.0580006
\(987\) −26.8116 −0.853423
\(988\) 80.0381 2.54635
\(989\) 4.36222 0.138710
\(990\) −61.2905 −1.94794
\(991\) −37.3445 −1.18629 −0.593143 0.805097i \(-0.702113\pi\)
−0.593143 + 0.805097i \(0.702113\pi\)
\(992\) 49.4340 1.56953
\(993\) −6.73160 −0.213621
\(994\) −11.2280 −0.356130
\(995\) 70.7797 2.24387
\(996\) 108.965 3.45270
\(997\) −33.7762 −1.06970 −0.534852 0.844946i \(-0.679633\pi\)
−0.534852 + 0.844946i \(0.679633\pi\)
\(998\) −11.8789 −0.376020
\(999\) −90.1184 −2.85122
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 \(a_p\))