Properties

Label 8002.2.a.d.1.19
Level 8002
Weight 2
Character 8002.1
Self dual Yes
Analytic conductor 63.896
Analytic rank 1
Dimension 69
CM No

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Newspace parameters

Level: \( N \) = \( 8002 = 2 \cdot 4001 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8002.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8962916974\)
Analytic rank: \(1\)
Dimension: \(69\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-1.96903 q^{3}\) \(+1.00000 q^{4}\) \(+3.30115 q^{5}\) \(-1.96903 q^{6}\) \(+1.85739 q^{7}\) \(+1.00000 q^{8}\) \(+0.877064 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-1.96903 q^{3}\) \(+1.00000 q^{4}\) \(+3.30115 q^{5}\) \(-1.96903 q^{6}\) \(+1.85739 q^{7}\) \(+1.00000 q^{8}\) \(+0.877064 q^{9}\) \(+3.30115 q^{10}\) \(-3.08990 q^{11}\) \(-1.96903 q^{12}\) \(+2.43216 q^{13}\) \(+1.85739 q^{14}\) \(-6.50006 q^{15}\) \(+1.00000 q^{16}\) \(-4.43573 q^{17}\) \(+0.877064 q^{18}\) \(+1.86336 q^{19}\) \(+3.30115 q^{20}\) \(-3.65725 q^{21}\) \(-3.08990 q^{22}\) \(-7.06371 q^{23}\) \(-1.96903 q^{24}\) \(+5.89761 q^{25}\) \(+2.43216 q^{26}\) \(+4.18012 q^{27}\) \(+1.85739 q^{28}\) \(+1.65879 q^{29}\) \(-6.50006 q^{30}\) \(-9.92897 q^{31}\) \(+1.00000 q^{32}\) \(+6.08410 q^{33}\) \(-4.43573 q^{34}\) \(+6.13153 q^{35}\) \(+0.877064 q^{36}\) \(-9.20402 q^{37}\) \(+1.86336 q^{38}\) \(-4.78898 q^{39}\) \(+3.30115 q^{40}\) \(-9.80139 q^{41}\) \(-3.65725 q^{42}\) \(+1.14766 q^{43}\) \(-3.08990 q^{44}\) \(+2.89532 q^{45}\) \(-7.06371 q^{46}\) \(+1.76021 q^{47}\) \(-1.96903 q^{48}\) \(-3.55010 q^{49}\) \(+5.89761 q^{50}\) \(+8.73408 q^{51}\) \(+2.43216 q^{52}\) \(-3.91707 q^{53}\) \(+4.18012 q^{54}\) \(-10.2002 q^{55}\) \(+1.85739 q^{56}\) \(-3.66900 q^{57}\) \(+1.65879 q^{58}\) \(+11.0174 q^{59}\) \(-6.50006 q^{60}\) \(-11.4546 q^{61}\) \(-9.92897 q^{62}\) \(+1.62905 q^{63}\) \(+1.00000 q^{64}\) \(+8.02891 q^{65}\) \(+6.08410 q^{66}\) \(-3.36449 q^{67}\) \(-4.43573 q^{68}\) \(+13.9086 q^{69}\) \(+6.13153 q^{70}\) \(+1.81745 q^{71}\) \(+0.877064 q^{72}\) \(+3.70540 q^{73}\) \(-9.20402 q^{74}\) \(-11.6125 q^{75}\) \(+1.86336 q^{76}\) \(-5.73916 q^{77}\) \(-4.78898 q^{78}\) \(-8.92708 q^{79}\) \(+3.30115 q^{80}\) \(-10.8620 q^{81}\) \(-9.80139 q^{82}\) \(+7.98237 q^{83}\) \(-3.65725 q^{84}\) \(-14.6430 q^{85}\) \(+1.14766 q^{86}\) \(-3.26619 q^{87}\) \(-3.08990 q^{88}\) \(-9.55337 q^{89}\) \(+2.89532 q^{90}\) \(+4.51746 q^{91}\) \(-7.06371 q^{92}\) \(+19.5504 q^{93}\) \(+1.76021 q^{94}\) \(+6.15122 q^{95}\) \(-1.96903 q^{96}\) \(-18.5452 q^{97}\) \(-3.55010 q^{98}\) \(-2.71004 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(69q \) \(\mathstrut +\mathstrut 69q^{2} \) \(\mathstrut -\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 33q^{5} \) \(\mathstrut -\mathstrut 25q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 54q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(69q \) \(\mathstrut +\mathstrut 69q^{2} \) \(\mathstrut -\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 33q^{5} \) \(\mathstrut -\mathstrut 25q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 54q^{9} \) \(\mathstrut -\mathstrut 33q^{10} \) \(\mathstrut -\mathstrut 30q^{11} \) \(\mathstrut -\mathstrut 25q^{12} \) \(\mathstrut -\mathstrut 58q^{13} \) \(\mathstrut -\mathstrut 19q^{14} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 69q^{16} \) \(\mathstrut -\mathstrut 80q^{17} \) \(\mathstrut +\mathstrut 54q^{18} \) \(\mathstrut -\mathstrut 40q^{19} \) \(\mathstrut -\mathstrut 33q^{20} \) \(\mathstrut -\mathstrut 32q^{21} \) \(\mathstrut -\mathstrut 30q^{22} \) \(\mathstrut -\mathstrut 45q^{23} \) \(\mathstrut -\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 42q^{25} \) \(\mathstrut -\mathstrut 58q^{26} \) \(\mathstrut -\mathstrut 76q^{27} \) \(\mathstrut -\mathstrut 19q^{28} \) \(\mathstrut -\mathstrut 44q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut -\mathstrut 12q^{31} \) \(\mathstrut +\mathstrut 69q^{32} \) \(\mathstrut -\mathstrut 41q^{33} \) \(\mathstrut -\mathstrut 80q^{34} \) \(\mathstrut -\mathstrut 49q^{35} \) \(\mathstrut +\mathstrut 54q^{36} \) \(\mathstrut -\mathstrut 47q^{37} \) \(\mathstrut -\mathstrut 40q^{38} \) \(\mathstrut -\mathstrut 14q^{39} \) \(\mathstrut -\mathstrut 33q^{40} \) \(\mathstrut -\mathstrut 94q^{41} \) \(\mathstrut -\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 30q^{44} \) \(\mathstrut -\mathstrut 89q^{45} \) \(\mathstrut -\mathstrut 45q^{46} \) \(\mathstrut -\mathstrut 85q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 32q^{49} \) \(\mathstrut +\mathstrut 42q^{50} \) \(\mathstrut -\mathstrut 10q^{51} \) \(\mathstrut -\mathstrut 58q^{52} \) \(\mathstrut -\mathstrut 41q^{53} \) \(\mathstrut -\mathstrut 76q^{54} \) \(\mathstrut -\mathstrut 27q^{55} \) \(\mathstrut -\mathstrut 19q^{56} \) \(\mathstrut -\mathstrut 72q^{57} \) \(\mathstrut -\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 75q^{59} \) \(\mathstrut +\mathstrut 2q^{60} \) \(\mathstrut -\mathstrut 98q^{61} \) \(\mathstrut -\mathstrut 12q^{62} \) \(\mathstrut -\mathstrut 61q^{63} \) \(\mathstrut +\mathstrut 69q^{64} \) \(\mathstrut -\mathstrut 47q^{65} \) \(\mathstrut -\mathstrut 41q^{66} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 80q^{68} \) \(\mathstrut -\mathstrut 74q^{69} \) \(\mathstrut -\mathstrut 49q^{70} \) \(\mathstrut -\mathstrut 22q^{71} \) \(\mathstrut +\mathstrut 54q^{72} \) \(\mathstrut -\mathstrut 129q^{73} \) \(\mathstrut -\mathstrut 47q^{74} \) \(\mathstrut -\mathstrut 106q^{75} \) \(\mathstrut -\mathstrut 40q^{76} \) \(\mathstrut -\mathstrut 108q^{77} \) \(\mathstrut -\mathstrut 14q^{78} \) \(\mathstrut +\mathstrut 21q^{79} \) \(\mathstrut -\mathstrut 33q^{80} \) \(\mathstrut +\mathstrut 13q^{81} \) \(\mathstrut -\mathstrut 94q^{82} \) \(\mathstrut -\mathstrut 111q^{83} \) \(\mathstrut -\mathstrut 32q^{84} \) \(\mathstrut -\mathstrut 67q^{85} \) \(\mathstrut -\mathstrut 10q^{86} \) \(\mathstrut -\mathstrut 38q^{87} \) \(\mathstrut -\mathstrut 30q^{88} \) \(\mathstrut -\mathstrut 112q^{89} \) \(\mathstrut -\mathstrut 89q^{90} \) \(\mathstrut -\mathstrut 55q^{91} \) \(\mathstrut -\mathstrut 45q^{92} \) \(\mathstrut -\mathstrut 90q^{93} \) \(\mathstrut -\mathstrut 85q^{94} \) \(\mathstrut -\mathstrut 38q^{95} \) \(\mathstrut -\mathstrut 25q^{96} \) \(\mathstrut -\mathstrut 98q^{97} \) \(\mathstrut +\mathstrut 32q^{98} \) \(\mathstrut -\mathstrut 51q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.96903 −1.13682 −0.568409 0.822746i \(-0.692441\pi\)
−0.568409 + 0.822746i \(0.692441\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.30115 1.47632 0.738160 0.674626i \(-0.235695\pi\)
0.738160 + 0.674626i \(0.235695\pi\)
\(6\) −1.96903 −0.803852
\(7\) 1.85739 0.702028 0.351014 0.936370i \(-0.385837\pi\)
0.351014 + 0.936370i \(0.385837\pi\)
\(8\) 1.00000 0.353553
\(9\) 0.877064 0.292355
\(10\) 3.30115 1.04392
\(11\) −3.08990 −0.931641 −0.465820 0.884879i \(-0.654241\pi\)
−0.465820 + 0.884879i \(0.654241\pi\)
\(12\) −1.96903 −0.568409
\(13\) 2.43216 0.674558 0.337279 0.941405i \(-0.390493\pi\)
0.337279 + 0.941405i \(0.390493\pi\)
\(14\) 1.85739 0.496409
\(15\) −6.50006 −1.67831
\(16\) 1.00000 0.250000
\(17\) −4.43573 −1.07582 −0.537912 0.843001i \(-0.680787\pi\)
−0.537912 + 0.843001i \(0.680787\pi\)
\(18\) 0.877064 0.206726
\(19\) 1.86336 0.427483 0.213742 0.976890i \(-0.431435\pi\)
0.213742 + 0.976890i \(0.431435\pi\)
\(20\) 3.30115 0.738160
\(21\) −3.65725 −0.798078
\(22\) −3.08990 −0.658769
\(23\) −7.06371 −1.47288 −0.736442 0.676500i \(-0.763496\pi\)
−0.736442 + 0.676500i \(0.763496\pi\)
\(24\) −1.96903 −0.401926
\(25\) 5.89761 1.17952
\(26\) 2.43216 0.476985
\(27\) 4.18012 0.804464
\(28\) 1.85739 0.351014
\(29\) 1.65879 0.308029 0.154014 0.988069i \(-0.450780\pi\)
0.154014 + 0.988069i \(0.450780\pi\)
\(30\) −6.50006 −1.18674
\(31\) −9.92897 −1.78330 −0.891648 0.452729i \(-0.850451\pi\)
−0.891648 + 0.452729i \(0.850451\pi\)
\(32\) 1.00000 0.176777
\(33\) 6.08410 1.05911
\(34\) −4.43573 −0.760722
\(35\) 6.13153 1.03642
\(36\) 0.877064 0.146177
\(37\) −9.20402 −1.51313 −0.756566 0.653918i \(-0.773124\pi\)
−0.756566 + 0.653918i \(0.773124\pi\)
\(38\) 1.86336 0.302276
\(39\) −4.78898 −0.766850
\(40\) 3.30115 0.521958
\(41\) −9.80139 −1.53072 −0.765360 0.643602i \(-0.777439\pi\)
−0.765360 + 0.643602i \(0.777439\pi\)
\(42\) −3.65725 −0.564326
\(43\) 1.14766 0.175017 0.0875085 0.996164i \(-0.472110\pi\)
0.0875085 + 0.996164i \(0.472110\pi\)
\(44\) −3.08990 −0.465820
\(45\) 2.89532 0.431609
\(46\) −7.06371 −1.04149
\(47\) 1.76021 0.256753 0.128376 0.991726i \(-0.459023\pi\)
0.128376 + 0.991726i \(0.459023\pi\)
\(48\) −1.96903 −0.284204
\(49\) −3.55010 −0.507157
\(50\) 5.89761 0.834048
\(51\) 8.73408 1.22302
\(52\) 2.43216 0.337279
\(53\) −3.91707 −0.538051 −0.269025 0.963133i \(-0.586702\pi\)
−0.269025 + 0.963133i \(0.586702\pi\)
\(54\) 4.18012 0.568842
\(55\) −10.2002 −1.37540
\(56\) 1.85739 0.248204
\(57\) −3.66900 −0.485971
\(58\) 1.65879 0.217809
\(59\) 11.0174 1.43434 0.717169 0.696900i \(-0.245438\pi\)
0.717169 + 0.696900i \(0.245438\pi\)
\(60\) −6.50006 −0.839153
\(61\) −11.4546 −1.46661 −0.733306 0.679899i \(-0.762024\pi\)
−0.733306 + 0.679899i \(0.762024\pi\)
\(62\) −9.92897 −1.26098
\(63\) 1.62905 0.205241
\(64\) 1.00000 0.125000
\(65\) 8.02891 0.995864
\(66\) 6.08410 0.748901
\(67\) −3.36449 −0.411038 −0.205519 0.978653i \(-0.565888\pi\)
−0.205519 + 0.978653i \(0.565888\pi\)
\(68\) −4.43573 −0.537912
\(69\) 13.9086 1.67440
\(70\) 6.13153 0.732858
\(71\) 1.81745 0.215692 0.107846 0.994168i \(-0.465605\pi\)
0.107846 + 0.994168i \(0.465605\pi\)
\(72\) 0.877064 0.103363
\(73\) 3.70540 0.433684 0.216842 0.976207i \(-0.430424\pi\)
0.216842 + 0.976207i \(0.430424\pi\)
\(74\) −9.20402 −1.06995
\(75\) −11.6125 −1.34090
\(76\) 1.86336 0.213742
\(77\) −5.73916 −0.654038
\(78\) −4.78898 −0.542245
\(79\) −8.92708 −1.00438 −0.502188 0.864759i \(-0.667471\pi\)
−0.502188 + 0.864759i \(0.667471\pi\)
\(80\) 3.30115 0.369080
\(81\) −10.8620 −1.20688
\(82\) −9.80139 −1.08238
\(83\) 7.98237 0.876179 0.438090 0.898931i \(-0.355655\pi\)
0.438090 + 0.898931i \(0.355655\pi\)
\(84\) −3.65725 −0.399039
\(85\) −14.6430 −1.58826
\(86\) 1.14766 0.123756
\(87\) −3.26619 −0.350173
\(88\) −3.08990 −0.329385
\(89\) −9.55337 −1.01266 −0.506328 0.862341i \(-0.668997\pi\)
−0.506328 + 0.862341i \(0.668997\pi\)
\(90\) 2.89532 0.305194
\(91\) 4.51746 0.473559
\(92\) −7.06371 −0.736442
\(93\) 19.5504 2.02728
\(94\) 1.76021 0.181551
\(95\) 6.15122 0.631102
\(96\) −1.96903 −0.200963
\(97\) −18.5452 −1.88298 −0.941490 0.337040i \(-0.890574\pi\)
−0.941490 + 0.337040i \(0.890574\pi\)
\(98\) −3.55010 −0.358614
\(99\) −2.71004 −0.272369
\(100\) 5.89761 0.589761
\(101\) −17.4314 −1.73448 −0.867242 0.497887i \(-0.834110\pi\)
−0.867242 + 0.497887i \(0.834110\pi\)
\(102\) 8.73408 0.864802
\(103\) 8.97142 0.883981 0.441990 0.897020i \(-0.354273\pi\)
0.441990 + 0.897020i \(0.354273\pi\)
\(104\) 2.43216 0.238492
\(105\) −12.0731 −1.17822
\(106\) −3.91707 −0.380459
\(107\) 10.4022 1.00562 0.502812 0.864396i \(-0.332299\pi\)
0.502812 + 0.864396i \(0.332299\pi\)
\(108\) 4.18012 0.402232
\(109\) 1.43512 0.137459 0.0687296 0.997635i \(-0.478105\pi\)
0.0687296 + 0.997635i \(0.478105\pi\)
\(110\) −10.2002 −0.972555
\(111\) 18.1230 1.72015
\(112\) 1.85739 0.175507
\(113\) −11.6128 −1.09244 −0.546222 0.837640i \(-0.683935\pi\)
−0.546222 + 0.837640i \(0.683935\pi\)
\(114\) −3.66900 −0.343633
\(115\) −23.3184 −2.17445
\(116\) 1.65879 0.154014
\(117\) 2.13315 0.197210
\(118\) 11.0174 1.01423
\(119\) −8.23889 −0.755258
\(120\) −6.50006 −0.593371
\(121\) −1.45250 −0.132046
\(122\) −11.4546 −1.03705
\(123\) 19.2992 1.74015
\(124\) −9.92897 −0.891648
\(125\) 2.96314 0.265031
\(126\) 1.62905 0.145127
\(127\) 3.51605 0.311999 0.155999 0.987757i \(-0.450140\pi\)
0.155999 + 0.987757i \(0.450140\pi\)
\(128\) 1.00000 0.0883883
\(129\) −2.25978 −0.198962
\(130\) 8.02891 0.704182
\(131\) 19.4772 1.70173 0.850864 0.525386i \(-0.176079\pi\)
0.850864 + 0.525386i \(0.176079\pi\)
\(132\) 6.08410 0.529553
\(133\) 3.46098 0.300105
\(134\) −3.36449 −0.290648
\(135\) 13.7992 1.18765
\(136\) −4.43573 −0.380361
\(137\) 5.15592 0.440500 0.220250 0.975443i \(-0.429313\pi\)
0.220250 + 0.975443i \(0.429313\pi\)
\(138\) 13.9086 1.18398
\(139\) 10.7889 0.915099 0.457550 0.889184i \(-0.348727\pi\)
0.457550 + 0.889184i \(0.348727\pi\)
\(140\) 6.13153 0.518209
\(141\) −3.46589 −0.291881
\(142\) 1.81745 0.152517
\(143\) −7.51512 −0.628446
\(144\) 0.877064 0.0730886
\(145\) 5.47591 0.454749
\(146\) 3.70540 0.306661
\(147\) 6.99024 0.576545
\(148\) −9.20402 −0.756566
\(149\) 20.4133 1.67232 0.836161 0.548485i \(-0.184795\pi\)
0.836161 + 0.548485i \(0.184795\pi\)
\(150\) −11.6125 −0.948160
\(151\) −6.13396 −0.499174 −0.249587 0.968352i \(-0.580295\pi\)
−0.249587 + 0.968352i \(0.580295\pi\)
\(152\) 1.86336 0.151138
\(153\) −3.89042 −0.314522
\(154\) −5.73916 −0.462474
\(155\) −32.7771 −2.63272
\(156\) −4.78898 −0.383425
\(157\) −3.51678 −0.280670 −0.140335 0.990104i \(-0.544818\pi\)
−0.140335 + 0.990104i \(0.544818\pi\)
\(158\) −8.92708 −0.710201
\(159\) 7.71281 0.611666
\(160\) 3.30115 0.260979
\(161\) −13.1201 −1.03401
\(162\) −10.8620 −0.853395
\(163\) −0.253671 −0.0198690 −0.00993451 0.999951i \(-0.503162\pi\)
−0.00993451 + 0.999951i \(0.503162\pi\)
\(164\) −9.80139 −0.765360
\(165\) 20.0845 1.56358
\(166\) 7.98237 0.619552
\(167\) −16.2070 −1.25413 −0.627066 0.778966i \(-0.715744\pi\)
−0.627066 + 0.778966i \(0.715744\pi\)
\(168\) −3.65725 −0.282163
\(169\) −7.08462 −0.544971
\(170\) −14.6430 −1.12307
\(171\) 1.63428 0.124977
\(172\) 1.14766 0.0875085
\(173\) 9.63707 0.732693 0.366346 0.930479i \(-0.380609\pi\)
0.366346 + 0.930479i \(0.380609\pi\)
\(174\) −3.26619 −0.247609
\(175\) 10.9542 0.828057
\(176\) −3.08990 −0.232910
\(177\) −21.6935 −1.63058
\(178\) −9.55337 −0.716055
\(179\) −3.01116 −0.225065 −0.112532 0.993648i \(-0.535896\pi\)
−0.112532 + 0.993648i \(0.535896\pi\)
\(180\) 2.89532 0.215804
\(181\) −0.836448 −0.0621727 −0.0310864 0.999517i \(-0.509897\pi\)
−0.0310864 + 0.999517i \(0.509897\pi\)
\(182\) 4.51746 0.334857
\(183\) 22.5544 1.66727
\(184\) −7.06371 −0.520743
\(185\) −30.3839 −2.23387
\(186\) 19.5504 1.43351
\(187\) 13.7060 1.00228
\(188\) 1.76021 0.128376
\(189\) 7.76411 0.564756
\(190\) 6.15122 0.446257
\(191\) 1.65960 0.120085 0.0600423 0.998196i \(-0.480876\pi\)
0.0600423 + 0.998196i \(0.480876\pi\)
\(192\) −1.96903 −0.142102
\(193\) 15.6955 1.12979 0.564893 0.825164i \(-0.308917\pi\)
0.564893 + 0.825164i \(0.308917\pi\)
\(194\) −18.5452 −1.33147
\(195\) −15.8091 −1.13212
\(196\) −3.55010 −0.253579
\(197\) 4.17827 0.297689 0.148845 0.988861i \(-0.452445\pi\)
0.148845 + 0.988861i \(0.452445\pi\)
\(198\) −2.71004 −0.192594
\(199\) 12.3731 0.877107 0.438553 0.898705i \(-0.355491\pi\)
0.438553 + 0.898705i \(0.355491\pi\)
\(200\) 5.89761 0.417024
\(201\) 6.62477 0.467275
\(202\) −17.4314 −1.22647
\(203\) 3.08101 0.216245
\(204\) 8.73408 0.611508
\(205\) −32.3559 −2.25983
\(206\) 8.97142 0.625069
\(207\) −6.19532 −0.430605
\(208\) 2.43216 0.168640
\(209\) −5.75759 −0.398261
\(210\) −12.0731 −0.833126
\(211\) 8.69248 0.598415 0.299207 0.954188i \(-0.403278\pi\)
0.299207 + 0.954188i \(0.403278\pi\)
\(212\) −3.91707 −0.269025
\(213\) −3.57861 −0.245202
\(214\) 10.4022 0.711083
\(215\) 3.78861 0.258381
\(216\) 4.18012 0.284421
\(217\) −18.4420 −1.25192
\(218\) 1.43512 0.0971983
\(219\) −7.29603 −0.493020
\(220\) −10.2002 −0.687700
\(221\) −10.7884 −0.725706
\(222\) 18.1230 1.21633
\(223\) 24.9148 1.66842 0.834210 0.551447i \(-0.185924\pi\)
0.834210 + 0.551447i \(0.185924\pi\)
\(224\) 1.85739 0.124102
\(225\) 5.17258 0.344838
\(226\) −11.6128 −0.772475
\(227\) 5.98015 0.396916 0.198458 0.980109i \(-0.436407\pi\)
0.198458 + 0.980109i \(0.436407\pi\)
\(228\) −3.66900 −0.242985
\(229\) 16.3355 1.07948 0.539739 0.841833i \(-0.318523\pi\)
0.539739 + 0.841833i \(0.318523\pi\)
\(230\) −23.3184 −1.53757
\(231\) 11.3005 0.743522
\(232\) 1.65879 0.108905
\(233\) −16.5570 −1.08468 −0.542342 0.840158i \(-0.682462\pi\)
−0.542342 + 0.840158i \(0.682462\pi\)
\(234\) 2.13315 0.139449
\(235\) 5.81071 0.379049
\(236\) 11.0174 0.717169
\(237\) 17.5777 1.14179
\(238\) −8.23889 −0.534048
\(239\) 6.85890 0.443665 0.221833 0.975085i \(-0.428796\pi\)
0.221833 + 0.975085i \(0.428796\pi\)
\(240\) −6.50006 −0.419577
\(241\) 1.98551 0.127898 0.0639489 0.997953i \(-0.479631\pi\)
0.0639489 + 0.997953i \(0.479631\pi\)
\(242\) −1.45250 −0.0933703
\(243\) 8.84711 0.567542
\(244\) −11.4546 −0.733306
\(245\) −11.7194 −0.748726
\(246\) 19.2992 1.23047
\(247\) 4.53197 0.288362
\(248\) −9.92897 −0.630491
\(249\) −15.7175 −0.996056
\(250\) 2.96314 0.187405
\(251\) 2.62668 0.165795 0.0828974 0.996558i \(-0.473583\pi\)
0.0828974 + 0.996558i \(0.473583\pi\)
\(252\) 1.62905 0.102620
\(253\) 21.8262 1.37220
\(254\) 3.51605 0.220617
\(255\) 28.8325 1.80556
\(256\) 1.00000 0.0625000
\(257\) 15.5398 0.969345 0.484672 0.874696i \(-0.338939\pi\)
0.484672 + 0.874696i \(0.338939\pi\)
\(258\) −2.25978 −0.140688
\(259\) −17.0955 −1.06226
\(260\) 8.02891 0.497932
\(261\) 1.45486 0.0900536
\(262\) 19.4772 1.20330
\(263\) −18.0404 −1.11242 −0.556208 0.831043i \(-0.687744\pi\)
−0.556208 + 0.831043i \(0.687744\pi\)
\(264\) 6.08410 0.374450
\(265\) −12.9308 −0.794335
\(266\) 3.46098 0.212206
\(267\) 18.8108 1.15120
\(268\) −3.36449 −0.205519
\(269\) 2.55414 0.155729 0.0778644 0.996964i \(-0.475190\pi\)
0.0778644 + 0.996964i \(0.475190\pi\)
\(270\) 13.7992 0.839793
\(271\) 15.7943 0.959435 0.479718 0.877423i \(-0.340739\pi\)
0.479718 + 0.877423i \(0.340739\pi\)
\(272\) −4.43573 −0.268956
\(273\) −8.89500 −0.538350
\(274\) 5.15592 0.311480
\(275\) −18.2230 −1.09889
\(276\) 13.9086 0.837201
\(277\) −17.2823 −1.03839 −0.519196 0.854655i \(-0.673768\pi\)
−0.519196 + 0.854655i \(0.673768\pi\)
\(278\) 10.7889 0.647073
\(279\) −8.70834 −0.521355
\(280\) 6.13153 0.366429
\(281\) −2.70883 −0.161595 −0.0807977 0.996731i \(-0.525747\pi\)
−0.0807977 + 0.996731i \(0.525747\pi\)
\(282\) −3.46589 −0.206391
\(283\) −18.6728 −1.10998 −0.554992 0.831855i \(-0.687279\pi\)
−0.554992 + 0.831855i \(0.687279\pi\)
\(284\) 1.81745 0.107846
\(285\) −12.1119 −0.717448
\(286\) −7.51512 −0.444379
\(287\) −18.2050 −1.07461
\(288\) 0.877064 0.0516815
\(289\) 2.67574 0.157397
\(290\) 5.47591 0.321556
\(291\) 36.5160 2.14061
\(292\) 3.70540 0.216842
\(293\) 14.7638 0.862513 0.431256 0.902229i \(-0.358070\pi\)
0.431256 + 0.902229i \(0.358070\pi\)
\(294\) 6.99024 0.407679
\(295\) 36.3700 2.11754
\(296\) −9.20402 −0.534973
\(297\) −12.9162 −0.749471
\(298\) 20.4133 1.18251
\(299\) −17.1800 −0.993547
\(300\) −11.6125 −0.670450
\(301\) 2.13166 0.122867
\(302\) −6.13396 −0.352969
\(303\) 34.3228 1.97179
\(304\) 1.86336 0.106871
\(305\) −37.8134 −2.16519
\(306\) −3.89042 −0.222401
\(307\) 22.9778 1.31141 0.655705 0.755017i \(-0.272371\pi\)
0.655705 + 0.755017i \(0.272371\pi\)
\(308\) −5.73916 −0.327019
\(309\) −17.6650 −1.00492
\(310\) −32.7771 −1.86161
\(311\) −23.7259 −1.34537 −0.672686 0.739928i \(-0.734860\pi\)
−0.672686 + 0.739928i \(0.734860\pi\)
\(312\) −4.78898 −0.271122
\(313\) 22.8174 1.28972 0.644858 0.764302i \(-0.276916\pi\)
0.644858 + 0.764302i \(0.276916\pi\)
\(314\) −3.51678 −0.198463
\(315\) 5.37774 0.303001
\(316\) −8.92708 −0.502188
\(317\) −3.37029 −0.189294 −0.0946471 0.995511i \(-0.530172\pi\)
−0.0946471 + 0.995511i \(0.530172\pi\)
\(318\) 7.71281 0.432513
\(319\) −5.12549 −0.286972
\(320\) 3.30115 0.184540
\(321\) −20.4823 −1.14321
\(322\) −13.1201 −0.731153
\(323\) −8.26535 −0.459897
\(324\) −10.8620 −0.603442
\(325\) 14.3439 0.795656
\(326\) −0.253671 −0.0140495
\(327\) −2.82578 −0.156266
\(328\) −9.80139 −0.541191
\(329\) 3.26939 0.180247
\(330\) 20.0845 1.10562
\(331\) −17.7755 −0.977029 −0.488515 0.872556i \(-0.662461\pi\)
−0.488515 + 0.872556i \(0.662461\pi\)
\(332\) 7.98237 0.438090
\(333\) −8.07251 −0.442371
\(334\) −16.2070 −0.886805
\(335\) −11.1067 −0.606823
\(336\) −3.65725 −0.199519
\(337\) 2.85351 0.155441 0.0777204 0.996975i \(-0.475236\pi\)
0.0777204 + 0.996975i \(0.475236\pi\)
\(338\) −7.08462 −0.385353
\(339\) 22.8660 1.24191
\(340\) −14.6430 −0.794130
\(341\) 30.6796 1.66139
\(342\) 1.63428 0.0883718
\(343\) −19.5957 −1.05807
\(344\) 1.14766 0.0618778
\(345\) 45.9145 2.47195
\(346\) 9.63707 0.518092
\(347\) 10.0494 0.539478 0.269739 0.962933i \(-0.413063\pi\)
0.269739 + 0.962933i \(0.413063\pi\)
\(348\) −3.26619 −0.175086
\(349\) 26.6497 1.42652 0.713262 0.700897i \(-0.247217\pi\)
0.713262 + 0.700897i \(0.247217\pi\)
\(350\) 10.9542 0.585525
\(351\) 10.1667 0.542658
\(352\) −3.08990 −0.164692
\(353\) 2.24877 0.119690 0.0598450 0.998208i \(-0.480939\pi\)
0.0598450 + 0.998208i \(0.480939\pi\)
\(354\) −21.6935 −1.15299
\(355\) 5.99968 0.318430
\(356\) −9.55337 −0.506328
\(357\) 16.2226 0.858591
\(358\) −3.01116 −0.159145
\(359\) −21.4690 −1.13309 −0.566544 0.824031i \(-0.691720\pi\)
−0.566544 + 0.824031i \(0.691720\pi\)
\(360\) 2.89532 0.152597
\(361\) −15.5279 −0.817258
\(362\) −0.836448 −0.0439627
\(363\) 2.86001 0.150112
\(364\) 4.51746 0.236779
\(365\) 12.2321 0.640257
\(366\) 22.5544 1.17894
\(367\) −17.9391 −0.936412 −0.468206 0.883619i \(-0.655099\pi\)
−0.468206 + 0.883619i \(0.655099\pi\)
\(368\) −7.06371 −0.368221
\(369\) −8.59644 −0.447513
\(370\) −30.3839 −1.57958
\(371\) −7.27553 −0.377727
\(372\) 19.5504 1.01364
\(373\) 24.2363 1.25491 0.627455 0.778653i \(-0.284097\pi\)
0.627455 + 0.778653i \(0.284097\pi\)
\(374\) 13.7060 0.708720
\(375\) −5.83450 −0.301292
\(376\) 1.76021 0.0907757
\(377\) 4.03442 0.207783
\(378\) 7.76411 0.399343
\(379\) 9.25112 0.475198 0.237599 0.971363i \(-0.423640\pi\)
0.237599 + 0.971363i \(0.423640\pi\)
\(380\) 6.15122 0.315551
\(381\) −6.92319 −0.354686
\(382\) 1.65960 0.0849126
\(383\) −2.97151 −0.151837 −0.0759185 0.997114i \(-0.524189\pi\)
−0.0759185 + 0.997114i \(0.524189\pi\)
\(384\) −1.96903 −0.100481
\(385\) −18.9458 −0.965569
\(386\) 15.6955 0.798879
\(387\) 1.00657 0.0511670
\(388\) −18.5452 −0.941490
\(389\) −12.6105 −0.639379 −0.319690 0.947522i \(-0.603579\pi\)
−0.319690 + 0.947522i \(0.603579\pi\)
\(390\) −15.8091 −0.800527
\(391\) 31.3327 1.58456
\(392\) −3.55010 −0.179307
\(393\) −38.3510 −1.93455
\(394\) 4.17827 0.210498
\(395\) −29.4697 −1.48278
\(396\) −2.71004 −0.136185
\(397\) −25.7601 −1.29286 −0.646432 0.762972i \(-0.723739\pi\)
−0.646432 + 0.762972i \(0.723739\pi\)
\(398\) 12.3731 0.620208
\(399\) −6.81476 −0.341165
\(400\) 5.89761 0.294880
\(401\) −29.4609 −1.47121 −0.735603 0.677412i \(-0.763101\pi\)
−0.735603 + 0.677412i \(0.763101\pi\)
\(402\) 6.62477 0.330413
\(403\) −24.1488 −1.20294
\(404\) −17.4314 −0.867242
\(405\) −35.8570 −1.78175
\(406\) 3.08101 0.152908
\(407\) 28.4395 1.40969
\(408\) 8.73408 0.432401
\(409\) 9.91199 0.490116 0.245058 0.969508i \(-0.421193\pi\)
0.245058 + 0.969508i \(0.421193\pi\)
\(410\) −32.3559 −1.59794
\(411\) −10.1521 −0.500768
\(412\) 8.97142 0.441990
\(413\) 20.4635 1.00694
\(414\) −6.19532 −0.304483
\(415\) 26.3510 1.29352
\(416\) 2.43216 0.119246
\(417\) −21.2435 −1.04030
\(418\) −5.75759 −0.281613
\(419\) −15.2195 −0.743521 −0.371760 0.928329i \(-0.621246\pi\)
−0.371760 + 0.928329i \(0.621246\pi\)
\(420\) −12.0731 −0.589109
\(421\) 27.9218 1.36082 0.680412 0.732830i \(-0.261801\pi\)
0.680412 + 0.732830i \(0.261801\pi\)
\(422\) 8.69248 0.423143
\(423\) 1.54381 0.0750628
\(424\) −3.91707 −0.190230
\(425\) −26.1602 −1.26896
\(426\) −3.57861 −0.173384
\(427\) −21.2757 −1.02960
\(428\) 10.4022 0.502812
\(429\) 14.7975 0.714429
\(430\) 3.78861 0.182703
\(431\) −21.4912 −1.03520 −0.517598 0.855624i \(-0.673174\pi\)
−0.517598 + 0.855624i \(0.673174\pi\)
\(432\) 4.18012 0.201116
\(433\) −15.6415 −0.751681 −0.375840 0.926684i \(-0.622646\pi\)
−0.375840 + 0.926684i \(0.622646\pi\)
\(434\) −18.4420 −0.885244
\(435\) −10.7822 −0.516967
\(436\) 1.43512 0.0687296
\(437\) −13.1622 −0.629634
\(438\) −7.29603 −0.348618
\(439\) −0.372896 −0.0177974 −0.00889869 0.999960i \(-0.502833\pi\)
−0.00889869 + 0.999960i \(0.502833\pi\)
\(440\) −10.2002 −0.486277
\(441\) −3.11366 −0.148270
\(442\) −10.7884 −0.513152
\(443\) −23.0059 −1.09305 −0.546523 0.837444i \(-0.684049\pi\)
−0.546523 + 0.837444i \(0.684049\pi\)
\(444\) 18.1230 0.860077
\(445\) −31.5371 −1.49500
\(446\) 24.9148 1.17975
\(447\) −40.1943 −1.90112
\(448\) 1.85739 0.0877535
\(449\) 0.341228 0.0161036 0.00805178 0.999968i \(-0.497437\pi\)
0.00805178 + 0.999968i \(0.497437\pi\)
\(450\) 5.17258 0.243838
\(451\) 30.2853 1.42608
\(452\) −11.6128 −0.546222
\(453\) 12.0779 0.567470
\(454\) 5.98015 0.280662
\(455\) 14.9128 0.699124
\(456\) −3.66900 −0.171817
\(457\) −15.9510 −0.746156 −0.373078 0.927800i \(-0.621698\pi\)
−0.373078 + 0.927800i \(0.621698\pi\)
\(458\) 16.3355 0.763306
\(459\) −18.5419 −0.865461
\(460\) −23.3184 −1.08722
\(461\) −10.0048 −0.465970 −0.232985 0.972480i \(-0.574849\pi\)
−0.232985 + 0.972480i \(0.574849\pi\)
\(462\) 11.3005 0.525749
\(463\) 10.9141 0.507221 0.253610 0.967306i \(-0.418382\pi\)
0.253610 + 0.967306i \(0.418382\pi\)
\(464\) 1.65879 0.0770072
\(465\) 64.5389 2.99292
\(466\) −16.5570 −0.766987
\(467\) 12.8464 0.594460 0.297230 0.954806i \(-0.403937\pi\)
0.297230 + 0.954806i \(0.403937\pi\)
\(468\) 2.13315 0.0986051
\(469\) −6.24917 −0.288560
\(470\) 5.81071 0.268028
\(471\) 6.92463 0.319070
\(472\) 11.0174 0.507115
\(473\) −3.54617 −0.163053
\(474\) 17.5777 0.807369
\(475\) 10.9893 0.504226
\(476\) −8.23889 −0.377629
\(477\) −3.43552 −0.157302
\(478\) 6.85890 0.313719
\(479\) −19.9150 −0.909938 −0.454969 0.890507i \(-0.650350\pi\)
−0.454969 + 0.890507i \(0.650350\pi\)
\(480\) −6.50006 −0.296686
\(481\) −22.3856 −1.02070
\(482\) 1.98551 0.0904374
\(483\) 25.8337 1.17548
\(484\) −1.45250 −0.0660228
\(485\) −61.2206 −2.77988
\(486\) 8.84711 0.401313
\(487\) 4.82401 0.218597 0.109298 0.994009i \(-0.465140\pi\)
0.109298 + 0.994009i \(0.465140\pi\)
\(488\) −11.4546 −0.518526
\(489\) 0.499484 0.0225875
\(490\) −11.7194 −0.529429
\(491\) −42.5241 −1.91908 −0.959542 0.281565i \(-0.909147\pi\)
−0.959542 + 0.281565i \(0.909147\pi\)
\(492\) 19.2992 0.870075
\(493\) −7.35793 −0.331385
\(494\) 4.53197 0.203903
\(495\) −8.94626 −0.402104
\(496\) −9.92897 −0.445824
\(497\) 3.37572 0.151422
\(498\) −15.7175 −0.704318
\(499\) −8.65225 −0.387328 −0.193664 0.981068i \(-0.562037\pi\)
−0.193664 + 0.981068i \(0.562037\pi\)
\(500\) 2.96314 0.132516
\(501\) 31.9119 1.42572
\(502\) 2.62668 0.117235
\(503\) 1.89418 0.0844575 0.0422288 0.999108i \(-0.486554\pi\)
0.0422288 + 0.999108i \(0.486554\pi\)
\(504\) 1.62905 0.0725636
\(505\) −57.5435 −2.56065
\(506\) 21.8262 0.970292
\(507\) 13.9498 0.619533
\(508\) 3.51605 0.155999
\(509\) 11.1608 0.494692 0.247346 0.968927i \(-0.420442\pi\)
0.247346 + 0.968927i \(0.420442\pi\)
\(510\) 28.8325 1.27673
\(511\) 6.88237 0.304458
\(512\) 1.00000 0.0441942
\(513\) 7.78905 0.343895
\(514\) 15.5398 0.685430
\(515\) 29.6160 1.30504
\(516\) −2.25978 −0.0994812
\(517\) −5.43887 −0.239201
\(518\) −17.0955 −0.751131
\(519\) −18.9756 −0.832938
\(520\) 8.02891 0.352091
\(521\) −1.45362 −0.0636841 −0.0318420 0.999493i \(-0.510137\pi\)
−0.0318420 + 0.999493i \(0.510137\pi\)
\(522\) 1.45486 0.0636775
\(523\) −14.4576 −0.632185 −0.316092 0.948728i \(-0.602371\pi\)
−0.316092 + 0.948728i \(0.602371\pi\)
\(524\) 19.4772 0.850864
\(525\) −21.5690 −0.941350
\(526\) −18.0404 −0.786597
\(527\) 44.0423 1.91851
\(528\) 6.08410 0.264776
\(529\) 26.8960 1.16939
\(530\) −12.9308 −0.561680
\(531\) 9.66292 0.419335
\(532\) 3.46098 0.150053
\(533\) −23.8385 −1.03256
\(534\) 18.8108 0.814024
\(535\) 34.3394 1.48462
\(536\) −3.36449 −0.145324
\(537\) 5.92905 0.255857
\(538\) 2.55414 0.110117
\(539\) 10.9695 0.472488
\(540\) 13.7992 0.593823
\(541\) 43.6182 1.87529 0.937647 0.347588i \(-0.112999\pi\)
0.937647 + 0.347588i \(0.112999\pi\)
\(542\) 15.7943 0.678423
\(543\) 1.64699 0.0706790
\(544\) −4.43573 −0.190181
\(545\) 4.73754 0.202934
\(546\) −8.89500 −0.380671
\(547\) −26.5465 −1.13505 −0.567523 0.823357i \(-0.692098\pi\)
−0.567523 + 0.823357i \(0.692098\pi\)
\(548\) 5.15592 0.220250
\(549\) −10.0464 −0.428771
\(550\) −18.2230 −0.777033
\(551\) 3.09091 0.131677
\(552\) 13.9086 0.591990
\(553\) −16.5811 −0.705099
\(554\) −17.2823 −0.734253
\(555\) 59.8266 2.53950
\(556\) 10.7889 0.457550
\(557\) 3.49412 0.148051 0.0740254 0.997256i \(-0.476415\pi\)
0.0740254 + 0.997256i \(0.476415\pi\)
\(558\) −8.70834 −0.368653
\(559\) 2.79129 0.118059
\(560\) 6.13153 0.259104
\(561\) −26.9874 −1.13941
\(562\) −2.70883 −0.114265
\(563\) −24.0819 −1.01493 −0.507466 0.861672i \(-0.669418\pi\)
−0.507466 + 0.861672i \(0.669418\pi\)
\(564\) −3.46589 −0.145940
\(565\) −38.3358 −1.61280
\(566\) −18.6728 −0.784878
\(567\) −20.1749 −0.847266
\(568\) 1.81745 0.0762585
\(569\) −19.0014 −0.796581 −0.398291 0.917259i \(-0.630396\pi\)
−0.398291 + 0.917259i \(0.630396\pi\)
\(570\) −12.1119 −0.507312
\(571\) −0.168188 −0.00703846 −0.00351923 0.999994i \(-0.501120\pi\)
−0.00351923 + 0.999994i \(0.501120\pi\)
\(572\) −7.51512 −0.314223
\(573\) −3.26780 −0.136514
\(574\) −18.2050 −0.759863
\(575\) −41.6590 −1.73730
\(576\) 0.877064 0.0365443
\(577\) −11.3984 −0.474523 −0.237261 0.971446i \(-0.576250\pi\)
−0.237261 + 0.971446i \(0.576250\pi\)
\(578\) 2.67574 0.111296
\(579\) −30.9048 −1.28436
\(580\) 5.47591 0.227375
\(581\) 14.8264 0.615102
\(582\) 36.5160 1.51364
\(583\) 12.1034 0.501270
\(584\) 3.70540 0.153330
\(585\) 7.04187 0.291145
\(586\) 14.7638 0.609889
\(587\) −38.3179 −1.58155 −0.790774 0.612109i \(-0.790322\pi\)
−0.790774 + 0.612109i \(0.790322\pi\)
\(588\) 6.99024 0.288273
\(589\) −18.5012 −0.762329
\(590\) 36.3700 1.49733
\(591\) −8.22711 −0.338418
\(592\) −9.20402 −0.378283
\(593\) −5.71708 −0.234772 −0.117386 0.993086i \(-0.537452\pi\)
−0.117386 + 0.993086i \(0.537452\pi\)
\(594\) −12.9162 −0.529956
\(595\) −27.1978 −1.11500
\(596\) 20.4133 0.836161
\(597\) −24.3630 −0.997111
\(598\) −17.1800 −0.702544
\(599\) −39.3916 −1.60950 −0.804749 0.593615i \(-0.797700\pi\)
−0.804749 + 0.593615i \(0.797700\pi\)
\(600\) −11.6125 −0.474080
\(601\) 2.40324 0.0980301 0.0490150 0.998798i \(-0.484392\pi\)
0.0490150 + 0.998798i \(0.484392\pi\)
\(602\) 2.13166 0.0868799
\(603\) −2.95087 −0.120169
\(604\) −6.13396 −0.249587
\(605\) −4.79493 −0.194942
\(606\) 34.3228 1.39427
\(607\) 4.40536 0.178808 0.0894040 0.995995i \(-0.471504\pi\)
0.0894040 + 0.995995i \(0.471504\pi\)
\(608\) 1.86336 0.0755691
\(609\) −6.06660 −0.245831
\(610\) −37.8134 −1.53102
\(611\) 4.28110 0.173195
\(612\) −3.89042 −0.157261
\(613\) 20.4673 0.826668 0.413334 0.910580i \(-0.364364\pi\)
0.413334 + 0.910580i \(0.364364\pi\)
\(614\) 22.9778 0.927307
\(615\) 63.7096 2.56902
\(616\) −5.73916 −0.231237
\(617\) −19.6640 −0.791643 −0.395821 0.918328i \(-0.629540\pi\)
−0.395821 + 0.918328i \(0.629540\pi\)
\(618\) −17.6650 −0.710589
\(619\) 11.7181 0.470989 0.235495 0.971876i \(-0.424329\pi\)
0.235495 + 0.971876i \(0.424329\pi\)
\(620\) −32.7771 −1.31636
\(621\) −29.5271 −1.18488
\(622\) −23.7259 −0.951322
\(623\) −17.7443 −0.710912
\(624\) −4.78898 −0.191713
\(625\) −19.7063 −0.788251
\(626\) 22.8174 0.911967
\(627\) 11.3368 0.452750
\(628\) −3.51678 −0.140335
\(629\) 40.8266 1.62786
\(630\) 5.37774 0.214254
\(631\) −12.7538 −0.507722 −0.253861 0.967241i \(-0.581701\pi\)
−0.253861 + 0.967241i \(0.581701\pi\)
\(632\) −8.92708 −0.355100
\(633\) −17.1157 −0.680289
\(634\) −3.37029 −0.133851
\(635\) 11.6070 0.460610
\(636\) 7.71281 0.305833
\(637\) −8.63439 −0.342107
\(638\) −5.12549 −0.202920
\(639\) 1.59402 0.0630584
\(640\) 3.30115 0.130490
\(641\) −26.6301 −1.05183 −0.525914 0.850538i \(-0.676276\pi\)
−0.525914 + 0.850538i \(0.676276\pi\)
\(642\) −20.4823 −0.808372
\(643\) −6.55098 −0.258345 −0.129173 0.991622i \(-0.541232\pi\)
−0.129173 + 0.991622i \(0.541232\pi\)
\(644\) −13.1201 −0.517003
\(645\) −7.45987 −0.293732
\(646\) −8.26535 −0.325196
\(647\) 35.0038 1.37614 0.688071 0.725643i \(-0.258458\pi\)
0.688071 + 0.725643i \(0.258458\pi\)
\(648\) −10.8620 −0.426698
\(649\) −34.0426 −1.33629
\(650\) 14.3439 0.562614
\(651\) 36.3127 1.42321
\(652\) −0.253671 −0.00993451
\(653\) −0.218475 −0.00854957 −0.00427478 0.999991i \(-0.501361\pi\)
−0.00427478 + 0.999991i \(0.501361\pi\)
\(654\) −2.82578 −0.110497
\(655\) 64.2971 2.51230
\(656\) −9.80139 −0.382680
\(657\) 3.24987 0.126789
\(658\) 3.26939 0.127454
\(659\) 46.1873 1.79920 0.899601 0.436713i \(-0.143857\pi\)
0.899601 + 0.436713i \(0.143857\pi\)
\(660\) 20.0845 0.781790
\(661\) −3.13371 −0.121887 −0.0609435 0.998141i \(-0.519411\pi\)
−0.0609435 + 0.998141i \(0.519411\pi\)
\(662\) −17.7755 −0.690864
\(663\) 21.2426 0.824995
\(664\) 7.98237 0.309776
\(665\) 11.4252 0.443051
\(666\) −8.07251 −0.312803
\(667\) −11.7172 −0.453691
\(668\) −16.2070 −0.627066
\(669\) −49.0579 −1.89669
\(670\) −11.1067 −0.429089
\(671\) 35.3936 1.36636
\(672\) −3.65725 −0.141082
\(673\) 35.9208 1.38465 0.692323 0.721588i \(-0.256587\pi\)
0.692323 + 0.721588i \(0.256587\pi\)
\(674\) 2.85351 0.109913
\(675\) 24.6527 0.948882
\(676\) −7.08462 −0.272485
\(677\) 2.06627 0.0794131 0.0397065 0.999211i \(-0.487358\pi\)
0.0397065 + 0.999211i \(0.487358\pi\)
\(678\) 22.8660 0.878164
\(679\) −34.4457 −1.32190
\(680\) −14.6430 −0.561535
\(681\) −11.7751 −0.451222
\(682\) 30.6796 1.17478
\(683\) 1.28584 0.0492013 0.0246007 0.999697i \(-0.492169\pi\)
0.0246007 + 0.999697i \(0.492169\pi\)
\(684\) 1.63428 0.0624883
\(685\) 17.0205 0.650319
\(686\) −19.5957 −0.748166
\(687\) −32.1649 −1.22717
\(688\) 1.14766 0.0437542
\(689\) −9.52692 −0.362947
\(690\) 45.9145 1.74793
\(691\) 15.2029 0.578344 0.289172 0.957277i \(-0.406620\pi\)
0.289172 + 0.957277i \(0.406620\pi\)
\(692\) 9.63707 0.366346
\(693\) −5.03361 −0.191211
\(694\) 10.0494 0.381469
\(695\) 35.6157 1.35098
\(696\) −3.26619 −0.123805
\(697\) 43.4764 1.64678
\(698\) 26.6497 1.00871
\(699\) 32.6011 1.23309
\(700\) 10.9542 0.414028
\(701\) 46.1050 1.74136 0.870680 0.491849i \(-0.163679\pi\)
0.870680 + 0.491849i \(0.163679\pi\)
\(702\) 10.1667 0.383717
\(703\) −17.1504 −0.646838
\(704\) −3.08990 −0.116455
\(705\) −11.4414 −0.430910
\(706\) 2.24877 0.0846336
\(707\) −32.3768 −1.21766
\(708\) −21.6935 −0.815290
\(709\) −33.4378 −1.25578 −0.627891 0.778302i \(-0.716081\pi\)
−0.627891 + 0.778302i \(0.716081\pi\)
\(710\) 5.99968 0.225164
\(711\) −7.82962 −0.293634
\(712\) −9.55337 −0.358028
\(713\) 70.1354 2.62659
\(714\) 16.2226 0.607115
\(715\) −24.8086 −0.927788
\(716\) −3.01116 −0.112532
\(717\) −13.5053 −0.504366
\(718\) −21.4690 −0.801214
\(719\) −48.3873 −1.80454 −0.902271 0.431168i \(-0.858101\pi\)
−0.902271 + 0.431168i \(0.858101\pi\)
\(720\) 2.89532 0.107902
\(721\) 16.6634 0.620579
\(722\) −15.5279 −0.577889
\(723\) −3.90952 −0.145397
\(724\) −0.836448 −0.0310864
\(725\) 9.78287 0.363327
\(726\) 2.86001 0.106145
\(727\) −13.4339 −0.498236 −0.249118 0.968473i \(-0.580141\pi\)
−0.249118 + 0.968473i \(0.580141\pi\)
\(728\) 4.51746 0.167428
\(729\) 15.1657 0.561691
\(730\) 12.2321 0.452730
\(731\) −5.09073 −0.188287
\(732\) 22.5544 0.833635
\(733\) 19.9571 0.737133 0.368566 0.929601i \(-0.379849\pi\)
0.368566 + 0.929601i \(0.379849\pi\)
\(734\) −17.9391 −0.662143
\(735\) 23.0758 0.851165
\(736\) −7.06371 −0.260372
\(737\) 10.3959 0.382940
\(738\) −8.59644 −0.316439
\(739\) 33.8681 1.24586 0.622928 0.782279i \(-0.285943\pi\)
0.622928 + 0.782279i \(0.285943\pi\)
\(740\) −30.3839 −1.11693
\(741\) −8.92357 −0.327816
\(742\) −7.27553 −0.267093
\(743\) −48.0257 −1.76189 −0.880946 0.473217i \(-0.843093\pi\)
−0.880946 + 0.473217i \(0.843093\pi\)
\(744\) 19.5504 0.716753
\(745\) 67.3873 2.46888
\(746\) 24.2363 0.887355
\(747\) 7.00105 0.256155
\(748\) 13.7060 0.501141
\(749\) 19.3210 0.705975
\(750\) −5.83450 −0.213046
\(751\) −32.5747 −1.18867 −0.594333 0.804219i \(-0.702584\pi\)
−0.594333 + 0.804219i \(0.702584\pi\)
\(752\) 1.76021 0.0641881
\(753\) −5.17201 −0.188478
\(754\) 4.03442 0.146925
\(755\) −20.2491 −0.736941
\(756\) 7.76411 0.282378
\(757\) 8.56134 0.311167 0.155584 0.987823i \(-0.450274\pi\)
0.155584 + 0.987823i \(0.450274\pi\)
\(758\) 9.25112 0.336016
\(759\) −42.9763 −1.55994
\(760\) 6.15122 0.223128
\(761\) −43.7731 −1.58677 −0.793387 0.608718i \(-0.791684\pi\)
−0.793387 + 0.608718i \(0.791684\pi\)
\(762\) −6.92319 −0.250801
\(763\) 2.66557 0.0965002
\(764\) 1.65960 0.0600423
\(765\) −12.8429 −0.464335
\(766\) −2.97151 −0.107365
\(767\) 26.7959 0.967544
\(768\) −1.96903 −0.0710511
\(769\) 30.0122 1.08227 0.541134 0.840936i \(-0.317995\pi\)
0.541134 + 0.840936i \(0.317995\pi\)
\(770\) −18.9458 −0.682760
\(771\) −30.5982 −1.10197
\(772\) 15.6955 0.564893
\(773\) 30.6254 1.10152 0.550759 0.834665i \(-0.314338\pi\)
0.550759 + 0.834665i \(0.314338\pi\)
\(774\) 1.00657 0.0361805
\(775\) −58.5572 −2.10344
\(776\) −18.5452 −0.665734
\(777\) 33.6614 1.20760
\(778\) −12.6105 −0.452109
\(779\) −18.2635 −0.654357
\(780\) −15.8091 −0.566058
\(781\) −5.61574 −0.200947
\(782\) 31.3327 1.12046
\(783\) 6.93392 0.247798
\(784\) −3.55010 −0.126789
\(785\) −11.6094 −0.414358
\(786\) −38.3510 −1.36794
\(787\) 19.3665 0.690341 0.345171 0.938540i \(-0.387821\pi\)
0.345171 + 0.938540i \(0.387821\pi\)
\(788\) 4.17827 0.148845
\(789\) 35.5219 1.26461
\(790\) −29.4697 −1.04848
\(791\) −21.5696 −0.766927
\(792\) −2.71004 −0.0962971
\(793\) −27.8594 −0.989315
\(794\) −25.7601 −0.914192
\(795\) 25.4612 0.903015
\(796\) 12.3731 0.438553
\(797\) −33.2779 −1.17876 −0.589382 0.807855i \(-0.700629\pi\)
−0.589382 + 0.807855i \(0.700629\pi\)
\(798\) −6.81476 −0.241240
\(799\) −7.80781 −0.276220
\(800\) 5.89761 0.208512
\(801\) −8.37891 −0.296054
\(802\) −29.4609 −1.04030
\(803\) −11.4493 −0.404038
\(804\) 6.62477 0.233638
\(805\) −43.3113 −1.52652
\(806\) −24.1488 −0.850605
\(807\) −5.02917 −0.177035
\(808\) −17.4314 −0.613233
\(809\) −5.16129 −0.181461 −0.0907307 0.995875i \(-0.528920\pi\)
−0.0907307 + 0.995875i \(0.528920\pi\)
\(810\) −35.8570 −1.25988
\(811\) 30.1396 1.05835 0.529173 0.848514i \(-0.322502\pi\)
0.529173 + 0.848514i \(0.322502\pi\)
\(812\) 3.08101 0.108122
\(813\) −31.0994 −1.09070
\(814\) 28.4395 0.996805
\(815\) −0.837406 −0.0293331
\(816\) 8.73408 0.305754
\(817\) 2.13851 0.0748168
\(818\) 9.91199 0.346565
\(819\) 3.96210 0.138447
\(820\) −32.3559 −1.12992
\(821\) 19.5959 0.683903 0.341951 0.939718i \(-0.388912\pi\)
0.341951 + 0.939718i \(0.388912\pi\)
\(822\) −10.1521 −0.354096
\(823\) 38.4553 1.34047 0.670234 0.742150i \(-0.266194\pi\)
0.670234 + 0.742150i \(0.266194\pi\)
\(824\) 8.97142 0.312534
\(825\) 35.8816 1.24924
\(826\) 20.4635 0.712017
\(827\) 47.8490 1.66387 0.831937 0.554870i \(-0.187232\pi\)
0.831937 + 0.554870i \(0.187232\pi\)
\(828\) −6.19532 −0.215302
\(829\) −51.4777 −1.78790 −0.893948 0.448171i \(-0.852076\pi\)
−0.893948 + 0.448171i \(0.852076\pi\)
\(830\) 26.3510 0.914657
\(831\) 34.0292 1.18046
\(832\) 2.43216 0.0843198
\(833\) 15.7473 0.545612
\(834\) −21.2435 −0.735604
\(835\) −53.5016 −1.85150
\(836\) −5.75759 −0.199130
\(837\) −41.5043 −1.43460
\(838\) −15.2195 −0.525749
\(839\) 29.8656 1.03107 0.515537 0.856868i \(-0.327593\pi\)
0.515537 + 0.856868i \(0.327593\pi\)
\(840\) −12.0731 −0.416563
\(841\) −26.2484 −0.905118
\(842\) 27.9218 0.962247
\(843\) 5.33376 0.183705
\(844\) 8.69248 0.299207
\(845\) −23.3874 −0.804552
\(846\) 1.54381 0.0530774
\(847\) −2.69786 −0.0926996
\(848\) −3.91707 −0.134513
\(849\) 36.7673 1.26185
\(850\) −26.1602 −0.897288
\(851\) 65.0145 2.22867
\(852\) −3.57861 −0.122601
\(853\) 43.5825 1.49224 0.746118 0.665814i \(-0.231915\pi\)
0.746118 + 0.665814i \(0.231915\pi\)
\(854\) −21.2757 −0.728039
\(855\) 5.39501 0.184506
\(856\) 10.4022 0.355541
\(857\) 6.03342 0.206098 0.103049 0.994676i \(-0.467140\pi\)
0.103049 + 0.994676i \(0.467140\pi\)
\(858\) 14.7975 0.505177
\(859\) −39.0553 −1.33255 −0.666274 0.745707i \(-0.732112\pi\)
−0.666274 + 0.745707i \(0.732112\pi\)
\(860\) 3.78861 0.129191
\(861\) 35.8461 1.22163
\(862\) −21.4912 −0.731993
\(863\) −20.1470 −0.685813 −0.342906 0.939370i \(-0.611411\pi\)
−0.342906 + 0.939370i \(0.611411\pi\)
\(864\) 4.18012 0.142210
\(865\) 31.8134 1.08169
\(866\) −15.6415 −0.531519
\(867\) −5.26861 −0.178931
\(868\) −18.4420 −0.625962
\(869\) 27.5838 0.935717
\(870\) −10.7822 −0.365551
\(871\) −8.18296 −0.277269
\(872\) 1.43512 0.0485992
\(873\) −16.2653 −0.550498
\(874\) −13.1622 −0.445218
\(875\) 5.50371 0.186059
\(876\) −7.29603 −0.246510
\(877\) −8.94746 −0.302134 −0.151067 0.988523i \(-0.548271\pi\)
−0.151067 + 0.988523i \(0.548271\pi\)
\(878\) −0.372896 −0.0125846
\(879\) −29.0704 −0.980520
\(880\) −10.2002 −0.343850
\(881\) −1.80227 −0.0607201 −0.0303601 0.999539i \(-0.509665\pi\)
−0.0303601 + 0.999539i \(0.509665\pi\)
\(882\) −3.11366 −0.104842
\(883\) −31.8607 −1.07220 −0.536099 0.844155i \(-0.680103\pi\)
−0.536099 + 0.844155i \(0.680103\pi\)
\(884\) −10.7884 −0.362853
\(885\) −71.6134 −2.40726
\(886\) −23.0059 −0.772900
\(887\) 7.16627 0.240620 0.120310 0.992736i \(-0.461611\pi\)
0.120310 + 0.992736i \(0.461611\pi\)
\(888\) 18.1230 0.608167
\(889\) 6.53068 0.219032
\(890\) −31.5371 −1.05713
\(891\) 33.5624 1.12438
\(892\) 24.9148 0.834210
\(893\) 3.27989 0.109757
\(894\) −40.1943 −1.34430
\(895\) −9.94030 −0.332267
\(896\) 1.85739 0.0620511
\(897\) 33.8279 1.12948
\(898\) 0.341228 0.0113869
\(899\) −16.4700 −0.549307
\(900\) 5.17258 0.172419
\(901\) 17.3751 0.578848
\(902\) 30.2853 1.00839
\(903\) −4.19729 −0.139677
\(904\) −11.6128 −0.386238
\(905\) −2.76124 −0.0917868
\(906\) 12.0779 0.401262
\(907\) 4.75130 0.157764 0.0788822 0.996884i \(-0.474865\pi\)
0.0788822 + 0.996884i \(0.474865\pi\)
\(908\) 5.98015 0.198458
\(909\) −15.2884 −0.507084
\(910\) 14.9128 0.494356
\(911\) −39.1743 −1.29790 −0.648951 0.760830i \(-0.724792\pi\)
−0.648951 + 0.760830i \(0.724792\pi\)
\(912\) −3.66900 −0.121493
\(913\) −24.6647 −0.816284
\(914\) −15.9510 −0.527612
\(915\) 74.4556 2.46143
\(916\) 16.3355 0.539739
\(917\) 36.1767 1.19466
\(918\) −18.5419 −0.611974
\(919\) 46.7454 1.54199 0.770995 0.636841i \(-0.219759\pi\)
0.770995 + 0.636841i \(0.219759\pi\)
\(920\) −23.3184 −0.768784
\(921\) −45.2438 −1.49083
\(922\) −10.0048 −0.329491
\(923\) 4.42032 0.145497
\(924\) 11.3005 0.371761
\(925\) −54.2817 −1.78477
\(926\) 10.9141 0.358659
\(927\) 7.86851 0.258436
\(928\) 1.65879 0.0544523
\(929\) 42.1050 1.38142 0.690711 0.723131i \(-0.257298\pi\)
0.690711 + 0.723131i \(0.257298\pi\)
\(930\) 64.5389 2.11631
\(931\) −6.61510 −0.216801
\(932\) −16.5570 −0.542342
\(933\) 46.7169 1.52944
\(934\) 12.8464 0.420347
\(935\) 45.2456 1.47969
\(936\) 2.13315 0.0697243
\(937\) −27.4100 −0.895444 −0.447722 0.894173i \(-0.647765\pi\)
−0.447722 + 0.894173i \(0.647765\pi\)
\(938\) −6.24917 −0.204043
\(939\) −44.9281 −1.46617
\(940\) 5.81071 0.189524
\(941\) −20.1827 −0.657937 −0.328969 0.944341i \(-0.606701\pi\)
−0.328969 + 0.944341i \(0.606701\pi\)
\(942\) 6.92463 0.225617
\(943\) 69.2342 2.25457
\(944\) 11.0174 0.358584
\(945\) 25.6305 0.833761
\(946\) −3.54617 −0.115296
\(947\) −0.716471 −0.0232822 −0.0116411 0.999932i \(-0.503706\pi\)
−0.0116411 + 0.999932i \(0.503706\pi\)
\(948\) 17.5777 0.570896
\(949\) 9.01210 0.292545
\(950\) 10.9893 0.356541
\(951\) 6.63619 0.215193
\(952\) −8.23889 −0.267024
\(953\) 12.7870 0.414212 0.207106 0.978318i \(-0.433595\pi\)
0.207106 + 0.978318i \(0.433595\pi\)
\(954\) −3.43552 −0.111229
\(955\) 5.47860 0.177283
\(956\) 6.85890 0.221833
\(957\) 10.0922 0.326235
\(958\) −19.9150 −0.643423
\(959\) 9.57655 0.309243
\(960\) −6.50006 −0.209788
\(961\) 67.5845 2.18015
\(962\) −22.3856 −0.721741
\(963\) 9.12343 0.293998
\(964\) 1.98551 0.0639489
\(965\) 51.8132 1.66793
\(966\) 25.8337 0.831187
\(967\) 17.3260 0.557167 0.278583 0.960412i \(-0.410135\pi\)
0.278583 + 0.960412i \(0.410135\pi\)
\(968\) −1.45250 −0.0466851
\(969\) 16.2747 0.522819
\(970\) −61.2206 −1.96567
\(971\) 23.9207 0.767650 0.383825 0.923406i \(-0.374607\pi\)
0.383825 + 0.923406i \(0.374607\pi\)
\(972\) 8.84711 0.283771
\(973\) 20.0391 0.642425
\(974\) 4.82401 0.154571
\(975\) −28.2435 −0.904516
\(976\) −11.4546 −0.366653
\(977\) 41.0508 1.31333 0.656666 0.754182i \(-0.271966\pi\)
0.656666 + 0.754182i \(0.271966\pi\)
\(978\) 0.499484 0.0159717
\(979\) 29.5190 0.943431
\(980\) −11.7194 −0.374363
\(981\) 1.25869 0.0401868
\(982\) −42.5241 −1.35700
\(983\) 49.5424 1.58016 0.790079 0.613005i \(-0.210040\pi\)
0.790079 + 0.613005i \(0.210040\pi\)
\(984\) 19.2992 0.615236
\(985\) 13.7931 0.439484
\(986\) −7.35793 −0.234324
\(987\) −6.43752 −0.204908
\(988\) 4.53197 0.144181
\(989\) −8.10676 −0.257780
\(990\) −8.94626 −0.284331
\(991\) −13.5708 −0.431092 −0.215546 0.976494i \(-0.569153\pi\)
−0.215546 + 0.976494i \(0.569153\pi\)
\(992\) −9.92897 −0.315245
\(993\) 35.0004 1.11070
\(994\) 3.37572 0.107071
\(995\) 40.8455 1.29489
\(996\) −15.7175 −0.498028
\(997\) −38.8697 −1.23102 −0.615508 0.788131i \(-0.711049\pi\)
−0.615508 + 0.788131i \(0.711049\pi\)
\(998\) −8.65225 −0.273882
\(999\) −38.4739 −1.21726
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 \(a_p\))