Properties

Label 4033.2.a.d.1.15
Level 4033
Weight 2
Character 4033.1
Self dual Yes
Analytic conductor 32.204
Analytic rank 1
Dimension 79
CM No

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Newspace parameters

Level: \( N \) = \( 4033 = 37 \cdot 109 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4033.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.2036671352\)
Analytic rank: \(1\)
Dimension: \(79\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 4033.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.08653 q^{2}\) \(+2.88703 q^{3}\) \(+2.35363 q^{4}\) \(-4.18679 q^{5}\) \(-6.02388 q^{6}\) \(-1.99666 q^{7}\) \(-0.737856 q^{8}\) \(+5.33492 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.08653 q^{2}\) \(+2.88703 q^{3}\) \(+2.35363 q^{4}\) \(-4.18679 q^{5}\) \(-6.02388 q^{6}\) \(-1.99666 q^{7}\) \(-0.737856 q^{8}\) \(+5.33492 q^{9}\) \(+8.73588 q^{10}\) \(+3.06980 q^{11}\) \(+6.79498 q^{12}\) \(+0.158092 q^{13}\) \(+4.16610 q^{14}\) \(-12.0874 q^{15}\) \(-3.16769 q^{16}\) \(-3.54579 q^{17}\) \(-11.1315 q^{18}\) \(+4.28964 q^{19}\) \(-9.85414 q^{20}\) \(-5.76441 q^{21}\) \(-6.40523 q^{22}\) \(-1.05297 q^{23}\) \(-2.13021 q^{24}\) \(+12.5292 q^{25}\) \(-0.329864 q^{26}\) \(+6.74097 q^{27}\) \(-4.69940 q^{28}\) \(-7.99932 q^{29}\) \(+25.2207 q^{30}\) \(+1.29591 q^{31}\) \(+8.08521 q^{32}\) \(+8.86258 q^{33}\) \(+7.39842 q^{34}\) \(+8.35960 q^{35}\) \(+12.5564 q^{36}\) \(-1.00000 q^{37}\) \(-8.95048 q^{38}\) \(+0.456415 q^{39}\) \(+3.08925 q^{40}\) \(-0.110396 q^{41}\) \(+12.0276 q^{42}\) \(+3.87431 q^{43}\) \(+7.22515 q^{44}\) \(-22.3362 q^{45}\) \(+2.19706 q^{46}\) \(-3.80279 q^{47}\) \(-9.14521 q^{48}\) \(-3.01335 q^{49}\) \(-26.1426 q^{50}\) \(-10.2368 q^{51}\) \(+0.372089 q^{52}\) \(+8.59885 q^{53}\) \(-14.0653 q^{54}\) \(-12.8526 q^{55}\) \(+1.47325 q^{56}\) \(+12.3843 q^{57}\) \(+16.6909 q^{58}\) \(-11.5903 q^{59}\) \(-28.4492 q^{60}\) \(-10.5347 q^{61}\) \(-2.70396 q^{62}\) \(-10.6520 q^{63}\) \(-10.5347 q^{64}\) \(-0.661897 q^{65}\) \(-18.4921 q^{66}\) \(+3.45692 q^{67}\) \(-8.34547 q^{68}\) \(-3.03996 q^{69}\) \(-17.4426 q^{70}\) \(+8.33434 q^{71}\) \(-3.93640 q^{72}\) \(+13.1132 q^{73}\) \(+2.08653 q^{74}\) \(+36.1721 q^{75}\) \(+10.0962 q^{76}\) \(-6.12934 q^{77}\) \(-0.952325 q^{78}\) \(+1.18523 q^{79}\) \(+13.2625 q^{80}\) \(+3.45659 q^{81}\) \(+0.230346 q^{82}\) \(+0.476753 q^{83}\) \(-13.5673 q^{84}\) \(+14.8455 q^{85}\) \(-8.08387 q^{86}\) \(-23.0942 q^{87}\) \(-2.26507 q^{88}\) \(+1.85481 q^{89}\) \(+46.6052 q^{90}\) \(-0.315655 q^{91}\) \(-2.47831 q^{92}\) \(+3.74132 q^{93}\) \(+7.93465 q^{94}\) \(-17.9598 q^{95}\) \(+23.3422 q^{96}\) \(-5.50030 q^{97}\) \(+6.28745 q^{98}\) \(+16.3771 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut -\mathstrut 13q^{10} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut -\mathstrut 40q^{12} \) \(\mathstrut -\mathstrut 18q^{13} \) \(\mathstrut -\mathstrut 42q^{14} \) \(\mathstrut -\mathstrut 49q^{15} \) \(\mathstrut +\mathstrut 83q^{16} \) \(\mathstrut -\mathstrut 62q^{17} \) \(\mathstrut -\mathstrut 33q^{18} \) \(\mathstrut -\mathstrut 25q^{19} \) \(\mathstrut -\mathstrut 39q^{20} \) \(\mathstrut -\mathstrut 15q^{21} \) \(\mathstrut -\mathstrut 31q^{22} \) \(\mathstrut -\mathstrut 94q^{23} \) \(\mathstrut -\mathstrut 39q^{24} \) \(\mathstrut +\mathstrut 71q^{25} \) \(\mathstrut -\mathstrut 35q^{26} \) \(\mathstrut -\mathstrut 47q^{27} \) \(\mathstrut -\mathstrut 13q^{28} \) \(\mathstrut -\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 15q^{30} \) \(\mathstrut -\mathstrut 37q^{31} \) \(\mathstrut -\mathstrut 105q^{32} \) \(\mathstrut -\mathstrut 60q^{33} \) \(\mathstrut +\mathstrut 9q^{34} \) \(\mathstrut -\mathstrut 60q^{35} \) \(\mathstrut +\mathstrut 43q^{36} \) \(\mathstrut -\mathstrut 79q^{37} \) \(\mathstrut -\mathstrut 80q^{38} \) \(\mathstrut -\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 64q^{40} \) \(\mathstrut -\mathstrut 37q^{41} \) \(\mathstrut -\mathstrut 30q^{42} \) \(\mathstrut -\mathstrut 20q^{43} \) \(\mathstrut -\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 8q^{45} \) \(\mathstrut +\mathstrut 61q^{46} \) \(\mathstrut -\mathstrut 148q^{47} \) \(\mathstrut -\mathstrut 39q^{48} \) \(\mathstrut +\mathstrut 82q^{49} \) \(\mathstrut -\mathstrut 90q^{50} \) \(\mathstrut -\mathstrut 45q^{51} \) \(\mathstrut -\mathstrut 27q^{52} \) \(\mathstrut -\mathstrut 70q^{53} \) \(\mathstrut -\mathstrut 41q^{54} \) \(\mathstrut -\mathstrut 105q^{55} \) \(\mathstrut -\mathstrut 68q^{56} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut -\mathstrut 14q^{58} \) \(\mathstrut -\mathstrut 96q^{59} \) \(\mathstrut -\mathstrut 74q^{60} \) \(\mathstrut -\mathstrut 21q^{61} \) \(\mathstrut +\mathstrut 4q^{62} \) \(\mathstrut -\mathstrut 60q^{63} \) \(\mathstrut +\mathstrut 132q^{64} \) \(\mathstrut -\mathstrut 15q^{65} \) \(\mathstrut +\mathstrut 71q^{66} \) \(\mathstrut -\mathstrut 44q^{67} \) \(\mathstrut -\mathstrut 166q^{68} \) \(\mathstrut -\mathstrut 72q^{69} \) \(\mathstrut -\mathstrut 9q^{70} \) \(\mathstrut -\mathstrut 55q^{71} \) \(\mathstrut -\mathstrut 126q^{72} \) \(\mathstrut -\mathstrut 27q^{73} \) \(\mathstrut +\mathstrut 11q^{74} \) \(\mathstrut -\mathstrut 39q^{75} \) \(\mathstrut -\mathstrut 4q^{76} \) \(\mathstrut -\mathstrut 104q^{77} \) \(\mathstrut -\mathstrut 47q^{78} \) \(\mathstrut -\mathstrut 49q^{79} \) \(\mathstrut -\mathstrut 82q^{80} \) \(\mathstrut +\mathstrut 55q^{81} \) \(\mathstrut +\mathstrut 20q^{82} \) \(\mathstrut -\mathstrut 52q^{83} \) \(\mathstrut -\mathstrut 29q^{84} \) \(\mathstrut +\mathstrut 3q^{85} \) \(\mathstrut -\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 113q^{87} \) \(\mathstrut +\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 68q^{89} \) \(\mathstrut -\mathstrut 39q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 179q^{92} \) \(\mathstrut -\mathstrut 53q^{93} \) \(\mathstrut -\mathstrut 33q^{94} \) \(\mathstrut -\mathstrut 86q^{95} \) \(\mathstrut +\mathstrut 33q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut -\mathstrut 116q^{98} \) \(\mathstrut +\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.08653 −1.47540 −0.737701 0.675127i \(-0.764089\pi\)
−0.737701 + 0.675127i \(0.764089\pi\)
\(3\) 2.88703 1.66683 0.833413 0.552651i \(-0.186384\pi\)
0.833413 + 0.552651i \(0.186384\pi\)
\(4\) 2.35363 1.17681
\(5\) −4.18679 −1.87239 −0.936195 0.351482i \(-0.885678\pi\)
−0.936195 + 0.351482i \(0.885678\pi\)
\(6\) −6.02388 −2.45924
\(7\) −1.99666 −0.754667 −0.377333 0.926077i \(-0.623159\pi\)
−0.377333 + 0.926077i \(0.623159\pi\)
\(8\) −0.737856 −0.260871
\(9\) 5.33492 1.77831
\(10\) 8.73588 2.76253
\(11\) 3.06980 0.925578 0.462789 0.886468i \(-0.346849\pi\)
0.462789 + 0.886468i \(0.346849\pi\)
\(12\) 6.79498 1.96154
\(13\) 0.158092 0.0438467 0.0219234 0.999760i \(-0.493021\pi\)
0.0219234 + 0.999760i \(0.493021\pi\)
\(14\) 4.16610 1.11344
\(15\) −12.0874 −3.12095
\(16\) −3.16769 −0.791923
\(17\) −3.54579 −0.859981 −0.429991 0.902833i \(-0.641483\pi\)
−0.429991 + 0.902833i \(0.641483\pi\)
\(18\) −11.1315 −2.62372
\(19\) 4.28964 0.984111 0.492055 0.870564i \(-0.336246\pi\)
0.492055 + 0.870564i \(0.336246\pi\)
\(20\) −9.85414 −2.20345
\(21\) −5.76441 −1.25790
\(22\) −6.40523 −1.36560
\(23\) −1.05297 −0.219560 −0.109780 0.993956i \(-0.535015\pi\)
−0.109780 + 0.993956i \(0.535015\pi\)
\(24\) −2.13021 −0.434827
\(25\) 12.5292 2.50584
\(26\) −0.329864 −0.0646916
\(27\) 6.74097 1.29730
\(28\) −4.69940 −0.888102
\(29\) −7.99932 −1.48544 −0.742718 0.669604i \(-0.766464\pi\)
−0.742718 + 0.669604i \(0.766464\pi\)
\(30\) 25.2207 4.60465
\(31\) 1.29591 0.232752 0.116376 0.993205i \(-0.462872\pi\)
0.116376 + 0.993205i \(0.462872\pi\)
\(32\) 8.08521 1.42928
\(33\) 8.86258 1.54278
\(34\) 7.39842 1.26882
\(35\) 8.35960 1.41303
\(36\) 12.5564 2.09273
\(37\) −1.00000 −0.164399
\(38\) −8.95048 −1.45196
\(39\) 0.456415 0.0730849
\(40\) 3.08925 0.488453
\(41\) −0.110396 −0.0172410 −0.00862051 0.999963i \(-0.502744\pi\)
−0.00862051 + 0.999963i \(0.502744\pi\)
\(42\) 12.0276 1.85591
\(43\) 3.87431 0.590826 0.295413 0.955370i \(-0.404543\pi\)
0.295413 + 0.955370i \(0.404543\pi\)
\(44\) 7.22515 1.08923
\(45\) −22.3362 −3.32968
\(46\) 2.19706 0.323940
\(47\) −3.80279 −0.554693 −0.277347 0.960770i \(-0.589455\pi\)
−0.277347 + 0.960770i \(0.589455\pi\)
\(48\) −9.14521 −1.32000
\(49\) −3.01335 −0.430478
\(50\) −26.1426 −3.69713
\(51\) −10.2368 −1.43344
\(52\) 0.372089 0.0515995
\(53\) 8.59885 1.18114 0.590571 0.806986i \(-0.298902\pi\)
0.590571 + 0.806986i \(0.298902\pi\)
\(54\) −14.0653 −1.91404
\(55\) −12.8526 −1.73304
\(56\) 1.47325 0.196871
\(57\) 12.3843 1.64034
\(58\) 16.6909 2.19162
\(59\) −11.5903 −1.50893 −0.754466 0.656339i \(-0.772104\pi\)
−0.754466 + 0.656339i \(0.772104\pi\)
\(60\) −28.4492 −3.67277
\(61\) −10.5347 −1.34883 −0.674417 0.738351i \(-0.735605\pi\)
−0.674417 + 0.738351i \(0.735605\pi\)
\(62\) −2.70396 −0.343403
\(63\) −10.6520 −1.34203
\(64\) −10.5347 −1.31684
\(65\) −0.661897 −0.0820982
\(66\) −18.4921 −2.27622
\(67\) 3.45692 0.422330 0.211165 0.977450i \(-0.432274\pi\)
0.211165 + 0.977450i \(0.432274\pi\)
\(68\) −8.34547 −1.01204
\(69\) −3.03996 −0.365968
\(70\) −17.4426 −2.08479
\(71\) 8.33434 0.989104 0.494552 0.869148i \(-0.335332\pi\)
0.494552 + 0.869148i \(0.335332\pi\)
\(72\) −3.93640 −0.463909
\(73\) 13.1132 1.53479 0.767395 0.641175i \(-0.221553\pi\)
0.767395 + 0.641175i \(0.221553\pi\)
\(74\) 2.08653 0.242555
\(75\) 36.1721 4.17680
\(76\) 10.0962 1.15812
\(77\) −6.12934 −0.698503
\(78\) −0.952325 −0.107830
\(79\) 1.18523 0.133349 0.0666746 0.997775i \(-0.478761\pi\)
0.0666746 + 0.997775i \(0.478761\pi\)
\(80\) 13.2625 1.48279
\(81\) 3.45659 0.384066
\(82\) 0.230346 0.0254374
\(83\) 0.476753 0.0523304 0.0261652 0.999658i \(-0.491670\pi\)
0.0261652 + 0.999658i \(0.491670\pi\)
\(84\) −13.5673 −1.48031
\(85\) 14.8455 1.61022
\(86\) −8.08387 −0.871707
\(87\) −23.0942 −2.47596
\(88\) −2.26507 −0.241457
\(89\) 1.85481 0.196609 0.0983046 0.995156i \(-0.468658\pi\)
0.0983046 + 0.995156i \(0.468658\pi\)
\(90\) 46.6052 4.91262
\(91\) −0.315655 −0.0330897
\(92\) −2.47831 −0.258381
\(93\) 3.74132 0.387957
\(94\) 7.93465 0.818396
\(95\) −17.9598 −1.84264
\(96\) 23.3422 2.38236
\(97\) −5.50030 −0.558471 −0.279236 0.960223i \(-0.590081\pi\)
−0.279236 + 0.960223i \(0.590081\pi\)
\(98\) 6.28745 0.635128
\(99\) 16.3771 1.64596
\(100\) 29.4891 2.94891
\(101\) −4.35362 −0.433201 −0.216600 0.976260i \(-0.569497\pi\)
−0.216600 + 0.976260i \(0.569497\pi\)
\(102\) 21.3594 2.11490
\(103\) 10.3794 1.02272 0.511358 0.859368i \(-0.329143\pi\)
0.511358 + 0.859368i \(0.329143\pi\)
\(104\) −0.116649 −0.0114384
\(105\) 24.1344 2.35527
\(106\) −17.9418 −1.74266
\(107\) 0.428744 0.0414482 0.0207241 0.999785i \(-0.493403\pi\)
0.0207241 + 0.999785i \(0.493403\pi\)
\(108\) 15.8657 1.52668
\(109\) −1.00000 −0.0957826
\(110\) 26.8174 2.55694
\(111\) −2.88703 −0.274024
\(112\) 6.32481 0.597638
\(113\) −0.0188257 −0.00177098 −0.000885488 1.00000i \(-0.500282\pi\)
−0.000885488 1.00000i \(0.500282\pi\)
\(114\) −25.8403 −2.42016
\(115\) 4.40858 0.411102
\(116\) −18.8274 −1.74808
\(117\) 0.843406 0.0779729
\(118\) 24.1836 2.22628
\(119\) 7.07974 0.648999
\(120\) 8.91873 0.814165
\(121\) −1.57636 −0.143305
\(122\) 21.9811 1.99007
\(123\) −0.318717 −0.0287378
\(124\) 3.05008 0.273906
\(125\) −31.5232 −2.81952
\(126\) 22.2258 1.98003
\(127\) −7.48308 −0.664016 −0.332008 0.943277i \(-0.607726\pi\)
−0.332008 + 0.943277i \(0.607726\pi\)
\(128\) 5.81057 0.513587
\(129\) 11.1852 0.984804
\(130\) 1.38107 0.121128
\(131\) −1.39904 −0.122234 −0.0611172 0.998131i \(-0.519466\pi\)
−0.0611172 + 0.998131i \(0.519466\pi\)
\(132\) 20.8592 1.81556
\(133\) −8.56496 −0.742676
\(134\) −7.21299 −0.623108
\(135\) −28.2230 −2.42905
\(136\) 2.61628 0.224344
\(137\) −22.2379 −1.89991 −0.949957 0.312381i \(-0.898873\pi\)
−0.949957 + 0.312381i \(0.898873\pi\)
\(138\) 6.34298 0.539951
\(139\) 6.16989 0.523323 0.261662 0.965160i \(-0.415730\pi\)
0.261662 + 0.965160i \(0.415730\pi\)
\(140\) 19.6754 1.66287
\(141\) −10.9787 −0.924577
\(142\) −17.3899 −1.45933
\(143\) 0.485309 0.0405836
\(144\) −16.8994 −1.40828
\(145\) 33.4915 2.78132
\(146\) −27.3612 −2.26443
\(147\) −8.69961 −0.717531
\(148\) −2.35363 −0.193467
\(149\) 17.9682 1.47201 0.736007 0.676974i \(-0.236709\pi\)
0.736007 + 0.676974i \(0.236709\pi\)
\(150\) −75.4744 −6.16246
\(151\) −8.44332 −0.687107 −0.343554 0.939133i \(-0.611631\pi\)
−0.343554 + 0.939133i \(0.611631\pi\)
\(152\) −3.16514 −0.256726
\(153\) −18.9165 −1.52931
\(154\) 12.7891 1.03057
\(155\) −5.42569 −0.435802
\(156\) 1.07423 0.0860073
\(157\) −18.7783 −1.49867 −0.749336 0.662190i \(-0.769627\pi\)
−0.749336 + 0.662190i \(0.769627\pi\)
\(158\) −2.47303 −0.196744
\(159\) 24.8251 1.96876
\(160\) −33.8511 −2.67616
\(161\) 2.10243 0.165695
\(162\) −7.21230 −0.566652
\(163\) 11.4355 0.895700 0.447850 0.894109i \(-0.352190\pi\)
0.447850 + 0.894109i \(0.352190\pi\)
\(164\) −0.259832 −0.0202895
\(165\) −37.1057 −2.88868
\(166\) −0.994761 −0.0772084
\(167\) −12.1767 −0.942258 −0.471129 0.882064i \(-0.656153\pi\)
−0.471129 + 0.882064i \(0.656153\pi\)
\(168\) 4.25330 0.328149
\(169\) −12.9750 −0.998077
\(170\) −30.9756 −2.37572
\(171\) 22.8849 1.75005
\(172\) 9.11867 0.695292
\(173\) −18.1908 −1.38302 −0.691510 0.722367i \(-0.743054\pi\)
−0.691510 + 0.722367i \(0.743054\pi\)
\(174\) 48.1869 3.65304
\(175\) −25.0166 −1.89108
\(176\) −9.72417 −0.732987
\(177\) −33.4616 −2.51513
\(178\) −3.87012 −0.290078
\(179\) −8.66274 −0.647483 −0.323742 0.946145i \(-0.604941\pi\)
−0.323742 + 0.946145i \(0.604941\pi\)
\(180\) −52.5710 −3.91841
\(181\) −16.9078 −1.25675 −0.628374 0.777912i \(-0.716279\pi\)
−0.628374 + 0.777912i \(0.716279\pi\)
\(182\) 0.658626 0.0488206
\(183\) −30.4140 −2.24827
\(184\) 0.776942 0.0572769
\(185\) 4.18679 0.307819
\(186\) −7.80639 −0.572392
\(187\) −10.8849 −0.795980
\(188\) −8.95034 −0.652771
\(189\) −13.4594 −0.979029
\(190\) 37.4738 2.71863
\(191\) 0.249458 0.0180502 0.00902508 0.999959i \(-0.497127\pi\)
0.00902508 + 0.999959i \(0.497127\pi\)
\(192\) −30.4139 −2.19494
\(193\) −3.13628 −0.225754 −0.112877 0.993609i \(-0.536007\pi\)
−0.112877 + 0.993609i \(0.536007\pi\)
\(194\) 11.4766 0.823970
\(195\) −1.91091 −0.136843
\(196\) −7.09229 −0.506592
\(197\) −24.4710 −1.74348 −0.871742 0.489965i \(-0.837010\pi\)
−0.871742 + 0.489965i \(0.837010\pi\)
\(198\) −34.1714 −2.42846
\(199\) −1.83804 −0.130295 −0.0651476 0.997876i \(-0.520752\pi\)
−0.0651476 + 0.997876i \(0.520752\pi\)
\(200\) −9.24475 −0.653702
\(201\) 9.98023 0.703951
\(202\) 9.08397 0.639146
\(203\) 15.9719 1.12101
\(204\) −24.0936 −1.68689
\(205\) 0.462206 0.0322819
\(206\) −21.6570 −1.50892
\(207\) −5.61752 −0.390445
\(208\) −0.500786 −0.0347233
\(209\) 13.1683 0.910872
\(210\) −50.3572 −3.47498
\(211\) 19.6474 1.35258 0.676291 0.736635i \(-0.263586\pi\)
0.676291 + 0.736635i \(0.263586\pi\)
\(212\) 20.2385 1.38998
\(213\) 24.0614 1.64866
\(214\) −0.894589 −0.0611529
\(215\) −16.2209 −1.10626
\(216\) −4.97386 −0.338428
\(217\) −2.58749 −0.175650
\(218\) 2.08653 0.141318
\(219\) 37.8583 2.55822
\(220\) −30.2502 −2.03947
\(221\) −0.560560 −0.0377074
\(222\) 6.02388 0.404296
\(223\) −28.5126 −1.90935 −0.954673 0.297655i \(-0.903795\pi\)
−0.954673 + 0.297655i \(0.903795\pi\)
\(224\) −16.1434 −1.07863
\(225\) 66.8423 4.45615
\(226\) 0.0392805 0.00261290
\(227\) −27.4752 −1.82359 −0.911796 0.410643i \(-0.865304\pi\)
−0.911796 + 0.410643i \(0.865304\pi\)
\(228\) 29.1480 1.93038
\(229\) 18.1710 1.20077 0.600387 0.799710i \(-0.295013\pi\)
0.600387 + 0.799710i \(0.295013\pi\)
\(230\) −9.19865 −0.606541
\(231\) −17.6956 −1.16428
\(232\) 5.90234 0.387508
\(233\) −19.8201 −1.29846 −0.649230 0.760592i \(-0.724909\pi\)
−0.649230 + 0.760592i \(0.724909\pi\)
\(234\) −1.75980 −0.115041
\(235\) 15.9215 1.03860
\(236\) −27.2793 −1.77573
\(237\) 3.42180 0.222270
\(238\) −14.7721 −0.957535
\(239\) −8.85584 −0.572836 −0.286418 0.958105i \(-0.592465\pi\)
−0.286418 + 0.958105i \(0.592465\pi\)
\(240\) 38.2891 2.47155
\(241\) 7.69249 0.495517 0.247759 0.968822i \(-0.420306\pi\)
0.247759 + 0.968822i \(0.420306\pi\)
\(242\) 3.28913 0.211433
\(243\) −10.2436 −0.657129
\(244\) −24.7948 −1.58733
\(245\) 12.6162 0.806022
\(246\) 0.665014 0.0423998
\(247\) 0.678157 0.0431501
\(248\) −0.956193 −0.0607183
\(249\) 1.37640 0.0872256
\(250\) 65.7743 4.15993
\(251\) −31.4555 −1.98545 −0.992727 0.120383i \(-0.961588\pi\)
−0.992727 + 0.120383i \(0.961588\pi\)
\(252\) −25.0709 −1.57932
\(253\) −3.23241 −0.203220
\(254\) 15.6137 0.979692
\(255\) 42.8593 2.68395
\(256\) 8.94542 0.559089
\(257\) 0.406951 0.0253849 0.0126925 0.999919i \(-0.495960\pi\)
0.0126925 + 0.999919i \(0.495960\pi\)
\(258\) −23.3384 −1.45298
\(259\) 1.99666 0.124066
\(260\) −1.55786 −0.0966143
\(261\) −42.6757 −2.64156
\(262\) 2.91914 0.180345
\(263\) 0.648543 0.0399909 0.0199954 0.999800i \(-0.493635\pi\)
0.0199954 + 0.999800i \(0.493635\pi\)
\(264\) −6.53930 −0.402466
\(265\) −36.0016 −2.21156
\(266\) 17.8711 1.09575
\(267\) 5.35487 0.327713
\(268\) 8.13631 0.497004
\(269\) 0.582066 0.0354892 0.0177446 0.999843i \(-0.494351\pi\)
0.0177446 + 0.999843i \(0.494351\pi\)
\(270\) 58.8883 3.58383
\(271\) 18.5576 1.12729 0.563647 0.826016i \(-0.309398\pi\)
0.563647 + 0.826016i \(0.309398\pi\)
\(272\) 11.2320 0.681039
\(273\) −0.911306 −0.0551547
\(274\) 46.4002 2.80314
\(275\) 38.4621 2.31935
\(276\) −7.15493 −0.430676
\(277\) −12.0589 −0.724549 −0.362274 0.932071i \(-0.618000\pi\)
−0.362274 + 0.932071i \(0.618000\pi\)
\(278\) −12.8737 −0.772113
\(279\) 6.91356 0.413904
\(280\) −6.16818 −0.368619
\(281\) 14.9185 0.889962 0.444981 0.895540i \(-0.353210\pi\)
0.444981 + 0.895540i \(0.353210\pi\)
\(282\) 22.9075 1.36412
\(283\) 2.97531 0.176864 0.0884318 0.996082i \(-0.471814\pi\)
0.0884318 + 0.996082i \(0.471814\pi\)
\(284\) 19.6159 1.16399
\(285\) −51.8505 −3.07136
\(286\) −1.01261 −0.0598771
\(287\) 0.220424 0.0130112
\(288\) 43.1339 2.54169
\(289\) −4.42736 −0.260433
\(290\) −69.8811 −4.10356
\(291\) −15.8795 −0.930873
\(292\) 30.8637 1.80616
\(293\) 22.5892 1.31967 0.659837 0.751409i \(-0.270625\pi\)
0.659837 + 0.751409i \(0.270625\pi\)
\(294\) 18.1520 1.05865
\(295\) 48.5263 2.82531
\(296\) 0.737856 0.0428870
\(297\) 20.6934 1.20075
\(298\) −37.4913 −2.17181
\(299\) −0.166466 −0.00962699
\(300\) 85.1358 4.91531
\(301\) −7.73568 −0.445877
\(302\) 17.6173 1.01376
\(303\) −12.5690 −0.722070
\(304\) −13.5883 −0.779340
\(305\) 44.1067 2.52554
\(306\) 39.4700 2.25635
\(307\) 1.08596 0.0619788 0.0309894 0.999520i \(-0.490134\pi\)
0.0309894 + 0.999520i \(0.490134\pi\)
\(308\) −14.4262 −0.822008
\(309\) 29.9657 1.70469
\(310\) 11.3209 0.642984
\(311\) −26.2601 −1.48907 −0.744536 0.667582i \(-0.767329\pi\)
−0.744536 + 0.667582i \(0.767329\pi\)
\(312\) −0.336768 −0.0190657
\(313\) −29.8583 −1.68769 −0.843844 0.536588i \(-0.819713\pi\)
−0.843844 + 0.536588i \(0.819713\pi\)
\(314\) 39.1816 2.21114
\(315\) 44.5978 2.51280
\(316\) 2.78960 0.156927
\(317\) −5.37419 −0.301844 −0.150922 0.988546i \(-0.548224\pi\)
−0.150922 + 0.988546i \(0.548224\pi\)
\(318\) −51.7984 −2.90471
\(319\) −24.5563 −1.37489
\(320\) 44.1065 2.46563
\(321\) 1.23780 0.0690870
\(322\) −4.38679 −0.244466
\(323\) −15.2102 −0.846317
\(324\) 8.13553 0.451974
\(325\) 1.98076 0.109873
\(326\) −23.8606 −1.32152
\(327\) −2.88703 −0.159653
\(328\) 0.0814566 0.00449769
\(329\) 7.59288 0.418609
\(330\) 77.4224 4.26196
\(331\) 5.39626 0.296605 0.148303 0.988942i \(-0.452619\pi\)
0.148303 + 0.988942i \(0.452619\pi\)
\(332\) 1.12210 0.0615831
\(333\) −5.33492 −0.292352
\(334\) 25.4070 1.39021
\(335\) −14.4734 −0.790767
\(336\) 18.2599 0.996158
\(337\) −4.63676 −0.252581 −0.126290 0.991993i \(-0.540307\pi\)
−0.126290 + 0.991993i \(0.540307\pi\)
\(338\) 27.0728 1.47257
\(339\) −0.0543504 −0.00295191
\(340\) 34.9407 1.89493
\(341\) 3.97817 0.215430
\(342\) −47.7501 −2.58203
\(343\) 19.9933 1.07953
\(344\) −2.85868 −0.154130
\(345\) 12.7277 0.685235
\(346\) 37.9557 2.04051
\(347\) −26.9002 −1.44408 −0.722040 0.691851i \(-0.756796\pi\)
−0.722040 + 0.691851i \(0.756796\pi\)
\(348\) −54.3552 −2.91375
\(349\) −2.90982 −0.155759 −0.0778795 0.996963i \(-0.524815\pi\)
−0.0778795 + 0.996963i \(0.524815\pi\)
\(350\) 52.1980 2.79010
\(351\) 1.06569 0.0568824
\(352\) 24.8199 1.32291
\(353\) −8.09966 −0.431101 −0.215551 0.976493i \(-0.569155\pi\)
−0.215551 + 0.976493i \(0.569155\pi\)
\(354\) 69.8188 3.71083
\(355\) −34.8941 −1.85199
\(356\) 4.36552 0.231372
\(357\) 20.4394 1.08177
\(358\) 18.0751 0.955299
\(359\) −27.8454 −1.46962 −0.734811 0.678272i \(-0.762729\pi\)
−0.734811 + 0.678272i \(0.762729\pi\)
\(360\) 16.4809 0.868618
\(361\) −0.598986 −0.0315256
\(362\) 35.2787 1.85421
\(363\) −4.55099 −0.238865
\(364\) −0.742935 −0.0389404
\(365\) −54.9024 −2.87372
\(366\) 63.4600 3.31710
\(367\) 12.4733 0.651099 0.325550 0.945525i \(-0.394451\pi\)
0.325550 + 0.945525i \(0.394451\pi\)
\(368\) 3.33550 0.173875
\(369\) −0.588955 −0.0306598
\(370\) −8.73588 −0.454157
\(371\) −17.1690 −0.891369
\(372\) 8.80567 0.456553
\(373\) 8.61311 0.445970 0.222985 0.974822i \(-0.428420\pi\)
0.222985 + 0.974822i \(0.428420\pi\)
\(374\) 22.7116 1.17439
\(375\) −91.0083 −4.69965
\(376\) 2.80591 0.144704
\(377\) −1.26463 −0.0651316
\(378\) 28.0836 1.44446
\(379\) 4.81080 0.247114 0.123557 0.992337i \(-0.460570\pi\)
0.123557 + 0.992337i \(0.460570\pi\)
\(380\) −42.2707 −2.16844
\(381\) −21.6039 −1.10680
\(382\) −0.520503 −0.0266313
\(383\) 8.51216 0.434951 0.217476 0.976066i \(-0.430218\pi\)
0.217476 + 0.976066i \(0.430218\pi\)
\(384\) 16.7753 0.856060
\(385\) 25.6623 1.30787
\(386\) 6.54396 0.333079
\(387\) 20.6691 1.05067
\(388\) −12.9457 −0.657216
\(389\) 11.5429 0.585249 0.292624 0.956227i \(-0.405471\pi\)
0.292624 + 0.956227i \(0.405471\pi\)
\(390\) 3.98719 0.201899
\(391\) 3.73362 0.188817
\(392\) 2.22341 0.112299
\(393\) −4.03906 −0.203743
\(394\) 51.0595 2.57234
\(395\) −4.96232 −0.249681
\(396\) 38.5456 1.93699
\(397\) 8.01852 0.402438 0.201219 0.979546i \(-0.435510\pi\)
0.201219 + 0.979546i \(0.435510\pi\)
\(398\) 3.83513 0.192238
\(399\) −24.7272 −1.23791
\(400\) −39.6887 −1.98443
\(401\) 30.6008 1.52813 0.764065 0.645139i \(-0.223201\pi\)
0.764065 + 0.645139i \(0.223201\pi\)
\(402\) −20.8241 −1.03861
\(403\) 0.204872 0.0102054
\(404\) −10.2468 −0.509797
\(405\) −14.4720 −0.719120
\(406\) −33.3260 −1.65394
\(407\) −3.06980 −0.152164
\(408\) 7.55328 0.373943
\(409\) −13.2434 −0.654844 −0.327422 0.944878i \(-0.606180\pi\)
−0.327422 + 0.944878i \(0.606180\pi\)
\(410\) −0.964410 −0.0476288
\(411\) −64.2014 −3.16682
\(412\) 24.4293 1.20355
\(413\) 23.1420 1.13874
\(414\) 11.7212 0.576064
\(415\) −1.99606 −0.0979829
\(416\) 1.27821 0.0626692
\(417\) 17.8126 0.872289
\(418\) −27.4762 −1.34390
\(419\) −17.2542 −0.842924 −0.421462 0.906846i \(-0.638483\pi\)
−0.421462 + 0.906846i \(0.638483\pi\)
\(420\) 56.8033 2.77172
\(421\) −8.73585 −0.425759 −0.212880 0.977078i \(-0.568284\pi\)
−0.212880 + 0.977078i \(0.568284\pi\)
\(422\) −40.9949 −1.99560
\(423\) −20.2876 −0.986415
\(424\) −6.34471 −0.308126
\(425\) −44.4260 −2.15498
\(426\) −50.2051 −2.43244
\(427\) 21.0343 1.01792
\(428\) 1.00910 0.0487769
\(429\) 1.40110 0.0676457
\(430\) 33.8455 1.63217
\(431\) 9.41660 0.453582 0.226791 0.973943i \(-0.427177\pi\)
0.226791 + 0.973943i \(0.427177\pi\)
\(432\) −21.3533 −1.02736
\(433\) −32.3039 −1.55242 −0.776212 0.630472i \(-0.782862\pi\)
−0.776212 + 0.630472i \(0.782862\pi\)
\(434\) 5.39888 0.259155
\(435\) 96.6907 4.63597
\(436\) −2.35363 −0.112718
\(437\) −4.51688 −0.216071
\(438\) −78.9926 −3.77441
\(439\) 25.3124 1.20809 0.604047 0.796949i \(-0.293554\pi\)
0.604047 + 0.796949i \(0.293554\pi\)
\(440\) 9.48335 0.452101
\(441\) −16.0759 −0.765521
\(442\) 1.16963 0.0556336
\(443\) 34.6939 1.64836 0.824178 0.566331i \(-0.191638\pi\)
0.824178 + 0.566331i \(0.191638\pi\)
\(444\) −6.79498 −0.322476
\(445\) −7.76569 −0.368129
\(446\) 59.4926 2.81706
\(447\) 51.8747 2.45359
\(448\) 21.0342 0.993773
\(449\) 20.4845 0.966722 0.483361 0.875421i \(-0.339416\pi\)
0.483361 + 0.875421i \(0.339416\pi\)
\(450\) −139.469 −6.57462
\(451\) −0.338894 −0.0159579
\(452\) −0.0443088 −0.00208411
\(453\) −24.3761 −1.14529
\(454\) 57.3279 2.69053
\(455\) 1.32158 0.0619568
\(456\) −9.13783 −0.427918
\(457\) −8.29217 −0.387891 −0.193946 0.981012i \(-0.562129\pi\)
−0.193946 + 0.981012i \(0.562129\pi\)
\(458\) −37.9144 −1.77163
\(459\) −23.9021 −1.11565
\(460\) 10.3761 0.483790
\(461\) 4.11590 0.191697 0.0958483 0.995396i \(-0.469444\pi\)
0.0958483 + 0.995396i \(0.469444\pi\)
\(462\) 36.9224 1.71779
\(463\) −13.7422 −0.638656 −0.319328 0.947644i \(-0.603457\pi\)
−0.319328 + 0.947644i \(0.603457\pi\)
\(464\) 25.3394 1.17635
\(465\) −15.6641 −0.726406
\(466\) 41.3554 1.91575
\(467\) −23.1326 −1.07045 −0.535224 0.844710i \(-0.679773\pi\)
−0.535224 + 0.844710i \(0.679773\pi\)
\(468\) 1.98506 0.0917596
\(469\) −6.90230 −0.318719
\(470\) −33.2207 −1.53236
\(471\) −54.2134 −2.49802
\(472\) 8.55199 0.393637
\(473\) 11.8933 0.546856
\(474\) −7.13970 −0.327937
\(475\) 53.7458 2.46603
\(476\) 16.6631 0.763751
\(477\) 45.8741 2.10043
\(478\) 18.4780 0.845165
\(479\) −28.2284 −1.28979 −0.644893 0.764272i \(-0.723098\pi\)
−0.644893 + 0.764272i \(0.723098\pi\)
\(480\) −97.7290 −4.46070
\(481\) −0.158092 −0.00720836
\(482\) −16.0507 −0.731087
\(483\) 6.06977 0.276184
\(484\) −3.71016 −0.168644
\(485\) 23.0286 1.04568
\(486\) 21.3737 0.969531
\(487\) 24.1370 1.09375 0.546876 0.837214i \(-0.315817\pi\)
0.546876 + 0.837214i \(0.315817\pi\)
\(488\) 7.77311 0.351872
\(489\) 33.0147 1.49298
\(490\) −26.3242 −1.18921
\(491\) 30.4537 1.37436 0.687179 0.726488i \(-0.258849\pi\)
0.687179 + 0.726488i \(0.258849\pi\)
\(492\) −0.750141 −0.0338190
\(493\) 28.3639 1.27745
\(494\) −1.41500 −0.0636637
\(495\) −68.5675 −3.08188
\(496\) −4.10504 −0.184322
\(497\) −16.6408 −0.746444
\(498\) −2.87190 −0.128693
\(499\) 26.1562 1.17091 0.585457 0.810704i \(-0.300915\pi\)
0.585457 + 0.810704i \(0.300915\pi\)
\(500\) −74.1939 −3.31805
\(501\) −35.1543 −1.57058
\(502\) 65.6330 2.92935
\(503\) 28.7989 1.28408 0.642039 0.766672i \(-0.278089\pi\)
0.642039 + 0.766672i \(0.278089\pi\)
\(504\) 7.85965 0.350097
\(505\) 18.2277 0.811121
\(506\) 6.74454 0.299831
\(507\) −37.4592 −1.66362
\(508\) −17.6124 −0.781423
\(509\) 20.1854 0.894703 0.447351 0.894358i \(-0.352367\pi\)
0.447351 + 0.894358i \(0.352367\pi\)
\(510\) −89.4274 −3.95991
\(511\) −26.1827 −1.15825
\(512\) −30.2861 −1.33847
\(513\) 28.9163 1.27669
\(514\) −0.849117 −0.0374530
\(515\) −43.4565 −1.91492
\(516\) 26.3258 1.15893
\(517\) −11.6738 −0.513412
\(518\) −4.16610 −0.183048
\(519\) −52.5172 −2.30525
\(520\) 0.488384 0.0214171
\(521\) −41.7702 −1.82998 −0.914992 0.403472i \(-0.867803\pi\)
−0.914992 + 0.403472i \(0.867803\pi\)
\(522\) 89.0444 3.89737
\(523\) 0.815699 0.0356680 0.0178340 0.999841i \(-0.494323\pi\)
0.0178340 + 0.999841i \(0.494323\pi\)
\(524\) −3.29281 −0.143847
\(525\) −72.2235 −3.15209
\(526\) −1.35321 −0.0590027
\(527\) −4.59502 −0.200162
\(528\) −28.0739 −1.22176
\(529\) −21.8912 −0.951793
\(530\) 75.1185 3.26294
\(531\) −61.8335 −2.68334
\(532\) −20.1587 −0.873991
\(533\) −0.0174527 −0.000755962 0
\(534\) −11.1731 −0.483509
\(535\) −1.79506 −0.0776073
\(536\) −2.55071 −0.110174
\(537\) −25.0095 −1.07924
\(538\) −1.21450 −0.0523609
\(539\) −9.25035 −0.398441
\(540\) −66.4264 −2.85854
\(541\) 37.5645 1.61502 0.807511 0.589852i \(-0.200814\pi\)
0.807511 + 0.589852i \(0.200814\pi\)
\(542\) −38.7211 −1.66321
\(543\) −48.8133 −2.09478
\(544\) −28.6685 −1.22915
\(545\) 4.18679 0.179342
\(546\) 1.90147 0.0813754
\(547\) 34.6399 1.48109 0.740547 0.672005i \(-0.234567\pi\)
0.740547 + 0.672005i \(0.234567\pi\)
\(548\) −52.3398 −2.23584
\(549\) −56.2019 −2.39864
\(550\) −80.2525 −3.42198
\(551\) −34.3142 −1.46183
\(552\) 2.24305 0.0954706
\(553\) −2.36651 −0.100634
\(554\) 25.1613 1.06900
\(555\) 12.0874 0.513080
\(556\) 14.5216 0.615854
\(557\) −26.0112 −1.10213 −0.551064 0.834463i \(-0.685778\pi\)
−0.551064 + 0.834463i \(0.685778\pi\)
\(558\) −14.4254 −0.610675
\(559\) 0.612496 0.0259058
\(560\) −26.4806 −1.11901
\(561\) −31.4249 −1.32676
\(562\) −31.1279 −1.31305
\(563\) −0.0410395 −0.00172961 −0.000864805 1.00000i \(-0.500275\pi\)
−0.000864805 1.00000i \(0.500275\pi\)
\(564\) −25.8399 −1.08805
\(565\) 0.0788194 0.00331596
\(566\) −6.20808 −0.260945
\(567\) −6.90164 −0.289842
\(568\) −6.14954 −0.258029
\(569\) −26.4683 −1.10961 −0.554804 0.831981i \(-0.687207\pi\)
−0.554804 + 0.831981i \(0.687207\pi\)
\(570\) 108.188 4.53149
\(571\) 14.5483 0.608828 0.304414 0.952540i \(-0.401539\pi\)
0.304414 + 0.952540i \(0.401539\pi\)
\(572\) 1.14224 0.0477593
\(573\) 0.720192 0.0300865
\(574\) −0.459922 −0.0191968
\(575\) −13.1929 −0.550183
\(576\) −56.2017 −2.34174
\(577\) −8.48698 −0.353318 −0.176659 0.984272i \(-0.556529\pi\)
−0.176659 + 0.984272i \(0.556529\pi\)
\(578\) 9.23783 0.384243
\(579\) −9.05452 −0.376293
\(580\) 78.8265 3.27309
\(581\) −0.951913 −0.0394920
\(582\) 33.1332 1.37341
\(583\) 26.3967 1.09324
\(584\) −9.67568 −0.400383
\(585\) −3.53116 −0.145996
\(586\) −47.1331 −1.94705
\(587\) 20.2853 0.837264 0.418632 0.908156i \(-0.362510\pi\)
0.418632 + 0.908156i \(0.362510\pi\)
\(588\) −20.4756 −0.844401
\(589\) 5.55898 0.229054
\(590\) −101.252 −4.16847
\(591\) −70.6483 −2.90608
\(592\) 3.16769 0.130191
\(593\) −10.7798 −0.442675 −0.221337 0.975197i \(-0.571042\pi\)
−0.221337 + 0.975197i \(0.571042\pi\)
\(594\) −43.1775 −1.77159
\(595\) −29.6414 −1.21518
\(596\) 42.2905 1.73229
\(597\) −5.30647 −0.217179
\(598\) 0.347338 0.0142037
\(599\) 35.7897 1.46233 0.731164 0.682202i \(-0.238978\pi\)
0.731164 + 0.682202i \(0.238978\pi\)
\(600\) −26.6898 −1.08961
\(601\) 28.9614 1.18136 0.590681 0.806905i \(-0.298859\pi\)
0.590681 + 0.806905i \(0.298859\pi\)
\(602\) 16.1408 0.657848
\(603\) 18.4424 0.751033
\(604\) −19.8724 −0.808597
\(605\) 6.59988 0.268323
\(606\) 26.2257 1.06534
\(607\) 19.0091 0.771556 0.385778 0.922592i \(-0.373933\pi\)
0.385778 + 0.922592i \(0.373933\pi\)
\(608\) 34.6827 1.40657
\(609\) 46.1114 1.86853
\(610\) −92.0302 −3.72619
\(611\) −0.601189 −0.0243215
\(612\) −44.5224 −1.79971
\(613\) −40.4964 −1.63564 −0.817818 0.575477i \(-0.804816\pi\)
−0.817818 + 0.575477i \(0.804816\pi\)
\(614\) −2.26589 −0.0914437
\(615\) 1.33440 0.0538083
\(616\) 4.52257 0.182219
\(617\) −2.83996 −0.114333 −0.0571663 0.998365i \(-0.518207\pi\)
−0.0571663 + 0.998365i \(0.518207\pi\)
\(618\) −62.5244 −2.51510
\(619\) 0.302818 0.0121713 0.00608564 0.999981i \(-0.498063\pi\)
0.00608564 + 0.999981i \(0.498063\pi\)
\(620\) −12.7701 −0.512858
\(621\) −7.09806 −0.284835
\(622\) 54.7926 2.19698
\(623\) −3.70342 −0.148374
\(624\) −1.44578 −0.0578776
\(625\) 69.3350 2.77340
\(626\) 62.3003 2.49002
\(627\) 38.0173 1.51826
\(628\) −44.1971 −1.76366
\(629\) 3.54579 0.141380
\(630\) −93.0548 −3.70739
\(631\) 23.5429 0.937227 0.468613 0.883403i \(-0.344754\pi\)
0.468613 + 0.883403i \(0.344754\pi\)
\(632\) −0.874531 −0.0347870
\(633\) 56.7225 2.25452
\(634\) 11.2134 0.445342
\(635\) 31.3301 1.24330
\(636\) 58.4290 2.31686
\(637\) −0.476385 −0.0188751
\(638\) 51.2375 2.02851
\(639\) 44.4630 1.75893
\(640\) −24.3277 −0.961635
\(641\) −4.73413 −0.186987 −0.0934935 0.995620i \(-0.529803\pi\)
−0.0934935 + 0.995620i \(0.529803\pi\)
\(642\) −2.58270 −0.101931
\(643\) 9.65759 0.380858 0.190429 0.981701i \(-0.439012\pi\)
0.190429 + 0.981701i \(0.439012\pi\)
\(644\) 4.94834 0.194992
\(645\) −46.8302 −1.84394
\(646\) 31.7366 1.24866
\(647\) 34.6508 1.36226 0.681132 0.732160i \(-0.261488\pi\)
0.681132 + 0.732160i \(0.261488\pi\)
\(648\) −2.55047 −0.100192
\(649\) −35.5799 −1.39664
\(650\) −4.13293 −0.162107
\(651\) −7.47014 −0.292778
\(652\) 26.9150 1.05407
\(653\) −9.15488 −0.358258 −0.179129 0.983826i \(-0.557328\pi\)
−0.179129 + 0.983826i \(0.557328\pi\)
\(654\) 6.02388 0.235552
\(655\) 5.85748 0.228871
\(656\) 0.349702 0.0136536
\(657\) 69.9581 2.72932
\(658\) −15.8428 −0.617617
\(659\) 9.19005 0.357994 0.178997 0.983850i \(-0.442715\pi\)
0.178997 + 0.983850i \(0.442715\pi\)
\(660\) −87.3331 −3.39944
\(661\) 0.209045 0.00813091 0.00406546 0.999992i \(-0.498706\pi\)
0.00406546 + 0.999992i \(0.498706\pi\)
\(662\) −11.2595 −0.437612
\(663\) −1.61835 −0.0628516
\(664\) −0.351775 −0.0136515
\(665\) 35.8597 1.39058
\(666\) 11.1315 0.431336
\(667\) 8.42307 0.326143
\(668\) −28.6593 −1.10886
\(669\) −82.3167 −3.18255
\(670\) 30.1993 1.16670
\(671\) −32.3395 −1.24845
\(672\) −46.6065 −1.79788
\(673\) −34.4177 −1.32671 −0.663353 0.748307i \(-0.730867\pi\)
−0.663353 + 0.748307i \(0.730867\pi\)
\(674\) 9.67477 0.372658
\(675\) 84.4590 3.25083
\(676\) −30.5383 −1.17455
\(677\) −7.74387 −0.297621 −0.148811 0.988866i \(-0.547544\pi\)
−0.148811 + 0.988866i \(0.547544\pi\)
\(678\) 0.113404 0.00435525
\(679\) 10.9822 0.421460
\(680\) −10.9538 −0.420060
\(681\) −79.3216 −3.03961
\(682\) −8.30059 −0.317846
\(683\) −1.52810 −0.0584710 −0.0292355 0.999573i \(-0.509307\pi\)
−0.0292355 + 0.999573i \(0.509307\pi\)
\(684\) 53.8625 2.05948
\(685\) 93.1055 3.55738
\(686\) −41.7166 −1.59275
\(687\) 52.4602 2.00148
\(688\) −12.2726 −0.467889
\(689\) 1.35941 0.0517893
\(690\) −26.5567 −1.01100
\(691\) 8.93879 0.340048 0.170024 0.985440i \(-0.445616\pi\)
0.170024 + 0.985440i \(0.445616\pi\)
\(692\) −42.8143 −1.62756
\(693\) −32.6995 −1.24215
\(694\) 56.1283 2.13060
\(695\) −25.8320 −0.979865
\(696\) 17.0402 0.645908
\(697\) 0.391443 0.0148269
\(698\) 6.07144 0.229807
\(699\) −57.2212 −2.16431
\(700\) −58.8797 −2.22544
\(701\) −49.3797 −1.86505 −0.932523 0.361110i \(-0.882398\pi\)
−0.932523 + 0.361110i \(0.882398\pi\)
\(702\) −2.22360 −0.0839244
\(703\) −4.28964 −0.161787
\(704\) −32.3393 −1.21883
\(705\) 45.9657 1.73117
\(706\) 16.9002 0.636048
\(707\) 8.69269 0.326922
\(708\) −78.7561 −2.95984
\(709\) 22.5113 0.845430 0.422715 0.906263i \(-0.361077\pi\)
0.422715 + 0.906263i \(0.361077\pi\)
\(710\) 72.8078 2.73243
\(711\) 6.32312 0.237135
\(712\) −1.36858 −0.0512897
\(713\) −1.36456 −0.0511030
\(714\) −42.6475 −1.59604
\(715\) −2.03189 −0.0759883
\(716\) −20.3889 −0.761967
\(717\) −25.5670 −0.954818
\(718\) 58.1003 2.16828
\(719\) 0.654194 0.0243973 0.0121987 0.999926i \(-0.496117\pi\)
0.0121987 + 0.999926i \(0.496117\pi\)
\(720\) 70.7542 2.63685
\(721\) −20.7242 −0.771810
\(722\) 1.24980 0.0465129
\(723\) 22.2084 0.825940
\(724\) −39.7947 −1.47896
\(725\) −100.225 −3.72227
\(726\) 9.49579 0.352422
\(727\) −7.06728 −0.262111 −0.131055 0.991375i \(-0.541837\pi\)
−0.131055 + 0.991375i \(0.541837\pi\)
\(728\) 0.232908 0.00863215
\(729\) −39.9434 −1.47939
\(730\) 114.556 4.23990
\(731\) −13.7375 −0.508099
\(732\) −71.5833 −2.64580
\(733\) −45.6776 −1.68714 −0.843570 0.537019i \(-0.819550\pi\)
−0.843570 + 0.537019i \(0.819550\pi\)
\(734\) −26.0259 −0.960634
\(735\) 36.4234 1.34350
\(736\) −8.51351 −0.313812
\(737\) 10.6120 0.390900
\(738\) 1.22888 0.0452355
\(739\) 16.9935 0.625117 0.312559 0.949898i \(-0.398814\pi\)
0.312559 + 0.949898i \(0.398814\pi\)
\(740\) 9.85414 0.362245
\(741\) 1.95786 0.0719236
\(742\) 35.8237 1.31513
\(743\) −26.2424 −0.962739 −0.481370 0.876518i \(-0.659861\pi\)
−0.481370 + 0.876518i \(0.659861\pi\)
\(744\) −2.76055 −0.101207
\(745\) −75.2292 −2.75618
\(746\) −17.9716 −0.657986
\(747\) 2.54344 0.0930594
\(748\) −25.6189 −0.936720
\(749\) −0.856056 −0.0312796
\(750\) 189.892 6.93388
\(751\) 47.1976 1.72226 0.861132 0.508382i \(-0.169756\pi\)
0.861132 + 0.508382i \(0.169756\pi\)
\(752\) 12.0461 0.439275
\(753\) −90.8129 −3.30941
\(754\) 2.63869 0.0960953
\(755\) 35.3504 1.28653
\(756\) −31.6785 −1.15213
\(757\) −37.8309 −1.37499 −0.687494 0.726190i \(-0.741289\pi\)
−0.687494 + 0.726190i \(0.741289\pi\)
\(758\) −10.0379 −0.364593
\(759\) −9.33206 −0.338732
\(760\) 13.2518 0.480692
\(761\) 27.9204 1.01211 0.506056 0.862500i \(-0.331103\pi\)
0.506056 + 0.862500i \(0.331103\pi\)
\(762\) 45.0772 1.63297
\(763\) 1.99666 0.0722840
\(764\) 0.587131 0.0212417
\(765\) 79.1994 2.86346
\(766\) −17.7609 −0.641728
\(767\) −1.83234 −0.0661618
\(768\) 25.8256 0.931903
\(769\) 27.4464 0.989743 0.494871 0.868966i \(-0.335215\pi\)
0.494871 + 0.868966i \(0.335215\pi\)
\(770\) −53.5452 −1.92963
\(771\) 1.17488 0.0423122
\(772\) −7.38164 −0.265671
\(773\) 14.6265 0.526079 0.263039 0.964785i \(-0.415275\pi\)
0.263039 + 0.964785i \(0.415275\pi\)
\(774\) −43.1268 −1.55016
\(775\) 16.2367 0.583239
\(776\) 4.05843 0.145689
\(777\) 5.76441 0.206797
\(778\) −24.0847 −0.863478
\(779\) −0.473561 −0.0169671
\(780\) −4.49758 −0.161039
\(781\) 25.5847 0.915493
\(782\) −7.79034 −0.278582
\(783\) −53.9232 −1.92706
\(784\) 9.54535 0.340906
\(785\) 78.6208 2.80610
\(786\) 8.42763 0.300604
\(787\) 2.66927 0.0951491 0.0475746 0.998868i \(-0.484851\pi\)
0.0475746 + 0.998868i \(0.484851\pi\)
\(788\) −57.5955 −2.05176
\(789\) 1.87236 0.0666578
\(790\) 10.3541 0.368381
\(791\) 0.0375886 0.00133650
\(792\) −12.0839 −0.429384
\(793\) −1.66545 −0.0591420
\(794\) −16.7309 −0.593758
\(795\) −103.937 −3.68628
\(796\) −4.32606 −0.153333
\(797\) −52.0129 −1.84239 −0.921195 0.389102i \(-0.872786\pi\)
−0.921195 + 0.389102i \(0.872786\pi\)
\(798\) 51.5943 1.82642
\(799\) 13.4839 0.477026
\(800\) 101.301 3.58154
\(801\) 9.89524 0.349631
\(802\) −63.8496 −2.25461
\(803\) 40.2550 1.42057
\(804\) 23.4897 0.828419
\(805\) −8.80243 −0.310245
\(806\) −0.427473 −0.0150571
\(807\) 1.68044 0.0591543
\(808\) 3.21234 0.113010
\(809\) 0.926175 0.0325626 0.0162813 0.999867i \(-0.494817\pi\)
0.0162813 + 0.999867i \(0.494817\pi\)
\(810\) 30.1964 1.06099
\(811\) 43.2951 1.52030 0.760149 0.649749i \(-0.225126\pi\)
0.760149 + 0.649749i \(0.225126\pi\)
\(812\) 37.5920 1.31922
\(813\) 53.5763 1.87900
\(814\) 6.40523 0.224503
\(815\) −47.8782 −1.67710
\(816\) 32.4270 1.13517
\(817\) 16.6194 0.581439
\(818\) 27.6328 0.966159
\(819\) −1.68400 −0.0588436
\(820\) 1.08786 0.0379898
\(821\) −9.91403 −0.346002 −0.173001 0.984922i \(-0.555346\pi\)
−0.173001 + 0.984922i \(0.555346\pi\)
\(822\) 133.959 4.67234
\(823\) −22.0778 −0.769582 −0.384791 0.923004i \(-0.625727\pi\)
−0.384791 + 0.923004i \(0.625727\pi\)
\(824\) −7.65852 −0.266797
\(825\) 111.041 3.86595
\(826\) −48.2865 −1.68010
\(827\) 26.1769 0.910258 0.455129 0.890425i \(-0.349593\pi\)
0.455129 + 0.890425i \(0.349593\pi\)
\(828\) −13.2216 −0.459481
\(829\) 39.0943 1.35780 0.678900 0.734231i \(-0.262457\pi\)
0.678900 + 0.734231i \(0.262457\pi\)
\(830\) 4.16485 0.144564
\(831\) −34.8143 −1.20770
\(832\) −1.66545 −0.0577390
\(833\) 10.6847 0.370203
\(834\) −37.1667 −1.28698
\(835\) 50.9811 1.76427
\(836\) 30.9933 1.07193
\(837\) 8.73567 0.301949
\(838\) 36.0015 1.24365
\(839\) 50.8751 1.75640 0.878201 0.478291i \(-0.158744\pi\)
0.878201 + 0.478291i \(0.158744\pi\)
\(840\) −17.8077 −0.614424
\(841\) 34.9891 1.20652
\(842\) 18.2277 0.628166
\(843\) 43.0700 1.48341
\(844\) 46.2426 1.59174
\(845\) 54.3236 1.86879
\(846\) 42.3307 1.45536
\(847\) 3.14745 0.108148
\(848\) −27.2385 −0.935374
\(849\) 8.58978 0.294801
\(850\) 92.6963 3.17946
\(851\) 1.05297 0.0360955
\(852\) 56.6317 1.94017
\(853\) −8.56741 −0.293342 −0.146671 0.989185i \(-0.546856\pi\)
−0.146671 + 0.989185i \(0.546856\pi\)
\(854\) −43.8888 −1.50184
\(855\) −95.8142 −3.27678
\(856\) −0.316351 −0.0108127
\(857\) −32.8619 −1.12254 −0.561271 0.827632i \(-0.689688\pi\)
−0.561271 + 0.827632i \(0.689688\pi\)
\(858\) −2.92344 −0.0998047
\(859\) −33.7271 −1.15075 −0.575376 0.817889i \(-0.695144\pi\)
−0.575376 + 0.817889i \(0.695144\pi\)
\(860\) −38.1780 −1.30186
\(861\) 0.636370 0.0216874
\(862\) −19.6481 −0.669216
\(863\) 17.0282 0.579646 0.289823 0.957080i \(-0.406404\pi\)
0.289823 + 0.957080i \(0.406404\pi\)
\(864\) 54.5021 1.85420
\(865\) 76.1610 2.58955
\(866\) 67.4031 2.29045
\(867\) −12.7819 −0.434096
\(868\) −6.08998 −0.206707
\(869\) 3.63842 0.123425
\(870\) −201.749 −6.83992
\(871\) 0.546511 0.0185178
\(872\) 0.737856 0.0249869
\(873\) −29.3437 −0.993132
\(874\) 9.42462 0.318792
\(875\) 62.9412 2.12780
\(876\) 89.1043 3.01055
\(877\) 10.0570 0.339600 0.169800 0.985479i \(-0.445688\pi\)
0.169800 + 0.985479i \(0.445688\pi\)
\(878\) −52.8151 −1.78242
\(879\) 65.2155 2.19966
\(880\) 40.7130 1.37244
\(881\) 57.3994 1.93384 0.966918 0.255088i \(-0.0821043\pi\)
0.966918 + 0.255088i \(0.0821043\pi\)
\(882\) 33.5430 1.12945
\(883\) −33.7958 −1.13732 −0.568659 0.822573i \(-0.692538\pi\)
−0.568659 + 0.822573i \(0.692538\pi\)
\(884\) −1.31935 −0.0443745
\(885\) 140.097 4.70930
\(886\) −72.3900 −2.43199
\(887\) −17.6359 −0.592157 −0.296078 0.955164i \(-0.595679\pi\)
−0.296078 + 0.955164i \(0.595679\pi\)
\(888\) 2.13021 0.0714851
\(889\) 14.9412 0.501111
\(890\) 16.2034 0.543138
\(891\) 10.6110 0.355483
\(892\) −67.1081 −2.24695
\(893\) −16.3126 −0.545880
\(894\) −108.238 −3.62003
\(895\) 36.2691 1.21234
\(896\) −11.6017 −0.387587
\(897\) −0.480592 −0.0160465
\(898\) −42.7415 −1.42630
\(899\) −10.3664 −0.345738
\(900\) 157.322 5.24406
\(901\) −30.4897 −1.01576
\(902\) 0.707114 0.0235443
\(903\) −22.3331 −0.743199
\(904\) 0.0138907 0.000461997 0
\(905\) 70.7894 2.35312
\(906\) 50.8615 1.68976
\(907\) −29.6536 −0.984633 −0.492317 0.870416i \(-0.663850\pi\)
−0.492317 + 0.870416i \(0.663850\pi\)
\(908\) −64.6664 −2.14603
\(909\) −23.2262 −0.770364
\(910\) −2.75753 −0.0914112
\(911\) −32.5549 −1.07859 −0.539296 0.842116i \(-0.681310\pi\)
−0.539296 + 0.842116i \(0.681310\pi\)
\(912\) −39.2297 −1.29902
\(913\) 1.46353 0.0484359
\(914\) 17.3019 0.572296
\(915\) 127.337 4.20964
\(916\) 42.7678 1.41309
\(917\) 2.79340 0.0922463
\(918\) 49.8725 1.64604
\(919\) 45.9636 1.51620 0.758099 0.652140i \(-0.226128\pi\)
0.758099 + 0.652140i \(0.226128\pi\)
\(920\) −3.25289 −0.107245
\(921\) 3.13519 0.103308
\(922\) −8.58797 −0.282830
\(923\) 1.31759 0.0433690
\(924\) −41.6488 −1.37014
\(925\) −12.5292 −0.411958
\(926\) 28.6737 0.942275
\(927\) 55.3734 1.81870
\(928\) −64.6762 −2.12310
\(929\) −6.80955 −0.223414 −0.111707 0.993741i \(-0.535632\pi\)
−0.111707 + 0.993741i \(0.535632\pi\)
\(930\) 32.6837 1.07174
\(931\) −12.9262 −0.423638
\(932\) −46.6492 −1.52805
\(933\) −75.8135 −2.48202
\(934\) 48.2669 1.57934
\(935\) 45.5726 1.49038
\(936\) −0.622312 −0.0203409
\(937\) −49.0367 −1.60196 −0.800980 0.598692i \(-0.795688\pi\)
−0.800980 + 0.598692i \(0.795688\pi\)
\(938\) 14.4019 0.470239
\(939\) −86.2016 −2.81308
\(940\) 37.4732 1.22224
\(941\) −39.2197 −1.27853 −0.639263 0.768988i \(-0.720760\pi\)
−0.639263 + 0.768988i \(0.720760\pi\)
\(942\) 113.118 3.68559
\(943\) 0.116244 0.00378544
\(944\) 36.7146 1.19496
\(945\) 56.3518 1.83312
\(946\) −24.8158 −0.806833
\(947\) 20.6620 0.671424 0.335712 0.941965i \(-0.391023\pi\)
0.335712 + 0.941965i \(0.391023\pi\)
\(948\) 8.05364 0.261570
\(949\) 2.07310 0.0672955
\(950\) −112.142 −3.63838
\(951\) −15.5154 −0.503122
\(952\) −5.22383 −0.169305
\(953\) −32.9748 −1.06816 −0.534079 0.845434i \(-0.679342\pi\)
−0.534079 + 0.845434i \(0.679342\pi\)
\(954\) −95.7180 −3.09898
\(955\) −1.04443 −0.0337969
\(956\) −20.8433 −0.674122
\(957\) −70.8946 −2.29170
\(958\) 58.8995 1.90296
\(959\) 44.4016 1.43380
\(960\) 127.337 4.10977
\(961\) −29.3206 −0.945827
\(962\) 0.329864 0.0106352
\(963\) 2.28731 0.0737077
\(964\) 18.1053 0.583131
\(965\) 13.1309 0.422700
\(966\) −12.6648 −0.407483
\(967\) −11.2566 −0.361986 −0.180993 0.983484i \(-0.557931\pi\)
−0.180993 + 0.983484i \(0.557931\pi\)
\(968\) 1.16312 0.0373842
\(969\) −43.9122 −1.41066
\(970\) −48.0500 −1.54279
\(971\) −47.6527 −1.52925 −0.764623 0.644477i \(-0.777075\pi\)
−0.764623 + 0.644477i \(0.777075\pi\)
\(972\) −24.1097 −0.773319
\(973\) −12.3192 −0.394935
\(974\) −50.3627 −1.61373
\(975\) 5.71852 0.183139
\(976\) 33.3708 1.06817
\(977\) 22.4780 0.719136 0.359568 0.933119i \(-0.382924\pi\)
0.359568 + 0.933119i \(0.382924\pi\)
\(978\) −68.8863 −2.20274
\(979\) 5.69388 0.181977
\(980\) 29.6939 0.948538
\(981\) −5.33492 −0.170331
\(982\) −63.5428 −2.02773
\(983\) 50.6589 1.61577 0.807884 0.589342i \(-0.200613\pi\)
0.807884 + 0.589342i \(0.200613\pi\)
\(984\) 0.235167 0.00749686
\(985\) 102.455 3.26448
\(986\) −59.1823 −1.88475
\(987\) 21.9208 0.697748
\(988\) 1.59613 0.0507796
\(989\) −4.07954 −0.129722
\(990\) 143.068 4.54701
\(991\) 49.7518 1.58042 0.790209 0.612838i \(-0.209972\pi\)
0.790209 + 0.612838i \(0.209972\pi\)
\(992\) 10.4777 0.332667
\(993\) 15.5791 0.494389
\(994\) 34.7217 1.10131
\(995\) 7.69549 0.243963
\(996\) 3.23953 0.102648
\(997\) 5.18402 0.164180 0.0820898 0.996625i \(-0.473841\pi\)
0.0820898 + 0.996625i \(0.473841\pi\)
\(998\) −54.5759 −1.72757
\(999\) −6.74097 −0.213275
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 \(a_p\))