Properties

Label 4033.2.a.d.1.7
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 1.7
Character \(\chi\) = 4033.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.60105 q^{2}\) \(+3.31359 q^{3}\) \(+4.76544 q^{4}\) \(-1.17110 q^{5}\) \(-8.61880 q^{6}\) \(+2.01510 q^{7}\) \(-7.19305 q^{8}\) \(+7.97988 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.60105 q^{2}\) \(+3.31359 q^{3}\) \(+4.76544 q^{4}\) \(-1.17110 q^{5}\) \(-8.61880 q^{6}\) \(+2.01510 q^{7}\) \(-7.19305 q^{8}\) \(+7.97988 q^{9}\) \(+3.04608 q^{10}\) \(-2.35764 q^{11}\) \(+15.7907 q^{12}\) \(-1.55402 q^{13}\) \(-5.24137 q^{14}\) \(-3.88054 q^{15}\) \(+9.17857 q^{16}\) \(-5.14771 q^{17}\) \(-20.7560 q^{18}\) \(+1.38186 q^{19}\) \(-5.58080 q^{20}\) \(+6.67721 q^{21}\) \(+6.13233 q^{22}\) \(-7.77240 q^{23}\) \(-23.8348 q^{24}\) \(-3.62853 q^{25}\) \(+4.04207 q^{26}\) \(+16.5013 q^{27}\) \(+9.60284 q^{28}\) \(+0.340737 q^{29}\) \(+10.0935 q^{30}\) \(-5.28638 q^{31}\) \(-9.48779 q^{32}\) \(-7.81225 q^{33}\) \(+13.3894 q^{34}\) \(-2.35988 q^{35}\) \(+38.0277 q^{36}\) \(-1.00000 q^{37}\) \(-3.59428 q^{38}\) \(-5.14937 q^{39}\) \(+8.42377 q^{40}\) \(+2.43498 q^{41}\) \(-17.3677 q^{42}\) \(-11.7440 q^{43}\) \(-11.2352 q^{44}\) \(-9.34522 q^{45}\) \(+20.2164 q^{46}\) \(-8.86853 q^{47}\) \(+30.4140 q^{48}\) \(-2.93938 q^{49}\) \(+9.43797 q^{50}\) \(-17.0574 q^{51}\) \(-7.40558 q^{52}\) \(-12.4091 q^{53}\) \(-42.9206 q^{54}\) \(+2.76103 q^{55}\) \(-14.4947 q^{56}\) \(+4.57891 q^{57}\) \(-0.886273 q^{58}\) \(+2.65306 q^{59}\) \(-18.4925 q^{60}\) \(+4.90042 q^{61}\) \(+13.7501 q^{62}\) \(+16.0802 q^{63}\) \(+6.32104 q^{64}\) \(+1.81991 q^{65}\) \(+20.3200 q^{66}\) \(-2.27072 q^{67}\) \(-24.5311 q^{68}\) \(-25.7545 q^{69}\) \(+6.13815 q^{70}\) \(-1.52159 q^{71}\) \(-57.3996 q^{72}\) \(+13.1359 q^{73}\) \(+2.60105 q^{74}\) \(-12.0235 q^{75}\) \(+6.58517 q^{76}\) \(-4.75088 q^{77}\) \(+13.3938 q^{78}\) \(+5.42043 q^{79}\) \(-10.7490 q^{80}\) \(+30.7388 q^{81}\) \(-6.33348 q^{82}\) \(-10.4900 q^{83}\) \(+31.8199 q^{84}\) \(+6.02848 q^{85}\) \(+30.5466 q^{86}\) \(+1.12906 q^{87}\) \(+16.9586 q^{88}\) \(+9.49778 q^{89}\) \(+24.3073 q^{90}\) \(-3.13150 q^{91}\) \(-37.0389 q^{92}\) \(-17.5169 q^{93}\) \(+23.0675 q^{94}\) \(-1.61829 q^{95}\) \(-31.4386 q^{96}\) \(+0.204257 q^{97}\) \(+7.64546 q^{98}\) \(-18.8137 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut -\mathstrut 13q^{10} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut -\mathstrut 40q^{12} \) \(\mathstrut -\mathstrut 18q^{13} \) \(\mathstrut -\mathstrut 42q^{14} \) \(\mathstrut -\mathstrut 49q^{15} \) \(\mathstrut +\mathstrut 83q^{16} \) \(\mathstrut -\mathstrut 62q^{17} \) \(\mathstrut -\mathstrut 33q^{18} \) \(\mathstrut -\mathstrut 25q^{19} \) \(\mathstrut -\mathstrut 39q^{20} \) \(\mathstrut -\mathstrut 15q^{21} \) \(\mathstrut -\mathstrut 31q^{22} \) \(\mathstrut -\mathstrut 94q^{23} \) \(\mathstrut -\mathstrut 39q^{24} \) \(\mathstrut +\mathstrut 71q^{25} \) \(\mathstrut -\mathstrut 35q^{26} \) \(\mathstrut -\mathstrut 47q^{27} \) \(\mathstrut -\mathstrut 13q^{28} \) \(\mathstrut -\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 15q^{30} \) \(\mathstrut -\mathstrut 37q^{31} \) \(\mathstrut -\mathstrut 105q^{32} \) \(\mathstrut -\mathstrut 60q^{33} \) \(\mathstrut +\mathstrut 9q^{34} \) \(\mathstrut -\mathstrut 60q^{35} \) \(\mathstrut +\mathstrut 43q^{36} \) \(\mathstrut -\mathstrut 79q^{37} \) \(\mathstrut -\mathstrut 80q^{38} \) \(\mathstrut -\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 64q^{40} \) \(\mathstrut -\mathstrut 37q^{41} \) \(\mathstrut -\mathstrut 30q^{42} \) \(\mathstrut -\mathstrut 20q^{43} \) \(\mathstrut -\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 8q^{45} \) \(\mathstrut +\mathstrut 61q^{46} \) \(\mathstrut -\mathstrut 148q^{47} \) \(\mathstrut -\mathstrut 39q^{48} \) \(\mathstrut +\mathstrut 82q^{49} \) \(\mathstrut -\mathstrut 90q^{50} \) \(\mathstrut -\mathstrut 45q^{51} \) \(\mathstrut -\mathstrut 27q^{52} \) \(\mathstrut -\mathstrut 70q^{53} \) \(\mathstrut -\mathstrut 41q^{54} \) \(\mathstrut -\mathstrut 105q^{55} \) \(\mathstrut -\mathstrut 68q^{56} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut -\mathstrut 14q^{58} \) \(\mathstrut -\mathstrut 96q^{59} \) \(\mathstrut -\mathstrut 74q^{60} \) \(\mathstrut -\mathstrut 21q^{61} \) \(\mathstrut +\mathstrut 4q^{62} \) \(\mathstrut -\mathstrut 60q^{63} \) \(\mathstrut +\mathstrut 132q^{64} \) \(\mathstrut -\mathstrut 15q^{65} \) \(\mathstrut +\mathstrut 71q^{66} \) \(\mathstrut -\mathstrut 44q^{67} \) \(\mathstrut -\mathstrut 166q^{68} \) \(\mathstrut -\mathstrut 72q^{69} \) \(\mathstrut -\mathstrut 9q^{70} \) \(\mathstrut -\mathstrut 55q^{71} \) \(\mathstrut -\mathstrut 126q^{72} \) \(\mathstrut -\mathstrut 27q^{73} \) \(\mathstrut +\mathstrut 11q^{74} \) \(\mathstrut -\mathstrut 39q^{75} \) \(\mathstrut -\mathstrut 4q^{76} \) \(\mathstrut -\mathstrut 104q^{77} \) \(\mathstrut -\mathstrut 47q^{78} \) \(\mathstrut -\mathstrut 49q^{79} \) \(\mathstrut -\mathstrut 82q^{80} \) \(\mathstrut +\mathstrut 55q^{81} \) \(\mathstrut +\mathstrut 20q^{82} \) \(\mathstrut -\mathstrut 52q^{83} \) \(\mathstrut -\mathstrut 29q^{84} \) \(\mathstrut +\mathstrut 3q^{85} \) \(\mathstrut -\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 113q^{87} \) \(\mathstrut +\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 68q^{89} \) \(\mathstrut -\mathstrut 39q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 179q^{92} \) \(\mathstrut -\mathstrut 53q^{93} \) \(\mathstrut -\mathstrut 33q^{94} \) \(\mathstrut -\mathstrut 86q^{95} \) \(\mathstrut +\mathstrut 33q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut -\mathstrut 116q^{98} \) \(\mathstrut +\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.60105 −1.83922 −0.919609 0.392835i \(-0.871494\pi\)
−0.919609 + 0.392835i \(0.871494\pi\)
\(3\) 3.31359 1.91310 0.956551 0.291565i \(-0.0941761\pi\)
0.956551 + 0.291565i \(0.0941761\pi\)
\(4\) 4.76544 2.38272
\(5\) −1.17110 −0.523731 −0.261866 0.965104i \(-0.584338\pi\)
−0.261866 + 0.965104i \(0.584338\pi\)
\(6\) −8.61880 −3.51861
\(7\) 2.01510 0.761636 0.380818 0.924650i \(-0.375642\pi\)
0.380818 + 0.924650i \(0.375642\pi\)
\(8\) −7.19305 −2.54313
\(9\) 7.97988 2.65996
\(10\) 3.04608 0.963255
\(11\) −2.35764 −0.710856 −0.355428 0.934704i \(-0.615665\pi\)
−0.355428 + 0.934704i \(0.615665\pi\)
\(12\) 15.7907 4.55839
\(13\) −1.55402 −0.431007 −0.215503 0.976503i \(-0.569139\pi\)
−0.215503 + 0.976503i \(0.569139\pi\)
\(14\) −5.24137 −1.40081
\(15\) −3.88054 −1.00195
\(16\) 9.17857 2.29464
\(17\) −5.14771 −1.24850 −0.624252 0.781223i \(-0.714596\pi\)
−0.624252 + 0.781223i \(0.714596\pi\)
\(18\) −20.7560 −4.89224
\(19\) 1.38186 0.317020 0.158510 0.987357i \(-0.449331\pi\)
0.158510 + 0.987357i \(0.449331\pi\)
\(20\) −5.58080 −1.24791
\(21\) 6.67721 1.45709
\(22\) 6.13233 1.30742
\(23\) −7.77240 −1.62066 −0.810329 0.585976i \(-0.800711\pi\)
−0.810329 + 0.585976i \(0.800711\pi\)
\(24\) −23.8348 −4.86526
\(25\) −3.62853 −0.725706
\(26\) 4.04207 0.792715
\(27\) 16.5013 3.17567
\(28\) 9.60284 1.81477
\(29\) 0.340737 0.0632733 0.0316366 0.999499i \(-0.489928\pi\)
0.0316366 + 0.999499i \(0.489928\pi\)
\(30\) 10.0935 1.84281
\(31\) −5.28638 −0.949462 −0.474731 0.880131i \(-0.657455\pi\)
−0.474731 + 0.880131i \(0.657455\pi\)
\(32\) −9.48779 −1.67722
\(33\) −7.81225 −1.35994
\(34\) 13.3894 2.29627
\(35\) −2.35988 −0.398892
\(36\) 38.0277 6.33794
\(37\) −1.00000 −0.164399
\(38\) −3.59428 −0.583069
\(39\) −5.14937 −0.824559
\(40\) 8.42377 1.33191
\(41\) 2.43498 0.380279 0.190140 0.981757i \(-0.439106\pi\)
0.190140 + 0.981757i \(0.439106\pi\)
\(42\) −17.3677 −2.67990
\(43\) −11.7440 −1.79094 −0.895469 0.445125i \(-0.853159\pi\)
−0.895469 + 0.445125i \(0.853159\pi\)
\(44\) −11.2352 −1.69377
\(45\) −9.34522 −1.39310
\(46\) 20.2164 2.98074
\(47\) −8.86853 −1.29361 −0.646804 0.762656i \(-0.723895\pi\)
−0.646804 + 0.762656i \(0.723895\pi\)
\(48\) 30.4140 4.38988
\(49\) −2.93938 −0.419911
\(50\) 9.43797 1.33473
\(51\) −17.0574 −2.38851
\(52\) −7.40558 −1.02697
\(53\) −12.4091 −1.70452 −0.852262 0.523115i \(-0.824770\pi\)
−0.852262 + 0.523115i \(0.824770\pi\)
\(54\) −42.9206 −5.84075
\(55\) 2.76103 0.372297
\(56\) −14.4947 −1.93694
\(57\) 4.57891 0.606491
\(58\) −0.886273 −0.116373
\(59\) 2.65306 0.345399 0.172700 0.984975i \(-0.444751\pi\)
0.172700 + 0.984975i \(0.444751\pi\)
\(60\) −18.4925 −2.38737
\(61\) 4.90042 0.627434 0.313717 0.949516i \(-0.398426\pi\)
0.313717 + 0.949516i \(0.398426\pi\)
\(62\) 13.7501 1.74627
\(63\) 16.0802 2.02592
\(64\) 6.32104 0.790130
\(65\) 1.81991 0.225731
\(66\) 20.3200 2.50122
\(67\) −2.27072 −0.277413 −0.138706 0.990334i \(-0.544294\pi\)
−0.138706 + 0.990334i \(0.544294\pi\)
\(68\) −24.5311 −2.97484
\(69\) −25.7545 −3.10048
\(70\) 6.13815 0.733650
\(71\) −1.52159 −0.180580 −0.0902899 0.995916i \(-0.528779\pi\)
−0.0902899 + 0.995916i \(0.528779\pi\)
\(72\) −57.3996 −6.76461
\(73\) 13.1359 1.53744 0.768720 0.639586i \(-0.220894\pi\)
0.768720 + 0.639586i \(0.220894\pi\)
\(74\) 2.60105 0.302366
\(75\) −12.0235 −1.38835
\(76\) 6.58517 0.755370
\(77\) −4.75088 −0.541413
\(78\) 13.3938 1.51654
\(79\) 5.42043 0.609846 0.304923 0.952377i \(-0.401369\pi\)
0.304923 + 0.952377i \(0.401369\pi\)
\(80\) −10.7490 −1.20178
\(81\) 30.7388 3.41542
\(82\) −6.33348 −0.699416
\(83\) −10.4900 −1.15143 −0.575713 0.817652i \(-0.695275\pi\)
−0.575713 + 0.817652i \(0.695275\pi\)
\(84\) 31.8199 3.47183
\(85\) 6.02848 0.653880
\(86\) 30.5466 3.29392
\(87\) 1.12906 0.121048
\(88\) 16.9586 1.80780
\(89\) 9.49778 1.00676 0.503381 0.864065i \(-0.332089\pi\)
0.503381 + 0.864065i \(0.332089\pi\)
\(90\) 24.3073 2.56222
\(91\) −3.13150 −0.328270
\(92\) −37.0389 −3.86158
\(93\) −17.5169 −1.81642
\(94\) 23.0675 2.37923
\(95\) −1.61829 −0.166033
\(96\) −31.4386 −3.20869
\(97\) 0.204257 0.0207392 0.0103696 0.999946i \(-0.496699\pi\)
0.0103696 + 0.999946i \(0.496699\pi\)
\(98\) 7.64546 0.772308
\(99\) −18.8137 −1.89085
\(100\) −17.2916 −1.72916
\(101\) 7.08007 0.704493 0.352247 0.935907i \(-0.385418\pi\)
0.352247 + 0.935907i \(0.385418\pi\)
\(102\) 44.3671 4.39300
\(103\) −12.9537 −1.27637 −0.638183 0.769885i \(-0.720314\pi\)
−0.638183 + 0.769885i \(0.720314\pi\)
\(104\) 11.1781 1.09610
\(105\) −7.81967 −0.763122
\(106\) 32.2767 3.13499
\(107\) −17.1427 −1.65725 −0.828624 0.559806i \(-0.810876\pi\)
−0.828624 + 0.559806i \(0.810876\pi\)
\(108\) 78.6359 7.56674
\(109\) −1.00000 −0.0957826
\(110\) −7.18157 −0.684735
\(111\) −3.31359 −0.314512
\(112\) 18.4957 1.74768
\(113\) 8.74945 0.823079 0.411539 0.911392i \(-0.364991\pi\)
0.411539 + 0.911392i \(0.364991\pi\)
\(114\) −11.9100 −1.11547
\(115\) 9.10224 0.848788
\(116\) 1.62376 0.150763
\(117\) −12.4009 −1.14646
\(118\) −6.90074 −0.635264
\(119\) −10.3731 −0.950905
\(120\) 27.9129 2.54809
\(121\) −5.44153 −0.494684
\(122\) −12.7462 −1.15399
\(123\) 8.06851 0.727513
\(124\) −25.1919 −2.26230
\(125\) 10.1049 0.903806
\(126\) −41.8255 −3.72611
\(127\) 10.3941 0.922323 0.461162 0.887316i \(-0.347433\pi\)
0.461162 + 0.887316i \(0.347433\pi\)
\(128\) 2.53425 0.223998
\(129\) −38.9147 −3.42625
\(130\) −4.73366 −0.415169
\(131\) 7.19472 0.628605 0.314303 0.949323i \(-0.398229\pi\)
0.314303 + 0.949323i \(0.398229\pi\)
\(132\) −37.2289 −3.24036
\(133\) 2.78458 0.241454
\(134\) 5.90625 0.510222
\(135\) −19.3246 −1.66320
\(136\) 37.0277 3.17510
\(137\) −3.87169 −0.330781 −0.165390 0.986228i \(-0.552888\pi\)
−0.165390 + 0.986228i \(0.552888\pi\)
\(138\) 66.9888 5.70246
\(139\) 4.52603 0.383893 0.191946 0.981405i \(-0.438520\pi\)
0.191946 + 0.981405i \(0.438520\pi\)
\(140\) −11.2459 −0.950449
\(141\) −29.3867 −2.47480
\(142\) 3.95773 0.332126
\(143\) 3.66381 0.306383
\(144\) 73.2438 6.10365
\(145\) −0.399037 −0.0331382
\(146\) −34.1671 −2.82769
\(147\) −9.73989 −0.803332
\(148\) −4.76544 −0.391717
\(149\) −19.2671 −1.57842 −0.789210 0.614123i \(-0.789510\pi\)
−0.789210 + 0.614123i \(0.789510\pi\)
\(150\) 31.2736 2.55348
\(151\) 11.8631 0.965403 0.482702 0.875785i \(-0.339656\pi\)
0.482702 + 0.875785i \(0.339656\pi\)
\(152\) −9.93977 −0.806222
\(153\) −41.0781 −3.32097
\(154\) 12.3573 0.995776
\(155\) 6.19087 0.497263
\(156\) −24.5390 −1.96470
\(157\) 0.972753 0.0776341 0.0388171 0.999246i \(-0.487641\pi\)
0.0388171 + 0.999246i \(0.487641\pi\)
\(158\) −14.0988 −1.12164
\(159\) −41.1187 −3.26093
\(160\) 11.1111 0.878412
\(161\) −15.6622 −1.23435
\(162\) −79.9530 −6.28170
\(163\) 21.1239 1.65455 0.827275 0.561797i \(-0.189890\pi\)
0.827275 + 0.561797i \(0.189890\pi\)
\(164\) 11.6037 0.906100
\(165\) 9.14892 0.712242
\(166\) 27.2849 2.11772
\(167\) −5.59785 −0.433175 −0.216587 0.976263i \(-0.569493\pi\)
−0.216587 + 0.976263i \(0.569493\pi\)
\(168\) −48.0295 −3.70556
\(169\) −10.5850 −0.814233
\(170\) −15.6803 −1.20263
\(171\) 11.0271 0.843260
\(172\) −55.9652 −4.26731
\(173\) −13.4509 −1.02265 −0.511325 0.859387i \(-0.670845\pi\)
−0.511325 + 0.859387i \(0.670845\pi\)
\(174\) −2.93675 −0.222634
\(175\) −7.31184 −0.552724
\(176\) −21.6398 −1.63116
\(177\) 8.79116 0.660784
\(178\) −24.7042 −1.85165
\(179\) 12.0761 0.902607 0.451304 0.892370i \(-0.350959\pi\)
0.451304 + 0.892370i \(0.350959\pi\)
\(180\) −44.5341 −3.31938
\(181\) 18.3471 1.36373 0.681863 0.731480i \(-0.261170\pi\)
0.681863 + 0.731480i \(0.261170\pi\)
\(182\) 8.14517 0.603760
\(183\) 16.2380 1.20035
\(184\) 55.9072 4.12154
\(185\) 1.17110 0.0861009
\(186\) 45.5623 3.34079
\(187\) 12.1365 0.887506
\(188\) −42.2625 −3.08231
\(189\) 33.2517 2.41870
\(190\) 4.20925 0.305371
\(191\) −6.32726 −0.457824 −0.228912 0.973447i \(-0.573517\pi\)
−0.228912 + 0.973447i \(0.573517\pi\)
\(192\) 20.9453 1.51160
\(193\) 11.7279 0.844192 0.422096 0.906551i \(-0.361295\pi\)
0.422096 + 0.906551i \(0.361295\pi\)
\(194\) −0.531283 −0.0381439
\(195\) 6.03042 0.431847
\(196\) −14.0074 −1.00053
\(197\) 13.6565 0.972984 0.486492 0.873685i \(-0.338276\pi\)
0.486492 + 0.873685i \(0.338276\pi\)
\(198\) 48.9353 3.47768
\(199\) −26.2231 −1.85890 −0.929452 0.368944i \(-0.879720\pi\)
−0.929452 + 0.368944i \(0.879720\pi\)
\(200\) 26.1002 1.84556
\(201\) −7.52423 −0.530718
\(202\) −18.4156 −1.29572
\(203\) 0.686619 0.0481912
\(204\) −81.2861 −5.69117
\(205\) −2.85160 −0.199164
\(206\) 33.6932 2.34751
\(207\) −62.0228 −4.31088
\(208\) −14.2636 −0.989006
\(209\) −3.25792 −0.225355
\(210\) 20.3393 1.40355
\(211\) −27.5009 −1.89324 −0.946620 0.322352i \(-0.895526\pi\)
−0.946620 + 0.322352i \(0.895526\pi\)
\(212\) −59.1350 −4.06141
\(213\) −5.04193 −0.345468
\(214\) 44.5890 3.04804
\(215\) 13.7533 0.937969
\(216\) −118.694 −8.07613
\(217\) −10.6526 −0.723144
\(218\) 2.60105 0.176165
\(219\) 43.5269 2.94128
\(220\) 13.1575 0.887080
\(221\) 7.99963 0.538113
\(222\) 8.61880 0.578456
\(223\) −1.12091 −0.0750615 −0.0375308 0.999295i \(-0.511949\pi\)
−0.0375308 + 0.999295i \(0.511949\pi\)
\(224\) −19.1188 −1.27743
\(225\) −28.9552 −1.93035
\(226\) −22.7577 −1.51382
\(227\) −7.85794 −0.521550 −0.260775 0.965400i \(-0.583978\pi\)
−0.260775 + 0.965400i \(0.583978\pi\)
\(228\) 21.8205 1.44510
\(229\) −1.03088 −0.0681226 −0.0340613 0.999420i \(-0.510844\pi\)
−0.0340613 + 0.999420i \(0.510844\pi\)
\(230\) −23.6754 −1.56111
\(231\) −15.7425 −1.03578
\(232\) −2.45094 −0.160912
\(233\) 19.9886 1.30950 0.654748 0.755847i \(-0.272775\pi\)
0.654748 + 0.755847i \(0.272775\pi\)
\(234\) 32.2552 2.10859
\(235\) 10.3859 0.677503
\(236\) 12.6430 0.822990
\(237\) 17.9611 1.16670
\(238\) 26.9810 1.74892
\(239\) 18.3141 1.18464 0.592321 0.805702i \(-0.298212\pi\)
0.592321 + 0.805702i \(0.298212\pi\)
\(240\) −35.6178 −2.29912
\(241\) 29.0472 1.87109 0.935547 0.353202i \(-0.114907\pi\)
0.935547 + 0.353202i \(0.114907\pi\)
\(242\) 14.1537 0.909832
\(243\) 52.3520 3.35838
\(244\) 23.3527 1.49500
\(245\) 3.44230 0.219920
\(246\) −20.9866 −1.33805
\(247\) −2.14743 −0.136638
\(248\) 38.0252 2.41460
\(249\) −34.7595 −2.20279
\(250\) −26.2832 −1.66230
\(251\) 17.8973 1.12967 0.564834 0.825205i \(-0.308940\pi\)
0.564834 + 0.825205i \(0.308940\pi\)
\(252\) 76.6295 4.82720
\(253\) 18.3245 1.15205
\(254\) −27.0354 −1.69635
\(255\) 19.9759 1.25094
\(256\) −19.2338 −1.20211
\(257\) 19.8595 1.23880 0.619402 0.785074i \(-0.287375\pi\)
0.619402 + 0.785074i \(0.287375\pi\)
\(258\) 101.219 6.30161
\(259\) −2.01510 −0.125212
\(260\) 8.67266 0.537855
\(261\) 2.71904 0.168304
\(262\) −18.7138 −1.15614
\(263\) −15.6347 −0.964075 −0.482038 0.876150i \(-0.660103\pi\)
−0.482038 + 0.876150i \(0.660103\pi\)
\(264\) 56.1939 3.45850
\(265\) 14.5323 0.892712
\(266\) −7.24282 −0.444086
\(267\) 31.4717 1.92604
\(268\) −10.8210 −0.660997
\(269\) 14.9388 0.910834 0.455417 0.890278i \(-0.349490\pi\)
0.455417 + 0.890278i \(0.349490\pi\)
\(270\) 50.2642 3.05898
\(271\) 5.92517 0.359929 0.179964 0.983673i \(-0.442402\pi\)
0.179964 + 0.983673i \(0.442402\pi\)
\(272\) −47.2486 −2.86487
\(273\) −10.3765 −0.628014
\(274\) 10.0704 0.608378
\(275\) 8.55477 0.515872
\(276\) −122.732 −7.38759
\(277\) −4.94849 −0.297326 −0.148663 0.988888i \(-0.547497\pi\)
−0.148663 + 0.988888i \(0.547497\pi\)
\(278\) −11.7724 −0.706063
\(279\) −42.1847 −2.52553
\(280\) 16.9747 1.01443
\(281\) 13.0469 0.778310 0.389155 0.921172i \(-0.372767\pi\)
0.389155 + 0.921172i \(0.372767\pi\)
\(282\) 76.4361 4.55170
\(283\) 6.21184 0.369255 0.184628 0.982809i \(-0.440892\pi\)
0.184628 + 0.982809i \(0.440892\pi\)
\(284\) −7.25107 −0.430272
\(285\) −5.36235 −0.317638
\(286\) −9.52975 −0.563506
\(287\) 4.90672 0.289634
\(288\) −75.7114 −4.46134
\(289\) 9.49893 0.558761
\(290\) 1.03791 0.0609483
\(291\) 0.676825 0.0396762
\(292\) 62.5983 3.66329
\(293\) 18.0544 1.05475 0.527374 0.849633i \(-0.323177\pi\)
0.527374 + 0.849633i \(0.323177\pi\)
\(294\) 25.3339 1.47750
\(295\) −3.10700 −0.180896
\(296\) 7.19305 0.418087
\(297\) −38.9041 −2.25744
\(298\) 50.1146 2.90306
\(299\) 12.0784 0.698514
\(300\) −57.2971 −3.30805
\(301\) −23.6652 −1.36404
\(302\) −30.8564 −1.77559
\(303\) 23.4604 1.34777
\(304\) 12.6835 0.727447
\(305\) −5.73887 −0.328607
\(306\) 106.846 6.10798
\(307\) −19.4518 −1.11017 −0.555087 0.831792i \(-0.687315\pi\)
−0.555087 + 0.831792i \(0.687315\pi\)
\(308\) −22.6401 −1.29004
\(309\) −42.9232 −2.44182
\(310\) −16.1027 −0.914574
\(311\) −11.2484 −0.637837 −0.318918 0.947782i \(-0.603320\pi\)
−0.318918 + 0.947782i \(0.603320\pi\)
\(312\) 37.0397 2.09696
\(313\) 5.87260 0.331939 0.165969 0.986131i \(-0.446925\pi\)
0.165969 + 0.986131i \(0.446925\pi\)
\(314\) −2.53018 −0.142786
\(315\) −18.8315 −1.06104
\(316\) 25.8308 1.45309
\(317\) 33.9138 1.90479 0.952395 0.304867i \(-0.0986120\pi\)
0.952395 + 0.304867i \(0.0986120\pi\)
\(318\) 106.952 5.99756
\(319\) −0.803336 −0.0449782
\(320\) −7.40256 −0.413816
\(321\) −56.8039 −3.17048
\(322\) 40.7380 2.27024
\(323\) −7.11340 −0.395800
\(324\) 146.484 8.13800
\(325\) 5.63879 0.312784
\(326\) −54.9442 −3.04308
\(327\) −3.31359 −0.183242
\(328\) −17.5149 −0.967098
\(329\) −17.8710 −0.985259
\(330\) −23.7968 −1.30997
\(331\) 11.6242 0.638926 0.319463 0.947599i \(-0.396497\pi\)
0.319463 + 0.947599i \(0.396497\pi\)
\(332\) −49.9894 −2.74353
\(333\) −7.97988 −0.437295
\(334\) 14.5603 0.796703
\(335\) 2.65924 0.145290
\(336\) 61.2872 3.34349
\(337\) 1.15699 0.0630252 0.0315126 0.999503i \(-0.489968\pi\)
0.0315126 + 0.999503i \(0.489968\pi\)
\(338\) 27.5322 1.49755
\(339\) 28.9921 1.57463
\(340\) 28.7284 1.55801
\(341\) 12.4634 0.674930
\(342\) −28.6819 −1.55094
\(343\) −20.0288 −1.08145
\(344\) 84.4749 4.55458
\(345\) 30.1611 1.62382
\(346\) 34.9864 1.88088
\(347\) −3.98509 −0.213931 −0.106966 0.994263i \(-0.534113\pi\)
−0.106966 + 0.994263i \(0.534113\pi\)
\(348\) 5.38049 0.288424
\(349\) 31.2330 1.67186 0.835932 0.548833i \(-0.184928\pi\)
0.835932 + 0.548833i \(0.184928\pi\)
\(350\) 19.0184 1.01658
\(351\) −25.6432 −1.36873
\(352\) 22.3688 1.19226
\(353\) −19.8095 −1.05436 −0.527178 0.849755i \(-0.676750\pi\)
−0.527178 + 0.849755i \(0.676750\pi\)
\(354\) −22.8662 −1.21533
\(355\) 1.78193 0.0945753
\(356\) 45.2611 2.39883
\(357\) −34.3724 −1.81918
\(358\) −31.4104 −1.66009
\(359\) 22.2377 1.17366 0.586830 0.809710i \(-0.300376\pi\)
0.586830 + 0.809710i \(0.300376\pi\)
\(360\) 67.2206 3.54284
\(361\) −17.0905 −0.899498
\(362\) −47.7215 −2.50819
\(363\) −18.0310 −0.946382
\(364\) −14.9230 −0.782176
\(365\) −15.3834 −0.805205
\(366\) −42.2357 −2.20770
\(367\) −36.7255 −1.91706 −0.958529 0.284996i \(-0.908008\pi\)
−0.958529 + 0.284996i \(0.908008\pi\)
\(368\) −71.3395 −3.71883
\(369\) 19.4308 1.01153
\(370\) −3.04608 −0.158358
\(371\) −25.0056 −1.29823
\(372\) −83.4758 −4.32802
\(373\) 6.15603 0.318747 0.159374 0.987218i \(-0.449053\pi\)
0.159374 + 0.987218i \(0.449053\pi\)
\(374\) −31.5675 −1.63232
\(375\) 33.4833 1.72907
\(376\) 63.7918 3.28981
\(377\) −0.529511 −0.0272712
\(378\) −86.4892 −4.44852
\(379\) −20.8972 −1.07341 −0.536707 0.843768i \(-0.680332\pi\)
−0.536707 + 0.843768i \(0.680332\pi\)
\(380\) −7.71188 −0.395611
\(381\) 34.4416 1.76450
\(382\) 16.4575 0.842039
\(383\) 4.65311 0.237763 0.118881 0.992908i \(-0.462069\pi\)
0.118881 + 0.992908i \(0.462069\pi\)
\(384\) 8.39746 0.428531
\(385\) 5.56375 0.283555
\(386\) −30.5048 −1.55265
\(387\) −93.7154 −4.76382
\(388\) 0.973377 0.0494157
\(389\) −5.22504 −0.264920 −0.132460 0.991188i \(-0.542288\pi\)
−0.132460 + 0.991188i \(0.542288\pi\)
\(390\) −15.6854 −0.794261
\(391\) 40.0101 2.02340
\(392\) 21.1431 1.06789
\(393\) 23.8403 1.20259
\(394\) −35.5211 −1.78953
\(395\) −6.34785 −0.319395
\(396\) −89.6556 −4.50536
\(397\) −2.91895 −0.146498 −0.0732490 0.997314i \(-0.523337\pi\)
−0.0732490 + 0.997314i \(0.523337\pi\)
\(398\) 68.2074 3.41893
\(399\) 9.22695 0.461926
\(400\) −33.3047 −1.66524
\(401\) −20.5757 −1.02750 −0.513751 0.857939i \(-0.671745\pi\)
−0.513751 + 0.857939i \(0.671745\pi\)
\(402\) 19.5709 0.976107
\(403\) 8.21512 0.409224
\(404\) 33.7397 1.67861
\(405\) −35.9981 −1.78876
\(406\) −1.78593 −0.0886341
\(407\) 2.35764 0.116864
\(408\) 122.695 6.07429
\(409\) 6.93499 0.342913 0.171457 0.985192i \(-0.445153\pi\)
0.171457 + 0.985192i \(0.445153\pi\)
\(410\) 7.41713 0.366306
\(411\) −12.8292 −0.632817
\(412\) −61.7301 −3.04123
\(413\) 5.34618 0.263068
\(414\) 161.324 7.92865
\(415\) 12.2848 0.603037
\(416\) 14.7442 0.722893
\(417\) 14.9974 0.734426
\(418\) 8.47401 0.414478
\(419\) −25.9334 −1.26693 −0.633464 0.773772i \(-0.718367\pi\)
−0.633464 + 0.773772i \(0.718367\pi\)
\(420\) −37.2642 −1.81831
\(421\) −10.8959 −0.531033 −0.265516 0.964106i \(-0.585542\pi\)
−0.265516 + 0.964106i \(0.585542\pi\)
\(422\) 71.5311 3.48208
\(423\) −70.7698 −3.44095
\(424\) 89.2594 4.33482
\(425\) 18.6786 0.906046
\(426\) 13.1143 0.635390
\(427\) 9.87483 0.477876
\(428\) −81.6926 −3.94876
\(429\) 12.1404 0.586143
\(430\) −35.7731 −1.72513
\(431\) 4.17511 0.201108 0.100554 0.994932i \(-0.467938\pi\)
0.100554 + 0.994932i \(0.467938\pi\)
\(432\) 151.458 7.28703
\(433\) −10.3484 −0.497311 −0.248656 0.968592i \(-0.579989\pi\)
−0.248656 + 0.968592i \(0.579989\pi\)
\(434\) 27.7079 1.33002
\(435\) −1.32224 −0.0633967
\(436\) −4.76544 −0.228223
\(437\) −10.7403 −0.513781
\(438\) −113.216 −5.40965
\(439\) 4.36848 0.208496 0.104248 0.994551i \(-0.466756\pi\)
0.104248 + 0.994551i \(0.466756\pi\)
\(440\) −19.8602 −0.946799
\(441\) −23.4559 −1.11695
\(442\) −20.8074 −0.989707
\(443\) 29.3371 1.39385 0.696924 0.717145i \(-0.254551\pi\)
0.696924 + 0.717145i \(0.254551\pi\)
\(444\) −15.7907 −0.749395
\(445\) −11.1228 −0.527273
\(446\) 2.91553 0.138055
\(447\) −63.8432 −3.01968
\(448\) 12.7375 0.601792
\(449\) −20.4087 −0.963147 −0.481573 0.876406i \(-0.659934\pi\)
−0.481573 + 0.876406i \(0.659934\pi\)
\(450\) 75.3139 3.55033
\(451\) −5.74080 −0.270324
\(452\) 41.6950 1.96117
\(453\) 39.3094 1.84691
\(454\) 20.4389 0.959244
\(455\) 3.66729 0.171925
\(456\) −32.9363 −1.54238
\(457\) 35.4834 1.65985 0.829923 0.557878i \(-0.188384\pi\)
0.829923 + 0.557878i \(0.188384\pi\)
\(458\) 2.68137 0.125292
\(459\) −84.9438 −3.96483
\(460\) 43.3762 2.02243
\(461\) −21.2896 −0.991555 −0.495777 0.868450i \(-0.665117\pi\)
−0.495777 + 0.868450i \(0.665117\pi\)
\(462\) 40.9469 1.90502
\(463\) −35.3079 −1.64090 −0.820449 0.571720i \(-0.806276\pi\)
−0.820449 + 0.571720i \(0.806276\pi\)
\(464\) 3.12748 0.145190
\(465\) 20.5140 0.951314
\(466\) −51.9913 −2.40845
\(467\) −7.82770 −0.362223 −0.181111 0.983463i \(-0.557969\pi\)
−0.181111 + 0.983463i \(0.557969\pi\)
\(468\) −59.0956 −2.73169
\(469\) −4.57572 −0.211287
\(470\) −27.0143 −1.24608
\(471\) 3.22330 0.148522
\(472\) −19.0836 −0.878394
\(473\) 27.6880 1.27310
\(474\) −46.7176 −2.14581
\(475\) −5.01411 −0.230063
\(476\) −49.4327 −2.26574
\(477\) −99.0233 −4.53396
\(478\) −47.6359 −2.17881
\(479\) 8.66092 0.395728 0.197864 0.980230i \(-0.436600\pi\)
0.197864 + 0.980230i \(0.436600\pi\)
\(480\) 36.8177 1.68049
\(481\) 1.55402 0.0708570
\(482\) −75.5531 −3.44135
\(483\) −51.8979 −2.36144
\(484\) −25.9313 −1.17870
\(485\) −0.239205 −0.0108618
\(486\) −136.170 −6.17679
\(487\) −10.5472 −0.477939 −0.238970 0.971027i \(-0.576810\pi\)
−0.238970 + 0.971027i \(0.576810\pi\)
\(488\) −35.2490 −1.59565
\(489\) 69.9959 3.16532
\(490\) −8.95358 −0.404481
\(491\) 26.1954 1.18218 0.591091 0.806605i \(-0.298697\pi\)
0.591091 + 0.806605i \(0.298697\pi\)
\(492\) 38.4500 1.73346
\(493\) −1.75402 −0.0789969
\(494\) 5.58556 0.251306
\(495\) 22.0327 0.990295
\(496\) −48.5214 −2.17868
\(497\) −3.06616 −0.137536
\(498\) 90.4111 4.05142
\(499\) 9.86402 0.441574 0.220787 0.975322i \(-0.429137\pi\)
0.220787 + 0.975322i \(0.429137\pi\)
\(500\) 48.1541 2.15352
\(501\) −18.5490 −0.828708
\(502\) −46.5517 −2.07770
\(503\) −28.1812 −1.25654 −0.628269 0.777996i \(-0.716236\pi\)
−0.628269 + 0.777996i \(0.716236\pi\)
\(504\) −115.666 −5.15217
\(505\) −8.29145 −0.368965
\(506\) −47.6629 −2.11888
\(507\) −35.0745 −1.55771
\(508\) 49.5323 2.19764
\(509\) −34.2811 −1.51949 −0.759743 0.650224i \(-0.774675\pi\)
−0.759743 + 0.650224i \(0.774675\pi\)
\(510\) −51.9582 −2.30075
\(511\) 26.4701 1.17097
\(512\) 44.9595 1.98695
\(513\) 22.8024 1.00675
\(514\) −51.6556 −2.27843
\(515\) 15.1701 0.668472
\(516\) −185.446 −8.16379
\(517\) 20.9088 0.919569
\(518\) 5.24137 0.230292
\(519\) −44.5707 −1.95644
\(520\) −13.0907 −0.574064
\(521\) −3.03895 −0.133139 −0.0665694 0.997782i \(-0.521205\pi\)
−0.0665694 + 0.997782i \(0.521205\pi\)
\(522\) −7.07235 −0.309548
\(523\) −3.06818 −0.134162 −0.0670812 0.997748i \(-0.521369\pi\)
−0.0670812 + 0.997748i \(0.521369\pi\)
\(524\) 34.2860 1.49779
\(525\) −24.2285 −1.05742
\(526\) 40.6665 1.77314
\(527\) 27.2128 1.18541
\(528\) −71.7053 −3.12057
\(529\) 37.4102 1.62653
\(530\) −37.7992 −1.64189
\(531\) 21.1711 0.918747
\(532\) 13.2698 0.575317
\(533\) −3.78399 −0.163903
\(534\) −81.8594 −3.54240
\(535\) 20.0758 0.867952
\(536\) 16.3334 0.705495
\(537\) 40.0151 1.72678
\(538\) −38.8565 −1.67522
\(539\) 6.92999 0.298496
\(540\) −92.0903 −3.96294
\(541\) −30.9230 −1.32949 −0.664743 0.747072i \(-0.731459\pi\)
−0.664743 + 0.747072i \(0.731459\pi\)
\(542\) −15.4117 −0.661987
\(543\) 60.7946 2.60895
\(544\) 48.8404 2.09401
\(545\) 1.17110 0.0501643
\(546\) 26.9897 1.15505
\(547\) −15.2506 −0.652068 −0.326034 0.945358i \(-0.605712\pi\)
−0.326034 + 0.945358i \(0.605712\pi\)
\(548\) −18.4503 −0.788158
\(549\) 39.1047 1.66895
\(550\) −22.2514 −0.948801
\(551\) 0.470850 0.0200589
\(552\) 185.254 7.88492
\(553\) 10.9227 0.464480
\(554\) 12.8712 0.546847
\(555\) 3.88054 0.164720
\(556\) 21.5685 0.914710
\(557\) −11.3654 −0.481568 −0.240784 0.970579i \(-0.577405\pi\)
−0.240784 + 0.970579i \(0.577405\pi\)
\(558\) 109.724 4.64500
\(559\) 18.2503 0.771906
\(560\) −21.6603 −0.915315
\(561\) 40.2152 1.69789
\(562\) −33.9355 −1.43148
\(563\) 29.6159 1.24816 0.624081 0.781359i \(-0.285473\pi\)
0.624081 + 0.781359i \(0.285473\pi\)
\(564\) −140.041 −5.89677
\(565\) −10.2465 −0.431072
\(566\) −16.1573 −0.679141
\(567\) 61.9417 2.60131
\(568\) 10.9449 0.459237
\(569\) 1.60709 0.0673729 0.0336864 0.999432i \(-0.489275\pi\)
0.0336864 + 0.999432i \(0.489275\pi\)
\(570\) 13.9477 0.584206
\(571\) 3.23101 0.135213 0.0676067 0.997712i \(-0.478464\pi\)
0.0676067 + 0.997712i \(0.478464\pi\)
\(572\) 17.4597 0.730026
\(573\) −20.9659 −0.875865
\(574\) −12.7626 −0.532701
\(575\) 28.2024 1.17612
\(576\) 50.4411 2.10171
\(577\) −21.1213 −0.879293 −0.439646 0.898171i \(-0.644896\pi\)
−0.439646 + 0.898171i \(0.644896\pi\)
\(578\) −24.7072 −1.02768
\(579\) 38.8614 1.61502
\(580\) −1.90159 −0.0789591
\(581\) −21.1384 −0.876967
\(582\) −1.76045 −0.0729731
\(583\) 29.2563 1.21167
\(584\) −94.4871 −3.90990
\(585\) 14.5226 0.600436
\(586\) −46.9603 −1.93991
\(587\) −10.6658 −0.440224 −0.220112 0.975475i \(-0.570642\pi\)
−0.220112 + 0.975475i \(0.570642\pi\)
\(588\) −46.4149 −1.91412
\(589\) −7.30502 −0.300998
\(590\) 8.08144 0.332708
\(591\) 45.2520 1.86142
\(592\) −9.17857 −0.377237
\(593\) −5.11354 −0.209988 −0.104994 0.994473i \(-0.533482\pi\)
−0.104994 + 0.994473i \(0.533482\pi\)
\(594\) 101.191 4.15193
\(595\) 12.1480 0.498018
\(596\) −91.8162 −3.76094
\(597\) −86.8925 −3.55627
\(598\) −31.4166 −1.28472
\(599\) −13.1369 −0.536760 −0.268380 0.963313i \(-0.586488\pi\)
−0.268380 + 0.963313i \(0.586488\pi\)
\(600\) 86.4853 3.53075
\(601\) 10.9783 0.447813 0.223907 0.974611i \(-0.428119\pi\)
0.223907 + 0.974611i \(0.428119\pi\)
\(602\) 61.5544 2.50877
\(603\) −18.1201 −0.737906
\(604\) 56.5328 2.30029
\(605\) 6.37256 0.259082
\(606\) −61.0217 −2.47884
\(607\) 21.1662 0.859108 0.429554 0.903041i \(-0.358671\pi\)
0.429554 + 0.903041i \(0.358671\pi\)
\(608\) −13.1108 −0.531712
\(609\) 2.27517 0.0921947
\(610\) 14.9271 0.604380
\(611\) 13.7818 0.557554
\(612\) −195.755 −7.91294
\(613\) −20.7641 −0.838656 −0.419328 0.907835i \(-0.637734\pi\)
−0.419328 + 0.907835i \(0.637734\pi\)
\(614\) 50.5951 2.04185
\(615\) −9.44902 −0.381021
\(616\) 34.1733 1.37688
\(617\) 0.876748 0.0352966 0.0176483 0.999844i \(-0.494382\pi\)
0.0176483 + 0.999844i \(0.494382\pi\)
\(618\) 111.645 4.49104
\(619\) −15.0009 −0.602936 −0.301468 0.953476i \(-0.597477\pi\)
−0.301468 + 0.953476i \(0.597477\pi\)
\(620\) 29.5022 1.18484
\(621\) −128.254 −5.14667
\(622\) 29.2575 1.17312
\(623\) 19.1390 0.766786
\(624\) −47.2639 −1.89207
\(625\) 6.30887 0.252355
\(626\) −15.2749 −0.610508
\(627\) −10.7954 −0.431128
\(628\) 4.63560 0.184981
\(629\) 5.14771 0.205253
\(630\) 48.9817 1.95148
\(631\) −25.4666 −1.01381 −0.506905 0.862002i \(-0.669210\pi\)
−0.506905 + 0.862002i \(0.669210\pi\)
\(632\) −38.9894 −1.55092
\(633\) −91.1267 −3.62196
\(634\) −88.2114 −3.50332
\(635\) −12.1725 −0.483049
\(636\) −195.949 −7.76989
\(637\) 4.56784 0.180984
\(638\) 2.08951 0.0827247
\(639\) −12.1421 −0.480335
\(640\) −2.96785 −0.117315
\(641\) −39.2307 −1.54952 −0.774760 0.632256i \(-0.782129\pi\)
−0.774760 + 0.632256i \(0.782129\pi\)
\(642\) 147.750 5.83121
\(643\) 22.5283 0.888431 0.444216 0.895920i \(-0.353482\pi\)
0.444216 + 0.895920i \(0.353482\pi\)
\(644\) −74.6371 −2.94111
\(645\) 45.5729 1.79443
\(646\) 18.5023 0.727963
\(647\) 4.50467 0.177097 0.0885485 0.996072i \(-0.471777\pi\)
0.0885485 + 0.996072i \(0.471777\pi\)
\(648\) −221.106 −8.68585
\(649\) −6.25497 −0.245529
\(650\) −14.6668 −0.575278
\(651\) −35.2983 −1.38345
\(652\) 100.665 3.94233
\(653\) −11.4086 −0.446454 −0.223227 0.974766i \(-0.571659\pi\)
−0.223227 + 0.974766i \(0.571659\pi\)
\(654\) 8.61880 0.337022
\(655\) −8.42572 −0.329220
\(656\) 22.3496 0.872605
\(657\) 104.823 4.08953
\(658\) 46.4832 1.81210
\(659\) −36.7225 −1.43051 −0.715253 0.698865i \(-0.753689\pi\)
−0.715253 + 0.698865i \(0.753689\pi\)
\(660\) 43.5987 1.69708
\(661\) −44.5905 −1.73437 −0.867184 0.497987i \(-0.834073\pi\)
−0.867184 + 0.497987i \(0.834073\pi\)
\(662\) −30.2352 −1.17512
\(663\) 26.5075 1.02947
\(664\) 75.4550 2.92822
\(665\) −3.26102 −0.126457
\(666\) 20.7560 0.804280
\(667\) −2.64834 −0.102544
\(668\) −26.6763 −1.03214
\(669\) −3.71423 −0.143600
\(670\) −6.91680 −0.267219
\(671\) −11.5534 −0.446015
\(672\) −63.3520 −2.44385
\(673\) −38.8733 −1.49846 −0.749228 0.662312i \(-0.769576\pi\)
−0.749228 + 0.662312i \(0.769576\pi\)
\(674\) −3.00938 −0.115917
\(675\) −59.8753 −2.30460
\(676\) −50.4424 −1.94009
\(677\) 46.0772 1.77089 0.885446 0.464742i \(-0.153853\pi\)
0.885446 + 0.464742i \(0.153853\pi\)
\(678\) −75.4098 −2.89609
\(679\) 0.411599 0.0157957
\(680\) −43.3631 −1.66290
\(681\) −26.0380 −0.997778
\(682\) −32.4178 −1.24134
\(683\) −22.8501 −0.874336 −0.437168 0.899380i \(-0.644018\pi\)
−0.437168 + 0.899380i \(0.644018\pi\)
\(684\) 52.5488 2.00925
\(685\) 4.53413 0.173240
\(686\) 52.0959 1.98903
\(687\) −3.41592 −0.130326
\(688\) −107.793 −4.10956
\(689\) 19.2840 0.734661
\(690\) −78.4504 −2.98656
\(691\) −1.11427 −0.0423887 −0.0211944 0.999775i \(-0.506747\pi\)
−0.0211944 + 0.999775i \(0.506747\pi\)
\(692\) −64.0994 −2.43669
\(693\) −37.9114 −1.44014
\(694\) 10.3654 0.393466
\(695\) −5.30043 −0.201057
\(696\) −8.12141 −0.307841
\(697\) −12.5346 −0.474780
\(698\) −81.2385 −3.07492
\(699\) 66.2340 2.50520
\(700\) −34.8442 −1.31699
\(701\) −29.7925 −1.12525 −0.562624 0.826713i \(-0.690208\pi\)
−0.562624 + 0.826713i \(0.690208\pi\)
\(702\) 66.6992 2.51740
\(703\) −1.38186 −0.0521177
\(704\) −14.9028 −0.561669
\(705\) 34.4147 1.29613
\(706\) 51.5256 1.93919
\(707\) 14.2670 0.536567
\(708\) 41.8938 1.57446
\(709\) −2.06602 −0.0775908 −0.0387954 0.999247i \(-0.512352\pi\)
−0.0387954 + 0.999247i \(0.512352\pi\)
\(710\) −4.63489 −0.173945
\(711\) 43.2544 1.62217
\(712\) −68.3180 −2.56032
\(713\) 41.0878 1.53875
\(714\) 89.4041 3.34586
\(715\) −4.29068 −0.160462
\(716\) 57.5478 2.15066
\(717\) 60.6855 2.26634
\(718\) −57.8412 −2.15861
\(719\) −20.1793 −0.752561 −0.376281 0.926506i \(-0.622797\pi\)
−0.376281 + 0.926506i \(0.622797\pi\)
\(720\) −85.7757 −3.19667
\(721\) −26.1030 −0.972126
\(722\) 44.4531 1.65437
\(723\) 96.2505 3.57959
\(724\) 87.4319 3.24938
\(725\) −1.23637 −0.0459178
\(726\) 46.8995 1.74060
\(727\) 0.633812 0.0235068 0.0117534 0.999931i \(-0.496259\pi\)
0.0117534 + 0.999931i \(0.496259\pi\)
\(728\) 22.5250 0.834832
\(729\) 81.2565 3.00950
\(730\) 40.0130 1.48095
\(731\) 60.4545 2.23599
\(732\) 77.3812 2.86009
\(733\) −1.78868 −0.0660664 −0.0330332 0.999454i \(-0.510517\pi\)
−0.0330332 + 0.999454i \(0.510517\pi\)
\(734\) 95.5248 3.52589
\(735\) 11.4064 0.420730
\(736\) 73.7429 2.71820
\(737\) 5.35354 0.197200
\(738\) −50.5404 −1.86042
\(739\) −8.68464 −0.319470 −0.159735 0.987160i \(-0.551064\pi\)
−0.159735 + 0.987160i \(0.551064\pi\)
\(740\) 5.58080 0.205154
\(741\) −7.11570 −0.261402
\(742\) 65.0408 2.38772
\(743\) 14.1827 0.520314 0.260157 0.965566i \(-0.416226\pi\)
0.260157 + 0.965566i \(0.416226\pi\)
\(744\) 126.000 4.61938
\(745\) 22.5636 0.826668
\(746\) −16.0121 −0.586246
\(747\) −83.7088 −3.06274
\(748\) 57.8356 2.11468
\(749\) −34.5442 −1.26222
\(750\) −87.0917 −3.18014
\(751\) 18.0447 0.658461 0.329230 0.944250i \(-0.393211\pi\)
0.329230 + 0.944250i \(0.393211\pi\)
\(752\) −81.4004 −2.96837
\(753\) 59.3043 2.16117
\(754\) 1.37728 0.0501577
\(755\) −13.8928 −0.505612
\(756\) 158.459 5.76310
\(757\) −23.2227 −0.844042 −0.422021 0.906586i \(-0.638679\pi\)
−0.422021 + 0.906586i \(0.638679\pi\)
\(758\) 54.3545 1.97424
\(759\) 60.7200 2.20399
\(760\) 11.6404 0.422243
\(761\) −4.21127 −0.152658 −0.0763292 0.997083i \(-0.524320\pi\)
−0.0763292 + 0.997083i \(0.524320\pi\)
\(762\) −89.5843 −3.24530
\(763\) −2.01510 −0.0729515
\(764\) −30.1522 −1.09087
\(765\) 48.1065 1.73929
\(766\) −12.1029 −0.437297
\(767\) −4.12290 −0.148869
\(768\) −63.7329 −2.29976
\(769\) −31.8961 −1.15020 −0.575101 0.818083i \(-0.695037\pi\)
−0.575101 + 0.818083i \(0.695037\pi\)
\(770\) −14.4716 −0.521519
\(771\) 65.8064 2.36996
\(772\) 55.8886 2.01147
\(773\) −36.7766 −1.32276 −0.661382 0.750050i \(-0.730030\pi\)
−0.661382 + 0.750050i \(0.730030\pi\)
\(774\) 243.758 8.76170
\(775\) 19.1818 0.689030
\(776\) −1.46923 −0.0527424
\(777\) −6.67721 −0.239544
\(778\) 13.5906 0.487245
\(779\) 3.36479 0.120556
\(780\) 28.7376 1.02897
\(781\) 3.58737 0.128366
\(782\) −104.068 −3.72147
\(783\) 5.62259 0.200935
\(784\) −26.9793 −0.963545
\(785\) −1.13919 −0.0406594
\(786\) −62.0098 −2.21182
\(787\) 17.4528 0.622126 0.311063 0.950389i \(-0.399315\pi\)
0.311063 + 0.950389i \(0.399315\pi\)
\(788\) 65.0792 2.31835
\(789\) −51.8069 −1.84437
\(790\) 16.5111 0.587437
\(791\) 17.6310 0.626886
\(792\) 135.328 4.80866
\(793\) −7.61533 −0.270428
\(794\) 7.59233 0.269442
\(795\) 48.1541 1.70785
\(796\) −124.965 −4.42925
\(797\) 20.3278 0.720049 0.360024 0.932943i \(-0.382768\pi\)
0.360024 + 0.932943i \(0.382768\pi\)
\(798\) −23.9997 −0.849582
\(799\) 45.6526 1.61507
\(800\) 34.4267 1.21717
\(801\) 75.7911 2.67795
\(802\) 53.5184 1.88980
\(803\) −30.9697 −1.09290
\(804\) −35.8563 −1.26455
\(805\) 18.3419 0.646468
\(806\) −21.3679 −0.752652
\(807\) 49.5010 1.74252
\(808\) −50.9273 −1.79162
\(809\) −24.8228 −0.872722 −0.436361 0.899772i \(-0.643733\pi\)
−0.436361 + 0.899772i \(0.643733\pi\)
\(810\) 93.6329 3.28992
\(811\) 37.3397 1.31118 0.655588 0.755119i \(-0.272421\pi\)
0.655588 + 0.755119i \(0.272421\pi\)
\(812\) 3.27204 0.114826
\(813\) 19.6336 0.688580
\(814\) −6.13233 −0.214938
\(815\) −24.7381 −0.866539
\(816\) −156.563 −5.48079
\(817\) −16.2285 −0.567763
\(818\) −18.0382 −0.630692
\(819\) −24.9890 −0.873185
\(820\) −13.5891 −0.474553
\(821\) 3.33407 0.116360 0.0581800 0.998306i \(-0.481470\pi\)
0.0581800 + 0.998306i \(0.481470\pi\)
\(822\) 33.3693 1.16389
\(823\) −5.27587 −0.183905 −0.0919526 0.995763i \(-0.529311\pi\)
−0.0919526 + 0.995763i \(0.529311\pi\)
\(824\) 93.1766 3.24596
\(825\) 28.3470 0.986916
\(826\) −13.9057 −0.483840
\(827\) −12.0864 −0.420285 −0.210143 0.977671i \(-0.567393\pi\)
−0.210143 + 0.977671i \(0.567393\pi\)
\(828\) −295.566 −10.2716
\(829\) −8.73730 −0.303459 −0.151730 0.988422i \(-0.548484\pi\)
−0.151730 + 0.988422i \(0.548484\pi\)
\(830\) −31.9533 −1.10912
\(831\) −16.3973 −0.568815
\(832\) −9.82300 −0.340551
\(833\) 15.1311 0.524260
\(834\) −39.0090 −1.35077
\(835\) 6.55564 0.226867
\(836\) −15.5255 −0.536959
\(837\) −87.2320 −3.01518
\(838\) 67.4539 2.33016
\(839\) 12.3880 0.427682 0.213841 0.976868i \(-0.431402\pi\)
0.213841 + 0.976868i \(0.431402\pi\)
\(840\) 56.2473 1.94072
\(841\) −28.8839 −0.995996
\(842\) 28.3407 0.976685
\(843\) 43.2319 1.48899
\(844\) −131.054 −4.51106
\(845\) 12.3961 0.426439
\(846\) 184.076 6.32865
\(847\) −10.9652 −0.376769
\(848\) −113.898 −3.91127
\(849\) 20.5835 0.706423
\(850\) −48.5840 −1.66642
\(851\) 7.77240 0.266434
\(852\) −24.0271 −0.823153
\(853\) −16.6881 −0.571390 −0.285695 0.958321i \(-0.592225\pi\)
−0.285695 + 0.958321i \(0.592225\pi\)
\(854\) −25.6849 −0.878919
\(855\) −12.9138 −0.441641
\(856\) 123.308 4.21459
\(857\) −13.1614 −0.449586 −0.224793 0.974407i \(-0.572171\pi\)
−0.224793 + 0.974407i \(0.572171\pi\)
\(858\) −31.5777 −1.07804
\(859\) −13.3957 −0.457054 −0.228527 0.973538i \(-0.573391\pi\)
−0.228527 + 0.973538i \(0.573391\pi\)
\(860\) 65.5407 2.23492
\(861\) 16.2588 0.554100
\(862\) −10.8597 −0.369882
\(863\) 1.35740 0.0462066 0.0231033 0.999733i \(-0.492645\pi\)
0.0231033 + 0.999733i \(0.492645\pi\)
\(864\) −156.561 −5.32630
\(865\) 15.7523 0.535594
\(866\) 26.9166 0.914664
\(867\) 31.4756 1.06897
\(868\) −50.7643 −1.72305
\(869\) −12.7794 −0.433512
\(870\) 3.43922 0.116600
\(871\) 3.52873 0.119567
\(872\) 7.19305 0.243587
\(873\) 1.62995 0.0551654
\(874\) 27.9361 0.944954
\(875\) 20.3623 0.688371
\(876\) 207.425 7.00825
\(877\) −18.2859 −0.617472 −0.308736 0.951148i \(-0.599906\pi\)
−0.308736 + 0.951148i \(0.599906\pi\)
\(878\) −11.3626 −0.383470
\(879\) 59.8248 2.01784
\(880\) 25.3423 0.854289
\(881\) 29.2080 0.984041 0.492020 0.870584i \(-0.336259\pi\)
0.492020 + 0.870584i \(0.336259\pi\)
\(882\) 61.0098 2.05431
\(883\) −3.73447 −0.125675 −0.0628375 0.998024i \(-0.520015\pi\)
−0.0628375 + 0.998024i \(0.520015\pi\)
\(884\) 38.1218 1.28217
\(885\) −10.2953 −0.346073
\(886\) −76.3072 −2.56359
\(887\) −13.9402 −0.468065 −0.234032 0.972229i \(-0.575192\pi\)
−0.234032 + 0.972229i \(0.575192\pi\)
\(888\) 23.8348 0.799844
\(889\) 20.9450 0.702474
\(890\) 28.9310 0.969769
\(891\) −72.4710 −2.42787
\(892\) −5.34162 −0.178851
\(893\) −12.2551 −0.410100
\(894\) 166.059 5.55385
\(895\) −14.1423 −0.472724
\(896\) 5.10676 0.170605
\(897\) 40.0230 1.33633
\(898\) 53.0840 1.77144
\(899\) −1.80127 −0.0600756
\(900\) −137.984 −4.59948
\(901\) 63.8786 2.12810
\(902\) 14.9321 0.497184
\(903\) −78.4169 −2.60955
\(904\) −62.9352 −2.09319
\(905\) −21.4862 −0.714225
\(906\) −102.245 −3.39688
\(907\) 23.5667 0.782520 0.391260 0.920280i \(-0.372039\pi\)
0.391260 + 0.920280i \(0.372039\pi\)
\(908\) −37.4466 −1.24271
\(909\) 56.4981 1.87392
\(910\) −9.53879 −0.316208
\(911\) −41.9131 −1.38864 −0.694322 0.719665i \(-0.744295\pi\)
−0.694322 + 0.719665i \(0.744295\pi\)
\(912\) 42.0278 1.39168
\(913\) 24.7316 0.818497
\(914\) −92.2941 −3.05282
\(915\) −19.0163 −0.628658
\(916\) −4.91261 −0.162317
\(917\) 14.4981 0.478768
\(918\) 220.943 7.29219
\(919\) 12.4132 0.409472 0.204736 0.978817i \(-0.434366\pi\)
0.204736 + 0.978817i \(0.434366\pi\)
\(920\) −65.4729 −2.15858
\(921\) −64.4553 −2.12388
\(922\) 55.3752 1.82369
\(923\) 2.36458 0.0778311
\(924\) −75.0198 −2.46797
\(925\) 3.62853 0.119305
\(926\) 91.8375 3.01797
\(927\) −103.369 −3.39508
\(928\) −3.23284 −0.106123
\(929\) 39.0517 1.28124 0.640622 0.767856i \(-0.278677\pi\)
0.640622 + 0.767856i \(0.278677\pi\)
\(930\) −53.3579 −1.74967
\(931\) −4.06180 −0.133120
\(932\) 95.2545 3.12016
\(933\) −37.2725 −1.22025
\(934\) 20.3602 0.666206
\(935\) −14.2130 −0.464814
\(936\) 89.2000 2.91559
\(937\) −1.48337 −0.0484597 −0.0242299 0.999706i \(-0.507713\pi\)
−0.0242299 + 0.999706i \(0.507713\pi\)
\(938\) 11.9017 0.388603
\(939\) 19.4594 0.635033
\(940\) 49.4935 1.61430
\(941\) −43.1849 −1.40779 −0.703894 0.710305i \(-0.748557\pi\)
−0.703894 + 0.710305i \(0.748557\pi\)
\(942\) −8.38396 −0.273164
\(943\) −18.9256 −0.616302
\(944\) 24.3513 0.792567
\(945\) −38.9410 −1.26675
\(946\) −72.0179 −2.34150
\(947\) −58.3054 −1.89467 −0.947336 0.320242i \(-0.896236\pi\)
−0.947336 + 0.320242i \(0.896236\pi\)
\(948\) 85.5925 2.77992
\(949\) −20.4134 −0.662646
\(950\) 13.0419 0.423136
\(951\) 112.376 3.64406
\(952\) 74.6146 2.41827
\(953\) 9.81020 0.317783 0.158892 0.987296i \(-0.449208\pi\)
0.158892 + 0.987296i \(0.449208\pi\)
\(954\) 257.564 8.33895
\(955\) 7.40984 0.239777
\(956\) 87.2749 2.82267
\(957\) −2.66193 −0.0860478
\(958\) −22.5275 −0.727829
\(959\) −7.80184 −0.251934
\(960\) −24.5291 −0.791672
\(961\) −3.05419 −0.0985224
\(962\) −4.04207 −0.130322
\(963\) −136.797 −4.40821
\(964\) 138.423 4.45830
\(965\) −13.7345 −0.442129
\(966\) 134.989 4.34320
\(967\) −60.6263 −1.94961 −0.974805 0.223059i \(-0.928396\pi\)
−0.974805 + 0.223059i \(0.928396\pi\)
\(968\) 39.1412 1.25805
\(969\) −23.5709 −0.757207
\(970\) 0.622184 0.0199771
\(971\) 38.4076 1.23256 0.616280 0.787527i \(-0.288639\pi\)
0.616280 + 0.787527i \(0.288639\pi\)
\(972\) 249.480 8.00208
\(973\) 9.12040 0.292387
\(974\) 27.4337 0.879034
\(975\) 18.6846 0.598388
\(976\) 44.9788 1.43974
\(977\) 54.7936 1.75300 0.876501 0.481400i \(-0.159872\pi\)
0.876501 + 0.481400i \(0.159872\pi\)
\(978\) −182.063 −5.82172
\(979\) −22.3923 −0.715662
\(980\) 16.4041 0.524009
\(981\) −7.97988 −0.254778
\(982\) −68.1355 −2.17429
\(983\) 60.2024 1.92016 0.960079 0.279729i \(-0.0902446\pi\)
0.960079 + 0.279729i \(0.0902446\pi\)
\(984\) −58.0372 −1.85016
\(985\) −15.9931 −0.509582
\(986\) 4.56228 0.145293
\(987\) −59.2171 −1.88490
\(988\) −10.2335 −0.325570
\(989\) 91.2787 2.90250
\(990\) −57.3080 −1.82137
\(991\) 8.66741 0.275329 0.137665 0.990479i \(-0.456040\pi\)
0.137665 + 0.990479i \(0.456040\pi\)
\(992\) 50.1560 1.59246
\(993\) 38.5180 1.22233
\(994\) 7.97522 0.252959
\(995\) 30.7098 0.973566
\(996\) −165.644 −5.24865
\(997\) 41.6409 1.31878 0.659390 0.751801i \(-0.270815\pi\)
0.659390 + 0.751801i \(0.270815\pi\)
\(998\) −25.6568 −0.812151
\(999\) −16.5013 −0.522077
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 \(a_p\))