Properties

Label 4033.2.a.d.1.2
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 1.2
Character \(\chi\) = 4033.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.77527 q^{2}\) \(+1.86757 q^{3}\) \(+5.70214 q^{4}\) \(+1.50597 q^{5}\) \(-5.18302 q^{6}\) \(-3.04702 q^{7}\) \(-10.2744 q^{8}\) \(+0.487817 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.77527 q^{2}\) \(+1.86757 q^{3}\) \(+5.70214 q^{4}\) \(+1.50597 q^{5}\) \(-5.18302 q^{6}\) \(-3.04702 q^{7}\) \(-10.2744 q^{8}\) \(+0.487817 q^{9}\) \(-4.17947 q^{10}\) \(-4.97460 q^{11}\) \(+10.6491 q^{12}\) \(+4.84844 q^{13}\) \(+8.45631 q^{14}\) \(+2.81250 q^{15}\) \(+17.1101 q^{16}\) \(-1.65425 q^{17}\) \(-1.35383 q^{18}\) \(+7.46249 q^{19}\) \(+8.58723 q^{20}\) \(-5.69052 q^{21}\) \(+13.8059 q^{22}\) \(-5.06186 q^{23}\) \(-19.1882 q^{24}\) \(-2.73206 q^{25}\) \(-13.4557 q^{26}\) \(-4.69168 q^{27}\) \(-17.3745 q^{28}\) \(-3.53076 q^{29}\) \(-7.80545 q^{30}\) \(+7.56226 q^{31}\) \(-26.9363 q^{32}\) \(-9.29040 q^{33}\) \(+4.59099 q^{34}\) \(-4.58871 q^{35}\) \(+2.78160 q^{36}\) \(-1.00000 q^{37}\) \(-20.7105 q^{38}\) \(+9.05480 q^{39}\) \(-15.4730 q^{40}\) \(+9.30932 q^{41}\) \(+15.7928 q^{42}\) \(+3.86049 q^{43}\) \(-28.3658 q^{44}\) \(+0.734637 q^{45}\) \(+14.0480 q^{46}\) \(-3.71430 q^{47}\) \(+31.9543 q^{48}\) \(+2.28433 q^{49}\) \(+7.58222 q^{50}\) \(-3.08943 q^{51}\) \(+27.6465 q^{52}\) \(+2.18318 q^{53}\) \(+13.0207 q^{54}\) \(-7.49157 q^{55}\) \(+31.3064 q^{56}\) \(+13.9367 q^{57}\) \(+9.79883 q^{58}\) \(-7.82573 q^{59}\) \(+16.0372 q^{60}\) \(+6.93522 q^{61}\) \(-20.9873 q^{62}\) \(-1.48639 q^{63}\) \(+40.5353 q^{64}\) \(+7.30159 q^{65}\) \(+25.7834 q^{66}\) \(-13.1252 q^{67}\) \(-9.43276 q^{68}\) \(-9.45338 q^{69}\) \(+12.7349 q^{70}\) \(+9.15497 q^{71}\) \(-5.01205 q^{72}\) \(-11.8430 q^{73}\) \(+2.77527 q^{74}\) \(-5.10232 q^{75}\) \(+42.5522 q^{76}\) \(+15.1577 q^{77}\) \(-25.1295 q^{78}\) \(-6.00754 q^{79}\) \(+25.7672 q^{80}\) \(-10.2255 q^{81}\) \(-25.8359 q^{82}\) \(+17.2265 q^{83}\) \(-32.4481 q^{84}\) \(-2.49124 q^{85}\) \(-10.7139 q^{86}\) \(-6.59395 q^{87}\) \(+51.1112 q^{88}\) \(-15.1661 q^{89}\) \(-2.03882 q^{90}\) \(-14.7733 q^{91}\) \(-28.8634 q^{92}\) \(+14.1230 q^{93}\) \(+10.3082 q^{94}\) \(+11.2383 q^{95}\) \(-50.3054 q^{96}\) \(-7.08860 q^{97}\) \(-6.33964 q^{98}\) \(-2.42669 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut -\mathstrut 13q^{10} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut -\mathstrut 40q^{12} \) \(\mathstrut -\mathstrut 18q^{13} \) \(\mathstrut -\mathstrut 42q^{14} \) \(\mathstrut -\mathstrut 49q^{15} \) \(\mathstrut +\mathstrut 83q^{16} \) \(\mathstrut -\mathstrut 62q^{17} \) \(\mathstrut -\mathstrut 33q^{18} \) \(\mathstrut -\mathstrut 25q^{19} \) \(\mathstrut -\mathstrut 39q^{20} \) \(\mathstrut -\mathstrut 15q^{21} \) \(\mathstrut -\mathstrut 31q^{22} \) \(\mathstrut -\mathstrut 94q^{23} \) \(\mathstrut -\mathstrut 39q^{24} \) \(\mathstrut +\mathstrut 71q^{25} \) \(\mathstrut -\mathstrut 35q^{26} \) \(\mathstrut -\mathstrut 47q^{27} \) \(\mathstrut -\mathstrut 13q^{28} \) \(\mathstrut -\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 15q^{30} \) \(\mathstrut -\mathstrut 37q^{31} \) \(\mathstrut -\mathstrut 105q^{32} \) \(\mathstrut -\mathstrut 60q^{33} \) \(\mathstrut +\mathstrut 9q^{34} \) \(\mathstrut -\mathstrut 60q^{35} \) \(\mathstrut +\mathstrut 43q^{36} \) \(\mathstrut -\mathstrut 79q^{37} \) \(\mathstrut -\mathstrut 80q^{38} \) \(\mathstrut -\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 64q^{40} \) \(\mathstrut -\mathstrut 37q^{41} \) \(\mathstrut -\mathstrut 30q^{42} \) \(\mathstrut -\mathstrut 20q^{43} \) \(\mathstrut -\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 8q^{45} \) \(\mathstrut +\mathstrut 61q^{46} \) \(\mathstrut -\mathstrut 148q^{47} \) \(\mathstrut -\mathstrut 39q^{48} \) \(\mathstrut +\mathstrut 82q^{49} \) \(\mathstrut -\mathstrut 90q^{50} \) \(\mathstrut -\mathstrut 45q^{51} \) \(\mathstrut -\mathstrut 27q^{52} \) \(\mathstrut -\mathstrut 70q^{53} \) \(\mathstrut -\mathstrut 41q^{54} \) \(\mathstrut -\mathstrut 105q^{55} \) \(\mathstrut -\mathstrut 68q^{56} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut -\mathstrut 14q^{58} \) \(\mathstrut -\mathstrut 96q^{59} \) \(\mathstrut -\mathstrut 74q^{60} \) \(\mathstrut -\mathstrut 21q^{61} \) \(\mathstrut +\mathstrut 4q^{62} \) \(\mathstrut -\mathstrut 60q^{63} \) \(\mathstrut +\mathstrut 132q^{64} \) \(\mathstrut -\mathstrut 15q^{65} \) \(\mathstrut +\mathstrut 71q^{66} \) \(\mathstrut -\mathstrut 44q^{67} \) \(\mathstrut -\mathstrut 166q^{68} \) \(\mathstrut -\mathstrut 72q^{69} \) \(\mathstrut -\mathstrut 9q^{70} \) \(\mathstrut -\mathstrut 55q^{71} \) \(\mathstrut -\mathstrut 126q^{72} \) \(\mathstrut -\mathstrut 27q^{73} \) \(\mathstrut +\mathstrut 11q^{74} \) \(\mathstrut -\mathstrut 39q^{75} \) \(\mathstrut -\mathstrut 4q^{76} \) \(\mathstrut -\mathstrut 104q^{77} \) \(\mathstrut -\mathstrut 47q^{78} \) \(\mathstrut -\mathstrut 49q^{79} \) \(\mathstrut -\mathstrut 82q^{80} \) \(\mathstrut +\mathstrut 55q^{81} \) \(\mathstrut +\mathstrut 20q^{82} \) \(\mathstrut -\mathstrut 52q^{83} \) \(\mathstrut -\mathstrut 29q^{84} \) \(\mathstrut +\mathstrut 3q^{85} \) \(\mathstrut -\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 113q^{87} \) \(\mathstrut +\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 68q^{89} \) \(\mathstrut -\mathstrut 39q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 179q^{92} \) \(\mathstrut -\mathstrut 53q^{93} \) \(\mathstrut -\mathstrut 33q^{94} \) \(\mathstrut -\mathstrut 86q^{95} \) \(\mathstrut +\mathstrut 33q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut -\mathstrut 116q^{98} \) \(\mathstrut +\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.77527 −1.96241 −0.981207 0.192958i \(-0.938192\pi\)
−0.981207 + 0.192958i \(0.938192\pi\)
\(3\) 1.86757 1.07824 0.539121 0.842228i \(-0.318757\pi\)
0.539121 + 0.842228i \(0.318757\pi\)
\(4\) 5.70214 2.85107
\(5\) 1.50597 0.673489 0.336744 0.941596i \(-0.390674\pi\)
0.336744 + 0.941596i \(0.390674\pi\)
\(6\) −5.18302 −2.11596
\(7\) −3.04702 −1.15167 −0.575833 0.817568i \(-0.695322\pi\)
−0.575833 + 0.817568i \(0.695322\pi\)
\(8\) −10.2744 −3.63256
\(9\) 0.487817 0.162606
\(10\) −4.17947 −1.32166
\(11\) −4.97460 −1.49990 −0.749948 0.661496i \(-0.769922\pi\)
−0.749948 + 0.661496i \(0.769922\pi\)
\(12\) 10.6491 3.07414
\(13\) 4.84844 1.34472 0.672358 0.740226i \(-0.265282\pi\)
0.672358 + 0.740226i \(0.265282\pi\)
\(14\) 8.45631 2.26004
\(15\) 2.81250 0.726184
\(16\) 17.1101 4.27752
\(17\) −1.65425 −0.401214 −0.200607 0.979672i \(-0.564292\pi\)
−0.200607 + 0.979672i \(0.564292\pi\)
\(18\) −1.35383 −0.319100
\(19\) 7.46249 1.71201 0.856007 0.516965i \(-0.172938\pi\)
0.856007 + 0.516965i \(0.172938\pi\)
\(20\) 8.58723 1.92016
\(21\) −5.69052 −1.24177
\(22\) 13.8059 2.94342
\(23\) −5.06186 −1.05547 −0.527736 0.849409i \(-0.676959\pi\)
−0.527736 + 0.849409i \(0.676959\pi\)
\(24\) −19.1882 −3.91678
\(25\) −2.73206 −0.546413
\(26\) −13.4557 −2.63889
\(27\) −4.69168 −0.902914
\(28\) −17.3745 −3.28348
\(29\) −3.53076 −0.655646 −0.327823 0.944739i \(-0.606315\pi\)
−0.327823 + 0.944739i \(0.606315\pi\)
\(30\) −7.80545 −1.42507
\(31\) 7.56226 1.35822 0.679111 0.734036i \(-0.262366\pi\)
0.679111 + 0.734036i \(0.262366\pi\)
\(32\) −26.9363 −4.76171
\(33\) −9.29040 −1.61725
\(34\) 4.59099 0.787349
\(35\) −4.58871 −0.775634
\(36\) 2.78160 0.463600
\(37\) −1.00000 −0.164399
\(38\) −20.7105 −3.35968
\(39\) 9.05480 1.44993
\(40\) −15.4730 −2.44649
\(41\) 9.30932 1.45387 0.726936 0.686705i \(-0.240944\pi\)
0.726936 + 0.686705i \(0.240944\pi\)
\(42\) 15.7928 2.43687
\(43\) 3.86049 0.588719 0.294359 0.955695i \(-0.404894\pi\)
0.294359 + 0.955695i \(0.404894\pi\)
\(44\) −28.3658 −4.27631
\(45\) 0.734637 0.109513
\(46\) 14.0480 2.07127
\(47\) −3.71430 −0.541787 −0.270893 0.962609i \(-0.587319\pi\)
−0.270893 + 0.962609i \(0.587319\pi\)
\(48\) 31.9543 4.61220
\(49\) 2.28433 0.326333
\(50\) 7.58222 1.07229
\(51\) −3.08943 −0.432606
\(52\) 27.6465 3.83388
\(53\) 2.18318 0.299883 0.149941 0.988695i \(-0.452092\pi\)
0.149941 + 0.988695i \(0.452092\pi\)
\(54\) 13.0207 1.77189
\(55\) −7.49157 −1.01016
\(56\) 31.3064 4.18350
\(57\) 13.9367 1.84596
\(58\) 9.79883 1.28665
\(59\) −7.82573 −1.01882 −0.509412 0.860523i \(-0.670137\pi\)
−0.509412 + 0.860523i \(0.670137\pi\)
\(60\) 16.0372 2.07040
\(61\) 6.93522 0.887964 0.443982 0.896036i \(-0.353565\pi\)
0.443982 + 0.896036i \(0.353565\pi\)
\(62\) −20.9873 −2.66539
\(63\) −1.48639 −0.187267
\(64\) 40.5353 5.06692
\(65\) 7.30159 0.905651
\(66\) 25.7834 3.17372
\(67\) −13.1252 −1.60349 −0.801747 0.597664i \(-0.796096\pi\)
−0.801747 + 0.597664i \(0.796096\pi\)
\(68\) −9.43276 −1.14389
\(69\) −9.45338 −1.13805
\(70\) 12.7349 1.52211
\(71\) 9.15497 1.08650 0.543248 0.839573i \(-0.317195\pi\)
0.543248 + 0.839573i \(0.317195\pi\)
\(72\) −5.01205 −0.590676
\(73\) −11.8430 −1.38612 −0.693059 0.720881i \(-0.743738\pi\)
−0.693059 + 0.720881i \(0.743738\pi\)
\(74\) 2.77527 0.322619
\(75\) −5.10232 −0.589165
\(76\) 42.5522 4.88107
\(77\) 15.1577 1.72738
\(78\) −25.1295 −2.84536
\(79\) −6.00754 −0.675902 −0.337951 0.941164i \(-0.609734\pi\)
−0.337951 + 0.941164i \(0.609734\pi\)
\(80\) 25.7672 2.88086
\(81\) −10.2255 −1.13617
\(82\) −25.8359 −2.85310
\(83\) 17.2265 1.89086 0.945430 0.325827i \(-0.105643\pi\)
0.945430 + 0.325827i \(0.105643\pi\)
\(84\) −32.4481 −3.54038
\(85\) −2.49124 −0.270213
\(86\) −10.7139 −1.15531
\(87\) −6.59395 −0.706945
\(88\) 51.1112 5.44847
\(89\) −15.1661 −1.60760 −0.803800 0.594900i \(-0.797192\pi\)
−0.803800 + 0.594900i \(0.797192\pi\)
\(90\) −2.03882 −0.214910
\(91\) −14.7733 −1.54866
\(92\) −28.8634 −3.00922
\(93\) 14.1230 1.46449
\(94\) 10.3082 1.06321
\(95\) 11.2383 1.15302
\(96\) −50.3054 −5.13427
\(97\) −7.08860 −0.719738 −0.359869 0.933003i \(-0.617179\pi\)
−0.359869 + 0.933003i \(0.617179\pi\)
\(98\) −6.33964 −0.640400
\(99\) −2.42669 −0.243892
\(100\) −15.5786 −1.55786
\(101\) −6.28711 −0.625591 −0.312796 0.949820i \(-0.601265\pi\)
−0.312796 + 0.949820i \(0.601265\pi\)
\(102\) 8.57400 0.848953
\(103\) −9.26369 −0.912778 −0.456389 0.889780i \(-0.650857\pi\)
−0.456389 + 0.889780i \(0.650857\pi\)
\(104\) −49.8150 −4.88476
\(105\) −8.56974 −0.836321
\(106\) −6.05891 −0.588494
\(107\) −5.38708 −0.520789 −0.260394 0.965502i \(-0.583853\pi\)
−0.260394 + 0.965502i \(0.583853\pi\)
\(108\) −26.7526 −2.57427
\(109\) −1.00000 −0.0957826
\(110\) 20.7912 1.98236
\(111\) −1.86757 −0.177262
\(112\) −52.1348 −4.92627
\(113\) −1.86056 −0.175027 −0.0875135 0.996163i \(-0.527892\pi\)
−0.0875135 + 0.996163i \(0.527892\pi\)
\(114\) −38.6782 −3.62255
\(115\) −7.62300 −0.710848
\(116\) −20.1329 −1.86929
\(117\) 2.36515 0.218659
\(118\) 21.7185 1.99935
\(119\) 5.04053 0.462065
\(120\) −28.8968 −2.63791
\(121\) 13.7466 1.24969
\(122\) −19.2471 −1.74255
\(123\) 17.3858 1.56763
\(124\) 43.1210 3.87238
\(125\) −11.6442 −1.04149
\(126\) 4.12514 0.367496
\(127\) −5.25893 −0.466654 −0.233327 0.972398i \(-0.574961\pi\)
−0.233327 + 0.972398i \(0.574961\pi\)
\(128\) −58.6241 −5.18168
\(129\) 7.20973 0.634782
\(130\) −20.2639 −1.77726
\(131\) −5.59196 −0.488572 −0.244286 0.969703i \(-0.578553\pi\)
−0.244286 + 0.969703i \(0.578553\pi\)
\(132\) −52.9752 −4.61090
\(133\) −22.7384 −1.97167
\(134\) 36.4259 3.14672
\(135\) −7.06551 −0.608102
\(136\) 16.9965 1.45744
\(137\) 8.44838 0.721794 0.360897 0.932606i \(-0.382471\pi\)
0.360897 + 0.932606i \(0.382471\pi\)
\(138\) 26.2357 2.23333
\(139\) −17.2359 −1.46193 −0.730964 0.682416i \(-0.760929\pi\)
−0.730964 + 0.682416i \(0.760929\pi\)
\(140\) −26.1655 −2.21138
\(141\) −6.93672 −0.584177
\(142\) −25.4075 −2.13215
\(143\) −24.1190 −2.01694
\(144\) 8.34660 0.695550
\(145\) −5.31721 −0.441570
\(146\) 32.8675 2.72014
\(147\) 4.26615 0.351866
\(148\) −5.70214 −0.468713
\(149\) −1.99641 −0.163552 −0.0817761 0.996651i \(-0.526059\pi\)
−0.0817761 + 0.996651i \(0.526059\pi\)
\(150\) 14.1603 1.15619
\(151\) −5.23292 −0.425849 −0.212924 0.977069i \(-0.568299\pi\)
−0.212924 + 0.977069i \(0.568299\pi\)
\(152\) −76.6729 −6.21900
\(153\) −0.806972 −0.0652398
\(154\) −42.0667 −3.38983
\(155\) 11.3885 0.914747
\(156\) 51.6317 4.13385
\(157\) 1.21537 0.0969972 0.0484986 0.998823i \(-0.484556\pi\)
0.0484986 + 0.998823i \(0.484556\pi\)
\(158\) 16.6726 1.32640
\(159\) 4.07724 0.323346
\(160\) −40.5651 −3.20696
\(161\) 15.4236 1.21555
\(162\) 28.3785 2.22963
\(163\) −2.79396 −0.218840 −0.109420 0.993996i \(-0.534899\pi\)
−0.109420 + 0.993996i \(0.534899\pi\)
\(164\) 53.0830 4.14509
\(165\) −13.9910 −1.08920
\(166\) −47.8084 −3.71065
\(167\) −1.39187 −0.107706 −0.0538529 0.998549i \(-0.517150\pi\)
−0.0538529 + 0.998549i \(0.517150\pi\)
\(168\) 58.4669 4.51082
\(169\) 10.5074 0.808261
\(170\) 6.91388 0.530271
\(171\) 3.64033 0.278383
\(172\) 22.0130 1.67848
\(173\) 13.8539 1.05329 0.526646 0.850085i \(-0.323449\pi\)
0.526646 + 0.850085i \(0.323449\pi\)
\(174\) 18.3000 1.38732
\(175\) 8.32466 0.629285
\(176\) −85.1158 −6.41584
\(177\) −14.6151 −1.09854
\(178\) 42.0900 3.15478
\(179\) 21.1116 1.57796 0.788978 0.614421i \(-0.210610\pi\)
0.788978 + 0.614421i \(0.210610\pi\)
\(180\) 4.18900 0.312230
\(181\) −23.0872 −1.71606 −0.858029 0.513601i \(-0.828311\pi\)
−0.858029 + 0.513601i \(0.828311\pi\)
\(182\) 40.9999 3.03912
\(183\) 12.9520 0.957440
\(184\) 52.0078 3.83407
\(185\) −1.50597 −0.110721
\(186\) −39.1953 −2.87394
\(187\) 8.22922 0.601780
\(188\) −21.1795 −1.54467
\(189\) 14.2956 1.03985
\(190\) −31.1892 −2.26271
\(191\) −13.3647 −0.967037 −0.483518 0.875334i \(-0.660641\pi\)
−0.483518 + 0.875334i \(0.660641\pi\)
\(192\) 75.7026 5.46336
\(193\) −5.31023 −0.382238 −0.191119 0.981567i \(-0.561212\pi\)
−0.191119 + 0.981567i \(0.561212\pi\)
\(194\) 19.6728 1.41242
\(195\) 13.6362 0.976511
\(196\) 13.0256 0.930397
\(197\) −15.4164 −1.09838 −0.549188 0.835699i \(-0.685063\pi\)
−0.549188 + 0.835699i \(0.685063\pi\)
\(198\) 6.73474 0.478617
\(199\) −12.3582 −0.876049 −0.438025 0.898963i \(-0.644322\pi\)
−0.438025 + 0.898963i \(0.644322\pi\)
\(200\) 28.0704 1.98488
\(201\) −24.5122 −1.72895
\(202\) 17.4485 1.22767
\(203\) 10.7583 0.755085
\(204\) −17.6163 −1.23339
\(205\) 14.0195 0.979166
\(206\) 25.7093 1.79125
\(207\) −2.46927 −0.171626
\(208\) 82.9573 5.75205
\(209\) −37.1229 −2.56784
\(210\) 23.7834 1.64121
\(211\) 13.6874 0.942280 0.471140 0.882058i \(-0.343843\pi\)
0.471140 + 0.882058i \(0.343843\pi\)
\(212\) 12.4488 0.854986
\(213\) 17.0975 1.17150
\(214\) 14.9506 1.02200
\(215\) 5.81377 0.396496
\(216\) 48.2043 3.27989
\(217\) −23.0423 −1.56422
\(218\) 2.77527 0.187965
\(219\) −22.1176 −1.49457
\(220\) −42.7180 −2.88005
\(221\) −8.02053 −0.539519
\(222\) 5.18302 0.347861
\(223\) −7.15168 −0.478912 −0.239456 0.970907i \(-0.576969\pi\)
−0.239456 + 0.970907i \(0.576969\pi\)
\(224\) 82.0754 5.48389
\(225\) −1.33275 −0.0888499
\(226\) 5.16357 0.343475
\(227\) −23.2683 −1.54437 −0.772186 0.635397i \(-0.780837\pi\)
−0.772186 + 0.635397i \(0.780837\pi\)
\(228\) 79.4691 5.26297
\(229\) −21.3020 −1.40767 −0.703837 0.710362i \(-0.748531\pi\)
−0.703837 + 0.710362i \(0.748531\pi\)
\(230\) 21.1559 1.39498
\(231\) 28.3080 1.86253
\(232\) 36.2766 2.38168
\(233\) −27.9747 −1.83268 −0.916342 0.400397i \(-0.868872\pi\)
−0.916342 + 0.400397i \(0.868872\pi\)
\(234\) −6.56395 −0.429099
\(235\) −5.59362 −0.364887
\(236\) −44.6234 −2.90473
\(237\) −11.2195 −0.728785
\(238\) −13.9888 −0.906762
\(239\) 0.737685 0.0477169 0.0238585 0.999715i \(-0.492405\pi\)
0.0238585 + 0.999715i \(0.492405\pi\)
\(240\) 48.1221 3.10627
\(241\) 10.3748 0.668297 0.334148 0.942520i \(-0.391551\pi\)
0.334148 + 0.942520i \(0.391551\pi\)
\(242\) −38.1505 −2.45241
\(243\) −5.02178 −0.322147
\(244\) 39.5456 2.53165
\(245\) 3.44013 0.219782
\(246\) −48.2504 −3.07633
\(247\) 36.1815 2.30217
\(248\) −77.6979 −4.93382
\(249\) 32.1718 2.03880
\(250\) 32.3159 2.04384
\(251\) −23.8826 −1.50746 −0.753729 0.657185i \(-0.771747\pi\)
−0.753729 + 0.657185i \(0.771747\pi\)
\(252\) −8.47560 −0.533912
\(253\) 25.1807 1.58310
\(254\) 14.5950 0.915769
\(255\) −4.65257 −0.291355
\(256\) 81.6270 5.10169
\(257\) −22.1270 −1.38024 −0.690121 0.723694i \(-0.742443\pi\)
−0.690121 + 0.723694i \(0.742443\pi\)
\(258\) −20.0090 −1.24570
\(259\) 3.04702 0.189333
\(260\) 41.6347 2.58207
\(261\) −1.72237 −0.106612
\(262\) 15.5192 0.958780
\(263\) −23.4109 −1.44358 −0.721790 0.692112i \(-0.756681\pi\)
−0.721790 + 0.692112i \(0.756681\pi\)
\(264\) 95.4537 5.87477
\(265\) 3.28779 0.201968
\(266\) 63.1052 3.86923
\(267\) −28.3237 −1.73338
\(268\) −74.8415 −4.57167
\(269\) 25.2480 1.53940 0.769700 0.638406i \(-0.220406\pi\)
0.769700 + 0.638406i \(0.220406\pi\)
\(270\) 19.6087 1.19335
\(271\) −10.0829 −0.612490 −0.306245 0.951953i \(-0.599073\pi\)
−0.306245 + 0.951953i \(0.599073\pi\)
\(272\) −28.3044 −1.71620
\(273\) −27.5902 −1.66983
\(274\) −23.4466 −1.41646
\(275\) 13.5909 0.819563
\(276\) −53.9045 −3.24467
\(277\) 5.96381 0.358330 0.179165 0.983819i \(-0.442660\pi\)
0.179165 + 0.983819i \(0.442660\pi\)
\(278\) 47.8343 2.86891
\(279\) 3.68900 0.220855
\(280\) 47.1464 2.81754
\(281\) 14.4865 0.864190 0.432095 0.901828i \(-0.357774\pi\)
0.432095 + 0.901828i \(0.357774\pi\)
\(282\) 19.2513 1.14640
\(283\) −15.6869 −0.932491 −0.466245 0.884655i \(-0.654394\pi\)
−0.466245 + 0.884655i \(0.654394\pi\)
\(284\) 52.2029 3.09767
\(285\) 20.9882 1.24324
\(286\) 66.9369 3.95806
\(287\) −28.3657 −1.67437
\(288\) −13.1400 −0.774281
\(289\) −14.2635 −0.839027
\(290\) 14.7567 0.866544
\(291\) −13.2385 −0.776052
\(292\) −67.5304 −3.95192
\(293\) 11.0611 0.646198 0.323099 0.946365i \(-0.395275\pi\)
0.323099 + 0.946365i \(0.395275\pi\)
\(294\) −11.8397 −0.690506
\(295\) −11.7853 −0.686166
\(296\) 10.2744 0.597190
\(297\) 23.3392 1.35428
\(298\) 5.54058 0.320957
\(299\) −24.5422 −1.41931
\(300\) −29.0941 −1.67975
\(301\) −11.7630 −0.678007
\(302\) 14.5228 0.835692
\(303\) −11.7416 −0.674539
\(304\) 127.684 7.32318
\(305\) 10.4442 0.598034
\(306\) 2.23957 0.128028
\(307\) 21.5534 1.23012 0.615058 0.788482i \(-0.289133\pi\)
0.615058 + 0.788482i \(0.289133\pi\)
\(308\) 86.4312 4.92488
\(309\) −17.3006 −0.984196
\(310\) −31.6062 −1.79511
\(311\) −11.2228 −0.636385 −0.318193 0.948026i \(-0.603076\pi\)
−0.318193 + 0.948026i \(0.603076\pi\)
\(312\) −93.0330 −5.26696
\(313\) 18.4336 1.04193 0.520964 0.853579i \(-0.325573\pi\)
0.520964 + 0.853579i \(0.325573\pi\)
\(314\) −3.37299 −0.190349
\(315\) −2.23845 −0.126123
\(316\) −34.2558 −1.92704
\(317\) 28.9466 1.62581 0.812903 0.582399i \(-0.197886\pi\)
0.812903 + 0.582399i \(0.197886\pi\)
\(318\) −11.3154 −0.634539
\(319\) 17.5641 0.983402
\(320\) 61.0449 3.41251
\(321\) −10.0607 −0.561536
\(322\) −42.8047 −2.38541
\(323\) −12.3448 −0.686884
\(324\) −58.3071 −3.23928
\(325\) −13.2463 −0.734770
\(326\) 7.75400 0.429455
\(327\) −1.86757 −0.103277
\(328\) −95.6481 −5.28128
\(329\) 11.3176 0.623957
\(330\) 38.8289 2.13746
\(331\) −16.4158 −0.902294 −0.451147 0.892450i \(-0.648985\pi\)
−0.451147 + 0.892450i \(0.648985\pi\)
\(332\) 98.2281 5.39097
\(333\) −0.487817 −0.0267322
\(334\) 3.86281 0.211364
\(335\) −19.7661 −1.07994
\(336\) −97.3654 −5.31172
\(337\) 6.21803 0.338718 0.169359 0.985554i \(-0.445830\pi\)
0.169359 + 0.985554i \(0.445830\pi\)
\(338\) −29.1609 −1.58614
\(339\) −3.47473 −0.188721
\(340\) −14.2054 −0.770397
\(341\) −37.6192 −2.03719
\(342\) −10.1029 −0.546303
\(343\) 14.3687 0.775839
\(344\) −39.6643 −2.13856
\(345\) −14.2365 −0.766466
\(346\) −38.4483 −2.06700
\(347\) −17.5959 −0.944596 −0.472298 0.881439i \(-0.656575\pi\)
−0.472298 + 0.881439i \(0.656575\pi\)
\(348\) −37.5996 −2.01555
\(349\) 22.2994 1.19366 0.596830 0.802367i \(-0.296426\pi\)
0.596830 + 0.802367i \(0.296426\pi\)
\(350\) −23.1032 −1.23492
\(351\) −22.7473 −1.21416
\(352\) 133.997 7.14207
\(353\) −13.1549 −0.700166 −0.350083 0.936719i \(-0.613847\pi\)
−0.350083 + 0.936719i \(0.613847\pi\)
\(354\) 40.5609 2.15579
\(355\) 13.7871 0.731742
\(356\) −86.4790 −4.58338
\(357\) 9.41355 0.498218
\(358\) −58.5905 −3.09660
\(359\) 13.0453 0.688506 0.344253 0.938877i \(-0.388132\pi\)
0.344253 + 0.938877i \(0.388132\pi\)
\(360\) −7.54798 −0.397813
\(361\) 36.6888 1.93099
\(362\) 64.0733 3.36762
\(363\) 25.6727 1.34747
\(364\) −84.2394 −4.41534
\(365\) −17.8352 −0.933535
\(366\) −35.9454 −1.87889
\(367\) −26.4008 −1.37811 −0.689056 0.724708i \(-0.741975\pi\)
−0.689056 + 0.724708i \(0.741975\pi\)
\(368\) −86.6089 −4.51480
\(369\) 4.54125 0.236408
\(370\) 4.17947 0.217280
\(371\) −6.65219 −0.345364
\(372\) 80.5315 4.17537
\(373\) 28.5611 1.47884 0.739419 0.673245i \(-0.235100\pi\)
0.739419 + 0.673245i \(0.235100\pi\)
\(374\) −22.8383 −1.18094
\(375\) −21.7464 −1.12298
\(376\) 38.1624 1.96807
\(377\) −17.1187 −0.881658
\(378\) −39.6743 −2.04062
\(379\) −12.3531 −0.634535 −0.317267 0.948336i \(-0.602765\pi\)
−0.317267 + 0.948336i \(0.602765\pi\)
\(380\) 64.0821 3.28734
\(381\) −9.82142 −0.503166
\(382\) 37.0907 1.89773
\(383\) 35.7315 1.82579 0.912896 0.408192i \(-0.133841\pi\)
0.912896 + 0.408192i \(0.133841\pi\)
\(384\) −109.485 −5.58711
\(385\) 22.8270 1.16337
\(386\) 14.7373 0.750110
\(387\) 1.88321 0.0957291
\(388\) −40.4202 −2.05202
\(389\) 8.03533 0.407407 0.203704 0.979033i \(-0.434702\pi\)
0.203704 + 0.979033i \(0.434702\pi\)
\(390\) −37.8443 −1.91632
\(391\) 8.37359 0.423470
\(392\) −23.4702 −1.18542
\(393\) −10.4434 −0.526798
\(394\) 42.7848 2.15547
\(395\) −9.04716 −0.455212
\(396\) −13.8373 −0.695353
\(397\) 15.9147 0.798738 0.399369 0.916790i \(-0.369229\pi\)
0.399369 + 0.916790i \(0.369229\pi\)
\(398\) 34.2974 1.71917
\(399\) −42.4655 −2.12593
\(400\) −46.7459 −2.33729
\(401\) 14.8140 0.739776 0.369888 0.929076i \(-0.379396\pi\)
0.369888 + 0.929076i \(0.379396\pi\)
\(402\) 68.0279 3.39292
\(403\) 36.6652 1.82642
\(404\) −35.8500 −1.78360
\(405\) −15.3992 −0.765194
\(406\) −29.8572 −1.48179
\(407\) 4.97460 0.246582
\(408\) 31.7421 1.57147
\(409\) 9.07411 0.448686 0.224343 0.974510i \(-0.427976\pi\)
0.224343 + 0.974510i \(0.427976\pi\)
\(410\) −38.9080 −1.92153
\(411\) 15.7779 0.778269
\(412\) −52.8228 −2.60239
\(413\) 23.8452 1.17334
\(414\) 6.85288 0.336801
\(415\) 25.9426 1.27347
\(416\) −130.599 −6.40314
\(417\) −32.1892 −1.57631
\(418\) 103.026 5.03917
\(419\) −4.83572 −0.236240 −0.118120 0.992999i \(-0.537687\pi\)
−0.118120 + 0.992999i \(0.537687\pi\)
\(420\) −48.8658 −2.38441
\(421\) 21.7162 1.05838 0.529191 0.848503i \(-0.322496\pi\)
0.529191 + 0.848503i \(0.322496\pi\)
\(422\) −37.9863 −1.84914
\(423\) −1.81190 −0.0880977
\(424\) −22.4309 −1.08934
\(425\) 4.51952 0.219229
\(426\) −47.4504 −2.29898
\(427\) −21.1318 −1.02264
\(428\) −30.7179 −1.48480
\(429\) −45.0440 −2.17474
\(430\) −16.1348 −0.778088
\(431\) 12.6370 0.608704 0.304352 0.952560i \(-0.401560\pi\)
0.304352 + 0.952560i \(0.401560\pi\)
\(432\) −80.2750 −3.86223
\(433\) 25.1637 1.20929 0.604645 0.796495i \(-0.293315\pi\)
0.604645 + 0.796495i \(0.293315\pi\)
\(434\) 63.9488 3.06964
\(435\) −9.93027 −0.476120
\(436\) −5.70214 −0.273083
\(437\) −37.7741 −1.80698
\(438\) 61.3824 2.93297
\(439\) 24.4025 1.16467 0.582334 0.812949i \(-0.302140\pi\)
0.582334 + 0.812949i \(0.302140\pi\)
\(440\) 76.9717 3.66948
\(441\) 1.11434 0.0530636
\(442\) 22.2592 1.05876
\(443\) 30.1894 1.43434 0.717170 0.696899i \(-0.245437\pi\)
0.717170 + 0.696899i \(0.245437\pi\)
\(444\) −10.6491 −0.505386
\(445\) −22.8396 −1.08270
\(446\) 19.8478 0.939823
\(447\) −3.72843 −0.176349
\(448\) −123.512 −5.83539
\(449\) 14.3744 0.678371 0.339185 0.940720i \(-0.389849\pi\)
0.339185 + 0.940720i \(0.389849\pi\)
\(450\) 3.69874 0.174360
\(451\) −46.3101 −2.18066
\(452\) −10.6092 −0.499014
\(453\) −9.77284 −0.459168
\(454\) 64.5759 3.03070
\(455\) −22.2481 −1.04301
\(456\) −143.192 −6.70558
\(457\) −17.0020 −0.795321 −0.397660 0.917533i \(-0.630178\pi\)
−0.397660 + 0.917533i \(0.630178\pi\)
\(458\) 59.1188 2.76244
\(459\) 7.76120 0.362262
\(460\) −43.4674 −2.02668
\(461\) 30.0299 1.39863 0.699316 0.714812i \(-0.253488\pi\)
0.699316 + 0.714812i \(0.253488\pi\)
\(462\) −78.5625 −3.65506
\(463\) −11.6971 −0.543611 −0.271806 0.962352i \(-0.587621\pi\)
−0.271806 + 0.962352i \(0.587621\pi\)
\(464\) −60.4117 −2.80454
\(465\) 21.2688 0.986319
\(466\) 77.6374 3.59648
\(467\) −5.69237 −0.263412 −0.131706 0.991289i \(-0.542045\pi\)
−0.131706 + 0.991289i \(0.542045\pi\)
\(468\) 13.4864 0.623411
\(469\) 39.9926 1.84669
\(470\) 15.5238 0.716060
\(471\) 2.26979 0.104586
\(472\) 80.4050 3.70094
\(473\) −19.2044 −0.883018
\(474\) 31.1372 1.43018
\(475\) −20.3880 −0.935466
\(476\) 28.7418 1.31738
\(477\) 1.06499 0.0487627
\(478\) −2.04728 −0.0936403
\(479\) 17.6713 0.807423 0.403712 0.914886i \(-0.367720\pi\)
0.403712 + 0.914886i \(0.367720\pi\)
\(480\) −75.7582 −3.45787
\(481\) −4.84844 −0.221070
\(482\) −28.7928 −1.31148
\(483\) 28.8046 1.31066
\(484\) 78.3850 3.56295
\(485\) −10.6752 −0.484736
\(486\) 13.9368 0.632187
\(487\) −34.4430 −1.56076 −0.780380 0.625305i \(-0.784974\pi\)
−0.780380 + 0.625305i \(0.784974\pi\)
\(488\) −71.2555 −3.22558
\(489\) −5.21792 −0.235962
\(490\) −9.54728 −0.431302
\(491\) −18.2239 −0.822432 −0.411216 0.911538i \(-0.634896\pi\)
−0.411216 + 0.911538i \(0.634896\pi\)
\(492\) 99.1363 4.46941
\(493\) 5.84076 0.263055
\(494\) −100.413 −4.51781
\(495\) −3.65452 −0.164258
\(496\) 129.391 5.80982
\(497\) −27.8954 −1.25128
\(498\) −89.2854 −4.00098
\(499\) −22.4715 −1.00596 −0.502981 0.864297i \(-0.667763\pi\)
−0.502981 + 0.864297i \(0.667763\pi\)
\(500\) −66.3970 −2.96936
\(501\) −2.59941 −0.116133
\(502\) 66.2808 2.95826
\(503\) −37.0854 −1.65355 −0.826777 0.562530i \(-0.809828\pi\)
−0.826777 + 0.562530i \(0.809828\pi\)
\(504\) 15.2718 0.680261
\(505\) −9.46818 −0.421329
\(506\) −69.8834 −3.10669
\(507\) 19.6233 0.871501
\(508\) −29.9871 −1.33046
\(509\) 18.3451 0.813131 0.406566 0.913622i \(-0.366726\pi\)
0.406566 + 0.913622i \(0.366726\pi\)
\(510\) 12.9122 0.571760
\(511\) 36.0859 1.59634
\(512\) −109.289 −4.82994
\(513\) −35.0116 −1.54580
\(514\) 61.4083 2.70860
\(515\) −13.9508 −0.614746
\(516\) 41.1109 1.80981
\(517\) 18.4772 0.812624
\(518\) −8.45631 −0.371549
\(519\) 25.8731 1.13570
\(520\) −75.0197 −3.28983
\(521\) −11.0598 −0.484537 −0.242269 0.970209i \(-0.577892\pi\)
−0.242269 + 0.970209i \(0.577892\pi\)
\(522\) 4.78004 0.209217
\(523\) 17.0460 0.745371 0.372686 0.927958i \(-0.378437\pi\)
0.372686 + 0.927958i \(0.378437\pi\)
\(524\) −31.8861 −1.39295
\(525\) 15.5469 0.678521
\(526\) 64.9718 2.83290
\(527\) −12.5099 −0.544938
\(528\) −158.960 −6.91783
\(529\) 2.62246 0.114020
\(530\) −9.12452 −0.396344
\(531\) −3.81753 −0.165667
\(532\) −129.657 −5.62136
\(533\) 45.1357 1.95504
\(534\) 78.6060 3.40161
\(535\) −8.11276 −0.350745
\(536\) 134.854 5.82479
\(537\) 39.4274 1.70142
\(538\) −70.0702 −3.02094
\(539\) −11.3636 −0.489466
\(540\) −40.2885 −1.73374
\(541\) −29.0154 −1.24747 −0.623736 0.781635i \(-0.714386\pi\)
−0.623736 + 0.781635i \(0.714386\pi\)
\(542\) 27.9827 1.20196
\(543\) −43.1170 −1.85033
\(544\) 44.5593 1.91047
\(545\) −1.50597 −0.0645085
\(546\) 76.5702 3.27690
\(547\) 0.327963 0.0140227 0.00701134 0.999975i \(-0.497768\pi\)
0.00701134 + 0.999975i \(0.497768\pi\)
\(548\) 48.1738 2.05788
\(549\) 3.38312 0.144388
\(550\) −37.7185 −1.60832
\(551\) −26.3483 −1.12248
\(552\) 97.1282 4.13405
\(553\) 18.3051 0.778412
\(554\) −16.5512 −0.703193
\(555\) −2.81250 −0.119384
\(556\) −98.2814 −4.16806
\(557\) 20.3230 0.861113 0.430557 0.902564i \(-0.358317\pi\)
0.430557 + 0.902564i \(0.358317\pi\)
\(558\) −10.2380 −0.433408
\(559\) 18.7174 0.791660
\(560\) −78.5132 −3.31779
\(561\) 15.3686 0.648865
\(562\) −40.2039 −1.69590
\(563\) −18.1328 −0.764208 −0.382104 0.924119i \(-0.624800\pi\)
−0.382104 + 0.924119i \(0.624800\pi\)
\(564\) −39.5541 −1.66553
\(565\) −2.80195 −0.117879
\(566\) 43.5355 1.82993
\(567\) 31.1573 1.30848
\(568\) −94.0622 −3.94676
\(569\) −1.26921 −0.0532080 −0.0266040 0.999646i \(-0.508469\pi\)
−0.0266040 + 0.999646i \(0.508469\pi\)
\(570\) −58.2481 −2.43974
\(571\) −4.86424 −0.203562 −0.101781 0.994807i \(-0.532454\pi\)
−0.101781 + 0.994807i \(0.532454\pi\)
\(572\) −137.530 −5.75042
\(573\) −24.9595 −1.04270
\(574\) 78.7225 3.28581
\(575\) 13.8293 0.576723
\(576\) 19.7739 0.823910
\(577\) −24.5522 −1.02212 −0.511062 0.859544i \(-0.670748\pi\)
−0.511062 + 0.859544i \(0.670748\pi\)
\(578\) 39.5850 1.64652
\(579\) −9.91722 −0.412146
\(580\) −30.3195 −1.25895
\(581\) −52.4896 −2.17764
\(582\) 36.7403 1.52294
\(583\) −10.8604 −0.449793
\(584\) 121.680 5.03516
\(585\) 3.56184 0.147264
\(586\) −30.6976 −1.26811
\(587\) −16.4595 −0.679358 −0.339679 0.940541i \(-0.610318\pi\)
−0.339679 + 0.940541i \(0.610318\pi\)
\(588\) 24.3262 1.00319
\(589\) 56.4333 2.32529
\(590\) 32.7074 1.34654
\(591\) −28.7913 −1.18432
\(592\) −17.1101 −0.703220
\(593\) 0.822481 0.0337753 0.0168876 0.999857i \(-0.494624\pi\)
0.0168876 + 0.999857i \(0.494624\pi\)
\(594\) −64.7726 −2.65765
\(595\) 7.59087 0.311195
\(596\) −11.3838 −0.466298
\(597\) −23.0798 −0.944593
\(598\) 68.1112 2.78527
\(599\) −23.6924 −0.968043 −0.484022 0.875056i \(-0.660824\pi\)
−0.484022 + 0.875056i \(0.660824\pi\)
\(600\) 52.4235 2.14018
\(601\) −12.4631 −0.508381 −0.254190 0.967154i \(-0.581809\pi\)
−0.254190 + 0.967154i \(0.581809\pi\)
\(602\) 32.6455 1.33053
\(603\) −6.40268 −0.260737
\(604\) −29.8388 −1.21412
\(605\) 20.7019 0.841652
\(606\) 32.5862 1.32372
\(607\) −11.4328 −0.464043 −0.232022 0.972711i \(-0.574534\pi\)
−0.232022 + 0.972711i \(0.574534\pi\)
\(608\) −201.012 −8.15211
\(609\) 20.0919 0.814165
\(610\) −28.9855 −1.17359
\(611\) −18.0086 −0.728549
\(612\) −4.60146 −0.186003
\(613\) −16.0318 −0.647517 −0.323758 0.946140i \(-0.604946\pi\)
−0.323758 + 0.946140i \(0.604946\pi\)
\(614\) −59.8165 −2.41400
\(615\) 26.1824 1.05578
\(616\) −155.737 −6.27481
\(617\) 29.9747 1.20674 0.603368 0.797463i \(-0.293825\pi\)
0.603368 + 0.797463i \(0.293825\pi\)
\(618\) 48.0138 1.93140
\(619\) 11.7212 0.471115 0.235557 0.971860i \(-0.424308\pi\)
0.235557 + 0.971860i \(0.424308\pi\)
\(620\) 64.9388 2.60801
\(621\) 23.7486 0.953000
\(622\) 31.1463 1.24885
\(623\) 46.2113 1.85142
\(624\) 154.929 6.20210
\(625\) −3.87550 −0.155020
\(626\) −51.1582 −2.04469
\(627\) −69.3296 −2.76876
\(628\) 6.93021 0.276546
\(629\) 1.65425 0.0659593
\(630\) 6.21232 0.247505
\(631\) −8.35781 −0.332719 −0.166360 0.986065i \(-0.553201\pi\)
−0.166360 + 0.986065i \(0.553201\pi\)
\(632\) 61.7241 2.45525
\(633\) 25.5622 1.01601
\(634\) −80.3348 −3.19050
\(635\) −7.91977 −0.314287
\(636\) 23.2490 0.921881
\(637\) 11.0754 0.438825
\(638\) −48.7452 −1.92984
\(639\) 4.46595 0.176670
\(640\) −88.2859 −3.48981
\(641\) 25.9920 1.02662 0.513311 0.858203i \(-0.328419\pi\)
0.513311 + 0.858203i \(0.328419\pi\)
\(642\) 27.9213 1.10197
\(643\) −19.9678 −0.787452 −0.393726 0.919228i \(-0.628814\pi\)
−0.393726 + 0.919228i \(0.628814\pi\)
\(644\) 87.9475 3.46562
\(645\) 10.8576 0.427518
\(646\) 34.2603 1.34795
\(647\) −38.6465 −1.51935 −0.759675 0.650303i \(-0.774642\pi\)
−0.759675 + 0.650303i \(0.774642\pi\)
\(648\) 105.061 4.12719
\(649\) 38.9298 1.52813
\(650\) 36.7620 1.44192
\(651\) −43.0332 −1.68660
\(652\) −15.9316 −0.623928
\(653\) −15.2668 −0.597438 −0.298719 0.954341i \(-0.596559\pi\)
−0.298719 + 0.954341i \(0.596559\pi\)
\(654\) 5.18302 0.202672
\(655\) −8.42130 −0.329047
\(656\) 159.283 6.21897
\(657\) −5.77722 −0.225391
\(658\) −31.4093 −1.22446
\(659\) −39.6208 −1.54341 −0.771703 0.635984i \(-0.780595\pi\)
−0.771703 + 0.635984i \(0.780595\pi\)
\(660\) −79.7788 −3.10539
\(661\) 33.5220 1.30386 0.651928 0.758281i \(-0.273960\pi\)
0.651928 + 0.758281i \(0.273960\pi\)
\(662\) 45.5583 1.77067
\(663\) −14.9789 −0.581733
\(664\) −176.993 −6.86866
\(665\) −34.2432 −1.32789
\(666\) 1.35383 0.0524597
\(667\) 17.8722 0.692016
\(668\) −7.93661 −0.307077
\(669\) −13.3563 −0.516383
\(670\) 54.8562 2.11928
\(671\) −34.4999 −1.33185
\(672\) 153.282 5.91296
\(673\) 21.6676 0.835224 0.417612 0.908625i \(-0.362867\pi\)
0.417612 + 0.908625i \(0.362867\pi\)
\(674\) −17.2567 −0.664705
\(675\) 12.8180 0.493364
\(676\) 59.9146 2.30441
\(677\) −18.4380 −0.708631 −0.354315 0.935126i \(-0.615286\pi\)
−0.354315 + 0.935126i \(0.615286\pi\)
\(678\) 9.64333 0.370350
\(679\) 21.5991 0.828898
\(680\) 25.5961 0.981567
\(681\) −43.4552 −1.66521
\(682\) 104.403 3.99781
\(683\) 16.6759 0.638084 0.319042 0.947741i \(-0.396639\pi\)
0.319042 + 0.947741i \(0.396639\pi\)
\(684\) 20.7577 0.793690
\(685\) 12.7230 0.486120
\(686\) −39.8772 −1.52252
\(687\) −39.7829 −1.51781
\(688\) 66.0533 2.51826
\(689\) 10.5850 0.403257
\(690\) 39.5101 1.50412
\(691\) −22.5250 −0.856891 −0.428446 0.903568i \(-0.640939\pi\)
−0.428446 + 0.903568i \(0.640939\pi\)
\(692\) 78.9968 3.00301
\(693\) 7.39419 0.280882
\(694\) 48.8334 1.85369
\(695\) −25.9567 −0.984592
\(696\) 67.7491 2.56802
\(697\) −15.3999 −0.583314
\(698\) −61.8870 −2.34246
\(699\) −52.2447 −1.97608
\(700\) 47.4683 1.79413
\(701\) −32.8914 −1.24229 −0.621146 0.783695i \(-0.713332\pi\)
−0.621146 + 0.783695i \(0.713332\pi\)
\(702\) 63.1300 2.38269
\(703\) −7.46249 −0.281453
\(704\) −201.647 −7.59985
\(705\) −10.4465 −0.393437
\(706\) 36.5085 1.37402
\(707\) 19.1570 0.720472
\(708\) −83.3373 −3.13201
\(709\) 23.8091 0.894171 0.447086 0.894491i \(-0.352462\pi\)
0.447086 + 0.894491i \(0.352462\pi\)
\(710\) −38.2629 −1.43598
\(711\) −2.93059 −0.109906
\(712\) 155.823 5.83971
\(713\) −38.2791 −1.43356
\(714\) −26.1252 −0.977709
\(715\) −36.3225 −1.35838
\(716\) 120.381 4.49886
\(717\) 1.37768 0.0514504
\(718\) −36.2043 −1.35113
\(719\) 21.9492 0.818565 0.409283 0.912408i \(-0.365779\pi\)
0.409283 + 0.912408i \(0.365779\pi\)
\(720\) 12.5697 0.468445
\(721\) 28.2266 1.05121
\(722\) −101.821 −3.78940
\(723\) 19.3756 0.720586
\(724\) −131.646 −4.89260
\(725\) 9.64628 0.358254
\(726\) −71.2488 −2.64429
\(727\) 2.07020 0.0767794 0.0383897 0.999263i \(-0.487777\pi\)
0.0383897 + 0.999263i \(0.487777\pi\)
\(728\) 151.787 5.62561
\(729\) 21.2979 0.788812
\(730\) 49.4974 1.83198
\(731\) −6.38621 −0.236203
\(732\) 73.8541 2.72973
\(733\) 42.4892 1.56937 0.784687 0.619892i \(-0.212824\pi\)
0.784687 + 0.619892i \(0.212824\pi\)
\(734\) 73.2695 2.70443
\(735\) 6.42467 0.236978
\(736\) 136.348 5.02585
\(737\) 65.2924 2.40508
\(738\) −12.6032 −0.463930
\(739\) −1.78901 −0.0658099 −0.0329050 0.999458i \(-0.510476\pi\)
−0.0329050 + 0.999458i \(0.510476\pi\)
\(740\) −8.58723 −0.315673
\(741\) 67.5714 2.48230
\(742\) 18.4616 0.677748
\(743\) 16.4932 0.605075 0.302538 0.953137i \(-0.402166\pi\)
0.302538 + 0.953137i \(0.402166\pi\)
\(744\) −145.106 −5.31986
\(745\) −3.00652 −0.110151
\(746\) −79.2649 −2.90209
\(747\) 8.40341 0.307465
\(748\) 46.9241 1.71572
\(749\) 16.4145 0.599774
\(750\) 60.3522 2.20375
\(751\) −30.6686 −1.11911 −0.559556 0.828792i \(-0.689028\pi\)
−0.559556 + 0.828792i \(0.689028\pi\)
\(752\) −63.5521 −2.31751
\(753\) −44.6025 −1.62540
\(754\) 47.5091 1.73018
\(755\) −7.88060 −0.286804
\(756\) 81.5156 2.96470
\(757\) −39.1436 −1.42270 −0.711349 0.702839i \(-0.751915\pi\)
−0.711349 + 0.702839i \(0.751915\pi\)
\(758\) 34.2832 1.24522
\(759\) 47.0268 1.70696
\(760\) −115.467 −4.18842
\(761\) 42.9294 1.55619 0.778096 0.628146i \(-0.216186\pi\)
0.778096 + 0.628146i \(0.216186\pi\)
\(762\) 27.2571 0.987421
\(763\) 3.04702 0.110310
\(764\) −76.2074 −2.75709
\(765\) −1.21527 −0.0439383
\(766\) −99.1645 −3.58296
\(767\) −37.9426 −1.37003
\(768\) 152.444 5.50086
\(769\) 49.8051 1.79602 0.898009 0.439978i \(-0.145014\pi\)
0.898009 + 0.439978i \(0.145014\pi\)
\(770\) −63.3511 −2.28301
\(771\) −41.3236 −1.48823
\(772\) −30.2796 −1.08979
\(773\) −39.4379 −1.41848 −0.709242 0.704965i \(-0.750963\pi\)
−0.709242 + 0.704965i \(0.750963\pi\)
\(774\) −5.22643 −0.187860
\(775\) −20.6606 −0.742150
\(776\) 72.8314 2.61449
\(777\) 5.69052 0.204146
\(778\) −22.3002 −0.799502
\(779\) 69.4708 2.48905
\(780\) 77.7557 2.78410
\(781\) −45.5423 −1.62963
\(782\) −23.2390 −0.831024
\(783\) 16.5652 0.591992
\(784\) 39.0851 1.39590
\(785\) 1.83031 0.0653265
\(786\) 28.9832 1.03380
\(787\) 29.4680 1.05042 0.525211 0.850972i \(-0.323987\pi\)
0.525211 + 0.850972i \(0.323987\pi\)
\(788\) −87.9067 −3.13155
\(789\) −43.7216 −1.55653
\(790\) 25.1083 0.893314
\(791\) 5.66917 0.201573
\(792\) 24.9329 0.885953
\(793\) 33.6250 1.19406
\(794\) −44.1677 −1.56745
\(795\) 6.14018 0.217770
\(796\) −70.4681 −2.49768
\(797\) −36.8191 −1.30420 −0.652099 0.758133i \(-0.726112\pi\)
−0.652099 + 0.758133i \(0.726112\pi\)
\(798\) 117.853 4.17196
\(799\) 6.14439 0.217373
\(800\) 73.5917 2.60186
\(801\) −7.39827 −0.261405
\(802\) −41.1129 −1.45175
\(803\) 58.9141 2.07903
\(804\) −139.772 −4.92937
\(805\) 23.2274 0.818659
\(806\) −101.756 −3.58420
\(807\) 47.1525 1.65985
\(808\) 64.5966 2.27250
\(809\) 30.5530 1.07418 0.537092 0.843523i \(-0.319523\pi\)
0.537092 + 0.843523i \(0.319523\pi\)
\(810\) 42.7371 1.50163
\(811\) 1.46555 0.0514625 0.0257312 0.999669i \(-0.491809\pi\)
0.0257312 + 0.999669i \(0.491809\pi\)
\(812\) 61.3453 2.15280
\(813\) −18.8305 −0.660413
\(814\) −13.8059 −0.483895
\(815\) −4.20761 −0.147386
\(816\) −52.8604 −1.85048
\(817\) 28.8089 1.00789
\(818\) −25.1831 −0.880507
\(819\) −7.20667 −0.251822
\(820\) 79.9413 2.79167
\(821\) 10.2438 0.357512 0.178756 0.983893i \(-0.442793\pi\)
0.178756 + 0.983893i \(0.442793\pi\)
\(822\) −43.7881 −1.52729
\(823\) 33.9663 1.18399 0.591996 0.805941i \(-0.298340\pi\)
0.591996 + 0.805941i \(0.298340\pi\)
\(824\) 95.1792 3.31572
\(825\) 25.3820 0.883687
\(826\) −66.1768 −2.30259
\(827\) −12.8306 −0.446163 −0.223081 0.974800i \(-0.571612\pi\)
−0.223081 + 0.974800i \(0.571612\pi\)
\(828\) −14.0801 −0.489317
\(829\) −9.41832 −0.327112 −0.163556 0.986534i \(-0.552296\pi\)
−0.163556 + 0.986534i \(0.552296\pi\)
\(830\) −71.9978 −2.49908
\(831\) 11.1378 0.386367
\(832\) 196.533 6.81357
\(833\) −3.77885 −0.130929
\(834\) 89.3339 3.09338
\(835\) −2.09610 −0.0725387
\(836\) −211.680 −7.32110
\(837\) −35.4797 −1.22636
\(838\) 13.4204 0.463601
\(839\) 37.7212 1.30228 0.651141 0.758957i \(-0.274291\pi\)
0.651141 + 0.758957i \(0.274291\pi\)
\(840\) 88.0492 3.03799
\(841\) −16.5337 −0.570128
\(842\) −60.2683 −2.07698
\(843\) 27.0545 0.931806
\(844\) 78.0475 2.68650
\(845\) 15.8238 0.544354
\(846\) 5.02852 0.172884
\(847\) −41.8862 −1.43923
\(848\) 37.3544 1.28275
\(849\) −29.2964 −1.00545
\(850\) −12.5429 −0.430218
\(851\) 5.06186 0.173518
\(852\) 97.4926 3.34004
\(853\) −14.1384 −0.484090 −0.242045 0.970265i \(-0.577818\pi\)
−0.242045 + 0.970265i \(0.577818\pi\)
\(854\) 58.6464 2.00684
\(855\) 5.48222 0.187488
\(856\) 55.3492 1.89180
\(857\) 20.7096 0.707425 0.353712 0.935354i \(-0.384919\pi\)
0.353712 + 0.935354i \(0.384919\pi\)
\(858\) 125.009 4.26775
\(859\) −16.7201 −0.570481 −0.285241 0.958456i \(-0.592074\pi\)
−0.285241 + 0.958456i \(0.592074\pi\)
\(860\) 33.1509 1.13044
\(861\) −52.9749 −1.80538
\(862\) −35.0712 −1.19453
\(863\) 37.3327 1.27082 0.635409 0.772175i \(-0.280831\pi\)
0.635409 + 0.772175i \(0.280831\pi\)
\(864\) 126.376 4.29941
\(865\) 20.8635 0.709380
\(866\) −69.8361 −2.37313
\(867\) −26.6380 −0.904674
\(868\) −131.391 −4.45969
\(869\) 29.8851 1.01378
\(870\) 27.5592 0.934344
\(871\) −63.6366 −2.15624
\(872\) 10.2744 0.347936
\(873\) −3.45794 −0.117034
\(874\) 104.833 3.54605
\(875\) 35.4802 1.19945
\(876\) −126.118 −4.26112
\(877\) −41.0087 −1.38476 −0.692382 0.721531i \(-0.743439\pi\)
−0.692382 + 0.721531i \(0.743439\pi\)
\(878\) −67.7236 −2.28556
\(879\) 20.6574 0.696757
\(880\) −128.182 −4.32100
\(881\) 39.2597 1.32269 0.661346 0.750081i \(-0.269985\pi\)
0.661346 + 0.750081i \(0.269985\pi\)
\(882\) −3.09259 −0.104133
\(883\) 12.3124 0.414345 0.207173 0.978304i \(-0.433574\pi\)
0.207173 + 0.978304i \(0.433574\pi\)
\(884\) −45.7342 −1.53821
\(885\) −22.0098 −0.739853
\(886\) −83.7837 −2.81477
\(887\) −18.4172 −0.618391 −0.309195 0.950999i \(-0.600060\pi\)
−0.309195 + 0.950999i \(0.600060\pi\)
\(888\) 19.1882 0.643915
\(889\) 16.0241 0.537430
\(890\) 63.3861 2.12471
\(891\) 50.8677 1.70413
\(892\) −40.7798 −1.36541
\(893\) −27.7180 −0.927546
\(894\) 10.3474 0.346069
\(895\) 31.7934 1.06274
\(896\) 178.629 5.96757
\(897\) −45.8342 −1.53036
\(898\) −39.8929 −1.33124
\(899\) −26.7005 −0.890513
\(900\) −7.59952 −0.253317
\(901\) −3.61152 −0.120317
\(902\) 128.523 4.27935
\(903\) −21.9682 −0.731056
\(904\) 19.1162 0.635797
\(905\) −34.7685 −1.15575
\(906\) 27.1223 0.901078
\(907\) 7.27336 0.241508 0.120754 0.992682i \(-0.461469\pi\)
0.120754 + 0.992682i \(0.461469\pi\)
\(908\) −132.679 −4.40311
\(909\) −3.06696 −0.101725
\(910\) 61.7445 2.04681
\(911\) −0.691119 −0.0228978 −0.0114489 0.999934i \(-0.503644\pi\)
−0.0114489 + 0.999934i \(0.503644\pi\)
\(912\) 238.459 7.89616
\(913\) −85.6951 −2.83609
\(914\) 47.1852 1.56075
\(915\) 19.5053 0.644825
\(916\) −121.467 −4.01337
\(917\) 17.0388 0.562671
\(918\) −21.5395 −0.710908
\(919\) −24.7904 −0.817761 −0.408881 0.912588i \(-0.634081\pi\)
−0.408881 + 0.912588i \(0.634081\pi\)
\(920\) 78.3220 2.58220
\(921\) 40.2524 1.32636
\(922\) −83.3412 −2.74470
\(923\) 44.3873 1.46103
\(924\) 161.416 5.31021
\(925\) 2.73206 0.0898297
\(926\) 32.4627 1.06679
\(927\) −4.51899 −0.148423
\(928\) 95.1057 3.12200
\(929\) 10.9340 0.358733 0.179367 0.983782i \(-0.442595\pi\)
0.179367 + 0.983782i \(0.442595\pi\)
\(930\) −59.0268 −1.93557
\(931\) 17.0468 0.558686
\(932\) −159.516 −5.22510
\(933\) −20.9593 −0.686177
\(934\) 15.7979 0.516922
\(935\) 12.3929 0.405292
\(936\) −24.3006 −0.794291
\(937\) −8.64073 −0.282280 −0.141140 0.989990i \(-0.545077\pi\)
−0.141140 + 0.989990i \(0.545077\pi\)
\(938\) −110.990 −3.62397
\(939\) 34.4260 1.12345
\(940\) −31.8956 −1.04032
\(941\) −13.9654 −0.455260 −0.227630 0.973748i \(-0.573098\pi\)
−0.227630 + 0.973748i \(0.573098\pi\)
\(942\) −6.29929 −0.205242
\(943\) −47.1225 −1.53452
\(944\) −133.899 −4.35804
\(945\) 21.5287 0.700330
\(946\) 53.2974 1.73285
\(947\) −20.2021 −0.656479 −0.328239 0.944595i \(-0.606455\pi\)
−0.328239 + 0.944595i \(0.606455\pi\)
\(948\) −63.9752 −2.07782
\(949\) −57.4201 −1.86394
\(950\) 56.5823 1.83577
\(951\) 54.0599 1.75301
\(952\) −51.7886 −1.67848
\(953\) −20.7886 −0.673408 −0.336704 0.941611i \(-0.609312\pi\)
−0.336704 + 0.941611i \(0.609312\pi\)
\(954\) −2.95564 −0.0956925
\(955\) −20.1268 −0.651288
\(956\) 4.20638 0.136044
\(957\) 32.8022 1.06035
\(958\) −49.0427 −1.58450
\(959\) −25.7424 −0.831265
\(960\) 114.006 3.67951
\(961\) 26.1877 0.844766
\(962\) 13.4557 0.433831
\(963\) −2.62791 −0.0846833
\(964\) 59.1583 1.90536
\(965\) −7.99702 −0.257433
\(966\) −79.9407 −2.57205
\(967\) −23.6220 −0.759633 −0.379817 0.925062i \(-0.624013\pi\)
−0.379817 + 0.925062i \(0.624013\pi\)
\(968\) −141.239 −4.53958
\(969\) −23.0548 −0.740628
\(970\) 29.6266 0.951252
\(971\) 59.8678 1.92125 0.960624 0.277851i \(-0.0896221\pi\)
0.960624 + 0.277851i \(0.0896221\pi\)
\(972\) −28.6349 −0.918464
\(973\) 52.5181 1.68365
\(974\) 95.5886 3.06286
\(975\) −24.7383 −0.792260
\(976\) 118.662 3.79829
\(977\) −17.5645 −0.561938 −0.280969 0.959717i \(-0.590656\pi\)
−0.280969 + 0.959717i \(0.590656\pi\)
\(978\) 14.4811 0.463056
\(979\) 75.4450 2.41123
\(980\) 19.6161 0.626612
\(981\) −0.487817 −0.0155748
\(982\) 50.5762 1.61395
\(983\) 20.2279 0.645170 0.322585 0.946540i \(-0.395448\pi\)
0.322585 + 0.946540i \(0.395448\pi\)
\(984\) −178.629 −5.69450
\(985\) −23.2167 −0.739744
\(986\) −16.2097 −0.516222
\(987\) 21.1363 0.672777
\(988\) 206.312 6.56365
\(989\) −19.5413 −0.621376
\(990\) 10.1423 0.322343
\(991\) 8.58612 0.272747 0.136374 0.990657i \(-0.456455\pi\)
0.136374 + 0.990657i \(0.456455\pi\)
\(992\) −203.699 −6.46745
\(993\) −30.6576 −0.972891
\(994\) 77.4173 2.45553
\(995\) −18.6110 −0.590009
\(996\) 183.448 5.81277
\(997\) −15.8439 −0.501782 −0.250891 0.968015i \(-0.580724\pi\)
−0.250891 + 0.968015i \(0.580724\pi\)
\(998\) 62.3645 1.97411
\(999\) 4.69168 0.148438
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 \(a_p\))