Properties

Label 4033.2.a.d.1.12
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 1.12
Character \(\chi\) = 4033.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.25482 q^{2}\) \(-0.982243 q^{3}\) \(+3.08420 q^{4}\) \(+2.20296 q^{5}\) \(+2.21478 q^{6}\) \(+0.164703 q^{7}\) \(-2.44467 q^{8}\) \(-2.03520 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.25482 q^{2}\) \(-0.982243 q^{3}\) \(+3.08420 q^{4}\) \(+2.20296 q^{5}\) \(+2.21478 q^{6}\) \(+0.164703 q^{7}\) \(-2.44467 q^{8}\) \(-2.03520 q^{9}\) \(-4.96728 q^{10}\) \(-1.46838 q^{11}\) \(-3.02943 q^{12}\) \(-5.51963 q^{13}\) \(-0.371375 q^{14}\) \(-2.16385 q^{15}\) \(-0.656123 q^{16}\) \(-5.86965 q^{17}\) \(+4.58900 q^{18}\) \(+2.55171 q^{19}\) \(+6.79437 q^{20}\) \(-0.161778 q^{21}\) \(+3.31093 q^{22}\) \(+4.06900 q^{23}\) \(+2.40126 q^{24}\) \(-0.146950 q^{25}\) \(+12.4458 q^{26}\) \(+4.94579 q^{27}\) \(+0.507977 q^{28}\) \(+5.77836 q^{29}\) \(+4.87908 q^{30}\) \(+7.63079 q^{31}\) \(+6.36877 q^{32}\) \(+1.44231 q^{33}\) \(+13.2350 q^{34}\) \(+0.362835 q^{35}\) \(-6.27695 q^{36}\) \(-1.00000 q^{37}\) \(-5.75364 q^{38}\) \(+5.42162 q^{39}\) \(-5.38551 q^{40}\) \(+7.80952 q^{41}\) \(+0.364781 q^{42}\) \(+8.43068 q^{43}\) \(-4.52878 q^{44}\) \(-4.48347 q^{45}\) \(-9.17485 q^{46}\) \(-0.369843 q^{47}\) \(+0.644472 q^{48}\) \(-6.97287 q^{49}\) \(+0.331344 q^{50}\) \(+5.76542 q^{51}\) \(-17.0236 q^{52}\) \(-8.21907 q^{53}\) \(-11.1518 q^{54}\) \(-3.23479 q^{55}\) \(-0.402644 q^{56}\) \(-2.50640 q^{57}\) \(-13.0291 q^{58}\) \(+9.69520 q^{59}\) \(-6.67373 q^{60}\) \(+3.52752 q^{61}\) \(-17.2060 q^{62}\) \(-0.335203 q^{63}\) \(-13.0482 q^{64}\) \(-12.1595 q^{65}\) \(-3.25214 q^{66}\) \(+3.90371 q^{67}\) \(-18.1032 q^{68}\) \(-3.99675 q^{69}\) \(-0.818126 q^{70}\) \(-5.46321 q^{71}\) \(+4.97538 q^{72}\) \(+4.24726 q^{73}\) \(+2.25482 q^{74}\) \(+0.144340 q^{75}\) \(+7.86998 q^{76}\) \(-0.241847 q^{77}\) \(-12.2248 q^{78}\) \(+2.31589 q^{79}\) \(-1.44542 q^{80}\) \(+1.24763 q^{81}\) \(-17.6090 q^{82}\) \(-7.50362 q^{83}\) \(-0.498957 q^{84}\) \(-12.9306 q^{85}\) \(-19.0096 q^{86}\) \(-5.67575 q^{87}\) \(+3.58970 q^{88}\) \(-1.80665 q^{89}\) \(+10.1094 q^{90}\) \(-0.909100 q^{91}\) \(+12.5496 q^{92}\) \(-7.49529 q^{93}\) \(+0.833929 q^{94}\) \(+5.62133 q^{95}\) \(-6.25568 q^{96}\) \(+5.91157 q^{97}\) \(+15.7225 q^{98}\) \(+2.98845 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut -\mathstrut 13q^{10} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut -\mathstrut 40q^{12} \) \(\mathstrut -\mathstrut 18q^{13} \) \(\mathstrut -\mathstrut 42q^{14} \) \(\mathstrut -\mathstrut 49q^{15} \) \(\mathstrut +\mathstrut 83q^{16} \) \(\mathstrut -\mathstrut 62q^{17} \) \(\mathstrut -\mathstrut 33q^{18} \) \(\mathstrut -\mathstrut 25q^{19} \) \(\mathstrut -\mathstrut 39q^{20} \) \(\mathstrut -\mathstrut 15q^{21} \) \(\mathstrut -\mathstrut 31q^{22} \) \(\mathstrut -\mathstrut 94q^{23} \) \(\mathstrut -\mathstrut 39q^{24} \) \(\mathstrut +\mathstrut 71q^{25} \) \(\mathstrut -\mathstrut 35q^{26} \) \(\mathstrut -\mathstrut 47q^{27} \) \(\mathstrut -\mathstrut 13q^{28} \) \(\mathstrut -\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 15q^{30} \) \(\mathstrut -\mathstrut 37q^{31} \) \(\mathstrut -\mathstrut 105q^{32} \) \(\mathstrut -\mathstrut 60q^{33} \) \(\mathstrut +\mathstrut 9q^{34} \) \(\mathstrut -\mathstrut 60q^{35} \) \(\mathstrut +\mathstrut 43q^{36} \) \(\mathstrut -\mathstrut 79q^{37} \) \(\mathstrut -\mathstrut 80q^{38} \) \(\mathstrut -\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 64q^{40} \) \(\mathstrut -\mathstrut 37q^{41} \) \(\mathstrut -\mathstrut 30q^{42} \) \(\mathstrut -\mathstrut 20q^{43} \) \(\mathstrut -\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 8q^{45} \) \(\mathstrut +\mathstrut 61q^{46} \) \(\mathstrut -\mathstrut 148q^{47} \) \(\mathstrut -\mathstrut 39q^{48} \) \(\mathstrut +\mathstrut 82q^{49} \) \(\mathstrut -\mathstrut 90q^{50} \) \(\mathstrut -\mathstrut 45q^{51} \) \(\mathstrut -\mathstrut 27q^{52} \) \(\mathstrut -\mathstrut 70q^{53} \) \(\mathstrut -\mathstrut 41q^{54} \) \(\mathstrut -\mathstrut 105q^{55} \) \(\mathstrut -\mathstrut 68q^{56} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut -\mathstrut 14q^{58} \) \(\mathstrut -\mathstrut 96q^{59} \) \(\mathstrut -\mathstrut 74q^{60} \) \(\mathstrut -\mathstrut 21q^{61} \) \(\mathstrut +\mathstrut 4q^{62} \) \(\mathstrut -\mathstrut 60q^{63} \) \(\mathstrut +\mathstrut 132q^{64} \) \(\mathstrut -\mathstrut 15q^{65} \) \(\mathstrut +\mathstrut 71q^{66} \) \(\mathstrut -\mathstrut 44q^{67} \) \(\mathstrut -\mathstrut 166q^{68} \) \(\mathstrut -\mathstrut 72q^{69} \) \(\mathstrut -\mathstrut 9q^{70} \) \(\mathstrut -\mathstrut 55q^{71} \) \(\mathstrut -\mathstrut 126q^{72} \) \(\mathstrut -\mathstrut 27q^{73} \) \(\mathstrut +\mathstrut 11q^{74} \) \(\mathstrut -\mathstrut 39q^{75} \) \(\mathstrut -\mathstrut 4q^{76} \) \(\mathstrut -\mathstrut 104q^{77} \) \(\mathstrut -\mathstrut 47q^{78} \) \(\mathstrut -\mathstrut 49q^{79} \) \(\mathstrut -\mathstrut 82q^{80} \) \(\mathstrut +\mathstrut 55q^{81} \) \(\mathstrut +\mathstrut 20q^{82} \) \(\mathstrut -\mathstrut 52q^{83} \) \(\mathstrut -\mathstrut 29q^{84} \) \(\mathstrut +\mathstrut 3q^{85} \) \(\mathstrut -\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 113q^{87} \) \(\mathstrut +\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 68q^{89} \) \(\mathstrut -\mathstrut 39q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 179q^{92} \) \(\mathstrut -\mathstrut 53q^{93} \) \(\mathstrut -\mathstrut 33q^{94} \) \(\mathstrut -\mathstrut 86q^{95} \) \(\mathstrut +\mathstrut 33q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut -\mathstrut 116q^{98} \) \(\mathstrut +\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.25482 −1.59440 −0.797198 0.603718i \(-0.793685\pi\)
−0.797198 + 0.603718i \(0.793685\pi\)
\(3\) −0.982243 −0.567098 −0.283549 0.958958i \(-0.591512\pi\)
−0.283549 + 0.958958i \(0.591512\pi\)
\(4\) 3.08420 1.54210
\(5\) 2.20296 0.985195 0.492598 0.870257i \(-0.336047\pi\)
0.492598 + 0.870257i \(0.336047\pi\)
\(6\) 2.21478 0.904179
\(7\) 0.164703 0.0622519 0.0311260 0.999515i \(-0.490091\pi\)
0.0311260 + 0.999515i \(0.490091\pi\)
\(8\) −2.44467 −0.864320
\(9\) −2.03520 −0.678400
\(10\) −4.96728 −1.57079
\(11\) −1.46838 −0.442734 −0.221367 0.975191i \(-0.571052\pi\)
−0.221367 + 0.975191i \(0.571052\pi\)
\(12\) −3.02943 −0.874521
\(13\) −5.51963 −1.53087 −0.765435 0.643513i \(-0.777476\pi\)
−0.765435 + 0.643513i \(0.777476\pi\)
\(14\) −0.371375 −0.0992542
\(15\) −2.16385 −0.558703
\(16\) −0.656123 −0.164031
\(17\) −5.86965 −1.42360 −0.711800 0.702383i \(-0.752120\pi\)
−0.711800 + 0.702383i \(0.752120\pi\)
\(18\) 4.58900 1.08164
\(19\) 2.55171 0.585402 0.292701 0.956204i \(-0.405446\pi\)
0.292701 + 0.956204i \(0.405446\pi\)
\(20\) 6.79437 1.51927
\(21\) −0.161778 −0.0353029
\(22\) 3.31093 0.705893
\(23\) 4.06900 0.848446 0.424223 0.905558i \(-0.360547\pi\)
0.424223 + 0.905558i \(0.360547\pi\)
\(24\) 2.40126 0.490154
\(25\) −0.146950 −0.0293899
\(26\) 12.4458 2.44081
\(27\) 4.94579 0.951817
\(28\) 0.507977 0.0959986
\(29\) 5.77836 1.07301 0.536507 0.843896i \(-0.319743\pi\)
0.536507 + 0.843896i \(0.319743\pi\)
\(30\) 4.87908 0.890793
\(31\) 7.63079 1.37053 0.685265 0.728294i \(-0.259686\pi\)
0.685265 + 0.728294i \(0.259686\pi\)
\(32\) 6.36877 1.12585
\(33\) 1.44231 0.251074
\(34\) 13.2350 2.26978
\(35\) 0.362835 0.0613303
\(36\) −6.27695 −1.04616
\(37\) −1.00000 −0.164399
\(38\) −5.75364 −0.933363
\(39\) 5.42162 0.868154
\(40\) −5.38551 −0.851524
\(41\) 7.80952 1.21964 0.609821 0.792539i \(-0.291241\pi\)
0.609821 + 0.792539i \(0.291241\pi\)
\(42\) 0.364781 0.0562869
\(43\) 8.43068 1.28567 0.642833 0.766006i \(-0.277759\pi\)
0.642833 + 0.766006i \(0.277759\pi\)
\(44\) −4.52878 −0.682739
\(45\) −4.48347 −0.668356
\(46\) −9.17485 −1.35276
\(47\) −0.369843 −0.0539472 −0.0269736 0.999636i \(-0.508587\pi\)
−0.0269736 + 0.999636i \(0.508587\pi\)
\(48\) 0.644472 0.0930216
\(49\) −6.97287 −0.996125
\(50\) 0.331344 0.0468592
\(51\) 5.76542 0.807321
\(52\) −17.0236 −2.36075
\(53\) −8.21907 −1.12898 −0.564488 0.825441i \(-0.690926\pi\)
−0.564488 + 0.825441i \(0.690926\pi\)
\(54\) −11.1518 −1.51757
\(55\) −3.23479 −0.436180
\(56\) −0.402644 −0.0538055
\(57\) −2.50640 −0.331981
\(58\) −13.0291 −1.71081
\(59\) 9.69520 1.26221 0.631104 0.775698i \(-0.282602\pi\)
0.631104 + 0.775698i \(0.282602\pi\)
\(60\) −6.67373 −0.861574
\(61\) 3.52752 0.451653 0.225826 0.974168i \(-0.427492\pi\)
0.225826 + 0.974168i \(0.427492\pi\)
\(62\) −17.2060 −2.18517
\(63\) −0.335203 −0.0422317
\(64\) −13.0482 −1.63102
\(65\) −12.1595 −1.50821
\(66\) −3.25214 −0.400311
\(67\) 3.90371 0.476914 0.238457 0.971153i \(-0.423358\pi\)
0.238457 + 0.971153i \(0.423358\pi\)
\(68\) −18.1032 −2.19533
\(69\) −3.99675 −0.481152
\(70\) −0.818126 −0.0977848
\(71\) −5.46321 −0.648364 −0.324182 0.945995i \(-0.605089\pi\)
−0.324182 + 0.945995i \(0.605089\pi\)
\(72\) 4.97538 0.586354
\(73\) 4.24726 0.497104 0.248552 0.968618i \(-0.420045\pi\)
0.248552 + 0.968618i \(0.420045\pi\)
\(74\) 2.25482 0.262117
\(75\) 0.144340 0.0166670
\(76\) 7.86998 0.902748
\(77\) −0.241847 −0.0275610
\(78\) −12.2248 −1.38418
\(79\) 2.31589 0.260558 0.130279 0.991477i \(-0.458413\pi\)
0.130279 + 0.991477i \(0.458413\pi\)
\(80\) −1.44542 −0.161602
\(81\) 1.24763 0.138626
\(82\) −17.6090 −1.94459
\(83\) −7.50362 −0.823629 −0.411814 0.911268i \(-0.635105\pi\)
−0.411814 + 0.911268i \(0.635105\pi\)
\(84\) −0.498957 −0.0544406
\(85\) −12.9306 −1.40252
\(86\) −19.0096 −2.04986
\(87\) −5.67575 −0.608504
\(88\) 3.58970 0.382664
\(89\) −1.80665 −0.191504 −0.0957522 0.995405i \(-0.530526\pi\)
−0.0957522 + 0.995405i \(0.530526\pi\)
\(90\) 10.1094 1.06562
\(91\) −0.909100 −0.0952996
\(92\) 12.5496 1.30839
\(93\) −7.49529 −0.777225
\(94\) 0.833929 0.0860132
\(95\) 5.62133 0.576736
\(96\) −6.25568 −0.638467
\(97\) 5.91157 0.600229 0.300114 0.953903i \(-0.402975\pi\)
0.300114 + 0.953903i \(0.402975\pi\)
\(98\) 15.7225 1.58822
\(99\) 2.98845 0.300351
\(100\) −0.453221 −0.0453221
\(101\) −2.83089 −0.281684 −0.140842 0.990032i \(-0.544981\pi\)
−0.140842 + 0.990032i \(0.544981\pi\)
\(102\) −13.0000 −1.28719
\(103\) −8.84765 −0.871785 −0.435893 0.899999i \(-0.643567\pi\)
−0.435893 + 0.899999i \(0.643567\pi\)
\(104\) 13.4936 1.32316
\(105\) −0.356392 −0.0347803
\(106\) 18.5325 1.80004
\(107\) −8.73896 −0.844827 −0.422413 0.906403i \(-0.638817\pi\)
−0.422413 + 0.906403i \(0.638817\pi\)
\(108\) 15.2538 1.46780
\(109\) −1.00000 −0.0957826
\(110\) 7.29387 0.695443
\(111\) 0.982243 0.0932304
\(112\) −0.108065 −0.0102112
\(113\) 1.52099 0.143083 0.0715413 0.997438i \(-0.477208\pi\)
0.0715413 + 0.997438i \(0.477208\pi\)
\(114\) 5.65147 0.529309
\(115\) 8.96387 0.835885
\(116\) 17.8216 1.65469
\(117\) 11.2335 1.03854
\(118\) −21.8609 −2.01246
\(119\) −0.966749 −0.0886218
\(120\) 5.28988 0.482898
\(121\) −8.84385 −0.803987
\(122\) −7.95391 −0.720113
\(123\) −7.67085 −0.691657
\(124\) 23.5349 2.11349
\(125\) −11.3385 −1.01415
\(126\) 0.755822 0.0673340
\(127\) −5.06517 −0.449461 −0.224731 0.974421i \(-0.572150\pi\)
−0.224731 + 0.974421i \(0.572150\pi\)
\(128\) 16.6837 1.47464
\(129\) −8.28098 −0.729099
\(130\) 27.4175 2.40468
\(131\) 9.21320 0.804961 0.402480 0.915429i \(-0.368148\pi\)
0.402480 + 0.915429i \(0.368148\pi\)
\(132\) 4.44836 0.387180
\(133\) 0.420274 0.0364424
\(134\) −8.80215 −0.760390
\(135\) 10.8954 0.937726
\(136\) 14.3493 1.23044
\(137\) 12.2131 1.04343 0.521716 0.853119i \(-0.325292\pi\)
0.521716 + 0.853119i \(0.325292\pi\)
\(138\) 9.01193 0.767147
\(139\) −5.06124 −0.429289 −0.214644 0.976692i \(-0.568859\pi\)
−0.214644 + 0.976692i \(0.568859\pi\)
\(140\) 1.11905 0.0945774
\(141\) 0.363276 0.0305934
\(142\) 12.3185 1.03375
\(143\) 8.10493 0.677768
\(144\) 1.33534 0.111278
\(145\) 12.7295 1.05713
\(146\) −9.57680 −0.792581
\(147\) 6.84906 0.564901
\(148\) −3.08420 −0.253519
\(149\) −21.9792 −1.80061 −0.900305 0.435261i \(-0.856656\pi\)
−0.900305 + 0.435261i \(0.856656\pi\)
\(150\) −0.325461 −0.0265737
\(151\) −6.96943 −0.567165 −0.283582 0.958948i \(-0.591523\pi\)
−0.283582 + 0.958948i \(0.591523\pi\)
\(152\) −6.23808 −0.505975
\(153\) 11.9459 0.965769
\(154\) 0.545321 0.0439432
\(155\) 16.8104 1.35024
\(156\) 16.7213 1.33878
\(157\) −5.70152 −0.455031 −0.227516 0.973774i \(-0.573060\pi\)
−0.227516 + 0.973774i \(0.573060\pi\)
\(158\) −5.22191 −0.415433
\(159\) 8.07313 0.640241
\(160\) 14.0302 1.10918
\(161\) 0.670177 0.0528174
\(162\) −2.81318 −0.221024
\(163\) −21.1576 −1.65719 −0.828597 0.559845i \(-0.810861\pi\)
−0.828597 + 0.559845i \(0.810861\pi\)
\(164\) 24.0861 1.88081
\(165\) 3.17735 0.247357
\(166\) 16.9193 1.31319
\(167\) −21.1413 −1.63596 −0.817980 0.575247i \(-0.804906\pi\)
−0.817980 + 0.575247i \(0.804906\pi\)
\(168\) 0.395494 0.0305130
\(169\) 17.4663 1.34356
\(170\) 29.1562 2.23618
\(171\) −5.19324 −0.397137
\(172\) 26.0019 1.98262
\(173\) −1.56608 −0.119067 −0.0595334 0.998226i \(-0.518961\pi\)
−0.0595334 + 0.998226i \(0.518961\pi\)
\(174\) 12.7978 0.970197
\(175\) −0.0242030 −0.00182958
\(176\) 0.963440 0.0726220
\(177\) −9.52304 −0.715796
\(178\) 4.07366 0.305334
\(179\) −9.43139 −0.704935 −0.352468 0.935824i \(-0.614657\pi\)
−0.352468 + 0.935824i \(0.614657\pi\)
\(180\) −13.8279 −1.03067
\(181\) −15.9628 −1.18651 −0.593254 0.805015i \(-0.702157\pi\)
−0.593254 + 0.805015i \(0.702157\pi\)
\(182\) 2.04985 0.151945
\(183\) −3.46488 −0.256131
\(184\) −9.94735 −0.733328
\(185\) −2.20296 −0.161965
\(186\) 16.9005 1.23920
\(187\) 8.61889 0.630276
\(188\) −1.14067 −0.0831919
\(189\) 0.814587 0.0592525
\(190\) −12.6751 −0.919545
\(191\) −19.1227 −1.38367 −0.691835 0.722056i \(-0.743197\pi\)
−0.691835 + 0.722056i \(0.743197\pi\)
\(192\) 12.8165 0.924948
\(193\) −11.9264 −0.858484 −0.429242 0.903190i \(-0.641219\pi\)
−0.429242 + 0.903190i \(0.641219\pi\)
\(194\) −13.3295 −0.957002
\(195\) 11.9436 0.855301
\(196\) −21.5057 −1.53612
\(197\) −5.73361 −0.408502 −0.204251 0.978919i \(-0.565476\pi\)
−0.204251 + 0.978919i \(0.565476\pi\)
\(198\) −6.73841 −0.478878
\(199\) 14.4102 1.02151 0.510755 0.859727i \(-0.329366\pi\)
0.510755 + 0.859727i \(0.329366\pi\)
\(200\) 0.359242 0.0254023
\(201\) −3.83439 −0.270457
\(202\) 6.38313 0.449115
\(203\) 0.951713 0.0667972
\(204\) 17.7817 1.24497
\(205\) 17.2041 1.20159
\(206\) 19.9498 1.38997
\(207\) −8.28123 −0.575585
\(208\) 3.62156 0.251110
\(209\) −3.74689 −0.259178
\(210\) 0.803599 0.0554536
\(211\) 23.7280 1.63351 0.816753 0.576987i \(-0.195772\pi\)
0.816753 + 0.576987i \(0.195772\pi\)
\(212\) −25.3492 −1.74099
\(213\) 5.36620 0.367686
\(214\) 19.7047 1.34699
\(215\) 18.5725 1.26663
\(216\) −12.0908 −0.822674
\(217\) 1.25681 0.0853181
\(218\) 2.25482 0.152715
\(219\) −4.17184 −0.281907
\(220\) −9.97674 −0.672632
\(221\) 32.3983 2.17934
\(222\) −2.21478 −0.148646
\(223\) −3.79616 −0.254210 −0.127105 0.991889i \(-0.540568\pi\)
−0.127105 + 0.991889i \(0.540568\pi\)
\(224\) 1.04896 0.0700863
\(225\) 0.299072 0.0199381
\(226\) −3.42955 −0.228130
\(227\) −12.8835 −0.855106 −0.427553 0.903990i \(-0.640624\pi\)
−0.427553 + 0.903990i \(0.640624\pi\)
\(228\) −7.73023 −0.511947
\(229\) 2.83708 0.187480 0.0937398 0.995597i \(-0.470118\pi\)
0.0937398 + 0.995597i \(0.470118\pi\)
\(230\) −20.2119 −1.33273
\(231\) 0.237553 0.0156298
\(232\) −14.1262 −0.927427
\(233\) 1.37489 0.0900719 0.0450359 0.998985i \(-0.485660\pi\)
0.0450359 + 0.998985i \(0.485660\pi\)
\(234\) −25.3296 −1.65585
\(235\) −0.814752 −0.0531485
\(236\) 29.9019 1.94645
\(237\) −2.27477 −0.147762
\(238\) 2.17984 0.141298
\(239\) −18.8303 −1.21803 −0.609017 0.793157i \(-0.708436\pi\)
−0.609017 + 0.793157i \(0.708436\pi\)
\(240\) 1.41975 0.0916444
\(241\) 13.2071 0.850743 0.425372 0.905019i \(-0.360143\pi\)
0.425372 + 0.905019i \(0.360143\pi\)
\(242\) 19.9413 1.28187
\(243\) −16.0628 −1.03043
\(244\) 10.8796 0.696493
\(245\) −15.3610 −0.981378
\(246\) 17.2964 1.10278
\(247\) −14.0845 −0.896175
\(248\) −18.6547 −1.18458
\(249\) 7.37037 0.467078
\(250\) 25.5663 1.61696
\(251\) −24.4842 −1.54543 −0.772715 0.634753i \(-0.781102\pi\)
−0.772715 + 0.634753i \(0.781102\pi\)
\(252\) −1.03383 −0.0651254
\(253\) −5.97485 −0.375636
\(254\) 11.4210 0.716619
\(255\) 12.7010 0.795369
\(256\) −11.5223 −0.720142
\(257\) 7.50671 0.468256 0.234128 0.972206i \(-0.424777\pi\)
0.234128 + 0.972206i \(0.424777\pi\)
\(258\) 18.6721 1.16247
\(259\) −0.164703 −0.0102342
\(260\) −37.5024 −2.32580
\(261\) −11.7601 −0.727932
\(262\) −20.7741 −1.28343
\(263\) −12.2348 −0.754427 −0.377214 0.926126i \(-0.623118\pi\)
−0.377214 + 0.926126i \(0.623118\pi\)
\(264\) −3.52596 −0.217008
\(265\) −18.1063 −1.11226
\(266\) −0.947642 −0.0581036
\(267\) 1.77457 0.108602
\(268\) 12.0398 0.735448
\(269\) 23.1546 1.41176 0.705881 0.708330i \(-0.250551\pi\)
0.705881 + 0.708330i \(0.250551\pi\)
\(270\) −24.5671 −1.49511
\(271\) 8.65013 0.525458 0.262729 0.964870i \(-0.415377\pi\)
0.262729 + 0.964870i \(0.415377\pi\)
\(272\) 3.85121 0.233514
\(273\) 0.892957 0.0540442
\(274\) −27.5382 −1.66364
\(275\) 0.215778 0.0130119
\(276\) −12.3268 −0.741984
\(277\) 21.0793 1.26653 0.633266 0.773934i \(-0.281714\pi\)
0.633266 + 0.773934i \(0.281714\pi\)
\(278\) 11.4122 0.684456
\(279\) −15.5302 −0.929767
\(280\) −0.887010 −0.0530090
\(281\) −30.6679 −1.82949 −0.914747 0.404027i \(-0.867610\pi\)
−0.914747 + 0.404027i \(0.867610\pi\)
\(282\) −0.819121 −0.0487779
\(283\) 0.587072 0.0348978 0.0174489 0.999848i \(-0.494446\pi\)
0.0174489 + 0.999848i \(0.494446\pi\)
\(284\) −16.8496 −0.999840
\(285\) −5.52151 −0.327066
\(286\) −18.2751 −1.08063
\(287\) 1.28625 0.0759251
\(288\) −12.9617 −0.763776
\(289\) 17.4528 1.02663
\(290\) −28.7027 −1.68548
\(291\) −5.80659 −0.340389
\(292\) 13.0994 0.766584
\(293\) −12.7241 −0.743353 −0.371676 0.928362i \(-0.621217\pi\)
−0.371676 + 0.928362i \(0.621217\pi\)
\(294\) −15.4434 −0.900675
\(295\) 21.3582 1.24352
\(296\) 2.44467 0.142093
\(297\) −7.26231 −0.421402
\(298\) 49.5591 2.87088
\(299\) −22.4594 −1.29886
\(300\) 0.445173 0.0257021
\(301\) 1.38856 0.0800352
\(302\) 15.7148 0.904285
\(303\) 2.78062 0.159742
\(304\) −1.67424 −0.0960240
\(305\) 7.77100 0.444966
\(306\) −26.9358 −1.53982
\(307\) −5.09662 −0.290880 −0.145440 0.989367i \(-0.546460\pi\)
−0.145440 + 0.989367i \(0.546460\pi\)
\(308\) −0.745904 −0.0425018
\(309\) 8.69054 0.494388
\(310\) −37.9043 −2.15282
\(311\) 13.7564 0.780053 0.390026 0.920804i \(-0.372466\pi\)
0.390026 + 0.920804i \(0.372466\pi\)
\(312\) −13.2540 −0.750362
\(313\) 3.00027 0.169585 0.0847927 0.996399i \(-0.472977\pi\)
0.0847927 + 0.996399i \(0.472977\pi\)
\(314\) 12.8559 0.725500
\(315\) −0.738441 −0.0416064
\(316\) 7.14267 0.401807
\(317\) −31.0840 −1.74585 −0.872925 0.487854i \(-0.837780\pi\)
−0.872925 + 0.487854i \(0.837780\pi\)
\(318\) −18.2034 −1.02080
\(319\) −8.48484 −0.475060
\(320\) −28.7446 −1.60687
\(321\) 8.58378 0.479100
\(322\) −1.51113 −0.0842118
\(323\) −14.9776 −0.833378
\(324\) 3.84794 0.213774
\(325\) 0.811107 0.0449921
\(326\) 47.7066 2.64222
\(327\) 0.982243 0.0543182
\(328\) −19.0917 −1.05416
\(329\) −0.0609143 −0.00335832
\(330\) −7.16435 −0.394384
\(331\) 5.25452 0.288815 0.144407 0.989518i \(-0.453872\pi\)
0.144407 + 0.989518i \(0.453872\pi\)
\(332\) −23.1426 −1.27012
\(333\) 2.03520 0.111528
\(334\) 47.6697 2.60837
\(335\) 8.59973 0.469853
\(336\) 0.106147 0.00579077
\(337\) −3.28474 −0.178931 −0.0894656 0.995990i \(-0.528516\pi\)
−0.0894656 + 0.995990i \(0.528516\pi\)
\(338\) −39.3833 −2.14217
\(339\) −1.49398 −0.0811419
\(340\) −39.8806 −2.16283
\(341\) −11.2049 −0.606780
\(342\) 11.7098 0.633193
\(343\) −2.30138 −0.124263
\(344\) −20.6102 −1.11123
\(345\) −8.80469 −0.474029
\(346\) 3.53122 0.189840
\(347\) 14.0046 0.751808 0.375904 0.926659i \(-0.377332\pi\)
0.375904 + 0.926659i \(0.377332\pi\)
\(348\) −17.5051 −0.938374
\(349\) 20.4532 1.09483 0.547417 0.836860i \(-0.315611\pi\)
0.547417 + 0.836860i \(0.315611\pi\)
\(350\) 0.0545734 0.00291707
\(351\) −27.2989 −1.45711
\(352\) −9.35179 −0.498452
\(353\) −19.7082 −1.04896 −0.524481 0.851422i \(-0.675741\pi\)
−0.524481 + 0.851422i \(0.675741\pi\)
\(354\) 21.4727 1.14126
\(355\) −12.0353 −0.638765
\(356\) −5.57206 −0.295319
\(357\) 0.949583 0.0502572
\(358\) 21.2661 1.12395
\(359\) −1.72725 −0.0911609 −0.0455805 0.998961i \(-0.514514\pi\)
−0.0455805 + 0.998961i \(0.514514\pi\)
\(360\) 10.9606 0.577673
\(361\) −12.4888 −0.657304
\(362\) 35.9933 1.89176
\(363\) 8.68681 0.455939
\(364\) −2.80384 −0.146961
\(365\) 9.35657 0.489745
\(366\) 7.81267 0.408375
\(367\) −31.6988 −1.65466 −0.827332 0.561713i \(-0.810142\pi\)
−0.827332 + 0.561713i \(0.810142\pi\)
\(368\) −2.66977 −0.139171
\(369\) −15.8939 −0.827405
\(370\) 4.96728 0.258237
\(371\) −1.35371 −0.0702809
\(372\) −23.1170 −1.19856
\(373\) 11.8488 0.613509 0.306754 0.951789i \(-0.400757\pi\)
0.306754 + 0.951789i \(0.400757\pi\)
\(374\) −19.4340 −1.00491
\(375\) 11.1372 0.575123
\(376\) 0.904143 0.0466276
\(377\) −31.8944 −1.64265
\(378\) −1.83674 −0.0944719
\(379\) −10.1128 −0.519459 −0.259729 0.965681i \(-0.583633\pi\)
−0.259729 + 0.965681i \(0.583633\pi\)
\(380\) 17.3373 0.889383
\(381\) 4.97523 0.254889
\(382\) 43.1181 2.20612
\(383\) −21.9162 −1.11987 −0.559933 0.828538i \(-0.689173\pi\)
−0.559933 + 0.828538i \(0.689173\pi\)
\(384\) −16.3874 −0.836266
\(385\) −0.532780 −0.0271530
\(386\) 26.8919 1.36876
\(387\) −17.1581 −0.872196
\(388\) 18.2324 0.925612
\(389\) −28.8889 −1.46472 −0.732362 0.680915i \(-0.761582\pi\)
−0.732362 + 0.680915i \(0.761582\pi\)
\(390\) −26.9307 −1.36369
\(391\) −23.8836 −1.20785
\(392\) 17.0463 0.860970
\(393\) −9.04960 −0.456492
\(394\) 12.9282 0.651315
\(395\) 5.10183 0.256701
\(396\) 9.21697 0.463170
\(397\) 4.43968 0.222821 0.111411 0.993774i \(-0.464463\pi\)
0.111411 + 0.993774i \(0.464463\pi\)
\(398\) −32.4923 −1.62869
\(399\) −0.412812 −0.0206664
\(400\) 0.0964170 0.00482085
\(401\) 17.2839 0.863119 0.431559 0.902085i \(-0.357964\pi\)
0.431559 + 0.902085i \(0.357964\pi\)
\(402\) 8.64585 0.431216
\(403\) −42.1191 −2.09810
\(404\) −8.73101 −0.434384
\(405\) 2.74848 0.136573
\(406\) −2.14594 −0.106501
\(407\) 1.46838 0.0727850
\(408\) −14.0945 −0.697783
\(409\) 24.8549 1.22900 0.614498 0.788918i \(-0.289359\pi\)
0.614498 + 0.788918i \(0.289359\pi\)
\(410\) −38.7921 −1.91580
\(411\) −11.9962 −0.591729
\(412\) −27.2879 −1.34438
\(413\) 1.59683 0.0785748
\(414\) 18.6726 0.917711
\(415\) −16.5302 −0.811435
\(416\) −35.1532 −1.72353
\(417\) 4.97136 0.243449
\(418\) 8.44854 0.413232
\(419\) −9.44275 −0.461309 −0.230654 0.973036i \(-0.574087\pi\)
−0.230654 + 0.973036i \(0.574087\pi\)
\(420\) −1.09918 −0.0536347
\(421\) 1.50629 0.0734120 0.0367060 0.999326i \(-0.488313\pi\)
0.0367060 + 0.999326i \(0.488313\pi\)
\(422\) −53.5024 −2.60446
\(423\) 0.752705 0.0365978
\(424\) 20.0929 0.975796
\(425\) 0.862542 0.0418394
\(426\) −12.0998 −0.586237
\(427\) 0.580994 0.0281162
\(428\) −26.9527 −1.30281
\(429\) −7.96101 −0.384361
\(430\) −41.8775 −2.01951
\(431\) −13.2053 −0.636075 −0.318038 0.948078i \(-0.603024\pi\)
−0.318038 + 0.948078i \(0.603024\pi\)
\(432\) −3.24505 −0.156127
\(433\) 18.0813 0.868932 0.434466 0.900688i \(-0.356937\pi\)
0.434466 + 0.900688i \(0.356937\pi\)
\(434\) −2.83389 −0.136031
\(435\) −12.5035 −0.599496
\(436\) −3.08420 −0.147706
\(437\) 10.3829 0.496682
\(438\) 9.40674 0.449472
\(439\) −14.2156 −0.678472 −0.339236 0.940701i \(-0.610168\pi\)
−0.339236 + 0.940701i \(0.610168\pi\)
\(440\) 7.90799 0.376999
\(441\) 14.1912 0.675771
\(442\) −73.0522 −3.47474
\(443\) −10.6497 −0.505984 −0.252992 0.967468i \(-0.581415\pi\)
−0.252992 + 0.967468i \(0.581415\pi\)
\(444\) 3.02943 0.143770
\(445\) −3.97998 −0.188669
\(446\) 8.55965 0.405311
\(447\) 21.5889 1.02112
\(448\) −2.14907 −0.101534
\(449\) 13.6692 0.645089 0.322544 0.946554i \(-0.395462\pi\)
0.322544 + 0.946554i \(0.395462\pi\)
\(450\) −0.674351 −0.0317892
\(451\) −11.4674 −0.539977
\(452\) 4.69103 0.220647
\(453\) 6.84568 0.321638
\(454\) 29.0499 1.36338
\(455\) −2.00271 −0.0938887
\(456\) 6.12731 0.286937
\(457\) −0.00708470 −0.000331408 0 −0.000165704 1.00000i \(-0.500053\pi\)
−0.000165704 1.00000i \(0.500053\pi\)
\(458\) −6.39710 −0.298917
\(459\) −29.0300 −1.35501
\(460\) 27.6463 1.28902
\(461\) 9.63524 0.448758 0.224379 0.974502i \(-0.427965\pi\)
0.224379 + 0.974502i \(0.427965\pi\)
\(462\) −0.535638 −0.0249201
\(463\) 24.1464 1.12218 0.561089 0.827755i \(-0.310382\pi\)
0.561089 + 0.827755i \(0.310382\pi\)
\(464\) −3.79131 −0.176007
\(465\) −16.5119 −0.765719
\(466\) −3.10012 −0.143610
\(467\) 26.2685 1.21556 0.607780 0.794105i \(-0.292060\pi\)
0.607780 + 0.794105i \(0.292060\pi\)
\(468\) 34.6465 1.60153
\(469\) 0.642953 0.0296888
\(470\) 1.83712 0.0847398
\(471\) 5.60028 0.258047
\(472\) −23.7015 −1.09095
\(473\) −12.3795 −0.569208
\(474\) 5.12919 0.235591
\(475\) −0.374973 −0.0172049
\(476\) −2.98165 −0.136663
\(477\) 16.7274 0.765897
\(478\) 42.4590 1.94203
\(479\) 36.0550 1.64739 0.823697 0.567030i \(-0.191908\pi\)
0.823697 + 0.567030i \(0.191908\pi\)
\(480\) −13.7810 −0.629015
\(481\) 5.51963 0.251673
\(482\) −29.7796 −1.35642
\(483\) −0.658277 −0.0299526
\(484\) −27.2762 −1.23983
\(485\) 13.0230 0.591342
\(486\) 36.2188 1.64292
\(487\) 39.5869 1.79385 0.896926 0.442180i \(-0.145795\pi\)
0.896926 + 0.442180i \(0.145795\pi\)
\(488\) −8.62361 −0.390372
\(489\) 20.7819 0.939792
\(490\) 34.6362 1.56470
\(491\) −0.832067 −0.0375507 −0.0187753 0.999824i \(-0.505977\pi\)
−0.0187753 + 0.999824i \(0.505977\pi\)
\(492\) −23.6584 −1.06660
\(493\) −33.9169 −1.52754
\(494\) 31.7579 1.42886
\(495\) 6.58345 0.295904
\(496\) −5.00674 −0.224809
\(497\) −0.899807 −0.0403619
\(498\) −16.6188 −0.744708
\(499\) −16.5920 −0.742759 −0.371380 0.928481i \(-0.621115\pi\)
−0.371380 + 0.928481i \(0.621115\pi\)
\(500\) −34.9703 −1.56392
\(501\) 20.7659 0.927750
\(502\) 55.2074 2.46403
\(503\) 21.0814 0.939973 0.469986 0.882674i \(-0.344259\pi\)
0.469986 + 0.882674i \(0.344259\pi\)
\(504\) 0.819460 0.0365017
\(505\) −6.23634 −0.277513
\(506\) 13.4722 0.598912
\(507\) −17.1562 −0.761932
\(508\) −15.6220 −0.693114
\(509\) −16.3778 −0.725935 −0.362967 0.931802i \(-0.618236\pi\)
−0.362967 + 0.931802i \(0.618236\pi\)
\(510\) −28.6385 −1.26813
\(511\) 0.699537 0.0309457
\(512\) −7.38670 −0.326449
\(513\) 12.6202 0.557196
\(514\) −16.9263 −0.746585
\(515\) −19.4911 −0.858879
\(516\) −25.5402 −1.12434
\(517\) 0.543072 0.0238843
\(518\) 0.371375 0.0163173
\(519\) 1.53827 0.0675226
\(520\) 29.7260 1.30357
\(521\) −18.6781 −0.818301 −0.409150 0.912467i \(-0.634175\pi\)
−0.409150 + 0.912467i \(0.634175\pi\)
\(522\) 26.5169 1.16061
\(523\) −24.3894 −1.06647 −0.533236 0.845966i \(-0.679024\pi\)
−0.533236 + 0.845966i \(0.679024\pi\)
\(524\) 28.4153 1.24133
\(525\) 0.0237733 0.00103755
\(526\) 27.5871 1.20286
\(527\) −44.7901 −1.95109
\(528\) −0.946332 −0.0411838
\(529\) −6.44322 −0.280140
\(530\) 40.8264 1.77339
\(531\) −19.7317 −0.856281
\(532\) 1.29621 0.0561978
\(533\) −43.1057 −1.86711
\(534\) −4.00133 −0.173154
\(535\) −19.2516 −0.832320
\(536\) −9.54326 −0.412206
\(537\) 9.26392 0.399768
\(538\) −52.2094 −2.25091
\(539\) 10.2388 0.441018
\(540\) 33.6035 1.44607
\(541\) −26.5119 −1.13984 −0.569919 0.821701i \(-0.693025\pi\)
−0.569919 + 0.821701i \(0.693025\pi\)
\(542\) −19.5045 −0.837788
\(543\) 15.6794 0.672867
\(544\) −37.3824 −1.60276
\(545\) −2.20296 −0.0943646
\(546\) −2.01345 −0.0861679
\(547\) −10.2219 −0.437058 −0.218529 0.975830i \(-0.570126\pi\)
−0.218529 + 0.975830i \(0.570126\pi\)
\(548\) 37.6675 1.60908
\(549\) −7.17921 −0.306401
\(550\) −0.486540 −0.0207461
\(551\) 14.7447 0.628145
\(552\) 9.77071 0.415869
\(553\) 0.381435 0.0162203
\(554\) −47.5299 −2.01935
\(555\) 2.16385 0.0918501
\(556\) −15.6099 −0.662005
\(557\) −7.30882 −0.309684 −0.154842 0.987939i \(-0.549487\pi\)
−0.154842 + 0.987939i \(0.549487\pi\)
\(558\) 35.0177 1.48242
\(559\) −46.5342 −1.96819
\(560\) −0.238064 −0.0100601
\(561\) −8.46584 −0.357428
\(562\) 69.1505 2.91694
\(563\) 3.67009 0.154676 0.0773378 0.997005i \(-0.475358\pi\)
0.0773378 + 0.997005i \(0.475358\pi\)
\(564\) 1.12041 0.0471780
\(565\) 3.35068 0.140964
\(566\) −1.32374 −0.0556409
\(567\) 0.205489 0.00862971
\(568\) 13.3557 0.560393
\(569\) 37.1544 1.55759 0.778797 0.627276i \(-0.215830\pi\)
0.778797 + 0.627276i \(0.215830\pi\)
\(570\) 12.4500 0.521472
\(571\) −11.8237 −0.494805 −0.247402 0.968913i \(-0.579577\pi\)
−0.247402 + 0.968913i \(0.579577\pi\)
\(572\) 24.9972 1.04519
\(573\) 18.7831 0.784676
\(574\) −2.90026 −0.121055
\(575\) −0.597938 −0.0249357
\(576\) 26.5556 1.10648
\(577\) −23.5618 −0.980889 −0.490444 0.871472i \(-0.663166\pi\)
−0.490444 + 0.871472i \(0.663166\pi\)
\(578\) −39.3528 −1.63686
\(579\) 11.7147 0.486845
\(580\) 39.2603 1.63020
\(581\) −1.23587 −0.0512725
\(582\) 13.0928 0.542714
\(583\) 12.0687 0.499836
\(584\) −10.3831 −0.429657
\(585\) 24.7471 1.02317
\(586\) 28.6906 1.18520
\(587\) 6.98323 0.288229 0.144114 0.989561i \(-0.453967\pi\)
0.144114 + 0.989561i \(0.453967\pi\)
\(588\) 21.1238 0.871132
\(589\) 19.4716 0.802312
\(590\) −48.1588 −1.98266
\(591\) 5.63179 0.231661
\(592\) 0.656123 0.0269665
\(593\) −13.3384 −0.547741 −0.273871 0.961767i \(-0.588304\pi\)
−0.273871 + 0.961767i \(0.588304\pi\)
\(594\) 16.3752 0.671882
\(595\) −2.12971 −0.0873098
\(596\) −67.7883 −2.77672
\(597\) −14.1543 −0.579296
\(598\) 50.6418 2.07090
\(599\) 2.33637 0.0954615 0.0477308 0.998860i \(-0.484801\pi\)
0.0477308 + 0.998860i \(0.484801\pi\)
\(600\) −0.352863 −0.0144056
\(601\) 26.4783 1.08007 0.540037 0.841641i \(-0.318410\pi\)
0.540037 + 0.841641i \(0.318410\pi\)
\(602\) −3.13095 −0.127608
\(603\) −7.94482 −0.323538
\(604\) −21.4951 −0.874624
\(605\) −19.4827 −0.792084
\(606\) −6.26978 −0.254692
\(607\) 9.19531 0.373226 0.186613 0.982434i \(-0.440249\pi\)
0.186613 + 0.982434i \(0.440249\pi\)
\(608\) 16.2512 0.659075
\(609\) −0.934814 −0.0378806
\(610\) −17.5222 −0.709452
\(611\) 2.04140 0.0825861
\(612\) 36.8435 1.48931
\(613\) −11.1909 −0.451998 −0.225999 0.974128i \(-0.572565\pi\)
−0.225999 + 0.974128i \(0.572565\pi\)
\(614\) 11.4920 0.463777
\(615\) −16.8986 −0.681417
\(616\) 0.591235 0.0238215
\(617\) −25.6710 −1.03348 −0.516739 0.856143i \(-0.672854\pi\)
−0.516739 + 0.856143i \(0.672854\pi\)
\(618\) −19.5956 −0.788250
\(619\) 0.103921 0.00417695 0.00208847 0.999998i \(-0.499335\pi\)
0.00208847 + 0.999998i \(0.499335\pi\)
\(620\) 51.8464 2.08220
\(621\) 20.1244 0.807565
\(622\) −31.0181 −1.24371
\(623\) −0.297561 −0.0119215
\(624\) −3.55725 −0.142404
\(625\) −24.2437 −0.969746
\(626\) −6.76506 −0.270386
\(627\) 3.68035 0.146979
\(628\) −17.5846 −0.701703
\(629\) 5.86965 0.234038
\(630\) 1.66505 0.0663372
\(631\) 31.5390 1.25555 0.627774 0.778395i \(-0.283966\pi\)
0.627774 + 0.778395i \(0.283966\pi\)
\(632\) −5.66158 −0.225206
\(633\) −23.3067 −0.926358
\(634\) 70.0887 2.78358
\(635\) −11.1584 −0.442807
\(636\) 24.8991 0.987314
\(637\) 38.4877 1.52494
\(638\) 19.1318 0.757434
\(639\) 11.1187 0.439850
\(640\) 36.7535 1.45281
\(641\) −18.2427 −0.720545 −0.360272 0.932847i \(-0.617316\pi\)
−0.360272 + 0.932847i \(0.617316\pi\)
\(642\) −19.3548 −0.763875
\(643\) −10.6664 −0.420641 −0.210321 0.977632i \(-0.567451\pi\)
−0.210321 + 0.977632i \(0.567451\pi\)
\(644\) 2.06696 0.0814496
\(645\) −18.2427 −0.718305
\(646\) 33.7718 1.32874
\(647\) −16.0421 −0.630680 −0.315340 0.948979i \(-0.602119\pi\)
−0.315340 + 0.948979i \(0.602119\pi\)
\(648\) −3.05004 −0.119817
\(649\) −14.2363 −0.558822
\(650\) −1.82890 −0.0717353
\(651\) −1.23450 −0.0483838
\(652\) −65.2543 −2.55556
\(653\) −8.69012 −0.340071 −0.170035 0.985438i \(-0.554388\pi\)
−0.170035 + 0.985438i \(0.554388\pi\)
\(654\) −2.21478 −0.0866047
\(655\) 20.2963 0.793044
\(656\) −5.12401 −0.200059
\(657\) −8.64402 −0.337235
\(658\) 0.137351 0.00535449
\(659\) 12.6363 0.492241 0.246121 0.969239i \(-0.420844\pi\)
0.246121 + 0.969239i \(0.420844\pi\)
\(660\) 9.79958 0.381448
\(661\) 7.58047 0.294846 0.147423 0.989074i \(-0.452902\pi\)
0.147423 + 0.989074i \(0.452902\pi\)
\(662\) −11.8480 −0.460485
\(663\) −31.8230 −1.23590
\(664\) 18.3438 0.711879
\(665\) 0.925849 0.0359029
\(666\) −4.58900 −0.177820
\(667\) 23.5122 0.910394
\(668\) −65.2038 −2.52281
\(669\) 3.72875 0.144162
\(670\) −19.3908 −0.749132
\(671\) −5.17975 −0.199962
\(672\) −1.03033 −0.0397458
\(673\) 21.8094 0.840691 0.420346 0.907364i \(-0.361909\pi\)
0.420346 + 0.907364i \(0.361909\pi\)
\(674\) 7.40649 0.285287
\(675\) −0.726781 −0.0279738
\(676\) 53.8695 2.07191
\(677\) 1.00890 0.0387752 0.0193876 0.999812i \(-0.493828\pi\)
0.0193876 + 0.999812i \(0.493828\pi\)
\(678\) 3.36865 0.129372
\(679\) 0.973653 0.0373654
\(680\) 31.6111 1.21223
\(681\) 12.6547 0.484929
\(682\) 25.2650 0.967448
\(683\) 0.173423 0.00663583 0.00331791 0.999994i \(-0.498944\pi\)
0.00331791 + 0.999994i \(0.498944\pi\)
\(684\) −16.0170 −0.612424
\(685\) 26.9049 1.02798
\(686\) 5.18918 0.198124
\(687\) −2.78670 −0.106319
\(688\) −5.53156 −0.210889
\(689\) 45.3662 1.72832
\(690\) 19.8530 0.755790
\(691\) 32.6202 1.24093 0.620466 0.784233i \(-0.286943\pi\)
0.620466 + 0.784233i \(0.286943\pi\)
\(692\) −4.83010 −0.183613
\(693\) 0.492207 0.0186974
\(694\) −31.5779 −1.19868
\(695\) −11.1497 −0.422933
\(696\) 13.8753 0.525942
\(697\) −45.8391 −1.73628
\(698\) −46.1182 −1.74560
\(699\) −1.35047 −0.0510796
\(700\) −0.0746469 −0.00282139
\(701\) 47.6177 1.79850 0.899248 0.437439i \(-0.144114\pi\)
0.899248 + 0.437439i \(0.144114\pi\)
\(702\) 61.5541 2.32321
\(703\) −2.55171 −0.0962396
\(704\) 19.1597 0.722108
\(705\) 0.800284 0.0301404
\(706\) 44.4384 1.67246
\(707\) −0.466255 −0.0175353
\(708\) −29.3709 −1.10383
\(709\) 36.8959 1.38565 0.692827 0.721103i \(-0.256365\pi\)
0.692827 + 0.721103i \(0.256365\pi\)
\(710\) 27.1373 1.01844
\(711\) −4.71330 −0.176763
\(712\) 4.41665 0.165521
\(713\) 31.0497 1.16282
\(714\) −2.14113 −0.0801299
\(715\) 17.8549 0.667734
\(716\) −29.0883 −1.08708
\(717\) 18.4960 0.690745
\(718\) 3.89464 0.145347
\(719\) −44.3594 −1.65432 −0.827162 0.561963i \(-0.810046\pi\)
−0.827162 + 0.561963i \(0.810046\pi\)
\(720\) 2.94171 0.109631
\(721\) −1.45724 −0.0542703
\(722\) 28.1599 1.04800
\(723\) −12.9726 −0.482455
\(724\) −49.2325 −1.82971
\(725\) −0.849127 −0.0315358
\(726\) −19.5872 −0.726948
\(727\) −0.821279 −0.0304595 −0.0152298 0.999884i \(-0.504848\pi\)
−0.0152298 + 0.999884i \(0.504848\pi\)
\(728\) 2.22244 0.0823693
\(729\) 12.0347 0.445730
\(730\) −21.0973 −0.780848
\(731\) −49.4851 −1.83027
\(732\) −10.6864 −0.394980
\(733\) −13.6899 −0.505646 −0.252823 0.967513i \(-0.581359\pi\)
−0.252823 + 0.967513i \(0.581359\pi\)
\(734\) 71.4750 2.63819
\(735\) 15.0882 0.556537
\(736\) 25.9145 0.955222
\(737\) −5.73214 −0.211146
\(738\) 35.8379 1.31921
\(739\) 10.2102 0.375589 0.187795 0.982208i \(-0.439866\pi\)
0.187795 + 0.982208i \(0.439866\pi\)
\(740\) −6.79437 −0.249766
\(741\) 13.8344 0.508219
\(742\) 3.05236 0.112056
\(743\) −8.70952 −0.319521 −0.159761 0.987156i \(-0.551072\pi\)
−0.159761 + 0.987156i \(0.551072\pi\)
\(744\) 18.3235 0.671771
\(745\) −48.4195 −1.77395
\(746\) −26.7169 −0.978176
\(747\) 15.2714 0.558749
\(748\) 26.5824 0.971947
\(749\) −1.43933 −0.0525921
\(750\) −25.1124 −0.916974
\(751\) 21.2111 0.774004 0.387002 0.922079i \(-0.373511\pi\)
0.387002 + 0.922079i \(0.373511\pi\)
\(752\) 0.242663 0.00884900
\(753\) 24.0495 0.876411
\(754\) 71.9160 2.61903
\(755\) −15.3534 −0.558768
\(756\) 2.51235 0.0913731
\(757\) −43.6388 −1.58608 −0.793039 0.609171i \(-0.791502\pi\)
−0.793039 + 0.609171i \(0.791502\pi\)
\(758\) 22.8025 0.828223
\(759\) 5.86876 0.213022
\(760\) −13.7423 −0.498484
\(761\) −8.35977 −0.303041 −0.151521 0.988454i \(-0.548417\pi\)
−0.151521 + 0.988454i \(0.548417\pi\)
\(762\) −11.2182 −0.406394
\(763\) −0.164703 −0.00596265
\(764\) −58.9781 −2.13375
\(765\) 26.3164 0.951471
\(766\) 49.4171 1.78551
\(767\) −53.5139 −1.93228
\(768\) 11.3177 0.408391
\(769\) 12.1551 0.438323 0.219161 0.975689i \(-0.429668\pi\)
0.219161 + 0.975689i \(0.429668\pi\)
\(770\) 1.20132 0.0432926
\(771\) −7.37341 −0.265547
\(772\) −36.7835 −1.32387
\(773\) −21.2250 −0.763411 −0.381705 0.924284i \(-0.624663\pi\)
−0.381705 + 0.924284i \(0.624663\pi\)
\(774\) 38.6884 1.39063
\(775\) −1.12134 −0.0402798
\(776\) −14.4518 −0.518789
\(777\) 0.161778 0.00580377
\(778\) 65.1391 2.33535
\(779\) 19.9276 0.713981
\(780\) 36.8365 1.31896
\(781\) 8.02208 0.287053
\(782\) 53.8532 1.92579
\(783\) 28.5785 1.02131
\(784\) 4.57506 0.163395
\(785\) −12.5603 −0.448295
\(786\) 20.4052 0.727829
\(787\) −43.3762 −1.54619 −0.773096 0.634288i \(-0.781293\pi\)
−0.773096 + 0.634288i \(0.781293\pi\)
\(788\) −17.6836 −0.629951
\(789\) 12.0175 0.427834
\(790\) −11.5037 −0.409283
\(791\) 0.250511 0.00890716
\(792\) −7.30576 −0.259599
\(793\) −19.4706 −0.691422
\(794\) −10.0107 −0.355265
\(795\) 17.7848 0.630762
\(796\) 44.4438 1.57527
\(797\) −6.90142 −0.244461 −0.122231 0.992502i \(-0.539005\pi\)
−0.122231 + 0.992502i \(0.539005\pi\)
\(798\) 0.930814 0.0329505
\(799\) 2.17085 0.0767992
\(800\) −0.935887 −0.0330886
\(801\) 3.67689 0.129917
\(802\) −38.9721 −1.37615
\(803\) −6.23661 −0.220085
\(804\) −11.8260 −0.417071
\(805\) 1.47638 0.0520354
\(806\) 94.9709 3.34521
\(807\) −22.7435 −0.800608
\(808\) 6.92057 0.243465
\(809\) 17.6983 0.622238 0.311119 0.950371i \(-0.399296\pi\)
0.311119 + 0.950371i \(0.399296\pi\)
\(810\) −6.19733 −0.217752
\(811\) 39.0802 1.37229 0.686145 0.727465i \(-0.259302\pi\)
0.686145 + 0.727465i \(0.259302\pi\)
\(812\) 2.93527 0.103008
\(813\) −8.49653 −0.297986
\(814\) −3.31093 −0.116048
\(815\) −46.6095 −1.63266
\(816\) −3.78283 −0.132425
\(817\) 21.5126 0.752632
\(818\) −56.0433 −1.95951
\(819\) 1.85020 0.0646512
\(820\) 53.0608 1.85296
\(821\) 32.5810 1.13708 0.568542 0.822655i \(-0.307508\pi\)
0.568542 + 0.822655i \(0.307508\pi\)
\(822\) 27.0492 0.943450
\(823\) 47.1518 1.64361 0.821804 0.569770i \(-0.192968\pi\)
0.821804 + 0.569770i \(0.192968\pi\)
\(824\) 21.6295 0.753501
\(825\) −0.211947 −0.00737903
\(826\) −3.60056 −0.125279
\(827\) −44.4088 −1.54425 −0.772123 0.635473i \(-0.780805\pi\)
−0.772123 + 0.635473i \(0.780805\pi\)
\(828\) −25.5409 −0.887609
\(829\) 24.8458 0.862931 0.431466 0.902129i \(-0.357997\pi\)
0.431466 + 0.902129i \(0.357997\pi\)
\(830\) 37.2726 1.29375
\(831\) −20.7050 −0.718248
\(832\) 72.0210 2.49688
\(833\) 40.9283 1.41808
\(834\) −11.2095 −0.388154
\(835\) −46.5734 −1.61174
\(836\) −11.5561 −0.399677
\(837\) 37.7403 1.30449
\(838\) 21.2917 0.735509
\(839\) −27.7744 −0.958879 −0.479440 0.877575i \(-0.659160\pi\)
−0.479440 + 0.877575i \(0.659160\pi\)
\(840\) 0.871259 0.0300613
\(841\) 4.38943 0.151360
\(842\) −3.39640 −0.117048
\(843\) 30.1233 1.03750
\(844\) 73.1820 2.51903
\(845\) 38.4776 1.32367
\(846\) −1.69721 −0.0583513
\(847\) −1.45661 −0.0500497
\(848\) 5.39272 0.185187
\(849\) −0.576647 −0.0197905
\(850\) −1.94487 −0.0667086
\(851\) −4.06900 −0.139484
\(852\) 16.5504 0.567008
\(853\) −12.8093 −0.438581 −0.219291 0.975660i \(-0.570374\pi\)
−0.219291 + 0.975660i \(0.570374\pi\)
\(854\) −1.31003 −0.0448284
\(855\) −11.4405 −0.391257
\(856\) 21.3638 0.730200
\(857\) 16.8746 0.576424 0.288212 0.957567i \(-0.406939\pi\)
0.288212 + 0.957567i \(0.406939\pi\)
\(858\) 17.9506 0.612824
\(859\) 5.81471 0.198395 0.0991977 0.995068i \(-0.468372\pi\)
0.0991977 + 0.995068i \(0.468372\pi\)
\(860\) 57.2812 1.95327
\(861\) −1.26341 −0.0430570
\(862\) 29.7754 1.01416
\(863\) −8.25272 −0.280926 −0.140463 0.990086i \(-0.544859\pi\)
−0.140463 + 0.990086i \(0.544859\pi\)
\(864\) 31.4986 1.07160
\(865\) −3.45002 −0.117304
\(866\) −40.7700 −1.38542
\(867\) −17.1429 −0.582203
\(868\) 3.87626 0.131569
\(869\) −3.40062 −0.115358
\(870\) 28.1930 0.955834
\(871\) −21.5470 −0.730093
\(872\) 2.44467 0.0827868
\(873\) −12.0312 −0.407195
\(874\) −23.4116 −0.791908
\(875\) −1.86749 −0.0631328
\(876\) −12.8668 −0.434728
\(877\) 39.6619 1.33929 0.669644 0.742682i \(-0.266447\pi\)
0.669644 + 0.742682i \(0.266447\pi\)
\(878\) 32.0535 1.08175
\(879\) 12.4982 0.421554
\(880\) 2.12242 0.0715469
\(881\) −15.0032 −0.505471 −0.252736 0.967535i \(-0.581330\pi\)
−0.252736 + 0.967535i \(0.581330\pi\)
\(882\) −31.9985 −1.07745
\(883\) 16.3675 0.550811 0.275405 0.961328i \(-0.411188\pi\)
0.275405 + 0.961328i \(0.411188\pi\)
\(884\) 99.9227 3.36076
\(885\) −20.9789 −0.705199
\(886\) 24.0132 0.806739
\(887\) 2.05599 0.0690333 0.0345166 0.999404i \(-0.489011\pi\)
0.0345166 + 0.999404i \(0.489011\pi\)
\(888\) −2.40126 −0.0805808
\(889\) −0.834250 −0.0279798
\(890\) 8.97413 0.300814
\(891\) −1.83200 −0.0613743
\(892\) −11.7081 −0.392016
\(893\) −0.943733 −0.0315808
\(894\) −48.6791 −1.62807
\(895\) −20.7770 −0.694499
\(896\) 2.74785 0.0917992
\(897\) 22.0606 0.736581
\(898\) −30.8215 −1.02853
\(899\) 44.0934 1.47060
\(900\) 0.922396 0.0307465
\(901\) 48.2431 1.60721
\(902\) 25.8568 0.860937
\(903\) −1.36390 −0.0453878
\(904\) −3.71831 −0.123669
\(905\) −35.1656 −1.16894
\(906\) −15.4357 −0.512818
\(907\) 21.7334 0.721644 0.360822 0.932635i \(-0.382496\pi\)
0.360822 + 0.932635i \(0.382496\pi\)
\(908\) −39.7352 −1.31866
\(909\) 5.76141 0.191094
\(910\) 4.51575 0.149696
\(911\) 42.7574 1.41661 0.708307 0.705904i \(-0.249459\pi\)
0.708307 + 0.705904i \(0.249459\pi\)
\(912\) 1.64451 0.0544550
\(913\) 11.0182 0.364648
\(914\) 0.0159747 0.000528396 0
\(915\) −7.63301 −0.252340
\(916\) 8.75011 0.289112
\(917\) 1.51744 0.0501103
\(918\) 65.4574 2.16042
\(919\) −32.6042 −1.07551 −0.537757 0.843100i \(-0.680728\pi\)
−0.537757 + 0.843100i \(0.680728\pi\)
\(920\) −21.9136 −0.722472
\(921\) 5.00612 0.164957
\(922\) −21.7257 −0.715498
\(923\) 30.1549 0.992560
\(924\) 0.732659 0.0241027
\(925\) 0.146950 0.00483167
\(926\) −54.4457 −1.78920
\(927\) 18.0067 0.591419
\(928\) 36.8010 1.20805
\(929\) −4.16366 −0.136605 −0.0683026 0.997665i \(-0.521758\pi\)
−0.0683026 + 0.997665i \(0.521758\pi\)
\(930\) 37.2312 1.22086
\(931\) −17.7927 −0.583134
\(932\) 4.24042 0.138900
\(933\) −13.5121 −0.442367
\(934\) −59.2306 −1.93808
\(935\) 18.9871 0.620945
\(936\) −27.4622 −0.897632
\(937\) −15.9896 −0.522359 −0.261179 0.965290i \(-0.584111\pi\)
−0.261179 + 0.965290i \(0.584111\pi\)
\(938\) −1.44974 −0.0473357
\(939\) −2.94699 −0.0961715
\(940\) −2.51285 −0.0819603
\(941\) −55.9491 −1.82389 −0.911944 0.410315i \(-0.865419\pi\)
−0.911944 + 0.410315i \(0.865419\pi\)
\(942\) −12.6276 −0.411430
\(943\) 31.7770 1.03480
\(944\) −6.36124 −0.207041
\(945\) 1.79450 0.0583752
\(946\) 27.9134 0.907543
\(947\) −38.4339 −1.24893 −0.624467 0.781051i \(-0.714684\pi\)
−0.624467 + 0.781051i \(0.714684\pi\)
\(948\) −7.01584 −0.227864
\(949\) −23.4433 −0.761002
\(950\) 0.845494 0.0274315
\(951\) 30.5320 0.990069
\(952\) 2.36338 0.0765975
\(953\) −14.2452 −0.461447 −0.230723 0.973019i \(-0.574109\pi\)
−0.230723 + 0.973019i \(0.574109\pi\)
\(954\) −37.7173 −1.22114
\(955\) −42.1266 −1.36318
\(956\) −58.0765 −1.87833
\(957\) 8.33417 0.269406
\(958\) −81.2974 −2.62660
\(959\) 2.01153 0.0649557
\(960\) 28.2342 0.911255
\(961\) 27.2290 0.878354
\(962\) −12.4458 −0.401267
\(963\) 17.7855 0.573130
\(964\) 40.7333 1.31193
\(965\) −26.2735 −0.845774
\(966\) 1.48429 0.0477564
\(967\) −40.7272 −1.30970 −0.654849 0.755760i \(-0.727268\pi\)
−0.654849 + 0.755760i \(0.727268\pi\)
\(968\) 21.6203 0.694901
\(969\) 14.7117 0.472607
\(970\) −29.3644 −0.942834
\(971\) 36.3446 1.16635 0.583177 0.812345i \(-0.301810\pi\)
0.583177 + 0.812345i \(0.301810\pi\)
\(972\) −49.5410 −1.58903
\(973\) −0.833601 −0.0267240
\(974\) −89.2611 −2.86011
\(975\) −0.796704 −0.0255150
\(976\) −2.31449 −0.0740850
\(977\) 33.3523 1.06704 0.533518 0.845789i \(-0.320870\pi\)
0.533518 + 0.845789i \(0.320870\pi\)
\(978\) −46.8595 −1.49840
\(979\) 2.65285 0.0847855
\(980\) −47.3763 −1.51338
\(981\) 2.03520 0.0649789
\(982\) 1.87616 0.0598706
\(983\) 10.8504 0.346075 0.173038 0.984915i \(-0.444642\pi\)
0.173038 + 0.984915i \(0.444642\pi\)
\(984\) 18.7527 0.597813
\(985\) −12.6309 −0.402455
\(986\) 76.4765 2.43551
\(987\) 0.0598327 0.00190450
\(988\) −43.4394 −1.38199
\(989\) 34.3045 1.09082
\(990\) −14.8445 −0.471788
\(991\) −31.5246 −1.00141 −0.500706 0.865618i \(-0.666926\pi\)
−0.500706 + 0.865618i \(0.666926\pi\)
\(992\) 48.5987 1.54301
\(993\) −5.16121 −0.163786
\(994\) 2.02890 0.0643528
\(995\) 31.7451 1.00639
\(996\) 22.7317 0.720281
\(997\) 58.4676 1.85169 0.925844 0.377906i \(-0.123356\pi\)
0.925844 + 0.377906i \(0.123356\pi\)
\(998\) 37.4119 1.18425
\(999\) −4.94579 −0.156478
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 \(a_p\))