Properties

Label 4015.2.a.h.1.22
Level 4015
Weight 2
Character 4015.1
Self dual Yes
Analytic conductor 32.060
Analytic rank 0
Dimension 37
CM No

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Newspace parameters

Level: \( N \) = \( 4015 = 5 \cdot 11 \cdot 73 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0599364115\)
Analytic rank: \(0\)
Dimension: \(37\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.22
Character \(\chi\) = 4015.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.829924 q^{2}\) \(+2.15264 q^{3}\) \(-1.31123 q^{4}\) \(+1.00000 q^{5}\) \(+1.78653 q^{6}\) \(-1.04291 q^{7}\) \(-2.74807 q^{8}\) \(+1.63385 q^{9}\) \(+O(q^{10})\) \(q\)\(+0.829924 q^{2}\) \(+2.15264 q^{3}\) \(-1.31123 q^{4}\) \(+1.00000 q^{5}\) \(+1.78653 q^{6}\) \(-1.04291 q^{7}\) \(-2.74807 q^{8}\) \(+1.63385 q^{9}\) \(+0.829924 q^{10}\) \(+1.00000 q^{11}\) \(-2.82259 q^{12}\) \(-4.99996 q^{13}\) \(-0.865533 q^{14}\) \(+2.15264 q^{15}\) \(+0.341763 q^{16}\) \(+2.47904 q^{17}\) \(+1.35597 q^{18}\) \(+2.20828 q^{19}\) \(-1.31123 q^{20}\) \(-2.24500 q^{21}\) \(+0.829924 q^{22}\) \(+5.73620 q^{23}\) \(-5.91560 q^{24}\) \(+1.00000 q^{25}\) \(-4.14959 q^{26}\) \(-2.94082 q^{27}\) \(+1.36748 q^{28}\) \(+7.55345 q^{29}\) \(+1.78653 q^{30}\) \(+10.9263 q^{31}\) \(+5.77977 q^{32}\) \(+2.15264 q^{33}\) \(+2.05741 q^{34}\) \(-1.04291 q^{35}\) \(-2.14235 q^{36}\) \(-2.81683 q^{37}\) \(+1.83271 q^{38}\) \(-10.7631 q^{39}\) \(-2.74807 q^{40}\) \(+4.54516 q^{41}\) \(-1.86318 q^{42}\) \(+6.23420 q^{43}\) \(-1.31123 q^{44}\) \(+1.63385 q^{45}\) \(+4.76061 q^{46}\) \(-7.66300 q^{47}\) \(+0.735691 q^{48}\) \(-5.91235 q^{49}\) \(+0.829924 q^{50}\) \(+5.33647 q^{51}\) \(+6.55608 q^{52}\) \(-4.99682 q^{53}\) \(-2.44066 q^{54}\) \(+1.00000 q^{55}\) \(+2.86598 q^{56}\) \(+4.75364 q^{57}\) \(+6.26880 q^{58}\) \(+12.1875 q^{59}\) \(-2.82259 q^{60}\) \(-1.05992 q^{61}\) \(+9.06802 q^{62}\) \(-1.70396 q^{63}\) \(+4.11325 q^{64}\) \(-4.99996 q^{65}\) \(+1.78653 q^{66}\) \(+7.00699 q^{67}\) \(-3.25058 q^{68}\) \(+12.3480 q^{69}\) \(-0.865533 q^{70}\) \(+13.6462 q^{71}\) \(-4.48994 q^{72}\) \(+1.00000 q^{73}\) \(-2.33775 q^{74}\) \(+2.15264 q^{75}\) \(-2.89556 q^{76}\) \(-1.04291 q^{77}\) \(-8.93257 q^{78}\) \(+15.2672 q^{79}\) \(+0.341763 q^{80}\) \(-11.2321 q^{81}\) \(+3.77214 q^{82}\) \(+3.03747 q^{83}\) \(+2.94370 q^{84}\) \(+2.47904 q^{85}\) \(+5.17392 q^{86}\) \(+16.2599 q^{87}\) \(-2.74807 q^{88}\) \(-16.0244 q^{89}\) \(+1.35597 q^{90}\) \(+5.21449 q^{91}\) \(-7.52145 q^{92}\) \(+23.5204 q^{93}\) \(-6.35971 q^{94}\) \(+2.20828 q^{95}\) \(+12.4418 q^{96}\) \(+2.92528 q^{97}\) \(-4.90680 q^{98}\) \(+1.63385 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut 5q^{10} \) \(\mathstrut +\mathstrut 37q^{11} \) \(\mathstrut +\mathstrut 6q^{12} \) \(\mathstrut +\mathstrut 11q^{13} \) \(\mathstrut +\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 43q^{16} \) \(\mathstrut +\mathstrut 38q^{17} \) \(\mathstrut +\mathstrut 11q^{18} \) \(\mathstrut +\mathstrut 34q^{19} \) \(\mathstrut +\mathstrut 43q^{20} \) \(\mathstrut +\mathstrut 39q^{21} \) \(\mathstrut +\mathstrut 5q^{22} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 37q^{25} \) \(\mathstrut -\mathstrut 9q^{26} \) \(\mathstrut +\mathstrut 3q^{27} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut +\mathstrut 9q^{30} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut +\mathstrut 14q^{32} \) \(\mathstrut +\mathstrut 3q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 6q^{35} \) \(\mathstrut +\mathstrut 20q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 15q^{38} \) \(\mathstrut +\mathstrut 14q^{39} \) \(\mathstrut +\mathstrut 12q^{40} \) \(\mathstrut +\mathstrut 62q^{41} \) \(\mathstrut -\mathstrut 13q^{42} \) \(\mathstrut +\mathstrut 30q^{43} \) \(\mathstrut +\mathstrut 43q^{44} \) \(\mathstrut +\mathstrut 50q^{45} \) \(\mathstrut +\mathstrut 31q^{46} \) \(\mathstrut +\mathstrut 5q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 59q^{49} \) \(\mathstrut +\mathstrut 5q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 13q^{54} \) \(\mathstrut +\mathstrut 37q^{55} \) \(\mathstrut +\mathstrut 22q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 40q^{58} \) \(\mathstrut +\mathstrut 15q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut +\mathstrut 57q^{61} \) \(\mathstrut +\mathstrut 20q^{62} \) \(\mathstrut -\mathstrut 29q^{63} \) \(\mathstrut +\mathstrut 10q^{64} \) \(\mathstrut +\mathstrut 11q^{65} \) \(\mathstrut +\mathstrut 9q^{66} \) \(\mathstrut -\mathstrut 14q^{67} \) \(\mathstrut +\mathstrut 53q^{68} \) \(\mathstrut +\mathstrut 24q^{69} \) \(\mathstrut +\mathstrut 11q^{70} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 15q^{72} \) \(\mathstrut +\mathstrut 37q^{73} \) \(\mathstrut +\mathstrut 7q^{74} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut +\mathstrut 59q^{76} \) \(\mathstrut +\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut q^{78} \) \(\mathstrut +\mathstrut 42q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 61q^{81} \) \(\mathstrut -\mathstrut 22q^{82} \) \(\mathstrut +\mathstrut 44q^{83} \) \(\mathstrut +\mathstrut 66q^{84} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut -\mathstrut q^{86} \) \(\mathstrut -\mathstrut 26q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 69q^{89} \) \(\mathstrut +\mathstrut 11q^{90} \) \(\mathstrut -\mathstrut 10q^{91} \) \(\mathstrut -\mathstrut 21q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut +\mathstrut 29q^{94} \) \(\mathstrut +\mathstrut 34q^{95} \) \(\mathstrut -\mathstrut 9q^{96} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut -\mathstrut 15q^{98} \) \(\mathstrut +\mathstrut 50q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.829924 0.586845 0.293423 0.955983i \(-0.405206\pi\)
0.293423 + 0.955983i \(0.405206\pi\)
\(3\) 2.15264 1.24283 0.621413 0.783483i \(-0.286559\pi\)
0.621413 + 0.783483i \(0.286559\pi\)
\(4\) −1.31123 −0.655613
\(5\) 1.00000 0.447214
\(6\) 1.78653 0.729347
\(7\) −1.04291 −0.394181 −0.197091 0.980385i \(-0.563149\pi\)
−0.197091 + 0.980385i \(0.563149\pi\)
\(8\) −2.74807 −0.971588
\(9\) 1.63385 0.544618
\(10\) 0.829924 0.262445
\(11\) 1.00000 0.301511
\(12\) −2.82259 −0.814813
\(13\) −4.99996 −1.38674 −0.693370 0.720582i \(-0.743875\pi\)
−0.693370 + 0.720582i \(0.743875\pi\)
\(14\) −0.865533 −0.231323
\(15\) 2.15264 0.555809
\(16\) 0.341763 0.0854407
\(17\) 2.47904 0.601255 0.300627 0.953742i \(-0.402804\pi\)
0.300627 + 0.953742i \(0.402804\pi\)
\(18\) 1.35597 0.319606
\(19\) 2.20828 0.506615 0.253308 0.967386i \(-0.418482\pi\)
0.253308 + 0.967386i \(0.418482\pi\)
\(20\) −1.31123 −0.293199
\(21\) −2.24500 −0.489899
\(22\) 0.829924 0.176940
\(23\) 5.73620 1.19608 0.598040 0.801466i \(-0.295946\pi\)
0.598040 + 0.801466i \(0.295946\pi\)
\(24\) −5.91560 −1.20752
\(25\) 1.00000 0.200000
\(26\) −4.14959 −0.813802
\(27\) −2.94082 −0.565961
\(28\) 1.36748 0.258430
\(29\) 7.55345 1.40264 0.701320 0.712846i \(-0.252594\pi\)
0.701320 + 0.712846i \(0.252594\pi\)
\(30\) 1.78653 0.326174
\(31\) 10.9263 1.96242 0.981212 0.192930i \(-0.0617991\pi\)
0.981212 + 0.192930i \(0.0617991\pi\)
\(32\) 5.77977 1.02173
\(33\) 2.15264 0.374726
\(34\) 2.05741 0.352843
\(35\) −1.04291 −0.176283
\(36\) −2.14235 −0.357058
\(37\) −2.81683 −0.463083 −0.231542 0.972825i \(-0.574377\pi\)
−0.231542 + 0.972825i \(0.574377\pi\)
\(38\) 1.83271 0.297305
\(39\) −10.7631 −1.72348
\(40\) −2.74807 −0.434508
\(41\) 4.54516 0.709834 0.354917 0.934898i \(-0.384509\pi\)
0.354917 + 0.934898i \(0.384509\pi\)
\(42\) −1.86318 −0.287495
\(43\) 6.23420 0.950707 0.475354 0.879795i \(-0.342320\pi\)
0.475354 + 0.879795i \(0.342320\pi\)
\(44\) −1.31123 −0.197675
\(45\) 1.63385 0.243560
\(46\) 4.76061 0.701914
\(47\) −7.66300 −1.11776 −0.558881 0.829248i \(-0.688769\pi\)
−0.558881 + 0.829248i \(0.688769\pi\)
\(48\) 0.735691 0.106188
\(49\) −5.91235 −0.844621
\(50\) 0.829924 0.117369
\(51\) 5.33647 0.747255
\(52\) 6.55608 0.909164
\(53\) −4.99682 −0.686366 −0.343183 0.939269i \(-0.611505\pi\)
−0.343183 + 0.939269i \(0.611505\pi\)
\(54\) −2.44066 −0.332132
\(55\) 1.00000 0.134840
\(56\) 2.86598 0.382982
\(57\) 4.75364 0.629635
\(58\) 6.26880 0.823133
\(59\) 12.1875 1.58668 0.793339 0.608780i \(-0.208341\pi\)
0.793339 + 0.608780i \(0.208341\pi\)
\(60\) −2.82259 −0.364395
\(61\) −1.05992 −0.135709 −0.0678544 0.997695i \(-0.521615\pi\)
−0.0678544 + 0.997695i \(0.521615\pi\)
\(62\) 9.06802 1.15164
\(63\) −1.70396 −0.214678
\(64\) 4.11325 0.514156
\(65\) −4.99996 −0.620169
\(66\) 1.78653 0.219906
\(67\) 7.00699 0.856040 0.428020 0.903769i \(-0.359211\pi\)
0.428020 + 0.903769i \(0.359211\pi\)
\(68\) −3.25058 −0.394190
\(69\) 12.3480 1.48652
\(70\) −0.865533 −0.103451
\(71\) 13.6462 1.61951 0.809753 0.586770i \(-0.199601\pi\)
0.809753 + 0.586770i \(0.199601\pi\)
\(72\) −4.48994 −0.529144
\(73\) 1.00000 0.117041
\(74\) −2.33775 −0.271758
\(75\) 2.15264 0.248565
\(76\) −2.89556 −0.332143
\(77\) −1.04291 −0.118850
\(78\) −8.93257 −1.01141
\(79\) 15.2672 1.71769 0.858845 0.512236i \(-0.171183\pi\)
0.858845 + 0.512236i \(0.171183\pi\)
\(80\) 0.341763 0.0382102
\(81\) −11.2321 −1.24801
\(82\) 3.77214 0.416563
\(83\) 3.03747 0.333406 0.166703 0.986007i \(-0.446688\pi\)
0.166703 + 0.986007i \(0.446688\pi\)
\(84\) 2.94370 0.321184
\(85\) 2.47904 0.268889
\(86\) 5.17392 0.557918
\(87\) 16.2599 1.74324
\(88\) −2.74807 −0.292945
\(89\) −16.0244 −1.69859 −0.849293 0.527922i \(-0.822972\pi\)
−0.849293 + 0.527922i \(0.822972\pi\)
\(90\) 1.35597 0.142932
\(91\) 5.21449 0.546627
\(92\) −7.52145 −0.784165
\(93\) 23.5204 2.43895
\(94\) −6.35971 −0.655954
\(95\) 2.20828 0.226565
\(96\) 12.4418 1.26983
\(97\) 2.92528 0.297017 0.148508 0.988911i \(-0.452553\pi\)
0.148508 + 0.988911i \(0.452553\pi\)
\(98\) −4.90680 −0.495662
\(99\) 1.63385 0.164208
\(100\) −1.31123 −0.131123
\(101\) 10.6303 1.05775 0.528875 0.848700i \(-0.322614\pi\)
0.528875 + 0.848700i \(0.322614\pi\)
\(102\) 4.42887 0.438523
\(103\) −13.6587 −1.34584 −0.672918 0.739717i \(-0.734959\pi\)
−0.672918 + 0.739717i \(0.734959\pi\)
\(104\) 13.7402 1.34734
\(105\) −2.24500 −0.219090
\(106\) −4.14698 −0.402790
\(107\) −6.82896 −0.660181 −0.330090 0.943949i \(-0.607079\pi\)
−0.330090 + 0.943949i \(0.607079\pi\)
\(108\) 3.85608 0.371051
\(109\) 12.6156 1.20836 0.604178 0.796849i \(-0.293502\pi\)
0.604178 + 0.796849i \(0.293502\pi\)
\(110\) 0.829924 0.0791302
\(111\) −6.06361 −0.575532
\(112\) −0.356426 −0.0336791
\(113\) 1.50690 0.141757 0.0708784 0.997485i \(-0.477420\pi\)
0.0708784 + 0.997485i \(0.477420\pi\)
\(114\) 3.94516 0.369498
\(115\) 5.73620 0.534903
\(116\) −9.90428 −0.919589
\(117\) −8.16920 −0.755243
\(118\) 10.1147 0.931134
\(119\) −2.58540 −0.237003
\(120\) −5.91560 −0.540018
\(121\) 1.00000 0.0909091
\(122\) −0.879653 −0.0796401
\(123\) 9.78408 0.882201
\(124\) −14.3269 −1.28659
\(125\) 1.00000 0.0894427
\(126\) −1.41415 −0.125983
\(127\) −4.36742 −0.387546 −0.193773 0.981046i \(-0.562072\pi\)
−0.193773 + 0.981046i \(0.562072\pi\)
\(128\) −8.14586 −0.719999
\(129\) 13.4200 1.18156
\(130\) −4.14959 −0.363943
\(131\) 16.7683 1.46505 0.732525 0.680741i \(-0.238342\pi\)
0.732525 + 0.680741i \(0.238342\pi\)
\(132\) −2.82259 −0.245675
\(133\) −2.30303 −0.199698
\(134\) 5.81528 0.502363
\(135\) −2.94082 −0.253105
\(136\) −6.81256 −0.584172
\(137\) −20.5287 −1.75388 −0.876942 0.480596i \(-0.840420\pi\)
−0.876942 + 0.480596i \(0.840420\pi\)
\(138\) 10.2479 0.872357
\(139\) 0.205962 0.0174694 0.00873472 0.999962i \(-0.497220\pi\)
0.00873472 + 0.999962i \(0.497220\pi\)
\(140\) 1.36748 0.115574
\(141\) −16.4957 −1.38919
\(142\) 11.3253 0.950400
\(143\) −4.99996 −0.418118
\(144\) 0.558390 0.0465325
\(145\) 7.55345 0.627280
\(146\) 0.829924 0.0686850
\(147\) −12.7271 −1.04972
\(148\) 3.69349 0.303603
\(149\) 0.357433 0.0292821 0.0146410 0.999893i \(-0.495339\pi\)
0.0146410 + 0.999893i \(0.495339\pi\)
\(150\) 1.78653 0.145869
\(151\) −5.41786 −0.440900 −0.220450 0.975398i \(-0.570753\pi\)
−0.220450 + 0.975398i \(0.570753\pi\)
\(152\) −6.06851 −0.492221
\(153\) 4.05038 0.327454
\(154\) −0.865533 −0.0697466
\(155\) 10.9263 0.877623
\(156\) 14.1129 1.12993
\(157\) −12.3225 −0.983441 −0.491720 0.870753i \(-0.663632\pi\)
−0.491720 + 0.870753i \(0.663632\pi\)
\(158\) 12.6706 1.00802
\(159\) −10.7563 −0.853034
\(160\) 5.77977 0.456931
\(161\) −5.98231 −0.471472
\(162\) −9.32178 −0.732388
\(163\) 7.40490 0.579997 0.289998 0.957027i \(-0.406345\pi\)
0.289998 + 0.957027i \(0.406345\pi\)
\(164\) −5.95972 −0.465376
\(165\) 2.15264 0.167583
\(166\) 2.52087 0.195658
\(167\) −18.2133 −1.40939 −0.704695 0.709510i \(-0.748916\pi\)
−0.704695 + 0.709510i \(0.748916\pi\)
\(168\) 6.16941 0.475980
\(169\) 11.9996 0.923047
\(170\) 2.05741 0.157796
\(171\) 3.60801 0.275912
\(172\) −8.17445 −0.623296
\(173\) −11.0730 −0.841866 −0.420933 0.907092i \(-0.638297\pi\)
−0.420933 + 0.907092i \(0.638297\pi\)
\(174\) 13.4945 1.02301
\(175\) −1.04291 −0.0788363
\(176\) 0.341763 0.0257613
\(177\) 26.2353 1.97196
\(178\) −13.2991 −0.996807
\(179\) −25.4658 −1.90340 −0.951700 0.307029i \(-0.900665\pi\)
−0.951700 + 0.307029i \(0.900665\pi\)
\(180\) −2.14235 −0.159681
\(181\) 17.9896 1.33716 0.668579 0.743641i \(-0.266903\pi\)
0.668579 + 0.743641i \(0.266903\pi\)
\(182\) 4.32763 0.320785
\(183\) −2.28162 −0.168662
\(184\) −15.7635 −1.16210
\(185\) −2.81683 −0.207097
\(186\) 19.5202 1.43129
\(187\) 2.47904 0.181285
\(188\) 10.0479 0.732820
\(189\) 3.06700 0.223091
\(190\) 1.83271 0.132959
\(191\) −0.0991286 −0.00717269 −0.00358635 0.999994i \(-0.501142\pi\)
−0.00358635 + 0.999994i \(0.501142\pi\)
\(192\) 8.85434 0.639007
\(193\) −7.35857 −0.529681 −0.264841 0.964292i \(-0.585319\pi\)
−0.264841 + 0.964292i \(0.585319\pi\)
\(194\) 2.42776 0.174303
\(195\) −10.7631 −0.770762
\(196\) 7.75242 0.553744
\(197\) 6.49007 0.462398 0.231199 0.972906i \(-0.425735\pi\)
0.231199 + 0.972906i \(0.425735\pi\)
\(198\) 1.35597 0.0963649
\(199\) −0.161833 −0.0114720 −0.00573600 0.999984i \(-0.501826\pi\)
−0.00573600 + 0.999984i \(0.501826\pi\)
\(200\) −2.74807 −0.194318
\(201\) 15.0835 1.06391
\(202\) 8.82231 0.620736
\(203\) −7.87754 −0.552895
\(204\) −6.99731 −0.489910
\(205\) 4.54516 0.317448
\(206\) −11.3357 −0.789797
\(207\) 9.37210 0.651406
\(208\) −1.70880 −0.118484
\(209\) 2.20828 0.152750
\(210\) −1.86318 −0.128572
\(211\) 22.5360 1.55144 0.775720 0.631078i \(-0.217387\pi\)
0.775720 + 0.631078i \(0.217387\pi\)
\(212\) 6.55195 0.449990
\(213\) 29.3753 2.01277
\(214\) −5.66752 −0.387424
\(215\) 6.23420 0.425169
\(216\) 8.08157 0.549881
\(217\) −11.3951 −0.773551
\(218\) 10.4700 0.709118
\(219\) 2.15264 0.145462
\(220\) −1.31123 −0.0884028
\(221\) −12.3951 −0.833784
\(222\) −5.03234 −0.337748
\(223\) −16.7780 −1.12354 −0.561771 0.827293i \(-0.689880\pi\)
−0.561771 + 0.827293i \(0.689880\pi\)
\(224\) −6.02776 −0.402746
\(225\) 1.63385 0.108924
\(226\) 1.25061 0.0831893
\(227\) 20.4542 1.35759 0.678797 0.734326i \(-0.262501\pi\)
0.678797 + 0.734326i \(0.262501\pi\)
\(228\) −6.23309 −0.412797
\(229\) −9.16392 −0.605569 −0.302784 0.953059i \(-0.597916\pi\)
−0.302784 + 0.953059i \(0.597916\pi\)
\(230\) 4.76061 0.313905
\(231\) −2.24500 −0.147710
\(232\) −20.7574 −1.36279
\(233\) −21.2588 −1.39271 −0.696356 0.717696i \(-0.745197\pi\)
−0.696356 + 0.717696i \(0.745197\pi\)
\(234\) −6.77982 −0.443211
\(235\) −7.66300 −0.499879
\(236\) −15.9806 −1.04025
\(237\) 32.8647 2.13479
\(238\) −2.14569 −0.139084
\(239\) −13.2380 −0.856295 −0.428148 0.903709i \(-0.640834\pi\)
−0.428148 + 0.903709i \(0.640834\pi\)
\(240\) 0.735691 0.0474887
\(241\) −6.99142 −0.450357 −0.225178 0.974318i \(-0.572296\pi\)
−0.225178 + 0.974318i \(0.572296\pi\)
\(242\) 0.829924 0.0533496
\(243\) −15.3562 −0.985098
\(244\) 1.38979 0.0889724
\(245\) −5.91235 −0.377726
\(246\) 8.12005 0.517715
\(247\) −11.0413 −0.702543
\(248\) −30.0263 −1.90667
\(249\) 6.53858 0.414365
\(250\) 0.829924 0.0524890
\(251\) 5.49663 0.346944 0.173472 0.984839i \(-0.444501\pi\)
0.173472 + 0.984839i \(0.444501\pi\)
\(252\) 2.23427 0.140746
\(253\) 5.73620 0.360632
\(254\) −3.62463 −0.227429
\(255\) 5.33647 0.334183
\(256\) −14.9869 −0.936684
\(257\) 7.03141 0.438608 0.219304 0.975657i \(-0.429621\pi\)
0.219304 + 0.975657i \(0.429621\pi\)
\(258\) 11.1376 0.693395
\(259\) 2.93768 0.182539
\(260\) 6.55608 0.406591
\(261\) 12.3412 0.763903
\(262\) 13.9164 0.859757
\(263\) 20.0010 1.23331 0.616656 0.787233i \(-0.288487\pi\)
0.616656 + 0.787233i \(0.288487\pi\)
\(264\) −5.91560 −0.364080
\(265\) −4.99682 −0.306952
\(266\) −1.91134 −0.117192
\(267\) −34.4948 −2.11105
\(268\) −9.18775 −0.561231
\(269\) −25.2922 −1.54209 −0.771046 0.636779i \(-0.780266\pi\)
−0.771046 + 0.636779i \(0.780266\pi\)
\(270\) −2.44066 −0.148534
\(271\) 12.3769 0.751844 0.375922 0.926651i \(-0.377326\pi\)
0.375922 + 0.926651i \(0.377326\pi\)
\(272\) 0.847242 0.0513716
\(273\) 11.2249 0.679362
\(274\) −17.0373 −1.02926
\(275\) 1.00000 0.0603023
\(276\) −16.1910 −0.974581
\(277\) −15.2397 −0.915667 −0.457833 0.889038i \(-0.651374\pi\)
−0.457833 + 0.889038i \(0.651374\pi\)
\(278\) 0.170933 0.0102519
\(279\) 17.8520 1.06877
\(280\) 2.86598 0.171275
\(281\) 26.7685 1.59687 0.798437 0.602078i \(-0.205660\pi\)
0.798437 + 0.602078i \(0.205660\pi\)
\(282\) −13.6902 −0.815237
\(283\) 18.6758 1.11016 0.555082 0.831796i \(-0.312687\pi\)
0.555082 + 0.831796i \(0.312687\pi\)
\(284\) −17.8933 −1.06177
\(285\) 4.75364 0.281581
\(286\) −4.14959 −0.245370
\(287\) −4.74017 −0.279803
\(288\) 9.44330 0.556452
\(289\) −10.8544 −0.638493
\(290\) 6.26880 0.368116
\(291\) 6.29706 0.369140
\(292\) −1.31123 −0.0767337
\(293\) −12.6535 −0.739226 −0.369613 0.929186i \(-0.620510\pi\)
−0.369613 + 0.929186i \(0.620510\pi\)
\(294\) −10.5626 −0.616022
\(295\) 12.1875 0.709584
\(296\) 7.74083 0.449926
\(297\) −2.94082 −0.170644
\(298\) 0.296643 0.0171840
\(299\) −28.6808 −1.65865
\(300\) −2.82259 −0.162963
\(301\) −6.50169 −0.374751
\(302\) −4.49642 −0.258740
\(303\) 22.8831 1.31460
\(304\) 0.754709 0.0432855
\(305\) −1.05992 −0.0606908
\(306\) 3.36151 0.192165
\(307\) 10.1608 0.579905 0.289953 0.957041i \(-0.406360\pi\)
0.289953 + 0.957041i \(0.406360\pi\)
\(308\) 1.36748 0.0779197
\(309\) −29.4023 −1.67264
\(310\) 9.06802 0.515029
\(311\) 9.06810 0.514205 0.257102 0.966384i \(-0.417232\pi\)
0.257102 + 0.966384i \(0.417232\pi\)
\(312\) 29.5777 1.67451
\(313\) 9.61319 0.543369 0.271685 0.962386i \(-0.412419\pi\)
0.271685 + 0.962386i \(0.412419\pi\)
\(314\) −10.2267 −0.577127
\(315\) −1.70396 −0.0960070
\(316\) −20.0187 −1.12614
\(317\) −3.81576 −0.214315 −0.107157 0.994242i \(-0.534175\pi\)
−0.107157 + 0.994242i \(0.534175\pi\)
\(318\) −8.92695 −0.500599
\(319\) 7.55345 0.422912
\(320\) 4.11325 0.229938
\(321\) −14.7003 −0.820490
\(322\) −4.96487 −0.276681
\(323\) 5.47442 0.304605
\(324\) 14.7278 0.818211
\(325\) −4.99996 −0.277348
\(326\) 6.14551 0.340368
\(327\) 27.1568 1.50178
\(328\) −12.4904 −0.689667
\(329\) 7.99178 0.440601
\(330\) 1.78653 0.0983451
\(331\) 3.71474 0.204180 0.102090 0.994775i \(-0.467447\pi\)
0.102090 + 0.994775i \(0.467447\pi\)
\(332\) −3.98281 −0.218585
\(333\) −4.60228 −0.252203
\(334\) −15.1157 −0.827094
\(335\) 7.00699 0.382833
\(336\) −0.767257 −0.0418573
\(337\) 17.0084 0.926504 0.463252 0.886227i \(-0.346682\pi\)
0.463252 + 0.886227i \(0.346682\pi\)
\(338\) 9.95877 0.541686
\(339\) 3.24380 0.176179
\(340\) −3.25058 −0.176287
\(341\) 10.9263 0.591693
\(342\) 2.99438 0.161917
\(343\) 13.4664 0.727115
\(344\) −17.1320 −0.923696
\(345\) 12.3480 0.664792
\(346\) −9.18977 −0.494045
\(347\) 30.3558 1.62959 0.814793 0.579751i \(-0.196850\pi\)
0.814793 + 0.579751i \(0.196850\pi\)
\(348\) −21.3203 −1.14289
\(349\) 14.6584 0.784647 0.392323 0.919827i \(-0.371671\pi\)
0.392323 + 0.919827i \(0.371671\pi\)
\(350\) −0.865533 −0.0462647
\(351\) 14.7040 0.784841
\(352\) 5.77977 0.308063
\(353\) 5.37992 0.286344 0.143172 0.989698i \(-0.454270\pi\)
0.143172 + 0.989698i \(0.454270\pi\)
\(354\) 21.7733 1.15724
\(355\) 13.6462 0.724265
\(356\) 21.0116 1.11361
\(357\) −5.56544 −0.294554
\(358\) −21.1347 −1.11700
\(359\) −37.1141 −1.95881 −0.979403 0.201917i \(-0.935283\pi\)
−0.979403 + 0.201917i \(0.935283\pi\)
\(360\) −4.48994 −0.236641
\(361\) −14.1235 −0.743341
\(362\) 14.9300 0.784705
\(363\) 2.15264 0.112984
\(364\) −6.83737 −0.358376
\(365\) 1.00000 0.0523424
\(366\) −1.89358 −0.0989788
\(367\) −7.98776 −0.416957 −0.208479 0.978027i \(-0.566851\pi\)
−0.208479 + 0.978027i \(0.566851\pi\)
\(368\) 1.96042 0.102194
\(369\) 7.42612 0.386588
\(370\) −2.33775 −0.121534
\(371\) 5.21121 0.270553
\(372\) −30.8406 −1.59901
\(373\) 5.56022 0.287897 0.143949 0.989585i \(-0.454020\pi\)
0.143949 + 0.989585i \(0.454020\pi\)
\(374\) 2.05741 0.106386
\(375\) 2.15264 0.111162
\(376\) 21.0584 1.08601
\(377\) −37.7670 −1.94510
\(378\) 2.54538 0.130920
\(379\) −9.54987 −0.490544 −0.245272 0.969454i \(-0.578877\pi\)
−0.245272 + 0.969454i \(0.578877\pi\)
\(380\) −2.89556 −0.148539
\(381\) −9.40147 −0.481652
\(382\) −0.0822692 −0.00420926
\(383\) 29.5944 1.51220 0.756102 0.654453i \(-0.227101\pi\)
0.756102 + 0.654453i \(0.227101\pi\)
\(384\) −17.5351 −0.894834
\(385\) −1.04291 −0.0531514
\(386\) −6.10705 −0.310841
\(387\) 10.1858 0.517772
\(388\) −3.83570 −0.194728
\(389\) 6.65207 0.337274 0.168637 0.985678i \(-0.446064\pi\)
0.168637 + 0.985678i \(0.446064\pi\)
\(390\) −8.93257 −0.452318
\(391\) 14.2202 0.719148
\(392\) 16.2475 0.820624
\(393\) 36.0960 1.82080
\(394\) 5.38627 0.271356
\(395\) 15.2672 0.768174
\(396\) −2.14235 −0.107657
\(397\) 21.4150 1.07479 0.537394 0.843331i \(-0.319409\pi\)
0.537394 + 0.843331i \(0.319409\pi\)
\(398\) −0.134309 −0.00673229
\(399\) −4.95760 −0.248190
\(400\) 0.341763 0.0170881
\(401\) −4.03434 −0.201465 −0.100733 0.994914i \(-0.532119\pi\)
−0.100733 + 0.994914i \(0.532119\pi\)
\(402\) 12.5182 0.624350
\(403\) −54.6312 −2.72137
\(404\) −13.9387 −0.693474
\(405\) −11.2321 −0.558127
\(406\) −6.53776 −0.324464
\(407\) −2.81683 −0.139625
\(408\) −14.6650 −0.726024
\(409\) 21.6220 1.06914 0.534570 0.845124i \(-0.320474\pi\)
0.534570 + 0.845124i \(0.320474\pi\)
\(410\) 3.77214 0.186293
\(411\) −44.1909 −2.17977
\(412\) 17.9097 0.882347
\(413\) −12.7104 −0.625439
\(414\) 7.77814 0.382275
\(415\) 3.03747 0.149104
\(416\) −28.8986 −1.41687
\(417\) 0.443361 0.0217115
\(418\) 1.83271 0.0896407
\(419\) 15.0268 0.734106 0.367053 0.930200i \(-0.380367\pi\)
0.367053 + 0.930200i \(0.380367\pi\)
\(420\) 2.94370 0.143638
\(421\) −1.89690 −0.0924490 −0.0462245 0.998931i \(-0.514719\pi\)
−0.0462245 + 0.998931i \(0.514719\pi\)
\(422\) 18.7031 0.910455
\(423\) −12.5202 −0.608754
\(424\) 13.7316 0.666865
\(425\) 2.47904 0.120251
\(426\) 24.3793 1.18118
\(427\) 1.10540 0.0534939
\(428\) 8.95431 0.432823
\(429\) −10.7631 −0.519648
\(430\) 5.17392 0.249509
\(431\) −13.3293 −0.642052 −0.321026 0.947070i \(-0.604028\pi\)
−0.321026 + 0.947070i \(0.604028\pi\)
\(432\) −1.00506 −0.0483561
\(433\) 14.0683 0.676077 0.338039 0.941132i \(-0.390237\pi\)
0.338039 + 0.941132i \(0.390237\pi\)
\(434\) −9.45709 −0.453955
\(435\) 16.2599 0.779600
\(436\) −16.5419 −0.792214
\(437\) 12.6672 0.605952
\(438\) 1.78653 0.0853636
\(439\) 8.53521 0.407363 0.203682 0.979037i \(-0.434709\pi\)
0.203682 + 0.979037i \(0.434709\pi\)
\(440\) −2.74807 −0.131009
\(441\) −9.65991 −0.459996
\(442\) −10.2870 −0.489302
\(443\) 6.33871 0.301161 0.150581 0.988598i \(-0.451886\pi\)
0.150581 + 0.988598i \(0.451886\pi\)
\(444\) 7.95076 0.377326
\(445\) −16.0244 −0.759631
\(446\) −13.9245 −0.659345
\(447\) 0.769425 0.0363925
\(448\) −4.28973 −0.202671
\(449\) −20.5376 −0.969230 −0.484615 0.874727i \(-0.661040\pi\)
−0.484615 + 0.874727i \(0.661040\pi\)
\(450\) 1.35597 0.0639213
\(451\) 4.54516 0.214023
\(452\) −1.97588 −0.0929375
\(453\) −11.6627 −0.547962
\(454\) 16.9755 0.796698
\(455\) 5.21449 0.244459
\(456\) −13.0633 −0.611746
\(457\) −16.5418 −0.773792 −0.386896 0.922123i \(-0.626453\pi\)
−0.386896 + 0.922123i \(0.626453\pi\)
\(458\) −7.60536 −0.355375
\(459\) −7.29040 −0.340287
\(460\) −7.52145 −0.350689
\(461\) −10.7185 −0.499212 −0.249606 0.968348i \(-0.580301\pi\)
−0.249606 + 0.968348i \(0.580301\pi\)
\(462\) −1.86318 −0.0866830
\(463\) 3.22102 0.149693 0.0748467 0.997195i \(-0.476153\pi\)
0.0748467 + 0.997195i \(0.476153\pi\)
\(464\) 2.58149 0.119843
\(465\) 23.5204 1.09073
\(466\) −17.6432 −0.817307
\(467\) 12.9028 0.597069 0.298534 0.954399i \(-0.403502\pi\)
0.298534 + 0.954399i \(0.403502\pi\)
\(468\) 10.7117 0.495147
\(469\) −7.30763 −0.337435
\(470\) −6.35971 −0.293351
\(471\) −26.5258 −1.22225
\(472\) −33.4921 −1.54160
\(473\) 6.23420 0.286649
\(474\) 27.2752 1.25279
\(475\) 2.20828 0.101323
\(476\) 3.39004 0.155382
\(477\) −8.16407 −0.373807
\(478\) −10.9865 −0.502513
\(479\) −38.6171 −1.76446 −0.882229 0.470820i \(-0.843958\pi\)
−0.882229 + 0.470820i \(0.843958\pi\)
\(480\) 12.4418 0.567886
\(481\) 14.0840 0.642176
\(482\) −5.80235 −0.264290
\(483\) −12.8778 −0.585958
\(484\) −1.31123 −0.0596012
\(485\) 2.92528 0.132830
\(486\) −12.7445 −0.578100
\(487\) −15.9532 −0.722907 −0.361453 0.932390i \(-0.617719\pi\)
−0.361453 + 0.932390i \(0.617719\pi\)
\(488\) 2.91273 0.131853
\(489\) 15.9401 0.720835
\(490\) −4.90680 −0.221667
\(491\) −27.1032 −1.22315 −0.611576 0.791186i \(-0.709464\pi\)
−0.611576 + 0.791186i \(0.709464\pi\)
\(492\) −12.8291 −0.578382
\(493\) 18.7253 0.843344
\(494\) −9.16348 −0.412284
\(495\) 1.63385 0.0734363
\(496\) 3.73421 0.167671
\(497\) −14.2317 −0.638379
\(498\) 5.42653 0.243168
\(499\) −16.7500 −0.749834 −0.374917 0.927058i \(-0.622329\pi\)
−0.374917 + 0.927058i \(0.622329\pi\)
\(500\) −1.31123 −0.0586398
\(501\) −39.2068 −1.75163
\(502\) 4.56179 0.203603
\(503\) −19.2636 −0.858923 −0.429462 0.903085i \(-0.641297\pi\)
−0.429462 + 0.903085i \(0.641297\pi\)
\(504\) 4.68258 0.208579
\(505\) 10.6303 0.473040
\(506\) 4.76061 0.211635
\(507\) 25.8308 1.14719
\(508\) 5.72667 0.254080
\(509\) −36.7666 −1.62965 −0.814827 0.579705i \(-0.803168\pi\)
−0.814827 + 0.579705i \(0.803168\pi\)
\(510\) 4.42887 0.196114
\(511\) −1.04291 −0.0461354
\(512\) 3.85368 0.170310
\(513\) −6.49417 −0.286724
\(514\) 5.83554 0.257395
\(515\) −13.6587 −0.601876
\(516\) −17.5966 −0.774649
\(517\) −7.66300 −0.337018
\(518\) 2.43806 0.107122
\(519\) −23.8362 −1.04629
\(520\) 13.7402 0.602549
\(521\) 34.6661 1.51875 0.759374 0.650655i \(-0.225505\pi\)
0.759374 + 0.650655i \(0.225505\pi\)
\(522\) 10.2423 0.448293
\(523\) 6.25512 0.273517 0.136759 0.990604i \(-0.456332\pi\)
0.136759 + 0.990604i \(0.456332\pi\)
\(524\) −21.9870 −0.960505
\(525\) −2.24500 −0.0979798
\(526\) 16.5993 0.723763
\(527\) 27.0867 1.17992
\(528\) 0.735691 0.0320169
\(529\) 9.90395 0.430606
\(530\) −4.14698 −0.180133
\(531\) 19.9126 0.864133
\(532\) 3.01980 0.130925
\(533\) −22.7256 −0.984355
\(534\) −28.6281 −1.23886
\(535\) −6.82896 −0.295242
\(536\) −19.2557 −0.831719
\(537\) −54.8186 −2.36560
\(538\) −20.9906 −0.904970
\(539\) −5.91235 −0.254663
\(540\) 3.85608 0.165939
\(541\) −23.6234 −1.01565 −0.507824 0.861461i \(-0.669550\pi\)
−0.507824 + 0.861461i \(0.669550\pi\)
\(542\) 10.2719 0.441216
\(543\) 38.7252 1.66186
\(544\) 14.3283 0.614319
\(545\) 12.6156 0.540393
\(546\) 9.31583 0.398681
\(547\) −12.1926 −0.521320 −0.260660 0.965431i \(-0.583940\pi\)
−0.260660 + 0.965431i \(0.583940\pi\)
\(548\) 26.9177 1.14987
\(549\) −1.73175 −0.0739094
\(550\) 0.829924 0.0353881
\(551\) 16.6802 0.710599
\(552\) −33.9330 −1.44429
\(553\) −15.9222 −0.677081
\(554\) −12.6478 −0.537355
\(555\) −6.06361 −0.257386
\(556\) −0.270062 −0.0114532
\(557\) 12.6831 0.537399 0.268700 0.963224i \(-0.413406\pi\)
0.268700 + 0.963224i \(0.413406\pi\)
\(558\) 14.8158 0.627204
\(559\) −31.1708 −1.31838
\(560\) −0.356426 −0.0150618
\(561\) 5.33647 0.225306
\(562\) 22.2158 0.937118
\(563\) −24.0000 −1.01148 −0.505740 0.862686i \(-0.668780\pi\)
−0.505740 + 0.862686i \(0.668780\pi\)
\(564\) 21.6295 0.910768
\(565\) 1.50690 0.0633956
\(566\) 15.4995 0.651494
\(567\) 11.7140 0.491942
\(568\) −37.5007 −1.57349
\(569\) −4.29859 −0.180206 −0.0901032 0.995932i \(-0.528720\pi\)
−0.0901032 + 0.995932i \(0.528720\pi\)
\(570\) 3.94516 0.165245
\(571\) −9.46649 −0.396160 −0.198080 0.980186i \(-0.563471\pi\)
−0.198080 + 0.980186i \(0.563471\pi\)
\(572\) 6.55608 0.274123
\(573\) −0.213388 −0.00891441
\(574\) −3.93398 −0.164201
\(575\) 5.73620 0.239216
\(576\) 6.72044 0.280019
\(577\) −34.7090 −1.44495 −0.722477 0.691395i \(-0.756997\pi\)
−0.722477 + 0.691395i \(0.756997\pi\)
\(578\) −9.00832 −0.374697
\(579\) −15.8403 −0.658302
\(580\) −9.90428 −0.411253
\(581\) −3.16780 −0.131422
\(582\) 5.22608 0.216628
\(583\) −4.99682 −0.206947
\(584\) −2.74807 −0.113716
\(585\) −8.16920 −0.337755
\(586\) −10.5015 −0.433811
\(587\) 21.1630 0.873489 0.436744 0.899586i \(-0.356131\pi\)
0.436744 + 0.899586i \(0.356131\pi\)
\(588\) 16.6882 0.688208
\(589\) 24.1284 0.994194
\(590\) 10.1147 0.416416
\(591\) 13.9708 0.574681
\(592\) −0.962686 −0.0395661
\(593\) 40.2295 1.65203 0.826014 0.563649i \(-0.190603\pi\)
0.826014 + 0.563649i \(0.190603\pi\)
\(594\) −2.44066 −0.100141
\(595\) −2.58540 −0.105991
\(596\) −0.468676 −0.0191977
\(597\) −0.348367 −0.0142577
\(598\) −23.8029 −0.973371
\(599\) 22.3013 0.911206 0.455603 0.890183i \(-0.349424\pi\)
0.455603 + 0.890183i \(0.349424\pi\)
\(600\) −5.91560 −0.241503
\(601\) 16.6444 0.678939 0.339470 0.940617i \(-0.389752\pi\)
0.339470 + 0.940617i \(0.389752\pi\)
\(602\) −5.39591 −0.219921
\(603\) 11.4484 0.466215
\(604\) 7.10404 0.289059
\(605\) 1.00000 0.0406558
\(606\) 18.9912 0.771467
\(607\) 17.8779 0.725641 0.362821 0.931859i \(-0.381814\pi\)
0.362821 + 0.931859i \(0.381814\pi\)
\(608\) 12.7634 0.517623
\(609\) −16.9575 −0.687152
\(610\) −0.879653 −0.0356161
\(611\) 38.3147 1.55005
\(612\) −5.31096 −0.214683
\(613\) 35.5502 1.43586 0.717930 0.696115i \(-0.245090\pi\)
0.717930 + 0.696115i \(0.245090\pi\)
\(614\) 8.43266 0.340315
\(615\) 9.78408 0.394532
\(616\) 2.86598 0.115473
\(617\) 2.87315 0.115669 0.0578343 0.998326i \(-0.481580\pi\)
0.0578343 + 0.998326i \(0.481580\pi\)
\(618\) −24.4017 −0.981581
\(619\) −1.78215 −0.0716308 −0.0358154 0.999358i \(-0.511403\pi\)
−0.0358154 + 0.999358i \(0.511403\pi\)
\(620\) −14.3269 −0.575381
\(621\) −16.8691 −0.676934
\(622\) 7.52584 0.301758
\(623\) 16.7120 0.669551
\(624\) −3.67843 −0.147255
\(625\) 1.00000 0.0400000
\(626\) 7.97822 0.318874
\(627\) 4.75364 0.189842
\(628\) 16.1575 0.644756
\(629\) −6.98301 −0.278431
\(630\) −1.41415 −0.0563413
\(631\) 11.5434 0.459537 0.229768 0.973245i \(-0.426203\pi\)
0.229768 + 0.973245i \(0.426203\pi\)
\(632\) −41.9552 −1.66889
\(633\) 48.5118 1.92817
\(634\) −3.16680 −0.125770
\(635\) −4.36742 −0.173316
\(636\) 14.1040 0.559260
\(637\) 29.5615 1.17127
\(638\) 6.26880 0.248184
\(639\) 22.2959 0.882012
\(640\) −8.14586 −0.321993
\(641\) −11.8352 −0.467461 −0.233730 0.972301i \(-0.575093\pi\)
−0.233730 + 0.972301i \(0.575093\pi\)
\(642\) −12.2001 −0.481501
\(643\) −20.2651 −0.799177 −0.399589 0.916695i \(-0.630847\pi\)
−0.399589 + 0.916695i \(0.630847\pi\)
\(644\) 7.84416 0.309103
\(645\) 13.4200 0.528412
\(646\) 4.54335 0.178756
\(647\) 7.94946 0.312526 0.156263 0.987716i \(-0.450055\pi\)
0.156263 + 0.987716i \(0.450055\pi\)
\(648\) 30.8665 1.21255
\(649\) 12.1875 0.478401
\(650\) −4.14959 −0.162760
\(651\) −24.5296 −0.961390
\(652\) −9.70949 −0.380253
\(653\) −18.0772 −0.707416 −0.353708 0.935356i \(-0.615079\pi\)
−0.353708 + 0.935356i \(0.615079\pi\)
\(654\) 22.5381 0.881311
\(655\) 16.7683 0.655190
\(656\) 1.55336 0.0606487
\(657\) 1.63385 0.0637427
\(658\) 6.63258 0.258565
\(659\) −44.4468 −1.73140 −0.865701 0.500561i \(-0.833127\pi\)
−0.865701 + 0.500561i \(0.833127\pi\)
\(660\) −2.82259 −0.109869
\(661\) −29.1686 −1.13453 −0.567264 0.823536i \(-0.691998\pi\)
−0.567264 + 0.823536i \(0.691998\pi\)
\(662\) 3.08295 0.119822
\(663\) −26.6821 −1.03625
\(664\) −8.34717 −0.323933
\(665\) −2.30303 −0.0893078
\(666\) −3.81954 −0.148004
\(667\) 43.3281 1.67767
\(668\) 23.8818 0.924015
\(669\) −36.1171 −1.39637
\(670\) 5.81528 0.224664
\(671\) −1.05992 −0.0409177
\(672\) −12.9756 −0.500544
\(673\) 12.7086 0.489880 0.244940 0.969538i \(-0.421232\pi\)
0.244940 + 0.969538i \(0.421232\pi\)
\(674\) 14.1157 0.543715
\(675\) −2.94082 −0.113192
\(676\) −15.7342 −0.605161
\(677\) 6.19998 0.238285 0.119142 0.992877i \(-0.461986\pi\)
0.119142 + 0.992877i \(0.461986\pi\)
\(678\) 2.69211 0.103390
\(679\) −3.05079 −0.117078
\(680\) −6.81256 −0.261250
\(681\) 44.0306 1.68725
\(682\) 9.06802 0.347232
\(683\) 19.4045 0.742492 0.371246 0.928534i \(-0.378931\pi\)
0.371246 + 0.928534i \(0.378931\pi\)
\(684\) −4.73092 −0.180891
\(685\) −20.5287 −0.784361
\(686\) 11.1761 0.426704
\(687\) −19.7266 −0.752617
\(688\) 2.13062 0.0812291
\(689\) 24.9839 0.951811
\(690\) 10.2479 0.390130
\(691\) 38.2011 1.45324 0.726620 0.687040i \(-0.241090\pi\)
0.726620 + 0.687040i \(0.241090\pi\)
\(692\) 14.5192 0.551938
\(693\) −1.70396 −0.0647279
\(694\) 25.1931 0.956315
\(695\) 0.205962 0.00781257
\(696\) −44.6832 −1.69371
\(697\) 11.2676 0.426791
\(698\) 12.1654 0.460466
\(699\) −45.7626 −1.73090
\(700\) 1.36748 0.0516861
\(701\) 7.88516 0.297818 0.148909 0.988851i \(-0.452424\pi\)
0.148909 + 0.988851i \(0.452424\pi\)
\(702\) 12.2032 0.460580
\(703\) −6.22035 −0.234605
\(704\) 4.11325 0.155024
\(705\) −16.4957 −0.621263
\(706\) 4.46493 0.168040
\(707\) −11.0864 −0.416945
\(708\) −34.4004 −1.29285
\(709\) 16.2668 0.610913 0.305457 0.952206i \(-0.401191\pi\)
0.305457 + 0.952206i \(0.401191\pi\)
\(710\) 11.3253 0.425032
\(711\) 24.9443 0.935485
\(712\) 44.0362 1.65033
\(713\) 62.6755 2.34722
\(714\) −4.61889 −0.172858
\(715\) −4.99996 −0.186988
\(716\) 33.3914 1.24789
\(717\) −28.4966 −1.06423
\(718\) −30.8019 −1.14952
\(719\) 10.4846 0.391009 0.195504 0.980703i \(-0.437366\pi\)
0.195504 + 0.980703i \(0.437366\pi\)
\(720\) 0.558390 0.0208100
\(721\) 14.2448 0.530503
\(722\) −11.7214 −0.436226
\(723\) −15.0500 −0.559715
\(724\) −23.5884 −0.876658
\(725\) 7.55345 0.280528
\(726\) 1.78653 0.0663043
\(727\) −28.6795 −1.06367 −0.531833 0.846850i \(-0.678496\pi\)
−0.531833 + 0.846850i \(0.678496\pi\)
\(728\) −14.3298 −0.531096
\(729\) 0.639991 0.0237034
\(730\) 0.829924 0.0307169
\(731\) 15.4548 0.571617
\(732\) 2.99172 0.110577
\(733\) 9.41565 0.347775 0.173887 0.984766i \(-0.444367\pi\)
0.173887 + 0.984766i \(0.444367\pi\)
\(734\) −6.62923 −0.244690
\(735\) −12.7271 −0.469448
\(736\) 33.1539 1.22207
\(737\) 7.00699 0.258106
\(738\) 6.16312 0.226868
\(739\) −28.5927 −1.05180 −0.525900 0.850546i \(-0.676271\pi\)
−0.525900 + 0.850546i \(0.676271\pi\)
\(740\) 3.69349 0.135776
\(741\) −23.7680 −0.873140
\(742\) 4.32491 0.158772
\(743\) −13.3726 −0.490593 −0.245297 0.969448i \(-0.578885\pi\)
−0.245297 + 0.969448i \(0.578885\pi\)
\(744\) −64.6357 −2.36966
\(745\) 0.357433 0.0130953
\(746\) 4.61456 0.168951
\(747\) 4.96278 0.181579
\(748\) −3.25058 −0.118853
\(749\) 7.12197 0.260231
\(750\) 1.78653 0.0652348
\(751\) 7.16088 0.261304 0.130652 0.991428i \(-0.458293\pi\)
0.130652 + 0.991428i \(0.458293\pi\)
\(752\) −2.61893 −0.0955024
\(753\) 11.8323 0.431192
\(754\) −31.3437 −1.14147
\(755\) −5.41786 −0.197176
\(756\) −4.02153 −0.146261
\(757\) −29.6488 −1.07760 −0.538802 0.842433i \(-0.681123\pi\)
−0.538802 + 0.842433i \(0.681123\pi\)
\(758\) −7.92567 −0.287873
\(759\) 12.3480 0.448202
\(760\) −6.06851 −0.220128
\(761\) −38.1278 −1.38213 −0.691066 0.722791i \(-0.742859\pi\)
−0.691066 + 0.722791i \(0.742859\pi\)
\(762\) −7.80251 −0.282655
\(763\) −13.1569 −0.476312
\(764\) 0.129980 0.00470251
\(765\) 4.05038 0.146442
\(766\) 24.5611 0.887430
\(767\) −60.9370 −2.20031
\(768\) −32.2615 −1.16414
\(769\) 7.37680 0.266014 0.133007 0.991115i \(-0.457537\pi\)
0.133007 + 0.991115i \(0.457537\pi\)
\(770\) −0.865533 −0.0311916
\(771\) 15.1361 0.545113
\(772\) 9.64874 0.347266
\(773\) −46.2555 −1.66369 −0.831847 0.555004i \(-0.812717\pi\)
−0.831847 + 0.555004i \(0.812717\pi\)
\(774\) 8.45343 0.303852
\(775\) 10.9263 0.392485
\(776\) −8.03885 −0.288578
\(777\) 6.32377 0.226864
\(778\) 5.52072 0.197927
\(779\) 10.0370 0.359613
\(780\) 14.1129 0.505322
\(781\) 13.6462 0.488300
\(782\) 11.8017 0.422029
\(783\) −22.2133 −0.793840
\(784\) −2.02062 −0.0721650
\(785\) −12.3225 −0.439808
\(786\) 29.9569 1.06853
\(787\) −35.5094 −1.26577 −0.632886 0.774245i \(-0.718130\pi\)
−0.632886 + 0.774245i \(0.718130\pi\)
\(788\) −8.50994 −0.303154
\(789\) 43.0548 1.53279
\(790\) 12.6706 0.450799
\(791\) −1.57155 −0.0558779
\(792\) −4.48994 −0.159543
\(793\) 5.29956 0.188193
\(794\) 17.7728 0.630734
\(795\) −10.7563 −0.381488
\(796\) 0.212199 0.00752119
\(797\) −35.0553 −1.24172 −0.620861 0.783920i \(-0.713217\pi\)
−0.620861 + 0.783920i \(0.713217\pi\)
\(798\) −4.11443 −0.145649
\(799\) −18.9968 −0.672060
\(800\) 5.77977 0.204346
\(801\) −26.1816 −0.925080
\(802\) −3.34820 −0.118229
\(803\) 1.00000 0.0352892
\(804\) −19.7779 −0.697513
\(805\) −5.98231 −0.210849
\(806\) −45.3398 −1.59702
\(807\) −54.4450 −1.91655
\(808\) −29.2127 −1.02770
\(809\) 42.7463 1.50288 0.751440 0.659802i \(-0.229360\pi\)
0.751440 + 0.659802i \(0.229360\pi\)
\(810\) −9.32178 −0.327534
\(811\) 7.93399 0.278600 0.139300 0.990250i \(-0.455515\pi\)
0.139300 + 0.990250i \(0.455515\pi\)
\(812\) 10.3292 0.362485
\(813\) 26.6430 0.934412
\(814\) −2.33775 −0.0819382
\(815\) 7.40490 0.259382
\(816\) 1.82381 0.0638460
\(817\) 13.7669 0.481643
\(818\) 17.9446 0.627420
\(819\) 8.51971 0.297703
\(820\) −5.95972 −0.208123
\(821\) −38.7862 −1.35365 −0.676824 0.736145i \(-0.736644\pi\)
−0.676824 + 0.736145i \(0.736644\pi\)
\(822\) −36.6751 −1.27919
\(823\) −23.8084 −0.829908 −0.414954 0.909842i \(-0.636202\pi\)
−0.414954 + 0.909842i \(0.636202\pi\)
\(824\) 37.5351 1.30760
\(825\) 2.15264 0.0749453
\(826\) −10.5487 −0.367036
\(827\) 21.2728 0.739728 0.369864 0.929086i \(-0.379404\pi\)
0.369864 + 0.929086i \(0.379404\pi\)
\(828\) −12.2889 −0.427070
\(829\) 32.2902 1.12148 0.560742 0.827991i \(-0.310516\pi\)
0.560742 + 0.827991i \(0.310516\pi\)
\(830\) 2.52087 0.0875007
\(831\) −32.8056 −1.13801
\(832\) −20.5661 −0.713001
\(833\) −14.6569 −0.507832
\(834\) 0.367956 0.0127413
\(835\) −18.2133 −0.630299
\(836\) −2.89556 −0.100145
\(837\) −32.1323 −1.11066
\(838\) 12.4711 0.430807
\(839\) −3.75627 −0.129681 −0.0648404 0.997896i \(-0.520654\pi\)
−0.0648404 + 0.997896i \(0.520654\pi\)
\(840\) 6.16941 0.212865
\(841\) 28.0546 0.967402
\(842\) −1.57428 −0.0542533
\(843\) 57.6229 1.98464
\(844\) −29.5497 −1.01714
\(845\) 11.9996 0.412799
\(846\) −10.3908 −0.357244
\(847\) −1.04291 −0.0358347
\(848\) −1.70773 −0.0586435
\(849\) 40.2023 1.37974
\(850\) 2.05741 0.0705687
\(851\) −16.1579 −0.553884
\(852\) −38.5177 −1.31959
\(853\) 14.0599 0.481401 0.240701 0.970599i \(-0.422623\pi\)
0.240701 + 0.970599i \(0.422623\pi\)
\(854\) 0.917396 0.0313926
\(855\) 3.60801 0.123391
\(856\) 18.7665 0.641424
\(857\) −47.6535 −1.62781 −0.813906 0.580997i \(-0.802663\pi\)
−0.813906 + 0.580997i \(0.802663\pi\)
\(858\) −8.93257 −0.304953
\(859\) 36.8435 1.25708 0.628542 0.777775i \(-0.283652\pi\)
0.628542 + 0.777775i \(0.283652\pi\)
\(860\) −8.17445 −0.278746
\(861\) −10.2039 −0.347747
\(862\) −11.0623 −0.376785
\(863\) −39.9755 −1.36078 −0.680391 0.732850i \(-0.738190\pi\)
−0.680391 + 0.732850i \(0.738190\pi\)
\(864\) −16.9973 −0.578259
\(865\) −11.0730 −0.376494
\(866\) 11.6756 0.396753
\(867\) −23.3656 −0.793536
\(868\) 14.9416 0.507150
\(869\) 15.2672 0.517903
\(870\) 13.4945 0.457505
\(871\) −35.0347 −1.18711
\(872\) −34.6685 −1.17402
\(873\) 4.77947 0.161761
\(874\) 10.5128 0.355600
\(875\) −1.04291 −0.0352567
\(876\) −2.82259 −0.0953666
\(877\) 43.9928 1.48553 0.742766 0.669551i \(-0.233513\pi\)
0.742766 + 0.669551i \(0.233513\pi\)
\(878\) 7.08358 0.239059
\(879\) −27.2385 −0.918730
\(880\) 0.341763 0.0115208
\(881\) 34.0757 1.14804 0.574019 0.818842i \(-0.305383\pi\)
0.574019 + 0.818842i \(0.305383\pi\)
\(882\) −8.01699 −0.269946
\(883\) 0.550601 0.0185292 0.00926460 0.999957i \(-0.497051\pi\)
0.00926460 + 0.999957i \(0.497051\pi\)
\(884\) 16.2527 0.546639
\(885\) 26.2353 0.881889
\(886\) 5.26065 0.176735
\(887\) 39.0533 1.31128 0.655642 0.755072i \(-0.272398\pi\)
0.655642 + 0.755072i \(0.272398\pi\)
\(888\) 16.6632 0.559180
\(889\) 4.55481 0.152763
\(890\) −13.2991 −0.445786
\(891\) −11.2321 −0.376289
\(892\) 21.9998 0.736608
\(893\) −16.9221 −0.566276
\(894\) 0.638565 0.0213568
\(895\) −25.4658 −0.851226
\(896\) 8.49536 0.283810
\(897\) −61.7393 −2.06142
\(898\) −17.0447 −0.568788
\(899\) 82.5314 2.75258
\(900\) −2.14235 −0.0714117
\(901\) −12.3873 −0.412681
\(902\) 3.77214 0.125598
\(903\) −13.9958 −0.465751
\(904\) −4.14105 −0.137729
\(905\) 17.9896 0.597995
\(906\) −9.67916 −0.321569
\(907\) 27.2645 0.905304 0.452652 0.891687i \(-0.350478\pi\)
0.452652 + 0.891687i \(0.350478\pi\)
\(908\) −26.8201 −0.890056
\(909\) 17.3683 0.576070
\(910\) 4.32763 0.143460
\(911\) −46.5648 −1.54276 −0.771380 0.636375i \(-0.780433\pi\)
−0.771380 + 0.636375i \(0.780433\pi\)
\(912\) 1.62462 0.0537964
\(913\) 3.03747 0.100526
\(914\) −13.7284 −0.454096
\(915\) −2.28162 −0.0754282
\(916\) 12.0160 0.397019
\(917\) −17.4877 −0.577495
\(918\) −6.05048 −0.199696
\(919\) −50.4399 −1.66386 −0.831930 0.554880i \(-0.812764\pi\)
−0.831930 + 0.554880i \(0.812764\pi\)
\(920\) −15.7635 −0.519706
\(921\) 21.8724 0.720721
\(922\) −8.89557 −0.292960
\(923\) −68.2305 −2.24583
\(924\) 2.94370 0.0968406
\(925\) −2.81683 −0.0926167
\(926\) 2.67320 0.0878469
\(927\) −22.3164 −0.732966
\(928\) 43.6572 1.43312
\(929\) 44.4410 1.45806 0.729032 0.684480i \(-0.239971\pi\)
0.729032 + 0.684480i \(0.239971\pi\)
\(930\) 19.5202 0.640092
\(931\) −13.0561 −0.427898
\(932\) 27.8751 0.913080
\(933\) 19.5203 0.639067
\(934\) 10.7083 0.350387
\(935\) 2.47904 0.0810732
\(936\) 22.4495 0.733785
\(937\) −48.3906 −1.58085 −0.790427 0.612557i \(-0.790141\pi\)
−0.790427 + 0.612557i \(0.790141\pi\)
\(938\) −6.06478 −0.198022
\(939\) 20.6937 0.675314
\(940\) 10.0479 0.327727
\(941\) 14.2855 0.465694 0.232847 0.972513i \(-0.425196\pi\)
0.232847 + 0.972513i \(0.425196\pi\)
\(942\) −22.0144 −0.717269
\(943\) 26.0719 0.849018
\(944\) 4.16523 0.135567
\(945\) 3.06700 0.0997695
\(946\) 5.17392 0.168219
\(947\) 31.6845 1.02961 0.514805 0.857308i \(-0.327864\pi\)
0.514805 + 0.857308i \(0.327864\pi\)
\(948\) −43.0930 −1.39960
\(949\) −4.99996 −0.162306
\(950\) 1.83271 0.0594609
\(951\) −8.21396 −0.266356
\(952\) 7.10486 0.230270
\(953\) −40.1753 −1.30141 −0.650704 0.759332i \(-0.725526\pi\)
−0.650704 + 0.759332i \(0.725526\pi\)
\(954\) −6.77556 −0.219367
\(955\) −0.0991286 −0.00320772
\(956\) 17.3580 0.561398
\(957\) 16.2599 0.525606
\(958\) −32.0492 −1.03546
\(959\) 21.4095 0.691349
\(960\) 8.85434 0.285773
\(961\) 88.3845 2.85111
\(962\) 11.6887 0.376858
\(963\) −11.1575 −0.359546
\(964\) 9.16732 0.295260
\(965\) −7.35857 −0.236881
\(966\) −10.6876 −0.343867
\(967\) 1.86766 0.0600597 0.0300299 0.999549i \(-0.490440\pi\)
0.0300299 + 0.999549i \(0.490440\pi\)
\(968\) −2.74807 −0.0883262
\(969\) 11.7844 0.378571
\(970\) 2.42776 0.0779506
\(971\) 42.4601 1.36261 0.681305 0.732000i \(-0.261413\pi\)
0.681305 + 0.732000i \(0.261413\pi\)
\(972\) 20.1354 0.645843
\(973\) −0.214799 −0.00688613
\(974\) −13.2399 −0.424235
\(975\) −10.7631 −0.344695
\(976\) −0.362241 −0.0115950
\(977\) 6.35485 0.203310 0.101655 0.994820i \(-0.467586\pi\)
0.101655 + 0.994820i \(0.467586\pi\)
\(978\) 13.2291 0.423019
\(979\) −16.0244 −0.512143
\(980\) 7.75242 0.247642
\(981\) 20.6121 0.658092
\(982\) −22.4936 −0.717801
\(983\) 57.0468 1.81951 0.909755 0.415146i \(-0.136270\pi\)
0.909755 + 0.415146i \(0.136270\pi\)
\(984\) −26.8873 −0.857136
\(985\) 6.49007 0.206791
\(986\) 15.5406 0.494913
\(987\) 17.2034 0.547591
\(988\) 14.4777 0.460596
\(989\) 35.7606 1.13712
\(990\) 1.35597 0.0430957
\(991\) −6.94726 −0.220687 −0.110343 0.993894i \(-0.535195\pi\)
−0.110343 + 0.993894i \(0.535195\pi\)
\(992\) 63.1516 2.00507
\(993\) 7.99649 0.253761
\(994\) −11.8112 −0.374630
\(995\) −0.161833 −0.00513044
\(996\) −8.57355 −0.271663
\(997\) −35.7252 −1.13143 −0.565714 0.824602i \(-0.691399\pi\)
−0.565714 + 0.824602i \(0.691399\pi\)
\(998\) −13.9012 −0.440036
\(999\) 8.28378 0.262087
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 \(a_p\))