Properties

Label 4033.2.a.d.1.14
Level 4033
Weight 2
Character 4033.1
Self dual Yes
Analytic conductor 32.204
Analytic rank 1
Dimension 79
CM No

Related objects

Downloads

Learn more about

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 1.14
Character \(\chi\) = 4033.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.13414 q^{2}\) \(-1.44031 q^{3}\) \(+2.55454 q^{4}\) \(+3.76689 q^{5}\) \(+3.07382 q^{6}\) \(+1.36855 q^{7}\) \(-1.18346 q^{8}\) \(-0.925504 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.13414 q^{2}\) \(-1.44031 q^{3}\) \(+2.55454 q^{4}\) \(+3.76689 q^{5}\) \(+3.07382 q^{6}\) \(+1.36855 q^{7}\) \(-1.18346 q^{8}\) \(-0.925504 q^{9}\) \(-8.03907 q^{10}\) \(-4.23559 q^{11}\) \(-3.67933 q^{12}\) \(+0.655939 q^{13}\) \(-2.92068 q^{14}\) \(-5.42550 q^{15}\) \(-2.58341 q^{16}\) \(+6.15511 q^{17}\) \(+1.97515 q^{18}\) \(-4.22451 q^{19}\) \(+9.62268 q^{20}\) \(-1.97114 q^{21}\) \(+9.03934 q^{22}\) \(-9.48602 q^{23}\) \(+1.70456 q^{24}\) \(+9.18950 q^{25}\) \(-1.39986 q^{26}\) \(+5.65395 q^{27}\) \(+3.49602 q^{28}\) \(+5.22133 q^{29}\) \(+11.5788 q^{30}\) \(+2.93870 q^{31}\) \(+7.88027 q^{32}\) \(+6.10057 q^{33}\) \(-13.1359 q^{34}\) \(+5.15519 q^{35}\) \(-2.36424 q^{36}\) \(-1.00000 q^{37}\) \(+9.01569 q^{38}\) \(-0.944756 q^{39}\) \(-4.45799 q^{40}\) \(-6.27351 q^{41}\) \(+4.20668 q^{42}\) \(+3.80023 q^{43}\) \(-10.8200 q^{44}\) \(-3.48628 q^{45}\) \(+20.2445 q^{46}\) \(-8.83363 q^{47}\) \(+3.72091 q^{48}\) \(-5.12707 q^{49}\) \(-19.6116 q^{50}\) \(-8.86528 q^{51}\) \(+1.67562 q^{52}\) \(+11.2691 q^{53}\) \(-12.0663 q^{54}\) \(-15.9550 q^{55}\) \(-1.61963 q^{56}\) \(+6.08461 q^{57}\) \(-11.1430 q^{58}\) \(-5.74271 q^{59}\) \(-13.8597 q^{60}\) \(-2.77791 q^{61}\) \(-6.27158 q^{62}\) \(-1.26660 q^{63}\) \(-11.6508 q^{64}\) \(+2.47085 q^{65}\) \(-13.0195 q^{66}\) \(-3.06684 q^{67}\) \(+15.7235 q^{68}\) \(+13.6628 q^{69}\) \(-11.0019 q^{70}\) \(+5.09721 q^{71}\) \(+1.09530 q^{72}\) \(-8.31385 q^{73}\) \(+2.13414 q^{74}\) \(-13.2357 q^{75}\) \(-10.7917 q^{76}\) \(-5.79663 q^{77}\) \(+2.01624 q^{78}\) \(-3.88915 q^{79}\) \(-9.73142 q^{80}\) \(-5.36693 q^{81}\) \(+13.3885 q^{82}\) \(-11.8513 q^{83}\) \(-5.03536 q^{84}\) \(+23.1857 q^{85}\) \(-8.11020 q^{86}\) \(-7.52033 q^{87}\) \(+5.01267 q^{88}\) \(-12.2838 q^{89}\) \(+7.44019 q^{90}\) \(+0.897687 q^{91}\) \(-24.2324 q^{92}\) \(-4.23264 q^{93}\) \(+18.8522 q^{94}\) \(-15.9133 q^{95}\) \(-11.3500 q^{96}\) \(+2.94967 q^{97}\) \(+10.9419 q^{98}\) \(+3.92006 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut -\mathstrut 13q^{10} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut -\mathstrut 40q^{12} \) \(\mathstrut -\mathstrut 18q^{13} \) \(\mathstrut -\mathstrut 42q^{14} \) \(\mathstrut -\mathstrut 49q^{15} \) \(\mathstrut +\mathstrut 83q^{16} \) \(\mathstrut -\mathstrut 62q^{17} \) \(\mathstrut -\mathstrut 33q^{18} \) \(\mathstrut -\mathstrut 25q^{19} \) \(\mathstrut -\mathstrut 39q^{20} \) \(\mathstrut -\mathstrut 15q^{21} \) \(\mathstrut -\mathstrut 31q^{22} \) \(\mathstrut -\mathstrut 94q^{23} \) \(\mathstrut -\mathstrut 39q^{24} \) \(\mathstrut +\mathstrut 71q^{25} \) \(\mathstrut -\mathstrut 35q^{26} \) \(\mathstrut -\mathstrut 47q^{27} \) \(\mathstrut -\mathstrut 13q^{28} \) \(\mathstrut -\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 15q^{30} \) \(\mathstrut -\mathstrut 37q^{31} \) \(\mathstrut -\mathstrut 105q^{32} \) \(\mathstrut -\mathstrut 60q^{33} \) \(\mathstrut +\mathstrut 9q^{34} \) \(\mathstrut -\mathstrut 60q^{35} \) \(\mathstrut +\mathstrut 43q^{36} \) \(\mathstrut -\mathstrut 79q^{37} \) \(\mathstrut -\mathstrut 80q^{38} \) \(\mathstrut -\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 64q^{40} \) \(\mathstrut -\mathstrut 37q^{41} \) \(\mathstrut -\mathstrut 30q^{42} \) \(\mathstrut -\mathstrut 20q^{43} \) \(\mathstrut -\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 8q^{45} \) \(\mathstrut +\mathstrut 61q^{46} \) \(\mathstrut -\mathstrut 148q^{47} \) \(\mathstrut -\mathstrut 39q^{48} \) \(\mathstrut +\mathstrut 82q^{49} \) \(\mathstrut -\mathstrut 90q^{50} \) \(\mathstrut -\mathstrut 45q^{51} \) \(\mathstrut -\mathstrut 27q^{52} \) \(\mathstrut -\mathstrut 70q^{53} \) \(\mathstrut -\mathstrut 41q^{54} \) \(\mathstrut -\mathstrut 105q^{55} \) \(\mathstrut -\mathstrut 68q^{56} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut -\mathstrut 14q^{58} \) \(\mathstrut -\mathstrut 96q^{59} \) \(\mathstrut -\mathstrut 74q^{60} \) \(\mathstrut -\mathstrut 21q^{61} \) \(\mathstrut +\mathstrut 4q^{62} \) \(\mathstrut -\mathstrut 60q^{63} \) \(\mathstrut +\mathstrut 132q^{64} \) \(\mathstrut -\mathstrut 15q^{65} \) \(\mathstrut +\mathstrut 71q^{66} \) \(\mathstrut -\mathstrut 44q^{67} \) \(\mathstrut -\mathstrut 166q^{68} \) \(\mathstrut -\mathstrut 72q^{69} \) \(\mathstrut -\mathstrut 9q^{70} \) \(\mathstrut -\mathstrut 55q^{71} \) \(\mathstrut -\mathstrut 126q^{72} \) \(\mathstrut -\mathstrut 27q^{73} \) \(\mathstrut +\mathstrut 11q^{74} \) \(\mathstrut -\mathstrut 39q^{75} \) \(\mathstrut -\mathstrut 4q^{76} \) \(\mathstrut -\mathstrut 104q^{77} \) \(\mathstrut -\mathstrut 47q^{78} \) \(\mathstrut -\mathstrut 49q^{79} \) \(\mathstrut -\mathstrut 82q^{80} \) \(\mathstrut +\mathstrut 55q^{81} \) \(\mathstrut +\mathstrut 20q^{82} \) \(\mathstrut -\mathstrut 52q^{83} \) \(\mathstrut -\mathstrut 29q^{84} \) \(\mathstrut +\mathstrut 3q^{85} \) \(\mathstrut -\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 113q^{87} \) \(\mathstrut +\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 68q^{89} \) \(\mathstrut -\mathstrut 39q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 179q^{92} \) \(\mathstrut -\mathstrut 53q^{93} \) \(\mathstrut -\mathstrut 33q^{94} \) \(\mathstrut -\mathstrut 86q^{95} \) \(\mathstrut +\mathstrut 33q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut -\mathstrut 116q^{98} \) \(\mathstrut +\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.13414 −1.50906 −0.754531 0.656264i \(-0.772136\pi\)
−0.754531 + 0.656264i \(0.772136\pi\)
\(3\) −1.44031 −0.831564 −0.415782 0.909464i \(-0.636492\pi\)
−0.415782 + 0.909464i \(0.636492\pi\)
\(4\) 2.55454 1.27727
\(5\) 3.76689 1.68461 0.842303 0.539004i \(-0.181199\pi\)
0.842303 + 0.539004i \(0.181199\pi\)
\(6\) 3.07382 1.25488
\(7\) 1.36855 0.517264 0.258632 0.965976i \(-0.416728\pi\)
0.258632 + 0.965976i \(0.416728\pi\)
\(8\) −1.18346 −0.418418
\(9\) −0.925504 −0.308501
\(10\) −8.03907 −2.54218
\(11\) −4.23559 −1.27708 −0.638540 0.769589i \(-0.720461\pi\)
−0.638540 + 0.769589i \(0.720461\pi\)
\(12\) −3.67933 −1.06213
\(13\) 0.655939 0.181925 0.0909624 0.995854i \(-0.471006\pi\)
0.0909624 + 0.995854i \(0.471006\pi\)
\(14\) −2.92068 −0.780584
\(15\) −5.42550 −1.40086
\(16\) −2.58341 −0.645851
\(17\) 6.15511 1.49283 0.746417 0.665478i \(-0.231772\pi\)
0.746417 + 0.665478i \(0.231772\pi\)
\(18\) 1.97515 0.465548
\(19\) −4.22451 −0.969170 −0.484585 0.874744i \(-0.661029\pi\)
−0.484585 + 0.874744i \(0.661029\pi\)
\(20\) 9.62268 2.15170
\(21\) −1.97114 −0.430138
\(22\) 9.03934 1.92719
\(23\) −9.48602 −1.97797 −0.988986 0.148007i \(-0.952714\pi\)
−0.988986 + 0.148007i \(0.952714\pi\)
\(24\) 1.70456 0.347941
\(25\) 9.18950 1.83790
\(26\) −1.39986 −0.274536
\(27\) 5.65395 1.08810
\(28\) 3.49602 0.660686
\(29\) 5.22133 0.969576 0.484788 0.874632i \(-0.338897\pi\)
0.484788 + 0.874632i \(0.338897\pi\)
\(30\) 11.5788 2.11398
\(31\) 2.93870 0.527805 0.263903 0.964549i \(-0.414990\pi\)
0.263903 + 0.964549i \(0.414990\pi\)
\(32\) 7.88027 1.39305
\(33\) 6.10057 1.06197
\(34\) −13.1359 −2.25278
\(35\) 5.15519 0.871386
\(36\) −2.36424 −0.394040
\(37\) −1.00000 −0.164399
\(38\) 9.01569 1.46254
\(39\) −0.944756 −0.151282
\(40\) −4.45799 −0.704869
\(41\) −6.27351 −0.979758 −0.489879 0.871791i \(-0.662959\pi\)
−0.489879 + 0.871791i \(0.662959\pi\)
\(42\) 4.20668 0.649105
\(43\) 3.80023 0.579529 0.289764 0.957098i \(-0.406423\pi\)
0.289764 + 0.957098i \(0.406423\pi\)
\(44\) −10.8200 −1.63118
\(45\) −3.48628 −0.519704
\(46\) 20.2445 2.98488
\(47\) −8.83363 −1.28852 −0.644258 0.764808i \(-0.722834\pi\)
−0.644258 + 0.764808i \(0.722834\pi\)
\(48\) 3.72091 0.537067
\(49\) −5.12707 −0.732438
\(50\) −19.6116 −2.77351
\(51\) −8.86528 −1.24139
\(52\) 1.67562 0.232367
\(53\) 11.2691 1.54793 0.773965 0.633228i \(-0.218271\pi\)
0.773965 + 0.633228i \(0.218271\pi\)
\(54\) −12.0663 −1.64201
\(55\) −15.9550 −2.15138
\(56\) −1.61963 −0.216432
\(57\) 6.08461 0.805927
\(58\) −11.1430 −1.46315
\(59\) −5.74271 −0.747637 −0.373819 0.927502i \(-0.621952\pi\)
−0.373819 + 0.927502i \(0.621952\pi\)
\(60\) −13.8597 −1.78927
\(61\) −2.77791 −0.355675 −0.177837 0.984060i \(-0.556910\pi\)
−0.177837 + 0.984060i \(0.556910\pi\)
\(62\) −6.27158 −0.796491
\(63\) −1.26660 −0.159577
\(64\) −11.6508 −1.45635
\(65\) 2.47085 0.306472
\(66\) −13.0195 −1.60258
\(67\) −3.06684 −0.374674 −0.187337 0.982296i \(-0.559986\pi\)
−0.187337 + 0.982296i \(0.559986\pi\)
\(68\) 15.7235 1.90675
\(69\) 13.6628 1.64481
\(70\) −11.0019 −1.31498
\(71\) 5.09721 0.604928 0.302464 0.953161i \(-0.402191\pi\)
0.302464 + 0.953161i \(0.402191\pi\)
\(72\) 1.09530 0.129083
\(73\) −8.31385 −0.973063 −0.486531 0.873663i \(-0.661738\pi\)
−0.486531 + 0.873663i \(0.661738\pi\)
\(74\) 2.13414 0.248088
\(75\) −13.2357 −1.52833
\(76\) −10.7917 −1.23789
\(77\) −5.79663 −0.660587
\(78\) 2.01624 0.228294
\(79\) −3.88915 −0.437564 −0.218782 0.975774i \(-0.570208\pi\)
−0.218782 + 0.975774i \(0.570208\pi\)
\(80\) −9.73142 −1.08801
\(81\) −5.36693 −0.596325
\(82\) 13.3885 1.47852
\(83\) −11.8513 −1.30085 −0.650424 0.759571i \(-0.725409\pi\)
−0.650424 + 0.759571i \(0.725409\pi\)
\(84\) −5.03536 −0.549402
\(85\) 23.1857 2.51484
\(86\) −8.11020 −0.874545
\(87\) −7.52033 −0.806264
\(88\) 5.01267 0.534353
\(89\) −12.2838 −1.30208 −0.651041 0.759042i \(-0.725667\pi\)
−0.651041 + 0.759042i \(0.725667\pi\)
\(90\) 7.44019 0.784265
\(91\) 0.897687 0.0941031
\(92\) −24.2324 −2.52641
\(93\) −4.23264 −0.438904
\(94\) 18.8522 1.94445
\(95\) −15.9133 −1.63267
\(96\) −11.3500 −1.15841
\(97\) 2.94967 0.299493 0.149747 0.988724i \(-0.452154\pi\)
0.149747 + 0.988724i \(0.452154\pi\)
\(98\) 10.9419 1.10529
\(99\) 3.92006 0.393981
\(100\) 23.4749 2.34749
\(101\) −0.425532 −0.0423420 −0.0211710 0.999776i \(-0.506739\pi\)
−0.0211710 + 0.999776i \(0.506739\pi\)
\(102\) 18.9197 1.87333
\(103\) 3.34237 0.329334 0.164667 0.986349i \(-0.447345\pi\)
0.164667 + 0.986349i \(0.447345\pi\)
\(104\) −0.776280 −0.0761206
\(105\) −7.42508 −0.724614
\(106\) −24.0498 −2.33592
\(107\) −5.85588 −0.566109 −0.283055 0.959104i \(-0.591348\pi\)
−0.283055 + 0.959104i \(0.591348\pi\)
\(108\) 14.4432 1.38980
\(109\) −1.00000 −0.0957826
\(110\) 34.0502 3.24656
\(111\) 1.44031 0.136708
\(112\) −3.53552 −0.334076
\(113\) 18.8082 1.76933 0.884664 0.466229i \(-0.154388\pi\)
0.884664 + 0.466229i \(0.154388\pi\)
\(114\) −12.9854 −1.21619
\(115\) −35.7329 −3.33211
\(116\) 13.3381 1.23841
\(117\) −0.607074 −0.0561240
\(118\) 12.2557 1.12823
\(119\) 8.42359 0.772190
\(120\) 6.42089 0.586144
\(121\) 6.94025 0.630932
\(122\) 5.92844 0.536736
\(123\) 9.03580 0.814731
\(124\) 7.50702 0.674150
\(125\) 15.7814 1.41153
\(126\) 2.70310 0.240811
\(127\) 4.72551 0.419321 0.209661 0.977774i \(-0.432764\pi\)
0.209661 + 0.977774i \(0.432764\pi\)
\(128\) 9.10378 0.804668
\(129\) −5.47351 −0.481915
\(130\) −5.27314 −0.462485
\(131\) −2.44067 −0.213242 −0.106621 0.994300i \(-0.534003\pi\)
−0.106621 + 0.994300i \(0.534003\pi\)
\(132\) 15.5842 1.35643
\(133\) −5.78147 −0.501317
\(134\) 6.54505 0.565406
\(135\) 21.2978 1.83302
\(136\) −7.28436 −0.624629
\(137\) 14.5983 1.24721 0.623606 0.781738i \(-0.285667\pi\)
0.623606 + 0.781738i \(0.285667\pi\)
\(138\) −29.1583 −2.48212
\(139\) −9.29174 −0.788115 −0.394057 0.919086i \(-0.628929\pi\)
−0.394057 + 0.919086i \(0.628929\pi\)
\(140\) 13.1691 1.11300
\(141\) 12.7232 1.07148
\(142\) −10.8781 −0.912874
\(143\) −2.77829 −0.232332
\(144\) 2.39095 0.199246
\(145\) 19.6682 1.63335
\(146\) 17.7429 1.46841
\(147\) 7.38457 0.609069
\(148\) −2.55454 −0.209982
\(149\) −6.01718 −0.492947 −0.246473 0.969150i \(-0.579272\pi\)
−0.246473 + 0.969150i \(0.579272\pi\)
\(150\) 28.2469 2.30635
\(151\) −10.6290 −0.864978 −0.432489 0.901639i \(-0.642365\pi\)
−0.432489 + 0.901639i \(0.642365\pi\)
\(152\) 4.99956 0.405518
\(153\) −5.69659 −0.460542
\(154\) 12.3708 0.996867
\(155\) 11.0698 0.889144
\(156\) −2.41342 −0.193228
\(157\) −20.1730 −1.60998 −0.804992 0.593286i \(-0.797830\pi\)
−0.804992 + 0.593286i \(0.797830\pi\)
\(158\) 8.29998 0.660311
\(159\) −16.2310 −1.28720
\(160\) 29.6841 2.34674
\(161\) −12.9821 −1.02313
\(162\) 11.4538 0.899892
\(163\) 21.0937 1.65219 0.826094 0.563532i \(-0.190558\pi\)
0.826094 + 0.563532i \(0.190558\pi\)
\(164\) −16.0259 −1.25141
\(165\) 22.9802 1.78901
\(166\) 25.2923 1.96306
\(167\) −16.4511 −1.27302 −0.636511 0.771268i \(-0.719623\pi\)
−0.636511 + 0.771268i \(0.719623\pi\)
\(168\) 2.33277 0.179977
\(169\) −12.5697 −0.966903
\(170\) −49.4814 −3.79505
\(171\) 3.90981 0.298990
\(172\) 9.70783 0.740215
\(173\) −4.92314 −0.374299 −0.187150 0.982331i \(-0.559925\pi\)
−0.187150 + 0.982331i \(0.559925\pi\)
\(174\) 16.0494 1.21670
\(175\) 12.5763 0.950679
\(176\) 10.9423 0.824803
\(177\) 8.27129 0.621708
\(178\) 26.2154 1.96492
\(179\) −10.5122 −0.785716 −0.392858 0.919599i \(-0.628514\pi\)
−0.392858 + 0.919599i \(0.628514\pi\)
\(180\) −8.90584 −0.663802
\(181\) −3.29512 −0.244924 −0.122462 0.992473i \(-0.539079\pi\)
−0.122462 + 0.992473i \(0.539079\pi\)
\(182\) −1.91579 −0.142008
\(183\) 4.00105 0.295766
\(184\) 11.2264 0.827619
\(185\) −3.76689 −0.276948
\(186\) 9.03302 0.662333
\(187\) −26.0706 −1.90647
\(188\) −22.5659 −1.64578
\(189\) 7.73772 0.562836
\(190\) 33.9612 2.46380
\(191\) 20.8180 1.50634 0.753170 0.657826i \(-0.228524\pi\)
0.753170 + 0.657826i \(0.228524\pi\)
\(192\) 16.7807 1.21104
\(193\) 6.40909 0.461336 0.230668 0.973032i \(-0.425909\pi\)
0.230668 + 0.973032i \(0.425909\pi\)
\(194\) −6.29500 −0.451954
\(195\) −3.55880 −0.254851
\(196\) −13.0973 −0.935521
\(197\) −18.9202 −1.34801 −0.674003 0.738729i \(-0.735426\pi\)
−0.674003 + 0.738729i \(0.735426\pi\)
\(198\) −8.36594 −0.594542
\(199\) 7.33651 0.520071 0.260036 0.965599i \(-0.416266\pi\)
0.260036 + 0.965599i \(0.416266\pi\)
\(200\) −10.8754 −0.769010
\(201\) 4.41720 0.311565
\(202\) 0.908144 0.0638968
\(203\) 7.14565 0.501527
\(204\) −22.6467 −1.58559
\(205\) −23.6317 −1.65051
\(206\) −7.13308 −0.496985
\(207\) 8.77936 0.610207
\(208\) −1.69456 −0.117496
\(209\) 17.8933 1.23771
\(210\) 15.8461 1.09349
\(211\) 18.6094 1.28113 0.640563 0.767906i \(-0.278701\pi\)
0.640563 + 0.767906i \(0.278701\pi\)
\(212\) 28.7874 1.97712
\(213\) −7.34157 −0.503036
\(214\) 12.4972 0.854294
\(215\) 14.3150 0.976278
\(216\) −6.69124 −0.455282
\(217\) 4.02176 0.273015
\(218\) 2.13414 0.144542
\(219\) 11.9745 0.809164
\(220\) −40.7578 −2.74789
\(221\) 4.03738 0.271584
\(222\) −3.07382 −0.206301
\(223\) 11.8957 0.796593 0.398297 0.917257i \(-0.369601\pi\)
0.398297 + 0.917257i \(0.369601\pi\)
\(224\) 10.7846 0.720574
\(225\) −8.50492 −0.566995
\(226\) −40.1393 −2.67003
\(227\) −9.19316 −0.610172 −0.305086 0.952325i \(-0.598685\pi\)
−0.305086 + 0.952325i \(0.598685\pi\)
\(228\) 15.5434 1.02939
\(229\) 7.32489 0.484042 0.242021 0.970271i \(-0.422190\pi\)
0.242021 + 0.970271i \(0.422190\pi\)
\(230\) 76.2588 5.02836
\(231\) 8.34895 0.549320
\(232\) −6.17925 −0.405688
\(233\) −5.87895 −0.385143 −0.192571 0.981283i \(-0.561683\pi\)
−0.192571 + 0.981283i \(0.561683\pi\)
\(234\) 1.29558 0.0846947
\(235\) −33.2753 −2.17064
\(236\) −14.6700 −0.954935
\(237\) 5.60159 0.363862
\(238\) −17.9771 −1.16528
\(239\) 23.9499 1.54919 0.774595 0.632458i \(-0.217954\pi\)
0.774595 + 0.632458i \(0.217954\pi\)
\(240\) 14.0163 0.904746
\(241\) 16.4993 1.06281 0.531406 0.847117i \(-0.321664\pi\)
0.531406 + 0.847117i \(0.321664\pi\)
\(242\) −14.8114 −0.952116
\(243\) −9.23180 −0.592220
\(244\) −7.09628 −0.454293
\(245\) −19.3131 −1.23387
\(246\) −19.2836 −1.22948
\(247\) −2.77102 −0.176316
\(248\) −3.47784 −0.220843
\(249\) 17.0695 1.08174
\(250\) −33.6797 −2.13009
\(251\) −21.7809 −1.37480 −0.687400 0.726279i \(-0.741248\pi\)
−0.687400 + 0.726279i \(0.741248\pi\)
\(252\) −3.23558 −0.203823
\(253\) 40.1789 2.52603
\(254\) −10.0849 −0.632782
\(255\) −33.3946 −2.09125
\(256\) 3.87281 0.242050
\(257\) −27.4537 −1.71251 −0.856257 0.516549i \(-0.827216\pi\)
−0.856257 + 0.516549i \(0.827216\pi\)
\(258\) 11.6812 0.727240
\(259\) −1.36855 −0.0850377
\(260\) 6.31189 0.391447
\(261\) −4.83236 −0.299116
\(262\) 5.20871 0.321795
\(263\) −19.0482 −1.17456 −0.587281 0.809383i \(-0.699802\pi\)
−0.587281 + 0.809383i \(0.699802\pi\)
\(264\) −7.21981 −0.444348
\(265\) 42.4495 2.60765
\(266\) 12.3384 0.756519
\(267\) 17.6925 1.08276
\(268\) −7.83436 −0.478560
\(269\) −28.1125 −1.71405 −0.857026 0.515274i \(-0.827690\pi\)
−0.857026 + 0.515274i \(0.827690\pi\)
\(270\) −45.4525 −2.76615
\(271\) 7.39562 0.449252 0.224626 0.974445i \(-0.427884\pi\)
0.224626 + 0.974445i \(0.427884\pi\)
\(272\) −15.9012 −0.964149
\(273\) −1.29295 −0.0782528
\(274\) −31.1547 −1.88212
\(275\) −38.9230 −2.34714
\(276\) 34.9022 2.10087
\(277\) −5.92276 −0.355864 −0.177932 0.984043i \(-0.556941\pi\)
−0.177932 + 0.984043i \(0.556941\pi\)
\(278\) 19.8298 1.18931
\(279\) −2.71978 −0.162829
\(280\) −6.10099 −0.364604
\(281\) 28.0893 1.67567 0.837834 0.545924i \(-0.183821\pi\)
0.837834 + 0.545924i \(0.183821\pi\)
\(282\) −27.1530 −1.61694
\(283\) 21.2649 1.26407 0.632033 0.774942i \(-0.282221\pi\)
0.632033 + 0.774942i \(0.282221\pi\)
\(284\) 13.0210 0.772656
\(285\) 22.9201 1.35767
\(286\) 5.92925 0.350604
\(287\) −8.58562 −0.506793
\(288\) −7.29322 −0.429757
\(289\) 20.8854 1.22856
\(290\) −41.9746 −2.46483
\(291\) −4.24844 −0.249048
\(292\) −21.2381 −1.24286
\(293\) −18.5883 −1.08594 −0.542971 0.839751i \(-0.682701\pi\)
−0.542971 + 0.839751i \(0.682701\pi\)
\(294\) −15.7597 −0.919123
\(295\) −21.6322 −1.25947
\(296\) 1.18346 0.0687875
\(297\) −23.9478 −1.38959
\(298\) 12.8415 0.743888
\(299\) −6.22225 −0.359842
\(300\) −33.8112 −1.95209
\(301\) 5.20081 0.299769
\(302\) 22.6838 1.30531
\(303\) 0.612899 0.0352101
\(304\) 10.9136 0.625940
\(305\) −10.4641 −0.599172
\(306\) 12.1573 0.694986
\(307\) −15.0461 −0.858725 −0.429363 0.903132i \(-0.641262\pi\)
−0.429363 + 0.903132i \(0.641262\pi\)
\(308\) −14.8077 −0.843748
\(309\) −4.81405 −0.273862
\(310\) −23.6244 −1.34177
\(311\) −23.7016 −1.34399 −0.671996 0.740555i \(-0.734563\pi\)
−0.671996 + 0.740555i \(0.734563\pi\)
\(312\) 1.11809 0.0632991
\(313\) 5.26113 0.297377 0.148688 0.988884i \(-0.452495\pi\)
0.148688 + 0.988884i \(0.452495\pi\)
\(314\) 43.0520 2.42957
\(315\) −4.77115 −0.268824
\(316\) −9.93500 −0.558887
\(317\) 6.33348 0.355723 0.177862 0.984055i \(-0.443082\pi\)
0.177862 + 0.984055i \(0.443082\pi\)
\(318\) 34.6392 1.94247
\(319\) −22.1154 −1.23823
\(320\) −43.8872 −2.45337
\(321\) 8.43429 0.470756
\(322\) 27.7056 1.54397
\(323\) −26.0024 −1.44681
\(324\) −13.7100 −0.761669
\(325\) 6.02775 0.334359
\(326\) −45.0169 −2.49326
\(327\) 1.44031 0.0796494
\(328\) 7.42447 0.409948
\(329\) −12.0893 −0.666503
\(330\) −49.0429 −2.69972
\(331\) −7.89057 −0.433705 −0.216853 0.976204i \(-0.569579\pi\)
−0.216853 + 0.976204i \(0.569579\pi\)
\(332\) −30.2746 −1.66153
\(333\) 0.925504 0.0507173
\(334\) 35.1088 1.92107
\(335\) −11.5525 −0.631178
\(336\) 5.09225 0.277805
\(337\) −26.5677 −1.44724 −0.723618 0.690201i \(-0.757522\pi\)
−0.723618 + 0.690201i \(0.757522\pi\)
\(338\) 26.8256 1.45912
\(339\) −27.0897 −1.47131
\(340\) 59.2287 3.21213
\(341\) −12.4471 −0.674049
\(342\) −8.34406 −0.451195
\(343\) −16.5965 −0.896128
\(344\) −4.49743 −0.242485
\(345\) 51.4664 2.77086
\(346\) 10.5067 0.564841
\(347\) −0.918185 −0.0492907 −0.0246454 0.999696i \(-0.507846\pi\)
−0.0246454 + 0.999696i \(0.507846\pi\)
\(348\) −19.2110 −1.02982
\(349\) 13.0948 0.700950 0.350475 0.936572i \(-0.386020\pi\)
0.350475 + 0.936572i \(0.386020\pi\)
\(350\) −26.8396 −1.43463
\(351\) 3.70864 0.197953
\(352\) −33.3776 −1.77903
\(353\) 9.58472 0.510143 0.255072 0.966922i \(-0.417901\pi\)
0.255072 + 0.966922i \(0.417901\pi\)
\(354\) −17.6521 −0.938197
\(355\) 19.2007 1.01907
\(356\) −31.3795 −1.66311
\(357\) −12.1326 −0.642125
\(358\) 22.4344 1.18569
\(359\) −21.5381 −1.13674 −0.568370 0.822773i \(-0.692426\pi\)
−0.568370 + 0.822773i \(0.692426\pi\)
\(360\) 4.12589 0.217453
\(361\) −1.15347 −0.0607092
\(362\) 7.03224 0.369606
\(363\) −9.99612 −0.524660
\(364\) 2.29318 0.120195
\(365\) −31.3174 −1.63923
\(366\) −8.53880 −0.446330
\(367\) −0.944153 −0.0492844 −0.0246422 0.999696i \(-0.507845\pi\)
−0.0246422 + 0.999696i \(0.507845\pi\)
\(368\) 24.5062 1.27748
\(369\) 5.80616 0.302257
\(370\) 8.03907 0.417931
\(371\) 15.4223 0.800689
\(372\) −10.8124 −0.560599
\(373\) −33.1288 −1.71535 −0.857673 0.514196i \(-0.828090\pi\)
−0.857673 + 0.514196i \(0.828090\pi\)
\(374\) 55.6381 2.87698
\(375\) −22.7301 −1.17378
\(376\) 10.4543 0.539138
\(377\) 3.42487 0.176390
\(378\) −16.5134 −0.849355
\(379\) 14.6053 0.750224 0.375112 0.926980i \(-0.377604\pi\)
0.375112 + 0.926980i \(0.377604\pi\)
\(380\) −40.6512 −2.08536
\(381\) −6.80621 −0.348693
\(382\) −44.4285 −2.27316
\(383\) −6.41574 −0.327829 −0.163914 0.986475i \(-0.552412\pi\)
−0.163914 + 0.986475i \(0.552412\pi\)
\(384\) −13.1123 −0.669133
\(385\) −21.8353 −1.11283
\(386\) −13.6779 −0.696185
\(387\) −3.51713 −0.178786
\(388\) 7.53505 0.382534
\(389\) 13.2814 0.673392 0.336696 0.941613i \(-0.390690\pi\)
0.336696 + 0.941613i \(0.390690\pi\)
\(390\) 7.59496 0.384586
\(391\) −58.3876 −2.95279
\(392\) 6.06770 0.306465
\(393\) 3.51532 0.177324
\(394\) 40.3782 2.03422
\(395\) −14.6500 −0.737123
\(396\) 10.0140 0.503220
\(397\) −27.3528 −1.37280 −0.686399 0.727225i \(-0.740810\pi\)
−0.686399 + 0.727225i \(0.740810\pi\)
\(398\) −15.6571 −0.784820
\(399\) 8.32711 0.416877
\(400\) −23.7402 −1.18701
\(401\) −0.492392 −0.0245889 −0.0122944 0.999924i \(-0.503914\pi\)
−0.0122944 + 0.999924i \(0.503914\pi\)
\(402\) −9.42691 −0.470172
\(403\) 1.92760 0.0960208
\(404\) −1.08704 −0.0540822
\(405\) −20.2167 −1.00457
\(406\) −15.2498 −0.756835
\(407\) 4.23559 0.209951
\(408\) 10.4917 0.519419
\(409\) −27.4873 −1.35916 −0.679581 0.733601i \(-0.737838\pi\)
−0.679581 + 0.733601i \(0.737838\pi\)
\(410\) 50.4332 2.49072
\(411\) −21.0260 −1.03714
\(412\) 8.53822 0.420648
\(413\) −7.85920 −0.386726
\(414\) −18.7363 −0.920841
\(415\) −44.6426 −2.19142
\(416\) 5.16898 0.253430
\(417\) 13.3830 0.655368
\(418\) −38.1868 −1.86778
\(419\) −4.38441 −0.214193 −0.107096 0.994249i \(-0.534155\pi\)
−0.107096 + 0.994249i \(0.534155\pi\)
\(420\) −18.9677 −0.925527
\(421\) 24.2082 1.17984 0.589918 0.807463i \(-0.299160\pi\)
0.589918 + 0.807463i \(0.299160\pi\)
\(422\) −39.7150 −1.93330
\(423\) 8.17556 0.397509
\(424\) −13.3366 −0.647681
\(425\) 56.5624 2.74368
\(426\) 15.6679 0.759113
\(427\) −3.80171 −0.183978
\(428\) −14.9591 −0.723074
\(429\) 4.00160 0.193199
\(430\) −30.5503 −1.47327
\(431\) 7.87818 0.379478 0.189739 0.981835i \(-0.439236\pi\)
0.189739 + 0.981835i \(0.439236\pi\)
\(432\) −14.6064 −0.702753
\(433\) −28.2580 −1.35799 −0.678996 0.734142i \(-0.737585\pi\)
−0.678996 + 0.734142i \(0.737585\pi\)
\(434\) −8.58298 −0.411996
\(435\) −28.3283 −1.35824
\(436\) −2.55454 −0.122340
\(437\) 40.0738 1.91699
\(438\) −25.5553 −1.22108
\(439\) 32.8960 1.57004 0.785021 0.619470i \(-0.212652\pi\)
0.785021 + 0.619470i \(0.212652\pi\)
\(440\) 18.8822 0.900174
\(441\) 4.74512 0.225958
\(442\) −8.61632 −0.409837
\(443\) −14.9879 −0.712095 −0.356047 0.934468i \(-0.615876\pi\)
−0.356047 + 0.934468i \(0.615876\pi\)
\(444\) 3.67933 0.174613
\(445\) −46.2719 −2.19350
\(446\) −25.3870 −1.20211
\(447\) 8.66662 0.409917
\(448\) −15.9447 −0.753315
\(449\) −19.8560 −0.937064 −0.468532 0.883446i \(-0.655217\pi\)
−0.468532 + 0.883446i \(0.655217\pi\)
\(450\) 18.1507 0.855631
\(451\) 26.5720 1.25123
\(452\) 48.0464 2.25991
\(453\) 15.3091 0.719284
\(454\) 19.6195 0.920787
\(455\) 3.38149 0.158527
\(456\) −7.20092 −0.337214
\(457\) 23.3544 1.09247 0.546236 0.837631i \(-0.316060\pi\)
0.546236 + 0.837631i \(0.316060\pi\)
\(458\) −15.6323 −0.730450
\(459\) 34.8007 1.62436
\(460\) −91.2810 −4.25600
\(461\) −13.3668 −0.622555 −0.311278 0.950319i \(-0.600757\pi\)
−0.311278 + 0.950319i \(0.600757\pi\)
\(462\) −17.8178 −0.828959
\(463\) 9.81123 0.455966 0.227983 0.973665i \(-0.426787\pi\)
0.227983 + 0.973665i \(0.426787\pi\)
\(464\) −13.4888 −0.626202
\(465\) −15.9439 −0.739380
\(466\) 12.5465 0.581205
\(467\) 32.5987 1.50849 0.754244 0.656594i \(-0.228003\pi\)
0.754244 + 0.656594i \(0.228003\pi\)
\(468\) −1.55080 −0.0716856
\(469\) −4.19713 −0.193805
\(470\) 71.0141 3.27564
\(471\) 29.0554 1.33880
\(472\) 6.79629 0.312825
\(473\) −16.0962 −0.740104
\(474\) −11.9546 −0.549091
\(475\) −38.8212 −1.78124
\(476\) 21.5184 0.986295
\(477\) −10.4296 −0.477539
\(478\) −51.1123 −2.33782
\(479\) −18.9961 −0.867952 −0.433976 0.900924i \(-0.642890\pi\)
−0.433976 + 0.900924i \(0.642890\pi\)
\(480\) −42.7544 −1.95146
\(481\) −0.655939 −0.0299082
\(482\) −35.2117 −1.60385
\(483\) 18.6983 0.850801
\(484\) 17.7291 0.805870
\(485\) 11.1111 0.504529
\(486\) 19.7019 0.893697
\(487\) 9.44711 0.428090 0.214045 0.976824i \(-0.431336\pi\)
0.214045 + 0.976824i \(0.431336\pi\)
\(488\) 3.28756 0.148821
\(489\) −30.3815 −1.37390
\(490\) 41.2168 1.86199
\(491\) 31.4925 1.42124 0.710619 0.703577i \(-0.248415\pi\)
0.710619 + 0.703577i \(0.248415\pi\)
\(492\) 23.0823 1.04063
\(493\) 32.1379 1.44742
\(494\) 5.91374 0.266072
\(495\) 14.7665 0.663703
\(496\) −7.59184 −0.340884
\(497\) 6.97580 0.312907
\(498\) −36.4287 −1.63241
\(499\) 1.61594 0.0723394 0.0361697 0.999346i \(-0.488484\pi\)
0.0361697 + 0.999346i \(0.488484\pi\)
\(500\) 40.3142 1.80291
\(501\) 23.6946 1.05860
\(502\) 46.4835 2.07466
\(503\) −26.6470 −1.18813 −0.594066 0.804416i \(-0.702478\pi\)
−0.594066 + 0.804416i \(0.702478\pi\)
\(504\) 1.49898 0.0667697
\(505\) −1.60294 −0.0713297
\(506\) −85.7474 −3.81193
\(507\) 18.1043 0.804042
\(508\) 12.0715 0.535587
\(509\) −33.1932 −1.47126 −0.735632 0.677381i \(-0.763115\pi\)
−0.735632 + 0.677381i \(0.763115\pi\)
\(510\) 71.2686 3.15583
\(511\) −11.3779 −0.503330
\(512\) −26.4727 −1.16994
\(513\) −23.8852 −1.05456
\(514\) 58.5900 2.58429
\(515\) 12.5904 0.554798
\(516\) −13.9823 −0.615536
\(517\) 37.4157 1.64554
\(518\) 2.92068 0.128327
\(519\) 7.09085 0.311254
\(520\) −2.92417 −0.128233
\(521\) 14.0609 0.616021 0.308010 0.951383i \(-0.400337\pi\)
0.308010 + 0.951383i \(0.400337\pi\)
\(522\) 10.3129 0.451384
\(523\) 2.53820 0.110988 0.0554940 0.998459i \(-0.482327\pi\)
0.0554940 + 0.998459i \(0.482327\pi\)
\(524\) −6.23478 −0.272368
\(525\) −18.1138 −0.790551
\(526\) 40.6515 1.77249
\(527\) 18.0880 0.787926
\(528\) −15.7602 −0.685877
\(529\) 66.9847 2.91238
\(530\) −90.5931 −3.93511
\(531\) 5.31490 0.230647
\(532\) −14.7690 −0.640317
\(533\) −4.11504 −0.178242
\(534\) −37.7583 −1.63396
\(535\) −22.0585 −0.953671
\(536\) 3.62949 0.156770
\(537\) 15.1408 0.653373
\(538\) 59.9960 2.58661
\(539\) 21.7162 0.935381
\(540\) 54.4061 2.34127
\(541\) 8.15077 0.350429 0.175214 0.984530i \(-0.443938\pi\)
0.175214 + 0.984530i \(0.443938\pi\)
\(542\) −15.7833 −0.677950
\(543\) 4.74600 0.203670
\(544\) 48.5040 2.07959
\(545\) −3.76689 −0.161356
\(546\) 2.75933 0.118088
\(547\) 1.65530 0.0707754 0.0353877 0.999374i \(-0.488733\pi\)
0.0353877 + 0.999374i \(0.488733\pi\)
\(548\) 37.2918 1.59303
\(549\) 2.57097 0.109726
\(550\) 83.0670 3.54199
\(551\) −22.0576 −0.939684
\(552\) −16.1695 −0.688218
\(553\) −5.32251 −0.226336
\(554\) 12.6400 0.537021
\(555\) 5.42550 0.230300
\(556\) −23.7361 −1.00664
\(557\) 41.4994 1.75839 0.879193 0.476466i \(-0.158083\pi\)
0.879193 + 0.476466i \(0.158083\pi\)
\(558\) 5.80437 0.245719
\(559\) 2.49272 0.105431
\(560\) −13.3179 −0.562786
\(561\) 37.5497 1.58535
\(562\) −59.9465 −2.52869
\(563\) 1.36805 0.0576565 0.0288283 0.999584i \(-0.490822\pi\)
0.0288283 + 0.999584i \(0.490822\pi\)
\(564\) 32.5018 1.36857
\(565\) 70.8486 2.98062
\(566\) −45.3821 −1.90755
\(567\) −7.34492 −0.308458
\(568\) −6.03237 −0.253113
\(569\) −42.5324 −1.78305 −0.891525 0.452972i \(-0.850364\pi\)
−0.891525 + 0.452972i \(0.850364\pi\)
\(570\) −48.9146 −2.04881
\(571\) 20.1118 0.841654 0.420827 0.907141i \(-0.361740\pi\)
0.420827 + 0.907141i \(0.361740\pi\)
\(572\) −7.09725 −0.296751
\(573\) −29.9844 −1.25262
\(574\) 18.3229 0.764783
\(575\) −87.1718 −3.63532
\(576\) 10.7828 0.449285
\(577\) −7.39345 −0.307793 −0.153897 0.988087i \(-0.549182\pi\)
−0.153897 + 0.988087i \(0.549182\pi\)
\(578\) −44.5724 −1.85397
\(579\) −9.23108 −0.383631
\(580\) 50.2432 2.08623
\(581\) −16.2191 −0.672882
\(582\) 9.06675 0.375829
\(583\) −47.7313 −1.97683
\(584\) 9.83915 0.407147
\(585\) −2.28679 −0.0945469
\(586\) 39.6701 1.63876
\(587\) −0.977209 −0.0403337 −0.0201669 0.999797i \(-0.506420\pi\)
−0.0201669 + 0.999797i \(0.506420\pi\)
\(588\) 18.8642 0.777945
\(589\) −12.4146 −0.511533
\(590\) 46.1661 1.90063
\(591\) 27.2509 1.12095
\(592\) 2.58341 0.106177
\(593\) −5.61013 −0.230381 −0.115190 0.993343i \(-0.536748\pi\)
−0.115190 + 0.993343i \(0.536748\pi\)
\(594\) 51.1079 2.09698
\(595\) 31.7308 1.30084
\(596\) −15.3711 −0.629626
\(597\) −10.5669 −0.432473
\(598\) 13.2791 0.543024
\(599\) 0.586628 0.0239690 0.0119845 0.999928i \(-0.496185\pi\)
0.0119845 + 0.999928i \(0.496185\pi\)
\(600\) 15.6640 0.639481
\(601\) −26.7621 −1.09165 −0.545825 0.837900i \(-0.683783\pi\)
−0.545825 + 0.837900i \(0.683783\pi\)
\(602\) −11.0992 −0.452371
\(603\) 2.83837 0.115587
\(604\) −27.1523 −1.10481
\(605\) 26.1432 1.06287
\(606\) −1.30801 −0.0531343
\(607\) −28.1114 −1.14101 −0.570504 0.821295i \(-0.693252\pi\)
−0.570504 + 0.821295i \(0.693252\pi\)
\(608\) −33.2903 −1.35010
\(609\) −10.2920 −0.417051
\(610\) 22.3318 0.904189
\(611\) −5.79432 −0.234413
\(612\) −14.5522 −0.588236
\(613\) 5.88354 0.237634 0.118817 0.992916i \(-0.462090\pi\)
0.118817 + 0.992916i \(0.462090\pi\)
\(614\) 32.1104 1.29587
\(615\) 34.0369 1.37250
\(616\) 6.86010 0.276401
\(617\) −43.7079 −1.75961 −0.879807 0.475331i \(-0.842328\pi\)
−0.879807 + 0.475331i \(0.842328\pi\)
\(618\) 10.2739 0.413275
\(619\) 11.2102 0.450577 0.225289 0.974292i \(-0.427667\pi\)
0.225289 + 0.974292i \(0.427667\pi\)
\(620\) 28.2781 1.13568
\(621\) −53.6335 −2.15224
\(622\) 50.5824 2.02817
\(623\) −16.8110 −0.673520
\(624\) 2.44069 0.0977057
\(625\) 13.4994 0.539975
\(626\) −11.2280 −0.448760
\(627\) −25.7720 −1.02923
\(628\) −51.5328 −2.05638
\(629\) −6.15511 −0.245421
\(630\) 10.1823 0.405672
\(631\) 34.6028 1.37751 0.688757 0.724992i \(-0.258157\pi\)
0.688757 + 0.724992i \(0.258157\pi\)
\(632\) 4.60267 0.183084
\(633\) −26.8033 −1.06534
\(634\) −13.5165 −0.536809
\(635\) 17.8005 0.706392
\(636\) −41.4628 −1.64411
\(637\) −3.36304 −0.133249
\(638\) 47.1973 1.86856
\(639\) −4.71749 −0.186621
\(640\) 34.2930 1.35555
\(641\) 7.71866 0.304869 0.152434 0.988314i \(-0.451289\pi\)
0.152434 + 0.988314i \(0.451289\pi\)
\(642\) −17.9999 −0.710400
\(643\) 16.4823 0.650000 0.325000 0.945714i \(-0.394636\pi\)
0.325000 + 0.945714i \(0.394636\pi\)
\(644\) −33.1633 −1.30682
\(645\) −20.6181 −0.811838
\(646\) 55.4926 2.18333
\(647\) 7.55485 0.297012 0.148506 0.988912i \(-0.452554\pi\)
0.148506 + 0.988912i \(0.452554\pi\)
\(648\) 6.35157 0.249513
\(649\) 24.3238 0.954792
\(650\) −12.8640 −0.504569
\(651\) −5.79258 −0.227029
\(652\) 53.8848 2.11029
\(653\) −9.64330 −0.377371 −0.188686 0.982038i \(-0.560423\pi\)
−0.188686 + 0.982038i \(0.560423\pi\)
\(654\) −3.07382 −0.120196
\(655\) −9.19373 −0.359229
\(656\) 16.2070 0.632778
\(657\) 7.69451 0.300191
\(658\) 25.8002 1.00580
\(659\) −41.2168 −1.60558 −0.802790 0.596262i \(-0.796652\pi\)
−0.802790 + 0.596262i \(0.796652\pi\)
\(660\) 58.7039 2.28504
\(661\) 40.6401 1.58072 0.790359 0.612644i \(-0.209894\pi\)
0.790359 + 0.612644i \(0.209894\pi\)
\(662\) 16.8396 0.654488
\(663\) −5.81508 −0.225839
\(664\) 14.0256 0.544298
\(665\) −21.7782 −0.844522
\(666\) −1.97515 −0.0765356
\(667\) −49.5296 −1.91779
\(668\) −42.0249 −1.62599
\(669\) −17.1335 −0.662418
\(670\) 24.6545 0.952487
\(671\) 11.7661 0.454225
\(672\) −15.5331 −0.599203
\(673\) 10.4961 0.404594 0.202297 0.979324i \(-0.435159\pi\)
0.202297 + 0.979324i \(0.435159\pi\)
\(674\) 56.6992 2.18397
\(675\) 51.9569 1.99982
\(676\) −32.1099 −1.23500
\(677\) −46.9452 −1.80425 −0.902125 0.431474i \(-0.857994\pi\)
−0.902125 + 0.431474i \(0.857994\pi\)
\(678\) 57.8131 2.22030
\(679\) 4.03677 0.154917
\(680\) −27.4394 −1.05225
\(681\) 13.2410 0.507397
\(682\) 26.5639 1.01718
\(683\) −26.5916 −1.01750 −0.508750 0.860914i \(-0.669892\pi\)
−0.508750 + 0.860914i \(0.669892\pi\)
\(684\) 9.98776 0.381891
\(685\) 54.9901 2.10106
\(686\) 35.4192 1.35231
\(687\) −10.5501 −0.402512
\(688\) −9.81752 −0.374290
\(689\) 7.39184 0.281607
\(690\) −109.836 −4.18140
\(691\) −42.3694 −1.61181 −0.805903 0.592047i \(-0.798320\pi\)
−0.805903 + 0.592047i \(0.798320\pi\)
\(692\) −12.5764 −0.478081
\(693\) 5.36481 0.203792
\(694\) 1.95953 0.0743828
\(695\) −35.0010 −1.32766
\(696\) 8.90004 0.337355
\(697\) −38.6142 −1.46262
\(698\) −27.9462 −1.05778
\(699\) 8.46752 0.320271
\(700\) 32.1267 1.21427
\(701\) −25.9240 −0.979134 −0.489567 0.871966i \(-0.662845\pi\)
−0.489567 + 0.871966i \(0.662845\pi\)
\(702\) −7.91475 −0.298723
\(703\) 4.22451 0.159331
\(704\) 49.3479 1.85987
\(705\) 47.9268 1.80503
\(706\) −20.4551 −0.769838
\(707\) −0.582363 −0.0219020
\(708\) 21.1293 0.794089
\(709\) 42.6047 1.60005 0.800027 0.599964i \(-0.204819\pi\)
0.800027 + 0.599964i \(0.204819\pi\)
\(710\) −40.9768 −1.53783
\(711\) 3.59943 0.134989
\(712\) 14.5375 0.544814
\(713\) −27.8765 −1.04398
\(714\) 25.8926 0.969007
\(715\) −10.4655 −0.391389
\(716\) −26.8537 −1.00357
\(717\) −34.4953 −1.28825
\(718\) 45.9653 1.71541
\(719\) 22.0989 0.824150 0.412075 0.911150i \(-0.364804\pi\)
0.412075 + 0.911150i \(0.364804\pi\)
\(720\) 9.00647 0.335651
\(721\) 4.57421 0.170352
\(722\) 2.46167 0.0916140
\(723\) −23.7641 −0.883796
\(724\) −8.41752 −0.312835
\(725\) 47.9814 1.78198
\(726\) 21.3331 0.791745
\(727\) −2.79577 −0.103689 −0.0518446 0.998655i \(-0.516510\pi\)
−0.0518446 + 0.998655i \(0.516510\pi\)
\(728\) −1.06238 −0.0393744
\(729\) 29.3974 1.08879
\(730\) 66.8356 2.47370
\(731\) 23.3908 0.865141
\(732\) 10.2209 0.377774
\(733\) 21.2125 0.783502 0.391751 0.920071i \(-0.371870\pi\)
0.391751 + 0.920071i \(0.371870\pi\)
\(734\) 2.01495 0.0743732
\(735\) 27.8169 1.02604
\(736\) −74.7524 −2.75541
\(737\) 12.9899 0.478488
\(738\) −12.3911 −0.456124
\(739\) 3.28407 0.120806 0.0604032 0.998174i \(-0.480761\pi\)
0.0604032 + 0.998174i \(0.480761\pi\)
\(740\) −9.62268 −0.353737
\(741\) 3.99114 0.146618
\(742\) −32.9134 −1.20829
\(743\) −25.3534 −0.930126 −0.465063 0.885277i \(-0.653968\pi\)
−0.465063 + 0.885277i \(0.653968\pi\)
\(744\) 5.00917 0.183645
\(745\) −22.6661 −0.830422
\(746\) 70.7015 2.58856
\(747\) 10.9684 0.401313
\(748\) −66.5983 −2.43507
\(749\) −8.01407 −0.292828
\(750\) 48.5092 1.77131
\(751\) −15.6180 −0.569907 −0.284954 0.958541i \(-0.591978\pi\)
−0.284954 + 0.958541i \(0.591978\pi\)
\(752\) 22.8208 0.832190
\(753\) 31.3713 1.14323
\(754\) −7.30914 −0.266183
\(755\) −40.0384 −1.45715
\(756\) 19.7663 0.718894
\(757\) 23.6116 0.858180 0.429090 0.903262i \(-0.358834\pi\)
0.429090 + 0.903262i \(0.358834\pi\)
\(758\) −31.1697 −1.13213
\(759\) −57.8702 −2.10055
\(760\) 18.8328 0.683138
\(761\) 16.8513 0.610860 0.305430 0.952215i \(-0.401200\pi\)
0.305430 + 0.952215i \(0.401200\pi\)
\(762\) 14.5254 0.526199
\(763\) −1.36855 −0.0495449
\(764\) 53.1805 1.92400
\(765\) −21.4584 −0.775832
\(766\) 13.6921 0.494714
\(767\) −3.76687 −0.136014
\(768\) −5.57805 −0.201280
\(769\) 6.15941 0.222114 0.111057 0.993814i \(-0.464576\pi\)
0.111057 + 0.993814i \(0.464576\pi\)
\(770\) 46.5995 1.67933
\(771\) 39.5419 1.42407
\(772\) 16.3723 0.589251
\(773\) −52.9284 −1.90370 −0.951852 0.306559i \(-0.900822\pi\)
−0.951852 + 0.306559i \(0.900822\pi\)
\(774\) 7.50603 0.269799
\(775\) 27.0051 0.970053
\(776\) −3.49083 −0.125313
\(777\) 1.97114 0.0707143
\(778\) −28.3443 −1.01619
\(779\) 26.5025 0.949552
\(780\) −9.09109 −0.325513
\(781\) −21.5897 −0.772541
\(782\) 124.607 4.45594
\(783\) 29.5211 1.05500
\(784\) 13.2453 0.473046
\(785\) −75.9897 −2.71219
\(786\) −7.50217 −0.267594
\(787\) 11.5430 0.411463 0.205732 0.978608i \(-0.434043\pi\)
0.205732 + 0.978608i \(0.434043\pi\)
\(788\) −48.3323 −1.72177
\(789\) 27.4353 0.976723
\(790\) 31.2652 1.11236
\(791\) 25.7400 0.915210
\(792\) −4.63925 −0.164849
\(793\) −1.82214 −0.0647061
\(794\) 58.3747 2.07164
\(795\) −61.1405 −2.16843
\(796\) 18.7414 0.664272
\(797\) −28.5349 −1.01076 −0.505380 0.862897i \(-0.668648\pi\)
−0.505380 + 0.862897i \(0.668648\pi\)
\(798\) −17.7712 −0.629094
\(799\) −54.3720 −1.92354
\(800\) 72.4157 2.56028
\(801\) 11.3687 0.401694
\(802\) 1.05083 0.0371062
\(803\) 35.2141 1.24268
\(804\) 11.2839 0.397953
\(805\) −48.9023 −1.72358
\(806\) −4.11377 −0.144901
\(807\) 40.4908 1.42534
\(808\) 0.503602 0.0177167
\(809\) −2.69962 −0.0949138 −0.0474569 0.998873i \(-0.515112\pi\)
−0.0474569 + 0.998873i \(0.515112\pi\)
\(810\) 43.1451 1.51596
\(811\) 20.4841 0.719294 0.359647 0.933088i \(-0.382897\pi\)
0.359647 + 0.933088i \(0.382897\pi\)
\(812\) 18.2539 0.640585
\(813\) −10.6520 −0.373582
\(814\) −9.03934 −0.316829
\(815\) 79.4579 2.78329
\(816\) 22.9026 0.801752
\(817\) −16.0541 −0.561662
\(818\) 58.6617 2.05106
\(819\) −0.830813 −0.0290310
\(820\) −60.3680 −2.10814
\(821\) 38.9491 1.35933 0.679666 0.733521i \(-0.262125\pi\)
0.679666 + 0.733521i \(0.262125\pi\)
\(822\) 44.8724 1.56510
\(823\) −25.4960 −0.888735 −0.444368 0.895845i \(-0.646572\pi\)
−0.444368 + 0.895845i \(0.646572\pi\)
\(824\) −3.95558 −0.137799
\(825\) 56.0612 1.95180
\(826\) 16.7726 0.583594
\(827\) 33.8527 1.17717 0.588586 0.808435i \(-0.299685\pi\)
0.588586 + 0.808435i \(0.299685\pi\)
\(828\) 22.4272 0.779400
\(829\) −37.1336 −1.28970 −0.644851 0.764308i \(-0.723081\pi\)
−0.644851 + 0.764308i \(0.723081\pi\)
\(830\) 95.2733 3.30699
\(831\) 8.53061 0.295924
\(832\) −7.64219 −0.264945
\(833\) −31.5577 −1.09341
\(834\) −28.5611 −0.988991
\(835\) −61.9694 −2.14454
\(836\) 45.7092 1.58089
\(837\) 16.6152 0.574306
\(838\) 9.35694 0.323230
\(839\) −28.9815 −1.00055 −0.500276 0.865866i \(-0.666768\pi\)
−0.500276 + 0.865866i \(0.666768\pi\)
\(840\) 8.78732 0.303191
\(841\) −1.73776 −0.0599229
\(842\) −51.6636 −1.78045
\(843\) −40.4574 −1.39343
\(844\) 47.5385 1.63634
\(845\) −47.3489 −1.62885
\(846\) −17.4478 −0.599867
\(847\) 9.49809 0.326358
\(848\) −29.1127 −0.999733
\(849\) −30.6280 −1.05115
\(850\) −120.712 −4.14039
\(851\) 9.48602 0.325177
\(852\) −18.7543 −0.642513
\(853\) −52.9216 −1.81200 −0.906000 0.423278i \(-0.860879\pi\)
−0.906000 + 0.423278i \(0.860879\pi\)
\(854\) 8.11338 0.277634
\(855\) 14.7278 0.503681
\(856\) 6.93022 0.236870
\(857\) 17.4274 0.595309 0.297655 0.954674i \(-0.403796\pi\)
0.297655 + 0.954674i \(0.403796\pi\)
\(858\) −8.53997 −0.291550
\(859\) 2.44307 0.0833565 0.0416783 0.999131i \(-0.486730\pi\)
0.0416783 + 0.999131i \(0.486730\pi\)
\(860\) 36.5684 1.24697
\(861\) 12.3660 0.421431
\(862\) −16.8131 −0.572657
\(863\) −7.88033 −0.268250 −0.134125 0.990964i \(-0.542822\pi\)
−0.134125 + 0.990964i \(0.542822\pi\)
\(864\) 44.5546 1.51578
\(865\) −18.5449 −0.630547
\(866\) 60.3064 2.04930
\(867\) −30.0815 −1.02162
\(868\) 10.2737 0.348713
\(869\) 16.4729 0.558804
\(870\) 60.4565 2.04967
\(871\) −2.01166 −0.0681624
\(872\) 1.18346 0.0400772
\(873\) −2.72993 −0.0923942
\(874\) −85.5231 −2.89286
\(875\) 21.5977 0.730134
\(876\) 30.5894 1.03352
\(877\) −55.7054 −1.88104 −0.940519 0.339741i \(-0.889660\pi\)
−0.940519 + 0.339741i \(0.889660\pi\)
\(878\) −70.2046 −2.36929
\(879\) 26.7730 0.903031
\(880\) 41.2183 1.38947
\(881\) −30.4788 −1.02686 −0.513429 0.858132i \(-0.671625\pi\)
−0.513429 + 0.858132i \(0.671625\pi\)
\(882\) −10.1267 −0.340985
\(883\) 22.8460 0.768828 0.384414 0.923161i \(-0.374404\pi\)
0.384414 + 0.923161i \(0.374404\pi\)
\(884\) 10.3136 0.346886
\(885\) 31.1571 1.04733
\(886\) 31.9862 1.07460
\(887\) 6.31334 0.211981 0.105991 0.994367i \(-0.466199\pi\)
0.105991 + 0.994367i \(0.466199\pi\)
\(888\) −1.70456 −0.0572012
\(889\) 6.46711 0.216900
\(890\) 98.7505 3.31012
\(891\) 22.7321 0.761555
\(892\) 30.3880 1.01746
\(893\) 37.3178 1.24879
\(894\) −18.4957 −0.618590
\(895\) −39.5982 −1.32362
\(896\) 12.4590 0.416226
\(897\) 8.96198 0.299232
\(898\) 42.3755 1.41409
\(899\) 15.3439 0.511747
\(900\) −21.7262 −0.724205
\(901\) 69.3626 2.31080
\(902\) −56.7084 −1.88818
\(903\) −7.49078 −0.249277
\(904\) −22.2589 −0.740319
\(905\) −12.4124 −0.412601
\(906\) −32.6717 −1.08545
\(907\) −1.87441 −0.0622388 −0.0311194 0.999516i \(-0.509907\pi\)
−0.0311194 + 0.999516i \(0.509907\pi\)
\(908\) −23.4843 −0.779354
\(909\) 0.393832 0.0130626
\(910\) −7.21656 −0.239227
\(911\) −37.7800 −1.25171 −0.625853 0.779941i \(-0.715249\pi\)
−0.625853 + 0.779941i \(0.715249\pi\)
\(912\) −15.7190 −0.520509
\(913\) 50.1972 1.66129
\(914\) −49.8414 −1.64861
\(915\) 15.0716 0.498250
\(916\) 18.7117 0.618252
\(917\) −3.34018 −0.110302
\(918\) −74.2694 −2.45126
\(919\) −3.47529 −0.114639 −0.0573196 0.998356i \(-0.518255\pi\)
−0.0573196 + 0.998356i \(0.518255\pi\)
\(920\) 42.2886 1.39421
\(921\) 21.6710 0.714085
\(922\) 28.5266 0.939475
\(923\) 3.34346 0.110051
\(924\) 21.3277 0.701631
\(925\) −9.18950 −0.302149
\(926\) −20.9385 −0.688082
\(927\) −3.09338 −0.101600
\(928\) 41.1454 1.35067
\(929\) −17.0406 −0.559084 −0.279542 0.960133i \(-0.590183\pi\)
−0.279542 + 0.960133i \(0.590183\pi\)
\(930\) 34.0264 1.11577
\(931\) 21.6594 0.709857
\(932\) −15.0180 −0.491931
\(933\) 34.1376 1.11762
\(934\) −69.5701 −2.27640
\(935\) −98.2051 −3.21165
\(936\) 0.718451 0.0234833
\(937\) −8.35854 −0.273062 −0.136531 0.990636i \(-0.543595\pi\)
−0.136531 + 0.990636i \(0.543595\pi\)
\(938\) 8.95724 0.292464
\(939\) −7.57766 −0.247288
\(940\) −85.0032 −2.77250
\(941\) 27.9252 0.910334 0.455167 0.890406i \(-0.349580\pi\)
0.455167 + 0.890406i \(0.349580\pi\)
\(942\) −62.0083 −2.02034
\(943\) 59.5107 1.93793
\(944\) 14.8358 0.482863
\(945\) 29.1472 0.948158
\(946\) 34.3515 1.11686
\(947\) 12.0136 0.390388 0.195194 0.980765i \(-0.437466\pi\)
0.195194 + 0.980765i \(0.437466\pi\)
\(948\) 14.3095 0.464750
\(949\) −5.45338 −0.177024
\(950\) 82.8497 2.68800
\(951\) −9.12218 −0.295807
\(952\) −9.96902 −0.323098
\(953\) −33.2861 −1.07824 −0.539122 0.842228i \(-0.681244\pi\)
−0.539122 + 0.842228i \(0.681244\pi\)
\(954\) 22.2582 0.720636
\(955\) 78.4193 2.53759
\(956\) 61.1809 1.97873
\(957\) 31.8531 1.02966
\(958\) 40.5402 1.30979
\(959\) 19.9785 0.645138
\(960\) 63.2112 2.04013
\(961\) −22.3641 −0.721422
\(962\) 1.39986 0.0451334
\(963\) 5.41964 0.174646
\(964\) 42.1480 1.35750
\(965\) 24.1424 0.777170
\(966\) −39.9047 −1.28391
\(967\) −2.75941 −0.0887366 −0.0443683 0.999015i \(-0.514128\pi\)
−0.0443683 + 0.999015i \(0.514128\pi\)
\(968\) −8.21354 −0.263993
\(969\) 37.4515 1.20312
\(970\) −23.7126 −0.761365
\(971\) −7.77037 −0.249363 −0.124681 0.992197i \(-0.539791\pi\)
−0.124681 + 0.992197i \(0.539791\pi\)
\(972\) −23.5830 −0.756425
\(973\) −12.7162 −0.407663
\(974\) −20.1614 −0.646014
\(975\) −8.68183 −0.278041
\(976\) 7.17647 0.229713
\(977\) −43.7443 −1.39950 −0.699751 0.714387i \(-0.746706\pi\)
−0.699751 + 0.714387i \(0.746706\pi\)
\(978\) 64.8383 2.07330
\(979\) 52.0293 1.66286
\(980\) −49.3361 −1.57598
\(981\) 0.925504 0.0295491
\(982\) −67.2093 −2.14474
\(983\) −12.8214 −0.408939 −0.204469 0.978873i \(-0.565547\pi\)
−0.204469 + 0.978873i \(0.565547\pi\)
\(984\) −10.6936 −0.340898
\(985\) −71.2703 −2.27086
\(986\) −68.5866 −2.18424
\(987\) 17.4123 0.554240
\(988\) −7.07869 −0.225203
\(989\) −36.0490 −1.14629
\(990\) −31.5136 −1.00157
\(991\) −9.02001 −0.286530 −0.143265 0.989684i \(-0.545760\pi\)
−0.143265 + 0.989684i \(0.545760\pi\)
\(992\) 23.1577 0.735258
\(993\) 11.3649 0.360654
\(994\) −14.8873 −0.472197
\(995\) 27.6359 0.876116
\(996\) 43.6048 1.38167
\(997\) 28.3580 0.898106 0.449053 0.893505i \(-0.351761\pi\)
0.449053 + 0.893505i \(0.351761\pi\)
\(998\) −3.44864 −0.109165
\(999\) −5.65395 −0.178883
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 \(a_p\))