Properties

Label 8023.2.a.c.1.7
Level 8023
Weight 2
Character 8023.1
Self dual Yes
Analytic conductor 64.064
Analytic rank 1
Dimension 158
CM No

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Newspace parameters

Level: \( N \) = \( 8023 = 71 \cdot 113 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8023.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0639775417\)
Analytic rank: \(1\)
Dimension: \(158\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 8023.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.70862 q^{2}\) \(+0.748763 q^{3}\) \(+5.33660 q^{4}\) \(-3.98594 q^{5}\) \(-2.02811 q^{6}\) \(+0.912141 q^{7}\) \(-9.03756 q^{8}\) \(-2.43935 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.70862 q^{2}\) \(+0.748763 q^{3}\) \(+5.33660 q^{4}\) \(-3.98594 q^{5}\) \(-2.02811 q^{6}\) \(+0.912141 q^{7}\) \(-9.03756 q^{8}\) \(-2.43935 q^{9}\) \(+10.7964 q^{10}\) \(-1.43215 q^{11}\) \(+3.99585 q^{12}\) \(-3.27590 q^{13}\) \(-2.47064 q^{14}\) \(-2.98453 q^{15}\) \(+13.8061 q^{16}\) \(+3.55832 q^{17}\) \(+6.60727 q^{18}\) \(-1.62050 q^{19}\) \(-21.2714 q^{20}\) \(+0.682978 q^{21}\) \(+3.87914 q^{22}\) \(-1.25726 q^{23}\) \(-6.76700 q^{24}\) \(+10.8877 q^{25}\) \(+8.87315 q^{26}\) \(-4.07279 q^{27}\) \(+4.86773 q^{28}\) \(+6.41914 q^{29}\) \(+8.08394 q^{30}\) \(-1.29634 q^{31}\) \(-19.3203 q^{32}\) \(-1.07234 q^{33}\) \(-9.63813 q^{34}\) \(-3.63574 q^{35}\) \(-13.0179 q^{36}\) \(-2.43016 q^{37}\) \(+4.38930 q^{38}\) \(-2.45287 q^{39}\) \(+36.0232 q^{40}\) \(+2.70524 q^{41}\) \(-1.84993 q^{42}\) \(+7.66248 q^{43}\) \(-7.64280 q^{44}\) \(+9.72312 q^{45}\) \(+3.40544 q^{46}\) \(-8.91948 q^{47}\) \(+10.3375 q^{48}\) \(-6.16800 q^{49}\) \(-29.4907 q^{50}\) \(+2.66434 q^{51}\) \(-17.4822 q^{52}\) \(-6.14645 q^{53}\) \(+11.0316 q^{54}\) \(+5.70846 q^{55}\) \(-8.24354 q^{56}\) \(-1.21337 q^{57}\) \(-17.3870 q^{58}\) \(-5.15399 q^{59}\) \(-15.9272 q^{60}\) \(+12.2559 q^{61}\) \(+3.51130 q^{62}\) \(-2.22504 q^{63}\) \(+24.7190 q^{64}\) \(+13.0575 q^{65}\) \(+2.90456 q^{66}\) \(+15.1183 q^{67}\) \(+18.9893 q^{68}\) \(-0.941392 q^{69}\) \(+9.84783 q^{70}\) \(-1.00000 q^{71}\) \(+22.0458 q^{72}\) \(+0.774711 q^{73}\) \(+6.58236 q^{74}\) \(+8.15235 q^{75}\) \(-8.64794 q^{76}\) \(-1.30632 q^{77}\) \(+6.64389 q^{78}\) \(+15.0796 q^{79}\) \(-55.0303 q^{80}\) \(+4.26850 q^{81}\) \(-7.32746 q^{82}\) \(-16.4118 q^{83}\) \(+3.64478 q^{84}\) \(-14.1833 q^{85}\) \(-20.7547 q^{86}\) \(+4.80642 q^{87}\) \(+12.9431 q^{88}\) \(+2.35548 q^{89}\) \(-26.3362 q^{90}\) \(-2.98808 q^{91}\) \(-6.70950 q^{92}\) \(-0.970655 q^{93}\) \(+24.1594 q^{94}\) \(+6.45921 q^{95}\) \(-14.4663 q^{96}\) \(-8.35135 q^{97}\) \(+16.7067 q^{98}\) \(+3.49352 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(158q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 158q^{4} \) \(\mathstrut -\mathstrut 31q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(158q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 158q^{4} \) \(\mathstrut -\mathstrut 31q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 10q^{11} \) \(\mathstrut -\mathstrut 46q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 27q^{14} \) \(\mathstrut -\mathstrut 41q^{15} \) \(\mathstrut +\mathstrut 150q^{16} \) \(\mathstrut -\mathstrut 137q^{17} \) \(\mathstrut -\mathstrut 67q^{18} \) \(\mathstrut -\mathstrut 42q^{19} \) \(\mathstrut -\mathstrut 66q^{20} \) \(\mathstrut -\mathstrut 46q^{21} \) \(\mathstrut -\mathstrut 8q^{22} \) \(\mathstrut -\mathstrut 26q^{23} \) \(\mathstrut -\mathstrut 48q^{24} \) \(\mathstrut +\mathstrut 129q^{25} \) \(\mathstrut -\mathstrut 67q^{26} \) \(\mathstrut -\mathstrut 89q^{27} \) \(\mathstrut -\mathstrut 21q^{28} \) \(\mathstrut -\mathstrut 79q^{29} \) \(\mathstrut -\mathstrut 11q^{30} \) \(\mathstrut +\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 147q^{32} \) \(\mathstrut -\mathstrut 112q^{33} \) \(\mathstrut -\mathstrut 28q^{34} \) \(\mathstrut -\mathstrut 53q^{35} \) \(\mathstrut +\mathstrut 141q^{36} \) \(\mathstrut -\mathstrut 60q^{37} \) \(\mathstrut -\mathstrut 53q^{38} \) \(\mathstrut -\mathstrut 3q^{39} \) \(\mathstrut -\mathstrut 48q^{40} \) \(\mathstrut -\mathstrut 128q^{41} \) \(\mathstrut +\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 63q^{43} \) \(\mathstrut -\mathstrut 88q^{45} \) \(\mathstrut -\mathstrut 2q^{46} \) \(\mathstrut -\mathstrut 92q^{47} \) \(\mathstrut -\mathstrut 131q^{48} \) \(\mathstrut +\mathstrut 122q^{49} \) \(\mathstrut -\mathstrut 116q^{50} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 89q^{52} \) \(\mathstrut -\mathstrut 94q^{53} \) \(\mathstrut -\mathstrut 71q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 104q^{56} \) \(\mathstrut -\mathstrut 93q^{57} \) \(\mathstrut -\mathstrut 65q^{58} \) \(\mathstrut -\mathstrut 54q^{59} \) \(\mathstrut -\mathstrut 12q^{60} \) \(\mathstrut +\mathstrut 17q^{61} \) \(\mathstrut -\mathstrut 97q^{62} \) \(\mathstrut -\mathstrut 28q^{63} \) \(\mathstrut +\mathstrut 163q^{64} \) \(\mathstrut -\mathstrut 163q^{65} \) \(\mathstrut -\mathstrut 65q^{66} \) \(\mathstrut -\mathstrut 35q^{67} \) \(\mathstrut -\mathstrut 217q^{68} \) \(\mathstrut -\mathstrut 46q^{69} \) \(\mathstrut -\mathstrut 79q^{70} \) \(\mathstrut -\mathstrut 158q^{71} \) \(\mathstrut -\mathstrut 99q^{72} \) \(\mathstrut -\mathstrut 165q^{73} \) \(\mathstrut -\mathstrut 94q^{75} \) \(\mathstrut -\mathstrut 93q^{76} \) \(\mathstrut -\mathstrut 140q^{77} \) \(\mathstrut +\mathstrut 25q^{78} \) \(\mathstrut -\mathstrut 61q^{79} \) \(\mathstrut -\mathstrut 134q^{80} \) \(\mathstrut +\mathstrut 114q^{81} \) \(\mathstrut +\mathstrut 10q^{82} \) \(\mathstrut -\mathstrut 158q^{83} \) \(\mathstrut -\mathstrut 160q^{84} \) \(\mathstrut +\mathstrut 23q^{85} \) \(\mathstrut -\mathstrut 122q^{86} \) \(\mathstrut -\mathstrut 71q^{87} \) \(\mathstrut -\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 251q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut -\mathstrut 57q^{91} \) \(\mathstrut -\mathstrut 58q^{92} \) \(\mathstrut -\mathstrut 52q^{93} \) \(\mathstrut -\mathstrut 64q^{94} \) \(\mathstrut -\mathstrut 84q^{95} \) \(\mathstrut -\mathstrut 98q^{96} \) \(\mathstrut -\mathstrut 48q^{97} \) \(\mathstrut -\mathstrut 84q^{98} \) \(\mathstrut +\mathstrut 85q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.70862 −1.91528 −0.957640 0.287967i \(-0.907021\pi\)
−0.957640 + 0.287967i \(0.907021\pi\)
\(3\) 0.748763 0.432299 0.216149 0.976360i \(-0.430650\pi\)
0.216149 + 0.976360i \(0.430650\pi\)
\(4\) 5.33660 2.66830
\(5\) −3.98594 −1.78257 −0.891284 0.453445i \(-0.850195\pi\)
−0.891284 + 0.453445i \(0.850195\pi\)
\(6\) −2.02811 −0.827973
\(7\) 0.912141 0.344757 0.172379 0.985031i \(-0.444855\pi\)
0.172379 + 0.985031i \(0.444855\pi\)
\(8\) −9.03756 −3.19526
\(9\) −2.43935 −0.813118
\(10\) 10.7964 3.41412
\(11\) −1.43215 −0.431809 −0.215905 0.976414i \(-0.569270\pi\)
−0.215905 + 0.976414i \(0.569270\pi\)
\(12\) 3.99585 1.15350
\(13\) −3.27590 −0.908570 −0.454285 0.890856i \(-0.650105\pi\)
−0.454285 + 0.890856i \(0.650105\pi\)
\(14\) −2.47064 −0.660307
\(15\) −2.98453 −0.770602
\(16\) 13.8061 3.45152
\(17\) 3.55832 0.863020 0.431510 0.902108i \(-0.357981\pi\)
0.431510 + 0.902108i \(0.357981\pi\)
\(18\) 6.60727 1.55735
\(19\) −1.62050 −0.371767 −0.185884 0.982572i \(-0.559515\pi\)
−0.185884 + 0.982572i \(0.559515\pi\)
\(20\) −21.2714 −4.75643
\(21\) 0.682978 0.149038
\(22\) 3.87914 0.827035
\(23\) −1.25726 −0.262157 −0.131079 0.991372i \(-0.541844\pi\)
−0.131079 + 0.991372i \(0.541844\pi\)
\(24\) −6.76700 −1.38131
\(25\) 10.8877 2.17755
\(26\) 8.87315 1.74017
\(27\) −4.07279 −0.783809
\(28\) 4.86773 0.919915
\(29\) 6.41914 1.19201 0.596003 0.802983i \(-0.296755\pi\)
0.596003 + 0.802983i \(0.296755\pi\)
\(30\) 8.08394 1.47592
\(31\) −1.29634 −0.232830 −0.116415 0.993201i \(-0.537140\pi\)
−0.116415 + 0.993201i \(0.537140\pi\)
\(32\) −19.3203 −3.41537
\(33\) −1.07234 −0.186671
\(34\) −9.63813 −1.65293
\(35\) −3.63574 −0.614553
\(36\) −13.0179 −2.16964
\(37\) −2.43016 −0.399515 −0.199758 0.979845i \(-0.564015\pi\)
−0.199758 + 0.979845i \(0.564015\pi\)
\(38\) 4.38930 0.712039
\(39\) −2.45287 −0.392774
\(40\) 36.0232 5.69577
\(41\) 2.70524 0.422488 0.211244 0.977433i \(-0.432249\pi\)
0.211244 + 0.977433i \(0.432249\pi\)
\(42\) −1.84993 −0.285450
\(43\) 7.66248 1.16852 0.584259 0.811567i \(-0.301385\pi\)
0.584259 + 0.811567i \(0.301385\pi\)
\(44\) −7.64280 −1.15220
\(45\) 9.72312 1.44944
\(46\) 3.40544 0.502105
\(47\) −8.91948 −1.30104 −0.650520 0.759489i \(-0.725449\pi\)
−0.650520 + 0.759489i \(0.725449\pi\)
\(48\) 10.3375 1.49209
\(49\) −6.16800 −0.881143
\(50\) −29.4907 −4.17062
\(51\) 2.66434 0.373083
\(52\) −17.4822 −2.42434
\(53\) −6.14645 −0.844280 −0.422140 0.906531i \(-0.638721\pi\)
−0.422140 + 0.906531i \(0.638721\pi\)
\(54\) 11.0316 1.50121
\(55\) 5.70846 0.769729
\(56\) −8.24354 −1.10159
\(57\) −1.21337 −0.160715
\(58\) −17.3870 −2.28302
\(59\) −5.15399 −0.670993 −0.335496 0.942041i \(-0.608904\pi\)
−0.335496 + 0.942041i \(0.608904\pi\)
\(60\) −15.9272 −2.05620
\(61\) 12.2559 1.56920 0.784601 0.620002i \(-0.212868\pi\)
0.784601 + 0.620002i \(0.212868\pi\)
\(62\) 3.51130 0.445935
\(63\) −2.22504 −0.280328
\(64\) 24.7190 3.08987
\(65\) 13.0575 1.61959
\(66\) 2.90456 0.357526
\(67\) 15.1183 1.84700 0.923499 0.383601i \(-0.125316\pi\)
0.923499 + 0.383601i \(0.125316\pi\)
\(68\) 18.9893 2.30280
\(69\) −0.941392 −0.113330
\(70\) 9.84783 1.17704
\(71\) −1.00000 −0.118678
\(72\) 22.0458 2.59812
\(73\) 0.774711 0.0906731 0.0453365 0.998972i \(-0.485564\pi\)
0.0453365 + 0.998972i \(0.485564\pi\)
\(74\) 6.58236 0.765184
\(75\) 8.15235 0.941352
\(76\) −8.64794 −0.991987
\(77\) −1.30632 −0.148869
\(78\) 6.64389 0.752272
\(79\) 15.0796 1.69659 0.848293 0.529527i \(-0.177630\pi\)
0.848293 + 0.529527i \(0.177630\pi\)
\(80\) −55.0303 −6.15257
\(81\) 4.26850 0.474278
\(82\) −7.32746 −0.809182
\(83\) −16.4118 −1.80143 −0.900714 0.434413i \(-0.856956\pi\)
−0.900714 + 0.434413i \(0.856956\pi\)
\(84\) 3.64478 0.397678
\(85\) −14.1833 −1.53839
\(86\) −20.7547 −2.23804
\(87\) 4.80642 0.515302
\(88\) 12.9431 1.37974
\(89\) 2.35548 0.249681 0.124840 0.992177i \(-0.460158\pi\)
0.124840 + 0.992177i \(0.460158\pi\)
\(90\) −26.3362 −2.77608
\(91\) −2.98808 −0.313236
\(92\) −6.70950 −0.699514
\(93\) −0.970655 −0.100652
\(94\) 24.1594 2.49186
\(95\) 6.45921 0.662701
\(96\) −14.4663 −1.47646
\(97\) −8.35135 −0.847951 −0.423976 0.905674i \(-0.639366\pi\)
−0.423976 + 0.905674i \(0.639366\pi\)
\(98\) 16.7067 1.68764
\(99\) 3.49352 0.351112
\(100\) 58.1035 5.81035
\(101\) −6.61098 −0.657818 −0.328909 0.944362i \(-0.606681\pi\)
−0.328909 + 0.944362i \(0.606681\pi\)
\(102\) −7.21668 −0.714558
\(103\) 0.0657150 0.00647509 0.00323754 0.999995i \(-0.498969\pi\)
0.00323754 + 0.999995i \(0.498969\pi\)
\(104\) 29.6061 2.90312
\(105\) −2.72231 −0.265671
\(106\) 16.6484 1.61703
\(107\) 4.41657 0.426965 0.213483 0.976947i \(-0.431519\pi\)
0.213483 + 0.976947i \(0.431519\pi\)
\(108\) −21.7348 −2.09144
\(109\) 10.9260 1.04652 0.523260 0.852173i \(-0.324716\pi\)
0.523260 + 0.852173i \(0.324716\pi\)
\(110\) −15.4620 −1.47425
\(111\) −1.81961 −0.172710
\(112\) 12.5931 1.18994
\(113\) −1.00000 −0.0940721
\(114\) 3.28655 0.307813
\(115\) 5.01137 0.467313
\(116\) 34.2564 3.18063
\(117\) 7.99107 0.738775
\(118\) 13.9602 1.28514
\(119\) 3.24569 0.297532
\(120\) 26.9729 2.46227
\(121\) −8.94895 −0.813541
\(122\) −33.1964 −3.00546
\(123\) 2.02559 0.182641
\(124\) −6.91807 −0.621261
\(125\) −23.4682 −2.09906
\(126\) 6.02677 0.536907
\(127\) 12.7108 1.12790 0.563950 0.825809i \(-0.309281\pi\)
0.563950 + 0.825809i \(0.309281\pi\)
\(128\) −28.3137 −2.50260
\(129\) 5.73739 0.505149
\(130\) −35.3679 −3.10197
\(131\) 20.4376 1.78564 0.892822 0.450409i \(-0.148722\pi\)
0.892822 + 0.450409i \(0.148722\pi\)
\(132\) −5.72265 −0.498093
\(133\) −1.47812 −0.128169
\(134\) −40.9498 −3.53752
\(135\) 16.2339 1.39719
\(136\) −32.1586 −2.75758
\(137\) 13.8559 1.18379 0.591893 0.806017i \(-0.298381\pi\)
0.591893 + 0.806017i \(0.298381\pi\)
\(138\) 2.54987 0.217059
\(139\) 7.62312 0.646585 0.323292 0.946299i \(-0.395210\pi\)
0.323292 + 0.946299i \(0.395210\pi\)
\(140\) −19.4025 −1.63981
\(141\) −6.67858 −0.562438
\(142\) 2.70862 0.227302
\(143\) 4.69157 0.392329
\(144\) −33.6779 −2.80649
\(145\) −25.5863 −2.12483
\(146\) −2.09839 −0.173664
\(147\) −4.61837 −0.380917
\(148\) −12.9688 −1.06603
\(149\) 17.1316 1.40347 0.701737 0.712436i \(-0.252408\pi\)
0.701737 + 0.712436i \(0.252408\pi\)
\(150\) −22.0816 −1.80295
\(151\) 4.75003 0.386552 0.193276 0.981144i \(-0.438089\pi\)
0.193276 + 0.981144i \(0.438089\pi\)
\(152\) 14.6453 1.18789
\(153\) −8.68001 −0.701737
\(154\) 3.53832 0.285126
\(155\) 5.16715 0.415036
\(156\) −13.0900 −1.04804
\(157\) 13.5555 1.08185 0.540924 0.841072i \(-0.318075\pi\)
0.540924 + 0.841072i \(0.318075\pi\)
\(158\) −40.8448 −3.24944
\(159\) −4.60224 −0.364981
\(160\) 77.0095 6.08813
\(161\) −1.14680 −0.0903805
\(162\) −11.5617 −0.908376
\(163\) −9.81288 −0.768604 −0.384302 0.923207i \(-0.625558\pi\)
−0.384302 + 0.923207i \(0.625558\pi\)
\(164\) 14.4368 1.12732
\(165\) 4.27429 0.332753
\(166\) 44.4532 3.45024
\(167\) 3.81946 0.295559 0.147779 0.989020i \(-0.452787\pi\)
0.147779 + 0.989020i \(0.452787\pi\)
\(168\) −6.17246 −0.476216
\(169\) −2.26850 −0.174500
\(170\) 38.4170 2.94645
\(171\) 3.95296 0.302291
\(172\) 40.8916 3.11796
\(173\) 5.50622 0.418630 0.209315 0.977848i \(-0.432877\pi\)
0.209315 + 0.977848i \(0.432877\pi\)
\(174\) −13.0187 −0.986949
\(175\) 9.93116 0.750725
\(176\) −19.7724 −1.49040
\(177\) −3.85912 −0.290069
\(178\) −6.38010 −0.478209
\(179\) −10.7058 −0.800190 −0.400095 0.916474i \(-0.631023\pi\)
−0.400095 + 0.916474i \(0.631023\pi\)
\(180\) 51.8884 3.86753
\(181\) −3.40862 −0.253361 −0.126681 0.991944i \(-0.540432\pi\)
−0.126681 + 0.991944i \(0.540432\pi\)
\(182\) 8.09357 0.599935
\(183\) 9.17673 0.678364
\(184\) 11.3626 0.837661
\(185\) 9.68647 0.712163
\(186\) 2.62913 0.192777
\(187\) −5.09605 −0.372660
\(188\) −47.5997 −3.47156
\(189\) −3.71496 −0.270224
\(190\) −17.4955 −1.26926
\(191\) 10.6151 0.768081 0.384040 0.923316i \(-0.374532\pi\)
0.384040 + 0.923316i \(0.374532\pi\)
\(192\) 18.5087 1.33575
\(193\) −3.51604 −0.253090 −0.126545 0.991961i \(-0.540389\pi\)
−0.126545 + 0.991961i \(0.540389\pi\)
\(194\) 22.6206 1.62406
\(195\) 9.77701 0.700146
\(196\) −32.9161 −2.35115
\(197\) 1.34905 0.0961162 0.0480581 0.998845i \(-0.484697\pi\)
0.0480581 + 0.998845i \(0.484697\pi\)
\(198\) −9.46259 −0.672477
\(199\) −19.9417 −1.41363 −0.706814 0.707400i \(-0.749868\pi\)
−0.706814 + 0.707400i \(0.749868\pi\)
\(200\) −98.3987 −6.95784
\(201\) 11.3201 0.798455
\(202\) 17.9066 1.25991
\(203\) 5.85517 0.410952
\(204\) 14.2185 0.995496
\(205\) −10.7829 −0.753113
\(206\) −0.177997 −0.0124016
\(207\) 3.06691 0.213165
\(208\) −45.2273 −3.13595
\(209\) 2.32079 0.160532
\(210\) 7.37370 0.508834
\(211\) 4.89531 0.337007 0.168503 0.985701i \(-0.446107\pi\)
0.168503 + 0.985701i \(0.446107\pi\)
\(212\) −32.8011 −2.25279
\(213\) −0.748763 −0.0513044
\(214\) −11.9628 −0.817759
\(215\) −30.5422 −2.08296
\(216\) 36.8081 2.50447
\(217\) −1.18245 −0.0802699
\(218\) −29.5943 −2.00438
\(219\) 0.580075 0.0391979
\(220\) 30.4638 2.05387
\(221\) −11.6567 −0.784115
\(222\) 4.92863 0.330788
\(223\) 15.2903 1.02391 0.511957 0.859011i \(-0.328921\pi\)
0.511957 + 0.859011i \(0.328921\pi\)
\(224\) −17.6228 −1.17747
\(225\) −26.5591 −1.77060
\(226\) 2.70862 0.180174
\(227\) −19.2461 −1.27741 −0.638704 0.769452i \(-0.720529\pi\)
−0.638704 + 0.769452i \(0.720529\pi\)
\(228\) −6.47526 −0.428835
\(229\) −17.9326 −1.18502 −0.592511 0.805562i \(-0.701863\pi\)
−0.592511 + 0.805562i \(0.701863\pi\)
\(230\) −13.5739 −0.895035
\(231\) −0.978126 −0.0643560
\(232\) −58.0134 −3.80877
\(233\) 11.7215 0.767898 0.383949 0.923354i \(-0.374564\pi\)
0.383949 + 0.923354i \(0.374564\pi\)
\(234\) −21.6447 −1.41496
\(235\) 35.5525 2.31919
\(236\) −27.5048 −1.79041
\(237\) 11.2910 0.733432
\(238\) −8.79134 −0.569858
\(239\) −18.4110 −1.19091 −0.595454 0.803389i \(-0.703028\pi\)
−0.595454 + 0.803389i \(0.703028\pi\)
\(240\) −41.2047 −2.65975
\(241\) −6.89501 −0.444147 −0.222073 0.975030i \(-0.571282\pi\)
−0.222073 + 0.975030i \(0.571282\pi\)
\(242\) 24.2393 1.55816
\(243\) 15.4145 0.988839
\(244\) 65.4046 4.18710
\(245\) 24.5853 1.57070
\(246\) −5.48653 −0.349808
\(247\) 5.30858 0.337777
\(248\) 11.7158 0.743953
\(249\) −12.2885 −0.778755
\(250\) 63.5664 4.02029
\(251\) −5.84727 −0.369076 −0.184538 0.982825i \(-0.559079\pi\)
−0.184538 + 0.982825i \(0.559079\pi\)
\(252\) −11.8741 −0.747999
\(253\) 1.80059 0.113202
\(254\) −34.4287 −2.16025
\(255\) −10.6199 −0.665045
\(256\) 27.2530 1.70331
\(257\) 4.37391 0.272837 0.136418 0.990651i \(-0.456441\pi\)
0.136418 + 0.990651i \(0.456441\pi\)
\(258\) −15.5404 −0.967502
\(259\) −2.21665 −0.137736
\(260\) 69.6829 4.32155
\(261\) −15.6586 −0.969241
\(262\) −55.3577 −3.42001
\(263\) 18.3415 1.13099 0.565493 0.824753i \(-0.308686\pi\)
0.565493 + 0.824753i \(0.308686\pi\)
\(264\) 9.69135 0.596461
\(265\) 24.4994 1.50499
\(266\) 4.00366 0.245480
\(267\) 1.76370 0.107937
\(268\) 80.6805 4.92834
\(269\) −29.4085 −1.79307 −0.896535 0.442973i \(-0.853924\pi\)
−0.896535 + 0.442973i \(0.853924\pi\)
\(270\) −43.9714 −2.67601
\(271\) 7.14665 0.434128 0.217064 0.976157i \(-0.430352\pi\)
0.217064 + 0.976157i \(0.430352\pi\)
\(272\) 49.1265 2.97873
\(273\) −2.23737 −0.135412
\(274\) −37.5302 −2.26728
\(275\) −15.5929 −0.940285
\(276\) −5.02383 −0.302399
\(277\) 6.64724 0.399394 0.199697 0.979858i \(-0.436004\pi\)
0.199697 + 0.979858i \(0.436004\pi\)
\(278\) −20.6481 −1.23839
\(279\) 3.16224 0.189318
\(280\) 32.8583 1.96366
\(281\) −20.8212 −1.24209 −0.621044 0.783776i \(-0.713291\pi\)
−0.621044 + 0.783776i \(0.713291\pi\)
\(282\) 18.0897 1.07723
\(283\) −8.34621 −0.496131 −0.248065 0.968743i \(-0.579795\pi\)
−0.248065 + 0.968743i \(0.579795\pi\)
\(284\) −5.33660 −0.316669
\(285\) 4.83642 0.286485
\(286\) −12.7077 −0.751420
\(287\) 2.46756 0.145656
\(288\) 47.1290 2.77710
\(289\) −4.33833 −0.255196
\(290\) 69.3036 4.06965
\(291\) −6.25319 −0.366568
\(292\) 4.13432 0.241943
\(293\) 27.0509 1.58033 0.790165 0.612895i \(-0.209995\pi\)
0.790165 + 0.612895i \(0.209995\pi\)
\(294\) 12.5094 0.729563
\(295\) 20.5435 1.19609
\(296\) 21.9627 1.27656
\(297\) 5.83284 0.338456
\(298\) −46.4029 −2.68805
\(299\) 4.11866 0.238188
\(300\) 43.5058 2.51181
\(301\) 6.98927 0.402855
\(302\) −12.8660 −0.740356
\(303\) −4.95006 −0.284374
\(304\) −22.3727 −1.28316
\(305\) −48.8511 −2.79721
\(306\) 23.5108 1.34402
\(307\) −4.94756 −0.282372 −0.141186 0.989983i \(-0.545092\pi\)
−0.141186 + 0.989983i \(0.545092\pi\)
\(308\) −6.97132 −0.397228
\(309\) 0.0492050 0.00279917
\(310\) −13.9958 −0.794910
\(311\) −12.4990 −0.708751 −0.354376 0.935103i \(-0.615307\pi\)
−0.354376 + 0.935103i \(0.615307\pi\)
\(312\) 22.1680 1.25502
\(313\) −25.9006 −1.46399 −0.731994 0.681311i \(-0.761410\pi\)
−0.731994 + 0.681311i \(0.761410\pi\)
\(314\) −36.7167 −2.07204
\(315\) 8.86886 0.499704
\(316\) 80.4737 4.52700
\(317\) 3.05519 0.171597 0.0857983 0.996313i \(-0.472656\pi\)
0.0857983 + 0.996313i \(0.472656\pi\)
\(318\) 12.4657 0.699041
\(319\) −9.19317 −0.514719
\(320\) −98.5285 −5.50791
\(321\) 3.30696 0.184577
\(322\) 3.10624 0.173104
\(323\) −5.76625 −0.320843
\(324\) 22.7793 1.26552
\(325\) −35.6671 −1.97846
\(326\) 26.5793 1.47209
\(327\) 8.18099 0.452410
\(328\) −24.4488 −1.34996
\(329\) −8.13583 −0.448543
\(330\) −11.5774 −0.637315
\(331\) 24.8088 1.36361 0.681807 0.731532i \(-0.261194\pi\)
0.681807 + 0.731532i \(0.261194\pi\)
\(332\) −87.5831 −4.80675
\(333\) 5.92801 0.324853
\(334\) −10.3455 −0.566078
\(335\) −60.2608 −3.29240
\(336\) 9.42926 0.514408
\(337\) −30.2374 −1.64714 −0.823569 0.567216i \(-0.808021\pi\)
−0.823569 + 0.567216i \(0.808021\pi\)
\(338\) 6.14449 0.334216
\(339\) −0.748763 −0.0406672
\(340\) −75.6905 −4.10489
\(341\) 1.85656 0.100538
\(342\) −10.7071 −0.578971
\(343\) −12.0111 −0.648537
\(344\) −69.2502 −3.73372
\(345\) 3.75233 0.202019
\(346\) −14.9142 −0.801793
\(347\) 23.3414 1.25303 0.626516 0.779408i \(-0.284480\pi\)
0.626516 + 0.779408i \(0.284480\pi\)
\(348\) 25.6499 1.37498
\(349\) −16.7935 −0.898935 −0.449467 0.893297i \(-0.648386\pi\)
−0.449467 + 0.893297i \(0.648386\pi\)
\(350\) −26.8997 −1.43785
\(351\) 13.3420 0.712145
\(352\) 27.6695 1.47479
\(353\) −7.11191 −0.378529 −0.189264 0.981926i \(-0.560610\pi\)
−0.189264 + 0.981926i \(0.560610\pi\)
\(354\) 10.4529 0.555564
\(355\) 3.98594 0.211552
\(356\) 12.5703 0.666223
\(357\) 2.43026 0.128623
\(358\) 28.9979 1.53259
\(359\) −7.30190 −0.385380 −0.192690 0.981260i \(-0.561721\pi\)
−0.192690 + 0.981260i \(0.561721\pi\)
\(360\) −87.8734 −4.63133
\(361\) −16.3740 −0.861789
\(362\) 9.23265 0.485258
\(363\) −6.70065 −0.351693
\(364\) −15.9462 −0.835808
\(365\) −3.08795 −0.161631
\(366\) −24.8562 −1.29926
\(367\) −7.54315 −0.393749 −0.196875 0.980429i \(-0.563079\pi\)
−0.196875 + 0.980429i \(0.563079\pi\)
\(368\) −17.3579 −0.904841
\(369\) −6.59904 −0.343532
\(370\) −26.2369 −1.36399
\(371\) −5.60643 −0.291071
\(372\) −5.18000 −0.268570
\(373\) −30.5427 −1.58144 −0.790720 0.612178i \(-0.790293\pi\)
−0.790720 + 0.612178i \(0.790293\pi\)
\(374\) 13.8032 0.713748
\(375\) −17.5721 −0.907421
\(376\) 80.6104 4.15716
\(377\) −21.0285 −1.08302
\(378\) 10.0624 0.517554
\(379\) 21.9396 1.12696 0.563481 0.826129i \(-0.309462\pi\)
0.563481 + 0.826129i \(0.309462\pi\)
\(380\) 34.4702 1.76828
\(381\) 9.51738 0.487590
\(382\) −28.7522 −1.47109
\(383\) −31.9447 −1.63230 −0.816148 0.577842i \(-0.803895\pi\)
−0.816148 + 0.577842i \(0.803895\pi\)
\(384\) −21.2003 −1.08187
\(385\) 5.20693 0.265370
\(386\) 9.52361 0.484739
\(387\) −18.6915 −0.950143
\(388\) −44.5678 −2.26259
\(389\) 14.8660 0.753736 0.376868 0.926267i \(-0.377001\pi\)
0.376868 + 0.926267i \(0.377001\pi\)
\(390\) −26.4822 −1.34098
\(391\) −4.47374 −0.226247
\(392\) 55.7437 2.81548
\(393\) 15.3030 0.771932
\(394\) −3.65407 −0.184089
\(395\) −60.1064 −3.02428
\(396\) 18.6435 0.936871
\(397\) 14.3745 0.721434 0.360717 0.932675i \(-0.382532\pi\)
0.360717 + 0.932675i \(0.382532\pi\)
\(398\) 54.0143 2.70749
\(399\) −1.10676 −0.0554075
\(400\) 150.317 7.51586
\(401\) 10.1155 0.505144 0.252572 0.967578i \(-0.418724\pi\)
0.252572 + 0.967578i \(0.418724\pi\)
\(402\) −30.6617 −1.52927
\(403\) 4.24669 0.211543
\(404\) −35.2802 −1.75525
\(405\) −17.0140 −0.845433
\(406\) −15.8594 −0.787089
\(407\) 3.48035 0.172514
\(408\) −24.0792 −1.19210
\(409\) −8.97727 −0.443898 −0.221949 0.975058i \(-0.571242\pi\)
−0.221949 + 0.975058i \(0.571242\pi\)
\(410\) 29.2068 1.44242
\(411\) 10.3748 0.511749
\(412\) 0.350694 0.0172775
\(413\) −4.70117 −0.231330
\(414\) −8.30707 −0.408270
\(415\) 65.4164 3.21117
\(416\) 63.2912 3.10311
\(417\) 5.70791 0.279518
\(418\) −6.28613 −0.307465
\(419\) −31.6460 −1.54601 −0.773005 0.634400i \(-0.781247\pi\)
−0.773005 + 0.634400i \(0.781247\pi\)
\(420\) −14.5279 −0.708888
\(421\) −6.22844 −0.303555 −0.151778 0.988415i \(-0.548500\pi\)
−0.151778 + 0.988415i \(0.548500\pi\)
\(422\) −13.2595 −0.645463
\(423\) 21.7578 1.05790
\(424\) 55.5489 2.69769
\(425\) 38.7421 1.87927
\(426\) 2.02811 0.0982624
\(427\) 11.1791 0.540993
\(428\) 23.5694 1.13927
\(429\) 3.51288 0.169603
\(430\) 82.7272 3.98946
\(431\) 31.5869 1.52149 0.760744 0.649052i \(-0.224834\pi\)
0.760744 + 0.649052i \(0.224834\pi\)
\(432\) −56.2293 −2.70533
\(433\) 5.81410 0.279408 0.139704 0.990193i \(-0.455385\pi\)
0.139704 + 0.990193i \(0.455385\pi\)
\(434\) 3.20280 0.153739
\(435\) −19.1581 −0.918562
\(436\) 58.3077 2.79243
\(437\) 2.03739 0.0974615
\(438\) −1.57120 −0.0750749
\(439\) 34.5312 1.64808 0.824042 0.566529i \(-0.191714\pi\)
0.824042 + 0.566529i \(0.191714\pi\)
\(440\) −51.5906 −2.45949
\(441\) 15.0459 0.716473
\(442\) 31.5735 1.50180
\(443\) 1.48642 0.0706218 0.0353109 0.999376i \(-0.488758\pi\)
0.0353109 + 0.999376i \(0.488758\pi\)
\(444\) −9.71054 −0.460842
\(445\) −9.38882 −0.445073
\(446\) −41.4155 −1.96108
\(447\) 12.8275 0.606720
\(448\) 22.5472 1.06526
\(449\) 29.4685 1.39071 0.695353 0.718668i \(-0.255248\pi\)
0.695353 + 0.718668i \(0.255248\pi\)
\(450\) 71.9383 3.39120
\(451\) −3.87431 −0.182434
\(452\) −5.33660 −0.251013
\(453\) 3.55665 0.167106
\(454\) 52.1303 2.44660
\(455\) 11.9103 0.558365
\(456\) 10.9659 0.513525
\(457\) −1.65144 −0.0772511 −0.0386255 0.999254i \(-0.512298\pi\)
−0.0386255 + 0.999254i \(0.512298\pi\)
\(458\) 48.5726 2.26965
\(459\) −14.4923 −0.676443
\(460\) 26.7437 1.24693
\(461\) −1.95428 −0.0910198 −0.0455099 0.998964i \(-0.514491\pi\)
−0.0455099 + 0.998964i \(0.514491\pi\)
\(462\) 2.64937 0.123260
\(463\) −13.6009 −0.632089 −0.316044 0.948744i \(-0.602355\pi\)
−0.316044 + 0.948744i \(0.602355\pi\)
\(464\) 88.6233 4.11423
\(465\) 3.86897 0.179419
\(466\) −31.7489 −1.47074
\(467\) −13.4410 −0.621977 −0.310988 0.950414i \(-0.600660\pi\)
−0.310988 + 0.950414i \(0.600660\pi\)
\(468\) 42.6451 1.97127
\(469\) 13.7901 0.636766
\(470\) −96.2982 −4.44190
\(471\) 10.1499 0.467681
\(472\) 46.5796 2.14400
\(473\) −10.9738 −0.504577
\(474\) −30.5831 −1.40473
\(475\) −17.6435 −0.809541
\(476\) 17.3210 0.793905
\(477\) 14.9934 0.686499
\(478\) 49.8683 2.28092
\(479\) −25.8889 −1.18289 −0.591447 0.806344i \(-0.701443\pi\)
−0.591447 + 0.806344i \(0.701443\pi\)
\(480\) 57.6619 2.63189
\(481\) 7.96094 0.362988
\(482\) 18.6759 0.850665
\(483\) −0.858682 −0.0390714
\(484\) −47.7570 −2.17077
\(485\) 33.2880 1.51153
\(486\) −41.7519 −1.89390
\(487\) −20.5703 −0.932131 −0.466066 0.884750i \(-0.654329\pi\)
−0.466066 + 0.884750i \(0.654329\pi\)
\(488\) −110.763 −5.01401
\(489\) −7.34753 −0.332267
\(490\) −66.5921 −3.00832
\(491\) 14.8702 0.671084 0.335542 0.942025i \(-0.391081\pi\)
0.335542 + 0.942025i \(0.391081\pi\)
\(492\) 10.8097 0.487341
\(493\) 22.8414 1.02872
\(494\) −14.3789 −0.646937
\(495\) −13.9250 −0.625880
\(496\) −17.8974 −0.803619
\(497\) −0.912141 −0.0409151
\(498\) 33.2849 1.49153
\(499\) 16.1355 0.722326 0.361163 0.932503i \(-0.382380\pi\)
0.361163 + 0.932503i \(0.382380\pi\)
\(500\) −125.240 −5.60092
\(501\) 2.85987 0.127770
\(502\) 15.8380 0.706885
\(503\) −6.46730 −0.288363 −0.144181 0.989551i \(-0.546055\pi\)
−0.144181 + 0.989551i \(0.546055\pi\)
\(504\) 20.1089 0.895722
\(505\) 26.3510 1.17260
\(506\) −4.87709 −0.216813
\(507\) −1.69857 −0.0754360
\(508\) 67.8324 3.00958
\(509\) 30.0668 1.33269 0.666343 0.745645i \(-0.267859\pi\)
0.666343 + 0.745645i \(0.267859\pi\)
\(510\) 28.7653 1.27375
\(511\) 0.706646 0.0312602
\(512\) −17.1905 −0.759719
\(513\) 6.59994 0.291394
\(514\) −11.8472 −0.522559
\(515\) −0.261936 −0.0115423
\(516\) 30.6181 1.34789
\(517\) 12.7740 0.561801
\(518\) 6.00404 0.263803
\(519\) 4.12285 0.180973
\(520\) −118.008 −5.17501
\(521\) −0.674971 −0.0295710 −0.0147855 0.999891i \(-0.504707\pi\)
−0.0147855 + 0.999891i \(0.504707\pi\)
\(522\) 42.4130 1.85637
\(523\) −3.42474 −0.149753 −0.0748766 0.997193i \(-0.523856\pi\)
−0.0748766 + 0.997193i \(0.523856\pi\)
\(524\) 109.067 4.76464
\(525\) 7.43609 0.324538
\(526\) −49.6801 −2.16615
\(527\) −4.61281 −0.200937
\(528\) −14.8048 −0.644298
\(529\) −21.4193 −0.931274
\(530\) −66.3595 −2.88247
\(531\) 12.5724 0.545596
\(532\) −7.88814 −0.341994
\(533\) −8.86209 −0.383860
\(534\) −4.77719 −0.206729
\(535\) −17.6042 −0.761095
\(536\) −136.633 −5.90164
\(537\) −8.01612 −0.345921
\(538\) 79.6564 3.43423
\(539\) 8.83349 0.380485
\(540\) 86.6338 3.72813
\(541\) 42.2052 1.81454 0.907272 0.420544i \(-0.138161\pi\)
0.907272 + 0.420544i \(0.138161\pi\)
\(542\) −19.3575 −0.831477
\(543\) −2.55225 −0.109528
\(544\) −68.7478 −2.94754
\(545\) −43.5504 −1.86549
\(546\) 6.06017 0.259351
\(547\) −34.7310 −1.48499 −0.742496 0.669851i \(-0.766358\pi\)
−0.742496 + 0.669851i \(0.766358\pi\)
\(548\) 73.9431 3.15869
\(549\) −29.8964 −1.27595
\(550\) 42.2351 1.80091
\(551\) −10.4022 −0.443149
\(552\) 8.50789 0.362120
\(553\) 13.7547 0.584910
\(554\) −18.0048 −0.764951
\(555\) 7.25287 0.307867
\(556\) 40.6815 1.72528
\(557\) −33.6060 −1.42393 −0.711965 0.702215i \(-0.752195\pi\)
−0.711965 + 0.702215i \(0.752195\pi\)
\(558\) −8.56529 −0.362598
\(559\) −25.1015 −1.06168
\(560\) −50.1954 −2.12114
\(561\) −3.81574 −0.161100
\(562\) 56.3966 2.37895
\(563\) −18.8058 −0.792570 −0.396285 0.918127i \(-0.629701\pi\)
−0.396285 + 0.918127i \(0.629701\pi\)
\(564\) −35.6409 −1.50075
\(565\) 3.98594 0.167690
\(566\) 22.6067 0.950230
\(567\) 3.89348 0.163511
\(568\) 9.03756 0.379208
\(569\) 17.2585 0.723516 0.361758 0.932272i \(-0.382177\pi\)
0.361758 + 0.932272i \(0.382177\pi\)
\(570\) −13.1000 −0.548698
\(571\) −1.14730 −0.0480130 −0.0240065 0.999712i \(-0.507642\pi\)
−0.0240065 + 0.999712i \(0.507642\pi\)
\(572\) 25.0370 1.04685
\(573\) 7.94819 0.332040
\(574\) −6.68368 −0.278971
\(575\) −13.6887 −0.570860
\(576\) −60.2984 −2.51243
\(577\) 29.7016 1.23650 0.618248 0.785983i \(-0.287843\pi\)
0.618248 + 0.785983i \(0.287843\pi\)
\(578\) 11.7509 0.488772
\(579\) −2.63268 −0.109411
\(580\) −136.544 −5.66968
\(581\) −14.9699 −0.621055
\(582\) 16.9375 0.702081
\(583\) 8.80263 0.364568
\(584\) −7.00150 −0.289724
\(585\) −31.8520 −1.31692
\(586\) −73.2704 −3.02677
\(587\) −0.801683 −0.0330890 −0.0165445 0.999863i \(-0.505267\pi\)
−0.0165445 + 0.999863i \(0.505267\pi\)
\(588\) −24.6464 −1.01640
\(589\) 2.10072 0.0865587
\(590\) −55.6445 −2.29085
\(591\) 1.01012 0.0415509
\(592\) −33.5510 −1.37894
\(593\) −2.85792 −0.117361 −0.0586804 0.998277i \(-0.518689\pi\)
−0.0586804 + 0.998277i \(0.518689\pi\)
\(594\) −15.7989 −0.648238
\(595\) −12.9372 −0.530372
\(596\) 91.4244 3.74489
\(597\) −14.9316 −0.611109
\(598\) −11.1559 −0.456197
\(599\) 10.3741 0.423876 0.211938 0.977283i \(-0.432023\pi\)
0.211938 + 0.977283i \(0.432023\pi\)
\(600\) −73.6773 −3.00786
\(601\) −6.48619 −0.264577 −0.132289 0.991211i \(-0.542233\pi\)
−0.132289 + 0.991211i \(0.542233\pi\)
\(602\) −18.9312 −0.771580
\(603\) −36.8790 −1.50183
\(604\) 25.3490 1.03144
\(605\) 35.6700 1.45019
\(606\) 13.4078 0.544655
\(607\) −1.64123 −0.0666157 −0.0333078 0.999445i \(-0.510604\pi\)
−0.0333078 + 0.999445i \(0.510604\pi\)
\(608\) 31.3084 1.26972
\(609\) 4.38414 0.177654
\(610\) 132.319 5.35744
\(611\) 29.2193 1.18209
\(612\) −46.3217 −1.87244
\(613\) 20.4776 0.827082 0.413541 0.910485i \(-0.364292\pi\)
0.413541 + 0.910485i \(0.364292\pi\)
\(614\) 13.4010 0.540822
\(615\) −8.07387 −0.325570
\(616\) 11.8060 0.475676
\(617\) −23.2480 −0.935930 −0.467965 0.883747i \(-0.655013\pi\)
−0.467965 + 0.883747i \(0.655013\pi\)
\(618\) −0.133277 −0.00536120
\(619\) 12.9089 0.518852 0.259426 0.965763i \(-0.416467\pi\)
0.259426 + 0.965763i \(0.416467\pi\)
\(620\) 27.5750 1.10744
\(621\) 5.12056 0.205481
\(622\) 33.8549 1.35746
\(623\) 2.14853 0.0860792
\(624\) −33.8646 −1.35567
\(625\) 39.1043 1.56417
\(626\) 70.1547 2.80395
\(627\) 1.73772 0.0693980
\(628\) 72.3403 2.88669
\(629\) −8.64728 −0.344790
\(630\) −24.0223 −0.957073
\(631\) −34.4391 −1.37100 −0.685499 0.728074i \(-0.740416\pi\)
−0.685499 + 0.728074i \(0.740416\pi\)
\(632\) −136.283 −5.42104
\(633\) 3.66543 0.145688
\(634\) −8.27533 −0.328656
\(635\) −50.6645 −2.01056
\(636\) −24.5603 −0.973879
\(637\) 20.2057 0.800580
\(638\) 24.9008 0.985831
\(639\) 2.43935 0.0964993
\(640\) 112.857 4.46106
\(641\) 3.65825 0.144492 0.0722461 0.997387i \(-0.476983\pi\)
0.0722461 + 0.997387i \(0.476983\pi\)
\(642\) −8.95729 −0.353516
\(643\) −21.4227 −0.844828 −0.422414 0.906403i \(-0.638817\pi\)
−0.422414 + 0.906403i \(0.638817\pi\)
\(644\) −6.12001 −0.241162
\(645\) −22.8689 −0.900462
\(646\) 15.6186 0.614504
\(647\) 7.43844 0.292435 0.146218 0.989252i \(-0.453290\pi\)
0.146218 + 0.989252i \(0.453290\pi\)
\(648\) −38.5769 −1.51544
\(649\) 7.38129 0.289741
\(650\) 96.6086 3.78930
\(651\) −0.885374 −0.0347006
\(652\) −52.3674 −2.05087
\(653\) −13.6620 −0.534637 −0.267319 0.963608i \(-0.586138\pi\)
−0.267319 + 0.963608i \(0.586138\pi\)
\(654\) −22.1592 −0.866491
\(655\) −81.4633 −3.18303
\(656\) 37.3488 1.45823
\(657\) −1.88979 −0.0737279
\(658\) 22.0368 0.859085
\(659\) 24.0406 0.936490 0.468245 0.883599i \(-0.344886\pi\)
0.468245 + 0.883599i \(0.344886\pi\)
\(660\) 22.8102 0.887884
\(661\) 18.8492 0.733148 0.366574 0.930389i \(-0.380531\pi\)
0.366574 + 0.930389i \(0.380531\pi\)
\(662\) −67.1974 −2.61170
\(663\) −8.72811 −0.338972
\(664\) 148.323 5.75603
\(665\) 5.89171 0.228471
\(666\) −16.0567 −0.622185
\(667\) −8.07054 −0.312493
\(668\) 20.3829 0.788639
\(669\) 11.4488 0.442637
\(670\) 163.223 6.30587
\(671\) −17.5522 −0.677595
\(672\) −13.1953 −0.509021
\(673\) −40.1378 −1.54720 −0.773599 0.633675i \(-0.781545\pi\)
−0.773599 + 0.633675i \(0.781545\pi\)
\(674\) 81.9016 3.15473
\(675\) −44.3435 −1.70678
\(676\) −12.1061 −0.465618
\(677\) 9.21275 0.354075 0.177037 0.984204i \(-0.443349\pi\)
0.177037 + 0.984204i \(0.443349\pi\)
\(678\) 2.02811 0.0778892
\(679\) −7.61761 −0.292337
\(680\) 128.182 4.91557
\(681\) −14.4108 −0.552222
\(682\) −5.02870 −0.192559
\(683\) 11.5761 0.442949 0.221474 0.975166i \(-0.428913\pi\)
0.221474 + 0.975166i \(0.428913\pi\)
\(684\) 21.0954 0.806602
\(685\) −55.2286 −2.11018
\(686\) 32.5334 1.24213
\(687\) −13.4273 −0.512284
\(688\) 105.789 4.03317
\(689\) 20.1351 0.767088
\(690\) −10.1636 −0.386923
\(691\) −12.3409 −0.469468 −0.234734 0.972060i \(-0.575422\pi\)
−0.234734 + 0.972060i \(0.575422\pi\)
\(692\) 29.3845 1.11703
\(693\) 3.18658 0.121048
\(694\) −63.2229 −2.39991
\(695\) −30.3853 −1.15258
\(696\) −43.4383 −1.64653
\(697\) 9.62612 0.364615
\(698\) 45.4871 1.72171
\(699\) 8.77659 0.331961
\(700\) 52.9986 2.00316
\(701\) −17.6089 −0.665078 −0.332539 0.943089i \(-0.607905\pi\)
−0.332539 + 0.943089i \(0.607905\pi\)
\(702\) −36.1385 −1.36396
\(703\) 3.93806 0.148527
\(704\) −35.4013 −1.33424
\(705\) 26.6204 1.00258
\(706\) 19.2634 0.724989
\(707\) −6.03015 −0.226787
\(708\) −20.5946 −0.773992
\(709\) 52.6488 1.97727 0.988634 0.150341i \(-0.0480371\pi\)
0.988634 + 0.150341i \(0.0480371\pi\)
\(710\) −10.7964 −0.405181
\(711\) −36.7845 −1.37952
\(712\) −21.2878 −0.797795
\(713\) 1.62984 0.0610381
\(714\) −6.58263 −0.246349
\(715\) −18.7003 −0.699353
\(716\) −57.1326 −2.13515
\(717\) −13.7855 −0.514828
\(718\) 19.7781 0.738110
\(719\) −28.7662 −1.07280 −0.536399 0.843965i \(-0.680216\pi\)
−0.536399 + 0.843965i \(0.680216\pi\)
\(720\) 134.238 5.00277
\(721\) 0.0599413 0.00223233
\(722\) 44.3509 1.65057
\(723\) −5.16273 −0.192004
\(724\) −18.1905 −0.676043
\(725\) 69.8900 2.59565
\(726\) 18.1495 0.673590
\(727\) −2.89966 −0.107542 −0.0537712 0.998553i \(-0.517124\pi\)
−0.0537712 + 0.998553i \(0.517124\pi\)
\(728\) 27.0050 1.00087
\(729\) −1.26372 −0.0468045
\(730\) 8.36408 0.309568
\(731\) 27.2656 1.00845
\(732\) 48.9726 1.81008
\(733\) 11.4829 0.424132 0.212066 0.977255i \(-0.431981\pi\)
0.212066 + 0.977255i \(0.431981\pi\)
\(734\) 20.4315 0.754140
\(735\) 18.4086 0.679010
\(736\) 24.2906 0.895364
\(737\) −21.6517 −0.797551
\(738\) 17.8743 0.657960
\(739\) 0.714710 0.0262910 0.0131455 0.999914i \(-0.495816\pi\)
0.0131455 + 0.999914i \(0.495816\pi\)
\(740\) 51.6928 1.90026
\(741\) 3.97487 0.146020
\(742\) 15.1857 0.557483
\(743\) −17.8664 −0.655455 −0.327727 0.944772i \(-0.606283\pi\)
−0.327727 + 0.944772i \(0.606283\pi\)
\(744\) 8.77235 0.321610
\(745\) −68.2856 −2.50179
\(746\) 82.7283 3.02890
\(747\) 40.0341 1.46477
\(748\) −27.1956 −0.994368
\(749\) 4.02853 0.147199
\(750\) 47.5962 1.73797
\(751\) 37.2948 1.36091 0.680454 0.732791i \(-0.261783\pi\)
0.680454 + 0.732791i \(0.261783\pi\)
\(752\) −123.143 −4.49057
\(753\) −4.37822 −0.159551
\(754\) 56.9580 2.07429
\(755\) −18.9334 −0.689056
\(756\) −19.8253 −0.721037
\(757\) −30.3008 −1.10130 −0.550651 0.834736i \(-0.685620\pi\)
−0.550651 + 0.834736i \(0.685620\pi\)
\(758\) −59.4260 −2.15845
\(759\) 1.34821 0.0489370
\(760\) −58.3755 −2.11750
\(761\) 0.132741 0.00481184 0.00240592 0.999997i \(-0.499234\pi\)
0.00240592 + 0.999997i \(0.499234\pi\)
\(762\) −25.7789 −0.933872
\(763\) 9.96606 0.360795
\(764\) 56.6485 2.04947
\(765\) 34.5980 1.25089
\(766\) 86.5259 3.12631
\(767\) 16.8840 0.609644
\(768\) 20.4061 0.736340
\(769\) 19.3907 0.699246 0.349623 0.936890i \(-0.386310\pi\)
0.349623 + 0.936890i \(0.386310\pi\)
\(770\) −14.1036 −0.508257
\(771\) 3.27502 0.117947
\(772\) −18.7637 −0.675321
\(773\) −25.3106 −0.910360 −0.455180 0.890399i \(-0.650425\pi\)
−0.455180 + 0.890399i \(0.650425\pi\)
\(774\) 50.6281 1.81979
\(775\) −14.1143 −0.506999
\(776\) 75.4759 2.70943
\(777\) −1.65974 −0.0595430
\(778\) −40.2663 −1.44362
\(779\) −4.38383 −0.157067
\(780\) 52.1760 1.86820
\(781\) 1.43215 0.0512463
\(782\) 12.1177 0.433326
\(783\) −26.1438 −0.934304
\(784\) −85.1559 −3.04128
\(785\) −54.0315 −1.92847
\(786\) −41.4498 −1.47847
\(787\) −55.4960 −1.97822 −0.989110 0.147180i \(-0.952980\pi\)
−0.989110 + 0.147180i \(0.952980\pi\)
\(788\) 7.19936 0.256467
\(789\) 13.7334 0.488924
\(790\) 162.805 5.79235
\(791\) −0.912141 −0.0324320
\(792\) −31.5729 −1.12189
\(793\) −40.1489 −1.42573
\(794\) −38.9349 −1.38175
\(795\) 18.3443 0.650604
\(796\) −106.421 −3.77198
\(797\) 10.6582 0.377534 0.188767 0.982022i \(-0.439551\pi\)
0.188767 + 0.982022i \(0.439551\pi\)
\(798\) 2.99780 0.106121
\(799\) −31.7384 −1.12282
\(800\) −210.354 −7.43714
\(801\) −5.74586 −0.203020
\(802\) −27.3990 −0.967493
\(803\) −1.10950 −0.0391534
\(804\) 60.4106 2.13052
\(805\) 4.57108 0.161109
\(806\) −11.5026 −0.405163
\(807\) −22.0200 −0.775142
\(808\) 59.7472 2.10190
\(809\) −13.2400 −0.465495 −0.232748 0.972537i \(-0.574772\pi\)
−0.232748 + 0.972537i \(0.574772\pi\)
\(810\) 46.0844 1.61924
\(811\) 3.35248 0.117721 0.0588607 0.998266i \(-0.481253\pi\)
0.0588607 + 0.998266i \(0.481253\pi\)
\(812\) 31.2467 1.09654
\(813\) 5.35115 0.187673
\(814\) −9.42692 −0.330413
\(815\) 39.1136 1.37009
\(816\) 36.7842 1.28770
\(817\) −12.4170 −0.434417
\(818\) 24.3160 0.850188
\(819\) 7.28899 0.254698
\(820\) −57.5442 −2.00953
\(821\) 54.9230 1.91683 0.958414 0.285382i \(-0.0921206\pi\)
0.958414 + 0.285382i \(0.0921206\pi\)
\(822\) −28.1012 −0.980143
\(823\) −10.8079 −0.376741 −0.188370 0.982098i \(-0.560321\pi\)
−0.188370 + 0.982098i \(0.560321\pi\)
\(824\) −0.593903 −0.0206896
\(825\) −11.6754 −0.406484
\(826\) 12.7337 0.443061
\(827\) −21.6437 −0.752626 −0.376313 0.926493i \(-0.622808\pi\)
−0.376313 + 0.926493i \(0.622808\pi\)
\(828\) 16.3668 0.568787
\(829\) −29.7101 −1.03188 −0.515938 0.856626i \(-0.672557\pi\)
−0.515938 + 0.856626i \(0.672557\pi\)
\(830\) −177.188 −6.15028
\(831\) 4.97721 0.172658
\(832\) −80.9769 −2.80737
\(833\) −21.9477 −0.760444
\(834\) −15.4605 −0.535355
\(835\) −15.2242 −0.526854
\(836\) 12.3851 0.428349
\(837\) 5.27973 0.182494
\(838\) 85.7169 2.96104
\(839\) 16.0247 0.553234 0.276617 0.960980i \(-0.410787\pi\)
0.276617 + 0.960980i \(0.410787\pi\)
\(840\) 24.6031 0.848887
\(841\) 12.2054 0.420876
\(842\) 16.8704 0.581394
\(843\) −15.5901 −0.536953
\(844\) 26.1243 0.899235
\(845\) 9.04210 0.311058
\(846\) −58.9334 −2.02617
\(847\) −8.16271 −0.280474
\(848\) −84.8584 −2.91405
\(849\) −6.24934 −0.214477
\(850\) −104.938 −3.59933
\(851\) 3.05534 0.104736
\(852\) −3.99585 −0.136896
\(853\) −38.6351 −1.32284 −0.661420 0.750016i \(-0.730046\pi\)
−0.661420 + 0.750016i \(0.730046\pi\)
\(854\) −30.2798 −1.03615
\(855\) −15.7563 −0.538854
\(856\) −39.9150 −1.36427
\(857\) −21.9064 −0.748310 −0.374155 0.927366i \(-0.622067\pi\)
−0.374155 + 0.927366i \(0.622067\pi\)
\(858\) −9.51504 −0.324838
\(859\) −36.4789 −1.24464 −0.622322 0.782761i \(-0.713811\pi\)
−0.622322 + 0.782761i \(0.713811\pi\)
\(860\) −162.992 −5.55797
\(861\) 1.84762 0.0629667
\(862\) −85.5569 −2.91408
\(863\) −51.4502 −1.75138 −0.875692 0.482869i \(-0.839595\pi\)
−0.875692 + 0.482869i \(0.839595\pi\)
\(864\) 78.6874 2.67700
\(865\) −21.9475 −0.746236
\(866\) −15.7482 −0.535145
\(867\) −3.24838 −0.110321
\(868\) −6.31026 −0.214184
\(869\) −21.5962 −0.732601
\(870\) 51.8920 1.75930
\(871\) −49.5261 −1.67813
\(872\) −98.7444 −3.34391
\(873\) 20.3719 0.689484
\(874\) −5.51850 −0.186666
\(875\) −21.4063 −0.723666
\(876\) 3.09563 0.104592
\(877\) −35.8209 −1.20959 −0.604793 0.796382i \(-0.706744\pi\)
−0.604793 + 0.796382i \(0.706744\pi\)
\(878\) −93.5317 −3.15654
\(879\) 20.2547 0.683174
\(880\) 78.8116 2.65674
\(881\) 25.6573 0.864415 0.432207 0.901774i \(-0.357735\pi\)
0.432207 + 0.901774i \(0.357735\pi\)
\(882\) −40.7536 −1.37225
\(883\) −25.2048 −0.848208 −0.424104 0.905613i \(-0.639411\pi\)
−0.424104 + 0.905613i \(0.639411\pi\)
\(884\) −62.2072 −2.09225
\(885\) 15.3822 0.517069
\(886\) −4.02614 −0.135261
\(887\) −0.569316 −0.0191157 −0.00955787 0.999954i \(-0.503042\pi\)
−0.00955787 + 0.999954i \(0.503042\pi\)
\(888\) 16.4449 0.551854
\(889\) 11.5940 0.388852
\(890\) 25.4307 0.852440
\(891\) −6.11313 −0.204798
\(892\) 81.5982 2.73211
\(893\) 14.4540 0.483684
\(894\) −34.7448 −1.16204
\(895\) 42.6728 1.42639
\(896\) −25.8261 −0.862790
\(897\) 3.08390 0.102968
\(898\) −79.8189 −2.66359
\(899\) −8.32142 −0.277535
\(900\) −141.735 −4.72450
\(901\) −21.8711 −0.728631
\(902\) 10.4940 0.349412
\(903\) 5.23331 0.174154
\(904\) 9.03756 0.300585
\(905\) 13.5866 0.451633
\(906\) −9.63360 −0.320055
\(907\) −31.3531 −1.04106 −0.520531 0.853843i \(-0.674266\pi\)
−0.520531 + 0.853843i \(0.674266\pi\)
\(908\) −102.709 −3.40851
\(909\) 16.1265 0.534883
\(910\) −32.2605 −1.06942
\(911\) 42.0364 1.39273 0.696364 0.717688i \(-0.254800\pi\)
0.696364 + 0.717688i \(0.254800\pi\)
\(912\) −16.7519 −0.554710
\(913\) 23.5041 0.777873
\(914\) 4.47311 0.147957
\(915\) −36.5779 −1.20923
\(916\) −95.6993 −3.16199
\(917\) 18.6420 0.615614
\(918\) 39.2541 1.29558
\(919\) −36.9675 −1.21945 −0.609723 0.792615i \(-0.708719\pi\)
−0.609723 + 0.792615i \(0.708719\pi\)
\(920\) −45.2906 −1.49319
\(921\) −3.70455 −0.122069
\(922\) 5.29339 0.174328
\(923\) 3.27590 0.107827
\(924\) −5.21987 −0.171721
\(925\) −26.4589 −0.869964
\(926\) 36.8397 1.21063
\(927\) −0.160302 −0.00526501
\(928\) −124.020 −4.07114
\(929\) −8.82033 −0.289386 −0.144693 0.989477i \(-0.546219\pi\)
−0.144693 + 0.989477i \(0.546219\pi\)
\(930\) −10.4796 −0.343639
\(931\) 9.99522 0.327580
\(932\) 62.5527 2.04898
\(933\) −9.35877 −0.306392
\(934\) 36.4066 1.19126
\(935\) 20.3126 0.664292
\(936\) −72.2198 −2.36058
\(937\) 12.6870 0.414465 0.207233 0.978292i \(-0.433554\pi\)
0.207233 + 0.978292i \(0.433554\pi\)
\(938\) −37.3520 −1.21958
\(939\) −19.3934 −0.632880
\(940\) 189.730 6.18830
\(941\) −19.0629 −0.621432 −0.310716 0.950503i \(-0.600569\pi\)
−0.310716 + 0.950503i \(0.600569\pi\)
\(942\) −27.4921 −0.895741
\(943\) −3.40119 −0.110758
\(944\) −71.1565 −2.31595
\(945\) 14.8076 0.481692
\(946\) 29.7239 0.966406
\(947\) −56.0404 −1.82107 −0.910533 0.413435i \(-0.864329\pi\)
−0.910533 + 0.413435i \(0.864329\pi\)
\(948\) 60.2558 1.95702
\(949\) −2.53787 −0.0823829
\(950\) 47.7896 1.55050
\(951\) 2.28761 0.0741810
\(952\) −29.3332 −0.950694
\(953\) 15.6501 0.506958 0.253479 0.967341i \(-0.418425\pi\)
0.253479 + 0.967341i \(0.418425\pi\)
\(954\) −40.6113 −1.31484
\(955\) −42.3111 −1.36916
\(956\) −98.2521 −3.17770
\(957\) −6.88351 −0.222512
\(958\) 70.1231 2.26558
\(959\) 12.6385 0.408118
\(960\) −73.7745 −2.38106
\(961\) −29.3195 −0.945790
\(962\) −21.5631 −0.695223
\(963\) −10.7736 −0.347173
\(964\) −36.7959 −1.18512
\(965\) 14.0147 0.451151
\(966\) 2.32584 0.0748327
\(967\) 30.2670 0.973320 0.486660 0.873592i \(-0.338215\pi\)
0.486660 + 0.873592i \(0.338215\pi\)
\(968\) 80.8767 2.59948
\(969\) −4.31756 −0.138700
\(970\) −90.1644 −2.89500
\(971\) 15.2688 0.490000 0.245000 0.969523i \(-0.421212\pi\)
0.245000 + 0.969523i \(0.421212\pi\)
\(972\) 82.2608 2.63852
\(973\) 6.95336 0.222915
\(974\) 55.7172 1.78529
\(975\) −26.7062 −0.855284
\(976\) 169.205 5.41613
\(977\) −4.47235 −0.143083 −0.0715415 0.997438i \(-0.522792\pi\)
−0.0715415 + 0.997438i \(0.522792\pi\)
\(978\) 19.9016 0.636384
\(979\) −3.37340 −0.107814
\(980\) 131.202 4.19109
\(981\) −26.6524 −0.850945
\(982\) −40.2777 −1.28531
\(983\) 47.5911 1.51792 0.758960 0.651138i \(-0.225708\pi\)
0.758960 + 0.651138i \(0.225708\pi\)
\(984\) −18.3064 −0.583585
\(985\) −5.37726 −0.171334
\(986\) −61.8686 −1.97030
\(987\) −6.09181 −0.193904
\(988\) 28.3298 0.901290
\(989\) −9.63375 −0.306335
\(990\) 37.7174 1.19874
\(991\) −22.4691 −0.713756 −0.356878 0.934151i \(-0.616159\pi\)
−0.356878 + 0.934151i \(0.616159\pi\)
\(992\) 25.0457 0.795202
\(993\) 18.5759 0.589489
\(994\) 2.47064 0.0783640
\(995\) 79.4864 2.51989
\(996\) −65.5790 −2.07795
\(997\) −35.4199 −1.12176 −0.560880 0.827897i \(-0.689537\pi\)
−0.560880 + 0.827897i \(0.689537\pi\)
\(998\) −43.7050 −1.38346
\(999\) 9.89751 0.313144
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 \(a_p\))