Properties

Label 8023.2.a.c.1.13
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 1.13
Character \(\chi\) = 8023.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.54054 q^{2}\) \(+2.90668 q^{3}\) \(+4.45432 q^{4}\) \(-2.39844 q^{5}\) \(-7.38453 q^{6}\) \(+0.864832 q^{7}\) \(-6.23529 q^{8}\) \(+5.44881 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.54054 q^{2}\) \(+2.90668 q^{3}\) \(+4.45432 q^{4}\) \(-2.39844 q^{5}\) \(-7.38453 q^{6}\) \(+0.864832 q^{7}\) \(-6.23529 q^{8}\) \(+5.44881 q^{9}\) \(+6.09333 q^{10}\) \(+0.754457 q^{11}\) \(+12.9473 q^{12}\) \(+6.48536 q^{13}\) \(-2.19714 q^{14}\) \(-6.97152 q^{15}\) \(+6.93234 q^{16}\) \(-2.24253 q^{17}\) \(-13.8429 q^{18}\) \(+4.96611 q^{19}\) \(-10.6834 q^{20}\) \(+2.51379 q^{21}\) \(-1.91672 q^{22}\) \(-5.99611 q^{23}\) \(-18.1240 q^{24}\) \(+0.752537 q^{25}\) \(-16.4763 q^{26}\) \(+7.11791 q^{27}\) \(+3.85224 q^{28}\) \(-8.64730 q^{29}\) \(+17.7114 q^{30}\) \(-4.93301 q^{31}\) \(-5.14127 q^{32}\) \(+2.19297 q^{33}\) \(+5.69724 q^{34}\) \(-2.07425 q^{35}\) \(+24.2707 q^{36}\) \(-8.49641 q^{37}\) \(-12.6166 q^{38}\) \(+18.8509 q^{39}\) \(+14.9550 q^{40}\) \(+7.04999 q^{41}\) \(-6.38638 q^{42}\) \(-4.93997 q^{43}\) \(+3.36059 q^{44}\) \(-13.0687 q^{45}\) \(+15.2333 q^{46}\) \(-3.26788 q^{47}\) \(+20.1501 q^{48}\) \(-6.25207 q^{49}\) \(-1.91185 q^{50}\) \(-6.51834 q^{51}\) \(+28.8879 q^{52}\) \(-3.16355 q^{53}\) \(-18.0833 q^{54}\) \(-1.80952 q^{55}\) \(-5.39248 q^{56}\) \(+14.4349 q^{57}\) \(+21.9688 q^{58}\) \(-8.33643 q^{59}\) \(-31.0534 q^{60}\) \(+7.09924 q^{61}\) \(+12.5325 q^{62}\) \(+4.71230 q^{63}\) \(-0.803098 q^{64}\) \(-15.5548 q^{65}\) \(-5.57131 q^{66}\) \(-5.01430 q^{67}\) \(-9.98897 q^{68}\) \(-17.4288 q^{69}\) \(+5.26971 q^{70}\) \(-1.00000 q^{71}\) \(-33.9749 q^{72}\) \(-6.83649 q^{73}\) \(+21.5854 q^{74}\) \(+2.18739 q^{75}\) \(+22.1206 q^{76}\) \(+0.652478 q^{77}\) \(-47.8913 q^{78}\) \(+14.1403 q^{79}\) \(-16.6268 q^{80}\) \(+4.34308 q^{81}\) \(-17.9108 q^{82}\) \(-10.5939 q^{83}\) \(+11.1972 q^{84}\) \(+5.37859 q^{85}\) \(+12.5502 q^{86}\) \(-25.1350 q^{87}\) \(-4.70426 q^{88}\) \(-16.5313 q^{89}\) \(+33.2014 q^{90}\) \(+5.60874 q^{91}\) \(-26.7086 q^{92}\) \(-14.3387 q^{93}\) \(+8.30216 q^{94}\) \(-11.9109 q^{95}\) \(-14.9440 q^{96}\) \(-4.88962 q^{97}\) \(+15.8836 q^{98}\) \(+4.11089 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(158q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 158q^{4} \) \(\mathstrut -\mathstrut 31q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(158q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 158q^{4} \) \(\mathstrut -\mathstrut 31q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 10q^{11} \) \(\mathstrut -\mathstrut 46q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 27q^{14} \) \(\mathstrut -\mathstrut 41q^{15} \) \(\mathstrut +\mathstrut 150q^{16} \) \(\mathstrut -\mathstrut 137q^{17} \) \(\mathstrut -\mathstrut 67q^{18} \) \(\mathstrut -\mathstrut 42q^{19} \) \(\mathstrut -\mathstrut 66q^{20} \) \(\mathstrut -\mathstrut 46q^{21} \) \(\mathstrut -\mathstrut 8q^{22} \) \(\mathstrut -\mathstrut 26q^{23} \) \(\mathstrut -\mathstrut 48q^{24} \) \(\mathstrut +\mathstrut 129q^{25} \) \(\mathstrut -\mathstrut 67q^{26} \) \(\mathstrut -\mathstrut 89q^{27} \) \(\mathstrut -\mathstrut 21q^{28} \) \(\mathstrut -\mathstrut 79q^{29} \) \(\mathstrut -\mathstrut 11q^{30} \) \(\mathstrut +\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 147q^{32} \) \(\mathstrut -\mathstrut 112q^{33} \) \(\mathstrut -\mathstrut 28q^{34} \) \(\mathstrut -\mathstrut 53q^{35} \) \(\mathstrut +\mathstrut 141q^{36} \) \(\mathstrut -\mathstrut 60q^{37} \) \(\mathstrut -\mathstrut 53q^{38} \) \(\mathstrut -\mathstrut 3q^{39} \) \(\mathstrut -\mathstrut 48q^{40} \) \(\mathstrut -\mathstrut 128q^{41} \) \(\mathstrut +\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 63q^{43} \) \(\mathstrut -\mathstrut 88q^{45} \) \(\mathstrut -\mathstrut 2q^{46} \) \(\mathstrut -\mathstrut 92q^{47} \) \(\mathstrut -\mathstrut 131q^{48} \) \(\mathstrut +\mathstrut 122q^{49} \) \(\mathstrut -\mathstrut 116q^{50} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 89q^{52} \) \(\mathstrut -\mathstrut 94q^{53} \) \(\mathstrut -\mathstrut 71q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 104q^{56} \) \(\mathstrut -\mathstrut 93q^{57} \) \(\mathstrut -\mathstrut 65q^{58} \) \(\mathstrut -\mathstrut 54q^{59} \) \(\mathstrut -\mathstrut 12q^{60} \) \(\mathstrut +\mathstrut 17q^{61} \) \(\mathstrut -\mathstrut 97q^{62} \) \(\mathstrut -\mathstrut 28q^{63} \) \(\mathstrut +\mathstrut 163q^{64} \) \(\mathstrut -\mathstrut 163q^{65} \) \(\mathstrut -\mathstrut 65q^{66} \) \(\mathstrut -\mathstrut 35q^{67} \) \(\mathstrut -\mathstrut 217q^{68} \) \(\mathstrut -\mathstrut 46q^{69} \) \(\mathstrut -\mathstrut 79q^{70} \) \(\mathstrut -\mathstrut 158q^{71} \) \(\mathstrut -\mathstrut 99q^{72} \) \(\mathstrut -\mathstrut 165q^{73} \) \(\mathstrut -\mathstrut 94q^{75} \) \(\mathstrut -\mathstrut 93q^{76} \) \(\mathstrut -\mathstrut 140q^{77} \) \(\mathstrut +\mathstrut 25q^{78} \) \(\mathstrut -\mathstrut 61q^{79} \) \(\mathstrut -\mathstrut 134q^{80} \) \(\mathstrut +\mathstrut 114q^{81} \) \(\mathstrut +\mathstrut 10q^{82} \) \(\mathstrut -\mathstrut 158q^{83} \) \(\mathstrut -\mathstrut 160q^{84} \) \(\mathstrut +\mathstrut 23q^{85} \) \(\mathstrut -\mathstrut 122q^{86} \) \(\mathstrut -\mathstrut 71q^{87} \) \(\mathstrut -\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 251q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut -\mathstrut 57q^{91} \) \(\mathstrut -\mathstrut 58q^{92} \) \(\mathstrut -\mathstrut 52q^{93} \) \(\mathstrut -\mathstrut 64q^{94} \) \(\mathstrut -\mathstrut 84q^{95} \) \(\mathstrut -\mathstrut 98q^{96} \) \(\mathstrut -\mathstrut 48q^{97} \) \(\mathstrut -\mathstrut 84q^{98} \) \(\mathstrut +\mathstrut 85q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.54054 −1.79643 −0.898215 0.439556i \(-0.855136\pi\)
−0.898215 + 0.439556i \(0.855136\pi\)
\(3\) 2.90668 1.67817 0.839087 0.543997i \(-0.183090\pi\)
0.839087 + 0.543997i \(0.183090\pi\)
\(4\) 4.45432 2.22716
\(5\) −2.39844 −1.07262 −0.536309 0.844022i \(-0.680182\pi\)
−0.536309 + 0.844022i \(0.680182\pi\)
\(6\) −7.38453 −3.01472
\(7\) 0.864832 0.326876 0.163438 0.986554i \(-0.447742\pi\)
0.163438 + 0.986554i \(0.447742\pi\)
\(8\) −6.23529 −2.20451
\(9\) 5.44881 1.81627
\(10\) 6.09333 1.92688
\(11\) 0.754457 0.227477 0.113739 0.993511i \(-0.463717\pi\)
0.113739 + 0.993511i \(0.463717\pi\)
\(12\) 12.9473 3.73756
\(13\) 6.48536 1.79871 0.899357 0.437215i \(-0.144035\pi\)
0.899357 + 0.437215i \(0.144035\pi\)
\(14\) −2.19714 −0.587209
\(15\) −6.97152 −1.80004
\(16\) 6.93234 1.73308
\(17\) −2.24253 −0.543894 −0.271947 0.962312i \(-0.587668\pi\)
−0.271947 + 0.962312i \(0.587668\pi\)
\(18\) −13.8429 −3.26280
\(19\) 4.96611 1.13930 0.569652 0.821886i \(-0.307078\pi\)
0.569652 + 0.821886i \(0.307078\pi\)
\(20\) −10.6834 −2.38889
\(21\) 2.51379 0.548554
\(22\) −1.91672 −0.408647
\(23\) −5.99611 −1.25028 −0.625138 0.780514i \(-0.714957\pi\)
−0.625138 + 0.780514i \(0.714957\pi\)
\(24\) −18.1240 −3.69955
\(25\) 0.752537 0.150507
\(26\) −16.4763 −3.23126
\(27\) 7.11791 1.36984
\(28\) 3.85224 0.728005
\(29\) −8.64730 −1.60576 −0.802882 0.596138i \(-0.796701\pi\)
−0.802882 + 0.596138i \(0.796701\pi\)
\(30\) 17.7114 3.23364
\(31\) −4.93301 −0.885996 −0.442998 0.896523i \(-0.646085\pi\)
−0.442998 + 0.896523i \(0.646085\pi\)
\(32\) −5.14127 −0.908857
\(33\) 2.19297 0.381747
\(34\) 5.69724 0.977068
\(35\) −2.07425 −0.350612
\(36\) 24.2707 4.04512
\(37\) −8.49641 −1.39680 −0.698400 0.715707i \(-0.746104\pi\)
−0.698400 + 0.715707i \(0.746104\pi\)
\(38\) −12.6166 −2.04668
\(39\) 18.8509 3.01856
\(40\) 14.9550 2.36459
\(41\) 7.04999 1.10102 0.550512 0.834827i \(-0.314433\pi\)
0.550512 + 0.834827i \(0.314433\pi\)
\(42\) −6.38638 −0.985440
\(43\) −4.93997 −0.753338 −0.376669 0.926348i \(-0.622931\pi\)
−0.376669 + 0.926348i \(0.622931\pi\)
\(44\) 3.36059 0.506629
\(45\) −13.0687 −1.94816
\(46\) 15.2333 2.24603
\(47\) −3.26788 −0.476669 −0.238335 0.971183i \(-0.576601\pi\)
−0.238335 + 0.971183i \(0.576601\pi\)
\(48\) 20.1501 2.90842
\(49\) −6.25207 −0.893152
\(50\) −1.91185 −0.270376
\(51\) −6.51834 −0.912750
\(52\) 28.8879 4.00603
\(53\) −3.16355 −0.434548 −0.217274 0.976111i \(-0.569716\pi\)
−0.217274 + 0.976111i \(0.569716\pi\)
\(54\) −18.0833 −2.46083
\(55\) −1.80952 −0.243996
\(56\) −5.39248 −0.720600
\(57\) 14.4349 1.91195
\(58\) 21.9688 2.88464
\(59\) −8.33643 −1.08531 −0.542655 0.839956i \(-0.682581\pi\)
−0.542655 + 0.839956i \(0.682581\pi\)
\(60\) −31.0534 −4.00898
\(61\) 7.09924 0.908964 0.454482 0.890756i \(-0.349824\pi\)
0.454482 + 0.890756i \(0.349824\pi\)
\(62\) 12.5325 1.59163
\(63\) 4.71230 0.593694
\(64\) −0.803098 −0.100387
\(65\) −15.5548 −1.92933
\(66\) −5.57131 −0.685781
\(67\) −5.01430 −0.612595 −0.306297 0.951936i \(-0.599090\pi\)
−0.306297 + 0.951936i \(0.599090\pi\)
\(68\) −9.98897 −1.21134
\(69\) −17.4288 −2.09818
\(70\) 5.26971 0.629851
\(71\) −1.00000 −0.118678
\(72\) −33.9749 −4.00398
\(73\) −6.83649 −0.800151 −0.400076 0.916482i \(-0.631016\pi\)
−0.400076 + 0.916482i \(0.631016\pi\)
\(74\) 21.5854 2.50925
\(75\) 2.18739 0.252578
\(76\) 22.1206 2.53741
\(77\) 0.652478 0.0743568
\(78\) −47.8913 −5.42262
\(79\) 14.1403 1.59091 0.795456 0.606012i \(-0.207232\pi\)
0.795456 + 0.606012i \(0.207232\pi\)
\(80\) −16.6268 −1.85894
\(81\) 4.34308 0.482565
\(82\) −17.9108 −1.97791
\(83\) −10.5939 −1.16283 −0.581414 0.813608i \(-0.697500\pi\)
−0.581414 + 0.813608i \(0.697500\pi\)
\(84\) 11.1972 1.22172
\(85\) 5.37859 0.583390
\(86\) 12.5502 1.35332
\(87\) −25.1350 −2.69475
\(88\) −4.70426 −0.501476
\(89\) −16.5313 −1.75231 −0.876157 0.482026i \(-0.839901\pi\)
−0.876157 + 0.482026i \(0.839901\pi\)
\(90\) 33.2014 3.49974
\(91\) 5.60874 0.587956
\(92\) −26.7086 −2.78457
\(93\) −14.3387 −1.48686
\(94\) 8.30216 0.856303
\(95\) −11.9109 −1.22204
\(96\) −14.9440 −1.52522
\(97\) −4.88962 −0.496466 −0.248233 0.968700i \(-0.579850\pi\)
−0.248233 + 0.968700i \(0.579850\pi\)
\(98\) 15.8836 1.60449
\(99\) 4.11089 0.413160
\(100\) 3.35204 0.335204
\(101\) 0.330137 0.0328498 0.0164249 0.999865i \(-0.494772\pi\)
0.0164249 + 0.999865i \(0.494772\pi\)
\(102\) 16.5601 1.63969
\(103\) −13.0320 −1.28409 −0.642043 0.766669i \(-0.721913\pi\)
−0.642043 + 0.766669i \(0.721913\pi\)
\(104\) −40.4381 −3.96528
\(105\) −6.02919 −0.588389
\(106\) 8.03712 0.780634
\(107\) −11.6794 −1.12909 −0.564545 0.825402i \(-0.690948\pi\)
−0.564545 + 0.825402i \(0.690948\pi\)
\(108\) 31.7055 3.05086
\(109\) −6.88946 −0.659891 −0.329945 0.944000i \(-0.607030\pi\)
−0.329945 + 0.944000i \(0.607030\pi\)
\(110\) 4.59716 0.438322
\(111\) −24.6964 −2.34407
\(112\) 5.99531 0.566503
\(113\) −1.00000 −0.0940721
\(114\) −36.6724 −3.43468
\(115\) 14.3813 1.34107
\(116\) −38.5179 −3.57629
\(117\) 35.3375 3.26695
\(118\) 21.1790 1.94968
\(119\) −1.93941 −0.177786
\(120\) 43.4695 3.96820
\(121\) −10.4308 −0.948254
\(122\) −18.0359 −1.63289
\(123\) 20.4921 1.84771
\(124\) −21.9732 −1.97325
\(125\) 10.1873 0.911180
\(126\) −11.9718 −1.06653
\(127\) 8.16770 0.724766 0.362383 0.932029i \(-0.381963\pi\)
0.362383 + 0.932029i \(0.381963\pi\)
\(128\) 12.3228 1.08920
\(129\) −14.3589 −1.26423
\(130\) 39.5174 3.46591
\(131\) 11.8604 1.03625 0.518125 0.855305i \(-0.326630\pi\)
0.518125 + 0.855305i \(0.326630\pi\)
\(132\) 9.76818 0.850211
\(133\) 4.29485 0.372411
\(134\) 12.7390 1.10048
\(135\) −17.0719 −1.46932
\(136\) 13.9829 1.19902
\(137\) 12.2080 1.04300 0.521501 0.853251i \(-0.325372\pi\)
0.521501 + 0.853251i \(0.325372\pi\)
\(138\) 44.2785 3.76924
\(139\) −15.7167 −1.33307 −0.666535 0.745474i \(-0.732223\pi\)
−0.666535 + 0.745474i \(0.732223\pi\)
\(140\) −9.23938 −0.780870
\(141\) −9.49869 −0.799934
\(142\) 2.54054 0.213197
\(143\) 4.89292 0.409167
\(144\) 37.7730 3.14775
\(145\) 20.7401 1.72237
\(146\) 17.3684 1.43742
\(147\) −18.1728 −1.49887
\(148\) −37.8457 −3.11090
\(149\) −8.87057 −0.726706 −0.363353 0.931652i \(-0.618368\pi\)
−0.363353 + 0.931652i \(0.618368\pi\)
\(150\) −5.55713 −0.453738
\(151\) 0.285061 0.0231980 0.0115990 0.999933i \(-0.496308\pi\)
0.0115990 + 0.999933i \(0.496308\pi\)
\(152\) −30.9651 −2.51160
\(153\) −12.2191 −0.987859
\(154\) −1.65764 −0.133577
\(155\) 11.8316 0.950334
\(156\) 83.9679 6.72281
\(157\) 13.3021 1.06163 0.530813 0.847489i \(-0.321887\pi\)
0.530813 + 0.847489i \(0.321887\pi\)
\(158\) −35.9240 −2.85796
\(159\) −9.19545 −0.729247
\(160\) 12.3311 0.974855
\(161\) −5.18563 −0.408685
\(162\) −11.0338 −0.866894
\(163\) −1.14068 −0.0893453 −0.0446727 0.999002i \(-0.514224\pi\)
−0.0446727 + 0.999002i \(0.514224\pi\)
\(164\) 31.4029 2.45216
\(165\) −5.25971 −0.409468
\(166\) 26.9141 2.08894
\(167\) −14.8599 −1.14990 −0.574948 0.818190i \(-0.694978\pi\)
−0.574948 + 0.818190i \(0.694978\pi\)
\(168\) −15.6742 −1.20929
\(169\) 29.0598 2.23537
\(170\) −13.6645 −1.04802
\(171\) 27.0594 2.06928
\(172\) −22.0042 −1.67781
\(173\) 23.3696 1.77676 0.888380 0.459108i \(-0.151831\pi\)
0.888380 + 0.459108i \(0.151831\pi\)
\(174\) 63.8563 4.84093
\(175\) 0.650818 0.0491972
\(176\) 5.23015 0.394237
\(177\) −24.2314 −1.82134
\(178\) 41.9983 3.14791
\(179\) 8.44406 0.631138 0.315569 0.948903i \(-0.397805\pi\)
0.315569 + 0.948903i \(0.397805\pi\)
\(180\) −58.2120 −4.33887
\(181\) −10.2294 −0.760349 −0.380174 0.924915i \(-0.624136\pi\)
−0.380174 + 0.924915i \(0.624136\pi\)
\(182\) −14.2492 −1.05622
\(183\) 20.6352 1.52540
\(184\) 37.3875 2.75624
\(185\) 20.3782 1.49823
\(186\) 36.4280 2.67103
\(187\) −1.69189 −0.123724
\(188\) −14.5562 −1.06162
\(189\) 6.15579 0.447768
\(190\) 30.2602 2.19530
\(191\) −1.65633 −0.119848 −0.0599238 0.998203i \(-0.519086\pi\)
−0.0599238 + 0.998203i \(0.519086\pi\)
\(192\) −2.33435 −0.168467
\(193\) −14.3713 −1.03447 −0.517233 0.855845i \(-0.673038\pi\)
−0.517233 + 0.855845i \(0.673038\pi\)
\(194\) 12.4223 0.891866
\(195\) −45.2128 −3.23775
\(196\) −27.8487 −1.98919
\(197\) 21.7851 1.55213 0.776063 0.630655i \(-0.217214\pi\)
0.776063 + 0.630655i \(0.217214\pi\)
\(198\) −10.4439 −0.742213
\(199\) 19.1160 1.35510 0.677548 0.735478i \(-0.263042\pi\)
0.677548 + 0.735478i \(0.263042\pi\)
\(200\) −4.69229 −0.331795
\(201\) −14.5750 −1.02804
\(202\) −0.838724 −0.0590124
\(203\) −7.47846 −0.524885
\(204\) −29.0348 −2.03284
\(205\) −16.9090 −1.18098
\(206\) 33.1084 2.30677
\(207\) −32.6717 −2.27084
\(208\) 44.9587 3.11732
\(209\) 3.74671 0.259166
\(210\) 15.3174 1.05700
\(211\) 7.51634 0.517446 0.258723 0.965952i \(-0.416698\pi\)
0.258723 + 0.965952i \(0.416698\pi\)
\(212\) −14.0915 −0.967807
\(213\) −2.90668 −0.199163
\(214\) 29.6719 2.02833
\(215\) 11.8482 0.808044
\(216\) −44.3822 −3.01983
\(217\) −4.26623 −0.289610
\(218\) 17.5029 1.18545
\(219\) −19.8715 −1.34279
\(220\) −8.06020 −0.543418
\(221\) −14.5436 −0.978310
\(222\) 62.7420 4.21097
\(223\) −20.3650 −1.36374 −0.681872 0.731472i \(-0.738834\pi\)
−0.681872 + 0.731472i \(0.738834\pi\)
\(224\) −4.44633 −0.297083
\(225\) 4.10043 0.273362
\(226\) 2.54054 0.168994
\(227\) −29.9297 −1.98650 −0.993251 0.115988i \(-0.962997\pi\)
−0.993251 + 0.115988i \(0.962997\pi\)
\(228\) 64.2977 4.25822
\(229\) 16.7831 1.10906 0.554529 0.832164i \(-0.312898\pi\)
0.554529 + 0.832164i \(0.312898\pi\)
\(230\) −36.5363 −2.40913
\(231\) 1.89655 0.124784
\(232\) 53.9185 3.53992
\(233\) −3.47543 −0.227683 −0.113841 0.993499i \(-0.536316\pi\)
−0.113841 + 0.993499i \(0.536316\pi\)
\(234\) −89.7761 −5.86885
\(235\) 7.83783 0.511283
\(236\) −37.1331 −2.41716
\(237\) 41.1015 2.66983
\(238\) 4.92715 0.319380
\(239\) 11.5586 0.747667 0.373833 0.927496i \(-0.378043\pi\)
0.373833 + 0.927496i \(0.378043\pi\)
\(240\) −48.3289 −3.11962
\(241\) 8.44147 0.543763 0.271881 0.962331i \(-0.412354\pi\)
0.271881 + 0.962331i \(0.412354\pi\)
\(242\) 26.4998 1.70347
\(243\) −8.72976 −0.560014
\(244\) 31.6223 2.02441
\(245\) 14.9952 0.958010
\(246\) −52.0609 −3.31928
\(247\) 32.2070 2.04928
\(248\) 30.7588 1.95318
\(249\) −30.7930 −1.95143
\(250\) −25.8812 −1.63687
\(251\) 26.1640 1.65146 0.825728 0.564069i \(-0.190765\pi\)
0.825728 + 0.564069i \(0.190765\pi\)
\(252\) 20.9901 1.32225
\(253\) −4.52381 −0.284409
\(254\) −20.7503 −1.30199
\(255\) 15.6339 0.979031
\(256\) −29.7004 −1.85628
\(257\) −2.86796 −0.178899 −0.0894493 0.995991i \(-0.528511\pi\)
−0.0894493 + 0.995991i \(0.528511\pi\)
\(258\) 36.4794 2.27111
\(259\) −7.34796 −0.456580
\(260\) −69.2859 −4.29693
\(261\) −47.1175 −2.91650
\(262\) −30.1318 −1.86155
\(263\) 19.4056 1.19660 0.598302 0.801271i \(-0.295842\pi\)
0.598302 + 0.801271i \(0.295842\pi\)
\(264\) −13.6738 −0.841564
\(265\) 7.58761 0.466103
\(266\) −10.9112 −0.669010
\(267\) −48.0512 −2.94069
\(268\) −22.3353 −1.36435
\(269\) 3.76334 0.229455 0.114728 0.993397i \(-0.463401\pi\)
0.114728 + 0.993397i \(0.463401\pi\)
\(270\) 43.3718 2.63952
\(271\) 31.2409 1.89775 0.948874 0.315655i \(-0.102224\pi\)
0.948874 + 0.315655i \(0.102224\pi\)
\(272\) −15.5460 −0.942615
\(273\) 16.3028 0.986693
\(274\) −31.0149 −1.87368
\(275\) 0.567757 0.0342370
\(276\) −77.6335 −4.67299
\(277\) −0.856384 −0.0514551 −0.0257276 0.999669i \(-0.508190\pi\)
−0.0257276 + 0.999669i \(0.508190\pi\)
\(278\) 39.9288 2.39477
\(279\) −26.8791 −1.60921
\(280\) 12.9336 0.772928
\(281\) −30.3893 −1.81287 −0.906436 0.422343i \(-0.861208\pi\)
−0.906436 + 0.422343i \(0.861208\pi\)
\(282\) 24.1318 1.43703
\(283\) 2.57768 0.153227 0.0766136 0.997061i \(-0.475589\pi\)
0.0766136 + 0.997061i \(0.475589\pi\)
\(284\) −4.45432 −0.264315
\(285\) −34.6213 −2.05079
\(286\) −12.4306 −0.735039
\(287\) 6.09706 0.359898
\(288\) −28.0138 −1.65073
\(289\) −11.9710 −0.704179
\(290\) −52.6909 −3.09412
\(291\) −14.2126 −0.833157
\(292\) −30.4519 −1.78207
\(293\) −12.5610 −0.733819 −0.366909 0.930257i \(-0.619584\pi\)
−0.366909 + 0.930257i \(0.619584\pi\)
\(294\) 46.1686 2.69261
\(295\) 19.9945 1.16412
\(296\) 52.9776 3.07926
\(297\) 5.37016 0.311608
\(298\) 22.5360 1.30548
\(299\) −38.8869 −2.24889
\(300\) 9.74332 0.562531
\(301\) −4.27224 −0.246248
\(302\) −0.724208 −0.0416735
\(303\) 0.959603 0.0551278
\(304\) 34.4267 1.97451
\(305\) −17.0271 −0.974971
\(306\) 31.0432 1.77462
\(307\) −18.2335 −1.04064 −0.520319 0.853972i \(-0.674187\pi\)
−0.520319 + 0.853972i \(0.674187\pi\)
\(308\) 2.90635 0.165605
\(309\) −37.8800 −2.15492
\(310\) −30.0585 −1.70721
\(311\) 13.5981 0.771080 0.385540 0.922691i \(-0.374015\pi\)
0.385540 + 0.922691i \(0.374015\pi\)
\(312\) −117.541 −6.65443
\(313\) 26.4258 1.49367 0.746836 0.665008i \(-0.231572\pi\)
0.746836 + 0.665008i \(0.231572\pi\)
\(314\) −33.7945 −1.90714
\(315\) −11.3022 −0.636807
\(316\) 62.9856 3.54322
\(317\) 4.07511 0.228881 0.114440 0.993430i \(-0.463493\pi\)
0.114440 + 0.993430i \(0.463493\pi\)
\(318\) 23.3614 1.31004
\(319\) −6.52402 −0.365275
\(320\) 1.92619 0.107677
\(321\) −33.9483 −1.89481
\(322\) 13.1743 0.734174
\(323\) −11.1367 −0.619661
\(324\) 19.3455 1.07475
\(325\) 4.88047 0.270720
\(326\) 2.89795 0.160503
\(327\) −20.0255 −1.10741
\(328\) −43.9588 −2.42722
\(329\) −2.82617 −0.155812
\(330\) 13.3625 0.735580
\(331\) −26.2802 −1.44449 −0.722246 0.691636i \(-0.756890\pi\)
−0.722246 + 0.691636i \(0.756890\pi\)
\(332\) −47.1885 −2.58981
\(333\) −46.2953 −2.53697
\(334\) 37.7522 2.06571
\(335\) 12.0265 0.657080
\(336\) 17.4265 0.950691
\(337\) 10.9635 0.597221 0.298610 0.954375i \(-0.403477\pi\)
0.298610 + 0.954375i \(0.403477\pi\)
\(338\) −73.8276 −4.01569
\(339\) −2.90668 −0.157869
\(340\) 23.9580 1.29930
\(341\) −3.72175 −0.201544
\(342\) −68.7453 −3.71732
\(343\) −11.4608 −0.618825
\(344\) 30.8022 1.66074
\(345\) 41.8020 2.25055
\(346\) −59.3714 −3.19183
\(347\) 22.7537 1.22148 0.610742 0.791829i \(-0.290871\pi\)
0.610742 + 0.791829i \(0.290871\pi\)
\(348\) −111.959 −6.00165
\(349\) −0.317408 −0.0169904 −0.00849522 0.999964i \(-0.502704\pi\)
−0.00849522 + 0.999964i \(0.502704\pi\)
\(350\) −1.65343 −0.0883793
\(351\) 46.1622 2.46395
\(352\) −3.87887 −0.206744
\(353\) 0.242761 0.0129209 0.00646044 0.999979i \(-0.497944\pi\)
0.00646044 + 0.999979i \(0.497944\pi\)
\(354\) 61.5606 3.27191
\(355\) 2.39844 0.127296
\(356\) −73.6357 −3.90268
\(357\) −5.63726 −0.298356
\(358\) −21.4524 −1.13380
\(359\) 22.6126 1.19345 0.596723 0.802448i \(-0.296469\pi\)
0.596723 + 0.802448i \(0.296469\pi\)
\(360\) 81.4869 4.29474
\(361\) 5.66224 0.298013
\(362\) 25.9883 1.36591
\(363\) −30.3190 −1.59134
\(364\) 24.9831 1.30947
\(365\) 16.3970 0.858256
\(366\) −52.4246 −2.74028
\(367\) −14.7954 −0.772315 −0.386157 0.922433i \(-0.626198\pi\)
−0.386157 + 0.922433i \(0.626198\pi\)
\(368\) −41.5671 −2.16683
\(369\) 38.4141 1.99976
\(370\) −51.7714 −2.69147
\(371\) −2.73594 −0.142043
\(372\) −63.8692 −3.31147
\(373\) −0.958361 −0.0496221 −0.0248110 0.999692i \(-0.507898\pi\)
−0.0248110 + 0.999692i \(0.507898\pi\)
\(374\) 4.29832 0.222261
\(375\) 29.6113 1.52912
\(376\) 20.3762 1.05082
\(377\) −56.0808 −2.88831
\(378\) −15.6390 −0.804384
\(379\) −9.34743 −0.480145 −0.240073 0.970755i \(-0.577171\pi\)
−0.240073 + 0.970755i \(0.577171\pi\)
\(380\) −53.0551 −2.72167
\(381\) 23.7409 1.21628
\(382\) 4.20796 0.215298
\(383\) 38.4182 1.96308 0.981540 0.191258i \(-0.0612567\pi\)
0.981540 + 0.191258i \(0.0612567\pi\)
\(384\) 35.8186 1.82786
\(385\) −1.56493 −0.0797564
\(386\) 36.5107 1.85835
\(387\) −26.9169 −1.36827
\(388\) −21.7800 −1.10571
\(389\) −34.7673 −1.76277 −0.881387 0.472395i \(-0.843390\pi\)
−0.881387 + 0.472395i \(0.843390\pi\)
\(390\) 114.865 5.81640
\(391\) 13.4465 0.680018
\(392\) 38.9835 1.96896
\(393\) 34.4745 1.73901
\(394\) −55.3459 −2.78829
\(395\) −33.9148 −1.70644
\(396\) 18.3112 0.920174
\(397\) 4.52356 0.227031 0.113515 0.993536i \(-0.463789\pi\)
0.113515 + 0.993536i \(0.463789\pi\)
\(398\) −48.5649 −2.43434
\(399\) 12.4838 0.624970
\(400\) 5.21684 0.260842
\(401\) −9.81605 −0.490190 −0.245095 0.969499i \(-0.578819\pi\)
−0.245095 + 0.969499i \(0.578819\pi\)
\(402\) 37.0283 1.84680
\(403\) −31.9924 −1.59365
\(404\) 1.47054 0.0731619
\(405\) −10.4166 −0.517607
\(406\) 18.9993 0.942920
\(407\) −6.41017 −0.317740
\(408\) 40.6437 2.01216
\(409\) 2.47050 0.122158 0.0610792 0.998133i \(-0.480546\pi\)
0.0610792 + 0.998133i \(0.480546\pi\)
\(410\) 42.9580 2.12154
\(411\) 35.4848 1.75034
\(412\) −58.0489 −2.85987
\(413\) −7.20961 −0.354762
\(414\) 83.0036 4.07940
\(415\) 25.4088 1.24727
\(416\) −33.3430 −1.63477
\(417\) −45.6834 −2.23712
\(418\) −9.51866 −0.465573
\(419\) 6.53790 0.319397 0.159699 0.987166i \(-0.448948\pi\)
0.159699 + 0.987166i \(0.448948\pi\)
\(420\) −26.8560 −1.31044
\(421\) −2.94410 −0.143487 −0.0717433 0.997423i \(-0.522856\pi\)
−0.0717433 + 0.997423i \(0.522856\pi\)
\(422\) −19.0955 −0.929555
\(423\) −17.8060 −0.865760
\(424\) 19.7257 0.957964
\(425\) −1.68759 −0.0818601
\(426\) 7.38453 0.357782
\(427\) 6.13965 0.297118
\(428\) −52.0238 −2.51467
\(429\) 14.2222 0.686653
\(430\) −30.1009 −1.45159
\(431\) −28.1340 −1.35517 −0.677583 0.735446i \(-0.736973\pi\)
−0.677583 + 0.735446i \(0.736973\pi\)
\(432\) 49.3438 2.37405
\(433\) 6.35756 0.305525 0.152762 0.988263i \(-0.451183\pi\)
0.152762 + 0.988263i \(0.451183\pi\)
\(434\) 10.8385 0.520265
\(435\) 60.2848 2.89044
\(436\) −30.6879 −1.46968
\(437\) −29.7774 −1.42444
\(438\) 50.4843 2.41223
\(439\) −22.3173 −1.06515 −0.532573 0.846384i \(-0.678775\pi\)
−0.532573 + 0.846384i \(0.678775\pi\)
\(440\) 11.2829 0.537891
\(441\) −34.0663 −1.62221
\(442\) 36.9486 1.75747
\(443\) 4.82135 0.229069 0.114535 0.993419i \(-0.463462\pi\)
0.114535 + 0.993419i \(0.463462\pi\)
\(444\) −110.006 −5.22063
\(445\) 39.6494 1.87956
\(446\) 51.7381 2.44987
\(447\) −25.7840 −1.21954
\(448\) −0.694544 −0.0328141
\(449\) −38.1210 −1.79904 −0.899520 0.436879i \(-0.856084\pi\)
−0.899520 + 0.436879i \(0.856084\pi\)
\(450\) −10.4173 −0.491076
\(451\) 5.31891 0.250458
\(452\) −4.45432 −0.209514
\(453\) 0.828583 0.0389302
\(454\) 76.0374 3.56861
\(455\) −13.4523 −0.630652
\(456\) −90.0059 −4.21491
\(457\) −26.5710 −1.24294 −0.621469 0.783438i \(-0.713464\pi\)
−0.621469 + 0.783438i \(0.713464\pi\)
\(458\) −42.6381 −1.99235
\(459\) −15.9622 −0.745049
\(460\) 64.0592 2.98677
\(461\) 36.1197 1.68226 0.841130 0.540832i \(-0.181891\pi\)
0.841130 + 0.540832i \(0.181891\pi\)
\(462\) −4.81825 −0.224165
\(463\) 34.7042 1.61284 0.806422 0.591341i \(-0.201401\pi\)
0.806422 + 0.591341i \(0.201401\pi\)
\(464\) −59.9460 −2.78292
\(465\) 34.3906 1.59483
\(466\) 8.82944 0.409016
\(467\) 19.4347 0.899330 0.449665 0.893197i \(-0.351543\pi\)
0.449665 + 0.893197i \(0.351543\pi\)
\(468\) 157.404 7.27602
\(469\) −4.33653 −0.200242
\(470\) −19.9123 −0.918485
\(471\) 38.6651 1.78159
\(472\) 51.9801 2.39258
\(473\) −3.72699 −0.171367
\(474\) −104.420 −4.79616
\(475\) 3.73718 0.171474
\(476\) −8.63878 −0.395958
\(477\) −17.2376 −0.789255
\(478\) −29.3652 −1.34313
\(479\) −3.85665 −0.176215 −0.0881074 0.996111i \(-0.528082\pi\)
−0.0881074 + 0.996111i \(0.528082\pi\)
\(480\) 35.8425 1.63598
\(481\) −55.1022 −2.51244
\(482\) −21.4459 −0.976832
\(483\) −15.0730 −0.685845
\(484\) −46.4621 −2.11191
\(485\) 11.7275 0.532518
\(486\) 22.1783 1.00603
\(487\) −7.97250 −0.361268 −0.180634 0.983550i \(-0.557815\pi\)
−0.180634 + 0.983550i \(0.557815\pi\)
\(488\) −44.2658 −2.00382
\(489\) −3.31561 −0.149937
\(490\) −38.0959 −1.72100
\(491\) −28.8480 −1.30189 −0.650947 0.759123i \(-0.725628\pi\)
−0.650947 + 0.759123i \(0.725628\pi\)
\(492\) 91.2784 4.11515
\(493\) 19.3919 0.873366
\(494\) −81.8230 −3.68139
\(495\) −9.85974 −0.443163
\(496\) −34.1973 −1.53551
\(497\) −0.864832 −0.0387930
\(498\) 78.2308 3.50560
\(499\) 24.4070 1.09261 0.546303 0.837588i \(-0.316035\pi\)
0.546303 + 0.837588i \(0.316035\pi\)
\(500\) 45.3775 2.02935
\(501\) −43.1931 −1.92973
\(502\) −66.4705 −2.96672
\(503\) 11.8602 0.528821 0.264411 0.964410i \(-0.414823\pi\)
0.264411 + 0.964410i \(0.414823\pi\)
\(504\) −29.3826 −1.30880
\(505\) −0.791815 −0.0352353
\(506\) 11.4929 0.510922
\(507\) 84.4677 3.75134
\(508\) 36.3816 1.61417
\(509\) 33.7485 1.49587 0.747937 0.663769i \(-0.231044\pi\)
0.747937 + 0.663769i \(0.231044\pi\)
\(510\) −39.7184 −1.75876
\(511\) −5.91242 −0.261550
\(512\) 50.8093 2.24547
\(513\) 35.3483 1.56067
\(514\) 7.28616 0.321379
\(515\) 31.2566 1.37733
\(516\) −63.9593 −2.81565
\(517\) −2.46547 −0.108431
\(518\) 18.6678 0.820214
\(519\) 67.9281 2.98171
\(520\) 96.9885 4.25323
\(521\) 0.416514 0.0182478 0.00912391 0.999958i \(-0.497096\pi\)
0.00912391 + 0.999958i \(0.497096\pi\)
\(522\) 119.704 5.23929
\(523\) 28.6460 1.25260 0.626302 0.779580i \(-0.284568\pi\)
0.626302 + 0.779580i \(0.284568\pi\)
\(524\) 52.8301 2.30790
\(525\) 1.89172 0.0825615
\(526\) −49.3007 −2.14961
\(527\) 11.0625 0.481888
\(528\) 15.2024 0.661599
\(529\) 12.9534 0.563191
\(530\) −19.2766 −0.837322
\(531\) −45.4236 −1.97122
\(532\) 19.1306 0.829418
\(533\) 45.7217 1.98043
\(534\) 122.076 5.28274
\(535\) 28.0124 1.21108
\(536\) 31.2657 1.35047
\(537\) 24.5442 1.05916
\(538\) −9.56091 −0.412200
\(539\) −4.71691 −0.203172
\(540\) −76.0438 −3.27240
\(541\) 7.92150 0.340572 0.170286 0.985395i \(-0.445531\pi\)
0.170286 + 0.985395i \(0.445531\pi\)
\(542\) −79.3686 −3.40917
\(543\) −29.7338 −1.27600
\(544\) 11.5295 0.494322
\(545\) 16.5240 0.707810
\(546\) −41.4179 −1.77252
\(547\) −18.3996 −0.786710 −0.393355 0.919387i \(-0.628686\pi\)
−0.393355 + 0.919387i \(0.628686\pi\)
\(548\) 54.3784 2.32293
\(549\) 38.6824 1.65092
\(550\) −1.44241 −0.0615044
\(551\) −42.9435 −1.82945
\(552\) 108.674 4.62546
\(553\) 12.2290 0.520030
\(554\) 2.17567 0.0924355
\(555\) 59.2329 2.51429
\(556\) −70.0071 −2.96896
\(557\) 19.2630 0.816199 0.408100 0.912937i \(-0.366192\pi\)
0.408100 + 0.912937i \(0.366192\pi\)
\(558\) 68.2872 2.89083
\(559\) −32.0375 −1.35504
\(560\) −14.3794 −0.607641
\(561\) −4.91780 −0.207630
\(562\) 77.2050 3.25670
\(563\) −19.5573 −0.824243 −0.412121 0.911129i \(-0.635212\pi\)
−0.412121 + 0.911129i \(0.635212\pi\)
\(564\) −42.3102 −1.78158
\(565\) 2.39844 0.100903
\(566\) −6.54869 −0.275262
\(567\) 3.75604 0.157739
\(568\) 6.23529 0.261627
\(569\) 47.1227 1.97549 0.987743 0.156088i \(-0.0498883\pi\)
0.987743 + 0.156088i \(0.0498883\pi\)
\(570\) 87.9567 3.68410
\(571\) 28.1737 1.17903 0.589516 0.807757i \(-0.299319\pi\)
0.589516 + 0.807757i \(0.299319\pi\)
\(572\) 21.7946 0.911280
\(573\) −4.81442 −0.201125
\(574\) −15.4898 −0.646531
\(575\) −4.51230 −0.188176
\(576\) −4.37592 −0.182330
\(577\) 6.97596 0.290413 0.145206 0.989401i \(-0.453615\pi\)
0.145206 + 0.989401i \(0.453615\pi\)
\(578\) 30.4129 1.26501
\(579\) −41.7727 −1.73601
\(580\) 92.3830 3.83599
\(581\) −9.16191 −0.380100
\(582\) 36.1076 1.49671
\(583\) −2.38676 −0.0988497
\(584\) 42.6275 1.76394
\(585\) −84.7549 −3.50419
\(586\) 31.9116 1.31825
\(587\) 13.2436 0.546622 0.273311 0.961926i \(-0.411881\pi\)
0.273311 + 0.961926i \(0.411881\pi\)
\(588\) −80.9474 −3.33821
\(589\) −24.4979 −1.00942
\(590\) −50.7966 −2.09126
\(591\) 63.3225 2.60474
\(592\) −58.9000 −2.42077
\(593\) −13.3338 −0.547554 −0.273777 0.961793i \(-0.588273\pi\)
−0.273777 + 0.961793i \(0.588273\pi\)
\(594\) −13.6431 −0.559782
\(595\) 4.65158 0.190696
\(596\) −39.5124 −1.61849
\(597\) 55.5641 2.27409
\(598\) 98.7936 4.03997
\(599\) 19.9071 0.813384 0.406692 0.913565i \(-0.366682\pi\)
0.406692 + 0.913565i \(0.366682\pi\)
\(600\) −13.6390 −0.556809
\(601\) −36.2171 −1.47733 −0.738664 0.674074i \(-0.764543\pi\)
−0.738664 + 0.674074i \(0.764543\pi\)
\(602\) 10.8538 0.442367
\(603\) −27.3220 −1.11264
\(604\) 1.26975 0.0516656
\(605\) 25.0177 1.01711
\(606\) −2.43791 −0.0990332
\(607\) 5.59905 0.227258 0.113629 0.993523i \(-0.463752\pi\)
0.113629 + 0.993523i \(0.463752\pi\)
\(608\) −25.5321 −1.03546
\(609\) −21.7375 −0.880849
\(610\) 43.2580 1.75147
\(611\) −21.1934 −0.857392
\(612\) −54.4280 −2.20012
\(613\) 19.2666 0.778171 0.389085 0.921202i \(-0.372791\pi\)
0.389085 + 0.921202i \(0.372791\pi\)
\(614\) 46.3228 1.86943
\(615\) −49.1492 −1.98189
\(616\) −4.06839 −0.163920
\(617\) −20.9597 −0.843806 −0.421903 0.906641i \(-0.638638\pi\)
−0.421903 + 0.906641i \(0.638638\pi\)
\(618\) 96.2356 3.87116
\(619\) 19.0538 0.765839 0.382919 0.923782i \(-0.374919\pi\)
0.382919 + 0.923782i \(0.374919\pi\)
\(620\) 52.7016 2.11655
\(621\) −42.6798 −1.71268
\(622\) −34.5466 −1.38519
\(623\) −14.2968 −0.572789
\(624\) 130.681 5.23141
\(625\) −28.1964 −1.12785
\(626\) −67.1356 −2.68328
\(627\) 10.8905 0.434925
\(628\) 59.2519 2.36441
\(629\) 19.0535 0.759712
\(630\) 28.7136 1.14398
\(631\) −37.7621 −1.50329 −0.751643 0.659570i \(-0.770738\pi\)
−0.751643 + 0.659570i \(0.770738\pi\)
\(632\) −88.1691 −3.50718
\(633\) 21.8476 0.868365
\(634\) −10.3530 −0.411168
\(635\) −19.5898 −0.777396
\(636\) −40.9595 −1.62415
\(637\) −40.5469 −1.60653
\(638\) 16.5745 0.656191
\(639\) −5.44881 −0.215552
\(640\) −29.5556 −1.16829
\(641\) 28.1792 1.11301 0.556507 0.830843i \(-0.312141\pi\)
0.556507 + 0.830843i \(0.312141\pi\)
\(642\) 86.2469 3.40389
\(643\) −12.1599 −0.479539 −0.239770 0.970830i \(-0.577072\pi\)
−0.239770 + 0.970830i \(0.577072\pi\)
\(644\) −23.0985 −0.910207
\(645\) 34.4391 1.35604
\(646\) 28.2931 1.11318
\(647\) −21.0256 −0.826600 −0.413300 0.910595i \(-0.635624\pi\)
−0.413300 + 0.910595i \(0.635624\pi\)
\(648\) −27.0804 −1.06382
\(649\) −6.28948 −0.246883
\(650\) −12.3990 −0.486329
\(651\) −12.4006 −0.486017
\(652\) −5.08098 −0.198986
\(653\) −22.2896 −0.872258 −0.436129 0.899884i \(-0.643651\pi\)
−0.436129 + 0.899884i \(0.643651\pi\)
\(654\) 50.8755 1.98939
\(655\) −28.4466 −1.11150
\(656\) 48.8729 1.90817
\(657\) −37.2507 −1.45329
\(658\) 7.17998 0.279905
\(659\) 1.40781 0.0548406 0.0274203 0.999624i \(-0.491271\pi\)
0.0274203 + 0.999624i \(0.491271\pi\)
\(660\) −23.4284 −0.911951
\(661\) −21.5702 −0.838983 −0.419491 0.907759i \(-0.637792\pi\)
−0.419491 + 0.907759i \(0.637792\pi\)
\(662\) 66.7659 2.59493
\(663\) −42.2737 −1.64178
\(664\) 66.0559 2.56346
\(665\) −10.3010 −0.399454
\(666\) 117.615 4.55748
\(667\) 51.8502 2.00765
\(668\) −66.1910 −2.56101
\(669\) −59.1947 −2.28860
\(670\) −30.5538 −1.18040
\(671\) 5.35607 0.206769
\(672\) −12.9241 −0.498557
\(673\) −22.2535 −0.857810 −0.428905 0.903349i \(-0.641101\pi\)
−0.428905 + 0.903349i \(0.641101\pi\)
\(674\) −27.8532 −1.07286
\(675\) 5.35649 0.206171
\(676\) 129.442 4.97853
\(677\) 32.1078 1.23400 0.617002 0.786962i \(-0.288347\pi\)
0.617002 + 0.786962i \(0.288347\pi\)
\(678\) 7.38453 0.283601
\(679\) −4.22870 −0.162283
\(680\) −33.5371 −1.28609
\(681\) −86.9960 −3.33370
\(682\) 9.45523 0.362059
\(683\) −46.4116 −1.77589 −0.887946 0.459948i \(-0.847868\pi\)
−0.887946 + 0.459948i \(0.847868\pi\)
\(684\) 120.531 4.60862
\(685\) −29.2803 −1.11874
\(686\) 29.1166 1.11168
\(687\) 48.7832 1.86119
\(688\) −34.2455 −1.30560
\(689\) −20.5168 −0.781627
\(690\) −106.200 −4.04295
\(691\) 16.1404 0.614011 0.307006 0.951708i \(-0.400673\pi\)
0.307006 + 0.951708i \(0.400673\pi\)
\(692\) 104.096 3.95713
\(693\) 3.55523 0.135052
\(694\) −57.8067 −2.19431
\(695\) 37.6956 1.42987
\(696\) 156.724 5.94060
\(697\) −15.8098 −0.598841
\(698\) 0.806385 0.0305221
\(699\) −10.1020 −0.382091
\(700\) 2.89895 0.109570
\(701\) −34.6658 −1.30931 −0.654655 0.755928i \(-0.727186\pi\)
−0.654655 + 0.755928i \(0.727186\pi\)
\(702\) −117.277 −4.42632
\(703\) −42.1941 −1.59138
\(704\) −0.605903 −0.0228358
\(705\) 22.7821 0.858023
\(706\) −0.616744 −0.0232115
\(707\) 0.285513 0.0107378
\(708\) −107.934 −4.05642
\(709\) −44.7348 −1.68005 −0.840025 0.542548i \(-0.817460\pi\)
−0.840025 + 0.542548i \(0.817460\pi\)
\(710\) −6.09333 −0.228679
\(711\) 77.0479 2.88952
\(712\) 103.077 3.86299
\(713\) 29.5789 1.10774
\(714\) 14.3217 0.535975
\(715\) −11.7354 −0.438879
\(716\) 37.6125 1.40565
\(717\) 33.5973 1.25472
\(718\) −57.4480 −2.14394
\(719\) 9.88601 0.368686 0.184343 0.982862i \(-0.440984\pi\)
0.184343 + 0.982862i \(0.440984\pi\)
\(720\) −90.5964 −3.37633
\(721\) −11.2705 −0.419736
\(722\) −14.3851 −0.535359
\(723\) 24.5367 0.912529
\(724\) −45.5653 −1.69342
\(725\) −6.50741 −0.241679
\(726\) 77.0265 2.85872
\(727\) −9.14325 −0.339104 −0.169552 0.985521i \(-0.554232\pi\)
−0.169552 + 0.985521i \(0.554232\pi\)
\(728\) −34.9721 −1.29615
\(729\) −38.4039 −1.42237
\(730\) −41.6570 −1.54180
\(731\) 11.0780 0.409736
\(732\) 91.9160 3.39731
\(733\) 13.3708 0.493860 0.246930 0.969033i \(-0.420578\pi\)
0.246930 + 0.969033i \(0.420578\pi\)
\(734\) 37.5883 1.38741
\(735\) 43.5864 1.60771
\(736\) 30.8276 1.13632
\(737\) −3.78308 −0.139351
\(738\) −97.5923 −3.59242
\(739\) −37.1917 −1.36812 −0.684059 0.729426i \(-0.739787\pi\)
−0.684059 + 0.729426i \(0.739787\pi\)
\(740\) 90.7709 3.33680
\(741\) 93.6155 3.43905
\(742\) 6.95076 0.255170
\(743\) −49.7980 −1.82691 −0.913456 0.406938i \(-0.866597\pi\)
−0.913456 + 0.406938i \(0.866597\pi\)
\(744\) 89.4061 3.27779
\(745\) 21.2756 0.779477
\(746\) 2.43475 0.0891426
\(747\) −57.7240 −2.11201
\(748\) −7.53624 −0.275552
\(749\) −10.1007 −0.369072
\(750\) −75.2285 −2.74696
\(751\) 37.8541 1.38131 0.690657 0.723182i \(-0.257321\pi\)
0.690657 + 0.723182i \(0.257321\pi\)
\(752\) −22.6540 −0.826108
\(753\) 76.0504 2.77143
\(754\) 142.475 5.18865
\(755\) −0.683704 −0.0248825
\(756\) 27.4199 0.997252
\(757\) −12.4834 −0.453718 −0.226859 0.973928i \(-0.572846\pi\)
−0.226859 + 0.973928i \(0.572846\pi\)
\(758\) 23.7475 0.862547
\(759\) −13.1493 −0.477289
\(760\) 74.2682 2.69399
\(761\) 2.55387 0.0925777 0.0462888 0.998928i \(-0.485261\pi\)
0.0462888 + 0.998928i \(0.485261\pi\)
\(762\) −60.3146 −2.18497
\(763\) −5.95823 −0.215702
\(764\) −7.37781 −0.266920
\(765\) 29.3069 1.05959
\(766\) −97.6029 −3.52654
\(767\) −54.0647 −1.95216
\(768\) −86.3297 −3.11515
\(769\) −10.8952 −0.392893 −0.196446 0.980515i \(-0.562940\pi\)
−0.196446 + 0.980515i \(0.562940\pi\)
\(770\) 3.97577 0.143277
\(771\) −8.33626 −0.300223
\(772\) −64.0142 −2.30392
\(773\) −12.1555 −0.437202 −0.218601 0.975814i \(-0.570149\pi\)
−0.218601 + 0.975814i \(0.570149\pi\)
\(774\) 68.3835 2.45799
\(775\) −3.71228 −0.133349
\(776\) 30.4882 1.09446
\(777\) −21.3582 −0.766221
\(778\) 88.3277 3.16670
\(779\) 35.0110 1.25440
\(780\) −201.392 −7.21100
\(781\) −0.754457 −0.0269966
\(782\) −34.1613 −1.22161
\(783\) −61.5507 −2.19964
\(784\) −43.3414 −1.54791
\(785\) −31.9044 −1.13872
\(786\) −87.5837 −3.12401
\(787\) −27.3912 −0.976391 −0.488195 0.872734i \(-0.662345\pi\)
−0.488195 + 0.872734i \(0.662345\pi\)
\(788\) 97.0380 3.45683
\(789\) 56.4061 2.00811
\(790\) 86.1618 3.06550
\(791\) −0.864832 −0.0307499
\(792\) −25.6326 −0.910815
\(793\) 46.0411 1.63497
\(794\) −11.4923 −0.407845
\(795\) 22.0548 0.782202
\(796\) 85.1488 3.01802
\(797\) −18.7348 −0.663619 −0.331809 0.943346i \(-0.607659\pi\)
−0.331809 + 0.943346i \(0.607659\pi\)
\(798\) −31.7155 −1.12271
\(799\) 7.32833 0.259258
\(800\) −3.86899 −0.136790
\(801\) −90.0759 −3.18267
\(802\) 24.9380 0.880592
\(803\) −5.15784 −0.182016
\(804\) −64.9217 −2.28961
\(805\) 12.4374 0.438362
\(806\) 81.2777 2.86289
\(807\) 10.9388 0.385066
\(808\) −2.05850 −0.0724178
\(809\) 17.0279 0.598670 0.299335 0.954148i \(-0.403235\pi\)
0.299335 + 0.954148i \(0.403235\pi\)
\(810\) 26.4639 0.929846
\(811\) −11.0296 −0.387300 −0.193650 0.981071i \(-0.562033\pi\)
−0.193650 + 0.981071i \(0.562033\pi\)
\(812\) −33.3115 −1.16900
\(813\) 90.8073 3.18475
\(814\) 16.2853 0.570798
\(815\) 2.73587 0.0958333
\(816\) −45.1873 −1.58187
\(817\) −24.5324 −0.858281
\(818\) −6.27640 −0.219449
\(819\) 30.5610 1.06789
\(820\) −75.3182 −2.63023
\(821\) −17.6725 −0.616775 −0.308387 0.951261i \(-0.599789\pi\)
−0.308387 + 0.951261i \(0.599789\pi\)
\(822\) −90.1505 −3.14436
\(823\) 6.30855 0.219902 0.109951 0.993937i \(-0.464931\pi\)
0.109951 + 0.993937i \(0.464931\pi\)
\(824\) 81.2586 2.83078
\(825\) 1.65029 0.0574557
\(826\) 18.3163 0.637304
\(827\) −42.7669 −1.48715 −0.743576 0.668652i \(-0.766872\pi\)
−0.743576 + 0.668652i \(0.766872\pi\)
\(828\) −145.530 −5.05752
\(829\) −0.0991423 −0.00344335 −0.00172168 0.999999i \(-0.500548\pi\)
−0.00172168 + 0.999999i \(0.500548\pi\)
\(830\) −64.5520 −2.24063
\(831\) −2.48924 −0.0863507
\(832\) −5.20837 −0.180568
\(833\) 14.0205 0.485780
\(834\) 116.060 4.01884
\(835\) 35.6408 1.23340
\(836\) 16.6891 0.577204
\(837\) −35.1128 −1.21367
\(838\) −16.6098 −0.573775
\(839\) 27.3247 0.943352 0.471676 0.881772i \(-0.343649\pi\)
0.471676 + 0.881772i \(0.343649\pi\)
\(840\) 37.5938 1.29711
\(841\) 45.7759 1.57848
\(842\) 7.47959 0.257764
\(843\) −88.3320 −3.04232
\(844\) 33.4802 1.15244
\(845\) −69.6984 −2.39770
\(846\) 45.2369 1.55528
\(847\) −9.02088 −0.309961
\(848\) −21.9308 −0.753108
\(849\) 7.49250 0.257142
\(850\) 4.28738 0.147056
\(851\) 50.9454 1.74639
\(852\) −12.9473 −0.443567
\(853\) −25.1711 −0.861843 −0.430921 0.902389i \(-0.641811\pi\)
−0.430921 + 0.902389i \(0.641811\pi\)
\(854\) −15.5980 −0.533752
\(855\) −64.9004 −2.21955
\(856\) 72.8245 2.48909
\(857\) −38.0878 −1.30105 −0.650527 0.759483i \(-0.725452\pi\)
−0.650527 + 0.759483i \(0.725452\pi\)
\(858\) −36.1319 −1.23352
\(859\) 9.06000 0.309123 0.154562 0.987983i \(-0.450604\pi\)
0.154562 + 0.987983i \(0.450604\pi\)
\(860\) 52.7759 1.79964
\(861\) 17.7222 0.603971
\(862\) 71.4754 2.43446
\(863\) 49.0771 1.67060 0.835302 0.549791i \(-0.185293\pi\)
0.835302 + 0.549791i \(0.185293\pi\)
\(864\) −36.5951 −1.24499
\(865\) −56.0508 −1.90578
\(866\) −16.1516 −0.548854
\(867\) −34.7960 −1.18174
\(868\) −19.0032 −0.645009
\(869\) 10.6683 0.361896
\(870\) −153.156 −5.19247
\(871\) −32.5195 −1.10188
\(872\) 42.9578 1.45473
\(873\) −26.6426 −0.901716
\(874\) 75.6504 2.55891
\(875\) 8.81031 0.297843
\(876\) −88.5142 −2.99062
\(877\) −12.3218 −0.416077 −0.208039 0.978121i \(-0.566708\pi\)
−0.208039 + 0.978121i \(0.566708\pi\)
\(878\) 56.6978 1.91346
\(879\) −36.5107 −1.23148
\(880\) −12.5442 −0.422866
\(881\) 12.5558 0.423017 0.211508 0.977376i \(-0.432162\pi\)
0.211508 + 0.977376i \(0.432162\pi\)
\(882\) 86.5467 2.91418
\(883\) −3.19155 −0.107404 −0.0537021 0.998557i \(-0.517102\pi\)
−0.0537021 + 0.998557i \(0.517102\pi\)
\(884\) −64.7820 −2.17885
\(885\) 58.1176 1.95360
\(886\) −12.2488 −0.411507
\(887\) 26.5796 0.892454 0.446227 0.894920i \(-0.352767\pi\)
0.446227 + 0.894920i \(0.352767\pi\)
\(888\) 153.989 5.16753
\(889\) 7.06369 0.236908
\(890\) −100.731 −3.37650
\(891\) 3.27667 0.109773
\(892\) −90.7124 −3.03728
\(893\) −16.2286 −0.543071
\(894\) 65.5051 2.19082
\(895\) −20.2526 −0.676970
\(896\) 10.6572 0.356031
\(897\) −113.032 −3.77403
\(898\) 96.8477 3.23185
\(899\) 42.6573 1.42270
\(900\) 18.2646 0.608821
\(901\) 7.09438 0.236348
\(902\) −13.5129 −0.449930
\(903\) −12.4181 −0.413247
\(904\) 6.23529 0.207383
\(905\) 24.5348 0.815563
\(906\) −2.10504 −0.0699354
\(907\) 37.1566 1.23376 0.616882 0.787056i \(-0.288395\pi\)
0.616882 + 0.787056i \(0.288395\pi\)
\(908\) −133.316 −4.42426
\(909\) 1.79885 0.0596642
\(910\) 34.1759 1.13292
\(911\) −48.6415 −1.61156 −0.805782 0.592212i \(-0.798255\pi\)
−0.805782 + 0.592212i \(0.798255\pi\)
\(912\) 100.068 3.31357
\(913\) −7.99262 −0.264517
\(914\) 67.5046 2.23285
\(915\) −49.4925 −1.63617
\(916\) 74.7573 2.47005
\(917\) 10.2573 0.338725
\(918\) 40.5524 1.33843
\(919\) 26.8077 0.884303 0.442152 0.896940i \(-0.354215\pi\)
0.442152 + 0.896940i \(0.354215\pi\)
\(920\) −89.6719 −2.95640
\(921\) −52.9989 −1.74637
\(922\) −91.7633 −3.02206
\(923\) −6.48536 −0.213468
\(924\) 8.44783 0.277913
\(925\) −6.39386 −0.210229
\(926\) −88.1674 −2.89736
\(927\) −71.0091 −2.33225
\(928\) 44.4581 1.45941
\(929\) −9.69227 −0.317993 −0.158997 0.987279i \(-0.550826\pi\)
−0.158997 + 0.987279i \(0.550826\pi\)
\(930\) −87.3706 −2.86499
\(931\) −31.0484 −1.01757
\(932\) −15.4807 −0.507086
\(933\) 39.5255 1.29401
\(934\) −49.3745 −1.61558
\(935\) 4.05792 0.132708
\(936\) −220.339 −7.20202
\(937\) −1.30603 −0.0426661 −0.0213330 0.999772i \(-0.506791\pi\)
−0.0213330 + 0.999772i \(0.506791\pi\)
\(938\) 11.0171 0.359721
\(939\) 76.8113 2.50664
\(940\) 34.9122 1.13871
\(941\) 29.9934 0.977756 0.488878 0.872352i \(-0.337406\pi\)
0.488878 + 0.872352i \(0.337406\pi\)
\(942\) −98.2300 −3.20051
\(943\) −42.2726 −1.37658
\(944\) −57.7909 −1.88093
\(945\) −14.7643 −0.480284
\(946\) 9.46856 0.307849
\(947\) 33.7358 1.09627 0.548134 0.836391i \(-0.315338\pi\)
0.548134 + 0.836391i \(0.315338\pi\)
\(948\) 183.079 5.94613
\(949\) −44.3371 −1.43924
\(950\) −9.49444 −0.308040
\(951\) 11.8450 0.384102
\(952\) 12.0928 0.391930
\(953\) 42.9836 1.39238 0.696188 0.717860i \(-0.254878\pi\)
0.696188 + 0.717860i \(0.254878\pi\)
\(954\) 43.7927 1.41784
\(955\) 3.97261 0.128551
\(956\) 51.4859 1.66517
\(957\) −18.9633 −0.612995
\(958\) 9.79796 0.316558
\(959\) 10.5579 0.340932
\(960\) 5.59881 0.180701
\(961\) −6.66536 −0.215012
\(962\) 139.989 4.51343
\(963\) −63.6388 −2.05073
\(964\) 37.6010 1.21105
\(965\) 34.4687 1.10959
\(966\) 38.2935 1.23207
\(967\) −29.1721 −0.938112 −0.469056 0.883168i \(-0.655406\pi\)
−0.469056 + 0.883168i \(0.655406\pi\)
\(968\) 65.0391 2.09043
\(969\) −32.3708 −1.03990
\(970\) −29.7941 −0.956631
\(971\) 45.3244 1.45453 0.727265 0.686357i \(-0.240791\pi\)
0.727265 + 0.686357i \(0.240791\pi\)
\(972\) −38.8851 −1.24724
\(973\) −13.5923 −0.435748
\(974\) 20.2544 0.648993
\(975\) 14.1860 0.454315
\(976\) 49.2143 1.57531
\(977\) −39.5448 −1.26515 −0.632575 0.774499i \(-0.718002\pi\)
−0.632575 + 0.774499i \(0.718002\pi\)
\(978\) 8.42343 0.269351
\(979\) −12.4721 −0.398612
\(980\) 66.7936 2.13364
\(981\) −37.5394 −1.19854
\(982\) 73.2895 2.33876
\(983\) −28.2671 −0.901580 −0.450790 0.892630i \(-0.648858\pi\)
−0.450790 + 0.892630i \(0.648858\pi\)
\(984\) −127.774 −4.07329
\(985\) −52.2504 −1.66484
\(986\) −49.2657 −1.56894
\(987\) −8.21477 −0.261479
\(988\) 143.460 4.56408
\(989\) 29.6206 0.941881
\(990\) 25.0490 0.796110
\(991\) −29.2232 −0.928305 −0.464153 0.885755i \(-0.653641\pi\)
−0.464153 + 0.885755i \(0.653641\pi\)
\(992\) 25.3620 0.805243
\(993\) −76.3883 −2.42411
\(994\) 2.19714 0.0696889
\(995\) −45.8486 −1.45350
\(996\) −137.162 −4.34614
\(997\) −26.4138 −0.836535 −0.418267 0.908324i \(-0.637363\pi\)
−0.418267 + 0.908324i \(0.637363\pi\)
\(998\) −62.0068 −1.96279
\(999\) −60.4766 −1.91340
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 \(a_p\))