Properties

Label 4009.2.a.c.1.8
Level 4009
Weight 2
Character 4009.1
Self dual Yes
Analytic conductor 32.012
Analytic rank 1
Dimension 71
CM No

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Newspace parameters

Level: \( N \) = \( 4009 = 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4009.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0120261703\)
Analytic rank: \(1\)
Dimension: \(71\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 4009.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.48400 q^{2}\) \(+0.221625 q^{3}\) \(+4.17025 q^{4}\) \(-2.50863 q^{5}\) \(-0.550515 q^{6}\) \(+2.33062 q^{7}\) \(-5.39089 q^{8}\) \(-2.95088 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.48400 q^{2}\) \(+0.221625 q^{3}\) \(+4.17025 q^{4}\) \(-2.50863 q^{5}\) \(-0.550515 q^{6}\) \(+2.33062 q^{7}\) \(-5.39089 q^{8}\) \(-2.95088 q^{9}\) \(+6.23143 q^{10}\) \(-4.94355 q^{11}\) \(+0.924230 q^{12}\) \(-3.44352 q^{13}\) \(-5.78925 q^{14}\) \(-0.555974 q^{15}\) \(+5.05047 q^{16}\) \(+4.24355 q^{17}\) \(+7.32999 q^{18}\) \(+1.00000 q^{19}\) \(-10.4616 q^{20}\) \(+0.516522 q^{21}\) \(+12.2798 q^{22}\) \(-3.69856 q^{23}\) \(-1.19475 q^{24}\) \(+1.29322 q^{25}\) \(+8.55371 q^{26}\) \(-1.31886 q^{27}\) \(+9.71925 q^{28}\) \(+3.97886 q^{29}\) \(+1.38104 q^{30}\) \(+8.72405 q^{31}\) \(-1.76358 q^{32}\) \(-1.09561 q^{33}\) \(-10.5410 q^{34}\) \(-5.84666 q^{35}\) \(-12.3059 q^{36}\) \(+9.05184 q^{37}\) \(-2.48400 q^{38}\) \(-0.763170 q^{39}\) \(+13.5238 q^{40}\) \(+10.8766 q^{41}\) \(-1.28304 q^{42}\) \(+1.63320 q^{43}\) \(-20.6158 q^{44}\) \(+7.40267 q^{45}\) \(+9.18722 q^{46}\) \(-6.41415 q^{47}\) \(+1.11931 q^{48}\) \(-1.56822 q^{49}\) \(-3.21237 q^{50}\) \(+0.940474 q^{51}\) \(-14.3603 q^{52}\) \(+10.2742 q^{53}\) \(+3.27605 q^{54}\) \(+12.4015 q^{55}\) \(-12.5641 q^{56}\) \(+0.221625 q^{57}\) \(-9.88347 q^{58}\) \(-2.69761 q^{59}\) \(-2.31855 q^{60}\) \(+14.5808 q^{61}\) \(-21.6705 q^{62}\) \(-6.87738 q^{63}\) \(-5.72022 q^{64}\) \(+8.63853 q^{65}\) \(+2.72150 q^{66}\) \(-0.0512046 q^{67}\) \(+17.6966 q^{68}\) \(-0.819693 q^{69}\) \(+14.5231 q^{70}\) \(-12.5130 q^{71}\) \(+15.9079 q^{72}\) \(+0.953806 q^{73}\) \(-22.4848 q^{74}\) \(+0.286610 q^{75}\) \(+4.17025 q^{76}\) \(-11.5215 q^{77}\) \(+1.89571 q^{78}\) \(+0.539584 q^{79}\) \(-12.6698 q^{80}\) \(+8.56036 q^{81}\) \(-27.0175 q^{82}\) \(+4.69541 q^{83}\) \(+2.15403 q^{84}\) \(-10.6455 q^{85}\) \(-4.05687 q^{86}\) \(+0.881813 q^{87}\) \(+26.6502 q^{88}\) \(-11.0504 q^{89}\) \(-18.3882 q^{90}\) \(-8.02554 q^{91}\) \(-15.4239 q^{92}\) \(+1.93347 q^{93}\) \(+15.9327 q^{94}\) \(-2.50863 q^{95}\) \(-0.390853 q^{96}\) \(-17.2966 q^{97}\) \(+3.89546 q^{98}\) \(+14.5878 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 9q^{12} \) \(\mathstrut -\mathstrut 15q^{13} \) \(\mathstrut -\mathstrut 53q^{14} \) \(\mathstrut -\mathstrut 33q^{15} \) \(\mathstrut +\mathstrut 53q^{16} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 35q^{18} \) \(\mathstrut +\mathstrut 71q^{19} \) \(\mathstrut -\mathstrut 33q^{20} \) \(\mathstrut -\mathstrut 38q^{21} \) \(\mathstrut -\mathstrut 6q^{22} \) \(\mathstrut -\mathstrut 65q^{23} \) \(\mathstrut -\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 51q^{25} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut -\mathstrut 23q^{27} \) \(\mathstrut -\mathstrut 29q^{28} \) \(\mathstrut -\mathstrut 97q^{29} \) \(\mathstrut -\mathstrut 27q^{30} \) \(\mathstrut -\mathstrut 53q^{31} \) \(\mathstrut -\mathstrut 78q^{32} \) \(\mathstrut -\mathstrut 17q^{33} \) \(\mathstrut -\mathstrut 24q^{34} \) \(\mathstrut -\mathstrut 38q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 33q^{37} \) \(\mathstrut -\mathstrut 15q^{38} \) \(\mathstrut -\mathstrut 86q^{39} \) \(\mathstrut +\mathstrut 25q^{40} \) \(\mathstrut -\mathstrut 69q^{41} \) \(\mathstrut +\mathstrut 64q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 94q^{44} \) \(\mathstrut -\mathstrut 34q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut -\mathstrut 37q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut +\mathstrut 74q^{49} \) \(\mathstrut -\mathstrut 41q^{50} \) \(\mathstrut -\mathstrut 46q^{51} \) \(\mathstrut -\mathstrut 30q^{52} \) \(\mathstrut -\mathstrut 50q^{53} \) \(\mathstrut -\mathstrut 17q^{54} \) \(\mathstrut -\mathstrut 30q^{55} \) \(\mathstrut -\mathstrut 116q^{56} \) \(\mathstrut -\mathstrut 8q^{57} \) \(\mathstrut +\mathstrut 11q^{58} \) \(\mathstrut -\mathstrut 93q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 18q^{61} \) \(\mathstrut -\mathstrut q^{62} \) \(\mathstrut -\mathstrut 84q^{63} \) \(\mathstrut +\mathstrut 93q^{64} \) \(\mathstrut -\mathstrut 78q^{65} \) \(\mathstrut -\mathstrut 53q^{66} \) \(\mathstrut -\mathstrut 5q^{67} \) \(\mathstrut -\mathstrut 9q^{68} \) \(\mathstrut -\mathstrut 69q^{69} \) \(\mathstrut -\mathstrut 10q^{70} \) \(\mathstrut -\mathstrut 221q^{71} \) \(\mathstrut -\mathstrut 73q^{72} \) \(\mathstrut -\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 58q^{74} \) \(\mathstrut -\mathstrut 70q^{75} \) \(\mathstrut +\mathstrut 69q^{76} \) \(\mathstrut -\mathstrut 2q^{77} \) \(\mathstrut +\mathstrut 7q^{78} \) \(\mathstrut -\mathstrut 68q^{79} \) \(\mathstrut -\mathstrut 71q^{80} \) \(\mathstrut +\mathstrut 39q^{81} \) \(\mathstrut +\mathstrut 26q^{82} \) \(\mathstrut -\mathstrut 45q^{83} \) \(\mathstrut -\mathstrut 10q^{84} \) \(\mathstrut -\mathstrut 44q^{85} \) \(\mathstrut -\mathstrut 80q^{86} \) \(\mathstrut -\mathstrut 7q^{87} \) \(\mathstrut -\mathstrut 46q^{88} \) \(\mathstrut -\mathstrut 143q^{89} \) \(\mathstrut +\mathstrut 41q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 46q^{92} \) \(\mathstrut +\mathstrut 32q^{93} \) \(\mathstrut +\mathstrut 41q^{94} \) \(\mathstrut -\mathstrut 18q^{95} \) \(\mathstrut -\mathstrut 140q^{96} \) \(\mathstrut -\mathstrut 18q^{97} \) \(\mathstrut -\mathstrut 97q^{98} \) \(\mathstrut -\mathstrut 142q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.48400 −1.75645 −0.878226 0.478246i \(-0.841273\pi\)
−0.878226 + 0.478246i \(0.841273\pi\)
\(3\) 0.221625 0.127955 0.0639775 0.997951i \(-0.479621\pi\)
0.0639775 + 0.997951i \(0.479621\pi\)
\(4\) 4.17025 2.08512
\(5\) −2.50863 −1.12189 −0.560947 0.827852i \(-0.689563\pi\)
−0.560947 + 0.827852i \(0.689563\pi\)
\(6\) −0.550515 −0.224747
\(7\) 2.33062 0.880891 0.440445 0.897779i \(-0.354821\pi\)
0.440445 + 0.897779i \(0.354821\pi\)
\(8\) −5.39089 −1.90597
\(9\) −2.95088 −0.983628
\(10\) 6.23143 1.97055
\(11\) −4.94355 −1.49054 −0.745268 0.666765i \(-0.767679\pi\)
−0.745268 + 0.666765i \(0.767679\pi\)
\(12\) 0.924230 0.266802
\(13\) −3.44352 −0.955062 −0.477531 0.878615i \(-0.658468\pi\)
−0.477531 + 0.878615i \(0.658468\pi\)
\(14\) −5.78925 −1.54724
\(15\) −0.555974 −0.143552
\(16\) 5.05047 1.26262
\(17\) 4.24355 1.02921 0.514605 0.857427i \(-0.327938\pi\)
0.514605 + 0.857427i \(0.327938\pi\)
\(18\) 7.32999 1.72769
\(19\) 1.00000 0.229416
\(20\) −10.4616 −2.33929
\(21\) 0.516522 0.112714
\(22\) 12.2798 2.61806
\(23\) −3.69856 −0.771204 −0.385602 0.922665i \(-0.626006\pi\)
−0.385602 + 0.922665i \(0.626006\pi\)
\(24\) −1.19475 −0.243878
\(25\) 1.29322 0.258645
\(26\) 8.55371 1.67752
\(27\) −1.31886 −0.253815
\(28\) 9.71925 1.83677
\(29\) 3.97886 0.738855 0.369427 0.929260i \(-0.379554\pi\)
0.369427 + 0.929260i \(0.379554\pi\)
\(30\) 1.38104 0.252142
\(31\) 8.72405 1.56689 0.783443 0.621464i \(-0.213462\pi\)
0.783443 + 0.621464i \(0.213462\pi\)
\(32\) −1.76358 −0.311760
\(33\) −1.09561 −0.190722
\(34\) −10.5410 −1.80776
\(35\) −5.84666 −0.988265
\(36\) −12.3059 −2.05099
\(37\) 9.05184 1.48811 0.744057 0.668117i \(-0.232899\pi\)
0.744057 + 0.668117i \(0.232899\pi\)
\(38\) −2.48400 −0.402958
\(39\) −0.763170 −0.122205
\(40\) 13.5238 2.13829
\(41\) 10.8766 1.69864 0.849322 0.527875i \(-0.177011\pi\)
0.849322 + 0.527875i \(0.177011\pi\)
\(42\) −1.28304 −0.197977
\(43\) 1.63320 0.249061 0.124531 0.992216i \(-0.460258\pi\)
0.124531 + 0.992216i \(0.460258\pi\)
\(44\) −20.6158 −3.10795
\(45\) 7.40267 1.10353
\(46\) 9.18722 1.35458
\(47\) −6.41415 −0.935600 −0.467800 0.883834i \(-0.654953\pi\)
−0.467800 + 0.883834i \(0.654953\pi\)
\(48\) 1.11931 0.161558
\(49\) −1.56822 −0.224032
\(50\) −3.21237 −0.454297
\(51\) 0.940474 0.131693
\(52\) −14.3603 −1.99142
\(53\) 10.2742 1.41127 0.705633 0.708577i \(-0.250663\pi\)
0.705633 + 0.708577i \(0.250663\pi\)
\(54\) 3.27605 0.445814
\(55\) 12.4015 1.67222
\(56\) −12.5641 −1.67895
\(57\) 0.221625 0.0293549
\(58\) −9.88347 −1.29776
\(59\) −2.69761 −0.351199 −0.175599 0.984462i \(-0.556186\pi\)
−0.175599 + 0.984462i \(0.556186\pi\)
\(60\) −2.31855 −0.299324
\(61\) 14.5808 1.86689 0.933443 0.358726i \(-0.116789\pi\)
0.933443 + 0.358726i \(0.116789\pi\)
\(62\) −21.6705 −2.75216
\(63\) −6.87738 −0.866468
\(64\) −5.72022 −0.715027
\(65\) 8.63853 1.07148
\(66\) 2.72150 0.334994
\(67\) −0.0512046 −0.00625564 −0.00312782 0.999995i \(-0.500996\pi\)
−0.00312782 + 0.999995i \(0.500996\pi\)
\(68\) 17.6966 2.14603
\(69\) −0.819693 −0.0986794
\(70\) 14.5231 1.73584
\(71\) −12.5130 −1.48503 −0.742513 0.669832i \(-0.766366\pi\)
−0.742513 + 0.669832i \(0.766366\pi\)
\(72\) 15.9079 1.87476
\(73\) 0.953806 0.111635 0.0558173 0.998441i \(-0.482224\pi\)
0.0558173 + 0.998441i \(0.482224\pi\)
\(74\) −22.4848 −2.61380
\(75\) 0.286610 0.0330949
\(76\) 4.17025 0.478360
\(77\) −11.5215 −1.31300
\(78\) 1.89571 0.214647
\(79\) 0.539584 0.0607079 0.0303540 0.999539i \(-0.490337\pi\)
0.0303540 + 0.999539i \(0.490337\pi\)
\(80\) −12.6698 −1.41652
\(81\) 8.56036 0.951151
\(82\) −27.0175 −2.98359
\(83\) 4.69541 0.515388 0.257694 0.966227i \(-0.417037\pi\)
0.257694 + 0.966227i \(0.417037\pi\)
\(84\) 2.15403 0.235024
\(85\) −10.6455 −1.15466
\(86\) −4.05687 −0.437464
\(87\) 0.881813 0.0945402
\(88\) 26.6502 2.84092
\(89\) −11.0504 −1.17134 −0.585671 0.810549i \(-0.699169\pi\)
−0.585671 + 0.810549i \(0.699169\pi\)
\(90\) −18.3882 −1.93829
\(91\) −8.02554 −0.841305
\(92\) −15.4239 −1.60805
\(93\) 1.93347 0.200491
\(94\) 15.9327 1.64334
\(95\) −2.50863 −0.257380
\(96\) −0.390853 −0.0398912
\(97\) −17.2966 −1.75621 −0.878103 0.478472i \(-0.841191\pi\)
−0.878103 + 0.478472i \(0.841191\pi\)
\(98\) 3.89546 0.393501
\(99\) 14.5878 1.46613
\(100\) 5.39306 0.539306
\(101\) −14.3360 −1.42649 −0.713243 0.700916i \(-0.752775\pi\)
−0.713243 + 0.700916i \(0.752775\pi\)
\(102\) −2.33614 −0.231312
\(103\) −4.26223 −0.419970 −0.209985 0.977705i \(-0.567342\pi\)
−0.209985 + 0.977705i \(0.567342\pi\)
\(104\) 18.5637 1.82032
\(105\) −1.29576 −0.126454
\(106\) −25.5210 −2.47882
\(107\) −13.4756 −1.30274 −0.651370 0.758760i \(-0.725805\pi\)
−0.651370 + 0.758760i \(0.725805\pi\)
\(108\) −5.49998 −0.529236
\(109\) 15.7658 1.51009 0.755044 0.655674i \(-0.227616\pi\)
0.755044 + 0.655674i \(0.227616\pi\)
\(110\) −30.8054 −2.93718
\(111\) 2.00611 0.190412
\(112\) 11.7707 1.11223
\(113\) −12.6181 −1.18701 −0.593505 0.804830i \(-0.702256\pi\)
−0.593505 + 0.804830i \(0.702256\pi\)
\(114\) −0.550515 −0.0515605
\(115\) 9.27832 0.865208
\(116\) 16.5928 1.54060
\(117\) 10.1614 0.939425
\(118\) 6.70086 0.616864
\(119\) 9.89008 0.906622
\(120\) 2.99720 0.273605
\(121\) 13.4387 1.22170
\(122\) −36.2188 −3.27910
\(123\) 2.41053 0.217350
\(124\) 36.3815 3.26715
\(125\) 9.29893 0.831722
\(126\) 17.0834 1.52191
\(127\) −9.26718 −0.822330 −0.411165 0.911561i \(-0.634878\pi\)
−0.411165 + 0.911561i \(0.634878\pi\)
\(128\) 17.7362 1.56767
\(129\) 0.361958 0.0318686
\(130\) −21.4581 −1.88200
\(131\) 5.98666 0.523057 0.261528 0.965196i \(-0.415773\pi\)
0.261528 + 0.965196i \(0.415773\pi\)
\(132\) −4.56898 −0.397678
\(133\) 2.33062 0.202090
\(134\) 0.127192 0.0109877
\(135\) 3.30854 0.284754
\(136\) −22.8765 −1.96164
\(137\) −0.504017 −0.0430610 −0.0215305 0.999768i \(-0.506854\pi\)
−0.0215305 + 0.999768i \(0.506854\pi\)
\(138\) 2.03612 0.173326
\(139\) −2.31136 −0.196047 −0.0980236 0.995184i \(-0.531252\pi\)
−0.0980236 + 0.995184i \(0.531252\pi\)
\(140\) −24.3820 −2.06066
\(141\) −1.42153 −0.119715
\(142\) 31.0824 2.60838
\(143\) 17.0232 1.42355
\(144\) −14.9033 −1.24195
\(145\) −9.98148 −0.828916
\(146\) −2.36925 −0.196081
\(147\) −0.347557 −0.0286660
\(148\) 37.7484 3.10290
\(149\) 15.9651 1.30792 0.653958 0.756531i \(-0.273107\pi\)
0.653958 + 0.756531i \(0.273107\pi\)
\(150\) −0.711939 −0.0581296
\(151\) −15.5455 −1.26508 −0.632539 0.774528i \(-0.717987\pi\)
−0.632539 + 0.774528i \(0.717987\pi\)
\(152\) −5.39089 −0.437259
\(153\) −12.5222 −1.01236
\(154\) 28.6195 2.30622
\(155\) −21.8854 −1.75788
\(156\) −3.18261 −0.254813
\(157\) 5.86492 0.468072 0.234036 0.972228i \(-0.424807\pi\)
0.234036 + 0.972228i \(0.424807\pi\)
\(158\) −1.34033 −0.106631
\(159\) 2.27701 0.180579
\(160\) 4.42417 0.349761
\(161\) −8.61993 −0.679346
\(162\) −21.2639 −1.67065
\(163\) −13.7970 −1.08067 −0.540333 0.841451i \(-0.681702\pi\)
−0.540333 + 0.841451i \(0.681702\pi\)
\(164\) 45.3582 3.54188
\(165\) 2.74849 0.213969
\(166\) −11.6634 −0.905254
\(167\) −1.56502 −0.121105 −0.0605524 0.998165i \(-0.519286\pi\)
−0.0605524 + 0.998165i \(0.519286\pi\)
\(168\) −2.78452 −0.214830
\(169\) −1.14215 −0.0878574
\(170\) 26.4434 2.02811
\(171\) −2.95088 −0.225660
\(172\) 6.81086 0.519323
\(173\) −8.92206 −0.678332 −0.339166 0.940727i \(-0.610145\pi\)
−0.339166 + 0.940727i \(0.610145\pi\)
\(174\) −2.19042 −0.166055
\(175\) 3.01401 0.227838
\(176\) −24.9673 −1.88198
\(177\) −0.597857 −0.0449377
\(178\) 27.4492 2.05740
\(179\) −22.4025 −1.67444 −0.837220 0.546865i \(-0.815821\pi\)
−0.837220 + 0.546865i \(0.815821\pi\)
\(180\) 30.8710 2.30099
\(181\) 3.50650 0.260636 0.130318 0.991472i \(-0.458400\pi\)
0.130318 + 0.991472i \(0.458400\pi\)
\(182\) 19.9354 1.47771
\(183\) 3.23147 0.238877
\(184\) 19.9386 1.46989
\(185\) −22.7077 −1.66950
\(186\) −4.80273 −0.352153
\(187\) −20.9782 −1.53408
\(188\) −26.7486 −1.95084
\(189\) −3.07376 −0.223583
\(190\) 6.23143 0.452076
\(191\) 9.43273 0.682528 0.341264 0.939967i \(-0.389145\pi\)
0.341264 + 0.939967i \(0.389145\pi\)
\(192\) −1.26774 −0.0914913
\(193\) 9.19990 0.662223 0.331112 0.943592i \(-0.392576\pi\)
0.331112 + 0.943592i \(0.392576\pi\)
\(194\) 42.9648 3.08469
\(195\) 1.91451 0.137101
\(196\) −6.53988 −0.467134
\(197\) −23.4229 −1.66882 −0.834408 0.551147i \(-0.814190\pi\)
−0.834408 + 0.551147i \(0.814190\pi\)
\(198\) −36.2362 −2.57519
\(199\) −6.96553 −0.493773 −0.246887 0.969044i \(-0.579408\pi\)
−0.246887 + 0.969044i \(0.579408\pi\)
\(200\) −6.97163 −0.492969
\(201\) −0.0113482 −0.000800440 0
\(202\) 35.6106 2.50556
\(203\) 9.27319 0.650850
\(204\) 3.92201 0.274596
\(205\) −27.2854 −1.90570
\(206\) 10.5874 0.737658
\(207\) 10.9140 0.758577
\(208\) −17.3914 −1.20588
\(209\) −4.94355 −0.341953
\(210\) 3.21867 0.222110
\(211\) 1.00000 0.0688428
\(212\) 42.8459 2.94267
\(213\) −2.77320 −0.190017
\(214\) 33.4735 2.28820
\(215\) −4.09710 −0.279420
\(216\) 7.10985 0.483764
\(217\) 20.3324 1.38026
\(218\) −39.1622 −2.65240
\(219\) 0.211387 0.0142842
\(220\) 51.7175 3.48679
\(221\) −14.6127 −0.982960
\(222\) −4.98318 −0.334449
\(223\) 22.5475 1.50989 0.754946 0.655787i \(-0.227663\pi\)
0.754946 + 0.655787i \(0.227663\pi\)
\(224\) −4.11023 −0.274626
\(225\) −3.81615 −0.254410
\(226\) 31.3433 2.08493
\(227\) −19.9149 −1.32180 −0.660900 0.750474i \(-0.729825\pi\)
−0.660900 + 0.750474i \(0.729825\pi\)
\(228\) 0.924230 0.0612086
\(229\) −24.8757 −1.64383 −0.821917 0.569607i \(-0.807095\pi\)
−0.821917 + 0.569607i \(0.807095\pi\)
\(230\) −23.0473 −1.51970
\(231\) −2.55345 −0.168005
\(232\) −21.4496 −1.40823
\(233\) 13.5434 0.887259 0.443630 0.896210i \(-0.353691\pi\)
0.443630 + 0.896210i \(0.353691\pi\)
\(234\) −25.2410 −1.65005
\(235\) 16.0907 1.04964
\(236\) −11.2497 −0.732293
\(237\) 0.119585 0.00776789
\(238\) −24.5669 −1.59244
\(239\) 23.1409 1.49686 0.748432 0.663212i \(-0.230807\pi\)
0.748432 + 0.663212i \(0.230807\pi\)
\(240\) −2.80793 −0.181251
\(241\) 9.30424 0.599339 0.299669 0.954043i \(-0.403124\pi\)
0.299669 + 0.954043i \(0.403124\pi\)
\(242\) −33.3817 −2.14586
\(243\) 5.85377 0.375520
\(244\) 60.8057 3.89269
\(245\) 3.93409 0.251340
\(246\) −5.98775 −0.381765
\(247\) −3.44352 −0.219106
\(248\) −47.0304 −2.98644
\(249\) 1.04062 0.0659465
\(250\) −23.0985 −1.46088
\(251\) −15.5023 −0.978498 −0.489249 0.872144i \(-0.662729\pi\)
−0.489249 + 0.872144i \(0.662729\pi\)
\(252\) −28.6804 −1.80669
\(253\) 18.2840 1.14951
\(254\) 23.0197 1.44438
\(255\) −2.35930 −0.147745
\(256\) −32.6162 −2.03851
\(257\) 6.49144 0.404925 0.202462 0.979290i \(-0.435106\pi\)
0.202462 + 0.979290i \(0.435106\pi\)
\(258\) −0.899103 −0.0559757
\(259\) 21.0964 1.31086
\(260\) 36.0248 2.23416
\(261\) −11.7411 −0.726758
\(262\) −14.8709 −0.918724
\(263\) 4.57133 0.281880 0.140940 0.990018i \(-0.454987\pi\)
0.140940 + 0.990018i \(0.454987\pi\)
\(264\) 5.90633 0.363510
\(265\) −25.7741 −1.58329
\(266\) −5.78925 −0.354962
\(267\) −2.44904 −0.149879
\(268\) −0.213536 −0.0130438
\(269\) −12.3664 −0.753994 −0.376997 0.926214i \(-0.623043\pi\)
−0.376997 + 0.926214i \(0.623043\pi\)
\(270\) −8.21840 −0.500156
\(271\) −12.7536 −0.774723 −0.387362 0.921928i \(-0.626613\pi\)
−0.387362 + 0.921928i \(0.626613\pi\)
\(272\) 21.4319 1.29950
\(273\) −1.77866 −0.107649
\(274\) 1.25198 0.0756347
\(275\) −6.39312 −0.385519
\(276\) −3.41832 −0.205759
\(277\) 32.3341 1.94277 0.971383 0.237520i \(-0.0763345\pi\)
0.971383 + 0.237520i \(0.0763345\pi\)
\(278\) 5.74142 0.344348
\(279\) −25.7437 −1.54123
\(280\) 31.5187 1.88360
\(281\) −15.8695 −0.946693 −0.473346 0.880876i \(-0.656954\pi\)
−0.473346 + 0.880876i \(0.656954\pi\)
\(282\) 3.53109 0.210273
\(283\) 30.0476 1.78614 0.893072 0.449913i \(-0.148545\pi\)
0.893072 + 0.449913i \(0.148545\pi\)
\(284\) −52.1825 −3.09646
\(285\) −0.555974 −0.0329331
\(286\) −42.2857 −2.50041
\(287\) 25.3493 1.49632
\(288\) 5.20412 0.306655
\(289\) 1.00768 0.0592751
\(290\) 24.7940 1.45595
\(291\) −3.83336 −0.224715
\(292\) 3.97761 0.232772
\(293\) 19.7465 1.15360 0.576802 0.816884i \(-0.304300\pi\)
0.576802 + 0.816884i \(0.304300\pi\)
\(294\) 0.863331 0.0503505
\(295\) 6.76731 0.394008
\(296\) −48.7975 −2.83630
\(297\) 6.51986 0.378321
\(298\) −39.6574 −2.29729
\(299\) 12.7361 0.736547
\(300\) 1.19524 0.0690070
\(301\) 3.80637 0.219395
\(302\) 38.6151 2.22205
\(303\) −3.17722 −0.182526
\(304\) 5.05047 0.289664
\(305\) −36.5779 −2.09445
\(306\) 31.1051 1.77816
\(307\) −3.84824 −0.219631 −0.109815 0.993952i \(-0.535026\pi\)
−0.109815 + 0.993952i \(0.535026\pi\)
\(308\) −48.0476 −2.73777
\(309\) −0.944616 −0.0537373
\(310\) 54.3633 3.08763
\(311\) 1.07263 0.0608234 0.0304117 0.999537i \(-0.490318\pi\)
0.0304117 + 0.999537i \(0.490318\pi\)
\(312\) 4.11417 0.232919
\(313\) −16.2107 −0.916285 −0.458143 0.888879i \(-0.651485\pi\)
−0.458143 + 0.888879i \(0.651485\pi\)
\(314\) −14.5685 −0.822146
\(315\) 17.2528 0.972085
\(316\) 2.25020 0.126584
\(317\) −19.3172 −1.08496 −0.542480 0.840069i \(-0.682515\pi\)
−0.542480 + 0.840069i \(0.682515\pi\)
\(318\) −5.65609 −0.317178
\(319\) −19.6697 −1.10129
\(320\) 14.3499 0.802184
\(321\) −2.98654 −0.166692
\(322\) 21.4119 1.19324
\(323\) 4.24355 0.236117
\(324\) 35.6988 1.98327
\(325\) −4.45325 −0.247022
\(326\) 34.2718 1.89814
\(327\) 3.49409 0.193223
\(328\) −58.6347 −3.23756
\(329\) −14.9489 −0.824161
\(330\) −6.82724 −0.375827
\(331\) −6.39605 −0.351559 −0.175779 0.984430i \(-0.556245\pi\)
−0.175779 + 0.984430i \(0.556245\pi\)
\(332\) 19.5810 1.07465
\(333\) −26.7109 −1.46375
\(334\) 3.88751 0.212715
\(335\) 0.128453 0.00701816
\(336\) 2.60868 0.142315
\(337\) 17.5536 0.956204 0.478102 0.878304i \(-0.341325\pi\)
0.478102 + 0.878304i \(0.341325\pi\)
\(338\) 2.83709 0.154317
\(339\) −2.79648 −0.151884
\(340\) −44.3943 −2.40762
\(341\) −43.1278 −2.33550
\(342\) 7.32999 0.396360
\(343\) −19.9692 −1.07824
\(344\) −8.80442 −0.474702
\(345\) 2.05631 0.110708
\(346\) 22.1624 1.19146
\(347\) 34.5541 1.85496 0.927481 0.373870i \(-0.121969\pi\)
0.927481 + 0.373870i \(0.121969\pi\)
\(348\) 3.67738 0.197128
\(349\) −18.4862 −0.989545 −0.494772 0.869023i \(-0.664749\pi\)
−0.494772 + 0.869023i \(0.664749\pi\)
\(350\) −7.48679 −0.400186
\(351\) 4.54153 0.242409
\(352\) 8.71834 0.464689
\(353\) 16.8822 0.898551 0.449275 0.893393i \(-0.351682\pi\)
0.449275 + 0.893393i \(0.351682\pi\)
\(354\) 1.48508 0.0789309
\(355\) 31.3906 1.66604
\(356\) −46.0830 −2.44239
\(357\) 2.19189 0.116007
\(358\) 55.6478 2.94108
\(359\) −5.96952 −0.315059 −0.157530 0.987514i \(-0.550353\pi\)
−0.157530 + 0.987514i \(0.550353\pi\)
\(360\) −39.9070 −2.10328
\(361\) 1.00000 0.0526316
\(362\) −8.71013 −0.457795
\(363\) 2.97835 0.156323
\(364\) −33.4685 −1.75422
\(365\) −2.39275 −0.125242
\(366\) −8.02698 −0.419577
\(367\) 20.0412 1.04614 0.523071 0.852289i \(-0.324786\pi\)
0.523071 + 0.852289i \(0.324786\pi\)
\(368\) −18.6795 −0.973735
\(369\) −32.0957 −1.67083
\(370\) 56.4059 2.93240
\(371\) 23.9452 1.24317
\(372\) 8.06303 0.418049
\(373\) 22.1700 1.14792 0.573959 0.818884i \(-0.305407\pi\)
0.573959 + 0.818884i \(0.305407\pi\)
\(374\) 52.1098 2.69453
\(375\) 2.06087 0.106423
\(376\) 34.5780 1.78322
\(377\) −13.7013 −0.705652
\(378\) 7.63522 0.392714
\(379\) −23.3293 −1.19835 −0.599173 0.800620i \(-0.704504\pi\)
−0.599173 + 0.800620i \(0.704504\pi\)
\(380\) −10.4616 −0.536669
\(381\) −2.05384 −0.105221
\(382\) −23.4309 −1.19883
\(383\) 15.9142 0.813180 0.406590 0.913611i \(-0.366718\pi\)
0.406590 + 0.913611i \(0.366718\pi\)
\(384\) 3.93077 0.200591
\(385\) 28.9032 1.47305
\(386\) −22.8525 −1.16316
\(387\) −4.81939 −0.244983
\(388\) −72.1312 −3.66191
\(389\) −23.6738 −1.20031 −0.600155 0.799884i \(-0.704894\pi\)
−0.600155 + 0.799884i \(0.704894\pi\)
\(390\) −4.75564 −0.240811
\(391\) −15.6950 −0.793731
\(392\) 8.45412 0.426998
\(393\) 1.32679 0.0669278
\(394\) 58.1826 2.93120
\(395\) −1.35362 −0.0681078
\(396\) 60.8349 3.05707
\(397\) −36.3576 −1.82473 −0.912367 0.409373i \(-0.865748\pi\)
−0.912367 + 0.409373i \(0.865748\pi\)
\(398\) 17.3024 0.867289
\(399\) 0.516522 0.0258585
\(400\) 6.53139 0.326569
\(401\) 22.3963 1.11842 0.559208 0.829027i \(-0.311105\pi\)
0.559208 + 0.829027i \(0.311105\pi\)
\(402\) 0.0281889 0.00140594
\(403\) −30.0415 −1.49647
\(404\) −59.7847 −2.97440
\(405\) −21.4748 −1.06709
\(406\) −23.0346 −1.14319
\(407\) −44.7482 −2.21809
\(408\) −5.07000 −0.251002
\(409\) −27.1435 −1.34216 −0.671079 0.741386i \(-0.734169\pi\)
−0.671079 + 0.741386i \(0.734169\pi\)
\(410\) 67.7770 3.34727
\(411\) −0.111703 −0.00550988
\(412\) −17.7746 −0.875690
\(413\) −6.28710 −0.309368
\(414\) −27.1104 −1.33240
\(415\) −11.7790 −0.578210
\(416\) 6.07293 0.297750
\(417\) −0.512255 −0.0250852
\(418\) 12.2798 0.600623
\(419\) 15.4957 0.757015 0.378508 0.925598i \(-0.376437\pi\)
0.378508 + 0.925598i \(0.376437\pi\)
\(420\) −5.40365 −0.263671
\(421\) −14.6595 −0.714462 −0.357231 0.934016i \(-0.616279\pi\)
−0.357231 + 0.934016i \(0.616279\pi\)
\(422\) −2.48400 −0.120919
\(423\) 18.9274 0.920282
\(424\) −55.3870 −2.68983
\(425\) 5.48785 0.266200
\(426\) 6.88863 0.333755
\(427\) 33.9824 1.64452
\(428\) −56.1968 −2.71637
\(429\) 3.77277 0.182151
\(430\) 10.1772 0.490788
\(431\) −32.7896 −1.57942 −0.789711 0.613479i \(-0.789769\pi\)
−0.789711 + 0.613479i \(0.789769\pi\)
\(432\) −6.66088 −0.320472
\(433\) −25.6682 −1.23354 −0.616768 0.787145i \(-0.711558\pi\)
−0.616768 + 0.787145i \(0.711558\pi\)
\(434\) −50.5057 −2.42435
\(435\) −2.21214 −0.106064
\(436\) 65.7472 3.14872
\(437\) −3.69856 −0.176926
\(438\) −0.525085 −0.0250895
\(439\) −31.6150 −1.50890 −0.754451 0.656356i \(-0.772097\pi\)
−0.754451 + 0.656356i \(0.772097\pi\)
\(440\) −66.8554 −3.18720
\(441\) 4.62764 0.220364
\(442\) 36.2980 1.72652
\(443\) 26.4232 1.25541 0.627703 0.778453i \(-0.283995\pi\)
0.627703 + 0.778453i \(0.283995\pi\)
\(444\) 8.36598 0.397032
\(445\) 27.7214 1.31412
\(446\) −56.0079 −2.65205
\(447\) 3.53827 0.167354
\(448\) −13.3316 −0.629860
\(449\) −4.55193 −0.214819 −0.107409 0.994215i \(-0.534256\pi\)
−0.107409 + 0.994215i \(0.534256\pi\)
\(450\) 9.47931 0.446859
\(451\) −53.7692 −2.53189
\(452\) −52.6206 −2.47506
\(453\) −3.44528 −0.161873
\(454\) 49.4686 2.32168
\(455\) 20.1331 0.943854
\(456\) −1.19475 −0.0559495
\(457\) −23.0502 −1.07824 −0.539121 0.842228i \(-0.681244\pi\)
−0.539121 + 0.842228i \(0.681244\pi\)
\(458\) 61.7913 2.88732
\(459\) −5.59665 −0.261229
\(460\) 38.6929 1.80407
\(461\) −5.06797 −0.236039 −0.118020 0.993011i \(-0.537655\pi\)
−0.118020 + 0.993011i \(0.537655\pi\)
\(462\) 6.34278 0.295093
\(463\) −25.6071 −1.19006 −0.595032 0.803702i \(-0.702861\pi\)
−0.595032 + 0.803702i \(0.702861\pi\)
\(464\) 20.0951 0.932892
\(465\) −4.85035 −0.224930
\(466\) −33.6418 −1.55843
\(467\) −33.1025 −1.53180 −0.765901 0.642958i \(-0.777707\pi\)
−0.765901 + 0.642958i \(0.777707\pi\)
\(468\) 42.3757 1.95882
\(469\) −0.119338 −0.00551053
\(470\) −39.9694 −1.84365
\(471\) 1.29981 0.0598922
\(472\) 14.5425 0.669374
\(473\) −8.07382 −0.371235
\(474\) −0.297049 −0.0136439
\(475\) 1.29322 0.0593372
\(476\) 41.2441 1.89042
\(477\) −30.3179 −1.38816
\(478\) −57.4821 −2.62917
\(479\) −1.66981 −0.0762954 −0.0381477 0.999272i \(-0.512146\pi\)
−0.0381477 + 0.999272i \(0.512146\pi\)
\(480\) 0.980505 0.0447537
\(481\) −31.1702 −1.42124
\(482\) −23.1117 −1.05271
\(483\) −1.91039 −0.0869257
\(484\) 56.0427 2.54740
\(485\) 43.3908 1.97028
\(486\) −14.5408 −0.659582
\(487\) −14.3500 −0.650263 −0.325131 0.945669i \(-0.605409\pi\)
−0.325131 + 0.945669i \(0.605409\pi\)
\(488\) −78.6038 −3.55822
\(489\) −3.05776 −0.138277
\(490\) −9.77228 −0.441466
\(491\) 25.3987 1.14623 0.573113 0.819477i \(-0.305736\pi\)
0.573113 + 0.819477i \(0.305736\pi\)
\(492\) 10.0525 0.453202
\(493\) 16.8845 0.760438
\(494\) 8.55371 0.384849
\(495\) −36.5955 −1.64484
\(496\) 44.0606 1.97838
\(497\) −29.1631 −1.30815
\(498\) −2.58489 −0.115832
\(499\) 0.531444 0.0237907 0.0118954 0.999929i \(-0.496214\pi\)
0.0118954 + 0.999929i \(0.496214\pi\)
\(500\) 38.7788 1.73424
\(501\) −0.346847 −0.0154960
\(502\) 38.5078 1.71869
\(503\) 2.66162 0.118676 0.0593378 0.998238i \(-0.481101\pi\)
0.0593378 + 0.998238i \(0.481101\pi\)
\(504\) 37.0752 1.65146
\(505\) 35.9638 1.60037
\(506\) −45.4175 −2.01905
\(507\) −0.253128 −0.0112418
\(508\) −38.6465 −1.71466
\(509\) −2.09432 −0.0928289 −0.0464144 0.998922i \(-0.514779\pi\)
−0.0464144 + 0.998922i \(0.514779\pi\)
\(510\) 5.86050 0.259507
\(511\) 2.22296 0.0983378
\(512\) 45.5462 2.01288
\(513\) −1.31886 −0.0582292
\(514\) −16.1247 −0.711231
\(515\) 10.6924 0.471162
\(516\) 1.50945 0.0664500
\(517\) 31.7087 1.39455
\(518\) −52.4034 −2.30247
\(519\) −1.97735 −0.0867960
\(520\) −46.5694 −2.04220
\(521\) −8.73101 −0.382512 −0.191256 0.981540i \(-0.561256\pi\)
−0.191256 + 0.981540i \(0.561256\pi\)
\(522\) 29.1650 1.27652
\(523\) 13.9520 0.610080 0.305040 0.952339i \(-0.401330\pi\)
0.305040 + 0.952339i \(0.401330\pi\)
\(524\) 24.9659 1.09064
\(525\) 0.667979 0.0291530
\(526\) −11.3552 −0.495109
\(527\) 37.0209 1.61266
\(528\) −5.53336 −0.240809
\(529\) −9.32064 −0.405245
\(530\) 64.0228 2.78097
\(531\) 7.96033 0.345449
\(532\) 9.71925 0.421383
\(533\) −37.4539 −1.62231
\(534\) 6.08342 0.263255
\(535\) 33.8054 1.46154
\(536\) 0.276038 0.0119230
\(537\) −4.96495 −0.214253
\(538\) 30.7182 1.32435
\(539\) 7.75259 0.333928
\(540\) 13.7974 0.593747
\(541\) 33.1935 1.42710 0.713550 0.700604i \(-0.247086\pi\)
0.713550 + 0.700604i \(0.247086\pi\)
\(542\) 31.6798 1.36076
\(543\) 0.777126 0.0333497
\(544\) −7.48383 −0.320867
\(545\) −39.5505 −1.69416
\(546\) 4.41818 0.189081
\(547\) −12.7655 −0.545813 −0.272907 0.962041i \(-0.587985\pi\)
−0.272907 + 0.962041i \(0.587985\pi\)
\(548\) −2.10187 −0.0897876
\(549\) −43.0264 −1.83632
\(550\) 15.8805 0.677146
\(551\) 3.97886 0.169505
\(552\) 4.41887 0.188080
\(553\) 1.25756 0.0534771
\(554\) −80.3178 −3.41237
\(555\) −5.03259 −0.213622
\(556\) −9.63896 −0.408783
\(557\) 26.3592 1.11688 0.558438 0.829546i \(-0.311401\pi\)
0.558438 + 0.829546i \(0.311401\pi\)
\(558\) 63.9472 2.70710
\(559\) −5.62397 −0.237869
\(560\) −29.5284 −1.24780
\(561\) −4.64928 −0.196293
\(562\) 39.4197 1.66282
\(563\) −4.98489 −0.210088 −0.105044 0.994468i \(-0.533498\pi\)
−0.105044 + 0.994468i \(0.533498\pi\)
\(564\) −5.92815 −0.249620
\(565\) 31.6541 1.33170
\(566\) −74.6382 −3.13728
\(567\) 19.9509 0.837860
\(568\) 67.4565 2.83041
\(569\) 34.9624 1.46570 0.732851 0.680389i \(-0.238189\pi\)
0.732851 + 0.680389i \(0.238189\pi\)
\(570\) 1.38104 0.0578454
\(571\) −2.19496 −0.0918562 −0.0459281 0.998945i \(-0.514625\pi\)
−0.0459281 + 0.998945i \(0.514625\pi\)
\(572\) 70.9911 2.96829
\(573\) 2.09053 0.0873329
\(574\) −62.9675 −2.62821
\(575\) −4.78307 −0.199468
\(576\) 16.8797 0.703320
\(577\) −16.4455 −0.684633 −0.342317 0.939585i \(-0.611212\pi\)
−0.342317 + 0.939585i \(0.611212\pi\)
\(578\) −2.50307 −0.104114
\(579\) 2.03892 0.0847348
\(580\) −41.6252 −1.72839
\(581\) 10.9432 0.454000
\(582\) 9.52206 0.394702
\(583\) −50.7909 −2.10354
\(584\) −5.14186 −0.212772
\(585\) −25.4913 −1.05393
\(586\) −49.0504 −2.02625
\(587\) −9.47010 −0.390873 −0.195436 0.980716i \(-0.562612\pi\)
−0.195436 + 0.980716i \(0.562612\pi\)
\(588\) −1.44940 −0.0597722
\(589\) 8.72405 0.359468
\(590\) −16.8100 −0.692056
\(591\) −5.19110 −0.213533
\(592\) 45.7161 1.87892
\(593\) 0.549011 0.0225452 0.0112726 0.999936i \(-0.496412\pi\)
0.0112726 + 0.999936i \(0.496412\pi\)
\(594\) −16.1953 −0.664502
\(595\) −24.8105 −1.01713
\(596\) 66.5786 2.72717
\(597\) −1.54373 −0.0631808
\(598\) −31.6364 −1.29371
\(599\) −39.6248 −1.61903 −0.809513 0.587103i \(-0.800269\pi\)
−0.809513 + 0.587103i \(0.800269\pi\)
\(600\) −1.54509 −0.0630778
\(601\) −30.7723 −1.25523 −0.627613 0.778525i \(-0.715968\pi\)
−0.627613 + 0.778525i \(0.715968\pi\)
\(602\) −9.45502 −0.385358
\(603\) 0.151099 0.00615322
\(604\) −64.8288 −2.63785
\(605\) −33.7127 −1.37062
\(606\) 7.89220 0.320599
\(607\) 18.6210 0.755801 0.377901 0.925846i \(-0.376646\pi\)
0.377901 + 0.925846i \(0.376646\pi\)
\(608\) −1.76358 −0.0715226
\(609\) 2.05517 0.0832796
\(610\) 90.8595 3.67880
\(611\) 22.0873 0.893556
\(612\) −52.2207 −2.11090
\(613\) −14.2846 −0.576951 −0.288475 0.957487i \(-0.593148\pi\)
−0.288475 + 0.957487i \(0.593148\pi\)
\(614\) 9.55902 0.385771
\(615\) −6.04713 −0.243844
\(616\) 62.1113 2.50254
\(617\) −34.9741 −1.40800 −0.704002 0.710198i \(-0.748606\pi\)
−0.704002 + 0.710198i \(0.748606\pi\)
\(618\) 2.34643 0.0943871
\(619\) −17.2219 −0.692206 −0.346103 0.938197i \(-0.612495\pi\)
−0.346103 + 0.938197i \(0.612495\pi\)
\(620\) −91.2676 −3.66540
\(621\) 4.87789 0.195743
\(622\) −2.66442 −0.106833
\(623\) −25.7543 −1.03182
\(624\) −3.85437 −0.154298
\(625\) −29.7937 −1.19175
\(626\) 40.2675 1.60941
\(627\) −1.09561 −0.0437546
\(628\) 24.4582 0.975988
\(629\) 38.4119 1.53158
\(630\) −42.8559 −1.70742
\(631\) 1.30626 0.0520014 0.0260007 0.999662i \(-0.491723\pi\)
0.0260007 + 0.999662i \(0.491723\pi\)
\(632\) −2.90884 −0.115707
\(633\) 0.221625 0.00880879
\(634\) 47.9838 1.90568
\(635\) 23.2479 0.922566
\(636\) 9.49570 0.376529
\(637\) 5.40021 0.213964
\(638\) 48.8594 1.93436
\(639\) 36.9245 1.46071
\(640\) −44.4935 −1.75876
\(641\) 38.0780 1.50399 0.751995 0.659169i \(-0.229092\pi\)
0.751995 + 0.659169i \(0.229092\pi\)
\(642\) 7.41855 0.292787
\(643\) −37.1455 −1.46487 −0.732437 0.680835i \(-0.761617\pi\)
−0.732437 + 0.680835i \(0.761617\pi\)
\(644\) −35.9473 −1.41652
\(645\) −0.908018 −0.0357532
\(646\) −10.5410 −0.414729
\(647\) 12.4874 0.490931 0.245465 0.969405i \(-0.421059\pi\)
0.245465 + 0.969405i \(0.421059\pi\)
\(648\) −46.1480 −1.81286
\(649\) 13.3358 0.523475
\(650\) 11.0619 0.433882
\(651\) 4.50617 0.176611
\(652\) −57.5370 −2.25332
\(653\) 31.8988 1.24830 0.624149 0.781305i \(-0.285446\pi\)
0.624149 + 0.781305i \(0.285446\pi\)
\(654\) −8.67930 −0.339388
\(655\) −15.0183 −0.586814
\(656\) 54.9321 2.14474
\(657\) −2.81457 −0.109807
\(658\) 37.1331 1.44760
\(659\) −28.1454 −1.09639 −0.548195 0.836351i \(-0.684685\pi\)
−0.548195 + 0.836351i \(0.684685\pi\)
\(660\) 11.4619 0.446153
\(661\) −11.4205 −0.444206 −0.222103 0.975023i \(-0.571292\pi\)
−0.222103 + 0.975023i \(0.571292\pi\)
\(662\) 15.8878 0.617496
\(663\) −3.23855 −0.125775
\(664\) −25.3124 −0.982313
\(665\) −5.84666 −0.226724
\(666\) 66.3499 2.57101
\(667\) −14.7160 −0.569808
\(668\) −6.52652 −0.252519
\(669\) 4.99708 0.193198
\(670\) −0.319078 −0.0123271
\(671\) −72.0811 −2.78266
\(672\) −0.910928 −0.0351398
\(673\) 34.8198 1.34221 0.671103 0.741364i \(-0.265821\pi\)
0.671103 + 0.741364i \(0.265821\pi\)
\(674\) −43.6031 −1.67953
\(675\) −1.70558 −0.0656480
\(676\) −4.76303 −0.183194
\(677\) 24.5439 0.943299 0.471650 0.881786i \(-0.343659\pi\)
0.471650 + 0.881786i \(0.343659\pi\)
\(678\) 6.94645 0.266777
\(679\) −40.3118 −1.54703
\(680\) 57.3887 2.20075
\(681\) −4.41364 −0.169131
\(682\) 107.129 4.10220
\(683\) 25.1092 0.960778 0.480389 0.877055i \(-0.340495\pi\)
0.480389 + 0.877055i \(0.340495\pi\)
\(684\) −12.3059 −0.470528
\(685\) 1.26439 0.0483099
\(686\) 49.6036 1.89387
\(687\) −5.51308 −0.210337
\(688\) 8.24844 0.314469
\(689\) −35.3794 −1.34785
\(690\) −5.10786 −0.194453
\(691\) −14.5623 −0.553975 −0.276987 0.960874i \(-0.589336\pi\)
−0.276987 + 0.960874i \(0.589336\pi\)
\(692\) −37.2072 −1.41441
\(693\) 33.9987 1.29150
\(694\) −85.8324 −3.25815
\(695\) 5.79835 0.219944
\(696\) −4.75376 −0.180191
\(697\) 46.1555 1.74826
\(698\) 45.9197 1.73809
\(699\) 3.00156 0.113529
\(700\) 12.5692 0.475070
\(701\) −24.1765 −0.913136 −0.456568 0.889689i \(-0.650921\pi\)
−0.456568 + 0.889689i \(0.650921\pi\)
\(702\) −11.2812 −0.425780
\(703\) 9.05184 0.341397
\(704\) 28.2782 1.06577
\(705\) 3.56610 0.134307
\(706\) −41.9354 −1.57826
\(707\) −33.4118 −1.25658
\(708\) −2.49321 −0.0937006
\(709\) 25.6750 0.964244 0.482122 0.876104i \(-0.339866\pi\)
0.482122 + 0.876104i \(0.339866\pi\)
\(710\) −77.9742 −2.92632
\(711\) −1.59225 −0.0597140
\(712\) 59.5716 2.23254
\(713\) −32.2665 −1.20839
\(714\) −5.44464 −0.203761
\(715\) −42.7050 −1.59708
\(716\) −93.4240 −3.49142
\(717\) 5.12860 0.191531
\(718\) 14.8283 0.553386
\(719\) 23.8298 0.888703 0.444352 0.895852i \(-0.353434\pi\)
0.444352 + 0.895852i \(0.353434\pi\)
\(720\) 37.3870 1.39333
\(721\) −9.93364 −0.369948
\(722\) −2.48400 −0.0924448
\(723\) 2.06205 0.0766884
\(724\) 14.6230 0.543458
\(725\) 5.14555 0.191101
\(726\) −7.39821 −0.274573
\(727\) −50.8608 −1.88632 −0.943161 0.332336i \(-0.892163\pi\)
−0.943161 + 0.332336i \(0.892163\pi\)
\(728\) 43.2648 1.60350
\(729\) −24.3837 −0.903101
\(730\) 5.94358 0.219982
\(731\) 6.93057 0.256336
\(732\) 13.4761 0.498089
\(733\) −12.9203 −0.477222 −0.238611 0.971115i \(-0.576692\pi\)
−0.238611 + 0.971115i \(0.576692\pi\)
\(734\) −49.7823 −1.83750
\(735\) 0.871892 0.0321602
\(736\) 6.52271 0.240430
\(737\) 0.253133 0.00932426
\(738\) 79.7256 2.93474
\(739\) 23.2148 0.853972 0.426986 0.904258i \(-0.359575\pi\)
0.426986 + 0.904258i \(0.359575\pi\)
\(740\) −94.6968 −3.48112
\(741\) −0.763170 −0.0280357
\(742\) −59.4798 −2.18357
\(743\) −15.6594 −0.574489 −0.287245 0.957857i \(-0.592739\pi\)
−0.287245 + 0.957857i \(0.592739\pi\)
\(744\) −10.4231 −0.382130
\(745\) −40.0506 −1.46734
\(746\) −55.0702 −2.01626
\(747\) −13.8556 −0.506950
\(748\) −87.4842 −3.19874
\(749\) −31.4066 −1.14757
\(750\) −5.11920 −0.186927
\(751\) −38.3303 −1.39869 −0.699346 0.714783i \(-0.746525\pi\)
−0.699346 + 0.714783i \(0.746525\pi\)
\(752\) −32.3945 −1.18131
\(753\) −3.43570 −0.125204
\(754\) 34.0340 1.23944
\(755\) 38.9980 1.41928
\(756\) −12.8184 −0.466199
\(757\) 36.7843 1.33695 0.668473 0.743736i \(-0.266948\pi\)
0.668473 + 0.743736i \(0.266948\pi\)
\(758\) 57.9499 2.10484
\(759\) 4.05219 0.147085
\(760\) 13.5238 0.490558
\(761\) 14.5656 0.528004 0.264002 0.964522i \(-0.414957\pi\)
0.264002 + 0.964522i \(0.414957\pi\)
\(762\) 5.10173 0.184816
\(763\) 36.7440 1.33022
\(764\) 39.3368 1.42316
\(765\) 31.4136 1.13576
\(766\) −39.5309 −1.42831
\(767\) 9.28929 0.335417
\(768\) −7.22855 −0.260838
\(769\) 17.6657 0.637041 0.318520 0.947916i \(-0.396814\pi\)
0.318520 + 0.947916i \(0.396814\pi\)
\(770\) −71.7956 −2.58733
\(771\) 1.43866 0.0518122
\(772\) 38.3659 1.38082
\(773\) −3.79132 −0.136364 −0.0681822 0.997673i \(-0.521720\pi\)
−0.0681822 + 0.997673i \(0.521720\pi\)
\(774\) 11.9714 0.430301
\(775\) 11.2822 0.405267
\(776\) 93.2442 3.34727
\(777\) 4.67548 0.167732
\(778\) 58.8057 2.10829
\(779\) 10.8766 0.389696
\(780\) 7.98398 0.285872
\(781\) 61.8589 2.21349
\(782\) 38.9864 1.39415
\(783\) −5.24756 −0.187533
\(784\) −7.92027 −0.282867
\(785\) −14.7129 −0.525127
\(786\) −3.29575 −0.117555
\(787\) −7.62789 −0.271905 −0.135952 0.990715i \(-0.543409\pi\)
−0.135952 + 0.990715i \(0.543409\pi\)
\(788\) −97.6795 −3.47969
\(789\) 1.01312 0.0360680
\(790\) 3.36238 0.119628
\(791\) −29.4079 −1.04563
\(792\) −78.6415 −2.79440
\(793\) −50.2095 −1.78299
\(794\) 90.3122 3.20506
\(795\) −5.71218 −0.202590
\(796\) −29.0480 −1.02958
\(797\) 28.6141 1.01356 0.506781 0.862075i \(-0.330835\pi\)
0.506781 + 0.862075i \(0.330835\pi\)
\(798\) −1.28304 −0.0454191
\(799\) −27.2187 −0.962930
\(800\) −2.28070 −0.0806350
\(801\) 32.6085 1.15216
\(802\) −55.6323 −1.96444
\(803\) −4.71519 −0.166395
\(804\) −0.0473248 −0.00166902
\(805\) 21.6242 0.762154
\(806\) 74.6230 2.62848
\(807\) −2.74070 −0.0964774
\(808\) 77.2839 2.71884
\(809\) −38.7781 −1.36337 −0.681683 0.731647i \(-0.738752\pi\)
−0.681683 + 0.731647i \(0.738752\pi\)
\(810\) 53.3433 1.87429
\(811\) 55.0715 1.93382 0.966910 0.255116i \(-0.0821137\pi\)
0.966910 + 0.255116i \(0.0821137\pi\)
\(812\) 38.6715 1.35710
\(813\) −2.82650 −0.0991298
\(814\) 111.155 3.89596
\(815\) 34.6116 1.21239
\(816\) 4.74984 0.166278
\(817\) 1.63320 0.0571385
\(818\) 67.4243 2.35744
\(819\) 23.6824 0.827530
\(820\) −113.787 −3.97362
\(821\) −2.36477 −0.0825310 −0.0412655 0.999148i \(-0.513139\pi\)
−0.0412655 + 0.999148i \(0.513139\pi\)
\(822\) 0.277469 0.00967784
\(823\) 33.0978 1.15372 0.576859 0.816844i \(-0.304278\pi\)
0.576859 + 0.816844i \(0.304278\pi\)
\(824\) 22.9772 0.800450
\(825\) −1.41687 −0.0493292
\(826\) 15.6171 0.543390
\(827\) −11.1874 −0.389025 −0.194513 0.980900i \(-0.562313\pi\)
−0.194513 + 0.980900i \(0.562313\pi\)
\(828\) 45.5142 1.58173
\(829\) −37.1760 −1.29118 −0.645589 0.763685i \(-0.723388\pi\)
−0.645589 + 0.763685i \(0.723388\pi\)
\(830\) 29.2591 1.01560
\(831\) 7.16603 0.248587
\(832\) 19.6977 0.682895
\(833\) −6.65483 −0.230576
\(834\) 1.27244 0.0440610
\(835\) 3.92605 0.135867
\(836\) −20.6158 −0.713014
\(837\) −11.5058 −0.397700
\(838\) −38.4913 −1.32966
\(839\) 24.0132 0.829029 0.414515 0.910043i \(-0.363951\pi\)
0.414515 + 0.910043i \(0.363951\pi\)
\(840\) 6.98532 0.241016
\(841\) −13.1687 −0.454093
\(842\) 36.4143 1.25492
\(843\) −3.51706 −0.121134
\(844\) 4.17025 0.143546
\(845\) 2.86522 0.0985666
\(846\) −47.0156 −1.61643
\(847\) 31.3205 1.07618
\(848\) 51.8894 1.78189
\(849\) 6.65929 0.228546
\(850\) −13.6318 −0.467567
\(851\) −33.4788 −1.14764
\(852\) −11.5649 −0.396208
\(853\) 33.9166 1.16128 0.580641 0.814160i \(-0.302802\pi\)
0.580641 + 0.814160i \(0.302802\pi\)
\(854\) −84.4121 −2.88852
\(855\) 7.40267 0.253166
\(856\) 72.6458 2.48298
\(857\) −3.91309 −0.133669 −0.0668343 0.997764i \(-0.521290\pi\)
−0.0668343 + 0.997764i \(0.521290\pi\)
\(858\) −9.37155 −0.319940
\(859\) 51.2580 1.74890 0.874451 0.485114i \(-0.161222\pi\)
0.874451 + 0.485114i \(0.161222\pi\)
\(860\) −17.0859 −0.582625
\(861\) 5.61802 0.191462
\(862\) 81.4494 2.77418
\(863\) 25.5023 0.868109 0.434055 0.900887i \(-0.357082\pi\)
0.434055 + 0.900887i \(0.357082\pi\)
\(864\) 2.32592 0.0791294
\(865\) 22.3821 0.761016
\(866\) 63.7598 2.16665
\(867\) 0.223326 0.00758455
\(868\) 84.7913 2.87800
\(869\) −2.66746 −0.0904874
\(870\) 5.49496 0.186296
\(871\) 0.176324 0.00597452
\(872\) −84.9916 −2.87818
\(873\) 51.0403 1.72745
\(874\) 9.18722 0.310762
\(875\) 21.6722 0.732656
\(876\) 0.881536 0.0297843
\(877\) −17.4490 −0.589211 −0.294606 0.955619i \(-0.595188\pi\)
−0.294606 + 0.955619i \(0.595188\pi\)
\(878\) 78.5317 2.65032
\(879\) 4.37632 0.147610
\(880\) 62.6336 2.11138
\(881\) 29.5358 0.995087 0.497544 0.867439i \(-0.334235\pi\)
0.497544 + 0.867439i \(0.334235\pi\)
\(882\) −11.4951 −0.387059
\(883\) −11.6888 −0.393359 −0.196679 0.980468i \(-0.563016\pi\)
−0.196679 + 0.980468i \(0.563016\pi\)
\(884\) −60.9388 −2.04959
\(885\) 1.49980 0.0504153
\(886\) −65.6353 −2.20506
\(887\) 32.2008 1.08120 0.540599 0.841281i \(-0.318198\pi\)
0.540599 + 0.841281i \(0.318198\pi\)
\(888\) −10.8147 −0.362918
\(889\) −21.5983 −0.724382
\(890\) −68.8599 −2.30819
\(891\) −42.3186 −1.41772
\(892\) 94.0286 3.14831
\(893\) −6.41415 −0.214641
\(894\) −8.78906 −0.293950
\(895\) 56.1996 1.87854
\(896\) 41.3362 1.38095
\(897\) 2.82263 0.0942449
\(898\) 11.3070 0.377319
\(899\) 34.7117 1.15770
\(900\) −15.9143 −0.530477
\(901\) 43.5989 1.45249
\(902\) 133.563 4.44715
\(903\) 0.843585 0.0280728
\(904\) 68.0228 2.26240
\(905\) −8.79651 −0.292406
\(906\) 8.55806 0.284323
\(907\) 7.45024 0.247381 0.123691 0.992321i \(-0.460527\pi\)
0.123691 + 0.992321i \(0.460527\pi\)
\(908\) −83.0501 −2.75612
\(909\) 42.3039 1.40313
\(910\) −50.0106 −1.65783
\(911\) 39.6783 1.31460 0.657300 0.753629i \(-0.271699\pi\)
0.657300 + 0.753629i \(0.271699\pi\)
\(912\) 1.11931 0.0370640
\(913\) −23.2120 −0.768204
\(914\) 57.2567 1.89388
\(915\) −8.10657 −0.267995
\(916\) −103.738 −3.42760
\(917\) 13.9526 0.460756
\(918\) 13.9021 0.458837
\(919\) 28.7383 0.947990 0.473995 0.880528i \(-0.342811\pi\)
0.473995 + 0.880528i \(0.342811\pi\)
\(920\) −50.0184 −1.64906
\(921\) −0.852865 −0.0281028
\(922\) 12.5888 0.414591
\(923\) 43.0890 1.41829
\(924\) −10.6485 −0.350311
\(925\) 11.7061 0.384893
\(926\) 63.6081 2.09029
\(927\) 12.5774 0.413094
\(928\) −7.01703 −0.230345
\(929\) 1.27637 0.0418764 0.0209382 0.999781i \(-0.493335\pi\)
0.0209382 + 0.999781i \(0.493335\pi\)
\(930\) 12.0483 0.395078
\(931\) −1.56822 −0.0513964
\(932\) 56.4794 1.85005
\(933\) 0.237722 0.00778266
\(934\) 82.2266 2.69054
\(935\) 52.6265 1.72107
\(936\) −54.7792 −1.79051
\(937\) −20.8315 −0.680534 −0.340267 0.940329i \(-0.610517\pi\)
−0.340267 + 0.940329i \(0.610517\pi\)
\(938\) 0.296436 0.00967898
\(939\) −3.59270 −0.117243
\(940\) 67.1023 2.18864
\(941\) −21.9126 −0.714331 −0.357165 0.934041i \(-0.616257\pi\)
−0.357165 + 0.934041i \(0.616257\pi\)
\(942\) −3.22873 −0.105198
\(943\) −40.2279 −1.31000
\(944\) −13.6242 −0.443430
\(945\) 7.71093 0.250837
\(946\) 20.0554 0.652056
\(947\) −3.85162 −0.125161 −0.0625804 0.998040i \(-0.519933\pi\)
−0.0625804 + 0.998040i \(0.519933\pi\)
\(948\) 0.498700 0.0161970
\(949\) −3.28445 −0.106618
\(950\) −3.21237 −0.104223
\(951\) −4.28116 −0.138826
\(952\) −53.3164 −1.72799
\(953\) −54.6977 −1.77183 −0.885916 0.463845i \(-0.846470\pi\)
−0.885916 + 0.463845i \(0.846470\pi\)
\(954\) 75.3096 2.43824
\(955\) −23.6632 −0.765724
\(956\) 96.5035 3.12115
\(957\) −4.35929 −0.140916
\(958\) 4.14780 0.134009
\(959\) −1.17467 −0.0379321
\(960\) 3.18029 0.102644
\(961\) 45.1091 1.45513
\(962\) 77.4268 2.49634
\(963\) 39.7651 1.28141
\(964\) 38.8010 1.24970
\(965\) −23.0791 −0.742944
\(966\) 4.74541 0.152681
\(967\) −31.3609 −1.00850 −0.504250 0.863558i \(-0.668231\pi\)
−0.504250 + 0.863558i \(0.668231\pi\)
\(968\) −72.4466 −2.32852
\(969\) 0.940474 0.0302124
\(970\) −107.783 −3.46070
\(971\) −29.9121 −0.959923 −0.479962 0.877289i \(-0.659349\pi\)
−0.479962 + 0.877289i \(0.659349\pi\)
\(972\) 24.4117 0.783005
\(973\) −5.38690 −0.172696
\(974\) 35.6455 1.14216
\(975\) −0.986949 −0.0316077
\(976\) 73.6401 2.35716
\(977\) −19.0711 −0.610139 −0.305070 0.952330i \(-0.598680\pi\)
−0.305070 + 0.952330i \(0.598680\pi\)
\(978\) 7.59547 0.242876
\(979\) 54.6283 1.74593
\(980\) 16.4061 0.524075
\(981\) −46.5230 −1.48536
\(982\) −63.0902 −2.01329
\(983\) 22.1866 0.707644 0.353822 0.935313i \(-0.384882\pi\)
0.353822 + 0.935313i \(0.384882\pi\)
\(984\) −12.9949 −0.414262
\(985\) 58.7595 1.87223
\(986\) −41.9410 −1.33567
\(987\) −3.31305 −0.105456
\(988\) −14.3603 −0.456863
\(989\) −6.04050 −0.192077
\(990\) 90.9031 2.88909
\(991\) −20.0570 −0.637132 −0.318566 0.947901i \(-0.603201\pi\)
−0.318566 + 0.947901i \(0.603201\pi\)
\(992\) −15.3856 −0.488492
\(993\) −1.41752 −0.0449837
\(994\) 72.4412 2.29769
\(995\) 17.4739 0.553961
\(996\) 4.33963 0.137507
\(997\) −16.4914 −0.522287 −0.261143 0.965300i \(-0.584100\pi\)
−0.261143 + 0.965300i \(0.584100\pi\)
\(998\) −1.32011 −0.0417872
\(999\) −11.9381 −0.377706
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 \(a_p\))