Properties

Label 6017.2.a.c.1.6
Level 6017
Weight 2
Character 6017.1
Self dual Yes
Analytic conductor 48.046
Analytic rank 1
Dimension 106
CM No

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Newspace parameters

Level: \( N \) = \( 6017 = 11 \cdot 547 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6017.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0459868962\)
Analytic rank: \(1\)
Dimension: \(106\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) = 6017.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.61585 q^{2}\) \(+1.81779 q^{3}\) \(+4.84270 q^{4}\) \(+3.74717 q^{5}\) \(-4.75507 q^{6}\) \(+0.406260 q^{7}\) \(-7.43608 q^{8}\) \(+0.304348 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.61585 q^{2}\) \(+1.81779 q^{3}\) \(+4.84270 q^{4}\) \(+3.74717 q^{5}\) \(-4.75507 q^{6}\) \(+0.406260 q^{7}\) \(-7.43608 q^{8}\) \(+0.304348 q^{9}\) \(-9.80206 q^{10}\) \(+1.00000 q^{11}\) \(+8.80299 q^{12}\) \(-3.01331 q^{13}\) \(-1.06272 q^{14}\) \(+6.81156 q^{15}\) \(+9.76632 q^{16}\) \(-6.49061 q^{17}\) \(-0.796131 q^{18}\) \(-1.64413 q^{19}\) \(+18.1464 q^{20}\) \(+0.738494 q^{21}\) \(-2.61585 q^{22}\) \(-1.93831 q^{23}\) \(-13.5172 q^{24}\) \(+9.04131 q^{25}\) \(+7.88239 q^{26}\) \(-4.90012 q^{27}\) \(+1.96740 q^{28}\) \(-7.98224 q^{29}\) \(-17.8181 q^{30}\) \(-2.09748 q^{31}\) \(-10.6751 q^{32}\) \(+1.81779 q^{33}\) \(+16.9785 q^{34}\) \(+1.52233 q^{35}\) \(+1.47387 q^{36}\) \(-4.51913 q^{37}\) \(+4.30082 q^{38}\) \(-5.47756 q^{39}\) \(-27.8643 q^{40}\) \(+8.72483 q^{41}\) \(-1.93179 q^{42}\) \(-11.3450 q^{43}\) \(+4.84270 q^{44}\) \(+1.14045 q^{45}\) \(+5.07033 q^{46}\) \(-1.52918 q^{47}\) \(+17.7531 q^{48}\) \(-6.83495 q^{49}\) \(-23.6508 q^{50}\) \(-11.7985 q^{51}\) \(-14.5926 q^{52}\) \(-5.40672 q^{53}\) \(+12.8180 q^{54}\) \(+3.74717 q^{55}\) \(-3.02098 q^{56}\) \(-2.98868 q^{57}\) \(+20.8804 q^{58}\) \(+5.97599 q^{59}\) \(+32.9863 q^{60}\) \(+13.7626 q^{61}\) \(+5.48671 q^{62}\) \(+0.123645 q^{63}\) \(+8.39191 q^{64}\) \(-11.2914 q^{65}\) \(-4.75507 q^{66}\) \(+7.92550 q^{67}\) \(-31.4320 q^{68}\) \(-3.52343 q^{69}\) \(-3.98219 q^{70}\) \(+12.1603 q^{71}\) \(-2.26316 q^{72}\) \(-6.94597 q^{73}\) \(+11.8214 q^{74}\) \(+16.4352 q^{75}\) \(-7.96204 q^{76}\) \(+0.406260 q^{77}\) \(+14.3285 q^{78}\) \(+7.28573 q^{79}\) \(+36.5961 q^{80}\) \(-9.82042 q^{81}\) \(-22.8229 q^{82}\) \(+8.02259 q^{83}\) \(+3.57630 q^{84}\) \(-24.3214 q^{85}\) \(+29.6768 q^{86}\) \(-14.5100 q^{87}\) \(-7.43608 q^{88}\) \(+0.679834 q^{89}\) \(-2.98324 q^{90}\) \(-1.22419 q^{91}\) \(-9.38663 q^{92}\) \(-3.81278 q^{93}\) \(+4.00012 q^{94}\) \(-6.16086 q^{95}\) \(-19.4051 q^{96}\) \(-14.7354 q^{97}\) \(+17.8792 q^{98}\) \(+0.304348 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(106q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 66q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(106q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 66q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut -\mathstrut 30q^{10} \) \(\mathstrut +\mathstrut 106q^{11} \) \(\mathstrut -\mathstrut 26q^{12} \) \(\mathstrut -\mathstrut 72q^{13} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut -\mathstrut 46q^{15} \) \(\mathstrut +\mathstrut 75q^{16} \) \(\mathstrut -\mathstrut 65q^{17} \) \(\mathstrut -\mathstrut 37q^{18} \) \(\mathstrut -\mathstrut 63q^{19} \) \(\mathstrut -\mathstrut 25q^{20} \) \(\mathstrut -\mathstrut 27q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut -\mathstrut 23q^{23} \) \(\mathstrut -\mathstrut 56q^{24} \) \(\mathstrut +\mathstrut 74q^{25} \) \(\mathstrut +\mathstrut 2q^{26} \) \(\mathstrut -\mathstrut 54q^{27} \) \(\mathstrut -\mathstrut 115q^{28} \) \(\mathstrut -\mathstrut 45q^{29} \) \(\mathstrut -\mathstrut 14q^{30} \) \(\mathstrut -\mathstrut 89q^{31} \) \(\mathstrut -\mathstrut 96q^{32} \) \(\mathstrut -\mathstrut 15q^{33} \) \(\mathstrut -\mathstrut 26q^{34} \) \(\mathstrut -\mathstrut 52q^{35} \) \(\mathstrut +\mathstrut 91q^{36} \) \(\mathstrut -\mathstrut 35q^{37} \) \(\mathstrut +\mathstrut 7q^{38} \) \(\mathstrut -\mathstrut 34q^{39} \) \(\mathstrut -\mathstrut 74q^{40} \) \(\mathstrut -\mathstrut 32q^{41} \) \(\mathstrut -\mathstrut 94q^{43} \) \(\mathstrut +\mathstrut 93q^{44} \) \(\mathstrut -\mathstrut 46q^{45} \) \(\mathstrut -\mathstrut 20q^{46} \) \(\mathstrut -\mathstrut 105q^{47} \) \(\mathstrut -\mathstrut 57q^{48} \) \(\mathstrut +\mathstrut 80q^{49} \) \(\mathstrut -\mathstrut 60q^{50} \) \(\mathstrut -\mathstrut 36q^{51} \) \(\mathstrut -\mathstrut 137q^{52} \) \(\mathstrut -\mathstrut 61q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 32q^{56} \) \(\mathstrut -\mathstrut 71q^{57} \) \(\mathstrut -\mathstrut 28q^{58} \) \(\mathstrut -\mathstrut 15q^{59} \) \(\mathstrut -\mathstrut 21q^{60} \) \(\mathstrut -\mathstrut 80q^{61} \) \(\mathstrut -\mathstrut 84q^{62} \) \(\mathstrut -\mathstrut 182q^{63} \) \(\mathstrut +\mathstrut 55q^{64} \) \(\mathstrut -\mathstrut 73q^{65} \) \(\mathstrut -\mathstrut 22q^{66} \) \(\mathstrut -\mathstrut 58q^{67} \) \(\mathstrut -\mathstrut 145q^{68} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 39q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut -\mathstrut 100q^{72} \) \(\mathstrut -\mathstrut 155q^{73} \) \(\mathstrut -\mathstrut 15q^{74} \) \(\mathstrut -\mathstrut 15q^{75} \) \(\mathstrut -\mathstrut 132q^{76} \) \(\mathstrut -\mathstrut 66q^{77} \) \(\mathstrut -\mathstrut 45q^{78} \) \(\mathstrut -\mathstrut 50q^{79} \) \(\mathstrut -\mathstrut 28q^{80} \) \(\mathstrut +\mathstrut 114q^{81} \) \(\mathstrut -\mathstrut 57q^{82} \) \(\mathstrut -\mathstrut 96q^{83} \) \(\mathstrut -\mathstrut 27q^{84} \) \(\mathstrut -\mathstrut 74q^{85} \) \(\mathstrut +\mathstrut 54q^{86} \) \(\mathstrut -\mathstrut 182q^{87} \) \(\mathstrut -\mathstrut 39q^{88} \) \(\mathstrut +\mathstrut 9q^{89} \) \(\mathstrut -\mathstrut 53q^{90} \) \(\mathstrut +\mathstrut 6q^{91} \) \(\mathstrut -\mathstrut 18q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut -\mathstrut 33q^{94} \) \(\mathstrut -\mathstrut 49q^{95} \) \(\mathstrut -\mathstrut 56q^{96} \) \(\mathstrut -\mathstrut 102q^{97} \) \(\mathstrut -\mathstrut 76q^{98} \) \(\mathstrut +\mathstrut 97q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.61585 −1.84969 −0.924844 0.380346i \(-0.875805\pi\)
−0.924844 + 0.380346i \(0.875805\pi\)
\(3\) 1.81779 1.04950 0.524750 0.851257i \(-0.324159\pi\)
0.524750 + 0.851257i \(0.324159\pi\)
\(4\) 4.84270 2.42135
\(5\) 3.74717 1.67579 0.837894 0.545834i \(-0.183787\pi\)
0.837894 + 0.545834i \(0.183787\pi\)
\(6\) −4.75507 −1.94125
\(7\) 0.406260 0.153552 0.0767760 0.997048i \(-0.475537\pi\)
0.0767760 + 0.997048i \(0.475537\pi\)
\(8\) −7.43608 −2.62905
\(9\) 0.304348 0.101449
\(10\) −9.80206 −3.09968
\(11\) 1.00000 0.301511
\(12\) 8.80299 2.54120
\(13\) −3.01331 −0.835742 −0.417871 0.908506i \(-0.637224\pi\)
−0.417871 + 0.908506i \(0.637224\pi\)
\(14\) −1.06272 −0.284023
\(15\) 6.81156 1.75874
\(16\) 9.76632 2.44158
\(17\) −6.49061 −1.57420 −0.787102 0.616823i \(-0.788419\pi\)
−0.787102 + 0.616823i \(0.788419\pi\)
\(18\) −0.796131 −0.187650
\(19\) −1.64413 −0.377190 −0.188595 0.982055i \(-0.560393\pi\)
−0.188595 + 0.982055i \(0.560393\pi\)
\(20\) 18.1464 4.05766
\(21\) 0.738494 0.161153
\(22\) −2.61585 −0.557702
\(23\) −1.93831 −0.404165 −0.202082 0.979369i \(-0.564771\pi\)
−0.202082 + 0.979369i \(0.564771\pi\)
\(24\) −13.5172 −2.75919
\(25\) 9.04131 1.80826
\(26\) 7.88239 1.54586
\(27\) −4.90012 −0.943028
\(28\) 1.96740 0.371803
\(29\) −7.98224 −1.48227 −0.741133 0.671359i \(-0.765711\pi\)
−0.741133 + 0.671359i \(0.765711\pi\)
\(30\) −17.8181 −3.25312
\(31\) −2.09748 −0.376719 −0.188360 0.982100i \(-0.560317\pi\)
−0.188360 + 0.982100i \(0.560317\pi\)
\(32\) −10.6751 −1.88711
\(33\) 1.81779 0.316436
\(34\) 16.9785 2.91179
\(35\) 1.52233 0.257320
\(36\) 1.47387 0.245644
\(37\) −4.51913 −0.742940 −0.371470 0.928445i \(-0.621146\pi\)
−0.371470 + 0.928445i \(0.621146\pi\)
\(38\) 4.30082 0.697684
\(39\) −5.47756 −0.877111
\(40\) −27.8643 −4.40573
\(41\) 8.72483 1.36259 0.681295 0.732009i \(-0.261417\pi\)
0.681295 + 0.732009i \(0.261417\pi\)
\(42\) −1.93179 −0.298082
\(43\) −11.3450 −1.73009 −0.865046 0.501693i \(-0.832711\pi\)
−0.865046 + 0.501693i \(0.832711\pi\)
\(44\) 4.84270 0.730064
\(45\) 1.14045 0.170008
\(46\) 5.07033 0.747579
\(47\) −1.52918 −0.223054 −0.111527 0.993761i \(-0.535574\pi\)
−0.111527 + 0.993761i \(0.535574\pi\)
\(48\) 17.7531 2.56244
\(49\) −6.83495 −0.976422
\(50\) −23.6508 −3.34472
\(51\) −11.7985 −1.65213
\(52\) −14.5926 −2.02362
\(53\) −5.40672 −0.742671 −0.371335 0.928499i \(-0.621100\pi\)
−0.371335 + 0.928499i \(0.621100\pi\)
\(54\) 12.8180 1.74431
\(55\) 3.74717 0.505269
\(56\) −3.02098 −0.403696
\(57\) −2.98868 −0.395861
\(58\) 20.8804 2.74173
\(59\) 5.97599 0.778008 0.389004 0.921236i \(-0.372819\pi\)
0.389004 + 0.921236i \(0.372819\pi\)
\(60\) 32.9863 4.25852
\(61\) 13.7626 1.76212 0.881062 0.473001i \(-0.156829\pi\)
0.881062 + 0.473001i \(0.156829\pi\)
\(62\) 5.48671 0.696813
\(63\) 0.123645 0.0155778
\(64\) 8.39191 1.04899
\(65\) −11.2914 −1.40053
\(66\) −4.75507 −0.585308
\(67\) 7.92550 0.968254 0.484127 0.874998i \(-0.339137\pi\)
0.484127 + 0.874998i \(0.339137\pi\)
\(68\) −31.4320 −3.81170
\(69\) −3.52343 −0.424171
\(70\) −3.98219 −0.475962
\(71\) 12.1603 1.44316 0.721581 0.692330i \(-0.243416\pi\)
0.721581 + 0.692330i \(0.243416\pi\)
\(72\) −2.26316 −0.266716
\(73\) −6.94597 −0.812964 −0.406482 0.913659i \(-0.633245\pi\)
−0.406482 + 0.913659i \(0.633245\pi\)
\(74\) 11.8214 1.37421
\(75\) 16.4352 1.89777
\(76\) −7.96204 −0.913309
\(77\) 0.406260 0.0462976
\(78\) 14.3285 1.62238
\(79\) 7.28573 0.819709 0.409854 0.912151i \(-0.365580\pi\)
0.409854 + 0.912151i \(0.365580\pi\)
\(80\) 36.5961 4.09157
\(81\) −9.82042 −1.09116
\(82\) −22.8229 −2.52037
\(83\) 8.02259 0.880594 0.440297 0.897852i \(-0.354873\pi\)
0.440297 + 0.897852i \(0.354873\pi\)
\(84\) 3.57630 0.390207
\(85\) −24.3214 −2.63803
\(86\) 29.6768 3.20013
\(87\) −14.5100 −1.55564
\(88\) −7.43608 −0.792689
\(89\) 0.679834 0.0720622 0.0360311 0.999351i \(-0.488528\pi\)
0.0360311 + 0.999351i \(0.488528\pi\)
\(90\) −2.98324 −0.314461
\(91\) −1.22419 −0.128330
\(92\) −9.38663 −0.978623
\(93\) −3.81278 −0.395366
\(94\) 4.00012 0.412581
\(95\) −6.16086 −0.632090
\(96\) −19.4051 −1.98052
\(97\) −14.7354 −1.49616 −0.748079 0.663610i \(-0.769024\pi\)
−0.748079 + 0.663610i \(0.769024\pi\)
\(98\) 17.8792 1.80608
\(99\) 0.304348 0.0305881
\(100\) 43.7843 4.37843
\(101\) −10.0124 −0.996272 −0.498136 0.867099i \(-0.665982\pi\)
−0.498136 + 0.867099i \(0.665982\pi\)
\(102\) 30.8633 3.05592
\(103\) 6.17742 0.608679 0.304340 0.952564i \(-0.401564\pi\)
0.304340 + 0.952564i \(0.401564\pi\)
\(104\) 22.4072 2.19721
\(105\) 2.76727 0.270058
\(106\) 14.1432 1.37371
\(107\) −14.5630 −1.40786 −0.703931 0.710268i \(-0.748574\pi\)
−0.703931 + 0.710268i \(0.748574\pi\)
\(108\) −23.7298 −2.28340
\(109\) 1.69123 0.161991 0.0809954 0.996714i \(-0.474190\pi\)
0.0809954 + 0.996714i \(0.474190\pi\)
\(110\) −9.80206 −0.934590
\(111\) −8.21481 −0.779715
\(112\) 3.96767 0.374909
\(113\) −10.6778 −1.00448 −0.502242 0.864727i \(-0.667491\pi\)
−0.502242 + 0.864727i \(0.667491\pi\)
\(114\) 7.81797 0.732220
\(115\) −7.26317 −0.677294
\(116\) −38.6556 −3.58908
\(117\) −0.917096 −0.0847856
\(118\) −15.6323 −1.43907
\(119\) −2.63688 −0.241722
\(120\) −50.6513 −4.62381
\(121\) 1.00000 0.0909091
\(122\) −36.0010 −3.25938
\(123\) 15.8599 1.43004
\(124\) −10.1575 −0.912168
\(125\) 15.1435 1.35448
\(126\) −0.323436 −0.0288140
\(127\) 8.81146 0.781891 0.390945 0.920414i \(-0.372148\pi\)
0.390945 + 0.920414i \(0.372148\pi\)
\(128\) −0.601782 −0.0531905
\(129\) −20.6227 −1.81573
\(130\) 29.5367 2.59054
\(131\) −7.45255 −0.651132 −0.325566 0.945519i \(-0.605555\pi\)
−0.325566 + 0.945519i \(0.605555\pi\)
\(132\) 8.80299 0.766202
\(133\) −0.667946 −0.0579183
\(134\) −20.7320 −1.79097
\(135\) −18.3616 −1.58031
\(136\) 48.2647 4.13866
\(137\) 21.5751 1.84329 0.921644 0.388037i \(-0.126847\pi\)
0.921644 + 0.388037i \(0.126847\pi\)
\(138\) 9.21677 0.784584
\(139\) 13.6880 1.16100 0.580501 0.814260i \(-0.302857\pi\)
0.580501 + 0.814260i \(0.302857\pi\)
\(140\) 7.37217 0.623062
\(141\) −2.77973 −0.234095
\(142\) −31.8096 −2.66940
\(143\) −3.01331 −0.251986
\(144\) 2.97236 0.247697
\(145\) −29.9108 −2.48396
\(146\) 18.1696 1.50373
\(147\) −12.4245 −1.02475
\(148\) −21.8848 −1.79892
\(149\) 3.22940 0.264563 0.132281 0.991212i \(-0.457770\pi\)
0.132281 + 0.991212i \(0.457770\pi\)
\(150\) −42.9920 −3.51028
\(151\) 3.62504 0.295002 0.147501 0.989062i \(-0.452877\pi\)
0.147501 + 0.989062i \(0.452877\pi\)
\(152\) 12.2259 0.991653
\(153\) −1.97540 −0.159702
\(154\) −1.06272 −0.0856362
\(155\) −7.85963 −0.631301
\(156\) −26.5262 −2.12379
\(157\) −20.4077 −1.62871 −0.814355 0.580367i \(-0.802909\pi\)
−0.814355 + 0.580367i \(0.802909\pi\)
\(158\) −19.0584 −1.51621
\(159\) −9.82827 −0.779433
\(160\) −40.0015 −3.16240
\(161\) −0.787456 −0.0620603
\(162\) 25.6888 2.01830
\(163\) −18.9494 −1.48423 −0.742114 0.670273i \(-0.766177\pi\)
−0.742114 + 0.670273i \(0.766177\pi\)
\(164\) 42.2517 3.29931
\(165\) 6.81156 0.530279
\(166\) −20.9859 −1.62883
\(167\) −12.6749 −0.980816 −0.490408 0.871493i \(-0.663152\pi\)
−0.490408 + 0.871493i \(0.663152\pi\)
\(168\) −5.49151 −0.423679
\(169\) −3.91995 −0.301535
\(170\) 63.6213 4.87953
\(171\) −0.500389 −0.0382657
\(172\) −54.9403 −4.18916
\(173\) 11.1155 0.845096 0.422548 0.906340i \(-0.361136\pi\)
0.422548 + 0.906340i \(0.361136\pi\)
\(174\) 37.9561 2.87744
\(175\) 3.67312 0.277662
\(176\) 9.76632 0.736164
\(177\) 10.8631 0.816519
\(178\) −1.77835 −0.133293
\(179\) −15.8713 −1.18628 −0.593139 0.805100i \(-0.702112\pi\)
−0.593139 + 0.805100i \(0.702112\pi\)
\(180\) 5.52283 0.411648
\(181\) −23.4620 −1.74392 −0.871959 0.489579i \(-0.837150\pi\)
−0.871959 + 0.489579i \(0.837150\pi\)
\(182\) 3.20230 0.237370
\(183\) 25.0175 1.84935
\(184\) 14.4134 1.06257
\(185\) −16.9340 −1.24501
\(186\) 9.97367 0.731305
\(187\) −6.49061 −0.474640
\(188\) −7.40537 −0.540092
\(189\) −1.99072 −0.144804
\(190\) 16.1159 1.16917
\(191\) −14.7215 −1.06521 −0.532606 0.846363i \(-0.678787\pi\)
−0.532606 + 0.846363i \(0.678787\pi\)
\(192\) 15.2547 1.10091
\(193\) −14.9958 −1.07942 −0.539712 0.841850i \(-0.681467\pi\)
−0.539712 + 0.841850i \(0.681467\pi\)
\(194\) 38.5458 2.76743
\(195\) −20.5254 −1.46985
\(196\) −33.0996 −2.36426
\(197\) −13.9415 −0.993293 −0.496647 0.867953i \(-0.665436\pi\)
−0.496647 + 0.867953i \(0.665436\pi\)
\(198\) −0.796131 −0.0565785
\(199\) −20.9879 −1.48779 −0.743895 0.668296i \(-0.767024\pi\)
−0.743895 + 0.668296i \(0.767024\pi\)
\(200\) −67.2319 −4.75402
\(201\) 14.4069 1.01618
\(202\) 26.1910 1.84279
\(203\) −3.24287 −0.227605
\(204\) −57.1367 −4.00037
\(205\) 32.6935 2.28341
\(206\) −16.1592 −1.12587
\(207\) −0.589920 −0.0410023
\(208\) −29.4290 −2.04053
\(209\) −1.64413 −0.113727
\(210\) −7.23877 −0.499522
\(211\) −10.0528 −0.692063 −0.346032 0.938223i \(-0.612471\pi\)
−0.346032 + 0.938223i \(0.612471\pi\)
\(212\) −26.1831 −1.79826
\(213\) 22.1048 1.51460
\(214\) 38.0948 2.60411
\(215\) −42.5116 −2.89927
\(216\) 36.4377 2.47927
\(217\) −0.852124 −0.0578459
\(218\) −4.42402 −0.299633
\(219\) −12.6263 −0.853206
\(220\) 18.1464 1.22343
\(221\) 19.5582 1.31563
\(222\) 21.4887 1.44223
\(223\) 15.5038 1.03821 0.519105 0.854711i \(-0.326266\pi\)
0.519105 + 0.854711i \(0.326266\pi\)
\(224\) −4.33687 −0.289770
\(225\) 2.75171 0.183447
\(226\) 27.9316 1.85798
\(227\) 19.0306 1.26310 0.631552 0.775333i \(-0.282418\pi\)
0.631552 + 0.775333i \(0.282418\pi\)
\(228\) −14.4733 −0.958517
\(229\) −11.7134 −0.774045 −0.387023 0.922070i \(-0.626496\pi\)
−0.387023 + 0.922070i \(0.626496\pi\)
\(230\) 18.9994 1.25278
\(231\) 0.738494 0.0485894
\(232\) 59.3566 3.89695
\(233\) 29.3282 1.92135 0.960677 0.277669i \(-0.0895617\pi\)
0.960677 + 0.277669i \(0.0895617\pi\)
\(234\) 2.39899 0.156827
\(235\) −5.73012 −0.373792
\(236\) 28.9399 1.88383
\(237\) 13.2439 0.860284
\(238\) 6.89768 0.447110
\(239\) −19.7215 −1.27568 −0.637840 0.770169i \(-0.720172\pi\)
−0.637840 + 0.770169i \(0.720172\pi\)
\(240\) 66.5239 4.29410
\(241\) 5.17290 0.333216 0.166608 0.986023i \(-0.446719\pi\)
0.166608 + 0.986023i \(0.446719\pi\)
\(242\) −2.61585 −0.168154
\(243\) −3.15106 −0.202141
\(244\) 66.6482 4.26672
\(245\) −25.6118 −1.63627
\(246\) −41.4872 −2.64513
\(247\) 4.95429 0.315234
\(248\) 15.5971 0.990414
\(249\) 14.5834 0.924183
\(250\) −39.6132 −2.50536
\(251\) −26.9332 −1.70001 −0.850004 0.526777i \(-0.823400\pi\)
−0.850004 + 0.526777i \(0.823400\pi\)
\(252\) 0.598773 0.0377192
\(253\) −1.93831 −0.121860
\(254\) −23.0495 −1.44625
\(255\) −44.2112 −2.76861
\(256\) −15.2096 −0.950602
\(257\) 12.4718 0.777969 0.388984 0.921244i \(-0.372826\pi\)
0.388984 + 0.921244i \(0.372826\pi\)
\(258\) 53.9461 3.35854
\(259\) −1.83594 −0.114080
\(260\) −54.6808 −3.39116
\(261\) −2.42938 −0.150375
\(262\) 19.4948 1.20439
\(263\) −22.5282 −1.38915 −0.694575 0.719420i \(-0.744408\pi\)
−0.694575 + 0.719420i \(0.744408\pi\)
\(264\) −13.5172 −0.831927
\(265\) −20.2599 −1.24456
\(266\) 1.74725 0.107131
\(267\) 1.23579 0.0756293
\(268\) 38.3808 2.34448
\(269\) 3.54782 0.216314 0.108157 0.994134i \(-0.465505\pi\)
0.108157 + 0.994134i \(0.465505\pi\)
\(270\) 48.0313 2.92309
\(271\) 20.4190 1.24037 0.620183 0.784457i \(-0.287058\pi\)
0.620183 + 0.784457i \(0.287058\pi\)
\(272\) −63.3894 −3.84354
\(273\) −2.22531 −0.134682
\(274\) −56.4374 −3.40951
\(275\) 9.04131 0.545212
\(276\) −17.0629 −1.02706
\(277\) 9.98239 0.599784 0.299892 0.953973i \(-0.403049\pi\)
0.299892 + 0.953973i \(0.403049\pi\)
\(278\) −35.8058 −2.14749
\(279\) −0.638365 −0.0382179
\(280\) −11.3202 −0.676509
\(281\) −4.16711 −0.248589 −0.124294 0.992245i \(-0.539667\pi\)
−0.124294 + 0.992245i \(0.539667\pi\)
\(282\) 7.27137 0.433004
\(283\) −21.9093 −1.30237 −0.651187 0.758917i \(-0.725729\pi\)
−0.651187 + 0.758917i \(0.725729\pi\)
\(284\) 58.8887 3.49440
\(285\) −11.1991 −0.663379
\(286\) 7.88239 0.466095
\(287\) 3.54455 0.209228
\(288\) −3.24895 −0.191446
\(289\) 25.1280 1.47812
\(290\) 78.2424 4.59455
\(291\) −26.7859 −1.57022
\(292\) −33.6372 −1.96847
\(293\) 1.15469 0.0674579 0.0337289 0.999431i \(-0.489262\pi\)
0.0337289 + 0.999431i \(0.489262\pi\)
\(294\) 32.5007 1.89548
\(295\) 22.3931 1.30378
\(296\) 33.6046 1.95323
\(297\) −4.90012 −0.284334
\(298\) −8.44764 −0.489359
\(299\) 5.84072 0.337777
\(300\) 79.5906 4.59516
\(301\) −4.60901 −0.265659
\(302\) −9.48258 −0.545661
\(303\) −18.2004 −1.04559
\(304\) −16.0571 −0.920940
\(305\) 51.5710 2.95294
\(306\) 5.16737 0.295399
\(307\) −28.8157 −1.64460 −0.822299 0.569055i \(-0.807309\pi\)
−0.822299 + 0.569055i \(0.807309\pi\)
\(308\) 1.96740 0.112103
\(309\) 11.2292 0.638809
\(310\) 20.5597 1.16771
\(311\) 7.02554 0.398382 0.199191 0.979961i \(-0.436169\pi\)
0.199191 + 0.979961i \(0.436169\pi\)
\(312\) 40.7316 2.30597
\(313\) 6.40546 0.362058 0.181029 0.983478i \(-0.442057\pi\)
0.181029 + 0.983478i \(0.442057\pi\)
\(314\) 53.3835 3.01261
\(315\) 0.463318 0.0261050
\(316\) 35.2826 1.98480
\(317\) −11.0741 −0.621983 −0.310992 0.950413i \(-0.600661\pi\)
−0.310992 + 0.950413i \(0.600661\pi\)
\(318\) 25.7093 1.44171
\(319\) −7.98224 −0.446920
\(320\) 31.4459 1.75788
\(321\) −26.4725 −1.47755
\(322\) 2.05987 0.114792
\(323\) 10.6714 0.593774
\(324\) −47.5573 −2.64207
\(325\) −27.2443 −1.51124
\(326\) 49.5688 2.74536
\(327\) 3.07430 0.170009
\(328\) −64.8786 −3.58232
\(329\) −0.621246 −0.0342504
\(330\) −17.8181 −0.980852
\(331\) 11.9337 0.655935 0.327968 0.944689i \(-0.393636\pi\)
0.327968 + 0.944689i \(0.393636\pi\)
\(332\) 38.8510 2.13223
\(333\) −1.37539 −0.0753708
\(334\) 33.1558 1.81420
\(335\) 29.6982 1.62259
\(336\) 7.21237 0.393467
\(337\) −28.8855 −1.57349 −0.786746 0.617277i \(-0.788236\pi\)
−0.786746 + 0.617277i \(0.788236\pi\)
\(338\) 10.2540 0.557745
\(339\) −19.4100 −1.05421
\(340\) −117.781 −6.38759
\(341\) −2.09748 −0.113585
\(342\) 1.30895 0.0707797
\(343\) −5.62059 −0.303483
\(344\) 84.3622 4.54850
\(345\) −13.2029 −0.710820
\(346\) −29.0766 −1.56317
\(347\) 32.1910 1.72810 0.864051 0.503405i \(-0.167920\pi\)
0.864051 + 0.503405i \(0.167920\pi\)
\(348\) −70.2676 −3.76674
\(349\) 14.0774 0.753547 0.376774 0.926305i \(-0.377033\pi\)
0.376774 + 0.926305i \(0.377033\pi\)
\(350\) −9.60836 −0.513589
\(351\) 14.7656 0.788129
\(352\) −10.6751 −0.568985
\(353\) 28.4325 1.51331 0.756656 0.653813i \(-0.226832\pi\)
0.756656 + 0.653813i \(0.226832\pi\)
\(354\) −28.4162 −1.51031
\(355\) 45.5668 2.41843
\(356\) 3.29223 0.174488
\(357\) −4.79328 −0.253687
\(358\) 41.5171 2.19425
\(359\) 27.0917 1.42984 0.714922 0.699204i \(-0.246462\pi\)
0.714922 + 0.699204i \(0.246462\pi\)
\(360\) −8.48045 −0.446959
\(361\) −16.2968 −0.857728
\(362\) 61.3732 3.22570
\(363\) 1.81779 0.0954091
\(364\) −5.92837 −0.310731
\(365\) −26.0278 −1.36235
\(366\) −65.4422 −3.42072
\(367\) 23.6316 1.23356 0.616781 0.787135i \(-0.288437\pi\)
0.616781 + 0.787135i \(0.288437\pi\)
\(368\) −18.9301 −0.986800
\(369\) 2.65539 0.138234
\(370\) 44.2968 2.30288
\(371\) −2.19654 −0.114039
\(372\) −18.4641 −0.957320
\(373\) −16.8513 −0.872528 −0.436264 0.899819i \(-0.643699\pi\)
−0.436264 + 0.899819i \(0.643699\pi\)
\(374\) 16.9785 0.877937
\(375\) 27.5276 1.42152
\(376\) 11.3711 0.586422
\(377\) 24.0530 1.23879
\(378\) 5.20744 0.267842
\(379\) 24.9236 1.28024 0.640120 0.768275i \(-0.278885\pi\)
0.640120 + 0.768275i \(0.278885\pi\)
\(380\) −29.8352 −1.53051
\(381\) 16.0174 0.820594
\(382\) 38.5094 1.97031
\(383\) 32.0931 1.63988 0.819940 0.572450i \(-0.194007\pi\)
0.819940 + 0.572450i \(0.194007\pi\)
\(384\) −1.09391 −0.0558234
\(385\) 1.52233 0.0775850
\(386\) 39.2269 1.99660
\(387\) −3.45282 −0.175517
\(388\) −71.3593 −3.62272
\(389\) −1.60480 −0.0813666 −0.0406833 0.999172i \(-0.512953\pi\)
−0.0406833 + 0.999172i \(0.512953\pi\)
\(390\) 53.6914 2.71877
\(391\) 12.5808 0.636237
\(392\) 50.8253 2.56706
\(393\) −13.5471 −0.683363
\(394\) 36.4690 1.83728
\(395\) 27.3009 1.37366
\(396\) 1.47387 0.0740646
\(397\) 12.0859 0.606575 0.303288 0.952899i \(-0.401916\pi\)
0.303288 + 0.952899i \(0.401916\pi\)
\(398\) 54.9012 2.75195
\(399\) −1.21418 −0.0607852
\(400\) 88.3003 4.41502
\(401\) 14.8137 0.739761 0.369880 0.929079i \(-0.379399\pi\)
0.369880 + 0.929079i \(0.379399\pi\)
\(402\) −37.6863 −1.87962
\(403\) 6.32037 0.314840
\(404\) −48.4871 −2.41232
\(405\) −36.7988 −1.82855
\(406\) 8.48287 0.420998
\(407\) −4.51913 −0.224005
\(408\) 87.7349 4.34353
\(409\) −25.8299 −1.27721 −0.638603 0.769537i \(-0.720487\pi\)
−0.638603 + 0.769537i \(0.720487\pi\)
\(410\) −85.5214 −4.22360
\(411\) 39.2190 1.93453
\(412\) 29.9154 1.47382
\(413\) 2.42781 0.119465
\(414\) 1.54314 0.0758414
\(415\) 30.0621 1.47569
\(416\) 32.1674 1.57714
\(417\) 24.8819 1.21847
\(418\) 4.30082 0.210360
\(419\) 15.4141 0.753027 0.376514 0.926411i \(-0.377123\pi\)
0.376514 + 0.926411i \(0.377123\pi\)
\(420\) 13.4010 0.653904
\(421\) 29.8792 1.45622 0.728112 0.685458i \(-0.240398\pi\)
0.728112 + 0.685458i \(0.240398\pi\)
\(422\) 26.2967 1.28010
\(423\) −0.465404 −0.0226287
\(424\) 40.2049 1.95252
\(425\) −58.6836 −2.84657
\(426\) −57.8230 −2.80154
\(427\) 5.59121 0.270578
\(428\) −70.5244 −3.40893
\(429\) −5.47756 −0.264459
\(430\) 111.204 5.36274
\(431\) −4.02678 −0.193963 −0.0969816 0.995286i \(-0.530919\pi\)
−0.0969816 + 0.995286i \(0.530919\pi\)
\(432\) −47.8561 −2.30248
\(433\) −10.3919 −0.499403 −0.249701 0.968323i \(-0.580332\pi\)
−0.249701 + 0.968323i \(0.580332\pi\)
\(434\) 2.22903 0.106997
\(435\) −54.3715 −2.60692
\(436\) 8.19013 0.392236
\(437\) 3.18683 0.152447
\(438\) 33.0285 1.57816
\(439\) −27.2829 −1.30214 −0.651071 0.759017i \(-0.725680\pi\)
−0.651071 + 0.759017i \(0.725680\pi\)
\(440\) −27.8643 −1.32838
\(441\) −2.08021 −0.0990574
\(442\) −51.1615 −2.43350
\(443\) −23.9806 −1.13935 −0.569676 0.821870i \(-0.692931\pi\)
−0.569676 + 0.821870i \(0.692931\pi\)
\(444\) −39.7818 −1.88796
\(445\) 2.54746 0.120761
\(446\) −40.5556 −1.92036
\(447\) 5.87036 0.277659
\(448\) 3.40930 0.161074
\(449\) −4.78234 −0.225692 −0.112846 0.993612i \(-0.535997\pi\)
−0.112846 + 0.993612i \(0.535997\pi\)
\(450\) −7.19807 −0.339320
\(451\) 8.72483 0.410836
\(452\) −51.7094 −2.43221
\(453\) 6.58955 0.309604
\(454\) −49.7813 −2.33635
\(455\) −4.58725 −0.215053
\(456\) 22.2241 1.04074
\(457\) −4.10829 −0.192178 −0.0960889 0.995373i \(-0.530633\pi\)
−0.0960889 + 0.995373i \(0.530633\pi\)
\(458\) 30.6406 1.43174
\(459\) 31.8048 1.48452
\(460\) −35.1733 −1.63996
\(461\) 13.1908 0.614357 0.307179 0.951652i \(-0.400615\pi\)
0.307179 + 0.951652i \(0.400615\pi\)
\(462\) −1.93179 −0.0898752
\(463\) −36.4953 −1.69608 −0.848039 0.529933i \(-0.822217\pi\)
−0.848039 + 0.529933i \(0.822217\pi\)
\(464\) −77.9571 −3.61907
\(465\) −14.2871 −0.662550
\(466\) −76.7183 −3.55391
\(467\) 3.68289 0.170424 0.0852118 0.996363i \(-0.472843\pi\)
0.0852118 + 0.996363i \(0.472843\pi\)
\(468\) −4.44122 −0.205295
\(469\) 3.21982 0.148677
\(470\) 14.9892 0.691398
\(471\) −37.0968 −1.70933
\(472\) −44.4380 −2.04542
\(473\) −11.3450 −0.521642
\(474\) −34.6441 −1.59126
\(475\) −14.8651 −0.682059
\(476\) −12.7696 −0.585293
\(477\) −1.64553 −0.0753435
\(478\) 51.5886 2.35961
\(479\) −8.83130 −0.403512 −0.201756 0.979436i \(-0.564665\pi\)
−0.201756 + 0.979436i \(0.564665\pi\)
\(480\) −72.7142 −3.31893
\(481\) 13.6175 0.620906
\(482\) −13.5315 −0.616345
\(483\) −1.43143 −0.0651322
\(484\) 4.84270 0.220123
\(485\) −55.2163 −2.50724
\(486\) 8.24272 0.373898
\(487\) −36.8666 −1.67059 −0.835293 0.549805i \(-0.814702\pi\)
−0.835293 + 0.549805i \(0.814702\pi\)
\(488\) −102.340 −4.63272
\(489\) −34.4459 −1.55770
\(490\) 66.9966 3.02660
\(491\) 23.7402 1.07138 0.535690 0.844415i \(-0.320052\pi\)
0.535690 + 0.844415i \(0.320052\pi\)
\(492\) 76.8046 3.46262
\(493\) 51.8096 2.33339
\(494\) −12.9597 −0.583084
\(495\) 1.14045 0.0512592
\(496\) −20.4847 −0.919790
\(497\) 4.94025 0.221600
\(498\) −38.1480 −1.70945
\(499\) 31.8301 1.42491 0.712455 0.701718i \(-0.247583\pi\)
0.712455 + 0.701718i \(0.247583\pi\)
\(500\) 73.3353 3.27966
\(501\) −23.0403 −1.02937
\(502\) 70.4533 3.14448
\(503\) −1.69168 −0.0754281 −0.0377141 0.999289i \(-0.512008\pi\)
−0.0377141 + 0.999289i \(0.512008\pi\)
\(504\) −0.919431 −0.0409547
\(505\) −37.5182 −1.66954
\(506\) 5.07033 0.225403
\(507\) −7.12564 −0.316461
\(508\) 42.6712 1.89323
\(509\) 38.9738 1.72748 0.863742 0.503934i \(-0.168115\pi\)
0.863742 + 0.503934i \(0.168115\pi\)
\(510\) 115.650 5.12107
\(511\) −2.82187 −0.124832
\(512\) 40.9898 1.81151
\(513\) 8.05645 0.355701
\(514\) −32.6244 −1.43900
\(515\) 23.1479 1.02002
\(516\) −99.8697 −4.39652
\(517\) −1.52918 −0.0672534
\(518\) 4.80256 0.211012
\(519\) 20.2056 0.886928
\(520\) 83.9638 3.68206
\(521\) −31.2559 −1.36935 −0.684674 0.728850i \(-0.740055\pi\)
−0.684674 + 0.728850i \(0.740055\pi\)
\(522\) 6.35491 0.278147
\(523\) −6.31710 −0.276228 −0.138114 0.990416i \(-0.544104\pi\)
−0.138114 + 0.990416i \(0.544104\pi\)
\(524\) −36.0904 −1.57662
\(525\) 6.67696 0.291406
\(526\) 58.9306 2.56950
\(527\) 13.6139 0.593032
\(528\) 17.7531 0.772604
\(529\) −19.2430 −0.836651
\(530\) 52.9970 2.30204
\(531\) 1.81878 0.0789284
\(532\) −3.23466 −0.140240
\(533\) −26.2906 −1.13877
\(534\) −3.23265 −0.139891
\(535\) −54.5703 −2.35928
\(536\) −58.9347 −2.54559
\(537\) −28.8507 −1.24500
\(538\) −9.28057 −0.400114
\(539\) −6.83495 −0.294402
\(540\) −88.9197 −3.82649
\(541\) −21.8392 −0.938942 −0.469471 0.882948i \(-0.655555\pi\)
−0.469471 + 0.882948i \(0.655555\pi\)
\(542\) −53.4131 −2.29429
\(543\) −42.6489 −1.83024
\(544\) 69.2880 2.97070
\(545\) 6.33735 0.271462
\(546\) 5.82110 0.249120
\(547\) 1.00000 0.0427569
\(548\) 104.482 4.46324
\(549\) 4.18863 0.178766
\(550\) −23.6508 −1.00847
\(551\) 13.1239 0.559096
\(552\) 26.2005 1.11517
\(553\) 2.95990 0.125868
\(554\) −26.1125 −1.10941
\(555\) −30.7823 −1.30664
\(556\) 66.2869 2.81119
\(557\) 34.1731 1.44796 0.723980 0.689821i \(-0.242311\pi\)
0.723980 + 0.689821i \(0.242311\pi\)
\(558\) 1.66987 0.0706913
\(559\) 34.1859 1.44591
\(560\) 14.8675 0.628268
\(561\) −11.7985 −0.498135
\(562\) 10.9006 0.459812
\(563\) −1.24870 −0.0526264 −0.0263132 0.999654i \(-0.508377\pi\)
−0.0263132 + 0.999654i \(0.508377\pi\)
\(564\) −13.4614 −0.566827
\(565\) −40.0116 −1.68330
\(566\) 57.3116 2.40899
\(567\) −3.98964 −0.167549
\(568\) −90.4250 −3.79415
\(569\) −8.39342 −0.351870 −0.175935 0.984402i \(-0.556295\pi\)
−0.175935 + 0.984402i \(0.556295\pi\)
\(570\) 29.2953 1.22704
\(571\) −13.9183 −0.582465 −0.291232 0.956652i \(-0.594065\pi\)
−0.291232 + 0.956652i \(0.594065\pi\)
\(572\) −14.5926 −0.610145
\(573\) −26.7606 −1.11794
\(574\) −9.27204 −0.387007
\(575\) −17.5248 −0.730836
\(576\) 2.55406 0.106419
\(577\) 11.6473 0.484883 0.242441 0.970166i \(-0.422052\pi\)
0.242441 + 0.970166i \(0.422052\pi\)
\(578\) −65.7311 −2.73405
\(579\) −27.2592 −1.13285
\(580\) −144.849 −6.01453
\(581\) 3.25926 0.135217
\(582\) 70.0680 2.90441
\(583\) −5.40672 −0.223924
\(584\) 51.6508 2.13733
\(585\) −3.43652 −0.142083
\(586\) −3.02051 −0.124776
\(587\) 24.8707 1.02653 0.513263 0.858232i \(-0.328437\pi\)
0.513263 + 0.858232i \(0.328437\pi\)
\(588\) −60.1680 −2.48129
\(589\) 3.44854 0.142095
\(590\) −58.5770 −2.41158
\(591\) −25.3427 −1.04246
\(592\) −44.1352 −1.81395
\(593\) 42.3587 1.73946 0.869732 0.493524i \(-0.164292\pi\)
0.869732 + 0.493524i \(0.164292\pi\)
\(594\) 12.8180 0.525929
\(595\) −9.88083 −0.405075
\(596\) 15.6390 0.640599
\(597\) −38.1515 −1.56144
\(598\) −15.2785 −0.624783
\(599\) −21.5127 −0.878987 −0.439494 0.898246i \(-0.644842\pi\)
−0.439494 + 0.898246i \(0.644842\pi\)
\(600\) −122.213 −4.98934
\(601\) 22.6113 0.922335 0.461168 0.887313i \(-0.347431\pi\)
0.461168 + 0.887313i \(0.347431\pi\)
\(602\) 12.0565 0.491386
\(603\) 2.41211 0.0982288
\(604\) 17.5550 0.714302
\(605\) 3.74717 0.152344
\(606\) 47.6097 1.93401
\(607\) −10.9909 −0.446107 −0.223054 0.974806i \(-0.571603\pi\)
−0.223054 + 0.974806i \(0.571603\pi\)
\(608\) 17.5513 0.711800
\(609\) −5.89484 −0.238871
\(610\) −134.902 −5.46203
\(611\) 4.60791 0.186416
\(612\) −9.56629 −0.386694
\(613\) −8.53005 −0.344526 −0.172263 0.985051i \(-0.555108\pi\)
−0.172263 + 0.985051i \(0.555108\pi\)
\(614\) 75.3777 3.04200
\(615\) 59.4298 2.39644
\(616\) −3.02098 −0.121719
\(617\) −22.1586 −0.892074 −0.446037 0.895015i \(-0.647165\pi\)
−0.446037 + 0.895015i \(0.647165\pi\)
\(618\) −29.3740 −1.18160
\(619\) −25.0431 −1.00657 −0.503283 0.864122i \(-0.667875\pi\)
−0.503283 + 0.864122i \(0.667875\pi\)
\(620\) −38.0618 −1.52860
\(621\) 9.49793 0.381139
\(622\) −18.3778 −0.736883
\(623\) 0.276189 0.0110653
\(624\) −53.4956 −2.14154
\(625\) 11.5387 0.461550
\(626\) −16.7557 −0.669694
\(627\) −2.98868 −0.119357
\(628\) −98.8282 −3.94367
\(629\) 29.3319 1.16954
\(630\) −1.21197 −0.0482861
\(631\) 8.28732 0.329913 0.164956 0.986301i \(-0.447252\pi\)
0.164956 + 0.986301i \(0.447252\pi\)
\(632\) −54.1773 −2.15506
\(633\) −18.2738 −0.726320
\(634\) 28.9682 1.15048
\(635\) 33.0181 1.31028
\(636\) −47.5953 −1.88728
\(637\) 20.5958 0.816037
\(638\) 20.8804 0.826662
\(639\) 3.70097 0.146408
\(640\) −2.25498 −0.0891359
\(641\) 19.8980 0.785925 0.392963 0.919554i \(-0.371450\pi\)
0.392963 + 0.919554i \(0.371450\pi\)
\(642\) 69.2482 2.73301
\(643\) 18.0543 0.711994 0.355997 0.934487i \(-0.384141\pi\)
0.355997 + 0.934487i \(0.384141\pi\)
\(644\) −3.81341 −0.150270
\(645\) −77.2770 −3.04278
\(646\) −27.9149 −1.09830
\(647\) −16.6657 −0.655196 −0.327598 0.944817i \(-0.606239\pi\)
−0.327598 + 0.944817i \(0.606239\pi\)
\(648\) 73.0254 2.86871
\(649\) 5.97599 0.234578
\(650\) 71.2671 2.79533
\(651\) −1.54898 −0.0607093
\(652\) −91.7660 −3.59384
\(653\) 6.26686 0.245241 0.122621 0.992454i \(-0.460870\pi\)
0.122621 + 0.992454i \(0.460870\pi\)
\(654\) −8.04193 −0.314464
\(655\) −27.9260 −1.09116
\(656\) 85.2095 3.32687
\(657\) −2.11399 −0.0824747
\(658\) 1.62509 0.0633526
\(659\) 19.3921 0.755409 0.377704 0.925926i \(-0.376714\pi\)
0.377704 + 0.925926i \(0.376714\pi\)
\(660\) 32.9863 1.28399
\(661\) 25.2995 0.984035 0.492018 0.870585i \(-0.336260\pi\)
0.492018 + 0.870585i \(0.336260\pi\)
\(662\) −31.2168 −1.21328
\(663\) 35.5527 1.38075
\(664\) −59.6567 −2.31513
\(665\) −2.50291 −0.0970587
\(666\) 3.59782 0.139413
\(667\) 15.4720 0.599079
\(668\) −61.3809 −2.37490
\(669\) 28.1825 1.08960
\(670\) −77.6863 −3.00128
\(671\) 13.7626 0.531300
\(672\) −7.88351 −0.304113
\(673\) −20.5174 −0.790888 −0.395444 0.918490i \(-0.629409\pi\)
−0.395444 + 0.918490i \(0.629409\pi\)
\(674\) 75.5602 2.91047
\(675\) −44.3035 −1.70524
\(676\) −18.9831 −0.730121
\(677\) −2.52438 −0.0970197 −0.0485099 0.998823i \(-0.515447\pi\)
−0.0485099 + 0.998823i \(0.515447\pi\)
\(678\) 50.7737 1.94995
\(679\) −5.98643 −0.229738
\(680\) 180.856 6.93552
\(681\) 34.5936 1.32563
\(682\) 5.48671 0.210097
\(683\) −15.0787 −0.576969 −0.288484 0.957485i \(-0.593151\pi\)
−0.288484 + 0.957485i \(0.593151\pi\)
\(684\) −2.42323 −0.0926546
\(685\) 80.8458 3.08896
\(686\) 14.7026 0.561350
\(687\) −21.2925 −0.812360
\(688\) −110.799 −4.22416
\(689\) 16.2921 0.620681
\(690\) 34.5368 1.31480
\(691\) 9.48717 0.360909 0.180455 0.983583i \(-0.442243\pi\)
0.180455 + 0.983583i \(0.442243\pi\)
\(692\) 53.8290 2.04627
\(693\) 0.123645 0.00469687
\(694\) −84.2069 −3.19645
\(695\) 51.2913 1.94559
\(696\) 107.898 4.08985
\(697\) −56.6295 −2.14499
\(698\) −36.8245 −1.39383
\(699\) 53.3124 2.01646
\(700\) 17.7878 0.672317
\(701\) 14.7547 0.557279 0.278639 0.960396i \(-0.410117\pi\)
0.278639 + 0.960396i \(0.410117\pi\)
\(702\) −38.6246 −1.45779
\(703\) 7.43005 0.280230
\(704\) 8.39191 0.316282
\(705\) −10.4161 −0.392294
\(706\) −74.3754 −2.79916
\(707\) −4.06764 −0.152980
\(708\) 52.6066 1.97708
\(709\) −19.5306 −0.733486 −0.366743 0.930322i \(-0.619527\pi\)
−0.366743 + 0.930322i \(0.619527\pi\)
\(710\) −119.196 −4.47335
\(711\) 2.21740 0.0831590
\(712\) −5.05530 −0.189455
\(713\) 4.06556 0.152257
\(714\) 12.5385 0.469242
\(715\) −11.2914 −0.422275
\(716\) −76.8600 −2.87239
\(717\) −35.8495 −1.33882
\(718\) −70.8679 −2.64477
\(719\) 9.80130 0.365527 0.182763 0.983157i \(-0.441496\pi\)
0.182763 + 0.983157i \(0.441496\pi\)
\(720\) 11.1380 0.415087
\(721\) 2.50964 0.0934639
\(722\) 42.6301 1.58653
\(723\) 9.40322 0.349710
\(724\) −113.619 −4.22263
\(725\) −72.1699 −2.68032
\(726\) −4.75507 −0.176477
\(727\) −37.1944 −1.37947 −0.689733 0.724064i \(-0.742272\pi\)
−0.689733 + 0.724064i \(0.742272\pi\)
\(728\) 9.10317 0.337386
\(729\) 23.7333 0.879011
\(730\) 68.0848 2.51993
\(731\) 73.6358 2.72352
\(732\) 121.152 4.47792
\(733\) −39.2717 −1.45054 −0.725268 0.688467i \(-0.758284\pi\)
−0.725268 + 0.688467i \(0.758284\pi\)
\(734\) −61.8169 −2.28170
\(735\) −46.5567 −1.71727
\(736\) 20.6916 0.762704
\(737\) 7.92550 0.291940
\(738\) −6.94611 −0.255690
\(739\) 4.69533 0.172720 0.0863602 0.996264i \(-0.472476\pi\)
0.0863602 + 0.996264i \(0.472476\pi\)
\(740\) −82.0060 −3.01460
\(741\) 9.00584 0.330838
\(742\) 5.74582 0.210936
\(743\) 41.5704 1.52507 0.762535 0.646947i \(-0.223954\pi\)
0.762535 + 0.646947i \(0.223954\pi\)
\(744\) 28.3521 1.03944
\(745\) 12.1011 0.443351
\(746\) 44.0806 1.61391
\(747\) 2.44166 0.0893358
\(748\) −31.4320 −1.14927
\(749\) −5.91639 −0.216180
\(750\) −72.0083 −2.62937
\(751\) 14.5781 0.531963 0.265981 0.963978i \(-0.414304\pi\)
0.265981 + 0.963978i \(0.414304\pi\)
\(752\) −14.9345 −0.544605
\(753\) −48.9588 −1.78416
\(754\) −62.9191 −2.29138
\(755\) 13.5837 0.494360
\(756\) −9.64047 −0.350621
\(757\) 37.7246 1.37112 0.685562 0.728014i \(-0.259557\pi\)
0.685562 + 0.728014i \(0.259557\pi\)
\(758\) −65.1965 −2.36804
\(759\) −3.52343 −0.127892
\(760\) 45.8126 1.66180
\(761\) −31.0762 −1.12651 −0.563256 0.826282i \(-0.690452\pi\)
−0.563256 + 0.826282i \(0.690452\pi\)
\(762\) −41.8991 −1.51784
\(763\) 0.687081 0.0248740
\(764\) −71.2919 −2.57925
\(765\) −7.40218 −0.267627
\(766\) −83.9508 −3.03327
\(767\) −18.0075 −0.650214
\(768\) −27.6479 −0.997657
\(769\) 4.40830 0.158967 0.0794837 0.996836i \(-0.474673\pi\)
0.0794837 + 0.996836i \(0.474673\pi\)
\(770\) −3.98219 −0.143508
\(771\) 22.6710 0.816478
\(772\) −72.6203 −2.61366
\(773\) 24.8597 0.894142 0.447071 0.894498i \(-0.352467\pi\)
0.447071 + 0.894498i \(0.352467\pi\)
\(774\) 9.03208 0.324651
\(775\) −18.9640 −0.681207
\(776\) 109.574 3.93348
\(777\) −3.33735 −0.119727
\(778\) 4.19792 0.150503
\(779\) −14.3448 −0.513956
\(780\) −99.3981 −3.55902
\(781\) 12.1603 0.435130
\(782\) −32.9095 −1.17684
\(783\) 39.1139 1.39782
\(784\) −66.7523 −2.38401
\(785\) −76.4711 −2.72937
\(786\) 35.4374 1.26401
\(787\) 23.9191 0.852625 0.426313 0.904576i \(-0.359812\pi\)
0.426313 + 0.904576i \(0.359812\pi\)
\(788\) −67.5146 −2.40511
\(789\) −40.9515 −1.45791
\(790\) −71.4152 −2.54084
\(791\) −4.33797 −0.154241
\(792\) −2.26316 −0.0804178
\(793\) −41.4711 −1.47268
\(794\) −31.6150 −1.12198
\(795\) −36.8282 −1.30616
\(796\) −101.638 −3.60246
\(797\) 47.5946 1.68589 0.842944 0.538002i \(-0.180821\pi\)
0.842944 + 0.538002i \(0.180821\pi\)
\(798\) 3.17613 0.112434
\(799\) 9.92533 0.351133
\(800\) −96.5170 −3.41239
\(801\) 0.206906 0.00731067
\(802\) −38.7505 −1.36833
\(803\) −6.94597 −0.245118
\(804\) 69.7681 2.46053
\(805\) −2.95074 −0.104000
\(806\) −16.5332 −0.582356
\(807\) 6.44917 0.227022
\(808\) 74.4531 2.61925
\(809\) −51.6584 −1.81621 −0.908107 0.418739i \(-0.862472\pi\)
−0.908107 + 0.418739i \(0.862472\pi\)
\(810\) 96.2603 3.38224
\(811\) 43.9447 1.54311 0.771554 0.636163i \(-0.219480\pi\)
0.771554 + 0.636163i \(0.219480\pi\)
\(812\) −15.7042 −0.551110
\(813\) 37.1174 1.30176
\(814\) 11.8214 0.414339
\(815\) −71.0066 −2.48725
\(816\) −115.228 −4.03380
\(817\) 18.6527 0.652574
\(818\) 67.5672 2.36243
\(819\) −0.372580 −0.0130190
\(820\) 158.325 5.52893
\(821\) −1.53166 −0.0534553 −0.0267277 0.999643i \(-0.508509\pi\)
−0.0267277 + 0.999643i \(0.508509\pi\)
\(822\) −102.591 −3.57828
\(823\) 9.87643 0.344271 0.172135 0.985073i \(-0.444933\pi\)
0.172135 + 0.985073i \(0.444933\pi\)
\(824\) −45.9358 −1.60025
\(825\) 16.4352 0.572199
\(826\) −6.35079 −0.220972
\(827\) 25.3600 0.881854 0.440927 0.897543i \(-0.354650\pi\)
0.440927 + 0.897543i \(0.354650\pi\)
\(828\) −2.85680 −0.0992808
\(829\) −2.02393 −0.0702940 −0.0351470 0.999382i \(-0.511190\pi\)
−0.0351470 + 0.999382i \(0.511190\pi\)
\(830\) −78.6380 −2.72956
\(831\) 18.1459 0.629473
\(832\) −25.2874 −0.876684
\(833\) 44.3630 1.53709
\(834\) −65.0874 −2.25379
\(835\) −47.4952 −1.64364
\(836\) −7.96204 −0.275373
\(837\) 10.2779 0.355257
\(838\) −40.3210 −1.39287
\(839\) 19.3795 0.669053 0.334526 0.942386i \(-0.391424\pi\)
0.334526 + 0.942386i \(0.391424\pi\)
\(840\) −20.5776 −0.709996
\(841\) 34.7162 1.19711
\(842\) −78.1597 −2.69356
\(843\) −7.57491 −0.260894
\(844\) −48.6827 −1.67573
\(845\) −14.6887 −0.505308
\(846\) 1.21743 0.0418561
\(847\) 0.406260 0.0139593
\(848\) −52.8038 −1.81329
\(849\) −39.8265 −1.36684
\(850\) 153.508 5.26527
\(851\) 8.75945 0.300270
\(852\) 107.047 3.66737
\(853\) 15.7500 0.539270 0.269635 0.962963i \(-0.413097\pi\)
0.269635 + 0.962963i \(0.413097\pi\)
\(854\) −14.6258 −0.500484
\(855\) −1.87505 −0.0641252
\(856\) 108.292 3.70135
\(857\) −15.5489 −0.531139 −0.265570 0.964092i \(-0.585560\pi\)
−0.265570 + 0.964092i \(0.585560\pi\)
\(858\) 14.3285 0.489167
\(859\) −35.3732 −1.20692 −0.603458 0.797394i \(-0.706211\pi\)
−0.603458 + 0.797394i \(0.706211\pi\)
\(860\) −205.871 −7.02013
\(861\) 6.44324 0.219585
\(862\) 10.5335 0.358772
\(863\) −38.9298 −1.32519 −0.662593 0.748980i \(-0.730544\pi\)
−0.662593 + 0.748980i \(0.730544\pi\)
\(864\) 52.3093 1.77960
\(865\) 41.6517 1.41620
\(866\) 27.1837 0.923740
\(867\) 45.6773 1.55128
\(868\) −4.12658 −0.140065
\(869\) 7.28573 0.247151
\(870\) 142.228 4.82198
\(871\) −23.8820 −0.809211
\(872\) −12.5762 −0.425882
\(873\) −4.48471 −0.151784
\(874\) −8.33629 −0.281979
\(875\) 6.15220 0.207982
\(876\) −61.1453 −2.06591
\(877\) −32.0277 −1.08150 −0.540750 0.841184i \(-0.681859\pi\)
−0.540750 + 0.841184i \(0.681859\pi\)
\(878\) 71.3681 2.40856
\(879\) 2.09898 0.0707970
\(880\) 36.5961 1.23365
\(881\) 50.3338 1.69579 0.847895 0.530165i \(-0.177870\pi\)
0.847895 + 0.530165i \(0.177870\pi\)
\(882\) 5.44152 0.183225
\(883\) 31.8313 1.07121 0.535604 0.844469i \(-0.320084\pi\)
0.535604 + 0.844469i \(0.320084\pi\)
\(884\) 94.7145 3.18559
\(885\) 40.7058 1.36831
\(886\) 62.7297 2.10745
\(887\) −0.781354 −0.0262353 −0.0131177 0.999914i \(-0.504176\pi\)
−0.0131177 + 0.999914i \(0.504176\pi\)
\(888\) 61.0860 2.04991
\(889\) 3.57975 0.120061
\(890\) −6.66377 −0.223370
\(891\) −9.82042 −0.328996
\(892\) 75.0800 2.51387
\(893\) 2.51418 0.0841339
\(894\) −15.3560 −0.513582
\(895\) −59.4726 −1.98795
\(896\) −0.244480 −0.00816750
\(897\) 10.6172 0.354497
\(898\) 12.5099 0.417461
\(899\) 16.7426 0.558397
\(900\) 13.3257 0.444189
\(901\) 35.0929 1.16911
\(902\) −22.8229 −0.759920
\(903\) −8.37820 −0.278809
\(904\) 79.4011 2.64084
\(905\) −87.9162 −2.92243
\(906\) −17.2373 −0.572671
\(907\) −46.6003 −1.54734 −0.773669 0.633591i \(-0.781580\pi\)
−0.773669 + 0.633591i \(0.781580\pi\)
\(908\) 92.1594 3.05842
\(909\) −3.04726 −0.101071
\(910\) 11.9996 0.397782
\(911\) −15.8917 −0.526514 −0.263257 0.964726i \(-0.584797\pi\)
−0.263257 + 0.964726i \(0.584797\pi\)
\(912\) −29.1885 −0.966526
\(913\) 8.02259 0.265509
\(914\) 10.7467 0.355469
\(915\) 93.7450 3.09911
\(916\) −56.7246 −1.87423
\(917\) −3.02767 −0.0999826
\(918\) −83.1966 −2.74590
\(919\) −18.5713 −0.612611 −0.306306 0.951933i \(-0.599093\pi\)
−0.306306 + 0.951933i \(0.599093\pi\)
\(920\) 54.0095 1.78064
\(921\) −52.3808 −1.72601
\(922\) −34.5052 −1.13637
\(923\) −36.6428 −1.20611
\(924\) 3.57630 0.117652
\(925\) −40.8588 −1.34343
\(926\) 95.4663 3.13722
\(927\) 1.88009 0.0617501
\(928\) 85.2113 2.79720
\(929\) −26.5792 −0.872035 −0.436018 0.899938i \(-0.643611\pi\)
−0.436018 + 0.899938i \(0.643611\pi\)
\(930\) 37.3731 1.22551
\(931\) 11.2376 0.368297
\(932\) 142.028 4.65227
\(933\) 12.7709 0.418102
\(934\) −9.63389 −0.315231
\(935\) −24.3214 −0.795396
\(936\) 6.81960 0.222906
\(937\) 3.86062 0.126121 0.0630605 0.998010i \(-0.479914\pi\)
0.0630605 + 0.998010i \(0.479914\pi\)
\(938\) −8.42257 −0.275007
\(939\) 11.6438 0.379980
\(940\) −27.7492 −0.905080
\(941\) 25.4012 0.828055 0.414028 0.910264i \(-0.364122\pi\)
0.414028 + 0.910264i \(0.364122\pi\)
\(942\) 97.0398 3.16173
\(943\) −16.9114 −0.550711
\(944\) 58.3635 1.89957
\(945\) −7.45959 −0.242660
\(946\) 29.6768 0.964876
\(947\) 10.1398 0.329499 0.164750 0.986335i \(-0.447318\pi\)
0.164750 + 0.986335i \(0.447318\pi\)
\(948\) 64.1362 2.08305
\(949\) 20.9304 0.679429
\(950\) 38.8850 1.26160
\(951\) −20.1303 −0.652771
\(952\) 19.6080 0.635500
\(953\) 55.5328 1.79888 0.899441 0.437041i \(-0.143974\pi\)
0.899441 + 0.437041i \(0.143974\pi\)
\(954\) 4.30446 0.139362
\(955\) −55.1641 −1.78507
\(956\) −95.5054 −3.08886
\(957\) −14.5100 −0.469042
\(958\) 23.1014 0.746372
\(959\) 8.76512 0.283040
\(960\) 57.1620 1.84490
\(961\) −26.6006 −0.858083
\(962\) −35.6215 −1.14848
\(963\) −4.43224 −0.142827
\(964\) 25.0508 0.806831
\(965\) −56.1920 −1.80888
\(966\) 3.74441 0.120474
\(967\) 35.4343 1.13949 0.569745 0.821821i \(-0.307042\pi\)
0.569745 + 0.821821i \(0.307042\pi\)
\(968\) −7.43608 −0.239005
\(969\) 19.3984 0.623166
\(970\) 144.438 4.63762
\(971\) 21.8054 0.699770 0.349885 0.936793i \(-0.386221\pi\)
0.349885 + 0.936793i \(0.386221\pi\)
\(972\) −15.2596 −0.489453
\(973\) 5.56089 0.178274
\(974\) 96.4377 3.09006
\(975\) −49.5243 −1.58605
\(976\) 134.410 4.30237
\(977\) −26.0413 −0.833136 −0.416568 0.909104i \(-0.636767\pi\)
−0.416568 + 0.909104i \(0.636767\pi\)
\(978\) 90.1055 2.88126
\(979\) 0.679834 0.0217276
\(980\) −124.030 −3.96199
\(981\) 0.514724 0.0164339
\(982\) −62.1009 −1.98172
\(983\) 23.9811 0.764877 0.382439 0.923981i \(-0.375084\pi\)
0.382439 + 0.923981i \(0.375084\pi\)
\(984\) −117.935 −3.75964
\(985\) −52.2414 −1.66455
\(986\) −135.526 −4.31604
\(987\) −1.12929 −0.0359458
\(988\) 23.9921 0.763291
\(989\) 21.9900 0.699242
\(990\) −2.98324 −0.0948136
\(991\) 10.5877 0.336329 0.168165 0.985759i \(-0.446216\pi\)
0.168165 + 0.985759i \(0.446216\pi\)
\(992\) 22.3909 0.710911
\(993\) 21.6929 0.688404
\(994\) −12.9230 −0.409892
\(995\) −78.6452 −2.49322
\(996\) 70.6228 2.23777
\(997\) 19.7017 0.623959 0.311979 0.950089i \(-0.399008\pi\)
0.311979 + 0.950089i \(0.399008\pi\)
\(998\) −83.2629 −2.63564
\(999\) 22.1443 0.700613
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 \(a_p\))