Properties

Label 8007.2.a.j.1.15
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 0
Dimension 64
CM No

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(0\)
Dimension: \(64\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.65285 q^{2}\) \(-1.00000 q^{3}\) \(+0.731922 q^{4}\) \(+2.84674 q^{5}\) \(+1.65285 q^{6}\) \(-0.210210 q^{7}\) \(+2.09595 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.65285 q^{2}\) \(-1.00000 q^{3}\) \(+0.731922 q^{4}\) \(+2.84674 q^{5}\) \(+1.65285 q^{6}\) \(-0.210210 q^{7}\) \(+2.09595 q^{8}\) \(+1.00000 q^{9}\) \(-4.70524 q^{10}\) \(+5.85789 q^{11}\) \(-0.731922 q^{12}\) \(+5.94416 q^{13}\) \(+0.347446 q^{14}\) \(-2.84674 q^{15}\) \(-4.92813 q^{16}\) \(+1.00000 q^{17}\) \(-1.65285 q^{18}\) \(-6.00132 q^{19}\) \(+2.08359 q^{20}\) \(+0.210210 q^{21}\) \(-9.68222 q^{22}\) \(-1.53863 q^{23}\) \(-2.09595 q^{24}\) \(+3.10394 q^{25}\) \(-9.82483 q^{26}\) \(-1.00000 q^{27}\) \(-0.153857 q^{28}\) \(+4.06149 q^{29}\) \(+4.70524 q^{30}\) \(+1.55353 q^{31}\) \(+3.95359 q^{32}\) \(-5.85789 q^{33}\) \(-1.65285 q^{34}\) \(-0.598414 q^{35}\) \(+0.731922 q^{36}\) \(+0.569477 q^{37}\) \(+9.91930 q^{38}\) \(-5.94416 q^{39}\) \(+5.96662 q^{40}\) \(-0.500994 q^{41}\) \(-0.347446 q^{42}\) \(-11.8990 q^{43}\) \(+4.28751 q^{44}\) \(+2.84674 q^{45}\) \(+2.54313 q^{46}\) \(+6.53043 q^{47}\) \(+4.92813 q^{48}\) \(-6.95581 q^{49}\) \(-5.13035 q^{50}\) \(-1.00000 q^{51}\) \(+4.35066 q^{52}\) \(+7.14559 q^{53}\) \(+1.65285 q^{54}\) \(+16.6759 q^{55}\) \(-0.440589 q^{56}\) \(+6.00132 q^{57}\) \(-6.71305 q^{58}\) \(+7.13227 q^{59}\) \(-2.08359 q^{60}\) \(-1.20114 q^{61}\) \(-2.56776 q^{62}\) \(-0.210210 q^{63}\) \(+3.32157 q^{64}\) \(+16.9215 q^{65}\) \(+9.68222 q^{66}\) \(+7.38532 q^{67}\) \(+0.731922 q^{68}\) \(+1.53863 q^{69}\) \(+0.989090 q^{70}\) \(+13.3151 q^{71}\) \(+2.09595 q^{72}\) \(-10.9391 q^{73}\) \(-0.941261 q^{74}\) \(-3.10394 q^{75}\) \(-4.39250 q^{76}\) \(-1.23139 q^{77}\) \(+9.82483 q^{78}\) \(+11.8246 q^{79}\) \(-14.0291 q^{80}\) \(+1.00000 q^{81}\) \(+0.828070 q^{82}\) \(-14.1343 q^{83}\) \(+0.153857 q^{84}\) \(+2.84674 q^{85}\) \(+19.6673 q^{86}\) \(-4.06149 q^{87}\) \(+12.2778 q^{88}\) \(+13.5101 q^{89}\) \(-4.70524 q^{90}\) \(-1.24952 q^{91}\) \(-1.12616 q^{92}\) \(-1.55353 q^{93}\) \(-10.7938 q^{94}\) \(-17.0842 q^{95}\) \(-3.95359 q^{96}\) \(+17.2545 q^{97}\) \(+11.4969 q^{98}\) \(+5.85789 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(64q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 64q^{3} \) \(\mathstrut +\mathstrut 77q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 64q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(64q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 64q^{3} \) \(\mathstrut +\mathstrut 77q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 64q^{9} \) \(\mathstrut +\mathstrut 12q^{10} \) \(\mathstrut -\mathstrut 7q^{11} \) \(\mathstrut -\mathstrut 77q^{12} \) \(\mathstrut +\mathstrut 24q^{13} \) \(\mathstrut -\mathstrut 14q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 103q^{16} \) \(\mathstrut +\mathstrut 64q^{17} \) \(\mathstrut +\mathstrut 5q^{18} \) \(\mathstrut +\mathstrut 26q^{19} \) \(\mathstrut -\mathstrut 24q^{20} \) \(\mathstrut -\mathstrut 5q^{21} \) \(\mathstrut +\mathstrut 25q^{22} \) \(\mathstrut +\mathstrut 20q^{23} \) \(\mathstrut -\mathstrut 18q^{24} \) \(\mathstrut +\mathstrut 141q^{25} \) \(\mathstrut +\mathstrut 9q^{26} \) \(\mathstrut -\mathstrut 64q^{27} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut +\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 31q^{32} \) \(\mathstrut +\mathstrut 7q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 3q^{35} \) \(\mathstrut +\mathstrut 77q^{36} \) \(\mathstrut +\mathstrut 50q^{37} \) \(\mathstrut +\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut +\mathstrut 28q^{40} \) \(\mathstrut -\mathstrut 9q^{41} \) \(\mathstrut +\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 59q^{43} \) \(\mathstrut -\mathstrut 6q^{44} \) \(\mathstrut -\mathstrut 3q^{45} \) \(\mathstrut +\mathstrut 11q^{47} \) \(\mathstrut -\mathstrut 103q^{48} \) \(\mathstrut +\mathstrut 163q^{49} \) \(\mathstrut +\mathstrut 20q^{50} \) \(\mathstrut -\mathstrut 64q^{51} \) \(\mathstrut +\mathstrut 65q^{52} \) \(\mathstrut +\mathstrut 39q^{53} \) \(\mathstrut -\mathstrut 5q^{54} \) \(\mathstrut +\mathstrut 35q^{55} \) \(\mathstrut -\mathstrut 34q^{56} \) \(\mathstrut -\mathstrut 26q^{57} \) \(\mathstrut -\mathstrut 27q^{58} \) \(\mathstrut -\mathstrut 65q^{59} \) \(\mathstrut +\mathstrut 24q^{60} \) \(\mathstrut +\mathstrut 15q^{61} \) \(\mathstrut +\mathstrut 18q^{62} \) \(\mathstrut +\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 152q^{64} \) \(\mathstrut +\mathstrut 49q^{65} \) \(\mathstrut -\mathstrut 25q^{66} \) \(\mathstrut +\mathstrut 56q^{67} \) \(\mathstrut +\mathstrut 77q^{68} \) \(\mathstrut -\mathstrut 20q^{69} \) \(\mathstrut +\mathstrut 28q^{70} \) \(\mathstrut -\mathstrut 18q^{71} \) \(\mathstrut +\mathstrut 18q^{72} \) \(\mathstrut +\mathstrut 37q^{73} \) \(\mathstrut -\mathstrut 76q^{74} \) \(\mathstrut -\mathstrut 141q^{75} \) \(\mathstrut +\mathstrut 30q^{76} \) \(\mathstrut +\mathstrut 80q^{77} \) \(\mathstrut -\mathstrut 9q^{78} \) \(\mathstrut +\mathstrut 20q^{79} \) \(\mathstrut -\mathstrut 144q^{80} \) \(\mathstrut +\mathstrut 64q^{81} \) \(\mathstrut +\mathstrut 27q^{82} \) \(\mathstrut +\mathstrut 3q^{83} \) \(\mathstrut -\mathstrut 14q^{84} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 12q^{86} \) \(\mathstrut -\mathstrut 5q^{87} \) \(\mathstrut +\mathstrut 108q^{88} \) \(\mathstrut +\mathstrut 42q^{89} \) \(\mathstrut +\mathstrut 12q^{90} \) \(\mathstrut +\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 18q^{92} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 60q^{94} \) \(\mathstrut +\mathstrut 42q^{95} \) \(\mathstrut -\mathstrut 31q^{96} \) \(\mathstrut +\mathstrut 72q^{97} \) \(\mathstrut +\mathstrut 18q^{98} \) \(\mathstrut -\mathstrut 7q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.65285 −1.16874 −0.584372 0.811486i \(-0.698659\pi\)
−0.584372 + 0.811486i \(0.698659\pi\)
\(3\) −1.00000 −0.577350
\(4\) 0.731922 0.365961
\(5\) 2.84674 1.27310 0.636551 0.771235i \(-0.280361\pi\)
0.636551 + 0.771235i \(0.280361\pi\)
\(6\) 1.65285 0.674774
\(7\) −0.210210 −0.0794519 −0.0397260 0.999211i \(-0.512648\pi\)
−0.0397260 + 0.999211i \(0.512648\pi\)
\(8\) 2.09595 0.741029
\(9\) 1.00000 0.333333
\(10\) −4.70524 −1.48793
\(11\) 5.85789 1.76622 0.883110 0.469167i \(-0.155446\pi\)
0.883110 + 0.469167i \(0.155446\pi\)
\(12\) −0.731922 −0.211288
\(13\) 5.94416 1.64861 0.824307 0.566143i \(-0.191565\pi\)
0.824307 + 0.566143i \(0.191565\pi\)
\(14\) 0.347446 0.0928589
\(15\) −2.84674 −0.735026
\(16\) −4.92813 −1.23203
\(17\) 1.00000 0.242536
\(18\) −1.65285 −0.389581
\(19\) −6.00132 −1.37680 −0.688399 0.725333i \(-0.741686\pi\)
−0.688399 + 0.725333i \(0.741686\pi\)
\(20\) 2.08359 0.465905
\(21\) 0.210210 0.0458716
\(22\) −9.68222 −2.06426
\(23\) −1.53863 −0.320826 −0.160413 0.987050i \(-0.551283\pi\)
−0.160413 + 0.987050i \(0.551283\pi\)
\(24\) −2.09595 −0.427833
\(25\) 3.10394 0.620788
\(26\) −9.82483 −1.92681
\(27\) −1.00000 −0.192450
\(28\) −0.153857 −0.0290763
\(29\) 4.06149 0.754201 0.377100 0.926172i \(-0.376921\pi\)
0.377100 + 0.926172i \(0.376921\pi\)
\(30\) 4.70524 0.859056
\(31\) 1.55353 0.279022 0.139511 0.990221i \(-0.455447\pi\)
0.139511 + 0.990221i \(0.455447\pi\)
\(32\) 3.95359 0.698902
\(33\) −5.85789 −1.01973
\(34\) −1.65285 −0.283462
\(35\) −0.598414 −0.101150
\(36\) 0.731922 0.121987
\(37\) 0.569477 0.0936214 0.0468107 0.998904i \(-0.485094\pi\)
0.0468107 + 0.998904i \(0.485094\pi\)
\(38\) 9.91930 1.60912
\(39\) −5.94416 −0.951828
\(40\) 5.96662 0.943405
\(41\) −0.500994 −0.0782422 −0.0391211 0.999234i \(-0.512456\pi\)
−0.0391211 + 0.999234i \(0.512456\pi\)
\(42\) −0.347446 −0.0536121
\(43\) −11.8990 −1.81458 −0.907290 0.420506i \(-0.861852\pi\)
−0.907290 + 0.420506i \(0.861852\pi\)
\(44\) 4.28751 0.646367
\(45\) 2.84674 0.424367
\(46\) 2.54313 0.374964
\(47\) 6.53043 0.952561 0.476281 0.879293i \(-0.341985\pi\)
0.476281 + 0.879293i \(0.341985\pi\)
\(48\) 4.92813 0.711315
\(49\) −6.95581 −0.993687
\(50\) −5.13035 −0.725541
\(51\) −1.00000 −0.140028
\(52\) 4.35066 0.603328
\(53\) 7.14559 0.981522 0.490761 0.871294i \(-0.336719\pi\)
0.490761 + 0.871294i \(0.336719\pi\)
\(54\) 1.65285 0.224925
\(55\) 16.6759 2.24858
\(56\) −0.440589 −0.0588762
\(57\) 6.00132 0.794894
\(58\) −6.71305 −0.881467
\(59\) 7.13227 0.928542 0.464271 0.885693i \(-0.346316\pi\)
0.464271 + 0.885693i \(0.346316\pi\)
\(60\) −2.08359 −0.268991
\(61\) −1.20114 −0.153791 −0.0768954 0.997039i \(-0.524501\pi\)
−0.0768954 + 0.997039i \(0.524501\pi\)
\(62\) −2.56776 −0.326105
\(63\) −0.210210 −0.0264840
\(64\) 3.32157 0.415197
\(65\) 16.9215 2.09885
\(66\) 9.68222 1.19180
\(67\) 7.38532 0.902260 0.451130 0.892458i \(-0.351021\pi\)
0.451130 + 0.892458i \(0.351021\pi\)
\(68\) 0.731922 0.0887585
\(69\) 1.53863 0.185229
\(70\) 0.989090 0.118219
\(71\) 13.3151 1.58022 0.790109 0.612967i \(-0.210024\pi\)
0.790109 + 0.612967i \(0.210024\pi\)
\(72\) 2.09595 0.247010
\(73\) −10.9391 −1.28033 −0.640163 0.768239i \(-0.721133\pi\)
−0.640163 + 0.768239i \(0.721133\pi\)
\(74\) −0.941261 −0.109419
\(75\) −3.10394 −0.358412
\(76\) −4.39250 −0.503854
\(77\) −1.23139 −0.140330
\(78\) 9.82483 1.11244
\(79\) 11.8246 1.33037 0.665184 0.746679i \(-0.268353\pi\)
0.665184 + 0.746679i \(0.268353\pi\)
\(80\) −14.0291 −1.56850
\(81\) 1.00000 0.111111
\(82\) 0.828070 0.0914450
\(83\) −14.1343 −1.55144 −0.775721 0.631076i \(-0.782614\pi\)
−0.775721 + 0.631076i \(0.782614\pi\)
\(84\) 0.153857 0.0167872
\(85\) 2.84674 0.308772
\(86\) 19.6673 2.12078
\(87\) −4.06149 −0.435438
\(88\) 12.2778 1.30882
\(89\) 13.5101 1.43207 0.716034 0.698066i \(-0.245956\pi\)
0.716034 + 0.698066i \(0.245956\pi\)
\(90\) −4.70524 −0.495976
\(91\) −1.24952 −0.130986
\(92\) −1.12616 −0.117410
\(93\) −1.55353 −0.161094
\(94\) −10.7938 −1.11330
\(95\) −17.0842 −1.75280
\(96\) −3.95359 −0.403511
\(97\) 17.2545 1.75193 0.875963 0.482378i \(-0.160227\pi\)
0.875963 + 0.482378i \(0.160227\pi\)
\(98\) 11.4969 1.16137
\(99\) 5.85789 0.588740
\(100\) 2.27184 0.227184
\(101\) −5.72965 −0.570121 −0.285061 0.958509i \(-0.592014\pi\)
−0.285061 + 0.958509i \(0.592014\pi\)
\(102\) 1.65285 0.163657
\(103\) 2.69854 0.265895 0.132948 0.991123i \(-0.457556\pi\)
0.132948 + 0.991123i \(0.457556\pi\)
\(104\) 12.4587 1.22167
\(105\) 0.598414 0.0583992
\(106\) −11.8106 −1.14715
\(107\) −0.371109 −0.0358765 −0.0179382 0.999839i \(-0.505710\pi\)
−0.0179382 + 0.999839i \(0.505710\pi\)
\(108\) −0.731922 −0.0704292
\(109\) −15.6145 −1.49560 −0.747800 0.663925i \(-0.768890\pi\)
−0.747800 + 0.663925i \(0.768890\pi\)
\(110\) −27.5628 −2.62801
\(111\) −0.569477 −0.0540523
\(112\) 1.03594 0.0978875
\(113\) 21.0031 1.97580 0.987902 0.155081i \(-0.0495639\pi\)
0.987902 + 0.155081i \(0.0495639\pi\)
\(114\) −9.91930 −0.929027
\(115\) −4.38008 −0.408445
\(116\) 2.97270 0.276008
\(117\) 5.94416 0.549538
\(118\) −11.7886 −1.08523
\(119\) −0.210210 −0.0192699
\(120\) −5.96662 −0.544675
\(121\) 23.3148 2.11953
\(122\) 1.98531 0.179742
\(123\) 0.500994 0.0451731
\(124\) 1.13706 0.102111
\(125\) −5.39760 −0.482776
\(126\) 0.347446 0.0309530
\(127\) −1.47857 −0.131202 −0.0656010 0.997846i \(-0.520896\pi\)
−0.0656010 + 0.997846i \(0.520896\pi\)
\(128\) −13.3972 −1.18416
\(129\) 11.8990 1.04765
\(130\) −27.9687 −2.45302
\(131\) 4.20037 0.366988 0.183494 0.983021i \(-0.441259\pi\)
0.183494 + 0.983021i \(0.441259\pi\)
\(132\) −4.28751 −0.373180
\(133\) 1.26154 0.109389
\(134\) −12.2068 −1.05451
\(135\) −2.84674 −0.245009
\(136\) 2.09595 0.179726
\(137\) −1.25383 −0.107122 −0.0535611 0.998565i \(-0.517057\pi\)
−0.0535611 + 0.998565i \(0.517057\pi\)
\(138\) −2.54313 −0.216485
\(139\) −9.42391 −0.799326 −0.399663 0.916662i \(-0.630873\pi\)
−0.399663 + 0.916662i \(0.630873\pi\)
\(140\) −0.437992 −0.0370171
\(141\) −6.53043 −0.549961
\(142\) −22.0080 −1.84687
\(143\) 34.8202 2.91181
\(144\) −4.92813 −0.410678
\(145\) 11.5620 0.960174
\(146\) 18.0807 1.49637
\(147\) 6.95581 0.573706
\(148\) 0.416812 0.0342617
\(149\) −12.6997 −1.04040 −0.520200 0.854044i \(-0.674143\pi\)
−0.520200 + 0.854044i \(0.674143\pi\)
\(150\) 5.13035 0.418891
\(151\) −6.93626 −0.564465 −0.282233 0.959346i \(-0.591075\pi\)
−0.282233 + 0.959346i \(0.591075\pi\)
\(152\) −12.5784 −1.02025
\(153\) 1.00000 0.0808452
\(154\) 2.03530 0.164009
\(155\) 4.42250 0.355224
\(156\) −4.35066 −0.348332
\(157\) −1.00000 −0.0798087
\(158\) −19.5443 −1.55486
\(159\) −7.14559 −0.566682
\(160\) 11.2548 0.889773
\(161\) 0.323435 0.0254903
\(162\) −1.65285 −0.129860
\(163\) 7.01983 0.549835 0.274918 0.961468i \(-0.411349\pi\)
0.274918 + 0.961468i \(0.411349\pi\)
\(164\) −0.366689 −0.0286336
\(165\) −16.6759 −1.29822
\(166\) 23.3619 1.81324
\(167\) −0.568370 −0.0439818 −0.0219909 0.999758i \(-0.507000\pi\)
−0.0219909 + 0.999758i \(0.507000\pi\)
\(168\) 0.440589 0.0339922
\(169\) 22.3331 1.71793
\(170\) −4.70524 −0.360876
\(171\) −6.00132 −0.458932
\(172\) −8.70913 −0.664065
\(173\) 15.5216 1.18008 0.590042 0.807373i \(-0.299111\pi\)
0.590042 + 0.807373i \(0.299111\pi\)
\(174\) 6.71305 0.508915
\(175\) −0.652479 −0.0493228
\(176\) −28.8684 −2.17604
\(177\) −7.13227 −0.536094
\(178\) −22.3302 −1.67372
\(179\) −16.3427 −1.22151 −0.610754 0.791820i \(-0.709134\pi\)
−0.610754 + 0.791820i \(0.709134\pi\)
\(180\) 2.08359 0.155302
\(181\) −18.7319 −1.39233 −0.696165 0.717882i \(-0.745112\pi\)
−0.696165 + 0.717882i \(0.745112\pi\)
\(182\) 2.06528 0.153089
\(183\) 1.20114 0.0887911
\(184\) −3.22489 −0.237742
\(185\) 1.62115 0.119190
\(186\) 2.56776 0.188277
\(187\) 5.85789 0.428371
\(188\) 4.77976 0.348600
\(189\) 0.210210 0.0152905
\(190\) 28.2377 2.04858
\(191\) 8.17914 0.591822 0.295911 0.955216i \(-0.404377\pi\)
0.295911 + 0.955216i \(0.404377\pi\)
\(192\) −3.32157 −0.239714
\(193\) 3.76066 0.270699 0.135349 0.990798i \(-0.456784\pi\)
0.135349 + 0.990798i \(0.456784\pi\)
\(194\) −28.5191 −2.04755
\(195\) −16.9215 −1.21177
\(196\) −5.09111 −0.363651
\(197\) 3.74230 0.266628 0.133314 0.991074i \(-0.457438\pi\)
0.133314 + 0.991074i \(0.457438\pi\)
\(198\) −9.68222 −0.688086
\(199\) 5.15903 0.365714 0.182857 0.983140i \(-0.441465\pi\)
0.182857 + 0.983140i \(0.441465\pi\)
\(200\) 6.50569 0.460022
\(201\) −7.38532 −0.520920
\(202\) 9.47026 0.666325
\(203\) −0.853767 −0.0599227
\(204\) −0.731922 −0.0512448
\(205\) −1.42620 −0.0996102
\(206\) −4.46030 −0.310764
\(207\) −1.53863 −0.106942
\(208\) −29.2936 −2.03115
\(209\) −35.1550 −2.43173
\(210\) −0.989090 −0.0682537
\(211\) 9.06044 0.623747 0.311873 0.950124i \(-0.399044\pi\)
0.311873 + 0.950124i \(0.399044\pi\)
\(212\) 5.23001 0.359199
\(213\) −13.3151 −0.912339
\(214\) 0.613388 0.0419304
\(215\) −33.8734 −2.31014
\(216\) −2.09595 −0.142611
\(217\) −0.326568 −0.0221689
\(218\) 25.8085 1.74797
\(219\) 10.9391 0.739197
\(220\) 12.2054 0.822891
\(221\) 5.94416 0.399848
\(222\) 0.941261 0.0631733
\(223\) −20.7564 −1.38995 −0.694974 0.719035i \(-0.744584\pi\)
−0.694974 + 0.719035i \(0.744584\pi\)
\(224\) −0.831084 −0.0555291
\(225\) 3.10394 0.206929
\(226\) −34.7150 −2.30921
\(227\) 2.50847 0.166493 0.0832466 0.996529i \(-0.473471\pi\)
0.0832466 + 0.996529i \(0.473471\pi\)
\(228\) 4.39250 0.290900
\(229\) 26.5594 1.75509 0.877546 0.479493i \(-0.159179\pi\)
0.877546 + 0.479493i \(0.159179\pi\)
\(230\) 7.23963 0.477367
\(231\) 1.23139 0.0810193
\(232\) 8.51268 0.558885
\(233\) 22.3359 1.46327 0.731636 0.681695i \(-0.238757\pi\)
0.731636 + 0.681695i \(0.238757\pi\)
\(234\) −9.82483 −0.642269
\(235\) 18.5904 1.21271
\(236\) 5.22026 0.339810
\(237\) −11.8246 −0.768088
\(238\) 0.347446 0.0225216
\(239\) 7.22761 0.467515 0.233758 0.972295i \(-0.424898\pi\)
0.233758 + 0.972295i \(0.424898\pi\)
\(240\) 14.0291 0.905576
\(241\) 7.00840 0.451451 0.225725 0.974191i \(-0.427525\pi\)
0.225725 + 0.974191i \(0.427525\pi\)
\(242\) −38.5360 −2.47719
\(243\) −1.00000 −0.0641500
\(244\) −0.879143 −0.0562814
\(245\) −19.8014 −1.26506
\(246\) −0.828070 −0.0527958
\(247\) −35.6728 −2.26981
\(248\) 3.25612 0.206764
\(249\) 14.1343 0.895726
\(250\) 8.92144 0.564241
\(251\) −6.24384 −0.394107 −0.197054 0.980393i \(-0.563137\pi\)
−0.197054 + 0.980393i \(0.563137\pi\)
\(252\) −0.153857 −0.00969210
\(253\) −9.01312 −0.566650
\(254\) 2.44386 0.153341
\(255\) −2.84674 −0.178270
\(256\) 15.5005 0.968782
\(257\) 20.5485 1.28178 0.640890 0.767633i \(-0.278565\pi\)
0.640890 + 0.767633i \(0.278565\pi\)
\(258\) −19.6673 −1.22443
\(259\) −0.119710 −0.00743840
\(260\) 12.3852 0.768098
\(261\) 4.06149 0.251400
\(262\) −6.94259 −0.428915
\(263\) −11.0544 −0.681643 −0.340821 0.940128i \(-0.610705\pi\)
−0.340821 + 0.940128i \(0.610705\pi\)
\(264\) −12.2778 −0.755647
\(265\) 20.3416 1.24958
\(266\) −2.08514 −0.127848
\(267\) −13.5101 −0.826804
\(268\) 5.40548 0.330192
\(269\) −6.38068 −0.389037 −0.194518 0.980899i \(-0.562314\pi\)
−0.194518 + 0.980899i \(0.562314\pi\)
\(270\) 4.70524 0.286352
\(271\) −7.66461 −0.465592 −0.232796 0.972526i \(-0.574787\pi\)
−0.232796 + 0.972526i \(0.574787\pi\)
\(272\) −4.92813 −0.298812
\(273\) 1.24952 0.0756246
\(274\) 2.07240 0.125198
\(275\) 18.1825 1.09645
\(276\) 1.12616 0.0677866
\(277\) 5.75758 0.345940 0.172970 0.984927i \(-0.444664\pi\)
0.172970 + 0.984927i \(0.444664\pi\)
\(278\) 15.5763 0.934206
\(279\) 1.55353 0.0930074
\(280\) −1.25424 −0.0749554
\(281\) 17.7636 1.05969 0.529845 0.848095i \(-0.322250\pi\)
0.529845 + 0.848095i \(0.322250\pi\)
\(282\) 10.7938 0.642764
\(283\) −30.0100 −1.78391 −0.891955 0.452124i \(-0.850666\pi\)
−0.891955 + 0.452124i \(0.850666\pi\)
\(284\) 9.74564 0.578298
\(285\) 17.0842 1.01198
\(286\) −57.5527 −3.40316
\(287\) 0.105314 0.00621649
\(288\) 3.95359 0.232967
\(289\) 1.00000 0.0588235
\(290\) −19.1103 −1.12220
\(291\) −17.2545 −1.01147
\(292\) −8.00658 −0.468549
\(293\) −2.13300 −0.124611 −0.0623055 0.998057i \(-0.519845\pi\)
−0.0623055 + 0.998057i \(0.519845\pi\)
\(294\) −11.4969 −0.670515
\(295\) 20.3037 1.18213
\(296\) 1.19359 0.0693761
\(297\) −5.85789 −0.339909
\(298\) 20.9907 1.21596
\(299\) −9.14587 −0.528919
\(300\) −2.27184 −0.131165
\(301\) 2.50129 0.144172
\(302\) 11.4646 0.659715
\(303\) 5.72965 0.329160
\(304\) 29.5753 1.69626
\(305\) −3.41935 −0.195791
\(306\) −1.65285 −0.0944873
\(307\) −29.6255 −1.69082 −0.845409 0.534119i \(-0.820643\pi\)
−0.845409 + 0.534119i \(0.820643\pi\)
\(308\) −0.901279 −0.0513551
\(309\) −2.69854 −0.153515
\(310\) −7.30974 −0.415165
\(311\) −10.9032 −0.618262 −0.309131 0.951019i \(-0.600038\pi\)
−0.309131 + 0.951019i \(0.600038\pi\)
\(312\) −12.4587 −0.705332
\(313\) −6.91690 −0.390967 −0.195483 0.980707i \(-0.562628\pi\)
−0.195483 + 0.980707i \(0.562628\pi\)
\(314\) 1.65285 0.0932759
\(315\) −0.598414 −0.0337168
\(316\) 8.65466 0.486863
\(317\) −11.9804 −0.672886 −0.336443 0.941704i \(-0.609224\pi\)
−0.336443 + 0.941704i \(0.609224\pi\)
\(318\) 11.8106 0.662306
\(319\) 23.7918 1.33208
\(320\) 9.45566 0.528588
\(321\) 0.371109 0.0207133
\(322\) −0.534591 −0.0297916
\(323\) −6.00132 −0.333922
\(324\) 0.731922 0.0406623
\(325\) 18.4503 1.02344
\(326\) −11.6027 −0.642616
\(327\) 15.6145 0.863485
\(328\) −1.05006 −0.0579797
\(329\) −1.37276 −0.0756828
\(330\) 27.5628 1.51728
\(331\) 24.3174 1.33660 0.668302 0.743890i \(-0.267021\pi\)
0.668302 + 0.743890i \(0.267021\pi\)
\(332\) −10.3452 −0.567767
\(333\) 0.569477 0.0312071
\(334\) 0.939432 0.0514034
\(335\) 21.0241 1.14867
\(336\) −1.03594 −0.0565154
\(337\) 5.25268 0.286132 0.143066 0.989713i \(-0.454304\pi\)
0.143066 + 0.989713i \(0.454304\pi\)
\(338\) −36.9133 −2.00782
\(339\) −21.0031 −1.14073
\(340\) 2.08359 0.112999
\(341\) 9.10040 0.492814
\(342\) 9.91930 0.536374
\(343\) 2.93365 0.158402
\(344\) −24.9397 −1.34466
\(345\) 4.38008 0.235816
\(346\) −25.6549 −1.37921
\(347\) 9.58455 0.514526 0.257263 0.966341i \(-0.417179\pi\)
0.257263 + 0.966341i \(0.417179\pi\)
\(348\) −2.97270 −0.159353
\(349\) 21.1760 1.13352 0.566762 0.823882i \(-0.308196\pi\)
0.566762 + 0.823882i \(0.308196\pi\)
\(350\) 1.07845 0.0576457
\(351\) −5.94416 −0.317276
\(352\) 23.1597 1.23441
\(353\) −6.29101 −0.334836 −0.167418 0.985886i \(-0.553543\pi\)
−0.167418 + 0.985886i \(0.553543\pi\)
\(354\) 11.7886 0.626556
\(355\) 37.9048 2.01178
\(356\) 9.88833 0.524080
\(357\) 0.210210 0.0111255
\(358\) 27.0120 1.42763
\(359\) −26.9110 −1.42031 −0.710153 0.704047i \(-0.751374\pi\)
−0.710153 + 0.704047i \(0.751374\pi\)
\(360\) 5.96662 0.314468
\(361\) 17.0158 0.895570
\(362\) 30.9610 1.62728
\(363\) −23.3148 −1.22371
\(364\) −0.914553 −0.0479356
\(365\) −31.1408 −1.62999
\(366\) −1.98531 −0.103774
\(367\) 37.1513 1.93928 0.969641 0.244532i \(-0.0786342\pi\)
0.969641 + 0.244532i \(0.0786342\pi\)
\(368\) 7.58257 0.395269
\(369\) −0.500994 −0.0260807
\(370\) −2.67953 −0.139302
\(371\) −1.50208 −0.0779839
\(372\) −1.13706 −0.0589539
\(373\) 25.9318 1.34270 0.671349 0.741142i \(-0.265715\pi\)
0.671349 + 0.741142i \(0.265715\pi\)
\(374\) −9.68222 −0.500656
\(375\) 5.39760 0.278731
\(376\) 13.6874 0.705875
\(377\) 24.1422 1.24339
\(378\) −0.347446 −0.0178707
\(379\) −10.2382 −0.525901 −0.262951 0.964809i \(-0.584696\pi\)
−0.262951 + 0.964809i \(0.584696\pi\)
\(380\) −12.5043 −0.641457
\(381\) 1.47857 0.0757495
\(382\) −13.5189 −0.691688
\(383\) −15.2298 −0.778205 −0.389103 0.921194i \(-0.627215\pi\)
−0.389103 + 0.921194i \(0.627215\pi\)
\(384\) 13.3972 0.683675
\(385\) −3.50544 −0.178654
\(386\) −6.21582 −0.316377
\(387\) −11.8990 −0.604860
\(388\) 12.6289 0.641136
\(389\) 9.97651 0.505829 0.252915 0.967489i \(-0.418611\pi\)
0.252915 + 0.967489i \(0.418611\pi\)
\(390\) 27.9687 1.41625
\(391\) −1.53863 −0.0778118
\(392\) −14.5790 −0.736351
\(393\) −4.20037 −0.211881
\(394\) −6.18546 −0.311619
\(395\) 33.6615 1.69369
\(396\) 4.28751 0.215456
\(397\) 22.1562 1.11199 0.555993 0.831187i \(-0.312338\pi\)
0.555993 + 0.831187i \(0.312338\pi\)
\(398\) −8.52711 −0.427426
\(399\) −1.26154 −0.0631559
\(400\) −15.2966 −0.764831
\(401\) −25.2019 −1.25852 −0.629261 0.777194i \(-0.716643\pi\)
−0.629261 + 0.777194i \(0.716643\pi\)
\(402\) 12.2068 0.608822
\(403\) 9.23444 0.460000
\(404\) −4.19365 −0.208642
\(405\) 2.84674 0.141456
\(406\) 1.41115 0.0700343
\(407\) 3.33593 0.165356
\(408\) −2.09595 −0.103765
\(409\) −25.0276 −1.23753 −0.618767 0.785574i \(-0.712368\pi\)
−0.618767 + 0.785574i \(0.712368\pi\)
\(410\) 2.35730 0.116419
\(411\) 1.25383 0.0618470
\(412\) 1.97512 0.0973073
\(413\) −1.49927 −0.0737745
\(414\) 2.54313 0.124988
\(415\) −40.2367 −1.97514
\(416\) 23.5008 1.15222
\(417\) 9.42391 0.461491
\(418\) 58.1061 2.84206
\(419\) 3.94598 0.192774 0.0963869 0.995344i \(-0.469271\pi\)
0.0963869 + 0.995344i \(0.469271\pi\)
\(420\) 0.437992 0.0213718
\(421\) 5.67669 0.276665 0.138332 0.990386i \(-0.455826\pi\)
0.138332 + 0.990386i \(0.455826\pi\)
\(422\) −14.9756 −0.729000
\(423\) 6.53043 0.317520
\(424\) 14.9768 0.727336
\(425\) 3.10394 0.150563
\(426\) 22.0080 1.06629
\(427\) 0.252493 0.0122190
\(428\) −0.271623 −0.0131294
\(429\) −34.8202 −1.68114
\(430\) 55.9877 2.69996
\(431\) 18.8191 0.906483 0.453242 0.891388i \(-0.350268\pi\)
0.453242 + 0.891388i \(0.350268\pi\)
\(432\) 4.92813 0.237105
\(433\) −20.4465 −0.982596 −0.491298 0.870991i \(-0.663477\pi\)
−0.491298 + 0.870991i \(0.663477\pi\)
\(434\) 0.539768 0.0259097
\(435\) −11.5620 −0.554357
\(436\) −11.4286 −0.547331
\(437\) 9.23381 0.441713
\(438\) −18.0807 −0.863932
\(439\) 11.7561 0.561089 0.280545 0.959841i \(-0.409485\pi\)
0.280545 + 0.959841i \(0.409485\pi\)
\(440\) 34.9518 1.66626
\(441\) −6.95581 −0.331229
\(442\) −9.82483 −0.467319
\(443\) −36.7025 −1.74379 −0.871894 0.489695i \(-0.837108\pi\)
−0.871894 + 0.489695i \(0.837108\pi\)
\(444\) −0.416812 −0.0197810
\(445\) 38.4597 1.82317
\(446\) 34.3072 1.62449
\(447\) 12.6997 0.600675
\(448\) −0.698228 −0.0329882
\(449\) −3.82195 −0.180369 −0.0901845 0.995925i \(-0.528746\pi\)
−0.0901845 + 0.995925i \(0.528746\pi\)
\(450\) −5.13035 −0.241847
\(451\) −2.93477 −0.138193
\(452\) 15.3726 0.723067
\(453\) 6.93626 0.325894
\(454\) −4.14614 −0.194588
\(455\) −3.55707 −0.166758
\(456\) 12.5784 0.589040
\(457\) 0.447567 0.0209363 0.0104682 0.999945i \(-0.496668\pi\)
0.0104682 + 0.999945i \(0.496668\pi\)
\(458\) −43.8987 −2.05125
\(459\) −1.00000 −0.0466760
\(460\) −3.20588 −0.149475
\(461\) −12.4428 −0.579518 −0.289759 0.957100i \(-0.593575\pi\)
−0.289759 + 0.957100i \(0.593575\pi\)
\(462\) −2.03530 −0.0946908
\(463\) 21.0256 0.977141 0.488570 0.872524i \(-0.337519\pi\)
0.488570 + 0.872524i \(0.337519\pi\)
\(464\) −20.0156 −0.929200
\(465\) −4.42250 −0.205088
\(466\) −36.9179 −1.71019
\(467\) −26.3427 −1.21899 −0.609497 0.792788i \(-0.708629\pi\)
−0.609497 + 0.792788i \(0.708629\pi\)
\(468\) 4.35066 0.201109
\(469\) −1.55247 −0.0716863
\(470\) −30.7273 −1.41734
\(471\) 1.00000 0.0460776
\(472\) 14.9488 0.688077
\(473\) −69.7029 −3.20494
\(474\) 19.5443 0.897698
\(475\) −18.6277 −0.854698
\(476\) −0.153857 −0.00705204
\(477\) 7.14559 0.327174
\(478\) −11.9462 −0.546405
\(479\) 0.464318 0.0212152 0.0106076 0.999944i \(-0.496623\pi\)
0.0106076 + 0.999944i \(0.496623\pi\)
\(480\) −11.2548 −0.513711
\(481\) 3.38506 0.154346
\(482\) −11.5838 −0.527630
\(483\) −0.323435 −0.0147168
\(484\) 17.0646 0.775665
\(485\) 49.1190 2.23038
\(486\) 1.65285 0.0749749
\(487\) 41.5963 1.88491 0.942454 0.334335i \(-0.108512\pi\)
0.942454 + 0.334335i \(0.108512\pi\)
\(488\) −2.51753 −0.113963
\(489\) −7.01983 −0.317448
\(490\) 32.7288 1.47854
\(491\) −35.5969 −1.60647 −0.803233 0.595666i \(-0.796888\pi\)
−0.803233 + 0.595666i \(0.796888\pi\)
\(492\) 0.366689 0.0165316
\(493\) 4.06149 0.182920
\(494\) 58.9619 2.65282
\(495\) 16.6759 0.749525
\(496\) −7.65600 −0.343765
\(497\) −2.79898 −0.125551
\(498\) −23.3619 −1.04687
\(499\) −14.2150 −0.636351 −0.318176 0.948032i \(-0.603070\pi\)
−0.318176 + 0.948032i \(0.603070\pi\)
\(500\) −3.95062 −0.176677
\(501\) 0.568370 0.0253929
\(502\) 10.3201 0.460610
\(503\) −27.1384 −1.21004 −0.605021 0.796210i \(-0.706835\pi\)
−0.605021 + 0.796210i \(0.706835\pi\)
\(504\) −0.440589 −0.0196254
\(505\) −16.3108 −0.725822
\(506\) 14.8974 0.662268
\(507\) −22.3331 −0.991847
\(508\) −1.08220 −0.0480148
\(509\) 27.5884 1.22284 0.611418 0.791308i \(-0.290600\pi\)
0.611418 + 0.791308i \(0.290600\pi\)
\(510\) 4.70524 0.208352
\(511\) 2.29951 0.101724
\(512\) 1.17441 0.0519022
\(513\) 6.00132 0.264965
\(514\) −33.9636 −1.49807
\(515\) 7.68206 0.338512
\(516\) 8.70913 0.383398
\(517\) 38.2545 1.68243
\(518\) 0.197863 0.00869358
\(519\) −15.5216 −0.681322
\(520\) 35.4666 1.55531
\(521\) −11.7955 −0.516768 −0.258384 0.966042i \(-0.583190\pi\)
−0.258384 + 0.966042i \(0.583190\pi\)
\(522\) −6.71305 −0.293822
\(523\) −24.7555 −1.08248 −0.541241 0.840868i \(-0.682045\pi\)
−0.541241 + 0.840868i \(0.682045\pi\)
\(524\) 3.07434 0.134303
\(525\) 0.652479 0.0284765
\(526\) 18.2713 0.796666
\(527\) 1.55353 0.0676728
\(528\) 28.8684 1.25634
\(529\) −20.6326 −0.897070
\(530\) −33.6217 −1.46044
\(531\) 7.13227 0.309514
\(532\) 0.923347 0.0400322
\(533\) −2.97799 −0.128991
\(534\) 22.3302 0.966322
\(535\) −1.05645 −0.0456744
\(536\) 15.4792 0.668601
\(537\) 16.3427 0.705238
\(538\) 10.5463 0.454684
\(539\) −40.7464 −1.75507
\(540\) −2.08359 −0.0896635
\(541\) −2.81676 −0.121102 −0.0605510 0.998165i \(-0.519286\pi\)
−0.0605510 + 0.998165i \(0.519286\pi\)
\(542\) 12.6685 0.544157
\(543\) 18.7319 0.803862
\(544\) 3.95359 0.169509
\(545\) −44.4505 −1.90405
\(546\) −2.06528 −0.0883857
\(547\) −19.1349 −0.818147 −0.409074 0.912501i \(-0.634148\pi\)
−0.409074 + 0.912501i \(0.634148\pi\)
\(548\) −0.917708 −0.0392025
\(549\) −1.20114 −0.0512636
\(550\) −30.0530 −1.28146
\(551\) −24.3743 −1.03838
\(552\) 3.22489 0.137260
\(553\) −2.48564 −0.105700
\(554\) −9.51644 −0.404315
\(555\) −1.62115 −0.0688141
\(556\) −6.89756 −0.292522
\(557\) −37.1017 −1.57205 −0.786025 0.618195i \(-0.787864\pi\)
−0.786025 + 0.618195i \(0.787864\pi\)
\(558\) −2.56776 −0.108702
\(559\) −70.7296 −2.99154
\(560\) 2.94906 0.124621
\(561\) −5.85789 −0.247320
\(562\) −29.3607 −1.23850
\(563\) −23.4607 −0.988750 −0.494375 0.869249i \(-0.664603\pi\)
−0.494375 + 0.869249i \(0.664603\pi\)
\(564\) −4.77976 −0.201264
\(565\) 59.7903 2.51540
\(566\) 49.6021 2.08493
\(567\) −0.210210 −0.00882799
\(568\) 27.9078 1.17099
\(569\) 32.6525 1.36886 0.684432 0.729077i \(-0.260050\pi\)
0.684432 + 0.729077i \(0.260050\pi\)
\(570\) −28.2377 −1.18275
\(571\) 21.2570 0.889579 0.444790 0.895635i \(-0.353278\pi\)
0.444790 + 0.895635i \(0.353278\pi\)
\(572\) 25.4857 1.06561
\(573\) −8.17914 −0.341688
\(574\) −0.174069 −0.00726549
\(575\) −4.77581 −0.199165
\(576\) 3.32157 0.138399
\(577\) 4.16749 0.173495 0.0867473 0.996230i \(-0.472353\pi\)
0.0867473 + 0.996230i \(0.472353\pi\)
\(578\) −1.65285 −0.0687496
\(579\) −3.76066 −0.156288
\(580\) 8.46250 0.351386
\(581\) 2.97118 0.123265
\(582\) 28.5191 1.18215
\(583\) 41.8581 1.73358
\(584\) −22.9278 −0.948759
\(585\) 16.9215 0.699618
\(586\) 3.52553 0.145638
\(587\) 18.1590 0.749503 0.374752 0.927125i \(-0.377728\pi\)
0.374752 + 0.927125i \(0.377728\pi\)
\(588\) 5.09111 0.209954
\(589\) −9.32323 −0.384157
\(590\) −33.5591 −1.38160
\(591\) −3.74230 −0.153937
\(592\) −2.80646 −0.115345
\(593\) −17.0261 −0.699176 −0.349588 0.936903i \(-0.613679\pi\)
−0.349588 + 0.936903i \(0.613679\pi\)
\(594\) 9.68222 0.397266
\(595\) −0.598414 −0.0245326
\(596\) −9.29518 −0.380746
\(597\) −5.15903 −0.211145
\(598\) 15.1168 0.618171
\(599\) −36.1876 −1.47859 −0.739293 0.673384i \(-0.764840\pi\)
−0.739293 + 0.673384i \(0.764840\pi\)
\(600\) −6.50569 −0.265594
\(601\) −9.97149 −0.406745 −0.203373 0.979101i \(-0.565190\pi\)
−0.203373 + 0.979101i \(0.565190\pi\)
\(602\) −4.13426 −0.168500
\(603\) 7.38532 0.300753
\(604\) −5.07680 −0.206572
\(605\) 66.3713 2.69838
\(606\) −9.47026 −0.384703
\(607\) −9.22939 −0.374609 −0.187305 0.982302i \(-0.559975\pi\)
−0.187305 + 0.982302i \(0.559975\pi\)
\(608\) −23.7267 −0.962246
\(609\) 0.853767 0.0345964
\(610\) 5.65168 0.228830
\(611\) 38.8179 1.57041
\(612\) 0.731922 0.0295862
\(613\) 0.424459 0.0171437 0.00857187 0.999963i \(-0.497271\pi\)
0.00857187 + 0.999963i \(0.497271\pi\)
\(614\) 48.9666 1.97613
\(615\) 1.42620 0.0575100
\(616\) −2.58092 −0.103988
\(617\) −12.0404 −0.484727 −0.242363 0.970186i \(-0.577923\pi\)
−0.242363 + 0.970186i \(0.577923\pi\)
\(618\) 4.46030 0.179419
\(619\) 10.3292 0.415166 0.207583 0.978217i \(-0.433440\pi\)
0.207583 + 0.978217i \(0.433440\pi\)
\(620\) 3.23692 0.129998
\(621\) 1.53863 0.0617431
\(622\) 18.0213 0.722590
\(623\) −2.83996 −0.113781
\(624\) 29.2936 1.17268
\(625\) −30.8853 −1.23541
\(626\) 11.4326 0.456940
\(627\) 35.1550 1.40396
\(628\) −0.731922 −0.0292069
\(629\) 0.569477 0.0227065
\(630\) 0.989090 0.0394063
\(631\) −3.47025 −0.138149 −0.0690743 0.997612i \(-0.522005\pi\)
−0.0690743 + 0.997612i \(0.522005\pi\)
\(632\) 24.7837 0.985841
\(633\) −9.06044 −0.360120
\(634\) 19.8018 0.786431
\(635\) −4.20911 −0.167033
\(636\) −5.23001 −0.207383
\(637\) −41.3465 −1.63821
\(638\) −39.3243 −1.55686
\(639\) 13.3151 0.526739
\(640\) −38.1385 −1.50756
\(641\) 35.4357 1.39963 0.699813 0.714326i \(-0.253266\pi\)
0.699813 + 0.714326i \(0.253266\pi\)
\(642\) −0.613388 −0.0242085
\(643\) 27.4759 1.08355 0.541773 0.840525i \(-0.317753\pi\)
0.541773 + 0.840525i \(0.317753\pi\)
\(644\) 0.236729 0.00932845
\(645\) 33.8734 1.33376
\(646\) 9.91930 0.390269
\(647\) −6.36602 −0.250274 −0.125137 0.992139i \(-0.539937\pi\)
−0.125137 + 0.992139i \(0.539937\pi\)
\(648\) 2.09595 0.0823366
\(649\) 41.7800 1.64001
\(650\) −30.4957 −1.19614
\(651\) 0.326568 0.0127992
\(652\) 5.13796 0.201218
\(653\) 12.1322 0.474769 0.237384 0.971416i \(-0.423710\pi\)
0.237384 + 0.971416i \(0.423710\pi\)
\(654\) −25.8085 −1.00919
\(655\) 11.9574 0.467213
\(656\) 2.46897 0.0963970
\(657\) −10.9391 −0.426776
\(658\) 2.26897 0.0884538
\(659\) −33.7255 −1.31376 −0.656880 0.753996i \(-0.728124\pi\)
−0.656880 + 0.753996i \(0.728124\pi\)
\(660\) −12.2054 −0.475096
\(661\) 47.2399 1.83742 0.918709 0.394935i \(-0.129233\pi\)
0.918709 + 0.394935i \(0.129233\pi\)
\(662\) −40.1931 −1.56215
\(663\) −5.94416 −0.230852
\(664\) −29.6248 −1.14966
\(665\) 3.59127 0.139264
\(666\) −0.941261 −0.0364731
\(667\) −6.24914 −0.241967
\(668\) −0.416002 −0.0160956
\(669\) 20.7564 0.802487
\(670\) −34.7497 −1.34250
\(671\) −7.03617 −0.271628
\(672\) 0.831084 0.0320597
\(673\) 25.1249 0.968493 0.484246 0.874932i \(-0.339094\pi\)
0.484246 + 0.874932i \(0.339094\pi\)
\(674\) −8.68191 −0.334415
\(675\) −3.10394 −0.119471
\(676\) 16.3461 0.628695
\(677\) 47.4437 1.82341 0.911705 0.410847i \(-0.134767\pi\)
0.911705 + 0.410847i \(0.134767\pi\)
\(678\) 34.7150 1.33322
\(679\) −3.62706 −0.139194
\(680\) 5.96662 0.228809
\(681\) −2.50847 −0.0961249
\(682\) −15.0416 −0.575973
\(683\) 28.0943 1.07500 0.537500 0.843264i \(-0.319369\pi\)
0.537500 + 0.843264i \(0.319369\pi\)
\(684\) −4.39250 −0.167951
\(685\) −3.56934 −0.136377
\(686\) −4.84890 −0.185132
\(687\) −26.5594 −1.01330
\(688\) 58.6398 2.23562
\(689\) 42.4746 1.61815
\(690\) −7.23963 −0.275608
\(691\) 8.06370 0.306758 0.153379 0.988167i \(-0.450985\pi\)
0.153379 + 0.988167i \(0.450985\pi\)
\(692\) 11.3606 0.431864
\(693\) −1.23139 −0.0467765
\(694\) −15.8419 −0.601349
\(695\) −26.8274 −1.01762
\(696\) −8.51268 −0.322672
\(697\) −0.500994 −0.0189765
\(698\) −35.0008 −1.32480
\(699\) −22.3359 −0.844821
\(700\) −0.477564 −0.0180502
\(701\) 19.9738 0.754398 0.377199 0.926132i \(-0.376887\pi\)
0.377199 + 0.926132i \(0.376887\pi\)
\(702\) 9.82483 0.370814
\(703\) −3.41761 −0.128898
\(704\) 19.4574 0.733328
\(705\) −18.5904 −0.700157
\(706\) 10.3981 0.391338
\(707\) 1.20443 0.0452972
\(708\) −5.22026 −0.196189
\(709\) −17.3105 −0.650109 −0.325055 0.945695i \(-0.605383\pi\)
−0.325055 + 0.945695i \(0.605383\pi\)
\(710\) −62.6510 −2.35125
\(711\) 11.8246 0.443456
\(712\) 28.3164 1.06120
\(713\) −2.39031 −0.0895177
\(714\) −0.347446 −0.0130029
\(715\) 99.1242 3.70704
\(716\) −11.9615 −0.447024
\(717\) −7.22761 −0.269920
\(718\) 44.4799 1.65997
\(719\) 42.5723 1.58768 0.793840 0.608127i \(-0.208079\pi\)
0.793840 + 0.608127i \(0.208079\pi\)
\(720\) −14.0291 −0.522835
\(721\) −0.567261 −0.0211259
\(722\) −28.1247 −1.04669
\(723\) −7.00840 −0.260645
\(724\) −13.7103 −0.509538
\(725\) 12.6066 0.468198
\(726\) 38.5360 1.43020
\(727\) 43.8139 1.62497 0.812484 0.582984i \(-0.198115\pi\)
0.812484 + 0.582984i \(0.198115\pi\)
\(728\) −2.61893 −0.0970642
\(729\) 1.00000 0.0370370
\(730\) 51.4712 1.90504
\(731\) −11.8990 −0.440100
\(732\) 0.879143 0.0324941
\(733\) 28.5615 1.05494 0.527472 0.849573i \(-0.323140\pi\)
0.527472 + 0.849573i \(0.323140\pi\)
\(734\) −61.4056 −2.26652
\(735\) 19.8014 0.730386
\(736\) −6.08310 −0.224226
\(737\) 43.2624 1.59359
\(738\) 0.828070 0.0304817
\(739\) 12.1462 0.446804 0.223402 0.974726i \(-0.428284\pi\)
0.223402 + 0.974726i \(0.428284\pi\)
\(740\) 1.18656 0.0436187
\(741\) 35.6728 1.31047
\(742\) 2.48271 0.0911431
\(743\) 17.7516 0.651243 0.325621 0.945500i \(-0.394427\pi\)
0.325621 + 0.945500i \(0.394427\pi\)
\(744\) −3.25612 −0.119375
\(745\) −36.1528 −1.32453
\(746\) −42.8614 −1.56927
\(747\) −14.1343 −0.517148
\(748\) 4.28751 0.156767
\(749\) 0.0780108 0.00285045
\(750\) −8.92144 −0.325765
\(751\) −15.6226 −0.570077 −0.285039 0.958516i \(-0.592006\pi\)
−0.285039 + 0.958516i \(0.592006\pi\)
\(752\) −32.1828 −1.17359
\(753\) 6.24384 0.227538
\(754\) −39.9035 −1.45320
\(755\) −19.7458 −0.718621
\(756\) 0.153857 0.00559574
\(757\) 22.9539 0.834273 0.417136 0.908844i \(-0.363034\pi\)
0.417136 + 0.908844i \(0.363034\pi\)
\(758\) 16.9222 0.614643
\(759\) 9.01312 0.327155
\(760\) −35.8076 −1.29888
\(761\) 25.4760 0.923505 0.461753 0.887009i \(-0.347221\pi\)
0.461753 + 0.887009i \(0.347221\pi\)
\(762\) −2.44386 −0.0885317
\(763\) 3.28233 0.118828
\(764\) 5.98649 0.216584
\(765\) 2.84674 0.102924
\(766\) 25.1726 0.909522
\(767\) 42.3954 1.53081
\(768\) −15.5005 −0.559327
\(769\) −39.6679 −1.43046 −0.715230 0.698889i \(-0.753678\pi\)
−0.715230 + 0.698889i \(0.753678\pi\)
\(770\) 5.79398 0.208800
\(771\) −20.5485 −0.740036
\(772\) 2.75251 0.0990651
\(773\) −8.15404 −0.293280 −0.146640 0.989190i \(-0.546846\pi\)
−0.146640 + 0.989190i \(0.546846\pi\)
\(774\) 19.6673 0.706926
\(775\) 4.82206 0.173213
\(776\) 36.1644 1.29823
\(777\) 0.119710 0.00429456
\(778\) −16.4897 −0.591184
\(779\) 3.00663 0.107724
\(780\) −12.3852 −0.443462
\(781\) 77.9986 2.79101
\(782\) 2.54313 0.0909421
\(783\) −4.06149 −0.145146
\(784\) 34.2792 1.22426
\(785\) −2.84674 −0.101605
\(786\) 6.94259 0.247634
\(787\) −14.5143 −0.517379 −0.258690 0.965960i \(-0.583291\pi\)
−0.258690 + 0.965960i \(0.583291\pi\)
\(788\) 2.73907 0.0975752
\(789\) 11.0544 0.393547
\(790\) −55.6375 −1.97949
\(791\) −4.41506 −0.156981
\(792\) 12.2778 0.436273
\(793\) −7.13980 −0.253542
\(794\) −36.6209 −1.29963
\(795\) −20.3416 −0.721444
\(796\) 3.77600 0.133837
\(797\) 42.1463 1.49290 0.746449 0.665442i \(-0.231757\pi\)
0.746449 + 0.665442i \(0.231757\pi\)
\(798\) 2.08514 0.0738130
\(799\) 6.53043 0.231030
\(800\) 12.2717 0.433870
\(801\) 13.5101 0.477356
\(802\) 41.6550 1.47089
\(803\) −64.0801 −2.26134
\(804\) −5.40548 −0.190636
\(805\) 0.920737 0.0324517
\(806\) −15.2632 −0.537622
\(807\) 6.38068 0.224611
\(808\) −12.0090 −0.422476
\(809\) −11.4192 −0.401477 −0.200739 0.979645i \(-0.564334\pi\)
−0.200739 + 0.979645i \(0.564334\pi\)
\(810\) −4.70524 −0.165325
\(811\) −48.2942 −1.69584 −0.847919 0.530125i \(-0.822145\pi\)
−0.847919 + 0.530125i \(0.822145\pi\)
\(812\) −0.624891 −0.0219294
\(813\) 7.66461 0.268809
\(814\) −5.51380 −0.193259
\(815\) 19.9836 0.699996
\(816\) 4.92813 0.172519
\(817\) 71.4096 2.49831
\(818\) 41.3669 1.44636
\(819\) −1.24952 −0.0436619
\(820\) −1.04387 −0.0364534
\(821\) 2.29552 0.0801144 0.0400572 0.999197i \(-0.487246\pi\)
0.0400572 + 0.999197i \(0.487246\pi\)
\(822\) −2.07240 −0.0722833
\(823\) 9.17424 0.319794 0.159897 0.987134i \(-0.448884\pi\)
0.159897 + 0.987134i \(0.448884\pi\)
\(824\) 5.65600 0.197036
\(825\) −18.1825 −0.633034
\(826\) 2.47808 0.0862234
\(827\) 47.9175 1.66625 0.833127 0.553082i \(-0.186549\pi\)
0.833127 + 0.553082i \(0.186549\pi\)
\(828\) −1.12616 −0.0391366
\(829\) 39.4460 1.37002 0.685008 0.728535i \(-0.259799\pi\)
0.685008 + 0.728535i \(0.259799\pi\)
\(830\) 66.5054 2.30844
\(831\) −5.75758 −0.199728
\(832\) 19.7440 0.684499
\(833\) −6.95581 −0.241005
\(834\) −15.5763 −0.539364
\(835\) −1.61800 −0.0559933
\(836\) −25.7307 −0.889916
\(837\) −1.55353 −0.0536978
\(838\) −6.52213 −0.225303
\(839\) 34.3489 1.18586 0.592929 0.805255i \(-0.297972\pi\)
0.592929 + 0.805255i \(0.297972\pi\)
\(840\) 1.25424 0.0432755
\(841\) −12.5043 −0.431182
\(842\) −9.38273 −0.323350
\(843\) −17.7636 −0.611812
\(844\) 6.63154 0.228267
\(845\) 63.5765 2.18710
\(846\) −10.7938 −0.371100
\(847\) −4.90101 −0.168401
\(848\) −35.2144 −1.20927
\(849\) 30.0100 1.02994
\(850\) −5.13035 −0.175970
\(851\) −0.876213 −0.0300362
\(852\) −9.74564 −0.333880
\(853\) −53.6133 −1.83568 −0.917842 0.396945i \(-0.870070\pi\)
−0.917842 + 0.396945i \(0.870070\pi\)
\(854\) −0.417333 −0.0142808
\(855\) −17.0842 −0.584267
\(856\) −0.777824 −0.0265855
\(857\) −17.1709 −0.586546 −0.293273 0.956029i \(-0.594744\pi\)
−0.293273 + 0.956029i \(0.594744\pi\)
\(858\) 57.5527 1.96482
\(859\) −54.5231 −1.86030 −0.930152 0.367174i \(-0.880325\pi\)
−0.930152 + 0.367174i \(0.880325\pi\)
\(860\) −24.7926 −0.845422
\(861\) −0.105314 −0.00358909
\(862\) −31.1052 −1.05945
\(863\) −10.8298 −0.368651 −0.184326 0.982865i \(-0.559010\pi\)
−0.184326 + 0.982865i \(0.559010\pi\)
\(864\) −3.95359 −0.134504
\(865\) 44.1859 1.50237
\(866\) 33.7951 1.14840
\(867\) −1.00000 −0.0339618
\(868\) −0.239022 −0.00811293
\(869\) 69.2670 2.34972
\(870\) 19.1103 0.647901
\(871\) 43.8996 1.48748
\(872\) −32.7272 −1.10828
\(873\) 17.2545 0.583975
\(874\) −15.2621 −0.516249
\(875\) 1.13463 0.0383575
\(876\) 8.00658 0.270517
\(877\) 13.9853 0.472250 0.236125 0.971723i \(-0.424123\pi\)
0.236125 + 0.971723i \(0.424123\pi\)
\(878\) −19.4311 −0.655770
\(879\) 2.13300 0.0719442
\(880\) −82.1810 −2.77032
\(881\) 40.7496 1.37289 0.686445 0.727182i \(-0.259170\pi\)
0.686445 + 0.727182i \(0.259170\pi\)
\(882\) 11.4969 0.387122
\(883\) 50.6880 1.70579 0.852894 0.522084i \(-0.174845\pi\)
0.852894 + 0.522084i \(0.174845\pi\)
\(884\) 4.35066 0.146329
\(885\) −20.3037 −0.682502
\(886\) 60.6638 2.03804
\(887\) 14.8357 0.498136 0.249068 0.968486i \(-0.419876\pi\)
0.249068 + 0.968486i \(0.419876\pi\)
\(888\) −1.19359 −0.0400543
\(889\) 0.310811 0.0104243
\(890\) −63.5683 −2.13081
\(891\) 5.85789 0.196247
\(892\) −15.1920 −0.508666
\(893\) −39.1912 −1.31148
\(894\) −20.9907 −0.702035
\(895\) −46.5233 −1.55510
\(896\) 2.81624 0.0940838
\(897\) 9.14587 0.305372
\(898\) 6.31712 0.210805
\(899\) 6.30965 0.210439
\(900\) 2.27184 0.0757280
\(901\) 7.14559 0.238054
\(902\) 4.85074 0.161512
\(903\) −2.50129 −0.0832377
\(904\) 44.0213 1.46413
\(905\) −53.3248 −1.77258
\(906\) −11.4646 −0.380887
\(907\) 11.8684 0.394083 0.197041 0.980395i \(-0.436867\pi\)
0.197041 + 0.980395i \(0.436867\pi\)
\(908\) 1.83601 0.0609300
\(909\) −5.72965 −0.190040
\(910\) 5.87931 0.194897
\(911\) 21.1556 0.700916 0.350458 0.936578i \(-0.386026\pi\)
0.350458 + 0.936578i \(0.386026\pi\)
\(912\) −29.5753 −0.979336
\(913\) −82.7972 −2.74019
\(914\) −0.739763 −0.0244692
\(915\) 3.41935 0.113040
\(916\) 19.4394 0.642295
\(917\) −0.882960 −0.0291579
\(918\) 1.65285 0.0545523
\(919\) 45.0715 1.48677 0.743386 0.668862i \(-0.233218\pi\)
0.743386 + 0.668862i \(0.233218\pi\)
\(920\) −9.18042 −0.302669
\(921\) 29.6255 0.976194
\(922\) 20.5661 0.677307
\(923\) 79.1474 2.60517
\(924\) 0.901279 0.0296499
\(925\) 1.76762 0.0581190
\(926\) −34.7522 −1.14203
\(927\) 2.69854 0.0886318
\(928\) 16.0575 0.527112
\(929\) −5.47683 −0.179689 −0.0898444 0.995956i \(-0.528637\pi\)
−0.0898444 + 0.995956i \(0.528637\pi\)
\(930\) 7.30974 0.239696
\(931\) 41.7440 1.36811
\(932\) 16.3481 0.535500
\(933\) 10.9032 0.356954
\(934\) 43.5406 1.42469
\(935\) 16.6759 0.545360
\(936\) 12.4587 0.407224
\(937\) −21.1231 −0.690061 −0.345030 0.938592i \(-0.612131\pi\)
−0.345030 + 0.938592i \(0.612131\pi\)
\(938\) 2.56600 0.0837829
\(939\) 6.91690 0.225725
\(940\) 13.6067 0.443803
\(941\) −0.116854 −0.00380933 −0.00190466 0.999998i \(-0.500606\pi\)
−0.00190466 + 0.999998i \(0.500606\pi\)
\(942\) −1.65285 −0.0538528
\(943\) 0.770845 0.0251022
\(944\) −35.1488 −1.14399
\(945\) 0.598414 0.0194664
\(946\) 115.209 3.74576
\(947\) 54.3483 1.76608 0.883041 0.469297i \(-0.155492\pi\)
0.883041 + 0.469297i \(0.155492\pi\)
\(948\) −8.65466 −0.281090
\(949\) −65.0239 −2.11077
\(950\) 30.7889 0.998923
\(951\) 11.9804 0.388491
\(952\) −0.440589 −0.0142796
\(953\) 40.8873 1.32447 0.662235 0.749296i \(-0.269608\pi\)
0.662235 + 0.749296i \(0.269608\pi\)
\(954\) −11.8106 −0.382382
\(955\) 23.2839 0.753449
\(956\) 5.29004 0.171092
\(957\) −23.7918 −0.769079
\(958\) −0.767449 −0.0247951
\(959\) 0.263568 0.00851107
\(960\) −9.45566 −0.305180
\(961\) −28.5865 −0.922147
\(962\) −5.59501 −0.180390
\(963\) −0.371109 −0.0119588
\(964\) 5.12960 0.165213
\(965\) 10.7056 0.344627
\(966\) 0.534591 0.0172002
\(967\) 18.4373 0.592905 0.296453 0.955048i \(-0.404196\pi\)
0.296453 + 0.955048i \(0.404196\pi\)
\(968\) 48.8666 1.57063
\(969\) 6.00132 0.192790
\(970\) −81.1865 −2.60674
\(971\) −20.8773 −0.669985 −0.334993 0.942221i \(-0.608734\pi\)
−0.334993 + 0.942221i \(0.608734\pi\)
\(972\) −0.731922 −0.0234764
\(973\) 1.98100 0.0635080
\(974\) −68.7526 −2.20297
\(975\) −18.4503 −0.590883
\(976\) 5.91940 0.189475
\(977\) −11.9099 −0.381033 −0.190517 0.981684i \(-0.561016\pi\)
−0.190517 + 0.981684i \(0.561016\pi\)
\(978\) 11.6027 0.371015
\(979\) 79.1406 2.52934
\(980\) −14.4931 −0.462964
\(981\) −15.6145 −0.498533
\(982\) 58.8364 1.87755
\(983\) −12.6322 −0.402904 −0.201452 0.979498i \(-0.564566\pi\)
−0.201452 + 0.979498i \(0.564566\pi\)
\(984\) 1.05006 0.0334746
\(985\) 10.6533 0.339444
\(986\) −6.71305 −0.213787
\(987\) 1.37276 0.0436955
\(988\) −26.1097 −0.830661
\(989\) 18.3081 0.582165
\(990\) −27.5628 −0.876003
\(991\) −16.5903 −0.527009 −0.263504 0.964658i \(-0.584878\pi\)
−0.263504 + 0.964658i \(0.584878\pi\)
\(992\) 6.14201 0.195009
\(993\) −24.3174 −0.771689
\(994\) 4.62630 0.146737
\(995\) 14.6864 0.465591
\(996\) 10.3452 0.327801
\(997\) 46.0986 1.45996 0.729978 0.683470i \(-0.239530\pi\)
0.729978 + 0.683470i \(0.239530\pi\)
\(998\) 23.4953 0.743731
\(999\) −0.569477 −0.0180174
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 \(a_p\))