Properties

Label 8007.2.a.e.1.16
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 1
Dimension 46
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: \(1\)
Dimension: \(46\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.41678 q^{2}\) \(+1.00000 q^{3}\) \(+0.00726459 q^{4}\) \(+2.31073 q^{5}\) \(-1.41678 q^{6}\) \(+2.67795 q^{7}\) \(+2.82327 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.41678 q^{2}\) \(+1.00000 q^{3}\) \(+0.00726459 q^{4}\) \(+2.31073 q^{5}\) \(-1.41678 q^{6}\) \(+2.67795 q^{7}\) \(+2.82327 q^{8}\) \(+1.00000 q^{9}\) \(-3.27380 q^{10}\) \(-4.03181 q^{11}\) \(+0.00726459 q^{12}\) \(-3.81653 q^{13}\) \(-3.79406 q^{14}\) \(+2.31073 q^{15}\) \(-4.01448 q^{16}\) \(-1.00000 q^{17}\) \(-1.41678 q^{18}\) \(-5.43435 q^{19}\) \(+0.0167865 q^{20}\) \(+2.67795 q^{21}\) \(+5.71219 q^{22}\) \(-4.96423 q^{23}\) \(+2.82327 q^{24}\) \(+0.339473 q^{25}\) \(+5.40718 q^{26}\) \(+1.00000 q^{27}\) \(+0.0194542 q^{28}\) \(+7.33326 q^{29}\) \(-3.27380 q^{30}\) \(+7.79303 q^{31}\) \(+0.0410945 q^{32}\) \(-4.03181 q^{33}\) \(+1.41678 q^{34}\) \(+6.18802 q^{35}\) \(+0.00726459 q^{36}\) \(-4.21869 q^{37}\) \(+7.69927 q^{38}\) \(-3.81653 q^{39}\) \(+6.52381 q^{40}\) \(-0.767137 q^{41}\) \(-3.79406 q^{42}\) \(-0.0132232 q^{43}\) \(-0.0292895 q^{44}\) \(+2.31073 q^{45}\) \(+7.03321 q^{46}\) \(-4.65762 q^{47}\) \(-4.01448 q^{48}\) \(+0.171415 q^{49}\) \(-0.480958 q^{50}\) \(-1.00000 q^{51}\) \(-0.0277255 q^{52}\) \(+7.15400 q^{53}\) \(-1.41678 q^{54}\) \(-9.31643 q^{55}\) \(+7.56057 q^{56}\) \(-5.43435 q^{57}\) \(-10.3896 q^{58}\) \(-1.07505 q^{59}\) \(+0.0167865 q^{60}\) \(+5.20154 q^{61}\) \(-11.0410 q^{62}\) \(+2.67795 q^{63}\) \(+7.97073 q^{64}\) \(-8.81896 q^{65}\) \(+5.71219 q^{66}\) \(+11.7690 q^{67}\) \(-0.00726459 q^{68}\) \(-4.96423 q^{69}\) \(-8.76706 q^{70}\) \(+8.38610 q^{71}\) \(+2.82327 q^{72}\) \(-15.9963 q^{73}\) \(+5.97695 q^{74}\) \(+0.339473 q^{75}\) \(-0.0394783 q^{76}\) \(-10.7970 q^{77}\) \(+5.40718 q^{78}\) \(+13.7133 q^{79}\) \(-9.27637 q^{80}\) \(+1.00000 q^{81}\) \(+1.08686 q^{82}\) \(-5.99969 q^{83}\) \(+0.0194542 q^{84}\) \(-2.31073 q^{85}\) \(+0.0187344 q^{86}\) \(+7.33326 q^{87}\) \(-11.3829 q^{88}\) \(+13.1505 q^{89}\) \(-3.27380 q^{90}\) \(-10.2205 q^{91}\) \(-0.0360631 q^{92}\) \(+7.79303 q^{93}\) \(+6.59882 q^{94}\) \(-12.5573 q^{95}\) \(+0.0410945 q^{96}\) \(-12.7568 q^{97}\) \(-0.242858 q^{98}\) \(-4.03181 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(46q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 46q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 46q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(46q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 46q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 46q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 25q^{11} \) \(\mathstrut +\mathstrut 43q^{12} \) \(\mathstrut -\mathstrut 8q^{13} \) \(\mathstrut -\mathstrut 28q^{14} \) \(\mathstrut -\mathstrut 19q^{15} \) \(\mathstrut +\mathstrut 33q^{16} \) \(\mathstrut -\mathstrut 46q^{17} \) \(\mathstrut -\mathstrut 5q^{18} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 56q^{20} \) \(\mathstrut +\mathstrut q^{21} \) \(\mathstrut -\mathstrut 19q^{22} \) \(\mathstrut -\mathstrut 64q^{23} \) \(\mathstrut -\mathstrut 18q^{24} \) \(\mathstrut +\mathstrut 11q^{25} \) \(\mathstrut -\mathstrut 13q^{26} \) \(\mathstrut +\mathstrut 46q^{27} \) \(\mathstrut -\mathstrut 38q^{28} \) \(\mathstrut -\mathstrut 51q^{29} \) \(\mathstrut -\mathstrut 10q^{30} \) \(\mathstrut -\mathstrut 19q^{31} \) \(\mathstrut -\mathstrut 61q^{32} \) \(\mathstrut -\mathstrut 25q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 39q^{35} \) \(\mathstrut +\mathstrut 43q^{36} \) \(\mathstrut -\mathstrut 46q^{37} \) \(\mathstrut -\mathstrut 48q^{38} \) \(\mathstrut -\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 10q^{40} \) \(\mathstrut -\mathstrut 53q^{41} \) \(\mathstrut -\mathstrut 28q^{42} \) \(\mathstrut -\mathstrut 33q^{43} \) \(\mathstrut -\mathstrut 62q^{44} \) \(\mathstrut -\mathstrut 19q^{45} \) \(\mathstrut +\mathstrut 2q^{46} \) \(\mathstrut -\mathstrut 45q^{47} \) \(\mathstrut +\mathstrut 33q^{48} \) \(\mathstrut +\mathstrut 21q^{49} \) \(\mathstrut -\mathstrut 60q^{50} \) \(\mathstrut -\mathstrut 46q^{51} \) \(\mathstrut -\mathstrut 63q^{52} \) \(\mathstrut -\mathstrut 47q^{53} \) \(\mathstrut -\mathstrut 5q^{54} \) \(\mathstrut +\mathstrut 5q^{55} \) \(\mathstrut -\mathstrut 82q^{56} \) \(\mathstrut -\mathstrut 2q^{57} \) \(\mathstrut -\mathstrut 21q^{58} \) \(\mathstrut -\mathstrut 65q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 37q^{61} \) \(\mathstrut -\mathstrut 46q^{62} \) \(\mathstrut +\mathstrut q^{63} \) \(\mathstrut +\mathstrut 74q^{64} \) \(\mathstrut -\mathstrut 85q^{65} \) \(\mathstrut -\mathstrut 19q^{66} \) \(\mathstrut -\mathstrut 52q^{67} \) \(\mathstrut -\mathstrut 43q^{68} \) \(\mathstrut -\mathstrut 64q^{69} \) \(\mathstrut -\mathstrut 20q^{70} \) \(\mathstrut -\mathstrut 48q^{71} \) \(\mathstrut -\mathstrut 18q^{72} \) \(\mathstrut -\mathstrut 39q^{73} \) \(\mathstrut -\mathstrut 16q^{74} \) \(\mathstrut +\mathstrut 11q^{75} \) \(\mathstrut +\mathstrut 42q^{76} \) \(\mathstrut -\mathstrut 78q^{77} \) \(\mathstrut -\mathstrut 13q^{78} \) \(\mathstrut -\mathstrut 26q^{79} \) \(\mathstrut -\mathstrut 78q^{80} \) \(\mathstrut +\mathstrut 46q^{81} \) \(\mathstrut +\mathstrut 3q^{82} \) \(\mathstrut -\mathstrut 47q^{83} \) \(\mathstrut -\mathstrut 38q^{84} \) \(\mathstrut +\mathstrut 19q^{85} \) \(\mathstrut -\mathstrut 6q^{86} \) \(\mathstrut -\mathstrut 51q^{87} \) \(\mathstrut -\mathstrut 58q^{88} \) \(\mathstrut -\mathstrut 58q^{89} \) \(\mathstrut -\mathstrut 10q^{90} \) \(\mathstrut -\mathstrut 43q^{91} \) \(\mathstrut -\mathstrut 68q^{92} \) \(\mathstrut -\mathstrut 19q^{93} \) \(\mathstrut -\mathstrut 78q^{95} \) \(\mathstrut -\mathstrut 61q^{96} \) \(\mathstrut -\mathstrut 44q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut -\mathstrut 25q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41678 −1.00181 −0.500907 0.865501i \(-0.667000\pi\)
−0.500907 + 0.865501i \(0.667000\pi\)
\(3\) 1.00000 0.577350
\(4\) 0.00726459 0.00363230
\(5\) 2.31073 1.03339 0.516695 0.856170i \(-0.327162\pi\)
0.516695 + 0.856170i \(0.327162\pi\)
\(6\) −1.41678 −0.578398
\(7\) 2.67795 1.01217 0.506085 0.862484i \(-0.331092\pi\)
0.506085 + 0.862484i \(0.331092\pi\)
\(8\) 2.82327 0.998176
\(9\) 1.00000 0.333333
\(10\) −3.27380 −1.03526
\(11\) −4.03181 −1.21564 −0.607818 0.794076i \(-0.707955\pi\)
−0.607818 + 0.794076i \(0.707955\pi\)
\(12\) 0.00726459 0.00209711
\(13\) −3.81653 −1.05851 −0.529257 0.848462i \(-0.677529\pi\)
−0.529257 + 0.848462i \(0.677529\pi\)
\(14\) −3.79406 −1.01401
\(15\) 2.31073 0.596628
\(16\) −4.01448 −1.00362
\(17\) −1.00000 −0.242536
\(18\) −1.41678 −0.333938
\(19\) −5.43435 −1.24673 −0.623363 0.781933i \(-0.714234\pi\)
−0.623363 + 0.781933i \(0.714234\pi\)
\(20\) 0.0167865 0.00375358
\(21\) 2.67795 0.584377
\(22\) 5.71219 1.21784
\(23\) −4.96423 −1.03511 −0.517556 0.855649i \(-0.673158\pi\)
−0.517556 + 0.855649i \(0.673158\pi\)
\(24\) 2.82327 0.576297
\(25\) 0.339473 0.0678945
\(26\) 5.40718 1.06043
\(27\) 1.00000 0.192450
\(28\) 0.0194542 0.00367650
\(29\) 7.33326 1.36175 0.680876 0.732399i \(-0.261599\pi\)
0.680876 + 0.732399i \(0.261599\pi\)
\(30\) −3.27380 −0.597710
\(31\) 7.79303 1.39967 0.699835 0.714304i \(-0.253257\pi\)
0.699835 + 0.714304i \(0.253257\pi\)
\(32\) 0.0410945 0.00726456
\(33\) −4.03181 −0.701848
\(34\) 1.41678 0.242976
\(35\) 6.18802 1.04597
\(36\) 0.00726459 0.00121077
\(37\) −4.21869 −0.693548 −0.346774 0.937949i \(-0.612723\pi\)
−0.346774 + 0.937949i \(0.612723\pi\)
\(38\) 7.69927 1.24899
\(39\) −3.81653 −0.611133
\(40\) 6.52381 1.03150
\(41\) −0.767137 −0.119807 −0.0599034 0.998204i \(-0.519079\pi\)
−0.0599034 + 0.998204i \(0.519079\pi\)
\(42\) −3.79406 −0.585437
\(43\) −0.0132232 −0.00201652 −0.00100826 0.999999i \(-0.500321\pi\)
−0.00100826 + 0.999999i \(0.500321\pi\)
\(44\) −0.0292895 −0.00441555
\(45\) 2.31073 0.344463
\(46\) 7.03321 1.03699
\(47\) −4.65762 −0.679383 −0.339692 0.940537i \(-0.610323\pi\)
−0.339692 + 0.940537i \(0.610323\pi\)
\(48\) −4.01448 −0.579440
\(49\) 0.171415 0.0244879
\(50\) −0.480958 −0.0680177
\(51\) −1.00000 −0.140028
\(52\) −0.0277255 −0.00384483
\(53\) 7.15400 0.982677 0.491338 0.870969i \(-0.336508\pi\)
0.491338 + 0.870969i \(0.336508\pi\)
\(54\) −1.41678 −0.192799
\(55\) −9.31643 −1.25623
\(56\) 7.56057 1.01032
\(57\) −5.43435 −0.719797
\(58\) −10.3896 −1.36422
\(59\) −1.07505 −0.139959 −0.0699797 0.997548i \(-0.522293\pi\)
−0.0699797 + 0.997548i \(0.522293\pi\)
\(60\) 0.0167865 0.00216713
\(61\) 5.20154 0.665989 0.332994 0.942929i \(-0.391941\pi\)
0.332994 + 0.942929i \(0.391941\pi\)
\(62\) −11.0410 −1.40221
\(63\) 2.67795 0.337390
\(64\) 7.97073 0.996341
\(65\) −8.81896 −1.09386
\(66\) 5.71219 0.703122
\(67\) 11.7690 1.43781 0.718906 0.695107i \(-0.244643\pi\)
0.718906 + 0.695107i \(0.244643\pi\)
\(68\) −0.00726459 −0.000880961 0
\(69\) −4.96423 −0.597623
\(70\) −8.76706 −1.04786
\(71\) 8.38610 0.995247 0.497623 0.867393i \(-0.334206\pi\)
0.497623 + 0.867393i \(0.334206\pi\)
\(72\) 2.82327 0.332725
\(73\) −15.9963 −1.87222 −0.936111 0.351705i \(-0.885602\pi\)
−0.936111 + 0.351705i \(0.885602\pi\)
\(74\) 5.97695 0.694806
\(75\) 0.339473 0.0391989
\(76\) −0.0394783 −0.00452847
\(77\) −10.7970 −1.23043
\(78\) 5.40718 0.612242
\(79\) 13.7133 1.54287 0.771433 0.636310i \(-0.219540\pi\)
0.771433 + 0.636310i \(0.219540\pi\)
\(80\) −9.27637 −1.03713
\(81\) 1.00000 0.111111
\(82\) 1.08686 0.120024
\(83\) −5.99969 −0.658551 −0.329276 0.944234i \(-0.606804\pi\)
−0.329276 + 0.944234i \(0.606804\pi\)
\(84\) 0.0194542 0.00212263
\(85\) −2.31073 −0.250634
\(86\) 0.0187344 0.00202018
\(87\) 7.33326 0.786208
\(88\) −11.3829 −1.21342
\(89\) 13.1505 1.39395 0.696976 0.717094i \(-0.254528\pi\)
0.696976 + 0.717094i \(0.254528\pi\)
\(90\) −3.27380 −0.345088
\(91\) −10.2205 −1.07140
\(92\) −0.0360631 −0.00375984
\(93\) 7.79303 0.808100
\(94\) 6.59882 0.680616
\(95\) −12.5573 −1.28835
\(96\) 0.0410945 0.00419419
\(97\) −12.7568 −1.29526 −0.647631 0.761954i \(-0.724240\pi\)
−0.647631 + 0.761954i \(0.724240\pi\)
\(98\) −0.242858 −0.0245324
\(99\) −4.03181 −0.405212
\(100\) 0.00246613 0.000246613 0
\(101\) −5.53926 −0.551177 −0.275588 0.961276i \(-0.588873\pi\)
−0.275588 + 0.961276i \(0.588873\pi\)
\(102\) 1.41678 0.140282
\(103\) −12.5811 −1.23965 −0.619825 0.784740i \(-0.712797\pi\)
−0.619825 + 0.784740i \(0.712797\pi\)
\(104\) −10.7751 −1.05658
\(105\) 6.18802 0.603889
\(106\) −10.1356 −0.984460
\(107\) −15.9193 −1.53898 −0.769490 0.638659i \(-0.779490\pi\)
−0.769490 + 0.638659i \(0.779490\pi\)
\(108\) 0.00726459 0.000699036 0
\(109\) 10.3418 0.990569 0.495285 0.868731i \(-0.335064\pi\)
0.495285 + 0.868731i \(0.335064\pi\)
\(110\) 13.1993 1.25851
\(111\) −4.21869 −0.400420
\(112\) −10.7506 −1.01583
\(113\) −4.48878 −0.422269 −0.211134 0.977457i \(-0.567716\pi\)
−0.211134 + 0.977457i \(0.567716\pi\)
\(114\) 7.69927 0.721103
\(115\) −11.4710 −1.06967
\(116\) 0.0532731 0.00494629
\(117\) −3.81653 −0.352838
\(118\) 1.52311 0.140213
\(119\) −2.67795 −0.245487
\(120\) 6.52381 0.595539
\(121\) 5.25550 0.477773
\(122\) −7.36943 −0.667197
\(123\) −0.767137 −0.0691704
\(124\) 0.0566132 0.00508402
\(125\) −10.7692 −0.963228
\(126\) −3.79406 −0.338002
\(127\) −11.5414 −1.02414 −0.512068 0.858945i \(-0.671120\pi\)
−0.512068 + 0.858945i \(0.671120\pi\)
\(128\) −11.3750 −1.00541
\(129\) −0.0132232 −0.00116424
\(130\) 12.4945 1.09584
\(131\) 1.04204 0.0910436 0.0455218 0.998963i \(-0.485505\pi\)
0.0455218 + 0.998963i \(0.485505\pi\)
\(132\) −0.0292895 −0.00254932
\(133\) −14.5529 −1.26190
\(134\) −16.6741 −1.44042
\(135\) 2.31073 0.198876
\(136\) −2.82327 −0.242093
\(137\) −5.64474 −0.482263 −0.241131 0.970493i \(-0.577518\pi\)
−0.241131 + 0.970493i \(0.577518\pi\)
\(138\) 7.03321 0.598707
\(139\) 10.1167 0.858088 0.429044 0.903284i \(-0.358851\pi\)
0.429044 + 0.903284i \(0.358851\pi\)
\(140\) 0.0449534 0.00379926
\(141\) −4.65762 −0.392242
\(142\) −11.8813 −0.997053
\(143\) 15.3875 1.28677
\(144\) −4.01448 −0.334540
\(145\) 16.9452 1.40722
\(146\) 22.6632 1.87562
\(147\) 0.171415 0.0141381
\(148\) −0.0306470 −0.00251917
\(149\) −12.1398 −0.994534 −0.497267 0.867598i \(-0.665663\pi\)
−0.497267 + 0.867598i \(0.665663\pi\)
\(150\) −0.480958 −0.0392701
\(151\) −14.2187 −1.15710 −0.578552 0.815645i \(-0.696382\pi\)
−0.578552 + 0.815645i \(0.696382\pi\)
\(152\) −15.3426 −1.24445
\(153\) −1.00000 −0.0808452
\(154\) 15.2970 1.23266
\(155\) 18.0076 1.44640
\(156\) −0.0277255 −0.00221982
\(157\) 1.00000 0.0798087
\(158\) −19.4287 −1.54567
\(159\) 7.15400 0.567349
\(160\) 0.0949584 0.00750712
\(161\) −13.2939 −1.04771
\(162\) −1.41678 −0.111313
\(163\) −16.2976 −1.27653 −0.638263 0.769818i \(-0.720347\pi\)
−0.638263 + 0.769818i \(0.720347\pi\)
\(164\) −0.00557294 −0.000435173 0
\(165\) −9.31643 −0.725283
\(166\) 8.50023 0.659746
\(167\) −17.1057 −1.32368 −0.661839 0.749646i \(-0.730224\pi\)
−0.661839 + 0.749646i \(0.730224\pi\)
\(168\) 7.56057 0.583310
\(169\) 1.56586 0.120451
\(170\) 3.27380 0.251089
\(171\) −5.43435 −0.415575
\(172\) −9.60612e−5 0 −7.32460e−6 0
\(173\) −16.7942 −1.27684 −0.638420 0.769688i \(-0.720412\pi\)
−0.638420 + 0.769688i \(0.720412\pi\)
\(174\) −10.3896 −0.787635
\(175\) 0.909091 0.0687208
\(176\) 16.1856 1.22004
\(177\) −1.07505 −0.0808056
\(178\) −18.6314 −1.39648
\(179\) −10.4357 −0.780001 −0.390001 0.920815i \(-0.627525\pi\)
−0.390001 + 0.920815i \(0.627525\pi\)
\(180\) 0.0167865 0.00125119
\(181\) −15.0002 −1.11496 −0.557479 0.830191i \(-0.688231\pi\)
−0.557479 + 0.830191i \(0.688231\pi\)
\(182\) 14.4801 1.07334
\(183\) 5.20154 0.384509
\(184\) −14.0153 −1.03322
\(185\) −9.74825 −0.716705
\(186\) −11.0410 −0.809566
\(187\) 4.03181 0.294835
\(188\) −0.0338357 −0.00246772
\(189\) 2.67795 0.194792
\(190\) 17.7909 1.29069
\(191\) −14.0987 −1.02015 −0.510073 0.860131i \(-0.670382\pi\)
−0.510073 + 0.860131i \(0.670382\pi\)
\(192\) 7.97073 0.575238
\(193\) −12.8316 −0.923639 −0.461820 0.886974i \(-0.652803\pi\)
−0.461820 + 0.886974i \(0.652803\pi\)
\(194\) 18.0736 1.29761
\(195\) −8.81896 −0.631539
\(196\) 0.00124526 8.89474e−5 0
\(197\) 13.2413 0.943404 0.471702 0.881758i \(-0.343640\pi\)
0.471702 + 0.881758i \(0.343640\pi\)
\(198\) 5.71219 0.405947
\(199\) −7.79202 −0.552362 −0.276181 0.961106i \(-0.589069\pi\)
−0.276181 + 0.961106i \(0.589069\pi\)
\(200\) 0.958422 0.0677707
\(201\) 11.7690 0.830122
\(202\) 7.84791 0.552177
\(203\) 19.6381 1.37832
\(204\) −0.00726459 −0.000508623 0
\(205\) −1.77265 −0.123807
\(206\) 17.8246 1.24190
\(207\) −4.96423 −0.345038
\(208\) 15.3213 1.06234
\(209\) 21.9103 1.51556
\(210\) −8.76706 −0.604985
\(211\) 19.8034 1.36332 0.681660 0.731669i \(-0.261258\pi\)
0.681660 + 0.731669i \(0.261258\pi\)
\(212\) 0.0519709 0.00356937
\(213\) 8.38610 0.574606
\(214\) 22.5542 1.54177
\(215\) −0.0305553 −0.00208385
\(216\) 2.82327 0.192099
\(217\) 20.8694 1.41670
\(218\) −14.6521 −0.992367
\(219\) −15.9963 −1.08093
\(220\) −0.0676800 −0.00456299
\(221\) 3.81653 0.256727
\(222\) 5.97695 0.401147
\(223\) −13.2992 −0.890583 −0.445292 0.895386i \(-0.646900\pi\)
−0.445292 + 0.895386i \(0.646900\pi\)
\(224\) 0.110049 0.00735296
\(225\) 0.339473 0.0226315
\(226\) 6.35961 0.423035
\(227\) 0.285761 0.0189666 0.00948330 0.999955i \(-0.496981\pi\)
0.00948330 + 0.999955i \(0.496981\pi\)
\(228\) −0.0394783 −0.00261452
\(229\) 15.0363 0.993629 0.496815 0.867857i \(-0.334503\pi\)
0.496815 + 0.867857i \(0.334503\pi\)
\(230\) 16.2519 1.07162
\(231\) −10.7970 −0.710390
\(232\) 20.7038 1.35927
\(233\) 11.9182 0.780789 0.390394 0.920648i \(-0.372339\pi\)
0.390394 + 0.920648i \(0.372339\pi\)
\(234\) 5.40718 0.353478
\(235\) −10.7625 −0.702068
\(236\) −0.00780979 −0.000508374 0
\(237\) 13.7133 0.890774
\(238\) 3.79406 0.245933
\(239\) −19.2522 −1.24532 −0.622662 0.782491i \(-0.713949\pi\)
−0.622662 + 0.782491i \(0.713949\pi\)
\(240\) −9.27637 −0.598787
\(241\) −2.32539 −0.149792 −0.0748958 0.997191i \(-0.523862\pi\)
−0.0748958 + 0.997191i \(0.523862\pi\)
\(242\) −7.44588 −0.478639
\(243\) 1.00000 0.0641500
\(244\) 0.0377871 0.00241907
\(245\) 0.396095 0.0253056
\(246\) 1.08686 0.0692960
\(247\) 20.7403 1.31968
\(248\) 22.0018 1.39712
\(249\) −5.99969 −0.380215
\(250\) 15.2576 0.964976
\(251\) −16.4310 −1.03711 −0.518557 0.855043i \(-0.673531\pi\)
−0.518557 + 0.855043i \(0.673531\pi\)
\(252\) 0.0194542 0.00122550
\(253\) 20.0148 1.25832
\(254\) 16.3517 1.02599
\(255\) −2.31073 −0.144704
\(256\) 0.174348 0.0108967
\(257\) −27.2932 −1.70250 −0.851250 0.524760i \(-0.824155\pi\)
−0.851250 + 0.524760i \(0.824155\pi\)
\(258\) 0.0187344 0.00116635
\(259\) −11.2974 −0.701988
\(260\) −0.0640661 −0.00397321
\(261\) 7.33326 0.453917
\(262\) −1.47634 −0.0912088
\(263\) 23.0316 1.42019 0.710094 0.704107i \(-0.248652\pi\)
0.710094 + 0.704107i \(0.248652\pi\)
\(264\) −11.3829 −0.700568
\(265\) 16.5310 1.01549
\(266\) 20.6183 1.26419
\(267\) 13.1505 0.804799
\(268\) 0.0854970 0.00522256
\(269\) −26.3989 −1.60957 −0.804786 0.593565i \(-0.797720\pi\)
−0.804786 + 0.593565i \(0.797720\pi\)
\(270\) −3.27380 −0.199237
\(271\) 12.7225 0.772838 0.386419 0.922323i \(-0.373712\pi\)
0.386419 + 0.922323i \(0.373712\pi\)
\(272\) 4.01448 0.243413
\(273\) −10.2205 −0.618571
\(274\) 7.99735 0.483138
\(275\) −1.36869 −0.0825351
\(276\) −0.0360631 −0.00217074
\(277\) −15.3201 −0.920497 −0.460249 0.887790i \(-0.652240\pi\)
−0.460249 + 0.887790i \(0.652240\pi\)
\(278\) −14.3331 −0.859645
\(279\) 7.79303 0.466557
\(280\) 17.4704 1.04406
\(281\) 10.7031 0.638495 0.319248 0.947671i \(-0.396570\pi\)
0.319248 + 0.947671i \(0.396570\pi\)
\(282\) 6.59882 0.392954
\(283\) 6.66693 0.396308 0.198154 0.980171i \(-0.436505\pi\)
0.198154 + 0.980171i \(0.436505\pi\)
\(284\) 0.0609216 0.00361503
\(285\) −12.5573 −0.743831
\(286\) −21.8007 −1.28910
\(287\) −2.05436 −0.121265
\(288\) 0.0410945 0.00242152
\(289\) 1.00000 0.0588235
\(290\) −24.0076 −1.40977
\(291\) −12.7568 −0.747820
\(292\) −0.116206 −0.00680046
\(293\) −0.808813 −0.0472514 −0.0236257 0.999721i \(-0.507521\pi\)
−0.0236257 + 0.999721i \(0.507521\pi\)
\(294\) −0.242858 −0.0141638
\(295\) −2.48415 −0.144633
\(296\) −11.9105 −0.692283
\(297\) −4.03181 −0.233949
\(298\) 17.1995 0.996338
\(299\) 18.9461 1.09568
\(300\) 0.00246613 0.000142382 0
\(301\) −0.0354111 −0.00204106
\(302\) 20.1448 1.15920
\(303\) −5.53926 −0.318222
\(304\) 21.8161 1.25124
\(305\) 12.0194 0.688226
\(306\) 1.41678 0.0809919
\(307\) 10.4262 0.595057 0.297528 0.954713i \(-0.403838\pi\)
0.297528 + 0.954713i \(0.403838\pi\)
\(308\) −0.0784357 −0.00446929
\(309\) −12.5811 −0.715712
\(310\) −25.5128 −1.44903
\(311\) 15.5470 0.881588 0.440794 0.897608i \(-0.354697\pi\)
0.440794 + 0.897608i \(0.354697\pi\)
\(312\) −10.7751 −0.610018
\(313\) 21.3908 1.20908 0.604540 0.796574i \(-0.293357\pi\)
0.604540 + 0.796574i \(0.293357\pi\)
\(314\) −1.41678 −0.0799535
\(315\) 6.18802 0.348655
\(316\) 0.0996215 0.00560415
\(317\) −6.26249 −0.351736 −0.175868 0.984414i \(-0.556273\pi\)
−0.175868 + 0.984414i \(0.556273\pi\)
\(318\) −10.1356 −0.568378
\(319\) −29.5663 −1.65540
\(320\) 18.4182 1.02961
\(321\) −15.9193 −0.888530
\(322\) 18.8346 1.04961
\(323\) 5.43435 0.302375
\(324\) 0.00726459 0.000403588 0
\(325\) −1.29561 −0.0718673
\(326\) 23.0901 1.27884
\(327\) 10.3418 0.571905
\(328\) −2.16583 −0.119588
\(329\) −12.4729 −0.687651
\(330\) 13.1993 0.726599
\(331\) −4.36548 −0.239949 −0.119974 0.992777i \(-0.538281\pi\)
−0.119974 + 0.992777i \(0.538281\pi\)
\(332\) −0.0435853 −0.00239205
\(333\) −4.21869 −0.231183
\(334\) 24.2350 1.32608
\(335\) 27.1950 1.48582
\(336\) −10.7506 −0.586491
\(337\) −15.2034 −0.828181 −0.414091 0.910236i \(-0.635900\pi\)
−0.414091 + 0.910236i \(0.635900\pi\)
\(338\) −2.21848 −0.120670
\(339\) −4.48878 −0.243797
\(340\) −0.0167865 −0.000910376 0
\(341\) −31.4200 −1.70149
\(342\) 7.69927 0.416329
\(343\) −18.2866 −0.987384
\(344\) −0.0373326 −0.00201284
\(345\) −11.4710 −0.617577
\(346\) 23.7937 1.27916
\(347\) 25.1469 1.34996 0.674979 0.737837i \(-0.264153\pi\)
0.674979 + 0.737837i \(0.264153\pi\)
\(348\) 0.0532731 0.00285574
\(349\) 27.3184 1.46232 0.731161 0.682205i \(-0.238979\pi\)
0.731161 + 0.682205i \(0.238979\pi\)
\(350\) −1.28798 −0.0688455
\(351\) −3.81653 −0.203711
\(352\) −0.165685 −0.00883106
\(353\) −31.0524 −1.65275 −0.826376 0.563119i \(-0.809601\pi\)
−0.826376 + 0.563119i \(0.809601\pi\)
\(354\) 1.52311 0.0809523
\(355\) 19.3780 1.02848
\(356\) 0.0955332 0.00506325
\(357\) −2.67795 −0.141732
\(358\) 14.7851 0.781416
\(359\) 23.2162 1.22531 0.612653 0.790352i \(-0.290102\pi\)
0.612653 + 0.790352i \(0.290102\pi\)
\(360\) 6.52381 0.343835
\(361\) 10.5321 0.554324
\(362\) 21.2520 1.11698
\(363\) 5.25550 0.275842
\(364\) −0.0742475 −0.00389163
\(365\) −36.9631 −1.93474
\(366\) −7.36943 −0.385207
\(367\) 32.8820 1.71643 0.858214 0.513292i \(-0.171574\pi\)
0.858214 + 0.513292i \(0.171574\pi\)
\(368\) 19.9288 1.03886
\(369\) −0.767137 −0.0399356
\(370\) 13.8111 0.718006
\(371\) 19.1580 0.994636
\(372\) 0.0566132 0.00293526
\(373\) −30.9935 −1.60478 −0.802392 0.596798i \(-0.796439\pi\)
−0.802392 + 0.596798i \(0.796439\pi\)
\(374\) −5.71219 −0.295370
\(375\) −10.7692 −0.556120
\(376\) −13.1497 −0.678144
\(377\) −27.9876 −1.44143
\(378\) −3.79406 −0.195146
\(379\) 14.7441 0.757353 0.378677 0.925529i \(-0.376379\pi\)
0.378677 + 0.925529i \(0.376379\pi\)
\(380\) −0.0912237 −0.00467968
\(381\) −11.5414 −0.591285
\(382\) 19.9748 1.02200
\(383\) −28.6639 −1.46466 −0.732329 0.680951i \(-0.761567\pi\)
−0.732329 + 0.680951i \(0.761567\pi\)
\(384\) −11.3750 −0.580476
\(385\) −24.9489 −1.27151
\(386\) 18.1796 0.925315
\(387\) −0.0132232 −0.000672173 0
\(388\) −0.0926733 −0.00470477
\(389\) −17.4660 −0.885559 −0.442780 0.896630i \(-0.646008\pi\)
−0.442780 + 0.896630i \(0.646008\pi\)
\(390\) 12.4945 0.632685
\(391\) 4.96423 0.251052
\(392\) 0.483951 0.0244432
\(393\) 1.04204 0.0525641
\(394\) −18.7600 −0.945115
\(395\) 31.6877 1.59438
\(396\) −0.0292895 −0.00147185
\(397\) −35.5696 −1.78519 −0.892595 0.450860i \(-0.851117\pi\)
−0.892595 + 0.450860i \(0.851117\pi\)
\(398\) 11.0396 0.553364
\(399\) −14.5529 −0.728557
\(400\) −1.36281 −0.0681403
\(401\) 2.08307 0.104024 0.0520118 0.998646i \(-0.483437\pi\)
0.0520118 + 0.998646i \(0.483437\pi\)
\(402\) −16.6741 −0.831628
\(403\) −29.7423 −1.48157
\(404\) −0.0402404 −0.00200204
\(405\) 2.31073 0.114821
\(406\) −27.8229 −1.38083
\(407\) 17.0089 0.843102
\(408\) −2.82327 −0.139773
\(409\) 5.47665 0.270803 0.135401 0.990791i \(-0.456768\pi\)
0.135401 + 0.990791i \(0.456768\pi\)
\(410\) 2.51145 0.124032
\(411\) −5.64474 −0.278434
\(412\) −0.0913964 −0.00450278
\(413\) −2.87893 −0.141663
\(414\) 7.03321 0.345664
\(415\) −13.8637 −0.680540
\(416\) −0.156838 −0.00768963
\(417\) 10.1167 0.495417
\(418\) −31.0420 −1.51831
\(419\) −0.816347 −0.0398812 −0.0199406 0.999801i \(-0.506348\pi\)
−0.0199406 + 0.999801i \(0.506348\pi\)
\(420\) 0.0449534 0.00219350
\(421\) 0.230345 0.0112263 0.00561316 0.999984i \(-0.498213\pi\)
0.00561316 + 0.999984i \(0.498213\pi\)
\(422\) −28.0570 −1.36579
\(423\) −4.65762 −0.226461
\(424\) 20.1976 0.980884
\(425\) −0.339473 −0.0164668
\(426\) −11.8813 −0.575649
\(427\) 13.9295 0.674094
\(428\) −0.115647 −0.00559003
\(429\) 15.3875 0.742916
\(430\) 0.0432901 0.00208763
\(431\) −25.5859 −1.23243 −0.616214 0.787579i \(-0.711334\pi\)
−0.616214 + 0.787579i \(0.711334\pi\)
\(432\) −4.01448 −0.193147
\(433\) 8.75978 0.420968 0.210484 0.977597i \(-0.432496\pi\)
0.210484 + 0.977597i \(0.432496\pi\)
\(434\) −29.5673 −1.41927
\(435\) 16.9452 0.812459
\(436\) 0.0751293 0.00359804
\(437\) 26.9773 1.29050
\(438\) 22.6632 1.08289
\(439\) 6.32351 0.301804 0.150902 0.988549i \(-0.451782\pi\)
0.150902 + 0.988549i \(0.451782\pi\)
\(440\) −26.3028 −1.25393
\(441\) 0.171415 0.00816264
\(442\) −5.40718 −0.257193
\(443\) −15.9795 −0.759211 −0.379606 0.925148i \(-0.623940\pi\)
−0.379606 + 0.925148i \(0.623940\pi\)
\(444\) −0.0306470 −0.00145444
\(445\) 30.3873 1.44050
\(446\) 18.8421 0.892199
\(447\) −12.1398 −0.574194
\(448\) 21.3452 1.00847
\(449\) 8.27207 0.390383 0.195192 0.980765i \(-0.437467\pi\)
0.195192 + 0.980765i \(0.437467\pi\)
\(450\) −0.480958 −0.0226726
\(451\) 3.09295 0.145641
\(452\) −0.0326091 −0.00153380
\(453\) −14.2187 −0.668055
\(454\) −0.404860 −0.0190010
\(455\) −23.6167 −1.10717
\(456\) −15.3426 −0.718484
\(457\) −9.56125 −0.447256 −0.223628 0.974675i \(-0.571790\pi\)
−0.223628 + 0.974675i \(0.571790\pi\)
\(458\) −21.3032 −0.995432
\(459\) −1.00000 −0.0466760
\(460\) −0.0833320 −0.00388538
\(461\) −5.59745 −0.260699 −0.130350 0.991468i \(-0.541610\pi\)
−0.130350 + 0.991468i \(0.541610\pi\)
\(462\) 15.2970 0.711679
\(463\) 23.1158 1.07428 0.537141 0.843492i \(-0.319504\pi\)
0.537141 + 0.843492i \(0.319504\pi\)
\(464\) −29.4392 −1.36668
\(465\) 18.0076 0.835082
\(466\) −16.8855 −0.782206
\(467\) −4.17250 −0.193080 −0.0965402 0.995329i \(-0.530778\pi\)
−0.0965402 + 0.995329i \(0.530778\pi\)
\(468\) −0.0277255 −0.00128161
\(469\) 31.5168 1.45531
\(470\) 15.2481 0.703342
\(471\) 1.00000 0.0460776
\(472\) −3.03515 −0.139704
\(473\) 0.0533135 0.00245136
\(474\) −19.4287 −0.892391
\(475\) −1.84481 −0.0846458
\(476\) −0.0194542 −0.000891682 0
\(477\) 7.15400 0.327559
\(478\) 27.2762 1.24758
\(479\) −12.9156 −0.590131 −0.295065 0.955477i \(-0.595341\pi\)
−0.295065 + 0.955477i \(0.595341\pi\)
\(480\) 0.0949584 0.00433424
\(481\) 16.1007 0.734130
\(482\) 3.29457 0.150063
\(483\) −13.2939 −0.604896
\(484\) 0.0381790 0.00173541
\(485\) −29.4776 −1.33851
\(486\) −1.41678 −0.0642664
\(487\) 28.8019 1.30514 0.652570 0.757728i \(-0.273691\pi\)
0.652570 + 0.757728i \(0.273691\pi\)
\(488\) 14.6853 0.664774
\(489\) −16.2976 −0.737003
\(490\) −0.561179 −0.0253515
\(491\) −31.0266 −1.40021 −0.700106 0.714039i \(-0.746864\pi\)
−0.700106 + 0.714039i \(0.746864\pi\)
\(492\) −0.00557294 −0.000251248 0
\(493\) −7.33326 −0.330273
\(494\) −29.3845 −1.32207
\(495\) −9.31643 −0.418742
\(496\) −31.2850 −1.40474
\(497\) 22.4576 1.00736
\(498\) 8.50023 0.380905
\(499\) −11.4975 −0.514701 −0.257350 0.966318i \(-0.582849\pi\)
−0.257350 + 0.966318i \(0.582849\pi\)
\(500\) −0.0782340 −0.00349873
\(501\) −17.1057 −0.764226
\(502\) 23.2791 1.03900
\(503\) 25.5582 1.13958 0.569791 0.821790i \(-0.307024\pi\)
0.569791 + 0.821790i \(0.307024\pi\)
\(504\) 7.56057 0.336774
\(505\) −12.7997 −0.569580
\(506\) −28.3566 −1.26060
\(507\) 1.56586 0.0695424
\(508\) −0.0838437 −0.00371996
\(509\) 4.64105 0.205711 0.102856 0.994696i \(-0.467202\pi\)
0.102856 + 0.994696i \(0.467202\pi\)
\(510\) 3.27380 0.144966
\(511\) −42.8372 −1.89501
\(512\) 22.5029 0.994497
\(513\) −5.43435 −0.239932
\(514\) 38.6684 1.70559
\(515\) −29.0715 −1.28104
\(516\) −9.60612e−5 0 −4.22886e−6 0
\(517\) 18.7786 0.825883
\(518\) 16.0060 0.703262
\(519\) −16.7942 −0.737184
\(520\) −24.8983 −1.09186
\(521\) −27.7432 −1.21545 −0.607727 0.794146i \(-0.707918\pi\)
−0.607727 + 0.794146i \(0.707918\pi\)
\(522\) −10.3896 −0.454741
\(523\) −12.2685 −0.536465 −0.268233 0.963354i \(-0.586440\pi\)
−0.268233 + 0.963354i \(0.586440\pi\)
\(524\) 0.00757001 0.000330697 0
\(525\) 0.909091 0.0396760
\(526\) −32.6307 −1.42277
\(527\) −7.79303 −0.339470
\(528\) 16.1856 0.704388
\(529\) 1.64353 0.0714580
\(530\) −23.4207 −1.01733
\(531\) −1.07505 −0.0466532
\(532\) −0.105721 −0.00458359
\(533\) 2.92780 0.126817
\(534\) −18.6314 −0.806259
\(535\) −36.7853 −1.59037
\(536\) 33.2270 1.43519
\(537\) −10.4357 −0.450334
\(538\) 37.4015 1.61249
\(539\) −0.691115 −0.0297684
\(540\) 0.0167865 0.000722376 0
\(541\) −7.52796 −0.323652 −0.161826 0.986819i \(-0.551738\pi\)
−0.161826 + 0.986819i \(0.551738\pi\)
\(542\) −18.0250 −0.774240
\(543\) −15.0002 −0.643722
\(544\) −0.0410945 −0.00176191
\(545\) 23.8972 1.02364
\(546\) 14.4801 0.619693
\(547\) −7.18480 −0.307200 −0.153600 0.988133i \(-0.549087\pi\)
−0.153600 + 0.988133i \(0.549087\pi\)
\(548\) −0.0410067 −0.00175172
\(549\) 5.20154 0.221996
\(550\) 1.93913 0.0826849
\(551\) −39.8515 −1.69773
\(552\) −14.0153 −0.596532
\(553\) 36.7235 1.56164
\(554\) 21.7052 0.922168
\(555\) −9.74825 −0.413790
\(556\) 0.0734937 0.00311683
\(557\) −23.3722 −0.990312 −0.495156 0.868804i \(-0.664889\pi\)
−0.495156 + 0.868804i \(0.664889\pi\)
\(558\) −11.0410 −0.467403
\(559\) 0.0504667 0.00213451
\(560\) −24.8417 −1.04975
\(561\) 4.03181 0.170223
\(562\) −15.1640 −0.639654
\(563\) −23.3413 −0.983721 −0.491860 0.870674i \(-0.663683\pi\)
−0.491860 + 0.870674i \(0.663683\pi\)
\(564\) −0.0338357 −0.00142474
\(565\) −10.3724 −0.436368
\(566\) −9.44558 −0.397027
\(567\) 2.67795 0.112463
\(568\) 23.6762 0.993431
\(569\) −41.1586 −1.72546 −0.862730 0.505665i \(-0.831247\pi\)
−0.862730 + 0.505665i \(0.831247\pi\)
\(570\) 17.7909 0.745181
\(571\) 7.05391 0.295197 0.147598 0.989047i \(-0.452846\pi\)
0.147598 + 0.989047i \(0.452846\pi\)
\(572\) 0.111784 0.00467392
\(573\) −14.0987 −0.588982
\(574\) 2.91057 0.121485
\(575\) −1.68522 −0.0702785
\(576\) 7.97073 0.332114
\(577\) 40.4953 1.68584 0.842920 0.538039i \(-0.180835\pi\)
0.842920 + 0.538039i \(0.180835\pi\)
\(578\) −1.41678 −0.0589303
\(579\) −12.8316 −0.533263
\(580\) 0.123100 0.00511144
\(581\) −16.0669 −0.666566
\(582\) 18.0736 0.749177
\(583\) −28.8436 −1.19458
\(584\) −45.1617 −1.86881
\(585\) −8.81896 −0.364619
\(586\) 1.14591 0.0473371
\(587\) 2.52694 0.104298 0.0521490 0.998639i \(-0.483393\pi\)
0.0521490 + 0.998639i \(0.483393\pi\)
\(588\) 0.00124526 5.13538e−5 0
\(589\) −42.3501 −1.74500
\(590\) 3.51949 0.144895
\(591\) 13.2413 0.544674
\(592\) 16.9358 0.696058
\(593\) 36.2539 1.48877 0.744386 0.667750i \(-0.232743\pi\)
0.744386 + 0.667750i \(0.232743\pi\)
\(594\) 5.71219 0.234374
\(595\) −6.18802 −0.253684
\(596\) −0.0881909 −0.00361244
\(597\) −7.79202 −0.318906
\(598\) −26.8424 −1.09767
\(599\) −43.1548 −1.76326 −0.881629 0.471944i \(-0.843553\pi\)
−0.881629 + 0.471944i \(0.843553\pi\)
\(600\) 0.958422 0.0391274
\(601\) 33.3337 1.35971 0.679854 0.733347i \(-0.262043\pi\)
0.679854 + 0.733347i \(0.262043\pi\)
\(602\) 0.0501697 0.00204476
\(603\) 11.7690 0.479271
\(604\) −0.103293 −0.00420295
\(605\) 12.1440 0.493725
\(606\) 7.84791 0.318799
\(607\) 26.9211 1.09269 0.546347 0.837559i \(-0.316018\pi\)
0.546347 + 0.837559i \(0.316018\pi\)
\(608\) −0.223322 −0.00905690
\(609\) 19.6381 0.795776
\(610\) −17.0288 −0.689475
\(611\) 17.7759 0.719137
\(612\) −0.00726459 −0.000293654 0
\(613\) −3.75524 −0.151673 −0.0758363 0.997120i \(-0.524163\pi\)
−0.0758363 + 0.997120i \(0.524163\pi\)
\(614\) −14.7717 −0.596136
\(615\) −1.77265 −0.0714800
\(616\) −30.4828 −1.22819
\(617\) −30.1904 −1.21542 −0.607709 0.794160i \(-0.707911\pi\)
−0.607709 + 0.794160i \(0.707911\pi\)
\(618\) 17.8246 0.717011
\(619\) 19.9694 0.802637 0.401318 0.915939i \(-0.368552\pi\)
0.401318 + 0.915939i \(0.368552\pi\)
\(620\) 0.130818 0.00525377
\(621\) −4.96423 −0.199208
\(622\) −22.0266 −0.883188
\(623\) 35.2164 1.41092
\(624\) 15.3213 0.613345
\(625\) −26.5821 −1.06328
\(626\) −30.3061 −1.21127
\(627\) 21.9103 0.875012
\(628\) 0.00726459 0.000289889 0
\(629\) 4.21869 0.168210
\(630\) −8.76706 −0.349288
\(631\) 13.6101 0.541810 0.270905 0.962606i \(-0.412677\pi\)
0.270905 + 0.962606i \(0.412677\pi\)
\(632\) 38.7163 1.54005
\(633\) 19.8034 0.787113
\(634\) 8.87257 0.352375
\(635\) −26.6691 −1.05833
\(636\) 0.0519709 0.00206078
\(637\) −0.654211 −0.0259208
\(638\) 41.8890 1.65840
\(639\) 8.38610 0.331749
\(640\) −26.2845 −1.03898
\(641\) 44.7544 1.76769 0.883847 0.467776i \(-0.154945\pi\)
0.883847 + 0.467776i \(0.154945\pi\)
\(642\) 22.5542 0.890143
\(643\) −45.0643 −1.77716 −0.888581 0.458721i \(-0.848308\pi\)
−0.888581 + 0.458721i \(0.848308\pi\)
\(644\) −0.0965751 −0.00380559
\(645\) −0.0305553 −0.00120311
\(646\) −7.69927 −0.302924
\(647\) 31.2551 1.22876 0.614382 0.789009i \(-0.289406\pi\)
0.614382 + 0.789009i \(0.289406\pi\)
\(648\) 2.82327 0.110908
\(649\) 4.33439 0.170140
\(650\) 1.83559 0.0719977
\(651\) 20.8694 0.817934
\(652\) −0.118395 −0.00463672
\(653\) −24.7805 −0.969735 −0.484868 0.874587i \(-0.661132\pi\)
−0.484868 + 0.874587i \(0.661132\pi\)
\(654\) −14.6521 −0.572943
\(655\) 2.40788 0.0940836
\(656\) 3.07965 0.120240
\(657\) −15.9963 −0.624074
\(658\) 17.6713 0.688899
\(659\) −6.55239 −0.255245 −0.127622 0.991823i \(-0.540735\pi\)
−0.127622 + 0.991823i \(0.540735\pi\)
\(660\) −0.0676800 −0.00263444
\(661\) 33.8232 1.31557 0.657786 0.753205i \(-0.271493\pi\)
0.657786 + 0.753205i \(0.271493\pi\)
\(662\) 6.18493 0.240384
\(663\) 3.81653 0.148222
\(664\) −16.9387 −0.657350
\(665\) −33.6279 −1.30403
\(666\) 5.97695 0.231602
\(667\) −36.4040 −1.40957
\(668\) −0.124266 −0.00480799
\(669\) −13.2992 −0.514178
\(670\) −38.5293 −1.48852
\(671\) −20.9716 −0.809600
\(672\) 0.110049 0.00424524
\(673\) −0.526357 −0.0202896 −0.0101448 0.999949i \(-0.503229\pi\)
−0.0101448 + 0.999949i \(0.503229\pi\)
\(674\) 21.5399 0.829684
\(675\) 0.339473 0.0130663
\(676\) 0.0113754 0.000437514 0
\(677\) −47.5145 −1.82613 −0.913066 0.407813i \(-0.866292\pi\)
−0.913066 + 0.407813i \(0.866292\pi\)
\(678\) 6.35961 0.244239
\(679\) −34.1622 −1.31103
\(680\) −6.52381 −0.250177
\(681\) 0.285761 0.0109504
\(682\) 44.5153 1.70458
\(683\) 11.1773 0.427687 0.213843 0.976868i \(-0.431402\pi\)
0.213843 + 0.976868i \(0.431402\pi\)
\(684\) −0.0394783 −0.00150949
\(685\) −13.0435 −0.498365
\(686\) 25.9081 0.989176
\(687\) 15.0363 0.573672
\(688\) 0.0530843 0.00202382
\(689\) −27.3034 −1.04018
\(690\) 16.2519 0.618698
\(691\) 11.3158 0.430472 0.215236 0.976562i \(-0.430948\pi\)
0.215236 + 0.976562i \(0.430948\pi\)
\(692\) −0.122003 −0.00463786
\(693\) −10.7970 −0.410144
\(694\) −35.6276 −1.35241
\(695\) 23.3770 0.886739
\(696\) 20.7038 0.784774
\(697\) 0.767137 0.0290574
\(698\) −38.7042 −1.46497
\(699\) 11.9182 0.450789
\(700\) 0.00660417 0.000249614 0
\(701\) −31.2986 −1.18213 −0.591065 0.806624i \(-0.701292\pi\)
−0.591065 + 0.806624i \(0.701292\pi\)
\(702\) 5.40718 0.204081
\(703\) 22.9258 0.864664
\(704\) −32.1365 −1.21119
\(705\) −10.7625 −0.405339
\(706\) 43.9944 1.65575
\(707\) −14.8339 −0.557884
\(708\) −0.00780979 −0.000293510 0
\(709\) 11.5913 0.435320 0.217660 0.976025i \(-0.430158\pi\)
0.217660 + 0.976025i \(0.430158\pi\)
\(710\) −27.4544 −1.03034
\(711\) 13.7133 0.514289
\(712\) 37.1274 1.39141
\(713\) −38.6864 −1.44882
\(714\) 3.79406 0.141989
\(715\) 35.5564 1.32973
\(716\) −0.0758111 −0.00283319
\(717\) −19.2522 −0.718988
\(718\) −32.8923 −1.22753
\(719\) 18.8419 0.702686 0.351343 0.936247i \(-0.385725\pi\)
0.351343 + 0.936247i \(0.385725\pi\)
\(720\) −9.27637 −0.345710
\(721\) −33.6915 −1.25474
\(722\) −14.9217 −0.555329
\(723\) −2.32539 −0.0864822
\(724\) −0.108971 −0.00404986
\(725\) 2.48944 0.0924555
\(726\) −7.44588 −0.276343
\(727\) −33.2405 −1.23282 −0.616411 0.787425i \(-0.711414\pi\)
−0.616411 + 0.787425i \(0.711414\pi\)
\(728\) −28.8551 −1.06944
\(729\) 1.00000 0.0370370
\(730\) 52.3685 1.93825
\(731\) 0.0132232 0.000489078 0
\(732\) 0.0377871 0.00139665
\(733\) 33.5915 1.24073 0.620365 0.784313i \(-0.286985\pi\)
0.620365 + 0.784313i \(0.286985\pi\)
\(734\) −46.5866 −1.71954
\(735\) 0.396095 0.0146102
\(736\) −0.204003 −0.00751963
\(737\) −47.4504 −1.74786
\(738\) 1.08686 0.0400080
\(739\) −0.813364 −0.0299201 −0.0149600 0.999888i \(-0.504762\pi\)
−0.0149600 + 0.999888i \(0.504762\pi\)
\(740\) −0.0708170 −0.00260329
\(741\) 20.7403 0.761915
\(742\) −27.1427 −0.996441
\(743\) −4.43118 −0.162564 −0.0812820 0.996691i \(-0.525901\pi\)
−0.0812820 + 0.996691i \(0.525901\pi\)
\(744\) 22.0018 0.806626
\(745\) −28.0519 −1.02774
\(746\) 43.9110 1.60770
\(747\) −5.99969 −0.219517
\(748\) 0.0292895 0.00107093
\(749\) −42.6312 −1.55771
\(750\) 15.2576 0.557129
\(751\) 2.64017 0.0963413 0.0481707 0.998839i \(-0.484661\pi\)
0.0481707 + 0.998839i \(0.484661\pi\)
\(752\) 18.6979 0.681842
\(753\) −16.4310 −0.598778
\(754\) 39.6522 1.44405
\(755\) −32.8557 −1.19574
\(756\) 0.0194542 0.000707543 0
\(757\) −1.93381 −0.0702856 −0.0351428 0.999382i \(-0.511189\pi\)
−0.0351428 + 0.999382i \(0.511189\pi\)
\(758\) −20.8891 −0.758727
\(759\) 20.0148 0.726492
\(760\) −35.4526 −1.28600
\(761\) 48.1701 1.74616 0.873082 0.487574i \(-0.162118\pi\)
0.873082 + 0.487574i \(0.162118\pi\)
\(762\) 16.3517 0.592358
\(763\) 27.6949 1.00262
\(764\) −0.102421 −0.00370547
\(765\) −2.31073 −0.0835446
\(766\) 40.6104 1.46732
\(767\) 4.10295 0.148149
\(768\) 0.174348 0.00629124
\(769\) 30.5605 1.10204 0.551020 0.834492i \(-0.314239\pi\)
0.551020 + 0.834492i \(0.314239\pi\)
\(770\) 35.3471 1.27382
\(771\) −27.2932 −0.982939
\(772\) −0.0932164 −0.00335493
\(773\) −33.2227 −1.19494 −0.597469 0.801892i \(-0.703827\pi\)
−0.597469 + 0.801892i \(0.703827\pi\)
\(774\) 0.0187344 0.000673393 0
\(775\) 2.64552 0.0950300
\(776\) −36.0160 −1.29290
\(777\) −11.2974 −0.405293
\(778\) 24.7454 0.887166
\(779\) 4.16889 0.149366
\(780\) −0.0640661 −0.00229394
\(781\) −33.8112 −1.20986
\(782\) −7.03321 −0.251507
\(783\) 7.33326 0.262069
\(784\) −0.688143 −0.0245765
\(785\) 2.31073 0.0824735
\(786\) −1.47634 −0.0526594
\(787\) −2.99505 −0.106762 −0.0533810 0.998574i \(-0.517000\pi\)
−0.0533810 + 0.998574i \(0.517000\pi\)
\(788\) 0.0961926 0.00342672
\(789\) 23.0316 0.819946
\(790\) −44.8945 −1.59728
\(791\) −12.0207 −0.427408
\(792\) −11.3829 −0.404473
\(793\) −19.8518 −0.704958
\(794\) 50.3944 1.78843
\(795\) 16.5310 0.586292
\(796\) −0.0566059 −0.00200634
\(797\) 23.7544 0.841422 0.420711 0.907195i \(-0.361781\pi\)
0.420711 + 0.907195i \(0.361781\pi\)
\(798\) 20.6183 0.729879
\(799\) 4.65762 0.164775
\(800\) 0.0139505 0.000493224 0
\(801\) 13.1505 0.464651
\(802\) −2.95125 −0.104212
\(803\) 64.4939 2.27594
\(804\) 0.0854970 0.00301525
\(805\) −30.7187 −1.08269
\(806\) 42.1383 1.48426
\(807\) −26.3989 −0.929287
\(808\) −15.6388 −0.550171
\(809\) 45.8999 1.61375 0.806877 0.590719i \(-0.201156\pi\)
0.806877 + 0.590719i \(0.201156\pi\)
\(810\) −3.27380 −0.115029
\(811\) 39.2703 1.37897 0.689483 0.724302i \(-0.257838\pi\)
0.689483 + 0.724302i \(0.257838\pi\)
\(812\) 0.142663 0.00500648
\(813\) 12.7225 0.446198
\(814\) −24.0979 −0.844632
\(815\) −37.6593 −1.31915
\(816\) 4.01448 0.140535
\(817\) 0.0718595 0.00251405
\(818\) −7.75921 −0.271294
\(819\) −10.2205 −0.357132
\(820\) −0.0128776 −0.000449704 0
\(821\) −23.3347 −0.814385 −0.407193 0.913342i \(-0.633492\pi\)
−0.407193 + 0.913342i \(0.633492\pi\)
\(822\) 7.99735 0.278940
\(823\) 26.0894 0.909419 0.454709 0.890640i \(-0.349743\pi\)
0.454709 + 0.890640i \(0.349743\pi\)
\(824\) −35.5197 −1.23739
\(825\) −1.36869 −0.0476517
\(826\) 4.07881 0.141920
\(827\) 5.87855 0.204417 0.102209 0.994763i \(-0.467409\pi\)
0.102209 + 0.994763i \(0.467409\pi\)
\(828\) −0.0360631 −0.00125328
\(829\) −7.39304 −0.256771 −0.128385 0.991724i \(-0.540979\pi\)
−0.128385 + 0.991724i \(0.540979\pi\)
\(830\) 19.6417 0.681775
\(831\) −15.3201 −0.531449
\(832\) −30.4205 −1.05464
\(833\) −0.171415 −0.00593919
\(834\) −14.3331 −0.496316
\(835\) −39.5266 −1.36788
\(836\) 0.159169 0.00550498
\(837\) 7.79303 0.269367
\(838\) 1.15658 0.0399535
\(839\) 17.8725 0.617029 0.308514 0.951220i \(-0.400168\pi\)
0.308514 + 0.951220i \(0.400168\pi\)
\(840\) 17.4704 0.602787
\(841\) 24.7767 0.854369
\(842\) −0.326348 −0.0112467
\(843\) 10.7031 0.368635
\(844\) 0.143863 0.00495198
\(845\) 3.61829 0.124473
\(846\) 6.59882 0.226872
\(847\) 14.0740 0.483587
\(848\) −28.7195 −0.986233
\(849\) 6.66693 0.228809
\(850\) 0.480958 0.0164967
\(851\) 20.9425 0.717900
\(852\) 0.0609216 0.00208714
\(853\) 11.3030 0.387007 0.193504 0.981100i \(-0.438015\pi\)
0.193504 + 0.981100i \(0.438015\pi\)
\(854\) −19.7350 −0.675317
\(855\) −12.5573 −0.429451
\(856\) −44.9445 −1.53617
\(857\) −7.40474 −0.252941 −0.126471 0.991970i \(-0.540365\pi\)
−0.126471 + 0.991970i \(0.540365\pi\)
\(858\) −21.8007 −0.744264
\(859\) 39.6964 1.35442 0.677211 0.735789i \(-0.263188\pi\)
0.677211 + 0.735789i \(0.263188\pi\)
\(860\) −0.000221972 0 −7.56917e−6 0
\(861\) −2.05436 −0.0700122
\(862\) 36.2495 1.23466
\(863\) 34.6242 1.17862 0.589311 0.807907i \(-0.299399\pi\)
0.589311 + 0.807907i \(0.299399\pi\)
\(864\) 0.0410945 0.00139806
\(865\) −38.8069 −1.31947
\(866\) −12.4107 −0.421732
\(867\) 1.00000 0.0339618
\(868\) 0.151607 0.00514589
\(869\) −55.2894 −1.87556
\(870\) −24.0076 −0.813934
\(871\) −44.9167 −1.52194
\(872\) 29.1978 0.988762
\(873\) −12.7568 −0.431754
\(874\) −38.2209 −1.29284
\(875\) −28.8394 −0.974951
\(876\) −0.116206 −0.00392625
\(877\) 3.74564 0.126481 0.0632407 0.997998i \(-0.479856\pi\)
0.0632407 + 0.997998i \(0.479856\pi\)
\(878\) −8.95901 −0.302352
\(879\) −0.808813 −0.0272806
\(880\) 37.4006 1.26077
\(881\) 20.2039 0.680688 0.340344 0.940301i \(-0.389457\pi\)
0.340344 + 0.940301i \(0.389457\pi\)
\(882\) −0.242858 −0.00817745
\(883\) 54.6753 1.83997 0.919986 0.391952i \(-0.128200\pi\)
0.919986 + 0.391952i \(0.128200\pi\)
\(884\) 0.0277255 0.000932509 0
\(885\) −2.48415 −0.0835037
\(886\) 22.6395 0.760589
\(887\) 2.42654 0.0814752 0.0407376 0.999170i \(-0.487029\pi\)
0.0407376 + 0.999170i \(0.487029\pi\)
\(888\) −11.9105 −0.399690
\(889\) −30.9074 −1.03660
\(890\) −43.0521 −1.44311
\(891\) −4.03181 −0.135071
\(892\) −0.0966135 −0.00323486
\(893\) 25.3111 0.847004
\(894\) 17.1995 0.575236
\(895\) −24.1141 −0.806045
\(896\) −30.4616 −1.01765
\(897\) 18.9461 0.632592
\(898\) −11.7197 −0.391091
\(899\) 57.1483 1.90600
\(900\) 0.00246613 8.22044e−5 0
\(901\) −7.15400 −0.238334
\(902\) −4.38203 −0.145906
\(903\) −0.0354111 −0.00117841
\(904\) −12.6730 −0.421498
\(905\) −34.6615 −1.15219
\(906\) 20.1448 0.669267
\(907\) 45.0778 1.49678 0.748391 0.663258i \(-0.230827\pi\)
0.748391 + 0.663258i \(0.230827\pi\)
\(908\) 0.00207593 6.88923e−5 0
\(909\) −5.53926 −0.183726
\(910\) 33.4597 1.10918
\(911\) −9.02246 −0.298927 −0.149464 0.988767i \(-0.547755\pi\)
−0.149464 + 0.988767i \(0.547755\pi\)
\(912\) 21.8161 0.722402
\(913\) 24.1896 0.800559
\(914\) 13.5462 0.448068
\(915\) 12.0194 0.397348
\(916\) 0.109233 0.00360916
\(917\) 2.79054 0.0921516
\(918\) 1.41678 0.0467607
\(919\) 29.6673 0.978633 0.489317 0.872106i \(-0.337246\pi\)
0.489317 + 0.872106i \(0.337246\pi\)
\(920\) −32.3857 −1.06772
\(921\) 10.4262 0.343556
\(922\) 7.93035 0.261172
\(923\) −32.0058 −1.05348
\(924\) −0.0784357 −0.00258035
\(925\) −1.43213 −0.0470881
\(926\) −32.7500 −1.07623
\(927\) −12.5811 −0.413217
\(928\) 0.301357 0.00989252
\(929\) 19.3430 0.634623 0.317312 0.948321i \(-0.397220\pi\)
0.317312 + 0.948321i \(0.397220\pi\)
\(930\) −25.5128 −0.836598
\(931\) −0.931531 −0.0305297
\(932\) 0.0865810 0.00283606
\(933\) 15.5470 0.508985
\(934\) 5.91152 0.193431
\(935\) 9.31643 0.304680
\(936\) −10.7751 −0.352194
\(937\) 15.9858 0.522233 0.261117 0.965307i \(-0.415909\pi\)
0.261117 + 0.965307i \(0.415909\pi\)
\(938\) −44.6524 −1.45795
\(939\) 21.3908 0.698063
\(940\) −0.0781851 −0.00255012
\(941\) 32.7348 1.06712 0.533562 0.845761i \(-0.320853\pi\)
0.533562 + 0.845761i \(0.320853\pi\)
\(942\) −1.41678 −0.0461612
\(943\) 3.80824 0.124013
\(944\) 4.31576 0.140466
\(945\) 6.18802 0.201296
\(946\) −0.0755334 −0.00245580
\(947\) −53.6036 −1.74188 −0.870941 0.491388i \(-0.836490\pi\)
−0.870941 + 0.491388i \(0.836490\pi\)
\(948\) 0.0996215 0.00323556
\(949\) 61.0502 1.98177
\(950\) 2.61369 0.0847994
\(951\) −6.26249 −0.203075
\(952\) −7.56057 −0.245039
\(953\) −6.11836 −0.198193 −0.0990966 0.995078i \(-0.531595\pi\)
−0.0990966 + 0.995078i \(0.531595\pi\)
\(954\) −10.1356 −0.328153
\(955\) −32.5783 −1.05421
\(956\) −0.139860 −0.00452338
\(957\) −29.5663 −0.955743
\(958\) 18.2986 0.591202
\(959\) −15.1163 −0.488132
\(960\) 18.4182 0.594445
\(961\) 29.7314 0.959077
\(962\) −22.8112 −0.735462
\(963\) −15.9193 −0.512993
\(964\) −0.0168930 −0.000544087 0
\(965\) −29.6504 −0.954479
\(966\) 18.8346 0.605993
\(967\) −46.7138 −1.50221 −0.751107 0.660181i \(-0.770480\pi\)
−0.751107 + 0.660181i \(0.770480\pi\)
\(968\) 14.8377 0.476901
\(969\) 5.43435 0.174576
\(970\) 41.7633 1.34094
\(971\) −41.8420 −1.34277 −0.671386 0.741108i \(-0.734301\pi\)
−0.671386 + 0.741108i \(0.734301\pi\)
\(972\) 0.00726459 0.000233012 0
\(973\) 27.0920 0.868530
\(974\) −40.8060 −1.30751
\(975\) −1.29561 −0.0414926
\(976\) −20.8815 −0.668399
\(977\) 32.7492 1.04774 0.523869 0.851799i \(-0.324488\pi\)
0.523869 + 0.851799i \(0.324488\pi\)
\(978\) 23.0901 0.738340
\(979\) −53.0204 −1.69454
\(980\) 0.00287747 9.19173e−5 0
\(981\) 10.3418 0.330190
\(982\) 43.9579 1.40275
\(983\) 1.85775 0.0592531 0.0296266 0.999561i \(-0.490568\pi\)
0.0296266 + 0.999561i \(0.490568\pi\)
\(984\) −2.16583 −0.0690443
\(985\) 30.5971 0.974904
\(986\) 10.3896 0.330873
\(987\) −12.4729 −0.397016
\(988\) 0.150670 0.00479345
\(989\) 0.0656430 0.00208733
\(990\) 13.1993 0.419502
\(991\) 12.6856 0.402972 0.201486 0.979491i \(-0.435423\pi\)
0.201486 + 0.979491i \(0.435423\pi\)
\(992\) 0.320251 0.0101680
\(993\) −4.36548 −0.138534
\(994\) −31.8174 −1.00919
\(995\) −18.0053 −0.570805
\(996\) −0.0435853 −0.00138105
\(997\) −62.4156 −1.97672 −0.988361 0.152128i \(-0.951388\pi\)
−0.988361 + 0.152128i \(0.951388\pi\)
\(998\) 16.2895 0.515635
\(999\) −4.21869 −0.133473
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 \(a_p\))