Properties

Label 6034.2.a.n.1.10
Level 6034
Weight 2
Character 6034.1
Self dual Yes
Analytic conductor 48.182
Analytic rank 0
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 6034 = 2 \cdot 7 \cdot 431 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6034.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1817325796\)
Analytic rank: \(0\)
Dimension: \(24\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 6034.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-0.0752307 q^{3}\) \(+1.00000 q^{4}\) \(-2.78876 q^{5}\) \(+0.0752307 q^{6}\) \(-1.00000 q^{7}\) \(-1.00000 q^{8}\) \(-2.99434 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-0.0752307 q^{3}\) \(+1.00000 q^{4}\) \(-2.78876 q^{5}\) \(+0.0752307 q^{6}\) \(-1.00000 q^{7}\) \(-1.00000 q^{8}\) \(-2.99434 q^{9}\) \(+2.78876 q^{10}\) \(+2.08969 q^{11}\) \(-0.0752307 q^{12}\) \(-3.50215 q^{13}\) \(+1.00000 q^{14}\) \(+0.209800 q^{15}\) \(+1.00000 q^{16}\) \(-5.12086 q^{17}\) \(+2.99434 q^{18}\) \(+1.33047 q^{19}\) \(-2.78876 q^{20}\) \(+0.0752307 q^{21}\) \(-2.08969 q^{22}\) \(-0.969938 q^{23}\) \(+0.0752307 q^{24}\) \(+2.77718 q^{25}\) \(+3.50215 q^{26}\) \(+0.450958 q^{27}\) \(-1.00000 q^{28}\) \(-0.965409 q^{29}\) \(-0.209800 q^{30}\) \(+2.05203 q^{31}\) \(-1.00000 q^{32}\) \(-0.157209 q^{33}\) \(+5.12086 q^{34}\) \(+2.78876 q^{35}\) \(-2.99434 q^{36}\) \(-4.89972 q^{37}\) \(-1.33047 q^{38}\) \(+0.263469 q^{39}\) \(+2.78876 q^{40}\) \(-7.97456 q^{41}\) \(-0.0752307 q^{42}\) \(-11.0838 q^{43}\) \(+2.08969 q^{44}\) \(+8.35049 q^{45}\) \(+0.969938 q^{46}\) \(-0.588653 q^{47}\) \(-0.0752307 q^{48}\) \(+1.00000 q^{49}\) \(-2.77718 q^{50}\) \(+0.385246 q^{51}\) \(-3.50215 q^{52}\) \(-0.927192 q^{53}\) \(-0.450958 q^{54}\) \(-5.82763 q^{55}\) \(+1.00000 q^{56}\) \(-0.100092 q^{57}\) \(+0.965409 q^{58}\) \(+4.91784 q^{59}\) \(+0.209800 q^{60}\) \(-9.55117 q^{61}\) \(-2.05203 q^{62}\) \(+2.99434 q^{63}\) \(+1.00000 q^{64}\) \(+9.76665 q^{65}\) \(+0.157209 q^{66}\) \(-15.9700 q^{67}\) \(-5.12086 q^{68}\) \(+0.0729691 q^{69}\) \(-2.78876 q^{70}\) \(-6.13198 q^{71}\) \(+2.99434 q^{72}\) \(+11.5714 q^{73}\) \(+4.89972 q^{74}\) \(-0.208929 q^{75}\) \(+1.33047 q^{76}\) \(-2.08969 q^{77}\) \(-0.263469 q^{78}\) \(-10.3141 q^{79}\) \(-2.78876 q^{80}\) \(+8.94910 q^{81}\) \(+7.97456 q^{82}\) \(-12.9099 q^{83}\) \(+0.0752307 q^{84}\) \(+14.2808 q^{85}\) \(+11.0838 q^{86}\) \(+0.0726284 q^{87}\) \(-2.08969 q^{88}\) \(+12.4413 q^{89}\) \(-8.35049 q^{90}\) \(+3.50215 q^{91}\) \(-0.969938 q^{92}\) \(-0.154376 q^{93}\) \(+0.588653 q^{94}\) \(-3.71035 q^{95}\) \(+0.0752307 q^{96}\) \(-7.10428 q^{97}\) \(-1.00000 q^{98}\) \(-6.25724 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 24q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 24q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut -\mathstrut 8q^{10} \) \(\mathstrut +\mathstrut 15q^{11} \) \(\mathstrut +\mathstrut 7q^{12} \) \(\mathstrut -\mathstrut 7q^{13} \) \(\mathstrut +\mathstrut 24q^{14} \) \(\mathstrut +\mathstrut 13q^{15} \) \(\mathstrut +\mathstrut 24q^{16} \) \(\mathstrut -\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 19q^{18} \) \(\mathstrut +\mathstrut 6q^{19} \) \(\mathstrut +\mathstrut 8q^{20} \) \(\mathstrut -\mathstrut 7q^{21} \) \(\mathstrut -\mathstrut 15q^{22} \) \(\mathstrut +\mathstrut 3q^{23} \) \(\mathstrut -\mathstrut 7q^{24} \) \(\mathstrut +\mathstrut 12q^{25} \) \(\mathstrut +\mathstrut 7q^{26} \) \(\mathstrut +\mathstrut 22q^{27} \) \(\mathstrut -\mathstrut 24q^{28} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 13q^{30} \) \(\mathstrut +\mathstrut 13q^{31} \) \(\mathstrut -\mathstrut 24q^{32} \) \(\mathstrut -\mathstrut 8q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut +\mathstrut 19q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 6q^{38} \) \(\mathstrut +\mathstrut 7q^{39} \) \(\mathstrut -\mathstrut 8q^{40} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 7q^{42} \) \(\mathstrut -\mathstrut 15q^{43} \) \(\mathstrut +\mathstrut 15q^{44} \) \(\mathstrut +\mathstrut 41q^{45} \) \(\mathstrut -\mathstrut 3q^{46} \) \(\mathstrut +\mathstrut 35q^{47} \) \(\mathstrut +\mathstrut 7q^{48} \) \(\mathstrut +\mathstrut 24q^{49} \) \(\mathstrut -\mathstrut 12q^{50} \) \(\mathstrut +\mathstrut 31q^{51} \) \(\mathstrut -\mathstrut 7q^{52} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 22q^{54} \) \(\mathstrut +\mathstrut 14q^{55} \) \(\mathstrut +\mathstrut 24q^{56} \) \(\mathstrut -\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 5q^{58} \) \(\mathstrut +\mathstrut 35q^{59} \) \(\mathstrut +\mathstrut 13q^{60} \) \(\mathstrut -\mathstrut 7q^{61} \) \(\mathstrut -\mathstrut 13q^{62} \) \(\mathstrut -\mathstrut 19q^{63} \) \(\mathstrut +\mathstrut 24q^{64} \) \(\mathstrut -\mathstrut 4q^{65} \) \(\mathstrut +\mathstrut 8q^{66} \) \(\mathstrut +\mathstrut 10q^{67} \) \(\mathstrut -\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut 6q^{69} \) \(\mathstrut +\mathstrut 8q^{70} \) \(\mathstrut +\mathstrut 58q^{71} \) \(\mathstrut -\mathstrut 19q^{72} \) \(\mathstrut +\mathstrut 9q^{73} \) \(\mathstrut -\mathstrut 2q^{74} \) \(\mathstrut +\mathstrut 7q^{75} \) \(\mathstrut +\mathstrut 6q^{76} \) \(\mathstrut -\mathstrut 15q^{77} \) \(\mathstrut -\mathstrut 7q^{78} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut +\mathstrut 8q^{80} \) \(\mathstrut +\mathstrut 16q^{81} \) \(\mathstrut -\mathstrut 25q^{82} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut -\mathstrut 7q^{84} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut +\mathstrut 15q^{86} \) \(\mathstrut +\mathstrut 30q^{87} \) \(\mathstrut -\mathstrut 15q^{88} \) \(\mathstrut +\mathstrut 45q^{89} \) \(\mathstrut -\mathstrut 41q^{90} \) \(\mathstrut +\mathstrut 7q^{91} \) \(\mathstrut +\mathstrut 3q^{92} \) \(\mathstrut +\mathstrut 25q^{93} \) \(\mathstrut -\mathstrut 35q^{94} \) \(\mathstrut -\mathstrut 10q^{95} \) \(\mathstrut -\mathstrut 7q^{96} \) \(\mathstrut -\mathstrut 9q^{97} \) \(\mathstrut -\mathstrut 24q^{98} \) \(\mathstrut +\mathstrut 64q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −0.0752307 −0.0434344 −0.0217172 0.999764i \(-0.506913\pi\)
−0.0217172 + 0.999764i \(0.506913\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.78876 −1.24717 −0.623585 0.781755i \(-0.714325\pi\)
−0.623585 + 0.781755i \(0.714325\pi\)
\(6\) 0.0752307 0.0307128
\(7\) −1.00000 −0.377964
\(8\) −1.00000 −0.353553
\(9\) −2.99434 −0.998113
\(10\) 2.78876 0.881883
\(11\) 2.08969 0.630065 0.315032 0.949081i \(-0.397985\pi\)
0.315032 + 0.949081i \(0.397985\pi\)
\(12\) −0.0752307 −0.0217172
\(13\) −3.50215 −0.971321 −0.485661 0.874147i \(-0.661421\pi\)
−0.485661 + 0.874147i \(0.661421\pi\)
\(14\) 1.00000 0.267261
\(15\) 0.209800 0.0541702
\(16\) 1.00000 0.250000
\(17\) −5.12086 −1.24199 −0.620996 0.783814i \(-0.713272\pi\)
−0.620996 + 0.783814i \(0.713272\pi\)
\(18\) 2.99434 0.705773
\(19\) 1.33047 0.305230 0.152615 0.988286i \(-0.451231\pi\)
0.152615 + 0.988286i \(0.451231\pi\)
\(20\) −2.78876 −0.623585
\(21\) 0.0752307 0.0164167
\(22\) −2.08969 −0.445523
\(23\) −0.969938 −0.202246 −0.101123 0.994874i \(-0.532244\pi\)
−0.101123 + 0.994874i \(0.532244\pi\)
\(24\) 0.0752307 0.0153564
\(25\) 2.77718 0.555435
\(26\) 3.50215 0.686828
\(27\) 0.450958 0.0867869
\(28\) −1.00000 −0.188982
\(29\) −0.965409 −0.179272 −0.0896360 0.995975i \(-0.528570\pi\)
−0.0896360 + 0.995975i \(0.528570\pi\)
\(30\) −0.209800 −0.0383041
\(31\) 2.05203 0.368556 0.184278 0.982874i \(-0.441005\pi\)
0.184278 + 0.982874i \(0.441005\pi\)
\(32\) −1.00000 −0.176777
\(33\) −0.157209 −0.0273665
\(34\) 5.12086 0.878221
\(35\) 2.78876 0.471386
\(36\) −2.99434 −0.499057
\(37\) −4.89972 −0.805509 −0.402755 0.915308i \(-0.631947\pi\)
−0.402755 + 0.915308i \(0.631947\pi\)
\(38\) −1.33047 −0.215830
\(39\) 0.263469 0.0421888
\(40\) 2.78876 0.440941
\(41\) −7.97456 −1.24542 −0.622708 0.782454i \(-0.713968\pi\)
−0.622708 + 0.782454i \(0.713968\pi\)
\(42\) −0.0752307 −0.0116083
\(43\) −11.0838 −1.69027 −0.845135 0.534553i \(-0.820480\pi\)
−0.845135 + 0.534553i \(0.820480\pi\)
\(44\) 2.08969 0.315032
\(45\) 8.35049 1.24482
\(46\) 0.969938 0.143010
\(47\) −0.588653 −0.0858639 −0.0429320 0.999078i \(-0.513670\pi\)
−0.0429320 + 0.999078i \(0.513670\pi\)
\(48\) −0.0752307 −0.0108586
\(49\) 1.00000 0.142857
\(50\) −2.77718 −0.392752
\(51\) 0.385246 0.0539452
\(52\) −3.50215 −0.485661
\(53\) −0.927192 −0.127360 −0.0636798 0.997970i \(-0.520284\pi\)
−0.0636798 + 0.997970i \(0.520284\pi\)
\(54\) −0.450958 −0.0613676
\(55\) −5.82763 −0.785798
\(56\) 1.00000 0.133631
\(57\) −0.100092 −0.0132575
\(58\) 0.965409 0.126764
\(59\) 4.91784 0.640248 0.320124 0.947376i \(-0.396275\pi\)
0.320124 + 0.947376i \(0.396275\pi\)
\(60\) 0.209800 0.0270851
\(61\) −9.55117 −1.22290 −0.611451 0.791283i \(-0.709414\pi\)
−0.611451 + 0.791283i \(0.709414\pi\)
\(62\) −2.05203 −0.260609
\(63\) 2.99434 0.377251
\(64\) 1.00000 0.125000
\(65\) 9.76665 1.21140
\(66\) 0.157209 0.0193510
\(67\) −15.9700 −1.95104 −0.975520 0.219911i \(-0.929423\pi\)
−0.975520 + 0.219911i \(0.929423\pi\)
\(68\) −5.12086 −0.620996
\(69\) 0.0729691 0.00878444
\(70\) −2.78876 −0.333320
\(71\) −6.13198 −0.727733 −0.363866 0.931451i \(-0.618544\pi\)
−0.363866 + 0.931451i \(0.618544\pi\)
\(72\) 2.99434 0.352886
\(73\) 11.5714 1.35433 0.677167 0.735830i \(-0.263208\pi\)
0.677167 + 0.735830i \(0.263208\pi\)
\(74\) 4.89972 0.569581
\(75\) −0.208929 −0.0241250
\(76\) 1.33047 0.152615
\(77\) −2.08969 −0.238142
\(78\) −0.263469 −0.0298320
\(79\) −10.3141 −1.16043 −0.580213 0.814464i \(-0.697031\pi\)
−0.580213 + 0.814464i \(0.697031\pi\)
\(80\) −2.78876 −0.311793
\(81\) 8.94910 0.994344
\(82\) 7.97456 0.880642
\(83\) −12.9099 −1.41704 −0.708521 0.705690i \(-0.750637\pi\)
−0.708521 + 0.705690i \(0.750637\pi\)
\(84\) 0.0752307 0.00820834
\(85\) 14.2808 1.54898
\(86\) 11.0838 1.19520
\(87\) 0.0726284 0.00778658
\(88\) −2.08969 −0.222761
\(89\) 12.4413 1.31878 0.659389 0.751802i \(-0.270815\pi\)
0.659389 + 0.751802i \(0.270815\pi\)
\(90\) −8.35049 −0.880219
\(91\) 3.50215 0.367125
\(92\) −0.969938 −0.101123
\(93\) −0.154376 −0.0160080
\(94\) 0.588653 0.0607150
\(95\) −3.71035 −0.380674
\(96\) 0.0752307 0.00767820
\(97\) −7.10428 −0.721331 −0.360665 0.932695i \(-0.617450\pi\)
−0.360665 + 0.932695i \(0.617450\pi\)
\(98\) −1.00000 −0.101015
\(99\) −6.25724 −0.628876
\(100\) 2.77718 0.277718
\(101\) 10.9266 1.08724 0.543620 0.839331i \(-0.317053\pi\)
0.543620 + 0.839331i \(0.317053\pi\)
\(102\) −0.385246 −0.0381450
\(103\) −9.34699 −0.920986 −0.460493 0.887663i \(-0.652327\pi\)
−0.460493 + 0.887663i \(0.652327\pi\)
\(104\) 3.50215 0.343414
\(105\) −0.209800 −0.0204744
\(106\) 0.927192 0.0900569
\(107\) 18.0723 1.74712 0.873558 0.486721i \(-0.161807\pi\)
0.873558 + 0.486721i \(0.161807\pi\)
\(108\) 0.450958 0.0433935
\(109\) −19.0724 −1.82681 −0.913404 0.407055i \(-0.866556\pi\)
−0.913404 + 0.407055i \(0.866556\pi\)
\(110\) 5.82763 0.555643
\(111\) 0.368609 0.0349868
\(112\) −1.00000 −0.0944911
\(113\) 8.37711 0.788052 0.394026 0.919099i \(-0.371082\pi\)
0.394026 + 0.919099i \(0.371082\pi\)
\(114\) 0.100092 0.00937446
\(115\) 2.70492 0.252235
\(116\) −0.965409 −0.0896360
\(117\) 10.4866 0.969489
\(118\) −4.91784 −0.452723
\(119\) 5.12086 0.469429
\(120\) −0.209800 −0.0191520
\(121\) −6.63321 −0.603019
\(122\) 9.55117 0.864722
\(123\) 0.599931 0.0540940
\(124\) 2.05203 0.184278
\(125\) 6.19892 0.554448
\(126\) −2.99434 −0.266757
\(127\) 2.10850 0.187099 0.0935494 0.995615i \(-0.470179\pi\)
0.0935494 + 0.995615i \(0.470179\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0.833844 0.0734159
\(130\) −9.76665 −0.856592
\(131\) −19.3765 −1.69294 −0.846468 0.532439i \(-0.821275\pi\)
−0.846468 + 0.532439i \(0.821275\pi\)
\(132\) −0.157209 −0.0136832
\(133\) −1.33047 −0.115366
\(134\) 15.9700 1.37959
\(135\) −1.25761 −0.108238
\(136\) 5.12086 0.439110
\(137\) −6.83121 −0.583630 −0.291815 0.956475i \(-0.594259\pi\)
−0.291815 + 0.956475i \(0.594259\pi\)
\(138\) −0.0729691 −0.00621154
\(139\) 14.5546 1.23451 0.617255 0.786764i \(-0.288245\pi\)
0.617255 + 0.786764i \(0.288245\pi\)
\(140\) 2.78876 0.235693
\(141\) 0.0442848 0.00372945
\(142\) 6.13198 0.514585
\(143\) −7.31840 −0.611995
\(144\) −2.99434 −0.249528
\(145\) 2.69229 0.223583
\(146\) −11.5714 −0.957658
\(147\) −0.0752307 −0.00620492
\(148\) −4.89972 −0.402755
\(149\) 17.7974 1.45802 0.729010 0.684503i \(-0.239981\pi\)
0.729010 + 0.684503i \(0.239981\pi\)
\(150\) 0.208929 0.0170590
\(151\) 12.7759 1.03969 0.519844 0.854261i \(-0.325990\pi\)
0.519844 + 0.854261i \(0.325990\pi\)
\(152\) −1.33047 −0.107915
\(153\) 15.3336 1.23965
\(154\) 2.08969 0.168392
\(155\) −5.72263 −0.459652
\(156\) 0.263469 0.0210944
\(157\) −6.02046 −0.480485 −0.240243 0.970713i \(-0.577227\pi\)
−0.240243 + 0.970713i \(0.577227\pi\)
\(158\) 10.3141 0.820546
\(159\) 0.0697533 0.00553180
\(160\) 2.78876 0.220471
\(161\) 0.969938 0.0764418
\(162\) −8.94910 −0.703107
\(163\) −10.9339 −0.856406 −0.428203 0.903683i \(-0.640853\pi\)
−0.428203 + 0.903683i \(0.640853\pi\)
\(164\) −7.97456 −0.622708
\(165\) 0.438417 0.0341307
\(166\) 12.9099 1.00200
\(167\) −14.8961 −1.15269 −0.576346 0.817206i \(-0.695522\pi\)
−0.576346 + 0.817206i \(0.695522\pi\)
\(168\) −0.0752307 −0.00580417
\(169\) −0.734957 −0.0565352
\(170\) −14.2808 −1.09529
\(171\) −3.98387 −0.304654
\(172\) −11.0838 −0.845135
\(173\) 22.4647 1.70796 0.853981 0.520303i \(-0.174181\pi\)
0.853981 + 0.520303i \(0.174181\pi\)
\(174\) −0.0726284 −0.00550594
\(175\) −2.77718 −0.209935
\(176\) 2.08969 0.157516
\(177\) −0.369972 −0.0278088
\(178\) −12.4413 −0.932517
\(179\) −5.83832 −0.436377 −0.218188 0.975907i \(-0.570015\pi\)
−0.218188 + 0.975907i \(0.570015\pi\)
\(180\) 8.35049 0.622409
\(181\) 23.4272 1.74133 0.870664 0.491879i \(-0.163690\pi\)
0.870664 + 0.491879i \(0.163690\pi\)
\(182\) −3.50215 −0.259597
\(183\) 0.718540 0.0531160
\(184\) 0.969938 0.0715048
\(185\) 13.6641 1.00461
\(186\) 0.154376 0.0113194
\(187\) −10.7010 −0.782535
\(188\) −0.588653 −0.0429320
\(189\) −0.450958 −0.0328024
\(190\) 3.71035 0.269177
\(191\) 7.68734 0.556236 0.278118 0.960547i \(-0.410289\pi\)
0.278118 + 0.960547i \(0.410289\pi\)
\(192\) −0.0752307 −0.00542931
\(193\) −13.1503 −0.946578 −0.473289 0.880907i \(-0.656933\pi\)
−0.473289 + 0.880907i \(0.656933\pi\)
\(194\) 7.10428 0.510058
\(195\) −0.734751 −0.0526166
\(196\) 1.00000 0.0714286
\(197\) −8.34788 −0.594762 −0.297381 0.954759i \(-0.596113\pi\)
−0.297381 + 0.954759i \(0.596113\pi\)
\(198\) 6.25724 0.444682
\(199\) 4.48691 0.318068 0.159034 0.987273i \(-0.449162\pi\)
0.159034 + 0.987273i \(0.449162\pi\)
\(200\) −2.77718 −0.196376
\(201\) 1.20143 0.0847423
\(202\) −10.9266 −0.768795
\(203\) 0.965409 0.0677585
\(204\) 0.385246 0.0269726
\(205\) 22.2391 1.55325
\(206\) 9.34699 0.651236
\(207\) 2.90432 0.201864
\(208\) −3.50215 −0.242830
\(209\) 2.78026 0.192315
\(210\) 0.209800 0.0144776
\(211\) −15.2276 −1.04831 −0.524157 0.851621i \(-0.675620\pi\)
−0.524157 + 0.851621i \(0.675620\pi\)
\(212\) −0.927192 −0.0636798
\(213\) 0.461313 0.0316087
\(214\) −18.0723 −1.23540
\(215\) 30.9102 2.10805
\(216\) −0.450958 −0.0306838
\(217\) −2.05203 −0.139301
\(218\) 19.0724 1.29175
\(219\) −0.870526 −0.0588247
\(220\) −5.82763 −0.392899
\(221\) 17.9340 1.20637
\(222\) −0.368609 −0.0247394
\(223\) 8.97511 0.601018 0.300509 0.953779i \(-0.402843\pi\)
0.300509 + 0.953779i \(0.402843\pi\)
\(224\) 1.00000 0.0668153
\(225\) −8.31581 −0.554387
\(226\) −8.37711 −0.557237
\(227\) 14.0786 0.934426 0.467213 0.884145i \(-0.345258\pi\)
0.467213 + 0.884145i \(0.345258\pi\)
\(228\) −0.100092 −0.00662875
\(229\) 23.3654 1.54403 0.772016 0.635603i \(-0.219249\pi\)
0.772016 + 0.635603i \(0.219249\pi\)
\(230\) −2.70492 −0.178357
\(231\) 0.157209 0.0103436
\(232\) 0.965409 0.0633822
\(233\) −20.1438 −1.31966 −0.659831 0.751414i \(-0.729372\pi\)
−0.659831 + 0.751414i \(0.729372\pi\)
\(234\) −10.4866 −0.685532
\(235\) 1.64161 0.107087
\(236\) 4.91784 0.320124
\(237\) 0.775936 0.0504025
\(238\) −5.12086 −0.331936
\(239\) 17.0756 1.10453 0.552264 0.833669i \(-0.313764\pi\)
0.552264 + 0.833669i \(0.313764\pi\)
\(240\) 0.209800 0.0135425
\(241\) −16.5972 −1.06912 −0.534560 0.845131i \(-0.679523\pi\)
−0.534560 + 0.845131i \(0.679523\pi\)
\(242\) 6.63321 0.426399
\(243\) −2.02612 −0.129976
\(244\) −9.55117 −0.611451
\(245\) −2.78876 −0.178167
\(246\) −0.599931 −0.0382502
\(247\) −4.65949 −0.296476
\(248\) −2.05203 −0.130304
\(249\) 0.971217 0.0615484
\(250\) −6.19892 −0.392054
\(251\) −20.4571 −1.29124 −0.645620 0.763659i \(-0.723401\pi\)
−0.645620 + 0.763659i \(0.723401\pi\)
\(252\) 2.99434 0.188626
\(253\) −2.02687 −0.127428
\(254\) −2.10850 −0.132299
\(255\) −1.07436 −0.0672789
\(256\) 1.00000 0.0625000
\(257\) 24.1486 1.50635 0.753176 0.657820i \(-0.228521\pi\)
0.753176 + 0.657820i \(0.228521\pi\)
\(258\) −0.833844 −0.0519129
\(259\) 4.89972 0.304454
\(260\) 9.76665 0.605702
\(261\) 2.89076 0.178934
\(262\) 19.3765 1.19709
\(263\) 5.53582 0.341353 0.170677 0.985327i \(-0.445405\pi\)
0.170677 + 0.985327i \(0.445405\pi\)
\(264\) 0.157209 0.00967552
\(265\) 2.58572 0.158839
\(266\) 1.33047 0.0815761
\(267\) −0.935969 −0.0572804
\(268\) −15.9700 −0.975520
\(269\) 9.23780 0.563239 0.281619 0.959526i \(-0.409128\pi\)
0.281619 + 0.959526i \(0.409128\pi\)
\(270\) 1.25761 0.0765359
\(271\) 28.4349 1.72729 0.863647 0.504096i \(-0.168174\pi\)
0.863647 + 0.504096i \(0.168174\pi\)
\(272\) −5.12086 −0.310498
\(273\) −0.263469 −0.0159459
\(274\) 6.83121 0.412689
\(275\) 5.80343 0.349960
\(276\) 0.0729691 0.00439222
\(277\) 1.95353 0.117376 0.0586881 0.998276i \(-0.481308\pi\)
0.0586881 + 0.998276i \(0.481308\pi\)
\(278\) −14.5546 −0.872930
\(279\) −6.14449 −0.367861
\(280\) −2.78876 −0.166660
\(281\) −12.9762 −0.774094 −0.387047 0.922060i \(-0.626505\pi\)
−0.387047 + 0.922060i \(0.626505\pi\)
\(282\) −0.0442848 −0.00263712
\(283\) 0.181693 0.0108005 0.00540025 0.999985i \(-0.498281\pi\)
0.00540025 + 0.999985i \(0.498281\pi\)
\(284\) −6.13198 −0.363866
\(285\) 0.279132 0.0165344
\(286\) 7.31840 0.432746
\(287\) 7.97456 0.470723
\(288\) 2.99434 0.176443
\(289\) 9.22323 0.542543
\(290\) −2.69229 −0.158097
\(291\) 0.534460 0.0313306
\(292\) 11.5714 0.677167
\(293\) −2.20882 −0.129041 −0.0645204 0.997916i \(-0.520552\pi\)
−0.0645204 + 0.997916i \(0.520552\pi\)
\(294\) 0.0752307 0.00438754
\(295\) −13.7147 −0.798498
\(296\) 4.89972 0.284791
\(297\) 0.942362 0.0546814
\(298\) −17.7974 −1.03098
\(299\) 3.39687 0.196446
\(300\) −0.208929 −0.0120625
\(301\) 11.0838 0.638862
\(302\) −12.7759 −0.735171
\(303\) −0.822018 −0.0472237
\(304\) 1.33047 0.0763075
\(305\) 26.6359 1.52517
\(306\) −15.3336 −0.876564
\(307\) 9.90028 0.565039 0.282519 0.959262i \(-0.408830\pi\)
0.282519 + 0.959262i \(0.408830\pi\)
\(308\) −2.08969 −0.119071
\(309\) 0.703180 0.0400025
\(310\) 5.72263 0.325023
\(311\) 17.0258 0.965446 0.482723 0.875773i \(-0.339648\pi\)
0.482723 + 0.875773i \(0.339648\pi\)
\(312\) −0.263469 −0.0149160
\(313\) 20.4525 1.15604 0.578022 0.816021i \(-0.303825\pi\)
0.578022 + 0.816021i \(0.303825\pi\)
\(314\) 6.02046 0.339754
\(315\) −8.35049 −0.470497
\(316\) −10.3141 −0.580213
\(317\) −15.2743 −0.857888 −0.428944 0.903331i \(-0.641114\pi\)
−0.428944 + 0.903331i \(0.641114\pi\)
\(318\) −0.0697533 −0.00391157
\(319\) −2.01740 −0.112953
\(320\) −2.78876 −0.155896
\(321\) −1.35959 −0.0758850
\(322\) −0.969938 −0.0540525
\(323\) −6.81313 −0.379093
\(324\) 8.94910 0.497172
\(325\) −9.72608 −0.539506
\(326\) 10.9339 0.605571
\(327\) 1.43483 0.0793464
\(328\) 7.97456 0.440321
\(329\) 0.588653 0.0324535
\(330\) −0.438417 −0.0241340
\(331\) 21.2142 1.16604 0.583020 0.812458i \(-0.301871\pi\)
0.583020 + 0.812458i \(0.301871\pi\)
\(332\) −12.9099 −0.708521
\(333\) 14.6714 0.803990
\(334\) 14.8961 0.815077
\(335\) 44.5363 2.43328
\(336\) 0.0752307 0.00410417
\(337\) 10.7870 0.587607 0.293803 0.955866i \(-0.405079\pi\)
0.293803 + 0.955866i \(0.405079\pi\)
\(338\) 0.734957 0.0399764
\(339\) −0.630215 −0.0342286
\(340\) 14.2808 0.774488
\(341\) 4.28811 0.232214
\(342\) 3.98387 0.215423
\(343\) −1.00000 −0.0539949
\(344\) 11.0838 0.597601
\(345\) −0.203493 −0.0109557
\(346\) −22.4647 −1.20771
\(347\) −11.8548 −0.636398 −0.318199 0.948024i \(-0.603078\pi\)
−0.318199 + 0.948024i \(0.603078\pi\)
\(348\) 0.0726284 0.00389329
\(349\) −15.9229 −0.852335 −0.426168 0.904644i \(-0.640137\pi\)
−0.426168 + 0.904644i \(0.640137\pi\)
\(350\) 2.77718 0.148446
\(351\) −1.57932 −0.0842980
\(352\) −2.08969 −0.111381
\(353\) −12.9708 −0.690365 −0.345183 0.938536i \(-0.612183\pi\)
−0.345183 + 0.938536i \(0.612183\pi\)
\(354\) 0.369972 0.0196638
\(355\) 17.1006 0.907607
\(356\) 12.4413 0.659389
\(357\) −0.385246 −0.0203894
\(358\) 5.83832 0.308565
\(359\) −5.07753 −0.267982 −0.133991 0.990983i \(-0.542779\pi\)
−0.133991 + 0.990983i \(0.542779\pi\)
\(360\) −8.35049 −0.440110
\(361\) −17.2299 −0.906835
\(362\) −23.4272 −1.23130
\(363\) 0.499020 0.0261918
\(364\) 3.50215 0.183562
\(365\) −32.2699 −1.68908
\(366\) −0.718540 −0.0375587
\(367\) −10.3721 −0.541420 −0.270710 0.962661i \(-0.587258\pi\)
−0.270710 + 0.962661i \(0.587258\pi\)
\(368\) −0.969938 −0.0505615
\(369\) 23.8785 1.24307
\(370\) −13.6641 −0.710365
\(371\) 0.927192 0.0481374
\(372\) −0.154376 −0.00800401
\(373\) −12.8516 −0.665431 −0.332716 0.943027i \(-0.607965\pi\)
−0.332716 + 0.943027i \(0.607965\pi\)
\(374\) 10.7010 0.553336
\(375\) −0.466349 −0.0240822
\(376\) 0.588653 0.0303575
\(377\) 3.38101 0.174131
\(378\) 0.450958 0.0231948
\(379\) 14.8366 0.762107 0.381054 0.924553i \(-0.375561\pi\)
0.381054 + 0.924553i \(0.375561\pi\)
\(380\) −3.71035 −0.190337
\(381\) −0.158624 −0.00812653
\(382\) −7.68734 −0.393318
\(383\) −30.9554 −1.58175 −0.790874 0.611979i \(-0.790374\pi\)
−0.790874 + 0.611979i \(0.790374\pi\)
\(384\) 0.0752307 0.00383910
\(385\) 5.82763 0.297004
\(386\) 13.1503 0.669332
\(387\) 33.1888 1.68708
\(388\) −7.10428 −0.360665
\(389\) −1.32860 −0.0673627 −0.0336814 0.999433i \(-0.510723\pi\)
−0.0336814 + 0.999433i \(0.510723\pi\)
\(390\) 0.734751 0.0372056
\(391\) 4.96692 0.251188
\(392\) −1.00000 −0.0505076
\(393\) 1.45771 0.0735317
\(394\) 8.34788 0.420560
\(395\) 28.7635 1.44725
\(396\) −6.25724 −0.314438
\(397\) 23.5864 1.18377 0.591884 0.806023i \(-0.298384\pi\)
0.591884 + 0.806023i \(0.298384\pi\)
\(398\) −4.48691 −0.224908
\(399\) 0.100092 0.00501086
\(400\) 2.77718 0.138859
\(401\) 30.4903 1.52261 0.761306 0.648393i \(-0.224559\pi\)
0.761306 + 0.648393i \(0.224559\pi\)
\(402\) −1.20143 −0.0599219
\(403\) −7.18653 −0.357986
\(404\) 10.9266 0.543620
\(405\) −24.9569 −1.24012
\(406\) −0.965409 −0.0479125
\(407\) −10.2389 −0.507523
\(408\) −0.385246 −0.0190725
\(409\) 15.5739 0.770081 0.385040 0.922900i \(-0.374187\pi\)
0.385040 + 0.922900i \(0.374187\pi\)
\(410\) −22.2391 −1.09831
\(411\) 0.513917 0.0253496
\(412\) −9.34699 −0.460493
\(413\) −4.91784 −0.241991
\(414\) −2.90432 −0.142740
\(415\) 36.0025 1.76729
\(416\) 3.50215 0.171707
\(417\) −1.09496 −0.0536202
\(418\) −2.78026 −0.135987
\(419\) 15.6330 0.763722 0.381861 0.924220i \(-0.375283\pi\)
0.381861 + 0.924220i \(0.375283\pi\)
\(420\) −0.209800 −0.0102372
\(421\) −22.5825 −1.10060 −0.550301 0.834966i \(-0.685487\pi\)
−0.550301 + 0.834966i \(0.685487\pi\)
\(422\) 15.2276 0.741270
\(423\) 1.76263 0.0857019
\(424\) 0.927192 0.0450284
\(425\) −14.2215 −0.689846
\(426\) −0.461313 −0.0223507
\(427\) 9.55117 0.462213
\(428\) 18.0723 0.873558
\(429\) 0.550568 0.0265817
\(430\) −30.9102 −1.49062
\(431\) 1.00000 0.0481683
\(432\) 0.450958 0.0216967
\(433\) 0.103257 0.00496222 0.00248111 0.999997i \(-0.499210\pi\)
0.00248111 + 0.999997i \(0.499210\pi\)
\(434\) 2.05203 0.0985008
\(435\) −0.202543 −0.00971120
\(436\) −19.0724 −0.913404
\(437\) −1.29047 −0.0617315
\(438\) 0.870526 0.0415953
\(439\) −19.2033 −0.916521 −0.458261 0.888818i \(-0.651527\pi\)
−0.458261 + 0.888818i \(0.651527\pi\)
\(440\) 5.82763 0.277822
\(441\) −2.99434 −0.142588
\(442\) −17.9340 −0.853034
\(443\) 17.9595 0.853283 0.426641 0.904421i \(-0.359697\pi\)
0.426641 + 0.904421i \(0.359697\pi\)
\(444\) 0.368609 0.0174934
\(445\) −34.6959 −1.64474
\(446\) −8.97511 −0.424984
\(447\) −1.33891 −0.0633283
\(448\) −1.00000 −0.0472456
\(449\) −21.5460 −1.01682 −0.508410 0.861115i \(-0.669766\pi\)
−0.508410 + 0.861115i \(0.669766\pi\)
\(450\) 8.31581 0.392011
\(451\) −16.6643 −0.784693
\(452\) 8.37711 0.394026
\(453\) −0.961140 −0.0451583
\(454\) −14.0786 −0.660739
\(455\) −9.76665 −0.457867
\(456\) 0.100092 0.00468723
\(457\) −10.5713 −0.494504 −0.247252 0.968951i \(-0.579528\pi\)
−0.247252 + 0.968951i \(0.579528\pi\)
\(458\) −23.3654 −1.09180
\(459\) −2.30929 −0.107789
\(460\) 2.70492 0.126118
\(461\) −21.8409 −1.01723 −0.508616 0.860993i \(-0.669843\pi\)
−0.508616 + 0.860993i \(0.669843\pi\)
\(462\) −0.157209 −0.00731400
\(463\) −31.2532 −1.45246 −0.726229 0.687453i \(-0.758729\pi\)
−0.726229 + 0.687453i \(0.758729\pi\)
\(464\) −0.965409 −0.0448180
\(465\) 0.430517 0.0199647
\(466\) 20.1438 0.933142
\(467\) −1.90340 −0.0880790 −0.0440395 0.999030i \(-0.514023\pi\)
−0.0440395 + 0.999030i \(0.514023\pi\)
\(468\) 10.4866 0.484744
\(469\) 15.9700 0.737424
\(470\) −1.64161 −0.0757219
\(471\) 0.452924 0.0208696
\(472\) −4.91784 −0.226362
\(473\) −23.1618 −1.06498
\(474\) −0.775936 −0.0356399
\(475\) 3.69494 0.169535
\(476\) 5.12086 0.234714
\(477\) 2.77633 0.127119
\(478\) −17.0756 −0.781019
\(479\) −19.3690 −0.884991 −0.442496 0.896771i \(-0.645907\pi\)
−0.442496 + 0.896771i \(0.645907\pi\)
\(480\) −0.209800 −0.00957602
\(481\) 17.1595 0.782408
\(482\) 16.5972 0.755982
\(483\) −0.0729691 −0.00332021
\(484\) −6.63321 −0.301509
\(485\) 19.8121 0.899623
\(486\) 2.02612 0.0919067
\(487\) 37.0416 1.67852 0.839258 0.543734i \(-0.182990\pi\)
0.839258 + 0.543734i \(0.182990\pi\)
\(488\) 9.55117 0.432361
\(489\) 0.822562 0.0371975
\(490\) 2.78876 0.125983
\(491\) 28.0123 1.26418 0.632088 0.774896i \(-0.282198\pi\)
0.632088 + 0.774896i \(0.282198\pi\)
\(492\) 0.599931 0.0270470
\(493\) 4.94373 0.222654
\(494\) 4.65949 0.209640
\(495\) 17.4499 0.784316
\(496\) 2.05203 0.0921390
\(497\) 6.13198 0.275057
\(498\) −0.971217 −0.0435213
\(499\) −18.2228 −0.815765 −0.407882 0.913034i \(-0.633733\pi\)
−0.407882 + 0.913034i \(0.633733\pi\)
\(500\) 6.19892 0.277224
\(501\) 1.12064 0.0500666
\(502\) 20.4571 0.913045
\(503\) −17.8430 −0.795579 −0.397789 0.917477i \(-0.630223\pi\)
−0.397789 + 0.917477i \(0.630223\pi\)
\(504\) −2.99434 −0.133379
\(505\) −30.4718 −1.35598
\(506\) 2.02687 0.0901052
\(507\) 0.0552913 0.00245557
\(508\) 2.10850 0.0935494
\(509\) 37.1841 1.64816 0.824078 0.566476i \(-0.191694\pi\)
0.824078 + 0.566476i \(0.191694\pi\)
\(510\) 1.07436 0.0475734
\(511\) −11.5714 −0.511890
\(512\) −1.00000 −0.0441942
\(513\) 0.599985 0.0264900
\(514\) −24.1486 −1.06515
\(515\) 26.0665 1.14863
\(516\) 0.833844 0.0367080
\(517\) −1.23010 −0.0540998
\(518\) −4.89972 −0.215281
\(519\) −1.69004 −0.0741844
\(520\) −9.76665 −0.428296
\(521\) −15.4721 −0.677844 −0.338922 0.940814i \(-0.610062\pi\)
−0.338922 + 0.940814i \(0.610062\pi\)
\(522\) −2.89076 −0.126525
\(523\) −3.16873 −0.138559 −0.0692794 0.997597i \(-0.522070\pi\)
−0.0692794 + 0.997597i \(0.522070\pi\)
\(524\) −19.3765 −0.846468
\(525\) 0.208929 0.00911840
\(526\) −5.53582 −0.241373
\(527\) −10.5082 −0.457744
\(528\) −0.157209 −0.00684162
\(529\) −22.0592 −0.959097
\(530\) −2.58572 −0.112316
\(531\) −14.7257 −0.639040
\(532\) −1.33047 −0.0576830
\(533\) 27.9281 1.20970
\(534\) 0.935969 0.0405033
\(535\) −50.3993 −2.17895
\(536\) 15.9700 0.689797
\(537\) 0.439221 0.0189538
\(538\) −9.23780 −0.398270
\(539\) 2.08969 0.0900092
\(540\) −1.25761 −0.0541191
\(541\) −17.6209 −0.757583 −0.378792 0.925482i \(-0.623660\pi\)
−0.378792 + 0.925482i \(0.623660\pi\)
\(542\) −28.4349 −1.22138
\(543\) −1.76244 −0.0756336
\(544\) 5.12086 0.219555
\(545\) 53.1884 2.27834
\(546\) 0.263469 0.0112754
\(547\) 36.6025 1.56501 0.782505 0.622644i \(-0.213942\pi\)
0.782505 + 0.622644i \(0.213942\pi\)
\(548\) −6.83121 −0.291815
\(549\) 28.5994 1.22059
\(550\) −5.80343 −0.247459
\(551\) −1.28444 −0.0547192
\(552\) −0.0729691 −0.00310577
\(553\) 10.3141 0.438600
\(554\) −1.95353 −0.0829975
\(555\) −1.02796 −0.0436346
\(556\) 14.5546 0.617255
\(557\) 6.68777 0.283370 0.141685 0.989912i \(-0.454748\pi\)
0.141685 + 0.989912i \(0.454748\pi\)
\(558\) 6.14449 0.260117
\(559\) 38.8172 1.64179
\(560\) 2.78876 0.117847
\(561\) 0.805043 0.0339890
\(562\) 12.9762 0.547367
\(563\) −8.91386 −0.375674 −0.187837 0.982200i \(-0.560148\pi\)
−0.187837 + 0.982200i \(0.560148\pi\)
\(564\) 0.0442848 0.00186473
\(565\) −23.3617 −0.982836
\(566\) −0.181693 −0.00763711
\(567\) −8.94910 −0.375827
\(568\) 6.13198 0.257292
\(569\) 31.9949 1.34130 0.670648 0.741776i \(-0.266016\pi\)
0.670648 + 0.741776i \(0.266016\pi\)
\(570\) −0.279132 −0.0116916
\(571\) 40.6907 1.70285 0.851426 0.524475i \(-0.175738\pi\)
0.851426 + 0.524475i \(0.175738\pi\)
\(572\) −7.31840 −0.305998
\(573\) −0.578323 −0.0241598
\(574\) −7.97456 −0.332852
\(575\) −2.69369 −0.112335
\(576\) −2.99434 −0.124764
\(577\) 27.9772 1.16471 0.582353 0.812936i \(-0.302132\pi\)
0.582353 + 0.812936i \(0.302132\pi\)
\(578\) −9.22323 −0.383636
\(579\) 0.989304 0.0411141
\(580\) 2.69229 0.111791
\(581\) 12.9099 0.535591
\(582\) −0.534460 −0.0221541
\(583\) −1.93754 −0.0802448
\(584\) −11.5714 −0.478829
\(585\) −29.2447 −1.20912
\(586\) 2.20882 0.0912457
\(587\) −24.9093 −1.02812 −0.514059 0.857755i \(-0.671859\pi\)
−0.514059 + 0.857755i \(0.671859\pi\)
\(588\) −0.0752307 −0.00310246
\(589\) 2.73016 0.112494
\(590\) 13.7147 0.564623
\(591\) 0.628016 0.0258331
\(592\) −4.89972 −0.201377
\(593\) 43.6980 1.79446 0.897232 0.441560i \(-0.145575\pi\)
0.897232 + 0.441560i \(0.145575\pi\)
\(594\) −0.942362 −0.0386656
\(595\) −14.2808 −0.585458
\(596\) 17.7974 0.729010
\(597\) −0.337553 −0.0138151
\(598\) −3.39687 −0.138908
\(599\) −32.1547 −1.31381 −0.656903 0.753975i \(-0.728134\pi\)
−0.656903 + 0.753975i \(0.728134\pi\)
\(600\) 0.208929 0.00852948
\(601\) −29.8922 −1.21933 −0.609664 0.792660i \(-0.708696\pi\)
−0.609664 + 0.792660i \(0.708696\pi\)
\(602\) −11.0838 −0.451744
\(603\) 47.8195 1.94736
\(604\) 12.7759 0.519844
\(605\) 18.4984 0.752067
\(606\) 0.822018 0.0333922
\(607\) −12.8160 −0.520186 −0.260093 0.965584i \(-0.583753\pi\)
−0.260093 + 0.965584i \(0.583753\pi\)
\(608\) −1.33047 −0.0539575
\(609\) −0.0726284 −0.00294305
\(610\) −26.6359 −1.07846
\(611\) 2.06155 0.0834014
\(612\) 15.3336 0.619824
\(613\) −36.8914 −1.49003 −0.745015 0.667048i \(-0.767558\pi\)
−0.745015 + 0.667048i \(0.767558\pi\)
\(614\) −9.90028 −0.399543
\(615\) −1.67306 −0.0674644
\(616\) 2.08969 0.0841959
\(617\) 47.1031 1.89630 0.948149 0.317827i \(-0.102953\pi\)
0.948149 + 0.317827i \(0.102953\pi\)
\(618\) −0.703180 −0.0282861
\(619\) −14.3723 −0.577672 −0.288836 0.957379i \(-0.593268\pi\)
−0.288836 + 0.957379i \(0.593268\pi\)
\(620\) −5.72263 −0.229826
\(621\) −0.437401 −0.0175523
\(622\) −17.0258 −0.682673
\(623\) −12.4413 −0.498451
\(624\) 0.263469 0.0105472
\(625\) −31.1732 −1.24693
\(626\) −20.4525 −0.817447
\(627\) −0.209161 −0.00835308
\(628\) −6.02046 −0.240243
\(629\) 25.0908 1.00044
\(630\) 8.35049 0.332692
\(631\) 29.1896 1.16202 0.581009 0.813897i \(-0.302658\pi\)
0.581009 + 0.813897i \(0.302658\pi\)
\(632\) 10.3141 0.410273
\(633\) 1.14559 0.0455330
\(634\) 15.2743 0.606618
\(635\) −5.88009 −0.233344
\(636\) 0.0697533 0.00276590
\(637\) −3.50215 −0.138760
\(638\) 2.01740 0.0798698
\(639\) 18.3612 0.726360
\(640\) 2.78876 0.110235
\(641\) −3.11595 −0.123073 −0.0615364 0.998105i \(-0.519600\pi\)
−0.0615364 + 0.998105i \(0.519600\pi\)
\(642\) 1.35959 0.0536588
\(643\) −31.7405 −1.25172 −0.625861 0.779935i \(-0.715252\pi\)
−0.625861 + 0.779935i \(0.715252\pi\)
\(644\) 0.969938 0.0382209
\(645\) −2.32539 −0.0915622
\(646\) 6.81313 0.268059
\(647\) −4.86494 −0.191261 −0.0956304 0.995417i \(-0.530487\pi\)
−0.0956304 + 0.995417i \(0.530487\pi\)
\(648\) −8.94910 −0.351554
\(649\) 10.2767 0.403397
\(650\) 9.72608 0.381488
\(651\) 0.154376 0.00605047
\(652\) −10.9339 −0.428203
\(653\) 45.8162 1.79293 0.896463 0.443118i \(-0.146128\pi\)
0.896463 + 0.443118i \(0.146128\pi\)
\(654\) −1.43483 −0.0561064
\(655\) 54.0365 2.11138
\(656\) −7.97456 −0.311354
\(657\) −34.6488 −1.35178
\(658\) −0.588653 −0.0229481
\(659\) −22.4375 −0.874043 −0.437021 0.899451i \(-0.643967\pi\)
−0.437021 + 0.899451i \(0.643967\pi\)
\(660\) 0.438417 0.0170654
\(661\) 47.1578 1.83423 0.917113 0.398628i \(-0.130513\pi\)
0.917113 + 0.398628i \(0.130513\pi\)
\(662\) −21.2142 −0.824515
\(663\) −1.34919 −0.0523981
\(664\) 12.9099 0.501000
\(665\) 3.71035 0.143881
\(666\) −14.6714 −0.568506
\(667\) 0.936387 0.0362571
\(668\) −14.8961 −0.576346
\(669\) −0.675204 −0.0261049
\(670\) −44.5363 −1.72059
\(671\) −19.9590 −0.770507
\(672\) −0.0752307 −0.00290209
\(673\) −34.4188 −1.32675 −0.663374 0.748288i \(-0.730876\pi\)
−0.663374 + 0.748288i \(0.730876\pi\)
\(674\) −10.7870 −0.415501
\(675\) 1.25239 0.0482045
\(676\) −0.734957 −0.0282676
\(677\) −41.5738 −1.59781 −0.798906 0.601456i \(-0.794587\pi\)
−0.798906 + 0.601456i \(0.794587\pi\)
\(678\) 0.630215 0.0242033
\(679\) 7.10428 0.272637
\(680\) −14.2808 −0.547646
\(681\) −1.05914 −0.0405863
\(682\) −4.28811 −0.164200
\(683\) −27.1052 −1.03715 −0.518576 0.855031i \(-0.673538\pi\)
−0.518576 + 0.855031i \(0.673538\pi\)
\(684\) −3.98387 −0.152327
\(685\) 19.0506 0.727886
\(686\) 1.00000 0.0381802
\(687\) −1.75780 −0.0670641
\(688\) −11.0838 −0.422567
\(689\) 3.24717 0.123707
\(690\) 0.203493 0.00774685
\(691\) 6.57740 0.250216 0.125108 0.992143i \(-0.460072\pi\)
0.125108 + 0.992143i \(0.460072\pi\)
\(692\) 22.4647 0.853981
\(693\) 6.25724 0.237693
\(694\) 11.8548 0.450001
\(695\) −40.5894 −1.53964
\(696\) −0.0726284 −0.00275297
\(697\) 40.8366 1.54680
\(698\) 15.9229 0.602692
\(699\) 1.51543 0.0573188
\(700\) −2.77718 −0.104967
\(701\) 21.3133 0.804992 0.402496 0.915422i \(-0.368143\pi\)
0.402496 + 0.915422i \(0.368143\pi\)
\(702\) 1.57932 0.0596077
\(703\) −6.51891 −0.245866
\(704\) 2.08969 0.0787581
\(705\) −0.123500 −0.00465126
\(706\) 12.9708 0.488162
\(707\) −10.9266 −0.410938
\(708\) −0.369972 −0.0139044
\(709\) 35.8331 1.34574 0.672870 0.739761i \(-0.265062\pi\)
0.672870 + 0.739761i \(0.265062\pi\)
\(710\) −17.1006 −0.641775
\(711\) 30.8839 1.15824
\(712\) −12.4413 −0.466258
\(713\) −1.99035 −0.0745390
\(714\) 0.385246 0.0144175
\(715\) 20.4092 0.763262
\(716\) −5.83832 −0.218188
\(717\) −1.28461 −0.0479745
\(718\) 5.07753 0.189492
\(719\) 42.4736 1.58400 0.791998 0.610524i \(-0.209041\pi\)
0.791998 + 0.610524i \(0.209041\pi\)
\(720\) 8.35049 0.311204
\(721\) 9.34699 0.348100
\(722\) 17.2299 0.641229
\(723\) 1.24862 0.0464366
\(724\) 23.4272 0.870664
\(725\) −2.68111 −0.0995740
\(726\) −0.499020 −0.0185204
\(727\) 47.3668 1.75674 0.878368 0.477985i \(-0.158633\pi\)
0.878368 + 0.477985i \(0.158633\pi\)
\(728\) −3.50215 −0.129798
\(729\) −26.6949 −0.988698
\(730\) 32.2699 1.19436
\(731\) 56.7588 2.09930
\(732\) 0.718540 0.0265580
\(733\) −9.38516 −0.346649 −0.173324 0.984865i \(-0.555451\pi\)
−0.173324 + 0.984865i \(0.555451\pi\)
\(734\) 10.3721 0.382842
\(735\) 0.209800 0.00773860
\(736\) 0.969938 0.0357524
\(737\) −33.3722 −1.22928
\(738\) −23.8785 −0.878981
\(739\) −23.8782 −0.878376 −0.439188 0.898395i \(-0.644734\pi\)
−0.439188 + 0.898395i \(0.644734\pi\)
\(740\) 13.6641 0.502304
\(741\) 0.350537 0.0128773
\(742\) −0.927192 −0.0340383
\(743\) 41.8944 1.53696 0.768479 0.639875i \(-0.221014\pi\)
0.768479 + 0.639875i \(0.221014\pi\)
\(744\) 0.154376 0.00565969
\(745\) −49.6327 −1.81840
\(746\) 12.8516 0.470531
\(747\) 38.6565 1.41437
\(748\) −10.7010 −0.391267
\(749\) −18.0723 −0.660348
\(750\) 0.466349 0.0170287
\(751\) 4.05812 0.148083 0.0740414 0.997255i \(-0.476410\pi\)
0.0740414 + 0.997255i \(0.476410\pi\)
\(752\) −0.588653 −0.0214660
\(753\) 1.53900 0.0560843
\(754\) −3.38101 −0.123129
\(755\) −35.6289 −1.29667
\(756\) −0.450958 −0.0164012
\(757\) 15.7867 0.573779 0.286890 0.957964i \(-0.407379\pi\)
0.286890 + 0.957964i \(0.407379\pi\)
\(758\) −14.8366 −0.538891
\(759\) 0.152483 0.00553477
\(760\) 3.71035 0.134589
\(761\) 10.8179 0.392149 0.196075 0.980589i \(-0.437181\pi\)
0.196075 + 0.980589i \(0.437181\pi\)
\(762\) 0.158624 0.00574633
\(763\) 19.0724 0.690468
\(764\) 7.68734 0.278118
\(765\) −42.7617 −1.54605
\(766\) 30.9554 1.11846
\(767\) −17.2230 −0.621886
\(768\) −0.0752307 −0.00271465
\(769\) −35.7110 −1.28777 −0.643886 0.765121i \(-0.722679\pi\)
−0.643886 + 0.765121i \(0.722679\pi\)
\(770\) −5.82763 −0.210013
\(771\) −1.81672 −0.0654275
\(772\) −13.1503 −0.473289
\(773\) 23.0290 0.828297 0.414149 0.910209i \(-0.364079\pi\)
0.414149 + 0.910209i \(0.364079\pi\)
\(774\) −33.1888 −1.19295
\(775\) 5.69886 0.204709
\(776\) 7.10428 0.255029
\(777\) −0.368609 −0.0132238
\(778\) 1.32860 0.0476326
\(779\) −10.6099 −0.380138
\(780\) −0.734751 −0.0263083
\(781\) −12.8139 −0.458518
\(782\) −4.96692 −0.177617
\(783\) −0.435359 −0.0155585
\(784\) 1.00000 0.0357143
\(785\) 16.7896 0.599247
\(786\) −1.45771 −0.0519948
\(787\) 34.5969 1.23324 0.616622 0.787259i \(-0.288501\pi\)
0.616622 + 0.787259i \(0.288501\pi\)
\(788\) −8.34788 −0.297381
\(789\) −0.416464 −0.0148265
\(790\) −28.7635 −1.02336
\(791\) −8.37711 −0.297856
\(792\) 6.25724 0.222341
\(793\) 33.4496 1.18783
\(794\) −23.5864 −0.837050
\(795\) −0.194525 −0.00689909
\(796\) 4.48691 0.159034
\(797\) 50.2237 1.77901 0.889507 0.456921i \(-0.151048\pi\)
0.889507 + 0.456921i \(0.151048\pi\)
\(798\) −0.100092 −0.00354321
\(799\) 3.01441 0.106642
\(800\) −2.77718 −0.0981880
\(801\) −37.2536 −1.31629
\(802\) −30.4903 −1.07665
\(803\) 24.1807 0.853317
\(804\) 1.20143 0.0423712
\(805\) −2.70492 −0.0953360
\(806\) 7.18653 0.253135
\(807\) −0.694966 −0.0244640
\(808\) −10.9266 −0.384398
\(809\) −8.12416 −0.285630 −0.142815 0.989749i \(-0.545615\pi\)
−0.142815 + 0.989749i \(0.545615\pi\)
\(810\) 24.9569 0.876895
\(811\) −31.1017 −1.09213 −0.546064 0.837743i \(-0.683875\pi\)
−0.546064 + 0.837743i \(0.683875\pi\)
\(812\) 0.965409 0.0338792
\(813\) −2.13917 −0.0750241
\(814\) 10.2389 0.358873
\(815\) 30.4919 1.06808
\(816\) 0.385246 0.0134863
\(817\) −14.7467 −0.515921
\(818\) −15.5739 −0.544529
\(819\) −10.4866 −0.366432
\(820\) 22.2391 0.776623
\(821\) −14.4847 −0.505521 −0.252761 0.967529i \(-0.581338\pi\)
−0.252761 + 0.967529i \(0.581338\pi\)
\(822\) −0.513917 −0.0179249
\(823\) −11.7369 −0.409123 −0.204561 0.978854i \(-0.565577\pi\)
−0.204561 + 0.978854i \(0.565577\pi\)
\(824\) 9.34699 0.325618
\(825\) −0.436596 −0.0152003
\(826\) 4.91784 0.171113
\(827\) 2.23957 0.0778774 0.0389387 0.999242i \(-0.487602\pi\)
0.0389387 + 0.999242i \(0.487602\pi\)
\(828\) 2.90432 0.100932
\(829\) −51.0609 −1.77342 −0.886709 0.462329i \(-0.847014\pi\)
−0.886709 + 0.462329i \(0.847014\pi\)
\(830\) −36.0025 −1.24966
\(831\) −0.146965 −0.00509817
\(832\) −3.50215 −0.121415
\(833\) −5.12086 −0.177427
\(834\) 1.09496 0.0379152
\(835\) 41.5415 1.43760
\(836\) 2.78026 0.0961573
\(837\) 0.925381 0.0319859
\(838\) −15.6330 −0.540033
\(839\) 8.82065 0.304523 0.152261 0.988340i \(-0.451344\pi\)
0.152261 + 0.988340i \(0.451344\pi\)
\(840\) 0.209800 0.00723879
\(841\) −28.0680 −0.967862
\(842\) 22.5825 0.778243
\(843\) 0.976207 0.0336224
\(844\) −15.2276 −0.524157
\(845\) 2.04962 0.0705090
\(846\) −1.76263 −0.0606004
\(847\) 6.63321 0.227920
\(848\) −0.927192 −0.0318399
\(849\) −0.0136688 −0.000469114 0
\(850\) 14.2215 0.487794
\(851\) 4.75243 0.162911
\(852\) 0.461313 0.0158043
\(853\) 3.92485 0.134384 0.0671922 0.997740i \(-0.478596\pi\)
0.0671922 + 0.997740i \(0.478596\pi\)
\(854\) −9.55117 −0.326834
\(855\) 11.1101 0.379956
\(856\) −18.0723 −0.617699
\(857\) 5.26994 0.180018 0.0900089 0.995941i \(-0.471310\pi\)
0.0900089 + 0.995941i \(0.471310\pi\)
\(858\) −0.550568 −0.0187961
\(859\) −40.2111 −1.37198 −0.685992 0.727609i \(-0.740632\pi\)
−0.685992 + 0.727609i \(0.740632\pi\)
\(860\) 30.9102 1.05403
\(861\) −0.599931 −0.0204456
\(862\) −1.00000 −0.0340601
\(863\) −25.0446 −0.852527 −0.426264 0.904599i \(-0.640170\pi\)
−0.426264 + 0.904599i \(0.640170\pi\)
\(864\) −0.450958 −0.0153419
\(865\) −62.6488 −2.13012
\(866\) −0.103257 −0.00350882
\(867\) −0.693869 −0.0235650
\(868\) −2.05203 −0.0696506
\(869\) −21.5532 −0.731144
\(870\) 0.202543 0.00686685
\(871\) 55.9291 1.89509
\(872\) 19.0724 0.645874
\(873\) 21.2726 0.719970
\(874\) 1.29047 0.0436508
\(875\) −6.19892 −0.209562
\(876\) −0.870526 −0.0294124
\(877\) 5.84031 0.197213 0.0986066 0.995126i \(-0.468561\pi\)
0.0986066 + 0.995126i \(0.468561\pi\)
\(878\) 19.2033 0.648078
\(879\) 0.166171 0.00560482
\(880\) −5.82763 −0.196450
\(881\) −28.8215 −0.971020 −0.485510 0.874231i \(-0.661366\pi\)
−0.485510 + 0.874231i \(0.661366\pi\)
\(882\) 2.99434 0.100825
\(883\) 7.79841 0.262437 0.131219 0.991353i \(-0.458111\pi\)
0.131219 + 0.991353i \(0.458111\pi\)
\(884\) 17.9340 0.603186
\(885\) 1.03176 0.0346823
\(886\) −17.9595 −0.603362
\(887\) 43.1409 1.44853 0.724265 0.689522i \(-0.242179\pi\)
0.724265 + 0.689522i \(0.242179\pi\)
\(888\) −0.368609 −0.0123697
\(889\) −2.10850 −0.0707167
\(890\) 34.6959 1.16301
\(891\) 18.7008 0.626501
\(892\) 8.97511 0.300509
\(893\) −0.783184 −0.0262082
\(894\) 1.33891 0.0447799
\(895\) 16.2817 0.544236
\(896\) 1.00000 0.0334077
\(897\) −0.255549 −0.00853252
\(898\) 21.5460 0.719000
\(899\) −1.98105 −0.0660718
\(900\) −8.31581 −0.277194
\(901\) 4.74802 0.158180
\(902\) 16.6643 0.554862
\(903\) −0.833844 −0.0277486
\(904\) −8.37711 −0.278618
\(905\) −65.3327 −2.17173
\(906\) 0.961140 0.0319317
\(907\) −29.1776 −0.968826 −0.484413 0.874839i \(-0.660967\pi\)
−0.484413 + 0.874839i \(0.660967\pi\)
\(908\) 14.0786 0.467213
\(909\) −32.7181 −1.08519
\(910\) 9.76665 0.323761
\(911\) 28.9357 0.958683 0.479341 0.877629i \(-0.340876\pi\)
0.479341 + 0.877629i \(0.340876\pi\)
\(912\) −0.100092 −0.00331437
\(913\) −26.9776 −0.892827
\(914\) 10.5713 0.349667
\(915\) −2.00384 −0.0662448
\(916\) 23.3654 0.772016
\(917\) 19.3765 0.639870
\(918\) 2.30929 0.0762181
\(919\) 6.48223 0.213829 0.106914 0.994268i \(-0.465903\pi\)
0.106914 + 0.994268i \(0.465903\pi\)
\(920\) −2.70492 −0.0891787
\(921\) −0.744804 −0.0245421
\(922\) 21.8409 0.719292
\(923\) 21.4751 0.706862
\(924\) 0.157209 0.00517178
\(925\) −13.6074 −0.447408
\(926\) 31.2532 1.02704
\(927\) 27.9881 0.919249
\(928\) 0.965409 0.0316911
\(929\) 22.3218 0.732356 0.366178 0.930545i \(-0.380666\pi\)
0.366178 + 0.930545i \(0.380666\pi\)
\(930\) −0.430517 −0.0141172
\(931\) 1.33047 0.0436043
\(932\) −20.1438 −0.659831
\(933\) −1.28086 −0.0419336
\(934\) 1.90340 0.0622813
\(935\) 29.8425 0.975954
\(936\) −10.4866 −0.342766
\(937\) 28.6441 0.935761 0.467881 0.883792i \(-0.345018\pi\)
0.467881 + 0.883792i \(0.345018\pi\)
\(938\) −15.9700 −0.521437
\(939\) −1.53866 −0.0502122
\(940\) 1.64161 0.0535435
\(941\) −7.70635 −0.251220 −0.125610 0.992080i \(-0.540089\pi\)
−0.125610 + 0.992080i \(0.540089\pi\)
\(942\) −0.452924 −0.0147570
\(943\) 7.73482 0.251881
\(944\) 4.91784 0.160062
\(945\) 1.25761 0.0409102
\(946\) 23.1618 0.753054
\(947\) −12.4639 −0.405022 −0.202511 0.979280i \(-0.564910\pi\)
−0.202511 + 0.979280i \(0.564910\pi\)
\(948\) 0.775936 0.0252012
\(949\) −40.5249 −1.31549
\(950\) −3.69494 −0.119880
\(951\) 1.14909 0.0372619
\(952\) −5.12086 −0.165968
\(953\) 25.7400 0.833802 0.416901 0.908952i \(-0.363116\pi\)
0.416901 + 0.908952i \(0.363116\pi\)
\(954\) −2.77633 −0.0898870
\(955\) −21.4381 −0.693721
\(956\) 17.0756 0.552264
\(957\) 0.151771 0.00490605
\(958\) 19.3690 0.625783
\(959\) 6.83121 0.220591
\(960\) 0.209800 0.00677127
\(961\) −26.7892 −0.864166
\(962\) −17.1595 −0.553246
\(963\) −54.1146 −1.74382
\(964\) −16.5972 −0.534560
\(965\) 36.6730 1.18054
\(966\) 0.0729691 0.00234774
\(967\) 11.1867 0.359740 0.179870 0.983690i \(-0.442432\pi\)
0.179870 + 0.983690i \(0.442432\pi\)
\(968\) 6.63321 0.213199
\(969\) 0.512557 0.0164657
\(970\) −19.8121 −0.636129
\(971\) −3.74736 −0.120258 −0.0601292 0.998191i \(-0.519151\pi\)
−0.0601292 + 0.998191i \(0.519151\pi\)
\(972\) −2.02612 −0.0649879
\(973\) −14.5546 −0.466601
\(974\) −37.0416 −1.18689
\(975\) 0.731699 0.0234331
\(976\) −9.55117 −0.305725
\(977\) −1.71856 −0.0549817 −0.0274909 0.999622i \(-0.508752\pi\)
−0.0274909 + 0.999622i \(0.508752\pi\)
\(978\) −0.822562 −0.0263026
\(979\) 25.9985 0.830915
\(980\) −2.78876 −0.0890836
\(981\) 57.1094 1.82336
\(982\) −28.0123 −0.893908
\(983\) 9.38753 0.299416 0.149708 0.988730i \(-0.452167\pi\)
0.149708 + 0.988730i \(0.452167\pi\)
\(984\) −0.599931 −0.0191251
\(985\) 23.2802 0.741769
\(986\) −4.94373 −0.157440
\(987\) −0.0442848 −0.00140960
\(988\) −4.65949 −0.148238
\(989\) 10.7506 0.341850
\(990\) −17.4499 −0.554595
\(991\) −31.3863 −0.997020 −0.498510 0.866884i \(-0.666119\pi\)
−0.498510 + 0.866884i \(0.666119\pi\)
\(992\) −2.05203 −0.0651521
\(993\) −1.59596 −0.0506463
\(994\) −6.13198 −0.194495
\(995\) −12.5129 −0.396686
\(996\) 0.971217 0.0307742
\(997\) −42.1729 −1.33563 −0.667814 0.744328i \(-0.732770\pi\)
−0.667814 + 0.744328i \(0.732770\pi\)
\(998\) 18.2228 0.576833
\(999\) −2.20957 −0.0699077
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 \(a_p\))