Properties

Label 6019.2.a.c.1.10
Level 6019
Weight 2
Character 6019.1
Self dual Yes
Analytic conductor 48.062
Analytic rank 1
Dimension 108
CM No

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Newspace parameters

Level: \( N \) = \( 6019 = 13 \cdot 463 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6019.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0619569766\)
Analytic rank: \(1\)
Dimension: \(108\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 6019.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.51181 q^{2}\) \(-2.99105 q^{3}\) \(+4.30921 q^{4}\) \(+1.76112 q^{5}\) \(+7.51295 q^{6}\) \(+3.89256 q^{7}\) \(-5.80031 q^{8}\) \(+5.94635 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.51181 q^{2}\) \(-2.99105 q^{3}\) \(+4.30921 q^{4}\) \(+1.76112 q^{5}\) \(+7.51295 q^{6}\) \(+3.89256 q^{7}\) \(-5.80031 q^{8}\) \(+5.94635 q^{9}\) \(-4.42360 q^{10}\) \(-5.42983 q^{11}\) \(-12.8890 q^{12}\) \(-1.00000 q^{13}\) \(-9.77739 q^{14}\) \(-5.26758 q^{15}\) \(+5.95087 q^{16}\) \(+3.49734 q^{17}\) \(-14.9361 q^{18}\) \(+4.03795 q^{19}\) \(+7.58902 q^{20}\) \(-11.6428 q^{21}\) \(+13.6387 q^{22}\) \(-6.04800 q^{23}\) \(+17.3490 q^{24}\) \(-1.89847 q^{25}\) \(+2.51181 q^{26}\) \(-8.81267 q^{27}\) \(+16.7739 q^{28}\) \(-9.38630 q^{29}\) \(+13.2312 q^{30}\) \(+6.27218 q^{31}\) \(-3.34687 q^{32}\) \(+16.2409 q^{33}\) \(-8.78468 q^{34}\) \(+6.85525 q^{35}\) \(+25.6241 q^{36}\) \(+7.54791 q^{37}\) \(-10.1426 q^{38}\) \(+2.99105 q^{39}\) \(-10.2150 q^{40}\) \(+9.87852 q^{41}\) \(+29.2446 q^{42}\) \(-5.32767 q^{43}\) \(-23.3983 q^{44}\) \(+10.4722 q^{45}\) \(+15.1914 q^{46}\) \(+8.51872 q^{47}\) \(-17.7993 q^{48}\) \(+8.15202 q^{49}\) \(+4.76859 q^{50}\) \(-10.4607 q^{51}\) \(-4.30921 q^{52}\) \(-6.65992 q^{53}\) \(+22.1358 q^{54}\) \(-9.56257 q^{55}\) \(-22.5780 q^{56}\) \(-12.0777 q^{57}\) \(+23.5767 q^{58}\) \(-4.16499 q^{59}\) \(-22.6991 q^{60}\) \(-15.3368 q^{61}\) \(-15.7545 q^{62}\) \(+23.1465 q^{63}\) \(-3.49503 q^{64}\) \(-1.76112 q^{65}\) \(-40.7941 q^{66}\) \(+3.15830 q^{67}\) \(+15.0708 q^{68}\) \(+18.0898 q^{69}\) \(-17.2191 q^{70}\) \(+10.8333 q^{71}\) \(-34.4907 q^{72}\) \(-2.84051 q^{73}\) \(-18.9590 q^{74}\) \(+5.67840 q^{75}\) \(+17.4004 q^{76}\) \(-21.1360 q^{77}\) \(-7.51295 q^{78}\) \(+9.78667 q^{79}\) \(+10.4802 q^{80}\) \(+8.52003 q^{81}\) \(-24.8130 q^{82}\) \(-2.31751 q^{83}\) \(-50.1714 q^{84}\) \(+6.15923 q^{85}\) \(+13.3821 q^{86}\) \(+28.0749 q^{87}\) \(+31.4947 q^{88}\) \(-13.4969 q^{89}\) \(-26.3043 q^{90}\) \(-3.89256 q^{91}\) \(-26.0621 q^{92}\) \(-18.7604 q^{93}\) \(-21.3974 q^{94}\) \(+7.11130 q^{95}\) \(+10.0106 q^{96}\) \(-12.2652 q^{97}\) \(-20.4764 q^{98}\) \(-32.2877 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(108q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 95q^{4} \) \(\mathstrut -\mathstrut 40q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 79q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(108q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 95q^{4} \) \(\mathstrut -\mathstrut 40q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 79q^{9} \) \(\mathstrut -\mathstrut q^{10} \) \(\mathstrut -\mathstrut 45q^{11} \) \(\mathstrut -\mathstrut 6q^{12} \) \(\mathstrut -\mathstrut 108q^{13} \) \(\mathstrut -\mathstrut 31q^{14} \) \(\mathstrut -\mathstrut 39q^{15} \) \(\mathstrut +\mathstrut 73q^{16} \) \(\mathstrut +\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 35q^{18} \) \(\mathstrut -\mathstrut 19q^{19} \) \(\mathstrut -\mathstrut 79q^{20} \) \(\mathstrut -\mathstrut 72q^{21} \) \(\mathstrut -\mathstrut 26q^{23} \) \(\mathstrut -\mathstrut 23q^{24} \) \(\mathstrut +\mathstrut 92q^{25} \) \(\mathstrut +\mathstrut 11q^{26} \) \(\mathstrut +\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut 21q^{28} \) \(\mathstrut -\mathstrut 94q^{29} \) \(\mathstrut -\mathstrut 24q^{30} \) \(\mathstrut -\mathstrut 36q^{31} \) \(\mathstrut -\mathstrut 77q^{32} \) \(\mathstrut -\mathstrut 32q^{33} \) \(\mathstrut -\mathstrut 58q^{34} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut +\mathstrut 17q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut q^{39} \) \(\mathstrut -\mathstrut 4q^{40} \) \(\mathstrut -\mathstrut 68q^{41} \) \(\mathstrut -\mathstrut 11q^{42} \) \(\mathstrut -\mathstrut 32q^{43} \) \(\mathstrut -\mathstrut 151q^{44} \) \(\mathstrut -\mathstrut 121q^{45} \) \(\mathstrut -\mathstrut 33q^{46} \) \(\mathstrut -\mathstrut 51q^{47} \) \(\mathstrut -\mathstrut 27q^{48} \) \(\mathstrut +\mathstrut 72q^{49} \) \(\mathstrut -\mathstrut 45q^{50} \) \(\mathstrut -\mathstrut 24q^{51} \) \(\mathstrut -\mathstrut 95q^{52} \) \(\mathstrut -\mathstrut 81q^{53} \) \(\mathstrut -\mathstrut 29q^{54} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut -\mathstrut 68q^{56} \) \(\mathstrut -\mathstrut 45q^{57} \) \(\mathstrut -\mathstrut 30q^{58} \) \(\mathstrut -\mathstrut 94q^{59} \) \(\mathstrut -\mathstrut 108q^{60} \) \(\mathstrut -\mathstrut 39q^{61} \) \(\mathstrut -\mathstrut 9q^{62} \) \(\mathstrut -\mathstrut 52q^{63} \) \(\mathstrut +\mathstrut 31q^{64} \) \(\mathstrut +\mathstrut 40q^{65} \) \(\mathstrut -\mathstrut 40q^{66} \) \(\mathstrut -\mathstrut 47q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut -\mathstrut 60q^{69} \) \(\mathstrut -\mathstrut 66q^{70} \) \(\mathstrut -\mathstrut 86q^{71} \) \(\mathstrut -\mathstrut 91q^{72} \) \(\mathstrut -\mathstrut 51q^{73} \) \(\mathstrut -\mathstrut 110q^{74} \) \(\mathstrut -\mathstrut 7q^{75} \) \(\mathstrut -\mathstrut 51q^{76} \) \(\mathstrut -\mathstrut 96q^{77} \) \(\mathstrut +\mathstrut 10q^{78} \) \(\mathstrut -\mathstrut 18q^{79} \) \(\mathstrut -\mathstrut 136q^{80} \) \(\mathstrut -\mathstrut 24q^{81} \) \(\mathstrut -\mathstrut 33q^{82} \) \(\mathstrut -\mathstrut 77q^{83} \) \(\mathstrut -\mathstrut 113q^{84} \) \(\mathstrut -\mathstrut 95q^{85} \) \(\mathstrut -\mathstrut 137q^{86} \) \(\mathstrut +\mathstrut 23q^{87} \) \(\mathstrut +\mathstrut 19q^{88} \) \(\mathstrut -\mathstrut 112q^{89} \) \(\mathstrut -\mathstrut 19q^{90} \) \(\mathstrut +\mathstrut 8q^{91} \) \(\mathstrut -\mathstrut 111q^{92} \) \(\mathstrut -\mathstrut 124q^{93} \) \(\mathstrut -\mathstrut 20q^{94} \) \(\mathstrut -\mathstrut 73q^{95} \) \(\mathstrut -\mathstrut 77q^{96} \) \(\mathstrut -\mathstrut 41q^{97} \) \(\mathstrut -\mathstrut 80q^{98} \) \(\mathstrut -\mathstrut 154q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.51181 −1.77612 −0.888060 0.459727i \(-0.847947\pi\)
−0.888060 + 0.459727i \(0.847947\pi\)
\(3\) −2.99105 −1.72688 −0.863440 0.504451i \(-0.831695\pi\)
−0.863440 + 0.504451i \(0.831695\pi\)
\(4\) 4.30921 2.15460
\(5\) 1.76112 0.787596 0.393798 0.919197i \(-0.371161\pi\)
0.393798 + 0.919197i \(0.371161\pi\)
\(6\) 7.51295 3.06715
\(7\) 3.89256 1.47125 0.735625 0.677389i \(-0.236889\pi\)
0.735625 + 0.677389i \(0.236889\pi\)
\(8\) −5.80031 −2.05072
\(9\) 5.94635 1.98212
\(10\) −4.42360 −1.39886
\(11\) −5.42983 −1.63716 −0.818578 0.574395i \(-0.805237\pi\)
−0.818578 + 0.574395i \(0.805237\pi\)
\(12\) −12.8890 −3.72075
\(13\) −1.00000 −0.277350
\(14\) −9.77739 −2.61312
\(15\) −5.26758 −1.36008
\(16\) 5.95087 1.48772
\(17\) 3.49734 0.848231 0.424115 0.905608i \(-0.360585\pi\)
0.424115 + 0.905608i \(0.360585\pi\)
\(18\) −14.9361 −3.52048
\(19\) 4.03795 0.926368 0.463184 0.886262i \(-0.346707\pi\)
0.463184 + 0.886262i \(0.346707\pi\)
\(20\) 7.58902 1.69696
\(21\) −11.6428 −2.54067
\(22\) 13.6387 2.90779
\(23\) −6.04800 −1.26109 −0.630547 0.776151i \(-0.717169\pi\)
−0.630547 + 0.776151i \(0.717169\pi\)
\(24\) 17.3490 3.54135
\(25\) −1.89847 −0.379693
\(26\) 2.51181 0.492607
\(27\) −8.81267 −1.69600
\(28\) 16.7739 3.16996
\(29\) −9.38630 −1.74299 −0.871497 0.490402i \(-0.836850\pi\)
−0.871497 + 0.490402i \(0.836850\pi\)
\(30\) 13.2312 2.41567
\(31\) 6.27218 1.12652 0.563258 0.826281i \(-0.309548\pi\)
0.563258 + 0.826281i \(0.309548\pi\)
\(32\) −3.34687 −0.591648
\(33\) 16.2409 2.82717
\(34\) −8.78468 −1.50656
\(35\) 6.85525 1.15875
\(36\) 25.6241 4.27068
\(37\) 7.54791 1.24087 0.620435 0.784258i \(-0.286956\pi\)
0.620435 + 0.784258i \(0.286956\pi\)
\(38\) −10.1426 −1.64534
\(39\) 2.99105 0.478951
\(40\) −10.2150 −1.61514
\(41\) 9.87852 1.54277 0.771383 0.636372i \(-0.219565\pi\)
0.771383 + 0.636372i \(0.219565\pi\)
\(42\) 29.2446 4.51254
\(43\) −5.32767 −0.812462 −0.406231 0.913770i \(-0.633157\pi\)
−0.406231 + 0.913770i \(0.633157\pi\)
\(44\) −23.3983 −3.52743
\(45\) 10.4722 1.56111
\(46\) 15.1914 2.23986
\(47\) 8.51872 1.24258 0.621292 0.783579i \(-0.286608\pi\)
0.621292 + 0.783579i \(0.286608\pi\)
\(48\) −17.7993 −2.56911
\(49\) 8.15202 1.16457
\(50\) 4.76859 0.674381
\(51\) −10.4607 −1.46479
\(52\) −4.30921 −0.597580
\(53\) −6.65992 −0.914810 −0.457405 0.889258i \(-0.651221\pi\)
−0.457405 + 0.889258i \(0.651221\pi\)
\(54\) 22.1358 3.01230
\(55\) −9.56257 −1.28942
\(56\) −22.5780 −3.01712
\(57\) −12.0777 −1.59973
\(58\) 23.5767 3.09577
\(59\) −4.16499 −0.542235 −0.271118 0.962546i \(-0.587393\pi\)
−0.271118 + 0.962546i \(0.587393\pi\)
\(60\) −22.6991 −2.93044
\(61\) −15.3368 −1.96368 −0.981838 0.189723i \(-0.939241\pi\)
−0.981838 + 0.189723i \(0.939241\pi\)
\(62\) −15.7545 −2.00083
\(63\) 23.1465 2.91619
\(64\) −3.49503 −0.436879
\(65\) −1.76112 −0.218440
\(66\) −40.7941 −5.02140
\(67\) 3.15830 0.385848 0.192924 0.981214i \(-0.438203\pi\)
0.192924 + 0.981214i \(0.438203\pi\)
\(68\) 15.0708 1.82760
\(69\) 18.0898 2.17776
\(70\) −17.2191 −2.05808
\(71\) 10.8333 1.28568 0.642838 0.766002i \(-0.277757\pi\)
0.642838 + 0.766002i \(0.277757\pi\)
\(72\) −34.4907 −4.06476
\(73\) −2.84051 −0.332456 −0.166228 0.986087i \(-0.553159\pi\)
−0.166228 + 0.986087i \(0.553159\pi\)
\(74\) −18.9590 −2.20393
\(75\) 5.67840 0.655685
\(76\) 17.4004 1.99596
\(77\) −21.1360 −2.40867
\(78\) −7.51295 −0.850674
\(79\) 9.78667 1.10109 0.550543 0.834807i \(-0.314421\pi\)
0.550543 + 0.834807i \(0.314421\pi\)
\(80\) 10.4802 1.17172
\(81\) 8.52003 0.946670
\(82\) −24.8130 −2.74014
\(83\) −2.31751 −0.254379 −0.127190 0.991878i \(-0.540596\pi\)
−0.127190 + 0.991878i \(0.540596\pi\)
\(84\) −50.1714 −5.47414
\(85\) 6.15923 0.668063
\(86\) 13.3821 1.44303
\(87\) 28.0749 3.00994
\(88\) 31.4947 3.35735
\(89\) −13.4969 −1.43067 −0.715334 0.698783i \(-0.753725\pi\)
−0.715334 + 0.698783i \(0.753725\pi\)
\(90\) −26.3043 −2.77271
\(91\) −3.89256 −0.408051
\(92\) −26.0621 −2.71716
\(93\) −18.7604 −1.94536
\(94\) −21.3974 −2.20698
\(95\) 7.11130 0.729604
\(96\) 10.0106 1.02171
\(97\) −12.2652 −1.24534 −0.622670 0.782485i \(-0.713952\pi\)
−0.622670 + 0.782485i \(0.713952\pi\)
\(98\) −20.4764 −2.06843
\(99\) −32.2877 −3.24504
\(100\) −8.18089 −0.818089
\(101\) −13.5097 −1.34427 −0.672134 0.740429i \(-0.734622\pi\)
−0.672134 + 0.740429i \(0.734622\pi\)
\(102\) 26.2754 2.60165
\(103\) 8.28325 0.816173 0.408086 0.912943i \(-0.366196\pi\)
0.408086 + 0.912943i \(0.366196\pi\)
\(104\) 5.80031 0.568767
\(105\) −20.5044 −2.00102
\(106\) 16.7285 1.62481
\(107\) −7.63331 −0.737940 −0.368970 0.929441i \(-0.620289\pi\)
−0.368970 + 0.929441i \(0.620289\pi\)
\(108\) −37.9756 −3.65421
\(109\) 4.26933 0.408928 0.204464 0.978874i \(-0.434455\pi\)
0.204464 + 0.978874i \(0.434455\pi\)
\(110\) 24.0194 2.29016
\(111\) −22.5761 −2.14283
\(112\) 23.1641 2.18880
\(113\) −11.6296 −1.09402 −0.547012 0.837125i \(-0.684235\pi\)
−0.547012 + 0.837125i \(0.684235\pi\)
\(114\) 30.3369 2.84131
\(115\) −10.6512 −0.993232
\(116\) −40.4476 −3.75546
\(117\) −5.94635 −0.549740
\(118\) 10.4617 0.963075
\(119\) 13.6136 1.24796
\(120\) 30.5536 2.78915
\(121\) 18.4831 1.68028
\(122\) 38.5232 3.48772
\(123\) −29.5471 −2.66417
\(124\) 27.0281 2.42720
\(125\) −12.1490 −1.08664
\(126\) −58.1398 −5.17950
\(127\) 4.77812 0.423990 0.211995 0.977271i \(-0.432004\pi\)
0.211995 + 0.977271i \(0.432004\pi\)
\(128\) 15.4726 1.36760
\(129\) 15.9353 1.40303
\(130\) 4.42360 0.387975
\(131\) 11.7456 1.02621 0.513107 0.858324i \(-0.328494\pi\)
0.513107 + 0.858324i \(0.328494\pi\)
\(132\) 69.9854 6.09144
\(133\) 15.7179 1.36292
\(134\) −7.93307 −0.685313
\(135\) −15.5201 −1.33576
\(136\) −20.2857 −1.73948
\(137\) −4.13947 −0.353659 −0.176830 0.984241i \(-0.556584\pi\)
−0.176830 + 0.984241i \(0.556584\pi\)
\(138\) −45.4383 −3.86796
\(139\) −12.8403 −1.08910 −0.544551 0.838728i \(-0.683300\pi\)
−0.544551 + 0.838728i \(0.683300\pi\)
\(140\) 29.5407 2.49665
\(141\) −25.4799 −2.14579
\(142\) −27.2112 −2.28352
\(143\) 5.42983 0.454066
\(144\) 35.3860 2.94883
\(145\) −16.5304 −1.37277
\(146\) 7.13483 0.590483
\(147\) −24.3831 −2.01108
\(148\) 32.5255 2.67358
\(149\) −16.8623 −1.38142 −0.690708 0.723134i \(-0.742701\pi\)
−0.690708 + 0.723134i \(0.742701\pi\)
\(150\) −14.2631 −1.16458
\(151\) 11.5132 0.936930 0.468465 0.883482i \(-0.344807\pi\)
0.468465 + 0.883482i \(0.344807\pi\)
\(152\) −23.4213 −1.89972
\(153\) 20.7964 1.68129
\(154\) 53.0896 4.27808
\(155\) 11.0460 0.887239
\(156\) 12.8890 1.03195
\(157\) 3.81230 0.304255 0.152127 0.988361i \(-0.451388\pi\)
0.152127 + 0.988361i \(0.451388\pi\)
\(158\) −24.5823 −1.95566
\(159\) 19.9201 1.57977
\(160\) −5.89423 −0.465980
\(161\) −23.5422 −1.85538
\(162\) −21.4007 −1.68140
\(163\) 13.2923 1.04113 0.520566 0.853822i \(-0.325721\pi\)
0.520566 + 0.853822i \(0.325721\pi\)
\(164\) 42.5686 3.32405
\(165\) 28.6021 2.22667
\(166\) 5.82115 0.451809
\(167\) −9.55572 −0.739444 −0.369722 0.929142i \(-0.620547\pi\)
−0.369722 + 0.929142i \(0.620547\pi\)
\(168\) 67.5319 5.21020
\(169\) 1.00000 0.0769231
\(170\) −15.4708 −1.18656
\(171\) 24.0110 1.83617
\(172\) −22.9581 −1.75054
\(173\) 17.8207 1.35489 0.677443 0.735576i \(-0.263088\pi\)
0.677443 + 0.735576i \(0.263088\pi\)
\(174\) −70.5188 −5.34602
\(175\) −7.38989 −0.558623
\(176\) −32.3122 −2.43563
\(177\) 12.4577 0.936376
\(178\) 33.9017 2.54104
\(179\) −16.5228 −1.23497 −0.617486 0.786582i \(-0.711849\pi\)
−0.617486 + 0.786582i \(0.711849\pi\)
\(180\) 45.1270 3.36357
\(181\) −13.5494 −1.00712 −0.503561 0.863960i \(-0.667977\pi\)
−0.503561 + 0.863960i \(0.667977\pi\)
\(182\) 9.77739 0.724748
\(183\) 45.8730 3.39103
\(184\) 35.0802 2.58615
\(185\) 13.2928 0.977303
\(186\) 47.1226 3.45519
\(187\) −18.9900 −1.38869
\(188\) 36.7090 2.67728
\(189\) −34.3038 −2.49524
\(190\) −17.8623 −1.29586
\(191\) 1.18068 0.0854311 0.0427156 0.999087i \(-0.486399\pi\)
0.0427156 + 0.999087i \(0.486399\pi\)
\(192\) 10.4538 0.754437
\(193\) 7.24026 0.521166 0.260583 0.965452i \(-0.416085\pi\)
0.260583 + 0.965452i \(0.416085\pi\)
\(194\) 30.8078 2.21187
\(195\) 5.26758 0.377219
\(196\) 35.1288 2.50920
\(197\) 16.5870 1.18177 0.590887 0.806755i \(-0.298778\pi\)
0.590887 + 0.806755i \(0.298778\pi\)
\(198\) 81.1007 5.76358
\(199\) −24.2241 −1.71720 −0.858599 0.512647i \(-0.828665\pi\)
−0.858599 + 0.512647i \(0.828665\pi\)
\(200\) 11.0117 0.778644
\(201\) −9.44663 −0.666314
\(202\) 33.9339 2.38758
\(203\) −36.5368 −2.56438
\(204\) −45.0774 −3.15605
\(205\) 17.3972 1.21508
\(206\) −20.8060 −1.44962
\(207\) −35.9635 −2.49964
\(208\) −5.95087 −0.412619
\(209\) −21.9254 −1.51661
\(210\) 51.5032 3.55406
\(211\) −14.2839 −0.983342 −0.491671 0.870781i \(-0.663614\pi\)
−0.491671 + 0.870781i \(0.663614\pi\)
\(212\) −28.6990 −1.97105
\(213\) −32.4029 −2.22021
\(214\) 19.1734 1.31067
\(215\) −9.38266 −0.639892
\(216\) 51.1162 3.47801
\(217\) 24.4148 1.65739
\(218\) −10.7238 −0.726306
\(219\) 8.49609 0.574112
\(220\) −41.2071 −2.77818
\(221\) −3.49734 −0.235257
\(222\) 56.7071 3.80593
\(223\) 18.5319 1.24099 0.620493 0.784212i \(-0.286932\pi\)
0.620493 + 0.784212i \(0.286932\pi\)
\(224\) −13.0279 −0.870462
\(225\) −11.2889 −0.752596
\(226\) 29.2115 1.94312
\(227\) 22.5663 1.49778 0.748890 0.662695i \(-0.230587\pi\)
0.748890 + 0.662695i \(0.230587\pi\)
\(228\) −52.0453 −3.44678
\(229\) −1.74389 −0.115239 −0.0576196 0.998339i \(-0.518351\pi\)
−0.0576196 + 0.998339i \(0.518351\pi\)
\(230\) 26.7539 1.76410
\(231\) 63.2186 4.15948
\(232\) 54.4434 3.57439
\(233\) −14.8912 −0.975558 −0.487779 0.872967i \(-0.662193\pi\)
−0.487779 + 0.872967i \(0.662193\pi\)
\(234\) 14.9361 0.976405
\(235\) 15.0025 0.978653
\(236\) −17.9478 −1.16830
\(237\) −29.2724 −1.90144
\(238\) −34.1949 −2.21653
\(239\) 19.1194 1.23673 0.618367 0.785889i \(-0.287795\pi\)
0.618367 + 0.785889i \(0.287795\pi\)
\(240\) −31.3467 −2.02342
\(241\) −14.8340 −0.955545 −0.477772 0.878484i \(-0.658556\pi\)
−0.477772 + 0.878484i \(0.658556\pi\)
\(242\) −46.4261 −2.98438
\(243\) 0.954196 0.0612117
\(244\) −66.0895 −4.23094
\(245\) 14.3567 0.917214
\(246\) 74.2168 4.73189
\(247\) −4.03795 −0.256928
\(248\) −36.3806 −2.31017
\(249\) 6.93177 0.439283
\(250\) 30.5160 1.93000
\(251\) 3.01486 0.190296 0.0951480 0.995463i \(-0.469668\pi\)
0.0951480 + 0.995463i \(0.469668\pi\)
\(252\) 99.7432 6.28323
\(253\) 32.8396 2.06461
\(254\) −12.0017 −0.753057
\(255\) −18.4225 −1.15366
\(256\) −31.8742 −1.99214
\(257\) 14.9671 0.933620 0.466810 0.884358i \(-0.345403\pi\)
0.466810 + 0.884358i \(0.345403\pi\)
\(258\) −40.0265 −2.49194
\(259\) 29.3807 1.82563
\(260\) −7.58902 −0.470651
\(261\) −55.8143 −3.45482
\(262\) −29.5027 −1.82268
\(263\) 27.2285 1.67898 0.839489 0.543376i \(-0.182854\pi\)
0.839489 + 0.543376i \(0.182854\pi\)
\(264\) −94.2021 −5.79774
\(265\) −11.7289 −0.720500
\(266\) −39.4806 −2.42071
\(267\) 40.3698 2.47059
\(268\) 13.6098 0.831351
\(269\) −2.42331 −0.147752 −0.0738758 0.997267i \(-0.523537\pi\)
−0.0738758 + 0.997267i \(0.523537\pi\)
\(270\) 38.9837 2.37247
\(271\) −26.9724 −1.63846 −0.819229 0.573466i \(-0.805598\pi\)
−0.819229 + 0.573466i \(0.805598\pi\)
\(272\) 20.8122 1.26193
\(273\) 11.6428 0.704656
\(274\) 10.3976 0.628141
\(275\) 10.3084 0.621617
\(276\) 77.9529 4.69221
\(277\) 22.5664 1.35588 0.677942 0.735115i \(-0.262872\pi\)
0.677942 + 0.735115i \(0.262872\pi\)
\(278\) 32.2525 1.93438
\(279\) 37.2966 2.23289
\(280\) −39.7626 −2.37627
\(281\) −29.9857 −1.78880 −0.894399 0.447270i \(-0.852396\pi\)
−0.894399 + 0.447270i \(0.852396\pi\)
\(282\) 64.0007 3.81119
\(283\) −22.2092 −1.32020 −0.660101 0.751177i \(-0.729487\pi\)
−0.660101 + 0.751177i \(0.729487\pi\)
\(284\) 46.6830 2.77012
\(285\) −21.2702 −1.25994
\(286\) −13.6387 −0.806475
\(287\) 38.4527 2.26979
\(288\) −19.9017 −1.17272
\(289\) −4.76858 −0.280505
\(290\) 41.5212 2.43821
\(291\) 36.6857 2.15055
\(292\) −12.2403 −0.716312
\(293\) −0.859670 −0.0502225 −0.0251112 0.999685i \(-0.507994\pi\)
−0.0251112 + 0.999685i \(0.507994\pi\)
\(294\) 61.2457 3.57192
\(295\) −7.33503 −0.427062
\(296\) −43.7802 −2.54467
\(297\) 47.8513 2.77662
\(298\) 42.3550 2.45356
\(299\) 6.04800 0.349765
\(300\) 24.4694 1.41274
\(301\) −20.7383 −1.19533
\(302\) −28.9190 −1.66410
\(303\) 40.4082 2.32139
\(304\) 24.0293 1.37817
\(305\) −27.0099 −1.54658
\(306\) −52.2368 −2.98618
\(307\) −26.9448 −1.53782 −0.768911 0.639356i \(-0.779201\pi\)
−0.768911 + 0.639356i \(0.779201\pi\)
\(308\) −91.0793 −5.18972
\(309\) −24.7756 −1.40943
\(310\) −27.7456 −1.57584
\(311\) −1.56447 −0.0887131 −0.0443565 0.999016i \(-0.514124\pi\)
−0.0443565 + 0.999016i \(0.514124\pi\)
\(312\) −17.3490 −0.982192
\(313\) 8.79620 0.497190 0.248595 0.968607i \(-0.420031\pi\)
0.248595 + 0.968607i \(0.420031\pi\)
\(314\) −9.57578 −0.540393
\(315\) 40.7637 2.29678
\(316\) 42.1728 2.37241
\(317\) 32.7422 1.83898 0.919492 0.393108i \(-0.128600\pi\)
0.919492 + 0.393108i \(0.128600\pi\)
\(318\) −50.0356 −2.80586
\(319\) 50.9661 2.85355
\(320\) −6.15516 −0.344084
\(321\) 22.8316 1.27433
\(322\) 59.1336 3.29539
\(323\) 14.1221 0.785774
\(324\) 36.7146 2.03970
\(325\) 1.89847 0.105308
\(326\) −33.3877 −1.84918
\(327\) −12.7698 −0.706170
\(328\) −57.2984 −3.16378
\(329\) 33.1596 1.82815
\(330\) −71.8431 −3.95483
\(331\) −11.3480 −0.623743 −0.311871 0.950124i \(-0.600956\pi\)
−0.311871 + 0.950124i \(0.600956\pi\)
\(332\) −9.98662 −0.548087
\(333\) 44.8825 2.45955
\(334\) 24.0022 1.31334
\(335\) 5.56214 0.303892
\(336\) −69.2849 −3.77980
\(337\) −26.1101 −1.42231 −0.711155 0.703035i \(-0.751828\pi\)
−0.711155 + 0.703035i \(0.751828\pi\)
\(338\) −2.51181 −0.136625
\(339\) 34.7847 1.88925
\(340\) 26.5414 1.43941
\(341\) −34.0569 −1.84428
\(342\) −60.3113 −3.26126
\(343\) 4.48432 0.242131
\(344\) 30.9021 1.66613
\(345\) 31.8583 1.71519
\(346\) −44.7624 −2.40644
\(347\) 4.21683 0.226371 0.113186 0.993574i \(-0.463895\pi\)
0.113186 + 0.993574i \(0.463895\pi\)
\(348\) 120.980 6.48523
\(349\) 12.4441 0.666118 0.333059 0.942906i \(-0.391919\pi\)
0.333059 + 0.942906i \(0.391919\pi\)
\(350\) 18.5620 0.992183
\(351\) 8.81267 0.470385
\(352\) 18.1729 0.968621
\(353\) −36.3534 −1.93490 −0.967449 0.253066i \(-0.918561\pi\)
−0.967449 + 0.253066i \(0.918561\pi\)
\(354\) −31.2913 −1.66312
\(355\) 19.0787 1.01259
\(356\) −58.1609 −3.08252
\(357\) −40.7190 −2.15508
\(358\) 41.5022 2.19346
\(359\) 18.5971 0.981517 0.490759 0.871296i \(-0.336720\pi\)
0.490759 + 0.871296i \(0.336720\pi\)
\(360\) −60.7421 −3.20139
\(361\) −2.69499 −0.141842
\(362\) 34.0337 1.78877
\(363\) −55.2838 −2.90165
\(364\) −16.7739 −0.879189
\(365\) −5.00247 −0.261841
\(366\) −115.225 −6.02288
\(367\) 26.7809 1.39795 0.698976 0.715145i \(-0.253640\pi\)
0.698976 + 0.715145i \(0.253640\pi\)
\(368\) −35.9908 −1.87615
\(369\) 58.7411 3.05794
\(370\) −33.3889 −1.73581
\(371\) −25.9241 −1.34591
\(372\) −80.8424 −4.19148
\(373\) −7.95613 −0.411953 −0.205976 0.978557i \(-0.566037\pi\)
−0.205976 + 0.978557i \(0.566037\pi\)
\(374\) 47.6994 2.46647
\(375\) 36.3382 1.87650
\(376\) −49.4112 −2.54819
\(377\) 9.38630 0.483419
\(378\) 86.1649 4.43184
\(379\) −8.11162 −0.416666 −0.208333 0.978058i \(-0.566804\pi\)
−0.208333 + 0.978058i \(0.566804\pi\)
\(380\) 30.6441 1.57201
\(381\) −14.2916 −0.732179
\(382\) −2.96565 −0.151736
\(383\) 5.95164 0.304115 0.152057 0.988372i \(-0.451410\pi\)
0.152057 + 0.988372i \(0.451410\pi\)
\(384\) −46.2793 −2.36168
\(385\) −37.2229 −1.89705
\(386\) −18.1862 −0.925653
\(387\) −31.6802 −1.61040
\(388\) −52.8532 −2.68322
\(389\) −21.1402 −1.07185 −0.535926 0.844265i \(-0.680037\pi\)
−0.535926 + 0.844265i \(0.680037\pi\)
\(390\) −13.2312 −0.669987
\(391\) −21.1519 −1.06970
\(392\) −47.2842 −2.38821
\(393\) −35.1315 −1.77215
\(394\) −41.6634 −2.09897
\(395\) 17.2355 0.867211
\(396\) −139.134 −6.99177
\(397\) −15.8358 −0.794774 −0.397387 0.917651i \(-0.630083\pi\)
−0.397387 + 0.917651i \(0.630083\pi\)
\(398\) 60.8464 3.04995
\(399\) −47.0131 −2.35360
\(400\) −11.2975 −0.564876
\(401\) −31.2313 −1.55962 −0.779808 0.626018i \(-0.784683\pi\)
−0.779808 + 0.626018i \(0.784683\pi\)
\(402\) 23.7282 1.18345
\(403\) −6.27218 −0.312439
\(404\) −58.2163 −2.89637
\(405\) 15.0048 0.745593
\(406\) 91.7735 4.55464
\(407\) −40.9839 −2.03150
\(408\) 60.6753 3.00388
\(409\) 26.6186 1.31621 0.658103 0.752928i \(-0.271359\pi\)
0.658103 + 0.752928i \(0.271359\pi\)
\(410\) −43.6986 −2.15812
\(411\) 12.3814 0.610727
\(412\) 35.6943 1.75853
\(413\) −16.2125 −0.797763
\(414\) 90.3336 4.43966
\(415\) −4.08140 −0.200348
\(416\) 3.34687 0.164094
\(417\) 38.4060 1.88075
\(418\) 55.0725 2.69368
\(419\) −1.24155 −0.0606539 −0.0303270 0.999540i \(-0.509655\pi\)
−0.0303270 + 0.999540i \(0.509655\pi\)
\(420\) −88.3577 −4.31141
\(421\) 29.1342 1.41992 0.709958 0.704244i \(-0.248714\pi\)
0.709958 + 0.704244i \(0.248714\pi\)
\(422\) 35.8784 1.74653
\(423\) 50.6553 2.46295
\(424\) 38.6296 1.87602
\(425\) −6.63959 −0.322067
\(426\) 81.3900 3.94336
\(427\) −59.6994 −2.88906
\(428\) −32.8935 −1.58997
\(429\) −16.2409 −0.784117
\(430\) 23.5675 1.13653
\(431\) −20.3554 −0.980484 −0.490242 0.871586i \(-0.663092\pi\)
−0.490242 + 0.871586i \(0.663092\pi\)
\(432\) −52.4430 −2.52317
\(433\) −12.8686 −0.618427 −0.309213 0.950993i \(-0.600066\pi\)
−0.309213 + 0.950993i \(0.600066\pi\)
\(434\) −61.3255 −2.94372
\(435\) 49.4431 2.37062
\(436\) 18.3975 0.881079
\(437\) −24.4215 −1.16824
\(438\) −21.3406 −1.01969
\(439\) −8.91008 −0.425255 −0.212628 0.977133i \(-0.568202\pi\)
−0.212628 + 0.977133i \(0.568202\pi\)
\(440\) 55.4659 2.64423
\(441\) 48.4748 2.30832
\(442\) 8.78468 0.417845
\(443\) 0.339655 0.0161375 0.00806876 0.999967i \(-0.497432\pi\)
0.00806876 + 0.999967i \(0.497432\pi\)
\(444\) −97.2853 −4.61696
\(445\) −23.7696 −1.12679
\(446\) −46.5486 −2.20414
\(447\) 50.4360 2.38554
\(448\) −13.6046 −0.642758
\(449\) 24.5888 1.16042 0.580210 0.814467i \(-0.302971\pi\)
0.580210 + 0.814467i \(0.302971\pi\)
\(450\) 28.3557 1.33670
\(451\) −53.6387 −2.52575
\(452\) −50.1145 −2.35719
\(453\) −34.4365 −1.61797
\(454\) −56.6824 −2.66024
\(455\) −6.85525 −0.321379
\(456\) 70.0542 3.28059
\(457\) −18.0417 −0.843955 −0.421977 0.906606i \(-0.638664\pi\)
−0.421977 + 0.906606i \(0.638664\pi\)
\(458\) 4.38032 0.204679
\(459\) −30.8209 −1.43860
\(460\) −45.8984 −2.14002
\(461\) 2.58467 0.120380 0.0601901 0.998187i \(-0.480829\pi\)
0.0601901 + 0.998187i \(0.480829\pi\)
\(462\) −158.793 −7.38774
\(463\) −1.00000 −0.0464739
\(464\) −55.8567 −2.59308
\(465\) −33.0392 −1.53216
\(466\) 37.4040 1.73271
\(467\) −32.0750 −1.48425 −0.742127 0.670259i \(-0.766183\pi\)
−0.742127 + 0.670259i \(0.766183\pi\)
\(468\) −25.6241 −1.18447
\(469\) 12.2939 0.567679
\(470\) −37.6834 −1.73821
\(471\) −11.4028 −0.525411
\(472\) 24.1582 1.11197
\(473\) 28.9284 1.33013
\(474\) 73.5267 3.37720
\(475\) −7.66590 −0.351736
\(476\) 58.6640 2.68886
\(477\) −39.6022 −1.81326
\(478\) −48.0245 −2.19659
\(479\) 1.54240 0.0704738 0.0352369 0.999379i \(-0.488781\pi\)
0.0352369 + 0.999379i \(0.488781\pi\)
\(480\) 17.6299 0.804691
\(481\) −7.54791 −0.344155
\(482\) 37.2604 1.69716
\(483\) 70.4158 3.20403
\(484\) 79.6476 3.62034
\(485\) −21.6004 −0.980824
\(486\) −2.39676 −0.108719
\(487\) 12.9024 0.584662 0.292331 0.956317i \(-0.405569\pi\)
0.292331 + 0.956317i \(0.405569\pi\)
\(488\) 88.9581 4.02694
\(489\) −39.7578 −1.79791
\(490\) −36.0613 −1.62908
\(491\) −12.8284 −0.578937 −0.289468 0.957188i \(-0.593478\pi\)
−0.289468 + 0.957188i \(0.593478\pi\)
\(492\) −127.325 −5.74024
\(493\) −32.8271 −1.47846
\(494\) 10.1426 0.456336
\(495\) −56.8624 −2.55578
\(496\) 37.3249 1.67594
\(497\) 42.1693 1.89155
\(498\) −17.4113 −0.780220
\(499\) −8.39311 −0.375727 −0.187864 0.982195i \(-0.560156\pi\)
−0.187864 + 0.982195i \(0.560156\pi\)
\(500\) −52.3526 −2.34128
\(501\) 28.5816 1.27693
\(502\) −7.57276 −0.337989
\(503\) −34.9071 −1.55643 −0.778216 0.627997i \(-0.783875\pi\)
−0.778216 + 0.627997i \(0.783875\pi\)
\(504\) −134.257 −5.98028
\(505\) −23.7922 −1.05874
\(506\) −82.4870 −3.66700
\(507\) −2.99105 −0.132837
\(508\) 20.5899 0.913530
\(509\) −5.51098 −0.244270 −0.122135 0.992514i \(-0.538974\pi\)
−0.122135 + 0.992514i \(0.538974\pi\)
\(510\) 46.2740 2.04905
\(511\) −11.0568 −0.489126
\(512\) 49.1170 2.17068
\(513\) −35.5851 −1.57112
\(514\) −37.5945 −1.65822
\(515\) 14.5878 0.642814
\(516\) 68.6686 3.02297
\(517\) −46.2552 −2.03430
\(518\) −73.7989 −3.24254
\(519\) −53.3026 −2.33973
\(520\) 10.2150 0.447958
\(521\) 2.94477 0.129013 0.0645064 0.997917i \(-0.479453\pi\)
0.0645064 + 0.997917i \(0.479453\pi\)
\(522\) 140.195 6.13617
\(523\) 37.9436 1.65916 0.829580 0.558388i \(-0.188580\pi\)
0.829580 + 0.558388i \(0.188580\pi\)
\(524\) 50.6141 2.21109
\(525\) 22.1035 0.964676
\(526\) −68.3928 −2.98207
\(527\) 21.9360 0.955546
\(528\) 96.6474 4.20604
\(529\) 13.5783 0.590359
\(530\) 29.4608 1.27970
\(531\) −24.7665 −1.07477
\(532\) 67.7319 2.93655
\(533\) −9.87852 −0.427886
\(534\) −101.401 −4.38807
\(535\) −13.4431 −0.581198
\(536\) −18.3191 −0.791266
\(537\) 49.4205 2.13265
\(538\) 6.08689 0.262425
\(539\) −44.2641 −1.90659
\(540\) −66.8795 −2.87804
\(541\) 8.13089 0.349574 0.174787 0.984606i \(-0.444076\pi\)
0.174787 + 0.984606i \(0.444076\pi\)
\(542\) 67.7497 2.91010
\(543\) 40.5270 1.73918
\(544\) −11.7052 −0.501854
\(545\) 7.51880 0.322070
\(546\) −29.2446 −1.25155
\(547\) 2.35221 0.100573 0.0502866 0.998735i \(-0.483987\pi\)
0.0502866 + 0.998735i \(0.483987\pi\)
\(548\) −17.8379 −0.761996
\(549\) −91.1980 −3.89223
\(550\) −25.8927 −1.10407
\(551\) −37.9014 −1.61465
\(552\) −104.927 −4.46597
\(553\) 38.0952 1.61997
\(554\) −56.6826 −2.40821
\(555\) −39.7592 −1.68769
\(556\) −55.3317 −2.34659
\(557\) 12.2887 0.520688 0.260344 0.965516i \(-0.416164\pi\)
0.260344 + 0.965516i \(0.416164\pi\)
\(558\) −93.6821 −3.96588
\(559\) 5.32767 0.225337
\(560\) 40.7947 1.72389
\(561\) 56.7999 2.39810
\(562\) 75.3185 3.17712
\(563\) 32.0547 1.35095 0.675473 0.737385i \(-0.263940\pi\)
0.675473 + 0.737385i \(0.263940\pi\)
\(564\) −109.798 −4.62334
\(565\) −20.4811 −0.861648
\(566\) 55.7855 2.34484
\(567\) 33.1647 1.39279
\(568\) −62.8365 −2.63656
\(569\) −1.66385 −0.0697521 −0.0348761 0.999392i \(-0.511104\pi\)
−0.0348761 + 0.999392i \(0.511104\pi\)
\(570\) 53.4268 2.23780
\(571\) −5.95208 −0.249087 −0.124543 0.992214i \(-0.539747\pi\)
−0.124543 + 0.992214i \(0.539747\pi\)
\(572\) 23.3983 0.978332
\(573\) −3.53147 −0.147529
\(574\) −96.5861 −4.03143
\(575\) 11.4819 0.478829
\(576\) −20.7827 −0.865945
\(577\) 15.7826 0.657038 0.328519 0.944497i \(-0.393451\pi\)
0.328519 + 0.944497i \(0.393451\pi\)
\(578\) 11.9778 0.498210
\(579\) −21.6560 −0.899991
\(580\) −71.2329 −2.95778
\(581\) −9.02103 −0.374256
\(582\) −92.1476 −3.81964
\(583\) 36.1622 1.49769
\(584\) 16.4758 0.681774
\(585\) −10.4722 −0.432973
\(586\) 2.15933 0.0892012
\(587\) 34.5161 1.42463 0.712316 0.701859i \(-0.247646\pi\)
0.712316 + 0.701859i \(0.247646\pi\)
\(588\) −105.072 −4.33309
\(589\) 25.3267 1.04357
\(590\) 18.4242 0.758514
\(591\) −49.6124 −2.04078
\(592\) 44.9166 1.84606
\(593\) −42.1148 −1.72945 −0.864724 0.502247i \(-0.832507\pi\)
−0.864724 + 0.502247i \(0.832507\pi\)
\(594\) −120.194 −4.93160
\(595\) 23.9752 0.982887
\(596\) −72.6633 −2.97641
\(597\) 72.4553 2.96540
\(598\) −15.1914 −0.621224
\(599\) 33.1014 1.35249 0.676243 0.736679i \(-0.263607\pi\)
0.676243 + 0.736679i \(0.263607\pi\)
\(600\) −32.9364 −1.34462
\(601\) 47.5637 1.94017 0.970083 0.242775i \(-0.0780576\pi\)
0.970083 + 0.242775i \(0.0780576\pi\)
\(602\) 52.0907 2.12306
\(603\) 18.7804 0.764796
\(604\) 49.6127 2.01871
\(605\) 32.5509 1.32338
\(606\) −101.498 −4.12307
\(607\) 5.03096 0.204200 0.102100 0.994774i \(-0.467444\pi\)
0.102100 + 0.994774i \(0.467444\pi\)
\(608\) −13.5145 −0.548084
\(609\) 109.283 4.42837
\(610\) 67.8438 2.74692
\(611\) −8.51872 −0.344631
\(612\) 89.6162 3.62252
\(613\) 30.0597 1.21410 0.607050 0.794663i \(-0.292353\pi\)
0.607050 + 0.794663i \(0.292353\pi\)
\(614\) 67.6804 2.73136
\(615\) −52.0359 −2.09829
\(616\) 122.595 4.93949
\(617\) −19.8182 −0.797850 −0.398925 0.916984i \(-0.630617\pi\)
−0.398925 + 0.916984i \(0.630617\pi\)
\(618\) 62.2316 2.50332
\(619\) 14.1960 0.570586 0.285293 0.958440i \(-0.407909\pi\)
0.285293 + 0.958440i \(0.407909\pi\)
\(620\) 47.5997 1.91165
\(621\) 53.2990 2.13881
\(622\) 3.92966 0.157565
\(623\) −52.5374 −2.10487
\(624\) 17.7993 0.712543
\(625\) −11.9035 −0.476140
\(626\) −22.0944 −0.883070
\(627\) 65.5798 2.61900
\(628\) 16.4280 0.655548
\(629\) 26.3976 1.05254
\(630\) −102.391 −4.07935
\(631\) −30.8457 −1.22795 −0.613974 0.789327i \(-0.710430\pi\)
−0.613974 + 0.789327i \(0.710430\pi\)
\(632\) −56.7657 −2.25802
\(633\) 42.7237 1.69811
\(634\) −82.2423 −3.26626
\(635\) 8.41483 0.333932
\(636\) 85.8400 3.40378
\(637\) −8.15202 −0.322995
\(638\) −128.017 −5.06825
\(639\) 64.4186 2.54836
\(640\) 27.2491 1.07711
\(641\) 19.9868 0.789432 0.394716 0.918803i \(-0.370843\pi\)
0.394716 + 0.918803i \(0.370843\pi\)
\(642\) −57.3486 −2.26337
\(643\) −5.15777 −0.203402 −0.101701 0.994815i \(-0.532429\pi\)
−0.101701 + 0.994815i \(0.532429\pi\)
\(644\) −101.448 −3.99762
\(645\) 28.0639 1.10502
\(646\) −35.4721 −1.39563
\(647\) −32.4123 −1.27426 −0.637129 0.770757i \(-0.719878\pi\)
−0.637129 + 0.770757i \(0.719878\pi\)
\(648\) −49.4188 −1.94135
\(649\) 22.6152 0.887724
\(650\) −4.76859 −0.187040
\(651\) −73.0259 −2.86211
\(652\) 57.2792 2.24323
\(653\) 22.1546 0.866975 0.433488 0.901159i \(-0.357283\pi\)
0.433488 + 0.901159i \(0.357283\pi\)
\(654\) 32.0753 1.25424
\(655\) 20.6853 0.808242
\(656\) 58.7858 2.29520
\(657\) −16.8907 −0.658967
\(658\) −83.2908 −3.24701
\(659\) −24.9857 −0.973303 −0.486652 0.873596i \(-0.661782\pi\)
−0.486652 + 0.873596i \(0.661782\pi\)
\(660\) 123.252 4.79759
\(661\) −1.78735 −0.0695198 −0.0347599 0.999396i \(-0.511067\pi\)
−0.0347599 + 0.999396i \(0.511067\pi\)
\(662\) 28.5041 1.10784
\(663\) 10.4607 0.406261
\(664\) 13.4422 0.521660
\(665\) 27.6811 1.07343
\(666\) −112.737 −4.36845
\(667\) 56.7683 2.19808
\(668\) −41.1776 −1.59321
\(669\) −55.4297 −2.14304
\(670\) −13.9711 −0.539750
\(671\) 83.2763 3.21484
\(672\) 38.9670 1.50318
\(673\) −17.9655 −0.692519 −0.346260 0.938139i \(-0.612548\pi\)
−0.346260 + 0.938139i \(0.612548\pi\)
\(674\) 65.5838 2.52619
\(675\) 16.7306 0.643959
\(676\) 4.30921 0.165739
\(677\) 44.0681 1.69367 0.846837 0.531852i \(-0.178504\pi\)
0.846837 + 0.531852i \(0.178504\pi\)
\(678\) −87.3728 −3.35553
\(679\) −47.7429 −1.83221
\(680\) −35.7254 −1.37001
\(681\) −67.4969 −2.58649
\(682\) 85.5446 3.27567
\(683\) −25.6391 −0.981053 −0.490527 0.871426i \(-0.663196\pi\)
−0.490527 + 0.871426i \(0.663196\pi\)
\(684\) 103.469 3.95622
\(685\) −7.29010 −0.278540
\(686\) −11.2638 −0.430053
\(687\) 5.21604 0.199004
\(688\) −31.7043 −1.20871
\(689\) 6.65992 0.253723
\(690\) −80.0222 −3.04639
\(691\) −19.6313 −0.746809 −0.373404 0.927669i \(-0.621810\pi\)
−0.373404 + 0.927669i \(0.621810\pi\)
\(692\) 76.7933 2.91924
\(693\) −125.682 −4.77426
\(694\) −10.5919 −0.402062
\(695\) −22.6133 −0.857772
\(696\) −162.843 −6.17254
\(697\) 34.5486 1.30862
\(698\) −31.2573 −1.18311
\(699\) 44.5404 1.68467
\(700\) −31.8446 −1.20361
\(701\) −25.9632 −0.980616 −0.490308 0.871549i \(-0.663116\pi\)
−0.490308 + 0.871549i \(0.663116\pi\)
\(702\) −22.1358 −0.835461
\(703\) 30.4781 1.14950
\(704\) 18.9774 0.715239
\(705\) −44.8731 −1.69002
\(706\) 91.3131 3.43661
\(707\) −52.5874 −1.97775
\(708\) 53.6827 2.01752
\(709\) 27.0719 1.01671 0.508353 0.861149i \(-0.330254\pi\)
0.508353 + 0.861149i \(0.330254\pi\)
\(710\) −47.9222 −1.79849
\(711\) 58.1950 2.18248
\(712\) 78.2861 2.93389
\(713\) −37.9341 −1.42064
\(714\) 102.278 3.82768
\(715\) 9.56257 0.357620
\(716\) −71.2003 −2.66088
\(717\) −57.1871 −2.13569
\(718\) −46.7125 −1.74329
\(719\) −5.33076 −0.198804 −0.0994020 0.995047i \(-0.531693\pi\)
−0.0994020 + 0.995047i \(0.531693\pi\)
\(720\) 62.3188 2.32249
\(721\) 32.2430 1.20079
\(722\) 6.76932 0.251928
\(723\) 44.3693 1.65011
\(724\) −58.3874 −2.16995
\(725\) 17.8196 0.661803
\(726\) 138.863 5.15367
\(727\) −7.59358 −0.281630 −0.140815 0.990036i \(-0.544972\pi\)
−0.140815 + 0.990036i \(0.544972\pi\)
\(728\) 22.5780 0.836798
\(729\) −28.4141 −1.05238
\(730\) 12.5653 0.465062
\(731\) −18.6327 −0.689156
\(732\) 197.677 7.30634
\(733\) −11.9586 −0.441701 −0.220851 0.975308i \(-0.570883\pi\)
−0.220851 + 0.975308i \(0.570883\pi\)
\(734\) −67.2686 −2.48293
\(735\) −42.9414 −1.58392
\(736\) 20.2419 0.746125
\(737\) −17.1491 −0.631694
\(738\) −147.547 −5.43127
\(739\) −13.5784 −0.499488 −0.249744 0.968312i \(-0.580346\pi\)
−0.249744 + 0.968312i \(0.580346\pi\)
\(740\) 57.2813 2.10570
\(741\) 12.0777 0.443685
\(742\) 65.1166 2.39051
\(743\) 0.116237 0.00426431 0.00213216 0.999998i \(-0.499321\pi\)
0.00213216 + 0.999998i \(0.499321\pi\)
\(744\) 108.816 3.98938
\(745\) −29.6965 −1.08800
\(746\) 19.9843 0.731678
\(747\) −13.7807 −0.504210
\(748\) −81.8319 −2.99207
\(749\) −29.7131 −1.08569
\(750\) −91.2749 −3.33289
\(751\) −28.2045 −1.02920 −0.514598 0.857432i \(-0.672059\pi\)
−0.514598 + 0.857432i \(0.672059\pi\)
\(752\) 50.6938 1.84861
\(753\) −9.01757 −0.328619
\(754\) −23.5767 −0.858611
\(755\) 20.2761 0.737922
\(756\) −147.822 −5.37625
\(757\) −27.5628 −1.00179 −0.500894 0.865509i \(-0.666995\pi\)
−0.500894 + 0.865509i \(0.666995\pi\)
\(758\) 20.3749 0.740049
\(759\) −98.2248 −3.56533
\(760\) −41.2477 −1.49621
\(761\) −14.5806 −0.528545 −0.264272 0.964448i \(-0.585132\pi\)
−0.264272 + 0.964448i \(0.585132\pi\)
\(762\) 35.8978 1.30044
\(763\) 16.6186 0.601635
\(764\) 5.08780 0.184070
\(765\) 36.6250 1.32418
\(766\) −14.9494 −0.540144
\(767\) 4.16499 0.150389
\(768\) 95.3373 3.44019
\(769\) 13.1329 0.473586 0.236793 0.971560i \(-0.423904\pi\)
0.236793 + 0.971560i \(0.423904\pi\)
\(770\) 93.4970 3.36940
\(771\) −44.7672 −1.61225
\(772\) 31.1998 1.12291
\(773\) 13.6355 0.490434 0.245217 0.969468i \(-0.421141\pi\)
0.245217 + 0.969468i \(0.421141\pi\)
\(774\) 79.5748 2.86026
\(775\) −11.9075 −0.427731
\(776\) 71.1418 2.55384
\(777\) −87.8790 −3.15264
\(778\) 53.1003 1.90374
\(779\) 39.8889 1.42917
\(780\) 22.6991 0.812759
\(781\) −58.8230 −2.10485
\(782\) 53.1297 1.89991
\(783\) 82.7184 2.95611
\(784\) 48.5116 1.73256
\(785\) 6.71390 0.239630
\(786\) 88.2438 3.14755
\(787\) 1.73206 0.0617413 0.0308707 0.999523i \(-0.490172\pi\)
0.0308707 + 0.999523i \(0.490172\pi\)
\(788\) 71.4768 2.54625
\(789\) −81.4415 −2.89940
\(790\) −43.2923 −1.54027
\(791\) −45.2690 −1.60958
\(792\) 187.279 6.65465
\(793\) 15.3368 0.544626
\(794\) 39.7765 1.41162
\(795\) 35.0817 1.24422
\(796\) −104.387 −3.69989
\(797\) 4.01249 0.142130 0.0710648 0.997472i \(-0.477360\pi\)
0.0710648 + 0.997472i \(0.477360\pi\)
\(798\) 118.088 4.18027
\(799\) 29.7929 1.05400
\(800\) 6.35392 0.224645
\(801\) −80.2572 −2.83575
\(802\) 78.4472 2.77007
\(803\) 15.4235 0.544283
\(804\) −40.7075 −1.43564
\(805\) −41.4606 −1.46129
\(806\) 15.7545 0.554930
\(807\) 7.24822 0.255149
\(808\) 78.3606 2.75672
\(809\) 21.3266 0.749803 0.374901 0.927065i \(-0.377677\pi\)
0.374901 + 0.927065i \(0.377677\pi\)
\(810\) −37.6892 −1.32426
\(811\) 19.6544 0.690158 0.345079 0.938574i \(-0.387852\pi\)
0.345079 + 0.938574i \(0.387852\pi\)
\(812\) −157.445 −5.52522
\(813\) 80.6757 2.82942
\(814\) 102.944 3.60818
\(815\) 23.4093 0.819991
\(816\) −62.2504 −2.17920
\(817\) −21.5129 −0.752639
\(818\) −66.8610 −2.33774
\(819\) −23.1465 −0.808805
\(820\) 74.9683 2.61801
\(821\) 42.1954 1.47263 0.736314 0.676640i \(-0.236565\pi\)
0.736314 + 0.676640i \(0.236565\pi\)
\(822\) −31.0997 −1.08472
\(823\) −27.1347 −0.945856 −0.472928 0.881101i \(-0.656803\pi\)
−0.472928 + 0.881101i \(0.656803\pi\)
\(824\) −48.0454 −1.67374
\(825\) −30.8328 −1.07346
\(826\) 40.7227 1.41692
\(827\) −6.67973 −0.232277 −0.116139 0.993233i \(-0.537052\pi\)
−0.116139 + 0.993233i \(0.537052\pi\)
\(828\) −154.974 −5.38573
\(829\) 11.3075 0.392724 0.196362 0.980531i \(-0.437087\pi\)
0.196362 + 0.980531i \(0.437087\pi\)
\(830\) 10.2517 0.355842
\(831\) −67.4971 −2.34145
\(832\) 3.49503 0.121168
\(833\) 28.5104 0.987828
\(834\) −96.4687 −3.34044
\(835\) −16.8288 −0.582383
\(836\) −94.4811 −3.26770
\(837\) −55.2746 −1.91057
\(838\) 3.11855 0.107729
\(839\) −28.5879 −0.986963 −0.493481 0.869756i \(-0.664276\pi\)
−0.493481 + 0.869756i \(0.664276\pi\)
\(840\) 118.932 4.10353
\(841\) 59.1027 2.03802
\(842\) −73.1798 −2.52194
\(843\) 89.6886 3.08904
\(844\) −61.5522 −2.11871
\(845\) 1.76112 0.0605843
\(846\) −127.237 −4.37449
\(847\) 71.9466 2.47211
\(848\) −39.6323 −1.36098
\(849\) 66.4288 2.27983
\(850\) 16.6774 0.572031
\(851\) −45.6497 −1.56485
\(852\) −139.631 −4.78367
\(853\) 33.2008 1.13677 0.568387 0.822761i \(-0.307568\pi\)
0.568387 + 0.822761i \(0.307568\pi\)
\(854\) 149.954 5.13131
\(855\) 42.2863 1.44616
\(856\) 44.2755 1.51331
\(857\) −22.7121 −0.775829 −0.387915 0.921695i \(-0.626804\pi\)
−0.387915 + 0.921695i \(0.626804\pi\)
\(858\) 40.7941 1.39269
\(859\) −22.5069 −0.767927 −0.383964 0.923348i \(-0.625441\pi\)
−0.383964 + 0.923348i \(0.625441\pi\)
\(860\) −40.4318 −1.37871
\(861\) −115.014 −3.91966
\(862\) 51.1289 1.74146
\(863\) −1.69455 −0.0576832 −0.0288416 0.999584i \(-0.509182\pi\)
−0.0288416 + 0.999584i \(0.509182\pi\)
\(864\) 29.4948 1.00343
\(865\) 31.3844 1.06710
\(866\) 32.3236 1.09840
\(867\) 14.2630 0.484398
\(868\) 105.209 3.57101
\(869\) −53.1400 −1.80265
\(870\) −124.192 −4.21050
\(871\) −3.15830 −0.107015
\(872\) −24.7634 −0.838596
\(873\) −72.9330 −2.46841
\(874\) 61.3422 2.07493
\(875\) −47.2907 −1.59872
\(876\) 36.6114 1.23699
\(877\) −35.7899 −1.20854 −0.604269 0.796781i \(-0.706535\pi\)
−0.604269 + 0.796781i \(0.706535\pi\)
\(878\) 22.3805 0.755304
\(879\) 2.57131 0.0867282
\(880\) −56.9056 −1.91829
\(881\) −21.8118 −0.734859 −0.367430 0.930051i \(-0.619762\pi\)
−0.367430 + 0.930051i \(0.619762\pi\)
\(882\) −121.760 −4.09986
\(883\) 45.7537 1.53973 0.769867 0.638204i \(-0.220322\pi\)
0.769867 + 0.638204i \(0.220322\pi\)
\(884\) −15.0708 −0.506886
\(885\) 21.9394 0.737485
\(886\) −0.853151 −0.0286622
\(887\) −42.1357 −1.41478 −0.707389 0.706825i \(-0.750127\pi\)
−0.707389 + 0.706825i \(0.750127\pi\)
\(888\) 130.949 4.39435
\(889\) 18.5991 0.623794
\(890\) 59.7048 2.00131
\(891\) −46.2624 −1.54985
\(892\) 79.8578 2.67384
\(893\) 34.3981 1.15109
\(894\) −126.686 −4.23701
\(895\) −29.0986 −0.972659
\(896\) 60.2280 2.01208
\(897\) −18.0898 −0.604002
\(898\) −61.7626 −2.06105
\(899\) −58.8726 −1.96351
\(900\) −48.6464 −1.62155
\(901\) −23.2920 −0.775970
\(902\) 134.730 4.48603
\(903\) 62.0291 2.06420
\(904\) 67.4554 2.24353
\(905\) −23.8621 −0.793205
\(906\) 86.4980 2.87370
\(907\) 19.5909 0.650504 0.325252 0.945627i \(-0.394551\pi\)
0.325252 + 0.945627i \(0.394551\pi\)
\(908\) 97.2430 3.22712
\(909\) −80.3336 −2.66450
\(910\) 17.2191 0.570808
\(911\) −18.7084 −0.619837 −0.309918 0.950763i \(-0.600302\pi\)
−0.309918 + 0.950763i \(0.600302\pi\)
\(912\) −71.8727 −2.37994
\(913\) 12.5837 0.416459
\(914\) 45.3174 1.49897
\(915\) 80.7878 2.67076
\(916\) −7.51477 −0.248295
\(917\) 45.7203 1.50982
\(918\) 77.4165 2.55512
\(919\) −26.3386 −0.868830 −0.434415 0.900713i \(-0.643045\pi\)
−0.434415 + 0.900713i \(0.643045\pi\)
\(920\) 61.7804 2.03684
\(921\) 80.5932 2.65564
\(922\) −6.49222 −0.213810
\(923\) −10.8333 −0.356582
\(924\) 272.422 8.96203
\(925\) −14.3295 −0.471150
\(926\) 2.51181 0.0825433
\(927\) 49.2551 1.61775
\(928\) 31.4147 1.03124
\(929\) −22.6383 −0.742737 −0.371368 0.928486i \(-0.621111\pi\)
−0.371368 + 0.928486i \(0.621111\pi\)
\(930\) 82.9884 2.72130
\(931\) 32.9174 1.07883
\(932\) −64.1695 −2.10194
\(933\) 4.67941 0.153197
\(934\) 80.5665 2.63622
\(935\) −33.4436 −1.09372
\(936\) 34.4907 1.12736
\(937\) −30.5897 −0.999323 −0.499661 0.866221i \(-0.666542\pi\)
−0.499661 + 0.866221i \(0.666542\pi\)
\(938\) −30.8800 −1.00827
\(939\) −26.3098 −0.858589
\(940\) 64.6488 2.10861
\(941\) 0.170224 0.00554915 0.00277457 0.999996i \(-0.499117\pi\)
0.00277457 + 0.999996i \(0.499117\pi\)
\(942\) 28.6416 0.933194
\(943\) −59.7452 −1.94557
\(944\) −24.7853 −0.806693
\(945\) −60.4131 −1.96524
\(946\) −72.6627 −2.36247
\(947\) 1.32065 0.0429153 0.0214576 0.999770i \(-0.493169\pi\)
0.0214576 + 0.999770i \(0.493169\pi\)
\(948\) −126.141 −4.09686
\(949\) 2.84051 0.0922068
\(950\) 19.2553 0.624725
\(951\) −97.9334 −3.17571
\(952\) −78.9632 −2.55921
\(953\) 3.28041 0.106263 0.0531314 0.998588i \(-0.483080\pi\)
0.0531314 + 0.998588i \(0.483080\pi\)
\(954\) 99.4734 3.22057
\(955\) 2.07932 0.0672852
\(956\) 82.3897 2.66467
\(957\) −152.442 −4.92775
\(958\) −3.87421 −0.125170
\(959\) −16.1131 −0.520321
\(960\) 18.4104 0.594192
\(961\) 8.34023 0.269040
\(962\) 18.9590 0.611261
\(963\) −45.3903 −1.46268
\(964\) −63.9230 −2.05882
\(965\) 12.7510 0.410468
\(966\) −176.871 −5.69074
\(967\) −14.4038 −0.463195 −0.231598 0.972812i \(-0.574395\pi\)
−0.231598 + 0.972812i \(0.574395\pi\)
\(968\) −107.208 −3.44578
\(969\) −42.2398 −1.35694
\(970\) 54.2562 1.74206
\(971\) 26.2939 0.843811 0.421905 0.906640i \(-0.361361\pi\)
0.421905 + 0.906640i \(0.361361\pi\)
\(972\) 4.11183 0.131887
\(973\) −49.9817 −1.60234
\(974\) −32.4083 −1.03843
\(975\) −5.67840 −0.181854
\(976\) −91.2673 −2.92139
\(977\) 0.996346 0.0318759 0.0159380 0.999873i \(-0.494927\pi\)
0.0159380 + 0.999873i \(0.494927\pi\)
\(978\) 99.8642 3.19331
\(979\) 73.2859 2.34223
\(980\) 61.8659 1.97623
\(981\) 25.3870 0.810543
\(982\) 32.2225 1.02826
\(983\) 29.4146 0.938181 0.469090 0.883150i \(-0.344582\pi\)
0.469090 + 0.883150i \(0.344582\pi\)
\(984\) 171.382 5.46346
\(985\) 29.2116 0.930759
\(986\) 82.4557 2.62592
\(987\) −99.1820 −3.15700
\(988\) −17.4004 −0.553579
\(989\) 32.2217 1.02459
\(990\) 142.828 4.53937
\(991\) −35.1949 −1.11800 −0.559001 0.829167i \(-0.688815\pi\)
−0.559001 + 0.829167i \(0.688815\pi\)
\(992\) −20.9922 −0.666502
\(993\) 33.9424 1.07713
\(994\) −105.921 −3.35962
\(995\) −42.6614 −1.35246
\(996\) 29.8704 0.946481
\(997\) −15.7106 −0.497561 −0.248780 0.968560i \(-0.580030\pi\)
−0.248780 + 0.968560i \(0.580030\pi\)
\(998\) 21.0819 0.667337
\(999\) −66.5172 −2.10451
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 \(a_p\))