Properties

Label 8021.2.a.a.1.20
Level 8021
Weight 2
Character 8021.1
Self dual Yes
Analytic conductor 64.048
Analytic rank 1
Dimension 134
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8021 = 13 \cdot 617 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8021.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0480074613\)
Analytic rank: \(1\)
Dimension: \(134\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 8021.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.09018 q^{2}\) \(-2.33308 q^{3}\) \(+2.36887 q^{4}\) \(+1.26900 q^{5}\) \(+4.87656 q^{6}\) \(+3.93400 q^{7}\) \(-0.771000 q^{8}\) \(+2.44324 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.09018 q^{2}\) \(-2.33308 q^{3}\) \(+2.36887 q^{4}\) \(+1.26900 q^{5}\) \(+4.87656 q^{6}\) \(+3.93400 q^{7}\) \(-0.771000 q^{8}\) \(+2.44324 q^{9}\) \(-2.65245 q^{10}\) \(+0.594536 q^{11}\) \(-5.52675 q^{12}\) \(+1.00000 q^{13}\) \(-8.22278 q^{14}\) \(-2.96068 q^{15}\) \(-3.12620 q^{16}\) \(+0.356619 q^{17}\) \(-5.10683 q^{18}\) \(+0.943128 q^{19}\) \(+3.00610 q^{20}\) \(-9.17832 q^{21}\) \(-1.24269 q^{22}\) \(+1.05114 q^{23}\) \(+1.79880 q^{24}\) \(-3.38963 q^{25}\) \(-2.09018 q^{26}\) \(+1.29896 q^{27}\) \(+9.31912 q^{28}\) \(-4.29692 q^{29}\) \(+6.18837 q^{30}\) \(+8.95361 q^{31}\) \(+8.07634 q^{32}\) \(-1.38710 q^{33}\) \(-0.745400 q^{34}\) \(+4.99227 q^{35}\) \(+5.78772 q^{36}\) \(-4.51017 q^{37}\) \(-1.97131 q^{38}\) \(-2.33308 q^{39}\) \(-0.978402 q^{40}\) \(+1.53286 q^{41}\) \(+19.1844 q^{42}\) \(-0.601067 q^{43}\) \(+1.40838 q^{44}\) \(+3.10049 q^{45}\) \(-2.19708 q^{46}\) \(+7.67167 q^{47}\) \(+7.29367 q^{48}\) \(+8.47636 q^{49}\) \(+7.08494 q^{50}\) \(-0.832020 q^{51}\) \(+2.36887 q^{52}\) \(-5.58352 q^{53}\) \(-2.71506 q^{54}\) \(+0.754468 q^{55}\) \(-3.03311 q^{56}\) \(-2.20039 q^{57}\) \(+8.98136 q^{58}\) \(-5.30846 q^{59}\) \(-7.01347 q^{60}\) \(-2.34686 q^{61}\) \(-18.7147 q^{62}\) \(+9.61172 q^{63}\) \(-10.6286 q^{64}\) \(+1.26900 q^{65}\) \(+2.89929 q^{66}\) \(-9.33733 q^{67}\) \(+0.844784 q^{68}\) \(-2.45240 q^{69}\) \(-10.4348 q^{70}\) \(+9.63204 q^{71}\) \(-1.88374 q^{72}\) \(-12.9931 q^{73}\) \(+9.42708 q^{74}\) \(+7.90826 q^{75}\) \(+2.23414 q^{76}\) \(+2.33890 q^{77}\) \(+4.87656 q^{78}\) \(-11.5251 q^{79}\) \(-3.96717 q^{80}\) \(-10.3603 q^{81}\) \(-3.20396 q^{82}\) \(-15.7864 q^{83}\) \(-21.7422 q^{84}\) \(+0.452552 q^{85}\) \(+1.25634 q^{86}\) \(+10.0250 q^{87}\) \(-0.458387 q^{88}\) \(-9.12560 q^{89}\) \(-6.48059 q^{90}\) \(+3.93400 q^{91}\) \(+2.49002 q^{92}\) \(-20.8895 q^{93}\) \(-16.0352 q^{94}\) \(+1.19683 q^{95}\) \(-18.8427 q^{96}\) \(-16.1829 q^{97}\) \(-17.7171 q^{98}\) \(+1.45259 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(134q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 33q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 101q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(134q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 33q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 101q^{9} \) \(\mathstrut -\mathstrut 33q^{10} \) \(\mathstrut -\mathstrut 47q^{11} \) \(\mathstrut -\mathstrut 53q^{12} \) \(\mathstrut +\mathstrut 134q^{13} \) \(\mathstrut -\mathstrut 28q^{14} \) \(\mathstrut -\mathstrut 30q^{15} \) \(\mathstrut +\mathstrut 30q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut -\mathstrut 14q^{18} \) \(\mathstrut -\mathstrut 87q^{19} \) \(\mathstrut -\mathstrut 12q^{20} \) \(\mathstrut -\mathstrut 24q^{21} \) \(\mathstrut -\mathstrut 52q^{22} \) \(\mathstrut -\mathstrut 44q^{23} \) \(\mathstrut -\mathstrut 36q^{24} \) \(\mathstrut +\mathstrut 58q^{25} \) \(\mathstrut -\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 117q^{27} \) \(\mathstrut -\mathstrut 71q^{28} \) \(\mathstrut -\mathstrut 42q^{29} \) \(\mathstrut -\mathstrut 21q^{30} \) \(\mathstrut -\mathstrut 82q^{31} \) \(\mathstrut -\mathstrut 31q^{32} \) \(\mathstrut +\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 30q^{34} \) \(\mathstrut -\mathstrut 54q^{35} \) \(\mathstrut +\mathstrut 32q^{36} \) \(\mathstrut -\mathstrut 55q^{37} \) \(\mathstrut -\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut 33q^{39} \) \(\mathstrut -\mathstrut 86q^{40} \) \(\mathstrut -\mathstrut 16q^{41} \) \(\mathstrut +\mathstrut 6q^{42} \) \(\mathstrut -\mathstrut 148q^{43} \) \(\mathstrut -\mathstrut 54q^{44} \) \(\mathstrut -\mathstrut 24q^{45} \) \(\mathstrut -\mathstrut 57q^{46} \) \(\mathstrut -\mathstrut 21q^{47} \) \(\mathstrut -\mathstrut 82q^{48} \) \(\mathstrut +\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 17q^{50} \) \(\mathstrut -\mathstrut 123q^{51} \) \(\mathstrut +\mathstrut 98q^{52} \) \(\mathstrut -\mathstrut 17q^{53} \) \(\mathstrut -\mathstrut 10q^{54} \) \(\mathstrut -\mathstrut 148q^{55} \) \(\mathstrut -\mathstrut 47q^{56} \) \(\mathstrut -\mathstrut q^{57} \) \(\mathstrut -\mathstrut 58q^{58} \) \(\mathstrut -\mathstrut 64q^{59} \) \(\mathstrut -\mathstrut 16q^{60} \) \(\mathstrut -\mathstrut 112q^{61} \) \(\mathstrut -\mathstrut 15q^{62} \) \(\mathstrut -\mathstrut 58q^{63} \) \(\mathstrut -\mathstrut 65q^{64} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 20q^{66} \) \(\mathstrut -\mathstrut 110q^{67} \) \(\mathstrut -\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 57q^{69} \) \(\mathstrut -\mathstrut 40q^{70} \) \(\mathstrut -\mathstrut 78q^{71} \) \(\mathstrut -\mathstrut 28q^{72} \) \(\mathstrut -\mathstrut 43q^{73} \) \(\mathstrut -\mathstrut 52q^{74} \) \(\mathstrut -\mathstrut 150q^{75} \) \(\mathstrut -\mathstrut 96q^{76} \) \(\mathstrut -\mathstrut 24q^{77} \) \(\mathstrut -\mathstrut 16q^{78} \) \(\mathstrut -\mathstrut 228q^{79} \) \(\mathstrut +\mathstrut 20q^{80} \) \(\mathstrut +\mathstrut 54q^{81} \) \(\mathstrut -\mathstrut 89q^{82} \) \(\mathstrut -\mathstrut 12q^{83} \) \(\mathstrut +\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 77q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut -\mathstrut 77q^{87} \) \(\mathstrut -\mathstrut 95q^{88} \) \(\mathstrut -\mathstrut 32q^{89} \) \(\mathstrut -\mathstrut 46q^{90} \) \(\mathstrut -\mathstrut 32q^{91} \) \(\mathstrut -\mathstrut 62q^{92} \) \(\mathstrut -\mathstrut 9q^{93} \) \(\mathstrut -\mathstrut 87q^{94} \) \(\mathstrut -\mathstrut 61q^{95} \) \(\mathstrut -\mathstrut 54q^{96} \) \(\mathstrut -\mathstrut 38q^{97} \) \(\mathstrut +\mathstrut 6q^{98} \) \(\mathstrut -\mathstrut 193q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.09018 −1.47798 −0.738991 0.673715i \(-0.764698\pi\)
−0.738991 + 0.673715i \(0.764698\pi\)
\(3\) −2.33308 −1.34700 −0.673501 0.739186i \(-0.735210\pi\)
−0.673501 + 0.739186i \(0.735210\pi\)
\(4\) 2.36887 1.18443
\(5\) 1.26900 0.567516 0.283758 0.958896i \(-0.408419\pi\)
0.283758 + 0.958896i \(0.408419\pi\)
\(6\) 4.87656 1.99085
\(7\) 3.93400 1.48691 0.743456 0.668785i \(-0.233185\pi\)
0.743456 + 0.668785i \(0.233185\pi\)
\(8\) −0.771000 −0.272590
\(9\) 2.44324 0.814414
\(10\) −2.65245 −0.838779
\(11\) 0.594536 0.179259 0.0896296 0.995975i \(-0.471432\pi\)
0.0896296 + 0.995975i \(0.471432\pi\)
\(12\) −5.52675 −1.59543
\(13\) 1.00000 0.277350
\(14\) −8.22278 −2.19763
\(15\) −2.96068 −0.764445
\(16\) −3.12620 −0.781551
\(17\) 0.356619 0.0864929 0.0432465 0.999064i \(-0.486230\pi\)
0.0432465 + 0.999064i \(0.486230\pi\)
\(18\) −5.10683 −1.20369
\(19\) 0.943128 0.216368 0.108184 0.994131i \(-0.465496\pi\)
0.108184 + 0.994131i \(0.465496\pi\)
\(20\) 3.00610 0.672185
\(21\) −9.17832 −2.00287
\(22\) −1.24269 −0.264942
\(23\) 1.05114 0.219179 0.109589 0.993977i \(-0.465046\pi\)
0.109589 + 0.993977i \(0.465046\pi\)
\(24\) 1.79880 0.367179
\(25\) −3.38963 −0.677925
\(26\) −2.09018 −0.409919
\(27\) 1.29896 0.249984
\(28\) 9.31912 1.76115
\(29\) −4.29692 −0.797918 −0.398959 0.916969i \(-0.630629\pi\)
−0.398959 + 0.916969i \(0.630629\pi\)
\(30\) 6.18837 1.12984
\(31\) 8.95361 1.60812 0.804058 0.594550i \(-0.202670\pi\)
0.804058 + 0.594550i \(0.202670\pi\)
\(32\) 8.07634 1.42771
\(33\) −1.38710 −0.241462
\(34\) −0.745400 −0.127835
\(35\) 4.99227 0.843847
\(36\) 5.78772 0.964620
\(37\) −4.51017 −0.741467 −0.370733 0.928739i \(-0.620894\pi\)
−0.370733 + 0.928739i \(0.620894\pi\)
\(38\) −1.97131 −0.319789
\(39\) −2.33308 −0.373591
\(40\) −0.978402 −0.154699
\(41\) 1.53286 0.239393 0.119696 0.992811i \(-0.461808\pi\)
0.119696 + 0.992811i \(0.461808\pi\)
\(42\) 19.1844 2.96021
\(43\) −0.601067 −0.0916619 −0.0458309 0.998949i \(-0.514594\pi\)
−0.0458309 + 0.998949i \(0.514594\pi\)
\(44\) 1.40838 0.212321
\(45\) 3.10049 0.462193
\(46\) −2.19708 −0.323942
\(47\) 7.67167 1.11903 0.559514 0.828821i \(-0.310988\pi\)
0.559514 + 0.828821i \(0.310988\pi\)
\(48\) 7.29367 1.05275
\(49\) 8.47636 1.21091
\(50\) 7.08494 1.00196
\(51\) −0.832020 −0.116506
\(52\) 2.36887 0.328503
\(53\) −5.58352 −0.766956 −0.383478 0.923550i \(-0.625274\pi\)
−0.383478 + 0.923550i \(0.625274\pi\)
\(54\) −2.71506 −0.369473
\(55\) 0.754468 0.101732
\(56\) −3.03311 −0.405317
\(57\) −2.20039 −0.291449
\(58\) 8.98136 1.17931
\(59\) −5.30846 −0.691103 −0.345552 0.938400i \(-0.612308\pi\)
−0.345552 + 0.938400i \(0.612308\pi\)
\(60\) −7.01347 −0.905435
\(61\) −2.34686 −0.300484 −0.150242 0.988649i \(-0.548005\pi\)
−0.150242 + 0.988649i \(0.548005\pi\)
\(62\) −18.7147 −2.37677
\(63\) 9.61172 1.21096
\(64\) −10.6286 −1.32858
\(65\) 1.26900 0.157401
\(66\) 2.89929 0.356877
\(67\) −9.33733 −1.14074 −0.570368 0.821389i \(-0.693200\pi\)
−0.570368 + 0.821389i \(0.693200\pi\)
\(68\) 0.844784 0.102445
\(69\) −2.45240 −0.295234
\(70\) −10.4348 −1.24719
\(71\) 9.63204 1.14311 0.571556 0.820563i \(-0.306340\pi\)
0.571556 + 0.820563i \(0.306340\pi\)
\(72\) −1.88374 −0.222001
\(73\) −12.9931 −1.52072 −0.760362 0.649499i \(-0.774978\pi\)
−0.760362 + 0.649499i \(0.774978\pi\)
\(74\) 9.42708 1.09588
\(75\) 7.90826 0.913167
\(76\) 2.23414 0.256274
\(77\) 2.33890 0.266543
\(78\) 4.87656 0.552161
\(79\) −11.5251 −1.29668 −0.648339 0.761352i \(-0.724536\pi\)
−0.648339 + 0.761352i \(0.724536\pi\)
\(80\) −3.96717 −0.443543
\(81\) −10.3603 −1.15114
\(82\) −3.20396 −0.353818
\(83\) −15.7864 −1.73278 −0.866389 0.499369i \(-0.833565\pi\)
−0.866389 + 0.499369i \(0.833565\pi\)
\(84\) −21.7422 −2.37227
\(85\) 0.452552 0.0490861
\(86\) 1.25634 0.135475
\(87\) 10.0250 1.07480
\(88\) −0.458387 −0.0488642
\(89\) −9.12560 −0.967311 −0.483656 0.875258i \(-0.660691\pi\)
−0.483656 + 0.875258i \(0.660691\pi\)
\(90\) −6.48059 −0.683114
\(91\) 3.93400 0.412395
\(92\) 2.49002 0.259603
\(93\) −20.8895 −2.16614
\(94\) −16.0352 −1.65391
\(95\) 1.19683 0.122793
\(96\) −18.8427 −1.92313
\(97\) −16.1829 −1.64312 −0.821562 0.570120i \(-0.806897\pi\)
−0.821562 + 0.570120i \(0.806897\pi\)
\(98\) −17.7171 −1.78970
\(99\) 1.45259 0.145991
\(100\) −8.02958 −0.802958
\(101\) 3.97644 0.395670 0.197835 0.980235i \(-0.436609\pi\)
0.197835 + 0.980235i \(0.436609\pi\)
\(102\) 1.73908 0.172194
\(103\) −12.2965 −1.21161 −0.605807 0.795612i \(-0.707150\pi\)
−0.605807 + 0.795612i \(0.707150\pi\)
\(104\) −0.771000 −0.0756027
\(105\) −11.6473 −1.13666
\(106\) 11.6706 1.13355
\(107\) 4.98167 0.481597 0.240798 0.970575i \(-0.422591\pi\)
0.240798 + 0.970575i \(0.422591\pi\)
\(108\) 3.07706 0.296090
\(109\) 8.72154 0.835372 0.417686 0.908591i \(-0.362841\pi\)
0.417686 + 0.908591i \(0.362841\pi\)
\(110\) −1.57698 −0.150359
\(111\) 10.5226 0.998757
\(112\) −12.2985 −1.16210
\(113\) 11.9136 1.12073 0.560366 0.828245i \(-0.310660\pi\)
0.560366 + 0.828245i \(0.310660\pi\)
\(114\) 4.59922 0.430756
\(115\) 1.33391 0.124387
\(116\) −10.1788 −0.945081
\(117\) 2.44324 0.225878
\(118\) 11.0957 1.02144
\(119\) 1.40294 0.128607
\(120\) 2.28269 0.208380
\(121\) −10.6465 −0.967866
\(122\) 4.90537 0.444111
\(123\) −3.57628 −0.322462
\(124\) 21.2099 1.90471
\(125\) −10.6465 −0.952250
\(126\) −20.0903 −1.78978
\(127\) −6.86625 −0.609281 −0.304641 0.952467i \(-0.598536\pi\)
−0.304641 + 0.952467i \(0.598536\pi\)
\(128\) 6.06309 0.535907
\(129\) 1.40234 0.123469
\(130\) −2.65245 −0.232635
\(131\) −16.5224 −1.44357 −0.721786 0.692116i \(-0.756679\pi\)
−0.721786 + 0.692116i \(0.756679\pi\)
\(132\) −3.28585 −0.285996
\(133\) 3.71027 0.321721
\(134\) 19.5167 1.68599
\(135\) 1.64838 0.141870
\(136\) −0.274954 −0.0235771
\(137\) −9.45389 −0.807700 −0.403850 0.914825i \(-0.632328\pi\)
−0.403850 + 0.914825i \(0.632328\pi\)
\(138\) 5.12596 0.436351
\(139\) 1.07259 0.0909763 0.0454881 0.998965i \(-0.485516\pi\)
0.0454881 + 0.998965i \(0.485516\pi\)
\(140\) 11.8260 0.999480
\(141\) −17.8986 −1.50733
\(142\) −20.1327 −1.68950
\(143\) 0.594536 0.0497176
\(144\) −7.63807 −0.636506
\(145\) −5.45282 −0.452832
\(146\) 27.1579 2.24760
\(147\) −19.7760 −1.63110
\(148\) −10.6840 −0.878218
\(149\) −1.92764 −0.157918 −0.0789592 0.996878i \(-0.525160\pi\)
−0.0789592 + 0.996878i \(0.525160\pi\)
\(150\) −16.5297 −1.34964
\(151\) 5.85703 0.476638 0.238319 0.971187i \(-0.423404\pi\)
0.238319 + 0.971187i \(0.423404\pi\)
\(152\) −0.727151 −0.0589798
\(153\) 0.871308 0.0704411
\(154\) −4.88874 −0.393946
\(155\) 11.3622 0.912632
\(156\) −5.52675 −0.442494
\(157\) 12.2998 0.981632 0.490816 0.871263i \(-0.336699\pi\)
0.490816 + 0.871263i \(0.336699\pi\)
\(158\) 24.0896 1.91647
\(159\) 13.0268 1.03309
\(160\) 10.2489 0.810248
\(161\) 4.13520 0.325900
\(162\) 21.6549 1.70137
\(163\) −6.75892 −0.529399 −0.264700 0.964331i \(-0.585273\pi\)
−0.264700 + 0.964331i \(0.585273\pi\)
\(164\) 3.63114 0.283545
\(165\) −1.76023 −0.137034
\(166\) 32.9964 2.56102
\(167\) 16.0606 1.24281 0.621405 0.783489i \(-0.286562\pi\)
0.621405 + 0.783489i \(0.286562\pi\)
\(168\) 7.07648 0.545963
\(169\) 1.00000 0.0769231
\(170\) −0.945916 −0.0725485
\(171\) 2.30429 0.176214
\(172\) −1.42385 −0.108567
\(173\) −23.9425 −1.82031 −0.910156 0.414266i \(-0.864038\pi\)
−0.910156 + 0.414266i \(0.864038\pi\)
\(174\) −20.9542 −1.58853
\(175\) −13.3348 −1.00802
\(176\) −1.85864 −0.140100
\(177\) 12.3850 0.930917
\(178\) 19.0742 1.42967
\(179\) −1.23871 −0.0925853 −0.0462926 0.998928i \(-0.514741\pi\)
−0.0462926 + 0.998928i \(0.514741\pi\)
\(180\) 7.34464 0.547437
\(181\) −17.4934 −1.30028 −0.650138 0.759816i \(-0.725289\pi\)
−0.650138 + 0.759816i \(0.725289\pi\)
\(182\) −8.22278 −0.609513
\(183\) 5.47540 0.404753
\(184\) −0.810432 −0.0597458
\(185\) −5.72342 −0.420794
\(186\) 43.6628 3.20151
\(187\) 0.212023 0.0155047
\(188\) 18.1732 1.32542
\(189\) 5.11010 0.371705
\(190\) −2.50160 −0.181485
\(191\) 12.8686 0.931141 0.465571 0.885011i \(-0.345849\pi\)
0.465571 + 0.885011i \(0.345849\pi\)
\(192\) 24.7974 1.78960
\(193\) 0.169081 0.0121707 0.00608537 0.999981i \(-0.498063\pi\)
0.00608537 + 0.999981i \(0.498063\pi\)
\(194\) 33.8252 2.42851
\(195\) −2.96068 −0.212019
\(196\) 20.0794 1.43424
\(197\) −18.6429 −1.32825 −0.664127 0.747620i \(-0.731197\pi\)
−0.664127 + 0.747620i \(0.731197\pi\)
\(198\) −3.03619 −0.215773
\(199\) −13.0939 −0.928204 −0.464102 0.885782i \(-0.653623\pi\)
−0.464102 + 0.885782i \(0.653623\pi\)
\(200\) 2.61340 0.184795
\(201\) 21.7847 1.53657
\(202\) −8.31148 −0.584794
\(203\) −16.9041 −1.18643
\(204\) −1.97095 −0.137994
\(205\) 1.94521 0.135859
\(206\) 25.7020 1.79074
\(207\) 2.56820 0.178502
\(208\) −3.12620 −0.216763
\(209\) 0.560723 0.0387860
\(210\) 24.3451 1.67997
\(211\) −9.27357 −0.638419 −0.319209 0.947684i \(-0.603417\pi\)
−0.319209 + 0.947684i \(0.603417\pi\)
\(212\) −13.2266 −0.908408
\(213\) −22.4723 −1.53977
\(214\) −10.4126 −0.711792
\(215\) −0.762757 −0.0520196
\(216\) −1.00150 −0.0681431
\(217\) 35.2235 2.39113
\(218\) −18.2296 −1.23467
\(219\) 30.3138 2.04842
\(220\) 1.78724 0.120495
\(221\) 0.356619 0.0239888
\(222\) −21.9941 −1.47615
\(223\) −21.7709 −1.45789 −0.728945 0.684573i \(-0.759989\pi\)
−0.728945 + 0.684573i \(0.759989\pi\)
\(224\) 31.7723 2.12288
\(225\) −8.28168 −0.552112
\(226\) −24.9015 −1.65642
\(227\) 2.61970 0.173875 0.0869376 0.996214i \(-0.472292\pi\)
0.0869376 + 0.996214i \(0.472292\pi\)
\(228\) −5.21243 −0.345202
\(229\) −14.3409 −0.947673 −0.473837 0.880613i \(-0.657131\pi\)
−0.473837 + 0.880613i \(0.657131\pi\)
\(230\) −2.78811 −0.183843
\(231\) −5.45684 −0.359034
\(232\) 3.31293 0.217504
\(233\) −0.783266 −0.0513135 −0.0256567 0.999671i \(-0.508168\pi\)
−0.0256567 + 0.999671i \(0.508168\pi\)
\(234\) −5.10683 −0.333844
\(235\) 9.73539 0.635067
\(236\) −12.5750 −0.818566
\(237\) 26.8890 1.74663
\(238\) −2.93240 −0.190080
\(239\) −21.5230 −1.39221 −0.696104 0.717941i \(-0.745085\pi\)
−0.696104 + 0.717941i \(0.745085\pi\)
\(240\) 9.25570 0.597453
\(241\) 28.9474 1.86466 0.932332 0.361603i \(-0.117770\pi\)
0.932332 + 0.361603i \(0.117770\pi\)
\(242\) 22.2532 1.43049
\(243\) 20.2745 1.30061
\(244\) −5.55940 −0.355904
\(245\) 10.7565 0.687210
\(246\) 7.47508 0.476594
\(247\) 0.943128 0.0600098
\(248\) −6.90323 −0.438356
\(249\) 36.8308 2.33406
\(250\) 22.2531 1.40741
\(251\) 14.4473 0.911908 0.455954 0.890003i \(-0.349298\pi\)
0.455954 + 0.890003i \(0.349298\pi\)
\(252\) 22.7689 1.43430
\(253\) 0.624943 0.0392898
\(254\) 14.3517 0.900508
\(255\) −1.05584 −0.0661191
\(256\) 8.58427 0.536517
\(257\) 31.4180 1.95980 0.979901 0.199485i \(-0.0639269\pi\)
0.979901 + 0.199485i \(0.0639269\pi\)
\(258\) −2.93114 −0.182485
\(259\) −17.7430 −1.10250
\(260\) 3.00610 0.186431
\(261\) −10.4984 −0.649836
\(262\) 34.5349 2.13358
\(263\) 13.5490 0.835470 0.417735 0.908569i \(-0.362824\pi\)
0.417735 + 0.908569i \(0.362824\pi\)
\(264\) 1.06945 0.0658202
\(265\) −7.08551 −0.435260
\(266\) −7.75514 −0.475498
\(267\) 21.2907 1.30297
\(268\) −22.1189 −1.35113
\(269\) −6.46595 −0.394236 −0.197118 0.980380i \(-0.563158\pi\)
−0.197118 + 0.980380i \(0.563158\pi\)
\(270\) −3.44542 −0.209682
\(271\) −21.9989 −1.33634 −0.668169 0.744009i \(-0.732922\pi\)
−0.668169 + 0.744009i \(0.732922\pi\)
\(272\) −1.11486 −0.0675986
\(273\) −9.17832 −0.555497
\(274\) 19.7604 1.19377
\(275\) −2.01525 −0.121524
\(276\) −5.80941 −0.349685
\(277\) 29.8503 1.79353 0.896766 0.442505i \(-0.145910\pi\)
0.896766 + 0.442505i \(0.145910\pi\)
\(278\) −2.24192 −0.134461
\(279\) 21.8759 1.30967
\(280\) −3.84904 −0.230024
\(281\) −20.9747 −1.25124 −0.625622 0.780126i \(-0.715155\pi\)
−0.625622 + 0.780126i \(0.715155\pi\)
\(282\) 37.4114 2.22781
\(283\) 1.44361 0.0858135 0.0429067 0.999079i \(-0.486338\pi\)
0.0429067 + 0.999079i \(0.486338\pi\)
\(284\) 22.8170 1.35394
\(285\) −2.79230 −0.165402
\(286\) −1.24269 −0.0734817
\(287\) 6.03027 0.355956
\(288\) 19.7325 1.16275
\(289\) −16.8728 −0.992519
\(290\) 11.3974 0.669277
\(291\) 37.7559 2.21329
\(292\) −30.7789 −1.80120
\(293\) 21.2415 1.24094 0.620470 0.784230i \(-0.286942\pi\)
0.620470 + 0.784230i \(0.286942\pi\)
\(294\) 41.3354 2.41073
\(295\) −6.73647 −0.392212
\(296\) 3.47734 0.202116
\(297\) 0.772276 0.0448120
\(298\) 4.02912 0.233401
\(299\) 1.05114 0.0607892
\(300\) 18.7336 1.08159
\(301\) −2.36460 −0.136293
\(302\) −12.2423 −0.704463
\(303\) −9.27733 −0.532969
\(304\) −2.94841 −0.169103
\(305\) −2.97817 −0.170530
\(306\) −1.82119 −0.104111
\(307\) −22.0317 −1.25741 −0.628707 0.777643i \(-0.716415\pi\)
−0.628707 + 0.777643i \(0.716415\pi\)
\(308\) 5.54055 0.315702
\(309\) 28.6887 1.63205
\(310\) −23.7490 −1.34885
\(311\) −1.80379 −0.102283 −0.0511417 0.998691i \(-0.516286\pi\)
−0.0511417 + 0.998691i \(0.516286\pi\)
\(312\) 1.79880 0.101837
\(313\) −2.45010 −0.138488 −0.0692440 0.997600i \(-0.522059\pi\)
−0.0692440 + 0.997600i \(0.522059\pi\)
\(314\) −25.7089 −1.45084
\(315\) 12.1973 0.687241
\(316\) −27.3015 −1.53583
\(317\) −2.03986 −0.114570 −0.0572849 0.998358i \(-0.518244\pi\)
−0.0572849 + 0.998358i \(0.518244\pi\)
\(318\) −27.2284 −1.52689
\(319\) −2.55467 −0.143034
\(320\) −13.4878 −0.753989
\(321\) −11.6226 −0.648712
\(322\) −8.64333 −0.481674
\(323\) 0.336338 0.0187143
\(324\) −24.5422 −1.36345
\(325\) −3.38963 −0.188023
\(326\) 14.1274 0.782443
\(327\) −20.3480 −1.12525
\(328\) −1.18183 −0.0652559
\(329\) 30.1804 1.66390
\(330\) 3.67921 0.202534
\(331\) −13.7142 −0.753798 −0.376899 0.926254i \(-0.623010\pi\)
−0.376899 + 0.926254i \(0.623010\pi\)
\(332\) −37.3958 −2.05236
\(333\) −11.0194 −0.603861
\(334\) −33.5697 −1.83685
\(335\) −11.8491 −0.647387
\(336\) 28.6933 1.56535
\(337\) 13.2739 0.723073 0.361536 0.932358i \(-0.382252\pi\)
0.361536 + 0.932358i \(0.382252\pi\)
\(338\) −2.09018 −0.113691
\(339\) −27.7952 −1.50963
\(340\) 1.07204 0.0581393
\(341\) 5.32324 0.288270
\(342\) −4.81639 −0.260441
\(343\) 5.80800 0.313602
\(344\) 0.463423 0.0249861
\(345\) −3.11211 −0.167550
\(346\) 50.0441 2.69039
\(347\) 3.36141 0.180450 0.0902249 0.995921i \(-0.471241\pi\)
0.0902249 + 0.995921i \(0.471241\pi\)
\(348\) 23.7480 1.27303
\(349\) 20.9003 1.11877 0.559383 0.828909i \(-0.311038\pi\)
0.559383 + 0.828909i \(0.311038\pi\)
\(350\) 27.8722 1.48983
\(351\) 1.29896 0.0693332
\(352\) 4.80167 0.255930
\(353\) 11.3589 0.604573 0.302286 0.953217i \(-0.402250\pi\)
0.302286 + 0.953217i \(0.402250\pi\)
\(354\) −25.8870 −1.37588
\(355\) 12.2231 0.648735
\(356\) −21.6173 −1.14572
\(357\) −3.27317 −0.173234
\(358\) 2.58912 0.136839
\(359\) 10.0049 0.528038 0.264019 0.964517i \(-0.414952\pi\)
0.264019 + 0.964517i \(0.414952\pi\)
\(360\) −2.39047 −0.125989
\(361\) −18.1105 −0.953185
\(362\) 36.5645 1.92179
\(363\) 24.8392 1.30372
\(364\) 9.31912 0.488455
\(365\) −16.4883 −0.863036
\(366\) −11.4446 −0.598218
\(367\) −8.72258 −0.455315 −0.227657 0.973741i \(-0.573107\pi\)
−0.227657 + 0.973741i \(0.573107\pi\)
\(368\) −3.28609 −0.171299
\(369\) 3.74515 0.194965
\(370\) 11.9630 0.621927
\(371\) −21.9656 −1.14040
\(372\) −49.4844 −2.56564
\(373\) 36.4617 1.88792 0.943959 0.330064i \(-0.107070\pi\)
0.943959 + 0.330064i \(0.107070\pi\)
\(374\) −0.443167 −0.0229156
\(375\) 24.8390 1.28268
\(376\) −5.91486 −0.305036
\(377\) −4.29692 −0.221303
\(378\) −10.6810 −0.549373
\(379\) 19.6000 1.00678 0.503392 0.864058i \(-0.332085\pi\)
0.503392 + 0.864058i \(0.332085\pi\)
\(380\) 2.83514 0.145440
\(381\) 16.0195 0.820703
\(382\) −26.8978 −1.37621
\(383\) 27.3446 1.39724 0.698621 0.715492i \(-0.253797\pi\)
0.698621 + 0.715492i \(0.253797\pi\)
\(384\) −14.1457 −0.721868
\(385\) 2.96808 0.151267
\(386\) −0.353411 −0.0179882
\(387\) −1.46855 −0.0746508
\(388\) −38.3351 −1.94617
\(389\) −12.4435 −0.630910 −0.315455 0.948940i \(-0.602157\pi\)
−0.315455 + 0.948940i \(0.602157\pi\)
\(390\) 6.18837 0.313360
\(391\) 0.374859 0.0189574
\(392\) −6.53527 −0.330081
\(393\) 38.5481 1.94449
\(394\) 38.9672 1.96314
\(395\) −14.6254 −0.735886
\(396\) 3.44100 0.172917
\(397\) −36.5064 −1.83220 −0.916102 0.400945i \(-0.868682\pi\)
−0.916102 + 0.400945i \(0.868682\pi\)
\(398\) 27.3687 1.37187
\(399\) −8.65633 −0.433359
\(400\) 10.5967 0.529833
\(401\) 3.79485 0.189506 0.0947529 0.995501i \(-0.469794\pi\)
0.0947529 + 0.995501i \(0.469794\pi\)
\(402\) −45.5340 −2.27103
\(403\) 8.95361 0.446011
\(404\) 9.41965 0.468645
\(405\) −13.1473 −0.653293
\(406\) 35.3327 1.75353
\(407\) −2.68145 −0.132915
\(408\) 0.641487 0.0317584
\(409\) 1.79064 0.0885413 0.0442706 0.999020i \(-0.485904\pi\)
0.0442706 + 0.999020i \(0.485904\pi\)
\(410\) −4.06584 −0.200797
\(411\) 22.0566 1.08797
\(412\) −29.1288 −1.43508
\(413\) −20.8835 −1.02761
\(414\) −5.36801 −0.263823
\(415\) −20.0330 −0.983380
\(416\) 8.07634 0.395975
\(417\) −2.50244 −0.122545
\(418\) −1.17201 −0.0573251
\(419\) −33.3636 −1.62992 −0.814960 0.579518i \(-0.803241\pi\)
−0.814960 + 0.579518i \(0.803241\pi\)
\(420\) −27.5910 −1.34630
\(421\) −32.7426 −1.59578 −0.797888 0.602806i \(-0.794049\pi\)
−0.797888 + 0.602806i \(0.794049\pi\)
\(422\) 19.3835 0.943572
\(423\) 18.7438 0.911353
\(424\) 4.30489 0.209064
\(425\) −1.20881 −0.0586357
\(426\) 46.9712 2.27576
\(427\) −9.23254 −0.446794
\(428\) 11.8009 0.570419
\(429\) −1.38710 −0.0669696
\(430\) 1.59430 0.0768841
\(431\) −0.419800 −0.0202210 −0.0101105 0.999949i \(-0.503218\pi\)
−0.0101105 + 0.999949i \(0.503218\pi\)
\(432\) −4.06080 −0.195375
\(433\) 20.5649 0.988284 0.494142 0.869381i \(-0.335482\pi\)
0.494142 + 0.869381i \(0.335482\pi\)
\(434\) −73.6236 −3.53405
\(435\) 12.7218 0.609965
\(436\) 20.6602 0.989443
\(437\) 0.991364 0.0474234
\(438\) −63.3615 −3.02753
\(439\) 9.91692 0.473309 0.236654 0.971594i \(-0.423949\pi\)
0.236654 + 0.971594i \(0.423949\pi\)
\(440\) −0.581695 −0.0277312
\(441\) 20.7098 0.986181
\(442\) −0.745400 −0.0354551
\(443\) 36.7168 1.74447 0.872235 0.489087i \(-0.162670\pi\)
0.872235 + 0.489087i \(0.162670\pi\)
\(444\) 24.9266 1.18296
\(445\) −11.5804 −0.548965
\(446\) 45.5052 2.15474
\(447\) 4.49733 0.212716
\(448\) −41.8130 −1.97548
\(449\) −14.6997 −0.693723 −0.346861 0.937916i \(-0.612753\pi\)
−0.346861 + 0.937916i \(0.612753\pi\)
\(450\) 17.3102 0.816012
\(451\) 0.911340 0.0429133
\(452\) 28.2216 1.32743
\(453\) −13.6649 −0.642033
\(454\) −5.47564 −0.256985
\(455\) 4.99227 0.234041
\(456\) 1.69650 0.0794459
\(457\) 36.3611 1.70090 0.850450 0.526056i \(-0.176330\pi\)
0.850450 + 0.526056i \(0.176330\pi\)
\(458\) 29.9751 1.40065
\(459\) 0.463233 0.0216219
\(460\) 3.15985 0.147329
\(461\) 24.9163 1.16047 0.580233 0.814451i \(-0.302961\pi\)
0.580233 + 0.814451i \(0.302961\pi\)
\(462\) 11.4058 0.530645
\(463\) 20.6262 0.958580 0.479290 0.877657i \(-0.340894\pi\)
0.479290 + 0.877657i \(0.340894\pi\)
\(464\) 13.4331 0.623614
\(465\) −26.5088 −1.22932
\(466\) 1.63717 0.0758404
\(467\) −0.512602 −0.0237204 −0.0118602 0.999930i \(-0.503775\pi\)
−0.0118602 + 0.999930i \(0.503775\pi\)
\(468\) 5.78772 0.267537
\(469\) −36.7331 −1.69618
\(470\) −20.3488 −0.938618
\(471\) −28.6964 −1.32226
\(472\) 4.09282 0.188387
\(473\) −0.357356 −0.0164312
\(474\) −56.2030 −2.58149
\(475\) −3.19685 −0.146682
\(476\) 3.32338 0.152327
\(477\) −13.6419 −0.624620
\(478\) 44.9871 2.05766
\(479\) −36.3578 −1.66123 −0.830615 0.556847i \(-0.812011\pi\)
−0.830615 + 0.556847i \(0.812011\pi\)
\(480\) −23.9115 −1.09141
\(481\) −4.51017 −0.205646
\(482\) −60.5053 −2.75594
\(483\) −9.64774 −0.438987
\(484\) −25.2202 −1.14637
\(485\) −20.5362 −0.932499
\(486\) −42.3774 −1.92228
\(487\) −23.8286 −1.07978 −0.539889 0.841736i \(-0.681534\pi\)
−0.539889 + 0.841736i \(0.681534\pi\)
\(488\) 1.80943 0.0819089
\(489\) 15.7691 0.713102
\(490\) −22.4831 −1.01568
\(491\) −14.5725 −0.657648 −0.328824 0.944391i \(-0.606652\pi\)
−0.328824 + 0.944391i \(0.606652\pi\)
\(492\) −8.47173 −0.381935
\(493\) −1.53237 −0.0690143
\(494\) −1.97131 −0.0886935
\(495\) 1.84335 0.0828524
\(496\) −27.9908 −1.25682
\(497\) 37.8924 1.69971
\(498\) −76.9831 −3.44969
\(499\) −8.33960 −0.373332 −0.186666 0.982423i \(-0.559768\pi\)
−0.186666 + 0.982423i \(0.559768\pi\)
\(500\) −25.2201 −1.12788
\(501\) −37.4707 −1.67407
\(502\) −30.1976 −1.34778
\(503\) 1.20170 0.0535812 0.0267906 0.999641i \(-0.491471\pi\)
0.0267906 + 0.999641i \(0.491471\pi\)
\(504\) −7.41063 −0.330096
\(505\) 5.04612 0.224549
\(506\) −1.30624 −0.0580697
\(507\) −2.33308 −0.103616
\(508\) −16.2652 −0.721653
\(509\) 4.83702 0.214397 0.107199 0.994238i \(-0.465812\pi\)
0.107199 + 0.994238i \(0.465812\pi\)
\(510\) 2.20689 0.0977229
\(511\) −51.1148 −2.26118
\(512\) −30.0689 −1.32887
\(513\) 1.22508 0.0540887
\(514\) −65.6694 −2.89655
\(515\) −15.6044 −0.687610
\(516\) 3.32195 0.146241
\(517\) 4.56108 0.200596
\(518\) 37.0861 1.62947
\(519\) 55.8596 2.45196
\(520\) −0.978402 −0.0429058
\(521\) 32.4755 1.42278 0.711388 0.702799i \(-0.248067\pi\)
0.711388 + 0.702799i \(0.248067\pi\)
\(522\) 21.9436 0.960447
\(523\) 21.3802 0.934893 0.467446 0.884021i \(-0.345174\pi\)
0.467446 + 0.884021i \(0.345174\pi\)
\(524\) −39.1395 −1.70982
\(525\) 31.1111 1.35780
\(526\) −28.3200 −1.23481
\(527\) 3.19303 0.139091
\(528\) 4.33635 0.188715
\(529\) −21.8951 −0.951961
\(530\) 14.8100 0.643306
\(531\) −12.9699 −0.562844
\(532\) 8.78913 0.381057
\(533\) 1.53286 0.0663955
\(534\) −44.5015 −1.92577
\(535\) 6.32177 0.273314
\(536\) 7.19908 0.310953
\(537\) 2.89000 0.124713
\(538\) 13.5150 0.582674
\(539\) 5.03950 0.217066
\(540\) 3.90480 0.168036
\(541\) 5.85414 0.251689 0.125844 0.992050i \(-0.459836\pi\)
0.125844 + 0.992050i \(0.459836\pi\)
\(542\) 45.9817 1.97509
\(543\) 40.8135 1.75147
\(544\) 2.88018 0.123487
\(545\) 11.0677 0.474087
\(546\) 19.1844 0.821015
\(547\) −37.0025 −1.58211 −0.791055 0.611745i \(-0.790468\pi\)
−0.791055 + 0.611745i \(0.790468\pi\)
\(548\) −22.3950 −0.956667
\(549\) −5.73395 −0.244719
\(550\) 4.21225 0.179611
\(551\) −4.05255 −0.172644
\(552\) 1.89080 0.0804778
\(553\) −45.3399 −1.92805
\(554\) −62.3927 −2.65081
\(555\) 13.3532 0.566811
\(556\) 2.54083 0.107755
\(557\) 7.66363 0.324718 0.162359 0.986732i \(-0.448090\pi\)
0.162359 + 0.986732i \(0.448090\pi\)
\(558\) −45.7245 −1.93567
\(559\) −0.601067 −0.0254224
\(560\) −15.6068 −0.659509
\(561\) −0.494666 −0.0208848
\(562\) 43.8409 1.84932
\(563\) −16.2677 −0.685604 −0.342802 0.939408i \(-0.611376\pi\)
−0.342802 + 0.939408i \(0.611376\pi\)
\(564\) −42.3994 −1.78534
\(565\) 15.1184 0.636034
\(566\) −3.01740 −0.126831
\(567\) −40.7574 −1.71165
\(568\) −7.42630 −0.311601
\(569\) −2.22546 −0.0932960 −0.0466480 0.998911i \(-0.514854\pi\)
−0.0466480 + 0.998911i \(0.514854\pi\)
\(570\) 5.83643 0.244461
\(571\) −4.02640 −0.168500 −0.0842498 0.996445i \(-0.526849\pi\)
−0.0842498 + 0.996445i \(0.526849\pi\)
\(572\) 1.40838 0.0588871
\(573\) −30.0235 −1.25425
\(574\) −12.6044 −0.526096
\(575\) −3.56299 −0.148587
\(576\) −25.9683 −1.08201
\(577\) −2.73297 −0.113775 −0.0568876 0.998381i \(-0.518118\pi\)
−0.0568876 + 0.998381i \(0.518118\pi\)
\(578\) 35.2673 1.46693
\(579\) −0.394480 −0.0163940
\(580\) −12.9170 −0.536349
\(581\) −62.1036 −2.57649
\(582\) −78.9168 −3.27120
\(583\) −3.31960 −0.137484
\(584\) 10.0177 0.414534
\(585\) 3.10049 0.128189
\(586\) −44.3986 −1.83409
\(587\) 4.70475 0.194186 0.0970929 0.995275i \(-0.469046\pi\)
0.0970929 + 0.995275i \(0.469046\pi\)
\(588\) −46.8467 −1.93192
\(589\) 8.44440 0.347946
\(590\) 14.0804 0.579683
\(591\) 43.4954 1.78916
\(592\) 14.0997 0.579494
\(593\) −7.51256 −0.308504 −0.154252 0.988032i \(-0.549297\pi\)
−0.154252 + 0.988032i \(0.549297\pi\)
\(594\) −1.61420 −0.0662313
\(595\) 1.78034 0.0729868
\(596\) −4.56632 −0.187044
\(597\) 30.5491 1.25029
\(598\) −2.19708 −0.0898455
\(599\) 11.6528 0.476121 0.238061 0.971250i \(-0.423488\pi\)
0.238061 + 0.971250i \(0.423488\pi\)
\(600\) −6.09726 −0.248920
\(601\) 18.4273 0.751663 0.375832 0.926688i \(-0.377357\pi\)
0.375832 + 0.926688i \(0.377357\pi\)
\(602\) 4.94245 0.201439
\(603\) −22.8134 −0.929032
\(604\) 13.8745 0.564546
\(605\) −13.5105 −0.549280
\(606\) 19.3913 0.787719
\(607\) 16.1309 0.654735 0.327367 0.944897i \(-0.393839\pi\)
0.327367 + 0.944897i \(0.393839\pi\)
\(608\) 7.61702 0.308911
\(609\) 39.4385 1.59813
\(610\) 6.22493 0.252040
\(611\) 7.67167 0.310363
\(612\) 2.06401 0.0834328
\(613\) 14.6581 0.592035 0.296018 0.955183i \(-0.404341\pi\)
0.296018 + 0.955183i \(0.404341\pi\)
\(614\) 46.0502 1.85844
\(615\) −4.53832 −0.183003
\(616\) −1.80329 −0.0726568
\(617\) 1.00000 0.0402585
\(618\) −59.9647 −2.41214
\(619\) −30.9896 −1.24558 −0.622789 0.782390i \(-0.714001\pi\)
−0.622789 + 0.782390i \(0.714001\pi\)
\(620\) 26.9155 1.08095
\(621\) 1.36539 0.0547912
\(622\) 3.77024 0.151173
\(623\) −35.9001 −1.43831
\(624\) 7.29367 0.291980
\(625\) 3.43771 0.137508
\(626\) 5.12117 0.204683
\(627\) −1.30821 −0.0522449
\(628\) 29.1366 1.16268
\(629\) −1.60841 −0.0641316
\(630\) −25.4946 −1.01573
\(631\) 24.2934 0.967105 0.483553 0.875315i \(-0.339346\pi\)
0.483553 + 0.875315i \(0.339346\pi\)
\(632\) 8.88587 0.353461
\(633\) 21.6359 0.859951
\(634\) 4.26368 0.169332
\(635\) −8.71331 −0.345777
\(636\) 30.8587 1.22363
\(637\) 8.47636 0.335846
\(638\) 5.33974 0.211402
\(639\) 23.5334 0.930967
\(640\) 7.69409 0.304136
\(641\) 45.4853 1.79656 0.898280 0.439423i \(-0.144817\pi\)
0.898280 + 0.439423i \(0.144817\pi\)
\(642\) 24.2934 0.958785
\(643\) 17.5784 0.693223 0.346612 0.938009i \(-0.387332\pi\)
0.346612 + 0.938009i \(0.387332\pi\)
\(644\) 9.79574 0.386006
\(645\) 1.77957 0.0700705
\(646\) −0.703008 −0.0276595
\(647\) 45.3923 1.78456 0.892278 0.451487i \(-0.149106\pi\)
0.892278 + 0.451487i \(0.149106\pi\)
\(648\) 7.98778 0.313790
\(649\) −3.15607 −0.123887
\(650\) 7.08494 0.277894
\(651\) −82.1791 −3.22085
\(652\) −16.0110 −0.627038
\(653\) −25.9357 −1.01494 −0.507471 0.861669i \(-0.669420\pi\)
−0.507471 + 0.861669i \(0.669420\pi\)
\(654\) 42.5311 1.66310
\(655\) −20.9671 −0.819251
\(656\) −4.79203 −0.187097
\(657\) −31.7452 −1.23850
\(658\) −63.0825 −2.45921
\(659\) −15.8752 −0.618411 −0.309205 0.950995i \(-0.600063\pi\)
−0.309205 + 0.950995i \(0.600063\pi\)
\(660\) −4.16976 −0.162308
\(661\) 6.26682 0.243751 0.121875 0.992545i \(-0.461109\pi\)
0.121875 + 0.992545i \(0.461109\pi\)
\(662\) 28.6651 1.11410
\(663\) −0.832020 −0.0323130
\(664\) 12.1713 0.472337
\(665\) 4.70835 0.182582
\(666\) 23.0326 0.892497
\(667\) −4.51669 −0.174887
\(668\) 38.0455 1.47203
\(669\) 50.7932 1.96378
\(670\) 24.7668 0.956826
\(671\) −1.39529 −0.0538646
\(672\) −74.1272 −2.85952
\(673\) −1.88677 −0.0727295 −0.0363648 0.999339i \(-0.511578\pi\)
−0.0363648 + 0.999339i \(0.511578\pi\)
\(674\) −27.7448 −1.06869
\(675\) −4.40298 −0.169471
\(676\) 2.36887 0.0911103
\(677\) 22.5363 0.866139 0.433069 0.901361i \(-0.357431\pi\)
0.433069 + 0.901361i \(0.357431\pi\)
\(678\) 58.0971 2.23121
\(679\) −63.6635 −2.44318
\(680\) −0.348917 −0.0133804
\(681\) −6.11195 −0.234210
\(682\) −11.1266 −0.426058
\(683\) −8.43173 −0.322631 −0.161316 0.986903i \(-0.551574\pi\)
−0.161316 + 0.986903i \(0.551574\pi\)
\(684\) 5.45856 0.208713
\(685\) −11.9970 −0.458383
\(686\) −12.1398 −0.463499
\(687\) 33.4584 1.27652
\(688\) 1.87906 0.0716384
\(689\) −5.58352 −0.212715
\(690\) 6.50487 0.247636
\(691\) −32.8082 −1.24808 −0.624042 0.781391i \(-0.714511\pi\)
−0.624042 + 0.781391i \(0.714511\pi\)
\(692\) −56.7165 −2.15604
\(693\) 5.71451 0.217076
\(694\) −7.02596 −0.266702
\(695\) 1.36113 0.0516305
\(696\) −7.72931 −0.292979
\(697\) 0.546648 0.0207058
\(698\) −43.6854 −1.65352
\(699\) 1.82742 0.0691194
\(700\) −31.5884 −1.19393
\(701\) −44.5816 −1.68382 −0.841911 0.539616i \(-0.818569\pi\)
−0.841911 + 0.539616i \(0.818569\pi\)
\(702\) −2.71506 −0.102473
\(703\) −4.25367 −0.160430
\(704\) −6.31909 −0.238160
\(705\) −22.7134 −0.855436
\(706\) −23.7422 −0.893548
\(707\) 15.6433 0.588327
\(708\) 29.3385 1.10261
\(709\) −37.1682 −1.39588 −0.697940 0.716157i \(-0.745900\pi\)
−0.697940 + 0.716157i \(0.745900\pi\)
\(710\) −25.5485 −0.958819
\(711\) −28.1587 −1.05603
\(712\) 7.03583 0.263679
\(713\) 9.41154 0.352465
\(714\) 6.84152 0.256038
\(715\) 0.754468 0.0282155
\(716\) −2.93433 −0.109661
\(717\) 50.2149 1.87531
\(718\) −20.9121 −0.780431
\(719\) −29.8968 −1.11496 −0.557482 0.830189i \(-0.688232\pi\)
−0.557482 + 0.830189i \(0.688232\pi\)
\(720\) −9.69275 −0.361228
\(721\) −48.3746 −1.80156
\(722\) 37.8543 1.40879
\(723\) −67.5364 −2.51171
\(724\) −41.4396 −1.54009
\(725\) 14.5650 0.540929
\(726\) −51.9184 −1.92687
\(727\) 16.3942 0.608028 0.304014 0.952668i \(-0.401673\pi\)
0.304014 + 0.952668i \(0.401673\pi\)
\(728\) −3.03311 −0.112415
\(729\) −16.2210 −0.600779
\(730\) 34.4635 1.27555
\(731\) −0.214352 −0.00792811
\(732\) 12.9705 0.479403
\(733\) −17.7639 −0.656126 −0.328063 0.944656i \(-0.606396\pi\)
−0.328063 + 0.944656i \(0.606396\pi\)
\(734\) 18.2318 0.672948
\(735\) −25.0958 −0.925673
\(736\) 8.48940 0.312923
\(737\) −5.55138 −0.204488
\(738\) −7.82805 −0.288155
\(739\) 53.4089 1.96468 0.982339 0.187110i \(-0.0599120\pi\)
0.982339 + 0.187110i \(0.0599120\pi\)
\(740\) −13.5580 −0.498403
\(741\) −2.20039 −0.0808333
\(742\) 45.9121 1.68549
\(743\) −31.4914 −1.15531 −0.577653 0.816282i \(-0.696031\pi\)
−0.577653 + 0.816282i \(0.696031\pi\)
\(744\) 16.1058 0.590466
\(745\) −2.44618 −0.0896212
\(746\) −76.2117 −2.79031
\(747\) −38.5699 −1.41120
\(748\) 0.502254 0.0183642
\(749\) 19.5979 0.716092
\(750\) −51.9181 −1.89578
\(751\) 50.6213 1.84720 0.923599 0.383360i \(-0.125233\pi\)
0.923599 + 0.383360i \(0.125233\pi\)
\(752\) −23.9832 −0.874578
\(753\) −33.7067 −1.22834
\(754\) 8.98136 0.327082
\(755\) 7.43260 0.270500
\(756\) 12.1051 0.440260
\(757\) 32.5132 1.18171 0.590857 0.806776i \(-0.298790\pi\)
0.590857 + 0.806776i \(0.298790\pi\)
\(758\) −40.9676 −1.48801
\(759\) −1.45804 −0.0529234
\(760\) −0.922759 −0.0334720
\(761\) −51.9771 −1.88417 −0.942085 0.335374i \(-0.891137\pi\)
−0.942085 + 0.335374i \(0.891137\pi\)
\(762\) −33.4837 −1.21299
\(763\) 34.3106 1.24213
\(764\) 30.4841 1.10287
\(765\) 1.10569 0.0399765
\(766\) −57.1552 −2.06510
\(767\) −5.30846 −0.191678
\(768\) −20.0277 −0.722689
\(769\) −48.9162 −1.76396 −0.881982 0.471284i \(-0.843791\pi\)
−0.881982 + 0.471284i \(0.843791\pi\)
\(770\) −6.20383 −0.223570
\(771\) −73.3006 −2.63986
\(772\) 0.400531 0.0144154
\(773\) 25.9124 0.932005 0.466002 0.884784i \(-0.345694\pi\)
0.466002 + 0.884784i \(0.345694\pi\)
\(774\) 3.06955 0.110333
\(775\) −30.3494 −1.09018
\(776\) 12.4770 0.447898
\(777\) 41.3958 1.48506
\(778\) 26.0092 0.932475
\(779\) 1.44568 0.0517970
\(780\) −7.01347 −0.251122
\(781\) 5.72659 0.204913
\(782\) −0.783523 −0.0280187
\(783\) −5.58152 −0.199467
\(784\) −26.4988 −0.946386
\(785\) 15.6085 0.557092
\(786\) −80.5726 −2.87393
\(787\) −25.6651 −0.914862 −0.457431 0.889245i \(-0.651230\pi\)
−0.457431 + 0.889245i \(0.651230\pi\)
\(788\) −44.1626 −1.57323
\(789\) −31.6110 −1.12538
\(790\) 30.5699 1.08763
\(791\) 46.8679 1.66643
\(792\) −1.11995 −0.0397957
\(793\) −2.34686 −0.0833394
\(794\) 76.3051 2.70797
\(795\) 16.5310 0.586296
\(796\) −31.0178 −1.09940
\(797\) 30.1552 1.06815 0.534076 0.845436i \(-0.320660\pi\)
0.534076 + 0.845436i \(0.320660\pi\)
\(798\) 18.0933 0.640497
\(799\) 2.73587 0.0967881
\(800\) −27.3758 −0.967880
\(801\) −22.2961 −0.787792
\(802\) −7.93194 −0.280086
\(803\) −7.72484 −0.272604
\(804\) 51.6051 1.81997
\(805\) 5.24759 0.184953
\(806\) −18.7147 −0.659197
\(807\) 15.0855 0.531036
\(808\) −3.06583 −0.107856
\(809\) −11.1658 −0.392569 −0.196285 0.980547i \(-0.562888\pi\)
−0.196285 + 0.980547i \(0.562888\pi\)
\(810\) 27.4802 0.965555
\(811\) −42.8489 −1.50463 −0.752315 0.658804i \(-0.771063\pi\)
−0.752315 + 0.658804i \(0.771063\pi\)
\(812\) −40.0436 −1.40525
\(813\) 51.3251 1.80005
\(814\) 5.60473 0.196446
\(815\) −8.57710 −0.300443
\(816\) 2.60106 0.0910555
\(817\) −0.566883 −0.0198327
\(818\) −3.74276 −0.130863
\(819\) 9.61172 0.335861
\(820\) 4.60794 0.160916
\(821\) 16.3169 0.569465 0.284732 0.958607i \(-0.408095\pi\)
0.284732 + 0.958607i \(0.408095\pi\)
\(822\) −46.1024 −1.60801
\(823\) −32.6925 −1.13959 −0.569794 0.821788i \(-0.692977\pi\)
−0.569794 + 0.821788i \(0.692977\pi\)
\(824\) 9.48062 0.330273
\(825\) 4.70174 0.163694
\(826\) 43.6503 1.51879
\(827\) 42.4194 1.47507 0.737534 0.675310i \(-0.235990\pi\)
0.737534 + 0.675310i \(0.235990\pi\)
\(828\) 6.08373 0.211424
\(829\) −29.6322 −1.02917 −0.514585 0.857439i \(-0.672054\pi\)
−0.514585 + 0.857439i \(0.672054\pi\)
\(830\) 41.8726 1.45342
\(831\) −69.6431 −2.41589
\(832\) −10.6286 −0.368481
\(833\) 3.02283 0.104735
\(834\) 5.23057 0.181120
\(835\) 20.3810 0.705315
\(836\) 1.32828 0.0459395
\(837\) 11.6304 0.402004
\(838\) 69.7361 2.40899
\(839\) 32.0792 1.10750 0.553748 0.832684i \(-0.313197\pi\)
0.553748 + 0.832684i \(0.313197\pi\)
\(840\) 8.98009 0.309843
\(841\) −10.5365 −0.363326
\(842\) 68.4380 2.35853
\(843\) 48.9355 1.68543
\(844\) −21.9678 −0.756164
\(845\) 1.26900 0.0436551
\(846\) −39.1779 −1.34696
\(847\) −41.8834 −1.43913
\(848\) 17.4552 0.599415
\(849\) −3.36804 −0.115591
\(850\) 2.52663 0.0866626
\(851\) −4.74084 −0.162514
\(852\) −53.2338 −1.82376
\(853\) 10.0400 0.343763 0.171882 0.985118i \(-0.445015\pi\)
0.171882 + 0.985118i \(0.445015\pi\)
\(854\) 19.2977 0.660354
\(855\) 2.92416 0.100004
\(856\) −3.84087 −0.131278
\(857\) 43.4488 1.48418 0.742091 0.670300i \(-0.233834\pi\)
0.742091 + 0.670300i \(0.233834\pi\)
\(858\) 2.89929 0.0989800
\(859\) −43.5521 −1.48598 −0.742988 0.669304i \(-0.766592\pi\)
−0.742988 + 0.669304i \(0.766592\pi\)
\(860\) −1.80687 −0.0616138
\(861\) −14.0691 −0.479473
\(862\) 0.877459 0.0298864
\(863\) 29.5209 1.00490 0.502451 0.864606i \(-0.332432\pi\)
0.502451 + 0.864606i \(0.332432\pi\)
\(864\) 10.4908 0.356905
\(865\) −30.3831 −1.03306
\(866\) −42.9843 −1.46067
\(867\) 39.3656 1.33693
\(868\) 83.4398 2.83213
\(869\) −6.85210 −0.232442
\(870\) −26.5910 −0.901518
\(871\) −9.33733 −0.316383
\(872\) −6.72431 −0.227714
\(873\) −39.5387 −1.33818
\(874\) −2.07213 −0.0700909
\(875\) −41.8832 −1.41591
\(876\) 71.8094 2.42622
\(877\) −27.8800 −0.941439 −0.470720 0.882283i \(-0.656006\pi\)
−0.470720 + 0.882283i \(0.656006\pi\)
\(878\) −20.7282 −0.699542
\(879\) −49.5580 −1.67155
\(880\) −2.35862 −0.0795091
\(881\) 44.4122 1.49629 0.748143 0.663537i \(-0.230946\pi\)
0.748143 + 0.663537i \(0.230946\pi\)
\(882\) −43.2873 −1.45756
\(883\) −10.0140 −0.336997 −0.168498 0.985702i \(-0.553892\pi\)
−0.168498 + 0.985702i \(0.553892\pi\)
\(884\) 0.844784 0.0284132
\(885\) 15.7167 0.528311
\(886\) −76.7449 −2.57830
\(887\) −34.8779 −1.17108 −0.585542 0.810642i \(-0.699118\pi\)
−0.585542 + 0.810642i \(0.699118\pi\)
\(888\) −8.11289 −0.272251
\(889\) −27.0118 −0.905948
\(890\) 24.2052 0.811361
\(891\) −6.15956 −0.206353
\(892\) −51.5724 −1.72677
\(893\) 7.23537 0.242122
\(894\) −9.40024 −0.314391
\(895\) −1.57192 −0.0525436
\(896\) 23.8522 0.796846
\(897\) −2.45240 −0.0818832
\(898\) 30.7251 1.02531
\(899\) −38.4730 −1.28315
\(900\) −19.6182 −0.653940
\(901\) −1.99119 −0.0663362
\(902\) −1.90487 −0.0634251
\(903\) 5.51679 0.183587
\(904\) −9.18535 −0.305500
\(905\) −22.1992 −0.737928
\(906\) 28.5621 0.948913
\(907\) −46.1010 −1.53076 −0.765380 0.643579i \(-0.777449\pi\)
−0.765380 + 0.643579i \(0.777449\pi\)
\(908\) 6.20571 0.205944
\(909\) 9.71540 0.322240
\(910\) −10.4348 −0.345909
\(911\) 0.856350 0.0283721 0.0141861 0.999899i \(-0.495484\pi\)
0.0141861 + 0.999899i \(0.495484\pi\)
\(912\) 6.87886 0.227782
\(913\) −9.38555 −0.310616
\(914\) −76.0013 −2.51390
\(915\) 6.94831 0.229704
\(916\) −33.9717 −1.12246
\(917\) −64.9993 −2.14647
\(918\) −0.968242 −0.0319568
\(919\) 3.77782 0.124619 0.0623095 0.998057i \(-0.480153\pi\)
0.0623095 + 0.998057i \(0.480153\pi\)
\(920\) −1.02844 −0.0339067
\(921\) 51.4015 1.69374
\(922\) −52.0796 −1.71515
\(923\) 9.63204 0.317042
\(924\) −12.9265 −0.425251
\(925\) 15.2878 0.502659
\(926\) −43.1125 −1.41676
\(927\) −30.0434 −0.986755
\(928\) −34.7034 −1.13919
\(929\) 14.3255 0.470004 0.235002 0.971995i \(-0.424490\pi\)
0.235002 + 0.971995i \(0.424490\pi\)
\(930\) 55.4083 1.81691
\(931\) 7.99429 0.262002
\(932\) −1.85545 −0.0607774
\(933\) 4.20837 0.137776
\(934\) 1.07143 0.0350583
\(935\) 0.269058 0.00879914
\(936\) −1.88374 −0.0615720
\(937\) −1.69404 −0.0553419 −0.0276709 0.999617i \(-0.508809\pi\)
−0.0276709 + 0.999617i \(0.508809\pi\)
\(938\) 76.7789 2.50692
\(939\) 5.71628 0.186544
\(940\) 23.0618 0.752195
\(941\) 57.7807 1.88360 0.941799 0.336178i \(-0.109134\pi\)
0.941799 + 0.336178i \(0.109134\pi\)
\(942\) 59.9807 1.95428
\(943\) 1.61126 0.0524698
\(944\) 16.5953 0.540132
\(945\) 6.48474 0.210948
\(946\) 0.746939 0.0242851
\(947\) 47.4372 1.54150 0.770751 0.637137i \(-0.219881\pi\)
0.770751 + 0.637137i \(0.219881\pi\)
\(948\) 63.6965 2.06877
\(949\) −12.9931 −0.421773
\(950\) 6.68201 0.216793
\(951\) 4.75914 0.154326
\(952\) −1.08167 −0.0350570
\(953\) −44.0583 −1.42719 −0.713594 0.700559i \(-0.752934\pi\)
−0.713594 + 0.700559i \(0.752934\pi\)
\(954\) 28.5141 0.923177
\(955\) 16.3303 0.528438
\(956\) −50.9852 −1.64898
\(957\) 5.96025 0.192667
\(958\) 75.9945 2.45527
\(959\) −37.1916 −1.20098
\(960\) 31.4680 1.01563
\(961\) 49.1672 1.58604
\(962\) 9.42708 0.303941
\(963\) 12.1714 0.392219
\(964\) 68.5725 2.20857
\(965\) 0.214565 0.00690709
\(966\) 20.1655 0.648816
\(967\) 20.4034 0.656128 0.328064 0.944656i \(-0.393604\pi\)
0.328064 + 0.944656i \(0.393604\pi\)
\(968\) 8.20847 0.263830
\(969\) −0.784702 −0.0252082
\(970\) 42.9243 1.37822
\(971\) −17.9394 −0.575704 −0.287852 0.957675i \(-0.592941\pi\)
−0.287852 + 0.957675i \(0.592941\pi\)
\(972\) 48.0275 1.54048
\(973\) 4.21959 0.135274
\(974\) 49.8062 1.59589
\(975\) 7.90826 0.253267
\(976\) 7.33676 0.234844
\(977\) −22.8010 −0.729470 −0.364735 0.931111i \(-0.618840\pi\)
−0.364735 + 0.931111i \(0.618840\pi\)
\(978\) −32.9602 −1.05395
\(979\) −5.42549 −0.173399
\(980\) 25.4808 0.813955
\(981\) 21.3088 0.680339
\(982\) 30.4592 0.971992
\(983\) 31.5278 1.00558 0.502791 0.864408i \(-0.332306\pi\)
0.502791 + 0.864408i \(0.332306\pi\)
\(984\) 2.75731 0.0878998
\(985\) −23.6580 −0.753806
\(986\) 3.20293 0.102002
\(987\) −70.4131 −2.24127
\(988\) 2.23414 0.0710776
\(989\) −0.631808 −0.0200903
\(990\) −3.85294 −0.122454
\(991\) 6.06283 0.192592 0.0962961 0.995353i \(-0.469300\pi\)
0.0962961 + 0.995353i \(0.469300\pi\)
\(992\) 72.3124 2.29592
\(993\) 31.9962 1.01537
\(994\) −79.2022 −2.51214
\(995\) −16.6163 −0.526771
\(996\) 87.2472 2.76453
\(997\) −3.19880 −0.101307 −0.0506535 0.998716i \(-0.516130\pi\)
−0.0506535 + 0.998716i \(0.516130\pi\)
\(998\) 17.4313 0.551778
\(999\) −5.85851 −0.185355
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 \(a_p\))