Properties

Label 6018.2.a.p.1.2
Level 6018
Weight 2
Character 6018.1
Self dual Yes
Analytic conductor 48.054
Analytic rank 0
Dimension 5
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0539719364\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: 5.5.1668357.1
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-2.44651\)
Character \(\chi\) = 6018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(-1.37256 q^{5}\) \(-1.00000 q^{6}\) \(+2.44651 q^{7}\) \(-1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(-1.37256 q^{5}\) \(-1.00000 q^{6}\) \(+2.44651 q^{7}\) \(-1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+1.37256 q^{10}\) \(+4.53685 q^{11}\) \(+1.00000 q^{12}\) \(-3.92241 q^{13}\) \(-2.44651 q^{14}\) \(-1.37256 q^{15}\) \(+1.00000 q^{16}\) \(-1.00000 q^{17}\) \(-1.00000 q^{18}\) \(+1.28222 q^{19}\) \(-1.37256 q^{20}\) \(+2.44651 q^{21}\) \(-4.53685 q^{22}\) \(+3.17888 q^{23}\) \(-1.00000 q^{24}\) \(-3.11609 q^{25}\) \(+3.92241 q^{26}\) \(+1.00000 q^{27}\) \(+2.44651 q^{28}\) \(-4.44468 q^{29}\) \(+1.37256 q^{30}\) \(+5.90783 q^{31}\) \(-1.00000 q^{32}\) \(+4.53685 q^{33}\) \(+1.00000 q^{34}\) \(-3.35797 q^{35}\) \(+1.00000 q^{36}\) \(-1.11972 q^{37}\) \(-1.28222 q^{38}\) \(-3.92241 q^{39}\) \(+1.37256 q^{40}\) \(+5.71415 q^{41}\) \(-2.44651 q^{42}\) \(-3.32679 q^{43}\) \(+4.53685 q^{44}\) \(-1.37256 q^{45}\) \(-3.17888 q^{46}\) \(+12.7605 q^{47}\) \(+1.00000 q^{48}\) \(-1.01458 q^{49}\) \(+3.11609 q^{50}\) \(-1.00000 q^{51}\) \(-3.92241 q^{52}\) \(+6.22101 q^{53}\) \(-1.00000 q^{54}\) \(-6.22708 q^{55}\) \(-2.44651 q^{56}\) \(+1.28222 q^{57}\) \(+4.44468 q^{58}\) \(-1.00000 q^{59}\) \(-1.37256 q^{60}\) \(+4.28402 q^{61}\) \(-5.90783 q^{62}\) \(+2.44651 q^{63}\) \(+1.00000 q^{64}\) \(+5.38373 q^{65}\) \(-4.53685 q^{66}\) \(-14.1086 q^{67}\) \(-1.00000 q^{68}\) \(+3.17888 q^{69}\) \(+3.35797 q^{70}\) \(-10.3817 q^{71}\) \(-1.00000 q^{72}\) \(+11.6347 q^{73}\) \(+1.11972 q^{74}\) \(-3.11609 q^{75}\) \(+1.28222 q^{76}\) \(+11.0995 q^{77}\) \(+3.92241 q^{78}\) \(+14.0873 q^{79}\) \(-1.37256 q^{80}\) \(+1.00000 q^{81}\) \(-5.71415 q^{82}\) \(+9.20886 q^{83}\) \(+2.44651 q^{84}\) \(+1.37256 q^{85}\) \(+3.32679 q^{86}\) \(-4.44468 q^{87}\) \(-4.53685 q^{88}\) \(+14.8009 q^{89}\) \(+1.37256 q^{90}\) \(-9.59622 q^{91}\) \(+3.17888 q^{92}\) \(+5.90783 q^{93}\) \(-12.7605 q^{94}\) \(-1.75992 q^{95}\) \(-1.00000 q^{96}\) \(-6.25100 q^{97}\) \(+1.01458 q^{98}\) \(+4.53685 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(5q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 5q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut -\mathstrut 5q^{8} \) \(\mathstrut +\mathstrut 5q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(5q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 5q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut -\mathstrut 5q^{8} \) \(\mathstrut +\mathstrut 5q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut +\mathstrut 6q^{11} \) \(\mathstrut +\mathstrut 5q^{12} \) \(\mathstrut -\mathstrut 2q^{13} \) \(\mathstrut +\mathstrut q^{14} \) \(\mathstrut -\mathstrut q^{15} \) \(\mathstrut +\mathstrut 5q^{16} \) \(\mathstrut -\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 5q^{18} \) \(\mathstrut +\mathstrut 4q^{19} \) \(\mathstrut -\mathstrut q^{20} \) \(\mathstrut -\mathstrut q^{21} \) \(\mathstrut -\mathstrut 6q^{22} \) \(\mathstrut +\mathstrut 12q^{23} \) \(\mathstrut -\mathstrut 5q^{24} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut +\mathstrut 2q^{26} \) \(\mathstrut +\mathstrut 5q^{27} \) \(\mathstrut -\mathstrut q^{28} \) \(\mathstrut +\mathstrut 19q^{29} \) \(\mathstrut +\mathstrut q^{30} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut -\mathstrut 5q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 4q^{35} \) \(\mathstrut +\mathstrut 5q^{36} \) \(\mathstrut -\mathstrut 11q^{37} \) \(\mathstrut -\mathstrut 4q^{38} \) \(\mathstrut -\mathstrut 2q^{39} \) \(\mathstrut +\mathstrut q^{40} \) \(\mathstrut +\mathstrut 6q^{41} \) \(\mathstrut +\mathstrut q^{42} \) \(\mathstrut +\mathstrut 2q^{43} \) \(\mathstrut +\mathstrut 6q^{44} \) \(\mathstrut -\mathstrut q^{45} \) \(\mathstrut -\mathstrut 12q^{46} \) \(\mathstrut +\mathstrut 22q^{47} \) \(\mathstrut +\mathstrut 5q^{48} \) \(\mathstrut -\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 4q^{50} \) \(\mathstrut -\mathstrut 5q^{51} \) \(\mathstrut -\mathstrut 2q^{52} \) \(\mathstrut +\mathstrut 15q^{53} \) \(\mathstrut -\mathstrut 5q^{54} \) \(\mathstrut -\mathstrut 36q^{55} \) \(\mathstrut +\mathstrut q^{56} \) \(\mathstrut +\mathstrut 4q^{57} \) \(\mathstrut -\mathstrut 19q^{58} \) \(\mathstrut -\mathstrut 5q^{59} \) \(\mathstrut -\mathstrut q^{60} \) \(\mathstrut +\mathstrut 16q^{61} \) \(\mathstrut -\mathstrut 5q^{62} \) \(\mathstrut -\mathstrut q^{63} \) \(\mathstrut +\mathstrut 5q^{64} \) \(\mathstrut -\mathstrut 2q^{65} \) \(\mathstrut -\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 25q^{67} \) \(\mathstrut -\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 4q^{70} \) \(\mathstrut -\mathstrut 5q^{72} \) \(\mathstrut -\mathstrut 10q^{73} \) \(\mathstrut +\mathstrut 11q^{74} \) \(\mathstrut +\mathstrut 4q^{75} \) \(\mathstrut +\mathstrut 4q^{76} \) \(\mathstrut +\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 2q^{78} \) \(\mathstrut +\mathstrut 10q^{79} \) \(\mathstrut -\mathstrut q^{80} \) \(\mathstrut +\mathstrut 5q^{81} \) \(\mathstrut -\mathstrut 6q^{82} \) \(\mathstrut +\mathstrut 19q^{83} \) \(\mathstrut -\mathstrut q^{84} \) \(\mathstrut +\mathstrut q^{85} \) \(\mathstrut -\mathstrut 2q^{86} \) \(\mathstrut +\mathstrut 19q^{87} \) \(\mathstrut -\mathstrut 6q^{88} \) \(\mathstrut +\mathstrut 23q^{89} \) \(\mathstrut +\mathstrut q^{90} \) \(\mathstrut -\mathstrut 17q^{91} \) \(\mathstrut +\mathstrut 12q^{92} \) \(\mathstrut +\mathstrut 5q^{93} \) \(\mathstrut -\mathstrut 22q^{94} \) \(\mathstrut +\mathstrut q^{95} \) \(\mathstrut -\mathstrut 5q^{96} \) \(\mathstrut +\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut 12q^{98} \) \(\mathstrut +\mathstrut 6q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) −1.37256 −0.613826 −0.306913 0.951738i \(-0.599296\pi\)
−0.306913 + 0.951738i \(0.599296\pi\)
\(6\) −1.00000 −0.408248
\(7\) 2.44651 0.924694 0.462347 0.886699i \(-0.347007\pi\)
0.462347 + 0.886699i \(0.347007\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 1.37256 0.434040
\(11\) 4.53685 1.36791 0.683956 0.729524i \(-0.260258\pi\)
0.683956 + 0.729524i \(0.260258\pi\)
\(12\) 1.00000 0.288675
\(13\) −3.92241 −1.08788 −0.543940 0.839124i \(-0.683068\pi\)
−0.543940 + 0.839124i \(0.683068\pi\)
\(14\) −2.44651 −0.653858
\(15\) −1.37256 −0.354392
\(16\) 1.00000 0.250000
\(17\) −1.00000 −0.242536
\(18\) −1.00000 −0.235702
\(19\) 1.28222 0.294161 0.147081 0.989125i \(-0.453012\pi\)
0.147081 + 0.989125i \(0.453012\pi\)
\(20\) −1.37256 −0.306913
\(21\) 2.44651 0.533873
\(22\) −4.53685 −0.967259
\(23\) 3.17888 0.662841 0.331421 0.943483i \(-0.392472\pi\)
0.331421 + 0.943483i \(0.392472\pi\)
\(24\) −1.00000 −0.204124
\(25\) −3.11609 −0.623218
\(26\) 3.92241 0.769248
\(27\) 1.00000 0.192450
\(28\) 2.44651 0.462347
\(29\) −4.44468 −0.825356 −0.412678 0.910877i \(-0.635406\pi\)
−0.412678 + 0.910877i \(0.635406\pi\)
\(30\) 1.37256 0.250593
\(31\) 5.90783 1.06108 0.530539 0.847661i \(-0.321990\pi\)
0.530539 + 0.847661i \(0.321990\pi\)
\(32\) −1.00000 −0.176777
\(33\) 4.53685 0.789764
\(34\) 1.00000 0.171499
\(35\) −3.35797 −0.567601
\(36\) 1.00000 0.166667
\(37\) −1.11972 −0.184082 −0.0920408 0.995755i \(-0.529339\pi\)
−0.0920408 + 0.995755i \(0.529339\pi\)
\(38\) −1.28222 −0.208003
\(39\) −3.92241 −0.628088
\(40\) 1.37256 0.217020
\(41\) 5.71415 0.892400 0.446200 0.894933i \(-0.352777\pi\)
0.446200 + 0.894933i \(0.352777\pi\)
\(42\) −2.44651 −0.377505
\(43\) −3.32679 −0.507330 −0.253665 0.967292i \(-0.581636\pi\)
−0.253665 + 0.967292i \(0.581636\pi\)
\(44\) 4.53685 0.683956
\(45\) −1.37256 −0.204609
\(46\) −3.17888 −0.468700
\(47\) 12.7605 1.86131 0.930656 0.365895i \(-0.119237\pi\)
0.930656 + 0.365895i \(0.119237\pi\)
\(48\) 1.00000 0.144338
\(49\) −1.01458 −0.144940
\(50\) 3.11609 0.440682
\(51\) −1.00000 −0.140028
\(52\) −3.92241 −0.543940
\(53\) 6.22101 0.854522 0.427261 0.904128i \(-0.359479\pi\)
0.427261 + 0.904128i \(0.359479\pi\)
\(54\) −1.00000 −0.136083
\(55\) −6.22708 −0.839659
\(56\) −2.44651 −0.326929
\(57\) 1.28222 0.169834
\(58\) 4.44468 0.583615
\(59\) −1.00000 −0.130189
\(60\) −1.37256 −0.177196
\(61\) 4.28402 0.548512 0.274256 0.961657i \(-0.411568\pi\)
0.274256 + 0.961657i \(0.411568\pi\)
\(62\) −5.90783 −0.750295
\(63\) 2.44651 0.308231
\(64\) 1.00000 0.125000
\(65\) 5.38373 0.667769
\(66\) −4.53685 −0.558447
\(67\) −14.1086 −1.72364 −0.861818 0.507218i \(-0.830674\pi\)
−0.861818 + 0.507218i \(0.830674\pi\)
\(68\) −1.00000 −0.121268
\(69\) 3.17888 0.382692
\(70\) 3.35797 0.401355
\(71\) −10.3817 −1.23208 −0.616039 0.787716i \(-0.711264\pi\)
−0.616039 + 0.787716i \(0.711264\pi\)
\(72\) −1.00000 −0.117851
\(73\) 11.6347 1.36174 0.680871 0.732404i \(-0.261602\pi\)
0.680871 + 0.732404i \(0.261602\pi\)
\(74\) 1.11972 0.130165
\(75\) −3.11609 −0.359815
\(76\) 1.28222 0.147081
\(77\) 11.0995 1.26490
\(78\) 3.92241 0.444126
\(79\) 14.0873 1.58495 0.792473 0.609908i \(-0.208793\pi\)
0.792473 + 0.609908i \(0.208793\pi\)
\(80\) −1.37256 −0.153456
\(81\) 1.00000 0.111111
\(82\) −5.71415 −0.631022
\(83\) 9.20886 1.01080 0.505402 0.862884i \(-0.331344\pi\)
0.505402 + 0.862884i \(0.331344\pi\)
\(84\) 2.44651 0.266936
\(85\) 1.37256 0.148875
\(86\) 3.32679 0.358737
\(87\) −4.44468 −0.476519
\(88\) −4.53685 −0.483630
\(89\) 14.8009 1.56889 0.784443 0.620200i \(-0.212949\pi\)
0.784443 + 0.620200i \(0.212949\pi\)
\(90\) 1.37256 0.144680
\(91\) −9.59622 −1.00596
\(92\) 3.17888 0.331421
\(93\) 5.90783 0.612613
\(94\) −12.7605 −1.31615
\(95\) −1.75992 −0.180564
\(96\) −1.00000 −0.102062
\(97\) −6.25100 −0.634692 −0.317346 0.948310i \(-0.602792\pi\)
−0.317346 + 0.948310i \(0.602792\pi\)
\(98\) 1.01458 0.102488
\(99\) 4.53685 0.455970
\(100\) −3.11609 −0.311609
\(101\) −7.31037 −0.727409 −0.363704 0.931514i \(-0.618488\pi\)
−0.363704 + 0.931514i \(0.618488\pi\)
\(102\) 1.00000 0.0990148
\(103\) 7.63233 0.752035 0.376018 0.926612i \(-0.377293\pi\)
0.376018 + 0.926612i \(0.377293\pi\)
\(104\) 3.92241 0.384624
\(105\) −3.35797 −0.327705
\(106\) −6.22101 −0.604238
\(107\) −4.49082 −0.434144 −0.217072 0.976156i \(-0.569651\pi\)
−0.217072 + 0.976156i \(0.569651\pi\)
\(108\) 1.00000 0.0962250
\(109\) −4.25283 −0.407347 −0.203674 0.979039i \(-0.565288\pi\)
−0.203674 + 0.979039i \(0.565288\pi\)
\(110\) 6.22708 0.593728
\(111\) −1.11972 −0.106280
\(112\) 2.44651 0.231174
\(113\) 9.44831 0.888822 0.444411 0.895823i \(-0.353413\pi\)
0.444411 + 0.895823i \(0.353413\pi\)
\(114\) −1.28222 −0.120091
\(115\) −4.36318 −0.406869
\(116\) −4.44468 −0.412678
\(117\) −3.92241 −0.362627
\(118\) 1.00000 0.0920575
\(119\) −2.44651 −0.224271
\(120\) 1.37256 0.125297
\(121\) 9.58299 0.871181
\(122\) −4.28402 −0.387857
\(123\) 5.71415 0.515227
\(124\) 5.90783 0.530539
\(125\) 11.1398 0.996373
\(126\) −2.44651 −0.217953
\(127\) 0.617352 0.0547811 0.0273906 0.999625i \(-0.491280\pi\)
0.0273906 + 0.999625i \(0.491280\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −3.32679 −0.292907
\(130\) −5.38373 −0.472184
\(131\) −4.86386 −0.424957 −0.212479 0.977166i \(-0.568154\pi\)
−0.212479 + 0.977166i \(0.568154\pi\)
\(132\) 4.53685 0.394882
\(133\) 3.13696 0.272009
\(134\) 14.1086 1.21879
\(135\) −1.37256 −0.118131
\(136\) 1.00000 0.0857493
\(137\) 4.51260 0.385538 0.192769 0.981244i \(-0.438253\pi\)
0.192769 + 0.981244i \(0.438253\pi\)
\(138\) −3.17888 −0.270604
\(139\) −10.2338 −0.868016 −0.434008 0.900909i \(-0.642901\pi\)
−0.434008 + 0.900909i \(0.642901\pi\)
\(140\) −3.35797 −0.283801
\(141\) 12.7605 1.07463
\(142\) 10.3817 0.871210
\(143\) −17.7954 −1.48812
\(144\) 1.00000 0.0833333
\(145\) 6.10057 0.506624
\(146\) −11.6347 −0.962896
\(147\) −1.01458 −0.0836814
\(148\) −1.11972 −0.0920408
\(149\) 15.1122 1.23804 0.619020 0.785375i \(-0.287530\pi\)
0.619020 + 0.785375i \(0.287530\pi\)
\(150\) 3.11609 0.254428
\(151\) −18.4536 −1.50173 −0.750865 0.660456i \(-0.770363\pi\)
−0.750865 + 0.660456i \(0.770363\pi\)
\(152\) −1.28222 −0.104002
\(153\) −1.00000 −0.0808452
\(154\) −11.0995 −0.894419
\(155\) −8.10882 −0.651316
\(156\) −3.92241 −0.314044
\(157\) −7.52286 −0.600390 −0.300195 0.953878i \(-0.597052\pi\)
−0.300195 + 0.953878i \(0.597052\pi\)
\(158\) −14.0873 −1.12073
\(159\) 6.22101 0.493358
\(160\) 1.37256 0.108510
\(161\) 7.77715 0.612926
\(162\) −1.00000 −0.0785674
\(163\) 10.9961 0.861282 0.430641 0.902523i \(-0.358288\pi\)
0.430641 + 0.902523i \(0.358288\pi\)
\(164\) 5.71415 0.446200
\(165\) −6.22708 −0.484777
\(166\) −9.20886 −0.714746
\(167\) −0.349234 −0.0270246 −0.0135123 0.999909i \(-0.504301\pi\)
−0.0135123 + 0.999909i \(0.504301\pi\)
\(168\) −2.44651 −0.188752
\(169\) 2.38530 0.183485
\(170\) −1.37256 −0.105270
\(171\) 1.28222 0.0980537
\(172\) −3.32679 −0.253665
\(173\) −2.38590 −0.181397 −0.0906983 0.995878i \(-0.528910\pi\)
−0.0906983 + 0.995878i \(0.528910\pi\)
\(174\) 4.44468 0.336950
\(175\) −7.62355 −0.576286
\(176\) 4.53685 0.341978
\(177\) −1.00000 −0.0751646
\(178\) −14.8009 −1.10937
\(179\) −1.29654 −0.0969081 −0.0484541 0.998825i \(-0.515429\pi\)
−0.0484541 + 0.998825i \(0.515429\pi\)
\(180\) −1.37256 −0.102304
\(181\) −7.64648 −0.568358 −0.284179 0.958771i \(-0.591721\pi\)
−0.284179 + 0.958771i \(0.591721\pi\)
\(182\) 9.59622 0.711319
\(183\) 4.28402 0.316684
\(184\) −3.17888 −0.234350
\(185\) 1.53688 0.112994
\(186\) −5.90783 −0.433183
\(187\) −4.53685 −0.331767
\(188\) 12.7605 0.930656
\(189\) 2.44651 0.177958
\(190\) 1.75992 0.127678
\(191\) 14.1519 1.02399 0.511997 0.858987i \(-0.328906\pi\)
0.511997 + 0.858987i \(0.328906\pi\)
\(192\) 1.00000 0.0721688
\(193\) 16.3671 1.17813 0.589064 0.808086i \(-0.299496\pi\)
0.589064 + 0.808086i \(0.299496\pi\)
\(194\) 6.25100 0.448795
\(195\) 5.38373 0.385537
\(196\) −1.01458 −0.0724702
\(197\) 4.28585 0.305354 0.152677 0.988276i \(-0.451211\pi\)
0.152677 + 0.988276i \(0.451211\pi\)
\(198\) −4.53685 −0.322420
\(199\) −20.6226 −1.46190 −0.730948 0.682434i \(-0.760922\pi\)
−0.730948 + 0.682434i \(0.760922\pi\)
\(200\) 3.11609 0.220341
\(201\) −14.1086 −0.995141
\(202\) 7.31037 0.514356
\(203\) −10.8739 −0.763202
\(204\) −1.00000 −0.0700140
\(205\) −7.84299 −0.547778
\(206\) −7.63233 −0.531769
\(207\) 3.17888 0.220947
\(208\) −3.92241 −0.271970
\(209\) 5.81723 0.402386
\(210\) 3.35797 0.231722
\(211\) −3.27881 −0.225722 −0.112861 0.993611i \(-0.536002\pi\)
−0.112861 + 0.993611i \(0.536002\pi\)
\(212\) 6.22101 0.427261
\(213\) −10.3817 −0.711340
\(214\) 4.49082 0.306986
\(215\) 4.56620 0.311412
\(216\) −1.00000 −0.0680414
\(217\) 14.4536 0.981172
\(218\) 4.25283 0.288038
\(219\) 11.6347 0.786202
\(220\) −6.22708 −0.419829
\(221\) 3.92241 0.263850
\(222\) 1.11972 0.0751510
\(223\) 7.89786 0.528880 0.264440 0.964402i \(-0.414813\pi\)
0.264440 + 0.964402i \(0.414813\pi\)
\(224\) −2.44651 −0.163464
\(225\) −3.11609 −0.207739
\(226\) −9.44831 −0.628492
\(227\) 3.21878 0.213638 0.106819 0.994278i \(-0.465933\pi\)
0.106819 + 0.994278i \(0.465933\pi\)
\(228\) 1.28222 0.0849170
\(229\) 8.63791 0.570809 0.285405 0.958407i \(-0.407872\pi\)
0.285405 + 0.958407i \(0.407872\pi\)
\(230\) 4.36318 0.287700
\(231\) 11.0995 0.730290
\(232\) 4.44468 0.291807
\(233\) −2.25951 −0.148026 −0.0740128 0.997257i \(-0.523581\pi\)
−0.0740128 + 0.997257i \(0.523581\pi\)
\(234\) 3.92241 0.256416
\(235\) −17.5145 −1.14252
\(236\) −1.00000 −0.0650945
\(237\) 14.0873 0.915068
\(238\) 2.44651 0.158584
\(239\) 25.9175 1.67647 0.838233 0.545312i \(-0.183589\pi\)
0.838233 + 0.545312i \(0.183589\pi\)
\(240\) −1.37256 −0.0885981
\(241\) 14.0196 0.903084 0.451542 0.892250i \(-0.350874\pi\)
0.451542 + 0.892250i \(0.350874\pi\)
\(242\) −9.58299 −0.616018
\(243\) 1.00000 0.0641500
\(244\) 4.28402 0.274256
\(245\) 1.39257 0.0889681
\(246\) −5.71415 −0.364321
\(247\) −5.02939 −0.320012
\(248\) −5.90783 −0.375147
\(249\) 9.20886 0.583588
\(250\) −11.1398 −0.704542
\(251\) −10.4937 −0.662359 −0.331179 0.943568i \(-0.607446\pi\)
−0.331179 + 0.943568i \(0.607446\pi\)
\(252\) 2.44651 0.154116
\(253\) 14.4221 0.906708
\(254\) −0.617352 −0.0387361
\(255\) 1.37256 0.0859528
\(256\) 1.00000 0.0625000
\(257\) 25.9848 1.62089 0.810445 0.585815i \(-0.199226\pi\)
0.810445 + 0.585815i \(0.199226\pi\)
\(258\) 3.32679 0.207117
\(259\) −2.73942 −0.170219
\(260\) 5.38373 0.333885
\(261\) −4.44468 −0.275119
\(262\) 4.86386 0.300490
\(263\) 16.6742 1.02818 0.514088 0.857738i \(-0.328131\pi\)
0.514088 + 0.857738i \(0.328131\pi\)
\(264\) −4.53685 −0.279224
\(265\) −8.53868 −0.524527
\(266\) −3.13696 −0.192340
\(267\) 14.8009 0.905797
\(268\) −14.1086 −0.861818
\(269\) −17.1270 −1.04425 −0.522127 0.852868i \(-0.674861\pi\)
−0.522127 + 0.852868i \(0.674861\pi\)
\(270\) 1.37256 0.0835311
\(271\) −16.7230 −1.01585 −0.507925 0.861401i \(-0.669587\pi\)
−0.507925 + 0.861401i \(0.669587\pi\)
\(272\) −1.00000 −0.0606339
\(273\) −9.59622 −0.580790
\(274\) −4.51260 −0.272616
\(275\) −14.1372 −0.852507
\(276\) 3.17888 0.191346
\(277\) 6.16976 0.370705 0.185353 0.982672i \(-0.440657\pi\)
0.185353 + 0.982672i \(0.440657\pi\)
\(278\) 10.2338 0.613780
\(279\) 5.90783 0.353692
\(280\) 3.35797 0.200677
\(281\) −21.8738 −1.30488 −0.652440 0.757840i \(-0.726255\pi\)
−0.652440 + 0.757840i \(0.726255\pi\)
\(282\) −12.7605 −0.759878
\(283\) −3.51379 −0.208873 −0.104436 0.994532i \(-0.533304\pi\)
−0.104436 + 0.994532i \(0.533304\pi\)
\(284\) −10.3817 −0.616039
\(285\) −1.75992 −0.104248
\(286\) 17.7954 1.05226
\(287\) 13.9797 0.825197
\(288\) −1.00000 −0.0589256
\(289\) 1.00000 0.0588235
\(290\) −6.10057 −0.358238
\(291\) −6.25100 −0.366440
\(292\) 11.6347 0.680871
\(293\) 9.89280 0.577944 0.288972 0.957338i \(-0.406687\pi\)
0.288972 + 0.957338i \(0.406687\pi\)
\(294\) 1.01458 0.0591717
\(295\) 1.37256 0.0799133
\(296\) 1.11972 0.0650827
\(297\) 4.53685 0.263255
\(298\) −15.1122 −0.875426
\(299\) −12.4689 −0.721092
\(300\) −3.11609 −0.179908
\(301\) −8.13902 −0.469125
\(302\) 18.4536 1.06188
\(303\) −7.31037 −0.419970
\(304\) 1.28222 0.0735403
\(305\) −5.88005 −0.336691
\(306\) 1.00000 0.0571662
\(307\) 13.8309 0.789370 0.394685 0.918817i \(-0.370854\pi\)
0.394685 + 0.918817i \(0.370854\pi\)
\(308\) 11.0995 0.632450
\(309\) 7.63233 0.434188
\(310\) 8.10882 0.460550
\(311\) 14.0500 0.796702 0.398351 0.917233i \(-0.369583\pi\)
0.398351 + 0.917233i \(0.369583\pi\)
\(312\) 3.92241 0.222063
\(313\) −6.65585 −0.376211 −0.188106 0.982149i \(-0.560235\pi\)
−0.188106 + 0.982149i \(0.560235\pi\)
\(314\) 7.52286 0.424540
\(315\) −3.35797 −0.189200
\(316\) 14.0873 0.792473
\(317\) −8.10346 −0.455136 −0.227568 0.973762i \(-0.573077\pi\)
−0.227568 + 0.973762i \(0.573077\pi\)
\(318\) −6.22101 −0.348857
\(319\) −20.1648 −1.12901
\(320\) −1.37256 −0.0767282
\(321\) −4.49082 −0.250653
\(322\) −7.77715 −0.433404
\(323\) −1.28222 −0.0713446
\(324\) 1.00000 0.0555556
\(325\) 12.2226 0.677987
\(326\) −10.9961 −0.609018
\(327\) −4.25283 −0.235182
\(328\) −5.71415 −0.315511
\(329\) 31.2187 1.72114
\(330\) 6.22708 0.342789
\(331\) −6.21793 −0.341768 −0.170884 0.985291i \(-0.554662\pi\)
−0.170884 + 0.985291i \(0.554662\pi\)
\(332\) 9.20886 0.505402
\(333\) −1.11972 −0.0613605
\(334\) 0.349234 0.0191093
\(335\) 19.3648 1.05801
\(336\) 2.44651 0.133468
\(337\) −5.56650 −0.303226 −0.151613 0.988440i \(-0.548447\pi\)
−0.151613 + 0.988440i \(0.548447\pi\)
\(338\) −2.38530 −0.129743
\(339\) 9.44831 0.513162
\(340\) 1.37256 0.0744373
\(341\) 26.8029 1.45146
\(342\) −1.28222 −0.0693344
\(343\) −19.6078 −1.05872
\(344\) 3.32679 0.179368
\(345\) −4.36318 −0.234906
\(346\) 2.38590 0.128267
\(347\) 24.3057 1.30480 0.652398 0.757877i \(-0.273763\pi\)
0.652398 + 0.757877i \(0.273763\pi\)
\(348\) −4.44468 −0.238260
\(349\) 24.6813 1.32116 0.660579 0.750757i \(-0.270311\pi\)
0.660579 + 0.750757i \(0.270311\pi\)
\(350\) 7.62355 0.407496
\(351\) −3.92241 −0.209363
\(352\) −4.53685 −0.241815
\(353\) 30.3271 1.61415 0.807075 0.590449i \(-0.201049\pi\)
0.807075 + 0.590449i \(0.201049\pi\)
\(354\) 1.00000 0.0531494
\(355\) 14.2494 0.756281
\(356\) 14.8009 0.784443
\(357\) −2.44651 −0.129483
\(358\) 1.29654 0.0685244
\(359\) 15.5771 0.822130 0.411065 0.911606i \(-0.365157\pi\)
0.411065 + 0.911606i \(0.365157\pi\)
\(360\) 1.37256 0.0723400
\(361\) −17.3559 −0.913469
\(362\) 7.64648 0.401890
\(363\) 9.58299 0.502977
\(364\) −9.59622 −0.502979
\(365\) −15.9693 −0.835872
\(366\) −4.28402 −0.223929
\(367\) 12.8664 0.671622 0.335811 0.941929i \(-0.390990\pi\)
0.335811 + 0.941929i \(0.390990\pi\)
\(368\) 3.17888 0.165710
\(369\) 5.71415 0.297467
\(370\) −1.53688 −0.0798988
\(371\) 15.2198 0.790171
\(372\) 5.90783 0.306307
\(373\) 21.6663 1.12184 0.560919 0.827871i \(-0.310448\pi\)
0.560919 + 0.827871i \(0.310448\pi\)
\(374\) 4.53685 0.234595
\(375\) 11.1398 0.575256
\(376\) −12.7605 −0.658073
\(377\) 17.4338 0.897889
\(378\) −2.44651 −0.125835
\(379\) 23.2861 1.19613 0.598064 0.801448i \(-0.295937\pi\)
0.598064 + 0.801448i \(0.295937\pi\)
\(380\) −1.75992 −0.0902818
\(381\) 0.617352 0.0316279
\(382\) −14.1519 −0.724073
\(383\) 0.383389 0.0195902 0.00979512 0.999952i \(-0.496882\pi\)
0.00979512 + 0.999952i \(0.496882\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −15.2346 −0.776428
\(386\) −16.3671 −0.833063
\(387\) −3.32679 −0.169110
\(388\) −6.25100 −0.317346
\(389\) −3.45139 −0.174993 −0.0874963 0.996165i \(-0.527887\pi\)
−0.0874963 + 0.996165i \(0.527887\pi\)
\(390\) −5.38373 −0.272616
\(391\) −3.17888 −0.160763
\(392\) 1.01458 0.0512442
\(393\) −4.86386 −0.245349
\(394\) −4.28585 −0.215918
\(395\) −19.3356 −0.972880
\(396\) 4.53685 0.227985
\(397\) 4.45900 0.223791 0.111895 0.993720i \(-0.464308\pi\)
0.111895 + 0.993720i \(0.464308\pi\)
\(398\) 20.6226 1.03372
\(399\) 3.13696 0.157045
\(400\) −3.11609 −0.155805
\(401\) −7.81142 −0.390084 −0.195042 0.980795i \(-0.562484\pi\)
−0.195042 + 0.980795i \(0.562484\pi\)
\(402\) 14.1086 0.703671
\(403\) −23.1729 −1.15433
\(404\) −7.31037 −0.363704
\(405\) −1.37256 −0.0682028
\(406\) 10.8739 0.539665
\(407\) −5.08002 −0.251807
\(408\) 1.00000 0.0495074
\(409\) 6.90534 0.341447 0.170724 0.985319i \(-0.445389\pi\)
0.170724 + 0.985319i \(0.445389\pi\)
\(410\) 7.84299 0.387337
\(411\) 4.51260 0.222590
\(412\) 7.63233 0.376018
\(413\) −2.44651 −0.120385
\(414\) −3.17888 −0.156233
\(415\) −12.6397 −0.620457
\(416\) 3.92241 0.192312
\(417\) −10.2338 −0.501149
\(418\) −5.81723 −0.284530
\(419\) 10.4229 0.509192 0.254596 0.967048i \(-0.418058\pi\)
0.254596 + 0.967048i \(0.418058\pi\)
\(420\) −3.35797 −0.163852
\(421\) −27.6947 −1.34976 −0.674880 0.737928i \(-0.735804\pi\)
−0.674880 + 0.737928i \(0.735804\pi\)
\(422\) 3.27881 0.159610
\(423\) 12.7605 0.620437
\(424\) −6.22101 −0.302119
\(425\) 3.11609 0.151153
\(426\) 10.3817 0.502994
\(427\) 10.4809 0.507206
\(428\) −4.49082 −0.217072
\(429\) −17.7954 −0.859169
\(430\) −4.56620 −0.220202
\(431\) 13.8370 0.666504 0.333252 0.942838i \(-0.391854\pi\)
0.333252 + 0.942838i \(0.391854\pi\)
\(432\) 1.00000 0.0481125
\(433\) −9.03973 −0.434422 −0.217211 0.976125i \(-0.569696\pi\)
−0.217211 + 0.976125i \(0.569696\pi\)
\(434\) −14.4536 −0.693793
\(435\) 6.10057 0.292500
\(436\) −4.25283 −0.203674
\(437\) 4.07601 0.194982
\(438\) −11.6347 −0.555929
\(439\) −6.09702 −0.290995 −0.145497 0.989359i \(-0.546478\pi\)
−0.145497 + 0.989359i \(0.546478\pi\)
\(440\) 6.22708 0.296864
\(441\) −1.01458 −0.0483135
\(442\) −3.92241 −0.186570
\(443\) −21.3040 −1.01219 −0.506093 0.862479i \(-0.668911\pi\)
−0.506093 + 0.862479i \(0.668911\pi\)
\(444\) −1.11972 −0.0531398
\(445\) −20.3150 −0.963023
\(446\) −7.89786 −0.373974
\(447\) 15.1122 0.714782
\(448\) 2.44651 0.115587
\(449\) 9.14428 0.431545 0.215773 0.976444i \(-0.430773\pi\)
0.215773 + 0.976444i \(0.430773\pi\)
\(450\) 3.11609 0.146894
\(451\) 25.9242 1.22072
\(452\) 9.44831 0.444411
\(453\) −18.4536 −0.867024
\(454\) −3.21878 −0.151065
\(455\) 13.1713 0.617482
\(456\) −1.28222 −0.0600454
\(457\) 24.4679 1.14456 0.572280 0.820058i \(-0.306059\pi\)
0.572280 + 0.820058i \(0.306059\pi\)
\(458\) −8.63791 −0.403623
\(459\) −1.00000 −0.0466760
\(460\) −4.36318 −0.203434
\(461\) −0.986656 −0.0459531 −0.0229766 0.999736i \(-0.507314\pi\)
−0.0229766 + 0.999736i \(0.507314\pi\)
\(462\) −11.0995 −0.516393
\(463\) 10.0240 0.465856 0.232928 0.972494i \(-0.425169\pi\)
0.232928 + 0.972494i \(0.425169\pi\)
\(464\) −4.44468 −0.206339
\(465\) −8.10882 −0.376038
\(466\) 2.25951 0.104670
\(467\) 8.99505 0.416241 0.208121 0.978103i \(-0.433265\pi\)
0.208121 + 0.978103i \(0.433265\pi\)
\(468\) −3.92241 −0.181313
\(469\) −34.5168 −1.59384
\(470\) 17.5145 0.807884
\(471\) −7.52286 −0.346635
\(472\) 1.00000 0.0460287
\(473\) −15.0931 −0.693983
\(474\) −14.0873 −0.647051
\(475\) −3.99551 −0.183327
\(476\) −2.44651 −0.112136
\(477\) 6.22101 0.284841
\(478\) −25.9175 −1.18544
\(479\) 25.8738 1.18220 0.591102 0.806597i \(-0.298693\pi\)
0.591102 + 0.806597i \(0.298693\pi\)
\(480\) 1.37256 0.0626483
\(481\) 4.39202 0.200259
\(482\) −14.0196 −0.638577
\(483\) 7.77715 0.353873
\(484\) 9.58299 0.435591
\(485\) 8.57984 0.389590
\(486\) −1.00000 −0.0453609
\(487\) 1.84849 0.0837631 0.0418816 0.999123i \(-0.486665\pi\)
0.0418816 + 0.999123i \(0.486665\pi\)
\(488\) −4.28402 −0.193928
\(489\) 10.9961 0.497261
\(490\) −1.39257 −0.0629100
\(491\) −35.3045 −1.59327 −0.796636 0.604460i \(-0.793389\pi\)
−0.796636 + 0.604460i \(0.793389\pi\)
\(492\) 5.71415 0.257614
\(493\) 4.44468 0.200178
\(494\) 5.02939 0.226283
\(495\) −6.22708 −0.279886
\(496\) 5.90783 0.265269
\(497\) −25.3989 −1.13930
\(498\) −9.20886 −0.412659
\(499\) −9.67804 −0.433249 −0.216624 0.976255i \(-0.569505\pi\)
−0.216624 + 0.976255i \(0.569505\pi\)
\(500\) 11.1398 0.498186
\(501\) −0.349234 −0.0156026
\(502\) 10.4937 0.468358
\(503\) −40.2304 −1.79378 −0.896892 0.442249i \(-0.854181\pi\)
−0.896892 + 0.442249i \(0.854181\pi\)
\(504\) −2.44651 −0.108976
\(505\) 10.0339 0.446502
\(506\) −14.4221 −0.641139
\(507\) 2.38530 0.105935
\(508\) 0.617352 0.0273906
\(509\) 7.40618 0.328273 0.164137 0.986438i \(-0.447516\pi\)
0.164137 + 0.986438i \(0.447516\pi\)
\(510\) −1.37256 −0.0607778
\(511\) 28.4645 1.25919
\(512\) −1.00000 −0.0441942
\(513\) 1.28222 0.0566113
\(514\) −25.9848 −1.14614
\(515\) −10.4758 −0.461619
\(516\) −3.32679 −0.146454
\(517\) 57.8925 2.54611
\(518\) 2.73942 0.120363
\(519\) −2.38590 −0.104729
\(520\) −5.38373 −0.236092
\(521\) −36.4063 −1.59499 −0.797495 0.603325i \(-0.793842\pi\)
−0.797495 + 0.603325i \(0.793842\pi\)
\(522\) 4.44468 0.194538
\(523\) 18.1574 0.793966 0.396983 0.917826i \(-0.370057\pi\)
0.396983 + 0.917826i \(0.370057\pi\)
\(524\) −4.86386 −0.212479
\(525\) −7.62355 −0.332719
\(526\) −16.6742 −0.727030
\(527\) −5.90783 −0.257349
\(528\) 4.53685 0.197441
\(529\) −12.8948 −0.560641
\(530\) 8.53868 0.370897
\(531\) −1.00000 −0.0433963
\(532\) 3.13696 0.136005
\(533\) −22.4132 −0.970825
\(534\) −14.8009 −0.640495
\(535\) 6.16390 0.266489
\(536\) 14.1086 0.609397
\(537\) −1.29654 −0.0559499
\(538\) 17.1270 0.738399
\(539\) −4.60301 −0.198266
\(540\) −1.37256 −0.0590654
\(541\) −21.7888 −0.936774 −0.468387 0.883523i \(-0.655165\pi\)
−0.468387 + 0.883523i \(0.655165\pi\)
\(542\) 16.7230 0.718314
\(543\) −7.64648 −0.328142
\(544\) 1.00000 0.0428746
\(545\) 5.83725 0.250040
\(546\) 9.59622 0.410680
\(547\) 18.3549 0.784799 0.392399 0.919795i \(-0.371645\pi\)
0.392399 + 0.919795i \(0.371645\pi\)
\(548\) 4.51260 0.192769
\(549\) 4.28402 0.182837
\(550\) 14.1372 0.602814
\(551\) −5.69905 −0.242788
\(552\) −3.17888 −0.135302
\(553\) 34.4647 1.46559
\(554\) −6.16976 −0.262128
\(555\) 1.53688 0.0652371
\(556\) −10.2338 −0.434008
\(557\) 19.9045 0.843382 0.421691 0.906740i \(-0.361437\pi\)
0.421691 + 0.906740i \(0.361437\pi\)
\(558\) −5.90783 −0.250098
\(559\) 13.0490 0.551915
\(560\) −3.35797 −0.141900
\(561\) −4.53685 −0.191546
\(562\) 21.8738 0.922690
\(563\) 1.46278 0.0616487 0.0308244 0.999525i \(-0.490187\pi\)
0.0308244 + 0.999525i \(0.490187\pi\)
\(564\) 12.7605 0.537315
\(565\) −12.9683 −0.545582
\(566\) 3.51379 0.147695
\(567\) 2.44651 0.102744
\(568\) 10.3817 0.435605
\(569\) −12.7127 −0.532942 −0.266471 0.963843i \(-0.585858\pi\)
−0.266471 + 0.963843i \(0.585858\pi\)
\(570\) 1.75992 0.0737148
\(571\) −10.7548 −0.450073 −0.225037 0.974350i \(-0.572250\pi\)
−0.225037 + 0.974350i \(0.572250\pi\)
\(572\) −17.7954 −0.744062
\(573\) 14.1519 0.591203
\(574\) −13.9797 −0.583502
\(575\) −9.90566 −0.413095
\(576\) 1.00000 0.0416667
\(577\) −1.00812 −0.0419688 −0.0209844 0.999780i \(-0.506680\pi\)
−0.0209844 + 0.999780i \(0.506680\pi\)
\(578\) −1.00000 −0.0415945
\(579\) 16.3671 0.680193
\(580\) 6.10057 0.253312
\(581\) 22.5296 0.934684
\(582\) 6.25100 0.259112
\(583\) 28.2238 1.16891
\(584\) −11.6347 −0.481448
\(585\) 5.38373 0.222590
\(586\) −9.89280 −0.408668
\(587\) −45.4167 −1.87455 −0.937273 0.348596i \(-0.886658\pi\)
−0.937273 + 0.348596i \(0.886658\pi\)
\(588\) −1.01458 −0.0418407
\(589\) 7.57513 0.312128
\(590\) −1.37256 −0.0565072
\(591\) 4.28585 0.176296
\(592\) −1.11972 −0.0460204
\(593\) −10.5736 −0.434207 −0.217103 0.976149i \(-0.569661\pi\)
−0.217103 + 0.976149i \(0.569661\pi\)
\(594\) −4.53685 −0.186149
\(595\) 3.35797 0.137663
\(596\) 15.1122 0.619020
\(597\) −20.6226 −0.844026
\(598\) 12.4689 0.509889
\(599\) 25.8614 1.05667 0.528335 0.849036i \(-0.322817\pi\)
0.528335 + 0.849036i \(0.322817\pi\)
\(600\) 3.11609 0.127214
\(601\) −28.1495 −1.14824 −0.574122 0.818770i \(-0.694656\pi\)
−0.574122 + 0.818770i \(0.694656\pi\)
\(602\) 8.13902 0.331722
\(603\) −14.1086 −0.574545
\(604\) −18.4536 −0.750865
\(605\) −13.1532 −0.534753
\(606\) 7.31037 0.296963
\(607\) 35.9274 1.45825 0.729124 0.684382i \(-0.239928\pi\)
0.729124 + 0.684382i \(0.239928\pi\)
\(608\) −1.28222 −0.0520008
\(609\) −10.8739 −0.440635
\(610\) 5.88005 0.238076
\(611\) −50.0520 −2.02489
\(612\) −1.00000 −0.0404226
\(613\) 18.1800 0.734285 0.367142 0.930165i \(-0.380336\pi\)
0.367142 + 0.930165i \(0.380336\pi\)
\(614\) −13.8309 −0.558169
\(615\) −7.84299 −0.316260
\(616\) −11.0995 −0.447210
\(617\) 15.3181 0.616682 0.308341 0.951276i \(-0.400226\pi\)
0.308341 + 0.951276i \(0.400226\pi\)
\(618\) −7.63233 −0.307017
\(619\) −6.33812 −0.254750 −0.127375 0.991855i \(-0.540655\pi\)
−0.127375 + 0.991855i \(0.540655\pi\)
\(620\) −8.10882 −0.325658
\(621\) 3.17888 0.127564
\(622\) −14.0500 −0.563354
\(623\) 36.2104 1.45074
\(624\) −3.92241 −0.157022
\(625\) 0.290476 0.0116190
\(626\) 6.65585 0.266021
\(627\) 5.81723 0.232318
\(628\) −7.52286 −0.300195
\(629\) 1.11972 0.0446464
\(630\) 3.35797 0.133785
\(631\) −8.70564 −0.346566 −0.173283 0.984872i \(-0.555438\pi\)
−0.173283 + 0.984872i \(0.555438\pi\)
\(632\) −14.0873 −0.560363
\(633\) −3.27881 −0.130321
\(634\) 8.10346 0.321829
\(635\) −0.847350 −0.0336260
\(636\) 6.22101 0.246679
\(637\) 3.97961 0.157678
\(638\) 20.1648 0.798333
\(639\) −10.3817 −0.410692
\(640\) 1.37256 0.0542550
\(641\) −9.56592 −0.377831 −0.188916 0.981993i \(-0.560497\pi\)
−0.188916 + 0.981993i \(0.560497\pi\)
\(642\) 4.49082 0.177239
\(643\) −19.2741 −0.760098 −0.380049 0.924966i \(-0.624093\pi\)
−0.380049 + 0.924966i \(0.624093\pi\)
\(644\) 7.77715 0.306463
\(645\) 4.56620 0.179794
\(646\) 1.28222 0.0504482
\(647\) −23.7598 −0.934096 −0.467048 0.884232i \(-0.654682\pi\)
−0.467048 + 0.884232i \(0.654682\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −4.53685 −0.178087
\(650\) −12.2226 −0.479409
\(651\) 14.4536 0.566480
\(652\) 10.9961 0.430641
\(653\) 37.2182 1.45646 0.728230 0.685333i \(-0.240343\pi\)
0.728230 + 0.685333i \(0.240343\pi\)
\(654\) 4.25283 0.166299
\(655\) 6.67591 0.260850
\(656\) 5.71415 0.223100
\(657\) 11.6347 0.453914
\(658\) −31.2187 −1.21703
\(659\) 10.3196 0.401995 0.200997 0.979592i \(-0.435582\pi\)
0.200997 + 0.979592i \(0.435582\pi\)
\(660\) −6.22708 −0.242389
\(661\) 5.50184 0.213997 0.106998 0.994259i \(-0.465876\pi\)
0.106998 + 0.994259i \(0.465876\pi\)
\(662\) 6.21793 0.241667
\(663\) 3.92241 0.152334
\(664\) −9.20886 −0.357373
\(665\) −4.30566 −0.166966
\(666\) 1.11972 0.0433885
\(667\) −14.1291 −0.547080
\(668\) −0.349234 −0.0135123
\(669\) 7.89786 0.305349
\(670\) −19.3648 −0.748127
\(671\) 19.4359 0.750316
\(672\) −2.44651 −0.0943762
\(673\) 11.7544 0.453100 0.226550 0.974000i \(-0.427255\pi\)
0.226550 + 0.974000i \(0.427255\pi\)
\(674\) 5.56650 0.214413
\(675\) −3.11609 −0.119938
\(676\) 2.38530 0.0917424
\(677\) −36.9735 −1.42101 −0.710503 0.703694i \(-0.751533\pi\)
−0.710503 + 0.703694i \(0.751533\pi\)
\(678\) −9.44831 −0.362860
\(679\) −15.2931 −0.586896
\(680\) −1.37256 −0.0526351
\(681\) 3.21878 0.123344
\(682\) −26.8029 −1.02634
\(683\) −14.5844 −0.558056 −0.279028 0.960283i \(-0.590012\pi\)
−0.279028 + 0.960283i \(0.590012\pi\)
\(684\) 1.28222 0.0490269
\(685\) −6.19380 −0.236653
\(686\) 19.6078 0.748628
\(687\) 8.63791 0.329557
\(688\) −3.32679 −0.126833
\(689\) −24.4014 −0.929618
\(690\) 4.36318 0.166104
\(691\) −16.4570 −0.626056 −0.313028 0.949744i \(-0.601343\pi\)
−0.313028 + 0.949744i \(0.601343\pi\)
\(692\) −2.38590 −0.0906983
\(693\) 11.0995 0.421633
\(694\) −24.3057 −0.922630
\(695\) 14.0464 0.532810
\(696\) 4.44468 0.168475
\(697\) −5.71415 −0.216439
\(698\) −24.6813 −0.934199
\(699\) −2.25951 −0.0854626
\(700\) −7.62355 −0.288143
\(701\) 30.3060 1.14464 0.572320 0.820030i \(-0.306043\pi\)
0.572320 + 0.820030i \(0.306043\pi\)
\(702\) 3.92241 0.148042
\(703\) −1.43573 −0.0541497
\(704\) 4.53685 0.170989
\(705\) −17.5145 −0.659635
\(706\) −30.3271 −1.14138
\(707\) −17.8849 −0.672631
\(708\) −1.00000 −0.0375823
\(709\) 47.8644 1.79759 0.898793 0.438374i \(-0.144445\pi\)
0.898793 + 0.438374i \(0.144445\pi\)
\(710\) −14.2494 −0.534771
\(711\) 14.0873 0.528315
\(712\) −14.8009 −0.554685
\(713\) 18.7802 0.703326
\(714\) 2.44651 0.0915584
\(715\) 24.4252 0.913449
\(716\) −1.29654 −0.0484541
\(717\) 25.9175 0.967908
\(718\) −15.5771 −0.581334
\(719\) −21.2687 −0.793190 −0.396595 0.917994i \(-0.629808\pi\)
−0.396595 + 0.917994i \(0.629808\pi\)
\(720\) −1.37256 −0.0511521
\(721\) 18.6726 0.695403
\(722\) 17.3559 0.645920
\(723\) 14.0196 0.521396
\(724\) −7.64648 −0.284179
\(725\) 13.8500 0.514377
\(726\) −9.58299 −0.355658
\(727\) 7.60032 0.281880 0.140940 0.990018i \(-0.454987\pi\)
0.140940 + 0.990018i \(0.454987\pi\)
\(728\) 9.59622 0.355660
\(729\) 1.00000 0.0370370
\(730\) 15.9693 0.591050
\(731\) 3.32679 0.123046
\(732\) 4.28402 0.158342
\(733\) 43.2703 1.59823 0.799113 0.601181i \(-0.205303\pi\)
0.799113 + 0.601181i \(0.205303\pi\)
\(734\) −12.8664 −0.474908
\(735\) 1.39257 0.0513658
\(736\) −3.17888 −0.117175
\(737\) −64.0084 −2.35778
\(738\) −5.71415 −0.210341
\(739\) 25.2377 0.928384 0.464192 0.885735i \(-0.346345\pi\)
0.464192 + 0.885735i \(0.346345\pi\)
\(740\) 1.53688 0.0564970
\(741\) −5.02939 −0.184759
\(742\) −15.2198 −0.558735
\(743\) −12.6389 −0.463675 −0.231838 0.972755i \(-0.574474\pi\)
−0.231838 + 0.972755i \(0.574474\pi\)
\(744\) −5.90783 −0.216591
\(745\) −20.7423 −0.759940
\(746\) −21.6663 −0.793259
\(747\) 9.20886 0.336935
\(748\) −4.53685 −0.165884
\(749\) −10.9868 −0.401450
\(750\) −11.1398 −0.406768
\(751\) −30.5853 −1.11607 −0.558036 0.829817i \(-0.688445\pi\)
−0.558036 + 0.829817i \(0.688445\pi\)
\(752\) 12.7605 0.465328
\(753\) −10.4937 −0.382413
\(754\) −17.4338 −0.634903
\(755\) 25.3285 0.921800
\(756\) 2.44651 0.0889788
\(757\) 30.5441 1.11014 0.555072 0.831802i \(-0.312691\pi\)
0.555072 + 0.831802i \(0.312691\pi\)
\(758\) −23.2861 −0.845790
\(759\) 14.4221 0.523488
\(760\) 1.75992 0.0638389
\(761\) 33.5608 1.21658 0.608289 0.793716i \(-0.291856\pi\)
0.608289 + 0.793716i \(0.291856\pi\)
\(762\) −0.617352 −0.0223643
\(763\) −10.4046 −0.376672
\(764\) 14.1519 0.511997
\(765\) 1.37256 0.0496249
\(766\) −0.383389 −0.0138524
\(767\) 3.92241 0.141630
\(768\) 1.00000 0.0360844
\(769\) −11.9763 −0.431875 −0.215938 0.976407i \(-0.569281\pi\)
−0.215938 + 0.976407i \(0.569281\pi\)
\(770\) 15.2346 0.549017
\(771\) 25.9848 0.935821
\(772\) 16.3671 0.589064
\(773\) 53.1645 1.91219 0.956097 0.293050i \(-0.0946703\pi\)
0.956097 + 0.293050i \(0.0946703\pi\)
\(774\) 3.32679 0.119579
\(775\) −18.4093 −0.661283
\(776\) 6.25100 0.224398
\(777\) −2.73942 −0.0982761
\(778\) 3.45139 0.123738
\(779\) 7.32679 0.262509
\(780\) 5.38373 0.192768
\(781\) −47.1001 −1.68537
\(782\) 3.17888 0.113676
\(783\) −4.44468 −0.158840
\(784\) −1.01458 −0.0362351
\(785\) 10.3255 0.368535
\(786\) 4.86386 0.173488
\(787\) 10.3491 0.368905 0.184453 0.982841i \(-0.440949\pi\)
0.184453 + 0.982841i \(0.440949\pi\)
\(788\) 4.28585 0.152677
\(789\) 16.6742 0.593617
\(790\) 19.3356 0.687930
\(791\) 23.1154 0.821889
\(792\) −4.53685 −0.161210
\(793\) −16.8037 −0.596716
\(794\) −4.45900 −0.158244
\(795\) −8.53868 −0.302836
\(796\) −20.6226 −0.730948
\(797\) −11.0883 −0.392769 −0.196385 0.980527i \(-0.562920\pi\)
−0.196385 + 0.980527i \(0.562920\pi\)
\(798\) −3.13696 −0.111047
\(799\) −12.7605 −0.451435
\(800\) 3.11609 0.110170
\(801\) 14.8009 0.522962
\(802\) 7.81142 0.275831
\(803\) 52.7850 1.86274
\(804\) −14.1086 −0.497571
\(805\) −10.6746 −0.376229
\(806\) 23.1729 0.816231
\(807\) −17.1270 −0.602900
\(808\) 7.31037 0.257178
\(809\) 36.1007 1.26923 0.634616 0.772828i \(-0.281158\pi\)
0.634616 + 0.772828i \(0.281158\pi\)
\(810\) 1.37256 0.0482267
\(811\) −10.0801 −0.353960 −0.176980 0.984214i \(-0.556633\pi\)
−0.176980 + 0.984214i \(0.556633\pi\)
\(812\) −10.8739 −0.381601
\(813\) −16.7230 −0.586501
\(814\) 5.08002 0.178055
\(815\) −15.0928 −0.528677
\(816\) −1.00000 −0.0350070
\(817\) −4.26567 −0.149237
\(818\) −6.90534 −0.241440
\(819\) −9.59622 −0.335319
\(820\) −7.84299 −0.273889
\(821\) 21.5479 0.752025 0.376013 0.926614i \(-0.377295\pi\)
0.376013 + 0.926614i \(0.377295\pi\)
\(822\) −4.51260 −0.157395
\(823\) −28.9849 −1.01035 −0.505175 0.863017i \(-0.668572\pi\)
−0.505175 + 0.863017i \(0.668572\pi\)
\(824\) −7.63233 −0.265885
\(825\) −14.1372 −0.492195
\(826\) 2.44651 0.0851250
\(827\) −8.30302 −0.288724 −0.144362 0.989525i \(-0.546113\pi\)
−0.144362 + 0.989525i \(0.546113\pi\)
\(828\) 3.17888 0.110474
\(829\) 11.8225 0.410611 0.205305 0.978698i \(-0.434181\pi\)
0.205305 + 0.978698i \(0.434181\pi\)
\(830\) 12.6397 0.438729
\(831\) 6.16976 0.214027
\(832\) −3.92241 −0.135985
\(833\) 1.01458 0.0351532
\(834\) 10.2338 0.354366
\(835\) 0.479344 0.0165884
\(836\) 5.81723 0.201193
\(837\) 5.90783 0.204204
\(838\) −10.4229 −0.360053
\(839\) 46.9065 1.61939 0.809696 0.586849i \(-0.199632\pi\)
0.809696 + 0.586849i \(0.199632\pi\)
\(840\) 3.35797 0.115861
\(841\) −9.24486 −0.318788
\(842\) 27.6947 0.954424
\(843\) −21.8738 −0.753373
\(844\) −3.27881 −0.112861
\(845\) −3.27396 −0.112628
\(846\) −12.7605 −0.438715
\(847\) 23.4449 0.805576
\(848\) 6.22101 0.213630
\(849\) −3.51379 −0.120593
\(850\) −3.11609 −0.106881
\(851\) −3.55947 −0.122017
\(852\) −10.3817 −0.355670
\(853\) −22.8736 −0.783176 −0.391588 0.920141i \(-0.628074\pi\)
−0.391588 + 0.920141i \(0.628074\pi\)
\(854\) −10.4809 −0.358649
\(855\) −1.75992 −0.0601879
\(856\) 4.49082 0.153493
\(857\) −41.6744 −1.42357 −0.711785 0.702397i \(-0.752113\pi\)
−0.711785 + 0.702397i \(0.752113\pi\)
\(858\) 17.7954 0.607524
\(859\) −28.1161 −0.959310 −0.479655 0.877457i \(-0.659238\pi\)
−0.479655 + 0.877457i \(0.659238\pi\)
\(860\) 4.56620 0.155706
\(861\) 13.9797 0.476428
\(862\) −13.8370 −0.471290
\(863\) −37.6570 −1.28186 −0.640930 0.767600i \(-0.721451\pi\)
−0.640930 + 0.767600i \(0.721451\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 3.27478 0.111346
\(866\) 9.03973 0.307183
\(867\) 1.00000 0.0339618
\(868\) 14.4536 0.490586
\(869\) 63.9119 2.16806
\(870\) −6.10057 −0.206829
\(871\) 55.3396 1.87511
\(872\) 4.25283 0.144019
\(873\) −6.25100 −0.211564
\(874\) −4.07601 −0.137873
\(875\) 27.2536 0.921340
\(876\) 11.6347 0.393101
\(877\) 20.0188 0.675986 0.337993 0.941149i \(-0.390252\pi\)
0.337993 + 0.941149i \(0.390252\pi\)
\(878\) 6.09702 0.205764
\(879\) 9.89280 0.333676
\(880\) −6.22708 −0.209915
\(881\) −5.20291 −0.175290 −0.0876452 0.996152i \(-0.527934\pi\)
−0.0876452 + 0.996152i \(0.527934\pi\)
\(882\) 1.01458 0.0341628
\(883\) 7.60991 0.256094 0.128047 0.991768i \(-0.459129\pi\)
0.128047 + 0.991768i \(0.459129\pi\)
\(884\) 3.92241 0.131925
\(885\) 1.37256 0.0461380
\(886\) 21.3040 0.715723
\(887\) −9.66067 −0.324374 −0.162187 0.986760i \(-0.551855\pi\)
−0.162187 + 0.986760i \(0.551855\pi\)
\(888\) 1.11972 0.0375755
\(889\) 1.51036 0.0506558
\(890\) 20.3150 0.680960
\(891\) 4.53685 0.151990
\(892\) 7.89786 0.264440
\(893\) 16.3618 0.547526
\(894\) −15.1122 −0.505427
\(895\) 1.77958 0.0594847
\(896\) −2.44651 −0.0817322
\(897\) −12.4689 −0.416323
\(898\) −9.14428 −0.305148
\(899\) −26.2584 −0.875766
\(900\) −3.11609 −0.103870
\(901\) −6.22101 −0.207252
\(902\) −25.9242 −0.863182
\(903\) −8.13902 −0.270850
\(904\) −9.44831 −0.314246
\(905\) 10.4952 0.348873
\(906\) 18.4536 0.613079
\(907\) −5.93790 −0.197165 −0.0985824 0.995129i \(-0.531431\pi\)
−0.0985824 + 0.995129i \(0.531431\pi\)
\(908\) 3.21878 0.106819
\(909\) −7.31037 −0.242470
\(910\) −13.1713 −0.436626
\(911\) −5.78904 −0.191799 −0.0958997 0.995391i \(-0.530573\pi\)
−0.0958997 + 0.995391i \(0.530573\pi\)
\(912\) 1.28222 0.0424585
\(913\) 41.7792 1.38269
\(914\) −24.4679 −0.809326
\(915\) −5.88005 −0.194389
\(916\) 8.63791 0.285405
\(917\) −11.8995 −0.392955
\(918\) 1.00000 0.0330049
\(919\) −9.84962 −0.324909 −0.162454 0.986716i \(-0.551941\pi\)
−0.162454 + 0.986716i \(0.551941\pi\)
\(920\) 4.36318 0.143850
\(921\) 13.8309 0.455743
\(922\) 0.986656 0.0324938
\(923\) 40.7212 1.34035
\(924\) 11.0995 0.365145
\(925\) 3.48916 0.114723
\(926\) −10.0240 −0.329410
\(927\) 7.63233 0.250678
\(928\) 4.44468 0.145904
\(929\) −26.2741 −0.862026 −0.431013 0.902346i \(-0.641844\pi\)
−0.431013 + 0.902346i \(0.641844\pi\)
\(930\) 8.10882 0.265899
\(931\) −1.30092 −0.0426358
\(932\) −2.25951 −0.0740128
\(933\) 14.0500 0.459976
\(934\) −8.99505 −0.294327
\(935\) 6.22708 0.203647
\(936\) 3.92241 0.128208
\(937\) 43.4759 1.42029 0.710147 0.704053i \(-0.248628\pi\)
0.710147 + 0.704053i \(0.248628\pi\)
\(938\) 34.5168 1.12701
\(939\) −6.65585 −0.217206
\(940\) −17.5145 −0.571261
\(941\) −49.9516 −1.62838 −0.814188 0.580601i \(-0.802818\pi\)
−0.814188 + 0.580601i \(0.802818\pi\)
\(942\) 7.52286 0.245108
\(943\) 18.1646 0.591520
\(944\) −1.00000 −0.0325472
\(945\) −3.35797 −0.109235
\(946\) 15.0931 0.490720
\(947\) 7.25843 0.235867 0.117934 0.993021i \(-0.462373\pi\)
0.117934 + 0.993021i \(0.462373\pi\)
\(948\) 14.0873 0.457534
\(949\) −45.6362 −1.48141
\(950\) 3.99551 0.129631
\(951\) −8.10346 −0.262773
\(952\) 2.44651 0.0792919
\(953\) −50.4910 −1.63556 −0.817781 0.575529i \(-0.804796\pi\)
−0.817781 + 0.575529i \(0.804796\pi\)
\(954\) −6.22101 −0.201413
\(955\) −19.4242 −0.628554
\(956\) 25.9175 0.838233
\(957\) −20.1648 −0.651836
\(958\) −25.8738 −0.835944
\(959\) 11.0401 0.356504
\(960\) −1.37256 −0.0442990
\(961\) 3.90243 0.125885
\(962\) −4.39202 −0.141604
\(963\) −4.49082 −0.144715
\(964\) 14.0196 0.451542
\(965\) −22.4647 −0.723165
\(966\) −7.77715 −0.250226
\(967\) 30.9893 0.996548 0.498274 0.867020i \(-0.333967\pi\)
0.498274 + 0.867020i \(0.333967\pi\)
\(968\) −9.58299 −0.308009
\(969\) −1.28222 −0.0411908
\(970\) −8.57984 −0.275482
\(971\) 41.1170 1.31951 0.659754 0.751482i \(-0.270661\pi\)
0.659754 + 0.751482i \(0.270661\pi\)
\(972\) 1.00000 0.0320750
\(973\) −25.0370 −0.802649
\(974\) −1.84849 −0.0592295
\(975\) 12.2226 0.391436
\(976\) 4.28402 0.137128
\(977\) −26.5130 −0.848228 −0.424114 0.905609i \(-0.639414\pi\)
−0.424114 + 0.905609i \(0.639414\pi\)
\(978\) −10.9961 −0.351617
\(979\) 67.1492 2.14610
\(980\) 1.39257 0.0444841
\(981\) −4.25283 −0.135782
\(982\) 35.3045 1.12661
\(983\) 55.9913 1.78585 0.892923 0.450210i \(-0.148651\pi\)
0.892923 + 0.450210i \(0.148651\pi\)
\(984\) −5.71415 −0.182160
\(985\) −5.88257 −0.187434
\(986\) −4.44468 −0.141547
\(987\) 31.2187 0.993703
\(988\) −5.02939 −0.160006
\(989\) −10.5754 −0.336279
\(990\) 6.22708 0.197909
\(991\) 18.0439 0.573182 0.286591 0.958053i \(-0.407478\pi\)
0.286591 + 0.958053i \(0.407478\pi\)
\(992\) −5.90783 −0.187574
\(993\) −6.21793 −0.197320
\(994\) 25.3989 0.805603
\(995\) 28.3056 0.897349
\(996\) 9.20886 0.291794
\(997\) −13.3287 −0.422124 −0.211062 0.977473i \(-0.567692\pi\)
−0.211062 + 0.977473i \(0.567692\pi\)
\(998\) 9.67804 0.306353
\(999\) −1.11972 −0.0354265
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 \(a_p\))