Properties

Label 6034.2.a.n.1.1
Level 6034
Weight 2
Character 6034.1
Self dual Yes
Analytic conductor 48.182
Analytic rank 0
Dimension 24
CM No

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 6034.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-2.83864 q^{3}\) \(+1.00000 q^{4}\) \(+0.330019 q^{5}\) \(+2.83864 q^{6}\) \(-1.00000 q^{7}\) \(-1.00000 q^{8}\) \(+5.05788 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-2.83864 q^{3}\) \(+1.00000 q^{4}\) \(+0.330019 q^{5}\) \(+2.83864 q^{6}\) \(-1.00000 q^{7}\) \(-1.00000 q^{8}\) \(+5.05788 q^{9}\) \(-0.330019 q^{10}\) \(+3.07808 q^{11}\) \(-2.83864 q^{12}\) \(+2.69265 q^{13}\) \(+1.00000 q^{14}\) \(-0.936805 q^{15}\) \(+1.00000 q^{16}\) \(-6.41032 q^{17}\) \(-5.05788 q^{18}\) \(+3.15184 q^{19}\) \(+0.330019 q^{20}\) \(+2.83864 q^{21}\) \(-3.07808 q^{22}\) \(-6.50437 q^{23}\) \(+2.83864 q^{24}\) \(-4.89109 q^{25}\) \(-2.69265 q^{26}\) \(-5.84159 q^{27}\) \(-1.00000 q^{28}\) \(+3.58221 q^{29}\) \(+0.936805 q^{30}\) \(-0.453720 q^{31}\) \(-1.00000 q^{32}\) \(-8.73757 q^{33}\) \(+6.41032 q^{34}\) \(-0.330019 q^{35}\) \(+5.05788 q^{36}\) \(+0.0743955 q^{37}\) \(-3.15184 q^{38}\) \(-7.64347 q^{39}\) \(-0.330019 q^{40}\) \(+9.21562 q^{41}\) \(-2.83864 q^{42}\) \(+7.47572 q^{43}\) \(+3.07808 q^{44}\) \(+1.66920 q^{45}\) \(+6.50437 q^{46}\) \(+10.2092 q^{47}\) \(-2.83864 q^{48}\) \(+1.00000 q^{49}\) \(+4.89109 q^{50}\) \(+18.1966 q^{51}\) \(+2.69265 q^{52}\) \(+3.91618 q^{53}\) \(+5.84159 q^{54}\) \(+1.01582 q^{55}\) \(+1.00000 q^{56}\) \(-8.94694 q^{57}\) \(-3.58221 q^{58}\) \(+7.17457 q^{59}\) \(-0.936805 q^{60}\) \(-7.56905 q^{61}\) \(+0.453720 q^{62}\) \(-5.05788 q^{63}\) \(+1.00000 q^{64}\) \(+0.888626 q^{65}\) \(+8.73757 q^{66}\) \(+1.60280 q^{67}\) \(-6.41032 q^{68}\) \(+18.4636 q^{69}\) \(+0.330019 q^{70}\) \(-5.69325 q^{71}\) \(-5.05788 q^{72}\) \(-6.01855 q^{73}\) \(-0.0743955 q^{74}\) \(+13.8840 q^{75}\) \(+3.15184 q^{76}\) \(-3.07808 q^{77}\) \(+7.64347 q^{78}\) \(-5.72181 q^{79}\) \(+0.330019 q^{80}\) \(+1.40852 q^{81}\) \(-9.21562 q^{82}\) \(+9.56326 q^{83}\) \(+2.83864 q^{84}\) \(-2.11552 q^{85}\) \(-7.47572 q^{86}\) \(-10.1686 q^{87}\) \(-3.07808 q^{88}\) \(-8.49202 q^{89}\) \(-1.66920 q^{90}\) \(-2.69265 q^{91}\) \(-6.50437 q^{92}\) \(+1.28795 q^{93}\) \(-10.2092 q^{94}\) \(+1.04017 q^{95}\) \(+2.83864 q^{96}\) \(+1.71641 q^{97}\) \(-1.00000 q^{98}\) \(+15.5686 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 24q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 24q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut -\mathstrut 8q^{10} \) \(\mathstrut +\mathstrut 15q^{11} \) \(\mathstrut +\mathstrut 7q^{12} \) \(\mathstrut -\mathstrut 7q^{13} \) \(\mathstrut +\mathstrut 24q^{14} \) \(\mathstrut +\mathstrut 13q^{15} \) \(\mathstrut +\mathstrut 24q^{16} \) \(\mathstrut -\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 19q^{18} \) \(\mathstrut +\mathstrut 6q^{19} \) \(\mathstrut +\mathstrut 8q^{20} \) \(\mathstrut -\mathstrut 7q^{21} \) \(\mathstrut -\mathstrut 15q^{22} \) \(\mathstrut +\mathstrut 3q^{23} \) \(\mathstrut -\mathstrut 7q^{24} \) \(\mathstrut +\mathstrut 12q^{25} \) \(\mathstrut +\mathstrut 7q^{26} \) \(\mathstrut +\mathstrut 22q^{27} \) \(\mathstrut -\mathstrut 24q^{28} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 13q^{30} \) \(\mathstrut +\mathstrut 13q^{31} \) \(\mathstrut -\mathstrut 24q^{32} \) \(\mathstrut -\mathstrut 8q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut +\mathstrut 19q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 6q^{38} \) \(\mathstrut +\mathstrut 7q^{39} \) \(\mathstrut -\mathstrut 8q^{40} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 7q^{42} \) \(\mathstrut -\mathstrut 15q^{43} \) \(\mathstrut +\mathstrut 15q^{44} \) \(\mathstrut +\mathstrut 41q^{45} \) \(\mathstrut -\mathstrut 3q^{46} \) \(\mathstrut +\mathstrut 35q^{47} \) \(\mathstrut +\mathstrut 7q^{48} \) \(\mathstrut +\mathstrut 24q^{49} \) \(\mathstrut -\mathstrut 12q^{50} \) \(\mathstrut +\mathstrut 31q^{51} \) \(\mathstrut -\mathstrut 7q^{52} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 22q^{54} \) \(\mathstrut +\mathstrut 14q^{55} \) \(\mathstrut +\mathstrut 24q^{56} \) \(\mathstrut -\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 5q^{58} \) \(\mathstrut +\mathstrut 35q^{59} \) \(\mathstrut +\mathstrut 13q^{60} \) \(\mathstrut -\mathstrut 7q^{61} \) \(\mathstrut -\mathstrut 13q^{62} \) \(\mathstrut -\mathstrut 19q^{63} \) \(\mathstrut +\mathstrut 24q^{64} \) \(\mathstrut -\mathstrut 4q^{65} \) \(\mathstrut +\mathstrut 8q^{66} \) \(\mathstrut +\mathstrut 10q^{67} \) \(\mathstrut -\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut 6q^{69} \) \(\mathstrut +\mathstrut 8q^{70} \) \(\mathstrut +\mathstrut 58q^{71} \) \(\mathstrut -\mathstrut 19q^{72} \) \(\mathstrut +\mathstrut 9q^{73} \) \(\mathstrut -\mathstrut 2q^{74} \) \(\mathstrut +\mathstrut 7q^{75} \) \(\mathstrut +\mathstrut 6q^{76} \) \(\mathstrut -\mathstrut 15q^{77} \) \(\mathstrut -\mathstrut 7q^{78} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut +\mathstrut 8q^{80} \) \(\mathstrut +\mathstrut 16q^{81} \) \(\mathstrut -\mathstrut 25q^{82} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut -\mathstrut 7q^{84} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut +\mathstrut 15q^{86} \) \(\mathstrut +\mathstrut 30q^{87} \) \(\mathstrut -\mathstrut 15q^{88} \) \(\mathstrut +\mathstrut 45q^{89} \) \(\mathstrut -\mathstrut 41q^{90} \) \(\mathstrut +\mathstrut 7q^{91} \) \(\mathstrut +\mathstrut 3q^{92} \) \(\mathstrut +\mathstrut 25q^{93} \) \(\mathstrut -\mathstrut 35q^{94} \) \(\mathstrut -\mathstrut 10q^{95} \) \(\mathstrut -\mathstrut 7q^{96} \) \(\mathstrut -\mathstrut 9q^{97} \) \(\mathstrut -\mathstrut 24q^{98} \) \(\mathstrut +\mathstrut 64q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −2.83864 −1.63889 −0.819445 0.573158i \(-0.805718\pi\)
−0.819445 + 0.573158i \(0.805718\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.330019 0.147589 0.0737944 0.997273i \(-0.476489\pi\)
0.0737944 + 0.997273i \(0.476489\pi\)
\(6\) 2.83864 1.15887
\(7\) −1.00000 −0.377964
\(8\) −1.00000 −0.353553
\(9\) 5.05788 1.68596
\(10\) −0.330019 −0.104361
\(11\) 3.07808 0.928076 0.464038 0.885815i \(-0.346400\pi\)
0.464038 + 0.885815i \(0.346400\pi\)
\(12\) −2.83864 −0.819445
\(13\) 2.69265 0.746808 0.373404 0.927669i \(-0.378191\pi\)
0.373404 + 0.927669i \(0.378191\pi\)
\(14\) 1.00000 0.267261
\(15\) −0.936805 −0.241882
\(16\) 1.00000 0.250000
\(17\) −6.41032 −1.55473 −0.777365 0.629050i \(-0.783444\pi\)
−0.777365 + 0.629050i \(0.783444\pi\)
\(18\) −5.05788 −1.19215
\(19\) 3.15184 0.723082 0.361541 0.932356i \(-0.382251\pi\)
0.361541 + 0.932356i \(0.382251\pi\)
\(20\) 0.330019 0.0737944
\(21\) 2.83864 0.619442
\(22\) −3.07808 −0.656249
\(23\) −6.50437 −1.35626 −0.678128 0.734944i \(-0.737208\pi\)
−0.678128 + 0.734944i \(0.737208\pi\)
\(24\) 2.83864 0.579435
\(25\) −4.89109 −0.978218
\(26\) −2.69265 −0.528073
\(27\) −5.84159 −1.12421
\(28\) −1.00000 −0.188982
\(29\) 3.58221 0.665199 0.332600 0.943068i \(-0.392074\pi\)
0.332600 + 0.943068i \(0.392074\pi\)
\(30\) 0.936805 0.171036
\(31\) −0.453720 −0.0814904 −0.0407452 0.999170i \(-0.512973\pi\)
−0.0407452 + 0.999170i \(0.512973\pi\)
\(32\) −1.00000 −0.176777
\(33\) −8.73757 −1.52102
\(34\) 6.41032 1.09936
\(35\) −0.330019 −0.0557833
\(36\) 5.05788 0.842980
\(37\) 0.0743955 0.0122305 0.00611527 0.999981i \(-0.498053\pi\)
0.00611527 + 0.999981i \(0.498053\pi\)
\(38\) −3.15184 −0.511296
\(39\) −7.64347 −1.22394
\(40\) −0.330019 −0.0521805
\(41\) 9.21562 1.43924 0.719619 0.694369i \(-0.244316\pi\)
0.719619 + 0.694369i \(0.244316\pi\)
\(42\) −2.83864 −0.438012
\(43\) 7.47572 1.14004 0.570018 0.821632i \(-0.306936\pi\)
0.570018 + 0.821632i \(0.306936\pi\)
\(44\) 3.07808 0.464038
\(45\) 1.66920 0.248829
\(46\) 6.50437 0.959018
\(47\) 10.2092 1.48916 0.744581 0.667532i \(-0.232649\pi\)
0.744581 + 0.667532i \(0.232649\pi\)
\(48\) −2.83864 −0.409723
\(49\) 1.00000 0.142857
\(50\) 4.89109 0.691704
\(51\) 18.1966 2.54803
\(52\) 2.69265 0.373404
\(53\) 3.91618 0.537929 0.268965 0.963150i \(-0.413319\pi\)
0.268965 + 0.963150i \(0.413319\pi\)
\(54\) 5.84159 0.794939
\(55\) 1.01582 0.136974
\(56\) 1.00000 0.133631
\(57\) −8.94694 −1.18505
\(58\) −3.58221 −0.470367
\(59\) 7.17457 0.934049 0.467025 0.884244i \(-0.345326\pi\)
0.467025 + 0.884244i \(0.345326\pi\)
\(60\) −0.936805 −0.120941
\(61\) −7.56905 −0.969118 −0.484559 0.874759i \(-0.661020\pi\)
−0.484559 + 0.874759i \(0.661020\pi\)
\(62\) 0.453720 0.0576224
\(63\) −5.05788 −0.637233
\(64\) 1.00000 0.125000
\(65\) 0.888626 0.110220
\(66\) 8.73757 1.07552
\(67\) 1.60280 0.195814 0.0979068 0.995196i \(-0.468785\pi\)
0.0979068 + 0.995196i \(0.468785\pi\)
\(68\) −6.41032 −0.777365
\(69\) 18.4636 2.22275
\(70\) 0.330019 0.0394448
\(71\) −5.69325 −0.675664 −0.337832 0.941206i \(-0.609694\pi\)
−0.337832 + 0.941206i \(0.609694\pi\)
\(72\) −5.05788 −0.596077
\(73\) −6.01855 −0.704417 −0.352209 0.935921i \(-0.614569\pi\)
−0.352209 + 0.935921i \(0.614569\pi\)
\(74\) −0.0743955 −0.00864830
\(75\) 13.8840 1.60319
\(76\) 3.15184 0.361541
\(77\) −3.07808 −0.350780
\(78\) 7.64347 0.865453
\(79\) −5.72181 −0.643754 −0.321877 0.946781i \(-0.604314\pi\)
−0.321877 + 0.946781i \(0.604314\pi\)
\(80\) 0.330019 0.0368972
\(81\) 1.40852 0.156502
\(82\) −9.21562 −1.01769
\(83\) 9.56326 1.04970 0.524852 0.851194i \(-0.324121\pi\)
0.524852 + 0.851194i \(0.324121\pi\)
\(84\) 2.83864 0.309721
\(85\) −2.11552 −0.229461
\(86\) −7.47572 −0.806128
\(87\) −10.1686 −1.09019
\(88\) −3.07808 −0.328125
\(89\) −8.49202 −0.900152 −0.450076 0.892990i \(-0.648603\pi\)
−0.450076 + 0.892990i \(0.648603\pi\)
\(90\) −1.66920 −0.175949
\(91\) −2.69265 −0.282267
\(92\) −6.50437 −0.678128
\(93\) 1.28795 0.133554
\(94\) −10.2092 −1.05300
\(95\) 1.04017 0.106719
\(96\) 2.83864 0.289718
\(97\) 1.71641 0.174275 0.0871374 0.996196i \(-0.472228\pi\)
0.0871374 + 0.996196i \(0.472228\pi\)
\(98\) −1.00000 −0.101015
\(99\) 15.5686 1.56470
\(100\) −4.89109 −0.489109
\(101\) 2.22710 0.221605 0.110802 0.993842i \(-0.464658\pi\)
0.110802 + 0.993842i \(0.464658\pi\)
\(102\) −18.1966 −1.80173
\(103\) −10.1067 −0.995844 −0.497922 0.867222i \(-0.665903\pi\)
−0.497922 + 0.867222i \(0.665903\pi\)
\(104\) −2.69265 −0.264036
\(105\) 0.936805 0.0914228
\(106\) −3.91618 −0.380373
\(107\) −10.1266 −0.978975 −0.489488 0.872010i \(-0.662816\pi\)
−0.489488 + 0.872010i \(0.662816\pi\)
\(108\) −5.84159 −0.562107
\(109\) −11.3383 −1.08601 −0.543004 0.839730i \(-0.682713\pi\)
−0.543004 + 0.839730i \(0.682713\pi\)
\(110\) −1.01582 −0.0968551
\(111\) −0.211182 −0.0200445
\(112\) −1.00000 −0.0944911
\(113\) −9.03856 −0.850276 −0.425138 0.905128i \(-0.639775\pi\)
−0.425138 + 0.905128i \(0.639775\pi\)
\(114\) 8.94694 0.837958
\(115\) −2.14657 −0.200168
\(116\) 3.58221 0.332600
\(117\) 13.6191 1.25909
\(118\) −7.17457 −0.660472
\(119\) 6.41032 0.587633
\(120\) 0.936805 0.0855182
\(121\) −1.52541 −0.138674
\(122\) 7.56905 0.685270
\(123\) −26.1598 −2.35875
\(124\) −0.453720 −0.0407452
\(125\) −3.26424 −0.291963
\(126\) 5.05788 0.450592
\(127\) −8.78251 −0.779321 −0.389661 0.920959i \(-0.627408\pi\)
−0.389661 + 0.920959i \(0.627408\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −21.2209 −1.86839
\(130\) −0.888626 −0.0779376
\(131\) 14.4953 1.26646 0.633231 0.773963i \(-0.281728\pi\)
0.633231 + 0.773963i \(0.281728\pi\)
\(132\) −8.73757 −0.760508
\(133\) −3.15184 −0.273299
\(134\) −1.60280 −0.138461
\(135\) −1.92783 −0.165921
\(136\) 6.41032 0.549680
\(137\) −6.55574 −0.560094 −0.280047 0.959986i \(-0.590350\pi\)
−0.280047 + 0.959986i \(0.590350\pi\)
\(138\) −18.4636 −1.57172
\(139\) 12.2483 1.03889 0.519445 0.854504i \(-0.326139\pi\)
0.519445 + 0.854504i \(0.326139\pi\)
\(140\) −0.330019 −0.0278917
\(141\) −28.9802 −2.44057
\(142\) 5.69325 0.477767
\(143\) 8.28821 0.693095
\(144\) 5.05788 0.421490
\(145\) 1.18220 0.0981760
\(146\) 6.01855 0.498098
\(147\) −2.83864 −0.234127
\(148\) 0.0743955 0.00611527
\(149\) 21.1229 1.73046 0.865229 0.501377i \(-0.167173\pi\)
0.865229 + 0.501377i \(0.167173\pi\)
\(150\) −13.8840 −1.13363
\(151\) 14.5996 1.18810 0.594051 0.804428i \(-0.297528\pi\)
0.594051 + 0.804428i \(0.297528\pi\)
\(152\) −3.15184 −0.255648
\(153\) −32.4226 −2.62121
\(154\) 3.07808 0.248039
\(155\) −0.149736 −0.0120271
\(156\) −7.64347 −0.611968
\(157\) 17.4928 1.39608 0.698038 0.716061i \(-0.254057\pi\)
0.698038 + 0.716061i \(0.254057\pi\)
\(158\) 5.72181 0.455203
\(159\) −11.1166 −0.881607
\(160\) −0.330019 −0.0260903
\(161\) 6.50437 0.512616
\(162\) −1.40852 −0.110664
\(163\) −11.4612 −0.897708 −0.448854 0.893605i \(-0.648168\pi\)
−0.448854 + 0.893605i \(0.648168\pi\)
\(164\) 9.21562 0.719619
\(165\) −2.88356 −0.224485
\(166\) −9.56326 −0.742253
\(167\) −8.42319 −0.651806 −0.325903 0.945403i \(-0.605668\pi\)
−0.325903 + 0.945403i \(0.605668\pi\)
\(168\) −2.83864 −0.219006
\(169\) −5.74962 −0.442278
\(170\) 2.11552 0.162253
\(171\) 15.9416 1.21909
\(172\) 7.47572 0.570018
\(173\) −10.6698 −0.811209 −0.405604 0.914049i \(-0.632939\pi\)
−0.405604 + 0.914049i \(0.632939\pi\)
\(174\) 10.1686 0.770880
\(175\) 4.89109 0.369731
\(176\) 3.07808 0.232019
\(177\) −20.3660 −1.53080
\(178\) 8.49202 0.636504
\(179\) 6.89780 0.515566 0.257783 0.966203i \(-0.417008\pi\)
0.257783 + 0.966203i \(0.417008\pi\)
\(180\) 1.66920 0.124414
\(181\) 12.5011 0.929199 0.464600 0.885521i \(-0.346198\pi\)
0.464600 + 0.885521i \(0.346198\pi\)
\(182\) 2.69265 0.199593
\(183\) 21.4858 1.58828
\(184\) 6.50437 0.479509
\(185\) 0.0245519 0.00180509
\(186\) −1.28795 −0.0944368
\(187\) −19.7315 −1.44291
\(188\) 10.2092 0.744581
\(189\) 5.84159 0.424913
\(190\) −1.04017 −0.0754616
\(191\) −0.0973263 −0.00704228 −0.00352114 0.999994i \(-0.501121\pi\)
−0.00352114 + 0.999994i \(0.501121\pi\)
\(192\) −2.83864 −0.204861
\(193\) −11.8903 −0.855884 −0.427942 0.903806i \(-0.640761\pi\)
−0.427942 + 0.903806i \(0.640761\pi\)
\(194\) −1.71641 −0.123231
\(195\) −2.52249 −0.180639
\(196\) 1.00000 0.0714286
\(197\) 7.03452 0.501189 0.250595 0.968092i \(-0.419374\pi\)
0.250595 + 0.968092i \(0.419374\pi\)
\(198\) −15.5686 −1.10641
\(199\) 2.73519 0.193892 0.0969461 0.995290i \(-0.469093\pi\)
0.0969461 + 0.995290i \(0.469093\pi\)
\(200\) 4.89109 0.345852
\(201\) −4.54978 −0.320917
\(202\) −2.22710 −0.156698
\(203\) −3.58221 −0.251422
\(204\) 18.1966 1.27402
\(205\) 3.04133 0.212416
\(206\) 10.1067 0.704168
\(207\) −32.8984 −2.28659
\(208\) 2.69265 0.186702
\(209\) 9.70162 0.671075
\(210\) −0.936805 −0.0646457
\(211\) −4.51356 −0.310726 −0.155363 0.987857i \(-0.549655\pi\)
−0.155363 + 0.987857i \(0.549655\pi\)
\(212\) 3.91618 0.268965
\(213\) 16.1611 1.10734
\(214\) 10.1266 0.692240
\(215\) 2.46713 0.168257
\(216\) 5.84159 0.397470
\(217\) 0.453720 0.0308005
\(218\) 11.3383 0.767924
\(219\) 17.0845 1.15446
\(220\) 1.01582 0.0684869
\(221\) −17.2608 −1.16108
\(222\) 0.211182 0.0141736
\(223\) 18.3038 1.22571 0.612855 0.790195i \(-0.290021\pi\)
0.612855 + 0.790195i \(0.290021\pi\)
\(224\) 1.00000 0.0668153
\(225\) −24.7385 −1.64924
\(226\) 9.03856 0.601236
\(227\) 6.09228 0.404359 0.202179 0.979349i \(-0.435198\pi\)
0.202179 + 0.979349i \(0.435198\pi\)
\(228\) −8.94694 −0.592526
\(229\) −22.2252 −1.46869 −0.734343 0.678779i \(-0.762510\pi\)
−0.734343 + 0.678779i \(0.762510\pi\)
\(230\) 2.14657 0.141540
\(231\) 8.73757 0.574890
\(232\) −3.58221 −0.235183
\(233\) −14.4571 −0.947117 −0.473559 0.880762i \(-0.657031\pi\)
−0.473559 + 0.880762i \(0.657031\pi\)
\(234\) −13.6191 −0.890310
\(235\) 3.36922 0.219784
\(236\) 7.17457 0.467025
\(237\) 16.2422 1.05504
\(238\) −6.41032 −0.415519
\(239\) 25.9559 1.67895 0.839474 0.543401i \(-0.182864\pi\)
0.839474 + 0.543401i \(0.182864\pi\)
\(240\) −0.936805 −0.0604705
\(241\) −3.21440 −0.207058 −0.103529 0.994626i \(-0.533013\pi\)
−0.103529 + 0.994626i \(0.533013\pi\)
\(242\) 1.52541 0.0980574
\(243\) 13.5265 0.867724
\(244\) −7.56905 −0.484559
\(245\) 0.330019 0.0210841
\(246\) 26.1598 1.66789
\(247\) 8.48681 0.540003
\(248\) 0.453720 0.0288112
\(249\) −27.1467 −1.72035
\(250\) 3.26424 0.206449
\(251\) 2.55475 0.161254 0.0806272 0.996744i \(-0.474308\pi\)
0.0806272 + 0.996744i \(0.474308\pi\)
\(252\) −5.05788 −0.318617
\(253\) −20.0210 −1.25871
\(254\) 8.78251 0.551063
\(255\) 6.00521 0.376061
\(256\) 1.00000 0.0625000
\(257\) −0.0593036 −0.00369926 −0.00184963 0.999998i \(-0.500589\pi\)
−0.00184963 + 0.999998i \(0.500589\pi\)
\(258\) 21.2209 1.32115
\(259\) −0.0743955 −0.00462271
\(260\) 0.888626 0.0551102
\(261\) 18.1184 1.12150
\(262\) −14.4953 −0.895523
\(263\) 0.204806 0.0126289 0.00631445 0.999980i \(-0.497990\pi\)
0.00631445 + 0.999980i \(0.497990\pi\)
\(264\) 8.73757 0.537760
\(265\) 1.29241 0.0793923
\(266\) 3.15184 0.193252
\(267\) 24.1058 1.47525
\(268\) 1.60280 0.0979068
\(269\) −15.3989 −0.938887 −0.469444 0.882963i \(-0.655545\pi\)
−0.469444 + 0.882963i \(0.655545\pi\)
\(270\) 1.92783 0.117324
\(271\) −10.3147 −0.626572 −0.313286 0.949659i \(-0.601430\pi\)
−0.313286 + 0.949659i \(0.601430\pi\)
\(272\) −6.41032 −0.388682
\(273\) 7.64347 0.462604
\(274\) 6.55574 0.396047
\(275\) −15.0552 −0.907861
\(276\) 18.4636 1.11138
\(277\) −21.6252 −1.29934 −0.649668 0.760218i \(-0.725092\pi\)
−0.649668 + 0.760218i \(0.725092\pi\)
\(278\) −12.2483 −0.734606
\(279\) −2.29486 −0.137390
\(280\) 0.330019 0.0197224
\(281\) −11.8424 −0.706461 −0.353230 0.935536i \(-0.614917\pi\)
−0.353230 + 0.935536i \(0.614917\pi\)
\(282\) 28.9802 1.72575
\(283\) 11.4577 0.681088 0.340544 0.940229i \(-0.389389\pi\)
0.340544 + 0.940229i \(0.389389\pi\)
\(284\) −5.69325 −0.337832
\(285\) −2.95266 −0.174900
\(286\) −8.28821 −0.490092
\(287\) −9.21562 −0.543981
\(288\) −5.05788 −0.298039
\(289\) 24.0922 1.41719
\(290\) −1.18220 −0.0694209
\(291\) −4.87226 −0.285617
\(292\) −6.01855 −0.352209
\(293\) 14.7623 0.862423 0.431212 0.902251i \(-0.358086\pi\)
0.431212 + 0.902251i \(0.358086\pi\)
\(294\) 2.83864 0.165553
\(295\) 2.36774 0.137855
\(296\) −0.0743955 −0.00432415
\(297\) −17.9809 −1.04336
\(298\) −21.1229 −1.22362
\(299\) −17.5140 −1.01286
\(300\) 13.8840 0.801595
\(301\) −7.47572 −0.430893
\(302\) −14.5996 −0.840114
\(303\) −6.32194 −0.363186
\(304\) 3.15184 0.180770
\(305\) −2.49793 −0.143031
\(306\) 32.4226 1.85348
\(307\) −17.6752 −1.00878 −0.504389 0.863477i \(-0.668282\pi\)
−0.504389 + 0.863477i \(0.668282\pi\)
\(308\) −3.07808 −0.175390
\(309\) 28.6893 1.63208
\(310\) 0.149736 0.00850443
\(311\) −4.89400 −0.277513 −0.138757 0.990327i \(-0.544311\pi\)
−0.138757 + 0.990327i \(0.544311\pi\)
\(312\) 7.64347 0.432727
\(313\) −6.78529 −0.383527 −0.191764 0.981441i \(-0.561421\pi\)
−0.191764 + 0.981441i \(0.561421\pi\)
\(314\) −17.4928 −0.987174
\(315\) −1.66920 −0.0940485
\(316\) −5.72181 −0.321877
\(317\) 23.1328 1.29927 0.649633 0.760248i \(-0.274922\pi\)
0.649633 + 0.760248i \(0.274922\pi\)
\(318\) 11.1166 0.623390
\(319\) 11.0263 0.617356
\(320\) 0.330019 0.0184486
\(321\) 28.7458 1.60443
\(322\) −6.50437 −0.362475
\(323\) −20.2043 −1.12420
\(324\) 1.40852 0.0782511
\(325\) −13.1700 −0.730540
\(326\) 11.4612 0.634775
\(327\) 32.1853 1.77985
\(328\) −9.21562 −0.508847
\(329\) −10.2092 −0.562850
\(330\) 2.88356 0.158735
\(331\) 10.9640 0.602636 0.301318 0.953524i \(-0.402573\pi\)
0.301318 + 0.953524i \(0.402573\pi\)
\(332\) 9.56326 0.524852
\(333\) 0.376284 0.0206202
\(334\) 8.42319 0.460896
\(335\) 0.528955 0.0288999
\(336\) 2.83864 0.154861
\(337\) 19.4040 1.05701 0.528503 0.848932i \(-0.322754\pi\)
0.528503 + 0.848932i \(0.322754\pi\)
\(338\) 5.74962 0.312738
\(339\) 25.6572 1.39351
\(340\) −2.11552 −0.114730
\(341\) −1.39659 −0.0756293
\(342\) −15.9416 −0.862025
\(343\) −1.00000 −0.0539949
\(344\) −7.47572 −0.403064
\(345\) 6.09333 0.328054
\(346\) 10.6698 0.573611
\(347\) 23.3104 1.25137 0.625685 0.780076i \(-0.284819\pi\)
0.625685 + 0.780076i \(0.284819\pi\)
\(348\) −10.1686 −0.545094
\(349\) 8.83540 0.472948 0.236474 0.971638i \(-0.424008\pi\)
0.236474 + 0.971638i \(0.424008\pi\)
\(350\) −4.89109 −0.261440
\(351\) −15.7294 −0.839571
\(352\) −3.07808 −0.164062
\(353\) 24.5084 1.30445 0.652225 0.758025i \(-0.273836\pi\)
0.652225 + 0.758025i \(0.273836\pi\)
\(354\) 20.3660 1.08244
\(355\) −1.87888 −0.0997205
\(356\) −8.49202 −0.450076
\(357\) −18.1966 −0.963065
\(358\) −6.89780 −0.364560
\(359\) 19.7712 1.04348 0.521742 0.853104i \(-0.325283\pi\)
0.521742 + 0.853104i \(0.325283\pi\)
\(360\) −1.66920 −0.0879743
\(361\) −9.06591 −0.477153
\(362\) −12.5011 −0.657043
\(363\) 4.33010 0.227272
\(364\) −2.69265 −0.141133
\(365\) −1.98623 −0.103964
\(366\) −21.4858 −1.12308
\(367\) 4.27937 0.223381 0.111691 0.993743i \(-0.464373\pi\)
0.111691 + 0.993743i \(0.464373\pi\)
\(368\) −6.50437 −0.339064
\(369\) 46.6115 2.42650
\(370\) −0.0245519 −0.00127639
\(371\) −3.91618 −0.203318
\(372\) 1.28795 0.0667769
\(373\) 17.8953 0.926585 0.463293 0.886205i \(-0.346668\pi\)
0.463293 + 0.886205i \(0.346668\pi\)
\(374\) 19.7315 1.02029
\(375\) 9.26602 0.478495
\(376\) −10.2092 −0.526498
\(377\) 9.64564 0.496776
\(378\) −5.84159 −0.300459
\(379\) 4.01937 0.206461 0.103231 0.994657i \(-0.467082\pi\)
0.103231 + 0.994657i \(0.467082\pi\)
\(380\) 1.04017 0.0533594
\(381\) 24.9304 1.27722
\(382\) 0.0973263 0.00497964
\(383\) −10.0772 −0.514921 −0.257461 0.966289i \(-0.582886\pi\)
−0.257461 + 0.966289i \(0.582886\pi\)
\(384\) 2.83864 0.144859
\(385\) −1.01582 −0.0517712
\(386\) 11.8903 0.605201
\(387\) 37.8113 1.92206
\(388\) 1.71641 0.0871374
\(389\) −20.8961 −1.05947 −0.529737 0.848162i \(-0.677710\pi\)
−0.529737 + 0.848162i \(0.677710\pi\)
\(390\) 2.52249 0.127731
\(391\) 41.6951 2.10861
\(392\) −1.00000 −0.0505076
\(393\) −41.1470 −2.07559
\(394\) −7.03452 −0.354394
\(395\) −1.88831 −0.0950109
\(396\) 15.5686 0.782350
\(397\) 27.2515 1.36771 0.683856 0.729617i \(-0.260302\pi\)
0.683856 + 0.729617i \(0.260302\pi\)
\(398\) −2.73519 −0.137103
\(399\) 8.94694 0.447907
\(400\) −4.89109 −0.244554
\(401\) 24.4179 1.21937 0.609686 0.792643i \(-0.291296\pi\)
0.609686 + 0.792643i \(0.291296\pi\)
\(402\) 4.54978 0.226923
\(403\) −1.22171 −0.0608577
\(404\) 2.22710 0.110802
\(405\) 0.464838 0.0230980
\(406\) 3.58221 0.177782
\(407\) 0.228995 0.0113509
\(408\) −18.1966 −0.900865
\(409\) 10.7500 0.531553 0.265776 0.964035i \(-0.414372\pi\)
0.265776 + 0.964035i \(0.414372\pi\)
\(410\) −3.04133 −0.150200
\(411\) 18.6094 0.917933
\(412\) −10.1067 −0.497922
\(413\) −7.17457 −0.353037
\(414\) 32.8984 1.61687
\(415\) 3.15605 0.154925
\(416\) −2.69265 −0.132018
\(417\) −34.7686 −1.70263
\(418\) −9.70162 −0.474522
\(419\) 35.8280 1.75031 0.875155 0.483842i \(-0.160759\pi\)
0.875155 + 0.483842i \(0.160759\pi\)
\(420\) 0.936805 0.0457114
\(421\) −7.31605 −0.356563 −0.178281 0.983980i \(-0.557054\pi\)
−0.178281 + 0.983980i \(0.557054\pi\)
\(422\) 4.51356 0.219716
\(423\) 51.6368 2.51067
\(424\) −3.91618 −0.190187
\(425\) 31.3534 1.52086
\(426\) −16.1611 −0.783007
\(427\) 7.56905 0.366292
\(428\) −10.1266 −0.489488
\(429\) −23.5272 −1.13591
\(430\) −2.46713 −0.118975
\(431\) 1.00000 0.0481683
\(432\) −5.84159 −0.281053
\(433\) 31.8948 1.53277 0.766383 0.642384i \(-0.222055\pi\)
0.766383 + 0.642384i \(0.222055\pi\)
\(434\) −0.453720 −0.0217792
\(435\) −3.35583 −0.160900
\(436\) −11.3383 −0.543004
\(437\) −20.5007 −0.980683
\(438\) −17.0845 −0.816328
\(439\) 14.7796 0.705392 0.352696 0.935738i \(-0.385265\pi\)
0.352696 + 0.935738i \(0.385265\pi\)
\(440\) −1.01582 −0.0484275
\(441\) 5.05788 0.240851
\(442\) 17.2608 0.821010
\(443\) 18.3398 0.871350 0.435675 0.900104i \(-0.356510\pi\)
0.435675 + 0.900104i \(0.356510\pi\)
\(444\) −0.211182 −0.0100223
\(445\) −2.80253 −0.132852
\(446\) −18.3038 −0.866708
\(447\) −59.9604 −2.83603
\(448\) −1.00000 −0.0472456
\(449\) −26.7154 −1.26078 −0.630388 0.776280i \(-0.717104\pi\)
−0.630388 + 0.776280i \(0.717104\pi\)
\(450\) 24.7385 1.16619
\(451\) 28.3664 1.33572
\(452\) −9.03856 −0.425138
\(453\) −41.4431 −1.94717
\(454\) −6.09228 −0.285925
\(455\) −0.888626 −0.0416594
\(456\) 8.94694 0.418979
\(457\) −11.2067 −0.524227 −0.262113 0.965037i \(-0.584419\pi\)
−0.262113 + 0.965037i \(0.584419\pi\)
\(458\) 22.2252 1.03852
\(459\) 37.4464 1.74785
\(460\) −2.14657 −0.100084
\(461\) 14.7644 0.687649 0.343824 0.939034i \(-0.388278\pi\)
0.343824 + 0.939034i \(0.388278\pi\)
\(462\) −8.73757 −0.406508
\(463\) −3.89885 −0.181195 −0.0905974 0.995888i \(-0.528878\pi\)
−0.0905974 + 0.995888i \(0.528878\pi\)
\(464\) 3.58221 0.166300
\(465\) 0.425047 0.0197111
\(466\) 14.4571 0.669713
\(467\) −0.801978 −0.0371111 −0.0185555 0.999828i \(-0.505907\pi\)
−0.0185555 + 0.999828i \(0.505907\pi\)
\(468\) 13.6191 0.629544
\(469\) −1.60280 −0.0740106
\(470\) −3.36922 −0.155411
\(471\) −49.6557 −2.28801
\(472\) −7.17457 −0.330236
\(473\) 23.0109 1.05804
\(474\) −16.2422 −0.746028
\(475\) −15.4159 −0.707331
\(476\) 6.41032 0.293816
\(477\) 19.8076 0.906927
\(478\) −25.9559 −1.18719
\(479\) 9.83182 0.449227 0.224614 0.974448i \(-0.427888\pi\)
0.224614 + 0.974448i \(0.427888\pi\)
\(480\) 0.936805 0.0427591
\(481\) 0.200321 0.00913386
\(482\) 3.21440 0.146412
\(483\) −18.4636 −0.840122
\(484\) −1.52541 −0.0693370
\(485\) 0.566447 0.0257210
\(486\) −13.5265 −0.613573
\(487\) −1.12362 −0.0509163 −0.0254582 0.999676i \(-0.508104\pi\)
−0.0254582 + 0.999676i \(0.508104\pi\)
\(488\) 7.56905 0.342635
\(489\) 32.5341 1.47124
\(490\) −0.330019 −0.0149087
\(491\) 3.87935 0.175073 0.0875363 0.996161i \(-0.472101\pi\)
0.0875363 + 0.996161i \(0.472101\pi\)
\(492\) −26.1598 −1.17938
\(493\) −22.9631 −1.03421
\(494\) −8.48681 −0.381840
\(495\) 5.13792 0.230932
\(496\) −0.453720 −0.0203726
\(497\) 5.69325 0.255377
\(498\) 27.1467 1.21647
\(499\) −30.7306 −1.37569 −0.687846 0.725857i \(-0.741443\pi\)
−0.687846 + 0.725857i \(0.741443\pi\)
\(500\) −3.26424 −0.145981
\(501\) 23.9104 1.06824
\(502\) −2.55475 −0.114024
\(503\) −15.1130 −0.673857 −0.336929 0.941530i \(-0.609388\pi\)
−0.336929 + 0.941530i \(0.609388\pi\)
\(504\) 5.05788 0.225296
\(505\) 0.734985 0.0327064
\(506\) 20.0210 0.890042
\(507\) 16.3211 0.724846
\(508\) −8.78251 −0.389661
\(509\) 12.6963 0.562756 0.281378 0.959597i \(-0.409209\pi\)
0.281378 + 0.959597i \(0.409209\pi\)
\(510\) −6.00521 −0.265915
\(511\) 6.01855 0.266245
\(512\) −1.00000 −0.0441942
\(513\) −18.4117 −0.812898
\(514\) 0.0593036 0.00261577
\(515\) −3.33540 −0.146975
\(516\) −21.2209 −0.934197
\(517\) 31.4247 1.38206
\(518\) 0.0743955 0.00326875
\(519\) 30.2877 1.32948
\(520\) −0.888626 −0.0389688
\(521\) −19.9584 −0.874394 −0.437197 0.899366i \(-0.644029\pi\)
−0.437197 + 0.899366i \(0.644029\pi\)
\(522\) −18.1184 −0.793020
\(523\) 10.8536 0.474597 0.237298 0.971437i \(-0.423738\pi\)
0.237298 + 0.971437i \(0.423738\pi\)
\(524\) 14.4953 0.633231
\(525\) −13.8840 −0.605949
\(526\) −0.204806 −0.00892998
\(527\) 2.90849 0.126696
\(528\) −8.73757 −0.380254
\(529\) 19.3069 0.839429
\(530\) −1.29241 −0.0561389
\(531\) 36.2881 1.57477
\(532\) −3.15184 −0.136650
\(533\) 24.8145 1.07483
\(534\) −24.1058 −1.04316
\(535\) −3.34197 −0.144486
\(536\) −1.60280 −0.0692305
\(537\) −19.5804 −0.844955
\(538\) 15.3989 0.663893
\(539\) 3.07808 0.132582
\(540\) −1.92783 −0.0829607
\(541\) 32.1501 1.38224 0.691120 0.722740i \(-0.257118\pi\)
0.691120 + 0.722740i \(0.257118\pi\)
\(542\) 10.3147 0.443053
\(543\) −35.4861 −1.52285
\(544\) 6.41032 0.274840
\(545\) −3.74184 −0.160283
\(546\) −7.64347 −0.327111
\(547\) −37.6713 −1.61071 −0.805353 0.592795i \(-0.798024\pi\)
−0.805353 + 0.592795i \(0.798024\pi\)
\(548\) −6.55574 −0.280047
\(549\) −38.2834 −1.63389
\(550\) 15.0552 0.641954
\(551\) 11.2905 0.480993
\(552\) −18.4636 −0.785862
\(553\) 5.72181 0.243316
\(554\) 21.6252 0.918769
\(555\) −0.0696940 −0.00295835
\(556\) 12.2483 0.519445
\(557\) −37.3679 −1.58333 −0.791663 0.610957i \(-0.790785\pi\)
−0.791663 + 0.610957i \(0.790785\pi\)
\(558\) 2.29486 0.0971491
\(559\) 20.1295 0.851388
\(560\) −0.330019 −0.0139458
\(561\) 56.0106 2.36477
\(562\) 11.8424 0.499543
\(563\) 18.5627 0.782325 0.391162 0.920322i \(-0.372073\pi\)
0.391162 + 0.920322i \(0.372073\pi\)
\(564\) −28.9802 −1.22029
\(565\) −2.98290 −0.125491
\(566\) −11.4577 −0.481602
\(567\) −1.40852 −0.0591523
\(568\) 5.69325 0.238883
\(569\) −16.0103 −0.671188 −0.335594 0.942007i \(-0.608937\pi\)
−0.335594 + 0.942007i \(0.608937\pi\)
\(570\) 2.95266 0.123673
\(571\) 11.3038 0.473051 0.236526 0.971625i \(-0.423991\pi\)
0.236526 + 0.971625i \(0.423991\pi\)
\(572\) 8.28821 0.346547
\(573\) 0.276274 0.0115415
\(574\) 9.21562 0.384653
\(575\) 31.8135 1.32671
\(576\) 5.05788 0.210745
\(577\) −11.5786 −0.482025 −0.241012 0.970522i \(-0.577479\pi\)
−0.241012 + 0.970522i \(0.577479\pi\)
\(578\) −24.0922 −1.00210
\(579\) 33.7523 1.40270
\(580\) 1.18220 0.0490880
\(581\) −9.56326 −0.396751
\(582\) 4.87226 0.201962
\(583\) 12.0543 0.499239
\(584\) 6.01855 0.249049
\(585\) 4.49456 0.185827
\(586\) −14.7623 −0.609825
\(587\) 0.201402 0.00831275 0.00415638 0.999991i \(-0.498677\pi\)
0.00415638 + 0.999991i \(0.498677\pi\)
\(588\) −2.83864 −0.117064
\(589\) −1.43005 −0.0589242
\(590\) −2.36774 −0.0974784
\(591\) −19.9685 −0.821394
\(592\) 0.0743955 0.00305764
\(593\) 29.3912 1.20695 0.603475 0.797382i \(-0.293782\pi\)
0.603475 + 0.797382i \(0.293782\pi\)
\(594\) 17.9809 0.737764
\(595\) 2.11552 0.0867280
\(596\) 21.1229 0.865229
\(597\) −7.76421 −0.317768
\(598\) 17.5140 0.716202
\(599\) 4.45914 0.182195 0.0910977 0.995842i \(-0.470962\pi\)
0.0910977 + 0.995842i \(0.470962\pi\)
\(600\) −13.8840 −0.566814
\(601\) 18.8668 0.769592 0.384796 0.923002i \(-0.374272\pi\)
0.384796 + 0.923002i \(0.374272\pi\)
\(602\) 7.47572 0.304688
\(603\) 8.10679 0.330134
\(604\) 14.5996 0.594051
\(605\) −0.503415 −0.0204667
\(606\) 6.32194 0.256811
\(607\) 5.78788 0.234923 0.117461 0.993077i \(-0.462524\pi\)
0.117461 + 0.993077i \(0.462524\pi\)
\(608\) −3.15184 −0.127824
\(609\) 10.1686 0.412052
\(610\) 2.49793 0.101138
\(611\) 27.4898 1.11212
\(612\) −32.4226 −1.31061
\(613\) 26.7243 1.07939 0.539693 0.841862i \(-0.318540\pi\)
0.539693 + 0.841862i \(0.318540\pi\)
\(614\) 17.6752 0.713313
\(615\) −8.63324 −0.348126
\(616\) 3.07808 0.124019
\(617\) 16.9714 0.683241 0.341620 0.939838i \(-0.389024\pi\)
0.341620 + 0.939838i \(0.389024\pi\)
\(618\) −28.6893 −1.15405
\(619\) −19.8861 −0.799290 −0.399645 0.916670i \(-0.630867\pi\)
−0.399645 + 0.916670i \(0.630867\pi\)
\(620\) −0.149736 −0.00601354
\(621\) 37.9959 1.52472
\(622\) 4.89400 0.196232
\(623\) 8.49202 0.340226
\(624\) −7.64347 −0.305984
\(625\) 23.3782 0.935127
\(626\) 6.78529 0.271195
\(627\) −27.5394 −1.09982
\(628\) 17.4928 0.698038
\(629\) −0.476899 −0.0190152
\(630\) 1.66920 0.0665023
\(631\) 17.1759 0.683763 0.341881 0.939743i \(-0.388936\pi\)
0.341881 + 0.939743i \(0.388936\pi\)
\(632\) 5.72181 0.227601
\(633\) 12.8124 0.509246
\(634\) −23.1328 −0.918720
\(635\) −2.89839 −0.115019
\(636\) −11.1166 −0.440803
\(637\) 2.69265 0.106687
\(638\) −11.0263 −0.436536
\(639\) −28.7958 −1.13914
\(640\) −0.330019 −0.0130451
\(641\) 1.29706 0.0512309 0.0256154 0.999672i \(-0.491845\pi\)
0.0256154 + 0.999672i \(0.491845\pi\)
\(642\) −28.7458 −1.13451
\(643\) −2.09592 −0.0826550 −0.0413275 0.999146i \(-0.513159\pi\)
−0.0413275 + 0.999146i \(0.513159\pi\)
\(644\) 6.50437 0.256308
\(645\) −7.00329 −0.275754
\(646\) 20.2043 0.794927
\(647\) 16.5203 0.649481 0.324741 0.945803i \(-0.394723\pi\)
0.324741 + 0.945803i \(0.394723\pi\)
\(648\) −1.40852 −0.0553319
\(649\) 22.0839 0.866869
\(650\) 13.1700 0.516570
\(651\) −1.28795 −0.0504786
\(652\) −11.4612 −0.448854
\(653\) 4.95189 0.193783 0.0968913 0.995295i \(-0.469110\pi\)
0.0968913 + 0.995295i \(0.469110\pi\)
\(654\) −32.1853 −1.25854
\(655\) 4.78373 0.186916
\(656\) 9.21562 0.359810
\(657\) −30.4411 −1.18762
\(658\) 10.2092 0.397995
\(659\) 22.4752 0.875511 0.437755 0.899094i \(-0.355774\pi\)
0.437755 + 0.899094i \(0.355774\pi\)
\(660\) −2.88356 −0.112242
\(661\) −14.7057 −0.571986 −0.285993 0.958232i \(-0.592323\pi\)
−0.285993 + 0.958232i \(0.592323\pi\)
\(662\) −10.9640 −0.426128
\(663\) 48.9971 1.90289
\(664\) −9.56326 −0.371126
\(665\) −1.04017 −0.0403359
\(666\) −0.376284 −0.0145807
\(667\) −23.3000 −0.902180
\(668\) −8.42319 −0.325903
\(669\) −51.9578 −2.00881
\(670\) −0.528955 −0.0204353
\(671\) −23.2982 −0.899416
\(672\) −2.83864 −0.109503
\(673\) 7.64237 0.294592 0.147296 0.989092i \(-0.452943\pi\)
0.147296 + 0.989092i \(0.452943\pi\)
\(674\) −19.4040 −0.747415
\(675\) 28.5717 1.09973
\(676\) −5.74962 −0.221139
\(677\) 44.5369 1.71169 0.855846 0.517230i \(-0.173037\pi\)
0.855846 + 0.517230i \(0.173037\pi\)
\(678\) −25.6572 −0.985360
\(679\) −1.71641 −0.0658697
\(680\) 2.11552 0.0811267
\(681\) −17.2938 −0.662699
\(682\) 1.39659 0.0534780
\(683\) −28.5032 −1.09064 −0.545322 0.838227i \(-0.683593\pi\)
−0.545322 + 0.838227i \(0.683593\pi\)
\(684\) 15.9416 0.609543
\(685\) −2.16352 −0.0826637
\(686\) 1.00000 0.0381802
\(687\) 63.0895 2.40701
\(688\) 7.47572 0.285009
\(689\) 10.5449 0.401729
\(690\) −6.09333 −0.231969
\(691\) 40.7632 1.55071 0.775353 0.631528i \(-0.217572\pi\)
0.775353 + 0.631528i \(0.217572\pi\)
\(692\) −10.6698 −0.405604
\(693\) −15.5686 −0.591401
\(694\) −23.3104 −0.884852
\(695\) 4.04218 0.153329
\(696\) 10.1686 0.385440
\(697\) −59.0750 −2.23763
\(698\) −8.83540 −0.334425
\(699\) 41.0386 1.55222
\(700\) 4.89109 0.184866
\(701\) 10.9502 0.413585 0.206793 0.978385i \(-0.433697\pi\)
0.206793 + 0.978385i \(0.433697\pi\)
\(702\) 15.7294 0.593667
\(703\) 0.234483 0.00884368
\(704\) 3.07808 0.116010
\(705\) −9.56401 −0.360201
\(706\) −24.5084 −0.922386
\(707\) −2.22710 −0.0837588
\(708\) −20.3660 −0.765402
\(709\) 10.5735 0.397097 0.198548 0.980091i \(-0.436377\pi\)
0.198548 + 0.980091i \(0.436377\pi\)
\(710\) 1.87888 0.0705130
\(711\) −28.9402 −1.08534
\(712\) 8.49202 0.318252
\(713\) 2.95116 0.110522
\(714\) 18.1966 0.680990
\(715\) 2.73526 0.102293
\(716\) 6.89780 0.257783
\(717\) −73.6795 −2.75161
\(718\) −19.7712 −0.737854
\(719\) 23.6357 0.881463 0.440732 0.897639i \(-0.354719\pi\)
0.440732 + 0.897639i \(0.354719\pi\)
\(720\) 1.66920 0.0622072
\(721\) 10.1067 0.376394
\(722\) 9.06591 0.337398
\(723\) 9.12453 0.339345
\(724\) 12.5011 0.464600
\(725\) −17.5209 −0.650710
\(726\) −4.33010 −0.160705
\(727\) 19.5599 0.725437 0.362718 0.931899i \(-0.381849\pi\)
0.362718 + 0.931899i \(0.381849\pi\)
\(728\) 2.69265 0.0997964
\(729\) −42.6224 −1.57861
\(730\) 1.98623 0.0735138
\(731\) −47.9217 −1.77245
\(732\) 21.4858 0.794139
\(733\) −21.4507 −0.792300 −0.396150 0.918186i \(-0.629654\pi\)
−0.396150 + 0.918186i \(0.629654\pi\)
\(734\) −4.27937 −0.157955
\(735\) −0.936805 −0.0345546
\(736\) 6.50437 0.239754
\(737\) 4.93356 0.181730
\(738\) −46.6115 −1.71579
\(739\) 45.7656 1.68351 0.841757 0.539856i \(-0.181521\pi\)
0.841757 + 0.539856i \(0.181521\pi\)
\(740\) 0.0245519 0.000902546 0
\(741\) −24.0910 −0.885005
\(742\) 3.91618 0.143768
\(743\) 26.4781 0.971389 0.485694 0.874129i \(-0.338567\pi\)
0.485694 + 0.874129i \(0.338567\pi\)
\(744\) −1.28795 −0.0472184
\(745\) 6.97096 0.255396
\(746\) −17.8953 −0.655195
\(747\) 48.3698 1.76976
\(748\) −19.7315 −0.721454
\(749\) 10.1266 0.370018
\(750\) −9.26602 −0.338347
\(751\) −3.24857 −0.118542 −0.0592710 0.998242i \(-0.518878\pi\)
−0.0592710 + 0.998242i \(0.518878\pi\)
\(752\) 10.2092 0.372291
\(753\) −7.25202 −0.264278
\(754\) −9.64564 −0.351274
\(755\) 4.81815 0.175350
\(756\) 5.84159 0.212456
\(757\) −9.47097 −0.344228 −0.172114 0.985077i \(-0.555060\pi\)
−0.172114 + 0.985077i \(0.555060\pi\)
\(758\) −4.01937 −0.145990
\(759\) 56.8324 2.06289
\(760\) −1.04017 −0.0377308
\(761\) −7.54176 −0.273388 −0.136694 0.990613i \(-0.543648\pi\)
−0.136694 + 0.990613i \(0.543648\pi\)
\(762\) −24.9304 −0.903132
\(763\) 11.3383 0.410473
\(764\) −0.0973263 −0.00352114
\(765\) −10.7001 −0.386862
\(766\) 10.0772 0.364104
\(767\) 19.3186 0.697555
\(768\) −2.83864 −0.102431
\(769\) 20.1783 0.727647 0.363824 0.931468i \(-0.381471\pi\)
0.363824 + 0.931468i \(0.381471\pi\)
\(770\) 1.01582 0.0366078
\(771\) 0.168342 0.00606267
\(772\) −11.8903 −0.427942
\(773\) −36.9712 −1.32976 −0.664881 0.746950i \(-0.731518\pi\)
−0.664881 + 0.746950i \(0.731518\pi\)
\(774\) −37.8113 −1.35910
\(775\) 2.21918 0.0797154
\(776\) −1.71641 −0.0616154
\(777\) 0.211182 0.00757612
\(778\) 20.8961 0.749162
\(779\) 29.0462 1.04069
\(780\) −2.52249 −0.0903196
\(781\) −17.5243 −0.627068
\(782\) −41.6951 −1.49101
\(783\) −20.9258 −0.747826
\(784\) 1.00000 0.0357143
\(785\) 5.77294 0.206045
\(786\) 41.1470 1.46766
\(787\) 21.8352 0.778339 0.389170 0.921166i \(-0.372762\pi\)
0.389170 + 0.921166i \(0.372762\pi\)
\(788\) 7.03452 0.250595
\(789\) −0.581372 −0.0206974
\(790\) 1.88831 0.0671829
\(791\) 9.03856 0.321374
\(792\) −15.5686 −0.553205
\(793\) −20.3808 −0.723745
\(794\) −27.2515 −0.967119
\(795\) −3.66870 −0.130115
\(796\) 2.73519 0.0969461
\(797\) 27.6137 0.978128 0.489064 0.872248i \(-0.337338\pi\)
0.489064 + 0.872248i \(0.337338\pi\)
\(798\) −8.94694 −0.316718
\(799\) −65.4441 −2.31525
\(800\) 4.89109 0.172926
\(801\) −42.9516 −1.51762
\(802\) −24.4179 −0.862226
\(803\) −18.5256 −0.653753
\(804\) −4.54978 −0.160458
\(805\) 2.14657 0.0756565
\(806\) 1.22171 0.0430329
\(807\) 43.7119 1.53873
\(808\) −2.22710 −0.0783492
\(809\) −38.1032 −1.33964 −0.669819 0.742525i \(-0.733628\pi\)
−0.669819 + 0.742525i \(0.733628\pi\)
\(810\) −0.464838 −0.0163327
\(811\) −22.5350 −0.791310 −0.395655 0.918399i \(-0.629482\pi\)
−0.395655 + 0.918399i \(0.629482\pi\)
\(812\) −3.58221 −0.125711
\(813\) 29.2797 1.02688
\(814\) −0.228995 −0.00802628
\(815\) −3.78240 −0.132492
\(816\) 18.1966 0.637008
\(817\) 23.5623 0.824339
\(818\) −10.7500 −0.375865
\(819\) −13.6191 −0.475891
\(820\) 3.04133 0.106208
\(821\) −49.7278 −1.73551 −0.867756 0.496991i \(-0.834438\pi\)
−0.867756 + 0.496991i \(0.834438\pi\)
\(822\) −18.6094 −0.649077
\(823\) −5.11618 −0.178339 −0.0891693 0.996016i \(-0.528421\pi\)
−0.0891693 + 0.996016i \(0.528421\pi\)
\(824\) 10.1067 0.352084
\(825\) 42.7362 1.48788
\(826\) 7.17457 0.249635
\(827\) 44.5796 1.55018 0.775092 0.631848i \(-0.217703\pi\)
0.775092 + 0.631848i \(0.217703\pi\)
\(828\) −32.8984 −1.14330
\(829\) 28.9940 1.00700 0.503502 0.863994i \(-0.332045\pi\)
0.503502 + 0.863994i \(0.332045\pi\)
\(830\) −3.15605 −0.109548
\(831\) 61.3863 2.12947
\(832\) 2.69265 0.0933509
\(833\) −6.41032 −0.222104
\(834\) 34.7686 1.20394
\(835\) −2.77981 −0.0961993
\(836\) 9.70162 0.335537
\(837\) 2.65044 0.0916127
\(838\) −35.8280 −1.23766
\(839\) 24.8167 0.856769 0.428384 0.903597i \(-0.359083\pi\)
0.428384 + 0.903597i \(0.359083\pi\)
\(840\) −0.936805 −0.0323228
\(841\) −16.1678 −0.557510
\(842\) 7.31605 0.252128
\(843\) 33.6164 1.15781
\(844\) −4.51356 −0.155363
\(845\) −1.89748 −0.0652754
\(846\) −51.6368 −1.77531
\(847\) 1.52541 0.0524139
\(848\) 3.91618 0.134482
\(849\) −32.5242 −1.11623
\(850\) −31.3534 −1.07541
\(851\) −0.483896 −0.0165877
\(852\) 16.1611 0.553669
\(853\) −37.0082 −1.26714 −0.633568 0.773687i \(-0.718410\pi\)
−0.633568 + 0.773687i \(0.718410\pi\)
\(854\) −7.56905 −0.259008
\(855\) 5.26104 0.179924
\(856\) 10.1266 0.346120
\(857\) 27.0014 0.922349 0.461174 0.887309i \(-0.347428\pi\)
0.461174 + 0.887309i \(0.347428\pi\)
\(858\) 23.5272 0.803207
\(859\) −6.55694 −0.223720 −0.111860 0.993724i \(-0.535681\pi\)
−0.111860 + 0.993724i \(0.535681\pi\)
\(860\) 2.46713 0.0841283
\(861\) 26.1598 0.891525
\(862\) −1.00000 −0.0340601
\(863\) 32.8848 1.11941 0.559706 0.828691i \(-0.310914\pi\)
0.559706 + 0.828691i \(0.310914\pi\)
\(864\) 5.84159 0.198735
\(865\) −3.52123 −0.119725
\(866\) −31.8948 −1.08383
\(867\) −68.3890 −2.32261
\(868\) 0.453720 0.0154002
\(869\) −17.6122 −0.597453
\(870\) 3.35583 0.113773
\(871\) 4.31579 0.146235
\(872\) 11.3383 0.383962
\(873\) 8.68139 0.293820
\(874\) 20.5007 0.693448
\(875\) 3.26424 0.110352
\(876\) 17.0845 0.577231
\(877\) 30.6105 1.03364 0.516822 0.856093i \(-0.327115\pi\)
0.516822 + 0.856093i \(0.327115\pi\)
\(878\) −14.7796 −0.498787
\(879\) −41.9049 −1.41342
\(880\) 1.01582 0.0342434
\(881\) 4.74842 0.159978 0.0799892 0.996796i \(-0.474511\pi\)
0.0799892 + 0.996796i \(0.474511\pi\)
\(882\) −5.05788 −0.170308
\(883\) −25.0104 −0.841666 −0.420833 0.907138i \(-0.638262\pi\)
−0.420833 + 0.907138i \(0.638262\pi\)
\(884\) −17.2608 −0.580542
\(885\) −6.72117 −0.225930
\(886\) −18.3398 −0.616138
\(887\) −5.84207 −0.196158 −0.0980788 0.995179i \(-0.531270\pi\)
−0.0980788 + 0.995179i \(0.531270\pi\)
\(888\) 0.211182 0.00708681
\(889\) 8.78251 0.294556
\(890\) 2.80253 0.0939409
\(891\) 4.33554 0.145246
\(892\) 18.3038 0.612855
\(893\) 32.1777 1.07679
\(894\) 59.9604 2.00538
\(895\) 2.27640 0.0760918
\(896\) 1.00000 0.0334077
\(897\) 49.7160 1.65997
\(898\) 26.7154 0.891504
\(899\) −1.62532 −0.0542074
\(900\) −24.7385 −0.824618
\(901\) −25.1040 −0.836334
\(902\) −28.3664 −0.944499
\(903\) 21.2209 0.706187
\(904\) 9.03856 0.300618
\(905\) 4.12560 0.137139
\(906\) 41.4431 1.37685
\(907\) −6.29419 −0.208995 −0.104498 0.994525i \(-0.533323\pi\)
−0.104498 + 0.994525i \(0.533323\pi\)
\(908\) 6.09228 0.202179
\(909\) 11.2644 0.373617
\(910\) 0.888626 0.0294577
\(911\) 60.0376 1.98913 0.994567 0.104094i \(-0.0331944\pi\)
0.994567 + 0.104094i \(0.0331944\pi\)
\(912\) −8.94694 −0.296263
\(913\) 29.4365 0.974205
\(914\) 11.2067 0.370684
\(915\) 7.09072 0.234412
\(916\) −22.2252 −0.734343
\(917\) −14.4953 −0.478677
\(918\) −37.4464 −1.23592
\(919\) 47.7603 1.57547 0.787733 0.616017i \(-0.211255\pi\)
0.787733 + 0.616017i \(0.211255\pi\)
\(920\) 2.14657 0.0707702
\(921\) 50.1736 1.65327
\(922\) −14.7644 −0.486241
\(923\) −15.3299 −0.504591
\(924\) 8.73757 0.287445
\(925\) −0.363875 −0.0119641
\(926\) 3.89885 0.128124
\(927\) −51.1185 −1.67895
\(928\) −3.58221 −0.117592
\(929\) 32.5774 1.06883 0.534416 0.845222i \(-0.320532\pi\)
0.534416 + 0.845222i \(0.320532\pi\)
\(930\) −0.425047 −0.0139378
\(931\) 3.15184 0.103297
\(932\) −14.4571 −0.473559
\(933\) 13.8923 0.454814
\(934\) 0.801978 0.0262415
\(935\) −6.51176 −0.212957
\(936\) −13.6191 −0.445155
\(937\) −18.1623 −0.593338 −0.296669 0.954980i \(-0.595876\pi\)
−0.296669 + 0.954980i \(0.595876\pi\)
\(938\) 1.60280 0.0523334
\(939\) 19.2610 0.628559
\(940\) 3.36922 0.109892
\(941\) 1.41149 0.0460133 0.0230067 0.999735i \(-0.492676\pi\)
0.0230067 + 0.999735i \(0.492676\pi\)
\(942\) 49.6557 1.61787
\(943\) −59.9418 −1.95197
\(944\) 7.17457 0.233512
\(945\) 1.92783 0.0627124
\(946\) −23.0109 −0.748148
\(947\) 4.00449 0.130128 0.0650642 0.997881i \(-0.479275\pi\)
0.0650642 + 0.997881i \(0.479275\pi\)
\(948\) 16.2422 0.527521
\(949\) −16.2059 −0.526064
\(950\) 15.4159 0.500159
\(951\) −65.6657 −2.12936
\(952\) −6.41032 −0.207760
\(953\) 17.7370 0.574558 0.287279 0.957847i \(-0.407249\pi\)
0.287279 + 0.957847i \(0.407249\pi\)
\(954\) −19.8076 −0.641294
\(955\) −0.0321195 −0.00103936
\(956\) 25.9559 0.839474
\(957\) −31.2998 −1.01178
\(958\) −9.83182 −0.317652
\(959\) 6.55574 0.211696
\(960\) −0.936805 −0.0302352
\(961\) −30.7941 −0.993359
\(962\) −0.200321 −0.00645862
\(963\) −51.2191 −1.65051
\(964\) −3.21440 −0.103529
\(965\) −3.92403 −0.126319
\(966\) 18.4636 0.594056
\(967\) 29.2920 0.941969 0.470984 0.882142i \(-0.343899\pi\)
0.470984 + 0.882142i \(0.343899\pi\)
\(968\) 1.52541 0.0490287
\(969\) 57.3527 1.84243
\(970\) −0.566447 −0.0181875
\(971\) 9.47562 0.304087 0.152044 0.988374i \(-0.451415\pi\)
0.152044 + 0.988374i \(0.451415\pi\)
\(972\) 13.5265 0.433862
\(973\) −12.2483 −0.392663
\(974\) 1.12362 0.0360033
\(975\) 37.3849 1.19728
\(976\) −7.56905 −0.242279
\(977\) −22.5524 −0.721517 −0.360758 0.932659i \(-0.617482\pi\)
−0.360758 + 0.932659i \(0.617482\pi\)
\(978\) −32.5341 −1.04033
\(979\) −26.1391 −0.835410
\(980\) 0.330019 0.0105421
\(981\) −57.3476 −1.83097
\(982\) −3.87935 −0.123795
\(983\) −17.3279 −0.552673 −0.276337 0.961061i \(-0.589120\pi\)
−0.276337 + 0.961061i \(0.589120\pi\)
\(984\) 26.1598 0.833945
\(985\) 2.32152 0.0739699
\(986\) 22.9631 0.731293
\(987\) 28.9802 0.922450
\(988\) 8.48681 0.270001
\(989\) −48.6249 −1.54618
\(990\) −5.13792 −0.163294
\(991\) −34.0054 −1.08022 −0.540109 0.841595i \(-0.681617\pi\)
−0.540109 + 0.841595i \(0.681617\pi\)
\(992\) 0.453720 0.0144056
\(993\) −31.1229 −0.987654
\(994\) −5.69325 −0.180579
\(995\) 0.902663 0.0286163
\(996\) −27.1467 −0.860175
\(997\) −23.0964 −0.731469 −0.365735 0.930719i \(-0.619182\pi\)
−0.365735 + 0.930719i \(0.619182\pi\)
\(998\) 30.7306 0.972761
\(999\) −0.434588 −0.0137497
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 \(a_p\))