Properties

Label 8018.2.a.d.1.10
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 30
CM No

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Newspace parameters

Level: \( N \) = \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(1\)
Dimension: \(30\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-1.46114 q^{3}\) \(+1.00000 q^{4}\) \(+1.82408 q^{5}\) \(-1.46114 q^{6}\) \(-2.77663 q^{7}\) \(+1.00000 q^{8}\) \(-0.865063 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-1.46114 q^{3}\) \(+1.00000 q^{4}\) \(+1.82408 q^{5}\) \(-1.46114 q^{6}\) \(-2.77663 q^{7}\) \(+1.00000 q^{8}\) \(-0.865063 q^{9}\) \(+1.82408 q^{10}\) \(-1.21614 q^{11}\) \(-1.46114 q^{12}\) \(+1.42796 q^{13}\) \(-2.77663 q^{14}\) \(-2.66525 q^{15}\) \(+1.00000 q^{16}\) \(+4.88240 q^{17}\) \(-0.865063 q^{18}\) \(+1.00000 q^{19}\) \(+1.82408 q^{20}\) \(+4.05705 q^{21}\) \(-1.21614 q^{22}\) \(+7.05784 q^{23}\) \(-1.46114 q^{24}\) \(-1.67272 q^{25}\) \(+1.42796 q^{26}\) \(+5.64741 q^{27}\) \(-2.77663 q^{28}\) \(-10.2436 q^{29}\) \(-2.66525 q^{30}\) \(-7.99282 q^{31}\) \(+1.00000 q^{32}\) \(+1.77695 q^{33}\) \(+4.88240 q^{34}\) \(-5.06481 q^{35}\) \(-0.865063 q^{36}\) \(-7.54026 q^{37}\) \(+1.00000 q^{38}\) \(-2.08645 q^{39}\) \(+1.82408 q^{40}\) \(-0.862262 q^{41}\) \(+4.05705 q^{42}\) \(-5.82798 q^{43}\) \(-1.21614 q^{44}\) \(-1.57795 q^{45}\) \(+7.05784 q^{46}\) \(+8.09691 q^{47}\) \(-1.46114 q^{48}\) \(+0.709678 q^{49}\) \(-1.67272 q^{50}\) \(-7.13388 q^{51}\) \(+1.42796 q^{52}\) \(+2.56029 q^{53}\) \(+5.64741 q^{54}\) \(-2.21834 q^{55}\) \(-2.77663 q^{56}\) \(-1.46114 q^{57}\) \(-10.2436 q^{58}\) \(-3.58628 q^{59}\) \(-2.66525 q^{60}\) \(-3.47477 q^{61}\) \(-7.99282 q^{62}\) \(+2.40196 q^{63}\) \(+1.00000 q^{64}\) \(+2.60472 q^{65}\) \(+1.77695 q^{66}\) \(+14.8212 q^{67}\) \(+4.88240 q^{68}\) \(-10.3125 q^{69}\) \(-5.06481 q^{70}\) \(-0.424097 q^{71}\) \(-0.865063 q^{72}\) \(+8.16655 q^{73}\) \(-7.54026 q^{74}\) \(+2.44408 q^{75}\) \(+1.00000 q^{76}\) \(+3.37677 q^{77}\) \(-2.08645 q^{78}\) \(+10.3349 q^{79}\) \(+1.82408 q^{80}\) \(-5.65648 q^{81}\) \(-0.862262 q^{82}\) \(-10.4403 q^{83}\) \(+4.05705 q^{84}\) \(+8.90591 q^{85}\) \(-5.82798 q^{86}\) \(+14.9674 q^{87}\) \(-1.21614 q^{88}\) \(+6.13887 q^{89}\) \(-1.57795 q^{90}\) \(-3.96492 q^{91}\) \(+7.05784 q^{92}\) \(+11.6786 q^{93}\) \(+8.09691 q^{94}\) \(+1.82408 q^{95}\) \(-1.46114 q^{96}\) \(-9.03631 q^{97}\) \(+0.709678 q^{98}\) \(+1.05204 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(30q \) \(\mathstrut +\mathstrut 30q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 10q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(30q \) \(\mathstrut +\mathstrut 30q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 10q^{9} \) \(\mathstrut -\mathstrut 12q^{10} \) \(\mathstrut -\mathstrut 17q^{11} \) \(\mathstrut -\mathstrut 10q^{12} \) \(\mathstrut -\mathstrut 19q^{13} \) \(\mathstrut -\mathstrut 15q^{14} \) \(\mathstrut -\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 30q^{16} \) \(\mathstrut -\mathstrut 18q^{17} \) \(\mathstrut +\mathstrut 10q^{18} \) \(\mathstrut +\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 12q^{20} \) \(\mathstrut -\mathstrut 14q^{21} \) \(\mathstrut -\mathstrut 17q^{22} \) \(\mathstrut -\mathstrut 15q^{23} \) \(\mathstrut -\mathstrut 10q^{24} \) \(\mathstrut -\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut 19q^{26} \) \(\mathstrut -\mathstrut 37q^{27} \) \(\mathstrut -\mathstrut 15q^{28} \) \(\mathstrut -\mathstrut 37q^{29} \) \(\mathstrut -\mathstrut 8q^{30} \) \(\mathstrut -\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 30q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut -\mathstrut 18q^{34} \) \(\mathstrut -\mathstrut 4q^{35} \) \(\mathstrut +\mathstrut 10q^{36} \) \(\mathstrut -\mathstrut 46q^{37} \) \(\mathstrut +\mathstrut 30q^{38} \) \(\mathstrut -\mathstrut 12q^{40} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 14q^{42} \) \(\mathstrut -\mathstrut 61q^{43} \) \(\mathstrut -\mathstrut 17q^{44} \) \(\mathstrut -\mathstrut 14q^{45} \) \(\mathstrut -\mathstrut 15q^{46} \) \(\mathstrut -\mathstrut 4q^{47} \) \(\mathstrut -\mathstrut 10q^{48} \) \(\mathstrut -\mathstrut q^{49} \) \(\mathstrut -\mathstrut 4q^{50} \) \(\mathstrut -\mathstrut 8q^{51} \) \(\mathstrut -\mathstrut 19q^{52} \) \(\mathstrut -\mathstrut 19q^{53} \) \(\mathstrut -\mathstrut 37q^{54} \) \(\mathstrut -\mathstrut 17q^{55} \) \(\mathstrut -\mathstrut 15q^{56} \) \(\mathstrut -\mathstrut 10q^{57} \) \(\mathstrut -\mathstrut 37q^{58} \) \(\mathstrut -\mathstrut 6q^{59} \) \(\mathstrut -\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut 32q^{61} \) \(\mathstrut -\mathstrut 11q^{62} \) \(\mathstrut -\mathstrut 24q^{63} \) \(\mathstrut +\mathstrut 30q^{64} \) \(\mathstrut -\mathstrut 24q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut -\mathstrut 44q^{67} \) \(\mathstrut -\mathstrut 18q^{68} \) \(\mathstrut -\mathstrut 2q^{69} \) \(\mathstrut -\mathstrut 4q^{70} \) \(\mathstrut +\mathstrut 10q^{71} \) \(\mathstrut +\mathstrut 10q^{72} \) \(\mathstrut -\mathstrut 58q^{73} \) \(\mathstrut -\mathstrut 46q^{74} \) \(\mathstrut -\mathstrut 42q^{75} \) \(\mathstrut +\mathstrut 30q^{76} \) \(\mathstrut -\mathstrut 32q^{77} \) \(\mathstrut -\mathstrut 42q^{79} \) \(\mathstrut -\mathstrut 12q^{80} \) \(\mathstrut -\mathstrut 38q^{81} \) \(\mathstrut -\mathstrut 28q^{82} \) \(\mathstrut -\mathstrut 25q^{83} \) \(\mathstrut -\mathstrut 14q^{84} \) \(\mathstrut -\mathstrut 48q^{85} \) \(\mathstrut -\mathstrut 61q^{86} \) \(\mathstrut -\mathstrut 15q^{87} \) \(\mathstrut -\mathstrut 17q^{88} \) \(\mathstrut -\mathstrut 39q^{89} \) \(\mathstrut -\mathstrut 14q^{90} \) \(\mathstrut -\mathstrut 21q^{91} \) \(\mathstrut -\mathstrut 15q^{92} \) \(\mathstrut -\mathstrut 45q^{93} \) \(\mathstrut -\mathstrut 4q^{94} \) \(\mathstrut -\mathstrut 12q^{95} \) \(\mathstrut -\mathstrut 10q^{96} \) \(\mathstrut -\mathstrut 33q^{97} \) \(\mathstrut -\mathstrut q^{98} \) \(\mathstrut -\mathstrut 38q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.46114 −0.843591 −0.421795 0.906691i \(-0.638600\pi\)
−0.421795 + 0.906691i \(0.638600\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.82408 0.815755 0.407878 0.913037i \(-0.366269\pi\)
0.407878 + 0.913037i \(0.366269\pi\)
\(6\) −1.46114 −0.596509
\(7\) −2.77663 −1.04947 −0.524734 0.851266i \(-0.675835\pi\)
−0.524734 + 0.851266i \(0.675835\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.865063 −0.288354
\(10\) 1.82408 0.576826
\(11\) −1.21614 −0.366680 −0.183340 0.983050i \(-0.558691\pi\)
−0.183340 + 0.983050i \(0.558691\pi\)
\(12\) −1.46114 −0.421795
\(13\) 1.42796 0.396045 0.198022 0.980197i \(-0.436548\pi\)
0.198022 + 0.980197i \(0.436548\pi\)
\(14\) −2.77663 −0.742086
\(15\) −2.66525 −0.688164
\(16\) 1.00000 0.250000
\(17\) 4.88240 1.18416 0.592078 0.805881i \(-0.298308\pi\)
0.592078 + 0.805881i \(0.298308\pi\)
\(18\) −0.865063 −0.203897
\(19\) 1.00000 0.229416
\(20\) 1.82408 0.407878
\(21\) 4.05705 0.885321
\(22\) −1.21614 −0.259282
\(23\) 7.05784 1.47166 0.735830 0.677166i \(-0.236792\pi\)
0.735830 + 0.677166i \(0.236792\pi\)
\(24\) −1.46114 −0.298254
\(25\) −1.67272 −0.334543
\(26\) 1.42796 0.280046
\(27\) 5.64741 1.08684
\(28\) −2.77663 −0.524734
\(29\) −10.2436 −1.90219 −0.951097 0.308893i \(-0.900042\pi\)
−0.951097 + 0.308893i \(0.900042\pi\)
\(30\) −2.66525 −0.486605
\(31\) −7.99282 −1.43555 −0.717776 0.696274i \(-0.754840\pi\)
−0.717776 + 0.696274i \(0.754840\pi\)
\(32\) 1.00000 0.176777
\(33\) 1.77695 0.309328
\(34\) 4.88240 0.837325
\(35\) −5.06481 −0.856109
\(36\) −0.865063 −0.144177
\(37\) −7.54026 −1.23961 −0.619805 0.784756i \(-0.712788\pi\)
−0.619805 + 0.784756i \(0.712788\pi\)
\(38\) 1.00000 0.162221
\(39\) −2.08645 −0.334100
\(40\) 1.82408 0.288413
\(41\) −0.862262 −0.134663 −0.0673313 0.997731i \(-0.521448\pi\)
−0.0673313 + 0.997731i \(0.521448\pi\)
\(42\) 4.05705 0.626017
\(43\) −5.82798 −0.888758 −0.444379 0.895839i \(-0.646576\pi\)
−0.444379 + 0.895839i \(0.646576\pi\)
\(44\) −1.21614 −0.183340
\(45\) −1.57795 −0.235227
\(46\) 7.05784 1.04062
\(47\) 8.09691 1.18106 0.590528 0.807017i \(-0.298920\pi\)
0.590528 + 0.807017i \(0.298920\pi\)
\(48\) −1.46114 −0.210898
\(49\) 0.709678 0.101383
\(50\) −1.67272 −0.236558
\(51\) −7.13388 −0.998943
\(52\) 1.42796 0.198022
\(53\) 2.56029 0.351683 0.175841 0.984419i \(-0.443735\pi\)
0.175841 + 0.984419i \(0.443735\pi\)
\(54\) 5.64741 0.768515
\(55\) −2.21834 −0.299121
\(56\) −2.77663 −0.371043
\(57\) −1.46114 −0.193533
\(58\) −10.2436 −1.34505
\(59\) −3.58628 −0.466894 −0.233447 0.972370i \(-0.575000\pi\)
−0.233447 + 0.972370i \(0.575000\pi\)
\(60\) −2.66525 −0.344082
\(61\) −3.47477 −0.444899 −0.222450 0.974944i \(-0.571405\pi\)
−0.222450 + 0.974944i \(0.571405\pi\)
\(62\) −7.99282 −1.01509
\(63\) 2.40196 0.302619
\(64\) 1.00000 0.125000
\(65\) 2.60472 0.323076
\(66\) 1.77695 0.218728
\(67\) 14.8212 1.81069 0.905347 0.424673i \(-0.139611\pi\)
0.905347 + 0.424673i \(0.139611\pi\)
\(68\) 4.88240 0.592078
\(69\) −10.3125 −1.24148
\(70\) −5.06481 −0.605360
\(71\) −0.424097 −0.0503310 −0.0251655 0.999683i \(-0.508011\pi\)
−0.0251655 + 0.999683i \(0.508011\pi\)
\(72\) −0.865063 −0.101949
\(73\) 8.16655 0.955822 0.477911 0.878408i \(-0.341394\pi\)
0.477911 + 0.878408i \(0.341394\pi\)
\(74\) −7.54026 −0.876537
\(75\) 2.44408 0.282218
\(76\) 1.00000 0.114708
\(77\) 3.37677 0.384818
\(78\) −2.08645 −0.236244
\(79\) 10.3349 1.16277 0.581386 0.813628i \(-0.302511\pi\)
0.581386 + 0.813628i \(0.302511\pi\)
\(80\) 1.82408 0.203939
\(81\) −5.65648 −0.628497
\(82\) −0.862262 −0.0952209
\(83\) −10.4403 −1.14597 −0.572983 0.819567i \(-0.694214\pi\)
−0.572983 + 0.819567i \(0.694214\pi\)
\(84\) 4.05705 0.442661
\(85\) 8.90591 0.965981
\(86\) −5.82798 −0.628447
\(87\) 14.9674 1.60467
\(88\) −1.21614 −0.129641
\(89\) 6.13887 0.650719 0.325359 0.945590i \(-0.394515\pi\)
0.325359 + 0.945590i \(0.394515\pi\)
\(90\) −1.57795 −0.166330
\(91\) −3.96492 −0.415636
\(92\) 7.05784 0.735830
\(93\) 11.6786 1.21102
\(94\) 8.09691 0.835133
\(95\) 1.82408 0.187147
\(96\) −1.46114 −0.149127
\(97\) −9.03631 −0.917499 −0.458749 0.888566i \(-0.651702\pi\)
−0.458749 + 0.888566i \(0.651702\pi\)
\(98\) 0.709678 0.0716883
\(99\) 1.05204 0.105734
\(100\) −1.67272 −0.167272
\(101\) −15.2409 −1.51653 −0.758265 0.651947i \(-0.773952\pi\)
−0.758265 + 0.651947i \(0.773952\pi\)
\(102\) −7.13388 −0.706359
\(103\) −1.13743 −0.112075 −0.0560373 0.998429i \(-0.517847\pi\)
−0.0560373 + 0.998429i \(0.517847\pi\)
\(104\) 1.42796 0.140023
\(105\) 7.40041 0.722206
\(106\) 2.56029 0.248677
\(107\) −3.71361 −0.359008 −0.179504 0.983757i \(-0.557449\pi\)
−0.179504 + 0.983757i \(0.557449\pi\)
\(108\) 5.64741 0.543422
\(109\) −7.68678 −0.736260 −0.368130 0.929774i \(-0.620002\pi\)
−0.368130 + 0.929774i \(0.620002\pi\)
\(110\) −2.21834 −0.211510
\(111\) 11.0174 1.04572
\(112\) −2.77663 −0.262367
\(113\) 3.56486 0.335354 0.167677 0.985842i \(-0.446374\pi\)
0.167677 + 0.985842i \(0.446374\pi\)
\(114\) −1.46114 −0.136849
\(115\) 12.8741 1.20052
\(116\) −10.2436 −0.951097
\(117\) −1.23528 −0.114201
\(118\) −3.58628 −0.330144
\(119\) −13.5566 −1.24273
\(120\) −2.66525 −0.243303
\(121\) −9.52101 −0.865546
\(122\) −3.47477 −0.314591
\(123\) 1.25989 0.113600
\(124\) −7.99282 −0.717776
\(125\) −12.1716 −1.08866
\(126\) 2.40196 0.213984
\(127\) 12.0562 1.06981 0.534906 0.844911i \(-0.320347\pi\)
0.534906 + 0.844911i \(0.320347\pi\)
\(128\) 1.00000 0.0883883
\(129\) 8.51550 0.749748
\(130\) 2.60472 0.228449
\(131\) −5.02274 −0.438839 −0.219419 0.975631i \(-0.570416\pi\)
−0.219419 + 0.975631i \(0.570416\pi\)
\(132\) 1.77695 0.154664
\(133\) −2.77663 −0.240764
\(134\) 14.8212 1.28035
\(135\) 10.3013 0.886599
\(136\) 4.88240 0.418662
\(137\) 6.60500 0.564303 0.282152 0.959370i \(-0.408952\pi\)
0.282152 + 0.959370i \(0.408952\pi\)
\(138\) −10.3125 −0.877859
\(139\) −8.51196 −0.721975 −0.360987 0.932571i \(-0.617560\pi\)
−0.360987 + 0.932571i \(0.617560\pi\)
\(140\) −5.06481 −0.428054
\(141\) −11.8307 −0.996328
\(142\) −0.424097 −0.0355894
\(143\) −1.73660 −0.145222
\(144\) −0.865063 −0.0720886
\(145\) −18.6852 −1.55172
\(146\) 8.16655 0.675869
\(147\) −1.03694 −0.0855254
\(148\) −7.54026 −0.619805
\(149\) −19.5391 −1.60071 −0.800353 0.599529i \(-0.795355\pi\)
−0.800353 + 0.599529i \(0.795355\pi\)
\(150\) 2.44408 0.199558
\(151\) 10.5323 0.857109 0.428555 0.903516i \(-0.359023\pi\)
0.428555 + 0.903516i \(0.359023\pi\)
\(152\) 1.00000 0.0811107
\(153\) −4.22358 −0.341457
\(154\) 3.37677 0.272108
\(155\) −14.5796 −1.17106
\(156\) −2.08645 −0.167050
\(157\) −10.4380 −0.833045 −0.416522 0.909125i \(-0.636751\pi\)
−0.416522 + 0.909125i \(0.636751\pi\)
\(158\) 10.3349 0.822204
\(159\) −3.74095 −0.296676
\(160\) 1.82408 0.144207
\(161\) −19.5970 −1.54446
\(162\) −5.65648 −0.444415
\(163\) 18.4883 1.44811 0.724057 0.689740i \(-0.242275\pi\)
0.724057 + 0.689740i \(0.242275\pi\)
\(164\) −0.862262 −0.0673313
\(165\) 3.24131 0.252336
\(166\) −10.4403 −0.810321
\(167\) −6.60100 −0.510801 −0.255400 0.966835i \(-0.582207\pi\)
−0.255400 + 0.966835i \(0.582207\pi\)
\(168\) 4.05705 0.313008
\(169\) −10.9609 −0.843148
\(170\) 8.90591 0.683052
\(171\) −0.865063 −0.0661530
\(172\) −5.82798 −0.444379
\(173\) 12.6258 0.959918 0.479959 0.877291i \(-0.340651\pi\)
0.479959 + 0.877291i \(0.340651\pi\)
\(174\) 14.9674 1.13468
\(175\) 4.64451 0.351092
\(176\) −1.21614 −0.0916699
\(177\) 5.24006 0.393867
\(178\) 6.13887 0.460128
\(179\) −15.6437 −1.16927 −0.584634 0.811297i \(-0.698762\pi\)
−0.584634 + 0.811297i \(0.698762\pi\)
\(180\) −1.57795 −0.117613
\(181\) 12.5304 0.931375 0.465687 0.884949i \(-0.345807\pi\)
0.465687 + 0.884949i \(0.345807\pi\)
\(182\) −3.96492 −0.293899
\(183\) 5.07714 0.375313
\(184\) 7.05784 0.520311
\(185\) −13.7541 −1.01122
\(186\) 11.6786 0.856320
\(187\) −5.93768 −0.434206
\(188\) 8.09691 0.590528
\(189\) −15.6808 −1.14061
\(190\) 1.82408 0.132333
\(191\) −26.2653 −1.90049 −0.950245 0.311505i \(-0.899167\pi\)
−0.950245 + 0.311505i \(0.899167\pi\)
\(192\) −1.46114 −0.105449
\(193\) −1.16834 −0.0840989 −0.0420494 0.999116i \(-0.513389\pi\)
−0.0420494 + 0.999116i \(0.513389\pi\)
\(194\) −9.03631 −0.648769
\(195\) −3.80587 −0.272544
\(196\) 0.709678 0.0506913
\(197\) −2.55178 −0.181807 −0.0909035 0.995860i \(-0.528975\pi\)
−0.0909035 + 0.995860i \(0.528975\pi\)
\(198\) 1.05204 0.0747650
\(199\) −8.74578 −0.619972 −0.309986 0.950741i \(-0.600324\pi\)
−0.309986 + 0.950741i \(0.600324\pi\)
\(200\) −1.67272 −0.118279
\(201\) −21.6558 −1.52748
\(202\) −15.2409 −1.07235
\(203\) 28.4428 1.99629
\(204\) −7.13388 −0.499472
\(205\) −1.57284 −0.109852
\(206\) −1.13743 −0.0792487
\(207\) −6.10547 −0.424360
\(208\) 1.42796 0.0990112
\(209\) −1.21614 −0.0841221
\(210\) 7.40041 0.510677
\(211\) −1.00000 −0.0688428
\(212\) 2.56029 0.175841
\(213\) 0.619665 0.0424588
\(214\) −3.71361 −0.253857
\(215\) −10.6307 −0.725009
\(216\) 5.64741 0.384257
\(217\) 22.1931 1.50657
\(218\) −7.68678 −0.520615
\(219\) −11.9325 −0.806323
\(220\) −2.21834 −0.149560
\(221\) 6.97187 0.468979
\(222\) 11.0174 0.739439
\(223\) 4.84894 0.324709 0.162355 0.986732i \(-0.448091\pi\)
0.162355 + 0.986732i \(0.448091\pi\)
\(224\) −2.77663 −0.185521
\(225\) 1.44700 0.0964670
\(226\) 3.56486 0.237131
\(227\) −14.6540 −0.972622 −0.486311 0.873786i \(-0.661658\pi\)
−0.486311 + 0.873786i \(0.661658\pi\)
\(228\) −1.46114 −0.0967665
\(229\) −27.3808 −1.80937 −0.904686 0.426078i \(-0.859895\pi\)
−0.904686 + 0.426078i \(0.859895\pi\)
\(230\) 12.8741 0.848892
\(231\) −4.93394 −0.324629
\(232\) −10.2436 −0.672527
\(233\) −11.7025 −0.766657 −0.383329 0.923612i \(-0.625222\pi\)
−0.383329 + 0.923612i \(0.625222\pi\)
\(234\) −1.23528 −0.0807525
\(235\) 14.7695 0.963453
\(236\) −3.58628 −0.233447
\(237\) −15.1008 −0.980904
\(238\) −13.5566 −0.878745
\(239\) 13.8794 0.897781 0.448891 0.893587i \(-0.351819\pi\)
0.448891 + 0.893587i \(0.351819\pi\)
\(240\) −2.66525 −0.172041
\(241\) −16.4042 −1.05669 −0.528343 0.849031i \(-0.677186\pi\)
−0.528343 + 0.849031i \(0.677186\pi\)
\(242\) −9.52101 −0.612033
\(243\) −8.67731 −0.556649
\(244\) −3.47477 −0.222450
\(245\) 1.29451 0.0827033
\(246\) 1.25989 0.0803275
\(247\) 1.42796 0.0908590
\(248\) −7.99282 −0.507544
\(249\) 15.2547 0.966727
\(250\) −12.1716 −0.769799
\(251\) −19.6656 −1.24128 −0.620642 0.784094i \(-0.713128\pi\)
−0.620642 + 0.784094i \(0.713128\pi\)
\(252\) 2.40196 0.151309
\(253\) −8.58331 −0.539628
\(254\) 12.0562 0.756472
\(255\) −13.0128 −0.814893
\(256\) 1.00000 0.0625000
\(257\) −12.8680 −0.802683 −0.401341 0.915929i \(-0.631456\pi\)
−0.401341 + 0.915929i \(0.631456\pi\)
\(258\) 8.51550 0.530152
\(259\) 20.9365 1.30093
\(260\) 2.60472 0.161538
\(261\) 8.86138 0.548506
\(262\) −5.02274 −0.310306
\(263\) −14.0847 −0.868501 −0.434250 0.900792i \(-0.642987\pi\)
−0.434250 + 0.900792i \(0.642987\pi\)
\(264\) 1.77695 0.109364
\(265\) 4.67018 0.286887
\(266\) −2.77663 −0.170246
\(267\) −8.96976 −0.548940
\(268\) 14.8212 0.905347
\(269\) −7.22519 −0.440528 −0.220264 0.975440i \(-0.570692\pi\)
−0.220264 + 0.975440i \(0.570692\pi\)
\(270\) 10.3013 0.626920
\(271\) −14.7499 −0.895990 −0.447995 0.894036i \(-0.647862\pi\)
−0.447995 + 0.894036i \(0.647862\pi\)
\(272\) 4.88240 0.296039
\(273\) 5.79331 0.350627
\(274\) 6.60500 0.399023
\(275\) 2.03425 0.122670
\(276\) −10.3125 −0.620740
\(277\) −6.43726 −0.386777 −0.193389 0.981122i \(-0.561948\pi\)
−0.193389 + 0.981122i \(0.561948\pi\)
\(278\) −8.51196 −0.510513
\(279\) 6.91429 0.413948
\(280\) −5.06481 −0.302680
\(281\) 13.9676 0.833240 0.416620 0.909081i \(-0.363215\pi\)
0.416620 + 0.909081i \(0.363215\pi\)
\(282\) −11.8307 −0.704510
\(283\) −6.75138 −0.401328 −0.200664 0.979660i \(-0.564310\pi\)
−0.200664 + 0.979660i \(0.564310\pi\)
\(284\) −0.424097 −0.0251655
\(285\) −2.66525 −0.157876
\(286\) −1.73660 −0.102687
\(287\) 2.39418 0.141324
\(288\) −0.865063 −0.0509743
\(289\) 6.83782 0.402225
\(290\) −18.6852 −1.09724
\(291\) 13.2033 0.773993
\(292\) 8.16655 0.477911
\(293\) −5.13724 −0.300121 −0.150060 0.988677i \(-0.547947\pi\)
−0.150060 + 0.988677i \(0.547947\pi\)
\(294\) −1.03694 −0.0604756
\(295\) −6.54167 −0.380871
\(296\) −7.54026 −0.438269
\(297\) −6.86803 −0.398524
\(298\) −19.5391 −1.13187
\(299\) 10.0783 0.582844
\(300\) 2.44408 0.141109
\(301\) 16.1821 0.932723
\(302\) 10.5323 0.606068
\(303\) 22.2692 1.27933
\(304\) 1.00000 0.0573539
\(305\) −6.33828 −0.362929
\(306\) −4.22358 −0.241446
\(307\) −19.8146 −1.13088 −0.565440 0.824790i \(-0.691294\pi\)
−0.565440 + 0.824790i \(0.691294\pi\)
\(308\) 3.37677 0.192409
\(309\) 1.66195 0.0945451
\(310\) −14.5796 −0.828064
\(311\) 14.9239 0.846255 0.423127 0.906070i \(-0.360932\pi\)
0.423127 + 0.906070i \(0.360932\pi\)
\(312\) −2.08645 −0.118122
\(313\) −18.1988 −1.02866 −0.514328 0.857594i \(-0.671959\pi\)
−0.514328 + 0.857594i \(0.671959\pi\)
\(314\) −10.4380 −0.589052
\(315\) 4.38138 0.246863
\(316\) 10.3349 0.581386
\(317\) −29.2845 −1.64478 −0.822391 0.568922i \(-0.807361\pi\)
−0.822391 + 0.568922i \(0.807361\pi\)
\(318\) −3.74095 −0.209782
\(319\) 12.4577 0.697496
\(320\) 1.82408 0.101969
\(321\) 5.42611 0.302856
\(322\) −19.5970 −1.09210
\(323\) 4.88240 0.271664
\(324\) −5.65648 −0.314249
\(325\) −2.38857 −0.132494
\(326\) 18.4883 1.02397
\(327\) 11.2315 0.621102
\(328\) −0.862262 −0.0476104
\(329\) −22.4821 −1.23948
\(330\) 3.24131 0.178428
\(331\) −11.3759 −0.625278 −0.312639 0.949872i \(-0.601213\pi\)
−0.312639 + 0.949872i \(0.601213\pi\)
\(332\) −10.4403 −0.572983
\(333\) 6.52280 0.357447
\(334\) −6.60100 −0.361191
\(335\) 27.0351 1.47708
\(336\) 4.05705 0.221330
\(337\) 2.84687 0.155079 0.0775394 0.996989i \(-0.475294\pi\)
0.0775394 + 0.996989i \(0.475294\pi\)
\(338\) −10.9609 −0.596196
\(339\) −5.20876 −0.282901
\(340\) 8.90591 0.482991
\(341\) 9.72038 0.526388
\(342\) −0.865063 −0.0467773
\(343\) 17.4659 0.943070
\(344\) −5.82798 −0.314223
\(345\) −18.8109 −1.01274
\(346\) 12.6258 0.678765
\(347\) −7.03087 −0.377437 −0.188718 0.982031i \(-0.560433\pi\)
−0.188718 + 0.982031i \(0.560433\pi\)
\(348\) 14.9674 0.802337
\(349\) 16.1992 0.867123 0.433561 0.901124i \(-0.357257\pi\)
0.433561 + 0.901124i \(0.357257\pi\)
\(350\) 4.64451 0.248260
\(351\) 8.06427 0.430439
\(352\) −1.21614 −0.0648204
\(353\) 22.9606 1.22207 0.611034 0.791604i \(-0.290754\pi\)
0.611034 + 0.791604i \(0.290754\pi\)
\(354\) 5.24006 0.278506
\(355\) −0.773588 −0.0410578
\(356\) 6.13887 0.325359
\(357\) 19.8082 1.04836
\(358\) −15.6437 −0.826798
\(359\) 36.5391 1.92846 0.964229 0.265071i \(-0.0853953\pi\)
0.964229 + 0.265071i \(0.0853953\pi\)
\(360\) −1.57795 −0.0831652
\(361\) 1.00000 0.0526316
\(362\) 12.5304 0.658582
\(363\) 13.9115 0.730167
\(364\) −3.96492 −0.207818
\(365\) 14.8965 0.779717
\(366\) 5.07714 0.265386
\(367\) 25.3408 1.32278 0.661389 0.750043i \(-0.269967\pi\)
0.661389 + 0.750043i \(0.269967\pi\)
\(368\) 7.05784 0.367915
\(369\) 0.745911 0.0388306
\(370\) −13.7541 −0.715040
\(371\) −7.10898 −0.369080
\(372\) 11.6786 0.605510
\(373\) −21.0985 −1.09244 −0.546219 0.837642i \(-0.683933\pi\)
−0.546219 + 0.837642i \(0.683933\pi\)
\(374\) −5.93768 −0.307030
\(375\) 17.7844 0.918384
\(376\) 8.09691 0.417566
\(377\) −14.6275 −0.753354
\(378\) −15.6808 −0.806531
\(379\) 24.4401 1.25540 0.627701 0.778455i \(-0.283996\pi\)
0.627701 + 0.778455i \(0.283996\pi\)
\(380\) 1.82408 0.0935736
\(381\) −17.6158 −0.902484
\(382\) −26.2653 −1.34385
\(383\) −25.8701 −1.32190 −0.660951 0.750429i \(-0.729847\pi\)
−0.660951 + 0.750429i \(0.729847\pi\)
\(384\) −1.46114 −0.0745636
\(385\) 6.15951 0.313918
\(386\) −1.16834 −0.0594669
\(387\) 5.04157 0.256277
\(388\) −9.03631 −0.458749
\(389\) 16.4882 0.835983 0.417992 0.908451i \(-0.362734\pi\)
0.417992 + 0.908451i \(0.362734\pi\)
\(390\) −3.80587 −0.192718
\(391\) 34.4592 1.74268
\(392\) 0.709678 0.0358441
\(393\) 7.33894 0.370201
\(394\) −2.55178 −0.128557
\(395\) 18.8518 0.948537
\(396\) 1.05204 0.0528668
\(397\) 35.6965 1.79156 0.895778 0.444502i \(-0.146619\pi\)
0.895778 + 0.444502i \(0.146619\pi\)
\(398\) −8.74578 −0.438386
\(399\) 4.05705 0.203107
\(400\) −1.67272 −0.0836358
\(401\) −19.5734 −0.977447 −0.488724 0.872439i \(-0.662537\pi\)
−0.488724 + 0.872439i \(0.662537\pi\)
\(402\) −21.6558 −1.08009
\(403\) −11.4134 −0.568543
\(404\) −15.2409 −0.758265
\(405\) −10.3179 −0.512700
\(406\) 28.4428 1.41159
\(407\) 9.17000 0.454540
\(408\) −7.13388 −0.353180
\(409\) 24.6509 1.21891 0.609454 0.792821i \(-0.291389\pi\)
0.609454 + 0.792821i \(0.291389\pi\)
\(410\) −1.57284 −0.0776770
\(411\) −9.65085 −0.476041
\(412\) −1.13743 −0.0560373
\(413\) 9.95777 0.489990
\(414\) −6.10547 −0.300068
\(415\) −19.0439 −0.934828
\(416\) 1.42796 0.0700115
\(417\) 12.4372 0.609051
\(418\) −1.21614 −0.0594833
\(419\) −32.3414 −1.57998 −0.789989 0.613120i \(-0.789914\pi\)
−0.789989 + 0.613120i \(0.789914\pi\)
\(420\) 7.40041 0.361103
\(421\) −17.8218 −0.868581 −0.434291 0.900773i \(-0.643001\pi\)
−0.434291 + 0.900773i \(0.643001\pi\)
\(422\) −1.00000 −0.0486792
\(423\) −7.00434 −0.340563
\(424\) 2.56029 0.124339
\(425\) −8.16687 −0.396151
\(426\) 0.619665 0.0300229
\(427\) 9.64816 0.466907
\(428\) −3.71361 −0.179504
\(429\) 2.53742 0.122508
\(430\) −10.6307 −0.512659
\(431\) 28.4446 1.37013 0.685064 0.728483i \(-0.259774\pi\)
0.685064 + 0.728483i \(0.259774\pi\)
\(432\) 5.64741 0.271711
\(433\) 9.12218 0.438384 0.219192 0.975682i \(-0.429658\pi\)
0.219192 + 0.975682i \(0.429658\pi\)
\(434\) 22.1931 1.06530
\(435\) 27.3018 1.30902
\(436\) −7.68678 −0.368130
\(437\) 7.05784 0.337622
\(438\) −11.9325 −0.570157
\(439\) −25.1019 −1.19805 −0.599023 0.800732i \(-0.704444\pi\)
−0.599023 + 0.800732i \(0.704444\pi\)
\(440\) −2.21834 −0.105755
\(441\) −0.613916 −0.0292341
\(442\) 6.97187 0.331618
\(443\) 10.1470 0.482098 0.241049 0.970513i \(-0.422508\pi\)
0.241049 + 0.970513i \(0.422508\pi\)
\(444\) 11.0174 0.522862
\(445\) 11.1978 0.530827
\(446\) 4.84894 0.229604
\(447\) 28.5494 1.35034
\(448\) −2.77663 −0.131183
\(449\) 5.78601 0.273059 0.136529 0.990636i \(-0.456405\pi\)
0.136529 + 0.990636i \(0.456405\pi\)
\(450\) 1.44700 0.0682125
\(451\) 1.04863 0.0493781
\(452\) 3.56486 0.167677
\(453\) −15.3892 −0.723050
\(454\) −14.6540 −0.687748
\(455\) −7.23235 −0.339058
\(456\) −1.46114 −0.0684243
\(457\) −23.9897 −1.12219 −0.561095 0.827751i \(-0.689620\pi\)
−0.561095 + 0.827751i \(0.689620\pi\)
\(458\) −27.3808 −1.27942
\(459\) 27.5729 1.28699
\(460\) 12.8741 0.600258
\(461\) −34.5981 −1.61139 −0.805696 0.592329i \(-0.798209\pi\)
−0.805696 + 0.592329i \(0.798209\pi\)
\(462\) −4.93394 −0.229548
\(463\) −6.30630 −0.293079 −0.146539 0.989205i \(-0.546813\pi\)
−0.146539 + 0.989205i \(0.546813\pi\)
\(464\) −10.2436 −0.475548
\(465\) 21.3028 0.987895
\(466\) −11.7025 −0.542108
\(467\) 7.16190 0.331413 0.165707 0.986175i \(-0.447010\pi\)
0.165707 + 0.986175i \(0.447010\pi\)
\(468\) −1.23528 −0.0571007
\(469\) −41.1529 −1.90026
\(470\) 14.7695 0.681264
\(471\) 15.2514 0.702749
\(472\) −3.58628 −0.165072
\(473\) 7.08763 0.325890
\(474\) −15.1008 −0.693604
\(475\) −1.67272 −0.0767495
\(476\) −13.5566 −0.621367
\(477\) −2.21481 −0.101409
\(478\) 13.8794 0.634827
\(479\) −26.1422 −1.19447 −0.597234 0.802067i \(-0.703733\pi\)
−0.597234 + 0.802067i \(0.703733\pi\)
\(480\) −2.66525 −0.121651
\(481\) −10.7672 −0.490942
\(482\) −16.4042 −0.747190
\(483\) 28.6340 1.30289
\(484\) −9.52101 −0.432773
\(485\) −16.4830 −0.748454
\(486\) −8.67731 −0.393611
\(487\) 22.2984 1.01044 0.505218 0.862992i \(-0.331412\pi\)
0.505218 + 0.862992i \(0.331412\pi\)
\(488\) −3.47477 −0.157296
\(489\) −27.0140 −1.22162
\(490\) 1.29451 0.0584801
\(491\) 25.7119 1.16036 0.580180 0.814488i \(-0.302982\pi\)
0.580180 + 0.814488i \(0.302982\pi\)
\(492\) 1.25989 0.0568001
\(493\) −50.0135 −2.25249
\(494\) 1.42796 0.0642470
\(495\) 1.91900 0.0862528
\(496\) −7.99282 −0.358888
\(497\) 1.17756 0.0528208
\(498\) 15.2547 0.683579
\(499\) −34.0529 −1.52442 −0.762209 0.647331i \(-0.775885\pi\)
−0.762209 + 0.647331i \(0.775885\pi\)
\(500\) −12.1716 −0.544330
\(501\) 9.64500 0.430907
\(502\) −19.6656 −0.877721
\(503\) 13.7182 0.611666 0.305833 0.952085i \(-0.401065\pi\)
0.305833 + 0.952085i \(0.401065\pi\)
\(504\) 2.40196 0.106992
\(505\) −27.8007 −1.23712
\(506\) −8.58331 −0.381575
\(507\) 16.0155 0.711272
\(508\) 12.0562 0.534906
\(509\) −28.2094 −1.25036 −0.625179 0.780481i \(-0.714974\pi\)
−0.625179 + 0.780481i \(0.714974\pi\)
\(510\) −13.0128 −0.576217
\(511\) −22.6755 −1.00310
\(512\) 1.00000 0.0441942
\(513\) 5.64741 0.249339
\(514\) −12.8680 −0.567582
\(515\) −2.07477 −0.0914254
\(516\) 8.51550 0.374874
\(517\) −9.84697 −0.433069
\(518\) 20.9365 0.919897
\(519\) −18.4480 −0.809778
\(520\) 2.60472 0.114225
\(521\) 6.67300 0.292349 0.146175 0.989259i \(-0.453304\pi\)
0.146175 + 0.989259i \(0.453304\pi\)
\(522\) 8.86138 0.387852
\(523\) 27.8938 1.21971 0.609854 0.792513i \(-0.291228\pi\)
0.609854 + 0.792513i \(0.291228\pi\)
\(524\) −5.02274 −0.219419
\(525\) −6.78630 −0.296178
\(526\) −14.0847 −0.614123
\(527\) −39.0241 −1.69992
\(528\) 1.77695 0.0773319
\(529\) 26.8131 1.16578
\(530\) 4.67018 0.202860
\(531\) 3.10236 0.134631
\(532\) −2.77663 −0.120382
\(533\) −1.23128 −0.0533325
\(534\) −8.96976 −0.388160
\(535\) −6.77393 −0.292863
\(536\) 14.8212 0.640177
\(537\) 22.8577 0.986384
\(538\) −7.22519 −0.311500
\(539\) −0.863067 −0.0371749
\(540\) 10.3013 0.443299
\(541\) −8.33901 −0.358522 −0.179261 0.983802i \(-0.557371\pi\)
−0.179261 + 0.983802i \(0.557371\pi\)
\(542\) −14.7499 −0.633561
\(543\) −18.3087 −0.785699
\(544\) 4.88240 0.209331
\(545\) −14.0213 −0.600608
\(546\) 5.79331 0.247931
\(547\) 8.05012 0.344198 0.172099 0.985080i \(-0.444945\pi\)
0.172099 + 0.985080i \(0.444945\pi\)
\(548\) 6.60500 0.282152
\(549\) 3.00590 0.128289
\(550\) 2.03425 0.0867409
\(551\) −10.2436 −0.436393
\(552\) −10.3125 −0.438929
\(553\) −28.6963 −1.22029
\(554\) −6.43726 −0.273493
\(555\) 20.0967 0.853055
\(556\) −8.51196 −0.360987
\(557\) 27.6121 1.16996 0.584980 0.811048i \(-0.301102\pi\)
0.584980 + 0.811048i \(0.301102\pi\)
\(558\) 6.91429 0.292705
\(559\) −8.32212 −0.351988
\(560\) −5.06481 −0.214027
\(561\) 8.67579 0.366292
\(562\) 13.9676 0.589190
\(563\) 30.0167 1.26505 0.632526 0.774539i \(-0.282018\pi\)
0.632526 + 0.774539i \(0.282018\pi\)
\(564\) −11.8307 −0.498164
\(565\) 6.50260 0.273566
\(566\) −6.75138 −0.283782
\(567\) 15.7059 0.659588
\(568\) −0.424097 −0.0177947
\(569\) 4.88122 0.204631 0.102316 0.994752i \(-0.467375\pi\)
0.102316 + 0.994752i \(0.467375\pi\)
\(570\) −2.66525 −0.111635
\(571\) −14.4168 −0.603323 −0.301662 0.953415i \(-0.597541\pi\)
−0.301662 + 0.953415i \(0.597541\pi\)
\(572\) −1.73660 −0.0726108
\(573\) 38.3773 1.60324
\(574\) 2.39418 0.0999313
\(575\) −11.8058 −0.492334
\(576\) −0.865063 −0.0360443
\(577\) −36.0190 −1.49949 −0.749745 0.661727i \(-0.769824\pi\)
−0.749745 + 0.661727i \(0.769824\pi\)
\(578\) 6.83782 0.284416
\(579\) 1.70711 0.0709450
\(580\) −18.6852 −0.775862
\(581\) 28.9887 1.20266
\(582\) 13.2033 0.547296
\(583\) −3.11367 −0.128955
\(584\) 8.16655 0.337934
\(585\) −2.25325 −0.0931603
\(586\) −5.13724 −0.212217
\(587\) 19.9494 0.823400 0.411700 0.911319i \(-0.364935\pi\)
0.411700 + 0.911319i \(0.364935\pi\)
\(588\) −1.03694 −0.0427627
\(589\) −7.99282 −0.329338
\(590\) −6.54167 −0.269316
\(591\) 3.72852 0.153371
\(592\) −7.54026 −0.309903
\(593\) −39.4333 −1.61933 −0.809665 0.586892i \(-0.800351\pi\)
−0.809665 + 0.586892i \(0.800351\pi\)
\(594\) −6.86803 −0.281799
\(595\) −24.7284 −1.01377
\(596\) −19.5391 −0.800353
\(597\) 12.7788 0.523003
\(598\) 10.0783 0.412133
\(599\) −12.9656 −0.529760 −0.264880 0.964281i \(-0.585332\pi\)
−0.264880 + 0.964281i \(0.585332\pi\)
\(600\) 2.44408 0.0997790
\(601\) 42.6830 1.74107 0.870537 0.492102i \(-0.163771\pi\)
0.870537 + 0.492102i \(0.163771\pi\)
\(602\) 16.1821 0.659535
\(603\) −12.8212 −0.522122
\(604\) 10.5323 0.428555
\(605\) −17.3671 −0.706074
\(606\) 22.2692 0.904623
\(607\) −12.4908 −0.506985 −0.253493 0.967337i \(-0.581579\pi\)
−0.253493 + 0.967337i \(0.581579\pi\)
\(608\) 1.00000 0.0405554
\(609\) −41.5589 −1.68405
\(610\) −6.33828 −0.256629
\(611\) 11.5621 0.467751
\(612\) −4.22358 −0.170728
\(613\) 9.86462 0.398428 0.199214 0.979956i \(-0.436161\pi\)
0.199214 + 0.979956i \(0.436161\pi\)
\(614\) −19.8146 −0.799653
\(615\) 2.29814 0.0926700
\(616\) 3.37677 0.136054
\(617\) −45.9061 −1.84811 −0.924054 0.382262i \(-0.875145\pi\)
−0.924054 + 0.382262i \(0.875145\pi\)
\(618\) 1.66195 0.0668534
\(619\) −31.1519 −1.25210 −0.626050 0.779783i \(-0.715329\pi\)
−0.626050 + 0.779783i \(0.715329\pi\)
\(620\) −14.5796 −0.585530
\(621\) 39.8585 1.59947
\(622\) 14.9239 0.598392
\(623\) −17.0454 −0.682908
\(624\) −2.08645 −0.0835250
\(625\) −13.8384 −0.553538
\(626\) −18.1988 −0.727369
\(627\) 1.77695 0.0709646
\(628\) −10.4380 −0.416522
\(629\) −36.8146 −1.46789
\(630\) 4.38138 0.174558
\(631\) 29.8730 1.18923 0.594613 0.804012i \(-0.297305\pi\)
0.594613 + 0.804012i \(0.297305\pi\)
\(632\) 10.3349 0.411102
\(633\) 1.46114 0.0580752
\(634\) −29.2845 −1.16304
\(635\) 21.9915 0.872705
\(636\) −3.74095 −0.148338
\(637\) 1.01339 0.0401520
\(638\) 12.4577 0.493204
\(639\) 0.366870 0.0145132
\(640\) 1.82408 0.0721033
\(641\) −33.7213 −1.33191 −0.665956 0.745991i \(-0.731976\pi\)
−0.665956 + 0.745991i \(0.731976\pi\)
\(642\) 5.42611 0.214151
\(643\) 27.0639 1.06730 0.533648 0.845707i \(-0.320821\pi\)
0.533648 + 0.845707i \(0.320821\pi\)
\(644\) −19.5970 −0.772230
\(645\) 15.5330 0.611611
\(646\) 4.88240 0.192095
\(647\) 25.4824 1.00182 0.500909 0.865500i \(-0.332999\pi\)
0.500909 + 0.865500i \(0.332999\pi\)
\(648\) −5.65648 −0.222207
\(649\) 4.36141 0.171200
\(650\) −2.38857 −0.0936875
\(651\) −32.4273 −1.27093
\(652\) 18.4883 0.724057
\(653\) 29.7431 1.16394 0.581968 0.813212i \(-0.302283\pi\)
0.581968 + 0.813212i \(0.302283\pi\)
\(654\) 11.2315 0.439186
\(655\) −9.16191 −0.357985
\(656\) −0.862262 −0.0336657
\(657\) −7.06458 −0.275616
\(658\) −22.4821 −0.876445
\(659\) −1.40224 −0.0546234 −0.0273117 0.999627i \(-0.508695\pi\)
−0.0273117 + 0.999627i \(0.508695\pi\)
\(660\) 3.24131 0.126168
\(661\) 23.4190 0.910892 0.455446 0.890263i \(-0.349480\pi\)
0.455446 + 0.890263i \(0.349480\pi\)
\(662\) −11.3759 −0.442139
\(663\) −10.1869 −0.395626
\(664\) −10.4403 −0.405160
\(665\) −5.06481 −0.196405
\(666\) 6.52280 0.252753
\(667\) −72.2978 −2.79938
\(668\) −6.60100 −0.255400
\(669\) −7.08499 −0.273922
\(670\) 27.0351 1.04446
\(671\) 4.22581 0.163135
\(672\) 4.05705 0.156504
\(673\) −12.2858 −0.473585 −0.236792 0.971560i \(-0.576096\pi\)
−0.236792 + 0.971560i \(0.576096\pi\)
\(674\) 2.84687 0.109657
\(675\) −9.44651 −0.363596
\(676\) −10.9609 −0.421574
\(677\) 47.2914 1.81756 0.908778 0.417280i \(-0.137017\pi\)
0.908778 + 0.417280i \(0.137017\pi\)
\(678\) −5.20876 −0.200041
\(679\) 25.0905 0.962885
\(680\) 8.90591 0.341526
\(681\) 21.4116 0.820495
\(682\) 9.72038 0.372212
\(683\) −31.2861 −1.19713 −0.598564 0.801075i \(-0.704262\pi\)
−0.598564 + 0.801075i \(0.704262\pi\)
\(684\) −0.865063 −0.0330765
\(685\) 12.0481 0.460334
\(686\) 17.4659 0.666851
\(687\) 40.0072 1.52637
\(688\) −5.82798 −0.222190
\(689\) 3.65599 0.139282
\(690\) −18.8109 −0.716118
\(691\) 8.50326 0.323479 0.161740 0.986833i \(-0.448290\pi\)
0.161740 + 0.986833i \(0.448290\pi\)
\(692\) 12.6258 0.479959
\(693\) −2.92112 −0.110964
\(694\) −7.03087 −0.266888
\(695\) −15.5265 −0.588955
\(696\) 14.9674 0.567338
\(697\) −4.20991 −0.159462
\(698\) 16.1992 0.613149
\(699\) 17.0990 0.646745
\(700\) 4.64451 0.175546
\(701\) −1.01268 −0.0382483 −0.0191242 0.999817i \(-0.506088\pi\)
−0.0191242 + 0.999817i \(0.506088\pi\)
\(702\) 8.06427 0.304366
\(703\) −7.54026 −0.284386
\(704\) −1.21614 −0.0458350
\(705\) −21.5803 −0.812760
\(706\) 22.9606 0.864132
\(707\) 42.3184 1.59155
\(708\) 5.24006 0.196934
\(709\) −9.19588 −0.345358 −0.172679 0.984978i \(-0.555242\pi\)
−0.172679 + 0.984978i \(0.555242\pi\)
\(710\) −0.773588 −0.0290322
\(711\) −8.94038 −0.335290
\(712\) 6.13887 0.230064
\(713\) −56.4120 −2.11265
\(714\) 19.8082 0.741301
\(715\) −3.16770 −0.118465
\(716\) −15.6437 −0.584634
\(717\) −20.2797 −0.757360
\(718\) 36.5391 1.36363
\(719\) 37.4818 1.39784 0.698918 0.715202i \(-0.253665\pi\)
0.698918 + 0.715202i \(0.253665\pi\)
\(720\) −1.57795 −0.0588067
\(721\) 3.15823 0.117619
\(722\) 1.00000 0.0372161
\(723\) 23.9688 0.891411
\(724\) 12.5304 0.465687
\(725\) 17.1347 0.636366
\(726\) 13.9115 0.516306
\(727\) −19.1272 −0.709387 −0.354694 0.934983i \(-0.615415\pi\)
−0.354694 + 0.934983i \(0.615415\pi\)
\(728\) −3.96492 −0.146950
\(729\) 29.6482 1.09808
\(730\) 14.8965 0.551343
\(731\) −28.4545 −1.05243
\(732\) 5.07714 0.187656
\(733\) 21.2864 0.786232 0.393116 0.919489i \(-0.371397\pi\)
0.393116 + 0.919489i \(0.371397\pi\)
\(734\) 25.3408 0.935346
\(735\) −1.89147 −0.0697678
\(736\) 7.05784 0.260155
\(737\) −18.0246 −0.663945
\(738\) 0.745911 0.0274574
\(739\) 25.6648 0.944095 0.472047 0.881573i \(-0.343515\pi\)
0.472047 + 0.881573i \(0.343515\pi\)
\(740\) −13.7541 −0.505610
\(741\) −2.08645 −0.0766478
\(742\) −7.10898 −0.260979
\(743\) 14.3271 0.525609 0.262804 0.964849i \(-0.415353\pi\)
0.262804 + 0.964849i \(0.415353\pi\)
\(744\) 11.6786 0.428160
\(745\) −35.6410 −1.30578
\(746\) −21.0985 −0.772470
\(747\) 9.03148 0.330445
\(748\) −5.93768 −0.217103
\(749\) 10.3113 0.376767
\(750\) 17.7844 0.649396
\(751\) 13.2594 0.483841 0.241921 0.970296i \(-0.422223\pi\)
0.241921 + 0.970296i \(0.422223\pi\)
\(752\) 8.09691 0.295264
\(753\) 28.7343 1.04714
\(754\) −14.6275 −0.532702
\(755\) 19.2119 0.699192
\(756\) −15.6808 −0.570304
\(757\) 19.9743 0.725977 0.362989 0.931794i \(-0.381756\pi\)
0.362989 + 0.931794i \(0.381756\pi\)
\(758\) 24.4401 0.887703
\(759\) 12.5414 0.455225
\(760\) 1.82408 0.0661665
\(761\) −29.0655 −1.05362 −0.526812 0.849982i \(-0.676613\pi\)
−0.526812 + 0.849982i \(0.676613\pi\)
\(762\) −17.6158 −0.638153
\(763\) 21.3434 0.772681
\(764\) −26.2653 −0.950245
\(765\) −7.70417 −0.278545
\(766\) −25.8701 −0.934726
\(767\) −5.12106 −0.184911
\(768\) −1.46114 −0.0527244
\(769\) 40.5879 1.46364 0.731819 0.681499i \(-0.238672\pi\)
0.731819 + 0.681499i \(0.238672\pi\)
\(770\) 6.15951 0.221973
\(771\) 18.8019 0.677136
\(772\) −1.16834 −0.0420494
\(773\) 38.5180 1.38540 0.692699 0.721227i \(-0.256422\pi\)
0.692699 + 0.721227i \(0.256422\pi\)
\(774\) 5.04157 0.181215
\(775\) 13.3697 0.480254
\(776\) −9.03631 −0.324385
\(777\) −30.5912 −1.09745
\(778\) 16.4882 0.591129
\(779\) −0.862262 −0.0308937
\(780\) −3.80587 −0.136272
\(781\) 0.515760 0.0184554
\(782\) 34.4592 1.23226
\(783\) −57.8499 −2.06739
\(784\) 0.709678 0.0253456
\(785\) −19.0398 −0.679561
\(786\) 7.33894 0.261771
\(787\) 12.7039 0.452845 0.226422 0.974029i \(-0.427297\pi\)
0.226422 + 0.974029i \(0.427297\pi\)
\(788\) −2.55178 −0.0909035
\(789\) 20.5798 0.732659
\(790\) 18.8518 0.670717
\(791\) −9.89829 −0.351943
\(792\) 1.05204 0.0373825
\(793\) −4.96184 −0.176200
\(794\) 35.6965 1.26682
\(795\) −6.82380 −0.242015
\(796\) −8.74578 −0.309986
\(797\) −6.89626 −0.244278 −0.122139 0.992513i \(-0.538975\pi\)
−0.122139 + 0.992513i \(0.538975\pi\)
\(798\) 4.05705 0.143618
\(799\) 39.5324 1.39855
\(800\) −1.67272 −0.0591394
\(801\) −5.31051 −0.187638
\(802\) −19.5734 −0.691159
\(803\) −9.93166 −0.350481
\(804\) −21.6558 −0.763742
\(805\) −35.7466 −1.25990
\(806\) −11.4134 −0.402021
\(807\) 10.5570 0.371625
\(808\) −15.2409 −0.536174
\(809\) −38.1999 −1.34304 −0.671518 0.740989i \(-0.734357\pi\)
−0.671518 + 0.740989i \(0.734357\pi\)
\(810\) −10.3179 −0.362534
\(811\) −21.7735 −0.764569 −0.382285 0.924045i \(-0.624863\pi\)
−0.382285 + 0.924045i \(0.624863\pi\)
\(812\) 28.4428 0.998145
\(813\) 21.5516 0.755849
\(814\) 9.17000 0.321408
\(815\) 33.7242 1.18131
\(816\) −7.13388 −0.249736
\(817\) −5.82798 −0.203895
\(818\) 24.6509 0.861898
\(819\) 3.42991 0.119851
\(820\) −1.57284 −0.0549259
\(821\) 1.08513 0.0378713 0.0189357 0.999821i \(-0.493972\pi\)
0.0189357 + 0.999821i \(0.493972\pi\)
\(822\) −9.65085 −0.336612
\(823\) −26.8699 −0.936626 −0.468313 0.883563i \(-0.655138\pi\)
−0.468313 + 0.883563i \(0.655138\pi\)
\(824\) −1.13743 −0.0396243
\(825\) −2.97234 −0.103483
\(826\) 9.95777 0.346475
\(827\) 22.8594 0.794901 0.397450 0.917624i \(-0.369895\pi\)
0.397450 + 0.917624i \(0.369895\pi\)
\(828\) −6.10547 −0.212180
\(829\) −36.0596 −1.25240 −0.626201 0.779662i \(-0.715391\pi\)
−0.626201 + 0.779662i \(0.715391\pi\)
\(830\) −19.0439 −0.661024
\(831\) 9.40575 0.326282
\(832\) 1.42796 0.0495056
\(833\) 3.46493 0.120053
\(834\) 12.4372 0.430664
\(835\) −12.0408 −0.416688
\(836\) −1.21614 −0.0420610
\(837\) −45.1387 −1.56022
\(838\) −32.3414 −1.11721
\(839\) −31.6285 −1.09194 −0.545968 0.837806i \(-0.683838\pi\)
−0.545968 + 0.837806i \(0.683838\pi\)
\(840\) 7.40041 0.255338
\(841\) 75.9319 2.61834
\(842\) −17.8218 −0.614180
\(843\) −20.4087 −0.702914
\(844\) −1.00000 −0.0344214
\(845\) −19.9937 −0.687803
\(846\) −7.00434 −0.240814
\(847\) 26.4363 0.908363
\(848\) 2.56029 0.0879207
\(849\) 9.86473 0.338557
\(850\) −8.16687 −0.280121
\(851\) −53.2179 −1.82429
\(852\) 0.619665 0.0212294
\(853\) 12.8704 0.440673 0.220336 0.975424i \(-0.429284\pi\)
0.220336 + 0.975424i \(0.429284\pi\)
\(854\) 9.64816 0.330153
\(855\) −1.57795 −0.0539647
\(856\) −3.71361 −0.126928
\(857\) −38.5153 −1.31566 −0.657829 0.753168i \(-0.728525\pi\)
−0.657829 + 0.753168i \(0.728525\pi\)
\(858\) 2.53742 0.0866260
\(859\) −21.8526 −0.745602 −0.372801 0.927911i \(-0.621603\pi\)
−0.372801 + 0.927911i \(0.621603\pi\)
\(860\) −10.6307 −0.362505
\(861\) −3.49824 −0.119220
\(862\) 28.4446 0.968827
\(863\) 2.74159 0.0933248 0.0466624 0.998911i \(-0.485141\pi\)
0.0466624 + 0.998911i \(0.485141\pi\)
\(864\) 5.64741 0.192129
\(865\) 23.0304 0.783059
\(866\) 9.12218 0.309984
\(867\) −9.99103 −0.339313
\(868\) 22.1931 0.753283
\(869\) −12.5687 −0.426365
\(870\) 27.3018 0.925618
\(871\) 21.1640 0.717116
\(872\) −7.68678 −0.260307
\(873\) 7.81698 0.264565
\(874\) 7.05784 0.238735
\(875\) 33.7960 1.14251
\(876\) −11.9325 −0.403162
\(877\) −57.1209 −1.92884 −0.964418 0.264382i \(-0.914832\pi\)
−0.964418 + 0.264382i \(0.914832\pi\)
\(878\) −25.1019 −0.847147
\(879\) 7.50623 0.253179
\(880\) −2.21834 −0.0747802
\(881\) −31.5977 −1.06455 −0.532277 0.846570i \(-0.678664\pi\)
−0.532277 + 0.846570i \(0.678664\pi\)
\(882\) −0.613916 −0.0206716
\(883\) −20.7145 −0.697100 −0.348550 0.937290i \(-0.613326\pi\)
−0.348550 + 0.937290i \(0.613326\pi\)
\(884\) 6.97187 0.234489
\(885\) 9.55832 0.321299
\(886\) 10.1470 0.340895
\(887\) 33.8950 1.13808 0.569041 0.822309i \(-0.307314\pi\)
0.569041 + 0.822309i \(0.307314\pi\)
\(888\) 11.0174 0.369719
\(889\) −33.4755 −1.12273
\(890\) 11.1978 0.375352
\(891\) 6.87906 0.230457
\(892\) 4.84894 0.162355
\(893\) 8.09691 0.270953
\(894\) 28.5494 0.954835
\(895\) −28.5355 −0.953837
\(896\) −2.77663 −0.0927607
\(897\) −14.7258 −0.491682
\(898\) 5.78601 0.193082
\(899\) 81.8754 2.73070
\(900\) 1.44700 0.0482335
\(901\) 12.5004 0.416447
\(902\) 1.04863 0.0349156
\(903\) −23.6444 −0.786837
\(904\) 3.56486 0.118565
\(905\) 22.8565 0.759774
\(906\) −15.3892 −0.511273
\(907\) −12.9369 −0.429563 −0.214781 0.976662i \(-0.568904\pi\)
−0.214781 + 0.976662i \(0.568904\pi\)
\(908\) −14.6540 −0.486311
\(909\) 13.1844 0.437298
\(910\) −7.23235 −0.239750
\(911\) 11.8616 0.392994 0.196497 0.980504i \(-0.437043\pi\)
0.196497 + 0.980504i \(0.437043\pi\)
\(912\) −1.46114 −0.0483833
\(913\) 12.6968 0.420203
\(914\) −23.9897 −0.793509
\(915\) 9.26113 0.306164
\(916\) −27.3808 −0.904686
\(917\) 13.9463 0.460547
\(918\) 27.5729 0.910041
\(919\) 38.9994 1.28647 0.643235 0.765669i \(-0.277592\pi\)
0.643235 + 0.765669i \(0.277592\pi\)
\(920\) 12.8741 0.424446
\(921\) 28.9520 0.954000
\(922\) −34.5981 −1.13943
\(923\) −0.605593 −0.0199333
\(924\) −4.93394 −0.162315
\(925\) 12.6127 0.414703
\(926\) −6.30630 −0.207238
\(927\) 0.983951 0.0323172
\(928\) −10.2436 −0.336263
\(929\) −5.05712 −0.165919 −0.0829594 0.996553i \(-0.526437\pi\)
−0.0829594 + 0.996553i \(0.526437\pi\)
\(930\) 21.3028 0.698547
\(931\) 0.709678 0.0232587
\(932\) −11.7025 −0.383329
\(933\) −21.8059 −0.713893
\(934\) 7.16190 0.234344
\(935\) −10.8308 −0.354206
\(936\) −1.23528 −0.0403763
\(937\) 46.6251 1.52317 0.761587 0.648062i \(-0.224420\pi\)
0.761587 + 0.648062i \(0.224420\pi\)
\(938\) −41.1529 −1.34369
\(939\) 26.5910 0.867765
\(940\) 14.7695 0.481726
\(941\) 57.4611 1.87318 0.936589 0.350429i \(-0.113964\pi\)
0.936589 + 0.350429i \(0.113964\pi\)
\(942\) 15.2514 0.496919
\(943\) −6.08570 −0.198178
\(944\) −3.58628 −0.116723
\(945\) −28.6030 −0.930457
\(946\) 7.08763 0.230439
\(947\) −13.2264 −0.429800 −0.214900 0.976636i \(-0.568943\pi\)
−0.214900 + 0.976636i \(0.568943\pi\)
\(948\) −15.1008 −0.490452
\(949\) 11.6615 0.378549
\(950\) −1.67272 −0.0542701
\(951\) 42.7889 1.38752
\(952\) −13.5566 −0.439373
\(953\) 32.1059 1.04001 0.520007 0.854162i \(-0.325929\pi\)
0.520007 + 0.854162i \(0.325929\pi\)
\(954\) −2.21481 −0.0717072
\(955\) −47.9101 −1.55033
\(956\) 13.8794 0.448891
\(957\) −18.2024 −0.588401
\(958\) −26.1422 −0.844616
\(959\) −18.3397 −0.592218
\(960\) −2.66525 −0.0860205
\(961\) 32.8851 1.06081
\(962\) −10.7672 −0.347148
\(963\) 3.21250 0.103522
\(964\) −16.4042 −0.528343
\(965\) −2.13115 −0.0686041
\(966\) 28.6340 0.921284
\(967\) −6.13235 −0.197203 −0.0986015 0.995127i \(-0.531437\pi\)
−0.0986015 + 0.995127i \(0.531437\pi\)
\(968\) −9.52101 −0.306017
\(969\) −7.13388 −0.229173
\(970\) −16.4830 −0.529237
\(971\) 47.2746 1.51711 0.758556 0.651607i \(-0.225905\pi\)
0.758556 + 0.651607i \(0.225905\pi\)
\(972\) −8.67731 −0.278325
\(973\) 23.6346 0.757689
\(974\) 22.2984 0.714486
\(975\) 3.49004 0.111771
\(976\) −3.47477 −0.111225
\(977\) 23.7397 0.759502 0.379751 0.925089i \(-0.376010\pi\)
0.379751 + 0.925089i \(0.376010\pi\)
\(978\) −27.0140 −0.863812
\(979\) −7.46572 −0.238605
\(980\) 1.29451 0.0413517
\(981\) 6.64955 0.212304
\(982\) 25.7119 0.820498
\(983\) −11.0704 −0.353092 −0.176546 0.984292i \(-0.556492\pi\)
−0.176546 + 0.984292i \(0.556492\pi\)
\(984\) 1.25989 0.0401637
\(985\) −4.65467 −0.148310
\(986\) −50.0135 −1.59275
\(987\) 32.8496 1.04561
\(988\) 1.42796 0.0454295
\(989\) −41.1329 −1.30795
\(990\) 1.91900 0.0609900
\(991\) 3.96292 0.125886 0.0629431 0.998017i \(-0.479951\pi\)
0.0629431 + 0.998017i \(0.479951\pi\)
\(992\) −7.99282 −0.253772
\(993\) 16.6219 0.527479
\(994\) 1.17756 0.0373499
\(995\) −15.9530 −0.505745
\(996\) 15.2547 0.483364
\(997\) 31.6596 1.00267 0.501335 0.865253i \(-0.332842\pi\)
0.501335 + 0.865253i \(0.332842\pi\)
\(998\) −34.0529 −1.07793
\(999\) −42.5829 −1.34726
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 \(a_p\))