Properties

Label 6034.2.a.n.1.13
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 1.13
Character \(\chi\) = 6034.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+0.632516 q^{3}\) \(+1.00000 q^{4}\) \(-0.321740 q^{5}\) \(-0.632516 q^{6}\) \(-1.00000 q^{7}\) \(-1.00000 q^{8}\) \(-2.59992 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+0.632516 q^{3}\) \(+1.00000 q^{4}\) \(-0.321740 q^{5}\) \(-0.632516 q^{6}\) \(-1.00000 q^{7}\) \(-1.00000 q^{8}\) \(-2.59992 q^{9}\) \(+0.321740 q^{10}\) \(-6.13579 q^{11}\) \(+0.632516 q^{12}\) \(-6.17301 q^{13}\) \(+1.00000 q^{14}\) \(-0.203506 q^{15}\) \(+1.00000 q^{16}\) \(-4.41675 q^{17}\) \(+2.59992 q^{18}\) \(-1.95390 q^{19}\) \(-0.321740 q^{20}\) \(-0.632516 q^{21}\) \(+6.13579 q^{22}\) \(-1.47676 q^{23}\) \(-0.632516 q^{24}\) \(-4.89648 q^{25}\) \(+6.17301 q^{26}\) \(-3.54204 q^{27}\) \(-1.00000 q^{28}\) \(+7.50658 q^{29}\) \(+0.203506 q^{30}\) \(+0.883615 q^{31}\) \(-1.00000 q^{32}\) \(-3.88099 q^{33}\) \(+4.41675 q^{34}\) \(+0.321740 q^{35}\) \(-2.59992 q^{36}\) \(-6.01483 q^{37}\) \(+1.95390 q^{38}\) \(-3.90453 q^{39}\) \(+0.321740 q^{40}\) \(+5.45149 q^{41}\) \(+0.632516 q^{42}\) \(-3.62475 q^{43}\) \(-6.13579 q^{44}\) \(+0.836500 q^{45}\) \(+1.47676 q^{46}\) \(+3.66636 q^{47}\) \(+0.632516 q^{48}\) \(+1.00000 q^{49}\) \(+4.89648 q^{50}\) \(-2.79367 q^{51}\) \(-6.17301 q^{52}\) \(-11.6099 q^{53}\) \(+3.54204 q^{54}\) \(+1.97413 q^{55}\) \(+1.00000 q^{56}\) \(-1.23588 q^{57}\) \(-7.50658 q^{58}\) \(-10.9745 q^{59}\) \(-0.203506 q^{60}\) \(+5.31575 q^{61}\) \(-0.883615 q^{62}\) \(+2.59992 q^{63}\) \(+1.00000 q^{64}\) \(+1.98611 q^{65}\) \(+3.88099 q^{66}\) \(+7.75011 q^{67}\) \(-4.41675 q^{68}\) \(-0.934074 q^{69}\) \(-0.321740 q^{70}\) \(+3.32133 q^{71}\) \(+2.59992 q^{72}\) \(-0.297693 q^{73}\) \(+6.01483 q^{74}\) \(-3.09710 q^{75}\) \(-1.95390 q^{76}\) \(+6.13579 q^{77}\) \(+3.90453 q^{78}\) \(+10.3255 q^{79}\) \(-0.321740 q^{80}\) \(+5.55937 q^{81}\) \(-5.45149 q^{82}\) \(-10.5391 q^{83}\) \(-0.632516 q^{84}\) \(+1.42105 q^{85}\) \(+3.62475 q^{86}\) \(+4.74804 q^{87}\) \(+6.13579 q^{88}\) \(+14.2235 q^{89}\) \(-0.836500 q^{90}\) \(+6.17301 q^{91}\) \(-1.47676 q^{92}\) \(+0.558901 q^{93}\) \(-3.66636 q^{94}\) \(+0.628649 q^{95}\) \(-0.632516 q^{96}\) \(-3.57404 q^{97}\) \(-1.00000 q^{98}\) \(+15.9526 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 24q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 24q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut -\mathstrut 8q^{10} \) \(\mathstrut +\mathstrut 15q^{11} \) \(\mathstrut +\mathstrut 7q^{12} \) \(\mathstrut -\mathstrut 7q^{13} \) \(\mathstrut +\mathstrut 24q^{14} \) \(\mathstrut +\mathstrut 13q^{15} \) \(\mathstrut +\mathstrut 24q^{16} \) \(\mathstrut -\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 19q^{18} \) \(\mathstrut +\mathstrut 6q^{19} \) \(\mathstrut +\mathstrut 8q^{20} \) \(\mathstrut -\mathstrut 7q^{21} \) \(\mathstrut -\mathstrut 15q^{22} \) \(\mathstrut +\mathstrut 3q^{23} \) \(\mathstrut -\mathstrut 7q^{24} \) \(\mathstrut +\mathstrut 12q^{25} \) \(\mathstrut +\mathstrut 7q^{26} \) \(\mathstrut +\mathstrut 22q^{27} \) \(\mathstrut -\mathstrut 24q^{28} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 13q^{30} \) \(\mathstrut +\mathstrut 13q^{31} \) \(\mathstrut -\mathstrut 24q^{32} \) \(\mathstrut -\mathstrut 8q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut +\mathstrut 19q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 6q^{38} \) \(\mathstrut +\mathstrut 7q^{39} \) \(\mathstrut -\mathstrut 8q^{40} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 7q^{42} \) \(\mathstrut -\mathstrut 15q^{43} \) \(\mathstrut +\mathstrut 15q^{44} \) \(\mathstrut +\mathstrut 41q^{45} \) \(\mathstrut -\mathstrut 3q^{46} \) \(\mathstrut +\mathstrut 35q^{47} \) \(\mathstrut +\mathstrut 7q^{48} \) \(\mathstrut +\mathstrut 24q^{49} \) \(\mathstrut -\mathstrut 12q^{50} \) \(\mathstrut +\mathstrut 31q^{51} \) \(\mathstrut -\mathstrut 7q^{52} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 22q^{54} \) \(\mathstrut +\mathstrut 14q^{55} \) \(\mathstrut +\mathstrut 24q^{56} \) \(\mathstrut -\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 5q^{58} \) \(\mathstrut +\mathstrut 35q^{59} \) \(\mathstrut +\mathstrut 13q^{60} \) \(\mathstrut -\mathstrut 7q^{61} \) \(\mathstrut -\mathstrut 13q^{62} \) \(\mathstrut -\mathstrut 19q^{63} \) \(\mathstrut +\mathstrut 24q^{64} \) \(\mathstrut -\mathstrut 4q^{65} \) \(\mathstrut +\mathstrut 8q^{66} \) \(\mathstrut +\mathstrut 10q^{67} \) \(\mathstrut -\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut 6q^{69} \) \(\mathstrut +\mathstrut 8q^{70} \) \(\mathstrut +\mathstrut 58q^{71} \) \(\mathstrut -\mathstrut 19q^{72} \) \(\mathstrut +\mathstrut 9q^{73} \) \(\mathstrut -\mathstrut 2q^{74} \) \(\mathstrut +\mathstrut 7q^{75} \) \(\mathstrut +\mathstrut 6q^{76} \) \(\mathstrut -\mathstrut 15q^{77} \) \(\mathstrut -\mathstrut 7q^{78} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut +\mathstrut 8q^{80} \) \(\mathstrut +\mathstrut 16q^{81} \) \(\mathstrut -\mathstrut 25q^{82} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut -\mathstrut 7q^{84} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut +\mathstrut 15q^{86} \) \(\mathstrut +\mathstrut 30q^{87} \) \(\mathstrut -\mathstrut 15q^{88} \) \(\mathstrut +\mathstrut 45q^{89} \) \(\mathstrut -\mathstrut 41q^{90} \) \(\mathstrut +\mathstrut 7q^{91} \) \(\mathstrut +\mathstrut 3q^{92} \) \(\mathstrut +\mathstrut 25q^{93} \) \(\mathstrut -\mathstrut 35q^{94} \) \(\mathstrut -\mathstrut 10q^{95} \) \(\mathstrut -\mathstrut 7q^{96} \) \(\mathstrut -\mathstrut 9q^{97} \) \(\mathstrut -\mathstrut 24q^{98} \) \(\mathstrut +\mathstrut 64q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 0.632516 0.365183 0.182592 0.983189i \(-0.441551\pi\)
0.182592 + 0.983189i \(0.441551\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.321740 −0.143887 −0.0719433 0.997409i \(-0.522920\pi\)
−0.0719433 + 0.997409i \(0.522920\pi\)
\(6\) −0.632516 −0.258224
\(7\) −1.00000 −0.377964
\(8\) −1.00000 −0.353553
\(9\) −2.59992 −0.866641
\(10\) 0.321740 0.101743
\(11\) −6.13579 −1.85001 −0.925006 0.379953i \(-0.875940\pi\)
−0.925006 + 0.379953i \(0.875940\pi\)
\(12\) 0.632516 0.182592
\(13\) −6.17301 −1.71209 −0.856043 0.516904i \(-0.827084\pi\)
−0.856043 + 0.516904i \(0.827084\pi\)
\(14\) 1.00000 0.267261
\(15\) −0.203506 −0.0525450
\(16\) 1.00000 0.250000
\(17\) −4.41675 −1.07122 −0.535610 0.844466i \(-0.679918\pi\)
−0.535610 + 0.844466i \(0.679918\pi\)
\(18\) 2.59992 0.612808
\(19\) −1.95390 −0.448256 −0.224128 0.974560i \(-0.571953\pi\)
−0.224128 + 0.974560i \(0.571953\pi\)
\(20\) −0.321740 −0.0719433
\(21\) −0.632516 −0.138026
\(22\) 6.13579 1.30816
\(23\) −1.47676 −0.307926 −0.153963 0.988077i \(-0.549204\pi\)
−0.153963 + 0.988077i \(0.549204\pi\)
\(24\) −0.632516 −0.129112
\(25\) −4.89648 −0.979297
\(26\) 6.17301 1.21063
\(27\) −3.54204 −0.681666
\(28\) −1.00000 −0.188982
\(29\) 7.50658 1.39394 0.696969 0.717101i \(-0.254532\pi\)
0.696969 + 0.717101i \(0.254532\pi\)
\(30\) 0.203506 0.0371549
\(31\) 0.883615 0.158702 0.0793510 0.996847i \(-0.474715\pi\)
0.0793510 + 0.996847i \(0.474715\pi\)
\(32\) −1.00000 −0.176777
\(33\) −3.88099 −0.675594
\(34\) 4.41675 0.757466
\(35\) 0.321740 0.0543840
\(36\) −2.59992 −0.433321
\(37\) −6.01483 −0.988831 −0.494416 0.869226i \(-0.664618\pi\)
−0.494416 + 0.869226i \(0.664618\pi\)
\(38\) 1.95390 0.316965
\(39\) −3.90453 −0.625225
\(40\) 0.321740 0.0508716
\(41\) 5.45149 0.851380 0.425690 0.904869i \(-0.360031\pi\)
0.425690 + 0.904869i \(0.360031\pi\)
\(42\) 0.632516 0.0975994
\(43\) −3.62475 −0.552770 −0.276385 0.961047i \(-0.589136\pi\)
−0.276385 + 0.961047i \(0.589136\pi\)
\(44\) −6.13579 −0.925006
\(45\) 0.836500 0.124698
\(46\) 1.47676 0.217736
\(47\) 3.66636 0.534794 0.267397 0.963586i \(-0.413837\pi\)
0.267397 + 0.963586i \(0.413837\pi\)
\(48\) 0.632516 0.0912958
\(49\) 1.00000 0.142857
\(50\) 4.89648 0.692467
\(51\) −2.79367 −0.391191
\(52\) −6.17301 −0.856043
\(53\) −11.6099 −1.59475 −0.797373 0.603487i \(-0.793778\pi\)
−0.797373 + 0.603487i \(0.793778\pi\)
\(54\) 3.54204 0.482011
\(55\) 1.97413 0.266192
\(56\) 1.00000 0.133631
\(57\) −1.23588 −0.163696
\(58\) −7.50658 −0.985663
\(59\) −10.9745 −1.42876 −0.714378 0.699760i \(-0.753290\pi\)
−0.714378 + 0.699760i \(0.753290\pi\)
\(60\) −0.203506 −0.0262725
\(61\) 5.31575 0.680611 0.340306 0.940315i \(-0.389469\pi\)
0.340306 + 0.940315i \(0.389469\pi\)
\(62\) −0.883615 −0.112219
\(63\) 2.59992 0.327560
\(64\) 1.00000 0.125000
\(65\) 1.98611 0.246346
\(66\) 3.88099 0.477717
\(67\) 7.75011 0.946827 0.473414 0.880840i \(-0.343022\pi\)
0.473414 + 0.880840i \(0.343022\pi\)
\(68\) −4.41675 −0.535610
\(69\) −0.934074 −0.112449
\(70\) −0.321740 −0.0384553
\(71\) 3.32133 0.394169 0.197085 0.980386i \(-0.436853\pi\)
0.197085 + 0.980386i \(0.436853\pi\)
\(72\) 2.59992 0.306404
\(73\) −0.297693 −0.0348423 −0.0174212 0.999848i \(-0.505546\pi\)
−0.0174212 + 0.999848i \(0.505546\pi\)
\(74\) 6.01483 0.699209
\(75\) −3.09710 −0.357623
\(76\) −1.95390 −0.224128
\(77\) 6.13579 0.699239
\(78\) 3.90453 0.442101
\(79\) 10.3255 1.16170 0.580852 0.814009i \(-0.302719\pi\)
0.580852 + 0.814009i \(0.302719\pi\)
\(80\) −0.321740 −0.0359716
\(81\) 5.55937 0.617708
\(82\) −5.45149 −0.602017
\(83\) −10.5391 −1.15682 −0.578411 0.815746i \(-0.696327\pi\)
−0.578411 + 0.815746i \(0.696327\pi\)
\(84\) −0.632516 −0.0690132
\(85\) 1.42105 0.154134
\(86\) 3.62475 0.390867
\(87\) 4.74804 0.509043
\(88\) 6.13579 0.654078
\(89\) 14.2235 1.50769 0.753846 0.657051i \(-0.228196\pi\)
0.753846 + 0.657051i \(0.228196\pi\)
\(90\) −0.836500 −0.0881748
\(91\) 6.17301 0.647108
\(92\) −1.47676 −0.153963
\(93\) 0.558901 0.0579553
\(94\) −3.66636 −0.378156
\(95\) 0.628649 0.0644981
\(96\) −0.632516 −0.0645559
\(97\) −3.57404 −0.362889 −0.181444 0.983401i \(-0.558077\pi\)
−0.181444 + 0.983401i \(0.558077\pi\)
\(98\) −1.00000 −0.101015
\(99\) 15.9526 1.60330
\(100\) −4.89648 −0.489648
\(101\) −6.37269 −0.634106 −0.317053 0.948408i \(-0.602693\pi\)
−0.317053 + 0.948408i \(0.602693\pi\)
\(102\) 2.79367 0.276614
\(103\) 3.02702 0.298261 0.149131 0.988818i \(-0.452353\pi\)
0.149131 + 0.988818i \(0.452353\pi\)
\(104\) 6.17301 0.605314
\(105\) 0.203506 0.0198601
\(106\) 11.6099 1.12766
\(107\) −1.85798 −0.179618 −0.0898090 0.995959i \(-0.528626\pi\)
−0.0898090 + 0.995959i \(0.528626\pi\)
\(108\) −3.54204 −0.340833
\(109\) −9.44677 −0.904837 −0.452418 0.891806i \(-0.649439\pi\)
−0.452418 + 0.891806i \(0.649439\pi\)
\(110\) −1.97413 −0.188226
\(111\) −3.80447 −0.361105
\(112\) −1.00000 −0.0944911
\(113\) 12.4241 1.16876 0.584380 0.811480i \(-0.301338\pi\)
0.584380 + 0.811480i \(0.301338\pi\)
\(114\) 1.23588 0.115750
\(115\) 0.475133 0.0443064
\(116\) 7.50658 0.696969
\(117\) 16.0494 1.48376
\(118\) 10.9745 1.01028
\(119\) 4.41675 0.404883
\(120\) 0.203506 0.0185775
\(121\) 26.6480 2.42254
\(122\) −5.31575 −0.481265
\(123\) 3.44816 0.310910
\(124\) 0.883615 0.0793510
\(125\) 3.18410 0.284794
\(126\) −2.59992 −0.231620
\(127\) −9.62882 −0.854419 −0.427210 0.904153i \(-0.640503\pi\)
−0.427210 + 0.904153i \(0.640503\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −2.29272 −0.201862
\(130\) −1.98611 −0.174193
\(131\) 14.6100 1.27648 0.638242 0.769836i \(-0.279662\pi\)
0.638242 + 0.769836i \(0.279662\pi\)
\(132\) −3.88099 −0.337797
\(133\) 1.95390 0.169425
\(134\) −7.75011 −0.669508
\(135\) 1.13962 0.0980826
\(136\) 4.41675 0.378733
\(137\) 4.48617 0.383280 0.191640 0.981465i \(-0.438619\pi\)
0.191640 + 0.981465i \(0.438619\pi\)
\(138\) 0.934074 0.0795137
\(139\) −13.0596 −1.10770 −0.553852 0.832615i \(-0.686842\pi\)
−0.553852 + 0.832615i \(0.686842\pi\)
\(140\) 0.321740 0.0271920
\(141\) 2.31903 0.195298
\(142\) −3.32133 −0.278720
\(143\) 37.8763 3.16738
\(144\) −2.59992 −0.216660
\(145\) −2.41517 −0.200569
\(146\) 0.297693 0.0246372
\(147\) 0.632516 0.0521691
\(148\) −6.01483 −0.494416
\(149\) −5.14666 −0.421631 −0.210815 0.977526i \(-0.567612\pi\)
−0.210815 + 0.977526i \(0.567612\pi\)
\(150\) 3.09710 0.252878
\(151\) 13.4881 1.09764 0.548822 0.835939i \(-0.315076\pi\)
0.548822 + 0.835939i \(0.315076\pi\)
\(152\) 1.95390 0.158483
\(153\) 11.4832 0.928363
\(154\) −6.13579 −0.494436
\(155\) −0.284294 −0.0228351
\(156\) −3.90453 −0.312613
\(157\) −5.47952 −0.437313 −0.218657 0.975802i \(-0.570167\pi\)
−0.218657 + 0.975802i \(0.570167\pi\)
\(158\) −10.3255 −0.821449
\(159\) −7.34347 −0.582375
\(160\) 0.321740 0.0254358
\(161\) 1.47676 0.116385
\(162\) −5.55937 −0.436785
\(163\) −11.4391 −0.895983 −0.447991 0.894038i \(-0.647860\pi\)
−0.447991 + 0.894038i \(0.647860\pi\)
\(164\) 5.45149 0.425690
\(165\) 1.24867 0.0972088
\(166\) 10.5391 0.817996
\(167\) −8.45450 −0.654228 −0.327114 0.944985i \(-0.606076\pi\)
−0.327114 + 0.944985i \(0.606076\pi\)
\(168\) 0.632516 0.0487997
\(169\) 25.1061 1.93124
\(170\) −1.42105 −0.108989
\(171\) 5.08000 0.388477
\(172\) −3.62475 −0.276385
\(173\) −12.9740 −0.986398 −0.493199 0.869916i \(-0.664173\pi\)
−0.493199 + 0.869916i \(0.664173\pi\)
\(174\) −4.74804 −0.359948
\(175\) 4.89648 0.370139
\(176\) −6.13579 −0.462503
\(177\) −6.94154 −0.521758
\(178\) −14.2235 −1.06610
\(179\) 18.4980 1.38260 0.691301 0.722567i \(-0.257038\pi\)
0.691301 + 0.722567i \(0.257038\pi\)
\(180\) 0.836500 0.0623490
\(181\) −7.81010 −0.580520 −0.290260 0.956948i \(-0.593742\pi\)
−0.290260 + 0.956948i \(0.593742\pi\)
\(182\) −6.17301 −0.457574
\(183\) 3.36230 0.248548
\(184\) 1.47676 0.108868
\(185\) 1.93521 0.142280
\(186\) −0.558901 −0.0409806
\(187\) 27.1003 1.98177
\(188\) 3.66636 0.267397
\(189\) 3.54204 0.257646
\(190\) −0.628649 −0.0456070
\(191\) −13.4955 −0.976503 −0.488252 0.872703i \(-0.662365\pi\)
−0.488252 + 0.872703i \(0.662365\pi\)
\(192\) 0.632516 0.0456479
\(193\) −0.696223 −0.0501152 −0.0250576 0.999686i \(-0.507977\pi\)
−0.0250576 + 0.999686i \(0.507977\pi\)
\(194\) 3.57404 0.256601
\(195\) 1.25624 0.0899615
\(196\) 1.00000 0.0714286
\(197\) −8.60111 −0.612804 −0.306402 0.951902i \(-0.599125\pi\)
−0.306402 + 0.951902i \(0.599125\pi\)
\(198\) −15.9526 −1.13370
\(199\) −11.1122 −0.787724 −0.393862 0.919170i \(-0.628861\pi\)
−0.393862 + 0.919170i \(0.628861\pi\)
\(200\) 4.89648 0.346234
\(201\) 4.90207 0.345766
\(202\) 6.37269 0.448381
\(203\) −7.50658 −0.526859
\(204\) −2.79367 −0.195596
\(205\) −1.75396 −0.122502
\(206\) −3.02702 −0.210902
\(207\) 3.83946 0.266861
\(208\) −6.17301 −0.428022
\(209\) 11.9888 0.829279
\(210\) −0.203506 −0.0140432
\(211\) −28.9543 −1.99329 −0.996647 0.0818258i \(-0.973925\pi\)
−0.996647 + 0.0818258i \(0.973925\pi\)
\(212\) −11.6099 −0.797373
\(213\) 2.10079 0.143944
\(214\) 1.85798 0.127009
\(215\) 1.16623 0.0795362
\(216\) 3.54204 0.241005
\(217\) −0.883615 −0.0599837
\(218\) 9.44677 0.639816
\(219\) −0.188296 −0.0127238
\(220\) 1.97413 0.133096
\(221\) 27.2647 1.83402
\(222\) 3.80447 0.255340
\(223\) −8.37454 −0.560801 −0.280400 0.959883i \(-0.590467\pi\)
−0.280400 + 0.959883i \(0.590467\pi\)
\(224\) 1.00000 0.0668153
\(225\) 12.7305 0.848699
\(226\) −12.4241 −0.826438
\(227\) 20.3147 1.34833 0.674167 0.738579i \(-0.264503\pi\)
0.674167 + 0.738579i \(0.264503\pi\)
\(228\) −1.23588 −0.0818479
\(229\) −4.69795 −0.310449 −0.155225 0.987879i \(-0.549610\pi\)
−0.155225 + 0.987879i \(0.549610\pi\)
\(230\) −0.475133 −0.0313293
\(231\) 3.88099 0.255350
\(232\) −7.50658 −0.492831
\(233\) −8.39479 −0.549961 −0.274980 0.961450i \(-0.588671\pi\)
−0.274980 + 0.961450i \(0.588671\pi\)
\(234\) −16.0494 −1.04918
\(235\) −1.17962 −0.0769497
\(236\) −10.9745 −0.714378
\(237\) 6.53102 0.424235
\(238\) −4.41675 −0.286295
\(239\) −15.1964 −0.982973 −0.491487 0.870885i \(-0.663546\pi\)
−0.491487 + 0.870885i \(0.663546\pi\)
\(240\) −0.203506 −0.0131362
\(241\) 25.8121 1.66270 0.831352 0.555747i \(-0.187567\pi\)
0.831352 + 0.555747i \(0.187567\pi\)
\(242\) −26.6480 −1.71300
\(243\) 14.1425 0.907243
\(244\) 5.31575 0.340306
\(245\) −0.321740 −0.0205552
\(246\) −3.44816 −0.219847
\(247\) 12.0615 0.767453
\(248\) −0.883615 −0.0561096
\(249\) −6.66618 −0.422452
\(250\) −3.18410 −0.201380
\(251\) 18.5296 1.16958 0.584790 0.811185i \(-0.301177\pi\)
0.584790 + 0.811185i \(0.301177\pi\)
\(252\) 2.59992 0.163780
\(253\) 9.06109 0.569666
\(254\) 9.62882 0.604166
\(255\) 0.898834 0.0562872
\(256\) 1.00000 0.0625000
\(257\) 10.9871 0.685359 0.342680 0.939452i \(-0.388665\pi\)
0.342680 + 0.939452i \(0.388665\pi\)
\(258\) 2.29272 0.142738
\(259\) 6.01483 0.373743
\(260\) 1.98611 0.123173
\(261\) −19.5165 −1.20804
\(262\) −14.6100 −0.902610
\(263\) −4.06441 −0.250622 −0.125311 0.992117i \(-0.539993\pi\)
−0.125311 + 0.992117i \(0.539993\pi\)
\(264\) 3.88099 0.238858
\(265\) 3.73538 0.229463
\(266\) −1.95390 −0.119802
\(267\) 8.99662 0.550584
\(268\) 7.75011 0.473414
\(269\) −8.60242 −0.524499 −0.262250 0.965000i \(-0.584464\pi\)
−0.262250 + 0.965000i \(0.584464\pi\)
\(270\) −1.13962 −0.0693549
\(271\) −19.0069 −1.15459 −0.577294 0.816537i \(-0.695891\pi\)
−0.577294 + 0.816537i \(0.695891\pi\)
\(272\) −4.41675 −0.267805
\(273\) 3.90453 0.236313
\(274\) −4.48617 −0.271020
\(275\) 30.0438 1.81171
\(276\) −0.934074 −0.0562247
\(277\) −30.6634 −1.84239 −0.921193 0.389105i \(-0.872784\pi\)
−0.921193 + 0.389105i \(0.872784\pi\)
\(278\) 13.0596 0.783264
\(279\) −2.29733 −0.137538
\(280\) −0.321740 −0.0192277
\(281\) −27.5384 −1.64280 −0.821402 0.570350i \(-0.806808\pi\)
−0.821402 + 0.570350i \(0.806808\pi\)
\(282\) −2.31903 −0.138096
\(283\) −1.18924 −0.0706932 −0.0353466 0.999375i \(-0.511254\pi\)
−0.0353466 + 0.999375i \(0.511254\pi\)
\(284\) 3.32133 0.197085
\(285\) 0.397631 0.0235536
\(286\) −37.8763 −2.23968
\(287\) −5.45149 −0.321792
\(288\) 2.59992 0.153202
\(289\) 2.50768 0.147510
\(290\) 2.41517 0.141824
\(291\) −2.26064 −0.132521
\(292\) −0.297693 −0.0174212
\(293\) −9.16357 −0.535342 −0.267671 0.963510i \(-0.586254\pi\)
−0.267671 + 0.963510i \(0.586254\pi\)
\(294\) −0.632516 −0.0368891
\(295\) 3.53093 0.205579
\(296\) 6.01483 0.349605
\(297\) 21.7332 1.26109
\(298\) 5.14666 0.298138
\(299\) 9.11606 0.527195
\(300\) −3.09710 −0.178811
\(301\) 3.62475 0.208927
\(302\) −13.4881 −0.776152
\(303\) −4.03083 −0.231565
\(304\) −1.95390 −0.112064
\(305\) −1.71029 −0.0979309
\(306\) −11.4832 −0.656451
\(307\) −28.0502 −1.60091 −0.800456 0.599391i \(-0.795409\pi\)
−0.800456 + 0.599391i \(0.795409\pi\)
\(308\) 6.13579 0.349619
\(309\) 1.91464 0.108920
\(310\) 0.284294 0.0161468
\(311\) −1.11890 −0.0634471 −0.0317235 0.999497i \(-0.510100\pi\)
−0.0317235 + 0.999497i \(0.510100\pi\)
\(312\) 3.90453 0.221051
\(313\) −10.7012 −0.604865 −0.302432 0.953171i \(-0.597799\pi\)
−0.302432 + 0.953171i \(0.597799\pi\)
\(314\) 5.47952 0.309227
\(315\) −0.836500 −0.0471314
\(316\) 10.3255 0.580852
\(317\) −4.27822 −0.240289 −0.120144 0.992756i \(-0.538336\pi\)
−0.120144 + 0.992756i \(0.538336\pi\)
\(318\) 7.34347 0.411801
\(319\) −46.0589 −2.57880
\(320\) −0.321740 −0.0179858
\(321\) −1.17520 −0.0655935
\(322\) −1.47676 −0.0822966
\(323\) 8.62990 0.480181
\(324\) 5.55937 0.308854
\(325\) 30.2261 1.67664
\(326\) 11.4391 0.633555
\(327\) −5.97524 −0.330431
\(328\) −5.45149 −0.301008
\(329\) −3.66636 −0.202133
\(330\) −1.24867 −0.0687370
\(331\) 1.17775 0.0647351 0.0323675 0.999476i \(-0.489695\pi\)
0.0323675 + 0.999476i \(0.489695\pi\)
\(332\) −10.5391 −0.578411
\(333\) 15.6381 0.856962
\(334\) 8.45450 0.462609
\(335\) −2.49352 −0.136236
\(336\) −0.632516 −0.0345066
\(337\) −7.61369 −0.414744 −0.207372 0.978262i \(-0.566491\pi\)
−0.207372 + 0.978262i \(0.566491\pi\)
\(338\) −25.1061 −1.36559
\(339\) 7.85844 0.426812
\(340\) 1.42105 0.0770670
\(341\) −5.42168 −0.293600
\(342\) −5.08000 −0.274695
\(343\) −1.00000 −0.0539949
\(344\) 3.62475 0.195434
\(345\) 0.300529 0.0161800
\(346\) 12.9740 0.697489
\(347\) 6.02573 0.323478 0.161739 0.986834i \(-0.448290\pi\)
0.161739 + 0.986834i \(0.448290\pi\)
\(348\) 4.74804 0.254521
\(349\) −6.80816 −0.364433 −0.182216 0.983258i \(-0.558327\pi\)
−0.182216 + 0.983258i \(0.558327\pi\)
\(350\) −4.89648 −0.261728
\(351\) 21.8651 1.16707
\(352\) 6.13579 0.327039
\(353\) 12.2006 0.649372 0.324686 0.945822i \(-0.394741\pi\)
0.324686 + 0.945822i \(0.394741\pi\)
\(354\) 6.94154 0.368939
\(355\) −1.06860 −0.0567156
\(356\) 14.2235 0.753846
\(357\) 2.79367 0.147856
\(358\) −18.4980 −0.977648
\(359\) 35.8380 1.89146 0.945729 0.324957i \(-0.105350\pi\)
0.945729 + 0.324957i \(0.105350\pi\)
\(360\) −0.836500 −0.0440874
\(361\) −15.1823 −0.799066
\(362\) 7.81010 0.410490
\(363\) 16.8553 0.884673
\(364\) 6.17301 0.323554
\(365\) 0.0957797 0.00501334
\(366\) −3.36230 −0.175750
\(367\) −32.0340 −1.67216 −0.836081 0.548607i \(-0.815158\pi\)
−0.836081 + 0.548607i \(0.815158\pi\)
\(368\) −1.47676 −0.0769814
\(369\) −14.1735 −0.737841
\(370\) −1.93521 −0.100607
\(371\) 11.6099 0.602757
\(372\) 0.558901 0.0289777
\(373\) 25.7329 1.33240 0.666201 0.745772i \(-0.267919\pi\)
0.666201 + 0.745772i \(0.267919\pi\)
\(374\) −27.1003 −1.40132
\(375\) 2.01399 0.104002
\(376\) −3.66636 −0.189078
\(377\) −46.3383 −2.38654
\(378\) −3.54204 −0.182183
\(379\) −25.3657 −1.30295 −0.651474 0.758671i \(-0.725849\pi\)
−0.651474 + 0.758671i \(0.725849\pi\)
\(380\) 0.628649 0.0322490
\(381\) −6.09038 −0.312020
\(382\) 13.4955 0.690492
\(383\) 21.4946 1.09832 0.549161 0.835717i \(-0.314947\pi\)
0.549161 + 0.835717i \(0.314947\pi\)
\(384\) −0.632516 −0.0322780
\(385\) −1.97413 −0.100611
\(386\) 0.696223 0.0354368
\(387\) 9.42408 0.479053
\(388\) −3.57404 −0.181444
\(389\) 3.47999 0.176443 0.0882213 0.996101i \(-0.471882\pi\)
0.0882213 + 0.996101i \(0.471882\pi\)
\(390\) −1.25624 −0.0636124
\(391\) 6.52248 0.329856
\(392\) −1.00000 −0.0505076
\(393\) 9.24107 0.466150
\(394\) 8.60111 0.433318
\(395\) −3.32211 −0.167154
\(396\) 15.9526 0.801648
\(397\) 33.7381 1.69327 0.846633 0.532178i \(-0.178626\pi\)
0.846633 + 0.532178i \(0.178626\pi\)
\(398\) 11.1122 0.557005
\(399\) 1.23588 0.0618712
\(400\) −4.89648 −0.244824
\(401\) −12.1011 −0.604300 −0.302150 0.953260i \(-0.597704\pi\)
−0.302150 + 0.953260i \(0.597704\pi\)
\(402\) −4.90207 −0.244493
\(403\) −5.45457 −0.271711
\(404\) −6.37269 −0.317053
\(405\) −1.78867 −0.0888799
\(406\) 7.50658 0.372546
\(407\) 36.9057 1.82935
\(408\) 2.79367 0.138307
\(409\) 1.22236 0.0604417 0.0302208 0.999543i \(-0.490379\pi\)
0.0302208 + 0.999543i \(0.490379\pi\)
\(410\) 1.75396 0.0866221
\(411\) 2.83758 0.139967
\(412\) 3.02702 0.149131
\(413\) 10.9745 0.540019
\(414\) −3.83946 −0.188699
\(415\) 3.39087 0.166451
\(416\) 6.17301 0.302657
\(417\) −8.26042 −0.404515
\(418\) −11.9888 −0.586389
\(419\) 5.23734 0.255861 0.127931 0.991783i \(-0.459167\pi\)
0.127931 + 0.991783i \(0.459167\pi\)
\(420\) 0.203506 0.00993007
\(421\) −6.17262 −0.300835 −0.150418 0.988623i \(-0.548062\pi\)
−0.150418 + 0.988623i \(0.548062\pi\)
\(422\) 28.9543 1.40947
\(423\) −9.53226 −0.463474
\(424\) 11.6099 0.563828
\(425\) 21.6265 1.04904
\(426\) −2.10079 −0.101784
\(427\) −5.31575 −0.257247
\(428\) −1.85798 −0.0898090
\(429\) 23.9574 1.15667
\(430\) −1.16623 −0.0562406
\(431\) 1.00000 0.0481683
\(432\) −3.54204 −0.170417
\(433\) −27.5362 −1.32330 −0.661652 0.749811i \(-0.730144\pi\)
−0.661652 + 0.749811i \(0.730144\pi\)
\(434\) 0.883615 0.0424149
\(435\) −1.52763 −0.0732444
\(436\) −9.44677 −0.452418
\(437\) 2.88545 0.138030
\(438\) 0.188296 0.00899711
\(439\) −13.7298 −0.655289 −0.327645 0.944801i \(-0.606255\pi\)
−0.327645 + 0.944801i \(0.606255\pi\)
\(440\) −1.97413 −0.0941130
\(441\) −2.59992 −0.123806
\(442\) −27.2647 −1.29685
\(443\) −3.62468 −0.172214 −0.0861068 0.996286i \(-0.527443\pi\)
−0.0861068 + 0.996286i \(0.527443\pi\)
\(444\) −3.80447 −0.180552
\(445\) −4.57628 −0.216937
\(446\) 8.37454 0.396546
\(447\) −3.25535 −0.153973
\(448\) −1.00000 −0.0472456
\(449\) 27.5415 1.29976 0.649882 0.760035i \(-0.274818\pi\)
0.649882 + 0.760035i \(0.274818\pi\)
\(450\) −12.7305 −0.600121
\(451\) −33.4492 −1.57506
\(452\) 12.4241 0.584380
\(453\) 8.53143 0.400841
\(454\) −20.3147 −0.953416
\(455\) −1.98611 −0.0931101
\(456\) 1.23588 0.0578752
\(457\) 7.70717 0.360526 0.180263 0.983618i \(-0.442305\pi\)
0.180263 + 0.983618i \(0.442305\pi\)
\(458\) 4.69795 0.219521
\(459\) 15.6443 0.730214
\(460\) 0.475133 0.0221532
\(461\) −7.23951 −0.337178 −0.168589 0.985686i \(-0.553921\pi\)
−0.168589 + 0.985686i \(0.553921\pi\)
\(462\) −3.88099 −0.180560
\(463\) −28.3503 −1.31755 −0.658775 0.752340i \(-0.728925\pi\)
−0.658775 + 0.752340i \(0.728925\pi\)
\(464\) 7.50658 0.348484
\(465\) −0.179821 −0.00833899
\(466\) 8.39479 0.388881
\(467\) −36.0164 −1.66664 −0.833320 0.552791i \(-0.813563\pi\)
−0.833320 + 0.552791i \(0.813563\pi\)
\(468\) 16.0494 0.741882
\(469\) −7.75011 −0.357867
\(470\) 1.17962 0.0544116
\(471\) −3.46589 −0.159700
\(472\) 10.9745 0.505141
\(473\) 22.2408 1.02263
\(474\) −6.53102 −0.299979
\(475\) 9.56726 0.438976
\(476\) 4.41675 0.202441
\(477\) 30.1849 1.38207
\(478\) 15.1964 0.695067
\(479\) 22.3916 1.02310 0.511548 0.859254i \(-0.329072\pi\)
0.511548 + 0.859254i \(0.329072\pi\)
\(480\) 0.203506 0.00928873
\(481\) 37.1296 1.69296
\(482\) −25.8121 −1.17571
\(483\) 0.934074 0.0425019
\(484\) 26.6480 1.21127
\(485\) 1.14991 0.0522148
\(486\) −14.1425 −0.641518
\(487\) 14.9153 0.675878 0.337939 0.941168i \(-0.390270\pi\)
0.337939 + 0.941168i \(0.390270\pi\)
\(488\) −5.31575 −0.240632
\(489\) −7.23544 −0.327198
\(490\) 0.321740 0.0145347
\(491\) 26.1480 1.18004 0.590021 0.807388i \(-0.299119\pi\)
0.590021 + 0.807388i \(0.299119\pi\)
\(492\) 3.44816 0.155455
\(493\) −33.1547 −1.49321
\(494\) −12.0615 −0.542671
\(495\) −5.13259 −0.230693
\(496\) 0.883615 0.0396755
\(497\) −3.32133 −0.148982
\(498\) 6.66618 0.298719
\(499\) 7.04939 0.315574 0.157787 0.987473i \(-0.449564\pi\)
0.157787 + 0.987473i \(0.449564\pi\)
\(500\) 3.18410 0.142397
\(501\) −5.34761 −0.238913
\(502\) −18.5296 −0.827018
\(503\) 34.3551 1.53182 0.765909 0.642948i \(-0.222289\pi\)
0.765909 + 0.642948i \(0.222289\pi\)
\(504\) −2.59992 −0.115810
\(505\) 2.05035 0.0912393
\(506\) −9.06109 −0.402815
\(507\) 15.8800 0.705256
\(508\) −9.62882 −0.427210
\(509\) −25.2305 −1.11832 −0.559160 0.829060i \(-0.688876\pi\)
−0.559160 + 0.829060i \(0.688876\pi\)
\(510\) −0.898834 −0.0398011
\(511\) 0.297693 0.0131692
\(512\) −1.00000 −0.0441942
\(513\) 6.92081 0.305561
\(514\) −10.9871 −0.484622
\(515\) −0.973914 −0.0429158
\(516\) −2.29272 −0.100931
\(517\) −22.4960 −0.989375
\(518\) −6.01483 −0.264276
\(519\) −8.20629 −0.360216
\(520\) −1.98611 −0.0870965
\(521\) −13.1434 −0.575825 −0.287912 0.957657i \(-0.592961\pi\)
−0.287912 + 0.957657i \(0.592961\pi\)
\(522\) 19.5165 0.854216
\(523\) −9.64825 −0.421889 −0.210944 0.977498i \(-0.567654\pi\)
−0.210944 + 0.977498i \(0.567654\pi\)
\(524\) 14.6100 0.638242
\(525\) 3.09710 0.135169
\(526\) 4.06441 0.177217
\(527\) −3.90271 −0.170005
\(528\) −3.88099 −0.168898
\(529\) −20.8192 −0.905182
\(530\) −3.73538 −0.162255
\(531\) 28.5328 1.23822
\(532\) 1.95390 0.0847125
\(533\) −33.6522 −1.45764
\(534\) −8.99662 −0.389322
\(535\) 0.597788 0.0258446
\(536\) −7.75011 −0.334754
\(537\) 11.7003 0.504904
\(538\) 8.60242 0.370877
\(539\) −6.13579 −0.264287
\(540\) 1.13962 0.0490413
\(541\) 28.9398 1.24422 0.622109 0.782930i \(-0.286276\pi\)
0.622109 + 0.782930i \(0.286276\pi\)
\(542\) 19.0069 0.816417
\(543\) −4.94001 −0.211996
\(544\) 4.41675 0.189367
\(545\) 3.03941 0.130194
\(546\) −3.90453 −0.167099
\(547\) 29.8837 1.27773 0.638867 0.769317i \(-0.279403\pi\)
0.638867 + 0.769317i \(0.279403\pi\)
\(548\) 4.48617 0.191640
\(549\) −13.8205 −0.589846
\(550\) −30.0438 −1.28107
\(551\) −14.6671 −0.624841
\(552\) 0.934074 0.0397568
\(553\) −10.3255 −0.439083
\(554\) 30.6634 1.30276
\(555\) 1.22405 0.0519581
\(556\) −13.0596 −0.553852
\(557\) 17.1092 0.724942 0.362471 0.931995i \(-0.381933\pi\)
0.362471 + 0.931995i \(0.381933\pi\)
\(558\) 2.29733 0.0972538
\(559\) 22.3757 0.946390
\(560\) 0.321740 0.0135960
\(561\) 17.1414 0.723709
\(562\) 27.5384 1.16164
\(563\) 4.80060 0.202321 0.101161 0.994870i \(-0.467744\pi\)
0.101161 + 0.994870i \(0.467744\pi\)
\(564\) 2.31903 0.0976489
\(565\) −3.99733 −0.168169
\(566\) 1.18924 0.0499876
\(567\) −5.55937 −0.233472
\(568\) −3.32133 −0.139360
\(569\) 26.4806 1.11013 0.555063 0.831808i \(-0.312694\pi\)
0.555063 + 0.831808i \(0.312694\pi\)
\(570\) −0.397631 −0.0166549
\(571\) −30.2918 −1.26767 −0.633837 0.773467i \(-0.718521\pi\)
−0.633837 + 0.773467i \(0.718521\pi\)
\(572\) 37.8763 1.58369
\(573\) −8.53615 −0.356603
\(574\) 5.45149 0.227541
\(575\) 7.23093 0.301551
\(576\) −2.59992 −0.108330
\(577\) −0.526807 −0.0219313 −0.0109656 0.999940i \(-0.503491\pi\)
−0.0109656 + 0.999940i \(0.503491\pi\)
\(578\) −2.50768 −0.104306
\(579\) −0.440372 −0.0183012
\(580\) −2.41517 −0.100284
\(581\) 10.5391 0.437237
\(582\) 2.26064 0.0937065
\(583\) 71.2361 2.95030
\(584\) 0.297693 0.0123186
\(585\) −5.16372 −0.213494
\(586\) 9.16357 0.378544
\(587\) −0.581325 −0.0239938 −0.0119969 0.999928i \(-0.503819\pi\)
−0.0119969 + 0.999928i \(0.503819\pi\)
\(588\) 0.632516 0.0260845
\(589\) −1.72650 −0.0711391
\(590\) −3.53093 −0.145366
\(591\) −5.44034 −0.223786
\(592\) −6.01483 −0.247208
\(593\) −36.5333 −1.50024 −0.750122 0.661300i \(-0.770005\pi\)
−0.750122 + 0.661300i \(0.770005\pi\)
\(594\) −21.7332 −0.891726
\(595\) −1.42105 −0.0582572
\(596\) −5.14666 −0.210815
\(597\) −7.02865 −0.287664
\(598\) −9.11606 −0.372783
\(599\) −20.0761 −0.820287 −0.410143 0.912021i \(-0.634521\pi\)
−0.410143 + 0.912021i \(0.634521\pi\)
\(600\) 3.09710 0.126439
\(601\) −23.5206 −0.959425 −0.479713 0.877426i \(-0.659259\pi\)
−0.479713 + 0.877426i \(0.659259\pi\)
\(602\) −3.62475 −0.147734
\(603\) −20.1497 −0.820559
\(604\) 13.4881 0.548822
\(605\) −8.57372 −0.348571
\(606\) 4.03083 0.163741
\(607\) 20.3789 0.827156 0.413578 0.910469i \(-0.364279\pi\)
0.413578 + 0.910469i \(0.364279\pi\)
\(608\) 1.95390 0.0792413
\(609\) −4.74804 −0.192400
\(610\) 1.71029 0.0692476
\(611\) −22.6325 −0.915613
\(612\) 11.4832 0.464181
\(613\) 9.08688 0.367016 0.183508 0.983018i \(-0.441255\pi\)
0.183508 + 0.983018i \(0.441255\pi\)
\(614\) 28.0502 1.13202
\(615\) −1.10941 −0.0447358
\(616\) −6.13579 −0.247218
\(617\) −12.4079 −0.499522 −0.249761 0.968308i \(-0.580352\pi\)
−0.249761 + 0.968308i \(0.580352\pi\)
\(618\) −1.91464 −0.0770181
\(619\) −14.9496 −0.600877 −0.300439 0.953801i \(-0.597133\pi\)
−0.300439 + 0.953801i \(0.597133\pi\)
\(620\) −0.284294 −0.0114175
\(621\) 5.23074 0.209903
\(622\) 1.11890 0.0448638
\(623\) −14.2235 −0.569854
\(624\) −3.90453 −0.156306
\(625\) 23.4580 0.938319
\(626\) 10.7012 0.427704
\(627\) 7.58308 0.302839
\(628\) −5.47952 −0.218657
\(629\) 26.5660 1.05925
\(630\) 0.836500 0.0333269
\(631\) 42.0127 1.67250 0.836251 0.548348i \(-0.184743\pi\)
0.836251 + 0.548348i \(0.184743\pi\)
\(632\) −10.3255 −0.410724
\(633\) −18.3140 −0.727918
\(634\) 4.27822 0.169910
\(635\) 3.09798 0.122939
\(636\) −7.34347 −0.291187
\(637\) −6.17301 −0.244584
\(638\) 46.0589 1.82349
\(639\) −8.63520 −0.341603
\(640\) 0.321740 0.0127179
\(641\) −13.3344 −0.526676 −0.263338 0.964704i \(-0.584823\pi\)
−0.263338 + 0.964704i \(0.584823\pi\)
\(642\) 1.17520 0.0463816
\(643\) 4.62498 0.182392 0.0911958 0.995833i \(-0.470931\pi\)
0.0911958 + 0.995833i \(0.470931\pi\)
\(644\) 1.47676 0.0581925
\(645\) 0.737659 0.0290453
\(646\) −8.62990 −0.339539
\(647\) 11.8158 0.464528 0.232264 0.972653i \(-0.425387\pi\)
0.232264 + 0.972653i \(0.425387\pi\)
\(648\) −5.55937 −0.218393
\(649\) 67.3372 2.64321
\(650\) −30.2261 −1.18556
\(651\) −0.558901 −0.0219050
\(652\) −11.4391 −0.447991
\(653\) −6.96223 −0.272453 −0.136227 0.990678i \(-0.543498\pi\)
−0.136227 + 0.990678i \(0.543498\pi\)
\(654\) 5.97524 0.233650
\(655\) −4.70063 −0.183669
\(656\) 5.45149 0.212845
\(657\) 0.773979 0.0301958
\(658\) 3.66636 0.142930
\(659\) 17.9936 0.700933 0.350466 0.936575i \(-0.386023\pi\)
0.350466 + 0.936575i \(0.386023\pi\)
\(660\) 1.24867 0.0486044
\(661\) −37.6774 −1.46548 −0.732741 0.680508i \(-0.761759\pi\)
−0.732741 + 0.680508i \(0.761759\pi\)
\(662\) −1.17775 −0.0457746
\(663\) 17.2453 0.669753
\(664\) 10.5391 0.408998
\(665\) −0.628649 −0.0243780
\(666\) −15.6381 −0.605963
\(667\) −11.0854 −0.429229
\(668\) −8.45450 −0.327114
\(669\) −5.29703 −0.204795
\(670\) 2.49352 0.0963332
\(671\) −32.6163 −1.25914
\(672\) 0.632516 0.0243998
\(673\) −11.4214 −0.440262 −0.220131 0.975470i \(-0.570648\pi\)
−0.220131 + 0.975470i \(0.570648\pi\)
\(674\) 7.61369 0.293268
\(675\) 17.3436 0.667554
\(676\) 25.1061 0.965620
\(677\) 46.1621 1.77415 0.887077 0.461622i \(-0.152732\pi\)
0.887077 + 0.461622i \(0.152732\pi\)
\(678\) −7.85844 −0.301801
\(679\) 3.57404 0.137159
\(680\) −1.42105 −0.0544946
\(681\) 12.8494 0.492389
\(682\) 5.42168 0.207607
\(683\) 16.0903 0.615680 0.307840 0.951438i \(-0.400394\pi\)
0.307840 + 0.951438i \(0.400394\pi\)
\(684\) 5.08000 0.194239
\(685\) −1.44338 −0.0551488
\(686\) 1.00000 0.0381802
\(687\) −2.97153 −0.113371
\(688\) −3.62475 −0.138192
\(689\) 71.6682 2.73034
\(690\) −0.300529 −0.0114410
\(691\) 31.2068 1.18716 0.593581 0.804774i \(-0.297714\pi\)
0.593581 + 0.804774i \(0.297714\pi\)
\(692\) −12.9740 −0.493199
\(693\) −15.9526 −0.605989
\(694\) −6.02573 −0.228734
\(695\) 4.20181 0.159384
\(696\) −4.74804 −0.179974
\(697\) −24.0779 −0.912015
\(698\) 6.80816 0.257693
\(699\) −5.30984 −0.200837
\(700\) 4.89648 0.185070
\(701\) −20.4699 −0.773136 −0.386568 0.922261i \(-0.626340\pi\)
−0.386568 + 0.922261i \(0.626340\pi\)
\(702\) −21.8651 −0.825244
\(703\) 11.7524 0.443250
\(704\) −6.13579 −0.231251
\(705\) −0.746126 −0.0281007
\(706\) −12.2006 −0.459176
\(707\) 6.37269 0.239670
\(708\) −6.94154 −0.260879
\(709\) 13.6881 0.514068 0.257034 0.966402i \(-0.417255\pi\)
0.257034 + 0.966402i \(0.417255\pi\)
\(710\) 1.06860 0.0401040
\(711\) −26.8454 −1.00678
\(712\) −14.2235 −0.533050
\(713\) −1.30489 −0.0488684
\(714\) −2.79367 −0.104550
\(715\) −12.1863 −0.455743
\(716\) 18.4980 0.691301
\(717\) −9.61197 −0.358965
\(718\) −35.8380 −1.33746
\(719\) −28.8229 −1.07491 −0.537457 0.843291i \(-0.680615\pi\)
−0.537457 + 0.843291i \(0.680615\pi\)
\(720\) 0.836500 0.0311745
\(721\) −3.02702 −0.112732
\(722\) 15.1823 0.565025
\(723\) 16.3266 0.607192
\(724\) −7.81010 −0.290260
\(725\) −36.7559 −1.36508
\(726\) −16.8553 −0.625558
\(727\) 33.8736 1.25630 0.628152 0.778091i \(-0.283812\pi\)
0.628152 + 0.778091i \(0.283812\pi\)
\(728\) −6.17301 −0.228787
\(729\) −7.73274 −0.286398
\(730\) −0.0957797 −0.00354497
\(731\) 16.0096 0.592138
\(732\) 3.36230 0.124274
\(733\) 20.6247 0.761791 0.380896 0.924618i \(-0.375616\pi\)
0.380896 + 0.924618i \(0.375616\pi\)
\(734\) 32.0340 1.18240
\(735\) −0.203506 −0.00750643
\(736\) 1.47676 0.0544341
\(737\) −47.5531 −1.75164
\(738\) 14.1735 0.521733
\(739\) 38.7895 1.42690 0.713448 0.700708i \(-0.247132\pi\)
0.713448 + 0.700708i \(0.247132\pi\)
\(740\) 1.93521 0.0711398
\(741\) 7.62908 0.280261
\(742\) −11.6099 −0.426214
\(743\) 16.3465 0.599697 0.299848 0.953987i \(-0.403064\pi\)
0.299848 + 0.953987i \(0.403064\pi\)
\(744\) −0.558901 −0.0204903
\(745\) 1.65589 0.0606670
\(746\) −25.7329 −0.942150
\(747\) 27.4010 1.00255
\(748\) 27.1003 0.990884
\(749\) 1.85798 0.0678892
\(750\) −2.01399 −0.0735406
\(751\) −48.9778 −1.78723 −0.893613 0.448838i \(-0.851838\pi\)
−0.893613 + 0.448838i \(0.851838\pi\)
\(752\) 3.66636 0.133698
\(753\) 11.7203 0.427111
\(754\) 46.3383 1.68754
\(755\) −4.33966 −0.157936
\(756\) 3.54204 0.128823
\(757\) −6.59531 −0.239711 −0.119855 0.992791i \(-0.538243\pi\)
−0.119855 + 0.992791i \(0.538243\pi\)
\(758\) 25.3657 0.921323
\(759\) 5.73129 0.208033
\(760\) −0.628649 −0.0228035
\(761\) 17.9108 0.649265 0.324632 0.945840i \(-0.394759\pi\)
0.324632 + 0.945840i \(0.394759\pi\)
\(762\) 6.09038 0.220631
\(763\) 9.44677 0.341996
\(764\) −13.4955 −0.488252
\(765\) −3.69461 −0.133579
\(766\) −21.4946 −0.776631
\(767\) 67.7456 2.44615
\(768\) 0.632516 0.0228240
\(769\) −37.5827 −1.35527 −0.677634 0.735400i \(-0.736994\pi\)
−0.677634 + 0.735400i \(0.736994\pi\)
\(770\) 1.97413 0.0711428
\(771\) 6.94955 0.250282
\(772\) −0.696223 −0.0250576
\(773\) −5.64442 −0.203016 −0.101508 0.994835i \(-0.532367\pi\)
−0.101508 + 0.994835i \(0.532367\pi\)
\(774\) −9.42408 −0.338742
\(775\) −4.32661 −0.155416
\(776\) 3.57404 0.128301
\(777\) 3.80447 0.136485
\(778\) −3.47999 −0.124764
\(779\) −10.6517 −0.381637
\(780\) 1.25624 0.0449808
\(781\) −20.3790 −0.729217
\(782\) −6.52248 −0.233243
\(783\) −26.5886 −0.950200
\(784\) 1.00000 0.0357143
\(785\) 1.76298 0.0629235
\(786\) −9.24107 −0.329618
\(787\) −19.8074 −0.706058 −0.353029 0.935612i \(-0.614848\pi\)
−0.353029 + 0.935612i \(0.614848\pi\)
\(788\) −8.60111 −0.306402
\(789\) −2.57081 −0.0915231
\(790\) 3.32211 0.118195
\(791\) −12.4241 −0.441750
\(792\) −15.9526 −0.566851
\(793\) −32.8142 −1.16527
\(794\) −33.7381 −1.19732
\(795\) 2.36269 0.0837959
\(796\) −11.1122 −0.393862
\(797\) −10.1365 −0.359053 −0.179527 0.983753i \(-0.557457\pi\)
−0.179527 + 0.983753i \(0.557457\pi\)
\(798\) −1.23588 −0.0437495
\(799\) −16.1934 −0.572881
\(800\) 4.89648 0.173117
\(801\) −36.9801 −1.30663
\(802\) 12.1011 0.427305
\(803\) 1.82658 0.0644587
\(804\) 4.90207 0.172883
\(805\) −0.475133 −0.0167462
\(806\) 5.45457 0.192129
\(807\) −5.44117 −0.191538
\(808\) 6.37269 0.224190
\(809\) −45.3280 −1.59365 −0.796824 0.604211i \(-0.793488\pi\)
−0.796824 + 0.604211i \(0.793488\pi\)
\(810\) 1.78867 0.0628476
\(811\) 37.0438 1.30078 0.650392 0.759598i \(-0.274604\pi\)
0.650392 + 0.759598i \(0.274604\pi\)
\(812\) −7.50658 −0.263429
\(813\) −12.0222 −0.421636
\(814\) −36.9057 −1.29355
\(815\) 3.68043 0.128920
\(816\) −2.79367 −0.0977979
\(817\) 7.08242 0.247783
\(818\) −1.22236 −0.0427387
\(819\) −16.0494 −0.560810
\(820\) −1.75396 −0.0612511
\(821\) 13.6798 0.477430 0.238715 0.971090i \(-0.423274\pi\)
0.238715 + 0.971090i \(0.423274\pi\)
\(822\) −2.83758 −0.0989719
\(823\) 42.9795 1.49817 0.749086 0.662473i \(-0.230493\pi\)
0.749086 + 0.662473i \(0.230493\pi\)
\(824\) −3.02702 −0.105451
\(825\) 19.0032 0.661606
\(826\) −10.9745 −0.381851
\(827\) −52.7622 −1.83472 −0.917360 0.398059i \(-0.869684\pi\)
−0.917360 + 0.398059i \(0.869684\pi\)
\(828\) 3.83946 0.133431
\(829\) 33.3332 1.15771 0.578854 0.815431i \(-0.303500\pi\)
0.578854 + 0.815431i \(0.303500\pi\)
\(830\) −3.39087 −0.117699
\(831\) −19.3951 −0.672809
\(832\) −6.17301 −0.214011
\(833\) −4.41675 −0.153031
\(834\) 8.26042 0.286035
\(835\) 2.72015 0.0941347
\(836\) 11.9888 0.414640
\(837\) −3.12980 −0.108182
\(838\) −5.23734 −0.180921
\(839\) −39.5637 −1.36589 −0.682945 0.730469i \(-0.739301\pi\)
−0.682945 + 0.730469i \(0.739301\pi\)
\(840\) −0.203506 −0.00702162
\(841\) 27.3488 0.943063
\(842\) 6.17262 0.212723
\(843\) −17.4185 −0.599925
\(844\) −28.9543 −0.996647
\(845\) −8.07764 −0.277879
\(846\) 9.53226 0.327726
\(847\) −26.6480 −0.915635
\(848\) −11.6099 −0.398686
\(849\) −0.752216 −0.0258160
\(850\) −21.6265 −0.741784
\(851\) 8.88245 0.304486
\(852\) 2.10079 0.0719720
\(853\) −15.1560 −0.518930 −0.259465 0.965752i \(-0.583546\pi\)
−0.259465 + 0.965752i \(0.583546\pi\)
\(854\) 5.31575 0.181901
\(855\) −1.63444 −0.0558967
\(856\) 1.85798 0.0635046
\(857\) 20.7256 0.707973 0.353987 0.935251i \(-0.384826\pi\)
0.353987 + 0.935251i \(0.384826\pi\)
\(858\) −23.9574 −0.817892
\(859\) 4.74521 0.161904 0.0809522 0.996718i \(-0.474204\pi\)
0.0809522 + 0.996718i \(0.474204\pi\)
\(860\) 1.16623 0.0397681
\(861\) −3.44816 −0.117513
\(862\) −1.00000 −0.0340601
\(863\) 44.3775 1.51063 0.755315 0.655362i \(-0.227484\pi\)
0.755315 + 0.655362i \(0.227484\pi\)
\(864\) 3.54204 0.120503
\(865\) 4.17427 0.141929
\(866\) 27.5362 0.935717
\(867\) 1.58615 0.0538684
\(868\) −0.883615 −0.0299918
\(869\) −63.3549 −2.14917
\(870\) 1.52763 0.0517916
\(871\) −47.8416 −1.62105
\(872\) 9.44677 0.319908
\(873\) 9.29223 0.314494
\(874\) −2.88545 −0.0976017
\(875\) −3.18410 −0.107642
\(876\) −0.188296 −0.00636192
\(877\) 34.5448 1.16649 0.583247 0.812295i \(-0.301782\pi\)
0.583247 + 0.812295i \(0.301782\pi\)
\(878\) 13.7298 0.463360
\(879\) −5.79611 −0.195498
\(880\) 1.97413 0.0665480
\(881\) 39.6145 1.33465 0.667323 0.744768i \(-0.267440\pi\)
0.667323 + 0.744768i \(0.267440\pi\)
\(882\) 2.59992 0.0875440
\(883\) 16.6696 0.560976 0.280488 0.959857i \(-0.409504\pi\)
0.280488 + 0.959857i \(0.409504\pi\)
\(884\) 27.2647 0.917010
\(885\) 2.23337 0.0750740
\(886\) 3.62468 0.121773
\(887\) 9.13035 0.306567 0.153284 0.988182i \(-0.451015\pi\)
0.153284 + 0.988182i \(0.451015\pi\)
\(888\) 3.80447 0.127670
\(889\) 9.62882 0.322940
\(890\) 4.57628 0.153397
\(891\) −34.1112 −1.14277
\(892\) −8.37454 −0.280400
\(893\) −7.16372 −0.239725
\(894\) 3.25535 0.108875
\(895\) −5.95154 −0.198938
\(896\) 1.00000 0.0334077
\(897\) 5.76605 0.192523
\(898\) −27.5415 −0.919072
\(899\) 6.63293 0.221221
\(900\) 12.7305 0.424349
\(901\) 51.2781 1.70832
\(902\) 33.4492 1.11374
\(903\) 2.29272 0.0762968
\(904\) −12.4241 −0.413219
\(905\) 2.51282 0.0835291
\(906\) −8.53143 −0.283438
\(907\) 32.8657 1.09129 0.545644 0.838017i \(-0.316285\pi\)
0.545644 + 0.838017i \(0.316285\pi\)
\(908\) 20.3147 0.674167
\(909\) 16.5685 0.549542
\(910\) 1.98611 0.0658388
\(911\) 24.8503 0.823326 0.411663 0.911336i \(-0.364948\pi\)
0.411663 + 0.911336i \(0.364948\pi\)
\(912\) −1.23588 −0.0409239
\(913\) 64.6660 2.14013
\(914\) −7.70717 −0.254930
\(915\) −1.08179 −0.0357627
\(916\) −4.69795 −0.155225
\(917\) −14.6100 −0.482465
\(918\) −15.6443 −0.516339
\(919\) 50.4332 1.66364 0.831819 0.555047i \(-0.187300\pi\)
0.831819 + 0.555047i \(0.187300\pi\)
\(920\) −0.475133 −0.0156647
\(921\) −17.7422 −0.584627
\(922\) 7.23951 0.238421
\(923\) −20.5026 −0.674851
\(924\) 3.88099 0.127675
\(925\) 29.4515 0.968359
\(926\) 28.3503 0.931649
\(927\) −7.87002 −0.258485
\(928\) −7.50658 −0.246416
\(929\) 40.6057 1.33223 0.666115 0.745849i \(-0.267956\pi\)
0.666115 + 0.745849i \(0.267956\pi\)
\(930\) 0.179821 0.00589656
\(931\) −1.95390 −0.0640366
\(932\) −8.39479 −0.274980
\(933\) −0.707723 −0.0231698
\(934\) 36.0164 1.17849
\(935\) −8.71924 −0.285150
\(936\) −16.0494 −0.524590
\(937\) −6.83152 −0.223176 −0.111588 0.993755i \(-0.535594\pi\)
−0.111588 + 0.993755i \(0.535594\pi\)
\(938\) 7.75011 0.253050
\(939\) −6.76865 −0.220887
\(940\) −1.17962 −0.0384748
\(941\) 51.2219 1.66978 0.834892 0.550413i \(-0.185530\pi\)
0.834892 + 0.550413i \(0.185530\pi\)
\(942\) 3.46589 0.112925
\(943\) −8.05055 −0.262162
\(944\) −10.9745 −0.357189
\(945\) −1.13962 −0.0370718
\(946\) −22.2408 −0.723109
\(947\) 1.34548 0.0437223 0.0218612 0.999761i \(-0.493041\pi\)
0.0218612 + 0.999761i \(0.493041\pi\)
\(948\) 6.53102 0.212118
\(949\) 1.83766 0.0596530
\(950\) −9.56726 −0.310403
\(951\) −2.70604 −0.0877495
\(952\) −4.41675 −0.143148
\(953\) −0.269103 −0.00871709 −0.00435854 0.999991i \(-0.501387\pi\)
−0.00435854 + 0.999991i \(0.501387\pi\)
\(954\) −30.1849 −0.977273
\(955\) 4.34206 0.140506
\(956\) −15.1964 −0.491487
\(957\) −29.1330 −0.941735
\(958\) −22.3916 −0.723439
\(959\) −4.48617 −0.144866
\(960\) −0.203506 −0.00656812
\(961\) −30.2192 −0.974814
\(962\) −37.1296 −1.19711
\(963\) 4.83061 0.155664
\(964\) 25.8121 0.831352
\(965\) 0.224003 0.00721091
\(966\) −0.934074 −0.0300533
\(967\) 10.4188 0.335046 0.167523 0.985868i \(-0.446423\pi\)
0.167523 + 0.985868i \(0.446423\pi\)
\(968\) −26.6480 −0.856498
\(969\) 5.45855 0.175354
\(970\) −1.14991 −0.0369215
\(971\) 33.6892 1.08114 0.540568 0.841300i \(-0.318209\pi\)
0.540568 + 0.841300i \(0.318209\pi\)
\(972\) 14.1425 0.453621
\(973\) 13.0596 0.418672
\(974\) −14.9153 −0.477918
\(975\) 19.1185 0.612281
\(976\) 5.31575 0.170153
\(977\) −40.8827 −1.30795 −0.653976 0.756515i \(-0.726900\pi\)
−0.653976 + 0.756515i \(0.726900\pi\)
\(978\) 7.23544 0.231364
\(979\) −87.2727 −2.78925
\(980\) −0.321740 −0.0102776
\(981\) 24.5609 0.784169
\(982\) −26.1480 −0.834416
\(983\) −7.36339 −0.234856 −0.117428 0.993081i \(-0.537465\pi\)
−0.117428 + 0.993081i \(0.537465\pi\)
\(984\) −3.44816 −0.109923
\(985\) 2.76732 0.0881742
\(986\) 33.1547 1.05586
\(987\) −2.31903 −0.0738157
\(988\) 12.0615 0.383727
\(989\) 5.35289 0.170212
\(990\) 5.13259 0.163124
\(991\) 1.35098 0.0429152 0.0214576 0.999770i \(-0.493169\pi\)
0.0214576 + 0.999770i \(0.493169\pi\)
\(992\) −0.883615 −0.0280548
\(993\) 0.744947 0.0236402
\(994\) 3.32133 0.105346
\(995\) 3.57524 0.113343
\(996\) −6.66618 −0.211226
\(997\) −15.7053 −0.497393 −0.248697 0.968581i \(-0.580002\pi\)
−0.248697 + 0.968581i \(0.580002\pi\)
\(998\) −7.04939 −0.223144
\(999\) 21.3048 0.674053
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 \(a_p\))