Properties

Label 6047.2.a.a.1.15
Level 6047
Weight 2
Character 6047.1
Self dual Yes
Analytic conductor 48.286
Analytic rank 1
Dimension 217
CM No

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Newspace parameters

Level: \( N \) = \( 6047 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6047.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2855381023\)
Analytic rank: \(1\)
Dimension: \(217\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 6047.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.50438 q^{2}\) \(+2.01082 q^{3}\) \(+4.27191 q^{4}\) \(+3.19046 q^{5}\) \(-5.03585 q^{6}\) \(+0.790850 q^{7}\) \(-5.68973 q^{8}\) \(+1.04339 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.50438 q^{2}\) \(+2.01082 q^{3}\) \(+4.27191 q^{4}\) \(+3.19046 q^{5}\) \(-5.03585 q^{6}\) \(+0.790850 q^{7}\) \(-5.68973 q^{8}\) \(+1.04339 q^{9}\) \(-7.99013 q^{10}\) \(-2.85059 q^{11}\) \(+8.59004 q^{12}\) \(-2.42137 q^{13}\) \(-1.98059 q^{14}\) \(+6.41544 q^{15}\) \(+5.70542 q^{16}\) \(+2.08136 q^{17}\) \(-2.61304 q^{18}\) \(+0.238553 q^{19}\) \(+13.6294 q^{20}\) \(+1.59026 q^{21}\) \(+7.13896 q^{22}\) \(+0.00126801 q^{23}\) \(-11.4410 q^{24}\) \(+5.17905 q^{25}\) \(+6.06402 q^{26}\) \(-3.93439 q^{27}\) \(+3.37844 q^{28}\) \(-9.31384 q^{29}\) \(-16.0667 q^{30}\) \(-9.00065 q^{31}\) \(-2.90906 q^{32}\) \(-5.73202 q^{33}\) \(-5.21251 q^{34}\) \(+2.52318 q^{35}\) \(+4.45726 q^{36}\) \(-0.877078 q^{37}\) \(-0.597427 q^{38}\) \(-4.86893 q^{39}\) \(-18.1529 q^{40}\) \(-5.36108 q^{41}\) \(-3.98260 q^{42}\) \(-1.10802 q^{43}\) \(-12.1775 q^{44}\) \(+3.32889 q^{45}\) \(-0.00317557 q^{46}\) \(-9.52505 q^{47}\) \(+11.4726 q^{48}\) \(-6.37456 q^{49}\) \(-12.9703 q^{50}\) \(+4.18523 q^{51}\) \(-10.3439 q^{52}\) \(+10.9698 q^{53}\) \(+9.85320 q^{54}\) \(-9.09471 q^{55}\) \(-4.49973 q^{56}\) \(+0.479687 q^{57}\) \(+23.3254 q^{58}\) \(-1.84744 q^{59}\) \(+27.4062 q^{60}\) \(+1.35042 q^{61}\) \(+22.5410 q^{62}\) \(+0.825164 q^{63}\) \(-4.12544 q^{64}\) \(-7.72528 q^{65}\) \(+14.3552 q^{66}\) \(-9.34063 q^{67}\) \(+8.89138 q^{68}\) \(+0.00254973 q^{69}\) \(-6.31899 q^{70}\) \(+3.61122 q^{71}\) \(-5.93660 q^{72}\) \(+11.6743 q^{73}\) \(+2.19654 q^{74}\) \(+10.4141 q^{75}\) \(+1.01908 q^{76}\) \(-2.25439 q^{77}\) \(+12.1936 q^{78}\) \(+8.15452 q^{79}\) \(+18.2029 q^{80}\) \(-11.0415 q^{81}\) \(+13.4262 q^{82}\) \(+5.00880 q^{83}\) \(+6.79344 q^{84}\) \(+6.64049 q^{85}\) \(+2.77490 q^{86}\) \(-18.7284 q^{87}\) \(+16.2191 q^{88}\) \(-18.2144 q^{89}\) \(-8.33681 q^{90}\) \(-1.91494 q^{91}\) \(+0.00541681 q^{92}\) \(-18.0987 q^{93}\) \(+23.8543 q^{94}\) \(+0.761094 q^{95}\) \(-5.84960 q^{96}\) \(+6.52392 q^{97}\) \(+15.9643 q^{98}\) \(-2.97427 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(217q \) \(\mathstrut -\mathstrut 20q^{2} \) \(\mathstrut -\mathstrut 27q^{3} \) \(\mathstrut +\mathstrut 184q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 48q^{7} \) \(\mathstrut -\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 152q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(217q \) \(\mathstrut -\mathstrut 20q^{2} \) \(\mathstrut -\mathstrut 27q^{3} \) \(\mathstrut +\mathstrut 184q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 48q^{7} \) \(\mathstrut -\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 152q^{9} \) \(\mathstrut -\mathstrut 46q^{10} \) \(\mathstrut -\mathstrut 32q^{11} \) \(\mathstrut -\mathstrut 72q^{12} \) \(\mathstrut -\mathstrut 80q^{13} \) \(\mathstrut -\mathstrut 22q^{14} \) \(\mathstrut -\mathstrut 43q^{15} \) \(\mathstrut +\mathstrut 122q^{16} \) \(\mathstrut -\mathstrut 61q^{17} \) \(\mathstrut -\mathstrut 88q^{18} \) \(\mathstrut -\mathstrut 43q^{19} \) \(\mathstrut -\mathstrut 41q^{20} \) \(\mathstrut -\mathstrut 61q^{21} \) \(\mathstrut -\mathstrut 93q^{22} \) \(\mathstrut -\mathstrut 60q^{23} \) \(\mathstrut -\mathstrut 41q^{24} \) \(\mathstrut +\mathstrut 26q^{25} \) \(\mathstrut -\mathstrut 9q^{26} \) \(\mathstrut -\mathstrut 93q^{27} \) \(\mathstrut -\mathstrut 126q^{28} \) \(\mathstrut -\mathstrut 47q^{29} \) \(\mathstrut -\mathstrut 36q^{30} \) \(\mathstrut -\mathstrut 100q^{31} \) \(\mathstrut -\mathstrut 114q^{32} \) \(\mathstrut -\mathstrut 133q^{33} \) \(\mathstrut -\mathstrut 75q^{34} \) \(\mathstrut -\mathstrut 37q^{35} \) \(\mathstrut +\mathstrut 75q^{36} \) \(\mathstrut -\mathstrut 264q^{37} \) \(\mathstrut -\mathstrut 35q^{38} \) \(\mathstrut -\mathstrut 47q^{39} \) \(\mathstrut -\mathstrut 118q^{40} \) \(\mathstrut -\mathstrut 72q^{41} \) \(\mathstrut -\mathstrut 64q^{42} \) \(\mathstrut -\mathstrut 107q^{43} \) \(\mathstrut -\mathstrut 59q^{44} \) \(\mathstrut -\mathstrut 69q^{45} \) \(\mathstrut -\mathstrut 111q^{46} \) \(\mathstrut -\mathstrut 54q^{47} \) \(\mathstrut -\mathstrut 135q^{48} \) \(\mathstrut +\mathstrut 33q^{49} \) \(\mathstrut -\mathstrut 42q^{50} \) \(\mathstrut -\mathstrut 26q^{51} \) \(\mathstrut -\mathstrut 173q^{52} \) \(\mathstrut -\mathstrut 103q^{53} \) \(\mathstrut -\mathstrut 28q^{54} \) \(\mathstrut -\mathstrut 78q^{55} \) \(\mathstrut -\mathstrut 44q^{56} \) \(\mathstrut -\mathstrut 205q^{57} \) \(\mathstrut -\mathstrut 189q^{58} \) \(\mathstrut -\mathstrut 38q^{59} \) \(\mathstrut -\mathstrut 105q^{60} \) \(\mathstrut -\mathstrut 108q^{61} \) \(\mathstrut -\mathstrut 14q^{62} \) \(\mathstrut -\mathstrut 116q^{63} \) \(\mathstrut +\mathstrut 39q^{64} \) \(\mathstrut -\mathstrut 146q^{65} \) \(\mathstrut +\mathstrut 5q^{66} \) \(\mathstrut -\mathstrut 206q^{67} \) \(\mathstrut -\mathstrut 62q^{68} \) \(\mathstrut -\mathstrut 55q^{69} \) \(\mathstrut -\mathstrut 125q^{70} \) \(\mathstrut -\mathstrut 78q^{71} \) \(\mathstrut -\mathstrut 225q^{72} \) \(\mathstrut -\mathstrut 326q^{73} \) \(\mathstrut +\mathstrut 3q^{74} \) \(\mathstrut -\mathstrut 95q^{75} \) \(\mathstrut -\mathstrut 84q^{76} \) \(\mathstrut -\mathstrut 79q^{77} \) \(\mathstrut -\mathstrut 86q^{78} \) \(\mathstrut -\mathstrut 117q^{79} \) \(\mathstrut -\mathstrut 39q^{80} \) \(\mathstrut +\mathstrut q^{81} \) \(\mathstrut -\mathstrut 96q^{82} \) \(\mathstrut -\mathstrut 23q^{83} \) \(\mathstrut -\mathstrut 57q^{84} \) \(\mathstrut -\mathstrut 224q^{85} \) \(\mathstrut -\mathstrut 7q^{86} \) \(\mathstrut -\mathstrut 45q^{87} \) \(\mathstrut -\mathstrut 250q^{88} \) \(\mathstrut -\mathstrut 104q^{89} \) \(\mathstrut -\mathstrut 36q^{90} \) \(\mathstrut -\mathstrut 96q^{91} \) \(\mathstrut -\mathstrut 137q^{92} \) \(\mathstrut -\mathstrut 155q^{93} \) \(\mathstrut -\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 38q^{95} \) \(\mathstrut -\mathstrut 33q^{96} \) \(\mathstrut -\mathstrut 447q^{97} \) \(\mathstrut -\mathstrut 46q^{98} \) \(\mathstrut -\mathstrut 94q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.50438 −1.77086 −0.885432 0.464770i \(-0.846137\pi\)
−0.885432 + 0.464770i \(0.846137\pi\)
\(3\) 2.01082 1.16095 0.580473 0.814279i \(-0.302868\pi\)
0.580473 + 0.814279i \(0.302868\pi\)
\(4\) 4.27191 2.13596
\(5\) 3.19046 1.42682 0.713409 0.700748i \(-0.247150\pi\)
0.713409 + 0.700748i \(0.247150\pi\)
\(6\) −5.03585 −2.05588
\(7\) 0.790850 0.298913 0.149457 0.988768i \(-0.452248\pi\)
0.149457 + 0.988768i \(0.452248\pi\)
\(8\) −5.68973 −2.01162
\(9\) 1.04339 0.347796
\(10\) −7.99013 −2.52670
\(11\) −2.85059 −0.859486 −0.429743 0.902951i \(-0.641396\pi\)
−0.429743 + 0.902951i \(0.641396\pi\)
\(12\) 8.59004 2.47973
\(13\) −2.42137 −0.671566 −0.335783 0.941939i \(-0.609001\pi\)
−0.335783 + 0.941939i \(0.609001\pi\)
\(14\) −1.98059 −0.529335
\(15\) 6.41544 1.65646
\(16\) 5.70542 1.42635
\(17\) 2.08136 0.504803 0.252402 0.967623i \(-0.418780\pi\)
0.252402 + 0.967623i \(0.418780\pi\)
\(18\) −2.61304 −0.615899
\(19\) 0.238553 0.0547278 0.0273639 0.999626i \(-0.491289\pi\)
0.0273639 + 0.999626i \(0.491289\pi\)
\(20\) 13.6294 3.04762
\(21\) 1.59026 0.347022
\(22\) 7.13896 1.52203
\(23\) 0.00126801 0.000264397 0 0.000132199 1.00000i \(-0.499958\pi\)
0.000132199 1.00000i \(0.499958\pi\)
\(24\) −11.4410 −2.33539
\(25\) 5.17905 1.03581
\(26\) 6.06402 1.18925
\(27\) −3.93439 −0.757174
\(28\) 3.37844 0.638466
\(29\) −9.31384 −1.72954 −0.864768 0.502171i \(-0.832535\pi\)
−0.864768 + 0.502171i \(0.832535\pi\)
\(30\) −16.0667 −2.93336
\(31\) −9.00065 −1.61656 −0.808282 0.588796i \(-0.799602\pi\)
−0.808282 + 0.588796i \(0.799602\pi\)
\(32\) −2.90906 −0.514255
\(33\) −5.73202 −0.997817
\(34\) −5.21251 −0.893938
\(35\) 2.52318 0.426495
\(36\) 4.45726 0.742877
\(37\) −0.877078 −0.144191 −0.0720954 0.997398i \(-0.522969\pi\)
−0.0720954 + 0.997398i \(0.522969\pi\)
\(38\) −0.597427 −0.0969155
\(39\) −4.86893 −0.779652
\(40\) −18.1529 −2.87022
\(41\) −5.36108 −0.837260 −0.418630 0.908157i \(-0.637490\pi\)
−0.418630 + 0.908157i \(0.637490\pi\)
\(42\) −3.98260 −0.614529
\(43\) −1.10802 −0.168971 −0.0844857 0.996425i \(-0.526925\pi\)
−0.0844857 + 0.996425i \(0.526925\pi\)
\(44\) −12.1775 −1.83582
\(45\) 3.32889 0.496242
\(46\) −0.00317557 −0.000468212 0
\(47\) −9.52505 −1.38937 −0.694685 0.719314i \(-0.744456\pi\)
−0.694685 + 0.719314i \(0.744456\pi\)
\(48\) 11.4726 1.65592
\(49\) −6.37456 −0.910651
\(50\) −12.9703 −1.83428
\(51\) 4.18523 0.586049
\(52\) −10.3439 −1.43444
\(53\) 10.9698 1.50681 0.753407 0.657554i \(-0.228409\pi\)
0.753407 + 0.657554i \(0.228409\pi\)
\(54\) 9.85320 1.34085
\(55\) −9.09471 −1.22633
\(56\) −4.49973 −0.601301
\(57\) 0.479687 0.0635360
\(58\) 23.3254 3.06277
\(59\) −1.84744 −0.240516 −0.120258 0.992743i \(-0.538372\pi\)
−0.120258 + 0.992743i \(0.538372\pi\)
\(60\) 27.4062 3.53813
\(61\) 1.35042 0.172904 0.0864520 0.996256i \(-0.472447\pi\)
0.0864520 + 0.996256i \(0.472447\pi\)
\(62\) 22.5410 2.86271
\(63\) 0.825164 0.103961
\(64\) −4.12544 −0.515680
\(65\) −7.72528 −0.958203
\(66\) 14.3552 1.76700
\(67\) −9.34063 −1.14114 −0.570570 0.821249i \(-0.693278\pi\)
−0.570570 + 0.821249i \(0.693278\pi\)
\(68\) 8.89138 1.07824
\(69\) 0.00254973 0.000306951 0
\(70\) −6.31899 −0.755264
\(71\) 3.61122 0.428573 0.214286 0.976771i \(-0.431257\pi\)
0.214286 + 0.976771i \(0.431257\pi\)
\(72\) −5.93660 −0.699635
\(73\) 11.6743 1.36638 0.683190 0.730241i \(-0.260592\pi\)
0.683190 + 0.730241i \(0.260592\pi\)
\(74\) 2.19654 0.255342
\(75\) 10.4141 1.20252
\(76\) 1.01908 0.116896
\(77\) −2.25439 −0.256912
\(78\) 12.1936 1.38066
\(79\) 8.15452 0.917455 0.458728 0.888577i \(-0.348305\pi\)
0.458728 + 0.888577i \(0.348305\pi\)
\(80\) 18.2029 2.03515
\(81\) −11.0415 −1.22683
\(82\) 13.4262 1.48267
\(83\) 5.00880 0.549787 0.274894 0.961475i \(-0.411357\pi\)
0.274894 + 0.961475i \(0.411357\pi\)
\(84\) 6.79344 0.741225
\(85\) 6.64049 0.720262
\(86\) 2.77490 0.299225
\(87\) −18.7284 −2.00790
\(88\) 16.2191 1.72896
\(89\) −18.2144 −1.93072 −0.965359 0.260926i \(-0.915972\pi\)
−0.965359 + 0.260926i \(0.915972\pi\)
\(90\) −8.33681 −0.878776
\(91\) −1.91494 −0.200740
\(92\) 0.00541681 0.000564741 0
\(93\) −18.0987 −1.87674
\(94\) 23.8543 2.46039
\(95\) 0.761094 0.0780866
\(96\) −5.84960 −0.597022
\(97\) 6.52392 0.662404 0.331202 0.943560i \(-0.392546\pi\)
0.331202 + 0.943560i \(0.392546\pi\)
\(98\) 15.9643 1.61264
\(99\) −2.97427 −0.298926
\(100\) 22.1245 2.21245
\(101\) −1.97455 −0.196475 −0.0982377 0.995163i \(-0.531321\pi\)
−0.0982377 + 0.995163i \(0.531321\pi\)
\(102\) −10.4814 −1.03781
\(103\) −8.44874 −0.832479 −0.416240 0.909255i \(-0.636652\pi\)
−0.416240 + 0.909255i \(0.636652\pi\)
\(104\) 13.7769 1.35094
\(105\) 5.07365 0.495138
\(106\) −27.4725 −2.66836
\(107\) 18.8832 1.82550 0.912752 0.408514i \(-0.133953\pi\)
0.912752 + 0.408514i \(0.133953\pi\)
\(108\) −16.8074 −1.61729
\(109\) −12.2294 −1.17136 −0.585681 0.810541i \(-0.699173\pi\)
−0.585681 + 0.810541i \(0.699173\pi\)
\(110\) 22.7766 2.17166
\(111\) −1.76364 −0.167398
\(112\) 4.51213 0.426356
\(113\) −14.3697 −1.35179 −0.675894 0.736999i \(-0.736242\pi\)
−0.675894 + 0.736999i \(0.736242\pi\)
\(114\) −1.20132 −0.112514
\(115\) 0.00404552 0.000377247 0
\(116\) −39.7879 −3.69421
\(117\) −2.52643 −0.233568
\(118\) 4.62668 0.425921
\(119\) 1.64604 0.150892
\(120\) −36.5021 −3.33217
\(121\) −2.87412 −0.261284
\(122\) −3.38197 −0.306189
\(123\) −10.7802 −0.972014
\(124\) −38.4500 −3.45291
\(125\) 0.571256 0.0510947
\(126\) −2.06652 −0.184101
\(127\) −5.24885 −0.465760 −0.232880 0.972505i \(-0.574815\pi\)
−0.232880 + 0.972505i \(0.574815\pi\)
\(128\) 16.1498 1.42745
\(129\) −2.22803 −0.196167
\(130\) 19.3470 1.69685
\(131\) −2.89568 −0.252997 −0.126499 0.991967i \(-0.540374\pi\)
−0.126499 + 0.991967i \(0.540374\pi\)
\(132\) −24.4867 −2.13129
\(133\) 0.188660 0.0163589
\(134\) 23.3925 2.02080
\(135\) −12.5525 −1.08035
\(136\) −11.8424 −1.01547
\(137\) 21.7114 1.85493 0.927463 0.373914i \(-0.121985\pi\)
0.927463 + 0.373914i \(0.121985\pi\)
\(138\) −0.00638549 −0.000543569 0
\(139\) 1.43807 0.121975 0.0609876 0.998139i \(-0.480575\pi\)
0.0609876 + 0.998139i \(0.480575\pi\)
\(140\) 10.7788 0.910975
\(141\) −19.1531 −1.61298
\(142\) −9.04386 −0.758944
\(143\) 6.90233 0.577202
\(144\) 5.95297 0.496081
\(145\) −29.7154 −2.46773
\(146\) −29.2370 −2.41967
\(147\) −12.8181 −1.05722
\(148\) −3.74680 −0.307985
\(149\) 7.86532 0.644352 0.322176 0.946680i \(-0.395586\pi\)
0.322176 + 0.946680i \(0.395586\pi\)
\(150\) −26.0809 −2.12950
\(151\) 0.0776229 0.00631687 0.00315843 0.999995i \(-0.498995\pi\)
0.00315843 + 0.999995i \(0.498995\pi\)
\(152\) −1.35730 −0.110092
\(153\) 2.17166 0.175569
\(154\) 5.64585 0.454956
\(155\) −28.7162 −2.30654
\(156\) −20.7996 −1.66530
\(157\) −12.9338 −1.03223 −0.516117 0.856518i \(-0.672623\pi\)
−0.516117 + 0.856518i \(0.672623\pi\)
\(158\) −20.4220 −1.62469
\(159\) 22.0582 1.74933
\(160\) −9.28126 −0.733748
\(161\) 0.00100280 7.90319e−5 0
\(162\) 27.6521 2.17256
\(163\) 1.78981 0.140188 0.0700942 0.997540i \(-0.477670\pi\)
0.0700942 + 0.997540i \(0.477670\pi\)
\(164\) −22.9021 −1.78835
\(165\) −18.2878 −1.42370
\(166\) −12.5439 −0.973598
\(167\) −12.0367 −0.931424 −0.465712 0.884936i \(-0.654202\pi\)
−0.465712 + 0.884936i \(0.654202\pi\)
\(168\) −9.04813 −0.698078
\(169\) −7.13698 −0.548999
\(170\) −16.6303 −1.27549
\(171\) 0.248903 0.0190341
\(172\) −4.73336 −0.360916
\(173\) 1.83863 0.139789 0.0698943 0.997554i \(-0.477734\pi\)
0.0698943 + 0.997554i \(0.477734\pi\)
\(174\) 46.9031 3.55571
\(175\) 4.09585 0.309617
\(176\) −16.2638 −1.22593
\(177\) −3.71486 −0.279226
\(178\) 45.6156 3.41904
\(179\) −3.58725 −0.268123 −0.134062 0.990973i \(-0.542802\pi\)
−0.134062 + 0.990973i \(0.542802\pi\)
\(180\) 14.2207 1.05995
\(181\) −14.7265 −1.09461 −0.547307 0.836932i \(-0.684347\pi\)
−0.547307 + 0.836932i \(0.684347\pi\)
\(182\) 4.79573 0.355483
\(183\) 2.71546 0.200732
\(184\) −0.00721461 −0.000531868 0
\(185\) −2.79829 −0.205734
\(186\) 45.3259 3.32346
\(187\) −5.93310 −0.433871
\(188\) −40.6902 −2.96764
\(189\) −3.11151 −0.226329
\(190\) −1.90607 −0.138281
\(191\) 14.9823 1.08408 0.542040 0.840353i \(-0.317652\pi\)
0.542040 + 0.840353i \(0.317652\pi\)
\(192\) −8.29550 −0.598676
\(193\) −21.3113 −1.53402 −0.767010 0.641635i \(-0.778257\pi\)
−0.767010 + 0.641635i \(0.778257\pi\)
\(194\) −16.3384 −1.17303
\(195\) −15.5341 −1.11242
\(196\) −27.2316 −1.94511
\(197\) 4.43248 0.315801 0.157900 0.987455i \(-0.449528\pi\)
0.157900 + 0.987455i \(0.449528\pi\)
\(198\) 7.44871 0.529357
\(199\) 24.3863 1.72870 0.864350 0.502891i \(-0.167730\pi\)
0.864350 + 0.502891i \(0.167730\pi\)
\(200\) −29.4674 −2.08366
\(201\) −18.7823 −1.32480
\(202\) 4.94503 0.347931
\(203\) −7.36585 −0.516981
\(204\) 17.8789 1.25178
\(205\) −17.1043 −1.19462
\(206\) 21.1588 1.47421
\(207\) 0.00132302 9.19564e−5 0
\(208\) −13.8149 −0.957892
\(209\) −0.680017 −0.0470378
\(210\) −12.7063 −0.876821
\(211\) 21.5620 1.48439 0.742193 0.670186i \(-0.233786\pi\)
0.742193 + 0.670186i \(0.233786\pi\)
\(212\) 46.8619 3.21849
\(213\) 7.26151 0.497550
\(214\) −47.2906 −3.23272
\(215\) −3.53510 −0.241091
\(216\) 22.3856 1.52315
\(217\) −7.11816 −0.483212
\(218\) 30.6270 2.07432
\(219\) 23.4750 1.58629
\(220\) −38.8518 −2.61939
\(221\) −5.03973 −0.339009
\(222\) 4.41683 0.296439
\(223\) −2.54423 −0.170374 −0.0851872 0.996365i \(-0.527149\pi\)
−0.0851872 + 0.996365i \(0.527149\pi\)
\(224\) −2.30063 −0.153718
\(225\) 5.40376 0.360251
\(226\) 35.9872 2.39383
\(227\) 0.315809 0.0209610 0.0104805 0.999945i \(-0.496664\pi\)
0.0104805 + 0.999945i \(0.496664\pi\)
\(228\) 2.04918 0.135710
\(229\) 4.74936 0.313847 0.156923 0.987611i \(-0.449842\pi\)
0.156923 + 0.987611i \(0.449842\pi\)
\(230\) −0.0101315 −0.000668053 0
\(231\) −4.53317 −0.298261
\(232\) 52.9932 3.47918
\(233\) −13.0529 −0.855123 −0.427562 0.903986i \(-0.640627\pi\)
−0.427562 + 0.903986i \(0.640627\pi\)
\(234\) 6.32713 0.413617
\(235\) −30.3893 −1.98238
\(236\) −7.89209 −0.513732
\(237\) 16.3973 1.06512
\(238\) −4.12231 −0.267210
\(239\) 25.4721 1.64766 0.823828 0.566840i \(-0.191834\pi\)
0.823828 + 0.566840i \(0.191834\pi\)
\(240\) 36.6028 2.36270
\(241\) 15.0431 0.969013 0.484506 0.874788i \(-0.338999\pi\)
0.484506 + 0.874788i \(0.338999\pi\)
\(242\) 7.19789 0.462698
\(243\) −10.3993 −0.667115
\(244\) 5.76889 0.369316
\(245\) −20.3378 −1.29933
\(246\) 26.9976 1.72130
\(247\) −0.577624 −0.0367534
\(248\) 51.2113 3.25192
\(249\) 10.0718 0.638274
\(250\) −1.43064 −0.0904817
\(251\) −4.65176 −0.293616 −0.146808 0.989165i \(-0.546900\pi\)
−0.146808 + 0.989165i \(0.546900\pi\)
\(252\) 3.52503 0.222056
\(253\) −0.00361457 −0.000227246 0
\(254\) 13.1451 0.824797
\(255\) 13.3528 0.836186
\(256\) −32.1943 −2.01214
\(257\) 8.22994 0.513370 0.256685 0.966495i \(-0.417370\pi\)
0.256685 + 0.966495i \(0.417370\pi\)
\(258\) 5.57982 0.347384
\(259\) −0.693638 −0.0431005
\(260\) −33.0017 −2.04668
\(261\) −9.71795 −0.601526
\(262\) 7.25189 0.448023
\(263\) −12.2692 −0.756551 −0.378275 0.925693i \(-0.623483\pi\)
−0.378275 + 0.925693i \(0.623483\pi\)
\(264\) 32.6137 2.00723
\(265\) 34.9987 2.14995
\(266\) −0.472475 −0.0289693
\(267\) −36.6257 −2.24146
\(268\) −39.9024 −2.43743
\(269\) 3.65920 0.223106 0.111553 0.993759i \(-0.464418\pi\)
0.111553 + 0.993759i \(0.464418\pi\)
\(270\) 31.4363 1.91315
\(271\) −25.7237 −1.56261 −0.781303 0.624152i \(-0.785444\pi\)
−0.781303 + 0.624152i \(0.785444\pi\)
\(272\) 11.8750 0.720028
\(273\) −3.85059 −0.233048
\(274\) −54.3735 −3.28482
\(275\) −14.7634 −0.890264
\(276\) 0.0108922 0.000655634 0
\(277\) 30.0391 1.80488 0.902438 0.430821i \(-0.141776\pi\)
0.902438 + 0.430821i \(0.141776\pi\)
\(278\) −3.60146 −0.216001
\(279\) −9.39117 −0.562235
\(280\) −14.3562 −0.857948
\(281\) 8.88843 0.530239 0.265120 0.964216i \(-0.414589\pi\)
0.265120 + 0.964216i \(0.414589\pi\)
\(282\) 47.9667 2.85638
\(283\) −2.24236 −0.133294 −0.0666471 0.997777i \(-0.521230\pi\)
−0.0666471 + 0.997777i \(0.521230\pi\)
\(284\) 15.4268 0.915413
\(285\) 1.53042 0.0906544
\(286\) −17.2860 −1.02215
\(287\) −4.23981 −0.250268
\(288\) −3.03528 −0.178856
\(289\) −12.6680 −0.745174
\(290\) 74.4187 4.37002
\(291\) 13.1184 0.769015
\(292\) 49.8718 2.91853
\(293\) −16.8304 −0.983245 −0.491623 0.870808i \(-0.663596\pi\)
−0.491623 + 0.870808i \(0.663596\pi\)
\(294\) 32.1013 1.87219
\(295\) −5.89418 −0.343173
\(296\) 4.99034 0.290058
\(297\) 11.2153 0.650780
\(298\) −19.6978 −1.14106
\(299\) −0.00307031 −0.000177560 0
\(300\) 44.4883 2.56853
\(301\) −0.876278 −0.0505078
\(302\) −0.194397 −0.0111863
\(303\) −3.97047 −0.228097
\(304\) 1.36104 0.0780613
\(305\) 4.30848 0.246703
\(306\) −5.43867 −0.310908
\(307\) −13.8030 −0.787780 −0.393890 0.919158i \(-0.628871\pi\)
−0.393890 + 0.919158i \(0.628871\pi\)
\(308\) −9.63057 −0.548753
\(309\) −16.9889 −0.966464
\(310\) 71.9163 4.08457
\(311\) 8.82172 0.500234 0.250117 0.968216i \(-0.419531\pi\)
0.250117 + 0.968216i \(0.419531\pi\)
\(312\) 27.7029 1.56837
\(313\) −18.4523 −1.04298 −0.521492 0.853256i \(-0.674624\pi\)
−0.521492 + 0.853256i \(0.674624\pi\)
\(314\) 32.3913 1.82794
\(315\) 2.63265 0.148333
\(316\) 34.8354 1.95964
\(317\) −22.0470 −1.23828 −0.619142 0.785279i \(-0.712520\pi\)
−0.619142 + 0.785279i \(0.712520\pi\)
\(318\) −55.2421 −3.09783
\(319\) 26.5500 1.48651
\(320\) −13.1621 −0.735781
\(321\) 37.9706 2.11931
\(322\) −0.00251140 −0.000139955 0
\(323\) 0.496514 0.0276268
\(324\) −47.1684 −2.62046
\(325\) −12.5404 −0.695615
\(326\) −4.48235 −0.248255
\(327\) −24.5911 −1.35989
\(328\) 30.5031 1.68425
\(329\) −7.53288 −0.415301
\(330\) 45.7996 2.52118
\(331\) −18.3796 −1.01023 −0.505116 0.863051i \(-0.668550\pi\)
−0.505116 + 0.863051i \(0.668550\pi\)
\(332\) 21.3972 1.17432
\(333\) −0.915133 −0.0501490
\(334\) 30.1443 1.64943
\(335\) −29.8009 −1.62820
\(336\) 9.07308 0.494977
\(337\) 28.9942 1.57941 0.789706 0.613485i \(-0.210233\pi\)
0.789706 + 0.613485i \(0.210233\pi\)
\(338\) 17.8737 0.972202
\(339\) −28.8949 −1.56935
\(340\) 28.3676 1.53845
\(341\) 25.6572 1.38941
\(342\) −0.623348 −0.0337068
\(343\) −10.5773 −0.571119
\(344\) 6.30434 0.339907
\(345\) 0.00813481 0.000437964 0
\(346\) −4.60463 −0.247546
\(347\) −3.99988 −0.214725 −0.107362 0.994220i \(-0.534241\pi\)
−0.107362 + 0.994220i \(0.534241\pi\)
\(348\) −80.0062 −4.28878
\(349\) −22.7879 −1.21981 −0.609904 0.792475i \(-0.708792\pi\)
−0.609904 + 0.792475i \(0.708792\pi\)
\(350\) −10.2576 −0.548290
\(351\) 9.52660 0.508492
\(352\) 8.29256 0.441995
\(353\) 11.8229 0.629272 0.314636 0.949212i \(-0.398118\pi\)
0.314636 + 0.949212i \(0.398118\pi\)
\(354\) 9.30342 0.494471
\(355\) 11.5215 0.611496
\(356\) −77.8101 −4.12393
\(357\) 3.30989 0.175178
\(358\) 8.98382 0.474810
\(359\) 24.0575 1.26971 0.634853 0.772633i \(-0.281061\pi\)
0.634853 + 0.772633i \(0.281061\pi\)
\(360\) −18.9405 −0.998252
\(361\) −18.9431 −0.997005
\(362\) 36.8808 1.93841
\(363\) −5.77934 −0.303337
\(364\) −8.18045 −0.428772
\(365\) 37.2466 1.94957
\(366\) −6.80053 −0.355469
\(367\) 11.8171 0.616846 0.308423 0.951249i \(-0.400199\pi\)
0.308423 + 0.951249i \(0.400199\pi\)
\(368\) 0.00723450 0.000377125 0
\(369\) −5.59369 −0.291196
\(370\) 7.00797 0.364327
\(371\) 8.67545 0.450407
\(372\) −77.3159 −4.00864
\(373\) 20.9736 1.08597 0.542987 0.839741i \(-0.317293\pi\)
0.542987 + 0.839741i \(0.317293\pi\)
\(374\) 14.8587 0.768327
\(375\) 1.14869 0.0593182
\(376\) 54.1950 2.79489
\(377\) 22.5522 1.16150
\(378\) 7.79241 0.400798
\(379\) −22.7950 −1.17090 −0.585450 0.810708i \(-0.699082\pi\)
−0.585450 + 0.810708i \(0.699082\pi\)
\(380\) 3.25133 0.166790
\(381\) −10.5545 −0.540722
\(382\) −37.5213 −1.91976
\(383\) 36.1951 1.84948 0.924742 0.380594i \(-0.124281\pi\)
0.924742 + 0.380594i \(0.124281\pi\)
\(384\) 32.4743 1.65720
\(385\) −7.19255 −0.366566
\(386\) 53.3716 2.71654
\(387\) −1.15609 −0.0587676
\(388\) 27.8696 1.41487
\(389\) 19.3851 0.982865 0.491433 0.870916i \(-0.336473\pi\)
0.491433 + 0.870916i \(0.336473\pi\)
\(390\) 38.9033 1.96995
\(391\) 0.00263917 0.000133469 0
\(392\) 36.2695 1.83189
\(393\) −5.82269 −0.293716
\(394\) −11.1006 −0.559240
\(395\) 26.0167 1.30904
\(396\) −12.7058 −0.638493
\(397\) 20.3149 1.01958 0.509789 0.860300i \(-0.329724\pi\)
0.509789 + 0.860300i \(0.329724\pi\)
\(398\) −61.0726 −3.06129
\(399\) 0.379360 0.0189918
\(400\) 29.5487 1.47743
\(401\) 26.5143 1.32406 0.662031 0.749476i \(-0.269695\pi\)
0.662031 + 0.749476i \(0.269695\pi\)
\(402\) 47.0380 2.34604
\(403\) 21.7939 1.08563
\(404\) −8.43512 −0.419663
\(405\) −35.2275 −1.75047
\(406\) 18.4469 0.915503
\(407\) 2.50019 0.123930
\(408\) −23.8128 −1.17891
\(409\) 4.15257 0.205331 0.102666 0.994716i \(-0.467263\pi\)
0.102666 + 0.994716i \(0.467263\pi\)
\(410\) 42.8357 2.11550
\(411\) 43.6576 2.15347
\(412\) −36.0923 −1.77814
\(413\) −1.46105 −0.0718934
\(414\) −0.00331335 −0.000162842 0
\(415\) 15.9804 0.784447
\(416\) 7.04391 0.345356
\(417\) 2.89169 0.141607
\(418\) 1.70302 0.0832975
\(419\) −16.3248 −0.797517 −0.398759 0.917056i \(-0.630559\pi\)
−0.398759 + 0.917056i \(0.630559\pi\)
\(420\) 21.6742 1.05759
\(421\) −19.2407 −0.937734 −0.468867 0.883269i \(-0.655338\pi\)
−0.468867 + 0.883269i \(0.655338\pi\)
\(422\) −53.9993 −2.62865
\(423\) −9.93832 −0.483218
\(424\) −62.4151 −3.03114
\(425\) 10.7795 0.522880
\(426\) −18.1856 −0.881093
\(427\) 1.06798 0.0516833
\(428\) 80.6672 3.89920
\(429\) 13.8793 0.670100
\(430\) 8.85322 0.426940
\(431\) 6.00449 0.289226 0.144613 0.989488i \(-0.453806\pi\)
0.144613 + 0.989488i \(0.453806\pi\)
\(432\) −22.4473 −1.08000
\(433\) −21.2896 −1.02311 −0.511555 0.859250i \(-0.670931\pi\)
−0.511555 + 0.859250i \(0.670931\pi\)
\(434\) 17.8266 0.855703
\(435\) −59.7524 −2.86491
\(436\) −52.2429 −2.50198
\(437\) 0.000302487 0 1.44699e−5 0
\(438\) −58.7903 −2.80911
\(439\) −9.02088 −0.430543 −0.215272 0.976554i \(-0.569064\pi\)
−0.215272 + 0.976554i \(0.569064\pi\)
\(440\) 51.7465 2.46692
\(441\) −6.65114 −0.316721
\(442\) 12.6214 0.600338
\(443\) 28.3534 1.34711 0.673555 0.739137i \(-0.264766\pi\)
0.673555 + 0.739137i \(0.264766\pi\)
\(444\) −7.53414 −0.357554
\(445\) −58.1122 −2.75478
\(446\) 6.37172 0.301710
\(447\) 15.8157 0.748059
\(448\) −3.26260 −0.154143
\(449\) 17.9961 0.849286 0.424643 0.905361i \(-0.360400\pi\)
0.424643 + 0.905361i \(0.360400\pi\)
\(450\) −13.5331 −0.637955
\(451\) 15.2822 0.719613
\(452\) −61.3861 −2.88736
\(453\) 0.156086 0.00733354
\(454\) −0.790904 −0.0371190
\(455\) −6.10954 −0.286420
\(456\) −2.72929 −0.127811
\(457\) 2.13183 0.0997230 0.0498615 0.998756i \(-0.484122\pi\)
0.0498615 + 0.998756i \(0.484122\pi\)
\(458\) −11.8942 −0.555780
\(459\) −8.18887 −0.382224
\(460\) 0.0172821 0.000805783 0
\(461\) −13.6079 −0.633784 −0.316892 0.948462i \(-0.602639\pi\)
−0.316892 + 0.948462i \(0.602639\pi\)
\(462\) 11.3528 0.528179
\(463\) −4.13632 −0.192231 −0.0961155 0.995370i \(-0.530642\pi\)
−0.0961155 + 0.995370i \(0.530642\pi\)
\(464\) −53.1393 −2.46693
\(465\) −57.7431 −2.67777
\(466\) 32.6894 1.51431
\(467\) −7.97191 −0.368896 −0.184448 0.982842i \(-0.559050\pi\)
−0.184448 + 0.982842i \(0.559050\pi\)
\(468\) −10.7927 −0.498891
\(469\) −7.38704 −0.341102
\(470\) 76.1063 3.51052
\(471\) −26.0076 −1.19837
\(472\) 10.5114 0.483828
\(473\) 3.15851 0.145229
\(474\) −41.0649 −1.88618
\(475\) 1.23548 0.0566876
\(476\) 7.03175 0.322300
\(477\) 11.4457 0.524064
\(478\) −63.7919 −2.91777
\(479\) 32.6113 1.49005 0.745023 0.667038i \(-0.232438\pi\)
0.745023 + 0.667038i \(0.232438\pi\)
\(480\) −18.6629 −0.851842
\(481\) 2.12373 0.0968337
\(482\) −37.6737 −1.71599
\(483\) 0.00201645 9.17518e−5 0
\(484\) −12.2780 −0.558091
\(485\) 20.8143 0.945130
\(486\) 26.0438 1.18137
\(487\) 27.1418 1.22991 0.614956 0.788562i \(-0.289174\pi\)
0.614956 + 0.788562i \(0.289174\pi\)
\(488\) −7.68355 −0.347818
\(489\) 3.59897 0.162751
\(490\) 50.9335 2.30094
\(491\) 20.3805 0.919759 0.459880 0.887981i \(-0.347893\pi\)
0.459880 + 0.887981i \(0.347893\pi\)
\(492\) −46.0519 −2.07618
\(493\) −19.3854 −0.873075
\(494\) 1.44659 0.0650852
\(495\) −9.48931 −0.426513
\(496\) −51.3525 −2.30579
\(497\) 2.85593 0.128106
\(498\) −25.2236 −1.13030
\(499\) −12.8047 −0.573216 −0.286608 0.958048i \(-0.592528\pi\)
−0.286608 + 0.958048i \(0.592528\pi\)
\(500\) 2.44036 0.109136
\(501\) −24.2035 −1.08133
\(502\) 11.6498 0.519955
\(503\) −10.0681 −0.448916 −0.224458 0.974484i \(-0.572061\pi\)
−0.224458 + 0.974484i \(0.572061\pi\)
\(504\) −4.69496 −0.209130
\(505\) −6.29974 −0.280335
\(506\) 0.00905225 0.000402421 0
\(507\) −14.3512 −0.637358
\(508\) −22.4226 −0.994843
\(509\) −14.7274 −0.652780 −0.326390 0.945235i \(-0.605832\pi\)
−0.326390 + 0.945235i \(0.605832\pi\)
\(510\) −33.4405 −1.48077
\(511\) 9.23266 0.408429
\(512\) 48.3272 2.13578
\(513\) −0.938560 −0.0414385
\(514\) −20.6109 −0.909107
\(515\) −26.9554 −1.18780
\(516\) −9.51793 −0.419004
\(517\) 27.1520 1.19414
\(518\) 1.73713 0.0763252
\(519\) 3.69715 0.162287
\(520\) 43.9548 1.92754
\(521\) 6.75940 0.296135 0.148067 0.988977i \(-0.452695\pi\)
0.148067 + 0.988977i \(0.452695\pi\)
\(522\) 24.3374 1.06522
\(523\) 13.0797 0.571933 0.285967 0.958240i \(-0.407685\pi\)
0.285967 + 0.958240i \(0.407685\pi\)
\(524\) −12.3701 −0.540391
\(525\) 8.23602 0.359449
\(526\) 30.7267 1.33975
\(527\) −18.7336 −0.816047
\(528\) −32.7036 −1.42324
\(529\) −23.0000 −1.00000
\(530\) −87.6499 −3.80727
\(531\) −1.92760 −0.0836505
\(532\) 0.805938 0.0349418
\(533\) 12.9811 0.562275
\(534\) 91.7248 3.96932
\(535\) 60.2460 2.60466
\(536\) 53.1457 2.29554
\(537\) −7.21330 −0.311277
\(538\) −9.16403 −0.395089
\(539\) 18.1713 0.782692
\(540\) −53.6233 −2.30758
\(541\) −4.39811 −0.189089 −0.0945447 0.995521i \(-0.530140\pi\)
−0.0945447 + 0.995521i \(0.530140\pi\)
\(542\) 64.4220 2.76716
\(543\) −29.6124 −1.27079
\(544\) −6.05480 −0.259598
\(545\) −39.0174 −1.67132
\(546\) 9.64334 0.412697
\(547\) −14.4596 −0.618249 −0.309125 0.951022i \(-0.600036\pi\)
−0.309125 + 0.951022i \(0.600036\pi\)
\(548\) 92.7490 3.96204
\(549\) 1.40902 0.0601353
\(550\) 36.9731 1.57654
\(551\) −2.22184 −0.0946537
\(552\) −0.0145073 −0.000617470 0
\(553\) 6.44901 0.274240
\(554\) −75.2293 −3.19619
\(555\) −5.62684 −0.238846
\(556\) 6.14329 0.260534
\(557\) 2.06157 0.0873516 0.0436758 0.999046i \(-0.486093\pi\)
0.0436758 + 0.999046i \(0.486093\pi\)
\(558\) 23.5190 0.995641
\(559\) 2.68292 0.113476
\(560\) 14.3958 0.608333
\(561\) −11.9304 −0.503701
\(562\) −22.2600 −0.938981
\(563\) 20.3908 0.859371 0.429686 0.902979i \(-0.358624\pi\)
0.429686 + 0.902979i \(0.358624\pi\)
\(564\) −81.8205 −3.44527
\(565\) −45.8460 −1.92876
\(566\) 5.61571 0.236046
\(567\) −8.73218 −0.366717
\(568\) −20.5469 −0.862128
\(569\) 19.1866 0.804344 0.402172 0.915564i \(-0.368255\pi\)
0.402172 + 0.915564i \(0.368255\pi\)
\(570\) −3.83276 −0.160537
\(571\) 21.0680 0.881668 0.440834 0.897589i \(-0.354683\pi\)
0.440834 + 0.897589i \(0.354683\pi\)
\(572\) 29.4862 1.23288
\(573\) 30.1267 1.25856
\(574\) 10.6181 0.443191
\(575\) 0.00656707 0.000273866 0
\(576\) −4.30443 −0.179351
\(577\) −25.4188 −1.05820 −0.529099 0.848560i \(-0.677470\pi\)
−0.529099 + 0.848560i \(0.677470\pi\)
\(578\) 31.7254 1.31960
\(579\) −42.8531 −1.78092
\(580\) −126.942 −5.27097
\(581\) 3.96121 0.164339
\(582\) −32.8535 −1.36182
\(583\) −31.2704 −1.29509
\(584\) −66.4239 −2.74864
\(585\) −8.06047 −0.333259
\(586\) 42.1498 1.74119
\(587\) −7.85314 −0.324134 −0.162067 0.986780i \(-0.551816\pi\)
−0.162067 + 0.986780i \(0.551816\pi\)
\(588\) −54.7577 −2.25817
\(589\) −2.14713 −0.0884710
\(590\) 14.7613 0.607712
\(591\) 8.91290 0.366628
\(592\) −5.00410 −0.205667
\(593\) 23.0173 0.945209 0.472604 0.881275i \(-0.343314\pi\)
0.472604 + 0.881275i \(0.343314\pi\)
\(594\) −28.0875 −1.15244
\(595\) 5.25163 0.215296
\(596\) 33.6000 1.37631
\(597\) 49.0364 2.00693
\(598\) 0.00768921 0.000314435 0
\(599\) −20.2450 −0.827188 −0.413594 0.910461i \(-0.635727\pi\)
−0.413594 + 0.910461i \(0.635727\pi\)
\(600\) −59.2536 −2.41902
\(601\) 19.1068 0.779381 0.389690 0.920946i \(-0.372582\pi\)
0.389690 + 0.920946i \(0.372582\pi\)
\(602\) 2.19453 0.0894424
\(603\) −9.74591 −0.396884
\(604\) 0.331599 0.0134926
\(605\) −9.16978 −0.372805
\(606\) 9.94355 0.403929
\(607\) 14.8454 0.602557 0.301279 0.953536i \(-0.402587\pi\)
0.301279 + 0.953536i \(0.402587\pi\)
\(608\) −0.693966 −0.0281440
\(609\) −14.8114 −0.600188
\(610\) −10.7901 −0.436877
\(611\) 23.0636 0.933055
\(612\) 9.27716 0.375007
\(613\) 28.7113 1.15964 0.579820 0.814745i \(-0.303123\pi\)
0.579820 + 0.814745i \(0.303123\pi\)
\(614\) 34.5680 1.39505
\(615\) −34.3937 −1.38689
\(616\) 12.8269 0.516810
\(617\) −40.4138 −1.62700 −0.813498 0.581567i \(-0.802440\pi\)
−0.813498 + 0.581567i \(0.802440\pi\)
\(618\) 42.5466 1.71147
\(619\) 35.2003 1.41482 0.707409 0.706805i \(-0.249864\pi\)
0.707409 + 0.706805i \(0.249864\pi\)
\(620\) −122.673 −4.92668
\(621\) −0.00498883 −0.000200195 0
\(622\) −22.0929 −0.885846
\(623\) −14.4048 −0.577117
\(624\) −27.7793 −1.11206
\(625\) −24.0727 −0.962907
\(626\) 46.2115 1.84698
\(627\) −1.36739 −0.0546083
\(628\) −55.2523 −2.20481
\(629\) −1.82551 −0.0727880
\(630\) −6.59316 −0.262678
\(631\) 8.37319 0.333331 0.166666 0.986013i \(-0.446700\pi\)
0.166666 + 0.986013i \(0.446700\pi\)
\(632\) −46.3970 −1.84558
\(633\) 43.3572 1.72329
\(634\) 55.2141 2.19283
\(635\) −16.7462 −0.664555
\(636\) 94.2308 3.73649
\(637\) 15.4351 0.611562
\(638\) −66.4911 −2.63241
\(639\) 3.76791 0.149056
\(640\) 51.5253 2.03672
\(641\) 23.5308 0.929412 0.464706 0.885465i \(-0.346160\pi\)
0.464706 + 0.885465i \(0.346160\pi\)
\(642\) −95.0928 −3.75301
\(643\) −13.2398 −0.522128 −0.261064 0.965322i \(-0.584073\pi\)
−0.261064 + 0.965322i \(0.584073\pi\)
\(644\) 0.00428389 0.000168809 0
\(645\) −7.10843 −0.279894
\(646\) −1.24346 −0.0489232
\(647\) −26.2806 −1.03320 −0.516599 0.856227i \(-0.672802\pi\)
−0.516599 + 0.856227i \(0.672802\pi\)
\(648\) 62.8232 2.46793
\(649\) 5.26629 0.206720
\(650\) 31.4059 1.23184
\(651\) −14.3133 −0.560984
\(652\) 7.64590 0.299436
\(653\) 22.6774 0.887434 0.443717 0.896167i \(-0.353659\pi\)
0.443717 + 0.896167i \(0.353659\pi\)
\(654\) 61.5854 2.40818
\(655\) −9.23857 −0.360981
\(656\) −30.5872 −1.19423
\(657\) 12.1809 0.475221
\(658\) 18.8652 0.735442
\(659\) −22.0958 −0.860732 −0.430366 0.902654i \(-0.641616\pi\)
−0.430366 + 0.902654i \(0.641616\pi\)
\(660\) −78.1239 −3.04097
\(661\) 28.1485 1.09485 0.547425 0.836855i \(-0.315608\pi\)
0.547425 + 0.836855i \(0.315608\pi\)
\(662\) 46.0294 1.78898
\(663\) −10.1340 −0.393571
\(664\) −28.4987 −1.10597
\(665\) 0.601912 0.0233411
\(666\) 2.29184 0.0888070
\(667\) −0.0118100 −0.000457285 0
\(668\) −51.4196 −1.98948
\(669\) −5.11599 −0.197796
\(670\) 74.6328 2.88332
\(671\) −3.84951 −0.148609
\(672\) −4.62616 −0.178458
\(673\) −43.9580 −1.69446 −0.847229 0.531228i \(-0.821731\pi\)
−0.847229 + 0.531228i \(0.821731\pi\)
\(674\) −72.6124 −2.79692
\(675\) −20.3764 −0.784288
\(676\) −30.4886 −1.17264
\(677\) 9.46161 0.363639 0.181820 0.983332i \(-0.441801\pi\)
0.181820 + 0.983332i \(0.441801\pi\)
\(678\) 72.3637 2.77911
\(679\) 5.15945 0.198001
\(680\) −37.7826 −1.44890
\(681\) 0.635034 0.0243345
\(682\) −64.2553 −2.46046
\(683\) −35.4647 −1.35702 −0.678510 0.734591i \(-0.737374\pi\)
−0.678510 + 0.734591i \(0.737374\pi\)
\(684\) 1.06329 0.0406561
\(685\) 69.2693 2.64664
\(686\) 26.4895 1.01137
\(687\) 9.55010 0.364359
\(688\) −6.32172 −0.241013
\(689\) −26.5619 −1.01193
\(690\) −0.0203727 −0.000775574 0
\(691\) 31.7405 1.20746 0.603732 0.797187i \(-0.293680\pi\)
0.603732 + 0.797187i \(0.293680\pi\)
\(692\) 7.85448 0.298582
\(693\) −2.35221 −0.0893529
\(694\) 10.0172 0.380248
\(695\) 4.58809 0.174036
\(696\) 106.560 4.03914
\(697\) −11.1583 −0.422651
\(698\) 57.0695 2.16011
\(699\) −26.2470 −0.992752
\(700\) 17.4971 0.661330
\(701\) −16.5673 −0.625738 −0.312869 0.949796i \(-0.601290\pi\)
−0.312869 + 0.949796i \(0.601290\pi\)
\(702\) −23.8582 −0.900470
\(703\) −0.209230 −0.00789125
\(704\) 11.7599 0.443219
\(705\) −61.1073 −2.30144
\(706\) −29.6091 −1.11435
\(707\) −1.56158 −0.0587291
\(708\) −15.8696 −0.596415
\(709\) −49.1851 −1.84719 −0.923593 0.383374i \(-0.874762\pi\)
−0.923593 + 0.383374i \(0.874762\pi\)
\(710\) −28.8541 −1.08288
\(711\) 8.50833 0.319087
\(712\) 103.635 3.88388
\(713\) −0.0114129 −0.000427415 0
\(714\) −8.28922 −0.310216
\(715\) 22.0216 0.823562
\(716\) −15.3244 −0.572700
\(717\) 51.2198 1.91284
\(718\) −60.2491 −2.24848
\(719\) 31.3364 1.16865 0.584326 0.811519i \(-0.301359\pi\)
0.584326 + 0.811519i \(0.301359\pi\)
\(720\) 18.9927 0.707817
\(721\) −6.68169 −0.248839
\(722\) 47.4407 1.76556
\(723\) 30.2490 1.12497
\(724\) −62.9105 −2.33805
\(725\) −48.2368 −1.79147
\(726\) 14.4736 0.537168
\(727\) 32.3337 1.19919 0.599596 0.800303i \(-0.295328\pi\)
0.599596 + 0.800303i \(0.295328\pi\)
\(728\) 10.8955 0.403814
\(729\) 12.2134 0.452350
\(730\) −93.2795 −3.45243
\(731\) −2.30618 −0.0852973
\(732\) 11.6002 0.428755
\(733\) −4.07873 −0.150651 −0.0753256 0.997159i \(-0.524000\pi\)
−0.0753256 + 0.997159i \(0.524000\pi\)
\(734\) −29.5944 −1.09235
\(735\) −40.8956 −1.50846
\(736\) −0.00368871 −0.000135968 0
\(737\) 26.6263 0.980794
\(738\) 14.0087 0.515668
\(739\) −42.2560 −1.55441 −0.777206 0.629246i \(-0.783364\pi\)
−0.777206 + 0.629246i \(0.783364\pi\)
\(740\) −11.9540 −0.439439
\(741\) −1.16150 −0.0426687
\(742\) −21.7266 −0.797609
\(743\) −45.2132 −1.65871 −0.829356 0.558721i \(-0.811292\pi\)
−0.829356 + 0.558721i \(0.811292\pi\)
\(744\) 102.977 3.77530
\(745\) 25.0940 0.919374
\(746\) −52.5260 −1.92311
\(747\) 5.22613 0.191214
\(748\) −25.3457 −0.926730
\(749\) 14.9338 0.545668
\(750\) −2.87676 −0.105044
\(751\) −39.2731 −1.43309 −0.716547 0.697539i \(-0.754279\pi\)
−0.716547 + 0.697539i \(0.754279\pi\)
\(752\) −54.3444 −1.98174
\(753\) −9.35384 −0.340873
\(754\) −56.4793 −2.05685
\(755\) 0.247653 0.00901302
\(756\) −13.2921 −0.483430
\(757\) 25.7317 0.935234 0.467617 0.883931i \(-0.345113\pi\)
0.467617 + 0.883931i \(0.345113\pi\)
\(758\) 57.0873 2.07350
\(759\) −0.00726824 −0.000263820 0
\(760\) −4.33042 −0.157081
\(761\) −6.65903 −0.241390 −0.120695 0.992690i \(-0.538512\pi\)
−0.120695 + 0.992690i \(0.538512\pi\)
\(762\) 26.4324 0.957545
\(763\) −9.67161 −0.350136
\(764\) 64.0031 2.31555
\(765\) 6.92861 0.250504
\(766\) −90.6463 −3.27518
\(767\) 4.47332 0.161522
\(768\) −64.7369 −2.33599
\(769\) −38.3908 −1.38441 −0.692204 0.721702i \(-0.743360\pi\)
−0.692204 + 0.721702i \(0.743360\pi\)
\(770\) 18.0129 0.649139
\(771\) 16.5489 0.595995
\(772\) −91.0400 −3.27660
\(773\) −47.6369 −1.71338 −0.856690 0.515831i \(-0.827483\pi\)
−0.856690 + 0.515831i \(0.827483\pi\)
\(774\) 2.89530 0.104069
\(775\) −46.6148 −1.67445
\(776\) −37.1194 −1.33251
\(777\) −1.39478 −0.0500374
\(778\) −48.5477 −1.74052
\(779\) −1.27890 −0.0458214
\(780\) −66.3605 −2.37609
\(781\) −10.2941 −0.368352
\(782\) −0.00660949 −0.000236355 0
\(783\) 36.6443 1.30956
\(784\) −36.3695 −1.29891
\(785\) −41.2650 −1.47281
\(786\) 14.5822 0.520131
\(787\) −7.55189 −0.269196 −0.134598 0.990900i \(-0.542974\pi\)
−0.134598 + 0.990900i \(0.542974\pi\)
\(788\) 18.9352 0.674537
\(789\) −24.6711 −0.878315
\(790\) −65.1557 −2.31813
\(791\) −11.3643 −0.404067
\(792\) 16.9228 0.601327
\(793\) −3.26987 −0.116117
\(794\) −50.8763 −1.80553
\(795\) 70.3759 2.49598
\(796\) 104.176 3.69243
\(797\) 4.73439 0.167701 0.0838503 0.996478i \(-0.473278\pi\)
0.0838503 + 0.996478i \(0.473278\pi\)
\(798\) −0.950062 −0.0336318
\(799\) −19.8250 −0.701359
\(800\) −15.0662 −0.532670
\(801\) −19.0046 −0.671496
\(802\) −66.4019 −2.34473
\(803\) −33.2788 −1.17438
\(804\) −80.2364 −2.82972
\(805\) 0.00319940 0.000112764 0
\(806\) −54.5801 −1.92250
\(807\) 7.35799 0.259014
\(808\) 11.2347 0.395235
\(809\) 8.95744 0.314927 0.157463 0.987525i \(-0.449668\pi\)
0.157463 + 0.987525i \(0.449668\pi\)
\(810\) 88.2230 3.09984
\(811\) 27.3832 0.961555 0.480777 0.876843i \(-0.340355\pi\)
0.480777 + 0.876843i \(0.340355\pi\)
\(812\) −31.4663 −1.10425
\(813\) −51.7257 −1.81410
\(814\) −6.26143 −0.219463
\(815\) 5.71031 0.200023
\(816\) 23.8785 0.835914
\(817\) −0.264321 −0.00924744
\(818\) −10.3996 −0.363614
\(819\) −1.99802 −0.0698166
\(820\) −73.0682 −2.55165
\(821\) 16.7438 0.584364 0.292182 0.956363i \(-0.405619\pi\)
0.292182 + 0.956363i \(0.405619\pi\)
\(822\) −109.335 −3.81350
\(823\) −40.4236 −1.40908 −0.704540 0.709665i \(-0.748846\pi\)
−0.704540 + 0.709665i \(0.748846\pi\)
\(824\) 48.0711 1.67464
\(825\) −29.6864 −1.03355
\(826\) 3.65901 0.127313
\(827\) −29.1603 −1.01400 −0.507001 0.861945i \(-0.669246\pi\)
−0.507001 + 0.861945i \(0.669246\pi\)
\(828\) 0.00565184 0.000196415 0
\(829\) −42.6598 −1.48164 −0.740818 0.671706i \(-0.765562\pi\)
−0.740818 + 0.671706i \(0.765562\pi\)
\(830\) −40.0210 −1.38915
\(831\) 60.4032 2.09536
\(832\) 9.98920 0.346313
\(833\) −13.2677 −0.459699
\(834\) −7.24188 −0.250766
\(835\) −38.4025 −1.32897
\(836\) −2.90498 −0.100471
\(837\) 35.4120 1.22402
\(838\) 40.8834 1.41229
\(839\) −18.9427 −0.653976 −0.326988 0.945028i \(-0.606034\pi\)
−0.326988 + 0.945028i \(0.606034\pi\)
\(840\) −28.8677 −0.996031
\(841\) 57.7476 1.99130
\(842\) 48.1860 1.66060
\(843\) 17.8730 0.615579
\(844\) 92.1108 3.17058
\(845\) −22.7703 −0.783321
\(846\) 24.8893 0.855713
\(847\) −2.27300 −0.0781012
\(848\) 62.5872 2.14925
\(849\) −4.50897 −0.154747
\(850\) −26.9958 −0.925950
\(851\) −0.00111214 −3.81237e−5 0
\(852\) 31.0205 1.06275
\(853\) −34.6981 −1.18804 −0.594020 0.804451i \(-0.702460\pi\)
−0.594020 + 0.804451i \(0.702460\pi\)
\(854\) −2.67463 −0.0915241
\(855\) 0.794117 0.0271582
\(856\) −107.440 −3.67223
\(857\) 54.0805 1.84735 0.923677 0.383172i \(-0.125168\pi\)
0.923677 + 0.383172i \(0.125168\pi\)
\(858\) −34.7591 −1.18666
\(859\) −52.1629 −1.77978 −0.889888 0.456178i \(-0.849218\pi\)
−0.889888 + 0.456178i \(0.849218\pi\)
\(860\) −15.1016 −0.514961
\(861\) −8.52549 −0.290548
\(862\) −15.0375 −0.512180
\(863\) 52.3833 1.78315 0.891574 0.452876i \(-0.149602\pi\)
0.891574 + 0.452876i \(0.149602\pi\)
\(864\) 11.4454 0.389380
\(865\) 5.86609 0.199453
\(866\) 53.3171 1.81179
\(867\) −25.4729 −0.865107
\(868\) −30.4082 −1.03212
\(869\) −23.2452 −0.788540
\(870\) 149.643 5.07336
\(871\) 22.6171 0.766351
\(872\) 69.5819 2.35634
\(873\) 6.80698 0.230381
\(874\) −0.000757541 0 −2.56242e−5 0
\(875\) 0.451778 0.0152729
\(876\) 100.283 3.38825
\(877\) −6.12184 −0.206720 −0.103360 0.994644i \(-0.532959\pi\)
−0.103360 + 0.994644i \(0.532959\pi\)
\(878\) 22.5917 0.762433
\(879\) −33.8430 −1.14149
\(880\) −51.8891 −1.74918
\(881\) 56.3363 1.89802 0.949009 0.315249i \(-0.102088\pi\)
0.949009 + 0.315249i \(0.102088\pi\)
\(882\) 16.6570 0.560869
\(883\) 8.55118 0.287770 0.143885 0.989594i \(-0.454040\pi\)
0.143885 + 0.989594i \(0.454040\pi\)
\(884\) −21.5293 −0.724108
\(885\) −11.8521 −0.398405
\(886\) −71.0076 −2.38555
\(887\) −37.0462 −1.24389 −0.621945 0.783061i \(-0.713657\pi\)
−0.621945 + 0.783061i \(0.713657\pi\)
\(888\) 10.0347 0.336741
\(889\) −4.15105 −0.139222
\(890\) 145.535 4.87834
\(891\) 31.4748 1.05445
\(892\) −10.8687 −0.363912
\(893\) −2.27223 −0.0760372
\(894\) −39.6086 −1.32471
\(895\) −11.4450 −0.382563
\(896\) 12.7721 0.426685
\(897\) −0.00617383 −0.000206138 0
\(898\) −45.0689 −1.50397
\(899\) 83.8305 2.79591
\(900\) 23.0844 0.769480
\(901\) 22.8320 0.760645
\(902\) −38.2725 −1.27434
\(903\) −1.76203 −0.0586368
\(904\) 81.7598 2.71929
\(905\) −46.9845 −1.56182
\(906\) −0.390897 −0.0129867
\(907\) 40.2951 1.33798 0.668988 0.743273i \(-0.266728\pi\)
0.668988 + 0.743273i \(0.266728\pi\)
\(908\) 1.34911 0.0447717
\(909\) −2.06023 −0.0683334
\(910\) 15.3006 0.507210
\(911\) −46.7577 −1.54915 −0.774576 0.632481i \(-0.782036\pi\)
−0.774576 + 0.632481i \(0.782036\pi\)
\(912\) 2.73681 0.0906249
\(913\) −14.2781 −0.472535
\(914\) −5.33892 −0.176596
\(915\) 8.66356 0.286408
\(916\) 20.2889 0.670363
\(917\) −2.29005 −0.0756242
\(918\) 20.5080 0.676866
\(919\) −33.9069 −1.11848 −0.559242 0.829004i \(-0.688908\pi\)
−0.559242 + 0.829004i \(0.688908\pi\)
\(920\) −0.0230179 −0.000758879 0
\(921\) −27.7554 −0.914570
\(922\) 34.0794 1.12234
\(923\) −8.74409 −0.287815
\(924\) −19.3653 −0.637072
\(925\) −4.54243 −0.149354
\(926\) 10.3589 0.340415
\(927\) −8.81532 −0.289533
\(928\) 27.0946 0.889422
\(929\) 30.1936 0.990620 0.495310 0.868716i \(-0.335054\pi\)
0.495310 + 0.868716i \(0.335054\pi\)
\(930\) 144.611 4.74197
\(931\) −1.52067 −0.0498379
\(932\) −55.7608 −1.82651
\(933\) 17.7389 0.580745
\(934\) 19.9647 0.653264
\(935\) −18.9293 −0.619055
\(936\) 14.3747 0.469851
\(937\) −54.1007 −1.76739 −0.883696 0.468061i \(-0.844953\pi\)
−0.883696 + 0.468061i \(0.844953\pi\)
\(938\) 18.4999 0.604045
\(939\) −37.1042 −1.21085
\(940\) −129.820 −4.23428
\(941\) −51.3561 −1.67416 −0.837081 0.547079i \(-0.815740\pi\)
−0.837081 + 0.547079i \(0.815740\pi\)
\(942\) 65.1329 2.12214
\(943\) −0.00679788 −0.000221369 0
\(944\) −10.5404 −0.343061
\(945\) −9.92717 −0.322931
\(946\) −7.91011 −0.257180
\(947\) 46.7235 1.51831 0.759154 0.650911i \(-0.225613\pi\)
0.759154 + 0.650911i \(0.225613\pi\)
\(948\) 70.0477 2.27504
\(949\) −28.2679 −0.917614
\(950\) −3.09411 −0.100386
\(951\) −44.3326 −1.43758
\(952\) −9.36554 −0.303539
\(953\) 25.8745 0.838158 0.419079 0.907950i \(-0.362353\pi\)
0.419079 + 0.907950i \(0.362353\pi\)
\(954\) −28.6645 −0.928046
\(955\) 47.8004 1.54679
\(956\) 108.815 3.51932
\(957\) 53.3871 1.72576
\(958\) −81.6710 −2.63867
\(959\) 17.1704 0.554462
\(960\) −26.4665 −0.854202
\(961\) 50.0116 1.61328
\(962\) −5.31862 −0.171479
\(963\) 19.7025 0.634903
\(964\) 64.2629 2.06977
\(965\) −67.9929 −2.18877
\(966\) −0.00504996 −0.000162480 0
\(967\) −40.4484 −1.30073 −0.650367 0.759620i \(-0.725385\pi\)
−0.650367 + 0.759620i \(0.725385\pi\)
\(968\) 16.3530 0.525605
\(969\) 0.998399 0.0320732
\(970\) −52.1270 −1.67370
\(971\) 0.0749970 0.00240677 0.00120338 0.999999i \(-0.499617\pi\)
0.00120338 + 0.999999i \(0.499617\pi\)
\(972\) −44.4249 −1.42493
\(973\) 1.13729 0.0364600
\(974\) −67.9733 −2.17801
\(975\) −25.2164 −0.807572
\(976\) 7.70473 0.246622
\(977\) −11.8737 −0.379873 −0.189937 0.981796i \(-0.560828\pi\)
−0.189937 + 0.981796i \(0.560828\pi\)
\(978\) −9.01319 −0.288210
\(979\) 51.9217 1.65942
\(980\) −86.8812 −2.77532
\(981\) −12.7600 −0.407395
\(982\) −51.0405 −1.62877
\(983\) 43.1551 1.37643 0.688217 0.725505i \(-0.258394\pi\)
0.688217 + 0.725505i \(0.258394\pi\)
\(984\) 61.3362 1.95533
\(985\) 14.1416 0.450590
\(986\) 48.5484 1.54610
\(987\) −15.1473 −0.482143
\(988\) −2.46756 −0.0785036
\(989\) −0.00140498 −4.46756e−5 0
\(990\) 23.7648 0.755296
\(991\) 33.6711 1.06960 0.534798 0.844980i \(-0.320388\pi\)
0.534798 + 0.844980i \(0.320388\pi\)
\(992\) 26.1835 0.831326
\(993\) −36.9580 −1.17283
\(994\) −7.15234 −0.226859
\(995\) 77.8036 2.46654
\(996\) 43.0258 1.36332
\(997\) 32.1354 1.01774 0.508870 0.860844i \(-0.330064\pi\)
0.508870 + 0.860844i \(0.330064\pi\)
\(998\) 32.0678 1.01509
\(999\) 3.45077 0.109177
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 \(a_p\))