Properties

Label 8011.2.a.b.1.11
Level 8011
Weight 2
Character 8011.1
Self dual Yes
Analytic conductor 63.968
Analytic rank 0
Dimension 358
CM No

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Newspace parameters

Level: \( N \) = \( 8011 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8011.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9681570592\)
Analytic rank: \(0\)
Dimension: \(358\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 8011.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.64605 q^{2}\) \(-0.0865598 q^{3}\) \(+5.00159 q^{4}\) \(-1.46630 q^{5}\) \(+0.229042 q^{6}\) \(-4.80741 q^{7}\) \(-7.94236 q^{8}\) \(-2.99251 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.64605 q^{2}\) \(-0.0865598 q^{3}\) \(+5.00159 q^{4}\) \(-1.46630 q^{5}\) \(+0.229042 q^{6}\) \(-4.80741 q^{7}\) \(-7.94236 q^{8}\) \(-2.99251 q^{9}\) \(+3.87990 q^{10}\) \(+2.57564 q^{11}\) \(-0.432937 q^{12}\) \(+4.36416 q^{13}\) \(+12.7207 q^{14}\) \(+0.126922 q^{15}\) \(+11.0127 q^{16}\) \(+5.06362 q^{17}\) \(+7.91833 q^{18}\) \(+3.86716 q^{19}\) \(-7.33382 q^{20}\) \(+0.416129 q^{21}\) \(-6.81528 q^{22}\) \(+5.72586 q^{23}\) \(+0.687489 q^{24}\) \(-2.84997 q^{25}\) \(-11.5478 q^{26}\) \(+0.518710 q^{27}\) \(-24.0447 q^{28}\) \(+4.16537 q^{29}\) \(-0.335843 q^{30}\) \(+1.73342 q^{31}\) \(-13.2555 q^{32}\) \(-0.222947 q^{33}\) \(-13.3986 q^{34}\) \(+7.04909 q^{35}\) \(-14.9673 q^{36}\) \(+6.26985 q^{37}\) \(-10.2327 q^{38}\) \(-0.377761 q^{39}\) \(+11.6459 q^{40}\) \(-5.65631 q^{41}\) \(-1.10110 q^{42}\) \(+3.61517 q^{43}\) \(+12.8823 q^{44}\) \(+4.38791 q^{45}\) \(-15.1509 q^{46}\) \(-3.93319 q^{47}\) \(-0.953259 q^{48}\) \(+16.1112 q^{49}\) \(+7.54117 q^{50}\) \(-0.438306 q^{51}\) \(+21.8277 q^{52}\) \(-0.0159586 q^{53}\) \(-1.37253 q^{54}\) \(-3.77666 q^{55}\) \(+38.1822 q^{56}\) \(-0.334741 q^{57}\) \(-11.0218 q^{58}\) \(+9.52594 q^{59}\) \(+0.634814 q^{60}\) \(-5.30684 q^{61}\) \(-4.58671 q^{62}\) \(+14.3862 q^{63}\) \(+13.0493 q^{64}\) \(-6.39915 q^{65}\) \(+0.589929 q^{66}\) \(+6.24632 q^{67}\) \(+25.3261 q^{68}\) \(-0.495629 q^{69}\) \(-18.6523 q^{70}\) \(+3.50484 q^{71}\) \(+23.7676 q^{72}\) \(+7.45362 q^{73}\) \(-16.5904 q^{74}\) \(+0.246693 q^{75}\) \(+19.3419 q^{76}\) \(-12.3822 q^{77}\) \(+0.999574 q^{78}\) \(+5.44143 q^{79}\) \(-16.1479 q^{80}\) \(+8.93262 q^{81}\) \(+14.9669 q^{82}\) \(-15.8453 q^{83}\) \(+2.08130 q^{84}\) \(-7.42477 q^{85}\) \(-9.56593 q^{86}\) \(-0.360554 q^{87}\) \(-20.4567 q^{88}\) \(+4.26134 q^{89}\) \(-11.6106 q^{90}\) \(-20.9803 q^{91}\) \(+28.6384 q^{92}\) \(-0.150044 q^{93}\) \(+10.4074 q^{94}\) \(-5.67041 q^{95}\) \(+1.14739 q^{96}\) \(-9.83726 q^{97}\) \(-42.6310 q^{98}\) \(-7.70762 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(358q \) \(\mathstrut +\mathstrut 33q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 391q^{4} \) \(\mathstrut +\mathstrut 76q^{5} \) \(\mathstrut +\mathstrut 32q^{6} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 99q^{8} \) \(\mathstrut +\mathstrut 451q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(358q \) \(\mathstrut +\mathstrut 33q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 391q^{4} \) \(\mathstrut +\mathstrut 76q^{5} \) \(\mathstrut +\mathstrut 32q^{6} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 99q^{8} \) \(\mathstrut +\mathstrut 451q^{9} \) \(\mathstrut +\mathstrut 21q^{10} \) \(\mathstrut +\mathstrut 70q^{11} \) \(\mathstrut +\mathstrut 20q^{12} \) \(\mathstrut +\mathstrut 53q^{13} \) \(\mathstrut +\mathstrut 69q^{14} \) \(\mathstrut +\mathstrut 28q^{15} \) \(\mathstrut +\mathstrut 449q^{16} \) \(\mathstrut +\mathstrut 88q^{17} \) \(\mathstrut +\mathstrut 86q^{18} \) \(\mathstrut +\mathstrut 44q^{19} \) \(\mathstrut +\mathstrut 136q^{20} \) \(\mathstrut +\mathstrut 125q^{21} \) \(\mathstrut +\mathstrut 17q^{22} \) \(\mathstrut +\mathstrut 104q^{23} \) \(\mathstrut +\mathstrut 84q^{24} \) \(\mathstrut +\mathstrut 444q^{25} \) \(\mathstrut +\mathstrut 100q^{26} \) \(\mathstrut +\mathstrut 32q^{27} \) \(\mathstrut +\mathstrut 46q^{28} \) \(\mathstrut +\mathstrut 373q^{29} \) \(\mathstrut +\mathstrut 99q^{30} \) \(\mathstrut +\mathstrut 30q^{31} \) \(\mathstrut +\mathstrut 221q^{32} \) \(\mathstrut +\mathstrut 56q^{33} \) \(\mathstrut +\mathstrut 26q^{34} \) \(\mathstrut +\mathstrut 164q^{35} \) \(\mathstrut +\mathstrut 599q^{36} \) \(\mathstrut +\mathstrut 81q^{37} \) \(\mathstrut +\mathstrut 66q^{38} \) \(\mathstrut +\mathstrut 143q^{39} \) \(\mathstrut +\mathstrut 42q^{40} \) \(\mathstrut +\mathstrut 182q^{41} \) \(\mathstrut +\mathstrut 32q^{42} \) \(\mathstrut +\mathstrut 40q^{43} \) \(\mathstrut +\mathstrut 184q^{44} \) \(\mathstrut +\mathstrut 198q^{45} \) \(\mathstrut +\mathstrut 54q^{46} \) \(\mathstrut +\mathstrut 66q^{47} \) \(\mathstrut +\mathstrut 5q^{48} \) \(\mathstrut +\mathstrut 479q^{49} \) \(\mathstrut +\mathstrut 184q^{50} \) \(\mathstrut +\mathstrut 123q^{51} \) \(\mathstrut +\mathstrut 64q^{52} \) \(\mathstrut +\mathstrut 221q^{53} \) \(\mathstrut +\mathstrut 67q^{54} \) \(\mathstrut +\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 174q^{56} \) \(\mathstrut +\mathstrut 84q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut +\mathstrut 127q^{59} \) \(\mathstrut +\mathstrut 29q^{60} \) \(\mathstrut +\mathstrut 174q^{61} \) \(\mathstrut +\mathstrut 86q^{62} \) \(\mathstrut +\mathstrut 48q^{63} \) \(\mathstrut +\mathstrut 549q^{64} \) \(\mathstrut +\mathstrut 202q^{65} \) \(\mathstrut +\mathstrut 32q^{66} \) \(\mathstrut +\mathstrut 29q^{67} \) \(\mathstrut +\mathstrut 172q^{68} \) \(\mathstrut +\mathstrut 249q^{69} \) \(\mathstrut +\mathstrut 12q^{70} \) \(\mathstrut +\mathstrut 185q^{71} \) \(\mathstrut +\mathstrut 218q^{72} \) \(\mathstrut +\mathstrut 57q^{73} \) \(\mathstrut +\mathstrut 272q^{74} \) \(\mathstrut +\mathstrut 24q^{75} \) \(\mathstrut +\mathstrut 84q^{76} \) \(\mathstrut +\mathstrut 384q^{77} \) \(\mathstrut +\mathstrut 12q^{78} \) \(\mathstrut +\mathstrut 93q^{79} \) \(\mathstrut +\mathstrut 215q^{80} \) \(\mathstrut +\mathstrut 702q^{81} \) \(\mathstrut +\mathstrut 48q^{82} \) \(\mathstrut +\mathstrut 121q^{83} \) \(\mathstrut +\mathstrut 179q^{84} \) \(\mathstrut +\mathstrut 177q^{85} \) \(\mathstrut +\mathstrut 209q^{86} \) \(\mathstrut +\mathstrut 91q^{87} \) \(\mathstrut +\mathstrut 36q^{88} \) \(\mathstrut +\mathstrut 186q^{89} \) \(\mathstrut +\mathstrut 66q^{90} \) \(\mathstrut +\mathstrut 32q^{91} \) \(\mathstrut +\mathstrut 272q^{92} \) \(\mathstrut +\mathstrut 220q^{93} \) \(\mathstrut +\mathstrut 60q^{94} \) \(\mathstrut +\mathstrut 170q^{95} \) \(\mathstrut +\mathstrut 162q^{96} \) \(\mathstrut +\mathstrut 22q^{97} \) \(\mathstrut +\mathstrut 196q^{98} \) \(\mathstrut +\mathstrut 152q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.64605 −1.87104 −0.935521 0.353272i \(-0.885069\pi\)
−0.935521 + 0.353272i \(0.885069\pi\)
\(3\) −0.0865598 −0.0499753 −0.0249877 0.999688i \(-0.507955\pi\)
−0.0249877 + 0.999688i \(0.507955\pi\)
\(4\) 5.00159 2.50079
\(5\) −1.46630 −0.655748 −0.327874 0.944721i \(-0.606332\pi\)
−0.327874 + 0.944721i \(0.606332\pi\)
\(6\) 0.229042 0.0935059
\(7\) −4.80741 −1.81703 −0.908515 0.417852i \(-0.862783\pi\)
−0.908515 + 0.417852i \(0.862783\pi\)
\(8\) −7.94236 −2.80805
\(9\) −2.99251 −0.997502
\(10\) 3.87990 1.22693
\(11\) 2.57564 0.776585 0.388292 0.921536i \(-0.373065\pi\)
0.388292 + 0.921536i \(0.373065\pi\)
\(12\) −0.432937 −0.124978
\(13\) 4.36416 1.21040 0.605200 0.796074i \(-0.293093\pi\)
0.605200 + 0.796074i \(0.293093\pi\)
\(14\) 12.7207 3.39974
\(15\) 0.126922 0.0327712
\(16\) 11.0127 2.75318
\(17\) 5.06362 1.22811 0.614054 0.789264i \(-0.289538\pi\)
0.614054 + 0.789264i \(0.289538\pi\)
\(18\) 7.91833 1.86637
\(19\) 3.86716 0.887187 0.443593 0.896228i \(-0.353703\pi\)
0.443593 + 0.896228i \(0.353703\pi\)
\(20\) −7.33382 −1.63989
\(21\) 0.416129 0.0908067
\(22\) −6.81528 −1.45302
\(23\) 5.72586 1.19392 0.596962 0.802270i \(-0.296374\pi\)
0.596962 + 0.802270i \(0.296374\pi\)
\(24\) 0.687489 0.140333
\(25\) −2.84997 −0.569994
\(26\) −11.5478 −2.26471
\(27\) 0.518710 0.0998259
\(28\) −24.0447 −4.54402
\(29\) 4.16537 0.773490 0.386745 0.922187i \(-0.373599\pi\)
0.386745 + 0.922187i \(0.373599\pi\)
\(30\) −0.335843 −0.0613163
\(31\) 1.73342 0.311331 0.155665 0.987810i \(-0.450248\pi\)
0.155665 + 0.987810i \(0.450248\pi\)
\(32\) −13.2555 −2.34326
\(33\) −0.222947 −0.0388101
\(34\) −13.3986 −2.29784
\(35\) 7.04909 1.19151
\(36\) −14.9673 −2.49455
\(37\) 6.26985 1.03076 0.515379 0.856962i \(-0.327651\pi\)
0.515379 + 0.856962i \(0.327651\pi\)
\(38\) −10.2327 −1.65996
\(39\) −0.377761 −0.0604901
\(40\) 11.6459 1.84137
\(41\) −5.65631 −0.883367 −0.441683 0.897171i \(-0.645619\pi\)
−0.441683 + 0.897171i \(0.645619\pi\)
\(42\) −1.10110 −0.169903
\(43\) 3.61517 0.551308 0.275654 0.961257i \(-0.411106\pi\)
0.275654 + 0.961257i \(0.411106\pi\)
\(44\) 12.8823 1.94208
\(45\) 4.38791 0.654110
\(46\) −15.1509 −2.23388
\(47\) −3.93319 −0.573715 −0.286858 0.957973i \(-0.592611\pi\)
−0.286858 + 0.957973i \(0.592611\pi\)
\(48\) −0.953259 −0.137591
\(49\) 16.1112 2.30160
\(50\) 7.54117 1.06648
\(51\) −0.438306 −0.0613751
\(52\) 21.8277 3.02696
\(53\) −0.0159586 −0.00219208 −0.00109604 0.999999i \(-0.500349\pi\)
−0.00109604 + 0.999999i \(0.500349\pi\)
\(54\) −1.37253 −0.186778
\(55\) −3.77666 −0.509244
\(56\) 38.1822 5.10231
\(57\) −0.334741 −0.0443375
\(58\) −11.0218 −1.44723
\(59\) 9.52594 1.24017 0.620086 0.784534i \(-0.287098\pi\)
0.620086 + 0.784534i \(0.287098\pi\)
\(60\) 0.634814 0.0819541
\(61\) −5.30684 −0.679471 −0.339736 0.940521i \(-0.610338\pi\)
−0.339736 + 0.940521i \(0.610338\pi\)
\(62\) −4.58671 −0.582513
\(63\) 14.3862 1.81249
\(64\) 13.0493 1.63116
\(65\) −6.39915 −0.793717
\(66\) 0.589929 0.0726153
\(67\) 6.24632 0.763109 0.381555 0.924346i \(-0.375389\pi\)
0.381555 + 0.924346i \(0.375389\pi\)
\(68\) 25.3261 3.07125
\(69\) −0.495629 −0.0596667
\(70\) −18.6523 −2.22937
\(71\) 3.50484 0.415948 0.207974 0.978134i \(-0.433313\pi\)
0.207974 + 0.978134i \(0.433313\pi\)
\(72\) 23.7676 2.80104
\(73\) 7.45362 0.872381 0.436190 0.899854i \(-0.356327\pi\)
0.436190 + 0.899854i \(0.356327\pi\)
\(74\) −16.5904 −1.92859
\(75\) 0.246693 0.0284857
\(76\) 19.3419 2.21867
\(77\) −12.3822 −1.41108
\(78\) 0.999574 0.113179
\(79\) 5.44143 0.612209 0.306104 0.951998i \(-0.400974\pi\)
0.306104 + 0.951998i \(0.400974\pi\)
\(80\) −16.1479 −1.80539
\(81\) 8.93262 0.992514
\(82\) 14.9669 1.65282
\(83\) −15.8453 −1.73924 −0.869621 0.493720i \(-0.835637\pi\)
−0.869621 + 0.493720i \(0.835637\pi\)
\(84\) 2.08130 0.227089
\(85\) −7.42477 −0.805330
\(86\) −9.56593 −1.03152
\(87\) −0.360554 −0.0386554
\(88\) −20.4567 −2.18069
\(89\) 4.26134 0.451701 0.225851 0.974162i \(-0.427484\pi\)
0.225851 + 0.974162i \(0.427484\pi\)
\(90\) −11.6106 −1.22387
\(91\) −20.9803 −2.19933
\(92\) 28.6384 2.98576
\(93\) −0.150044 −0.0155589
\(94\) 10.4074 1.07344
\(95\) −5.67041 −0.581771
\(96\) 1.14739 0.117105
\(97\) −9.83726 −0.998822 −0.499411 0.866365i \(-0.666450\pi\)
−0.499411 + 0.866365i \(0.666450\pi\)
\(98\) −42.6310 −4.30638
\(99\) −7.70762 −0.774645
\(100\) −14.2544 −1.42544
\(101\) 3.82878 0.380977 0.190489 0.981689i \(-0.438993\pi\)
0.190489 + 0.981689i \(0.438993\pi\)
\(102\) 1.15978 0.114835
\(103\) −14.2637 −1.40544 −0.702720 0.711467i \(-0.748031\pi\)
−0.702720 + 0.711467i \(0.748031\pi\)
\(104\) −34.6617 −3.39886
\(105\) −0.610168 −0.0595463
\(106\) 0.0422272 0.00410147
\(107\) 3.05407 0.295249 0.147624 0.989044i \(-0.452837\pi\)
0.147624 + 0.989044i \(0.452837\pi\)
\(108\) 2.59438 0.249644
\(109\) 3.96121 0.379415 0.189707 0.981841i \(-0.439246\pi\)
0.189707 + 0.981841i \(0.439246\pi\)
\(110\) 9.99323 0.952817
\(111\) −0.542718 −0.0515125
\(112\) −52.9426 −5.00261
\(113\) −6.37308 −0.599529 −0.299765 0.954013i \(-0.596908\pi\)
−0.299765 + 0.954013i \(0.596908\pi\)
\(114\) 0.885741 0.0829572
\(115\) −8.39581 −0.782913
\(116\) 20.8335 1.93434
\(117\) −13.0598 −1.20738
\(118\) −25.2061 −2.32041
\(119\) −24.3429 −2.23151
\(120\) −1.00806 −0.0920232
\(121\) −4.36608 −0.396916
\(122\) 14.0422 1.27132
\(123\) 0.489609 0.0441465
\(124\) 8.66984 0.778575
\(125\) 11.5104 1.02952
\(126\) −38.0667 −3.39125
\(127\) −8.99010 −0.797743 −0.398871 0.917007i \(-0.630598\pi\)
−0.398871 + 0.917007i \(0.630598\pi\)
\(128\) −8.01812 −0.708708
\(129\) −0.312928 −0.0275518
\(130\) 16.9325 1.48508
\(131\) −0.402871 −0.0351990 −0.0175995 0.999845i \(-0.505602\pi\)
−0.0175995 + 0.999845i \(0.505602\pi\)
\(132\) −1.11509 −0.0970561
\(133\) −18.5910 −1.61205
\(134\) −16.5281 −1.42781
\(135\) −0.760584 −0.0654606
\(136\) −40.2171 −3.44859
\(137\) 7.30938 0.624482 0.312241 0.950003i \(-0.398920\pi\)
0.312241 + 0.950003i \(0.398920\pi\)
\(138\) 1.31146 0.111639
\(139\) 5.86279 0.497276 0.248638 0.968597i \(-0.420017\pi\)
0.248638 + 0.968597i \(0.420017\pi\)
\(140\) 35.2567 2.97973
\(141\) 0.340456 0.0286716
\(142\) −9.27398 −0.778255
\(143\) 11.2405 0.939978
\(144\) −32.9556 −2.74630
\(145\) −6.10768 −0.507215
\(146\) −19.7227 −1.63226
\(147\) −1.39458 −0.115023
\(148\) 31.3592 2.57771
\(149\) 20.4152 1.67248 0.836241 0.548362i \(-0.184749\pi\)
0.836241 + 0.548362i \(0.184749\pi\)
\(150\) −0.652762 −0.0532978
\(151\) −14.0415 −1.14268 −0.571342 0.820712i \(-0.693577\pi\)
−0.571342 + 0.820712i \(0.693577\pi\)
\(152\) −30.7144 −2.49126
\(153\) −15.1529 −1.22504
\(154\) 32.7638 2.64018
\(155\) −2.54171 −0.204155
\(156\) −1.88940 −0.151273
\(157\) −15.8888 −1.26806 −0.634031 0.773308i \(-0.718601\pi\)
−0.634031 + 0.773308i \(0.718601\pi\)
\(158\) −14.3983 −1.14547
\(159\) 0.00138137 0.000109550 0
\(160\) 19.4365 1.53659
\(161\) −27.5265 −2.16940
\(162\) −23.6362 −1.85703
\(163\) 3.73850 0.292822 0.146411 0.989224i \(-0.453228\pi\)
0.146411 + 0.989224i \(0.453228\pi\)
\(164\) −28.2905 −2.20912
\(165\) 0.326907 0.0254496
\(166\) 41.9274 3.25419
\(167\) 2.35594 0.182308 0.0911541 0.995837i \(-0.470944\pi\)
0.0911541 + 0.995837i \(0.470944\pi\)
\(168\) −3.30504 −0.254990
\(169\) 6.04586 0.465066
\(170\) 19.6463 1.50680
\(171\) −11.5725 −0.884971
\(172\) 18.0816 1.37871
\(173\) 1.97358 0.150048 0.0750242 0.997182i \(-0.476097\pi\)
0.0750242 + 0.997182i \(0.476097\pi\)
\(174\) 0.954044 0.0723259
\(175\) 13.7010 1.03570
\(176\) 28.3648 2.13808
\(177\) −0.824564 −0.0619780
\(178\) −11.2757 −0.845152
\(179\) 6.11912 0.457365 0.228682 0.973501i \(-0.426558\pi\)
0.228682 + 0.973501i \(0.426558\pi\)
\(180\) 21.9465 1.63580
\(181\) −14.0159 −1.04180 −0.520898 0.853619i \(-0.674403\pi\)
−0.520898 + 0.853619i \(0.674403\pi\)
\(182\) 55.5149 4.11504
\(183\) 0.459359 0.0339568
\(184\) −45.4768 −3.35260
\(185\) −9.19347 −0.675918
\(186\) 0.397025 0.0291113
\(187\) 13.0421 0.953730
\(188\) −19.6722 −1.43474
\(189\) −2.49365 −0.181387
\(190\) 15.0042 1.08852
\(191\) 3.23956 0.234406 0.117203 0.993108i \(-0.462607\pi\)
0.117203 + 0.993108i \(0.462607\pi\)
\(192\) −1.12954 −0.0815179
\(193\) −19.8896 −1.43168 −0.715842 0.698262i \(-0.753957\pi\)
−0.715842 + 0.698262i \(0.753957\pi\)
\(194\) 26.0299 1.86884
\(195\) 0.553909 0.0396663
\(196\) 80.5815 5.75582
\(197\) 12.2142 0.870224 0.435112 0.900376i \(-0.356709\pi\)
0.435112 + 0.900376i \(0.356709\pi\)
\(198\) 20.3948 1.44939
\(199\) 25.5372 1.81029 0.905143 0.425108i \(-0.139764\pi\)
0.905143 + 0.425108i \(0.139764\pi\)
\(200\) 22.6355 1.60057
\(201\) −0.540680 −0.0381367
\(202\) −10.1311 −0.712824
\(203\) −20.0247 −1.40546
\(204\) −2.19223 −0.153487
\(205\) 8.29383 0.579266
\(206\) 37.7424 2.62964
\(207\) −17.1347 −1.19094
\(208\) 48.0612 3.33245
\(209\) 9.96041 0.688976
\(210\) 1.61454 0.111414
\(211\) 11.1326 0.766398 0.383199 0.923666i \(-0.374822\pi\)
0.383199 + 0.923666i \(0.374822\pi\)
\(212\) −0.0798183 −0.00548194
\(213\) −0.303378 −0.0207871
\(214\) −8.08124 −0.552422
\(215\) −5.30092 −0.361519
\(216\) −4.11978 −0.280316
\(217\) −8.33325 −0.565698
\(218\) −10.4816 −0.709901
\(219\) −0.645184 −0.0435975
\(220\) −18.8893 −1.27351
\(221\) 22.0984 1.48650
\(222\) 1.43606 0.0963819
\(223\) −16.3468 −1.09466 −0.547332 0.836915i \(-0.684357\pi\)
−0.547332 + 0.836915i \(0.684357\pi\)
\(224\) 63.7246 4.25778
\(225\) 8.52856 0.568571
\(226\) 16.8635 1.12174
\(227\) −28.6151 −1.89925 −0.949627 0.313383i \(-0.898538\pi\)
−0.949627 + 0.313383i \(0.898538\pi\)
\(228\) −1.67423 −0.110879
\(229\) −24.0500 −1.58927 −0.794635 0.607088i \(-0.792338\pi\)
−0.794635 + 0.607088i \(0.792338\pi\)
\(230\) 22.2157 1.46486
\(231\) 1.07180 0.0705191
\(232\) −33.0829 −2.17200
\(233\) −10.9982 −0.720517 −0.360259 0.932852i \(-0.617312\pi\)
−0.360259 + 0.932852i \(0.617312\pi\)
\(234\) 34.5568 2.25905
\(235\) 5.76723 0.376213
\(236\) 47.6449 3.10142
\(237\) −0.471009 −0.0305953
\(238\) 64.4125 4.17525
\(239\) 0.803309 0.0519617 0.0259809 0.999662i \(-0.491729\pi\)
0.0259809 + 0.999662i \(0.491729\pi\)
\(240\) 1.39776 0.0902251
\(241\) 15.1730 0.977376 0.488688 0.872459i \(-0.337476\pi\)
0.488688 + 0.872459i \(0.337476\pi\)
\(242\) 11.5529 0.742646
\(243\) −2.32934 −0.149427
\(244\) −26.5426 −1.69922
\(245\) −23.6238 −1.50927
\(246\) −1.29553 −0.0826000
\(247\) 16.8769 1.07385
\(248\) −13.7674 −0.874232
\(249\) 1.37156 0.0869192
\(250\) −30.4571 −1.92628
\(251\) 15.3394 0.968216 0.484108 0.875008i \(-0.339144\pi\)
0.484108 + 0.875008i \(0.339144\pi\)
\(252\) 71.9539 4.53267
\(253\) 14.7477 0.927183
\(254\) 23.7883 1.49261
\(255\) 0.642687 0.0402466
\(256\) −4.88223 −0.305140
\(257\) 9.78914 0.610630 0.305315 0.952251i \(-0.401238\pi\)
0.305315 + 0.952251i \(0.401238\pi\)
\(258\) 0.828025 0.0515506
\(259\) −30.1418 −1.87292
\(260\) −32.0059 −1.98492
\(261\) −12.4649 −0.771558
\(262\) 1.06602 0.0658588
\(263\) 21.6338 1.33399 0.666997 0.745060i \(-0.267579\pi\)
0.666997 + 0.745060i \(0.267579\pi\)
\(264\) 1.77073 0.108981
\(265\) 0.0234000 0.00143745
\(266\) 49.1928 3.01620
\(267\) −0.368861 −0.0225739
\(268\) 31.2415 1.90838
\(269\) 30.2003 1.84135 0.920674 0.390333i \(-0.127640\pi\)
0.920674 + 0.390333i \(0.127640\pi\)
\(270\) 2.01254 0.122480
\(271\) −11.1520 −0.677434 −0.338717 0.940888i \(-0.609993\pi\)
−0.338717 + 0.940888i \(0.609993\pi\)
\(272\) 55.7642 3.38120
\(273\) 1.81605 0.109912
\(274\) −19.3410 −1.16843
\(275\) −7.34050 −0.442649
\(276\) −2.47893 −0.149214
\(277\) 12.5708 0.755307 0.377653 0.925947i \(-0.376731\pi\)
0.377653 + 0.925947i \(0.376731\pi\)
\(278\) −15.5133 −0.930423
\(279\) −5.18726 −0.310553
\(280\) −55.9864 −3.34583
\(281\) 7.10484 0.423839 0.211920 0.977287i \(-0.432028\pi\)
0.211920 + 0.977287i \(0.432028\pi\)
\(282\) −0.900865 −0.0536458
\(283\) 13.8382 0.822594 0.411297 0.911501i \(-0.365076\pi\)
0.411297 + 0.911501i \(0.365076\pi\)
\(284\) 17.5298 1.04020
\(285\) 0.490829 0.0290742
\(286\) −29.7429 −1.75874
\(287\) 27.1922 1.60510
\(288\) 39.6672 2.33741
\(289\) 8.64024 0.508249
\(290\) 16.1612 0.949020
\(291\) 0.851511 0.0499165
\(292\) 37.2800 2.18164
\(293\) −18.9420 −1.10660 −0.553301 0.832981i \(-0.686632\pi\)
−0.553301 + 0.832981i \(0.686632\pi\)
\(294\) 3.69013 0.215213
\(295\) −13.9679 −0.813241
\(296\) −49.7974 −2.89442
\(297\) 1.33601 0.0775232
\(298\) −54.0198 −3.12928
\(299\) 24.9885 1.44512
\(300\) 1.23386 0.0712368
\(301\) −17.3796 −1.00174
\(302\) 37.1546 2.13801
\(303\) −0.331418 −0.0190395
\(304\) 42.5879 2.44258
\(305\) 7.78140 0.445562
\(306\) 40.0954 2.29210
\(307\) −16.6913 −0.952624 −0.476312 0.879276i \(-0.658027\pi\)
−0.476312 + 0.879276i \(0.658027\pi\)
\(308\) −61.9305 −3.52882
\(309\) 1.23466 0.0702373
\(310\) 6.72548 0.381982
\(311\) 19.5173 1.10673 0.553364 0.832940i \(-0.313344\pi\)
0.553364 + 0.832940i \(0.313344\pi\)
\(312\) 3.00031 0.169859
\(313\) −16.3993 −0.926946 −0.463473 0.886111i \(-0.653397\pi\)
−0.463473 + 0.886111i \(0.653397\pi\)
\(314\) 42.0425 2.37260
\(315\) −21.0945 −1.18854
\(316\) 27.2158 1.53101
\(317\) 4.16664 0.234022 0.117011 0.993131i \(-0.462669\pi\)
0.117011 + 0.993131i \(0.462669\pi\)
\(318\) −0.00365518 −0.000204972 0
\(319\) 10.7285 0.600681
\(320\) −19.1342 −1.06963
\(321\) −0.264360 −0.0147551
\(322\) 72.8366 4.05903
\(323\) 19.5818 1.08956
\(324\) 44.6773 2.48207
\(325\) −12.4377 −0.689921
\(326\) −9.89225 −0.547881
\(327\) −0.342881 −0.0189614
\(328\) 44.9244 2.48054
\(329\) 18.9085 1.04246
\(330\) −0.865012 −0.0476173
\(331\) 22.3730 1.22973 0.614865 0.788632i \(-0.289210\pi\)
0.614865 + 0.788632i \(0.289210\pi\)
\(332\) −79.2514 −4.34949
\(333\) −18.7626 −1.02818
\(334\) −6.23394 −0.341106
\(335\) −9.15896 −0.500408
\(336\) 4.58271 0.250007
\(337\) 20.6946 1.12731 0.563655 0.826011i \(-0.309395\pi\)
0.563655 + 0.826011i \(0.309395\pi\)
\(338\) −15.9977 −0.870158
\(339\) 0.551653 0.0299617
\(340\) −37.1357 −2.01396
\(341\) 4.46466 0.241775
\(342\) 30.6214 1.65582
\(343\) −43.8012 −2.36504
\(344\) −28.7130 −1.54810
\(345\) 0.726740 0.0391264
\(346\) −5.22219 −0.280747
\(347\) 11.9336 0.640630 0.320315 0.947311i \(-0.396211\pi\)
0.320315 + 0.947311i \(0.396211\pi\)
\(348\) −1.80334 −0.0966693
\(349\) −3.21568 −0.172131 −0.0860657 0.996289i \(-0.527429\pi\)
−0.0860657 + 0.996289i \(0.527429\pi\)
\(350\) −36.2535 −1.93783
\(351\) 2.26373 0.120829
\(352\) −34.1414 −1.81974
\(353\) −16.7078 −0.889268 −0.444634 0.895712i \(-0.646666\pi\)
−0.444634 + 0.895712i \(0.646666\pi\)
\(354\) 2.18184 0.115963
\(355\) −5.13913 −0.272757
\(356\) 21.3135 1.12961
\(357\) 2.10712 0.111520
\(358\) −16.1915 −0.855748
\(359\) −15.6914 −0.828160 −0.414080 0.910241i \(-0.635897\pi\)
−0.414080 + 0.910241i \(0.635897\pi\)
\(360\) −34.8503 −1.83677
\(361\) −4.04509 −0.212899
\(362\) 37.0869 1.94924
\(363\) 0.377927 0.0198360
\(364\) −104.935 −5.50008
\(365\) −10.9292 −0.572062
\(366\) −1.21549 −0.0635346
\(367\) −17.2242 −0.899094 −0.449547 0.893257i \(-0.648415\pi\)
−0.449547 + 0.893257i \(0.648415\pi\)
\(368\) 63.0572 3.28709
\(369\) 16.9265 0.881160
\(370\) 24.3264 1.26467
\(371\) 0.0767194 0.00398307
\(372\) −0.750460 −0.0389095
\(373\) 19.2770 0.998127 0.499063 0.866565i \(-0.333677\pi\)
0.499063 + 0.866565i \(0.333677\pi\)
\(374\) −34.5100 −1.78447
\(375\) −0.996338 −0.0514507
\(376\) 31.2388 1.61102
\(377\) 18.1783 0.936232
\(378\) 6.59834 0.339382
\(379\) −18.8645 −0.969004 −0.484502 0.874790i \(-0.660999\pi\)
−0.484502 + 0.874790i \(0.660999\pi\)
\(380\) −28.3610 −1.45489
\(381\) 0.778182 0.0398675
\(382\) −8.57204 −0.438584
\(383\) 34.7702 1.77667 0.888337 0.459192i \(-0.151861\pi\)
0.888337 + 0.459192i \(0.151861\pi\)
\(384\) 0.694047 0.0354179
\(385\) 18.1559 0.925312
\(386\) 52.6289 2.67874
\(387\) −10.8184 −0.549931
\(388\) −49.2019 −2.49785
\(389\) 32.2435 1.63481 0.817406 0.576062i \(-0.195411\pi\)
0.817406 + 0.576062i \(0.195411\pi\)
\(390\) −1.46567 −0.0742172
\(391\) 28.9936 1.46627
\(392\) −127.961 −6.46300
\(393\) 0.0348724 0.00175908
\(394\) −32.3194 −1.62823
\(395\) −7.97876 −0.401455
\(396\) −38.5504 −1.93723
\(397\) −9.49168 −0.476374 −0.238187 0.971219i \(-0.576553\pi\)
−0.238187 + 0.971219i \(0.576553\pi\)
\(398\) −67.5728 −3.38712
\(399\) 1.60923 0.0805625
\(400\) −31.3859 −1.56930
\(401\) 5.90272 0.294768 0.147384 0.989079i \(-0.452915\pi\)
0.147384 + 0.989079i \(0.452915\pi\)
\(402\) 1.43067 0.0713552
\(403\) 7.56490 0.376835
\(404\) 19.1500 0.952746
\(405\) −13.0979 −0.650839
\(406\) 52.9863 2.62966
\(407\) 16.1489 0.800471
\(408\) 3.48118 0.172344
\(409\) −24.3422 −1.20365 −0.601823 0.798629i \(-0.705559\pi\)
−0.601823 + 0.798629i \(0.705559\pi\)
\(410\) −21.9459 −1.08383
\(411\) −0.632699 −0.0312087
\(412\) −71.3409 −3.51472
\(413\) −45.7951 −2.25343
\(414\) 45.3392 2.22830
\(415\) 23.2339 1.14051
\(416\) −57.8491 −2.83628
\(417\) −0.507482 −0.0248515
\(418\) −26.3558 −1.28910
\(419\) −26.8175 −1.31012 −0.655060 0.755577i \(-0.727357\pi\)
−0.655060 + 0.755577i \(0.727357\pi\)
\(420\) −3.05181 −0.148913
\(421\) 0.355718 0.0173366 0.00866831 0.999962i \(-0.497241\pi\)
0.00866831 + 0.999962i \(0.497241\pi\)
\(422\) −29.4574 −1.43396
\(423\) 11.7701 0.572282
\(424\) 0.126749 0.00615547
\(425\) −14.4312 −0.700015
\(426\) 0.802754 0.0388936
\(427\) 25.5121 1.23462
\(428\) 15.2752 0.738356
\(429\) −0.972975 −0.0469757
\(430\) 14.0265 0.676418
\(431\) 18.4008 0.886336 0.443168 0.896439i \(-0.353855\pi\)
0.443168 + 0.896439i \(0.353855\pi\)
\(432\) 5.71241 0.274838
\(433\) 2.81257 0.135164 0.0675818 0.997714i \(-0.478472\pi\)
0.0675818 + 0.997714i \(0.478472\pi\)
\(434\) 22.0502 1.05844
\(435\) 0.528679 0.0253482
\(436\) 19.8123 0.948839
\(437\) 22.1428 1.05923
\(438\) 1.70719 0.0815727
\(439\) 16.8499 0.804201 0.402101 0.915595i \(-0.368280\pi\)
0.402101 + 0.915595i \(0.368280\pi\)
\(440\) 29.9956 1.42998
\(441\) −48.2128 −2.29585
\(442\) −58.4736 −2.78130
\(443\) −40.9646 −1.94629 −0.973144 0.230197i \(-0.926063\pi\)
−0.973144 + 0.230197i \(0.926063\pi\)
\(444\) −2.71445 −0.128822
\(445\) −6.24839 −0.296202
\(446\) 43.2545 2.04816
\(447\) −1.76714 −0.0835828
\(448\) −62.7333 −2.96387
\(449\) 25.8064 1.21788 0.608940 0.793216i \(-0.291595\pi\)
0.608940 + 0.793216i \(0.291595\pi\)
\(450\) −22.5670 −1.06382
\(451\) −14.5686 −0.686009
\(452\) −31.8756 −1.49930
\(453\) 1.21543 0.0571060
\(454\) 75.7171 3.55358
\(455\) 30.7633 1.44221
\(456\) 2.65863 0.124502
\(457\) 25.9497 1.21388 0.606939 0.794748i \(-0.292397\pi\)
0.606939 + 0.794748i \(0.292397\pi\)
\(458\) 63.6376 2.97359
\(459\) 2.62655 0.122597
\(460\) −41.9924 −1.95791
\(461\) −33.0910 −1.54120 −0.770602 0.637317i \(-0.780044\pi\)
−0.770602 + 0.637317i \(0.780044\pi\)
\(462\) −2.83603 −0.131944
\(463\) −0.598540 −0.0278165 −0.0139082 0.999903i \(-0.504427\pi\)
−0.0139082 + 0.999903i \(0.504427\pi\)
\(464\) 45.8721 2.12956
\(465\) 0.220010 0.0102027
\(466\) 29.1018 1.34812
\(467\) −14.7382 −0.682001 −0.341000 0.940063i \(-0.610766\pi\)
−0.341000 + 0.940063i \(0.610766\pi\)
\(468\) −65.3196 −3.01940
\(469\) −30.0286 −1.38659
\(470\) −15.2604 −0.703909
\(471\) 1.37533 0.0633718
\(472\) −75.6585 −3.48246
\(473\) 9.31138 0.428138
\(474\) 1.24632 0.0572451
\(475\) −11.0213 −0.505691
\(476\) −121.753 −5.58055
\(477\) 0.0477562 0.00218660
\(478\) −2.12560 −0.0972225
\(479\) −22.7965 −1.04160 −0.520800 0.853679i \(-0.674366\pi\)
−0.520800 + 0.853679i \(0.674366\pi\)
\(480\) −1.68242 −0.0767916
\(481\) 27.3626 1.24763
\(482\) −40.1484 −1.82871
\(483\) 2.38269 0.108416
\(484\) −21.8373 −0.992605
\(485\) 14.4244 0.654976
\(486\) 6.16355 0.279584
\(487\) −33.6072 −1.52289 −0.761443 0.648232i \(-0.775509\pi\)
−0.761443 + 0.648232i \(0.775509\pi\)
\(488\) 42.1488 1.90799
\(489\) −0.323604 −0.0146339
\(490\) 62.5098 2.82390
\(491\) −17.8021 −0.803397 −0.401699 0.915772i \(-0.631580\pi\)
−0.401699 + 0.915772i \(0.631580\pi\)
\(492\) 2.44882 0.110401
\(493\) 21.0919 0.949930
\(494\) −44.6571 −2.00922
\(495\) 11.3017 0.507972
\(496\) 19.0896 0.857150
\(497\) −16.8492 −0.755789
\(498\) −3.62922 −0.162629
\(499\) 1.92040 0.0859691 0.0429845 0.999076i \(-0.486313\pi\)
0.0429845 + 0.999076i \(0.486313\pi\)
\(500\) 57.5703 2.57462
\(501\) −0.203930 −0.00911092
\(502\) −40.5889 −1.81157
\(503\) 24.9087 1.11063 0.555313 0.831641i \(-0.312598\pi\)
0.555313 + 0.831641i \(0.312598\pi\)
\(504\) −114.260 −5.08957
\(505\) −5.61412 −0.249825
\(506\) −39.0233 −1.73480
\(507\) −0.523329 −0.0232418
\(508\) −44.9648 −1.99499
\(509\) 22.6361 1.00333 0.501663 0.865063i \(-0.332722\pi\)
0.501663 + 0.865063i \(0.332722\pi\)
\(510\) −1.70058 −0.0753031
\(511\) −35.8326 −1.58514
\(512\) 28.9549 1.27964
\(513\) 2.00594 0.0885642
\(514\) −25.9026 −1.14251
\(515\) 20.9148 0.921615
\(516\) −1.56514 −0.0689014
\(517\) −10.1305 −0.445538
\(518\) 79.7567 3.50431
\(519\) −0.170833 −0.00749872
\(520\) 50.8244 2.22880
\(521\) 17.3593 0.760526 0.380263 0.924878i \(-0.375834\pi\)
0.380263 + 0.924878i \(0.375834\pi\)
\(522\) 32.9828 1.44362
\(523\) 18.7533 0.820027 0.410013 0.912080i \(-0.365524\pi\)
0.410013 + 0.912080i \(0.365524\pi\)
\(524\) −2.01499 −0.0880254
\(525\) −1.18595 −0.0517593
\(526\) −57.2441 −2.49596
\(527\) 8.77737 0.382348
\(528\) −2.45525 −0.106851
\(529\) 9.78544 0.425454
\(530\) −0.0619177 −0.00268953
\(531\) −28.5065 −1.23707
\(532\) −92.9846 −4.03139
\(533\) −24.6850 −1.06923
\(534\) 0.976025 0.0422367
\(535\) −4.47818 −0.193609
\(536\) −49.6105 −2.14285
\(537\) −0.529670 −0.0228570
\(538\) −79.9117 −3.44524
\(539\) 41.4966 1.78739
\(540\) −3.80413 −0.163704
\(541\) 28.3782 1.22007 0.610037 0.792373i \(-0.291155\pi\)
0.610037 + 0.792373i \(0.291155\pi\)
\(542\) 29.5087 1.26751
\(543\) 1.21322 0.0520641
\(544\) −67.1208 −2.87778
\(545\) −5.80831 −0.248801
\(546\) −4.80536 −0.205650
\(547\) −28.9121 −1.23619 −0.618097 0.786102i \(-0.712096\pi\)
−0.618097 + 0.786102i \(0.712096\pi\)
\(548\) 36.5585 1.56170
\(549\) 15.8808 0.677774
\(550\) 19.4233 0.828214
\(551\) 16.1082 0.686231
\(552\) 3.93647 0.167547
\(553\) −26.1592 −1.11240
\(554\) −33.2630 −1.41321
\(555\) 0.795785 0.0337792
\(556\) 29.3233 1.24358
\(557\) 1.35712 0.0575032 0.0287516 0.999587i \(-0.490847\pi\)
0.0287516 + 0.999587i \(0.490847\pi\)
\(558\) 13.7258 0.581058
\(559\) 15.7772 0.667303
\(560\) 77.6297 3.28045
\(561\) −1.12892 −0.0476630
\(562\) −18.7998 −0.793021
\(563\) 31.0870 1.31016 0.655080 0.755559i \(-0.272635\pi\)
0.655080 + 0.755559i \(0.272635\pi\)
\(564\) 1.70282 0.0717018
\(565\) 9.34484 0.393140
\(566\) −36.6165 −1.53911
\(567\) −42.9428 −1.80343
\(568\) −27.8367 −1.16800
\(569\) 4.28242 0.179529 0.0897643 0.995963i \(-0.471389\pi\)
0.0897643 + 0.995963i \(0.471389\pi\)
\(570\) −1.29876 −0.0543991
\(571\) 24.1973 1.01263 0.506313 0.862350i \(-0.331008\pi\)
0.506313 + 0.862350i \(0.331008\pi\)
\(572\) 56.2204 2.35069
\(573\) −0.280416 −0.0117145
\(574\) −71.9519 −3.00321
\(575\) −16.3185 −0.680530
\(576\) −39.0501 −1.62709
\(577\) −16.8897 −0.703127 −0.351563 0.936164i \(-0.614350\pi\)
−0.351563 + 0.936164i \(0.614350\pi\)
\(578\) −22.8625 −0.950956
\(579\) 1.72164 0.0715489
\(580\) −30.5481 −1.26844
\(581\) 76.1746 3.16026
\(582\) −2.25314 −0.0933958
\(583\) −0.0411036 −0.00170234
\(584\) −59.1994 −2.44969
\(585\) 19.1495 0.791735
\(586\) 50.1215 2.07050
\(587\) 20.6711 0.853187 0.426593 0.904444i \(-0.359714\pi\)
0.426593 + 0.904444i \(0.359714\pi\)
\(588\) −6.97512 −0.287649
\(589\) 6.70340 0.276209
\(590\) 36.9597 1.52161
\(591\) −1.05726 −0.0434898
\(592\) 69.0481 2.83786
\(593\) 4.89814 0.201143 0.100571 0.994930i \(-0.467933\pi\)
0.100571 + 0.994930i \(0.467933\pi\)
\(594\) −3.53516 −0.145049
\(595\) 35.6939 1.46331
\(596\) 102.109 4.18253
\(597\) −2.21050 −0.0904696
\(598\) −66.1210 −2.70389
\(599\) 46.5479 1.90189 0.950947 0.309353i \(-0.100112\pi\)
0.950947 + 0.309353i \(0.100112\pi\)
\(600\) −1.95932 −0.0799891
\(601\) 47.8571 1.95213 0.976066 0.217473i \(-0.0697815\pi\)
0.976066 + 0.217473i \(0.0697815\pi\)
\(602\) 45.9873 1.87430
\(603\) −18.6922 −0.761204
\(604\) −70.2300 −2.85762
\(605\) 6.40197 0.260277
\(606\) 0.876949 0.0356236
\(607\) −43.5880 −1.76918 −0.884592 0.466366i \(-0.845563\pi\)
−0.884592 + 0.466366i \(0.845563\pi\)
\(608\) −51.2611 −2.07891
\(609\) 1.73333 0.0702381
\(610\) −20.5900 −0.833665
\(611\) −17.1651 −0.694424
\(612\) −75.7887 −3.06358
\(613\) −3.76272 −0.151975 −0.0759874 0.997109i \(-0.524211\pi\)
−0.0759874 + 0.997109i \(0.524211\pi\)
\(614\) 44.1661 1.78240
\(615\) −0.717912 −0.0289490
\(616\) 98.3436 3.96238
\(617\) 0.475122 0.0191277 0.00956384 0.999954i \(-0.496956\pi\)
0.00956384 + 0.999954i \(0.496956\pi\)
\(618\) −3.26697 −0.131417
\(619\) −33.9193 −1.36333 −0.681665 0.731664i \(-0.738744\pi\)
−0.681665 + 0.731664i \(0.738744\pi\)
\(620\) −12.7126 −0.510549
\(621\) 2.97006 0.119184
\(622\) −51.6439 −2.07073
\(623\) −20.4860 −0.820755
\(624\) −4.16017 −0.166540
\(625\) −2.62781 −0.105112
\(626\) 43.3935 1.73435
\(627\) −0.862171 −0.0344318
\(628\) −79.4691 −3.17116
\(629\) 31.7482 1.26588
\(630\) 55.8170 2.22380
\(631\) −4.28588 −0.170618 −0.0853092 0.996355i \(-0.527188\pi\)
−0.0853092 + 0.996355i \(0.527188\pi\)
\(632\) −43.2178 −1.71911
\(633\) −0.963634 −0.0383010
\(634\) −11.0251 −0.437864
\(635\) 13.1822 0.523118
\(636\) 0.00690905 0.000273962 0
\(637\) 70.3117 2.78585
\(638\) −28.3882 −1.12390
\(639\) −10.4883 −0.414909
\(640\) 11.7570 0.464734
\(641\) 14.7011 0.580657 0.290329 0.956927i \(-0.406235\pi\)
0.290329 + 0.956927i \(0.406235\pi\)
\(642\) 0.699511 0.0276075
\(643\) 7.20623 0.284186 0.142093 0.989853i \(-0.454617\pi\)
0.142093 + 0.989853i \(0.454617\pi\)
\(644\) −137.676 −5.42521
\(645\) 0.458846 0.0180671
\(646\) −51.8145 −2.03861
\(647\) 38.4156 1.51027 0.755137 0.655567i \(-0.227571\pi\)
0.755137 + 0.655567i \(0.227571\pi\)
\(648\) −70.9461 −2.78703
\(649\) 24.5354 0.963099
\(650\) 32.9108 1.29087
\(651\) 0.721324 0.0282709
\(652\) 18.6984 0.732287
\(653\) 9.36327 0.366413 0.183207 0.983074i \(-0.441352\pi\)
0.183207 + 0.983074i \(0.441352\pi\)
\(654\) 0.907282 0.0354775
\(655\) 0.590729 0.0230817
\(656\) −62.2913 −2.43207
\(657\) −22.3050 −0.870202
\(658\) −50.0328 −1.95048
\(659\) 0.773262 0.0301220 0.0150610 0.999887i \(-0.495206\pi\)
0.0150610 + 0.999887i \(0.495206\pi\)
\(660\) 1.63505 0.0636443
\(661\) 18.4117 0.716130 0.358065 0.933697i \(-0.383437\pi\)
0.358065 + 0.933697i \(0.383437\pi\)
\(662\) −59.2001 −2.30088
\(663\) −1.91284 −0.0742884
\(664\) 125.849 4.88388
\(665\) 27.2600 1.05710
\(666\) 49.6468 1.92377
\(667\) 23.8503 0.923488
\(668\) 11.7835 0.455915
\(669\) 1.41498 0.0547062
\(670\) 24.2351 0.936283
\(671\) −13.6685 −0.527667
\(672\) −5.51599 −0.212784
\(673\) −21.4652 −0.827424 −0.413712 0.910408i \(-0.635768\pi\)
−0.413712 + 0.910408i \(0.635768\pi\)
\(674\) −54.7591 −2.10924
\(675\) −1.47831 −0.0569002
\(676\) 30.2389 1.16304
\(677\) 41.1602 1.58191 0.790957 0.611871i \(-0.209583\pi\)
0.790957 + 0.611871i \(0.209583\pi\)
\(678\) −1.45970 −0.0560595
\(679\) 47.2917 1.81489
\(680\) 58.9702 2.26140
\(681\) 2.47692 0.0949158
\(682\) −11.8137 −0.452371
\(683\) −21.2727 −0.813978 −0.406989 0.913433i \(-0.633421\pi\)
−0.406989 + 0.913433i \(0.633421\pi\)
\(684\) −57.8809 −2.21313
\(685\) −10.7177 −0.409503
\(686\) 115.900 4.42509
\(687\) 2.08176 0.0794243
\(688\) 39.8128 1.51785
\(689\) −0.0696457 −0.00265329
\(690\) −1.92299 −0.0732070
\(691\) −18.9801 −0.722037 −0.361018 0.932559i \(-0.617571\pi\)
−0.361018 + 0.932559i \(0.617571\pi\)
\(692\) 9.87103 0.375240
\(693\) 37.0537 1.40755
\(694\) −31.5770 −1.19865
\(695\) −8.59660 −0.326088
\(696\) 2.86365 0.108546
\(697\) −28.6414 −1.08487
\(698\) 8.50885 0.322065
\(699\) 0.952004 0.0360081
\(700\) 68.5267 2.59006
\(701\) 4.59819 0.173671 0.0868356 0.996223i \(-0.472325\pi\)
0.0868356 + 0.996223i \(0.472325\pi\)
\(702\) −5.98995 −0.226076
\(703\) 24.2465 0.914475
\(704\) 33.6103 1.26674
\(705\) −0.499211 −0.0188014
\(706\) 44.2098 1.66386
\(707\) −18.4065 −0.692247
\(708\) −4.12413 −0.154994
\(709\) 43.3211 1.62696 0.813480 0.581593i \(-0.197570\pi\)
0.813480 + 0.581593i \(0.197570\pi\)
\(710\) 13.5984 0.510339
\(711\) −16.2835 −0.610680
\(712\) −33.8451 −1.26840
\(713\) 9.92530 0.371705
\(714\) −5.57554 −0.208659
\(715\) −16.4819 −0.616389
\(716\) 30.6053 1.14378
\(717\) −0.0695343 −0.00259681
\(718\) 41.5202 1.54952
\(719\) 10.3041 0.384277 0.192139 0.981368i \(-0.438458\pi\)
0.192139 + 0.981368i \(0.438458\pi\)
\(720\) 48.3228 1.80088
\(721\) 68.5712 2.55373
\(722\) 10.7035 0.398343
\(723\) −1.31337 −0.0488447
\(724\) −70.1019 −2.60532
\(725\) −11.8712 −0.440885
\(726\) −1.00001 −0.0371140
\(727\) −22.5526 −0.836428 −0.418214 0.908349i \(-0.637344\pi\)
−0.418214 + 0.908349i \(0.637344\pi\)
\(728\) 166.633 6.17583
\(729\) −26.5962 −0.985046
\(730\) 28.9193 1.07035
\(731\) 18.3058 0.677066
\(732\) 2.29753 0.0849190
\(733\) −46.1682 −1.70526 −0.852631 0.522514i \(-0.824994\pi\)
−0.852631 + 0.522514i \(0.824994\pi\)
\(734\) 45.5760 1.68224
\(735\) 2.04487 0.0754262
\(736\) −75.8991 −2.79768
\(737\) 16.0883 0.592619
\(738\) −44.7885 −1.64869
\(739\) −7.16285 −0.263490 −0.131745 0.991284i \(-0.542058\pi\)
−0.131745 + 0.991284i \(0.542058\pi\)
\(740\) −45.9820 −1.69033
\(741\) −1.46086 −0.0536660
\(742\) −0.203004 −0.00745250
\(743\) −10.3110 −0.378274 −0.189137 0.981951i \(-0.560569\pi\)
−0.189137 + 0.981951i \(0.560569\pi\)
\(744\) 1.19171 0.0436901
\(745\) −29.9348 −1.09673
\(746\) −51.0080 −1.86754
\(747\) 47.4170 1.73490
\(748\) 65.2310 2.38508
\(749\) −14.6822 −0.536475
\(750\) 2.63636 0.0962663
\(751\) 11.9353 0.435525 0.217762 0.976002i \(-0.430124\pi\)
0.217762 + 0.976002i \(0.430124\pi\)
\(752\) −43.3151 −1.57954
\(753\) −1.32778 −0.0483869
\(754\) −48.1008 −1.75173
\(755\) 20.5891 0.749313
\(756\) −12.4722 −0.453611
\(757\) −6.41756 −0.233250 −0.116625 0.993176i \(-0.537208\pi\)
−0.116625 + 0.993176i \(0.537208\pi\)
\(758\) 49.9164 1.81305
\(759\) −1.27656 −0.0463363
\(760\) 45.0364 1.63364
\(761\) −8.04158 −0.291507 −0.145754 0.989321i \(-0.546561\pi\)
−0.145754 + 0.989321i \(0.546561\pi\)
\(762\) −2.05911 −0.0745936
\(763\) −19.0431 −0.689408
\(764\) 16.2029 0.586202
\(765\) 22.2187 0.803318
\(766\) −92.0037 −3.32423
\(767\) 41.5727 1.50110
\(768\) 0.422605 0.0152495
\(769\) 34.7266 1.25227 0.626136 0.779714i \(-0.284635\pi\)
0.626136 + 0.779714i \(0.284635\pi\)
\(770\) −48.0415 −1.73130
\(771\) −0.847347 −0.0305164
\(772\) −99.4796 −3.58035
\(773\) 17.7661 0.639002 0.319501 0.947586i \(-0.396485\pi\)
0.319501 + 0.947586i \(0.396485\pi\)
\(774\) 28.6261 1.02894
\(775\) −4.94019 −0.177457
\(776\) 78.1311 2.80474
\(777\) 2.60907 0.0935997
\(778\) −85.3180 −3.05880
\(779\) −21.8738 −0.783711
\(780\) 2.77043 0.0991972
\(781\) 9.02720 0.323019
\(782\) −76.7185 −2.74345
\(783\) 2.16062 0.0772143
\(784\) 177.428 6.33671
\(785\) 23.2977 0.831529
\(786\) −0.0922742 −0.00329131
\(787\) −32.2652 −1.15013 −0.575065 0.818108i \(-0.695023\pi\)
−0.575065 + 0.818108i \(0.695023\pi\)
\(788\) 61.0903 2.17625
\(789\) −1.87261 −0.0666668
\(790\) 21.1122 0.751139
\(791\) 30.6380 1.08936
\(792\) 61.2167 2.17524
\(793\) −23.1599 −0.822431
\(794\) 25.1155 0.891315
\(795\) −0.00202550 −7.18372e−5 0
\(796\) 127.727 4.52715
\(797\) 44.4127 1.57318 0.786590 0.617476i \(-0.211845\pi\)
0.786590 + 0.617476i \(0.211845\pi\)
\(798\) −4.25812 −0.150736
\(799\) −19.9162 −0.704584
\(800\) 37.7778 1.33565
\(801\) −12.7521 −0.450573
\(802\) −15.6189 −0.551523
\(803\) 19.1979 0.677477
\(804\) −2.70426 −0.0953719
\(805\) 40.3621 1.42258
\(806\) −20.0171 −0.705073
\(807\) −2.61414 −0.0920220
\(808\) −30.4095 −1.06980
\(809\) −39.9511 −1.40461 −0.702303 0.711879i \(-0.747845\pi\)
−0.702303 + 0.711879i \(0.747845\pi\)
\(810\) 34.6577 1.21775
\(811\) 23.2696 0.817106 0.408553 0.912735i \(-0.366034\pi\)
0.408553 + 0.912735i \(0.366034\pi\)
\(812\) −100.155 −3.51475
\(813\) 0.965313 0.0338550
\(814\) −42.7308 −1.49771
\(815\) −5.48175 −0.192017
\(816\) −4.82694 −0.168977
\(817\) 13.9804 0.489114
\(818\) 64.4108 2.25207
\(819\) 62.7837 2.19384
\(820\) 41.4823 1.44863
\(821\) −25.7475 −0.898595 −0.449298 0.893382i \(-0.648326\pi\)
−0.449298 + 0.893382i \(0.648326\pi\)
\(822\) 1.67415 0.0583928
\(823\) 44.9842 1.56805 0.784025 0.620729i \(-0.213163\pi\)
0.784025 + 0.620729i \(0.213163\pi\)
\(824\) 113.287 3.94654
\(825\) 0.635392 0.0221215
\(826\) 121.176 4.21626
\(827\) −35.7382 −1.24274 −0.621369 0.783518i \(-0.713423\pi\)
−0.621369 + 0.783518i \(0.713423\pi\)
\(828\) −85.7006 −2.97830
\(829\) −39.2241 −1.36231 −0.681154 0.732140i \(-0.738522\pi\)
−0.681154 + 0.732140i \(0.738522\pi\)
\(830\) −61.4780 −2.13393
\(831\) −1.08813 −0.0377467
\(832\) 56.9492 1.97436
\(833\) 81.5809 2.82661
\(834\) 1.34282 0.0464982
\(835\) −3.45451 −0.119548
\(836\) 49.8179 1.72299
\(837\) 0.899142 0.0310789
\(838\) 70.9604 2.45129
\(839\) 13.2223 0.456486 0.228243 0.973604i \(-0.426702\pi\)
0.228243 + 0.973604i \(0.426702\pi\)
\(840\) 4.84618 0.167209
\(841\) −11.6497 −0.401713
\(842\) −0.941247 −0.0324375
\(843\) −0.614994 −0.0211815
\(844\) 55.6806 1.91660
\(845\) −8.86503 −0.304966
\(846\) −31.1443 −1.07076
\(847\) 20.9895 0.721208
\(848\) −0.175747 −0.00603519
\(849\) −1.19783 −0.0411094
\(850\) 38.1856 1.30976
\(851\) 35.9003 1.23065
\(852\) −1.51737 −0.0519843
\(853\) 18.4076 0.630264 0.315132 0.949048i \(-0.397951\pi\)
0.315132 + 0.949048i \(0.397951\pi\)
\(854\) −67.5065 −2.31002
\(855\) 16.9687 0.580318
\(856\) −24.2566 −0.829072
\(857\) −6.47183 −0.221074 −0.110537 0.993872i \(-0.535257\pi\)
−0.110537 + 0.993872i \(0.535257\pi\)
\(858\) 2.57454 0.0878935
\(859\) −33.4938 −1.14280 −0.571398 0.820673i \(-0.693599\pi\)
−0.571398 + 0.820673i \(0.693599\pi\)
\(860\) −26.5130 −0.904086
\(861\) −2.35375 −0.0802156
\(862\) −48.6895 −1.65837
\(863\) 17.5074 0.595960 0.297980 0.954572i \(-0.403687\pi\)
0.297980 + 0.954572i \(0.403687\pi\)
\(864\) −6.87576 −0.233918
\(865\) −2.89385 −0.0983940
\(866\) −7.44221 −0.252896
\(867\) −0.747898 −0.0253999
\(868\) −41.6795 −1.41469
\(869\) 14.0152 0.475432
\(870\) −1.39891 −0.0474276
\(871\) 27.2599 0.923667
\(872\) −31.4613 −1.06542
\(873\) 29.4381 0.996328
\(874\) −58.5910 −1.98187
\(875\) −55.3352 −1.87067
\(876\) −3.22695 −0.109028
\(877\) 12.1390 0.409905 0.204953 0.978772i \(-0.434296\pi\)
0.204953 + 0.978772i \(0.434296\pi\)
\(878\) −44.5857 −1.50469
\(879\) 1.63961 0.0553028
\(880\) −41.5912 −1.40204
\(881\) 26.4420 0.890852 0.445426 0.895319i \(-0.353052\pi\)
0.445426 + 0.895319i \(0.353052\pi\)
\(882\) 127.574 4.29563
\(883\) 12.1855 0.410076 0.205038 0.978754i \(-0.434268\pi\)
0.205038 + 0.978754i \(0.434268\pi\)
\(884\) 110.527 3.71743
\(885\) 1.20906 0.0406420
\(886\) 108.395 3.64158
\(887\) −16.2777 −0.546550 −0.273275 0.961936i \(-0.588107\pi\)
−0.273275 + 0.961936i \(0.588107\pi\)
\(888\) 4.31046 0.144650
\(889\) 43.2191 1.44952
\(890\) 16.5336 0.554207
\(891\) 23.0072 0.770771
\(892\) −81.7601 −2.73753
\(893\) −15.2103 −0.508993
\(894\) 4.67594 0.156387
\(895\) −8.97246 −0.299916
\(896\) 38.5464 1.28774
\(897\) −2.16300 −0.0722206
\(898\) −68.2851 −2.27870
\(899\) 7.22033 0.240811
\(900\) 42.6564 1.42188
\(901\) −0.0808082 −0.00269211
\(902\) 38.5493 1.28355
\(903\) 1.50438 0.0500625
\(904\) 50.6173 1.68351
\(905\) 20.5515 0.683156
\(906\) −3.21610 −0.106848
\(907\) 29.7376 0.987421 0.493710 0.869626i \(-0.335640\pi\)
0.493710 + 0.869626i \(0.335640\pi\)
\(908\) −143.121 −4.74964
\(909\) −11.4576 −0.380026
\(910\) −81.4014 −2.69843
\(911\) −52.3587 −1.73472 −0.867361 0.497680i \(-0.834185\pi\)
−0.867361 + 0.497680i \(0.834185\pi\)
\(912\) −3.68640 −0.122069
\(913\) −40.8117 −1.35067
\(914\) −68.6644 −2.27122
\(915\) −0.673557 −0.0222671
\(916\) −120.288 −3.97444
\(917\) 1.93677 0.0639576
\(918\) −6.94999 −0.229384
\(919\) 29.1886 0.962843 0.481421 0.876489i \(-0.340121\pi\)
0.481421 + 0.876489i \(0.340121\pi\)
\(920\) 66.6826 2.19846
\(921\) 1.44480 0.0476077
\(922\) 87.5606 2.88365
\(923\) 15.2957 0.503463
\(924\) 5.36069 0.176354
\(925\) −17.8689 −0.587526
\(926\) 1.58377 0.0520458
\(927\) 42.6841 1.40193
\(928\) −55.2141 −1.81249
\(929\) −22.9553 −0.753137 −0.376569 0.926389i \(-0.622896\pi\)
−0.376569 + 0.926389i \(0.622896\pi\)
\(930\) −0.582157 −0.0190897
\(931\) 62.3045 2.04195
\(932\) −55.0086 −1.80187
\(933\) −1.68942 −0.0553091
\(934\) 38.9979 1.27605
\(935\) −19.1235 −0.625407
\(936\) 103.725 3.39037
\(937\) 35.4762 1.15896 0.579479 0.814987i \(-0.303256\pi\)
0.579479 + 0.814987i \(0.303256\pi\)
\(938\) 79.4573 2.59437
\(939\) 1.41952 0.0463244
\(940\) 28.8453 0.940831
\(941\) 41.0396 1.33785 0.668926 0.743329i \(-0.266754\pi\)
0.668926 + 0.743329i \(0.266754\pi\)
\(942\) −3.63919 −0.118571
\(943\) −32.3872 −1.05467
\(944\) 104.907 3.41442
\(945\) 3.65644 0.118944
\(946\) −24.6384 −0.801063
\(947\) −57.4401 −1.86655 −0.933276 0.359160i \(-0.883063\pi\)
−0.933276 + 0.359160i \(0.883063\pi\)
\(948\) −2.35580 −0.0765127
\(949\) 32.5288 1.05593
\(950\) 29.1629 0.946170
\(951\) −0.360663 −0.0116953
\(952\) 193.340 6.26619
\(953\) 16.6030 0.537825 0.268913 0.963165i \(-0.413336\pi\)
0.268913 + 0.963165i \(0.413336\pi\)
\(954\) −0.126365 −0.00409123
\(955\) −4.75016 −0.153711
\(956\) 4.01782 0.129946
\(957\) −0.928657 −0.0300192
\(958\) 60.3208 1.94888
\(959\) −35.1392 −1.13470
\(960\) 1.65625 0.0534552
\(961\) −27.9953 −0.903073
\(962\) −72.4029 −2.33436
\(963\) −9.13934 −0.294511
\(964\) 75.8889 2.44422
\(965\) 29.1641 0.938825
\(966\) −6.30473 −0.202851
\(967\) 49.2291 1.58310 0.791550 0.611104i \(-0.209274\pi\)
0.791550 + 0.611104i \(0.209274\pi\)
\(968\) 34.6770 1.11456
\(969\) −1.69500 −0.0544512
\(970\) −38.1676 −1.22549
\(971\) −15.1993 −0.487768 −0.243884 0.969804i \(-0.578422\pi\)
−0.243884 + 0.969804i \(0.578422\pi\)
\(972\) −11.6504 −0.373686
\(973\) −28.1848 −0.903565
\(974\) 88.9263 2.84938
\(975\) 1.07661 0.0344790
\(976\) −58.4427 −1.87071
\(977\) −11.8933 −0.380499 −0.190250 0.981736i \(-0.560930\pi\)
−0.190250 + 0.981736i \(0.560930\pi\)
\(978\) 0.856272 0.0273805
\(979\) 10.9757 0.350784
\(980\) −118.157 −3.77437
\(981\) −11.8539 −0.378467
\(982\) 47.1053 1.50319
\(983\) −3.44831 −0.109984 −0.0549920 0.998487i \(-0.517513\pi\)
−0.0549920 + 0.998487i \(0.517513\pi\)
\(984\) −3.88865 −0.123966
\(985\) −17.9096 −0.570648
\(986\) −55.8102 −1.77736
\(987\) −1.63671 −0.0520972
\(988\) 84.4112 2.68548
\(989\) 20.6999 0.658220
\(990\) −29.9048 −0.950437
\(991\) −32.7835 −1.04140 −0.520702 0.853739i \(-0.674330\pi\)
−0.520702 + 0.853739i \(0.674330\pi\)
\(992\) −22.9773 −0.729530
\(993\) −1.93660 −0.0614562
\(994\) 44.5838 1.41411
\(995\) −37.4452 −1.18709
\(996\) 6.85999 0.217367
\(997\) −47.6704 −1.50974 −0.754868 0.655876i \(-0.772299\pi\)
−0.754868 + 0.655876i \(0.772299\pi\)
\(998\) −5.08149 −0.160852
\(999\) 3.25224 0.102896
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 \(a_p\))