Properties

Label 6023.2.a.b.1.12
Level 6023
Weight 2
Character 6023.1
Self dual Yes
Analytic conductor 48.094
Analytic rank 1
Dimension 99
CM No

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Newspace parameters

Level: \( N \) = \( 6023 = 19 \cdot 317 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6023.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0938971374\)
Analytic rank: \(1\)
Dimension: \(99\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 6023.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.30551 q^{2}\) \(+2.60917 q^{3}\) \(+3.31537 q^{4}\) \(-2.40173 q^{5}\) \(-6.01546 q^{6}\) \(+3.07987 q^{7}\) \(-3.03260 q^{8}\) \(+3.80775 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.30551 q^{2}\) \(+2.60917 q^{3}\) \(+3.31537 q^{4}\) \(-2.40173 q^{5}\) \(-6.01546 q^{6}\) \(+3.07987 q^{7}\) \(-3.03260 q^{8}\) \(+3.80775 q^{9}\) \(+5.53721 q^{10}\) \(+0.844336 q^{11}\) \(+8.65036 q^{12}\) \(-3.14234 q^{13}\) \(-7.10067 q^{14}\) \(-6.26651 q^{15}\) \(+0.360950 q^{16}\) \(+6.14818 q^{17}\) \(-8.77880 q^{18}\) \(-1.00000 q^{19}\) \(-7.96262 q^{20}\) \(+8.03590 q^{21}\) \(-1.94662 q^{22}\) \(-4.06495 q^{23}\) \(-7.91257 q^{24}\) \(+0.768298 q^{25}\) \(+7.24469 q^{26}\) \(+2.10755 q^{27}\) \(+10.2109 q^{28}\) \(-2.51541 q^{29}\) \(+14.4475 q^{30}\) \(-10.0867 q^{31}\) \(+5.23303 q^{32}\) \(+2.20301 q^{33}\) \(-14.1747 q^{34}\) \(-7.39701 q^{35}\) \(+12.6241 q^{36}\) \(+10.1752 q^{37}\) \(+2.30551 q^{38}\) \(-8.19888 q^{39}\) \(+7.28349 q^{40}\) \(-5.50353 q^{41}\) \(-18.5268 q^{42}\) \(-12.0050 q^{43}\) \(+2.79929 q^{44}\) \(-9.14517 q^{45}\) \(+9.37178 q^{46}\) \(+2.56130 q^{47}\) \(+0.941780 q^{48}\) \(+2.48561 q^{49}\) \(-1.77132 q^{50}\) \(+16.0416 q^{51}\) \(-10.4180 q^{52}\) \(+2.70214 q^{53}\) \(-4.85897 q^{54}\) \(-2.02787 q^{55}\) \(-9.34003 q^{56}\) \(-2.60917 q^{57}\) \(+5.79929 q^{58}\) \(-2.93389 q^{59}\) \(-20.7758 q^{60}\) \(+0.124901 q^{61}\) \(+23.2550 q^{62}\) \(+11.7274 q^{63}\) \(-12.7867 q^{64}\) \(+7.54704 q^{65}\) \(-5.07907 q^{66}\) \(-10.4066 q^{67}\) \(+20.3835 q^{68}\) \(-10.6061 q^{69}\) \(+17.0539 q^{70}\) \(+5.48170 q^{71}\) \(-11.5474 q^{72}\) \(-7.86690 q^{73}\) \(-23.4591 q^{74}\) \(+2.00462 q^{75}\) \(-3.31537 q^{76}\) \(+2.60045 q^{77}\) \(+18.9026 q^{78}\) \(-10.0905 q^{79}\) \(-0.866905 q^{80}\) \(-5.92430 q^{81}\) \(+12.6884 q^{82}\) \(+0.962786 q^{83}\) \(+26.6420 q^{84}\) \(-14.7662 q^{85}\) \(+27.6777 q^{86}\) \(-6.56311 q^{87}\) \(-2.56054 q^{88}\) \(-8.65056 q^{89}\) \(+21.0843 q^{90}\) \(-9.67800 q^{91}\) \(-13.4768 q^{92}\) \(-26.3179 q^{93}\) \(-5.90509 q^{94}\) \(+2.40173 q^{95}\) \(+13.6539 q^{96}\) \(-0.130985 q^{97}\) \(-5.73060 q^{98}\) \(+3.21502 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(99q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 80q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 58q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(99q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 80q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 58q^{9} \) \(\mathstrut -\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 27q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 13q^{14} \) \(\mathstrut -\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 38q^{16} \) \(\mathstrut -\mathstrut 36q^{17} \) \(\mathstrut -\mathstrut 14q^{18} \) \(\mathstrut -\mathstrut 99q^{19} \) \(\mathstrut -\mathstrut 34q^{20} \) \(\mathstrut -\mathstrut 20q^{21} \) \(\mathstrut -\mathstrut 53q^{22} \) \(\mathstrut -\mathstrut 38q^{23} \) \(\mathstrut -\mathstrut 25q^{24} \) \(\mathstrut -\mathstrut 8q^{25} \) \(\mathstrut -\mathstrut 3q^{26} \) \(\mathstrut -\mathstrut 3q^{27} \) \(\mathstrut -\mathstrut 63q^{28} \) \(\mathstrut -\mathstrut 34q^{29} \) \(\mathstrut -\mathstrut 30q^{30} \) \(\mathstrut -\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 43q^{32} \) \(\mathstrut -\mathstrut 41q^{33} \) \(\mathstrut -\mathstrut 14q^{34} \) \(\mathstrut -\mathstrut 25q^{35} \) \(\mathstrut -\mathstrut 16q^{36} \) \(\mathstrut -\mathstrut 80q^{37} \) \(\mathstrut +\mathstrut 4q^{38} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 10q^{40} \) \(\mathstrut -\mathstrut 32q^{41} \) \(\mathstrut -\mathstrut 37q^{42} \) \(\mathstrut -\mathstrut 76q^{43} \) \(\mathstrut -\mathstrut 21q^{44} \) \(\mathstrut -\mathstrut 53q^{45} \) \(\mathstrut -\mathstrut 23q^{46} \) \(\mathstrut -\mathstrut 31q^{47} \) \(\mathstrut -\mathstrut 74q^{48} \) \(\mathstrut -\mathstrut 32q^{49} \) \(\mathstrut -\mathstrut 29q^{50} \) \(\mathstrut -\mathstrut 30q^{51} \) \(\mathstrut -\mathstrut 71q^{52} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 80q^{54} \) \(\mathstrut -\mathstrut 45q^{55} \) \(\mathstrut -\mathstrut 33q^{56} \) \(\mathstrut +\mathstrut 3q^{57} \) \(\mathstrut -\mathstrut 91q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 61q^{61} \) \(\mathstrut -\mathstrut 46q^{62} \) \(\mathstrut -\mathstrut 43q^{63} \) \(\mathstrut -\mathstrut 30q^{64} \) \(\mathstrut -\mathstrut 46q^{65} \) \(\mathstrut -\mathstrut 75q^{66} \) \(\mathstrut -\mathstrut 26q^{67} \) \(\mathstrut -\mathstrut 55q^{68} \) \(\mathstrut -\mathstrut 45q^{69} \) \(\mathstrut -\mathstrut 76q^{70} \) \(\mathstrut -\mathstrut 41q^{71} \) \(\mathstrut -\mathstrut 77q^{72} \) \(\mathstrut -\mathstrut 143q^{73} \) \(\mathstrut -\mathstrut 64q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 80q^{76} \) \(\mathstrut -\mathstrut 58q^{77} \) \(\mathstrut -\mathstrut 34q^{78} \) \(\mathstrut -\mathstrut 22q^{79} \) \(\mathstrut -\mathstrut 36q^{80} \) \(\mathstrut -\mathstrut 81q^{81} \) \(\mathstrut -\mathstrut 109q^{82} \) \(\mathstrut -\mathstrut 7q^{83} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 80q^{85} \) \(\mathstrut +\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 57q^{87} \) \(\mathstrut -\mathstrut 120q^{88} \) \(\mathstrut -\mathstrut 28q^{89} \) \(\mathstrut -\mathstrut 12q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 107q^{92} \) \(\mathstrut -\mathstrut 121q^{93} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut +\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut -\mathstrut 128q^{97} \) \(\mathstrut +\mathstrut 54q^{98} \) \(\mathstrut -\mathstrut 34q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.30551 −1.63024 −0.815121 0.579291i \(-0.803329\pi\)
−0.815121 + 0.579291i \(0.803329\pi\)
\(3\) 2.60917 1.50640 0.753201 0.657790i \(-0.228509\pi\)
0.753201 + 0.657790i \(0.228509\pi\)
\(4\) 3.31537 1.65769
\(5\) −2.40173 −1.07409 −0.537043 0.843555i \(-0.680459\pi\)
−0.537043 + 0.843555i \(0.680459\pi\)
\(6\) −6.01546 −2.45580
\(7\) 3.07987 1.16408 0.582041 0.813159i \(-0.302254\pi\)
0.582041 + 0.813159i \(0.302254\pi\)
\(8\) −3.03260 −1.07219
\(9\) 3.80775 1.26925
\(10\) 5.53721 1.75102
\(11\) 0.844336 0.254577 0.127288 0.991866i \(-0.459373\pi\)
0.127288 + 0.991866i \(0.459373\pi\)
\(12\) 8.65036 2.49714
\(13\) −3.14234 −0.871528 −0.435764 0.900061i \(-0.643522\pi\)
−0.435764 + 0.900061i \(0.643522\pi\)
\(14\) −7.10067 −1.89773
\(15\) −6.26651 −1.61801
\(16\) 0.360950 0.0902376
\(17\) 6.14818 1.49115 0.745576 0.666421i \(-0.232175\pi\)
0.745576 + 0.666421i \(0.232175\pi\)
\(18\) −8.77880 −2.06918
\(19\) −1.00000 −0.229416
\(20\) −7.96262 −1.78050
\(21\) 8.03590 1.75358
\(22\) −1.94662 −0.415022
\(23\) −4.06495 −0.847600 −0.423800 0.905756i \(-0.639304\pi\)
−0.423800 + 0.905756i \(0.639304\pi\)
\(24\) −7.91257 −1.61515
\(25\) 0.768298 0.153660
\(26\) 7.24469 1.42080
\(27\) 2.10755 0.405598
\(28\) 10.2109 1.92968
\(29\) −2.51541 −0.467099 −0.233550 0.972345i \(-0.575034\pi\)
−0.233550 + 0.972345i \(0.575034\pi\)
\(30\) 14.4475 2.63774
\(31\) −10.0867 −1.81162 −0.905812 0.423679i \(-0.860738\pi\)
−0.905812 + 0.423679i \(0.860738\pi\)
\(32\) 5.23303 0.925078
\(33\) 2.20301 0.383495
\(34\) −14.1747 −2.43094
\(35\) −7.39701 −1.25032
\(36\) 12.6241 2.10402
\(37\) 10.1752 1.67280 0.836398 0.548123i \(-0.184658\pi\)
0.836398 + 0.548123i \(0.184658\pi\)
\(38\) 2.30551 0.374003
\(39\) −8.19888 −1.31287
\(40\) 7.28349 1.15162
\(41\) −5.50353 −0.859507 −0.429754 0.902946i \(-0.641400\pi\)
−0.429754 + 0.902946i \(0.641400\pi\)
\(42\) −18.5268 −2.85875
\(43\) −12.0050 −1.83075 −0.915375 0.402603i \(-0.868105\pi\)
−0.915375 + 0.402603i \(0.868105\pi\)
\(44\) 2.79929 0.422009
\(45\) −9.14517 −1.36328
\(46\) 9.37178 1.38179
\(47\) 2.56130 0.373603 0.186802 0.982398i \(-0.440188\pi\)
0.186802 + 0.982398i \(0.440188\pi\)
\(48\) 0.941780 0.135934
\(49\) 2.48561 0.355087
\(50\) −1.77132 −0.250502
\(51\) 16.0416 2.24627
\(52\) −10.4180 −1.44472
\(53\) 2.70214 0.371167 0.185584 0.982628i \(-0.440582\pi\)
0.185584 + 0.982628i \(0.440582\pi\)
\(54\) −4.85897 −0.661222
\(55\) −2.02787 −0.273437
\(56\) −9.34003 −1.24811
\(57\) −2.60917 −0.345592
\(58\) 5.79929 0.761485
\(59\) −2.93389 −0.381960 −0.190980 0.981594i \(-0.561167\pi\)
−0.190980 + 0.981594i \(0.561167\pi\)
\(60\) −20.7758 −2.68215
\(61\) 0.124901 0.0159920 0.00799598 0.999968i \(-0.497455\pi\)
0.00799598 + 0.999968i \(0.497455\pi\)
\(62\) 23.2550 2.95338
\(63\) 11.7274 1.47751
\(64\) −12.7867 −1.59834
\(65\) 7.54704 0.936095
\(66\) −5.07907 −0.625190
\(67\) −10.4066 −1.27136 −0.635681 0.771952i \(-0.719281\pi\)
−0.635681 + 0.771952i \(0.719281\pi\)
\(68\) 20.3835 2.47186
\(69\) −10.6061 −1.27683
\(70\) 17.0539 2.03833
\(71\) 5.48170 0.650558 0.325279 0.945618i \(-0.394542\pi\)
0.325279 + 0.945618i \(0.394542\pi\)
\(72\) −11.5474 −1.36087
\(73\) −7.86690 −0.920751 −0.460375 0.887724i \(-0.652285\pi\)
−0.460375 + 0.887724i \(0.652285\pi\)
\(74\) −23.4591 −2.72706
\(75\) 2.00462 0.231473
\(76\) −3.31537 −0.380299
\(77\) 2.60045 0.296348
\(78\) 18.9026 2.14030
\(79\) −10.0905 −1.13527 −0.567635 0.823280i \(-0.692141\pi\)
−0.567635 + 0.823280i \(0.692141\pi\)
\(80\) −0.866905 −0.0969229
\(81\) −5.92430 −0.658256
\(82\) 12.6884 1.40120
\(83\) 0.962786 0.105679 0.0528397 0.998603i \(-0.483173\pi\)
0.0528397 + 0.998603i \(0.483173\pi\)
\(84\) 26.6420 2.90688
\(85\) −14.7662 −1.60162
\(86\) 27.6777 2.98456
\(87\) −6.56311 −0.703640
\(88\) −2.56054 −0.272954
\(89\) −8.65056 −0.916958 −0.458479 0.888705i \(-0.651606\pi\)
−0.458479 + 0.888705i \(0.651606\pi\)
\(90\) 21.0843 2.22248
\(91\) −9.67800 −1.01453
\(92\) −13.4768 −1.40506
\(93\) −26.3179 −2.72904
\(94\) −5.90509 −0.609064
\(95\) 2.40173 0.246412
\(96\) 13.6539 1.39354
\(97\) −0.130985 −0.0132995 −0.00664974 0.999978i \(-0.502117\pi\)
−0.00664974 + 0.999978i \(0.502117\pi\)
\(98\) −5.73060 −0.578878
\(99\) 3.21502 0.323121
\(100\) 2.54719 0.254719
\(101\) −2.76506 −0.275134 −0.137567 0.990492i \(-0.543928\pi\)
−0.137567 + 0.990492i \(0.543928\pi\)
\(102\) −36.9841 −3.66197
\(103\) −11.0342 −1.08724 −0.543618 0.839333i \(-0.682946\pi\)
−0.543618 + 0.839333i \(0.682946\pi\)
\(104\) 9.52947 0.934441
\(105\) −19.3000 −1.88349
\(106\) −6.22981 −0.605092
\(107\) 13.0360 1.26024 0.630119 0.776499i \(-0.283006\pi\)
0.630119 + 0.776499i \(0.283006\pi\)
\(108\) 6.98730 0.672354
\(109\) −11.8198 −1.13213 −0.566067 0.824359i \(-0.691536\pi\)
−0.566067 + 0.824359i \(0.691536\pi\)
\(110\) 4.67526 0.445769
\(111\) 26.5488 2.51990
\(112\) 1.11168 0.105044
\(113\) 8.45082 0.794986 0.397493 0.917605i \(-0.369880\pi\)
0.397493 + 0.917605i \(0.369880\pi\)
\(114\) 6.01546 0.563399
\(115\) 9.76290 0.910395
\(116\) −8.33951 −0.774304
\(117\) −11.9652 −1.10619
\(118\) 6.76412 0.622687
\(119\) 18.9356 1.73582
\(120\) 19.0038 1.73480
\(121\) −10.2871 −0.935191
\(122\) −0.287961 −0.0260707
\(123\) −14.3596 −1.29476
\(124\) −33.4412 −3.00311
\(125\) 10.1634 0.909042
\(126\) −27.0376 −2.40870
\(127\) 11.7523 1.04285 0.521425 0.853297i \(-0.325401\pi\)
0.521425 + 0.853297i \(0.325401\pi\)
\(128\) 19.0138 1.68060
\(129\) −31.3231 −2.75785
\(130\) −17.3998 −1.52606
\(131\) −9.89520 −0.864547 −0.432274 0.901742i \(-0.642289\pi\)
−0.432274 + 0.901742i \(0.642289\pi\)
\(132\) 7.30381 0.635715
\(133\) −3.07987 −0.267059
\(134\) 23.9924 2.07263
\(135\) −5.06176 −0.435647
\(136\) −18.6450 −1.59879
\(137\) 14.3140 1.22293 0.611466 0.791271i \(-0.290580\pi\)
0.611466 + 0.791271i \(0.290580\pi\)
\(138\) 24.4525 2.08154
\(139\) −4.48599 −0.380497 −0.190248 0.981736i \(-0.560929\pi\)
−0.190248 + 0.981736i \(0.560929\pi\)
\(140\) −24.5239 −2.07264
\(141\) 6.68285 0.562797
\(142\) −12.6381 −1.06057
\(143\) −2.65319 −0.221871
\(144\) 1.37441 0.114534
\(145\) 6.04132 0.501705
\(146\) 18.1372 1.50105
\(147\) 6.48537 0.534904
\(148\) 33.7346 2.77297
\(149\) −6.33757 −0.519194 −0.259597 0.965717i \(-0.583590\pi\)
−0.259597 + 0.965717i \(0.583590\pi\)
\(150\) −4.62166 −0.377357
\(151\) 19.2425 1.56593 0.782965 0.622066i \(-0.213706\pi\)
0.782965 + 0.622066i \(0.213706\pi\)
\(152\) 3.03260 0.245977
\(153\) 23.4107 1.89264
\(154\) −5.99535 −0.483119
\(155\) 24.2255 1.94584
\(156\) −27.1824 −2.17633
\(157\) 7.49867 0.598459 0.299229 0.954181i \(-0.403270\pi\)
0.299229 + 0.954181i \(0.403270\pi\)
\(158\) 23.2637 1.85076
\(159\) 7.05033 0.559128
\(160\) −12.5683 −0.993613
\(161\) −12.5195 −0.986677
\(162\) 13.6585 1.07312
\(163\) −1.69924 −0.133095 −0.0665474 0.997783i \(-0.521198\pi\)
−0.0665474 + 0.997783i \(0.521198\pi\)
\(164\) −18.2463 −1.42479
\(165\) −5.29104 −0.411907
\(166\) −2.21971 −0.172283
\(167\) −3.52614 −0.272861 −0.136431 0.990650i \(-0.543563\pi\)
−0.136431 + 0.990650i \(0.543563\pi\)
\(168\) −24.3697 −1.88016
\(169\) −3.12571 −0.240439
\(170\) 34.0437 2.61103
\(171\) −3.80775 −0.291186
\(172\) −39.8011 −3.03481
\(173\) 9.03444 0.686876 0.343438 0.939175i \(-0.388408\pi\)
0.343438 + 0.939175i \(0.388408\pi\)
\(174\) 15.1313 1.14710
\(175\) 2.36626 0.178872
\(176\) 0.304763 0.0229724
\(177\) −7.65501 −0.575386
\(178\) 19.9439 1.49486
\(179\) −3.14057 −0.234737 −0.117369 0.993088i \(-0.537446\pi\)
−0.117369 + 0.993088i \(0.537446\pi\)
\(180\) −30.3197 −2.25989
\(181\) 18.1560 1.34952 0.674762 0.738035i \(-0.264246\pi\)
0.674762 + 0.738035i \(0.264246\pi\)
\(182\) 22.3127 1.65393
\(183\) 0.325888 0.0240903
\(184\) 12.3274 0.908786
\(185\) −24.4381 −1.79672
\(186\) 60.6761 4.44899
\(187\) 5.19113 0.379613
\(188\) 8.49165 0.619317
\(189\) 6.49098 0.472149
\(190\) −5.53721 −0.401711
\(191\) −0.0279119 −0.00201964 −0.00100982 0.999999i \(-0.500321\pi\)
−0.00100982 + 0.999999i \(0.500321\pi\)
\(192\) −33.3626 −2.40774
\(193\) −15.0972 −1.08672 −0.543362 0.839499i \(-0.682849\pi\)
−0.543362 + 0.839499i \(0.682849\pi\)
\(194\) 0.301987 0.0216814
\(195\) 19.6915 1.41014
\(196\) 8.24072 0.588623
\(197\) −18.9560 −1.35056 −0.675280 0.737561i \(-0.735977\pi\)
−0.675280 + 0.737561i \(0.735977\pi\)
\(198\) −7.41225 −0.526766
\(199\) −10.4289 −0.739288 −0.369644 0.929173i \(-0.620520\pi\)
−0.369644 + 0.929173i \(0.620520\pi\)
\(200\) −2.32994 −0.164752
\(201\) −27.1524 −1.91518
\(202\) 6.37488 0.448535
\(203\) −7.74713 −0.543742
\(204\) 53.1839 3.72362
\(205\) 13.2180 0.923184
\(206\) 25.4395 1.77246
\(207\) −15.4783 −1.07582
\(208\) −1.13423 −0.0786446
\(209\) −0.844336 −0.0584039
\(210\) 44.4964 3.07054
\(211\) 20.7296 1.42709 0.713543 0.700612i \(-0.247089\pi\)
0.713543 + 0.700612i \(0.247089\pi\)
\(212\) 8.95860 0.615279
\(213\) 14.3027 0.980002
\(214\) −30.0546 −2.05449
\(215\) 28.8328 1.96638
\(216\) −6.39136 −0.434877
\(217\) −31.0657 −2.10888
\(218\) 27.2507 1.84565
\(219\) −20.5260 −1.38702
\(220\) −6.72313 −0.453273
\(221\) −19.3196 −1.29958
\(222\) −61.2086 −4.10805
\(223\) 28.3112 1.89586 0.947929 0.318483i \(-0.103173\pi\)
0.947929 + 0.318483i \(0.103173\pi\)
\(224\) 16.1171 1.07687
\(225\) 2.92548 0.195032
\(226\) −19.4834 −1.29602
\(227\) −5.69973 −0.378305 −0.189152 0.981948i \(-0.560574\pi\)
−0.189152 + 0.981948i \(0.560574\pi\)
\(228\) −8.65036 −0.572884
\(229\) −15.3214 −1.01247 −0.506233 0.862396i \(-0.668963\pi\)
−0.506233 + 0.862396i \(0.668963\pi\)
\(230\) −22.5085 −1.48416
\(231\) 6.78500 0.446420
\(232\) 7.62823 0.500818
\(233\) −22.5553 −1.47765 −0.738824 0.673898i \(-0.764619\pi\)
−0.738824 + 0.673898i \(0.764619\pi\)
\(234\) 27.5860 1.80335
\(235\) −6.15154 −0.401282
\(236\) −9.72695 −0.633170
\(237\) −26.3278 −1.71017
\(238\) −43.6562 −2.82981
\(239\) −6.95185 −0.449678 −0.224839 0.974396i \(-0.572186\pi\)
−0.224839 + 0.974396i \(0.572186\pi\)
\(240\) −2.26190 −0.146005
\(241\) −9.55654 −0.615591 −0.307795 0.951453i \(-0.599591\pi\)
−0.307795 + 0.951453i \(0.599591\pi\)
\(242\) 23.7170 1.52459
\(243\) −21.7801 −1.39720
\(244\) 0.414094 0.0265097
\(245\) −5.96976 −0.381394
\(246\) 33.1063 2.11078
\(247\) 3.14234 0.199942
\(248\) 30.5890 1.94240
\(249\) 2.51207 0.159196
\(250\) −23.4318 −1.48196
\(251\) 3.59023 0.226613 0.113307 0.993560i \(-0.463856\pi\)
0.113307 + 0.993560i \(0.463856\pi\)
\(252\) 38.8806 2.44925
\(253\) −3.43218 −0.215779
\(254\) −27.0951 −1.70010
\(255\) −38.5276 −2.41269
\(256\) −18.2631 −1.14144
\(257\) 1.34236 0.0837341 0.0418670 0.999123i \(-0.486669\pi\)
0.0418670 + 0.999123i \(0.486669\pi\)
\(258\) 72.2157 4.49595
\(259\) 31.3384 1.94727
\(260\) 25.0213 1.55175
\(261\) −9.57803 −0.592865
\(262\) 22.8135 1.40942
\(263\) −16.8192 −1.03711 −0.518557 0.855043i \(-0.673531\pi\)
−0.518557 + 0.855043i \(0.673531\pi\)
\(264\) −6.68086 −0.411179
\(265\) −6.48980 −0.398666
\(266\) 7.10067 0.435370
\(267\) −22.5707 −1.38131
\(268\) −34.5016 −2.10752
\(269\) −13.6212 −0.830500 −0.415250 0.909707i \(-0.636306\pi\)
−0.415250 + 0.909707i \(0.636306\pi\)
\(270\) 11.6699 0.710209
\(271\) −9.98790 −0.606722 −0.303361 0.952876i \(-0.598109\pi\)
−0.303361 + 0.952876i \(0.598109\pi\)
\(272\) 2.21919 0.134558
\(273\) −25.2515 −1.52829
\(274\) −33.0012 −1.99367
\(275\) 0.648701 0.0391182
\(276\) −35.1633 −2.11658
\(277\) 22.5904 1.35732 0.678662 0.734451i \(-0.262560\pi\)
0.678662 + 0.734451i \(0.262560\pi\)
\(278\) 10.3425 0.620301
\(279\) −38.4076 −2.29940
\(280\) 22.4322 1.34058
\(281\) 12.5607 0.749307 0.374653 0.927165i \(-0.377762\pi\)
0.374653 + 0.927165i \(0.377762\pi\)
\(282\) −15.4074 −0.917495
\(283\) 12.1383 0.721545 0.360773 0.932654i \(-0.382513\pi\)
0.360773 + 0.932654i \(0.382513\pi\)
\(284\) 18.1739 1.07842
\(285\) 6.26651 0.371196
\(286\) 6.11695 0.361703
\(287\) −16.9502 −1.00054
\(288\) 19.9261 1.17415
\(289\) 20.8001 1.22353
\(290\) −13.9283 −0.817899
\(291\) −0.341761 −0.0200344
\(292\) −26.0817 −1.52632
\(293\) 21.5483 1.25887 0.629433 0.777055i \(-0.283287\pi\)
0.629433 + 0.777055i \(0.283287\pi\)
\(294\) −14.9521 −0.872023
\(295\) 7.04641 0.410258
\(296\) −30.8574 −1.79355
\(297\) 1.77948 0.103256
\(298\) 14.6113 0.846411
\(299\) 12.7734 0.738707
\(300\) 6.64605 0.383710
\(301\) −36.9739 −2.13114
\(302\) −44.3637 −2.55284
\(303\) −7.21451 −0.414462
\(304\) −0.360950 −0.0207019
\(305\) −0.299979 −0.0171767
\(306\) −53.9736 −3.08546
\(307\) 10.9893 0.627193 0.313596 0.949556i \(-0.398466\pi\)
0.313596 + 0.949556i \(0.398466\pi\)
\(308\) 8.62145 0.491253
\(309\) −28.7902 −1.63781
\(310\) −55.8521 −3.17219
\(311\) −6.84222 −0.387987 −0.193993 0.981003i \(-0.562144\pi\)
−0.193993 + 0.981003i \(0.562144\pi\)
\(312\) 24.8640 1.40764
\(313\) −20.5589 −1.16206 −0.581030 0.813882i \(-0.697350\pi\)
−0.581030 + 0.813882i \(0.697350\pi\)
\(314\) −17.2883 −0.975632
\(315\) −28.1660 −1.58697
\(316\) −33.4538 −1.88192
\(317\) −1.00000 −0.0561656
\(318\) −16.2546 −0.911513
\(319\) −2.12385 −0.118913
\(320\) 30.7102 1.71675
\(321\) 34.0131 1.89843
\(322\) 28.8639 1.60852
\(323\) −6.14818 −0.342094
\(324\) −19.6413 −1.09118
\(325\) −2.41425 −0.133919
\(326\) 3.91762 0.216977
\(327\) −30.8399 −1.70545
\(328\) 16.6900 0.921553
\(329\) 7.88846 0.434905
\(330\) 12.1985 0.671507
\(331\) 3.15236 0.173270 0.0866348 0.996240i \(-0.472389\pi\)
0.0866348 + 0.996240i \(0.472389\pi\)
\(332\) 3.19199 0.175183
\(333\) 38.7447 2.12319
\(334\) 8.12955 0.444829
\(335\) 24.9937 1.36555
\(336\) 2.90056 0.158239
\(337\) −4.12736 −0.224832 −0.112416 0.993661i \(-0.535859\pi\)
−0.112416 + 0.993661i \(0.535859\pi\)
\(338\) 7.20635 0.391974
\(339\) 22.0496 1.19757
\(340\) −48.9556 −2.65499
\(341\) −8.51656 −0.461198
\(342\) 8.77880 0.474703
\(343\) −13.9037 −0.750731
\(344\) 36.4065 1.96291
\(345\) 25.4730 1.37142
\(346\) −20.8290 −1.11977
\(347\) −10.0358 −0.538752 −0.269376 0.963035i \(-0.586817\pi\)
−0.269376 + 0.963035i \(0.586817\pi\)
\(348\) −21.7592 −1.16641
\(349\) −22.2393 −1.19044 −0.595221 0.803562i \(-0.702935\pi\)
−0.595221 + 0.803562i \(0.702935\pi\)
\(350\) −5.45543 −0.291605
\(351\) −6.62263 −0.353490
\(352\) 4.41844 0.235504
\(353\) 0.128942 0.00686288 0.00343144 0.999994i \(-0.498908\pi\)
0.00343144 + 0.999994i \(0.498908\pi\)
\(354\) 17.6487 0.938018
\(355\) −13.1655 −0.698755
\(356\) −28.6798 −1.52003
\(357\) 49.4061 2.61485
\(358\) 7.24061 0.382678
\(359\) −3.53690 −0.186671 −0.0933353 0.995635i \(-0.529753\pi\)
−0.0933353 + 0.995635i \(0.529753\pi\)
\(360\) 27.7337 1.46169
\(361\) 1.00000 0.0526316
\(362\) −41.8588 −2.20005
\(363\) −26.8407 −1.40877
\(364\) −32.0862 −1.68177
\(365\) 18.8941 0.988965
\(366\) −0.751338 −0.0392730
\(367\) 25.0769 1.30900 0.654502 0.756061i \(-0.272879\pi\)
0.654502 + 0.756061i \(0.272879\pi\)
\(368\) −1.46724 −0.0764854
\(369\) −20.9561 −1.09093
\(370\) 56.3423 2.92909
\(371\) 8.32224 0.432069
\(372\) −87.2536 −4.52389
\(373\) 17.4144 0.901686 0.450843 0.892603i \(-0.351124\pi\)
0.450843 + 0.892603i \(0.351124\pi\)
\(374\) −11.9682 −0.618860
\(375\) 26.5180 1.36938
\(376\) −7.76740 −0.400573
\(377\) 7.90426 0.407090
\(378\) −14.9650 −0.769717
\(379\) −12.0486 −0.618893 −0.309447 0.950917i \(-0.600144\pi\)
−0.309447 + 0.950917i \(0.600144\pi\)
\(380\) 7.96262 0.408474
\(381\) 30.6638 1.57095
\(382\) 0.0643512 0.00329250
\(383\) 20.7513 1.06034 0.530172 0.847890i \(-0.322128\pi\)
0.530172 + 0.847890i \(0.322128\pi\)
\(384\) 49.6102 2.53166
\(385\) −6.24557 −0.318303
\(386\) 34.8068 1.77162
\(387\) −45.7121 −2.32368
\(388\) −0.434263 −0.0220464
\(389\) −5.52185 −0.279969 −0.139984 0.990154i \(-0.544705\pi\)
−0.139984 + 0.990154i \(0.544705\pi\)
\(390\) −45.3989 −2.29886
\(391\) −24.9920 −1.26390
\(392\) −7.53787 −0.380720
\(393\) −25.8182 −1.30236
\(394\) 43.7033 2.20174
\(395\) 24.2346 1.21938
\(396\) 10.6590 0.535634
\(397\) −6.99177 −0.350907 −0.175453 0.984488i \(-0.556139\pi\)
−0.175453 + 0.984488i \(0.556139\pi\)
\(398\) 24.0440 1.20522
\(399\) −8.03590 −0.402298
\(400\) 0.277317 0.0138659
\(401\) 15.8587 0.791943 0.395972 0.918263i \(-0.370408\pi\)
0.395972 + 0.918263i \(0.370408\pi\)
\(402\) 62.6002 3.12221
\(403\) 31.6958 1.57888
\(404\) −9.16721 −0.456086
\(405\) 14.2286 0.707023
\(406\) 17.8611 0.886431
\(407\) 8.59130 0.425855
\(408\) −48.6478 −2.40843
\(409\) −28.1892 −1.39386 −0.696932 0.717137i \(-0.745452\pi\)
−0.696932 + 0.717137i \(0.745452\pi\)
\(410\) −30.4742 −1.50501
\(411\) 37.3477 1.84223
\(412\) −36.5826 −1.80230
\(413\) −9.03601 −0.444633
\(414\) 35.6854 1.75384
\(415\) −2.31235 −0.113509
\(416\) −16.4440 −0.806232
\(417\) −11.7047 −0.573181
\(418\) 1.94662 0.0952125
\(419\) −11.8947 −0.581096 −0.290548 0.956860i \(-0.593838\pi\)
−0.290548 + 0.956860i \(0.593838\pi\)
\(420\) −63.9868 −3.12224
\(421\) −11.0341 −0.537769 −0.268884 0.963172i \(-0.586655\pi\)
−0.268884 + 0.963172i \(0.586655\pi\)
\(422\) −47.7923 −2.32649
\(423\) 9.75277 0.474196
\(424\) −8.19452 −0.397961
\(425\) 4.72363 0.229130
\(426\) −32.9749 −1.59764
\(427\) 0.384680 0.0186160
\(428\) 43.2192 2.08908
\(429\) −6.92261 −0.334227
\(430\) −66.4743 −3.20568
\(431\) 19.0607 0.918120 0.459060 0.888405i \(-0.348186\pi\)
0.459060 + 0.888405i \(0.348186\pi\)
\(432\) 0.760720 0.0366002
\(433\) −1.40924 −0.0677239 −0.0338620 0.999427i \(-0.510781\pi\)
−0.0338620 + 0.999427i \(0.510781\pi\)
\(434\) 71.6223 3.43798
\(435\) 15.7628 0.755769
\(436\) −39.1871 −1.87672
\(437\) 4.06495 0.194453
\(438\) 47.3230 2.26118
\(439\) 7.83372 0.373883 0.186942 0.982371i \(-0.440143\pi\)
0.186942 + 0.982371i \(0.440143\pi\)
\(440\) 6.14971 0.293176
\(441\) 9.46458 0.450694
\(442\) 44.5416 2.11863
\(443\) −16.0685 −0.763437 −0.381719 0.924279i \(-0.624668\pi\)
−0.381719 + 0.924279i \(0.624668\pi\)
\(444\) 88.0193 4.17721
\(445\) 20.7763 0.984891
\(446\) −65.2717 −3.09070
\(447\) −16.5358 −0.782115
\(448\) −39.3814 −1.86060
\(449\) 34.1153 1.61000 0.805001 0.593273i \(-0.202165\pi\)
0.805001 + 0.593273i \(0.202165\pi\)
\(450\) −6.74473 −0.317950
\(451\) −4.64683 −0.218811
\(452\) 28.0176 1.31784
\(453\) 50.2068 2.35892
\(454\) 13.1408 0.616728
\(455\) 23.2439 1.08969
\(456\) 7.91257 0.370540
\(457\) 6.11868 0.286220 0.143110 0.989707i \(-0.454290\pi\)
0.143110 + 0.989707i \(0.454290\pi\)
\(458\) 35.3236 1.65057
\(459\) 12.9576 0.604808
\(460\) 32.3677 1.50915
\(461\) 37.6355 1.75286 0.876429 0.481531i \(-0.159919\pi\)
0.876429 + 0.481531i \(0.159919\pi\)
\(462\) −15.6429 −0.727772
\(463\) 30.7212 1.42774 0.713868 0.700280i \(-0.246941\pi\)
0.713868 + 0.700280i \(0.246941\pi\)
\(464\) −0.907937 −0.0421499
\(465\) 63.2084 2.93122
\(466\) 52.0015 2.40892
\(467\) 39.0635 1.80764 0.903821 0.427911i \(-0.140750\pi\)
0.903821 + 0.427911i \(0.140750\pi\)
\(468\) −39.6692 −1.83371
\(469\) −32.0508 −1.47997
\(470\) 14.1824 0.654186
\(471\) 19.5653 0.901520
\(472\) 8.89733 0.409533
\(473\) −10.1363 −0.466066
\(474\) 60.6989 2.78800
\(475\) −0.768298 −0.0352519
\(476\) 62.7785 2.87745
\(477\) 10.2891 0.471104
\(478\) 16.0276 0.733084
\(479\) 12.3208 0.562949 0.281475 0.959569i \(-0.409176\pi\)
0.281475 + 0.959569i \(0.409176\pi\)
\(480\) −32.7928 −1.49678
\(481\) −31.9740 −1.45789
\(482\) 22.0327 1.00356
\(483\) −32.6655 −1.48633
\(484\) −34.1056 −1.55025
\(485\) 0.314590 0.0142848
\(486\) 50.2143 2.27777
\(487\) −6.30218 −0.285579 −0.142790 0.989753i \(-0.545607\pi\)
−0.142790 + 0.989753i \(0.545607\pi\)
\(488\) −0.378776 −0.0171464
\(489\) −4.43360 −0.200494
\(490\) 13.7633 0.621764
\(491\) 21.0356 0.949323 0.474662 0.880168i \(-0.342570\pi\)
0.474662 + 0.880168i \(0.342570\pi\)
\(492\) −47.6075 −2.14631
\(493\) −15.4652 −0.696516
\(494\) −7.24469 −0.325954
\(495\) −7.72160 −0.347060
\(496\) −3.64080 −0.163477
\(497\) 16.8829 0.757303
\(498\) −5.79160 −0.259528
\(499\) −28.4324 −1.27281 −0.636405 0.771355i \(-0.719579\pi\)
−0.636405 + 0.771355i \(0.719579\pi\)
\(500\) 33.6955 1.50691
\(501\) −9.20029 −0.411039
\(502\) −8.27731 −0.369434
\(503\) −11.6335 −0.518710 −0.259355 0.965782i \(-0.583510\pi\)
−0.259355 + 0.965782i \(0.583510\pi\)
\(504\) −35.5645 −1.58417
\(505\) 6.64093 0.295517
\(506\) 7.91293 0.351773
\(507\) −8.15549 −0.362198
\(508\) 38.9633 1.72872
\(509\) 9.05113 0.401184 0.200592 0.979675i \(-0.435713\pi\)
0.200592 + 0.979675i \(0.435713\pi\)
\(510\) 88.8257 3.93327
\(511\) −24.2290 −1.07183
\(512\) 4.07810 0.180228
\(513\) −2.10755 −0.0930505
\(514\) −3.09482 −0.136507
\(515\) 26.5012 1.16778
\(516\) −103.848 −4.57164
\(517\) 2.16259 0.0951108
\(518\) −72.2509 −3.17452
\(519\) 23.5724 1.03471
\(520\) −22.8872 −1.00367
\(521\) −34.5083 −1.51184 −0.755918 0.654666i \(-0.772809\pi\)
−0.755918 + 0.654666i \(0.772809\pi\)
\(522\) 22.0822 0.966514
\(523\) −34.7348 −1.51885 −0.759424 0.650597i \(-0.774519\pi\)
−0.759424 + 0.650597i \(0.774519\pi\)
\(524\) −32.8063 −1.43315
\(525\) 6.17396 0.269454
\(526\) 38.7768 1.69075
\(527\) −62.0148 −2.70141
\(528\) 0.795178 0.0346057
\(529\) −6.47619 −0.281573
\(530\) 14.9623 0.649921
\(531\) −11.1715 −0.484803
\(532\) −10.2109 −0.442700
\(533\) 17.2940 0.749085
\(534\) 52.0371 2.25186
\(535\) −31.3089 −1.35360
\(536\) 31.5589 1.36314
\(537\) −8.19426 −0.353609
\(538\) 31.4038 1.35391
\(539\) 2.09869 0.0903970
\(540\) −16.7816 −0.722165
\(541\) −11.2467 −0.483535 −0.241768 0.970334i \(-0.577727\pi\)
−0.241768 + 0.970334i \(0.577727\pi\)
\(542\) 23.0272 0.989103
\(543\) 47.3720 2.03293
\(544\) 32.1736 1.37943
\(545\) 28.3880 1.21601
\(546\) 58.2176 2.49148
\(547\) −22.0700 −0.943644 −0.471822 0.881694i \(-0.656403\pi\)
−0.471822 + 0.881694i \(0.656403\pi\)
\(548\) 47.4564 2.02724
\(549\) 0.475592 0.0202978
\(550\) −1.49559 −0.0637720
\(551\) 2.51541 0.107160
\(552\) 32.1642 1.36900
\(553\) −31.0774 −1.32155
\(554\) −52.0823 −2.21276
\(555\) −63.7631 −2.70659
\(556\) −14.8727 −0.630744
\(557\) 24.0806 1.02033 0.510164 0.860077i \(-0.329585\pi\)
0.510164 + 0.860077i \(0.329585\pi\)
\(558\) 88.5491 3.74858
\(559\) 37.7239 1.59555
\(560\) −2.66996 −0.112826
\(561\) 13.5445 0.571850
\(562\) −28.9587 −1.22155
\(563\) −41.0811 −1.73136 −0.865682 0.500595i \(-0.833115\pi\)
−0.865682 + 0.500595i \(0.833115\pi\)
\(564\) 22.1561 0.932941
\(565\) −20.2966 −0.853883
\(566\) −27.9849 −1.17629
\(567\) −18.2461 −0.766264
\(568\) −16.6238 −0.697520
\(569\) −21.0383 −0.881971 −0.440985 0.897514i \(-0.645371\pi\)
−0.440985 + 0.897514i \(0.645371\pi\)
\(570\) −14.4475 −0.605139
\(571\) −29.5547 −1.23682 −0.618412 0.785854i \(-0.712224\pi\)
−0.618412 + 0.785854i \(0.712224\pi\)
\(572\) −8.79631 −0.367792
\(573\) −0.0728269 −0.00304239
\(574\) 39.0788 1.63112
\(575\) −3.12309 −0.130242
\(576\) −48.6885 −2.02869
\(577\) 11.3295 0.471655 0.235828 0.971795i \(-0.424220\pi\)
0.235828 + 0.971795i \(0.424220\pi\)
\(578\) −47.9547 −1.99465
\(579\) −39.3912 −1.63704
\(580\) 20.0292 0.831669
\(581\) 2.96526 0.123020
\(582\) 0.787933 0.0326609
\(583\) 2.28151 0.0944906
\(584\) 23.8572 0.987217
\(585\) 28.7372 1.18814
\(586\) −49.6798 −2.05225
\(587\) −27.9458 −1.15345 −0.576724 0.816939i \(-0.695669\pi\)
−0.576724 + 0.816939i \(0.695669\pi\)
\(588\) 21.5014 0.886704
\(589\) 10.0867 0.415615
\(590\) −16.2456 −0.668819
\(591\) −49.4594 −2.03449
\(592\) 3.67275 0.150949
\(593\) −7.47525 −0.306972 −0.153486 0.988151i \(-0.549050\pi\)
−0.153486 + 0.988151i \(0.549050\pi\)
\(594\) −4.10260 −0.168332
\(595\) −45.4781 −1.86442
\(596\) −21.0114 −0.860660
\(597\) −27.2108 −1.11367
\(598\) −29.4493 −1.20427
\(599\) −42.8856 −1.75226 −0.876128 0.482078i \(-0.839882\pi\)
−0.876128 + 0.482078i \(0.839882\pi\)
\(600\) −6.07921 −0.248183
\(601\) 38.3259 1.56335 0.781673 0.623689i \(-0.214367\pi\)
0.781673 + 0.623689i \(0.214367\pi\)
\(602\) 85.2438 3.47428
\(603\) −39.6255 −1.61368
\(604\) 63.7959 2.59582
\(605\) 24.7068 1.00447
\(606\) 16.6331 0.675674
\(607\) 1.81492 0.0736655 0.0368328 0.999321i \(-0.488273\pi\)
0.0368328 + 0.999321i \(0.488273\pi\)
\(608\) −5.23303 −0.212228
\(609\) −20.2135 −0.819094
\(610\) 0.691604 0.0280022
\(611\) −8.04846 −0.325606
\(612\) 77.6152 3.13741
\(613\) 20.7243 0.837045 0.418522 0.908206i \(-0.362548\pi\)
0.418522 + 0.908206i \(0.362548\pi\)
\(614\) −25.3359 −1.02248
\(615\) 34.4879 1.39069
\(616\) −7.88612 −0.317741
\(617\) −27.7305 −1.11639 −0.558195 0.829710i \(-0.688506\pi\)
−0.558195 + 0.829710i \(0.688506\pi\)
\(618\) 66.3760 2.67003
\(619\) 20.7828 0.835332 0.417666 0.908601i \(-0.362848\pi\)
0.417666 + 0.908601i \(0.362848\pi\)
\(620\) 80.3166 3.22559
\(621\) −8.56707 −0.343785
\(622\) 15.7748 0.632512
\(623\) −26.6426 −1.06741
\(624\) −2.95939 −0.118470
\(625\) −28.2512 −1.13005
\(626\) 47.3988 1.89444
\(627\) −2.20301 −0.0879799
\(628\) 24.8609 0.992057
\(629\) 62.5590 2.49439
\(630\) 64.9369 2.58715
\(631\) 2.78791 0.110985 0.0554924 0.998459i \(-0.482327\pi\)
0.0554924 + 0.998459i \(0.482327\pi\)
\(632\) 30.6005 1.21722
\(633\) 54.0870 2.14977
\(634\) 2.30551 0.0915635
\(635\) −28.2259 −1.12011
\(636\) 23.3745 0.926858
\(637\) −7.81063 −0.309468
\(638\) 4.89655 0.193856
\(639\) 20.8729 0.825720
\(640\) −45.6660 −1.80511
\(641\) −38.9042 −1.53662 −0.768312 0.640076i \(-0.778903\pi\)
−0.768312 + 0.640076i \(0.778903\pi\)
\(642\) −78.4175 −3.09489
\(643\) 7.95320 0.313644 0.156822 0.987627i \(-0.449875\pi\)
0.156822 + 0.987627i \(0.449875\pi\)
\(644\) −41.5069 −1.63560
\(645\) 75.2296 2.96216
\(646\) 14.1747 0.557695
\(647\) 17.4271 0.685131 0.342565 0.939494i \(-0.388704\pi\)
0.342565 + 0.939494i \(0.388704\pi\)
\(648\) 17.9661 0.705773
\(649\) −2.47719 −0.0972382
\(650\) 5.56608 0.218320
\(651\) −81.0557 −3.17682
\(652\) −5.63362 −0.220630
\(653\) −30.7322 −1.20264 −0.601322 0.799007i \(-0.705359\pi\)
−0.601322 + 0.799007i \(0.705359\pi\)
\(654\) 71.1016 2.78029
\(655\) 23.7656 0.928598
\(656\) −1.98650 −0.0775599
\(657\) −29.9552 −1.16866
\(658\) −18.1869 −0.709000
\(659\) −1.32947 −0.0517887 −0.0258944 0.999665i \(-0.508243\pi\)
−0.0258944 + 0.999665i \(0.508243\pi\)
\(660\) −17.5418 −0.682812
\(661\) −33.5193 −1.30375 −0.651874 0.758327i \(-0.726017\pi\)
−0.651874 + 0.758327i \(0.726017\pi\)
\(662\) −7.26780 −0.282471
\(663\) −50.4082 −1.95769
\(664\) −2.91975 −0.113308
\(665\) 7.39701 0.286844
\(666\) −89.3262 −3.46132
\(667\) 10.2250 0.395914
\(668\) −11.6905 −0.452318
\(669\) 73.8686 2.85592
\(670\) −57.6232 −2.22618
\(671\) 0.105459 0.00407118
\(672\) 42.0521 1.62220
\(673\) −27.7690 −1.07042 −0.535208 0.844720i \(-0.679767\pi\)
−0.535208 + 0.844720i \(0.679767\pi\)
\(674\) 9.51566 0.366530
\(675\) 1.61922 0.0623239
\(676\) −10.3629 −0.398573
\(677\) 41.8151 1.60708 0.803542 0.595249i \(-0.202946\pi\)
0.803542 + 0.595249i \(0.202946\pi\)
\(678\) −50.8355 −1.95233
\(679\) −0.403416 −0.0154817
\(680\) 44.7802 1.71724
\(681\) −14.8715 −0.569879
\(682\) 19.6350 0.751863
\(683\) 23.4050 0.895568 0.447784 0.894142i \(-0.352213\pi\)
0.447784 + 0.894142i \(0.352213\pi\)
\(684\) −12.6241 −0.482695
\(685\) −34.3784 −1.31353
\(686\) 32.0552 1.22387
\(687\) −39.9761 −1.52518
\(688\) −4.33322 −0.165202
\(689\) −8.49104 −0.323483
\(690\) −58.7283 −2.23575
\(691\) 2.60738 0.0991892 0.0495946 0.998769i \(-0.484207\pi\)
0.0495946 + 0.998769i \(0.484207\pi\)
\(692\) 29.9525 1.13862
\(693\) 9.90184 0.376140
\(694\) 23.1377 0.878295
\(695\) 10.7741 0.408686
\(696\) 19.9033 0.754434
\(697\) −33.8367 −1.28166
\(698\) 51.2729 1.94071
\(699\) −58.8506 −2.22593
\(700\) 7.84503 0.296514
\(701\) −47.5963 −1.79769 −0.898844 0.438269i \(-0.855592\pi\)
−0.898844 + 0.438269i \(0.855592\pi\)
\(702\) 15.2685 0.576273
\(703\) −10.1752 −0.383766
\(704\) −10.7963 −0.406900
\(705\) −16.0504 −0.604492
\(706\) −0.297276 −0.0111881
\(707\) −8.51604 −0.320278
\(708\) −25.3792 −0.953809
\(709\) 10.1603 0.381576 0.190788 0.981631i \(-0.438896\pi\)
0.190788 + 0.981631i \(0.438896\pi\)
\(710\) 30.3533 1.13914
\(711\) −38.4221 −1.44094
\(712\) 26.2337 0.983150
\(713\) 41.0019 1.53553
\(714\) −113.906 −4.26283
\(715\) 6.37224 0.238308
\(716\) −10.4122 −0.389120
\(717\) −18.1385 −0.677396
\(718\) 8.15437 0.304318
\(719\) 20.7575 0.774125 0.387063 0.922053i \(-0.373490\pi\)
0.387063 + 0.922053i \(0.373490\pi\)
\(720\) −3.30095 −0.123019
\(721\) −33.9840 −1.26563
\(722\) −2.30551 −0.0858022
\(723\) −24.9346 −0.927328
\(724\) 60.1939 2.23709
\(725\) −1.93258 −0.0717742
\(726\) 61.8816 2.29664
\(727\) 14.3863 0.533559 0.266779 0.963758i \(-0.414040\pi\)
0.266779 + 0.963758i \(0.414040\pi\)
\(728\) 29.3495 1.08777
\(729\) −39.0551 −1.44648
\(730\) −43.5606 −1.61225
\(731\) −73.8090 −2.72992
\(732\) 1.08044 0.0399342
\(733\) 14.7498 0.544798 0.272399 0.962184i \(-0.412183\pi\)
0.272399 + 0.962184i \(0.412183\pi\)
\(734\) −57.8150 −2.13399
\(735\) −15.5761 −0.574533
\(736\) −21.2720 −0.784097
\(737\) −8.78663 −0.323660
\(738\) 48.3144 1.77848
\(739\) −30.7085 −1.12963 −0.564815 0.825217i \(-0.691053\pi\)
−0.564815 + 0.825217i \(0.691053\pi\)
\(740\) −81.0214 −2.97841
\(741\) 8.19888 0.301194
\(742\) −19.1870 −0.704377
\(743\) −0.0550381 −0.00201915 −0.00100958 0.999999i \(-0.500321\pi\)
−0.00100958 + 0.999999i \(0.500321\pi\)
\(744\) 79.8117 2.92604
\(745\) 15.2211 0.557658
\(746\) −40.1492 −1.46996
\(747\) 3.66605 0.134134
\(748\) 17.2105 0.629279
\(749\) 40.1492 1.46702
\(750\) −61.1375 −2.23243
\(751\) −41.1707 −1.50234 −0.751170 0.660109i \(-0.770510\pi\)
−0.751170 + 0.660109i \(0.770510\pi\)
\(752\) 0.924501 0.0337131
\(753\) 9.36750 0.341371
\(754\) −18.2233 −0.663655
\(755\) −46.2152 −1.68194
\(756\) 21.5200 0.782675
\(757\) −8.00867 −0.291080 −0.145540 0.989352i \(-0.546492\pi\)
−0.145540 + 0.989352i \(0.546492\pi\)
\(758\) 27.7781 1.00894
\(759\) −8.95513 −0.325051
\(760\) −7.28349 −0.264200
\(761\) 15.5504 0.563702 0.281851 0.959458i \(-0.409052\pi\)
0.281851 + 0.959458i \(0.409052\pi\)
\(762\) −70.6956 −2.56103
\(763\) −36.4035 −1.31790
\(764\) −0.0925385 −0.00334792
\(765\) −56.2261 −2.03286
\(766\) −47.8424 −1.72861
\(767\) 9.21928 0.332889
\(768\) −47.6514 −1.71947
\(769\) 51.1094 1.84305 0.921527 0.388315i \(-0.126943\pi\)
0.921527 + 0.388315i \(0.126943\pi\)
\(770\) 14.3992 0.518911
\(771\) 3.50244 0.126137
\(772\) −50.0530 −1.80145
\(773\) 16.1831 0.582066 0.291033 0.956713i \(-0.406001\pi\)
0.291033 + 0.956713i \(0.406001\pi\)
\(774\) 105.390 3.78815
\(775\) −7.74959 −0.278373
\(776\) 0.397225 0.0142595
\(777\) 81.7670 2.93337
\(778\) 12.7307 0.456416
\(779\) 5.50353 0.197185
\(780\) 65.2846 2.33756
\(781\) 4.62840 0.165617
\(782\) 57.6193 2.06046
\(783\) −5.30134 −0.189454
\(784\) 0.897182 0.0320422
\(785\) −18.0098 −0.642796
\(786\) 59.5241 2.12316
\(787\) −2.87606 −0.102521 −0.0512603 0.998685i \(-0.516324\pi\)
−0.0512603 + 0.998685i \(0.516324\pi\)
\(788\) −62.8463 −2.23881
\(789\) −43.8840 −1.56231
\(790\) −55.8732 −1.98788
\(791\) 26.0274 0.925429
\(792\) −9.74988 −0.346447
\(793\) −0.392482 −0.0139374
\(794\) 16.1196 0.572063
\(795\) −16.9330 −0.600551
\(796\) −34.5758 −1.22551
\(797\) −4.77768 −0.169234 −0.0846171 0.996414i \(-0.526967\pi\)
−0.0846171 + 0.996414i \(0.526967\pi\)
\(798\) 18.5268 0.655843
\(799\) 15.7473 0.557099
\(800\) 4.02053 0.142147
\(801\) −32.9392 −1.16385
\(802\) −36.5623 −1.29106
\(803\) −6.64230 −0.234402
\(804\) −90.0204 −3.17477
\(805\) 30.0685 1.05977
\(806\) −73.0750 −2.57396
\(807\) −35.5400 −1.25107
\(808\) 8.38534 0.294995
\(809\) −50.7959 −1.78589 −0.892945 0.450166i \(-0.851365\pi\)
−0.892945 + 0.450166i \(0.851365\pi\)
\(810\) −32.8041 −1.15262
\(811\) 35.1819 1.23540 0.617702 0.786412i \(-0.288064\pi\)
0.617702 + 0.786412i \(0.288064\pi\)
\(812\) −25.6846 −0.901354
\(813\) −26.0601 −0.913967
\(814\) −19.8073 −0.694246
\(815\) 4.08112 0.142955
\(816\) 5.79023 0.202698
\(817\) 12.0050 0.420003
\(818\) 64.9904 2.27234
\(819\) −36.8514 −1.28769
\(820\) 43.8226 1.53035
\(821\) 3.76859 0.131525 0.0657623 0.997835i \(-0.479052\pi\)
0.0657623 + 0.997835i \(0.479052\pi\)
\(822\) −86.1055 −3.00327
\(823\) 43.8325 1.52791 0.763953 0.645272i \(-0.223256\pi\)
0.763953 + 0.645272i \(0.223256\pi\)
\(824\) 33.4625 1.16572
\(825\) 1.69257 0.0589277
\(826\) 20.8326 0.724859
\(827\) 16.7129 0.581166 0.290583 0.956850i \(-0.406151\pi\)
0.290583 + 0.956850i \(0.406151\pi\)
\(828\) −51.3163 −1.78337
\(829\) 4.78930 0.166339 0.0831697 0.996535i \(-0.473496\pi\)
0.0831697 + 0.996535i \(0.473496\pi\)
\(830\) 5.33114 0.185047
\(831\) 58.9420 2.04468
\(832\) 40.1802 1.39300
\(833\) 15.2820 0.529489
\(834\) 26.9853 0.934423
\(835\) 8.46883 0.293076
\(836\) −2.79929 −0.0968154
\(837\) −21.2582 −0.734791
\(838\) 27.4234 0.947327
\(839\) −12.5972 −0.434905 −0.217452 0.976071i \(-0.569775\pi\)
−0.217452 + 0.976071i \(0.569775\pi\)
\(840\) 58.5294 2.01946
\(841\) −22.6727 −0.781818
\(842\) 25.4392 0.876692
\(843\) 32.7729 1.12876
\(844\) 68.7264 2.36566
\(845\) 7.50710 0.258252
\(846\) −22.4851 −0.773054
\(847\) −31.6829 −1.08864
\(848\) 0.975338 0.0334933
\(849\) 31.6708 1.08694
\(850\) −10.8904 −0.373537
\(851\) −41.3617 −1.41786
\(852\) 47.4187 1.62454
\(853\) −3.93449 −0.134714 −0.0673572 0.997729i \(-0.521457\pi\)
−0.0673572 + 0.997729i \(0.521457\pi\)
\(854\) −0.886882 −0.0303485
\(855\) 9.14517 0.312758
\(856\) −39.5330 −1.35121
\(857\) −38.7534 −1.32379 −0.661896 0.749596i \(-0.730248\pi\)
−0.661896 + 0.749596i \(0.730248\pi\)
\(858\) 15.9601 0.544870
\(859\) 25.4345 0.867813 0.433906 0.900958i \(-0.357135\pi\)
0.433906 + 0.900958i \(0.357135\pi\)
\(860\) 95.5915 3.25964
\(861\) −44.2258 −1.50721
\(862\) −43.9445 −1.49676
\(863\) 41.1827 1.40187 0.700937 0.713223i \(-0.252765\pi\)
0.700937 + 0.713223i \(0.252765\pi\)
\(864\) 11.0289 0.375210
\(865\) −21.6983 −0.737763
\(866\) 3.24902 0.110406
\(867\) 54.2708 1.84313
\(868\) −102.995 −3.49586
\(869\) −8.51977 −0.289013
\(870\) −36.3413 −1.23209
\(871\) 32.7009 1.10803
\(872\) 35.8448 1.21386
\(873\) −0.498757 −0.0168804
\(874\) −9.37178 −0.317005
\(875\) 31.3020 1.05820
\(876\) −68.0515 −2.29925
\(877\) −21.4016 −0.722679 −0.361340 0.932434i \(-0.617681\pi\)
−0.361340 + 0.932434i \(0.617681\pi\)
\(878\) −18.0607 −0.609520
\(879\) 56.2231 1.89636
\(880\) −0.731959 −0.0246743
\(881\) 36.8108 1.24019 0.620093 0.784528i \(-0.287095\pi\)
0.620093 + 0.784528i \(0.287095\pi\)
\(882\) −21.8207 −0.734740
\(883\) −24.8980 −0.837884 −0.418942 0.908013i \(-0.637599\pi\)
−0.418942 + 0.908013i \(0.637599\pi\)
\(884\) −64.0518 −2.15430
\(885\) 18.3853 0.618014
\(886\) 37.0461 1.24459
\(887\) 27.1751 0.912450 0.456225 0.889865i \(-0.349201\pi\)
0.456225 + 0.889865i \(0.349201\pi\)
\(888\) −80.5121 −2.70181
\(889\) 36.1956 1.21396
\(890\) −47.8999 −1.60561
\(891\) −5.00210 −0.167577
\(892\) 93.8621 3.14274
\(893\) −2.56130 −0.0857105
\(894\) 38.1234 1.27504
\(895\) 7.54279 0.252128
\(896\) 58.5601 1.95635
\(897\) 33.3280 1.11279
\(898\) −78.6532 −2.62469
\(899\) 25.3721 0.846209
\(900\) 9.69907 0.323302
\(901\) 16.6132 0.553467
\(902\) 10.7133 0.356714
\(903\) −96.4711 −3.21036
\(904\) −25.6280 −0.852374
\(905\) −43.6057 −1.44950
\(906\) −115.752 −3.84561
\(907\) −38.3004 −1.27174 −0.635872 0.771795i \(-0.719359\pi\)
−0.635872 + 0.771795i \(0.719359\pi\)
\(908\) −18.8967 −0.627110
\(909\) −10.5287 −0.349214
\(910\) −53.5891 −1.77646
\(911\) −26.4863 −0.877530 −0.438765 0.898602i \(-0.644584\pi\)
−0.438765 + 0.898602i \(0.644584\pi\)
\(912\) −0.941780 −0.0311854
\(913\) 0.812915 0.0269036
\(914\) −14.1067 −0.466608
\(915\) −0.782694 −0.0258751
\(916\) −50.7962 −1.67835
\(917\) −30.4759 −1.00640
\(918\) −29.8738 −0.985982
\(919\) −15.4876 −0.510889 −0.255445 0.966824i \(-0.582222\pi\)
−0.255445 + 0.966824i \(0.582222\pi\)
\(920\) −29.6070 −0.976114
\(921\) 28.6729 0.944805
\(922\) −86.7689 −2.85758
\(923\) −17.2254 −0.566979
\(924\) 22.4948 0.740024
\(925\) 7.81759 0.257041
\(926\) −70.8281 −2.32756
\(927\) −42.0156 −1.37997
\(928\) −13.1632 −0.432103
\(929\) −26.7547 −0.877792 −0.438896 0.898538i \(-0.644630\pi\)
−0.438896 + 0.898538i \(0.644630\pi\)
\(930\) −145.727 −4.77859
\(931\) −2.48561 −0.0814626
\(932\) −74.7793 −2.44948
\(933\) −17.8525 −0.584464
\(934\) −90.0612 −2.94689
\(935\) −12.4677 −0.407736
\(936\) 36.2858 1.18604
\(937\) 29.5719 0.966072 0.483036 0.875600i \(-0.339534\pi\)
0.483036 + 0.875600i \(0.339534\pi\)
\(938\) 73.8935 2.41271
\(939\) −53.6417 −1.75053
\(940\) −20.3946 −0.665200
\(941\) −34.5602 −1.12663 −0.563315 0.826243i \(-0.690474\pi\)
−0.563315 + 0.826243i \(0.690474\pi\)
\(942\) −45.1079 −1.46970
\(943\) 22.3716 0.728519
\(944\) −1.05899 −0.0344672
\(945\) −15.5896 −0.507128
\(946\) 23.3693 0.759801
\(947\) 37.7324 1.22614 0.613069 0.790029i \(-0.289935\pi\)
0.613069 + 0.790029i \(0.289935\pi\)
\(948\) −87.2864 −2.83493
\(949\) 24.7205 0.802460
\(950\) 1.77132 0.0574691
\(951\) −2.60917 −0.0846080
\(952\) −57.4241 −1.86113
\(953\) −52.6080 −1.70414 −0.852070 0.523427i \(-0.824653\pi\)
−0.852070 + 0.523427i \(0.824653\pi\)
\(954\) −23.7215 −0.768013
\(955\) 0.0670369 0.00216926
\(956\) −23.0480 −0.745425
\(957\) −5.54147 −0.179130
\(958\) −28.4056 −0.917743
\(959\) 44.0854 1.42359
\(960\) 80.1280 2.58612
\(961\) 70.7415 2.28198
\(962\) 73.7163 2.37671
\(963\) 49.6378 1.59956
\(964\) −31.6835 −1.02046
\(965\) 36.2595 1.16723
\(966\) 75.3106 2.42308
\(967\) −37.8037 −1.21569 −0.607843 0.794057i \(-0.707965\pi\)
−0.607843 + 0.794057i \(0.707965\pi\)
\(968\) 31.1967 1.00270
\(969\) −16.0416 −0.515331
\(970\) −0.725289 −0.0232876
\(971\) −27.9189 −0.895961 −0.447981 0.894043i \(-0.647857\pi\)
−0.447981 + 0.894043i \(0.647857\pi\)
\(972\) −72.2092 −2.31611
\(973\) −13.8163 −0.442929
\(974\) 14.5297 0.465563
\(975\) −6.29918 −0.201735
\(976\) 0.0450831 0.00144308
\(977\) 27.2956 0.873263 0.436631 0.899640i \(-0.356171\pi\)
0.436631 + 0.899640i \(0.356171\pi\)
\(978\) 10.2217 0.326854
\(979\) −7.30398 −0.233436
\(980\) −19.7920 −0.632232
\(981\) −45.0069 −1.43696
\(982\) −48.4978 −1.54763
\(983\) −52.4363 −1.67246 −0.836229 0.548380i \(-0.815245\pi\)
−0.836229 + 0.548380i \(0.815245\pi\)
\(984\) 43.5471 1.38823
\(985\) 45.5272 1.45062
\(986\) 35.6551 1.13549
\(987\) 20.5823 0.655142
\(988\) 10.4180 0.331441
\(989\) 48.7998 1.55174
\(990\) 17.8022 0.565792
\(991\) −52.4246 −1.66532 −0.832661 0.553784i \(-0.813183\pi\)
−0.832661 + 0.553784i \(0.813183\pi\)
\(992\) −52.7840 −1.67589
\(993\) 8.22504 0.261014
\(994\) −38.9238 −1.23459
\(995\) 25.0475 0.794058
\(996\) 8.32844 0.263897
\(997\) −61.6117 −1.95126 −0.975631 0.219416i \(-0.929585\pi\)
−0.975631 + 0.219416i \(0.929585\pi\)
\(998\) 65.5512 2.07499
\(999\) 21.4447 0.678482
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 \(a_p\))