Properties

Label 4031.2.a.c.1.12
Level 4031
Weight 2
Character 4031.1
Self dual Yes
Analytic conductor 32.188
Analytic rank 1
Dimension 61
CM No

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Newspace parameters

Level: \( N \) = \( 4031 = 29 \cdot 139 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4031.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1876970548\)
Analytic rank: \(1\)
Dimension: \(61\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 4031.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.83395 q^{2}\) \(+2.22148 q^{3}\) \(+1.36337 q^{4}\) \(+1.24306 q^{5}\) \(-4.07408 q^{6}\) \(+2.01007 q^{7}\) \(+1.16755 q^{8}\) \(+1.93497 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.83395 q^{2}\) \(+2.22148 q^{3}\) \(+1.36337 q^{4}\) \(+1.24306 q^{5}\) \(-4.07408 q^{6}\) \(+2.01007 q^{7}\) \(+1.16755 q^{8}\) \(+1.93497 q^{9}\) \(-2.27970 q^{10}\) \(-5.64415 q^{11}\) \(+3.02870 q^{12}\) \(-2.77843 q^{13}\) \(-3.68637 q^{14}\) \(+2.76142 q^{15}\) \(-4.86796 q^{16}\) \(+0.668588 q^{17}\) \(-3.54864 q^{18}\) \(+4.24245 q^{19}\) \(+1.69474 q^{20}\) \(+4.46534 q^{21}\) \(+10.3511 q^{22}\) \(-4.21670 q^{23}\) \(+2.59369 q^{24}\) \(-3.45481 q^{25}\) \(+5.09550 q^{26}\) \(-2.36594 q^{27}\) \(+2.74047 q^{28}\) \(-1.00000 q^{29}\) \(-5.06431 q^{30}\) \(-5.44314 q^{31}\) \(+6.59250 q^{32}\) \(-12.5384 q^{33}\) \(-1.22616 q^{34}\) \(+2.49863 q^{35}\) \(+2.63808 q^{36}\) \(-1.36287 q^{37}\) \(-7.78044 q^{38}\) \(-6.17223 q^{39}\) \(+1.45133 q^{40}\) \(+5.79632 q^{41}\) \(-8.18920 q^{42}\) \(+4.48081 q^{43}\) \(-7.69506 q^{44}\) \(+2.40528 q^{45}\) \(+7.73321 q^{46}\) \(-2.51083 q^{47}\) \(-10.8141 q^{48}\) \(-2.95961 q^{49}\) \(+6.33595 q^{50}\) \(+1.48525 q^{51}\) \(-3.78803 q^{52}\) \(+9.20963 q^{53}\) \(+4.33902 q^{54}\) \(-7.01600 q^{55}\) \(+2.34686 q^{56}\) \(+9.42452 q^{57}\) \(+1.83395 q^{58}\) \(-8.56719 q^{59}\) \(+3.76484 q^{60}\) \(-9.37884 q^{61}\) \(+9.98243 q^{62}\) \(+3.88943 q^{63}\) \(-2.35438 q^{64}\) \(-3.45375 q^{65}\) \(+22.9947 q^{66}\) \(-1.24871 q^{67}\) \(+0.911532 q^{68}\) \(-9.36731 q^{69}\) \(-4.58236 q^{70}\) \(+0.728297 q^{71}\) \(+2.25917 q^{72}\) \(-9.77556 q^{73}\) \(+2.49944 q^{74}\) \(-7.67479 q^{75}\) \(+5.78402 q^{76}\) \(-11.3452 q^{77}\) \(+11.3196 q^{78}\) \(-4.46664 q^{79}\) \(-6.05115 q^{80}\) \(-11.0608 q^{81}\) \(-10.6302 q^{82}\) \(+2.99039 q^{83}\) \(+6.08790 q^{84}\) \(+0.831092 q^{85}\) \(-8.21757 q^{86}\) \(-2.22148 q^{87}\) \(-6.58982 q^{88}\) \(-7.01453 q^{89}\) \(-4.41115 q^{90}\) \(-5.58485 q^{91}\) \(-5.74891 q^{92}\) \(-12.0918 q^{93}\) \(+4.60473 q^{94}\) \(+5.27360 q^{95}\) \(+14.6451 q^{96}\) \(-9.31278 q^{97}\) \(+5.42777 q^{98}\) \(-10.9213 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut -\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 18q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 14q^{14} \) \(\mathstrut -\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 11q^{16} \) \(\mathstrut -\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 17q^{18} \) \(\mathstrut -\mathstrut 36q^{19} \) \(\mathstrut -\mathstrut 16q^{20} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 42q^{22} \) \(\mathstrut -\mathstrut 15q^{23} \) \(\mathstrut -\mathstrut 28q^{24} \) \(\mathstrut -\mathstrut 16q^{25} \) \(\mathstrut -\mathstrut 13q^{26} \) \(\mathstrut -\mathstrut 10q^{27} \) \(\mathstrut -\mathstrut 25q^{28} \) \(\mathstrut -\mathstrut 61q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut -\mathstrut 18q^{31} \) \(\mathstrut -\mathstrut 3q^{32} \) \(\mathstrut -\mathstrut 42q^{33} \) \(\mathstrut -\mathstrut 22q^{34} \) \(\mathstrut -\mathstrut 29q^{35} \) \(\mathstrut -\mathstrut 38q^{36} \) \(\mathstrut -\mathstrut 30q^{37} \) \(\mathstrut -\mathstrut 27q^{38} \) \(\mathstrut -\mathstrut 31q^{39} \) \(\mathstrut -\mathstrut 22q^{40} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 9q^{42} \) \(\mathstrut -\mathstrut 58q^{43} \) \(\mathstrut -\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut 31q^{45} \) \(\mathstrut -\mathstrut 40q^{46} \) \(\mathstrut -\mathstrut 6q^{47} \) \(\mathstrut -\mathstrut 37q^{48} \) \(\mathstrut -\mathstrut 37q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut -\mathstrut 44q^{51} \) \(\mathstrut -\mathstrut 43q^{52} \) \(\mathstrut -\mathstrut 27q^{53} \) \(\mathstrut -\mathstrut 18q^{54} \) \(\mathstrut -\mathstrut 38q^{55} \) \(\mathstrut -\mathstrut 22q^{56} \) \(\mathstrut -\mathstrut 50q^{57} \) \(\mathstrut +\mathstrut q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 76q^{61} \) \(\mathstrut -\mathstrut 17q^{62} \) \(\mathstrut -\mathstrut 6q^{63} \) \(\mathstrut -\mathstrut 60q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut -\mathstrut 7q^{66} \) \(\mathstrut -\mathstrut 45q^{67} \) \(\mathstrut -\mathstrut 31q^{68} \) \(\mathstrut -\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 48q^{70} \) \(\mathstrut -\mathstrut 28q^{71} \) \(\mathstrut -\mathstrut 40q^{72} \) \(\mathstrut -\mathstrut 50q^{73} \) \(\mathstrut -\mathstrut 17q^{74} \) \(\mathstrut -\mathstrut 35q^{75} \) \(\mathstrut -\mathstrut 100q^{76} \) \(\mathstrut +\mathstrut q^{77} \) \(\mathstrut -\mathstrut 6q^{78} \) \(\mathstrut -\mathstrut 66q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut -\mathstrut 63q^{81} \) \(\mathstrut -\mathstrut 5q^{82} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 24q^{84} \) \(\mathstrut -\mathstrut 77q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut -\mathstrut 62q^{88} \) \(\mathstrut -\mathstrut 30q^{89} \) \(\mathstrut +\mathstrut 50q^{90} \) \(\mathstrut -\mathstrut 52q^{91} \) \(\mathstrut -\mathstrut 53q^{92} \) \(\mathstrut -\mathstrut 42q^{93} \) \(\mathstrut -\mathstrut 92q^{94} \) \(\mathstrut -\mathstrut 20q^{95} \) \(\mathstrut -\mathstrut 47q^{96} \) \(\mathstrut -\mathstrut 34q^{97} \) \(\mathstrut +\mathstrut 36q^{98} \) \(\mathstrut -\mathstrut 29q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.83395 −1.29680 −0.648399 0.761301i \(-0.724561\pi\)
−0.648399 + 0.761301i \(0.724561\pi\)
\(3\) 2.22148 1.28257 0.641286 0.767302i \(-0.278401\pi\)
0.641286 + 0.767302i \(0.278401\pi\)
\(4\) 1.36337 0.681684
\(5\) 1.24306 0.555911 0.277956 0.960594i \(-0.410343\pi\)
0.277956 + 0.960594i \(0.410343\pi\)
\(6\) −4.07408 −1.66324
\(7\) 2.01007 0.759736 0.379868 0.925041i \(-0.375969\pi\)
0.379868 + 0.925041i \(0.375969\pi\)
\(8\) 1.16755 0.412791
\(9\) 1.93497 0.644990
\(10\) −2.27970 −0.720905
\(11\) −5.64415 −1.70178 −0.850888 0.525347i \(-0.823935\pi\)
−0.850888 + 0.525347i \(0.823935\pi\)
\(12\) 3.02870 0.874309
\(13\) −2.77843 −0.770598 −0.385299 0.922792i \(-0.625902\pi\)
−0.385299 + 0.922792i \(0.625902\pi\)
\(14\) −3.68637 −0.985224
\(15\) 2.76142 0.712996
\(16\) −4.86796 −1.21699
\(17\) 0.668588 0.162156 0.0810782 0.996708i \(-0.474164\pi\)
0.0810782 + 0.996708i \(0.474164\pi\)
\(18\) −3.54864 −0.836422
\(19\) 4.24245 0.973285 0.486642 0.873601i \(-0.338221\pi\)
0.486642 + 0.873601i \(0.338221\pi\)
\(20\) 1.69474 0.378956
\(21\) 4.46534 0.974416
\(22\) 10.3511 2.20686
\(23\) −4.21670 −0.879242 −0.439621 0.898183i \(-0.644887\pi\)
−0.439621 + 0.898183i \(0.644887\pi\)
\(24\) 2.59369 0.529434
\(25\) −3.45481 −0.690963
\(26\) 5.09550 0.999310
\(27\) −2.36594 −0.455326
\(28\) 2.74047 0.517900
\(29\) −1.00000 −0.185695
\(30\) −5.06431 −0.924612
\(31\) −5.44314 −0.977616 −0.488808 0.872391i \(-0.662568\pi\)
−0.488808 + 0.872391i \(0.662568\pi\)
\(32\) 6.59250 1.16540
\(33\) −12.5384 −2.18265
\(34\) −1.22616 −0.210284
\(35\) 2.49863 0.422346
\(36\) 2.63808 0.439680
\(37\) −1.36287 −0.224055 −0.112027 0.993705i \(-0.535734\pi\)
−0.112027 + 0.993705i \(0.535734\pi\)
\(38\) −7.78044 −1.26215
\(39\) −6.17223 −0.988348
\(40\) 1.45133 0.229475
\(41\) 5.79632 0.905234 0.452617 0.891705i \(-0.350491\pi\)
0.452617 + 0.891705i \(0.350491\pi\)
\(42\) −8.18920 −1.26362
\(43\) 4.48081 0.683316 0.341658 0.939824i \(-0.389011\pi\)
0.341658 + 0.939824i \(0.389011\pi\)
\(44\) −7.69506 −1.16007
\(45\) 2.40528 0.358557
\(46\) 7.73321 1.14020
\(47\) −2.51083 −0.366242 −0.183121 0.983090i \(-0.558620\pi\)
−0.183121 + 0.983090i \(0.558620\pi\)
\(48\) −10.8141 −1.56088
\(49\) −2.95961 −0.422801
\(50\) 6.33595 0.896039
\(51\) 1.48525 0.207977
\(52\) −3.78803 −0.525305
\(53\) 9.20963 1.26504 0.632520 0.774544i \(-0.282021\pi\)
0.632520 + 0.774544i \(0.282021\pi\)
\(54\) 4.33902 0.590465
\(55\) −7.01600 −0.946037
\(56\) 2.34686 0.313612
\(57\) 9.42452 1.24831
\(58\) 1.83395 0.240809
\(59\) −8.56719 −1.11535 −0.557677 0.830058i \(-0.688307\pi\)
−0.557677 + 0.830058i \(0.688307\pi\)
\(60\) 3.76484 0.486038
\(61\) −9.37884 −1.20084 −0.600419 0.799686i \(-0.704999\pi\)
−0.600419 + 0.799686i \(0.704999\pi\)
\(62\) 9.98243 1.26777
\(63\) 3.88943 0.490022
\(64\) −2.35438 −0.294297
\(65\) −3.45375 −0.428384
\(66\) 22.9947 2.83045
\(67\) −1.24871 −0.152555 −0.0762774 0.997087i \(-0.524303\pi\)
−0.0762774 + 0.997087i \(0.524303\pi\)
\(68\) 0.911532 0.110540
\(69\) −9.36731 −1.12769
\(70\) −4.58236 −0.547697
\(71\) 0.728297 0.0864329 0.0432165 0.999066i \(-0.486239\pi\)
0.0432165 + 0.999066i \(0.486239\pi\)
\(72\) 2.25917 0.266246
\(73\) −9.77556 −1.14414 −0.572072 0.820204i \(-0.693860\pi\)
−0.572072 + 0.820204i \(0.693860\pi\)
\(74\) 2.49944 0.290554
\(75\) −7.67479 −0.886209
\(76\) 5.78402 0.663473
\(77\) −11.3452 −1.29290
\(78\) 11.3196 1.28169
\(79\) −4.46664 −0.502536 −0.251268 0.967918i \(-0.580848\pi\)
−0.251268 + 0.967918i \(0.580848\pi\)
\(80\) −6.05115 −0.676539
\(81\) −11.0608 −1.22898
\(82\) −10.6302 −1.17390
\(83\) 2.99039 0.328237 0.164119 0.986441i \(-0.447522\pi\)
0.164119 + 0.986441i \(0.447522\pi\)
\(84\) 6.08790 0.664244
\(85\) 0.831092 0.0901446
\(86\) −8.21757 −0.886123
\(87\) −2.22148 −0.238168
\(88\) −6.58982 −0.702478
\(89\) −7.01453 −0.743539 −0.371769 0.928325i \(-0.621249\pi\)
−0.371769 + 0.928325i \(0.621249\pi\)
\(90\) −4.41115 −0.464976
\(91\) −5.58485 −0.585451
\(92\) −5.74891 −0.599366
\(93\) −12.0918 −1.25386
\(94\) 4.60473 0.474942
\(95\) 5.27360 0.541060
\(96\) 14.6451 1.49471
\(97\) −9.31278 −0.945569 −0.472785 0.881178i \(-0.656751\pi\)
−0.472785 + 0.881178i \(0.656751\pi\)
\(98\) 5.42777 0.548287
\(99\) −10.9213 −1.09763
\(100\) −4.71018 −0.471018
\(101\) 10.5508 1.04984 0.524920 0.851152i \(-0.324095\pi\)
0.524920 + 0.851152i \(0.324095\pi\)
\(102\) −2.72388 −0.269704
\(103\) −9.80880 −0.966490 −0.483245 0.875485i \(-0.660542\pi\)
−0.483245 + 0.875485i \(0.660542\pi\)
\(104\) −3.24396 −0.318096
\(105\) 5.55066 0.541689
\(106\) −16.8900 −1.64050
\(107\) 1.87151 0.180926 0.0904629 0.995900i \(-0.471165\pi\)
0.0904629 + 0.995900i \(0.471165\pi\)
\(108\) −3.22565 −0.310388
\(109\) −8.38731 −0.803358 −0.401679 0.915780i \(-0.631573\pi\)
−0.401679 + 0.915780i \(0.631573\pi\)
\(110\) 12.8670 1.22682
\(111\) −3.02759 −0.287366
\(112\) −9.78496 −0.924592
\(113\) −0.291141 −0.0273882 −0.0136941 0.999906i \(-0.504359\pi\)
−0.0136941 + 0.999906i \(0.504359\pi\)
\(114\) −17.2841 −1.61880
\(115\) −5.24159 −0.488781
\(116\) −1.36337 −0.126586
\(117\) −5.37618 −0.497028
\(118\) 15.7118 1.44639
\(119\) 1.34391 0.123196
\(120\) 3.22410 0.294318
\(121\) 20.8564 1.89604
\(122\) 17.2003 1.55724
\(123\) 12.8764 1.16103
\(124\) −7.42100 −0.666426
\(125\) −10.5098 −0.940025
\(126\) −7.13302 −0.635460
\(127\) 2.71896 0.241269 0.120634 0.992697i \(-0.461507\pi\)
0.120634 + 0.992697i \(0.461507\pi\)
\(128\) −8.86719 −0.783756
\(129\) 9.95402 0.876402
\(130\) 6.33399 0.555528
\(131\) −1.46073 −0.127624 −0.0638122 0.997962i \(-0.520326\pi\)
−0.0638122 + 0.997962i \(0.520326\pi\)
\(132\) −17.0944 −1.48788
\(133\) 8.52763 0.739440
\(134\) 2.29008 0.197833
\(135\) −2.94100 −0.253121
\(136\) 0.780609 0.0669367
\(137\) 5.65497 0.483137 0.241569 0.970384i \(-0.422338\pi\)
0.241569 + 0.970384i \(0.422338\pi\)
\(138\) 17.1792 1.46239
\(139\) −1.00000 −0.0848189
\(140\) 3.40656 0.287907
\(141\) −5.57776 −0.469732
\(142\) −1.33566 −0.112086
\(143\) 15.6819 1.31139
\(144\) −9.41936 −0.784947
\(145\) −1.24306 −0.103230
\(146\) 17.9279 1.48372
\(147\) −6.57471 −0.542273
\(148\) −1.85810 −0.152735
\(149\) −13.6240 −1.11612 −0.558060 0.829801i \(-0.688454\pi\)
−0.558060 + 0.829801i \(0.688454\pi\)
\(150\) 14.0752 1.14923
\(151\) 20.1573 1.64038 0.820191 0.572090i \(-0.193867\pi\)
0.820191 + 0.572090i \(0.193867\pi\)
\(152\) 4.95327 0.401763
\(153\) 1.29370 0.104589
\(154\) 20.8064 1.67663
\(155\) −6.76612 −0.543468
\(156\) −8.41503 −0.673741
\(157\) −4.29784 −0.343005 −0.171502 0.985184i \(-0.554862\pi\)
−0.171502 + 0.985184i \(0.554862\pi\)
\(158\) 8.19159 0.651688
\(159\) 20.4590 1.62250
\(160\) 8.19484 0.647859
\(161\) −8.47587 −0.667992
\(162\) 20.2849 1.59374
\(163\) −7.44700 −0.583294 −0.291647 0.956526i \(-0.594203\pi\)
−0.291647 + 0.956526i \(0.594203\pi\)
\(164\) 7.90253 0.617084
\(165\) −15.5859 −1.21336
\(166\) −5.48421 −0.425658
\(167\) −7.21906 −0.558627 −0.279314 0.960200i \(-0.590107\pi\)
−0.279314 + 0.960200i \(0.590107\pi\)
\(168\) 5.21350 0.402230
\(169\) −5.28031 −0.406178
\(170\) −1.52418 −0.116899
\(171\) 8.20901 0.627759
\(172\) 6.10899 0.465806
\(173\) −5.14445 −0.391125 −0.195563 0.980691i \(-0.562653\pi\)
−0.195563 + 0.980691i \(0.562653\pi\)
\(174\) 4.07408 0.308855
\(175\) −6.94443 −0.524949
\(176\) 27.4755 2.07105
\(177\) −19.0318 −1.43052
\(178\) 12.8643 0.964219
\(179\) 15.9114 1.18927 0.594635 0.803996i \(-0.297296\pi\)
0.594635 + 0.803996i \(0.297296\pi\)
\(180\) 3.27928 0.244423
\(181\) 17.1925 1.27791 0.638956 0.769244i \(-0.279367\pi\)
0.638956 + 0.769244i \(0.279367\pi\)
\(182\) 10.2423 0.759212
\(183\) −20.8349 −1.54016
\(184\) −4.92320 −0.362943
\(185\) −1.69413 −0.124555
\(186\) 22.1758 1.62601
\(187\) −3.77361 −0.275954
\(188\) −3.42319 −0.249662
\(189\) −4.75572 −0.345927
\(190\) −9.67152 −0.701646
\(191\) −19.4927 −1.41044 −0.705222 0.708987i \(-0.749153\pi\)
−0.705222 + 0.708987i \(0.749153\pi\)
\(192\) −5.23020 −0.377457
\(193\) −12.5093 −0.900442 −0.450221 0.892917i \(-0.648655\pi\)
−0.450221 + 0.892917i \(0.648655\pi\)
\(194\) 17.0792 1.22621
\(195\) −7.67243 −0.549434
\(196\) −4.03504 −0.288217
\(197\) 19.0707 1.35873 0.679367 0.733799i \(-0.262255\pi\)
0.679367 + 0.733799i \(0.262255\pi\)
\(198\) 20.0290 1.42340
\(199\) −10.5371 −0.746958 −0.373479 0.927639i \(-0.621835\pi\)
−0.373479 + 0.927639i \(0.621835\pi\)
\(200\) −4.03366 −0.285223
\(201\) −2.77399 −0.195662
\(202\) −19.3495 −1.36143
\(203\) −2.01007 −0.141079
\(204\) 2.02495 0.141775
\(205\) 7.20515 0.503230
\(206\) 17.9888 1.25334
\(207\) −8.15918 −0.567102
\(208\) 13.5253 0.937811
\(209\) −23.9450 −1.65631
\(210\) −10.1796 −0.702461
\(211\) 0.922142 0.0634829 0.0317414 0.999496i \(-0.489895\pi\)
0.0317414 + 0.999496i \(0.489895\pi\)
\(212\) 12.5561 0.862358
\(213\) 1.61790 0.110856
\(214\) −3.43225 −0.234624
\(215\) 5.56989 0.379863
\(216\) −2.76235 −0.187954
\(217\) −10.9411 −0.742730
\(218\) 15.3819 1.04179
\(219\) −21.7162 −1.46745
\(220\) −9.56539 −0.644898
\(221\) −1.85763 −0.124957
\(222\) 5.55245 0.372656
\(223\) 15.0369 1.00694 0.503472 0.864012i \(-0.332056\pi\)
0.503472 + 0.864012i \(0.332056\pi\)
\(224\) 13.2514 0.885396
\(225\) −6.68496 −0.445664
\(226\) 0.533937 0.0355170
\(227\) −3.88589 −0.257916 −0.128958 0.991650i \(-0.541163\pi\)
−0.128958 + 0.991650i \(0.541163\pi\)
\(228\) 12.8491 0.850952
\(229\) 11.7843 0.778728 0.389364 0.921084i \(-0.372695\pi\)
0.389364 + 0.921084i \(0.372695\pi\)
\(230\) 9.61281 0.633850
\(231\) −25.2030 −1.65824
\(232\) −1.16755 −0.0766534
\(233\) 12.3496 0.809047 0.404523 0.914528i \(-0.367437\pi\)
0.404523 + 0.914528i \(0.367437\pi\)
\(234\) 9.85965 0.644545
\(235\) −3.12110 −0.203598
\(236\) −11.6802 −0.760319
\(237\) −9.92255 −0.644539
\(238\) −2.46466 −0.159760
\(239\) 23.9266 1.54768 0.773842 0.633379i \(-0.218333\pi\)
0.773842 + 0.633379i \(0.218333\pi\)
\(240\) −13.4425 −0.867710
\(241\) 10.2786 0.662106 0.331053 0.943612i \(-0.392596\pi\)
0.331053 + 0.943612i \(0.392596\pi\)
\(242\) −38.2497 −2.45878
\(243\) −17.4735 −1.12093
\(244\) −12.7868 −0.818592
\(245\) −3.67896 −0.235040
\(246\) −23.6147 −1.50562
\(247\) −11.7874 −0.750012
\(248\) −6.35513 −0.403551
\(249\) 6.64308 0.420988
\(250\) 19.2744 1.21902
\(251\) −0.569540 −0.0359491 −0.0179745 0.999838i \(-0.505722\pi\)
−0.0179745 + 0.999838i \(0.505722\pi\)
\(252\) 5.30273 0.334041
\(253\) 23.7997 1.49627
\(254\) −4.98644 −0.312877
\(255\) 1.84625 0.115617
\(256\) 20.9707 1.31067
\(257\) 2.78147 0.173504 0.0867518 0.996230i \(-0.472351\pi\)
0.0867518 + 0.996230i \(0.472351\pi\)
\(258\) −18.2552 −1.13652
\(259\) −2.73947 −0.170222
\(260\) −4.70873 −0.292023
\(261\) −1.93497 −0.119772
\(262\) 2.67890 0.165503
\(263\) −21.4959 −1.32549 −0.662746 0.748844i \(-0.730609\pi\)
−0.662746 + 0.748844i \(0.730609\pi\)
\(264\) −14.6392 −0.900978
\(265\) 11.4481 0.703250
\(266\) −15.6392 −0.958904
\(267\) −15.5826 −0.953641
\(268\) −1.70246 −0.103994
\(269\) 7.66060 0.467075 0.233537 0.972348i \(-0.424970\pi\)
0.233537 + 0.972348i \(0.424970\pi\)
\(270\) 5.39364 0.328246
\(271\) 29.6818 1.80304 0.901519 0.432739i \(-0.142453\pi\)
0.901519 + 0.432739i \(0.142453\pi\)
\(272\) −3.25466 −0.197343
\(273\) −12.4066 −0.750883
\(274\) −10.3709 −0.626531
\(275\) 19.4995 1.17586
\(276\) −12.7711 −0.768730
\(277\) −25.8068 −1.55058 −0.775289 0.631607i \(-0.782396\pi\)
−0.775289 + 0.631607i \(0.782396\pi\)
\(278\) 1.83395 0.109993
\(279\) −10.5323 −0.630553
\(280\) 2.91728 0.174341
\(281\) 4.18325 0.249552 0.124776 0.992185i \(-0.460179\pi\)
0.124776 + 0.992185i \(0.460179\pi\)
\(282\) 10.2293 0.609147
\(283\) 11.3202 0.672917 0.336458 0.941698i \(-0.390771\pi\)
0.336458 + 0.941698i \(0.390771\pi\)
\(284\) 0.992937 0.0589200
\(285\) 11.7152 0.693948
\(286\) −28.7598 −1.70060
\(287\) 11.6510 0.687739
\(288\) 12.7563 0.751671
\(289\) −16.5530 −0.973705
\(290\) 2.27970 0.133869
\(291\) −20.6881 −1.21276
\(292\) −13.3277 −0.779945
\(293\) 5.66212 0.330785 0.165392 0.986228i \(-0.447111\pi\)
0.165392 + 0.986228i \(0.447111\pi\)
\(294\) 12.0577 0.703218
\(295\) −10.6495 −0.620038
\(296\) −1.59122 −0.0924878
\(297\) 13.3537 0.774862
\(298\) 24.9857 1.44738
\(299\) 11.7158 0.677543
\(300\) −10.4636 −0.604115
\(301\) 9.00675 0.519140
\(302\) −36.9675 −2.12724
\(303\) 23.4383 1.34649
\(304\) −20.6521 −1.18448
\(305\) −11.6584 −0.667559
\(306\) −2.37258 −0.135631
\(307\) −19.2092 −1.09632 −0.548162 0.836372i \(-0.684672\pi\)
−0.548162 + 0.836372i \(0.684672\pi\)
\(308\) −15.4676 −0.881350
\(309\) −21.7901 −1.23959
\(310\) 12.4087 0.704768
\(311\) 6.41115 0.363543 0.181772 0.983341i \(-0.441817\pi\)
0.181772 + 0.983341i \(0.441817\pi\)
\(312\) −7.20638 −0.407981
\(313\) 11.3444 0.641221 0.320611 0.947211i \(-0.396112\pi\)
0.320611 + 0.947211i \(0.396112\pi\)
\(314\) 7.88201 0.444808
\(315\) 4.83478 0.272409
\(316\) −6.08968 −0.342571
\(317\) −12.2839 −0.689931 −0.344966 0.938615i \(-0.612109\pi\)
−0.344966 + 0.938615i \(0.612109\pi\)
\(318\) −37.5208 −2.10406
\(319\) 5.64415 0.316012
\(320\) −2.92662 −0.163603
\(321\) 4.15752 0.232050
\(322\) 15.5443 0.866251
\(323\) 2.83645 0.157824
\(324\) −15.0800 −0.837775
\(325\) 9.59896 0.532455
\(326\) 13.6574 0.756415
\(327\) −18.6322 −1.03036
\(328\) 6.76749 0.373672
\(329\) −5.04695 −0.278247
\(330\) 28.5837 1.57348
\(331\) −13.0588 −0.717774 −0.358887 0.933381i \(-0.616844\pi\)
−0.358887 + 0.933381i \(0.616844\pi\)
\(332\) 4.07700 0.223754
\(333\) −2.63712 −0.144513
\(334\) 13.2394 0.724427
\(335\) −1.55222 −0.0848069
\(336\) −21.7371 −1.18586
\(337\) 2.95532 0.160987 0.0804933 0.996755i \(-0.474350\pi\)
0.0804933 + 0.996755i \(0.474350\pi\)
\(338\) 9.68383 0.526731
\(339\) −0.646763 −0.0351274
\(340\) 1.13309 0.0614502
\(341\) 30.7219 1.66368
\(342\) −15.0549 −0.814077
\(343\) −20.0195 −1.08095
\(344\) 5.23156 0.282067
\(345\) −11.6441 −0.626896
\(346\) 9.43466 0.507211
\(347\) −32.6814 −1.75443 −0.877216 0.480096i \(-0.840602\pi\)
−0.877216 + 0.480096i \(0.840602\pi\)
\(348\) −3.02870 −0.162355
\(349\) −15.7430 −0.842704 −0.421352 0.906897i \(-0.638444\pi\)
−0.421352 + 0.906897i \(0.638444\pi\)
\(350\) 12.7357 0.680753
\(351\) 6.57361 0.350873
\(352\) −37.2091 −1.98325
\(353\) 33.0831 1.76084 0.880419 0.474197i \(-0.157262\pi\)
0.880419 + 0.474197i \(0.157262\pi\)
\(354\) 34.9034 1.85510
\(355\) 0.905313 0.0480490
\(356\) −9.56339 −0.506859
\(357\) 2.98547 0.158008
\(358\) −29.1806 −1.54224
\(359\) 19.6864 1.03901 0.519505 0.854468i \(-0.326117\pi\)
0.519505 + 0.854468i \(0.326117\pi\)
\(360\) 2.80828 0.148009
\(361\) −1.00161 −0.0527165
\(362\) −31.5302 −1.65719
\(363\) 46.3322 2.43181
\(364\) −7.61421 −0.399093
\(365\) −12.1516 −0.636042
\(366\) 38.2101 1.99728
\(367\) 33.4889 1.74810 0.874052 0.485832i \(-0.161483\pi\)
0.874052 + 0.485832i \(0.161483\pi\)
\(368\) 20.5267 1.07003
\(369\) 11.2157 0.583867
\(370\) 3.10694 0.161522
\(371\) 18.5120 0.961096
\(372\) −16.4856 −0.854739
\(373\) −29.0100 −1.50208 −0.751041 0.660256i \(-0.770448\pi\)
−0.751041 + 0.660256i \(0.770448\pi\)
\(374\) 6.92061 0.357856
\(375\) −23.3473 −1.20565
\(376\) −2.93152 −0.151181
\(377\) 2.77843 0.143097
\(378\) 8.72174 0.448598
\(379\) −13.5860 −0.697865 −0.348933 0.937148i \(-0.613456\pi\)
−0.348933 + 0.937148i \(0.613456\pi\)
\(380\) 7.18986 0.368832
\(381\) 6.04012 0.309445
\(382\) 35.7486 1.82906
\(383\) 2.55541 0.130576 0.0652878 0.997866i \(-0.479203\pi\)
0.0652878 + 0.997866i \(0.479203\pi\)
\(384\) −19.6983 −1.00522
\(385\) −14.1027 −0.718738
\(386\) 22.9415 1.16769
\(387\) 8.67022 0.440732
\(388\) −12.6967 −0.644580
\(389\) 26.1040 1.32352 0.661762 0.749714i \(-0.269809\pi\)
0.661762 + 0.749714i \(0.269809\pi\)
\(390\) 14.0708 0.712504
\(391\) −2.81923 −0.142575
\(392\) −3.45549 −0.174528
\(393\) −3.24498 −0.163688
\(394\) −34.9747 −1.76200
\(395\) −5.55228 −0.279366
\(396\) −14.8897 −0.748236
\(397\) −24.5293 −1.23109 −0.615545 0.788102i \(-0.711064\pi\)
−0.615545 + 0.788102i \(0.711064\pi\)
\(398\) 19.3246 0.968654
\(399\) 18.9440 0.948384
\(400\) 16.8179 0.840895
\(401\) −14.0012 −0.699188 −0.349594 0.936901i \(-0.613681\pi\)
−0.349594 + 0.936901i \(0.613681\pi\)
\(402\) 5.08736 0.253734
\(403\) 15.1234 0.753349
\(404\) 14.3846 0.715659
\(405\) −13.7492 −0.683203
\(406\) 3.68637 0.182952
\(407\) 7.69226 0.381291
\(408\) 1.73411 0.0858511
\(409\) 9.37308 0.463469 0.231735 0.972779i \(-0.425560\pi\)
0.231735 + 0.972779i \(0.425560\pi\)
\(410\) −13.2139 −0.652587
\(411\) 12.5624 0.619658
\(412\) −13.3730 −0.658841
\(413\) −17.2207 −0.847374
\(414\) 14.9635 0.735417
\(415\) 3.71722 0.182471
\(416\) −18.3168 −0.898055
\(417\) −2.22148 −0.108786
\(418\) 43.9140 2.14790
\(419\) 1.38486 0.0676548 0.0338274 0.999428i \(-0.489230\pi\)
0.0338274 + 0.999428i \(0.489230\pi\)
\(420\) 7.56760 0.369261
\(421\) −33.1640 −1.61631 −0.808157 0.588967i \(-0.799535\pi\)
−0.808157 + 0.588967i \(0.799535\pi\)
\(422\) −1.69116 −0.0823245
\(423\) −4.85838 −0.236223
\(424\) 10.7527 0.522197
\(425\) −2.30985 −0.112044
\(426\) −2.96714 −0.143758
\(427\) −18.8521 −0.912319
\(428\) 2.55156 0.123334
\(429\) 34.8370 1.68195
\(430\) −10.2149 −0.492606
\(431\) −1.17561 −0.0566270 −0.0283135 0.999599i \(-0.509014\pi\)
−0.0283135 + 0.999599i \(0.509014\pi\)
\(432\) 11.5173 0.554127
\(433\) −10.3946 −0.499532 −0.249766 0.968306i \(-0.580354\pi\)
−0.249766 + 0.968306i \(0.580354\pi\)
\(434\) 20.0654 0.963171
\(435\) −2.76142 −0.132400
\(436\) −11.4350 −0.547637
\(437\) −17.8891 −0.855753
\(438\) 39.8264 1.90298
\(439\) 11.8005 0.563206 0.281603 0.959531i \(-0.409134\pi\)
0.281603 + 0.959531i \(0.409134\pi\)
\(440\) −8.19152 −0.390515
\(441\) −5.72675 −0.272702
\(442\) 3.40679 0.162045
\(443\) −18.0992 −0.859918 −0.429959 0.902848i \(-0.641472\pi\)
−0.429959 + 0.902848i \(0.641472\pi\)
\(444\) −4.12772 −0.195893
\(445\) −8.71945 −0.413342
\(446\) −27.5768 −1.30580
\(447\) −30.2654 −1.43150
\(448\) −4.73247 −0.223588
\(449\) 39.4251 1.86059 0.930293 0.366818i \(-0.119553\pi\)
0.930293 + 0.366818i \(0.119553\pi\)
\(450\) 12.2599 0.577936
\(451\) −32.7153 −1.54050
\(452\) −0.396932 −0.0186701
\(453\) 44.7791 2.10391
\(454\) 7.12653 0.334465
\(455\) −6.94228 −0.325459
\(456\) 11.0036 0.515290
\(457\) 8.62277 0.403356 0.201678 0.979452i \(-0.435361\pi\)
0.201678 + 0.979452i \(0.435361\pi\)
\(458\) −21.6118 −1.00985
\(459\) −1.58184 −0.0738340
\(460\) −7.14622 −0.333194
\(461\) −35.4156 −1.64947 −0.824734 0.565521i \(-0.808675\pi\)
−0.824734 + 0.565521i \(0.808675\pi\)
\(462\) 46.2211 2.15040
\(463\) −24.5238 −1.13972 −0.569859 0.821743i \(-0.693002\pi\)
−0.569859 + 0.821743i \(0.693002\pi\)
\(464\) 4.86796 0.225990
\(465\) −15.0308 −0.697037
\(466\) −22.6485 −1.04917
\(467\) 31.9863 1.48015 0.740075 0.672525i \(-0.234790\pi\)
0.740075 + 0.672525i \(0.234790\pi\)
\(468\) −7.32972 −0.338816
\(469\) −2.51001 −0.115901
\(470\) 5.72394 0.264026
\(471\) −9.54755 −0.439928
\(472\) −10.0026 −0.460408
\(473\) −25.2903 −1.16285
\(474\) 18.1974 0.835836
\(475\) −14.6569 −0.672503
\(476\) 1.83225 0.0839809
\(477\) 17.8204 0.815938
\(478\) −43.8802 −2.00703
\(479\) 11.1474 0.509337 0.254669 0.967028i \(-0.418034\pi\)
0.254669 + 0.967028i \(0.418034\pi\)
\(480\) 18.2047 0.830926
\(481\) 3.78665 0.172656
\(482\) −18.8505 −0.858617
\(483\) −18.8290 −0.856748
\(484\) 28.4350 1.29250
\(485\) −11.5763 −0.525653
\(486\) 32.0455 1.45361
\(487\) −16.3167 −0.739381 −0.369691 0.929155i \(-0.620536\pi\)
−0.369691 + 0.929155i \(0.620536\pi\)
\(488\) −10.9503 −0.495695
\(489\) −16.5434 −0.748117
\(490\) 6.74702 0.304799
\(491\) 9.01831 0.406990 0.203495 0.979076i \(-0.434770\pi\)
0.203495 + 0.979076i \(0.434770\pi\)
\(492\) 17.5553 0.791454
\(493\) −0.668588 −0.0301117
\(494\) 21.6174 0.972614
\(495\) −13.5757 −0.610184
\(496\) 26.4970 1.18975
\(497\) 1.46393 0.0656662
\(498\) −12.1831 −0.545936
\(499\) −15.3650 −0.687832 −0.343916 0.939000i \(-0.611754\pi\)
−0.343916 + 0.939000i \(0.611754\pi\)
\(500\) −14.3287 −0.640801
\(501\) −16.0370 −0.716479
\(502\) 1.04451 0.0466187
\(503\) 3.02824 0.135023 0.0675114 0.997719i \(-0.478494\pi\)
0.0675114 + 0.997719i \(0.478494\pi\)
\(504\) 4.54110 0.202277
\(505\) 13.1152 0.583618
\(506\) −43.6474 −1.94036
\(507\) −11.7301 −0.520952
\(508\) 3.70695 0.164469
\(509\) −18.3653 −0.814026 −0.407013 0.913422i \(-0.633430\pi\)
−0.407013 + 0.913422i \(0.633430\pi\)
\(510\) −3.38594 −0.149932
\(511\) −19.6496 −0.869247
\(512\) −20.7249 −0.915918
\(513\) −10.0374 −0.443162
\(514\) −5.10108 −0.224999
\(515\) −12.1929 −0.537283
\(516\) 13.5710 0.597430
\(517\) 14.1715 0.623262
\(518\) 5.02405 0.220744
\(519\) −11.4283 −0.501646
\(520\) −4.03242 −0.176833
\(521\) 21.7085 0.951066 0.475533 0.879698i \(-0.342255\pi\)
0.475533 + 0.879698i \(0.342255\pi\)
\(522\) 3.54864 0.155320
\(523\) 4.98493 0.217976 0.108988 0.994043i \(-0.465239\pi\)
0.108988 + 0.994043i \(0.465239\pi\)
\(524\) −1.99151 −0.0869996
\(525\) −15.4269 −0.673285
\(526\) 39.4223 1.71890
\(527\) −3.63922 −0.158527
\(528\) 61.0363 2.65626
\(529\) −5.21946 −0.226933
\(530\) −20.9952 −0.911973
\(531\) −16.5773 −0.719392
\(532\) 11.6263 0.504065
\(533\) −16.1047 −0.697572
\(534\) 28.5777 1.23668
\(535\) 2.32639 0.100579
\(536\) −1.45794 −0.0629732
\(537\) 35.3467 1.52532
\(538\) −14.0491 −0.605702
\(539\) 16.7045 0.719513
\(540\) −4.00966 −0.172548
\(541\) 6.47617 0.278432 0.139216 0.990262i \(-0.455542\pi\)
0.139216 + 0.990262i \(0.455542\pi\)
\(542\) −54.4348 −2.33818
\(543\) 38.1929 1.63901
\(544\) 4.40767 0.188977
\(545\) −10.4259 −0.446596
\(546\) 22.7531 0.973744
\(547\) −26.3303 −1.12580 −0.562901 0.826524i \(-0.690315\pi\)
−0.562901 + 0.826524i \(0.690315\pi\)
\(548\) 7.70981 0.329347
\(549\) −18.1478 −0.774528
\(550\) −35.7611 −1.52486
\(551\) −4.24245 −0.180734
\(552\) −10.9368 −0.465501
\(553\) −8.97827 −0.381795
\(554\) 47.3283 2.01079
\(555\) −3.76347 −0.159750
\(556\) −1.36337 −0.0578197
\(557\) −31.9958 −1.35570 −0.677852 0.735199i \(-0.737089\pi\)
−0.677852 + 0.735199i \(0.737089\pi\)
\(558\) 19.3157 0.817699
\(559\) −12.4496 −0.526563
\(560\) −12.1633 −0.513991
\(561\) −8.38300 −0.353931
\(562\) −7.67186 −0.323618
\(563\) −3.91721 −0.165091 −0.0825453 0.996587i \(-0.526305\pi\)
−0.0825453 + 0.996587i \(0.526305\pi\)
\(564\) −7.60454 −0.320209
\(565\) −0.361904 −0.0152254
\(566\) −20.7607 −0.872637
\(567\) −22.2330 −0.933699
\(568\) 0.850322 0.0356787
\(569\) −14.6616 −0.614645 −0.307322 0.951605i \(-0.599433\pi\)
−0.307322 + 0.951605i \(0.599433\pi\)
\(570\) −21.4851 −0.899911
\(571\) 22.3749 0.936362 0.468181 0.883633i \(-0.344910\pi\)
0.468181 + 0.883633i \(0.344910\pi\)
\(572\) 21.3802 0.893951
\(573\) −43.3027 −1.80899
\(574\) −21.3674 −0.891858
\(575\) 14.5679 0.607523
\(576\) −4.55565 −0.189819
\(577\) 45.6063 1.89861 0.949307 0.314351i \(-0.101787\pi\)
0.949307 + 0.314351i \(0.101787\pi\)
\(578\) 30.3573 1.26270
\(579\) −27.7892 −1.15488
\(580\) −1.69474 −0.0703704
\(581\) 6.01089 0.249374
\(582\) 37.9410 1.57270
\(583\) −51.9805 −2.15281
\(584\) −11.4135 −0.472292
\(585\) −6.68290 −0.276304
\(586\) −10.3840 −0.428961
\(587\) −35.4247 −1.46213 −0.731067 0.682305i \(-0.760977\pi\)
−0.731067 + 0.682305i \(0.760977\pi\)
\(588\) −8.96375 −0.369659
\(589\) −23.0922 −0.951499
\(590\) 19.5306 0.804063
\(591\) 42.3652 1.74267
\(592\) 6.63441 0.272673
\(593\) 1.00484 0.0412636 0.0206318 0.999787i \(-0.493432\pi\)
0.0206318 + 0.999787i \(0.493432\pi\)
\(594\) −24.4901 −1.00484
\(595\) 1.67056 0.0684861
\(596\) −18.5745 −0.760841
\(597\) −23.4080 −0.958028
\(598\) −21.4862 −0.878636
\(599\) 41.4102 1.69197 0.845987 0.533203i \(-0.179012\pi\)
0.845987 + 0.533203i \(0.179012\pi\)
\(600\) −8.96070 −0.365819
\(601\) −32.0025 −1.30541 −0.652704 0.757613i \(-0.726365\pi\)
−0.652704 + 0.757613i \(0.726365\pi\)
\(602\) −16.5179 −0.673220
\(603\) −2.41622 −0.0983963
\(604\) 27.4819 1.11822
\(605\) 25.9257 1.05403
\(606\) −42.9846 −1.74613
\(607\) −2.93277 −0.119037 −0.0595187 0.998227i \(-0.518957\pi\)
−0.0595187 + 0.998227i \(0.518957\pi\)
\(608\) 27.9683 1.13427
\(609\) −4.46534 −0.180945
\(610\) 21.3809 0.865689
\(611\) 6.97617 0.282226
\(612\) 1.76379 0.0712969
\(613\) −35.3141 −1.42632 −0.713162 0.700999i \(-0.752738\pi\)
−0.713162 + 0.700999i \(0.752738\pi\)
\(614\) 35.2286 1.42171
\(615\) 16.0061 0.645428
\(616\) −13.2460 −0.533698
\(617\) −19.1939 −0.772718 −0.386359 0.922348i \(-0.626267\pi\)
−0.386359 + 0.922348i \(0.626267\pi\)
\(618\) 39.9618 1.60750
\(619\) −10.1164 −0.406611 −0.203306 0.979115i \(-0.565168\pi\)
−0.203306 + 0.979115i \(0.565168\pi\)
\(620\) −9.22472 −0.370474
\(621\) 9.97646 0.400342
\(622\) −11.7577 −0.471442
\(623\) −14.0997 −0.564893
\(624\) 30.0462 1.20281
\(625\) 4.20979 0.168392
\(626\) −20.8050 −0.831534
\(627\) −53.1934 −2.12434
\(628\) −5.85954 −0.233821
\(629\) −0.911200 −0.0363319
\(630\) −8.86674 −0.353259
\(631\) −30.4959 −1.21402 −0.607011 0.794694i \(-0.707632\pi\)
−0.607011 + 0.794694i \(0.707632\pi\)
\(632\) −5.21502 −0.207442
\(633\) 2.04852 0.0814213
\(634\) 22.5280 0.894701
\(635\) 3.37982 0.134124
\(636\) 27.8932 1.10604
\(637\) 8.22307 0.325810
\(638\) −10.3511 −0.409803
\(639\) 1.40923 0.0557484
\(640\) −11.0224 −0.435699
\(641\) 28.8594 1.13988 0.569938 0.821688i \(-0.306967\pi\)
0.569938 + 0.821688i \(0.306967\pi\)
\(642\) −7.62468 −0.300922
\(643\) 15.3497 0.605334 0.302667 0.953096i \(-0.402123\pi\)
0.302667 + 0.953096i \(0.402123\pi\)
\(644\) −11.5557 −0.455360
\(645\) 12.3734 0.487202
\(646\) −5.20191 −0.204666
\(647\) −36.9647 −1.45323 −0.726615 0.687045i \(-0.758908\pi\)
−0.726615 + 0.687045i \(0.758908\pi\)
\(648\) −12.9140 −0.507311
\(649\) 48.3545 1.89808
\(650\) −17.6040 −0.690486
\(651\) −24.3054 −0.952605
\(652\) −10.1530 −0.397623
\(653\) 41.4900 1.62363 0.811815 0.583914i \(-0.198480\pi\)
0.811815 + 0.583914i \(0.198480\pi\)
\(654\) 34.1706 1.33617
\(655\) −1.81577 −0.0709479
\(656\) −28.2163 −1.10166
\(657\) −18.9154 −0.737961
\(658\) 9.25585 0.360831
\(659\) 44.7917 1.74484 0.872418 0.488760i \(-0.162551\pi\)
0.872418 + 0.488760i \(0.162551\pi\)
\(660\) −21.2493 −0.827128
\(661\) −0.574409 −0.0223419 −0.0111710 0.999938i \(-0.503556\pi\)
−0.0111710 + 0.999938i \(0.503556\pi\)
\(662\) 23.9491 0.930808
\(663\) −4.12668 −0.160267
\(664\) 3.49142 0.135493
\(665\) 10.6003 0.411063
\(666\) 4.83634 0.187404
\(667\) 4.21670 0.163271
\(668\) −9.84223 −0.380807
\(669\) 33.4041 1.29148
\(670\) 2.84669 0.109977
\(671\) 52.9356 2.04356
\(672\) 29.4377 1.13558
\(673\) 26.8878 1.03645 0.518225 0.855245i \(-0.326593\pi\)
0.518225 + 0.855245i \(0.326593\pi\)
\(674\) −5.41991 −0.208767
\(675\) 8.17389 0.314613
\(676\) −7.19902 −0.276885
\(677\) −45.8867 −1.76357 −0.881785 0.471651i \(-0.843658\pi\)
−0.881785 + 0.471651i \(0.843658\pi\)
\(678\) 1.18613 0.0455531
\(679\) −18.7194 −0.718383
\(680\) 0.970341 0.0372109
\(681\) −8.63243 −0.330795
\(682\) −56.3424 −2.15746
\(683\) −29.3011 −1.12118 −0.560588 0.828095i \(-0.689425\pi\)
−0.560588 + 0.828095i \(0.689425\pi\)
\(684\) 11.1919 0.427934
\(685\) 7.02945 0.268581
\(686\) 36.7148 1.40178
\(687\) 26.1786 0.998775
\(688\) −21.8124 −0.831590
\(689\) −25.5883 −0.974838
\(690\) 21.3547 0.812958
\(691\) 9.87689 0.375735 0.187867 0.982194i \(-0.439842\pi\)
0.187867 + 0.982194i \(0.439842\pi\)
\(692\) −7.01378 −0.266624
\(693\) −21.9525 −0.833908
\(694\) 59.9361 2.27514
\(695\) −1.24306 −0.0471518
\(696\) −2.59369 −0.0983134
\(697\) 3.87535 0.146789
\(698\) 28.8719 1.09282
\(699\) 27.4343 1.03766
\(700\) −9.46781 −0.357850
\(701\) 8.23788 0.311140 0.155570 0.987825i \(-0.450279\pi\)
0.155570 + 0.987825i \(0.450279\pi\)
\(702\) −12.0557 −0.455012
\(703\) −5.78192 −0.218069
\(704\) 13.2885 0.500828
\(705\) −6.93346 −0.261129
\(706\) −60.6728 −2.28345
\(707\) 21.2078 0.797601
\(708\) −25.9474 −0.975164
\(709\) −30.7693 −1.15557 −0.577783 0.816190i \(-0.696082\pi\)
−0.577783 + 0.816190i \(0.696082\pi\)
\(710\) −1.66030 −0.0623099
\(711\) −8.64281 −0.324131
\(712\) −8.18981 −0.306926
\(713\) 22.9521 0.859561
\(714\) −5.47520 −0.204904
\(715\) 19.4935 0.729014
\(716\) 21.6930 0.810707
\(717\) 53.1525 1.98501
\(718\) −36.1039 −1.34738
\(719\) −5.42888 −0.202463 −0.101231 0.994863i \(-0.532278\pi\)
−0.101231 + 0.994863i \(0.532278\pi\)
\(720\) −11.7088 −0.436361
\(721\) −19.7164 −0.734278
\(722\) 1.83691 0.0683627
\(723\) 22.8338 0.849198
\(724\) 23.4398 0.871132
\(725\) 3.45481 0.128309
\(726\) −84.9708 −3.15356
\(727\) −10.3202 −0.382754 −0.191377 0.981517i \(-0.561295\pi\)
−0.191377 + 0.981517i \(0.561295\pi\)
\(728\) −6.52059 −0.241669
\(729\) −5.63465 −0.208691
\(730\) 22.2854 0.824818
\(731\) 2.99581 0.110804
\(732\) −28.4056 −1.04990
\(733\) 0.0447480 0.00165280 0.000826402 1.00000i \(-0.499737\pi\)
0.000826402 1.00000i \(0.499737\pi\)
\(734\) −61.4169 −2.26694
\(735\) −8.17273 −0.301456
\(736\) −27.7986 −1.02467
\(737\) 7.04793 0.259614
\(738\) −20.5690 −0.757157
\(739\) 38.5738 1.41896 0.709480 0.704725i \(-0.248930\pi\)
0.709480 + 0.704725i \(0.248930\pi\)
\(740\) −2.30972 −0.0849069
\(741\) −26.1854 −0.961944
\(742\) −33.9501 −1.24635
\(743\) 39.8310 1.46126 0.730628 0.682776i \(-0.239227\pi\)
0.730628 + 0.682776i \(0.239227\pi\)
\(744\) −14.1178 −0.517583
\(745\) −16.9354 −0.620464
\(746\) 53.2029 1.94790
\(747\) 5.78631 0.211710
\(748\) −5.14483 −0.188113
\(749\) 3.76187 0.137456
\(750\) 42.8178 1.56348
\(751\) −30.2442 −1.10363 −0.551813 0.833968i \(-0.686064\pi\)
−0.551813 + 0.833968i \(0.686064\pi\)
\(752\) 12.2226 0.445713
\(753\) −1.26522 −0.0461073
\(754\) −5.09550 −0.185567
\(755\) 25.0567 0.911907
\(756\) −6.48379 −0.235813
\(757\) 51.6913 1.87875 0.939377 0.342887i \(-0.111405\pi\)
0.939377 + 0.342887i \(0.111405\pi\)
\(758\) 24.9160 0.904990
\(759\) 52.8705 1.91908
\(760\) 6.15719 0.223345
\(761\) −4.69002 −0.170013 −0.0850066 0.996380i \(-0.527091\pi\)
−0.0850066 + 0.996380i \(0.527091\pi\)
\(762\) −11.0773 −0.401287
\(763\) −16.8591 −0.610340
\(764\) −26.5758 −0.961477
\(765\) 1.60814 0.0581424
\(766\) −4.68650 −0.169330
\(767\) 23.8034 0.859490
\(768\) 46.5860 1.68103
\(769\) −26.4507 −0.953835 −0.476917 0.878948i \(-0.658246\pi\)
−0.476917 + 0.878948i \(0.658246\pi\)
\(770\) 25.8636 0.932058
\(771\) 6.17898 0.222531
\(772\) −17.0548 −0.613817
\(773\) −6.88315 −0.247570 −0.123785 0.992309i \(-0.539503\pi\)
−0.123785 + 0.992309i \(0.539503\pi\)
\(774\) −15.9007 −0.571541
\(775\) 18.8050 0.675496
\(776\) −10.8731 −0.390322
\(777\) −6.08568 −0.218323
\(778\) −47.8733 −1.71634
\(779\) 24.5906 0.881050
\(780\) −10.4603 −0.374540
\(781\) −4.11062 −0.147089
\(782\) 5.17033 0.184891
\(783\) 2.36594 0.0845519
\(784\) 14.4073 0.514545
\(785\) −5.34245 −0.190680
\(786\) 5.95113 0.212270
\(787\) −2.82562 −0.100722 −0.0503612 0.998731i \(-0.516037\pi\)
−0.0503612 + 0.998731i \(0.516037\pi\)
\(788\) 26.0004 0.926227
\(789\) −47.7526 −1.70004
\(790\) 10.1826 0.362281
\(791\) −0.585214 −0.0208078
\(792\) −12.7511 −0.453091
\(793\) 26.0585 0.925363
\(794\) 44.9854 1.59647
\(795\) 25.4317 0.901969
\(796\) −14.3660 −0.509190
\(797\) 15.2976 0.541868 0.270934 0.962598i \(-0.412668\pi\)
0.270934 + 0.962598i \(0.412668\pi\)
\(798\) −34.7423 −1.22986
\(799\) −1.67871 −0.0593885
\(800\) −22.7758 −0.805248
\(801\) −13.5729 −0.479575
\(802\) 25.6776 0.906706
\(803\) 55.1748 1.94708
\(804\) −3.78197 −0.133380
\(805\) −10.5360 −0.371344
\(806\) −27.7355 −0.976942
\(807\) 17.0179 0.599057
\(808\) 12.3185 0.433364
\(809\) −19.0327 −0.669154 −0.334577 0.942368i \(-0.608593\pi\)
−0.334577 + 0.942368i \(0.608593\pi\)
\(810\) 25.2153 0.885976
\(811\) 23.2544 0.816574 0.408287 0.912854i \(-0.366126\pi\)
0.408287 + 0.912854i \(0.366126\pi\)
\(812\) −2.74047 −0.0961717
\(813\) 65.9374 2.31253
\(814\) −14.1072 −0.494457
\(815\) −9.25704 −0.324260
\(816\) −7.23016 −0.253106
\(817\) 19.0096 0.665062
\(818\) −17.1898 −0.601026
\(819\) −10.8065 −0.377610
\(820\) 9.82328 0.343044
\(821\) 2.47894 0.0865157 0.0432578 0.999064i \(-0.486226\pi\)
0.0432578 + 0.999064i \(0.486226\pi\)
\(822\) −23.0388 −0.803571
\(823\) 2.75618 0.0960746 0.0480373 0.998846i \(-0.484703\pi\)
0.0480373 + 0.998846i \(0.484703\pi\)
\(824\) −11.4523 −0.398958
\(825\) 43.3177 1.50813
\(826\) 31.5818 1.09887
\(827\) 31.2781 1.08765 0.543823 0.839200i \(-0.316976\pi\)
0.543823 + 0.839200i \(0.316976\pi\)
\(828\) −11.1240 −0.386585
\(829\) −12.3196 −0.427878 −0.213939 0.976847i \(-0.568629\pi\)
−0.213939 + 0.976847i \(0.568629\pi\)
\(830\) −6.81718 −0.236628
\(831\) −57.3292 −1.98873
\(832\) 6.54148 0.226785
\(833\) −1.97876 −0.0685599
\(834\) 4.07408 0.141074
\(835\) −8.97369 −0.310547
\(836\) −32.6459 −1.12908
\(837\) 12.8781 0.445134
\(838\) −2.53976 −0.0877345
\(839\) −7.27794 −0.251262 −0.125631 0.992077i \(-0.540096\pi\)
−0.125631 + 0.992077i \(0.540096\pi\)
\(840\) 6.48067 0.223604
\(841\) 1.00000 0.0344828
\(842\) 60.8211 2.09603
\(843\) 9.29300 0.320068
\(844\) 1.25722 0.0432753
\(845\) −6.56372 −0.225799
\(846\) 8.91002 0.306333
\(847\) 41.9230 1.44049
\(848\) −44.8321 −1.53954
\(849\) 25.1476 0.863064
\(850\) 4.23614 0.145298
\(851\) 5.74682 0.196998
\(852\) 2.20579 0.0755691
\(853\) 29.2283 1.00076 0.500378 0.865807i \(-0.333194\pi\)
0.500378 + 0.865807i \(0.333194\pi\)
\(854\) 34.5739 1.18309
\(855\) 10.2043 0.348978
\(856\) 2.18508 0.0746845
\(857\) −47.8387 −1.63414 −0.817069 0.576539i \(-0.804403\pi\)
−0.817069 + 0.576539i \(0.804403\pi\)
\(858\) −63.8893 −2.18114
\(859\) −35.9446 −1.22641 −0.613207 0.789922i \(-0.710121\pi\)
−0.613207 + 0.789922i \(0.710121\pi\)
\(860\) 7.59382 0.258947
\(861\) 25.8825 0.882074
\(862\) 2.15600 0.0734338
\(863\) −16.0074 −0.544897 −0.272449 0.962170i \(-0.587834\pi\)
−0.272449 + 0.962170i \(0.587834\pi\)
\(864\) −15.5975 −0.530637
\(865\) −6.39484 −0.217431
\(866\) 19.0631 0.647792
\(867\) −36.7721 −1.24885
\(868\) −14.9168 −0.506308
\(869\) 25.2104 0.855204
\(870\) 5.06431 0.171696
\(871\) 3.46947 0.117558
\(872\) −9.79259 −0.331619
\(873\) −18.0199 −0.609883
\(874\) 32.8078 1.10974
\(875\) −21.1255 −0.714171
\(876\) −29.6072 −1.00033
\(877\) 39.1682 1.32262 0.661308 0.750115i \(-0.270002\pi\)
0.661308 + 0.750115i \(0.270002\pi\)
\(878\) −21.6415 −0.730364
\(879\) 12.5783 0.424255
\(880\) 34.1536 1.15132
\(881\) 11.6314 0.391872 0.195936 0.980617i \(-0.437225\pi\)
0.195936 + 0.980617i \(0.437225\pi\)
\(882\) 10.5026 0.353640
\(883\) −21.0579 −0.708656 −0.354328 0.935121i \(-0.615290\pi\)
−0.354328 + 0.935121i \(0.615290\pi\)
\(884\) −2.53263 −0.0851816
\(885\) −23.6576 −0.795243
\(886\) 33.1930 1.11514
\(887\) 8.46040 0.284072 0.142036 0.989861i \(-0.454635\pi\)
0.142036 + 0.989861i \(0.454635\pi\)
\(888\) −3.53486 −0.118622
\(889\) 5.46531 0.183301
\(890\) 15.9910 0.536020
\(891\) 62.4288 2.09144
\(892\) 20.5008 0.686417
\(893\) −10.6521 −0.356458
\(894\) 55.5052 1.85637
\(895\) 19.7787 0.661129
\(896\) −17.8237 −0.595448
\(897\) 26.0264 0.868997
\(898\) −72.3036 −2.41280
\(899\) 5.44314 0.181539
\(900\) −9.11406 −0.303802
\(901\) 6.15745 0.205134
\(902\) 59.9982 1.99772
\(903\) 20.0083 0.665834
\(904\) −0.339921 −0.0113056
\(905\) 21.3713 0.710406
\(906\) −82.1226 −2.72834
\(907\) −23.6662 −0.785823 −0.392911 0.919576i \(-0.628532\pi\)
−0.392911 + 0.919576i \(0.628532\pi\)
\(908\) −5.29791 −0.175817
\(909\) 20.4154 0.677136
\(910\) 12.7318 0.422055
\(911\) −6.05842 −0.200724 −0.100362 0.994951i \(-0.532000\pi\)
−0.100362 + 0.994951i \(0.532000\pi\)
\(912\) −45.8782 −1.51918
\(913\) −16.8782 −0.558587
\(914\) −15.8137 −0.523071
\(915\) −25.8989 −0.856192
\(916\) 16.0663 0.530847
\(917\) −2.93617 −0.0969609
\(918\) 2.90101 0.0957478
\(919\) 0.232766 0.00767825 0.00383912 0.999993i \(-0.498778\pi\)
0.00383912 + 0.999993i \(0.498778\pi\)
\(920\) −6.11981 −0.201764
\(921\) −42.6728 −1.40612
\(922\) 64.9504 2.13903
\(923\) −2.02352 −0.0666051
\(924\) −34.3610 −1.13039
\(925\) 4.70847 0.154813
\(926\) 44.9754 1.47798
\(927\) −18.9797 −0.623377
\(928\) −6.59250 −0.216409
\(929\) 28.9222 0.948908 0.474454 0.880280i \(-0.342645\pi\)
0.474454 + 0.880280i \(0.342645\pi\)
\(930\) 27.5657 0.903915
\(931\) −12.5560 −0.411506
\(932\) 16.8370 0.551515
\(933\) 14.2422 0.466270
\(934\) −58.6612 −1.91945
\(935\) −4.69081 −0.153406
\(936\) −6.27696 −0.205169
\(937\) −3.08688 −0.100844 −0.0504220 0.998728i \(-0.516057\pi\)
−0.0504220 + 0.998728i \(0.516057\pi\)
\(938\) 4.60322 0.150301
\(939\) 25.2013 0.822412
\(940\) −4.25521 −0.138790
\(941\) −54.7851 −1.78594 −0.892972 0.450113i \(-0.851384\pi\)
−0.892972 + 0.450113i \(0.851384\pi\)
\(942\) 17.5097 0.570498
\(943\) −24.4413 −0.795920
\(944\) 41.7048 1.35737
\(945\) −5.91162 −0.192305
\(946\) 46.3812 1.50798
\(947\) 21.6168 0.702452 0.351226 0.936291i \(-0.385765\pi\)
0.351226 + 0.936291i \(0.385765\pi\)
\(948\) −13.5281 −0.439372
\(949\) 27.1607 0.881675
\(950\) 26.8800 0.872101
\(951\) −27.2884 −0.884886
\(952\) 1.56908 0.0508542
\(953\) 10.1315 0.328191 0.164096 0.986444i \(-0.447529\pi\)
0.164096 + 0.986444i \(0.447529\pi\)
\(954\) −32.6816 −1.05811
\(955\) −24.2305 −0.784081
\(956\) 32.6208 1.05503
\(957\) 12.5384 0.405308
\(958\) −20.4437 −0.660507
\(959\) 11.3669 0.367057
\(960\) −6.50143 −0.209833
\(961\) −1.37227 −0.0442669
\(962\) −6.94452 −0.223900
\(963\) 3.62132 0.116695
\(964\) 14.0136 0.451347
\(965\) −15.5498 −0.500566
\(966\) 34.5314 1.11103
\(967\) 27.3427 0.879283 0.439641 0.898173i \(-0.355106\pi\)
0.439641 + 0.898173i \(0.355106\pi\)
\(968\) 24.3509 0.782669
\(969\) 6.30112 0.202421
\(970\) 21.2303 0.681665
\(971\) 41.6142 1.33546 0.667732 0.744402i \(-0.267265\pi\)
0.667732 + 0.744402i \(0.267265\pi\)
\(972\) −23.8228 −0.764118
\(973\) −2.01007 −0.0644400
\(974\) 29.9240 0.958828
\(975\) 21.3239 0.682911
\(976\) 45.6558 1.46141
\(977\) −3.08971 −0.0988486 −0.0494243 0.998778i \(-0.515739\pi\)
−0.0494243 + 0.998778i \(0.515739\pi\)
\(978\) 30.3397 0.970156
\(979\) 39.5911 1.26534
\(980\) −5.01577 −0.160223
\(981\) −16.2292 −0.518158
\(982\) −16.5391 −0.527784
\(983\) 39.5890 1.26269 0.631346 0.775501i \(-0.282503\pi\)
0.631346 + 0.775501i \(0.282503\pi\)
\(984\) 15.0338 0.479261
\(985\) 23.7060 0.755335
\(986\) 1.22616 0.0390488
\(987\) −11.2117 −0.356872
\(988\) −16.0705 −0.511271
\(989\) −18.8942 −0.600801
\(990\) 24.8972 0.791285
\(991\) 42.8562 1.36137 0.680686 0.732575i \(-0.261682\pi\)
0.680686 + 0.732575i \(0.261682\pi\)
\(992\) −35.8839 −1.13931
\(993\) −29.0098 −0.920597
\(994\) −2.68477 −0.0851558
\(995\) −13.0983 −0.415243
\(996\) 9.05697 0.286981
\(997\) 28.2944 0.896094 0.448047 0.894010i \(-0.352120\pi\)
0.448047 + 0.894010i \(0.352120\pi\)
\(998\) 28.1786 0.891979
\(999\) 3.22448 0.102018
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 \(a_p\))