Properties

Label 4033.2.a.d.1.9
Level 4033
Weight 2
Character 4033.1
Self dual Yes
Analytic conductor 32.204
Analytic rank 1
Dimension 79
CM No

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Newspace parameters

Level: \( N \) = \( 4033 = 37 \cdot 109 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4033.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.2036671352\)
Analytic rank: \(1\)
Dimension: \(79\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 4033.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.50108 q^{2}\) \(-2.74712 q^{3}\) \(+4.25541 q^{4}\) \(+3.75941 q^{5}\) \(+6.87078 q^{6}\) \(-1.77571 q^{7}\) \(-5.64098 q^{8}\) \(+4.54668 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.50108 q^{2}\) \(-2.74712 q^{3}\) \(+4.25541 q^{4}\) \(+3.75941 q^{5}\) \(+6.87078 q^{6}\) \(-1.77571 q^{7}\) \(-5.64098 q^{8}\) \(+4.54668 q^{9}\) \(-9.40258 q^{10}\) \(+4.50342 q^{11}\) \(-11.6901 q^{12}\) \(-2.22949 q^{13}\) \(+4.44119 q^{14}\) \(-10.3275 q^{15}\) \(+5.59772 q^{16}\) \(+2.78903 q^{17}\) \(-11.3716 q^{18}\) \(-6.60953 q^{19}\) \(+15.9978 q^{20}\) \(+4.87809 q^{21}\) \(-11.2634 q^{22}\) \(+5.39913 q^{23}\) \(+15.4965 q^{24}\) \(+9.13313 q^{25}\) \(+5.57615 q^{26}\) \(-4.24891 q^{27}\) \(-7.55638 q^{28}\) \(+1.55088 q^{29}\) \(+25.8300 q^{30}\) \(-4.02437 q^{31}\) \(-2.71842 q^{32}\) \(-12.3714 q^{33}\) \(-6.97558 q^{34}\) \(-6.67561 q^{35}\) \(+19.3480 q^{36}\) \(-1.00000 q^{37}\) \(+16.5310 q^{38}\) \(+6.12469 q^{39}\) \(-21.2067 q^{40}\) \(+11.6153 q^{41}\) \(-12.2005 q^{42}\) \(-10.9960 q^{43}\) \(+19.1639 q^{44}\) \(+17.0928 q^{45}\) \(-13.5037 q^{46}\) \(-9.73430 q^{47}\) \(-15.3776 q^{48}\) \(-3.84686 q^{49}\) \(-22.8427 q^{50}\) \(-7.66179 q^{51}\) \(-9.48742 q^{52}\) \(-10.7722 q^{53}\) \(+10.6269 q^{54}\) \(+16.9302 q^{55}\) \(+10.0167 q^{56}\) \(+18.1572 q^{57}\) \(-3.87888 q^{58}\) \(-2.95304 q^{59}\) \(-43.9480 q^{60}\) \(+6.72393 q^{61}\) \(+10.0653 q^{62}\) \(-8.07357 q^{63}\) \(-4.39647 q^{64}\) \(-8.38157 q^{65}\) \(+30.9420 q^{66}\) \(-3.18113 q^{67}\) \(+11.8685 q^{68}\) \(-14.8321 q^{69}\) \(+16.6962 q^{70}\) \(+10.1420 q^{71}\) \(-25.6477 q^{72}\) \(-6.37886 q^{73}\) \(+2.50108 q^{74}\) \(-25.0898 q^{75}\) \(-28.1263 q^{76}\) \(-7.99676 q^{77}\) \(-15.3184 q^{78}\) \(-10.5416 q^{79}\) \(+21.0441 q^{80}\) \(-1.96776 q^{81}\) \(-29.0508 q^{82}\) \(-6.27102 q^{83}\) \(+20.7583 q^{84}\) \(+10.4851 q^{85}\) \(+27.5019 q^{86}\) \(-4.26046 q^{87}\) \(-25.4037 q^{88}\) \(-16.4692 q^{89}\) \(-42.7505 q^{90}\) \(+3.95893 q^{91}\) \(+22.9755 q^{92}\) \(+11.0554 q^{93}\) \(+24.3463 q^{94}\) \(-24.8479 q^{95}\) \(+7.46782 q^{96}\) \(-12.3723 q^{97}\) \(+9.62132 q^{98}\) \(+20.4756 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut -\mathstrut 13q^{10} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut -\mathstrut 40q^{12} \) \(\mathstrut -\mathstrut 18q^{13} \) \(\mathstrut -\mathstrut 42q^{14} \) \(\mathstrut -\mathstrut 49q^{15} \) \(\mathstrut +\mathstrut 83q^{16} \) \(\mathstrut -\mathstrut 62q^{17} \) \(\mathstrut -\mathstrut 33q^{18} \) \(\mathstrut -\mathstrut 25q^{19} \) \(\mathstrut -\mathstrut 39q^{20} \) \(\mathstrut -\mathstrut 15q^{21} \) \(\mathstrut -\mathstrut 31q^{22} \) \(\mathstrut -\mathstrut 94q^{23} \) \(\mathstrut -\mathstrut 39q^{24} \) \(\mathstrut +\mathstrut 71q^{25} \) \(\mathstrut -\mathstrut 35q^{26} \) \(\mathstrut -\mathstrut 47q^{27} \) \(\mathstrut -\mathstrut 13q^{28} \) \(\mathstrut -\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 15q^{30} \) \(\mathstrut -\mathstrut 37q^{31} \) \(\mathstrut -\mathstrut 105q^{32} \) \(\mathstrut -\mathstrut 60q^{33} \) \(\mathstrut +\mathstrut 9q^{34} \) \(\mathstrut -\mathstrut 60q^{35} \) \(\mathstrut +\mathstrut 43q^{36} \) \(\mathstrut -\mathstrut 79q^{37} \) \(\mathstrut -\mathstrut 80q^{38} \) \(\mathstrut -\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 64q^{40} \) \(\mathstrut -\mathstrut 37q^{41} \) \(\mathstrut -\mathstrut 30q^{42} \) \(\mathstrut -\mathstrut 20q^{43} \) \(\mathstrut -\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 8q^{45} \) \(\mathstrut +\mathstrut 61q^{46} \) \(\mathstrut -\mathstrut 148q^{47} \) \(\mathstrut -\mathstrut 39q^{48} \) \(\mathstrut +\mathstrut 82q^{49} \) \(\mathstrut -\mathstrut 90q^{50} \) \(\mathstrut -\mathstrut 45q^{51} \) \(\mathstrut -\mathstrut 27q^{52} \) \(\mathstrut -\mathstrut 70q^{53} \) \(\mathstrut -\mathstrut 41q^{54} \) \(\mathstrut -\mathstrut 105q^{55} \) \(\mathstrut -\mathstrut 68q^{56} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut -\mathstrut 14q^{58} \) \(\mathstrut -\mathstrut 96q^{59} \) \(\mathstrut -\mathstrut 74q^{60} \) \(\mathstrut -\mathstrut 21q^{61} \) \(\mathstrut +\mathstrut 4q^{62} \) \(\mathstrut -\mathstrut 60q^{63} \) \(\mathstrut +\mathstrut 132q^{64} \) \(\mathstrut -\mathstrut 15q^{65} \) \(\mathstrut +\mathstrut 71q^{66} \) \(\mathstrut -\mathstrut 44q^{67} \) \(\mathstrut -\mathstrut 166q^{68} \) \(\mathstrut -\mathstrut 72q^{69} \) \(\mathstrut -\mathstrut 9q^{70} \) \(\mathstrut -\mathstrut 55q^{71} \) \(\mathstrut -\mathstrut 126q^{72} \) \(\mathstrut -\mathstrut 27q^{73} \) \(\mathstrut +\mathstrut 11q^{74} \) \(\mathstrut -\mathstrut 39q^{75} \) \(\mathstrut -\mathstrut 4q^{76} \) \(\mathstrut -\mathstrut 104q^{77} \) \(\mathstrut -\mathstrut 47q^{78} \) \(\mathstrut -\mathstrut 49q^{79} \) \(\mathstrut -\mathstrut 82q^{80} \) \(\mathstrut +\mathstrut 55q^{81} \) \(\mathstrut +\mathstrut 20q^{82} \) \(\mathstrut -\mathstrut 52q^{83} \) \(\mathstrut -\mathstrut 29q^{84} \) \(\mathstrut +\mathstrut 3q^{85} \) \(\mathstrut -\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 113q^{87} \) \(\mathstrut +\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 68q^{89} \) \(\mathstrut -\mathstrut 39q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 179q^{92} \) \(\mathstrut -\mathstrut 53q^{93} \) \(\mathstrut -\mathstrut 33q^{94} \) \(\mathstrut -\mathstrut 86q^{95} \) \(\mathstrut +\mathstrut 33q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut -\mathstrut 116q^{98} \) \(\mathstrut +\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.50108 −1.76853 −0.884266 0.466983i \(-0.845341\pi\)
−0.884266 + 0.466983i \(0.845341\pi\)
\(3\) −2.74712 −1.58605 −0.793026 0.609188i \(-0.791495\pi\)
−0.793026 + 0.609188i \(0.791495\pi\)
\(4\) 4.25541 2.12771
\(5\) 3.75941 1.68126 0.840629 0.541612i \(-0.182186\pi\)
0.840629 + 0.541612i \(0.182186\pi\)
\(6\) 6.87078 2.80498
\(7\) −1.77571 −0.671155 −0.335577 0.942013i \(-0.608931\pi\)
−0.335577 + 0.942013i \(0.608931\pi\)
\(8\) −5.64098 −1.99439
\(9\) 4.54668 1.51556
\(10\) −9.40258 −2.97336
\(11\) 4.50342 1.35783 0.678916 0.734216i \(-0.262450\pi\)
0.678916 + 0.734216i \(0.262450\pi\)
\(12\) −11.6901 −3.37465
\(13\) −2.22949 −0.618350 −0.309175 0.951005i \(-0.600053\pi\)
−0.309175 + 0.951005i \(0.600053\pi\)
\(14\) 4.44119 1.18696
\(15\) −10.3275 −2.66656
\(16\) 5.59772 1.39943
\(17\) 2.78903 0.676438 0.338219 0.941067i \(-0.390176\pi\)
0.338219 + 0.941067i \(0.390176\pi\)
\(18\) −11.3716 −2.68032
\(19\) −6.60953 −1.51633 −0.758165 0.652063i \(-0.773904\pi\)
−0.758165 + 0.652063i \(0.773904\pi\)
\(20\) 15.9978 3.57722
\(21\) 4.87809 1.06449
\(22\) −11.2634 −2.40137
\(23\) 5.39913 1.12580 0.562898 0.826526i \(-0.309686\pi\)
0.562898 + 0.826526i \(0.309686\pi\)
\(24\) 15.4965 3.16320
\(25\) 9.13313 1.82663
\(26\) 5.57615 1.09357
\(27\) −4.24891 −0.817703
\(28\) −7.55638 −1.42802
\(29\) 1.55088 0.287991 0.143996 0.989578i \(-0.454005\pi\)
0.143996 + 0.989578i \(0.454005\pi\)
\(30\) 25.8300 4.71590
\(31\) −4.02437 −0.722797 −0.361399 0.932411i \(-0.617701\pi\)
−0.361399 + 0.932411i \(0.617701\pi\)
\(32\) −2.71842 −0.480552
\(33\) −12.3714 −2.15359
\(34\) −6.97558 −1.19630
\(35\) −6.67561 −1.12838
\(36\) 19.3480 3.22467
\(37\) −1.00000 −0.164399
\(38\) 16.5310 2.68168
\(39\) 6.12469 0.980736
\(40\) −21.2067 −3.35308
\(41\) 11.6153 1.81400 0.907001 0.421128i \(-0.138366\pi\)
0.907001 + 0.421128i \(0.138366\pi\)
\(42\) −12.2005 −1.88258
\(43\) −10.9960 −1.67688 −0.838438 0.544997i \(-0.816531\pi\)
−0.838438 + 0.544997i \(0.816531\pi\)
\(44\) 19.1639 2.88907
\(45\) 17.0928 2.54804
\(46\) −13.5037 −1.99101
\(47\) −9.73430 −1.41989 −0.709947 0.704255i \(-0.751281\pi\)
−0.709947 + 0.704255i \(0.751281\pi\)
\(48\) −15.3776 −2.21957
\(49\) −3.84686 −0.549551
\(50\) −22.8427 −3.23045
\(51\) −7.66179 −1.07287
\(52\) −9.48742 −1.31567
\(53\) −10.7722 −1.47968 −0.739841 0.672782i \(-0.765099\pi\)
−0.739841 + 0.672782i \(0.765099\pi\)
\(54\) 10.6269 1.44613
\(55\) 16.9302 2.28286
\(56\) 10.0167 1.33854
\(57\) 18.1572 2.40498
\(58\) −3.87888 −0.509322
\(59\) −2.95304 −0.384453 −0.192227 0.981351i \(-0.561571\pi\)
−0.192227 + 0.981351i \(0.561571\pi\)
\(60\) −43.9480 −5.67366
\(61\) 6.72393 0.860911 0.430456 0.902612i \(-0.358353\pi\)
0.430456 + 0.902612i \(0.358353\pi\)
\(62\) 10.0653 1.27829
\(63\) −8.07357 −1.01717
\(64\) −4.39647 −0.549559
\(65\) −8.38157 −1.03961
\(66\) 30.9420 3.80870
\(67\) −3.18113 −0.388636 −0.194318 0.980939i \(-0.562249\pi\)
−0.194318 + 0.980939i \(0.562249\pi\)
\(68\) 11.8685 1.43926
\(69\) −14.8321 −1.78557
\(70\) 16.6962 1.99558
\(71\) 10.1420 1.20364 0.601818 0.798633i \(-0.294443\pi\)
0.601818 + 0.798633i \(0.294443\pi\)
\(72\) −25.6477 −3.02261
\(73\) −6.37886 −0.746589 −0.373294 0.927713i \(-0.621772\pi\)
−0.373294 + 0.927713i \(0.621772\pi\)
\(74\) 2.50108 0.290745
\(75\) −25.0898 −2.89712
\(76\) −28.1263 −3.22631
\(77\) −7.99676 −0.911315
\(78\) −15.3184 −1.73446
\(79\) −10.5416 −1.18602 −0.593009 0.805196i \(-0.702060\pi\)
−0.593009 + 0.805196i \(0.702060\pi\)
\(80\) 21.0441 2.35280
\(81\) −1.96776 −0.218640
\(82\) −29.0508 −3.20812
\(83\) −6.27102 −0.688334 −0.344167 0.938908i \(-0.611839\pi\)
−0.344167 + 0.938908i \(0.611839\pi\)
\(84\) 20.7583 2.26491
\(85\) 10.4851 1.13727
\(86\) 27.5019 2.96561
\(87\) −4.26046 −0.456769
\(88\) −25.4037 −2.70804
\(89\) −16.4692 −1.74573 −0.872864 0.487964i \(-0.837740\pi\)
−0.872864 + 0.487964i \(0.837740\pi\)
\(90\) −42.7505 −4.50630
\(91\) 3.95893 0.415009
\(92\) 22.9755 2.39536
\(93\) 11.0554 1.14639
\(94\) 24.3463 2.51113
\(95\) −24.8479 −2.54934
\(96\) 7.46782 0.762181
\(97\) −12.3723 −1.25622 −0.628111 0.778124i \(-0.716171\pi\)
−0.628111 + 0.778124i \(0.716171\pi\)
\(98\) 9.62132 0.971900
\(99\) 20.4756 2.05787
\(100\) 38.8652 3.88652
\(101\) 3.73452 0.371598 0.185799 0.982588i \(-0.440513\pi\)
0.185799 + 0.982588i \(0.440513\pi\)
\(102\) 19.1628 1.89740
\(103\) 1.87238 0.184491 0.0922456 0.995736i \(-0.470596\pi\)
0.0922456 + 0.995736i \(0.470596\pi\)
\(104\) 12.5765 1.23323
\(105\) 18.3387 1.78967
\(106\) 26.9423 2.61687
\(107\) −5.66160 −0.547328 −0.273664 0.961825i \(-0.588236\pi\)
−0.273664 + 0.961825i \(0.588236\pi\)
\(108\) −18.0809 −1.73983
\(109\) −1.00000 −0.0957826
\(110\) −42.3438 −4.03732
\(111\) 2.74712 0.260745
\(112\) −9.93993 −0.939235
\(113\) −7.62153 −0.716974 −0.358487 0.933535i \(-0.616707\pi\)
−0.358487 + 0.933535i \(0.616707\pi\)
\(114\) −45.4126 −4.25328
\(115\) 20.2975 1.89275
\(116\) 6.59964 0.612761
\(117\) −10.1368 −0.937146
\(118\) 7.38580 0.679918
\(119\) −4.95250 −0.453995
\(120\) 58.2574 5.31815
\(121\) 9.28078 0.843707
\(122\) −16.8171 −1.52255
\(123\) −31.9086 −2.87710
\(124\) −17.1253 −1.53790
\(125\) 15.5381 1.38977
\(126\) 20.1927 1.79891
\(127\) −5.33994 −0.473843 −0.236921 0.971529i \(-0.576138\pi\)
−0.236921 + 0.971529i \(0.576138\pi\)
\(128\) 16.4328 1.45246
\(129\) 30.2074 2.65961
\(130\) 20.9630 1.83858
\(131\) 2.03375 0.177689 0.0888447 0.996045i \(-0.471683\pi\)
0.0888447 + 0.996045i \(0.471683\pi\)
\(132\) −52.6456 −4.58221
\(133\) 11.7366 1.01769
\(134\) 7.95626 0.687316
\(135\) −15.9734 −1.37477
\(136\) −15.7328 −1.34908
\(137\) −3.64660 −0.311550 −0.155775 0.987793i \(-0.549788\pi\)
−0.155775 + 0.987793i \(0.549788\pi\)
\(138\) 37.0962 3.15784
\(139\) 20.6974 1.75553 0.877766 0.479090i \(-0.159033\pi\)
0.877766 + 0.479090i \(0.159033\pi\)
\(140\) −28.4075 −2.40087
\(141\) 26.7413 2.25202
\(142\) −25.3660 −2.12867
\(143\) −10.0403 −0.839616
\(144\) 25.4510 2.12092
\(145\) 5.83039 0.484187
\(146\) 15.9540 1.32037
\(147\) 10.5678 0.871617
\(148\) −4.25541 −0.349793
\(149\) 13.8189 1.13209 0.566044 0.824375i \(-0.308473\pi\)
0.566044 + 0.824375i \(0.308473\pi\)
\(150\) 62.7517 5.12365
\(151\) 4.94410 0.402345 0.201172 0.979556i \(-0.435525\pi\)
0.201172 + 0.979556i \(0.435525\pi\)
\(152\) 37.2842 3.02415
\(153\) 12.6808 1.02518
\(154\) 20.0006 1.61169
\(155\) −15.1292 −1.21521
\(156\) 26.0631 2.08672
\(157\) 22.3443 1.78327 0.891634 0.452756i \(-0.149559\pi\)
0.891634 + 0.452756i \(0.149559\pi\)
\(158\) 26.3653 2.09751
\(159\) 29.5927 2.34685
\(160\) −10.2196 −0.807932
\(161\) −9.58728 −0.755583
\(162\) 4.92154 0.386673
\(163\) −9.37314 −0.734161 −0.367081 0.930189i \(-0.619643\pi\)
−0.367081 + 0.930189i \(0.619643\pi\)
\(164\) 49.4278 3.85967
\(165\) −46.5092 −3.62074
\(166\) 15.6843 1.21734
\(167\) 14.8931 1.15246 0.576231 0.817287i \(-0.304523\pi\)
0.576231 + 0.817287i \(0.304523\pi\)
\(168\) −27.5172 −2.12300
\(169\) −8.02936 −0.617643
\(170\) −26.2240 −2.01129
\(171\) −30.0514 −2.29809
\(172\) −46.7926 −3.56790
\(173\) 20.4389 1.55394 0.776971 0.629536i \(-0.216755\pi\)
0.776971 + 0.629536i \(0.216755\pi\)
\(174\) 10.6558 0.807810
\(175\) −16.2178 −1.22595
\(176\) 25.2089 1.90019
\(177\) 8.11237 0.609763
\(178\) 41.1907 3.08738
\(179\) −15.7357 −1.17614 −0.588070 0.808810i \(-0.700112\pi\)
−0.588070 + 0.808810i \(0.700112\pi\)
\(180\) 72.7369 5.42149
\(181\) −5.37184 −0.399286 −0.199643 0.979869i \(-0.563978\pi\)
−0.199643 + 0.979869i \(0.563978\pi\)
\(182\) −9.90161 −0.733957
\(183\) −18.4715 −1.36545
\(184\) −30.4564 −2.24527
\(185\) −3.75941 −0.276397
\(186\) −27.6505 −2.02743
\(187\) 12.5602 0.918489
\(188\) −41.4235 −3.02112
\(189\) 7.54482 0.548805
\(190\) 62.1466 4.50859
\(191\) 5.53808 0.400722 0.200361 0.979722i \(-0.435789\pi\)
0.200361 + 0.979722i \(0.435789\pi\)
\(192\) 12.0776 0.871628
\(193\) −10.0808 −0.725628 −0.362814 0.931862i \(-0.618184\pi\)
−0.362814 + 0.931862i \(0.618184\pi\)
\(194\) 30.9443 2.22167
\(195\) 23.0252 1.64887
\(196\) −16.3700 −1.16928
\(197\) −0.686420 −0.0489054 −0.0244527 0.999701i \(-0.507784\pi\)
−0.0244527 + 0.999701i \(0.507784\pi\)
\(198\) −51.2111 −3.63942
\(199\) −17.1729 −1.21735 −0.608676 0.793419i \(-0.708299\pi\)
−0.608676 + 0.793419i \(0.708299\pi\)
\(200\) −51.5198 −3.64300
\(201\) 8.73894 0.616397
\(202\) −9.34033 −0.657184
\(203\) −2.75391 −0.193287
\(204\) −32.6041 −2.28274
\(205\) 43.6666 3.04980
\(206\) −4.68298 −0.326279
\(207\) 24.5481 1.70621
\(208\) −12.4801 −0.865339
\(209\) −29.7655 −2.05892
\(210\) −45.8666 −3.16510
\(211\) −4.67839 −0.322073 −0.161037 0.986948i \(-0.551484\pi\)
−0.161037 + 0.986948i \(0.551484\pi\)
\(212\) −45.8404 −3.14833
\(213\) −27.8614 −1.90903
\(214\) 14.1601 0.967967
\(215\) −41.3385 −2.81926
\(216\) 23.9680 1.63082
\(217\) 7.14610 0.485109
\(218\) 2.50108 0.169395
\(219\) 17.5235 1.18413
\(220\) 72.0449 4.85727
\(221\) −6.21812 −0.418276
\(222\) −6.87078 −0.461136
\(223\) −4.38034 −0.293329 −0.146665 0.989186i \(-0.546854\pi\)
−0.146665 + 0.989186i \(0.546854\pi\)
\(224\) 4.82711 0.322525
\(225\) 41.5254 2.76836
\(226\) 19.0621 1.26799
\(227\) −4.94781 −0.328398 −0.164199 0.986427i \(-0.552504\pi\)
−0.164199 + 0.986427i \(0.552504\pi\)
\(228\) 77.2663 5.11709
\(229\) −2.70576 −0.178802 −0.0894008 0.995996i \(-0.528495\pi\)
−0.0894008 + 0.995996i \(0.528495\pi\)
\(230\) −50.7657 −3.34739
\(231\) 21.9681 1.44539
\(232\) −8.74848 −0.574366
\(233\) 28.9503 1.89660 0.948299 0.317379i \(-0.102803\pi\)
0.948299 + 0.317379i \(0.102803\pi\)
\(234\) 25.3529 1.65737
\(235\) −36.5952 −2.38721
\(236\) −12.5664 −0.818004
\(237\) 28.9590 1.88109
\(238\) 12.3866 0.802904
\(239\) −0.0952732 −0.00616271 −0.00308136 0.999995i \(-0.500981\pi\)
−0.00308136 + 0.999995i \(0.500981\pi\)
\(240\) −57.8107 −3.73167
\(241\) 4.45281 0.286831 0.143415 0.989663i \(-0.454191\pi\)
0.143415 + 0.989663i \(0.454191\pi\)
\(242\) −23.2120 −1.49212
\(243\) 18.1524 1.16448
\(244\) 28.6131 1.83177
\(245\) −14.4619 −0.923937
\(246\) 79.8060 5.08825
\(247\) 14.7359 0.937623
\(248\) 22.7014 1.44154
\(249\) 17.2273 1.09173
\(250\) −38.8621 −2.45785
\(251\) −11.9965 −0.757215 −0.378607 0.925557i \(-0.623597\pi\)
−0.378607 + 0.925557i \(0.623597\pi\)
\(252\) −34.3564 −2.16425
\(253\) 24.3145 1.52864
\(254\) 13.3556 0.838006
\(255\) −28.8038 −1.80376
\(256\) −32.3068 −2.01917
\(257\) −5.09848 −0.318035 −0.159017 0.987276i \(-0.550833\pi\)
−0.159017 + 0.987276i \(0.550833\pi\)
\(258\) −75.5512 −4.70361
\(259\) 1.77571 0.110337
\(260\) −35.6671 −2.21198
\(261\) 7.05135 0.436468
\(262\) −5.08657 −0.314249
\(263\) −19.2074 −1.18438 −0.592188 0.805800i \(-0.701736\pi\)
−0.592188 + 0.805800i \(0.701736\pi\)
\(264\) 69.7870 4.29509
\(265\) −40.4972 −2.48773
\(266\) −29.3542 −1.79982
\(267\) 45.2428 2.76881
\(268\) −13.5370 −0.826904
\(269\) −10.2788 −0.626711 −0.313356 0.949636i \(-0.601453\pi\)
−0.313356 + 0.949636i \(0.601453\pi\)
\(270\) 39.9507 2.43132
\(271\) 5.71771 0.347326 0.173663 0.984805i \(-0.444440\pi\)
0.173663 + 0.984805i \(0.444440\pi\)
\(272\) 15.6122 0.946629
\(273\) −10.8757 −0.658225
\(274\) 9.12045 0.550987
\(275\) 41.1303 2.48025
\(276\) −63.1166 −3.79917
\(277\) 22.7137 1.36474 0.682368 0.731009i \(-0.260950\pi\)
0.682368 + 0.731009i \(0.260950\pi\)
\(278\) −51.7660 −3.10472
\(279\) −18.2975 −1.09544
\(280\) 37.6570 2.25043
\(281\) −22.4531 −1.33944 −0.669721 0.742613i \(-0.733586\pi\)
−0.669721 + 0.742613i \(0.733586\pi\)
\(282\) −66.8822 −3.98278
\(283\) −15.9034 −0.945360 −0.472680 0.881234i \(-0.656713\pi\)
−0.472680 + 0.881234i \(0.656713\pi\)
\(284\) 43.1585 2.56098
\(285\) 68.2602 4.04338
\(286\) 25.1117 1.48489
\(287\) −20.6254 −1.21748
\(288\) −12.3598 −0.728305
\(289\) −9.22133 −0.542431
\(290\) −14.5823 −0.856301
\(291\) 33.9883 1.99243
\(292\) −27.1447 −1.58852
\(293\) 28.0829 1.64062 0.820311 0.571918i \(-0.193800\pi\)
0.820311 + 0.571918i \(0.193800\pi\)
\(294\) −26.4309 −1.54148
\(295\) −11.1017 −0.646365
\(296\) 5.64098 0.327875
\(297\) −19.1346 −1.11030
\(298\) −34.5622 −2.00214
\(299\) −12.0373 −0.696136
\(300\) −106.768 −6.16423
\(301\) 19.5257 1.12544
\(302\) −12.3656 −0.711560
\(303\) −10.2592 −0.589374
\(304\) −36.9983 −2.12200
\(305\) 25.2780 1.44741
\(306\) −31.7157 −1.81307
\(307\) −12.7842 −0.729633 −0.364816 0.931079i \(-0.618868\pi\)
−0.364816 + 0.931079i \(0.618868\pi\)
\(308\) −34.0295 −1.93901
\(309\) −5.14366 −0.292613
\(310\) 37.8394 2.14914
\(311\) 14.7539 0.836619 0.418309 0.908305i \(-0.362623\pi\)
0.418309 + 0.908305i \(0.362623\pi\)
\(312\) −34.5493 −1.95597
\(313\) −5.22249 −0.295192 −0.147596 0.989048i \(-0.547154\pi\)
−0.147596 + 0.989048i \(0.547154\pi\)
\(314\) −55.8849 −3.15377
\(315\) −30.3518 −1.71013
\(316\) −44.8587 −2.52350
\(317\) −2.84700 −0.159904 −0.0799518 0.996799i \(-0.525477\pi\)
−0.0799518 + 0.996799i \(0.525477\pi\)
\(318\) −74.0137 −4.15048
\(319\) 6.98426 0.391044
\(320\) −16.5281 −0.923949
\(321\) 15.5531 0.868090
\(322\) 23.9786 1.33627
\(323\) −18.4341 −1.02570
\(324\) −8.37365 −0.465203
\(325\) −20.3623 −1.12949
\(326\) 23.4430 1.29839
\(327\) 2.74712 0.151916
\(328\) −65.5216 −3.61782
\(329\) 17.2853 0.952968
\(330\) 116.323 6.40340
\(331\) −17.4093 −0.956902 −0.478451 0.878114i \(-0.658802\pi\)
−0.478451 + 0.878114i \(0.658802\pi\)
\(332\) −26.6858 −1.46457
\(333\) −4.54668 −0.249156
\(334\) −37.2488 −2.03817
\(335\) −11.9591 −0.653398
\(336\) 27.3062 1.48967
\(337\) −12.7783 −0.696078 −0.348039 0.937480i \(-0.613152\pi\)
−0.348039 + 0.937480i \(0.613152\pi\)
\(338\) 20.0821 1.09232
\(339\) 20.9373 1.13716
\(340\) 44.6184 2.41977
\(341\) −18.1234 −0.981437
\(342\) 75.1610 4.06424
\(343\) 19.2609 1.03999
\(344\) 62.0283 3.34434
\(345\) −55.7597 −3.00200
\(346\) −51.1194 −2.74820
\(347\) 16.9491 0.909875 0.454938 0.890523i \(-0.349662\pi\)
0.454938 + 0.890523i \(0.349662\pi\)
\(348\) −18.1300 −0.971870
\(349\) −6.61386 −0.354032 −0.177016 0.984208i \(-0.556644\pi\)
−0.177016 + 0.984208i \(0.556644\pi\)
\(350\) 40.5620 2.16813
\(351\) 9.47292 0.505627
\(352\) −12.2422 −0.652509
\(353\) −17.1758 −0.914178 −0.457089 0.889421i \(-0.651108\pi\)
−0.457089 + 0.889421i \(0.651108\pi\)
\(354\) −20.2897 −1.07839
\(355\) 38.1279 2.02362
\(356\) −70.0831 −3.71440
\(357\) 13.6051 0.720059
\(358\) 39.3562 2.08004
\(359\) 5.68775 0.300188 0.150094 0.988672i \(-0.452042\pi\)
0.150094 + 0.988672i \(0.452042\pi\)
\(360\) −96.4201 −5.08179
\(361\) 24.6859 1.29926
\(362\) 13.4354 0.706150
\(363\) −25.4954 −1.33816
\(364\) 16.8469 0.883017
\(365\) −23.9807 −1.25521
\(366\) 46.1986 2.41484
\(367\) 10.7412 0.560686 0.280343 0.959900i \(-0.409552\pi\)
0.280343 + 0.959900i \(0.409552\pi\)
\(368\) 30.2228 1.57547
\(369\) 52.8109 2.74923
\(370\) 9.40258 0.488817
\(371\) 19.1284 0.993095
\(372\) 47.0454 2.43919
\(373\) −29.8133 −1.54367 −0.771836 0.635821i \(-0.780662\pi\)
−0.771836 + 0.635821i \(0.780662\pi\)
\(374\) −31.4140 −1.62438
\(375\) −42.6851 −2.20425
\(376\) 54.9110 2.83182
\(377\) −3.45768 −0.178079
\(378\) −18.8702 −0.970579
\(379\) −30.0416 −1.54313 −0.771567 0.636149i \(-0.780527\pi\)
−0.771567 + 0.636149i \(0.780527\pi\)
\(380\) −105.738 −5.42425
\(381\) 14.6695 0.751539
\(382\) −13.8512 −0.708689
\(383\) 18.5881 0.949810 0.474905 0.880037i \(-0.342482\pi\)
0.474905 + 0.880037i \(0.342482\pi\)
\(384\) −45.1428 −2.30368
\(385\) −30.0631 −1.53216
\(386\) 25.2128 1.28330
\(387\) −49.9953 −2.54140
\(388\) −52.6495 −2.67287
\(389\) 34.1304 1.73048 0.865241 0.501356i \(-0.167165\pi\)
0.865241 + 0.501356i \(0.167165\pi\)
\(390\) −57.5879 −2.91608
\(391\) 15.0583 0.761531
\(392\) 21.7001 1.09602
\(393\) −5.58695 −0.281824
\(394\) 1.71679 0.0864908
\(395\) −39.6300 −1.99400
\(396\) 87.1321 4.37855
\(397\) −26.9599 −1.35308 −0.676540 0.736405i \(-0.736522\pi\)
−0.676540 + 0.736405i \(0.736522\pi\)
\(398\) 42.9507 2.15293
\(399\) −32.2418 −1.61411
\(400\) 51.1247 2.55624
\(401\) −13.5162 −0.674968 −0.337484 0.941331i \(-0.609576\pi\)
−0.337484 + 0.941331i \(0.609576\pi\)
\(402\) −21.8568 −1.09012
\(403\) 8.97230 0.446942
\(404\) 15.8919 0.790652
\(405\) −7.39762 −0.367591
\(406\) 6.88776 0.341834
\(407\) −4.50342 −0.223226
\(408\) 43.2200 2.13971
\(409\) 13.2780 0.656556 0.328278 0.944581i \(-0.393532\pi\)
0.328278 + 0.944581i \(0.393532\pi\)
\(410\) −109.214 −5.39368
\(411\) 10.0177 0.494135
\(412\) 7.96776 0.392543
\(413\) 5.24374 0.258028
\(414\) −61.3968 −3.01749
\(415\) −23.5753 −1.15727
\(416\) 6.06069 0.297150
\(417\) −56.8583 −2.78436
\(418\) 74.4459 3.64127
\(419\) −29.3218 −1.43247 −0.716233 0.697861i \(-0.754135\pi\)
−0.716233 + 0.697861i \(0.754135\pi\)
\(420\) 78.0388 3.80790
\(421\) 28.5734 1.39258 0.696291 0.717760i \(-0.254832\pi\)
0.696291 + 0.717760i \(0.254832\pi\)
\(422\) 11.7010 0.569597
\(423\) −44.2587 −2.15193
\(424\) 60.7660 2.95106
\(425\) 25.4725 1.23560
\(426\) 69.6835 3.37618
\(427\) −11.9397 −0.577804
\(428\) −24.0925 −1.16455
\(429\) 27.5820 1.33167
\(430\) 103.391 4.98595
\(431\) 29.3912 1.41573 0.707863 0.706350i \(-0.249659\pi\)
0.707863 + 0.706350i \(0.249659\pi\)
\(432\) −23.7842 −1.14432
\(433\) −30.0483 −1.44403 −0.722014 0.691879i \(-0.756783\pi\)
−0.722014 + 0.691879i \(0.756783\pi\)
\(434\) −17.8730 −0.857931
\(435\) −16.0168 −0.767946
\(436\) −4.25541 −0.203797
\(437\) −35.6857 −1.70708
\(438\) −43.8277 −2.09417
\(439\) −1.81365 −0.0865608 −0.0432804 0.999063i \(-0.513781\pi\)
−0.0432804 + 0.999063i \(0.513781\pi\)
\(440\) −95.5028 −4.55292
\(441\) −17.4904 −0.832878
\(442\) 15.5520 0.739734
\(443\) 9.68617 0.460204 0.230102 0.973167i \(-0.426094\pi\)
0.230102 + 0.973167i \(0.426094\pi\)
\(444\) 11.6901 0.554790
\(445\) −61.9143 −2.93502
\(446\) 10.9556 0.518762
\(447\) −37.9622 −1.79555
\(448\) 7.80685 0.368839
\(449\) 9.52376 0.449454 0.224727 0.974422i \(-0.427851\pi\)
0.224727 + 0.974422i \(0.427851\pi\)
\(450\) −103.858 −4.89593
\(451\) 52.3085 2.46311
\(452\) −32.4328 −1.52551
\(453\) −13.5820 −0.638140
\(454\) 12.3749 0.580782
\(455\) 14.8832 0.697736
\(456\) −102.424 −4.79645
\(457\) 25.1797 1.17786 0.588929 0.808185i \(-0.299550\pi\)
0.588929 + 0.808185i \(0.299550\pi\)
\(458\) 6.76733 0.316217
\(459\) −11.8503 −0.553125
\(460\) 86.3743 4.02722
\(461\) 22.1288 1.03064 0.515319 0.856998i \(-0.327673\pi\)
0.515319 + 0.856998i \(0.327673\pi\)
\(462\) −54.9439 −2.55622
\(463\) 21.1050 0.980834 0.490417 0.871488i \(-0.336845\pi\)
0.490417 + 0.871488i \(0.336845\pi\)
\(464\) 8.68140 0.403024
\(465\) 41.5618 1.92738
\(466\) −72.4071 −3.35420
\(467\) −36.7561 −1.70087 −0.850435 0.526080i \(-0.823661\pi\)
−0.850435 + 0.526080i \(0.823661\pi\)
\(468\) −43.1362 −1.99397
\(469\) 5.64875 0.260835
\(470\) 91.5276 4.22185
\(471\) −61.3825 −2.82836
\(472\) 16.6581 0.766749
\(473\) −49.5197 −2.27692
\(474\) −72.4288 −3.32676
\(475\) −60.3657 −2.76977
\(476\) −21.0749 −0.965968
\(477\) −48.9779 −2.24254
\(478\) 0.238286 0.0108990
\(479\) −30.3823 −1.38820 −0.694102 0.719876i \(-0.744199\pi\)
−0.694102 + 0.719876i \(0.744199\pi\)
\(480\) 28.0745 1.28142
\(481\) 2.22949 0.101656
\(482\) −11.1369 −0.507270
\(483\) 26.3374 1.19839
\(484\) 39.4936 1.79516
\(485\) −46.5127 −2.11203
\(486\) −45.4007 −2.05942
\(487\) 33.0725 1.49866 0.749330 0.662197i \(-0.230376\pi\)
0.749330 + 0.662197i \(0.230376\pi\)
\(488\) −37.9295 −1.71699
\(489\) 25.7492 1.16442
\(490\) 36.1704 1.63401
\(491\) 8.48729 0.383026 0.191513 0.981490i \(-0.438661\pi\)
0.191513 + 0.981490i \(0.438661\pi\)
\(492\) −135.784 −6.12163
\(493\) 4.32544 0.194808
\(494\) −36.8557 −1.65822
\(495\) 76.9760 3.45982
\(496\) −22.5273 −1.01151
\(497\) −18.0093 −0.807826
\(498\) −43.0868 −1.93077
\(499\) 2.15049 0.0962692 0.0481346 0.998841i \(-0.484672\pi\)
0.0481346 + 0.998841i \(0.484672\pi\)
\(500\) 66.1211 2.95702
\(501\) −40.9131 −1.82786
\(502\) 30.0043 1.33916
\(503\) −2.94521 −0.131320 −0.0656601 0.997842i \(-0.520915\pi\)
−0.0656601 + 0.997842i \(0.520915\pi\)
\(504\) 45.5428 2.02864
\(505\) 14.0396 0.624752
\(506\) −60.8127 −2.70345
\(507\) 22.0576 0.979613
\(508\) −22.7236 −1.00820
\(509\) 27.1085 1.20156 0.600782 0.799413i \(-0.294856\pi\)
0.600782 + 0.799413i \(0.294856\pi\)
\(510\) 72.0406 3.19001
\(511\) 11.3270 0.501076
\(512\) 47.9364 2.11851
\(513\) 28.0833 1.23991
\(514\) 12.7517 0.562454
\(515\) 7.03904 0.310177
\(516\) 128.545 5.65888
\(517\) −43.8376 −1.92798
\(518\) −4.44119 −0.195135
\(519\) −56.1482 −2.46463
\(520\) 47.2803 2.07338
\(521\) −28.5679 −1.25158 −0.625790 0.779991i \(-0.715223\pi\)
−0.625790 + 0.779991i \(0.715223\pi\)
\(522\) −17.6360 −0.771907
\(523\) 8.28521 0.362287 0.181143 0.983457i \(-0.442020\pi\)
0.181143 + 0.983457i \(0.442020\pi\)
\(524\) 8.65444 0.378071
\(525\) 44.5522 1.94442
\(526\) 48.0392 2.09461
\(527\) −11.2241 −0.488928
\(528\) −69.2519 −3.01380
\(529\) 6.15058 0.267416
\(530\) 101.287 4.39962
\(531\) −13.4265 −0.582662
\(532\) 49.9441 2.16535
\(533\) −25.8962 −1.12169
\(534\) −113.156 −4.89674
\(535\) −21.2842 −0.920198
\(536\) 17.9447 0.775091
\(537\) 43.2278 1.86542
\(538\) 25.7082 1.10836
\(539\) −17.3240 −0.746198
\(540\) −67.9733 −2.92510
\(541\) 9.46904 0.407106 0.203553 0.979064i \(-0.434751\pi\)
0.203553 + 0.979064i \(0.434751\pi\)
\(542\) −14.3005 −0.614258
\(543\) 14.7571 0.633288
\(544\) −7.58173 −0.325064
\(545\) −3.75941 −0.161035
\(546\) 27.2009 1.16409
\(547\) −39.1040 −1.67197 −0.835983 0.548755i \(-0.815102\pi\)
−0.835983 + 0.548755i \(0.815102\pi\)
\(548\) −15.5178 −0.662888
\(549\) 30.5715 1.30476
\(550\) −102.870 −4.38640
\(551\) −10.2506 −0.436690
\(552\) 83.6673 3.56112
\(553\) 18.7187 0.796002
\(554\) −56.8089 −2.41358
\(555\) 10.3275 0.438380
\(556\) 88.0761 3.73526
\(557\) −8.96933 −0.380043 −0.190021 0.981780i \(-0.560856\pi\)
−0.190021 + 0.981780i \(0.560856\pi\)
\(558\) 45.7635 1.93732
\(559\) 24.5156 1.03690
\(560\) −37.3682 −1.57910
\(561\) −34.5043 −1.45677
\(562\) 56.1571 2.36885
\(563\) −36.8971 −1.55503 −0.777513 0.628867i \(-0.783519\pi\)
−0.777513 + 0.628867i \(0.783519\pi\)
\(564\) 113.795 4.79165
\(565\) −28.6524 −1.20542
\(566\) 39.7758 1.67190
\(567\) 3.49417 0.146742
\(568\) −57.2109 −2.40052
\(569\) −6.15740 −0.258131 −0.129066 0.991636i \(-0.541198\pi\)
−0.129066 + 0.991636i \(0.541198\pi\)
\(570\) −170.724 −7.15086
\(571\) −14.5119 −0.607303 −0.303652 0.952783i \(-0.598206\pi\)
−0.303652 + 0.952783i \(0.598206\pi\)
\(572\) −42.7258 −1.78646
\(573\) −15.2138 −0.635565
\(574\) 51.5857 2.15315
\(575\) 49.3109 2.05641
\(576\) −19.9893 −0.832888
\(577\) −42.7898 −1.78136 −0.890681 0.454629i \(-0.849772\pi\)
−0.890681 + 0.454629i \(0.849772\pi\)
\(578\) 23.0633 0.959308
\(579\) 27.6930 1.15088
\(580\) 24.8107 1.03021
\(581\) 11.1355 0.461978
\(582\) −85.0076 −3.52368
\(583\) −48.5119 −2.00916
\(584\) 35.9830 1.48899
\(585\) −38.1083 −1.57558
\(586\) −70.2377 −2.90149
\(587\) −29.9670 −1.23687 −0.618436 0.785835i \(-0.712233\pi\)
−0.618436 + 0.785835i \(0.712233\pi\)
\(588\) 44.9703 1.85455
\(589\) 26.5992 1.09600
\(590\) 27.7662 1.14312
\(591\) 1.88568 0.0775665
\(592\) −5.59772 −0.230065
\(593\) −16.3470 −0.671292 −0.335646 0.941988i \(-0.608955\pi\)
−0.335646 + 0.941988i \(0.608955\pi\)
\(594\) 47.8572 1.96361
\(595\) −18.6184 −0.763282
\(596\) 58.8052 2.40875
\(597\) 47.1759 1.93078
\(598\) 30.1063 1.23114
\(599\) −21.9570 −0.897138 −0.448569 0.893748i \(-0.648066\pi\)
−0.448569 + 0.893748i \(0.648066\pi\)
\(600\) 141.531 5.77798
\(601\) −17.1625 −0.700073 −0.350036 0.936736i \(-0.613831\pi\)
−0.350036 + 0.936736i \(0.613831\pi\)
\(602\) −48.8354 −1.99038
\(603\) −14.4635 −0.589001
\(604\) 21.0392 0.856072
\(605\) 34.8902 1.41849
\(606\) 25.6590 1.04233
\(607\) −40.3817 −1.63904 −0.819521 0.573049i \(-0.805760\pi\)
−0.819521 + 0.573049i \(0.805760\pi\)
\(608\) 17.9674 0.728676
\(609\) 7.56533 0.306562
\(610\) −63.2223 −2.55980
\(611\) 21.7026 0.877992
\(612\) 53.9621 2.18129
\(613\) −38.1289 −1.54001 −0.770007 0.638036i \(-0.779747\pi\)
−0.770007 + 0.638036i \(0.779747\pi\)
\(614\) 31.9743 1.29038
\(615\) −119.957 −4.83715
\(616\) 45.1095 1.81752
\(617\) 39.2989 1.58211 0.791057 0.611743i \(-0.209531\pi\)
0.791057 + 0.611743i \(0.209531\pi\)
\(618\) 12.8647 0.517495
\(619\) 47.8885 1.92480 0.962400 0.271637i \(-0.0875651\pi\)
0.962400 + 0.271637i \(0.0875651\pi\)
\(620\) −64.3811 −2.58561
\(621\) −22.9404 −0.920566
\(622\) −36.9008 −1.47959
\(623\) 29.2444 1.17165
\(624\) 34.2843 1.37247
\(625\) 12.7484 0.509936
\(626\) 13.0619 0.522057
\(627\) 81.7694 3.26555
\(628\) 95.0842 3.79427
\(629\) −2.78903 −0.111206
\(630\) 75.9124 3.02442
\(631\) −3.39586 −0.135187 −0.0675935 0.997713i \(-0.521532\pi\)
−0.0675935 + 0.997713i \(0.521532\pi\)
\(632\) 59.4647 2.36538
\(633\) 12.8521 0.510825
\(634\) 7.12059 0.282795
\(635\) −20.0750 −0.796651
\(636\) 125.929 4.99341
\(637\) 8.57655 0.339815
\(638\) −17.4682 −0.691573
\(639\) 46.1125 1.82418
\(640\) 61.7774 2.44197
\(641\) −4.24075 −0.167499 −0.0837497 0.996487i \(-0.526690\pi\)
−0.0837497 + 0.996487i \(0.526690\pi\)
\(642\) −38.8996 −1.53524
\(643\) 36.9933 1.45888 0.729438 0.684047i \(-0.239782\pi\)
0.729438 + 0.684047i \(0.239782\pi\)
\(644\) −40.7978 −1.60766
\(645\) 113.562 4.47149
\(646\) 46.1053 1.81399
\(647\) 1.07387 0.0422183 0.0211092 0.999777i \(-0.493280\pi\)
0.0211092 + 0.999777i \(0.493280\pi\)
\(648\) 11.1001 0.436054
\(649\) −13.2988 −0.522023
\(650\) 50.9277 1.99755
\(651\) −19.6312 −0.769407
\(652\) −39.8866 −1.56208
\(653\) −5.36182 −0.209824 −0.104912 0.994481i \(-0.533456\pi\)
−0.104912 + 0.994481i \(0.533456\pi\)
\(654\) −6.87078 −0.268669
\(655\) 7.64568 0.298742
\(656\) 65.0192 2.53857
\(657\) −29.0026 −1.13150
\(658\) −43.2319 −1.68536
\(659\) 45.0898 1.75645 0.878224 0.478250i \(-0.158729\pi\)
0.878224 + 0.478250i \(0.158729\pi\)
\(660\) −197.916 −7.70388
\(661\) −21.3253 −0.829457 −0.414729 0.909945i \(-0.636123\pi\)
−0.414729 + 0.909945i \(0.636123\pi\)
\(662\) 43.5421 1.69231
\(663\) 17.0819 0.663407
\(664\) 35.3747 1.37280
\(665\) 44.1226 1.71100
\(666\) 11.3716 0.440641
\(667\) 8.37340 0.324219
\(668\) 63.3762 2.45210
\(669\) 12.0333 0.465235
\(670\) 29.9108 1.15555
\(671\) 30.2807 1.16897
\(672\) −13.2607 −0.511541
\(673\) 41.9257 1.61612 0.808058 0.589103i \(-0.200519\pi\)
0.808058 + 0.589103i \(0.200519\pi\)
\(674\) 31.9596 1.23104
\(675\) −38.8058 −1.49364
\(676\) −34.1682 −1.31416
\(677\) 15.6844 0.602799 0.301399 0.953498i \(-0.402546\pi\)
0.301399 + 0.953498i \(0.402546\pi\)
\(678\) −52.3659 −2.01110
\(679\) 21.9697 0.843119
\(680\) −59.1461 −2.26815
\(681\) 13.5922 0.520856
\(682\) 45.3281 1.73570
\(683\) 47.2032 1.80618 0.903090 0.429451i \(-0.141293\pi\)
0.903090 + 0.429451i \(0.141293\pi\)
\(684\) −127.881 −4.88966
\(685\) −13.7091 −0.523796
\(686\) −48.1730 −1.83925
\(687\) 7.43305 0.283589
\(688\) −61.5527 −2.34667
\(689\) 24.0167 0.914962
\(690\) 139.460 5.30914
\(691\) −35.3951 −1.34649 −0.673246 0.739419i \(-0.735101\pi\)
−0.673246 + 0.739419i \(0.735101\pi\)
\(692\) 86.9761 3.30633
\(693\) −36.3587 −1.38115
\(694\) −42.3911 −1.60914
\(695\) 77.8100 2.95150
\(696\) 24.0331 0.910974
\(697\) 32.3953 1.22706
\(698\) 16.5418 0.626117
\(699\) −79.5300 −3.00810
\(700\) −69.0133 −2.60846
\(701\) 38.7447 1.46337 0.731683 0.681645i \(-0.238735\pi\)
0.731683 + 0.681645i \(0.238735\pi\)
\(702\) −23.6925 −0.894217
\(703\) 6.60953 0.249283
\(704\) −19.7991 −0.746208
\(705\) 100.531 3.78623
\(706\) 42.9582 1.61675
\(707\) −6.63141 −0.249400
\(708\) 34.5215 1.29740
\(709\) −37.8365 −1.42098 −0.710490 0.703707i \(-0.751527\pi\)
−0.710490 + 0.703707i \(0.751527\pi\)
\(710\) −95.3612 −3.57884
\(711\) −47.9291 −1.79748
\(712\) 92.9022 3.48166
\(713\) −21.7281 −0.813722
\(714\) −34.0275 −1.27345
\(715\) −37.7457 −1.41161
\(716\) −66.9618 −2.50248
\(717\) 0.261727 0.00977438
\(718\) −14.2255 −0.530892
\(719\) −26.3921 −0.984259 −0.492129 0.870522i \(-0.663781\pi\)
−0.492129 + 0.870522i \(0.663781\pi\)
\(720\) 95.6808 3.56581
\(721\) −3.32480 −0.123822
\(722\) −61.7414 −2.29778
\(723\) −12.2324 −0.454929
\(724\) −22.8594 −0.849563
\(725\) 14.1644 0.526052
\(726\) 63.7662 2.36658
\(727\) 4.00161 0.148411 0.0742057 0.997243i \(-0.476358\pi\)
0.0742057 + 0.997243i \(0.476358\pi\)
\(728\) −22.3322 −0.827688
\(729\) −43.9636 −1.62828
\(730\) 59.9777 2.21988
\(731\) −30.6682 −1.13430
\(732\) −78.6037 −2.90528
\(733\) −24.6358 −0.909944 −0.454972 0.890506i \(-0.650351\pi\)
−0.454972 + 0.890506i \(0.650351\pi\)
\(734\) −26.8646 −0.991591
\(735\) 39.7286 1.46541
\(736\) −14.6771 −0.541004
\(737\) −14.3259 −0.527703
\(738\) −132.085 −4.86210
\(739\) −8.83046 −0.324834 −0.162417 0.986722i \(-0.551929\pi\)
−0.162417 + 0.986722i \(0.551929\pi\)
\(740\) −15.9978 −0.588092
\(741\) −40.4813 −1.48712
\(742\) −47.8416 −1.75632
\(743\) −23.7277 −0.870485 −0.435242 0.900313i \(-0.643337\pi\)
−0.435242 + 0.900313i \(0.643337\pi\)
\(744\) −62.3634 −2.28635
\(745\) 51.9509 1.90333
\(746\) 74.5655 2.73004
\(747\) −28.5123 −1.04321
\(748\) 53.4487 1.95428
\(749\) 10.0533 0.367341
\(750\) 106.759 3.89828
\(751\) −18.5947 −0.678530 −0.339265 0.940691i \(-0.610178\pi\)
−0.339265 + 0.940691i \(0.610178\pi\)
\(752\) −54.4899 −1.98704
\(753\) 32.9559 1.20098
\(754\) 8.64794 0.314939
\(755\) 18.5869 0.676445
\(756\) 32.1063 1.16770
\(757\) 25.8715 0.940315 0.470157 0.882583i \(-0.344197\pi\)
0.470157 + 0.882583i \(0.344197\pi\)
\(758\) 75.1365 2.72908
\(759\) −66.7950 −2.42450
\(760\) 140.166 5.08437
\(761\) 21.1880 0.768065 0.384032 0.923320i \(-0.374535\pi\)
0.384032 + 0.923320i \(0.374535\pi\)
\(762\) −36.6895 −1.32912
\(763\) 1.77571 0.0642850
\(764\) 23.5668 0.852618
\(765\) 47.6723 1.72359
\(766\) −46.4905 −1.67977
\(767\) 6.58379 0.237727
\(768\) 88.7506 3.20251
\(769\) 18.3133 0.660394 0.330197 0.943912i \(-0.392885\pi\)
0.330197 + 0.943912i \(0.392885\pi\)
\(770\) 75.1902 2.70967
\(771\) 14.0061 0.504419
\(772\) −42.8978 −1.54392
\(773\) 24.6088 0.885118 0.442559 0.896740i \(-0.354071\pi\)
0.442559 + 0.896740i \(0.354071\pi\)
\(774\) 125.042 4.49456
\(775\) −36.7550 −1.32028
\(776\) 69.7921 2.50539
\(777\) −4.87809 −0.175000
\(778\) −85.3630 −3.06041
\(779\) −76.7715 −2.75063
\(780\) 97.9818 3.50831
\(781\) 45.6737 1.63434
\(782\) −37.6621 −1.34679
\(783\) −6.58955 −0.235491
\(784\) −21.5337 −0.769059
\(785\) 84.0013 2.99813
\(786\) 13.9734 0.498416
\(787\) 24.0390 0.856897 0.428449 0.903566i \(-0.359060\pi\)
0.428449 + 0.903566i \(0.359060\pi\)
\(788\) −2.92100 −0.104056
\(789\) 52.7649 1.87848
\(790\) 99.1180 3.52646
\(791\) 13.5336 0.481200
\(792\) −115.502 −4.10420
\(793\) −14.9910 −0.532345
\(794\) 67.4291 2.39297
\(795\) 111.251 3.94566
\(796\) −73.0776 −2.59017
\(797\) −51.9727 −1.84097 −0.920484 0.390779i \(-0.872206\pi\)
−0.920484 + 0.390779i \(0.872206\pi\)
\(798\) 80.6395 2.85461
\(799\) −27.1492 −0.960470
\(800\) −24.8276 −0.877789
\(801\) −74.8800 −2.64575
\(802\) 33.8052 1.19370
\(803\) −28.7267 −1.01374
\(804\) 37.1878 1.31151
\(805\) −36.0425 −1.27033
\(806\) −22.4405 −0.790432
\(807\) 28.2372 0.993996
\(808\) −21.0663 −0.741111
\(809\) −51.6974 −1.81759 −0.908793 0.417248i \(-0.862995\pi\)
−0.908793 + 0.417248i \(0.862995\pi\)
\(810\) 18.5021 0.650096
\(811\) −36.2942 −1.27446 −0.637230 0.770674i \(-0.719920\pi\)
−0.637230 + 0.770674i \(0.719920\pi\)
\(812\) −11.7190 −0.411257
\(813\) −15.7073 −0.550877
\(814\) 11.2634 0.394783
\(815\) −35.2374 −1.23431
\(816\) −42.8886 −1.50140
\(817\) 72.6785 2.54270
\(818\) −33.2094 −1.16114
\(819\) 18.0000 0.628970
\(820\) 185.819 6.48909
\(821\) 6.98642 0.243828 0.121914 0.992541i \(-0.461097\pi\)
0.121914 + 0.992541i \(0.461097\pi\)
\(822\) −25.0550 −0.873893
\(823\) 37.5741 1.30975 0.654875 0.755737i \(-0.272721\pi\)
0.654875 + 0.755737i \(0.272721\pi\)
\(824\) −10.5621 −0.367947
\(825\) −112.990 −3.93380
\(826\) −13.1150 −0.456330
\(827\) 32.0081 1.11303 0.556516 0.830837i \(-0.312138\pi\)
0.556516 + 0.830837i \(0.312138\pi\)
\(828\) 104.462 3.63032
\(829\) 5.74489 0.199528 0.0997642 0.995011i \(-0.468191\pi\)
0.0997642 + 0.995011i \(0.468191\pi\)
\(830\) 58.9638 2.04666
\(831\) −62.3974 −2.16454
\(832\) 9.80190 0.339820
\(833\) −10.7290 −0.371738
\(834\) 142.207 4.92424
\(835\) 55.9891 1.93758
\(836\) −126.664 −4.38078
\(837\) 17.0992 0.591033
\(838\) 73.3364 2.53336
\(839\) −1.50858 −0.0520820 −0.0260410 0.999661i \(-0.508290\pi\)
−0.0260410 + 0.999661i \(0.508290\pi\)
\(840\) −103.448 −3.56930
\(841\) −26.5948 −0.917061
\(842\) −71.4644 −2.46283
\(843\) 61.6815 2.12442
\(844\) −19.9085 −0.685278
\(845\) −30.1856 −1.03842
\(846\) 110.695 3.80576
\(847\) −16.4800 −0.566258
\(848\) −60.3001 −2.07071
\(849\) 43.6886 1.49939
\(850\) −63.7089 −2.18520
\(851\) −5.39913 −0.185080
\(852\) −118.562 −4.06185
\(853\) −42.4939 −1.45496 −0.727482 0.686127i \(-0.759309\pi\)
−0.727482 + 0.686127i \(0.759309\pi\)
\(854\) 29.8623 1.02187
\(855\) −112.975 −3.86367
\(856\) 31.9370 1.09158
\(857\) 14.0921 0.481376 0.240688 0.970603i \(-0.422627\pi\)
0.240688 + 0.970603i \(0.422627\pi\)
\(858\) −68.9850 −2.35511
\(859\) 22.2933 0.760636 0.380318 0.924856i \(-0.375815\pi\)
0.380318 + 0.924856i \(0.375815\pi\)
\(860\) −175.912 −5.99856
\(861\) 56.6604 1.93098
\(862\) −73.5099 −2.50376
\(863\) 50.3130 1.71267 0.856337 0.516417i \(-0.172734\pi\)
0.856337 + 0.516417i \(0.172734\pi\)
\(864\) 11.5503 0.392949
\(865\) 76.8382 2.61258
\(866\) 75.1532 2.55381
\(867\) 25.3321 0.860324
\(868\) 30.4096 1.03217
\(869\) −47.4731 −1.61041
\(870\) 40.0593 1.35814
\(871\) 7.09230 0.240313
\(872\) 5.64098 0.191028
\(873\) −56.2530 −1.90388
\(874\) 89.2529 3.01902
\(875\) −27.5911 −0.932751
\(876\) 74.5697 2.51948
\(877\) −10.1060 −0.341256 −0.170628 0.985336i \(-0.554580\pi\)
−0.170628 + 0.985336i \(0.554580\pi\)
\(878\) 4.53609 0.153086
\(879\) −77.1472 −2.60211
\(880\) 94.7705 3.19471
\(881\) −47.2631 −1.59233 −0.796167 0.605077i \(-0.793142\pi\)
−0.796167 + 0.605077i \(0.793142\pi\)
\(882\) 43.7450 1.47297
\(883\) 49.0860 1.65187 0.825937 0.563762i \(-0.190647\pi\)
0.825937 + 0.563762i \(0.190647\pi\)
\(884\) −26.4607 −0.889969
\(885\) 30.4977 1.02517
\(886\) −24.2259 −0.813886
\(887\) −8.79015 −0.295144 −0.147572 0.989051i \(-0.547146\pi\)
−0.147572 + 0.989051i \(0.547146\pi\)
\(888\) −15.4965 −0.520027
\(889\) 9.48217 0.318022
\(890\) 154.853 5.19067
\(891\) −8.86166 −0.296877
\(892\) −18.6402 −0.624118
\(893\) 64.3391 2.15303
\(894\) 94.9466 3.17549
\(895\) −59.1568 −1.97739
\(896\) −29.1798 −0.974828
\(897\) 33.0680 1.10411
\(898\) −23.8197 −0.794874
\(899\) −6.24131 −0.208159
\(900\) 176.708 5.89026
\(901\) −30.0441 −1.00091
\(902\) −130.828 −4.35609
\(903\) −53.6395 −1.78501
\(904\) 42.9929 1.42992
\(905\) −20.1949 −0.671302
\(906\) 33.9698 1.12857
\(907\) 36.5862 1.21483 0.607413 0.794386i \(-0.292207\pi\)
0.607413 + 0.794386i \(0.292207\pi\)
\(908\) −21.0550 −0.698735
\(909\) 16.9796 0.563179
\(910\) −37.2242 −1.23397
\(911\) −52.0158 −1.72336 −0.861679 0.507453i \(-0.830587\pi\)
−0.861679 + 0.507453i \(0.830587\pi\)
\(912\) 101.639 3.36560
\(913\) −28.2410 −0.934642
\(914\) −62.9765 −2.08308
\(915\) −69.4417 −2.29567
\(916\) −11.5141 −0.380438
\(917\) −3.61134 −0.119257
\(918\) 29.6386 0.978220
\(919\) −30.5085 −1.00638 −0.503191 0.864175i \(-0.667841\pi\)
−0.503191 + 0.864175i \(0.667841\pi\)
\(920\) −114.498 −3.77488
\(921\) 35.1197 1.15724
\(922\) −55.3459 −1.82272
\(923\) −22.6116 −0.744269
\(924\) 93.4832 3.07537
\(925\) −9.13313 −0.300295
\(926\) −52.7854 −1.73464
\(927\) 8.51311 0.279607
\(928\) −4.21593 −0.138395
\(929\) −17.6283 −0.578367 −0.289183 0.957274i \(-0.593384\pi\)
−0.289183 + 0.957274i \(0.593384\pi\)
\(930\) −103.950 −3.40864
\(931\) 25.4259 0.833301
\(932\) 123.196 4.03541
\(933\) −40.5308 −1.32692
\(934\) 91.9301 3.00804
\(935\) 47.2187 1.54422
\(936\) 57.1814 1.86903
\(937\) −13.6281 −0.445211 −0.222606 0.974909i \(-0.571456\pi\)
−0.222606 + 0.974909i \(0.571456\pi\)
\(938\) −14.1280 −0.461295
\(939\) 14.3468 0.468190
\(940\) −155.728 −5.07928
\(941\) −16.9766 −0.553421 −0.276711 0.960953i \(-0.589244\pi\)
−0.276711 + 0.960953i \(0.589244\pi\)
\(942\) 153.523 5.00204
\(943\) 62.7124 2.04220
\(944\) −16.5303 −0.538016
\(945\) 28.3640 0.922682
\(946\) 123.853 4.02680
\(947\) −52.7863 −1.71532 −0.857662 0.514214i \(-0.828084\pi\)
−0.857662 + 0.514214i \(0.828084\pi\)
\(948\) 123.232 4.00240
\(949\) 14.2216 0.461653
\(950\) 150.980 4.89842
\(951\) 7.82106 0.253615
\(952\) 27.9369 0.905441
\(953\) −29.5778 −0.958120 −0.479060 0.877782i \(-0.659022\pi\)
−0.479060 + 0.877782i \(0.659022\pi\)
\(954\) 122.498 3.96601
\(955\) 20.8199 0.673716
\(956\) −0.405427 −0.0131124
\(957\) −19.1866 −0.620215
\(958\) 75.9888 2.45509
\(959\) 6.47530 0.209098
\(960\) 45.4047 1.46543
\(961\) −14.8045 −0.477564
\(962\) −5.57615 −0.179782
\(963\) −25.7415 −0.829507
\(964\) 18.9486 0.610292
\(965\) −37.8976 −1.21997
\(966\) −65.8720 −2.11940
\(967\) −20.1261 −0.647210 −0.323605 0.946192i \(-0.604895\pi\)
−0.323605 + 0.946192i \(0.604895\pi\)
\(968\) −52.3527 −1.68268
\(969\) 50.6408 1.62682
\(970\) 116.332 3.73520
\(971\) −11.7292 −0.376407 −0.188203 0.982130i \(-0.560266\pi\)
−0.188203 + 0.982130i \(0.560266\pi\)
\(972\) 77.2460 2.47767
\(973\) −36.7526 −1.17823
\(974\) −82.7171 −2.65043
\(975\) 55.9376 1.79144
\(976\) 37.6387 1.20479
\(977\) 31.0277 0.992665 0.496333 0.868132i \(-0.334680\pi\)
0.496333 + 0.868132i \(0.334680\pi\)
\(978\) −64.4008 −2.05931
\(979\) −74.1675 −2.37040
\(980\) −61.5414 −1.96587
\(981\) −4.54668 −0.145164
\(982\) −21.2274 −0.677394
\(983\) −25.3519 −0.808599 −0.404299 0.914627i \(-0.632485\pi\)
−0.404299 + 0.914627i \(0.632485\pi\)
\(984\) 179.996 5.73805
\(985\) −2.58053 −0.0822226
\(986\) −10.8183 −0.344525
\(987\) −47.4848 −1.51146
\(988\) 62.7074 1.99499
\(989\) −59.3689 −1.88782
\(990\) −192.523 −6.11880
\(991\) −46.7573 −1.48529 −0.742647 0.669683i \(-0.766430\pi\)
−0.742647 + 0.669683i \(0.766430\pi\)
\(992\) 10.9399 0.347342
\(993\) 47.8255 1.51770
\(994\) 45.0427 1.42867
\(995\) −64.5597 −2.04668
\(996\) 73.3091 2.32289
\(997\) −5.36141 −0.169798 −0.0848989 0.996390i \(-0.527057\pi\)
−0.0848989 + 0.996390i \(0.527057\pi\)
\(998\) −5.37856 −0.170255
\(999\) 4.24891 0.134429
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 \(a_p\))