Properties

Label 4033.2.a.d.1.13
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 1.13
Character \(\chi\) = 4033.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.24777 q^{2}\) \(-0.430015 q^{3}\) \(+3.05245 q^{4}\) \(-2.54923 q^{5}\) \(+0.966572 q^{6}\) \(-1.16281 q^{7}\) \(-2.36567 q^{8}\) \(-2.81509 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.24777 q^{2}\) \(-0.430015 q^{3}\) \(+3.05245 q^{4}\) \(-2.54923 q^{5}\) \(+0.966572 q^{6}\) \(-1.16281 q^{7}\) \(-2.36567 q^{8}\) \(-2.81509 q^{9}\) \(+5.73008 q^{10}\) \(-4.74947 q^{11}\) \(-1.31260 q^{12}\) \(+7.05536 q^{13}\) \(+2.61373 q^{14}\) \(+1.09621 q^{15}\) \(-0.787431 q^{16}\) \(+0.294550 q^{17}\) \(+6.32766 q^{18}\) \(-2.10260 q^{19}\) \(-7.78141 q^{20}\) \(+0.500025 q^{21}\) \(+10.6757 q^{22}\) \(+0.0839506 q^{23}\) \(+1.01727 q^{24}\) \(+1.49858 q^{25}\) \(-15.8588 q^{26}\) \(+2.50057 q^{27}\) \(-3.54943 q^{28}\) \(+2.00176 q^{29}\) \(-2.46402 q^{30}\) \(-3.70206 q^{31}\) \(+6.50130 q^{32}\) \(+2.04234 q^{33}\) \(-0.662080 q^{34}\) \(+2.96427 q^{35}\) \(-8.59293 q^{36}\) \(-1.00000 q^{37}\) \(+4.72616 q^{38}\) \(-3.03391 q^{39}\) \(+6.03065 q^{40}\) \(-4.65519 q^{41}\) \(-1.12394 q^{42}\) \(+10.0771 q^{43}\) \(-14.4976 q^{44}\) \(+7.17631 q^{45}\) \(-0.188701 q^{46}\) \(+9.77592 q^{47}\) \(+0.338607 q^{48}\) \(-5.64787 q^{49}\) \(-3.36846 q^{50}\) \(-0.126661 q^{51}\) \(+21.5362 q^{52}\) \(-1.02973 q^{53}\) \(-5.62070 q^{54}\) \(+12.1075 q^{55}\) \(+2.75083 q^{56}\) \(+0.904149 q^{57}\) \(-4.49948 q^{58}\) \(-5.69236 q^{59}\) \(+3.34612 q^{60}\) \(+12.6845 q^{61}\) \(+8.32137 q^{62}\) \(+3.27341 q^{63}\) \(-13.0386 q^{64}\) \(-17.9858 q^{65}\) \(-4.59071 q^{66}\) \(+2.67338 q^{67}\) \(+0.899101 q^{68}\) \(-0.0361000 q^{69}\) \(-6.66299 q^{70}\) \(+1.82350 q^{71}\) \(+6.65957 q^{72}\) \(+2.80184 q^{73}\) \(+2.24777 q^{74}\) \(-0.644412 q^{75}\) \(-6.41810 q^{76}\) \(+5.52274 q^{77}\) \(+6.81952 q^{78}\) \(+10.8000 q^{79}\) \(+2.00734 q^{80}\) \(+7.36998 q^{81}\) \(+10.4638 q^{82}\) \(+3.88417 q^{83}\) \(+1.52630 q^{84}\) \(-0.750877 q^{85}\) \(-22.6510 q^{86}\) \(-0.860785 q^{87}\) \(+11.2357 q^{88}\) \(-0.146585 q^{89}\) \(-16.1307 q^{90}\) \(-8.20405 q^{91}\) \(+0.256255 q^{92}\) \(+1.59194 q^{93}\) \(-21.9740 q^{94}\) \(+5.36002 q^{95}\) \(-2.79566 q^{96}\) \(+16.0336 q^{97}\) \(+12.6951 q^{98}\) \(+13.3702 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut -\mathstrut 13q^{10} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut -\mathstrut 40q^{12} \) \(\mathstrut -\mathstrut 18q^{13} \) \(\mathstrut -\mathstrut 42q^{14} \) \(\mathstrut -\mathstrut 49q^{15} \) \(\mathstrut +\mathstrut 83q^{16} \) \(\mathstrut -\mathstrut 62q^{17} \) \(\mathstrut -\mathstrut 33q^{18} \) \(\mathstrut -\mathstrut 25q^{19} \) \(\mathstrut -\mathstrut 39q^{20} \) \(\mathstrut -\mathstrut 15q^{21} \) \(\mathstrut -\mathstrut 31q^{22} \) \(\mathstrut -\mathstrut 94q^{23} \) \(\mathstrut -\mathstrut 39q^{24} \) \(\mathstrut +\mathstrut 71q^{25} \) \(\mathstrut -\mathstrut 35q^{26} \) \(\mathstrut -\mathstrut 47q^{27} \) \(\mathstrut -\mathstrut 13q^{28} \) \(\mathstrut -\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 15q^{30} \) \(\mathstrut -\mathstrut 37q^{31} \) \(\mathstrut -\mathstrut 105q^{32} \) \(\mathstrut -\mathstrut 60q^{33} \) \(\mathstrut +\mathstrut 9q^{34} \) \(\mathstrut -\mathstrut 60q^{35} \) \(\mathstrut +\mathstrut 43q^{36} \) \(\mathstrut -\mathstrut 79q^{37} \) \(\mathstrut -\mathstrut 80q^{38} \) \(\mathstrut -\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 64q^{40} \) \(\mathstrut -\mathstrut 37q^{41} \) \(\mathstrut -\mathstrut 30q^{42} \) \(\mathstrut -\mathstrut 20q^{43} \) \(\mathstrut -\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 8q^{45} \) \(\mathstrut +\mathstrut 61q^{46} \) \(\mathstrut -\mathstrut 148q^{47} \) \(\mathstrut -\mathstrut 39q^{48} \) \(\mathstrut +\mathstrut 82q^{49} \) \(\mathstrut -\mathstrut 90q^{50} \) \(\mathstrut -\mathstrut 45q^{51} \) \(\mathstrut -\mathstrut 27q^{52} \) \(\mathstrut -\mathstrut 70q^{53} \) \(\mathstrut -\mathstrut 41q^{54} \) \(\mathstrut -\mathstrut 105q^{55} \) \(\mathstrut -\mathstrut 68q^{56} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut -\mathstrut 14q^{58} \) \(\mathstrut -\mathstrut 96q^{59} \) \(\mathstrut -\mathstrut 74q^{60} \) \(\mathstrut -\mathstrut 21q^{61} \) \(\mathstrut +\mathstrut 4q^{62} \) \(\mathstrut -\mathstrut 60q^{63} \) \(\mathstrut +\mathstrut 132q^{64} \) \(\mathstrut -\mathstrut 15q^{65} \) \(\mathstrut +\mathstrut 71q^{66} \) \(\mathstrut -\mathstrut 44q^{67} \) \(\mathstrut -\mathstrut 166q^{68} \) \(\mathstrut -\mathstrut 72q^{69} \) \(\mathstrut -\mathstrut 9q^{70} \) \(\mathstrut -\mathstrut 55q^{71} \) \(\mathstrut -\mathstrut 126q^{72} \) \(\mathstrut -\mathstrut 27q^{73} \) \(\mathstrut +\mathstrut 11q^{74} \) \(\mathstrut -\mathstrut 39q^{75} \) \(\mathstrut -\mathstrut 4q^{76} \) \(\mathstrut -\mathstrut 104q^{77} \) \(\mathstrut -\mathstrut 47q^{78} \) \(\mathstrut -\mathstrut 49q^{79} \) \(\mathstrut -\mathstrut 82q^{80} \) \(\mathstrut +\mathstrut 55q^{81} \) \(\mathstrut +\mathstrut 20q^{82} \) \(\mathstrut -\mathstrut 52q^{83} \) \(\mathstrut -\mathstrut 29q^{84} \) \(\mathstrut +\mathstrut 3q^{85} \) \(\mathstrut -\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 113q^{87} \) \(\mathstrut +\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 68q^{89} \) \(\mathstrut -\mathstrut 39q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 179q^{92} \) \(\mathstrut -\mathstrut 53q^{93} \) \(\mathstrut -\mathstrut 33q^{94} \) \(\mathstrut -\mathstrut 86q^{95} \) \(\mathstrut +\mathstrut 33q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut -\mathstrut 116q^{98} \) \(\mathstrut +\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.24777 −1.58941 −0.794705 0.606995i \(-0.792375\pi\)
−0.794705 + 0.606995i \(0.792375\pi\)
\(3\) −0.430015 −0.248269 −0.124135 0.992265i \(-0.539615\pi\)
−0.124135 + 0.992265i \(0.539615\pi\)
\(4\) 3.05245 1.52623
\(5\) −2.54923 −1.14005 −0.570026 0.821627i \(-0.693067\pi\)
−0.570026 + 0.821627i \(0.693067\pi\)
\(6\) 0.966572 0.394601
\(7\) −1.16281 −0.439501 −0.219750 0.975556i \(-0.570524\pi\)
−0.219750 + 0.975556i \(0.570524\pi\)
\(8\) −2.36567 −0.836391
\(9\) −2.81509 −0.938363
\(10\) 5.73008 1.81201
\(11\) −4.74947 −1.43202 −0.716010 0.698090i \(-0.754034\pi\)
−0.716010 + 0.698090i \(0.754034\pi\)
\(12\) −1.31260 −0.378915
\(13\) 7.05536 1.95681 0.978403 0.206709i \(-0.0662752\pi\)
0.978403 + 0.206709i \(0.0662752\pi\)
\(14\) 2.61373 0.698548
\(15\) 1.09621 0.283039
\(16\) −0.787431 −0.196858
\(17\) 0.294550 0.0714389 0.0357195 0.999362i \(-0.488628\pi\)
0.0357195 + 0.999362i \(0.488628\pi\)
\(18\) 6.32766 1.49144
\(19\) −2.10260 −0.482370 −0.241185 0.970479i \(-0.577536\pi\)
−0.241185 + 0.970479i \(0.577536\pi\)
\(20\) −7.78141 −1.73998
\(21\) 0.500025 0.109114
\(22\) 10.6757 2.27607
\(23\) 0.0839506 0.0175049 0.00875245 0.999962i \(-0.497214\pi\)
0.00875245 + 0.999962i \(0.497214\pi\)
\(24\) 1.01727 0.207650
\(25\) 1.49858 0.299716
\(26\) −15.8588 −3.11017
\(27\) 2.50057 0.481235
\(28\) −3.54943 −0.670778
\(29\) 2.00176 0.371717 0.185858 0.982577i \(-0.440493\pi\)
0.185858 + 0.982577i \(0.440493\pi\)
\(30\) −2.46402 −0.449866
\(31\) −3.70206 −0.664910 −0.332455 0.943119i \(-0.607877\pi\)
−0.332455 + 0.943119i \(0.607877\pi\)
\(32\) 6.50130 1.14928
\(33\) 2.04234 0.355526
\(34\) −0.662080 −0.113546
\(35\) 2.96427 0.501054
\(36\) −8.59293 −1.43215
\(37\) −1.00000 −0.164399
\(38\) 4.72616 0.766684
\(39\) −3.03391 −0.485814
\(40\) 6.03065 0.953529
\(41\) −4.65519 −0.727019 −0.363509 0.931591i \(-0.618422\pi\)
−0.363509 + 0.931591i \(0.618422\pi\)
\(42\) −1.12394 −0.173428
\(43\) 10.0771 1.53674 0.768372 0.640004i \(-0.221067\pi\)
0.768372 + 0.640004i \(0.221067\pi\)
\(44\) −14.4976 −2.18559
\(45\) 7.17631 1.06978
\(46\) −0.188701 −0.0278225
\(47\) 9.77592 1.42596 0.712982 0.701182i \(-0.247344\pi\)
0.712982 + 0.701182i \(0.247344\pi\)
\(48\) 0.338607 0.0488737
\(49\) −5.64787 −0.806839
\(50\) −3.36846 −0.476373
\(51\) −0.126661 −0.0177361
\(52\) 21.5362 2.98653
\(53\) −1.02973 −0.141444 −0.0707222 0.997496i \(-0.522530\pi\)
−0.0707222 + 0.997496i \(0.522530\pi\)
\(54\) −5.62070 −0.764881
\(55\) 12.1075 1.63258
\(56\) 2.75083 0.367595
\(57\) 0.904149 0.119758
\(58\) −4.49948 −0.590811
\(59\) −5.69236 −0.741082 −0.370541 0.928816i \(-0.620828\pi\)
−0.370541 + 0.928816i \(0.620828\pi\)
\(60\) 3.34612 0.431982
\(61\) 12.6845 1.62408 0.812041 0.583600i \(-0.198357\pi\)
0.812041 + 0.583600i \(0.198357\pi\)
\(62\) 8.32137 1.05681
\(63\) 3.27341 0.412411
\(64\) −13.0386 −1.62982
\(65\) −17.9858 −2.23086
\(66\) −4.59071 −0.565077
\(67\) 2.67338 0.326605 0.163302 0.986576i \(-0.447785\pi\)
0.163302 + 0.986576i \(0.447785\pi\)
\(68\) 0.899101 0.109032
\(69\) −0.0361000 −0.00434593
\(70\) −6.66299 −0.796380
\(71\) 1.82350 0.216410 0.108205 0.994129i \(-0.465490\pi\)
0.108205 + 0.994129i \(0.465490\pi\)
\(72\) 6.65957 0.784838
\(73\) 2.80184 0.327930 0.163965 0.986466i \(-0.447572\pi\)
0.163965 + 0.986466i \(0.447572\pi\)
\(74\) 2.24777 0.261298
\(75\) −0.644412 −0.0744103
\(76\) −6.41810 −0.736206
\(77\) 5.52274 0.629374
\(78\) 6.81952 0.772158
\(79\) 10.8000 1.21509 0.607545 0.794285i \(-0.292154\pi\)
0.607545 + 0.794285i \(0.292154\pi\)
\(80\) 2.00734 0.224428
\(81\) 7.36998 0.818887
\(82\) 10.4638 1.15553
\(83\) 3.88417 0.426343 0.213172 0.977015i \(-0.431621\pi\)
0.213172 + 0.977015i \(0.431621\pi\)
\(84\) 1.52630 0.166533
\(85\) −0.750877 −0.0814440
\(86\) −22.6510 −2.44252
\(87\) −0.860785 −0.0922858
\(88\) 11.2357 1.19773
\(89\) −0.146585 −0.0155380 −0.00776899 0.999970i \(-0.502473\pi\)
−0.00776899 + 0.999970i \(0.502473\pi\)
\(90\) −16.1307 −1.70032
\(91\) −8.20405 −0.860018
\(92\) 0.256255 0.0267165
\(93\) 1.59194 0.165076
\(94\) −21.9740 −2.26644
\(95\) 5.36002 0.549926
\(96\) −2.79566 −0.285330
\(97\) 16.0336 1.62797 0.813985 0.580886i \(-0.197294\pi\)
0.813985 + 0.580886i \(0.197294\pi\)
\(98\) 12.6951 1.28240
\(99\) 13.3702 1.34375
\(100\) 4.57435 0.457435
\(101\) −12.9748 −1.29104 −0.645522 0.763742i \(-0.723360\pi\)
−0.645522 + 0.763742i \(0.723360\pi\)
\(102\) 0.284704 0.0281899
\(103\) 2.59612 0.255804 0.127902 0.991787i \(-0.459176\pi\)
0.127902 + 0.991787i \(0.459176\pi\)
\(104\) −16.6907 −1.63665
\(105\) −1.27468 −0.124396
\(106\) 2.31460 0.224813
\(107\) −19.0742 −1.84398 −0.921988 0.387217i \(-0.873436\pi\)
−0.921988 + 0.387217i \(0.873436\pi\)
\(108\) 7.63288 0.734474
\(109\) −1.00000 −0.0957826
\(110\) −27.2149 −2.59484
\(111\) 0.430015 0.0408152
\(112\) 0.915632 0.0865191
\(113\) 5.69733 0.535960 0.267980 0.963425i \(-0.413644\pi\)
0.267980 + 0.963425i \(0.413644\pi\)
\(114\) −2.03232 −0.190344
\(115\) −0.214009 −0.0199565
\(116\) 6.11027 0.567325
\(117\) −19.8615 −1.83619
\(118\) 12.7951 1.17788
\(119\) −0.342506 −0.0313975
\(120\) −2.59327 −0.236732
\(121\) 11.5575 1.05068
\(122\) −28.5118 −2.58133
\(123\) 2.00180 0.180496
\(124\) −11.3004 −1.01480
\(125\) 8.92593 0.798359
\(126\) −7.35787 −0.655491
\(127\) −7.68914 −0.682301 −0.341150 0.940009i \(-0.610817\pi\)
−0.341150 + 0.940009i \(0.610817\pi\)
\(128\) 16.3050 1.44117
\(129\) −4.33330 −0.381526
\(130\) 40.4278 3.54575
\(131\) −10.1462 −0.886477 −0.443238 0.896404i \(-0.646170\pi\)
−0.443238 + 0.896404i \(0.646170\pi\)
\(132\) 6.23416 0.542614
\(133\) 2.44493 0.212002
\(134\) −6.00912 −0.519109
\(135\) −6.37454 −0.548633
\(136\) −0.696809 −0.0597509
\(137\) −10.8127 −0.923794 −0.461897 0.886934i \(-0.652831\pi\)
−0.461897 + 0.886934i \(0.652831\pi\)
\(138\) 0.0811443 0.00690746
\(139\) −13.7521 −1.16644 −0.583218 0.812316i \(-0.698207\pi\)
−0.583218 + 0.812316i \(0.698207\pi\)
\(140\) 9.04831 0.764722
\(141\) −4.20379 −0.354023
\(142\) −4.09881 −0.343964
\(143\) −33.5093 −2.80219
\(144\) 2.21669 0.184724
\(145\) −5.10294 −0.423776
\(146\) −6.29788 −0.521216
\(147\) 2.42867 0.200313
\(148\) −3.05245 −0.250910
\(149\) 23.5174 1.92662 0.963309 0.268396i \(-0.0864935\pi\)
0.963309 + 0.268396i \(0.0864935\pi\)
\(150\) 1.44849 0.118269
\(151\) 5.90896 0.480864 0.240432 0.970666i \(-0.422711\pi\)
0.240432 + 0.970666i \(0.422711\pi\)
\(152\) 4.97407 0.403450
\(153\) −0.829185 −0.0670356
\(154\) −12.4138 −1.00033
\(155\) 9.43741 0.758031
\(156\) −9.26087 −0.741463
\(157\) −10.1050 −0.806464 −0.403232 0.915098i \(-0.632113\pi\)
−0.403232 + 0.915098i \(0.632113\pi\)
\(158\) −24.2758 −1.93128
\(159\) 0.442799 0.0351163
\(160\) −16.5733 −1.31024
\(161\) −0.0976186 −0.00769342
\(162\) −16.5660 −1.30155
\(163\) 16.7315 1.31051 0.655255 0.755408i \(-0.272561\pi\)
0.655255 + 0.755408i \(0.272561\pi\)
\(164\) −14.2098 −1.10960
\(165\) −5.20641 −0.405318
\(166\) −8.73071 −0.677635
\(167\) 10.6026 0.820456 0.410228 0.911983i \(-0.365449\pi\)
0.410228 + 0.911983i \(0.365449\pi\)
\(168\) −1.18290 −0.0912624
\(169\) 36.7781 2.82909
\(170\) 1.68780 0.129448
\(171\) 5.91901 0.452638
\(172\) 30.7599 2.34542
\(173\) −11.7940 −0.896685 −0.448342 0.893862i \(-0.647985\pi\)
−0.448342 + 0.893862i \(0.647985\pi\)
\(174\) 1.93484 0.146680
\(175\) −1.74257 −0.131726
\(176\) 3.73988 0.281904
\(177\) 2.44780 0.183988
\(178\) 0.329489 0.0246962
\(179\) −15.1551 −1.13275 −0.566374 0.824148i \(-0.691654\pi\)
−0.566374 + 0.824148i \(0.691654\pi\)
\(180\) 21.9054 1.63273
\(181\) −2.19847 −0.163411 −0.0817055 0.996657i \(-0.526037\pi\)
−0.0817055 + 0.996657i \(0.526037\pi\)
\(182\) 18.4408 1.36692
\(183\) −5.45451 −0.403209
\(184\) −0.198600 −0.0146410
\(185\) 2.54923 0.187423
\(186\) −3.57831 −0.262374
\(187\) −1.39896 −0.102302
\(188\) 29.8405 2.17635
\(189\) −2.90769 −0.211503
\(190\) −12.0481 −0.874059
\(191\) −8.33547 −0.603134 −0.301567 0.953445i \(-0.597510\pi\)
−0.301567 + 0.953445i \(0.597510\pi\)
\(192\) 5.60677 0.404634
\(193\) 14.6536 1.05479 0.527395 0.849620i \(-0.323169\pi\)
0.527395 + 0.849620i \(0.323169\pi\)
\(194\) −36.0399 −2.58751
\(195\) 7.73413 0.553853
\(196\) −17.2399 −1.23142
\(197\) 24.7052 1.76018 0.880088 0.474811i \(-0.157484\pi\)
0.880088 + 0.474811i \(0.157484\pi\)
\(198\) −30.0531 −2.13578
\(199\) 17.1851 1.21822 0.609111 0.793085i \(-0.291526\pi\)
0.609111 + 0.793085i \(0.291526\pi\)
\(200\) −3.54515 −0.250680
\(201\) −1.14959 −0.0810859
\(202\) 29.1644 2.05200
\(203\) −2.32766 −0.163370
\(204\) −0.386627 −0.0270693
\(205\) 11.8672 0.828838
\(206\) −5.83548 −0.406577
\(207\) −0.236328 −0.0164259
\(208\) −5.55561 −0.385212
\(209\) 9.98625 0.690764
\(210\) 2.86518 0.197716
\(211\) −14.0705 −0.968655 −0.484328 0.874887i \(-0.660936\pi\)
−0.484328 + 0.874887i \(0.660936\pi\)
\(212\) −3.14321 −0.215876
\(213\) −0.784133 −0.0537279
\(214\) 42.8745 2.93084
\(215\) −25.6889 −1.75197
\(216\) −5.91553 −0.402501
\(217\) 4.30479 0.292228
\(218\) 2.24777 0.152238
\(219\) −1.20483 −0.0814150
\(220\) 36.9576 2.49168
\(221\) 2.07816 0.139792
\(222\) −0.966572 −0.0648721
\(223\) −18.9661 −1.27007 −0.635033 0.772485i \(-0.719014\pi\)
−0.635033 + 0.772485i \(0.719014\pi\)
\(224\) −7.55978 −0.505109
\(225\) −4.21864 −0.281243
\(226\) −12.8063 −0.851860
\(227\) −6.97613 −0.463022 −0.231511 0.972832i \(-0.574367\pi\)
−0.231511 + 0.972832i \(0.574367\pi\)
\(228\) 2.75987 0.182777
\(229\) 3.48427 0.230247 0.115123 0.993351i \(-0.463274\pi\)
0.115123 + 0.993351i \(0.463274\pi\)
\(230\) 0.481043 0.0317191
\(231\) −2.37486 −0.156254
\(232\) −4.73550 −0.310901
\(233\) −10.6089 −0.695014 −0.347507 0.937677i \(-0.612972\pi\)
−0.347507 + 0.937677i \(0.612972\pi\)
\(234\) 44.6439 2.91846
\(235\) −24.9211 −1.62567
\(236\) −17.3757 −1.13106
\(237\) −4.64414 −0.301669
\(238\) 0.769874 0.0499035
\(239\) 3.24797 0.210094 0.105047 0.994467i \(-0.466501\pi\)
0.105047 + 0.994467i \(0.466501\pi\)
\(240\) −0.863187 −0.0557185
\(241\) −10.8670 −0.700004 −0.350002 0.936749i \(-0.613819\pi\)
−0.350002 + 0.936749i \(0.613819\pi\)
\(242\) −25.9786 −1.66997
\(243\) −10.6709 −0.684540
\(244\) 38.7188 2.47872
\(245\) 14.3977 0.919838
\(246\) −4.49958 −0.286883
\(247\) −14.8346 −0.943904
\(248\) 8.75786 0.556125
\(249\) −1.67025 −0.105848
\(250\) −20.0634 −1.26892
\(251\) 0.598480 0.0377757 0.0188879 0.999822i \(-0.493987\pi\)
0.0188879 + 0.999822i \(0.493987\pi\)
\(252\) 9.99194 0.629433
\(253\) −0.398721 −0.0250674
\(254\) 17.2834 1.08446
\(255\) 0.322888 0.0202200
\(256\) −10.5728 −0.660798
\(257\) 9.01116 0.562101 0.281050 0.959693i \(-0.409317\pi\)
0.281050 + 0.959693i \(0.409317\pi\)
\(258\) 9.74024 0.606401
\(259\) 1.16281 0.0722535
\(260\) −54.9007 −3.40480
\(261\) −5.63512 −0.348805
\(262\) 22.8063 1.40898
\(263\) −23.4255 −1.44448 −0.722240 0.691642i \(-0.756887\pi\)
−0.722240 + 0.691642i \(0.756887\pi\)
\(264\) −4.83151 −0.297359
\(265\) 2.62502 0.161254
\(266\) −5.49562 −0.336958
\(267\) 0.0630337 0.00385760
\(268\) 8.16036 0.498473
\(269\) 15.8899 0.968823 0.484411 0.874840i \(-0.339034\pi\)
0.484411 + 0.874840i \(0.339034\pi\)
\(270\) 14.3285 0.872003
\(271\) 15.5382 0.943880 0.471940 0.881631i \(-0.343554\pi\)
0.471940 + 0.881631i \(0.343554\pi\)
\(272\) −0.231938 −0.0140633
\(273\) 3.52786 0.213516
\(274\) 24.3045 1.46829
\(275\) −7.11748 −0.429200
\(276\) −0.110193 −0.00663287
\(277\) −17.1127 −1.02820 −0.514101 0.857730i \(-0.671874\pi\)
−0.514101 + 0.857730i \(0.671874\pi\)
\(278\) 30.9115 1.85395
\(279\) 10.4216 0.623926
\(280\) −7.01250 −0.419077
\(281\) −16.0612 −0.958129 −0.479065 0.877780i \(-0.659024\pi\)
−0.479065 + 0.877780i \(0.659024\pi\)
\(282\) 9.44913 0.562688
\(283\) −2.50329 −0.148805 −0.0744024 0.997228i \(-0.523705\pi\)
−0.0744024 + 0.997228i \(0.523705\pi\)
\(284\) 5.56616 0.330291
\(285\) −2.30489 −0.136530
\(286\) 75.3210 4.45382
\(287\) 5.41310 0.319525
\(288\) −18.3017 −1.07844
\(289\) −16.9132 −0.994896
\(290\) 11.4702 0.673555
\(291\) −6.89470 −0.404175
\(292\) 8.55249 0.500496
\(293\) 16.0100 0.935312 0.467656 0.883911i \(-0.345099\pi\)
0.467656 + 0.883911i \(0.345099\pi\)
\(294\) −5.45908 −0.318380
\(295\) 14.5111 0.844872
\(296\) 2.36567 0.137502
\(297\) −11.8764 −0.689139
\(298\) −52.8615 −3.06219
\(299\) 0.592302 0.0342537
\(300\) −1.96704 −0.113567
\(301\) −11.7178 −0.675400
\(302\) −13.2820 −0.764291
\(303\) 5.57937 0.320526
\(304\) 1.65565 0.0949582
\(305\) −32.3357 −1.85154
\(306\) 1.86381 0.106547
\(307\) −9.45518 −0.539636 −0.269818 0.962911i \(-0.586963\pi\)
−0.269818 + 0.962911i \(0.586963\pi\)
\(308\) 16.8579 0.960568
\(309\) −1.11637 −0.0635081
\(310\) −21.2131 −1.20482
\(311\) −1.38739 −0.0786715 −0.0393357 0.999226i \(-0.512524\pi\)
−0.0393357 + 0.999226i \(0.512524\pi\)
\(312\) 7.17723 0.406331
\(313\) −12.6434 −0.714648 −0.357324 0.933980i \(-0.616311\pi\)
−0.357324 + 0.933980i \(0.616311\pi\)
\(314\) 22.7136 1.28180
\(315\) −8.34469 −0.470170
\(316\) 32.9664 1.85450
\(317\) 8.34217 0.468543 0.234271 0.972171i \(-0.424730\pi\)
0.234271 + 0.972171i \(0.424730\pi\)
\(318\) −0.995310 −0.0558142
\(319\) −9.50729 −0.532306
\(320\) 33.2383 1.85808
\(321\) 8.20220 0.457802
\(322\) 0.219424 0.0122280
\(323\) −0.619322 −0.0344600
\(324\) 22.4965 1.24981
\(325\) 10.5730 0.586487
\(326\) −37.6084 −2.08294
\(327\) 0.430015 0.0237799
\(328\) 11.0127 0.608072
\(329\) −11.3675 −0.626713
\(330\) 11.7028 0.644217
\(331\) −16.9375 −0.930970 −0.465485 0.885056i \(-0.654120\pi\)
−0.465485 + 0.885056i \(0.654120\pi\)
\(332\) 11.8563 0.650697
\(333\) 2.81509 0.154266
\(334\) −23.8322 −1.30404
\(335\) −6.81505 −0.372346
\(336\) −0.393735 −0.0214800
\(337\) −29.5763 −1.61112 −0.805561 0.592512i \(-0.798136\pi\)
−0.805561 + 0.592512i \(0.798136\pi\)
\(338\) −82.6686 −4.49658
\(339\) −2.44993 −0.133062
\(340\) −2.29202 −0.124302
\(341\) 17.5828 0.952164
\(342\) −13.3045 −0.719428
\(343\) 14.7071 0.794107
\(344\) −23.8391 −1.28532
\(345\) 0.0920272 0.00495458
\(346\) 26.5103 1.42520
\(347\) −6.29530 −0.337949 −0.168975 0.985620i \(-0.554046\pi\)
−0.168975 + 0.985620i \(0.554046\pi\)
\(348\) −2.62751 −0.140849
\(349\) 12.2184 0.654035 0.327018 0.945018i \(-0.393956\pi\)
0.327018 + 0.945018i \(0.393956\pi\)
\(350\) 3.91688 0.209366
\(351\) 17.6424 0.941684
\(352\) −30.8778 −1.64579
\(353\) −27.3453 −1.45545 −0.727723 0.685871i \(-0.759421\pi\)
−0.727723 + 0.685871i \(0.759421\pi\)
\(354\) −5.50208 −0.292432
\(355\) −4.64853 −0.246718
\(356\) −0.447444 −0.0237145
\(357\) 0.147283 0.00779502
\(358\) 34.0652 1.80040
\(359\) 17.1295 0.904060 0.452030 0.892003i \(-0.350700\pi\)
0.452030 + 0.892003i \(0.350700\pi\)
\(360\) −16.9768 −0.894756
\(361\) −14.5791 −0.767319
\(362\) 4.94165 0.259727
\(363\) −4.96990 −0.260852
\(364\) −25.0425 −1.31258
\(365\) −7.14254 −0.373857
\(366\) 12.2605 0.640865
\(367\) 26.6592 1.39160 0.695799 0.718236i \(-0.255050\pi\)
0.695799 + 0.718236i \(0.255050\pi\)
\(368\) −0.0661052 −0.00344597
\(369\) 13.1048 0.682207
\(370\) −5.73008 −0.297893
\(371\) 1.19738 0.0621650
\(372\) 4.85932 0.251944
\(373\) 1.17442 0.0608089 0.0304045 0.999538i \(-0.490320\pi\)
0.0304045 + 0.999538i \(0.490320\pi\)
\(374\) 3.14453 0.162600
\(375\) −3.83828 −0.198208
\(376\) −23.1266 −1.19266
\(377\) 14.1231 0.727378
\(378\) 6.53581 0.336166
\(379\) −16.5853 −0.851928 −0.425964 0.904740i \(-0.640065\pi\)
−0.425964 + 0.904740i \(0.640065\pi\)
\(380\) 16.3612 0.839313
\(381\) 3.30644 0.169394
\(382\) 18.7362 0.958627
\(383\) −13.4128 −0.685364 −0.342682 0.939451i \(-0.611335\pi\)
−0.342682 + 0.939451i \(0.611335\pi\)
\(384\) −7.01139 −0.357799
\(385\) −14.0787 −0.717519
\(386\) −32.9379 −1.67649
\(387\) −28.3679 −1.44202
\(388\) 48.9420 2.48465
\(389\) 11.7260 0.594531 0.297265 0.954795i \(-0.403925\pi\)
0.297265 + 0.954795i \(0.403925\pi\)
\(390\) −17.3845 −0.880300
\(391\) 0.0247277 0.00125053
\(392\) 13.3610 0.674833
\(393\) 4.36301 0.220085
\(394\) −55.5316 −2.79764
\(395\) −27.5316 −1.38527
\(396\) 40.8119 2.05087
\(397\) 3.57515 0.179431 0.0897157 0.995967i \(-0.471404\pi\)
0.0897157 + 0.995967i \(0.471404\pi\)
\(398\) −38.6282 −1.93625
\(399\) −1.05135 −0.0526335
\(400\) −1.18003 −0.0590015
\(401\) −9.37817 −0.468323 −0.234162 0.972198i \(-0.575235\pi\)
−0.234162 + 0.972198i \(0.575235\pi\)
\(402\) 2.58401 0.128879
\(403\) −26.1194 −1.30110
\(404\) −39.6051 −1.97043
\(405\) −18.7878 −0.933573
\(406\) 5.23204 0.259662
\(407\) 4.74947 0.235423
\(408\) 0.299638 0.0148343
\(409\) −9.26333 −0.458042 −0.229021 0.973421i \(-0.573552\pi\)
−0.229021 + 0.973421i \(0.573552\pi\)
\(410\) −26.6746 −1.31736
\(411\) 4.64963 0.229349
\(412\) 7.92455 0.390414
\(413\) 6.61914 0.325706
\(414\) 0.531211 0.0261076
\(415\) −9.90165 −0.486053
\(416\) 45.8690 2.24892
\(417\) 5.91359 0.289590
\(418\) −22.4468 −1.09791
\(419\) −24.2130 −1.18288 −0.591441 0.806348i \(-0.701441\pi\)
−0.591441 + 0.806348i \(0.701441\pi\)
\(420\) −3.89090 −0.189857
\(421\) −9.74620 −0.475001 −0.237500 0.971387i \(-0.576328\pi\)
−0.237500 + 0.971387i \(0.576328\pi\)
\(422\) 31.6273 1.53959
\(423\) −27.5201 −1.33807
\(424\) 2.43601 0.118303
\(425\) 0.441408 0.0214114
\(426\) 1.76255 0.0853957
\(427\) −14.7497 −0.713786
\(428\) −58.2233 −2.81433
\(429\) 14.4095 0.695696
\(430\) 57.7426 2.78459
\(431\) −2.88528 −0.138979 −0.0694896 0.997583i \(-0.522137\pi\)
−0.0694896 + 0.997583i \(0.522137\pi\)
\(432\) −1.96903 −0.0947349
\(433\) 9.16473 0.440429 0.220214 0.975452i \(-0.429324\pi\)
0.220214 + 0.975452i \(0.429324\pi\)
\(434\) −9.67617 −0.464471
\(435\) 2.19434 0.105211
\(436\) −3.05245 −0.146186
\(437\) −0.176515 −0.00844384
\(438\) 2.70818 0.129402
\(439\) 9.64524 0.460342 0.230171 0.973150i \(-0.426071\pi\)
0.230171 + 0.973150i \(0.426071\pi\)
\(440\) −28.6424 −1.36547
\(441\) 15.8993 0.757107
\(442\) −4.67122 −0.222187
\(443\) −29.8736 −1.41934 −0.709669 0.704536i \(-0.751155\pi\)
−0.709669 + 0.704536i \(0.751155\pi\)
\(444\) 1.31260 0.0622932
\(445\) 0.373679 0.0177141
\(446\) 42.6315 2.01866
\(447\) −10.1128 −0.478319
\(448\) 15.1614 0.716307
\(449\) 4.58987 0.216609 0.108305 0.994118i \(-0.465458\pi\)
0.108305 + 0.994118i \(0.465458\pi\)
\(450\) 9.48252 0.447010
\(451\) 22.1097 1.04111
\(452\) 17.3908 0.817996
\(453\) −2.54094 −0.119384
\(454\) 15.6807 0.735932
\(455\) 20.9140 0.980464
\(456\) −2.13892 −0.100164
\(457\) −9.83523 −0.460073 −0.230036 0.973182i \(-0.573885\pi\)
−0.230036 + 0.973182i \(0.573885\pi\)
\(458\) −7.83182 −0.365957
\(459\) 0.736544 0.0343789
\(460\) −0.653254 −0.0304581
\(461\) −14.4415 −0.672607 −0.336303 0.941754i \(-0.609177\pi\)
−0.336303 + 0.941754i \(0.609177\pi\)
\(462\) 5.33813 0.248352
\(463\) 3.42847 0.159334 0.0796672 0.996822i \(-0.474614\pi\)
0.0796672 + 0.996822i \(0.474614\pi\)
\(464\) −1.57624 −0.0731753
\(465\) −4.05822 −0.188196
\(466\) 23.8464 1.10466
\(467\) 7.08429 0.327822 0.163911 0.986475i \(-0.447589\pi\)
0.163911 + 0.986475i \(0.447589\pi\)
\(468\) −60.6262 −2.80245
\(469\) −3.10863 −0.143543
\(470\) 56.0168 2.58386
\(471\) 4.34528 0.200220
\(472\) 13.4663 0.619835
\(473\) −47.8609 −2.20065
\(474\) 10.4389 0.479477
\(475\) −3.15092 −0.144574
\(476\) −1.04548 −0.0479197
\(477\) 2.89878 0.132726
\(478\) −7.30068 −0.333925
\(479\) −0.855569 −0.0390919 −0.0195460 0.999809i \(-0.506222\pi\)
−0.0195460 + 0.999809i \(0.506222\pi\)
\(480\) 7.12677 0.325291
\(481\) −7.05536 −0.321697
\(482\) 24.4264 1.11259
\(483\) 0.0419774 0.00191004
\(484\) 35.2788 1.60358
\(485\) −40.8735 −1.85597
\(486\) 23.9857 1.08801
\(487\) 34.3690 1.55741 0.778704 0.627392i \(-0.215877\pi\)
0.778704 + 0.627392i \(0.215877\pi\)
\(488\) −30.0073 −1.35837
\(489\) −7.19478 −0.325359
\(490\) −32.3627 −1.46200
\(491\) −35.2937 −1.59278 −0.796392 0.604781i \(-0.793261\pi\)
−0.796392 + 0.604781i \(0.793261\pi\)
\(492\) 6.11040 0.275478
\(493\) 0.589618 0.0265551
\(494\) 33.3448 1.50025
\(495\) −34.0837 −1.53195
\(496\) 2.91512 0.130893
\(497\) −2.12039 −0.0951124
\(498\) 3.75433 0.168236
\(499\) −33.3454 −1.49274 −0.746372 0.665529i \(-0.768206\pi\)
−0.746372 + 0.665529i \(0.768206\pi\)
\(500\) 27.2460 1.21848
\(501\) −4.55929 −0.203694
\(502\) −1.34524 −0.0600411
\(503\) −20.5881 −0.917979 −0.458989 0.888442i \(-0.651788\pi\)
−0.458989 + 0.888442i \(0.651788\pi\)
\(504\) −7.74382 −0.344937
\(505\) 33.0758 1.47186
\(506\) 0.896232 0.0398424
\(507\) −15.8151 −0.702374
\(508\) −23.4707 −1.04135
\(509\) 1.56105 0.0691925 0.0345963 0.999401i \(-0.488985\pi\)
0.0345963 + 0.999401i \(0.488985\pi\)
\(510\) −0.725777 −0.0321379
\(511\) −3.25801 −0.144126
\(512\) −8.84493 −0.390894
\(513\) −5.25771 −0.232133
\(514\) −20.2550 −0.893409
\(515\) −6.61812 −0.291629
\(516\) −13.2272 −0.582295
\(517\) −46.4305 −2.04201
\(518\) −2.61373 −0.114841
\(519\) 5.07161 0.222619
\(520\) 42.5484 1.86587
\(521\) 38.6568 1.69359 0.846793 0.531923i \(-0.178530\pi\)
0.846793 + 0.531923i \(0.178530\pi\)
\(522\) 12.6664 0.554395
\(523\) −40.7829 −1.78331 −0.891655 0.452716i \(-0.850455\pi\)
−0.891655 + 0.452716i \(0.850455\pi\)
\(524\) −30.9708 −1.35296
\(525\) 0.749329 0.0327034
\(526\) 52.6551 2.29587
\(527\) −1.09044 −0.0475004
\(528\) −1.60820 −0.0699881
\(529\) −22.9930 −0.999694
\(530\) −5.90044 −0.256299
\(531\) 16.0245 0.695404
\(532\) 7.46303 0.323563
\(533\) −32.8441 −1.42263
\(534\) −0.141685 −0.00613131
\(535\) 48.6247 2.10223
\(536\) −6.32433 −0.273169
\(537\) 6.51693 0.281226
\(538\) −35.7167 −1.53986
\(539\) 26.8244 1.15541
\(540\) −19.4580 −0.837338
\(541\) −26.3166 −1.13144 −0.565719 0.824598i \(-0.691401\pi\)
−0.565719 + 0.824598i \(0.691401\pi\)
\(542\) −34.9263 −1.50021
\(543\) 0.945374 0.0405699
\(544\) 1.91496 0.0821033
\(545\) 2.54923 0.109197
\(546\) −7.92980 −0.339364
\(547\) −19.8536 −0.848877 −0.424439 0.905457i \(-0.639528\pi\)
−0.424439 + 0.905457i \(0.639528\pi\)
\(548\) −33.0054 −1.40992
\(549\) −35.7079 −1.52398
\(550\) 15.9984 0.682175
\(551\) −4.20890 −0.179305
\(552\) 0.0854007 0.00363489
\(553\) −12.5583 −0.534033
\(554\) 38.4653 1.63424
\(555\) −1.09621 −0.0465314
\(556\) −41.9776 −1.78025
\(557\) −1.64757 −0.0698098 −0.0349049 0.999391i \(-0.511113\pi\)
−0.0349049 + 0.999391i \(0.511113\pi\)
\(558\) −23.4254 −0.991675
\(559\) 71.0976 3.00711
\(560\) −2.33416 −0.0986362
\(561\) 0.601573 0.0253984
\(562\) 36.1018 1.52286
\(563\) −3.61375 −0.152301 −0.0761507 0.997096i \(-0.524263\pi\)
−0.0761507 + 0.997096i \(0.524263\pi\)
\(564\) −12.8319 −0.540319
\(565\) −14.5238 −0.611021
\(566\) 5.62680 0.236512
\(567\) −8.56989 −0.359901
\(568\) −4.31381 −0.181003
\(569\) −23.5827 −0.988638 −0.494319 0.869281i \(-0.664583\pi\)
−0.494319 + 0.869281i \(0.664583\pi\)
\(570\) 5.18085 0.217002
\(571\) −42.5523 −1.78076 −0.890378 0.455221i \(-0.849560\pi\)
−0.890378 + 0.455221i \(0.849560\pi\)
\(572\) −102.285 −4.27677
\(573\) 3.58437 0.149739
\(574\) −12.1674 −0.507857
\(575\) 0.125807 0.00524651
\(576\) 36.7047 1.52936
\(577\) −14.1166 −0.587682 −0.293841 0.955854i \(-0.594934\pi\)
−0.293841 + 0.955854i \(0.594934\pi\)
\(578\) 38.0170 1.58130
\(579\) −6.30126 −0.261872
\(580\) −15.5765 −0.646779
\(581\) −4.51656 −0.187378
\(582\) 15.4977 0.642400
\(583\) 4.89068 0.202551
\(584\) −6.62823 −0.274278
\(585\) 50.6315 2.09335
\(586\) −35.9867 −1.48660
\(587\) 30.4626 1.25733 0.628664 0.777677i \(-0.283602\pi\)
0.628664 + 0.777677i \(0.283602\pi\)
\(588\) 7.41340 0.305723
\(589\) 7.78396 0.320732
\(590\) −32.6177 −1.34285
\(591\) −10.6236 −0.436997
\(592\) 0.787431 0.0323632
\(593\) −12.6272 −0.518539 −0.259269 0.965805i \(-0.583482\pi\)
−0.259269 + 0.965805i \(0.583482\pi\)
\(594\) 26.6954 1.09532
\(595\) 0.873127 0.0357947
\(596\) 71.7857 2.94046
\(597\) −7.38985 −0.302447
\(598\) −1.33136 −0.0544432
\(599\) −33.8513 −1.38313 −0.691564 0.722315i \(-0.743078\pi\)
−0.691564 + 0.722315i \(0.743078\pi\)
\(600\) 1.52447 0.0622361
\(601\) 14.0076 0.571380 0.285690 0.958322i \(-0.407777\pi\)
0.285690 + 0.958322i \(0.407777\pi\)
\(602\) 26.3388 1.07349
\(603\) −7.52579 −0.306474
\(604\) 18.0368 0.733908
\(605\) −29.4628 −1.19783
\(606\) −12.5411 −0.509448
\(607\) −7.10471 −0.288371 −0.144186 0.989551i \(-0.546056\pi\)
−0.144186 + 0.989551i \(0.546056\pi\)
\(608\) −13.6697 −0.554378
\(609\) 1.00093 0.0405597
\(610\) 72.6831 2.94285
\(611\) 68.9726 2.79033
\(612\) −2.53105 −0.102312
\(613\) 7.39456 0.298663 0.149332 0.988787i \(-0.452288\pi\)
0.149332 + 0.988787i \(0.452288\pi\)
\(614\) 21.2530 0.857703
\(615\) −5.10305 −0.205775
\(616\) −13.0650 −0.526403
\(617\) 40.6914 1.63818 0.819088 0.573668i \(-0.194480\pi\)
0.819088 + 0.573668i \(0.194480\pi\)
\(618\) 2.50934 0.100940
\(619\) 32.8933 1.32210 0.661048 0.750344i \(-0.270112\pi\)
0.661048 + 0.750344i \(0.270112\pi\)
\(620\) 28.8073 1.15693
\(621\) 0.209924 0.00842398
\(622\) 3.11852 0.125041
\(623\) 0.170451 0.00682896
\(624\) 2.38899 0.0956362
\(625\) −30.2472 −1.20989
\(626\) 28.4195 1.13587
\(627\) −4.29423 −0.171495
\(628\) −30.8449 −1.23085
\(629\) −0.294550 −0.0117445
\(630\) 18.7569 0.747293
\(631\) −17.9048 −0.712778 −0.356389 0.934338i \(-0.615992\pi\)
−0.356389 + 0.934338i \(0.615992\pi\)
\(632\) −25.5492 −1.01629
\(633\) 6.05053 0.240487
\(634\) −18.7512 −0.744707
\(635\) 19.6014 0.777858
\(636\) 1.35162 0.0535954
\(637\) −39.8478 −1.57883
\(638\) 21.3702 0.846053
\(639\) −5.13332 −0.203071
\(640\) −41.5653 −1.64301
\(641\) −7.64672 −0.302027 −0.151014 0.988532i \(-0.548254\pi\)
−0.151014 + 0.988532i \(0.548254\pi\)
\(642\) −18.4366 −0.727636
\(643\) 16.5325 0.651978 0.325989 0.945374i \(-0.394303\pi\)
0.325989 + 0.945374i \(0.394303\pi\)
\(644\) −0.297976 −0.0117419
\(645\) 11.0466 0.434959
\(646\) 1.39209 0.0547711
\(647\) 15.2064 0.597826 0.298913 0.954280i \(-0.403376\pi\)
0.298913 + 0.954280i \(0.403376\pi\)
\(648\) −17.4350 −0.684910
\(649\) 27.0357 1.06125
\(650\) −23.7657 −0.932168
\(651\) −1.85112 −0.0725513
\(652\) 51.0721 2.00014
\(653\) 18.6645 0.730399 0.365200 0.930929i \(-0.381001\pi\)
0.365200 + 0.930929i \(0.381001\pi\)
\(654\) −0.966572 −0.0377960
\(655\) 25.8650 1.01063
\(656\) 3.66564 0.143119
\(657\) −7.88742 −0.307718
\(658\) 25.5516 0.996104
\(659\) 12.9082 0.502833 0.251416 0.967879i \(-0.419104\pi\)
0.251416 + 0.967879i \(0.419104\pi\)
\(660\) −15.8923 −0.618608
\(661\) −39.8418 −1.54967 −0.774834 0.632165i \(-0.782167\pi\)
−0.774834 + 0.632165i \(0.782167\pi\)
\(662\) 38.0716 1.47969
\(663\) −0.893638 −0.0347060
\(664\) −9.18868 −0.356590
\(665\) −6.23269 −0.241693
\(666\) −6.32766 −0.245192
\(667\) 0.168049 0.00650687
\(668\) 32.3641 1.25220
\(669\) 8.15572 0.315318
\(670\) 15.3187 0.591811
\(671\) −60.2446 −2.32572
\(672\) 3.25082 0.125403
\(673\) −31.0630 −1.19739 −0.598695 0.800977i \(-0.704314\pi\)
−0.598695 + 0.800977i \(0.704314\pi\)
\(674\) 66.4806 2.56074
\(675\) 3.74731 0.144234
\(676\) 112.264 4.31783
\(677\) 21.9780 0.844682 0.422341 0.906437i \(-0.361208\pi\)
0.422341 + 0.906437i \(0.361208\pi\)
\(678\) 5.50688 0.211490
\(679\) −18.6441 −0.715495
\(680\) 1.77633 0.0681191
\(681\) 2.99984 0.114954
\(682\) −39.5221 −1.51338
\(683\) 37.3784 1.43025 0.715123 0.698999i \(-0.246371\pi\)
0.715123 + 0.698999i \(0.246371\pi\)
\(684\) 18.0675 0.690828
\(685\) 27.5642 1.05317
\(686\) −33.0581 −1.26216
\(687\) −1.49829 −0.0571632
\(688\) −7.93502 −0.302520
\(689\) −7.26513 −0.276779
\(690\) −0.206856 −0.00787486
\(691\) 13.0529 0.496556 0.248278 0.968689i \(-0.420135\pi\)
0.248278 + 0.968689i \(0.420135\pi\)
\(692\) −36.0008 −1.36854
\(693\) −15.5470 −0.590581
\(694\) 14.1504 0.537141
\(695\) 35.0572 1.32980
\(696\) 2.03633 0.0771870
\(697\) −1.37119 −0.0519374
\(698\) −27.4641 −1.03953
\(699\) 4.56200 0.172551
\(700\) −5.31911 −0.201043
\(701\) −44.0974 −1.66554 −0.832769 0.553621i \(-0.813246\pi\)
−0.832769 + 0.553621i \(0.813246\pi\)
\(702\) −39.6561 −1.49672
\(703\) 2.10260 0.0793011
\(704\) 61.9263 2.33393
\(705\) 10.7164 0.403604
\(706\) 61.4659 2.31330
\(707\) 15.0873 0.567415
\(708\) 7.47179 0.280807
\(709\) −26.3781 −0.990651 −0.495326 0.868707i \(-0.664951\pi\)
−0.495326 + 0.868707i \(0.664951\pi\)
\(710\) 10.4488 0.392137
\(711\) −30.4028 −1.14020
\(712\) 0.346772 0.0129958
\(713\) −0.310790 −0.0116392
\(714\) −0.331057 −0.0123895
\(715\) 85.4229 3.19463
\(716\) −46.2603 −1.72883
\(717\) −1.39667 −0.0521598
\(718\) −38.5031 −1.43692
\(719\) 15.9648 0.595387 0.297693 0.954662i \(-0.403783\pi\)
0.297693 + 0.954662i \(0.403783\pi\)
\(720\) −5.65085 −0.210595
\(721\) −3.01880 −0.112426
\(722\) 32.7703 1.21959
\(723\) 4.67296 0.173789
\(724\) −6.71073 −0.249402
\(725\) 2.99980 0.111410
\(726\) 11.1712 0.414601
\(727\) −4.30426 −0.159636 −0.0798181 0.996809i \(-0.525434\pi\)
−0.0798181 + 0.996809i \(0.525434\pi\)
\(728\) 19.4081 0.719311
\(729\) −17.5213 −0.648937
\(730\) 16.0548 0.594213
\(731\) 2.96821 0.109783
\(732\) −16.6497 −0.615389
\(733\) 16.6432 0.614731 0.307365 0.951592i \(-0.400553\pi\)
0.307365 + 0.951592i \(0.400553\pi\)
\(734\) −59.9236 −2.21182
\(735\) −6.19124 −0.228367
\(736\) 0.545788 0.0201180
\(737\) −12.6971 −0.467705
\(738\) −29.4565 −1.08431
\(739\) −2.54039 −0.0934498 −0.0467249 0.998908i \(-0.514878\pi\)
−0.0467249 + 0.998908i \(0.514878\pi\)
\(740\) 7.78141 0.286050
\(741\) 6.37910 0.234342
\(742\) −2.69144 −0.0988057
\(743\) −7.43169 −0.272642 −0.136321 0.990665i \(-0.543528\pi\)
−0.136321 + 0.990665i \(0.543528\pi\)
\(744\) −3.76601 −0.138069
\(745\) −59.9512 −2.19644
\(746\) −2.63981 −0.0966503
\(747\) −10.9343 −0.400065
\(748\) −4.27026 −0.156136
\(749\) 22.1797 0.810430
\(750\) 8.62755 0.315034
\(751\) −8.16338 −0.297886 −0.148943 0.988846i \(-0.547587\pi\)
−0.148943 + 0.988846i \(0.547587\pi\)
\(752\) −7.69786 −0.280712
\(753\) −0.257355 −0.00937854
\(754\) −31.7455 −1.15610
\(755\) −15.0633 −0.548210
\(756\) −8.87559 −0.322802
\(757\) 19.8339 0.720877 0.360438 0.932783i \(-0.382627\pi\)
0.360438 + 0.932783i \(0.382627\pi\)
\(758\) 37.2798 1.35406
\(759\) 0.171456 0.00622345
\(760\) −12.6800 −0.459954
\(761\) 10.2965 0.373247 0.186624 0.982431i \(-0.440246\pi\)
0.186624 + 0.982431i \(0.440246\pi\)
\(762\) −7.43211 −0.269237
\(763\) 1.16281 0.0420966
\(764\) −25.4436 −0.920519
\(765\) 2.11378 0.0764240
\(766\) 30.1489 1.08933
\(767\) −40.1617 −1.45015
\(768\) 4.54644 0.164056
\(769\) −29.7110 −1.07141 −0.535703 0.844406i \(-0.679953\pi\)
−0.535703 + 0.844406i \(0.679953\pi\)
\(770\) 31.6457 1.14043
\(771\) −3.87493 −0.139552
\(772\) 44.7295 1.60985
\(773\) 37.5946 1.35218 0.676092 0.736817i \(-0.263672\pi\)
0.676092 + 0.736817i \(0.263672\pi\)
\(774\) 63.7645 2.29197
\(775\) −5.54784 −0.199284
\(776\) −37.9304 −1.36162
\(777\) −0.500025 −0.0179383
\(778\) −26.3573 −0.944953
\(779\) 9.78801 0.350692
\(780\) 23.6081 0.845305
\(781\) −8.66068 −0.309904
\(782\) −0.0555820 −0.00198761
\(783\) 5.00554 0.178883
\(784\) 4.44731 0.158832
\(785\) 25.7599 0.919410
\(786\) −9.80703 −0.349805
\(787\) −48.6549 −1.73436 −0.867180 0.497994i \(-0.834070\pi\)
−0.867180 + 0.497994i \(0.834070\pi\)
\(788\) 75.4116 2.68643
\(789\) 10.0733 0.358620
\(790\) 61.8846 2.20176
\(791\) −6.62491 −0.235555
\(792\) −31.6295 −1.12390
\(793\) 89.4936 3.17801
\(794\) −8.03609 −0.285190
\(795\) −1.12880 −0.0400343
\(796\) 52.4568 1.85928
\(797\) 39.1366 1.38629 0.693144 0.720799i \(-0.256225\pi\)
0.693144 + 0.720799i \(0.256225\pi\)
\(798\) 2.36320 0.0836563
\(799\) 2.87950 0.101869
\(800\) 9.74274 0.344458
\(801\) 0.412650 0.0145803
\(802\) 21.0799 0.744358
\(803\) −13.3073 −0.469603
\(804\) −3.50907 −0.123755
\(805\) 0.248852 0.00877089
\(806\) 58.7103 2.06798
\(807\) −6.83288 −0.240529
\(808\) 30.6942 1.07982
\(809\) 26.4619 0.930350 0.465175 0.885219i \(-0.345991\pi\)
0.465175 + 0.885219i \(0.345991\pi\)
\(810\) 42.2306 1.48383
\(811\) 27.6638 0.971408 0.485704 0.874123i \(-0.338563\pi\)
0.485704 + 0.874123i \(0.338563\pi\)
\(812\) −7.10509 −0.249340
\(813\) −6.68166 −0.234336
\(814\) −10.6757 −0.374183
\(815\) −42.6524 −1.49405
\(816\) 0.0997367 0.00349148
\(817\) −21.1881 −0.741279
\(818\) 20.8218 0.728017
\(819\) 23.0951 0.807008
\(820\) 36.2240 1.26500
\(821\) −2.02895 −0.0708107 −0.0354054 0.999373i \(-0.511272\pi\)
−0.0354054 + 0.999373i \(0.511272\pi\)
\(822\) −10.4513 −0.364531
\(823\) 25.8220 0.900097 0.450048 0.893004i \(-0.351407\pi\)
0.450048 + 0.893004i \(0.351407\pi\)
\(824\) −6.14158 −0.213952
\(825\) 3.06062 0.106557
\(826\) −14.8783 −0.517681
\(827\) 26.4839 0.920936 0.460468 0.887676i \(-0.347682\pi\)
0.460468 + 0.887676i \(0.347682\pi\)
\(828\) −0.721381 −0.0250697
\(829\) 53.6005 1.86162 0.930812 0.365500i \(-0.119102\pi\)
0.930812 + 0.365500i \(0.119102\pi\)
\(830\) 22.2566 0.772538
\(831\) 7.35871 0.255271
\(832\) −91.9917 −3.18924
\(833\) −1.66358 −0.0576397
\(834\) −13.2924 −0.460277
\(835\) −27.0286 −0.935362
\(836\) 30.4826 1.05426
\(837\) −9.25727 −0.319978
\(838\) 54.4252 1.88009
\(839\) −52.5306 −1.81356 −0.906779 0.421607i \(-0.861466\pi\)
−0.906779 + 0.421607i \(0.861466\pi\)
\(840\) 3.01548 0.104044
\(841\) −24.9930 −0.861827
\(842\) 21.9072 0.754971
\(843\) 6.90654 0.237874
\(844\) −42.9496 −1.47839
\(845\) −93.7560 −3.22530
\(846\) 61.8587 2.12675
\(847\) −13.4392 −0.461776
\(848\) 0.810842 0.0278444
\(849\) 1.07645 0.0369436
\(850\) −0.992182 −0.0340315
\(851\) −0.0839506 −0.00287779
\(852\) −2.39353 −0.0820010
\(853\) 10.3780 0.355338 0.177669 0.984090i \(-0.443144\pi\)
0.177669 + 0.984090i \(0.443144\pi\)
\(854\) 33.1538 1.13450
\(855\) −15.0889 −0.516030
\(856\) 45.1234 1.54229
\(857\) 53.7916 1.83749 0.918744 0.394854i \(-0.129205\pi\)
0.918744 + 0.394854i \(0.129205\pi\)
\(858\) −32.3891 −1.10575
\(859\) −31.3370 −1.06920 −0.534602 0.845104i \(-0.679539\pi\)
−0.534602 + 0.845104i \(0.679539\pi\)
\(860\) −78.4141 −2.67390
\(861\) −2.32771 −0.0793282
\(862\) 6.48544 0.220895
\(863\) −0.927314 −0.0315661 −0.0157831 0.999875i \(-0.505024\pi\)
−0.0157831 + 0.999875i \(0.505024\pi\)
\(864\) 16.2570 0.553074
\(865\) 30.0658 1.02227
\(866\) −20.6002 −0.700022
\(867\) 7.27294 0.247002
\(868\) 13.1402 0.446007
\(869\) −51.2941 −1.74003
\(870\) −4.93236 −0.167223
\(871\) 18.8616 0.639102
\(872\) 2.36567 0.0801118
\(873\) −45.1361 −1.52763
\(874\) 0.396764 0.0134207
\(875\) −10.3792 −0.350880
\(876\) −3.67769 −0.124258
\(877\) 31.7024 1.07051 0.535257 0.844689i \(-0.320215\pi\)
0.535257 + 0.844689i \(0.320215\pi\)
\(878\) −21.6802 −0.731673
\(879\) −6.88452 −0.232209
\(880\) −9.53383 −0.321385
\(881\) 39.2656 1.32289 0.661445 0.749993i \(-0.269943\pi\)
0.661445 + 0.749993i \(0.269943\pi\)
\(882\) −35.7378 −1.20335
\(883\) 28.9049 0.972729 0.486364 0.873756i \(-0.338323\pi\)
0.486364 + 0.873756i \(0.338323\pi\)
\(884\) 6.34348 0.213354
\(885\) −6.24000 −0.209755
\(886\) 67.1489 2.25591
\(887\) −17.7689 −0.596620 −0.298310 0.954469i \(-0.596423\pi\)
−0.298310 + 0.954469i \(0.596423\pi\)
\(888\) −1.01727 −0.0341375
\(889\) 8.94101 0.299872
\(890\) −0.839944 −0.0281550
\(891\) −35.0035 −1.17266
\(892\) −57.8933 −1.93841
\(893\) −20.5549 −0.687842
\(894\) 22.7312 0.760246
\(895\) 38.6339 1.29139
\(896\) −18.9596 −0.633397
\(897\) −0.254698 −0.00850413
\(898\) −10.3169 −0.344281
\(899\) −7.41063 −0.247158
\(900\) −12.8772 −0.429240
\(901\) −0.303308 −0.0101046
\(902\) −49.6975 −1.65474
\(903\) 5.03880 0.167681
\(904\) −13.4780 −0.448272
\(905\) 5.60441 0.186297
\(906\) 5.71144 0.189750
\(907\) 16.8000 0.557835 0.278918 0.960315i \(-0.410024\pi\)
0.278918 + 0.960315i \(0.410024\pi\)
\(908\) −21.2943 −0.706676
\(909\) 36.5253 1.21147
\(910\) −47.0098 −1.55836
\(911\) 11.8168 0.391507 0.195754 0.980653i \(-0.437285\pi\)
0.195754 + 0.980653i \(0.437285\pi\)
\(912\) −0.711955 −0.0235752
\(913\) −18.4478 −0.610532
\(914\) 22.1073 0.731245
\(915\) 13.9048 0.459679
\(916\) 10.6356 0.351409
\(917\) 11.7981 0.389607
\(918\) −1.65558 −0.0546423
\(919\) 38.3081 1.26367 0.631834 0.775103i \(-0.282302\pi\)
0.631834 + 0.775103i \(0.282302\pi\)
\(920\) 0.506276 0.0166914
\(921\) 4.06586 0.133975
\(922\) 32.4611 1.06905
\(923\) 12.8655 0.423472
\(924\) −7.24914 −0.238479
\(925\) −1.49858 −0.0492731
\(926\) −7.70639 −0.253248
\(927\) −7.30831 −0.240036
\(928\) 13.0140 0.427206
\(929\) 21.7794 0.714557 0.357279 0.933998i \(-0.383705\pi\)
0.357279 + 0.933998i \(0.383705\pi\)
\(930\) 9.12194 0.299120
\(931\) 11.8752 0.389195
\(932\) −32.3833 −1.06075
\(933\) 0.596597 0.0195317
\(934\) −15.9238 −0.521044
\(935\) 3.56627 0.116630
\(936\) 46.9857 1.53578
\(937\) −46.4791 −1.51840 −0.759202 0.650855i \(-0.774411\pi\)
−0.759202 + 0.650855i \(0.774411\pi\)
\(938\) 6.98747 0.228149
\(939\) 5.43685 0.177425
\(940\) −76.0705 −2.48115
\(941\) −5.60750 −0.182799 −0.0913996 0.995814i \(-0.529134\pi\)
−0.0913996 + 0.995814i \(0.529134\pi\)
\(942\) −9.76717 −0.318232
\(943\) −0.390806 −0.0127264
\(944\) 4.48234 0.145888
\(945\) 7.41238 0.241125
\(946\) 107.580 3.49773
\(947\) −19.9986 −0.649868 −0.324934 0.945737i \(-0.605342\pi\)
−0.324934 + 0.945737i \(0.605342\pi\)
\(948\) −14.1760 −0.460416
\(949\) 19.7680 0.641696
\(950\) 7.08254 0.229788
\(951\) −3.58725 −0.116325
\(952\) 0.810257 0.0262606
\(953\) −47.9112 −1.55199 −0.775997 0.630736i \(-0.782753\pi\)
−0.775997 + 0.630736i \(0.782753\pi\)
\(954\) −6.51579 −0.210956
\(955\) 21.2490 0.687603
\(956\) 9.91428 0.320651
\(957\) 4.08827 0.132155
\(958\) 1.92312 0.0621331
\(959\) 12.5732 0.406008
\(960\) −14.2929 −0.461303
\(961\) −17.2947 −0.557895
\(962\) 15.8588 0.511308
\(963\) 53.6957 1.73032
\(964\) −33.1710 −1.06837
\(965\) −37.3554 −1.20251
\(966\) −0.0943554 −0.00303584
\(967\) 6.65369 0.213968 0.106984 0.994261i \(-0.465881\pi\)
0.106984 + 0.994261i \(0.465881\pi\)
\(968\) −27.3413 −0.878782
\(969\) 0.266317 0.00855535
\(970\) 91.8741 2.94990
\(971\) 31.1185 0.998640 0.499320 0.866418i \(-0.333583\pi\)
0.499320 + 0.866418i \(0.333583\pi\)
\(972\) −32.5725 −1.04476
\(973\) 15.9911 0.512650
\(974\) −77.2535 −2.47536
\(975\) −4.54656 −0.145606
\(976\) −9.98815 −0.319713
\(977\) −9.70385 −0.310454 −0.155227 0.987879i \(-0.549611\pi\)
−0.155227 + 0.987879i \(0.549611\pi\)
\(978\) 16.1722 0.517129
\(979\) 0.696202 0.0222507
\(980\) 43.9484 1.40388
\(981\) 2.81509 0.0898788
\(982\) 79.3321 2.53159
\(983\) 22.6855 0.723554 0.361777 0.932265i \(-0.382170\pi\)
0.361777 + 0.932265i \(0.382170\pi\)
\(984\) −4.73560 −0.150965
\(985\) −62.9794 −2.00669
\(986\) −1.32532 −0.0422069
\(987\) 4.88821 0.155593
\(988\) −45.2820 −1.44061
\(989\) 0.845978 0.0269005
\(990\) 76.6122 2.43490
\(991\) 1.67284 0.0531396 0.0265698 0.999647i \(-0.491542\pi\)
0.0265698 + 0.999647i \(0.491542\pi\)
\(992\) −24.0682 −0.764167
\(993\) 7.28338 0.231131
\(994\) 4.76614 0.151173
\(995\) −43.8089 −1.38883
\(996\) −5.09836 −0.161548
\(997\) 6.58580 0.208575 0.104287 0.994547i \(-0.466744\pi\)
0.104287 + 0.994547i \(0.466744\pi\)
\(998\) 74.9526 2.37258
\(999\) −2.50057 −0.0791146
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 \(a_p\))