Properties

Label 4033.2.a.d.1.17
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 1.17
Character \(\chi\) = 4033.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.97055 q^{2}\) \(-1.02182 q^{3}\) \(+1.88308 q^{4}\) \(-1.99471 q^{5}\) \(+2.01355 q^{6}\) \(-4.59826 q^{7}\) \(+0.230406 q^{8}\) \(-1.95588 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.97055 q^{2}\) \(-1.02182 q^{3}\) \(+1.88308 q^{4}\) \(-1.99471 q^{5}\) \(+2.01355 q^{6}\) \(-4.59826 q^{7}\) \(+0.230406 q^{8}\) \(-1.95588 q^{9}\) \(+3.93068 q^{10}\) \(+0.147869 q^{11}\) \(-1.92416 q^{12}\) \(-5.98055 q^{13}\) \(+9.06110 q^{14}\) \(+2.03823 q^{15}\) \(-4.22018 q^{16}\) \(+5.78675 q^{17}\) \(+3.85417 q^{18}\) \(+4.95304 q^{19}\) \(-3.75619 q^{20}\) \(+4.69859 q^{21}\) \(-0.291384 q^{22}\) \(-4.12678 q^{23}\) \(-0.235434 q^{24}\) \(-1.02114 q^{25}\) \(+11.7850 q^{26}\) \(+5.06402 q^{27}\) \(-8.65886 q^{28}\) \(-8.55493 q^{29}\) \(-4.01645 q^{30}\) \(-4.53282 q^{31}\) \(+7.85527 q^{32}\) \(-0.151096 q^{33}\) \(-11.4031 q^{34}\) \(+9.17218 q^{35}\) \(-3.68307 q^{36}\) \(-1.00000 q^{37}\) \(-9.76023 q^{38}\) \(+6.11105 q^{39}\) \(-0.459593 q^{40}\) \(+10.2013 q^{41}\) \(-9.25882 q^{42}\) \(+7.52821 q^{43}\) \(+0.278449 q^{44}\) \(+3.90142 q^{45}\) \(+8.13203 q^{46}\) \(-3.29908 q^{47}\) \(+4.31226 q^{48}\) \(+14.1440 q^{49}\) \(+2.01221 q^{50}\) \(-5.91302 q^{51}\) \(-11.2618 q^{52}\) \(+8.58786 q^{53}\) \(-9.97892 q^{54}\) \(-0.294956 q^{55}\) \(-1.05947 q^{56}\) \(-5.06112 q^{57}\) \(+16.8579 q^{58}\) \(+2.91642 q^{59}\) \(+3.83815 q^{60}\) \(+8.46825 q^{61}\) \(+8.93216 q^{62}\) \(+8.99365 q^{63}\) \(-7.03886 q^{64}\) \(+11.9295 q^{65}\) \(+0.297743 q^{66}\) \(-9.46516 q^{67}\) \(+10.8969 q^{68}\) \(+4.21683 q^{69}\) \(-18.0743 q^{70}\) \(+13.3751 q^{71}\) \(-0.450647 q^{72}\) \(-6.62409 q^{73}\) \(+1.97055 q^{74}\) \(+1.04342 q^{75}\) \(+9.32695 q^{76}\) \(-0.679942 q^{77}\) \(-12.0421 q^{78}\) \(-9.72416 q^{79}\) \(+8.41802 q^{80}\) \(+0.693127 q^{81}\) \(-20.1022 q^{82}\) \(-1.11380 q^{83}\) \(+8.84780 q^{84}\) \(-11.5429 q^{85}\) \(-14.8347 q^{86}\) \(+8.74160 q^{87}\) \(+0.0340700 q^{88}\) \(+7.87689 q^{89}\) \(-7.68794 q^{90}\) \(+27.5001 q^{91}\) \(-7.77104 q^{92}\) \(+4.63173 q^{93}\) \(+6.50102 q^{94}\) \(-9.87988 q^{95}\) \(-8.02667 q^{96}\) \(+17.5649 q^{97}\) \(-27.8714 q^{98}\) \(-0.289215 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut -\mathstrut 13q^{10} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut -\mathstrut 40q^{12} \) \(\mathstrut -\mathstrut 18q^{13} \) \(\mathstrut -\mathstrut 42q^{14} \) \(\mathstrut -\mathstrut 49q^{15} \) \(\mathstrut +\mathstrut 83q^{16} \) \(\mathstrut -\mathstrut 62q^{17} \) \(\mathstrut -\mathstrut 33q^{18} \) \(\mathstrut -\mathstrut 25q^{19} \) \(\mathstrut -\mathstrut 39q^{20} \) \(\mathstrut -\mathstrut 15q^{21} \) \(\mathstrut -\mathstrut 31q^{22} \) \(\mathstrut -\mathstrut 94q^{23} \) \(\mathstrut -\mathstrut 39q^{24} \) \(\mathstrut +\mathstrut 71q^{25} \) \(\mathstrut -\mathstrut 35q^{26} \) \(\mathstrut -\mathstrut 47q^{27} \) \(\mathstrut -\mathstrut 13q^{28} \) \(\mathstrut -\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 15q^{30} \) \(\mathstrut -\mathstrut 37q^{31} \) \(\mathstrut -\mathstrut 105q^{32} \) \(\mathstrut -\mathstrut 60q^{33} \) \(\mathstrut +\mathstrut 9q^{34} \) \(\mathstrut -\mathstrut 60q^{35} \) \(\mathstrut +\mathstrut 43q^{36} \) \(\mathstrut -\mathstrut 79q^{37} \) \(\mathstrut -\mathstrut 80q^{38} \) \(\mathstrut -\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 64q^{40} \) \(\mathstrut -\mathstrut 37q^{41} \) \(\mathstrut -\mathstrut 30q^{42} \) \(\mathstrut -\mathstrut 20q^{43} \) \(\mathstrut -\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 8q^{45} \) \(\mathstrut +\mathstrut 61q^{46} \) \(\mathstrut -\mathstrut 148q^{47} \) \(\mathstrut -\mathstrut 39q^{48} \) \(\mathstrut +\mathstrut 82q^{49} \) \(\mathstrut -\mathstrut 90q^{50} \) \(\mathstrut -\mathstrut 45q^{51} \) \(\mathstrut -\mathstrut 27q^{52} \) \(\mathstrut -\mathstrut 70q^{53} \) \(\mathstrut -\mathstrut 41q^{54} \) \(\mathstrut -\mathstrut 105q^{55} \) \(\mathstrut -\mathstrut 68q^{56} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut -\mathstrut 14q^{58} \) \(\mathstrut -\mathstrut 96q^{59} \) \(\mathstrut -\mathstrut 74q^{60} \) \(\mathstrut -\mathstrut 21q^{61} \) \(\mathstrut +\mathstrut 4q^{62} \) \(\mathstrut -\mathstrut 60q^{63} \) \(\mathstrut +\mathstrut 132q^{64} \) \(\mathstrut -\mathstrut 15q^{65} \) \(\mathstrut +\mathstrut 71q^{66} \) \(\mathstrut -\mathstrut 44q^{67} \) \(\mathstrut -\mathstrut 166q^{68} \) \(\mathstrut -\mathstrut 72q^{69} \) \(\mathstrut -\mathstrut 9q^{70} \) \(\mathstrut -\mathstrut 55q^{71} \) \(\mathstrut -\mathstrut 126q^{72} \) \(\mathstrut -\mathstrut 27q^{73} \) \(\mathstrut +\mathstrut 11q^{74} \) \(\mathstrut -\mathstrut 39q^{75} \) \(\mathstrut -\mathstrut 4q^{76} \) \(\mathstrut -\mathstrut 104q^{77} \) \(\mathstrut -\mathstrut 47q^{78} \) \(\mathstrut -\mathstrut 49q^{79} \) \(\mathstrut -\mathstrut 82q^{80} \) \(\mathstrut +\mathstrut 55q^{81} \) \(\mathstrut +\mathstrut 20q^{82} \) \(\mathstrut -\mathstrut 52q^{83} \) \(\mathstrut -\mathstrut 29q^{84} \) \(\mathstrut +\mathstrut 3q^{85} \) \(\mathstrut -\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 113q^{87} \) \(\mathstrut +\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 68q^{89} \) \(\mathstrut -\mathstrut 39q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 179q^{92} \) \(\mathstrut -\mathstrut 53q^{93} \) \(\mathstrut -\mathstrut 33q^{94} \) \(\mathstrut -\mathstrut 86q^{95} \) \(\mathstrut +\mathstrut 33q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut -\mathstrut 116q^{98} \) \(\mathstrut +\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.97055 −1.39339 −0.696695 0.717367i \(-0.745347\pi\)
−0.696695 + 0.717367i \(0.745347\pi\)
\(3\) −1.02182 −0.589948 −0.294974 0.955505i \(-0.595311\pi\)
−0.294974 + 0.955505i \(0.595311\pi\)
\(4\) 1.88308 0.941538
\(5\) −1.99471 −0.892061 −0.446030 0.895018i \(-0.647163\pi\)
−0.446030 + 0.895018i \(0.647163\pi\)
\(6\) 2.01355 0.822029
\(7\) −4.59826 −1.73798 −0.868989 0.494832i \(-0.835230\pi\)
−0.868989 + 0.494832i \(0.835230\pi\)
\(8\) 0.230406 0.0814609
\(9\) −1.95588 −0.651961
\(10\) 3.93068 1.24299
\(11\) 0.147869 0.0445843 0.0222922 0.999751i \(-0.492904\pi\)
0.0222922 + 0.999751i \(0.492904\pi\)
\(12\) −1.92416 −0.555459
\(13\) −5.98055 −1.65871 −0.829353 0.558725i \(-0.811291\pi\)
−0.829353 + 0.558725i \(0.811291\pi\)
\(14\) 9.06110 2.42168
\(15\) 2.03823 0.526270
\(16\) −4.22018 −1.05504
\(17\) 5.78675 1.40349 0.701746 0.712427i \(-0.252404\pi\)
0.701746 + 0.712427i \(0.252404\pi\)
\(18\) 3.85417 0.908436
\(19\) 4.95304 1.13631 0.568153 0.822923i \(-0.307658\pi\)
0.568153 + 0.822923i \(0.307658\pi\)
\(20\) −3.75619 −0.839909
\(21\) 4.69859 1.02532
\(22\) −0.291384 −0.0621234
\(23\) −4.12678 −0.860493 −0.430247 0.902711i \(-0.641573\pi\)
−0.430247 + 0.902711i \(0.641573\pi\)
\(24\) −0.235434 −0.0480577
\(25\) −1.02114 −0.204228
\(26\) 11.7850 2.31123
\(27\) 5.06402 0.974572
\(28\) −8.65886 −1.63637
\(29\) −8.55493 −1.58861 −0.794306 0.607519i \(-0.792165\pi\)
−0.794306 + 0.607519i \(0.792165\pi\)
\(30\) −4.01645 −0.733299
\(31\) −4.53282 −0.814118 −0.407059 0.913402i \(-0.633446\pi\)
−0.407059 + 0.913402i \(0.633446\pi\)
\(32\) 7.85527 1.38863
\(33\) −0.151096 −0.0263024
\(34\) −11.4031 −1.95561
\(35\) 9.17218 1.55038
\(36\) −3.68307 −0.613846
\(37\) −1.00000 −0.164399
\(38\) −9.76023 −1.58332
\(39\) 6.11105 0.978551
\(40\) −0.459593 −0.0726680
\(41\) 10.2013 1.59317 0.796587 0.604524i \(-0.206637\pi\)
0.796587 + 0.604524i \(0.206637\pi\)
\(42\) −9.25882 −1.42867
\(43\) 7.52821 1.14804 0.574021 0.818841i \(-0.305383\pi\)
0.574021 + 0.818841i \(0.305383\pi\)
\(44\) 0.278449 0.0419778
\(45\) 3.90142 0.581589
\(46\) 8.13203 1.19900
\(47\) −3.29908 −0.481221 −0.240610 0.970622i \(-0.577348\pi\)
−0.240610 + 0.970622i \(0.577348\pi\)
\(48\) 4.31226 0.622422
\(49\) 14.1440 2.02057
\(50\) 2.01221 0.284569
\(51\) −5.91302 −0.827988
\(52\) −11.2618 −1.56173
\(53\) 8.58786 1.17963 0.589817 0.807537i \(-0.299200\pi\)
0.589817 + 0.807537i \(0.299200\pi\)
\(54\) −9.97892 −1.35796
\(55\) −0.294956 −0.0397719
\(56\) −1.05947 −0.141577
\(57\) −5.06112 −0.670362
\(58\) 16.8579 2.21356
\(59\) 2.91642 0.379686 0.189843 0.981814i \(-0.439202\pi\)
0.189843 + 0.981814i \(0.439202\pi\)
\(60\) 3.83815 0.495503
\(61\) 8.46825 1.08425 0.542124 0.840299i \(-0.317620\pi\)
0.542124 + 0.840299i \(0.317620\pi\)
\(62\) 8.93216 1.13438
\(63\) 8.99365 1.13309
\(64\) −7.03886 −0.879857
\(65\) 11.9295 1.47967
\(66\) 0.297743 0.0366496
\(67\) −9.46516 −1.15635 −0.578177 0.815911i \(-0.696236\pi\)
−0.578177 + 0.815911i \(0.696236\pi\)
\(68\) 10.8969 1.32144
\(69\) 4.21683 0.507646
\(70\) −18.0743 −2.16029
\(71\) 13.3751 1.58734 0.793668 0.608351i \(-0.208169\pi\)
0.793668 + 0.608351i \(0.208169\pi\)
\(72\) −0.450647 −0.0531093
\(73\) −6.62409 −0.775291 −0.387646 0.921808i \(-0.626712\pi\)
−0.387646 + 0.921808i \(0.626712\pi\)
\(74\) 1.97055 0.229072
\(75\) 1.04342 0.120484
\(76\) 9.32695 1.06987
\(77\) −0.679942 −0.0774866
\(78\) −12.0421 −1.36350
\(79\) −9.72416 −1.09405 −0.547027 0.837115i \(-0.684240\pi\)
−0.547027 + 0.837115i \(0.684240\pi\)
\(80\) 8.41802 0.941164
\(81\) 0.693127 0.0770141
\(82\) −20.1022 −2.21991
\(83\) −1.11380 −0.122256 −0.0611278 0.998130i \(-0.519470\pi\)
−0.0611278 + 0.998130i \(0.519470\pi\)
\(84\) 8.84780 0.965375
\(85\) −11.5429 −1.25200
\(86\) −14.8347 −1.59967
\(87\) 8.74160 0.937198
\(88\) 0.0340700 0.00363188
\(89\) 7.87689 0.834949 0.417474 0.908689i \(-0.362915\pi\)
0.417474 + 0.908689i \(0.362915\pi\)
\(90\) −7.68794 −0.810380
\(91\) 27.5001 2.88279
\(92\) −7.77104 −0.810187
\(93\) 4.63173 0.480288
\(94\) 6.50102 0.670529
\(95\) −9.87988 −1.01365
\(96\) −8.02667 −0.819219
\(97\) 17.5649 1.78345 0.891725 0.452577i \(-0.149495\pi\)
0.891725 + 0.452577i \(0.149495\pi\)
\(98\) −27.8714 −2.81544
\(99\) −0.289215 −0.0290672
\(100\) −1.92288 −0.192288
\(101\) −12.7841 −1.27207 −0.636034 0.771661i \(-0.719426\pi\)
−0.636034 + 0.771661i \(0.719426\pi\)
\(102\) 11.6519 1.15371
\(103\) 1.20833 0.119060 0.0595302 0.998227i \(-0.481040\pi\)
0.0595302 + 0.998227i \(0.481040\pi\)
\(104\) −1.37796 −0.135120
\(105\) −9.37232 −0.914645
\(106\) −16.9228 −1.64369
\(107\) −9.61471 −0.929490 −0.464745 0.885445i \(-0.653854\pi\)
−0.464745 + 0.885445i \(0.653854\pi\)
\(108\) 9.53594 0.917596
\(109\) −1.00000 −0.0957826
\(110\) 0.581227 0.0554178
\(111\) 1.02182 0.0969869
\(112\) 19.4055 1.83364
\(113\) −9.29285 −0.874197 −0.437099 0.899414i \(-0.643994\pi\)
−0.437099 + 0.899414i \(0.643994\pi\)
\(114\) 9.97320 0.934076
\(115\) 8.23172 0.767612
\(116\) −16.1096 −1.49574
\(117\) 11.6973 1.08141
\(118\) −5.74697 −0.529051
\(119\) −26.6090 −2.43924
\(120\) 0.469622 0.0428704
\(121\) −10.9781 −0.998012
\(122\) −16.6871 −1.51078
\(123\) −10.4239 −0.939890
\(124\) −8.53564 −0.766523
\(125\) 12.0104 1.07424
\(126\) −17.7225 −1.57884
\(127\) 18.8334 1.67119 0.835596 0.549345i \(-0.185123\pi\)
0.835596 + 0.549345i \(0.185123\pi\)
\(128\) −1.84010 −0.162643
\(129\) −7.69248 −0.677285
\(130\) −23.5076 −2.06175
\(131\) 21.7971 1.90442 0.952210 0.305444i \(-0.0988049\pi\)
0.952210 + 0.305444i \(0.0988049\pi\)
\(132\) −0.284525 −0.0247647
\(133\) −22.7754 −1.97487
\(134\) 18.6516 1.61125
\(135\) −10.1012 −0.869377
\(136\) 1.33330 0.114330
\(137\) −8.60123 −0.734853 −0.367426 0.930053i \(-0.619761\pi\)
−0.367426 + 0.930053i \(0.619761\pi\)
\(138\) −8.30948 −0.707350
\(139\) 17.0727 1.44808 0.724042 0.689756i \(-0.242282\pi\)
0.724042 + 0.689756i \(0.242282\pi\)
\(140\) 17.2719 1.45974
\(141\) 3.37107 0.283896
\(142\) −26.3564 −2.21178
\(143\) −0.884341 −0.0739523
\(144\) 8.25417 0.687848
\(145\) 17.0646 1.41714
\(146\) 13.0531 1.08028
\(147\) −14.4526 −1.19203
\(148\) −1.88308 −0.154788
\(149\) 1.40424 0.115040 0.0575198 0.998344i \(-0.481681\pi\)
0.0575198 + 0.998344i \(0.481681\pi\)
\(150\) −2.05611 −0.167881
\(151\) −6.12834 −0.498717 −0.249359 0.968411i \(-0.580220\pi\)
−0.249359 + 0.968411i \(0.580220\pi\)
\(152\) 1.14121 0.0925645
\(153\) −11.3182 −0.915023
\(154\) 1.33986 0.107969
\(155\) 9.04165 0.726243
\(156\) 11.5076 0.921343
\(157\) −13.1395 −1.04864 −0.524322 0.851520i \(-0.675681\pi\)
−0.524322 + 0.851520i \(0.675681\pi\)
\(158\) 19.1620 1.52444
\(159\) −8.77526 −0.695923
\(160\) −15.6690 −1.23874
\(161\) 18.9760 1.49552
\(162\) −1.36584 −0.107311
\(163\) −8.64246 −0.676929 −0.338465 0.940979i \(-0.609908\pi\)
−0.338465 + 0.940979i \(0.609908\pi\)
\(164\) 19.2098 1.50003
\(165\) 0.301393 0.0234634
\(166\) 2.19480 0.170350
\(167\) 6.36306 0.492388 0.246194 0.969221i \(-0.420820\pi\)
0.246194 + 0.969221i \(0.420820\pi\)
\(168\) 1.08258 0.0835232
\(169\) 22.7670 1.75131
\(170\) 22.7458 1.74453
\(171\) −9.68757 −0.740827
\(172\) 14.1762 1.08092
\(173\) 16.9767 1.29071 0.645357 0.763881i \(-0.276709\pi\)
0.645357 + 0.763881i \(0.276709\pi\)
\(174\) −17.2258 −1.30588
\(175\) 4.69545 0.354943
\(176\) −0.624035 −0.0470384
\(177\) −2.98006 −0.223995
\(178\) −15.5218 −1.16341
\(179\) −1.68099 −0.125643 −0.0628216 0.998025i \(-0.520010\pi\)
−0.0628216 + 0.998025i \(0.520010\pi\)
\(180\) 7.34666 0.547588
\(181\) 17.1230 1.27274 0.636371 0.771383i \(-0.280435\pi\)
0.636371 + 0.771383i \(0.280435\pi\)
\(182\) −54.1904 −4.01686
\(183\) −8.65303 −0.639650
\(184\) −0.950835 −0.0700965
\(185\) 1.99471 0.146654
\(186\) −9.12706 −0.669228
\(187\) 0.855684 0.0625738
\(188\) −6.21243 −0.453088
\(189\) −23.2857 −1.69378
\(190\) 19.4688 1.41242
\(191\) −8.62110 −0.623801 −0.311901 0.950115i \(-0.600966\pi\)
−0.311901 + 0.950115i \(0.600966\pi\)
\(192\) 7.19245 0.519070
\(193\) −9.64784 −0.694467 −0.347233 0.937779i \(-0.612879\pi\)
−0.347233 + 0.937779i \(0.612879\pi\)
\(194\) −34.6126 −2.48504
\(195\) −12.1898 −0.872927
\(196\) 26.6342 1.90244
\(197\) −21.0894 −1.50256 −0.751280 0.659984i \(-0.770563\pi\)
−0.751280 + 0.659984i \(0.770563\pi\)
\(198\) 0.569914 0.0405020
\(199\) 14.6718 1.04006 0.520029 0.854148i \(-0.325921\pi\)
0.520029 + 0.854148i \(0.325921\pi\)
\(200\) −0.235276 −0.0166366
\(201\) 9.67170 0.682189
\(202\) 25.1918 1.77249
\(203\) 39.3378 2.76097
\(204\) −11.1347 −0.779582
\(205\) −20.3486 −1.42121
\(206\) −2.38108 −0.165898
\(207\) 8.07150 0.561008
\(208\) 25.2390 1.75001
\(209\) 0.732404 0.0506614
\(210\) 18.4687 1.27446
\(211\) −12.2705 −0.844736 −0.422368 0.906425i \(-0.638801\pi\)
−0.422368 + 0.906425i \(0.638801\pi\)
\(212\) 16.1716 1.11067
\(213\) −13.6670 −0.936447
\(214\) 18.9463 1.29514
\(215\) −15.0166 −1.02412
\(216\) 1.16678 0.0793894
\(217\) 20.8431 1.41492
\(218\) 1.97055 0.133463
\(219\) 6.76863 0.457382
\(220\) −0.555425 −0.0374468
\(221\) −34.6079 −2.32798
\(222\) −2.01355 −0.135141
\(223\) 8.42206 0.563983 0.281991 0.959417i \(-0.409005\pi\)
0.281991 + 0.959417i \(0.409005\pi\)
\(224\) −36.1205 −2.41340
\(225\) 1.99723 0.133148
\(226\) 18.3120 1.21810
\(227\) −10.0213 −0.665139 −0.332570 0.943079i \(-0.607916\pi\)
−0.332570 + 0.943079i \(0.607916\pi\)
\(228\) −9.53047 −0.631171
\(229\) 20.0915 1.32768 0.663841 0.747874i \(-0.268925\pi\)
0.663841 + 0.747874i \(0.268925\pi\)
\(230\) −16.2210 −1.06958
\(231\) 0.694778 0.0457131
\(232\) −1.97111 −0.129410
\(233\) −1.77267 −0.116132 −0.0580659 0.998313i \(-0.518493\pi\)
−0.0580659 + 0.998313i \(0.518493\pi\)
\(234\) −23.0501 −1.50683
\(235\) 6.58071 0.429278
\(236\) 5.49185 0.357489
\(237\) 9.93635 0.645435
\(238\) 52.4343 3.39881
\(239\) 8.81715 0.570334 0.285167 0.958478i \(-0.407951\pi\)
0.285167 + 0.958478i \(0.407951\pi\)
\(240\) −8.60171 −0.555238
\(241\) 6.64155 0.427820 0.213910 0.976853i \(-0.431380\pi\)
0.213910 + 0.976853i \(0.431380\pi\)
\(242\) 21.6330 1.39062
\(243\) −15.9003 −1.02001
\(244\) 15.9463 1.02086
\(245\) −28.2131 −1.80247
\(246\) 20.5408 1.30963
\(247\) −29.6219 −1.88480
\(248\) −1.04439 −0.0663188
\(249\) 1.13810 0.0721244
\(250\) −23.6671 −1.49684
\(251\) 11.8620 0.748720 0.374360 0.927283i \(-0.377862\pi\)
0.374360 + 0.927283i \(0.377862\pi\)
\(252\) 16.9357 1.06685
\(253\) −0.610225 −0.0383645
\(254\) −37.1121 −2.32862
\(255\) 11.7947 0.738616
\(256\) 17.7037 1.10648
\(257\) −18.7509 −1.16965 −0.584824 0.811160i \(-0.698837\pi\)
−0.584824 + 0.811160i \(0.698837\pi\)
\(258\) 15.1584 0.943723
\(259\) 4.59826 0.285722
\(260\) 22.4641 1.39316
\(261\) 16.7324 1.03571
\(262\) −42.9523 −2.65360
\(263\) −12.7417 −0.785685 −0.392842 0.919606i \(-0.628508\pi\)
−0.392842 + 0.919606i \(0.628508\pi\)
\(264\) −0.0348134 −0.00214262
\(265\) −17.1303 −1.05231
\(266\) 44.8800 2.75177
\(267\) −8.04877 −0.492577
\(268\) −17.8236 −1.08875
\(269\) −20.3942 −1.24345 −0.621727 0.783234i \(-0.713569\pi\)
−0.621727 + 0.783234i \(0.713569\pi\)
\(270\) 19.9050 1.21138
\(271\) −15.1779 −0.921992 −0.460996 0.887402i \(-0.652508\pi\)
−0.460996 + 0.887402i \(0.652508\pi\)
\(272\) −24.4211 −1.48075
\(273\) −28.1002 −1.70070
\(274\) 16.9492 1.02394
\(275\) −0.150995 −0.00910535
\(276\) 7.94061 0.477968
\(277\) 24.2305 1.45587 0.727935 0.685647i \(-0.240480\pi\)
0.727935 + 0.685647i \(0.240480\pi\)
\(278\) −33.6425 −2.01775
\(279\) 8.86566 0.530773
\(280\) 2.11333 0.126295
\(281\) −2.17622 −0.129822 −0.0649111 0.997891i \(-0.520676\pi\)
−0.0649111 + 0.997891i \(0.520676\pi\)
\(282\) −6.64287 −0.395577
\(283\) −7.25351 −0.431177 −0.215588 0.976484i \(-0.569167\pi\)
−0.215588 + 0.976484i \(0.569167\pi\)
\(284\) 25.1864 1.49454
\(285\) 10.0955 0.598003
\(286\) 1.74264 0.103044
\(287\) −46.9081 −2.76890
\(288\) −15.3640 −0.905331
\(289\) 16.4865 0.969792
\(290\) −33.6267 −1.97463
\(291\) −17.9482 −1.05214
\(292\) −12.4737 −0.729966
\(293\) −15.6834 −0.916234 −0.458117 0.888892i \(-0.651476\pi\)
−0.458117 + 0.888892i \(0.651476\pi\)
\(294\) 28.4796 1.66096
\(295\) −5.81742 −0.338703
\(296\) −0.230406 −0.0133921
\(297\) 0.748814 0.0434506
\(298\) −2.76712 −0.160295
\(299\) 24.6804 1.42731
\(300\) 1.96484 0.113440
\(301\) −34.6167 −1.99527
\(302\) 12.0762 0.694908
\(303\) 13.0631 0.750455
\(304\) −20.9027 −1.19885
\(305\) −16.8917 −0.967215
\(306\) 22.3031 1.27498
\(307\) −5.37871 −0.306979 −0.153489 0.988150i \(-0.549051\pi\)
−0.153489 + 0.988150i \(0.549051\pi\)
\(308\) −1.28038 −0.0729565
\(309\) −1.23470 −0.0702394
\(310\) −17.8170 −1.01194
\(311\) 6.01019 0.340807 0.170403 0.985374i \(-0.445493\pi\)
0.170403 + 0.985374i \(0.445493\pi\)
\(312\) 1.40802 0.0797136
\(313\) −0.833868 −0.0471330 −0.0235665 0.999722i \(-0.507502\pi\)
−0.0235665 + 0.999722i \(0.507502\pi\)
\(314\) 25.8920 1.46117
\(315\) −17.9397 −1.01079
\(316\) −18.3113 −1.03009
\(317\) −2.80052 −0.157293 −0.0786465 0.996903i \(-0.525060\pi\)
−0.0786465 + 0.996903i \(0.525060\pi\)
\(318\) 17.2921 0.969693
\(319\) −1.26501 −0.0708271
\(320\) 14.0405 0.784886
\(321\) 9.82451 0.548351
\(322\) −37.3932 −2.08384
\(323\) 28.6620 1.59480
\(324\) 1.30521 0.0725117
\(325\) 6.10697 0.338754
\(326\) 17.0304 0.943227
\(327\) 1.02182 0.0565068
\(328\) 2.35044 0.129781
\(329\) 15.1700 0.836351
\(330\) −0.593910 −0.0326937
\(331\) 13.2177 0.726513 0.363256 0.931689i \(-0.381665\pi\)
0.363256 + 0.931689i \(0.381665\pi\)
\(332\) −2.09737 −0.115108
\(333\) 1.95588 0.107182
\(334\) −12.5387 −0.686089
\(335\) 18.8802 1.03154
\(336\) −19.8289 −1.08176
\(337\) −0.664361 −0.0361900 −0.0180950 0.999836i \(-0.505760\pi\)
−0.0180950 + 0.999836i \(0.505760\pi\)
\(338\) −44.8635 −2.44025
\(339\) 9.49562 0.515731
\(340\) −21.7361 −1.17881
\(341\) −0.670266 −0.0362969
\(342\) 19.0899 1.03226
\(343\) −32.8498 −1.77372
\(344\) 1.73455 0.0935205
\(345\) −8.41134 −0.452851
\(346\) −33.4535 −1.79847
\(347\) −23.3057 −1.25112 −0.625558 0.780178i \(-0.715129\pi\)
−0.625558 + 0.780178i \(0.715129\pi\)
\(348\) 16.4611 0.882408
\(349\) −30.1020 −1.61132 −0.805662 0.592375i \(-0.798190\pi\)
−0.805662 + 0.592375i \(0.798190\pi\)
\(350\) −9.25264 −0.494574
\(351\) −30.2856 −1.61653
\(352\) 1.16155 0.0619111
\(353\) −30.6406 −1.63083 −0.815417 0.578874i \(-0.803492\pi\)
−0.815417 + 0.578874i \(0.803492\pi\)
\(354\) 5.87237 0.312113
\(355\) −26.6795 −1.41600
\(356\) 14.8328 0.786136
\(357\) 27.1896 1.43903
\(358\) 3.31248 0.175070
\(359\) 22.9484 1.21117 0.605585 0.795781i \(-0.292939\pi\)
0.605585 + 0.795781i \(0.292939\pi\)
\(360\) 0.898910 0.0473767
\(361\) 5.53264 0.291191
\(362\) −33.7418 −1.77343
\(363\) 11.2177 0.588776
\(364\) 51.7848 2.71426
\(365\) 13.2131 0.691607
\(366\) 17.0512 0.891283
\(367\) 30.3728 1.58545 0.792724 0.609580i \(-0.208662\pi\)
0.792724 + 0.609580i \(0.208662\pi\)
\(368\) 17.4157 0.907858
\(369\) −19.9525 −1.03869
\(370\) −3.93068 −0.204346
\(371\) −39.4892 −2.05018
\(372\) 8.72189 0.452209
\(373\) 5.48861 0.284189 0.142095 0.989853i \(-0.454616\pi\)
0.142095 + 0.989853i \(0.454616\pi\)
\(374\) −1.68617 −0.0871897
\(375\) −12.2725 −0.633749
\(376\) −0.760129 −0.0392007
\(377\) 51.1632 2.63504
\(378\) 45.8856 2.36010
\(379\) 1.37247 0.0704992 0.0352496 0.999379i \(-0.488777\pi\)
0.0352496 + 0.999379i \(0.488777\pi\)
\(380\) −18.6046 −0.954393
\(381\) −19.2443 −0.985917
\(382\) 16.9883 0.869199
\(383\) 7.86117 0.401687 0.200844 0.979623i \(-0.435632\pi\)
0.200844 + 0.979623i \(0.435632\pi\)
\(384\) 1.88025 0.0959511
\(385\) 1.35629 0.0691227
\(386\) 19.0116 0.967664
\(387\) −14.7243 −0.748479
\(388\) 33.0761 1.67919
\(389\) 24.1926 1.22661 0.613306 0.789846i \(-0.289839\pi\)
0.613306 + 0.789846i \(0.289839\pi\)
\(390\) 24.0206 1.21633
\(391\) −23.8806 −1.20770
\(392\) 3.25886 0.164597
\(393\) −22.2727 −1.12351
\(394\) 41.5578 2.09365
\(395\) 19.3969 0.975963
\(396\) −0.544614 −0.0273679
\(397\) −24.4275 −1.22598 −0.612990 0.790091i \(-0.710033\pi\)
−0.612990 + 0.790091i \(0.710033\pi\)
\(398\) −28.9116 −1.44921
\(399\) 23.2723 1.16507
\(400\) 4.30938 0.215469
\(401\) −30.6409 −1.53013 −0.765067 0.643950i \(-0.777294\pi\)
−0.765067 + 0.643950i \(0.777294\pi\)
\(402\) −19.0586 −0.950556
\(403\) 27.1088 1.35038
\(404\) −24.0735 −1.19770
\(405\) −1.38259 −0.0687013
\(406\) −77.5171 −3.84711
\(407\) −0.147869 −0.00732962
\(408\) −1.36240 −0.0674486
\(409\) −1.34065 −0.0662908 −0.0331454 0.999451i \(-0.510552\pi\)
−0.0331454 + 0.999451i \(0.510552\pi\)
\(410\) 40.0980 1.98030
\(411\) 8.78891 0.433525
\(412\) 2.27538 0.112100
\(413\) −13.4105 −0.659886
\(414\) −15.9053 −0.781703
\(415\) 2.22171 0.109059
\(416\) −46.9788 −2.30333
\(417\) −17.4452 −0.854294
\(418\) −1.44324 −0.0705912
\(419\) 0.699066 0.0341516 0.0170758 0.999854i \(-0.494564\pi\)
0.0170758 + 0.999854i \(0.494564\pi\)
\(420\) −17.6488 −0.861173
\(421\) 36.1837 1.76349 0.881744 0.471728i \(-0.156370\pi\)
0.881744 + 0.471728i \(0.156370\pi\)
\(422\) 24.1796 1.17705
\(423\) 6.45262 0.313737
\(424\) 1.97870 0.0960940
\(425\) −5.90907 −0.286632
\(426\) 26.9315 1.30484
\(427\) −38.9392 −1.88440
\(428\) −18.1052 −0.875149
\(429\) 0.903637 0.0436280
\(430\) 29.5910 1.42700
\(431\) −19.3507 −0.932088 −0.466044 0.884761i \(-0.654321\pi\)
−0.466044 + 0.884761i \(0.654321\pi\)
\(432\) −21.3711 −1.02822
\(433\) 37.5133 1.80277 0.901387 0.433014i \(-0.142550\pi\)
0.901387 + 0.433014i \(0.142550\pi\)
\(434\) −41.0723 −1.97154
\(435\) −17.4370 −0.836038
\(436\) −1.88308 −0.0901830
\(437\) −20.4401 −0.977783
\(438\) −13.3379 −0.637312
\(439\) −20.9945 −1.00201 −0.501006 0.865444i \(-0.667036\pi\)
−0.501006 + 0.865444i \(0.667036\pi\)
\(440\) −0.0679598 −0.00323985
\(441\) −27.6639 −1.31733
\(442\) 68.1968 3.24379
\(443\) −15.6328 −0.742737 −0.371369 0.928485i \(-0.621111\pi\)
−0.371369 + 0.928485i \(0.621111\pi\)
\(444\) 1.92416 0.0913168
\(445\) −15.7121 −0.744825
\(446\) −16.5961 −0.785848
\(447\) −1.43488 −0.0678674
\(448\) 32.3665 1.52917
\(449\) −19.5869 −0.924364 −0.462182 0.886785i \(-0.652933\pi\)
−0.462182 + 0.886785i \(0.652933\pi\)
\(450\) −3.93564 −0.185528
\(451\) 1.50846 0.0710306
\(452\) −17.4991 −0.823090
\(453\) 6.26207 0.294218
\(454\) 19.7476 0.926799
\(455\) −54.8547 −2.57163
\(456\) −1.16611 −0.0546082
\(457\) 28.8389 1.34903 0.674513 0.738263i \(-0.264354\pi\)
0.674513 + 0.738263i \(0.264354\pi\)
\(458\) −39.5913 −1.84998
\(459\) 29.3042 1.36780
\(460\) 15.5010 0.722736
\(461\) −0.777552 −0.0362142 −0.0181071 0.999836i \(-0.505764\pi\)
−0.0181071 + 0.999836i \(0.505764\pi\)
\(462\) −1.36910 −0.0636962
\(463\) −21.4915 −0.998796 −0.499398 0.866373i \(-0.666445\pi\)
−0.499398 + 0.866373i \(0.666445\pi\)
\(464\) 36.1033 1.67606
\(465\) −9.23895 −0.428446
\(466\) 3.49315 0.161817
\(467\) −13.0787 −0.605212 −0.302606 0.953116i \(-0.597857\pi\)
−0.302606 + 0.953116i \(0.597857\pi\)
\(468\) 22.0268 1.01819
\(469\) 43.5233 2.00972
\(470\) −12.9676 −0.598153
\(471\) 13.4262 0.618646
\(472\) 0.671962 0.0309296
\(473\) 1.11319 0.0511847
\(474\) −19.5801 −0.899344
\(475\) −5.05774 −0.232065
\(476\) −50.1067 −2.29664
\(477\) −16.7969 −0.769075
\(478\) −17.3746 −0.794698
\(479\) −12.9537 −0.591870 −0.295935 0.955208i \(-0.595631\pi\)
−0.295935 + 0.955208i \(0.595631\pi\)
\(480\) 16.0109 0.730793
\(481\) 5.98055 0.272690
\(482\) −13.0875 −0.596120
\(483\) −19.3901 −0.882278
\(484\) −20.6727 −0.939666
\(485\) −35.0370 −1.59095
\(486\) 31.3324 1.42127
\(487\) 3.00195 0.136031 0.0680157 0.997684i \(-0.478333\pi\)
0.0680157 + 0.997684i \(0.478333\pi\)
\(488\) 1.95114 0.0883238
\(489\) 8.83104 0.399353
\(490\) 55.5954 2.51154
\(491\) 13.1521 0.593546 0.296773 0.954948i \(-0.404089\pi\)
0.296773 + 0.954948i \(0.404089\pi\)
\(492\) −19.6290 −0.884942
\(493\) −49.5052 −2.22960
\(494\) 58.3715 2.62626
\(495\) 0.576900 0.0259297
\(496\) 19.1293 0.858931
\(497\) −61.5023 −2.75876
\(498\) −2.24269 −0.100498
\(499\) 26.0363 1.16554 0.582772 0.812635i \(-0.301968\pi\)
0.582772 + 0.812635i \(0.301968\pi\)
\(500\) 22.6165 1.01144
\(501\) −6.50190 −0.290484
\(502\) −23.3746 −1.04326
\(503\) −40.9404 −1.82544 −0.912722 0.408582i \(-0.866023\pi\)
−0.912722 + 0.408582i \(0.866023\pi\)
\(504\) 2.07219 0.0923028
\(505\) 25.5006 1.13476
\(506\) 1.20248 0.0534567
\(507\) −23.2638 −1.03318
\(508\) 35.4647 1.57349
\(509\) 5.31906 0.235763 0.117882 0.993028i \(-0.462390\pi\)
0.117882 + 0.993028i \(0.462390\pi\)
\(510\) −23.2422 −1.02918
\(511\) 30.4593 1.34744
\(512\) −31.2059 −1.37912
\(513\) 25.0823 1.10741
\(514\) 36.9496 1.62978
\(515\) −2.41027 −0.106209
\(516\) −14.4855 −0.637690
\(517\) −0.487834 −0.0214549
\(518\) −9.06110 −0.398122
\(519\) −17.3471 −0.761455
\(520\) 2.74862 0.120535
\(521\) 11.9207 0.522254 0.261127 0.965304i \(-0.415906\pi\)
0.261127 + 0.965304i \(0.415906\pi\)
\(522\) −32.9722 −1.44315
\(523\) −30.4181 −1.33009 −0.665045 0.746803i \(-0.731588\pi\)
−0.665045 + 0.746803i \(0.731588\pi\)
\(524\) 41.0456 1.79308
\(525\) −4.79791 −0.209398
\(526\) 25.1081 1.09477
\(527\) −26.2303 −1.14261
\(528\) 0.637652 0.0277502
\(529\) −5.96969 −0.259552
\(530\) 33.7561 1.46627
\(531\) −5.70418 −0.247541
\(532\) −42.8877 −1.85942
\(533\) −61.0093 −2.64261
\(534\) 15.8605 0.686352
\(535\) 19.1786 0.829161
\(536\) −2.18083 −0.0941976
\(537\) 1.71767 0.0741230
\(538\) 40.1878 1.73262
\(539\) 2.09146 0.0900856
\(540\) −19.0214 −0.818551
\(541\) 22.9775 0.987882 0.493941 0.869496i \(-0.335556\pi\)
0.493941 + 0.869496i \(0.335556\pi\)
\(542\) 29.9089 1.28470
\(543\) −17.4966 −0.750852
\(544\) 45.4565 1.94893
\(545\) 1.99471 0.0854439
\(546\) 55.3728 2.36974
\(547\) −3.91647 −0.167456 −0.0837282 0.996489i \(-0.526683\pi\)
−0.0837282 + 0.996489i \(0.526683\pi\)
\(548\) −16.1968 −0.691891
\(549\) −16.5629 −0.706887
\(550\) 0.297544 0.0126873
\(551\) −42.3729 −1.80515
\(552\) 0.971583 0.0413533
\(553\) 44.7142 1.90144
\(554\) −47.7474 −2.02859
\(555\) −2.03823 −0.0865182
\(556\) 32.1491 1.36342
\(557\) 31.8265 1.34853 0.674266 0.738488i \(-0.264460\pi\)
0.674266 + 0.738488i \(0.264460\pi\)
\(558\) −17.4703 −0.739575
\(559\) −45.0229 −1.90426
\(560\) −38.7082 −1.63572
\(561\) −0.874355 −0.0369153
\(562\) 4.28835 0.180893
\(563\) −45.5972 −1.92169 −0.960846 0.277082i \(-0.910633\pi\)
−0.960846 + 0.277082i \(0.910633\pi\)
\(564\) 6.34798 0.267298
\(565\) 18.5365 0.779837
\(566\) 14.2934 0.600797
\(567\) −3.18718 −0.133849
\(568\) 3.08171 0.129306
\(569\) 36.6562 1.53671 0.768353 0.640026i \(-0.221076\pi\)
0.768353 + 0.640026i \(0.221076\pi\)
\(570\) −19.8936 −0.833253
\(571\) −36.5350 −1.52894 −0.764471 0.644658i \(-0.777000\pi\)
−0.764471 + 0.644658i \(0.777000\pi\)
\(572\) −1.66528 −0.0696289
\(573\) 8.80922 0.368010
\(574\) 92.4349 3.85816
\(575\) 4.21401 0.175736
\(576\) 13.7672 0.573633
\(577\) 44.5360 1.85406 0.927028 0.374992i \(-0.122354\pi\)
0.927028 + 0.374992i \(0.122354\pi\)
\(578\) −32.4874 −1.35130
\(579\) 9.85836 0.409700
\(580\) 32.1339 1.33429
\(581\) 5.12154 0.212477
\(582\) 35.3679 1.46605
\(583\) 1.26988 0.0525932
\(584\) −1.52623 −0.0631559
\(585\) −23.3326 −0.964685
\(586\) 30.9049 1.27667
\(587\) 2.45740 0.101428 0.0507138 0.998713i \(-0.483850\pi\)
0.0507138 + 0.998713i \(0.483850\pi\)
\(588\) −27.2153 −1.12234
\(589\) −22.4512 −0.925088
\(590\) 11.4635 0.471946
\(591\) 21.5496 0.886433
\(592\) 4.22018 0.173448
\(593\) −6.85210 −0.281382 −0.140691 0.990054i \(-0.544932\pi\)
−0.140691 + 0.990054i \(0.544932\pi\)
\(594\) −1.47558 −0.0605437
\(595\) 53.0771 2.17595
\(596\) 2.64428 0.108314
\(597\) −14.9920 −0.613581
\(598\) −48.6340 −1.98879
\(599\) −9.11532 −0.372442 −0.186221 0.982508i \(-0.559624\pi\)
−0.186221 + 0.982508i \(0.559624\pi\)
\(600\) 0.240410 0.00981471
\(601\) 29.8340 1.21695 0.608477 0.793571i \(-0.291781\pi\)
0.608477 + 0.793571i \(0.291781\pi\)
\(602\) 68.2139 2.78019
\(603\) 18.5128 0.753898
\(604\) −11.5401 −0.469561
\(605\) 21.8982 0.890288
\(606\) −25.7415 −1.04568
\(607\) 14.1509 0.574368 0.287184 0.957875i \(-0.407281\pi\)
0.287184 + 0.957875i \(0.407281\pi\)
\(608\) 38.9075 1.57791
\(609\) −40.1961 −1.62883
\(610\) 33.2859 1.34771
\(611\) 19.7303 0.798204
\(612\) −21.3130 −0.861528
\(613\) −22.6702 −0.915641 −0.457820 0.889045i \(-0.651370\pi\)
−0.457820 + 0.889045i \(0.651370\pi\)
\(614\) 10.5990 0.427742
\(615\) 20.7926 0.838439
\(616\) −0.156663 −0.00631212
\(617\) 36.9447 1.48734 0.743669 0.668548i \(-0.233084\pi\)
0.743669 + 0.668548i \(0.233084\pi\)
\(618\) 2.43303 0.0978710
\(619\) −42.5386 −1.70977 −0.854884 0.518818i \(-0.826372\pi\)
−0.854884 + 0.518818i \(0.826372\pi\)
\(620\) 17.0261 0.683785
\(621\) −20.8981 −0.838612
\(622\) −11.8434 −0.474877
\(623\) −36.2200 −1.45112
\(624\) −25.7897 −1.03241
\(625\) −18.8516 −0.754064
\(626\) 1.64318 0.0656747
\(627\) −0.748385 −0.0298876
\(628\) −24.7426 −0.987338
\(629\) −5.78675 −0.230733
\(630\) 35.3511 1.40842
\(631\) −38.7494 −1.54259 −0.771295 0.636478i \(-0.780390\pi\)
−0.771295 + 0.636478i \(0.780390\pi\)
\(632\) −2.24051 −0.0891226
\(633\) 12.5382 0.498350
\(634\) 5.51858 0.219171
\(635\) −37.5671 −1.49080
\(636\) −16.5245 −0.655238
\(637\) −84.5887 −3.35153
\(638\) 2.49277 0.0986899
\(639\) −26.1602 −1.03488
\(640\) 3.67046 0.145088
\(641\) −25.7708 −1.01789 −0.508944 0.860800i \(-0.669964\pi\)
−0.508944 + 0.860800i \(0.669964\pi\)
\(642\) −19.3597 −0.764067
\(643\) 12.1811 0.480374 0.240187 0.970727i \(-0.422791\pi\)
0.240187 + 0.970727i \(0.422791\pi\)
\(644\) 35.7332 1.40809
\(645\) 15.3443 0.604180
\(646\) −56.4800 −2.22218
\(647\) −34.6555 −1.36245 −0.681224 0.732075i \(-0.738552\pi\)
−0.681224 + 0.732075i \(0.738552\pi\)
\(648\) 0.159701 0.00627363
\(649\) 0.431250 0.0169280
\(650\) −12.0341 −0.472016
\(651\) −21.2979 −0.834729
\(652\) −16.2744 −0.637355
\(653\) 32.8451 1.28533 0.642665 0.766147i \(-0.277829\pi\)
0.642665 + 0.766147i \(0.277829\pi\)
\(654\) −2.01355 −0.0787361
\(655\) −43.4788 −1.69886
\(656\) −43.0513 −1.68087
\(657\) 12.9560 0.505460
\(658\) −29.8934 −1.16536
\(659\) 0.334015 0.0130114 0.00650569 0.999979i \(-0.497929\pi\)
0.00650569 + 0.999979i \(0.497929\pi\)
\(660\) 0.567545 0.0220917
\(661\) 35.1421 1.36687 0.683435 0.730011i \(-0.260485\pi\)
0.683435 + 0.730011i \(0.260485\pi\)
\(662\) −26.0462 −1.01232
\(663\) 35.3631 1.37339
\(664\) −0.256627 −0.00995904
\(665\) 45.4302 1.76171
\(666\) −3.85417 −0.149346
\(667\) 35.3043 1.36699
\(668\) 11.9821 0.463602
\(669\) −8.60583 −0.332721
\(670\) −37.2045 −1.43734
\(671\) 1.25220 0.0483405
\(672\) 36.9087 1.42378
\(673\) −2.05265 −0.0791240 −0.0395620 0.999217i \(-0.512596\pi\)
−0.0395620 + 0.999217i \(0.512596\pi\)
\(674\) 1.30916 0.0504269
\(675\) −5.17107 −0.199034
\(676\) 42.8719 1.64892
\(677\) −37.4889 −1.44081 −0.720407 0.693552i \(-0.756045\pi\)
−0.720407 + 0.693552i \(0.756045\pi\)
\(678\) −18.7116 −0.718615
\(679\) −80.7681 −3.09960
\(680\) −2.65955 −0.101989
\(681\) 10.2400 0.392398
\(682\) 1.32079 0.0505758
\(683\) −0.722222 −0.0276351 −0.0138175 0.999905i \(-0.504398\pi\)
−0.0138175 + 0.999905i \(0.504398\pi\)
\(684\) −18.2424 −0.697517
\(685\) 17.1569 0.655533
\(686\) 64.7322 2.47149
\(687\) −20.5299 −0.783263
\(688\) −31.7704 −1.21124
\(689\) −51.3602 −1.95667
\(690\) 16.5750 0.630999
\(691\) 35.6903 1.35772 0.678861 0.734266i \(-0.262474\pi\)
0.678861 + 0.734266i \(0.262474\pi\)
\(692\) 31.9684 1.21526
\(693\) 1.32989 0.0505182
\(694\) 45.9251 1.74329
\(695\) −34.0550 −1.29178
\(696\) 2.01412 0.0763450
\(697\) 59.0323 2.23601
\(698\) 59.3176 2.24520
\(699\) 1.81135 0.0685117
\(700\) 8.84189 0.334192
\(701\) 21.8072 0.823648 0.411824 0.911263i \(-0.364892\pi\)
0.411824 + 0.911263i \(0.364892\pi\)
\(702\) 59.6794 2.25246
\(703\) −4.95304 −0.186808
\(704\) −1.04083 −0.0392278
\(705\) −6.72431 −0.253252
\(706\) 60.3789 2.27239
\(707\) 58.7847 2.21083
\(708\) −5.61168 −0.210900
\(709\) 6.15257 0.231065 0.115532 0.993304i \(-0.463143\pi\)
0.115532 + 0.993304i \(0.463143\pi\)
\(710\) 52.5733 1.97304
\(711\) 19.0193 0.713280
\(712\) 1.81488 0.0680156
\(713\) 18.7059 0.700543
\(714\) −53.5785 −2.00512
\(715\) 1.76400 0.0659699
\(716\) −3.16544 −0.118298
\(717\) −9.00954 −0.336467
\(718\) −45.2210 −1.68763
\(719\) 2.59823 0.0968977 0.0484489 0.998826i \(-0.484572\pi\)
0.0484489 + 0.998826i \(0.484572\pi\)
\(720\) −16.4647 −0.613602
\(721\) −5.55621 −0.206924
\(722\) −10.9023 −0.405743
\(723\) −6.78647 −0.252392
\(724\) 32.2439 1.19833
\(725\) 8.73577 0.324438
\(726\) −22.1050 −0.820395
\(727\) −26.5290 −0.983905 −0.491953 0.870622i \(-0.663717\pi\)
−0.491953 + 0.870622i \(0.663717\pi\)
\(728\) 6.33619 0.234835
\(729\) 14.1679 0.524737
\(730\) −26.0372 −0.963679
\(731\) 43.5639 1.61127
\(732\) −16.2943 −0.602255
\(733\) −14.6904 −0.542604 −0.271302 0.962494i \(-0.587454\pi\)
−0.271302 + 0.962494i \(0.587454\pi\)
\(734\) −59.8512 −2.20915
\(735\) 28.8287 1.06336
\(736\) −32.4170 −1.19491
\(737\) −1.39961 −0.0515552
\(738\) 39.3175 1.44730
\(739\) 5.78051 0.212639 0.106320 0.994332i \(-0.466093\pi\)
0.106320 + 0.994332i \(0.466093\pi\)
\(740\) 3.75619 0.138080
\(741\) 30.2683 1.11193
\(742\) 77.8155 2.85670
\(743\) −4.40453 −0.161586 −0.0807932 0.996731i \(-0.525745\pi\)
−0.0807932 + 0.996731i \(0.525745\pi\)
\(744\) 1.06718 0.0391246
\(745\) −2.80104 −0.102622
\(746\) −10.8156 −0.395987
\(747\) 2.17846 0.0797058
\(748\) 1.61132 0.0589156
\(749\) 44.2109 1.61543
\(750\) 24.1836 0.883059
\(751\) −17.5718 −0.641202 −0.320601 0.947214i \(-0.603885\pi\)
−0.320601 + 0.947214i \(0.603885\pi\)
\(752\) 13.9227 0.507710
\(753\) −12.1208 −0.441706
\(754\) −100.820 −3.67164
\(755\) 12.2243 0.444886
\(756\) −43.8487 −1.59476
\(757\) 10.9831 0.399186 0.199593 0.979879i \(-0.436038\pi\)
0.199593 + 0.979879i \(0.436038\pi\)
\(758\) −2.70453 −0.0982329
\(759\) 0.623540 0.0226331
\(760\) −2.27638 −0.0825731
\(761\) −4.03291 −0.146193 −0.0730964 0.997325i \(-0.523288\pi\)
−0.0730964 + 0.997325i \(0.523288\pi\)
\(762\) 37.9219 1.37377
\(763\) 4.59826 0.166468
\(764\) −16.2342 −0.587332
\(765\) 22.5765 0.816256
\(766\) −15.4909 −0.559707
\(767\) −17.4418 −0.629788
\(768\) −18.0900 −0.652768
\(769\) 28.2518 1.01879 0.509394 0.860533i \(-0.329870\pi\)
0.509394 + 0.860533i \(0.329870\pi\)
\(770\) −2.67263 −0.0963150
\(771\) 19.1601 0.690032
\(772\) −18.1676 −0.653867
\(773\) −35.9229 −1.29206 −0.646028 0.763314i \(-0.723571\pi\)
−0.646028 + 0.763314i \(0.723571\pi\)
\(774\) 29.0150 1.04292
\(775\) 4.62863 0.166265
\(776\) 4.04707 0.145281
\(777\) −4.69859 −0.168561
\(778\) −47.6727 −1.70915
\(779\) 50.5274 1.81033
\(780\) −22.9542 −0.821894
\(781\) 1.97777 0.0707703
\(782\) 47.0580 1.68279
\(783\) −43.3224 −1.54822
\(784\) −59.6900 −2.13179
\(785\) 26.2094 0.935454
\(786\) 43.8895 1.56549
\(787\) 42.7074 1.52235 0.761177 0.648544i \(-0.224622\pi\)
0.761177 + 0.648544i \(0.224622\pi\)
\(788\) −39.7130 −1.41472
\(789\) 13.0197 0.463513
\(790\) −38.2225 −1.35990
\(791\) 42.7309 1.51934
\(792\) −0.0666370 −0.00236784
\(793\) −50.6448 −1.79845
\(794\) 48.1356 1.70827
\(795\) 17.5041 0.620806
\(796\) 27.6282 0.979254
\(797\) 39.0827 1.38438 0.692190 0.721716i \(-0.256646\pi\)
0.692190 + 0.721716i \(0.256646\pi\)
\(798\) −45.8593 −1.62340
\(799\) −19.0910 −0.675390
\(800\) −8.02131 −0.283596
\(801\) −15.4063 −0.544354
\(802\) 60.3795 2.13208
\(803\) −0.979501 −0.0345658
\(804\) 18.2125 0.642307
\(805\) −37.8516 −1.33409
\(806\) −53.4192 −1.88161
\(807\) 20.8392 0.733574
\(808\) −2.94554 −0.103624
\(809\) 4.36769 0.153560 0.0767800 0.997048i \(-0.475536\pi\)
0.0767800 + 0.997048i \(0.475536\pi\)
\(810\) 2.72446 0.0957277
\(811\) 18.2529 0.640945 0.320472 0.947258i \(-0.396158\pi\)
0.320472 + 0.947258i \(0.396158\pi\)
\(812\) 74.0760 2.59956
\(813\) 15.5091 0.543928
\(814\) 0.291384 0.0102130
\(815\) 17.2392 0.603862
\(816\) 24.9540 0.873564
\(817\) 37.2876 1.30453
\(818\) 2.64182 0.0923690
\(819\) −53.7870 −1.87947
\(820\) −38.3179 −1.33812
\(821\) 32.1393 1.12167 0.560835 0.827928i \(-0.310480\pi\)
0.560835 + 0.827928i \(0.310480\pi\)
\(822\) −17.3190 −0.604070
\(823\) 40.7252 1.41959 0.709796 0.704407i \(-0.248787\pi\)
0.709796 + 0.704407i \(0.248787\pi\)
\(824\) 0.278407 0.00969875
\(825\) 0.154290 0.00537168
\(826\) 26.4260 0.919479
\(827\) −11.3478 −0.394601 −0.197300 0.980343i \(-0.563217\pi\)
−0.197300 + 0.980343i \(0.563217\pi\)
\(828\) 15.1992 0.528210
\(829\) −27.2925 −0.947908 −0.473954 0.880550i \(-0.657174\pi\)
−0.473954 + 0.880550i \(0.657174\pi\)
\(830\) −4.37799 −0.151962
\(831\) −24.7592 −0.858887
\(832\) 42.0962 1.45942
\(833\) 81.8476 2.83585
\(834\) 34.3766 1.19037
\(835\) −12.6924 −0.439240
\(836\) 1.37917 0.0476996
\(837\) −22.9543 −0.793417
\(838\) −1.37755 −0.0475865
\(839\) 8.36928 0.288940 0.144470 0.989509i \(-0.453852\pi\)
0.144470 + 0.989509i \(0.453852\pi\)
\(840\) −2.15944 −0.0745078
\(841\) 44.1869 1.52369
\(842\) −71.3020 −2.45723
\(843\) 2.22370 0.0765884
\(844\) −23.1063 −0.795350
\(845\) −45.4135 −1.56227
\(846\) −12.7152 −0.437159
\(847\) 50.4803 1.73452
\(848\) −36.2423 −1.24457
\(849\) 7.41179 0.254372
\(850\) 11.6441 0.399390
\(851\) 4.12678 0.141464
\(852\) −25.7360 −0.881700
\(853\) 31.4511 1.07686 0.538432 0.842669i \(-0.319017\pi\)
0.538432 + 0.842669i \(0.319017\pi\)
\(854\) 76.7317 2.62570
\(855\) 19.3239 0.660863
\(856\) −2.21529 −0.0757170
\(857\) 53.5519 1.82930 0.914648 0.404251i \(-0.132468\pi\)
0.914648 + 0.404251i \(0.132468\pi\)
\(858\) −1.78066 −0.0607909
\(859\) −17.6230 −0.601290 −0.300645 0.953736i \(-0.597202\pi\)
−0.300645 + 0.953736i \(0.597202\pi\)
\(860\) −28.2774 −0.964251
\(861\) 47.9317 1.63351
\(862\) 38.1315 1.29876
\(863\) 30.2351 1.02921 0.514607 0.857426i \(-0.327938\pi\)
0.514607 + 0.857426i \(0.327938\pi\)
\(864\) 39.7793 1.35332
\(865\) −33.8636 −1.15140
\(866\) −73.9219 −2.51197
\(867\) −16.8462 −0.572127
\(868\) 39.2491 1.33220
\(869\) −1.43791 −0.0487777
\(870\) 34.3604 1.16493
\(871\) 56.6069 1.91805
\(872\) −0.230406 −0.00780253
\(873\) −34.3550 −1.16274
\(874\) 40.2783 1.36243
\(875\) −55.2270 −1.86701
\(876\) 12.7458 0.430642
\(877\) 4.92419 0.166278 0.0831391 0.996538i \(-0.473505\pi\)
0.0831391 + 0.996538i \(0.473505\pi\)
\(878\) 41.3707 1.39619
\(879\) 16.0256 0.540531
\(880\) 1.24477 0.0419611
\(881\) 21.9024 0.737912 0.368956 0.929447i \(-0.379715\pi\)
0.368956 + 0.929447i \(0.379715\pi\)
\(882\) 54.5132 1.83556
\(883\) −34.0815 −1.14693 −0.573466 0.819229i \(-0.694402\pi\)
−0.573466 + 0.819229i \(0.694402\pi\)
\(884\) −65.1694 −2.19188
\(885\) 5.94436 0.199817
\(886\) 30.8053 1.03492
\(887\) −14.6698 −0.492565 −0.246282 0.969198i \(-0.579209\pi\)
−0.246282 + 0.969198i \(0.579209\pi\)
\(888\) 0.235434 0.00790064
\(889\) −86.6007 −2.90449
\(890\) 30.9615 1.03783
\(891\) 0.102492 0.00343362
\(892\) 15.8594 0.531011
\(893\) −16.3405 −0.546814
\(894\) 2.82750 0.0945658
\(895\) 3.35309 0.112081
\(896\) 8.46125 0.282670
\(897\) −25.2190 −0.842036
\(898\) 38.5971 1.28800
\(899\) 38.7780 1.29332
\(900\) 3.76093 0.125364
\(901\) 49.6958 1.65561
\(902\) −2.97250 −0.0989733
\(903\) 35.3720 1.17711
\(904\) −2.14113 −0.0712129
\(905\) −34.1554 −1.13536
\(906\) −12.3397 −0.409960
\(907\) 41.1637 1.36682 0.683409 0.730036i \(-0.260497\pi\)
0.683409 + 0.730036i \(0.260497\pi\)
\(908\) −18.8709 −0.626254
\(909\) 25.0043 0.829339
\(910\) 108.094 3.58328
\(911\) −25.6140 −0.848629 −0.424315 0.905515i \(-0.639485\pi\)
−0.424315 + 0.905515i \(0.639485\pi\)
\(912\) 21.3588 0.707262
\(913\) −0.164697 −0.00545068
\(914\) −56.8285 −1.87972
\(915\) 17.2603 0.570607
\(916\) 37.8337 1.25006
\(917\) −100.229 −3.30984
\(918\) −57.7455 −1.90589
\(919\) 6.19134 0.204233 0.102117 0.994772i \(-0.467438\pi\)
0.102117 + 0.994772i \(0.467438\pi\)
\(920\) 1.89664 0.0625303
\(921\) 5.49607 0.181102
\(922\) 1.53221 0.0504606
\(923\) −79.9907 −2.63293
\(924\) 1.30832 0.0430406
\(925\) 1.02114 0.0335748
\(926\) 42.3502 1.39171
\(927\) −2.36335 −0.0776227
\(928\) −67.2013 −2.20599
\(929\) −1.27625 −0.0418723 −0.0209361 0.999781i \(-0.506665\pi\)
−0.0209361 + 0.999781i \(0.506665\pi\)
\(930\) 18.2058 0.596992
\(931\) 70.0557 2.29598
\(932\) −3.33808 −0.109342
\(933\) −6.14133 −0.201058
\(934\) 25.7723 0.843297
\(935\) −1.70684 −0.0558196
\(936\) 2.69512 0.0880927
\(937\) 19.3880 0.633378 0.316689 0.948529i \(-0.397429\pi\)
0.316689 + 0.948529i \(0.397429\pi\)
\(938\) −85.7648 −2.80032
\(939\) 0.852064 0.0278061
\(940\) 12.3920 0.404182
\(941\) 44.8429 1.46184 0.730919 0.682464i \(-0.239092\pi\)
0.730919 + 0.682464i \(0.239092\pi\)
\(942\) −26.4570 −0.862015
\(943\) −42.0985 −1.37091
\(944\) −12.3078 −0.400586
\(945\) 46.4481 1.51096
\(946\) −2.19360 −0.0713202
\(947\) −44.8399 −1.45710 −0.728551 0.684992i \(-0.759806\pi\)
−0.728551 + 0.684992i \(0.759806\pi\)
\(948\) 18.7109 0.607702
\(949\) 39.6157 1.28598
\(950\) 9.96654 0.323357
\(951\) 2.86163 0.0927948
\(952\) −6.13087 −0.198702
\(953\) 7.68868 0.249061 0.124530 0.992216i \(-0.460258\pi\)
0.124530 + 0.992216i \(0.460258\pi\)
\(954\) 33.0991 1.07162
\(955\) 17.1966 0.556469
\(956\) 16.6033 0.536991
\(957\) 1.29262 0.0417844
\(958\) 25.5259 0.824706
\(959\) 39.5507 1.27716
\(960\) −14.3468 −0.463042
\(961\) −10.4536 −0.337211
\(962\) −11.7850 −0.379963
\(963\) 18.8053 0.605991
\(964\) 12.5065 0.402809
\(965\) 19.2446 0.619507
\(966\) 38.2091 1.22936
\(967\) 15.1427 0.486956 0.243478 0.969906i \(-0.421712\pi\)
0.243478 + 0.969906i \(0.421712\pi\)
\(968\) −2.52943 −0.0812989
\(969\) −29.2874 −0.940848
\(970\) 69.0421 2.21681
\(971\) 43.2548 1.38811 0.694056 0.719921i \(-0.255822\pi\)
0.694056 + 0.719921i \(0.255822\pi\)
\(972\) −29.9415 −0.960374
\(973\) −78.5044 −2.51674
\(974\) −5.91550 −0.189545
\(975\) −6.24022 −0.199847
\(976\) −35.7375 −1.14393
\(977\) 51.2904 1.64093 0.820463 0.571700i \(-0.193716\pi\)
0.820463 + 0.571700i \(0.193716\pi\)
\(978\) −17.4020 −0.556455
\(979\) 1.16475 0.0372256
\(980\) −53.1274 −1.69709
\(981\) 1.95588 0.0624465
\(982\) −25.9169 −0.827042
\(983\) 20.1997 0.644269 0.322134 0.946694i \(-0.395600\pi\)
0.322134 + 0.946694i \(0.395600\pi\)
\(984\) −2.40173 −0.0765643
\(985\) 42.0673 1.34037
\(986\) 97.5527 3.10671
\(987\) −15.5011 −0.493404
\(988\) −55.7803 −1.77461
\(989\) −31.0673 −0.987882
\(990\) −1.13681 −0.0361303
\(991\) 35.6963 1.13393 0.566965 0.823742i \(-0.308118\pi\)
0.566965 + 0.823742i \(0.308118\pi\)
\(992\) −35.6065 −1.13051
\(993\) −13.5062 −0.428605
\(994\) 121.194 3.84402
\(995\) −29.2660 −0.927795
\(996\) 2.14314 0.0679079
\(997\) 35.9659 1.13905 0.569526 0.821973i \(-0.307127\pi\)
0.569526 + 0.821973i \(0.307127\pi\)
\(998\) −51.3059 −1.62406
\(999\) −5.06402 −0.160219
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 \(a_p\))