Properties

Label 6001.2.a.b.1.3
Level 6001
Weight 2
Character 6001.1
Self dual Yes
Analytic conductor 47.918
Analytic rank 1
Dimension 114
CM No

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Newspace parameters

Level: \( N \) = \( 6001 = 17 \cdot 353 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.918226253\)
Analytic rank: \(1\)
Dimension: \(114\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 6001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.75487 q^{2}\) \(-1.38395 q^{3}\) \(+5.58934 q^{4}\) \(+1.31563 q^{5}\) \(+3.81261 q^{6}\) \(-4.81832 q^{7}\) \(-9.88817 q^{8}\) \(-1.08468 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.75487 q^{2}\) \(-1.38395 q^{3}\) \(+5.58934 q^{4}\) \(+1.31563 q^{5}\) \(+3.81261 q^{6}\) \(-4.81832 q^{7}\) \(-9.88817 q^{8}\) \(-1.08468 q^{9}\) \(-3.62439 q^{10}\) \(-5.09469 q^{11}\) \(-7.73536 q^{12}\) \(+5.27345 q^{13}\) \(+13.2739 q^{14}\) \(-1.82076 q^{15}\) \(+16.0620 q^{16}\) \(+1.00000 q^{17}\) \(+2.98816 q^{18}\) \(+6.13889 q^{19}\) \(+7.35348 q^{20}\) \(+6.66832 q^{21}\) \(+14.0352 q^{22}\) \(-3.61162 q^{23}\) \(+13.6847 q^{24}\) \(-3.26912 q^{25}\) \(-14.5277 q^{26}\) \(+5.65300 q^{27}\) \(-26.9312 q^{28}\) \(-6.73759 q^{29}\) \(+5.01598 q^{30}\) \(-6.43208 q^{31}\) \(-24.4725 q^{32}\) \(+7.05080 q^{33}\) \(-2.75487 q^{34}\) \(-6.33912 q^{35}\) \(-6.06265 q^{36}\) \(+5.38614 q^{37}\) \(-16.9119 q^{38}\) \(-7.29819 q^{39}\) \(-13.0092 q^{40}\) \(-3.59917 q^{41}\) \(-18.3704 q^{42}\) \(+11.4833 q^{43}\) \(-28.4760 q^{44}\) \(-1.42704 q^{45}\) \(+9.94955 q^{46}\) \(-4.09995 q^{47}\) \(-22.2290 q^{48}\) \(+16.2162 q^{49}\) \(+9.00603 q^{50}\) \(-1.38395 q^{51}\) \(+29.4751 q^{52}\) \(+13.0616 q^{53}\) \(-15.5733 q^{54}\) \(-6.70272 q^{55}\) \(+47.6444 q^{56}\) \(-8.49592 q^{57}\) \(+18.5612 q^{58}\) \(-10.3127 q^{59}\) \(-10.1769 q^{60}\) \(+1.62534 q^{61}\) \(+17.7196 q^{62}\) \(+5.22634 q^{63}\) \(+35.2946 q^{64}\) \(+6.93789 q^{65}\) \(-19.4241 q^{66}\) \(-8.49693 q^{67}\) \(+5.58934 q^{68}\) \(+4.99830 q^{69}\) \(+17.4635 q^{70}\) \(+5.46230 q^{71}\) \(+10.7255 q^{72}\) \(-4.51414 q^{73}\) \(-14.8381 q^{74}\) \(+4.52431 q^{75}\) \(+34.3123 q^{76}\) \(+24.5479 q^{77}\) \(+20.1056 q^{78}\) \(-12.2658 q^{79}\) \(+21.1316 q^{80}\) \(-4.56942 q^{81}\) \(+9.91527 q^{82}\) \(-0.164706 q^{83}\) \(+37.2715 q^{84}\) \(+1.31563 q^{85}\) \(-31.6350 q^{86}\) \(+9.32448 q^{87}\) \(+50.3772 q^{88}\) \(+3.49655 q^{89}\) \(+3.93131 q^{90}\) \(-25.4092 q^{91}\) \(-20.1865 q^{92}\) \(+8.90167 q^{93}\) \(+11.2948 q^{94}\) \(+8.07649 q^{95}\) \(+33.8687 q^{96}\) \(+14.0705 q^{97}\) \(-44.6736 q^{98}\) \(+5.52612 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut -\mathstrut 19q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 49q^{12} \) \(\mathstrut -\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 39q^{15} \) \(\mathstrut +\mathstrut 110q^{16} \) \(\mathstrut +\mathstrut 114q^{17} \) \(\mathstrut -\mathstrut 21q^{18} \) \(\mathstrut -\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 88q^{20} \) \(\mathstrut -\mathstrut 30q^{21} \) \(\mathstrut -\mathstrut 36q^{22} \) \(\mathstrut -\mathstrut 77q^{23} \) \(\mathstrut -\mathstrut 72q^{24} \) \(\mathstrut +\mathstrut 119q^{25} \) \(\mathstrut -\mathstrut 79q^{26} \) \(\mathstrut -\mathstrut 77q^{27} \) \(\mathstrut -\mathstrut 92q^{28} \) \(\mathstrut -\mathstrut 65q^{29} \) \(\mathstrut -\mathstrut 10q^{30} \) \(\mathstrut -\mathstrut 131q^{31} \) \(\mathstrut -\mathstrut 30q^{32} \) \(\mathstrut -\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 33q^{35} \) \(\mathstrut +\mathstrut 109q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 14q^{38} \) \(\mathstrut -\mathstrut 83q^{39} \) \(\mathstrut -\mathstrut 42q^{40} \) \(\mathstrut -\mathstrut 99q^{41} \) \(\mathstrut +\mathstrut 29q^{42} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 98q^{44} \) \(\mathstrut -\mathstrut 73q^{45} \) \(\mathstrut -\mathstrut 35q^{46} \) \(\mathstrut -\mathstrut 113q^{47} \) \(\mathstrut -\mathstrut 86q^{48} \) \(\mathstrut +\mathstrut 101q^{49} \) \(\mathstrut -\mathstrut 44q^{50} \) \(\mathstrut -\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut 3q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut -\mathstrut 78q^{54} \) \(\mathstrut -\mathstrut 63q^{55} \) \(\mathstrut -\mathstrut 117q^{56} \) \(\mathstrut -\mathstrut 64q^{57} \) \(\mathstrut -\mathstrut 31q^{58} \) \(\mathstrut -\mathstrut 134q^{59} \) \(\mathstrut -\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 30q^{61} \) \(\mathstrut -\mathstrut 30q^{62} \) \(\mathstrut -\mathstrut 154q^{63} \) \(\mathstrut +\mathstrut 117q^{64} \) \(\mathstrut -\mathstrut 66q^{65} \) \(\mathstrut -\mathstrut 12q^{66} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut +\mathstrut 110q^{68} \) \(\mathstrut -\mathstrut 35q^{69} \) \(\mathstrut +\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 233q^{71} \) \(\mathstrut +\mathstrut 16q^{72} \) \(\mathstrut -\mathstrut 56q^{73} \) \(\mathstrut -\mathstrut 64q^{74} \) \(\mathstrut -\mathstrut 100q^{75} \) \(\mathstrut -\mathstrut 64q^{76} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 50q^{78} \) \(\mathstrut -\mathstrut 154q^{79} \) \(\mathstrut -\mathstrut 128q^{80} \) \(\mathstrut +\mathstrut 118q^{81} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 53q^{83} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 27q^{85} \) \(\mathstrut -\mathstrut 52q^{86} \) \(\mathstrut -\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 52q^{88} \) \(\mathstrut -\mathstrut 118q^{89} \) \(\mathstrut -\mathstrut 5q^{90} \) \(\mathstrut -\mathstrut 95q^{91} \) \(\mathstrut -\mathstrut 102q^{92} \) \(\mathstrut +\mathstrut 47q^{93} \) \(\mathstrut -\mathstrut 3q^{94} \) \(\mathstrut -\mathstrut 158q^{95} \) \(\mathstrut -\mathstrut 144q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut +\mathstrut 3q^{98} \) \(\mathstrut -\mathstrut 131q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.75487 −1.94799 −0.973995 0.226568i \(-0.927249\pi\)
−0.973995 + 0.226568i \(0.927249\pi\)
\(3\) −1.38395 −0.799024 −0.399512 0.916728i \(-0.630820\pi\)
−0.399512 + 0.916728i \(0.630820\pi\)
\(4\) 5.58934 2.79467
\(5\) 1.31563 0.588367 0.294183 0.955749i \(-0.404952\pi\)
0.294183 + 0.955749i \(0.404952\pi\)
\(6\) 3.81261 1.55649
\(7\) −4.81832 −1.82115 −0.910577 0.413339i \(-0.864362\pi\)
−0.910577 + 0.413339i \(0.864362\pi\)
\(8\) −9.88817 −3.49600
\(9\) −1.08468 −0.361561
\(10\) −3.62439 −1.14613
\(11\) −5.09469 −1.53611 −0.768054 0.640385i \(-0.778775\pi\)
−0.768054 + 0.640385i \(0.778775\pi\)
\(12\) −7.73536 −2.23301
\(13\) 5.27345 1.46259 0.731295 0.682061i \(-0.238916\pi\)
0.731295 + 0.682061i \(0.238916\pi\)
\(14\) 13.2739 3.54759
\(15\) −1.82076 −0.470119
\(16\) 16.0620 4.01550
\(17\) 1.00000 0.242536
\(18\) 2.98816 0.704317
\(19\) 6.13889 1.40836 0.704179 0.710022i \(-0.251315\pi\)
0.704179 + 0.710022i \(0.251315\pi\)
\(20\) 7.35348 1.64429
\(21\) 6.66832 1.45515
\(22\) 14.0352 2.99232
\(23\) −3.61162 −0.753074 −0.376537 0.926402i \(-0.622885\pi\)
−0.376537 + 0.926402i \(0.622885\pi\)
\(24\) 13.6847 2.79339
\(25\) −3.26912 −0.653825
\(26\) −14.5277 −2.84911
\(27\) 5.65300 1.08792
\(28\) −26.9312 −5.08952
\(29\) −6.73759 −1.25114 −0.625569 0.780169i \(-0.715133\pi\)
−0.625569 + 0.780169i \(0.715133\pi\)
\(30\) 5.01598 0.915788
\(31\) −6.43208 −1.15523 −0.577617 0.816308i \(-0.696017\pi\)
−0.577617 + 0.816308i \(0.696017\pi\)
\(32\) −24.4725 −4.32616
\(33\) 7.05080 1.22739
\(34\) −2.75487 −0.472457
\(35\) −6.33912 −1.07151
\(36\) −6.06265 −1.01044
\(37\) 5.38614 0.885475 0.442738 0.896651i \(-0.354007\pi\)
0.442738 + 0.896651i \(0.354007\pi\)
\(38\) −16.9119 −2.74347
\(39\) −7.29819 −1.16865
\(40\) −13.0092 −2.05693
\(41\) −3.59917 −0.562096 −0.281048 0.959694i \(-0.590682\pi\)
−0.281048 + 0.959694i \(0.590682\pi\)
\(42\) −18.3704 −2.83461
\(43\) 11.4833 1.75118 0.875591 0.483053i \(-0.160472\pi\)
0.875591 + 0.483053i \(0.160472\pi\)
\(44\) −28.4760 −4.29291
\(45\) −1.42704 −0.212730
\(46\) 9.94955 1.46698
\(47\) −4.09995 −0.598039 −0.299020 0.954247i \(-0.596660\pi\)
−0.299020 + 0.954247i \(0.596660\pi\)
\(48\) −22.2290 −3.20848
\(49\) 16.2162 2.31660
\(50\) 9.00603 1.27364
\(51\) −1.38395 −0.193792
\(52\) 29.4751 4.08746
\(53\) 13.0616 1.79414 0.897072 0.441883i \(-0.145690\pi\)
0.897072 + 0.441883i \(0.145690\pi\)
\(54\) −15.5733 −2.11926
\(55\) −6.70272 −0.903795
\(56\) 47.6444 6.36675
\(57\) −8.49592 −1.12531
\(58\) 18.5612 2.43721
\(59\) −10.3127 −1.34260 −0.671299 0.741186i \(-0.734263\pi\)
−0.671299 + 0.741186i \(0.734263\pi\)
\(60\) −10.1769 −1.31383
\(61\) 1.62534 0.208103 0.104052 0.994572i \(-0.466819\pi\)
0.104052 + 0.994572i \(0.466819\pi\)
\(62\) 17.7196 2.25039
\(63\) 5.22634 0.658457
\(64\) 35.2946 4.41182
\(65\) 6.93789 0.860540
\(66\) −19.4241 −2.39094
\(67\) −8.49693 −1.03806 −0.519032 0.854755i \(-0.673708\pi\)
−0.519032 + 0.854755i \(0.673708\pi\)
\(68\) 5.58934 0.677807
\(69\) 4.99830 0.601724
\(70\) 17.4635 2.08728
\(71\) 5.46230 0.648256 0.324128 0.946013i \(-0.394929\pi\)
0.324128 + 0.946013i \(0.394929\pi\)
\(72\) 10.7255 1.26401
\(73\) −4.51414 −0.528340 −0.264170 0.964476i \(-0.585098\pi\)
−0.264170 + 0.964476i \(0.585098\pi\)
\(74\) −14.8381 −1.72490
\(75\) 4.52431 0.522422
\(76\) 34.3123 3.93589
\(77\) 24.5479 2.79749
\(78\) 20.1056 2.27651
\(79\) −12.2658 −1.38001 −0.690006 0.723804i \(-0.742392\pi\)
−0.690006 + 0.723804i \(0.742392\pi\)
\(80\) 21.1316 2.36259
\(81\) −4.56942 −0.507713
\(82\) 9.91527 1.09496
\(83\) −0.164706 −0.0180788 −0.00903939 0.999959i \(-0.502877\pi\)
−0.00903939 + 0.999959i \(0.502877\pi\)
\(84\) 37.2715 4.06665
\(85\) 1.31563 0.142700
\(86\) −31.6350 −3.41129
\(87\) 9.32448 0.999690
\(88\) 50.3772 5.37023
\(89\) 3.49655 0.370633 0.185317 0.982679i \(-0.440669\pi\)
0.185317 + 0.982679i \(0.440669\pi\)
\(90\) 3.93131 0.414396
\(91\) −25.4092 −2.66360
\(92\) −20.1865 −2.10459
\(93\) 8.90167 0.923061
\(94\) 11.2948 1.16497
\(95\) 8.07649 0.828631
\(96\) 33.8687 3.45671
\(97\) 14.0705 1.42864 0.714320 0.699819i \(-0.246736\pi\)
0.714320 + 0.699819i \(0.246736\pi\)
\(98\) −44.6736 −4.51272
\(99\) 5.52612 0.555396
\(100\) −18.2722 −1.82722
\(101\) 0.940015 0.0935350 0.0467675 0.998906i \(-0.485108\pi\)
0.0467675 + 0.998906i \(0.485108\pi\)
\(102\) 3.81261 0.377505
\(103\) 8.90741 0.877674 0.438837 0.898567i \(-0.355391\pi\)
0.438837 + 0.898567i \(0.355391\pi\)
\(104\) −52.1447 −5.11321
\(105\) 8.77302 0.856159
\(106\) −35.9830 −3.49498
\(107\) 19.5910 1.89394 0.946968 0.321329i \(-0.104130\pi\)
0.946968 + 0.321329i \(0.104130\pi\)
\(108\) 31.5965 3.04037
\(109\) 0.372597 0.0356883 0.0178441 0.999841i \(-0.494320\pi\)
0.0178441 + 0.999841i \(0.494320\pi\)
\(110\) 18.4652 1.76058
\(111\) −7.45414 −0.707516
\(112\) −77.3919 −7.31285
\(113\) 17.0229 1.60138 0.800690 0.599078i \(-0.204466\pi\)
0.800690 + 0.599078i \(0.204466\pi\)
\(114\) 23.4052 2.19210
\(115\) −4.75154 −0.443084
\(116\) −37.6586 −3.49652
\(117\) −5.72001 −0.528815
\(118\) 28.4102 2.61537
\(119\) −4.81832 −0.441695
\(120\) 18.0040 1.64353
\(121\) 14.9559 1.35963
\(122\) −4.47761 −0.405384
\(123\) 4.98108 0.449128
\(124\) −35.9510 −3.22850
\(125\) −10.8791 −0.973055
\(126\) −14.3979 −1.28267
\(127\) −8.22937 −0.730239 −0.365119 0.930961i \(-0.618972\pi\)
−0.365119 + 0.930961i \(0.618972\pi\)
\(128\) −48.2872 −4.26803
\(129\) −15.8923 −1.39924
\(130\) −19.1130 −1.67632
\(131\) 6.83787 0.597427 0.298714 0.954343i \(-0.403442\pi\)
0.298714 + 0.954343i \(0.403442\pi\)
\(132\) 39.4093 3.43014
\(133\) −29.5791 −2.56484
\(134\) 23.4080 2.02214
\(135\) 7.43724 0.640096
\(136\) −9.88817 −0.847904
\(137\) 0.806727 0.0689233 0.0344617 0.999406i \(-0.489028\pi\)
0.0344617 + 0.999406i \(0.489028\pi\)
\(138\) −13.7697 −1.17215
\(139\) 2.93234 0.248717 0.124359 0.992237i \(-0.460313\pi\)
0.124359 + 0.992237i \(0.460313\pi\)
\(140\) −35.4314 −2.99450
\(141\) 5.67413 0.477848
\(142\) −15.0480 −1.26280
\(143\) −26.8666 −2.24670
\(144\) −17.4222 −1.45185
\(145\) −8.86415 −0.736128
\(146\) 12.4359 1.02920
\(147\) −22.4424 −1.85102
\(148\) 30.1049 2.47461
\(149\) 10.8265 0.886942 0.443471 0.896289i \(-0.353747\pi\)
0.443471 + 0.896289i \(0.353747\pi\)
\(150\) −12.4639 −1.01767
\(151\) −0.0538371 −0.00438120 −0.00219060 0.999998i \(-0.500697\pi\)
−0.00219060 + 0.999998i \(0.500697\pi\)
\(152\) −60.7024 −4.92362
\(153\) −1.08468 −0.0876913
\(154\) −67.6263 −5.44948
\(155\) −8.46222 −0.679702
\(156\) −40.7920 −3.26598
\(157\) −7.41195 −0.591538 −0.295769 0.955259i \(-0.595576\pi\)
−0.295769 + 0.955259i \(0.595576\pi\)
\(158\) 33.7908 2.68825
\(159\) −18.0766 −1.43357
\(160\) −32.1967 −2.54537
\(161\) 17.4019 1.37146
\(162\) 12.5882 0.989021
\(163\) 10.5688 0.827815 0.413907 0.910319i \(-0.364164\pi\)
0.413907 + 0.910319i \(0.364164\pi\)
\(164\) −20.1170 −1.57087
\(165\) 9.27623 0.722154
\(166\) 0.453743 0.0352173
\(167\) 8.09223 0.626196 0.313098 0.949721i \(-0.398633\pi\)
0.313098 + 0.949721i \(0.398633\pi\)
\(168\) −65.9375 −5.08719
\(169\) 14.8092 1.13917
\(170\) −3.62439 −0.277978
\(171\) −6.65874 −0.509207
\(172\) 64.1839 4.89397
\(173\) −4.69446 −0.356913 −0.178457 0.983948i \(-0.557110\pi\)
−0.178457 + 0.983948i \(0.557110\pi\)
\(174\) −25.6878 −1.94739
\(175\) 15.7517 1.19072
\(176\) −81.8310 −6.16824
\(177\) 14.2723 1.07277
\(178\) −9.63255 −0.721990
\(179\) −1.54529 −0.115500 −0.0577501 0.998331i \(-0.518393\pi\)
−0.0577501 + 0.998331i \(0.518393\pi\)
\(180\) −7.97619 −0.594510
\(181\) 5.86638 0.436044 0.218022 0.975944i \(-0.430039\pi\)
0.218022 + 0.975944i \(0.430039\pi\)
\(182\) 69.9991 5.18867
\(183\) −2.24939 −0.166280
\(184\) 35.7123 2.63274
\(185\) 7.08615 0.520984
\(186\) −24.5230 −1.79811
\(187\) −5.09469 −0.372561
\(188\) −22.9160 −1.67132
\(189\) −27.2379 −1.98127
\(190\) −22.2497 −1.61417
\(191\) −24.3587 −1.76253 −0.881266 0.472621i \(-0.843308\pi\)
−0.881266 + 0.472621i \(0.843308\pi\)
\(192\) −48.8460 −3.52515
\(193\) 7.18898 0.517474 0.258737 0.965948i \(-0.416694\pi\)
0.258737 + 0.965948i \(0.416694\pi\)
\(194\) −38.7624 −2.78298
\(195\) −9.60170 −0.687592
\(196\) 90.6379 6.47413
\(197\) −18.1768 −1.29505 −0.647523 0.762046i \(-0.724195\pi\)
−0.647523 + 0.762046i \(0.724195\pi\)
\(198\) −15.2238 −1.08191
\(199\) −9.60114 −0.680607 −0.340304 0.940316i \(-0.610530\pi\)
−0.340304 + 0.940316i \(0.610530\pi\)
\(200\) 32.3257 2.28577
\(201\) 11.7593 0.829439
\(202\) −2.58962 −0.182205
\(203\) 32.4638 2.27852
\(204\) −7.73536 −0.541584
\(205\) −4.73517 −0.330719
\(206\) −24.5388 −1.70970
\(207\) 3.91745 0.272282
\(208\) 84.7021 5.87304
\(209\) −31.2758 −2.16339
\(210\) −24.1686 −1.66779
\(211\) 16.9496 1.16686 0.583429 0.812164i \(-0.301711\pi\)
0.583429 + 0.812164i \(0.301711\pi\)
\(212\) 73.0055 5.01404
\(213\) −7.55956 −0.517972
\(214\) −53.9708 −3.68937
\(215\) 15.1077 1.03034
\(216\) −55.8978 −3.80336
\(217\) 30.9918 2.10386
\(218\) −1.02646 −0.0695205
\(219\) 6.24734 0.422156
\(220\) −37.4638 −2.52581
\(221\) 5.27345 0.354730
\(222\) 20.5352 1.37823
\(223\) 10.8772 0.728391 0.364196 0.931322i \(-0.381344\pi\)
0.364196 + 0.931322i \(0.381344\pi\)
\(224\) 117.916 7.87861
\(225\) 3.54596 0.236397
\(226\) −46.8960 −3.11947
\(227\) −16.7208 −1.10980 −0.554899 0.831918i \(-0.687243\pi\)
−0.554899 + 0.831918i \(0.687243\pi\)
\(228\) −47.4866 −3.14487
\(229\) −5.12306 −0.338541 −0.169271 0.985570i \(-0.554141\pi\)
−0.169271 + 0.985570i \(0.554141\pi\)
\(230\) 13.0899 0.863123
\(231\) −33.9730 −2.23526
\(232\) 66.6224 4.37397
\(233\) 17.1101 1.12092 0.560461 0.828181i \(-0.310624\pi\)
0.560461 + 0.828181i \(0.310624\pi\)
\(234\) 15.7579 1.03013
\(235\) −5.39401 −0.351866
\(236\) −57.6411 −3.75212
\(237\) 16.9753 1.10266
\(238\) 13.2739 0.860417
\(239\) −10.8259 −0.700269 −0.350135 0.936699i \(-0.613864\pi\)
−0.350135 + 0.936699i \(0.613864\pi\)
\(240\) −29.2451 −1.88776
\(241\) 8.02923 0.517208 0.258604 0.965983i \(-0.416738\pi\)
0.258604 + 0.965983i \(0.416738\pi\)
\(242\) −41.2017 −2.64854
\(243\) −10.6351 −0.682244
\(244\) 9.08457 0.581580
\(245\) 21.3345 1.36301
\(246\) −13.7222 −0.874898
\(247\) 32.3731 2.05985
\(248\) 63.6015 4.03870
\(249\) 0.227944 0.0144454
\(250\) 29.9705 1.89550
\(251\) 27.3790 1.72815 0.864074 0.503365i \(-0.167905\pi\)
0.864074 + 0.503365i \(0.167905\pi\)
\(252\) 29.2118 1.84017
\(253\) 18.4001 1.15680
\(254\) 22.6709 1.42250
\(255\) −1.82076 −0.114021
\(256\) 62.4361 3.90226
\(257\) −13.4438 −0.838604 −0.419302 0.907847i \(-0.637725\pi\)
−0.419302 + 0.907847i \(0.637725\pi\)
\(258\) 43.7812 2.72570
\(259\) −25.9521 −1.61259
\(260\) 38.7782 2.40492
\(261\) 7.30813 0.452362
\(262\) −18.8375 −1.16378
\(263\) 17.1270 1.05610 0.528048 0.849214i \(-0.322924\pi\)
0.528048 + 0.849214i \(0.322924\pi\)
\(264\) −69.7196 −4.29094
\(265\) 17.1842 1.05561
\(266\) 81.4868 4.99628
\(267\) −4.83905 −0.296145
\(268\) −47.4922 −2.90105
\(269\) −2.30480 −0.140526 −0.0702630 0.997529i \(-0.522384\pi\)
−0.0702630 + 0.997529i \(0.522384\pi\)
\(270\) −20.4887 −1.24690
\(271\) −2.55742 −0.155352 −0.0776762 0.996979i \(-0.524750\pi\)
−0.0776762 + 0.996979i \(0.524750\pi\)
\(272\) 16.0620 0.973902
\(273\) 35.1650 2.12828
\(274\) −2.22243 −0.134262
\(275\) 16.6552 1.00435
\(276\) 27.9372 1.68162
\(277\) −11.1856 −0.672078 −0.336039 0.941848i \(-0.609087\pi\)
−0.336039 + 0.941848i \(0.609087\pi\)
\(278\) −8.07822 −0.484499
\(279\) 6.97675 0.417687
\(280\) 62.6823 3.74598
\(281\) 6.12385 0.365318 0.182659 0.983176i \(-0.441530\pi\)
0.182659 + 0.983176i \(0.441530\pi\)
\(282\) −15.6315 −0.930843
\(283\) −25.8471 −1.53645 −0.768226 0.640178i \(-0.778860\pi\)
−0.768226 + 0.640178i \(0.778860\pi\)
\(284\) 30.5306 1.81166
\(285\) −11.1775 −0.662096
\(286\) 74.0141 4.37655
\(287\) 17.3420 1.02366
\(288\) 26.5448 1.56417
\(289\) 1.00000 0.0588235
\(290\) 24.4196 1.43397
\(291\) −19.4728 −1.14152
\(292\) −25.2310 −1.47653
\(293\) 11.4962 0.671617 0.335808 0.941930i \(-0.390991\pi\)
0.335808 + 0.941930i \(0.390991\pi\)
\(294\) 61.8261 3.60577
\(295\) −13.5677 −0.789940
\(296\) −53.2590 −3.09562
\(297\) −28.8003 −1.67116
\(298\) −29.8257 −1.72775
\(299\) −19.0457 −1.10144
\(300\) 25.2879 1.46000
\(301\) −55.3301 −3.18917
\(302\) 0.148314 0.00853454
\(303\) −1.30093 −0.0747367
\(304\) 98.6029 5.65526
\(305\) 2.13834 0.122441
\(306\) 2.98816 0.170822
\(307\) 6.71400 0.383188 0.191594 0.981474i \(-0.438634\pi\)
0.191594 + 0.981474i \(0.438634\pi\)
\(308\) 137.206 7.81805
\(309\) −12.3274 −0.701282
\(310\) 23.3123 1.32405
\(311\) 0.693118 0.0393031 0.0196515 0.999807i \(-0.493744\pi\)
0.0196515 + 0.999807i \(0.493744\pi\)
\(312\) 72.1657 4.08558
\(313\) −0.300505 −0.0169855 −0.00849277 0.999964i \(-0.502703\pi\)
−0.00849277 + 0.999964i \(0.502703\pi\)
\(314\) 20.4190 1.15231
\(315\) 6.87592 0.387414
\(316\) −68.5577 −3.85667
\(317\) −27.9780 −1.57140 −0.785701 0.618606i \(-0.787698\pi\)
−0.785701 + 0.618606i \(0.787698\pi\)
\(318\) 49.7987 2.79257
\(319\) 34.3259 1.92188
\(320\) 46.4345 2.59577
\(321\) −27.1130 −1.51330
\(322\) −47.9401 −2.67160
\(323\) 6.13889 0.341577
\(324\) −25.5400 −1.41889
\(325\) −17.2396 −0.956278
\(326\) −29.1158 −1.61258
\(327\) −0.515655 −0.0285158
\(328\) 35.5892 1.96509
\(329\) 19.7549 1.08912
\(330\) −25.5549 −1.40675
\(331\) −3.91937 −0.215428 −0.107714 0.994182i \(-0.534353\pi\)
−0.107714 + 0.994182i \(0.534353\pi\)
\(332\) −0.920594 −0.0505242
\(333\) −5.84224 −0.320153
\(334\) −22.2931 −1.21982
\(335\) −11.1788 −0.610763
\(336\) 107.107 5.84314
\(337\) −27.8817 −1.51881 −0.759405 0.650618i \(-0.774510\pi\)
−0.759405 + 0.650618i \(0.774510\pi\)
\(338\) −40.7976 −2.21910
\(339\) −23.5589 −1.27954
\(340\) 7.35348 0.398799
\(341\) 32.7695 1.77457
\(342\) 18.3440 0.991930
\(343\) −44.4067 −2.39774
\(344\) −113.549 −6.12213
\(345\) 6.57590 0.354034
\(346\) 12.9326 0.695264
\(347\) −5.18556 −0.278376 −0.139188 0.990266i \(-0.544449\pi\)
−0.139188 + 0.990266i \(0.544449\pi\)
\(348\) 52.1177 2.79380
\(349\) −12.9154 −0.691346 −0.345673 0.938355i \(-0.612349\pi\)
−0.345673 + 0.938355i \(0.612349\pi\)
\(350\) −43.3939 −2.31950
\(351\) 29.8108 1.59118
\(352\) 124.680 6.64545
\(353\) 1.00000 0.0532246
\(354\) −39.3183 −2.08974
\(355\) 7.18636 0.381412
\(356\) 19.5434 1.03580
\(357\) 6.66832 0.352925
\(358\) 4.25707 0.224993
\(359\) −27.8674 −1.47079 −0.735393 0.677641i \(-0.763002\pi\)
−0.735393 + 0.677641i \(0.763002\pi\)
\(360\) 14.1108 0.743704
\(361\) 18.6860 0.983473
\(362\) −16.1611 −0.849410
\(363\) −20.6982 −1.08638
\(364\) −142.020 −7.44389
\(365\) −5.93892 −0.310857
\(366\) 6.19679 0.323911
\(367\) 6.50514 0.339565 0.169783 0.985482i \(-0.445693\pi\)
0.169783 + 0.985482i \(0.445693\pi\)
\(368\) −58.0098 −3.02397
\(369\) 3.90396 0.203232
\(370\) −19.5215 −1.01487
\(371\) −62.9348 −3.26741
\(372\) 49.7544 2.57965
\(373\) 27.7373 1.43618 0.718092 0.695948i \(-0.245016\pi\)
0.718092 + 0.695948i \(0.245016\pi\)
\(374\) 14.0352 0.725745
\(375\) 15.0561 0.777495
\(376\) 40.5410 2.09074
\(377\) −35.5303 −1.82990
\(378\) 75.0371 3.85949
\(379\) −15.4252 −0.792341 −0.396171 0.918177i \(-0.629661\pi\)
−0.396171 + 0.918177i \(0.629661\pi\)
\(380\) 45.1422 2.31575
\(381\) 11.3890 0.583479
\(382\) 67.1051 3.43339
\(383\) 8.25417 0.421768 0.210884 0.977511i \(-0.432366\pi\)
0.210884 + 0.977511i \(0.432366\pi\)
\(384\) 66.8271 3.41026
\(385\) 32.2959 1.64595
\(386\) −19.8047 −1.00803
\(387\) −12.4557 −0.633158
\(388\) 78.6446 3.99257
\(389\) −22.3600 −1.13370 −0.566848 0.823823i \(-0.691837\pi\)
−0.566848 + 0.823823i \(0.691837\pi\)
\(390\) 26.4515 1.33942
\(391\) −3.61162 −0.182647
\(392\) −160.349 −8.09883
\(393\) −9.46327 −0.477359
\(394\) 50.0749 2.52274
\(395\) −16.1372 −0.811953
\(396\) 30.8873 1.55215
\(397\) −24.5964 −1.23446 −0.617228 0.786784i \(-0.711745\pi\)
−0.617228 + 0.786784i \(0.711745\pi\)
\(398\) 26.4500 1.32582
\(399\) 40.9361 2.04937
\(400\) −52.5087 −2.62543
\(401\) 17.0749 0.852681 0.426341 0.904563i \(-0.359802\pi\)
0.426341 + 0.904563i \(0.359802\pi\)
\(402\) −32.3955 −1.61574
\(403\) −33.9192 −1.68964
\(404\) 5.25406 0.261399
\(405\) −6.01166 −0.298722
\(406\) −89.4338 −4.43853
\(407\) −27.4407 −1.36019
\(408\) 13.6847 0.677496
\(409\) 32.9225 1.62791 0.813956 0.580927i \(-0.197310\pi\)
0.813956 + 0.580927i \(0.197310\pi\)
\(410\) 13.0448 0.644237
\(411\) −1.11647 −0.0550714
\(412\) 49.7865 2.45281
\(413\) 49.6899 2.44508
\(414\) −10.7921 −0.530402
\(415\) −0.216691 −0.0106369
\(416\) −129.054 −6.32741
\(417\) −4.05821 −0.198731
\(418\) 86.1608 4.21426
\(419\) 26.0108 1.27071 0.635355 0.772220i \(-0.280854\pi\)
0.635355 + 0.772220i \(0.280854\pi\)
\(420\) 49.0354 2.39268
\(421\) −6.62047 −0.322662 −0.161331 0.986900i \(-0.551579\pi\)
−0.161331 + 0.986900i \(0.551579\pi\)
\(422\) −46.6940 −2.27303
\(423\) 4.44714 0.216227
\(424\) −129.155 −6.27232
\(425\) −3.26912 −0.158576
\(426\) 20.8256 1.00901
\(427\) −7.83141 −0.378988
\(428\) 109.501 5.29292
\(429\) 37.1820 1.79517
\(430\) −41.6199 −2.00709
\(431\) 28.2510 1.36080 0.680401 0.732840i \(-0.261806\pi\)
0.680401 + 0.732840i \(0.261806\pi\)
\(432\) 90.7985 4.36854
\(433\) −12.4363 −0.597651 −0.298825 0.954308i \(-0.596595\pi\)
−0.298825 + 0.954308i \(0.596595\pi\)
\(434\) −85.3785 −4.09830
\(435\) 12.2675 0.588184
\(436\) 2.08257 0.0997369
\(437\) −22.1713 −1.06060
\(438\) −17.2106 −0.822356
\(439\) 32.0340 1.52890 0.764450 0.644683i \(-0.223011\pi\)
0.764450 + 0.644683i \(0.223011\pi\)
\(440\) 66.2777 3.15966
\(441\) −17.5894 −0.837592
\(442\) −14.5277 −0.691012
\(443\) −33.6093 −1.59683 −0.798414 0.602109i \(-0.794327\pi\)
−0.798414 + 0.602109i \(0.794327\pi\)
\(444\) −41.6637 −1.97727
\(445\) 4.60015 0.218068
\(446\) −29.9653 −1.41890
\(447\) −14.9833 −0.708688
\(448\) −170.061 −8.03461
\(449\) −13.2498 −0.625295 −0.312648 0.949869i \(-0.601216\pi\)
−0.312648 + 0.949869i \(0.601216\pi\)
\(450\) −9.76867 −0.460500
\(451\) 18.3367 0.863441
\(452\) 95.1468 4.47533
\(453\) 0.0745079 0.00350068
\(454\) 46.0637 2.16188
\(455\) −33.4290 −1.56718
\(456\) 84.0091 3.93409
\(457\) −25.2382 −1.18059 −0.590297 0.807186i \(-0.700989\pi\)
−0.590297 + 0.807186i \(0.700989\pi\)
\(458\) 14.1134 0.659475
\(459\) 5.65300 0.263859
\(460\) −26.5580 −1.23827
\(461\) −0.317499 −0.0147874 −0.00739369 0.999973i \(-0.502354\pi\)
−0.00739369 + 0.999973i \(0.502354\pi\)
\(462\) 93.5915 4.35427
\(463\) 32.0904 1.49137 0.745684 0.666300i \(-0.232123\pi\)
0.745684 + 0.666300i \(0.232123\pi\)
\(464\) −108.219 −5.02395
\(465\) 11.7113 0.543098
\(466\) −47.1362 −2.18354
\(467\) 3.11978 0.144366 0.0721832 0.997391i \(-0.477003\pi\)
0.0721832 + 0.997391i \(0.477003\pi\)
\(468\) −31.9711 −1.47786
\(469\) 40.9409 1.89048
\(470\) 14.8598 0.685432
\(471\) 10.2578 0.472653
\(472\) 101.974 4.69372
\(473\) −58.5038 −2.69001
\(474\) −46.7647 −2.14798
\(475\) −20.0688 −0.920819
\(476\) −26.9312 −1.23439
\(477\) −14.1676 −0.648692
\(478\) 29.8240 1.36412
\(479\) −1.51347 −0.0691524 −0.0345762 0.999402i \(-0.511008\pi\)
−0.0345762 + 0.999402i \(0.511008\pi\)
\(480\) 44.5586 2.03381
\(481\) 28.4035 1.29509
\(482\) −22.1195 −1.00752
\(483\) −24.0834 −1.09583
\(484\) 83.5936 3.79971
\(485\) 18.5115 0.840564
\(486\) 29.2985 1.32901
\(487\) −9.89872 −0.448554 −0.224277 0.974525i \(-0.572002\pi\)
−0.224277 + 0.974525i \(0.572002\pi\)
\(488\) −16.0716 −0.727529
\(489\) −14.6267 −0.661444
\(490\) −58.7739 −2.65513
\(491\) −13.7986 −0.622721 −0.311360 0.950292i \(-0.600785\pi\)
−0.311360 + 0.950292i \(0.600785\pi\)
\(492\) 27.8409 1.25516
\(493\) −6.73759 −0.303446
\(494\) −89.1839 −4.01257
\(495\) 7.27032 0.326776
\(496\) −103.312 −4.63885
\(497\) −26.3191 −1.18057
\(498\) −0.627958 −0.0281395
\(499\) −37.5978 −1.68311 −0.841555 0.540172i \(-0.818359\pi\)
−0.841555 + 0.540172i \(0.818359\pi\)
\(500\) −60.8069 −2.71937
\(501\) −11.1992 −0.500345
\(502\) −75.4258 −3.36642
\(503\) −13.3935 −0.597187 −0.298593 0.954380i \(-0.596517\pi\)
−0.298593 + 0.954380i \(0.596517\pi\)
\(504\) −51.6790 −2.30196
\(505\) 1.23671 0.0550329
\(506\) −50.6899 −2.25344
\(507\) −20.4953 −0.910226
\(508\) −45.9967 −2.04078
\(509\) −28.7976 −1.27643 −0.638216 0.769858i \(-0.720327\pi\)
−0.638216 + 0.769858i \(0.720327\pi\)
\(510\) 5.01598 0.222111
\(511\) 21.7506 0.962188
\(512\) −75.4292 −3.33353
\(513\) 34.7031 1.53218
\(514\) 37.0361 1.63359
\(515\) 11.7188 0.516394
\(516\) −88.8273 −3.91040
\(517\) 20.8880 0.918653
\(518\) 71.4949 3.14130
\(519\) 6.49690 0.285182
\(520\) −68.6031 −3.00844
\(521\) −2.06407 −0.0904285 −0.0452143 0.998977i \(-0.514397\pi\)
−0.0452143 + 0.998977i \(0.514397\pi\)
\(522\) −20.1330 −0.881197
\(523\) 20.3347 0.889175 0.444587 0.895736i \(-0.353350\pi\)
0.444587 + 0.895736i \(0.353350\pi\)
\(524\) 38.2191 1.66961
\(525\) −21.7996 −0.951411
\(526\) −47.1827 −2.05727
\(527\) −6.43208 −0.280186
\(528\) 113.250 4.92858
\(529\) −9.95623 −0.432880
\(530\) −47.3402 −2.05633
\(531\) 11.1860 0.485431
\(532\) −165.328 −7.16787
\(533\) −18.9800 −0.822117
\(534\) 13.3310 0.576887
\(535\) 25.7745 1.11433
\(536\) 84.0191 3.62907
\(537\) 2.13860 0.0922874
\(538\) 6.34943 0.273743
\(539\) −82.6167 −3.55855
\(540\) 41.5692 1.78885
\(541\) 31.0928 1.33679 0.668393 0.743809i \(-0.266983\pi\)
0.668393 + 0.743809i \(0.266983\pi\)
\(542\) 7.04539 0.302625
\(543\) −8.11877 −0.348410
\(544\) −24.4725 −1.04925
\(545\) 0.490199 0.0209978
\(546\) −96.8752 −4.14588
\(547\) 16.3923 0.700884 0.350442 0.936584i \(-0.386031\pi\)
0.350442 + 0.936584i \(0.386031\pi\)
\(548\) 4.50907 0.192618
\(549\) −1.76298 −0.0752420
\(550\) −45.8830 −1.95646
\(551\) −41.3613 −1.76205
\(552\) −49.4240 −2.10363
\(553\) 59.1006 2.51321
\(554\) 30.8149 1.30920
\(555\) −9.80688 −0.416279
\(556\) 16.3898 0.695083
\(557\) −31.0733 −1.31662 −0.658310 0.752747i \(-0.728728\pi\)
−0.658310 + 0.752747i \(0.728728\pi\)
\(558\) −19.2201 −0.813651
\(559\) 60.5564 2.56126
\(560\) −101.819 −4.30263
\(561\) 7.05080 0.297685
\(562\) −16.8704 −0.711637
\(563\) 7.46822 0.314748 0.157374 0.987539i \(-0.449697\pi\)
0.157374 + 0.987539i \(0.449697\pi\)
\(564\) 31.7146 1.33543
\(565\) 22.3958 0.942199
\(566\) 71.2056 2.99300
\(567\) 22.0169 0.924624
\(568\) −54.0122 −2.26630
\(569\) −4.01374 −0.168265 −0.0841324 0.996455i \(-0.526812\pi\)
−0.0841324 + 0.996455i \(0.526812\pi\)
\(570\) 30.7925 1.28976
\(571\) −12.6101 −0.527718 −0.263859 0.964561i \(-0.584995\pi\)
−0.263859 + 0.964561i \(0.584995\pi\)
\(572\) −150.166 −6.27877
\(573\) 33.7112 1.40831
\(574\) −47.7749 −1.99409
\(575\) 11.8068 0.492378
\(576\) −38.2834 −1.59514
\(577\) −8.66150 −0.360583 −0.180291 0.983613i \(-0.557704\pi\)
−0.180291 + 0.983613i \(0.557704\pi\)
\(578\) −2.75487 −0.114588
\(579\) −9.94919 −0.413474
\(580\) −49.5447 −2.05723
\(581\) 0.793604 0.0329242
\(582\) 53.6452 2.22367
\(583\) −66.5447 −2.75600
\(584\) 44.6365 1.84707
\(585\) −7.52540 −0.311137
\(586\) −31.6707 −1.30830
\(587\) 21.6722 0.894508 0.447254 0.894407i \(-0.352402\pi\)
0.447254 + 0.894407i \(0.352402\pi\)
\(588\) −125.438 −5.17299
\(589\) −39.4858 −1.62698
\(590\) 37.3772 1.53880
\(591\) 25.1558 1.03477
\(592\) 86.5121 3.55563
\(593\) 41.3352 1.69743 0.848716 0.528849i \(-0.177376\pi\)
0.848716 + 0.528849i \(0.177376\pi\)
\(594\) 79.3412 3.25541
\(595\) −6.33912 −0.259878
\(596\) 60.5130 2.47871
\(597\) 13.2875 0.543821
\(598\) 52.4684 2.14559
\(599\) −32.4854 −1.32732 −0.663659 0.748035i \(-0.730998\pi\)
−0.663659 + 0.748035i \(0.730998\pi\)
\(600\) −44.7371 −1.82638
\(601\) −4.99245 −0.203646 −0.101823 0.994803i \(-0.532468\pi\)
−0.101823 + 0.994803i \(0.532468\pi\)
\(602\) 152.427 6.21248
\(603\) 9.21646 0.375323
\(604\) −0.300914 −0.0122440
\(605\) 19.6764 0.799960
\(606\) 3.58391 0.145586
\(607\) 11.7942 0.478711 0.239355 0.970932i \(-0.423064\pi\)
0.239355 + 0.970932i \(0.423064\pi\)
\(608\) −150.234 −6.09279
\(609\) −44.9284 −1.82059
\(610\) −5.89087 −0.238514
\(611\) −21.6209 −0.874687
\(612\) −6.06265 −0.245068
\(613\) 27.9795 1.13008 0.565042 0.825062i \(-0.308860\pi\)
0.565042 + 0.825062i \(0.308860\pi\)
\(614\) −18.4962 −0.746447
\(615\) 6.55324 0.264252
\(616\) −242.734 −9.78001
\(617\) −7.29682 −0.293759 −0.146879 0.989154i \(-0.546923\pi\)
−0.146879 + 0.989154i \(0.546923\pi\)
\(618\) 33.9605 1.36609
\(619\) 25.9805 1.04425 0.522123 0.852870i \(-0.325140\pi\)
0.522123 + 0.852870i \(0.325140\pi\)
\(620\) −47.2982 −1.89954
\(621\) −20.4164 −0.819284
\(622\) −1.90945 −0.0765621
\(623\) −16.8475 −0.674980
\(624\) −117.224 −4.69270
\(625\) 2.03279 0.0813117
\(626\) 0.827853 0.0330877
\(627\) 43.2841 1.72860
\(628\) −41.4279 −1.65315
\(629\) 5.38614 0.214759
\(630\) −18.9423 −0.754679
\(631\) −28.4391 −1.13214 −0.566071 0.824357i \(-0.691537\pi\)
−0.566071 + 0.824357i \(0.691537\pi\)
\(632\) 121.286 4.82452
\(633\) −23.4574 −0.932348
\(634\) 77.0760 3.06108
\(635\) −10.8268 −0.429648
\(636\) −101.036 −4.00634
\(637\) 85.5153 3.38824
\(638\) −94.5637 −3.74381
\(639\) −5.92486 −0.234384
\(640\) −63.5280 −2.51117
\(641\) −16.9746 −0.670458 −0.335229 0.942137i \(-0.608814\pi\)
−0.335229 + 0.942137i \(0.608814\pi\)
\(642\) 74.6929 2.94789
\(643\) −25.3326 −0.999019 −0.499509 0.866308i \(-0.666486\pi\)
−0.499509 + 0.866308i \(0.666486\pi\)
\(644\) 97.2652 3.83279
\(645\) −20.9083 −0.823264
\(646\) −16.9119 −0.665389
\(647\) −36.8206 −1.44757 −0.723784 0.690026i \(-0.757599\pi\)
−0.723784 + 0.690026i \(0.757599\pi\)
\(648\) 45.1832 1.77496
\(649\) 52.5400 2.06238
\(650\) 47.4928 1.86282
\(651\) −42.8911 −1.68104
\(652\) 59.0728 2.31347
\(653\) 38.8027 1.51847 0.759234 0.650818i \(-0.225574\pi\)
0.759234 + 0.650818i \(0.225574\pi\)
\(654\) 1.42057 0.0555485
\(655\) 8.99608 0.351506
\(656\) −57.8099 −2.25710
\(657\) 4.89640 0.191027
\(658\) −54.4222 −2.12160
\(659\) 24.4183 0.951201 0.475601 0.879661i \(-0.342231\pi\)
0.475601 + 0.879661i \(0.342231\pi\)
\(660\) 51.8480 2.01818
\(661\) 41.5089 1.61451 0.807254 0.590204i \(-0.200953\pi\)
0.807254 + 0.590204i \(0.200953\pi\)
\(662\) 10.7974 0.419652
\(663\) −7.29819 −0.283438
\(664\) 1.62864 0.0632033
\(665\) −38.9151 −1.50906
\(666\) 16.0946 0.623655
\(667\) 24.3336 0.942200
\(668\) 45.2302 1.75001
\(669\) −15.0535 −0.582002
\(670\) 30.7962 1.18976
\(671\) −8.28061 −0.319669
\(672\) −163.190 −6.29520
\(673\) −25.8865 −0.997850 −0.498925 0.866645i \(-0.666272\pi\)
−0.498925 + 0.866645i \(0.666272\pi\)
\(674\) 76.8105 2.95863
\(675\) −18.4803 −0.711309
\(676\) 82.7738 3.18361
\(677\) −23.7726 −0.913657 −0.456828 0.889555i \(-0.651015\pi\)
−0.456828 + 0.889555i \(0.651015\pi\)
\(678\) 64.9017 2.49254
\(679\) −67.7960 −2.60177
\(680\) −13.0092 −0.498878
\(681\) 23.1407 0.886755
\(682\) −90.2758 −3.45684
\(683\) −9.56096 −0.365840 −0.182920 0.983128i \(-0.558555\pi\)
−0.182920 + 0.983128i \(0.558555\pi\)
\(684\) −37.2179 −1.42306
\(685\) 1.06135 0.0405522
\(686\) 122.335 4.67077
\(687\) 7.09006 0.270503
\(688\) 184.444 7.03188
\(689\) 68.8795 2.62410
\(690\) −18.1158 −0.689656
\(691\) −48.4330 −1.84248 −0.921239 0.388997i \(-0.872822\pi\)
−0.921239 + 0.388997i \(0.872822\pi\)
\(692\) −26.2389 −0.997454
\(693\) −26.6266 −1.01146
\(694\) 14.2856 0.542273
\(695\) 3.85786 0.146337
\(696\) −92.2021 −3.49491
\(697\) −3.59917 −0.136328
\(698\) 35.5803 1.34674
\(699\) −23.6796 −0.895643
\(700\) 88.0415 3.32766
\(701\) −11.6295 −0.439239 −0.219620 0.975586i \(-0.570482\pi\)
−0.219620 + 0.975586i \(0.570482\pi\)
\(702\) −82.1250 −3.09961
\(703\) 33.0649 1.24707
\(704\) −179.815 −6.77704
\(705\) 7.46504 0.281150
\(706\) −2.75487 −0.103681
\(707\) −4.52929 −0.170342
\(708\) 79.7724 2.99803
\(709\) −24.1336 −0.906356 −0.453178 0.891420i \(-0.649710\pi\)
−0.453178 + 0.891420i \(0.649710\pi\)
\(710\) −19.7975 −0.742987
\(711\) 13.3045 0.498958
\(712\) −34.5745 −1.29573
\(713\) 23.2302 0.869977
\(714\) −18.3704 −0.687494
\(715\) −35.3464 −1.32188
\(716\) −8.63713 −0.322785
\(717\) 14.9825 0.559532
\(718\) 76.7712 2.86508
\(719\) −48.0895 −1.79344 −0.896718 0.442603i \(-0.854055\pi\)
−0.896718 + 0.442603i \(0.854055\pi\)
\(720\) −22.9211 −0.854218
\(721\) −42.9188 −1.59838
\(722\) −51.4775 −1.91580
\(723\) −11.1121 −0.413262
\(724\) 32.7891 1.21860
\(725\) 22.0260 0.818025
\(726\) 57.0211 2.11625
\(727\) 34.4811 1.27883 0.639417 0.768861i \(-0.279176\pi\)
0.639417 + 0.768861i \(0.279176\pi\)
\(728\) 251.250 9.31195
\(729\) 28.4268 1.05284
\(730\) 16.3610 0.605547
\(731\) 11.4833 0.424724
\(732\) −12.5726 −0.464697
\(733\) −35.4817 −1.31055 −0.655273 0.755392i \(-0.727446\pi\)
−0.655273 + 0.755392i \(0.727446\pi\)
\(734\) −17.9208 −0.661470
\(735\) −29.5259 −1.08908
\(736\) 88.3852 3.25792
\(737\) 43.2892 1.59458
\(738\) −10.7549 −0.395894
\(739\) 8.06191 0.296562 0.148281 0.988945i \(-0.452626\pi\)
0.148281 + 0.988945i \(0.452626\pi\)
\(740\) 39.6069 1.45598
\(741\) −44.8028 −1.64587
\(742\) 173.378 6.36489
\(743\) −19.3678 −0.710536 −0.355268 0.934765i \(-0.615610\pi\)
−0.355268 + 0.934765i \(0.615610\pi\)
\(744\) −88.0213 −3.22702
\(745\) 14.2437 0.521847
\(746\) −76.4129 −2.79767
\(747\) 0.178653 0.00653657
\(748\) −28.4760 −1.04118
\(749\) −94.3958 −3.44915
\(750\) −41.4777 −1.51455
\(751\) −7.95756 −0.290375 −0.145188 0.989404i \(-0.546379\pi\)
−0.145188 + 0.989404i \(0.546379\pi\)
\(752\) −65.8534 −2.40143
\(753\) −37.8912 −1.38083
\(754\) 97.8815 3.56463
\(755\) −0.0708296 −0.00257775
\(756\) −152.242 −5.53699
\(757\) −47.5578 −1.72852 −0.864260 0.503046i \(-0.832213\pi\)
−0.864260 + 0.503046i \(0.832213\pi\)
\(758\) 42.4946 1.54347
\(759\) −25.4648 −0.924313
\(760\) −79.8618 −2.89689
\(761\) 3.39134 0.122936 0.0614680 0.998109i \(-0.480422\pi\)
0.0614680 + 0.998109i \(0.480422\pi\)
\(762\) −31.3754 −1.13661
\(763\) −1.79529 −0.0649939
\(764\) −136.149 −4.92569
\(765\) −1.42704 −0.0515946
\(766\) −22.7392 −0.821601
\(767\) −54.3834 −1.96367
\(768\) −86.4085 −3.11800
\(769\) 16.0805 0.579877 0.289939 0.957045i \(-0.406365\pi\)
0.289939 + 0.957045i \(0.406365\pi\)
\(770\) −88.9711 −3.20629
\(771\) 18.6056 0.670065
\(772\) 40.1816 1.44617
\(773\) −48.9441 −1.76040 −0.880198 0.474607i \(-0.842590\pi\)
−0.880198 + 0.474607i \(0.842590\pi\)
\(774\) 34.3139 1.23339
\(775\) 21.0273 0.755321
\(776\) −139.131 −4.99452
\(777\) 35.9165 1.28850
\(778\) 61.5989 2.20843
\(779\) −22.0949 −0.791633
\(780\) −53.6671 −1.92159
\(781\) −27.8288 −0.995792
\(782\) 9.94955 0.355795
\(783\) −38.0875 −1.36114
\(784\) 260.465 9.30232
\(785\) −9.75137 −0.348041
\(786\) 26.0701 0.929890
\(787\) −32.7361 −1.16692 −0.583459 0.812143i \(-0.698301\pi\)
−0.583459 + 0.812143i \(0.698301\pi\)
\(788\) −101.596 −3.61922
\(789\) −23.7029 −0.843846
\(790\) 44.4561 1.58168
\(791\) −82.0218 −2.91636
\(792\) −54.6432 −1.94166
\(793\) 8.57114 0.304370
\(794\) 67.7599 2.40471
\(795\) −23.7820 −0.843462
\(796\) −53.6640 −1.90207
\(797\) −6.87112 −0.243387 −0.121694 0.992568i \(-0.538833\pi\)
−0.121694 + 0.992568i \(0.538833\pi\)
\(798\) −112.774 −3.99215
\(799\) −4.09995 −0.145046
\(800\) 80.0035 2.82855
\(801\) −3.79264 −0.134006
\(802\) −47.0393 −1.66102
\(803\) 22.9981 0.811587
\(804\) 65.7268 2.31801
\(805\) 22.8944 0.806923
\(806\) 93.4432 3.29140
\(807\) 3.18972 0.112284
\(808\) −9.29503 −0.326998
\(809\) 16.0637 0.564770 0.282385 0.959301i \(-0.408874\pi\)
0.282385 + 0.959301i \(0.408874\pi\)
\(810\) 16.5614 0.581907
\(811\) −43.7462 −1.53614 −0.768068 0.640369i \(-0.778782\pi\)
−0.768068 + 0.640369i \(0.778782\pi\)
\(812\) 181.451 6.36769
\(813\) 3.53935 0.124130
\(814\) 75.5957 2.64963
\(815\) 13.9046 0.487059
\(816\) −22.2290 −0.778171
\(817\) 70.4946 2.46629
\(818\) −90.6973 −3.17116
\(819\) 27.5608 0.963054
\(820\) −26.4665 −0.924249
\(821\) 32.7099 1.14158 0.570791 0.821095i \(-0.306637\pi\)
0.570791 + 0.821095i \(0.306637\pi\)
\(822\) 3.07574 0.107279
\(823\) 51.9900 1.81226 0.906129 0.423000i \(-0.139023\pi\)
0.906129 + 0.423000i \(0.139023\pi\)
\(824\) −88.0780 −3.06834
\(825\) −23.0500 −0.802496
\(826\) −136.889 −4.76299
\(827\) −3.56395 −0.123931 −0.0619654 0.998078i \(-0.519737\pi\)
−0.0619654 + 0.998078i \(0.519737\pi\)
\(828\) 21.8960 0.760937
\(829\) 43.5030 1.51092 0.755460 0.655194i \(-0.227413\pi\)
0.755460 + 0.655194i \(0.227413\pi\)
\(830\) 0.596957 0.0207207
\(831\) 15.4803 0.537006
\(832\) 186.124 6.45269
\(833\) 16.2162 0.561859
\(834\) 11.1799 0.387127
\(835\) 10.6464 0.368433
\(836\) −174.811 −6.04596
\(837\) −36.3605 −1.25680
\(838\) −71.6565 −2.47533
\(839\) −47.9142 −1.65418 −0.827091 0.562068i \(-0.810006\pi\)
−0.827091 + 0.562068i \(0.810006\pi\)
\(840\) −86.7491 −2.99313
\(841\) 16.3951 0.565347
\(842\) 18.2386 0.628543
\(843\) −8.47511 −0.291898
\(844\) 94.7370 3.26098
\(845\) 19.4834 0.670251
\(846\) −12.2513 −0.421209
\(847\) −72.0624 −2.47609
\(848\) 209.795 7.20439
\(849\) 35.7712 1.22766
\(850\) 9.00603 0.308904
\(851\) −19.4527 −0.666828
\(852\) −42.2529 −1.44756
\(853\) −11.7507 −0.402337 −0.201168 0.979557i \(-0.564474\pi\)
−0.201168 + 0.979557i \(0.564474\pi\)
\(854\) 21.5746 0.738266
\(855\) −8.76042 −0.299600
\(856\) −193.719 −6.62119
\(857\) 39.3138 1.34293 0.671467 0.741035i \(-0.265665\pi\)
0.671467 + 0.741035i \(0.265665\pi\)
\(858\) −102.432 −3.49697
\(859\) −50.7875 −1.73285 −0.866424 0.499309i \(-0.833587\pi\)
−0.866424 + 0.499309i \(0.833587\pi\)
\(860\) 84.4421 2.87945
\(861\) −24.0004 −0.817932
\(862\) −77.8280 −2.65083
\(863\) 33.5353 1.14155 0.570777 0.821105i \(-0.306642\pi\)
0.570777 + 0.821105i \(0.306642\pi\)
\(864\) −138.343 −4.70652
\(865\) −6.17616 −0.209996
\(866\) 34.2605 1.16422
\(867\) −1.38395 −0.0470014
\(868\) 173.224 5.87959
\(869\) 62.4906 2.11985
\(870\) −33.7956 −1.14578
\(871\) −44.8081 −1.51826
\(872\) −3.68430 −0.124766
\(873\) −15.2620 −0.516540
\(874\) 61.0792 2.06603
\(875\) 52.4189 1.77208
\(876\) 34.9185 1.17979
\(877\) −3.59414 −0.121366 −0.0606828 0.998157i \(-0.519328\pi\)
−0.0606828 + 0.998157i \(0.519328\pi\)
\(878\) −88.2497 −2.97828
\(879\) −15.9102 −0.536638
\(880\) −107.659 −3.62919
\(881\) −41.9150 −1.41215 −0.706076 0.708136i \(-0.749536\pi\)
−0.706076 + 0.708136i \(0.749536\pi\)
\(882\) 48.4567 1.63162
\(883\) −6.93214 −0.233285 −0.116643 0.993174i \(-0.537213\pi\)
−0.116643 + 0.993174i \(0.537213\pi\)
\(884\) 29.4751 0.991354
\(885\) 18.7770 0.631181
\(886\) 92.5896 3.11061
\(887\) −10.9871 −0.368911 −0.184455 0.982841i \(-0.559052\pi\)
−0.184455 + 0.982841i \(0.559052\pi\)
\(888\) 73.7079 2.47347
\(889\) 39.6518 1.32988
\(890\) −12.6728 −0.424795
\(891\) 23.2798 0.779903
\(892\) 60.7963 2.03561
\(893\) −25.1691 −0.842253
\(894\) 41.2773 1.38052
\(895\) −2.03302 −0.0679564
\(896\) 232.663 7.77274
\(897\) 26.3582 0.880076
\(898\) 36.5015 1.21807
\(899\) 43.3367 1.44536
\(900\) 19.8196 0.660652
\(901\) 13.0616 0.435144
\(902\) −50.5153 −1.68197
\(903\) 76.5741 2.54823
\(904\) −168.325 −5.59842
\(905\) 7.71797 0.256554
\(906\) −0.205260 −0.00681930
\(907\) 2.94876 0.0979119 0.0489560 0.998801i \(-0.484411\pi\)
0.0489560 + 0.998801i \(0.484411\pi\)
\(908\) −93.4581 −3.10152
\(909\) −1.01962 −0.0338186
\(910\) 92.0927 3.05284
\(911\) −9.70709 −0.321610 −0.160805 0.986986i \(-0.551409\pi\)
−0.160805 + 0.986986i \(0.551409\pi\)
\(912\) −136.462 −4.51869
\(913\) 0.839124 0.0277710
\(914\) 69.5282 2.29979
\(915\) −2.95936 −0.0978334
\(916\) −28.6345 −0.946110
\(917\) −32.9470 −1.08801
\(918\) −15.5733 −0.513995
\(919\) −34.8141 −1.14841 −0.574206 0.818711i \(-0.694689\pi\)
−0.574206 + 0.818711i \(0.694689\pi\)
\(920\) 46.9841 1.54902
\(921\) −9.29184 −0.306176
\(922\) 0.874669 0.0288057
\(923\) 28.8052 0.948133
\(924\) −189.887 −6.24681
\(925\) −17.6079 −0.578946
\(926\) −88.4050 −2.90517
\(927\) −9.66171 −0.317332
\(928\) 164.885 5.41263
\(929\) 11.6150 0.381074 0.190537 0.981680i \(-0.438977\pi\)
0.190537 + 0.981680i \(0.438977\pi\)
\(930\) −32.2631 −1.05795
\(931\) 99.5496 3.26261
\(932\) 95.6342 3.13260
\(933\) −0.959240 −0.0314041
\(934\) −8.59461 −0.281224
\(935\) −6.70272 −0.219202
\(936\) 56.5604 1.84874
\(937\) 18.2768 0.597078 0.298539 0.954397i \(-0.403501\pi\)
0.298539 + 0.954397i \(0.403501\pi\)
\(938\) −112.787 −3.68263
\(939\) 0.415884 0.0135719
\(940\) −30.1489 −0.983349
\(941\) −7.46183 −0.243249 −0.121624 0.992576i \(-0.538810\pi\)
−0.121624 + 0.992576i \(0.538810\pi\)
\(942\) −28.2589 −0.920724
\(943\) 12.9988 0.423300
\(944\) −165.643 −5.39121
\(945\) −35.8350 −1.16571
\(946\) 161.171 5.24011
\(947\) −10.5432 −0.342607 −0.171303 0.985218i \(-0.554798\pi\)
−0.171303 + 0.985218i \(0.554798\pi\)
\(948\) 94.8805 3.08158
\(949\) −23.8051 −0.772745
\(950\) 55.2870 1.79375
\(951\) 38.7202 1.25559
\(952\) 47.6444 1.54416
\(953\) 25.0948 0.812900 0.406450 0.913673i \(-0.366767\pi\)
0.406450 + 0.913673i \(0.366767\pi\)
\(954\) 39.0301 1.26365
\(955\) −32.0469 −1.03701
\(956\) −60.5096 −1.95702
\(957\) −47.5054 −1.53563
\(958\) 4.16943 0.134708
\(959\) −3.88707 −0.125520
\(960\) −64.2631 −2.07408
\(961\) 10.3716 0.334568
\(962\) −78.2481 −2.52282
\(963\) −21.2500 −0.684772
\(964\) 44.8781 1.44542
\(965\) 9.45802 0.304464
\(966\) 66.3467 2.13467
\(967\) −23.1106 −0.743187 −0.371594 0.928395i \(-0.621189\pi\)
−0.371594 + 0.928395i \(0.621189\pi\)
\(968\) −147.887 −4.75326
\(969\) −8.49592 −0.272928
\(970\) −50.9969 −1.63741
\(971\) −13.6255 −0.437264 −0.218632 0.975807i \(-0.570159\pi\)
−0.218632 + 0.975807i \(0.570159\pi\)
\(972\) −59.4434 −1.90665
\(973\) −14.1289 −0.452953
\(974\) 27.2697 0.873778
\(975\) 23.8587 0.764089
\(976\) 26.1062 0.835640
\(977\) −55.4372 −1.77359 −0.886797 0.462159i \(-0.847075\pi\)
−0.886797 + 0.462159i \(0.847075\pi\)
\(978\) 40.2948 1.28849
\(979\) −17.8138 −0.569333
\(980\) 119.246 3.80916
\(981\) −0.404149 −0.0129035
\(982\) 38.0133 1.21305
\(983\) −28.6291 −0.913128 −0.456564 0.889691i \(-0.650920\pi\)
−0.456564 + 0.889691i \(0.650920\pi\)
\(984\) −49.2537 −1.57015
\(985\) −23.9139 −0.761961
\(986\) 18.5612 0.591109
\(987\) −27.3398 −0.870234
\(988\) 180.944 5.75660
\(989\) −41.4732 −1.31877
\(990\) −20.0288 −0.636558
\(991\) −15.6685 −0.497726 −0.248863 0.968539i \(-0.580057\pi\)
−0.248863 + 0.968539i \(0.580057\pi\)
\(992\) 157.409 4.99773
\(993\) 5.42422 0.172132
\(994\) 72.5059 2.29975
\(995\) −12.6315 −0.400446
\(996\) 1.27406 0.0403700
\(997\) 1.25717 0.0398150 0.0199075 0.999802i \(-0.493663\pi\)
0.0199075 + 0.999802i \(0.493663\pi\)
\(998\) 103.577 3.27868
\(999\) 30.4478 0.963326
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 \(a_p\))