Properties

Label 6001.2.a.b.1.20
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 1.20
Character \(\chi\) = 6001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.09110 q^{2}\) \(-1.81594 q^{3}\) \(+2.37271 q^{4}\) \(+1.01486 q^{5}\) \(+3.79732 q^{6}\) \(+2.98461 q^{7}\) \(-0.779370 q^{8}\) \(+0.297648 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.09110 q^{2}\) \(-1.81594 q^{3}\) \(+2.37271 q^{4}\) \(+1.01486 q^{5}\) \(+3.79732 q^{6}\) \(+2.98461 q^{7}\) \(-0.779370 q^{8}\) \(+0.297648 q^{9}\) \(-2.12218 q^{10}\) \(-2.86797 q^{11}\) \(-4.30870 q^{12}\) \(+0.868290 q^{13}\) \(-6.24112 q^{14}\) \(-1.84293 q^{15}\) \(-3.11567 q^{16}\) \(+1.00000 q^{17}\) \(-0.622412 q^{18}\) \(+1.72172 q^{19}\) \(+2.40797 q^{20}\) \(-5.41988 q^{21}\) \(+5.99722 q^{22}\) \(-6.20821 q^{23}\) \(+1.41529 q^{24}\) \(-3.97006 q^{25}\) \(-1.81568 q^{26}\) \(+4.90732 q^{27}\) \(+7.08160 q^{28}\) \(-0.219151 q^{29}\) \(+3.85375 q^{30}\) \(+5.98951 q^{31}\) \(+8.07393 q^{32}\) \(+5.20807 q^{33}\) \(-2.09110 q^{34}\) \(+3.02896 q^{35}\) \(+0.706231 q^{36}\) \(+4.78509 q^{37}\) \(-3.60030 q^{38}\) \(-1.57677 q^{39}\) \(-0.790951 q^{40}\) \(+9.96704 q^{41}\) \(+11.3335 q^{42}\) \(+3.15469 q^{43}\) \(-6.80485 q^{44}\) \(+0.302071 q^{45}\) \(+12.9820 q^{46}\) \(-11.3131 q^{47}\) \(+5.65788 q^{48}\) \(+1.90788 q^{49}\) \(+8.30180 q^{50}\) \(-1.81594 q^{51}\) \(+2.06020 q^{52}\) \(+4.10300 q^{53}\) \(-10.2617 q^{54}\) \(-2.91059 q^{55}\) \(-2.32611 q^{56}\) \(-3.12655 q^{57}\) \(+0.458267 q^{58}\) \(-12.2362 q^{59}\) \(-4.37273 q^{60}\) \(+3.65797 q^{61}\) \(-12.5247 q^{62}\) \(+0.888362 q^{63}\) \(-10.6521 q^{64}\) \(+0.881193 q^{65}\) \(-10.8906 q^{66}\) \(-11.9679 q^{67}\) \(+2.37271 q^{68}\) \(+11.2738 q^{69}\) \(-6.33386 q^{70}\) \(-5.83543 q^{71}\) \(-0.231978 q^{72}\) \(-13.4525 q^{73}\) \(-10.0061 q^{74}\) \(+7.20940 q^{75}\) \(+4.08515 q^{76}\) \(-8.55976 q^{77}\) \(+3.29718 q^{78}\) \(+9.40040 q^{79}\) \(-3.16197 q^{80}\) \(-9.80435 q^{81}\) \(-20.8421 q^{82}\) \(-12.4585 q^{83}\) \(-12.8598 q^{84}\) \(+1.01486 q^{85}\) \(-6.59678 q^{86}\) \(+0.397965 q^{87}\) \(+2.23521 q^{88}\) \(+3.38629 q^{89}\) \(-0.631661 q^{90}\) \(+2.59151 q^{91}\) \(-14.7303 q^{92}\) \(-10.8766 q^{93}\) \(+23.6568 q^{94}\) \(+1.74731 q^{95}\) \(-14.6618 q^{96}\) \(+5.45836 q^{97}\) \(-3.98958 q^{98}\) \(-0.853645 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut -\mathstrut 19q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 49q^{12} \) \(\mathstrut -\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 39q^{15} \) \(\mathstrut +\mathstrut 110q^{16} \) \(\mathstrut +\mathstrut 114q^{17} \) \(\mathstrut -\mathstrut 21q^{18} \) \(\mathstrut -\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 88q^{20} \) \(\mathstrut -\mathstrut 30q^{21} \) \(\mathstrut -\mathstrut 36q^{22} \) \(\mathstrut -\mathstrut 77q^{23} \) \(\mathstrut -\mathstrut 72q^{24} \) \(\mathstrut +\mathstrut 119q^{25} \) \(\mathstrut -\mathstrut 79q^{26} \) \(\mathstrut -\mathstrut 77q^{27} \) \(\mathstrut -\mathstrut 92q^{28} \) \(\mathstrut -\mathstrut 65q^{29} \) \(\mathstrut -\mathstrut 10q^{30} \) \(\mathstrut -\mathstrut 131q^{31} \) \(\mathstrut -\mathstrut 30q^{32} \) \(\mathstrut -\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 33q^{35} \) \(\mathstrut +\mathstrut 109q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 14q^{38} \) \(\mathstrut -\mathstrut 83q^{39} \) \(\mathstrut -\mathstrut 42q^{40} \) \(\mathstrut -\mathstrut 99q^{41} \) \(\mathstrut +\mathstrut 29q^{42} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 98q^{44} \) \(\mathstrut -\mathstrut 73q^{45} \) \(\mathstrut -\mathstrut 35q^{46} \) \(\mathstrut -\mathstrut 113q^{47} \) \(\mathstrut -\mathstrut 86q^{48} \) \(\mathstrut +\mathstrut 101q^{49} \) \(\mathstrut -\mathstrut 44q^{50} \) \(\mathstrut -\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut 3q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut -\mathstrut 78q^{54} \) \(\mathstrut -\mathstrut 63q^{55} \) \(\mathstrut -\mathstrut 117q^{56} \) \(\mathstrut -\mathstrut 64q^{57} \) \(\mathstrut -\mathstrut 31q^{58} \) \(\mathstrut -\mathstrut 134q^{59} \) \(\mathstrut -\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 30q^{61} \) \(\mathstrut -\mathstrut 30q^{62} \) \(\mathstrut -\mathstrut 154q^{63} \) \(\mathstrut +\mathstrut 117q^{64} \) \(\mathstrut -\mathstrut 66q^{65} \) \(\mathstrut -\mathstrut 12q^{66} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut +\mathstrut 110q^{68} \) \(\mathstrut -\mathstrut 35q^{69} \) \(\mathstrut +\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 233q^{71} \) \(\mathstrut +\mathstrut 16q^{72} \) \(\mathstrut -\mathstrut 56q^{73} \) \(\mathstrut -\mathstrut 64q^{74} \) \(\mathstrut -\mathstrut 100q^{75} \) \(\mathstrut -\mathstrut 64q^{76} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 50q^{78} \) \(\mathstrut -\mathstrut 154q^{79} \) \(\mathstrut -\mathstrut 128q^{80} \) \(\mathstrut +\mathstrut 118q^{81} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 53q^{83} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 27q^{85} \) \(\mathstrut -\mathstrut 52q^{86} \) \(\mathstrut -\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 52q^{88} \) \(\mathstrut -\mathstrut 118q^{89} \) \(\mathstrut -\mathstrut 5q^{90} \) \(\mathstrut -\mathstrut 95q^{91} \) \(\mathstrut -\mathstrut 102q^{92} \) \(\mathstrut +\mathstrut 47q^{93} \) \(\mathstrut -\mathstrut 3q^{94} \) \(\mathstrut -\mathstrut 158q^{95} \) \(\mathstrut -\mathstrut 144q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut +\mathstrut 3q^{98} \) \(\mathstrut -\mathstrut 131q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.09110 −1.47863 −0.739316 0.673358i \(-0.764851\pi\)
−0.739316 + 0.673358i \(0.764851\pi\)
\(3\) −1.81594 −1.04843 −0.524217 0.851584i \(-0.675642\pi\)
−0.524217 + 0.851584i \(0.675642\pi\)
\(4\) 2.37271 1.18635
\(5\) 1.01486 0.453859 0.226930 0.973911i \(-0.427131\pi\)
0.226930 + 0.973911i \(0.427131\pi\)
\(6\) 3.79732 1.55025
\(7\) 2.98461 1.12808 0.564038 0.825749i \(-0.309247\pi\)
0.564038 + 0.825749i \(0.309247\pi\)
\(8\) −0.779370 −0.275549
\(9\) 0.297648 0.0992159
\(10\) −2.12218 −0.671091
\(11\) −2.86797 −0.864725 −0.432363 0.901700i \(-0.642320\pi\)
−0.432363 + 0.901700i \(0.642320\pi\)
\(12\) −4.30870 −1.24381
\(13\) 0.868290 0.240820 0.120410 0.992724i \(-0.461579\pi\)
0.120410 + 0.992724i \(0.461579\pi\)
\(14\) −6.24112 −1.66801
\(15\) −1.84293 −0.475842
\(16\) −3.11567 −0.778918
\(17\) 1.00000 0.242536
\(18\) −0.622412 −0.146704
\(19\) 1.72172 0.394991 0.197495 0.980304i \(-0.436719\pi\)
0.197495 + 0.980304i \(0.436719\pi\)
\(20\) 2.40797 0.538437
\(21\) −5.41988 −1.18271
\(22\) 5.99722 1.27861
\(23\) −6.20821 −1.29450 −0.647251 0.762277i \(-0.724081\pi\)
−0.647251 + 0.762277i \(0.724081\pi\)
\(24\) 1.41529 0.288895
\(25\) −3.97006 −0.794012
\(26\) −1.81568 −0.356085
\(27\) 4.90732 0.944414
\(28\) 7.08160 1.33830
\(29\) −0.219151 −0.0406953 −0.0203476 0.999793i \(-0.506477\pi\)
−0.0203476 + 0.999793i \(0.506477\pi\)
\(30\) 3.85375 0.703595
\(31\) 5.98951 1.07575 0.537874 0.843025i \(-0.319228\pi\)
0.537874 + 0.843025i \(0.319228\pi\)
\(32\) 8.07393 1.42728
\(33\) 5.20807 0.906608
\(34\) −2.09110 −0.358621
\(35\) 3.02896 0.511987
\(36\) 0.706231 0.117705
\(37\) 4.78509 0.786664 0.393332 0.919396i \(-0.371322\pi\)
0.393332 + 0.919396i \(0.371322\pi\)
\(38\) −3.60030 −0.584046
\(39\) −1.57677 −0.252485
\(40\) −0.790951 −0.125060
\(41\) 9.96704 1.55659 0.778295 0.627899i \(-0.216085\pi\)
0.778295 + 0.627899i \(0.216085\pi\)
\(42\) 11.3335 1.74880
\(43\) 3.15469 0.481085 0.240543 0.970639i \(-0.422675\pi\)
0.240543 + 0.970639i \(0.422675\pi\)
\(44\) −6.80485 −1.02587
\(45\) 0.302071 0.0450300
\(46\) 12.9820 1.91409
\(47\) −11.3131 −1.65018 −0.825090 0.565002i \(-0.808876\pi\)
−0.825090 + 0.565002i \(0.808876\pi\)
\(48\) 5.65788 0.816645
\(49\) 1.90788 0.272555
\(50\) 8.30180 1.17405
\(51\) −1.81594 −0.254283
\(52\) 2.06020 0.285698
\(53\) 4.10300 0.563590 0.281795 0.959475i \(-0.409070\pi\)
0.281795 + 0.959475i \(0.409070\pi\)
\(54\) −10.2617 −1.39644
\(55\) −2.91059 −0.392463
\(56\) −2.32611 −0.310840
\(57\) −3.12655 −0.414122
\(58\) 0.458267 0.0601734
\(59\) −12.2362 −1.59302 −0.796509 0.604627i \(-0.793322\pi\)
−0.796509 + 0.604627i \(0.793322\pi\)
\(60\) −4.37273 −0.564517
\(61\) 3.65797 0.468355 0.234178 0.972194i \(-0.424760\pi\)
0.234178 + 0.972194i \(0.424760\pi\)
\(62\) −12.5247 −1.59064
\(63\) 0.888362 0.111923
\(64\) −10.6521 −1.33151
\(65\) 0.881193 0.109299
\(66\) −10.8906 −1.34054
\(67\) −11.9679 −1.46212 −0.731059 0.682315i \(-0.760973\pi\)
−0.731059 + 0.682315i \(0.760973\pi\)
\(68\) 2.37271 0.287733
\(69\) 11.2738 1.35720
\(70\) −6.33386 −0.757041
\(71\) −5.83543 −0.692538 −0.346269 0.938135i \(-0.612552\pi\)
−0.346269 + 0.938135i \(0.612552\pi\)
\(72\) −0.231978 −0.0273388
\(73\) −13.4525 −1.57450 −0.787248 0.616636i \(-0.788495\pi\)
−0.787248 + 0.616636i \(0.788495\pi\)
\(74\) −10.0061 −1.16319
\(75\) 7.20940 0.832470
\(76\) 4.08515 0.468599
\(77\) −8.55976 −0.975476
\(78\) 3.29718 0.373332
\(79\) 9.40040 1.05763 0.528814 0.848738i \(-0.322637\pi\)
0.528814 + 0.848738i \(0.322637\pi\)
\(80\) −3.16197 −0.353519
\(81\) −9.80435 −1.08937
\(82\) −20.8421 −2.30162
\(83\) −12.4585 −1.36750 −0.683749 0.729717i \(-0.739652\pi\)
−0.683749 + 0.729717i \(0.739652\pi\)
\(84\) −12.8598 −1.40312
\(85\) 1.01486 0.110077
\(86\) −6.59678 −0.711349
\(87\) 0.397965 0.0426664
\(88\) 2.23521 0.238274
\(89\) 3.38629 0.358946 0.179473 0.983763i \(-0.442561\pi\)
0.179473 + 0.983763i \(0.442561\pi\)
\(90\) −0.631661 −0.0665829
\(91\) 2.59151 0.271664
\(92\) −14.7303 −1.53574
\(93\) −10.8766 −1.12785
\(94\) 23.6568 2.44001
\(95\) 1.74731 0.179270
\(96\) −14.6618 −1.49641
\(97\) 5.45836 0.554213 0.277106 0.960839i \(-0.410625\pi\)
0.277106 + 0.960839i \(0.410625\pi\)
\(98\) −3.98958 −0.403008
\(99\) −0.853645 −0.0857945
\(100\) −9.41979 −0.941979
\(101\) 0.434914 0.0432756 0.0216378 0.999766i \(-0.493112\pi\)
0.0216378 + 0.999766i \(0.493112\pi\)
\(102\) 3.79732 0.375991
\(103\) −1.14666 −0.112984 −0.0564921 0.998403i \(-0.517992\pi\)
−0.0564921 + 0.998403i \(0.517992\pi\)
\(104\) −0.676720 −0.0663578
\(105\) −5.50041 −0.536785
\(106\) −8.57979 −0.833343
\(107\) 8.98893 0.868992 0.434496 0.900674i \(-0.356926\pi\)
0.434496 + 0.900674i \(0.356926\pi\)
\(108\) 11.6436 1.12041
\(109\) 7.50538 0.718885 0.359442 0.933167i \(-0.382967\pi\)
0.359442 + 0.933167i \(0.382967\pi\)
\(110\) 6.08633 0.580309
\(111\) −8.68945 −0.824766
\(112\) −9.29906 −0.878679
\(113\) 11.6881 1.09952 0.549761 0.835322i \(-0.314719\pi\)
0.549761 + 0.835322i \(0.314719\pi\)
\(114\) 6.53794 0.612334
\(115\) −6.30046 −0.587521
\(116\) −0.519981 −0.0482790
\(117\) 0.258445 0.0238932
\(118\) 25.5871 2.35549
\(119\) 2.98461 0.273599
\(120\) 1.43632 0.131118
\(121\) −2.77475 −0.252250
\(122\) −7.64919 −0.692526
\(123\) −18.0996 −1.63198
\(124\) 14.2114 1.27622
\(125\) −9.10335 −0.814229
\(126\) −1.85766 −0.165493
\(127\) 11.7746 1.04483 0.522413 0.852692i \(-0.325032\pi\)
0.522413 + 0.852692i \(0.325032\pi\)
\(128\) 6.12670 0.541529
\(129\) −5.72873 −0.504387
\(130\) −1.84266 −0.161612
\(131\) −7.72977 −0.675353 −0.337676 0.941262i \(-0.609641\pi\)
−0.337676 + 0.941262i \(0.609641\pi\)
\(132\) 12.3572 1.07556
\(133\) 5.13867 0.445579
\(134\) 25.0262 2.16193
\(135\) 4.98024 0.428631
\(136\) −0.779370 −0.0668304
\(137\) −7.44727 −0.636264 −0.318132 0.948046i \(-0.603055\pi\)
−0.318132 + 0.948046i \(0.603055\pi\)
\(138\) −23.5746 −2.00680
\(139\) 10.8714 0.922103 0.461051 0.887373i \(-0.347472\pi\)
0.461051 + 0.887373i \(0.347472\pi\)
\(140\) 7.18683 0.607398
\(141\) 20.5439 1.73011
\(142\) 12.2025 1.02401
\(143\) −2.49023 −0.208243
\(144\) −0.927373 −0.0772811
\(145\) −0.222407 −0.0184699
\(146\) 28.1306 2.32810
\(147\) −3.46461 −0.285756
\(148\) 11.3536 0.933262
\(149\) −14.2643 −1.16858 −0.584289 0.811546i \(-0.698627\pi\)
−0.584289 + 0.811546i \(0.698627\pi\)
\(150\) −15.0756 −1.23092
\(151\) −5.01201 −0.407872 −0.203936 0.978984i \(-0.565373\pi\)
−0.203936 + 0.978984i \(0.565373\pi\)
\(152\) −1.34186 −0.108839
\(153\) 0.297648 0.0240634
\(154\) 17.8993 1.44237
\(155\) 6.07852 0.488238
\(156\) −3.74120 −0.299536
\(157\) −1.86289 −0.148675 −0.0743374 0.997233i \(-0.523684\pi\)
−0.0743374 + 0.997233i \(0.523684\pi\)
\(158\) −19.6572 −1.56384
\(159\) −7.45081 −0.590888
\(160\) 8.19391 0.647785
\(161\) −18.5291 −1.46030
\(162\) 20.5019 1.61078
\(163\) −13.3781 −1.04785 −0.523925 0.851764i \(-0.675533\pi\)
−0.523925 + 0.851764i \(0.675533\pi\)
\(164\) 23.6489 1.84667
\(165\) 5.28546 0.411472
\(166\) 26.0520 2.02203
\(167\) 4.81218 0.372378 0.186189 0.982514i \(-0.440386\pi\)
0.186189 + 0.982514i \(0.440386\pi\)
\(168\) 4.22409 0.325896
\(169\) −12.2461 −0.942006
\(170\) −2.12218 −0.162763
\(171\) 0.512467 0.0391894
\(172\) 7.48515 0.570738
\(173\) 19.2610 1.46439 0.732193 0.681097i \(-0.238497\pi\)
0.732193 + 0.681097i \(0.238497\pi\)
\(174\) −0.832186 −0.0630879
\(175\) −11.8491 −0.895706
\(176\) 8.93565 0.673550
\(177\) 22.2202 1.67018
\(178\) −7.08107 −0.530749
\(179\) −11.3991 −0.852010 −0.426005 0.904721i \(-0.640079\pi\)
−0.426005 + 0.904721i \(0.640079\pi\)
\(180\) 0.716726 0.0534216
\(181\) 0.0779341 0.00579279 0.00289640 0.999996i \(-0.499078\pi\)
0.00289640 + 0.999996i \(0.499078\pi\)
\(182\) −5.41910 −0.401691
\(183\) −6.64267 −0.491040
\(184\) 4.83850 0.356699
\(185\) 4.85620 0.357035
\(186\) 22.7441 1.66768
\(187\) −2.86797 −0.209727
\(188\) −26.8426 −1.95770
\(189\) 14.6464 1.06537
\(190\) −3.65380 −0.265075
\(191\) 25.8975 1.87388 0.936939 0.349493i \(-0.113646\pi\)
0.936939 + 0.349493i \(0.113646\pi\)
\(192\) 19.3435 1.39600
\(193\) −18.7292 −1.34816 −0.674080 0.738658i \(-0.735460\pi\)
−0.674080 + 0.738658i \(0.735460\pi\)
\(194\) −11.4140 −0.819477
\(195\) −1.60020 −0.114592
\(196\) 4.52685 0.323346
\(197\) −12.6599 −0.901979 −0.450989 0.892529i \(-0.648929\pi\)
−0.450989 + 0.892529i \(0.648929\pi\)
\(198\) 1.78506 0.126859
\(199\) 25.7766 1.82726 0.913629 0.406549i \(-0.133268\pi\)
0.913629 + 0.406549i \(0.133268\pi\)
\(200\) 3.09415 0.218789
\(201\) 21.7331 1.53293
\(202\) −0.909451 −0.0639887
\(203\) −0.654079 −0.0459074
\(204\) −4.30870 −0.301669
\(205\) 10.1151 0.706472
\(206\) 2.39779 0.167062
\(207\) −1.84786 −0.128435
\(208\) −2.70531 −0.187579
\(209\) −4.93785 −0.341558
\(210\) 11.5019 0.793708
\(211\) −12.1503 −0.836460 −0.418230 0.908341i \(-0.637349\pi\)
−0.418230 + 0.908341i \(0.637349\pi\)
\(212\) 9.73522 0.668617
\(213\) 10.5968 0.726081
\(214\) −18.7968 −1.28492
\(215\) 3.20157 0.218345
\(216\) −3.82462 −0.260232
\(217\) 17.8763 1.21353
\(218\) −15.6945 −1.06297
\(219\) 24.4290 1.65076
\(220\) −6.90597 −0.465600
\(221\) 0.868290 0.0584075
\(222\) 18.1705 1.21953
\(223\) 7.32543 0.490547 0.245273 0.969454i \(-0.421122\pi\)
0.245273 + 0.969454i \(0.421122\pi\)
\(224\) 24.0975 1.61008
\(225\) −1.18168 −0.0787786
\(226\) −24.4409 −1.62579
\(227\) 7.10532 0.471596 0.235798 0.971802i \(-0.424230\pi\)
0.235798 + 0.971802i \(0.424230\pi\)
\(228\) −7.41840 −0.491295
\(229\) −11.1217 −0.734944 −0.367472 0.930035i \(-0.619777\pi\)
−0.367472 + 0.930035i \(0.619777\pi\)
\(230\) 13.1749 0.868728
\(231\) 15.5440 1.02272
\(232\) 0.170800 0.0112135
\(233\) −29.1623 −1.91049 −0.955243 0.295823i \(-0.904406\pi\)
−0.955243 + 0.295823i \(0.904406\pi\)
\(234\) −0.540434 −0.0353293
\(235\) −11.4812 −0.748949
\(236\) −29.0329 −1.88988
\(237\) −17.0706 −1.10885
\(238\) −6.24112 −0.404552
\(239\) −22.8964 −1.48104 −0.740522 0.672033i \(-0.765421\pi\)
−0.740522 + 0.672033i \(0.765421\pi\)
\(240\) 5.74196 0.370642
\(241\) 3.15808 0.203430 0.101715 0.994814i \(-0.467567\pi\)
0.101715 + 0.994814i \(0.467567\pi\)
\(242\) 5.80229 0.372985
\(243\) 3.08219 0.197722
\(244\) 8.67930 0.555635
\(245\) 1.93623 0.123701
\(246\) 37.8481 2.41310
\(247\) 1.49496 0.0951218
\(248\) −4.66805 −0.296421
\(249\) 22.6239 1.43373
\(250\) 19.0360 1.20394
\(251\) 16.6537 1.05117 0.525586 0.850740i \(-0.323846\pi\)
0.525586 + 0.850740i \(0.323846\pi\)
\(252\) 2.10782 0.132780
\(253\) 17.8050 1.11939
\(254\) −24.6219 −1.54491
\(255\) −1.84293 −0.115409
\(256\) 8.49258 0.530786
\(257\) 17.5087 1.09216 0.546080 0.837733i \(-0.316119\pi\)
0.546080 + 0.837733i \(0.316119\pi\)
\(258\) 11.9794 0.745803
\(259\) 14.2816 0.887417
\(260\) 2.09081 0.129667
\(261\) −0.0652298 −0.00403762
\(262\) 16.1637 0.998599
\(263\) −17.0874 −1.05366 −0.526829 0.849972i \(-0.676619\pi\)
−0.526829 + 0.849972i \(0.676619\pi\)
\(264\) −4.05901 −0.249815
\(265\) 4.16397 0.255791
\(266\) −10.7455 −0.658848
\(267\) −6.14930 −0.376331
\(268\) −28.3964 −1.73459
\(269\) −22.4341 −1.36783 −0.683916 0.729561i \(-0.739724\pi\)
−0.683916 + 0.729561i \(0.739724\pi\)
\(270\) −10.4142 −0.633787
\(271\) −4.21022 −0.255753 −0.127876 0.991790i \(-0.540816\pi\)
−0.127876 + 0.991790i \(0.540816\pi\)
\(272\) −3.11567 −0.188915
\(273\) −4.70603 −0.284822
\(274\) 15.5730 0.940800
\(275\) 11.3860 0.686602
\(276\) 26.7493 1.61012
\(277\) 27.1206 1.62952 0.814759 0.579800i \(-0.196869\pi\)
0.814759 + 0.579800i \(0.196869\pi\)
\(278\) −22.7333 −1.36345
\(279\) 1.78277 0.106731
\(280\) −2.36068 −0.141078
\(281\) 9.15554 0.546174 0.273087 0.961989i \(-0.411955\pi\)
0.273087 + 0.961989i \(0.411955\pi\)
\(282\) −42.9593 −2.55819
\(283\) 27.0950 1.61063 0.805314 0.592849i \(-0.201997\pi\)
0.805314 + 0.592849i \(0.201997\pi\)
\(284\) −13.8458 −0.821595
\(285\) −3.17301 −0.187953
\(286\) 5.20732 0.307916
\(287\) 29.7477 1.75595
\(288\) 2.40319 0.141609
\(289\) 1.00000 0.0588235
\(290\) 0.465077 0.0273102
\(291\) −9.91207 −0.581056
\(292\) −31.9189 −1.86791
\(293\) −0.0277554 −0.00162149 −0.000810745 1.00000i \(-0.500258\pi\)
−0.000810745 1.00000i \(0.500258\pi\)
\(294\) 7.24484 0.422528
\(295\) −12.4180 −0.723005
\(296\) −3.72936 −0.216765
\(297\) −14.0740 −0.816658
\(298\) 29.8281 1.72790
\(299\) −5.39053 −0.311742
\(300\) 17.1058 0.987604
\(301\) 9.41551 0.542701
\(302\) 10.4806 0.603093
\(303\) −0.789780 −0.0453717
\(304\) −5.36433 −0.307665
\(305\) 3.71233 0.212567
\(306\) −0.622412 −0.0355809
\(307\) −27.8195 −1.58774 −0.793871 0.608086i \(-0.791938\pi\)
−0.793871 + 0.608086i \(0.791938\pi\)
\(308\) −20.3098 −1.15726
\(309\) 2.08227 0.118456
\(310\) −12.7108 −0.721925
\(311\) −1.57795 −0.0894775 −0.0447387 0.998999i \(-0.514246\pi\)
−0.0447387 + 0.998999i \(0.514246\pi\)
\(312\) 1.22888 0.0695719
\(313\) 24.4018 1.37927 0.689636 0.724156i \(-0.257771\pi\)
0.689636 + 0.724156i \(0.257771\pi\)
\(314\) 3.89549 0.219835
\(315\) 0.901563 0.0507973
\(316\) 22.3044 1.25472
\(317\) 23.1314 1.29919 0.649594 0.760281i \(-0.274939\pi\)
0.649594 + 0.760281i \(0.274939\pi\)
\(318\) 15.5804 0.873706
\(319\) 0.628518 0.0351903
\(320\) −10.8104 −0.604317
\(321\) −16.3234 −0.911082
\(322\) 38.7462 2.15924
\(323\) 1.72172 0.0957993
\(324\) −23.2629 −1.29238
\(325\) −3.44716 −0.191214
\(326\) 27.9749 1.54939
\(327\) −13.6293 −0.753704
\(328\) −7.76801 −0.428917
\(329\) −33.7650 −1.86153
\(330\) −11.0524 −0.608416
\(331\) 23.1059 1.27001 0.635007 0.772507i \(-0.280997\pi\)
0.635007 + 0.772507i \(0.280997\pi\)
\(332\) −29.5604 −1.62234
\(333\) 1.42427 0.0780496
\(334\) −10.0628 −0.550610
\(335\) −12.1458 −0.663595
\(336\) 16.8866 0.921238
\(337\) 22.1749 1.20794 0.603971 0.797006i \(-0.293584\pi\)
0.603971 + 0.797006i \(0.293584\pi\)
\(338\) 25.6078 1.39288
\(339\) −21.2249 −1.15278
\(340\) 2.40797 0.130590
\(341\) −17.1777 −0.930227
\(342\) −1.07162 −0.0579467
\(343\) −15.1980 −0.820613
\(344\) −2.45867 −0.132563
\(345\) 11.4413 0.615978
\(346\) −40.2767 −2.16529
\(347\) −33.2416 −1.78450 −0.892251 0.451541i \(-0.850875\pi\)
−0.892251 + 0.451541i \(0.850875\pi\)
\(348\) 0.944256 0.0506174
\(349\) −24.9642 −1.33630 −0.668152 0.744025i \(-0.732914\pi\)
−0.668152 + 0.744025i \(0.732914\pi\)
\(350\) 24.7776 1.32442
\(351\) 4.26098 0.227434
\(352\) −23.1558 −1.23421
\(353\) 1.00000 0.0532246
\(354\) −46.4648 −2.46958
\(355\) −5.92214 −0.314315
\(356\) 8.03467 0.425837
\(357\) −5.41988 −0.286850
\(358\) 23.8367 1.25981
\(359\) −5.77716 −0.304907 −0.152453 0.988311i \(-0.548717\pi\)
−0.152453 + 0.988311i \(0.548717\pi\)
\(360\) −0.235425 −0.0124080
\(361\) −16.0357 −0.843982
\(362\) −0.162968 −0.00856541
\(363\) 5.03879 0.264468
\(364\) 6.14889 0.322289
\(365\) −13.6524 −0.714600
\(366\) 13.8905 0.726068
\(367\) 32.5860 1.70098 0.850488 0.525994i \(-0.176307\pi\)
0.850488 + 0.525994i \(0.176307\pi\)
\(368\) 19.3428 1.00831
\(369\) 2.96667 0.154439
\(370\) −10.1548 −0.527923
\(371\) 12.2458 0.635772
\(372\) −25.8070 −1.33803
\(373\) −7.80508 −0.404132 −0.202066 0.979372i \(-0.564766\pi\)
−0.202066 + 0.979372i \(0.564766\pi\)
\(374\) 5.99722 0.310109
\(375\) 16.5312 0.853666
\(376\) 8.81706 0.454705
\(377\) −0.190287 −0.00980026
\(378\) −30.6271 −1.57529
\(379\) 16.5589 0.850574 0.425287 0.905058i \(-0.360173\pi\)
0.425287 + 0.905058i \(0.360173\pi\)
\(380\) 4.14585 0.212678
\(381\) −21.3820 −1.09543
\(382\) −54.1543 −2.77078
\(383\) 18.8729 0.964359 0.482180 0.876072i \(-0.339845\pi\)
0.482180 + 0.876072i \(0.339845\pi\)
\(384\) −11.1257 −0.567758
\(385\) −8.68696 −0.442728
\(386\) 39.1648 1.99343
\(387\) 0.938986 0.0477313
\(388\) 12.9511 0.657492
\(389\) 4.08555 0.207145 0.103573 0.994622i \(-0.466973\pi\)
0.103573 + 0.994622i \(0.466973\pi\)
\(390\) 3.34617 0.169440
\(391\) −6.20821 −0.313963
\(392\) −1.48695 −0.0751022
\(393\) 14.0368 0.708064
\(394\) 26.4731 1.33369
\(395\) 9.54008 0.480014
\(396\) −2.02545 −0.101783
\(397\) −2.99310 −0.150219 −0.0751097 0.997175i \(-0.523931\pi\)
−0.0751097 + 0.997175i \(0.523931\pi\)
\(398\) −53.9016 −2.70184
\(399\) −9.33153 −0.467161
\(400\) 12.3694 0.618470
\(401\) −19.8881 −0.993166 −0.496583 0.867989i \(-0.665412\pi\)
−0.496583 + 0.867989i \(0.665412\pi\)
\(402\) −45.4461 −2.26665
\(403\) 5.20064 0.259062
\(404\) 1.03193 0.0513402
\(405\) −9.95004 −0.494421
\(406\) 1.36775 0.0678801
\(407\) −13.7235 −0.680248
\(408\) 1.41529 0.0700674
\(409\) −19.8486 −0.981451 −0.490725 0.871314i \(-0.663268\pi\)
−0.490725 + 0.871314i \(0.663268\pi\)
\(410\) −21.1518 −1.04461
\(411\) 13.5238 0.667081
\(412\) −2.72070 −0.134039
\(413\) −36.5203 −1.79704
\(414\) 3.86406 0.189908
\(415\) −12.6436 −0.620651
\(416\) 7.01052 0.343719
\(417\) −19.7419 −0.966765
\(418\) 10.3256 0.505039
\(419\) −16.2220 −0.792498 −0.396249 0.918143i \(-0.629688\pi\)
−0.396249 + 0.918143i \(0.629688\pi\)
\(420\) −13.0509 −0.636817
\(421\) 8.91700 0.434588 0.217294 0.976106i \(-0.430277\pi\)
0.217294 + 0.976106i \(0.430277\pi\)
\(422\) 25.4075 1.23682
\(423\) −3.36731 −0.163724
\(424\) −3.19776 −0.155297
\(425\) −3.97006 −0.192576
\(426\) −22.1590 −1.07361
\(427\) 10.9176 0.528340
\(428\) 21.3281 1.03093
\(429\) 4.52211 0.218330
\(430\) −6.69480 −0.322852
\(431\) −35.5417 −1.71198 −0.855992 0.516988i \(-0.827053\pi\)
−0.855992 + 0.516988i \(0.827053\pi\)
\(432\) −15.2896 −0.735621
\(433\) 22.5134 1.08193 0.540963 0.841047i \(-0.318060\pi\)
0.540963 + 0.841047i \(0.318060\pi\)
\(434\) −37.3813 −1.79436
\(435\) 0.403879 0.0193645
\(436\) 17.8081 0.852852
\(437\) −10.6888 −0.511316
\(438\) −51.0835 −2.44086
\(439\) −37.9037 −1.80904 −0.904522 0.426428i \(-0.859772\pi\)
−0.904522 + 0.426428i \(0.859772\pi\)
\(440\) 2.26842 0.108143
\(441\) 0.567877 0.0270418
\(442\) −1.81568 −0.0863633
\(443\) 2.51325 0.119408 0.0597040 0.998216i \(-0.480984\pi\)
0.0597040 + 0.998216i \(0.480984\pi\)
\(444\) −20.6175 −0.978465
\(445\) 3.43661 0.162911
\(446\) −15.3182 −0.725339
\(447\) 25.9032 1.22518
\(448\) −31.7922 −1.50204
\(449\) −41.4836 −1.95773 −0.978865 0.204507i \(-0.934441\pi\)
−0.978865 + 0.204507i \(0.934441\pi\)
\(450\) 2.47101 0.116485
\(451\) −28.5852 −1.34602
\(452\) 27.7324 1.30442
\(453\) 9.10153 0.427627
\(454\) −14.8579 −0.697318
\(455\) 2.63001 0.123297
\(456\) 2.43674 0.114111
\(457\) 30.2560 1.41532 0.707659 0.706555i \(-0.249752\pi\)
0.707659 + 0.706555i \(0.249752\pi\)
\(458\) 23.2567 1.08671
\(459\) 4.90732 0.229054
\(460\) −14.9492 −0.697008
\(461\) 39.6776 1.84797 0.923986 0.382427i \(-0.124911\pi\)
0.923986 + 0.382427i \(0.124911\pi\)
\(462\) −32.5042 −1.51223
\(463\) −10.7520 −0.499686 −0.249843 0.968286i \(-0.580379\pi\)
−0.249843 + 0.968286i \(0.580379\pi\)
\(464\) 0.682802 0.0316983
\(465\) −11.0382 −0.511886
\(466\) 60.9813 2.82491
\(467\) 6.51316 0.301393 0.150696 0.988580i \(-0.451848\pi\)
0.150696 + 0.988580i \(0.451848\pi\)
\(468\) 0.613214 0.0283458
\(469\) −35.7196 −1.64938
\(470\) 24.0083 1.10742
\(471\) 3.38290 0.155876
\(472\) 9.53653 0.438954
\(473\) −9.04755 −0.416007
\(474\) 35.6963 1.63959
\(475\) −6.83535 −0.313627
\(476\) 7.08160 0.324585
\(477\) 1.22125 0.0559171
\(478\) 47.8787 2.18992
\(479\) 7.54319 0.344657 0.172329 0.985040i \(-0.444871\pi\)
0.172329 + 0.985040i \(0.444871\pi\)
\(480\) −14.8797 −0.679161
\(481\) 4.15485 0.189445
\(482\) −6.60387 −0.300798
\(483\) 33.6477 1.53103
\(484\) −6.58368 −0.299258
\(485\) 5.53947 0.251534
\(486\) −6.44516 −0.292359
\(487\) −34.5474 −1.56549 −0.782747 0.622340i \(-0.786182\pi\)
−0.782747 + 0.622340i \(0.786182\pi\)
\(488\) −2.85092 −0.129055
\(489\) 24.2938 1.09860
\(490\) −4.04886 −0.182909
\(491\) 5.75212 0.259589 0.129795 0.991541i \(-0.458568\pi\)
0.129795 + 0.991541i \(0.458568\pi\)
\(492\) −42.9450 −1.93611
\(493\) −0.219151 −0.00987006
\(494\) −3.12611 −0.140650
\(495\) −0.866329 −0.0389386
\(496\) −18.6614 −0.837920
\(497\) −17.4165 −0.781235
\(498\) −47.3089 −2.11996
\(499\) −27.6169 −1.23630 −0.618151 0.786059i \(-0.712118\pi\)
−0.618151 + 0.786059i \(0.712118\pi\)
\(500\) −21.5996 −0.965963
\(501\) −8.73864 −0.390414
\(502\) −34.8246 −1.55430
\(503\) 4.01701 0.179110 0.0895548 0.995982i \(-0.471456\pi\)
0.0895548 + 0.995982i \(0.471456\pi\)
\(504\) −0.692363 −0.0308403
\(505\) 0.441377 0.0196410
\(506\) −37.2320 −1.65516
\(507\) 22.2382 0.987632
\(508\) 27.9377 1.23953
\(509\) −17.0152 −0.754184 −0.377092 0.926176i \(-0.623076\pi\)
−0.377092 + 0.926176i \(0.623076\pi\)
\(510\) 3.85375 0.170647
\(511\) −40.1505 −1.77615
\(512\) −30.0123 −1.32637
\(513\) 8.44905 0.373035
\(514\) −36.6124 −1.61490
\(515\) −1.16370 −0.0512789
\(516\) −13.5926 −0.598381
\(517\) 32.4455 1.42695
\(518\) −29.8643 −1.31216
\(519\) −34.9769 −1.53531
\(520\) −0.686775 −0.0301171
\(521\) −4.25927 −0.186602 −0.0933009 0.995638i \(-0.529742\pi\)
−0.0933009 + 0.995638i \(0.529742\pi\)
\(522\) 0.136402 0.00597016
\(523\) −36.2561 −1.58537 −0.792684 0.609633i \(-0.791317\pi\)
−0.792684 + 0.609633i \(0.791317\pi\)
\(524\) −18.3405 −0.801208
\(525\) 21.5172 0.939089
\(526\) 35.7316 1.55797
\(527\) 5.98951 0.260907
\(528\) −16.2266 −0.706174
\(529\) 15.5419 0.675734
\(530\) −8.70728 −0.378220
\(531\) −3.64208 −0.158053
\(532\) 12.1926 0.528615
\(533\) 8.65428 0.374859
\(534\) 12.8588 0.556456
\(535\) 9.12250 0.394400
\(536\) 9.32746 0.402885
\(537\) 20.7001 0.893277
\(538\) 46.9120 2.02252
\(539\) −5.47175 −0.235685
\(540\) 11.8166 0.508508
\(541\) −29.7495 −1.27903 −0.639516 0.768778i \(-0.720865\pi\)
−0.639516 + 0.768778i \(0.720865\pi\)
\(542\) 8.80400 0.378164
\(543\) −0.141524 −0.00607337
\(544\) 8.07393 0.346167
\(545\) 7.61691 0.326272
\(546\) 9.84078 0.421147
\(547\) 34.0493 1.45584 0.727922 0.685660i \(-0.240486\pi\)
0.727922 + 0.685660i \(0.240486\pi\)
\(548\) −17.6702 −0.754834
\(549\) 1.08879 0.0464683
\(550\) −23.8093 −1.01523
\(551\) −0.377317 −0.0160743
\(552\) −8.78643 −0.373975
\(553\) 28.0565 1.19308
\(554\) −56.7119 −2.40946
\(555\) −8.81857 −0.374328
\(556\) 25.7947 1.09394
\(557\) −33.7253 −1.42899 −0.714493 0.699643i \(-0.753342\pi\)
−0.714493 + 0.699643i \(0.753342\pi\)
\(558\) −3.72794 −0.157816
\(559\) 2.73918 0.115855
\(560\) −9.43724 −0.398796
\(561\) 5.20807 0.219885
\(562\) −19.1452 −0.807591
\(563\) −12.2703 −0.517131 −0.258566 0.965994i \(-0.583250\pi\)
−0.258566 + 0.965994i \(0.583250\pi\)
\(564\) 48.7446 2.05252
\(565\) 11.8617 0.499028
\(566\) −56.6583 −2.38153
\(567\) −29.2621 −1.22889
\(568\) 4.54796 0.190828
\(569\) −10.4652 −0.438723 −0.219362 0.975644i \(-0.570397\pi\)
−0.219362 + 0.975644i \(0.570397\pi\)
\(570\) 6.63509 0.277913
\(571\) −24.5470 −1.02726 −0.513631 0.858011i \(-0.671700\pi\)
−0.513631 + 0.858011i \(0.671700\pi\)
\(572\) −5.90859 −0.247050
\(573\) −47.0284 −1.96464
\(574\) −62.2055 −2.59641
\(575\) 24.6470 1.02785
\(576\) −3.17056 −0.132107
\(577\) −33.0579 −1.37622 −0.688109 0.725608i \(-0.741559\pi\)
−0.688109 + 0.725608i \(0.741559\pi\)
\(578\) −2.09110 −0.0869784
\(579\) 34.0112 1.41346
\(580\) −0.527708 −0.0219119
\(581\) −37.1837 −1.54264
\(582\) 20.7272 0.859168
\(583\) −11.7673 −0.487351
\(584\) 10.4845 0.433851
\(585\) 0.262285 0.0108442
\(586\) 0.0580394 0.00239759
\(587\) −4.57179 −0.188698 −0.0943489 0.995539i \(-0.530077\pi\)
−0.0943489 + 0.995539i \(0.530077\pi\)
\(588\) −8.22050 −0.339008
\(589\) 10.3123 0.424911
\(590\) 25.9674 1.06906
\(591\) 22.9896 0.945666
\(592\) −14.9088 −0.612747
\(593\) 5.36899 0.220478 0.110239 0.993905i \(-0.464838\pi\)
0.110239 + 0.993905i \(0.464838\pi\)
\(594\) 29.4302 1.20754
\(595\) 3.02896 0.124175
\(596\) −33.8450 −1.38635
\(597\) −46.8089 −1.91576
\(598\) 11.2721 0.460952
\(599\) −0.612818 −0.0250391 −0.0125195 0.999922i \(-0.503985\pi\)
−0.0125195 + 0.999922i \(0.503985\pi\)
\(600\) −5.61879 −0.229386
\(601\) −9.75933 −0.398091 −0.199046 0.979990i \(-0.563784\pi\)
−0.199046 + 0.979990i \(0.563784\pi\)
\(602\) −19.6888 −0.802455
\(603\) −3.56223 −0.145065
\(604\) −11.8920 −0.483880
\(605\) −2.81598 −0.114486
\(606\) 1.65151 0.0670880
\(607\) 6.89616 0.279906 0.139953 0.990158i \(-0.455305\pi\)
0.139953 + 0.990158i \(0.455305\pi\)
\(608\) 13.9011 0.563763
\(609\) 1.18777 0.0481309
\(610\) −7.76286 −0.314309
\(611\) −9.82302 −0.397397
\(612\) 0.706231 0.0285477
\(613\) −15.3003 −0.617973 −0.308987 0.951066i \(-0.599990\pi\)
−0.308987 + 0.951066i \(0.599990\pi\)
\(614\) 58.1734 2.34769
\(615\) −18.3685 −0.740690
\(616\) 6.67122 0.268791
\(617\) −21.0660 −0.848085 −0.424042 0.905642i \(-0.639389\pi\)
−0.424042 + 0.905642i \(0.639389\pi\)
\(618\) −4.35425 −0.175154
\(619\) −40.4684 −1.62656 −0.813281 0.581871i \(-0.802321\pi\)
−0.813281 + 0.581871i \(0.802321\pi\)
\(620\) 14.4225 0.579223
\(621\) −30.4657 −1.22254
\(622\) 3.29966 0.132304
\(623\) 10.1067 0.404918
\(624\) 4.91269 0.196665
\(625\) 10.6117 0.424467
\(626\) −51.0267 −2.03944
\(627\) 8.96686 0.358102
\(628\) −4.42009 −0.176381
\(629\) 4.78509 0.190794
\(630\) −1.88526 −0.0751105
\(631\) −6.58365 −0.262091 −0.131045 0.991376i \(-0.541833\pi\)
−0.131045 + 0.991376i \(0.541833\pi\)
\(632\) −7.32639 −0.291428
\(633\) 22.0642 0.876974
\(634\) −48.3701 −1.92102
\(635\) 11.9496 0.474204
\(636\) −17.6786 −0.701002
\(637\) 1.65660 0.0656367
\(638\) −1.31430 −0.0520334
\(639\) −1.73690 −0.0687108
\(640\) 6.21774 0.245778
\(641\) 0.415617 0.0164159 0.00820795 0.999966i \(-0.497387\pi\)
0.00820795 + 0.999966i \(0.497387\pi\)
\(642\) 34.1338 1.34716
\(643\) −11.8308 −0.466560 −0.233280 0.972410i \(-0.574946\pi\)
−0.233280 + 0.972410i \(0.574946\pi\)
\(644\) −43.9641 −1.73243
\(645\) −5.81386 −0.228921
\(646\) −3.60030 −0.141652
\(647\) −19.6497 −0.772510 −0.386255 0.922392i \(-0.626232\pi\)
−0.386255 + 0.922392i \(0.626232\pi\)
\(648\) 7.64122 0.300175
\(649\) 35.0930 1.37752
\(650\) 7.20837 0.282736
\(651\) −32.4624 −1.27230
\(652\) −31.7422 −1.24312
\(653\) 4.94129 0.193368 0.0966838 0.995315i \(-0.469176\pi\)
0.0966838 + 0.995315i \(0.469176\pi\)
\(654\) 28.5003 1.11445
\(655\) −7.84463 −0.306515
\(656\) −31.0540 −1.21246
\(657\) −4.00411 −0.156215
\(658\) 70.6062 2.75251
\(659\) −26.9771 −1.05088 −0.525439 0.850831i \(-0.676099\pi\)
−0.525439 + 0.850831i \(0.676099\pi\)
\(660\) 12.5408 0.488152
\(661\) 23.6325 0.919196 0.459598 0.888127i \(-0.347993\pi\)
0.459598 + 0.888127i \(0.347993\pi\)
\(662\) −48.3167 −1.87788
\(663\) −1.57677 −0.0612365
\(664\) 9.70978 0.376813
\(665\) 5.21503 0.202230
\(666\) −2.97830 −0.115407
\(667\) 1.36053 0.0526801
\(668\) 11.4179 0.441772
\(669\) −13.3026 −0.514307
\(670\) 25.3981 0.981213
\(671\) −10.4910 −0.404999
\(672\) −43.7597 −1.68807
\(673\) 16.3553 0.630452 0.315226 0.949017i \(-0.397920\pi\)
0.315226 + 0.949017i \(0.397920\pi\)
\(674\) −46.3699 −1.78610
\(675\) −19.4823 −0.749876
\(676\) −29.0564 −1.11755
\(677\) 22.4546 0.863001 0.431500 0.902113i \(-0.357984\pi\)
0.431500 + 0.902113i \(0.357984\pi\)
\(678\) 44.3834 1.70453
\(679\) 16.2911 0.625194
\(680\) −0.790951 −0.0303316
\(681\) −12.9028 −0.494438
\(682\) 35.9204 1.37546
\(683\) −39.5745 −1.51428 −0.757138 0.653255i \(-0.773403\pi\)
−0.757138 + 0.653255i \(0.773403\pi\)
\(684\) 1.21594 0.0464925
\(685\) −7.55794 −0.288774
\(686\) 31.7805 1.21339
\(687\) 20.1964 0.770541
\(688\) −9.82898 −0.374726
\(689\) 3.56259 0.135724
\(690\) −23.9249 −0.910805
\(691\) 31.7324 1.20716 0.603578 0.797304i \(-0.293741\pi\)
0.603578 + 0.797304i \(0.293741\pi\)
\(692\) 45.7007 1.73728
\(693\) −2.54779 −0.0967827
\(694\) 69.5115 2.63862
\(695\) 11.0330 0.418505
\(696\) −0.310162 −0.0117567
\(697\) 9.96704 0.377529
\(698\) 52.2027 1.97590
\(699\) 52.9571 2.00302
\(700\) −28.1144 −1.06262
\(701\) −15.8612 −0.599068 −0.299534 0.954086i \(-0.596831\pi\)
−0.299534 + 0.954086i \(0.596831\pi\)
\(702\) −8.91013 −0.336291
\(703\) 8.23861 0.310725
\(704\) 30.5498 1.15139
\(705\) 20.8491 0.785224
\(706\) −2.09110 −0.0786997
\(707\) 1.29805 0.0488182
\(708\) 52.7221 1.98142
\(709\) 22.0290 0.827317 0.413658 0.910432i \(-0.364251\pi\)
0.413658 + 0.910432i \(0.364251\pi\)
\(710\) 12.3838 0.464756
\(711\) 2.79801 0.104933
\(712\) −2.63917 −0.0989071
\(713\) −37.1842 −1.39256
\(714\) 11.3335 0.424146
\(715\) −2.52723 −0.0945132
\(716\) −27.0468 −1.01079
\(717\) 41.5785 1.55278
\(718\) 12.0806 0.450845
\(719\) 3.09202 0.115313 0.0576564 0.998336i \(-0.481637\pi\)
0.0576564 + 0.998336i \(0.481637\pi\)
\(720\) −0.941154 −0.0350747
\(721\) −3.42234 −0.127455
\(722\) 33.5322 1.24794
\(723\) −5.73489 −0.213283
\(724\) 0.184915 0.00687230
\(725\) 0.870042 0.0323126
\(726\) −10.5366 −0.391051
\(727\) −49.1080 −1.82131 −0.910657 0.413164i \(-0.864424\pi\)
−0.910657 + 0.413164i \(0.864424\pi\)
\(728\) −2.01974 −0.0748566
\(729\) 23.8160 0.882073
\(730\) 28.5486 1.05663
\(731\) 3.15469 0.116680
\(732\) −15.7611 −0.582548
\(733\) 36.5012 1.34820 0.674101 0.738640i \(-0.264531\pi\)
0.674101 + 0.738640i \(0.264531\pi\)
\(734\) −68.1407 −2.51512
\(735\) −3.51609 −0.129693
\(736\) −50.1247 −1.84762
\(737\) 34.3237 1.26433
\(738\) −6.20360 −0.228358
\(739\) 42.5923 1.56678 0.783391 0.621529i \(-0.213488\pi\)
0.783391 + 0.621529i \(0.213488\pi\)
\(740\) 11.5223 0.423569
\(741\) −2.71476 −0.0997290
\(742\) −25.6073 −0.940074
\(743\) 25.5163 0.936104 0.468052 0.883701i \(-0.344956\pi\)
0.468052 + 0.883701i \(0.344956\pi\)
\(744\) 8.47691 0.310779
\(745\) −14.4763 −0.530370
\(746\) 16.3212 0.597562
\(747\) −3.70824 −0.135678
\(748\) −6.80485 −0.248810
\(749\) 26.8284 0.980289
\(750\) −34.5684 −1.26226
\(751\) 17.9162 0.653771 0.326886 0.945064i \(-0.394001\pi\)
0.326886 + 0.945064i \(0.394001\pi\)
\(752\) 35.2478 1.28536
\(753\) −30.2422 −1.10209
\(754\) 0.397909 0.0144910
\(755\) −5.08649 −0.185116
\(756\) 34.7517 1.26391
\(757\) −23.7269 −0.862369 −0.431185 0.902264i \(-0.641904\pi\)
−0.431185 + 0.902264i \(0.641904\pi\)
\(758\) −34.6264 −1.25769
\(759\) −32.3328 −1.17361
\(760\) −1.36180 −0.0493977
\(761\) −15.7229 −0.569953 −0.284977 0.958534i \(-0.591986\pi\)
−0.284977 + 0.958534i \(0.591986\pi\)
\(762\) 44.7119 1.61974
\(763\) 22.4006 0.810957
\(764\) 61.4472 2.22308
\(765\) 0.302071 0.0109214
\(766\) −39.4651 −1.42593
\(767\) −10.6246 −0.383631
\(768\) −15.4220 −0.556495
\(769\) 27.9600 1.00826 0.504131 0.863627i \(-0.331813\pi\)
0.504131 + 0.863627i \(0.331813\pi\)
\(770\) 18.1653 0.654633
\(771\) −31.7947 −1.14506
\(772\) −44.4390 −1.59940
\(773\) 45.1752 1.62484 0.812420 0.583073i \(-0.198150\pi\)
0.812420 + 0.583073i \(0.198150\pi\)
\(774\) −1.96352 −0.0705771
\(775\) −23.7787 −0.854157
\(776\) −4.25409 −0.152713
\(777\) −25.9346 −0.930399
\(778\) −8.54330 −0.306292
\(779\) 17.1605 0.614839
\(780\) −3.79680 −0.135947
\(781\) 16.7358 0.598855
\(782\) 12.9820 0.464235
\(783\) −1.07544 −0.0384332
\(784\) −5.94434 −0.212298
\(785\) −1.89057 −0.0674774
\(786\) −29.3524 −1.04697
\(787\) −27.7085 −0.987702 −0.493851 0.869547i \(-0.664411\pi\)
−0.493851 + 0.869547i \(0.664411\pi\)
\(788\) −30.0382 −1.07007
\(789\) 31.0298 1.10469
\(790\) −19.9493 −0.709764
\(791\) 34.8843 1.24034
\(792\) 0.665305 0.0236406
\(793\) 3.17618 0.112790
\(794\) 6.25888 0.222119
\(795\) −7.56153 −0.268180
\(796\) 61.1605 2.16777
\(797\) 18.4155 0.652310 0.326155 0.945316i \(-0.394247\pi\)
0.326155 + 0.945316i \(0.394247\pi\)
\(798\) 19.5132 0.690759
\(799\) −11.3131 −0.400227
\(800\) −32.0540 −1.13328
\(801\) 1.00792 0.0356131
\(802\) 41.5881 1.46853
\(803\) 38.5814 1.36151
\(804\) 51.5663 1.81860
\(805\) −18.8044 −0.662768
\(806\) −10.8751 −0.383058
\(807\) 40.7390 1.43408
\(808\) −0.338959 −0.0119246
\(809\) −11.8305 −0.415939 −0.207970 0.978135i \(-0.566686\pi\)
−0.207970 + 0.978135i \(0.566686\pi\)
\(810\) 20.8065 0.731067
\(811\) 39.1848 1.37597 0.687983 0.725727i \(-0.258497\pi\)
0.687983 + 0.725727i \(0.258497\pi\)
\(812\) −1.55194 −0.0544624
\(813\) 7.64552 0.268140
\(814\) 28.6972 1.00584
\(815\) −13.5768 −0.475576
\(816\) 5.65788 0.198066
\(817\) 5.43150 0.190024
\(818\) 41.5055 1.45121
\(819\) 0.771356 0.0269534
\(820\) 24.0003 0.838126
\(821\) −10.1772 −0.355188 −0.177594 0.984104i \(-0.556831\pi\)
−0.177594 + 0.984104i \(0.556831\pi\)
\(822\) −28.2797 −0.986368
\(823\) −39.7117 −1.38426 −0.692131 0.721771i \(-0.743328\pi\)
−0.692131 + 0.721771i \(0.743328\pi\)
\(824\) 0.893675 0.0311327
\(825\) −20.6763 −0.719858
\(826\) 76.3676 2.65717
\(827\) −0.717797 −0.0249603 −0.0124801 0.999922i \(-0.503973\pi\)
−0.0124801 + 0.999922i \(0.503973\pi\)
\(828\) −4.38443 −0.152370
\(829\) −22.4349 −0.779198 −0.389599 0.920985i \(-0.627386\pi\)
−0.389599 + 0.920985i \(0.627386\pi\)
\(830\) 26.4391 0.917715
\(831\) −49.2494 −1.70844
\(832\) −9.24909 −0.320654
\(833\) 1.90788 0.0661042
\(834\) 41.2823 1.42949
\(835\) 4.88369 0.169007
\(836\) −11.7161 −0.405209
\(837\) 29.3924 1.01595
\(838\) 33.9219 1.17181
\(839\) −9.96119 −0.343898 −0.171949 0.985106i \(-0.555007\pi\)
−0.171949 + 0.985106i \(0.555007\pi\)
\(840\) 4.28686 0.147911
\(841\) −28.9520 −0.998344
\(842\) −18.6464 −0.642596
\(843\) −16.6259 −0.572628
\(844\) −28.8291 −0.992338
\(845\) −12.4280 −0.427538
\(846\) 7.04138 0.242088
\(847\) −8.28155 −0.284557
\(848\) −12.7836 −0.438991
\(849\) −49.2029 −1.68864
\(850\) 8.30180 0.284749
\(851\) −29.7069 −1.01834
\(852\) 25.1431 0.861389
\(853\) 3.62093 0.123978 0.0619891 0.998077i \(-0.480256\pi\)
0.0619891 + 0.998077i \(0.480256\pi\)
\(854\) −22.8298 −0.781221
\(855\) 0.520082 0.0177864
\(856\) −7.00570 −0.239450
\(857\) −7.33351 −0.250508 −0.125254 0.992125i \(-0.539975\pi\)
−0.125254 + 0.992125i \(0.539975\pi\)
\(858\) −9.45620 −0.322829
\(859\) −48.8409 −1.66643 −0.833215 0.552950i \(-0.813502\pi\)
−0.833215 + 0.552950i \(0.813502\pi\)
\(860\) 7.59638 0.259034
\(861\) −54.0201 −1.84100
\(862\) 74.3214 2.53140
\(863\) 20.6073 0.701479 0.350740 0.936473i \(-0.385930\pi\)
0.350740 + 0.936473i \(0.385930\pi\)
\(864\) 39.6213 1.34795
\(865\) 19.5472 0.664625
\(866\) −47.0778 −1.59977
\(867\) −1.81594 −0.0616726
\(868\) 42.4154 1.43967
\(869\) −26.9600 −0.914557
\(870\) −0.844552 −0.0286330
\(871\) −10.3916 −0.352108
\(872\) −5.84947 −0.198088
\(873\) 1.62467 0.0549867
\(874\) 22.3514 0.756048
\(875\) −27.1699 −0.918511
\(876\) 57.9628 1.95838
\(877\) 11.7031 0.395184 0.197592 0.980284i \(-0.436688\pi\)
0.197592 + 0.980284i \(0.436688\pi\)
\(878\) 79.2604 2.67491
\(879\) 0.0504023 0.00170003
\(880\) 9.06844 0.305697
\(881\) 14.8342 0.499776 0.249888 0.968275i \(-0.419606\pi\)
0.249888 + 0.968275i \(0.419606\pi\)
\(882\) −1.18749 −0.0399848
\(883\) −46.7951 −1.57478 −0.787391 0.616454i \(-0.788569\pi\)
−0.787391 + 0.616454i \(0.788569\pi\)
\(884\) 2.06020 0.0692920
\(885\) 22.5504 0.758024
\(886\) −5.25545 −0.176560
\(887\) −43.5365 −1.46181 −0.730906 0.682478i \(-0.760902\pi\)
−0.730906 + 0.682478i \(0.760902\pi\)
\(888\) 6.77230 0.227264
\(889\) 35.1426 1.17864
\(890\) −7.18630 −0.240885
\(891\) 28.1186 0.942008
\(892\) 17.3811 0.581962
\(893\) −19.4780 −0.651805
\(894\) −54.1662 −1.81159
\(895\) −11.5685 −0.386692
\(896\) 18.2858 0.610885
\(897\) 9.78889 0.326842
\(898\) 86.7464 2.89476
\(899\) −1.31261 −0.0437779
\(900\) −2.80378 −0.0934593
\(901\) 4.10300 0.136691
\(902\) 59.7745 1.99027
\(903\) −17.0980 −0.568986
\(904\) −9.10933 −0.302972
\(905\) 0.0790921 0.00262911
\(906\) −19.0322 −0.632303
\(907\) 12.7894 0.424664 0.212332 0.977198i \(-0.431894\pi\)
0.212332 + 0.977198i \(0.431894\pi\)
\(908\) 16.8588 0.559480
\(909\) 0.129451 0.00429363
\(910\) −5.49963 −0.182311
\(911\) −54.8850 −1.81842 −0.909210 0.416337i \(-0.863314\pi\)
−0.909210 + 0.416337i \(0.863314\pi\)
\(912\) 9.74132 0.322567
\(913\) 35.7306 1.18251
\(914\) −63.2684 −2.09273
\(915\) −6.74138 −0.222863
\(916\) −26.3886 −0.871904
\(917\) −23.0703 −0.761849
\(918\) −10.2617 −0.338687
\(919\) 15.8466 0.522732 0.261366 0.965240i \(-0.415827\pi\)
0.261366 + 0.965240i \(0.415827\pi\)
\(920\) 4.91039 0.161891
\(921\) 50.5186 1.66464
\(922\) −82.9700 −2.73247
\(923\) −5.06685 −0.166777
\(924\) 36.8815 1.21331
\(925\) −18.9971 −0.624621
\(926\) 22.4834 0.738852
\(927\) −0.341302 −0.0112098
\(928\) −1.76941 −0.0580837
\(929\) −25.7385 −0.844451 −0.422226 0.906491i \(-0.638751\pi\)
−0.422226 + 0.906491i \(0.638751\pi\)
\(930\) 23.0821 0.756891
\(931\) 3.28485 0.107657
\(932\) −69.1936 −2.26651
\(933\) 2.86547 0.0938113
\(934\) −13.6197 −0.445649
\(935\) −2.91059 −0.0951863
\(936\) −0.201424 −0.00658375
\(937\) 37.2581 1.21717 0.608585 0.793489i \(-0.291737\pi\)
0.608585 + 0.793489i \(0.291737\pi\)
\(938\) 74.6934 2.43883
\(939\) −44.3123 −1.44608
\(940\) −27.2415 −0.888518
\(941\) −1.59855 −0.0521112 −0.0260556 0.999660i \(-0.508295\pi\)
−0.0260556 + 0.999660i \(0.508295\pi\)
\(942\) −7.07399 −0.230483
\(943\) −61.8775 −2.01501
\(944\) 38.1240 1.24083
\(945\) 14.8641 0.483528
\(946\) 18.9193 0.615121
\(947\) −43.8586 −1.42521 −0.712606 0.701564i \(-0.752485\pi\)
−0.712606 + 0.701564i \(0.752485\pi\)
\(948\) −40.5035 −1.31549
\(949\) −11.6807 −0.379171
\(950\) 14.2934 0.463740
\(951\) −42.0053 −1.36211
\(952\) −2.32611 −0.0753898
\(953\) 15.6224 0.506060 0.253030 0.967458i \(-0.418573\pi\)
0.253030 + 0.967458i \(0.418573\pi\)
\(954\) −2.55376 −0.0826809
\(955\) 26.2823 0.850476
\(956\) −54.3264 −1.75704
\(957\) −1.14135 −0.0368947
\(958\) −15.7736 −0.509621
\(959\) −22.2272 −0.717753
\(960\) 19.6310 0.633587
\(961\) 4.87427 0.157235
\(962\) −8.68821 −0.280119
\(963\) 2.67553 0.0862179
\(964\) 7.49320 0.241340
\(965\) −19.0076 −0.611875
\(966\) −70.3609 −2.26382
\(967\) −7.61090 −0.244750 −0.122375 0.992484i \(-0.539051\pi\)
−0.122375 + 0.992484i \(0.539051\pi\)
\(968\) 2.16256 0.0695073
\(969\) −3.12655 −0.100439
\(970\) −11.5836 −0.371927
\(971\) −33.2528 −1.06713 −0.533567 0.845758i \(-0.679149\pi\)
−0.533567 + 0.845758i \(0.679149\pi\)
\(972\) 7.31313 0.234569
\(973\) 32.4470 1.04020
\(974\) 72.2422 2.31479
\(975\) 6.25985 0.200476
\(976\) −11.3970 −0.364811
\(977\) 30.1237 0.963743 0.481872 0.876242i \(-0.339957\pi\)
0.481872 + 0.876242i \(0.339957\pi\)
\(978\) −50.8008 −1.62443
\(979\) −9.71177 −0.310389
\(980\) 4.59412 0.146754
\(981\) 2.23396 0.0713248
\(982\) −12.0283 −0.383837
\(983\) −30.2007 −0.963253 −0.481627 0.876377i \(-0.659954\pi\)
−0.481627 + 0.876377i \(0.659954\pi\)
\(984\) 14.1063 0.449691
\(985\) −12.8480 −0.409371
\(986\) 0.458267 0.0145942
\(987\) 61.3154 1.95169
\(988\) 3.54709 0.112848
\(989\) −19.5850 −0.622766
\(990\) 1.81158 0.0575759
\(991\) −51.5450 −1.63738 −0.818691 0.574234i \(-0.805300\pi\)
−0.818691 + 0.574234i \(0.805300\pi\)
\(992\) 48.3589 1.53540
\(993\) −41.9589 −1.33153
\(994\) 36.4196 1.15516
\(995\) 26.1597 0.829318
\(996\) 53.6800 1.70091
\(997\) 37.6421 1.19214 0.596069 0.802933i \(-0.296728\pi\)
0.596069 + 0.802933i \(0.296728\pi\)
\(998\) 57.7498 1.82804
\(999\) 23.4820 0.742936
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 \(a_p\))