Properties

Label 6013.2.a.e.1.20
Level 6013
Weight 2
Character 6013.1
Self dual Yes
Analytic conductor 48.014
Analytic rank 0
Dimension 109
CM No

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Newspace parameters

Level: \( N \) = \( 6013 = 7 \cdot 859 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6013.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0140467354\)
Analytic rank: \(0\)
Dimension: \(109\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 6013.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.74589 q^{2}\) \(-1.96009 q^{3}\) \(+1.04812 q^{4}\) \(-3.28540 q^{5}\) \(+3.42209 q^{6}\) \(+1.00000 q^{7}\) \(+1.66188 q^{8}\) \(+0.841938 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.74589 q^{2}\) \(-1.96009 q^{3}\) \(+1.04812 q^{4}\) \(-3.28540 q^{5}\) \(+3.42209 q^{6}\) \(+1.00000 q^{7}\) \(+1.66188 q^{8}\) \(+0.841938 q^{9}\) \(+5.73592 q^{10}\) \(+1.91069 q^{11}\) \(-2.05440 q^{12}\) \(-3.31629 q^{13}\) \(-1.74589 q^{14}\) \(+6.43966 q^{15}\) \(-4.99768 q^{16}\) \(-1.86606 q^{17}\) \(-1.46993 q^{18}\) \(+8.48604 q^{19}\) \(-3.44348 q^{20}\) \(-1.96009 q^{21}\) \(-3.33585 q^{22}\) \(+2.57229 q^{23}\) \(-3.25743 q^{24}\) \(+5.79382 q^{25}\) \(+5.78986 q^{26}\) \(+4.22999 q^{27}\) \(+1.04812 q^{28}\) \(+0.829641 q^{29}\) \(-11.2429 q^{30}\) \(-2.16770 q^{31}\) \(+5.40163 q^{32}\) \(-3.74512 q^{33}\) \(+3.25793 q^{34}\) \(-3.28540 q^{35}\) \(+0.882450 q^{36}\) \(+2.77673 q^{37}\) \(-14.8157 q^{38}\) \(+6.50021 q^{39}\) \(-5.45993 q^{40}\) \(+10.8038 q^{41}\) \(+3.42209 q^{42}\) \(-2.93374 q^{43}\) \(+2.00263 q^{44}\) \(-2.76610 q^{45}\) \(-4.49092 q^{46}\) \(+11.9434 q^{47}\) \(+9.79589 q^{48}\) \(+1.00000 q^{49}\) \(-10.1154 q^{50}\) \(+3.65764 q^{51}\) \(-3.47586 q^{52}\) \(+2.58333 q^{53}\) \(-7.38507 q^{54}\) \(-6.27737 q^{55}\) \(+1.66188 q^{56}\) \(-16.6334 q^{57}\) \(-1.44846 q^{58}\) \(-8.63134 q^{59}\) \(+6.74952 q^{60}\) \(+3.85505 q^{61}\) \(+3.78455 q^{62}\) \(+0.841938 q^{63}\) \(+0.564743 q^{64}\) \(+10.8953 q^{65}\) \(+6.53855 q^{66}\) \(+2.23311 q^{67}\) \(-1.95585 q^{68}\) \(-5.04190 q^{69}\) \(+5.73592 q^{70}\) \(-8.59384 q^{71}\) \(+1.39920 q^{72}\) \(+2.15469 q^{73}\) \(-4.84785 q^{74}\) \(-11.3564 q^{75}\) \(+8.89436 q^{76}\) \(+1.91069 q^{77}\) \(-11.3486 q^{78}\) \(-6.24433 q^{79}\) \(+16.4194 q^{80}\) \(-10.8170 q^{81}\) \(-18.8621 q^{82}\) \(+9.36943 q^{83}\) \(-2.05440 q^{84}\) \(+6.13076 q^{85}\) \(+5.12198 q^{86}\) \(-1.62617 q^{87}\) \(+3.17534 q^{88}\) \(+9.54575 q^{89}\) \(+4.82929 q^{90}\) \(-3.31629 q^{91}\) \(+2.69606 q^{92}\) \(+4.24888 q^{93}\) \(-20.8518 q^{94}\) \(-27.8800 q^{95}\) \(-10.5877 q^{96}\) \(+16.4209 q^{97}\) \(-1.74589 q^{98}\) \(+1.60868 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(109q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 38q^{3} \) \(\mathstrut +\mathstrut 111q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 109q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(109q \) \(\mathstrut +\mathstrut 19q^{2} \) \(\mathstrut +\mathstrut 38q^{3} \) \(\mathstrut +\mathstrut 111q^{4} \) \(\mathstrut +\mathstrut 43q^{5} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 109q^{7} \) \(\mathstrut +\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut 15q^{10} \) \(\mathstrut +\mathstrut 48q^{11} \) \(\mathstrut +\mathstrut 72q^{12} \) \(\mathstrut +\mathstrut 29q^{13} \) \(\mathstrut +\mathstrut 19q^{14} \) \(\mathstrut +\mathstrut 29q^{15} \) \(\mathstrut +\mathstrut 115q^{16} \) \(\mathstrut +\mathstrut 72q^{17} \) \(\mathstrut +\mathstrut 33q^{18} \) \(\mathstrut +\mathstrut 58q^{19} \) \(\mathstrut +\mathstrut 88q^{20} \) \(\mathstrut +\mathstrut 38q^{21} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 65q^{23} \) \(\mathstrut +\mathstrut 46q^{24} \) \(\mathstrut +\mathstrut 124q^{25} \) \(\mathstrut +\mathstrut 49q^{26} \) \(\mathstrut +\mathstrut 131q^{27} \) \(\mathstrut +\mathstrut 111q^{28} \) \(\mathstrut +\mathstrut 25q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut +\mathstrut 41q^{31} \) \(\mathstrut +\mathstrut 75q^{32} \) \(\mathstrut +\mathstrut 54q^{33} \) \(\mathstrut +\mathstrut 23q^{34} \) \(\mathstrut +\mathstrut 43q^{35} \) \(\mathstrut +\mathstrut 111q^{36} \) \(\mathstrut +\mathstrut 25q^{37} \) \(\mathstrut +\mathstrut 54q^{38} \) \(\mathstrut +\mathstrut 27q^{39} \) \(\mathstrut +\mathstrut 30q^{40} \) \(\mathstrut +\mathstrut 109q^{41} \) \(\mathstrut +\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 38q^{43} \) \(\mathstrut +\mathstrut 68q^{44} \) \(\mathstrut +\mathstrut 84q^{45} \) \(\mathstrut -\mathstrut 9q^{46} \) \(\mathstrut +\mathstrut 121q^{47} \) \(\mathstrut +\mathstrut 106q^{48} \) \(\mathstrut +\mathstrut 109q^{49} \) \(\mathstrut +\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 38q^{52} \) \(\mathstrut +\mathstrut 61q^{53} \) \(\mathstrut +\mathstrut 31q^{54} \) \(\mathstrut +\mathstrut 50q^{55} \) \(\mathstrut +\mathstrut 48q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 20q^{58} \) \(\mathstrut +\mathstrut 181q^{59} \) \(\mathstrut +\mathstrut 25q^{60} \) \(\mathstrut +\mathstrut 34q^{61} \) \(\mathstrut +\mathstrut 75q^{62} \) \(\mathstrut +\mathstrut 119q^{63} \) \(\mathstrut +\mathstrut 96q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 19q^{66} \) \(\mathstrut +\mathstrut 87q^{67} \) \(\mathstrut +\mathstrut 150q^{68} \) \(\mathstrut +\mathstrut 89q^{69} \) \(\mathstrut +\mathstrut 15q^{70} \) \(\mathstrut +\mathstrut 83q^{71} \) \(\mathstrut +\mathstrut 65q^{72} \) \(\mathstrut +\mathstrut 32q^{73} \) \(\mathstrut -\mathstrut 19q^{74} \) \(\mathstrut +\mathstrut 112q^{75} \) \(\mathstrut +\mathstrut 84q^{76} \) \(\mathstrut +\mathstrut 48q^{77} \) \(\mathstrut -\mathstrut 34q^{78} \) \(\mathstrut -\mathstrut 9q^{79} \) \(\mathstrut +\mathstrut 137q^{80} \) \(\mathstrut +\mathstrut 109q^{81} \) \(\mathstrut -\mathstrut 19q^{82} \) \(\mathstrut +\mathstrut 136q^{83} \) \(\mathstrut +\mathstrut 72q^{84} \) \(\mathstrut -\mathstrut 32q^{85} \) \(\mathstrut -\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 28q^{87} \) \(\mathstrut -\mathstrut 24q^{88} \) \(\mathstrut +\mathstrut 142q^{89} \) \(\mathstrut +\mathstrut 19q^{90} \) \(\mathstrut +\mathstrut 29q^{91} \) \(\mathstrut +\mathstrut 96q^{92} \) \(\mathstrut +\mathstrut 29q^{93} \) \(\mathstrut +\mathstrut 9q^{94} \) \(\mathstrut +\mathstrut 52q^{95} \) \(\mathstrut +\mathstrut 88q^{96} \) \(\mathstrut +\mathstrut 75q^{97} \) \(\mathstrut +\mathstrut 19q^{98} \) \(\mathstrut +\mathstrut 84q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.74589 −1.23453 −0.617264 0.786756i \(-0.711759\pi\)
−0.617264 + 0.786756i \(0.711759\pi\)
\(3\) −1.96009 −1.13166 −0.565828 0.824523i \(-0.691443\pi\)
−0.565828 + 0.824523i \(0.691443\pi\)
\(4\) 1.04812 0.524059
\(5\) −3.28540 −1.46927 −0.734637 0.678461i \(-0.762647\pi\)
−0.734637 + 0.678461i \(0.762647\pi\)
\(6\) 3.42209 1.39706
\(7\) 1.00000 0.377964
\(8\) 1.66188 0.587563
\(9\) 0.841938 0.280646
\(10\) 5.73592 1.81386
\(11\) 1.91069 0.576095 0.288047 0.957616i \(-0.406994\pi\)
0.288047 + 0.957616i \(0.406994\pi\)
\(12\) −2.05440 −0.593054
\(13\) −3.31629 −0.919772 −0.459886 0.887978i \(-0.652110\pi\)
−0.459886 + 0.887978i \(0.652110\pi\)
\(14\) −1.74589 −0.466608
\(15\) 6.43966 1.66271
\(16\) −4.99768 −1.24942
\(17\) −1.86606 −0.452587 −0.226293 0.974059i \(-0.572661\pi\)
−0.226293 + 0.974059i \(0.572661\pi\)
\(18\) −1.46993 −0.346465
\(19\) 8.48604 1.94683 0.973416 0.229046i \(-0.0735607\pi\)
0.973416 + 0.229046i \(0.0735607\pi\)
\(20\) −3.44348 −0.769985
\(21\) −1.96009 −0.427726
\(22\) −3.33585 −0.711205
\(23\) 2.57229 0.536359 0.268179 0.963369i \(-0.413578\pi\)
0.268179 + 0.963369i \(0.413578\pi\)
\(24\) −3.25743 −0.664919
\(25\) 5.79382 1.15876
\(26\) 5.78986 1.13548
\(27\) 4.22999 0.814061
\(28\) 1.04812 0.198076
\(29\) 0.829641 0.154060 0.0770302 0.997029i \(-0.475456\pi\)
0.0770302 + 0.997029i \(0.475456\pi\)
\(30\) −11.2429 −2.05266
\(31\) −2.16770 −0.389330 −0.194665 0.980870i \(-0.562362\pi\)
−0.194665 + 0.980870i \(0.562362\pi\)
\(32\) 5.40163 0.954882
\(33\) −3.74512 −0.651941
\(34\) 3.25793 0.558731
\(35\) −3.28540 −0.555333
\(36\) 0.882450 0.147075
\(37\) 2.77673 0.456491 0.228246 0.973604i \(-0.426701\pi\)
0.228246 + 0.973604i \(0.426701\pi\)
\(38\) −14.8157 −2.40342
\(39\) 6.50021 1.04087
\(40\) −5.45993 −0.863291
\(41\) 10.8038 1.68726 0.843632 0.536922i \(-0.180413\pi\)
0.843632 + 0.536922i \(0.180413\pi\)
\(42\) 3.42209 0.528039
\(43\) −2.93374 −0.447391 −0.223696 0.974659i \(-0.571812\pi\)
−0.223696 + 0.974659i \(0.571812\pi\)
\(44\) 2.00263 0.301907
\(45\) −2.76610 −0.412346
\(46\) −4.49092 −0.662149
\(47\) 11.9434 1.74212 0.871062 0.491173i \(-0.163432\pi\)
0.871062 + 0.491173i \(0.163432\pi\)
\(48\) 9.79589 1.41392
\(49\) 1.00000 0.142857
\(50\) −10.1154 −1.43053
\(51\) 3.65764 0.512173
\(52\) −3.47586 −0.482015
\(53\) 2.58333 0.354847 0.177424 0.984135i \(-0.443224\pi\)
0.177424 + 0.984135i \(0.443224\pi\)
\(54\) −7.38507 −1.00498
\(55\) −6.27737 −0.846441
\(56\) 1.66188 0.222078
\(57\) −16.6334 −2.20314
\(58\) −1.44846 −0.190192
\(59\) −8.63134 −1.12370 −0.561852 0.827238i \(-0.689911\pi\)
−0.561852 + 0.827238i \(0.689911\pi\)
\(60\) 6.74952 0.871359
\(61\) 3.85505 0.493588 0.246794 0.969068i \(-0.420623\pi\)
0.246794 + 0.969068i \(0.420623\pi\)
\(62\) 3.78455 0.480639
\(63\) 0.841938 0.106074
\(64\) 0.564743 0.0705928
\(65\) 10.8953 1.35140
\(66\) 6.53855 0.804840
\(67\) 2.23311 0.272818 0.136409 0.990653i \(-0.456444\pi\)
0.136409 + 0.990653i \(0.456444\pi\)
\(68\) −1.95585 −0.237182
\(69\) −5.04190 −0.606974
\(70\) 5.73592 0.685574
\(71\) −8.59384 −1.01990 −0.509950 0.860204i \(-0.670336\pi\)
−0.509950 + 0.860204i \(0.670336\pi\)
\(72\) 1.39920 0.164897
\(73\) 2.15469 0.252187 0.126093 0.992018i \(-0.459756\pi\)
0.126093 + 0.992018i \(0.459756\pi\)
\(74\) −4.84785 −0.563551
\(75\) −11.3564 −1.31132
\(76\) 8.89436 1.02025
\(77\) 1.91069 0.217743
\(78\) −11.3486 −1.28498
\(79\) −6.24433 −0.702542 −0.351271 0.936274i \(-0.614250\pi\)
−0.351271 + 0.936274i \(0.614250\pi\)
\(80\) 16.4194 1.83574
\(81\) −10.8170 −1.20188
\(82\) −18.8621 −2.08297
\(83\) 9.36943 1.02843 0.514214 0.857662i \(-0.328084\pi\)
0.514214 + 0.857662i \(0.328084\pi\)
\(84\) −2.05440 −0.224153
\(85\) 6.13076 0.664974
\(86\) 5.12198 0.552317
\(87\) −1.62617 −0.174343
\(88\) 3.17534 0.338492
\(89\) 9.54575 1.01185 0.505923 0.862578i \(-0.331152\pi\)
0.505923 + 0.862578i \(0.331152\pi\)
\(90\) 4.82929 0.509052
\(91\) −3.31629 −0.347641
\(92\) 2.69606 0.281083
\(93\) 4.24888 0.440588
\(94\) −20.8518 −2.15070
\(95\) −27.8800 −2.86043
\(96\) −10.5877 −1.08060
\(97\) 16.4209 1.66729 0.833646 0.552300i \(-0.186250\pi\)
0.833646 + 0.552300i \(0.186250\pi\)
\(98\) −1.74589 −0.176361
\(99\) 1.60868 0.161679
\(100\) 6.07260 0.607260
\(101\) 1.09604 0.109060 0.0545302 0.998512i \(-0.482634\pi\)
0.0545302 + 0.998512i \(0.482634\pi\)
\(102\) −6.38583 −0.632291
\(103\) −13.3210 −1.31256 −0.656280 0.754518i \(-0.727871\pi\)
−0.656280 + 0.754518i \(0.727871\pi\)
\(104\) −5.51127 −0.540424
\(105\) 6.43966 0.628446
\(106\) −4.51019 −0.438068
\(107\) 14.0155 1.35493 0.677464 0.735556i \(-0.263079\pi\)
0.677464 + 0.735556i \(0.263079\pi\)
\(108\) 4.43352 0.426616
\(109\) −13.3420 −1.27793 −0.638967 0.769234i \(-0.720638\pi\)
−0.638967 + 0.769234i \(0.720638\pi\)
\(110\) 10.9596 1.04495
\(111\) −5.44263 −0.516591
\(112\) −4.99768 −0.472237
\(113\) 10.1519 0.955007 0.477503 0.878630i \(-0.341542\pi\)
0.477503 + 0.878630i \(0.341542\pi\)
\(114\) 29.0400 2.71984
\(115\) −8.45097 −0.788057
\(116\) 0.869561 0.0807367
\(117\) −2.79211 −0.258131
\(118\) 15.0693 1.38724
\(119\) −1.86606 −0.171062
\(120\) 10.7019 0.976948
\(121\) −7.34926 −0.668115
\(122\) −6.73047 −0.609348
\(123\) −21.1763 −1.90940
\(124\) −2.27200 −0.204032
\(125\) −2.60802 −0.233268
\(126\) −1.46993 −0.130952
\(127\) −5.41375 −0.480393 −0.240196 0.970724i \(-0.577212\pi\)
−0.240196 + 0.970724i \(0.577212\pi\)
\(128\) −11.7892 −1.04203
\(129\) 5.75039 0.506293
\(130\) −19.0220 −1.66834
\(131\) 0.315403 0.0275569 0.0137784 0.999905i \(-0.495614\pi\)
0.0137784 + 0.999905i \(0.495614\pi\)
\(132\) −3.92532 −0.341655
\(133\) 8.48604 0.735833
\(134\) −3.89876 −0.336801
\(135\) −13.8972 −1.19608
\(136\) −3.10117 −0.265923
\(137\) −13.4607 −1.15002 −0.575011 0.818146i \(-0.695002\pi\)
−0.575011 + 0.818146i \(0.695002\pi\)
\(138\) 8.80258 0.749326
\(139\) 12.5108 1.06115 0.530577 0.847637i \(-0.321975\pi\)
0.530577 + 0.847637i \(0.321975\pi\)
\(140\) −3.44348 −0.291027
\(141\) −23.4101 −1.97149
\(142\) 15.0039 1.25910
\(143\) −6.33640 −0.529876
\(144\) −4.20774 −0.350645
\(145\) −2.72570 −0.226357
\(146\) −3.76183 −0.311332
\(147\) −1.96009 −0.161665
\(148\) 2.91034 0.239228
\(149\) −19.8234 −1.62400 −0.811999 0.583658i \(-0.801621\pi\)
−0.811999 + 0.583658i \(0.801621\pi\)
\(150\) 19.8270 1.61886
\(151\) −9.24647 −0.752467 −0.376233 0.926525i \(-0.622781\pi\)
−0.376233 + 0.926525i \(0.622781\pi\)
\(152\) 14.1028 1.14389
\(153\) −1.57111 −0.127017
\(154\) −3.33585 −0.268810
\(155\) 7.12175 0.572033
\(156\) 6.81298 0.545475
\(157\) 7.62036 0.608171 0.304086 0.952645i \(-0.401649\pi\)
0.304086 + 0.952645i \(0.401649\pi\)
\(158\) 10.9019 0.867307
\(159\) −5.06354 −0.401565
\(160\) −17.7465 −1.40298
\(161\) 2.57229 0.202724
\(162\) 18.8852 1.48376
\(163\) 4.42505 0.346597 0.173299 0.984869i \(-0.444557\pi\)
0.173299 + 0.984869i \(0.444557\pi\)
\(164\) 11.3236 0.884225
\(165\) 12.3042 0.957880
\(166\) −16.3580 −1.26962
\(167\) −8.29704 −0.642044 −0.321022 0.947072i \(-0.604026\pi\)
−0.321022 + 0.947072i \(0.604026\pi\)
\(168\) −3.25743 −0.251316
\(169\) −2.00224 −0.154019
\(170\) −10.7036 −0.820928
\(171\) 7.14472 0.546371
\(172\) −3.07490 −0.234459
\(173\) −9.53468 −0.724908 −0.362454 0.932002i \(-0.618061\pi\)
−0.362454 + 0.932002i \(0.618061\pi\)
\(174\) 2.83910 0.215232
\(175\) 5.79382 0.437972
\(176\) −9.54903 −0.719785
\(177\) 16.9182 1.27165
\(178\) −16.6658 −1.24915
\(179\) 7.01788 0.524541 0.262271 0.964994i \(-0.415529\pi\)
0.262271 + 0.964994i \(0.415529\pi\)
\(180\) −2.89920 −0.216093
\(181\) −22.2976 −1.65736 −0.828682 0.559720i \(-0.810909\pi\)
−0.828682 + 0.559720i \(0.810909\pi\)
\(182\) 5.78986 0.429173
\(183\) −7.55622 −0.558572
\(184\) 4.27483 0.315144
\(185\) −9.12265 −0.670711
\(186\) −7.41805 −0.543918
\(187\) −3.56547 −0.260733
\(188\) 12.5181 0.912975
\(189\) 4.22999 0.307686
\(190\) 48.6753 3.53128
\(191\) −6.16315 −0.445950 −0.222975 0.974824i \(-0.571577\pi\)
−0.222975 + 0.974824i \(0.571577\pi\)
\(192\) −1.10694 −0.0798868
\(193\) −10.2000 −0.734214 −0.367107 0.930179i \(-0.619652\pi\)
−0.367107 + 0.930179i \(0.619652\pi\)
\(194\) −28.6690 −2.05832
\(195\) −21.3558 −1.52932
\(196\) 1.04812 0.0748655
\(197\) −1.74104 −0.124044 −0.0620219 0.998075i \(-0.519755\pi\)
−0.0620219 + 0.998075i \(0.519755\pi\)
\(198\) −2.80858 −0.199597
\(199\) −10.6091 −0.752062 −0.376031 0.926607i \(-0.622711\pi\)
−0.376031 + 0.926607i \(0.622711\pi\)
\(200\) 9.62863 0.680847
\(201\) −4.37709 −0.308736
\(202\) −1.91357 −0.134638
\(203\) 0.829641 0.0582294
\(204\) 3.83364 0.268408
\(205\) −35.4946 −2.47905
\(206\) 23.2570 1.62039
\(207\) 2.16571 0.150527
\(208\) 16.5738 1.14918
\(209\) 16.2142 1.12156
\(210\) −11.2429 −0.775834
\(211\) −6.15523 −0.423743 −0.211872 0.977297i \(-0.567956\pi\)
−0.211872 + 0.977297i \(0.567956\pi\)
\(212\) 2.70763 0.185961
\(213\) 16.8447 1.15418
\(214\) −24.4694 −1.67270
\(215\) 9.63850 0.657340
\(216\) 7.02973 0.478312
\(217\) −2.16770 −0.147153
\(218\) 23.2936 1.57764
\(219\) −4.22337 −0.285389
\(220\) −6.57942 −0.443585
\(221\) 6.18840 0.416277
\(222\) 9.50221 0.637746
\(223\) −10.8906 −0.729287 −0.364644 0.931147i \(-0.618809\pi\)
−0.364644 + 0.931147i \(0.618809\pi\)
\(224\) 5.40163 0.360912
\(225\) 4.87804 0.325203
\(226\) −17.7240 −1.17898
\(227\) 6.65267 0.441553 0.220776 0.975324i \(-0.429141\pi\)
0.220776 + 0.975324i \(0.429141\pi\)
\(228\) −17.4337 −1.15458
\(229\) 5.25229 0.347081 0.173541 0.984827i \(-0.444479\pi\)
0.173541 + 0.984827i \(0.444479\pi\)
\(230\) 14.7544 0.972879
\(231\) −3.74512 −0.246411
\(232\) 1.37876 0.0905202
\(233\) 27.3980 1.79491 0.897453 0.441111i \(-0.145416\pi\)
0.897453 + 0.441111i \(0.145416\pi\)
\(234\) 4.87470 0.318669
\(235\) −39.2388 −2.55966
\(236\) −9.04665 −0.588887
\(237\) 12.2394 0.795036
\(238\) 3.25793 0.211180
\(239\) −15.3051 −0.990005 −0.495003 0.868891i \(-0.664833\pi\)
−0.495003 + 0.868891i \(0.664833\pi\)
\(240\) −32.1834 −2.07743
\(241\) −5.67145 −0.365330 −0.182665 0.983175i \(-0.558472\pi\)
−0.182665 + 0.983175i \(0.558472\pi\)
\(242\) 12.8310 0.824806
\(243\) 8.51220 0.546058
\(244\) 4.04054 0.258669
\(245\) −3.28540 −0.209896
\(246\) 36.9714 2.35721
\(247\) −28.1421 −1.79064
\(248\) −3.60245 −0.228756
\(249\) −18.3649 −1.16383
\(250\) 4.55331 0.287976
\(251\) 12.8211 0.809259 0.404629 0.914481i \(-0.367401\pi\)
0.404629 + 0.914481i \(0.367401\pi\)
\(252\) 0.882450 0.0555891
\(253\) 4.91484 0.308993
\(254\) 9.45179 0.593058
\(255\) −12.0168 −0.752522
\(256\) 19.4532 1.21582
\(257\) 21.7714 1.35806 0.679032 0.734109i \(-0.262400\pi\)
0.679032 + 0.734109i \(0.262400\pi\)
\(258\) −10.0395 −0.625033
\(259\) 2.77673 0.172538
\(260\) 11.4196 0.708211
\(261\) 0.698506 0.0432365
\(262\) −0.550657 −0.0340197
\(263\) −15.1009 −0.931161 −0.465581 0.885006i \(-0.654154\pi\)
−0.465581 + 0.885006i \(0.654154\pi\)
\(264\) −6.22393 −0.383057
\(265\) −8.48725 −0.521367
\(266\) −14.8157 −0.908406
\(267\) −18.7105 −1.14506
\(268\) 2.34056 0.142973
\(269\) 26.2716 1.60181 0.800903 0.598794i \(-0.204353\pi\)
0.800903 + 0.598794i \(0.204353\pi\)
\(270\) 24.2629 1.47659
\(271\) −2.05618 −0.124904 −0.0624520 0.998048i \(-0.519892\pi\)
−0.0624520 + 0.998048i \(0.519892\pi\)
\(272\) 9.32600 0.565472
\(273\) 6.50021 0.393410
\(274\) 23.5008 1.41973
\(275\) 11.0702 0.667558
\(276\) −5.28450 −0.318090
\(277\) −5.60176 −0.336577 −0.168289 0.985738i \(-0.553824\pi\)
−0.168289 + 0.985738i \(0.553824\pi\)
\(278\) −21.8425 −1.31002
\(279\) −1.82507 −0.109264
\(280\) −5.45993 −0.326293
\(281\) 29.4980 1.75970 0.879851 0.475250i \(-0.157642\pi\)
0.879851 + 0.475250i \(0.157642\pi\)
\(282\) 40.8714 2.43385
\(283\) −11.6430 −0.692107 −0.346053 0.938215i \(-0.612478\pi\)
−0.346053 + 0.938215i \(0.612478\pi\)
\(284\) −9.00735 −0.534488
\(285\) 54.6472 3.23702
\(286\) 11.0626 0.654147
\(287\) 10.8038 0.637726
\(288\) 4.54784 0.267984
\(289\) −13.5178 −0.795165
\(290\) 4.75876 0.279444
\(291\) −32.1864 −1.88680
\(292\) 2.25836 0.132161
\(293\) −6.47962 −0.378543 −0.189272 0.981925i \(-0.560613\pi\)
−0.189272 + 0.981925i \(0.560613\pi\)
\(294\) 3.42209 0.199580
\(295\) 28.3574 1.65103
\(296\) 4.61459 0.268217
\(297\) 8.08220 0.468977
\(298\) 34.6094 2.00487
\(299\) −8.53043 −0.493328
\(300\) −11.9028 −0.687210
\(301\) −2.93374 −0.169098
\(302\) 16.1433 0.928941
\(303\) −2.14834 −0.123419
\(304\) −42.4106 −2.43241
\(305\) −12.6654 −0.725216
\(306\) 2.74298 0.156806
\(307\) 25.6854 1.46595 0.732973 0.680258i \(-0.238132\pi\)
0.732973 + 0.680258i \(0.238132\pi\)
\(308\) 2.00263 0.114110
\(309\) 26.1104 1.48537
\(310\) −12.4338 −0.706190
\(311\) −28.0808 −1.59232 −0.796158 0.605089i \(-0.793138\pi\)
−0.796158 + 0.605089i \(0.793138\pi\)
\(312\) 10.8026 0.611574
\(313\) 22.6216 1.27865 0.639325 0.768936i \(-0.279214\pi\)
0.639325 + 0.768936i \(0.279214\pi\)
\(314\) −13.3043 −0.750804
\(315\) −2.76610 −0.155852
\(316\) −6.54479 −0.368173
\(317\) 16.2021 0.909999 0.454999 0.890492i \(-0.349639\pi\)
0.454999 + 0.890492i \(0.349639\pi\)
\(318\) 8.84036 0.495743
\(319\) 1.58519 0.0887534
\(320\) −1.85540 −0.103720
\(321\) −27.4716 −1.53331
\(322\) −4.49092 −0.250269
\(323\) −15.8355 −0.881110
\(324\) −11.3374 −0.629857
\(325\) −19.2140 −1.06580
\(326\) −7.72564 −0.427884
\(327\) 26.1515 1.44618
\(328\) 17.9545 0.991374
\(329\) 11.9434 0.658461
\(330\) −21.4817 −1.18253
\(331\) 4.70979 0.258873 0.129437 0.991588i \(-0.458683\pi\)
0.129437 + 0.991588i \(0.458683\pi\)
\(332\) 9.82026 0.538957
\(333\) 2.33783 0.128113
\(334\) 14.4857 0.792621
\(335\) −7.33666 −0.400844
\(336\) 9.79589 0.534410
\(337\) −11.9069 −0.648609 −0.324304 0.945953i \(-0.605130\pi\)
−0.324304 + 0.945953i \(0.605130\pi\)
\(338\) 3.49569 0.190141
\(339\) −19.8985 −1.08074
\(340\) 6.42575 0.348485
\(341\) −4.14180 −0.224291
\(342\) −12.4739 −0.674510
\(343\) 1.00000 0.0539949
\(344\) −4.87552 −0.262871
\(345\) 16.5646 0.891810
\(346\) 16.6465 0.894919
\(347\) −27.0007 −1.44947 −0.724737 0.689026i \(-0.758039\pi\)
−0.724737 + 0.689026i \(0.758039\pi\)
\(348\) −1.70441 −0.0913662
\(349\) 26.8913 1.43946 0.719730 0.694254i \(-0.244265\pi\)
0.719730 + 0.694254i \(0.244265\pi\)
\(350\) −10.1154 −0.540688
\(351\) −14.0278 −0.748751
\(352\) 10.3208 0.550103
\(353\) −6.88105 −0.366241 −0.183121 0.983090i \(-0.558620\pi\)
−0.183121 + 0.983090i \(0.558620\pi\)
\(354\) −29.5372 −1.56988
\(355\) 28.2342 1.49851
\(356\) 10.0051 0.530267
\(357\) 3.65764 0.193583
\(358\) −12.2524 −0.647561
\(359\) 16.8498 0.889298 0.444649 0.895705i \(-0.353328\pi\)
0.444649 + 0.895705i \(0.353328\pi\)
\(360\) −4.59692 −0.242279
\(361\) 53.0129 2.79015
\(362\) 38.9290 2.04606
\(363\) 14.4052 0.756076
\(364\) −3.47586 −0.182184
\(365\) −7.07899 −0.370531
\(366\) 13.1923 0.689573
\(367\) 8.12816 0.424286 0.212143 0.977239i \(-0.431956\pi\)
0.212143 + 0.977239i \(0.431956\pi\)
\(368\) −12.8555 −0.670138
\(369\) 9.09610 0.473524
\(370\) 15.9271 0.828011
\(371\) 2.58333 0.134120
\(372\) 4.45332 0.230894
\(373\) 9.87937 0.511534 0.255767 0.966738i \(-0.417672\pi\)
0.255767 + 0.966738i \(0.417672\pi\)
\(374\) 6.22490 0.321882
\(375\) 5.11195 0.263980
\(376\) 19.8485 1.02361
\(377\) −2.75133 −0.141701
\(378\) −7.38507 −0.379847
\(379\) 9.70783 0.498657 0.249329 0.968419i \(-0.419790\pi\)
0.249329 + 0.968419i \(0.419790\pi\)
\(380\) −29.2215 −1.49903
\(381\) 10.6114 0.543639
\(382\) 10.7602 0.550537
\(383\) 9.86406 0.504030 0.252015 0.967723i \(-0.418907\pi\)
0.252015 + 0.967723i \(0.418907\pi\)
\(384\) 23.1079 1.17922
\(385\) −6.27737 −0.319925
\(386\) 17.8081 0.906407
\(387\) −2.47003 −0.125559
\(388\) 17.2110 0.873758
\(389\) 27.3709 1.38776 0.693879 0.720091i \(-0.255900\pi\)
0.693879 + 0.720091i \(0.255900\pi\)
\(390\) 37.2847 1.88798
\(391\) −4.80005 −0.242749
\(392\) 1.66188 0.0839376
\(393\) −0.618216 −0.0311849
\(394\) 3.03965 0.153136
\(395\) 20.5151 1.03223
\(396\) 1.68609 0.0847291
\(397\) −5.39048 −0.270540 −0.135270 0.990809i \(-0.543190\pi\)
−0.135270 + 0.990809i \(0.543190\pi\)
\(398\) 18.5223 0.928441
\(399\) −16.6334 −0.832710
\(400\) −28.9557 −1.44778
\(401\) 28.7668 1.43655 0.718273 0.695761i \(-0.244933\pi\)
0.718273 + 0.695761i \(0.244933\pi\)
\(402\) 7.64190 0.381143
\(403\) 7.18871 0.358095
\(404\) 1.14878 0.0571540
\(405\) 35.5380 1.76590
\(406\) −1.44846 −0.0718858
\(407\) 5.30547 0.262982
\(408\) 6.07856 0.300934
\(409\) −13.2751 −0.656411 −0.328206 0.944606i \(-0.606444\pi\)
−0.328206 + 0.944606i \(0.606444\pi\)
\(410\) 61.9696 3.06046
\(411\) 26.3840 1.30143
\(412\) −13.9620 −0.687858
\(413\) −8.63134 −0.424720
\(414\) −3.78107 −0.185830
\(415\) −30.7823 −1.51104
\(416\) −17.9133 −0.878274
\(417\) −24.5223 −1.20086
\(418\) −28.3081 −1.38460
\(419\) 29.6675 1.44935 0.724676 0.689089i \(-0.241989\pi\)
0.724676 + 0.689089i \(0.241989\pi\)
\(420\) 6.74952 0.329343
\(421\) 28.2124 1.37499 0.687494 0.726190i \(-0.258711\pi\)
0.687494 + 0.726190i \(0.258711\pi\)
\(422\) 10.7463 0.523123
\(423\) 10.0556 0.488920
\(424\) 4.29317 0.208495
\(425\) −10.8116 −0.524442
\(426\) −29.4089 −1.42486
\(427\) 3.85505 0.186559
\(428\) 14.6899 0.710061
\(429\) 12.4199 0.599638
\(430\) −16.8277 −0.811505
\(431\) 21.7657 1.04842 0.524208 0.851590i \(-0.324362\pi\)
0.524208 + 0.851590i \(0.324362\pi\)
\(432\) −21.1401 −1.01711
\(433\) 17.0310 0.818459 0.409230 0.912431i \(-0.365797\pi\)
0.409230 + 0.912431i \(0.365797\pi\)
\(434\) 3.78455 0.181664
\(435\) 5.34260 0.256158
\(436\) −13.9840 −0.669712
\(437\) 21.8285 1.04420
\(438\) 7.37352 0.352320
\(439\) 8.11277 0.387202 0.193601 0.981080i \(-0.437983\pi\)
0.193601 + 0.981080i \(0.437983\pi\)
\(440\) −10.4322 −0.497337
\(441\) 0.841938 0.0400923
\(442\) −10.8042 −0.513905
\(443\) 6.76886 0.321598 0.160799 0.986987i \(-0.448593\pi\)
0.160799 + 0.986987i \(0.448593\pi\)
\(444\) −5.70451 −0.270724
\(445\) −31.3615 −1.48668
\(446\) 19.0137 0.900325
\(447\) 38.8556 1.83781
\(448\) 0.564743 0.0266816
\(449\) −34.2148 −1.61470 −0.807348 0.590075i \(-0.799098\pi\)
−0.807348 + 0.590075i \(0.799098\pi\)
\(450\) −8.51650 −0.401472
\(451\) 20.6426 0.972024
\(452\) 10.6403 0.500479
\(453\) 18.1239 0.851534
\(454\) −11.6148 −0.545109
\(455\) 10.8953 0.510780
\(456\) −27.6426 −1.29449
\(457\) 7.17176 0.335481 0.167740 0.985831i \(-0.446353\pi\)
0.167740 + 0.985831i \(0.446353\pi\)
\(458\) −9.16990 −0.428481
\(459\) −7.89342 −0.368433
\(460\) −8.85761 −0.412988
\(461\) 4.96680 0.231327 0.115664 0.993288i \(-0.463101\pi\)
0.115664 + 0.993288i \(0.463101\pi\)
\(462\) 6.53855 0.304201
\(463\) 25.9335 1.20523 0.602615 0.798032i \(-0.294125\pi\)
0.602615 + 0.798032i \(0.294125\pi\)
\(464\) −4.14628 −0.192486
\(465\) −13.9592 −0.647344
\(466\) −47.8338 −2.21586
\(467\) −21.8989 −1.01336 −0.506679 0.862135i \(-0.669127\pi\)
−0.506679 + 0.862135i \(0.669127\pi\)
\(468\) −2.92646 −0.135276
\(469\) 2.23311 0.103116
\(470\) 68.5065 3.15997
\(471\) −14.9366 −0.688241
\(472\) −14.3442 −0.660247
\(473\) −5.60547 −0.257740
\(474\) −21.3686 −0.981494
\(475\) 49.1666 2.25592
\(476\) −1.95585 −0.0896464
\(477\) 2.17500 0.0995864
\(478\) 26.7210 1.22219
\(479\) −10.2278 −0.467319 −0.233659 0.972319i \(-0.575070\pi\)
−0.233659 + 0.972319i \(0.575070\pi\)
\(480\) 34.7846 1.58769
\(481\) −9.20843 −0.419868
\(482\) 9.90170 0.451010
\(483\) −5.04190 −0.229414
\(484\) −7.70289 −0.350131
\(485\) −53.9492 −2.44971
\(486\) −14.8613 −0.674124
\(487\) −40.0561 −1.81511 −0.907557 0.419930i \(-0.862055\pi\)
−0.907557 + 0.419930i \(0.862055\pi\)
\(488\) 6.40662 0.290014
\(489\) −8.67349 −0.392229
\(490\) 5.73592 0.259123
\(491\) −18.8272 −0.849658 −0.424829 0.905274i \(-0.639666\pi\)
−0.424829 + 0.905274i \(0.639666\pi\)
\(492\) −22.1952 −1.00064
\(493\) −1.54816 −0.0697257
\(494\) 49.1330 2.21060
\(495\) −5.28516 −0.237550
\(496\) 10.8335 0.486437
\(497\) −8.59384 −0.385486
\(498\) 32.0630 1.43678
\(499\) −40.7116 −1.82250 −0.911251 0.411851i \(-0.864882\pi\)
−0.911251 + 0.411851i \(0.864882\pi\)
\(500\) −2.73351 −0.122246
\(501\) 16.2629 0.726573
\(502\) −22.3841 −0.999052
\(503\) 4.82188 0.214997 0.107499 0.994205i \(-0.465716\pi\)
0.107499 + 0.994205i \(0.465716\pi\)
\(504\) 1.39920 0.0623253
\(505\) −3.60094 −0.160240
\(506\) −8.58075 −0.381461
\(507\) 3.92457 0.174296
\(508\) −5.67424 −0.251754
\(509\) −21.9411 −0.972524 −0.486262 0.873813i \(-0.661640\pi\)
−0.486262 + 0.873813i \(0.661640\pi\)
\(510\) 20.9800 0.929009
\(511\) 2.15469 0.0953177
\(512\) −10.3845 −0.458936
\(513\) 35.8958 1.58484
\(514\) −38.0104 −1.67657
\(515\) 43.7648 1.92851
\(516\) 6.02708 0.265327
\(517\) 22.8201 1.00363
\(518\) −4.84785 −0.213002
\(519\) 18.6888 0.820347
\(520\) 18.1067 0.794031
\(521\) −17.4090 −0.762702 −0.381351 0.924430i \(-0.624541\pi\)
−0.381351 + 0.924430i \(0.624541\pi\)
\(522\) −1.21951 −0.0533766
\(523\) −5.44139 −0.237935 −0.118968 0.992898i \(-0.537958\pi\)
−0.118968 + 0.992898i \(0.537958\pi\)
\(524\) 0.330579 0.0144414
\(525\) −11.3564 −0.495634
\(526\) 26.3644 1.14954
\(527\) 4.04506 0.176206
\(528\) 18.7169 0.814549
\(529\) −16.3833 −0.712320
\(530\) 14.8178 0.643642
\(531\) −7.26705 −0.315363
\(532\) 8.89436 0.385620
\(533\) −35.8284 −1.55190
\(534\) 32.6664 1.41361
\(535\) −46.0464 −1.99076
\(536\) 3.71116 0.160298
\(537\) −13.7557 −0.593600
\(538\) −45.8672 −1.97747
\(539\) 1.91069 0.0822993
\(540\) −14.5659 −0.626815
\(541\) −5.90035 −0.253676 −0.126838 0.991923i \(-0.540483\pi\)
−0.126838 + 0.991923i \(0.540483\pi\)
\(542\) 3.58986 0.154198
\(543\) 43.7051 1.87557
\(544\) −10.0798 −0.432167
\(545\) 43.8338 1.87763
\(546\) −11.3486 −0.485676
\(547\) −15.3011 −0.654227 −0.327113 0.944985i \(-0.606076\pi\)
−0.327113 + 0.944985i \(0.606076\pi\)
\(548\) −14.1083 −0.602679
\(549\) 3.24571 0.138524
\(550\) −19.3273 −0.824119
\(551\) 7.04037 0.299930
\(552\) −8.37903 −0.356635
\(553\) −6.24433 −0.265536
\(554\) 9.78003 0.415514
\(555\) 17.8812 0.759014
\(556\) 13.1128 0.556107
\(557\) 1.46309 0.0619931 0.0309966 0.999519i \(-0.490132\pi\)
0.0309966 + 0.999519i \(0.490132\pi\)
\(558\) 3.18636 0.134889
\(559\) 9.72913 0.411498
\(560\) 16.4194 0.693845
\(561\) 6.98863 0.295060
\(562\) −51.5001 −2.17240
\(563\) 31.4951 1.32736 0.663679 0.748017i \(-0.268994\pi\)
0.663679 + 0.748017i \(0.268994\pi\)
\(564\) −24.5365 −1.03317
\(565\) −33.3529 −1.40317
\(566\) 20.3274 0.854425
\(567\) −10.8170 −0.454269
\(568\) −14.2819 −0.599256
\(569\) −6.50207 −0.272581 −0.136290 0.990669i \(-0.543518\pi\)
−0.136290 + 0.990669i \(0.543518\pi\)
\(570\) −95.4078 −3.99619
\(571\) 16.3126 0.682663 0.341331 0.939943i \(-0.389122\pi\)
0.341331 + 0.939943i \(0.389122\pi\)
\(572\) −6.64129 −0.277686
\(573\) 12.0803 0.504662
\(574\) −18.8621 −0.787290
\(575\) 14.9034 0.621513
\(576\) 0.475479 0.0198116
\(577\) 10.6963 0.445295 0.222647 0.974899i \(-0.428530\pi\)
0.222647 + 0.974899i \(0.428530\pi\)
\(578\) 23.6005 0.981653
\(579\) 19.9929 0.830878
\(580\) −2.85685 −0.118624
\(581\) 9.36943 0.388710
\(582\) 56.1938 2.32931
\(583\) 4.93594 0.204426
\(584\) 3.58083 0.148176
\(585\) 9.17318 0.379264
\(586\) 11.3127 0.467322
\(587\) −24.0346 −0.992012 −0.496006 0.868319i \(-0.665201\pi\)
−0.496006 + 0.868319i \(0.665201\pi\)
\(588\) −2.05440 −0.0847220
\(589\) −18.3952 −0.757960
\(590\) −49.5087 −2.03824
\(591\) 3.41259 0.140375
\(592\) −13.8772 −0.570350
\(593\) −44.4349 −1.82472 −0.912360 0.409388i \(-0.865742\pi\)
−0.912360 + 0.409388i \(0.865742\pi\)
\(594\) −14.1106 −0.578965
\(595\) 6.13076 0.251336
\(596\) −20.7773 −0.851070
\(597\) 20.7948 0.851076
\(598\) 14.8932 0.609027
\(599\) 47.5175 1.94151 0.970756 0.240068i \(-0.0771697\pi\)
0.970756 + 0.240068i \(0.0771697\pi\)
\(600\) −18.8729 −0.770485
\(601\) −7.71627 −0.314753 −0.157377 0.987539i \(-0.550304\pi\)
−0.157377 + 0.987539i \(0.550304\pi\)
\(602\) 5.12198 0.208756
\(603\) 1.88014 0.0765653
\(604\) −9.69138 −0.394337
\(605\) 24.1452 0.981643
\(606\) 3.75076 0.152364
\(607\) −16.3509 −0.663663 −0.331832 0.943339i \(-0.607667\pi\)
−0.331832 + 0.943339i \(0.607667\pi\)
\(608\) 45.8384 1.85899
\(609\) −1.62617 −0.0658956
\(610\) 22.1123 0.895299
\(611\) −39.6077 −1.60236
\(612\) −1.64671 −0.0665642
\(613\) −9.78766 −0.395320 −0.197660 0.980271i \(-0.563334\pi\)
−0.197660 + 0.980271i \(0.563334\pi\)
\(614\) −44.8438 −1.80975
\(615\) 69.5725 2.80544
\(616\) 3.17534 0.127938
\(617\) 41.2809 1.66191 0.830953 0.556342i \(-0.187796\pi\)
0.830953 + 0.556342i \(0.187796\pi\)
\(618\) −45.5857 −1.83373
\(619\) −28.1587 −1.13180 −0.565898 0.824476i \(-0.691470\pi\)
−0.565898 + 0.824476i \(0.691470\pi\)
\(620\) 7.46443 0.299779
\(621\) 10.8807 0.436629
\(622\) 49.0259 1.96576
\(623\) 9.54575 0.382442
\(624\) −32.4860 −1.30048
\(625\) −20.4007 −0.816029
\(626\) −39.4948 −1.57853
\(627\) −31.7812 −1.26922
\(628\) 7.98703 0.318717
\(629\) −5.18155 −0.206602
\(630\) 4.82929 0.192404
\(631\) −31.8845 −1.26930 −0.634650 0.772799i \(-0.718856\pi\)
−0.634650 + 0.772799i \(0.718856\pi\)
\(632\) −10.3773 −0.412787
\(633\) 12.0648 0.479532
\(634\) −28.2870 −1.12342
\(635\) 17.7863 0.705828
\(636\) −5.30718 −0.210444
\(637\) −3.31629 −0.131396
\(638\) −2.76756 −0.109569
\(639\) −7.23548 −0.286231
\(640\) 38.7323 1.53103
\(641\) −27.6404 −1.09173 −0.545864 0.837874i \(-0.683799\pi\)
−0.545864 + 0.837874i \(0.683799\pi\)
\(642\) 47.9622 1.89292
\(643\) 39.8607 1.57195 0.785976 0.618257i \(-0.212161\pi\)
0.785976 + 0.618257i \(0.212161\pi\)
\(644\) 2.69606 0.106239
\(645\) −18.8923 −0.743883
\(646\) 27.6470 1.08775
\(647\) 30.4658 1.19773 0.598867 0.800849i \(-0.295618\pi\)
0.598867 + 0.800849i \(0.295618\pi\)
\(648\) −17.9765 −0.706182
\(649\) −16.4918 −0.647360
\(650\) 33.5454 1.31576
\(651\) 4.24888 0.166527
\(652\) 4.63797 0.181637
\(653\) −19.0497 −0.745473 −0.372736 0.927937i \(-0.621580\pi\)
−0.372736 + 0.927937i \(0.621580\pi\)
\(654\) −45.6575 −1.78535
\(655\) −1.03622 −0.0404886
\(656\) −53.9938 −2.10810
\(657\) 1.81411 0.0707753
\(658\) −20.8518 −0.812888
\(659\) 11.9209 0.464371 0.232186 0.972671i \(-0.425412\pi\)
0.232186 + 0.972671i \(0.425412\pi\)
\(660\) 12.8962 0.501985
\(661\) 22.9270 0.891755 0.445878 0.895094i \(-0.352892\pi\)
0.445878 + 0.895094i \(0.352892\pi\)
\(662\) −8.22276 −0.319586
\(663\) −12.1298 −0.471082
\(664\) 15.5709 0.604267
\(665\) −27.8800 −1.08114
\(666\) −4.08159 −0.158158
\(667\) 2.13407 0.0826316
\(668\) −8.69627 −0.336469
\(669\) 21.3465 0.825302
\(670\) 12.8090 0.494853
\(671\) 7.36580 0.284354
\(672\) −10.5877 −0.408428
\(673\) −21.8310 −0.841524 −0.420762 0.907171i \(-0.638237\pi\)
−0.420762 + 0.907171i \(0.638237\pi\)
\(674\) 20.7880 0.800726
\(675\) 24.5078 0.943305
\(676\) −2.09859 −0.0807149
\(677\) 30.4099 1.16875 0.584373 0.811485i \(-0.301341\pi\)
0.584373 + 0.811485i \(0.301341\pi\)
\(678\) 34.7405 1.33420
\(679\) 16.4209 0.630177
\(680\) 10.1886 0.390714
\(681\) −13.0398 −0.499686
\(682\) 7.23111 0.276894
\(683\) 51.8359 1.98345 0.991723 0.128400i \(-0.0409840\pi\)
0.991723 + 0.128400i \(0.0409840\pi\)
\(684\) 7.48851 0.286330
\(685\) 44.2236 1.68970
\(686\) −1.74589 −0.0666582
\(687\) −10.2949 −0.392777
\(688\) 14.6619 0.558980
\(689\) −8.56705 −0.326378
\(690\) −28.9200 −1.10096
\(691\) 22.8195 0.868095 0.434047 0.900890i \(-0.357085\pi\)
0.434047 + 0.900890i \(0.357085\pi\)
\(692\) −9.99346 −0.379894
\(693\) 1.60868 0.0611088
\(694\) 47.1401 1.78941
\(695\) −41.1030 −1.55913
\(696\) −2.70249 −0.102438
\(697\) −20.1605 −0.763633
\(698\) −46.9492 −1.77705
\(699\) −53.7025 −2.03122
\(700\) 6.07260 0.229523
\(701\) 41.7773 1.57791 0.788953 0.614454i \(-0.210624\pi\)
0.788953 + 0.614454i \(0.210624\pi\)
\(702\) 24.4910 0.924354
\(703\) 23.5634 0.888712
\(704\) 1.07905 0.0406682
\(705\) 76.9114 2.89665
\(706\) 12.0135 0.452135
\(707\) 1.09604 0.0412210
\(708\) 17.7322 0.666418
\(709\) −13.6129 −0.511242 −0.255621 0.966777i \(-0.582280\pi\)
−0.255621 + 0.966777i \(0.582280\pi\)
\(710\) −49.2936 −1.84996
\(711\) −5.25734 −0.197166
\(712\) 15.8639 0.594524
\(713\) −5.57594 −0.208821
\(714\) −6.38583 −0.238984
\(715\) 20.8176 0.778533
\(716\) 7.35556 0.274890
\(717\) 29.9993 1.12035
\(718\) −29.4178 −1.09786
\(719\) 33.1382 1.23584 0.617922 0.786239i \(-0.287975\pi\)
0.617922 + 0.786239i \(0.287975\pi\)
\(720\) 13.8241 0.515194
\(721\) −13.3210 −0.496101
\(722\) −92.5544 −3.44452
\(723\) 11.1165 0.413428
\(724\) −23.3704 −0.868556
\(725\) 4.80679 0.178520
\(726\) −25.1498 −0.933397
\(727\) 33.4495 1.24057 0.620287 0.784375i \(-0.287016\pi\)
0.620287 + 0.784375i \(0.287016\pi\)
\(728\) −5.51127 −0.204261
\(729\) 15.7662 0.583934
\(730\) 12.3591 0.457431
\(731\) 5.47455 0.202483
\(732\) −7.91981 −0.292724
\(733\) 1.13408 0.0418884 0.0209442 0.999781i \(-0.493333\pi\)
0.0209442 + 0.999781i \(0.493333\pi\)
\(734\) −14.1908 −0.523793
\(735\) 6.43966 0.237530
\(736\) 13.8945 0.512159
\(737\) 4.26679 0.157169
\(738\) −15.8808 −0.584579
\(739\) −1.24976 −0.0459733 −0.0229867 0.999736i \(-0.507318\pi\)
−0.0229867 + 0.999736i \(0.507318\pi\)
\(740\) −9.56161 −0.351492
\(741\) 55.1610 2.02639
\(742\) −4.51019 −0.165574
\(743\) 28.9431 1.06182 0.530910 0.847428i \(-0.321850\pi\)
0.530910 + 0.847428i \(0.321850\pi\)
\(744\) 7.06112 0.258873
\(745\) 65.1278 2.38610
\(746\) −17.2482 −0.631503
\(747\) 7.88848 0.288625
\(748\) −3.73703 −0.136639
\(749\) 14.0155 0.512115
\(750\) −8.92487 −0.325890
\(751\) −15.4679 −0.564431 −0.282215 0.959351i \(-0.591069\pi\)
−0.282215 + 0.959351i \(0.591069\pi\)
\(752\) −59.6894 −2.17665
\(753\) −25.1304 −0.915803
\(754\) 4.80350 0.174933
\(755\) 30.3783 1.10558
\(756\) 4.43352 0.161246
\(757\) 44.1814 1.60580 0.802899 0.596114i \(-0.203290\pi\)
0.802899 + 0.596114i \(0.203290\pi\)
\(758\) −16.9488 −0.615606
\(759\) −9.63351 −0.349674
\(760\) −46.3332 −1.68068
\(761\) 10.4630 0.379283 0.189642 0.981853i \(-0.439267\pi\)
0.189642 + 0.981853i \(0.439267\pi\)
\(762\) −18.5263 −0.671138
\(763\) −13.3420 −0.483014
\(764\) −6.45970 −0.233704
\(765\) 5.16172 0.186622
\(766\) −17.2215 −0.622239
\(767\) 28.6240 1.03355
\(768\) −38.1299 −1.37589
\(769\) −4.42904 −0.159715 −0.0798577 0.996806i \(-0.525447\pi\)
−0.0798577 + 0.996806i \(0.525447\pi\)
\(770\) 10.9596 0.394956
\(771\) −42.6738 −1.53686
\(772\) −10.6908 −0.384771
\(773\) 0.340986 0.0122644 0.00613221 0.999981i \(-0.498048\pi\)
0.00613221 + 0.999981i \(0.498048\pi\)
\(774\) 4.31239 0.155006
\(775\) −12.5593 −0.451142
\(776\) 27.2896 0.979639
\(777\) −5.44263 −0.195253
\(778\) −47.7864 −1.71323
\(779\) 91.6812 3.28482
\(780\) −22.3833 −0.801452
\(781\) −16.4202 −0.587560
\(782\) 8.38033 0.299680
\(783\) 3.50937 0.125415
\(784\) −4.99768 −0.178489
\(785\) −25.0359 −0.893570
\(786\) 1.07934 0.0384986
\(787\) −31.0067 −1.10527 −0.552635 0.833424i \(-0.686377\pi\)
−0.552635 + 0.833424i \(0.686377\pi\)
\(788\) −1.82481 −0.0650062
\(789\) 29.5991 1.05375
\(790\) −35.8170 −1.27431
\(791\) 10.1519 0.360959
\(792\) 2.67344 0.0949965
\(793\) −12.7844 −0.453989
\(794\) 9.41116 0.333989
\(795\) 16.6357 0.590009
\(796\) −11.1196 −0.394125
\(797\) 30.2850 1.07275 0.536374 0.843980i \(-0.319793\pi\)
0.536374 + 0.843980i \(0.319793\pi\)
\(798\) 29.0400 1.02800
\(799\) −22.2871 −0.788462
\(800\) 31.2961 1.10648
\(801\) 8.03693 0.283971
\(802\) −50.2236 −1.77346
\(803\) 4.11694 0.145284
\(804\) −4.58771 −0.161796
\(805\) −8.45097 −0.297858
\(806\) −12.5507 −0.442078
\(807\) −51.4945 −1.81269
\(808\) 1.82149 0.0640798
\(809\) −47.4570 −1.66850 −0.834250 0.551386i \(-0.814099\pi\)
−0.834250 + 0.551386i \(0.814099\pi\)
\(810\) −62.0452 −2.18005
\(811\) −33.1888 −1.16542 −0.582709 0.812681i \(-0.698007\pi\)
−0.582709 + 0.812681i \(0.698007\pi\)
\(812\) 0.869561 0.0305156
\(813\) 4.03029 0.141348
\(814\) −9.26274 −0.324659
\(815\) −14.5381 −0.509246
\(816\) −18.2798 −0.639919
\(817\) −24.8959 −0.870996
\(818\) 23.1768 0.810358
\(819\) −2.79211 −0.0975642
\(820\) −37.2025 −1.29917
\(821\) 14.9224 0.520795 0.260398 0.965501i \(-0.416146\pi\)
0.260398 + 0.965501i \(0.416146\pi\)
\(822\) −46.0635 −1.60665
\(823\) 31.7130 1.10545 0.552723 0.833365i \(-0.313589\pi\)
0.552723 + 0.833365i \(0.313589\pi\)
\(824\) −22.1379 −0.771211
\(825\) −21.6986 −0.755447
\(826\) 15.0693 0.524329
\(827\) −48.7849 −1.69642 −0.848209 0.529662i \(-0.822319\pi\)
−0.848209 + 0.529662i \(0.822319\pi\)
\(828\) 2.26991 0.0788849
\(829\) 27.6527 0.960419 0.480210 0.877154i \(-0.340561\pi\)
0.480210 + 0.877154i \(0.340561\pi\)
\(830\) 53.7424 1.86542
\(831\) 10.9799 0.380890
\(832\) −1.87285 −0.0649293
\(833\) −1.86606 −0.0646553
\(834\) 42.8131 1.48250
\(835\) 27.2591 0.943339
\(836\) 16.9944 0.587763
\(837\) −9.16934 −0.316939
\(838\) −51.7961 −1.78927
\(839\) 2.95740 0.102101 0.0510504 0.998696i \(-0.483743\pi\)
0.0510504 + 0.998696i \(0.483743\pi\)
\(840\) 10.7019 0.369252
\(841\) −28.3117 −0.976265
\(842\) −49.2556 −1.69746
\(843\) −57.8186 −1.99138
\(844\) −6.45140 −0.222066
\(845\) 6.57817 0.226296
\(846\) −17.5559 −0.603586
\(847\) −7.34926 −0.252524
\(848\) −12.9106 −0.443353
\(849\) 22.8214 0.783227
\(850\) 18.8759 0.647438
\(851\) 7.14254 0.244843
\(852\) 17.6552 0.604856
\(853\) −52.0891 −1.78350 −0.891748 0.452532i \(-0.850521\pi\)
−0.891748 + 0.452532i \(0.850521\pi\)
\(854\) −6.73047 −0.230312
\(855\) −23.4732 −0.802768
\(856\) 23.2920 0.796105
\(857\) 48.1988 1.64644 0.823219 0.567723i \(-0.192176\pi\)
0.823219 + 0.567723i \(0.192176\pi\)
\(858\) −21.6837 −0.740269
\(859\) −1.00000 −0.0341196
\(860\) 10.1023 0.344485
\(861\) −21.1763 −0.721687
\(862\) −38.0004 −1.29430
\(863\) 28.3074 0.963596 0.481798 0.876282i \(-0.339984\pi\)
0.481798 + 0.876282i \(0.339984\pi\)
\(864\) 22.8488 0.777333
\(865\) 31.3252 1.06509
\(866\) −29.7342 −1.01041
\(867\) 26.4961 0.899854
\(868\) −2.27200 −0.0771168
\(869\) −11.9310 −0.404731
\(870\) −9.32758 −0.316234
\(871\) −7.40564 −0.250931
\(872\) −22.1728 −0.750866
\(873\) 13.8254 0.467919
\(874\) −38.1101 −1.28909
\(875\) −2.60802 −0.0881672
\(876\) −4.42659 −0.149560
\(877\) −13.7382 −0.463907 −0.231953 0.972727i \(-0.574512\pi\)
−0.231953 + 0.972727i \(0.574512\pi\)
\(878\) −14.1640 −0.478011
\(879\) 12.7006 0.428381
\(880\) 31.3723 1.05756
\(881\) −34.2910 −1.15529 −0.577647 0.816286i \(-0.696029\pi\)
−0.577647 + 0.816286i \(0.696029\pi\)
\(882\) −1.46993 −0.0494951
\(883\) 46.4387 1.56279 0.781394 0.624038i \(-0.214509\pi\)
0.781394 + 0.624038i \(0.214509\pi\)
\(884\) 6.48617 0.218153
\(885\) −55.5829 −1.86840
\(886\) −11.8177 −0.397022
\(887\) −43.5715 −1.46299 −0.731494 0.681848i \(-0.761177\pi\)
−0.731494 + 0.681848i \(0.761177\pi\)
\(888\) −9.04499 −0.303530
\(889\) −5.41375 −0.181571
\(890\) 54.7537 1.83535
\(891\) −20.6679 −0.692399
\(892\) −11.4146 −0.382189
\(893\) 101.352 3.39162
\(894\) −67.8375 −2.26883
\(895\) −23.0565 −0.770694
\(896\) −11.7892 −0.393851
\(897\) 16.7204 0.558277
\(898\) 59.7352 1.99339
\(899\) −1.79841 −0.0599804
\(900\) 5.11276 0.170425
\(901\) −4.82065 −0.160599
\(902\) −36.0397 −1.19999
\(903\) 5.75039 0.191361
\(904\) 16.8712 0.561126
\(905\) 73.2563 2.43512
\(906\) −31.6422 −1.05124
\(907\) 8.11369 0.269411 0.134705 0.990886i \(-0.456991\pi\)
0.134705 + 0.990886i \(0.456991\pi\)
\(908\) 6.97277 0.231400
\(909\) 0.922801 0.0306074
\(910\) −19.0220 −0.630572
\(911\) 28.4699 0.943249 0.471625 0.881799i \(-0.343668\pi\)
0.471625 + 0.881799i \(0.343668\pi\)
\(912\) 83.1283 2.75265
\(913\) 17.9021 0.592473
\(914\) −12.5211 −0.414160
\(915\) 24.8252 0.820695
\(916\) 5.50502 0.181891
\(917\) 0.315403 0.0104155
\(918\) 13.7810 0.454841
\(919\) 42.8095 1.41215 0.706077 0.708135i \(-0.250463\pi\)
0.706077 + 0.708135i \(0.250463\pi\)
\(920\) −14.0445 −0.463033
\(921\) −50.3457 −1.65895
\(922\) −8.67147 −0.285580
\(923\) 28.4996 0.938077
\(924\) −3.92532 −0.129134
\(925\) 16.0879 0.528966
\(926\) −45.2769 −1.48789
\(927\) −11.2155 −0.368365
\(928\) 4.48141 0.147110
\(929\) −28.9205 −0.948850 −0.474425 0.880296i \(-0.657344\pi\)
−0.474425 + 0.880296i \(0.657344\pi\)
\(930\) 24.3712 0.799164
\(931\) 8.48604 0.278119
\(932\) 28.7163 0.940635
\(933\) 55.0408 1.80195
\(934\) 38.2329 1.25102
\(935\) 11.7140 0.383088
\(936\) −4.64015 −0.151668
\(937\) 5.43546 0.177569 0.0887844 0.996051i \(-0.471702\pi\)
0.0887844 + 0.996051i \(0.471702\pi\)
\(938\) −3.89876 −0.127299
\(939\) −44.3404 −1.44699
\(940\) −41.1269 −1.34141
\(941\) −38.5710 −1.25738 −0.628689 0.777657i \(-0.716408\pi\)
−0.628689 + 0.777657i \(0.716408\pi\)
\(942\) 26.0775 0.849652
\(943\) 27.7904 0.904979
\(944\) 43.1367 1.40398
\(945\) −13.8972 −0.452075
\(946\) 9.78652 0.318187
\(947\) 56.9289 1.84994 0.924970 0.380040i \(-0.124090\pi\)
0.924970 + 0.380040i \(0.124090\pi\)
\(948\) 12.8283 0.416645
\(949\) −7.14555 −0.231955
\(950\) −85.8393 −2.78499
\(951\) −31.7575 −1.02981
\(952\) −3.10117 −0.100510
\(953\) −35.1039 −1.13713 −0.568563 0.822640i \(-0.692500\pi\)
−0.568563 + 0.822640i \(0.692500\pi\)
\(954\) −3.79730 −0.122942
\(955\) 20.2484 0.655222
\(956\) −16.0415 −0.518821
\(957\) −3.10710 −0.100438
\(958\) 17.8565 0.576918
\(959\) −13.4607 −0.434667
\(960\) 3.63675 0.117376
\(961\) −26.3011 −0.848422
\(962\) 16.0769 0.518339
\(963\) 11.8002 0.380255
\(964\) −5.94434 −0.191454
\(965\) 33.5111 1.07876
\(966\) 8.80258 0.283218
\(967\) −17.1347 −0.551016 −0.275508 0.961299i \(-0.588846\pi\)
−0.275508 + 0.961299i \(0.588846\pi\)
\(968\) −12.2136 −0.392559
\(969\) 31.0389 0.997114
\(970\) 94.1891 3.02423
\(971\) −24.3608 −0.781774 −0.390887 0.920439i \(-0.627832\pi\)
−0.390887 + 0.920439i \(0.627832\pi\)
\(972\) 8.92179 0.286166
\(973\) 12.5108 0.401079
\(974\) 69.9333 2.24081
\(975\) 37.6610 1.20612
\(976\) −19.2663 −0.616699
\(977\) 32.1297 1.02792 0.513960 0.857814i \(-0.328178\pi\)
0.513960 + 0.857814i \(0.328178\pi\)
\(978\) 15.1429 0.484217
\(979\) 18.2390 0.582920
\(980\) −3.44348 −0.109998
\(981\) −11.2332 −0.358647
\(982\) 32.8701 1.04893
\(983\) −38.8126 −1.23793 −0.618965 0.785419i \(-0.712448\pi\)
−0.618965 + 0.785419i \(0.712448\pi\)
\(984\) −35.1925 −1.12189
\(985\) 5.72000 0.182254
\(986\) 2.70291 0.0860783
\(987\) −23.4101 −0.745152
\(988\) −29.4963 −0.938401
\(989\) −7.54642 −0.239962
\(990\) 9.22729 0.293262
\(991\) −56.8249 −1.80510 −0.902551 0.430584i \(-0.858308\pi\)
−0.902551 + 0.430584i \(0.858308\pi\)
\(992\) −11.7091 −0.371764
\(993\) −9.23160 −0.292956
\(994\) 15.0039 0.475893
\(995\) 34.8552 1.10498
\(996\) −19.2486 −0.609914
\(997\) 52.3753 1.65874 0.829371 0.558698i \(-0.188699\pi\)
0.829371 + 0.558698i \(0.188699\pi\)
\(998\) 71.0778 2.24993
\(999\) 11.7455 0.371612
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 \(a_p\))