Properties

Label 8015.2.a.l.1.11
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.12264 q^{2}\) \(-2.04208 q^{3}\) \(+2.50559 q^{4}\) \(-1.00000 q^{5}\) \(+4.33460 q^{6}\) \(-1.00000 q^{7}\) \(-1.07319 q^{8}\) \(+1.17010 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.12264 q^{2}\) \(-2.04208 q^{3}\) \(+2.50559 q^{4}\) \(-1.00000 q^{5}\) \(+4.33460 q^{6}\) \(-1.00000 q^{7}\) \(-1.07319 q^{8}\) \(+1.17010 q^{9}\) \(+2.12264 q^{10}\) \(+3.06648 q^{11}\) \(-5.11662 q^{12}\) \(+4.61144 q^{13}\) \(+2.12264 q^{14}\) \(+2.04208 q^{15}\) \(-2.73319 q^{16}\) \(-5.63379 q^{17}\) \(-2.48369 q^{18}\) \(-3.26056 q^{19}\) \(-2.50559 q^{20}\) \(+2.04208 q^{21}\) \(-6.50903 q^{22}\) \(+4.76193 q^{23}\) \(+2.19154 q^{24}\) \(+1.00000 q^{25}\) \(-9.78843 q^{26}\) \(+3.73681 q^{27}\) \(-2.50559 q^{28}\) \(-3.51013 q^{29}\) \(-4.33460 q^{30}\) \(-2.15089 q^{31}\) \(+7.94796 q^{32}\) \(-6.26201 q^{33}\) \(+11.9585 q^{34}\) \(+1.00000 q^{35}\) \(+2.93178 q^{36}\) \(+5.31424 q^{37}\) \(+6.92099 q^{38}\) \(-9.41694 q^{39}\) \(+1.07319 q^{40}\) \(-9.14281 q^{41}\) \(-4.33460 q^{42}\) \(+2.94660 q^{43}\) \(+7.68335 q^{44}\) \(-1.17010 q^{45}\) \(-10.1079 q^{46}\) \(+1.74188 q^{47}\) \(+5.58140 q^{48}\) \(+1.00000 q^{49}\) \(-2.12264 q^{50}\) \(+11.5046 q^{51}\) \(+11.5544 q^{52}\) \(-10.4360 q^{53}\) \(-7.93190 q^{54}\) \(-3.06648 q^{55}\) \(+1.07319 q^{56}\) \(+6.65833 q^{57}\) \(+7.45073 q^{58}\) \(+12.7186 q^{59}\) \(+5.11662 q^{60}\) \(+6.25110 q^{61}\) \(+4.56556 q^{62}\) \(-1.17010 q^{63}\) \(-11.4042 q^{64}\) \(-4.61144 q^{65}\) \(+13.2920 q^{66}\) \(-2.70719 q^{67}\) \(-14.1160 q^{68}\) \(-9.72424 q^{69}\) \(-2.12264 q^{70}\) \(+11.6344 q^{71}\) \(-1.25573 q^{72}\) \(+7.59479 q^{73}\) \(-11.2802 q^{74}\) \(-2.04208 q^{75}\) \(-8.16964 q^{76}\) \(-3.06648 q^{77}\) \(+19.9888 q^{78}\) \(-4.26352 q^{79}\) \(+2.73319 q^{80}\) \(-11.1412 q^{81}\) \(+19.4069 q^{82}\) \(+13.3150 q^{83}\) \(+5.11662 q^{84}\) \(+5.63379 q^{85}\) \(-6.25456 q^{86}\) \(+7.16797 q^{87}\) \(-3.29091 q^{88}\) \(-3.77914 q^{89}\) \(+2.48369 q^{90}\) \(-4.61144 q^{91}\) \(+11.9314 q^{92}\) \(+4.39229 q^{93}\) \(-3.69739 q^{94}\) \(+3.26056 q^{95}\) \(-16.2304 q^{96}\) \(+6.32500 q^{97}\) \(-2.12264 q^{98}\) \(+3.58808 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(62q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut -\mathstrut 62q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 62q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(62q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut -\mathstrut 62q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 62q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 13q^{11} \) \(\mathstrut +\mathstrut 37q^{12} \) \(\mathstrut +\mathstrut 31q^{13} \) \(\mathstrut -\mathstrut 2q^{14} \) \(\mathstrut -\mathstrut 11q^{15} \) \(\mathstrut +\mathstrut 64q^{16} \) \(\mathstrut +\mathstrut 30q^{17} \) \(\mathstrut +\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut 64q^{20} \) \(\mathstrut -\mathstrut 11q^{21} \) \(\mathstrut +\mathstrut 7q^{22} \) \(\mathstrut +\mathstrut 29q^{24} \) \(\mathstrut +\mathstrut 62q^{25} \) \(\mathstrut +\mathstrut 59q^{27} \) \(\mathstrut -\mathstrut 64q^{28} \) \(\mathstrut -\mathstrut 29q^{29} \) \(\mathstrut -\mathstrut 3q^{30} \) \(\mathstrut +\mathstrut 20q^{31} \) \(\mathstrut +\mathstrut 22q^{32} \) \(\mathstrut +\mathstrut 72q^{33} \) \(\mathstrut +\mathstrut 13q^{34} \) \(\mathstrut +\mathstrut 62q^{35} \) \(\mathstrut +\mathstrut 53q^{36} \) \(\mathstrut +\mathstrut 35q^{37} \) \(\mathstrut +\mathstrut 34q^{38} \) \(\mathstrut -\mathstrut 6q^{39} \) \(\mathstrut -\mathstrut 15q^{40} \) \(\mathstrut +\mathstrut 13q^{41} \) \(\mathstrut -\mathstrut 3q^{42} \) \(\mathstrut -\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 44q^{44} \) \(\mathstrut -\mathstrut 69q^{45} \) \(\mathstrut -\mathstrut 19q^{46} \) \(\mathstrut +\mathstrut 58q^{47} \) \(\mathstrut +\mathstrut 64q^{48} \) \(\mathstrut +\mathstrut 62q^{49} \) \(\mathstrut +\mathstrut 2q^{50} \) \(\mathstrut -\mathstrut 30q^{51} \) \(\mathstrut +\mathstrut 82q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 22q^{54} \) \(\mathstrut +\mathstrut 13q^{55} \) \(\mathstrut -\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 21q^{57} \) \(\mathstrut +\mathstrut 18q^{58} \) \(\mathstrut -\mathstrut 11q^{59} \) \(\mathstrut -\mathstrut 37q^{60} \) \(\mathstrut +\mathstrut 24q^{61} \) \(\mathstrut +\mathstrut 48q^{62} \) \(\mathstrut -\mathstrut 69q^{63} \) \(\mathstrut +\mathstrut 65q^{64} \) \(\mathstrut -\mathstrut 31q^{65} \) \(\mathstrut +\mathstrut 25q^{66} \) \(\mathstrut -\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 65q^{68} \) \(\mathstrut +\mathstrut 27q^{69} \) \(\mathstrut +\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 35q^{71} \) \(\mathstrut +\mathstrut 53q^{72} \) \(\mathstrut +\mathstrut 116q^{73} \) \(\mathstrut -\mathstrut 69q^{74} \) \(\mathstrut +\mathstrut 11q^{75} \) \(\mathstrut +\mathstrut 65q^{76} \) \(\mathstrut +\mathstrut 13q^{77} \) \(\mathstrut +\mathstrut 102q^{78} \) \(\mathstrut -\mathstrut 83q^{79} \) \(\mathstrut -\mathstrut 64q^{80} \) \(\mathstrut +\mathstrut 126q^{81} \) \(\mathstrut +\mathstrut 71q^{82} \) \(\mathstrut +\mathstrut 84q^{83} \) \(\mathstrut -\mathstrut 37q^{84} \) \(\mathstrut -\mathstrut 30q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 49q^{87} \) \(\mathstrut +\mathstrut 20q^{88} \) \(\mathstrut -\mathstrut 16q^{89} \) \(\mathstrut -\mathstrut 18q^{90} \) \(\mathstrut -\mathstrut 31q^{91} \) \(\mathstrut +\mathstrut 19q^{92} \) \(\mathstrut +\mathstrut 65q^{93} \) \(\mathstrut +\mathstrut 54q^{94} \) \(\mathstrut -\mathstrut 20q^{95} \) \(\mathstrut +\mathstrut 17q^{96} \) \(\mathstrut +\mathstrut 155q^{97} \) \(\mathstrut +\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut 6q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.12264 −1.50093 −0.750466 0.660909i \(-0.770171\pi\)
−0.750466 + 0.660909i \(0.770171\pi\)
\(3\) −2.04208 −1.17900 −0.589498 0.807770i \(-0.700674\pi\)
−0.589498 + 0.807770i \(0.700674\pi\)
\(4\) 2.50559 1.25280
\(5\) −1.00000 −0.447214
\(6\) 4.33460 1.76959
\(7\) −1.00000 −0.377964
\(8\) −1.07319 −0.379429
\(9\) 1.17010 0.390032
\(10\) 2.12264 0.671237
\(11\) 3.06648 0.924579 0.462290 0.886729i \(-0.347028\pi\)
0.462290 + 0.886729i \(0.347028\pi\)
\(12\) −5.11662 −1.47704
\(13\) 4.61144 1.27898 0.639492 0.768798i \(-0.279145\pi\)
0.639492 + 0.768798i \(0.279145\pi\)
\(14\) 2.12264 0.567299
\(15\) 2.04208 0.527263
\(16\) −2.73319 −0.683299
\(17\) −5.63379 −1.36639 −0.683197 0.730234i \(-0.739411\pi\)
−0.683197 + 0.730234i \(0.739411\pi\)
\(18\) −2.48369 −0.585411
\(19\) −3.26056 −0.748024 −0.374012 0.927424i \(-0.622018\pi\)
−0.374012 + 0.927424i \(0.622018\pi\)
\(20\) −2.50559 −0.560267
\(21\) 2.04208 0.445619
\(22\) −6.50903 −1.38773
\(23\) 4.76193 0.992931 0.496465 0.868057i \(-0.334631\pi\)
0.496465 + 0.868057i \(0.334631\pi\)
\(24\) 2.19154 0.447345
\(25\) 1.00000 0.200000
\(26\) −9.78843 −1.91967
\(27\) 3.73681 0.719150
\(28\) −2.50559 −0.473512
\(29\) −3.51013 −0.651815 −0.325907 0.945402i \(-0.605670\pi\)
−0.325907 + 0.945402i \(0.605670\pi\)
\(30\) −4.33460 −0.791386
\(31\) −2.15089 −0.386311 −0.193156 0.981168i \(-0.561872\pi\)
−0.193156 + 0.981168i \(0.561872\pi\)
\(32\) 7.94796 1.40501
\(33\) −6.26201 −1.09008
\(34\) 11.9585 2.05086
\(35\) 1.00000 0.169031
\(36\) 2.93178 0.488630
\(37\) 5.31424 0.873656 0.436828 0.899545i \(-0.356102\pi\)
0.436828 + 0.899545i \(0.356102\pi\)
\(38\) 6.92099 1.12273
\(39\) −9.41694 −1.50792
\(40\) 1.07319 0.169686
\(41\) −9.14281 −1.42787 −0.713933 0.700214i \(-0.753088\pi\)
−0.713933 + 0.700214i \(0.753088\pi\)
\(42\) −4.33460 −0.668843
\(43\) 2.94660 0.449352 0.224676 0.974434i \(-0.427868\pi\)
0.224676 + 0.974434i \(0.427868\pi\)
\(44\) 7.68335 1.15831
\(45\) −1.17010 −0.174427
\(46\) −10.1079 −1.49032
\(47\) 1.74188 0.254080 0.127040 0.991898i \(-0.459452\pi\)
0.127040 + 0.991898i \(0.459452\pi\)
\(48\) 5.58140 0.805606
\(49\) 1.00000 0.142857
\(50\) −2.12264 −0.300186
\(51\) 11.5046 1.61097
\(52\) 11.5544 1.60231
\(53\) −10.4360 −1.43350 −0.716750 0.697330i \(-0.754371\pi\)
−0.716750 + 0.697330i \(0.754371\pi\)
\(54\) −7.93190 −1.07940
\(55\) −3.06648 −0.413484
\(56\) 1.07319 0.143411
\(57\) 6.65833 0.881918
\(58\) 7.45073 0.978329
\(59\) 12.7186 1.65582 0.827909 0.560862i \(-0.189530\pi\)
0.827909 + 0.560862i \(0.189530\pi\)
\(60\) 5.11662 0.660553
\(61\) 6.25110 0.800371 0.400185 0.916434i \(-0.368946\pi\)
0.400185 + 0.916434i \(0.368946\pi\)
\(62\) 4.56556 0.579826
\(63\) −1.17010 −0.147418
\(64\) −11.4042 −1.42553
\(65\) −4.61144 −0.571979
\(66\) 13.2920 1.63613
\(67\) −2.70719 −0.330736 −0.165368 0.986232i \(-0.552881\pi\)
−0.165368 + 0.986232i \(0.552881\pi\)
\(68\) −14.1160 −1.71181
\(69\) −9.72424 −1.17066
\(70\) −2.12264 −0.253704
\(71\) 11.6344 1.38075 0.690374 0.723453i \(-0.257446\pi\)
0.690374 + 0.723453i \(0.257446\pi\)
\(72\) −1.25573 −0.147989
\(73\) 7.59479 0.888903 0.444452 0.895803i \(-0.353399\pi\)
0.444452 + 0.895803i \(0.353399\pi\)
\(74\) −11.2802 −1.31130
\(75\) −2.04208 −0.235799
\(76\) −8.16964 −0.937122
\(77\) −3.06648 −0.349458
\(78\) 19.9888 2.26328
\(79\) −4.26352 −0.479683 −0.239842 0.970812i \(-0.577096\pi\)
−0.239842 + 0.970812i \(0.577096\pi\)
\(80\) 2.73319 0.305580
\(81\) −11.1412 −1.23791
\(82\) 19.4069 2.14313
\(83\) 13.3150 1.46151 0.730756 0.682638i \(-0.239168\pi\)
0.730756 + 0.682638i \(0.239168\pi\)
\(84\) 5.11662 0.558269
\(85\) 5.63379 0.611070
\(86\) −6.25456 −0.674446
\(87\) 7.16797 0.768487
\(88\) −3.29091 −0.350812
\(89\) −3.77914 −0.400588 −0.200294 0.979736i \(-0.564190\pi\)
−0.200294 + 0.979736i \(0.564190\pi\)
\(90\) 2.48369 0.261804
\(91\) −4.61144 −0.483411
\(92\) 11.9314 1.24394
\(93\) 4.39229 0.455459
\(94\) −3.69739 −0.381357
\(95\) 3.26056 0.334527
\(96\) −16.2304 −1.65651
\(97\) 6.32500 0.642206 0.321103 0.947044i \(-0.395946\pi\)
0.321103 + 0.947044i \(0.395946\pi\)
\(98\) −2.12264 −0.214419
\(99\) 3.58808 0.360615
\(100\) 2.50559 0.250559
\(101\) 0.223535 0.0222425 0.0111213 0.999938i \(-0.496460\pi\)
0.0111213 + 0.999938i \(0.496460\pi\)
\(102\) −24.4202 −2.41796
\(103\) 8.72842 0.860037 0.430019 0.902820i \(-0.358507\pi\)
0.430019 + 0.902820i \(0.358507\pi\)
\(104\) −4.94894 −0.485284
\(105\) −2.04208 −0.199287
\(106\) 22.1519 2.15159
\(107\) −12.2087 −1.18026 −0.590128 0.807310i \(-0.700923\pi\)
−0.590128 + 0.807310i \(0.700923\pi\)
\(108\) 9.36293 0.900948
\(109\) −6.81227 −0.652497 −0.326249 0.945284i \(-0.605785\pi\)
−0.326249 + 0.945284i \(0.605785\pi\)
\(110\) 6.50903 0.620612
\(111\) −10.8521 −1.03004
\(112\) 2.73319 0.258263
\(113\) 11.5652 1.08796 0.543979 0.839099i \(-0.316917\pi\)
0.543979 + 0.839099i \(0.316917\pi\)
\(114\) −14.1332 −1.32370
\(115\) −4.76193 −0.444052
\(116\) −8.79495 −0.816591
\(117\) 5.39583 0.498845
\(118\) −26.9969 −2.48527
\(119\) 5.63379 0.516448
\(120\) −2.19154 −0.200059
\(121\) −1.59669 −0.145153
\(122\) −13.2688 −1.20130
\(123\) 18.6704 1.68345
\(124\) −5.38925 −0.483969
\(125\) −1.00000 −0.0894427
\(126\) 2.48369 0.221265
\(127\) −9.82591 −0.871909 −0.435954 0.899969i \(-0.643589\pi\)
−0.435954 + 0.899969i \(0.643589\pi\)
\(128\) 8.31117 0.734610
\(129\) −6.01719 −0.529784
\(130\) 9.78843 0.858502
\(131\) −6.88741 −0.601756 −0.300878 0.953663i \(-0.597280\pi\)
−0.300878 + 0.953663i \(0.597280\pi\)
\(132\) −15.6900 −1.36564
\(133\) 3.26056 0.282727
\(134\) 5.74639 0.496412
\(135\) −3.73681 −0.321614
\(136\) 6.04611 0.518450
\(137\) −8.90601 −0.760892 −0.380446 0.924803i \(-0.624229\pi\)
−0.380446 + 0.924803i \(0.624229\pi\)
\(138\) 20.6410 1.75708
\(139\) 13.2483 1.12370 0.561851 0.827238i \(-0.310089\pi\)
0.561851 + 0.827238i \(0.310089\pi\)
\(140\) 2.50559 0.211761
\(141\) −3.55707 −0.299559
\(142\) −24.6956 −2.07241
\(143\) 14.1409 1.18252
\(144\) −3.19810 −0.266508
\(145\) 3.51013 0.291500
\(146\) −16.1210 −1.33418
\(147\) −2.04208 −0.168428
\(148\) 13.3153 1.09451
\(149\) −8.98809 −0.736333 −0.368167 0.929760i \(-0.620014\pi\)
−0.368167 + 0.929760i \(0.620014\pi\)
\(150\) 4.33460 0.353918
\(151\) −13.3460 −1.08609 −0.543043 0.839705i \(-0.682728\pi\)
−0.543043 + 0.839705i \(0.682728\pi\)
\(152\) 3.49919 0.283822
\(153\) −6.59207 −0.532937
\(154\) 6.50903 0.524513
\(155\) 2.15089 0.172764
\(156\) −23.5950 −1.88911
\(157\) 3.65570 0.291756 0.145878 0.989303i \(-0.453399\pi\)
0.145878 + 0.989303i \(0.453399\pi\)
\(158\) 9.04991 0.719972
\(159\) 21.3112 1.69009
\(160\) −7.94796 −0.628341
\(161\) −4.76193 −0.375293
\(162\) 23.6487 1.85801
\(163\) 9.04593 0.708532 0.354266 0.935145i \(-0.384731\pi\)
0.354266 + 0.935145i \(0.384731\pi\)
\(164\) −22.9081 −1.78882
\(165\) 6.26201 0.487496
\(166\) −28.2630 −2.19363
\(167\) 17.0657 1.32058 0.660291 0.751010i \(-0.270433\pi\)
0.660291 + 0.751010i \(0.270433\pi\)
\(168\) −2.19154 −0.169081
\(169\) 8.26542 0.635801
\(170\) −11.9585 −0.917174
\(171\) −3.81517 −0.291753
\(172\) 7.38297 0.562946
\(173\) 17.0726 1.29800 0.649002 0.760787i \(-0.275187\pi\)
0.649002 + 0.760787i \(0.275187\pi\)
\(174\) −15.2150 −1.15345
\(175\) −1.00000 −0.0755929
\(176\) −8.38129 −0.631764
\(177\) −25.9724 −1.95220
\(178\) 8.02175 0.601255
\(179\) −17.0019 −1.27078 −0.635392 0.772190i \(-0.719162\pi\)
−0.635392 + 0.772190i \(0.719162\pi\)
\(180\) −2.93178 −0.218522
\(181\) 3.54374 0.263404 0.131702 0.991289i \(-0.457956\pi\)
0.131702 + 0.991289i \(0.457956\pi\)
\(182\) 9.78843 0.725566
\(183\) −12.7652 −0.943634
\(184\) −5.11044 −0.376747
\(185\) −5.31424 −0.390711
\(186\) −9.32324 −0.683613
\(187\) −17.2759 −1.26334
\(188\) 4.36445 0.318310
\(189\) −3.73681 −0.271813
\(190\) −6.92099 −0.502102
\(191\) −25.1507 −1.81984 −0.909922 0.414779i \(-0.863859\pi\)
−0.909922 + 0.414779i \(0.863859\pi\)
\(192\) 23.2884 1.68070
\(193\) −11.2607 −0.810566 −0.405283 0.914191i \(-0.632827\pi\)
−0.405283 + 0.914191i \(0.632827\pi\)
\(194\) −13.4257 −0.963908
\(195\) 9.41694 0.674361
\(196\) 2.50559 0.178971
\(197\) −5.77791 −0.411659 −0.205829 0.978588i \(-0.565989\pi\)
−0.205829 + 0.978588i \(0.565989\pi\)
\(198\) −7.61619 −0.541259
\(199\) −10.1673 −0.720739 −0.360370 0.932810i \(-0.617349\pi\)
−0.360370 + 0.932810i \(0.617349\pi\)
\(200\) −1.07319 −0.0758858
\(201\) 5.52831 0.389937
\(202\) −0.474483 −0.0333845
\(203\) 3.51013 0.246363
\(204\) 28.8259 2.01822
\(205\) 9.14281 0.638561
\(206\) −18.5273 −1.29086
\(207\) 5.57191 0.387275
\(208\) −12.6040 −0.873928
\(209\) −9.99846 −0.691608
\(210\) 4.33460 0.299116
\(211\) 25.3243 1.74340 0.871698 0.490043i \(-0.163019\pi\)
0.871698 + 0.490043i \(0.163019\pi\)
\(212\) −26.1485 −1.79588
\(213\) −23.7584 −1.62790
\(214\) 25.9146 1.77148
\(215\) −2.94660 −0.200956
\(216\) −4.01030 −0.272866
\(217\) 2.15089 0.146012
\(218\) 14.4600 0.979354
\(219\) −15.5092 −1.04801
\(220\) −7.68335 −0.518011
\(221\) −25.9799 −1.74760
\(222\) 23.0351 1.54602
\(223\) 14.7787 0.989652 0.494826 0.868992i \(-0.335232\pi\)
0.494826 + 0.868992i \(0.335232\pi\)
\(224\) −7.94796 −0.531045
\(225\) 1.17010 0.0780063
\(226\) −24.5486 −1.63295
\(227\) −26.0088 −1.72627 −0.863134 0.504975i \(-0.831502\pi\)
−0.863134 + 0.504975i \(0.831502\pi\)
\(228\) 16.6831 1.10486
\(229\) 1.00000 0.0660819
\(230\) 10.1079 0.666492
\(231\) 6.26201 0.412010
\(232\) 3.76703 0.247317
\(233\) 2.54395 0.166660 0.0833299 0.996522i \(-0.473444\pi\)
0.0833299 + 0.996522i \(0.473444\pi\)
\(234\) −11.4534 −0.748732
\(235\) −1.74188 −0.113628
\(236\) 31.8676 2.07440
\(237\) 8.70645 0.565545
\(238\) −11.9585 −0.775154
\(239\) −25.9383 −1.67781 −0.838904 0.544279i \(-0.816803\pi\)
−0.838904 + 0.544279i \(0.816803\pi\)
\(240\) −5.58140 −0.360278
\(241\) 10.9253 0.703757 0.351879 0.936046i \(-0.385543\pi\)
0.351879 + 0.936046i \(0.385543\pi\)
\(242\) 3.38919 0.217865
\(243\) 11.5407 0.740337
\(244\) 15.6627 1.00270
\(245\) −1.00000 −0.0638877
\(246\) −39.6304 −2.52674
\(247\) −15.0359 −0.956712
\(248\) 2.30831 0.146578
\(249\) −27.1903 −1.72312
\(250\) 2.12264 0.134247
\(251\) −10.8962 −0.687760 −0.343880 0.939014i \(-0.611741\pi\)
−0.343880 + 0.939014i \(0.611741\pi\)
\(252\) −2.93178 −0.184685
\(253\) 14.6024 0.918043
\(254\) 20.8568 1.30868
\(255\) −11.5046 −0.720449
\(256\) 5.16689 0.322931
\(257\) 8.55327 0.533538 0.266769 0.963760i \(-0.414044\pi\)
0.266769 + 0.963760i \(0.414044\pi\)
\(258\) 12.7723 0.795170
\(259\) −5.31424 −0.330211
\(260\) −11.5544 −0.716573
\(261\) −4.10719 −0.254228
\(262\) 14.6195 0.903194
\(263\) −26.8373 −1.65486 −0.827429 0.561570i \(-0.810197\pi\)
−0.827429 + 0.561570i \(0.810197\pi\)
\(264\) 6.72031 0.413606
\(265\) 10.4360 0.641081
\(266\) −6.92099 −0.424353
\(267\) 7.71731 0.472292
\(268\) −6.78312 −0.414345
\(269\) 23.1962 1.41430 0.707150 0.707064i \(-0.249981\pi\)
0.707150 + 0.707064i \(0.249981\pi\)
\(270\) 7.93190 0.482720
\(271\) −16.5502 −1.00535 −0.502675 0.864475i \(-0.667651\pi\)
−0.502675 + 0.864475i \(0.667651\pi\)
\(272\) 15.3982 0.933655
\(273\) 9.41694 0.569939
\(274\) 18.9042 1.14205
\(275\) 3.06648 0.184916
\(276\) −24.3650 −1.46660
\(277\) 23.6464 1.42077 0.710387 0.703812i \(-0.248520\pi\)
0.710387 + 0.703812i \(0.248520\pi\)
\(278\) −28.1213 −1.68660
\(279\) −2.51674 −0.150674
\(280\) −1.07319 −0.0641352
\(281\) −11.1360 −0.664319 −0.332159 0.943223i \(-0.607777\pi\)
−0.332159 + 0.943223i \(0.607777\pi\)
\(282\) 7.55037 0.449618
\(283\) 16.2753 0.967467 0.483733 0.875215i \(-0.339280\pi\)
0.483733 + 0.875215i \(0.339280\pi\)
\(284\) 29.1510 1.72980
\(285\) −6.65833 −0.394406
\(286\) −30.0160 −1.77489
\(287\) 9.14281 0.539683
\(288\) 9.29987 0.548000
\(289\) 14.7395 0.867032
\(290\) −7.45073 −0.437522
\(291\) −12.9162 −0.757159
\(292\) 19.0295 1.11361
\(293\) 21.0407 1.22921 0.614605 0.788835i \(-0.289315\pi\)
0.614605 + 0.788835i \(0.289315\pi\)
\(294\) 4.33460 0.252799
\(295\) −12.7186 −0.740504
\(296\) −5.70318 −0.331490
\(297\) 11.4589 0.664911
\(298\) 19.0785 1.10519
\(299\) 21.9594 1.26994
\(300\) −5.11662 −0.295408
\(301\) −2.94660 −0.169839
\(302\) 28.3288 1.63014
\(303\) −0.456476 −0.0262239
\(304\) 8.91175 0.511124
\(305\) −6.25110 −0.357937
\(306\) 13.9926 0.799902
\(307\) −29.7346 −1.69704 −0.848522 0.529161i \(-0.822507\pi\)
−0.848522 + 0.529161i \(0.822507\pi\)
\(308\) −7.68335 −0.437800
\(309\) −17.8242 −1.01398
\(310\) −4.56556 −0.259306
\(311\) 29.5926 1.67804 0.839022 0.544098i \(-0.183128\pi\)
0.839022 + 0.544098i \(0.183128\pi\)
\(312\) 10.1061 0.572148
\(313\) −34.4107 −1.94501 −0.972504 0.232885i \(-0.925184\pi\)
−0.972504 + 0.232885i \(0.925184\pi\)
\(314\) −7.75972 −0.437906
\(315\) 1.17010 0.0659274
\(316\) −10.6826 −0.600945
\(317\) −1.77424 −0.0996513 −0.0498257 0.998758i \(-0.515867\pi\)
−0.0498257 + 0.998758i \(0.515867\pi\)
\(318\) −45.2361 −2.53671
\(319\) −10.7638 −0.602654
\(320\) 11.4042 0.637517
\(321\) 24.9311 1.39152
\(322\) 10.1079 0.563288
\(323\) 18.3693 1.02210
\(324\) −27.9152 −1.55084
\(325\) 4.61144 0.255797
\(326\) −19.2012 −1.06346
\(327\) 13.9112 0.769292
\(328\) 9.81195 0.541774
\(329\) −1.74188 −0.0960332
\(330\) −13.2920 −0.731699
\(331\) −24.1241 −1.32598 −0.662989 0.748629i \(-0.730712\pi\)
−0.662989 + 0.748629i \(0.730712\pi\)
\(332\) 33.3620 1.83098
\(333\) 6.21817 0.340754
\(334\) −36.2242 −1.98210
\(335\) 2.70719 0.147910
\(336\) −5.58140 −0.304491
\(337\) −10.5005 −0.571997 −0.285998 0.958230i \(-0.592325\pi\)
−0.285998 + 0.958230i \(0.592325\pi\)
\(338\) −17.5445 −0.954294
\(339\) −23.6170 −1.28270
\(340\) 14.1160 0.765546
\(341\) −6.59566 −0.357175
\(342\) 8.09822 0.437902
\(343\) −1.00000 −0.0539949
\(344\) −3.16225 −0.170497
\(345\) 9.72424 0.523536
\(346\) −36.2389 −1.94821
\(347\) 2.78571 0.149545 0.0747723 0.997201i \(-0.476177\pi\)
0.0747723 + 0.997201i \(0.476177\pi\)
\(348\) 17.9600 0.962757
\(349\) −18.0677 −0.967143 −0.483571 0.875305i \(-0.660661\pi\)
−0.483571 + 0.875305i \(0.660661\pi\)
\(350\) 2.12264 0.113460
\(351\) 17.2321 0.919782
\(352\) 24.3723 1.29905
\(353\) −26.8713 −1.43021 −0.715106 0.699016i \(-0.753622\pi\)
−0.715106 + 0.699016i \(0.753622\pi\)
\(354\) 55.1299 2.93012
\(355\) −11.6344 −0.617489
\(356\) −9.46898 −0.501855
\(357\) −11.5046 −0.608891
\(358\) 36.0890 1.90736
\(359\) −29.2865 −1.54568 −0.772842 0.634599i \(-0.781165\pi\)
−0.772842 + 0.634599i \(0.781165\pi\)
\(360\) 1.25573 0.0661829
\(361\) −8.36873 −0.440460
\(362\) −7.52208 −0.395352
\(363\) 3.26056 0.171135
\(364\) −11.5544 −0.605615
\(365\) −7.59479 −0.397530
\(366\) 27.0960 1.41633
\(367\) 23.1745 1.20970 0.604850 0.796339i \(-0.293233\pi\)
0.604850 + 0.796339i \(0.293233\pi\)
\(368\) −13.0153 −0.678468
\(369\) −10.6980 −0.556913
\(370\) 11.2802 0.586430
\(371\) 10.4360 0.541812
\(372\) 11.0053 0.570597
\(373\) −16.7267 −0.866074 −0.433037 0.901376i \(-0.642558\pi\)
−0.433037 + 0.901376i \(0.642558\pi\)
\(374\) 36.6705 1.89619
\(375\) 2.04208 0.105453
\(376\) −1.86937 −0.0964053
\(377\) −16.1868 −0.833661
\(378\) 7.93190 0.407973
\(379\) 29.6413 1.52257 0.761287 0.648415i \(-0.224568\pi\)
0.761287 + 0.648415i \(0.224568\pi\)
\(380\) 8.16964 0.419094
\(381\) 20.0653 1.02798
\(382\) 53.3859 2.73146
\(383\) −9.28910 −0.474651 −0.237325 0.971430i \(-0.576271\pi\)
−0.237325 + 0.971430i \(0.576271\pi\)
\(384\) −16.9721 −0.866103
\(385\) 3.06648 0.156282
\(386\) 23.9025 1.21660
\(387\) 3.44780 0.175261
\(388\) 15.8479 0.804553
\(389\) 33.5409 1.70059 0.850296 0.526305i \(-0.176423\pi\)
0.850296 + 0.526305i \(0.176423\pi\)
\(390\) −19.9888 −1.01217
\(391\) −26.8277 −1.35673
\(392\) −1.07319 −0.0542042
\(393\) 14.0647 0.709468
\(394\) 12.2644 0.617872
\(395\) 4.26352 0.214521
\(396\) 8.99025 0.451777
\(397\) 11.5278 0.578566 0.289283 0.957244i \(-0.406583\pi\)
0.289283 + 0.957244i \(0.406583\pi\)
\(398\) 21.5815 1.08178
\(399\) −6.65833 −0.333334
\(400\) −2.73319 −0.136660
\(401\) 26.0596 1.30135 0.650677 0.759355i \(-0.274485\pi\)
0.650677 + 0.759355i \(0.274485\pi\)
\(402\) −11.7346 −0.585268
\(403\) −9.91870 −0.494086
\(404\) 0.560087 0.0278654
\(405\) 11.1412 0.553609
\(406\) −7.45073 −0.369774
\(407\) 16.2960 0.807764
\(408\) −12.3466 −0.611250
\(409\) 7.62205 0.376886 0.188443 0.982084i \(-0.439656\pi\)
0.188443 + 0.982084i \(0.439656\pi\)
\(410\) −19.4069 −0.958437
\(411\) 18.1868 0.897089
\(412\) 21.8699 1.07745
\(413\) −12.7186 −0.625840
\(414\) −11.8271 −0.581273
\(415\) −13.3150 −0.653608
\(416\) 36.6516 1.79699
\(417\) −27.0540 −1.32484
\(418\) 21.2231 1.03806
\(419\) 1.50873 0.0737061 0.0368531 0.999321i \(-0.488267\pi\)
0.0368531 + 0.999321i \(0.488267\pi\)
\(420\) −5.11662 −0.249666
\(421\) 2.85527 0.139158 0.0695788 0.997576i \(-0.477834\pi\)
0.0695788 + 0.997576i \(0.477834\pi\)
\(422\) −53.7543 −2.61672
\(423\) 2.03817 0.0990992
\(424\) 11.1998 0.543912
\(425\) −5.63379 −0.273279
\(426\) 50.4304 2.44336
\(427\) −6.25110 −0.302512
\(428\) −30.5899 −1.47862
\(429\) −28.8769 −1.39419
\(430\) 6.25456 0.301622
\(431\) −18.7728 −0.904256 −0.452128 0.891953i \(-0.649335\pi\)
−0.452128 + 0.891953i \(0.649335\pi\)
\(432\) −10.2134 −0.491394
\(433\) 25.3428 1.21790 0.608948 0.793210i \(-0.291592\pi\)
0.608948 + 0.793210i \(0.291592\pi\)
\(434\) −4.56556 −0.219154
\(435\) −7.16797 −0.343678
\(436\) −17.0688 −0.817446
\(437\) −15.5266 −0.742736
\(438\) 32.9204 1.57300
\(439\) −21.2610 −1.01473 −0.507367 0.861730i \(-0.669381\pi\)
−0.507367 + 0.861730i \(0.669381\pi\)
\(440\) 3.29091 0.156888
\(441\) 1.17010 0.0557188
\(442\) 55.1459 2.62302
\(443\) 4.89366 0.232505 0.116252 0.993220i \(-0.462912\pi\)
0.116252 + 0.993220i \(0.462912\pi\)
\(444\) −27.1910 −1.29043
\(445\) 3.77914 0.179148
\(446\) −31.3697 −1.48540
\(447\) 18.3544 0.868134
\(448\) 11.4042 0.538800
\(449\) −13.3205 −0.628635 −0.314318 0.949318i \(-0.601776\pi\)
−0.314318 + 0.949318i \(0.601776\pi\)
\(450\) −2.48369 −0.117082
\(451\) −28.0363 −1.32018
\(452\) 28.9776 1.36299
\(453\) 27.2537 1.28049
\(454\) 55.2074 2.59101
\(455\) 4.61144 0.216188
\(456\) −7.14564 −0.334625
\(457\) 39.9404 1.86833 0.934167 0.356835i \(-0.116144\pi\)
0.934167 + 0.356835i \(0.116144\pi\)
\(458\) −2.12264 −0.0991844
\(459\) −21.0524 −0.982642
\(460\) −11.9314 −0.556307
\(461\) 5.78241 0.269314 0.134657 0.990892i \(-0.457007\pi\)
0.134657 + 0.990892i \(0.457007\pi\)
\(462\) −13.2920 −0.618398
\(463\) 25.0507 1.16420 0.582102 0.813115i \(-0.302230\pi\)
0.582102 + 0.813115i \(0.302230\pi\)
\(464\) 9.59387 0.445384
\(465\) −4.39229 −0.203688
\(466\) −5.39989 −0.250145
\(467\) 18.8812 0.873718 0.436859 0.899530i \(-0.356091\pi\)
0.436859 + 0.899530i \(0.356091\pi\)
\(468\) 13.5197 0.624950
\(469\) 2.70719 0.125007
\(470\) 3.69739 0.170548
\(471\) −7.46523 −0.343980
\(472\) −13.6494 −0.628266
\(473\) 9.03569 0.415461
\(474\) −18.4806 −0.848844
\(475\) −3.26056 −0.149605
\(476\) 14.1160 0.647004
\(477\) −12.2112 −0.559111
\(478\) 55.0576 2.51828
\(479\) −5.35204 −0.244541 −0.122271 0.992497i \(-0.539018\pi\)
−0.122271 + 0.992497i \(0.539018\pi\)
\(480\) 16.2304 0.740812
\(481\) 24.5063 1.11739
\(482\) −23.1904 −1.05629
\(483\) 9.72424 0.442468
\(484\) −4.00065 −0.181848
\(485\) −6.32500 −0.287203
\(486\) −24.4968 −1.11120
\(487\) −18.9679 −0.859517 −0.429759 0.902944i \(-0.641401\pi\)
−0.429759 + 0.902944i \(0.641401\pi\)
\(488\) −6.70860 −0.303684
\(489\) −18.4725 −0.835356
\(490\) 2.12264 0.0958910
\(491\) −26.3558 −1.18942 −0.594710 0.803940i \(-0.702733\pi\)
−0.594710 + 0.803940i \(0.702733\pi\)
\(492\) 46.7803 2.10902
\(493\) 19.7753 0.890636
\(494\) 31.9158 1.43596
\(495\) −3.58808 −0.161272
\(496\) 5.87880 0.263966
\(497\) −11.6344 −0.521874
\(498\) 57.7152 2.58628
\(499\) 2.51107 0.112411 0.0562054 0.998419i \(-0.482100\pi\)
0.0562054 + 0.998419i \(0.482100\pi\)
\(500\) −2.50559 −0.112053
\(501\) −34.8495 −1.55696
\(502\) 23.1286 1.03228
\(503\) −14.0204 −0.625138 −0.312569 0.949895i \(-0.601190\pi\)
−0.312569 + 0.949895i \(0.601190\pi\)
\(504\) 1.25573 0.0559347
\(505\) −0.223535 −0.00994717
\(506\) −30.9955 −1.37792
\(507\) −16.8787 −0.749607
\(508\) −24.6197 −1.09232
\(509\) 17.3762 0.770189 0.385094 0.922877i \(-0.374169\pi\)
0.385094 + 0.922877i \(0.374169\pi\)
\(510\) 24.4202 1.08134
\(511\) −7.59479 −0.335974
\(512\) −27.5898 −1.21931
\(513\) −12.1841 −0.537942
\(514\) −18.1555 −0.800804
\(515\) −8.72842 −0.384620
\(516\) −15.0766 −0.663711
\(517\) 5.34146 0.234917
\(518\) 11.2802 0.495624
\(519\) −34.8636 −1.53034
\(520\) 4.94894 0.217026
\(521\) −34.0736 −1.49279 −0.746395 0.665503i \(-0.768217\pi\)
−0.746395 + 0.665503i \(0.768217\pi\)
\(522\) 8.71807 0.381580
\(523\) 23.6750 1.03523 0.517617 0.855612i \(-0.326819\pi\)
0.517617 + 0.855612i \(0.326819\pi\)
\(524\) −17.2570 −0.753877
\(525\) 2.04208 0.0891237
\(526\) 56.9658 2.48383
\(527\) 12.1176 0.527853
\(528\) 17.1153 0.744847
\(529\) −0.324034 −0.0140885
\(530\) −22.1519 −0.962219
\(531\) 14.8820 0.645822
\(532\) 8.16964 0.354199
\(533\) −42.1615 −1.82622
\(534\) −16.3811 −0.708878
\(535\) 12.2087 0.527827
\(536\) 2.90532 0.125491
\(537\) 34.7193 1.49825
\(538\) −49.2372 −2.12277
\(539\) 3.06648 0.132083
\(540\) −9.36293 −0.402916
\(541\) −0.272589 −0.0117195 −0.00585976 0.999983i \(-0.501865\pi\)
−0.00585976 + 0.999983i \(0.501865\pi\)
\(542\) 35.1300 1.50896
\(543\) −7.23661 −0.310553
\(544\) −44.7771 −1.91980
\(545\) 6.81227 0.291806
\(546\) −19.9888 −0.855440
\(547\) 2.18910 0.0935991 0.0467995 0.998904i \(-0.485098\pi\)
0.0467995 + 0.998904i \(0.485098\pi\)
\(548\) −22.3148 −0.953242
\(549\) 7.31438 0.312170
\(550\) −6.50903 −0.277546
\(551\) 11.4450 0.487573
\(552\) 10.4359 0.444183
\(553\) 4.26352 0.181303
\(554\) −50.1927 −2.13248
\(555\) 10.8521 0.460647
\(556\) 33.1947 1.40777
\(557\) −10.6716 −0.452169 −0.226085 0.974108i \(-0.572593\pi\)
−0.226085 + 0.974108i \(0.572593\pi\)
\(558\) 5.34214 0.226151
\(559\) 13.5881 0.574714
\(560\) −2.73319 −0.115499
\(561\) 35.2788 1.48947
\(562\) 23.6377 0.997097
\(563\) −42.5192 −1.79197 −0.895986 0.444083i \(-0.853529\pi\)
−0.895986 + 0.444083i \(0.853529\pi\)
\(564\) −8.91256 −0.375286
\(565\) −11.5652 −0.486550
\(566\) −34.5466 −1.45210
\(567\) 11.1412 0.467885
\(568\) −12.4859 −0.523896
\(569\) 39.2890 1.64708 0.823541 0.567256i \(-0.191995\pi\)
0.823541 + 0.567256i \(0.191995\pi\)
\(570\) 14.1332 0.591976
\(571\) 31.3362 1.31138 0.655689 0.755031i \(-0.272378\pi\)
0.655689 + 0.755031i \(0.272378\pi\)
\(572\) 35.4313 1.48146
\(573\) 51.3599 2.14559
\(574\) −19.4069 −0.810027
\(575\) 4.76193 0.198586
\(576\) −13.3441 −0.556002
\(577\) 9.38736 0.390801 0.195400 0.980724i \(-0.437399\pi\)
0.195400 + 0.980724i \(0.437399\pi\)
\(578\) −31.2867 −1.30136
\(579\) 22.9954 0.955654
\(580\) 8.79495 0.365190
\(581\) −13.3150 −0.552400
\(582\) 27.4163 1.13644
\(583\) −32.0019 −1.32538
\(584\) −8.15064 −0.337276
\(585\) −5.39583 −0.223090
\(586\) −44.6618 −1.84496
\(587\) −22.9190 −0.945968 −0.472984 0.881071i \(-0.656823\pi\)
−0.472984 + 0.881071i \(0.656823\pi\)
\(588\) −5.11662 −0.211006
\(589\) 7.01311 0.288970
\(590\) 26.9969 1.11145
\(591\) 11.7990 0.485344
\(592\) −14.5249 −0.596968
\(593\) −7.94890 −0.326422 −0.163211 0.986591i \(-0.552185\pi\)
−0.163211 + 0.986591i \(0.552185\pi\)
\(594\) −24.3230 −0.997986
\(595\) −5.63379 −0.230963
\(596\) −22.5205 −0.922475
\(597\) 20.7624 0.849749
\(598\) −46.6118 −1.90610
\(599\) 37.2515 1.52205 0.761027 0.648720i \(-0.224695\pi\)
0.761027 + 0.648720i \(0.224695\pi\)
\(600\) 2.19154 0.0894691
\(601\) −7.57068 −0.308814 −0.154407 0.988007i \(-0.549347\pi\)
−0.154407 + 0.988007i \(0.549347\pi\)
\(602\) 6.25456 0.254917
\(603\) −3.16767 −0.128998
\(604\) −33.4397 −1.36064
\(605\) 1.59669 0.0649146
\(606\) 0.968934 0.0393602
\(607\) −34.3256 −1.39323 −0.696617 0.717443i \(-0.745312\pi\)
−0.696617 + 0.717443i \(0.745312\pi\)
\(608\) −25.9148 −1.05098
\(609\) −7.16797 −0.290461
\(610\) 13.2688 0.537239
\(611\) 8.03260 0.324964
\(612\) −16.5170 −0.667661
\(613\) 29.1949 1.17917 0.589585 0.807707i \(-0.299292\pi\)
0.589585 + 0.807707i \(0.299292\pi\)
\(614\) 63.1158 2.54715
\(615\) −18.6704 −0.752861
\(616\) 3.29091 0.132595
\(617\) −30.7230 −1.23686 −0.618430 0.785840i \(-0.712231\pi\)
−0.618430 + 0.785840i \(0.712231\pi\)
\(618\) 37.8342 1.52192
\(619\) 24.3738 0.979666 0.489833 0.871816i \(-0.337058\pi\)
0.489833 + 0.871816i \(0.337058\pi\)
\(620\) 5.38925 0.216437
\(621\) 17.7944 0.714066
\(622\) −62.8144 −2.51863
\(623\) 3.77914 0.151408
\(624\) 25.7383 1.03036
\(625\) 1.00000 0.0400000
\(626\) 73.0415 2.91933
\(627\) 20.4177 0.815403
\(628\) 9.15968 0.365511
\(629\) −29.9393 −1.19376
\(630\) −2.48369 −0.0989525
\(631\) −1.75619 −0.0699129 −0.0349564 0.999389i \(-0.511129\pi\)
−0.0349564 + 0.999389i \(0.511129\pi\)
\(632\) 4.57556 0.182006
\(633\) −51.7143 −2.05546
\(634\) 3.76607 0.149570
\(635\) 9.82591 0.389929
\(636\) 53.3973 2.11734
\(637\) 4.61144 0.182712
\(638\) 22.8475 0.904543
\(639\) 13.6133 0.538536
\(640\) −8.31117 −0.328528
\(641\) 18.8825 0.745816 0.372908 0.927868i \(-0.378361\pi\)
0.372908 + 0.927868i \(0.378361\pi\)
\(642\) −52.9197 −2.08857
\(643\) 2.69666 0.106346 0.0531730 0.998585i \(-0.483067\pi\)
0.0531730 + 0.998585i \(0.483067\pi\)
\(644\) −11.9314 −0.470165
\(645\) 6.01719 0.236927
\(646\) −38.9914 −1.53410
\(647\) −10.7195 −0.421426 −0.210713 0.977548i \(-0.567579\pi\)
−0.210713 + 0.977548i \(0.567579\pi\)
\(648\) 11.9566 0.469698
\(649\) 39.0013 1.53093
\(650\) −9.78843 −0.383934
\(651\) −4.39229 −0.172147
\(652\) 22.6654 0.887646
\(653\) −34.9606 −1.36811 −0.684057 0.729429i \(-0.739786\pi\)
−0.684057 + 0.729429i \(0.739786\pi\)
\(654\) −29.5285 −1.15465
\(655\) 6.88741 0.269113
\(656\) 24.9891 0.975659
\(657\) 8.88663 0.346701
\(658\) 3.69739 0.144139
\(659\) 21.1440 0.823653 0.411826 0.911262i \(-0.364891\pi\)
0.411826 + 0.911262i \(0.364891\pi\)
\(660\) 15.6900 0.610733
\(661\) 18.2657 0.710455 0.355227 0.934780i \(-0.384403\pi\)
0.355227 + 0.934780i \(0.384403\pi\)
\(662\) 51.2066 1.99020
\(663\) 53.0530 2.06041
\(664\) −14.2895 −0.554540
\(665\) −3.26056 −0.126439
\(666\) −13.1989 −0.511448
\(667\) −16.7150 −0.647207
\(668\) 42.7596 1.65442
\(669\) −30.1792 −1.16680
\(670\) −5.74639 −0.222002
\(671\) 19.1689 0.740006
\(672\) 16.2304 0.626100
\(673\) 25.0722 0.966464 0.483232 0.875492i \(-0.339463\pi\)
0.483232 + 0.875492i \(0.339463\pi\)
\(674\) 22.2887 0.858528
\(675\) 3.73681 0.143830
\(676\) 20.7098 0.796529
\(677\) −42.5619 −1.63579 −0.817893 0.575371i \(-0.804858\pi\)
−0.817893 + 0.575371i \(0.804858\pi\)
\(678\) 50.1303 1.92524
\(679\) −6.32500 −0.242731
\(680\) −6.04611 −0.231858
\(681\) 53.1122 2.03526
\(682\) 14.0002 0.536095
\(683\) −40.4792 −1.54890 −0.774448 0.632638i \(-0.781972\pi\)
−0.774448 + 0.632638i \(0.781972\pi\)
\(684\) −9.55925 −0.365507
\(685\) 8.90601 0.340281
\(686\) 2.12264 0.0810427
\(687\) −2.04208 −0.0779103
\(688\) −8.05362 −0.307042
\(689\) −48.1252 −1.83343
\(690\) −20.6410 −0.785791
\(691\) 25.5214 0.970881 0.485440 0.874270i \(-0.338659\pi\)
0.485440 + 0.874270i \(0.338659\pi\)
\(692\) 42.7769 1.62613
\(693\) −3.58808 −0.136300
\(694\) −5.91305 −0.224456
\(695\) −13.2483 −0.502535
\(696\) −7.69258 −0.291586
\(697\) 51.5086 1.95103
\(698\) 38.3512 1.45162
\(699\) −5.19495 −0.196491
\(700\) −2.50559 −0.0947025
\(701\) 36.6153 1.38294 0.691470 0.722405i \(-0.256963\pi\)
0.691470 + 0.722405i \(0.256963\pi\)
\(702\) −36.5775 −1.38053
\(703\) −17.3274 −0.653516
\(704\) −34.9709 −1.31802
\(705\) 3.55707 0.133967
\(706\) 57.0380 2.14665
\(707\) −0.223535 −0.00840689
\(708\) −65.0762 −2.44571
\(709\) 39.2437 1.47383 0.736915 0.675986i \(-0.236282\pi\)
0.736915 + 0.675986i \(0.236282\pi\)
\(710\) 24.6956 0.926809
\(711\) −4.98872 −0.187092
\(712\) 4.05573 0.151995
\(713\) −10.2424 −0.383580
\(714\) 24.4202 0.913903
\(715\) −14.1409 −0.528840
\(716\) −42.5999 −1.59203
\(717\) 52.9681 1.97813
\(718\) 62.1647 2.31997
\(719\) 1.23151 0.0459274 0.0229637 0.999736i \(-0.492690\pi\)
0.0229637 + 0.999736i \(0.492690\pi\)
\(720\) 3.19810 0.119186
\(721\) −8.72842 −0.325064
\(722\) 17.7638 0.661100
\(723\) −22.3103 −0.829727
\(724\) 8.87917 0.329992
\(725\) −3.51013 −0.130363
\(726\) −6.92100 −0.256862
\(727\) 34.6280 1.28428 0.642140 0.766587i \(-0.278047\pi\)
0.642140 + 0.766587i \(0.278047\pi\)
\(728\) 4.94894 0.183420
\(729\) 9.85641 0.365052
\(730\) 16.1210 0.596665
\(731\) −16.6005 −0.613992
\(732\) −31.9845 −1.18218
\(733\) 4.30702 0.159083 0.0795416 0.996832i \(-0.474654\pi\)
0.0795416 + 0.996832i \(0.474654\pi\)
\(734\) −49.1911 −1.81568
\(735\) 2.04208 0.0753233
\(736\) 37.8476 1.39508
\(737\) −8.30156 −0.305792
\(738\) 22.7079 0.835889
\(739\) −15.0350 −0.553072 −0.276536 0.961004i \(-0.589187\pi\)
−0.276536 + 0.961004i \(0.589187\pi\)
\(740\) −13.3153 −0.489481
\(741\) 30.7045 1.12796
\(742\) −22.1519 −0.813223
\(743\) −14.3180 −0.525278 −0.262639 0.964894i \(-0.584593\pi\)
−0.262639 + 0.964894i \(0.584593\pi\)
\(744\) −4.71375 −0.172814
\(745\) 8.98809 0.329298
\(746\) 35.5046 1.29992
\(747\) 15.5798 0.570036
\(748\) −43.2864 −1.58271
\(749\) 12.2087 0.446095
\(750\) −4.33460 −0.158277
\(751\) 44.7372 1.63248 0.816242 0.577710i \(-0.196054\pi\)
0.816242 + 0.577710i \(0.196054\pi\)
\(752\) −4.76091 −0.173612
\(753\) 22.2509 0.810866
\(754\) 34.3586 1.25127
\(755\) 13.3460 0.485712
\(756\) −9.36293 −0.340526
\(757\) 42.4048 1.54123 0.770614 0.637302i \(-0.219950\pi\)
0.770614 + 0.637302i \(0.219950\pi\)
\(758\) −62.9178 −2.28528
\(759\) −29.8192 −1.08237
\(760\) −3.49919 −0.126929
\(761\) −5.37407 −0.194810 −0.0974050 0.995245i \(-0.531054\pi\)
−0.0974050 + 0.995245i \(0.531054\pi\)
\(762\) −42.5914 −1.54292
\(763\) 6.81227 0.246621
\(764\) −63.0175 −2.27989
\(765\) 6.59207 0.238337
\(766\) 19.7174 0.712418
\(767\) 58.6510 2.11777
\(768\) −10.5512 −0.380734
\(769\) 45.2364 1.63127 0.815633 0.578570i \(-0.196389\pi\)
0.815633 + 0.578570i \(0.196389\pi\)
\(770\) −6.50903 −0.234569
\(771\) −17.4665 −0.629039
\(772\) −28.2148 −1.01547
\(773\) 42.2415 1.51932 0.759660 0.650320i \(-0.225365\pi\)
0.759660 + 0.650320i \(0.225365\pi\)
\(774\) −7.31843 −0.263056
\(775\) −2.15089 −0.0772622
\(776\) −6.78791 −0.243672
\(777\) 10.8521 0.389317
\(778\) −71.1952 −2.55247
\(779\) 29.8107 1.06808
\(780\) 23.5950 0.844837
\(781\) 35.6766 1.27661
\(782\) 56.9455 2.03637
\(783\) −13.1167 −0.468753
\(784\) −2.73319 −0.0976141
\(785\) −3.65570 −0.130477
\(786\) −29.8542 −1.06486
\(787\) 8.00191 0.285237 0.142619 0.989778i \(-0.454448\pi\)
0.142619 + 0.989778i \(0.454448\pi\)
\(788\) −14.4771 −0.515724
\(789\) 54.8039 1.95107
\(790\) −9.04991 −0.321981
\(791\) −11.5652 −0.411210
\(792\) −3.85068 −0.136828
\(793\) 28.8266 1.02366
\(794\) −24.4694 −0.868388
\(795\) −21.3112 −0.755832
\(796\) −25.4751 −0.902939
\(797\) 25.2981 0.896105 0.448053 0.894007i \(-0.352118\pi\)
0.448053 + 0.894007i \(0.352118\pi\)
\(798\) 14.1332 0.500311
\(799\) −9.81340 −0.347173
\(800\) 7.94796 0.281003
\(801\) −4.42195 −0.156242
\(802\) −55.3151 −1.95324
\(803\) 23.2893 0.821862
\(804\) 13.8517 0.488511
\(805\) 4.76193 0.167836
\(806\) 21.0538 0.741589
\(807\) −47.3686 −1.66745
\(808\) −0.239895 −0.00843947
\(809\) 55.1741 1.93982 0.969908 0.243470i \(-0.0782858\pi\)
0.969908 + 0.243470i \(0.0782858\pi\)
\(810\) −23.6487 −0.830929
\(811\) 7.02071 0.246531 0.123265 0.992374i \(-0.460663\pi\)
0.123265 + 0.992374i \(0.460663\pi\)
\(812\) 8.79495 0.308642
\(813\) 33.7968 1.18530
\(814\) −34.5906 −1.21240
\(815\) −9.04593 −0.316865
\(816\) −31.4444 −1.10078
\(817\) −9.60756 −0.336126
\(818\) −16.1789 −0.565680
\(819\) −5.39583 −0.188546
\(820\) 22.9081 0.799987
\(821\) −19.9345 −0.695719 −0.347860 0.937547i \(-0.613091\pi\)
−0.347860 + 0.937547i \(0.613091\pi\)
\(822\) −38.6040 −1.34647
\(823\) 12.8969 0.449559 0.224780 0.974410i \(-0.427834\pi\)
0.224780 + 0.974410i \(0.427834\pi\)
\(824\) −9.36724 −0.326323
\(825\) −6.26201 −0.218015
\(826\) 26.9969 0.939344
\(827\) 17.2107 0.598476 0.299238 0.954178i \(-0.403268\pi\)
0.299238 + 0.954178i \(0.403268\pi\)
\(828\) 13.9609 0.485176
\(829\) −16.0537 −0.557569 −0.278785 0.960354i \(-0.589932\pi\)
−0.278785 + 0.960354i \(0.589932\pi\)
\(830\) 28.2630 0.981022
\(831\) −48.2878 −1.67509
\(832\) −52.5900 −1.82323
\(833\) −5.63379 −0.195199
\(834\) 57.4259 1.98850
\(835\) −17.0657 −0.590582
\(836\) −25.0520 −0.866443
\(837\) −8.03747 −0.277816
\(838\) −3.20248 −0.110628
\(839\) 41.4646 1.43152 0.715758 0.698348i \(-0.246081\pi\)
0.715758 + 0.698348i \(0.246081\pi\)
\(840\) 2.19154 0.0756152
\(841\) −16.6790 −0.575137
\(842\) −6.06071 −0.208866
\(843\) 22.7406 0.783229
\(844\) 63.4523 2.18412
\(845\) −8.26542 −0.284339
\(846\) −4.32630 −0.148741
\(847\) 1.59669 0.0548628
\(848\) 28.5237 0.979509
\(849\) −33.2355 −1.14064
\(850\) 11.9585 0.410173
\(851\) 25.3060 0.867480
\(852\) −59.5288 −2.03942
\(853\) 11.1093 0.380377 0.190188 0.981748i \(-0.439090\pi\)
0.190188 + 0.981748i \(0.439090\pi\)
\(854\) 13.2688 0.454049
\(855\) 3.81517 0.130476
\(856\) 13.1022 0.447824
\(857\) −21.6269 −0.738760 −0.369380 0.929278i \(-0.620430\pi\)
−0.369380 + 0.929278i \(0.620430\pi\)
\(858\) 61.2952 2.09258
\(859\) 38.1861 1.30289 0.651446 0.758695i \(-0.274163\pi\)
0.651446 + 0.758695i \(0.274163\pi\)
\(860\) −7.38297 −0.251757
\(861\) −18.6704 −0.636284
\(862\) 39.8479 1.35723
\(863\) −55.7673 −1.89834 −0.949171 0.314760i \(-0.898076\pi\)
−0.949171 + 0.314760i \(0.898076\pi\)
\(864\) 29.7000 1.01042
\(865\) −17.0726 −0.580485
\(866\) −53.7935 −1.82798
\(867\) −30.0994 −1.02223
\(868\) 5.38925 0.182923
\(869\) −13.0740 −0.443505
\(870\) 15.2150 0.515837
\(871\) −12.4841 −0.423006
\(872\) 7.31085 0.247576
\(873\) 7.40085 0.250481
\(874\) 32.9573 1.11480
\(875\) 1.00000 0.0338062
\(876\) −38.8597 −1.31295
\(877\) −8.33568 −0.281476 −0.140738 0.990047i \(-0.544948\pi\)
−0.140738 + 0.990047i \(0.544948\pi\)
\(878\) 45.1295 1.52305
\(879\) −42.9668 −1.44923
\(880\) 8.38129 0.282533
\(881\) −15.6621 −0.527669 −0.263834 0.964568i \(-0.584987\pi\)
−0.263834 + 0.964568i \(0.584987\pi\)
\(882\) −2.48369 −0.0836301
\(883\) 12.1951 0.410398 0.205199 0.978720i \(-0.434216\pi\)
0.205199 + 0.978720i \(0.434216\pi\)
\(884\) −65.0950 −2.18938
\(885\) 25.9724 0.873052
\(886\) −10.3875 −0.348973
\(887\) 43.0680 1.44608 0.723040 0.690806i \(-0.242744\pi\)
0.723040 + 0.690806i \(0.242744\pi\)
\(888\) 11.6464 0.390826
\(889\) 9.82591 0.329550
\(890\) −8.02175 −0.268890
\(891\) −34.1642 −1.14454
\(892\) 37.0293 1.23983
\(893\) −5.67952 −0.190058
\(894\) −38.9598 −1.30301
\(895\) 17.0019 0.568312
\(896\) −8.31117 −0.277657
\(897\) −44.8428 −1.49726
\(898\) 28.2747 0.943539
\(899\) 7.54990 0.251803
\(900\) 2.93178 0.0977260
\(901\) 58.7944 1.95873
\(902\) 59.5108 1.98149
\(903\) 6.01719 0.200240
\(904\) −12.4116 −0.412803
\(905\) −3.54374 −0.117798
\(906\) −57.8497 −1.92193
\(907\) 51.2419 1.70146 0.850729 0.525604i \(-0.176161\pi\)
0.850729 + 0.525604i \(0.176161\pi\)
\(908\) −65.1675 −2.16266
\(909\) 0.261557 0.00867530
\(910\) −9.78843 −0.324483
\(911\) −8.94013 −0.296200 −0.148100 0.988972i \(-0.547316\pi\)
−0.148100 + 0.988972i \(0.547316\pi\)
\(912\) −18.1985 −0.602613
\(913\) 40.8303 1.35128
\(914\) −84.7791 −2.80424
\(915\) 12.7652 0.422006
\(916\) 2.50559 0.0827871
\(917\) 6.88741 0.227442
\(918\) 44.6866 1.47488
\(919\) 22.2120 0.732707 0.366354 0.930476i \(-0.380606\pi\)
0.366354 + 0.930476i \(0.380606\pi\)
\(920\) 5.11044 0.168486
\(921\) 60.7205 2.00081
\(922\) −12.2740 −0.404221
\(923\) 53.6513 1.76596
\(924\) 15.6900 0.516164
\(925\) 5.31424 0.174731
\(926\) −53.1736 −1.74739
\(927\) 10.2131 0.335442
\(928\) −27.8984 −0.915809
\(929\) 15.5265 0.509408 0.254704 0.967019i \(-0.418022\pi\)
0.254704 + 0.967019i \(0.418022\pi\)
\(930\) 9.32324 0.305721
\(931\) −3.26056 −0.106861
\(932\) 6.37410 0.208791
\(933\) −60.4305 −1.97841
\(934\) −40.0780 −1.31139
\(935\) 17.2759 0.564983
\(936\) −5.79074 −0.189276
\(937\) 7.01098 0.229039 0.114519 0.993421i \(-0.463467\pi\)
0.114519 + 0.993421i \(0.463467\pi\)
\(938\) −5.74639 −0.187626
\(939\) 70.2695 2.29316
\(940\) −4.36445 −0.142353
\(941\) 26.1510 0.852499 0.426250 0.904606i \(-0.359835\pi\)
0.426250 + 0.904606i \(0.359835\pi\)
\(942\) 15.8460 0.516290
\(943\) −43.5374 −1.41777
\(944\) −34.7624 −1.13142
\(945\) 3.73681 0.121559
\(946\) −19.1795 −0.623579
\(947\) 39.6232 1.28758 0.643791 0.765202i \(-0.277361\pi\)
0.643791 + 0.765202i \(0.277361\pi\)
\(948\) 21.8148 0.708512
\(949\) 35.0230 1.13689
\(950\) 6.92099 0.224547
\(951\) 3.62314 0.117488
\(952\) −6.04611 −0.195956
\(953\) 42.3360 1.37140 0.685699 0.727886i \(-0.259497\pi\)
0.685699 + 0.727886i \(0.259497\pi\)
\(954\) 25.9199 0.839187
\(955\) 25.1507 0.813859
\(956\) −64.9908 −2.10195
\(957\) 21.9805 0.710527
\(958\) 11.3605 0.367040
\(959\) 8.90601 0.287590
\(960\) −23.2884 −0.751630
\(961\) −26.3737 −0.850764
\(962\) −52.0181 −1.67713
\(963\) −14.2853 −0.460337
\(964\) 27.3742 0.881664
\(965\) 11.2607 0.362496
\(966\) −20.6410 −0.664115
\(967\) −23.7374 −0.763342 −0.381671 0.924298i \(-0.624651\pi\)
−0.381671 + 0.924298i \(0.624651\pi\)
\(968\) 1.71354 0.0550754
\(969\) −37.5116 −1.20505
\(970\) 13.4257 0.431073
\(971\) −15.0226 −0.482097 −0.241049 0.970513i \(-0.577491\pi\)
−0.241049 + 0.970513i \(0.577491\pi\)
\(972\) 28.9163 0.927491
\(973\) −13.2483 −0.424720
\(974\) 40.2620 1.29008
\(975\) −9.41694 −0.301584
\(976\) −17.0855 −0.546892
\(977\) 10.2097 0.326637 0.163319 0.986573i \(-0.447780\pi\)
0.163319 + 0.986573i \(0.447780\pi\)
\(978\) 39.2105 1.25381
\(979\) −11.5887 −0.370375
\(980\) −2.50559 −0.0800382
\(981\) −7.97101 −0.254495
\(982\) 55.9438 1.78524
\(983\) 9.38284 0.299266 0.149633 0.988742i \(-0.452191\pi\)
0.149633 + 0.988742i \(0.452191\pi\)
\(984\) −20.0368 −0.638749
\(985\) 5.77791 0.184099
\(986\) −41.9758 −1.33678
\(987\) 3.55707 0.113223
\(988\) −37.6738 −1.19856
\(989\) 14.0315 0.446175
\(990\) 7.61619 0.242058
\(991\) 2.18631 0.0694503 0.0347251 0.999397i \(-0.488944\pi\)
0.0347251 + 0.999397i \(0.488944\pi\)
\(992\) −17.0952 −0.542772
\(993\) 49.2633 1.56332
\(994\) 24.6956 0.783297
\(995\) 10.1673 0.322324
\(996\) −68.1279 −2.15871
\(997\) 58.6579 1.85772 0.928858 0.370436i \(-0.120792\pi\)
0.928858 + 0.370436i \(0.120792\pi\)
\(998\) −5.33008 −0.168721
\(999\) 19.8583 0.628290
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 \(a_p\))