Properties

Label 6001.2.a.b.1.4
Level 6001
Weight 2
Character 6001.1
Self dual Yes
Analytic conductor 47.918
Analytic rank 1
Dimension 114
CM No

Related objects

Downloads

Learn more about

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 1.4
Character \(\chi\) = 6001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.73023 q^{2}\) \(-3.10574 q^{3}\) \(+5.45415 q^{4}\) \(-3.71411 q^{5}\) \(+8.47938 q^{6}\) \(+1.88828 q^{7}\) \(-9.43061 q^{8}\) \(+6.64562 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.73023 q^{2}\) \(-3.10574 q^{3}\) \(+5.45415 q^{4}\) \(-3.71411 q^{5}\) \(+8.47938 q^{6}\) \(+1.88828 q^{7}\) \(-9.43061 q^{8}\) \(+6.64562 q^{9}\) \(+10.1404 q^{10}\) \(+0.489363 q^{11}\) \(-16.9392 q^{12}\) \(+5.48712 q^{13}\) \(-5.15543 q^{14}\) \(+11.5351 q^{15}\) \(+14.8394 q^{16}\) \(+1.00000 q^{17}\) \(-18.1441 q^{18}\) \(-0.332704 q^{19}\) \(-20.2573 q^{20}\) \(-5.86450 q^{21}\) \(-1.33607 q^{22}\) \(+8.82357 q^{23}\) \(+29.2890 q^{24}\) \(+8.79459 q^{25}\) \(-14.9811 q^{26}\) \(-11.3223 q^{27}\) \(+10.2989 q^{28}\) \(+0.482276 q^{29}\) \(-31.4933 q^{30}\) \(-5.74916 q^{31}\) \(-21.6538 q^{32}\) \(-1.51984 q^{33}\) \(-2.73023 q^{34}\) \(-7.01326 q^{35}\) \(+36.2462 q^{36}\) \(+8.83875 q^{37}\) \(+0.908359 q^{38}\) \(-17.0416 q^{39}\) \(+35.0263 q^{40}\) \(-4.82872 q^{41}\) \(+16.0114 q^{42}\) \(+4.70608 q^{43}\) \(+2.66906 q^{44}\) \(-24.6825 q^{45}\) \(-24.0904 q^{46}\) \(-9.37780 q^{47}\) \(-46.0874 q^{48}\) \(-3.43441 q^{49}\) \(-24.0112 q^{50}\) \(-3.10574 q^{51}\) \(+29.9276 q^{52}\) \(+6.17027 q^{53}\) \(+30.9126 q^{54}\) \(-1.81755 q^{55}\) \(-17.8076 q^{56}\) \(+1.03329 q^{57}\) \(-1.31672 q^{58}\) \(+1.46121 q^{59}\) \(+62.9139 q^{60}\) \(-6.01970 q^{61}\) \(+15.6965 q^{62}\) \(+12.5488 q^{63}\) \(+29.4409 q^{64}\) \(-20.3798 q^{65}\) \(+4.14950 q^{66}\) \(+6.95743 q^{67}\) \(+5.45415 q^{68}\) \(-27.4037 q^{69}\) \(+19.1478 q^{70}\) \(-10.4009 q^{71}\) \(-62.6722 q^{72}\) \(-14.5071 q^{73}\) \(-24.1318 q^{74}\) \(-27.3137 q^{75}\) \(-1.81462 q^{76}\) \(+0.924054 q^{77}\) \(+46.5274 q^{78}\) \(+3.18488 q^{79}\) \(-55.1152 q^{80}\) \(+15.2274 q^{81}\) \(+13.1835 q^{82}\) \(-7.61897 q^{83}\) \(-31.9858 q^{84}\) \(-3.71411 q^{85}\) \(-12.8487 q^{86}\) \(-1.49782 q^{87}\) \(-4.61500 q^{88}\) \(-10.6162 q^{89}\) \(+67.3890 q^{90}\) \(+10.3612 q^{91}\) \(+48.1250 q^{92}\) \(+17.8554 q^{93}\) \(+25.6035 q^{94}\) \(+1.23570 q^{95}\) \(+67.2510 q^{96}\) \(-13.5666 q^{97}\) \(+9.37672 q^{98}\) \(+3.25212 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut -\mathstrut 19q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 49q^{12} \) \(\mathstrut -\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 39q^{15} \) \(\mathstrut +\mathstrut 110q^{16} \) \(\mathstrut +\mathstrut 114q^{17} \) \(\mathstrut -\mathstrut 21q^{18} \) \(\mathstrut -\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 88q^{20} \) \(\mathstrut -\mathstrut 30q^{21} \) \(\mathstrut -\mathstrut 36q^{22} \) \(\mathstrut -\mathstrut 77q^{23} \) \(\mathstrut -\mathstrut 72q^{24} \) \(\mathstrut +\mathstrut 119q^{25} \) \(\mathstrut -\mathstrut 79q^{26} \) \(\mathstrut -\mathstrut 77q^{27} \) \(\mathstrut -\mathstrut 92q^{28} \) \(\mathstrut -\mathstrut 65q^{29} \) \(\mathstrut -\mathstrut 10q^{30} \) \(\mathstrut -\mathstrut 131q^{31} \) \(\mathstrut -\mathstrut 30q^{32} \) \(\mathstrut -\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 33q^{35} \) \(\mathstrut +\mathstrut 109q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 14q^{38} \) \(\mathstrut -\mathstrut 83q^{39} \) \(\mathstrut -\mathstrut 42q^{40} \) \(\mathstrut -\mathstrut 99q^{41} \) \(\mathstrut +\mathstrut 29q^{42} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 98q^{44} \) \(\mathstrut -\mathstrut 73q^{45} \) \(\mathstrut -\mathstrut 35q^{46} \) \(\mathstrut -\mathstrut 113q^{47} \) \(\mathstrut -\mathstrut 86q^{48} \) \(\mathstrut +\mathstrut 101q^{49} \) \(\mathstrut -\mathstrut 44q^{50} \) \(\mathstrut -\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut 3q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut -\mathstrut 78q^{54} \) \(\mathstrut -\mathstrut 63q^{55} \) \(\mathstrut -\mathstrut 117q^{56} \) \(\mathstrut -\mathstrut 64q^{57} \) \(\mathstrut -\mathstrut 31q^{58} \) \(\mathstrut -\mathstrut 134q^{59} \) \(\mathstrut -\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 30q^{61} \) \(\mathstrut -\mathstrut 30q^{62} \) \(\mathstrut -\mathstrut 154q^{63} \) \(\mathstrut +\mathstrut 117q^{64} \) \(\mathstrut -\mathstrut 66q^{65} \) \(\mathstrut -\mathstrut 12q^{66} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut +\mathstrut 110q^{68} \) \(\mathstrut -\mathstrut 35q^{69} \) \(\mathstrut +\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 233q^{71} \) \(\mathstrut +\mathstrut 16q^{72} \) \(\mathstrut -\mathstrut 56q^{73} \) \(\mathstrut -\mathstrut 64q^{74} \) \(\mathstrut -\mathstrut 100q^{75} \) \(\mathstrut -\mathstrut 64q^{76} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 50q^{78} \) \(\mathstrut -\mathstrut 154q^{79} \) \(\mathstrut -\mathstrut 128q^{80} \) \(\mathstrut +\mathstrut 118q^{81} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 53q^{83} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 27q^{85} \) \(\mathstrut -\mathstrut 52q^{86} \) \(\mathstrut -\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 52q^{88} \) \(\mathstrut -\mathstrut 118q^{89} \) \(\mathstrut -\mathstrut 5q^{90} \) \(\mathstrut -\mathstrut 95q^{91} \) \(\mathstrut -\mathstrut 102q^{92} \) \(\mathstrut +\mathstrut 47q^{93} \) \(\mathstrut -\mathstrut 3q^{94} \) \(\mathstrut -\mathstrut 158q^{95} \) \(\mathstrut -\mathstrut 144q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut +\mathstrut 3q^{98} \) \(\mathstrut -\mathstrut 131q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.73023 −1.93056 −0.965281 0.261212i \(-0.915878\pi\)
−0.965281 + 0.261212i \(0.915878\pi\)
\(3\) −3.10574 −1.79310 −0.896550 0.442943i \(-0.853934\pi\)
−0.896550 + 0.442943i \(0.853934\pi\)
\(4\) 5.45415 2.72707
\(5\) −3.71411 −1.66100 −0.830500 0.557019i \(-0.811945\pi\)
−0.830500 + 0.557019i \(0.811945\pi\)
\(6\) 8.47938 3.46169
\(7\) 1.88828 0.713702 0.356851 0.934161i \(-0.383850\pi\)
0.356851 + 0.934161i \(0.383850\pi\)
\(8\) −9.43061 −3.33422
\(9\) 6.64562 2.21521
\(10\) 10.1404 3.20666
\(11\) 0.489363 0.147549 0.0737743 0.997275i \(-0.476496\pi\)
0.0737743 + 0.997275i \(0.476496\pi\)
\(12\) −16.9392 −4.88991
\(13\) 5.48712 1.52185 0.760927 0.648838i \(-0.224745\pi\)
0.760927 + 0.648838i \(0.224745\pi\)
\(14\) −5.15543 −1.37785
\(15\) 11.5351 2.97834
\(16\) 14.8394 3.70986
\(17\) 1.00000 0.242536
\(18\) −18.1441 −4.27660
\(19\) −0.332704 −0.0763276 −0.0381638 0.999271i \(-0.512151\pi\)
−0.0381638 + 0.999271i \(0.512151\pi\)
\(20\) −20.2573 −4.52967
\(21\) −5.86450 −1.27974
\(22\) −1.33607 −0.284852
\(23\) 8.82357 1.83984 0.919921 0.392104i \(-0.128253\pi\)
0.919921 + 0.392104i \(0.128253\pi\)
\(24\) 29.2890 5.97860
\(25\) 8.79459 1.75892
\(26\) −14.9811 −2.93803
\(27\) −11.3223 −2.17899
\(28\) 10.2989 1.94632
\(29\) 0.482276 0.0895564 0.0447782 0.998997i \(-0.485742\pi\)
0.0447782 + 0.998997i \(0.485742\pi\)
\(30\) −31.4933 −5.74987
\(31\) −5.74916 −1.03258 −0.516290 0.856414i \(-0.672687\pi\)
−0.516290 + 0.856414i \(0.672687\pi\)
\(32\) −21.6538 −3.82789
\(33\) −1.51984 −0.264569
\(34\) −2.73023 −0.468230
\(35\) −7.01326 −1.18546
\(36\) 36.2462 6.04103
\(37\) 8.83875 1.45308 0.726541 0.687124i \(-0.241127\pi\)
0.726541 + 0.687124i \(0.241127\pi\)
\(38\) 0.908359 0.147355
\(39\) −17.0416 −2.72883
\(40\) 35.0263 5.53814
\(41\) −4.82872 −0.754120 −0.377060 0.926189i \(-0.623065\pi\)
−0.377060 + 0.926189i \(0.623065\pi\)
\(42\) 16.0114 2.47061
\(43\) 4.70608 0.717671 0.358836 0.933401i \(-0.383174\pi\)
0.358836 + 0.933401i \(0.383174\pi\)
\(44\) 2.66906 0.402376
\(45\) −24.6825 −3.67946
\(46\) −24.0904 −3.55193
\(47\) −9.37780 −1.36789 −0.683947 0.729532i \(-0.739738\pi\)
−0.683947 + 0.729532i \(0.739738\pi\)
\(48\) −46.0874 −6.65214
\(49\) −3.43441 −0.490630
\(50\) −24.0112 −3.39570
\(51\) −3.10574 −0.434891
\(52\) 29.9276 4.15021
\(53\) 6.17027 0.847552 0.423776 0.905767i \(-0.360704\pi\)
0.423776 + 0.905767i \(0.360704\pi\)
\(54\) 30.9126 4.20667
\(55\) −1.81755 −0.245078
\(56\) −17.8076 −2.37964
\(57\) 1.03329 0.136863
\(58\) −1.31672 −0.172894
\(59\) 1.46121 0.190234 0.0951170 0.995466i \(-0.469677\pi\)
0.0951170 + 0.995466i \(0.469677\pi\)
\(60\) 62.9139 8.12214
\(61\) −6.01970 −0.770744 −0.385372 0.922761i \(-0.625927\pi\)
−0.385372 + 0.922761i \(0.625927\pi\)
\(62\) 15.6965 1.99346
\(63\) 12.5488 1.58100
\(64\) 29.4409 3.68012
\(65\) −20.3798 −2.52780
\(66\) 4.14950 0.510768
\(67\) 6.95743 0.849986 0.424993 0.905197i \(-0.360277\pi\)
0.424993 + 0.905197i \(0.360277\pi\)
\(68\) 5.45415 0.661412
\(69\) −27.4037 −3.29902
\(70\) 19.1478 2.28860
\(71\) −10.4009 −1.23436 −0.617181 0.786821i \(-0.711726\pi\)
−0.617181 + 0.786821i \(0.711726\pi\)
\(72\) −62.6722 −7.38599
\(73\) −14.5071 −1.69793 −0.848963 0.528452i \(-0.822773\pi\)
−0.848963 + 0.528452i \(0.822773\pi\)
\(74\) −24.1318 −2.80526
\(75\) −27.3137 −3.15392
\(76\) −1.81462 −0.208151
\(77\) 0.924054 0.105306
\(78\) 46.5274 5.26819
\(79\) 3.18488 0.358327 0.179163 0.983819i \(-0.442661\pi\)
0.179163 + 0.983819i \(0.442661\pi\)
\(80\) −55.1152 −6.16207
\(81\) 15.2274 1.69193
\(82\) 13.1835 1.45588
\(83\) −7.61897 −0.836290 −0.418145 0.908380i \(-0.637320\pi\)
−0.418145 + 0.908380i \(0.637320\pi\)
\(84\) −31.9858 −3.48994
\(85\) −3.71411 −0.402852
\(86\) −12.8487 −1.38551
\(87\) −1.49782 −0.160583
\(88\) −4.61500 −0.491960
\(89\) −10.6162 −1.12531 −0.562657 0.826690i \(-0.690221\pi\)
−0.562657 + 0.826690i \(0.690221\pi\)
\(90\) 67.3890 7.10342
\(91\) 10.3612 1.08615
\(92\) 48.1250 5.01738
\(93\) 17.8554 1.85152
\(94\) 25.6035 2.64080
\(95\) 1.23570 0.126780
\(96\) 67.2510 6.86378
\(97\) −13.5666 −1.37747 −0.688737 0.725011i \(-0.741835\pi\)
−0.688737 + 0.725011i \(0.741835\pi\)
\(98\) 9.37672 0.947192
\(99\) 3.25212 0.326851
\(100\) 47.9670 4.79670
\(101\) 17.6559 1.75682 0.878412 0.477905i \(-0.158604\pi\)
0.878412 + 0.477905i \(0.158604\pi\)
\(102\) 8.47938 0.839584
\(103\) 5.54877 0.546737 0.273368 0.961909i \(-0.411862\pi\)
0.273368 + 0.961909i \(0.411862\pi\)
\(104\) −51.7469 −5.07420
\(105\) 21.7814 2.12564
\(106\) −16.8462 −1.63625
\(107\) −6.62995 −0.640942 −0.320471 0.947258i \(-0.603841\pi\)
−0.320471 + 0.947258i \(0.603841\pi\)
\(108\) −61.7537 −5.94225
\(109\) 3.56639 0.341598 0.170799 0.985306i \(-0.445365\pi\)
0.170799 + 0.985306i \(0.445365\pi\)
\(110\) 4.96232 0.473139
\(111\) −27.4508 −2.60552
\(112\) 28.0209 2.64773
\(113\) 12.7847 1.20268 0.601341 0.798993i \(-0.294633\pi\)
0.601341 + 0.798993i \(0.294633\pi\)
\(114\) −2.82113 −0.264223
\(115\) −32.7717 −3.05598
\(116\) 2.63040 0.244227
\(117\) 36.4653 3.37122
\(118\) −3.98945 −0.367259
\(119\) 1.88828 0.173098
\(120\) −108.783 −9.93044
\(121\) −10.7605 −0.978229
\(122\) 16.4352 1.48797
\(123\) 14.9968 1.35221
\(124\) −31.3568 −2.81592
\(125\) −14.0935 −1.26056
\(126\) −34.2610 −3.05221
\(127\) 4.13427 0.366857 0.183428 0.983033i \(-0.441280\pi\)
0.183428 + 0.983033i \(0.441280\pi\)
\(128\) −37.0729 −3.27682
\(129\) −14.6159 −1.28686
\(130\) 55.6414 4.88007
\(131\) −2.51700 −0.219911 −0.109956 0.993937i \(-0.535071\pi\)
−0.109956 + 0.993937i \(0.535071\pi\)
\(132\) −8.28941 −0.721500
\(133\) −0.628238 −0.0544751
\(134\) −18.9954 −1.64095
\(135\) 42.0524 3.61929
\(136\) −9.43061 −0.808668
\(137\) −4.34490 −0.371210 −0.185605 0.982624i \(-0.559424\pi\)
−0.185605 + 0.982624i \(0.559424\pi\)
\(138\) 74.8184 6.36896
\(139\) −14.4175 −1.22287 −0.611437 0.791293i \(-0.709408\pi\)
−0.611437 + 0.791293i \(0.709408\pi\)
\(140\) −38.2514 −3.23283
\(141\) 29.1250 2.45277
\(142\) 28.3969 2.38302
\(143\) 2.68520 0.224547
\(144\) 98.6171 8.21810
\(145\) −1.79122 −0.148753
\(146\) 39.6077 3.27795
\(147\) 10.6664 0.879748
\(148\) 48.2078 3.96266
\(149\) 8.91601 0.730428 0.365214 0.930924i \(-0.380996\pi\)
0.365214 + 0.930924i \(0.380996\pi\)
\(150\) 74.5727 6.08883
\(151\) −23.3970 −1.90402 −0.952012 0.306062i \(-0.900988\pi\)
−0.952012 + 0.306062i \(0.900988\pi\)
\(152\) 3.13760 0.254493
\(153\) 6.64562 0.537266
\(154\) −2.52288 −0.203299
\(155\) 21.3530 1.71511
\(156\) −92.9472 −7.44173
\(157\) −7.57057 −0.604197 −0.302098 0.953277i \(-0.597687\pi\)
−0.302098 + 0.953277i \(0.597687\pi\)
\(158\) −8.69545 −0.691773
\(159\) −19.1633 −1.51974
\(160\) 80.4245 6.35812
\(161\) 16.6613 1.31310
\(162\) −41.5743 −3.26638
\(163\) −22.9019 −1.79381 −0.896907 0.442219i \(-0.854192\pi\)
−0.896907 + 0.442219i \(0.854192\pi\)
\(164\) −26.3366 −2.05654
\(165\) 5.64483 0.439450
\(166\) 20.8015 1.61451
\(167\) −5.06068 −0.391607 −0.195803 0.980643i \(-0.562731\pi\)
−0.195803 + 0.980643i \(0.562731\pi\)
\(168\) 55.3058 4.26693
\(169\) 17.1085 1.31604
\(170\) 10.1404 0.777730
\(171\) −2.21103 −0.169081
\(172\) 25.6677 1.95714
\(173\) 14.9806 1.13895 0.569477 0.822007i \(-0.307146\pi\)
0.569477 + 0.822007i \(0.307146\pi\)
\(174\) 4.08940 0.310017
\(175\) 16.6066 1.25534
\(176\) 7.26187 0.547384
\(177\) −4.53815 −0.341108
\(178\) 28.9846 2.17249
\(179\) −2.28495 −0.170785 −0.0853924 0.996347i \(-0.527214\pi\)
−0.0853924 + 0.996347i \(0.527214\pi\)
\(180\) −134.622 −10.0341
\(181\) −9.98093 −0.741877 −0.370938 0.928657i \(-0.620964\pi\)
−0.370938 + 0.928657i \(0.620964\pi\)
\(182\) −28.2885 −2.09688
\(183\) 18.6956 1.38202
\(184\) −83.2116 −6.13444
\(185\) −32.8281 −2.41357
\(186\) −48.7493 −3.57447
\(187\) 0.489363 0.0357858
\(188\) −51.1479 −3.73035
\(189\) −21.3797 −1.55515
\(190\) −3.37374 −0.244757
\(191\) 9.37472 0.678331 0.339166 0.940727i \(-0.389855\pi\)
0.339166 + 0.940727i \(0.389855\pi\)
\(192\) −91.4359 −6.59882
\(193\) −3.57459 −0.257305 −0.128652 0.991690i \(-0.541065\pi\)
−0.128652 + 0.991690i \(0.541065\pi\)
\(194\) 37.0398 2.65930
\(195\) 63.2942 4.53259
\(196\) −18.7318 −1.33798
\(197\) −3.72825 −0.265627 −0.132814 0.991141i \(-0.542401\pi\)
−0.132814 + 0.991141i \(0.542401\pi\)
\(198\) −8.87904 −0.631006
\(199\) 16.2589 1.15257 0.576283 0.817250i \(-0.304503\pi\)
0.576283 + 0.817250i \(0.304503\pi\)
\(200\) −82.9384 −5.86463
\(201\) −21.6080 −1.52411
\(202\) −48.2045 −3.39166
\(203\) 0.910670 0.0639165
\(204\) −16.9392 −1.18598
\(205\) 17.9344 1.25259
\(206\) −15.1494 −1.05551
\(207\) 58.6381 4.07563
\(208\) 81.4257 5.64586
\(209\) −0.162813 −0.0112620
\(210\) −59.4681 −4.10369
\(211\) −17.6162 −1.21275 −0.606375 0.795179i \(-0.707377\pi\)
−0.606375 + 0.795179i \(0.707377\pi\)
\(212\) 33.6536 2.31134
\(213\) 32.3026 2.21334
\(214\) 18.1013 1.23738
\(215\) −17.4789 −1.19205
\(216\) 106.777 7.26523
\(217\) −10.8560 −0.736954
\(218\) −9.73705 −0.659476
\(219\) 45.0552 3.04455
\(220\) −9.91318 −0.668346
\(221\) 5.48712 0.369104
\(222\) 74.9471 5.03012
\(223\) 21.3039 1.42662 0.713308 0.700851i \(-0.247196\pi\)
0.713308 + 0.700851i \(0.247196\pi\)
\(224\) −40.8884 −2.73197
\(225\) 58.4455 3.89637
\(226\) −34.9051 −2.32185
\(227\) −23.3592 −1.55040 −0.775201 0.631715i \(-0.782351\pi\)
−0.775201 + 0.631715i \(0.782351\pi\)
\(228\) 5.63573 0.373236
\(229\) 24.0406 1.58865 0.794324 0.607494i \(-0.207825\pi\)
0.794324 + 0.607494i \(0.207825\pi\)
\(230\) 89.4742 5.89975
\(231\) −2.86987 −0.188824
\(232\) −4.54815 −0.298601
\(233\) 24.7168 1.61925 0.809626 0.586946i \(-0.199670\pi\)
0.809626 + 0.586946i \(0.199670\pi\)
\(234\) −99.5586 −6.50835
\(235\) 34.8302 2.27207
\(236\) 7.96968 0.518782
\(237\) −9.89141 −0.642516
\(238\) −5.15543 −0.334177
\(239\) 15.3728 0.994386 0.497193 0.867640i \(-0.334364\pi\)
0.497193 + 0.867640i \(0.334364\pi\)
\(240\) 171.173 11.0492
\(241\) −2.36423 −0.152294 −0.0761468 0.997097i \(-0.524262\pi\)
−0.0761468 + 0.997097i \(0.524262\pi\)
\(242\) 29.3787 1.88853
\(243\) −13.3253 −0.854818
\(244\) −32.8323 −2.10187
\(245\) 12.7558 0.814936
\(246\) −40.9446 −2.61053
\(247\) −1.82559 −0.116159
\(248\) 54.2181 3.44285
\(249\) 23.6625 1.49955
\(250\) 38.4785 2.43360
\(251\) −4.03403 −0.254626 −0.127313 0.991863i \(-0.540635\pi\)
−0.127313 + 0.991863i \(0.540635\pi\)
\(252\) 68.4428 4.31149
\(253\) 4.31793 0.271466
\(254\) −11.2875 −0.708240
\(255\) 11.5351 0.722353
\(256\) 42.3357 2.64598
\(257\) −20.6869 −1.29041 −0.645207 0.764008i \(-0.723229\pi\)
−0.645207 + 0.764008i \(0.723229\pi\)
\(258\) 39.9047 2.48436
\(259\) 16.6900 1.03707
\(260\) −111.154 −6.89349
\(261\) 3.20502 0.198386
\(262\) 6.87198 0.424552
\(263\) 4.81240 0.296745 0.148373 0.988932i \(-0.452597\pi\)
0.148373 + 0.988932i \(0.452597\pi\)
\(264\) 14.3330 0.882134
\(265\) −22.9170 −1.40778
\(266\) 1.71523 0.105168
\(267\) 32.9711 2.01780
\(268\) 37.9469 2.31797
\(269\) −21.4166 −1.30579 −0.652896 0.757448i \(-0.726446\pi\)
−0.652896 + 0.757448i \(0.726446\pi\)
\(270\) −114.813 −6.98728
\(271\) 9.59117 0.582622 0.291311 0.956628i \(-0.405908\pi\)
0.291311 + 0.956628i \(0.405908\pi\)
\(272\) 14.8394 0.899772
\(273\) −32.1792 −1.94757
\(274\) 11.8626 0.716644
\(275\) 4.30375 0.259526
\(276\) −149.464 −8.99667
\(277\) 25.2227 1.51549 0.757744 0.652552i \(-0.226302\pi\)
0.757744 + 0.652552i \(0.226302\pi\)
\(278\) 39.3630 2.36084
\(279\) −38.2067 −2.28738
\(280\) 66.1393 3.95258
\(281\) −28.2834 −1.68725 −0.843623 0.536935i \(-0.819582\pi\)
−0.843623 + 0.536935i \(0.819582\pi\)
\(282\) −79.5179 −4.73523
\(283\) −6.79798 −0.404098 −0.202049 0.979375i \(-0.564760\pi\)
−0.202049 + 0.979375i \(0.564760\pi\)
\(284\) −56.7282 −3.36620
\(285\) −3.83776 −0.227329
\(286\) −7.33120 −0.433503
\(287\) −9.11797 −0.538217
\(288\) −143.903 −8.47956
\(289\) 1.00000 0.0588235
\(290\) 4.89045 0.287177
\(291\) 42.1342 2.46995
\(292\) −79.1238 −4.63037
\(293\) 25.8654 1.51107 0.755536 0.655107i \(-0.227376\pi\)
0.755536 + 0.655107i \(0.227376\pi\)
\(294\) −29.1217 −1.69841
\(295\) −5.42711 −0.315978
\(296\) −83.3548 −4.84490
\(297\) −5.54074 −0.321506
\(298\) −24.3427 −1.41014
\(299\) 48.4160 2.79997
\(300\) −148.973 −8.60096
\(301\) 8.88639 0.512203
\(302\) 63.8792 3.67584
\(303\) −54.8345 −3.15016
\(304\) −4.93714 −0.283164
\(305\) 22.3578 1.28020
\(306\) −18.1441 −1.03723
\(307\) −2.79061 −0.159268 −0.0796342 0.996824i \(-0.525375\pi\)
−0.0796342 + 0.996824i \(0.525375\pi\)
\(308\) 5.03992 0.287176
\(309\) −17.2330 −0.980353
\(310\) −58.2986 −3.31114
\(311\) 15.4616 0.876749 0.438375 0.898792i \(-0.355554\pi\)
0.438375 + 0.898792i \(0.355554\pi\)
\(312\) 160.712 9.09855
\(313\) −15.3716 −0.868851 −0.434426 0.900708i \(-0.643049\pi\)
−0.434426 + 0.900708i \(0.643049\pi\)
\(314\) 20.6694 1.16644
\(315\) −46.6075 −2.62603
\(316\) 17.3708 0.977184
\(317\) 8.42410 0.473145 0.236572 0.971614i \(-0.423976\pi\)
0.236572 + 0.971614i \(0.423976\pi\)
\(318\) 52.3201 2.93396
\(319\) 0.236008 0.0132139
\(320\) −109.347 −6.11267
\(321\) 20.5909 1.14927
\(322\) −45.4893 −2.53502
\(323\) −0.332704 −0.0185122
\(324\) 83.0524 4.61402
\(325\) 48.2570 2.67682
\(326\) 62.5274 3.46307
\(327\) −11.0763 −0.612519
\(328\) 45.5378 2.51440
\(329\) −17.7079 −0.976268
\(330\) −15.4117 −0.848385
\(331\) −0.912109 −0.0501341 −0.0250670 0.999686i \(-0.507980\pi\)
−0.0250670 + 0.999686i \(0.507980\pi\)
\(332\) −41.5550 −2.28062
\(333\) 58.7390 3.21887
\(334\) 13.8168 0.756022
\(335\) −25.8407 −1.41183
\(336\) −87.0257 −4.74764
\(337\) 4.59478 0.250294 0.125147 0.992138i \(-0.460060\pi\)
0.125147 + 0.992138i \(0.460060\pi\)
\(338\) −46.7101 −2.54069
\(339\) −39.7059 −2.15653
\(340\) −20.2573 −1.09861
\(341\) −2.81343 −0.152356
\(342\) 6.03661 0.326422
\(343\) −19.7031 −1.06387
\(344\) −44.3812 −2.39288
\(345\) 101.780 5.47967
\(346\) −40.9004 −2.19882
\(347\) −25.7120 −1.38029 −0.690147 0.723669i \(-0.742454\pi\)
−0.690147 + 0.723669i \(0.742454\pi\)
\(348\) −8.16935 −0.437923
\(349\) −17.9258 −0.959544 −0.479772 0.877393i \(-0.659281\pi\)
−0.479772 + 0.877393i \(0.659281\pi\)
\(350\) −45.3399 −2.42352
\(351\) −62.1271 −3.31610
\(352\) −10.5966 −0.564799
\(353\) 1.00000 0.0532246
\(354\) 12.3902 0.658531
\(355\) 38.6302 2.05028
\(356\) −57.9023 −3.06881
\(357\) −5.86450 −0.310382
\(358\) 6.23842 0.329711
\(359\) −1.81147 −0.0956059 −0.0478029 0.998857i \(-0.515222\pi\)
−0.0478029 + 0.998857i \(0.515222\pi\)
\(360\) 232.771 12.2681
\(361\) −18.8893 −0.994174
\(362\) 27.2502 1.43224
\(363\) 33.4194 1.75406
\(364\) 56.5115 2.96201
\(365\) 53.8809 2.82025
\(366\) −51.0433 −2.66808
\(367\) −16.0234 −0.836416 −0.418208 0.908351i \(-0.637342\pi\)
−0.418208 + 0.908351i \(0.637342\pi\)
\(368\) 130.937 6.82555
\(369\) −32.0899 −1.67053
\(370\) 89.6281 4.65954
\(371\) 11.6512 0.604899
\(372\) 97.3860 5.04923
\(373\) 26.3507 1.36439 0.682194 0.731171i \(-0.261026\pi\)
0.682194 + 0.731171i \(0.261026\pi\)
\(374\) −1.33607 −0.0690867
\(375\) 43.7708 2.26032
\(376\) 88.4384 4.56086
\(377\) 2.64631 0.136292
\(378\) 58.3715 3.00231
\(379\) 17.1585 0.881374 0.440687 0.897661i \(-0.354735\pi\)
0.440687 + 0.897661i \(0.354735\pi\)
\(380\) 6.73969 0.345739
\(381\) −12.8400 −0.657811
\(382\) −25.5951 −1.30956
\(383\) −24.1693 −1.23499 −0.617497 0.786574i \(-0.711853\pi\)
−0.617497 + 0.786574i \(0.711853\pi\)
\(384\) 115.139 5.87566
\(385\) −3.43203 −0.174913
\(386\) 9.75946 0.496743
\(387\) 31.2748 1.58979
\(388\) −73.9940 −3.75647
\(389\) −38.4853 −1.95128 −0.975640 0.219378i \(-0.929597\pi\)
−0.975640 + 0.219378i \(0.929597\pi\)
\(390\) −172.808 −8.75046
\(391\) 8.82357 0.446227
\(392\) 32.3886 1.63587
\(393\) 7.81714 0.394323
\(394\) 10.1790 0.512810
\(395\) −11.8290 −0.595181
\(396\) 17.7376 0.891346
\(397\) 18.6066 0.933839 0.466919 0.884300i \(-0.345364\pi\)
0.466919 + 0.884300i \(0.345364\pi\)
\(398\) −44.3906 −2.22510
\(399\) 1.95114 0.0976794
\(400\) 130.507 6.52533
\(401\) −34.1431 −1.70503 −0.852513 0.522706i \(-0.824922\pi\)
−0.852513 + 0.522706i \(0.824922\pi\)
\(402\) 58.9947 2.94239
\(403\) −31.5464 −1.57144
\(404\) 96.2976 4.79099
\(405\) −56.5562 −2.81030
\(406\) −2.48634 −0.123395
\(407\) 4.32536 0.214400
\(408\) 29.2890 1.45002
\(409\) −17.0858 −0.844838 −0.422419 0.906401i \(-0.638819\pi\)
−0.422419 + 0.906401i \(0.638819\pi\)
\(410\) −48.9650 −2.41821
\(411\) 13.4941 0.665616
\(412\) 30.2638 1.49099
\(413\) 2.75918 0.135770
\(414\) −160.095 −7.86826
\(415\) 28.2977 1.38908
\(416\) −118.817 −5.82548
\(417\) 44.7769 2.19274
\(418\) 0.444518 0.0217421
\(419\) 18.4805 0.902831 0.451415 0.892314i \(-0.350919\pi\)
0.451415 + 0.892314i \(0.350919\pi\)
\(420\) 118.799 5.79679
\(421\) −33.3756 −1.62663 −0.813314 0.581825i \(-0.802339\pi\)
−0.813314 + 0.581825i \(0.802339\pi\)
\(422\) 48.0963 2.34129
\(423\) −62.3213 −3.03017
\(424\) −58.1894 −2.82593
\(425\) 8.79459 0.426600
\(426\) −88.1934 −4.27298
\(427\) −11.3669 −0.550081
\(428\) −36.1607 −1.74789
\(429\) −8.33952 −0.402636
\(430\) 47.7214 2.30133
\(431\) 31.4371 1.51427 0.757135 0.653259i \(-0.226599\pi\)
0.757135 + 0.653259i \(0.226599\pi\)
\(432\) −168.017 −8.08372
\(433\) 39.5437 1.90035 0.950175 0.311716i \(-0.100904\pi\)
0.950175 + 0.311716i \(0.100904\pi\)
\(434\) 29.6394 1.42274
\(435\) 5.56308 0.266729
\(436\) 19.4516 0.931562
\(437\) −2.93564 −0.140431
\(438\) −123.011 −5.87770
\(439\) −12.6570 −0.604084 −0.302042 0.953295i \(-0.597668\pi\)
−0.302042 + 0.953295i \(0.597668\pi\)
\(440\) 17.1406 0.817145
\(441\) −22.8238 −1.08685
\(442\) −14.9811 −0.712578
\(443\) −7.99741 −0.379968 −0.189984 0.981787i \(-0.560844\pi\)
−0.189984 + 0.981787i \(0.560844\pi\)
\(444\) −149.721 −7.10544
\(445\) 39.4297 1.86915
\(446\) −58.1646 −2.75417
\(447\) −27.6908 −1.30973
\(448\) 55.5927 2.62651
\(449\) −2.48995 −0.117508 −0.0587541 0.998272i \(-0.518713\pi\)
−0.0587541 + 0.998272i \(0.518713\pi\)
\(450\) −159.570 −7.52218
\(451\) −2.36300 −0.111269
\(452\) 69.7295 3.27980
\(453\) 72.6651 3.41410
\(454\) 63.7758 2.99315
\(455\) −38.4826 −1.80409
\(456\) −9.74458 −0.456332
\(457\) 1.67177 0.0782022 0.0391011 0.999235i \(-0.487551\pi\)
0.0391011 + 0.999235i \(0.487551\pi\)
\(458\) −65.6364 −3.06699
\(459\) −11.3223 −0.528482
\(460\) −178.742 −8.33387
\(461\) −7.96759 −0.371088 −0.185544 0.982636i \(-0.559405\pi\)
−0.185544 + 0.982636i \(0.559405\pi\)
\(462\) 7.83540 0.364536
\(463\) −3.44446 −0.160078 −0.0800389 0.996792i \(-0.525504\pi\)
−0.0800389 + 0.996792i \(0.525504\pi\)
\(464\) 7.15669 0.332241
\(465\) −66.3169 −3.07537
\(466\) −67.4825 −3.12607
\(467\) −19.0809 −0.882960 −0.441480 0.897271i \(-0.645546\pi\)
−0.441480 + 0.897271i \(0.645546\pi\)
\(468\) 198.887 9.19356
\(469\) 13.1376 0.606636
\(470\) −95.0943 −4.38637
\(471\) 23.5122 1.08339
\(472\) −13.7801 −0.634283
\(473\) 2.30299 0.105891
\(474\) 27.0058 1.24042
\(475\) −2.92600 −0.134254
\(476\) 10.2989 0.472051
\(477\) 41.0053 1.87750
\(478\) −41.9714 −1.91973
\(479\) −0.317062 −0.0144869 −0.00724346 0.999974i \(-0.502306\pi\)
−0.00724346 + 0.999974i \(0.502306\pi\)
\(480\) −249.778 −11.4007
\(481\) 48.4993 2.21138
\(482\) 6.45490 0.294013
\(483\) −51.7458 −2.35452
\(484\) −58.6895 −2.66770
\(485\) 50.3876 2.28798
\(486\) 36.3811 1.65028
\(487\) −36.3431 −1.64686 −0.823431 0.567416i \(-0.807943\pi\)
−0.823431 + 0.567416i \(0.807943\pi\)
\(488\) 56.7694 2.56983
\(489\) 71.1273 3.21649
\(490\) −34.8262 −1.57329
\(491\) 23.0676 1.04103 0.520514 0.853853i \(-0.325740\pi\)
0.520514 + 0.853853i \(0.325740\pi\)
\(492\) 81.7945 3.68758
\(493\) 0.482276 0.0217206
\(494\) 4.98427 0.224253
\(495\) −12.0787 −0.542899
\(496\) −85.3143 −3.83072
\(497\) −19.6398 −0.880967
\(498\) −64.6041 −2.89498
\(499\) 35.8699 1.60576 0.802879 0.596142i \(-0.203300\pi\)
0.802879 + 0.596142i \(0.203300\pi\)
\(500\) −76.8682 −3.43765
\(501\) 15.7171 0.702190
\(502\) 11.0138 0.491571
\(503\) −12.3750 −0.551776 −0.275888 0.961190i \(-0.588972\pi\)
−0.275888 + 0.961190i \(0.588972\pi\)
\(504\) −118.343 −5.27140
\(505\) −65.5758 −2.91808
\(506\) −11.7889 −0.524082
\(507\) −53.1345 −2.35979
\(508\) 22.5489 1.00045
\(509\) −22.9858 −1.01883 −0.509414 0.860522i \(-0.670138\pi\)
−0.509414 + 0.860522i \(0.670138\pi\)
\(510\) −31.4933 −1.39455
\(511\) −27.3934 −1.21181
\(512\) −41.4402 −1.83141
\(513\) 3.76699 0.166317
\(514\) 56.4800 2.49123
\(515\) −20.6087 −0.908129
\(516\) −79.7171 −3.50935
\(517\) −4.58915 −0.201831
\(518\) −45.5675 −2.00212
\(519\) −46.5258 −2.04226
\(520\) 192.193 8.42824
\(521\) −2.92055 −0.127952 −0.0639758 0.997951i \(-0.520378\pi\)
−0.0639758 + 0.997951i \(0.520378\pi\)
\(522\) −8.75044 −0.382996
\(523\) −9.77817 −0.427569 −0.213785 0.976881i \(-0.568579\pi\)
−0.213785 + 0.976881i \(0.568579\pi\)
\(524\) −13.7281 −0.599714
\(525\) −51.5759 −2.25096
\(526\) −13.1389 −0.572885
\(527\) −5.74916 −0.250437
\(528\) −22.5535 −0.981514
\(529\) 54.8554 2.38502
\(530\) 62.5688 2.71781
\(531\) 9.71068 0.421408
\(532\) −3.42650 −0.148558
\(533\) −26.4958 −1.14766
\(534\) −90.0187 −3.89549
\(535\) 24.6244 1.06460
\(536\) −65.6128 −2.83404
\(537\) 7.09645 0.306234
\(538\) 58.4721 2.52091
\(539\) −1.68067 −0.0723918
\(540\) 229.360 9.87008
\(541\) −5.62524 −0.241848 −0.120924 0.992662i \(-0.538586\pi\)
−0.120924 + 0.992662i \(0.538586\pi\)
\(542\) −26.1861 −1.12479
\(543\) 30.9982 1.33026
\(544\) −21.6538 −0.928399
\(545\) −13.2459 −0.567394
\(546\) 87.8566 3.75991
\(547\) −19.7322 −0.843686 −0.421843 0.906669i \(-0.638617\pi\)
−0.421843 + 0.906669i \(0.638617\pi\)
\(548\) −23.6977 −1.01232
\(549\) −40.0046 −1.70736
\(550\) −11.7502 −0.501031
\(551\) −0.160455 −0.00683562
\(552\) 258.434 10.9997
\(553\) 6.01393 0.255739
\(554\) −68.8638 −2.92574
\(555\) 101.955 4.32777
\(556\) −78.6350 −3.33487
\(557\) 27.0923 1.14794 0.573970 0.818877i \(-0.305403\pi\)
0.573970 + 0.818877i \(0.305403\pi\)
\(558\) 104.313 4.41593
\(559\) 25.8229 1.09219
\(560\) −104.073 −4.39788
\(561\) −1.51984 −0.0641675
\(562\) 77.2202 3.25734
\(563\) −7.40450 −0.312063 −0.156031 0.987752i \(-0.549870\pi\)
−0.156031 + 0.987752i \(0.549870\pi\)
\(564\) 158.852 6.68888
\(565\) −47.4837 −1.99765
\(566\) 18.5600 0.780137
\(567\) 28.7535 1.20754
\(568\) 98.0871 4.11564
\(569\) −27.7703 −1.16419 −0.582096 0.813120i \(-0.697767\pi\)
−0.582096 + 0.813120i \(0.697767\pi\)
\(570\) 10.4780 0.438874
\(571\) −11.5386 −0.482876 −0.241438 0.970416i \(-0.577619\pi\)
−0.241438 + 0.970416i \(0.577619\pi\)
\(572\) 14.6455 0.612357
\(573\) −29.1154 −1.21632
\(574\) 24.8941 1.03906
\(575\) 77.5997 3.23613
\(576\) 195.653 8.15222
\(577\) −32.1425 −1.33811 −0.669055 0.743213i \(-0.733301\pi\)
−0.669055 + 0.743213i \(0.733301\pi\)
\(578\) −2.73023 −0.113563
\(579\) 11.1018 0.461373
\(580\) −9.76960 −0.405660
\(581\) −14.3867 −0.596862
\(582\) −115.036 −4.76839
\(583\) 3.01950 0.125055
\(584\) 136.811 5.66127
\(585\) −135.436 −5.59959
\(586\) −70.6185 −2.91722
\(587\) 7.24354 0.298973 0.149486 0.988764i \(-0.452238\pi\)
0.149486 + 0.988764i \(0.452238\pi\)
\(588\) 58.1760 2.39914
\(589\) 1.91277 0.0788144
\(590\) 14.8172 0.610016
\(591\) 11.5790 0.476296
\(592\) 131.162 5.39072
\(593\) 14.1958 0.582951 0.291476 0.956578i \(-0.405854\pi\)
0.291476 + 0.956578i \(0.405854\pi\)
\(594\) 15.1275 0.620688
\(595\) −7.01326 −0.287516
\(596\) 48.6292 1.99193
\(597\) −50.4960 −2.06666
\(598\) −132.187 −5.40552
\(599\) −41.0042 −1.67539 −0.837693 0.546142i \(-0.816096\pi\)
−0.837693 + 0.546142i \(0.816096\pi\)
\(600\) 257.585 10.5159
\(601\) −19.2506 −0.785250 −0.392625 0.919699i \(-0.628433\pi\)
−0.392625 + 0.919699i \(0.628433\pi\)
\(602\) −24.2619 −0.988840
\(603\) 46.2364 1.88289
\(604\) −127.611 −5.19241
\(605\) 39.9657 1.62484
\(606\) 149.711 6.08158
\(607\) −22.0815 −0.896259 −0.448130 0.893969i \(-0.647910\pi\)
−0.448130 + 0.893969i \(0.647910\pi\)
\(608\) 7.20431 0.292173
\(609\) −2.82830 −0.114609
\(610\) −61.0419 −2.47152
\(611\) −51.4571 −2.08173
\(612\) 36.2462 1.46516
\(613\) −22.8577 −0.923214 −0.461607 0.887085i \(-0.652727\pi\)
−0.461607 + 0.887085i \(0.652727\pi\)
\(614\) 7.61900 0.307478
\(615\) −55.6996 −2.24602
\(616\) −8.71439 −0.351113
\(617\) −26.1765 −1.05383 −0.526913 0.849919i \(-0.676651\pi\)
−0.526913 + 0.849919i \(0.676651\pi\)
\(618\) 47.0501 1.89263
\(619\) 17.5333 0.704724 0.352362 0.935864i \(-0.385379\pi\)
0.352362 + 0.935864i \(0.385379\pi\)
\(620\) 116.462 4.67724
\(621\) −99.9035 −4.00899
\(622\) −42.2138 −1.69262
\(623\) −20.0463 −0.803139
\(624\) −252.887 −10.1236
\(625\) 8.37191 0.334876
\(626\) 41.9678 1.67737
\(627\) 0.505656 0.0201940
\(628\) −41.2910 −1.64769
\(629\) 8.83875 0.352424
\(630\) 127.249 5.06972
\(631\) 0.116003 0.00461802 0.00230901 0.999997i \(-0.499265\pi\)
0.00230901 + 0.999997i \(0.499265\pi\)
\(632\) −30.0354 −1.19474
\(633\) 54.7114 2.17458
\(634\) −22.9997 −0.913435
\(635\) −15.3551 −0.609349
\(636\) −104.519 −4.14446
\(637\) −18.8450 −0.746667
\(638\) −0.644356 −0.0255103
\(639\) −69.1206 −2.73437
\(640\) 137.693 5.44279
\(641\) 31.7091 1.25243 0.626216 0.779649i \(-0.284603\pi\)
0.626216 + 0.779649i \(0.284603\pi\)
\(642\) −56.2179 −2.21874
\(643\) 4.04807 0.159640 0.0798202 0.996809i \(-0.474565\pi\)
0.0798202 + 0.996809i \(0.474565\pi\)
\(644\) 90.8734 3.58091
\(645\) 54.2849 2.13747
\(646\) 0.908359 0.0357389
\(647\) 39.8631 1.56718 0.783590 0.621279i \(-0.213386\pi\)
0.783590 + 0.621279i \(0.213386\pi\)
\(648\) −143.604 −5.64128
\(649\) 0.715065 0.0280688
\(650\) −131.753 −5.16776
\(651\) 33.7159 1.32143
\(652\) −124.910 −4.89186
\(653\) −17.4076 −0.681212 −0.340606 0.940206i \(-0.610632\pi\)
−0.340606 + 0.940206i \(0.610632\pi\)
\(654\) 30.2407 1.18251
\(655\) 9.34840 0.365272
\(656\) −71.6555 −2.79768
\(657\) −96.4086 −3.76126
\(658\) 48.3466 1.88475
\(659\) −18.7947 −0.732138 −0.366069 0.930588i \(-0.619297\pi\)
−0.366069 + 0.930588i \(0.619297\pi\)
\(660\) 30.7877 1.19841
\(661\) −4.61400 −0.179464 −0.0897320 0.995966i \(-0.528601\pi\)
−0.0897320 + 0.995966i \(0.528601\pi\)
\(662\) 2.49027 0.0967870
\(663\) −17.0416 −0.661840
\(664\) 71.8515 2.78838
\(665\) 2.33334 0.0904832
\(666\) −160.371 −6.21424
\(667\) 4.25539 0.164770
\(668\) −27.6017 −1.06794
\(669\) −66.1644 −2.55807
\(670\) 70.5509 2.72562
\(671\) −2.94582 −0.113722
\(672\) 126.989 4.89869
\(673\) −18.9647 −0.731037 −0.365518 0.930804i \(-0.619108\pi\)
−0.365518 + 0.930804i \(0.619108\pi\)
\(674\) −12.5448 −0.483208
\(675\) −99.5754 −3.83266
\(676\) 93.3122 3.58893
\(677\) 12.8848 0.495203 0.247601 0.968862i \(-0.420358\pi\)
0.247601 + 0.968862i \(0.420358\pi\)
\(678\) 108.406 4.16331
\(679\) −25.6174 −0.983106
\(680\) 35.0263 1.34320
\(681\) 72.5474 2.78002
\(682\) 7.68131 0.294132
\(683\) −13.3476 −0.510731 −0.255366 0.966845i \(-0.582196\pi\)
−0.255366 + 0.966845i \(0.582196\pi\)
\(684\) −12.0593 −0.461097
\(685\) 16.1374 0.616579
\(686\) 53.7938 2.05386
\(687\) −74.6639 −2.84861
\(688\) 69.8356 2.66246
\(689\) 33.8570 1.28985
\(690\) −277.884 −10.5788
\(691\) 26.1747 0.995734 0.497867 0.867253i \(-0.334117\pi\)
0.497867 + 0.867253i \(0.334117\pi\)
\(692\) 81.7064 3.10601
\(693\) 6.14091 0.233274
\(694\) 70.1997 2.66474
\(695\) 53.5480 2.03119
\(696\) 14.1254 0.535421
\(697\) −4.82872 −0.182901
\(698\) 48.9414 1.85246
\(699\) −76.7640 −2.90348
\(700\) 90.5750 3.42341
\(701\) 9.87840 0.373102 0.186551 0.982445i \(-0.440269\pi\)
0.186551 + 0.982445i \(0.440269\pi\)
\(702\) 169.621 6.40193
\(703\) −2.94069 −0.110910
\(704\) 14.4073 0.542996
\(705\) −108.173 −4.07405
\(706\) −2.73023 −0.102753
\(707\) 33.3391 1.25385
\(708\) −24.7518 −0.930228
\(709\) −33.9452 −1.27484 −0.637419 0.770518i \(-0.719998\pi\)
−0.637419 + 0.770518i \(0.719998\pi\)
\(710\) −105.469 −3.95819
\(711\) 21.1655 0.793768
\(712\) 100.117 3.75205
\(713\) −50.7281 −1.89978
\(714\) 16.0114 0.599212
\(715\) −9.97311 −0.372973
\(716\) −12.4624 −0.465743
\(717\) −47.7440 −1.78303
\(718\) 4.94573 0.184573
\(719\) −32.9145 −1.22750 −0.613752 0.789499i \(-0.710340\pi\)
−0.613752 + 0.789499i \(0.710340\pi\)
\(720\) −366.275 −13.6503
\(721\) 10.4776 0.390207
\(722\) 51.5721 1.91932
\(723\) 7.34269 0.273078
\(724\) −54.4375 −2.02315
\(725\) 4.24142 0.157522
\(726\) −91.2425 −3.38633
\(727\) 11.4999 0.426508 0.213254 0.976997i \(-0.431594\pi\)
0.213254 + 0.976997i \(0.431594\pi\)
\(728\) −97.7125 −3.62146
\(729\) −4.29729 −0.159159
\(730\) −147.107 −5.44468
\(731\) 4.70608 0.174061
\(732\) 101.969 3.76887
\(733\) 8.26852 0.305405 0.152702 0.988272i \(-0.451202\pi\)
0.152702 + 0.988272i \(0.451202\pi\)
\(734\) 43.7476 1.61475
\(735\) −39.6161 −1.46126
\(736\) −191.064 −7.04270
\(737\) 3.40471 0.125414
\(738\) 87.6126 3.22507
\(739\) −41.6012 −1.53032 −0.765162 0.643837i \(-0.777341\pi\)
−0.765162 + 0.643837i \(0.777341\pi\)
\(740\) −179.049 −6.58197
\(741\) 5.66980 0.208285
\(742\) −31.8104 −1.16780
\(743\) −13.8321 −0.507450 −0.253725 0.967276i \(-0.581656\pi\)
−0.253725 + 0.967276i \(0.581656\pi\)
\(744\) −168.387 −6.17338
\(745\) −33.1150 −1.21324
\(746\) −71.9435 −2.63404
\(747\) −50.6327 −1.85256
\(748\) 2.66906 0.0975905
\(749\) −12.5192 −0.457441
\(750\) −119.504 −4.36368
\(751\) −16.5109 −0.602491 −0.301245 0.953547i \(-0.597402\pi\)
−0.301245 + 0.953547i \(0.597402\pi\)
\(752\) −139.161 −5.07469
\(753\) 12.5287 0.456570
\(754\) −7.22502 −0.263120
\(755\) 86.8991 3.16258
\(756\) −116.608 −4.24100
\(757\) −16.7520 −0.608863 −0.304432 0.952534i \(-0.598467\pi\)
−0.304432 + 0.952534i \(0.598467\pi\)
\(758\) −46.8467 −1.70155
\(759\) −13.4104 −0.486766
\(760\) −11.6534 −0.422713
\(761\) 43.9955 1.59483 0.797417 0.603429i \(-0.206199\pi\)
0.797417 + 0.603429i \(0.206199\pi\)
\(762\) 35.0560 1.26995
\(763\) 6.73433 0.243799
\(764\) 51.1311 1.84986
\(765\) −24.6825 −0.892399
\(766\) 65.9877 2.38423
\(767\) 8.01786 0.289508
\(768\) −131.484 −4.74450
\(769\) 33.2541 1.19917 0.599587 0.800309i \(-0.295331\pi\)
0.599587 + 0.800309i \(0.295331\pi\)
\(770\) 9.37024 0.337680
\(771\) 64.2482 2.31384
\(772\) −19.4964 −0.701689
\(773\) −18.5456 −0.667039 −0.333520 0.942743i \(-0.608236\pi\)
−0.333520 + 0.942743i \(0.608236\pi\)
\(774\) −85.3875 −3.06919
\(775\) −50.5616 −1.81622
\(776\) 127.941 4.59281
\(777\) −51.8348 −1.85956
\(778\) 105.074 3.76707
\(779\) 1.60654 0.0575602
\(780\) 345.216 12.3607
\(781\) −5.08983 −0.182129
\(782\) −24.0904 −0.861470
\(783\) −5.46049 −0.195142
\(784\) −50.9647 −1.82017
\(785\) 28.1179 1.00357
\(786\) −21.3426 −0.761265
\(787\) −13.0023 −0.463482 −0.231741 0.972778i \(-0.574442\pi\)
−0.231741 + 0.972778i \(0.574442\pi\)
\(788\) −20.3344 −0.724385
\(789\) −14.9461 −0.532094
\(790\) 32.2958 1.14903
\(791\) 24.1410 0.858356
\(792\) −30.6695 −1.08979
\(793\) −33.0308 −1.17296
\(794\) −50.8003 −1.80283
\(795\) 71.1744 2.52430
\(796\) 88.6786 3.14313
\(797\) 10.8613 0.384729 0.192364 0.981324i \(-0.438384\pi\)
0.192364 + 0.981324i \(0.438384\pi\)
\(798\) −5.32707 −0.188576
\(799\) −9.37780 −0.331763
\(800\) −190.436 −6.73294
\(801\) −70.5512 −2.49280
\(802\) 93.2185 3.29166
\(803\) −7.09924 −0.250527
\(804\) −117.853 −4.15636
\(805\) −61.8820 −2.18105
\(806\) 86.1287 3.03376
\(807\) 66.5143 2.34141
\(808\) −166.505 −5.85764
\(809\) −12.1153 −0.425953 −0.212976 0.977057i \(-0.568316\pi\)
−0.212976 + 0.977057i \(0.568316\pi\)
\(810\) 154.411 5.42546
\(811\) −1.56410 −0.0549230 −0.0274615 0.999623i \(-0.508742\pi\)
−0.0274615 + 0.999623i \(0.508742\pi\)
\(812\) 4.96693 0.174305
\(813\) −29.7877 −1.04470
\(814\) −11.8092 −0.413913
\(815\) 85.0601 2.97952
\(816\) −46.0874 −1.61338
\(817\) −1.56573 −0.0547781
\(818\) 46.6481 1.63101
\(819\) 68.8566 2.40604
\(820\) 97.8168 3.41591
\(821\) 37.1552 1.29672 0.648362 0.761332i \(-0.275454\pi\)
0.648362 + 0.761332i \(0.275454\pi\)
\(822\) −36.8420 −1.28501
\(823\) −34.0078 −1.18544 −0.592719 0.805409i \(-0.701945\pi\)
−0.592719 + 0.805409i \(0.701945\pi\)
\(824\) −52.3283 −1.82294
\(825\) −13.3663 −0.465356
\(826\) −7.53319 −0.262113
\(827\) −39.5015 −1.37360 −0.686801 0.726845i \(-0.740986\pi\)
−0.686801 + 0.726845i \(0.740986\pi\)
\(828\) 319.821 11.1145
\(829\) −55.2152 −1.91770 −0.958852 0.283906i \(-0.908370\pi\)
−0.958852 + 0.283906i \(0.908370\pi\)
\(830\) −77.2591 −2.68170
\(831\) −78.3353 −2.71742
\(832\) 161.546 5.60060
\(833\) −3.43441 −0.118995
\(834\) −122.251 −4.23321
\(835\) 18.7959 0.650459
\(836\) −0.888008 −0.0307124
\(837\) 65.0940 2.24998
\(838\) −50.4560 −1.74297
\(839\) 16.5066 0.569871 0.284935 0.958547i \(-0.408028\pi\)
0.284935 + 0.958547i \(0.408028\pi\)
\(840\) −205.412 −7.08737
\(841\) −28.7674 −0.991980
\(842\) 91.1230 3.14031
\(843\) 87.8409 3.02540
\(844\) −96.0814 −3.30726
\(845\) −63.5428 −2.18594
\(846\) 170.151 5.84993
\(847\) −20.3188 −0.698164
\(848\) 91.5632 3.14429
\(849\) 21.1128 0.724588
\(850\) −24.0112 −0.823579
\(851\) 77.9893 2.67344
\(852\) 176.183 6.03593
\(853\) 45.0347 1.54196 0.770979 0.636860i \(-0.219767\pi\)
0.770979 + 0.636860i \(0.219767\pi\)
\(854\) 31.0341 1.06197
\(855\) 8.21199 0.280844
\(856\) 62.5245 2.13704
\(857\) 29.9362 1.02260 0.511301 0.859402i \(-0.329164\pi\)
0.511301 + 0.859402i \(0.329164\pi\)
\(858\) 22.7688 0.777314
\(859\) 45.5819 1.55523 0.777617 0.628738i \(-0.216428\pi\)
0.777617 + 0.628738i \(0.216428\pi\)
\(860\) −95.3325 −3.25081
\(861\) 28.3180 0.965076
\(862\) −85.8303 −2.92339
\(863\) 23.0996 0.786320 0.393160 0.919470i \(-0.371382\pi\)
0.393160 + 0.919470i \(0.371382\pi\)
\(864\) 245.172 8.34091
\(865\) −55.6395 −1.89180
\(866\) −107.963 −3.66875
\(867\) −3.10574 −0.105476
\(868\) −59.2103 −2.00973
\(869\) 1.55856 0.0528706
\(870\) −15.1885 −0.514937
\(871\) 38.1763 1.29355
\(872\) −33.6332 −1.13896
\(873\) −90.1581 −3.05139
\(874\) 8.01497 0.271110
\(875\) −26.6125 −0.899666
\(876\) 245.738 8.30271
\(877\) 6.42386 0.216918 0.108459 0.994101i \(-0.465408\pi\)
0.108459 + 0.994101i \(0.465408\pi\)
\(878\) 34.5564 1.16622
\(879\) −80.3312 −2.70950
\(880\) −26.9714 −0.909205
\(881\) 32.9297 1.10943 0.554715 0.832040i \(-0.312827\pi\)
0.554715 + 0.832040i \(0.312827\pi\)
\(882\) 62.3141 2.09823
\(883\) 20.2052 0.679960 0.339980 0.940433i \(-0.389580\pi\)
0.339980 + 0.940433i \(0.389580\pi\)
\(884\) 29.9276 1.00657
\(885\) 16.8552 0.566581
\(886\) 21.8348 0.733553
\(887\) 10.2533 0.344271 0.172135 0.985073i \(-0.444933\pi\)
0.172135 + 0.985073i \(0.444933\pi\)
\(888\) 258.878 8.68738
\(889\) 7.80664 0.261826
\(890\) −107.652 −3.60850
\(891\) 7.45173 0.249642
\(892\) 116.195 3.89049
\(893\) 3.12004 0.104408
\(894\) 75.6022 2.52852
\(895\) 8.48653 0.283673
\(896\) −70.0040 −2.33867
\(897\) −150.367 −5.02062
\(898\) 6.79814 0.226857
\(899\) −2.77268 −0.0924741
\(900\) 318.770 10.6257
\(901\) 6.17027 0.205562
\(902\) 6.45153 0.214812
\(903\) −27.5988 −0.918431
\(904\) −120.567 −4.01001
\(905\) 37.0703 1.23226
\(906\) −198.392 −6.59114
\(907\) −20.5685 −0.682966 −0.341483 0.939888i \(-0.610929\pi\)
−0.341483 + 0.939888i \(0.610929\pi\)
\(908\) −127.404 −4.22806
\(909\) 117.334 3.89173
\(910\) 105.066 3.48292
\(911\) −45.9796 −1.52337 −0.761685 0.647947i \(-0.775628\pi\)
−0.761685 + 0.647947i \(0.775628\pi\)
\(912\) 15.3335 0.507742
\(913\) −3.72844 −0.123393
\(914\) −4.56432 −0.150974
\(915\) −69.4375 −2.29553
\(916\) 131.121 4.33236
\(917\) −4.75279 −0.156951
\(918\) 30.9126 1.02027
\(919\) 14.9234 0.492278 0.246139 0.969235i \(-0.420838\pi\)
0.246139 + 0.969235i \(0.420838\pi\)
\(920\) 309.057 10.1893
\(921\) 8.66690 0.285584
\(922\) 21.7533 0.716408
\(923\) −57.0711 −1.87852
\(924\) −15.6527 −0.514936
\(925\) 77.7332 2.55585
\(926\) 9.40417 0.309040
\(927\) 36.8750 1.21113
\(928\) −10.4431 −0.342812
\(929\) 53.1100 1.74248 0.871241 0.490855i \(-0.163315\pi\)
0.871241 + 0.490855i \(0.163315\pi\)
\(930\) 181.060 5.93720
\(931\) 1.14264 0.0374486
\(932\) 134.809 4.41582
\(933\) −48.0198 −1.57210
\(934\) 52.0953 1.70461
\(935\) −1.81755 −0.0594402
\(936\) −343.890 −11.2404
\(937\) 26.7036 0.872369 0.436184 0.899857i \(-0.356330\pi\)
0.436184 + 0.899857i \(0.356330\pi\)
\(938\) −35.8685 −1.17115
\(939\) 47.7400 1.55794
\(940\) 189.969 6.19610
\(941\) −0.757355 −0.0246891 −0.0123445 0.999924i \(-0.503929\pi\)
−0.0123445 + 0.999924i \(0.503929\pi\)
\(942\) −64.1937 −2.09154
\(943\) −42.6066 −1.38746
\(944\) 21.6836 0.705741
\(945\) 79.4066 2.58310
\(946\) −6.28768 −0.204430
\(947\) 13.5317 0.439722 0.219861 0.975531i \(-0.429440\pi\)
0.219861 + 0.975531i \(0.429440\pi\)
\(948\) −53.9492 −1.75219
\(949\) −79.6021 −2.58399
\(950\) 7.98865 0.259186
\(951\) −26.1631 −0.848395
\(952\) −17.8076 −0.577148
\(953\) −50.2605 −1.62810 −0.814048 0.580798i \(-0.802741\pi\)
−0.814048 + 0.580798i \(0.802741\pi\)
\(954\) −111.954 −3.62464
\(955\) −34.8187 −1.12671
\(956\) 83.8457 2.71176
\(957\) −0.732980 −0.0236939
\(958\) 0.865651 0.0279679
\(959\) −8.20437 −0.264933
\(960\) 339.603 10.9606
\(961\) 2.05288 0.0662218
\(962\) −132.414 −4.26920
\(963\) −44.0601 −1.41982
\(964\) −12.8949 −0.415316
\(965\) 13.2764 0.427383
\(966\) 141.278 4.54554
\(967\) 60.4776 1.94483 0.972414 0.233262i \(-0.0749401\pi\)
0.972414 + 0.233262i \(0.0749401\pi\)
\(968\) 101.478 3.26164
\(969\) 1.03329 0.0331942
\(970\) −137.570 −4.41710
\(971\) 23.4587 0.752825 0.376413 0.926452i \(-0.377157\pi\)
0.376413 + 0.926452i \(0.377157\pi\)
\(972\) −72.6781 −2.33115
\(973\) −27.2242 −0.872767
\(974\) 99.2249 3.17937
\(975\) −149.874 −4.79980
\(976\) −89.3289 −2.85935
\(977\) −24.5612 −0.785784 −0.392892 0.919585i \(-0.628525\pi\)
−0.392892 + 0.919585i \(0.628525\pi\)
\(978\) −194.194 −6.20963
\(979\) −5.19518 −0.166039
\(980\) 69.5718 2.22239
\(981\) 23.7008 0.756710
\(982\) −62.9799 −2.00977
\(983\) −19.2821 −0.615003 −0.307502 0.951548i \(-0.599493\pi\)
−0.307502 + 0.951548i \(0.599493\pi\)
\(984\) −141.429 −4.50858
\(985\) 13.8471 0.441207
\(986\) −1.31672 −0.0419330
\(987\) 54.9961 1.75055
\(988\) −9.95703 −0.316775
\(989\) 41.5245 1.32040
\(990\) 32.9777 1.04810
\(991\) 27.2784 0.866528 0.433264 0.901267i \(-0.357362\pi\)
0.433264 + 0.901267i \(0.357362\pi\)
\(992\) 124.491 3.95260
\(993\) 2.83277 0.0898954
\(994\) 53.6212 1.70076
\(995\) −60.3874 −1.91441
\(996\) 129.059 4.08939
\(997\) 40.6600 1.28771 0.643857 0.765146i \(-0.277333\pi\)
0.643857 + 0.765146i \(0.277333\pi\)
\(998\) −97.9331 −3.10002
\(999\) −100.075 −3.16624
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 \(a_p\))