Properties

Label 4009.2.a.c.1.9
Level 4009
Weight 2
Character 4009.1
Self dual Yes
Analytic conductor 32.012
Analytic rank 1
Dimension 71
CM No

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Newspace parameters

Level: \( N \) = \( 4009 = 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4009.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0120261703\)
Analytic rank: \(1\)
Dimension: \(71\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 4009.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.35519 q^{2}\) \(+0.815593 q^{3}\) \(+3.54692 q^{4}\) \(+1.05865 q^{5}\) \(-1.92088 q^{6}\) \(-4.06376 q^{7}\) \(-3.64328 q^{8}\) \(-2.33481 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.35519 q^{2}\) \(+0.815593 q^{3}\) \(+3.54692 q^{4}\) \(+1.05865 q^{5}\) \(-1.92088 q^{6}\) \(-4.06376 q^{7}\) \(-3.64328 q^{8}\) \(-2.33481 q^{9}\) \(-2.49333 q^{10}\) \(+3.34628 q^{11}\) \(+2.89284 q^{12}\) \(+2.90167 q^{13}\) \(+9.57091 q^{14}\) \(+0.863432 q^{15}\) \(+1.48678 q^{16}\) \(+7.81825 q^{17}\) \(+5.49891 q^{18}\) \(+1.00000 q^{19}\) \(+3.75496 q^{20}\) \(-3.31437 q^{21}\) \(-7.88113 q^{22}\) \(-5.53700 q^{23}\) \(-2.97144 q^{24}\) \(-3.87925 q^{25}\) \(-6.83397 q^{26}\) \(-4.35103 q^{27}\) \(-14.4138 q^{28}\) \(+4.90550 q^{29}\) \(-2.03354 q^{30}\) \(-10.2234 q^{31}\) \(+3.78490 q^{32}\) \(+2.72921 q^{33}\) \(-18.4135 q^{34}\) \(-4.30212 q^{35}\) \(-8.28137 q^{36}\) \(-4.34401 q^{37}\) \(-2.35519 q^{38}\) \(+2.36658 q^{39}\) \(-3.85698 q^{40}\) \(-2.46182 q^{41}\) \(+7.80597 q^{42}\) \(-5.12426 q^{43}\) \(+11.8690 q^{44}\) \(-2.47176 q^{45}\) \(+13.0407 q^{46}\) \(-8.47533 q^{47}\) \(+1.21261 q^{48}\) \(+9.51411 q^{49}\) \(+9.13637 q^{50}\) \(+6.37651 q^{51}\) \(+10.2920 q^{52}\) \(+8.14686 q^{53}\) \(+10.2475 q^{54}\) \(+3.54256 q^{55}\) \(+14.8054 q^{56}\) \(+0.815593 q^{57}\) \(-11.5534 q^{58}\) \(+4.16450 q^{59}\) \(+3.06252 q^{60}\) \(+11.1105 q^{61}\) \(+24.0781 q^{62}\) \(+9.48809 q^{63}\) \(-11.8877 q^{64}\) \(+3.07186 q^{65}\) \(-6.42780 q^{66}\) \(+4.88499 q^{67}\) \(+27.7307 q^{68}\) \(-4.51594 q^{69}\) \(+10.1323 q^{70}\) \(-15.7871 q^{71}\) \(+8.50636 q^{72}\) \(+5.09224 q^{73}\) \(+10.2310 q^{74}\) \(-3.16389 q^{75}\) \(+3.54692 q^{76}\) \(-13.5985 q^{77}\) \(-5.57374 q^{78}\) \(-6.78921 q^{79}\) \(+1.57399 q^{80}\) \(+3.45575 q^{81}\) \(+5.79806 q^{82}\) \(-7.77213 q^{83}\) \(-11.7558 q^{84}\) \(+8.27683 q^{85}\) \(+12.0686 q^{86}\) \(+4.00089 q^{87}\) \(-12.1915 q^{88}\) \(+1.21312 q^{89}\) \(+5.82145 q^{90}\) \(-11.7917 q^{91}\) \(-19.6393 q^{92}\) \(-8.33814 q^{93}\) \(+19.9610 q^{94}\) \(+1.05865 q^{95}\) \(+3.08694 q^{96}\) \(+4.15615 q^{97}\) \(-22.4075 q^{98}\) \(-7.81293 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 9q^{12} \) \(\mathstrut -\mathstrut 15q^{13} \) \(\mathstrut -\mathstrut 53q^{14} \) \(\mathstrut -\mathstrut 33q^{15} \) \(\mathstrut +\mathstrut 53q^{16} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 35q^{18} \) \(\mathstrut +\mathstrut 71q^{19} \) \(\mathstrut -\mathstrut 33q^{20} \) \(\mathstrut -\mathstrut 38q^{21} \) \(\mathstrut -\mathstrut 6q^{22} \) \(\mathstrut -\mathstrut 65q^{23} \) \(\mathstrut -\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 51q^{25} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut -\mathstrut 23q^{27} \) \(\mathstrut -\mathstrut 29q^{28} \) \(\mathstrut -\mathstrut 97q^{29} \) \(\mathstrut -\mathstrut 27q^{30} \) \(\mathstrut -\mathstrut 53q^{31} \) \(\mathstrut -\mathstrut 78q^{32} \) \(\mathstrut -\mathstrut 17q^{33} \) \(\mathstrut -\mathstrut 24q^{34} \) \(\mathstrut -\mathstrut 38q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 33q^{37} \) \(\mathstrut -\mathstrut 15q^{38} \) \(\mathstrut -\mathstrut 86q^{39} \) \(\mathstrut +\mathstrut 25q^{40} \) \(\mathstrut -\mathstrut 69q^{41} \) \(\mathstrut +\mathstrut 64q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 94q^{44} \) \(\mathstrut -\mathstrut 34q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut -\mathstrut 37q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut +\mathstrut 74q^{49} \) \(\mathstrut -\mathstrut 41q^{50} \) \(\mathstrut -\mathstrut 46q^{51} \) \(\mathstrut -\mathstrut 30q^{52} \) \(\mathstrut -\mathstrut 50q^{53} \) \(\mathstrut -\mathstrut 17q^{54} \) \(\mathstrut -\mathstrut 30q^{55} \) \(\mathstrut -\mathstrut 116q^{56} \) \(\mathstrut -\mathstrut 8q^{57} \) \(\mathstrut +\mathstrut 11q^{58} \) \(\mathstrut -\mathstrut 93q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 18q^{61} \) \(\mathstrut -\mathstrut q^{62} \) \(\mathstrut -\mathstrut 84q^{63} \) \(\mathstrut +\mathstrut 93q^{64} \) \(\mathstrut -\mathstrut 78q^{65} \) \(\mathstrut -\mathstrut 53q^{66} \) \(\mathstrut -\mathstrut 5q^{67} \) \(\mathstrut -\mathstrut 9q^{68} \) \(\mathstrut -\mathstrut 69q^{69} \) \(\mathstrut -\mathstrut 10q^{70} \) \(\mathstrut -\mathstrut 221q^{71} \) \(\mathstrut -\mathstrut 73q^{72} \) \(\mathstrut -\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 58q^{74} \) \(\mathstrut -\mathstrut 70q^{75} \) \(\mathstrut +\mathstrut 69q^{76} \) \(\mathstrut -\mathstrut 2q^{77} \) \(\mathstrut +\mathstrut 7q^{78} \) \(\mathstrut -\mathstrut 68q^{79} \) \(\mathstrut -\mathstrut 71q^{80} \) \(\mathstrut +\mathstrut 39q^{81} \) \(\mathstrut +\mathstrut 26q^{82} \) \(\mathstrut -\mathstrut 45q^{83} \) \(\mathstrut -\mathstrut 10q^{84} \) \(\mathstrut -\mathstrut 44q^{85} \) \(\mathstrut -\mathstrut 80q^{86} \) \(\mathstrut -\mathstrut 7q^{87} \) \(\mathstrut -\mathstrut 46q^{88} \) \(\mathstrut -\mathstrut 143q^{89} \) \(\mathstrut +\mathstrut 41q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 46q^{92} \) \(\mathstrut +\mathstrut 32q^{93} \) \(\mathstrut +\mathstrut 41q^{94} \) \(\mathstrut -\mathstrut 18q^{95} \) \(\mathstrut -\mathstrut 140q^{96} \) \(\mathstrut -\mathstrut 18q^{97} \) \(\mathstrut -\mathstrut 97q^{98} \) \(\mathstrut -\mathstrut 142q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.35519 −1.66537 −0.832685 0.553747i \(-0.813198\pi\)
−0.832685 + 0.553747i \(0.813198\pi\)
\(3\) 0.815593 0.470883 0.235441 0.971889i \(-0.424346\pi\)
0.235441 + 0.971889i \(0.424346\pi\)
\(4\) 3.54692 1.77346
\(5\) 1.05865 0.473445 0.236722 0.971577i \(-0.423927\pi\)
0.236722 + 0.971577i \(0.423927\pi\)
\(6\) −1.92088 −0.784194
\(7\) −4.06376 −1.53596 −0.767978 0.640477i \(-0.778737\pi\)
−0.767978 + 0.640477i \(0.778737\pi\)
\(8\) −3.64328 −1.28809
\(9\) −2.33481 −0.778269
\(10\) −2.49333 −0.788461
\(11\) 3.34628 1.00894 0.504471 0.863428i \(-0.331687\pi\)
0.504471 + 0.863428i \(0.331687\pi\)
\(12\) 2.89284 0.835091
\(13\) 2.90167 0.804777 0.402389 0.915469i \(-0.368180\pi\)
0.402389 + 0.915469i \(0.368180\pi\)
\(14\) 9.57091 2.55793
\(15\) 0.863432 0.222937
\(16\) 1.48678 0.371696
\(17\) 7.81825 1.89620 0.948102 0.317966i \(-0.103000\pi\)
0.948102 + 0.317966i \(0.103000\pi\)
\(18\) 5.49891 1.29611
\(19\) 1.00000 0.229416
\(20\) 3.75496 0.839635
\(21\) −3.31437 −0.723255
\(22\) −7.88113 −1.68026
\(23\) −5.53700 −1.15455 −0.577273 0.816551i \(-0.695883\pi\)
−0.577273 + 0.816551i \(0.695883\pi\)
\(24\) −2.97144 −0.606542
\(25\) −3.87925 −0.775850
\(26\) −6.83397 −1.34025
\(27\) −4.35103 −0.837357
\(28\) −14.4138 −2.72395
\(29\) 4.90550 0.910928 0.455464 0.890254i \(-0.349473\pi\)
0.455464 + 0.890254i \(0.349473\pi\)
\(30\) −2.03354 −0.371273
\(31\) −10.2234 −1.83618 −0.918089 0.396374i \(-0.870268\pi\)
−0.918089 + 0.396374i \(0.870268\pi\)
\(32\) 3.78490 0.669083
\(33\) 2.72921 0.475094
\(34\) −18.4135 −3.15788
\(35\) −4.30212 −0.727190
\(36\) −8.28137 −1.38023
\(37\) −4.34401 −0.714150 −0.357075 0.934076i \(-0.616226\pi\)
−0.357075 + 0.934076i \(0.616226\pi\)
\(38\) −2.35519 −0.382062
\(39\) 2.36658 0.378956
\(40\) −3.85698 −0.609842
\(41\) −2.46182 −0.384472 −0.192236 0.981349i \(-0.561574\pi\)
−0.192236 + 0.981349i \(0.561574\pi\)
\(42\) 7.80597 1.20449
\(43\) −5.12426 −0.781443 −0.390721 0.920509i \(-0.627774\pi\)
−0.390721 + 0.920509i \(0.627774\pi\)
\(44\) 11.8690 1.78932
\(45\) −2.47176 −0.368468
\(46\) 13.0407 1.92275
\(47\) −8.47533 −1.23625 −0.618127 0.786078i \(-0.712108\pi\)
−0.618127 + 0.786078i \(0.712108\pi\)
\(48\) 1.21261 0.175025
\(49\) 9.51411 1.35916
\(50\) 9.13637 1.29208
\(51\) 6.37651 0.892890
\(52\) 10.2920 1.42724
\(53\) 8.14686 1.11906 0.559529 0.828811i \(-0.310982\pi\)
0.559529 + 0.828811i \(0.310982\pi\)
\(54\) 10.2475 1.39451
\(55\) 3.54256 0.477679
\(56\) 14.8054 1.97846
\(57\) 0.815593 0.108028
\(58\) −11.5534 −1.51703
\(59\) 4.16450 0.542172 0.271086 0.962555i \(-0.412617\pi\)
0.271086 + 0.962555i \(0.412617\pi\)
\(60\) 3.06252 0.395370
\(61\) 11.1105 1.42256 0.711279 0.702910i \(-0.248116\pi\)
0.711279 + 0.702910i \(0.248116\pi\)
\(62\) 24.0781 3.05792
\(63\) 9.48809 1.19539
\(64\) −11.8877 −1.48597
\(65\) 3.07186 0.381018
\(66\) −6.42780 −0.791207
\(67\) 4.88499 0.596797 0.298398 0.954441i \(-0.403548\pi\)
0.298398 + 0.954441i \(0.403548\pi\)
\(68\) 27.7307 3.36284
\(69\) −4.51594 −0.543656
\(70\) 10.1323 1.21104
\(71\) −15.7871 −1.87359 −0.936793 0.349885i \(-0.886221\pi\)
−0.936793 + 0.349885i \(0.886221\pi\)
\(72\) 8.50636 1.00248
\(73\) 5.09224 0.596002 0.298001 0.954566i \(-0.403680\pi\)
0.298001 + 0.954566i \(0.403680\pi\)
\(74\) 10.2310 1.18932
\(75\) −3.16389 −0.365334
\(76\) 3.54692 0.406859
\(77\) −13.5985 −1.54969
\(78\) −5.57374 −0.631102
\(79\) −6.78921 −0.763846 −0.381923 0.924194i \(-0.624738\pi\)
−0.381923 + 0.924194i \(0.624738\pi\)
\(80\) 1.57399 0.175978
\(81\) 3.45575 0.383973
\(82\) 5.79806 0.640288
\(83\) −7.77213 −0.853102 −0.426551 0.904463i \(-0.640272\pi\)
−0.426551 + 0.904463i \(0.640272\pi\)
\(84\) −11.7558 −1.28266
\(85\) 8.27683 0.897748
\(86\) 12.0686 1.30139
\(87\) 4.00089 0.428940
\(88\) −12.1915 −1.29961
\(89\) 1.21312 0.128591 0.0642954 0.997931i \(-0.479520\pi\)
0.0642954 + 0.997931i \(0.479520\pi\)
\(90\) 5.82145 0.613635
\(91\) −11.7917 −1.23610
\(92\) −19.6393 −2.04754
\(93\) −8.33814 −0.864625
\(94\) 19.9610 2.05882
\(95\) 1.05865 0.108616
\(96\) 3.08694 0.315060
\(97\) 4.15615 0.421993 0.210996 0.977487i \(-0.432329\pi\)
0.210996 + 0.977487i \(0.432329\pi\)
\(98\) −22.4075 −2.26350
\(99\) −7.81293 −0.785229
\(100\) −13.7594 −1.37594
\(101\) −2.33289 −0.232131 −0.116065 0.993242i \(-0.537028\pi\)
−0.116065 + 0.993242i \(0.537028\pi\)
\(102\) −15.0179 −1.48699
\(103\) 8.58403 0.845810 0.422905 0.906174i \(-0.361010\pi\)
0.422905 + 0.906174i \(0.361010\pi\)
\(104\) −10.5716 −1.03663
\(105\) −3.50878 −0.342421
\(106\) −19.1874 −1.86364
\(107\) 17.4673 1.68863 0.844316 0.535846i \(-0.180007\pi\)
0.844316 + 0.535846i \(0.180007\pi\)
\(108\) −15.4327 −1.48502
\(109\) −2.51329 −0.240729 −0.120365 0.992730i \(-0.538406\pi\)
−0.120365 + 0.992730i \(0.538406\pi\)
\(110\) −8.34340 −0.795512
\(111\) −3.54294 −0.336281
\(112\) −6.04193 −0.570909
\(113\) 10.4302 0.981189 0.490594 0.871388i \(-0.336780\pi\)
0.490594 + 0.871388i \(0.336780\pi\)
\(114\) −1.92088 −0.179907
\(115\) −5.86178 −0.546614
\(116\) 17.3994 1.61549
\(117\) −6.77483 −0.626334
\(118\) −9.80819 −0.902917
\(119\) −31.7715 −2.91249
\(120\) −3.14572 −0.287164
\(121\) 0.197616 0.0179651
\(122\) −26.1674 −2.36909
\(123\) −2.00784 −0.181041
\(124\) −36.2616 −3.25639
\(125\) −9.40006 −0.840767
\(126\) −22.3462 −1.99076
\(127\) −15.3610 −1.36307 −0.681536 0.731785i \(-0.738688\pi\)
−0.681536 + 0.731785i \(0.738688\pi\)
\(128\) 20.4281 1.80560
\(129\) −4.17931 −0.367968
\(130\) −7.23482 −0.634536
\(131\) −7.82477 −0.683653 −0.341827 0.939763i \(-0.611046\pi\)
−0.341827 + 0.939763i \(0.611046\pi\)
\(132\) 9.68027 0.842559
\(133\) −4.06376 −0.352372
\(134\) −11.5051 −0.993888
\(135\) −4.60624 −0.396442
\(136\) −28.4841 −2.44249
\(137\) 14.0762 1.20261 0.601306 0.799019i \(-0.294647\pi\)
0.601306 + 0.799019i \(0.294647\pi\)
\(138\) 10.6359 0.905388
\(139\) 14.1465 1.19989 0.599947 0.800040i \(-0.295188\pi\)
0.599947 + 0.800040i \(0.295188\pi\)
\(140\) −15.2592 −1.28964
\(141\) −6.91242 −0.582131
\(142\) 37.1816 3.12021
\(143\) 9.70980 0.811974
\(144\) −3.47136 −0.289280
\(145\) 5.19323 0.431274
\(146\) −11.9932 −0.992564
\(147\) 7.75964 0.640005
\(148\) −15.4078 −1.26652
\(149\) −20.1160 −1.64797 −0.823984 0.566613i \(-0.808254\pi\)
−0.823984 + 0.566613i \(0.808254\pi\)
\(150\) 7.45156 0.608417
\(151\) −12.8877 −1.04879 −0.524395 0.851475i \(-0.675708\pi\)
−0.524395 + 0.851475i \(0.675708\pi\)
\(152\) −3.64328 −0.295509
\(153\) −18.2541 −1.47576
\(154\) 32.0270 2.58081
\(155\) −10.8231 −0.869329
\(156\) 8.39406 0.672063
\(157\) 2.28696 0.182519 0.0912594 0.995827i \(-0.470911\pi\)
0.0912594 + 0.995827i \(0.470911\pi\)
\(158\) 15.9899 1.27209
\(159\) 6.64452 0.526945
\(160\) 4.00691 0.316774
\(161\) 22.5010 1.77333
\(162\) −8.13895 −0.639456
\(163\) 6.88038 0.538913 0.269457 0.963013i \(-0.413156\pi\)
0.269457 + 0.963013i \(0.413156\pi\)
\(164\) −8.73188 −0.681845
\(165\) 2.88929 0.224931
\(166\) 18.3048 1.42073
\(167\) −6.36028 −0.492173 −0.246087 0.969248i \(-0.579145\pi\)
−0.246087 + 0.969248i \(0.579145\pi\)
\(168\) 12.0752 0.931621
\(169\) −4.58033 −0.352333
\(170\) −19.4935 −1.49508
\(171\) −2.33481 −0.178547
\(172\) −18.1753 −1.38586
\(173\) −21.2737 −1.61741 −0.808706 0.588213i \(-0.799832\pi\)
−0.808706 + 0.588213i \(0.799832\pi\)
\(174\) −9.42285 −0.714344
\(175\) 15.7643 1.19167
\(176\) 4.97520 0.375020
\(177\) 3.39654 0.255300
\(178\) −2.85714 −0.214151
\(179\) −9.63670 −0.720281 −0.360140 0.932898i \(-0.617271\pi\)
−0.360140 + 0.932898i \(0.617271\pi\)
\(180\) −8.76711 −0.653462
\(181\) 23.4314 1.74164 0.870819 0.491603i \(-0.163589\pi\)
0.870819 + 0.491603i \(0.163589\pi\)
\(182\) 27.7716 2.05857
\(183\) 9.06167 0.669858
\(184\) 20.1729 1.48716
\(185\) −4.59880 −0.338111
\(186\) 19.6379 1.43992
\(187\) 26.1621 1.91316
\(188\) −30.0613 −2.19244
\(189\) 17.6815 1.28614
\(190\) −2.49333 −0.180885
\(191\) 3.01536 0.218184 0.109092 0.994032i \(-0.465206\pi\)
0.109092 + 0.994032i \(0.465206\pi\)
\(192\) −9.69555 −0.699716
\(193\) −17.5746 −1.26505 −0.632523 0.774541i \(-0.717981\pi\)
−0.632523 + 0.774541i \(0.717981\pi\)
\(194\) −9.78851 −0.702774
\(195\) 2.50539 0.179415
\(196\) 33.7458 2.41041
\(197\) 8.88922 0.633331 0.316665 0.948537i \(-0.397437\pi\)
0.316665 + 0.948537i \(0.397437\pi\)
\(198\) 18.4009 1.30770
\(199\) −25.9490 −1.83948 −0.919738 0.392534i \(-0.871599\pi\)
−0.919738 + 0.392534i \(0.871599\pi\)
\(200\) 14.1332 0.999368
\(201\) 3.98417 0.281021
\(202\) 5.49439 0.386584
\(203\) −19.9347 −1.39914
\(204\) 22.6170 1.58350
\(205\) −2.60622 −0.182026
\(206\) −20.2170 −1.40859
\(207\) 12.9278 0.898547
\(208\) 4.31415 0.299133
\(209\) 3.34628 0.231467
\(210\) 8.26383 0.570258
\(211\) 1.00000 0.0688428
\(212\) 28.8962 1.98460
\(213\) −12.8759 −0.882239
\(214\) −41.1389 −2.81220
\(215\) −5.42482 −0.369970
\(216\) 15.8520 1.07859
\(217\) 41.5454 2.82029
\(218\) 5.91927 0.400903
\(219\) 4.15320 0.280647
\(220\) 12.5652 0.847143
\(221\) 22.6860 1.52602
\(222\) 8.34430 0.560033
\(223\) −26.7138 −1.78889 −0.894444 0.447180i \(-0.852428\pi\)
−0.894444 + 0.447180i \(0.852428\pi\)
\(224\) −15.3809 −1.02768
\(225\) 9.05730 0.603820
\(226\) −24.5650 −1.63404
\(227\) 2.97136 0.197216 0.0986080 0.995126i \(-0.468561\pi\)
0.0986080 + 0.995126i \(0.468561\pi\)
\(228\) 2.89284 0.191583
\(229\) −6.05167 −0.399906 −0.199953 0.979806i \(-0.564079\pi\)
−0.199953 + 0.979806i \(0.564079\pi\)
\(230\) 13.8056 0.910314
\(231\) −11.0908 −0.729723
\(232\) −17.8721 −1.17336
\(233\) −23.3870 −1.53213 −0.766066 0.642762i \(-0.777788\pi\)
−0.766066 + 0.642762i \(0.777788\pi\)
\(234\) 15.9560 1.04308
\(235\) −8.97245 −0.585298
\(236\) 14.7711 0.961520
\(237\) −5.53724 −0.359682
\(238\) 74.8278 4.85037
\(239\) 0.891708 0.0576798 0.0288399 0.999584i \(-0.490819\pi\)
0.0288399 + 0.999584i \(0.490819\pi\)
\(240\) 1.28374 0.0828649
\(241\) −0.680321 −0.0438234 −0.0219117 0.999760i \(-0.506975\pi\)
−0.0219117 + 0.999760i \(0.506975\pi\)
\(242\) −0.465423 −0.0299185
\(243\) 15.8716 1.01816
\(244\) 39.4081 2.52285
\(245\) 10.0722 0.643487
\(246\) 4.72885 0.301501
\(247\) 2.90167 0.184629
\(248\) 37.2467 2.36517
\(249\) −6.33890 −0.401711
\(250\) 22.1389 1.40019
\(251\) −22.9201 −1.44671 −0.723353 0.690479i \(-0.757400\pi\)
−0.723353 + 0.690479i \(0.757400\pi\)
\(252\) 33.6535 2.11997
\(253\) −18.5284 −1.16487
\(254\) 36.1781 2.27002
\(255\) 6.75052 0.422734
\(256\) −24.3365 −1.52103
\(257\) −27.3317 −1.70490 −0.852452 0.522806i \(-0.824885\pi\)
−0.852452 + 0.522806i \(0.824885\pi\)
\(258\) 9.84307 0.612803
\(259\) 17.6530 1.09690
\(260\) 10.8956 0.675719
\(261\) −11.4534 −0.708947
\(262\) 18.4288 1.13854
\(263\) 13.2661 0.818021 0.409010 0.912530i \(-0.365874\pi\)
0.409010 + 0.912530i \(0.365874\pi\)
\(264\) −9.94327 −0.611966
\(265\) 8.62471 0.529812
\(266\) 9.57091 0.586830
\(267\) 0.989415 0.0605512
\(268\) 17.3267 1.05839
\(269\) 4.79322 0.292248 0.146124 0.989266i \(-0.453320\pi\)
0.146124 + 0.989266i \(0.453320\pi\)
\(270\) 10.8486 0.660223
\(271\) −0.696460 −0.0423069 −0.0211535 0.999776i \(-0.506734\pi\)
−0.0211535 + 0.999776i \(0.506734\pi\)
\(272\) 11.6241 0.704812
\(273\) −9.61720 −0.582059
\(274\) −33.1521 −2.00279
\(275\) −12.9811 −0.782788
\(276\) −16.0177 −0.964151
\(277\) −3.51672 −0.211299 −0.105650 0.994403i \(-0.533692\pi\)
−0.105650 + 0.994403i \(0.533692\pi\)
\(278\) −33.3178 −1.99827
\(279\) 23.8697 1.42904
\(280\) 15.6738 0.936690
\(281\) −33.4025 −1.99263 −0.996314 0.0857861i \(-0.972660\pi\)
−0.996314 + 0.0857861i \(0.972660\pi\)
\(282\) 16.2801 0.969463
\(283\) −7.93631 −0.471765 −0.235882 0.971782i \(-0.575798\pi\)
−0.235882 + 0.971782i \(0.575798\pi\)
\(284\) −55.9956 −3.32273
\(285\) 0.863432 0.0511453
\(286\) −22.8684 −1.35224
\(287\) 10.0042 0.590532
\(288\) −8.83702 −0.520727
\(289\) 44.1251 2.59559
\(290\) −12.2310 −0.718231
\(291\) 3.38972 0.198709
\(292\) 18.0618 1.05698
\(293\) −1.05604 −0.0616945 −0.0308473 0.999524i \(-0.509821\pi\)
−0.0308473 + 0.999524i \(0.509821\pi\)
\(294\) −18.2754 −1.06584
\(295\) 4.40877 0.256689
\(296\) 15.8264 0.919893
\(297\) −14.5598 −0.844845
\(298\) 47.3770 2.74448
\(299\) −16.0665 −0.929152
\(300\) −11.2221 −0.647905
\(301\) 20.8237 1.20026
\(302\) 30.3531 1.74662
\(303\) −1.90269 −0.109306
\(304\) 1.48678 0.0852730
\(305\) 11.7622 0.673503
\(306\) 42.9919 2.45768
\(307\) 11.9040 0.679395 0.339697 0.940535i \(-0.389675\pi\)
0.339697 + 0.940535i \(0.389675\pi\)
\(308\) −48.2327 −2.74831
\(309\) 7.00107 0.398277
\(310\) 25.4904 1.44775
\(311\) −19.6767 −1.11576 −0.557881 0.829921i \(-0.688385\pi\)
−0.557881 + 0.829921i \(0.688385\pi\)
\(312\) −8.62211 −0.488131
\(313\) 2.40808 0.136113 0.0680564 0.997681i \(-0.478320\pi\)
0.0680564 + 0.997681i \(0.478320\pi\)
\(314\) −5.38621 −0.303962
\(315\) 10.0446 0.565950
\(316\) −24.0808 −1.35465
\(317\) −5.62913 −0.316163 −0.158082 0.987426i \(-0.550531\pi\)
−0.158082 + 0.987426i \(0.550531\pi\)
\(318\) −15.6491 −0.877558
\(319\) 16.4152 0.919074
\(320\) −12.5850 −0.703523
\(321\) 14.2462 0.795148
\(322\) −52.9942 −2.95325
\(323\) 7.81825 0.435019
\(324\) 12.2573 0.680959
\(325\) −11.2563 −0.624387
\(326\) −16.2046 −0.897490
\(327\) −2.04982 −0.113355
\(328\) 8.96911 0.495236
\(329\) 34.4417 1.89883
\(330\) −6.80482 −0.374593
\(331\) 11.2081 0.616052 0.308026 0.951378i \(-0.400332\pi\)
0.308026 + 0.951378i \(0.400332\pi\)
\(332\) −27.5671 −1.51294
\(333\) 10.1424 0.555801
\(334\) 14.9797 0.819651
\(335\) 5.17152 0.282550
\(336\) −4.92776 −0.268831
\(337\) −23.1766 −1.26251 −0.631256 0.775575i \(-0.717460\pi\)
−0.631256 + 0.775575i \(0.717460\pi\)
\(338\) 10.7875 0.586765
\(339\) 8.50678 0.462025
\(340\) 29.3572 1.59212
\(341\) −34.2104 −1.85260
\(342\) 5.49891 0.297347
\(343\) −10.2167 −0.551652
\(344\) 18.6691 1.00657
\(345\) −4.78082 −0.257391
\(346\) 50.1037 2.69359
\(347\) −7.00451 −0.376022 −0.188011 0.982167i \(-0.560204\pi\)
−0.188011 + 0.982167i \(0.560204\pi\)
\(348\) 14.1908 0.760708
\(349\) −19.8934 −1.06487 −0.532436 0.846471i \(-0.678723\pi\)
−0.532436 + 0.846471i \(0.678723\pi\)
\(350\) −37.1280 −1.98457
\(351\) −12.6252 −0.673886
\(352\) 12.6654 0.675066
\(353\) −15.7660 −0.839142 −0.419571 0.907723i \(-0.637819\pi\)
−0.419571 + 0.907723i \(0.637819\pi\)
\(354\) −7.99949 −0.425168
\(355\) −16.7131 −0.887039
\(356\) 4.30285 0.228051
\(357\) −25.9126 −1.37144
\(358\) 22.6963 1.19953
\(359\) 0.780277 0.0411815 0.0205907 0.999788i \(-0.493445\pi\)
0.0205907 + 0.999788i \(0.493445\pi\)
\(360\) 9.00530 0.474621
\(361\) 1.00000 0.0526316
\(362\) −55.1853 −2.90047
\(363\) 0.161174 0.00845945
\(364\) −41.8240 −2.19218
\(365\) 5.39093 0.282174
\(366\) −21.3420 −1.11556
\(367\) 12.4372 0.649218 0.324609 0.945848i \(-0.394767\pi\)
0.324609 + 0.945848i \(0.394767\pi\)
\(368\) −8.23233 −0.429140
\(369\) 5.74788 0.299223
\(370\) 10.8311 0.563080
\(371\) −33.1069 −1.71882
\(372\) −29.5747 −1.53338
\(373\) −36.3071 −1.87991 −0.939955 0.341298i \(-0.889134\pi\)
−0.939955 + 0.341298i \(0.889134\pi\)
\(374\) −61.6167 −3.18612
\(375\) −7.66662 −0.395903
\(376\) 30.8780 1.59241
\(377\) 14.2341 0.733094
\(378\) −41.6434 −2.14190
\(379\) −33.8596 −1.73925 −0.869626 0.493711i \(-0.835640\pi\)
−0.869626 + 0.493711i \(0.835640\pi\)
\(380\) 3.75496 0.192625
\(381\) −12.5284 −0.641847
\(382\) −7.10175 −0.363357
\(383\) 25.9094 1.32391 0.661954 0.749544i \(-0.269727\pi\)
0.661954 + 0.749544i \(0.269727\pi\)
\(384\) 16.6610 0.850227
\(385\) −14.3961 −0.733693
\(386\) 41.3915 2.10677
\(387\) 11.9642 0.608173
\(388\) 14.7415 0.748387
\(389\) −23.3379 −1.18328 −0.591640 0.806202i \(-0.701519\pi\)
−0.591640 + 0.806202i \(0.701519\pi\)
\(390\) −5.90067 −0.298792
\(391\) −43.2897 −2.18925
\(392\) −34.6626 −1.75073
\(393\) −6.38183 −0.321921
\(394\) −20.9358 −1.05473
\(395\) −7.18744 −0.361639
\(396\) −27.7118 −1.39257
\(397\) 31.6373 1.58783 0.793915 0.608028i \(-0.208039\pi\)
0.793915 + 0.608028i \(0.208039\pi\)
\(398\) 61.1148 3.06341
\(399\) −3.31437 −0.165926
\(400\) −5.76761 −0.288380
\(401\) −5.11584 −0.255473 −0.127736 0.991808i \(-0.540771\pi\)
−0.127736 + 0.991808i \(0.540771\pi\)
\(402\) −9.38347 −0.468005
\(403\) −29.6649 −1.47771
\(404\) −8.27455 −0.411674
\(405\) 3.65845 0.181790
\(406\) 46.9501 2.33009
\(407\) −14.5363 −0.720537
\(408\) −23.2314 −1.15013
\(409\) −4.36186 −0.215680 −0.107840 0.994168i \(-0.534393\pi\)
−0.107840 + 0.994168i \(0.534393\pi\)
\(410\) 6.13814 0.303141
\(411\) 11.4805 0.566289
\(412\) 30.4468 1.50001
\(413\) −16.9235 −0.832752
\(414\) −30.4475 −1.49641
\(415\) −8.22800 −0.403897
\(416\) 10.9825 0.538463
\(417\) 11.5378 0.565010
\(418\) −7.88113 −0.385479
\(419\) −11.7294 −0.573019 −0.286509 0.958077i \(-0.592495\pi\)
−0.286509 + 0.958077i \(0.592495\pi\)
\(420\) −12.4453 −0.607270
\(421\) 14.8381 0.723164 0.361582 0.932340i \(-0.382237\pi\)
0.361582 + 0.932340i \(0.382237\pi\)
\(422\) −2.35519 −0.114649
\(423\) 19.7883 0.962138
\(424\) −29.6813 −1.44145
\(425\) −30.3289 −1.47117
\(426\) 30.3251 1.46925
\(427\) −45.1505 −2.18499
\(428\) 61.9552 2.99472
\(429\) 7.91924 0.382345
\(430\) 12.7765 0.616137
\(431\) −26.5767 −1.28015 −0.640077 0.768311i \(-0.721098\pi\)
−0.640077 + 0.768311i \(0.721098\pi\)
\(432\) −6.46905 −0.311242
\(433\) −32.3118 −1.55281 −0.776403 0.630237i \(-0.782958\pi\)
−0.776403 + 0.630237i \(0.782958\pi\)
\(434\) −97.8473 −4.69682
\(435\) 4.23556 0.203080
\(436\) −8.91442 −0.426923
\(437\) −5.53700 −0.264871
\(438\) −9.78157 −0.467381
\(439\) −0.252507 −0.0120515 −0.00602574 0.999982i \(-0.501918\pi\)
−0.00602574 + 0.999982i \(0.501918\pi\)
\(440\) −12.9065 −0.615295
\(441\) −22.2136 −1.05779
\(442\) −53.4297 −2.54139
\(443\) −29.0251 −1.37902 −0.689511 0.724275i \(-0.742175\pi\)
−0.689511 + 0.724275i \(0.742175\pi\)
\(444\) −12.5665 −0.596381
\(445\) 1.28428 0.0608807
\(446\) 62.9160 2.97916
\(447\) −16.4065 −0.776000
\(448\) 48.3089 2.28238
\(449\) 8.10323 0.382415 0.191208 0.981550i \(-0.438760\pi\)
0.191208 + 0.981550i \(0.438760\pi\)
\(450\) −21.3317 −1.00558
\(451\) −8.23795 −0.387910
\(452\) 36.9950 1.74010
\(453\) −10.5111 −0.493857
\(454\) −6.99811 −0.328438
\(455\) −12.4833 −0.585226
\(456\) −2.97144 −0.139150
\(457\) 17.1469 0.802099 0.401050 0.916056i \(-0.368645\pi\)
0.401050 + 0.916056i \(0.368645\pi\)
\(458\) 14.2528 0.665991
\(459\) −34.0175 −1.58780
\(460\) −20.7912 −0.969396
\(461\) 17.9364 0.835381 0.417691 0.908589i \(-0.362840\pi\)
0.417691 + 0.908589i \(0.362840\pi\)
\(462\) 26.1210 1.21526
\(463\) −3.68266 −0.171148 −0.0855739 0.996332i \(-0.527272\pi\)
−0.0855739 + 0.996332i \(0.527272\pi\)
\(464\) 7.29342 0.338588
\(465\) −8.82721 −0.409352
\(466\) 55.0808 2.55157
\(467\) 31.3913 1.45262 0.726308 0.687369i \(-0.241234\pi\)
0.726308 + 0.687369i \(0.241234\pi\)
\(468\) −24.0298 −1.11078
\(469\) −19.8514 −0.916653
\(470\) 21.1318 0.974738
\(471\) 1.86522 0.0859450
\(472\) −15.1725 −0.698369
\(473\) −17.1472 −0.788431
\(474\) 13.0412 0.599004
\(475\) −3.87925 −0.177992
\(476\) −112.691 −5.16517
\(477\) −19.0214 −0.870928
\(478\) −2.10014 −0.0960582
\(479\) 14.9656 0.683796 0.341898 0.939737i \(-0.388930\pi\)
0.341898 + 0.939737i \(0.388930\pi\)
\(480\) 3.26801 0.149163
\(481\) −12.6049 −0.574732
\(482\) 1.60229 0.0729821
\(483\) 18.3517 0.835031
\(484\) 0.700928 0.0318603
\(485\) 4.39993 0.199790
\(486\) −37.3806 −1.69562
\(487\) 19.5342 0.885178 0.442589 0.896725i \(-0.354060\pi\)
0.442589 + 0.896725i \(0.354060\pi\)
\(488\) −40.4788 −1.83239
\(489\) 5.61159 0.253765
\(490\) −23.7218 −1.07164
\(491\) 22.7050 1.02466 0.512332 0.858787i \(-0.328782\pi\)
0.512332 + 0.858787i \(0.328782\pi\)
\(492\) −7.12166 −0.321069
\(493\) 38.3524 1.72730
\(494\) −6.83397 −0.307475
\(495\) −8.27120 −0.371763
\(496\) −15.2000 −0.682500
\(497\) 64.1550 2.87774
\(498\) 14.9293 0.668998
\(499\) 44.5243 1.99318 0.996590 0.0825176i \(-0.0262961\pi\)
0.996590 + 0.0825176i \(0.0262961\pi\)
\(500\) −33.3412 −1.49107
\(501\) −5.18740 −0.231756
\(502\) 53.9812 2.40930
\(503\) 29.7657 1.32719 0.663594 0.748093i \(-0.269030\pi\)
0.663594 + 0.748093i \(0.269030\pi\)
\(504\) −34.5678 −1.53977
\(505\) −2.46972 −0.109901
\(506\) 43.6379 1.93994
\(507\) −3.73569 −0.165908
\(508\) −54.4843 −2.41735
\(509\) −35.7821 −1.58602 −0.793008 0.609212i \(-0.791486\pi\)
−0.793008 + 0.609212i \(0.791486\pi\)
\(510\) −15.8988 −0.704009
\(511\) −20.6936 −0.915433
\(512\) 16.4609 0.727475
\(513\) −4.35103 −0.192103
\(514\) 64.3713 2.83930
\(515\) 9.08753 0.400444
\(516\) −14.8237 −0.652576
\(517\) −28.3609 −1.24731
\(518\) −41.5761 −1.82675
\(519\) −17.3507 −0.761612
\(520\) −11.1917 −0.490787
\(521\) 15.2653 0.668785 0.334393 0.942434i \(-0.391469\pi\)
0.334393 + 0.942434i \(0.391469\pi\)
\(522\) 26.9749 1.18066
\(523\) −0.665276 −0.0290905 −0.0145453 0.999894i \(-0.504630\pi\)
−0.0145453 + 0.999894i \(0.504630\pi\)
\(524\) −27.7538 −1.21243
\(525\) 12.8573 0.561137
\(526\) −31.2441 −1.36231
\(527\) −79.9292 −3.48177
\(528\) 4.05774 0.176591
\(529\) 7.65842 0.332975
\(530\) −20.3128 −0.882333
\(531\) −9.72332 −0.421956
\(532\) −14.4138 −0.624918
\(533\) −7.14338 −0.309414
\(534\) −2.33026 −0.100840
\(535\) 18.4919 0.799474
\(536\) −17.7974 −0.768731
\(537\) −7.85963 −0.339168
\(538\) −11.2889 −0.486701
\(539\) 31.8369 1.37131
\(540\) −16.3380 −0.703074
\(541\) −4.60724 −0.198081 −0.0990403 0.995083i \(-0.531577\pi\)
−0.0990403 + 0.995083i \(0.531577\pi\)
\(542\) 1.64029 0.0704567
\(543\) 19.1104 0.820108
\(544\) 29.5913 1.26872
\(545\) −2.66070 −0.113972
\(546\) 22.6503 0.969344
\(547\) −12.0929 −0.517054 −0.258527 0.966004i \(-0.583237\pi\)
−0.258527 + 0.966004i \(0.583237\pi\)
\(548\) 49.9271 2.13278
\(549\) −25.9410 −1.10713
\(550\) 30.5729 1.30363
\(551\) 4.90550 0.208981
\(552\) 16.4529 0.700280
\(553\) 27.5897 1.17323
\(554\) 8.28254 0.351891
\(555\) −3.75075 −0.159211
\(556\) 50.1766 2.12796
\(557\) 24.5146 1.03872 0.519359 0.854556i \(-0.326171\pi\)
0.519359 + 0.854556i \(0.326171\pi\)
\(558\) −56.2176 −2.37988
\(559\) −14.8689 −0.628887
\(560\) −6.39632 −0.270294
\(561\) 21.3376 0.900875
\(562\) 78.6693 3.31846
\(563\) −15.3476 −0.646823 −0.323412 0.946258i \(-0.604830\pi\)
−0.323412 + 0.946258i \(0.604830\pi\)
\(564\) −24.5178 −1.03238
\(565\) 11.0420 0.464539
\(566\) 18.6915 0.785663
\(567\) −14.0433 −0.589765
\(568\) 57.5169 2.41336
\(569\) −9.28783 −0.389366 −0.194683 0.980866i \(-0.562368\pi\)
−0.194683 + 0.980866i \(0.562368\pi\)
\(570\) −2.03354 −0.0851758
\(571\) 15.9374 0.666960 0.333480 0.942757i \(-0.391777\pi\)
0.333480 + 0.942757i \(0.391777\pi\)
\(572\) 34.4399 1.44000
\(573\) 2.45931 0.102739
\(574\) −23.5619 −0.983454
\(575\) 21.4794 0.895754
\(576\) 27.7556 1.15648
\(577\) −39.7523 −1.65491 −0.827455 0.561532i \(-0.810212\pi\)
−0.827455 + 0.561532i \(0.810212\pi\)
\(578\) −103.923 −4.32262
\(579\) −14.3337 −0.595689
\(580\) 18.4199 0.764846
\(581\) 31.5840 1.31033
\(582\) −7.98344 −0.330924
\(583\) 27.2617 1.12906
\(584\) −18.5525 −0.767707
\(585\) −7.17221 −0.296534
\(586\) 2.48717 0.102744
\(587\) 17.4164 0.718852 0.359426 0.933174i \(-0.382973\pi\)
0.359426 + 0.933174i \(0.382973\pi\)
\(588\) 27.5228 1.13502
\(589\) −10.2234 −0.421248
\(590\) −10.3835 −0.427482
\(591\) 7.24999 0.298225
\(592\) −6.45860 −0.265447
\(593\) 17.9171 0.735768 0.367884 0.929872i \(-0.380082\pi\)
0.367884 + 0.929872i \(0.380082\pi\)
\(594\) 34.2911 1.40698
\(595\) −33.6350 −1.37890
\(596\) −71.3498 −2.92260
\(597\) −21.1638 −0.866177
\(598\) 37.8397 1.54738
\(599\) 4.65533 0.190212 0.0951059 0.995467i \(-0.469681\pi\)
0.0951059 + 0.995467i \(0.469681\pi\)
\(600\) 11.5269 0.470585
\(601\) −34.9283 −1.42476 −0.712378 0.701796i \(-0.752382\pi\)
−0.712378 + 0.701796i \(0.752382\pi\)
\(602\) −49.0439 −1.99888
\(603\) −11.4055 −0.464469
\(604\) −45.7117 −1.85998
\(605\) 0.209207 0.00850548
\(606\) 4.48118 0.182036
\(607\) 45.9974 1.86698 0.933489 0.358607i \(-0.116748\pi\)
0.933489 + 0.358607i \(0.116748\pi\)
\(608\) 3.78490 0.153498
\(609\) −16.2586 −0.658833
\(610\) −27.7023 −1.12163
\(611\) −24.5926 −0.994909
\(612\) −64.7458 −2.61720
\(613\) 0.916594 0.0370209 0.0185104 0.999829i \(-0.494108\pi\)
0.0185104 + 0.999829i \(0.494108\pi\)
\(614\) −28.0361 −1.13144
\(615\) −2.12561 −0.0857130
\(616\) 49.5431 1.99615
\(617\) −40.2900 −1.62201 −0.811007 0.585036i \(-0.801080\pi\)
−0.811007 + 0.585036i \(0.801080\pi\)
\(618\) −16.4889 −0.663279
\(619\) −13.0772 −0.525617 −0.262808 0.964848i \(-0.584649\pi\)
−0.262808 + 0.964848i \(0.584649\pi\)
\(620\) −38.3885 −1.54172
\(621\) 24.0917 0.966766
\(622\) 46.3423 1.85816
\(623\) −4.92984 −0.197510
\(624\) 3.51859 0.140856
\(625\) 9.44483 0.377793
\(626\) −5.67148 −0.226678
\(627\) 2.72921 0.108994
\(628\) 8.11164 0.323690
\(629\) −33.9625 −1.35418
\(630\) −23.6570 −0.942516
\(631\) −1.30780 −0.0520626 −0.0260313 0.999661i \(-0.508287\pi\)
−0.0260313 + 0.999661i \(0.508287\pi\)
\(632\) 24.7350 0.983906
\(633\) 0.815593 0.0324169
\(634\) 13.2577 0.526529
\(635\) −16.2620 −0.645339
\(636\) 23.5676 0.934515
\(637\) 27.6068 1.09382
\(638\) −38.6609 −1.53060
\(639\) 36.8599 1.45815
\(640\) 21.6263 0.854853
\(641\) −8.07067 −0.318772 −0.159386 0.987216i \(-0.550951\pi\)
−0.159386 + 0.987216i \(0.550951\pi\)
\(642\) −33.5526 −1.32422
\(643\) 14.3952 0.567691 0.283845 0.958870i \(-0.408390\pi\)
0.283845 + 0.958870i \(0.408390\pi\)
\(644\) 79.8093 3.14493
\(645\) −4.42445 −0.174213
\(646\) −18.4135 −0.724468
\(647\) 13.6290 0.535810 0.267905 0.963445i \(-0.413669\pi\)
0.267905 + 0.963445i \(0.413669\pi\)
\(648\) −12.5903 −0.494593
\(649\) 13.9356 0.547021
\(650\) 26.5107 1.03983
\(651\) 33.8842 1.32802
\(652\) 24.4042 0.955740
\(653\) 29.9937 1.17374 0.586872 0.809680i \(-0.300359\pi\)
0.586872 + 0.809680i \(0.300359\pi\)
\(654\) 4.82771 0.188779
\(655\) −8.28373 −0.323672
\(656\) −3.66020 −0.142907
\(657\) −11.8894 −0.463850
\(658\) −81.1166 −3.16226
\(659\) −33.1760 −1.29235 −0.646176 0.763188i \(-0.723633\pi\)
−0.646176 + 0.763188i \(0.723633\pi\)
\(660\) 10.2481 0.398905
\(661\) −27.9290 −1.08631 −0.543155 0.839632i \(-0.682771\pi\)
−0.543155 + 0.839632i \(0.682771\pi\)
\(662\) −26.3972 −1.02595
\(663\) 18.5025 0.718578
\(664\) 28.3161 1.09888
\(665\) −4.30212 −0.166829
\(666\) −23.8873 −0.925615
\(667\) −27.1617 −1.05171
\(668\) −22.5594 −0.872849
\(669\) −21.7876 −0.842357
\(670\) −12.1799 −0.470551
\(671\) 37.1790 1.43528
\(672\) −12.5446 −0.483917
\(673\) 44.6394 1.72072 0.860361 0.509685i \(-0.170238\pi\)
0.860361 + 0.509685i \(0.170238\pi\)
\(674\) 54.5854 2.10255
\(675\) 16.8787 0.649663
\(676\) −16.2461 −0.624848
\(677\) −46.8823 −1.80183 −0.900917 0.433991i \(-0.857105\pi\)
−0.900917 + 0.433991i \(0.857105\pi\)
\(678\) −20.0351 −0.769443
\(679\) −16.8896 −0.648162
\(680\) −30.1548 −1.15638
\(681\) 2.42342 0.0928656
\(682\) 80.5720 3.08526
\(683\) −11.1401 −0.426264 −0.213132 0.977023i \(-0.568366\pi\)
−0.213132 + 0.977023i \(0.568366\pi\)
\(684\) −8.28137 −0.316646
\(685\) 14.9018 0.569370
\(686\) 24.0623 0.918705
\(687\) −4.93570 −0.188309
\(688\) −7.61867 −0.290459
\(689\) 23.6395 0.900592
\(690\) 11.2597 0.428651
\(691\) −33.4231 −1.27148 −0.635738 0.771905i \(-0.719304\pi\)
−0.635738 + 0.771905i \(0.719304\pi\)
\(692\) −75.4562 −2.86841
\(693\) 31.7498 1.20608
\(694\) 16.4970 0.626216
\(695\) 14.9763 0.568084
\(696\) −14.5764 −0.552516
\(697\) −19.2471 −0.729037
\(698\) 46.8528 1.77340
\(699\) −19.0743 −0.721455
\(700\) 55.9147 2.11338
\(701\) 1.17001 0.0441907 0.0220953 0.999756i \(-0.492966\pi\)
0.0220953 + 0.999756i \(0.492966\pi\)
\(702\) 29.7348 1.12227
\(703\) −4.34401 −0.163837
\(704\) −39.7797 −1.49926
\(705\) −7.31787 −0.275607
\(706\) 37.1320 1.39748
\(707\) 9.48028 0.356543
\(708\) 12.0472 0.452763
\(709\) −29.1309 −1.09403 −0.547016 0.837122i \(-0.684236\pi\)
−0.547016 + 0.837122i \(0.684236\pi\)
\(710\) 39.3625 1.47725
\(711\) 15.8515 0.594478
\(712\) −4.41975 −0.165637
\(713\) 56.6070 2.11995
\(714\) 61.0290 2.28395
\(715\) 10.2793 0.384425
\(716\) −34.1806 −1.27739
\(717\) 0.727271 0.0271604
\(718\) −1.83770 −0.0685824
\(719\) 2.98339 0.111262 0.0556308 0.998451i \(-0.482283\pi\)
0.0556308 + 0.998451i \(0.482283\pi\)
\(720\) −3.67497 −0.136958
\(721\) −34.8834 −1.29913
\(722\) −2.35519 −0.0876511
\(723\) −0.554865 −0.0206357
\(724\) 83.1091 3.08872
\(725\) −19.0296 −0.706743
\(726\) −0.379596 −0.0140881
\(727\) 1.04362 0.0387056 0.0193528 0.999813i \(-0.493839\pi\)
0.0193528 + 0.999813i \(0.493839\pi\)
\(728\) 42.9604 1.59222
\(729\) 2.57750 0.0954628
\(730\) −12.6967 −0.469924
\(731\) −40.0628 −1.48177
\(732\) 32.1410 1.18797
\(733\) −3.94867 −0.145847 −0.0729237 0.997338i \(-0.523233\pi\)
−0.0729237 + 0.997338i \(0.523233\pi\)
\(734\) −29.2920 −1.08119
\(735\) 8.21478 0.303007
\(736\) −20.9570 −0.772486
\(737\) 16.3466 0.602134
\(738\) −13.5373 −0.498317
\(739\) 8.68242 0.319388 0.159694 0.987167i \(-0.448949\pi\)
0.159694 + 0.987167i \(0.448949\pi\)
\(740\) −16.3116 −0.599626
\(741\) 2.36658 0.0869384
\(742\) 77.9729 2.86248
\(743\) 2.95345 0.108351 0.0541757 0.998531i \(-0.482747\pi\)
0.0541757 + 0.998531i \(0.482747\pi\)
\(744\) 30.3782 1.11372
\(745\) −21.2959 −0.780222
\(746\) 85.5101 3.13075
\(747\) 18.1464 0.663943
\(748\) 92.7947 3.39291
\(749\) −70.9830 −2.59366
\(750\) 18.0564 0.659325
\(751\) −38.1300 −1.39138 −0.695691 0.718341i \(-0.744902\pi\)
−0.695691 + 0.718341i \(0.744902\pi\)
\(752\) −12.6010 −0.459511
\(753\) −18.6935 −0.681229
\(754\) −33.5240 −1.22087
\(755\) −13.6437 −0.496544
\(756\) 62.7149 2.28092
\(757\) 5.07316 0.184387 0.0921937 0.995741i \(-0.470612\pi\)
0.0921937 + 0.995741i \(0.470612\pi\)
\(758\) 79.7458 2.89650
\(759\) −15.1116 −0.548517
\(760\) −3.85698 −0.139907
\(761\) 32.2741 1.16993 0.584967 0.811057i \(-0.301107\pi\)
0.584967 + 0.811057i \(0.301107\pi\)
\(762\) 29.5066 1.06891
\(763\) 10.2134 0.369749
\(764\) 10.6952 0.386940
\(765\) −19.3248 −0.698690
\(766\) −61.0216 −2.20480
\(767\) 12.0840 0.436328
\(768\) −19.8487 −0.716227
\(769\) 50.4795 1.82034 0.910169 0.414237i \(-0.135952\pi\)
0.910169 + 0.414237i \(0.135952\pi\)
\(770\) 33.9055 1.22187
\(771\) −22.2915 −0.802810
\(772\) −62.3356 −2.24351
\(773\) 9.63174 0.346430 0.173215 0.984884i \(-0.444584\pi\)
0.173215 + 0.984884i \(0.444584\pi\)
\(774\) −28.1779 −1.01283
\(775\) 39.6591 1.42460
\(776\) −15.1420 −0.543567
\(777\) 14.3977 0.516513
\(778\) 54.9653 1.97060
\(779\) −2.46182 −0.0882039
\(780\) 8.88641 0.318185
\(781\) −52.8282 −1.89034
\(782\) 101.955 3.64592
\(783\) −21.3440 −0.762771
\(784\) 14.1454 0.505194
\(785\) 2.42110 0.0864126
\(786\) 15.0304 0.536117
\(787\) −30.8820 −1.10082 −0.550412 0.834893i \(-0.685529\pi\)
−0.550412 + 0.834893i \(0.685529\pi\)
\(788\) 31.5293 1.12319
\(789\) 10.8197 0.385192
\(790\) 16.9278 0.602263
\(791\) −42.3857 −1.50706
\(792\) 28.4647 1.01145
\(793\) 32.2391 1.14484
\(794\) −74.5118 −2.64433
\(795\) 7.03426 0.249479
\(796\) −92.0389 −3.26223
\(797\) 4.67012 0.165424 0.0827121 0.996573i \(-0.473642\pi\)
0.0827121 + 0.996573i \(0.473642\pi\)
\(798\) 7.80597 0.276328
\(799\) −66.2622 −2.34419
\(800\) −14.6826 −0.519108
\(801\) −2.83241 −0.100078
\(802\) 12.0488 0.425457
\(803\) 17.0401 0.601332
\(804\) 14.1315 0.498380
\(805\) 23.8208 0.839574
\(806\) 69.8665 2.46094
\(807\) 3.90932 0.137614
\(808\) 8.49936 0.299006
\(809\) 40.6331 1.42858 0.714292 0.699847i \(-0.246749\pi\)
0.714292 + 0.699847i \(0.246749\pi\)
\(810\) −8.61634 −0.302747
\(811\) −3.17941 −0.111644 −0.0558221 0.998441i \(-0.517778\pi\)
−0.0558221 + 0.998441i \(0.517778\pi\)
\(812\) −70.7068 −2.48132
\(813\) −0.568028 −0.0199216
\(814\) 34.2357 1.19996
\(815\) 7.28395 0.255146
\(816\) 9.48050 0.331884
\(817\) −5.12426 −0.179275
\(818\) 10.2730 0.359187
\(819\) 27.5313 0.962020
\(820\) −9.24404 −0.322816
\(821\) −51.9477 −1.81299 −0.906493 0.422220i \(-0.861251\pi\)
−0.906493 + 0.422220i \(0.861251\pi\)
\(822\) −27.0386 −0.943081
\(823\) 26.6951 0.930534 0.465267 0.885170i \(-0.345958\pi\)
0.465267 + 0.885170i \(0.345958\pi\)
\(824\) −31.2740 −1.08948
\(825\) −10.5873 −0.368601
\(826\) 39.8581 1.38684
\(827\) 22.5541 0.784284 0.392142 0.919905i \(-0.371734\pi\)
0.392142 + 0.919905i \(0.371734\pi\)
\(828\) 45.8540 1.59354
\(829\) −34.3884 −1.19436 −0.597180 0.802107i \(-0.703712\pi\)
−0.597180 + 0.802107i \(0.703712\pi\)
\(830\) 19.3785 0.672638
\(831\) −2.86821 −0.0994972
\(832\) −34.4942 −1.19587
\(833\) 74.3837 2.57724
\(834\) −27.1738 −0.940950
\(835\) −6.73334 −0.233017
\(836\) 11.8690 0.410498
\(837\) 44.4824 1.53754
\(838\) 27.6250 0.954289
\(839\) −23.8833 −0.824543 −0.412272 0.911061i \(-0.635265\pi\)
−0.412272 + 0.911061i \(0.635265\pi\)
\(840\) 12.7835 0.441071
\(841\) −4.93612 −0.170211
\(842\) −34.9465 −1.20434
\(843\) −27.2429 −0.938294
\(844\) 3.54692 0.122090
\(845\) −4.84899 −0.166810
\(846\) −46.6051 −1.60232
\(847\) −0.803063 −0.0275936
\(848\) 12.1126 0.415949
\(849\) −6.47280 −0.222146
\(850\) 71.4304 2.45004
\(851\) 24.0528 0.824519
\(852\) −45.6696 −1.56461
\(853\) 13.5779 0.464900 0.232450 0.972608i \(-0.425326\pi\)
0.232450 + 0.972608i \(0.425326\pi\)
\(854\) 106.338 3.63881
\(855\) −2.47176 −0.0845323
\(856\) −63.6384 −2.17512
\(857\) 42.6481 1.45683 0.728415 0.685136i \(-0.240257\pi\)
0.728415 + 0.685136i \(0.240257\pi\)
\(858\) −18.6513 −0.636746
\(859\) −28.4263 −0.969894 −0.484947 0.874544i \(-0.661161\pi\)
−0.484947 + 0.874544i \(0.661161\pi\)
\(860\) −19.2414 −0.656126
\(861\) 8.15939 0.278071
\(862\) 62.5932 2.13193
\(863\) −30.8627 −1.05058 −0.525288 0.850924i \(-0.676043\pi\)
−0.525288 + 0.850924i \(0.676043\pi\)
\(864\) −16.4682 −0.560261
\(865\) −22.5216 −0.765756
\(866\) 76.1004 2.58600
\(867\) 35.9881 1.22222
\(868\) 147.358 5.00166
\(869\) −22.7186 −0.770677
\(870\) −9.97554 −0.338203
\(871\) 14.1746 0.480289
\(872\) 9.15661 0.310082
\(873\) −9.70381 −0.328424
\(874\) 13.0407 0.441108
\(875\) 38.1996 1.29138
\(876\) 14.7311 0.497716
\(877\) −6.78441 −0.229093 −0.114547 0.993418i \(-0.536542\pi\)
−0.114547 + 0.993418i \(0.536542\pi\)
\(878\) 0.594701 0.0200702
\(879\) −0.861299 −0.0290509
\(880\) 5.26702 0.177551
\(881\) 18.7865 0.632932 0.316466 0.948604i \(-0.397504\pi\)
0.316466 + 0.948604i \(0.397504\pi\)
\(882\) 52.3173 1.76161
\(883\) 10.9100 0.367152 0.183576 0.983006i \(-0.441233\pi\)
0.183576 + 0.983006i \(0.441233\pi\)
\(884\) 80.4652 2.70634
\(885\) 3.59576 0.120870
\(886\) 68.3595 2.29658
\(887\) 17.9859 0.603906 0.301953 0.953323i \(-0.402361\pi\)
0.301953 + 0.953323i \(0.402361\pi\)
\(888\) 12.9079 0.433162
\(889\) 62.4235 2.09362
\(890\) −3.02472 −0.101389
\(891\) 11.5639 0.387406
\(892\) −94.7516 −3.17252
\(893\) −8.47533 −0.283616
\(894\) 38.6404 1.29233
\(895\) −10.2019 −0.341013
\(896\) −83.0146 −2.77332
\(897\) −13.1038 −0.437522
\(898\) −19.0846 −0.636863
\(899\) −50.1509 −1.67263
\(900\) 32.1255 1.07085
\(901\) 63.6942 2.12196
\(902\) 19.4019 0.646014
\(903\) 16.9837 0.565182
\(904\) −38.0001 −1.26386
\(905\) 24.8057 0.824570
\(906\) 24.7557 0.822455
\(907\) 38.6298 1.28268 0.641341 0.767256i \(-0.278378\pi\)
0.641341 + 0.767256i \(0.278378\pi\)
\(908\) 10.5392 0.349754
\(909\) 5.44684 0.180660
\(910\) 29.4005 0.974618
\(911\) −18.4358 −0.610805 −0.305402 0.952223i \(-0.598791\pi\)
−0.305402 + 0.952223i \(0.598791\pi\)
\(912\) 1.21261 0.0401536
\(913\) −26.0078 −0.860731
\(914\) −40.3842 −1.33579
\(915\) 9.59319 0.317141
\(916\) −21.4648 −0.709216
\(917\) 31.7980 1.05006
\(918\) 80.1176 2.64427
\(919\) 14.0343 0.462948 0.231474 0.972841i \(-0.425645\pi\)
0.231474 + 0.972841i \(0.425645\pi\)
\(920\) 21.3561 0.704090
\(921\) 9.70878 0.319915
\(922\) −42.2436 −1.39122
\(923\) −45.8089 −1.50782
\(924\) −39.3382 −1.29413
\(925\) 16.8515 0.554074
\(926\) 8.67336 0.285024
\(927\) −20.0421 −0.658268
\(928\) 18.5668 0.609486
\(929\) −5.79232 −0.190040 −0.0950199 0.995475i \(-0.530291\pi\)
−0.0950199 + 0.995475i \(0.530291\pi\)
\(930\) 20.7898 0.681723
\(931\) 9.51411 0.311812
\(932\) −82.9517 −2.71717
\(933\) −16.0482 −0.525393
\(934\) −73.9325 −2.41914
\(935\) 27.6966 0.905776
\(936\) 24.6826 0.806777
\(937\) −39.6431 −1.29508 −0.647542 0.762030i \(-0.724203\pi\)
−0.647542 + 0.762030i \(0.724203\pi\)
\(938\) 46.7539 1.52657
\(939\) 1.96401 0.0640932
\(940\) −31.8245 −1.03800
\(941\) 29.3255 0.955985 0.477992 0.878364i \(-0.341365\pi\)
0.477992 + 0.878364i \(0.341365\pi\)
\(942\) −4.39296 −0.143130
\(943\) 13.6311 0.443890
\(944\) 6.19172 0.201523
\(945\) 18.7186 0.608917
\(946\) 40.3850 1.31303
\(947\) 41.5570 1.35042 0.675211 0.737625i \(-0.264053\pi\)
0.675211 + 0.737625i \(0.264053\pi\)
\(948\) −19.6401 −0.637881
\(949\) 14.7760 0.479649
\(950\) 9.13637 0.296423
\(951\) −4.59108 −0.148876
\(952\) 115.752 3.75156
\(953\) −57.7073 −1.86932 −0.934661 0.355540i \(-0.884297\pi\)
−0.934661 + 0.355540i \(0.884297\pi\)
\(954\) 44.7989 1.45042
\(955\) 3.19223 0.103298
\(956\) 3.16281 0.102293
\(957\) 13.3881 0.432776
\(958\) −35.2468 −1.13877
\(959\) −57.2023 −1.84716
\(960\) −10.2642 −0.331277
\(961\) 73.5180 2.37155
\(962\) 29.6868 0.957142
\(963\) −40.7829 −1.31421
\(964\) −2.41304 −0.0777189
\(965\) −18.6054 −0.598930
\(966\) −43.2217 −1.39064
\(967\) −16.3938 −0.527188 −0.263594 0.964634i \(-0.584908\pi\)
−0.263594 + 0.964634i \(0.584908\pi\)
\(968\) −0.719971 −0.0231407
\(969\) 6.37651 0.204843
\(970\) −10.3627 −0.332725
\(971\) 5.62352 0.180467 0.0902337 0.995921i \(-0.471239\pi\)
0.0902337 + 0.995921i \(0.471239\pi\)
\(972\) 56.2952 1.80567
\(973\) −57.4881 −1.84298
\(974\) −46.0067 −1.47415
\(975\) −9.18055 −0.294013
\(976\) 16.5190 0.528760
\(977\) 48.0619 1.53764 0.768818 0.639467i \(-0.220845\pi\)
0.768818 + 0.639467i \(0.220845\pi\)
\(978\) −13.2164 −0.422613
\(979\) 4.05946 0.129741
\(980\) 35.7251 1.14120
\(981\) 5.86804 0.187352
\(982\) −53.4747 −1.70645
\(983\) −21.2619 −0.678151 −0.339075 0.940759i \(-0.610114\pi\)
−0.339075 + 0.940759i \(0.610114\pi\)
\(984\) 7.31514 0.233198
\(985\) 9.41062 0.299847
\(986\) −90.3271 −2.87660
\(987\) 28.0904 0.894127
\(988\) 10.2920 0.327431
\(989\) 28.3731 0.902211
\(990\) 19.4802 0.619123
\(991\) 16.5905 0.527015 0.263507 0.964657i \(-0.415121\pi\)
0.263507 + 0.964657i \(0.415121\pi\)
\(992\) −38.6946 −1.22856
\(993\) 9.14123 0.290088
\(994\) −151.097 −4.79251
\(995\) −27.4710 −0.870890
\(996\) −22.4835 −0.712418
\(997\) 16.5687 0.524737 0.262369 0.964968i \(-0.415496\pi\)
0.262369 + 0.964968i \(0.415496\pi\)
\(998\) −104.863 −3.31938
\(999\) 18.9009 0.597999
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 \(a_p\))