Properties

Label 6017.2.a.c.1.7
Level 6017
Weight 2
Character 6017.1
Self dual Yes
Analytic conductor 48.046
Analytic rank 1
Dimension 106
CM No

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Newspace parameters

Level: \( N \) = \( 6017 = 11 \cdot 547 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6017.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0459868962\)
Analytic rank: \(1\)
Dimension: \(106\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 6017.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.58511 q^{2}\) \(-2.87890 q^{3}\) \(+4.68281 q^{4}\) \(-1.51557 q^{5}\) \(+7.44229 q^{6}\) \(+0.161489 q^{7}\) \(-6.93538 q^{8}\) \(+5.28808 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.58511 q^{2}\) \(-2.87890 q^{3}\) \(+4.68281 q^{4}\) \(-1.51557 q^{5}\) \(+7.44229 q^{6}\) \(+0.161489 q^{7}\) \(-6.93538 q^{8}\) \(+5.28808 q^{9}\) \(+3.91792 q^{10}\) \(+1.00000 q^{11}\) \(-13.4814 q^{12}\) \(-6.99617 q^{13}\) \(-0.417469 q^{14}\) \(+4.36317 q^{15}\) \(+8.56312 q^{16}\) \(-4.66254 q^{17}\) \(-13.6703 q^{18}\) \(+4.03748 q^{19}\) \(-7.09712 q^{20}\) \(-0.464912 q^{21}\) \(-2.58511 q^{22}\) \(+4.97780 q^{23}\) \(+19.9663 q^{24}\) \(-2.70305 q^{25}\) \(+18.0859 q^{26}\) \(-6.58715 q^{27}\) \(+0.756225 q^{28}\) \(-1.95167 q^{29}\) \(-11.2793 q^{30}\) \(-0.546934 q^{31}\) \(-8.26588 q^{32}\) \(-2.87890 q^{33}\) \(+12.0532 q^{34}\) \(-0.244748 q^{35}\) \(+24.7631 q^{36}\) \(-3.94217 q^{37}\) \(-10.4373 q^{38}\) \(+20.1413 q^{39}\) \(+10.5110 q^{40}\) \(+4.07011 q^{41}\) \(+1.20185 q^{42}\) \(+5.47625 q^{43}\) \(+4.68281 q^{44}\) \(-8.01444 q^{45}\) \(-12.8682 q^{46}\) \(-2.72261 q^{47}\) \(-24.6524 q^{48}\) \(-6.97392 q^{49}\) \(+6.98770 q^{50}\) \(+13.4230 q^{51}\) \(-32.7618 q^{52}\) \(+13.7242 q^{53}\) \(+17.0285 q^{54}\) \(-1.51557 q^{55}\) \(-1.11999 q^{56}\) \(-11.6235 q^{57}\) \(+5.04528 q^{58}\) \(-0.114947 q^{59}\) \(+20.4319 q^{60}\) \(-2.36507 q^{61}\) \(+1.41389 q^{62}\) \(+0.853969 q^{63}\) \(+4.24200 q^{64}\) \(+10.6032 q^{65}\) \(+7.44229 q^{66}\) \(+4.13899 q^{67}\) \(-21.8338 q^{68}\) \(-14.3306 q^{69}\) \(+0.632702 q^{70}\) \(+5.67318 q^{71}\) \(-36.6748 q^{72}\) \(-14.8910 q^{73}\) \(+10.1909 q^{74}\) \(+7.78183 q^{75}\) \(+18.9068 q^{76}\) \(+0.161489 q^{77}\) \(-52.0675 q^{78}\) \(-7.56851 q^{79}\) \(-12.9780 q^{80}\) \(+3.09954 q^{81}\) \(-10.5217 q^{82}\) \(-9.11300 q^{83}\) \(-2.17710 q^{84}\) \(+7.06640 q^{85}\) \(-14.1567 q^{86}\) \(+5.61865 q^{87}\) \(-6.93538 q^{88}\) \(+10.4253 q^{89}\) \(+20.7182 q^{90}\) \(-1.12981 q^{91}\) \(+23.3101 q^{92}\) \(+1.57457 q^{93}\) \(+7.03827 q^{94}\) \(-6.11907 q^{95}\) \(+23.7967 q^{96}\) \(-6.91061 q^{97}\) \(+18.0284 q^{98}\) \(+5.28808 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(106q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 66q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(106q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 66q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut -\mathstrut 30q^{10} \) \(\mathstrut +\mathstrut 106q^{11} \) \(\mathstrut -\mathstrut 26q^{12} \) \(\mathstrut -\mathstrut 72q^{13} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut -\mathstrut 46q^{15} \) \(\mathstrut +\mathstrut 75q^{16} \) \(\mathstrut -\mathstrut 65q^{17} \) \(\mathstrut -\mathstrut 37q^{18} \) \(\mathstrut -\mathstrut 63q^{19} \) \(\mathstrut -\mathstrut 25q^{20} \) \(\mathstrut -\mathstrut 27q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut -\mathstrut 23q^{23} \) \(\mathstrut -\mathstrut 56q^{24} \) \(\mathstrut +\mathstrut 74q^{25} \) \(\mathstrut +\mathstrut 2q^{26} \) \(\mathstrut -\mathstrut 54q^{27} \) \(\mathstrut -\mathstrut 115q^{28} \) \(\mathstrut -\mathstrut 45q^{29} \) \(\mathstrut -\mathstrut 14q^{30} \) \(\mathstrut -\mathstrut 89q^{31} \) \(\mathstrut -\mathstrut 96q^{32} \) \(\mathstrut -\mathstrut 15q^{33} \) \(\mathstrut -\mathstrut 26q^{34} \) \(\mathstrut -\mathstrut 52q^{35} \) \(\mathstrut +\mathstrut 91q^{36} \) \(\mathstrut -\mathstrut 35q^{37} \) \(\mathstrut +\mathstrut 7q^{38} \) \(\mathstrut -\mathstrut 34q^{39} \) \(\mathstrut -\mathstrut 74q^{40} \) \(\mathstrut -\mathstrut 32q^{41} \) \(\mathstrut -\mathstrut 94q^{43} \) \(\mathstrut +\mathstrut 93q^{44} \) \(\mathstrut -\mathstrut 46q^{45} \) \(\mathstrut -\mathstrut 20q^{46} \) \(\mathstrut -\mathstrut 105q^{47} \) \(\mathstrut -\mathstrut 57q^{48} \) \(\mathstrut +\mathstrut 80q^{49} \) \(\mathstrut -\mathstrut 60q^{50} \) \(\mathstrut -\mathstrut 36q^{51} \) \(\mathstrut -\mathstrut 137q^{52} \) \(\mathstrut -\mathstrut 61q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 32q^{56} \) \(\mathstrut -\mathstrut 71q^{57} \) \(\mathstrut -\mathstrut 28q^{58} \) \(\mathstrut -\mathstrut 15q^{59} \) \(\mathstrut -\mathstrut 21q^{60} \) \(\mathstrut -\mathstrut 80q^{61} \) \(\mathstrut -\mathstrut 84q^{62} \) \(\mathstrut -\mathstrut 182q^{63} \) \(\mathstrut +\mathstrut 55q^{64} \) \(\mathstrut -\mathstrut 73q^{65} \) \(\mathstrut -\mathstrut 22q^{66} \) \(\mathstrut -\mathstrut 58q^{67} \) \(\mathstrut -\mathstrut 145q^{68} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 39q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut -\mathstrut 100q^{72} \) \(\mathstrut -\mathstrut 155q^{73} \) \(\mathstrut -\mathstrut 15q^{74} \) \(\mathstrut -\mathstrut 15q^{75} \) \(\mathstrut -\mathstrut 132q^{76} \) \(\mathstrut -\mathstrut 66q^{77} \) \(\mathstrut -\mathstrut 45q^{78} \) \(\mathstrut -\mathstrut 50q^{79} \) \(\mathstrut -\mathstrut 28q^{80} \) \(\mathstrut +\mathstrut 114q^{81} \) \(\mathstrut -\mathstrut 57q^{82} \) \(\mathstrut -\mathstrut 96q^{83} \) \(\mathstrut -\mathstrut 27q^{84} \) \(\mathstrut -\mathstrut 74q^{85} \) \(\mathstrut +\mathstrut 54q^{86} \) \(\mathstrut -\mathstrut 182q^{87} \) \(\mathstrut -\mathstrut 39q^{88} \) \(\mathstrut +\mathstrut 9q^{89} \) \(\mathstrut -\mathstrut 53q^{90} \) \(\mathstrut +\mathstrut 6q^{91} \) \(\mathstrut -\mathstrut 18q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut -\mathstrut 33q^{94} \) \(\mathstrut -\mathstrut 49q^{95} \) \(\mathstrut -\mathstrut 56q^{96} \) \(\mathstrut -\mathstrut 102q^{97} \) \(\mathstrut -\mathstrut 76q^{98} \) \(\mathstrut +\mathstrut 97q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.58511 −1.82795 −0.913976 0.405769i \(-0.867004\pi\)
−0.913976 + 0.405769i \(0.867004\pi\)
\(3\) −2.87890 −1.66214 −0.831068 0.556172i \(-0.812270\pi\)
−0.831068 + 0.556172i \(0.812270\pi\)
\(4\) 4.68281 2.34141
\(5\) −1.51557 −0.677783 −0.338891 0.940826i \(-0.610052\pi\)
−0.338891 + 0.940826i \(0.610052\pi\)
\(6\) 7.44229 3.03830
\(7\) 0.161489 0.0610373 0.0305186 0.999534i \(-0.490284\pi\)
0.0305186 + 0.999534i \(0.490284\pi\)
\(8\) −6.93538 −2.45203
\(9\) 5.28808 1.76269
\(10\) 3.91792 1.23895
\(11\) 1.00000 0.301511
\(12\) −13.4814 −3.89173
\(13\) −6.99617 −1.94039 −0.970194 0.242329i \(-0.922089\pi\)
−0.970194 + 0.242329i \(0.922089\pi\)
\(14\) −0.417469 −0.111573
\(15\) 4.36317 1.12657
\(16\) 8.56312 2.14078
\(17\) −4.66254 −1.13083 −0.565417 0.824805i \(-0.691285\pi\)
−0.565417 + 0.824805i \(0.691285\pi\)
\(18\) −13.6703 −3.22212
\(19\) 4.03748 0.926261 0.463131 0.886290i \(-0.346726\pi\)
0.463131 + 0.886290i \(0.346726\pi\)
\(20\) −7.09712 −1.58696
\(21\) −0.464912 −0.101452
\(22\) −2.58511 −0.551148
\(23\) 4.97780 1.03794 0.518972 0.854792i \(-0.326315\pi\)
0.518972 + 0.854792i \(0.326315\pi\)
\(24\) 19.9663 4.07560
\(25\) −2.70305 −0.540611
\(26\) 18.0859 3.54694
\(27\) −6.58715 −1.26770
\(28\) 0.756225 0.142913
\(29\) −1.95167 −0.362415 −0.181208 0.983445i \(-0.558001\pi\)
−0.181208 + 0.983445i \(0.558001\pi\)
\(30\) −11.2793 −2.05931
\(31\) −0.546934 −0.0982323 −0.0491162 0.998793i \(-0.515640\pi\)
−0.0491162 + 0.998793i \(0.515640\pi\)
\(32\) −8.26588 −1.46121
\(33\) −2.87890 −0.501153
\(34\) 12.0532 2.06711
\(35\) −0.244748 −0.0413700
\(36\) 24.7631 4.12718
\(37\) −3.94217 −0.648088 −0.324044 0.946042i \(-0.605043\pi\)
−0.324044 + 0.946042i \(0.605043\pi\)
\(38\) −10.4373 −1.69316
\(39\) 20.1413 3.22519
\(40\) 10.5110 1.66194
\(41\) 4.07011 0.635644 0.317822 0.948150i \(-0.397048\pi\)
0.317822 + 0.948150i \(0.397048\pi\)
\(42\) 1.20185 0.185450
\(43\) 5.47625 0.835120 0.417560 0.908649i \(-0.362885\pi\)
0.417560 + 0.908649i \(0.362885\pi\)
\(44\) 4.68281 0.705961
\(45\) −8.01444 −1.19472
\(46\) −12.8682 −1.89731
\(47\) −2.72261 −0.397134 −0.198567 0.980087i \(-0.563629\pi\)
−0.198567 + 0.980087i \(0.563629\pi\)
\(48\) −24.6524 −3.55826
\(49\) −6.97392 −0.996274
\(50\) 6.98770 0.988210
\(51\) 13.4230 1.87960
\(52\) −32.7618 −4.54324
\(53\) 13.7242 1.88516 0.942581 0.333978i \(-0.108391\pi\)
0.942581 + 0.333978i \(0.108391\pi\)
\(54\) 17.0285 2.31729
\(55\) −1.51557 −0.204359
\(56\) −1.11999 −0.149665
\(57\) −11.6235 −1.53957
\(58\) 5.04528 0.662477
\(59\) −0.114947 −0.0149648 −0.00748240 0.999972i \(-0.502382\pi\)
−0.00748240 + 0.999972i \(0.502382\pi\)
\(60\) 20.4319 2.63775
\(61\) −2.36507 −0.302816 −0.151408 0.988471i \(-0.548381\pi\)
−0.151408 + 0.988471i \(0.548381\pi\)
\(62\) 1.41389 0.179564
\(63\) 0.853969 0.107590
\(64\) 4.24200 0.530250
\(65\) 10.6032 1.31516
\(66\) 7.44229 0.916083
\(67\) 4.13899 0.505658 0.252829 0.967511i \(-0.418639\pi\)
0.252829 + 0.967511i \(0.418639\pi\)
\(68\) −21.8338 −2.64774
\(69\) −14.3306 −1.72520
\(70\) 0.632702 0.0756224
\(71\) 5.67318 0.673282 0.336641 0.941633i \(-0.390709\pi\)
0.336641 + 0.941633i \(0.390709\pi\)
\(72\) −36.6748 −4.32217
\(73\) −14.8910 −1.74286 −0.871430 0.490520i \(-0.836807\pi\)
−0.871430 + 0.490520i \(0.836807\pi\)
\(74\) 10.1909 1.18467
\(75\) 7.78183 0.898568
\(76\) 18.9068 2.16875
\(77\) 0.161489 0.0184034
\(78\) −52.0675 −5.89549
\(79\) −7.56851 −0.851524 −0.425762 0.904835i \(-0.639994\pi\)
−0.425762 + 0.904835i \(0.639994\pi\)
\(80\) −12.9780 −1.45098
\(81\) 3.09954 0.344393
\(82\) −10.5217 −1.16193
\(83\) −9.11300 −1.00028 −0.500141 0.865944i \(-0.666719\pi\)
−0.500141 + 0.865944i \(0.666719\pi\)
\(84\) −2.17710 −0.237541
\(85\) 7.06640 0.766459
\(86\) −14.1567 −1.52656
\(87\) 5.61865 0.602383
\(88\) −6.93538 −0.739314
\(89\) 10.4253 1.10508 0.552542 0.833485i \(-0.313658\pi\)
0.552542 + 0.833485i \(0.313658\pi\)
\(90\) 20.7182 2.18389
\(91\) −1.12981 −0.118436
\(92\) 23.3101 2.43025
\(93\) 1.57457 0.163275
\(94\) 7.03827 0.725942
\(95\) −6.11907 −0.627804
\(96\) 23.7967 2.42874
\(97\) −6.91061 −0.701667 −0.350833 0.936438i \(-0.614102\pi\)
−0.350833 + 0.936438i \(0.614102\pi\)
\(98\) 18.0284 1.82114
\(99\) 5.28808 0.531472
\(100\) −12.6579 −1.26579
\(101\) −5.03261 −0.500763 −0.250382 0.968147i \(-0.580556\pi\)
−0.250382 + 0.968147i \(0.580556\pi\)
\(102\) −34.7000 −3.43581
\(103\) 2.72640 0.268641 0.134320 0.990938i \(-0.457115\pi\)
0.134320 + 0.990938i \(0.457115\pi\)
\(104\) 48.5211 4.75788
\(105\) 0.704606 0.0687625
\(106\) −35.4786 −3.44598
\(107\) 13.6287 1.31753 0.658766 0.752348i \(-0.271079\pi\)
0.658766 + 0.752348i \(0.271079\pi\)
\(108\) −30.8464 −2.96820
\(109\) −15.2555 −1.46122 −0.730608 0.682797i \(-0.760763\pi\)
−0.730608 + 0.682797i \(0.760763\pi\)
\(110\) 3.91792 0.373559
\(111\) 11.3491 1.07721
\(112\) 1.38285 0.130667
\(113\) 5.26182 0.494990 0.247495 0.968889i \(-0.420393\pi\)
0.247495 + 0.968889i \(0.420393\pi\)
\(114\) 30.0481 2.81426
\(115\) −7.54419 −0.703500
\(116\) −9.13929 −0.848562
\(117\) −36.9963 −3.42031
\(118\) 0.297151 0.0273549
\(119\) −0.752952 −0.0690230
\(120\) −30.2603 −2.76237
\(121\) 1.00000 0.0909091
\(122\) 6.11397 0.553533
\(123\) −11.7175 −1.05653
\(124\) −2.56119 −0.230002
\(125\) 11.6745 1.04420
\(126\) −2.20761 −0.196669
\(127\) 0.925858 0.0821566 0.0410783 0.999156i \(-0.486921\pi\)
0.0410783 + 0.999156i \(0.486921\pi\)
\(128\) 5.56571 0.491944
\(129\) −15.7656 −1.38808
\(130\) −27.4104 −2.40405
\(131\) 10.4749 0.915192 0.457596 0.889160i \(-0.348711\pi\)
0.457596 + 0.889160i \(0.348711\pi\)
\(132\) −13.4814 −1.17340
\(133\) 0.652010 0.0565365
\(134\) −10.6997 −0.924318
\(135\) 9.98328 0.859224
\(136\) 32.3365 2.77283
\(137\) −3.09197 −0.264165 −0.132082 0.991239i \(-0.542166\pi\)
−0.132082 + 0.991239i \(0.542166\pi\)
\(138\) 37.0462 3.15358
\(139\) 14.6916 1.24612 0.623061 0.782173i \(-0.285889\pi\)
0.623061 + 0.782173i \(0.285889\pi\)
\(140\) −1.14611 −0.0968640
\(141\) 7.83814 0.660090
\(142\) −14.6658 −1.23073
\(143\) −6.99617 −0.585049
\(144\) 45.2824 3.77354
\(145\) 2.95788 0.245639
\(146\) 38.4949 3.18586
\(147\) 20.0772 1.65594
\(148\) −18.4604 −1.51744
\(149\) 8.05954 0.660263 0.330132 0.943935i \(-0.392907\pi\)
0.330132 + 0.943935i \(0.392907\pi\)
\(150\) −20.1169 −1.64254
\(151\) 7.99433 0.650570 0.325285 0.945616i \(-0.394540\pi\)
0.325285 + 0.945616i \(0.394540\pi\)
\(152\) −28.0014 −2.27122
\(153\) −24.6559 −1.99331
\(154\) −0.417469 −0.0336406
\(155\) 0.828916 0.0665801
\(156\) 94.3179 7.55148
\(157\) −9.44993 −0.754187 −0.377093 0.926175i \(-0.623076\pi\)
−0.377093 + 0.926175i \(0.623076\pi\)
\(158\) 19.5655 1.55654
\(159\) −39.5106 −3.13339
\(160\) 12.5275 0.990386
\(161\) 0.803862 0.0633532
\(162\) −8.01266 −0.629534
\(163\) 8.41794 0.659344 0.329672 0.944096i \(-0.393062\pi\)
0.329672 + 0.944096i \(0.393062\pi\)
\(164\) 19.0596 1.48830
\(165\) 4.36317 0.339672
\(166\) 23.5582 1.82847
\(167\) −19.7872 −1.53118 −0.765590 0.643329i \(-0.777553\pi\)
−0.765590 + 0.643329i \(0.777553\pi\)
\(168\) 3.22434 0.248764
\(169\) 35.9464 2.76511
\(170\) −18.2675 −1.40105
\(171\) 21.3505 1.63271
\(172\) 25.6442 1.95536
\(173\) −7.68459 −0.584249 −0.292124 0.956380i \(-0.594362\pi\)
−0.292124 + 0.956380i \(0.594362\pi\)
\(174\) −14.5249 −1.10113
\(175\) −0.436515 −0.0329974
\(176\) 8.56312 0.645469
\(177\) 0.330921 0.0248735
\(178\) −26.9507 −2.02004
\(179\) 10.5445 0.788135 0.394067 0.919082i \(-0.371068\pi\)
0.394067 + 0.919082i \(0.371068\pi\)
\(180\) −37.5301 −2.79733
\(181\) 15.0626 1.11959 0.559796 0.828630i \(-0.310879\pi\)
0.559796 + 0.828630i \(0.310879\pi\)
\(182\) 2.92068 0.216495
\(183\) 6.80880 0.503321
\(184\) −34.5229 −2.54506
\(185\) 5.97462 0.439263
\(186\) −4.07044 −0.298459
\(187\) −4.66254 −0.340959
\(188\) −12.7495 −0.929852
\(189\) −1.06376 −0.0773769
\(190\) 15.8185 1.14759
\(191\) −11.1598 −0.807496 −0.403748 0.914870i \(-0.632293\pi\)
−0.403748 + 0.914870i \(0.632293\pi\)
\(192\) −12.2123 −0.881347
\(193\) −2.87338 −0.206830 −0.103415 0.994638i \(-0.532977\pi\)
−0.103415 + 0.994638i \(0.532977\pi\)
\(194\) 17.8647 1.28261
\(195\) −30.5255 −2.18598
\(196\) −32.6576 −2.33268
\(197\) 1.34645 0.0959306 0.0479653 0.998849i \(-0.484726\pi\)
0.0479653 + 0.998849i \(0.484726\pi\)
\(198\) −13.6703 −0.971505
\(199\) −9.04600 −0.641254 −0.320627 0.947206i \(-0.603894\pi\)
−0.320627 + 0.947206i \(0.603894\pi\)
\(200\) 18.7467 1.32559
\(201\) −11.9157 −0.840471
\(202\) 13.0099 0.915371
\(203\) −0.315174 −0.0221208
\(204\) 62.8575 4.40090
\(205\) −6.16853 −0.430829
\(206\) −7.04807 −0.491062
\(207\) 26.3230 1.82957
\(208\) −59.9090 −4.15394
\(209\) 4.03748 0.279278
\(210\) −1.82149 −0.125695
\(211\) 9.37452 0.645369 0.322684 0.946507i \(-0.395415\pi\)
0.322684 + 0.946507i \(0.395415\pi\)
\(212\) 64.2678 4.41393
\(213\) −16.3325 −1.11909
\(214\) −35.2316 −2.40838
\(215\) −8.29962 −0.566030
\(216\) 45.6844 3.10843
\(217\) −0.0883242 −0.00599583
\(218\) 39.4373 2.67103
\(219\) 42.8697 2.89687
\(220\) −7.09712 −0.478488
\(221\) 32.6200 2.19426
\(222\) −29.3387 −1.96909
\(223\) 20.9816 1.40503 0.702515 0.711668i \(-0.252060\pi\)
0.702515 + 0.711668i \(0.252060\pi\)
\(224\) −1.33485 −0.0891886
\(225\) −14.2940 −0.952931
\(226\) −13.6024 −0.904818
\(227\) 3.20659 0.212829 0.106415 0.994322i \(-0.466063\pi\)
0.106415 + 0.994322i \(0.466063\pi\)
\(228\) −54.4307 −3.60476
\(229\) 12.1614 0.803651 0.401825 0.915716i \(-0.368376\pi\)
0.401825 + 0.915716i \(0.368376\pi\)
\(230\) 19.5026 1.28596
\(231\) −0.464912 −0.0305890
\(232\) 13.5355 0.888652
\(233\) 12.3003 0.805817 0.402909 0.915240i \(-0.367999\pi\)
0.402909 + 0.915240i \(0.367999\pi\)
\(234\) 95.6396 6.25216
\(235\) 4.12631 0.269171
\(236\) −0.538274 −0.0350387
\(237\) 21.7890 1.41535
\(238\) 1.94647 0.126171
\(239\) 18.9956 1.22872 0.614360 0.789026i \(-0.289414\pi\)
0.614360 + 0.789026i \(0.289414\pi\)
\(240\) 37.3624 2.41173
\(241\) 22.0061 1.41754 0.708769 0.705440i \(-0.249251\pi\)
0.708769 + 0.705440i \(0.249251\pi\)
\(242\) −2.58511 −0.166177
\(243\) 10.8382 0.695271
\(244\) −11.0752 −0.709016
\(245\) 10.5695 0.675257
\(246\) 30.2909 1.93128
\(247\) −28.2469 −1.79731
\(248\) 3.79320 0.240868
\(249\) 26.2354 1.66260
\(250\) −30.1799 −1.90875
\(251\) −19.7167 −1.24451 −0.622253 0.782816i \(-0.713783\pi\)
−0.622253 + 0.782816i \(0.713783\pi\)
\(252\) 3.99898 0.251912
\(253\) 4.97780 0.312952
\(254\) −2.39345 −0.150178
\(255\) −20.3435 −1.27396
\(256\) −22.8720 −1.42950
\(257\) 3.09154 0.192845 0.0964225 0.995340i \(-0.469260\pi\)
0.0964225 + 0.995340i \(0.469260\pi\)
\(258\) 40.7558 2.53735
\(259\) −0.636618 −0.0395575
\(260\) 49.6527 3.07933
\(261\) −10.3206 −0.638827
\(262\) −27.0787 −1.67293
\(263\) 21.5974 1.33175 0.665876 0.746062i \(-0.268058\pi\)
0.665876 + 0.746062i \(0.268058\pi\)
\(264\) 19.9663 1.22884
\(265\) −20.7999 −1.27773
\(266\) −1.68552 −0.103346
\(267\) −30.0135 −1.83680
\(268\) 19.3821 1.18395
\(269\) 13.3903 0.816419 0.408210 0.912888i \(-0.366153\pi\)
0.408210 + 0.912888i \(0.366153\pi\)
\(270\) −25.8079 −1.57062
\(271\) −6.57861 −0.399622 −0.199811 0.979834i \(-0.564033\pi\)
−0.199811 + 0.979834i \(0.564033\pi\)
\(272\) −39.9259 −2.42086
\(273\) 3.25261 0.196857
\(274\) 7.99308 0.482880
\(275\) −2.70305 −0.163000
\(276\) −67.1075 −4.03940
\(277\) −22.2248 −1.33536 −0.667678 0.744450i \(-0.732712\pi\)
−0.667678 + 0.744450i \(0.732712\pi\)
\(278\) −37.9794 −2.27785
\(279\) −2.89223 −0.173153
\(280\) 1.69742 0.101440
\(281\) −10.1465 −0.605288 −0.302644 0.953104i \(-0.597869\pi\)
−0.302644 + 0.953104i \(0.597869\pi\)
\(282\) −20.2625 −1.20661
\(283\) 2.43092 0.144503 0.0722515 0.997386i \(-0.476982\pi\)
0.0722515 + 0.997386i \(0.476982\pi\)
\(284\) 26.5664 1.57643
\(285\) 17.6162 1.04349
\(286\) 18.0859 1.06944
\(287\) 0.657280 0.0387980
\(288\) −43.7106 −2.57567
\(289\) 4.73932 0.278784
\(290\) −7.64646 −0.449016
\(291\) 19.8950 1.16626
\(292\) −69.7318 −4.08074
\(293\) 8.83366 0.516068 0.258034 0.966136i \(-0.416925\pi\)
0.258034 + 0.966136i \(0.416925\pi\)
\(294\) −51.9019 −3.02698
\(295\) 0.174210 0.0101429
\(296\) 27.3404 1.58913
\(297\) −6.58715 −0.382225
\(298\) −20.8348 −1.20693
\(299\) −34.8255 −2.01401
\(300\) 36.4409 2.10391
\(301\) 0.884356 0.0509735
\(302\) −20.6663 −1.18921
\(303\) 14.4884 0.832336
\(304\) 34.5734 1.98292
\(305\) 3.58442 0.205243
\(306\) 63.7383 3.64368
\(307\) 20.7216 1.18265 0.591323 0.806434i \(-0.298606\pi\)
0.591323 + 0.806434i \(0.298606\pi\)
\(308\) 0.756225 0.0430899
\(309\) −7.84905 −0.446517
\(310\) −2.14284 −0.121705
\(311\) 3.17697 0.180149 0.0900747 0.995935i \(-0.471289\pi\)
0.0900747 + 0.995935i \(0.471289\pi\)
\(312\) −139.687 −7.90825
\(313\) 32.6979 1.84819 0.924096 0.382160i \(-0.124820\pi\)
0.924096 + 0.382160i \(0.124820\pi\)
\(314\) 24.4291 1.37862
\(315\) −1.29425 −0.0729226
\(316\) −35.4419 −1.99376
\(317\) 1.74848 0.0982045 0.0491022 0.998794i \(-0.484364\pi\)
0.0491022 + 0.998794i \(0.484364\pi\)
\(318\) 102.139 5.72769
\(319\) −1.95167 −0.109272
\(320\) −6.42904 −0.359394
\(321\) −39.2356 −2.18992
\(322\) −2.07808 −0.115807
\(323\) −18.8249 −1.04745
\(324\) 14.5146 0.806364
\(325\) 18.9110 1.04899
\(326\) −21.7613 −1.20525
\(327\) 43.9192 2.42874
\(328\) −28.2278 −1.55862
\(329\) −0.439674 −0.0242400
\(330\) −11.2793 −0.620905
\(331\) 13.6593 0.750782 0.375391 0.926866i \(-0.377508\pi\)
0.375391 + 0.926866i \(0.377508\pi\)
\(332\) −42.6745 −2.34207
\(333\) −20.8465 −1.14238
\(334\) 51.1522 2.79892
\(335\) −6.27291 −0.342726
\(336\) −3.98110 −0.217187
\(337\) 29.2215 1.59180 0.795898 0.605431i \(-0.206999\pi\)
0.795898 + 0.605431i \(0.206999\pi\)
\(338\) −92.9255 −5.05448
\(339\) −15.1483 −0.822741
\(340\) 33.0907 1.79459
\(341\) −0.546934 −0.0296182
\(342\) −55.1935 −2.98452
\(343\) −2.25664 −0.121847
\(344\) −37.9799 −2.04774
\(345\) 21.7190 1.16931
\(346\) 19.8655 1.06798
\(347\) 5.25371 0.282034 0.141017 0.990007i \(-0.454963\pi\)
0.141017 + 0.990007i \(0.454963\pi\)
\(348\) 26.3111 1.41042
\(349\) −29.1507 −1.56040 −0.780200 0.625531i \(-0.784882\pi\)
−0.780200 + 0.625531i \(0.784882\pi\)
\(350\) 1.12844 0.0603177
\(351\) 46.0848 2.45983
\(352\) −8.26588 −0.440573
\(353\) −11.8078 −0.628467 −0.314234 0.949346i \(-0.601748\pi\)
−0.314234 + 0.949346i \(0.601748\pi\)
\(354\) −0.855467 −0.0454676
\(355\) −8.59809 −0.456339
\(356\) 48.8199 2.58745
\(357\) 2.16768 0.114726
\(358\) −27.2588 −1.44067
\(359\) −37.5797 −1.98338 −0.991689 0.128656i \(-0.958934\pi\)
−0.991689 + 0.128656i \(0.958934\pi\)
\(360\) 55.5832 2.92949
\(361\) −2.69877 −0.142040
\(362\) −38.9385 −2.04656
\(363\) −2.87890 −0.151103
\(364\) −5.29068 −0.277307
\(365\) 22.5683 1.18128
\(366\) −17.6015 −0.920047
\(367\) 21.8766 1.14195 0.570975 0.820967i \(-0.306565\pi\)
0.570975 + 0.820967i \(0.306565\pi\)
\(368\) 42.6255 2.22201
\(369\) 21.5231 1.12045
\(370\) −15.4451 −0.802951
\(371\) 2.21631 0.115065
\(372\) 7.37342 0.382294
\(373\) −16.3409 −0.846100 −0.423050 0.906106i \(-0.639041\pi\)
−0.423050 + 0.906106i \(0.639041\pi\)
\(374\) 12.0532 0.623257
\(375\) −33.6097 −1.73560
\(376\) 18.8824 0.973783
\(377\) 13.6542 0.703226
\(378\) 2.74993 0.141441
\(379\) 23.9542 1.23044 0.615222 0.788354i \(-0.289066\pi\)
0.615222 + 0.788354i \(0.289066\pi\)
\(380\) −28.6545 −1.46994
\(381\) −2.66545 −0.136555
\(382\) 28.8494 1.47606
\(383\) 9.53268 0.487097 0.243549 0.969889i \(-0.421688\pi\)
0.243549 + 0.969889i \(0.421688\pi\)
\(384\) −16.0231 −0.817677
\(385\) −0.244748 −0.0124735
\(386\) 7.42801 0.378076
\(387\) 28.9588 1.47206
\(388\) −32.3611 −1.64289
\(389\) 17.4434 0.884417 0.442209 0.896912i \(-0.354195\pi\)
0.442209 + 0.896912i \(0.354195\pi\)
\(390\) 78.9119 3.99586
\(391\) −23.2092 −1.17374
\(392\) 48.3668 2.44289
\(393\) −30.1561 −1.52117
\(394\) −3.48073 −0.175357
\(395\) 11.4706 0.577148
\(396\) 24.7631 1.24439
\(397\) −21.0785 −1.05790 −0.528950 0.848653i \(-0.677414\pi\)
−0.528950 + 0.848653i \(0.677414\pi\)
\(398\) 23.3849 1.17218
\(399\) −1.87707 −0.0939712
\(400\) −23.1466 −1.15733
\(401\) −8.79432 −0.439167 −0.219584 0.975594i \(-0.570470\pi\)
−0.219584 + 0.975594i \(0.570470\pi\)
\(402\) 30.8035 1.53634
\(403\) 3.82645 0.190609
\(404\) −23.5668 −1.17249
\(405\) −4.69756 −0.233424
\(406\) 0.814759 0.0404358
\(407\) −3.94217 −0.195406
\(408\) −93.0937 −4.60882
\(409\) −22.7627 −1.12554 −0.562772 0.826612i \(-0.690265\pi\)
−0.562772 + 0.826612i \(0.690265\pi\)
\(410\) 15.9463 0.787534
\(411\) 8.90147 0.439077
\(412\) 12.7672 0.628997
\(413\) −0.0185627 −0.000913411 0
\(414\) −68.0479 −3.34437
\(415\) 13.8114 0.677974
\(416\) 57.8295 2.83532
\(417\) −42.2956 −2.07122
\(418\) −10.4373 −0.510507
\(419\) −7.39567 −0.361302 −0.180651 0.983547i \(-0.557820\pi\)
−0.180651 + 0.983547i \(0.557820\pi\)
\(420\) 3.29954 0.161001
\(421\) 14.3276 0.698285 0.349143 0.937070i \(-0.386473\pi\)
0.349143 + 0.937070i \(0.386473\pi\)
\(422\) −24.2342 −1.17970
\(423\) −14.3974 −0.700025
\(424\) −95.1824 −4.62247
\(425\) 12.6031 0.611341
\(426\) 42.2214 2.04564
\(427\) −0.381934 −0.0184831
\(428\) 63.8205 3.08488
\(429\) 20.1413 0.972431
\(430\) 21.4555 1.03467
\(431\) 8.81640 0.424671 0.212336 0.977197i \(-0.431893\pi\)
0.212336 + 0.977197i \(0.431893\pi\)
\(432\) −56.4066 −2.71386
\(433\) −13.3556 −0.641829 −0.320915 0.947108i \(-0.603990\pi\)
−0.320915 + 0.947108i \(0.603990\pi\)
\(434\) 0.228328 0.0109601
\(435\) −8.51545 −0.408285
\(436\) −71.4388 −3.42130
\(437\) 20.0978 0.961406
\(438\) −110.823 −5.29534
\(439\) 1.22712 0.0585675 0.0292837 0.999571i \(-0.490677\pi\)
0.0292837 + 0.999571i \(0.490677\pi\)
\(440\) 10.5110 0.501094
\(441\) −36.8786 −1.75613
\(442\) −84.3263 −4.01099
\(443\) −34.7240 −1.64979 −0.824894 0.565288i \(-0.808765\pi\)
−0.824894 + 0.565288i \(0.808765\pi\)
\(444\) 53.1458 2.52219
\(445\) −15.8003 −0.749006
\(446\) −54.2398 −2.56833
\(447\) −23.2026 −1.09745
\(448\) 0.685038 0.0323650
\(449\) −11.6811 −0.551266 −0.275633 0.961263i \(-0.588887\pi\)
−0.275633 + 0.961263i \(0.588887\pi\)
\(450\) 36.9515 1.74191
\(451\) 4.07011 0.191654
\(452\) 24.6401 1.15897
\(453\) −23.0149 −1.08133
\(454\) −8.28941 −0.389041
\(455\) 1.71230 0.0802739
\(456\) 80.6134 3.77507
\(457\) −2.17391 −0.101691 −0.0508456 0.998707i \(-0.516192\pi\)
−0.0508456 + 0.998707i \(0.516192\pi\)
\(458\) −31.4387 −1.46903
\(459\) 30.7129 1.43356
\(460\) −35.3281 −1.64718
\(461\) 1.29809 0.0604579 0.0302290 0.999543i \(-0.490376\pi\)
0.0302290 + 0.999543i \(0.490376\pi\)
\(462\) 1.20185 0.0559152
\(463\) −2.86111 −0.132967 −0.0664834 0.997788i \(-0.521178\pi\)
−0.0664834 + 0.997788i \(0.521178\pi\)
\(464\) −16.7123 −0.775851
\(465\) −2.38637 −0.110665
\(466\) −31.7976 −1.47299
\(467\) 0.427463 0.0197806 0.00989032 0.999951i \(-0.496852\pi\)
0.00989032 + 0.999951i \(0.496852\pi\)
\(468\) −173.247 −8.00833
\(469\) 0.668403 0.0308640
\(470\) −10.6670 −0.492031
\(471\) 27.2054 1.25356
\(472\) 0.797200 0.0366941
\(473\) 5.47625 0.251798
\(474\) −56.3271 −2.58719
\(475\) −10.9135 −0.500747
\(476\) −3.52593 −0.161611
\(477\) 72.5746 3.32296
\(478\) −49.1057 −2.24604
\(479\) 14.1486 0.646468 0.323234 0.946319i \(-0.395230\pi\)
0.323234 + 0.946319i \(0.395230\pi\)
\(480\) −36.0654 −1.64615
\(481\) 27.5801 1.25754
\(482\) −56.8883 −2.59119
\(483\) −2.31424 −0.105302
\(484\) 4.68281 0.212855
\(485\) 10.4735 0.475577
\(486\) −28.0180 −1.27092
\(487\) −17.3031 −0.784076 −0.392038 0.919949i \(-0.628230\pi\)
−0.392038 + 0.919949i \(0.628230\pi\)
\(488\) 16.4027 0.742513
\(489\) −24.2344 −1.09592
\(490\) −27.3232 −1.23434
\(491\) 8.70093 0.392667 0.196334 0.980537i \(-0.437096\pi\)
0.196334 + 0.980537i \(0.437096\pi\)
\(492\) −54.8706 −2.47376
\(493\) 9.09973 0.409831
\(494\) 73.0214 3.28539
\(495\) −8.01444 −0.360222
\(496\) −4.68346 −0.210294
\(497\) 0.916159 0.0410953
\(498\) −67.8216 −3.03916
\(499\) −16.8790 −0.755606 −0.377803 0.925886i \(-0.623320\pi\)
−0.377803 + 0.925886i \(0.623320\pi\)
\(500\) 54.6695 2.44490
\(501\) 56.9654 2.54503
\(502\) 50.9699 2.27490
\(503\) −31.8644 −1.42076 −0.710382 0.703816i \(-0.751478\pi\)
−0.710382 + 0.703816i \(0.751478\pi\)
\(504\) −5.92260 −0.263814
\(505\) 7.62726 0.339409
\(506\) −12.8682 −0.572060
\(507\) −103.486 −4.59598
\(508\) 4.33562 0.192362
\(509\) 19.5984 0.868684 0.434342 0.900748i \(-0.356981\pi\)
0.434342 + 0.900748i \(0.356981\pi\)
\(510\) 52.5902 2.32873
\(511\) −2.40474 −0.106379
\(512\) 47.9953 2.12111
\(513\) −26.5955 −1.17422
\(514\) −7.99198 −0.352511
\(515\) −4.13205 −0.182080
\(516\) −73.8273 −3.25006
\(517\) −2.72261 −0.119740
\(518\) 1.64573 0.0723093
\(519\) 22.1232 0.971100
\(520\) −73.5370 −3.22481
\(521\) −43.8426 −1.92078 −0.960389 0.278662i \(-0.910109\pi\)
−0.960389 + 0.278662i \(0.910109\pi\)
\(522\) 26.6798 1.16774
\(523\) −9.32950 −0.407950 −0.203975 0.978976i \(-0.565386\pi\)
−0.203975 + 0.978976i \(0.565386\pi\)
\(524\) 49.0518 2.14284
\(525\) 1.25668 0.0548462
\(526\) −55.8317 −2.43438
\(527\) 2.55011 0.111084
\(528\) −24.6524 −1.07286
\(529\) 1.77849 0.0773258
\(530\) 53.7702 2.33563
\(531\) −0.607848 −0.0263783
\(532\) 3.05324 0.132375
\(533\) −28.4752 −1.23340
\(534\) 77.5884 3.35758
\(535\) −20.6552 −0.893000
\(536\) −28.7054 −1.23989
\(537\) −30.3567 −1.30999
\(538\) −34.6154 −1.49237
\(539\) −6.97392 −0.300388
\(540\) 46.7498 2.01179
\(541\) 5.07859 0.218345 0.109173 0.994023i \(-0.465180\pi\)
0.109173 + 0.994023i \(0.465180\pi\)
\(542\) 17.0065 0.730490
\(543\) −43.3637 −1.86091
\(544\) 38.5400 1.65239
\(545\) 23.1208 0.990386
\(546\) −8.40836 −0.359845
\(547\) 1.00000 0.0427569
\(548\) −14.4791 −0.618517
\(549\) −12.5067 −0.533772
\(550\) 6.98770 0.297957
\(551\) −7.87981 −0.335691
\(552\) 99.3881 4.23024
\(553\) −1.22223 −0.0519747
\(554\) 57.4535 2.44097
\(555\) −17.2003 −0.730114
\(556\) 68.7979 2.91768
\(557\) 38.7081 1.64012 0.820058 0.572280i \(-0.193941\pi\)
0.820058 + 0.572280i \(0.193941\pi\)
\(558\) 7.47675 0.316516
\(559\) −38.3128 −1.62046
\(560\) −2.09581 −0.0885641
\(561\) 13.4230 0.566720
\(562\) 26.2298 1.10644
\(563\) 13.0177 0.548632 0.274316 0.961640i \(-0.411549\pi\)
0.274316 + 0.961640i \(0.411549\pi\)
\(564\) 36.7045 1.54554
\(565\) −7.97464 −0.335496
\(566\) −6.28420 −0.264144
\(567\) 0.500543 0.0210208
\(568\) −39.3456 −1.65091
\(569\) −1.88665 −0.0790925 −0.0395462 0.999218i \(-0.512591\pi\)
−0.0395462 + 0.999218i \(0.512591\pi\)
\(570\) −45.5399 −1.90746
\(571\) −0.986817 −0.0412970 −0.0206485 0.999787i \(-0.506573\pi\)
−0.0206485 + 0.999787i \(0.506573\pi\)
\(572\) −32.7618 −1.36984
\(573\) 32.1280 1.34217
\(574\) −1.69914 −0.0709209
\(575\) −13.4553 −0.561123
\(576\) 22.4320 0.934667
\(577\) 15.2056 0.633019 0.316510 0.948589i \(-0.397489\pi\)
0.316510 + 0.948589i \(0.397489\pi\)
\(578\) −12.2517 −0.509603
\(579\) 8.27217 0.343780
\(580\) 13.8512 0.575140
\(581\) −1.47165 −0.0610545
\(582\) −51.4308 −2.13188
\(583\) 13.7242 0.568398
\(584\) 103.275 4.27354
\(585\) 56.0704 2.31823
\(586\) −22.8360 −0.943347
\(587\) −14.1367 −0.583484 −0.291742 0.956497i \(-0.594235\pi\)
−0.291742 + 0.956497i \(0.594235\pi\)
\(588\) 94.0180 3.87724
\(589\) −2.20824 −0.0909888
\(590\) −0.450352 −0.0185407
\(591\) −3.87630 −0.159450
\(592\) −33.7572 −1.38741
\(593\) 33.4461 1.37347 0.686733 0.726910i \(-0.259044\pi\)
0.686733 + 0.726910i \(0.259044\pi\)
\(594\) 17.0285 0.698690
\(595\) 1.14115 0.0467826
\(596\) 37.7413 1.54595
\(597\) 26.0425 1.06585
\(598\) 90.0280 3.68152
\(599\) 31.4078 1.28329 0.641645 0.767002i \(-0.278252\pi\)
0.641645 + 0.767002i \(0.278252\pi\)
\(600\) −53.9699 −2.20331
\(601\) −34.3757 −1.40222 −0.701108 0.713055i \(-0.747311\pi\)
−0.701108 + 0.713055i \(0.747311\pi\)
\(602\) −2.28616 −0.0931770
\(603\) 21.8873 0.891319
\(604\) 37.4360 1.52325
\(605\) −1.51557 −0.0616166
\(606\) −37.4541 −1.52147
\(607\) −17.9097 −0.726931 −0.363466 0.931608i \(-0.618407\pi\)
−0.363466 + 0.931608i \(0.618407\pi\)
\(608\) −33.3733 −1.35347
\(609\) 0.907354 0.0367678
\(610\) −9.26614 −0.375175
\(611\) 19.0479 0.770594
\(612\) −115.459 −4.66715
\(613\) 16.8330 0.679879 0.339939 0.940447i \(-0.389593\pi\)
0.339939 + 0.940447i \(0.389593\pi\)
\(614\) −53.5678 −2.16182
\(615\) 17.7586 0.716096
\(616\) −1.11999 −0.0451257
\(617\) 41.4502 1.66872 0.834360 0.551219i \(-0.185837\pi\)
0.834360 + 0.551219i \(0.185837\pi\)
\(618\) 20.2907 0.816211
\(619\) −26.6160 −1.06979 −0.534894 0.844919i \(-0.679649\pi\)
−0.534894 + 0.844919i \(0.679649\pi\)
\(620\) 3.88166 0.155891
\(621\) −32.7895 −1.31580
\(622\) −8.21283 −0.329305
\(623\) 1.68358 0.0674513
\(624\) 172.472 6.90442
\(625\) −4.17823 −0.167129
\(626\) −84.5277 −3.37841
\(627\) −11.6235 −0.464198
\(628\) −44.2523 −1.76586
\(629\) 18.3805 0.732879
\(630\) 3.34578 0.133299
\(631\) −44.0330 −1.75293 −0.876463 0.481468i \(-0.840104\pi\)
−0.876463 + 0.481468i \(0.840104\pi\)
\(632\) 52.4905 2.08796
\(633\) −26.9883 −1.07269
\(634\) −4.52002 −0.179513
\(635\) −1.40320 −0.0556843
\(636\) −185.021 −7.33655
\(637\) 48.7907 1.93316
\(638\) 5.04528 0.199744
\(639\) 30.0002 1.18679
\(640\) −8.43521 −0.333431
\(641\) −20.5714 −0.812521 −0.406260 0.913757i \(-0.633167\pi\)
−0.406260 + 0.913757i \(0.633167\pi\)
\(642\) 101.428 4.00306
\(643\) 43.0152 1.69635 0.848177 0.529713i \(-0.177700\pi\)
0.848177 + 0.529713i \(0.177700\pi\)
\(644\) 3.76434 0.148336
\(645\) 23.8938 0.940818
\(646\) 48.6646 1.91468
\(647\) −7.20143 −0.283117 −0.141559 0.989930i \(-0.545211\pi\)
−0.141559 + 0.989930i \(0.545211\pi\)
\(648\) −21.4965 −0.844461
\(649\) −0.114947 −0.00451206
\(650\) −48.8872 −1.91751
\(651\) 0.254277 0.00996589
\(652\) 39.4196 1.54379
\(653\) 0.250362 0.00979742 0.00489871 0.999988i \(-0.498441\pi\)
0.00489871 + 0.999988i \(0.498441\pi\)
\(654\) −113.536 −4.43961
\(655\) −15.8754 −0.620301
\(656\) 34.8528 1.36077
\(657\) −78.7448 −3.07213
\(658\) 1.13661 0.0443095
\(659\) −5.67795 −0.221182 −0.110591 0.993866i \(-0.535274\pi\)
−0.110591 + 0.993866i \(0.535274\pi\)
\(660\) 20.4319 0.795311
\(661\) −24.6075 −0.957122 −0.478561 0.878054i \(-0.658841\pi\)
−0.478561 + 0.878054i \(0.658841\pi\)
\(662\) −35.3108 −1.37239
\(663\) −93.9097 −3.64715
\(664\) 63.2021 2.45272
\(665\) −0.988166 −0.0383194
\(666\) 53.8905 2.08822
\(667\) −9.71500 −0.376166
\(668\) −92.6598 −3.58512
\(669\) −60.4039 −2.33535
\(670\) 16.2162 0.626486
\(671\) −2.36507 −0.0913025
\(672\) 3.84291 0.148243
\(673\) −27.7457 −1.06952 −0.534758 0.845005i \(-0.679597\pi\)
−0.534758 + 0.845005i \(0.679597\pi\)
\(674\) −75.5409 −2.90973
\(675\) 17.8054 0.685331
\(676\) 168.330 6.47424
\(677\) 47.0005 1.80638 0.903188 0.429245i \(-0.141220\pi\)
0.903188 + 0.429245i \(0.141220\pi\)
\(678\) 39.1600 1.50393
\(679\) −1.11599 −0.0428278
\(680\) −49.0082 −1.87938
\(681\) −9.23147 −0.353751
\(682\) 1.41389 0.0541406
\(683\) 16.5936 0.634937 0.317469 0.948269i \(-0.397167\pi\)
0.317469 + 0.948269i \(0.397167\pi\)
\(684\) 99.9804 3.82285
\(685\) 4.68608 0.179046
\(686\) 5.83368 0.222731
\(687\) −35.0116 −1.33578
\(688\) 46.8938 1.78781
\(689\) −96.0167 −3.65795
\(690\) −56.1461 −2.13744
\(691\) 38.5825 1.46775 0.733874 0.679285i \(-0.237710\pi\)
0.733874 + 0.679285i \(0.237710\pi\)
\(692\) −35.9855 −1.36796
\(693\) 0.853969 0.0324396
\(694\) −13.5814 −0.515544
\(695\) −22.2661 −0.844600
\(696\) −38.9675 −1.47706
\(697\) −18.9771 −0.718808
\(698\) 75.3578 2.85233
\(699\) −35.4113 −1.33938
\(700\) −2.04412 −0.0772604
\(701\) −2.14089 −0.0808603 −0.0404302 0.999182i \(-0.512873\pi\)
−0.0404302 + 0.999182i \(0.512873\pi\)
\(702\) −119.135 −4.49645
\(703\) −15.9164 −0.600299
\(704\) 4.24200 0.159876
\(705\) −11.8792 −0.447398
\(706\) 30.5246 1.14881
\(707\) −0.812714 −0.0305652
\(708\) 1.54964 0.0582390
\(709\) 25.9461 0.974428 0.487214 0.873283i \(-0.338013\pi\)
0.487214 + 0.873283i \(0.338013\pi\)
\(710\) 22.2270 0.834166
\(711\) −40.0229 −1.50098
\(712\) −72.3037 −2.70969
\(713\) −2.72253 −0.101960
\(714\) −5.60369 −0.209713
\(715\) 10.6032 0.396536
\(716\) 49.3781 1.84534
\(717\) −54.6864 −2.04230
\(718\) 97.1477 3.62552
\(719\) 1.93803 0.0722765 0.0361382 0.999347i \(-0.488494\pi\)
0.0361382 + 0.999347i \(0.488494\pi\)
\(720\) −68.6286 −2.55764
\(721\) 0.440286 0.0163971
\(722\) 6.97663 0.259643
\(723\) −63.3535 −2.35614
\(724\) 70.5352 2.62142
\(725\) 5.27546 0.195926
\(726\) 7.44229 0.276209
\(727\) −36.5797 −1.35667 −0.678333 0.734754i \(-0.737297\pi\)
−0.678333 + 0.734754i \(0.737297\pi\)
\(728\) 7.83565 0.290408
\(729\) −40.5007 −1.50003
\(730\) −58.3417 −2.15932
\(731\) −25.5332 −0.944381
\(732\) 31.8844 1.17848
\(733\) −14.3156 −0.528761 −0.264380 0.964419i \(-0.585167\pi\)
−0.264380 + 0.964419i \(0.585167\pi\)
\(734\) −56.5536 −2.08743
\(735\) −30.4284 −1.12237
\(736\) −41.1459 −1.51666
\(737\) 4.13899 0.152461
\(738\) −55.6396 −2.04812
\(739\) 32.2885 1.18775 0.593876 0.804557i \(-0.297597\pi\)
0.593876 + 0.804557i \(0.297597\pi\)
\(740\) 27.9780 1.02849
\(741\) 81.3200 2.98737
\(742\) −5.72942 −0.210334
\(743\) −43.3774 −1.59136 −0.795682 0.605715i \(-0.792887\pi\)
−0.795682 + 0.605715i \(0.792887\pi\)
\(744\) −10.9202 −0.400356
\(745\) −12.2148 −0.447515
\(746\) 42.2431 1.54663
\(747\) −48.1903 −1.76319
\(748\) −21.8338 −0.798324
\(749\) 2.20088 0.0804186
\(750\) 86.8850 3.17259
\(751\) 5.03165 0.183607 0.0918037 0.995777i \(-0.470737\pi\)
0.0918037 + 0.995777i \(0.470737\pi\)
\(752\) −23.3141 −0.850176
\(753\) 56.7624 2.06854
\(754\) −35.2976 −1.28546
\(755\) −12.1160 −0.440945
\(756\) −4.98137 −0.181171
\(757\) −43.1143 −1.56702 −0.783509 0.621381i \(-0.786572\pi\)
−0.783509 + 0.621381i \(0.786572\pi\)
\(758\) −61.9243 −2.24919
\(759\) −14.3306 −0.520168
\(760\) 42.4381 1.53939
\(761\) −15.4426 −0.559793 −0.279896 0.960030i \(-0.590300\pi\)
−0.279896 + 0.960030i \(0.590300\pi\)
\(762\) 6.89050 0.249617
\(763\) −2.46361 −0.0891886
\(764\) −52.2594 −1.89068
\(765\) 37.3677 1.35103
\(766\) −24.6431 −0.890390
\(767\) 0.804187 0.0290375
\(768\) 65.8462 2.37602
\(769\) −52.1705 −1.88132 −0.940658 0.339356i \(-0.889791\pi\)
−0.940658 + 0.339356i \(0.889791\pi\)
\(770\) 0.632702 0.0228010
\(771\) −8.90024 −0.320534
\(772\) −13.4555 −0.484274
\(773\) −37.7145 −1.35650 −0.678249 0.734833i \(-0.737261\pi\)
−0.678249 + 0.734833i \(0.737261\pi\)
\(774\) −74.8619 −2.69085
\(775\) 1.47839 0.0531054
\(776\) 47.9277 1.72051
\(777\) 1.83276 0.0657500
\(778\) −45.0933 −1.61667
\(779\) 16.4330 0.588773
\(780\) −142.945 −5.11826
\(781\) 5.67318 0.203002
\(782\) 59.9985 2.14554
\(783\) 12.8559 0.459433
\(784\) −59.7185 −2.13280
\(785\) 14.3220 0.511175
\(786\) 77.9569 2.78063
\(787\) −51.9526 −1.85191 −0.925955 0.377633i \(-0.876738\pi\)
−0.925955 + 0.377633i \(0.876738\pi\)
\(788\) 6.30518 0.224613
\(789\) −62.1768 −2.21355
\(790\) −29.6528 −1.05500
\(791\) 0.849729 0.0302129
\(792\) −36.6748 −1.30318
\(793\) 16.5464 0.587581
\(794\) 54.4904 1.93379
\(795\) 59.8810 2.12376
\(796\) −42.3607 −1.50144
\(797\) −21.6111 −0.765506 −0.382753 0.923851i \(-0.625024\pi\)
−0.382753 + 0.923851i \(0.625024\pi\)
\(798\) 4.85245 0.171775
\(799\) 12.6943 0.449092
\(800\) 22.3431 0.789948
\(801\) 55.1300 1.94792
\(802\) 22.7343 0.802777
\(803\) −14.8910 −0.525492
\(804\) −55.7992 −1.96789
\(805\) −1.21831 −0.0429397
\(806\) −9.89180 −0.348424
\(807\) −38.5493 −1.35700
\(808\) 34.9031 1.22789
\(809\) −40.3141 −1.41737 −0.708684 0.705526i \(-0.750711\pi\)
−0.708684 + 0.705526i \(0.750711\pi\)
\(810\) 12.1437 0.426687
\(811\) −49.2849 −1.73063 −0.865313 0.501232i \(-0.832880\pi\)
−0.865313 + 0.501232i \(0.832880\pi\)
\(812\) −1.47590 −0.0517939
\(813\) 18.9392 0.664226
\(814\) 10.1909 0.357192
\(815\) −12.7580 −0.446892
\(816\) 114.943 4.02380
\(817\) 22.1102 0.773539
\(818\) 58.8442 2.05744
\(819\) −5.97451 −0.208766
\(820\) −28.8861 −1.00875
\(821\) −6.67849 −0.233081 −0.116540 0.993186i \(-0.537180\pi\)
−0.116540 + 0.993186i \(0.537180\pi\)
\(822\) −23.0113 −0.802612
\(823\) −54.4162 −1.89683 −0.948415 0.317033i \(-0.897313\pi\)
−0.948415 + 0.317033i \(0.897313\pi\)
\(824\) −18.9086 −0.658714
\(825\) 7.78183 0.270928
\(826\) 0.0479867 0.00166967
\(827\) 3.10943 0.108125 0.0540627 0.998538i \(-0.482783\pi\)
0.0540627 + 0.998538i \(0.482783\pi\)
\(828\) 123.266 4.28378
\(829\) 19.2971 0.670216 0.335108 0.942180i \(-0.391227\pi\)
0.335108 + 0.942180i \(0.391227\pi\)
\(830\) −35.7040 −1.23930
\(831\) 63.9829 2.21954
\(832\) −29.6777 −1.02889
\(833\) 32.5162 1.12662
\(834\) 109.339 3.78610
\(835\) 29.9889 1.03781
\(836\) 18.9068 0.653904
\(837\) 3.60274 0.124529
\(838\) 19.1186 0.660443
\(839\) −14.9063 −0.514622 −0.257311 0.966329i \(-0.582837\pi\)
−0.257311 + 0.966329i \(0.582837\pi\)
\(840\) −4.88671 −0.168608
\(841\) −25.1910 −0.868655
\(842\) −37.0385 −1.27643
\(843\) 29.2107 1.00607
\(844\) 43.8991 1.51107
\(845\) −54.4792 −1.87414
\(846\) 37.2189 1.27961
\(847\) 0.161489 0.00554884
\(848\) 117.522 4.03572
\(849\) −6.99837 −0.240183
\(850\) −32.5805 −1.11750
\(851\) −19.6233 −0.672678
\(852\) −76.4822 −2.62024
\(853\) −46.4502 −1.59043 −0.795213 0.606330i \(-0.792641\pi\)
−0.795213 + 0.606330i \(0.792641\pi\)
\(854\) 0.987342 0.0337862
\(855\) −32.3581 −1.10662
\(856\) −94.5199 −3.23062
\(857\) 49.7322 1.69882 0.849409 0.527734i \(-0.176958\pi\)
0.849409 + 0.527734i \(0.176958\pi\)
\(858\) −52.0675 −1.77756
\(859\) 17.6664 0.602770 0.301385 0.953502i \(-0.402551\pi\)
0.301385 + 0.953502i \(0.402551\pi\)
\(860\) −38.8656 −1.32531
\(861\) −1.89225 −0.0644875
\(862\) −22.7914 −0.776278
\(863\) 26.3017 0.895320 0.447660 0.894204i \(-0.352257\pi\)
0.447660 + 0.894204i \(0.352257\pi\)
\(864\) 54.4486 1.85238
\(865\) 11.6465 0.395994
\(866\) 34.5258 1.17323
\(867\) −13.6440 −0.463376
\(868\) −0.413606 −0.0140387
\(869\) −7.56851 −0.256744
\(870\) 22.0134 0.746325
\(871\) −28.9570 −0.981172
\(872\) 105.803 3.58294
\(873\) −36.5439 −1.23682
\(874\) −51.9550 −1.75740
\(875\) 1.88531 0.0637351
\(876\) 200.751 6.78275
\(877\) 41.9397 1.41620 0.708102 0.706111i \(-0.249552\pi\)
0.708102 + 0.706111i \(0.249552\pi\)
\(878\) −3.17226 −0.107059
\(879\) −25.4313 −0.857775
\(880\) −12.9780 −0.437488
\(881\) 54.7979 1.84619 0.923094 0.384574i \(-0.125652\pi\)
0.923094 + 0.384574i \(0.125652\pi\)
\(882\) 95.3355 3.21011
\(883\) −32.4485 −1.09198 −0.545990 0.837792i \(-0.683846\pi\)
−0.545990 + 0.837792i \(0.683846\pi\)
\(884\) 152.753 5.13765
\(885\) −0.501533 −0.0168588
\(886\) 89.7655 3.01573
\(887\) −2.47299 −0.0830347 −0.0415174 0.999138i \(-0.513219\pi\)
−0.0415174 + 0.999138i \(0.513219\pi\)
\(888\) −78.7104 −2.64135
\(889\) 0.149516 0.00501461
\(890\) 40.8456 1.36915
\(891\) 3.09954 0.103838
\(892\) 98.2529 3.28975
\(893\) −10.9925 −0.367850
\(894\) 59.9815 2.00608
\(895\) −15.9809 −0.534184
\(896\) 0.898803 0.0300269
\(897\) 100.259 3.34756
\(898\) 30.1970 1.00769
\(899\) 1.06743 0.0356009
\(900\) −66.9360 −2.23120
\(901\) −63.9896 −2.13180
\(902\) −10.5217 −0.350334
\(903\) −2.54598 −0.0847248
\(904\) −36.4927 −1.21373
\(905\) −22.8284 −0.758840
\(906\) 59.4961 1.97663
\(907\) 49.8744 1.65605 0.828026 0.560690i \(-0.189464\pi\)
0.828026 + 0.560690i \(0.189464\pi\)
\(908\) 15.0159 0.498319
\(909\) −26.6128 −0.882692
\(910\) −4.42649 −0.146737
\(911\) −49.5070 −1.64024 −0.820120 0.572192i \(-0.806093\pi\)
−0.820120 + 0.572192i \(0.806093\pi\)
\(912\) −99.5335 −3.29588
\(913\) −9.11300 −0.301596
\(914\) 5.61980 0.185887
\(915\) −10.3192 −0.341142
\(916\) 56.9498 1.88167
\(917\) 1.69158 0.0558609
\(918\) −79.3963 −2.62047
\(919\) −44.3554 −1.46315 −0.731574 0.681762i \(-0.761214\pi\)
−0.731574 + 0.681762i \(0.761214\pi\)
\(920\) 52.3218 1.72500
\(921\) −59.6556 −1.96572
\(922\) −3.35570 −0.110514
\(923\) −39.6905 −1.30643
\(924\) −2.17710 −0.0716213
\(925\) 10.6559 0.350363
\(926\) 7.39629 0.243057
\(927\) 14.4174 0.473531
\(928\) 16.1322 0.529566
\(929\) −10.8535 −0.356091 −0.178046 0.984022i \(-0.556977\pi\)
−0.178046 + 0.984022i \(0.556977\pi\)
\(930\) 6.16903 0.202291
\(931\) −28.1571 −0.922810
\(932\) 57.5999 1.88675
\(933\) −9.14619 −0.299433
\(934\) −1.10504 −0.0361581
\(935\) 7.06640 0.231096
\(936\) 256.583 8.38669
\(937\) 38.0257 1.24225 0.621123 0.783713i \(-0.286677\pi\)
0.621123 + 0.783713i \(0.286677\pi\)
\(938\) −1.72790 −0.0564178
\(939\) −94.1340 −3.07195
\(940\) 19.3227 0.630238
\(941\) −24.8764 −0.810947 −0.405474 0.914107i \(-0.632893\pi\)
−0.405474 + 0.914107i \(0.632893\pi\)
\(942\) −70.3291 −2.29145
\(943\) 20.2602 0.659763
\(944\) −0.984303 −0.0320363
\(945\) 1.61219 0.0524447
\(946\) −14.1567 −0.460275
\(947\) −40.0294 −1.30078 −0.650391 0.759600i \(-0.725395\pi\)
−0.650391 + 0.759600i \(0.725395\pi\)
\(948\) 102.034 3.31391
\(949\) 104.180 3.38183
\(950\) 28.2127 0.915341
\(951\) −5.03371 −0.163229
\(952\) 5.22201 0.169246
\(953\) 17.9403 0.581144 0.290572 0.956853i \(-0.406154\pi\)
0.290572 + 0.956853i \(0.406154\pi\)
\(954\) −187.614 −6.07421
\(955\) 16.9135 0.547307
\(956\) 88.9527 2.87694
\(957\) 5.61865 0.181625
\(958\) −36.5758 −1.18171
\(959\) −0.499320 −0.0161239
\(960\) 18.5086 0.597361
\(961\) −30.7009 −0.990350
\(962\) −71.2976 −2.29873
\(963\) 72.0694 2.32240
\(964\) 103.051 3.31903
\(965\) 4.35480 0.140186
\(966\) 5.98258 0.192486
\(967\) 51.1550 1.64503 0.822516 0.568742i \(-0.192570\pi\)
0.822516 + 0.568742i \(0.192570\pi\)
\(968\) −6.93538 −0.222912
\(969\) 54.1951 1.74100
\(970\) −27.0752 −0.869332
\(971\) −16.8976 −0.542269 −0.271134 0.962542i \(-0.587399\pi\)
−0.271134 + 0.962542i \(0.587399\pi\)
\(972\) 50.7533 1.62791
\(973\) 2.37253 0.0760599
\(974\) 44.7304 1.43325
\(975\) −54.4430 −1.74357
\(976\) −20.2524 −0.648263
\(977\) 27.2904 0.873098 0.436549 0.899681i \(-0.356201\pi\)
0.436549 + 0.899681i \(0.356201\pi\)
\(978\) 62.6487 2.00329
\(979\) 10.4253 0.333195
\(980\) 49.4948 1.58105
\(981\) −80.6725 −2.57567
\(982\) −22.4929 −0.717777
\(983\) 5.15037 0.164271 0.0821356 0.996621i \(-0.473826\pi\)
0.0821356 + 0.996621i \(0.473826\pi\)
\(984\) 81.2650 2.59063
\(985\) −2.04064 −0.0650201
\(986\) −23.5238 −0.749152
\(987\) 1.26578 0.0402901
\(988\) −132.275 −4.20823
\(989\) 27.2597 0.866807
\(990\) 20.7182 0.658469
\(991\) 3.83886 0.121946 0.0609728 0.998139i \(-0.480580\pi\)
0.0609728 + 0.998139i \(0.480580\pi\)
\(992\) 4.52089 0.143538
\(993\) −39.3238 −1.24790
\(994\) −2.36837 −0.0751203
\(995\) 13.7098 0.434631
\(996\) 122.856 3.89283
\(997\) 36.0307 1.14110 0.570551 0.821262i \(-0.306730\pi\)
0.570551 + 0.821262i \(0.306730\pi\)
\(998\) 43.6340 1.38121
\(999\) 25.9676 0.821580
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 \(a_p\))