Properties

Label 8007.2.a.j.1.12
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 0
Dimension 64
CM No

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(0\)
Dimension: \(64\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.82641 q^{2}\) \(-1.00000 q^{3}\) \(+1.33579 q^{4}\) \(+0.0479756 q^{5}\) \(+1.82641 q^{6}\) \(-0.416922 q^{7}\) \(+1.21313 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.82641 q^{2}\) \(-1.00000 q^{3}\) \(+1.33579 q^{4}\) \(+0.0479756 q^{5}\) \(+1.82641 q^{6}\) \(-0.416922 q^{7}\) \(+1.21313 q^{8}\) \(+1.00000 q^{9}\) \(-0.0876232 q^{10}\) \(+2.02005 q^{11}\) \(-1.33579 q^{12}\) \(-4.18708 q^{13}\) \(+0.761473 q^{14}\) \(-0.0479756 q^{15}\) \(-4.88725 q^{16}\) \(+1.00000 q^{17}\) \(-1.82641 q^{18}\) \(-3.54630 q^{19}\) \(+0.0640852 q^{20}\) \(+0.416922 q^{21}\) \(-3.68944 q^{22}\) \(-4.19836 q^{23}\) \(-1.21313 q^{24}\) \(-4.99770 q^{25}\) \(+7.64733 q^{26}\) \(-1.00000 q^{27}\) \(-0.556919 q^{28}\) \(-0.335745 q^{29}\) \(+0.0876232 q^{30}\) \(-8.59798 q^{31}\) \(+6.49988 q^{32}\) \(-2.02005 q^{33}\) \(-1.82641 q^{34}\) \(-0.0200021 q^{35}\) \(+1.33579 q^{36}\) \(+6.45995 q^{37}\) \(+6.47701 q^{38}\) \(+4.18708 q^{39}\) \(+0.0582005 q^{40}\) \(-4.65889 q^{41}\) \(-0.761473 q^{42}\) \(-8.67098 q^{43}\) \(+2.69835 q^{44}\) \(+0.0479756 q^{45}\) \(+7.66794 q^{46}\) \(-10.7000 q^{47}\) \(+4.88725 q^{48}\) \(-6.82618 q^{49}\) \(+9.12786 q^{50}\) \(-1.00000 q^{51}\) \(-5.59304 q^{52}\) \(+10.3834 q^{53}\) \(+1.82641 q^{54}\) \(+0.0969129 q^{55}\) \(-0.505780 q^{56}\) \(+3.54630 q^{57}\) \(+0.613209 q^{58}\) \(-9.03342 q^{59}\) \(-0.0640852 q^{60}\) \(+11.8588 q^{61}\) \(+15.7035 q^{62}\) \(-0.416922 q^{63}\) \(-2.09698 q^{64}\) \(-0.200877 q^{65}\) \(+3.68944 q^{66}\) \(-6.64855 q^{67}\) \(+1.33579 q^{68}\) \(+4.19836 q^{69}\) \(+0.0365321 q^{70}\) \(+2.46716 q^{71}\) \(+1.21313 q^{72}\) \(+10.7246 q^{73}\) \(-11.7985 q^{74}\) \(+4.99770 q^{75}\) \(-4.73710 q^{76}\) \(-0.842203 q^{77}\) \(-7.64733 q^{78}\) \(+5.42684 q^{79}\) \(-0.234468 q^{80}\) \(+1.00000 q^{81}\) \(+8.50905 q^{82}\) \(-3.38586 q^{83}\) \(+0.556919 q^{84}\) \(+0.0479756 q^{85}\) \(+15.8368 q^{86}\) \(+0.335745 q^{87}\) \(+2.45058 q^{88}\) \(-1.09398 q^{89}\) \(-0.0876232 q^{90}\) \(+1.74569 q^{91}\) \(-5.60811 q^{92}\) \(+8.59798 q^{93}\) \(+19.5427 q^{94}\) \(-0.170136 q^{95}\) \(-6.49988 q^{96}\) \(-12.9976 q^{97}\) \(+12.4674 q^{98}\) \(+2.02005 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(64q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 64q^{3} \) \(\mathstrut +\mathstrut 77q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 64q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(64q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 64q^{3} \) \(\mathstrut +\mathstrut 77q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 64q^{9} \) \(\mathstrut +\mathstrut 12q^{10} \) \(\mathstrut -\mathstrut 7q^{11} \) \(\mathstrut -\mathstrut 77q^{12} \) \(\mathstrut +\mathstrut 24q^{13} \) \(\mathstrut -\mathstrut 14q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 103q^{16} \) \(\mathstrut +\mathstrut 64q^{17} \) \(\mathstrut +\mathstrut 5q^{18} \) \(\mathstrut +\mathstrut 26q^{19} \) \(\mathstrut -\mathstrut 24q^{20} \) \(\mathstrut -\mathstrut 5q^{21} \) \(\mathstrut +\mathstrut 25q^{22} \) \(\mathstrut +\mathstrut 20q^{23} \) \(\mathstrut -\mathstrut 18q^{24} \) \(\mathstrut +\mathstrut 141q^{25} \) \(\mathstrut +\mathstrut 9q^{26} \) \(\mathstrut -\mathstrut 64q^{27} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut +\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 31q^{32} \) \(\mathstrut +\mathstrut 7q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 3q^{35} \) \(\mathstrut +\mathstrut 77q^{36} \) \(\mathstrut +\mathstrut 50q^{37} \) \(\mathstrut +\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut +\mathstrut 28q^{40} \) \(\mathstrut -\mathstrut 9q^{41} \) \(\mathstrut +\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 59q^{43} \) \(\mathstrut -\mathstrut 6q^{44} \) \(\mathstrut -\mathstrut 3q^{45} \) \(\mathstrut +\mathstrut 11q^{47} \) \(\mathstrut -\mathstrut 103q^{48} \) \(\mathstrut +\mathstrut 163q^{49} \) \(\mathstrut +\mathstrut 20q^{50} \) \(\mathstrut -\mathstrut 64q^{51} \) \(\mathstrut +\mathstrut 65q^{52} \) \(\mathstrut +\mathstrut 39q^{53} \) \(\mathstrut -\mathstrut 5q^{54} \) \(\mathstrut +\mathstrut 35q^{55} \) \(\mathstrut -\mathstrut 34q^{56} \) \(\mathstrut -\mathstrut 26q^{57} \) \(\mathstrut -\mathstrut 27q^{58} \) \(\mathstrut -\mathstrut 65q^{59} \) \(\mathstrut +\mathstrut 24q^{60} \) \(\mathstrut +\mathstrut 15q^{61} \) \(\mathstrut +\mathstrut 18q^{62} \) \(\mathstrut +\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 152q^{64} \) \(\mathstrut +\mathstrut 49q^{65} \) \(\mathstrut -\mathstrut 25q^{66} \) \(\mathstrut +\mathstrut 56q^{67} \) \(\mathstrut +\mathstrut 77q^{68} \) \(\mathstrut -\mathstrut 20q^{69} \) \(\mathstrut +\mathstrut 28q^{70} \) \(\mathstrut -\mathstrut 18q^{71} \) \(\mathstrut +\mathstrut 18q^{72} \) \(\mathstrut +\mathstrut 37q^{73} \) \(\mathstrut -\mathstrut 76q^{74} \) \(\mathstrut -\mathstrut 141q^{75} \) \(\mathstrut +\mathstrut 30q^{76} \) \(\mathstrut +\mathstrut 80q^{77} \) \(\mathstrut -\mathstrut 9q^{78} \) \(\mathstrut +\mathstrut 20q^{79} \) \(\mathstrut -\mathstrut 144q^{80} \) \(\mathstrut +\mathstrut 64q^{81} \) \(\mathstrut +\mathstrut 27q^{82} \) \(\mathstrut +\mathstrut 3q^{83} \) \(\mathstrut -\mathstrut 14q^{84} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 12q^{86} \) \(\mathstrut -\mathstrut 5q^{87} \) \(\mathstrut +\mathstrut 108q^{88} \) \(\mathstrut +\mathstrut 42q^{89} \) \(\mathstrut +\mathstrut 12q^{90} \) \(\mathstrut +\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 18q^{92} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 60q^{94} \) \(\mathstrut +\mathstrut 42q^{95} \) \(\mathstrut -\mathstrut 31q^{96} \) \(\mathstrut +\mathstrut 72q^{97} \) \(\mathstrut +\mathstrut 18q^{98} \) \(\mathstrut -\mathstrut 7q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.82641 −1.29147 −0.645735 0.763562i \(-0.723449\pi\)
−0.645735 + 0.763562i \(0.723449\pi\)
\(3\) −1.00000 −0.577350
\(4\) 1.33579 0.667894
\(5\) 0.0479756 0.0214553 0.0107277 0.999942i \(-0.496585\pi\)
0.0107277 + 0.999942i \(0.496585\pi\)
\(6\) 1.82641 0.745630
\(7\) −0.416922 −0.157582 −0.0787909 0.996891i \(-0.525106\pi\)
−0.0787909 + 0.996891i \(0.525106\pi\)
\(8\) 1.21313 0.428905
\(9\) 1.00000 0.333333
\(10\) −0.0876232 −0.0277089
\(11\) 2.02005 0.609067 0.304534 0.952502i \(-0.401499\pi\)
0.304534 + 0.952502i \(0.401499\pi\)
\(12\) −1.33579 −0.385609
\(13\) −4.18708 −1.16129 −0.580643 0.814158i \(-0.697199\pi\)
−0.580643 + 0.814158i \(0.697199\pi\)
\(14\) 0.761473 0.203512
\(15\) −0.0479756 −0.0123872
\(16\) −4.88725 −1.22181
\(17\) 1.00000 0.242536
\(18\) −1.82641 −0.430490
\(19\) −3.54630 −0.813577 −0.406788 0.913522i \(-0.633351\pi\)
−0.406788 + 0.913522i \(0.633351\pi\)
\(20\) 0.0640852 0.0143299
\(21\) 0.416922 0.0909799
\(22\) −3.68944 −0.786592
\(23\) −4.19836 −0.875418 −0.437709 0.899117i \(-0.644210\pi\)
−0.437709 + 0.899117i \(0.644210\pi\)
\(24\) −1.21313 −0.247629
\(25\) −4.99770 −0.999540
\(26\) 7.64733 1.49977
\(27\) −1.00000 −0.192450
\(28\) −0.556919 −0.105248
\(29\) −0.335745 −0.0623463 −0.0311731 0.999514i \(-0.509924\pi\)
−0.0311731 + 0.999514i \(0.509924\pi\)
\(30\) 0.0876232 0.0159977
\(31\) −8.59798 −1.54424 −0.772122 0.635475i \(-0.780804\pi\)
−0.772122 + 0.635475i \(0.780804\pi\)
\(32\) 6.49988 1.14903
\(33\) −2.02005 −0.351645
\(34\) −1.82641 −0.313227
\(35\) −0.0200021 −0.00338097
\(36\) 1.33579 0.222631
\(37\) 6.45995 1.06201 0.531004 0.847369i \(-0.321815\pi\)
0.531004 + 0.847369i \(0.321815\pi\)
\(38\) 6.47701 1.05071
\(39\) 4.18708 0.670469
\(40\) 0.0582005 0.00920230
\(41\) −4.65889 −0.727596 −0.363798 0.931478i \(-0.618520\pi\)
−0.363798 + 0.931478i \(0.618520\pi\)
\(42\) −0.761473 −0.117498
\(43\) −8.67098 −1.32231 −0.661156 0.750249i \(-0.729934\pi\)
−0.661156 + 0.750249i \(0.729934\pi\)
\(44\) 2.69835 0.406792
\(45\) 0.0479756 0.00715178
\(46\) 7.66794 1.13058
\(47\) −10.7000 −1.56076 −0.780379 0.625306i \(-0.784974\pi\)
−0.780379 + 0.625306i \(0.784974\pi\)
\(48\) 4.88725 0.705413
\(49\) −6.82618 −0.975168
\(50\) 9.12786 1.29088
\(51\) −1.00000 −0.140028
\(52\) −5.59304 −0.775615
\(53\) 10.3834 1.42627 0.713134 0.701028i \(-0.247275\pi\)
0.713134 + 0.701028i \(0.247275\pi\)
\(54\) 1.82641 0.248543
\(55\) 0.0969129 0.0130677
\(56\) −0.505780 −0.0675877
\(57\) 3.54630 0.469719
\(58\) 0.613209 0.0805183
\(59\) −9.03342 −1.17605 −0.588026 0.808842i \(-0.700095\pi\)
−0.588026 + 0.808842i \(0.700095\pi\)
\(60\) −0.0640852 −0.00827336
\(61\) 11.8588 1.51837 0.759183 0.650878i \(-0.225599\pi\)
0.759183 + 0.650878i \(0.225599\pi\)
\(62\) 15.7035 1.99434
\(63\) −0.416922 −0.0525273
\(64\) −2.09698 −0.262122
\(65\) −0.200877 −0.0249158
\(66\) 3.68944 0.454139
\(67\) −6.64855 −0.812250 −0.406125 0.913818i \(-0.633120\pi\)
−0.406125 + 0.913818i \(0.633120\pi\)
\(68\) 1.33579 0.161988
\(69\) 4.19836 0.505423
\(70\) 0.0365321 0.00436642
\(71\) 2.46716 0.292798 0.146399 0.989226i \(-0.453232\pi\)
0.146399 + 0.989226i \(0.453232\pi\)
\(72\) 1.21313 0.142968
\(73\) 10.7246 1.25522 0.627609 0.778529i \(-0.284034\pi\)
0.627609 + 0.778529i \(0.284034\pi\)
\(74\) −11.7985 −1.37155
\(75\) 4.99770 0.577084
\(76\) −4.73710 −0.543383
\(77\) −0.842203 −0.0959779
\(78\) −7.64733 −0.865890
\(79\) 5.42684 0.610567 0.305283 0.952262i \(-0.401249\pi\)
0.305283 + 0.952262i \(0.401249\pi\)
\(80\) −0.234468 −0.0262144
\(81\) 1.00000 0.111111
\(82\) 8.50905 0.939668
\(83\) −3.38586 −0.371646 −0.185823 0.982583i \(-0.559495\pi\)
−0.185823 + 0.982583i \(0.559495\pi\)
\(84\) 0.556919 0.0607649
\(85\) 0.0479756 0.00520368
\(86\) 15.8368 1.70773
\(87\) 0.335745 0.0359956
\(88\) 2.45058 0.261232
\(89\) −1.09398 −0.115962 −0.0579810 0.998318i \(-0.518466\pi\)
−0.0579810 + 0.998318i \(0.518466\pi\)
\(90\) −0.0876232 −0.00923630
\(91\) 1.74569 0.182998
\(92\) −5.60811 −0.584686
\(93\) 8.59798 0.891569
\(94\) 19.5427 2.01567
\(95\) −0.170136 −0.0174556
\(96\) −6.49988 −0.663391
\(97\) −12.9976 −1.31971 −0.659855 0.751393i \(-0.729382\pi\)
−0.659855 + 0.751393i \(0.729382\pi\)
\(98\) 12.4674 1.25940
\(99\) 2.02005 0.203022
\(100\) −6.67586 −0.667586
\(101\) −10.6831 −1.06301 −0.531503 0.847056i \(-0.678373\pi\)
−0.531503 + 0.847056i \(0.678373\pi\)
\(102\) 1.82641 0.180842
\(103\) −10.9569 −1.07962 −0.539810 0.841787i \(-0.681504\pi\)
−0.539810 + 0.841787i \(0.681504\pi\)
\(104\) −5.07946 −0.498082
\(105\) 0.0200021 0.00195200
\(106\) −18.9644 −1.84198
\(107\) 13.8446 1.33841 0.669206 0.743077i \(-0.266634\pi\)
0.669206 + 0.743077i \(0.266634\pi\)
\(108\) −1.33579 −0.128536
\(109\) 18.5572 1.77746 0.888729 0.458432i \(-0.151589\pi\)
0.888729 + 0.458432i \(0.151589\pi\)
\(110\) −0.177003 −0.0168766
\(111\) −6.45995 −0.613151
\(112\) 2.03760 0.192535
\(113\) 8.29831 0.780640 0.390320 0.920679i \(-0.372364\pi\)
0.390320 + 0.920679i \(0.372364\pi\)
\(114\) −6.47701 −0.606628
\(115\) −0.201419 −0.0187824
\(116\) −0.448484 −0.0416407
\(117\) −4.18708 −0.387095
\(118\) 16.4988 1.51883
\(119\) −0.416922 −0.0382192
\(120\) −0.0582005 −0.00531295
\(121\) −6.91941 −0.629037
\(122\) −21.6591 −1.96092
\(123\) 4.65889 0.420078
\(124\) −11.4851 −1.03139
\(125\) −0.479645 −0.0429008
\(126\) 0.761473 0.0678374
\(127\) 14.5279 1.28914 0.644572 0.764544i \(-0.277036\pi\)
0.644572 + 0.764544i \(0.277036\pi\)
\(128\) −9.16981 −0.810505
\(129\) 8.67098 0.763437
\(130\) 0.366885 0.0321780
\(131\) 4.55832 0.398262 0.199131 0.979973i \(-0.436188\pi\)
0.199131 + 0.979973i \(0.436188\pi\)
\(132\) −2.69835 −0.234862
\(133\) 1.47853 0.128205
\(134\) 12.1430 1.04900
\(135\) −0.0479756 −0.00412908
\(136\) 1.21313 0.104025
\(137\) 4.84068 0.413567 0.206783 0.978387i \(-0.433700\pi\)
0.206783 + 0.978387i \(0.433700\pi\)
\(138\) −7.66794 −0.652738
\(139\) 12.9447 1.09796 0.548979 0.835836i \(-0.315017\pi\)
0.548979 + 0.835836i \(0.315017\pi\)
\(140\) −0.0267185 −0.00225813
\(141\) 10.7000 0.901104
\(142\) −4.50606 −0.378140
\(143\) −8.45809 −0.707301
\(144\) −4.88725 −0.407271
\(145\) −0.0161076 −0.00133766
\(146\) −19.5875 −1.62108
\(147\) 6.82618 0.563013
\(148\) 8.62912 0.709309
\(149\) −8.74514 −0.716430 −0.358215 0.933639i \(-0.616615\pi\)
−0.358215 + 0.933639i \(0.616615\pi\)
\(150\) −9.12786 −0.745287
\(151\) 0.743467 0.0605025 0.0302512 0.999542i \(-0.490369\pi\)
0.0302512 + 0.999542i \(0.490369\pi\)
\(152\) −4.30211 −0.348947
\(153\) 1.00000 0.0808452
\(154\) 1.53821 0.123953
\(155\) −0.412493 −0.0331322
\(156\) 5.59304 0.447802
\(157\) −1.00000 −0.0798087
\(158\) −9.91165 −0.788528
\(159\) −10.3834 −0.823456
\(160\) 0.311835 0.0246528
\(161\) 1.75039 0.137950
\(162\) −1.82641 −0.143497
\(163\) 1.29011 0.101049 0.0505245 0.998723i \(-0.483911\pi\)
0.0505245 + 0.998723i \(0.483911\pi\)
\(164\) −6.22328 −0.485956
\(165\) −0.0969129 −0.00754466
\(166\) 6.18398 0.479970
\(167\) 1.21096 0.0937073 0.0468536 0.998902i \(-0.485081\pi\)
0.0468536 + 0.998902i \(0.485081\pi\)
\(168\) 0.505780 0.0390218
\(169\) 4.53160 0.348585
\(170\) −0.0876232 −0.00672040
\(171\) −3.54630 −0.271192
\(172\) −11.5826 −0.883164
\(173\) 14.6723 1.11551 0.557756 0.830005i \(-0.311663\pi\)
0.557756 + 0.830005i \(0.311663\pi\)
\(174\) −0.613209 −0.0464873
\(175\) 2.08365 0.157509
\(176\) −9.87247 −0.744166
\(177\) 9.03342 0.678993
\(178\) 1.99806 0.149761
\(179\) −9.47781 −0.708404 −0.354202 0.935169i \(-0.615248\pi\)
−0.354202 + 0.935169i \(0.615248\pi\)
\(180\) 0.0640852 0.00477663
\(181\) 22.1067 1.64318 0.821590 0.570079i \(-0.193087\pi\)
0.821590 + 0.570079i \(0.193087\pi\)
\(182\) −3.18834 −0.236336
\(183\) −11.8588 −0.876628
\(184\) −5.09314 −0.375471
\(185\) 0.309920 0.0227857
\(186\) −15.7035 −1.15143
\(187\) 2.02005 0.147721
\(188\) −14.2930 −1.04242
\(189\) 0.416922 0.0303266
\(190\) 0.310738 0.0225433
\(191\) −16.8321 −1.21793 −0.608966 0.793197i \(-0.708415\pi\)
−0.608966 + 0.793197i \(0.708415\pi\)
\(192\) 2.09698 0.151336
\(193\) −11.2057 −0.806607 −0.403303 0.915066i \(-0.632138\pi\)
−0.403303 + 0.915066i \(0.632138\pi\)
\(194\) 23.7391 1.70437
\(195\) 0.200877 0.0143851
\(196\) −9.11832 −0.651308
\(197\) −20.4516 −1.45712 −0.728560 0.684982i \(-0.759810\pi\)
−0.728560 + 0.684982i \(0.759810\pi\)
\(198\) −3.68944 −0.262197
\(199\) −10.1594 −0.720178 −0.360089 0.932918i \(-0.617254\pi\)
−0.360089 + 0.932918i \(0.617254\pi\)
\(200\) −6.06284 −0.428708
\(201\) 6.64855 0.468953
\(202\) 19.5117 1.37284
\(203\) 0.139980 0.00982464
\(204\) −1.33579 −0.0935238
\(205\) −0.223513 −0.0156108
\(206\) 20.0119 1.39430
\(207\) −4.19836 −0.291806
\(208\) 20.4633 1.41887
\(209\) −7.16369 −0.495523
\(210\) −0.0365321 −0.00252095
\(211\) 28.4268 1.95698 0.978491 0.206289i \(-0.0661386\pi\)
0.978491 + 0.206289i \(0.0661386\pi\)
\(212\) 13.8700 0.952595
\(213\) −2.46716 −0.169047
\(214\) −25.2861 −1.72852
\(215\) −0.415995 −0.0283706
\(216\) −1.21313 −0.0825429
\(217\) 3.58469 0.243345
\(218\) −33.8932 −2.29553
\(219\) −10.7246 −0.724701
\(220\) 0.129455 0.00872786
\(221\) −4.18708 −0.281653
\(222\) 11.7985 0.791866
\(223\) −5.86594 −0.392813 −0.196406 0.980523i \(-0.562927\pi\)
−0.196406 + 0.980523i \(0.562927\pi\)
\(224\) −2.70995 −0.181066
\(225\) −4.99770 −0.333180
\(226\) −15.1562 −1.00817
\(227\) 0.403365 0.0267722 0.0133861 0.999910i \(-0.495739\pi\)
0.0133861 + 0.999910i \(0.495739\pi\)
\(228\) 4.73710 0.313722
\(229\) −26.3942 −1.74418 −0.872089 0.489348i \(-0.837235\pi\)
−0.872089 + 0.489348i \(0.837235\pi\)
\(230\) 0.367874 0.0242569
\(231\) 0.842203 0.0554129
\(232\) −0.407301 −0.0267406
\(233\) −23.2593 −1.52377 −0.761884 0.647713i \(-0.775725\pi\)
−0.761884 + 0.647713i \(0.775725\pi\)
\(234\) 7.64733 0.499922
\(235\) −0.513340 −0.0334866
\(236\) −12.0667 −0.785477
\(237\) −5.42684 −0.352511
\(238\) 0.761473 0.0493589
\(239\) −16.6546 −1.07729 −0.538647 0.842532i \(-0.681064\pi\)
−0.538647 + 0.842532i \(0.681064\pi\)
\(240\) 0.234468 0.0151349
\(241\) 28.5383 1.83832 0.919158 0.393889i \(-0.128871\pi\)
0.919158 + 0.393889i \(0.128871\pi\)
\(242\) 12.6377 0.812382
\(243\) −1.00000 −0.0641500
\(244\) 15.8408 1.01411
\(245\) −0.327490 −0.0209225
\(246\) −8.50905 −0.542517
\(247\) 14.8486 0.944795
\(248\) −10.4304 −0.662334
\(249\) 3.38586 0.214570
\(250\) 0.876031 0.0554050
\(251\) −20.5372 −1.29629 −0.648147 0.761515i \(-0.724456\pi\)
−0.648147 + 0.761515i \(0.724456\pi\)
\(252\) −0.556919 −0.0350826
\(253\) −8.48088 −0.533188
\(254\) −26.5340 −1.66489
\(255\) −0.0479756 −0.00300435
\(256\) 20.9418 1.30886
\(257\) 15.0003 0.935695 0.467848 0.883809i \(-0.345030\pi\)
0.467848 + 0.883809i \(0.345030\pi\)
\(258\) −15.8368 −0.985956
\(259\) −2.69330 −0.167353
\(260\) −0.268329 −0.0166411
\(261\) −0.335745 −0.0207821
\(262\) −8.32537 −0.514343
\(263\) 10.3625 0.638980 0.319490 0.947590i \(-0.396488\pi\)
0.319490 + 0.947590i \(0.396488\pi\)
\(264\) −2.45058 −0.150822
\(265\) 0.498149 0.0306011
\(266\) −2.70041 −0.165573
\(267\) 1.09398 0.0669506
\(268\) −8.88105 −0.542496
\(269\) 7.00773 0.427269 0.213634 0.976914i \(-0.431470\pi\)
0.213634 + 0.976914i \(0.431470\pi\)
\(270\) 0.0876232 0.00533258
\(271\) 19.5375 1.18682 0.593409 0.804901i \(-0.297782\pi\)
0.593409 + 0.804901i \(0.297782\pi\)
\(272\) −4.88725 −0.296333
\(273\) −1.74569 −0.105654
\(274\) −8.84108 −0.534109
\(275\) −10.0956 −0.608787
\(276\) 5.60811 0.337569
\(277\) 5.05535 0.303747 0.151873 0.988400i \(-0.451469\pi\)
0.151873 + 0.988400i \(0.451469\pi\)
\(278\) −23.6425 −1.41798
\(279\) −8.59798 −0.514748
\(280\) −0.0242651 −0.00145012
\(281\) −7.43753 −0.443686 −0.221843 0.975082i \(-0.571207\pi\)
−0.221843 + 0.975082i \(0.571207\pi\)
\(282\) −19.5427 −1.16375
\(283\) −4.08341 −0.242734 −0.121367 0.992608i \(-0.538728\pi\)
−0.121367 + 0.992608i \(0.538728\pi\)
\(284\) 3.29561 0.195558
\(285\) 0.170136 0.0100780
\(286\) 15.4480 0.913458
\(287\) 1.94239 0.114656
\(288\) 6.49988 0.383009
\(289\) 1.00000 0.0588235
\(290\) 0.0294191 0.00172755
\(291\) 12.9976 0.761935
\(292\) 14.3258 0.838352
\(293\) 34.1062 1.99250 0.996251 0.0865044i \(-0.0275697\pi\)
0.996251 + 0.0865044i \(0.0275697\pi\)
\(294\) −12.4674 −0.727115
\(295\) −0.433384 −0.0252326
\(296\) 7.83674 0.455501
\(297\) −2.02005 −0.117215
\(298\) 15.9722 0.925247
\(299\) 17.5788 1.01661
\(300\) 6.67586 0.385431
\(301\) 3.61512 0.208372
\(302\) −1.35788 −0.0781371
\(303\) 10.6831 0.613727
\(304\) 17.3316 0.994038
\(305\) 0.568933 0.0325770
\(306\) −1.82641 −0.104409
\(307\) −22.8826 −1.30598 −0.652990 0.757366i \(-0.726486\pi\)
−0.652990 + 0.757366i \(0.726486\pi\)
\(308\) −1.12500 −0.0641030
\(309\) 10.9569 0.623318
\(310\) 0.753383 0.0427893
\(311\) −14.0114 −0.794512 −0.397256 0.917708i \(-0.630038\pi\)
−0.397256 + 0.917708i \(0.630038\pi\)
\(312\) 5.07946 0.287568
\(313\) −11.4559 −0.647523 −0.323762 0.946139i \(-0.604948\pi\)
−0.323762 + 0.946139i \(0.604948\pi\)
\(314\) 1.82641 0.103070
\(315\) −0.0200021 −0.00112699
\(316\) 7.24910 0.407794
\(317\) −15.2293 −0.855362 −0.427681 0.903930i \(-0.640669\pi\)
−0.427681 + 0.903930i \(0.640669\pi\)
\(318\) 18.9644 1.06347
\(319\) −0.678221 −0.0379731
\(320\) −0.100604 −0.00562392
\(321\) −13.8446 −0.772733
\(322\) −3.19693 −0.178158
\(323\) −3.54630 −0.197321
\(324\) 1.33579 0.0742104
\(325\) 20.9257 1.16075
\(326\) −2.35627 −0.130502
\(327\) −18.5572 −1.02622
\(328\) −5.65182 −0.312070
\(329\) 4.46108 0.245947
\(330\) 0.177003 0.00974370
\(331\) −11.9976 −0.659446 −0.329723 0.944078i \(-0.606955\pi\)
−0.329723 + 0.944078i \(0.606955\pi\)
\(332\) −4.52279 −0.248220
\(333\) 6.45995 0.354003
\(334\) −2.21172 −0.121020
\(335\) −0.318968 −0.0174271
\(336\) −2.03760 −0.111160
\(337\) 24.7430 1.34784 0.673918 0.738806i \(-0.264610\pi\)
0.673918 + 0.738806i \(0.264610\pi\)
\(338\) −8.27658 −0.450186
\(339\) −8.29831 −0.450703
\(340\) 0.0640852 0.00347551
\(341\) −17.3683 −0.940548
\(342\) 6.47701 0.350237
\(343\) 5.76444 0.311251
\(344\) −10.5190 −0.567147
\(345\) 0.201419 0.0108440
\(346\) −26.7976 −1.44065
\(347\) −3.60475 −0.193513 −0.0967566 0.995308i \(-0.530847\pi\)
−0.0967566 + 0.995308i \(0.530847\pi\)
\(348\) 0.448484 0.0240413
\(349\) −23.2803 −1.24617 −0.623084 0.782155i \(-0.714121\pi\)
−0.623084 + 0.782155i \(0.714121\pi\)
\(350\) −3.80561 −0.203418
\(351\) 4.18708 0.223490
\(352\) 13.1301 0.699835
\(353\) 19.1996 1.02189 0.510947 0.859612i \(-0.329295\pi\)
0.510947 + 0.859612i \(0.329295\pi\)
\(354\) −16.4988 −0.876899
\(355\) 0.118364 0.00628209
\(356\) −1.46133 −0.0774502
\(357\) 0.416922 0.0220659
\(358\) 17.3104 0.914883
\(359\) 25.3997 1.34054 0.670272 0.742115i \(-0.266177\pi\)
0.670272 + 0.742115i \(0.266177\pi\)
\(360\) 0.0582005 0.00306743
\(361\) −6.42376 −0.338093
\(362\) −40.3760 −2.12212
\(363\) 6.91941 0.363175
\(364\) 2.33186 0.122223
\(365\) 0.514518 0.0269311
\(366\) 21.6591 1.13214
\(367\) −1.08568 −0.0566719 −0.0283360 0.999598i \(-0.509021\pi\)
−0.0283360 + 0.999598i \(0.509021\pi\)
\(368\) 20.5184 1.06960
\(369\) −4.65889 −0.242532
\(370\) −0.566042 −0.0294271
\(371\) −4.32907 −0.224754
\(372\) 11.4851 0.595473
\(373\) 22.9203 1.18677 0.593383 0.804920i \(-0.297792\pi\)
0.593383 + 0.804920i \(0.297792\pi\)
\(374\) −3.68944 −0.190777
\(375\) 0.479645 0.0247688
\(376\) −12.9805 −0.669418
\(377\) 1.40579 0.0724018
\(378\) −0.761473 −0.0391659
\(379\) 33.1341 1.70198 0.850991 0.525180i \(-0.176002\pi\)
0.850991 + 0.525180i \(0.176002\pi\)
\(380\) −0.227265 −0.0116585
\(381\) −14.5279 −0.744288
\(382\) 30.7425 1.57292
\(383\) 26.7400 1.36635 0.683175 0.730255i \(-0.260599\pi\)
0.683175 + 0.730255i \(0.260599\pi\)
\(384\) 9.16981 0.467945
\(385\) −0.0404052 −0.00205924
\(386\) 20.4663 1.04171
\(387\) −8.67098 −0.440771
\(388\) −17.3621 −0.881426
\(389\) 33.2292 1.68479 0.842393 0.538864i \(-0.181146\pi\)
0.842393 + 0.538864i \(0.181146\pi\)
\(390\) −0.366885 −0.0185779
\(391\) −4.19836 −0.212320
\(392\) −8.28102 −0.418255
\(393\) −4.55832 −0.229937
\(394\) 37.3532 1.88183
\(395\) 0.260356 0.0130999
\(396\) 2.69835 0.135597
\(397\) −9.31156 −0.467334 −0.233667 0.972317i \(-0.575073\pi\)
−0.233667 + 0.972317i \(0.575073\pi\)
\(398\) 18.5552 0.930088
\(399\) −1.47853 −0.0740191
\(400\) 24.4250 1.22125
\(401\) −12.4630 −0.622371 −0.311186 0.950349i \(-0.600726\pi\)
−0.311186 + 0.950349i \(0.600726\pi\)
\(402\) −12.1430 −0.605638
\(403\) 36.0004 1.79331
\(404\) −14.2703 −0.709975
\(405\) 0.0479756 0.00238393
\(406\) −0.255661 −0.0126882
\(407\) 13.0494 0.646835
\(408\) −1.21313 −0.0600588
\(409\) −35.9173 −1.77599 −0.887997 0.459848i \(-0.847904\pi\)
−0.887997 + 0.459848i \(0.847904\pi\)
\(410\) 0.408227 0.0201609
\(411\) −4.84068 −0.238773
\(412\) −14.6361 −0.721071
\(413\) 3.76623 0.185324
\(414\) 7.66794 0.376859
\(415\) −0.162438 −0.00797379
\(416\) −27.2155 −1.33435
\(417\) −12.9447 −0.633907
\(418\) 13.0839 0.639953
\(419\) −22.0013 −1.07483 −0.537416 0.843317i \(-0.680600\pi\)
−0.537416 + 0.843317i \(0.680600\pi\)
\(420\) 0.0267185 0.00130373
\(421\) 11.4962 0.560291 0.280146 0.959958i \(-0.409617\pi\)
0.280146 + 0.959958i \(0.409617\pi\)
\(422\) −51.9191 −2.52738
\(423\) −10.7000 −0.520253
\(424\) 12.5964 0.611734
\(425\) −4.99770 −0.242424
\(426\) 4.50606 0.218319
\(427\) −4.94420 −0.239267
\(428\) 18.4935 0.893917
\(429\) 8.45809 0.408361
\(430\) 0.759779 0.0366398
\(431\) −21.2051 −1.02141 −0.510707 0.859755i \(-0.670616\pi\)
−0.510707 + 0.859755i \(0.670616\pi\)
\(432\) 4.88725 0.235138
\(433\) −40.5132 −1.94694 −0.973469 0.228818i \(-0.926514\pi\)
−0.973469 + 0.228818i \(0.926514\pi\)
\(434\) −6.54713 −0.314272
\(435\) 0.0161076 0.000772298 0
\(436\) 24.7885 1.18715
\(437\) 14.8886 0.712220
\(438\) 19.5875 0.935929
\(439\) 9.11896 0.435224 0.217612 0.976035i \(-0.430173\pi\)
0.217612 + 0.976035i \(0.430173\pi\)
\(440\) 0.117568 0.00560482
\(441\) −6.82618 −0.325056
\(442\) 7.64733 0.363746
\(443\) 37.1433 1.76473 0.882366 0.470564i \(-0.155949\pi\)
0.882366 + 0.470564i \(0.155949\pi\)
\(444\) −8.62912 −0.409520
\(445\) −0.0524844 −0.00248800
\(446\) 10.7136 0.507306
\(447\) 8.74514 0.413631
\(448\) 0.874276 0.0413057
\(449\) −17.7362 −0.837021 −0.418511 0.908212i \(-0.637448\pi\)
−0.418511 + 0.908212i \(0.637448\pi\)
\(450\) 9.12786 0.430292
\(451\) −9.41117 −0.443155
\(452\) 11.0848 0.521384
\(453\) −0.743467 −0.0349311
\(454\) −0.736711 −0.0345755
\(455\) 0.0837502 0.00392627
\(456\) 4.30211 0.201465
\(457\) 31.3861 1.46818 0.734090 0.679052i \(-0.237609\pi\)
0.734090 + 0.679052i \(0.237609\pi\)
\(458\) 48.2067 2.25255
\(459\) −1.00000 −0.0466760
\(460\) −0.269052 −0.0125446
\(461\) −7.31929 −0.340894 −0.170447 0.985367i \(-0.554521\pi\)
−0.170447 + 0.985367i \(0.554521\pi\)
\(462\) −1.53821 −0.0715641
\(463\) 28.8899 1.34263 0.671314 0.741173i \(-0.265730\pi\)
0.671314 + 0.741173i \(0.265730\pi\)
\(464\) 1.64087 0.0761754
\(465\) 0.412493 0.0191289
\(466\) 42.4811 1.96790
\(467\) 18.4058 0.851721 0.425860 0.904789i \(-0.359971\pi\)
0.425860 + 0.904789i \(0.359971\pi\)
\(468\) −5.59304 −0.258538
\(469\) 2.77193 0.127996
\(470\) 0.937571 0.0432469
\(471\) 1.00000 0.0460776
\(472\) −10.9587 −0.504415
\(473\) −17.5158 −0.805377
\(474\) 9.91165 0.455257
\(475\) 17.7233 0.813202
\(476\) −0.556919 −0.0255264
\(477\) 10.3834 0.475423
\(478\) 30.4181 1.39129
\(479\) −27.5798 −1.26015 −0.630077 0.776533i \(-0.716977\pi\)
−0.630077 + 0.776533i \(0.716977\pi\)
\(480\) −0.311835 −0.0142333
\(481\) −27.0483 −1.23330
\(482\) −52.1228 −2.37413
\(483\) −1.75039 −0.0796454
\(484\) −9.24286 −0.420130
\(485\) −0.623569 −0.0283148
\(486\) 1.82641 0.0828478
\(487\) 20.2700 0.918521 0.459260 0.888302i \(-0.348114\pi\)
0.459260 + 0.888302i \(0.348114\pi\)
\(488\) 14.3862 0.651235
\(489\) −1.29011 −0.0583407
\(490\) 0.598132 0.0270208
\(491\) 4.36081 0.196800 0.0984002 0.995147i \(-0.468627\pi\)
0.0984002 + 0.995147i \(0.468627\pi\)
\(492\) 6.22328 0.280567
\(493\) −0.335745 −0.0151212
\(494\) −27.1197 −1.22017
\(495\) 0.0969129 0.00435591
\(496\) 42.0205 1.88677
\(497\) −1.02862 −0.0461397
\(498\) −6.18398 −0.277111
\(499\) −15.9772 −0.715236 −0.357618 0.933868i \(-0.616411\pi\)
−0.357618 + 0.933868i \(0.616411\pi\)
\(500\) −0.640704 −0.0286532
\(501\) −1.21096 −0.0541019
\(502\) 37.5094 1.67412
\(503\) 16.0122 0.713951 0.356975 0.934114i \(-0.383808\pi\)
0.356975 + 0.934114i \(0.383808\pi\)
\(504\) −0.505780 −0.0225292
\(505\) −0.512527 −0.0228072
\(506\) 15.4896 0.688597
\(507\) −4.53160 −0.201255
\(508\) 19.4062 0.861011
\(509\) −37.7521 −1.67333 −0.836666 0.547713i \(-0.815498\pi\)
−0.836666 + 0.547713i \(0.815498\pi\)
\(510\) 0.0876232 0.00388002
\(511\) −4.47132 −0.197800
\(512\) −19.9088 −0.879854
\(513\) 3.54630 0.156573
\(514\) −27.3968 −1.20842
\(515\) −0.525665 −0.0231636
\(516\) 11.5826 0.509895
\(517\) −21.6146 −0.950607
\(518\) 4.91907 0.216132
\(519\) −14.6723 −0.644041
\(520\) −0.243690 −0.0106865
\(521\) −29.2891 −1.28318 −0.641589 0.767048i \(-0.721725\pi\)
−0.641589 + 0.767048i \(0.721725\pi\)
\(522\) 0.613209 0.0268394
\(523\) −2.05422 −0.0898246 −0.0449123 0.998991i \(-0.514301\pi\)
−0.0449123 + 0.998991i \(0.514301\pi\)
\(524\) 6.08894 0.265997
\(525\) −2.08365 −0.0909380
\(526\) −18.9262 −0.825223
\(527\) −8.59798 −0.374534
\(528\) 9.87247 0.429644
\(529\) −5.37380 −0.233643
\(530\) −0.909826 −0.0395203
\(531\) −9.03342 −0.392017
\(532\) 1.97500 0.0856272
\(533\) 19.5071 0.844946
\(534\) −1.99806 −0.0864647
\(535\) 0.664205 0.0287161
\(536\) −8.06554 −0.348378
\(537\) 9.47781 0.408997
\(538\) −12.7990 −0.551804
\(539\) −13.7892 −0.593943
\(540\) −0.0640852 −0.00275779
\(541\) −17.7552 −0.763354 −0.381677 0.924296i \(-0.624653\pi\)
−0.381677 + 0.924296i \(0.624653\pi\)
\(542\) −35.6836 −1.53274
\(543\) −22.1067 −0.948691
\(544\) 6.49988 0.278680
\(545\) 0.890293 0.0381360
\(546\) 3.18834 0.136448
\(547\) −20.1108 −0.859877 −0.429938 0.902858i \(-0.641465\pi\)
−0.429938 + 0.902858i \(0.641465\pi\)
\(548\) 6.46611 0.276219
\(549\) 11.8588 0.506122
\(550\) 18.4387 0.786230
\(551\) 1.19065 0.0507235
\(552\) 5.09314 0.216779
\(553\) −2.26257 −0.0962142
\(554\) −9.23316 −0.392280
\(555\) −0.309920 −0.0131554
\(556\) 17.2914 0.733320
\(557\) 35.9402 1.52283 0.761417 0.648262i \(-0.224504\pi\)
0.761417 + 0.648262i \(0.224504\pi\)
\(558\) 15.7035 0.664781
\(559\) 36.3060 1.53558
\(560\) 0.0977551 0.00413091
\(561\) −2.02005 −0.0852865
\(562\) 13.5840 0.573006
\(563\) 41.1183 1.73293 0.866464 0.499239i \(-0.166387\pi\)
0.866464 + 0.499239i \(0.166387\pi\)
\(564\) 14.2930 0.601842
\(565\) 0.398116 0.0167489
\(566\) 7.45800 0.313483
\(567\) −0.416922 −0.0175091
\(568\) 2.99298 0.125583
\(569\) 10.9142 0.457548 0.228774 0.973480i \(-0.426528\pi\)
0.228774 + 0.973480i \(0.426528\pi\)
\(570\) −0.310738 −0.0130154
\(571\) 19.1926 0.803184 0.401592 0.915819i \(-0.368457\pi\)
0.401592 + 0.915819i \(0.368457\pi\)
\(572\) −11.2982 −0.472402
\(573\) 16.8321 0.703173
\(574\) −3.54761 −0.148075
\(575\) 20.9821 0.875015
\(576\) −2.09698 −0.0873740
\(577\) 20.3142 0.845692 0.422846 0.906202i \(-0.361031\pi\)
0.422846 + 0.906202i \(0.361031\pi\)
\(578\) −1.82641 −0.0759688
\(579\) 11.2057 0.465695
\(580\) −0.0215163 −0.000893414 0
\(581\) 1.41164 0.0585647
\(582\) −23.7391 −0.984016
\(583\) 20.9749 0.868693
\(584\) 13.0103 0.538370
\(585\) −0.200877 −0.00830526
\(586\) −62.2920 −2.57326
\(587\) −24.8794 −1.02688 −0.513441 0.858125i \(-0.671630\pi\)
−0.513441 + 0.858125i \(0.671630\pi\)
\(588\) 9.11832 0.376033
\(589\) 30.4910 1.25636
\(590\) 0.791538 0.0325871
\(591\) 20.4516 0.841268
\(592\) −31.5714 −1.29758
\(593\) −15.6683 −0.643418 −0.321709 0.946839i \(-0.604257\pi\)
−0.321709 + 0.946839i \(0.604257\pi\)
\(594\) 3.68944 0.151380
\(595\) −0.0200021 −0.000820006 0
\(596\) −11.6816 −0.478499
\(597\) 10.1594 0.415795
\(598\) −32.1062 −1.31292
\(599\) −7.84620 −0.320587 −0.160293 0.987069i \(-0.551244\pi\)
−0.160293 + 0.987069i \(0.551244\pi\)
\(600\) 6.06284 0.247515
\(601\) 14.4851 0.590860 0.295430 0.955364i \(-0.404537\pi\)
0.295430 + 0.955364i \(0.404537\pi\)
\(602\) −6.60271 −0.269106
\(603\) −6.64855 −0.270750
\(604\) 0.993114 0.0404092
\(605\) −0.331963 −0.0134962
\(606\) −19.5117 −0.792610
\(607\) 7.05011 0.286155 0.143078 0.989711i \(-0.454300\pi\)
0.143078 + 0.989711i \(0.454300\pi\)
\(608\) −23.0505 −0.934822
\(609\) −0.139980 −0.00567226
\(610\) −1.03911 −0.0420722
\(611\) 44.8018 1.81249
\(612\) 1.33579 0.0539960
\(613\) 9.27112 0.374457 0.187229 0.982316i \(-0.440049\pi\)
0.187229 + 0.982316i \(0.440049\pi\)
\(614\) 41.7931 1.68663
\(615\) 0.223513 0.00901290
\(616\) −1.02170 −0.0411654
\(617\) 11.9586 0.481433 0.240717 0.970595i \(-0.422618\pi\)
0.240717 + 0.970595i \(0.422618\pi\)
\(618\) −20.0119 −0.804997
\(619\) −33.5510 −1.34853 −0.674264 0.738491i \(-0.735539\pi\)
−0.674264 + 0.738491i \(0.735539\pi\)
\(620\) −0.551003 −0.0221288
\(621\) 4.19836 0.168474
\(622\) 25.5906 1.02609
\(623\) 0.456106 0.0182735
\(624\) −20.4633 −0.819186
\(625\) 24.9655 0.998619
\(626\) 20.9231 0.836256
\(627\) 7.16369 0.286090
\(628\) −1.33579 −0.0533037
\(629\) 6.45995 0.257575
\(630\) 0.0365321 0.00145547
\(631\) 2.60155 0.103566 0.0517831 0.998658i \(-0.483510\pi\)
0.0517831 + 0.998658i \(0.483510\pi\)
\(632\) 6.58344 0.261875
\(633\) −28.4268 −1.12986
\(634\) 27.8150 1.10467
\(635\) 0.696985 0.0276590
\(636\) −13.8700 −0.549981
\(637\) 28.5817 1.13245
\(638\) 1.23871 0.0490411
\(639\) 2.46716 0.0975995
\(640\) −0.439927 −0.0173896
\(641\) 23.1525 0.914468 0.457234 0.889346i \(-0.348840\pi\)
0.457234 + 0.889346i \(0.348840\pi\)
\(642\) 25.2861 0.997961
\(643\) −22.1570 −0.873786 −0.436893 0.899514i \(-0.643921\pi\)
−0.436893 + 0.899514i \(0.643921\pi\)
\(644\) 2.33815 0.0921359
\(645\) 0.415995 0.0163798
\(646\) 6.47701 0.254835
\(647\) −12.8584 −0.505516 −0.252758 0.967530i \(-0.581338\pi\)
−0.252758 + 0.967530i \(0.581338\pi\)
\(648\) 1.21313 0.0476561
\(649\) −18.2479 −0.716294
\(650\) −38.2191 −1.49907
\(651\) −3.58469 −0.140495
\(652\) 1.72331 0.0674900
\(653\) 14.6787 0.574421 0.287211 0.957867i \(-0.407272\pi\)
0.287211 + 0.957867i \(0.407272\pi\)
\(654\) 33.8932 1.32533
\(655\) 0.218688 0.00854484
\(656\) 22.7691 0.888985
\(657\) 10.7246 0.418406
\(658\) −8.14777 −0.317633
\(659\) 6.97850 0.271844 0.135922 0.990720i \(-0.456600\pi\)
0.135922 + 0.990720i \(0.456600\pi\)
\(660\) −0.129455 −0.00503903
\(661\) 26.4295 1.02799 0.513994 0.857794i \(-0.328165\pi\)
0.513994 + 0.857794i \(0.328165\pi\)
\(662\) 21.9125 0.851654
\(663\) 4.18708 0.162613
\(664\) −4.10748 −0.159401
\(665\) 0.0709334 0.00275068
\(666\) −11.7985 −0.457184
\(667\) 1.40958 0.0545790
\(668\) 1.61759 0.0625865
\(669\) 5.86594 0.226790
\(670\) 0.582568 0.0225066
\(671\) 23.9554 0.924786
\(672\) 2.70995 0.104538
\(673\) 2.32359 0.0895678 0.0447839 0.998997i \(-0.485740\pi\)
0.0447839 + 0.998997i \(0.485740\pi\)
\(674\) −45.1909 −1.74069
\(675\) 4.99770 0.192361
\(676\) 6.05325 0.232817
\(677\) −26.4166 −1.01527 −0.507636 0.861572i \(-0.669480\pi\)
−0.507636 + 0.861572i \(0.669480\pi\)
\(678\) 15.1562 0.582069
\(679\) 5.41900 0.207962
\(680\) 0.0582005 0.00223189
\(681\) −0.403365 −0.0154570
\(682\) 31.7218 1.21469
\(683\) 31.1416 1.19160 0.595801 0.803132i \(-0.296835\pi\)
0.595801 + 0.803132i \(0.296835\pi\)
\(684\) −4.73710 −0.181128
\(685\) 0.232234 0.00887321
\(686\) −10.5283 −0.401971
\(687\) 26.3942 1.00700
\(688\) 42.3772 1.61562
\(689\) −43.4760 −1.65631
\(690\) −0.367874 −0.0140047
\(691\) 37.4409 1.42432 0.712160 0.702017i \(-0.247717\pi\)
0.712160 + 0.702017i \(0.247717\pi\)
\(692\) 19.5990 0.745043
\(693\) −0.842203 −0.0319926
\(694\) 6.58377 0.249916
\(695\) 0.621032 0.0235571
\(696\) 0.407301 0.0154387
\(697\) −4.65889 −0.176468
\(698\) 42.5195 1.60939
\(699\) 23.2593 0.879748
\(700\) 2.78332 0.105199
\(701\) −7.06251 −0.266747 −0.133374 0.991066i \(-0.542581\pi\)
−0.133374 + 0.991066i \(0.542581\pi\)
\(702\) −7.64733 −0.288630
\(703\) −22.9089 −0.864026
\(704\) −4.23599 −0.159650
\(705\) 0.513340 0.0193335
\(706\) −35.0665 −1.31974
\(707\) 4.45402 0.167511
\(708\) 12.0667 0.453495
\(709\) 29.2730 1.09937 0.549686 0.835372i \(-0.314747\pi\)
0.549686 + 0.835372i \(0.314747\pi\)
\(710\) −0.216181 −0.00811312
\(711\) 5.42684 0.203522
\(712\) −1.32714 −0.0497367
\(713\) 36.0974 1.35186
\(714\) −0.761473 −0.0284974
\(715\) −0.405782 −0.0151754
\(716\) −12.6603 −0.473139
\(717\) 16.6546 0.621976
\(718\) −46.3904 −1.73127
\(719\) 29.7963 1.11121 0.555606 0.831445i \(-0.312486\pi\)
0.555606 + 0.831445i \(0.312486\pi\)
\(720\) −0.234468 −0.00873812
\(721\) 4.56819 0.170128
\(722\) 11.7324 0.436636
\(723\) −28.5383 −1.06135
\(724\) 29.5299 1.09747
\(725\) 1.67795 0.0623176
\(726\) −12.6377 −0.469029
\(727\) 15.2817 0.566766 0.283383 0.959007i \(-0.408543\pi\)
0.283383 + 0.959007i \(0.408543\pi\)
\(728\) 2.11774 0.0784886
\(729\) 1.00000 0.0370370
\(730\) −0.939723 −0.0347807
\(731\) −8.67098 −0.320708
\(732\) −15.8408 −0.585495
\(733\) 44.9771 1.66127 0.830634 0.556819i \(-0.187978\pi\)
0.830634 + 0.556819i \(0.187978\pi\)
\(734\) 1.98290 0.0731901
\(735\) 0.327490 0.0120796
\(736\) −27.2888 −1.00588
\(737\) −13.4304 −0.494715
\(738\) 8.50905 0.313223
\(739\) −43.5685 −1.60269 −0.801347 0.598200i \(-0.795883\pi\)
−0.801347 + 0.598200i \(0.795883\pi\)
\(740\) 0.413987 0.0152185
\(741\) −14.8486 −0.545478
\(742\) 7.90667 0.290263
\(743\) −38.9216 −1.42789 −0.713947 0.700200i \(-0.753094\pi\)
−0.713947 + 0.700200i \(0.753094\pi\)
\(744\) 10.4304 0.382399
\(745\) −0.419553 −0.0153712
\(746\) −41.8619 −1.53267
\(747\) −3.38586 −0.123882
\(748\) 2.69835 0.0986616
\(749\) −5.77214 −0.210909
\(750\) −0.876031 −0.0319881
\(751\) 33.4902 1.22208 0.611038 0.791601i \(-0.290752\pi\)
0.611038 + 0.791601i \(0.290752\pi\)
\(752\) 52.2936 1.90695
\(753\) 20.5372 0.748416
\(754\) −2.56755 −0.0935048
\(755\) 0.0356682 0.00129810
\(756\) 0.556919 0.0202550
\(757\) −41.9871 −1.52605 −0.763023 0.646371i \(-0.776286\pi\)
−0.763023 + 0.646371i \(0.776286\pi\)
\(758\) −60.5165 −2.19806
\(759\) 8.48088 0.307836
\(760\) −0.206396 −0.00748678
\(761\) 10.9918 0.398451 0.199226 0.979954i \(-0.436157\pi\)
0.199226 + 0.979954i \(0.436157\pi\)
\(762\) 26.5340 0.961225
\(763\) −7.73692 −0.280095
\(764\) −22.4842 −0.813448
\(765\) 0.0479756 0.00173456
\(766\) −48.8383 −1.76460
\(767\) 37.8236 1.36573
\(768\) −20.9418 −0.755673
\(769\) 43.2895 1.56106 0.780530 0.625118i \(-0.214949\pi\)
0.780530 + 0.625118i \(0.214949\pi\)
\(770\) 0.0737965 0.00265944
\(771\) −15.0003 −0.540224
\(772\) −14.9685 −0.538727
\(773\) −35.5396 −1.27827 −0.639136 0.769094i \(-0.720708\pi\)
−0.639136 + 0.769094i \(0.720708\pi\)
\(774\) 15.8368 0.569242
\(775\) 42.9701 1.54353
\(776\) −15.7678 −0.566031
\(777\) 2.69330 0.0966215
\(778\) −60.6902 −2.17585
\(779\) 16.5218 0.591955
\(780\) 0.268329 0.00960773
\(781\) 4.98379 0.178334
\(782\) 7.66794 0.274205
\(783\) 0.335745 0.0119985
\(784\) 33.3612 1.19147
\(785\) −0.0479756 −0.00171232
\(786\) 8.32537 0.296956
\(787\) 47.3781 1.68885 0.844424 0.535675i \(-0.179943\pi\)
0.844424 + 0.535675i \(0.179943\pi\)
\(788\) −27.3191 −0.973201
\(789\) −10.3625 −0.368915
\(790\) −0.475517 −0.0169181
\(791\) −3.45975 −0.123015
\(792\) 2.45058 0.0870774
\(793\) −49.6537 −1.76326
\(794\) 17.0068 0.603548
\(795\) −0.498149 −0.0176675
\(796\) −13.5707 −0.481002
\(797\) −3.91050 −0.138517 −0.0692585 0.997599i \(-0.522063\pi\)
−0.0692585 + 0.997599i \(0.522063\pi\)
\(798\) 2.70041 0.0955935
\(799\) −10.7000 −0.378540
\(800\) −32.4844 −1.14850
\(801\) −1.09398 −0.0386540
\(802\) 22.7626 0.803774
\(803\) 21.6642 0.764512
\(804\) 8.88105 0.313210
\(805\) 0.0839759 0.00295976
\(806\) −65.7516 −2.31600
\(807\) −7.00773 −0.246684
\(808\) −12.9599 −0.455929
\(809\) 7.66232 0.269393 0.134696 0.990887i \(-0.456994\pi\)
0.134696 + 0.990887i \(0.456994\pi\)
\(810\) −0.0876232 −0.00307877
\(811\) −42.4011 −1.48890 −0.744452 0.667676i \(-0.767289\pi\)
−0.744452 + 0.667676i \(0.767289\pi\)
\(812\) 0.186983 0.00656181
\(813\) −19.5375 −0.685210
\(814\) −23.8336 −0.835368
\(815\) 0.0618936 0.00216804
\(816\) 4.88725 0.171088
\(817\) 30.7499 1.07580
\(818\) 65.5998 2.29364
\(819\) 1.74569 0.0609992
\(820\) −0.298565 −0.0104264
\(821\) −5.84868 −0.204120 −0.102060 0.994778i \(-0.532543\pi\)
−0.102060 + 0.994778i \(0.532543\pi\)
\(822\) 8.84108 0.308368
\(823\) 40.2911 1.40446 0.702230 0.711950i \(-0.252188\pi\)
0.702230 + 0.711950i \(0.252188\pi\)
\(824\) −13.2922 −0.463054
\(825\) 10.0956 0.351483
\(826\) −6.87870 −0.239341
\(827\) −10.1546 −0.353111 −0.176556 0.984291i \(-0.556496\pi\)
−0.176556 + 0.984291i \(0.556496\pi\)
\(828\) −5.60811 −0.194895
\(829\) 24.4609 0.849563 0.424782 0.905296i \(-0.360351\pi\)
0.424782 + 0.905296i \(0.360351\pi\)
\(830\) 0.296680 0.0102979
\(831\) −5.05535 −0.175368
\(832\) 8.78020 0.304399
\(833\) −6.82618 −0.236513
\(834\) 23.6425 0.818671
\(835\) 0.0580967 0.00201052
\(836\) −9.56917 −0.330957
\(837\) 8.59798 0.297190
\(838\) 40.1834 1.38811
\(839\) −24.8467 −0.857803 −0.428902 0.903351i \(-0.641099\pi\)
−0.428902 + 0.903351i \(0.641099\pi\)
\(840\) 0.0242651 0.000837225 0
\(841\) −28.8873 −0.996113
\(842\) −20.9968 −0.723599
\(843\) 7.43753 0.256162
\(844\) 37.9722 1.30706
\(845\) 0.217406 0.00747900
\(846\) 19.5427 0.671891
\(847\) 2.88486 0.0991248
\(848\) −50.7462 −1.74263
\(849\) 4.08341 0.140142
\(850\) 9.12786 0.313083
\(851\) −27.1212 −0.929702
\(852\) −3.29561 −0.112906
\(853\) −25.8759 −0.885974 −0.442987 0.896528i \(-0.646081\pi\)
−0.442987 + 0.896528i \(0.646081\pi\)
\(854\) 9.03016 0.309006
\(855\) −0.170136 −0.00581852
\(856\) 16.7953 0.574052
\(857\) 17.5004 0.597801 0.298900 0.954284i \(-0.403380\pi\)
0.298900 + 0.954284i \(0.403380\pi\)
\(858\) −15.4480 −0.527385
\(859\) 14.8968 0.508271 0.254136 0.967169i \(-0.418209\pi\)
0.254136 + 0.967169i \(0.418209\pi\)
\(860\) −0.555681 −0.0189486
\(861\) −1.94239 −0.0661966
\(862\) 38.7293 1.31912
\(863\) −1.96213 −0.0667917 −0.0333959 0.999442i \(-0.510632\pi\)
−0.0333959 + 0.999442i \(0.510632\pi\)
\(864\) −6.49988 −0.221130
\(865\) 0.703910 0.0239337
\(866\) 73.9938 2.51441
\(867\) −1.00000 −0.0339618
\(868\) 4.78838 0.162528
\(869\) 10.9625 0.371876
\(870\) −0.0294191 −0.000997400 0
\(871\) 27.8380 0.943254
\(872\) 22.5123 0.762362
\(873\) −12.9976 −0.439903
\(874\) −27.1928 −0.919810
\(875\) 0.199975 0.00676038
\(876\) −14.3258 −0.484023
\(877\) −4.59256 −0.155080 −0.0775399 0.996989i \(-0.524707\pi\)
−0.0775399 + 0.996989i \(0.524707\pi\)
\(878\) −16.6550 −0.562079
\(879\) −34.1062 −1.15037
\(880\) −0.473637 −0.0159663
\(881\) 38.9793 1.31325 0.656623 0.754219i \(-0.271984\pi\)
0.656623 + 0.754219i \(0.271984\pi\)
\(882\) 12.4674 0.419800
\(883\) 29.7894 1.00249 0.501246 0.865305i \(-0.332875\pi\)
0.501246 + 0.865305i \(0.332875\pi\)
\(884\) −5.59304 −0.188114
\(885\) 0.433384 0.0145680
\(886\) −67.8391 −2.27910
\(887\) 9.61151 0.322723 0.161361 0.986895i \(-0.448412\pi\)
0.161361 + 0.986895i \(0.448412\pi\)
\(888\) −7.83674 −0.262984
\(889\) −6.05701 −0.203146
\(890\) 0.0958583 0.00321318
\(891\) 2.02005 0.0676741
\(892\) −7.83565 −0.262357
\(893\) 37.9455 1.26980
\(894\) −15.9722 −0.534192
\(895\) −0.454703 −0.0151990
\(896\) 3.82310 0.127721
\(897\) −17.5788 −0.586940
\(898\) 32.3936 1.08099
\(899\) 2.88673 0.0962778
\(900\) −6.67586 −0.222529
\(901\) 10.3834 0.345921
\(902\) 17.1887 0.572321
\(903\) −3.61512 −0.120304
\(904\) 10.0669 0.334821
\(905\) 1.06058 0.0352550
\(906\) 1.35788 0.0451125
\(907\) 10.0338 0.333167 0.166584 0.986027i \(-0.446726\pi\)
0.166584 + 0.986027i \(0.446726\pi\)
\(908\) 0.538809 0.0178810
\(909\) −10.6831 −0.354336
\(910\) −0.152963 −0.00507066
\(911\) −3.49954 −0.115945 −0.0579724 0.998318i \(-0.518464\pi\)
−0.0579724 + 0.998318i \(0.518464\pi\)
\(912\) −17.3316 −0.573908
\(913\) −6.83959 −0.226358
\(914\) −57.3240 −1.89611
\(915\) −0.568933 −0.0188084
\(916\) −35.2570 −1.16492
\(917\) −1.90046 −0.0627588
\(918\) 1.82641 0.0602806
\(919\) 47.7480 1.57506 0.787530 0.616276i \(-0.211359\pi\)
0.787530 + 0.616276i \(0.211359\pi\)
\(920\) −0.244346 −0.00805586
\(921\) 22.8826 0.754008
\(922\) 13.3681 0.440254
\(923\) −10.3302 −0.340023
\(924\) 1.12500 0.0370099
\(925\) −32.2849 −1.06152
\(926\) −52.7649 −1.73396
\(927\) −10.9569 −0.359873
\(928\) −2.18230 −0.0716376
\(929\) 11.0666 0.363082 0.181541 0.983383i \(-0.441891\pi\)
0.181541 + 0.983383i \(0.441891\pi\)
\(930\) −0.753383 −0.0247044
\(931\) 24.2077 0.793374
\(932\) −31.0695 −1.01772
\(933\) 14.0114 0.458712
\(934\) −33.6167 −1.09997
\(935\) 0.0969129 0.00316939
\(936\) −5.07946 −0.166027
\(937\) 52.1126 1.70244 0.851222 0.524806i \(-0.175862\pi\)
0.851222 + 0.524806i \(0.175862\pi\)
\(938\) −5.06269 −0.165303
\(939\) 11.4559 0.373848
\(940\) −0.685713 −0.0223655
\(941\) 14.3980 0.469361 0.234680 0.972073i \(-0.424596\pi\)
0.234680 + 0.972073i \(0.424596\pi\)
\(942\) −1.82641 −0.0595078
\(943\) 19.5597 0.636950
\(944\) 44.1486 1.43691
\(945\) 0.0200021 0.000650668 0
\(946\) 31.9911 1.04012
\(947\) 40.6237 1.32009 0.660047 0.751225i \(-0.270536\pi\)
0.660047 + 0.751225i \(0.270536\pi\)
\(948\) −7.24910 −0.235440
\(949\) −44.9047 −1.45767
\(950\) −32.3701 −1.05023
\(951\) 15.2293 0.493844
\(952\) −0.505780 −0.0163924
\(953\) −55.2538 −1.78985 −0.894923 0.446220i \(-0.852770\pi\)
−0.894923 + 0.446220i \(0.852770\pi\)
\(954\) −18.9644 −0.613994
\(955\) −0.807532 −0.0261311
\(956\) −22.2469 −0.719517
\(957\) 0.678221 0.0219238
\(958\) 50.3722 1.62745
\(959\) −2.01819 −0.0651706
\(960\) 0.100604 0.00324697
\(961\) 42.9253 1.38469
\(962\) 49.4014 1.59276
\(963\) 13.8446 0.446137
\(964\) 38.1211 1.22780
\(965\) −0.537602 −0.0173060
\(966\) 3.19693 0.102860
\(967\) −7.52986 −0.242144 −0.121072 0.992644i \(-0.538633\pi\)
−0.121072 + 0.992644i \(0.538633\pi\)
\(968\) −8.39412 −0.269797
\(969\) 3.54630 0.113924
\(970\) 1.13889 0.0365677
\(971\) −52.0194 −1.66938 −0.834692 0.550718i \(-0.814354\pi\)
−0.834692 + 0.550718i \(0.814354\pi\)
\(972\) −1.33579 −0.0428454
\(973\) −5.39695 −0.173018
\(974\) −37.0214 −1.18624
\(975\) −20.9257 −0.670160
\(976\) −57.9569 −1.85516
\(977\) 47.5767 1.52211 0.761057 0.648685i \(-0.224681\pi\)
0.761057 + 0.648685i \(0.224681\pi\)
\(978\) 2.35627 0.0753452
\(979\) −2.20990 −0.0706286
\(980\) −0.437457 −0.0139740
\(981\) 18.5572 0.592486
\(982\) −7.96464 −0.254162
\(983\) 24.7261 0.788639 0.394320 0.918973i \(-0.370980\pi\)
0.394320 + 0.918973i \(0.370980\pi\)
\(984\) 5.65182 0.180173
\(985\) −0.981180 −0.0312630
\(986\) 0.613209 0.0195286
\(987\) −4.46108 −0.141998
\(988\) 19.8346 0.631023
\(989\) 36.4039 1.15758
\(990\) −0.177003 −0.00562553
\(991\) −52.5370 −1.66889 −0.834446 0.551090i \(-0.814212\pi\)
−0.834446 + 0.551090i \(0.814212\pi\)
\(992\) −55.8859 −1.77438
\(993\) 11.9976 0.380731
\(994\) 1.87868 0.0595880
\(995\) −0.487401 −0.0154517
\(996\) 4.52279 0.143310
\(997\) 6.09253 0.192952 0.0964761 0.995335i \(-0.469243\pi\)
0.0964761 + 0.995335i \(0.469243\pi\)
\(998\) 29.1809 0.923705
\(999\) −6.45995 −0.204384
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 \(a_p\))