Properties

Label 8015.2.a.l.1.16
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.46418 q^{2}\) \(-1.88953 q^{3}\) \(+0.143813 q^{4}\) \(-1.00000 q^{5}\) \(+2.76661 q^{6}\) \(-1.00000 q^{7}\) \(+2.71779 q^{8}\) \(+0.570340 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.46418 q^{2}\) \(-1.88953 q^{3}\) \(+0.143813 q^{4}\) \(-1.00000 q^{5}\) \(+2.76661 q^{6}\) \(-1.00000 q^{7}\) \(+2.71779 q^{8}\) \(+0.570340 q^{9}\) \(+1.46418 q^{10}\) \(-0.769647 q^{11}\) \(-0.271739 q^{12}\) \(+1.91852 q^{13}\) \(+1.46418 q^{14}\) \(+1.88953 q^{15}\) \(-4.26694 q^{16}\) \(+2.52935 q^{17}\) \(-0.835078 q^{18}\) \(+3.94494 q^{19}\) \(-0.143813 q^{20}\) \(+1.88953 q^{21}\) \(+1.12690 q^{22}\) \(-6.34157 q^{23}\) \(-5.13535 q^{24}\) \(+1.00000 q^{25}\) \(-2.80906 q^{26}\) \(+4.59093 q^{27}\) \(-0.143813 q^{28}\) \(+0.0132311 q^{29}\) \(-2.76661 q^{30}\) \(-1.12165 q^{31}\) \(+0.811986 q^{32}\) \(+1.45427 q^{33}\) \(-3.70342 q^{34}\) \(+1.00000 q^{35}\) \(+0.0820221 q^{36}\) \(+0.322083 q^{37}\) \(-5.77609 q^{38}\) \(-3.62511 q^{39}\) \(-2.71779 q^{40}\) \(+1.44715 q^{41}\) \(-2.76661 q^{42}\) \(+11.2694 q^{43}\) \(-0.110685 q^{44}\) \(-0.570340 q^{45}\) \(+9.28517 q^{46}\) \(-10.0385 q^{47}\) \(+8.06254 q^{48}\) \(+1.00000 q^{49}\) \(-1.46418 q^{50}\) \(-4.77929 q^{51}\) \(+0.275908 q^{52}\) \(+11.5769 q^{53}\) \(-6.72193 q^{54}\) \(+0.769647 q^{55}\) \(-2.71779 q^{56}\) \(-7.45410 q^{57}\) \(-0.0193727 q^{58}\) \(+8.40858 q^{59}\) \(+0.271739 q^{60}\) \(+10.5914 q^{61}\) \(+1.64229 q^{62}\) \(-0.570340 q^{63}\) \(+7.34500 q^{64}\) \(-1.91852 q^{65}\) \(-2.12931 q^{66}\) \(+9.82891 q^{67}\) \(+0.363753 q^{68}\) \(+11.9826 q^{69}\) \(-1.46418 q^{70}\) \(+11.9043 q^{71}\) \(+1.55006 q^{72}\) \(-7.51649 q^{73}\) \(-0.471586 q^{74}\) \(-1.88953 q^{75}\) \(+0.567333 q^{76}\) \(+0.769647 q^{77}\) \(+5.30781 q^{78}\) \(-13.3557 q^{79}\) \(+4.26694 q^{80}\) \(-10.3857 q^{81}\) \(-2.11888 q^{82}\) \(-4.86670 q^{83}\) \(+0.271739 q^{84}\) \(-2.52935 q^{85}\) \(-16.5004 q^{86}\) \(-0.0250006 q^{87}\) \(-2.09174 q^{88}\) \(+3.44228 q^{89}\) \(+0.835078 q^{90}\) \(-1.91852 q^{91}\) \(-0.911998 q^{92}\) \(+2.11939 q^{93}\) \(+14.6982 q^{94}\) \(-3.94494 q^{95}\) \(-1.53428 q^{96}\) \(-11.6821 q^{97}\) \(-1.46418 q^{98}\) \(-0.438960 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(62q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut -\mathstrut 62q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 62q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(62q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut -\mathstrut 62q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 62q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 13q^{11} \) \(\mathstrut +\mathstrut 37q^{12} \) \(\mathstrut +\mathstrut 31q^{13} \) \(\mathstrut -\mathstrut 2q^{14} \) \(\mathstrut -\mathstrut 11q^{15} \) \(\mathstrut +\mathstrut 64q^{16} \) \(\mathstrut +\mathstrut 30q^{17} \) \(\mathstrut +\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut 64q^{20} \) \(\mathstrut -\mathstrut 11q^{21} \) \(\mathstrut +\mathstrut 7q^{22} \) \(\mathstrut +\mathstrut 29q^{24} \) \(\mathstrut +\mathstrut 62q^{25} \) \(\mathstrut +\mathstrut 59q^{27} \) \(\mathstrut -\mathstrut 64q^{28} \) \(\mathstrut -\mathstrut 29q^{29} \) \(\mathstrut -\mathstrut 3q^{30} \) \(\mathstrut +\mathstrut 20q^{31} \) \(\mathstrut +\mathstrut 22q^{32} \) \(\mathstrut +\mathstrut 72q^{33} \) \(\mathstrut +\mathstrut 13q^{34} \) \(\mathstrut +\mathstrut 62q^{35} \) \(\mathstrut +\mathstrut 53q^{36} \) \(\mathstrut +\mathstrut 35q^{37} \) \(\mathstrut +\mathstrut 34q^{38} \) \(\mathstrut -\mathstrut 6q^{39} \) \(\mathstrut -\mathstrut 15q^{40} \) \(\mathstrut +\mathstrut 13q^{41} \) \(\mathstrut -\mathstrut 3q^{42} \) \(\mathstrut -\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 44q^{44} \) \(\mathstrut -\mathstrut 69q^{45} \) \(\mathstrut -\mathstrut 19q^{46} \) \(\mathstrut +\mathstrut 58q^{47} \) \(\mathstrut +\mathstrut 64q^{48} \) \(\mathstrut +\mathstrut 62q^{49} \) \(\mathstrut +\mathstrut 2q^{50} \) \(\mathstrut -\mathstrut 30q^{51} \) \(\mathstrut +\mathstrut 82q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 22q^{54} \) \(\mathstrut +\mathstrut 13q^{55} \) \(\mathstrut -\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 21q^{57} \) \(\mathstrut +\mathstrut 18q^{58} \) \(\mathstrut -\mathstrut 11q^{59} \) \(\mathstrut -\mathstrut 37q^{60} \) \(\mathstrut +\mathstrut 24q^{61} \) \(\mathstrut +\mathstrut 48q^{62} \) \(\mathstrut -\mathstrut 69q^{63} \) \(\mathstrut +\mathstrut 65q^{64} \) \(\mathstrut -\mathstrut 31q^{65} \) \(\mathstrut +\mathstrut 25q^{66} \) \(\mathstrut -\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 65q^{68} \) \(\mathstrut +\mathstrut 27q^{69} \) \(\mathstrut +\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 35q^{71} \) \(\mathstrut +\mathstrut 53q^{72} \) \(\mathstrut +\mathstrut 116q^{73} \) \(\mathstrut -\mathstrut 69q^{74} \) \(\mathstrut +\mathstrut 11q^{75} \) \(\mathstrut +\mathstrut 65q^{76} \) \(\mathstrut +\mathstrut 13q^{77} \) \(\mathstrut +\mathstrut 102q^{78} \) \(\mathstrut -\mathstrut 83q^{79} \) \(\mathstrut -\mathstrut 64q^{80} \) \(\mathstrut +\mathstrut 126q^{81} \) \(\mathstrut +\mathstrut 71q^{82} \) \(\mathstrut +\mathstrut 84q^{83} \) \(\mathstrut -\mathstrut 37q^{84} \) \(\mathstrut -\mathstrut 30q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 49q^{87} \) \(\mathstrut +\mathstrut 20q^{88} \) \(\mathstrut -\mathstrut 16q^{89} \) \(\mathstrut -\mathstrut 18q^{90} \) \(\mathstrut -\mathstrut 31q^{91} \) \(\mathstrut +\mathstrut 19q^{92} \) \(\mathstrut +\mathstrut 65q^{93} \) \(\mathstrut +\mathstrut 54q^{94} \) \(\mathstrut -\mathstrut 20q^{95} \) \(\mathstrut +\mathstrut 17q^{96} \) \(\mathstrut +\mathstrut 155q^{97} \) \(\mathstrut +\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut 6q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.46418 −1.03533 −0.517665 0.855584i \(-0.673198\pi\)
−0.517665 + 0.855584i \(0.673198\pi\)
\(3\) −1.88953 −1.09092 −0.545462 0.838136i \(-0.683646\pi\)
−0.545462 + 0.838136i \(0.683646\pi\)
\(4\) 0.143813 0.0719064
\(5\) −1.00000 −0.447214
\(6\) 2.76661 1.12946
\(7\) −1.00000 −0.377964
\(8\) 2.71779 0.960882
\(9\) 0.570340 0.190113
\(10\) 1.46418 0.463013
\(11\) −0.769647 −0.232057 −0.116029 0.993246i \(-0.537016\pi\)
−0.116029 + 0.993246i \(0.537016\pi\)
\(12\) −0.271739 −0.0784443
\(13\) 1.91852 0.532102 0.266051 0.963959i \(-0.414281\pi\)
0.266051 + 0.963959i \(0.414281\pi\)
\(14\) 1.46418 0.391318
\(15\) 1.88953 0.487876
\(16\) −4.26694 −1.06674
\(17\) 2.52935 0.613458 0.306729 0.951797i \(-0.400766\pi\)
0.306729 + 0.951797i \(0.400766\pi\)
\(18\) −0.835078 −0.196830
\(19\) 3.94494 0.905032 0.452516 0.891756i \(-0.350527\pi\)
0.452516 + 0.891756i \(0.350527\pi\)
\(20\) −0.143813 −0.0321575
\(21\) 1.88953 0.412330
\(22\) 1.12690 0.240256
\(23\) −6.34157 −1.32231 −0.661154 0.750250i \(-0.729933\pi\)
−0.661154 + 0.750250i \(0.729933\pi\)
\(24\) −5.13535 −1.04825
\(25\) 1.00000 0.200000
\(26\) −2.80906 −0.550901
\(27\) 4.59093 0.883524
\(28\) −0.143813 −0.0271780
\(29\) 0.0132311 0.00245696 0.00122848 0.999999i \(-0.499609\pi\)
0.00122848 + 0.999999i \(0.499609\pi\)
\(30\) −2.76661 −0.505112
\(31\) −1.12165 −0.201454 −0.100727 0.994914i \(-0.532117\pi\)
−0.100727 + 0.994914i \(0.532117\pi\)
\(32\) 0.811986 0.143540
\(33\) 1.45427 0.253157
\(34\) −3.70342 −0.635130
\(35\) 1.00000 0.169031
\(36\) 0.0820221 0.0136704
\(37\) 0.322083 0.0529501 0.0264751 0.999649i \(-0.491572\pi\)
0.0264751 + 0.999649i \(0.491572\pi\)
\(38\) −5.77609 −0.937006
\(39\) −3.62511 −0.580483
\(40\) −2.71779 −0.429720
\(41\) 1.44715 0.226007 0.113003 0.993595i \(-0.463953\pi\)
0.113003 + 0.993595i \(0.463953\pi\)
\(42\) −2.76661 −0.426897
\(43\) 11.2694 1.71857 0.859286 0.511496i \(-0.170908\pi\)
0.859286 + 0.511496i \(0.170908\pi\)
\(44\) −0.110685 −0.0166864
\(45\) −0.570340 −0.0850212
\(46\) 9.28517 1.36902
\(47\) −10.0385 −1.46427 −0.732135 0.681159i \(-0.761476\pi\)
−0.732135 + 0.681159i \(0.761476\pi\)
\(48\) 8.06254 1.16373
\(49\) 1.00000 0.142857
\(50\) −1.46418 −0.207066
\(51\) −4.77929 −0.669235
\(52\) 0.275908 0.0382615
\(53\) 11.5769 1.59020 0.795101 0.606477i \(-0.207418\pi\)
0.795101 + 0.606477i \(0.207418\pi\)
\(54\) −6.72193 −0.914738
\(55\) 0.769647 0.103779
\(56\) −2.71779 −0.363179
\(57\) −7.45410 −0.987320
\(58\) −0.0193727 −0.00254376
\(59\) 8.40858 1.09470 0.547352 0.836902i \(-0.315636\pi\)
0.547352 + 0.836902i \(0.315636\pi\)
\(60\) 0.271739 0.0350814
\(61\) 10.5914 1.35609 0.678046 0.735019i \(-0.262827\pi\)
0.678046 + 0.735019i \(0.262827\pi\)
\(62\) 1.64229 0.208571
\(63\) −0.570340 −0.0718561
\(64\) 7.34500 0.918124
\(65\) −1.91852 −0.237963
\(66\) −2.12931 −0.262101
\(67\) 9.82891 1.20079 0.600396 0.799703i \(-0.295010\pi\)
0.600396 + 0.799703i \(0.295010\pi\)
\(68\) 0.363753 0.0441115
\(69\) 11.9826 1.44254
\(70\) −1.46418 −0.175003
\(71\) 11.9043 1.41278 0.706389 0.707823i \(-0.250323\pi\)
0.706389 + 0.707823i \(0.250323\pi\)
\(72\) 1.55006 0.182677
\(73\) −7.51649 −0.879738 −0.439869 0.898062i \(-0.644975\pi\)
−0.439869 + 0.898062i \(0.644975\pi\)
\(74\) −0.471586 −0.0548208
\(75\) −1.88953 −0.218185
\(76\) 0.567333 0.0650775
\(77\) 0.769647 0.0877094
\(78\) 5.30781 0.600991
\(79\) −13.3557 −1.50263 −0.751317 0.659941i \(-0.770581\pi\)
−0.751317 + 0.659941i \(0.770581\pi\)
\(80\) 4.26694 0.477059
\(81\) −10.3857 −1.15397
\(82\) −2.11888 −0.233991
\(83\) −4.86670 −0.534190 −0.267095 0.963670i \(-0.586064\pi\)
−0.267095 + 0.963670i \(0.586064\pi\)
\(84\) 0.271739 0.0296492
\(85\) −2.52935 −0.274347
\(86\) −16.5004 −1.77929
\(87\) −0.0250006 −0.00268035
\(88\) −2.09174 −0.222980
\(89\) 3.44228 0.364881 0.182440 0.983217i \(-0.441600\pi\)
0.182440 + 0.983217i \(0.441600\pi\)
\(90\) 0.835078 0.0880250
\(91\) −1.91852 −0.201116
\(92\) −0.911998 −0.0950823
\(93\) 2.11939 0.219770
\(94\) 14.6982 1.51600
\(95\) −3.94494 −0.404742
\(96\) −1.53428 −0.156591
\(97\) −11.6821 −1.18614 −0.593069 0.805152i \(-0.702084\pi\)
−0.593069 + 0.805152i \(0.702084\pi\)
\(98\) −1.46418 −0.147904
\(99\) −0.438960 −0.0441172
\(100\) 0.143813 0.0143813
\(101\) −2.74927 −0.273562 −0.136781 0.990601i \(-0.543676\pi\)
−0.136781 + 0.990601i \(0.543676\pi\)
\(102\) 6.99773 0.692879
\(103\) −0.582543 −0.0573997 −0.0286998 0.999588i \(-0.509137\pi\)
−0.0286998 + 0.999588i \(0.509137\pi\)
\(104\) 5.21413 0.511288
\(105\) −1.88953 −0.184400
\(106\) −16.9506 −1.64638
\(107\) 3.23972 0.313196 0.156598 0.987662i \(-0.449947\pi\)
0.156598 + 0.987662i \(0.449947\pi\)
\(108\) 0.660234 0.0635310
\(109\) 1.52795 0.146351 0.0731757 0.997319i \(-0.476687\pi\)
0.0731757 + 0.997319i \(0.476687\pi\)
\(110\) −1.12690 −0.107446
\(111\) −0.608587 −0.0577645
\(112\) 4.26694 0.403188
\(113\) −14.7035 −1.38319 −0.691595 0.722285i \(-0.743092\pi\)
−0.691595 + 0.722285i \(0.743092\pi\)
\(114\) 10.9141 1.02220
\(115\) 6.34157 0.591354
\(116\) 0.00190280 0.000176671 0
\(117\) 1.09421 0.101160
\(118\) −12.3117 −1.13338
\(119\) −2.52935 −0.231865
\(120\) 5.13535 0.468791
\(121\) −10.4076 −0.946149
\(122\) −15.5077 −1.40400
\(123\) −2.73444 −0.246556
\(124\) −0.161307 −0.0144858
\(125\) −1.00000 −0.0894427
\(126\) 0.835078 0.0743947
\(127\) 19.0927 1.69420 0.847102 0.531430i \(-0.178345\pi\)
0.847102 + 0.531430i \(0.178345\pi\)
\(128\) −12.3783 −1.09410
\(129\) −21.2940 −1.87483
\(130\) 2.80906 0.246370
\(131\) −20.0269 −1.74976 −0.874881 0.484337i \(-0.839061\pi\)
−0.874881 + 0.484337i \(0.839061\pi\)
\(132\) 0.209143 0.0182036
\(133\) −3.94494 −0.342070
\(134\) −14.3913 −1.24322
\(135\) −4.59093 −0.395124
\(136\) 6.87423 0.589461
\(137\) 0.958552 0.0818947 0.0409473 0.999161i \(-0.486962\pi\)
0.0409473 + 0.999161i \(0.486962\pi\)
\(138\) −17.5447 −1.49350
\(139\) −6.50772 −0.551978 −0.275989 0.961161i \(-0.589005\pi\)
−0.275989 + 0.961161i \(0.589005\pi\)
\(140\) 0.143813 0.0121544
\(141\) 18.9682 1.59741
\(142\) −17.4300 −1.46269
\(143\) −1.47659 −0.123478
\(144\) −2.43361 −0.202801
\(145\) −0.0132311 −0.00109878
\(146\) 11.0055 0.910819
\(147\) −1.88953 −0.155846
\(148\) 0.0463196 0.00380745
\(149\) −0.640380 −0.0524620 −0.0262310 0.999656i \(-0.508351\pi\)
−0.0262310 + 0.999656i \(0.508351\pi\)
\(150\) 2.76661 0.225893
\(151\) −7.01626 −0.570975 −0.285488 0.958382i \(-0.592156\pi\)
−0.285488 + 0.958382i \(0.592156\pi\)
\(152\) 10.7215 0.869629
\(153\) 1.44259 0.116626
\(154\) −1.12690 −0.0908081
\(155\) 1.12165 0.0900928
\(156\) −0.521337 −0.0417404
\(157\) 20.0864 1.60307 0.801535 0.597947i \(-0.204017\pi\)
0.801535 + 0.597947i \(0.204017\pi\)
\(158\) 19.5551 1.55572
\(159\) −21.8749 −1.73479
\(160\) −0.811986 −0.0641932
\(161\) 6.34157 0.499785
\(162\) 15.2065 1.19474
\(163\) 10.5575 0.826926 0.413463 0.910521i \(-0.364319\pi\)
0.413463 + 0.910521i \(0.364319\pi\)
\(164\) 0.208119 0.0162513
\(165\) −1.45427 −0.113215
\(166\) 7.12571 0.553063
\(167\) −18.1655 −1.40569 −0.702845 0.711343i \(-0.748087\pi\)
−0.702845 + 0.711343i \(0.748087\pi\)
\(168\) 5.13535 0.396201
\(169\) −9.31927 −0.716867
\(170\) 3.70342 0.284039
\(171\) 2.24996 0.172059
\(172\) 1.62069 0.123576
\(173\) 10.6660 0.810920 0.405460 0.914113i \(-0.367111\pi\)
0.405460 + 0.914113i \(0.367111\pi\)
\(174\) 0.0366054 0.00277504
\(175\) −1.00000 −0.0755929
\(176\) 3.28404 0.247544
\(177\) −15.8883 −1.19424
\(178\) −5.04010 −0.377772
\(179\) −13.4786 −1.00744 −0.503721 0.863867i \(-0.668036\pi\)
−0.503721 + 0.863867i \(0.668036\pi\)
\(180\) −0.0820221 −0.00611357
\(181\) −4.65420 −0.345944 −0.172972 0.984927i \(-0.555337\pi\)
−0.172972 + 0.984927i \(0.555337\pi\)
\(182\) 2.80906 0.208221
\(183\) −20.0129 −1.47939
\(184\) −17.2350 −1.27058
\(185\) −0.322083 −0.0236800
\(186\) −3.10316 −0.227535
\(187\) −1.94671 −0.142357
\(188\) −1.44367 −0.105290
\(189\) −4.59093 −0.333941
\(190\) 5.77609 0.419042
\(191\) −1.02369 −0.0740715 −0.0370357 0.999314i \(-0.511792\pi\)
−0.0370357 + 0.999314i \(0.511792\pi\)
\(192\) −13.8786 −1.00160
\(193\) 22.9306 1.65058 0.825289 0.564710i \(-0.191012\pi\)
0.825289 + 0.564710i \(0.191012\pi\)
\(194\) 17.1047 1.22804
\(195\) 3.62511 0.259600
\(196\) 0.143813 0.0102723
\(197\) 5.61528 0.400072 0.200036 0.979789i \(-0.435894\pi\)
0.200036 + 0.979789i \(0.435894\pi\)
\(198\) 0.642716 0.0456758
\(199\) 10.2793 0.728680 0.364340 0.931266i \(-0.381295\pi\)
0.364340 + 0.931266i \(0.381295\pi\)
\(200\) 2.71779 0.192176
\(201\) −18.5721 −1.30997
\(202\) 4.02541 0.283227
\(203\) −0.0132311 −0.000928642 0
\(204\) −0.687323 −0.0481223
\(205\) −1.44715 −0.101073
\(206\) 0.852946 0.0594275
\(207\) −3.61685 −0.251388
\(208\) −8.18623 −0.567613
\(209\) −3.03621 −0.210019
\(210\) 2.76661 0.190914
\(211\) −19.5451 −1.34554 −0.672769 0.739853i \(-0.734895\pi\)
−0.672769 + 0.739853i \(0.734895\pi\)
\(212\) 1.66490 0.114346
\(213\) −22.4936 −1.54123
\(214\) −4.74353 −0.324261
\(215\) −11.2694 −0.768568
\(216\) 12.4772 0.848963
\(217\) 1.12165 0.0761423
\(218\) −2.23719 −0.151522
\(219\) 14.2027 0.959727
\(220\) 0.110685 0.00746238
\(221\) 4.85262 0.326422
\(222\) 0.891079 0.0598053
\(223\) 16.7732 1.12322 0.561610 0.827402i \(-0.310182\pi\)
0.561610 + 0.827402i \(0.310182\pi\)
\(224\) −0.811986 −0.0542531
\(225\) 0.570340 0.0380227
\(226\) 21.5285 1.43206
\(227\) 6.28497 0.417148 0.208574 0.978007i \(-0.433118\pi\)
0.208574 + 0.978007i \(0.433118\pi\)
\(228\) −1.07199 −0.0709946
\(229\) 1.00000 0.0660819
\(230\) −9.28517 −0.612246
\(231\) −1.45427 −0.0956843
\(232\) 0.0359593 0.00236085
\(233\) 24.2098 1.58604 0.793018 0.609198i \(-0.208509\pi\)
0.793018 + 0.609198i \(0.208509\pi\)
\(234\) −1.60212 −0.104734
\(235\) 10.0385 0.654842
\(236\) 1.20926 0.0787162
\(237\) 25.2361 1.63926
\(238\) 3.70342 0.240057
\(239\) −21.2084 −1.37186 −0.685929 0.727669i \(-0.740604\pi\)
−0.685929 + 0.727669i \(0.740604\pi\)
\(240\) −8.06254 −0.520434
\(241\) −23.0932 −1.48756 −0.743781 0.668423i \(-0.766969\pi\)
−0.743781 + 0.668423i \(0.766969\pi\)
\(242\) 15.2386 0.979576
\(243\) 5.85142 0.375369
\(244\) 1.52318 0.0975117
\(245\) −1.00000 −0.0638877
\(246\) 4.00370 0.255267
\(247\) 7.56846 0.481570
\(248\) −3.04839 −0.193573
\(249\) 9.19581 0.582760
\(250\) 1.46418 0.0926027
\(251\) 12.4348 0.784878 0.392439 0.919778i \(-0.371631\pi\)
0.392439 + 0.919778i \(0.371631\pi\)
\(252\) −0.0820221 −0.00516691
\(253\) 4.88077 0.306851
\(254\) −27.9551 −1.75406
\(255\) 4.77929 0.299291
\(256\) 3.43409 0.214630
\(257\) −21.7890 −1.35916 −0.679582 0.733600i \(-0.737839\pi\)
−0.679582 + 0.733600i \(0.737839\pi\)
\(258\) 31.1781 1.94107
\(259\) −0.322083 −0.0200133
\(260\) −0.275908 −0.0171111
\(261\) 0.00754623 0.000467100 0
\(262\) 29.3230 1.81158
\(263\) −17.4968 −1.07890 −0.539450 0.842018i \(-0.681368\pi\)
−0.539450 + 0.842018i \(0.681368\pi\)
\(264\) 3.95241 0.243254
\(265\) −11.5769 −0.711160
\(266\) 5.77609 0.354155
\(267\) −6.50430 −0.398057
\(268\) 1.41352 0.0863446
\(269\) 6.69885 0.408436 0.204218 0.978925i \(-0.434535\pi\)
0.204218 + 0.978925i \(0.434535\pi\)
\(270\) 6.72193 0.409083
\(271\) −29.1923 −1.77330 −0.886652 0.462438i \(-0.846975\pi\)
−0.886652 + 0.462438i \(0.846975\pi\)
\(272\) −10.7926 −0.654397
\(273\) 3.62511 0.219402
\(274\) −1.40349 −0.0847879
\(275\) −0.769647 −0.0464115
\(276\) 1.72325 0.103728
\(277\) 7.87863 0.473381 0.236691 0.971585i \(-0.423937\pi\)
0.236691 + 0.971585i \(0.423937\pi\)
\(278\) 9.52845 0.571479
\(279\) −0.639720 −0.0382990
\(280\) 2.71779 0.162419
\(281\) −12.6238 −0.753075 −0.376538 0.926401i \(-0.622885\pi\)
−0.376538 + 0.926401i \(0.622885\pi\)
\(282\) −27.7727 −1.65384
\(283\) −15.9248 −0.946632 −0.473316 0.880893i \(-0.656943\pi\)
−0.473316 + 0.880893i \(0.656943\pi\)
\(284\) 1.71199 0.101588
\(285\) 7.45410 0.441543
\(286\) 2.16198 0.127841
\(287\) −1.44715 −0.0854226
\(288\) 0.463108 0.0272889
\(289\) −10.6024 −0.623670
\(290\) 0.0193727 0.00113760
\(291\) 22.0737 1.29399
\(292\) −1.08097 −0.0632588
\(293\) 11.0663 0.646499 0.323250 0.946314i \(-0.395225\pi\)
0.323250 + 0.946314i \(0.395225\pi\)
\(294\) 2.76661 0.161352
\(295\) −8.40858 −0.489567
\(296\) 0.875353 0.0508788
\(297\) −3.53339 −0.205028
\(298\) 0.937630 0.0543154
\(299\) −12.1664 −0.703603
\(300\) −0.271739 −0.0156889
\(301\) −11.2694 −0.649559
\(302\) 10.2730 0.591148
\(303\) 5.19483 0.298435
\(304\) −16.8328 −0.965430
\(305\) −10.5914 −0.606463
\(306\) −2.11221 −0.120747
\(307\) −32.9383 −1.87989 −0.939944 0.341329i \(-0.889123\pi\)
−0.939944 + 0.341329i \(0.889123\pi\)
\(308\) 0.110685 0.00630687
\(309\) 1.10074 0.0626186
\(310\) −1.64229 −0.0932757
\(311\) −12.1127 −0.686848 −0.343424 0.939180i \(-0.611587\pi\)
−0.343424 + 0.939180i \(0.611587\pi\)
\(312\) −9.85228 −0.557776
\(313\) 17.0096 0.961442 0.480721 0.876874i \(-0.340375\pi\)
0.480721 + 0.876874i \(0.340375\pi\)
\(314\) −29.4101 −1.65971
\(315\) 0.570340 0.0321350
\(316\) −1.92072 −0.108049
\(317\) 33.2939 1.86997 0.934985 0.354687i \(-0.115412\pi\)
0.934985 + 0.354687i \(0.115412\pi\)
\(318\) 32.0286 1.79608
\(319\) −0.0101833 −0.000570155 0
\(320\) −7.34500 −0.410598
\(321\) −6.12157 −0.341673
\(322\) −9.28517 −0.517442
\(323\) 9.97814 0.555199
\(324\) −1.49360 −0.0829778
\(325\) 1.91852 0.106420
\(326\) −15.4580 −0.856140
\(327\) −2.88712 −0.159658
\(328\) 3.93304 0.217166
\(329\) 10.0385 0.553442
\(330\) 2.12931 0.117215
\(331\) 0.893604 0.0491169 0.0245584 0.999698i \(-0.492182\pi\)
0.0245584 + 0.999698i \(0.492182\pi\)
\(332\) −0.699894 −0.0384117
\(333\) 0.183697 0.0100665
\(334\) 26.5975 1.45535
\(335\) −9.82891 −0.537011
\(336\) −8.06254 −0.439847
\(337\) 19.7816 1.07757 0.538786 0.842442i \(-0.318883\pi\)
0.538786 + 0.842442i \(0.318883\pi\)
\(338\) 13.6451 0.742193
\(339\) 27.7828 1.50895
\(340\) −0.363753 −0.0197273
\(341\) 0.863272 0.0467488
\(342\) −3.29433 −0.178137
\(343\) −1.00000 −0.0539949
\(344\) 30.6279 1.65134
\(345\) −11.9826 −0.645122
\(346\) −15.6169 −0.839569
\(347\) −3.00075 −0.161089 −0.0805444 0.996751i \(-0.525666\pi\)
−0.0805444 + 0.996751i \(0.525666\pi\)
\(348\) −0.00359541 −0.000192734 0
\(349\) 1.20119 0.0642981 0.0321491 0.999483i \(-0.489765\pi\)
0.0321491 + 0.999483i \(0.489765\pi\)
\(350\) 1.46418 0.0782635
\(351\) 8.80780 0.470125
\(352\) −0.624943 −0.0333096
\(353\) 19.6422 1.04545 0.522724 0.852502i \(-0.324916\pi\)
0.522724 + 0.852502i \(0.324916\pi\)
\(354\) 23.2633 1.23643
\(355\) −11.9043 −0.631814
\(356\) 0.495043 0.0262372
\(357\) 4.77929 0.252947
\(358\) 19.7351 1.04303
\(359\) 11.6099 0.612749 0.306374 0.951911i \(-0.400884\pi\)
0.306374 + 0.951911i \(0.400884\pi\)
\(360\) −1.55006 −0.0816954
\(361\) −3.43744 −0.180918
\(362\) 6.81457 0.358166
\(363\) 19.6656 1.03218
\(364\) −0.275908 −0.0144615
\(365\) 7.51649 0.393431
\(366\) 29.3023 1.53166
\(367\) −4.96078 −0.258951 −0.129475 0.991583i \(-0.541329\pi\)
−0.129475 + 0.991583i \(0.541329\pi\)
\(368\) 27.0591 1.41055
\(369\) 0.825367 0.0429669
\(370\) 0.471586 0.0245166
\(371\) −11.5769 −0.601040
\(372\) 0.304795 0.0158029
\(373\) −15.7111 −0.813489 −0.406745 0.913542i \(-0.633336\pi\)
−0.406745 + 0.913542i \(0.633336\pi\)
\(374\) 2.85032 0.147387
\(375\) 1.88953 0.0975751
\(376\) −27.2826 −1.40699
\(377\) 0.0253842 0.00130735
\(378\) 6.72193 0.345739
\(379\) 32.2233 1.65520 0.827601 0.561317i \(-0.189705\pi\)
0.827601 + 0.561317i \(0.189705\pi\)
\(380\) −0.567333 −0.0291036
\(381\) −36.0763 −1.84825
\(382\) 1.49886 0.0766883
\(383\) −9.02809 −0.461314 −0.230657 0.973035i \(-0.574087\pi\)
−0.230657 + 0.973035i \(0.574087\pi\)
\(384\) 23.3893 1.19358
\(385\) −0.769647 −0.0392249
\(386\) −33.5744 −1.70889
\(387\) 6.42740 0.326723
\(388\) −1.68004 −0.0852909
\(389\) 24.8774 1.26134 0.630668 0.776053i \(-0.282781\pi\)
0.630668 + 0.776053i \(0.282781\pi\)
\(390\) −5.30781 −0.268771
\(391\) −16.0400 −0.811180
\(392\) 2.71779 0.137269
\(393\) 37.8416 1.90886
\(394\) −8.22177 −0.414207
\(395\) 13.3557 0.671998
\(396\) −0.0631281 −0.00317231
\(397\) 27.9280 1.40167 0.700833 0.713326i \(-0.252812\pi\)
0.700833 + 0.713326i \(0.252812\pi\)
\(398\) −15.0507 −0.754424
\(399\) 7.45410 0.373172
\(400\) −4.26694 −0.213347
\(401\) −25.6395 −1.28037 −0.640187 0.768219i \(-0.721143\pi\)
−0.640187 + 0.768219i \(0.721143\pi\)
\(402\) 27.1928 1.35625
\(403\) −2.15190 −0.107194
\(404\) −0.395379 −0.0196709
\(405\) 10.3857 0.516071
\(406\) 0.0193727 0.000961450 0
\(407\) −0.247890 −0.0122875
\(408\) −12.9891 −0.643056
\(409\) 23.9644 1.18497 0.592483 0.805583i \(-0.298148\pi\)
0.592483 + 0.805583i \(0.298148\pi\)
\(410\) 2.11888 0.104644
\(411\) −1.81122 −0.0893408
\(412\) −0.0837771 −0.00412740
\(413\) −8.40858 −0.413759
\(414\) 5.29570 0.260270
\(415\) 4.86670 0.238897
\(416\) 1.55781 0.0763781
\(417\) 12.2966 0.602165
\(418\) 4.44555 0.217439
\(419\) −7.90795 −0.386329 −0.193164 0.981166i \(-0.561875\pi\)
−0.193164 + 0.981166i \(0.561875\pi\)
\(420\) −0.271739 −0.0132595
\(421\) −27.1541 −1.32341 −0.661704 0.749765i \(-0.730167\pi\)
−0.661704 + 0.749765i \(0.730167\pi\)
\(422\) 28.6174 1.39307
\(423\) −5.72537 −0.278377
\(424\) 31.4634 1.52800
\(425\) 2.52935 0.122692
\(426\) 32.9345 1.59568
\(427\) −10.5914 −0.512555
\(428\) 0.465913 0.0225208
\(429\) 2.79006 0.134705
\(430\) 16.5004 0.795721
\(431\) −25.8805 −1.24662 −0.623311 0.781974i \(-0.714213\pi\)
−0.623311 + 0.781974i \(0.714213\pi\)
\(432\) −19.5892 −0.942487
\(433\) 16.6908 0.802108 0.401054 0.916054i \(-0.368644\pi\)
0.401054 + 0.916054i \(0.368644\pi\)
\(434\) −1.64229 −0.0788323
\(435\) 0.0250006 0.00119869
\(436\) 0.219739 0.0105236
\(437\) −25.0171 −1.19673
\(438\) −20.7952 −0.993633
\(439\) 26.8538 1.28166 0.640832 0.767681i \(-0.278590\pi\)
0.640832 + 0.767681i \(0.278590\pi\)
\(440\) 2.09174 0.0997196
\(441\) 0.570340 0.0271590
\(442\) −7.10509 −0.337954
\(443\) −32.1592 −1.52793 −0.763965 0.645258i \(-0.776750\pi\)
−0.763965 + 0.645258i \(0.776750\pi\)
\(444\) −0.0875225 −0.00415364
\(445\) −3.44228 −0.163180
\(446\) −24.5590 −1.16290
\(447\) 1.21002 0.0572320
\(448\) −7.34500 −0.347018
\(449\) −3.72511 −0.175799 −0.0878994 0.996129i \(-0.528015\pi\)
−0.0878994 + 0.996129i \(0.528015\pi\)
\(450\) −0.835078 −0.0393660
\(451\) −1.11379 −0.0524466
\(452\) −2.11455 −0.0994602
\(453\) 13.2575 0.622890
\(454\) −9.20231 −0.431886
\(455\) 1.91852 0.0899417
\(456\) −20.2587 −0.948698
\(457\) −22.5746 −1.05599 −0.527997 0.849246i \(-0.677057\pi\)
−0.527997 + 0.849246i \(0.677057\pi\)
\(458\) −1.46418 −0.0684165
\(459\) 11.6121 0.542005
\(460\) 0.911998 0.0425221
\(461\) 27.0328 1.25904 0.629521 0.776983i \(-0.283251\pi\)
0.629521 + 0.776983i \(0.283251\pi\)
\(462\) 2.12931 0.0990647
\(463\) 4.32309 0.200911 0.100455 0.994942i \(-0.467970\pi\)
0.100455 + 0.994942i \(0.467970\pi\)
\(464\) −0.0564564 −0.00262092
\(465\) −2.11939 −0.0982843
\(466\) −35.4474 −1.64207
\(467\) 4.23657 0.196045 0.0980224 0.995184i \(-0.468748\pi\)
0.0980224 + 0.995184i \(0.468748\pi\)
\(468\) 0.157361 0.00727403
\(469\) −9.82891 −0.453857
\(470\) −14.6982 −0.677977
\(471\) −37.9540 −1.74883
\(472\) 22.8527 1.05188
\(473\) −8.67348 −0.398807
\(474\) −36.9500 −1.69717
\(475\) 3.94494 0.181006
\(476\) −0.363753 −0.0166726
\(477\) 6.60274 0.302319
\(478\) 31.0528 1.42032
\(479\) 14.8047 0.676443 0.338222 0.941066i \(-0.390175\pi\)
0.338222 + 0.941066i \(0.390175\pi\)
\(480\) 1.53428 0.0700298
\(481\) 0.617924 0.0281749
\(482\) 33.8125 1.54012
\(483\) −11.9826 −0.545228
\(484\) −1.49675 −0.0680342
\(485\) 11.6821 0.530457
\(486\) −8.56751 −0.388630
\(487\) 6.37497 0.288877 0.144439 0.989514i \(-0.453862\pi\)
0.144439 + 0.989514i \(0.453862\pi\)
\(488\) 28.7852 1.30305
\(489\) −19.9487 −0.902112
\(490\) 1.46418 0.0661448
\(491\) 30.6198 1.38185 0.690925 0.722926i \(-0.257203\pi\)
0.690925 + 0.722926i \(0.257203\pi\)
\(492\) −0.393247 −0.0177290
\(493\) 0.0334661 0.00150724
\(494\) −11.0816 −0.498583
\(495\) 0.438960 0.0197298
\(496\) 4.78600 0.214898
\(497\) −11.9043 −0.533980
\(498\) −13.4643 −0.603349
\(499\) −43.0440 −1.92691 −0.963456 0.267866i \(-0.913681\pi\)
−0.963456 + 0.267866i \(0.913681\pi\)
\(500\) −0.143813 −0.00643150
\(501\) 34.3244 1.53350
\(502\) −18.2068 −0.812607
\(503\) 26.7587 1.19311 0.596556 0.802571i \(-0.296535\pi\)
0.596556 + 0.802571i \(0.296535\pi\)
\(504\) −1.55006 −0.0690452
\(505\) 2.74927 0.122341
\(506\) −7.14631 −0.317692
\(507\) 17.6091 0.782047
\(508\) 2.74577 0.121824
\(509\) 15.9496 0.706953 0.353477 0.935443i \(-0.384999\pi\)
0.353477 + 0.935443i \(0.384999\pi\)
\(510\) −6.99773 −0.309865
\(511\) 7.51649 0.332510
\(512\) 19.7286 0.871888
\(513\) 18.1109 0.799617
\(514\) 31.9030 1.40718
\(515\) 0.582543 0.0256699
\(516\) −3.06234 −0.134812
\(517\) 7.72613 0.339795
\(518\) 0.471586 0.0207203
\(519\) −20.1537 −0.884651
\(520\) −5.21413 −0.228655
\(521\) −2.30278 −0.100887 −0.0504433 0.998727i \(-0.516063\pi\)
−0.0504433 + 0.998727i \(0.516063\pi\)
\(522\) −0.0110490 −0.000483602 0
\(523\) 15.1414 0.662088 0.331044 0.943615i \(-0.392599\pi\)
0.331044 + 0.943615i \(0.392599\pi\)
\(524\) −2.88013 −0.125819
\(525\) 1.88953 0.0824660
\(526\) 25.6184 1.11702
\(527\) −2.83704 −0.123583
\(528\) −6.20531 −0.270051
\(529\) 17.2155 0.748498
\(530\) 16.9506 0.736285
\(531\) 4.79575 0.208118
\(532\) −0.567333 −0.0245970
\(533\) 2.77639 0.120259
\(534\) 9.52344 0.412120
\(535\) −3.23972 −0.140065
\(536\) 26.7129 1.15382
\(537\) 25.4684 1.09904
\(538\) −9.80830 −0.422866
\(539\) −0.769647 −0.0331511
\(540\) −0.660234 −0.0284119
\(541\) −31.7684 −1.36583 −0.682916 0.730497i \(-0.739288\pi\)
−0.682916 + 0.730497i \(0.739288\pi\)
\(542\) 42.7426 1.83595
\(543\) 8.79427 0.377398
\(544\) 2.05380 0.0880559
\(545\) −1.52795 −0.0654503
\(546\) −5.30781 −0.227153
\(547\) 5.69976 0.243704 0.121852 0.992548i \(-0.461117\pi\)
0.121852 + 0.992548i \(0.461117\pi\)
\(548\) 0.137852 0.00588875
\(549\) 6.04071 0.257811
\(550\) 1.12690 0.0480511
\(551\) 0.0521960 0.00222362
\(552\) 32.5662 1.38611
\(553\) 13.3557 0.567942
\(554\) −11.5357 −0.490105
\(555\) 0.608587 0.0258331
\(556\) −0.935893 −0.0396907
\(557\) −32.6181 −1.38207 −0.691036 0.722821i \(-0.742845\pi\)
−0.691036 + 0.722821i \(0.742845\pi\)
\(558\) 0.936662 0.0396521
\(559\) 21.6206 0.914456
\(560\) −4.26694 −0.180311
\(561\) 3.67837 0.155301
\(562\) 18.4835 0.779681
\(563\) −27.4771 −1.15802 −0.579011 0.815320i \(-0.696561\pi\)
−0.579011 + 0.815320i \(0.696561\pi\)
\(564\) 2.72786 0.114864
\(565\) 14.7035 0.618582
\(566\) 23.3167 0.980076
\(567\) 10.3857 0.436160
\(568\) 32.3533 1.35751
\(569\) 22.4018 0.939134 0.469567 0.882897i \(-0.344410\pi\)
0.469567 + 0.882897i \(0.344410\pi\)
\(570\) −10.9141 −0.457142
\(571\) 40.6912 1.70287 0.851437 0.524457i \(-0.175732\pi\)
0.851437 + 0.524457i \(0.175732\pi\)
\(572\) −0.212352 −0.00887887
\(573\) 1.93429 0.0808063
\(574\) 2.11888 0.0884405
\(575\) −6.34157 −0.264462
\(576\) 4.18914 0.174548
\(577\) −17.9973 −0.749237 −0.374619 0.927179i \(-0.622226\pi\)
−0.374619 + 0.927179i \(0.622226\pi\)
\(578\) 15.5238 0.645703
\(579\) −43.3281 −1.80065
\(580\) −0.00190280 −7.90096e−5 0
\(581\) 4.86670 0.201905
\(582\) −32.3199 −1.33970
\(583\) −8.91009 −0.369018
\(584\) −20.4282 −0.845325
\(585\) −1.09421 −0.0452400
\(586\) −16.2030 −0.669339
\(587\) 30.6407 1.26468 0.632338 0.774693i \(-0.282095\pi\)
0.632338 + 0.774693i \(0.282095\pi\)
\(588\) −0.271739 −0.0112063
\(589\) −4.42483 −0.182322
\(590\) 12.3117 0.506863
\(591\) −10.6103 −0.436448
\(592\) −1.37431 −0.0564838
\(593\) 34.1853 1.40382 0.701910 0.712265i \(-0.252331\pi\)
0.701910 + 0.712265i \(0.252331\pi\)
\(594\) 5.17351 0.212272
\(595\) 2.52935 0.103693
\(596\) −0.0920948 −0.00377235
\(597\) −19.4231 −0.794934
\(598\) 17.8138 0.728461
\(599\) 6.79367 0.277582 0.138791 0.990322i \(-0.455678\pi\)
0.138791 + 0.990322i \(0.455678\pi\)
\(600\) −5.13535 −0.209650
\(601\) 6.73902 0.274891 0.137445 0.990509i \(-0.456111\pi\)
0.137445 + 0.990509i \(0.456111\pi\)
\(602\) 16.5004 0.672507
\(603\) 5.60582 0.228287
\(604\) −1.00903 −0.0410568
\(605\) 10.4076 0.423131
\(606\) −7.60615 −0.308979
\(607\) 7.00689 0.284401 0.142200 0.989838i \(-0.454582\pi\)
0.142200 + 0.989838i \(0.454582\pi\)
\(608\) 3.20324 0.129908
\(609\) 0.0250006 0.00101308
\(610\) 15.5077 0.627889
\(611\) −19.2592 −0.779142
\(612\) 0.207463 0.00838618
\(613\) −47.6840 −1.92594 −0.962970 0.269610i \(-0.913105\pi\)
−0.962970 + 0.269610i \(0.913105\pi\)
\(614\) 48.2275 1.94630
\(615\) 2.73444 0.110263
\(616\) 2.09174 0.0842785
\(617\) 16.7927 0.676047 0.338024 0.941138i \(-0.390242\pi\)
0.338024 + 0.941138i \(0.390242\pi\)
\(618\) −1.61167 −0.0648309
\(619\) 44.0610 1.77096 0.885481 0.464676i \(-0.153829\pi\)
0.885481 + 0.464676i \(0.153829\pi\)
\(620\) 0.161307 0.00647824
\(621\) −29.1137 −1.16829
\(622\) 17.7351 0.711114
\(623\) −3.44228 −0.137912
\(624\) 15.4682 0.619222
\(625\) 1.00000 0.0400000
\(626\) −24.9051 −0.995408
\(627\) 5.73703 0.229115
\(628\) 2.88868 0.115271
\(629\) 0.814661 0.0324827
\(630\) −0.835078 −0.0332703
\(631\) 35.1985 1.40123 0.700615 0.713539i \(-0.252909\pi\)
0.700615 + 0.713539i \(0.252909\pi\)
\(632\) −36.2979 −1.44385
\(633\) 36.9311 1.46788
\(634\) −48.7481 −1.93603
\(635\) −19.0927 −0.757671
\(636\) −3.14588 −0.124742
\(637\) 1.91852 0.0760146
\(638\) 0.0149101 0.000590298 0
\(639\) 6.78949 0.268588
\(640\) 12.3783 0.489297
\(641\) −13.0336 −0.514795 −0.257398 0.966306i \(-0.582865\pi\)
−0.257398 + 0.966306i \(0.582865\pi\)
\(642\) 8.96306 0.353744
\(643\) 27.7186 1.09311 0.546557 0.837422i \(-0.315938\pi\)
0.546557 + 0.837422i \(0.315938\pi\)
\(644\) 0.911998 0.0359377
\(645\) 21.2940 0.838449
\(646\) −14.6098 −0.574813
\(647\) 5.32167 0.209216 0.104608 0.994514i \(-0.466641\pi\)
0.104608 + 0.994514i \(0.466641\pi\)
\(648\) −28.2262 −1.10883
\(649\) −6.47164 −0.254034
\(650\) −2.80906 −0.110180
\(651\) −2.11939 −0.0830654
\(652\) 1.51830 0.0594612
\(653\) 12.4627 0.487702 0.243851 0.969813i \(-0.421589\pi\)
0.243851 + 0.969813i \(0.421589\pi\)
\(654\) 4.22725 0.165299
\(655\) 20.0269 0.782518
\(656\) −6.17491 −0.241090
\(657\) −4.28695 −0.167250
\(658\) −14.6982 −0.572995
\(659\) 12.5914 0.490491 0.245245 0.969461i \(-0.421131\pi\)
0.245245 + 0.969461i \(0.421131\pi\)
\(660\) −0.209143 −0.00814089
\(661\) 46.5201 1.80942 0.904712 0.426025i \(-0.140086\pi\)
0.904712 + 0.426025i \(0.140086\pi\)
\(662\) −1.30839 −0.0508521
\(663\) −9.16918 −0.356102
\(664\) −13.2267 −0.513294
\(665\) 3.94494 0.152978
\(666\) −0.268965 −0.0104222
\(667\) −0.0839060 −0.00324885
\(668\) −2.61243 −0.101078
\(669\) −31.6936 −1.22535
\(670\) 14.3913 0.555983
\(671\) −8.15166 −0.314691
\(672\) 1.53428 0.0591860
\(673\) 31.0920 1.19851 0.599255 0.800558i \(-0.295464\pi\)
0.599255 + 0.800558i \(0.295464\pi\)
\(674\) −28.9638 −1.11564
\(675\) 4.59093 0.176705
\(676\) −1.34023 −0.0515473
\(677\) 17.2356 0.662418 0.331209 0.943557i \(-0.392544\pi\)
0.331209 + 0.943557i \(0.392544\pi\)
\(678\) −40.6789 −1.56226
\(679\) 11.6821 0.448318
\(680\) −6.87423 −0.263615
\(681\) −11.8757 −0.455077
\(682\) −1.26398 −0.0484004
\(683\) 40.4199 1.54662 0.773312 0.634025i \(-0.218598\pi\)
0.773312 + 0.634025i \(0.218598\pi\)
\(684\) 0.323572 0.0123721
\(685\) −0.958552 −0.0366244
\(686\) 1.46418 0.0559025
\(687\) −1.88953 −0.0720902
\(688\) −48.0860 −1.83326
\(689\) 22.2105 0.846151
\(690\) 17.5447 0.667913
\(691\) −7.98035 −0.303587 −0.151793 0.988412i \(-0.548505\pi\)
−0.151793 + 0.988412i \(0.548505\pi\)
\(692\) 1.53390 0.0583103
\(693\) 0.438960 0.0166747
\(694\) 4.39363 0.166780
\(695\) 6.50772 0.246852
\(696\) −0.0679464 −0.00257550
\(697\) 3.66035 0.138646
\(698\) −1.75875 −0.0665697
\(699\) −45.7452 −1.73024
\(700\) −0.143813 −0.00543561
\(701\) −5.54488 −0.209427 −0.104714 0.994502i \(-0.533393\pi\)
−0.104714 + 0.994502i \(0.533393\pi\)
\(702\) −12.8962 −0.486734
\(703\) 1.27060 0.0479215
\(704\) −5.65305 −0.213058
\(705\) −18.9682 −0.714382
\(706\) −28.7596 −1.08238
\(707\) 2.74927 0.103397
\(708\) −2.28494 −0.0858733
\(709\) 4.91070 0.184425 0.0922125 0.995739i \(-0.470606\pi\)
0.0922125 + 0.995739i \(0.470606\pi\)
\(710\) 17.4300 0.654135
\(711\) −7.61729 −0.285671
\(712\) 9.35537 0.350607
\(713\) 7.11299 0.266384
\(714\) −6.99773 −0.261883
\(715\) 1.47659 0.0552212
\(716\) −1.93840 −0.0724415
\(717\) 40.0740 1.49659
\(718\) −16.9990 −0.634397
\(719\) 32.9807 1.22997 0.614987 0.788537i \(-0.289161\pi\)
0.614987 + 0.788537i \(0.289161\pi\)
\(720\) 2.43361 0.0906952
\(721\) 0.582543 0.0216950
\(722\) 5.03302 0.187309
\(723\) 43.6353 1.62282
\(724\) −0.669333 −0.0248756
\(725\) 0.0132311 0.000491391 0
\(726\) −28.7939 −1.06864
\(727\) 20.0670 0.744245 0.372122 0.928184i \(-0.378630\pi\)
0.372122 + 0.928184i \(0.378630\pi\)
\(728\) −5.21413 −0.193249
\(729\) 20.1007 0.744472
\(730\) −11.0055 −0.407330
\(731\) 28.5043 1.05427
\(732\) −2.87810 −0.106378
\(733\) 33.3438 1.23158 0.615791 0.787909i \(-0.288836\pi\)
0.615791 + 0.787909i \(0.288836\pi\)
\(734\) 7.26346 0.268099
\(735\) 1.88953 0.0696965
\(736\) −5.14927 −0.189804
\(737\) −7.56479 −0.278653
\(738\) −1.20848 −0.0444849
\(739\) 3.20237 0.117801 0.0589005 0.998264i \(-0.481241\pi\)
0.0589005 + 0.998264i \(0.481241\pi\)
\(740\) −0.0463196 −0.00170274
\(741\) −14.3009 −0.525355
\(742\) 16.9506 0.622274
\(743\) −43.5545 −1.59786 −0.798929 0.601425i \(-0.794600\pi\)
−0.798929 + 0.601425i \(0.794600\pi\)
\(744\) 5.76005 0.211174
\(745\) 0.640380 0.0234617
\(746\) 23.0038 0.842229
\(747\) −2.77568 −0.101557
\(748\) −0.279961 −0.0102364
\(749\) −3.23972 −0.118377
\(750\) −2.76661 −0.101022
\(751\) 5.49291 0.200439 0.100220 0.994965i \(-0.468045\pi\)
0.100220 + 0.994965i \(0.468045\pi\)
\(752\) 42.8338 1.56199
\(753\) −23.4960 −0.856242
\(754\) −0.0371669 −0.00135354
\(755\) 7.01626 0.255348
\(756\) −0.660234 −0.0240125
\(757\) −10.2688 −0.373228 −0.186614 0.982433i \(-0.559751\pi\)
−0.186614 + 0.982433i \(0.559751\pi\)
\(758\) −47.1807 −1.71368
\(759\) −9.22238 −0.334751
\(760\) −10.7215 −0.388910
\(761\) 53.2524 1.93040 0.965200 0.261515i \(-0.0842219\pi\)
0.965200 + 0.261515i \(0.0842219\pi\)
\(762\) 52.8221 1.91354
\(763\) −1.52795 −0.0553156
\(764\) −0.147219 −0.00532621
\(765\) −1.44259 −0.0521569
\(766\) 13.2187 0.477612
\(767\) 16.1321 0.582495
\(768\) −6.48882 −0.234145
\(769\) 46.5471 1.67853 0.839266 0.543721i \(-0.182985\pi\)
0.839266 + 0.543721i \(0.182985\pi\)
\(770\) 1.12690 0.0406106
\(771\) 41.1711 1.48274
\(772\) 3.29771 0.118687
\(773\) −48.5510 −1.74626 −0.873129 0.487490i \(-0.837913\pi\)
−0.873129 + 0.487490i \(0.837913\pi\)
\(774\) −9.41085 −0.338266
\(775\) −1.12165 −0.0402907
\(776\) −31.7495 −1.13974
\(777\) 0.608587 0.0218329
\(778\) −36.4249 −1.30590
\(779\) 5.70892 0.204543
\(780\) 0.521337 0.0186669
\(781\) −9.16210 −0.327846
\(782\) 23.4855 0.839838
\(783\) 0.0607431 0.00217078
\(784\) −4.26694 −0.152391
\(785\) −20.0864 −0.716915
\(786\) −55.4068 −1.97629
\(787\) 36.6763 1.30737 0.653685 0.756767i \(-0.273222\pi\)
0.653685 + 0.756767i \(0.273222\pi\)
\(788\) 0.807549 0.0287677
\(789\) 33.0608 1.17700
\(790\) −19.5551 −0.695739
\(791\) 14.7035 0.522797
\(792\) −1.19300 −0.0423914
\(793\) 20.3199 0.721580
\(794\) −40.8915 −1.45118
\(795\) 21.8749 0.775821
\(796\) 1.47829 0.0523967
\(797\) −41.0353 −1.45355 −0.726773 0.686878i \(-0.758981\pi\)
−0.726773 + 0.686878i \(0.758981\pi\)
\(798\) −10.9141 −0.386356
\(799\) −25.3910 −0.898268
\(800\) 0.811986 0.0287081
\(801\) 1.96327 0.0693687
\(802\) 37.5407 1.32561
\(803\) 5.78504 0.204150
\(804\) −2.67090 −0.0941953
\(805\) −6.34157 −0.223511
\(806\) 3.15077 0.110981
\(807\) −12.6577 −0.445572
\(808\) −7.47191 −0.262861
\(809\) −18.8459 −0.662587 −0.331294 0.943528i \(-0.607485\pi\)
−0.331294 + 0.943528i \(0.607485\pi\)
\(810\) −15.2065 −0.534304
\(811\) −10.5096 −0.369043 −0.184521 0.982829i \(-0.559073\pi\)
−0.184521 + 0.982829i \(0.559073\pi\)
\(812\) −0.00190280 −6.67753e−5 0
\(813\) 55.1598 1.93454
\(814\) 0.362955 0.0127216
\(815\) −10.5575 −0.369812
\(816\) 20.3930 0.713897
\(817\) 44.4572 1.55536
\(818\) −35.0882 −1.22683
\(819\) −1.09421 −0.0382348
\(820\) −0.208119 −0.00726782
\(821\) −34.8324 −1.21566 −0.607829 0.794068i \(-0.707959\pi\)
−0.607829 + 0.794068i \(0.707959\pi\)
\(822\) 2.65194 0.0924971
\(823\) −11.5837 −0.403782 −0.201891 0.979408i \(-0.564709\pi\)
−0.201891 + 0.979408i \(0.564709\pi\)
\(824\) −1.58323 −0.0551543
\(825\) 1.45427 0.0506313
\(826\) 12.3117 0.428377
\(827\) −44.0885 −1.53311 −0.766553 0.642181i \(-0.778030\pi\)
−0.766553 + 0.642181i \(0.778030\pi\)
\(828\) −0.520149 −0.0180764
\(829\) 17.0857 0.593410 0.296705 0.954969i \(-0.404112\pi\)
0.296705 + 0.954969i \(0.404112\pi\)
\(830\) −7.12571 −0.247337
\(831\) −14.8869 −0.516422
\(832\) 14.0915 0.488536
\(833\) 2.52935 0.0876368
\(834\) −18.0043 −0.623439
\(835\) 18.1655 0.628644
\(836\) −0.436646 −0.0151017
\(837\) −5.14940 −0.177989
\(838\) 11.5786 0.399977
\(839\) 2.86237 0.0988199 0.0494100 0.998779i \(-0.484266\pi\)
0.0494100 + 0.998779i \(0.484266\pi\)
\(840\) −5.13535 −0.177186
\(841\) −28.9998 −0.999994
\(842\) 39.7584 1.37016
\(843\) 23.8532 0.821547
\(844\) −2.81083 −0.0967527
\(845\) 9.31927 0.320593
\(846\) 8.38296 0.288212
\(847\) 10.4076 0.357611
\(848\) −49.3978 −1.69633
\(849\) 30.0905 1.03270
\(850\) −3.70342 −0.127026
\(851\) −2.04251 −0.0700164
\(852\) −3.23486 −0.110824
\(853\) 37.8443 1.29576 0.647882 0.761741i \(-0.275655\pi\)
0.647882 + 0.761741i \(0.275655\pi\)
\(854\) 15.5077 0.530663
\(855\) −2.24996 −0.0769469
\(856\) 8.80487 0.300944
\(857\) −30.0978 −1.02812 −0.514061 0.857754i \(-0.671859\pi\)
−0.514061 + 0.857754i \(0.671859\pi\)
\(858\) −4.08514 −0.139464
\(859\) 6.33170 0.216035 0.108017 0.994149i \(-0.465550\pi\)
0.108017 + 0.994149i \(0.465550\pi\)
\(860\) −1.62069 −0.0552650
\(861\) 2.73444 0.0931895
\(862\) 37.8937 1.29066
\(863\) −9.95428 −0.338847 −0.169424 0.985543i \(-0.554191\pi\)
−0.169424 + 0.985543i \(0.554191\pi\)
\(864\) 3.72777 0.126821
\(865\) −10.6660 −0.362654
\(866\) −24.4382 −0.830445
\(867\) 20.0336 0.680376
\(868\) 0.161307 0.00547512
\(869\) 10.2792 0.348697
\(870\) −0.0366054 −0.00124104
\(871\) 18.8570 0.638945
\(872\) 4.15265 0.140626
\(873\) −6.66277 −0.225501
\(874\) 36.6295 1.23901
\(875\) 1.00000 0.0338062
\(876\) 2.04252 0.0690105
\(877\) 42.5212 1.43584 0.717920 0.696125i \(-0.245094\pi\)
0.717920 + 0.696125i \(0.245094\pi\)
\(878\) −39.3188 −1.32694
\(879\) −20.9101 −0.705281
\(880\) −3.28404 −0.110705
\(881\) −14.6939 −0.495051 −0.247525 0.968881i \(-0.579617\pi\)
−0.247525 + 0.968881i \(0.579617\pi\)
\(882\) −0.835078 −0.0281185
\(883\) 33.6629 1.13285 0.566424 0.824114i \(-0.308327\pi\)
0.566424 + 0.824114i \(0.308327\pi\)
\(884\) 0.697868 0.0234718
\(885\) 15.8883 0.534080
\(886\) 47.0867 1.58191
\(887\) −43.7898 −1.47032 −0.735159 0.677894i \(-0.762893\pi\)
−0.735159 + 0.677894i \(0.762893\pi\)
\(888\) −1.65401 −0.0555049
\(889\) −19.0927 −0.640349
\(890\) 5.04010 0.168945
\(891\) 7.99335 0.267787
\(892\) 2.41221 0.0807666
\(893\) −39.6014 −1.32521
\(894\) −1.77168 −0.0592540
\(895\) 13.4786 0.450542
\(896\) 12.3783 0.413531
\(897\) 22.9889 0.767577
\(898\) 5.45422 0.182010
\(899\) −0.0148406 −0.000494963 0
\(900\) 0.0820221 0.00273407
\(901\) 29.2819 0.975522
\(902\) 1.63079 0.0542994
\(903\) 21.2940 0.708619
\(904\) −39.9610 −1.32908
\(905\) 4.65420 0.154711
\(906\) −19.4113 −0.644897
\(907\) 53.9213 1.79043 0.895213 0.445638i \(-0.147023\pi\)
0.895213 + 0.445638i \(0.147023\pi\)
\(908\) 0.903859 0.0299956
\(909\) −1.56802 −0.0520078
\(910\) −2.80906 −0.0931193
\(911\) −52.9483 −1.75425 −0.877127 0.480259i \(-0.840543\pi\)
−0.877127 + 0.480259i \(0.840543\pi\)
\(912\) 31.8062 1.05321
\(913\) 3.74565 0.123963
\(914\) 33.0532 1.09330
\(915\) 20.0129 0.661605
\(916\) 0.143813 0.00475171
\(917\) 20.0269 0.661348
\(918\) −17.0021 −0.561153
\(919\) −4.10537 −0.135424 −0.0677119 0.997705i \(-0.521570\pi\)
−0.0677119 + 0.997705i \(0.521570\pi\)
\(920\) 17.2350 0.568222
\(921\) 62.2380 2.05081
\(922\) −39.5808 −1.30352
\(923\) 22.8386 0.751743
\(924\) −0.209143 −0.00688031
\(925\) 0.322083 0.0105900
\(926\) −6.32976 −0.208009
\(927\) −0.332248 −0.0109124
\(928\) 0.0107435 0.000352672 0
\(929\) −39.5635 −1.29804 −0.649018 0.760773i \(-0.724820\pi\)
−0.649018 + 0.760773i \(0.724820\pi\)
\(930\) 3.10316 0.101757
\(931\) 3.94494 0.129290
\(932\) 3.48168 0.114046
\(933\) 22.8874 0.749298
\(934\) −6.20308 −0.202971
\(935\) 1.94671 0.0636641
\(936\) 2.97383 0.0972026
\(937\) 30.4221 0.993848 0.496924 0.867794i \(-0.334463\pi\)
0.496924 + 0.867794i \(0.334463\pi\)
\(938\) 14.3913 0.469891
\(939\) −32.1403 −1.04886
\(940\) 1.44367 0.0470873
\(941\) −7.29449 −0.237793 −0.118897 0.992907i \(-0.537936\pi\)
−0.118897 + 0.992907i \(0.537936\pi\)
\(942\) 55.5713 1.81061
\(943\) −9.17720 −0.298851
\(944\) −35.8789 −1.16776
\(945\) 4.59093 0.149343
\(946\) 12.6995 0.412897
\(947\) 18.6095 0.604728 0.302364 0.953193i \(-0.402224\pi\)
0.302364 + 0.953193i \(0.402224\pi\)
\(948\) 3.62927 0.117873
\(949\) −14.4206 −0.468111
\(950\) −5.77609 −0.187401
\(951\) −62.9099 −2.03999
\(952\) −6.87423 −0.222795
\(953\) −48.0943 −1.55793 −0.778963 0.627070i \(-0.784254\pi\)
−0.778963 + 0.627070i \(0.784254\pi\)
\(954\) −9.66758 −0.312999
\(955\) 1.02369 0.0331258
\(956\) −3.05004 −0.0986453
\(957\) 0.0192417 0.000621995 0
\(958\) −21.6767 −0.700342
\(959\) −0.958552 −0.0309533
\(960\) 13.8786 0.447931
\(961\) −29.7419 −0.959416
\(962\) −0.904749 −0.0291703
\(963\) 1.84774 0.0595427
\(964\) −3.32109 −0.106965
\(965\) −22.9306 −0.738161
\(966\) 17.5447 0.564490
\(967\) 34.0401 1.09466 0.547328 0.836918i \(-0.315645\pi\)
0.547328 + 0.836918i \(0.315645\pi\)
\(968\) −28.2857 −0.909138
\(969\) −18.8540 −0.605679
\(970\) −17.1047 −0.549198
\(971\) 24.5832 0.788912 0.394456 0.918915i \(-0.370933\pi\)
0.394456 + 0.918915i \(0.370933\pi\)
\(972\) 0.841508 0.0269914
\(973\) 6.50772 0.208628
\(974\) −9.33408 −0.299083
\(975\) −3.62511 −0.116097
\(976\) −45.1930 −1.44659
\(977\) 48.4573 1.55029 0.775143 0.631785i \(-0.217678\pi\)
0.775143 + 0.631785i \(0.217678\pi\)
\(978\) 29.2084 0.933983
\(979\) −2.64934 −0.0846732
\(980\) −0.143813 −0.00459393
\(981\) 0.871453 0.0278233
\(982\) −44.8327 −1.43067
\(983\) −18.1849 −0.580007 −0.290003 0.957026i \(-0.593656\pi\)
−0.290003 + 0.957026i \(0.593656\pi\)
\(984\) −7.43162 −0.236911
\(985\) −5.61528 −0.178918
\(986\) −0.0490003 −0.00156049
\(987\) −18.9682 −0.603763
\(988\) 1.08844 0.0346279
\(989\) −71.4658 −2.27248
\(990\) −0.642716 −0.0204268
\(991\) 23.4407 0.744619 0.372310 0.928109i \(-0.378566\pi\)
0.372310 + 0.928109i \(0.378566\pi\)
\(992\) −0.910762 −0.0289167
\(993\) −1.68849 −0.0535828
\(994\) 17.4300 0.552845
\(995\) −10.2793 −0.325876
\(996\) 1.32247 0.0419042
\(997\) −21.4383 −0.678959 −0.339479 0.940613i \(-0.610251\pi\)
−0.339479 + 0.940613i \(0.610251\pi\)
\(998\) 63.0239 1.99499
\(999\) 1.47866 0.0467827
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 \(a_p\))