Properties

Label 6017.2.a.c.1.20
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 1.20
Character \(\chi\) = 6017.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.99930 q^{2}\) \(-0.450091 q^{3}\) \(+1.99721 q^{4}\) \(+2.88473 q^{5}\) \(+0.899867 q^{6}\) \(-0.362986 q^{7}\) \(+0.00557515 q^{8}\) \(-2.79742 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.99930 q^{2}\) \(-0.450091 q^{3}\) \(+1.99721 q^{4}\) \(+2.88473 q^{5}\) \(+0.899867 q^{6}\) \(-0.362986 q^{7}\) \(+0.00557515 q^{8}\) \(-2.79742 q^{9}\) \(-5.76745 q^{10}\) \(+1.00000 q^{11}\) \(-0.898926 q^{12}\) \(+2.94993 q^{13}\) \(+0.725718 q^{14}\) \(-1.29839 q^{15}\) \(-4.00557 q^{16}\) \(+4.78518 q^{17}\) \(+5.59289 q^{18}\) \(+5.95874 q^{19}\) \(+5.76142 q^{20}\) \(+0.163377 q^{21}\) \(-1.99930 q^{22}\) \(-6.31286 q^{23}\) \(-0.00250932 q^{24}\) \(+3.32167 q^{25}\) \(-5.89781 q^{26}\) \(+2.60936 q^{27}\) \(-0.724959 q^{28}\) \(-7.37252 q^{29}\) \(+2.59587 q^{30}\) \(-5.35187 q^{31}\) \(+7.99720 q^{32}\) \(-0.450091 q^{33}\) \(-9.56701 q^{34}\) \(-1.04712 q^{35}\) \(-5.58704 q^{36}\) \(-5.10578 q^{37}\) \(-11.9133 q^{38}\) \(-1.32774 q^{39}\) \(+0.0160828 q^{40}\) \(-1.57761 q^{41}\) \(-0.326639 q^{42}\) \(-2.22083 q^{43}\) \(+1.99721 q^{44}\) \(-8.06980 q^{45}\) \(+12.6213 q^{46}\) \(-6.25798 q^{47}\) \(+1.80287 q^{48}\) \(-6.86824 q^{49}\) \(-6.64102 q^{50}\) \(-2.15376 q^{51}\) \(+5.89164 q^{52}\) \(+10.2942 q^{53}\) \(-5.21691 q^{54}\) \(+2.88473 q^{55}\) \(-0.00202370 q^{56}\) \(-2.68197 q^{57}\) \(+14.7399 q^{58}\) \(+1.54222 q^{59}\) \(-2.59316 q^{60}\) \(-7.30567 q^{61}\) \(+10.7000 q^{62}\) \(+1.01542 q^{63}\) \(-7.97768 q^{64}\) \(+8.50976 q^{65}\) \(+0.899867 q^{66}\) \(+4.96765 q^{67}\) \(+9.55701 q^{68}\) \(+2.84136 q^{69}\) \(+2.09350 q^{70}\) \(-1.36024 q^{71}\) \(-0.0155960 q^{72}\) \(+2.67836 q^{73}\) \(+10.2080 q^{74}\) \(-1.49505 q^{75}\) \(+11.9009 q^{76}\) \(-0.362986 q^{77}\) \(+2.65455 q^{78}\) \(-13.9977 q^{79}\) \(-11.5550 q^{80}\) \(+7.21781 q^{81}\) \(+3.15411 q^{82}\) \(-13.8090 q^{83}\) \(+0.326297 q^{84}\) \(+13.8039 q^{85}\) \(+4.44012 q^{86}\) \(+3.31830 q^{87}\) \(+0.00557515 q^{88}\) \(-13.8671 q^{89}\) \(+16.1340 q^{90}\) \(-1.07078 q^{91}\) \(-12.6081 q^{92}\) \(+2.40883 q^{93}\) \(+12.5116 q^{94}\) \(+17.1894 q^{95}\) \(-3.59946 q^{96}\) \(-1.81081 q^{97}\) \(+13.7317 q^{98}\) \(-2.79742 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(106q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 66q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(106q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 66q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut -\mathstrut 30q^{10} \) \(\mathstrut +\mathstrut 106q^{11} \) \(\mathstrut -\mathstrut 26q^{12} \) \(\mathstrut -\mathstrut 72q^{13} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut -\mathstrut 46q^{15} \) \(\mathstrut +\mathstrut 75q^{16} \) \(\mathstrut -\mathstrut 65q^{17} \) \(\mathstrut -\mathstrut 37q^{18} \) \(\mathstrut -\mathstrut 63q^{19} \) \(\mathstrut -\mathstrut 25q^{20} \) \(\mathstrut -\mathstrut 27q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut -\mathstrut 23q^{23} \) \(\mathstrut -\mathstrut 56q^{24} \) \(\mathstrut +\mathstrut 74q^{25} \) \(\mathstrut +\mathstrut 2q^{26} \) \(\mathstrut -\mathstrut 54q^{27} \) \(\mathstrut -\mathstrut 115q^{28} \) \(\mathstrut -\mathstrut 45q^{29} \) \(\mathstrut -\mathstrut 14q^{30} \) \(\mathstrut -\mathstrut 89q^{31} \) \(\mathstrut -\mathstrut 96q^{32} \) \(\mathstrut -\mathstrut 15q^{33} \) \(\mathstrut -\mathstrut 26q^{34} \) \(\mathstrut -\mathstrut 52q^{35} \) \(\mathstrut +\mathstrut 91q^{36} \) \(\mathstrut -\mathstrut 35q^{37} \) \(\mathstrut +\mathstrut 7q^{38} \) \(\mathstrut -\mathstrut 34q^{39} \) \(\mathstrut -\mathstrut 74q^{40} \) \(\mathstrut -\mathstrut 32q^{41} \) \(\mathstrut -\mathstrut 94q^{43} \) \(\mathstrut +\mathstrut 93q^{44} \) \(\mathstrut -\mathstrut 46q^{45} \) \(\mathstrut -\mathstrut 20q^{46} \) \(\mathstrut -\mathstrut 105q^{47} \) \(\mathstrut -\mathstrut 57q^{48} \) \(\mathstrut +\mathstrut 80q^{49} \) \(\mathstrut -\mathstrut 60q^{50} \) \(\mathstrut -\mathstrut 36q^{51} \) \(\mathstrut -\mathstrut 137q^{52} \) \(\mathstrut -\mathstrut 61q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 32q^{56} \) \(\mathstrut -\mathstrut 71q^{57} \) \(\mathstrut -\mathstrut 28q^{58} \) \(\mathstrut -\mathstrut 15q^{59} \) \(\mathstrut -\mathstrut 21q^{60} \) \(\mathstrut -\mathstrut 80q^{61} \) \(\mathstrut -\mathstrut 84q^{62} \) \(\mathstrut -\mathstrut 182q^{63} \) \(\mathstrut +\mathstrut 55q^{64} \) \(\mathstrut -\mathstrut 73q^{65} \) \(\mathstrut -\mathstrut 22q^{66} \) \(\mathstrut -\mathstrut 58q^{67} \) \(\mathstrut -\mathstrut 145q^{68} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 39q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut -\mathstrut 100q^{72} \) \(\mathstrut -\mathstrut 155q^{73} \) \(\mathstrut -\mathstrut 15q^{74} \) \(\mathstrut -\mathstrut 15q^{75} \) \(\mathstrut -\mathstrut 132q^{76} \) \(\mathstrut -\mathstrut 66q^{77} \) \(\mathstrut -\mathstrut 45q^{78} \) \(\mathstrut -\mathstrut 50q^{79} \) \(\mathstrut -\mathstrut 28q^{80} \) \(\mathstrut +\mathstrut 114q^{81} \) \(\mathstrut -\mathstrut 57q^{82} \) \(\mathstrut -\mathstrut 96q^{83} \) \(\mathstrut -\mathstrut 27q^{84} \) \(\mathstrut -\mathstrut 74q^{85} \) \(\mathstrut +\mathstrut 54q^{86} \) \(\mathstrut -\mathstrut 182q^{87} \) \(\mathstrut -\mathstrut 39q^{88} \) \(\mathstrut +\mathstrut 9q^{89} \) \(\mathstrut -\mathstrut 53q^{90} \) \(\mathstrut +\mathstrut 6q^{91} \) \(\mathstrut -\mathstrut 18q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut -\mathstrut 33q^{94} \) \(\mathstrut -\mathstrut 49q^{95} \) \(\mathstrut -\mathstrut 56q^{96} \) \(\mathstrut -\mathstrut 102q^{97} \) \(\mathstrut -\mathstrut 76q^{98} \) \(\mathstrut +\mathstrut 97q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.99930 −1.41372 −0.706860 0.707353i \(-0.749889\pi\)
−0.706860 + 0.707353i \(0.749889\pi\)
\(3\) −0.450091 −0.259860 −0.129930 0.991523i \(-0.541475\pi\)
−0.129930 + 0.991523i \(0.541475\pi\)
\(4\) 1.99721 0.998606
\(5\) 2.88473 1.29009 0.645045 0.764144i \(-0.276839\pi\)
0.645045 + 0.764144i \(0.276839\pi\)
\(6\) 0.899867 0.367369
\(7\) −0.362986 −0.137196 −0.0685979 0.997644i \(-0.521853\pi\)
−0.0685979 + 0.997644i \(0.521853\pi\)
\(8\) 0.00557515 0.00197111
\(9\) −2.79742 −0.932473
\(10\) −5.76745 −1.82383
\(11\) 1.00000 0.301511
\(12\) −0.898926 −0.259498
\(13\) 2.94993 0.818164 0.409082 0.912498i \(-0.365849\pi\)
0.409082 + 0.912498i \(0.365849\pi\)
\(14\) 0.725718 0.193956
\(15\) −1.29839 −0.335243
\(16\) −4.00557 −1.00139
\(17\) 4.78518 1.16058 0.580288 0.814412i \(-0.302940\pi\)
0.580288 + 0.814412i \(0.302940\pi\)
\(18\) 5.59289 1.31826
\(19\) 5.95874 1.36703 0.683515 0.729937i \(-0.260451\pi\)
0.683515 + 0.729937i \(0.260451\pi\)
\(20\) 5.76142 1.28829
\(21\) 0.163377 0.0356517
\(22\) −1.99930 −0.426253
\(23\) −6.31286 −1.31632 −0.658161 0.752877i \(-0.728666\pi\)
−0.658161 + 0.752877i \(0.728666\pi\)
\(24\) −0.00250932 −0.000512214 0
\(25\) 3.32167 0.664334
\(26\) −5.89781 −1.15666
\(27\) 2.60936 0.502172
\(28\) −0.724959 −0.137004
\(29\) −7.37252 −1.36904 −0.684521 0.728993i \(-0.739989\pi\)
−0.684521 + 0.728993i \(0.739989\pi\)
\(30\) 2.59587 0.473940
\(31\) −5.35187 −0.961225 −0.480612 0.876933i \(-0.659586\pi\)
−0.480612 + 0.876933i \(0.659586\pi\)
\(32\) 7.99720 1.41372
\(33\) −0.450091 −0.0783507
\(34\) −9.56701 −1.64073
\(35\) −1.04712 −0.176995
\(36\) −5.58704 −0.931173
\(37\) −5.10578 −0.839385 −0.419693 0.907666i \(-0.637862\pi\)
−0.419693 + 0.907666i \(0.637862\pi\)
\(38\) −11.9133 −1.93260
\(39\) −1.32774 −0.212608
\(40\) 0.0160828 0.00254292
\(41\) −1.57761 −0.246381 −0.123190 0.992383i \(-0.539313\pi\)
−0.123190 + 0.992383i \(0.539313\pi\)
\(42\) −0.326639 −0.0504015
\(43\) −2.22083 −0.338674 −0.169337 0.985558i \(-0.554163\pi\)
−0.169337 + 0.985558i \(0.554163\pi\)
\(44\) 1.99721 0.301091
\(45\) −8.06980 −1.20297
\(46\) 12.6213 1.86091
\(47\) −6.25798 −0.912820 −0.456410 0.889770i \(-0.650865\pi\)
−0.456410 + 0.889770i \(0.650865\pi\)
\(48\) 1.80287 0.260222
\(49\) −6.86824 −0.981177
\(50\) −6.64102 −0.939182
\(51\) −2.15376 −0.301587
\(52\) 5.89164 0.817023
\(53\) 10.2942 1.41402 0.707011 0.707203i \(-0.250043\pi\)
0.707011 + 0.707203i \(0.250043\pi\)
\(54\) −5.21691 −0.709931
\(55\) 2.88473 0.388977
\(56\) −0.00202370 −0.000270428 0
\(57\) −2.68197 −0.355236
\(58\) 14.7399 1.93544
\(59\) 1.54222 0.200780 0.100390 0.994948i \(-0.467991\pi\)
0.100390 + 0.994948i \(0.467991\pi\)
\(60\) −2.59316 −0.334775
\(61\) −7.30567 −0.935395 −0.467698 0.883889i \(-0.654916\pi\)
−0.467698 + 0.883889i \(0.654916\pi\)
\(62\) 10.7000 1.35890
\(63\) 1.01542 0.127931
\(64\) −7.97768 −0.997210
\(65\) 8.50976 1.05551
\(66\) 0.899867 0.110766
\(67\) 4.96765 0.606895 0.303447 0.952848i \(-0.401862\pi\)
0.303447 + 0.952848i \(0.401862\pi\)
\(68\) 9.55701 1.15896
\(69\) 2.84136 0.342060
\(70\) 2.09350 0.250221
\(71\) −1.36024 −0.161431 −0.0807157 0.996737i \(-0.525721\pi\)
−0.0807157 + 0.996737i \(0.525721\pi\)
\(72\) −0.0155960 −0.00183801
\(73\) 2.67836 0.313479 0.156739 0.987640i \(-0.449902\pi\)
0.156739 + 0.987640i \(0.449902\pi\)
\(74\) 10.2080 1.18666
\(75\) −1.49505 −0.172634
\(76\) 11.9009 1.36512
\(77\) −0.362986 −0.0413661
\(78\) 2.65455 0.300568
\(79\) −13.9977 −1.57487 −0.787433 0.616400i \(-0.788590\pi\)
−0.787433 + 0.616400i \(0.788590\pi\)
\(80\) −11.5550 −1.29189
\(81\) 7.21781 0.801978
\(82\) 3.15411 0.348313
\(83\) −13.8090 −1.51573 −0.757865 0.652412i \(-0.773757\pi\)
−0.757865 + 0.652412i \(0.773757\pi\)
\(84\) 0.326297 0.0356020
\(85\) 13.8039 1.49725
\(86\) 4.44012 0.478791
\(87\) 3.31830 0.355759
\(88\) 0.00557515 0.000594313 0
\(89\) −13.8671 −1.46990 −0.734952 0.678119i \(-0.762795\pi\)
−0.734952 + 0.678119i \(0.762795\pi\)
\(90\) 16.1340 1.70067
\(91\) −1.07078 −0.112249
\(92\) −12.6081 −1.31449
\(93\) 2.40883 0.249784
\(94\) 12.5116 1.29047
\(95\) 17.1894 1.76359
\(96\) −3.59946 −0.367369
\(97\) −1.81081 −0.183860 −0.0919298 0.995765i \(-0.529304\pi\)
−0.0919298 + 0.995765i \(0.529304\pi\)
\(98\) 13.7317 1.38711
\(99\) −2.79742 −0.281151
\(100\) 6.63407 0.663407
\(101\) 0.721995 0.0718412 0.0359206 0.999355i \(-0.488564\pi\)
0.0359206 + 0.999355i \(0.488564\pi\)
\(102\) 4.30602 0.426360
\(103\) −1.58775 −0.156446 −0.0782228 0.996936i \(-0.524925\pi\)
−0.0782228 + 0.996936i \(0.524925\pi\)
\(104\) 0.0164463 0.00161269
\(105\) 0.471297 0.0459939
\(106\) −20.5813 −1.99903
\(107\) −12.0469 −1.16462 −0.582310 0.812967i \(-0.697851\pi\)
−0.582310 + 0.812967i \(0.697851\pi\)
\(108\) 5.21145 0.501472
\(109\) 10.1318 0.970447 0.485223 0.874390i \(-0.338738\pi\)
0.485223 + 0.874390i \(0.338738\pi\)
\(110\) −5.76745 −0.549905
\(111\) 2.29806 0.218123
\(112\) 1.45396 0.137387
\(113\) −4.46767 −0.420283 −0.210142 0.977671i \(-0.567393\pi\)
−0.210142 + 0.977671i \(0.567393\pi\)
\(114\) 5.36208 0.502205
\(115\) −18.2109 −1.69818
\(116\) −14.7245 −1.36713
\(117\) −8.25219 −0.762916
\(118\) −3.08336 −0.283846
\(119\) −1.73695 −0.159226
\(120\) −0.00723872 −0.000660802 0
\(121\) 1.00000 0.0909091
\(122\) 14.6062 1.32239
\(123\) 0.710066 0.0640245
\(124\) −10.6888 −0.959884
\(125\) −4.84154 −0.433040
\(126\) −2.03014 −0.180859
\(127\) −19.9414 −1.76951 −0.884756 0.466054i \(-0.845675\pi\)
−0.884756 + 0.466054i \(0.845675\pi\)
\(128\) −0.0446012 −0.00394222
\(129\) 0.999577 0.0880078
\(130\) −17.0136 −1.49219
\(131\) −9.76658 −0.853310 −0.426655 0.904414i \(-0.640308\pi\)
−0.426655 + 0.904414i \(0.640308\pi\)
\(132\) −0.898926 −0.0782415
\(133\) −2.16294 −0.187551
\(134\) −9.93183 −0.857980
\(135\) 7.52731 0.647848
\(136\) 0.0266781 0.00228763
\(137\) 5.99462 0.512155 0.256078 0.966656i \(-0.417570\pi\)
0.256078 + 0.966656i \(0.417570\pi\)
\(138\) −5.68074 −0.483577
\(139\) 16.4970 1.39926 0.699629 0.714506i \(-0.253349\pi\)
0.699629 + 0.714506i \(0.253349\pi\)
\(140\) −2.09131 −0.176748
\(141\) 2.81666 0.237205
\(142\) 2.71954 0.228219
\(143\) 2.94993 0.246686
\(144\) 11.2053 0.933771
\(145\) −21.2677 −1.76619
\(146\) −5.35486 −0.443172
\(147\) 3.09133 0.254969
\(148\) −10.1973 −0.838215
\(149\) 7.46531 0.611582 0.305791 0.952099i \(-0.401079\pi\)
0.305791 + 0.952099i \(0.401079\pi\)
\(150\) 2.98906 0.244056
\(151\) −21.4943 −1.74918 −0.874592 0.484859i \(-0.838871\pi\)
−0.874592 + 0.484859i \(0.838871\pi\)
\(152\) 0.0332209 0.00269457
\(153\) −13.3861 −1.08221
\(154\) 0.725718 0.0584801
\(155\) −15.4387 −1.24007
\(156\) −2.65177 −0.212312
\(157\) 3.64099 0.290583 0.145291 0.989389i \(-0.453588\pi\)
0.145291 + 0.989389i \(0.453588\pi\)
\(158\) 27.9857 2.22642
\(159\) −4.63334 −0.367448
\(160\) 23.0698 1.82382
\(161\) 2.29148 0.180594
\(162\) −14.4306 −1.13377
\(163\) 13.0863 1.02500 0.512500 0.858687i \(-0.328720\pi\)
0.512500 + 0.858687i \(0.328720\pi\)
\(164\) −3.15081 −0.246037
\(165\) −1.29839 −0.101080
\(166\) 27.6083 2.14282
\(167\) 5.73006 0.443405 0.221703 0.975114i \(-0.428839\pi\)
0.221703 + 0.975114i \(0.428839\pi\)
\(168\) 0.000910849 0 7.02735e−5 0
\(169\) −4.29790 −0.330608
\(170\) −27.5983 −2.11669
\(171\) −16.6691 −1.27472
\(172\) −4.43548 −0.338202
\(173\) −8.11004 −0.616595 −0.308297 0.951290i \(-0.599759\pi\)
−0.308297 + 0.951290i \(0.599759\pi\)
\(174\) −6.63429 −0.502944
\(175\) −1.20572 −0.0911437
\(176\) −4.00557 −0.301931
\(177\) −0.694138 −0.0521746
\(178\) 27.7244 2.07803
\(179\) −2.25991 −0.168914 −0.0844568 0.996427i \(-0.526916\pi\)
−0.0844568 + 0.996427i \(0.526916\pi\)
\(180\) −16.1171 −1.20130
\(181\) −13.5140 −1.00449 −0.502243 0.864726i \(-0.667492\pi\)
−0.502243 + 0.864726i \(0.667492\pi\)
\(182\) 2.14082 0.158688
\(183\) 3.28821 0.243072
\(184\) −0.0351952 −0.00259462
\(185\) −14.7288 −1.08288
\(186\) −4.81598 −0.353124
\(187\) 4.78518 0.349927
\(188\) −12.4985 −0.911547
\(189\) −0.947162 −0.0688959
\(190\) −34.3667 −2.49323
\(191\) −11.9490 −0.864602 −0.432301 0.901729i \(-0.642298\pi\)
−0.432301 + 0.901729i \(0.642298\pi\)
\(192\) 3.59068 0.259135
\(193\) 10.5114 0.756628 0.378314 0.925677i \(-0.376504\pi\)
0.378314 + 0.925677i \(0.376504\pi\)
\(194\) 3.62035 0.259926
\(195\) −3.83016 −0.274284
\(196\) −13.7173 −0.979809
\(197\) 1.58035 0.112595 0.0562976 0.998414i \(-0.482070\pi\)
0.0562976 + 0.998414i \(0.482070\pi\)
\(198\) 5.59289 0.397469
\(199\) 19.7211 1.39799 0.698996 0.715126i \(-0.253631\pi\)
0.698996 + 0.715126i \(0.253631\pi\)
\(200\) 0.0185188 0.00130948
\(201\) −2.23589 −0.157708
\(202\) −1.44349 −0.101563
\(203\) 2.67612 0.187827
\(204\) −4.30152 −0.301167
\(205\) −4.55097 −0.317853
\(206\) 3.17439 0.221170
\(207\) 17.6597 1.22744
\(208\) −11.8162 −0.819303
\(209\) 5.95874 0.412175
\(210\) −0.942266 −0.0650225
\(211\) 26.9365 1.85439 0.927193 0.374585i \(-0.122215\pi\)
0.927193 + 0.374585i \(0.122215\pi\)
\(212\) 20.5598 1.41205
\(213\) 0.612233 0.0419495
\(214\) 24.0854 1.64645
\(215\) −6.40651 −0.436920
\(216\) 0.0145476 0.000989839 0
\(217\) 1.94265 0.131876
\(218\) −20.2565 −1.37194
\(219\) −1.20551 −0.0814606
\(220\) 5.76142 0.388435
\(221\) 14.1159 0.949541
\(222\) −4.59453 −0.308364
\(223\) 24.8508 1.66413 0.832067 0.554676i \(-0.187158\pi\)
0.832067 + 0.554676i \(0.187158\pi\)
\(224\) −2.90287 −0.193956
\(225\) −9.29209 −0.619473
\(226\) 8.93223 0.594163
\(227\) 12.0407 0.799167 0.399583 0.916697i \(-0.369155\pi\)
0.399583 + 0.916697i \(0.369155\pi\)
\(228\) −5.35647 −0.354741
\(229\) −25.2139 −1.66618 −0.833092 0.553135i \(-0.813431\pi\)
−0.833092 + 0.553135i \(0.813431\pi\)
\(230\) 36.4091 2.40075
\(231\) 0.163377 0.0107494
\(232\) −0.0411029 −0.00269854
\(233\) 19.2270 1.25960 0.629802 0.776756i \(-0.283136\pi\)
0.629802 + 0.776756i \(0.283136\pi\)
\(234\) 16.4986 1.07855
\(235\) −18.0526 −1.17762
\(236\) 3.08014 0.200500
\(237\) 6.30024 0.409245
\(238\) 3.47269 0.225101
\(239\) −7.08298 −0.458160 −0.229080 0.973408i \(-0.573572\pi\)
−0.229080 + 0.973408i \(0.573572\pi\)
\(240\) 5.20079 0.335710
\(241\) 4.87192 0.313828 0.156914 0.987612i \(-0.449845\pi\)
0.156914 + 0.987612i \(0.449845\pi\)
\(242\) −1.99930 −0.128520
\(243\) −11.0768 −0.710574
\(244\) −14.5910 −0.934091
\(245\) −19.8130 −1.26581
\(246\) −1.41964 −0.0905127
\(247\) 17.5779 1.11845
\(248\) −0.0298375 −0.00189468
\(249\) 6.21528 0.393877
\(250\) 9.67970 0.612198
\(251\) 2.75389 0.173824 0.0869120 0.996216i \(-0.472300\pi\)
0.0869120 + 0.996216i \(0.472300\pi\)
\(252\) 2.02801 0.127753
\(253\) −6.31286 −0.396886
\(254\) 39.8689 2.50160
\(255\) −6.21302 −0.389075
\(256\) 16.0445 1.00278
\(257\) 21.0756 1.31466 0.657329 0.753604i \(-0.271686\pi\)
0.657329 + 0.753604i \(0.271686\pi\)
\(258\) −1.99846 −0.124418
\(259\) 1.85333 0.115160
\(260\) 16.9958 1.05403
\(261\) 20.6240 1.27659
\(262\) 19.5264 1.20634
\(263\) −18.3199 −1.12965 −0.564827 0.825210i \(-0.691057\pi\)
−0.564827 + 0.825210i \(0.691057\pi\)
\(264\) −0.00250932 −0.000154438 0
\(265\) 29.6961 1.82422
\(266\) 4.32437 0.265144
\(267\) 6.24143 0.381969
\(268\) 9.92145 0.606049
\(269\) 3.33904 0.203585 0.101792 0.994806i \(-0.467542\pi\)
0.101792 + 0.994806i \(0.467542\pi\)
\(270\) −15.0494 −0.915876
\(271\) 19.5346 1.18664 0.593322 0.804965i \(-0.297816\pi\)
0.593322 + 0.804965i \(0.297816\pi\)
\(272\) −19.1674 −1.16219
\(273\) 0.481950 0.0291689
\(274\) −11.9851 −0.724045
\(275\) 3.32167 0.200304
\(276\) 5.67480 0.341583
\(277\) −12.1734 −0.731426 −0.365713 0.930728i \(-0.619175\pi\)
−0.365713 + 0.930728i \(0.619175\pi\)
\(278\) −32.9825 −1.97816
\(279\) 14.9714 0.896316
\(280\) −0.00583783 −0.000348877 0
\(281\) 0.912342 0.0544258 0.0272129 0.999630i \(-0.491337\pi\)
0.0272129 + 0.999630i \(0.491337\pi\)
\(282\) −5.63135 −0.335342
\(283\) −28.0355 −1.66654 −0.833270 0.552866i \(-0.813534\pi\)
−0.833270 + 0.552866i \(0.813534\pi\)
\(284\) −2.71670 −0.161206
\(285\) −7.73677 −0.458287
\(286\) −5.89781 −0.348745
\(287\) 0.572649 0.0338024
\(288\) −22.3715 −1.31825
\(289\) 5.89790 0.346935
\(290\) 42.5206 2.49690
\(291\) 0.815027 0.0477778
\(292\) 5.34926 0.313042
\(293\) −4.25992 −0.248867 −0.124433 0.992228i \(-0.539711\pi\)
−0.124433 + 0.992228i \(0.539711\pi\)
\(294\) −6.18051 −0.360454
\(295\) 4.44888 0.259024
\(296\) −0.0284655 −0.00165452
\(297\) 2.60936 0.151411
\(298\) −14.9254 −0.864606
\(299\) −18.6225 −1.07697
\(300\) −2.98593 −0.172393
\(301\) 0.806132 0.0464646
\(302\) 42.9737 2.47286
\(303\) −0.324963 −0.0186687
\(304\) −23.8682 −1.36893
\(305\) −21.0749 −1.20674
\(306\) 26.7629 1.52994
\(307\) 2.23668 0.127654 0.0638269 0.997961i \(-0.479669\pi\)
0.0638269 + 0.997961i \(0.479669\pi\)
\(308\) −0.724959 −0.0413084
\(309\) 0.714631 0.0406539
\(310\) 30.8666 1.75311
\(311\) −3.46332 −0.196387 −0.0981936 0.995167i \(-0.531306\pi\)
−0.0981936 + 0.995167i \(0.531306\pi\)
\(312\) −0.00740233 −0.000419075 0
\(313\) 10.2811 0.581122 0.290561 0.956856i \(-0.406158\pi\)
0.290561 + 0.956856i \(0.406158\pi\)
\(314\) −7.27944 −0.410802
\(315\) 2.92922 0.165043
\(316\) −27.9564 −1.57267
\(317\) 6.21650 0.349153 0.174577 0.984644i \(-0.444144\pi\)
0.174577 + 0.984644i \(0.444144\pi\)
\(318\) 9.26345 0.519468
\(319\) −7.37252 −0.412782
\(320\) −23.0134 −1.28649
\(321\) 5.42220 0.302638
\(322\) −4.58136 −0.255309
\(323\) 28.5136 1.58654
\(324\) 14.4155 0.800860
\(325\) 9.79869 0.543534
\(326\) −26.1635 −1.44906
\(327\) −4.56021 −0.252180
\(328\) −0.00879539 −0.000485644 0
\(329\) 2.27156 0.125235
\(330\) 2.59587 0.142898
\(331\) 9.83914 0.540808 0.270404 0.962747i \(-0.412843\pi\)
0.270404 + 0.962747i \(0.412843\pi\)
\(332\) −27.5794 −1.51362
\(333\) 14.2830 0.782704
\(334\) −11.4561 −0.626851
\(335\) 14.3303 0.782949
\(336\) −0.654416 −0.0357013
\(337\) 6.62815 0.361058 0.180529 0.983570i \(-0.442219\pi\)
0.180529 + 0.983570i \(0.442219\pi\)
\(338\) 8.59281 0.467387
\(339\) 2.01086 0.109215
\(340\) 27.5694 1.49516
\(341\) −5.35187 −0.289820
\(342\) 33.3266 1.80209
\(343\) 5.03397 0.271809
\(344\) −0.0123815 −0.000667565 0
\(345\) 8.19656 0.441288
\(346\) 16.2144 0.871693
\(347\) −17.2173 −0.924273 −0.462137 0.886809i \(-0.652917\pi\)
−0.462137 + 0.886809i \(0.652917\pi\)
\(348\) 6.62735 0.355263
\(349\) −34.5913 −1.85163 −0.925814 0.377979i \(-0.876619\pi\)
−0.925814 + 0.377979i \(0.876619\pi\)
\(350\) 2.41060 0.128852
\(351\) 7.69744 0.410859
\(352\) 7.99720 0.426252
\(353\) −5.61003 −0.298592 −0.149296 0.988793i \(-0.547701\pi\)
−0.149296 + 0.988793i \(0.547701\pi\)
\(354\) 1.38779 0.0737603
\(355\) −3.92394 −0.208261
\(356\) −27.6954 −1.46785
\(357\) 0.781785 0.0413765
\(358\) 4.51825 0.238797
\(359\) 15.1262 0.798332 0.399166 0.916879i \(-0.369300\pi\)
0.399166 + 0.916879i \(0.369300\pi\)
\(360\) −0.0449903 −0.00237120
\(361\) 16.5066 0.868769
\(362\) 27.0185 1.42006
\(363\) −0.450091 −0.0236236
\(364\) −2.13858 −0.112092
\(365\) 7.72636 0.404416
\(366\) −6.57413 −0.343636
\(367\) −24.2695 −1.26686 −0.633429 0.773800i \(-0.718353\pi\)
−0.633429 + 0.773800i \(0.718353\pi\)
\(368\) 25.2866 1.31816
\(369\) 4.41323 0.229743
\(370\) 29.4473 1.53089
\(371\) −3.73666 −0.193998
\(372\) 4.81094 0.249436
\(373\) −27.7565 −1.43718 −0.718588 0.695436i \(-0.755211\pi\)
−0.718588 + 0.695436i \(0.755211\pi\)
\(374\) −9.56701 −0.494698
\(375\) 2.17913 0.112530
\(376\) −0.0348892 −0.00179927
\(377\) −21.7484 −1.12010
\(378\) 1.89366 0.0973995
\(379\) −17.5987 −0.903986 −0.451993 0.892021i \(-0.649287\pi\)
−0.451993 + 0.892021i \(0.649287\pi\)
\(380\) 34.3308 1.76113
\(381\) 8.97544 0.459826
\(382\) 23.8898 1.22231
\(383\) −0.178230 −0.00910710 −0.00455355 0.999990i \(-0.501449\pi\)
−0.00455355 + 0.999990i \(0.501449\pi\)
\(384\) 0.0200746 0.00102443
\(385\) −1.04712 −0.0533660
\(386\) −21.0155 −1.06966
\(387\) 6.21260 0.315804
\(388\) −3.61657 −0.183603
\(389\) 35.8756 1.81896 0.909482 0.415743i \(-0.136478\pi\)
0.909482 + 0.415743i \(0.136478\pi\)
\(390\) 7.65765 0.387760
\(391\) −30.2082 −1.52769
\(392\) −0.0382915 −0.00193401
\(393\) 4.39585 0.221741
\(394\) −3.15960 −0.159178
\(395\) −40.3796 −2.03172
\(396\) −5.58704 −0.280759
\(397\) 1.08125 0.0542663 0.0271331 0.999632i \(-0.491362\pi\)
0.0271331 + 0.999632i \(0.491362\pi\)
\(398\) −39.4284 −1.97637
\(399\) 0.973518 0.0487369
\(400\) −13.3052 −0.665258
\(401\) 8.17621 0.408301 0.204150 0.978940i \(-0.434557\pi\)
0.204150 + 0.978940i \(0.434557\pi\)
\(402\) 4.47023 0.222955
\(403\) −15.7877 −0.786439
\(404\) 1.44198 0.0717411
\(405\) 20.8214 1.03462
\(406\) −5.35037 −0.265534
\(407\) −5.10578 −0.253084
\(408\) −0.0120076 −0.000594462 0
\(409\) 8.35355 0.413057 0.206528 0.978441i \(-0.433783\pi\)
0.206528 + 0.978441i \(0.433783\pi\)
\(410\) 9.09876 0.449356
\(411\) −2.69812 −0.133089
\(412\) −3.17107 −0.156227
\(413\) −0.559803 −0.0275461
\(414\) −35.3071 −1.73525
\(415\) −39.8351 −1.95543
\(416\) 23.5912 1.15665
\(417\) −7.42515 −0.363611
\(418\) −11.9133 −0.582700
\(419\) 28.4073 1.38779 0.693893 0.720078i \(-0.255894\pi\)
0.693893 + 0.720078i \(0.255894\pi\)
\(420\) 0.941280 0.0459298
\(421\) −10.7396 −0.523415 −0.261707 0.965147i \(-0.584286\pi\)
−0.261707 + 0.965147i \(0.584286\pi\)
\(422\) −53.8542 −2.62158
\(423\) 17.5062 0.851180
\(424\) 0.0573919 0.00278720
\(425\) 15.8948 0.771009
\(426\) −1.22404 −0.0593049
\(427\) 2.65185 0.128332
\(428\) −24.0602 −1.16300
\(429\) −1.32774 −0.0641037
\(430\) 12.8086 0.617683
\(431\) 15.3331 0.738567 0.369284 0.929317i \(-0.379603\pi\)
0.369284 + 0.929317i \(0.379603\pi\)
\(432\) −10.4520 −0.502871
\(433\) 9.93526 0.477458 0.238729 0.971086i \(-0.423269\pi\)
0.238729 + 0.971086i \(0.423269\pi\)
\(434\) −3.88395 −0.186436
\(435\) 9.57240 0.458962
\(436\) 20.2353 0.969094
\(437\) −37.6167 −1.79945
\(438\) 2.41017 0.115163
\(439\) −18.5476 −0.885229 −0.442615 0.896712i \(-0.645949\pi\)
−0.442615 + 0.896712i \(0.645949\pi\)
\(440\) 0.0160828 0.000766718 0
\(441\) 19.2133 0.914921
\(442\) −28.2220 −1.34239
\(443\) 21.0964 1.00232 0.501161 0.865354i \(-0.332906\pi\)
0.501161 + 0.865354i \(0.332906\pi\)
\(444\) 4.58972 0.217819
\(445\) −40.0027 −1.89631
\(446\) −49.6843 −2.35262
\(447\) −3.36006 −0.158926
\(448\) 2.89578 0.136813
\(449\) 6.32141 0.298326 0.149163 0.988813i \(-0.452342\pi\)
0.149163 + 0.988813i \(0.452342\pi\)
\(450\) 18.5777 0.875762
\(451\) −1.57761 −0.0742866
\(452\) −8.92289 −0.419697
\(453\) 9.67440 0.454543
\(454\) −24.0729 −1.12980
\(455\) −3.08892 −0.144811
\(456\) −0.0149524 −0.000700211 0
\(457\) 32.9867 1.54305 0.771526 0.636198i \(-0.219494\pi\)
0.771526 + 0.636198i \(0.219494\pi\)
\(458\) 50.4103 2.35552
\(459\) 12.4863 0.582809
\(460\) −36.3710 −1.69581
\(461\) −5.82537 −0.271315 −0.135657 0.990756i \(-0.543315\pi\)
−0.135657 + 0.990756i \(0.543315\pi\)
\(462\) −0.326639 −0.0151966
\(463\) −18.6868 −0.868452 −0.434226 0.900804i \(-0.642978\pi\)
−0.434226 + 0.900804i \(0.642978\pi\)
\(464\) 29.5311 1.37095
\(465\) 6.94882 0.322244
\(466\) −38.4406 −1.78073
\(467\) −33.0998 −1.53168 −0.765838 0.643033i \(-0.777676\pi\)
−0.765838 + 0.643033i \(0.777676\pi\)
\(468\) −16.4814 −0.761852
\(469\) −1.80319 −0.0832634
\(470\) 36.0926 1.66483
\(471\) −1.63877 −0.0755108
\(472\) 0.00859810 0.000395760 0
\(473\) −2.22083 −0.102114
\(474\) −12.5961 −0.578557
\(475\) 19.7930 0.908163
\(476\) −3.46906 −0.159004
\(477\) −28.7973 −1.31854
\(478\) 14.1610 0.647710
\(479\) −22.7700 −1.04039 −0.520193 0.854049i \(-0.674140\pi\)
−0.520193 + 0.854049i \(0.674140\pi\)
\(480\) −10.3835 −0.473939
\(481\) −15.0617 −0.686755
\(482\) −9.74045 −0.443665
\(483\) −1.03137 −0.0469291
\(484\) 1.99721 0.0907823
\(485\) −5.22369 −0.237196
\(486\) 22.1458 1.00455
\(487\) −43.1115 −1.95357 −0.976784 0.214227i \(-0.931277\pi\)
−0.976784 + 0.214227i \(0.931277\pi\)
\(488\) −0.0407302 −0.00184377
\(489\) −5.89003 −0.266356
\(490\) 39.6122 1.78950
\(491\) 10.6550 0.480855 0.240427 0.970667i \(-0.422712\pi\)
0.240427 + 0.970667i \(0.422712\pi\)
\(492\) 1.41815 0.0639352
\(493\) −35.2788 −1.58888
\(494\) −35.1435 −1.58118
\(495\) −8.06980 −0.362710
\(496\) 21.4373 0.962563
\(497\) 0.493749 0.0221477
\(498\) −12.4262 −0.556833
\(499\) −35.5199 −1.59009 −0.795046 0.606550i \(-0.792553\pi\)
−0.795046 + 0.606550i \(0.792553\pi\)
\(500\) −9.66957 −0.432436
\(501\) −2.57905 −0.115223
\(502\) −5.50586 −0.245738
\(503\) 10.3276 0.460487 0.230243 0.973133i \(-0.426048\pi\)
0.230243 + 0.973133i \(0.426048\pi\)
\(504\) 0.00566114 0.000252167 0
\(505\) 2.08276 0.0926817
\(506\) 12.6213 0.561086
\(507\) 1.93445 0.0859118
\(508\) −39.8272 −1.76705
\(509\) 15.9761 0.708126 0.354063 0.935222i \(-0.384800\pi\)
0.354063 + 0.935222i \(0.384800\pi\)
\(510\) 12.4217 0.550043
\(511\) −0.972208 −0.0430080
\(512\) −31.9887 −1.41371
\(513\) 15.5485 0.686484
\(514\) −42.1365 −1.85856
\(515\) −4.58023 −0.201829
\(516\) 1.99637 0.0878851
\(517\) −6.25798 −0.275225
\(518\) −3.70536 −0.162804
\(519\) 3.65025 0.160228
\(520\) 0.0474432 0.00208052
\(521\) 28.6127 1.25355 0.626773 0.779202i \(-0.284375\pi\)
0.626773 + 0.779202i \(0.284375\pi\)
\(522\) −41.2336 −1.80475
\(523\) −15.2230 −0.665654 −0.332827 0.942988i \(-0.608003\pi\)
−0.332827 + 0.942988i \(0.608003\pi\)
\(524\) −19.5059 −0.852121
\(525\) 0.542682 0.0236846
\(526\) 36.6270 1.59701
\(527\) −25.6096 −1.11557
\(528\) 1.80287 0.0784598
\(529\) 16.8522 0.732706
\(530\) −59.3715 −2.57893
\(531\) −4.31423 −0.187222
\(532\) −4.31985 −0.187289
\(533\) −4.65383 −0.201580
\(534\) −12.4785 −0.539998
\(535\) −34.7521 −1.50246
\(536\) 0.0276954 0.00119626
\(537\) 1.01716 0.0438939
\(538\) −6.67576 −0.287812
\(539\) −6.86824 −0.295836
\(540\) 15.0336 0.646944
\(541\) −8.49099 −0.365056 −0.182528 0.983201i \(-0.558428\pi\)
−0.182528 + 0.983201i \(0.558428\pi\)
\(542\) −39.0556 −1.67758
\(543\) 6.08252 0.261026
\(544\) 38.2680 1.64073
\(545\) 29.2274 1.25196
\(546\) −0.963563 −0.0412367
\(547\) 1.00000 0.0427569
\(548\) 11.9725 0.511441
\(549\) 20.4370 0.872231
\(550\) −6.64102 −0.283174
\(551\) −43.9309 −1.87152
\(552\) 0.0158410 0.000674238 0
\(553\) 5.08097 0.216065
\(554\) 24.3382 1.03403
\(555\) 6.62930 0.281398
\(556\) 32.9480 1.39731
\(557\) 27.7864 1.17735 0.588674 0.808371i \(-0.299650\pi\)
0.588674 + 0.808371i \(0.299650\pi\)
\(558\) −29.9324 −1.26714
\(559\) −6.55131 −0.277091
\(560\) 4.19430 0.177241
\(561\) −2.15376 −0.0909319
\(562\) −1.82405 −0.0769429
\(563\) −13.1368 −0.553652 −0.276826 0.960920i \(-0.589282\pi\)
−0.276826 + 0.960920i \(0.589282\pi\)
\(564\) 5.62546 0.236875
\(565\) −12.8880 −0.542204
\(566\) 56.0515 2.35602
\(567\) −2.61996 −0.110028
\(568\) −0.00758357 −0.000318200 0
\(569\) −46.5668 −1.95218 −0.976091 0.217362i \(-0.930255\pi\)
−0.976091 + 0.217362i \(0.930255\pi\)
\(570\) 15.4681 0.647889
\(571\) −18.8015 −0.786820 −0.393410 0.919363i \(-0.628705\pi\)
−0.393410 + 0.919363i \(0.628705\pi\)
\(572\) 5.89164 0.246342
\(573\) 5.37815 0.224676
\(574\) −1.14490 −0.0477871
\(575\) −20.9692 −0.874477
\(576\) 22.3169 0.929871
\(577\) 11.7678 0.489899 0.244950 0.969536i \(-0.421229\pi\)
0.244950 + 0.969536i \(0.421229\pi\)
\(578\) −11.7917 −0.490470
\(579\) −4.73109 −0.196617
\(580\) −42.4761 −1.76373
\(581\) 5.01245 0.207952
\(582\) −1.62949 −0.0675444
\(583\) 10.2942 0.426344
\(584\) 0.0149323 0.000617903 0
\(585\) −23.8054 −0.984230
\(586\) 8.51686 0.351828
\(587\) 26.2281 1.08255 0.541275 0.840845i \(-0.317942\pi\)
0.541275 + 0.840845i \(0.317942\pi\)
\(588\) 6.17404 0.254613
\(589\) −31.8904 −1.31402
\(590\) −8.89466 −0.366188
\(591\) −0.711300 −0.0292590
\(592\) 20.4516 0.840554
\(593\) −4.98548 −0.204729 −0.102365 0.994747i \(-0.532641\pi\)
−0.102365 + 0.994747i \(0.532641\pi\)
\(594\) −5.21691 −0.214052
\(595\) −5.01063 −0.205416
\(596\) 14.9098 0.610729
\(597\) −8.87628 −0.363282
\(598\) 37.2320 1.52253
\(599\) −43.6838 −1.78487 −0.892436 0.451175i \(-0.851005\pi\)
−0.892436 + 0.451175i \(0.851005\pi\)
\(600\) −0.00833514 −0.000340281 0
\(601\) −14.8578 −0.606061 −0.303030 0.952981i \(-0.597998\pi\)
−0.303030 + 0.952981i \(0.597998\pi\)
\(602\) −1.61170 −0.0656880
\(603\) −13.8966 −0.565913
\(604\) −42.9287 −1.74675
\(605\) 2.88473 0.117281
\(606\) 0.649700 0.0263923
\(607\) −29.4908 −1.19699 −0.598497 0.801125i \(-0.704235\pi\)
−0.598497 + 0.801125i \(0.704235\pi\)
\(608\) 47.6532 1.93259
\(609\) −1.20450 −0.0488086
\(610\) 42.1351 1.70600
\(611\) −18.4606 −0.746836
\(612\) −26.7349 −1.08070
\(613\) −4.60138 −0.185848 −0.0929241 0.995673i \(-0.529621\pi\)
−0.0929241 + 0.995673i \(0.529621\pi\)
\(614\) −4.47179 −0.180467
\(615\) 2.04835 0.0825974
\(616\) −0.00202370 −8.15372e−5 0
\(617\) −43.3837 −1.74656 −0.873281 0.487217i \(-0.838012\pi\)
−0.873281 + 0.487217i \(0.838012\pi\)
\(618\) −1.42876 −0.0574733
\(619\) 29.6577 1.19205 0.596023 0.802968i \(-0.296747\pi\)
0.596023 + 0.802968i \(0.296747\pi\)
\(620\) −30.8344 −1.23834
\(621\) −16.4726 −0.661021
\(622\) 6.92423 0.277636
\(623\) 5.03354 0.201665
\(624\) 5.31834 0.212904
\(625\) −30.5749 −1.22299
\(626\) −20.5550 −0.821544
\(627\) −2.68197 −0.107108
\(628\) 7.27182 0.290177
\(629\) −24.4321 −0.974170
\(630\) −5.85640 −0.233325
\(631\) 1.37930 0.0549090 0.0274545 0.999623i \(-0.491260\pi\)
0.0274545 + 0.999623i \(0.491260\pi\)
\(632\) −0.0780394 −0.00310424
\(633\) −12.1239 −0.481881
\(634\) −12.4287 −0.493605
\(635\) −57.5255 −2.28283
\(636\) −9.25376 −0.366935
\(637\) −20.2608 −0.802764
\(638\) 14.7399 0.583558
\(639\) 3.80517 0.150530
\(640\) −0.128662 −0.00508583
\(641\) 16.9572 0.669769 0.334885 0.942259i \(-0.391303\pi\)
0.334885 + 0.942259i \(0.391303\pi\)
\(642\) −10.8406 −0.427845
\(643\) −36.2657 −1.43018 −0.715091 0.699032i \(-0.753615\pi\)
−0.715091 + 0.699032i \(0.753615\pi\)
\(644\) 4.57657 0.180342
\(645\) 2.88351 0.113538
\(646\) −57.0074 −2.24292
\(647\) −34.3265 −1.34951 −0.674757 0.738040i \(-0.735752\pi\)
−0.674757 + 0.738040i \(0.735752\pi\)
\(648\) 0.0402404 0.00158079
\(649\) 1.54222 0.0605374
\(650\) −19.5906 −0.768405
\(651\) −0.874370 −0.0342693
\(652\) 26.1361 1.02357
\(653\) 37.6520 1.47344 0.736718 0.676200i \(-0.236374\pi\)
0.736718 + 0.676200i \(0.236374\pi\)
\(654\) 9.11724 0.356512
\(655\) −28.1740 −1.10085
\(656\) 6.31921 0.246724
\(657\) −7.49251 −0.292311
\(658\) −4.54153 −0.177047
\(659\) 28.8648 1.12441 0.562207 0.826997i \(-0.309952\pi\)
0.562207 + 0.826997i \(0.309952\pi\)
\(660\) −2.59316 −0.100939
\(661\) −3.78825 −0.147346 −0.0736729 0.997282i \(-0.523472\pi\)
−0.0736729 + 0.997282i \(0.523472\pi\)
\(662\) −19.6714 −0.764552
\(663\) −6.35345 −0.246748
\(664\) −0.0769870 −0.00298768
\(665\) −6.23949 −0.241957
\(666\) −28.5561 −1.10652
\(667\) 46.5417 1.80210
\(668\) 11.4441 0.442787
\(669\) −11.1851 −0.432442
\(670\) −28.6507 −1.10687
\(671\) −7.30567 −0.282032
\(672\) 1.30655 0.0504014
\(673\) −12.7411 −0.491133 −0.245567 0.969380i \(-0.578974\pi\)
−0.245567 + 0.969380i \(0.578974\pi\)
\(674\) −13.2517 −0.510435
\(675\) 8.66744 0.333610
\(676\) −8.58382 −0.330147
\(677\) 32.7051 1.25696 0.628480 0.777826i \(-0.283677\pi\)
0.628480 + 0.777826i \(0.283677\pi\)
\(678\) −4.02031 −0.154399
\(679\) 0.657297 0.0252248
\(680\) 0.0769590 0.00295124
\(681\) −5.41939 −0.207671
\(682\) 10.7000 0.409725
\(683\) −0.452736 −0.0173235 −0.00866174 0.999962i \(-0.502757\pi\)
−0.00866174 + 0.999962i \(0.502757\pi\)
\(684\) −33.2917 −1.27294
\(685\) 17.2929 0.660727
\(686\) −10.0644 −0.384262
\(687\) 11.3486 0.432974
\(688\) 8.89571 0.339146
\(689\) 30.3673 1.15690
\(690\) −16.3874 −0.623858
\(691\) 44.3008 1.68528 0.842641 0.538475i \(-0.180999\pi\)
0.842641 + 0.538475i \(0.180999\pi\)
\(692\) −16.1975 −0.615735
\(693\) 1.01542 0.0385727
\(694\) 34.4226 1.30666
\(695\) 47.5894 1.80517
\(696\) 0.0185000 0.000701242 0
\(697\) −7.54912 −0.285943
\(698\) 69.1584 2.61768
\(699\) −8.65390 −0.327321
\(700\) −2.40807 −0.0910166
\(701\) −44.9069 −1.69611 −0.848055 0.529908i \(-0.822226\pi\)
−0.848055 + 0.529908i \(0.822226\pi\)
\(702\) −15.3895 −0.580840
\(703\) −30.4240 −1.14746
\(704\) −7.97768 −0.300670
\(705\) 8.12529 0.306016
\(706\) 11.2161 0.422125
\(707\) −0.262074 −0.00985631
\(708\) −1.38634 −0.0521019
\(709\) 40.9845 1.53921 0.769603 0.638523i \(-0.220454\pi\)
0.769603 + 0.638523i \(0.220454\pi\)
\(710\) 7.84514 0.294423
\(711\) 39.1575 1.46852
\(712\) −0.0773109 −0.00289735
\(713\) 33.7856 1.26528
\(714\) −1.56303 −0.0584948
\(715\) 8.50976 0.318247
\(716\) −4.51352 −0.168678
\(717\) 3.18798 0.119057
\(718\) −30.2419 −1.12862
\(719\) 29.3296 1.09381 0.546905 0.837195i \(-0.315806\pi\)
0.546905 + 0.837195i \(0.315806\pi\)
\(720\) 32.3241 1.20465
\(721\) 0.576330 0.0214637
\(722\) −33.0017 −1.22820
\(723\) −2.19281 −0.0815514
\(724\) −26.9903 −1.00309
\(725\) −24.4890 −0.909500
\(726\) 0.899867 0.0333972
\(727\) −46.1201 −1.71050 −0.855250 0.518216i \(-0.826596\pi\)
−0.855250 + 0.518216i \(0.826596\pi\)
\(728\) −0.00596978 −0.000221255 0
\(729\) −16.6679 −0.617329
\(730\) −15.4473 −0.571731
\(731\) −10.6271 −0.393057
\(732\) 6.56726 0.242733
\(733\) 29.6637 1.09565 0.547826 0.836592i \(-0.315455\pi\)
0.547826 + 0.836592i \(0.315455\pi\)
\(734\) 48.5221 1.79098
\(735\) 8.91766 0.328933
\(736\) −50.4852 −1.86091
\(737\) 4.96765 0.182986
\(738\) −8.82337 −0.324793
\(739\) 21.2245 0.780756 0.390378 0.920655i \(-0.372344\pi\)
0.390378 + 0.920655i \(0.372344\pi\)
\(740\) −29.4165 −1.08137
\(741\) −7.91164 −0.290641
\(742\) 7.47072 0.274259
\(743\) 10.8253 0.397142 0.198571 0.980087i \(-0.436370\pi\)
0.198571 + 0.980087i \(0.436370\pi\)
\(744\) 0.0134296 0.000492352 0
\(745\) 21.5354 0.788996
\(746\) 55.4936 2.03177
\(747\) 38.6294 1.41338
\(748\) 9.55701 0.349439
\(749\) 4.37286 0.159781
\(750\) −4.35674 −0.159086
\(751\) 35.0967 1.28070 0.640349 0.768084i \(-0.278790\pi\)
0.640349 + 0.768084i \(0.278790\pi\)
\(752\) 25.0668 0.914091
\(753\) −1.23950 −0.0451699
\(754\) 43.4817 1.58351
\(755\) −62.0054 −2.25661
\(756\) −1.89168 −0.0687998
\(757\) −27.5117 −0.999928 −0.499964 0.866046i \(-0.666653\pi\)
−0.499964 + 0.866046i \(0.666653\pi\)
\(758\) 35.1852 1.27798
\(759\) 2.84136 0.103135
\(760\) 0.0958333 0.00347624
\(761\) 12.5518 0.455004 0.227502 0.973778i \(-0.426944\pi\)
0.227502 + 0.973778i \(0.426944\pi\)
\(762\) −17.9446 −0.650065
\(763\) −3.67768 −0.133141
\(764\) −23.8648 −0.863397
\(765\) −38.6154 −1.39614
\(766\) 0.356335 0.0128749
\(767\) 4.54944 0.164271
\(768\) −7.22149 −0.260583
\(769\) −38.4223 −1.38554 −0.692772 0.721156i \(-0.743611\pi\)
−0.692772 + 0.721156i \(0.743611\pi\)
\(770\) 2.09350 0.0754446
\(771\) −9.48592 −0.341627
\(772\) 20.9935 0.755573
\(773\) 15.1409 0.544579 0.272289 0.962215i \(-0.412219\pi\)
0.272289 + 0.962215i \(0.412219\pi\)
\(774\) −12.4209 −0.446459
\(775\) −17.7771 −0.638574
\(776\) −0.0100955 −0.000362408 0
\(777\) −0.834165 −0.0299255
\(778\) −71.7262 −2.57151
\(779\) −9.40055 −0.336810
\(780\) −7.64964 −0.273901
\(781\) −1.36024 −0.0486734
\(782\) 60.3952 2.15973
\(783\) −19.2376 −0.687495
\(784\) 27.5112 0.982543
\(785\) 10.5033 0.374878
\(786\) −8.78863 −0.313480
\(787\) −11.6738 −0.416126 −0.208063 0.978115i \(-0.566716\pi\)
−0.208063 + 0.978115i \(0.566716\pi\)
\(788\) 3.15629 0.112438
\(789\) 8.24561 0.293552
\(790\) 80.7311 2.87228
\(791\) 1.62170 0.0576611
\(792\) −0.0155960 −0.000554181 0
\(793\) −21.5512 −0.765307
\(794\) −2.16174 −0.0767174
\(795\) −13.3659 −0.474041
\(796\) 39.3872 1.39604
\(797\) −6.47142 −0.229229 −0.114615 0.993410i \(-0.536563\pi\)
−0.114615 + 0.993410i \(0.536563\pi\)
\(798\) −1.94636 −0.0689003
\(799\) −29.9455 −1.05940
\(800\) 26.5640 0.939180
\(801\) 38.7919 1.37065
\(802\) −16.3467 −0.577223
\(803\) 2.67836 0.0945174
\(804\) −4.46555 −0.157488
\(805\) 6.61030 0.232982
\(806\) 31.5643 1.11181
\(807\) −1.50287 −0.0529036
\(808\) 0.00402523 0.000141607 0
\(809\) 17.6367 0.620075 0.310037 0.950724i \(-0.399658\pi\)
0.310037 + 0.950724i \(0.399658\pi\)
\(810\) −41.6283 −1.46267
\(811\) −44.0942 −1.54836 −0.774179 0.632967i \(-0.781837\pi\)
−0.774179 + 0.632967i \(0.781837\pi\)
\(812\) 5.34477 0.187565
\(813\) −8.79235 −0.308361
\(814\) 10.2080 0.357790
\(815\) 37.7505 1.32234
\(816\) 8.62705 0.302007
\(817\) −13.2334 −0.462977
\(818\) −16.7013 −0.583947
\(819\) 2.99543 0.104669
\(820\) −9.08925 −0.317410
\(821\) 44.2170 1.54318 0.771591 0.636119i \(-0.219461\pi\)
0.771591 + 0.636119i \(0.219461\pi\)
\(822\) 5.39437 0.188150
\(823\) −32.7749 −1.14246 −0.571231 0.820789i \(-0.693534\pi\)
−0.571231 + 0.820789i \(0.693534\pi\)
\(824\) −0.00885194 −0.000308372 0
\(825\) −1.49505 −0.0520510
\(826\) 1.11922 0.0389425
\(827\) −15.2971 −0.531931 −0.265965 0.963983i \(-0.585691\pi\)
−0.265965 + 0.963983i \(0.585691\pi\)
\(828\) 35.2702 1.22572
\(829\) −21.8347 −0.758349 −0.379175 0.925325i \(-0.623792\pi\)
−0.379175 + 0.925325i \(0.623792\pi\)
\(830\) 79.6424 2.76443
\(831\) 5.47911 0.190068
\(832\) −23.5336 −0.815881
\(833\) −32.8657 −1.13873
\(834\) 14.8451 0.514045
\(835\) 16.5297 0.572033
\(836\) 11.9009 0.411600
\(837\) −13.9650 −0.482700
\(838\) −56.7948 −1.96194
\(839\) 36.0537 1.24471 0.622356 0.782735i \(-0.286176\pi\)
0.622356 + 0.782735i \(0.286176\pi\)
\(840\) 0.00262755 9.06592e−5 0
\(841\) 25.3540 0.874276
\(842\) 21.4717 0.739962
\(843\) −0.410637 −0.0141431
\(844\) 53.7979 1.85180
\(845\) −12.3983 −0.426514
\(846\) −35.0002 −1.20333
\(847\) −0.362986 −0.0124723
\(848\) −41.2343 −1.41599
\(849\) 12.6185 0.433067
\(850\) −31.7784 −1.08999
\(851\) 32.2321 1.10490
\(852\) 1.22276 0.0418911
\(853\) −28.1833 −0.964976 −0.482488 0.875903i \(-0.660267\pi\)
−0.482488 + 0.875903i \(0.660267\pi\)
\(854\) −5.30186 −0.181426
\(855\) −48.0858 −1.64450
\(856\) −0.0671634 −0.00229560
\(857\) 17.1424 0.585574 0.292787 0.956178i \(-0.405417\pi\)
0.292787 + 0.956178i \(0.405417\pi\)
\(858\) 2.65455 0.0906248
\(859\) 44.0304 1.50230 0.751148 0.660134i \(-0.229500\pi\)
0.751148 + 0.660134i \(0.229500\pi\)
\(860\) −12.7952 −0.436311
\(861\) −0.257744 −0.00878389
\(862\) −30.6554 −1.04413
\(863\) 16.4341 0.559423 0.279711 0.960084i \(-0.409761\pi\)
0.279711 + 0.960084i \(0.409761\pi\)
\(864\) 20.8676 0.709930
\(865\) −23.3953 −0.795463
\(866\) −19.8636 −0.674992
\(867\) −2.65459 −0.0901546
\(868\) 3.87989 0.131692
\(869\) −13.9977 −0.474840
\(870\) −19.1381 −0.648843
\(871\) 14.6542 0.496540
\(872\) 0.0564861 0.00191286
\(873\) 5.06559 0.171444
\(874\) 75.2072 2.54392
\(875\) 1.75741 0.0594113
\(876\) −2.40765 −0.0813470
\(877\) −49.1356 −1.65919 −0.829595 0.558365i \(-0.811429\pi\)
−0.829595 + 0.558365i \(0.811429\pi\)
\(878\) 37.0823 1.25147
\(879\) 1.91735 0.0646706
\(880\) −11.5550 −0.389519
\(881\) 28.3615 0.955522 0.477761 0.878490i \(-0.341448\pi\)
0.477761 + 0.878490i \(0.341448\pi\)
\(882\) −38.4133 −1.29344
\(883\) −18.6310 −0.626983 −0.313491 0.949591i \(-0.601499\pi\)
−0.313491 + 0.949591i \(0.601499\pi\)
\(884\) 28.1925 0.948217
\(885\) −2.00240 −0.0673100
\(886\) −42.1782 −1.41700
\(887\) −15.7780 −0.529772 −0.264886 0.964280i \(-0.585334\pi\)
−0.264886 + 0.964280i \(0.585334\pi\)
\(888\) 0.0128121 0.000429945 0
\(889\) 7.23844 0.242770
\(890\) 79.9775 2.68085
\(891\) 7.21781 0.241806
\(892\) 49.6323 1.66181
\(893\) −37.2897 −1.24785
\(894\) 6.71779 0.224676
\(895\) −6.51923 −0.217914
\(896\) 0.0161896 0.000540856 0
\(897\) 8.38182 0.279861
\(898\) −12.6384 −0.421749
\(899\) 39.4568 1.31596
\(900\) −18.5583 −0.618609
\(901\) 49.2597 1.64108
\(902\) 3.15411 0.105020
\(903\) −0.362832 −0.0120743
\(904\) −0.0249080 −0.000828426 0
\(905\) −38.9842 −1.29588
\(906\) −19.3421 −0.642597
\(907\) −46.9638 −1.55941 −0.779703 0.626149i \(-0.784630\pi\)
−0.779703 + 0.626149i \(0.784630\pi\)
\(908\) 24.0477 0.798052
\(909\) −2.01972 −0.0669900
\(910\) 6.17569 0.204722
\(911\) −35.8940 −1.18922 −0.594610 0.804014i \(-0.702694\pi\)
−0.594610 + 0.804014i \(0.702694\pi\)
\(912\) 10.7428 0.355731
\(913\) −13.8090 −0.457010
\(914\) −65.9504 −2.18144
\(915\) 9.48561 0.313585
\(916\) −50.3575 −1.66386
\(917\) 3.54513 0.117071
\(918\) −24.9638 −0.823929
\(919\) −10.5660 −0.348540 −0.174270 0.984698i \(-0.555757\pi\)
−0.174270 + 0.984698i \(0.555757\pi\)
\(920\) −0.101529 −0.00334730
\(921\) −1.00671 −0.0331721
\(922\) 11.6467 0.383563
\(923\) −4.01263 −0.132077
\(924\) 0.326297 0.0107344
\(925\) −16.9597 −0.557632
\(926\) 37.3607 1.22775
\(927\) 4.44160 0.145881
\(928\) −58.9595 −1.93544
\(929\) 48.8465 1.60260 0.801302 0.598261i \(-0.204141\pi\)
0.801302 + 0.598261i \(0.204141\pi\)
\(930\) −13.8928 −0.455563
\(931\) −40.9261 −1.34130
\(932\) 38.4004 1.25785
\(933\) 1.55881 0.0510331
\(934\) 66.1765 2.16536
\(935\) 13.8039 0.451437
\(936\) −0.0460072 −0.00150379
\(937\) 12.3683 0.404056 0.202028 0.979380i \(-0.435247\pi\)
0.202028 + 0.979380i \(0.435247\pi\)
\(938\) 3.60511 0.117711
\(939\) −4.62743 −0.151010
\(940\) −36.0548 −1.17598
\(941\) 11.5598 0.376838 0.188419 0.982089i \(-0.439664\pi\)
0.188419 + 0.982089i \(0.439664\pi\)
\(942\) 3.27641 0.106751
\(943\) 9.95921 0.324317
\(944\) −6.17746 −0.201059
\(945\) −2.73231 −0.0888819
\(946\) 4.44012 0.144361
\(947\) −51.2889 −1.66667 −0.833333 0.552772i \(-0.813570\pi\)
−0.833333 + 0.552772i \(0.813570\pi\)
\(948\) 12.5829 0.408674
\(949\) 7.90099 0.256477
\(950\) −39.5721 −1.28389
\(951\) −2.79799 −0.0907310
\(952\) −0.00968376 −0.000313853 0
\(953\) −18.7483 −0.607317 −0.303658 0.952781i \(-0.598208\pi\)
−0.303658 + 0.952781i \(0.598208\pi\)
\(954\) 57.5745 1.86404
\(955\) −34.4698 −1.11542
\(956\) −14.1462 −0.457521
\(957\) 3.31830 0.107265
\(958\) 45.5241 1.47082
\(959\) −2.17596 −0.0702655
\(960\) 10.3581 0.334307
\(961\) −2.35747 −0.0760473
\(962\) 30.1129 0.970879
\(963\) 33.7003 1.08598
\(964\) 9.73026 0.313391
\(965\) 30.3226 0.976118
\(966\) 2.06203 0.0663447
\(967\) 30.6557 0.985822 0.492911 0.870080i \(-0.335933\pi\)
0.492911 + 0.870080i \(0.335933\pi\)
\(968\) 0.00557515 0.000179192 0
\(969\) −12.8337 −0.412278
\(970\) 10.4437 0.335328
\(971\) −5.40827 −0.173560 −0.0867799 0.996228i \(-0.527658\pi\)
−0.0867799 + 0.996228i \(0.527658\pi\)
\(972\) −22.1226 −0.709584
\(973\) −5.98818 −0.191972
\(974\) 86.1929 2.76180
\(975\) −4.41030 −0.141243
\(976\) 29.2634 0.936698
\(977\) 30.1414 0.964308 0.482154 0.876086i \(-0.339855\pi\)
0.482154 + 0.876086i \(0.339855\pi\)
\(978\) 11.7759 0.376553
\(979\) −13.8671 −0.443193
\(980\) −39.5708 −1.26404
\(981\) −28.3428 −0.904915
\(982\) −21.3026 −0.679794
\(983\) −52.9684 −1.68943 −0.844715 0.535217i \(-0.820230\pi\)
−0.844715 + 0.535217i \(0.820230\pi\)
\(984\) 0.00395872 0.000126200 0
\(985\) 4.55888 0.145258
\(986\) 70.5330 2.24623
\(987\) −1.02241 −0.0325436
\(988\) 35.1067 1.11689
\(989\) 14.0198 0.445804
\(990\) 16.1340 0.512771
\(991\) −29.8129 −0.947039 −0.473520 0.880783i \(-0.657017\pi\)
−0.473520 + 0.880783i \(0.657017\pi\)
\(992\) −42.8000 −1.35890
\(993\) −4.42851 −0.140534
\(994\) −0.987155 −0.0313106
\(995\) 56.8900 1.80354
\(996\) 12.4132 0.393328
\(997\) −49.4140 −1.56496 −0.782479 0.622677i \(-0.786045\pi\)
−0.782479 + 0.622677i \(0.786045\pi\)
\(998\) 71.0151 2.24794
\(999\) −13.3228 −0.421516
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 \(a_p\))