Properties

Label 462.2.g.a.419.1
Level $462$
Weight $2$
Character 462.419
Analytic conductor $3.689$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.68908857338\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{5})\)
Defining polynomial: \(x^{4} + 3 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 419.1
Root \(-0.618034i\) of defining polynomial
Character \(\chi\) \(=\) 462.419
Dual form 462.2.g.a.419.3

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} +(-1.61803 + 0.618034i) q^{3} -1.00000 q^{4} -3.23607 q^{5} +(0.618034 + 1.61803i) q^{6} +(0.381966 + 2.61803i) q^{7} +1.00000i q^{8} +(2.23607 - 2.00000i) q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +(-1.61803 + 0.618034i) q^{3} -1.00000 q^{4} -3.23607 q^{5} +(0.618034 + 1.61803i) q^{6} +(0.381966 + 2.61803i) q^{7} +1.00000i q^{8} +(2.23607 - 2.00000i) q^{9} +3.23607i q^{10} +1.00000i q^{11} +(1.61803 - 0.618034i) q^{12} -6.00000i q^{13} +(2.61803 - 0.381966i) q^{14} +(5.23607 - 2.00000i) q^{15} +1.00000 q^{16} +7.23607 q^{17} +(-2.00000 - 2.23607i) q^{18} -2.00000i q^{19} +3.23607 q^{20} +(-2.23607 - 4.00000i) q^{21} +1.00000 q^{22} -1.23607i q^{23} +(-0.618034 - 1.61803i) q^{24} +5.47214 q^{25} -6.00000 q^{26} +(-2.38197 + 4.61803i) q^{27} +(-0.381966 - 2.61803i) q^{28} -0.472136i q^{29} +(-2.00000 - 5.23607i) q^{30} -0.763932i q^{31} -1.00000i q^{32} +(-0.618034 - 1.61803i) q^{33} -7.23607i q^{34} +(-1.23607 - 8.47214i) q^{35} +(-2.23607 + 2.00000i) q^{36} -4.47214 q^{37} -2.00000 q^{38} +(3.70820 + 9.70820i) q^{39} -3.23607i q^{40} +12.1803 q^{41} +(-4.00000 + 2.23607i) q^{42} +10.9443 q^{43} -1.00000i q^{44} +(-7.23607 + 6.47214i) q^{45} -1.23607 q^{46} +1.52786 q^{47} +(-1.61803 + 0.618034i) q^{48} +(-6.70820 + 2.00000i) q^{49} -5.47214i q^{50} +(-11.7082 + 4.47214i) q^{51} +6.00000i q^{52} -7.70820i q^{53} +(4.61803 + 2.38197i) q^{54} -3.23607i q^{55} +(-2.61803 + 0.381966i) q^{56} +(1.23607 + 3.23607i) q^{57} -0.472136 q^{58} +3.23607 q^{59} +(-5.23607 + 2.00000i) q^{60} +3.52786i q^{61} -0.763932 q^{62} +(6.09017 + 5.09017i) q^{63} -1.00000 q^{64} +19.4164i q^{65} +(-1.61803 + 0.618034i) q^{66} +1.52786 q^{67} -7.23607 q^{68} +(0.763932 + 2.00000i) q^{69} +(-8.47214 + 1.23607i) q^{70} +6.18034i q^{71} +(2.00000 + 2.23607i) q^{72} -14.1803i q^{73} +4.47214i q^{74} +(-8.85410 + 3.38197i) q^{75} +2.00000i q^{76} +(-2.61803 + 0.381966i) q^{77} +(9.70820 - 3.70820i) q^{78} +7.23607 q^{79} -3.23607 q^{80} +(1.00000 - 8.94427i) q^{81} -12.1803i q^{82} +6.00000 q^{83} +(2.23607 + 4.00000i) q^{84} -23.4164 q^{85} -10.9443i q^{86} +(0.291796 + 0.763932i) q^{87} -1.00000 q^{88} -12.9443 q^{89} +(6.47214 + 7.23607i) q^{90} +(15.7082 - 2.29180i) q^{91} +1.23607i q^{92} +(0.472136 + 1.23607i) q^{93} -1.52786i q^{94} +6.47214i q^{95} +(0.618034 + 1.61803i) q^{96} +2.47214i q^{97} +(2.00000 + 6.70820i) q^{98} +(2.00000 + 2.23607i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{3} - 4q^{4} - 4q^{5} - 2q^{6} + 6q^{7} + O(q^{10}) \) \( 4q - 2q^{3} - 4q^{4} - 4q^{5} - 2q^{6} + 6q^{7} + 2q^{12} + 6q^{14} + 12q^{15} + 4q^{16} + 20q^{17} - 8q^{18} + 4q^{20} + 4q^{22} + 2q^{24} + 4q^{25} - 24q^{26} - 14q^{27} - 6q^{28} - 8q^{30} + 2q^{33} + 4q^{35} - 8q^{38} - 12q^{39} + 4q^{41} - 16q^{42} + 8q^{43} - 20q^{45} + 4q^{46} + 24q^{47} - 2q^{48} - 20q^{51} + 14q^{54} - 6q^{56} - 4q^{57} + 16q^{58} + 4q^{59} - 12q^{60} - 12q^{62} + 2q^{63} - 4q^{64} - 2q^{66} + 24q^{67} - 20q^{68} + 12q^{69} - 16q^{70} + 8q^{72} - 22q^{75} - 6q^{77} + 12q^{78} + 20q^{79} - 4q^{80} + 4q^{81} + 24q^{83} - 40q^{85} + 28q^{87} - 4q^{88} - 16q^{89} + 8q^{90} + 36q^{91} - 16q^{93} - 2q^{96} + 8q^{98} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −1.61803 + 0.618034i −0.934172 + 0.356822i
\(4\) −1.00000 −0.500000
\(5\) −3.23607 −1.44721 −0.723607 0.690212i \(-0.757517\pi\)
−0.723607 + 0.690212i \(0.757517\pi\)
\(6\) 0.618034 + 1.61803i 0.252311 + 0.660560i
\(7\) 0.381966 + 2.61803i 0.144370 + 0.989524i
\(8\) 1.00000i 0.353553i
\(9\) 2.23607 2.00000i 0.745356 0.666667i
\(10\) 3.23607i 1.02333i
\(11\) 1.00000i 0.301511i
\(12\) 1.61803 0.618034i 0.467086 0.178411i
\(13\) 6.00000i 1.66410i −0.554700 0.832050i \(-0.687167\pi\)
0.554700 0.832050i \(-0.312833\pi\)
\(14\) 2.61803 0.381966i 0.699699 0.102085i
\(15\) 5.23607 2.00000i 1.35195 0.516398i
\(16\) 1.00000 0.250000
\(17\) 7.23607 1.75500 0.877502 0.479573i \(-0.159208\pi\)
0.877502 + 0.479573i \(0.159208\pi\)
\(18\) −2.00000 2.23607i −0.471405 0.527046i
\(19\) 2.00000i 0.458831i −0.973329 0.229416i \(-0.926318\pi\)
0.973329 0.229416i \(-0.0736815\pi\)
\(20\) 3.23607 0.723607
\(21\) −2.23607 4.00000i −0.487950 0.872872i
\(22\) 1.00000 0.213201
\(23\) 1.23607i 0.257738i −0.991662 0.128869i \(-0.958865\pi\)
0.991662 0.128869i \(-0.0411347\pi\)
\(24\) −0.618034 1.61803i −0.126156 0.330280i
\(25\) 5.47214 1.09443
\(26\) −6.00000 −1.17670
\(27\) −2.38197 + 4.61803i −0.458410 + 0.888741i
\(28\) −0.381966 2.61803i −0.0721848 0.494762i
\(29\) 0.472136i 0.0876734i −0.999039 0.0438367i \(-0.986042\pi\)
0.999039 0.0438367i \(-0.0139581\pi\)
\(30\) −2.00000 5.23607i −0.365148 0.955971i
\(31\) 0.763932i 0.137206i −0.997644 0.0686031i \(-0.978146\pi\)
0.997644 0.0686031i \(-0.0218542\pi\)
\(32\) 1.00000i 0.176777i
\(33\) −0.618034 1.61803i −0.107586 0.281664i
\(34\) 7.23607i 1.24098i
\(35\) −1.23607 8.47214i −0.208934 1.43205i
\(36\) −2.23607 + 2.00000i −0.372678 + 0.333333i
\(37\) −4.47214 −0.735215 −0.367607 0.929981i \(-0.619823\pi\)
−0.367607 + 0.929981i \(0.619823\pi\)
\(38\) −2.00000 −0.324443
\(39\) 3.70820 + 9.70820i 0.593788 + 1.55456i
\(40\) 3.23607i 0.511667i
\(41\) 12.1803 1.90225 0.951125 0.308807i \(-0.0999297\pi\)
0.951125 + 0.308807i \(0.0999297\pi\)
\(42\) −4.00000 + 2.23607i −0.617213 + 0.345033i
\(43\) 10.9443 1.66899 0.834493 0.551019i \(-0.185761\pi\)
0.834493 + 0.551019i \(0.185761\pi\)
\(44\) 1.00000i 0.150756i
\(45\) −7.23607 + 6.47214i −1.07869 + 0.964809i
\(46\) −1.23607 −0.182248
\(47\) 1.52786 0.222862 0.111431 0.993772i \(-0.464457\pi\)
0.111431 + 0.993772i \(0.464457\pi\)
\(48\) −1.61803 + 0.618034i −0.233543 + 0.0892055i
\(49\) −6.70820 + 2.00000i −0.958315 + 0.285714i
\(50\) 5.47214i 0.773877i
\(51\) −11.7082 + 4.47214i −1.63948 + 0.626224i
\(52\) 6.00000i 0.832050i
\(53\) 7.70820i 1.05880i −0.848371 0.529402i \(-0.822416\pi\)
0.848371 0.529402i \(-0.177584\pi\)
\(54\) 4.61803 + 2.38197i 0.628435 + 0.324145i
\(55\) 3.23607i 0.436351i
\(56\) −2.61803 + 0.381966i −0.349850 + 0.0510424i
\(57\) 1.23607 + 3.23607i 0.163721 + 0.428628i
\(58\) −0.472136 −0.0619945
\(59\) 3.23607 0.421300 0.210650 0.977562i \(-0.432442\pi\)
0.210650 + 0.977562i \(0.432442\pi\)
\(60\) −5.23607 + 2.00000i −0.675973 + 0.258199i
\(61\) 3.52786i 0.451697i 0.974162 + 0.225848i \(0.0725154\pi\)
−0.974162 + 0.225848i \(0.927485\pi\)
\(62\) −0.763932 −0.0970195
\(63\) 6.09017 + 5.09017i 0.767289 + 0.641301i
\(64\) −1.00000 −0.125000
\(65\) 19.4164i 2.40831i
\(66\) −1.61803 + 0.618034i −0.199166 + 0.0760747i
\(67\) 1.52786 0.186658 0.0933292 0.995635i \(-0.470249\pi\)
0.0933292 + 0.995635i \(0.470249\pi\)
\(68\) −7.23607 −0.877502
\(69\) 0.763932 + 2.00000i 0.0919666 + 0.240772i
\(70\) −8.47214 + 1.23607i −1.01261 + 0.147738i
\(71\) 6.18034i 0.733471i 0.930325 + 0.366736i \(0.119525\pi\)
−0.930325 + 0.366736i \(0.880475\pi\)
\(72\) 2.00000 + 2.23607i 0.235702 + 0.263523i
\(73\) 14.1803i 1.65968i −0.557999 0.829842i \(-0.688431\pi\)
0.557999 0.829842i \(-0.311569\pi\)
\(74\) 4.47214i 0.519875i
\(75\) −8.85410 + 3.38197i −1.02238 + 0.390516i
\(76\) 2.00000i 0.229416i
\(77\) −2.61803 + 0.381966i −0.298353 + 0.0435291i
\(78\) 9.70820 3.70820i 1.09924 0.419871i
\(79\) 7.23607 0.814121 0.407061 0.913401i \(-0.366554\pi\)
0.407061 + 0.913401i \(0.366554\pi\)
\(80\) −3.23607 −0.361803
\(81\) 1.00000 8.94427i 0.111111 0.993808i
\(82\) 12.1803i 1.34509i
\(83\) 6.00000 0.658586 0.329293 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) 2.23607 + 4.00000i 0.243975 + 0.436436i
\(85\) −23.4164 −2.53987
\(86\) 10.9443i 1.18015i
\(87\) 0.291796 + 0.763932i 0.0312838 + 0.0819021i
\(88\) −1.00000 −0.106600
\(89\) −12.9443 −1.37209 −0.686045 0.727559i \(-0.740655\pi\)
−0.686045 + 0.727559i \(0.740655\pi\)
\(90\) 6.47214 + 7.23607i 0.682223 + 0.762749i
\(91\) 15.7082 2.29180i 1.64667 0.240246i
\(92\) 1.23607i 0.128869i
\(93\) 0.472136 + 1.23607i 0.0489582 + 0.128174i
\(94\) 1.52786i 0.157587i
\(95\) 6.47214i 0.664027i
\(96\) 0.618034 + 1.61803i 0.0630778 + 0.165140i
\(97\) 2.47214i 0.251007i 0.992093 + 0.125504i \(0.0400547\pi\)
−0.992093 + 0.125504i \(0.959945\pi\)
\(98\) 2.00000 + 6.70820i 0.202031 + 0.677631i
\(99\) 2.00000 + 2.23607i 0.201008 + 0.224733i
\(100\) −5.47214 −0.547214
\(101\) −6.76393 −0.673036 −0.336518 0.941677i \(-0.609249\pi\)
−0.336518 + 0.941677i \(0.609249\pi\)
\(102\) 4.47214 + 11.7082i 0.442807 + 1.15928i
\(103\) 9.70820i 0.956578i −0.878203 0.478289i \(-0.841257\pi\)
0.878203 0.478289i \(-0.158743\pi\)
\(104\) 6.00000 0.588348
\(105\) 7.23607 + 12.9443i 0.706168 + 1.26323i
\(106\) −7.70820 −0.748687
\(107\) 8.94427i 0.864675i −0.901712 0.432338i \(-0.857689\pi\)
0.901712 0.432338i \(-0.142311\pi\)
\(108\) 2.38197 4.61803i 0.229205 0.444371i
\(109\) 8.76393 0.839432 0.419716 0.907655i \(-0.362130\pi\)
0.419716 + 0.907655i \(0.362130\pi\)
\(110\) −3.23607 −0.308547
\(111\) 7.23607 2.76393i 0.686817 0.262341i
\(112\) 0.381966 + 2.61803i 0.0360924 + 0.247381i
\(113\) 8.00000i 0.752577i 0.926503 + 0.376288i \(0.122800\pi\)
−0.926503 + 0.376288i \(0.877200\pi\)
\(114\) 3.23607 1.23607i 0.303086 0.115768i
\(115\) 4.00000i 0.373002i
\(116\) 0.472136i 0.0438367i
\(117\) −12.0000 13.4164i −1.10940 1.24035i
\(118\) 3.23607i 0.297904i
\(119\) 2.76393 + 18.9443i 0.253369 + 1.73662i
\(120\) 2.00000 + 5.23607i 0.182574 + 0.477985i
\(121\) −1.00000 −0.0909091
\(122\) 3.52786 0.319398
\(123\) −19.7082 + 7.52786i −1.77703 + 0.678765i
\(124\) 0.763932i 0.0686031i
\(125\) −1.52786 −0.136656
\(126\) 5.09017 6.09017i 0.453468 0.542555i
\(127\) −17.7082 −1.57135 −0.785675 0.618640i \(-0.787684\pi\)
−0.785675 + 0.618640i \(0.787684\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −17.7082 + 6.76393i −1.55912 + 0.595531i
\(130\) 19.4164 1.70293
\(131\) −9.41641 −0.822715 −0.411358 0.911474i \(-0.634945\pi\)
−0.411358 + 0.911474i \(0.634945\pi\)
\(132\) 0.618034 + 1.61803i 0.0537930 + 0.140832i
\(133\) 5.23607 0.763932i 0.454025 0.0662413i
\(134\) 1.52786i 0.131987i
\(135\) 7.70820 14.9443i 0.663417 1.28620i
\(136\) 7.23607i 0.620488i
\(137\) 6.47214i 0.552952i −0.961021 0.276476i \(-0.910833\pi\)
0.961021 0.276476i \(-0.0891666\pi\)
\(138\) 2.00000 0.763932i 0.170251 0.0650302i
\(139\) 10.0000i 0.848189i 0.905618 + 0.424094i \(0.139408\pi\)
−0.905618 + 0.424094i \(0.860592\pi\)
\(140\) 1.23607 + 8.47214i 0.104467 + 0.716026i
\(141\) −2.47214 + 0.944272i −0.208191 + 0.0795220i
\(142\) 6.18034 0.518643
\(143\) 6.00000 0.501745
\(144\) 2.23607 2.00000i 0.186339 0.166667i
\(145\) 1.52786i 0.126882i
\(146\) −14.1803 −1.17357
\(147\) 9.61803 7.38197i 0.793282 0.608854i
\(148\) 4.47214 0.367607
\(149\) 2.00000i 0.163846i 0.996639 + 0.0819232i \(0.0261062\pi\)
−0.996639 + 0.0819232i \(0.973894\pi\)
\(150\) 3.38197 + 8.85410i 0.276136 + 0.722934i
\(151\) 12.1803 0.991222 0.495611 0.868545i \(-0.334944\pi\)
0.495611 + 0.868545i \(0.334944\pi\)
\(152\) 2.00000 0.162221
\(153\) 16.1803 14.4721i 1.30810 1.17000i
\(154\) 0.381966 + 2.61803i 0.0307797 + 0.210967i
\(155\) 2.47214i 0.198567i
\(156\) −3.70820 9.70820i −0.296894 0.777278i
\(157\) 13.4164i 1.07075i −0.844616 0.535373i \(-0.820171\pi\)
0.844616 0.535373i \(-0.179829\pi\)
\(158\) 7.23607i 0.575671i
\(159\) 4.76393 + 12.4721i 0.377804 + 0.989105i
\(160\) 3.23607i 0.255834i
\(161\) 3.23607 0.472136i 0.255038 0.0372095i
\(162\) −8.94427 1.00000i −0.702728 0.0785674i
\(163\) 18.4721 1.44685 0.723425 0.690403i \(-0.242567\pi\)
0.723425 + 0.690403i \(0.242567\pi\)
\(164\) −12.1803 −0.951125
\(165\) 2.00000 + 5.23607i 0.155700 + 0.407627i
\(166\) 6.00000i 0.465690i
\(167\) 13.8885 1.07473 0.537364 0.843350i \(-0.319420\pi\)
0.537364 + 0.843350i \(0.319420\pi\)
\(168\) 4.00000 2.23607i 0.308607 0.172516i
\(169\) −23.0000 −1.76923
\(170\) 23.4164i 1.79596i
\(171\) −4.00000 4.47214i −0.305888 0.341993i
\(172\) −10.9443 −0.834493
\(173\) 7.70820 0.586044 0.293022 0.956106i \(-0.405339\pi\)
0.293022 + 0.956106i \(0.405339\pi\)
\(174\) 0.763932 0.291796i 0.0579135 0.0221210i
\(175\) 2.09017 + 14.3262i 0.158002 + 1.08296i
\(176\) 1.00000i 0.0753778i
\(177\) −5.23607 + 2.00000i −0.393567 + 0.150329i
\(178\) 12.9443i 0.970214i
\(179\) 12.9443i 0.967500i 0.875206 + 0.483750i \(0.160726\pi\)
−0.875206 + 0.483750i \(0.839274\pi\)
\(180\) 7.23607 6.47214i 0.539345 0.482405i
\(181\) 3.52786i 0.262224i −0.991368 0.131112i \(-0.958145\pi\)
0.991368 0.131112i \(-0.0418548\pi\)
\(182\) −2.29180 15.7082i −0.169879 1.16437i
\(183\) −2.18034 5.70820i −0.161175 0.421963i
\(184\) 1.23607 0.0911241
\(185\) 14.4721 1.06401
\(186\) 1.23607 0.472136i 0.0906329 0.0346187i
\(187\) 7.23607i 0.529154i
\(188\) −1.52786 −0.111431
\(189\) −13.0000 4.47214i −0.945611 0.325300i
\(190\) 6.47214 0.469538
\(191\) 11.7082i 0.847176i −0.905855 0.423588i \(-0.860770\pi\)
0.905855 0.423588i \(-0.139230\pi\)
\(192\) 1.61803 0.618034i 0.116772 0.0446028i
\(193\) −2.94427 −0.211933 −0.105967 0.994370i \(-0.533794\pi\)
−0.105967 + 0.994370i \(0.533794\pi\)
\(194\) 2.47214 0.177489
\(195\) −12.0000 31.4164i −0.859338 2.24978i
\(196\) 6.70820 2.00000i 0.479157 0.142857i
\(197\) 14.9443i 1.06474i −0.846513 0.532368i \(-0.821302\pi\)
0.846513 0.532368i \(-0.178698\pi\)
\(198\) 2.23607 2.00000i 0.158910 0.142134i
\(199\) 20.1803i 1.43055i −0.698845 0.715273i \(-0.746302\pi\)
0.698845 0.715273i \(-0.253698\pi\)
\(200\) 5.47214i 0.386938i
\(201\) −2.47214 + 0.944272i −0.174371 + 0.0666038i
\(202\) 6.76393i 0.475909i
\(203\) 1.23607 0.180340i 0.0867550 0.0126574i
\(204\) 11.7082 4.47214i 0.819738 0.313112i
\(205\) −39.4164 −2.75296
\(206\) −9.70820 −0.676403
\(207\) −2.47214 2.76393i −0.171825 0.192107i
\(208\) 6.00000i 0.416025i
\(209\) 2.00000 0.138343
\(210\) 12.9443 7.23607i 0.893240 0.499336i
\(211\) 9.41641 0.648252 0.324126 0.946014i \(-0.394930\pi\)
0.324126 + 0.946014i \(0.394930\pi\)
\(212\) 7.70820i 0.529402i
\(213\) −3.81966 10.0000i −0.261719 0.685189i
\(214\) −8.94427 −0.611418
\(215\) −35.4164 −2.41538
\(216\) −4.61803 2.38197i −0.314217 0.162072i
\(217\) 2.00000 0.291796i 0.135769 0.0198084i
\(218\) 8.76393i 0.593568i
\(219\) 8.76393 + 22.9443i 0.592212 + 1.55043i
\(220\) 3.23607i 0.218176i
\(221\) 43.4164i 2.92050i
\(222\) −2.76393 7.23607i −0.185503 0.485653i
\(223\) 23.5967i 1.58016i 0.613007 + 0.790078i \(0.289960\pi\)
−0.613007 + 0.790078i \(0.710040\pi\)
\(224\) 2.61803 0.381966i 0.174925 0.0255212i
\(225\) 12.2361 10.9443i 0.815738 0.729618i
\(226\) 8.00000 0.532152
\(227\) −22.0000 −1.46019 −0.730096 0.683345i \(-0.760525\pi\)
−0.730096 + 0.683345i \(0.760525\pi\)
\(228\) −1.23607 3.23607i −0.0818606 0.214314i
\(229\) 2.00000i 0.132164i 0.997814 + 0.0660819i \(0.0210498\pi\)
−0.997814 + 0.0660819i \(0.978950\pi\)
\(230\) 4.00000 0.263752
\(231\) 4.00000 2.23607i 0.263181 0.147122i
\(232\) 0.472136 0.0309972
\(233\) 25.4164i 1.66508i −0.553962 0.832542i \(-0.686885\pi\)
0.553962 0.832542i \(-0.313115\pi\)
\(234\) −13.4164 + 12.0000i −0.877058 + 0.784465i
\(235\) −4.94427 −0.322529
\(236\) −3.23607 −0.210650
\(237\) −11.7082 + 4.47214i −0.760530 + 0.290496i
\(238\) 18.9443 2.76393i 1.22797 0.179159i
\(239\) 21.8885i 1.41585i −0.706287 0.707926i \(-0.749631\pi\)
0.706287 0.707926i \(-0.250369\pi\)
\(240\) 5.23607 2.00000i 0.337987 0.129099i
\(241\) 18.1803i 1.17110i 0.810637 + 0.585549i \(0.199121\pi\)
−0.810637 + 0.585549i \(0.800879\pi\)
\(242\) 1.00000i 0.0642824i
\(243\) 3.90983 + 15.0902i 0.250816 + 0.968035i
\(244\) 3.52786i 0.225848i
\(245\) 21.7082 6.47214i 1.38689 0.413490i
\(246\) 7.52786 + 19.7082i 0.479959 + 1.25655i
\(247\) −12.0000 −0.763542
\(248\) 0.763932 0.0485097
\(249\) −9.70820 + 3.70820i −0.615232 + 0.234998i
\(250\) 1.52786i 0.0966306i
\(251\) −1.70820 −0.107821 −0.0539104 0.998546i \(-0.517169\pi\)
−0.0539104 + 0.998546i \(0.517169\pi\)
\(252\) −6.09017 5.09017i −0.383645 0.320651i
\(253\) 1.23607 0.0777109
\(254\) 17.7082i 1.11111i
\(255\) 37.8885 14.4721i 2.37267 0.906280i
\(256\) 1.00000 0.0625000
\(257\) 0.944272 0.0589021 0.0294510 0.999566i \(-0.490624\pi\)
0.0294510 + 0.999566i \(0.490624\pi\)
\(258\) 6.76393 + 17.7082i 0.421104 + 1.10246i
\(259\) −1.70820 11.7082i −0.106143 0.727512i
\(260\) 19.4164i 1.20415i
\(261\) −0.944272 1.05573i −0.0584490 0.0653479i
\(262\) 9.41641i 0.581748i
\(263\) 21.5279i 1.32746i −0.747970 0.663732i \(-0.768971\pi\)
0.747970 0.663732i \(-0.231029\pi\)
\(264\) 1.61803 0.618034i 0.0995831 0.0380374i
\(265\) 24.9443i 1.53231i
\(266\) −0.763932 5.23607i −0.0468397 0.321044i
\(267\) 20.9443 8.00000i 1.28177 0.489592i
\(268\) −1.52786 −0.0933292
\(269\) 23.5967 1.43872 0.719360 0.694638i \(-0.244435\pi\)
0.719360 + 0.694638i \(0.244435\pi\)
\(270\) −14.9443 7.70820i −0.909479 0.469106i
\(271\) 23.7082i 1.44017i 0.693885 + 0.720085i \(0.255897\pi\)
−0.693885 + 0.720085i \(0.744103\pi\)
\(272\) 7.23607 0.438751
\(273\) −24.0000 + 13.4164i −1.45255 + 0.811998i
\(274\) −6.47214 −0.390996
\(275\) 5.47214i 0.329982i
\(276\) −0.763932 2.00000i −0.0459833 0.120386i
\(277\) −24.1803 −1.45286 −0.726428 0.687243i \(-0.758821\pi\)
−0.726428 + 0.687243i \(0.758821\pi\)
\(278\) 10.0000 0.599760
\(279\) −1.52786 1.70820i −0.0914708 0.102267i
\(280\) 8.47214 1.23607i 0.506307 0.0738692i
\(281\) 25.4164i 1.51622i 0.652129 + 0.758108i \(0.273876\pi\)
−0.652129 + 0.758108i \(0.726124\pi\)
\(282\) 0.944272 + 2.47214i 0.0562306 + 0.147214i
\(283\) 14.9443i 0.888345i −0.895941 0.444172i \(-0.853498\pi\)
0.895941 0.444172i \(-0.146502\pi\)
\(284\) 6.18034i 0.366736i
\(285\) −4.00000 10.4721i −0.236940 0.620316i
\(286\) 6.00000i 0.354787i
\(287\) 4.65248 + 31.8885i 0.274627 + 1.88232i
\(288\) −2.00000 2.23607i −0.117851 0.131762i
\(289\) 35.3607 2.08004
\(290\) 1.52786 0.0897193
\(291\) −1.52786 4.00000i −0.0895650 0.234484i
\(292\) 14.1803i 0.829842i
\(293\) 18.1803 1.06211 0.531053 0.847338i \(-0.321796\pi\)
0.531053 + 0.847338i \(0.321796\pi\)
\(294\) −7.38197 9.61803i −0.430525 0.560935i
\(295\) −10.4721 −0.609711
\(296\) 4.47214i 0.259938i
\(297\) −4.61803 2.38197i −0.267966 0.138216i
\(298\) 2.00000 0.115857
\(299\) −7.41641 −0.428902
\(300\) 8.85410 3.38197i 0.511192 0.195258i
\(301\) 4.18034 + 28.6525i 0.240951 + 1.65150i
\(302\) 12.1803i 0.700900i
\(303\) 10.9443 4.18034i 0.628732 0.240154i
\(304\) 2.00000i 0.114708i
\(305\) 11.4164i 0.653702i
\(306\) −14.4721 16.1803i −0.827317 0.924968i
\(307\) 3.52786i 0.201346i −0.994920 0.100673i \(-0.967900\pi\)
0.994920 0.100673i \(-0.0320996\pi\)
\(308\) 2.61803 0.381966i 0.149176 0.0217645i
\(309\) 6.00000 + 15.7082i 0.341328 + 0.893609i
\(310\) 2.47214 0.140408
\(311\) −10.4721 −0.593820 −0.296910 0.954905i \(-0.595956\pi\)
−0.296910 + 0.954905i \(0.595956\pi\)
\(312\) −9.70820 + 3.70820i −0.549619 + 0.209936i
\(313\) 8.00000i 0.452187i −0.974106 0.226093i \(-0.927405\pi\)
0.974106 0.226093i \(-0.0725954\pi\)
\(314\) −13.4164 −0.757132
\(315\) −19.7082 16.4721i −1.11043 0.928100i
\(316\) −7.23607 −0.407061
\(317\) 12.2918i 0.690376i 0.938534 + 0.345188i \(0.112185\pi\)
−0.938534 + 0.345188i \(0.887815\pi\)
\(318\) 12.4721 4.76393i 0.699403 0.267148i
\(319\) 0.472136 0.0264345
\(320\) 3.23607 0.180902
\(321\) 5.52786 + 14.4721i 0.308535 + 0.807756i
\(322\) −0.472136 3.23607i −0.0263111 0.180339i
\(323\) 14.4721i 0.805251i
\(324\) −1.00000 + 8.94427i −0.0555556 + 0.496904i
\(325\) 32.8328i 1.82124i
\(326\) 18.4721i 1.02308i
\(327\) −14.1803 + 5.41641i −0.784175 + 0.299528i
\(328\) 12.1803i 0.672547i
\(329\) 0.583592 + 4.00000i 0.0321745 + 0.220527i
\(330\) 5.23607 2.00000i 0.288236 0.110096i
\(331\) 8.94427 0.491622 0.245811 0.969318i \(-0.420946\pi\)
0.245811 + 0.969318i \(0.420946\pi\)
\(332\) −6.00000 −0.329293
\(333\) −10.0000 + 8.94427i −0.547997 + 0.490143i
\(334\) 13.8885i 0.759947i
\(335\) −4.94427 −0.270134
\(336\) −2.23607 4.00000i −0.121988 0.218218i
\(337\) 13.4164 0.730838 0.365419 0.930843i \(-0.380926\pi\)
0.365419 + 0.930843i \(0.380926\pi\)
\(338\) 23.0000i 1.25104i
\(339\) −4.94427 12.9443i −0.268536 0.703036i
\(340\) 23.4164 1.26993
\(341\) 0.763932 0.0413692
\(342\) −4.47214 + 4.00000i −0.241825 + 0.216295i
\(343\) −7.79837 16.7984i −0.421073 0.907027i
\(344\) 10.9443i 0.590076i
\(345\) −2.47214 6.47214i −0.133095 0.348448i
\(346\) 7.70820i 0.414396i
\(347\) 16.9443i 0.909616i 0.890589 + 0.454808i \(0.150292\pi\)
−0.890589 + 0.454808i \(0.849708\pi\)
\(348\) −0.291796 0.763932i −0.0156419 0.0409511i
\(349\) 22.0000i 1.17763i 0.808267 + 0.588817i \(0.200406\pi\)
−0.808267 + 0.588817i \(0.799594\pi\)
\(350\) 14.3262 2.09017i 0.765770 0.111724i
\(351\) 27.7082 + 14.2918i 1.47895 + 0.762840i
\(352\) 1.00000 0.0533002
\(353\) 0.944272 0.0502585 0.0251293 0.999684i \(-0.492000\pi\)
0.0251293 + 0.999684i \(0.492000\pi\)
\(354\) 2.00000 + 5.23607i 0.106299 + 0.278294i
\(355\) 20.0000i 1.06149i
\(356\) 12.9443 0.686045
\(357\) −16.1803 28.9443i −0.856354 1.53189i
\(358\) 12.9443 0.684126
\(359\) 18.8328i 0.993958i 0.867763 + 0.496979i \(0.165557\pi\)
−0.867763 + 0.496979i \(0.834443\pi\)
\(360\) −6.47214 7.23607i −0.341112 0.381374i
\(361\) 15.0000 0.789474
\(362\) −3.52786 −0.185420
\(363\) 1.61803 0.618034i 0.0849248 0.0324384i
\(364\) −15.7082 + 2.29180i −0.823334 + 0.120123i
\(365\) 45.8885i 2.40192i
\(366\) −5.70820 + 2.18034i −0.298373 + 0.113968i
\(367\) 26.6525i 1.39125i 0.718406 + 0.695624i \(0.244872\pi\)
−0.718406 + 0.695624i \(0.755128\pi\)
\(368\) 1.23607i 0.0644345i
\(369\) 27.2361 24.3607i 1.41785 1.26817i
\(370\) 14.4721i 0.752371i
\(371\) 20.1803 2.94427i 1.04771 0.152859i
\(372\) −0.472136 1.23607i −0.0244791 0.0640871i
\(373\) −7.81966 −0.404887 −0.202443 0.979294i \(-0.564888\pi\)
−0.202443 + 0.979294i \(0.564888\pi\)
\(374\) 7.23607 0.374168
\(375\) 2.47214 0.944272i 0.127661 0.0487620i
\(376\) 1.52786i 0.0787936i
\(377\) −2.83282 −0.145897
\(378\) −4.47214 + 13.0000i −0.230022 + 0.668648i
\(379\) −12.3607 −0.634925 −0.317463 0.948271i \(-0.602831\pi\)
−0.317463 + 0.948271i \(0.602831\pi\)
\(380\) 6.47214i 0.332014i
\(381\) 28.6525 10.9443i 1.46791 0.560692i
\(382\) −11.7082 −0.599044
\(383\) 20.0000 1.02195 0.510976 0.859595i \(-0.329284\pi\)
0.510976 + 0.859595i \(0.329284\pi\)
\(384\) −0.618034 1.61803i −0.0315389 0.0825700i
\(385\) 8.47214 1.23607i 0.431780 0.0629959i
\(386\) 2.94427i 0.149859i
\(387\) 24.4721 21.8885i 1.24399 1.11266i
\(388\) 2.47214i 0.125504i
\(389\) 17.2361i 0.873903i 0.899485 + 0.436952i \(0.143942\pi\)
−0.899485 + 0.436952i \(0.856058\pi\)
\(390\) −31.4164 + 12.0000i −1.59083 + 0.607644i
\(391\) 8.94427i 0.452331i
\(392\) −2.00000 6.70820i −0.101015 0.338815i
\(393\) 15.2361 5.81966i 0.768558 0.293563i
\(394\) −14.9443 −0.752882
\(395\) −23.4164 −1.17821
\(396\) −2.00000 2.23607i −0.100504 0.112367i
\(397\) 14.9443i 0.750032i 0.927018 + 0.375016i \(0.122363\pi\)
−0.927018 + 0.375016i \(0.877637\pi\)
\(398\) −20.1803 −1.01155
\(399\) −8.00000 + 4.47214i −0.400501 + 0.223887i
\(400\) 5.47214 0.273607
\(401\) 2.47214i 0.123453i 0.998093 + 0.0617263i \(0.0196606\pi\)
−0.998093 + 0.0617263i \(0.980339\pi\)
\(402\) 0.944272 + 2.47214i 0.0470960 + 0.123299i
\(403\) −4.58359 −0.228325
\(404\) 6.76393 0.336518
\(405\) −3.23607 + 28.9443i −0.160802 + 1.43825i
\(406\) −0.180340 1.23607i −0.00895012 0.0613450i
\(407\) 4.47214i 0.221676i
\(408\) −4.47214 11.7082i −0.221404 0.579642i
\(409\) 5.23607i 0.258907i 0.991586 + 0.129453i \(0.0413223\pi\)
−0.991586 + 0.129453i \(0.958678\pi\)
\(410\) 39.4164i 1.94664i
\(411\) 4.00000 + 10.4721i 0.197305 + 0.516552i
\(412\) 9.70820i 0.478289i
\(413\) 1.23607 + 8.47214i 0.0608229 + 0.416887i
\(414\) −2.76393 + 2.47214i −0.135840 + 0.121499i
\(415\) −19.4164 −0.953114
\(416\) −6.00000 −0.294174
\(417\) −6.18034 16.1803i −0.302653 0.792355i
\(418\) 2.00000i 0.0978232i
\(419\) −9.12461 −0.445766 −0.222883 0.974845i \(-0.571547\pi\)
−0.222883 + 0.974845i \(0.571547\pi\)
\(420\) −7.23607 12.9443i −0.353084 0.631616i
\(421\) 4.47214 0.217959 0.108979 0.994044i \(-0.465242\pi\)
0.108979 + 0.994044i \(0.465242\pi\)
\(422\) 9.41641i 0.458384i
\(423\) 3.41641 3.05573i 0.166111 0.148575i
\(424\) 7.70820 0.374343
\(425\) 39.5967 1.92072
\(426\) −10.0000 + 3.81966i −0.484502 + 0.185063i
\(427\) −9.23607 + 1.34752i −0.446965 + 0.0652113i
\(428\) 8.94427i 0.432338i
\(429\) −9.70820 + 3.70820i −0.468717 + 0.179034i
\(430\) 35.4164i 1.70793i
\(431\) 5.88854i 0.283641i 0.989892 + 0.141821i \(0.0452956\pi\)
−0.989892 + 0.141821i \(0.954704\pi\)
\(432\) −2.38197 + 4.61803i −0.114602 + 0.222185i
\(433\) 26.4721i 1.27217i −0.771619 0.636085i \(-0.780553\pi\)
0.771619 0.636085i \(-0.219447\pi\)
\(434\) −0.291796 2.00000i −0.0140067 0.0960031i
\(435\) −0.944272 2.47214i −0.0452744 0.118530i
\(436\) −8.76393 −0.419716
\(437\) −2.47214 −0.118258
\(438\) 22.9443 8.76393i 1.09632 0.418757i
\(439\) 17.2361i 0.822633i 0.911493 + 0.411316i \(0.134931\pi\)
−0.911493 + 0.411316i \(0.865069\pi\)
\(440\) 3.23607 0.154273
\(441\) −11.0000 + 17.8885i −0.523810 + 0.851835i
\(442\) −43.4164 −2.06511
\(443\) 29.8885i 1.42005i −0.704178 0.710024i \(-0.748684\pi\)
0.704178 0.710024i \(-0.251316\pi\)
\(444\) −7.23607 + 2.76393i −0.343409 + 0.131170i
\(445\) 41.8885 1.98571
\(446\) 23.5967 1.11734
\(447\) −1.23607 3.23607i −0.0584640 0.153061i
\(448\) −0.381966 2.61803i −0.0180462 0.123690i
\(449\) 31.4164i 1.48263i 0.671156 + 0.741316i \(0.265798\pi\)
−0.671156 + 0.741316i \(0.734202\pi\)
\(450\) −10.9443 12.2361i −0.515918 0.576814i
\(451\) 12.1803i 0.573550i
\(452\) 8.00000i 0.376288i
\(453\) −19.7082 + 7.52786i −0.925972 + 0.353690i
\(454\) 22.0000i 1.03251i
\(455\) −50.8328 + 7.41641i −2.38308 + 0.347687i
\(456\) −3.23607 + 1.23607i −0.151543 + 0.0578842i
\(457\) −2.00000 −0.0935561 −0.0467780 0.998905i \(-0.514895\pi\)
−0.0467780 + 0.998905i \(0.514895\pi\)
\(458\) 2.00000 0.0934539
\(459\) −17.2361 + 33.4164i −0.804511 + 1.55974i
\(460\) 4.00000i 0.186501i
\(461\) −41.2361 −1.92056 −0.960278 0.279047i \(-0.909982\pi\)
−0.960278 + 0.279047i \(0.909982\pi\)
\(462\) −2.23607 4.00000i −0.104031 0.186097i
\(463\) −26.4721 −1.23026 −0.615132 0.788424i \(-0.710897\pi\)
−0.615132 + 0.788424i \(0.710897\pi\)
\(464\) 0.472136i 0.0219184i
\(465\) −1.52786 4.00000i −0.0708530 0.185496i
\(466\) −25.4164 −1.17739
\(467\) −22.6525 −1.04823 −0.524116 0.851647i \(-0.675604\pi\)
−0.524116 + 0.851647i \(0.675604\pi\)
\(468\) 12.0000 + 13.4164i 0.554700 + 0.620174i
\(469\) 0.583592 + 4.00000i 0.0269478 + 0.184703i
\(470\) 4.94427i 0.228062i
\(471\) 8.29180 + 21.7082i 0.382066 + 1.00026i
\(472\) 3.23607i 0.148952i
\(473\) 10.9443i 0.503218i
\(474\) 4.47214 + 11.7082i 0.205412 + 0.537776i
\(475\) 10.9443i 0.502158i
\(476\) −2.76393 18.9443i −0.126685 0.868309i
\(477\) −15.4164 17.2361i −0.705869 0.789185i
\(478\) −21.8885 −1.00116
\(479\) −0.944272 −0.0431449 −0.0215724 0.999767i \(-0.506867\pi\)
−0.0215724 + 0.999767i \(0.506867\pi\)
\(480\) −2.00000 5.23607i −0.0912871 0.238993i
\(481\) 26.8328i 1.22347i
\(482\) 18.1803 0.828092
\(483\) −4.94427 + 2.76393i −0.224972 + 0.125763i
\(484\) 1.00000 0.0454545
\(485\) 8.00000i 0.363261i
\(486\) 15.0902 3.90983i 0.684504 0.177353i
\(487\) 1.52786 0.0692341 0.0346171 0.999401i \(-0.488979\pi\)
0.0346171 + 0.999401i \(0.488979\pi\)
\(488\) −3.52786 −0.159699
\(489\) −29.8885 + 11.4164i −1.35161 + 0.516268i
\(490\) −6.47214 21.7082i −0.292381 0.980677i
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 19.7082 7.52786i 0.888514 0.339382i
\(493\) 3.41641i 0.153867i
\(494\) 12.0000i 0.539906i
\(495\) −6.47214 7.23607i −0.290901 0.325237i
\(496\) 0.763932i 0.0343016i
\(497\) −16.1803 + 2.36068i −0.725787 + 0.105891i
\(498\) 3.70820 + 9.70820i 0.166169 + 0.435035i
\(499\) 19.0557 0.853052 0.426526 0.904475i \(-0.359737\pi\)
0.426526 + 0.904475i \(0.359737\pi\)
\(500\) 1.52786 0.0683282
\(501\) −22.4721 + 8.58359i −1.00398 + 0.383487i
\(502\) 1.70820i 0.0762409i
\(503\) −4.58359 −0.204372 −0.102186 0.994765i \(-0.532584\pi\)
−0.102186 + 0.994765i \(0.532584\pi\)
\(504\) −5.09017 + 6.09017i −0.226734 + 0.271278i
\(505\) 21.8885 0.974027
\(506\) 1.23607i 0.0549499i
\(507\) 37.2148 14.2148i 1.65277 0.631301i
\(508\) 17.7082 0.785675
\(509\) 17.1246 0.759035 0.379518 0.925185i \(-0.376090\pi\)
0.379518 + 0.925185i \(0.376090\pi\)
\(510\) −14.4721 37.8885i −0.640837 1.67773i
\(511\) 37.1246 5.41641i 1.64230 0.239608i
\(512\) 1.00000i 0.0441942i
\(513\) 9.23607 + 4.76393i 0.407782 + 0.210333i
\(514\) 0.944272i 0.0416500i
\(515\) 31.4164i 1.38437i
\(516\) 17.7082 6.76393i 0.779560 0.297766i
\(517\) 1.52786i 0.0671954i
\(518\) −11.7082 + 1.70820i −0.514429 + 0.0750542i
\(519\) −12.4721 + 4.76393i −0.547466 + 0.209113i
\(520\) −19.4164 −0.851466
\(521\) 19.0557 0.834847 0.417423 0.908712i \(-0.362933\pi\)
0.417423 + 0.908712i \(0.362933\pi\)
\(522\) −1.05573 + 0.944272i −0.0462080 + 0.0413297i
\(523\) 29.7771i 1.30206i 0.759052 + 0.651031i \(0.225663\pi\)
−0.759052 + 0.651031i \(0.774337\pi\)
\(524\) 9.41641 0.411358
\(525\) −12.2361 21.8885i −0.534026 0.955294i
\(526\) −21.5279 −0.938659
\(527\) 5.52786i 0.240798i
\(528\) −0.618034 1.61803i −0.0268965 0.0704159i
\(529\) 21.4721 0.933571
\(530\) 24.9443 1.08351
\(531\) 7.23607 6.47214i 0.314019 0.280867i
\(532\) −5.23607 + 0.763932i −0.227012 + 0.0331207i
\(533\) 73.0820i 3.16553i
\(534\) −8.00000 20.9443i −0.346194 0.906347i
\(535\) 28.9443i 1.25137i
\(536\) 1.52786i 0.0659937i
\(537\) −8.00000 20.9443i −0.345225 0.903812i
\(538\) 23.5967i 1.01733i
\(539\) −2.00000 6.70820i −0.0861461 0.288943i
\(540\) −7.70820 + 14.9443i −0.331708 + 0.643099i
\(541\) −23.5967 −1.01450 −0.507252 0.861798i \(-0.669339\pi\)
−0.507252 + 0.861798i \(0.669339\pi\)
\(542\) 23.7082 1.01835
\(543\) 2.18034 + 5.70820i 0.0935673 + 0.244962i
\(544\) 7.23607i 0.310244i
\(545\) −28.3607 −1.21484
\(546\) 13.4164 + 24.0000i 0.574169 + 1.02711i
\(547\) 24.8328 1.06177 0.530887 0.847442i \(-0.321859\pi\)
0.530887 + 0.847442i \(0.321859\pi\)
\(548\) 6.47214i 0.276476i
\(549\) 7.05573 + 7.88854i 0.301131 + 0.336675i
\(550\) 5.47214 0.233333
\(551\) −0.944272 −0.0402273
\(552\) −2.00000 + 0.763932i −0.0851257 + 0.0325151i
\(553\) 2.76393 + 18.9443i 0.117534 + 0.805592i
\(554\) 24.1803i 1.02732i
\(555\) −23.4164 + 8.94427i −0.993971 + 0.379663i
\(556\) 10.0000i 0.424094i
\(557\) 9.05573i 0.383704i 0.981424 + 0.191852i \(0.0614493\pi\)
−0.981424 + 0.191852i \(0.938551\pi\)
\(558\) −1.70820 + 1.52786i −0.0723140 + 0.0646796i
\(559\) 65.6656i 2.77736i
\(560\) −1.23607 8.47214i −0.0522334 0.358013i
\(561\) −4.47214 11.7082i −0.188814 0.494321i
\(562\) 25.4164 1.07213
\(563\) −23.5279 −0.991581 −0.495791 0.868442i \(-0.665122\pi\)
−0.495791 + 0.868442i \(0.665122\pi\)
\(564\) 2.47214 0.944272i 0.104096 0.0397610i
\(565\) 25.8885i 1.08914i
\(566\) −14.9443 −0.628155
\(567\) 23.7984 0.798374i 0.999438 0.0335286i
\(568\) −6.18034 −0.259321
\(569\) 6.00000i 0.251533i 0.992060 + 0.125767i \(0.0401390\pi\)
−0.992060 + 0.125767i \(0.959861\pi\)
\(570\) −10.4721 + 4.00000i −0.438630 + 0.167542i
\(571\) −26.9443 −1.12758 −0.563791 0.825917i \(-0.690658\pi\)
−0.563791 + 0.825917i \(0.690658\pi\)
\(572\) −6.00000 −0.250873
\(573\) 7.23607 + 18.9443i 0.302291 + 0.791408i
\(574\) 31.8885 4.65248i 1.33100 0.194191i
\(575\) 6.76393i 0.282075i
\(576\) −2.23607 + 2.00000i −0.0931695 + 0.0833333i
\(577\) 37.5279i 1.56231i −0.624340 0.781153i \(-0.714632\pi\)
0.624340 0.781153i \(-0.285368\pi\)
\(578\) 35.3607i 1.47081i
\(579\) 4.76393 1.81966i 0.197982 0.0756225i
\(580\) 1.52786i 0.0634411i
\(581\) 2.29180 + 15.7082i 0.0950797 + 0.651686i
\(582\) −4.00000 + 1.52786i −0.165805 + 0.0633320i
\(583\) 7.70820 0.319241
\(584\) 14.1803 0.586787
\(585\) 38.8328 + 43.4164i 1.60554 + 1.79505i
\(586\) 18.1803i 0.751023i
\(587\) 27.5967 1.13904 0.569520 0.821978i \(-0.307129\pi\)
0.569520 + 0.821978i \(0.307129\pi\)
\(588\) −9.61803 + 7.38197i −0.396641 + 0.304427i
\(589\) −1.52786 −0.0629545
\(590\) 10.4721i 0.431131i
\(591\) 9.23607 + 24.1803i 0.379921 + 0.994646i
\(592\) −4.47214 −0.183804
\(593\) 1.70820 0.0701475 0.0350738 0.999385i \(-0.488833\pi\)
0.0350738 + 0.999385i \(0.488833\pi\)
\(594\) −2.38197 + 4.61803i −0.0977332 + 0.189480i
\(595\) −8.94427 61.3050i −0.366679 2.51326i
\(596\) 2.00000i 0.0819232i
\(597\) 12.4721 + 32.6525i 0.510451 + 1.33638i
\(598\) 7.41641i 0.303279i
\(599\) 15.7082i 0.641820i −0.947110 0.320910i \(-0.896011\pi\)
0.947110 0.320910i \(-0.103989\pi\)
\(600\) −3.38197 8.85410i −0.138068 0.361467i
\(601\) 9.23607i 0.376747i −0.982097 0.188374i \(-0.939678\pi\)
0.982097 0.188374i \(-0.0603216\pi\)
\(602\) 28.6525 4.18034i 1.16779 0.170378i
\(603\) 3.41641 3.05573i 0.139127 0.124439i
\(604\) −12.1803 −0.495611
\(605\) 3.23607 0.131565
\(606\) −4.18034 10.9443i −0.169815 0.444581i
\(607\) 1.23607i 0.0501705i 0.999685 + 0.0250852i \(0.00798571\pi\)
−0.999685 + 0.0250852i \(0.992014\pi\)
\(608\) −2.00000 −0.0811107
\(609\) −1.88854 + 1.05573i −0.0765277 + 0.0427803i
\(610\) −11.4164 −0.462237
\(611\) 9.16718i 0.370865i
\(612\) −16.1803 + 14.4721i −0.654051 + 0.585001i
\(613\) −4.18034 −0.168842 −0.0844212 0.996430i \(-0.526904\pi\)
−0.0844212 + 0.996430i \(0.526904\pi\)
\(614\) −3.52786 −0.142373
\(615\) 63.7771 24.3607i 2.57174 0.982317i
\(616\) −0.381966 2.61803i −0.0153898 0.105484i
\(617\) 11.0557i 0.445087i −0.974923 0.222543i \(-0.928564\pi\)
0.974923 0.222543i \(-0.0714359\pi\)
\(618\) 15.7082 6.00000i 0.631877 0.241355i
\(619\) 21.2361i 0.853550i −0.904358 0.426775i \(-0.859650\pi\)
0.904358 0.426775i \(-0.140350\pi\)
\(620\) 2.47214i 0.0992834i
\(621\) 5.70820 + 2.94427i 0.229062 + 0.118150i
\(622\) 10.4721i 0.419894i
\(623\) −4.94427 33.8885i −0.198088 1.35772i
\(624\) 3.70820 + 9.70820i 0.148447 + 0.388639i
\(625\) −22.4164 −0.896656
\(626\) −8.00000 −0.319744
\(627\) −3.23607 + 1.23607i −0.129236 + 0.0493638i
\(628\) 13.4164i 0.535373i
\(629\) −32.3607 −1.29030
\(630\) −16.4721 + 19.7082i −0.656266 + 0.785194i
\(631\) −32.9443 −1.31149 −0.655745 0.754982i \(-0.727646\pi\)
−0.655745 + 0.754982i \(0.727646\pi\)
\(632\) 7.23607i 0.287835i
\(633\) −15.2361 + 5.81966i −0.605579 + 0.231311i
\(634\) 12.2918 0.488170
\(635\) 57.3050 2.27408
\(636\) −4.76393 12.4721i −0.188902 0.494552i
\(637\) 12.0000 + 40.2492i 0.475457 + 1.59473i
\(638\) 0.472136i 0.0186920i
\(639\) 12.3607 + 13.8197i 0.488981 + 0.546697i
\(640\) 3.23607i 0.127917i
\(641\) 32.3607i 1.27817i −0.769136 0.639085i \(-0.779313\pi\)
0.769136 0.639085i \(-0.220687\pi\)
\(642\) 14.4721 5.52786i 0.571170 0.218167i
\(643\) 32.0689i 1.26467i 0.774694 + 0.632337i \(0.217904\pi\)
−0.774694 + 0.632337i \(0.782096\pi\)
\(644\) −3.23607 + 0.472136i −0.127519 + 0.0186048i
\(645\) 57.3050 21.8885i 2.25638 0.861861i
\(646\) −14.4721 −0.569399
\(647\) 5.88854 0.231503 0.115751 0.993278i \(-0.463072\pi\)
0.115751 + 0.993278i \(0.463072\pi\)
\(648\) 8.94427 + 1.00000i 0.351364 + 0.0392837i
\(649\) 3.23607i 0.127027i
\(650\) −32.8328 −1.28781
\(651\) −3.05573 + 1.70820i −0.119763 + 0.0669498i
\(652\) −18.4721 −0.723425
\(653\) 21.2361i 0.831032i −0.909586 0.415516i \(-0.863601\pi\)
0.909586 0.415516i \(-0.136399\pi\)
\(654\) 5.41641 + 14.1803i 0.211798 + 0.554495i
\(655\) 30.4721 1.19064
\(656\) 12.1803 0.475562
\(657\) −28.3607 31.7082i −1.10646 1.23705i
\(658\) 4.00000 0.583592i 0.155936 0.0227508i
\(659\) 9.88854i 0.385203i 0.981277 + 0.192601i \(0.0616925\pi\)
−0.981277 + 0.192601i \(0.938308\pi\)
\(660\) −2.00000 5.23607i −0.0778499 0.203814i
\(661\) 44.4721i 1.72977i −0.501974 0.864883i \(-0.667393\pi\)
0.501974 0.864883i \(-0.332607\pi\)
\(662\) 8.94427i 0.347629i
\(663\) 26.8328 + 70.2492i 1.04210 + 2.72825i
\(664\) 6.00000i 0.232845i
\(665\) −16.9443 + 2.47214i −0.657071 + 0.0958653i
\(666\) 8.94427 + 10.0000i 0.346583 + 0.387492i
\(667\) −0.583592 −0.0225968
\(668\) −13.8885 −0.537364
\(669\) −14.5836 38.1803i −0.563834 1.47614i
\(670\) 4.94427i 0.191014i
\(671\) −3.52786 −0.136192
\(672\) −4.00000 + 2.23607i −0.154303 + 0.0862582i
\(673\) −11.3050 −0.435774 −0.217887 0.975974i \(-0.569916\pi\)
−0.217887 + 0.975974i \(0.569916\pi\)
\(674\) 13.4164i 0.516781i
\(675\) −13.0344 + 25.2705i −0.501696 + 0.972662i
\(676\) 23.0000 0.884615
\(677\) 2.76393 0.106227 0.0531133 0.998588i \(-0.483086\pi\)
0.0531133 + 0.998588i \(0.483086\pi\)
\(678\) −12.9443 + 4.94427i −0.497122 + 0.189884i
\(679\) −6.47214 + 0.944272i −0.248378 + 0.0362378i
\(680\) 23.4164i 0.897978i
\(681\) 35.5967 13.5967i 1.36407 0.521029i
\(682\) 0.763932i 0.0292525i
\(683\) 33.8885i 1.29671i 0.761339 + 0.648355i \(0.224543\pi\)
−0.761339 + 0.648355i \(0.775457\pi\)
\(684\) 4.00000 + 4.47214i 0.152944 + 0.170996i
\(685\) 20.9443i 0.800239i
\(686\) −16.7984 + 7.79837i −0.641365 + 0.297743i
\(687\) −1.23607 3.23607i −0.0471589 0.123464i
\(688\) 10.9443 0.417246
\(689\) −46.2492 −1.76196
\(690\) −6.47214 + 2.47214i −0.246390 + 0.0941126i
\(691\) 29.5967i 1.12591i 0.826486 + 0.562957i \(0.190336\pi\)
−0.826486 + 0.562957i \(0.809664\pi\)
\(692\) −7.70820 −0.293022
\(693\) −5.09017 + 6.09017i −0.193360 + 0.231346i
\(694\) 16.9443 0.643196
\(695\) 32.3607i 1.22751i
\(696\) −0.763932 + 0.291796i −0.0289568 + 0.0110605i
\(697\) 88.1378 3.33846
\(698\) 22.0000 0.832712
\(699\) 15.7082 + 41.1246i 0.594139 + 1.55548i
\(700\) −2.09017 14.3262i −0.0790010 0.541481i
\(701\) 17.4164i 0.657809i 0.944363 + 0.328904i \(0.106679\pi\)
−0.944363 + 0.328904i \(0.893321\pi\)
\(702\) 14.2918 27.7082i 0.539409 1.04578i
\(703\) 8.94427i 0.337340i
\(704\) 1.00000i 0.0376889i
\(705\) 8.00000 3.05573i 0.301297 0.115085i
\(706\) 0.944272i 0.0355381i
\(707\) −2.58359 17.7082i −0.0971660 0.665986i
\(708\) 5.23607 2.00000i 0.196783 0.0751646i
\(709\) −22.5836 −0.848145 −0.424072 0.905628i \(-0.639400\pi\)
−0.424072 + 0.905628i \(0.639400\pi\)
\(710\) −20.0000 −0.750587
\(711\) 16.1803 14.4721i 0.606810 0.542748i
\(712\) 12.9443i 0.485107i
\(713\) −0.944272 −0.0353633
\(714\) −28.9443 + 16.1803i −1.08321 + 0.605534i
\(715\) −19.4164 −0.726132
\(716\) 12.9443i 0.483750i
\(717\) 13.5279 + 35.4164i 0.505207 + 1.32265i
\(718\) 18.8328 0.702834
\(719\) −17.5279 −0.653679 −0.326840 0.945080i \(-0.605984\pi\)
−0.326840 + 0.945080i \(0.605984\pi\)
\(720\) −7.23607 + 6.47214i −0.269672 + 0.241202i
\(721\) 25.4164 3.70820i 0.946556 0.138101i
\(722\) 15.0000i 0.558242i
\(723\) −11.2361 29.4164i −0.417874 1.09401i
\(724\) 3.52786i 0.131112i
\(725\) 2.58359i 0.0959522i
\(726\) −0.618034 1.61803i −0.0229374 0.0600509i
\(727\) 2.29180i 0.0849980i 0.999097 + 0.0424990i \(0.0135319\pi\)
−0.999097 + 0.0424990i \(0.986468\pi\)
\(728\) 2.29180 + 15.7082i 0.0849396 + 0.582185i
\(729\) −15.6525 22.0000i −0.579721 0.814815i
\(730\) 45.8885 1.69841
\(731\) 79.1935 2.92908
\(732\) 2.18034 + 5.70820i 0.0805877 + 0.210981i
\(733\) 26.5836i 0.981887i −0.871191 0.490944i \(-0.836652\pi\)
0.871191 0.490944i \(-0.163348\pi\)
\(734\) 26.6525 0.983761
\(735\) −31.1246 + 23.8885i −1.14805 + 0.881142i
\(736\) −1.23607 −0.0455621
\(737\) 1.52786i 0.0562796i
\(738\) −24.3607 27.2361i −0.896729 1.00257i
\(739\) 9.41641 0.346388 0.173194 0.984888i \(-0.444591\pi\)
0.173194 + 0.984888i \(0.444591\pi\)
\(740\) −14.4721 −0.532006
\(741\) 19.4164 7.41641i 0.713280 0.272449i
\(742\) −2.94427 20.1803i −0.108088 0.740844i
\(743\) 1.52786i 0.0560519i −0.999607 0.0280259i \(-0.991078\pi\)
0.999607 0.0280259i \(-0.00892210\pi\)
\(744\) −1.23607 + 0.472136i −0.0453165 + 0.0173093i
\(745\) 6.47214i 0.237121i
\(746\) 7.81966i 0.286298i
\(747\) 13.4164 12.0000i 0.490881 0.439057i
\(748\) 7.23607i 0.264577i
\(749\) 23.4164 3.41641i 0.855617 0.124833i
\(750\) −0.944272 2.47214i −0.0344799 0.0902696i
\(751\) −32.3607 −1.18086 −0.590429 0.807090i \(-0.701041\pi\)
−0.590429 + 0.807090i \(0.701041\pi\)
\(752\) 1.52786 0.0557155
\(753\) 2.76393 1.05573i 0.100723 0.0384729i
\(754\) 2.83282i 0.103165i
\(755\) −39.4164 −1.43451
\(756\) 13.0000 + 4.47214i 0.472805 + 0.162650i
\(757\) −1.41641 −0.0514802 −0.0257401 0.999669i \(-0.508194\pi\)
−0.0257401 + 0.999669i \(0.508194\pi\)
\(758\) 12.3607i 0.448960i
\(759\) −2.00000 + 0.763932i −0.0725954 + 0.0277290i
\(760\) −6.47214 −0.234769
\(761\) −33.1246 −1.20077 −0.600383 0.799713i \(-0.704985\pi\)
−0.600383 + 0.799713i \(0.704985\pi\)
\(762\) −10.9443 28.6525i −0.396469 1.03797i
\(763\) 3.34752 + 22.9443i 0.121189 + 0.830638i
\(764\) 11.7082i 0.423588i
\(765\) −52.3607 + 46.8328i −1.89310 + 1.69324i
\(766\) 20.0000i 0.722629i
\(767\) 19.4164i 0.701086i
\(768\) −1.61803 + 0.618034i −0.0583858 + 0.0223014i
\(769\) 51.4853i 1.85661i −0.371823 0.928304i \(-0.621267\pi\)
0.371823 0.928304i \(-0.378733\pi\)
\(770\) −1.23607 8.47214i −0.0445448 0.305315i
\(771\) −1.52786 + 0.583592i −0.0550247 + 0.0210176i
\(772\) 2.94427 0.105967
\(773\) 1.12461 0.0404495 0.0202247 0.999795i \(-0.493562\pi\)
0.0202247 + 0.999795i \(0.493562\pi\)
\(774\) −21.8885 24.4721i −0.786767 0.879633i
\(775\) 4.18034i 0.150162i
\(776\) −2.47214 −0.0887445
\(777\) 10.0000 + 17.8885i 0.358748 + 0.641748i
\(778\) 17.2361 0.617943
\(779\) 24.3607i 0.872812i
\(780\) 12.0000 + 31.4164i 0.429669 + 1.12489i
\(781\) −6.18034 −0.221150
\(782\) −8.94427