Properties

Label 273.2.t.b.4.2
Level $273$
Weight $2$
Character 273.4
Analytic conductor $2.180$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.t (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-7})\)
Defining polynomial: \(x^{4} - x^{3} - x^{2} - 2 x + 4\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 4.2
Root \(-0.895644 + 1.09445i\) of defining polynomial
Character \(\chi\) \(=\) 273.4
Dual form 273.2.t.b.205.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.18890i q^{2} +(-0.500000 - 0.866025i) q^{3} -2.79129 q^{4} +(1.50000 - 0.866025i) q^{5} +(1.89564 - 1.09445i) q^{6} +(2.29129 + 1.32288i) q^{7} -1.73205i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+2.18890i q^{2} +(-0.500000 - 0.866025i) q^{3} -2.79129 q^{4} +(1.50000 - 0.866025i) q^{5} +(1.89564 - 1.09445i) q^{6} +(2.29129 + 1.32288i) q^{7} -1.73205i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.89564 + 3.28335i) q^{10} +(3.00000 - 1.73205i) q^{11} +(1.39564 + 2.41733i) q^{12} +(-1.00000 + 3.46410i) q^{13} +(-2.89564 + 5.01540i) q^{14} +(-1.50000 - 0.866025i) q^{15} -1.79129 q^{16} +1.00000 q^{17} +(-1.89564 - 1.09445i) q^{18} +(4.58258 + 2.64575i) q^{19} +(-4.18693 + 2.41733i) q^{20} -2.64575i q^{21} +(3.79129 + 6.56670i) q^{22} -8.58258 q^{23} +(-1.50000 + 0.866025i) q^{24} +(-1.00000 + 1.73205i) q^{25} +(-7.58258 - 2.18890i) q^{26} +1.00000 q^{27} +(-6.39564 - 3.69253i) q^{28} +(3.50000 - 6.06218i) q^{29} +(1.89564 - 3.28335i) q^{30} +(5.29129 + 3.05493i) q^{31} -7.38505i q^{32} +(-3.00000 - 1.73205i) q^{33} +2.18890i q^{34} +4.58258 q^{35} +(1.39564 - 2.41733i) q^{36} -7.02355i q^{37} +(-5.79129 + 10.0308i) q^{38} +(3.50000 - 0.866025i) q^{39} +(-1.50000 - 2.59808i) q^{40} +(-3.08258 - 1.77973i) q^{41} +5.79129 q^{42} +(-2.29129 - 3.96863i) q^{43} +(-8.37386 + 4.83465i) q^{44} +1.73205i q^{45} -18.7864i q^{46} +(-0.708712 + 0.409175i) q^{47} +(0.895644 + 1.55130i) q^{48} +(3.50000 + 6.06218i) q^{49} +(-3.79129 - 2.18890i) q^{50} +(-0.500000 - 0.866025i) q^{51} +(2.79129 - 9.66930i) q^{52} +(3.08258 - 5.33918i) q^{53} +2.18890i q^{54} +(3.00000 - 5.19615i) q^{55} +(2.29129 - 3.96863i) q^{56} -5.29150i q^{57} +(13.2695 + 7.66115i) q^{58} +4.28245i q^{59} +(4.18693 + 2.41733i) q^{60} +(2.58258 - 4.47315i) q^{61} +(-6.68693 + 11.5821i) q^{62} +(-2.29129 + 1.32288i) q^{63} +12.5826 q^{64} +(1.50000 + 6.06218i) q^{65} +(3.79129 - 6.56670i) q^{66} +(-12.1652 + 7.02355i) q^{67} -2.79129 q^{68} +(4.29129 + 7.43273i) q^{69} +10.0308i q^{70} +(-3.87386 + 2.23658i) q^{71} +(1.50000 + 0.866025i) q^{72} +(-7.50000 - 4.33013i) q^{73} +15.3739 q^{74} +2.00000 q^{75} +(-12.7913 - 7.38505i) q^{76} +9.16515 q^{77} +(1.89564 + 7.66115i) q^{78} +(0.708712 + 1.22753i) q^{79} +(-2.68693 + 1.55130i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.89564 - 6.74745i) q^{82} -3.46410i q^{83} +7.38505i q^{84} +(1.50000 - 0.866025i) q^{85} +(8.68693 - 5.01540i) q^{86} -7.00000 q^{87} +(-3.00000 - 5.19615i) q^{88} -15.5885i q^{89} -3.79129 q^{90} +(-6.87386 + 6.61438i) q^{91} +23.9564 q^{92} -6.10985i q^{93} +(-0.895644 - 1.55130i) q^{94} +9.16515 q^{95} +(-6.39564 + 3.69253i) q^{96} +(9.08258 - 5.24383i) q^{97} +(-13.2695 + 7.66115i) q^{98} +3.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{3} - 2q^{4} + 6q^{5} + 3q^{6} - 2q^{9} + O(q^{10}) \) \( 4q - 2q^{3} - 2q^{4} + 6q^{5} + 3q^{6} - 2q^{9} + 3q^{10} + 12q^{11} + q^{12} - 4q^{13} - 7q^{14} - 6q^{15} + 2q^{16} + 4q^{17} - 3q^{18} - 3q^{20} + 6q^{22} - 16q^{23} - 6q^{24} - 4q^{25} - 12q^{26} + 4q^{27} - 21q^{28} + 14q^{29} + 3q^{30} + 12q^{31} - 12q^{33} + q^{36} - 14q^{38} + 14q^{39} - 6q^{40} + 6q^{41} + 14q^{42} - 6q^{44} - 12q^{47} - q^{48} + 14q^{49} - 6q^{50} - 2q^{51} + 2q^{52} - 6q^{53} + 12q^{55} + 21q^{58} + 3q^{60} - 8q^{61} - 13q^{62} + 32q^{64} + 6q^{65} + 6q^{66} - 12q^{67} - 2q^{68} + 8q^{69} + 12q^{71} + 6q^{72} - 30q^{73} + 34q^{74} + 8q^{75} - 42q^{76} + 3q^{78} + 12q^{79} + 3q^{80} - 2q^{81} + 11q^{82} + 6q^{85} + 21q^{86} - 28q^{87} - 12q^{88} - 6q^{90} + 50q^{92} + q^{94} - 21q^{96} + 18q^{97} - 21q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.18890i 1.54779i 0.633316 + 0.773893i \(0.281693\pi\)
−0.633316 + 0.773893i \(0.718307\pi\)
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) −2.79129 −1.39564
\(5\) 1.50000 0.866025i 0.670820 0.387298i −0.125567 0.992085i \(-0.540075\pi\)
0.796387 + 0.604787i \(0.206742\pi\)
\(6\) 1.89564 1.09445i 0.773893 0.446808i
\(7\) 2.29129 + 1.32288i 0.866025 + 0.500000i
\(8\) 1.73205i 0.612372i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 1.89564 + 3.28335i 0.599455 + 1.03829i
\(11\) 3.00000 1.73205i 0.904534 0.522233i 0.0258656 0.999665i \(-0.491766\pi\)
0.878668 + 0.477432i \(0.158432\pi\)
\(12\) 1.39564 + 2.41733i 0.402888 + 0.697822i
\(13\) −1.00000 + 3.46410i −0.277350 + 0.960769i
\(14\) −2.89564 + 5.01540i −0.773893 + 1.34042i
\(15\) −1.50000 0.866025i −0.387298 0.223607i
\(16\) −1.79129 −0.447822
\(17\) 1.00000 0.242536 0.121268 0.992620i \(-0.461304\pi\)
0.121268 + 0.992620i \(0.461304\pi\)
\(18\) −1.89564 1.09445i −0.446808 0.257964i
\(19\) 4.58258 + 2.64575i 1.05131 + 0.606977i 0.923017 0.384759i \(-0.125715\pi\)
0.128298 + 0.991736i \(0.459049\pi\)
\(20\) −4.18693 + 2.41733i −0.936226 + 0.540531i
\(21\) 2.64575i 0.577350i
\(22\) 3.79129 + 6.56670i 0.808305 + 1.40003i
\(23\) −8.58258 −1.78959 −0.894795 0.446476i \(-0.852679\pi\)
−0.894795 + 0.446476i \(0.852679\pi\)
\(24\) −1.50000 + 0.866025i −0.306186 + 0.176777i
\(25\) −1.00000 + 1.73205i −0.200000 + 0.346410i
\(26\) −7.58258 2.18890i −1.48707 0.429279i
\(27\) 1.00000 0.192450
\(28\) −6.39564 3.69253i −1.20866 0.697822i
\(29\) 3.50000 6.06218i 0.649934 1.12572i −0.333205 0.942855i \(-0.608130\pi\)
0.983138 0.182864i \(-0.0585367\pi\)
\(30\) 1.89564 3.28335i 0.346096 0.599455i
\(31\) 5.29129 + 3.05493i 0.950343 + 0.548681i 0.893188 0.449684i \(-0.148463\pi\)
0.0571558 + 0.998365i \(0.481797\pi\)
\(32\) 7.38505i 1.30551i
\(33\) −3.00000 1.73205i −0.522233 0.301511i
\(34\) 2.18890i 0.375393i
\(35\) 4.58258 0.774597
\(36\) 1.39564 2.41733i 0.232607 0.402888i
\(37\) 7.02355i 1.15467i −0.816509 0.577333i \(-0.804094\pi\)
0.816509 0.577333i \(-0.195906\pi\)
\(38\) −5.79129 + 10.0308i −0.939471 + 1.62721i
\(39\) 3.50000 0.866025i 0.560449 0.138675i
\(40\) −1.50000 2.59808i −0.237171 0.410792i
\(41\) −3.08258 1.77973i −0.481417 0.277946i 0.239590 0.970874i \(-0.422987\pi\)
−0.721007 + 0.692928i \(0.756320\pi\)
\(42\) 5.79129 0.893615
\(43\) −2.29129 3.96863i −0.349418 0.605210i 0.636728 0.771088i \(-0.280287\pi\)
−0.986146 + 0.165878i \(0.946954\pi\)
\(44\) −8.37386 + 4.83465i −1.26241 + 0.728851i
\(45\) 1.73205i 0.258199i
\(46\) 18.7864i 2.76990i
\(47\) −0.708712 + 0.409175i −0.103376 + 0.0596843i −0.550797 0.834639i \(-0.685676\pi\)
0.447421 + 0.894324i \(0.352343\pi\)
\(48\) 0.895644 + 1.55130i 0.129275 + 0.223911i
\(49\) 3.50000 + 6.06218i 0.500000 + 0.866025i
\(50\) −3.79129 2.18890i −0.536169 0.309557i
\(51\) −0.500000 0.866025i −0.0700140 0.121268i
\(52\) 2.79129 9.66930i 0.387082 1.34089i
\(53\) 3.08258 5.33918i 0.423424 0.733392i −0.572848 0.819662i \(-0.694161\pi\)
0.996272 + 0.0862695i \(0.0274946\pi\)
\(54\) 2.18890i 0.297872i
\(55\) 3.00000 5.19615i 0.404520 0.700649i
\(56\) 2.29129 3.96863i 0.306186 0.530330i
\(57\) 5.29150i 0.700877i
\(58\) 13.2695 + 7.66115i 1.74237 + 1.00596i
\(59\) 4.28245i 0.557528i 0.960360 + 0.278764i \(0.0899247\pi\)
−0.960360 + 0.278764i \(0.910075\pi\)
\(60\) 4.18693 + 2.41733i 0.540531 + 0.312075i
\(61\) 2.58258 4.47315i 0.330665 0.572728i −0.651977 0.758238i \(-0.726060\pi\)
0.982642 + 0.185510i \(0.0593937\pi\)
\(62\) −6.68693 + 11.5821i −0.849241 + 1.47093i
\(63\) −2.29129 + 1.32288i −0.288675 + 0.166667i
\(64\) 12.5826 1.57282
\(65\) 1.50000 + 6.06218i 0.186052 + 0.751921i
\(66\) 3.79129 6.56670i 0.466675 0.808305i
\(67\) −12.1652 + 7.02355i −1.48621 + 0.858064i −0.999877 0.0157098i \(-0.994999\pi\)
−0.486333 + 0.873773i \(0.661666\pi\)
\(68\) −2.79129 −0.338493
\(69\) 4.29129 + 7.43273i 0.516610 + 0.894795i
\(70\) 10.0308i 1.19891i
\(71\) −3.87386 + 2.23658i −0.459743 + 0.265433i −0.711936 0.702244i \(-0.752181\pi\)
0.252193 + 0.967677i \(0.418848\pi\)
\(72\) 1.50000 + 0.866025i 0.176777 + 0.102062i
\(73\) −7.50000 4.33013i −0.877809 0.506803i −0.00787336 0.999969i \(-0.502506\pi\)
−0.869935 + 0.493166i \(0.835840\pi\)
\(74\) 15.3739 1.78718
\(75\) 2.00000 0.230940
\(76\) −12.7913 7.38505i −1.46726 0.847124i
\(77\) 9.16515 1.04447
\(78\) 1.89564 + 7.66115i 0.214639 + 0.867455i
\(79\) 0.708712 + 1.22753i 0.0797363 + 0.138107i 0.903136 0.429354i \(-0.141259\pi\)
−0.823400 + 0.567462i \(0.807925\pi\)
\(80\) −2.68693 + 1.55130i −0.300408 + 0.173441i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 3.89564 6.74745i 0.430202 0.745132i
\(83\) 3.46410i 0.380235i −0.981761 0.190117i \(-0.939113\pi\)
0.981761 0.190117i \(-0.0608868\pi\)
\(84\) 7.38505i 0.805775i
\(85\) 1.50000 0.866025i 0.162698 0.0939336i
\(86\) 8.68693 5.01540i 0.936736 0.540825i
\(87\) −7.00000 −0.750479
\(88\) −3.00000 5.19615i −0.319801 0.553912i
\(89\) 15.5885i 1.65237i −0.563397 0.826187i \(-0.690506\pi\)
0.563397 0.826187i \(-0.309494\pi\)
\(90\) −3.79129 −0.399637
\(91\) −6.87386 + 6.61438i −0.720577 + 0.693375i
\(92\) 23.9564 2.49763
\(93\) 6.10985i 0.633562i
\(94\) −0.895644 1.55130i −0.0923786 0.160004i
\(95\) 9.16515 0.940325
\(96\) −6.39564 + 3.69253i −0.652753 + 0.376867i
\(97\) 9.08258 5.24383i 0.922196 0.532430i 0.0378609 0.999283i \(-0.487946\pi\)
0.884335 + 0.466853i \(0.154612\pi\)
\(98\) −13.2695 + 7.66115i −1.34042 + 0.773893i
\(99\) 3.46410i 0.348155i
\(100\) 2.79129 4.83465i 0.279129 0.483465i
\(101\) −6.58258 11.4014i −0.654991 1.13448i −0.981896 0.189420i \(-0.939339\pi\)
0.326905 0.945057i \(-0.393994\pi\)
\(102\) 1.89564 1.09445i 0.187697 0.108367i
\(103\) −1.70871 2.95958i −0.168364 0.291616i 0.769481 0.638670i \(-0.220515\pi\)
−0.937845 + 0.347055i \(0.887182\pi\)
\(104\) 6.00000 + 1.73205i 0.588348 + 0.169842i
\(105\) −2.29129 3.96863i −0.223607 0.387298i
\(106\) 11.6869 + 6.74745i 1.13514 + 0.655371i
\(107\) −1.41742 −0.137028 −0.0685138 0.997650i \(-0.521826\pi\)
−0.0685138 + 0.997650i \(0.521826\pi\)
\(108\) −2.79129 −0.268592
\(109\) −16.6652 9.62163i −1.59623 0.921585i −0.992204 0.124622i \(-0.960228\pi\)
−0.604028 0.796963i \(-0.706438\pi\)
\(110\) 11.3739 + 6.56670i 1.08446 + 0.626111i
\(111\) −6.08258 + 3.51178i −0.577333 + 0.333323i
\(112\) −4.10436 2.36965i −0.387825 0.223911i
\(113\) −6.08258 10.5353i −0.572201 0.991080i −0.996340 0.0854834i \(-0.972757\pi\)
0.424139 0.905597i \(-0.360577\pi\)
\(114\) 11.5826 1.08481
\(115\) −12.8739 + 7.43273i −1.20049 + 0.693106i
\(116\) −9.76951 + 16.9213i −0.907076 + 1.57110i
\(117\) −2.50000 2.59808i −0.231125 0.240192i
\(118\) −9.37386 −0.862934
\(119\) 2.29129 + 1.32288i 0.210042 + 0.121268i
\(120\) −1.50000 + 2.59808i −0.136931 + 0.237171i
\(121\) 0.500000 0.866025i 0.0454545 0.0787296i
\(122\) 9.79129 + 5.65300i 0.886462 + 0.511799i
\(123\) 3.55945i 0.320945i
\(124\) −14.7695 8.52718i −1.32634 0.765763i
\(125\) 12.1244i 1.08444i
\(126\) −2.89564 5.01540i −0.257964 0.446808i
\(127\) −3.29129 + 5.70068i −0.292055 + 0.505853i −0.974295 0.225274i \(-0.927672\pi\)
0.682241 + 0.731128i \(0.261006\pi\)
\(128\) 12.7719i 1.12889i
\(129\) −2.29129 + 3.96863i −0.201737 + 0.349418i
\(130\) −13.2695 + 3.28335i −1.16381 + 0.287969i
\(131\) −0.708712 1.22753i −0.0619205 0.107249i 0.833403 0.552665i \(-0.186389\pi\)
−0.895324 + 0.445416i \(0.853056\pi\)
\(132\) 8.37386 + 4.83465i 0.728851 + 0.420802i
\(133\) 7.00000 + 12.1244i 0.606977 + 1.05131i
\(134\) −15.3739 26.6283i −1.32810 2.30034i
\(135\) 1.50000 0.866025i 0.129099 0.0745356i
\(136\) 1.73205i 0.148522i
\(137\) 8.66025i 0.739895i 0.929053 + 0.369948i \(0.120624\pi\)
−0.929053 + 0.369948i \(0.879376\pi\)
\(138\) −16.2695 + 9.39320i −1.38495 + 0.799603i
\(139\) 3.29129 + 5.70068i 0.279163 + 0.483525i 0.971177 0.238359i \(-0.0766096\pi\)
−0.692014 + 0.721884i \(0.743276\pi\)
\(140\) −12.7913 −1.08106
\(141\) 0.708712 + 0.409175i 0.0596843 + 0.0344588i
\(142\) −4.89564 8.47950i −0.410833 0.711584i
\(143\) 3.00000 + 12.1244i 0.250873 + 1.01389i
\(144\) 0.895644 1.55130i 0.0746370 0.129275i
\(145\) 12.1244i 1.00687i
\(146\) 9.47822 16.4168i 0.784423 1.35866i
\(147\) 3.50000 6.06218i 0.288675 0.500000i
\(148\) 19.6048i 1.61150i
\(149\) 3.16515 + 1.82740i 0.259299 + 0.149707i 0.624015 0.781412i \(-0.285500\pi\)
−0.364716 + 0.931119i \(0.618834\pi\)
\(150\) 4.37780i 0.357446i
\(151\) 14.4564 + 8.34643i 1.17645 + 0.679223i 0.955190 0.295993i \(-0.0956503\pi\)
0.221258 + 0.975215i \(0.428984\pi\)
\(152\) 4.58258 7.93725i 0.371696 0.643796i
\(153\) −0.500000 + 0.866025i −0.0404226 + 0.0700140i
\(154\) 20.0616i 1.61661i
\(155\) 10.5826 0.850013
\(156\) −9.76951 + 2.41733i −0.782187 + 0.193541i
\(157\) −5.08258 + 8.80328i −0.405634 + 0.702578i −0.994395 0.105729i \(-0.966282\pi\)
0.588761 + 0.808307i \(0.299616\pi\)
\(158\) −2.68693 + 1.55130i −0.213761 + 0.123415i
\(159\) −6.16515 −0.488928
\(160\) −6.39564 11.0776i −0.505620 0.875760i
\(161\) −19.6652 11.3537i −1.54983 0.894795i
\(162\) 1.89564 1.09445i 0.148936 0.0859882i
\(163\) 3.00000 + 1.73205i 0.234978 + 0.135665i 0.612866 0.790186i \(-0.290016\pi\)
−0.377888 + 0.925851i \(0.623350\pi\)
\(164\) 8.60436 + 4.96773i 0.671887 + 0.387914i
\(165\) −6.00000 −0.467099
\(166\) 7.58258 0.588522
\(167\) 3.87386 + 2.23658i 0.299769 + 0.173071i 0.642339 0.766421i \(-0.277964\pi\)
−0.342570 + 0.939492i \(0.611298\pi\)
\(168\) −4.58258 −0.353553
\(169\) −11.0000 6.92820i −0.846154 0.532939i
\(170\) 1.89564 + 3.28335i 0.145389 + 0.251822i
\(171\) −4.58258 + 2.64575i −0.350438 + 0.202326i
\(172\) 6.39564 + 11.0776i 0.487663 + 0.844658i
\(173\) −12.1652 + 21.0707i −0.924899 + 1.60197i −0.133176 + 0.991092i \(0.542518\pi\)
−0.791723 + 0.610880i \(0.790816\pi\)
\(174\) 15.3223i 1.16158i
\(175\) −4.58258 + 2.64575i −0.346410 + 0.200000i
\(176\) −5.37386 + 3.10260i −0.405070 + 0.233867i
\(177\) 3.70871 2.14123i 0.278764 0.160944i
\(178\) 34.1216 2.55752
\(179\) −0.417424 0.723000i −0.0311998 0.0540396i 0.850004 0.526776i \(-0.176599\pi\)
−0.881204 + 0.472737i \(0.843266\pi\)
\(180\) 4.83465i 0.360354i
\(181\) 22.0000 1.63525 0.817624 0.575753i \(-0.195291\pi\)
0.817624 + 0.575753i \(0.195291\pi\)
\(182\) −14.4782 15.0462i −1.07320 1.11530i
\(183\) −5.16515 −0.381819
\(184\) 14.8655i 1.09590i
\(185\) −6.08258 10.5353i −0.447200 0.774573i
\(186\) 13.3739 0.980619
\(187\) 3.00000 1.73205i 0.219382 0.126660i
\(188\) 1.97822 1.14213i 0.144276 0.0832981i
\(189\) 2.29129 + 1.32288i 0.166667 + 0.0962250i
\(190\) 20.0616i 1.45542i
\(191\) 7.16515 12.4104i 0.518452 0.897985i −0.481318 0.876546i \(-0.659842\pi\)
0.999770 0.0214394i \(-0.00682490\pi\)
\(192\) −6.29129 10.8968i −0.454035 0.786411i
\(193\) −3.16515 + 1.82740i −0.227833 + 0.131539i −0.609572 0.792731i \(-0.708659\pi\)
0.381739 + 0.924270i \(0.375325\pi\)
\(194\) 11.4782 + 19.8809i 0.824088 + 1.42736i
\(195\) 4.50000 4.33013i 0.322252 0.310087i
\(196\) −9.76951 16.9213i −0.697822 1.20866i
\(197\) 15.2477 + 8.80328i 1.08636 + 0.627208i 0.932604 0.360902i \(-0.117531\pi\)
0.153752 + 0.988110i \(0.450864\pi\)
\(198\) −7.58258 −0.538870
\(199\) 2.58258 0.183074 0.0915370 0.995802i \(-0.470822\pi\)
0.0915370 + 0.995802i \(0.470822\pi\)
\(200\) 3.00000 + 1.73205i 0.212132 + 0.122474i
\(201\) 12.1652 + 7.02355i 0.858064 + 0.495403i
\(202\) 24.9564 14.4086i 1.75593 1.01379i
\(203\) 16.0390 9.26013i 1.12572 0.649934i
\(204\) 1.39564 + 2.41733i 0.0977146 + 0.169247i
\(205\) −6.16515 −0.430593
\(206\) 6.47822 3.74020i 0.451359 0.260592i
\(207\) 4.29129 7.43273i 0.298265 0.516610i
\(208\) 1.79129 6.20520i 0.124203 0.430253i
\(209\) 18.3303 1.26793
\(210\) 8.68693 5.01540i 0.599455 0.346096i
\(211\) −3.29129 + 5.70068i −0.226582 + 0.392451i −0.956793 0.290771i \(-0.906088\pi\)
0.730211 + 0.683222i \(0.239422\pi\)
\(212\) −8.60436 + 14.9032i −0.590950 + 1.02355i
\(213\) 3.87386 + 2.23658i 0.265433 + 0.153248i
\(214\) 3.10260i 0.212089i
\(215\) −6.87386 3.96863i −0.468794 0.270658i
\(216\) 1.73205i 0.117851i
\(217\) 8.08258 + 13.9994i 0.548681 + 0.950343i
\(218\) 21.0608 36.4784i 1.42642 2.47063i
\(219\) 8.66025i 0.585206i
\(220\) −8.37386 + 14.5040i −0.564566 + 0.977857i
\(221\) −1.00000 + 3.46410i −0.0672673 + 0.233021i
\(222\) −7.68693 13.3142i −0.515913 0.893588i
\(223\) −2.29129 1.32288i −0.153436 0.0885863i 0.421316 0.906914i \(-0.361568\pi\)
−0.574752 + 0.818327i \(0.694902\pi\)
\(224\) 9.76951 16.9213i 0.652753 1.13060i
\(225\) −1.00000 1.73205i −0.0666667 0.115470i
\(226\) 23.0608 13.3142i 1.53398 0.885645i
\(227\) 27.2759i 1.81036i 0.425026 + 0.905181i \(0.360265\pi\)
−0.425026 + 0.905181i \(0.639735\pi\)
\(228\) 14.7701i 0.978174i
\(229\) −9.08258 + 5.24383i −0.600193 + 0.346522i −0.769118 0.639107i \(-0.779304\pi\)
0.168924 + 0.985629i \(0.445971\pi\)
\(230\) −16.2695 28.1796i −1.07278 1.85811i
\(231\) −4.58258 7.93725i −0.301511 0.522233i
\(232\) −10.5000 6.06218i −0.689359 0.398001i
\(233\) −10.0826 17.4635i −0.660531 1.14407i −0.980476 0.196638i \(-0.936998\pi\)
0.319945 0.947436i \(-0.396336\pi\)
\(234\) 5.68693 5.47225i 0.371766 0.357732i
\(235\) −0.708712 + 1.22753i −0.0462313 + 0.0800749i
\(236\) 11.9536i 0.778110i
\(237\) 0.708712 1.22753i 0.0460358 0.0797363i
\(238\) −2.89564 + 5.01540i −0.187697 + 0.325100i
\(239\) 2.01810i 0.130540i 0.997868 + 0.0652701i \(0.0207909\pi\)
−0.997868 + 0.0652701i \(0.979209\pi\)
\(240\) 2.68693 + 1.55130i 0.173441 + 0.100136i
\(241\) 14.1425i 0.910996i −0.890237 0.455498i \(-0.849461\pi\)
0.890237 0.455498i \(-0.150539\pi\)
\(242\) 1.89564 + 1.09445i 0.121857 + 0.0703539i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) −7.20871 + 12.4859i −0.461491 + 0.799325i
\(245\) 10.5000 + 6.06218i 0.670820 + 0.387298i
\(246\) −7.79129 −0.496754
\(247\) −13.7477 + 13.2288i −0.874747 + 0.841726i
\(248\) 5.29129 9.16478i 0.335997 0.581964i
\(249\) −3.00000 + 1.73205i −0.190117 + 0.109764i
\(250\) −26.5390 −1.67847
\(251\) 10.2913 + 17.8250i 0.649580 + 1.12511i 0.983223 + 0.182407i \(0.0583887\pi\)
−0.333643 + 0.942700i \(0.608278\pi\)
\(252\) 6.39564 3.69253i 0.402888 0.232607i
\(253\) −25.7477 + 14.8655i −1.61875 + 0.934583i
\(254\) −12.4782 7.20430i −0.782953 0.452038i
\(255\) −1.50000 0.866025i −0.0939336 0.0542326i
\(256\) −2.79129 −0.174455
\(257\) −9.33030 −0.582008 −0.291004 0.956722i \(-0.593989\pi\)
−0.291004 + 0.956722i \(0.593989\pi\)
\(258\) −8.68693 5.01540i −0.540825 0.312245i
\(259\) 9.29129 16.0930i 0.577333 0.999969i
\(260\) −4.18693 16.9213i −0.259662 1.04941i
\(261\) 3.50000 + 6.06218i 0.216645 + 0.375239i
\(262\) 2.68693 1.55130i 0.165999 0.0958397i
\(263\) 2.41742 + 4.18710i 0.149065 + 0.258188i 0.930882 0.365320i \(-0.119040\pi\)
−0.781817 + 0.623508i \(0.785707\pi\)
\(264\) −3.00000 + 5.19615i −0.184637 + 0.319801i
\(265\) 10.6784i 0.655966i
\(266\) −26.5390 + 15.3223i −1.62721 + 0.939471i
\(267\) −13.5000 + 7.79423i −0.826187 + 0.476999i
\(268\) 33.9564 19.6048i 2.07422 1.19755i
\(269\) 16.1652 0.985607 0.492803 0.870141i \(-0.335972\pi\)
0.492803 + 0.870141i \(0.335972\pi\)
\(270\) 1.89564 + 3.28335i 0.115365 + 0.199818i
\(271\) 11.5921i 0.704167i −0.935969 0.352084i \(-0.885473\pi\)
0.935969 0.352084i \(-0.114527\pi\)
\(272\) −1.79129 −0.108613
\(273\) 9.16515 + 2.64575i 0.554700 + 0.160128i
\(274\) −18.9564 −1.14520
\(275\) 6.92820i 0.417786i
\(276\) −11.9782 20.7469i −0.721004 1.24882i
\(277\) 9.33030 0.560604 0.280302 0.959912i \(-0.409565\pi\)
0.280302 + 0.959912i \(0.409565\pi\)
\(278\) −12.4782 + 7.20430i −0.748394 + 0.432085i
\(279\) −5.29129 + 3.05493i −0.316781 + 0.182894i
\(280\) 7.93725i 0.474342i
\(281\) 3.65480i 0.218027i 0.994040 + 0.109014i \(0.0347692\pi\)
−0.994040 + 0.109014i \(0.965231\pi\)
\(282\) −0.895644 + 1.55130i −0.0533348 + 0.0923786i
\(283\) 15.1652 + 26.2668i 0.901475 + 1.56140i 0.825581 + 0.564284i \(0.190848\pi\)
0.0758940 + 0.997116i \(0.475819\pi\)
\(284\) 10.8131 6.24293i 0.641638 0.370450i
\(285\) −4.58258 7.93725i −0.271448 0.470162i
\(286\) −26.5390 + 6.56670i −1.56928 + 0.388297i
\(287\) −4.70871 8.15573i −0.277946 0.481417i
\(288\) 6.39564 + 3.69253i 0.376867 + 0.217584i
\(289\) −16.0000 −0.941176
\(290\) 26.5390 1.55842
\(291\) −9.08258 5.24383i −0.532430 0.307399i
\(292\) 20.9347 + 12.0866i 1.22511 + 0.707317i
\(293\) 16.8303 9.71698i 0.983237 0.567672i 0.0799910 0.996796i \(-0.474511\pi\)
0.903246 + 0.429124i \(0.141178\pi\)
\(294\) 13.2695 + 7.66115i 0.773893 + 0.446808i
\(295\) 3.70871 + 6.42368i 0.215930 + 0.374001i
\(296\) −12.1652 −0.707085
\(297\) 3.00000 1.73205i 0.174078 0.100504i
\(298\) −4.00000 + 6.92820i −0.231714 + 0.401340i
\(299\) 8.58258 29.7309i 0.496343 1.71938i
\(300\) −5.58258 −0.322310
\(301\) 12.1244i 0.698836i
\(302\) −18.2695 + 31.6437i −1.05129 + 1.82089i
\(303\) −6.58258 + 11.4014i −0.378159 + 0.654991i
\(304\) −8.20871 4.73930i −0.470802 0.271818i
\(305\) 8.94630i 0.512264i
\(306\) −1.89564 1.09445i −0.108367 0.0625656i
\(307\) 20.9753i 1.19712i −0.801076 0.598562i \(-0.795739\pi\)
0.801076 0.598562i \(-0.204261\pi\)
\(308\) −25.5826 −1.45770
\(309\) −1.70871 + 2.95958i −0.0972052 + 0.168364i
\(310\) 23.1642i 1.31564i
\(311\) 4.29129 7.43273i 0.243337 0.421471i −0.718326 0.695707i \(-0.755091\pi\)
0.961663 + 0.274235i \(0.0884247\pi\)
\(312\) −1.50000 6.06218i −0.0849208 0.343203i
\(313\) 6.91742 + 11.9813i 0.390996 + 0.677225i 0.992581 0.121584i \(-0.0387973\pi\)
−0.601585 + 0.798809i \(0.705464\pi\)
\(314\) −19.2695 11.1253i −1.08744 0.627834i
\(315\) −2.29129 + 3.96863i −0.129099 + 0.223607i
\(316\) −1.97822 3.42638i −0.111284 0.192749i
\(317\) −1.66515 + 0.961376i −0.0935242 + 0.0539962i −0.546033 0.837764i \(-0.683863\pi\)
0.452508 + 0.891760i \(0.350529\pi\)
\(318\) 13.4949i 0.756757i
\(319\) 24.2487i 1.35767i
\(320\) 18.8739 10.8968i 1.05508 0.609151i
\(321\) 0.708712 + 1.22753i 0.0395565 + 0.0685138i
\(322\) 24.8521 43.0451i 1.38495 2.39881i
\(323\) 4.58258 + 2.64575i 0.254981 + 0.147214i
\(324\) 1.39564 + 2.41733i 0.0775358 + 0.134296i
\(325\) −5.00000 5.19615i −0.277350 0.288231i
\(326\) −3.79129 + 6.56670i −0.209980 + 0.363696i
\(327\) 19.2433i 1.06415i
\(328\) −3.08258 + 5.33918i −0.170207 + 0.294807i
\(329\) −2.16515 −0.119369
\(330\) 13.1334i 0.722970i
\(331\) −22.5826 13.0381i −1.24125 0.716636i −0.271902 0.962325i \(-0.587653\pi\)
−0.969349 + 0.245689i \(0.920986\pi\)
\(332\) 9.66930i 0.530672i
\(333\) 6.08258 + 3.51178i 0.333323 + 0.192444i
\(334\) −4.89564 + 8.47950i −0.267878 + 0.463978i
\(335\) −12.1652 + 21.0707i −0.664653 + 1.15121i
\(336\) 4.73930i 0.258550i
\(337\) 23.4955 1.27988 0.639939 0.768425i \(-0.278959\pi\)
0.639939 + 0.768425i \(0.278959\pi\)
\(338\) 15.1652 24.0779i 0.824875 1.30967i
\(339\) −6.08258 + 10.5353i −0.330360 + 0.572201i
\(340\) −4.18693 + 2.41733i −0.227068 + 0.131098i
\(341\) 21.1652 1.14616
\(342\) −5.79129 10.0308i −0.313157 0.542404i
\(343\) 18.5203i 1.00000i
\(344\) −6.87386 + 3.96863i −0.370614 + 0.213974i
\(345\) 12.8739 + 7.43273i 0.693106 + 0.400165i
\(346\) −46.1216 26.6283i −2.47951 1.43155i
\(347\) −25.7477 −1.38221 −0.691105 0.722754i \(-0.742876\pi\)
−0.691105 + 0.722754i \(0.742876\pi\)
\(348\) 19.5390 1.04740
\(349\) 9.08258 + 5.24383i 0.486179 + 0.280696i 0.722988 0.690861i \(-0.242768\pi\)
−0.236809 + 0.971556i \(0.576102\pi\)
\(350\) −5.79129 10.0308i −0.309557 0.536169i
\(351\) −1.00000 + 3.46410i −0.0533761 + 0.184900i
\(352\) −12.7913 22.1552i −0.681778 1.18087i
\(353\) −16.7477 + 9.66930i −0.891392 + 0.514645i −0.874397 0.485210i \(-0.838743\pi\)
−0.0169942 + 0.999856i \(0.505410\pi\)
\(354\) 4.68693 + 8.11800i 0.249108 + 0.431467i
\(355\) −3.87386 + 6.70973i −0.205603 + 0.356115i
\(356\) 43.5119i 2.30612i
\(357\) 2.64575i 0.140028i
\(358\) 1.58258 0.913701i 0.0836417 0.0482906i
\(359\) 16.0390 9.26013i 0.846507 0.488731i −0.0129639 0.999916i \(-0.504127\pi\)
0.859471 + 0.511185i \(0.170793\pi\)
\(360\) 3.00000 0.158114
\(361\) 4.50000 + 7.79423i 0.236842 + 0.410223i
\(362\) 48.1558i 2.53101i
\(363\) −1.00000 −0.0524864
\(364\) 19.1869 18.4626i 1.00567 0.967705i
\(365\) −15.0000 −0.785136
\(366\) 11.3060i 0.590974i
\(367\) −7.58258 13.1334i −0.395807 0.685558i 0.597397 0.801946i \(-0.296202\pi\)
−0.993204 + 0.116388i \(0.962868\pi\)
\(368\) 15.3739 0.801418
\(369\) 3.08258 1.77973i 0.160472 0.0926488i
\(370\) 23.0608 13.3142i 1.19887 0.692170i
\(371\) 14.1261 8.15573i 0.733392 0.423424i
\(372\) 17.0544i 0.884227i
\(373\) 13.0000 22.5167i 0.673114 1.16587i −0.303902 0.952703i \(-0.598289\pi\)
0.977016 0.213165i \(-0.0683772\pi\)
\(374\) 3.79129 + 6.56670i 0.196043 + 0.339556i
\(375\) 10.5000 6.06218i 0.542218 0.313050i
\(376\) 0.708712 + 1.22753i 0.0365490 + 0.0633048i
\(377\) 17.5000 + 18.1865i 0.901296 + 0.936654i
\(378\) −2.89564 + 5.01540i −0.148936 + 0.257964i
\(379\) 16.0390 + 9.26013i 0.823869 + 0.475661i 0.851749 0.523950i \(-0.175542\pi\)
−0.0278799 + 0.999611i \(0.508876\pi\)
\(380\) −25.5826 −1.31236
\(381\) 6.58258 0.337236
\(382\) 27.1652 + 15.6838i 1.38989 + 0.802453i
\(383\) −15.3303 8.85095i −0.783342 0.452263i 0.0542715 0.998526i \(-0.482716\pi\)
−0.837613 + 0.546264i \(0.816050\pi\)
\(384\) 11.0608 6.38595i 0.564444 0.325882i
\(385\) 13.7477 7.93725i 0.700649 0.404520i
\(386\) −4.00000 6.92820i −0.203595 0.352636i
\(387\) 4.58258 0.232945
\(388\) −25.3521 + 14.6370i −1.28706 + 0.743083i
\(389\) −13.6652 + 23.6687i −0.692851 + 1.20005i 0.278049 + 0.960567i \(0.410312\pi\)
−0.970900 + 0.239486i \(0.923021\pi\)
\(390\) 9.47822 + 9.85005i 0.479948 + 0.498777i
\(391\) −8.58258 −0.434040
\(392\) 10.5000 6.06218i 0.530330 0.306186i
\(393\) −0.708712 + 1.22753i −0.0357498 + 0.0619205i
\(394\) −19.2695 + 33.3758i −0.970784 + 1.68145i
\(395\) 2.12614 + 1.22753i 0.106978 + 0.0617635i
\(396\) 9.66930i 0.485901i
\(397\) 31.9129 + 18.4249i 1.60166 + 0.924720i 0.991155 + 0.132708i \(0.0423673\pi\)
0.610506 + 0.792011i \(0.290966\pi\)
\(398\) 5.65300i 0.283359i
\(399\) 7.00000 12.1244i 0.350438 0.606977i
\(400\) 1.79129 3.10260i 0.0895644 0.155130i
\(401\) 34.7364i 1.73465i 0.497741 + 0.867326i \(0.334163\pi\)
−0.497741 + 0.867326i \(0.665837\pi\)
\(402\) −15.3739 + 26.6283i −0.766779 + 1.32810i
\(403\) −15.8739 + 15.2746i −0.790733 + 0.760884i
\(404\) 18.3739 + 31.8245i 0.914134 + 1.58333i
\(405\) −1.50000 0.866025i −0.0745356 0.0430331i
\(406\) 20.2695 + 35.1078i 1.00596 + 1.74237i
\(407\) −12.1652 21.0707i −0.603004 1.04443i
\(408\) −1.50000 + 0.866025i −0.0742611 + 0.0428746i
\(409\) 31.2723i 1.54631i −0.634215 0.773157i \(-0.718676\pi\)
0.634215 0.773157i \(-0.281324\pi\)
\(410\) 13.4949i 0.666466i
\(411\) 7.50000 4.33013i 0.369948 0.213589i
\(412\) 4.76951 + 8.26103i 0.234977 + 0.406992i
\(413\) −5.66515 + 9.81233i −0.278764 + 0.482833i
\(414\) 16.2695 + 9.39320i 0.799603 + 0.461651i
\(415\) −3.00000 5.19615i −0.147264 0.255069i
\(416\) 25.5826 + 7.38505i 1.25429 + 0.362082i
\(417\) 3.29129 5.70068i 0.161175 0.279163i
\(418\) 40.1232i 1.96249i
\(419\) −5.87386 + 10.1738i −0.286957 + 0.497024i −0.973082 0.230460i \(-0.925977\pi\)
0.686125 + 0.727484i \(0.259310\pi\)
\(420\) 6.39564 + 11.0776i 0.312075 + 0.540531i
\(421\) 40.5046i 1.97407i −0.160492 0.987037i \(-0.551308\pi\)
0.160492 0.987037i \(-0.448692\pi\)
\(422\) −12.4782 7.20430i −0.607430 0.350700i
\(423\) 0.818350i 0.0397896i
\(424\) −9.24773 5.33918i −0.449109 0.259293i
\(425\) −1.00000 + 1.73205i −0.0485071 + 0.0840168i
\(426\) −4.89564 + 8.47950i −0.237195 + 0.410833i
\(427\) 11.8348 6.83285i 0.572728 0.330665i
\(428\) 3.95644 0.191242
\(429\) 9.00000 8.66025i 0.434524 0.418121i
\(430\) 8.68693 15.0462i 0.418921 0.725593i
\(431\) −7.41742 + 4.28245i −0.357285 + 0.206278i −0.667889 0.744261i \(-0.732802\pi\)
0.310604 + 0.950539i \(0.399469\pi\)
\(432\) −1.79129 −0.0861834
\(433\) 7.66515 + 13.2764i 0.368364 + 0.638025i 0.989310 0.145829i \(-0.0465848\pi\)
−0.620946 + 0.783853i \(0.713251\pi\)
\(434\) −30.6434 + 17.6920i −1.47093 + 0.849241i
\(435\) −10.5000 + 6.06218i −0.503436 + 0.290659i
\(436\) 46.5172 + 26.8567i 2.22777 + 1.28620i
\(437\) −39.3303 22.7074i −1.88142 1.08624i
\(438\) −18.9564 −0.905774
\(439\) −10.5826 −0.505079 −0.252539 0.967587i \(-0.581266\pi\)
−0.252539 + 0.967587i \(0.581266\pi\)
\(440\) −9.00000 5.19615i −0.429058 0.247717i
\(441\) −7.00000 −0.333333
\(442\) −7.58258 2.18890i −0.360666 0.104115i
\(443\) 2.87386 + 4.97768i 0.136541 + 0.236497i 0.926185 0.377069i \(-0.123068\pi\)
−0.789644 + 0.613565i \(0.789735\pi\)
\(444\) 16.9782 9.80238i 0.805751 0.465200i
\(445\) −13.5000 23.3827i −0.639961 1.10845i
\(446\) 2.89564 5.01540i 0.137113 0.237486i
\(447\) 3.65480i 0.172866i
\(448\) 28.8303 + 16.6452i 1.36210 + 0.786411i
\(449\) −10.6652 + 6.15753i −0.503320 + 0.290592i −0.730083 0.683358i \(-0.760519\pi\)
0.226764 + 0.973950i \(0.427185\pi\)
\(450\) 3.79129 2.18890i 0.178723 0.103186i
\(451\) −12.3303 −0.580611
\(452\) 16.9782 + 29.4071i 0.798588 + 1.38320i
\(453\) 16.6929i 0.784299i
\(454\) −59.7042 −2.80206
\(455\) −4.58258 + 15.8745i −0.214834 + 0.744208i
\(456\) −9.16515 −0.429198
\(457\) 3.75015i 0.175425i −0.996146 0.0877124i \(-0.972044\pi\)
0.996146 0.0877124i \(-0.0279556\pi\)
\(458\) −11.4782 19.8809i −0.536342 0.928972i
\(459\) 1.00000 0.0466760
\(460\) 35.9347 20.7469i 1.67546 0.967328i
\(461\) −27.4129 + 15.8268i −1.27675 + 0.737129i −0.976248 0.216654i \(-0.930486\pi\)
−0.300497 + 0.953783i \(0.597152\pi\)
\(462\) 17.3739 10.0308i 0.808305 0.466675i
\(463\) 38.4865i 1.78862i −0.447448 0.894310i \(-0.647667\pi\)
0.447448 0.894310i \(-0.352333\pi\)
\(464\) −6.26951 + 10.8591i −0.291055 + 0.504121i
\(465\) −5.29129 9.16478i −0.245378 0.425006i
\(466\) 38.2259 22.0698i 1.77078 1.02236i
\(467\) 14.4564 + 25.0393i 0.668964 + 1.15868i 0.978194 + 0.207693i \(0.0665954\pi\)
−0.309230 + 0.950987i \(0.600071\pi\)
\(468\) 6.97822 + 7.25198i 0.322568 + 0.335223i
\(469\) −37.1652 −1.71613
\(470\) −2.68693 1.55130i −0.123939 0.0715562i
\(471\) 10.1652 0.468385
\(472\) 7.41742 0.341415
\(473\) −13.7477 7.93725i −0.632121 0.364955i
\(474\) 2.68693 + 1.55130i 0.123415 + 0.0712536i
\(475\) −9.16515 + 5.29150i −0.420526 + 0.242791i
\(476\) −6.39564 3.69253i −0.293144 0.169247i
\(477\) 3.08258 + 5.33918i 0.141141 + 0.244464i
\(478\) −4.41742 −0.202048
\(479\) 24.4955 14.1425i 1.11923 0.646185i 0.178023 0.984026i \(-0.443030\pi\)
0.941203 + 0.337841i \(0.109697\pi\)
\(480\) −6.39564 + 11.0776i −0.291920 + 0.505620i
\(481\) 24.3303 + 7.02355i 1.10937 + 0.320246i
\(482\) 30.9564 1.41003
\(483\) 22.7074i 1.03322i
\(484\) −1.39564 + 2.41733i −0.0634384 + 0.109878i
\(485\) 9.08258 15.7315i 0.412419 0.714330i
\(486\) −1.89564 1.09445i −0.0859882 0.0496453i
\(487\) 11.0200i 0.499362i 0.968328 + 0.249681i \(0.0803257\pi\)
−0.968328 + 0.249681i \(0.919674\pi\)
\(488\) −7.74773 4.47315i −0.350723 0.202490i
\(489\) 3.46410i 0.156652i
\(490\) −13.2695 + 22.9835i −0.599455 + 1.03829i
\(491\) −1.87386 + 3.24563i −0.0845663 + 0.146473i −0.905206 0.424972i \(-0.860284\pi\)
0.820640 + 0.571445i \(0.193617\pi\)
\(492\) 9.93545i 0.447925i
\(493\) 3.50000 6.06218i 0.157632 0.273027i
\(494\) −28.9564 30.0924i −1.30281 1.35392i
\(495\) 3.00000 + 5.19615i 0.134840 + 0.233550i
\(496\) −9.47822 5.47225i −0.425585 0.245711i
\(497\) −11.8348 −0.530866
\(498\) −3.79129 6.56670i −0.169892 0.294261i
\(499\) −21.7087 + 12.5335i −0.971815 + 0.561078i −0.899789 0.436325i \(-0.856280\pi\)
−0.0720262 + 0.997403i \(0.522947\pi\)
\(500\) 33.8426i 1.51349i
\(501\) 4.47315i 0.199846i
\(502\) −39.0172 + 22.5266i −1.74142 + 1.00541i
\(503\) −0.873864 1.51358i −0.0389636 0.0674870i 0.845886 0.533364i \(-0.179072\pi\)
−0.884850 + 0.465877i \(0.845739\pi\)
\(504\) 2.29129 + 3.96863i 0.102062 + 0.176777i
\(505\) −19.7477 11.4014i −0.878762 0.507354i
\(506\) −32.5390 56.3592i −1.44654 2.50547i
\(507\) −0.500000 + 12.9904i −0.0222058 + 0.576923i
\(508\) 9.18693 15.9122i 0.407604 0.705991i
\(509\) 27.9989i 1.24103i −0.784195 0.620514i \(-0.786924\pi\)
0.784195 0.620514i \(-0.213076\pi\)
\(510\) 1.89564 3.28335i 0.0839405 0.145389i
\(511\) −11.4564 19.8431i −0.506803 0.877809i
\(512\) 19.4340i 0.858868i
\(513\) 4.58258 + 2.64575i 0.202326 + 0.116813i
\(514\) 20.4231i 0.900825i
\(515\) −5.12614 2.95958i −0.225885 0.130415i
\(516\) 6.39564 11.0776i 0.281553 0.487663i
\(517\) −1.41742 + 2.45505i −0.0623382 + 0.107973i
\(518\) 35.2259 + 20.3377i 1.54774 + 0.893588i
\(519\) 24.3303 1.06798
\(520\) 10.5000 2.59808i 0.460455 0.113933i
\(521\) −1.66515 + 2.88413i −0.0729516 + 0.126356i −0.900194 0.435490i \(-0.856575\pi\)
0.827242 + 0.561846i \(0.189909\pi\)
\(522\) −13.2695 + 7.66115i −0.580791 + 0.335320i
\(523\) −9.74773 −0.426238 −0.213119 0.977026i \(-0.568362\pi\)
−0.213119 + 0.977026i \(0.568362\pi\)
\(524\) 1.97822 + 3.42638i 0.0864189 + 0.149682i
\(525\) 4.58258 + 2.64575i 0.200000 + 0.115470i
\(526\) −9.16515 + 5.29150i −0.399620 + 0.230720i
\(527\) 5.29129 + 3.05493i 0.230492 + 0.133075i
\(528\) 5.37386 + 3.10260i 0.233867 + 0.135023i
\(529\) 50.6606 2.20264
\(530\) 23.3739 1.01530
\(531\) −3.70871 2.14123i −0.160944 0.0929213i
\(532\) −19.5390 33.8426i −0.847124 1.46726i
\(533\) 9.24773 8.89863i 0.400564 0.385442i
\(534\) −17.0608 29.5502i −0.738293 1.27876i
\(535\) −2.12614 + 1.22753i −0.0919209 + 0.0530706i
\(536\) 12.1652 + 21.0707i 0.525455 + 0.910114i
\(537\) −0.417424 + 0.723000i −0.0180132 + 0.0311998i
\(538\) 35.3839i 1.52551i
\(539\) 21.0000 + 12.1244i 0.904534 + 0.522233i
\(540\) −4.18693 + 2.41733i −0.180177 + 0.104025i
\(541\) 7.33485 4.23478i 0.315350 0.182067i −0.333968 0.942584i \(-0.608388\pi\)
0.649318 + 0.760517i \(0.275054\pi\)
\(542\) 25.3739 1.08990
\(543\) −11.0000 19.0526i −0.472055 0.817624i
\(544\) 7.38505i 0.316632i
\(545\) −33.3303 −1.42771
\(546\) −5.79129 + 20.0616i −0.247844 + 0.858558i
\(547\) −8.00000 −0.342055 −0.171028 0.985266i \(-0.554709\pi\)
−0.171028 + 0.985266i \(0.554709\pi\)
\(548\) 24.1733i 1.03263i
\(549\) 2.58258 + 4.47315i 0.110222 + 0.190909i
\(550\) −15.1652 −0.646644
\(551\) 32.0780 18.5203i 1.36657 0.788990i
\(552\) 12.8739 7.43273i 0.547948 0.316358i
\(553\) 3.75015i 0.159473i
\(554\) 20.4231i 0.867695i
\(555\) −6.08258 + 10.5353i −0.258191 + 0.447200i
\(556\) −9.18693 15.9122i −0.389613 0.674829i
\(557\) −21.1652 + 12.2197i −0.896796 + 0.517766i −0.876159 0.482021i \(-0.839903\pi\)
−0.0206368 + 0.999787i \(0.506569\pi\)
\(558\) −6.68693 11.5821i −0.283080 0.490310i
\(559\) 16.0390 3.96863i 0.678378 0.167855i
\(560\) −8.20871 −0.346881
\(561\) −3.00000 1.73205i −0.126660 0.0731272i
\(562\) −8.00000 −0.337460
\(563\) 5.41742 0.228317 0.114159 0.993463i \(-0.463583\pi\)
0.114159 + 0.993463i \(0.463583\pi\)
\(564\) −1.97822 1.14213i −0.0832981 0.0480922i
\(565\) −18.2477 10.5353i −0.767688 0.443225i
\(566\) −57.4955 + 33.1950i −2.41671 + 1.39529i
\(567\) 2.64575i 0.111111i
\(568\) 3.87386 + 6.70973i 0.162544 + 0.281534i
\(569\) −5.33030 −0.223458 −0.111729 0.993739i \(-0.535639\pi\)
−0.111729 + 0.993739i \(0.535639\pi\)
\(570\) 17.3739 10.0308i 0.727711 0.420144i
\(571\) −23.8739 + 41.3507i −0.999090 + 1.73047i −0.462609 + 0.886562i \(0.653087\pi\)
−0.536481 + 0.843913i \(0.680247\pi\)
\(572\) −8.37386 33.8426i −0.350129 1.41503i
\(573\) −14.3303 −0.598657
\(574\) 17.8521 10.3069i 0.745132 0.430202i
\(575\) 8.58258 14.8655i 0.357918 0.619932i
\(576\) −6.29129 + 10.8968i −0.262137 + 0.454035i
\(577\) 12.0826 + 6.97588i 0.503004 + 0.290410i 0.729953 0.683497i \(-0.239542\pi\)
−0.226949 + 0.973907i \(0.572875\pi\)
\(578\) 35.0224i 1.45674i
\(579\) 3.16515 + 1.82740i 0.131539 + 0.0759442i
\(580\) 33.8426i 1.40524i
\(581\) 4.58258 7.93725i 0.190117 0.329293i
\(582\) 11.4782 19.8809i 0.475788 0.824088i
\(583\) 21.3567i 0.884505i
\(584\) −7.50000 + 12.9904i −0.310352 + 0.537546i
\(585\) −6.00000 1.73205i −0.248069 0.0716115i
\(586\) 21.2695 + 36.8399i 0.878635 + 1.52184i
\(587\) −18.8739 10.8968i −0.779008 0.449760i 0.0570708 0.998370i \(-0.481824\pi\)
−0.836079 + 0.548610i \(0.815157\pi\)
\(588\) −9.76951 + 16.9213i −0.402888 + 0.697822i
\(589\) 16.1652 + 27.9989i 0.666073 + 1.15367i
\(590\) −14.0608 + 8.11800i −0.578874 + 0.334213i
\(591\) 17.6066i 0.724237i
\(592\) 12.5812i 0.517084i
\(593\) −15.2477 + 8.80328i −0.626149 + 0.361507i −0.779259 0.626702i \(-0.784404\pi\)
0.153110 + 0.988209i \(0.451071\pi\)
\(594\) 3.79129 + 6.56670i 0.155558 + 0.269435i
\(595\) 4.58258 0.187867
\(596\) −8.83485 5.10080i −0.361889 0.208937i
\(597\) −1.29129 2.23658i −0.0528489 0.0915370i
\(598\) 65.0780 + 18.7864i 2.66124 + 0.768233i
\(599\) −4.12614 + 7.14668i −0.168589 + 0.292005i −0.937924 0.346841i \(-0.887255\pi\)
0.769335 + 0.638846i \(0.220588\pi\)
\(600\) 3.46410i 0.141421i
\(601\) −13.0826 + 22.6597i −0.533649 + 0.924308i 0.465578 + 0.885007i \(0.345846\pi\)
−0.999227 + 0.0393010i \(0.987487\pi\)
\(602\) 26.5390 1.08165
\(603\) 14.0471i 0.572042i
\(604\) −40.3521 23.2973i −1.64190 0.947953i
\(605\) 1.73205i 0.0704179i
\(606\) −24.9564 14.4086i −1.01379 0.585310i
\(607\) 4.00000 6.92820i 0.162355 0.281207i −0.773358 0.633970i \(-0.781424\pi\)
0.935713 + 0.352763i \(0.114758\pi\)
\(608\) 19.5390 33.8426i 0.792412 1.37250i
\(609\) −16.0390 9.26013i −0.649934 0.375239i
\(610\) 19.5826 0.792875
\(611\) −0.708712 2.86423i −0.0286714 0.115874i
\(612\) 1.39564 2.41733i 0.0564156 0.0977146i
\(613\) 21.1652 12.2197i 0.854852 0.493549i −0.00743271 0.999972i \(-0.502366\pi\)
0.862285 + 0.506423i \(0.169033\pi\)
\(614\) 45.9129 1.85289
\(615\) 3.08258 + 5.33918i 0.124301 + 0.215296i
\(616\) 15.8745i 0.639602i
\(617\) −18.2477 + 10.5353i −0.734626 + 0.424136i −0.820112 0.572203i \(-0.806089\pi\)
0.0854862 + 0.996339i \(0.472756\pi\)
\(618\) −6.47822 3.74020i −0.260592 0.150453i
\(619\) −1.03901 0.599876i −0.0417615 0.0241110i 0.478974 0.877829i \(-0.341009\pi\)
−0.520735 + 0.853718i \(0.674342\pi\)
\(620\) −29.5390 −1.18632
\(621\) −8.58258 −0.344407
\(622\) 16.2695 + 9.39320i 0.652348 + 0.376633i
\(623\) 20.6216 35.7176i 0.826187 1.43100i
\(624\) −6.26951 + 1.55130i −0.250981 + 0.0621017i
\(625\) 5.50000 + 9.52628i 0.220000 + 0.381051i
\(626\) −26.2259 + 15.1416i −1.04820 + 0.605178i
\(627\) −9.16515 15.8745i −0.366021 0.633967i
\(628\) 14.1869 24.5725i 0.566120 0.980549i
\(629\) 7.02355i 0.280047i
\(630\) −8.68693 5.01540i −0.346096 0.199818i
\(631\) −30.8739 + 17.8250i −1.22907 + 0.709603i −0.966835 0.255401i \(-0.917793\pi\)
−0.262234 + 0.965004i \(0.584459\pi\)
\(632\) 2.12614 1.22753i 0.0845732 0.0488283i
\(633\) 6.58258 0.261634
\(634\) −2.10436 3.64485i −0.0835747 0.144756i
\(635\) 11.4014i 0.452449i
\(636\) 17.2087 0.682370
\(637\) −24.5000 + 6.06218i −0.970725 + 0.240192i
\(638\) 53.0780 2.10138
\(639\) 4.47315i 0.176955i
\(640\) 11.0608 + 19.1579i 0.437216 + 0.757281i
\(641\) −16.4955 −0.651531 −0.325766 0.945451i \(-0.605622\pi\)
−0.325766 + 0.945451i \(0.605622\pi\)
\(642\) −2.68693 + 1.55130i −0.106045 + 0.0612250i
\(643\) 29.4564 17.0067i 1.16165 0.670678i 0.209950 0.977712i \(-0.432670\pi\)
0.951699 + 0.307034i \(0.0993365\pi\)
\(644\) 54.8911 + 31.6914i 2.16301 + 1.24882i
\(645\) 7.93725i 0.312529i
\(646\) −5.79129 + 10.0308i −0.227855 + 0.394657i
\(647\) 19.1652 + 33.1950i 0.753460 + 1.30503i 0.946136 + 0.323768i \(0.104950\pi\)
−0.192677 + 0.981262i \(0.561717\pi\)
\(648\) −1.50000 + 0.866025i −0.0589256 + 0.0340207i
\(649\) 7.41742 + 12.8474i 0.291159 + 0.504303i
\(650\) 11.3739 10.9445i 0.446120 0.429279i
\(651\) 8.08258 13.9994i 0.316781 0.548681i
\(652\) −8.37386 4.83465i −0.327946 0.189340i
\(653\) 26.4955 1.03685 0.518424 0.855124i \(-0.326519\pi\)
0.518424 + 0.855124i \(0.326519\pi\)
\(654\) −42.1216 −1.64708
\(655\) −2.12614 1.22753i −0.0830750 0.0479634i
\(656\) 5.52178 + 3.18800i 0.215589 + 0.124471i
\(657\) 7.50000 4.33013i 0.292603 0.168934i
\(658\) 4.73930i 0.184757i
\(659\) −10.0390 17.3881i −0.391064 0.677344i 0.601526 0.798853i \(-0.294560\pi\)
−0.992590 + 0.121510i \(0.961226\pi\)
\(660\) 16.7477 0.651904
\(661\) 4.74773 2.74110i 0.184665 0.106616i −0.404818 0.914397i \(-0.632665\pi\)
0.589483 + 0.807781i \(0.299332\pi\)
\(662\) 28.5390 49.4310i 1.10920 1.92119i
\(663\) 3.50000 0.866025i 0.135929 0.0336336i
\(664\) −6.00000 −0.232845
\(665\) 21.0000 + 12.1244i 0.814345 + 0.470162i
\(666\) −7.68693 + 13.3142i −0.297863 + 0.515913i
\(667\) −30.0390 + 52.0291i −1.16312 + 2.01457i
\(668\) −10.8131 6.24293i −0.418370 0.241546i
\(669\) 2.64575i 0.102291i
\(670\) −46.1216 26.6283i −1.78183 1.02874i
\(671\) 17.8926i 0.690737i
\(672\) −19.5390 −0.753734
\(673\) 17.6652 30.5969i 0.680942 1.17943i −0.293752 0.955882i \(-0.594904\pi\)
0.974694 0.223544i \(-0.0717626\pi\)
\(674\) 51.4292i 1.98098i
\(675\) −1.00000 + 1.73205i −0.0384900 + 0.0666667i
\(676\) 30.7042 + 19.3386i 1.18093 + 0.743793i
\(677\) −14.9174 25.8377i −0.573323 0.993025i −0.996222 0.0868478i \(-0.972321\pi\)
0.422898 0.906177i \(-0.361013\pi\)
\(678\) −23.0608 13.3142i −0.885645 0.511327i
\(679\) 27.7477 1.06486
\(680\) −1.50000 2.59808i −0.0575224 0.0996317i
\(681\) 23.6216 13.6379i 0.905181 0.522607i
\(682\) 46.3284i 1.77401i
\(683\) 39.1142i 1.49666i −0.663325 0.748331i \(-0.730855\pi\)
0.663325 0.748331i \(-0.269145\pi\)
\(684\) 12.7913 7.38505i 0.489087 0.282375i
\(685\) 7.50000 + 12.9904i 0.286560 + 0.496337i
\(686\) −40.5390 −1.54779
\(687\) 9.08258 + 5.24383i 0.346522 + 0.200064i
\(688\) 4.10436 + 7.10895i 0.156477 + 0.271026i
\(689\) 15.4129 + 16.0175i 0.587184 + 0.610219i
\(690\) −16.2695 + 28.1796i −0.619370 + 1.07278i
\(691\) 7.55585i 0.287438i −0.989619 0.143719i \(-0.954094\pi\)
0.989619 0.143719i \(-0.0459062\pi\)
\(692\) 33.9564 58.8143i 1.29083 2.23578i
\(693\) −4.58258 + 7.93725i −0.174078 + 0.301511i
\(694\) 56.3592i 2.13937i
\(695\) 9.87386 + 5.70068i 0.374537 + 0.216239i
\(696\) 12.1244i 0.459573i
\(697\) −3.08258 1.77973i −0.116761 0.0674119i
\(698\) −11.4782 + 19.8809i −0.434457 + 0.752502i
\(699\) −10.0826 + 17.4635i −0.381358 + 0.660531i
\(700\) 12.7913 7.38505i 0.483465 0.279129i
\(701\) 34.0000 1.28416 0.642081 0.766637i \(-0.278071\pi\)
0.642081 + 0.766637i \(0.278071\pi\)
\(702\) −7.58258 2.18890i −0.286186 0.0826147i
\(703\) 18.5826 32.1860i 0.700855 1.21392i
\(704\) 37.7477 21.7937i 1.42267 0.821379i
\(705\) 1.41742 0.0533833
\(706\) −21.1652 36.6591i −0.796561 1.37968i
\(707\) 34.8317i 1.30998i
\(708\) −10.3521 + 5.97678i −0.389055 + 0.224621i
\(709\) 25.5826 + 14.7701i 0.960774 + 0.554703i 0.896411 0.443224i \(-0.146165\pi\)
0.0643627 + 0.997927i \(0.479499\pi\)
\(710\) −14.6869 8.47950i −0.551191 0.318230i
\(711\) −1.41742 −0.0531576
\(712\) −27.0000 −1.01187
\(713\) −45.4129 26.2191i −1.70073 0.981914i
\(714\) 5.79129 0.216734
\(715\) 15.0000 + 15.5885i 0.560968 + 0.582975i
\(716\) 1.16515 + 2.01810i 0.0435438 + 0.0754200i
\(717\) 1.74773 1.00905i 0.0652701 0.0376837i
\(718\) 20.2695 + 35.1078i 0.756451 + 1.31021i
\(719\) 17.1652 29.7309i 0.640152 1.10878i −0.345246 0.938512i \(-0.612205\pi\)
0.985398 0.170264i \(-0.0544620\pi\)
\(720\) 3.10260i 0.115627i
\(721\) 9.04165i 0.336729i
\(722\) −17.0608 + 9.85005i −0.634937 + 0.366581i
\(723\) −12.2477 + 7.07123i −0.455498 + 0.262982i
\(724\) −61.4083 −2.28222
\(725\) 7.00000 + 12.1244i 0.259973 + 0.450287i
\(726\) 2.18890i 0.0812377i
\(727\) 28.0000 1.03846 0.519231 0.854634i \(-0.326218\pi\)
0.519231 + 0.854634i \(0.326218\pi\)
\(728\) 11.4564 + 11.9059i 0.424604 + 0.441261i
\(729\) 1.00000 0.0370370
\(730\) 32.8335i 1.21522i
\(731\) −2.29129 3.96863i −0.0847463 0.146785i
\(732\) 14.4174 0.532883
\(733\) −25.8303 + 14.9131i −0.954064 + 0.550829i −0.894341 0.447386i \(-0.852355\pi\)
−0.0597230 + 0.998215i \(0.519022\pi\)
\(734\) 28.7477 16.5975i 1.06110 0.612625i
\(735\) 12.1244i 0.447214i
\(736\) 63.3828i 2.33632i
\(737\) −24.3303 + 42.1413i −0.896218 + 1.55230i
\(738\) 3.89564 + 6.74745i 0.143401 + 0.248377i
\(739\) 16.5826 9.57395i 0.610000 0.352184i −0.162966 0.986632i \(-0.552106\pi\)
0.772965 + 0.634448i \(0.218773\pi\)
\(740\) 16.9782 + 29.4071i 0.624132 + 1.08103i
\(741\) 18.3303 + 5.29150i 0.673380 + 0.194388i
\(742\) 17.8521 + 30.9207i 0.655371 + 1.13514i
\(743\) 6.70871 + 3.87328i 0.246119 + 0.142097i 0.617986 0.786189i \(-0.287949\pi\)
−0.371867 + 0.928286i \(0.621282\pi\)
\(744\) −10.5826 −0.387976
\(745\) 6.33030 0.231924
\(746\) 49.2867 + 28.4557i 1.80452 + 1.04184i
\(747\) 3.00000 + 1.73205i 0.109764 + 0.0633724i
\(748\) −8.37386 + 4.83465i −0.306179 + 0.176772i
\(749\) −3.24773 1.87508i −0.118669 0.0685138i
\(750\) 13.2695 + 22.9835i 0.484534 + 0.839237i
\(751\) −12.9129 −0.471198 −0.235599 0.971850i \(-0.575705\pi\)
−0.235599 + 0.971850i \(0.575705\pi\)
\(752\) 1.26951 0.732950i 0.0462942 0.0267280i
\(753\) 10.2913 17.8250i 0.375035 0.649580i
\(754\) −39.8085 + 38.3058i −1.44974 + 1.39501i
\(755\) 28.9129 1.05225
\(756\) −6.39564 3.69253i −0.232607 0.134296i
\(757\) −2.24773 + 3.89318i −0.0816950 + 0.141500i −0.903978 0.427579i \(-0.859367\pi\)
0.822283 + 0.569079i \(0.192700\pi\)
\(758\) −20.2695 + 35.1078i −0.736222 + 1.27517i
\(759\) 25.7477 + 14.8655i 0.934583 + 0.539582i
\(760\) 15.8745i 0.575829i
\(761\) −1.25227 0.723000i −0.0453949 0.0262087i 0.477131 0.878832i \(-0.341677\pi\)
−0.522526 + 0.852624i \(0.675010\pi\)
\(762\) 14.4086i 0.521969i
\(763\) −25.4564 44.0918i −0.921585 1.59623i
\(764\) −20.0000 + 34.6410i −0.723575 + 1.25327i
\(765\) 1.73205i 0.0626224i
\(766\) 19.3739 33.5565i 0.700006 1.21245i
\(767\) −14.8348 4.28245i −0.535655 0.154630i
\(768\) 1.39564 + 2.41733i 0.0503610 + 0.0872277i
\(769\) −2.91742 1.68438i −0.105205 0.0607401i 0.446474 0.894796i \(-0.352679\pi\)
−0.551679 + 0.834056i \(0.686013\pi\)
\(770\) 17.3739 + 30.0924i 0.626111 + 1.08446i
\(771\) 4.66515 + 8.08028i 0.168011 + 0.291004i
\(772\) 8.83485 5.10080i 0.317973 0.183582i
\(773\) 24.5348i 0.882454i −0.897396 0.441227i \(-0.854543\pi\)
0.897396 0.441227i \(-0.145457\pi\)
\(774\) 10.0308i 0.360550i
\(775\) −10.5826 + 6.10985i −0.380137 + 0.219472i