Properties

Label 273.2.t.b.205.1
Level $273$
Weight $2$
Character 273.205
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 205.1
Root \(-0.895644 - 1.09445i\) of defining polynomial
Character \(\chi\) \(=\) 273.205
Dual form 273.2.t.b.4.2

$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\)

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 \(-0.718307\pi\)
0.633316 0.773893i \(-0.281693\pi\)
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) −2.79129 −1.39564
\(5\) 1.50000 + 0.866025i 0.670820 + 0.387298i 0.796387 0.604787i \(-0.206742\pi\)
−0.125567 + 0.992085i \(0.540075\pi\)
\(6\) 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 0.878668 0.477432i \(-0.158432\pi\)
0.0258656 + 0.999665i \(0.491766\pi\)
\(12\) 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 0.128298 0.991736i \(-0.459049\pi\)
0.923017 + 0.384759i \(0.125715\pi\)
\(20\) −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 0.983138 + 0.182864i \(0.0585367\pi\)
−0.333205 + 0.942855i \(0.608130\pi\)
\(30\) 1.89564 + 3.28335i 0.346096 + 0.599455i
\(31\) 5.29129 3.05493i 0.950343 0.548681i 0.0571558 0.998365i \(-0.481797\pi\)
0.893188 + 0.449684i \(0.148463\pi\)
\(32\) 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 \(0.195906\pi\)
−0.816509 + 0.577333i \(0.804094\pi\)
\(38\) −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 −0.721007 0.692928i \(-0.756320\pi\)
0.239590 + 0.970874i \(0.422987\pi\)
\(42\) 5.79129 0.893615
\(43\) −2.29129 + 3.96863i −0.349418 + 0.605210i −0.986146 0.165878i \(-0.946954\pi\)
0.636728 + 0.771088i \(0.280287\pi\)
\(44\) −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 0.447421 0.894324i \(-0.352343\pi\)
−0.550797 + 0.834639i \(0.685676\pi\)
\(48\) 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 0.996272 0.0862695i \(-0.0274946\pi\)
−0.572848 + 0.819662i \(0.694161\pi\)
\(54\) 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 \(-0.910075\pi\)
0.960360 0.278764i \(-0.0899247\pi\)
\(60\) 4.18693 2.41733i 0.540531 0.312075i
\(61\) 2.58258 + 4.47315i 0.330665 + 0.572728i 0.982642 0.185510i \(-0.0593937\pi\)
−0.651977 + 0.758238i \(0.726060\pi\)
\(62\) −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 −0.486333 0.873773i \(-0.661666\pi\)
−0.999877 + 0.0157098i \(0.994999\pi\)
\(68\) −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 0.252193 0.967677i \(-0.418848\pi\)
−0.711936 + 0.702244i \(0.752181\pi\)
\(72\) 1.50000 0.866025i 0.176777 0.102062i
\(73\) −7.50000 + 4.33013i −0.877809 + 0.506803i −0.869935 0.493166i \(-0.835840\pi\)
−0.00787336 + 0.999969i \(0.502506\pi\)
\(74\) 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 −0.823400 0.567462i \(-0.807925\pi\)
0.903136 + 0.429354i \(0.141259\pi\)
\(80\) −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 \(0.0608868\pi\)
−0.981761 + 0.190117i \(0.939113\pi\)
\(84\) 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 \(0.309494\pi\)
−0.563397 + 0.826187i \(0.690506\pi\)
\(90\) −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 0.884335 0.466853i \(-0.154612\pi\)
0.0378609 + 0.999283i \(0.487946\pi\)
\(98\) −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 0.326905 + 0.945057i \(0.393994\pi\)
−0.981896 + 0.189420i \(0.939339\pi\)
\(102\) 1.89564 + 1.09445i 0.187697 + 0.108367i
\(103\) −1.70871 + 2.95958i −0.168364 + 0.291616i −0.937845 0.347055i \(-0.887182\pi\)
0.769481 + 0.638670i \(0.220515\pi\)
\(104\) 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 −0.604028 + 0.796963i \(0.706438\pi\)
−0.992204 + 0.124622i \(0.960228\pi\)
\(110\) 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 0.424139 + 0.905597i \(0.360577\pi\)
−0.996340 + 0.0854834i \(0.972757\pi\)
\(114\) 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 0.682241 0.731128i \(-0.261006\pi\)
−0.974295 + 0.225274i \(0.927672\pi\)
\(128\) 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 −0.895324 0.445416i \(-0.853056\pi\)
0.833403 + 0.552665i \(0.186389\pi\)
\(132\) 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 \(-0.879376\pi\)
0.929053 0.369948i \(-0.120624\pi\)
\(138\) −16.2695 9.39320i −1.38495 0.799603i
\(139\) 3.29129 5.70068i 0.279163 0.483525i −0.692014 0.721884i \(-0.743276\pi\)
0.971177 + 0.238359i \(0.0766096\pi\)
\(140\) −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 −0.364716 0.931119i \(-0.618834\pi\)
0.624015 + 0.781412i \(0.285500\pi\)
\(150\) 4.37780i 0.357446i
\(151\) 14.4564 8.34643i 1.17645 0.679223i 0.221258 0.975215i \(-0.428984\pi\)
0.955190 + 0.295993i \(0.0956503\pi\)
\(152\) 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 0.588761 0.808307i \(-0.299616\pi\)
−0.994395 + 0.105729i \(0.966282\pi\)
\(158\) −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 −0.377888 0.925851i \(-0.623350\pi\)
0.612866 + 0.790186i \(0.290016\pi\)
\(164\) 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 −0.342570 0.939492i \(-0.611298\pi\)
0.642339 + 0.766421i \(0.277964\pi\)
\(168\) −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 −0.791723 0.610880i \(-0.790816\pi\)
−0.133176 0.991092i \(-0.542518\pi\)
\(174\) 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 −0.881204 0.472737i \(-0.843266\pi\)
0.850004 + 0.526776i \(0.176599\pi\)
\(180\) 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 0.999770 + 0.0214394i \(0.00682490\pi\)
−0.481318 + 0.876546i \(0.659842\pi\)
\(192\) −6.29129 + 10.8968i −0.454035 + 0.786411i
\(193\) −3.16515 1.82740i −0.227833 0.131539i 0.381739 0.924270i \(-0.375325\pi\)
−0.609572 + 0.792731i \(0.708659\pi\)
\(194\) 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 0.153752 0.988110i \(-0.450864\pi\)
0.932604 + 0.360902i \(0.117531\pi\)
\(198\) −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 0.730211 0.683222i \(-0.239422\pi\)
−0.956793 + 0.290771i \(0.906088\pi\)
\(212\) −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 −0.574752 0.818327i \(-0.694902\pi\)
0.421316 + 0.906914i \(0.361568\pi\)
\(224\) 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 \(-0.639735\pi\)
0.425026 0.905181i \(-0.360265\pi\)
\(228\) 14.7701i 0.978174i
\(229\) −9.08258 5.24383i −0.600193 0.346522i 0.168924 0.985629i \(-0.445971\pi\)
−0.769118 + 0.639107i \(0.779304\pi\)
\(230\) −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 0.319945 + 0.947436i \(0.396336\pi\)
−0.980476 + 0.196638i \(0.936998\pi\)
\(234\) 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 \(-0.979209\pi\)
0.997868 0.0652701i \(-0.0207909\pi\)
\(240\) 2.68693 1.55130i 0.173441 0.100136i
\(241\) 14.1425i 0.910996i 0.890237 + 0.455498i \(0.150539\pi\)
−0.890237 + 0.455498i \(0.849461\pi\)
\(242\) 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 −0.333643 0.942700i \(-0.608278\pi\)
0.983223 0.182407i \(-0.0583887\pi\)
\(252\) 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 −0.781817 0.623508i \(-0.785707\pi\)
0.930882 + 0.365320i \(0.119040\pi\)
\(264\) −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 \(0.114527\pi\)
−0.935969 + 0.352084i \(0.885473\pi\)
\(272\) −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 \(-0.965231\pi\)
0.994040 0.109014i \(-0.0347692\pi\)
\(282\) −0.895644 1.55130i −0.0533348 0.0923786i
\(283\) 15.1652 26.2668i 0.901475 1.56140i 0.0758940 0.997116i \(-0.475819\pi\)
0.825581 0.564284i \(-0.190848\pi\)
\(284\) 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 0.903246 0.429124i \(-0.141178\pi\)
0.0799910 + 0.996796i \(0.474511\pi\)
\(294\) 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 \(0.204261\pi\)
−0.801076 + 0.598562i \(0.795739\pi\)
\(308\) −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 0.961663 0.274235i \(-0.0884247\pi\)
−0.718326 + 0.695707i \(0.755091\pi\)
\(312\) −1.50000 + 6.06218i −0.0849208 + 0.343203i
\(313\) 6.91742 11.9813i 0.390996 0.677225i −0.601585 0.798809i \(-0.705464\pi\)
0.992581 + 0.121584i \(0.0387973\pi\)
\(314\) −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 0.452508 0.891760i \(-0.350529\pi\)
−0.546033 + 0.837764i \(0.683863\pi\)
\(318\) 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 −0.969349 0.245689i \(-0.920986\pi\)
−0.271902 + 0.962325i \(0.587653\pi\)
\(332\) 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 −0.236809 0.971556i \(-0.576102\pi\)
0.722988 + 0.690861i \(0.242768\pi\)
\(350\) −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 −0.0169942 0.999856i \(-0.505410\pi\)
−0.874397 + 0.485210i \(0.838743\pi\)
\(354\) 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 0.859471 0.511185i \(-0.170793\pi\)
−0.0129639 + 0.999916i \(0.504127\pi\)
\(360\) 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 −0.993204 0.116388i \(-0.962868\pi\)
0.597397 + 0.801946i \(0.296202\pi\)
\(368\) 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 0.977016 + 0.213165i \(0.0683772\pi\)
−0.303902 + 0.952703i \(0.598289\pi\)
\(374\) 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 −0.0278799 0.999611i \(-0.508876\pi\)
0.851749 + 0.523950i \(0.175542\pi\)
\(380\) −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 −0.837613 0.546264i \(-0.816050\pi\)
0.0542715 + 0.998526i \(0.482716\pi\)
\(384\) 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 −0.970900 0.239486i \(-0.923021\pi\)
0.278049 0.960567i \(-0.410312\pi\)
\(390\) 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 0.610506 0.792011i \(-0.290966\pi\)
0.991155 0.132708i \(-0.0423673\pi\)
\(398\) 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 \(-0.665837\pi\)
0.497741 0.867326i \(-0.334163\pi\)
\(402\) −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 \(0.281324\pi\)
−0.634215 + 0.773157i \(0.718676\pi\)
\(410\) 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 0.686125 0.727484i \(-0.259310\pi\)
−0.973082 + 0.230460i \(0.925977\pi\)
\(420\) 6.39564 11.0776i 0.312075 0.540531i
\(421\) 40.5046i 1.97407i 0.160492 + 0.987037i \(0.448692\pi\)
−0.160492 + 0.987037i \(0.551308\pi\)
\(422\) −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 0.310604 0.950539i \(-0.399469\pi\)
−0.667889 + 0.744261i \(0.732802\pi\)
\(432\) −1.79129 −0.0861834
\(433\) 7.66515 13.2764i 0.368364 0.638025i −0.620946 0.783853i \(-0.713251\pi\)
0.989310 + 0.145829i \(0.0465848\pi\)
\(434\) −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 −0.789644 0.613565i \(-0.789735\pi\)
0.926185 + 0.377069i \(0.123068\pi\)
\(444\) 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 0.226764 0.973950i \(-0.427185\pi\)
−0.730083 + 0.683358i \(0.760519\pi\)
\(450\) 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 \(0.0279556\pi\)
−0.996146 + 0.0877124i \(0.972044\pi\)
\(458\) −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 −0.300497 0.953783i \(-0.597152\pi\)
−0.976248 + 0.216654i \(0.930486\pi\)
\(462\) 17.3739 + 10.0308i 0.808305 + 0.466675i
\(463\) 38.4865i 1.78862i 0.447448 + 0.894310i \(0.352333\pi\)
−0.447448 + 0.894310i \(0.647667\pi\)
\(464\) −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 −0.309230 0.950987i \(-0.600071\pi\)
0.978194 0.207693i \(-0.0665954\pi\)
\(468\) 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 0.941203 0.337841i \(-0.109697\pi\)
0.178023 + 0.984026i \(0.443030\pi\)
\(480\) −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 \(-0.919674\pi\)
0.968328 0.249681i \(-0.0803257\pi\)
\(488\) −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 0.820640 0.571445i \(-0.193617\pi\)
−0.905206 + 0.424972i \(0.860284\pi\)
\(492\) 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 −0.0720262 0.997403i \(-0.522947\pi\)
−0.899789 + 0.436325i \(0.856280\pi\)
\(500\) 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 −0.884850 0.465877i \(-0.845739\pi\)
0.845886 + 0.533364i \(0.179072\pi\)
\(504\) 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 \(0.213076\pi\)
−0.784195 + 0.620514i \(0.786924\pi\)
\(510\) 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 0.827242 0.561846i \(-0.189909\pi\)
−0.900194 + 0.435490i \(0.856575\pi\)
\(522\) −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 0.649318 0.760517i \(-0.275054\pi\)
−0.333968 + 0.942584i \(0.608388\pi\)
\(542\) 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 −0.0206368 0.999787i \(-0.506569\pi\)
−0.876159 + 0.482021i \(0.839903\pi\)
\(558\) −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 −0.536481 0.843913i \(-0.680247\pi\)
−0.462609 0.886562i \(-0.653087\pi\)
\(572\) −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 −0.226949 0.973907i \(-0.572875\pi\)
0.729953 + 0.683497i \(0.239542\pi\)
\(578\) 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 −0.836079 0.548610i \(-0.815157\pi\)
0.0570708 + 0.998370i \(0.481824\pi\)
\(588\) −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 0.153110 0.988209i \(-0.451071\pi\)
−0.779259 + 0.626702i \(0.784404\pi\)
\(594\) 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 0.769335 0.638846i \(-0.220588\pi\)
−0.937924 + 0.346841i \(0.887255\pi\)
\(600\) 3.46410i 0.141421i
\(601\) −13.0826 22.6597i −0.533649 0.924308i −0.999227 0.0393010i \(-0.987487\pi\)
0.465578 0.885007i \(-0.345846\pi\)
\(602\) 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 0.935713 0.352763i \(-0.114758\pi\)
−0.773358 + 0.633970i \(0.781424\pi\)
\(608\) 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 0.862285 0.506423i \(-0.169033\pi\)
−0.00743271 + 0.999972i \(0.502366\pi\)
\(614\) 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 0.0854862 0.996339i \(-0.472756\pi\)
−0.820112 + 0.572203i \(0.806089\pi\)
\(618\) −6.47822 + 3.74020i −0.260592 + 0.150453i
\(619\) −1.03901 + 0.599876i −0.0417615 + 0.0241110i −0.520735 0.853718i \(-0.674342\pi\)
0.478974 + 0.877829i \(0.341009\pi\)
\(620\) −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 −0.262234 0.965004i \(-0.584459\pi\)
−0.966835 + 0.255401i \(0.917793\pi\)
\(632\) 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 0.951699 0.307034i \(-0.0993365\pi\)
0.209950 + 0.977712i \(0.432670\pi\)
\(644\) 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 −0.192677 0.981262i \(-0.561717\pi\)
0.946136 0.323768i \(-0.104950\pi\)
\(648\) −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 −0.992590 0.121510i \(-0.961226\pi\)
0.601526 + 0.798853i \(0.294560\pi\)
\(660\) 16.7477 0.651904
\(661\) 4.74773 + 2.74110i 0.184665 + 0.106616i 0.589483 0.807781i \(-0.299332\pi\)
−0.404818 + 0.914397i \(0.632665\pi\)
\(662\) 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 0.974694 + 0.223544i \(0.0717626\pi\)
−0.293752 + 0.955882i \(0.594904\pi\)
\(674\) 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 0.422898 + 0.906177i \(0.361013\pi\)
−0.996222 + 0.0868478i \(0.972321\pi\)
\(678\) −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 \(0.269145\pi\)
−0.663325 + 0.748331i \(0.730855\pi\)
\(684\) 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 \(0.0459062\pi\)
−0.989619 + 0.143719i \(0.954094\pi\)
\(692\) 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 0.0643627 0.997927i \(-0.479499\pi\)
0.896411 + 0.443224i \(0.146165\pi\)
\(710\) −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 0.985398 + 0.170264i \(0.0544620\pi\)
−0.345246 + 0.938512i \(0.612205\pi\)
\(720\) 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 −0.0597230 0.998215i \(-0.519022\pi\)
−0.894341 + 0.447386i \(0.852355\pi\)
\(734\) 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 0.772965 0.634448i \(-0.218773\pi\)
−0.162966 + 0.986632i \(0.552106\pi\)
\(740\) 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 −0.371867 0.928286i \(-0.621282\pi\)
0.617986 + 0.786189i \(0.287949\pi\)
\(744\) −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 0.822283 0.569079i \(-0.192700\pi\)
−0.903978 + 0.427579i \(0.859367\pi\)
\(758\) −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 −0.522526 0.852624i \(-0.675010\pi\)
0.477131 + 0.878832i \(0.341677\pi\)
\(762\) 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 −0.551679 0.834056i \(-0.686013\pi\)
0.446474 + 0.894796i \(0.352679\pi\)
\(770\) 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 \(0.145457\pi\)
−0.897396 + 0.441227i \(0.854543\pi\)
\(774\) 10.0308i 0.360550i
\(775\) −10.5826 6.10985i −0.380137 0.219472i