Properties

Label 273.2.bl.b.88.2
Level $273$
Weight $2$
Character 273.88
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.bl (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: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 88.2
Root \(-0.895644 + 1.09445i\) of defining polynomial
Character \(\chi\) \(=\) 273.88
Dual form 273.2.bl.b.121.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.89564 + 1.09445i) q^{2} +1.00000 q^{3} +(1.39564 + 2.41733i) q^{4} +(-1.50000 + 0.866025i) q^{5} +(1.89564 + 1.09445i) q^{6} +2.64575i q^{7} +1.73205i q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(1.89564 + 1.09445i) q^{2} +1.00000 q^{3} +(1.39564 + 2.41733i) q^{4} +(-1.50000 + 0.866025i) q^{5} +(1.89564 + 1.09445i) q^{6} +2.64575i q^{7} +1.73205i q^{8} +1.00000 q^{9} -3.79129 q^{10} -3.46410i 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} +(0.895644 - 1.55130i) q^{16} +(-0.500000 - 0.866025i) q^{17} +(1.89564 + 1.09445i) q^{18} +5.29150i q^{19} +(-4.18693 - 2.41733i) q^{20} +2.64575i q^{21} +(3.79129 - 6.56670i) q^{22} +(4.29129 - 7.43273i) q^{23} +1.73205i q^{24} +(-1.00000 + 1.73205i) q^{25} +(1.89564 - 7.66115i) q^{26} +1.00000 q^{27} +(-6.39564 + 3.69253i) q^{28} +(3.50000 + 6.06218i) q^{29} -3.79129 q^{30} +(-5.29129 - 3.05493i) q^{31} +(6.39564 - 3.69253i) q^{32} -3.46410i q^{33} -2.18890i q^{34} +(-2.29129 - 3.96863i) q^{35} +(1.39564 + 2.41733i) q^{36} +(-6.08258 - 3.51178i) q^{37} +(-5.79129 + 10.0308i) q^{38} +(-1.00000 - 3.46410i) q^{39} +(-1.50000 - 2.59808i) q^{40} +(-3.08258 + 1.77973i) q^{41} +(-2.89564 + 5.01540i) q^{42} +(-2.29129 + 3.96863i) q^{43} +(8.37386 - 4.83465i) q^{44} +(-1.50000 + 0.866025i) q^{45} +(16.2695 - 9.39320i) q^{46} +(0.708712 - 0.409175i) q^{47} +(0.895644 - 1.55130i) q^{48} -7.00000 q^{49} +(-3.79129 + 2.18890i) q^{50} +(-0.500000 - 0.866025i) q^{51} +(6.97822 - 7.25198i) q^{52} +(3.08258 - 5.33918i) q^{53} +(1.89564 + 1.09445i) q^{54} +(3.00000 + 5.19615i) q^{55} -4.58258 q^{56} +5.29150i q^{57} +15.3223i q^{58} +(-3.70871 + 2.14123i) q^{59} +(-4.18693 - 2.41733i) q^{60} -5.16515 q^{61} +(-6.68693 - 11.5821i) q^{62} +2.64575i q^{63} +12.5826 q^{64} +(4.50000 + 4.33013i) q^{65} +(3.79129 - 6.56670i) q^{66} +14.0471i q^{67} +(1.39564 - 2.41733i) q^{68} +(4.29129 - 7.43273i) q^{69} -10.0308i q^{70} +(-3.87386 - 2.23658i) q^{71} +1.73205i q^{72} +(7.50000 + 4.33013i) q^{73} +(-7.68693 - 13.3142i) q^{74} +(-1.00000 + 1.73205i) q^{75} +(-12.7913 + 7.38505i) q^{76} +9.16515 q^{77} +(1.89564 - 7.66115i) q^{78} +(0.708712 + 1.22753i) q^{79} +3.10260i q^{80} +1.00000 q^{81} -7.79129 q^{82} +3.46410i q^{83} +(-6.39564 + 3.69253i) q^{84} +(1.50000 + 0.866025i) q^{85} +(-8.68693 + 5.01540i) q^{86} +(3.50000 + 6.06218i) q^{87} +6.00000 q^{88} +(-13.5000 - 7.79423i) q^{89} -3.79129 q^{90} +(9.16515 - 2.64575i) q^{91} +23.9564 q^{92} +(-5.29129 - 3.05493i) q^{93} +1.79129 q^{94} +(-4.58258 - 7.93725i) 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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 3q^{2} + 4q^{3} + q^{4} - 6q^{5} + 3q^{6} + 4q^{9} + O(q^{10}) \) \( 4q + 3q^{2} + 4q^{3} + q^{4} - 6q^{5} + 3q^{6} + 4q^{9} - 6q^{10} + q^{12} - 4q^{13} - 7q^{14} - 6q^{15} - q^{16} - 2q^{17} + 3q^{18} - 3q^{20} + 6q^{22} + 8q^{23} - 4q^{25} + 3q^{26} + 4q^{27} - 21q^{28} + 14q^{29} - 6q^{30} - 12q^{31} + 21q^{32} + q^{36} - 6q^{37} - 14q^{38} - 4q^{39} - 6q^{40} + 6q^{41} - 7q^{42} + 6q^{44} - 6q^{45} + 33q^{46} + 12q^{47} - q^{48} - 28q^{49} - 6q^{50} - 2q^{51} + 5q^{52} - 6q^{53} + 3q^{54} + 12q^{55} - 24q^{59} - 3q^{60} + 16q^{61} - 13q^{62} + 32q^{64} + 18q^{65} + 6q^{66} + q^{68} + 8q^{69} + 12q^{71} + 30q^{73} - 17q^{74} - 4q^{75} - 42q^{76} + 3q^{78} + 12q^{79} + 4q^{81} - 22q^{82} - 21q^{84} + 6q^{85} - 21q^{86} + 14q^{87} + 24q^{88} - 54q^{89} - 6q^{90} + 50q^{92} - 12q^{93} - 2q^{94} + 21q^{96} + 18q^{97} - 21q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.89564 + 1.09445i 1.34042 + 0.773893i 0.986869 0.161521i \(-0.0516399\pi\)
0.353553 + 0.935414i \(0.384973\pi\)
\(3\) 1.00000 0.577350
\(4\) 1.39564 + 2.41733i 0.697822 + 1.20866i
\(5\) −1.50000 + 0.866025i −0.670820 + 0.387298i −0.796387 0.604787i \(-0.793258\pi\)
0.125567 + 0.992085i \(0.459925\pi\)
\(6\) 1.89564 + 1.09445i 0.773893 + 0.446808i
\(7\) 2.64575i 1.00000i
\(8\) 1.73205i 0.612372i
\(9\) 1.00000 0.333333
\(10\) −3.79129 −1.19891
\(11\) 3.46410i 1.04447i −0.852803 0.522233i \(-0.825099\pi\)
0.852803 0.522233i \(-0.174901\pi\)
\(12\) 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
\(16\) 0.895644 1.55130i 0.223911 0.387825i
\(17\) −0.500000 0.866025i −0.121268 0.210042i 0.799000 0.601331i \(-0.205363\pi\)
−0.920268 + 0.391289i \(0.872029\pi\)
\(18\) 1.89564 + 1.09445i 0.446808 + 0.257964i
\(19\) 5.29150i 1.21395i 0.794719 + 0.606977i \(0.207618\pi\)
−0.794719 + 0.606977i \(0.792382\pi\)
\(20\) −4.18693 2.41733i −0.936226 0.540531i
\(21\) 2.64575i 0.577350i
\(22\) 3.79129 6.56670i 0.808305 1.40003i
\(23\) 4.29129 7.43273i 0.894795 1.54983i 0.0607377 0.998154i \(-0.480655\pi\)
0.834058 0.551677i \(-0.186012\pi\)
\(24\) 1.73205i 0.353553i
\(25\) −1.00000 + 1.73205i −0.200000 + 0.346410i
\(26\) 1.89564 7.66115i 0.371766 1.50248i
\(27\) 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 \(0.608130\pi\)
\(30\) −3.79129 −0.692191
\(31\) −5.29129 3.05493i −0.950343 0.548681i −0.0571558 0.998365i \(-0.518203\pi\)
−0.893188 + 0.449684i \(0.851537\pi\)
\(32\) 6.39564 3.69253i 1.13060 0.652753i
\(33\) 3.46410i 0.603023i
\(34\) 2.18890i 0.375393i
\(35\) −2.29129 3.96863i −0.387298 0.670820i
\(36\) 1.39564 + 2.41733i 0.232607 + 0.402888i
\(37\) −6.08258 3.51178i −0.999969 0.577333i −0.0917301 0.995784i \(-0.529240\pi\)
−0.908239 + 0.418451i \(0.862573\pi\)
\(38\) −5.79129 + 10.0308i −0.939471 + 1.62721i
\(39\) −1.00000 3.46410i −0.160128 0.554700i
\(40\) −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 \(0.422987\pi\)
\(42\) −2.89564 + 5.01540i −0.446808 + 0.773893i
\(43\) −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
\(45\) −1.50000 + 0.866025i −0.223607 + 0.129099i
\(46\) 16.2695 9.39320i 2.39881 1.38495i
\(47\) 0.708712 0.409175i 0.103376 0.0596843i −0.447421 0.894324i \(-0.647657\pi\)
0.550797 + 0.834639i \(0.314324\pi\)
\(48\) 0.895644 1.55130i 0.129275 0.223911i
\(49\) −7.00000 −1.00000
\(50\) −3.79129 + 2.18890i −0.536169 + 0.309557i
\(51\) −0.500000 0.866025i −0.0700140 0.121268i
\(52\) 6.97822 7.25198i 0.967705 1.00567i
\(53\) 3.08258 5.33918i 0.423424 0.733392i −0.572848 0.819662i \(-0.694161\pi\)
0.996272 + 0.0862695i \(0.0274946\pi\)
\(54\) 1.89564 + 1.09445i 0.257964 + 0.148936i
\(55\) 3.00000 + 5.19615i 0.404520 + 0.700649i
\(56\) −4.58258 −0.612372
\(57\) 5.29150i 0.700877i
\(58\) 15.3223i 2.01192i
\(59\) −3.70871 + 2.14123i −0.482833 + 0.278764i −0.721596 0.692314i \(-0.756591\pi\)
0.238763 + 0.971078i \(0.423258\pi\)
\(60\) −4.18693 2.41733i −0.540531 0.312075i
\(61\) −5.16515 −0.661330 −0.330665 0.943748i \(-0.607273\pi\)
−0.330665 + 0.943748i \(0.607273\pi\)
\(62\) −6.68693 11.5821i −0.849241 1.47093i
\(63\) 2.64575i 0.333333i
\(64\) 12.5826 1.57282
\(65\) 4.50000 + 4.33013i 0.558156 + 0.537086i
\(66\) 3.79129 6.56670i 0.466675 0.808305i
\(67\) 14.0471i 1.71613i 0.513543 + 0.858064i \(0.328333\pi\)
−0.513543 + 0.858064i \(0.671667\pi\)
\(68\) 1.39564 2.41733i 0.169247 0.293144i
\(69\) 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 \(0.752181\pi\)
\(72\) 1.73205i 0.204124i
\(73\) 7.50000 + 4.33013i 0.877809 + 0.506803i 0.869935 0.493166i \(-0.164160\pi\)
0.00787336 + 0.999969i \(0.497494\pi\)
\(74\) −7.68693 13.3142i −0.893588 1.54774i
\(75\) −1.00000 + 1.73205i −0.115470 + 0.200000i
\(76\) −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 \(0.807925\pi\)
\(80\) 3.10260i 0.346881i
\(81\) 1.00000 0.111111
\(82\) −7.79129 −0.860404
\(83\) 3.46410i 0.380235i 0.981761 + 0.190117i \(0.0608868\pi\)
−0.981761 + 0.190117i \(0.939113\pi\)
\(84\) −6.39564 + 3.69253i −0.697822 + 0.402888i
\(85\) 1.50000 + 0.866025i 0.162698 + 0.0939336i
\(86\) −8.68693 + 5.01540i −0.936736 + 0.540825i
\(87\) 3.50000 + 6.06218i 0.375239 + 0.649934i
\(88\) 6.00000 0.639602
\(89\) −13.5000 7.79423i −1.43100 0.826187i −0.433800 0.901009i \(-0.642828\pi\)
−0.997197 + 0.0748225i \(0.976161\pi\)
\(90\) −3.79129 −0.399637
\(91\) 9.16515 2.64575i 0.960769 0.277350i
\(92\) 23.9564 2.49763
\(93\) −5.29129 3.05493i −0.548681 0.316781i
\(94\) 1.79129 0.184757
\(95\) −4.58258 7.93725i −0.470162 0.814345i
\(96\) 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
\(100\) −5.58258 −0.558258
\(101\) 13.1652 1.30998 0.654991 0.755637i \(-0.272673\pi\)
0.654991 + 0.755637i \(0.272673\pi\)
\(102\) 2.18890i 0.216734i
\(103\) −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
\(107\) 0.708712 1.22753i 0.0685138 0.118669i −0.829733 0.558160i \(-0.811508\pi\)
0.898247 + 0.439490i \(0.144841\pi\)
\(108\) 1.39564 + 2.41733i 0.134296 + 0.232607i
\(109\) 16.6652 + 9.62163i 1.59623 + 0.921585i 0.992204 + 0.124622i \(0.0397717\pi\)
0.604028 + 0.796963i \(0.293562\pi\)
\(110\) 13.1334i 1.25222i
\(111\) −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 \(0.972757\pi\)
\(114\) −5.79129 + 10.0308i −0.542404 + 0.939471i
\(115\) 14.8655i 1.38621i
\(116\) −9.76951 + 16.9213i −0.907076 + 1.57110i
\(117\) −1.00000 3.46410i −0.0924500 0.320256i
\(118\) −9.37386 −0.862934
\(119\) 2.29129 1.32288i 0.210042 0.121268i
\(120\) −1.50000 2.59808i −0.136931 0.237171i
\(121\) −1.00000 −0.0909091
\(122\) −9.79129 5.65300i −0.886462 0.511799i
\(123\) −3.08258 + 1.77973i −0.277946 + 0.160472i
\(124\) 17.0544i 1.53153i
\(125\) 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 \(0.927672\pi\)
\(128\) 11.0608 + 6.38595i 0.977645 + 0.564444i
\(129\) −2.29129 + 3.96863i −0.201737 + 0.349418i
\(130\) 3.79129 + 13.1334i 0.332518 + 1.15188i
\(131\) −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
\(133\) −14.0000 −1.21395
\(134\) −15.3739 + 26.6283i −1.32810 + 2.30034i
\(135\) −1.50000 + 0.866025i −0.129099 + 0.0745356i
\(136\) 1.50000 0.866025i 0.128624 0.0742611i
\(137\) −7.50000 + 4.33013i −0.640768 + 0.369948i −0.784910 0.619609i \(-0.787291\pi\)
0.144142 + 0.989557i \(0.453958\pi\)
\(138\) 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 \(0.0766096\pi\)
\(140\) 6.39564 11.0776i 0.540531 0.936226i
\(141\) 0.708712 0.409175i 0.0596843 0.0344588i
\(142\) −4.89564 8.47950i −0.410833 0.711584i
\(143\) −12.0000 + 3.46410i −1.00349 + 0.289683i
\(144\) 0.895644 1.55130i 0.0746370 0.129275i
\(145\) −10.5000 6.06218i −0.871978 0.503436i
\(146\) 9.47822 + 16.4168i 0.784423 + 1.35866i
\(147\) −7.00000 −0.577350
\(148\) 19.6048i 1.61150i
\(149\) 3.65480i 0.299413i 0.988730 + 0.149707i \(0.0478329\pi\)
−0.988730 + 0.149707i \(0.952167\pi\)
\(150\) −3.79129 + 2.18890i −0.309557 + 0.178723i
\(151\) −14.4564 8.34643i −1.17645 0.679223i −0.221258 0.975215i \(-0.571016\pi\)
−0.955190 + 0.295993i \(0.904350\pi\)
\(152\) −9.16515 −0.743392
\(153\) −0.500000 0.866025i −0.0404226 0.0700140i
\(154\) 17.3739 + 10.0308i 1.40003 + 0.808305i
\(155\) 10.5826 0.850013
\(156\) 6.97822 7.25198i 0.558705 0.580623i
\(157\) −5.08258 + 8.80328i −0.405634 + 0.702578i −0.994395 0.105729i \(-0.966282\pi\)
0.588761 + 0.808307i \(0.299616\pi\)
\(158\) 3.10260i 0.246830i
\(159\) 3.08258 5.33918i 0.244464 0.423424i
\(160\) −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
\(163\) 3.46410i 0.271329i 0.990755 + 0.135665i \(0.0433170\pi\)
−0.990755 + 0.135665i \(0.956683\pi\)
\(164\) −8.60436 4.96773i −0.671887 0.387914i
\(165\) 3.00000 + 5.19615i 0.233550 + 0.404520i
\(166\) −3.79129 + 6.56670i −0.294261 + 0.509675i
\(167\) 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
\(171\) 5.29150i 0.404651i
\(172\) −12.7913 −0.975327
\(173\) 24.3303 1.84980 0.924899 0.380212i \(-0.124149\pi\)
0.924899 + 0.380212i \(0.124149\pi\)
\(174\) 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
\(178\) −17.0608 29.5502i −1.27876 2.21488i
\(179\) 0.834849 0.0623995 0.0311998 0.999513i \(-0.490067\pi\)
0.0311998 + 0.999513i \(0.490067\pi\)
\(180\) −4.18693 2.41733i −0.312075 0.180177i
\(181\) 22.0000 1.63525 0.817624 0.575753i \(-0.195291\pi\)
0.817624 + 0.575753i \(0.195291\pi\)
\(182\) 20.2695 + 5.01540i 1.50248 + 0.371766i
\(183\) −5.16515 −0.381819
\(184\) 12.8739 + 7.43273i 0.949074 + 0.547948i
\(185\) 12.1652 0.894400
\(186\) −6.68693 11.5821i −0.490310 0.849241i
\(187\) −3.00000 + 1.73205i −0.219382 + 0.126660i
\(188\) 1.97822 + 1.14213i 0.144276 + 0.0832981i
\(189\) 2.64575i 0.192450i
\(190\) 20.0616i 1.45542i
\(191\) −14.3303 −1.03690 −0.518452 0.855107i \(-0.673492\pi\)
−0.518452 + 0.855107i \(0.673492\pi\)
\(192\) 12.5826 0.908069
\(193\) 3.65480i 0.263078i 0.991311 + 0.131539i \(0.0419919\pi\)
−0.991311 + 0.131539i \(0.958008\pi\)
\(194\) 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 \(0.117531\pi\)
\(198\) 3.79129 6.56670i 0.269435 0.466675i
\(199\) −1.29129 2.23658i −0.0915370 0.158547i 0.816621 0.577174i \(-0.195845\pi\)
−0.908158 + 0.418627i \(0.862511\pi\)
\(200\) −3.00000 1.73205i −0.212132 0.122474i
\(201\) 14.0471i 0.990807i
\(202\) 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
\(205\) 3.08258 5.33918i 0.215296 0.372904i
\(206\) 7.48040i 0.521184i
\(207\) 4.29129 7.43273i 0.298265 0.516610i
\(208\) −6.26951 1.55130i −0.434712 0.107563i
\(209\) 18.3303 1.26793
\(210\) 10.0308i 0.692191i
\(211\) −3.29129 5.70068i −0.226582 0.392451i 0.730211 0.683222i \(-0.239422\pi\)
−0.956793 + 0.290771i \(0.906088\pi\)
\(212\) 17.2087 1.18190
\(213\) −3.87386 2.23658i −0.265433 0.153248i
\(214\) 2.68693 1.55130i 0.183675 0.106045i
\(215\) 7.93725i 0.541316i
\(216\) 1.73205i 0.117851i
\(217\) 8.08258 13.9994i 0.548681 0.950343i
\(218\) 21.0608 + 36.4784i 1.42642 + 2.47063i
\(219\) 7.50000 + 4.33013i 0.506803 + 0.292603i
\(220\) −8.37386 + 14.5040i −0.564566 + 0.977857i
\(221\) −2.50000 + 2.59808i −0.168168 + 0.174766i
\(222\) −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
\(227\) −23.6216 + 13.6379i −1.56782 + 0.905181i −0.571397 + 0.820674i \(0.693598\pi\)
−0.996423 + 0.0845077i \(0.973068\pi\)
\(228\) −12.7913 + 7.38505i −0.847124 + 0.489087i
\(229\) 9.08258 5.24383i 0.600193 0.346522i −0.168924 0.985629i \(-0.554029\pi\)
0.769118 + 0.639107i \(0.220696\pi\)
\(230\) −16.2695 + 28.1796i −1.07278 + 1.85811i
\(231\) 9.16515 0.603023
\(232\) −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 \(-0.396336\pi\)
\(234\) 1.89564 7.66115i 0.123922 0.500825i
\(235\) −0.708712 + 1.22753i −0.0462313 + 0.0800749i
\(236\) −10.3521 5.97678i −0.673863 0.389055i
\(237\) 0.708712 + 1.22753i 0.0460358 + 0.0797363i
\(238\) 5.79129 0.375393
\(239\) 2.01810i 0.130540i −0.997868 0.0652701i \(-0.979209\pi\)
0.997868 0.0652701i \(-0.0207909\pi\)
\(240\) 3.10260i 0.200272i
\(241\) 12.2477 7.07123i 0.788945 0.455498i −0.0506457 0.998717i \(-0.516128\pi\)
0.839591 + 0.543219i \(0.182795\pi\)
\(242\) −1.89564 1.09445i −0.121857 0.0703539i
\(243\) 1.00000 0.0641500
\(244\) −7.20871 12.4859i −0.461491 0.799325i
\(245\) 10.5000 6.06218i 0.670820 0.387298i
\(246\) −7.79129 −0.496754
\(247\) 18.3303 5.29150i 1.16633 0.336690i
\(248\) 5.29129 9.16478i 0.335997 0.581964i
\(249\) 3.46410i 0.219529i
\(250\) 13.2695 22.9835i 0.839237 1.45360i
\(251\) 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
\(254\) 14.4086i 0.904076i
\(255\) 1.50000 + 0.866025i 0.0939336 + 0.0542326i
\(256\) 1.39564 + 2.41733i 0.0872277 + 0.151083i
\(257\) 4.66515 8.08028i 0.291004 0.504034i −0.683043 0.730378i \(-0.739344\pi\)
0.974047 + 0.226344i \(0.0726773\pi\)
\(258\) −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
\(262\) 3.10260i 0.191679i
\(263\) −4.83485 −0.298130 −0.149065 0.988827i \(-0.547626\pi\)
−0.149065 + 0.988827i \(0.547626\pi\)
\(264\) 6.00000 0.369274
\(265\) 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
\(269\) −8.08258 13.9994i −0.492803 0.853560i 0.507162 0.861851i \(-0.330694\pi\)
−0.999966 + 0.00829015i \(0.997361\pi\)
\(270\) −3.79129 −0.230730
\(271\) −10.0390 5.79603i −0.609827 0.352084i 0.163071 0.986614i \(-0.447860\pi\)
−0.772898 + 0.634531i \(0.781193\pi\)
\(272\) −1.79129 −0.108613
\(273\) 9.16515 2.64575i 0.554700 0.160128i
\(274\) −18.9564 −1.14520
\(275\) 6.00000 + 3.46410i 0.361814 + 0.208893i
\(276\) 23.9564 1.44201
\(277\) −4.66515 8.08028i −0.280302 0.485497i 0.691157 0.722704i \(-0.257101\pi\)
−0.971459 + 0.237208i \(0.923768\pi\)
\(278\) 12.4782 7.20430i 0.748394 0.432085i
\(279\) −5.29129 3.05493i −0.316781 0.182894i
\(280\) 6.87386 3.96863i 0.410792 0.237171i
\(281\) 3.65480i 0.218027i −0.994040 0.109014i \(-0.965231\pi\)
0.994040 0.109014i \(-0.0347692\pi\)
\(282\) 1.79129 0.106670
\(283\) −30.3303 −1.80295 −0.901475 0.432832i \(-0.857514\pi\)
−0.901475 + 0.432832i \(0.857514\pi\)
\(284\) 12.4859i 0.740899i
\(285\) −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
\(289\) 8.00000 13.8564i 0.470588 0.815083i
\(290\) −13.2695 22.9835i −0.779212 1.34964i
\(291\) 9.08258 + 5.24383i 0.532430 + 0.307399i
\(292\) 24.1733i 1.41463i
\(293\) 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
\(296\) 6.08258 10.5353i 0.353543 0.612354i
\(297\) 3.46410i 0.201008i
\(298\) −4.00000 + 6.92820i −0.231714 + 0.401340i
\(299\) −30.0390 7.43273i −1.73720 0.429846i
\(300\) −5.58258 −0.322310
\(301\) −10.5000 6.06218i −0.605210 0.349418i
\(302\) −18.2695 31.6437i −1.05129 1.82089i
\(303\) 13.1652 0.756318
\(304\) 8.20871 + 4.73930i 0.470802 + 0.271818i
\(305\) 7.74773 4.47315i 0.443634 0.256132i
\(306\) 2.18890i 0.125131i
\(307\) 20.9753i 1.19712i 0.801076 + 0.598562i \(0.204261\pi\)
−0.801076 + 0.598562i \(0.795739\pi\)
\(308\) 12.7913 + 22.1552i 0.728851 + 1.26241i
\(309\) −1.70871 2.95958i −0.0972052 0.168364i
\(310\) 20.0608 + 11.5821i 1.13938 + 0.657819i
\(311\) 4.29129 7.43273i 0.243337 0.421471i −0.718326 0.695707i \(-0.755091\pi\)
0.961663 + 0.274235i \(0.0884247\pi\)
\(312\) 6.00000 1.73205i 0.339683 0.0980581i
\(313\) 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 −0.452508 0.891760i \(-0.649471\pi\)
0.546033 + 0.837764i \(0.316137\pi\)
\(318\) 11.6869 6.74745i 0.655371 0.378378i
\(319\) 21.0000 12.1244i 1.17577 0.678834i
\(320\) −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
\(325\) 7.00000 + 1.73205i 0.388290 + 0.0960769i
\(326\) −3.79129 + 6.56670i −0.209980 + 0.363696i
\(327\) 16.6652 + 9.62163i 0.921585 + 0.532077i
\(328\) −3.08258 5.33918i −0.170207 0.294807i
\(329\) 1.08258 + 1.87508i 0.0596843 + 0.103376i
\(330\) 13.1334i 0.722970i
\(331\) 26.0761i 1.43327i −0.697447 0.716636i \(-0.745681\pi\)
0.697447 0.716636i \(-0.254319\pi\)
\(332\) −8.37386 + 4.83465i −0.459575 + 0.265336i
\(333\) −6.08258 3.51178i −0.333323 0.192444i
\(334\) 9.79129 0.535755
\(335\) −12.1652 21.0707i −0.664653 1.15121i
\(336\) 4.10436 + 2.36965i 0.223911 + 0.129275i
\(337\) 23.4955 1.27988 0.639939 0.768425i \(-0.278959\pi\)
0.639939 + 0.768425i \(0.278959\pi\)
\(338\) −28.4347 + 1.09445i −1.54664 + 0.0595303i
\(339\) −6.08258 + 10.5353i −0.330360 + 0.572201i
\(340\) 4.83465i 0.262196i
\(341\) −10.5826 + 18.3296i −0.573079 + 0.992601i
\(342\) −5.79129 + 10.0308i −0.313157 + 0.542404i
\(343\) 18.5203i 1.00000i
\(344\) −6.87386 3.96863i −0.370614 0.213974i
\(345\) 14.8655i 0.800329i
\(346\) 46.1216 + 26.6283i 2.47951 + 1.43155i
\(347\) 12.8739 + 22.2982i 0.691105 + 1.19703i 0.971476 + 0.237138i \(0.0762092\pi\)
−0.280371 + 0.959892i \(0.590457\pi\)
\(348\) −9.76951 + 16.9213i −0.523701 + 0.907076i
\(349\) 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
\(353\) 19.3386i 1.02929i 0.857403 + 0.514645i \(0.172076\pi\)
−0.857403 + 0.514645i \(0.827924\pi\)
\(354\) −9.37386 −0.498215
\(355\) 7.74773 0.411207
\(356\) 43.5119i 2.30612i
\(357\) 2.29129 1.32288i 0.121268 0.0700140i
\(358\) 1.58258 + 0.913701i 0.0836417 + 0.0482906i
\(359\) −16.0390 + 9.26013i −0.846507 + 0.488731i −0.859471 0.511185i \(-0.829207\pi\)
0.0129639 + 0.999916i \(0.495873\pi\)
\(360\) −1.50000 2.59808i −0.0790569 0.136931i
\(361\) −9.00000 −0.473684
\(362\) 41.7042 + 24.0779i 2.19192 + 1.26551i
\(363\) −1.00000 −0.0524864
\(364\) 19.1869 + 18.4626i 1.00567 + 0.967705i
\(365\) −15.0000 −0.785136
\(366\) −9.79129 5.65300i −0.511799 0.295487i
\(367\) 15.1652 0.791614 0.395807 0.918334i \(-0.370465\pi\)
0.395807 + 0.918334i \(0.370465\pi\)
\(368\) −7.68693 13.3142i −0.400709 0.694048i
\(369\) −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
\(373\) −26.0000 −1.34623 −0.673114 0.739538i \(-0.735044\pi\)
−0.673114 + 0.739538i \(0.735044\pi\)
\(374\) −7.58258 −0.392086
\(375\) 12.1244i 0.626099i
\(376\) 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 \(0.175542\pi\)
\(380\) 12.7913 22.1552i 0.656179 1.13654i
\(381\) −3.29129 5.70068i −0.168618 0.292055i
\(382\) −27.1652 15.6838i −1.38989 0.802453i
\(383\) 17.7019i 0.904525i −0.891885 0.452263i \(-0.850617\pi\)
0.891885 0.452263i \(-0.149383\pi\)
\(384\) 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
\(387\) −2.29129 + 3.96863i −0.116473 + 0.201737i
\(388\) 29.2741i 1.48617i
\(389\) −13.6652 + 23.6687i −0.692851 + 1.20005i 0.278049 + 0.960567i \(0.410312\pi\)
−0.970900 + 0.239486i \(0.923021\pi\)
\(390\) 3.79129 + 13.1334i 0.191979 + 0.665036i
\(391\) −8.58258 −0.434040
\(392\) 12.1244i 0.612372i
\(393\) −0.708712 1.22753i −0.0357498 0.0619205i
\(394\) 38.5390 1.94157
\(395\) −2.12614 1.22753i −0.106978 0.0617635i
\(396\) 8.37386 4.83465i 0.420802 0.242950i
\(397\) 36.8498i 1.84944i 0.380649 + 0.924720i \(0.375701\pi\)
−0.380649 + 0.924720i \(0.624299\pi\)
\(398\) 5.65300i 0.283359i
\(399\) −14.0000 −0.700877
\(400\) 1.79129 + 3.10260i 0.0895644 + 0.155130i
\(401\) 30.0826 + 17.3682i 1.50225 + 0.867326i 0.999997 + 0.00260643i \(0.000829654\pi\)
0.502256 + 0.864719i \(0.332504\pi\)
\(402\) −15.3739 + 26.6283i −0.766779 + 1.32810i
\(403\) −5.29129 + 21.3845i −0.263578 + 1.06524i
\(404\) 18.3739 + 31.8245i 0.914134 + 1.58333i
\(405\) −1.50000 + 0.866025i −0.0745356 + 0.0430331i
\(406\) −40.5390 −2.01192
\(407\) −12.1652 + 21.0707i −0.603004 + 1.04443i
\(408\) 1.50000 0.866025i 0.0742611 0.0428746i
\(409\) 27.0826 15.6361i 1.33915 0.773157i 0.352466 0.935825i \(-0.385343\pi\)
0.986681 + 0.162668i \(0.0520098\pi\)
\(410\) 11.6869 6.74745i 0.577176 0.333233i
\(411\) −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
\(416\) −19.1869 18.4626i −0.940717 0.905205i
\(417\) 3.29129 5.70068i 0.161175 0.279163i
\(418\) 34.7477 + 20.0616i 1.69957 + 0.981245i
\(419\) −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 \(0.551308\pi\)
\(422\) 14.4086i 0.701400i
\(423\) 0.708712 0.409175i 0.0344588 0.0198948i
\(424\) 9.24773 + 5.33918i 0.449109 + 0.259293i
\(425\) 2.00000 0.0970143
\(426\) −4.89564 8.47950i −0.237195 0.410833i
\(427\) 13.6657i 0.661330i
\(428\) 3.95644 0.191242
\(429\) −12.0000 + 3.46410i −0.579365 + 0.167248i
\(430\) 8.68693 15.0462i 0.418921 0.725593i
\(431\) 8.56490i 0.412557i 0.978493 + 0.206278i \(0.0661353\pi\)
−0.978493 + 0.206278i \(0.933865\pi\)
\(432\) 0.895644 1.55130i 0.0430917 0.0746370i
\(433\) 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
\(436\) 53.7135i 2.57241i
\(437\) 39.3303 + 22.7074i 1.88142 + 1.08624i
\(438\) 9.47822 + 16.4168i 0.452887 + 0.784423i
\(439\) 5.29129 9.16478i 0.252539 0.437411i −0.711685 0.702499i \(-0.752068\pi\)
0.964224 + 0.265088i \(0.0854009\pi\)
\(440\) −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 \(0.789735\pi\)
\(444\) 19.6048i 0.930401i
\(445\) 27.0000 1.27992
\(446\) −5.79129 −0.274225
\(447\) 3.65480i 0.172866i
\(448\) 33.2904i 1.57282i
\(449\) −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
\(451\) 6.16515 + 10.6784i 0.290306 + 0.502824i
\(452\) −33.9564 −1.59718
\(453\) −14.4564 8.34643i −0.679223 0.392149i
\(454\) −59.7042 −2.80206
\(455\) −11.4564 + 11.9059i −0.537086 + 0.558156i
\(456\) −9.16515 −0.429198
\(457\) −3.24773 1.87508i −0.151922 0.0877124i 0.422112 0.906544i \(-0.361289\pi\)
−0.574034 + 0.818831i \(0.694622\pi\)
\(458\) 22.9564 1.07268
\(459\) −0.500000 0.866025i −0.0233380 0.0404226i
\(460\) −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 \(0.647667\pi\)
\(464\) 12.5390 0.582109
\(465\) 10.5826 0.490755
\(466\) 44.1395i 2.04472i
\(467\) 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
\(471\) −5.08258 + 8.80328i −0.234193 + 0.405634i
\(472\) −3.70871 6.42368i −0.170707 0.295674i
\(473\) 13.7477 + 7.93725i 0.632121 + 0.364955i
\(474\) 3.10260i 0.142507i
\(475\) −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
\(478\) 2.20871 3.82560i 0.101024 0.174979i
\(479\) 28.2849i 1.29237i −0.763181 0.646185i \(-0.776363\pi\)
0.763181 0.646185i \(-0.223637\pi\)
\(480\) −6.39564 + 11.0776i −0.291920 + 0.505620i
\(481\) −6.08258 + 24.5824i −0.277342 + 1.12086i
\(482\) 30.9564 1.41003
\(483\) 19.6652 + 11.3537i 0.894795 + 0.516610i
\(484\) −1.39564 2.41733i −0.0634384 0.109878i
\(485\) −18.1652 −0.824837
\(486\) 1.89564 + 1.09445i 0.0859882 + 0.0496453i
\(487\) −9.54356 + 5.50998i −0.432460 + 0.249681i −0.700394 0.713756i \(-0.746992\pi\)
0.267934 + 0.963437i \(0.413659\pi\)
\(488\) 8.94630i 0.404980i
\(489\) 3.46410i 0.156652i
\(490\) 26.5390 1.19891
\(491\) −1.87386 3.24563i −0.0845663 0.146473i 0.820640 0.571445i \(-0.193617\pi\)
−0.905206 + 0.424972i \(0.860284\pi\)
\(492\) −8.60436 4.96773i −0.387914 0.223962i
\(493\) 3.50000 6.06218i 0.157632 0.273027i
\(494\) 40.5390 + 10.0308i 1.82394 + 0.451307i
\(495\) 3.00000 + 5.19615i 0.134840 + 0.233550i
\(496\) −9.47822 + 5.47225i −0.425585 + 0.245711i
\(497\) 5.91742 10.2493i 0.265433 0.459743i
\(498\) −3.79129 + 6.56670i −0.169892 + 0.294261i
\(499\) 21.7087 12.5335i 0.971815 0.561078i 0.0720262 0.997403i \(-0.477053\pi\)
0.899789 + 0.436325i \(0.143720\pi\)
\(500\) 29.3085 16.9213i 1.31072 0.756743i
\(501\) 3.87386 2.23658i 0.173071 0.0999229i
\(502\) 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 \(0.179072\pi\)
\(504\) −4.58258 −0.204124
\(505\) −19.7477 + 11.4014i −0.878762 + 0.507354i
\(506\) −32.5390 56.3592i −1.44654 2.50547i
\(507\) −11.0000 + 6.92820i −0.488527 + 0.307692i
\(508\) 9.18693 15.9122i 0.407604 0.705991i
\(509\) −24.2477 13.9994i −1.07476 0.620514i −0.145283 0.989390i \(-0.546409\pi\)
−0.929479 + 0.368876i \(0.879743\pi\)
\(510\) 1.89564 + 3.28335i 0.0839405 + 0.145389i
\(511\) −11.4564 + 19.8431i −0.506803 + 0.877809i
\(512\) 19.4340i 0.858868i
\(513\) 5.29150i 0.233626i
\(514\) 17.6869 10.2116i 0.780137 0.450412i
\(515\) 5.12614 + 2.95958i 0.225885 + 0.130415i
\(516\) −12.7913 −0.563105
\(517\) −1.41742 2.45505i −0.0623382 0.107973i
\(518\) 35.2259 20.3377i 1.54774 0.893588i
\(519\) 24.3303 1.06798
\(520\) −7.50000 + 7.79423i −0.328897 + 0.341800i
\(521\) −1.66515 + 2.88413i −0.0729516 + 0.126356i −0.900194 0.435490i \(-0.856575\pi\)
0.827242 + 0.561846i \(0.189909\pi\)
\(522\) 15.3223i 0.670639i
\(523\) 4.87386 8.44178i 0.213119 0.369133i −0.739570 0.673080i \(-0.764971\pi\)
0.952689 + 0.303946i \(0.0983044\pi\)
\(524\) 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
\(527\) 6.10985i 0.266149i
\(528\) −5.37386 3.10260i −0.233867 0.135023i
\(529\) −25.3303 43.8734i −1.10132 1.90754i
\(530\) −11.6869 + 20.2424i −0.507648 + 0.879272i
\(531\) −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
\(535\) 2.45505i 0.106141i
\(536\) −24.3303 −1.05091
\(537\) 0.834849 0.0360264
\(538\) 35.3839i 1.52551i
\(539\) 24.2487i 1.04447i
\(540\) −4.18693 2.41733i −0.180177 0.104025i
\(541\) −7.33485 + 4.23478i −0.315350 + 0.182067i −0.649318 0.760517i \(-0.724946\pi\)
0.333968 + 0.942584i \(0.391612\pi\)
\(542\) −12.6869 21.9744i −0.544950 0.943882i
\(543\) 22.0000 0.944110
\(544\) −6.39564 3.69253i −0.274211 0.158316i
\(545\) −33.3303 −1.42771
\(546\) 20.2695 + 5.01540i 0.867455 + 0.214639i
\(547\) −8.00000 −0.342055 −0.171028 0.985266i \(-0.554709\pi\)
−0.171028 + 0.985266i \(0.554709\pi\)
\(548\) −20.9347 12.0866i −0.894284 0.516315i
\(549\) −5.16515 −0.220443
\(550\) 7.58258 + 13.1334i 0.323322 + 0.560010i
\(551\) −32.0780 + 18.5203i −1.36657 + 0.788990i
\(552\) 12.8739 + 7.43273i 0.547948 + 0.316358i
\(553\) −3.24773 + 1.87508i −0.138107 + 0.0797363i
\(554\) 20.4231i 0.867695i
\(555\) 12.1652 0.516382
\(556\) 18.3739 0.779225
\(557\) 24.4394i 1.03553i 0.855523 + 0.517766i \(0.173236\pi\)
−0.855523 + 0.517766i \(0.826764\pi\)
\(558\) −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
\(562\) 4.00000 6.92820i 0.168730 0.292249i
\(563\) −2.70871 4.69163i −0.114159 0.197729i 0.803284 0.595596i \(-0.203084\pi\)
−0.917443 + 0.397867i \(0.869751\pi\)
\(564\) 1.97822 + 1.14213i 0.0832981 + 0.0480922i
\(565\) 21.0707i 0.886449i
\(566\) −57.4955 33.1950i −2.41671 1.39529i
\(567\) 2.64575i 0.111111i
\(568\) 3.87386 6.70973i 0.162544 0.281534i
\(569\) 2.66515 4.61618i 0.111729 0.193520i −0.804738 0.593629i \(-0.797694\pi\)
0.916467 + 0.400109i \(0.131028\pi\)
\(570\) 20.0616i 0.840288i
\(571\) −23.8739 + 41.3507i −0.999090 + 1.73047i −0.462609 + 0.886562i \(0.653087\pi\)
−0.536481 + 0.843913i \(0.680247\pi\)
\(572\) −25.1216 24.1733i −1.05039 1.01073i
\(573\) −14.3303 −0.598657
\(574\) 20.6138i 0.860404i
\(575\) 8.58258 + 14.8655i 0.357918 + 0.619932i
\(576\) 12.5826 0.524274
\(577\) −12.0826 6.97588i −0.503004 0.290410i 0.226949 0.973907i \(-0.427125\pi\)
−0.729953 + 0.683497i \(0.760458\pi\)
\(578\) 30.3303 17.5112i 1.26157 0.728370i
\(579\) 3.65480i 0.151888i
\(580\) 33.8426i 1.40524i
\(581\) −9.16515 −0.380235
\(582\) 11.4782 + 19.8809i 0.475788 + 0.824088i
\(583\) −18.4955 10.6784i −0.766003 0.442252i
\(584\) −7.50000 + 12.9904i −0.310352 + 0.537546i
\(585\) 4.50000 + 4.33013i 0.186052 + 0.179029i
\(586\) 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
\(591\) 15.2477 8.80328i 0.627208 0.362119i
\(592\) −10.8956 + 6.29060i −0.447808 + 0.258542i
\(593\) 15.2477 8.80328i 0.626149 0.361507i −0.153110 0.988209i \(-0.548929\pi\)
0.779259 + 0.626702i \(0.215596\pi\)
\(594\) 3.79129 6.56670i 0.155558 0.269435i
\(595\) −2.29129 + 3.96863i −0.0939336 + 0.162698i
\(596\) −8.83485 + 5.10080i −0.361889 + 0.208937i
\(597\) −1.29129 2.23658i −0.0528489 0.0915370i
\(598\) −48.8085 46.9660i −1.99593 1.92058i
\(599\) −4.12614 + 7.14668i −0.168589 + 0.292005i −0.937924 0.346841i \(-0.887255\pi\)
0.769335 + 0.638846i \(0.220588\pi\)
\(600\) −3.00000 1.73205i −0.122474 0.0707107i
\(601\) −13.0826 22.6597i −0.533649 0.924308i −0.999227 0.0393010i \(-0.987487\pi\)
0.465578 0.885007i \(-0.345846\pi\)
\(602\) −13.2695 22.9835i −0.540825 0.936736i
\(603\) 14.0471i 0.572042i
\(604\) 46.5946i 1.89591i
\(605\) 1.50000 0.866025i 0.0609837 0.0352089i
\(606\) 24.9564 + 14.4086i 1.01379 + 0.585310i
\(607\) −8.00000 −0.324710 −0.162355 0.986732i \(-0.551909\pi\)
−0.162355 + 0.986732i \(0.551909\pi\)
\(608\) 19.5390 + 33.8426i 0.792412 + 1.37250i
\(609\) −16.0390 + 9.26013i −0.649934 + 0.375239i
\(610\) 19.5826 0.792875
\(611\) −2.12614 2.04588i −0.0860143 0.0827673i
\(612\) 1.39564 2.41733i 0.0564156 0.0977146i
\(613\) 24.4394i 0.987099i −0.869718 0.493549i \(-0.835699\pi\)
0.869718 0.493549i \(-0.164301\pi\)
\(614\) −22.9564 + 39.7617i −0.926446 + 1.60465i
\(615\) 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 \(0.806089\pi\)
\(618\) 7.48040i 0.300906i
\(619\) 1.03901 + 0.599876i 0.0417615 + 0.0241110i 0.520735 0.853718i \(-0.325658\pi\)
−0.478974 + 0.877829i \(0.658991\pi\)
\(620\) 14.7695 + 25.5815i 0.593158 + 1.02738i
\(621\) 4.29129 7.43273i 0.172203 0.298265i
\(622\) 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
\(626\) 30.2831i 1.21036i
\(627\) 18.3303 0.732042
\(628\) −28.3739 −1.13224
\(629\) 7.02355i 0.280047i
\(630\) 10.0308i 0.399637i
\(631\) −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
\(633\) −3.29129 5.70068i −0.130817 0.226582i
\(634\) 4.20871 0.167149
\(635\) 9.87386 + 5.70068i 0.391832 + 0.226224i
\(636\) 17.2087 0.682370
\(637\) 7.00000 + 24.2487i 0.277350 + 0.960769i
\(638\) 53.0780 2.10138
\(639\) −3.87386 2.23658i −0.153248 0.0884776i
\(640\) −22.1216 −0.874433
\(641\) 8.24773 + 14.2855i 0.325766 + 0.564243i 0.981667 0.190604i \(-0.0610446\pi\)
−0.655901 + 0.754847i \(0.727711\pi\)
\(642\) 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 \(0.432670\pi\)
\(644\) 63.3828i 2.49763i
\(645\) 7.93725i 0.312529i
\(646\) 11.5826 0.455710
\(647\) −38.3303 −1.50692 −0.753460 0.657494i \(-0.771617\pi\)
−0.753460 + 0.657494i \(0.771617\pi\)
\(648\) 1.73205i 0.0680414i
\(649\) 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
\(653\) −13.2477 + 22.9457i −0.518424 + 0.897936i 0.481347 + 0.876530i \(0.340148\pi\)
−0.999771 + 0.0214061i \(0.993186\pi\)
\(654\) 21.0608 + 36.4784i 0.823542 + 1.42642i
\(655\) 2.12614 + 1.22753i 0.0830750 + 0.0479634i
\(656\) 6.37600i 0.248941i
\(657\) 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 \(0.294560\pi\)
\(660\) −8.37386 + 14.5040i −0.325952 + 0.564566i
\(661\) 5.48220i 0.213233i −0.994300 0.106616i \(-0.965998\pi\)
0.994300 0.106616i \(-0.0340017\pi\)
\(662\) 28.5390 49.4310i 1.10920 1.92119i
\(663\) −2.50000 + 2.59808i −0.0970920 + 0.100901i
\(664\) −6.00000 −0.232845
\(665\) 21.0000 12.1244i 0.814345 0.470162i
\(666\) −7.68693 13.3142i −0.297863 0.515913i
\(667\) 60.0780 2.32623
\(668\) 10.8131 + 6.24293i 0.418370 + 0.241546i
\(669\) −2.29129 + 1.32288i −0.0885863 + 0.0511453i
\(670\) 53.2566i 2.05748i
\(671\) 17.8926i 0.690737i
\(672\) 9.76951 + 16.9213i 0.376867 + 0.652753i
\(673\) 17.6652 + 30.5969i 0.680942 + 1.17943i 0.974694 + 0.223544i \(0.0717626\pi\)
−0.293752 + 0.955882i \(0.594904\pi\)
\(674\) 44.5390 + 25.7146i 1.71558 + 0.990490i
\(675\) −1.00000 + 1.73205i −0.0384900 + 0.0666667i
\(676\) −32.0998 16.9213i −1.23461 0.650819i
\(677\) −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
\(679\) −13.8739 + 24.0302i −0.532430 + 0.922196i
\(680\) −1.50000 + 2.59808i −0.0575224 + 0.0996317i
\(681\) −23.6216 + 13.6379i −0.905181 + 0.522607i
\(682\) −40.1216 + 23.1642i −1.53634 + 0.887003i
\(683\) 33.8739 19.5571i 1.29615 0.748331i 0.316411 0.948622i \(-0.397522\pi\)
0.979736 + 0.200291i \(0.0641888\pi\)
\(684\) −12.7913 + 7.38505i −0.489087 + 0.282375i
\(685\) 7.50000 12.9904i 0.286560 0.496337i
\(686\) 20.2695 35.1078i 0.773893 1.34042i
\(687\) 9.08258 5.24383i 0.346522 0.200064i
\(688\) 4.10436 + 7.10895i 0.156477 + 0.271026i
\(689\) −21.5780 5.33918i −0.822057 0.203406i
\(690\) −16.2695 + 28.1796i −0.619370 + 1.07278i
\(691\) −6.54356 3.77793i −0.248929 0.143719i 0.370345 0.928894i \(-0.379240\pi\)
−0.619274 + 0.785175i \(0.712573\pi\)
\(692\) 33.9564 + 58.8143i 1.29083 + 2.23578i
\(693\) 9.16515 0.348155
\(694\) 56.3592i 2.13937i
\(695\) 11.4014i 0.432478i
\(696\) −10.5000 + 6.06218i −0.398001 + 0.229786i
\(697\) 3.08258 + 1.77973i 0.116761 + 0.0674119i
\(698\) 22.9564 0.868914
\(699\) −10.0826 17.4635i −0.381358 0.660531i
\(700\) 14.7701i 0.558258i
\(701\) 34.0000 1.28416 0.642081 0.766637i \(-0.278071\pi\)
0.642081 + 0.766637i \(0.278071\pi\)
\(702\) 1.89564 7.66115i 0.0715465 0.289152i
\(703\) 18.5826 32.1860i 0.700855 1.21392i
\(704\) 43.5873i 1.64276i
\(705\) −0.708712 + 1.22753i −0.0266916 + 0.0462313i
\(706\) −21.1652 + 36.6591i −0.796561 + 1.37968i
\(707\) 34.8317i 1.30998i
\(708\) −10.3521 5.97678i −0.389055 0.224621i
\(709\) 29.5402i 1.10941i 0.832048 + 0.554703i \(0.187168\pi\)
−0.832048 + 0.554703i \(0.812832\pi\)
\(710\) 14.6869 + 8.47950i 0.551191 + 0.318230i
\(711\) 0.708712 + 1.22753i 0.0265788 + 0.0460358i
\(712\) 13.5000 23.3827i 0.505934 0.876303i
\(713\) −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
\(717\) 2.01810i 0.0753674i
\(718\) −40.5390 −1.51290
\(719\) −34.3303 −1.28030 −0.640152 0.768248i \(-0.721129\pi\)
−0.640152 + 0.768248i \(0.721129\pi\)
\(720\) 3.10260i 0.115627i
\(721\) 7.83030 4.52083i 0.291616 0.168364i
\(722\) −17.0608 9.85005i −0.634937 0.366581i
\(723\) 12.2477 7.07123i 0.455498 0.262982i
\(724\) 30.7042 + 53.1812i 1.14111 + 1.97646i
\(725\) −14.0000 −0.519947
\(726\) −1.89564 1.09445i −0.0703539 0.0406189i
\(727\) 28.0000 1.03846 0.519231 0.854634i \(-0.326218\pi\)
0.519231 + 0.854634i \(0.326218\pi\)
\(728\) 4.58258 + 15.8745i 0.169842 + 0.588348i
\(729\) 1.00000 0.0370370
\(730\) −28.4347 16.4168i −1.05241 0.607611i
\(731\) 4.58258 0.169493
\(732\) −7.20871 12.4859i −0.266442 0.461491i
\(733\) 25.8303 14.9131i 0.954064 0.550829i 0.0597230 0.998215i \(-0.480978\pi\)
0.894341 + 0.447386i \(0.147645\pi\)
\(734\) 28.7477 + 16.5975i 1.06110 + 0.612625i
\(735\) 10.5000 6.06218i 0.387298 0.223607i
\(736\) 63.3828i 2.33632i
\(737\) 48.6606 1.79244
\(738\) −7.79129 −0.286801
\(739\) 19.1479i 0.704367i −0.935931 0.352184i \(-0.885439\pi\)
0.935931 0.352184i \(-0.114561\pi\)
\(740\) 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 \(0.287949\pi\)
\(744\) 5.29129 9.16478i 0.193988 0.335997i
\(745\) −3.16515 5.48220i −0.115962 0.200852i
\(746\) −49.2867 28.4557i −1.80452 1.04184i
\(747\) 3.46410i 0.126745i
\(748\) −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
\(751\) 6.45644 11.1829i 0.235599 0.408069i −0.723848 0.689960i \(-0.757628\pi\)
0.959447 + 0.281891i \(0.0909615\pi\)
\(752\) 1.46590i 0.0534559i
\(753\) 10.2913 17.8250i 0.375035 0.649580i
\(754\) 53.0780 15.3223i 1.93299 0.558006i
\(755\) 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 \(0.859367\pi\)
\(758\) 40.5390 1.47244
\(759\) −25.7477 14.8655i −0.934583 0.539582i
\(760\) 13.7477 7.93725i 0.498682 0.287914i
\(761\) 1.44600i 0.0524175i −0.999656 0.0262087i \(-0.991657\pi\)
0.999656 0.0262087i \(-0.00834345\pi\)
\(762\) 14.4086i 0.521969i
\(763\) −25.4564 + 44.0918i −0.921585 + 1.59623i
\(764\) −20.0000 34.6410i −0.723575 1.25327i
\(765\) 1.50000 + 0.866025i 0.0542326 + 0.0313112i
\(766\) 19.3739 33.5565i 0.700006 1.21245i
\(767\) 11.1261 + 10.7061i 0.401742 + 0.386576i
\(768\) 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 \(0.352679\pi\)
\(770\) −34.7477 −1.25222
\(771\) 4.66515 8.08028i 0.168011 0.291004i
\(772\) −8.83485 + 5.10080i −0.317973 + 0.183582i
\(773\) 21.2477 12.2674i 0.764228 0.441227i −0.0665839 0.997781i \(-0.521210\pi\)
0.830812 + 0.556554i \(0.187877\pi\)
\(774\) −8.68693 + 5.01540i −0.312245 + 0.180275i
\(775\) 10.5826 6.10985i 0.380137 0.219472i