Properties

Label 273.2.bl.b.121.1
Level $273$
Weight $2$
Character 273.121
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 121.1
Root \(1.39564 + 0.228425i\) of defining polynomial
Character \(\chi\) \(=\) 273.121
Dual form 273.2.bl.b.88.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.395644 + 0.228425i) q^{2} +1.00000 q^{3} +(-0.895644 + 1.55130i) q^{4} +(-1.50000 - 0.866025i) q^{5} +(-0.395644 + 0.228425i) q^{6} +2.64575i q^{7} -1.73205i q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(-0.395644 + 0.228425i) q^{2} +1.00000 q^{3} +(-0.895644 + 1.55130i) q^{4} +(-1.50000 - 0.866025i) q^{5} +(-0.395644 + 0.228425i) q^{6} +2.64575i q^{7} -1.73205i q^{8} +1.00000 q^{9} +0.791288 q^{10} +3.46410i q^{11} +(-0.895644 + 1.55130i) q^{12} +(-1.00000 + 3.46410i) q^{13} +(-0.604356 - 1.04678i) q^{14} +(-1.50000 - 0.866025i) q^{15} +(-1.39564 - 2.41733i) q^{16} +(-0.500000 + 0.866025i) q^{17} +(-0.395644 + 0.228425i) q^{18} +5.29150i q^{19} +(2.68693 - 1.55130i) q^{20} +2.64575i q^{21} +(-0.791288 - 1.37055i) q^{22} +(-0.291288 - 0.504525i) q^{23} -1.73205i q^{24} +(-1.00000 - 1.73205i) q^{25} +(-0.395644 - 1.59898i) q^{26} +1.00000 q^{27} +(-4.10436 - 2.36965i) q^{28} +(3.50000 - 6.06218i) q^{29} +0.791288 q^{30} +(-0.708712 + 0.409175i) q^{31} +(4.10436 + 2.36965i) q^{32} +3.46410i q^{33} -0.456850i q^{34} +(2.29129 - 3.96863i) q^{35} +(-0.895644 + 1.55130i) q^{36} +(3.08258 - 1.77973i) q^{37} +(-1.20871 - 2.09355i) q^{38} +(-1.00000 + 3.46410i) q^{39} +(-1.50000 + 2.59808i) q^{40} +(6.08258 + 3.51178i) q^{41} +(-0.604356 - 1.04678i) q^{42} +(2.29129 + 3.96863i) q^{43} +(-5.37386 - 3.10260i) q^{44} +(-1.50000 - 0.866025i) q^{45} +(0.230493 + 0.133075i) q^{46} +(5.29129 + 3.05493i) q^{47} +(-1.39564 - 2.41733i) q^{48} -7.00000 q^{49} +(0.791288 + 0.456850i) q^{50} +(-0.500000 + 0.866025i) q^{51} +(-4.47822 - 4.65390i) q^{52} +(-6.08258 - 10.5353i) q^{53} +(-0.395644 + 0.228425i) q^{54} +(3.00000 - 5.19615i) q^{55} +4.58258 q^{56} +5.29150i q^{57} +3.19795i q^{58} +(-8.29129 - 4.78698i) q^{59} +(2.68693 - 1.55130i) q^{60} +13.1652 q^{61} +(0.186932 - 0.323775i) q^{62} +2.64575i q^{63} +3.41742 q^{64} +(4.50000 - 4.33013i) q^{65} +(-0.791288 - 1.37055i) q^{66} +7.11890i q^{67} +(-0.895644 - 1.55130i) q^{68} +(-0.291288 - 0.504525i) q^{69} +2.09355i q^{70} +(9.87386 - 5.70068i) q^{71} -1.73205i q^{72} +(7.50000 - 4.33013i) q^{73} +(-0.813068 + 1.40828i) q^{74} +(-1.00000 - 1.73205i) q^{75} +(-8.20871 - 4.73930i) q^{76} -9.16515 q^{77} +(-0.395644 - 1.59898i) q^{78} +(5.29129 - 9.16478i) q^{79} +4.83465i q^{80} +1.00000 q^{81} -3.20871 q^{82} -3.46410i q^{83} +(-4.10436 - 2.36965i) q^{84} +(1.50000 - 0.866025i) q^{85} +(-1.81307 - 1.04678i) q^{86} +(3.50000 - 6.06218i) q^{87} +6.00000 q^{88} +(-13.5000 + 7.79423i) q^{89} +0.791288 q^{90} +(-9.16515 - 2.64575i) q^{91} +1.04356 q^{92} +(-0.708712 + 0.409175i) q^{93} -2.79129 q^{94} +(4.58258 - 7.93725i) q^{95} +(4.10436 + 2.36965i) q^{96} +(-0.0825757 + 0.0476751i) q^{97} +(2.76951 - 1.59898i) 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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.395644 + 0.228425i −0.279763 + 0.161521i −0.633316 0.773893i \(-0.718307\pi\)
0.353553 + 0.935414i \(0.384973\pi\)
\(3\) 1.00000 0.577350
\(4\) −0.895644 + 1.55130i −0.447822 + 0.775650i
\(5\) −1.50000 0.866025i −0.670820 0.387298i 0.125567 0.992085i \(-0.459925\pi\)
−0.796387 + 0.604787i \(0.793258\pi\)
\(6\) −0.395644 + 0.228425i −0.161521 + 0.0932542i
\(7\) 2.64575i 1.00000i
\(8\) 1.73205i 0.612372i
\(9\) 1.00000 0.333333
\(10\) 0.791288 0.250227
\(11\) 3.46410i 1.04447i 0.852803 + 0.522233i \(0.174901\pi\)
−0.852803 + 0.522233i \(0.825099\pi\)
\(12\) −0.895644 + 1.55130i −0.258550 + 0.447822i
\(13\) −1.00000 + 3.46410i −0.277350 + 0.960769i
\(14\) −0.604356 1.04678i −0.161521 0.279763i
\(15\) −1.50000 0.866025i −0.387298 0.223607i
\(16\) −1.39564 2.41733i −0.348911 0.604332i
\(17\) −0.500000 + 0.866025i −0.121268 + 0.210042i −0.920268 0.391289i \(-0.872029\pi\)
0.799000 + 0.601331i \(0.205363\pi\)
\(18\) −0.395644 + 0.228425i −0.0932542 + 0.0538403i
\(19\) 5.29150i 1.21395i 0.794719 + 0.606977i \(0.207618\pi\)
−0.794719 + 0.606977i \(0.792382\pi\)
\(20\) 2.68693 1.55130i 0.600816 0.346881i
\(21\) 2.64575i 0.577350i
\(22\) −0.791288 1.37055i −0.168703 0.292202i
\(23\) −0.291288 0.504525i −0.0607377 0.105201i 0.834058 0.551677i \(-0.186012\pi\)
−0.894795 + 0.446476i \(0.852679\pi\)
\(24\) 1.73205i 0.353553i
\(25\) −1.00000 1.73205i −0.200000 0.346410i
\(26\) −0.395644 1.59898i −0.0775922 0.313585i
\(27\) 1.00000 0.192450
\(28\) −4.10436 2.36965i −0.775650 0.447822i
\(29\) 3.50000 6.06218i 0.649934 1.12572i −0.333205 0.942855i \(-0.608130\pi\)
0.983138 0.182864i \(-0.0585367\pi\)
\(30\) 0.791288 0.144469
\(31\) −0.708712 + 0.409175i −0.127288 + 0.0734900i −0.562292 0.826939i \(-0.690080\pi\)
0.435004 + 0.900429i \(0.356747\pi\)
\(32\) 4.10436 + 2.36965i 0.725555 + 0.418899i
\(33\) 3.46410i 0.603023i
\(34\) 0.456850i 0.0783492i
\(35\) 2.29129 3.96863i 0.387298 0.670820i
\(36\) −0.895644 + 1.55130i −0.149274 + 0.258550i
\(37\) 3.08258 1.77973i 0.506772 0.292585i −0.224734 0.974420i \(-0.572151\pi\)
0.731506 + 0.681835i \(0.238818\pi\)
\(38\) −1.20871 2.09355i −0.196079 0.339619i
\(39\) −1.00000 + 3.46410i −0.160128 + 0.554700i
\(40\) −1.50000 + 2.59808i −0.237171 + 0.410792i
\(41\) 6.08258 + 3.51178i 0.949939 + 0.548447i 0.893062 0.449934i \(-0.148552\pi\)
0.0568768 + 0.998381i \(0.481886\pi\)
\(42\) −0.604356 1.04678i −0.0932542 0.161521i
\(43\) 2.29129 + 3.96863i 0.349418 + 0.605210i 0.986146 0.165878i \(-0.0530460\pi\)
−0.636728 + 0.771088i \(0.719713\pi\)
\(44\) −5.37386 3.10260i −0.810140 0.467735i
\(45\) −1.50000 0.866025i −0.223607 0.129099i
\(46\) 0.230493 + 0.133075i 0.0339843 + 0.0196208i
\(47\) 5.29129 + 3.05493i 0.771814 + 0.445607i 0.833521 0.552487i \(-0.186321\pi\)
−0.0617076 + 0.998094i \(0.519655\pi\)
\(48\) −1.39564 2.41733i −0.201444 0.348911i
\(49\) −7.00000 −1.00000
\(50\) 0.791288 + 0.456850i 0.111905 + 0.0646084i
\(51\) −0.500000 + 0.866025i −0.0700140 + 0.121268i
\(52\) −4.47822 4.65390i −0.621017 0.645380i
\(53\) −6.08258 10.5353i −0.835506 1.44714i −0.893618 0.448829i \(-0.851841\pi\)
0.0581117 0.998310i \(-0.481492\pi\)
\(54\) −0.395644 + 0.228425i −0.0538403 + 0.0310847i
\(55\) 3.00000 5.19615i 0.404520 0.700649i
\(56\) 4.58258 0.612372
\(57\) 5.29150i 0.700877i
\(58\) 3.19795i 0.419912i
\(59\) −8.29129 4.78698i −1.07943 0.623211i −0.148690 0.988884i \(-0.547506\pi\)
−0.930744 + 0.365672i \(0.880839\pi\)
\(60\) 2.68693 1.55130i 0.346881 0.200272i
\(61\) 13.1652 1.68562 0.842812 0.538207i \(-0.180898\pi\)
0.842812 + 0.538207i \(0.180898\pi\)
\(62\) 0.186932 0.323775i 0.0237404 0.0411195i
\(63\) 2.64575i 0.333333i
\(64\) 3.41742 0.427178
\(65\) 4.50000 4.33013i 0.558156 0.537086i
\(66\) −0.791288 1.37055i −0.0974008 0.168703i
\(67\) 7.11890i 0.869713i 0.900500 + 0.434856i \(0.143201\pi\)
−0.900500 + 0.434856i \(0.856799\pi\)
\(68\) −0.895644 1.55130i −0.108613 0.188123i
\(69\) −0.291288 0.504525i −0.0350669 0.0607377i
\(70\) 2.09355i 0.250227i
\(71\) 9.87386 5.70068i 1.17181 0.676546i 0.217706 0.976014i \(-0.430143\pi\)
0.954106 + 0.299468i \(0.0968093\pi\)
\(72\) 1.73205i 0.204124i
\(73\) 7.50000 4.33013i 0.877809 0.506803i 0.00787336 0.999969i \(-0.497494\pi\)
0.869935 + 0.493166i \(0.164160\pi\)
\(74\) −0.813068 + 1.40828i −0.0945173 + 0.163709i
\(75\) −1.00000 1.73205i −0.115470 0.200000i
\(76\) −8.20871 4.73930i −0.941604 0.543635i
\(77\) −9.16515 −1.04447
\(78\) −0.395644 1.59898i −0.0447979 0.181048i
\(79\) 5.29129 9.16478i 0.595316 1.03112i −0.398186 0.917305i \(-0.630360\pi\)
0.993502 0.113813i \(-0.0363066\pi\)
\(80\) 4.83465i 0.540531i
\(81\) 1.00000 0.111111
\(82\) −3.20871 −0.354343
\(83\) 3.46410i 0.380235i −0.981761 0.190117i \(-0.939113\pi\)
0.981761 0.190117i \(-0.0608868\pi\)
\(84\) −4.10436 2.36965i −0.447822 0.258550i
\(85\) 1.50000 0.866025i 0.162698 0.0939336i
\(86\) −1.81307 1.04678i −0.195508 0.112877i
\(87\) 3.50000 6.06218i 0.375239 0.649934i
\(88\) 6.00000 0.639602
\(89\) −13.5000 + 7.79423i −1.43100 + 0.826187i −0.997197 0.0748225i \(-0.976161\pi\)
−0.433800 + 0.901009i \(0.642828\pi\)
\(90\) 0.791288 0.0834091
\(91\) −9.16515 2.64575i −0.960769 0.277350i
\(92\) 1.04356 0.108799
\(93\) −0.708712 + 0.409175i −0.0734900 + 0.0424295i
\(94\) −2.79129 −0.287899
\(95\) 4.58258 7.93725i 0.470162 0.814345i
\(96\) 4.10436 + 2.36965i 0.418899 + 0.241852i
\(97\) −0.0825757 + 0.0476751i −0.00838429 + 0.00484067i −0.504186 0.863595i \(-0.668208\pi\)
0.495802 + 0.868436i \(0.334874\pi\)
\(98\) 2.76951 1.59898i 0.279763 0.161521i
\(99\) 3.46410i 0.348155i
\(100\) 3.58258 0.358258
\(101\) −5.16515 −0.513952 −0.256976 0.966418i \(-0.582726\pi\)
−0.256976 + 0.966418i \(0.582726\pi\)
\(102\) 0.456850i 0.0452349i
\(103\) −6.29129 + 10.8968i −0.619899 + 1.07370i 0.369605 + 0.929189i \(0.379493\pi\)
−0.989504 + 0.144507i \(0.953840\pi\)
\(104\) 6.00000 + 1.73205i 0.588348 + 0.169842i
\(105\) 2.29129 3.96863i 0.223607 0.387298i
\(106\) 4.81307 + 2.77883i 0.467487 + 0.269903i
\(107\) 5.29129 + 9.16478i 0.511528 + 0.885993i 0.999911 + 0.0133631i \(0.00425372\pi\)
−0.488383 + 0.872630i \(0.662413\pi\)
\(108\) −0.895644 + 1.55130i −0.0861834 + 0.149274i
\(109\) −1.66515 + 0.961376i −0.159493 + 0.0920831i −0.577622 0.816304i \(-0.696019\pi\)
0.418129 + 0.908387i \(0.362686\pi\)
\(110\) 2.74110i 0.261354i
\(111\) 3.08258 1.77973i 0.292585 0.168924i
\(112\) 6.39564 3.69253i 0.604332 0.348911i
\(113\) 3.08258 + 5.33918i 0.289984 + 0.502268i 0.973806 0.227382i \(-0.0730166\pi\)
−0.683821 + 0.729649i \(0.739683\pi\)
\(114\) −1.20871 2.09355i −0.113206 0.196079i
\(115\) 1.00905i 0.0940945i
\(116\) 6.26951 + 10.8591i 0.582109 + 1.00824i
\(117\) −1.00000 + 3.46410i −0.0924500 + 0.320256i
\(118\) 4.37386 0.402647
\(119\) −2.29129 1.32288i −0.210042 0.121268i
\(120\) −1.50000 + 2.59808i −0.136931 + 0.237171i
\(121\) −1.00000 −0.0909091
\(122\) −5.20871 + 3.00725i −0.471575 + 0.272264i
\(123\) 6.08258 + 3.51178i 0.548447 + 0.316646i
\(124\) 1.46590i 0.131642i
\(125\) 12.1244i 1.08444i
\(126\) −0.604356 1.04678i −0.0538403 0.0932542i
\(127\) 1.29129 2.23658i 0.114583 0.198464i −0.803030 0.595939i \(-0.796780\pi\)
0.917613 + 0.397475i \(0.130113\pi\)
\(128\) −9.56080 + 5.51993i −0.845063 + 0.487897i
\(129\) 2.29129 + 3.96863i 0.201737 + 0.349418i
\(130\) −0.791288 + 2.74110i −0.0694005 + 0.240411i
\(131\) −5.29129 + 9.16478i −0.462302 + 0.800730i −0.999075 0.0429960i \(-0.986310\pi\)
0.536773 + 0.843727i \(0.319643\pi\)
\(132\) −5.37386 3.10260i −0.467735 0.270047i
\(133\) −14.0000 −1.21395
\(134\) −1.62614 2.81655i −0.140477 0.243313i
\(135\) −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 0.144142 0.989557i \(-0.453958\pi\)
−0.784910 + 0.619609i \(0.787291\pi\)
\(138\) 0.230493 + 0.133075i 0.0196208 + 0.0113281i
\(139\) −1.29129 2.23658i −0.109526 0.189704i 0.806053 0.591844i \(-0.201600\pi\)
−0.915578 + 0.402140i \(0.868266\pi\)
\(140\) 4.10436 + 7.10895i 0.346881 + 0.600816i
\(141\) 5.29129 + 3.05493i 0.445607 + 0.257271i
\(142\) −2.60436 + 4.51088i −0.218553 + 0.378544i
\(143\) −12.0000 3.46410i −1.00349 0.289683i
\(144\) −1.39564 2.41733i −0.116304 0.201444i
\(145\) −10.5000 + 6.06218i −0.871978 + 0.503436i
\(146\) −1.97822 + 3.42638i −0.163719 + 0.283569i
\(147\) −7.00000 −0.577350
\(148\) 6.37600i 0.524104i
\(149\) 17.5112i 1.43457i 0.696778 + 0.717287i \(0.254616\pi\)
−0.696778 + 0.717287i \(0.745384\pi\)
\(150\) 0.791288 + 0.456850i 0.0646084 + 0.0373017i
\(151\) 8.45644 4.88233i 0.688175 0.397318i −0.114753 0.993394i \(-0.536608\pi\)
0.802928 + 0.596076i \(0.203274\pi\)
\(152\) 9.16515 0.743392
\(153\) −0.500000 + 0.866025i −0.0404226 + 0.0700140i
\(154\) 3.62614 2.09355i 0.292202 0.168703i
\(155\) 1.41742 0.113850
\(156\) −4.47822 4.65390i −0.358545 0.372610i
\(157\) 4.08258 + 7.07123i 0.325825 + 0.564345i 0.981679 0.190542i \(-0.0610246\pi\)
−0.655854 + 0.754888i \(0.727691\pi\)
\(158\) 4.83465i 0.384624i
\(159\) −6.08258 10.5353i −0.482380 0.835506i
\(160\) −4.10436 7.10895i −0.324478 0.562012i
\(161\) 1.33485 0.770675i 0.105201 0.0607377i
\(162\) −0.395644 + 0.228425i −0.0310847 + 0.0179468i
\(163\) 3.46410i 0.271329i −0.990755 0.135665i \(-0.956683\pi\)
0.990755 0.135665i \(-0.0433170\pi\)
\(164\) −10.8956 + 6.29060i −0.850807 + 0.491214i
\(165\) 3.00000 5.19615i 0.233550 0.404520i
\(166\) 0.791288 + 1.37055i 0.0614158 + 0.106375i
\(167\) −9.87386 5.70068i −0.764063 0.441132i 0.0666899 0.997774i \(-0.478756\pi\)
−0.830752 + 0.556642i \(0.812089\pi\)
\(168\) 4.58258 0.353553
\(169\) −11.0000 6.92820i −0.846154 0.532939i
\(170\) −0.395644 + 0.685275i −0.0303445 + 0.0525582i
\(171\) 5.29150i 0.404651i
\(172\) −8.20871 −0.625908
\(173\) −12.3303 −0.937456 −0.468728 0.883343i \(-0.655287\pi\)
−0.468728 + 0.883343i \(0.655287\pi\)
\(174\) 3.19795i 0.242436i
\(175\) 4.58258 2.64575i 0.346410 0.200000i
\(176\) 8.37386 4.83465i 0.631204 0.364426i
\(177\) −8.29129 4.78698i −0.623211 0.359811i
\(178\) 3.56080 6.16748i 0.266893 0.462272i
\(179\) 19.1652 1.43247 0.716235 0.697859i \(-0.245864\pi\)
0.716235 + 0.697859i \(0.245864\pi\)
\(180\) 2.68693 1.55130i 0.200272 0.115627i
\(181\) 22.0000 1.63525 0.817624 0.575753i \(-0.195291\pi\)
0.817624 + 0.575753i \(0.195291\pi\)
\(182\) 4.23049 1.04678i 0.313585 0.0775922i
\(183\) 13.1652 0.973196
\(184\) −0.873864 + 0.504525i −0.0644221 + 0.0371941i
\(185\) −6.16515 −0.453271
\(186\) 0.186932 0.323775i 0.0137065 0.0237404i
\(187\) −3.00000 1.73205i −0.219382 0.126660i
\(188\) −9.47822 + 5.47225i −0.691270 + 0.399105i
\(189\) 2.64575i 0.192450i
\(190\) 4.18710i 0.303764i
\(191\) 22.3303 1.61576 0.807882 0.589344i \(-0.200614\pi\)
0.807882 + 0.589344i \(0.200614\pi\)
\(192\) 3.41742 0.246631
\(193\) 17.5112i 1.26048i 0.776399 + 0.630242i \(0.217044\pi\)
−0.776399 + 0.630242i \(0.782956\pi\)
\(194\) 0.0217804 0.0377247i 0.00156374 0.00270848i
\(195\) 4.50000 4.33013i 0.322252 0.310087i
\(196\) 6.26951 10.8591i 0.447822 0.775650i
\(197\) −12.2477 7.07123i −0.872614 0.503804i −0.00439826 0.999990i \(-0.501400\pi\)
−0.868216 + 0.496186i \(0.834733\pi\)
\(198\) −0.791288 1.37055i −0.0562344 0.0974008i
\(199\) 3.29129 5.70068i 0.233313 0.404110i −0.725468 0.688256i \(-0.758377\pi\)
0.958781 + 0.284146i \(0.0917099\pi\)
\(200\) −3.00000 + 1.73205i −0.212132 + 0.122474i
\(201\) 7.11890i 0.502129i
\(202\) 2.04356 1.17985i 0.143784 0.0830140i
\(203\) 16.0390 + 9.26013i 1.12572 + 0.649934i
\(204\) −0.895644 1.55130i −0.0627076 0.108613i
\(205\) −6.08258 10.5353i −0.424826 0.735819i
\(206\) 5.74835i 0.400507i
\(207\) −0.291288 0.504525i −0.0202459 0.0350669i
\(208\) 9.76951 2.41733i 0.677393 0.167611i
\(209\) −18.3303 −1.26793
\(210\) 2.09355i 0.144469i
\(211\) 1.29129 2.23658i 0.0888959 0.153972i −0.818149 0.575007i \(-0.804999\pi\)
0.907045 + 0.421034i \(0.138333\pi\)
\(212\) 21.7913 1.49663
\(213\) 9.87386 5.70068i 0.676546 0.390604i
\(214\) −4.18693 2.41733i −0.286213 0.165245i
\(215\) 7.93725i 0.541316i
\(216\) 1.73205i 0.117851i
\(217\) −1.08258 1.87508i −0.0734900 0.127288i
\(218\) 0.439205 0.760725i 0.0297467 0.0515228i
\(219\) 7.50000 4.33013i 0.506803 0.292603i
\(220\) 5.37386 + 9.30780i 0.362306 + 0.627532i
\(221\) −2.50000 2.59808i −0.168168 0.174766i
\(222\) −0.813068 + 1.40828i −0.0545696 + 0.0945173i
\(223\) 2.29129 + 1.32288i 0.153436 + 0.0885863i 0.574752 0.818327i \(-0.305098\pi\)
−0.421316 + 0.906914i \(0.638432\pi\)
\(224\) −6.26951 + 10.8591i −0.418899 + 0.725555i
\(225\) −1.00000 1.73205i −0.0666667 0.115470i
\(226\) −2.43920 1.40828i −0.162253 0.0936771i
\(227\) 17.6216 + 10.1738i 1.16959 + 0.675261i 0.953583 0.301132i \(-0.0973644\pi\)
0.216004 + 0.976393i \(0.430698\pi\)
\(228\) −8.20871 4.73930i −0.543635 0.313868i
\(229\) −0.0825757 0.0476751i −0.00545676 0.00315046i 0.497269 0.867596i \(-0.334336\pi\)
−0.502726 + 0.864446i \(0.667669\pi\)
\(230\) −0.230493 0.399225i −0.0151982 0.0263241i
\(231\) −9.16515 −0.603023
\(232\) −10.5000 6.06218i −0.689359 0.398001i
\(233\) −0.917424 + 1.58903i −0.0601025 + 0.104101i −0.894511 0.447046i \(-0.852476\pi\)
0.834409 + 0.551146i \(0.185809\pi\)
\(234\) −0.395644 1.59898i −0.0258641 0.104528i
\(235\) −5.29129 9.16478i −0.345166 0.597844i
\(236\) 14.8521 8.57485i 0.966788 0.558175i
\(237\) 5.29129 9.16478i 0.343706 0.595316i
\(238\) 1.20871 0.0783492
\(239\) 29.7309i 1.92313i −0.274572 0.961566i \(-0.588536\pi\)
0.274572 0.961566i \(-0.411464\pi\)
\(240\) 4.83465i 0.312075i
\(241\) −15.2477 8.80328i −0.982192 0.567069i −0.0792611 0.996854i \(-0.525256\pi\)
−0.902931 + 0.429785i \(0.858589\pi\)
\(242\) 0.395644 0.228425i 0.0254330 0.0146837i
\(243\) 1.00000 0.0641500
\(244\) −11.7913 + 20.4231i −0.754860 + 1.30746i
\(245\) 10.5000 + 6.06218i 0.670820 + 0.387298i
\(246\) −3.20871 −0.204580
\(247\) −18.3303 5.29150i −1.16633 0.336690i
\(248\) 0.708712 + 1.22753i 0.0450033 + 0.0779479i
\(249\) 3.46410i 0.219529i
\(250\) −2.76951 4.79693i −0.175159 0.303384i
\(251\) 5.70871 + 9.88778i 0.360331 + 0.624111i 0.988015 0.154357i \(-0.0493305\pi\)
−0.627684 + 0.778468i \(0.715997\pi\)
\(252\) −4.10436 2.36965i −0.258550 0.149274i
\(253\) 1.74773 1.00905i 0.109879 0.0634385i
\(254\) 1.17985i 0.0740304i
\(255\) 1.50000 0.866025i 0.0939336 0.0542326i
\(256\) −0.895644 + 1.55130i −0.0559777 + 0.0969563i
\(257\) −13.6652 23.6687i −0.852409 1.47642i −0.879028 0.476770i \(-0.841808\pi\)
0.0266196 0.999646i \(-0.491526\pi\)
\(258\) −1.81307 1.04678i −0.112877 0.0651694i
\(259\) 4.70871 + 8.15573i 0.292585 + 0.506772i
\(260\) 2.68693 + 10.8591i 0.166636 + 0.673453i
\(261\) 3.50000 6.06218i 0.216645 0.375239i
\(262\) 4.83465i 0.298686i
\(263\) −23.1652 −1.42842 −0.714212 0.699929i \(-0.753215\pi\)
−0.714212 + 0.699929i \(0.753215\pi\)
\(264\) 6.00000 0.369274
\(265\) 21.0707i 1.29436i
\(266\) 5.53901 3.19795i 0.339619 0.196079i
\(267\) −13.5000 + 7.79423i −0.826187 + 0.476999i
\(268\) −11.0436 6.37600i −0.674593 0.389476i
\(269\) 1.08258 1.87508i 0.0660058 0.114325i −0.831134 0.556072i \(-0.812308\pi\)
0.897140 + 0.441747i \(0.145641\pi\)
\(270\) 0.791288 0.0481562
\(271\) 22.0390 12.7242i 1.33877 0.772942i 0.352149 0.935944i \(-0.385451\pi\)
0.986626 + 0.163002i \(0.0521177\pi\)
\(272\) 2.79129 0.169247
\(273\) −9.16515 2.64575i −0.554700 0.160128i
\(274\) 3.95644 0.239017
\(275\) 6.00000 3.46410i 0.361814 0.208893i
\(276\) 1.04356 0.0628150
\(277\) 13.6652 23.6687i 0.821059 1.42212i −0.0838347 0.996480i \(-0.526717\pi\)
0.904894 0.425637i \(-0.139950\pi\)
\(278\) 1.02178 + 0.589925i 0.0612823 + 0.0353814i
\(279\) −0.708712 + 0.409175i −0.0424295 + 0.0244967i
\(280\) −6.87386 3.96863i −0.410792 0.237171i
\(281\) 17.5112i 1.04463i −0.852752 0.522316i \(-0.825068\pi\)
0.852752 0.522316i \(-0.174932\pi\)
\(282\) −2.79129 −0.166219
\(283\) 6.33030 0.376297 0.188149 0.982141i \(-0.439751\pi\)
0.188149 + 0.982141i \(0.439751\pi\)
\(284\) 20.4231i 1.21189i
\(285\) 4.58258 7.93725i 0.271448 0.470162i
\(286\) 5.53901 1.37055i 0.327529 0.0810424i
\(287\) −9.29129 + 16.0930i −0.548447 + 0.949939i
\(288\) 4.10436 + 2.36965i 0.241852 + 0.139633i
\(289\) 8.00000 + 13.8564i 0.470588 + 0.815083i
\(290\) 2.76951 4.79693i 0.162631 0.281685i
\(291\) −0.0825757 + 0.0476751i −0.00484067 + 0.00279476i
\(292\) 15.5130i 0.907830i
\(293\) −19.8303 + 11.4490i −1.15850 + 0.668860i −0.950944 0.309364i \(-0.899884\pi\)
−0.207555 + 0.978223i \(0.566551\pi\)
\(294\) 2.76951 1.59898i 0.161521 0.0932542i
\(295\) 8.29129 + 14.3609i 0.482737 + 0.836126i
\(296\) −3.08258 5.33918i −0.179171 0.310333i
\(297\) 3.46410i 0.201008i
\(298\) −4.00000 6.92820i −0.231714 0.401340i
\(299\) 2.03901 0.504525i 0.117919 0.0291775i
\(300\) 3.58258 0.206840
\(301\) −10.5000 + 6.06218i −0.605210 + 0.349418i
\(302\) −2.23049 + 3.86333i −0.128350 + 0.222309i
\(303\) −5.16515 −0.296730
\(304\) 12.7913 7.38505i 0.733631 0.423562i
\(305\) −19.7477 11.4014i −1.13075 0.652840i
\(306\) 0.456850i 0.0261164i
\(307\) 0.190700i 0.0108838i 0.999985 + 0.00544192i \(0.00173223\pi\)
−0.999985 + 0.00544192i \(0.998268\pi\)
\(308\) 8.20871 14.2179i 0.467735 0.810140i
\(309\) −6.29129 + 10.8968i −0.357899 + 0.619899i
\(310\) −0.560795 + 0.323775i −0.0318510 + 0.0183892i
\(311\) −0.291288 0.504525i −0.0165174 0.0286090i 0.857649 0.514236i \(-0.171925\pi\)
−0.874166 + 0.485627i \(0.838591\pi\)
\(312\) 6.00000 + 1.73205i 0.339683 + 0.0980581i
\(313\) 16.0826 27.8558i 0.909041 1.57451i 0.0936417 0.995606i \(-0.470149\pi\)
0.815399 0.578899i \(-0.196517\pi\)
\(314\) −3.23049 1.86513i −0.182307 0.105255i
\(315\) 2.29129 3.96863i 0.129099 0.223607i
\(316\) 9.47822 + 16.4168i 0.533192 + 0.923515i
\(317\) −16.6652 9.62163i −0.936008 0.540405i −0.0473014 0.998881i \(-0.515062\pi\)
−0.888707 + 0.458476i \(0.848395\pi\)
\(318\) 4.81307 + 2.77883i 0.269903 + 0.155829i
\(319\) 21.0000 + 12.1244i 1.17577 + 0.678834i
\(320\) −5.12614 2.95958i −0.286560 0.165445i
\(321\) 5.29129 + 9.16478i 0.295331 + 0.511528i
\(322\) −0.352083 + 0.609826i −0.0196208 + 0.0339843i
\(323\) −4.58258 2.64575i −0.254981 0.147214i
\(324\) −0.895644 + 1.55130i −0.0497580 + 0.0861834i
\(325\) 7.00000 1.73205i 0.388290 0.0960769i
\(326\) 0.791288 + 1.37055i 0.0438254 + 0.0759078i
\(327\) −1.66515 + 0.961376i −0.0920831 + 0.0531642i
\(328\) 6.08258 10.5353i 0.335854 0.581716i
\(329\) −8.08258 + 13.9994i −0.445607 + 0.771814i
\(330\) 2.74110i 0.150893i
\(331\) 15.4931i 0.851578i 0.904822 + 0.425789i \(0.140003\pi\)
−0.904822 + 0.425789i \(0.859997\pi\)
\(332\) 5.37386 + 3.10260i 0.294929 + 0.170277i
\(333\) 3.08258 1.77973i 0.168924 0.0975284i
\(334\) 5.20871 0.285008
\(335\) 6.16515 10.6784i 0.336838 0.583421i
\(336\) 6.39564 3.69253i 0.348911 0.201444i
\(337\) −31.4955 −1.71567 −0.857833 0.513928i \(-0.828190\pi\)
−0.857833 + 0.513928i \(0.828190\pi\)
\(338\) 5.93466 + 0.228425i 0.322803 + 0.0124247i
\(339\) 3.08258 + 5.33918i 0.167423 + 0.289984i
\(340\) 3.10260i 0.168262i
\(341\) −1.41742 2.45505i −0.0767578 0.132948i
\(342\) −1.20871 2.09355i −0.0653597 0.113206i
\(343\) 18.5203i 1.00000i
\(344\) 6.87386 3.96863i 0.370614 0.213974i
\(345\) 1.00905i 0.0543255i
\(346\) 4.87841 2.81655i 0.262265 0.151419i
\(347\) −0.873864 + 1.51358i −0.0469115 + 0.0812530i −0.888528 0.458823i \(-0.848271\pi\)
0.841616 + 0.540076i \(0.181605\pi\)
\(348\) 6.26951 + 10.8591i 0.336081 + 0.582109i
\(349\) −0.0825757 0.0476751i −0.00442018 0.00255199i 0.497788 0.867299i \(-0.334146\pi\)
−0.502208 + 0.864747i \(0.667479\pi\)
\(350\) −1.20871 + 2.09355i −0.0646084 + 0.111905i
\(351\) −1.00000 + 3.46410i −0.0533761 + 0.184900i
\(352\) −8.20871 + 14.2179i −0.437526 + 0.757817i
\(353\) 12.4104i 0.660539i 0.943887 + 0.330270i \(0.107140\pi\)
−0.943887 + 0.330270i \(0.892860\pi\)
\(354\) 4.37386 0.232468
\(355\) −19.7477 −1.04810
\(356\) 27.9234i 1.47994i
\(357\) −2.29129 1.32288i −0.121268 0.0700140i
\(358\) −7.58258 + 4.37780i −0.400752 + 0.231374i
\(359\) 16.0390 + 9.26013i 0.846507 + 0.488731i 0.859471 0.511185i \(-0.170793\pi\)
−0.0129639 + 0.999916i \(0.504127\pi\)
\(360\) −1.50000 + 2.59808i −0.0790569 + 0.136931i
\(361\) −9.00000 −0.473684
\(362\) −8.70417 + 5.02535i −0.457481 + 0.264127i
\(363\) −1.00000 −0.0524864
\(364\) 12.3131 11.8483i 0.645380 0.621017i
\(365\) −15.0000 −0.785136
\(366\) −5.20871 + 3.00725i −0.272264 + 0.157192i
\(367\) −3.16515 −0.165220 −0.0826098 0.996582i \(-0.526326\pi\)
−0.0826098 + 0.996582i \(0.526326\pi\)
\(368\) −0.813068 + 1.40828i −0.0423841 + 0.0734114i
\(369\) 6.08258 + 3.51178i 0.316646 + 0.182816i
\(370\) 2.43920 1.40828i 0.126808 0.0732128i
\(371\) 27.8739 16.0930i 1.44714 0.835506i
\(372\) 1.46590i 0.0760034i
\(373\) −26.0000 −1.34623 −0.673114 0.739538i \(-0.735044\pi\)
−0.673114 + 0.739538i \(0.735044\pi\)
\(374\) 1.58258 0.0818330
\(375\) 12.1244i 0.626099i
\(376\) 5.29129 9.16478i 0.272877 0.472637i
\(377\) 17.5000 + 18.1865i 0.901296 + 0.936654i
\(378\) −0.604356 1.04678i −0.0310847 0.0538403i
\(379\) −16.0390 9.26013i −0.823869 0.475661i 0.0278799 0.999611i \(-0.491124\pi\)
−0.851749 + 0.523950i \(0.824458\pi\)
\(380\) 8.20871 + 14.2179i 0.421098 + 0.729363i
\(381\) 1.29129 2.23658i 0.0661547 0.114583i
\(382\) −8.83485 + 5.10080i −0.452030 + 0.260980i
\(383\) 24.6301i 1.25854i −0.777187 0.629270i \(-0.783354\pi\)
0.777187 0.629270i \(-0.216646\pi\)
\(384\) −9.56080 + 5.51993i −0.487897 + 0.281688i
\(385\) 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
\(388\) 0.170800i 0.00867104i
\(389\) 4.66515 + 8.08028i 0.236533 + 0.409686i 0.959717 0.280969i \(-0.0906557\pi\)
−0.723184 + 0.690655i \(0.757322\pi\)
\(390\) −0.791288 + 2.74110i −0.0400684 + 0.138801i
\(391\) 0.582576 0.0294621
\(392\) 12.1244i 0.612372i
\(393\) −5.29129 + 9.16478i −0.266910 + 0.462302i
\(394\) 6.46099 0.325500
\(395\) −15.8739 + 9.16478i −0.798701 + 0.461130i
\(396\) −5.37386 3.10260i −0.270047 0.155912i
\(397\) 16.0652i 0.806290i 0.915136 + 0.403145i \(0.132083\pi\)
−0.915136 + 0.403145i \(0.867917\pi\)
\(398\) 3.00725i 0.150740i
\(399\) −14.0000 −0.700877
\(400\) −2.79129 + 4.83465i −0.139564 + 0.241733i
\(401\) 20.9174 12.0767i 1.04457 0.603081i 0.123443 0.992352i \(-0.460606\pi\)
0.921123 + 0.389271i \(0.127273\pi\)
\(402\) −1.62614 2.81655i −0.0811043 0.140477i
\(403\) −0.708712 2.86423i −0.0353035 0.142677i
\(404\) 4.62614 8.01270i 0.230159 0.398647i
\(405\) −1.50000 0.866025i −0.0745356 0.0430331i
\(406\) −8.46099 −0.419912
\(407\) 6.16515 + 10.6784i 0.305595 + 0.529306i
\(408\) 1.50000 + 0.866025i 0.0742611 + 0.0428746i
\(409\) 17.9174 + 10.3446i 0.885960 + 0.511509i 0.872619 0.488402i \(-0.162420\pi\)
0.0133409 + 0.999911i \(0.495753\pi\)
\(410\) 4.81307 + 2.77883i 0.237700 + 0.137236i
\(411\) −7.50000 4.33013i −0.369948 0.213589i
\(412\) −11.2695 19.5194i −0.555209 0.961650i
\(413\) 12.6652 21.9367i 0.623211 1.07943i
\(414\) 0.230493 + 0.133075i 0.0113281 + 0.00654028i
\(415\) −3.00000 + 5.19615i −0.147264 + 0.255069i
\(416\) −12.3131 + 11.8483i −0.603698 + 0.580909i
\(417\) −1.29129 2.23658i −0.0632346 0.109526i
\(418\) 7.25227 4.18710i 0.354720 0.204798i
\(419\) 7.87386 13.6379i 0.384663 0.666257i −0.607059 0.794657i \(-0.707651\pi\)
0.991722 + 0.128400i \(0.0409842\pi\)
\(420\) 4.10436 + 7.10895i 0.200272 + 0.346881i
\(421\) 33.5764i 1.63641i 0.574923 + 0.818207i \(0.305032\pi\)
−0.574923 + 0.818207i \(0.694968\pi\)
\(422\) 1.17985i 0.0574342i
\(423\) 5.29129 + 3.05493i 0.257271 + 0.148536i
\(424\) −18.2477 + 10.5353i −0.886188 + 0.511641i
\(425\) 2.00000 0.0970143
\(426\) −2.60436 + 4.51088i −0.126181 + 0.218553i
\(427\) 34.8317i 1.68562i
\(428\) −18.9564 −0.916294
\(429\) −12.0000 3.46410i −0.579365 0.167248i
\(430\) 1.81307 + 3.14033i 0.0874339 + 0.151440i
\(431\) 19.1479i 0.922322i −0.887316 0.461161i \(-0.847433\pi\)
0.887316 0.461161i \(-0.152567\pi\)
\(432\) −1.39564 2.41733i −0.0671479 0.116304i
\(433\) −10.6652 18.4726i −0.512534 0.887736i −0.999894 0.0145345i \(-0.995373\pi\)
0.487360 0.873201i \(-0.337960\pi\)
\(434\) 0.856629 + 0.494575i 0.0411195 + 0.0237404i
\(435\) −10.5000 + 6.06218i −0.503436 + 0.290659i
\(436\) 3.44420i 0.164947i
\(437\) 2.66970 1.54135i 0.127709 0.0737328i
\(438\) −1.97822 + 3.42638i −0.0945230 + 0.163719i
\(439\) 0.708712 + 1.22753i 0.0338250 + 0.0585866i 0.882442 0.470421i \(-0.155898\pi\)
−0.848617 + 0.529007i \(0.822564\pi\)
\(440\) −9.00000 5.19615i −0.429058 0.247717i
\(441\) −7.00000 −0.333333
\(442\) 1.58258 + 0.456850i 0.0752754 + 0.0217302i
\(443\) −10.8739 + 18.8341i −0.516633 + 0.894834i 0.483181 + 0.875521i \(0.339481\pi\)
−0.999813 + 0.0193136i \(0.993852\pi\)
\(444\) 6.37600i 0.302592i
\(445\) 27.0000 1.27992
\(446\) −1.20871 −0.0572342
\(447\) 17.5112i 0.828252i
\(448\) 9.04165i 0.427178i
\(449\) 7.66515 4.42548i 0.361741 0.208851i −0.308103 0.951353i \(-0.599694\pi\)
0.669844 + 0.742502i \(0.266361\pi\)
\(450\) 0.791288 + 0.456850i 0.0373017 + 0.0215361i
\(451\) −12.1652 + 21.0707i −0.572835 + 0.992179i
\(452\) −11.0436 −0.519445
\(453\) 8.45644 4.88233i 0.397318 0.229392i
\(454\) −9.29583 −0.436275
\(455\) 11.4564 + 11.9059i 0.537086 + 0.558156i
\(456\) 9.16515 0.429198
\(457\) 24.2477 13.9994i 1.13426 0.654866i 0.189258 0.981927i \(-0.439392\pi\)
0.945003 + 0.327062i \(0.106058\pi\)
\(458\) 0.0435608 0.00203546
\(459\) −0.500000 + 0.866025i −0.0233380 + 0.0404226i
\(460\) −1.56534 0.903750i −0.0729844 0.0421376i
\(461\) 18.4129 10.6307i 0.857573 0.495120i −0.00562564 0.999984i \(-0.501791\pi\)
0.863199 + 0.504864i \(0.168457\pi\)
\(462\) 3.62614 2.09355i 0.168703 0.0974008i
\(463\) 3.84550i 0.178716i 0.996000 + 0.0893578i \(0.0284815\pi\)
−0.996000 + 0.0893578i \(0.971519\pi\)
\(464\) −19.5390 −0.907076
\(465\) 1.41742 0.0657315
\(466\) 0.838251i 0.0388312i
\(467\) −8.45644 + 14.6470i −0.391317 + 0.677782i −0.992624 0.121237i \(-0.961314\pi\)
0.601306 + 0.799019i \(0.294647\pi\)
\(468\) −4.47822 4.65390i −0.207006 0.215127i
\(469\) −18.8348 −0.869713
\(470\) 4.18693 + 2.41733i 0.193129 + 0.111503i
\(471\) 4.08258 + 7.07123i 0.188115 + 0.325825i
\(472\) −8.29129 + 14.3609i −0.381637 + 0.661015i
\(473\) −13.7477 + 7.93725i −0.632121 + 0.364955i
\(474\) 4.83465i 0.222063i
\(475\) 9.16515 5.29150i 0.420526 0.242791i
\(476\) 4.10436 2.36965i 0.188123 0.108613i
\(477\) −6.08258 10.5353i −0.278502 0.482380i
\(478\) 6.79129 + 11.7629i 0.310626 + 0.538020i
\(479\) 35.2131i 1.60893i −0.594001 0.804464i \(-0.702453\pi\)
0.594001 0.804464i \(-0.297547\pi\)
\(480\) −4.10436 7.10895i −0.187337 0.324478i
\(481\) 3.08258 + 12.4581i 0.140553 + 0.568040i
\(482\) 8.04356 0.366374
\(483\) 1.33485 0.770675i 0.0607377 0.0350669i
\(484\) 0.895644 1.55130i 0.0407111 0.0705137i
\(485\) 0.165151 0.00749914
\(486\) −0.395644 + 0.228425i −0.0179468 + 0.0103616i
\(487\) −32.4564 18.7387i −1.47074 0.849133i −0.471281 0.881983i \(-0.656208\pi\)
−0.999460 + 0.0328498i \(0.989542\pi\)
\(488\) 22.8027i 1.03223i
\(489\) 3.46410i 0.156652i
\(490\) −5.53901 −0.250227
\(491\) 11.8739 20.5661i 0.535860 0.928137i −0.463261 0.886222i \(-0.653321\pi\)
0.999121 0.0419149i \(-0.0133458\pi\)
\(492\) −10.8956 + 6.29060i −0.491214 + 0.283602i
\(493\) 3.50000 + 6.06218i 0.157632 + 0.273027i
\(494\) 8.46099 2.09355i 0.380678 0.0941933i
\(495\) 3.00000 5.19615i 0.134840 0.233550i
\(496\) 1.97822 + 1.14213i 0.0888247 + 0.0512830i
\(497\) 15.0826 + 26.1238i 0.676546 + 1.17181i
\(498\) 0.791288 + 1.37055i 0.0354585 + 0.0614158i
\(499\) 26.2913 + 15.1793i 1.17696 + 0.679518i 0.955309 0.295608i \(-0.0955223\pi\)
0.221650 + 0.975126i \(0.428856\pi\)
\(500\) −18.8085 10.8591i −0.841143 0.485634i
\(501\) −9.87386 5.70068i −0.441132 0.254688i
\(502\) −4.51723 2.60803i −0.201614 0.116402i
\(503\) 12.8739 + 22.2982i 0.574017 + 0.994227i 0.996148 + 0.0876919i \(0.0279491\pi\)
−0.422130 + 0.906535i \(0.638718\pi\)
\(504\) 4.58258 0.204124
\(505\) 7.74773 + 4.47315i 0.344769 + 0.199053i
\(506\) −0.460985 + 0.798450i −0.0204933 + 0.0354954i
\(507\) −11.0000 6.92820i −0.488527 0.307692i
\(508\) 2.31307 + 4.00635i 0.102626 + 0.177753i
\(509\) 3.24773 1.87508i 0.143953 0.0831113i −0.426294 0.904585i \(-0.640181\pi\)
0.570247 + 0.821474i \(0.306848\pi\)
\(510\) −0.395644 + 0.685275i −0.0175194 + 0.0303445i
\(511\) 11.4564 + 19.8431i 0.506803 + 0.877809i
\(512\) 22.8981i 1.01196i
\(513\) 5.29150i 0.233626i
\(514\) 10.8131 + 6.24293i 0.476944 + 0.275364i
\(515\) 18.8739 10.8968i 0.831682 0.480172i
\(516\) −8.20871 −0.361368
\(517\) −10.5826 + 18.3296i −0.465421 + 0.806133i
\(518\) −3.72595 2.15118i −0.163709 0.0945173i
\(519\) −12.3303 −0.541240
\(520\) −7.50000 7.79423i −0.328897 0.341800i
\(521\) 16.6652 + 28.8649i 0.730114 + 1.26459i 0.956834 + 0.290634i \(0.0938662\pi\)
−0.226721 + 0.973960i \(0.572800\pi\)
\(522\) 3.19795i 0.139971i
\(523\) −8.87386 15.3700i −0.388027 0.672082i 0.604157 0.796865i \(-0.293510\pi\)
−0.992184 + 0.124783i \(0.960177\pi\)
\(524\) −9.47822 16.4168i −0.414058 0.717169i
\(525\) 4.58258 2.64575i 0.200000 0.115470i
\(526\) 9.16515 5.29150i 0.399620 0.230720i
\(527\) 0.818350i 0.0356479i
\(528\) 8.37386 4.83465i 0.364426 0.210401i
\(529\) 11.3303 19.6247i 0.492622 0.853246i
\(530\) −4.81307 8.33648i −0.209066 0.362113i
\(531\) −8.29129 4.78698i −0.359811 0.207737i
\(532\) 12.5390 21.7182i 0.543635 0.941604i
\(533\) −18.2477 + 17.5589i −0.790397 + 0.760560i
\(534\) 3.56080 6.16748i 0.154091 0.266893i
\(535\) 18.3296i 0.792456i
\(536\) 12.3303 0.532588
\(537\) 19.1652 0.827037
\(538\) 0.989150i 0.0426453i
\(539\) 24.2487i 1.04447i
\(540\) 2.68693 1.55130i 0.115627 0.0667574i
\(541\) −25.6652 14.8178i −1.10343 0.637066i −0.166311 0.986073i \(-0.553186\pi\)
−0.937120 + 0.349007i \(0.886519\pi\)
\(542\) −5.81307 + 10.0685i −0.249693 + 0.432480i
\(543\) 22.0000 0.944110
\(544\) −4.10436 + 2.36965i −0.175973 + 0.101598i
\(545\) 3.33030 0.142654
\(546\) 4.23049 1.04678i 0.181048 0.0447979i
\(547\) −8.00000 −0.342055 −0.171028 0.985266i \(-0.554709\pi\)
−0.171028 + 0.985266i \(0.554709\pi\)
\(548\) 13.4347 7.75650i 0.573900 0.331341i
\(549\) 13.1652 0.561875
\(550\) −1.58258 + 2.74110i −0.0674813 + 0.116881i
\(551\) 32.0780 + 18.5203i 1.36657 + 0.788990i
\(552\) −0.873864 + 0.504525i −0.0371941 + 0.0214740i
\(553\) 24.2477 + 13.9994i 1.03112 + 0.595316i
\(554\) 12.4859i 0.530473i
\(555\) −6.16515 −0.261696
\(556\) 4.62614 0.196192
\(557\) 3.27340i 0.138698i −0.997592 0.0693492i \(-0.977908\pi\)
0.997592 0.0693492i \(-0.0220923\pi\)
\(558\) 0.186932 0.323775i 0.00791345 0.0137065i
\(559\) −16.0390 + 3.96863i −0.678378 + 0.167855i
\(560\) −12.7913 −0.540531
\(561\) −3.00000 1.73205i −0.126660 0.0731272i
\(562\) 4.00000 + 6.92820i 0.168730 + 0.292249i
\(563\) −7.29129 + 12.6289i −0.307291 + 0.532244i −0.977769 0.209686i \(-0.932756\pi\)
0.670478 + 0.741930i \(0.266089\pi\)
\(564\) −9.47822 + 5.47225i −0.399105 + 0.230423i
\(565\) 10.6784i 0.449242i
\(566\) −2.50455 + 1.44600i −0.105274 + 0.0607799i
\(567\) 2.64575i 0.111111i
\(568\) −9.87386 17.1020i −0.414298 0.717585i
\(569\) −15.6652 27.1328i −0.656717 1.13747i −0.981460 0.191665i \(-0.938611\pi\)
0.324743 0.945802i \(-0.394722\pi\)
\(570\) 4.18710i 0.175378i
\(571\) −10.1261 17.5390i −0.423766 0.733984i 0.572539 0.819878i \(-0.305959\pi\)
−0.996304 + 0.0858941i \(0.972625\pi\)
\(572\) 16.1216 15.5130i 0.674078 0.648631i
\(573\) 22.3303 0.932862
\(574\) 8.48945i 0.354343i
\(575\) −0.582576 + 1.00905i −0.0242951 + 0.0420803i
\(576\) 3.41742 0.142393
\(577\) −2.91742 + 1.68438i −0.121454 + 0.0701215i −0.559496 0.828833i \(-0.689005\pi\)
0.438042 + 0.898954i \(0.355672\pi\)
\(578\) −6.33030 3.65480i −0.263306 0.152020i
\(579\) 17.5112i 0.727741i
\(580\) 21.7182i 0.901800i
\(581\) 9.16515 0.380235
\(582\) 0.0217804 0.0377247i 0.000902826 0.00156374i
\(583\) 36.4955 21.0707i 1.51149 0.872658i
\(584\) −7.50000 12.9904i −0.310352 0.537546i
\(585\) 4.50000 4.33013i 0.186052 0.179029i
\(586\) 5.23049 9.05948i 0.216070 0.374244i
\(587\) −5.12614 2.95958i −0.211578 0.122155i 0.390466 0.920617i \(-0.372314\pi\)
−0.602045 + 0.798462i \(0.705647\pi\)
\(588\) 6.26951 10.8591i 0.258550 0.447822i
\(589\) −2.16515 3.75015i −0.0892135 0.154522i
\(590\) −6.56080 3.78788i −0.270104 0.155944i
\(591\) −12.2477 7.07123i −0.503804 0.290871i
\(592\) −8.60436 4.96773i −0.353637 0.204172i
\(593\) −12.2477 7.07123i −0.502954 0.290381i 0.226979 0.973900i \(-0.427115\pi\)
−0.729933 + 0.683519i \(0.760449\pi\)
\(594\) −0.791288 1.37055i −0.0324669 0.0562344i
\(595\) 2.29129 + 3.96863i 0.0939336 + 0.162698i
\(596\) −27.1652 15.6838i −1.11273 0.642434i
\(597\) 3.29129 5.70068i 0.134703 0.233313i
\(598\) −0.691478 + 0.665375i −0.0282766 + 0.0272092i
\(599\) −17.8739 30.9584i −0.730306 1.26493i −0.956752 0.290904i \(-0.906044\pi\)
0.226446 0.974024i \(-0.427289\pi\)
\(600\) −3.00000 + 1.73205i −0.122474 + 0.0707107i
\(601\) −3.91742 + 6.78518i −0.159795 + 0.276773i −0.934795 0.355189i \(-0.884417\pi\)
0.775000 + 0.631962i \(0.217750\pi\)
\(602\) 2.76951 4.79693i 0.112877 0.195508i
\(603\) 7.11890i 0.289904i
\(604\) 17.4913i 0.711711i
\(605\) 1.50000 + 0.866025i 0.0609837 + 0.0352089i
\(606\) 2.04356 1.17985i 0.0830140 0.0479281i
\(607\) −8.00000 −0.324710 −0.162355 0.986732i \(-0.551909\pi\)
−0.162355 + 0.986732i \(0.551909\pi\)
\(608\) −12.5390 + 21.7182i −0.508524 + 0.880790i
\(609\) 16.0390 + 9.26013i 0.649934 + 0.375239i
\(610\) 10.4174 0.421789
\(611\) −15.8739 + 15.2746i −0.642188 + 0.617945i
\(612\) −0.895644 1.55130i −0.0362043 0.0627076i
\(613\) 3.27340i 0.132211i 0.997813 + 0.0661057i \(0.0210575\pi\)
−0.997813 + 0.0661057i \(0.978943\pi\)
\(614\) −0.0435608 0.0754495i −0.00175797 0.00304489i
\(615\) −6.08258 10.5353i −0.245273 0.424826i
\(616\) 15.8745i 0.639602i
\(617\) 9.24773 5.33918i 0.372299 0.214947i −0.302163 0.953256i \(-0.597709\pi\)
0.674463 + 0.738309i \(0.264375\pi\)
\(618\) 5.74835i 0.231233i
\(619\) −31.0390 + 17.9204i −1.24756 + 0.720281i −0.970623 0.240606i \(-0.922654\pi\)
−0.276940 + 0.960887i \(0.589320\pi\)
\(620\) −1.26951 + 2.19885i −0.0509846 + 0.0883080i
\(621\) −0.291288 0.504525i −0.0116890 0.0202459i
\(622\) 0.230493 + 0.133075i 0.00924191 + 0.00533582i
\(623\) −20.6216 35.7176i −0.826187 1.43100i
\(624\) 9.76951 2.41733i 0.391093 0.0967705i
\(625\) 5.50000 9.52628i 0.220000 0.381051i
\(626\) 14.6947i 0.587317i
\(627\) −18.3303 −0.732042
\(628\) −14.6261 −0.583646
\(629\) 3.55945i 0.141925i
\(630\) 2.09355i 0.0834091i
\(631\) −17.1261 + 9.88778i −0.681781 + 0.393626i −0.800526 0.599299i \(-0.795446\pi\)
0.118745 + 0.992925i \(0.462113\pi\)
\(632\) −15.8739 9.16478i −0.631428 0.364555i
\(633\) 1.29129 2.23658i 0.0513241 0.0888959i
\(634\) 8.79129 0.349147
\(635\) −3.87386 + 2.23658i −0.153730 + 0.0887558i
\(636\) 21.7913 0.864081
\(637\) 7.00000 24.2487i 0.277350 0.960769i
\(638\) −11.0780 −0.438583
\(639\) 9.87386 5.70068i 0.390604 0.225515i
\(640\) 19.1216 0.755847
\(641\) −19.2477 + 33.3380i −0.760240 + 1.31677i 0.182487 + 0.983208i \(0.441585\pi\)
−0.942727 + 0.333565i \(0.891748\pi\)
\(642\) −4.18693 2.41733i −0.165245 0.0954043i
\(643\) 6.54356 3.77793i 0.258053 0.148987i −0.365393 0.930853i \(-0.619065\pi\)
0.623446 + 0.781866i \(0.285732\pi\)
\(644\) 2.76100i 0.108799i
\(645\) 7.93725i 0.312529i
\(646\) 2.41742 0.0951123
\(647\) −1.66970 −0.0656426 −0.0328213 0.999461i \(-0.510449\pi\)
−0.0328213 + 0.999461i \(0.510449\pi\)
\(648\) 1.73205i 0.0680414i
\(649\) 16.5826 28.7219i 0.650923 1.12743i
\(650\) −2.37386 + 2.28425i −0.0931106 + 0.0895957i
\(651\) −1.08258 1.87508i −0.0424295 0.0734900i
\(652\) 5.37386 + 3.10260i 0.210457 + 0.121507i
\(653\) 14.2477 + 24.6778i 0.557557 + 0.965716i 0.997700 + 0.0677888i \(0.0215944\pi\)
−0.440143 + 0.897928i \(0.645072\pi\)
\(654\) 0.439205 0.760725i 0.0171743 0.0297467i
\(655\) 15.8739 9.16478i 0.620243 0.358098i
\(656\) 19.6048i 0.765437i
\(657\) 7.50000 4.33013i 0.292603 0.168934i
\(658\) 7.38505i 0.287899i
\(659\) 22.0390 + 38.1727i 0.858518 + 1.48700i 0.873342 + 0.487107i \(0.161948\pi\)
−0.0148242 + 0.999890i \(0.504719\pi\)
\(660\) 5.37386 + 9.30780i 0.209177 + 0.362306i
\(661\) 26.2668i 1.02166i −0.859682 0.510830i \(-0.829338\pi\)
0.859682 0.510830i \(-0.170662\pi\)
\(662\) −3.53901 6.12975i −0.137548 0.238240i
\(663\) −2.50000 2.59808i −0.0970920 0.100901i
\(664\) −6.00000 −0.232845
\(665\) 21.0000 + 12.1244i 0.814345 + 0.470162i
\(666\) −0.813068 + 1.40828i −0.0315058 + 0.0545696i
\(667\) −4.07803 −0.157902
\(668\) 17.6869 10.2116i 0.684328 0.395097i
\(669\) 2.29129 + 1.32288i 0.0885863 + 0.0511453i
\(670\) 5.63310i 0.217626i
\(671\) 45.6054i 1.76058i
\(672\) −6.26951 + 10.8591i −0.241852 + 0.418899i
\(673\) −0.665151 + 1.15208i −0.0256397 + 0.0444093i −0.878561 0.477631i \(-0.841496\pi\)
0.852921 + 0.522040i \(0.174829\pi\)
\(674\) 12.4610 7.19435i 0.479979 0.277116i
\(675\) −1.00000 1.73205i −0.0384900 0.0666667i
\(676\) 20.5998 10.8591i 0.792300 0.417658i
\(677\) −24.0826 + 41.7122i −0.925569 + 1.60313i −0.134924 + 0.990856i \(0.543079\pi\)
−0.790644 + 0.612276i \(0.790254\pi\)
\(678\) −2.43920 1.40828i −0.0936771 0.0540845i
\(679\) −0.126136 0.218475i −0.00484067 0.00838429i
\(680\) −1.50000 2.59808i −0.0575224 0.0996317i
\(681\) 17.6216 + 10.1738i 0.675261 + 0.389862i
\(682\) 1.12159 + 0.647551i 0.0429479 + 0.0247960i
\(683\) 20.1261 + 11.6198i 0.770105 + 0.444620i 0.832912 0.553405i \(-0.186672\pi\)
−0.0628069 + 0.998026i \(0.520005\pi\)
\(684\) −8.20871 4.73930i −0.313868 0.181212i
\(685\) 7.50000 + 12.9904i 0.286560 + 0.496337i
\(686\) 4.23049 + 7.32743i 0.161521 + 0.279763i
\(687\) −0.0825757 0.0476751i −0.00315046 0.00181892i
\(688\) 6.39564 11.0776i 0.243832 0.422329i
\(689\) 42.5780 10.5353i 1.62209 0.401364i
\(690\) −0.230493 0.399225i −0.00877470 0.0151982i
\(691\) −29.4564 + 17.0067i −1.12058 + 0.646965i −0.941548 0.336879i \(-0.890629\pi\)
−0.179028 + 0.983844i \(0.557295\pi\)
\(692\) 11.0436 19.1280i 0.419813 0.727138i
\(693\) −9.16515 −0.348155
\(694\) 0.798450i 0.0303087i
\(695\) 4.47315i 0.169676i
\(696\) −10.5000 6.06218i −0.398001 0.229786i
\(697\) −6.08258 + 3.51178i −0.230394 + 0.133018i
\(698\) 0.0435608 0.00164880
\(699\) −0.917424 + 1.58903i −0.0347002 + 0.0601025i
\(700\) 9.47860i 0.358258i
\(701\) 34.0000 1.28416 0.642081 0.766637i \(-0.278071\pi\)
0.642081 + 0.766637i \(0.278071\pi\)
\(702\) −0.395644 1.59898i −0.0149326 0.0603495i
\(703\) 9.41742 + 16.3115i 0.355185 + 0.615198i
\(704\) 11.8383i 0.446173i
\(705\) −5.29129 9.16478i −0.199281 0.345166i
\(706\) −2.83485 4.91010i −0.106691 0.184794i
\(707\) 13.6657i 0.513952i
\(708\) 14.8521 8.57485i 0.558175 0.322263i
\(709\) 18.9572i 0.711953i −0.934495 0.355976i \(-0.884148\pi\)
0.934495 0.355976i \(-0.115852\pi\)
\(710\) 7.81307 4.51088i 0.293219 0.169290i
\(711\) 5.29129 9.16478i 0.198439 0.343706i
\(712\) 13.5000 + 23.3827i 0.505934 + 0.876303i
\(713\) 0.412878 + 0.238375i 0.0154624 + 0.00892723i
\(714\) 1.20871 0.0452349
\(715\) 15.0000 + 15.5885i 0.560968 + 0.582975i
\(716\) −17.1652 + 29.7309i −0.641492 + 1.11110i
\(717\) 29.7309i 1.11032i
\(718\) −8.46099 −0.315761
\(719\) 2.33030 0.0869056 0.0434528 0.999055i \(-0.486164\pi\)
0.0434528 + 0.999055i \(0.486164\pi\)
\(720\) 4.83465i 0.180177i
\(721\) −28.8303 16.6452i −1.07370 0.619899i
\(722\) 3.56080 2.05583i 0.132519 0.0765099i
\(723\) −15.2477 8.80328i −0.567069 0.327397i
\(724\) −19.7042 + 34.1286i −0.732300 + 1.26838i
\(725\) −14.0000 −0.519947
\(726\) 0.395644 0.228425i 0.0146837 0.00847765i
\(727\) 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
\(730\) 5.93466 3.42638i 0.219652 0.126816i
\(731\) −4.58258 −0.169493
\(732\) −11.7913 + 20.4231i −0.435819 + 0.754860i
\(733\) −10.8303 6.25288i −0.400026 0.230955i 0.286469 0.958090i \(-0.407518\pi\)
−0.686495 + 0.727134i \(0.740852\pi\)
\(734\) 1.25227 0.723000i 0.0462222 0.0266864i
\(735\) 10.5000 + 6.06218i 0.387298 + 0.223607i
\(736\) 2.76100i 0.101772i
\(737\) −24.6606 −0.908385
\(738\) −3.20871 −0.118114
\(739\) 8.56490i 0.315065i 0.987514 + 0.157533i \(0.0503539\pi\)
−0.987514 + 0.157533i \(0.949646\pi\)
\(740\) 5.52178 9.56400i 0.202985 0.351580i
\(741\) −18.3303 5.29150i −0.673380 0.194388i
\(742\) −7.35208 + 12.7342i −0.269903 + 0.467487i
\(743\) 11.2913 + 6.51903i 0.414237 + 0.239160i 0.692609 0.721314i \(-0.256461\pi\)
−0.278372 + 0.960473i \(0.589795\pi\)
\(744\) 0.708712 + 1.22753i 0.0259826 + 0.0450033i
\(745\) 15.1652 26.2668i 0.555608 0.962342i
\(746\) 10.2867 5.93905i 0.376624 0.217444i
\(747\) 3.46410i 0.126745i
\(748\) 5.37386 3.10260i 0.196488 0.113442i
\(749\) −24.2477 + 13.9994i −0.885993 + 0.511528i
\(750\) −2.76951 4.79693i −0.101128 0.175159i
\(751\) −16.4564 28.5034i −0.600504 1.04010i −0.992745 0.120241i \(-0.961633\pi\)
0.392241 0.919863i \(-0.371700\pi\)
\(752\) 17.0544i 0.621908i
\(753\) 5.70871 + 9.88778i 0.208037 + 0.360331i
\(754\) −11.0780 3.19795i −0.403438 0.116463i
\(755\) −16.9129 −0.615523
\(756\) −4.10436 2.36965i −0.149274 0.0861834i
\(757\) 25.2477 43.7303i 0.917644 1.58941i 0.114661 0.993405i \(-0.463422\pi\)
0.802983 0.596002i \(-0.203245\pi\)
\(758\) 8.46099 0.307317
\(759\) 1.74773 1.00905i 0.0634385 0.0366262i
\(760\) −13.7477 7.93725i −0.498682 0.287914i
\(761\) 33.1950i 1.20332i 0.798753 + 0.601659i \(0.205493\pi\)
−0.798753 + 0.601659i \(0.794507\pi\)
\(762\) 1.17985i 0.0427415i
\(763\) −2.54356 4.40558i −0.0920831 0.159493i
\(764\) −20.0000 + 34.6410i −0.723575 + 1.25327i
\(765\) 1.50000 0.866025i 0.0542326 0.0313112i
\(766\) 5.62614 + 9.74475i 0.203281 + 0.352092i
\(767\) 24.8739 23.9349i 0.898143 0.864239i
\(768\) −0.895644 + 1.55130i −0.0323188 + 0.0559777i
\(769\) −12.0826 6.97588i −0.435709 0.251557i 0.266067 0.963955i \(-0.414276\pi\)
−0.701776 + 0.712398i \(0.747609\pi\)
\(770\) −7.25227 −0.261354
\(771\) −13.6652 23.6687i −0.492138 0.852409i
\(772\) −27.1652 15.6838i −0.977695 0.564473i
\(773\) −6.24773 3.60713i −0.224715 0.129739i 0.383417 0.923576i \(-0.374747\pi\)
−0.608132 + 0.793836i \(0.708081\pi\)
\(774\) −1.81307 1.04678i −0.0651694 0.0376256i