Properties

Label 273.2.t.b.4.1
Level $273$
Weight $2$
Character 273.4
Analytic conductor $2.180$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 4.1
Root \(1.39564 - 0.228425i\) of defining polynomial
Character \(\chi\) \(=\) 273.4
Dual form 273.2.t.b.205.2

$q$-expansion

\(f(q)\) \(=\) \(q-0.456850i q^{2} +(-0.500000 - 0.866025i) q^{3} +1.79129 q^{4} +(1.50000 - 0.866025i) q^{5} +(-0.395644 + 0.228425i) q^{6} +(-2.29129 - 1.32288i) q^{7} -1.73205i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q-0.456850i q^{2} +(-0.500000 - 0.866025i) q^{3} +1.79129 q^{4} +(1.50000 - 0.866025i) q^{5} +(-0.395644 + 0.228425i) q^{6} +(-2.29129 - 1.32288i) q^{7} -1.73205i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.395644 - 0.685275i) q^{10} +(3.00000 - 1.73205i) 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} +2.79129 q^{16} +1.00000 q^{17} +(0.395644 + 0.228425i) q^{18} +(-4.58258 - 2.64575i) q^{19} +(2.68693 - 1.55130i) q^{20} +2.64575i q^{21} +(-0.791288 - 1.37055i) q^{22} +0.582576 q^{23} +(-1.50000 + 0.866025i) q^{24} +(-1.00000 + 1.73205i) q^{25} +(1.58258 + 0.456850i) q^{26} +1.00000 q^{27} +(-4.10436 - 2.36965i) q^{28} +(3.50000 - 6.06218i) q^{29} +(-0.395644 + 0.685275i) q^{30} +(0.708712 + 0.409175i) q^{31} -4.73930i q^{32} +(-3.00000 - 1.73205i) q^{33} -0.456850i q^{34} -4.58258 q^{35} +(-0.895644 + 1.55130i) q^{36} +3.55945i q^{37} +(-1.20871 + 2.09355i) q^{38} +(3.50000 - 0.866025i) q^{39} +(-1.50000 - 2.59808i) q^{40} +(6.08258 + 3.51178i) q^{41} +1.20871 q^{42} +(2.29129 + 3.96863i) q^{43} +(5.37386 - 3.10260i) q^{44} +1.73205i q^{45} -0.266150i q^{46} +(-5.29129 + 3.05493i) q^{47} +(-1.39564 - 2.41733i) q^{48} +(3.50000 + 6.06218i) q^{49} +(0.791288 + 0.456850i) q^{50} +(-0.500000 - 0.866025i) q^{51} +(-1.79129 + 6.20520i) q^{52} +(-6.08258 + 10.5353i) q^{53} -0.456850i q^{54} +(3.00000 - 5.19615i) q^{55} +(-2.29129 + 3.96863i) q^{56} +5.29150i q^{57} +(-2.76951 - 1.59898i) q^{58} +9.57395i q^{59} +(-2.68693 - 1.55130i) q^{60} +(-6.58258 + 11.4014i) q^{61} +(0.186932 - 0.323775i) q^{62} +(2.29129 - 1.32288i) q^{63} +3.41742 q^{64} +(1.50000 + 6.06218i) q^{65} +(-0.791288 + 1.37055i) q^{66} +(6.16515 - 3.55945i) q^{67} +1.79129 q^{68} +(-0.291288 - 0.504525i) q^{69} +2.09355i q^{70} +(9.87386 - 5.70068i) q^{71} +(1.50000 + 0.866025i) q^{72} +(-7.50000 - 4.33013i) q^{73} +1.62614 q^{74} +2.00000 q^{75} +(-8.20871 - 4.73930i) q^{76} -9.16515 q^{77} +(-0.395644 - 1.59898i) q^{78} +(5.29129 + 9.16478i) q^{79} +(4.18693 - 2.41733i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.60436 - 2.77883i) q^{82} -3.46410i q^{83} +4.73930i q^{84} +(1.50000 - 0.866025i) q^{85} +(1.81307 - 1.04678i) q^{86} -7.00000 q^{87} +(-3.00000 - 5.19615i) q^{88} -15.5885i q^{89} +0.791288 q^{90} +(6.87386 - 6.61438i) q^{91} +1.04356 q^{92} -0.818350i q^{93} +(1.39564 + 2.41733i) q^{94} -9.16515 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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{3} - 2q^{4} + 6q^{5} + 3q^{6} - 2q^{9} + O(q^{10}) \) \( 4q - 2q^{3} - 2q^{4} + 6q^{5} + 3q^{6} - 2q^{9} + 3q^{10} + 12q^{11} + q^{12} - 4q^{13} - 7q^{14} - 6q^{15} + 2q^{16} + 4q^{17} - 3q^{18} - 3q^{20} + 6q^{22} - 16q^{23} - 6q^{24} - 4q^{25} - 12q^{26} + 4q^{27} - 21q^{28} + 14q^{29} + 3q^{30} + 12q^{31} - 12q^{33} + q^{36} - 14q^{38} + 14q^{39} - 6q^{40} + 6q^{41} + 14q^{42} - 6q^{44} - 12q^{47} - q^{48} + 14q^{49} - 6q^{50} - 2q^{51} + 2q^{52} - 6q^{53} + 12q^{55} + 21q^{58} + 3q^{60} - 8q^{61} - 13q^{62} + 32q^{64} + 6q^{65} + 6q^{66} - 12q^{67} - 2q^{68} + 8q^{69} + 12q^{71} + 6q^{72} - 30q^{73} + 34q^{74} + 8q^{75} - 42q^{76} + 3q^{78} + 12q^{79} + 3q^{80} - 2q^{81} + 11q^{82} + 6q^{85} + 21q^{86} - 28q^{87} - 12q^{88} - 6q^{90} + 50q^{92} + q^{94} - 21q^{96} + 18q^{97} - 21q^{98} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.456850i 0.323042i −0.986869 0.161521i \(-0.948360\pi\)
0.986869 0.161521i \(-0.0516399\pi\)
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) 1.79129 0.895644
\(5\) 1.50000 0.866025i 0.670820 0.387298i −0.125567 0.992085i \(-0.540075\pi\)
0.796387 + 0.604787i \(0.206742\pi\)
\(6\) −0.395644 + 0.228425i −0.161521 + 0.0932542i
\(7\) −2.29129 1.32288i −0.866025 0.500000i
\(8\) 1.73205i 0.612372i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −0.395644 0.685275i −0.125114 0.216703i
\(11\) 3.00000 1.73205i 0.904534 0.522233i 0.0258656 0.999665i \(-0.491766\pi\)
0.878668 + 0.477432i \(0.158432\pi\)
\(12\) −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
\(16\) 2.79129 0.697822
\(17\) 1.00000 0.242536 0.121268 0.992620i \(-0.461304\pi\)
0.121268 + 0.992620i \(0.461304\pi\)
\(18\) 0.395644 + 0.228425i 0.0932542 + 0.0538403i
\(19\) −4.58258 2.64575i −1.05131 0.606977i −0.128298 0.991736i \(-0.540951\pi\)
−0.923017 + 0.384759i \(0.874285\pi\)
\(20\) 2.68693 1.55130i 0.600816 0.346881i
\(21\) 2.64575i 0.577350i
\(22\) −0.791288 1.37055i −0.168703 0.292202i
\(23\) 0.582576 0.121475 0.0607377 0.998154i \(-0.480655\pi\)
0.0607377 + 0.998154i \(0.480655\pi\)
\(24\) −1.50000 + 0.866025i −0.306186 + 0.176777i
\(25\) −1.00000 + 1.73205i −0.200000 + 0.346410i
\(26\) 1.58258 + 0.456850i 0.310369 + 0.0895957i
\(27\) 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 \(-0.0585367\pi\)
\(30\) −0.395644 + 0.685275i −0.0722344 + 0.125114i
\(31\) 0.708712 + 0.409175i 0.127288 + 0.0734900i 0.562292 0.826939i \(-0.309920\pi\)
−0.435004 + 0.900429i \(0.643253\pi\)
\(32\) 4.73930i 0.837798i
\(33\) −3.00000 1.73205i −0.522233 0.301511i
\(34\) 0.456850i 0.0783492i
\(35\) −4.58258 −0.774597
\(36\) −0.895644 + 1.55130i −0.149274 + 0.258550i
\(37\) 3.55945i 0.585170i 0.956239 + 0.292585i \(0.0945155\pi\)
−0.956239 + 0.292585i \(0.905485\pi\)
\(38\) −1.20871 + 2.09355i −0.196079 + 0.339619i
\(39\) 3.50000 0.866025i 0.560449 0.138675i
\(40\) −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 \(0.481886\pi\)
\(42\) 1.20871 0.186508
\(43\) 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
\(45\) 1.73205i 0.258199i
\(46\) 0.266150i 0.0392417i
\(47\) −5.29129 + 3.05493i −0.771814 + 0.445607i −0.833521 0.552487i \(-0.813679\pi\)
0.0617076 + 0.998094i \(0.480345\pi\)
\(48\) −1.39564 2.41733i −0.201444 0.348911i
\(49\) 3.50000 + 6.06218i 0.500000 + 0.866025i
\(50\) 0.791288 + 0.456850i 0.111905 + 0.0646084i
\(51\) −0.500000 0.866025i −0.0700140 0.121268i
\(52\) −1.79129 + 6.20520i −0.248407 + 0.860507i
\(53\) −6.08258 + 10.5353i −0.835506 + 1.44714i 0.0581117 + 0.998310i \(0.481492\pi\)
−0.893618 + 0.448829i \(0.851841\pi\)
\(54\) 0.456850i 0.0621694i
\(55\) 3.00000 5.19615i 0.404520 0.700649i
\(56\) −2.29129 + 3.96863i −0.306186 + 0.530330i
\(57\) 5.29150i 0.700877i
\(58\) −2.76951 1.59898i −0.363654 0.209956i
\(59\) 9.57395i 1.24642i 0.782053 + 0.623211i \(0.214172\pi\)
−0.782053 + 0.623211i \(0.785828\pi\)
\(60\) −2.68693 1.55130i −0.346881 0.200272i
\(61\) −6.58258 + 11.4014i −0.842812 + 1.45979i 0.0446950 + 0.999001i \(0.485768\pi\)
−0.887507 + 0.460793i \(0.847565\pi\)
\(62\) 0.186932 0.323775i 0.0237404 0.0411195i
\(63\) 2.29129 1.32288i 0.288675 0.166667i
\(64\) 3.41742 0.427178
\(65\) 1.50000 + 6.06218i 0.186052 + 0.751921i
\(66\) −0.791288 + 1.37055i −0.0974008 + 0.168703i
\(67\) 6.16515 3.55945i 0.753193 0.434856i −0.0736534 0.997284i \(-0.523466\pi\)
0.826847 + 0.562428i \(0.190133\pi\)
\(68\) 1.79129 0.217226
\(69\) −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 \(0.0968093\pi\)
\(72\) 1.50000 + 0.866025i 0.176777 + 0.102062i
\(73\) −7.50000 4.33013i −0.877809 0.506803i −0.00787336 0.999969i \(-0.502506\pi\)
−0.869935 + 0.493166i \(0.835840\pi\)
\(74\) 1.62614 0.189035
\(75\) 2.00000 0.230940
\(76\) −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 0.993502 + 0.113813i \(0.0363066\pi\)
−0.398186 + 0.917305i \(0.630360\pi\)
\(80\) 4.18693 2.41733i 0.468113 0.270265i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 1.60436 2.77883i 0.177171 0.306870i
\(83\) 3.46410i 0.380235i −0.981761 0.190117i \(-0.939113\pi\)
0.981761 0.190117i \(-0.0608868\pi\)
\(84\) 4.73930i 0.517100i
\(85\) 1.50000 0.866025i 0.162698 0.0939336i
\(86\) 1.81307 1.04678i 0.195508 0.112877i
\(87\) −7.00000 −0.750479
\(88\) −3.00000 5.19615i −0.319801 0.553912i
\(89\) 15.5885i 1.65237i −0.563397 0.826187i \(-0.690506\pi\)
0.563397 0.826187i \(-0.309494\pi\)
\(90\) 0.791288 0.0834091
\(91\) 6.87386 6.61438i 0.720577 0.693375i
\(92\) 1.04356 0.108799
\(93\) 0.818350i 0.0848590i
\(94\) 1.39564 + 2.41733i 0.143950 + 0.249328i
\(95\) −9.16515 −0.940325
\(96\) −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
\(100\) −1.79129 + 3.10260i −0.179129 + 0.310260i
\(101\) 2.58258 + 4.47315i 0.256976 + 0.445095i 0.965430 0.260661i \(-0.0839406\pi\)
−0.708454 + 0.705757i \(0.750607\pi\)
\(102\) −0.395644 + 0.228425i −0.0391746 + 0.0226175i
\(103\) −6.29129 10.8968i −0.619899 1.07370i −0.989504 0.144507i \(-0.953840\pi\)
0.369605 0.929189i \(-0.379493\pi\)
\(104\) 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
\(107\) −10.5826 −1.02306 −0.511528 0.859267i \(-0.670920\pi\)
−0.511528 + 0.859267i \(0.670920\pi\)
\(108\) 1.79129 0.172367
\(109\) 1.66515 + 0.961376i 0.159493 + 0.0920831i 0.577622 0.816304i \(-0.303981\pi\)
−0.418129 + 0.908387i \(0.637314\pi\)
\(110\) −2.37386 1.37055i −0.226339 0.130677i
\(111\) 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 \(0.739683\pi\)
\(114\) 2.41742 0.226413
\(115\) 0.873864 0.504525i 0.0814882 0.0470472i
\(116\) 6.26951 10.8591i 0.582109 1.00824i
\(117\) −2.50000 2.59808i −0.231125 0.240192i
\(118\) 4.37386 0.402647
\(119\) −2.29129 1.32288i −0.210042 0.121268i
\(120\) −1.50000 + 2.59808i −0.136931 + 0.237171i
\(121\) 0.500000 0.866025i 0.0454545 0.0787296i
\(122\) 5.20871 + 3.00725i 0.471575 + 0.272264i
\(123\) 7.02355i 0.633292i
\(124\) 1.26951 + 0.732950i 0.114005 + 0.0658209i
\(125\) 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 \(0.130113\pi\)
\(128\) 11.0399i 0.975795i
\(129\) 2.29129 3.96863i 0.201737 0.349418i
\(130\) 2.76951 0.685275i 0.242902 0.0601026i
\(131\) −5.29129 9.16478i −0.462302 0.800730i 0.536773 0.843727i \(-0.319643\pi\)
−0.999075 + 0.0429960i \(0.986310\pi\)
\(132\) −5.37386 3.10260i −0.467735 0.270047i
\(133\) 7.00000 + 12.1244i 0.606977 + 1.05131i
\(134\) −1.62614 2.81655i −0.140477 0.243313i
\(135\) 1.50000 0.866025i 0.129099 0.0745356i
\(136\) 1.73205i 0.148522i
\(137\) 8.66025i 0.739895i 0.929053 + 0.369948i \(0.120624\pi\)
−0.929053 + 0.369948i \(0.879376\pi\)
\(138\) −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 \(0.868266\pi\)
\(140\) −8.20871 −0.693763
\(141\) 5.29129 + 3.05493i 0.445607 + 0.257271i
\(142\) −2.60436 4.51088i −0.218553 0.378544i
\(143\) 3.00000 + 12.1244i 0.250873 + 1.01389i
\(144\) −1.39564 + 2.41733i −0.116304 + 0.201444i
\(145\) 12.1244i 1.00687i
\(146\) −1.97822 + 3.42638i −0.163719 + 0.283569i
\(147\) 3.50000 6.06218i 0.288675 0.500000i
\(148\) 6.37600i 0.524104i
\(149\) −15.1652 8.75560i −1.24238 0.717287i −0.272800 0.962071i \(-0.587950\pi\)
−0.969578 + 0.244784i \(0.921283\pi\)
\(150\) 0.913701i 0.0746033i
\(151\) −8.45644 4.88233i −0.688175 0.397318i 0.114753 0.993394i \(-0.463392\pi\)
−0.802928 + 0.596076i \(0.796726\pi\)
\(152\) −4.58258 + 7.93725i −0.371696 + 0.643796i
\(153\) −0.500000 + 0.866025i −0.0404226 + 0.0700140i
\(154\) 4.18710i 0.337406i
\(155\) 1.41742 0.113850
\(156\) 6.26951 1.55130i 0.501962 0.124203i
\(157\) 4.08258 7.07123i 0.325825 0.564345i −0.655854 0.754888i \(-0.727691\pi\)
0.981679 + 0.190542i \(0.0610246\pi\)
\(158\) 4.18693 2.41733i 0.333094 0.192312i
\(159\) 12.1652 0.964759
\(160\) −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
\(163\) 3.00000 + 1.73205i 0.234978 + 0.135665i 0.612866 0.790186i \(-0.290016\pi\)
−0.377888 + 0.925851i \(0.623350\pi\)
\(164\) 10.8956 + 6.29060i 0.850807 + 0.491214i
\(165\) −6.00000 −0.467099
\(166\) −1.58258 −0.122832
\(167\) −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
\(171\) 4.58258 2.64575i 0.350438 0.202326i
\(172\) 4.10436 + 7.10895i 0.312954 + 0.542053i
\(173\) 6.16515 10.6784i 0.468728 0.811860i −0.530633 0.847601i \(-0.678046\pi\)
0.999361 + 0.0357412i \(0.0113792\pi\)
\(174\) 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
\(178\) −7.12159 −0.533786
\(179\) −9.58258 16.5975i −0.716235 1.24056i −0.962481 0.271349i \(-0.912530\pi\)
0.246246 0.969207i \(-0.420803\pi\)
\(180\) 3.10260i 0.231254i
\(181\) 22.0000 1.63525 0.817624 0.575753i \(-0.195291\pi\)
0.817624 + 0.575753i \(0.195291\pi\)
\(182\) −3.02178 3.14033i −0.223989 0.232776i
\(183\) 13.1652 0.973196
\(184\) 1.00905i 0.0743882i
\(185\) 3.08258 + 5.33918i 0.226635 + 0.392544i
\(186\) −0.373864 −0.0274130
\(187\) 3.00000 1.73205i 0.219382 0.126660i
\(188\) −9.47822 + 5.47225i −0.691270 + 0.399105i
\(189\) −2.29129 1.32288i −0.166667 0.0962250i
\(190\) 4.18710i 0.303764i
\(191\) −11.1652 + 19.3386i −0.807882 + 1.39929i 0.106446 + 0.994318i \(0.466053\pi\)
−0.914328 + 0.404974i \(0.867280\pi\)
\(192\) −1.70871 2.95958i −0.123316 0.213589i
\(193\) 15.1652 8.75560i 1.09161 0.630242i 0.157606 0.987502i \(-0.449622\pi\)
0.934005 + 0.357260i \(0.116289\pi\)
\(194\) 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 \(0.834733\pi\)
\(198\) 1.58258 0.112469
\(199\) −6.58258 −0.466626 −0.233313 0.972402i \(-0.574957\pi\)
−0.233313 + 0.972402i \(0.574957\pi\)
\(200\) 3.00000 + 1.73205i 0.212132 + 0.122474i
\(201\) −6.16515 3.55945i −0.434856 0.251064i
\(202\) 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
\(205\) 12.1652 0.849651
\(206\) −4.97822 + 2.87418i −0.346849 + 0.200253i
\(207\) −0.291288 + 0.504525i −0.0202459 + 0.0350669i
\(208\) −2.79129 + 9.66930i −0.193541 + 0.670446i
\(209\) −18.3303 −1.26793
\(210\) 1.81307 1.04678i 0.125114 0.0722344i
\(211\) 1.29129 2.23658i 0.0888959 0.153972i −0.818149 0.575007i \(-0.804999\pi\)
0.907045 + 0.421034i \(0.138333\pi\)
\(212\) −10.8956 + 18.8718i −0.748316 + 1.29612i
\(213\) −9.87386 5.70068i −0.676546 0.390604i
\(214\) 4.83465i 0.330490i
\(215\) 6.87386 + 3.96863i 0.468794 + 0.270658i
\(216\) 1.73205i 0.117851i
\(217\) −1.08258 1.87508i −0.0734900 0.127288i
\(218\) 0.439205 0.760725i 0.0297467 0.0515228i
\(219\) 8.66025i 0.585206i
\(220\) 5.37386 9.30780i 0.362306 0.627532i
\(221\) −1.00000 + 3.46410i −0.0672673 + 0.233021i
\(222\) −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
\(227\) 20.3477i 1.35052i −0.737579 0.675261i \(-0.764031\pi\)
0.737579 0.675261i \(-0.235969\pi\)
\(228\) 9.47860i 0.627736i
\(229\) 0.0825757 0.0476751i 0.00545676 0.00315046i −0.497269 0.867596i \(-0.665664\pi\)
0.502726 + 0.864446i \(0.332331\pi\)
\(230\) −0.230493 0.399225i −0.0151982 0.0263241i
\(231\) 4.58258 + 7.93725i 0.301511 + 0.522233i
\(232\) −10.5000 6.06218i −0.689359 0.398001i
\(233\) −0.917424 1.58903i −0.0601025 0.104101i 0.834409 0.551146i \(-0.185809\pi\)
−0.894511 + 0.447046i \(0.852476\pi\)
\(234\) −1.18693 + 1.14213i −0.0775922 + 0.0746631i
\(235\) −5.29129 + 9.16478i −0.345166 + 0.597844i
\(236\) 17.1497i 1.11635i
\(237\) 5.29129 9.16478i 0.343706 0.595316i
\(238\) −0.604356 + 1.04678i −0.0391746 + 0.0678524i
\(239\) 29.7309i 1.92313i −0.274572 0.961566i \(-0.588536\pi\)
0.274572 0.961566i \(-0.411464\pi\)
\(240\) −4.18693 2.41733i −0.270265 0.156038i
\(241\) 17.6066i 1.13414i 0.823670 + 0.567069i \(0.191923\pi\)
−0.823670 + 0.567069i \(0.808077\pi\)
\(242\) −0.395644 0.228425i −0.0254330 0.0146837i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) −11.7913 + 20.4231i −0.754860 + 1.30746i
\(245\) 10.5000 + 6.06218i 0.670820 + 0.387298i
\(246\) −3.20871 −0.204580
\(247\) 13.7477 13.2288i 0.874747 0.841726i
\(248\) 0.708712 1.22753i 0.0450033 0.0779479i
\(249\) −3.00000 + 1.73205i −0.190117 + 0.109764i
\(250\) 5.53901 0.350318
\(251\) 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
\(254\) −1.02178 0.589925i −0.0641122 0.0370152i
\(255\) −1.50000 0.866025i −0.0939336 0.0542326i
\(256\) 1.79129 0.111955
\(257\) 27.3303 1.70482 0.852409 0.522876i \(-0.175141\pi\)
0.852409 + 0.522876i \(0.175141\pi\)
\(258\) −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
\(262\) −4.18693 + 2.41733i −0.258670 + 0.149343i
\(263\) 11.5826 + 20.0616i 0.714212 + 1.23705i 0.963263 + 0.268561i \(0.0865482\pi\)
−0.249050 + 0.968491i \(0.580118\pi\)
\(264\) −3.00000 + 5.19615i −0.184637 + 0.319801i
\(265\) 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
\(269\) −2.16515 −0.132012 −0.0660058 0.997819i \(-0.521026\pi\)
−0.0660058 + 0.997819i \(0.521026\pi\)
\(270\) −0.395644 0.685275i −0.0240781 0.0417045i
\(271\) 25.4485i 1.54588i 0.634477 + 0.772942i \(0.281216\pi\)
−0.634477 + 0.772942i \(0.718784\pi\)
\(272\) 2.79129 0.169247
\(273\) −9.16515 2.64575i −0.554700 0.160128i
\(274\) 3.95644 0.239017
\(275\) 6.92820i 0.417786i
\(276\) −0.521780 0.903750i −0.0314075 0.0543994i
\(277\) −27.3303 −1.64212 −0.821059 0.570843i \(-0.806617\pi\)
−0.821059 + 0.570843i \(0.806617\pi\)
\(278\) −1.02178 + 0.589925i −0.0612823 + 0.0353814i
\(279\) −0.708712 + 0.409175i −0.0424295 + 0.0244967i
\(280\) 7.93725i 0.474342i
\(281\) 17.5112i 1.04463i −0.852752 0.522316i \(-0.825068\pi\)
0.852752 0.522316i \(-0.174932\pi\)
\(282\) 1.39564 2.41733i 0.0831094 0.143950i
\(283\) −3.16515 5.48220i −0.188149 0.325883i 0.756484 0.654012i \(-0.226915\pi\)
−0.944633 + 0.328129i \(0.893582\pi\)
\(284\) 17.6869 10.2116i 1.04953 0.605944i
\(285\) 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
\(289\) −16.0000 −0.941176
\(290\) −5.53901 −0.325262
\(291\) 0.0825757 + 0.0476751i 0.00484067 + 0.00279476i
\(292\) −13.4347 7.75650i −0.786204 0.453915i
\(293\) −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
\(296\) 6.16515 0.358342
\(297\) 3.00000 1.73205i 0.174078 0.100504i
\(298\) −4.00000 + 6.92820i −0.231714 + 0.401340i
\(299\) −0.582576 + 2.01810i −0.0336912 + 0.116710i
\(300\) 3.58258 0.206840
\(301\) 12.1244i 0.698836i
\(302\) −2.23049 + 3.86333i −0.128350 + 0.222309i
\(303\) 2.58258 4.47315i 0.148365 0.256976i
\(304\) −12.7913 7.38505i −0.733631 0.423562i
\(305\) 22.8027i 1.30568i
\(306\) 0.395644 + 0.228425i 0.0226175 + 0.0130582i
\(307\) 0.190700i 0.0108838i 0.999985 + 0.00544192i \(0.00173223\pi\)
−0.999985 + 0.00544192i \(0.998268\pi\)
\(308\) −16.4174 −0.935470
\(309\) −6.29129 + 10.8968i −0.357899 + 0.619899i
\(310\) 0.647551i 0.0367784i
\(311\) −0.291288 + 0.504525i −0.0165174 + 0.0286090i −0.874166 0.485627i \(-0.838591\pi\)
0.857649 + 0.514236i \(0.171925\pi\)
\(312\) −1.50000 6.06218i −0.0849208 0.343203i
\(313\) 16.0826 + 27.8558i 0.909041 + 1.57451i 0.815399 + 0.578899i \(0.196517\pi\)
0.0936417 + 0.995606i \(0.470149\pi\)
\(314\) −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 \(-0.484938\pi\)
0.888707 + 0.458476i \(0.151605\pi\)
\(318\) 5.55765i 0.311658i
\(319\) 24.2487i 1.35767i
\(320\) 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
\(325\) −5.00000 5.19615i −0.277350 0.288231i
\(326\) 0.791288 1.37055i 0.0438254 0.0759078i
\(327\) 1.92275i 0.106328i
\(328\) 6.08258 10.5353i 0.335854 0.581716i
\(329\) 16.1652 0.891214
\(330\) 2.74110i 0.150893i
\(331\) −13.4174 7.74655i −0.737488 0.425789i 0.0836671 0.996494i \(-0.473337\pi\)
−0.821155 + 0.570705i \(0.806670\pi\)
\(332\) 6.20520i 0.340555i
\(333\) −3.08258 1.77973i −0.168924 0.0975284i
\(334\) −2.60436 + 4.51088i −0.142504 + 0.246824i
\(335\) 6.16515 10.6784i 0.336838 0.583421i
\(336\) 7.38505i 0.402888i
\(337\) −31.4955 −1.71567 −0.857833 0.513928i \(-0.828190\pi\)
−0.857833 + 0.513928i \(0.828190\pi\)
\(338\) −3.16515 + 5.02535i −0.172162 + 0.273343i
\(339\) 3.08258 5.33918i 0.167423 0.289984i
\(340\) 2.68693 1.55130i 0.145719 0.0841311i
\(341\) 2.83485 0.153516
\(342\) −1.20871 2.09355i −0.0653597 0.113206i
\(343\) 18.5203i 1.00000i
\(344\) 6.87386 3.96863i 0.370614 0.213974i
\(345\) −0.873864 0.504525i −0.0470472 0.0271627i
\(346\) −4.87841 2.81655i −0.262265 0.151419i
\(347\) 1.74773 0.0938229 0.0469115 0.998899i \(-0.485062\pi\)
0.0469115 + 0.998899i \(0.485062\pi\)
\(348\) −12.5390 −0.672162
\(349\) −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
\(353\) 10.7477 6.20520i 0.572044 0.330270i −0.185921 0.982565i \(-0.559527\pi\)
0.757965 + 0.652295i \(0.226194\pi\)
\(354\) −2.18693 3.78788i −0.116234 0.201323i
\(355\) 9.87386 17.1020i 0.524050 0.907682i
\(356\) 27.9234i 1.47994i
\(357\) 2.64575i 0.140028i
\(358\) −7.58258 + 4.37780i −0.400752 + 0.231374i
\(359\) −16.0390 + 9.26013i −0.846507 + 0.488731i −0.859471 0.511185i \(-0.829207\pi\)
0.0129639 + 0.999916i \(0.495873\pi\)
\(360\) 3.00000 0.158114
\(361\) 4.50000 + 7.79423i 0.236842 + 0.410223i
\(362\) 10.0507i 0.528253i
\(363\) −1.00000 −0.0524864
\(364\) 12.3131 11.8483i 0.645380 0.621017i
\(365\) −15.0000 −0.785136
\(366\) 6.01450i 0.314383i
\(367\) 1.58258 + 2.74110i 0.0826098 + 0.143084i 0.904370 0.426749i \(-0.140341\pi\)
−0.821760 + 0.569833i \(0.807008\pi\)
\(368\) 1.62614 0.0847682
\(369\) −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
\(373\) 13.0000 22.5167i 0.673114 1.16587i −0.303902 0.952703i \(-0.598289\pi\)
0.977016 0.213165i \(-0.0683772\pi\)
\(374\) −0.791288 1.37055i −0.0409165 0.0708695i
\(375\) 10.5000 6.06218i 0.542218 0.313050i
\(376\) 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 \(0.824458\pi\)
\(380\) −16.4174 −0.842196
\(381\) −2.58258 −0.132309
\(382\) 8.83485 + 5.10080i 0.452030 + 0.260980i
\(383\) 21.3303 + 12.3151i 1.08993 + 0.629270i 0.933557 0.358429i \(-0.116687\pi\)
0.156370 + 0.987698i \(0.450021\pi\)
\(384\) −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
\(387\) −4.58258 −0.232945
\(388\) −0.147917 + 0.0853998i −0.00750934 + 0.00433552i
\(389\) 4.66515 8.08028i 0.236533 0.409686i −0.723184 0.690655i \(-0.757322\pi\)
0.959717 + 0.280969i \(0.0906557\pi\)
\(390\) −1.97822 2.05583i −0.100171 0.104101i
\(391\) 0.582576 0.0294621
\(392\) 10.5000 6.06218i 0.530330 0.306186i
\(393\) −5.29129 + 9.16478i −0.266910 + 0.462302i
\(394\) −3.23049 + 5.59538i −0.162750 + 0.281891i
\(395\) 15.8739 + 9.16478i 0.798701 + 0.461130i
\(396\) 6.20520i 0.311823i
\(397\) −13.9129 8.03260i −0.698267 0.403145i 0.108434 0.994104i \(-0.465416\pi\)
−0.806702 + 0.590959i \(0.798750\pi\)
\(398\) 3.00725i 0.150740i
\(399\) 7.00000 12.1244i 0.350438 0.606977i
\(400\) −2.79129 + 4.83465i −0.139564 + 0.241733i
\(401\) 24.1534i 1.20616i 0.797680 + 0.603081i \(0.206060\pi\)
−0.797680 + 0.603081i \(0.793940\pi\)
\(402\) −1.62614 + 2.81655i −0.0811043 + 0.140477i
\(403\) −2.12614 + 2.04588i −0.105910 + 0.101912i
\(404\) 4.62614 + 8.01270i 0.230159 + 0.398647i
\(405\) −1.50000 0.866025i −0.0745356 0.0430331i
\(406\) 4.23049 + 7.32743i 0.209956 + 0.363654i
\(407\) 6.16515 + 10.6784i 0.305595 + 0.529306i
\(408\) −1.50000 + 0.866025i −0.0742611 + 0.0428746i
\(409\) 20.6893i 1.02302i −0.859278 0.511509i \(-0.829087\pi\)
0.859278 0.511509i \(-0.170913\pi\)
\(410\) 5.55765i 0.274473i
\(411\) 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
\(416\) 16.4174 + 4.73930i 0.804930 + 0.232363i
\(417\) −1.29129 + 2.23658i −0.0632346 + 0.109526i
\(418\) 8.37420i 0.409596i
\(419\) 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 \(0.694968\pi\)
\(422\) −1.02178 0.589925i −0.0497395 0.0287171i
\(423\) 6.10985i 0.297071i
\(424\) 18.2477 + 10.5353i 0.886188 + 0.511641i
\(425\) −1.00000 + 1.73205i −0.0485071 + 0.0840168i
\(426\) −2.60436 + 4.51088i −0.126181 + 0.218553i
\(427\) 30.1652 17.4159i 1.45979 0.842812i
\(428\) −18.9564 −0.916294
\(429\) 9.00000 8.66025i 0.434524 0.418121i
\(430\) 1.81307 3.14033i 0.0874339 0.151440i
\(431\) −16.5826 + 9.57395i −0.798755 + 0.461161i −0.843035 0.537858i \(-0.819234\pi\)
0.0442809 + 0.999019i \(0.485900\pi\)
\(432\) 2.79129 0.134296
\(433\) −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
\(436\) 2.98277 + 1.72210i 0.142849 + 0.0824737i
\(437\) −2.66970 1.54135i −0.127709 0.0737328i
\(438\) 3.95644 0.189046
\(439\) −1.41742 −0.0676500 −0.0338250 0.999428i \(-0.510769\pi\)
−0.0338250 + 0.999428i \(0.510769\pi\)
\(440\) −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 −0.999813 0.0193136i \(-0.993852\pi\)
0.483181 0.875521i \(-0.339481\pi\)
\(444\) 5.52178 3.18800i 0.262052 0.151296i
\(445\) −13.5000 23.3827i −0.639961 1.10845i
\(446\) 0.604356 1.04678i 0.0286171 0.0495663i
\(447\) 17.5112i 0.828252i
\(448\) −7.83030 4.52083i −0.369947 0.213589i
\(449\) 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
\(451\) 24.3303 1.14567
\(452\) 5.52178 + 9.56400i 0.259723 + 0.449853i
\(453\) 9.76465i 0.458784i
\(454\) −9.29583 −0.436275
\(455\) 4.58258 15.8745i 0.214834 0.744208i
\(456\) 9.16515 0.429198
\(457\) 27.9989i 1.30973i 0.755745 + 0.654866i \(0.227275\pi\)
−0.755745 + 0.654866i \(0.772725\pi\)
\(458\) −0.0217804 0.0377247i −0.00101773 0.00176276i
\(459\) 1.00000 0.0466760
\(460\) 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 \(0.971519\pi\)
\(464\) 9.76951 16.9213i 0.453538 0.785551i
\(465\) −0.708712 1.22753i −0.0328657 0.0569251i
\(466\) −0.725947 + 0.419126i −0.0336288 + 0.0194156i
\(467\) −8.45644 14.6470i −0.391317 0.677782i 0.601306 0.799019i \(-0.294647\pi\)
−0.992624 + 0.121237i \(0.961314\pi\)
\(468\) −4.47822 4.65390i −0.207006 0.215127i
\(469\) −18.8348 −0.869713
\(470\) 4.18693 + 2.41733i 0.193129 + 0.111503i
\(471\) −8.16515 −0.376230
\(472\) 16.5826 0.763275
\(473\) 13.7477 + 7.93725i 0.632121 + 0.364955i
\(474\) −4.18693 2.41733i −0.192312 0.111031i
\(475\) 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
\(478\) −13.5826 −0.621253
\(479\) −30.4955 + 17.6066i −1.39337 + 0.804464i −0.993687 0.112188i \(-0.964214\pi\)
−0.399686 + 0.916652i \(0.630881\pi\)
\(480\) −4.10436 + 7.10895i −0.187337 + 0.324478i
\(481\) −12.3303 3.55945i −0.562213 0.162297i
\(482\) 8.04356 0.366374
\(483\) 1.54135i 0.0701339i
\(484\) 0.895644 1.55130i 0.0407111 0.0705137i
\(485\) −0.0825757 + 0.143025i −0.00374957 + 0.00649444i
\(486\) 0.395644 + 0.228425i 0.0179468 + 0.0103616i
\(487\) 37.4775i 1.69827i 0.528179 + 0.849133i \(0.322875\pi\)
−0.528179 + 0.849133i \(0.677125\pi\)
\(488\) 19.7477 + 11.4014i 0.893938 + 0.516115i
\(489\) 3.46410i 0.156652i
\(490\) 2.76951 4.79693i 0.125114 0.216703i
\(491\) 11.8739 20.5661i 0.535860 0.928137i −0.463261 0.886222i \(-0.653321\pi\)
0.999121 0.0419149i \(-0.0133458\pi\)
\(492\) 12.5812i 0.567205i
\(493\) 3.50000 6.06218i 0.157632 0.273027i
\(494\) −6.04356 6.28065i −0.271913 0.282580i
\(495\) 3.00000 + 5.19615i 0.134840 + 0.233550i
\(496\) 1.97822 + 1.14213i 0.0888247 + 0.0512830i
\(497\) −30.1652 −1.35309
\(498\) 0.791288 + 1.37055i 0.0354585 + 0.0614158i
\(499\) −26.2913 + 15.1793i −1.17696 + 0.679518i −0.955309 0.295608i \(-0.904478\pi\)
−0.221650 + 0.975126i \(0.571144\pi\)
\(500\) 21.7182i 0.971268i
\(501\) 11.4014i 0.509375i
\(502\) 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 \(0.638718\pi\)
\(504\) −2.29129 3.96863i −0.102062 0.176777i
\(505\) 7.74773 + 4.47315i 0.344769 + 0.199053i
\(506\) −0.460985 0.798450i −0.0204933 0.0354954i
\(507\) −0.500000 + 12.9904i −0.0222058 + 0.576923i
\(508\) 2.31307 4.00635i 0.102626 0.177753i
\(509\) 3.75015i 0.166223i 0.996540 + 0.0831113i \(0.0264857\pi\)
−0.996540 + 0.0831113i \(0.973514\pi\)
\(510\) −0.395644 + 0.685275i −0.0175194 + 0.0303445i
\(511\) 11.4564 + 19.8431i 0.506803 + 0.877809i
\(512\) 22.8981i 1.01196i
\(513\) −4.58258 2.64575i −0.202326 0.116813i
\(514\) 12.4859i 0.550727i
\(515\) −18.8739 10.8968i −0.831682 0.480172i
\(516\) 4.10436 7.10895i 0.180684 0.312954i
\(517\) −10.5826 + 18.3296i −0.465421 + 0.806133i
\(518\) −3.72595 2.15118i −0.163709 0.0945173i
\(519\) −12.3303 −0.541240
\(520\) 10.5000 2.59808i 0.460455 0.113933i
\(521\) 16.6652 28.8649i 0.730114 1.26459i −0.226721 0.973960i \(-0.572800\pi\)
0.956834 0.290634i \(-0.0938662\pi\)
\(522\) 2.76951 1.59898i 0.121218 0.0699853i
\(523\) 17.7477 0.776054 0.388027 0.921648i \(-0.373157\pi\)
0.388027 + 0.921648i \(0.373157\pi\)
\(524\) −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
\(527\) 0.708712 + 0.409175i 0.0308720 + 0.0178239i
\(528\) −8.37386 4.83465i −0.364426 0.210401i
\(529\) −22.6606 −0.985244
\(530\) 9.62614 0.418133
\(531\) −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
\(535\) −15.8739 + 9.16478i −0.686287 + 0.396228i
\(536\) −6.16515 10.6784i −0.266294 0.461235i
\(537\) −9.58258 + 16.5975i −0.413519 + 0.716235i
\(538\) 0.989150i 0.0426453i
\(539\) 21.0000 + 12.1244i 0.904534 + 0.522233i
\(540\) 2.68693 1.55130i 0.115627 0.0667574i
\(541\) 25.6652 14.8178i 1.10343 0.637066i 0.166311 0.986073i \(-0.446814\pi\)
0.937120 + 0.349007i \(0.113481\pi\)
\(542\) 11.6261 0.499385
\(543\) −11.0000 19.0526i −0.472055 0.817624i
\(544\) 4.73930i 0.203196i
\(545\) 3.33030 0.142654
\(546\) −1.20871 + 4.18710i −0.0517281 + 0.179191i
\(547\) −8.00000 −0.342055 −0.171028 0.985266i \(-0.554709\pi\)
−0.171028 + 0.985266i \(0.554709\pi\)
\(548\) 15.5130i 0.662683i
\(549\) −6.58258 11.4014i −0.280937 0.486598i
\(550\) 3.16515 0.134963
\(551\) −32.0780 + 18.5203i −1.36657 + 0.788990i
\(552\) −0.873864 + 0.504525i −0.0371941 + 0.0214740i
\(553\) 27.9989i 1.19063i
\(554\) 12.4859i 0.530473i
\(555\) 3.08258 5.33918i 0.130848 0.226635i
\(556\) −2.31307 4.00635i −0.0980959 0.169907i
\(557\) −2.83485 + 1.63670i −0.120116 + 0.0693492i −0.558854 0.829266i \(-0.688759\pi\)
0.438738 + 0.898615i \(0.355426\pi\)
\(558\) 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
\(562\) −8.00000 −0.337460
\(563\) 14.5826 0.614582 0.307291 0.951616i \(-0.400577\pi\)
0.307291 + 0.951616i \(0.400577\pi\)
\(564\) 9.47822 + 5.47225i 0.399105 + 0.230423i
\(565\) 9.24773 + 5.33918i 0.389055 + 0.224621i
\(566\) −2.50455 + 1.44600i −0.105274 + 0.0607799i
\(567\) 2.64575i 0.111111i
\(568\) −9.87386 17.1020i −0.414298 0.717585i
\(569\) 31.3303 1.31343 0.656717 0.754137i \(-0.271944\pi\)
0.656717 + 0.754137i \(0.271944\pi\)
\(570\) 3.62614 2.09355i 0.151882 0.0876892i
\(571\) −10.1261 + 17.5390i −0.423766 + 0.733984i −0.996304 0.0858941i \(-0.972625\pi\)
0.572539 + 0.819878i \(0.305959\pi\)
\(572\) 5.37386 + 21.7182i 0.224693 + 0.908084i
\(573\) 22.3303 0.932862
\(574\) −7.35208 + 4.24473i −0.306870 + 0.177171i
\(575\) −0.582576 + 1.00905i −0.0242951 + 0.0420803i
\(576\) −1.70871 + 2.95958i −0.0711963 + 0.123316i
\(577\) 2.91742 + 1.68438i 0.121454 + 0.0701215i 0.559496 0.828833i \(-0.310995\pi\)
−0.438042 + 0.898954i \(0.644328\pi\)
\(578\) 7.30960i 0.304039i
\(579\) −15.1652 8.75560i −0.630242 0.363870i
\(580\) 21.7182i 0.901800i
\(581\) −4.58258 + 7.93725i −0.190117 + 0.329293i
\(582\) 0.0217804 0.0377247i 0.000902826 0.00156374i
\(583\) 42.1413i 1.74532i
\(584\) −7.50000 + 12.9904i −0.310352 + 0.537546i
\(585\) −6.00000 1.73205i −0.248069 0.0716115i
\(586\) 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
\(591\) 14.1425i 0.581743i
\(592\) 9.93545i 0.408345i
\(593\) 12.2477 7.07123i 0.502954 0.290381i −0.226979 0.973900i \(-0.572885\pi\)
0.729933 + 0.683519i \(0.239551\pi\)
\(594\) −0.791288 1.37055i −0.0324669 0.0562344i
\(595\) −4.58258 −0.187867
\(596\) −27.1652 15.6838i −1.11273 0.642434i
\(597\) 3.29129 + 5.70068i 0.134703 + 0.233313i
\(598\) 0.921970 + 0.266150i 0.0377022 + 0.0108837i
\(599\) −17.8739 + 30.9584i −0.730306 + 1.26493i 0.226446 + 0.974024i \(0.427289\pi\)
−0.956752 + 0.290904i \(0.906044\pi\)
\(600\) 3.46410i 0.141421i
\(601\) −3.91742 + 6.78518i −0.159795 + 0.276773i −0.934795 0.355189i \(-0.884417\pi\)
0.775000 + 0.631962i \(0.217750\pi\)
\(602\) −5.53901 −0.225753
\(603\) 7.11890i 0.289904i
\(604\) −15.1479 8.74565i −0.616360 0.355856i
\(605\) 1.73205i 0.0704179i
\(606\) −2.04356 1.17985i −0.0830140 0.0479281i
\(607\) 4.00000 6.92820i 0.162355 0.281207i −0.773358 0.633970i \(-0.781424\pi\)
0.935713 + 0.352763i \(0.114758\pi\)
\(608\) −12.5390 + 21.7182i −0.508524 + 0.880790i
\(609\) 16.0390 + 9.26013i 0.649934 + 0.375239i
\(610\) 10.4174 0.421789
\(611\) −5.29129 21.3845i −0.214063 0.865124i
\(612\) −0.895644 + 1.55130i −0.0362043 + 0.0627076i
\(613\) 2.83485 1.63670i 0.114498 0.0661057i −0.441657 0.897184i \(-0.645609\pi\)
0.556156 + 0.831078i \(0.312276\pi\)
\(614\) 0.0871215 0.00351594
\(615\) −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 \(0.264375\pi\)
\(618\) 4.97822 + 2.87418i 0.200253 + 0.115616i
\(619\) 31.0390 + 17.9204i 1.24756 + 0.720281i 0.970623 0.240606i \(-0.0773462\pi\)
0.276940 + 0.960887i \(0.410680\pi\)
\(620\) 2.53901 0.101969
\(621\) 0.582576 0.0233780
\(622\) 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
\(626\) 12.7259 7.34733i 0.508631 0.293658i
\(627\) 9.16515 + 15.8745i 0.366021 + 0.633967i
\(628\) 7.31307 12.6666i 0.291823 0.505453i
\(629\) 3.55945i 0.141925i
\(630\) −1.81307 1.04678i −0.0722344 0.0417045i
\(631\) −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
\(633\) −2.58258 −0.102648
\(634\) −4.39564 7.61348i −0.174573 0.302370i
\(635\) 4.47315i 0.177512i
\(636\) 21.7913 0.864081
\(637\) −24.5000 + 6.06218i −0.970725 + 0.240192i
\(638\) −11.0780 −0.438583
\(639\) 11.4014i 0.451031i
\(640\) −9.56080 16.5598i −0.377924 0.654583i
\(641\) 38.4955 1.52048 0.760240 0.649643i \(-0.225082\pi\)
0.760240 + 0.649643i \(0.225082\pi\)
\(642\) 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 \(0.285732\pi\)
\(644\) −2.39110 1.38050i −0.0942225 0.0543994i
\(645\) 7.93725i 0.312529i
\(646\) −1.20871 + 2.09355i −0.0475561 + 0.0823697i
\(647\) 0.834849 + 1.44600i 0.0328213 + 0.0568481i 0.881969 0.471307i \(-0.156217\pi\)
−0.849148 + 0.528155i \(0.822884\pi\)
\(648\) −1.50000 + 0.866025i −0.0589256 + 0.0340207i
\(649\) 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
\(653\) −28.4955 −1.11511 −0.557557 0.830139i \(-0.688261\pi\)
−0.557557 + 0.830139i \(0.688261\pi\)
\(654\) −0.878409 −0.0343485
\(655\) −15.8739 9.16478i −0.620243 0.358098i
\(656\) 16.9782 + 9.80238i 0.662888 + 0.382719i
\(657\) 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 \(0.504719\pi\)
\(660\) −10.7477 −0.418355
\(661\) −22.7477 + 13.1334i −0.884784 + 0.510830i −0.872233 0.489091i \(-0.837329\pi\)
−0.0125512 + 0.999921i \(0.503995\pi\)
\(662\) −3.53901 + 6.12975i −0.137548 + 0.238240i
\(663\) 3.50000 0.866025i 0.135929 0.0336336i
\(664\) −6.00000 −0.232845
\(665\) 21.0000 + 12.1244i 0.814345 + 0.470162i
\(666\) −0.813068 + 1.40828i −0.0315058 + 0.0545696i
\(667\) 2.03901 3.53168i 0.0789510 0.136747i
\(668\) −17.6869 10.2116i −0.684328 0.395097i
\(669\) 2.64575i 0.102291i
\(670\) −4.87841 2.81655i −0.188469 0.108813i
\(671\) 45.6054i 1.76058i
\(672\) 12.5390 0.483703
\(673\) −0.665151 + 1.15208i −0.0256397 + 0.0444093i −0.878561 0.477631i \(-0.841496\pi\)
0.852921 + 0.522040i \(0.174829\pi\)
\(674\) 14.3887i 0.554232i
\(675\) −1.00000 + 1.73205i −0.0384900 + 0.0666667i
\(676\) −19.7042 12.4104i −0.757853 0.477323i
\(677\) −24.0826 41.7122i −0.925569 1.60313i −0.790644 0.612276i \(-0.790254\pi\)
−0.134924 0.990856i \(-0.543079\pi\)
\(678\) −2.43920 1.40828i −0.0936771 0.0540845i
\(679\) 0.252273 0.00968135
\(680\) −1.50000 2.59808i −0.0575224 0.0996317i
\(681\) −17.6216 + 10.1738i −0.675261 + 0.389862i
\(682\) 1.29510i 0.0495920i
\(683\) 23.2397i 0.889241i −0.895719 0.444620i \(-0.853339\pi\)
0.895719 0.444620i \(-0.146661\pi\)
\(684\) 8.20871 4.73930i 0.313868 0.181212i
\(685\) 7.50000 + 12.9904i 0.286560 + 0.496337i
\(686\) −8.46099 −0.323042
\(687\) −0.0825757 0.0476751i −0.00315046 0.00181892i
\(688\) 6.39564 + 11.0776i 0.243832 + 0.422329i
\(689\) −30.4129 31.6060i −1.15864 1.20409i
\(690\) −0.230493 + 0.399225i −0.00877470 + 0.0151982i
\(691\) 34.0134i 1.29393i −0.762520 0.646965i \(-0.776038\pi\)
0.762520 0.646965i \(-0.223962\pi\)
\(692\) 11.0436 19.1280i 0.419813 0.727138i
\(693\) 4.58258 7.93725i 0.174078 0.301511i
\(694\) 0.798450i 0.0303087i
\(695\) −3.87386 2.23658i −0.146944 0.0848382i
\(696\) 12.1244i 0.459573i
\(697\) 6.08258 + 3.51178i 0.230394 + 0.133018i
\(698\) −0.0217804 + 0.0377247i −0.000824400 + 0.00142790i
\(699\) −0.917424 + 1.58903i −0.0347002 + 0.0601025i
\(700\) 8.20871 4.73930i 0.310260 0.179129i
\(701\) 34.0000 1.28416 0.642081 0.766637i \(-0.278071\pi\)
0.642081 + 0.766637i \(0.278071\pi\)
\(702\) 1.58258 + 0.456850i 0.0597305 + 0.0172427i
\(703\) 9.41742 16.3115i 0.355185 0.615198i
\(704\) 10.2523 5.91915i 0.386397 0.223086i
\(705\) 10.5826 0.398563
\(706\) −2.83485 4.91010i −0.106691 0.184794i
\(707\) 13.6657i 0.513952i
\(708\) 14.8521 8.57485i 0.558175 0.322263i
\(709\) 16.4174 + 9.47860i 0.616569 + 0.355976i 0.775532 0.631308i \(-0.217482\pi\)
−0.158963 + 0.987285i \(0.550815\pi\)
\(710\) −7.81307 4.51088i −0.293219 0.169290i
\(711\) −10.5826 −0.396878
\(712\) −27.0000 −1.01187
\(713\) 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
\(717\) −25.7477 + 14.8655i −0.961566 + 0.555161i
\(718\) 4.23049 + 7.32743i 0.157881 + 0.273457i
\(719\) −1.16515 + 2.01810i −0.0434528 + 0.0752625i −0.886934 0.461896i \(-0.847169\pi\)
0.843481 + 0.537159i \(0.180502\pi\)
\(720\) 4.83465i 0.180177i
\(721\) 33.2904i 1.23980i
\(722\) 3.56080 2.05583i 0.132519 0.0765099i
\(723\) 15.2477 8.80328i 0.567069 0.327397i
\(724\) 39.4083 1.46460
\(725\) 7.00000 + 12.1244i 0.259973 + 0.450287i
\(726\) 0.456850i 0.0169553i
\(727\) 28.0000 1.03846 0.519231 0.854634i \(-0.326218\pi\)
0.519231 + 0.854634i \(0.326218\pi\)
\(728\) −11.4564 11.9059i −0.424604 0.441261i
\(729\) 1.00000 0.0370370
\(730\) 6.85275i 0.253632i
\(731\) 2.29129 + 3.96863i 0.0847463 + 0.146785i
\(732\) 23.5826 0.871637
\(733\) 10.8303 6.25288i 0.400026 0.230955i −0.286469 0.958090i \(-0.592482\pi\)
0.686495 + 0.727134i \(0.259148\pi\)
\(734\) 1.25227 0.723000i 0.0462222 0.0266864i
\(735\) 12.1244i 0.447214i
\(736\) 2.76100i 0.101772i
\(737\) 12.3303 21.3567i 0.454193 0.786685i
\(738\) 1.60436 + 2.77883i 0.0590572 + 0.102290i
\(739\) 7.41742 4.28245i 0.272854 0.157533i −0.357330 0.933978i \(-0.616313\pi\)
0.630184 + 0.776446i \(0.282979\pi\)
\(740\) 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 \(0.589795\pi\)
\(744\) −1.41742 −0.0519653
\(745\) −30.3303 −1.11122
\(746\) −10.2867 5.93905i −0.376624 0.217444i
\(747\) 3.00000 + 1.73205i 0.109764 + 0.0633724i
\(748\) 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
\(751\) 32.9129 1.20101 0.600504 0.799622i \(-0.294967\pi\)
0.600504 + 0.799622i \(0.294967\pi\)
\(752\) −14.7695 + 8.52718i −0.538589 + 0.310954i
\(753\) 5.70871 9.88778i 0.208037 0.360331i
\(754\) 8.30852 7.99488i 0.302579 0.291156i
\(755\) −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 \(-0.203245\pi\)
\(758\) −4.23049 + 7.32743i −0.153658 + 0.266144i
\(759\) −1.74773 1.00905i −0.0634385 0.0366262i
\(760\) 15.8745i 0.575829i
\(761\) −28.7477 16.5975i −1.04210 0.601659i −0.121676 0.992570i \(-0.538827\pi\)
−0.920429 + 0.390911i \(0.872160\pi\)
\(762\) 1.17985i 0.0427415i
\(763\) −2.54356 4.40558i −0.0920831 0.159493i
\(764\) −20.0000 + 34.6410i −0.723575 + 1.25327i
\(765\) 1.73205i 0.0626224i
\(766\) 5.62614 9.74475i 0.203281 0.352092i
\(767\) −33.1652 9.57395i −1.19752 0.345695i
\(768\) −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 \(0.747609\pi\)
\(770\) 3.62614 + 6.28065i 0.130677 + 0.226339i
\(771\) −13.6652 23.6687i −0.492138 0.852409i
\(772\) 27.1652 15.6838i 0.977695 0.564473i
\(773\) 7.21425i 0.259479i 0.991548 + 0.129739i \(0.0414141\pi\)
−0.991548 + 0.129739i \(0.958586\pi\)
\(774\) 2.09355i 0.0752511i
\(775\)