Properties

Label 91.2.f.b.29.1
Level $91$
Weight $2$
Character 91.29
Analytic conductor $0.727$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 91.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.726638658394\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 29.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 91.29
Dual form 91.2.f.b.22.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 1.50000i) q^{2} +(-1.36603 - 2.36603i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.73205 q^{5} +(-2.36603 + 4.09808i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.73205 q^{8} +(-2.23205 + 3.86603i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 1.50000i) q^{2} +(-1.36603 - 2.36603i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.73205 q^{5} +(-2.36603 + 4.09808i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.73205 q^{8} +(-2.23205 + 3.86603i) q^{9} +(-1.50000 - 2.59808i) q^{10} +(-0.633975 - 1.09808i) q^{11} +2.73205 q^{12} +(3.59808 + 0.232051i) q^{13} +1.73205 q^{14} +(-2.36603 - 4.09808i) q^{15} +(2.50000 + 4.33013i) q^{16} +(3.86603 - 6.69615i) q^{17} +7.73205 q^{18} +(-1.00000 + 1.73205i) q^{19} +(-0.866025 + 1.50000i) q^{20} +2.73205 q^{21} +(-1.09808 + 1.90192i) q^{22} +(-2.36603 - 4.09808i) q^{23} +(2.36603 + 4.09808i) q^{24} -2.00000 q^{25} +(-2.76795 - 5.59808i) q^{26} +4.00000 q^{27} +(-0.500000 - 0.866025i) q^{28} +(1.50000 + 2.59808i) q^{29} +(-4.09808 + 7.09808i) q^{30} +4.19615 q^{31} +(2.59808 - 4.50000i) q^{32} +(-1.73205 + 3.00000i) q^{33} -13.3923 q^{34} +(-0.866025 + 1.50000i) q^{35} +(-2.23205 - 3.86603i) q^{36} +(3.50000 + 6.06218i) q^{37} +3.46410 q^{38} +(-4.36603 - 8.83013i) q^{39} -3.00000 q^{40} +(2.59808 + 4.50000i) q^{41} +(-2.36603 - 4.09808i) q^{42} +(0.0980762 - 0.169873i) q^{43} +1.26795 q^{44} +(-3.86603 + 6.69615i) q^{45} +(-4.09808 + 7.09808i) q^{46} +12.9282 q^{47} +(6.83013 - 11.8301i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(1.73205 + 3.00000i) q^{50} -21.1244 q^{51} +(-2.00000 + 3.00000i) q^{52} -9.92820 q^{53} +(-3.46410 - 6.00000i) q^{54} +(-1.09808 - 1.90192i) q^{55} +(0.866025 - 1.50000i) q^{56} +5.46410 q^{57} +(2.59808 - 4.50000i) q^{58} +(-3.63397 + 6.29423i) q^{59} +4.73205 q^{60} +(2.40192 - 4.16025i) q^{61} +(-3.63397 - 6.29423i) q^{62} +(-2.23205 - 3.86603i) q^{63} +1.00000 q^{64} +(6.23205 + 0.401924i) q^{65} +6.00000 q^{66} +(3.09808 + 5.36603i) q^{67} +(3.86603 + 6.69615i) q^{68} +(-6.46410 + 11.1962i) q^{69} +3.00000 q^{70} +(-3.00000 + 5.19615i) q^{71} +(3.86603 - 6.69615i) q^{72} -3.19615 q^{73} +(6.06218 - 10.5000i) q^{74} +(2.73205 + 4.73205i) q^{75} +(-1.00000 - 1.73205i) q^{76} +1.26795 q^{77} +(-9.46410 + 14.1962i) q^{78} +16.1962 q^{79} +(4.33013 + 7.50000i) q^{80} +(1.23205 + 2.13397i) q^{81} +(4.50000 - 7.79423i) q^{82} -2.19615 q^{83} +(-1.36603 + 2.36603i) q^{84} +(6.69615 - 11.5981i) q^{85} -0.339746 q^{86} +(4.09808 - 7.09808i) q^{87} +(1.09808 + 1.90192i) q^{88} +(-6.46410 - 11.1962i) q^{89} +13.3923 q^{90} +(-2.00000 + 3.00000i) q^{91} +4.73205 q^{92} +(-5.73205 - 9.92820i) q^{93} +(-11.1962 - 19.3923i) q^{94} +(-1.73205 + 3.00000i) q^{95} -14.1962 q^{96} +(-3.19615 + 5.53590i) q^{97} +(-0.866025 + 1.50000i) q^{98} +5.66025 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{3} - 2 q^{4} - 6 q^{6} - 2 q^{7} - 2 q^{9} + O(q^{10}) \) \( 4 q - 2 q^{3} - 2 q^{4} - 6 q^{6} - 2 q^{7} - 2 q^{9} - 6 q^{10} - 6 q^{11} + 4 q^{12} + 4 q^{13} - 6 q^{15} + 10 q^{16} + 12 q^{17} + 24 q^{18} - 4 q^{19} + 4 q^{21} + 6 q^{22} - 6 q^{23} + 6 q^{24} - 8 q^{25} - 18 q^{26} + 16 q^{27} - 2 q^{28} + 6 q^{29} - 6 q^{30} - 4 q^{31} - 12 q^{34} - 2 q^{36} + 14 q^{37} - 14 q^{39} - 12 q^{40} - 6 q^{42} - 10 q^{43} + 12 q^{44} - 12 q^{45} - 6 q^{46} + 24 q^{47} + 10 q^{48} - 2 q^{49} - 36 q^{51} - 8 q^{52} - 12 q^{53} + 6 q^{55} + 8 q^{57} - 18 q^{59} + 12 q^{60} + 20 q^{61} - 18 q^{62} - 2 q^{63} + 4 q^{64} + 18 q^{65} + 24 q^{66} + 2 q^{67} + 12 q^{68} - 12 q^{69} + 12 q^{70} - 12 q^{71} + 12 q^{72} + 8 q^{73} + 4 q^{75} - 4 q^{76} + 12 q^{77} - 24 q^{78} + 44 q^{79} - 2 q^{81} + 18 q^{82} + 12 q^{83} - 2 q^{84} + 6 q^{85} - 36 q^{86} + 6 q^{87} - 6 q^{88} - 12 q^{89} + 12 q^{90} - 8 q^{91} + 12 q^{92} - 16 q^{93} - 24 q^{94} - 36 q^{96} + 8 q^{97} - 12 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(66\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 1.50000i −0.612372 1.06066i −0.990839 0.135045i \(-0.956882\pi\)
0.378467 0.925615i \(-0.376451\pi\)
\(3\) −1.36603 2.36603i −0.788675 1.36603i −0.926779 0.375608i \(-0.877434\pi\)
0.138104 0.990418i \(-0.455899\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 1.73205 0.774597 0.387298 0.921954i \(-0.373408\pi\)
0.387298 + 0.921954i \(0.373408\pi\)
\(6\) −2.36603 + 4.09808i −0.965926 + 1.67303i
\(7\) −0.500000 + 0.866025i −0.188982 + 0.327327i
\(8\) −1.73205 −0.612372
\(9\) −2.23205 + 3.86603i −0.744017 + 1.28868i
\(10\) −1.50000 2.59808i −0.474342 0.821584i
\(11\) −0.633975 1.09808i −0.191151 0.331082i 0.754481 0.656322i \(-0.227889\pi\)
−0.945632 + 0.325239i \(0.894555\pi\)
\(12\) 2.73205 0.788675
\(13\) 3.59808 + 0.232051i 0.997927 + 0.0643593i
\(14\) 1.73205 0.462910
\(15\) −2.36603 4.09808i −0.610905 1.05812i
\(16\) 2.50000 + 4.33013i 0.625000 + 1.08253i
\(17\) 3.86603 6.69615i 0.937649 1.62406i 0.167808 0.985820i \(-0.446331\pi\)
0.769841 0.638236i \(-0.220336\pi\)
\(18\) 7.73205 1.82246
\(19\) −1.00000 + 1.73205i −0.229416 + 0.397360i −0.957635 0.287984i \(-0.907015\pi\)
0.728219 + 0.685344i \(0.240348\pi\)
\(20\) −0.866025 + 1.50000i −0.193649 + 0.335410i
\(21\) 2.73205 0.596182
\(22\) −1.09808 + 1.90192i −0.234111 + 0.405492i
\(23\) −2.36603 4.09808i −0.493350 0.854508i 0.506620 0.862169i \(-0.330895\pi\)
−0.999971 + 0.00766135i \(0.997561\pi\)
\(24\) 2.36603 + 4.09808i 0.482963 + 0.836516i
\(25\) −2.00000 −0.400000
\(26\) −2.76795 5.59808i −0.542839 1.09787i
\(27\) 4.00000 0.769800
\(28\) −0.500000 0.866025i −0.0944911 0.163663i
\(29\) 1.50000 + 2.59808i 0.278543 + 0.482451i 0.971023 0.238987i \(-0.0768152\pi\)
−0.692480 + 0.721437i \(0.743482\pi\)
\(30\) −4.09808 + 7.09808i −0.748203 + 1.29593i
\(31\) 4.19615 0.753651 0.376826 0.926284i \(-0.377016\pi\)
0.376826 + 0.926284i \(0.377016\pi\)
\(32\) 2.59808 4.50000i 0.459279 0.795495i
\(33\) −1.73205 + 3.00000i −0.301511 + 0.522233i
\(34\) −13.3923 −2.29676
\(35\) −0.866025 + 1.50000i −0.146385 + 0.253546i
\(36\) −2.23205 3.86603i −0.372008 0.644338i
\(37\) 3.50000 + 6.06218i 0.575396 + 0.996616i 0.995998 + 0.0893706i \(0.0284856\pi\)
−0.420602 + 0.907245i \(0.638181\pi\)
\(38\) 3.46410 0.561951
\(39\) −4.36603 8.83013i −0.699124 1.41395i
\(40\) −3.00000 −0.474342
\(41\) 2.59808 + 4.50000i 0.405751 + 0.702782i 0.994409 0.105601i \(-0.0336766\pi\)
−0.588657 + 0.808383i \(0.700343\pi\)
\(42\) −2.36603 4.09808i −0.365086 0.632347i
\(43\) 0.0980762 0.169873i 0.0149565 0.0259054i −0.858450 0.512897i \(-0.828572\pi\)
0.873407 + 0.486991i \(0.161906\pi\)
\(44\) 1.26795 0.191151
\(45\) −3.86603 + 6.69615i −0.576313 + 0.998203i
\(46\) −4.09808 + 7.09808i −0.604228 + 1.04655i
\(47\) 12.9282 1.88577 0.942886 0.333115i \(-0.108100\pi\)
0.942886 + 0.333115i \(0.108100\pi\)
\(48\) 6.83013 11.8301i 0.985844 1.70753i
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) 1.73205 + 3.00000i 0.244949 + 0.424264i
\(51\) −21.1244 −2.95800
\(52\) −2.00000 + 3.00000i −0.277350 + 0.416025i
\(53\) −9.92820 −1.36374 −0.681872 0.731472i \(-0.738834\pi\)
−0.681872 + 0.731472i \(0.738834\pi\)
\(54\) −3.46410 6.00000i −0.471405 0.816497i
\(55\) −1.09808 1.90192i −0.148065 0.256455i
\(56\) 0.866025 1.50000i 0.115728 0.200446i
\(57\) 5.46410 0.723738
\(58\) 2.59808 4.50000i 0.341144 0.590879i
\(59\) −3.63397 + 6.29423i −0.473103 + 0.819439i −0.999526 0.0307841i \(-0.990200\pi\)
0.526423 + 0.850223i \(0.323533\pi\)
\(60\) 4.73205 0.610905
\(61\) 2.40192 4.16025i 0.307535 0.532666i −0.670288 0.742101i \(-0.733829\pi\)
0.977822 + 0.209435i \(0.0671626\pi\)
\(62\) −3.63397 6.29423i −0.461515 0.799368i
\(63\) −2.23205 3.86603i −0.281212 0.487073i
\(64\) 1.00000 0.125000
\(65\) 6.23205 + 0.401924i 0.772991 + 0.0498525i
\(66\) 6.00000 0.738549
\(67\) 3.09808 + 5.36603i 0.378490 + 0.655564i 0.990843 0.135020i \(-0.0431100\pi\)
−0.612353 + 0.790585i \(0.709777\pi\)
\(68\) 3.86603 + 6.69615i 0.468824 + 0.812028i
\(69\) −6.46410 + 11.1962i −0.778186 + 1.34786i
\(70\) 3.00000 0.358569
\(71\) −3.00000 + 5.19615i −0.356034 + 0.616670i −0.987294 0.158901i \(-0.949205\pi\)
0.631260 + 0.775571i \(0.282538\pi\)
\(72\) 3.86603 6.69615i 0.455615 0.789149i
\(73\) −3.19615 −0.374081 −0.187041 0.982352i \(-0.559890\pi\)
−0.187041 + 0.982352i \(0.559890\pi\)
\(74\) 6.06218 10.5000i 0.704714 1.22060i
\(75\) 2.73205 + 4.73205i 0.315470 + 0.546410i
\(76\) −1.00000 1.73205i −0.114708 0.198680i
\(77\) 1.26795 0.144496
\(78\) −9.46410 + 14.1962i −1.07160 + 1.60740i
\(79\) 16.1962 1.82221 0.911105 0.412175i \(-0.135231\pi\)
0.911105 + 0.412175i \(0.135231\pi\)
\(80\) 4.33013 + 7.50000i 0.484123 + 0.838525i
\(81\) 1.23205 + 2.13397i 0.136895 + 0.237108i
\(82\) 4.50000 7.79423i 0.496942 0.860729i
\(83\) −2.19615 −0.241059 −0.120530 0.992710i \(-0.538459\pi\)
−0.120530 + 0.992710i \(0.538459\pi\)
\(84\) −1.36603 + 2.36603i −0.149046 + 0.258155i
\(85\) 6.69615 11.5981i 0.726300 1.25799i
\(86\) −0.339746 −0.0366357
\(87\) 4.09808 7.09808i 0.439360 0.760994i
\(88\) 1.09808 + 1.90192i 0.117055 + 0.202746i
\(89\) −6.46410 11.1962i −0.685193 1.18679i −0.973376 0.229214i \(-0.926384\pi\)
0.288183 0.957575i \(-0.406949\pi\)
\(90\) 13.3923 1.41167
\(91\) −2.00000 + 3.00000i −0.209657 + 0.314485i
\(92\) 4.73205 0.493350
\(93\) −5.73205 9.92820i −0.594386 1.02951i
\(94\) −11.1962 19.3923i −1.15479 2.00016i
\(95\) −1.73205 + 3.00000i −0.177705 + 0.307794i
\(96\) −14.1962 −1.44889
\(97\) −3.19615 + 5.53590i −0.324520 + 0.562085i −0.981415 0.191897i \(-0.938536\pi\)
0.656895 + 0.753982i \(0.271869\pi\)
\(98\) −0.866025 + 1.50000i −0.0874818 + 0.151523i
\(99\) 5.66025 0.568877
\(100\) 1.00000 1.73205i 0.100000 0.173205i
\(101\) 3.86603 + 6.69615i 0.384684 + 0.666292i 0.991725 0.128378i \(-0.0409771\pi\)
−0.607041 + 0.794670i \(0.707644\pi\)
\(102\) 18.2942 + 31.6865i 1.81140 + 3.13743i
\(103\) −14.3923 −1.41812 −0.709058 0.705150i \(-0.750880\pi\)
−0.709058 + 0.705150i \(0.750880\pi\)
\(104\) −6.23205 0.401924i −0.611103 0.0394119i
\(105\) 4.73205 0.461801
\(106\) 8.59808 + 14.8923i 0.835119 + 1.44647i
\(107\) 3.92820 + 6.80385i 0.379754 + 0.657753i 0.991026 0.133667i \(-0.0426754\pi\)
−0.611273 + 0.791420i \(0.709342\pi\)
\(108\) −2.00000 + 3.46410i −0.192450 + 0.333333i
\(109\) −8.39230 −0.803837 −0.401919 0.915675i \(-0.631656\pi\)
−0.401919 + 0.915675i \(0.631656\pi\)
\(110\) −1.90192 + 3.29423i −0.181341 + 0.314092i
\(111\) 9.56218 16.5622i 0.907602 1.57201i
\(112\) −5.00000 −0.472456
\(113\) −6.69615 + 11.5981i −0.629921 + 1.09106i 0.357646 + 0.933857i \(0.383579\pi\)
−0.987567 + 0.157198i \(0.949754\pi\)
\(114\) −4.73205 8.19615i −0.443197 0.767640i
\(115\) −4.09808 7.09808i −0.382148 0.661899i
\(116\) −3.00000 −0.278543
\(117\) −8.92820 + 13.3923i −0.825413 + 1.23812i
\(118\) 12.5885 1.15886
\(119\) 3.86603 + 6.69615i 0.354398 + 0.613835i
\(120\) 4.09808 + 7.09808i 0.374101 + 0.647963i
\(121\) 4.69615 8.13397i 0.426923 0.739452i
\(122\) −8.32051 −0.753303
\(123\) 7.09808 12.2942i 0.640012 1.10853i
\(124\) −2.09808 + 3.63397i −0.188413 + 0.326341i
\(125\) −12.1244 −1.08444
\(126\) −3.86603 + 6.69615i −0.344413 + 0.596541i
\(127\) −9.19615 15.9282i −0.816027 1.41340i −0.908588 0.417693i \(-0.862839\pi\)
0.0925619 0.995707i \(-0.470494\pi\)
\(128\) −6.06218 10.5000i −0.535826 0.928078i
\(129\) −0.535898 −0.0471832
\(130\) −4.79423 9.69615i −0.420482 0.850409i
\(131\) −3.46410 −0.302660 −0.151330 0.988483i \(-0.548356\pi\)
−0.151330 + 0.988483i \(0.548356\pi\)
\(132\) −1.73205 3.00000i −0.150756 0.261116i
\(133\) −1.00000 1.73205i −0.0867110 0.150188i
\(134\) 5.36603 9.29423i 0.463554 0.802899i
\(135\) 6.92820 0.596285
\(136\) −6.69615 + 11.5981i −0.574190 + 0.994527i
\(137\) −4.03590 + 6.99038i −0.344810 + 0.597229i −0.985319 0.170722i \(-0.945390\pi\)
0.640509 + 0.767951i \(0.278723\pi\)
\(138\) 22.3923 1.90616
\(139\) 5.29423 9.16987i 0.449051 0.777778i −0.549274 0.835642i \(-0.685096\pi\)
0.998324 + 0.0578639i \(0.0184290\pi\)
\(140\) −0.866025 1.50000i −0.0731925 0.126773i
\(141\) −17.6603 30.5885i −1.48726 2.57601i
\(142\) 10.3923 0.872103
\(143\) −2.02628 4.09808i −0.169446 0.342698i
\(144\) −22.3205 −1.86004
\(145\) 2.59808 + 4.50000i 0.215758 + 0.373705i
\(146\) 2.76795 + 4.79423i 0.229077 + 0.396773i
\(147\) −1.36603 + 2.36603i −0.112668 + 0.195146i
\(148\) −7.00000 −0.575396
\(149\) 3.23205 5.59808i 0.264780 0.458612i −0.702726 0.711461i \(-0.748034\pi\)
0.967506 + 0.252848i \(0.0813674\pi\)
\(150\) 4.73205 8.19615i 0.386370 0.669213i
\(151\) 2.00000 0.162758 0.0813788 0.996683i \(-0.474068\pi\)
0.0813788 + 0.996683i \(0.474068\pi\)
\(152\) 1.73205 3.00000i 0.140488 0.243332i
\(153\) 17.2583 + 29.8923i 1.39525 + 2.41665i
\(154\) −1.09808 1.90192i −0.0884855 0.153261i
\(155\) 7.26795 0.583776
\(156\) 9.83013 + 0.633975i 0.787040 + 0.0507586i
\(157\) 1.19615 0.0954634 0.0477317 0.998860i \(-0.484801\pi\)
0.0477317 + 0.998860i \(0.484801\pi\)
\(158\) −14.0263 24.2942i −1.11587 1.93275i
\(159\) 13.5622 + 23.4904i 1.07555 + 1.86291i
\(160\) 4.50000 7.79423i 0.355756 0.616188i
\(161\) 4.73205 0.372938
\(162\) 2.13397 3.69615i 0.167661 0.290397i
\(163\) −8.09808 + 14.0263i −0.634290 + 1.09862i 0.352375 + 0.935859i \(0.385374\pi\)
−0.986665 + 0.162764i \(0.947959\pi\)
\(164\) −5.19615 −0.405751
\(165\) −3.00000 + 5.19615i −0.233550 + 0.404520i
\(166\) 1.90192 + 3.29423i 0.147618 + 0.255682i
\(167\) 3.29423 + 5.70577i 0.254915 + 0.441526i 0.964872 0.262719i \(-0.0846192\pi\)
−0.709957 + 0.704245i \(0.751286\pi\)
\(168\) −4.73205 −0.365086
\(169\) 12.8923 + 1.66987i 0.991716 + 0.128452i
\(170\) −23.1962 −1.77906
\(171\) −4.46410 7.73205i −0.341378 0.591285i
\(172\) 0.0980762 + 0.169873i 0.00747824 + 0.0129527i
\(173\) −4.26795 + 7.39230i −0.324486 + 0.562027i −0.981408 0.191932i \(-0.938525\pi\)
0.656922 + 0.753958i \(0.271858\pi\)
\(174\) −14.1962 −1.07621
\(175\) 1.00000 1.73205i 0.0755929 0.130931i
\(176\) 3.16987 5.49038i 0.238938 0.413853i
\(177\) 19.8564 1.49250
\(178\) −11.1962 + 19.3923i −0.839187 + 1.45351i
\(179\) 3.46410 + 6.00000i 0.258919 + 0.448461i 0.965953 0.258719i \(-0.0833004\pi\)
−0.707034 + 0.707180i \(0.749967\pi\)
\(180\) −3.86603 6.69615i −0.288157 0.499102i
\(181\) 5.58846 0.415387 0.207693 0.978194i \(-0.433404\pi\)
0.207693 + 0.978194i \(0.433404\pi\)
\(182\) 6.23205 + 0.401924i 0.461950 + 0.0297926i
\(183\) −13.1244 −0.970180
\(184\) 4.09808 + 7.09808i 0.302114 + 0.523277i
\(185\) 6.06218 + 10.5000i 0.445700 + 0.771975i
\(186\) −9.92820 + 17.1962i −0.727971 + 1.26088i
\(187\) −9.80385 −0.716928
\(188\) −6.46410 + 11.1962i −0.471443 + 0.816563i
\(189\) −2.00000 + 3.46410i −0.145479 + 0.251976i
\(190\) 6.00000 0.435286
\(191\) −2.36603 + 4.09808i −0.171200 + 0.296526i −0.938840 0.344355i \(-0.888098\pi\)
0.767640 + 0.640881i \(0.221431\pi\)
\(192\) −1.36603 2.36603i −0.0985844 0.170753i
\(193\) −2.50000 4.33013i −0.179954 0.311689i 0.761911 0.647682i \(-0.224262\pi\)
−0.941865 + 0.335993i \(0.890928\pi\)
\(194\) 11.0718 0.794909
\(195\) −7.56218 15.2942i −0.541539 1.09524i
\(196\) 1.00000 0.0714286
\(197\) −6.00000 10.3923i −0.427482 0.740421i 0.569166 0.822222i \(-0.307266\pi\)
−0.996649 + 0.0818013i \(0.973933\pi\)
\(198\) −4.90192 8.49038i −0.348365 0.603385i
\(199\) −1.00000 + 1.73205i −0.0708881 + 0.122782i −0.899291 0.437351i \(-0.855917\pi\)
0.828403 + 0.560133i \(0.189250\pi\)
\(200\) 3.46410 0.244949
\(201\) 8.46410 14.6603i 0.597012 1.03405i
\(202\) 6.69615 11.5981i 0.471140 0.816038i
\(203\) −3.00000 −0.210559
\(204\) 10.5622 18.2942i 0.739500 1.28085i
\(205\) 4.50000 + 7.79423i 0.314294 + 0.544373i
\(206\) 12.4641 + 21.5885i 0.868415 + 1.50414i
\(207\) 21.1244 1.46824
\(208\) 7.99038 + 16.1603i 0.554033 + 1.12051i
\(209\) 2.53590 0.175412
\(210\) −4.09808 7.09808i −0.282794 0.489814i
\(211\) 0.901924 + 1.56218i 0.0620910 + 0.107545i 0.895400 0.445263i \(-0.146890\pi\)
−0.833309 + 0.552808i \(0.813556\pi\)
\(212\) 4.96410 8.59808i 0.340936 0.590518i
\(213\) 16.3923 1.12318
\(214\) 6.80385 11.7846i 0.465101 0.805579i
\(215\) 0.169873 0.294229i 0.0115852 0.0200662i
\(216\) −6.92820 −0.471405
\(217\) −2.09808 + 3.63397i −0.142427 + 0.246690i
\(218\) 7.26795 + 12.5885i 0.492248 + 0.852598i
\(219\) 4.36603 + 7.56218i 0.295029 + 0.511005i
\(220\) 2.19615 0.148065
\(221\) 15.4641 23.1962i 1.04023 1.56034i
\(222\) −33.1244 −2.22316
\(223\) 5.00000 + 8.66025i 0.334825 + 0.579934i 0.983451 0.181173i \(-0.0579895\pi\)
−0.648626 + 0.761107i \(0.724656\pi\)
\(224\) 2.59808 + 4.50000i 0.173591 + 0.300669i
\(225\) 4.46410 7.73205i 0.297607 0.515470i
\(226\) 23.1962 1.54299
\(227\) −2.83013 + 4.90192i −0.187842 + 0.325352i −0.944531 0.328424i \(-0.893483\pi\)
0.756688 + 0.653776i \(0.226816\pi\)
\(228\) −2.73205 + 4.73205i −0.180934 + 0.313388i
\(229\) −14.3923 −0.951070 −0.475535 0.879697i \(-0.657746\pi\)
−0.475535 + 0.879697i \(0.657746\pi\)
\(230\) −7.09808 + 12.2942i −0.468033 + 0.810657i
\(231\) −1.73205 3.00000i −0.113961 0.197386i
\(232\) −2.59808 4.50000i −0.170572 0.295439i
\(233\) −1.85641 −0.121617 −0.0608086 0.998149i \(-0.519368\pi\)
−0.0608086 + 0.998149i \(0.519368\pi\)
\(234\) 27.8205 + 1.79423i 1.81868 + 0.117292i
\(235\) 22.3923 1.46071
\(236\) −3.63397 6.29423i −0.236552 0.409719i
\(237\) −22.1244 38.3205i −1.43713 2.48918i
\(238\) 6.69615 11.5981i 0.434047 0.751792i
\(239\) −15.8038 −1.02227 −0.511133 0.859502i \(-0.670774\pi\)
−0.511133 + 0.859502i \(0.670774\pi\)
\(240\) 11.8301 20.4904i 0.763631 1.32265i
\(241\) 10.5981 18.3564i 0.682682 1.18244i −0.291477 0.956578i \(-0.594147\pi\)
0.974159 0.225862i \(-0.0725199\pi\)
\(242\) −16.2679 −1.04574
\(243\) 9.36603 16.2224i 0.600831 1.04067i
\(244\) 2.40192 + 4.16025i 0.153767 + 0.266333i
\(245\) −0.866025 1.50000i −0.0553283 0.0958315i
\(246\) −24.5885 −1.56770
\(247\) −4.00000 + 6.00000i −0.254514 + 0.381771i
\(248\) −7.26795 −0.461515
\(249\) 3.00000 + 5.19615i 0.190117 + 0.329293i
\(250\) 10.5000 + 18.1865i 0.664078 + 1.15022i
\(251\) 0.803848 1.39230i 0.0507384 0.0878815i −0.839541 0.543297i \(-0.817176\pi\)
0.890279 + 0.455415i \(0.150509\pi\)
\(252\) 4.46410 0.281212
\(253\) −3.00000 + 5.19615i −0.188608 + 0.326679i
\(254\) −15.9282 + 27.5885i −0.999424 + 1.73105i
\(255\) −36.5885 −2.29126
\(256\) −9.50000 + 16.4545i −0.593750 + 1.02841i
\(257\) −3.06218 5.30385i −0.191013 0.330845i 0.754573 0.656216i \(-0.227844\pi\)
−0.945586 + 0.325371i \(0.894511\pi\)
\(258\) 0.464102 + 0.803848i 0.0288937 + 0.0500454i
\(259\) −7.00000 −0.434959
\(260\) −3.46410 + 5.19615i −0.214834 + 0.322252i
\(261\) −13.3923 −0.828963
\(262\) 3.00000 + 5.19615i 0.185341 + 0.321019i
\(263\) −0.633975 1.09808i −0.0390925 0.0677103i 0.845817 0.533473i \(-0.179113\pi\)
−0.884910 + 0.465763i \(0.845780\pi\)
\(264\) 3.00000 5.19615i 0.184637 0.319801i
\(265\) −17.1962 −1.05635
\(266\) −1.73205 + 3.00000i −0.106199 + 0.183942i
\(267\) −17.6603 + 30.5885i −1.08079 + 1.87198i
\(268\) −6.19615 −0.378490
\(269\) −2.53590 + 4.39230i −0.154616 + 0.267804i −0.932919 0.360086i \(-0.882748\pi\)
0.778303 + 0.627889i \(0.216081\pi\)
\(270\) −6.00000 10.3923i −0.365148 0.632456i
\(271\) −2.90192 5.02628i −0.176279 0.305325i 0.764324 0.644832i \(-0.223073\pi\)
−0.940603 + 0.339508i \(0.889740\pi\)
\(272\) 38.6603 2.34412
\(273\) 9.83013 + 0.633975i 0.594946 + 0.0383699i
\(274\) 13.9808 0.844609
\(275\) 1.26795 + 2.19615i 0.0764602 + 0.132433i
\(276\) −6.46410 11.1962i −0.389093 0.673929i
\(277\) −8.50000 + 14.7224i −0.510716 + 0.884585i 0.489207 + 0.872167i \(0.337286\pi\)
−0.999923 + 0.0124177i \(0.996047\pi\)
\(278\) −18.3397 −1.09994
\(279\) −9.36603 + 16.2224i −0.560729 + 0.971212i
\(280\) 1.50000 2.59808i 0.0896421 0.155265i
\(281\) 13.3923 0.798918 0.399459 0.916751i \(-0.369198\pi\)
0.399459 + 0.916751i \(0.369198\pi\)
\(282\) −30.5885 + 52.9808i −1.82152 + 3.15496i
\(283\) −5.09808 8.83013i −0.303049 0.524897i 0.673776 0.738936i \(-0.264671\pi\)
−0.976825 + 0.214039i \(0.931338\pi\)
\(284\) −3.00000 5.19615i −0.178017 0.308335i
\(285\) 9.46410 0.560605
\(286\) −4.39230 + 6.58846i −0.259722 + 0.389584i
\(287\) −5.19615 −0.306719
\(288\) 11.5981 + 20.0885i 0.683423 + 1.18372i
\(289\) −21.3923 37.0526i −1.25837 2.17956i
\(290\) 4.50000 7.79423i 0.264249 0.457693i
\(291\) 17.4641 1.02376
\(292\) 1.59808 2.76795i 0.0935203 0.161982i
\(293\) 0.401924 0.696152i 0.0234806 0.0406697i −0.854046 0.520197i \(-0.825859\pi\)
0.877527 + 0.479527i \(0.159192\pi\)
\(294\) 4.73205 0.275979
\(295\) −6.29423 + 10.9019i −0.366464 + 0.634735i
\(296\) −6.06218 10.5000i −0.352357 0.610300i
\(297\) −2.53590 4.39230i −0.147148 0.254867i
\(298\) −11.1962 −0.648576
\(299\) −7.56218 15.2942i −0.437332 0.884488i
\(300\) −5.46410 −0.315470
\(301\) 0.0980762 + 0.169873i 0.00565302 + 0.00979132i
\(302\) −1.73205 3.00000i −0.0996683 0.172631i
\(303\) 10.5622 18.2942i 0.606781 1.05098i
\(304\) −10.0000 −0.573539
\(305\) 4.16025 7.20577i 0.238215 0.412601i
\(306\) 29.8923 51.7750i 1.70883 2.95978i
\(307\) −4.58846 −0.261877 −0.130939 0.991390i \(-0.541799\pi\)
−0.130939 + 0.991390i \(0.541799\pi\)
\(308\) −0.633975 + 1.09808i −0.0361241 + 0.0625687i
\(309\) 19.6603 + 34.0526i 1.11843 + 1.93718i
\(310\) −6.29423 10.9019i −0.357488 0.619188i
\(311\) 1.26795 0.0718988 0.0359494 0.999354i \(-0.488554\pi\)
0.0359494 + 0.999354i \(0.488554\pi\)
\(312\) 7.56218 + 15.2942i 0.428124 + 0.865865i
\(313\) 28.7846 1.62700 0.813501 0.581563i \(-0.197559\pi\)
0.813501 + 0.581563i \(0.197559\pi\)
\(314\) −1.03590 1.79423i −0.0584591 0.101254i
\(315\) −3.86603 6.69615i −0.217826 0.377285i
\(316\) −8.09808 + 14.0263i −0.455552 + 0.789040i
\(317\) −6.46410 −0.363060 −0.181530 0.983385i \(-0.558105\pi\)
−0.181530 + 0.983385i \(0.558105\pi\)
\(318\) 23.4904 40.6865i 1.31728 2.28159i
\(319\) 1.90192 3.29423i 0.106487 0.184441i
\(320\) 1.73205 0.0968246
\(321\) 10.7321 18.5885i 0.599005 1.03751i
\(322\) −4.09808 7.09808i −0.228377 0.395560i
\(323\) 7.73205 + 13.3923i 0.430223 + 0.745168i
\(324\) −2.46410 −0.136895
\(325\) −7.19615 0.464102i −0.399171 0.0257437i
\(326\) 28.0526 1.55369
\(327\) 11.4641 + 19.8564i 0.633966 + 1.09806i
\(328\) −4.50000 7.79423i −0.248471 0.430364i
\(329\) −6.46410 + 11.1962i −0.356377 + 0.617264i
\(330\) 10.3923 0.572078
\(331\) −12.4904 + 21.6340i −0.686533 + 1.18911i 0.286419 + 0.958105i \(0.407535\pi\)
−0.972952 + 0.231006i \(0.925798\pi\)
\(332\) 1.09808 1.90192i 0.0602648 0.104382i
\(333\) −31.2487 −1.71242
\(334\) 5.70577 9.88269i 0.312206 0.540757i
\(335\) 5.36603 + 9.29423i 0.293177 + 0.507798i
\(336\) 6.83013 + 11.8301i 0.372614 + 0.645386i
\(337\) 11.0000 0.599208 0.299604 0.954064i \(-0.403145\pi\)
0.299604 + 0.954064i \(0.403145\pi\)
\(338\) −8.66025 20.7846i −0.471056 1.13053i
\(339\) 36.5885 1.98721
\(340\) 6.69615 + 11.5981i 0.363150 + 0.628994i
\(341\) −2.66025 4.60770i −0.144061 0.249521i
\(342\) −7.73205 + 13.3923i −0.418101 + 0.724173i
\(343\) 1.00000 0.0539949
\(344\) −0.169873 + 0.294229i −0.00915894 + 0.0158637i
\(345\) −11.1962 + 19.3923i −0.602781 + 1.04405i
\(346\) 14.7846 0.794826
\(347\) −3.63397 + 6.29423i −0.195082 + 0.337892i −0.946927 0.321448i \(-0.895831\pi\)
0.751845 + 0.659339i \(0.229164\pi\)
\(348\) 4.09808 + 7.09808i 0.219680 + 0.380497i
\(349\) 12.3923 + 21.4641i 0.663345 + 1.14895i 0.979731 + 0.200317i \(0.0641971\pi\)
−0.316386 + 0.948630i \(0.602470\pi\)
\(350\) −3.46410 −0.185164
\(351\) 14.3923 + 0.928203i 0.768204 + 0.0495438i
\(352\) −6.58846 −0.351166
\(353\) −10.3301 17.8923i −0.549817 0.952311i −0.998287 0.0585131i \(-0.981364\pi\)
0.448469 0.893798i \(-0.351969\pi\)
\(354\) −17.1962 29.7846i −0.913965 1.58303i
\(355\) −5.19615 + 9.00000i −0.275783 + 0.477670i
\(356\) 12.9282 0.685193
\(357\) 10.5622 18.2942i 0.559010 0.968233i
\(358\) 6.00000 10.3923i 0.317110 0.549250i
\(359\) 18.9282 0.998992 0.499496 0.866316i \(-0.333518\pi\)
0.499496 + 0.866316i \(0.333518\pi\)
\(360\) 6.69615 11.5981i 0.352918 0.611272i
\(361\) 7.50000 + 12.9904i 0.394737 + 0.683704i
\(362\) −4.83975 8.38269i −0.254371 0.440584i
\(363\) −25.6603 −1.34681
\(364\) −1.59808 3.23205i −0.0837620 0.169405i
\(365\) −5.53590 −0.289762
\(366\) 11.3660 + 19.6865i 0.594112 + 1.02903i
\(367\) −2.09808 3.63397i −0.109519 0.189692i 0.806057 0.591838i \(-0.201598\pi\)
−0.915575 + 0.402146i \(0.868264\pi\)
\(368\) 11.8301 20.4904i 0.616688 1.06813i
\(369\) −23.1962 −1.20754
\(370\) 10.5000 18.1865i 0.545869 0.945473i
\(371\) 4.96410 8.59808i 0.257723 0.446390i
\(372\) 11.4641 0.594386
\(373\) 5.69615 9.86603i 0.294936 0.510843i −0.680034 0.733180i \(-0.738035\pi\)
0.974970 + 0.222337i \(0.0713685\pi\)
\(374\) 8.49038 + 14.7058i 0.439027 + 0.760417i
\(375\) 16.5622 + 28.6865i 0.855267 + 1.48137i
\(376\) −22.3923 −1.15479
\(377\) 4.79423 + 9.69615i 0.246915 + 0.499377i
\(378\) 6.92820 0.356348
\(379\) −13.2942 23.0263i −0.682879 1.18278i −0.974098 0.226124i \(-0.927394\pi\)
0.291220 0.956656i \(-0.405939\pi\)
\(380\) −1.73205 3.00000i −0.0888523 0.153897i
\(381\) −25.1244 + 43.5167i −1.28716 + 2.22943i
\(382\) 8.19615 0.419352
\(383\) 5.83013 10.0981i 0.297906 0.515988i −0.677751 0.735291i \(-0.737045\pi\)
0.975657 + 0.219304i \(0.0703786\pi\)
\(384\) −16.5622 + 28.6865i −0.845185 + 1.46390i
\(385\) 2.19615 0.111926
\(386\) −4.33013 + 7.50000i −0.220398 + 0.381740i
\(387\) 0.437822 + 0.758330i 0.0222558 + 0.0385481i
\(388\) −3.19615 5.53590i −0.162260 0.281043i
\(389\) −23.5359 −1.19332 −0.596659 0.802495i \(-0.703505\pi\)
−0.596659 + 0.802495i \(0.703505\pi\)
\(390\) −16.3923 + 24.5885i −0.830057 + 1.24508i
\(391\) −36.5885 −1.85036
\(392\) 0.866025 + 1.50000i 0.0437409 + 0.0757614i
\(393\) 4.73205 + 8.19615i 0.238700 + 0.413441i
\(394\) −10.3923 + 18.0000i −0.523557 + 0.906827i
\(395\) 28.0526 1.41148
\(396\) −2.83013 + 4.90192i −0.142219 + 0.246331i
\(397\) 9.39230 16.2679i 0.471386 0.816465i −0.528078 0.849196i \(-0.677087\pi\)
0.999464 + 0.0327309i \(0.0104204\pi\)
\(398\) 3.46410 0.173640
\(399\) −2.73205 + 4.73205i −0.136774 + 0.236899i
\(400\) −5.00000 8.66025i −0.250000 0.433013i
\(401\) 5.42820 + 9.40192i 0.271072 + 0.469510i 0.969136 0.246525i \(-0.0792887\pi\)
−0.698065 + 0.716034i \(0.745955\pi\)
\(402\) −29.3205 −1.46237
\(403\) 15.0981 + 0.973721i 0.752089 + 0.0485045i
\(404\) −7.73205 −0.384684
\(405\) 2.13397 + 3.69615i 0.106038 + 0.183663i
\(406\) 2.59808 + 4.50000i 0.128940 + 0.223331i
\(407\) 4.43782 7.68653i 0.219975 0.381007i
\(408\) 36.5885 1.81140
\(409\) 8.40192 14.5526i 0.415448 0.719578i −0.580027 0.814597i \(-0.696958\pi\)
0.995475 + 0.0950195i \(0.0302913\pi\)
\(410\) 7.79423 13.5000i 0.384930 0.666717i
\(411\) 22.0526 1.08777
\(412\) 7.19615 12.4641i 0.354529 0.614062i
\(413\) −3.63397 6.29423i −0.178816 0.309719i
\(414\) −18.2942 31.6865i −0.899112 1.55731i
\(415\) −3.80385 −0.186724
\(416\) 10.3923 15.5885i 0.509525 0.764287i
\(417\) −28.9282 −1.41662
\(418\) −2.19615 3.80385i −0.107417 0.186052i
\(419\) 16.0981 + 27.8827i 0.786442 + 1.36216i 0.928134 + 0.372247i \(0.121413\pi\)
−0.141691 + 0.989911i \(0.545254\pi\)
\(420\) −2.36603 + 4.09808i −0.115450 + 0.199966i
\(421\) −32.1769 −1.56821 −0.784103 0.620630i \(-0.786877\pi\)
−0.784103 + 0.620630i \(0.786877\pi\)
\(422\) 1.56218 2.70577i 0.0760456 0.131715i
\(423\) −28.8564 + 49.9808i −1.40305 + 2.43015i
\(424\) 17.1962 0.835119
\(425\) −7.73205 + 13.3923i −0.375060 + 0.649622i
\(426\) −14.1962 24.5885i −0.687806 1.19131i
\(427\) 2.40192 + 4.16025i 0.116237 + 0.201329i
\(428\) −7.85641 −0.379754
\(429\) −6.92820 + 10.3923i −0.334497 + 0.501745i
\(430\) −0.588457 −0.0283779
\(431\) −0.339746 0.588457i −0.0163650 0.0283450i 0.857727 0.514106i \(-0.171876\pi\)
−0.874092 + 0.485761i \(0.838543\pi\)
\(432\) 10.0000 + 17.3205i 0.481125 + 0.833333i
\(433\) 6.79423 11.7679i 0.326510 0.565532i −0.655307 0.755363i \(-0.727461\pi\)
0.981817 + 0.189831i \(0.0607941\pi\)
\(434\) 7.26795 0.348873
\(435\) 7.09808 12.2942i 0.340327 0.589463i
\(436\) 4.19615 7.26795i 0.200959 0.348072i
\(437\) 9.46410 0.452729
\(438\) 7.56218 13.0981i 0.361335 0.625850i
\(439\) −7.29423 12.6340i −0.348135 0.602987i 0.637784 0.770216i \(-0.279851\pi\)
−0.985918 + 0.167229i \(0.946518\pi\)
\(440\) 1.90192 + 3.29423i 0.0906707 + 0.157046i
\(441\) 4.46410 0.212576
\(442\) −48.1865 3.10770i −2.29200 0.147818i
\(443\) 23.3205 1.10799 0.553995 0.832520i \(-0.313103\pi\)
0.553995 + 0.832520i \(0.313103\pi\)
\(444\) 9.56218 + 16.5622i 0.453801 + 0.786006i
\(445\) −11.1962 19.3923i −0.530749 0.919283i
\(446\) 8.66025 15.0000i 0.410075 0.710271i
\(447\) −17.6603 −0.835301
\(448\) −0.500000 + 0.866025i −0.0236228 + 0.0409159i
\(449\) 6.00000 10.3923i 0.283158 0.490443i −0.689003 0.724758i \(-0.741951\pi\)
0.972161 + 0.234315i \(0.0752847\pi\)
\(450\) −15.4641 −0.728985
\(451\) 3.29423 5.70577i 0.155119 0.268674i
\(452\) −6.69615 11.5981i −0.314961 0.545528i
\(453\) −2.73205 4.73205i −0.128363 0.222331i
\(454\) 9.80385 0.460117
\(455\) −3.46410 + 5.19615i −0.162400 + 0.243599i
\(456\) −9.46410 −0.443197
\(457\) −5.50000 9.52628i −0.257279 0.445621i 0.708233 0.705979i \(-0.249493\pi\)
−0.965512 + 0.260358i \(0.916159\pi\)
\(458\) 12.4641 + 21.5885i 0.582409 + 1.00876i
\(459\) 15.4641 26.7846i 0.721802 1.25020i
\(460\) 8.19615 0.382148
\(461\) 7.79423 13.5000i 0.363013 0.628758i −0.625442 0.780271i \(-0.715081\pi\)
0.988455 + 0.151513i \(0.0484146\pi\)
\(462\) −3.00000 + 5.19615i −0.139573 + 0.241747i
\(463\) −4.58846 −0.213244 −0.106622 0.994300i \(-0.534003\pi\)
−0.106622 + 0.994300i \(0.534003\pi\)
\(464\) −7.50000 + 12.9904i −0.348179 + 0.603063i
\(465\) −9.92820 17.1962i −0.460409 0.797452i
\(466\) 1.60770 + 2.78461i 0.0744750 + 0.128995i
\(467\) 25.5167 1.18077 0.590385 0.807122i \(-0.298976\pi\)
0.590385 + 0.807122i \(0.298976\pi\)
\(468\) −7.13397 14.4282i −0.329768 0.666944i
\(469\) −6.19615 −0.286112
\(470\) −19.3923 33.5885i −0.894500 1.54932i
\(471\) −1.63397 2.83013i −0.0752896 0.130405i
\(472\) 6.29423 10.9019i 0.289715 0.501802i
\(473\) −0.248711 −0.0114358
\(474\) −38.3205 + 66.3731i −1.76012 + 3.04862i
\(475\) 2.00000 3.46410i 0.0917663 0.158944i
\(476\) −7.73205 −0.354398
\(477\) 22.1603 38.3827i 1.01465 1.75742i
\(478\) 13.6865 + 23.7058i 0.626007 + 1.08428i
\(479\) −0.633975 1.09808i −0.0289670 0.0501724i 0.851178 0.524876i \(-0.175888\pi\)
−0.880146 + 0.474704i \(0.842555\pi\)
\(480\) −24.5885 −1.12230
\(481\) 11.1865 + 22.6244i 0.510062 + 1.03158i
\(482\) −36.7128 −1.67222
\(483\) −6.46410 11.1962i −0.294127 0.509443i
\(484\) 4.69615 + 8.13397i 0.213461 + 0.369726i
\(485\) −5.53590 + 9.58846i −0.251372 + 0.435389i
\(486\) −32.4449 −1.47173
\(487\) −20.3923 + 35.3205i −0.924064 + 1.60052i −0.131003 + 0.991382i \(0.541820\pi\)
−0.793060 + 0.609143i \(0.791514\pi\)
\(488\) −4.16025 + 7.20577i −0.188326 + 0.326190i
\(489\) 44.2487 2.00100
\(490\) −1.50000 + 2.59808i −0.0677631 + 0.117369i
\(491\) −3.80385 6.58846i −0.171665 0.297333i 0.767337 0.641244i \(-0.221581\pi\)
−0.939002 + 0.343911i \(0.888248\pi\)
\(492\) 7.09808 + 12.2942i 0.320006 + 0.554267i
\(493\) 23.1962 1.04470
\(494\) 12.4641 + 0.803848i 0.560786 + 0.0361668i
\(495\) 9.80385 0.440650
\(496\) 10.4904 + 18.1699i 0.471032 + 0.815851i
\(497\) −3.00000 5.19615i −0.134568 0.233079i
\(498\) 5.19615 9.00000i 0.232845 0.403300i
\(499\) −38.9808 −1.74502 −0.872509 0.488598i \(-0.837509\pi\)
−0.872509 + 0.488598i \(0.837509\pi\)
\(500\) 6.06218 10.5000i 0.271109 0.469574i
\(501\) 9.00000 15.5885i 0.402090 0.696441i
\(502\) −2.78461 −0.124283
\(503\) 9.29423 16.0981i 0.414409 0.717778i −0.580957 0.813934i \(-0.697322\pi\)
0.995366 + 0.0961565i \(0.0306549\pi\)
\(504\) 3.86603 + 6.69615i 0.172206 + 0.298270i
\(505\) 6.69615 + 11.5981i 0.297975 + 0.516108i
\(506\) 10.3923 0.461994
\(507\) −13.6603 32.7846i −0.606673 1.45602i
\(508\) 18.3923 0.816027
\(509\) −6.86603 11.8923i −0.304331 0.527117i 0.672781 0.739842i \(-0.265100\pi\)
−0.977112 + 0.212725i \(0.931766\pi\)
\(510\) 31.6865 + 54.8827i 1.40310 + 2.43025i
\(511\) 1.59808 2.76795i 0.0706947 0.122447i
\(512\) 8.66025 0.382733
\(513\) −4.00000 + 6.92820i −0.176604 + 0.305888i
\(514\) −5.30385 + 9.18653i −0.233943 + 0.405201i
\(515\) −24.9282 −1.09847
\(516\) 0.267949 0.464102i 0.0117958 0.0204309i
\(517\) −8.19615 14.1962i −0.360466 0.624346i
\(518\) 6.06218 + 10.5000i 0.266357 + 0.461344i
\(519\) 23.3205 1.02366
\(520\) −10.7942 0.696152i −0.473358 0.0305283i
\(521\) −24.1244 −1.05691 −0.528454 0.848962i \(-0.677228\pi\)
−0.528454 + 0.848962i \(0.677228\pi\)
\(522\) 11.5981 + 20.0885i 0.507634 + 0.879248i
\(523\) 14.5885 + 25.2679i 0.637909 + 1.10489i 0.985891 + 0.167389i \(0.0535336\pi\)
−0.347982 + 0.937501i \(0.613133\pi\)
\(524\) 1.73205 3.00000i 0.0756650 0.131056i
\(525\) −5.46410 −0.238473
\(526\) −1.09808 + 1.90192i −0.0478784 + 0.0829278i
\(527\) 16.2224 28.0981i 0.706660 1.22397i
\(528\) −17.3205 −0.753778
\(529\) 0.303848 0.526279i 0.0132108 0.0228817i
\(530\) 14.8923 + 25.7942i 0.646880 + 1.12043i
\(531\) −16.2224 28.0981i −0.703994 1.21935i
\(532\) 2.00000 0.0867110
\(533\) 8.30385 + 16.7942i 0.359680 + 0.727439i
\(534\) 61.1769 2.64738
\(535\) 6.80385 + 11.7846i 0.294156 + 0.509493i
\(536\) −5.36603 9.29423i −0.231777 0.401450i
\(537\) 9.46410 16.3923i 0.408406 0.707380i
\(538\) 8.78461 0.378731
\(539\) −0.633975 + 1.09808i −0.0273072 + 0.0472975i
\(540\) −3.46410 + 6.00000i −0.149071 + 0.258199i
\(541\) −14.6077 −0.628034 −0.314017 0.949417i \(-0.601675\pi\)
−0.314017 + 0.949417i \(0.601675\pi\)
\(542\) −5.02628 + 8.70577i −0.215897 + 0.373945i
\(543\) −7.63397 13.2224i −0.327605 0.567429i
\(544\) −20.0885 34.7942i −0.861285 1.49179i
\(545\) −14.5359 −0.622649
\(546\) −7.56218 15.2942i −0.323631 0.654533i
\(547\) 17.8038 0.761238 0.380619 0.924732i \(-0.375711\pi\)
0.380619 + 0.924732i \(0.375711\pi\)
\(548\) −4.03590 6.99038i −0.172405 0.298614i
\(549\) 10.7224 + 18.5718i 0.457622 + 0.792625i
\(550\) 2.19615 3.80385i 0.0936443 0.162197i
\(551\) −6.00000 −0.255609
\(552\) 11.1962 19.3923i 0.476540 0.825391i
\(553\) −8.09808 + 14.0263i −0.344365 + 0.596458i
\(554\) 29.4449 1.25099
\(555\) 16.5622 28.6865i 0.703025 1.21768i
\(556\) 5.29423 + 9.16987i 0.224525 + 0.388889i
\(557\) −21.8205 37.7942i −0.924565 1.60139i −0.792260 0.610184i \(-0.791096\pi\)
−0.132305 0.991209i \(-0.542238\pi\)
\(558\) 32.4449 1.37350
\(559\) 0.392305 0.588457i 0.0165927 0.0248891i
\(560\) −8.66025 −0.365963
\(561\) 13.3923 + 23.1962i 0.565424 + 0.979342i
\(562\) −11.5981 20.0885i −0.489235 0.847380i
\(563\) −14.0263 + 24.2942i −0.591137 + 1.02388i 0.402942 + 0.915225i \(0.367987\pi\)
−0.994080 + 0.108654i \(0.965346\pi\)
\(564\) 35.3205 1.48726
\(565\) −11.5981 + 20.0885i −0.487935 + 0.845128i
\(566\) −8.83013 + 15.2942i −0.371158 + 0.642864i
\(567\) −2.46410 −0.103483
\(568\) 5.19615 9.00000i 0.218026 0.377632i
\(569\) −21.4641 37.1769i −0.899822 1.55854i −0.827721 0.561140i \(-0.810363\pi\)
−0.0721010 0.997397i \(-0.522970\pi\)
\(570\) −8.19615 14.1962i −0.343299 0.594611i
\(571\) 16.7846 0.702414 0.351207 0.936298i \(-0.385771\pi\)
0.351207 + 0.936298i \(0.385771\pi\)
\(572\) 4.56218 + 0.294229i 0.190754 + 0.0123023i
\(573\) 12.9282 0.540083
\(574\) 4.50000 + 7.79423i 0.187826 + 0.325325i
\(575\) 4.73205 + 8.19615i 0.197340 + 0.341803i
\(576\) −2.23205 + 3.86603i −0.0930021 + 0.161084i
\(577\) 43.1962 1.79828 0.899140 0.437662i \(-0.144193\pi\)
0.899140 + 0.437662i \(0.144193\pi\)
\(578\) −37.0526 + 64.1769i −1.54118 + 2.66941i
\(579\) −6.83013 + 11.8301i −0.283850 + 0.491643i
\(580\) −5.19615 −0.215758
\(581\) 1.09808 1.90192i 0.0455559 0.0789051i
\(582\) −15.1244 26.1962i −0.626925 1.08587i
\(583\) 6.29423 + 10.9019i 0.260680 + 0.451512i
\(584\) 5.53590 0.229077
\(585\) −15.4641 + 23.1962i −0.639362 + 0.959043i
\(586\) −1.39230 −0.0575156
\(587\) −8.19615 14.1962i −0.338291 0.585938i 0.645820 0.763490i \(-0.276516\pi\)
−0.984111 + 0.177552i \(0.943182\pi\)
\(588\) −1.36603 2.36603i −0.0563339 0.0975732i
\(589\) −4.19615 + 7.26795i −0.172899 + 0.299471i
\(590\) 21.8038 0.897650
\(591\) −16.3923 + 28.3923i −0.674289 + 1.16790i
\(592\) −17.5000 + 30.3109i −0.719246 + 1.24577i
\(593\) −17.4449 −0.716375 −0.358187 0.933650i \(-0.616605\pi\)
−0.358187 + 0.933650i \(0.616605\pi\)
\(594\) −4.39230 + 7.60770i −0.180218 + 0.312148i
\(595\) 6.69615 + 11.5981i 0.274515 + 0.475475i
\(596\) 3.23205 + 5.59808i 0.132390 + 0.229306i
\(597\) 5.46410 0.223631
\(598\) −16.3923 + 24.5885i −0.670331 + 1.00550i
\(599\) 43.8564 1.79192 0.895962 0.444131i \(-0.146487\pi\)
0.895962 + 0.444131i \(0.146487\pi\)
\(600\) −4.73205 8.19615i −0.193185 0.334607i
\(601\) 14.9904 + 25.9641i 0.611470 + 1.05910i 0.990993 + 0.133915i \(0.0427550\pi\)
−0.379522 + 0.925183i \(0.623912\pi\)
\(602\) 0.169873 0.294229i 0.00692351 0.0119919i
\(603\) −27.6603 −1.12641
\(604\) −1.00000 + 1.73205i −0.0406894 + 0.0704761i
\(605\) 8.13397 14.0885i 0.330693 0.572777i
\(606\) −36.5885 −1.48630
\(607\) 7.19615 12.4641i 0.292083 0.505902i −0.682219 0.731148i \(-0.738985\pi\)
0.974302 + 0.225245i \(0.0723184\pi\)
\(608\) 5.19615 + 9.00000i 0.210732 + 0.364998i
\(609\) 4.09808 + 7.09808i 0.166062 + 0.287629i
\(610\) −14.4115 −0.583506
\(611\) 46.5167 + 3.00000i 1.88186 + 0.121367i
\(612\) −34.5167 −1.39525
\(613\) −1.69615 2.93782i −0.0685070 0.118658i 0.829737 0.558154i \(-0.188490\pi\)
−0.898244 + 0.439497i \(0.855157\pi\)
\(614\) 3.97372 + 6.88269i 0.160366 + 0.277763i
\(615\) 12.2942 21.2942i 0.495751 0.858666i
\(616\) −2.19615 −0.0884855
\(617\) −24.6962 + 42.7750i −0.994230 + 1.72206i −0.404214 + 0.914664i \(0.632455\pi\)
−0.590016 + 0.807392i \(0.700878\pi\)
\(618\) 34.0526 58.9808i 1.36979 2.37255i
\(619\) 35.3731 1.42176 0.710882 0.703311i \(-0.248296\pi\)
0.710882 + 0.703311i \(0.248296\pi\)
\(620\) −3.63397 + 6.29423i −0.145944 + 0.252782i
\(621\) −9.46410 16.3923i −0.379781 0.657801i
\(622\) −1.09808 1.90192i −0.0440288 0.0762602i
\(623\) 12.9282 0.517958
\(624\) 27.3205 40.9808i 1.09370 1.64054i
\(625\) −11.0000 −0.440000
\(626\) −24.9282 43.1769i −0.996331 1.72570i
\(627\) −3.46410 6.00000i −0.138343 0.239617i
\(628\) −0.598076 + 1.03590i −0.0238658 + 0.0413368i
\(629\) 54.1244 2.15808
\(630\) −6.69615 + 11.5981i −0.266781 + 0.462078i
\(631\) 6.39230 11.0718i 0.254474 0.440761i −0.710279 0.703920i \(-0.751431\pi\)
0.964752 + 0.263159i \(0.0847645\pi\)
\(632\) −28.0526 −1.11587
\(633\) 2.46410 4.26795i 0.0979392 0.169636i
\(634\) 5.59808 + 9.69615i 0.222328 + 0.385083i
\(635\) −15.9282 27.5885i −0.632091 1.09481i
\(636\) −27.1244 −1.07555
\(637\) −1.59808 3.23205i −0.0633181 0.128059i
\(638\) −6.58846 −0.260840
\(639\) −13.3923 23.1962i −0.529791 0.917626i
\(640\) −10.5000 18.1865i −0.415049 0.718886i
\(641\) −14.4282 + 24.9904i −0.569880 + 0.987061i 0.426698 + 0.904394i \(0.359677\pi\)
−0.996577 + 0.0826663i \(0.973656\pi\)
\(642\) −37.1769 −1.46726
\(643\) 0.392305 0.679492i 0.0154710 0.0267965i −0.858186 0.513338i \(-0.828409\pi\)
0.873657 + 0.486542i \(0.161742\pi\)
\(644\) −2.36603 + 4.09808i −0.0932345 + 0.161487i
\(645\) −0.928203 −0.0365480
\(646\) 13.3923 23.1962i 0.526913 0.912640i
\(647\) −22.5167 39.0000i −0.885221 1.53325i −0.845460 0.534039i \(-0.820674\pi\)
−0.0397614 0.999209i \(-0.512660\pi\)
\(648\) −2.13397 3.69615i −0.0838304 0.145199i
\(649\) 9.21539 0.361736
\(650\) 5.53590 + 11.1962i 0.217136 + 0.439149i
\(651\) 11.4641 0.449314
\(652\) −8.09808 14.0263i −0.317145 0.549311i
\(653\) 18.9282 + 32.7846i 0.740718 + 1.28296i 0.952169 + 0.305572i \(0.0988478\pi\)
−0.211451 + 0.977389i \(0.567819\pi\)
\(654\) 19.8564 34.3923i 0.776447 1.34485i
\(655\) −6.00000 −0.234439
\(656\) −12.9904 + 22.5000i −0.507189 + 0.878477i
\(657\) 7.13397 12.3564i 0.278323 0.482069i
\(658\) 22.3923 0.872943
\(659\) −14.1962 + 24.5885i −0.553004 + 0.957830i 0.445052 + 0.895505i \(0.353185\pi\)
−0.998056 + 0.0623257i \(0.980148\pi\)
\(660\) −3.00000 5.19615i −0.116775 0.202260i
\(661\) 16.5981 + 28.7487i 0.645590 + 1.11820i 0.984165 + 0.177256i \(0.0567220\pi\)
−0.338574 + 0.940940i \(0.609945\pi\)
\(662\) 43.2679 1.68166
\(663\) −76.0070 4.90192i −2.95187 0.190375i
\(664\) 3.80385 0.147618
\(665\) −1.73205 3.00000i −0.0671660 0.116335i
\(666\) 27.0622 + 46.8731i 1.04864 + 1.81629i
\(667\) 7.09808 12.2942i 0.274839 0.476034i
\(668\) −6.58846 −0.254915
\(669\) 13.6603 23.6603i 0.528136 0.914758i
\(670\) 9.29423 16.0981i 0.359067 0.621923i
\(671\) −6.09103 −0.235142
\(672\) 7.09808 12.2942i 0.273814 0.474260i
\(673\) 22.0885 + 38.2583i 0.851447 + 1.47475i 0.879902 + 0.475155i \(0.157608\pi\)
−0.0284546 + 0.999595i \(0.509059\pi\)
\(674\) −9.52628 16.5000i −0.366939 0.635556i
\(675\) −8.00000 −0.307920
\(676\) −7.89230 + 10.3301i −0.303550 + 0.397313i
\(677\) −23.0718 −0.886721 −0.443361 0.896343i \(-0.646214\pi\)
−0.443361 + 0.896343i \(0.646214\pi\)
\(678\) −31.6865 54.8827i −1.21691 2.10776i
\(679\) −3.19615 5.53590i −0.122657 0.212448i
\(680\) −11.5981 + 20.0885i −0.444766 + 0.770357i
\(681\) 15.4641 0.592586
\(682\) −4.60770 + 7.98076i −0.176438 + 0.305599i
\(683\) −7.73205 + 13.3923i −0.295859 + 0.512442i −0.975184 0.221395i \(-0.928939\pi\)
0.679326 + 0.733837i \(0.262272\pi\)
\(684\) 8.92820 0.341378
\(685\) −6.99038 + 12.1077i −0.267089 + 0.462611i
\(686\) −0.866025 1.50000i −0.0330650 0.0572703i
\(687\) 19.6603 + 34.0526i 0.750085 + 1.29919i
\(688\) 0.980762 0.0373912
\(689\) −35.7224 2.30385i −1.36092 0.0877696i
\(690\) 38.7846 1.47650
\(691\) −0.196152 0.339746i −0.00746199 0.0129245i 0.862270 0.506448i \(-0.169042\pi\)
−0.869732 + 0.493524i \(0.835709\pi\)
\(692\) −4.26795 7.39230i −0.162243 0.281013i
\(693\) −2.83013 + 4.90192i −0.107508 + 0.186209i
\(694\) 12.5885 0.477851
\(695\) 9.16987 15.8827i 0.347833 0.602465i
\(696\) −7.09808 + 12.2942i −0.269052 + 0.466012i
\(697\) 40.1769 1.52181
\(698\) 21.4641 37.1769i 0.812428 1.40717i
\(699\) 2.53590 + 4.39230i 0.0959165 + 0.166132i
\(700\) 1.00000 + 1.73205i 0.0377964 + 0.0654654i
\(701\) 20.7846 0.785024 0.392512 0.919747i \(-0.371606\pi\)
0.392512 + 0.919747i \(0.371606\pi\)
\(702\) −11.0718 22.3923i −0.417878 0.845143i
\(703\) −14.0000 −0.528020
\(704\) −0.633975 1.09808i −0.0238938 0.0413853i
\(705\) −30.5885 52.9808i −1.15203 1.99537i
\(706\) −17.8923 + 30.9904i −0.673386 + 1.16634i
\(707\) −7.73205 −0.290794
\(708\) −9.92820 + 17.1962i −0.373125 + 0.646271i
\(709\) −15.0885 + 26.1340i −0.566659 + 0.981482i 0.430234 + 0.902717i \(0.358431\pi\)
−0.996893 + 0.0787648i \(0.974902\pi\)
\(710\) 18.0000 0.675528
\(711\) −36.1506 + 62.6147i −1.35575 + 2.34824i
\(712\) 11.1962 + 19.3923i 0.419594 + 0.726757i
\(713\) −9.92820 17.1962i −0.371814 0.644001i
\(714\) −36.5885 −1.36929
\(715\) −3.50962 7.09808i −0.131252 0.265453i
\(716\) −6.92820 −0.258919
\(717\) 21.5885 + 37.3923i 0.806236 + 1.39644i
\(718\) −16.3923 28.3923i −0.611755 1.05959i
\(719\) 3.63397 6.29423i 0.135524 0.234735i −0.790273 0.612755i \(-0.790061\pi\)
0.925798 + 0.378019i \(0.123395\pi\)
\(720\) −38.6603 −1.44078
\(721\) 7.19615 12.4641i 0.267999 0.464187i
\(722\) 12.9904 22.5000i 0.483452 0.837363i
\(723\) −57.9090 −2.15366
\(724\) −2.79423 + 4.83975i −0.103847 + 0.179868i
\(725\) −3.00000 5.19615i −0.111417 0.192980i
\(726\) 22.2224 + 38.4904i 0.824752 + 1.42851i
\(727\) −41.1769 −1.52717 −0.763584 0.645709i \(-0.776562\pi\)
−0.763584 + 0.645709i \(0.776562\pi\)
\(728\) 3.46410 5.19615i 0.128388 0.192582i
\(729\) −43.7846 −1.62165
\(730\) 4.79423 + 8.30385i 0.177442 + 0.307339i
\(731\) −0.758330 1.31347i −0.0280479 0.0485803i
\(732\) 6.56218 11.3660i 0.242545 0.420100i
\(733\) 23.5885 0.871260 0.435630 0.900126i \(-0.356526\pi\)
0.435630 + 0.900126i \(0.356526\pi\)
\(734\) −3.63397 + 6.29423i −0.134132 + 0.232324i
\(735\) −2.36603 + 4.09808i −0.0872722 + 0.151160i
\(736\) −24.5885 −0.906343
\(737\) 3.92820 6.80385i 0.144697 0.250623i
\(738\) 20.0885 + 34.7942i 0.739466 + 1.28079i
\(739\) −20.3923 35.3205i −0.750143 1.29929i −0.947753 0.319005i \(-0.896651\pi\)
0.197610 0.980281i \(-0.436682\pi\)
\(740\) −12.1244 −0.445700
\(741\) 19.6603 + 1.26795i 0.722237 + 0.0465793i
\(742\) −17.1962 −0.631291
\(743\) 3.80385 + 6.58846i 0.139550 + 0.241707i 0.927326 0.374254i \(-0.122101\pi\)
−0.787777 + 0.615961i \(0.788768\pi\)
\(744\) 9.92820 + 17.1962i 0.363986 + 0.630442i
\(745\) 5.59808 9.69615i 0.205098 0.355240i
\(746\) −19.7321 −0.722442
\(747\) 4.90192 8.49038i 0.179352 0.310647i
\(748\) 4.90192 8.49038i 0.179232 0.310439i
\(749\) −7.85641 −0.287067
\(750\) 28.6865 49.6865i 1.04748 1.81430i
\(751\) −17.9019 31.0070i −0.653250 1.13146i −0.982329 0.187161i \(-0.940072\pi\)
0.329079 0.944302i \(-0.393262\pi\)
\(752\) 32.3205 + 55.9808i 1.17861 + 2.04141i
\(753\) −4.39230 −0.160064
\(754\) 10.3923 15.5885i 0.378465 0.567698i
\(755\) 3.46410 0.126072
\(756\) −2.00000 3.46410i −0.0727393 0.125988i
\(757\) 8.00000 + 13.8564i 0.290765 + 0.503620i 0.973991 0.226587i \(-0.0727569\pi\)
−0.683226 + 0.730207i \(0.739424\pi\)
\(758\) −23.0263 + 39.8827i −0.836352 + 1.44860i
\(759\) 16.3923 0.595003
\(760\) 3.00000 5.19615i 0.108821 0.188484i
\(761\) −20.6603 + 35.7846i −0.748934 + 1.29719i 0.199401 + 0.979918i \(0.436100\pi\)
−0.948334 + 0.317273i \(0.897233\pi\)
\(762\) 87.0333 3.15288
\(763\) 4.19615 7.26795i 0.151911 0.263117i
\(764\) −2.36603 4.09808i −0.0855998 0.148263i
\(765\) 29.8923 + 51.7750i 1.08076 + 1.87193i
\(766\) −20.1962 −0.729717
\(767\) −14.5359 + 21.8038i −0.524861 + 0.787291i
\(768\) 51.9090 1.87310
\(769\) −7.58846 13.1436i −0.273647 0.473970i 0.696146 0.717900i \(-0.254897\pi\)
−0.969793 + 0.243930i \(0.921563\pi\)
\(770\) −1.90192 3.29423i −0.0685406 0.118716i
\(771\) −8.36603 + 14.4904i −0.301295 + 0.521858i
\(772\) 5.00000 0.179954
\(773\) 6.46410 11.1962i 0.232498 0.402698i −0.726045 0.687647i \(-0.758644\pi\)
0.958542 + 0.284950i \(0.0919769\pi\)
\(774\) 0.758330 1.31347i 0.0272576 0.0472116i
\(775\) −8.39230 −0.301460
\(776\) 5.53590 9.58846i 0.198727 0.344206i