Properties

Label 91.2.f.b.29.2
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 29.2
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 91.29
Dual form 91.2.f.b.22.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 1.50000i) q^{2} +(0.366025 + 0.633975i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.73205 q^{5} +(-0.633975 + 1.09808i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.73205 q^{8} +(1.23205 - 2.13397i) q^{9} +O(q^{10})\) \(q+(0.866025 + 1.50000i) q^{2} +(0.366025 + 0.633975i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.73205 q^{5} +(-0.633975 + 1.09808i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.73205 q^{8} +(1.23205 - 2.13397i) q^{9} +(-1.50000 - 2.59808i) q^{10} +(-2.36603 - 4.09808i) q^{11} -0.732051 q^{12} +(-1.59808 + 3.23205i) q^{13} -1.73205 q^{14} +(-0.633975 - 1.09808i) q^{15} +(2.50000 + 4.33013i) q^{16} +(2.13397 - 3.69615i) q^{17} +4.26795 q^{18} +(-1.00000 + 1.73205i) q^{19} +(0.866025 - 1.50000i) q^{20} -0.732051 q^{21} +(4.09808 - 7.09808i) q^{22} +(-0.633975 - 1.09808i) q^{23} +(0.633975 + 1.09808i) q^{24} -2.00000 q^{25} +(-6.23205 + 0.401924i) q^{26} +4.00000 q^{27} +(-0.500000 - 0.866025i) q^{28} +(1.50000 + 2.59808i) q^{29} +(1.09808 - 1.90192i) q^{30} -6.19615 q^{31} +(-2.59808 + 4.50000i) q^{32} +(1.73205 - 3.00000i) q^{33} +7.39230 q^{34} +(0.866025 - 1.50000i) q^{35} +(1.23205 + 2.13397i) q^{36} +(3.50000 + 6.06218i) q^{37} -3.46410 q^{38} +(-2.63397 + 0.169873i) q^{39} -3.00000 q^{40} +(-2.59808 - 4.50000i) q^{41} +(-0.633975 - 1.09808i) q^{42} +(-5.09808 + 8.83013i) q^{43} +4.73205 q^{44} +(-2.13397 + 3.69615i) q^{45} +(1.09808 - 1.90192i) q^{46} -0.928203 q^{47} +(-1.83013 + 3.16987i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-1.73205 - 3.00000i) q^{50} +3.12436 q^{51} +(-2.00000 - 3.00000i) q^{52} +3.92820 q^{53} +(3.46410 + 6.00000i) q^{54} +(4.09808 + 7.09808i) q^{55} +(-0.866025 + 1.50000i) q^{56} -1.46410 q^{57} +(-2.59808 + 4.50000i) q^{58} +(-5.36603 + 9.29423i) q^{59} +1.26795 q^{60} +(7.59808 - 13.1603i) q^{61} +(-5.36603 - 9.29423i) q^{62} +(1.23205 + 2.13397i) q^{63} +1.00000 q^{64} +(2.76795 - 5.59808i) q^{65} +6.00000 q^{66} +(-2.09808 - 3.63397i) q^{67} +(2.13397 + 3.69615i) q^{68} +(0.464102 - 0.803848i) q^{69} +3.00000 q^{70} +(-3.00000 + 5.19615i) q^{71} +(2.13397 - 3.69615i) q^{72} +7.19615 q^{73} +(-6.06218 + 10.5000i) q^{74} +(-0.732051 - 1.26795i) q^{75} +(-1.00000 - 1.73205i) q^{76} +4.73205 q^{77} +(-2.53590 - 3.80385i) q^{78} +5.80385 q^{79} +(-4.33013 - 7.50000i) q^{80} +(-2.23205 - 3.86603i) q^{81} +(4.50000 - 7.79423i) q^{82} +8.19615 q^{83} +(0.366025 - 0.633975i) q^{84} +(-3.69615 + 6.40192i) q^{85} -17.6603 q^{86} +(-1.09808 + 1.90192i) q^{87} +(-4.09808 - 7.09808i) q^{88} +(0.464102 + 0.803848i) q^{89} -7.39230 q^{90} +(-2.00000 - 3.00000i) q^{91} +1.26795 q^{92} +(-2.26795 - 3.92820i) q^{93} +(-0.803848 - 1.39230i) q^{94} +(1.73205 - 3.00000i) q^{95} -3.80385 q^{96} +(7.19615 - 12.4641i) q^{97} +(0.866025 - 1.50000i) q^{98} -11.6603 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{3} - 2q^{4} - 6q^{6} - 2q^{7} - 2q^{9} + O(q^{10}) \) \( 4q - 2q^{3} - 2q^{4} - 6q^{6} - 2q^{7} - 2q^{9} - 6q^{10} - 6q^{11} + 4q^{12} + 4q^{13} - 6q^{15} + 10q^{16} + 12q^{17} + 24q^{18} - 4q^{19} + 4q^{21} + 6q^{22} - 6q^{23} + 6q^{24} - 8q^{25} - 18q^{26} + 16q^{27} - 2q^{28} + 6q^{29} - 6q^{30} - 4q^{31} - 12q^{34} - 2q^{36} + 14q^{37} - 14q^{39} - 12q^{40} - 6q^{42} - 10q^{43} + 12q^{44} - 12q^{45} - 6q^{46} + 24q^{47} + 10q^{48} - 2q^{49} - 36q^{51} - 8q^{52} - 12q^{53} + 6q^{55} + 8q^{57} - 18q^{59} + 12q^{60} + 20q^{61} - 18q^{62} - 2q^{63} + 4q^{64} + 18q^{65} + 24q^{66} + 2q^{67} + 12q^{68} - 12q^{69} + 12q^{70} - 12q^{71} + 12q^{72} + 8q^{73} + 4q^{75} - 4q^{76} + 12q^{77} - 24q^{78} + 44q^{79} - 2q^{81} + 18q^{82} + 12q^{83} - 2q^{84} + 6q^{85} - 36q^{86} + 6q^{87} - 6q^{88} - 12q^{89} + 12q^{90} - 8q^{91} + 12q^{92} - 16q^{93} - 24q^{94} - 36q^{96} + 8q^{97} - 12q^{99} + O(q^{100}) \)

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 \(0.0431180\pi\)
−0.378467 + 0.925615i \(0.623549\pi\)
\(3\) 0.366025 + 0.633975i 0.211325 + 0.366025i 0.952129 0.305695i \(-0.0988889\pi\)
−0.740805 + 0.671721i \(0.765556\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −1.73205 −0.774597 −0.387298 0.921954i \(-0.626592\pi\)
−0.387298 + 0.921954i \(0.626592\pi\)
\(6\) −0.633975 + 1.09808i −0.258819 + 0.448288i
\(7\) −0.500000 + 0.866025i −0.188982 + 0.327327i
\(8\) 1.73205 0.612372
\(9\) 1.23205 2.13397i 0.410684 0.711325i
\(10\) −1.50000 2.59808i −0.474342 0.821584i
\(11\) −2.36603 4.09808i −0.713384 1.23562i −0.963580 0.267421i \(-0.913828\pi\)
0.250196 0.968195i \(-0.419505\pi\)
\(12\) −0.732051 −0.211325
\(13\) −1.59808 + 3.23205i −0.443227 + 0.896410i
\(14\) −1.73205 −0.462910
\(15\) −0.633975 1.09808i −0.163692 0.283522i
\(16\) 2.50000 + 4.33013i 0.625000 + 1.08253i
\(17\) 2.13397 3.69615i 0.517565 0.896449i −0.482227 0.876046i \(-0.660172\pi\)
0.999792 0.0204023i \(-0.00649471\pi\)
\(18\) 4.26795 1.00597
\(19\) −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
\(21\) −0.732051 −0.159747
\(22\) 4.09808 7.09808i 0.873713 1.51331i
\(23\) −0.633975 1.09808i −0.132193 0.228965i 0.792329 0.610094i \(-0.208868\pi\)
−0.924522 + 0.381130i \(0.875535\pi\)
\(24\) 0.633975 + 1.09808i 0.129410 + 0.224144i
\(25\) −2.00000 −0.400000
\(26\) −6.23205 + 0.401924i −1.22221 + 0.0788237i
\(27\) 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 \(0.743482\pi\)
\(30\) 1.09808 1.90192i 0.200480 0.347242i
\(31\) −6.19615 −1.11286 −0.556431 0.830894i \(-0.687830\pi\)
−0.556431 + 0.830894i \(0.687830\pi\)
\(32\) −2.59808 + 4.50000i −0.459279 + 0.795495i
\(33\) 1.73205 3.00000i 0.301511 0.522233i
\(34\) 7.39230 1.26777
\(35\) 0.866025 1.50000i 0.146385 0.253546i
\(36\) 1.23205 + 2.13397i 0.205342 + 0.355662i
\(37\) 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
\(39\) −2.63397 + 0.169873i −0.421773 + 0.0272014i
\(40\) −3.00000 −0.474342
\(41\) −2.59808 4.50000i −0.405751 0.702782i 0.588657 0.808383i \(-0.299657\pi\)
−0.994409 + 0.105601i \(0.966323\pi\)
\(42\) −0.633975 1.09808i −0.0978244 0.169437i
\(43\) −5.09808 + 8.83013i −0.777449 + 1.34658i 0.155958 + 0.987764i \(0.450153\pi\)
−0.933408 + 0.358818i \(0.883180\pi\)
\(44\) 4.73205 0.713384
\(45\) −2.13397 + 3.69615i −0.318114 + 0.550990i
\(46\) 1.09808 1.90192i 0.161903 0.280423i
\(47\) −0.928203 −0.135392 −0.0676962 0.997706i \(-0.521565\pi\)
−0.0676962 + 0.997706i \(0.521565\pi\)
\(48\) −1.83013 + 3.16987i −0.264156 + 0.457532i
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) −1.73205 3.00000i −0.244949 0.424264i
\(51\) 3.12436 0.437497
\(52\) −2.00000 3.00000i −0.277350 0.416025i
\(53\) 3.92820 0.539580 0.269790 0.962919i \(-0.413046\pi\)
0.269790 + 0.962919i \(0.413046\pi\)
\(54\) 3.46410 + 6.00000i 0.471405 + 0.816497i
\(55\) 4.09808 + 7.09808i 0.552584 + 0.957104i
\(56\) −0.866025 + 1.50000i −0.115728 + 0.200446i
\(57\) −1.46410 −0.193925
\(58\) −2.59808 + 4.50000i −0.341144 + 0.590879i
\(59\) −5.36603 + 9.29423i −0.698597 + 1.21001i 0.270356 + 0.962760i \(0.412859\pi\)
−0.968953 + 0.247245i \(0.920475\pi\)
\(60\) 1.26795 0.163692
\(61\) 7.59808 13.1603i 0.972834 1.68500i 0.285929 0.958251i \(-0.407698\pi\)
0.686905 0.726747i \(-0.258969\pi\)
\(62\) −5.36603 9.29423i −0.681486 1.18037i
\(63\) 1.23205 + 2.13397i 0.155224 + 0.268856i
\(64\) 1.00000 0.125000
\(65\) 2.76795 5.59808i 0.343322 0.694356i
\(66\) 6.00000 0.738549
\(67\) −2.09808 3.63397i −0.256321 0.443961i 0.708933 0.705276i \(-0.249177\pi\)
−0.965253 + 0.261316i \(0.915844\pi\)
\(68\) 2.13397 + 3.69615i 0.258782 + 0.448224i
\(69\) 0.464102 0.803848i 0.0558713 0.0967719i
\(70\) 3.00000 0.358569
\(71\) −3.00000 + 5.19615i −0.356034 + 0.616670i −0.987294 0.158901i \(-0.949205\pi\)
0.631260 + 0.775571i \(0.282538\pi\)
\(72\) 2.13397 3.69615i 0.251491 0.435596i
\(73\) 7.19615 0.842246 0.421123 0.907004i \(-0.361636\pi\)
0.421123 + 0.907004i \(0.361636\pi\)
\(74\) −6.06218 + 10.5000i −0.704714 + 1.22060i
\(75\) −0.732051 1.26795i −0.0845299 0.146410i
\(76\) −1.00000 1.73205i −0.114708 0.198680i
\(77\) 4.73205 0.539267
\(78\) −2.53590 3.80385i −0.287134 0.430701i
\(79\) 5.80385 0.652984 0.326492 0.945200i \(-0.394133\pi\)
0.326492 + 0.945200i \(0.394133\pi\)
\(80\) −4.33013 7.50000i −0.484123 0.838525i
\(81\) −2.23205 3.86603i −0.248006 0.429558i
\(82\) 4.50000 7.79423i 0.496942 0.860729i
\(83\) 8.19615 0.899645 0.449822 0.893118i \(-0.351487\pi\)
0.449822 + 0.893118i \(0.351487\pi\)
\(84\) 0.366025 0.633975i 0.0399366 0.0691723i
\(85\) −3.69615 + 6.40192i −0.400904 + 0.694386i
\(86\) −17.6603 −1.90435
\(87\) −1.09808 + 1.90192i −0.117726 + 0.203908i
\(88\) −4.09808 7.09808i −0.436856 0.756657i
\(89\) 0.464102 + 0.803848i 0.0491947 + 0.0852077i 0.889574 0.456791i \(-0.151001\pi\)
−0.840379 + 0.541998i \(0.817668\pi\)
\(90\) −7.39230 −0.779217
\(91\) −2.00000 3.00000i −0.209657 0.314485i
\(92\) 1.26795 0.132193
\(93\) −2.26795 3.92820i −0.235175 0.407336i
\(94\) −0.803848 1.39230i −0.0829105 0.143605i
\(95\) 1.73205 3.00000i 0.177705 0.307794i
\(96\) −3.80385 −0.388229
\(97\) 7.19615 12.4641i 0.730659 1.26554i −0.225944 0.974140i \(-0.572546\pi\)
0.956602 0.291397i \(-0.0941202\pi\)
\(98\) 0.866025 1.50000i 0.0874818 0.151523i
\(99\) −11.6603 −1.17190
\(100\) 1.00000 1.73205i 0.100000 0.173205i
\(101\) 2.13397 + 3.69615i 0.212338 + 0.367781i 0.952446 0.304708i \(-0.0985588\pi\)
−0.740108 + 0.672489i \(0.765225\pi\)
\(102\) 2.70577 + 4.68653i 0.267911 + 0.464036i
\(103\) 6.39230 0.629853 0.314926 0.949116i \(-0.398020\pi\)
0.314926 + 0.949116i \(0.398020\pi\)
\(104\) −2.76795 + 5.59808i −0.271420 + 0.548937i
\(105\) 1.26795 0.123739
\(106\) 3.40192 + 5.89230i 0.330424 + 0.572311i
\(107\) −9.92820 17.1962i −0.959796 1.66241i −0.722991 0.690858i \(-0.757233\pi\)
−0.236805 0.971557i \(-0.576100\pi\)
\(108\) −2.00000 + 3.46410i −0.192450 + 0.333333i
\(109\) 12.3923 1.18697 0.593484 0.804846i \(-0.297752\pi\)
0.593484 + 0.804846i \(0.297752\pi\)
\(110\) −7.09808 + 12.2942i −0.676775 + 1.17221i
\(111\) −2.56218 + 4.43782i −0.243191 + 0.421219i
\(112\) −5.00000 −0.472456
\(113\) 3.69615 6.40192i 0.347705 0.602242i −0.638137 0.769923i \(-0.720294\pi\)
0.985841 + 0.167681i \(0.0536278\pi\)
\(114\) −1.26795 2.19615i −0.118754 0.205689i
\(115\) 1.09808 + 1.90192i 0.102396 + 0.177355i
\(116\) −3.00000 −0.278543
\(117\) 4.92820 + 7.39230i 0.455613 + 0.683419i
\(118\) −18.5885 −1.71121
\(119\) 2.13397 + 3.69615i 0.195621 + 0.338826i
\(120\) −1.09808 1.90192i −0.100240 0.173621i
\(121\) −5.69615 + 9.86603i −0.517832 + 0.896911i
\(122\) 26.3205 2.38295
\(123\) 1.90192 3.29423i 0.171491 0.297031i
\(124\) 3.09808 5.36603i 0.278215 0.481883i
\(125\) 12.1244 1.08444
\(126\) −2.13397 + 3.69615i −0.190110 + 0.329279i
\(127\) 1.19615 + 2.07180i 0.106141 + 0.183842i 0.914204 0.405254i \(-0.132817\pi\)
−0.808063 + 0.589097i \(0.799484\pi\)
\(128\) 6.06218 + 10.5000i 0.535826 + 0.928078i
\(129\) −7.46410 −0.657178
\(130\) 10.7942 0.696152i 0.946716 0.0610566i
\(131\) 3.46410 0.302660 0.151330 0.988483i \(-0.451644\pi\)
0.151330 + 0.988483i \(0.451644\pi\)
\(132\) 1.73205 + 3.00000i 0.150756 + 0.261116i
\(133\) −1.00000 1.73205i −0.0867110 0.150188i
\(134\) 3.63397 6.29423i 0.313928 0.543739i
\(135\) −6.92820 −0.596285
\(136\) 3.69615 6.40192i 0.316942 0.548960i
\(137\) −10.9641 + 18.9904i −0.936726 + 1.62246i −0.165200 + 0.986260i \(0.552827\pi\)
−0.771526 + 0.636198i \(0.780506\pi\)
\(138\) 1.60770 0.136856
\(139\) −10.2942 + 17.8301i −0.873145 + 1.51233i −0.0144194 + 0.999896i \(0.504590\pi\)
−0.858726 + 0.512436i \(0.828743\pi\)
\(140\) 0.866025 + 1.50000i 0.0731925 + 0.126773i
\(141\) −0.339746 0.588457i −0.0286118 0.0495570i
\(142\) −10.3923 −0.872103
\(143\) 17.0263 1.09808i 1.42381 0.0918257i
\(144\) 12.3205 1.02671
\(145\) −2.59808 4.50000i −0.215758 0.373705i
\(146\) 6.23205 + 10.7942i 0.515768 + 0.893337i
\(147\) 0.366025 0.633975i 0.0301893 0.0522893i
\(148\) −7.00000 −0.575396
\(149\) −0.232051 + 0.401924i −0.0190103 + 0.0329269i −0.875374 0.483446i \(-0.839385\pi\)
0.856364 + 0.516373i \(0.172718\pi\)
\(150\) 1.26795 2.19615i 0.103528 0.179315i
\(151\) 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
\(153\) −5.25833 9.10770i −0.425111 0.736314i
\(154\) 4.09808 + 7.09808i 0.330232 + 0.571979i
\(155\) 10.7321 0.862019
\(156\) 1.16987 2.36603i 0.0936648 0.189434i
\(157\) −9.19615 −0.733933 −0.366966 0.930234i \(-0.619604\pi\)
−0.366966 + 0.930234i \(0.619604\pi\)
\(158\) 5.02628 + 8.70577i 0.399869 + 0.692594i
\(159\) 1.43782 + 2.49038i 0.114027 + 0.197500i
\(160\) 4.50000 7.79423i 0.355756 0.616188i
\(161\) 1.26795 0.0999284
\(162\) 3.86603 6.69615i 0.303744 0.526099i
\(163\) −2.90192 + 5.02628i −0.227296 + 0.393689i −0.957006 0.290069i \(-0.906322\pi\)
0.729710 + 0.683757i \(0.239655\pi\)
\(164\) 5.19615 0.405751
\(165\) −3.00000 + 5.19615i −0.233550 + 0.404520i
\(166\) 7.09808 + 12.2942i 0.550918 + 0.954217i
\(167\) −12.2942 21.2942i −0.951356 1.64780i −0.742495 0.669852i \(-0.766358\pi\)
−0.208861 0.977945i \(-0.566976\pi\)
\(168\) −1.26795 −0.0978244
\(169\) −7.89230 10.3301i −0.607100 0.794625i
\(170\) −12.8038 −0.982010
\(171\) 2.46410 + 4.26795i 0.188435 + 0.326378i
\(172\) −5.09808 8.83013i −0.388725 0.673291i
\(173\) −7.73205 + 13.3923i −0.587857 + 1.01820i 0.406656 + 0.913581i \(0.366695\pi\)
−0.994513 + 0.104617i \(0.966638\pi\)
\(174\) −3.80385 −0.288369
\(175\) 1.00000 1.73205i 0.0755929 0.130931i
\(176\) 11.8301 20.4904i 0.891729 1.54452i
\(177\) −7.85641 −0.590524
\(178\) −0.803848 + 1.39230i −0.0602509 + 0.104358i
\(179\) −3.46410 6.00000i −0.258919 0.448461i 0.707034 0.707180i \(-0.250033\pi\)
−0.965953 + 0.258719i \(0.916700\pi\)
\(180\) −2.13397 3.69615i −0.159057 0.275495i
\(181\) −25.5885 −1.90198 −0.950988 0.309229i \(-0.899929\pi\)
−0.950988 + 0.309229i \(0.899929\pi\)
\(182\) 2.76795 5.59808i 0.205174 0.414957i
\(183\) 11.1244 0.822336
\(184\) −1.09808 1.90192i −0.0809513 0.140212i
\(185\) −6.06218 10.5000i −0.445700 0.771975i
\(186\) 3.92820 6.80385i 0.288030 0.498882i
\(187\) −20.1962 −1.47689
\(188\) 0.464102 0.803848i 0.0338481 0.0586266i
\(189\) −2.00000 + 3.46410i −0.145479 + 0.251976i
\(190\) 6.00000 0.435286
\(191\) −0.633975 + 1.09808i −0.0458728 + 0.0794540i −0.888050 0.459747i \(-0.847940\pi\)
0.842177 + 0.539201i \(0.181274\pi\)
\(192\) 0.366025 + 0.633975i 0.0264156 + 0.0457532i
\(193\) −2.50000 4.33013i −0.179954 0.311689i 0.761911 0.647682i \(-0.224262\pi\)
−0.941865 + 0.335993i \(0.890928\pi\)
\(194\) 24.9282 1.78974
\(195\) 4.56218 0.294229i 0.326704 0.0210702i
\(196\) 1.00000 0.0714286
\(197\) −6.00000 10.3923i −0.427482 0.740421i 0.569166 0.822222i \(-0.307266\pi\)
−0.996649 + 0.0818013i \(0.973933\pi\)
\(198\) −10.0981 17.4904i −0.717639 1.24299i
\(199\) −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
\(201\) 1.53590 2.66025i 0.108334 0.187640i
\(202\) −3.69615 + 6.40192i −0.260060 + 0.450438i
\(203\) −3.00000 −0.210559
\(204\) −1.56218 + 2.70577i −0.109374 + 0.189442i
\(205\) 4.50000 + 7.79423i 0.314294 + 0.544373i
\(206\) 5.53590 + 9.58846i 0.385704 + 0.668059i
\(207\) −3.12436 −0.217158
\(208\) −17.9904 + 1.16025i −1.24741 + 0.0804491i
\(209\) 9.46410 0.654646
\(210\) 1.09808 + 1.90192i 0.0757745 + 0.131245i
\(211\) 6.09808 + 10.5622i 0.419809 + 0.727130i 0.995920 0.0902411i \(-0.0287638\pi\)
−0.576111 + 0.817371i \(0.695430\pi\)
\(212\) −1.96410 + 3.40192i −0.134895 + 0.233645i
\(213\) −4.39230 −0.300956
\(214\) 17.1962 29.7846i 1.17550 2.03603i
\(215\) 8.83013 15.2942i 0.602210 1.04306i
\(216\) 6.92820 0.471405
\(217\) 3.09808 5.36603i 0.210311 0.364270i
\(218\) 10.7321 + 18.5885i 0.726866 + 1.25897i
\(219\) 2.63397 + 4.56218i 0.177988 + 0.308283i
\(220\) −8.19615 −0.552584
\(221\) 8.53590 + 12.8038i 0.574187 + 0.861280i
\(222\) −8.87564 −0.595694
\(223\) 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
\(225\) −2.46410 + 4.26795i −0.164273 + 0.284530i
\(226\) 12.8038 0.851699
\(227\) 5.83013 10.0981i 0.386959 0.670233i −0.605080 0.796165i \(-0.706859\pi\)
0.992039 + 0.125932i \(0.0401921\pi\)
\(228\) 0.732051 1.26795i 0.0484812 0.0839720i
\(229\) 6.39230 0.422415 0.211208 0.977441i \(-0.432260\pi\)
0.211208 + 0.977441i \(0.432260\pi\)
\(230\) −1.90192 + 3.29423i −0.125409 + 0.217215i
\(231\) 1.73205 + 3.00000i 0.113961 + 0.197386i
\(232\) 2.59808 + 4.50000i 0.170572 + 0.295439i
\(233\) 25.8564 1.69391 0.846955 0.531665i \(-0.178433\pi\)
0.846955 + 0.531665i \(0.178433\pi\)
\(234\) −6.82051 + 13.7942i −0.445871 + 0.901757i
\(235\) 1.60770 0.104874
\(236\) −5.36603 9.29423i −0.349299 0.605003i
\(237\) 2.12436 + 3.67949i 0.137992 + 0.239009i
\(238\) −3.69615 + 6.40192i −0.239586 + 0.414975i
\(239\) −26.1962 −1.69449 −0.847244 0.531204i \(-0.821740\pi\)
−0.847244 + 0.531204i \(0.821740\pi\)
\(240\) 3.16987 5.49038i 0.204614 0.354403i
\(241\) 5.40192 9.35641i 0.347969 0.602699i −0.637920 0.770103i \(-0.720205\pi\)
0.985888 + 0.167404i \(0.0535383\pi\)
\(242\) −19.7321 −1.26842
\(243\) 7.63397 13.2224i 0.489720 0.848219i
\(244\) 7.59808 + 13.1603i 0.486417 + 0.842499i
\(245\) 0.866025 + 1.50000i 0.0553283 + 0.0958315i
\(246\) 6.58846 0.420065
\(247\) −4.00000 6.00000i −0.254514 0.381771i
\(248\) −10.7321 −0.681486
\(249\) 3.00000 + 5.19615i 0.190117 + 0.329293i
\(250\) 10.5000 + 18.1865i 0.664078 + 1.15022i
\(251\) 11.1962 19.3923i 0.706695 1.22403i −0.259382 0.965775i \(-0.583519\pi\)
0.966076 0.258256i \(-0.0831480\pi\)
\(252\) −2.46410 −0.155224
\(253\) −3.00000 + 5.19615i −0.188608 + 0.326679i
\(254\) −2.07180 + 3.58846i −0.129996 + 0.225160i
\(255\) −5.41154 −0.338884
\(256\) −9.50000 + 16.4545i −0.593750 + 1.02841i
\(257\) 9.06218 + 15.6962i 0.565283 + 0.979099i 0.997023 + 0.0771011i \(0.0245664\pi\)
−0.431740 + 0.901998i \(0.642100\pi\)
\(258\) −6.46410 11.1962i −0.402437 0.697042i
\(259\) −7.00000 −0.434959
\(260\) 3.46410 + 5.19615i 0.214834 + 0.322252i
\(261\) 7.39230 0.457572
\(262\) 3.00000 + 5.19615i 0.185341 + 0.321019i
\(263\) −2.36603 4.09808i −0.145895 0.252698i 0.783811 0.620999i \(-0.213273\pi\)
−0.929707 + 0.368301i \(0.879940\pi\)
\(264\) 3.00000 5.19615i 0.184637 0.319801i
\(265\) −6.80385 −0.417957
\(266\) 1.73205 3.00000i 0.106199 0.183942i
\(267\) −0.339746 + 0.588457i −0.0207921 + 0.0360130i
\(268\) 4.19615 0.256321
\(269\) −9.46410 + 16.3923i −0.577036 + 0.999456i 0.418781 + 0.908087i \(0.362458\pi\)
−0.995817 + 0.0913690i \(0.970876\pi\)
\(270\) −6.00000 10.3923i −0.365148 0.632456i
\(271\) −8.09808 14.0263i −0.491923 0.852036i 0.508034 0.861337i \(-0.330373\pi\)
−0.999957 + 0.00930143i \(0.997039\pi\)
\(272\) 21.3397 1.29391
\(273\) 1.16987 2.36603i 0.0708039 0.143198i
\(274\) −37.9808 −2.29450
\(275\) 4.73205 + 8.19615i 0.285353 + 0.494247i
\(276\) 0.464102 + 0.803848i 0.0279356 + 0.0483859i
\(277\) −8.50000 + 14.7224i −0.510716 + 0.884585i 0.489207 + 0.872167i \(0.337286\pi\)
−0.999923 + 0.0124177i \(0.996047\pi\)
\(278\) −35.6603 −2.13876
\(279\) −7.63397 + 13.2224i −0.457034 + 0.791606i
\(280\) 1.50000 2.59808i 0.0896421 0.155265i
\(281\) −7.39230 −0.440988 −0.220494 0.975388i \(-0.570767\pi\)
−0.220494 + 0.975388i \(0.570767\pi\)
\(282\) 0.588457 1.01924i 0.0350421 0.0606947i
\(283\) 0.0980762 + 0.169873i 0.00583003 + 0.0100979i 0.868926 0.494943i \(-0.164811\pi\)
−0.863096 + 0.505040i \(0.831478\pi\)
\(284\) −3.00000 5.19615i −0.178017 0.308335i
\(285\) 2.53590 0.150214
\(286\) 16.3923 + 24.5885i 0.969297 + 1.45395i
\(287\) 5.19615 0.306719
\(288\) 6.40192 + 11.0885i 0.377237 + 0.653394i
\(289\) −0.607695 1.05256i −0.0357468 0.0619152i
\(290\) 4.50000 7.79423i 0.264249 0.457693i
\(291\) 10.5359 0.617625
\(292\) −3.59808 + 6.23205i −0.210561 + 0.364703i
\(293\) 5.59808 9.69615i 0.327043 0.566455i −0.654881 0.755732i \(-0.727281\pi\)
0.981924 + 0.189277i \(0.0606144\pi\)
\(294\) 1.26795 0.0739483
\(295\) 9.29423 16.0981i 0.541131 0.937266i
\(296\) 6.06218 + 10.5000i 0.352357 + 0.610300i
\(297\) −9.46410 16.3923i −0.549163 0.951178i
\(298\) −0.803848 −0.0465656
\(299\) 4.56218 0.294229i 0.263838 0.0170157i
\(300\) 1.46410 0.0845299
\(301\) −5.09808 8.83013i −0.293848 0.508960i
\(302\) 1.73205 + 3.00000i 0.0996683 + 0.172631i
\(303\) −1.56218 + 2.70577i −0.0897448 + 0.155443i
\(304\) −10.0000 −0.573539
\(305\) −13.1603 + 22.7942i −0.753554 + 1.30519i
\(306\) 9.10770 15.7750i 0.520652 0.901796i
\(307\) 26.5885 1.51748 0.758742 0.651392i \(-0.225814\pi\)
0.758742 + 0.651392i \(0.225814\pi\)
\(308\) −2.36603 + 4.09808i −0.134817 + 0.233510i
\(309\) 2.33975 + 4.05256i 0.133103 + 0.230542i
\(310\) 9.29423 + 16.0981i 0.527877 + 0.914309i
\(311\) 4.73205 0.268330 0.134165 0.990959i \(-0.457165\pi\)
0.134165 + 0.990959i \(0.457165\pi\)
\(312\) −4.56218 + 0.294229i −0.258282 + 0.0166574i
\(313\) −12.7846 −0.722629 −0.361314 0.932444i \(-0.617672\pi\)
−0.361314 + 0.932444i \(0.617672\pi\)
\(314\) −7.96410 13.7942i −0.449440 0.778453i
\(315\) −2.13397 3.69615i −0.120236 0.208255i
\(316\) −2.90192 + 5.02628i −0.163246 + 0.282750i
\(317\) 0.464102 0.0260665 0.0130333 0.999915i \(-0.495851\pi\)
0.0130333 + 0.999915i \(0.495851\pi\)
\(318\) −2.49038 + 4.31347i −0.139654 + 0.241887i
\(319\) 7.09808 12.2942i 0.397416 0.688345i
\(320\) −1.73205 −0.0968246
\(321\) 7.26795 12.5885i 0.405657 0.702619i
\(322\) 1.09808 + 1.90192i 0.0611934 + 0.105990i
\(323\) 4.26795 + 7.39230i 0.237475 + 0.411319i
\(324\) 4.46410 0.248006
\(325\) 3.19615 6.46410i 0.177291 0.358564i
\(326\) −10.0526 −0.556760
\(327\) 4.53590 + 7.85641i 0.250836 + 0.434460i
\(328\) −4.50000 7.79423i −0.248471 0.430364i
\(329\) 0.464102 0.803848i 0.0255868 0.0443176i
\(330\) −10.3923 −0.572078
\(331\) 13.4904 23.3660i 0.741498 1.28431i −0.210315 0.977634i \(-0.567449\pi\)
0.951813 0.306679i \(-0.0992179\pi\)
\(332\) −4.09808 + 7.09808i −0.224911 + 0.389558i
\(333\) 17.2487 0.945224
\(334\) 21.2942 36.8827i 1.16517 2.01813i
\(335\) 3.63397 + 6.29423i 0.198545 + 0.343890i
\(336\) −1.83013 3.16987i −0.0998416 0.172931i
\(337\) 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
\(339\) 5.41154 0.293915
\(340\) −3.69615 6.40192i −0.200452 0.347193i
\(341\) 14.6603 + 25.3923i 0.793897 + 1.37507i
\(342\) −4.26795 + 7.39230i −0.230784 + 0.399730i
\(343\) 1.00000 0.0539949
\(344\) −8.83013 + 15.2942i −0.476089 + 0.824610i
\(345\) −0.803848 + 1.39230i −0.0432777 + 0.0749592i
\(346\) −26.7846 −1.43995
\(347\) −5.36603 + 9.29423i −0.288063 + 0.498940i −0.973347 0.229336i \(-0.926345\pi\)
0.685284 + 0.728276i \(0.259678\pi\)
\(348\) −1.09808 1.90192i −0.0588631 0.101954i
\(349\) −8.39230 14.5359i −0.449230 0.778089i 0.549106 0.835753i \(-0.314968\pi\)
−0.998336 + 0.0576637i \(0.981635\pi\)
\(350\) 3.46410 0.185164
\(351\) −6.39230 + 12.9282i −0.341196 + 0.690056i
\(352\) 24.5885 1.31057
\(353\) −1.66987 2.89230i −0.0888784 0.153942i 0.818159 0.574992i \(-0.194995\pi\)
−0.907037 + 0.421050i \(0.861662\pi\)
\(354\) −6.80385 11.7846i −0.361620 0.626345i
\(355\) 5.19615 9.00000i 0.275783 0.477670i
\(356\) −0.928203 −0.0491947
\(357\) −1.56218 + 2.70577i −0.0826792 + 0.143205i
\(358\) 6.00000 10.3923i 0.317110 0.549250i
\(359\) 5.07180 0.267679 0.133840 0.991003i \(-0.457269\pi\)
0.133840 + 0.991003i \(0.457269\pi\)
\(360\) −3.69615 + 6.40192i −0.194804 + 0.337411i
\(361\) 7.50000 + 12.9904i 0.394737 + 0.683704i
\(362\) −22.1603 38.3827i −1.16472 2.01735i
\(363\) −8.33975 −0.437723
\(364\) 3.59808 0.232051i 0.188590 0.0121628i
\(365\) −12.4641 −0.652401
\(366\) 9.63397 + 16.6865i 0.503576 + 0.872219i
\(367\) 3.09808 + 5.36603i 0.161718 + 0.280104i 0.935485 0.353366i \(-0.114963\pi\)
−0.773767 + 0.633471i \(0.781630\pi\)
\(368\) 3.16987 5.49038i 0.165241 0.286206i
\(369\) −12.8038 −0.666542
\(370\) 10.5000 18.1865i 0.545869 0.945473i
\(371\) −1.96410 + 3.40192i −0.101971 + 0.176619i
\(372\) 4.53590 0.235175
\(373\) −4.69615 + 8.13397i −0.243158 + 0.421161i −0.961612 0.274413i \(-0.911517\pi\)
0.718454 + 0.695574i \(0.244850\pi\)
\(374\) −17.4904 30.2942i −0.904406 1.56648i
\(375\) 4.43782 + 7.68653i 0.229168 + 0.396931i
\(376\) −1.60770 −0.0829105
\(377\) −10.7942 + 0.696152i −0.555931 + 0.0358537i
\(378\) −6.92820 −0.356348
\(379\) 2.29423 + 3.97372i 0.117847 + 0.204116i 0.918914 0.394458i \(-0.129068\pi\)
−0.801067 + 0.598574i \(0.795734\pi\)
\(380\) 1.73205 + 3.00000i 0.0888523 + 0.153897i
\(381\) −0.875644 + 1.51666i −0.0448606 + 0.0777009i
\(382\) −2.19615 −0.112365
\(383\) −2.83013 + 4.90192i −0.144613 + 0.250477i −0.929228 0.369506i \(-0.879527\pi\)
0.784616 + 0.619982i \(0.212860\pi\)
\(384\) −4.43782 + 7.68653i −0.226467 + 0.392252i
\(385\) −8.19615 −0.417715
\(386\) 4.33013 7.50000i 0.220398 0.381740i
\(387\) 12.5622 + 21.7583i 0.638571 + 1.10604i
\(388\) 7.19615 + 12.4641i 0.365329 + 0.632769i
\(389\) −30.4641 −1.54459 −0.772296 0.635263i \(-0.780892\pi\)
−0.772296 + 0.635263i \(0.780892\pi\)
\(390\) 4.39230 + 6.58846i 0.222413 + 0.333620i
\(391\) −5.41154 −0.273673
\(392\) −0.866025 1.50000i −0.0437409 0.0757614i
\(393\) 1.26795 + 2.19615i 0.0639596 + 0.110781i
\(394\) 10.3923 18.0000i 0.523557 0.906827i
\(395\) −10.0526 −0.505799
\(396\) 5.83013 10.0981i 0.292975 0.507447i
\(397\) −11.3923 + 19.7321i −0.571763 + 0.990323i 0.424622 + 0.905371i \(0.360407\pi\)
−0.996385 + 0.0849523i \(0.972926\pi\)
\(398\) −3.46410 −0.173640
\(399\) 0.732051 1.26795i 0.0366484 0.0634769i
\(400\) −5.00000 8.66025i −0.250000 0.433013i
\(401\) −8.42820 14.5981i −0.420884 0.728993i 0.575142 0.818054i \(-0.304947\pi\)
−0.996026 + 0.0890606i \(0.971614\pi\)
\(402\) 5.32051 0.265363
\(403\) 9.90192 20.0263i 0.493250 0.997580i
\(404\) −4.26795 −0.212338
\(405\) 3.86603 + 6.69615i 0.192104 + 0.332734i
\(406\) −2.59808 4.50000i −0.128940 0.223331i
\(407\) 16.5622 28.6865i 0.820957 1.42194i
\(408\) 5.41154 0.267911
\(409\) 13.5981 23.5526i 0.672382 1.16460i −0.304845 0.952402i \(-0.598605\pi\)
0.977227 0.212197i \(-0.0680619\pi\)
\(410\) −7.79423 + 13.5000i −0.384930 + 0.666717i
\(411\) −16.0526 −0.791814
\(412\) −3.19615 + 5.53590i −0.157463 + 0.272734i
\(413\) −5.36603 9.29423i −0.264045 0.457339i
\(414\) −2.70577 4.68653i −0.132981 0.230331i
\(415\) −14.1962 −0.696862
\(416\) −10.3923 15.5885i −0.509525 0.764287i
\(417\) −15.0718 −0.738069
\(418\) 8.19615 + 14.1962i 0.400887 + 0.694357i
\(419\) 10.9019 + 18.8827i 0.532594 + 0.922480i 0.999276 + 0.0380543i \(0.0121160\pi\)
−0.466682 + 0.884425i \(0.654551\pi\)
\(420\) −0.633975 + 1.09808i −0.0309348 + 0.0535806i
\(421\) 30.1769 1.47073 0.735366 0.677670i \(-0.237010\pi\)
0.735366 + 0.677670i \(0.237010\pi\)
\(422\) −10.5622 + 18.2942i −0.514159 + 0.890549i
\(423\) −1.14359 + 1.98076i −0.0556034 + 0.0963079i
\(424\) 6.80385 0.330424
\(425\) −4.26795 + 7.39230i −0.207026 + 0.358579i
\(426\) −3.80385 6.58846i −0.184297 0.319212i
\(427\) 7.59808 + 13.1603i 0.367697 + 0.636869i
\(428\) 19.8564 0.959796
\(429\) 6.92820 + 10.3923i 0.334497 + 0.501745i
\(430\) 30.5885 1.47511
\(431\) −17.6603 30.5885i −0.850665 1.47339i −0.880610 0.473843i \(-0.842867\pi\)
0.0299451 0.999552i \(-0.490467\pi\)
\(432\) 10.0000 + 17.3205i 0.481125 + 0.833333i
\(433\) −8.79423 + 15.2321i −0.422624 + 0.732006i −0.996195 0.0871498i \(-0.972224\pi\)
0.573572 + 0.819155i \(0.305557\pi\)
\(434\) 10.7321 0.515155
\(435\) 1.90192 3.29423i 0.0911903 0.157946i
\(436\) −6.19615 + 10.7321i −0.296742 + 0.513972i
\(437\) 2.53590 0.121308
\(438\) −4.56218 + 7.90192i −0.217989 + 0.377569i
\(439\) 8.29423 + 14.3660i 0.395862 + 0.685653i 0.993211 0.116329i \(-0.0371125\pi\)
−0.597349 + 0.801982i \(0.703779\pi\)
\(440\) 7.09808 + 12.2942i 0.338388 + 0.586104i
\(441\) −2.46410 −0.117338
\(442\) −11.8135 + 23.8923i −0.561909 + 1.13644i
\(443\) −11.3205 −0.537854 −0.268927 0.963161i \(-0.586669\pi\)
−0.268927 + 0.963161i \(0.586669\pi\)
\(444\) −2.56218 4.43782i −0.121596 0.210610i
\(445\) −0.803848 1.39230i −0.0381060 0.0660016i
\(446\) −8.66025 + 15.0000i −0.410075 + 0.710271i
\(447\) −0.339746 −0.0160694
\(448\) −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 \(0.0752847\pi\)
\(450\) −8.53590 −0.402386
\(451\) −12.2942 + 21.2942i −0.578913 + 1.00271i
\(452\) 3.69615 + 6.40192i 0.173852 + 0.301121i
\(453\) 0.732051 + 1.26795i 0.0343947 + 0.0595734i
\(454\) 20.1962 0.947852
\(455\) 3.46410 + 5.19615i 0.162400 + 0.243599i
\(456\) −2.53590 −0.118754
\(457\) −5.50000 9.52628i −0.257279 0.445621i 0.708233 0.705979i \(-0.249493\pi\)
−0.965512 + 0.260358i \(0.916159\pi\)
\(458\) 5.53590 + 9.58846i 0.258676 + 0.448039i
\(459\) 8.53590 14.7846i 0.398422 0.690086i
\(460\) −2.19615 −0.102396
\(461\) −7.79423 + 13.5000i −0.363013 + 0.628758i −0.988455 0.151513i \(-0.951585\pi\)
0.625442 + 0.780271i \(0.284919\pi\)
\(462\) −3.00000 + 5.19615i −0.139573 + 0.241747i
\(463\) 26.5885 1.23567 0.617835 0.786308i \(-0.288010\pi\)
0.617835 + 0.786308i \(0.288010\pi\)
\(464\) −7.50000 + 12.9904i −0.348179 + 0.603063i
\(465\) 3.92820 + 6.80385i 0.182166 + 0.315521i
\(466\) 22.3923 + 38.7846i 1.03730 + 1.79666i
\(467\) −19.5167 −0.903123 −0.451562 0.892240i \(-0.649133\pi\)
−0.451562 + 0.892240i \(0.649133\pi\)
\(468\) −8.86603 + 0.571797i −0.409832 + 0.0264313i
\(469\) 4.19615 0.193760
\(470\) 1.39230 + 2.41154i 0.0642222 + 0.111236i
\(471\) −3.36603 5.83013i −0.155098 0.268638i
\(472\) −9.29423 + 16.0981i −0.427802 + 0.740974i
\(473\) 48.2487 2.21848
\(474\) −3.67949 + 6.37307i −0.169005 + 0.292725i
\(475\) 2.00000 3.46410i 0.0917663 0.158944i
\(476\) −4.26795 −0.195621
\(477\) 4.83975 8.38269i 0.221597 0.383817i
\(478\) −22.6865 39.2942i −1.03766 1.79728i
\(479\) −2.36603 4.09808i −0.108106 0.187246i 0.806897 0.590693i \(-0.201145\pi\)
−0.915003 + 0.403447i \(0.867812\pi\)
\(480\) 6.58846 0.300721
\(481\) −25.1865 + 1.62436i −1.14841 + 0.0740642i
\(482\) 18.7128 0.852345
\(483\) 0.464102 + 0.803848i 0.0211174 + 0.0365763i
\(484\) −5.69615 9.86603i −0.258916 0.448456i
\(485\) −12.4641 + 21.5885i −0.565966 + 0.980281i
\(486\) 26.4449 1.19956
\(487\) 0.392305 0.679492i 0.0177770 0.0307907i −0.857000 0.515316i \(-0.827674\pi\)
0.874777 + 0.484526i \(0.161008\pi\)
\(488\) 13.1603 22.7942i 0.595737 1.03185i
\(489\) −4.24871 −0.192133
\(490\) −1.50000 + 2.59808i −0.0677631 + 0.117369i
\(491\) −14.1962 24.5885i −0.640663 1.10966i −0.985285 0.170920i \(-0.945326\pi\)
0.344622 0.938742i \(-0.388007\pi\)
\(492\) 1.90192 + 3.29423i 0.0857453 + 0.148515i
\(493\) 12.8038 0.576656
\(494\) 5.53590 11.1962i 0.249072 0.503739i
\(495\) 20.1962 0.907750
\(496\) −15.4904 26.8301i −0.695539 1.20471i
\(497\) −3.00000 5.19615i −0.134568 0.233079i
\(498\) −5.19615 + 9.00000i −0.232845 + 0.403300i
\(499\) 12.9808 0.581099 0.290549 0.956860i \(-0.406162\pi\)
0.290549 + 0.956860i \(0.406162\pi\)
\(500\) −6.06218 + 10.5000i −0.271109 + 0.469574i
\(501\) 9.00000 15.5885i 0.402090 0.696441i
\(502\) 38.7846 1.73104
\(503\) −6.29423 + 10.9019i −0.280646 + 0.486093i −0.971544 0.236859i \(-0.923882\pi\)
0.690898 + 0.722952i \(0.257215\pi\)
\(504\) 2.13397 + 3.69615i 0.0950548 + 0.164640i
\(505\) −3.69615 6.40192i −0.164477 0.284882i
\(506\) −10.3923 −0.461994
\(507\) 3.66025 8.78461i 0.162558 0.390138i
\(508\) −2.39230 −0.106141
\(509\) −5.13397 8.89230i −0.227559 0.394144i 0.729525 0.683954i \(-0.239741\pi\)
−0.957084 + 0.289810i \(0.906408\pi\)
\(510\) −4.68653 8.11731i −0.207523 0.359441i
\(511\) −3.59808 + 6.23205i −0.159170 + 0.275690i
\(512\) −8.66025 −0.382733
\(513\) −4.00000 + 6.92820i −0.176604 + 0.305888i
\(514\) −15.6962 + 27.1865i −0.692328 + 1.19915i
\(515\) −11.0718 −0.487882
\(516\) 3.73205 6.46410i 0.164294 0.284566i
\(517\) 2.19615 + 3.80385i 0.0965867 + 0.167293i
\(518\) −6.06218 10.5000i −0.266357 0.461344i
\(519\) −11.3205 −0.496915
\(520\) 4.79423 9.69615i 0.210241 0.425204i
\(521\) 0.124356 0.00544812 0.00272406 0.999996i \(-0.499133\pi\)
0.00272406 + 0.999996i \(0.499133\pi\)
\(522\) 6.40192 + 11.0885i 0.280205 + 0.485329i
\(523\) −16.5885 28.7321i −0.725363 1.25636i −0.958825 0.283999i \(-0.908339\pi\)
0.233462 0.972366i \(-0.424995\pi\)
\(524\) −1.73205 + 3.00000i −0.0756650 + 0.131056i
\(525\) 1.46410 0.0638986
\(526\) 4.09808 7.09808i 0.178685 0.309491i
\(527\) −13.2224 + 22.9019i −0.575978 + 0.997623i
\(528\) 17.3205 0.753778
\(529\) 10.6962 18.5263i 0.465050 0.805490i
\(530\) −5.89230 10.2058i −0.255945 0.443310i
\(531\) 13.2224 + 22.9019i 0.573805 + 0.993859i
\(532\) 2.00000 0.0867110
\(533\) 18.6962 1.20577i 0.809820 0.0522278i
\(534\) −1.17691 −0.0509301
\(535\) 17.1962 + 29.7846i 0.743455 + 1.28770i
\(536\) −3.63397 6.29423i −0.156964 0.271869i
\(537\) 2.53590 4.39230i 0.109432 0.189542i
\(538\) −32.7846 −1.41344
\(539\) −2.36603 + 4.09808i −0.101912 + 0.176517i
\(540\) 3.46410 6.00000i 0.149071 0.258199i
\(541\) −35.3923 −1.52163 −0.760817 0.648966i \(-0.775202\pi\)
−0.760817 + 0.648966i \(0.775202\pi\)
\(542\) 14.0263 24.2942i 0.602480 1.04353i
\(543\) −9.36603 16.2224i −0.401935 0.696171i
\(544\) 11.0885 + 19.2058i 0.475414 + 0.823441i
\(545\) −21.4641 −0.919421
\(546\) 4.56218 0.294229i 0.195243 0.0125918i
\(547\) 28.1962 1.20558 0.602790 0.797900i \(-0.294056\pi\)
0.602790 + 0.797900i \(0.294056\pi\)
\(548\) −10.9641 18.9904i −0.468363 0.811229i
\(549\) −18.7224 32.4282i −0.799054 1.38400i
\(550\) −8.19615 + 14.1962i −0.349485 + 0.605326i
\(551\) −6.00000 −0.255609
\(552\) 0.803848 1.39230i 0.0342140 0.0592604i
\(553\) −2.90192 + 5.02628i −0.123402 + 0.213739i
\(554\) −29.4449 −1.25099
\(555\) 4.43782 7.68653i 0.188375 0.326275i
\(556\) −10.2942 17.8301i −0.436573 0.756166i
\(557\) 12.8205 + 22.2058i 0.543222 + 0.940889i 0.998716 + 0.0506499i \(0.0161293\pi\)
−0.455494 + 0.890239i \(0.650537\pi\)
\(558\) −26.4449 −1.11950
\(559\) −20.3923 30.5885i −0.862503 1.29375i
\(560\) 8.66025 0.365963
\(561\) −7.39230 12.8038i −0.312103 0.540579i
\(562\) −6.40192 11.0885i −0.270049 0.467738i
\(563\) 5.02628 8.70577i 0.211832 0.366905i −0.740456 0.672105i \(-0.765390\pi\)
0.952288 + 0.305201i \(0.0987236\pi\)
\(564\) 0.679492 0.0286118
\(565\) −6.40192 + 11.0885i −0.269331 + 0.466495i
\(566\) −0.169873 + 0.294229i −0.00714029 + 0.0123674i
\(567\) 4.46410 0.187475
\(568\) −5.19615 + 9.00000i −0.218026 + 0.377632i
\(569\) −14.5359 25.1769i −0.609377 1.05547i −0.991343 0.131295i \(-0.958086\pi\)
0.381967 0.924176i \(-0.375247\pi\)
\(570\) 2.19615 + 3.80385i 0.0919867 + 0.159326i
\(571\) −24.7846 −1.03720 −0.518602 0.855016i \(-0.673547\pi\)
−0.518602 + 0.855016i \(0.673547\pi\)
\(572\) −7.56218 + 15.2942i −0.316191 + 0.639484i
\(573\) −0.928203 −0.0387762
\(574\) 4.50000 + 7.79423i 0.187826 + 0.325325i
\(575\) 1.26795 + 2.19615i 0.0528771 + 0.0915859i
\(576\) 1.23205 2.13397i 0.0513355 0.0889156i
\(577\) 32.8038 1.36564 0.682821 0.730586i \(-0.260753\pi\)
0.682821 + 0.730586i \(0.260753\pi\)
\(578\) 1.05256 1.82309i 0.0437807 0.0758304i
\(579\) 1.83013 3.16987i 0.0760575 0.131735i
\(580\) 5.19615 0.215758
\(581\) −4.09808 + 7.09808i −0.170017 + 0.294478i
\(582\) 9.12436 + 15.8038i 0.378217 + 0.655091i
\(583\) −9.29423 16.0981i −0.384928 0.666714i
\(584\) 12.4641 0.515768
\(585\) −8.53590 12.8038i −0.352916 0.529374i
\(586\) 19.3923 0.801089
\(587\) 2.19615 + 3.80385i 0.0906449 + 0.157002i 0.907783 0.419441i \(-0.137774\pi\)
−0.817138 + 0.576442i \(0.804441\pi\)
\(588\) 0.366025 + 0.633975i 0.0150946 + 0.0261447i
\(589\) 6.19615 10.7321i 0.255308 0.442206i
\(590\) 32.1962 1.32549
\(591\) 4.39230 7.60770i 0.180675 0.312939i
\(592\) −17.5000 + 30.3109i −0.719246 + 1.24577i
\(593\) 41.4449 1.70194 0.850968 0.525217i \(-0.176016\pi\)
0.850968 + 0.525217i \(0.176016\pi\)
\(594\) 16.3923 28.3923i 0.672584 1.16495i
\(595\) −3.69615 6.40192i −0.151527 0.262453i
\(596\) −0.232051 0.401924i −0.00950517 0.0164634i
\(597\) −1.46410 −0.0599217
\(598\) 4.39230 + 6.58846i 0.179615 + 0.269422i
\(599\) 16.1436 0.659609 0.329805 0.944049i \(-0.393017\pi\)
0.329805 + 0.944049i \(0.393017\pi\)
\(600\) −1.26795 2.19615i −0.0517638 0.0896575i
\(601\) −10.9904 19.0359i −0.448307 0.776490i 0.549969 0.835185i \(-0.314640\pi\)
−0.998276 + 0.0586946i \(0.981306\pi\)
\(602\) 8.83013 15.2942i 0.359889 0.623346i
\(603\) −10.3397 −0.421067
\(604\) −1.00000 + 1.73205i −0.0406894 + 0.0704761i
\(605\) 9.86603 17.0885i 0.401111 0.694745i
\(606\) −5.41154 −0.219829
\(607\) −3.19615 + 5.53590i −0.129728 + 0.224695i −0.923571 0.383427i \(-0.874744\pi\)
0.793843 + 0.608122i \(0.208077\pi\)
\(608\) −5.19615 9.00000i −0.210732 0.364998i
\(609\) −1.09808 1.90192i −0.0444963 0.0770698i
\(610\) −45.5885 −1.84582
\(611\) 1.48334 3.00000i 0.0600095 0.121367i
\(612\) 10.5167 0.425111
\(613\) 8.69615 + 15.0622i 0.351234 + 0.608356i 0.986466 0.163966i \(-0.0524287\pi\)
−0.635232 + 0.772322i \(0.719095\pi\)
\(614\) 23.0263 + 39.8827i 0.929265 + 1.60953i
\(615\) −3.29423 + 5.70577i −0.132836 + 0.230079i
\(616\) 8.19615 0.330232
\(617\) −14.3038 + 24.7750i −0.575851 + 0.997404i 0.420097 + 0.907479i \(0.361996\pi\)
−0.995949 + 0.0899245i \(0.971337\pi\)
\(618\) −4.05256 + 7.01924i −0.163018 + 0.282355i
\(619\) −37.3731 −1.50215 −0.751075 0.660217i \(-0.770464\pi\)
−0.751075 + 0.660217i \(0.770464\pi\)
\(620\) −5.36603 + 9.29423i −0.215505 + 0.373265i
\(621\) −2.53590 4.39230i −0.101762 0.176257i
\(622\) 4.09808 + 7.09808i 0.164318 + 0.284607i
\(623\) −0.928203 −0.0371877
\(624\) −7.32051 10.9808i −0.293055 0.439582i
\(625\) −11.0000 −0.440000
\(626\) −11.0718 19.1769i −0.442518 0.766464i
\(627\) 3.46410 + 6.00000i 0.138343 + 0.239617i
\(628\) 4.59808 7.96410i 0.183483 0.317802i
\(629\) 29.8756 1.19122
\(630\) 3.69615 6.40192i 0.147258 0.255059i
\(631\) −14.3923 + 24.9282i −0.572949 + 0.992376i 0.423313 + 0.905984i \(0.360867\pi\)
−0.996261 + 0.0863924i \(0.972466\pi\)
\(632\) 10.0526 0.399869
\(633\) −4.46410 + 7.73205i −0.177432 + 0.307321i
\(634\) 0.401924 + 0.696152i 0.0159624 + 0.0276477i
\(635\) −2.07180 3.58846i −0.0822167 0.142404i
\(636\) −2.87564 −0.114027
\(637\) 3.59808 0.232051i 0.142561 0.00919419i
\(638\) 24.5885 0.973466
\(639\) 7.39230 + 12.8038i 0.292435 + 0.506512i
\(640\) −10.5000 18.1865i −0.415049 0.718886i
\(641\) −0.571797 + 0.990381i −0.0225846 + 0.0391177i −0.877097 0.480314i \(-0.840523\pi\)
0.854512 + 0.519431i \(0.173856\pi\)
\(642\) 25.1769 0.993654
\(643\) −20.3923 + 35.3205i −0.804194 + 1.39290i 0.112640 + 0.993636i \(0.464069\pi\)
−0.916834 + 0.399269i \(0.869264\pi\)
\(644\) −0.633975 + 1.09808i −0.0249821 + 0.0432703i
\(645\) 12.9282 0.509048
\(646\) −7.39230 + 12.8038i −0.290846 + 0.503761i
\(647\) 22.5167 + 39.0000i 0.885221 + 1.53325i 0.845460 + 0.534039i \(0.179326\pi\)
0.0397614 + 0.999209i \(0.487340\pi\)
\(648\) −3.86603 6.69615i −0.151872 0.263050i
\(649\) 50.7846 1.99347
\(650\) 12.4641 0.803848i 0.488882 0.0315295i
\(651\) 4.53590 0.177776
\(652\) −2.90192 5.02628i −0.113648 0.196844i
\(653\) 5.07180 + 8.78461i 0.198475 + 0.343768i 0.948034 0.318169i \(-0.103068\pi\)
−0.749559 + 0.661937i \(0.769735\pi\)
\(654\) −7.85641 + 13.6077i −0.307210 + 0.532103i
\(655\) −6.00000 −0.234439
\(656\) 12.9904 22.5000i 0.507189 0.878477i
\(657\) 8.86603 15.3564i 0.345897 0.599110i
\(658\) 1.60770 0.0626745
\(659\) −3.80385 + 6.58846i −0.148177 + 0.256650i −0.930554 0.366156i \(-0.880674\pi\)
0.782377 + 0.622805i \(0.214007\pi\)
\(660\) −3.00000 5.19615i −0.116775 0.202260i
\(661\) 11.4019 + 19.7487i 0.443483 + 0.768136i 0.997945 0.0640734i \(-0.0204092\pi\)
−0.554462 + 0.832209i \(0.687076\pi\)
\(662\) 46.7321 1.81629
\(663\) −4.99296 + 10.0981i −0.193910 + 0.392177i
\(664\) 14.1962 0.550918
\(665\) 1.73205 + 3.00000i 0.0671660 + 0.116335i
\(666\) 14.9378 + 25.8731i 0.578829 + 1.00256i
\(667\) 1.90192 3.29423i 0.0736428 0.127553i
\(668\) 24.5885 0.951356
\(669\) −3.66025 + 6.33975i −0.141514 + 0.245109i
\(670\) −6.29423 + 10.9019i −0.243167 + 0.421178i
\(671\) −71.9090 −2.77601
\(672\) 1.90192 3.29423i 0.0733683 0.127078i
\(673\) −9.08846 15.7417i −0.350334 0.606797i 0.635974 0.771711i \(-0.280599\pi\)
−0.986308 + 0.164914i \(0.947265\pi\)
\(674\) 9.52628 + 16.5000i 0.366939 + 0.635556i
\(675\) −8.00000 −0.307920
\(676\) 12.8923 1.66987i 0.495858 0.0642259i
\(677\) −36.9282 −1.41927 −0.709633 0.704571i \(-0.751139\pi\)
−0.709633 + 0.704571i \(0.751139\pi\)
\(678\) 4.68653 + 8.11731i 0.179985 + 0.311744i
\(679\) 7.19615 + 12.4641i 0.276163 + 0.478328i
\(680\) −6.40192 + 11.0885i −0.245503 + 0.425223i
\(681\) 8.53590 0.327096
\(682\) −25.3923 + 43.9808i −0.972322 + 1.68411i
\(683\) −4.26795 + 7.39230i −0.163309 + 0.282859i −0.936053 0.351858i \(-0.885550\pi\)
0.772745 + 0.634717i \(0.218883\pi\)
\(684\) −4.92820 −0.188435
\(685\) 18.9904 32.8923i 0.725585 1.25675i
\(686\) 0.866025 + 1.50000i 0.0330650 + 0.0572703i
\(687\) 2.33975 + 4.05256i 0.0892669 + 0.154615i
\(688\) −50.9808 −1.94362
\(689\) −6.27757 + 12.6962i −0.239156 + 0.483685i
\(690\) −2.78461 −0.106008
\(691\) 10.1962 + 17.6603i 0.387880 + 0.671828i 0.992164 0.124941i \(-0.0398742\pi\)
−0.604284 + 0.796769i \(0.706541\pi\)
\(692\) −7.73205 13.3923i −0.293928 0.509099i
\(693\) 5.83013 10.0981i 0.221468 0.383594i
\(694\) −18.5885 −0.705608
\(695\) 17.8301 30.8827i 0.676335 1.17145i
\(696\) −1.90192 + 3.29423i −0.0720922 + 0.124867i
\(697\) −22.1769 −0.840011
\(698\) 14.5359 25.1769i 0.550192 0.952960i
\(699\) 9.46410 + 16.3923i 0.357965 + 0.620014i
\(700\) 1.00000 + 1.73205i 0.0377964 + 0.0654654i
\(701\) −20.7846 −0.785024 −0.392512 0.919747i \(-0.628394\pi\)
−0.392512 + 0.919747i \(0.628394\pi\)
\(702\) −24.9282 + 1.60770i −0.940854 + 0.0606785i
\(703\) −14.0000 −0.528020
\(704\) −2.36603 4.09808i −0.0891729 0.154452i
\(705\) 0.588457 + 1.01924i 0.0221626 + 0.0383867i
\(706\) 2.89230 5.00962i 0.108853 0.188539i
\(707\) −4.26795 −0.160513
\(708\) 3.92820 6.80385i 0.147631 0.255704i
\(709\) 16.0885 27.8660i 0.604215 1.04653i −0.387960 0.921676i \(-0.626820\pi\)
0.992175 0.124854i \(-0.0398464\pi\)
\(710\) 18.0000 0.675528
\(711\) 7.15064 12.3853i 0.268170 0.464484i
\(712\) 0.803848 + 1.39230i 0.0301255 + 0.0521788i
\(713\) 3.92820 + 6.80385i 0.147112 + 0.254806i
\(714\) −5.41154 −0.202522
\(715\) −29.4904 + 1.90192i −1.10288 + 0.0711279i
\(716\) 6.92820 0.258919
\(717\) −9.58846 16.6077i −0.358087 0.620226i
\(718\) 4.39230 + 7.60770i 0.163919 + 0.283917i
\(719\) 5.36603 9.29423i 0.200119 0.346616i −0.748448 0.663194i \(-0.769200\pi\)
0.948567 + 0.316578i \(0.102534\pi\)
\(720\) −21.3397 −0.795285
\(721\) −3.19615 + 5.53590i −0.119031 + 0.206168i
\(722\) −12.9904 + 22.5000i −0.483452 + 0.837363i
\(723\) 7.90897 0.294138
\(724\) 12.7942 22.1603i 0.475494 0.823579i
\(725\) −3.00000 5.19615i −0.111417 0.192980i
\(726\) −7.22243 12.5096i −0.268050 0.464276i
\(727\) 21.1769 0.785408 0.392704 0.919665i \(-0.371540\pi\)
0.392704 + 0.919665i \(0.371540\pi\)
\(728\) −3.46410 5.19615i −0.128388 0.192582i
\(729\) −2.21539 −0.0820515
\(730\) −10.7942 18.6962i −0.399512 0.691976i
\(731\) 21.7583 + 37.6865i 0.804761 + 1.39389i
\(732\) −5.56218 + 9.63397i −0.205584 + 0.356082i
\(733\) −7.58846 −0.280286 −0.140143 0.990131i \(-0.544756\pi\)
−0.140143 + 0.990131i \(0.544756\pi\)
\(734\) −5.36603 + 9.29423i −0.198064 + 0.343056i
\(735\) −0.633975 + 1.09808i −0.0233845 + 0.0405032i
\(736\) 6.58846 0.242854
\(737\) −9.92820 + 17.1962i −0.365710 + 0.633428i
\(738\) −11.0885 19.2058i −0.408172 0.706974i
\(739\) 0.392305 + 0.679492i 0.0144312 + 0.0249955i 0.873151 0.487450i \(-0.162073\pi\)
−0.858720 + 0.512446i \(0.828740\pi\)
\(740\) 12.1244 0.445700
\(741\) 2.33975 4.73205i 0.0859527 0.173836i
\(742\) −6.80385 −0.249777
\(743\) 14.1962 + 24.5885i 0.520806 + 0.902063i 0.999707 + 0.0241941i \(0.00770196\pi\)
−0.478901 + 0.877869i \(0.658965\pi\)
\(744\) −3.92820 6.80385i −0.144015 0.249441i
\(745\) 0.401924 0.696152i 0.0147253 0.0255051i
\(746\) −16.2679 −0.595612
\(747\) 10.0981 17.4904i 0.369469 0.639940i
\(748\) 10.0981 17.4904i 0.369222 0.639512i
\(749\) 19.8564 0.725537
\(750\) −7.68653 + 13.3135i −0.280673 + 0.486139i
\(751\) −23.0981 40.0070i −0.842861 1.45988i −0.887466 0.460873i \(-0.847536\pi\)
0.0446053 0.999005i \(-0.485797\pi\)
\(752\) −2.32051 4.01924i −0.0846202 0.146567i
\(753\) 16.3923 0.597369
\(754\) −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 \(0.739424\pi\)
\(758\) −3.97372 + 6.88269i −0.144332 + 0.249990i
\(759\) −4.39230 −0.159431
\(760\) 3.00000 5.19615i 0.108821 0.188484i
\(761\) −3.33975 + 5.78461i −0.121066 + 0.209692i −0.920188 0.391476i \(-0.871965\pi\)
0.799123 + 0.601168i \(0.205298\pi\)
\(762\) −3.03332 −0.109886
\(763\) −6.19615 + 10.7321i −0.224316 + 0.388526i
\(764\) −0.633975 1.09808i −0.0229364 0.0397270i
\(765\) 9.10770 + 15.7750i 0.329289 + 0.570346i
\(766\) −9.80385 −0.354227
\(767\) −21.4641 32.1962i −0.775024 1.16254i
\(768\) −13.9090 −0.501897
\(769\) 23.5885 + 40.8564i 0.850622 + 1.47332i 0.880648 + 0.473771i \(0.157107\pi\)
−0.0300268 + 0.999549i \(0.509559\pi\)
\(770\) −7.09808 12.2942i −0.255797 0.443053i
\(771\) −6.63397 + 11.4904i −0.238917 + 0.413816i
\(772\) 5.00000 0.179954
\(773\) −0.464102 + 0.803848i −0.0166926 + 0.0289124i −0.874251 0.485474i \(-0.838647\pi\)
0.857558 + 0.514387i \(0.171980\pi\)
\(774\) −21.7583 + 37.6865i −0.782087 + 1.35461i
\(775\) 12.3923 0.445145
\(776\) 12.4641 21.5885i 0.447435 0.774980i
\(777\) −2.56218 4.43782i