Properties

Label 546.2.s.a.43.1
Level $546$
Weight $2$
Character 546.43
Analytic conductor $4.360$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.s (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 43.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 546.43
Dual form 546.2.s.a.127.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +0.732051i q^{5} +(0.866025 - 0.500000i) q^{6} +(0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +0.732051i q^{5} +(0.866025 - 0.500000i) q^{6} +(0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.366025 - 0.633975i) q^{10} +(1.50000 + 0.866025i) q^{11} -1.00000 q^{12} +(1.59808 - 3.23205i) q^{13} -1.00000 q^{14} +(-0.633975 - 0.366025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.86603 + 3.23205i) q^{17} +1.00000i q^{18} +(0.866025 - 0.500000i) q^{19} +(-0.633975 + 0.366025i) q^{20} +1.00000i q^{21} +(-0.866025 - 1.50000i) q^{22} +(-1.73205 + 3.00000i) q^{23} +(0.866025 + 0.500000i) q^{24} +4.46410 q^{25} +(-3.00000 + 2.00000i) q^{26} +1.00000 q^{27} +(0.866025 + 0.500000i) q^{28} +(-3.23205 + 5.59808i) q^{29} +(0.366025 + 0.633975i) q^{30} +2.19615i q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.50000 + 0.866025i) q^{33} -3.73205i q^{34} +(0.366025 + 0.633975i) q^{35} +(0.500000 - 0.866025i) q^{36} +(5.83013 + 3.36603i) q^{37} -1.00000 q^{38} +(2.00000 + 3.00000i) q^{39} +0.732051 q^{40} +(2.59808 + 1.50000i) q^{41} +(0.500000 - 0.866025i) q^{42} +(1.63397 + 2.83013i) q^{43} +1.73205i q^{44} +(0.633975 - 0.366025i) q^{45} +(3.00000 - 1.73205i) q^{46} +2.46410i q^{47} +(-0.500000 - 0.866025i) q^{48} +(0.500000 - 0.866025i) q^{49} +(-3.86603 - 2.23205i) q^{50} -3.73205 q^{51} +(3.59808 - 0.232051i) q^{52} +7.00000 q^{53} +(-0.866025 - 0.500000i) q^{54} +(-0.633975 + 1.09808i) q^{55} +(-0.500000 - 0.866025i) q^{56} +1.00000i q^{57} +(5.59808 - 3.23205i) q^{58} +(0.803848 - 0.464102i) q^{59} -0.732051i q^{60} +(-2.59808 - 4.50000i) q^{61} +(1.09808 - 1.90192i) q^{62} +(-0.866025 - 0.500000i) q^{63} -1.00000 q^{64} +(2.36603 + 1.16987i) q^{65} +1.73205 q^{66} +(7.73205 + 4.46410i) q^{67} +(-1.86603 + 3.23205i) q^{68} +(-1.73205 - 3.00000i) q^{69} -0.732051i q^{70} +(-1.90192 + 1.09808i) q^{71} +(-0.866025 + 0.500000i) q^{72} -5.46410i q^{73} +(-3.36603 - 5.83013i) q^{74} +(-2.23205 + 3.86603i) q^{75} +(0.866025 + 0.500000i) q^{76} +1.73205 q^{77} +(-0.232051 - 3.59808i) q^{78} +2.07180 q^{79} +(-0.633975 - 0.366025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.50000 - 2.59808i) q^{82} +0.196152i q^{83} +(-0.866025 + 0.500000i) q^{84} +(-2.36603 + 1.36603i) q^{85} -3.26795i q^{86} +(-3.23205 - 5.59808i) q^{87} +(0.866025 - 1.50000i) q^{88} +(-9.06218 - 5.23205i) q^{89} -0.732051 q^{90} +(-0.232051 - 3.59808i) q^{91} -3.46410 q^{92} +(-1.90192 - 1.09808i) q^{93} +(1.23205 - 2.13397i) q^{94} +(0.366025 + 0.633975i) q^{95} +1.00000i q^{96} +(13.5622 - 7.83013i) q^{97} +(-0.866025 + 0.500000i) q^{98} -1.73205i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{3} + 2q^{4} - 2q^{9} + O(q^{10}) \) \( 4q - 2q^{3} + 2q^{4} - 2q^{9} - 2q^{10} + 6q^{11} - 4q^{12} - 4q^{13} - 4q^{14} - 6q^{15} - 2q^{16} + 4q^{17} - 6q^{20} + 4q^{25} - 12q^{26} + 4q^{27} - 6q^{29} - 2q^{30} - 6q^{33} - 2q^{35} + 2q^{36} + 6q^{37} - 4q^{38} + 8q^{39} - 4q^{40} + 2q^{42} + 10q^{43} + 6q^{45} + 12q^{46} - 2q^{48} + 2q^{49} - 12q^{50} - 8q^{51} + 4q^{52} + 28q^{53} - 6q^{55} - 2q^{56} + 12q^{58} + 24q^{59} - 6q^{62} - 4q^{64} + 6q^{65} + 24q^{67} - 4q^{68} - 18q^{71} - 10q^{74} - 2q^{75} + 6q^{78} + 36q^{79} - 6q^{80} - 2q^{81} - 6q^{82} - 6q^{85} - 6q^{87} - 12q^{89} + 4q^{90} + 6q^{91} - 18q^{93} - 2q^{94} - 2q^{95} + 30q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0.732051i 0.327383i 0.986512 + 0.163692i \(0.0523402\pi\)
−0.986512 + 0.163692i \(0.947660\pi\)
\(6\) 0.866025 0.500000i 0.353553 0.204124i
\(7\) 0.866025 0.500000i 0.327327 0.188982i
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0.366025 0.633975i 0.115747 0.200480i
\(11\) 1.50000 + 0.866025i 0.452267 + 0.261116i 0.708787 0.705422i \(-0.249243\pi\)
−0.256520 + 0.966539i \(0.582576\pi\)
\(12\) −1.00000 −0.288675
\(13\) 1.59808 3.23205i 0.443227 0.896410i
\(14\) −1.00000 −0.267261
\(15\) −0.633975 0.366025i −0.163692 0.0945074i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.86603 + 3.23205i 0.452578 + 0.783887i 0.998545 0.0539188i \(-0.0171712\pi\)
−0.545968 + 0.837806i \(0.683838\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 0.866025 0.500000i 0.198680 0.114708i −0.397360 0.917663i \(-0.630073\pi\)
0.596040 + 0.802955i \(0.296740\pi\)
\(20\) −0.633975 + 0.366025i −0.141761 + 0.0818458i
\(21\) 1.00000i 0.218218i
\(22\) −0.866025 1.50000i −0.184637 0.319801i
\(23\) −1.73205 + 3.00000i −0.361158 + 0.625543i −0.988152 0.153481i \(-0.950952\pi\)
0.626994 + 0.779024i \(0.284285\pi\)
\(24\) 0.866025 + 0.500000i 0.176777 + 0.102062i
\(25\) 4.46410 0.892820
\(26\) −3.00000 + 2.00000i −0.588348 + 0.392232i
\(27\) 1.00000 0.192450
\(28\) 0.866025 + 0.500000i 0.163663 + 0.0944911i
\(29\) −3.23205 + 5.59808i −0.600177 + 1.03954i 0.392617 + 0.919702i \(0.371570\pi\)
−0.992794 + 0.119835i \(0.961764\pi\)
\(30\) 0.366025 + 0.633975i 0.0668268 + 0.115747i
\(31\) 2.19615i 0.394441i 0.980359 + 0.197220i \(0.0631914\pi\)
−0.980359 + 0.197220i \(0.936809\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) −1.50000 + 0.866025i −0.261116 + 0.150756i
\(34\) 3.73205i 0.640041i
\(35\) 0.366025 + 0.633975i 0.0618696 + 0.107161i
\(36\) 0.500000 0.866025i 0.0833333 0.144338i
\(37\) 5.83013 + 3.36603i 0.958467 + 0.553371i 0.895701 0.444657i \(-0.146674\pi\)
0.0627661 + 0.998028i \(0.480008\pi\)
\(38\) −1.00000 −0.162221
\(39\) 2.00000 + 3.00000i 0.320256 + 0.480384i
\(40\) 0.732051 0.115747
\(41\) 2.59808 + 1.50000i 0.405751 + 0.234261i 0.688963 0.724797i \(-0.258066\pi\)
−0.283211 + 0.959058i \(0.591400\pi\)
\(42\) 0.500000 0.866025i 0.0771517 0.133631i
\(43\) 1.63397 + 2.83013i 0.249179 + 0.431590i 0.963298 0.268434i \(-0.0865060\pi\)
−0.714119 + 0.700024i \(0.753173\pi\)
\(44\) 1.73205i 0.261116i
\(45\) 0.633975 0.366025i 0.0945074 0.0545638i
\(46\) 3.00000 1.73205i 0.442326 0.255377i
\(47\) 2.46410i 0.359426i 0.983719 + 0.179713i \(0.0575169\pi\)
−0.983719 + 0.179713i \(0.942483\pi\)
\(48\) −0.500000 0.866025i −0.0721688 0.125000i
\(49\) 0.500000 0.866025i 0.0714286 0.123718i
\(50\) −3.86603 2.23205i −0.546739 0.315660i
\(51\) −3.73205 −0.522592
\(52\) 3.59808 0.232051i 0.498963 0.0321797i
\(53\) 7.00000 0.961524 0.480762 0.876851i \(-0.340360\pi\)
0.480762 + 0.876851i \(0.340360\pi\)
\(54\) −0.866025 0.500000i −0.117851 0.0680414i
\(55\) −0.633975 + 1.09808i −0.0854851 + 0.148065i
\(56\) −0.500000 0.866025i −0.0668153 0.115728i
\(57\) 1.00000i 0.132453i
\(58\) 5.59808 3.23205i 0.735063 0.424389i
\(59\) 0.803848 0.464102i 0.104652 0.0604209i −0.446760 0.894654i \(-0.647422\pi\)
0.551413 + 0.834233i \(0.314089\pi\)
\(60\) 0.732051i 0.0945074i
\(61\) −2.59808 4.50000i −0.332650 0.576166i 0.650381 0.759608i \(-0.274609\pi\)
−0.983030 + 0.183442i \(0.941276\pi\)
\(62\) 1.09808 1.90192i 0.139456 0.241545i
\(63\) −0.866025 0.500000i −0.109109 0.0629941i
\(64\) −1.00000 −0.125000
\(65\) 2.36603 + 1.16987i 0.293469 + 0.145105i
\(66\) 1.73205 0.213201
\(67\) 7.73205 + 4.46410i 0.944620 + 0.545377i 0.891406 0.453206i \(-0.149720\pi\)
0.0532147 + 0.998583i \(0.483053\pi\)
\(68\) −1.86603 + 3.23205i −0.226289 + 0.391944i
\(69\) −1.73205 3.00000i −0.208514 0.361158i
\(70\) 0.732051i 0.0874968i
\(71\) −1.90192 + 1.09808i −0.225717 + 0.130318i −0.608595 0.793481i \(-0.708266\pi\)
0.382878 + 0.923799i \(0.374933\pi\)
\(72\) −0.866025 + 0.500000i −0.102062 + 0.0589256i
\(73\) 5.46410i 0.639525i −0.947498 0.319762i \(-0.896397\pi\)
0.947498 0.319762i \(-0.103603\pi\)
\(74\) −3.36603 5.83013i −0.391293 0.677738i
\(75\) −2.23205 + 3.86603i −0.257735 + 0.446410i
\(76\) 0.866025 + 0.500000i 0.0993399 + 0.0573539i
\(77\) 1.73205 0.197386
\(78\) −0.232051 3.59808i −0.0262746 0.407402i
\(79\) 2.07180 0.233095 0.116548 0.993185i \(-0.462817\pi\)
0.116548 + 0.993185i \(0.462817\pi\)
\(80\) −0.633975 0.366025i −0.0708805 0.0409229i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −1.50000 2.59808i −0.165647 0.286910i
\(83\) 0.196152i 0.0215305i 0.999942 + 0.0107653i \(0.00342676\pi\)
−0.999942 + 0.0107653i \(0.996573\pi\)
\(84\) −0.866025 + 0.500000i −0.0944911 + 0.0545545i
\(85\) −2.36603 + 1.36603i −0.256631 + 0.148166i
\(86\) 3.26795i 0.352392i
\(87\) −3.23205 5.59808i −0.346512 0.600177i
\(88\) 0.866025 1.50000i 0.0923186 0.159901i
\(89\) −9.06218 5.23205i −0.960589 0.554596i −0.0642347 0.997935i \(-0.520461\pi\)
−0.896354 + 0.443339i \(0.853794\pi\)
\(90\) −0.732051 −0.0771649
\(91\) −0.232051 3.59808i −0.0243255 0.377181i
\(92\) −3.46410 −0.361158
\(93\) −1.90192 1.09808i −0.197220 0.113865i
\(94\) 1.23205 2.13397i 0.127076 0.220103i
\(95\) 0.366025 + 0.633975i 0.0375534 + 0.0650444i
\(96\) 1.00000i 0.102062i
\(97\) 13.5622 7.83013i 1.37703 0.795029i 0.385230 0.922821i \(-0.374122\pi\)
0.991801 + 0.127792i \(0.0407889\pi\)
\(98\) −0.866025 + 0.500000i −0.0874818 + 0.0505076i
\(99\) 1.73205i 0.174078i
\(100\) 2.23205 + 3.86603i 0.223205 + 0.386603i
\(101\) 1.53590 2.66025i 0.152828 0.264705i −0.779438 0.626479i \(-0.784495\pi\)
0.932266 + 0.361774i \(0.117829\pi\)
\(102\) 3.23205 + 1.86603i 0.320021 + 0.184764i
\(103\) −14.7321 −1.45159 −0.725796 0.687910i \(-0.758528\pi\)
−0.725796 + 0.687910i \(0.758528\pi\)
\(104\) −3.23205 1.59808i −0.316929 0.156704i
\(105\) −0.732051 −0.0714408
\(106\) −6.06218 3.50000i −0.588811 0.339950i
\(107\) −5.42820 + 9.40192i −0.524764 + 0.908918i 0.474820 + 0.880083i \(0.342513\pi\)
−0.999584 + 0.0288353i \(0.990820\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) 4.73205i 0.453248i 0.973982 + 0.226624i \(0.0727689\pi\)
−0.973982 + 0.226624i \(0.927231\pi\)
\(110\) 1.09808 0.633975i 0.104697 0.0604471i
\(111\) −5.83013 + 3.36603i −0.553371 + 0.319489i
\(112\) 1.00000i 0.0944911i
\(113\) −7.63397 13.2224i −0.718144 1.24386i −0.961734 0.273984i \(-0.911659\pi\)
0.243590 0.969878i \(-0.421675\pi\)
\(114\) 0.500000 0.866025i 0.0468293 0.0811107i
\(115\) −2.19615 1.26795i −0.204792 0.118237i
\(116\) −6.46410 −0.600177
\(117\) −3.59808 + 0.232051i −0.332642 + 0.0214531i
\(118\) −0.928203 −0.0854480
\(119\) 3.23205 + 1.86603i 0.296282 + 0.171058i
\(120\) −0.366025 + 0.633975i −0.0334134 + 0.0578737i
\(121\) −4.00000 6.92820i −0.363636 0.629837i
\(122\) 5.19615i 0.470438i
\(123\) −2.59808 + 1.50000i −0.234261 + 0.135250i
\(124\) −1.90192 + 1.09808i −0.170798 + 0.0986102i
\(125\) 6.92820i 0.619677i
\(126\) 0.500000 + 0.866025i 0.0445435 + 0.0771517i
\(127\) −7.73205 + 13.3923i −0.686109 + 1.18837i 0.286978 + 0.957937i \(0.407349\pi\)
−0.973087 + 0.230438i \(0.925984\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) −3.26795 −0.287727
\(130\) −1.46410 2.19615i −0.128410 0.192615i
\(131\) −13.8564 −1.21064 −0.605320 0.795982i \(-0.706955\pi\)
−0.605320 + 0.795982i \(0.706955\pi\)
\(132\) −1.50000 0.866025i −0.130558 0.0753778i
\(133\) 0.500000 0.866025i 0.0433555 0.0750939i
\(134\) −4.46410 7.73205i −0.385640 0.667947i
\(135\) 0.732051i 0.0630049i
\(136\) 3.23205 1.86603i 0.277146 0.160010i
\(137\) 12.4641 7.19615i 1.06488 0.614809i 0.138102 0.990418i \(-0.455900\pi\)
0.926778 + 0.375609i \(0.122567\pi\)
\(138\) 3.46410i 0.294884i
\(139\) −5.79423 10.0359i −0.491460 0.851234i 0.508492 0.861067i \(-0.330203\pi\)
−0.999952 + 0.00983316i \(0.996870\pi\)
\(140\) −0.366025 + 0.633975i −0.0309348 + 0.0535806i
\(141\) −2.13397 1.23205i −0.179713 0.103757i
\(142\) 2.19615 0.184297
\(143\) 5.19615 3.46410i 0.434524 0.289683i
\(144\) 1.00000 0.0833333
\(145\) −4.09808 2.36603i −0.340327 0.196488i
\(146\) −2.73205 + 4.73205i −0.226106 + 0.391627i
\(147\) 0.500000 + 0.866025i 0.0412393 + 0.0714286i
\(148\) 6.73205i 0.553371i
\(149\) 12.0000 6.92820i 0.983078 0.567581i 0.0798802 0.996804i \(-0.474546\pi\)
0.903198 + 0.429224i \(0.141213\pi\)
\(150\) 3.86603 2.23205i 0.315660 0.182246i
\(151\) 5.19615i 0.422857i 0.977393 + 0.211428i \(0.0678115\pi\)
−0.977393 + 0.211428i \(0.932188\pi\)
\(152\) −0.500000 0.866025i −0.0405554 0.0702439i
\(153\) 1.86603 3.23205i 0.150859 0.261296i
\(154\) −1.50000 0.866025i −0.120873 0.0697863i
\(155\) −1.60770 −0.129133
\(156\) −1.59808 + 3.23205i −0.127948 + 0.258771i
\(157\) −0.535898 −0.0427693 −0.0213847 0.999771i \(-0.506807\pi\)
−0.0213847 + 0.999771i \(0.506807\pi\)
\(158\) −1.79423 1.03590i −0.142741 0.0824117i
\(159\) −3.50000 + 6.06218i −0.277568 + 0.480762i
\(160\) 0.366025 + 0.633975i 0.0289368 + 0.0501201i
\(161\) 3.46410i 0.273009i
\(162\) 0.866025 0.500000i 0.0680414 0.0392837i
\(163\) 2.36603 1.36603i 0.185321 0.106995i −0.404469 0.914552i \(-0.632544\pi\)
0.589790 + 0.807556i \(0.299210\pi\)
\(164\) 3.00000i 0.234261i
\(165\) −0.633975 1.09808i −0.0493549 0.0854851i
\(166\) 0.0980762 0.169873i 0.00761219 0.0131847i
\(167\) −12.0000 6.92820i −0.928588 0.536120i −0.0422232 0.999108i \(-0.513444\pi\)
−0.886365 + 0.462988i \(0.846777\pi\)
\(168\) 1.00000 0.0771517
\(169\) −7.89230 10.3301i −0.607100 0.794625i
\(170\) 2.73205 0.209539
\(171\) −0.866025 0.500000i −0.0662266 0.0382360i
\(172\) −1.63397 + 2.83013i −0.124589 + 0.215795i
\(173\) −4.56218 7.90192i −0.346856 0.600772i 0.638833 0.769345i \(-0.279417\pi\)
−0.985689 + 0.168573i \(0.946084\pi\)
\(174\) 6.46410i 0.490042i
\(175\) 3.86603 2.23205i 0.292244 0.168727i
\(176\) −1.50000 + 0.866025i −0.113067 + 0.0652791i
\(177\) 0.928203i 0.0697680i
\(178\) 5.23205 + 9.06218i 0.392159 + 0.679239i
\(179\) 5.73205 9.92820i 0.428434 0.742069i −0.568301 0.822821i \(-0.692399\pi\)
0.996734 + 0.0807523i \(0.0257323\pi\)
\(180\) 0.633975 + 0.366025i 0.0472537 + 0.0272819i
\(181\) 2.66025 0.197735 0.0988676 0.995101i \(-0.468478\pi\)
0.0988676 + 0.995101i \(0.468478\pi\)
\(182\) −1.59808 + 3.23205i −0.118457 + 0.239576i
\(183\) 5.19615 0.384111
\(184\) 3.00000 + 1.73205i 0.221163 + 0.127688i
\(185\) −2.46410 + 4.26795i −0.181164 + 0.313786i
\(186\) 1.09808 + 1.90192i 0.0805149 + 0.139456i
\(187\) 6.46410i 0.472702i
\(188\) −2.13397 + 1.23205i −0.155636 + 0.0898565i
\(189\) 0.866025 0.500000i 0.0629941 0.0363696i
\(190\) 0.732051i 0.0531085i
\(191\) −11.5622 20.0263i −0.836610 1.44905i −0.892713 0.450626i \(-0.851201\pi\)
0.0561031 0.998425i \(-0.482132\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) −1.03590 0.598076i −0.0745656 0.0430505i 0.462254 0.886748i \(-0.347041\pi\)
−0.536819 + 0.843697i \(0.680374\pi\)
\(194\) −15.6603 −1.12434
\(195\) −2.19615 + 1.46410i −0.157270 + 0.104846i
\(196\) 1.00000 0.0714286
\(197\) 23.0885 + 13.3301i 1.64498 + 0.949732i 0.979024 + 0.203745i \(0.0653114\pi\)
0.665961 + 0.745987i \(0.268022\pi\)
\(198\) −0.866025 + 1.50000i −0.0615457 + 0.106600i
\(199\) −8.09808 14.0263i −0.574057 0.994297i −0.996143 0.0877408i \(-0.972035\pi\)
0.422086 0.906556i \(-0.361298\pi\)
\(200\) 4.46410i 0.315660i
\(201\) −7.73205 + 4.46410i −0.545377 + 0.314873i
\(202\) −2.66025 + 1.53590i −0.187175 + 0.108065i
\(203\) 6.46410i 0.453691i
\(204\) −1.86603 3.23205i −0.130648 0.226289i
\(205\) −1.09808 + 1.90192i −0.0766930 + 0.132836i
\(206\) 12.7583 + 7.36603i 0.888915 + 0.513215i
\(207\) 3.46410 0.240772
\(208\) 2.00000 + 3.00000i 0.138675 + 0.208013i
\(209\) 1.73205 0.119808
\(210\) 0.633975 + 0.366025i 0.0437484 + 0.0252582i
\(211\) −13.0000 + 22.5167i −0.894957 + 1.55011i −0.0610990 + 0.998132i \(0.519461\pi\)
−0.833858 + 0.551979i \(0.813873\pi\)
\(212\) 3.50000 + 6.06218i 0.240381 + 0.416352i
\(213\) 2.19615i 0.150478i
\(214\) 9.40192 5.42820i 0.642702 0.371064i
\(215\) −2.07180 + 1.19615i −0.141295 + 0.0815769i
\(216\) 1.00000i 0.0680414i
\(217\) 1.09808 + 1.90192i 0.0745423 + 0.129111i
\(218\) 2.36603 4.09808i 0.160247 0.277557i
\(219\) 4.73205 + 2.73205i 0.319762 + 0.184615i
\(220\) −1.26795 −0.0854851
\(221\) 13.4282 0.866025i 0.903279 0.0582552i
\(222\) 6.73205 0.451826
\(223\) 21.1244 + 12.1962i 1.41459 + 0.816715i 0.995817 0.0913753i \(-0.0291263\pi\)
0.418775 + 0.908090i \(0.362460\pi\)
\(224\) 0.500000 0.866025i 0.0334077 0.0578638i
\(225\) −2.23205 3.86603i −0.148803 0.257735i
\(226\) 15.2679i 1.01561i
\(227\) 15.9282 9.19615i 1.05719 0.610370i 0.132538 0.991178i \(-0.457687\pi\)
0.924654 + 0.380808i \(0.124354\pi\)
\(228\) −0.866025 + 0.500000i −0.0573539 + 0.0331133i
\(229\) 19.9282i 1.31689i −0.752628 0.658446i \(-0.771214\pi\)
0.752628 0.658446i \(-0.228786\pi\)
\(230\) 1.26795 + 2.19615i 0.0836061 + 0.144810i
\(231\) −0.866025 + 1.50000i −0.0569803 + 0.0986928i
\(232\) 5.59808 + 3.23205i 0.367532 + 0.212195i
\(233\) 9.12436 0.597756 0.298878 0.954291i \(-0.403388\pi\)
0.298878 + 0.954291i \(0.403388\pi\)
\(234\) 3.23205 + 1.59808i 0.211286 + 0.104470i
\(235\) −1.80385 −0.117670
\(236\) 0.803848 + 0.464102i 0.0523260 + 0.0302104i
\(237\) −1.03590 + 1.79423i −0.0672888 + 0.116548i
\(238\) −1.86603 3.23205i −0.120956 0.209503i
\(239\) 0.732051i 0.0473524i 0.999720 + 0.0236762i \(0.00753708\pi\)
−0.999720 + 0.0236762i \(0.992463\pi\)
\(240\) 0.633975 0.366025i 0.0409229 0.0236268i
\(241\) −6.92820 + 4.00000i −0.446285 + 0.257663i −0.706260 0.707953i \(-0.749619\pi\)
0.259975 + 0.965615i \(0.416286\pi\)
\(242\) 8.00000i 0.514259i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 2.59808 4.50000i 0.166325 0.288083i
\(245\) 0.633975 + 0.366025i 0.0405032 + 0.0233845i
\(246\) 3.00000 0.191273
\(247\) −0.232051 3.59808i −0.0147650 0.228940i
\(248\) 2.19615 0.139456
\(249\) −0.169873 0.0980762i −0.0107653 0.00621533i
\(250\) 3.46410 6.00000i 0.219089 0.379473i
\(251\) 6.56218 + 11.3660i 0.414201 + 0.717417i 0.995344 0.0963841i \(-0.0307277\pi\)
−0.581143 + 0.813801i \(0.697394\pi\)
\(252\) 1.00000i 0.0629941i
\(253\) −5.19615 + 3.00000i −0.326679 + 0.188608i
\(254\) 13.3923 7.73205i 0.840308 0.485152i
\(255\) 2.73205i 0.171088i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 10.3301 17.8923i 0.644376 1.11609i −0.340070 0.940400i \(-0.610451\pi\)
0.984445 0.175691i \(-0.0562160\pi\)
\(258\) 2.83013 + 1.63397i 0.176196 + 0.101727i
\(259\) 6.73205 0.418309
\(260\) 0.169873 + 2.63397i 0.0105351 + 0.163352i
\(261\) 6.46410 0.400118
\(262\) 12.0000 + 6.92820i 0.741362 + 0.428026i
\(263\) 7.56218 13.0981i 0.466304 0.807662i −0.532955 0.846143i \(-0.678919\pi\)
0.999259 + 0.0384813i \(0.0122520\pi\)
\(264\) 0.866025 + 1.50000i 0.0533002 + 0.0923186i
\(265\) 5.12436i 0.314787i
\(266\) −0.866025 + 0.500000i −0.0530994 + 0.0306570i
\(267\) 9.06218 5.23205i 0.554596 0.320196i
\(268\) 8.92820i 0.545377i
\(269\) 4.92820 + 8.53590i 0.300478 + 0.520443i 0.976244 0.216673i \(-0.0695205\pi\)
−0.675766 + 0.737116i \(0.736187\pi\)
\(270\) 0.366025 0.633975i 0.0222756 0.0385825i
\(271\) −24.2942 14.0263i −1.47577 0.852036i −0.476143 0.879368i \(-0.657965\pi\)
−0.999626 + 0.0273321i \(0.991299\pi\)
\(272\) −3.73205 −0.226289
\(273\) 3.23205 + 1.59808i 0.195613 + 0.0967200i
\(274\) −14.3923 −0.869471
\(275\) 6.69615 + 3.86603i 0.403793 + 0.233130i
\(276\) 1.73205 3.00000i 0.104257 0.180579i
\(277\) 4.66025 + 8.07180i 0.280008 + 0.484987i 0.971386 0.237505i \(-0.0763297\pi\)
−0.691379 + 0.722493i \(0.742996\pi\)
\(278\) 11.5885i 0.695029i
\(279\) 1.90192 1.09808i 0.113865 0.0657401i
\(280\) 0.633975 0.366025i 0.0378872 0.0218742i
\(281\) 0.339746i 0.0202675i −0.999949 0.0101338i \(-0.996774\pi\)
0.999949 0.0101338i \(-0.00322574\pi\)
\(282\) 1.23205 + 2.13397i 0.0733676 + 0.127076i
\(283\) −4.92820 + 8.53590i −0.292951 + 0.507406i −0.974506 0.224360i \(-0.927971\pi\)
0.681555 + 0.731767i \(0.261304\pi\)
\(284\) −1.90192 1.09808i −0.112858 0.0651588i
\(285\) −0.732051 −0.0433629
\(286\) −6.23205 + 0.401924i −0.368509 + 0.0237663i
\(287\) 3.00000 0.177084
\(288\) −0.866025 0.500000i −0.0510310 0.0294628i
\(289\) 1.53590 2.66025i 0.0903470 0.156486i
\(290\) 2.36603 + 4.09808i 0.138938 + 0.240647i
\(291\) 15.6603i 0.918020i
\(292\) 4.73205 2.73205i 0.276922 0.159881i
\(293\) −14.7846 + 8.53590i −0.863726 + 0.498673i −0.865258 0.501326i \(-0.832846\pi\)
0.00153218 + 0.999999i \(0.499512\pi\)
\(294\) 1.00000i 0.0583212i
\(295\) 0.339746 + 0.588457i 0.0197808 + 0.0342613i
\(296\) 3.36603 5.83013i 0.195646 0.338869i
\(297\) 1.50000 + 0.866025i 0.0870388 + 0.0502519i
\(298\) −13.8564 −0.802680
\(299\) 6.92820 + 10.3923i 0.400668 + 0.601003i
\(300\) −4.46410 −0.257735
\(301\) 2.83013 + 1.63397i 0.163126 + 0.0941807i
\(302\) 2.59808 4.50000i 0.149502 0.258946i
\(303\) 1.53590 + 2.66025i 0.0882351 + 0.152828i
\(304\) 1.00000i 0.0573539i
\(305\) 3.29423 1.90192i 0.188627 0.108904i
\(306\) −3.23205 + 1.86603i −0.184764 + 0.106674i
\(307\) 8.60770i 0.491267i 0.969363 + 0.245634i \(0.0789960\pi\)
−0.969363 + 0.245634i \(0.921004\pi\)
\(308\) 0.866025 + 1.50000i 0.0493464 + 0.0854704i
\(309\) 7.36603 12.7583i 0.419039 0.725796i
\(310\) 1.39230 + 0.803848i 0.0790776 + 0.0456555i
\(311\) −4.26795 −0.242013 −0.121007 0.992652i \(-0.538612\pi\)
−0.121007 + 0.992652i \(0.538612\pi\)
\(312\) 3.00000 2.00000i 0.169842 0.113228i
\(313\) 13.5167 0.764007 0.382003 0.924161i \(-0.375234\pi\)
0.382003 + 0.924161i \(0.375234\pi\)
\(314\) 0.464102 + 0.267949i 0.0261908 + 0.0151212i
\(315\) 0.366025 0.633975i 0.0206232 0.0357204i
\(316\) 1.03590 + 1.79423i 0.0582738 + 0.100933i
\(317\) 11.8564i 0.665922i 0.942941 + 0.332961i \(0.108048\pi\)
−0.942941 + 0.332961i \(0.891952\pi\)
\(318\) 6.06218 3.50000i 0.339950 0.196270i
\(319\) −9.69615 + 5.59808i −0.542880 + 0.313432i
\(320\) 0.732051i 0.0409229i
\(321\) −5.42820 9.40192i −0.302973 0.524764i
\(322\) 1.73205 3.00000i 0.0965234 0.167183i
\(323\) 3.23205 + 1.86603i 0.179836 + 0.103828i
\(324\) −1.00000 −0.0555556
\(325\) 7.13397 14.4282i 0.395722 0.800333i
\(326\) −2.73205 −0.151314
\(327\) −4.09808 2.36603i −0.226624 0.130842i
\(328\) 1.50000 2.59808i 0.0828236 0.143455i
\(329\) 1.23205 + 2.13397i 0.0679252 + 0.117650i
\(330\) 1.26795i 0.0697983i
\(331\) 24.1244 13.9282i 1.32599 0.765563i 0.341317 0.939948i \(-0.389127\pi\)
0.984678 + 0.174385i \(0.0557937\pi\)
\(332\) −0.169873 + 0.0980762i −0.00932299 + 0.00538263i
\(333\) 6.73205i 0.368914i
\(334\) 6.92820 + 12.0000i 0.379094 + 0.656611i
\(335\) −3.26795 + 5.66025i −0.178547 + 0.309253i
\(336\) −0.866025 0.500000i −0.0472456 0.0272772i
\(337\) −19.0000 −1.03500 −0.517498 0.855684i \(-0.673136\pi\)
−0.517498 + 0.855684i \(0.673136\pi\)
\(338\) 1.66987 + 12.8923i 0.0908291 + 0.701249i
\(339\) 15.2679 0.829241
\(340\) −2.36603 1.36603i −0.128316 0.0740831i
\(341\) −1.90192 + 3.29423i −0.102995 + 0.178392i
\(342\) 0.500000 + 0.866025i 0.0270369 + 0.0468293i
\(343\) 1.00000i 0.0539949i
\(344\) 2.83013 1.63397i 0.152590 0.0880980i
\(345\) 2.19615 1.26795i 0.118237 0.0682641i
\(346\) 9.12436i 0.490528i
\(347\) −2.69615 4.66987i −0.144737 0.250692i 0.784538 0.620081i \(-0.212900\pi\)
−0.929275 + 0.369389i \(0.879567\pi\)
\(348\) 3.23205 5.59808i 0.173256 0.300088i
\(349\) −20.5359 11.8564i −1.09926 0.634659i −0.163235 0.986587i \(-0.552193\pi\)
−0.936027 + 0.351928i \(0.885526\pi\)
\(350\) −4.46410 −0.238616
\(351\) 1.59808 3.23205i 0.0852990 0.172514i
\(352\) 1.73205 0.0923186
\(353\) −8.19615 4.73205i −0.436237 0.251862i 0.265763 0.964038i \(-0.414376\pi\)
−0.702000 + 0.712177i \(0.747709\pi\)
\(354\) 0.464102 0.803848i 0.0246667 0.0427240i
\(355\) −0.803848 1.39230i −0.0426638 0.0738959i
\(356\) 10.4641i 0.554596i
\(357\) −3.23205 + 1.86603i −0.171058 + 0.0987605i
\(358\) −9.92820 + 5.73205i −0.524722 + 0.302948i
\(359\) 3.80385i 0.200759i −0.994949 0.100380i \(-0.967994\pi\)
0.994949 0.100380i \(-0.0320058\pi\)
\(360\) −0.366025 0.633975i −0.0192912 0.0334134i
\(361\) −9.00000 + 15.5885i −0.473684 + 0.820445i
\(362\) −2.30385 1.33013i −0.121088 0.0699099i
\(363\) 8.00000 0.419891
\(364\) 3.00000 2.00000i 0.157243 0.104828i
\(365\) 4.00000 0.209370
\(366\) −4.50000 2.59808i −0.235219 0.135804i
\(367\) −12.6603 + 21.9282i −0.660860 + 1.14464i 0.319530 + 0.947576i \(0.396475\pi\)
−0.980390 + 0.197067i \(0.936858\pi\)
\(368\) −1.73205 3.00000i −0.0902894 0.156386i
\(369\) 3.00000i 0.156174i
\(370\) 4.26795 2.46410i 0.221880 0.128103i
\(371\) 6.06218 3.50000i 0.314733 0.181711i
\(372\) 2.19615i 0.113865i
\(373\) −4.83013 8.36603i −0.250094 0.433176i 0.713457 0.700699i \(-0.247128\pi\)
−0.963552 + 0.267523i \(0.913795\pi\)
\(374\) 3.23205 5.59808i 0.167125 0.289470i
\(375\) −6.00000 3.46410i −0.309839 0.178885i
\(376\) 2.46410 0.127076
\(377\) 12.9282 + 19.3923i 0.665836 + 0.998755i
\(378\) −1.00000 −0.0514344
\(379\) 24.6340 + 14.2224i 1.26536 + 0.730557i 0.974107 0.226088i \(-0.0725937\pi\)
0.291255 + 0.956645i \(0.405927\pi\)
\(380\) −0.366025 + 0.633975i −0.0187767 + 0.0325222i
\(381\) −7.73205 13.3923i −0.396125 0.686109i
\(382\) 23.1244i 1.18314i
\(383\) −4.79423 + 2.76795i −0.244974 + 0.141436i −0.617461 0.786602i \(-0.711838\pi\)
0.372487 + 0.928037i \(0.378505\pi\)
\(384\) −0.866025 + 0.500000i −0.0441942 + 0.0255155i
\(385\) 1.26795i 0.0646207i
\(386\) 0.598076 + 1.03590i 0.0304413 + 0.0527258i
\(387\) 1.63397 2.83013i 0.0830596 0.143863i
\(388\) 13.5622 + 7.83013i 0.688515 + 0.397514i
\(389\) −8.39230 −0.425507 −0.212753 0.977106i \(-0.568243\pi\)
−0.212753 + 0.977106i \(0.568243\pi\)
\(390\) 2.63397 0.169873i 0.133376 0.00860185i
\(391\) −12.9282 −0.653807
\(392\) −0.866025 0.500000i −0.0437409 0.0252538i
\(393\) 6.92820 12.0000i 0.349482 0.605320i
\(394\) −13.3301 23.0885i −0.671562 1.16318i
\(395\) 1.51666i 0.0763115i
\(396\) 1.50000 0.866025i 0.0753778 0.0435194i
\(397\) 6.99038 4.03590i 0.350837 0.202556i −0.314217 0.949351i \(-0.601742\pi\)
0.665054 + 0.746795i \(0.268409\pi\)
\(398\) 16.1962i 0.811840i
\(399\) 0.500000 + 0.866025i 0.0250313 + 0.0433555i
\(400\) −2.23205 + 3.86603i −0.111603 + 0.193301i
\(401\) −33.5885 19.3923i −1.67733 0.968405i −0.963354 0.268233i \(-0.913560\pi\)
−0.713973 0.700173i \(-0.753106\pi\)
\(402\) 8.92820 0.445298
\(403\) 7.09808 + 3.50962i 0.353580 + 0.174827i
\(404\) 3.07180 0.152828
\(405\) −0.633975 0.366025i −0.0315025 0.0181879i
\(406\) 3.23205 5.59808i 0.160404 0.277828i
\(407\) 5.83013 + 10.0981i 0.288989 + 0.500543i
\(408\) 3.73205i 0.184764i
\(409\) −33.5429 + 19.3660i −1.65859 + 0.957588i −0.685226 + 0.728331i \(0.740297\pi\)
−0.973366 + 0.229258i \(0.926370\pi\)
\(410\) 1.90192 1.09808i 0.0939293 0.0542301i
\(411\) 14.3923i 0.709920i
\(412\) −7.36603 12.7583i −0.362898 0.628558i
\(413\) 0.464102 0.803848i 0.0228369 0.0395548i
\(414\) −3.00000 1.73205i −0.147442 0.0851257i
\(415\) −0.143594 −0.00704873
\(416\) −0.232051 3.59808i −0.0113772 0.176410i
\(417\) 11.5885 0.567489
\(418\) −1.50000 0.866025i −0.0733674 0.0423587i
\(419\) −0.366025 + 0.633975i −0.0178815 + 0.0309717i −0.874828 0.484434i \(-0.839025\pi\)
0.856946 + 0.515406i \(0.172359\pi\)
\(420\) −0.366025 0.633975i −0.0178602 0.0309348i
\(421\) 22.3923i 1.09133i 0.838002 + 0.545667i \(0.183724\pi\)
−0.838002 + 0.545667i \(0.816276\pi\)
\(422\) 22.5167 13.0000i 1.09609 0.632830i
\(423\) 2.13397 1.23205i 0.103757 0.0599044i
\(424\) 7.00000i 0.339950i
\(425\) 8.33013 + 14.4282i 0.404071 + 0.699871i
\(426\) −1.09808 + 1.90192i −0.0532020 + 0.0921485i
\(427\) −4.50000 2.59808i −0.217770 0.125730i
\(428\) −10.8564 −0.524764
\(429\) 0.401924 + 6.23205i 0.0194051 + 0.300886i
\(430\) 2.39230 0.115367
\(431\) −12.2942 7.09808i −0.592192 0.341902i 0.173772 0.984786i \(-0.444405\pi\)
−0.765964 + 0.642884i \(0.777738\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) −13.5359 23.4449i −0.650494 1.12669i −0.983003 0.183588i \(-0.941229\pi\)
0.332509 0.943100i \(-0.392105\pi\)
\(434\) 2.19615i 0.105419i
\(435\) 4.09808 2.36603i 0.196488 0.113442i
\(436\) −4.09808 + 2.36603i −0.196262 + 0.113312i
\(437\) 3.46410i 0.165710i
\(438\) −2.73205 4.73205i −0.130542 0.226106i
\(439\) −12.5885 + 21.8038i −0.600814 + 1.04064i 0.391884 + 0.920015i \(0.371824\pi\)
−0.992698 + 0.120626i \(0.961510\pi\)
\(440\) 1.09808 + 0.633975i 0.0523487 + 0.0302236i
\(441\) −1.00000 −0.0476190
\(442\) −12.0622 5.96410i −0.573739 0.283683i
\(443\) −33.6410 −1.59833 −0.799166 0.601110i \(-0.794725\pi\)
−0.799166 + 0.601110i \(0.794725\pi\)
\(444\) −5.83013 3.36603i −0.276686 0.159744i
\(445\) 3.83013 6.63397i 0.181565 0.314481i
\(446\) −12.1962 21.1244i −0.577505 1.00027i
\(447\) 13.8564i 0.655386i
\(448\) −0.866025 + 0.500000i −0.0409159 + 0.0236228i
\(449\) 17.8301 10.2942i 0.841456 0.485815i −0.0163031 0.999867i \(-0.505190\pi\)
0.857759 + 0.514052i \(0.171856\pi\)
\(450\) 4.46410i 0.210440i
\(451\) 2.59808 + 4.50000i 0.122339 + 0.211897i
\(452\) 7.63397 13.2224i 0.359072 0.621931i
\(453\) −4.50000 2.59808i −0.211428 0.122068i
\(454\) −18.3923 −0.863194
\(455\) 2.63397 0.169873i 0.123483 0.00796377i
\(456\) 1.00000 0.0468293
\(457\) 10.2679 + 5.92820i 0.480314 + 0.277310i 0.720548 0.693406i \(-0.243891\pi\)
−0.240233 + 0.970715i \(0.577224\pi\)
\(458\) −9.96410 + 17.2583i −0.465592 + 0.806429i
\(459\) 1.86603 + 3.23205i 0.0870986 + 0.150859i
\(460\) 2.53590i 0.118237i
\(461\) −23.3205 + 13.4641i −1.08614 + 0.627086i −0.932547 0.361048i \(-0.882419\pi\)
−0.153597 + 0.988134i \(0.549086\pi\)
\(462\) 1.50000 0.866025i 0.0697863 0.0402911i
\(463\) 6.26795i 0.291296i −0.989336 0.145648i \(-0.953473\pi\)
0.989336 0.145648i \(-0.0465267\pi\)
\(464\) −3.23205 5.59808i −0.150044 0.259884i
\(465\) 0.803848 1.39230i 0.0372775 0.0645666i
\(466\) −7.90192 4.56218i −0.366050 0.211339i
\(467\) 13.8564 0.641198 0.320599 0.947215i \(-0.396116\pi\)
0.320599 + 0.947215i \(0.396116\pi\)
\(468\) −2.00000 3.00000i −0.0924500 0.138675i
\(469\) 8.92820 0.412266
\(470\) 1.56218 + 0.901924i 0.0720579 + 0.0416026i
\(471\) 0.267949 0.464102i 0.0123464 0.0213847i
\(472\) −0.464102 0.803848i −0.0213620 0.0370001i
\(473\) 5.66025i 0.260259i
\(474\) 1.79423 1.03590i 0.0824117 0.0475804i
\(475\) 3.86603 2.23205i 0.177385 0.102414i
\(476\) 3.73205i 0.171058i
\(477\) −3.50000 6.06218i −0.160254 0.277568i
\(478\) 0.366025 0.633975i 0.0167416 0.0289973i
\(479\) −28.1147 16.2321i −1.28460 0.741661i −0.306910 0.951738i \(-0.599295\pi\)
−0.977685 + 0.210077i \(0.932628\pi\)
\(480\) −0.732051 −0.0334134
\(481\) 20.1962 13.4641i 0.920865 0.613910i
\(482\) 8.00000 0.364390
\(483\) −3.00000 1.73205i −0.136505 0.0788110i
\(484\) 4.00000 6.92820i 0.181818 0.314918i
\(485\) 5.73205 + 9.92820i 0.260279 + 0.450816i
\(486\) 1.00000i 0.0453609i
\(487\) −14.4282 + 8.33013i −0.653804 + 0.377474i −0.789912 0.613220i \(-0.789874\pi\)
0.136108 + 0.990694i \(0.456541\pi\)
\(488\) −4.50000 + 2.59808i −0.203705 + 0.117609i
\(489\) 2.73205i 0.123548i
\(490\) −0.366025 0.633975i −0.0165353 0.0286401i
\(491\) 17.7321 30.7128i 0.800236 1.38605i −0.119224 0.992867i \(-0.538041\pi\)
0.919460 0.393182i \(-0.128626\pi\)
\(492\) −2.59808 1.50000i −0.117130 0.0676252i
\(493\) −24.1244 −1.08651
\(494\) −1.59808 + 3.23205i −0.0719008 + 0.145417i
\(495\) 1.26795 0.0569901
\(496\) −1.90192 1.09808i −0.0853989 0.0493051i
\(497\) −1.09808 + 1.90192i −0.0492554 + 0.0853129i
\(498\) 0.0980762 + 0.169873i 0.00439490 + 0.00761219i
\(499\) 11.5167i 0.515557i −0.966204 0.257778i \(-0.917010\pi\)
0.966204 0.257778i \(-0.0829904\pi\)
\(500\) −6.00000 + 3.46410i −0.268328 + 0.154919i
\(501\) 12.0000 6.92820i 0.536120 0.309529i
\(502\) 13.1244i 0.585769i
\(503\) −3.46410 6.00000i −0.154457 0.267527i 0.778404 0.627763i \(-0.216029\pi\)
−0.932861 + 0.360236i \(0.882696\pi\)
\(504\) −0.500000 + 0.866025i −0.0222718 + 0.0385758i
\(505\) 1.94744 + 1.12436i 0.0866600 + 0.0500332i
\(506\) 6.00000 0.266733
\(507\) 12.8923 1.66987i 0.572567 0.0741617i
\(508\) −15.4641 −0.686109
\(509\) −19.3468 11.1699i −0.857531 0.495096i 0.00565352 0.999984i \(-0.498200\pi\)
−0.863185 + 0.504888i \(0.831534\pi\)
\(510\) −1.36603 + 2.36603i −0.0604886 + 0.104769i
\(511\) −2.73205 4.73205i −0.120859 0.209334i
\(512\) 1.00000i 0.0441942i
\(513\) 0.866025 0.500000i 0.0382360 0.0220755i
\(514\) −17.8923 + 10.3301i −0.789196 + 0.455642i
\(515\) 10.7846i 0.475227i
\(516\) −1.63397 2.83013i −0.0719317 0.124589i
\(517\) −2.13397 + 3.69615i −0.0938521 + 0.162557i
\(518\) −5.83013 3.36603i −0.256161 0.147895i
\(519\) 9.12436 0.400515
\(520\) 1.16987 2.36603i 0.0513023 0.103757i
\(521\) 7.05256 0.308978 0.154489 0.987994i \(-0.450627\pi\)
0.154489 + 0.987994i \(0.450627\pi\)
\(522\) −5.59808 3.23205i −0.245021 0.141463i
\(523\) 6.93782 12.0167i 0.303370 0.525452i −0.673527 0.739162i \(-0.735222\pi\)
0.976897 + 0.213711i \(0.0685549\pi\)
\(524\) −6.92820 12.0000i −0.302660 0.524222i
\(525\) 4.46410i 0.194829i
\(526\) −13.0981 + 7.56218i −0.571103 + 0.329727i
\(527\) −7.09808 + 4.09808i −0.309197 + 0.178515i
\(528\) 1.73205i 0.0753778i
\(529\) 5.50000 + 9.52628i 0.239130 + 0.414186i
\(530\) 2.56218 4.43782i 0.111294 0.192767i
\(531\) −0.803848 0.464102i −0.0348840 0.0201403i
\(532\) 1.00000 0.0433555
\(533\) 9.00000 6.00000i 0.389833 0.259889i
\(534\) −10.4641 −0.452826
\(535\) −6.88269 3.97372i −0.297564 0.171799i
\(536\) 4.46410 7.73205i 0.192820 0.333974i
\(537\) 5.73205 + 9.92820i 0.247356 + 0.428434i
\(538\) 9.85641i 0.424940i
\(539\) 1.50000 0.866025i 0.0646096 0.0373024i
\(540\) −0.633975 + 0.366025i −0.0272819 + 0.0157512i
\(541\) 24.3397i 1.04645i −0.852195 0.523224i \(-0.824729\pi\)
0.852195 0.523224i \(-0.175271\pi\)
\(542\) 14.0263 + 24.2942i 0.602480 + 1.04353i
\(543\) −1.33013 + 2.30385i −0.0570812 + 0.0988676i
\(544\) 3.23205 + 1.86603i 0.138573 + 0.0800052i
\(545\) −3.46410 −0.148386
\(546\) −2.00000 3.00000i −0.0855921 0.128388i
\(547\) −1.26795 −0.0542136 −0.0271068 0.999633i \(-0.508629\pi\)
−0.0271068 + 0.999633i \(0.508629\pi\)
\(548\) 12.4641 + 7.19615i 0.532440 + 0.307404i
\(549\) −2.59808 + 4.50000i −0.110883 + 0.192055i
\(550\) −3.86603 6.69615i −0.164848 0.285525i
\(551\) 6.46410i 0.275380i
\(552\) −3.00000 + 1.73205i −0.127688 + 0.0737210i
\(553\) 1.79423 1.03590i 0.0762984 0.0440509i
\(554\) 9.32051i 0.395990i
\(555\) −2.46410 4.26795i −0.104595 0.181164i
\(556\) 5.79423 10.0359i 0.245730 0.425617i
\(557\) 11.3038 + 6.52628i 0.478959 + 0.276527i 0.719983 0.693992i \(-0.244150\pi\)
−0.241023 + 0.970519i \(0.577483\pi\)
\(558\) −2.19615 −0.0929705
\(559\) 11.7583 0.758330i 0.497324 0.0320740i
\(560\) −0.732051 −0.0309348
\(561\) −5.59808 3.23205i −0.236351 0.136457i
\(562\) −0.169873 + 0.294229i −0.00716566 + 0.0124113i
\(563\) −18.0981 31.3468i −0.762743 1.32111i −0.941432 0.337204i \(-0.890519\pi\)
0.178689 0.983906i \(-0.442815\pi\)
\(564\) 2.46410i 0.103757i
\(565\) 9.67949 5.58846i 0.407219 0.235108i
\(566\) 8.53590 4.92820i 0.358791 0.207148i
\(567\) 1.00000i 0.0419961i
\(568\) 1.09808 + 1.90192i 0.0460743 + 0.0798029i
\(569\) −19.2224 + 33.2942i −0.805846 + 1.39577i 0.109872 + 0.993946i \(0.464956\pi\)
−0.915718 + 0.401821i \(0.868377\pi\)
\(570\) 0.633975 + 0.366025i 0.0265543 + 0.0153311i
\(571\) −16.9808 −0.710623 −0.355311 0.934748i \(-0.615625\pi\)
−0.355311 + 0.934748i \(0.615625\pi\)
\(572\) 5.59808 + 2.76795i 0.234067 + 0.115734i
\(573\) 23.1244 0.966034
\(574\) −2.59808 1.50000i −0.108442 0.0626088i
\(575\) −7.73205 + 13.3923i −0.322449 + 0.558498i
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) 10.3397i 0.430449i −0.976565 0.215225i \(-0.930952\pi\)
0.976565 0.215225i \(-0.0690484\pi\)
\(578\) −2.66025 + 1.53590i −0.110652 + 0.0638850i
\(579\) 1.03590 0.598076i 0.0430505 0.0248552i
\(580\) 4.73205i 0.196488i
\(581\) 0.0980762 + 0.169873i 0.00406889 + 0.00704752i
\(582\) 7.83013 13.5622i 0.324569 0.562170i
\(583\) 10.5000 + 6.06218i 0.434866 + 0.251070i
\(584\) −5.46410 −0.226106
\(585\) −0.169873 2.63397i −0.00702338 0.108901i
\(586\) 17.0718 0.705229
\(587\) 10.6865 + 6.16987i 0.441080 + 0.254658i 0.704056 0.710145i \(-0.251370\pi\)
−0.262975 + 0.964803i \(0.584704\pi\)
\(588\) −0.500000 + 0.866025i −0.0206197 + 0.0357143i
\(589\) 1.09808 + 1.90192i 0.0452454 + 0.0783674i
\(590\) 0.679492i 0.0279742i
\(591\) −23.0885 + 13.3301i −0.949732 + 0.548328i
\(592\) −5.83013 + 3.36603i −0.239617 + 0.138343i
\(593\) 0.464102i 0.0190584i 0.999955 + 0.00952918i \(0.00303328\pi\)
−0.999955 + 0.00952918i \(0.996967\pi\)
\(594\) −0.866025 1.50000i −0.0355335 0.0615457i
\(595\) −1.36603 + 2.36603i −0.0560016 + 0.0969976i
\(596\) 12.0000 + 6.92820i 0.491539 + 0.283790i
\(597\) 16.1962 0.662864
\(598\) −0.803848 12.4641i −0.0328718 0.509695i
\(599\) −28.6410 −1.17024 −0.585120 0.810947i \(-0.698953\pi\)
−0.585120 + 0.810947i \(0.698953\pi\)
\(600\) 3.86603 + 2.23205i 0.157830 + 0.0911231i
\(601\) 11.3660 19.6865i 0.463630 0.803030i −0.535509 0.844530i \(-0.679880\pi\)
0.999139 + 0.0414993i \(0.0132134\pi\)
\(602\) −1.63397 2.83013i −0.0665958 0.115347i
\(603\) 8.92820i 0.363585i
\(604\) −4.50000 + 2.59808i −0.183102 + 0.105714i
\(605\) 5.07180 2.92820i 0.206198 0.119048i
\(606\) 3.07180i 0.124783i
\(607\) 15.7583 + 27.2942i 0.639611 + 1.10784i 0.985518 + 0.169570i \(0.0542378\pi\)
−0.345907 + 0.938269i \(0.612429\pi\)
\(608\) 0.500000 0.866025i 0.0202777 0.0351220i
\(609\) −5.59808 3.23205i −0.226845 0.130969i
\(610\) −3.80385 −0.154013
\(611\) 7.96410 + 3.93782i 0.322193 + 0.159307i
\(612\) 3.73205 0.150859
\(613\) 3.46410 + 2.00000i 0.139914 + 0.0807792i 0.568323 0.822806i \(-0.307592\pi\)
−0.428409 + 0.903585i \(0.640926\pi\)
\(614\) 4.30385 7.45448i 0.173689 0.300838i
\(615\) −1.09808 1.90192i −0.0442787 0.0766930i
\(616\) 1.73205i 0.0697863i
\(617\) 1.90192 1.09808i 0.0765686 0.0442069i −0.461227 0.887282i \(-0.652591\pi\)
0.537795 + 0.843075i \(0.319257\pi\)
\(618\) −12.7583 + 7.36603i −0.513215 + 0.296305i
\(619\) 22.0718i 0.887140i 0.896240 + 0.443570i \(0.146288\pi\)
−0.896240 + 0.443570i \(0.853712\pi\)
\(620\) −0.803848 1.39230i −0.0322833 0.0559163i
\(621\) −1.73205 + 3.00000i −0.0695048 + 0.120386i
\(622\) 3.69615 + 2.13397i 0.148202 + 0.0855646i
\(623\) −10.4641 −0.419235
\(624\) −3.59808 + 0.232051i −0.144038 + 0.00928947i
\(625\) 17.2487 0.689948
\(626\) −11.7058 6.75833i −0.467857 0.270117i
\(627\) −0.866025 + 1.50000i −0.0345857 + 0.0599042i
\(628\) −0.267949 0.464102i −0.0106923 0.0185197i
\(629\) 25.1244i 1.00177i
\(630\) −0.633975 + 0.366025i −0.0252582 + 0.0145828i
\(631\) 14.5526 8.40192i 0.579328 0.334475i −0.181538 0.983384i \(-0.558108\pi\)
0.760866 + 0.648909i \(0.224774\pi\)
\(632\) 2.07180i 0.0824117i
\(633\) −13.0000 22.5167i −0.516704 0.894957i
\(634\) 5.92820 10.2679i 0.235439 0.407792i
\(635\) −9.80385 5.66025i −0.389054 0.224620i
\(636\) −7.00000 −0.277568
\(637\) −2.00000 3.00000i −0.0792429 0.118864i
\(638\) 11.1962 0.443260
\(639\) 1.90192 + 1.09808i 0.0752389 + 0.0434392i
\(640\) −0.366025 + 0.633975i −0.0144684 + 0.0250600i
\(641\) 15.5885 + 27.0000i 0.615707 + 1.06644i 0.990260 + 0.139230i \(0.0444629\pi\)
−0.374553 + 0.927206i \(0.622204\pi\)
\(642\) 10.8564i 0.428468i
\(643\) 28.4545 16.4282i 1.12214 0.647865i 0.180190 0.983632i \(-0.442329\pi\)
0.941945 + 0.335767i \(0.108995\pi\)
\(644\) −3.00000 + 1.73205i −0.118217 + 0.0682524i
\(645\) 2.39230i 0.0941969i
\(646\) −1.86603 3.23205i −0.0734178 0.127163i
\(647\) 17.9186 31.0359i 0.704452 1.22015i −0.262437 0.964949i \(-0.584526\pi\)
0.966889 0.255198i \(-0.0821406\pi\)
\(648\) 0.866025 + 0.500000i 0.0340207 + 0.0196419i
\(649\) 1.60770 0.0631076
\(650\) −13.3923 + 8.92820i −0.525289 + 0.350193i
\(651\) −2.19615 −0.0860740
\(652\) 2.36603 + 1.36603i 0.0926607 + 0.0534977i
\(653\) −23.3564 + 40.4545i −0.914007 + 1.58311i −0.105658 + 0.994403i \(0.533695\pi\)
−0.808349 + 0.588704i \(0.799638\pi\)
\(654\) 2.36603 + 4.09808i 0.0925189 + 0.160247i
\(655\) 10.1436i 0.396343i
\(656\) −2.59808 + 1.50000i −0.101438 + 0.0585652i
\(657\) −4.73205 + 2.73205i −0.184615 + 0.106587i
\(658\) 2.46410i 0.0960607i
\(659\) −9.30385 16.1147i −0.362426 0.627741i 0.625933 0.779877i \(-0.284718\pi\)
−0.988360 + 0.152136i \(0.951385\pi\)
\(660\) 0.633975 1.09808i 0.0246774 0.0427426i
\(661\) 10.7321 + 6.19615i 0.417428 + 0.241002i 0.693976 0.719998i \(-0.255857\pi\)
−0.276548 + 0.961000i \(0.589190\pi\)
\(662\) −27.8564 −1.08267
\(663\) −5.96410 + 12.0622i −0.231627 + 0.468456i
\(664\) 0.196152 0.00761219
\(665\) 0.633975 + 0.366025i 0.0245845 + 0.0141939i
\(666\) −3.36603 + 5.83013i −0.130431 + 0.225913i
\(667\) −11.1962 19.3923i −0.433517 0.750873i
\(668\) 13.8564i 0.536120i
\(669\) −21.1244 + 12.1962i −0.816715 + 0.471530i
\(670\) 5.66025 3.26795i 0.218675 0.126252i
\(671\) 9.00000i 0.347441i
\(672\) 0.500000 + 0.866025i 0.0192879 + 0.0334077i
\(673\) −16.3564 + 28.3301i −0.630493 + 1.09205i 0.356958 + 0.934120i \(0.383814\pi\)
−0.987451 + 0.157926i \(0.949519\pi\)
\(674\) 16.4545 + 9.50000i 0.633803 + 0.365926i
\(675\) 4.46410 0.171823
\(676\) 5.00000 12.0000i 0.192308 0.461538i
\(677\) 36.7321 1.41173 0.705864 0.708348i \(-0.250559\pi\)
0.705864 + 0.708348i \(0.250559\pi\)
\(678\) −13.2224 7.63397i −0.507804 0.293181i
\(679\) 7.83013 13.5622i 0.300493 0.520469i
\(680\) 1.36603 + 2.36603i 0.0523847 + 0.0907329i
\(681\) 18.3923i 0.704795i
\(682\) 3.29423 1.90192i 0.126143 0.0728284i
\(683\) 25.6410 14.8038i 0.981126 0.566453i 0.0785163 0.996913i \(-0.474982\pi\)
0.902610 + 0.430459i \(0.141648\pi\)
\(684\) 1.00000i 0.0382360i
\(685\) 5.26795 + 9.12436i 0.201278 + 0.348624i
\(686\) −0.500000 + 0.866025i −0.0190901 + 0.0330650i
\(687\) 17.2583 + 9.96410i 0.658446 + 0.380154i
\(688\) −3.26795 −0.124589
\(689\) 11.1865 22.6244i 0.426173 0.861919i
\(690\) −2.53590 −0.0965400
\(691\) 37.8564 + 21.8564i 1.44013 + 0.831457i 0.997857 0.0654260i \(-0.0208406\pi\)
0.442268 + 0.896883i \(0.354174\pi\)
\(692\) 4.56218 7.90192i 0.173428 0.300386i
\(693\) −0.866025 1.50000i −0.0328976 0.0569803i
\(694\) 5.39230i 0.204689i
\(695\) 7.34679 4.24167i 0.278680 0.160896i
\(696\) −5.59808 + 3.23205i −0.212195 + 0.122511i
\(697\) 11.1962i 0.424085i
\(698\) 11.8564 + 20.5359i 0.448772 + 0.777295i
\(699\) −4.56218 + 7.90192i −0.172557 + 0.298878i
\(700\) 3.86603 + 2.23205i 0.146122 + 0.0843636i
\(701\) −1.14359 −0.0431929 −0.0215965 0.999767i \(-0.506875\pi\)
−0.0215965 + 0.999767i \(0.506875\pi\)
\(702\) −3.00000 + 2.00000i −0.113228 + 0.0754851i
\(703\) 6.73205 0.253904
\(704\) −1.50000 0.866025i −0.0565334 0.0326396i
\(705\) 0.901924 1.56218i 0.0339684 0.0588350i
\(706\) 4.73205 + 8.19615i 0.178093 + 0.308466i
\(707\) 3.07180i 0.115527i
\(708\) −0.803848 + 0.464102i −0.0302104 + 0.0174420i
\(709\) −27.7583 + 16.0263i −1.04249 + 0.601880i −0.920536 0.390657i \(-0.872248\pi\)
−0.121950 + 0.992536i \(0.538915\pi\)
\(710\) 1.60770i 0.0603357i
\(711\) −1.03590 1.79423i −0.0388492 0.0672888i
\(712\) −5.23205 + 9.06218i −0.196079 + 0.339619i
\(713\) −6.58846 3.80385i −0.246740 0.142455i
\(714\) 3.73205 0.139668
\(715\) 2.53590 + 3.80385i 0.0948372 + 0.142256i
\(716\) 11.4641 0.428434
\(717\) −0.633975 0.366025i −0.0236762 0.0136695i
\(718\) −1.90192 + 3.29423i −0.0709792 + 0.122940i
\(719\) 13.2583 + 22.9641i 0.494452 + 0.856416i 0.999980 0.00639415i \(-0.00203533\pi\)
−0.505527 + 0.862811i \(0.668702\pi\)
\(720\) 0.732051i 0.0272819i
\(721\) −12.7583 + 7.36603i −0.475145 + 0.274325i
\(722\) 15.5885 9.00000i 0.580142 0.334945i
\(723\) 8.00000i 0.297523i
\(724\) 1.33013 + 2.30385i 0.0494338 + 0.0856218i
\(725\) −14.4282 + 24.9904i −0.535850 + 0.928119i
\(726\) −6.92820 4.00000i −0.257130 0.148454i
\(727\) 19.3205 0.716558 0.358279 0.933615i \(-0.383364\pi\)
0.358279 + 0.933615i \(0.383364\pi\)
\(728\) −3.59808 + 0.232051i −0.133354 + 0.00860038i
\(729\) 1.00000 0.0370370
\(730\) −3.46410 2.00000i −0.128212 0.0740233i
\(731\) −6.09808 + 10.5622i −0.225545 + 0.390656i
\(732\) 2.59808 + 4.50000i 0.0960277 + 0.166325i
\(733\) 48.1769i 1.77945i −0.456492 0.889727i \(-0.650894\pi\)
0.456492 0.889727i \(-0.349106\pi\)
\(734\) 21.9282 12.6603i 0.809385 0.467299i
\(735\) −0.633975 + 0.366025i −0.0233845 + 0.0135011i
\(736\) 3.46410i 0.127688i
\(737\) 7.73205 + 13.3923i 0.284814 + 0.493312i
\(738\) −1.50000 + 2.59808i −0.0552158 + 0.0956365i
\(739\) 13.1436 + 7.58846i 0.483495 + 0.279146i 0.721872 0.692027i \(-0.243282\pi\)
−0.238377 + 0.971173i \(0.576615\pi\)
\(740\) −4.92820 −0.181164
\(741\) 3.23205 + 1.59808i 0.118732 + 0.0587068i
\(742\) −7.00000 −0.256978
\(743\) −12.1699 7.02628i −0.446469 0.257769i 0.259869 0.965644i \(-0.416321\pi\)
−0.706338 + 0.707875i \(0.749654\pi\)
\(744\) −1.09808 + 1.90192i −0.0402574 + 0.0697279i
\(745\) 5.07180 + 8.78461i 0.185816 + 0.321843i
\(746\) 9.66025i 0.353687i
\(747\) 0.169873 0.0980762i 0.00621533 0.00358842i
\(748\) −5.59808 + 3.23205i −0.204686 + 0.118175i
\(749\) 10.8564i 0.396684i
\(750\) 3.46410 + 6.00000i 0.126491 + 0.219089i
\(751\) −9.57180 + 16.5788i −0.349280 + 0.604970i −0.986122 0.166024i \(-0.946907\pi\)
0.636842 + 0.770994i \(0.280240\pi\)
\(752\) −2.13397 1.23205i −0.0778180 0.0449283i
\(753\) −13.1244 −0.478278
\(754\) −1.50000 23.2583i −0.0546268 0.847018i
\(755\) −3.80385 −0.138436
\(756\) 0.866025 + 0.500000i 0.0314970 + 0.0181848i
\(757\) 0.294229 0.509619i 0.0106939 0.0185224i −0.860629 0.509233i \(-0.829929\pi\)
0.871323 + 0.490710i \(0.163263\pi\)
\(758\) −14.2224 24.6340i −0.516582 0.894746i
\(759\) 6.00000i 0.217786i
\(760\) 0.633975 0.366025i 0.0229967 0.0132771i
\(761\) 13.2679 7.66025i 0.480963 0.277684i −0.239855 0.970809i \(-0.577100\pi\)
0.720818 + 0.693125i \(0.243767\pi\)
\(762\) 15.4641i 0.560205i
\(763\) 2.36603 + 4.09808i 0.0856559 + 0.148360i
\(764\) 11.5622 20.0263i 0.418305 0.724525i
\(765\) 2.36603 + 1.36603i 0.0855438 + 0.0493888i
\(766\) 5.53590 0.200020
\(767\) −0.215390 3.33975i −0.00777729 0.120591i
\(768\) 1.00000 0.0360844
\(769\) 36.6340 + 21.1506i 1.32105 + 0.762711i 0.983897 0.178737i \(-0.0572010\pi\)
0.337158 + 0.941448i \(0.390534\pi\)
\(770\) 0.633975 1.09808i 0.0228469 0.0395719i
\(771\) 10.3301 + 17.8923i 0.372030 + 0.644376i
\(772\) 1.19615i 0.0430505i
\(773\) −40.8564 + 23.5885i −1.46950 + 0.848418i −0.999415 0.0342018i \(-0.989111\pi\)
−0.470088 + 0.882620i \(0.655778\pi\)
\(774\) −2.83013 + 1.63397i −0.101727 + 0.0587320i
\(775\) 9.80385i 0.352