Properties

Label 546.2.s.c.127.2
Level $546$
Weight $2$
Character 546.127
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 127.2
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 546.127
Dual form 546.2.s.c.43.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +3.46410i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +3.46410i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.73205 + 3.00000i) q^{10} +(3.46410 - 2.00000i) q^{11} -1.00000 q^{12} +(2.59808 + 2.50000i) q^{13} -1.00000 q^{14} +(3.00000 - 1.73205i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.23205 - 5.59808i) q^{17} +1.00000i q^{18} +(6.46410 + 3.73205i) q^{19} +(3.00000 + 1.73205i) q^{20} +1.00000i q^{21} +(2.00000 - 3.46410i) q^{22} +(2.86603 + 4.96410i) q^{23} +(-0.866025 + 0.500000i) q^{24} -7.00000 q^{25} +(3.50000 + 0.866025i) q^{26} +1.00000 q^{27} +(-0.866025 + 0.500000i) q^{28} +(-4.00000 - 6.92820i) q^{29} +(1.73205 - 3.00000i) q^{30} +6.46410i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-3.46410 - 2.00000i) q^{33} -6.46410i q^{34} +(1.73205 - 3.00000i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-4.26795 + 2.46410i) q^{37} +7.46410 q^{38} +(0.866025 - 3.50000i) q^{39} +3.46410 q^{40} +(-6.00000 + 3.46410i) q^{41} +(0.500000 + 0.866025i) q^{42} +(2.23205 - 3.86603i) q^{43} -4.00000i q^{44} +(-3.00000 - 1.73205i) q^{45} +(4.96410 + 2.86603i) q^{46} -0.535898i q^{47} +(-0.500000 + 0.866025i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-6.06218 + 3.50000i) q^{50} -6.46410 q^{51} +(3.46410 - 1.00000i) q^{52} -8.26795 q^{53} +(0.866025 - 0.500000i) q^{54} +(6.92820 + 12.0000i) q^{55} +(-0.500000 + 0.866025i) q^{56} -7.46410i q^{57} +(-6.92820 - 4.00000i) q^{58} +(-5.42820 - 3.13397i) q^{59} -3.46410i q^{60} +(2.59808 - 4.50000i) q^{61} +(3.23205 + 5.59808i) q^{62} +(0.866025 - 0.500000i) q^{63} -1.00000 q^{64} +(-8.66025 + 9.00000i) q^{65} -4.00000 q^{66} +(6.23205 - 3.59808i) q^{67} +(-3.23205 - 5.59808i) q^{68} +(2.86603 - 4.96410i) q^{69} -3.46410i q^{70} +(1.66987 + 0.964102i) q^{71} +(0.866025 + 0.500000i) q^{72} -10.9282i q^{73} +(-2.46410 + 4.26795i) q^{74} +(3.50000 + 6.06218i) q^{75} +(6.46410 - 3.73205i) q^{76} -4.00000 q^{77} +(-1.00000 - 3.46410i) q^{78} -9.46410 q^{79} +(3.00000 - 1.73205i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.46410 + 6.00000i) q^{82} -1.73205i q^{83} +(0.866025 + 0.500000i) q^{84} +(19.3923 + 11.1962i) q^{85} -4.46410i q^{86} +(-4.00000 + 6.92820i) q^{87} +(-2.00000 - 3.46410i) q^{88} +(-10.1603 + 5.86603i) q^{89} -3.46410 q^{90} +(-1.00000 - 3.46410i) q^{91} +5.73205 q^{92} +(5.59808 - 3.23205i) q^{93} +(-0.267949 - 0.464102i) q^{94} +(-12.9282 + 22.3923i) q^{95} +1.00000i q^{96} +(10.7321 + 6.19615i) q^{97} +(0.866025 + 0.500000i) q^{98} +4.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{3} + 2q^{4} - 2q^{9} + O(q^{10}) \) \( 4q - 2q^{3} + 2q^{4} - 2q^{9} - 4q^{12} - 4q^{14} + 12q^{15} - 2q^{16} + 6q^{17} + 12q^{19} + 12q^{20} + 8q^{22} + 8q^{23} - 28q^{25} + 14q^{26} + 4q^{27} - 16q^{29} + 2q^{36} - 24q^{37} + 16q^{38} - 24q^{41} + 2q^{42} + 2q^{43} - 12q^{45} + 6q^{46} - 2q^{48} + 2q^{49} - 12q^{51} - 40q^{53} - 2q^{56} + 6q^{59} + 6q^{62} - 4q^{64} - 16q^{66} + 18q^{67} - 6q^{68} + 8q^{69} + 24q^{71} + 4q^{74} + 14q^{75} + 12q^{76} - 16q^{77} - 4q^{78} - 24q^{79} + 12q^{80} - 2q^{81} + 36q^{85} - 16q^{87} - 8q^{88} - 6q^{89} - 4q^{91} + 16q^{92} + 12q^{93} - 8q^{94} - 24q^{95} + 36q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)

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
\(5\) 3.46410i 1.54919i 0.632456 + 0.774597i \(0.282047\pi\)
−0.632456 + 0.774597i \(0.717953\pi\)
\(6\) −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
\(10\) 1.73205 + 3.00000i 0.547723 + 0.948683i
\(11\) 3.46410 2.00000i 1.04447 0.603023i 0.123371 0.992361i \(-0.460630\pi\)
0.921095 + 0.389338i \(0.127296\pi\)
\(12\) −1.00000 −0.288675
\(13\) 2.59808 + 2.50000i 0.720577 + 0.693375i
\(14\) −1.00000 −0.267261
\(15\) 3.00000 1.73205i 0.774597 0.447214i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 3.23205 5.59808i 0.783887 1.35773i −0.145774 0.989318i \(-0.546567\pi\)
0.929661 0.368415i \(-0.120099\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 6.46410 + 3.73205i 1.48297 + 0.856191i 0.999813 0.0193444i \(-0.00615788\pi\)
0.483154 + 0.875536i \(0.339491\pi\)
\(20\) 3.00000 + 1.73205i 0.670820 + 0.387298i
\(21\) 1.00000i 0.218218i
\(22\) 2.00000 3.46410i 0.426401 0.738549i
\(23\) 2.86603 + 4.96410i 0.597608 + 1.03509i 0.993173 + 0.116649i \(0.0372153\pi\)
−0.395566 + 0.918438i \(0.629451\pi\)
\(24\) −0.866025 + 0.500000i −0.176777 + 0.102062i
\(25\) −7.00000 −1.40000
\(26\) 3.50000 + 0.866025i 0.686406 + 0.169842i
\(27\) 1.00000 0.192450
\(28\) −0.866025 + 0.500000i −0.163663 + 0.0944911i
\(29\) −4.00000 6.92820i −0.742781 1.28654i −0.951224 0.308500i \(-0.900173\pi\)
0.208443 0.978035i \(-0.433160\pi\)
\(30\) 1.73205 3.00000i 0.316228 0.547723i
\(31\) 6.46410i 1.16099i 0.814265 + 0.580493i \(0.197140\pi\)
−0.814265 + 0.580493i \(0.802860\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) −3.46410 2.00000i −0.603023 0.348155i
\(34\) 6.46410i 1.10858i
\(35\) 1.73205 3.00000i 0.292770 0.507093i
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) −4.26795 + 2.46410i −0.701647 + 0.405096i −0.807960 0.589237i \(-0.799429\pi\)
0.106314 + 0.994333i \(0.466095\pi\)
\(38\) 7.46410 1.21084
\(39\) 0.866025 3.50000i 0.138675 0.560449i
\(40\) 3.46410 0.547723
\(41\) −6.00000 + 3.46410i −0.937043 + 0.541002i −0.889032 0.457845i \(-0.848621\pi\)
−0.0480106 + 0.998847i \(0.515288\pi\)
\(42\) 0.500000 + 0.866025i 0.0771517 + 0.133631i
\(43\) 2.23205 3.86603i 0.340385 0.589563i −0.644120 0.764925i \(-0.722776\pi\)
0.984504 + 0.175361i \(0.0561094\pi\)
\(44\) 4.00000i 0.603023i
\(45\) −3.00000 1.73205i −0.447214 0.258199i
\(46\) 4.96410 + 2.86603i 0.731917 + 0.422572i
\(47\) 0.535898i 0.0781688i −0.999236 0.0390844i \(-0.987556\pi\)
0.999236 0.0390844i \(-0.0124441\pi\)
\(48\) −0.500000 + 0.866025i −0.0721688 + 0.125000i
\(49\) 0.500000 + 0.866025i 0.0714286 + 0.123718i
\(50\) −6.06218 + 3.50000i −0.857321 + 0.494975i
\(51\) −6.46410 −0.905155
\(52\) 3.46410 1.00000i 0.480384 0.138675i
\(53\) −8.26795 −1.13569 −0.567845 0.823135i \(-0.692223\pi\)
−0.567845 + 0.823135i \(0.692223\pi\)
\(54\) 0.866025 0.500000i 0.117851 0.0680414i
\(55\) 6.92820 + 12.0000i 0.934199 + 1.61808i
\(56\) −0.500000 + 0.866025i −0.0668153 + 0.115728i
\(57\) 7.46410i 0.988644i
\(58\) −6.92820 4.00000i −0.909718 0.525226i
\(59\) −5.42820 3.13397i −0.706692 0.408009i 0.103143 0.994667i \(-0.467110\pi\)
−0.809835 + 0.586658i \(0.800443\pi\)
\(60\) 3.46410i 0.447214i
\(61\) 2.59808 4.50000i 0.332650 0.576166i −0.650381 0.759608i \(-0.725391\pi\)
0.983030 + 0.183442i \(0.0587240\pi\)
\(62\) 3.23205 + 5.59808i 0.410471 + 0.710956i
\(63\) 0.866025 0.500000i 0.109109 0.0629941i
\(64\) −1.00000 −0.125000
\(65\) −8.66025 + 9.00000i −1.07417 + 1.11631i
\(66\) −4.00000 −0.492366
\(67\) 6.23205 3.59808i 0.761366 0.439575i −0.0684199 0.997657i \(-0.521796\pi\)
0.829786 + 0.558082i \(0.188462\pi\)
\(68\) −3.23205 5.59808i −0.391944 0.678866i
\(69\) 2.86603 4.96410i 0.345029 0.597608i
\(70\) 3.46410i 0.414039i
\(71\) 1.66987 + 0.964102i 0.198177 + 0.114418i 0.595805 0.803129i \(-0.296833\pi\)
−0.397628 + 0.917547i \(0.630166\pi\)
\(72\) 0.866025 + 0.500000i 0.102062 + 0.0589256i
\(73\) 10.9282i 1.27905i −0.768771 0.639525i \(-0.779131\pi\)
0.768771 0.639525i \(-0.220869\pi\)
\(74\) −2.46410 + 4.26795i −0.286446 + 0.496139i
\(75\) 3.50000 + 6.06218i 0.404145 + 0.700000i
\(76\) 6.46410 3.73205i 0.741483 0.428096i
\(77\) −4.00000 −0.455842
\(78\) −1.00000 3.46410i −0.113228 0.392232i
\(79\) −9.46410 −1.06479 −0.532397 0.846495i \(-0.678709\pi\)
−0.532397 + 0.846495i \(0.678709\pi\)
\(80\) 3.00000 1.73205i 0.335410 0.193649i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −3.46410 + 6.00000i −0.382546 + 0.662589i
\(83\) 1.73205i 0.190117i −0.995472 0.0950586i \(-0.969696\pi\)
0.995472 0.0950586i \(-0.0303039\pi\)
\(84\) 0.866025 + 0.500000i 0.0944911 + 0.0545545i
\(85\) 19.3923 + 11.1962i 2.10339 + 1.21439i
\(86\) 4.46410i 0.481376i
\(87\) −4.00000 + 6.92820i −0.428845 + 0.742781i
\(88\) −2.00000 3.46410i −0.213201 0.369274i
\(89\) −10.1603 + 5.86603i −1.07698 + 0.621797i −0.930081 0.367353i \(-0.880264\pi\)
−0.146903 + 0.989151i \(0.546931\pi\)
\(90\) −3.46410 −0.365148
\(91\) −1.00000 3.46410i −0.104828 0.363137i
\(92\) 5.73205 0.597608
\(93\) 5.59808 3.23205i 0.580493 0.335148i
\(94\) −0.267949 0.464102i −0.0276368 0.0478684i
\(95\) −12.9282 + 22.3923i −1.32641 + 2.29740i
\(96\) 1.00000i 0.102062i
\(97\) 10.7321 + 6.19615i 1.08967 + 0.629124i 0.933490 0.358604i \(-0.116747\pi\)
0.156185 + 0.987728i \(0.450080\pi\)
\(98\) 0.866025 + 0.500000i 0.0874818 + 0.0505076i
\(99\) 4.00000i 0.402015i
\(100\) −3.50000 + 6.06218i −0.350000 + 0.606218i
\(101\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(102\) −5.59808 + 3.23205i −0.554292 + 0.320021i
\(103\) −10.6603 −1.05039 −0.525193 0.850983i \(-0.676007\pi\)
−0.525193 + 0.850983i \(0.676007\pi\)
\(104\) 2.50000 2.59808i 0.245145 0.254762i
\(105\) −3.46410 −0.338062
\(106\) −7.16025 + 4.13397i −0.695465 + 0.401527i
\(107\) −4.26795 7.39230i −0.412598 0.714641i 0.582575 0.812777i \(-0.302045\pi\)
−0.995173 + 0.0981360i \(0.968712\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) 12.0000i 1.14939i 0.818367 + 0.574696i \(0.194880\pi\)
−0.818367 + 0.574696i \(0.805120\pi\)
\(110\) 12.0000 + 6.92820i 1.14416 + 0.660578i
\(111\) 4.26795 + 2.46410i 0.405096 + 0.233882i
\(112\) 1.00000i 0.0944911i
\(113\) 2.19615 3.80385i 0.206597 0.357836i −0.744044 0.668131i \(-0.767095\pi\)
0.950640 + 0.310295i \(0.100428\pi\)
\(114\) −3.73205 6.46410i −0.349539 0.605419i
\(115\) −17.1962 + 9.92820i −1.60355 + 0.925810i
\(116\) −8.00000 −0.742781
\(117\) −3.46410 + 1.00000i −0.320256 + 0.0924500i
\(118\) −6.26795 −0.577011
\(119\) −5.59808 + 3.23205i −0.513175 + 0.296282i
\(120\) −1.73205 3.00000i −0.158114 0.273861i
\(121\) 2.50000 4.33013i 0.227273 0.393648i
\(122\) 5.19615i 0.470438i
\(123\) 6.00000 + 3.46410i 0.541002 + 0.312348i
\(124\) 5.59808 + 3.23205i 0.502722 + 0.290247i
\(125\) 6.92820i 0.619677i
\(126\) 0.500000 0.866025i 0.0445435 0.0771517i
\(127\) 2.53590 + 4.39230i 0.225025 + 0.389754i 0.956327 0.292300i \(-0.0944204\pi\)
−0.731302 + 0.682054i \(0.761087\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) −4.46410 −0.393042
\(130\) −3.00000 + 12.1244i −0.263117 + 1.06338i
\(131\) 19.0000 1.66004 0.830019 0.557735i \(-0.188330\pi\)
0.830019 + 0.557735i \(0.188330\pi\)
\(132\) −3.46410 + 2.00000i −0.301511 + 0.174078i
\(133\) −3.73205 6.46410i −0.323610 0.560509i
\(134\) 3.59808 6.23205i 0.310826 0.538367i
\(135\) 3.46410i 0.298142i
\(136\) −5.59808 3.23205i −0.480031 0.277146i
\(137\) −12.0000 6.92820i −1.02523 0.591916i −0.109615 0.993974i \(-0.534962\pi\)
−0.915614 + 0.402058i \(0.868295\pi\)
\(138\) 5.73205i 0.487945i
\(139\) −1.46410 + 2.53590i −0.124183 + 0.215092i −0.921413 0.388584i \(-0.872964\pi\)
0.797230 + 0.603676i \(0.206298\pi\)
\(140\) −1.73205 3.00000i −0.146385 0.253546i
\(141\) −0.464102 + 0.267949i −0.0390844 + 0.0225654i
\(142\) 1.92820 0.161811
\(143\) 14.0000 + 3.46410i 1.17074 + 0.289683i
\(144\) 1.00000 0.0833333
\(145\) 24.0000 13.8564i 1.99309 1.15071i
\(146\) −5.46410 9.46410i −0.452212 0.783255i
\(147\) 0.500000 0.866025i 0.0412393 0.0714286i
\(148\) 4.92820i 0.405096i
\(149\) −9.99038 5.76795i −0.818444 0.472529i 0.0314357 0.999506i \(-0.489992\pi\)
−0.849880 + 0.526977i \(0.823325\pi\)
\(150\) 6.06218 + 3.50000i 0.494975 + 0.285774i
\(151\) 12.0000i 0.976546i −0.872691 0.488273i \(-0.837627\pi\)
0.872691 0.488273i \(-0.162373\pi\)
\(152\) 3.73205 6.46410i 0.302709 0.524308i
\(153\) 3.23205 + 5.59808i 0.261296 + 0.452578i
\(154\) −3.46410 + 2.00000i −0.279145 + 0.161165i
\(155\) −22.3923 −1.79859
\(156\) −2.59808 2.50000i −0.208013 0.200160i
\(157\) −2.92820 −0.233696 −0.116848 0.993150i \(-0.537279\pi\)
−0.116848 + 0.993150i \(0.537279\pi\)
\(158\) −8.19615 + 4.73205i −0.652051 + 0.376462i
\(159\) 4.13397 + 7.16025i 0.327846 + 0.567845i
\(160\) 1.73205 3.00000i 0.136931 0.237171i
\(161\) 5.73205i 0.451749i
\(162\) −0.866025 0.500000i −0.0680414 0.0392837i
\(163\) 1.16025 + 0.669873i 0.0908781 + 0.0524685i 0.544750 0.838598i \(-0.316624\pi\)
−0.453872 + 0.891067i \(0.649958\pi\)
\(164\) 6.92820i 0.541002i
\(165\) 6.92820 12.0000i 0.539360 0.934199i
\(166\) −0.866025 1.50000i −0.0672166 0.116423i
\(167\) 17.3205 10.0000i 1.34030 0.773823i 0.353450 0.935454i \(-0.385009\pi\)
0.986851 + 0.161630i \(0.0516752\pi\)
\(168\) 1.00000 0.0771517
\(169\) 0.500000 + 12.9904i 0.0384615 + 0.999260i
\(170\) 22.3923 1.71741
\(171\) −6.46410 + 3.73205i −0.494322 + 0.285397i
\(172\) −2.23205 3.86603i −0.170192 0.294782i
\(173\) 0.535898 0.928203i 0.0407436 0.0705700i −0.844934 0.534870i \(-0.820361\pi\)
0.885678 + 0.464300i \(0.153694\pi\)
\(174\) 8.00000i 0.606478i
\(175\) 6.06218 + 3.50000i 0.458258 + 0.264575i
\(176\) −3.46410 2.00000i −0.261116 0.150756i
\(177\) 6.26795i 0.471128i
\(178\) −5.86603 + 10.1603i −0.439677 + 0.761543i
\(179\) −8.46410 14.6603i −0.632637 1.09576i −0.987011 0.160655i \(-0.948639\pi\)
0.354374 0.935104i \(-0.384694\pi\)
\(180\) −3.00000 + 1.73205i −0.223607 + 0.129099i
\(181\) −24.7846 −1.84223 −0.921113 0.389296i \(-0.872718\pi\)
−0.921113 + 0.389296i \(0.872718\pi\)
\(182\) −2.59808 2.50000i −0.192582 0.185312i
\(183\) −5.19615 −0.384111
\(184\) 4.96410 2.86603i 0.365958 0.211286i
\(185\) −8.53590 14.7846i −0.627572 1.08699i
\(186\) 3.23205 5.59808i 0.236985 0.410471i
\(187\) 25.8564i 1.89081i
\(188\) −0.464102 0.267949i −0.0338481 0.0195422i
\(189\) −0.866025 0.500000i −0.0629941 0.0363696i
\(190\) 25.8564i 1.87582i
\(191\) 13.2583 22.9641i 0.959339 1.66162i 0.235229 0.971940i \(-0.424416\pi\)
0.724110 0.689684i \(-0.242251\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) 15.4641 8.92820i 1.11313 0.642666i 0.173492 0.984835i \(-0.444495\pi\)
0.939638 + 0.342169i \(0.111162\pi\)
\(194\) 12.3923 0.889716
\(195\) 12.1244 + 3.00000i 0.868243 + 0.214834i
\(196\) 1.00000 0.0714286
\(197\) 2.25833 1.30385i 0.160899 0.0928953i −0.417388 0.908728i \(-0.637054\pi\)
0.578288 + 0.815833i \(0.303721\pi\)
\(198\) 2.00000 + 3.46410i 0.142134 + 0.246183i
\(199\) −11.0622 + 19.1603i −0.784177 + 1.35823i 0.145312 + 0.989386i \(0.453581\pi\)
−0.929489 + 0.368849i \(0.879752\pi\)
\(200\) 7.00000i 0.494975i
\(201\) −6.23205 3.59808i −0.439575 0.253789i
\(202\) 0 0
\(203\) 8.00000i 0.561490i
\(204\) −3.23205 + 5.59808i −0.226289 + 0.391944i
\(205\) −12.0000 20.7846i −0.838116 1.45166i
\(206\) −9.23205 + 5.33013i −0.643227 + 0.371368i
\(207\) −5.73205 −0.398405
\(208\) 0.866025 3.50000i 0.0600481 0.242681i
\(209\) 29.8564 2.06521
\(210\) −3.00000 + 1.73205i −0.207020 + 0.119523i
\(211\) 4.53590 + 7.85641i 0.312264 + 0.540857i 0.978852 0.204569i \(-0.0655793\pi\)
−0.666588 + 0.745426i \(0.732246\pi\)
\(212\) −4.13397 + 7.16025i −0.283923 + 0.491768i
\(213\) 1.92820i 0.132118i
\(214\) −7.39230 4.26795i −0.505328 0.291751i
\(215\) 13.3923 + 7.73205i 0.913348 + 0.527321i
\(216\) 1.00000i 0.0680414i
\(217\) 3.23205 5.59808i 0.219406 0.380022i
\(218\) 6.00000 + 10.3923i 0.406371 + 0.703856i
\(219\) −9.46410 + 5.46410i −0.639525 + 0.369230i
\(220\) 13.8564 0.934199
\(221\) 22.3923 6.46410i 1.50627 0.434823i
\(222\) 4.92820 0.330759
\(223\) −6.52628 + 3.76795i −0.437032 + 0.252321i −0.702338 0.711844i \(-0.747860\pi\)
0.265306 + 0.964164i \(0.414527\pi\)
\(224\) 0.500000 + 0.866025i 0.0334077 + 0.0578638i
\(225\) 3.50000 6.06218i 0.233333 0.404145i
\(226\) 4.39230i 0.292172i
\(227\) −11.5359 6.66025i −0.765664 0.442057i 0.0656613 0.997842i \(-0.479084\pi\)
−0.831326 + 0.555785i \(0.812418\pi\)
\(228\) −6.46410 3.73205i −0.428096 0.247161i
\(229\) 19.9282i 1.31689i 0.752628 + 0.658446i \(0.228786\pi\)
−0.752628 + 0.658446i \(0.771214\pi\)
\(230\) −9.92820 + 17.1962i −0.654646 + 1.13388i
\(231\) 2.00000 + 3.46410i 0.131590 + 0.227921i
\(232\) −6.92820 + 4.00000i −0.454859 + 0.262613i
\(233\) −13.4641 −0.882063 −0.441031 0.897492i \(-0.645387\pi\)
−0.441031 + 0.897492i \(0.645387\pi\)
\(234\) −2.50000 + 2.59808i −0.163430 + 0.169842i
\(235\) 1.85641 0.121099
\(236\) −5.42820 + 3.13397i −0.353346 + 0.204004i
\(237\) 4.73205 + 8.19615i 0.307380 + 0.532397i
\(238\) −3.23205 + 5.59808i −0.209503 + 0.362869i
\(239\) 12.8564i 0.831612i −0.909453 0.415806i \(-0.863500\pi\)
0.909453 0.415806i \(-0.136500\pi\)
\(240\) −3.00000 1.73205i −0.193649 0.111803i
\(241\) 13.7321 + 7.92820i 0.884559 + 0.510700i 0.872159 0.489223i \(-0.162719\pi\)
0.0124002 + 0.999923i \(0.496053\pi\)
\(242\) 5.00000i 0.321412i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) −2.59808 4.50000i −0.166325 0.288083i
\(245\) −3.00000 + 1.73205i −0.191663 + 0.110657i
\(246\) 6.92820 0.441726
\(247\) 7.46410 + 25.8564i 0.474929 + 1.64520i
\(248\) 6.46410 0.410471
\(249\) −1.50000 + 0.866025i −0.0950586 + 0.0548821i
\(250\) −3.46410 6.00000i −0.219089 0.379473i
\(251\) −5.03590 + 8.72243i −0.317863 + 0.550555i −0.980042 0.198791i \(-0.936299\pi\)
0.662179 + 0.749346i \(0.269632\pi\)
\(252\) 1.00000i 0.0629941i
\(253\) 19.8564 + 11.4641i 1.24836 + 0.720742i
\(254\) 4.39230 + 2.53590i 0.275598 + 0.159116i
\(255\) 22.3923i 1.40226i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 0.232051 + 0.401924i 0.0144749 + 0.0250713i 0.873172 0.487412i \(-0.162059\pi\)
−0.858697 + 0.512483i \(0.828726\pi\)
\(258\) −3.86603 + 2.23205i −0.240688 + 0.138961i
\(259\) 4.92820 0.306224
\(260\) 3.46410 + 12.0000i 0.214834 + 0.744208i
\(261\) 8.00000 0.495188
\(262\) 16.4545 9.50000i 1.01656 0.586912i
\(263\) 8.66025 + 15.0000i 0.534014 + 0.924940i 0.999210 + 0.0397320i \(0.0126504\pi\)
−0.465196 + 0.885208i \(0.654016\pi\)
\(264\) −2.00000 + 3.46410i −0.123091 + 0.213201i
\(265\) 28.6410i 1.75940i
\(266\) −6.46410 3.73205i −0.396339 0.228827i
\(267\) 10.1603 + 5.86603i 0.621797 + 0.358995i
\(268\) 7.19615i 0.439575i
\(269\) −11.1962 + 19.3923i −0.682641 + 1.18237i 0.291530 + 0.956562i \(0.405836\pi\)
−0.974172 + 0.225808i \(0.927498\pi\)
\(270\) 1.73205 + 3.00000i 0.105409 + 0.182574i
\(271\) 10.7942 6.23205i 0.655703 0.378570i −0.134935 0.990854i \(-0.543083\pi\)
0.790638 + 0.612284i \(0.209749\pi\)
\(272\) −6.46410 −0.391944
\(273\) −2.50000 + 2.59808i −0.151307 + 0.157243i
\(274\) −13.8564 −0.837096
\(275\) −24.2487 + 14.0000i −1.46225 + 0.844232i
\(276\) −2.86603 4.96410i −0.172514 0.298804i
\(277\) 3.66025 6.33975i 0.219923 0.380918i −0.734861 0.678218i \(-0.762753\pi\)
0.954784 + 0.297299i \(0.0960859\pi\)
\(278\) 2.92820i 0.175622i
\(279\) −5.59808 3.23205i −0.335148 0.193498i
\(280\) −3.00000 1.73205i −0.179284 0.103510i
\(281\) 2.39230i 0.142713i −0.997451 0.0713565i \(-0.977267\pi\)
0.997451 0.0713565i \(-0.0227328\pi\)
\(282\) −0.267949 + 0.464102i −0.0159561 + 0.0276368i
\(283\) −5.73205 9.92820i −0.340735 0.590170i 0.643834 0.765165i \(-0.277343\pi\)
−0.984569 + 0.174994i \(0.944009\pi\)
\(284\) 1.66987 0.964102i 0.0990887 0.0572089i
\(285\) 25.8564 1.53160
\(286\) 13.8564 4.00000i 0.819346 0.236525i
\(287\) 6.92820 0.408959
\(288\) 0.866025 0.500000i 0.0510310 0.0294628i
\(289\) −12.3923 21.4641i −0.728959 1.26259i
\(290\) 13.8564 24.0000i 0.813676 1.40933i
\(291\) 12.3923i 0.726450i
\(292\) −9.46410 5.46410i −0.553845 0.319762i
\(293\) −28.9808 16.7321i −1.69307 0.977497i −0.952012 0.306060i \(-0.900989\pi\)
−0.741062 0.671437i \(-0.765678\pi\)
\(294\) 1.00000i 0.0583212i
\(295\) 10.8564 18.8038i 0.632084 1.09480i
\(296\) 2.46410 + 4.26795i 0.143223 + 0.248070i
\(297\) 3.46410 2.00000i 0.201008 0.116052i
\(298\) −11.5359 −0.668257
\(299\) −4.96410 + 20.0622i −0.287081 + 1.16023i
\(300\) 7.00000 0.404145
\(301\) −3.86603 + 2.23205i −0.222834 + 0.128653i
\(302\) −6.00000 10.3923i −0.345261 0.598010i
\(303\) 0 0
\(304\) 7.46410i 0.428096i
\(305\) 15.5885 + 9.00000i 0.892592 + 0.515339i
\(306\) 5.59808 + 3.23205i 0.320021 + 0.184764i
\(307\) 22.0000i 1.25561i −0.778372 0.627803i \(-0.783954\pi\)
0.778372 0.627803i \(-0.216046\pi\)
\(308\) −2.00000 + 3.46410i −0.113961 + 0.197386i
\(309\) 5.33013 + 9.23205i 0.303220 + 0.525193i
\(310\) −19.3923 + 11.1962i −1.10141 + 0.635899i
\(311\) −13.3205 −0.755337 −0.377668 0.925941i \(-0.623274\pi\)
−0.377668 + 0.925941i \(0.623274\pi\)
\(312\) −3.50000 0.866025i −0.198148 0.0490290i
\(313\) 0.679492 0.0384072 0.0192036 0.999816i \(-0.493887\pi\)
0.0192036 + 0.999816i \(0.493887\pi\)
\(314\) −2.53590 + 1.46410i −0.143109 + 0.0826240i
\(315\) 1.73205 + 3.00000i 0.0975900 + 0.169031i
\(316\) −4.73205 + 8.19615i −0.266199 + 0.461070i
\(317\) 16.4641i 0.924716i −0.886693 0.462358i \(-0.847003\pi\)
0.886693 0.462358i \(-0.152997\pi\)
\(318\) 7.16025 + 4.13397i 0.401527 + 0.231822i
\(319\) −27.7128 16.0000i −1.55162 0.895828i
\(320\) 3.46410i 0.193649i
\(321\) −4.26795 + 7.39230i −0.238214 + 0.412598i
\(322\) −2.86603 4.96410i −0.159717 0.276639i
\(323\) 41.7846 24.1244i 2.32496 1.34232i
\(324\) −1.00000 −0.0555556
\(325\) −18.1865 17.5000i −1.00881 0.970725i
\(326\) 1.33975 0.0742017
\(327\) 10.3923 6.00000i 0.574696 0.331801i
\(328\) 3.46410 + 6.00000i 0.191273 + 0.331295i
\(329\) −0.267949 + 0.464102i −0.0147725 + 0.0255868i
\(330\) 13.8564i 0.762770i
\(331\) 18.4641 + 10.6603i 1.01488 + 0.585941i 0.912616 0.408817i \(-0.134059\pi\)
0.102262 + 0.994757i \(0.467392\pi\)
\(332\) −1.50000 0.866025i −0.0823232 0.0475293i
\(333\) 4.92820i 0.270064i
\(334\) 10.0000 17.3205i 0.547176 0.947736i
\(335\) 12.4641 + 21.5885i 0.680987 + 1.17950i
\(336\) 0.866025 0.500000i 0.0472456 0.0272772i
\(337\) −6.00000 −0.326841 −0.163420 0.986557i \(-0.552253\pi\)
−0.163420 + 0.986557i \(0.552253\pi\)
\(338\) 6.92820 + 11.0000i 0.376845 + 0.598321i
\(339\) −4.39230 −0.238557
\(340\) 19.3923 11.1962i 1.05170 0.607197i
\(341\) 12.9282 + 22.3923i 0.700101 + 1.21261i
\(342\) −3.73205 + 6.46410i −0.201806 + 0.349539i
\(343\) 1.00000i 0.0539949i
\(344\) −3.86603 2.23205i −0.208442 0.120344i
\(345\) 17.1962 + 9.92820i 0.925810 + 0.534516i
\(346\) 1.07180i 0.0576202i
\(347\) −12.8564 + 22.2679i −0.690168 + 1.19541i 0.281614 + 0.959528i \(0.409130\pi\)
−0.971783 + 0.235879i \(0.924203\pi\)
\(348\) 4.00000 + 6.92820i 0.214423 + 0.371391i
\(349\) −30.8660 + 17.8205i −1.65222 + 0.953910i −0.676064 + 0.736843i \(0.736316\pi\)
−0.976157 + 0.217067i \(0.930351\pi\)
\(350\) 7.00000 0.374166
\(351\) 2.59808 + 2.50000i 0.138675 + 0.133440i
\(352\) −4.00000 −0.213201
\(353\) 8.08846 4.66987i 0.430505 0.248552i −0.269057 0.963124i \(-0.586712\pi\)
0.699562 + 0.714572i \(0.253379\pi\)
\(354\) 3.13397 + 5.42820i 0.166569 + 0.288506i
\(355\) −3.33975 + 5.78461i −0.177255 + 0.307015i
\(356\) 11.7321i 0.621797i
\(357\) 5.59808 + 3.23205i 0.296282 + 0.171058i
\(358\) −14.6603 8.46410i −0.774819 0.447342i
\(359\) 8.00000i 0.422224i −0.977462 0.211112i \(-0.932292\pi\)
0.977462 0.211112i \(-0.0677085\pi\)
\(360\) −1.73205 + 3.00000i −0.0912871 + 0.158114i
\(361\) 18.3564 + 31.7942i 0.966127 + 1.67338i
\(362\) −21.4641 + 12.3923i −1.12813 + 0.651325i
\(363\) −5.00000 −0.262432
\(364\) −3.50000 0.866025i −0.183450 0.0453921i
\(365\) 37.8564 1.98149
\(366\) −4.50000 + 2.59808i −0.235219 + 0.135804i
\(367\) 16.5263 + 28.6244i 0.862665 + 1.49418i 0.869347 + 0.494202i \(0.164540\pi\)
−0.00668260 + 0.999978i \(0.502127\pi\)
\(368\) 2.86603 4.96410i 0.149402 0.258772i
\(369\) 6.92820i 0.360668i
\(370\) −14.7846 8.53590i −0.768615 0.443760i
\(371\) 7.16025 + 4.13397i 0.371742 + 0.214625i
\(372\) 6.46410i 0.335148i
\(373\) 13.1244 22.7321i 0.679553 1.17702i −0.295562 0.955324i \(-0.595507\pi\)
0.975116 0.221697i \(-0.0711597\pi\)
\(374\) −12.9282 22.3923i −0.668501 1.15788i
\(375\) −6.00000 + 3.46410i −0.309839 + 0.178885i
\(376\) −0.535898 −0.0276368
\(377\) 6.92820 28.0000i 0.356821 1.44207i
\(378\) −1.00000 −0.0514344
\(379\) −8.32051 + 4.80385i −0.427396 + 0.246757i −0.698237 0.715867i \(-0.746032\pi\)
0.270841 + 0.962624i \(0.412698\pi\)
\(380\) 12.9282 + 22.3923i 0.663203 + 1.14870i
\(381\) 2.53590 4.39230i 0.129918 0.225025i
\(382\) 26.5167i 1.35671i
\(383\) 6.33975 + 3.66025i 0.323946 + 0.187030i 0.653150 0.757229i \(-0.273447\pi\)
−0.329204 + 0.944259i \(0.606780\pi\)
\(384\) 0.866025 + 0.500000i 0.0441942 + 0.0255155i
\(385\) 13.8564i 0.706188i
\(386\) 8.92820 15.4641i 0.454434 0.787102i
\(387\) 2.23205 + 3.86603i 0.113462 + 0.196521i
\(388\) 10.7321 6.19615i 0.544837 0.314562i
\(389\) 14.6603 0.743304 0.371652 0.928372i \(-0.378791\pi\)
0.371652 + 0.928372i \(0.378791\pi\)
\(390\) 12.0000 3.46410i 0.607644 0.175412i
\(391\) 37.0526 1.87383
\(392\) 0.866025 0.500000i 0.0437409 0.0252538i
\(393\) −9.50000 16.4545i −0.479212 0.830019i
\(394\) 1.30385 2.25833i 0.0656869 0.113773i
\(395\) 32.7846i 1.64957i
\(396\) 3.46410 + 2.00000i 0.174078 + 0.100504i
\(397\) −25.7942 14.8923i −1.29458 0.747423i −0.315114 0.949054i \(-0.602043\pi\)
−0.979462 + 0.201631i \(0.935376\pi\)
\(398\) 22.1244i 1.10899i
\(399\) −3.73205 + 6.46410i −0.186836 + 0.323610i
\(400\) 3.50000 + 6.06218i 0.175000 + 0.303109i
\(401\) −14.1962 + 8.19615i −0.708922 + 0.409296i −0.810662 0.585515i \(-0.800892\pi\)
0.101740 + 0.994811i \(0.467559\pi\)
\(402\) −7.19615 −0.358911
\(403\) −16.1603 + 16.7942i −0.805000 + 0.836580i
\(404\) 0 0
\(405\) 3.00000 1.73205i 0.149071 0.0860663i
\(406\) 4.00000 + 6.92820i 0.198517 + 0.343841i
\(407\) −9.85641 + 17.0718i −0.488564 + 0.846218i
\(408\) 6.46410i 0.320021i
\(409\) 5.53590 + 3.19615i 0.273733 + 0.158040i 0.630583 0.776122i \(-0.282816\pi\)
−0.356850 + 0.934162i \(0.616149\pi\)
\(410\) −20.7846 12.0000i −1.02648 0.592638i
\(411\) 13.8564i 0.683486i
\(412\) −5.33013 + 9.23205i −0.262597 + 0.454830i
\(413\) 3.13397 + 5.42820i 0.154213 + 0.267104i
\(414\) −4.96410 + 2.86603i −0.243972 + 0.140857i
\(415\) 6.00000 0.294528
\(416\) −1.00000 3.46410i −0.0490290 0.169842i
\(417\) 2.92820 0.143395
\(418\) 25.8564 14.9282i 1.26468 0.730162i
\(419\) 2.50000 + 4.33013i 0.122133 + 0.211541i 0.920609 0.390487i \(-0.127693\pi\)
−0.798476 + 0.602027i \(0.794360\pi\)
\(420\) −1.73205 + 3.00000i −0.0845154 + 0.146385i
\(421\) 1.60770i 0.0783543i 0.999232 + 0.0391771i \(0.0124737\pi\)
−0.999232 + 0.0391771i \(0.987526\pi\)
\(422\) 7.85641 + 4.53590i 0.382444 + 0.220804i
\(423\) 0.464102 + 0.267949i 0.0225654 + 0.0130281i
\(424\) 8.26795i 0.401527i
\(425\) −22.6244 + 39.1865i −1.09744 + 1.90083i
\(426\) −0.964102 1.66987i −0.0467109 0.0809056i
\(427\) −4.50000 + 2.59808i −0.217770 + 0.125730i
\(428\) −8.53590 −0.412598
\(429\) −4.00000 13.8564i −0.193122 0.668994i
\(430\) 15.4641 0.745745
\(431\) 4.20577 2.42820i 0.202585 0.116962i −0.395276 0.918563i \(-0.629351\pi\)
0.597861 + 0.801600i \(0.296018\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) 4.92820 8.53590i 0.236834 0.410209i −0.722970 0.690880i \(-0.757223\pi\)
0.959804 + 0.280670i \(0.0905568\pi\)
\(434\) 6.46410i 0.310287i
\(435\) −24.0000 13.8564i −1.15071 0.664364i
\(436\) 10.3923 + 6.00000i 0.497701 + 0.287348i
\(437\) 42.7846i 2.04667i
\(438\) −5.46410 + 9.46410i −0.261085 + 0.452212i
\(439\) −6.80385 11.7846i −0.324730 0.562449i 0.656728 0.754128i \(-0.271940\pi\)
−0.981458 + 0.191679i \(0.938607\pi\)
\(440\) 12.0000 6.92820i 0.572078 0.330289i
\(441\) −1.00000 −0.0476190
\(442\) 16.1603 16.7942i 0.768665 0.798820i
\(443\) −22.3923 −1.06389 −0.531945 0.846779i \(-0.678539\pi\)
−0.531945 + 0.846779i \(0.678539\pi\)
\(444\) 4.26795 2.46410i 0.202548 0.116941i
\(445\) −20.3205 35.1962i −0.963284 1.66846i
\(446\) −3.76795 + 6.52628i −0.178418 + 0.309028i
\(447\) 11.5359i 0.545629i
\(448\) 0.866025 + 0.500000i 0.0409159 + 0.0236228i
\(449\) 15.5885 + 9.00000i 0.735665 + 0.424736i 0.820491 0.571660i \(-0.193700\pi\)
−0.0848262 + 0.996396i \(0.527033\pi\)
\(450\) 7.00000i 0.329983i
\(451\) −13.8564 + 24.0000i −0.652473 + 1.13012i
\(452\) −2.19615 3.80385i −0.103298 0.178918i
\(453\) −10.3923 + 6.00000i −0.488273 + 0.281905i
\(454\) −13.3205 −0.625162
\(455\) 12.0000 3.46410i 0.562569 0.162400i
\(456\) −7.46410 −0.349539
\(457\) 1.03590 0.598076i 0.0484573 0.0279768i −0.475576 0.879675i \(-0.657760\pi\)
0.524033 + 0.851698i \(0.324427\pi\)
\(458\) 9.96410 + 17.2583i 0.465592 + 0.806429i
\(459\) 3.23205 5.59808i 0.150859 0.261296i
\(460\) 19.8564i 0.925810i
\(461\) −4.39230 2.53590i −0.204570 0.118109i 0.394215 0.919018i \(-0.371016\pi\)
−0.598785 + 0.800910i \(0.704350\pi\)
\(462\) 3.46410 + 2.00000i 0.161165 + 0.0930484i
\(463\) 8.24871i 0.383350i 0.981458 + 0.191675i \(0.0613920\pi\)
−0.981458 + 0.191675i \(0.938608\pi\)
\(464\) −4.00000 + 6.92820i −0.185695 + 0.321634i
\(465\) 11.1962 + 19.3923i 0.519209 + 0.899297i
\(466\) −11.6603 + 6.73205i −0.540151 + 0.311856i
\(467\) 39.6410 1.83437 0.917184 0.398465i \(-0.130457\pi\)
0.917184 + 0.398465i \(0.130457\pi\)
\(468\) −0.866025 + 3.50000i −0.0400320 + 0.161788i
\(469\) −7.19615 −0.332287
\(470\) 1.60770 0.928203i 0.0741574 0.0428148i
\(471\) 1.46410 + 2.53590i 0.0674622 + 0.116848i
\(472\) −3.13397 + 5.42820i −0.144253 + 0.249853i
\(473\) 17.8564i 0.821038i
\(474\) 8.19615 + 4.73205i 0.376462 + 0.217350i
\(475\) −45.2487 26.1244i −2.07615 1.19867i
\(476\) 6.46410i 0.296282i
\(477\) 4.13397 7.16025i 0.189282 0.327846i
\(478\) −6.42820 11.1340i −0.294019 0.509256i
\(479\) −3.80385 + 2.19615i −0.173802 + 0.100345i −0.584377 0.811482i \(-0.698661\pi\)
0.410575 + 0.911827i \(0.365328\pi\)
\(480\) −3.46410 −0.158114
\(481\) −17.2487 4.26795i −0.786474 0.194602i
\(482\) 15.8564 0.722240
\(483\) −4.96410 + 2.86603i −0.225874 + 0.130409i
\(484\) −2.50000 4.33013i −0.113636 0.196824i
\(485\) −21.4641 + 37.1769i −0.974635 + 1.68812i
\(486\) 1.00000i 0.0453609i
\(487\) 0.339746 + 0.196152i 0.0153954 + 0.00888851i 0.507678 0.861547i \(-0.330504\pi\)
−0.492283 + 0.870435i \(0.663837\pi\)
\(488\) −4.50000 2.59808i −0.203705 0.117609i
\(489\) 1.33975i 0.0605854i
\(490\) −1.73205 + 3.00000i −0.0782461 + 0.135526i
\(491\) −4.92820 8.53590i −0.222407 0.385220i 0.733132 0.680087i \(-0.238058\pi\)
−0.955538 + 0.294867i \(0.904725\pi\)
\(492\) 6.00000 3.46410i 0.270501 0.156174i
\(493\) −51.7128 −2.32903
\(494\) 19.3923 + 18.6603i 0.872501 + 0.839565i
\(495\) −13.8564 −0.622799
\(496\) 5.59808 3.23205i 0.251361 0.145123i
\(497\) −0.964102 1.66987i −0.0432459 0.0749040i
\(498\) −0.866025 + 1.50000i −0.0388075 + 0.0672166i
\(499\) 0.267949i 0.0119951i 0.999982 + 0.00599753i \(0.00190908\pi\)
−0.999982 + 0.00599753i \(0.998091\pi\)
\(500\) −6.00000 3.46410i −0.268328 0.154919i
\(501\) −17.3205 10.0000i −0.773823 0.446767i
\(502\) 10.0718i 0.449526i
\(503\) 3.46410 6.00000i 0.154457 0.267527i −0.778404 0.627763i \(-0.783971\pi\)
0.932861 + 0.360236i \(0.117304\pi\)
\(504\) −0.500000 0.866025i −0.0222718 0.0385758i
\(505\) 0 0
\(506\) 22.9282 1.01928
\(507\) 11.0000 6.92820i 0.488527 0.307692i
\(508\) 5.07180 0.225025
\(509\) −29.6603 + 17.1244i −1.31467 + 0.759024i −0.982865 0.184325i \(-0.940990\pi\)
−0.331802 + 0.943349i \(0.607657\pi\)
\(510\) −11.1962 19.3923i −0.495774 0.858706i
\(511\) −5.46410 + 9.46410i −0.241718 + 0.418667i
\(512\) 1.00000i 0.0441942i
\(513\) 6.46410 + 3.73205i 0.285397 + 0.164774i
\(514\) 0.401924 + 0.232051i 0.0177281 + 0.0102353i
\(515\) 36.9282i 1.62725i
\(516\) −2.23205 + 3.86603i −0.0982606 + 0.170192i
\(517\) −1.07180 1.85641i −0.0471376 0.0816447i
\(518\) 4.26795 2.46410i 0.187523 0.108266i
\(519\) −1.07180 −0.0470467
\(520\) 9.00000 + 8.66025i 0.394676 + 0.379777i
\(521\) −30.0000 −1.31432 −0.657162 0.753749i \(-0.728243\pi\)
−0.657162 + 0.753749i \(0.728243\pi\)
\(522\) 6.92820 4.00000i 0.303239 0.175075i
\(523\) −7.46410 12.9282i −0.326382 0.565311i 0.655409 0.755274i \(-0.272496\pi\)
−0.981791 + 0.189963i \(0.939163\pi\)
\(524\) 9.50000 16.4545i 0.415009 0.718817i
\(525\) 7.00000i 0.305505i
\(526\) 15.0000 + 8.66025i 0.654031 + 0.377605i
\(527\) 36.1865 + 20.8923i 1.57631 + 0.910083i
\(528\) 4.00000i 0.174078i
\(529\) −4.92820 + 8.53590i −0.214270 + 0.371126i
\(530\) −14.3205 24.8038i −0.622043 1.07741i
\(531\) 5.42820 3.13397i 0.235564 0.136003i
\(532\) −7.46410 −0.323610
\(533\) −24.2487 6.00000i −1.05033 0.259889i
\(534\) 11.7321 0.507695
\(535\) 25.6077 14.7846i 1.10712 0.639194i
\(536\) −3.59808 6.23205i −0.155413 0.269184i
\(537\) −8.46410 + 14.6603i −0.365253 + 0.632637i
\(538\) 22.3923i 0.965401i
\(539\) 3.46410 + 2.00000i 0.149209 + 0.0861461i
\(540\) 3.00000 + 1.73205i 0.129099 + 0.0745356i
\(541\) 17.3205i 0.744667i −0.928099 0.372333i \(-0.878558\pi\)
0.928099 0.372333i \(-0.121442\pi\)
\(542\) 6.23205 10.7942i 0.267690 0.463652i
\(543\) 12.3923 + 21.4641i 0.531805 + 0.921113i
\(544\) −5.59808 + 3.23205i −0.240016 + 0.138573i
\(545\) −41.5692 −1.78063
\(546\) −0.866025 + 3.50000i −0.0370625 + 0.149786i
\(547\) −20.0000 −0.855138 −0.427569 0.903983i \(-0.640630\pi\)
−0.427569 + 0.903983i \(0.640630\pi\)
\(548\) −12.0000 + 6.92820i −0.512615 + 0.295958i
\(549\) 2.59808 + 4.50000i 0.110883 + 0.192055i
\(550\) −14.0000 + 24.2487i −0.596962 + 1.03397i
\(551\) 59.7128i 2.54385i
\(552\) −4.96410 2.86603i −0.211286 0.121986i
\(553\) 8.19615 + 4.73205i 0.348536 + 0.201227i
\(554\) 7.32051i 0.311019i
\(555\) −8.53590 + 14.7846i −0.362329 + 0.627572i
\(556\) 1.46410 + 2.53590i 0.0620917 + 0.107546i
\(557\) 21.3109 12.3038i 0.902971 0.521331i 0.0248083 0.999692i \(-0.492102\pi\)
0.878163 + 0.478361i \(0.158769\pi\)
\(558\) −6.46410 −0.273647
\(559\) 15.4641 4.46410i 0.654062 0.188811i
\(560\) −3.46410 −0.146385
\(561\) −22.3923 + 12.9282i −0.945404 + 0.545829i
\(562\) −1.19615 2.07180i −0.0504566 0.0873935i
\(563\) −6.92820 + 12.0000i −0.291989 + 0.505740i −0.974280 0.225341i \(-0.927650\pi\)
0.682291 + 0.731081i \(0.260984\pi\)
\(564\) 0.535898i 0.0225654i
\(565\) 13.1769 + 7.60770i 0.554357 + 0.320058i
\(566\) −9.92820 5.73205i −0.417314 0.240936i
\(567\) 1.00000i 0.0419961i
\(568\) 0.964102 1.66987i 0.0404528 0.0700663i
\(569\) 7.73205 + 13.3923i 0.324144 + 0.561435i 0.981339 0.192286i \(-0.0615903\pi\)
−0.657194 + 0.753721i \(0.728257\pi\)
\(570\) 22.3923 12.9282i 0.937910 0.541503i
\(571\) 3.39230 0.141964 0.0709818 0.997478i \(-0.477387\pi\)
0.0709818 + 0.997478i \(0.477387\pi\)
\(572\) 10.0000 10.3923i 0.418121 0.434524i
\(573\) −26.5167 −1.10775
\(574\) 6.00000 3.46410i 0.250435 0.144589i
\(575\) −20.0622 34.7487i −0.836651 1.44912i
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) 1.21539i 0.0505974i −0.999680 0.0252987i \(-0.991946\pi\)
0.999680 0.0252987i \(-0.00805368\pi\)
\(578\) −21.4641 12.3923i −0.892789 0.515452i
\(579\) −15.4641 8.92820i −0.642666 0.371043i
\(580\) 27.7128i 1.15071i
\(581\) −0.866025 + 1.50000i −0.0359288 + 0.0622305i
\(582\) −6.19615 10.7321i −0.256839 0.444858i
\(583\) −28.6410 + 16.5359i −1.18619 + 0.684847i
\(584\) −10.9282 −0.452212
\(585\) −3.46410 12.0000i −0.143223 0.496139i
\(586\) −33.4641 −1.38239
\(587\) 7.03590 4.06218i 0.290403 0.167664i −0.347721 0.937598i \(-0.613044\pi\)
0.638123 + 0.769934i \(0.279711\pi\)
\(588\) −0.500000 0.866025i −0.0206197 0.0357143i
\(589\) −24.1244 + 41.7846i −0.994027 + 1.72170i
\(590\) 21.7128i 0.893902i
\(591\) −2.25833 1.30385i −0.0928953 0.0536331i
\(592\) 4.26795 + 2.46410i 0.175412 + 0.101274i
\(593\) 4.26795i 0.175264i 0.996153 + 0.0876318i \(0.0279299\pi\)
−0.996153 + 0.0876318i \(0.972070\pi\)
\(594\) 2.00000 3.46410i 0.0820610 0.142134i
\(595\) −11.1962 19.3923i −0.458997 0.795007i
\(596\) −9.99038 + 5.76795i −0.409222 + 0.236264i
\(597\) 22.1244 0.905490
\(598\) 5.73205 + 19.8564i 0.234401 + 0.811989i
\(599\) −19.0526 −0.778466 −0.389233 0.921139i \(-0.627260\pi\)
−0.389233 + 0.921139i \(0.627260\pi\)
\(600\) 6.06218 3.50000i 0.247487 0.142887i
\(601\) 12.1244 + 21.0000i 0.494563 + 0.856608i 0.999980 0.00626702i \(-0.00199487\pi\)
−0.505418 + 0.862875i \(0.668662\pi\)
\(602\) −2.23205 + 3.86603i −0.0909716 + 0.157567i
\(603\) 7.19615i 0.293050i
\(604\) −10.3923 6.00000i −0.422857 0.244137i
\(605\) 15.0000 + 8.66025i 0.609837 + 0.352089i
\(606\) 0 0
\(607\) 7.59808 13.1603i 0.308396 0.534158i −0.669615 0.742708i \(-0.733541\pi\)
0.978012 + 0.208550i \(0.0668744\pi\)
\(608\) −3.73205 6.46410i −0.151355 0.262154i
\(609\) 6.92820 4.00000i 0.280745 0.162088i
\(610\) 18.0000 0.728799
\(611\) 1.33975 1.39230i 0.0542003 0.0563266i
\(612\) 6.46410 0.261296
\(613\) 29.7846 17.1962i 1.20299 0.694546i 0.241770 0.970333i \(-0.422272\pi\)
0.961219 + 0.275787i \(0.0889386\pi\)
\(614\) −11.0000 19.0526i −0.443924 0.768899i
\(615\) −12.0000 + 20.7846i −0.483887 + 0.838116i
\(616\) 4.00000i 0.161165i
\(617\) −5.07180 2.92820i −0.204183 0.117885i 0.394422 0.918929i \(-0.370945\pi\)
−0.598605 + 0.801044i \(0.704278\pi\)
\(618\) 9.23205 + 5.33013i 0.371368 + 0.214409i
\(619\) 30.7846i 1.23734i 0.785652 + 0.618669i \(0.212328\pi\)
−0.785652 + 0.618669i \(0.787672\pi\)
\(620\) −11.1962 + 19.3923i −0.449648 + 0.778814i
\(621\) 2.86603 + 4.96410i 0.115010 + 0.199203i
\(622\) −11.5359 + 6.66025i −0.462547 + 0.267052i
\(623\) 11.7321 0.470035
\(624\) −3.46410 + 1.00000i −0.138675 + 0.0400320i
\(625\) −11.0000 −0.440000
\(626\) 0.588457 0.339746i 0.0235195 0.0135790i
\(627\) −14.9282 25.8564i −0.596175 1.03261i
\(628\) −1.46410 + 2.53590i −0.0584240 + 0.101193i
\(629\) 31.8564i 1.27020i
\(630\) 3.00000 + 1.73205i 0.119523 + 0.0690066i
\(631\) 30.2487 + 17.4641i 1.20418 + 0.695235i 0.961482 0.274867i \(-0.0886337\pi\)
0.242700 + 0.970101i \(0.421967\pi\)
\(632\) 9.46410i 0.376462i
\(633\) 4.53590 7.85641i 0.180286 0.312264i
\(634\) −8.23205 14.2583i −0.326937 0.566271i
\(635\) −15.2154 + 8.78461i −0.603804 + 0.348607i
\(636\) 8.26795 0.327846
\(637\) −0.866025 + 3.50000i −0.0343132 + 0.138675i
\(638\) −32.0000 −1.26689
\(639\) −1.66987 + 0.964102i −0.0660592 + 0.0381393i
\(640\) −1.73205 3.00000i −0.0684653 0.118585i
\(641\) −13.3205 + 23.0718i −0.526128 + 0.911281i 0.473408 + 0.880843i \(0.343024\pi\)
−0.999537 + 0.0304380i \(0.990310\pi\)
\(642\) 8.53590i 0.336885i
\(643\) −17.5359 10.1244i −0.691548 0.399266i 0.112643 0.993635i \(-0.464068\pi\)
−0.804192 + 0.594370i \(0.797402\pi\)
\(644\) −4.96410 2.86603i −0.195613 0.112937i
\(645\) 15.4641i 0.608898i
\(646\) 24.1244 41.7846i 0.949160 1.64399i
\(647\) 18.6603 + 32.3205i 0.733610 + 1.27065i 0.955330 + 0.295540i \(0.0954995\pi\)
−0.221720 + 0.975110i \(0.571167\pi\)
\(648\) −0.866025 + 0.500000i −0.0340207 + 0.0196419i
\(649\) −25.0718 −0.984154
\(650\) −24.5000 6.06218i −0.960969 0.237778i
\(651\) −6.46410 −0.253348
\(652\) 1.16025 0.669873i 0.0454391 0.0262343i
\(653\) 18.7942 + 32.5526i 0.735475 + 1.27388i 0.954515 + 0.298164i \(0.0963743\pi\)
−0.219040 + 0.975716i \(0.570292\pi\)
\(654\) 6.00000 10.3923i 0.234619 0.406371i
\(655\) 65.8179i 2.57172i
\(656\) 6.00000 + 3.46410i 0.234261 + 0.135250i
\(657\) 9.46410 + 5.46410i 0.369230 + 0.213175i
\(658\) 0.535898i 0.0208915i
\(659\) −0.803848 + 1.39230i −0.0313135 + 0.0542365i −0.881257 0.472637i \(-0.843302\pi\)
0.849944 + 0.526873i \(0.176636\pi\)
\(660\) −6.92820 12.0000i −0.269680 0.467099i
\(661\) 43.9186 25.3564i 1.70823 0.986250i 0.771487 0.636245i \(-0.219513\pi\)
0.936748 0.350005i \(-0.113820\pi\)
\(662\) 21.3205 0.828645
\(663\) −16.7942 16.1603i −0.652234 0.627612i
\(664\) −1.73205 −0.0672166
\(665\) 22.3923 12.9282i 0.868336 0.501334i
\(666\) −2.46410 4.26795i −0.0954820 0.165380i
\(667\) 22.9282 39.7128i 0.887784 1.53769i
\(668\) 20.0000i 0.773823i
\(669\) 6.52628 + 3.76795i 0.252321 + 0.145677i
\(670\) 21.5885 + 12.4641i 0.834035 + 0.481530i
\(671\) 20.7846i 0.802381i
\(672\) 0.500000 0.866025i 0.0192879 0.0334077i
\(673\) 19.8205 + 34.3301i 0.764024 + 1.32333i 0.940761 + 0.339071i \(0.110113\pi\)
−0.176736 + 0.984258i \(0.556554\pi\)
\(674\) −5.19615 + 3.00000i −0.200148 + 0.115556i
\(675\) −7.00000 −0.269430
\(676\) 11.5000 + 6.06218i 0.442308 + 0.233161i
\(677\) 1.07180 0.0411925 0.0205962 0.999788i \(-0.493444\pi\)
0.0205962 + 0.999788i \(0.493444\pi\)
\(678\) −3.80385 + 2.19615i −0.146086 + 0.0843427i
\(679\) −6.19615 10.7321i −0.237787 0.411858i
\(680\) 11.1962 19.3923i 0.429353 0.743661i
\(681\) 13.3205i 0.510443i
\(682\) 22.3923 + 12.9282i 0.857446 + 0.495046i
\(683\) 44.3205 + 25.5885i 1.69588 + 0.979115i 0.949592 + 0.313489i \(0.101498\pi\)
0.746285 + 0.665626i \(0.231836\pi\)
\(684\) 7.46410i 0.285397i
\(685\) 24.0000 41.5692i 0.916993 1.58828i
\(686\) −0.500000 0.866025i −0.0190901 0.0330650i
\(687\) 17.2583 9.96410i 0.658446 0.380154i
\(688\) −4.46410 −0.170192
\(689\) −21.4808 20.6699i −0.818352 0.787459i
\(690\) 19.8564 0.755920
\(691\) −35.6603 + 20.5885i −1.35658 + 0.783222i −0.989161 0.146834i \(-0.953092\pi\)
−0.367419 + 0.930056i \(0.619758\pi\)
\(692\) −0.535898 0.928203i −0.0203718 0.0352850i
\(693\) 2.00000 3.46410i 0.0759737 0.131590i
\(694\) 25.7128i 0.976045i
\(695\) −8.78461 5.07180i −0.333219 0.192384i
\(696\) 6.92820 + 4.00000i 0.262613 + 0.151620i
\(697\) 44.7846i 1.69634i
\(698\) −17.8205 + 30.8660i −0.674516 + 1.16830i
\(699\) 6.73205 + 11.6603i 0.254630 + 0.441031i
\(700\) 6.06218 3.50000i 0.229129 0.132288i
\(701\) 2.12436 0.0802358 0.0401179 0.999195i \(-0.487227\pi\)
0.0401179 + 0.999195i \(0.487227\pi\)
\(702\) 3.50000 + 0.866025i 0.132099 + 0.0326860i
\(703\) −36.7846 −1.38736
\(704\) −3.46410 + 2.00000i −0.130558 + 0.0753778i
\(705\) −0.928203 1.60770i −0.0349582 0.0605493i
\(706\) 4.66987 8.08846i 0.175753 0.304413i
\(707\) 0 0
\(708\) 5.42820 + 3.13397i 0.204004 + 0.117782i
\(709\) −6.67949 3.85641i −0.250854 0.144830i 0.369301 0.929310i \(-0.379597\pi\)
−0.620155 + 0.784479i \(0.712930\pi\)
\(710\) 6.67949i 0.250677i
\(711\) 4.73205 8.19615i 0.177466 0.307380i
\(712\) 5.86603 + 10.1603i 0.219839 + 0.380772i
\(713\) −32.0885 + 18.5263i −1.20172 + 0.693815i
\(714\) 6.46410 0.241913
\(715\) −12.0000 + 48.4974i −0.448775 + 1.81370i
\(716\) −16.9282 −0.632637
\(717\) −11.1340 + 6.42820i −0.415806 + 0.240066i
\(718\) −4.00000 6.92820i −0.149279 0.258558i
\(719\) 17.2679 29.9090i 0.643986 1.11542i −0.340549 0.940227i \(-0.610613\pi\)
0.984535 0.175189i \(-0.0560538\pi\)
\(720\) 3.46410i 0.129099i
\(721\) 9.23205 + 5.33013i 0.343820 + 0.198504i
\(722\) 31.7942 + 18.3564i 1.18326 + 0.683155i
\(723\) 15.8564i 0.589706i
\(724\) −12.3923 + 21.4641i −0.460556 + 0.797707i
\(725\) 28.0000 + 48.4974i 1.03989 + 1.80115i
\(726\) −4.33013 + 2.50000i −0.160706 + 0.0927837i
\(727\) 22.9090 0.849646 0.424823 0.905276i \(-0.360336\pi\)
0.424823 + 0.905276i \(0.360336\pi\)
\(728\) −3.46410 + 1.00000i −0.128388 + 0.0370625i
\(729\) 1.00000 0.0370370
\(730\) 32.7846 18.9282i 1.21341 0.700564i
\(731\) −14.4282 24.9904i −0.533646 0.924303i
\(732\) −2.59808 + 4.50000i −0.0960277 + 0.166325i
\(733\) 4.85641i 0.179375i −0.995970 0.0896877i \(-0.971413\pi\)
0.995970 0.0896877i \(-0.0285869\pi\)
\(734\) 28.6244 + 16.5263i 1.05654 + 0.609996i
\(735\) 3.00000 + 1.73205i 0.110657 + 0.0638877i
\(736\) 5.73205i 0.211286i
\(737\) 14.3923 24.9282i 0.530147 0.918242i
\(738\) −3.46410 6.00000i −0.127515 0.220863i
\(739\) 6.69615 3.86603i 0.246322 0.142214i −0.371757 0.928330i \(-0.621245\pi\)
0.618079 + 0.786116i \(0.287911\pi\)
\(740\) −17.0718 −0.627572
\(741\) 18.6603 19.3923i 0.685502 0.712394i
\(742\) 8.26795 0.303526
\(743\) 1.54552 0.892305i 0.0566995 0.0327355i −0.471382 0.881929i \(-0.656245\pi\)
0.528082 + 0.849194i \(0.322911\pi\)
\(744\) −3.23205 5.59808i −0.118493 0.205235i
\(745\) 19.9808 34.6077i 0.732038 1.26793i
\(746\) 26.2487i 0.961034i
\(747\) 1.50000 + 0.866025i 0.0548821 + 0.0316862i
\(748\) −22.3923 12.9282i −0.818744 0.472702i
\(749\) 8.53590i 0.311895i
\(750\) −3.46410 + 6.00000i −0.126491 + 0.219089i
\(751\) 14.6603 + 25.3923i 0.534960 + 0.926578i 0.999165 + 0.0408506i \(0.0130068\pi\)
−0.464205 + 0.885728i \(0.653660\pi\)
\(752\) −0.464102 + 0.267949i −0.0169240 + 0.00977110i
\(753\) 10.0718 0.367037
\(754\) −8.00000 27.7128i −0.291343 1.00924i
\(755\) 41.5692 1.51286
\(756\) −0.866025 + 0.500000i −0.0314970 + 0.0181848i
\(757\) −9.92820 17.1962i −0.360847 0.625005i 0.627254 0.778815i \(-0.284179\pi\)
−0.988100 + 0.153810i \(0.950846\pi\)
\(758\) −4.80385 + 8.32051i −0.174484 + 0.302214i
\(759\) 22.9282i 0.832241i
\(760\) 22.3923 + 12.9282i 0.812254 + 0.468955i
\(761\) 6.00000 + 3.46410i 0.217500 + 0.125574i 0.604792 0.796383i \(-0.293256\pi\)
−0.387292 + 0.921957i \(0.626590\pi\)
\(762\) 5.07180i 0.183732i
\(763\) 6.00000 10.3923i 0.217215 0.376227i
\(764\) −13.2583 22.9641i −0.479670 0.830812i
\(765\) −19.3923 + 11.1962i −0.701130 + 0.404798i
\(766\) 7.32051 0.264501
\(767\) −6.26795 21.7128i −0.226323 0.784004i
\(768\) 1.00000 0.0360844
\(769\) 36.9282 21.3205i 1.33167 0.768837i 0.346110 0.938194i \(-0.387502\pi\)
0.985555 + 0.169357i \(0.0541690\pi\)
\(770\) −6.92820 12.0000i −0.249675 0.432450i
\(771\) 0.232051 0.401924i 0.00835711 0.0144749i
\(772\) 17.8564i 0.642666i
\(773\) 11.1962 + 6.46410i 0.402698 + 0.232498i 0.687647 0.726045i \(-0.258644\pi\)
−0.284950 + 0.958542i \(0.591977\pi\)
\(774\) 3.86603 + 2.23205i 0.138961 + 0.0802294i
\(775\) 45.2487i 1.62538i