Properties

Label 546.2.s.c.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.c.127.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -3.46410i q^{5} +(0.866025 - 0.500000i) q^{6} +(0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(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} +(-0.232051 - 0.401924i) q^{17} +1.00000i q^{18} +(-0.464102 + 0.267949i) q^{19} +(3.00000 - 1.73205i) q^{20} +1.00000i q^{21} +(2.00000 + 3.46410i) q^{22} +(1.13397 - 1.96410i) 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} -0.464102i q^{31} +(0.866025 - 0.500000i) q^{32} +(3.46410 - 2.00000i) q^{33} +0.464102i q^{34} +(-1.73205 - 3.00000i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-7.73205 - 4.46410i) q^{37} +0.535898 q^{38} +(-0.866025 - 3.50000i) q^{39} -3.46410 q^{40} +(-6.00000 - 3.46410i) q^{41} +(0.500000 - 0.866025i) q^{42} +(-1.23205 - 2.13397i) q^{43} -4.00000i q^{44} +(-3.00000 + 1.73205i) q^{45} +(-1.96410 + 1.13397i) q^{46} -7.46410i q^{47} +(-0.500000 - 0.866025i) q^{48} +(0.500000 - 0.866025i) q^{49} +(6.06218 + 3.50000i) q^{50} +0.464102 q^{51} +(-3.46410 - 1.00000i) q^{52} -11.7321 q^{53} +(-0.866025 - 0.500000i) q^{54} +(-6.92820 + 12.0000i) q^{55} +(-0.500000 - 0.866025i) q^{56} -0.535898i q^{57} +(6.92820 - 4.00000i) q^{58} +(8.42820 - 4.86603i) q^{59} +3.46410i q^{60} +(-2.59808 - 4.50000i) q^{61} +(-0.232051 + 0.401924i) q^{62} +(-0.866025 - 0.500000i) q^{63} -1.00000 q^{64} +(8.66025 + 9.00000i) q^{65} -4.00000 q^{66} +(2.76795 + 1.59808i) q^{67} +(0.232051 - 0.401924i) q^{68} +(1.13397 + 1.96410i) q^{69} +3.46410i q^{70} +(10.3301 - 5.96410i) q^{71} +(-0.866025 + 0.500000i) q^{72} +2.92820i q^{73} +(4.46410 + 7.73205i) q^{74} +(3.50000 - 6.06218i) q^{75} +(-0.464102 - 0.267949i) q^{76} -4.00000 q^{77} +(-1.00000 + 3.46410i) q^{78} -2.53590 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} +(-1.39230 + 0.803848i) q^{85} +2.46410i q^{86} +(-4.00000 - 6.92820i) q^{87} +(-2.00000 + 3.46410i) q^{88} +(7.16025 + 4.13397i) q^{89} +3.46410 q^{90} +(-1.00000 + 3.46410i) q^{91} +2.26795 q^{92} +(0.401924 + 0.232051i) q^{93} +(-3.73205 + 6.46410i) q^{94} +(0.928203 + 1.60770i) q^{95} +1.00000i q^{96} +(7.26795 - 4.19615i) 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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

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

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
\(5\) 3.46410i 1.54919i −0.632456 0.774597i \(-0.717953\pi\)
0.632456 0.774597i \(-0.282047\pi\)
\(6\) 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 \(-0.539370\pi\)
−0.921095 + 0.389338i \(0.872704\pi\)
\(12\) −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
\(17\) −0.232051 0.401924i −0.0562806 0.0974808i 0.836512 0.547948i \(-0.184591\pi\)
−0.892793 + 0.450467i \(0.851257\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −0.464102 + 0.267949i −0.106472 + 0.0614718i −0.552291 0.833652i \(-0.686246\pi\)
0.445818 + 0.895123i \(0.352913\pi\)
\(20\) 3.00000 1.73205i 0.670820 0.387298i
\(21\) 1.00000i 0.218218i
\(22\) 2.00000 + 3.46410i 0.426401 + 0.738549i
\(23\) 1.13397 1.96410i 0.236450 0.409543i −0.723243 0.690594i \(-0.757349\pi\)
0.959693 + 0.281050i \(0.0906827\pi\)
\(24\) 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 0.208443 + 0.978035i \(0.433160\pi\)
−0.951224 + 0.308500i \(0.900173\pi\)
\(30\) −1.73205 3.00000i −0.316228 0.547723i
\(31\) 0.464102i 0.0833551i −0.999131 0.0416776i \(-0.986730\pi\)
0.999131 0.0416776i \(-0.0132702\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 3.46410 2.00000i 0.603023 0.348155i
\(34\) 0.464102i 0.0795928i
\(35\) −1.73205 3.00000i −0.292770 0.507093i
\(36\) 0.500000 0.866025i 0.0833333 0.144338i
\(37\) −7.73205 4.46410i −1.27114 0.733894i −0.295939 0.955207i \(-0.595632\pi\)
−0.975203 + 0.221313i \(0.928966\pi\)
\(38\) 0.535898 0.0869342
\(39\) −0.866025 3.50000i −0.138675 0.560449i
\(40\) −3.46410 −0.547723
\(41\) −6.00000 3.46410i −0.937043 0.541002i −0.0480106 0.998847i \(-0.515288\pi\)
−0.889032 + 0.457845i \(0.848621\pi\)
\(42\) 0.500000 0.866025i 0.0771517 0.133631i
\(43\) −1.23205 2.13397i −0.187886 0.325428i 0.756659 0.653809i \(-0.226830\pi\)
−0.944545 + 0.328381i \(0.893497\pi\)
\(44\) 4.00000i 0.603023i
\(45\) −3.00000 + 1.73205i −0.447214 + 0.258199i
\(46\) −1.96410 + 1.13397i −0.289591 + 0.167195i
\(47\) 7.46410i 1.08875i −0.838842 0.544376i \(-0.816767\pi\)
0.838842 0.544376i \(-0.183233\pi\)
\(48\) −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
\(51\) 0.464102 0.0649872
\(52\) −3.46410 1.00000i −0.480384 0.138675i
\(53\) −11.7321 −1.61152 −0.805761 0.592241i \(-0.798243\pi\)
−0.805761 + 0.592241i \(0.798243\pi\)
\(54\) −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
\(57\) 0.535898i 0.0709815i
\(58\) 6.92820 4.00000i 0.909718 0.525226i
\(59\) 8.42820 4.86603i 1.09726 0.633503i 0.161759 0.986830i \(-0.448283\pi\)
0.935500 + 0.353328i \(0.114950\pi\)
\(60\) 3.46410i 0.447214i
\(61\) −2.59808 4.50000i −0.332650 0.576166i 0.650381 0.759608i \(-0.274609\pi\)
−0.983030 + 0.183442i \(0.941276\pi\)
\(62\) −0.232051 + 0.401924i −0.0294705 + 0.0510444i
\(63\) −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
\(67\) 2.76795 + 1.59808i 0.338159 + 0.195236i 0.659458 0.751742i \(-0.270786\pi\)
−0.321299 + 0.946978i \(0.604119\pi\)
\(68\) 0.232051 0.401924i 0.0281403 0.0487404i
\(69\) 1.13397 + 1.96410i 0.136514 + 0.236450i
\(70\) 3.46410i 0.414039i
\(71\) 10.3301 5.96410i 1.22596 0.707809i 0.259778 0.965668i \(-0.416351\pi\)
0.966182 + 0.257860i \(0.0830172\pi\)
\(72\) −0.866025 + 0.500000i −0.102062 + 0.0589256i
\(73\) 2.92820i 0.342720i 0.985208 + 0.171360i \(0.0548162\pi\)
−0.985208 + 0.171360i \(0.945184\pi\)
\(74\) 4.46410 + 7.73205i 0.518941 + 0.898833i
\(75\) 3.50000 6.06218i 0.404145 0.700000i
\(76\) −0.464102 0.267949i −0.0532361 0.0307359i
\(77\) −4.00000 −0.455842
\(78\) −1.00000 + 3.46410i −0.113228 + 0.392232i
\(79\) −2.53590 −0.285311 −0.142655 0.989772i \(-0.545564\pi\)
−0.142655 + 0.989772i \(0.545564\pi\)
\(80\) 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 \(0.0303039\pi\)
−0.995472 + 0.0950586i \(0.969696\pi\)
\(84\) −0.866025 + 0.500000i −0.0944911 + 0.0545545i
\(85\) −1.39230 + 0.803848i −0.151017 + 0.0871895i
\(86\) 2.46410i 0.265711i
\(87\) −4.00000 6.92820i −0.428845 0.742781i
\(88\) −2.00000 + 3.46410i −0.213201 + 0.369274i
\(89\) 7.16025 + 4.13397i 0.758985 + 0.438200i 0.828931 0.559350i \(-0.188949\pi\)
−0.0699459 + 0.997551i \(0.522283\pi\)
\(90\) 3.46410 0.365148
\(91\) −1.00000 + 3.46410i −0.104828 + 0.363137i
\(92\) 2.26795 0.236450
\(93\) 0.401924 + 0.232051i 0.0416776 + 0.0240625i
\(94\) −3.73205 + 6.46410i −0.384932 + 0.666721i
\(95\) 0.928203 + 1.60770i 0.0952316 + 0.164946i
\(96\) 1.00000i 0.102062i
\(97\) 7.26795 4.19615i 0.737948 0.426055i −0.0833745 0.996518i \(-0.526570\pi\)
0.821323 + 0.570464i \(0.193236\pi\)
\(98\) −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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(102\) −0.401924 0.232051i −0.0397964 0.0229765i
\(103\) 6.66025 0.656254 0.328127 0.944634i \(-0.393583\pi\)
0.328127 + 0.944634i \(0.393583\pi\)
\(104\) 2.50000 + 2.59808i 0.245145 + 0.254762i
\(105\) 3.46410 0.338062
\(106\) 10.1603 + 5.86603i 0.986851 + 0.569759i
\(107\) −7.73205 + 13.3923i −0.747486 + 1.29468i 0.201539 + 0.979481i \(0.435406\pi\)
−0.949024 + 0.315202i \(0.897928\pi\)
\(108\) 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
\(111\) 7.73205 4.46410i 0.733894 0.423714i
\(112\) 1.00000i 0.0944911i
\(113\) −8.19615 14.1962i −0.771029 1.33546i −0.936999 0.349331i \(-0.886409\pi\)
0.165970 0.986131i \(-0.446924\pi\)
\(114\) −0.267949 + 0.464102i −0.0250957 + 0.0434671i
\(115\) −6.80385 3.92820i −0.634462 0.366307i
\(116\) −8.00000 −0.742781
\(117\) 3.46410 + 1.00000i 0.320256 + 0.0924500i
\(118\) −9.73205 −0.895908
\(119\) −0.401924 0.232051i −0.0368443 0.0212721i
\(120\) 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
\(124\) 0.401924 0.232051i 0.0360938 0.0208388i
\(125\) 6.92820i 0.619677i
\(126\) 0.500000 + 0.866025i 0.0445435 + 0.0771517i
\(127\) 9.46410 16.3923i 0.839803 1.45458i −0.0502557 0.998736i \(-0.516004\pi\)
0.890059 0.455845i \(-0.150663\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 2.46410 0.216952
\(130\) −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
\(133\) −0.267949 + 0.464102i −0.0232341 + 0.0402427i
\(134\) −1.59808 2.76795i −0.138053 0.239114i
\(135\) 3.46410i 0.298142i
\(136\) −0.401924 + 0.232051i −0.0344647 + 0.0198982i
\(137\) −12.0000 + 6.92820i −1.02523 + 0.591916i −0.915614 0.402058i \(-0.868295\pi\)
−0.109615 + 0.993974i \(0.534962\pi\)
\(138\) 2.26795i 0.193061i
\(139\) 5.46410 + 9.46410i 0.463459 + 0.802735i 0.999131 0.0416919i \(-0.0132748\pi\)
−0.535671 + 0.844426i \(0.679941\pi\)
\(140\) 1.73205 3.00000i 0.146385 0.253546i
\(141\) 6.46410 + 3.73205i 0.544376 + 0.314295i
\(142\) −11.9282 −1.00099
\(143\) 14.0000 3.46410i 1.17074 0.289683i
\(144\) 1.00000 0.0833333
\(145\) 24.0000 + 13.8564i 1.99309 + 1.15071i
\(146\) 1.46410 2.53590i 0.121170 0.209872i
\(147\) 0.500000 + 0.866025i 0.0412393 + 0.0714286i
\(148\) 8.92820i 0.733894i
\(149\) 15.9904 9.23205i 1.30998 0.756319i 0.327890 0.944716i \(-0.393662\pi\)
0.982093 + 0.188397i \(0.0603291\pi\)
\(150\) −6.06218 + 3.50000i −0.494975 + 0.285774i
\(151\) 12.0000i 0.976546i −0.872691 0.488273i \(-0.837627\pi\)
0.872691 0.488273i \(-0.162373\pi\)
\(152\) 0.267949 + 0.464102i 0.0217335 + 0.0376436i
\(153\) −0.232051 + 0.401924i −0.0187602 + 0.0324936i
\(154\) 3.46410 + 2.00000i 0.279145 + 0.161165i
\(155\) −1.60770 −0.129133
\(156\) 2.59808 2.50000i 0.208013 0.200160i
\(157\) 10.9282 0.872166 0.436083 0.899907i \(-0.356365\pi\)
0.436083 + 0.899907i \(0.356365\pi\)
\(158\) 2.19615 + 1.26795i 0.174717 + 0.100873i
\(159\) 5.86603 10.1603i 0.465206 0.805761i
\(160\) −1.73205 3.00000i −0.136931 0.237171i
\(161\) 2.26795i 0.178739i
\(162\) 0.866025 0.500000i 0.0680414 0.0392837i
\(163\) −16.1603 + 9.33013i −1.26577 + 0.730792i −0.974185 0.225753i \(-0.927516\pi\)
−0.291584 + 0.956545i \(0.594182\pi\)
\(164\) 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 \(-0.614991\pi\)
−0.986851 + 0.161630i \(0.948325\pi\)
\(168\) 1.00000 0.0771517
\(169\) 0.500000 12.9904i 0.0384615 0.999260i
\(170\) 1.60770 0.123305
\(171\) 0.464102 + 0.267949i 0.0354907 + 0.0204906i
\(172\) 1.23205 2.13397i 0.0939430 0.162714i
\(173\) 7.46410 + 12.9282i 0.567485 + 0.982913i 0.996814 + 0.0797647i \(0.0254169\pi\)
−0.429329 + 0.903148i \(0.641250\pi\)
\(174\) 8.00000i 0.606478i
\(175\) −6.06218 + 3.50000i −0.458258 + 0.264575i
\(176\) 3.46410 2.00000i 0.261116 0.150756i
\(177\) 9.73205i 0.731506i
\(178\) −4.13397 7.16025i −0.309854 0.536684i
\(179\) −1.53590 + 2.66025i −0.114798 + 0.198837i −0.917699 0.397276i \(-0.869956\pi\)
0.802901 + 0.596113i \(0.203289\pi\)
\(180\) −3.00000 1.73205i −0.223607 0.129099i
\(181\) 16.7846 1.24759 0.623795 0.781588i \(-0.285590\pi\)
0.623795 + 0.781588i \(0.285590\pi\)
\(182\) 2.59808 2.50000i 0.192582 0.185312i
\(183\) 5.19615 0.384111
\(184\) −1.96410 1.13397i −0.144795 0.0835977i
\(185\) −15.4641 + 26.7846i −1.13694 + 1.96924i
\(186\) −0.232051 0.401924i −0.0170148 0.0294705i
\(187\) 1.85641i 0.135754i
\(188\) 6.46410 3.73205i 0.471443 0.272188i
\(189\) 0.866025 0.500000i 0.0629941 0.0363696i
\(190\) 1.85641i 0.134678i
\(191\) −9.25833 16.0359i −0.669909 1.16032i −0.977929 0.208937i \(-0.933000\pi\)
0.308020 0.951380i \(-0.400334\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) 8.53590 + 4.92820i 0.614427 + 0.354740i 0.774696 0.632334i \(-0.217903\pi\)
−0.160269 + 0.987073i \(0.551236\pi\)
\(194\) −8.39230 −0.602532
\(195\) −12.1244 + 3.00000i −0.868243 + 0.214834i
\(196\) 1.00000 0.0714286
\(197\) −20.2583 11.6962i −1.44335 0.833316i −0.445275 0.895394i \(-0.646894\pi\)
−0.998071 + 0.0620775i \(0.980227\pi\)
\(198\) 2.00000 3.46410i 0.142134 0.246183i
\(199\) 1.06218 + 1.83975i 0.0752958 + 0.130416i 0.901215 0.433373i \(-0.142677\pi\)
−0.825919 + 0.563789i \(0.809343\pi\)
\(200\) 7.00000i 0.494975i
\(201\) −2.76795 + 1.59808i −0.195236 + 0.112720i
\(202\) 0 0
\(203\) 8.00000i 0.561490i
\(204\) 0.232051 + 0.401924i 0.0162468 + 0.0281403i
\(205\) −12.0000 + 20.7846i −0.838116 + 1.45166i
\(206\) −5.76795 3.33013i −0.401872 0.232021i
\(207\) −2.26795 −0.157633
\(208\) −0.866025 3.50000i −0.0600481 0.242681i
\(209\) 2.14359 0.148275
\(210\) −3.00000 1.73205i −0.207020 0.119523i
\(211\) 11.4641 19.8564i 0.789221 1.36697i −0.137223 0.990540i \(-0.543818\pi\)
0.926445 0.376431i \(-0.122849\pi\)
\(212\) −5.86603 10.1603i −0.402880 0.697809i
\(213\) 11.9282i 0.817307i
\(214\) 13.3923 7.73205i 0.915479 0.528552i
\(215\) −7.39230 + 4.26795i −0.504151 + 0.291072i
\(216\) 1.00000i 0.0680414i
\(217\) −0.232051 0.401924i −0.0157526 0.0272844i
\(218\) 6.00000 10.3923i 0.406371 0.703856i
\(219\) −2.53590 1.46410i −0.171360 0.0989348i
\(220\) −13.8564 −0.934199
\(221\) 1.60770 + 0.464102i 0.108145 + 0.0312189i
\(222\) −8.92820 −0.599222
\(223\) 12.5263 + 7.23205i 0.838822 + 0.484294i 0.856864 0.515543i \(-0.172410\pi\)
−0.0180418 + 0.999837i \(0.505743\pi\)
\(224\) 0.500000 0.866025i 0.0334077 0.0578638i
\(225\) 3.50000 + 6.06218i 0.233333 + 0.404145i
\(226\) 16.3923i 1.09040i
\(227\) −18.4641 + 10.6603i −1.22551 + 0.707546i −0.966086 0.258219i \(-0.916864\pi\)
−0.259419 + 0.965765i \(0.583531\pi\)
\(228\) 0.464102 0.267949i 0.0307359 0.0177454i
\(229\) 6.07180i 0.401236i 0.979670 + 0.200618i \(0.0642949\pi\)
−0.979670 + 0.200618i \(0.935705\pi\)
\(230\) 3.92820 + 6.80385i 0.259018 + 0.448632i
\(231\) 2.00000 3.46410i 0.131590 0.227921i
\(232\) 6.92820 + 4.00000i 0.454859 + 0.262613i
\(233\) −6.53590 −0.428181 −0.214090 0.976814i \(-0.568679\pi\)
−0.214090 + 0.976814i \(0.568679\pi\)
\(234\) −2.50000 2.59808i −0.163430 0.169842i
\(235\) −25.8564 −1.68669
\(236\) 8.42820 + 4.86603i 0.548629 + 0.316751i
\(237\) 1.26795 2.19615i 0.0823622 0.142655i
\(238\) 0.232051 + 0.401924i 0.0150416 + 0.0260528i
\(239\) 14.8564i 0.960981i 0.877000 + 0.480491i \(0.159541\pi\)
−0.877000 + 0.480491i \(0.840459\pi\)
\(240\) −3.00000 + 1.73205i −0.193649 + 0.111803i
\(241\) 10.2679 5.92820i 0.661417 0.381869i −0.131400 0.991329i \(-0.541947\pi\)
0.792817 + 0.609460i \(0.208614\pi\)
\(242\) 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
\(247\) 0.535898 1.85641i 0.0340984 0.118120i
\(248\) −0.464102 −0.0294705
\(249\) −1.50000 0.866025i −0.0950586 0.0548821i
\(250\) 3.46410 6.00000i 0.219089 0.379473i
\(251\) −11.9641 20.7224i −0.755167 1.30799i −0.945291 0.326228i \(-0.894222\pi\)
0.190124 0.981760i \(-0.439111\pi\)
\(252\) 1.00000i 0.0629941i
\(253\) −7.85641 + 4.53590i −0.493928 + 0.285169i
\(254\) −16.3923 + 9.46410i −1.02854 + 0.593831i
\(255\) 1.60770i 0.100678i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −3.23205 + 5.59808i −0.201610 + 0.349198i −0.949047 0.315134i \(-0.897951\pi\)
0.747437 + 0.664332i \(0.231284\pi\)
\(258\) −2.13397 1.23205i −0.132855 0.0767041i
\(259\) −8.92820 −0.554772
\(260\) −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 0.465196 + 0.885208i \(0.345984\pi\)
−0.999210 + 0.0397320i \(0.987350\pi\)
\(264\) −2.00000 3.46410i −0.123091 0.213201i
\(265\) 40.6410i 2.49656i
\(266\) 0.464102 0.267949i 0.0284559 0.0164290i
\(267\) −7.16025 + 4.13397i −0.438200 + 0.252995i
\(268\) 3.19615i 0.195236i
\(269\) −0.803848 1.39230i −0.0490115 0.0848903i 0.840479 0.541844i \(-0.182274\pi\)
−0.889490 + 0.456954i \(0.848940\pi\)
\(270\) −1.73205 + 3.00000i −0.105409 + 0.182574i
\(271\) −4.79423 2.76795i −0.291229 0.168141i 0.347267 0.937766i \(-0.387110\pi\)
−0.638496 + 0.769625i \(0.720443\pi\)
\(272\) 0.464102 0.0281403
\(273\) −2.50000 2.59808i −0.151307 0.157243i
\(274\) 13.8564 0.837096
\(275\) 24.2487 + 14.0000i 1.46225 + 0.844232i
\(276\) −1.13397 + 1.96410i −0.0682572 + 0.118225i
\(277\) −13.6603 23.6603i −0.820765 1.42161i −0.905113 0.425171i \(-0.860214\pi\)
0.0843481 0.996436i \(-0.473119\pi\)
\(278\) 10.9282i 0.655430i
\(279\) −0.401924 + 0.232051i −0.0240625 + 0.0138925i
\(280\) −3.00000 + 1.73205i −0.179284 + 0.103510i
\(281\) 18.3923i 1.09719i 0.836087 + 0.548596i \(0.184838\pi\)
−0.836087 + 0.548596i \(0.815162\pi\)
\(282\) −3.73205 6.46410i −0.222240 0.384932i
\(283\) −2.26795 + 3.92820i −0.134816 + 0.233507i −0.925527 0.378682i \(-0.876378\pi\)
0.790711 + 0.612189i \(0.209711\pi\)
\(284\) 10.3301 + 5.96410i 0.612980 + 0.353904i
\(285\) −1.85641 −0.109964
\(286\) −13.8564 4.00000i −0.819346 0.236525i
\(287\) −6.92820 −0.408959
\(288\) −0.866025 0.500000i −0.0510310 0.0294628i
\(289\) 8.39230 14.5359i 0.493665 0.855053i
\(290\) −13.8564 24.0000i −0.813676 1.40933i
\(291\) 8.39230i 0.491966i
\(292\) −2.53590 + 1.46410i −0.148402 + 0.0856801i
\(293\) 22.9808 13.2679i 1.34255 0.775122i 0.355369 0.934726i \(-0.384355\pi\)
0.987181 + 0.159604i \(0.0510218\pi\)
\(294\) 1.00000i 0.0583212i
\(295\) −16.8564 29.1962i −0.981418 1.69987i
\(296\) −4.46410 + 7.73205i −0.259471 + 0.449416i
\(297\) −3.46410 2.00000i −0.201008 0.116052i
\(298\) −18.4641 −1.06960
\(299\) 1.96410 + 7.93782i 0.113587 + 0.459056i
\(300\) 7.00000 0.404145
\(301\) −2.13397 1.23205i −0.123000 0.0710142i
\(302\) −6.00000 + 10.3923i −0.345261 + 0.598010i
\(303\) 0 0
\(304\) 0.535898i 0.0307359i
\(305\) −15.5885 + 9.00000i −0.892592 + 0.515339i
\(306\) 0.401924 0.232051i 0.0229765 0.0132655i
\(307\) 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
\(309\) −3.33013 + 5.76795i −0.189444 + 0.328127i
\(310\) 1.39230 + 0.803848i 0.0790776 + 0.0456555i
\(311\) 21.3205 1.20898 0.604488 0.796615i \(-0.293378\pi\)
0.604488 + 0.796615i \(0.293378\pi\)
\(312\) −3.50000 + 0.866025i −0.198148 + 0.0490290i
\(313\) 35.3205 1.99643 0.998217 0.0596964i \(-0.0190133\pi\)
0.998217 + 0.0596964i \(0.0190133\pi\)
\(314\) −9.46410 5.46410i −0.534090 0.308357i
\(315\) −1.73205 + 3.00000i −0.0975900 + 0.169031i
\(316\) −1.26795 2.19615i −0.0713277 0.123543i
\(317\) 9.53590i 0.535589i −0.963476 0.267795i \(-0.913705\pi\)
0.963476 0.267795i \(-0.0862949\pi\)
\(318\) −10.1603 + 5.86603i −0.569759 + 0.328950i
\(319\) 27.7128 16.0000i 1.55162 0.895828i
\(320\) 3.46410i 0.193649i
\(321\) −7.73205 13.3923i −0.431561 0.747486i
\(322\) −1.13397 + 1.96410i −0.0631939 + 0.109455i
\(323\) 0.215390 + 0.124356i 0.0119846 + 0.00691933i
\(324\) −1.00000 −0.0555556
\(325\) 18.1865 17.5000i 1.00881 0.970725i
\(326\) 18.6603 1.03350
\(327\) −10.3923 6.00000i −0.574696 0.331801i
\(328\) −3.46410 + 6.00000i −0.191273 + 0.331295i
\(329\) −3.73205 6.46410i −0.205755 0.356377i
\(330\) 13.8564i 0.762770i
\(331\) 11.5359 6.66025i 0.634070 0.366081i −0.148256 0.988949i \(-0.547366\pi\)
0.782327 + 0.622868i \(0.214033\pi\)
\(332\) −1.50000 + 0.866025i −0.0823232 + 0.0475293i
\(333\) 8.92820i 0.489263i
\(334\) 10.0000 + 17.3205i 0.547176 + 0.947736i
\(335\) 5.53590 9.58846i 0.302458 0.523873i
\(336\) −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
\(339\) 16.3923 0.890308
\(340\) −1.39230 0.803848i −0.0755083 0.0435948i
\(341\) −0.928203 + 1.60770i −0.0502650 + 0.0870616i
\(342\) −0.267949 0.464102i −0.0144890 0.0250957i
\(343\) 1.00000i 0.0539949i
\(344\) −2.13397 + 1.23205i −0.115056 + 0.0664277i
\(345\) 6.80385 3.92820i 0.366307 0.211487i
\(346\) 14.9282i 0.802545i
\(347\) 14.8564 + 25.7321i 0.797534 + 1.38137i 0.921218 + 0.389047i \(0.127196\pi\)
−0.123684 + 0.992322i \(0.539471\pi\)
\(348\) 4.00000 6.92820i 0.214423 0.371391i
\(349\) −29.1340 16.8205i −1.55951 0.900381i −0.997304 0.0733812i \(-0.976621\pi\)
−0.562202 0.827000i \(-0.690046\pi\)
\(350\) 7.00000 0.374166
\(351\) −2.59808 + 2.50000i −0.138675 + 0.133440i
\(352\) −4.00000 −0.213201
\(353\) −23.0885 13.3301i −1.22887 0.709491i −0.262080 0.965046i \(-0.584408\pi\)
−0.966795 + 0.255555i \(0.917742\pi\)
\(354\) 4.86603 8.42820i 0.258626 0.447954i
\(355\) −20.6603 35.7846i −1.09653 1.89925i
\(356\) 8.26795i 0.438200i
\(357\) 0.401924 0.232051i 0.0212721 0.0122814i
\(358\) 2.66025 1.53590i 0.140599 0.0811748i
\(359\) 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
\(361\) −9.35641 + 16.2058i −0.492442 + 0.852935i
\(362\) −14.5359 8.39230i −0.763990 0.441090i
\(363\) −5.00000 −0.262432
\(364\) −3.50000 + 0.866025i −0.183450 + 0.0453921i
\(365\) 10.1436 0.530940
\(366\) −4.50000 2.59808i −0.235219 0.135804i
\(367\) −2.52628 + 4.37564i −0.131871 + 0.228407i −0.924398 0.381430i \(-0.875432\pi\)
0.792527 + 0.609837i \(0.208765\pi\)
\(368\) 1.13397 + 1.96410i 0.0591125 + 0.102386i
\(369\) 6.92820i 0.360668i
\(370\) 26.7846 15.4641i 1.39247 0.803940i
\(371\) −10.1603 + 5.86603i −0.527494 + 0.304549i
\(372\) 0.464102i 0.0240625i
\(373\) −11.1244 19.2679i −0.575997 0.997657i −0.995932 0.0901025i \(-0.971281\pi\)
0.419935 0.907554i \(-0.362053\pi\)
\(374\) 0.928203 1.60770i 0.0479962 0.0831319i
\(375\) −6.00000 3.46410i −0.309839 0.178885i
\(376\) −7.46410 −0.384932
\(377\) −6.92820 28.0000i −0.356821 1.44207i
\(378\) −1.00000 −0.0514344
\(379\) 26.3205 + 15.1962i 1.35199 + 0.780574i 0.988529 0.151034i \(-0.0482603\pi\)
0.363465 + 0.931608i \(0.381594\pi\)
\(380\) −0.928203 + 1.60770i −0.0476158 + 0.0824730i
\(381\) 9.46410 + 16.3923i 0.484861 + 0.839803i
\(382\) 18.5167i 0.947395i
\(383\) 23.6603 13.6603i 1.20898 0.698006i 0.246445 0.969157i \(-0.420737\pi\)
0.962537 + 0.271150i \(0.0874040\pi\)
\(384\) −0.866025 + 0.500000i −0.0441942 + 0.0255155i
\(385\) 13.8564i 0.706188i
\(386\) −4.92820 8.53590i −0.250839 0.434466i
\(387\) −1.23205 + 2.13397i −0.0626287 + 0.108476i
\(388\) 7.26795 + 4.19615i 0.368974 + 0.213027i
\(389\) −2.66025 −0.134880 −0.0674401 0.997723i \(-0.521483\pi\)
−0.0674401 + 0.997723i \(0.521483\pi\)
\(390\) 12.0000 + 3.46410i 0.607644 + 0.175412i
\(391\) −1.05256 −0.0532302
\(392\) −0.866025 0.500000i −0.0437409 0.0252538i
\(393\) −9.50000 + 16.4545i −0.479212 + 0.830019i
\(394\) 11.6962 + 20.2583i 0.589244 + 1.02060i
\(395\) 8.78461i 0.442002i
\(396\) −3.46410 + 2.00000i −0.174078 + 0.100504i
\(397\) −10.2058 + 5.89230i −0.512213 + 0.295726i −0.733743 0.679427i \(-0.762228\pi\)
0.221530 + 0.975154i \(0.428895\pi\)
\(398\) 2.12436i 0.106484i
\(399\) −0.267949 0.464102i −0.0134142 0.0232341i
\(400\) 3.50000 6.06218i 0.175000 0.303109i
\(401\) −3.80385 2.19615i −0.189955 0.109671i 0.402006 0.915637i \(-0.368313\pi\)
−0.591962 + 0.805966i \(0.701646\pi\)
\(402\) 3.19615 0.159410
\(403\) 1.16025 + 1.20577i 0.0577964 + 0.0600637i
\(404\) 0 0
\(405\) 3.00000 + 1.73205i 0.149071 + 0.0860663i
\(406\) 4.00000 6.92820i 0.198517 0.343841i
\(407\) 17.8564 + 30.9282i 0.885109 + 1.53305i
\(408\) 0.464102i 0.0229765i
\(409\) 12.4641 7.19615i 0.616310 0.355827i −0.159121 0.987259i \(-0.550866\pi\)
0.775431 + 0.631432i \(0.217533\pi\)
\(410\) 20.7846 12.0000i 1.02648 0.592638i
\(411\) 13.8564i 0.683486i
\(412\) 3.33013 + 5.76795i 0.164064 + 0.284166i
\(413\) 4.86603 8.42820i 0.239441 0.414725i
\(414\) 1.96410 + 1.13397i 0.0965303 + 0.0557318i
\(415\) 6.00000 0.294528
\(416\) −1.00000 + 3.46410i −0.0490290 + 0.169842i
\(417\) −10.9282 −0.535156
\(418\) −1.85641 1.07180i −0.0907998 0.0524233i
\(419\) 2.50000 4.33013i 0.122133 0.211541i −0.798476 0.602027i \(-0.794360\pi\)
0.920609 + 0.390487i \(0.127693\pi\)
\(420\) 1.73205 + 3.00000i 0.0845154 + 0.146385i
\(421\) 22.3923i 1.09133i 0.838002 + 0.545667i \(0.183724\pi\)
−0.838002 + 0.545667i \(0.816276\pi\)
\(422\) −19.8564 + 11.4641i −0.966595 + 0.558064i
\(423\) −6.46410 + 3.73205i −0.314295 + 0.181459i
\(424\) 11.7321i 0.569759i
\(425\) 1.62436 + 2.81347i 0.0787928 + 0.136473i
\(426\) 5.96410 10.3301i 0.288962 0.500496i
\(427\) −4.50000 2.59808i −0.217770 0.125730i
\(428\) −15.4641 −0.747486
\(429\) −4.00000 + 13.8564i −0.193122 + 0.668994i
\(430\) 8.53590 0.411638
\(431\) 19.7942 + 11.4282i 0.953454 + 0.550477i 0.894152 0.447763i \(-0.147779\pi\)
0.0593021 + 0.998240i \(0.481112\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) −8.92820 15.4641i −0.429062 0.743157i 0.567728 0.823216i \(-0.307823\pi\)
−0.996790 + 0.0800589i \(0.974489\pi\)
\(434\) 0.464102i 0.0222776i
\(435\) −24.0000 + 13.8564i −1.15071 + 0.664364i
\(436\) −10.3923 + 6.00000i −0.497701 + 0.287348i
\(437\) 1.21539i 0.0581400i
\(438\) 1.46410 + 2.53590i 0.0699575 + 0.121170i
\(439\) −17.1962 + 29.7846i −0.820728 + 1.42154i 0.0844136 + 0.996431i \(0.473098\pi\)
−0.905141 + 0.425111i \(0.860235\pi\)
\(440\) 12.0000 + 6.92820i 0.572078 + 0.330289i
\(441\) −1.00000 −0.0476190
\(442\) −1.16025 1.20577i −0.0551877 0.0573527i
\(443\) −1.60770 −0.0763839 −0.0381920 0.999270i \(-0.512160\pi\)
−0.0381920 + 0.999270i \(0.512160\pi\)
\(444\) 7.73205 + 4.46410i 0.366947 + 0.211857i
\(445\) 14.3205 24.8038i 0.678857 1.17582i
\(446\) −7.23205 12.5263i −0.342448 0.593137i
\(447\) 18.4641i 0.873322i
\(448\) −0.866025 + 0.500000i −0.0409159 + 0.0236228i
\(449\) −15.5885 + 9.00000i −0.735665 + 0.424736i −0.820491 0.571660i \(-0.806300\pi\)
0.0848262 + 0.996396i \(0.472967\pi\)
\(450\) 7.00000i 0.329983i
\(451\) 13.8564 + 24.0000i 0.652473 + 1.13012i
\(452\) 8.19615 14.1962i 0.385515 0.667731i
\(453\) 10.3923 + 6.00000i 0.488273 + 0.281905i
\(454\) 21.3205 1.00062
\(455\) 12.0000 + 3.46410i 0.562569 + 0.162400i
\(456\) −0.535898 −0.0250957
\(457\) 7.96410 + 4.59808i 0.372545 + 0.215089i 0.674570 0.738211i \(-0.264329\pi\)
−0.302025 + 0.953300i \(0.597663\pi\)
\(458\) 3.03590 5.25833i 0.141858 0.245706i
\(459\) −0.232051 0.401924i −0.0108312 0.0187602i
\(460\) 7.85641i 0.366307i
\(461\) 16.3923 9.46410i 0.763466 0.440787i −0.0670730 0.997748i \(-0.521366\pi\)
0.830539 + 0.556961i \(0.188033\pi\)
\(462\) −3.46410 + 2.00000i −0.161165 + 0.0930484i
\(463\) 40.2487i 1.87052i −0.353966 0.935258i \(-0.615167\pi\)
0.353966 0.935258i \(-0.384833\pi\)
\(464\) −4.00000 6.92820i −0.185695 0.321634i
\(465\) 0.803848 1.39230i 0.0372775 0.0645666i
\(466\) 5.66025 + 3.26795i 0.262206 + 0.151385i
\(467\) −29.6410 −1.37162 −0.685811 0.727779i \(-0.740552\pi\)
−0.685811 + 0.727779i \(0.740552\pi\)
\(468\) 0.866025 + 3.50000i 0.0400320 + 0.161788i
\(469\) 3.19615 0.147585
\(470\) 22.3923 + 12.9282i 1.03288 + 0.596334i
\(471\) −5.46410 + 9.46410i −0.251773 + 0.436083i
\(472\) −4.86603 8.42820i −0.223977 0.387939i
\(473\) 9.85641i 0.453198i
\(474\) −2.19615 + 1.26795i −0.100873 + 0.0582388i
\(475\) 3.24871 1.87564i 0.149061 0.0860605i
\(476\) 0.464102i 0.0212721i
\(477\) 5.86603 + 10.1603i 0.268587 + 0.465206i
\(478\) 7.42820 12.8660i 0.339758 0.588478i
\(479\) −14.1962 8.19615i −0.648639 0.374492i 0.139296 0.990251i \(-0.455516\pi\)
−0.787935 + 0.615759i \(0.788849\pi\)
\(480\) 3.46410 0.158114
\(481\) 31.2487 7.73205i 1.42482 0.352551i
\(482\) −11.8564 −0.540045
\(483\) 1.96410 + 1.13397i 0.0893697 + 0.0515976i
\(484\) −2.50000 + 4.33013i −0.113636 + 0.196824i
\(485\) −14.5359 25.1769i −0.660041 1.14322i
\(486\) 1.00000i 0.0453609i
\(487\) 17.6603 10.1962i 0.800262 0.462032i −0.0433004 0.999062i \(-0.513787\pi\)
0.843563 + 0.537030i \(0.180454\pi\)
\(488\) −4.50000 + 2.59808i −0.203705 + 0.117609i
\(489\) 18.6603i 0.843846i
\(490\) 1.73205 + 3.00000i 0.0782461 + 0.135526i
\(491\) 8.92820 15.4641i 0.402924 0.697885i −0.591153 0.806559i \(-0.701327\pi\)
0.994077 + 0.108674i \(0.0346605\pi\)
\(492\) 6.00000 + 3.46410i 0.270501 + 0.156174i
\(493\) 3.71281 0.167217
\(494\) −1.39230 + 1.33975i −0.0626428 + 0.0602780i
\(495\) 13.8564 0.622799
\(496\) 0.401924 + 0.232051i 0.0180469 + 0.0104194i
\(497\) 5.96410 10.3301i 0.267527 0.463370i
\(498\) 0.866025 + 1.50000i 0.0388075 + 0.0672166i
\(499\) 3.73205i 0.167070i 0.996505 + 0.0835348i \(0.0266210\pi\)
−0.996505 + 0.0835348i \(0.973379\pi\)
\(500\) −6.00000 + 3.46410i −0.268328 + 0.154919i
\(501\) 17.3205 10.0000i 0.773823 0.446767i
\(502\) 23.9282i 1.06797i
\(503\) −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
\(505\) 0 0
\(506\) 9.07180 0.403291
\(507\) 11.0000 + 6.92820i 0.488527 + 0.307692i
\(508\) 18.9282 0.839803
\(509\) −12.3397 7.12436i −0.546950 0.315782i 0.200941 0.979603i \(-0.435600\pi\)
−0.747891 + 0.663822i \(0.768933\pi\)
\(510\) −0.803848 + 1.39230i −0.0355950 + 0.0616523i
\(511\) 1.46410 + 2.53590i 0.0647680 + 0.112182i
\(512\) 1.00000i 0.0441942i
\(513\) −0.464102 + 0.267949i −0.0204906 + 0.0118302i
\(514\) 5.59808 3.23205i 0.246921 0.142560i
\(515\) 23.0718i 1.01666i
\(516\) 1.23205 + 2.13397i 0.0542380 + 0.0939430i
\(517\) −14.9282 + 25.8564i −0.656542 + 1.13716i
\(518\) 7.73205 + 4.46410i 0.339727 + 0.196141i
\(519\) −14.9282 −0.655275
\(520\) 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
\(523\) −0.535898 + 0.928203i −0.0234332 + 0.0405875i −0.877504 0.479569i \(-0.840793\pi\)
0.854071 + 0.520156i \(0.174126\pi\)
\(524\) 9.50000 + 16.4545i 0.415009 + 0.718817i
\(525\) 7.00000i 0.305505i
\(526\) 15.0000 8.66025i 0.654031 0.377605i
\(527\) −0.186533 + 0.107695i −0.00812553 + 0.00469127i
\(528\) 4.00000i 0.174078i
\(529\) 8.92820 + 15.4641i 0.388183 + 0.672352i
\(530\) 20.3205 35.1962i 0.882666 1.52882i
\(531\) −8.42820 4.86603i −0.365753 0.211168i
\(532\) −0.535898 −0.0232341
\(533\) 24.2487 6.00000i 1.05033 0.259889i
\(534\) 8.26795 0.357789
\(535\) 46.3923 + 26.7846i 2.00571 + 1.15800i
\(536\) 1.59808 2.76795i 0.0690264 0.119557i
\(537\) −1.53590 2.66025i −0.0662789 0.114798i
\(538\) 1.60770i 0.0693127i
\(539\) −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 \(0.121442\pi\)
−0.928099 + 0.372333i \(0.878558\pi\)
\(542\) 2.76795 + 4.79423i 0.118894 + 0.205930i
\(543\) −8.39230 + 14.5359i −0.360148 + 0.623795i
\(544\) −0.401924 0.232051i −0.0172323 0.00994910i
\(545\) 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
\(551\) 4.28719i 0.182640i
\(552\) 1.96410 1.13397i 0.0835977 0.0482652i
\(553\) −2.19615 + 1.26795i −0.0933899 + 0.0539187i
\(554\) 27.3205i 1.16074i
\(555\) −15.4641 26.7846i −0.656415 1.13694i
\(556\) −5.46410 + 9.46410i −0.231730 + 0.401367i
\(557\) −39.3109 22.6962i −1.66566 0.961667i −0.969938 0.243351i \(-0.921753\pi\)
−0.695718 0.718315i \(-0.744914\pi\)
\(558\) 0.464102 0.0196470
\(559\) 8.53590 + 2.46410i 0.361030 + 0.104220i
\(560\) 3.46410 0.146385
\(561\) −1.60770 0.928203i −0.0678769 0.0391888i
\(562\) 9.19615 15.9282i 0.387916 0.671891i
\(563\) 6.92820 + 12.0000i 0.291989 + 0.505740i 0.974280 0.225341i \(-0.0723496\pi\)
−0.682291 + 0.731081i \(0.739016\pi\)
\(564\) 7.46410i 0.314295i
\(565\) −49.1769 + 28.3923i −2.06889 + 1.19447i
\(566\) 3.92820 2.26795i 0.165115 0.0953290i
\(567\) 1.00000i 0.0419961i
\(568\) −5.96410 10.3301i −0.250248 0.433443i
\(569\) 4.26795 7.39230i 0.178922 0.309902i −0.762590 0.646882i \(-0.776072\pi\)
0.941511 + 0.336981i \(0.109406\pi\)
\(570\) 1.60770 + 0.928203i 0.0673389 + 0.0388782i
\(571\) −17.3923 −0.727845 −0.363923 0.931429i \(-0.618563\pi\)
−0.363923 + 0.931429i \(0.618563\pi\)
\(572\) 10.0000 + 10.3923i 0.418121 + 0.434524i
\(573\) 18.5167 0.773545
\(574\) 6.00000 + 3.46410i 0.250435 + 0.144589i
\(575\) −7.93782 + 13.7487i −0.331030 + 0.573361i
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) 42.7846i 1.78115i −0.454840 0.890573i \(-0.650303\pi\)
0.454840 0.890573i \(-0.349697\pi\)
\(578\) −14.5359 + 8.39230i −0.604614 + 0.349074i
\(579\) −8.53590 + 4.92820i −0.354740 + 0.204809i
\(580\) 27.7128i 1.15071i
\(581\) 0.866025 + 1.50000i 0.0359288 + 0.0622305i
\(582\) 4.19615 7.26795i 0.173936 0.301266i
\(583\) 40.6410 + 23.4641i 1.68318 + 0.971784i
\(584\) 2.92820 0.121170
\(585\) 3.46410 12.0000i 0.143223 0.496139i
\(586\) −26.5359 −1.09619
\(587\) 13.9641 + 8.06218i 0.576360 + 0.332762i 0.759686 0.650291i \(-0.225353\pi\)
−0.183325 + 0.983052i \(0.558686\pi\)
\(588\) −0.500000 + 0.866025i −0.0206197 + 0.0357143i
\(589\) 0.124356 + 0.215390i 0.00512399 + 0.00887500i
\(590\) 33.7128i 1.38793i
\(591\) 20.2583 11.6962i 0.833316 0.481115i
\(592\) 7.73205 4.46410i 0.317785 0.183473i
\(593\) 7.73205i 0.317517i 0.987317 + 0.158759i \(0.0507492\pi\)
−0.987317 + 0.158759i \(0.949251\pi\)
\(594\) 2.00000 + 3.46410i 0.0820610 + 0.142134i
\(595\) −0.803848 + 1.39230i −0.0329545 + 0.0570789i
\(596\) 15.9904 + 9.23205i 0.654992 + 0.378160i
\(597\) −2.12436 −0.0869441
\(598\) 2.26795 7.85641i 0.0927433 0.321272i
\(599\) 19.0526 0.778466 0.389233 0.921139i \(-0.372740\pi\)
0.389233 + 0.921139i \(0.372740\pi\)
\(600\) −6.06218 3.50000i −0.247487 0.142887i
\(601\) −12.1244 + 21.0000i −0.494563 + 0.856608i −0.999980 0.00626702i \(-0.998005\pi\)
0.505418 + 0.862875i \(0.331338\pi\)
\(602\) 1.23205 + 2.13397i 0.0502146 + 0.0869743i
\(603\) 3.19615i 0.130157i
\(604\) 10.3923 6.00000i 0.422857 0.244137i
\(605\) 15.0000 8.66025i 0.609837 0.352089i
\(606\) 0 0
\(607\) 2.40192 + 4.16025i 0.0974911 + 0.168860i 0.910646 0.413188i \(-0.135585\pi\)
−0.813154 + 0.582048i \(0.802252\pi\)
\(608\) −0.267949 + 0.464102i −0.0108668 + 0.0188218i
\(609\) −6.92820 4.00000i −0.280745 0.162088i
\(610\) 18.0000 0.728799
\(611\) 18.6603 + 19.3923i 0.754913 + 0.784529i
\(612\) −0.464102 −0.0187602
\(613\) −11.7846 6.80385i −0.475976 0.274805i 0.242762 0.970086i \(-0.421947\pi\)
−0.718738 + 0.695281i \(0.755280\pi\)
\(614\) −11.0000 + 19.0526i −0.443924 + 0.768899i
\(615\) −12.0000 20.7846i −0.483887 0.838116i
\(616\) 4.00000i 0.161165i
\(617\) −18.9282 + 10.9282i −0.762021 + 0.439953i −0.830021 0.557732i \(-0.811672\pi\)
0.0680000 + 0.997685i \(0.478338\pi\)
\(618\) 5.76795 3.33013i 0.232021 0.133957i
\(619\) 10.7846i 0.433470i −0.976230 0.216735i \(-0.930459\pi\)
0.976230 0.216735i \(-0.0695408\pi\)
\(620\) −0.803848 1.39230i −0.0322833 0.0559163i
\(621\) 1.13397 1.96410i 0.0455048 0.0788167i
\(622\) −18.4641 10.6603i −0.740343 0.427437i
\(623\) 8.26795 0.331248
\(624\) 3.46410 + 1.00000i 0.138675 + 0.0400320i
\(625\) −11.0000 −0.440000
\(626\) −30.5885 17.6603i −1.22256 0.705846i
\(627\) −1.07180 + 1.85641i −0.0428034 + 0.0741377i
\(628\) 5.46410 + 9.46410i 0.218041 + 0.377659i
\(629\) 4.14359i 0.165216i
\(630\) 3.00000 1.73205i 0.119523 0.0690066i
\(631\) −18.2487 + 10.5359i −0.726470 + 0.419427i −0.817129 0.576454i \(-0.804436\pi\)
0.0906596 + 0.995882i \(0.471102\pi\)
\(632\) 2.53590i 0.100873i
\(633\) 11.4641 + 19.8564i 0.455657 + 0.789221i
\(634\) −4.76795 + 8.25833i −0.189359 + 0.327980i
\(635\) −56.7846 32.7846i −2.25343 1.30102i
\(636\) 11.7321 0.465206
\(637\) 0.866025 + 3.50000i 0.0343132 + 0.138675i
\(638\) −32.0000 −1.26689
\(639\) −10.3301 5.96410i −0.408654 0.235936i
\(640\) 1.73205 3.00000i 0.0684653 0.118585i
\(641\) 21.3205 + 36.9282i 0.842109 + 1.45858i 0.888108 + 0.459635i \(0.152020\pi\)
−0.0459986 + 0.998942i \(0.514647\pi\)
\(642\) 15.4641i 0.610319i
\(643\) −24.4641 + 14.1244i −0.964770 + 0.557010i −0.897638 0.440734i \(-0.854718\pi\)
−0.0671322 + 0.997744i \(0.521385\pi\)
\(644\) 1.96410 1.13397i 0.0773964 0.0446849i
\(645\) 8.53590i 0.336101i
\(646\) −0.124356 0.215390i −0.00489271 0.00847442i
\(647\) 1.33975 2.32051i 0.0526708 0.0912286i −0.838488 0.544920i \(-0.816560\pi\)
0.891159 + 0.453692i \(0.149893\pi\)
\(648\) 0.866025 + 0.500000i 0.0340207 + 0.0196419i
\(649\) −38.9282 −1.52807
\(650\) −24.5000 + 6.06218i −0.960969 + 0.237778i
\(651\) 0.464102 0.0181896
\(652\) −16.1603 9.33013i −0.632884 0.365396i
\(653\) 3.20577 5.55256i 0.125452 0.217288i −0.796458 0.604694i \(-0.793295\pi\)
0.921909 + 0.387406i \(0.126629\pi\)
\(654\) 6.00000 + 10.3923i 0.234619 + 0.406371i
\(655\) 65.8179i 2.57172i
\(656\) 6.00000 3.46410i 0.234261 0.135250i
\(657\) 2.53590 1.46410i 0.0989348 0.0571200i
\(658\) 7.46410i 0.290981i
\(659\) −11.1962 19.3923i −0.436140 0.755417i 0.561248 0.827648i \(-0.310321\pi\)
−0.997388 + 0.0722309i \(0.976988\pi\)
\(660\) 6.92820 12.0000i 0.269680 0.467099i
\(661\) 4.08142 + 2.35641i 0.158749 + 0.0916536i 0.577270 0.816553i \(-0.304118\pi\)
−0.418521 + 0.908207i \(0.637451\pi\)
\(662\) −13.3205 −0.517716
\(663\) −1.20577 + 1.16025i −0.0468283 + 0.0450605i
\(664\) 1.73205 0.0672166
\(665\) 1.60770 + 0.928203i 0.0623437 + 0.0359942i
\(666\) 4.46410 7.73205i 0.172980 0.299611i
\(667\) 9.07180 + 15.7128i 0.351261 + 0.608403i
\(668\) 20.0000i 0.773823i
\(669\) −12.5263 + 7.23205i −0.484294 + 0.279607i
\(670\) −9.58846 + 5.53590i −0.370434 + 0.213870i
\(671\) 20.7846i 0.802381i
\(672\) 0.500000 + 0.866025i 0.0192879 + 0.0334077i
\(673\) −14.8205 + 25.6699i −0.571289 + 0.989501i 0.425145 + 0.905125i \(0.360223\pi\)
−0.996434 + 0.0843758i \(0.973110\pi\)
\(674\) 5.19615 + 3.00000i 0.200148 + 0.115556i
\(675\) −7.00000 −0.269430
\(676\) 11.5000 6.06218i 0.442308 0.233161i
\(677\) 14.9282 0.573737 0.286869 0.957970i \(-0.407386\pi\)
0.286869 + 0.957970i \(0.407386\pi\)
\(678\) −14.1962 8.19615i −0.545200 0.314771i
\(679\) 4.19615 7.26795i 0.161034 0.278918i
\(680\) 0.803848 + 1.39230i 0.0308261 + 0.0533925i
\(681\) 21.3205i 0.817004i
\(682\) 1.60770 0.928203i 0.0615618 0.0355427i
\(683\) 9.67949 5.58846i 0.370375 0.213836i −0.303247 0.952912i \(-0.598071\pi\)
0.673622 + 0.739076i \(0.264737\pi\)
\(684\) 0.535898i 0.0204906i
\(685\) 24.0000 + 41.5692i 0.916993 + 1.58828i
\(686\) −0.500000 + 0.866025i −0.0190901 + 0.0330650i
\(687\) −5.25833 3.03590i −0.200618 0.115827i
\(688\) 2.46410 0.0939430
\(689\) 30.4808 29.3301i 1.16122 1.11739i
\(690\) −7.85641 −0.299088
\(691\) −18.3397 10.5885i −0.697677 0.402804i 0.108805 0.994063i \(-0.465298\pi\)
−0.806482 + 0.591259i \(0.798631\pi\)
\(692\) −7.46410 + 12.9282i −0.283743 + 0.491457i
\(693\) 2.00000 + 3.46410i 0.0759737 + 0.131590i
\(694\) 29.7128i 1.12788i
\(695\) 32.7846 18.9282i 1.24359 0.717988i
\(696\) −6.92820 + 4.00000i −0.262613 + 0.151620i
\(697\) 3.21539i 0.121792i
\(698\) 16.8205 + 29.1340i 0.636666 + 1.10274i
\(699\) 3.26795 5.66025i 0.123605 0.214090i
\(700\) −6.06218 3.50000i −0.229129 0.132288i
\(701\) −22.1244 −0.835625 −0.417813 0.908533i \(-0.637203\pi\)
−0.417813 + 0.908533i \(0.637203\pi\)
\(702\) 3.50000 0.866025i 0.132099 0.0326860i
\(703\) 4.78461 0.180455
\(704\) 3.46410 + 2.00000i 0.130558 + 0.0753778i
\(705\) 12.9282 22.3923i 0.486904 0.843343i
\(706\) 13.3301 + 23.0885i 0.501686 + 0.868946i
\(707\) 0 0
\(708\) −8.42820 + 4.86603i −0.316751 + 0.182876i
\(709\) −41.3205 + 23.8564i −1.55182 + 0.895946i −0.553831 + 0.832629i \(0.686835\pi\)
−0.997993 + 0.0633169i \(0.979832\pi\)
\(710\) 41.3205i 1.55073i
\(711\) 1.26795 + 2.19615i 0.0475518 + 0.0823622i
\(712\) 4.13397 7.16025i 0.154927 0.268342i
\(713\) −0.911543 0.526279i −0.0341375 0.0197093i
\(714\) −0.464102 −0.0173686
\(715\) −12.0000 48.4974i −0.448775 1.81370i
\(716\) −3.07180 −0.114798
\(717\) −12.8660 7.42820i −0.480491 0.277411i
\(718\) −4.00000 + 6.92820i −0.149279 + 0.258558i
\(719\) 20.7321 + 35.9090i 0.773175 + 1.33918i 0.935814 + 0.352493i \(0.114666\pi\)
−0.162639 + 0.986686i \(0.552001\pi\)
\(720\) 3.46410i 0.129099i
\(721\) 5.76795 3.33013i 0.214810 0.124020i
\(722\) 16.2058 9.35641i 0.603116 0.348209i
\(723\) 11.8564i 0.440945i
\(724\) 8.39230 + 14.5359i 0.311898 + 0.540222i
\(725\) 28.0000 48.4974i 1.03989 1.80115i
\(726\) 4.33013 + 2.50000i 0.160706 + 0.0927837i
\(727\) −42.9090 −1.59141 −0.795703 0.605687i \(-0.792898\pi\)
−0.795703 + 0.605687i \(0.792898\pi\)
\(728\) 3.46410 + 1.00000i 0.128388 + 0.0370625i
\(729\) 1.00000 0.0370370
\(730\) −8.78461 5.07180i −0.325133 0.187716i
\(731\) −0.571797 + 0.990381i −0.0211487 + 0.0366306i
\(732\) 2.59808 + 4.50000i 0.0960277 + 0.166325i
\(733\) 22.8564i 0.844221i 0.906544 + 0.422110i \(0.138711\pi\)
−0.906544 + 0.422110i \(0.861289\pi\)
\(734\) 4.37564 2.52628i 0.161508 0.0932467i
\(735\) 3.00000 1.73205i 0.110657 0.0638877i
\(736\) 2.26795i 0.0835977i
\(737\) −6.39230 11.0718i −0.235464 0.407835i
\(738\) 3.46410 6.00000i 0.127515 0.220863i
\(739\) −3.69615 2.13397i −0.135965 0.0784995i 0.430474 0.902603i \(-0.358346\pi\)
−0.566440 + 0.824103i \(0.691680\pi\)
\(740\) −30.9282 −1.13694
\(741\) 1.33975 + 1.39230i 0.0492168 + 0.0511476i
\(742\) 11.7321 0.430697
\(743\) 34.4545 + 19.8923i 1.26401 + 0.729778i 0.973848 0.227199i \(-0.0729568\pi\)
0.290164 + 0.956977i \(0.406290\pi\)
\(744\) 0.232051 0.401924i 0.00850740 0.0147352i
\(745\) −31.9808 55.3923i −1.17168 2.02942i
\(746\) 22.2487i 0.814583i
\(747\) 1.50000 0.866025i 0.0548821 0.0316862i
\(748\) −1.60770 + 0.928203i −0.0587832 + 0.0339385i
\(749\) 15.4641i 0.565046i
\(750\) 3.46410 + 6.00000i 0.126491 + 0.219089i
\(751\) −2.66025 + 4.60770i −0.0970740 + 0.168137i −0.910472 0.413570i \(-0.864282\pi\)
0.813398 + 0.581707i \(0.197615\pi\)
\(752\) 6.46410 + 3.73205i 0.235722 + 0.136094i
\(753\) 23.9282 0.871992
\(754\) −8.00000 + 27.7128i −0.291343 + 1.00924i
\(755\) −41.5692 −1.51286
\(756\) 0.866025 + 0.500000i 0.0314970 + 0.0181848i
\(757\) 3.92820 6.80385i 0.142773 0.247290i −0.785767 0.618523i \(-0.787731\pi\)
0.928540 + 0.371233i \(0.121065\pi\)
\(758\) −15.1962 26.3205i −0.551949 0.956004i
\(759\) 9.07180i 0.329285i
\(760\) 1.60770 0.928203i 0.0583172 0.0336695i
\(761\) 6.00000 3.46410i 0.217500 0.125574i −0.387292 0.921957i \(-0.626590\pi\)
0.604792 + 0.796383i \(0.293256\pi\)
\(762\) 18.9282i 0.685696i
\(763\) 6.00000 + 10.3923i 0.217215 + 0.376227i
\(764\) 9.25833 16.0359i 0.334955 0.580158i
\(765\) 1.39230 + 0.803848i 0.0503389 + 0.0290632i
\(766\) −27.3205 −0.987130
\(767\) −9.73205 + 33.7128i −0.351404 + 1.21730i
\(768\) 1.00000 0.0360844
\(769\) 23.0718 + 13.3205i 0.831990 + 0.480350i 0.854534 0.519396i \(-0.173843\pi\)
−0.0225434 + 0.999746i \(0.507176\pi\)
\(770\) 6.92820 12.0000i 0.249675 0.432450i
\(771\) −3.23205 5.59808i −0.116399 0.201610i
\(772\) 9.85641i 0.354740i
\(773\) 0.803848 0.464102i 0.0289124 0.0166926i −0.485474 0.874251i \(-0.661353\pi\)
0.514387 + 0.857558i \(0.328020\pi\)
\(774\) 2.13397 1.23205i 0.0767041 0.0442852i
\(775\) 3.24871i 0.116697i