Properties

Label 546.2.s.d.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.d.127.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +0.732051i q^{5} +(-0.866025 + 0.500000i) q^{6} +(0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +0.732051i q^{5} +(-0.866025 + 0.500000i) q^{6} +(0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.366025 - 0.633975i) q^{10} +(-3.23205 - 1.86603i) q^{11} +1.00000 q^{12} +(-0.866025 - 3.50000i) q^{13} -1.00000 q^{14} +(0.633975 + 0.366025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.133975 + 0.232051i) q^{17} +1.00000i q^{18} +(3.86603 - 2.23205i) q^{19} +(-0.633975 + 0.366025i) q^{20} -1.00000i q^{21} +(1.86603 + 3.23205i) q^{22} +(1.73205 - 3.00000i) q^{23} +(-0.866025 - 0.500000i) q^{24} +4.46410 q^{25} +(-1.00000 + 3.46410i) q^{26} -1.00000 q^{27} +(0.866025 + 0.500000i) q^{28} +(1.50000 - 2.59808i) q^{29} +(-0.366025 - 0.633975i) q^{30} -7.66025i q^{31} +(0.866025 - 0.500000i) q^{32} +(-3.23205 + 1.86603i) q^{33} -0.267949i q^{34} +(0.366025 + 0.633975i) q^{35} +(0.500000 - 0.866025i) q^{36} +(1.09808 + 0.633975i) q^{37} -4.46410 q^{38} +(-3.46410 - 1.00000i) q^{39} +0.732051 q^{40} +(-6.06218 - 3.50000i) q^{41} +(-0.500000 + 0.866025i) q^{42} +(0.366025 + 0.633975i) q^{43} -3.73205i q^{44} +(0.633975 - 0.366025i) q^{45} +(-3.00000 + 1.73205i) q^{46} +4.46410i q^{47} +(0.500000 + 0.866025i) q^{48} +(0.500000 - 0.866025i) q^{49} +(-3.86603 - 2.23205i) q^{50} +0.267949 q^{51} +(2.59808 - 2.50000i) q^{52} -10.4641 q^{53} +(0.866025 + 0.500000i) q^{54} +(1.36603 - 2.36603i) q^{55} +(-0.500000 - 0.866025i) q^{56} -4.46410i q^{57} +(-2.59808 + 1.50000i) q^{58} +(0.803848 - 0.464102i) q^{59} +0.732051i q^{60} +(5.86603 + 10.1603i) q^{61} +(-3.83013 + 6.63397i) q^{62} +(-0.866025 - 0.500000i) q^{63} -1.00000 q^{64} +(2.56218 - 0.633975i) q^{65} +3.73205 q^{66} +(-11.1962 - 6.46410i) q^{67} +(-0.133975 + 0.232051i) q^{68} +(-1.73205 - 3.00000i) q^{69} -0.732051i q^{70} +(1.90192 - 1.09808i) q^{71} +(-0.866025 + 0.500000i) q^{72} +6.53590i q^{73} +(-0.633975 - 1.09808i) q^{74} +(2.23205 - 3.86603i) q^{75} +(3.86603 + 2.23205i) q^{76} -3.73205 q^{77} +(2.50000 + 2.59808i) q^{78} +10.8564 q^{79} +(-0.633975 - 0.366025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.50000 + 6.06218i) q^{82} -5.66025i q^{83} +(0.866025 - 0.500000i) q^{84} +(-0.169873 + 0.0980762i) q^{85} -0.732051i q^{86} +(-1.50000 - 2.59808i) q^{87} +(-1.86603 + 3.23205i) q^{88} +(5.59808 + 3.23205i) q^{89} -0.732051 q^{90} +(-2.50000 - 2.59808i) q^{91} +3.46410 q^{92} +(-6.63397 - 3.83013i) q^{93} +(2.23205 - 3.86603i) q^{94} +(1.63397 + 2.83013i) q^{95} -1.00000i q^{96} +(0.633975 - 0.366025i) q^{97} +(-0.866025 + 0.500000i) q^{98} +3.73205i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{3} + 2q^{4} - 2q^{9} + O(q^{10}) \) \( 4q + 2q^{3} + 2q^{4} - 2q^{9} - 2q^{10} - 6q^{11} + 4q^{12} - 4q^{14} + 6q^{15} - 2q^{16} + 4q^{17} + 12q^{19} - 6q^{20} + 4q^{22} + 4q^{25} - 4q^{26} - 4q^{27} + 6q^{29} + 2q^{30} - 6q^{33} - 2q^{35} + 2q^{36} - 6q^{37} - 4q^{38} - 4q^{40} - 2q^{42} - 2q^{43} + 6q^{45} - 12q^{46} + 2q^{48} + 2q^{49} - 12q^{50} + 8q^{51} - 28q^{53} + 2q^{55} - 2q^{56} + 24q^{59} + 20q^{61} + 2q^{62} - 4q^{64} - 14q^{65} + 8q^{66} - 24q^{67} - 4q^{68} + 18q^{71} - 6q^{74} + 2q^{75} + 12q^{76} - 8q^{77} + 10q^{78} - 12q^{79} - 6q^{80} - 2q^{81} + 14q^{82} - 18q^{85} - 6q^{87} - 4q^{88} + 12q^{89} + 4q^{90} - 10q^{91} - 30q^{93} + 2q^{94} + 10q^{95} + 6q^{97} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0.732051i 0.327383i 0.986512 + 0.163692i \(0.0523402\pi\)
−0.986512 + 0.163692i \(0.947660\pi\)
\(6\) −0.866025 + 0.500000i −0.353553 + 0.204124i
\(7\) 0.866025 0.500000i 0.327327 0.188982i
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0.366025 0.633975i 0.115747 0.200480i
\(11\) −3.23205 1.86603i −0.974500 0.562628i −0.0738948 0.997266i \(-0.523543\pi\)
−0.900605 + 0.434638i \(0.856876\pi\)
\(12\) 1.00000 0.288675
\(13\) −0.866025 3.50000i −0.240192 0.970725i
\(14\) −1.00000 −0.267261
\(15\) 0.633975 + 0.366025i 0.163692 + 0.0945074i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0.133975 + 0.232051i 0.0324936 + 0.0562806i 0.881815 0.471596i \(-0.156322\pi\)
−0.849321 + 0.527876i \(0.822988\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 3.86603 2.23205i 0.886927 0.512068i 0.0139909 0.999902i \(-0.495546\pi\)
0.872936 + 0.487835i \(0.162213\pi\)
\(20\) −0.633975 + 0.366025i −0.141761 + 0.0818458i
\(21\) 1.00000i 0.218218i
\(22\) 1.86603 + 3.23205i 0.397838 + 0.689076i
\(23\) 1.73205 3.00000i 0.361158 0.625543i −0.626994 0.779024i \(-0.715715\pi\)
0.988152 + 0.153481i \(0.0490483\pi\)
\(24\) −0.866025 0.500000i −0.176777 0.102062i
\(25\) 4.46410 0.892820
\(26\) −1.00000 + 3.46410i −0.196116 + 0.679366i
\(27\) −1.00000 −0.192450
\(28\) 0.866025 + 0.500000i 0.163663 + 0.0944911i
\(29\) 1.50000 2.59808i 0.278543 0.482451i −0.692480 0.721437i \(-0.743482\pi\)
0.971023 + 0.238987i \(0.0768152\pi\)
\(30\) −0.366025 0.633975i −0.0668268 0.115747i
\(31\) 7.66025i 1.37582i −0.725795 0.687911i \(-0.758528\pi\)
0.725795 0.687911i \(-0.241472\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) −3.23205 + 1.86603i −0.562628 + 0.324833i
\(34\) 0.267949i 0.0459529i
\(35\) 0.366025 + 0.633975i 0.0618696 + 0.107161i
\(36\) 0.500000 0.866025i 0.0833333 0.144338i
\(37\) 1.09808 + 0.633975i 0.180523 + 0.104225i 0.587538 0.809196i \(-0.300097\pi\)
−0.407016 + 0.913421i \(0.633431\pi\)
\(38\) −4.46410 −0.724173
\(39\) −3.46410 1.00000i −0.554700 0.160128i
\(40\) 0.732051 0.115747
\(41\) −6.06218 3.50000i −0.946753 0.546608i −0.0546823 0.998504i \(-0.517415\pi\)
−0.892071 + 0.451896i \(0.850748\pi\)
\(42\) −0.500000 + 0.866025i −0.0771517 + 0.133631i
\(43\) 0.366025 + 0.633975i 0.0558184 + 0.0966802i 0.892584 0.450880i \(-0.148890\pi\)
−0.836766 + 0.547561i \(0.815557\pi\)
\(44\) 3.73205i 0.562628i
\(45\) 0.633975 0.366025i 0.0945074 0.0545638i
\(46\) −3.00000 + 1.73205i −0.442326 + 0.255377i
\(47\) 4.46410i 0.651156i 0.945515 + 0.325578i \(0.105559\pi\)
−0.945515 + 0.325578i \(0.894441\pi\)
\(48\) 0.500000 + 0.866025i 0.0721688 + 0.125000i
\(49\) 0.500000 0.866025i 0.0714286 0.123718i
\(50\) −3.86603 2.23205i −0.546739 0.315660i
\(51\) 0.267949 0.0375204
\(52\) 2.59808 2.50000i 0.360288 0.346688i
\(53\) −10.4641 −1.43735 −0.718677 0.695344i \(-0.755252\pi\)
−0.718677 + 0.695344i \(0.755252\pi\)
\(54\) 0.866025 + 0.500000i 0.117851 + 0.0680414i
\(55\) 1.36603 2.36603i 0.184195 0.319035i
\(56\) −0.500000 0.866025i −0.0668153 0.115728i
\(57\) 4.46410i 0.591285i
\(58\) −2.59808 + 1.50000i −0.341144 + 0.196960i
\(59\) 0.803848 0.464102i 0.104652 0.0604209i −0.446760 0.894654i \(-0.647422\pi\)
0.551413 + 0.834233i \(0.314089\pi\)
\(60\) 0.732051i 0.0945074i
\(61\) 5.86603 + 10.1603i 0.751068 + 1.30089i 0.947306 + 0.320331i \(0.103794\pi\)
−0.196238 + 0.980556i \(0.562873\pi\)
\(62\) −3.83013 + 6.63397i −0.486427 + 0.842516i
\(63\) −0.866025 0.500000i −0.109109 0.0629941i
\(64\) −1.00000 −0.125000
\(65\) 2.56218 0.633975i 0.317799 0.0786349i
\(66\) 3.73205 0.459384
\(67\) −11.1962 6.46410i −1.36783 0.789716i −0.377177 0.926141i \(-0.623105\pi\)
−0.990650 + 0.136425i \(0.956439\pi\)
\(68\) −0.133975 + 0.232051i −0.0162468 + 0.0281403i
\(69\) −1.73205 3.00000i −0.208514 0.361158i
\(70\) 0.732051i 0.0874968i
\(71\) 1.90192 1.09808i 0.225717 0.130318i −0.382878 0.923799i \(-0.625067\pi\)
0.608595 + 0.793481i \(0.291734\pi\)
\(72\) −0.866025 + 0.500000i −0.102062 + 0.0589256i
\(73\) 6.53590i 0.764969i 0.923962 + 0.382485i \(0.124931\pi\)
−0.923962 + 0.382485i \(0.875069\pi\)
\(74\) −0.633975 1.09808i −0.0736980 0.127649i
\(75\) 2.23205 3.86603i 0.257735 0.446410i
\(76\) 3.86603 + 2.23205i 0.443464 + 0.256034i
\(77\) −3.73205 −0.425307
\(78\) 2.50000 + 2.59808i 0.283069 + 0.294174i
\(79\) 10.8564 1.22144 0.610721 0.791846i \(-0.290880\pi\)
0.610721 + 0.791846i \(0.290880\pi\)
\(80\) −0.633975 0.366025i −0.0708805 0.0409229i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 3.50000 + 6.06218i 0.386510 + 0.669456i
\(83\) 5.66025i 0.621294i −0.950525 0.310647i \(-0.899454\pi\)
0.950525 0.310647i \(-0.100546\pi\)
\(84\) 0.866025 0.500000i 0.0944911 0.0545545i
\(85\) −0.169873 + 0.0980762i −0.0184253 + 0.0106379i
\(86\) 0.732051i 0.0789391i
\(87\) −1.50000 2.59808i −0.160817 0.278543i
\(88\) −1.86603 + 3.23205i −0.198919 + 0.344538i
\(89\) 5.59808 + 3.23205i 0.593395 + 0.342597i 0.766439 0.642317i \(-0.222027\pi\)
−0.173044 + 0.984914i \(0.555360\pi\)
\(90\) −0.732051 −0.0771649
\(91\) −2.50000 2.59808i −0.262071 0.272352i
\(92\) 3.46410 0.361158
\(93\) −6.63397 3.83013i −0.687911 0.397166i
\(94\) 2.23205 3.86603i 0.230218 0.398750i
\(95\) 1.63397 + 2.83013i 0.167642 + 0.290365i
\(96\) 1.00000i 0.102062i
\(97\) 0.633975 0.366025i 0.0643704 0.0371642i −0.467469 0.884009i \(-0.654834\pi\)
0.531840 + 0.846845i \(0.321501\pi\)
\(98\) −0.866025 + 0.500000i −0.0874818 + 0.0505076i
\(99\) 3.73205i 0.375085i
\(100\) 2.23205 + 3.86603i 0.223205 + 0.386603i
\(101\) −5.00000 + 8.66025i −0.497519 + 0.861727i −0.999996 0.00286291i \(-0.999089\pi\)
0.502477 + 0.864590i \(0.332422\pi\)
\(102\) −0.232051 0.133975i −0.0229765 0.0132655i
\(103\) 12.1962 1.20172 0.600861 0.799353i \(-0.294824\pi\)
0.600861 + 0.799353i \(0.294824\pi\)
\(104\) −3.50000 + 0.866025i −0.343203 + 0.0849208i
\(105\) 0.732051 0.0714408
\(106\) 9.06218 + 5.23205i 0.880197 + 0.508182i
\(107\) 0.767949 1.33013i 0.0742405 0.128588i −0.826515 0.562914i \(-0.809680\pi\)
0.900756 + 0.434326i \(0.143013\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) 3.66025i 0.350589i −0.984516 0.175294i \(-0.943912\pi\)
0.984516 0.175294i \(-0.0560877\pi\)
\(110\) −2.36603 + 1.36603i −0.225592 + 0.130245i
\(111\) 1.09808 0.633975i 0.104225 0.0601742i
\(112\) 1.00000i 0.0944911i
\(113\) 5.09808 + 8.83013i 0.479587 + 0.830668i 0.999726 0.0234130i \(-0.00745328\pi\)
−0.520139 + 0.854081i \(0.674120\pi\)
\(114\) −2.23205 + 3.86603i −0.209051 + 0.362086i
\(115\) 2.19615 + 1.26795i 0.204792 + 0.118237i
\(116\) 3.00000 0.278543
\(117\) −2.59808 + 2.50000i −0.240192 + 0.231125i
\(118\) −0.928203 −0.0854480
\(119\) 0.232051 + 0.133975i 0.0212721 + 0.0122814i
\(120\) 0.366025 0.633975i 0.0334134 0.0578737i
\(121\) 1.46410 + 2.53590i 0.133100 + 0.230536i
\(122\) 11.7321i 1.06217i
\(123\) −6.06218 + 3.50000i −0.546608 + 0.315584i
\(124\) 6.63397 3.83013i 0.595749 0.343956i
\(125\) 6.92820i 0.619677i
\(126\) 0.500000 + 0.866025i 0.0445435 + 0.0771517i
\(127\) −6.26795 + 10.8564i −0.556191 + 0.963350i 0.441619 + 0.897203i \(0.354404\pi\)
−0.997810 + 0.0661478i \(0.978929\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 0.732051 0.0644535
\(130\) −2.53590 0.732051i −0.222413 0.0642051i
\(131\) 18.9282 1.65376 0.826882 0.562375i \(-0.190112\pi\)
0.826882 + 0.562375i \(0.190112\pi\)
\(132\) −3.23205 1.86603i −0.281314 0.162417i
\(133\) 2.23205 3.86603i 0.193543 0.335227i
\(134\) 6.46410 + 11.1962i 0.558413 + 0.967200i
\(135\) 0.732051i 0.0630049i
\(136\) 0.232051 0.133975i 0.0198982 0.0114882i
\(137\) 13.3923 7.73205i 1.14418 0.660594i 0.196719 0.980460i \(-0.436971\pi\)
0.947463 + 0.319866i \(0.103638\pi\)
\(138\) 3.46410i 0.294884i
\(139\) 9.06218 + 15.6962i 0.768644 + 1.33133i 0.938298 + 0.345827i \(0.112401\pi\)
−0.169655 + 0.985504i \(0.554265\pi\)
\(140\) −0.366025 + 0.633975i −0.0309348 + 0.0535806i
\(141\) 3.86603 + 2.23205i 0.325578 + 0.187973i
\(142\) −2.19615 −0.184297
\(143\) −3.73205 + 12.9282i −0.312090 + 1.08111i
\(144\) 1.00000 0.0833333
\(145\) 1.90192 + 1.09808i 0.157946 + 0.0911903i
\(146\) 3.26795 5.66025i 0.270457 0.468446i
\(147\) −0.500000 0.866025i −0.0412393 0.0714286i
\(148\) 1.26795i 0.104225i
\(149\) −16.3923 + 9.46410i −1.34291 + 0.775329i −0.987233 0.159280i \(-0.949083\pi\)
−0.355676 + 0.934609i \(0.615749\pi\)
\(150\) −3.86603 + 2.23205i −0.315660 + 0.182246i
\(151\) 13.1962i 1.07389i 0.843618 + 0.536944i \(0.180421\pi\)
−0.843618 + 0.536944i \(0.819579\pi\)
\(152\) −2.23205 3.86603i −0.181043 0.313576i
\(153\) 0.133975 0.232051i 0.0108312 0.0187602i
\(154\) 3.23205 + 1.86603i 0.260446 + 0.150369i
\(155\) 5.60770 0.450421
\(156\) −0.866025 3.50000i −0.0693375 0.280224i
\(157\) −15.4641 −1.23417 −0.617085 0.786897i \(-0.711686\pi\)
−0.617085 + 0.786897i \(0.711686\pi\)
\(158\) −9.40192 5.42820i −0.747977 0.431845i
\(159\) −5.23205 + 9.06218i −0.414929 + 0.718677i
\(160\) 0.366025 + 0.633975i 0.0289368 + 0.0501201i
\(161\) 3.46410i 0.273009i
\(162\) 0.866025 0.500000i 0.0680414 0.0392837i
\(163\) −6.75833 + 3.90192i −0.529353 + 0.305622i −0.740753 0.671777i \(-0.765531\pi\)
0.211400 + 0.977400i \(0.432198\pi\)
\(164\) 7.00000i 0.546608i
\(165\) −1.36603 2.36603i −0.106345 0.184195i
\(166\) −2.83013 + 4.90192i −0.219660 + 0.380463i
\(167\) 5.07180 + 2.92820i 0.392467 + 0.226591i 0.683229 0.730204i \(-0.260575\pi\)
−0.290761 + 0.956796i \(0.593909\pi\)
\(168\) −1.00000 −0.0771517
\(169\) −11.5000 + 6.06218i −0.884615 + 0.466321i
\(170\) 0.196152 0.0150442
\(171\) −3.86603 2.23205i −0.295642 0.170689i
\(172\) −0.366025 + 0.633975i −0.0279092 + 0.0483401i
\(173\) 10.3660 + 17.9545i 0.788114 + 1.36505i 0.927121 + 0.374763i \(0.122276\pi\)
−0.139007 + 0.990291i \(0.544391\pi\)
\(174\) 3.00000i 0.227429i
\(175\) 3.86603 2.23205i 0.292244 0.168727i
\(176\) 3.23205 1.86603i 0.243625 0.140657i
\(177\) 0.928203i 0.0697680i
\(178\) −3.23205 5.59808i −0.242252 0.419594i
\(179\) 11.1962 19.3923i 0.836840 1.44945i −0.0556840 0.998448i \(-0.517734\pi\)
0.892524 0.451000i \(-0.148933\pi\)
\(180\) 0.633975 + 0.366025i 0.0472537 + 0.0272819i
\(181\) −1.19615 −0.0889093 −0.0444547 0.999011i \(-0.514155\pi\)
−0.0444547 + 0.999011i \(0.514155\pi\)
\(182\) 0.866025 + 3.50000i 0.0641941 + 0.259437i
\(183\) 11.7321 0.867258
\(184\) −3.00000 1.73205i −0.221163 0.127688i
\(185\) −0.464102 + 0.803848i −0.0341214 + 0.0591000i
\(186\) 3.83013 + 6.63397i 0.280839 + 0.486427i
\(187\) 1.00000i 0.0731272i
\(188\) −3.86603 + 2.23205i −0.281959 + 0.162789i
\(189\) −0.866025 + 0.500000i −0.0629941 + 0.0363696i
\(190\) 3.26795i 0.237082i
\(191\) 2.09808 + 3.63397i 0.151811 + 0.262945i 0.931893 0.362732i \(-0.118156\pi\)
−0.780082 + 0.625677i \(0.784823\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −14.8923 8.59808i −1.07197 0.618903i −0.143252 0.989686i \(-0.545756\pi\)
−0.928719 + 0.370783i \(0.879089\pi\)
\(194\) −0.732051 −0.0525582
\(195\) 0.732051 2.53590i 0.0524232 0.181599i
\(196\) 1.00000 0.0714286
\(197\) 1.96410 + 1.13397i 0.139936 + 0.0807923i 0.568334 0.822798i \(-0.307588\pi\)
−0.428397 + 0.903591i \(0.640922\pi\)
\(198\) 1.86603 3.23205i 0.132613 0.229692i
\(199\) −2.09808 3.63397i −0.148729 0.257606i 0.782029 0.623242i \(-0.214185\pi\)
−0.930758 + 0.365636i \(0.880851\pi\)
\(200\) 4.46410i 0.315660i
\(201\) −11.1962 + 6.46410i −0.789716 + 0.455943i
\(202\) 8.66025 5.00000i 0.609333 0.351799i
\(203\) 3.00000i 0.210559i
\(204\) 0.133975 + 0.232051i 0.00938010 + 0.0162468i
\(205\) 2.56218 4.43782i 0.178950 0.309951i
\(206\) −10.5622 6.09808i −0.735902 0.424873i
\(207\) −3.46410 −0.240772
\(208\) 3.46410 + 1.00000i 0.240192 + 0.0693375i
\(209\) −16.6603 −1.15241
\(210\) −0.633975 0.366025i −0.0437484 0.0252582i
\(211\) 7.92820 13.7321i 0.545800 0.945353i −0.452756 0.891634i \(-0.649559\pi\)
0.998556 0.0537189i \(-0.0171075\pi\)
\(212\) −5.23205 9.06218i −0.359339 0.622393i
\(213\) 2.19615i 0.150478i
\(214\) −1.33013 + 0.767949i −0.0909256 + 0.0524959i
\(215\) −0.464102 + 0.267949i −0.0316515 + 0.0182740i
\(216\) 1.00000i 0.0680414i
\(217\) −3.83013 6.63397i −0.260006 0.450344i
\(218\) −1.83013 + 3.16987i −0.123952 + 0.214691i
\(219\) 5.66025 + 3.26795i 0.382485 + 0.220828i
\(220\) 2.73205 0.184195
\(221\) 0.696152 0.669873i 0.0468283 0.0450605i
\(222\) −1.26795 −0.0850992
\(223\) 7.26795 + 4.19615i 0.486698 + 0.280995i 0.723204 0.690635i \(-0.242669\pi\)
−0.236506 + 0.971630i \(0.576002\pi\)
\(224\) 0.500000 0.866025i 0.0334077 0.0578638i
\(225\) −2.23205 3.86603i −0.148803 0.257735i
\(226\) 10.1962i 0.678238i
\(227\) 7.39230 4.26795i 0.490645 0.283274i −0.234197 0.972189i \(-0.575246\pi\)
0.724842 + 0.688915i \(0.241913\pi\)
\(228\) 3.86603 2.23205i 0.256034 0.147821i
\(229\) 10.3205i 0.681998i −0.940064 0.340999i \(-0.889235\pi\)
0.940064 0.340999i \(-0.110765\pi\)
\(230\) −1.26795 2.19615i −0.0836061 0.144810i
\(231\) −1.86603 + 3.23205i −0.122775 + 0.212653i
\(232\) −2.59808 1.50000i −0.170572 0.0984798i
\(233\) −2.19615 −0.143875 −0.0719374 0.997409i \(-0.522918\pi\)
−0.0719374 + 0.997409i \(0.522918\pi\)
\(234\) 3.50000 0.866025i 0.228802 0.0566139i
\(235\) −3.26795 −0.213177
\(236\) 0.803848 + 0.464102i 0.0523260 + 0.0302104i
\(237\) 5.42820 9.40192i 0.352600 0.610721i
\(238\) −0.133975 0.232051i −0.00868428 0.0150416i
\(239\) 13.8038i 0.892897i −0.894809 0.446448i \(-0.852689\pi\)
0.894809 0.446448i \(-0.147311\pi\)
\(240\) −0.633975 + 0.366025i −0.0409229 + 0.0236268i
\(241\) −11.0718 + 6.39230i −0.713197 + 0.411765i −0.812244 0.583318i \(-0.801754\pi\)
0.0990466 + 0.995083i \(0.468421\pi\)
\(242\) 2.92820i 0.188232i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −5.86603 + 10.1603i −0.375534 + 0.650444i
\(245\) 0.633975 + 0.366025i 0.0405032 + 0.0233845i
\(246\) 7.00000 0.446304
\(247\) −11.1603 11.5981i −0.710110 0.737968i
\(248\) −7.66025 −0.486427
\(249\) −4.90192 2.83013i −0.310647 0.179352i
\(250\) 3.46410 6.00000i 0.219089 0.379473i
\(251\) 9.09808 + 15.7583i 0.574265 + 0.994657i 0.996121 + 0.0879939i \(0.0280456\pi\)
−0.421856 + 0.906663i \(0.638621\pi\)
\(252\) 1.00000i 0.0629941i
\(253\) −11.1962 + 6.46410i −0.703896 + 0.406395i
\(254\) 10.8564 6.26795i 0.681192 0.393286i
\(255\) 0.196152i 0.0122835i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 5.52628 9.57180i 0.344720 0.597072i −0.640583 0.767889i \(-0.721307\pi\)
0.985303 + 0.170817i \(0.0546406\pi\)
\(258\) −0.633975 0.366025i −0.0394695 0.0227877i
\(259\) 1.26795 0.0787865
\(260\) 1.83013 + 1.90192i 0.113500 + 0.117952i
\(261\) −3.00000 −0.185695
\(262\) −16.3923 9.46410i −1.01272 0.584694i
\(263\) 9.36603 16.2224i 0.577534 1.00032i −0.418227 0.908342i \(-0.637348\pi\)
0.995761 0.0919756i \(-0.0293182\pi\)
\(264\) 1.86603 + 3.23205i 0.114846 + 0.198919i
\(265\) 7.66025i 0.470566i
\(266\) −3.86603 + 2.23205i −0.237041 + 0.136856i
\(267\) 5.59808 3.23205i 0.342597 0.197798i
\(268\) 12.9282i 0.789716i
\(269\) 11.8564 + 20.5359i 0.722898 + 1.25210i 0.959833 + 0.280570i \(0.0905236\pi\)
−0.236936 + 0.971525i \(0.576143\pi\)
\(270\) −0.366025 + 0.633975i −0.0222756 + 0.0385825i
\(271\) 18.6340 + 10.7583i 1.13193 + 0.653522i 0.944420 0.328740i \(-0.106624\pi\)
0.187513 + 0.982262i \(0.439957\pi\)
\(272\) −0.267949 −0.0162468
\(273\) −3.50000 + 0.866025i −0.211830 + 0.0524142i
\(274\) −15.4641 −0.934221
\(275\) −14.4282 8.33013i −0.870053 0.502326i
\(276\) 1.73205 3.00000i 0.104257 0.180579i
\(277\) −13.1962 22.8564i −0.792880 1.37331i −0.924177 0.381965i \(-0.875247\pi\)
0.131297 0.991343i \(-0.458086\pi\)
\(278\) 18.1244i 1.08703i
\(279\) −6.63397 + 3.83013i −0.397166 + 0.229304i
\(280\) 0.633975 0.366025i 0.0378872 0.0218742i
\(281\) 18.1962i 1.08549i 0.839897 + 0.542746i \(0.182615\pi\)
−0.839897 + 0.542746i \(0.817385\pi\)
\(282\) −2.23205 3.86603i −0.132917 0.230218i
\(283\) −11.4641 + 19.8564i −0.681470 + 1.18034i 0.293062 + 0.956093i \(0.405326\pi\)
−0.974532 + 0.224247i \(0.928008\pi\)
\(284\) 1.90192 + 1.09808i 0.112858 + 0.0651588i
\(285\) 3.26795 0.193577
\(286\) 9.69615 9.33013i 0.573346 0.551702i
\(287\) −7.00000 −0.413197
\(288\) −0.866025 0.500000i −0.0510310 0.0294628i
\(289\) 8.46410 14.6603i 0.497888 0.862368i
\(290\) −1.09808 1.90192i −0.0644813 0.111685i
\(291\) 0.732051i 0.0429136i
\(292\) −5.66025 + 3.26795i −0.331241 + 0.191242i
\(293\) −11.0718 + 6.39230i −0.646821 + 0.373442i −0.787237 0.616650i \(-0.788489\pi\)
0.140416 + 0.990093i \(0.455156\pi\)
\(294\) 1.00000i 0.0583212i
\(295\) 0.339746 + 0.588457i 0.0197808 + 0.0342613i
\(296\) 0.633975 1.09808i 0.0368490 0.0638244i
\(297\) 3.23205 + 1.86603i 0.187543 + 0.108278i
\(298\) 18.9282 1.09648
\(299\) −12.0000 3.46410i −0.693978 0.200334i
\(300\) 4.46410 0.257735
\(301\) 0.633975 + 0.366025i 0.0365417 + 0.0210974i
\(302\) 6.59808 11.4282i 0.379677 0.657619i
\(303\) 5.00000 + 8.66025i 0.287242 + 0.497519i
\(304\) 4.46410i 0.256034i
\(305\) −7.43782 + 4.29423i −0.425888 + 0.245887i
\(306\) −0.232051 + 0.133975i −0.0132655 + 0.00765882i
\(307\) 33.7846i 1.92819i −0.265558 0.964095i \(-0.585556\pi\)
0.265558 0.964095i \(-0.414444\pi\)
\(308\) −1.86603 3.23205i −0.106327 0.184163i
\(309\) 6.09808 10.5622i 0.346907 0.600861i
\(310\) −4.85641 2.80385i −0.275825 0.159248i
\(311\) 19.1962 1.08851 0.544257 0.838919i \(-0.316812\pi\)
0.544257 + 0.838919i \(0.316812\pi\)
\(312\) −1.00000 + 3.46410i −0.0566139 + 0.196116i
\(313\) 1.80385 0.101959 0.0509797 0.998700i \(-0.483766\pi\)
0.0509797 + 0.998700i \(0.483766\pi\)
\(314\) 13.3923 + 7.73205i 0.755771 + 0.436345i
\(315\) 0.366025 0.633975i 0.0206232 0.0357204i
\(316\) 5.42820 + 9.40192i 0.305360 + 0.528900i
\(317\) 18.0000i 1.01098i −0.862832 0.505490i \(-0.831312\pi\)
0.862832 0.505490i \(-0.168688\pi\)
\(318\) 9.06218 5.23205i 0.508182 0.293399i
\(319\) −9.69615 + 5.59808i −0.542880 + 0.313432i
\(320\) 0.732051i 0.0409229i
\(321\) −0.767949 1.33013i −0.0428627 0.0742405i
\(322\) −1.73205 + 3.00000i −0.0965234 + 0.167183i
\(323\) 1.03590 + 0.598076i 0.0576389 + 0.0332779i
\(324\) −1.00000 −0.0555556
\(325\) −3.86603 15.6244i −0.214449 0.866683i
\(326\) 7.80385 0.432215
\(327\) −3.16987 1.83013i −0.175294 0.101206i
\(328\) −3.50000 + 6.06218i −0.193255 + 0.334728i
\(329\) 2.23205 + 3.86603i 0.123057 + 0.213141i
\(330\) 2.73205i 0.150394i
\(331\) −14.6603 + 8.46410i −0.805800 + 0.465229i −0.845495 0.533983i \(-0.820695\pi\)
0.0396949 + 0.999212i \(0.487361\pi\)
\(332\) 4.90192 2.83013i 0.269028 0.155323i
\(333\) 1.26795i 0.0694832i
\(334\) −2.92820 5.07180i −0.160224 0.277516i
\(335\) 4.73205 8.19615i 0.258540 0.447804i
\(336\) 0.866025 + 0.500000i 0.0472456 + 0.0272772i
\(337\) −27.7846 −1.51352 −0.756762 0.653690i \(-0.773220\pi\)
−0.756762 + 0.653690i \(0.773220\pi\)
\(338\) 12.9904 + 0.500000i 0.706584 + 0.0271964i
\(339\) 10.1962 0.553779
\(340\) −0.169873 0.0980762i −0.00921266 0.00531893i
\(341\) −14.2942 + 24.7583i −0.774076 + 1.34074i
\(342\) 2.23205 + 3.86603i 0.120695 + 0.209051i
\(343\) 1.00000i 0.0539949i
\(344\) 0.633975 0.366025i 0.0341816 0.0197348i
\(345\) 2.19615 1.26795i 0.118237 0.0682641i
\(346\) 20.7321i 1.11456i
\(347\) −11.4282 19.7942i −0.613498 1.06261i −0.990646 0.136457i \(-0.956429\pi\)
0.377148 0.926153i \(-0.376905\pi\)
\(348\) 1.50000 2.59808i 0.0804084 0.139272i
\(349\) 20.5359 + 11.8564i 1.09926 + 0.634659i 0.936027 0.351928i \(-0.114474\pi\)
0.163235 + 0.986587i \(0.447807\pi\)
\(350\) −4.46410 −0.238616
\(351\) 0.866025 + 3.50000i 0.0462250 + 0.186816i
\(352\) −3.73205 −0.198919
\(353\) −1.26795 0.732051i −0.0674861 0.0389631i 0.465877 0.884849i \(-0.345739\pi\)
−0.533363 + 0.845886i \(0.679072\pi\)
\(354\) −0.464102 + 0.803848i −0.0246667 + 0.0427240i
\(355\) 0.803848 + 1.39230i 0.0426638 + 0.0738959i
\(356\) 6.46410i 0.342597i
\(357\) 0.232051 0.133975i 0.0122814 0.00709069i
\(358\) −19.3923 + 11.1962i −1.02492 + 0.591735i
\(359\) 15.8038i 0.834095i 0.908885 + 0.417048i \(0.136935\pi\)
−0.908885 + 0.417048i \(0.863065\pi\)
\(360\) −0.366025 0.633975i −0.0192912 0.0334134i
\(361\) 0.464102 0.803848i 0.0244264 0.0423078i
\(362\) 1.03590 + 0.598076i 0.0544456 + 0.0314342i
\(363\) 2.92820 0.153691
\(364\) 1.00000 3.46410i 0.0524142 0.181568i
\(365\) −4.78461 −0.250438
\(366\) −10.1603 5.86603i −0.531085 0.306622i
\(367\) −8.12436 + 14.0718i −0.424088 + 0.734542i −0.996335 0.0855396i \(-0.972739\pi\)
0.572247 + 0.820081i \(0.306072\pi\)
\(368\) 1.73205 + 3.00000i 0.0902894 + 0.156386i
\(369\) 7.00000i 0.364405i
\(370\) 0.803848 0.464102i 0.0417900 0.0241275i
\(371\) −9.06218 + 5.23205i −0.470485 + 0.271635i
\(372\) 7.66025i 0.397166i
\(373\) 10.2942 + 17.8301i 0.533015 + 0.923209i 0.999257 + 0.0385516i \(0.0122744\pi\)
−0.466242 + 0.884657i \(0.654392\pi\)
\(374\) −0.500000 + 0.866025i −0.0258544 + 0.0447811i
\(375\) 6.00000 + 3.46410i 0.309839 + 0.178885i
\(376\) 4.46410 0.230218
\(377\) −10.3923 3.00000i −0.535231 0.154508i
\(378\) 1.00000 0.0514344
\(379\) −12.6340 7.29423i −0.648964 0.374679i 0.139095 0.990279i \(-0.455581\pi\)
−0.788059 + 0.615600i \(0.788914\pi\)
\(380\) −1.63397 + 2.83013i −0.0838211 + 0.145182i
\(381\) 6.26795 + 10.8564i 0.321117 + 0.556191i
\(382\) 4.19615i 0.214694i
\(383\) 12.6506 7.30385i 0.646417 0.373209i −0.140665 0.990057i \(-0.544924\pi\)
0.787082 + 0.616848i \(0.211591\pi\)
\(384\) 0.866025 0.500000i 0.0441942 0.0255155i
\(385\) 2.73205i 0.139238i
\(386\) 8.59808 + 14.8923i 0.437631 + 0.757998i
\(387\) 0.366025 0.633975i 0.0186061 0.0322267i
\(388\) 0.633975 + 0.366025i 0.0321852 + 0.0185821i
\(389\) 33.1769 1.68214 0.841068 0.540929i \(-0.181927\pi\)
0.841068 + 0.540929i \(0.181927\pi\)
\(390\) −1.90192 + 1.83013i −0.0963077 + 0.0926721i
\(391\) 0.928203 0.0469413
\(392\) −0.866025 0.500000i −0.0437409 0.0252538i
\(393\) 9.46410 16.3923i 0.477401 0.826882i
\(394\) −1.13397 1.96410i −0.0571288 0.0989500i
\(395\) 7.94744i 0.399879i
\(396\) −3.23205 + 1.86603i −0.162417 + 0.0937713i
\(397\) −14.2583 + 8.23205i −0.715605 + 0.413155i −0.813133 0.582078i \(-0.802240\pi\)
0.0975279 + 0.995233i \(0.468906\pi\)
\(398\) 4.19615i 0.210334i
\(399\) −2.23205 3.86603i −0.111742 0.193543i
\(400\) −2.23205 + 3.86603i −0.111603 + 0.193301i
\(401\) −8.66025 5.00000i −0.432472 0.249688i 0.267927 0.963439i \(-0.413661\pi\)
−0.700399 + 0.713751i \(0.746995\pi\)
\(402\) 12.9282 0.644800
\(403\) −26.8109 + 6.63397i −1.33555 + 0.330462i
\(404\) −10.0000 −0.497519
\(405\) −0.633975 0.366025i −0.0315025 0.0181879i
\(406\) −1.50000 + 2.59808i −0.0744438 + 0.128940i
\(407\) −2.36603 4.09808i −0.117280 0.203134i
\(408\) 0.267949i 0.0132655i
\(409\) 11.4904 6.63397i 0.568163 0.328029i −0.188252 0.982121i \(-0.560282\pi\)
0.756415 + 0.654092i \(0.226949\pi\)
\(410\) −4.43782 + 2.56218i −0.219168 + 0.126537i
\(411\) 15.4641i 0.762788i
\(412\) 6.09808 + 10.5622i 0.300431 + 0.520361i
\(413\) 0.464102 0.803848i 0.0228369 0.0395548i
\(414\) 3.00000 + 1.73205i 0.147442 + 0.0851257i
\(415\) 4.14359 0.203401
\(416\) −2.50000 2.59808i −0.122573 0.127381i
\(417\) 18.1244 0.887554
\(418\) 14.4282 + 8.33013i 0.705706 + 0.407440i
\(419\) 3.09808 5.36603i 0.151351 0.262147i −0.780373 0.625314i \(-0.784971\pi\)
0.931724 + 0.363166i \(0.118304\pi\)
\(420\) 0.366025 + 0.633975i 0.0178602 + 0.0309348i
\(421\) 14.3923i 0.701438i −0.936481 0.350719i \(-0.885937\pi\)
0.936481 0.350719i \(-0.114063\pi\)
\(422\) −13.7321 + 7.92820i −0.668466 + 0.385939i
\(423\) 3.86603 2.23205i 0.187973 0.108526i
\(424\) 10.4641i 0.508182i
\(425\) 0.598076 + 1.03590i 0.0290110 + 0.0502485i
\(426\) −1.09808 + 1.90192i −0.0532020 + 0.0921485i
\(427\) 10.1603 + 5.86603i 0.491689 + 0.283877i
\(428\) 1.53590 0.0742405
\(429\) 9.33013 + 9.69615i 0.450463 + 0.468135i
\(430\) 0.535898 0.0258433
\(431\) 18.2942 + 10.5622i 0.881202 + 0.508762i 0.871055 0.491186i \(-0.163437\pi\)
0.0101474 + 0.999949i \(0.496770\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) 4.46410 + 7.73205i 0.214531 + 0.371579i 0.953127 0.302569i \(-0.0978444\pi\)
−0.738596 + 0.674148i \(0.764511\pi\)
\(434\) 7.66025i 0.367704i
\(435\) 1.90192 1.09808i 0.0911903 0.0526487i
\(436\) 3.16987 1.83013i 0.151809 0.0876472i
\(437\) 15.4641i 0.739748i
\(438\) −3.26795 5.66025i −0.156149 0.270457i
\(439\) −8.19615 + 14.1962i −0.391181 + 0.677545i −0.992606 0.121384i \(-0.961267\pi\)
0.601425 + 0.798930i \(0.294600\pi\)
\(440\) −2.36603 1.36603i −0.112796 0.0651227i
\(441\) −1.00000 −0.0476190
\(442\) −0.937822 + 0.232051i −0.0446077 + 0.0110375i
\(443\) −31.3923 −1.49149 −0.745747 0.666230i \(-0.767907\pi\)
−0.745747 + 0.666230i \(0.767907\pi\)
\(444\) 1.09808 + 0.633975i 0.0521124 + 0.0300871i
\(445\) −2.36603 + 4.09808i −0.112160 + 0.194267i
\(446\) −4.19615 7.26795i −0.198694 0.344147i
\(447\) 18.9282i 0.895273i
\(448\) −0.866025 + 0.500000i −0.0409159 + 0.0236228i
\(449\) −9.29423 + 5.36603i −0.438622 + 0.253238i −0.703013 0.711177i \(-0.748162\pi\)
0.264391 + 0.964416i \(0.414829\pi\)
\(450\) 4.46410i 0.210440i
\(451\) 13.0622 + 22.6244i 0.615074 + 1.06534i
\(452\) −5.09808 + 8.83013i −0.239793 + 0.415334i
\(453\) 11.4282 + 6.59808i 0.536944 + 0.310005i
\(454\) −8.53590 −0.400610
\(455\) 1.90192 1.83013i 0.0891636 0.0857977i
\(456\) −4.46410 −0.209051
\(457\) 5.87564 + 3.39230i 0.274851 + 0.158685i 0.631090 0.775710i \(-0.282608\pi\)
−0.356239 + 0.934395i \(0.615941\pi\)
\(458\) −5.16025 + 8.93782i −0.241123 + 0.417637i
\(459\) −0.133975 0.232051i −0.00625340 0.0108312i
\(460\) 2.53590i 0.118237i
\(461\) −24.0000 + 13.8564i −1.11779 + 0.645357i −0.940836 0.338862i \(-0.889958\pi\)
−0.176955 + 0.984219i \(0.556625\pi\)
\(462\) 3.23205 1.86603i 0.150369 0.0868154i
\(463\) 1.19615i 0.0555899i −0.999614 0.0277950i \(-0.991151\pi\)
0.999614 0.0277950i \(-0.00884855\pi\)
\(464\) 1.50000 + 2.59808i 0.0696358 + 0.120613i
\(465\) 2.80385 4.85641i 0.130025 0.225210i
\(466\) 1.90192 + 1.09808i 0.0881049 + 0.0508674i
\(467\) 9.85641 0.456100 0.228050 0.973649i \(-0.426765\pi\)
0.228050 + 0.973649i \(0.426765\pi\)
\(468\) −3.46410 1.00000i −0.160128 0.0462250i
\(469\) −12.9282 −0.596969
\(470\) 2.83013 + 1.63397i 0.130544 + 0.0753696i
\(471\) −7.73205 + 13.3923i −0.356274 + 0.617085i
\(472\) −0.464102 0.803848i −0.0213620 0.0370001i
\(473\) 2.73205i 0.125620i
\(474\) −9.40192 + 5.42820i −0.431845 + 0.249326i
\(475\) 17.2583 9.96410i 0.791866 0.457184i
\(476\) 0.267949i 0.0122814i
\(477\) 5.23205 + 9.06218i 0.239559 + 0.414929i
\(478\) −6.90192 + 11.9545i −0.315687 + 0.546785i
\(479\) 27.1865 + 15.6962i 1.24218 + 0.717176i 0.969539 0.244939i \(-0.0787679\pi\)
0.272646 + 0.962114i \(0.412101\pi\)
\(480\) 0.732051 0.0334134
\(481\) 1.26795 4.39230i 0.0578135 0.200272i
\(482\) 12.7846 0.582323
\(483\) −3.00000 1.73205i −0.136505 0.0788110i
\(484\) −1.46410 + 2.53590i −0.0665501 + 0.115268i
\(485\) 0.267949 + 0.464102i 0.0121669 + 0.0210738i
\(486\) 1.00000i 0.0453609i
\(487\) 18.3564 10.5981i 0.831808 0.480245i −0.0226632 0.999743i \(-0.507215\pi\)
0.854471 + 0.519498i \(0.173881\pi\)
\(488\) 10.1603 5.86603i 0.459933 0.265542i
\(489\) 7.80385i 0.352902i
\(490\) −0.366025 0.633975i −0.0165353 0.0286401i
\(491\) 18.1244 31.3923i 0.817941 1.41671i −0.0892562 0.996009i \(-0.528449\pi\)
0.907197 0.420706i \(-0.138218\pi\)
\(492\) −6.06218 3.50000i −0.273304 0.157792i
\(493\) 0.803848 0.0362035
\(494\) 3.86603 + 15.6244i 0.173941 + 0.702973i
\(495\) −2.73205 −0.122797
\(496\) 6.63397 + 3.83013i 0.297874 + 0.171978i
\(497\) 1.09808 1.90192i 0.0492554 0.0853129i
\(498\) 2.83013 + 4.90192i 0.126821 + 0.219660i
\(499\) 12.9808i 0.581099i −0.956860 0.290549i \(-0.906162\pi\)
0.956860 0.290549i \(-0.0938380\pi\)
\(500\) −6.00000 + 3.46410i −0.268328 + 0.154919i
\(501\) 5.07180 2.92820i 0.226591 0.130822i
\(502\) 18.1962i 0.812134i
\(503\) 11.8564 + 20.5359i 0.528651 + 0.915650i 0.999442 + 0.0334056i \(0.0106353\pi\)
−0.470791 + 0.882245i \(0.656031\pi\)
\(504\) −0.500000 + 0.866025i −0.0222718 + 0.0385758i
\(505\) −6.33975 3.66025i −0.282115 0.162879i
\(506\) 12.9282 0.574729
\(507\) −0.500000 + 12.9904i −0.0222058 + 0.576923i
\(508\) −12.5359 −0.556191
\(509\) −22.5622 13.0263i −1.00005 0.577380i −0.0917876 0.995779i \(-0.529258\pi\)
−0.908263 + 0.418399i \(0.862591\pi\)
\(510\) 0.0980762 0.169873i 0.00434289 0.00752210i
\(511\) 3.26795 + 5.66025i 0.144566 + 0.250395i
\(512\) 1.00000i 0.0441942i
\(513\) −3.86603 + 2.23205i −0.170689 + 0.0985475i
\(514\) −9.57180 + 5.52628i −0.422194 + 0.243754i
\(515\) 8.92820i 0.393424i
\(516\) 0.366025 + 0.633975i 0.0161134 + 0.0279092i
\(517\) 8.33013 14.4282i 0.366359 0.634552i
\(518\) −1.09808 0.633975i −0.0482467 0.0278552i
\(519\) 20.7321 0.910036
\(520\) −0.633975 2.56218i −0.0278016 0.112359i
\(521\) −2.26795 −0.0993607 −0.0496803 0.998765i \(-0.515820\pi\)
−0.0496803 + 0.998765i \(0.515820\pi\)
\(522\) 2.59808 + 1.50000i 0.113715 + 0.0656532i
\(523\) 9.40192 16.2846i 0.411117 0.712076i −0.583895 0.811829i \(-0.698472\pi\)
0.995012 + 0.0997531i \(0.0318053\pi\)
\(524\) 9.46410 + 16.3923i 0.413441 + 0.716101i
\(525\) 4.46410i 0.194829i
\(526\) −16.2224 + 9.36603i −0.707332 + 0.408378i
\(527\) 1.77757 1.02628i 0.0774321 0.0447054i
\(528\) 3.73205i 0.162417i
\(529\) 5.50000 + 9.52628i 0.239130 + 0.414186i
\(530\) −3.83013 + 6.63397i −0.166370 + 0.288161i
\(531\) −0.803848 0.464102i −0.0348840 0.0201403i
\(532\) 4.46410 0.193543
\(533\) −7.00000 + 24.2487i −0.303204 + 1.05033i
\(534\) −6.46410 −0.279729
\(535\) 0.973721 + 0.562178i 0.0420976 + 0.0243051i
\(536\) −6.46410 + 11.1962i −0.279207 + 0.483600i
\(537\) −11.1962 19.3923i −0.483150 0.836840i
\(538\) 23.7128i 1.02233i
\(539\) −3.23205 + 1.86603i −0.139214 + 0.0803754i
\(540\) 0.633975 0.366025i 0.0272819 0.0157512i
\(541\) 30.1962i 1.29823i 0.760689 + 0.649117i \(0.224861\pi\)
−0.760689 + 0.649117i \(0.775139\pi\)
\(542\) −10.7583 18.6340i −0.462110 0.800398i
\(543\) −0.598076 + 1.03590i −0.0256659 + 0.0444547i
\(544\) 0.232051 + 0.133975i 0.00994910 + 0.00574411i
\(545\) 2.67949 0.114777
\(546\) 3.46410 + 1.00000i 0.148250 + 0.0427960i
\(547\) −12.8756 −0.550523 −0.275261 0.961369i \(-0.588764\pi\)
−0.275261 + 0.961369i \(0.588764\pi\)
\(548\) 13.3923 + 7.73205i 0.572091 + 0.330297i
\(549\) 5.86603 10.1603i 0.250356 0.433629i
\(550\) 8.33013 + 14.4282i 0.355198 + 0.615221i
\(551\) 13.3923i 0.570531i
\(552\) −3.00000 + 1.73205i −0.127688 + 0.0737210i
\(553\) 9.40192 5.42820i 0.399810 0.230831i
\(554\) 26.3923i 1.12130i
\(555\) 0.464102 + 0.803848i 0.0197000 + 0.0341214i
\(556\) −9.06218 + 15.6962i −0.384322 + 0.665665i
\(557\) 31.7487 + 18.3301i 1.34524 + 0.776672i 0.987570 0.157177i \(-0.0502394\pi\)
0.357666 + 0.933850i \(0.383573\pi\)
\(558\) 7.66025 0.324284
\(559\) 1.90192 1.83013i 0.0804428 0.0774061i
\(560\) −0.732051 −0.0309348
\(561\) −0.866025 0.500000i −0.0365636 0.0211100i
\(562\) 9.09808 15.7583i 0.383779 0.664725i
\(563\) −16.6340 28.8109i −0.701038 1.21423i −0.968102 0.250555i \(-0.919387\pi\)
0.267064 0.963679i \(-0.413947\pi\)
\(564\) 4.46410i 0.187973i
\(565\) −6.46410 + 3.73205i −0.271947 + 0.157009i
\(566\) 19.8564 11.4641i 0.834627 0.481872i
\(567\) 1.00000i 0.0419961i
\(568\) −1.09808 1.90192i −0.0460743 0.0798029i
\(569\) 11.3660 19.6865i 0.476489 0.825302i −0.523149 0.852242i \(-0.675243\pi\)
0.999637 + 0.0269391i \(0.00857603\pi\)
\(570\) −2.83013 1.63397i −0.118541 0.0684397i
\(571\) −19.8038 −0.828765 −0.414383 0.910103i \(-0.636002\pi\)
−0.414383 + 0.910103i \(0.636002\pi\)
\(572\) −13.0622 + 3.23205i −0.546157 + 0.135139i
\(573\) 4.19615 0.175297
\(574\) 6.06218 + 3.50000i 0.253030 + 0.146087i
\(575\) 7.73205 13.3923i 0.322449 0.558498i
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) 13.2679i 0.552352i −0.961107 0.276176i \(-0.910933\pi\)
0.961107 0.276176i \(-0.0890673\pi\)
\(578\) −14.6603 + 8.46410i −0.609786 + 0.352060i
\(579\) −14.8923 + 8.59808i −0.618903 + 0.357324i
\(580\) 2.19615i 0.0911903i
\(581\) −2.83013 4.90192i −0.117413 0.203366i
\(582\) −0.366025 + 0.633975i −0.0151722 + 0.0262791i
\(583\) 33.8205 + 19.5263i 1.40070 + 0.808696i
\(584\) 6.53590 0.270457
\(585\) −1.83013 1.90192i −0.0756664 0.0786349i
\(586\) 12.7846 0.528127
\(587\) −27.1699 15.6865i −1.12142 0.647453i −0.179657 0.983729i \(-0.557499\pi\)
−0.941763 + 0.336277i \(0.890832\pi\)
\(588\) 0.500000 0.866025i 0.0206197 0.0357143i
\(589\) −17.0981 29.6147i −0.704514 1.22025i
\(590\) 0.679492i 0.0279742i
\(591\) 1.96410 1.13397i 0.0807923 0.0466455i
\(592\) −1.09808 + 0.633975i −0.0451307 + 0.0260562i
\(593\) 13.6795i 0.561749i 0.959744 + 0.280875i \(0.0906245\pi\)
−0.959744 + 0.280875i \(0.909375\pi\)
\(594\) −1.86603 3.23205i −0.0765639 0.132613i
\(595\) −0.0980762 + 0.169873i −0.00402073 + 0.00696411i
\(596\) −16.3923 9.46410i −0.671455 0.387665i
\(597\) −4.19615 −0.171737
\(598\) 8.66025 + 9.00000i 0.354144 + 0.368037i
\(599\) −21.7128 −0.887161 −0.443581 0.896234i \(-0.646292\pi\)
−0.443581 + 0.896234i \(0.646292\pi\)
\(600\) −3.86603 2.23205i −0.157830 0.0911231i
\(601\) 6.43782 11.1506i 0.262604 0.454844i −0.704329 0.709874i \(-0.748752\pi\)
0.966933 + 0.255030i \(0.0820853\pi\)
\(602\) −0.366025 0.633975i −0.0149181 0.0258389i
\(603\) 12.9282i 0.526477i
\(604\) −11.4282 + 6.59808i −0.465007 + 0.268472i
\(605\) −1.85641 + 1.07180i −0.0754737 + 0.0435747i
\(606\) 10.0000i 0.406222i
\(607\) −19.9545 34.5622i −0.809927 1.40284i −0.912914 0.408153i \(-0.866173\pi\)
0.102986 0.994683i \(-0.467160\pi\)
\(608\) 2.23205 3.86603i 0.0905216 0.156788i
\(609\) −2.59808 1.50000i −0.105279 0.0607831i
\(610\) 8.58846 0.347736
\(611\) 15.6244 3.86603i 0.632094 0.156403i
\(612\) 0.267949 0.0108312
\(613\) 36.2487 + 20.9282i 1.46407 + 0.845282i 0.999196 0.0400938i \(-0.0127657\pi\)
0.464876 + 0.885376i \(0.346099\pi\)
\(614\) −16.8923 + 29.2583i −0.681718 + 1.18077i
\(615\) −2.56218 4.43782i −0.103317 0.178950i
\(616\) 3.73205i 0.150369i
\(617\) 35.9545 20.7583i 1.44747 0.835699i 0.449143 0.893460i \(-0.351730\pi\)
0.998330 + 0.0577612i \(0.0183962\pi\)
\(618\) −10.5622 + 6.09808i −0.424873 + 0.245301i
\(619\) 2.32051i 0.0932691i 0.998912 + 0.0466345i \(0.0148496\pi\)
−0.998912 + 0.0466345i \(0.985150\pi\)
\(620\) 2.80385 + 4.85641i 0.112605 + 0.195038i
\(621\) −1.73205 + 3.00000i −0.0695048 + 0.120386i
\(622\) −16.6244 9.59808i −0.666576 0.384848i
\(623\) 6.46410 0.258979
\(624\) 2.59808 2.50000i 0.104006 0.100080i
\(625\) 17.2487 0.689948
\(626\) −1.56218 0.901924i −0.0624372 0.0360481i
\(627\) −8.33013 + 14.4282i −0.332673 + 0.576207i
\(628\) −7.73205 13.3923i −0.308542 0.534411i
\(629\) 0.339746i 0.0135466i
\(630\) −0.633975 + 0.366025i −0.0252582 + 0.0145828i
\(631\) −13.8397 + 7.99038i −0.550952 + 0.318092i −0.749506 0.661998i \(-0.769709\pi\)
0.198554 + 0.980090i \(0.436375\pi\)
\(632\) 10.8564i 0.431845i
\(633\) −7.92820 13.7321i −0.315118 0.545800i
\(634\) −9.00000 + 15.5885i −0.357436 + 0.619097i
\(635\) −7.94744 4.58846i −0.315385 0.182087i
\(636\) −10.4641 −0.414929
\(637\) −3.46410 1.00000i −0.137253 0.0396214i
\(638\) 11.1962 0.443260
\(639\) −1.90192 1.09808i −0.0752389 0.0434392i
\(640\) −0.366025 + 0.633975i −0.0144684 + 0.0250600i
\(641\) −8.12436 14.0718i −0.320893 0.555803i 0.659780 0.751459i \(-0.270650\pi\)
−0.980672 + 0.195656i \(0.937316\pi\)
\(642\) 1.53590i 0.0606171i
\(643\) 1.45448 0.839746i 0.0573592 0.0331163i −0.471046 0.882109i \(-0.656123\pi\)
0.528405 + 0.848992i \(0.322790\pi\)
\(644\) 3.00000 1.73205i 0.118217 0.0682524i
\(645\) 0.535898i 0.0211010i
\(646\) −0.598076 1.03590i −0.0235310 0.0407569i
\(647\) 0.866025 1.50000i 0.0340470 0.0589711i −0.848500 0.529196i \(-0.822494\pi\)
0.882547 + 0.470225i \(0.155827\pi\)
\(648\) 0.866025 + 0.500000i 0.0340207 + 0.0196419i
\(649\) −3.46410 −0.135978
\(650\) −4.46410 + 15.4641i −0.175096 + 0.606552i
\(651\) −7.66025 −0.300229
\(652\) −6.75833 3.90192i −0.264677 0.152811i
\(653\) −5.83975 + 10.1147i −0.228527 + 0.395820i −0.957372 0.288859i \(-0.906724\pi\)
0.728845 + 0.684679i \(0.240058\pi\)
\(654\) 1.83013 + 3.16987i 0.0715636 + 0.123952i
\(655\) 13.8564i 0.541415i
\(656\) 6.06218 3.50000i 0.236688 0.136652i
\(657\) 5.66025 3.26795i 0.220828 0.127495i
\(658\) 4.46410i 0.174029i
\(659\) −16.9641 29.3827i −0.660828 1.14459i −0.980399 0.197025i \(-0.936872\pi\)
0.319571 0.947562i \(-0.396461\pi\)
\(660\) 1.36603 2.36603i 0.0531725 0.0920974i
\(661\) 23.9090 + 13.8038i 0.929951 + 0.536907i 0.886796 0.462161i \(-0.152926\pi\)
0.0431549 + 0.999068i \(0.486259\pi\)
\(662\) 16.9282 0.657933
\(663\) −0.232051 0.937822i −0.00901211 0.0364220i
\(664\) −5.66025 −0.219660
\(665\) 2.83013 + 1.63397i 0.109748 + 0.0633628i
\(666\) −0.633975 + 1.09808i −0.0245660 + 0.0425496i
\(667\) −5.19615 9.00000i −0.201196 0.348481i
\(668\) 5.85641i 0.226591i
\(669\) 7.26795 4.19615i 0.280995 0.162233i
\(670\) −8.19615 + 4.73205i −0.316645 + 0.182815i
\(671\) 43.7846i 1.69029i
\(672\) −0.500000 0.866025i −0.0192879 0.0334077i
\(673\) −23.9641 + 41.5070i −0.923748 + 1.59998i −0.130186 + 0.991490i \(0.541557\pi\)
−0.793562 + 0.608489i \(0.791776\pi\)
\(674\) 24.0622 + 13.8923i 0.926840 + 0.535112i
\(675\) −4.46410 −0.171823
\(676\) −11.0000 6.92820i −0.423077 0.266469i
\(677\) −47.7654 −1.83577 −0.917886 0.396844i \(-0.870105\pi\)
−0.917886 + 0.396844i \(0.870105\pi\)
\(678\) −8.83013 5.09808i −0.339119 0.195790i
\(679\) 0.366025 0.633975i 0.0140468 0.0243297i
\(680\) 0.0980762 + 0.169873i 0.00376105 + 0.00651433i
\(681\) 8.53590i 0.327096i
\(682\) 24.7583 14.2942i 0.948045 0.547354i
\(683\) −22.8564 + 13.1962i −0.874576 + 0.504937i −0.868866 0.495047i \(-0.835151\pi\)
−0.00570987 + 0.999984i \(0.501818\pi\)
\(684\) 4.46410i 0.170689i
\(685\) 5.66025 + 9.80385i 0.216267 + 0.374586i
\(686\) −0.500000 + 0.866025i −0.0190901 + 0.0330650i
\(687\) −8.93782 5.16025i −0.340999 0.196876i
\(688\) −0.732051 −0.0279092
\(689\) 9.06218 + 36.6244i 0.345241 + 1.39528i
\(690\) −2.53590 −0.0965400
\(691\) 35.3205 + 20.3923i 1.34366 + 0.775760i 0.987342 0.158607i \(-0.0507002\pi\)
0.356314 + 0.934366i \(0.384033\pi\)
\(692\) −10.3660 + 17.9545i −0.394057 + 0.682527i
\(693\) 1.86603 + 3.23205i 0.0708844 + 0.122775i
\(694\) 22.8564i 0.867617i
\(695\) −11.4904 + 6.63397i −0.435855 + 0.251641i
\(696\) −2.59808 + 1.50000i −0.0984798 + 0.0568574i
\(697\) 1.87564i 0.0710451i
\(698\) −11.8564 20.5359i −0.448772 0.777295i
\(699\) −1.09808 + 1.90192i −0.0415331 + 0.0719374i
\(700\) 3.86603 + 2.23205i 0.146122 + 0.0843636i
\(701\) −14.3205 −0.540878 −0.270439 0.962737i \(-0.587169\pi\)
−0.270439 + 0.962737i \(0.587169\pi\)
\(702\) 1.00000 3.46410i 0.0377426 0.130744i
\(703\) 5.66025 0.213481
\(704\) 3.23205 + 1.86603i 0.121812 + 0.0703285i
\(705\) −1.63397 + 2.83013i −0.0615390 + 0.106589i
\(706\) 0.732051 + 1.26795i 0.0275511 + 0.0477199i
\(707\) 10.0000i 0.376089i
\(708\) 0.803848 0.464102i 0.0302104 0.0174420i
\(709\) 20.8301 12.0263i 0.782292 0.451656i −0.0549501 0.998489i \(-0.517500\pi\)
0.837242 + 0.546833i \(0.184167\pi\)
\(710\) 1.60770i 0.0603357i
\(711\) −5.42820 9.40192i −0.203574 0.352600i
\(712\) 3.23205 5.59808i 0.121126 0.209797i
\(713\) −22.9808 13.2679i −0.860636 0.496889i
\(714\) −0.267949 −0.0100277
\(715\) −9.46410 2.73205i −0.353937 0.102173i
\(716\) 22.3923 0.836840
\(717\) −11.9545 6.90192i −0.446448 0.257757i
\(718\) 7.90192 13.6865i 0.294897 0.510777i
\(719\) 1.52628 + 2.64359i 0.0569206 + 0.0985894i 0.893082 0.449895i \(-0.148538\pi\)
−0.836161 + 0.548484i \(0.815205\pi\)
\(720\) 0.732051i 0.0272819i
\(721\) 10.5622 6.09808i 0.393356 0.227104i
\(722\) −0.803848 + 0.464102i −0.0299161 + 0.0172721i
\(723\) 12.7846i 0.475465i
\(724\) −0.598076 1.03590i −0.0222273 0.0384989i
\(725\) 6.69615 11.5981i 0.248689 0.430742i
\(726\) −2.53590 1.46410i −0.0941160 0.0543379i
\(727\) −1.46410 −0.0543005 −0.0271503 0.999631i \(-0.508643\pi\)
−0.0271503 + 0.999631i \(0.508643\pi\)
\(728\) −2.59808 + 2.50000i −0.0962911 + 0.0926562i
\(729\) 1.00000 0.0370370
\(730\) 4.14359 + 2.39230i 0.153361 + 0.0885432i
\(731\) −0.0980762 + 0.169873i −0.00362748 + 0.00628298i
\(732\) 5.86603 + 10.1603i 0.216815 + 0.375534i
\(733\) 6.85641i 0.253247i −0.991951 0.126624i \(-0.959586\pi\)
0.991951 0.126624i \(-0.0404140\pi\)
\(734\) 14.0718 8.12436i 0.519399 0.299875i
\(735\) 0.633975 0.366025i 0.0233845 0.0135011i
\(736\) 3.46410i 0.127688i
\(737\) 24.1244 + 41.7846i 0.888632 + 1.53916i
\(738\) 3.50000 6.06218i 0.128837 0.223152i
\(739\) 5.53590 + 3.19615i 0.203641 + 0.117572i 0.598353 0.801233i \(-0.295822\pi\)
−0.394712 + 0.918805i \(0.629155\pi\)
\(740\) −0.928203 −0.0341214
\(741\) −15.6244 + 3.86603i −0.573975 + 0.142022i
\(742\) 10.4641 0.384149
\(743\) −16.9019 9.75833i −0.620071 0.357998i 0.156825 0.987626i \(-0.449874\pi\)
−0.776897 + 0.629628i \(0.783207\pi\)
\(744\) −3.83013 + 6.63397i −0.140419 + 0.243213i
\(745\) −6.92820 12.0000i −0.253830 0.439646i
\(746\) 20.5885i 0.753797i
\(747\) −4.90192 + 2.83013i −0.179352 + 0.103549i
\(748\) 0.866025 0.500000i 0.0316650 0.0182818i
\(749\) 1.53590i 0.0561205i
\(750\) −3.46410 6.00000i −0.126491 0.219089i
\(751\) −3.42820 + 5.93782i −0.125097 + 0.216674i −0.921771 0.387735i \(-0.873258\pi\)
0.796674 + 0.604409i \(0.206591\pi\)
\(752\) −3.86603 2.23205i −0.140979 0.0813945i
\(753\) 18.1962 0.663105
\(754\) 7.50000 + 7.79423i 0.273134 + 0.283849i
\(755\) −9.66025 −0.351573
\(756\) −0.866025 0.500000i −0.0314970 0.0181848i
\(757\) 19.0263 32.9545i 0.691522 1.19775i −0.279817 0.960053i \(-0.590274\pi\)
0.971339 0.237698i \(-0.0763928\pi\)
\(758\) 7.29423 + 12.6340i 0.264938 + 0.458887i
\(759\) 12.9282i 0.469264i
\(760\) 2.83013 1.63397i 0.102659 0.0592705i
\(761\) −0.588457 + 0.339746i −0.0213316 + 0.0123158i −0.510628 0.859802i \(-0.670587\pi\)
0.489296 + 0.872118i \(0.337254\pi\)
\(762\) 12.5359i 0.454128i
\(763\) −1.83013 3.16987i −0.0662550 0.114757i
\(764\) −2.09808 + 3.63397i −0.0759057 + 0.131473i
\(765\) 0.169873 + 0.0980762i 0.00614177 + 0.00354595i
\(766\) −14.6077 −0.527797
\(767\) −2.32051 2.41154i −0.0837887 0.0870758i
\(768\) −1.00000 −0.0360844
\(769\) 21.1699 + 12.2224i 0.763405 + 0.440752i 0.830517 0.556993i \(-0.188045\pi\)
−0.0671118 + 0.997745i \(0.521378\pi\)
\(770\) −1.36603 + 2.36603i −0.0492281 + 0.0852656i
\(771\) −5.52628 9.57180i −0.199024 0.344720i
\(772\) 17.1962i 0.618903i
\(773\) 36.7128 21.1962i 1.32047 0.762373i 0.336665 0.941625i \(-0.390701\pi\)
0.983803 + 0.179252i \(0.0573677\pi\)
\(774\) −0.633975 + 0.366025i −0.0227877 + 0.0131565i
\(775\) 34.1962i 1.22836i
\(776\) −0.366025