Properties

Label 546.2.l.j.211.1
Level $546$
Weight $2$
Character 546.211
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.l (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-19})\)
Defining polynomial: \(x^{4} - x^{3} - 4 x^{2} - 5 x + 25\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 211.1
Root \(-1.63746 + 1.52274i\) of defining polynomial
Character \(\chi\) \(=\) 546.211
Dual form 546.2.l.j.295.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.27492 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.27492 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.63746 + 2.83616i) q^{10} +(2.00000 + 3.46410i) q^{11} +1.00000 q^{12} +(3.50000 - 0.866025i) q^{13} +1.00000 q^{14} +(1.63746 + 2.83616i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +1.00000 q^{18} +(4.27492 - 7.40437i) q^{19} +(1.63746 - 2.83616i) q^{20} +1.00000 q^{21} +(2.00000 - 3.46410i) q^{22} +(-1.13746 - 1.97014i) q^{23} +(-0.500000 - 0.866025i) q^{24} +5.72508 q^{25} +(-2.50000 - 2.59808i) q^{26} +1.00000 q^{27} +(-0.500000 - 0.866025i) q^{28} +(-0.362541 - 0.627940i) q^{29} +(1.63746 - 2.83616i) q^{30} +6.27492 q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.00000 - 3.46410i) q^{33} +3.00000 q^{34} +(1.63746 - 2.83616i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(3.63746 + 6.30026i) q^{37} -8.54983 q^{38} +(-2.50000 - 2.59808i) q^{39} -3.27492 q^{40} +(-0.362541 - 0.627940i) q^{41} +(-0.500000 - 0.866025i) q^{42} +(-5.41238 + 9.37451i) q^{43} -4.00000 q^{44} +(1.63746 - 2.83616i) q^{45} +(-1.13746 + 1.97014i) q^{46} +8.54983 q^{47} +(-0.500000 + 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-2.86254 - 4.95807i) q^{50} +3.00000 q^{51} +(-1.00000 + 3.46410i) q^{52} +11.5498 q^{53} +(-0.500000 - 0.866025i) q^{54} +(-6.54983 - 11.3446i) q^{55} +(-0.500000 + 0.866025i) q^{56} -8.54983 q^{57} +(-0.362541 + 0.627940i) q^{58} +(-5.41238 + 9.37451i) q^{59} -3.27492 q^{60} +(4.50000 - 7.79423i) q^{61} +(-3.13746 - 5.43424i) q^{62} +(-0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +(-11.4622 + 2.83616i) q^{65} -4.00000 q^{66} +(5.13746 + 8.89834i) q^{67} +(-1.50000 - 2.59808i) q^{68} +(-1.13746 + 1.97014i) q^{69} -3.27492 q^{70} +(1.13746 - 1.97014i) q^{71} +(-0.500000 + 0.866025i) q^{72} +13.2749 q^{73} +(3.63746 - 6.30026i) q^{74} +(-2.86254 - 4.95807i) q^{75} +(4.27492 + 7.40437i) q^{76} -4.00000 q^{77} +(-1.00000 + 3.46410i) q^{78} -8.00000 q^{79} +(1.63746 + 2.83616i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.362541 + 0.627940i) q^{82} +10.8248 q^{83} +(-0.500000 + 0.866025i) q^{84} +(4.91238 - 8.50848i) q^{85} +10.8248 q^{86} +(-0.362541 + 0.627940i) q^{87} +(2.00000 + 3.46410i) q^{88} +(-4.13746 - 7.16629i) q^{89} -3.27492 q^{90} +(-1.00000 + 3.46410i) q^{91} +2.27492 q^{92} +(-3.13746 - 5.43424i) q^{93} +(-4.27492 - 7.40437i) q^{94} +(-14.0000 + 24.2487i) q^{95} +1.00000 q^{96} +(-7.27492 + 12.6005i) q^{97} +(-0.500000 + 0.866025i) q^{98} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} - 2q^{3} - 2q^{4} + 2q^{5} - 2q^{6} - 2q^{7} + 4q^{8} - 2q^{9} + O(q^{10}) \) \( 4q - 2q^{2} - 2q^{3} - 2q^{4} + 2q^{5} - 2q^{6} - 2q^{7} + 4q^{8} - 2q^{9} - q^{10} + 8q^{11} + 4q^{12} + 14q^{13} + 4q^{14} - q^{15} - 2q^{16} - 6q^{17} + 4q^{18} + 2q^{19} - q^{20} + 4q^{21} + 8q^{22} + 3q^{23} - 2q^{24} + 38q^{25} - 10q^{26} + 4q^{27} - 2q^{28} - 9q^{29} - q^{30} + 10q^{31} - 2q^{32} + 8q^{33} + 12q^{34} - q^{35} - 2q^{36} + 7q^{37} - 4q^{38} - 10q^{39} + 2q^{40} - 9q^{41} - 2q^{42} + q^{43} - 16q^{44} - q^{45} + 3q^{46} + 4q^{47} - 2q^{48} - 2q^{49} - 19q^{50} + 12q^{51} - 4q^{52} + 16q^{53} - 2q^{54} + 4q^{55} - 2q^{56} - 4q^{57} - 9q^{58} + q^{59} + 2q^{60} + 18q^{61} - 5q^{62} - 2q^{63} + 4q^{64} + 7q^{65} - 16q^{66} + 13q^{67} - 6q^{68} + 3q^{69} + 2q^{70} - 3q^{71} - 2q^{72} + 38q^{73} + 7q^{74} - 19q^{75} + 2q^{76} - 16q^{77} - 4q^{78} - 32q^{79} - q^{80} - 2q^{81} - 9q^{82} - 2q^{83} - 2q^{84} - 3q^{85} - 2q^{86} - 9q^{87} + 8q^{88} - 9q^{89} + 2q^{90} - 4q^{91} - 6q^{92} - 5q^{93} - 2q^{94} - 56q^{95} + 4q^{96} - 14q^{97} - 2q^{98} - 16q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −3.27492 −1.46459 −0.732294 0.680989i \(-0.761550\pi\)
−0.732294 + 0.680989i \(0.761550\pi\)
\(6\) −0.500000 + 0.866025i −0.204124 + 0.353553i
\(7\) −0.500000 + 0.866025i −0.188982 + 0.327327i
\(8\) 1.00000 0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 1.63746 + 2.83616i 0.517810 + 0.896873i
\(11\) 2.00000 + 3.46410i 0.603023 + 1.04447i 0.992361 + 0.123371i \(0.0393705\pi\)
−0.389338 + 0.921095i \(0.627296\pi\)
\(12\) 1.00000 0.288675
\(13\) 3.50000 0.866025i 0.970725 0.240192i
\(14\) 1.00000 0.267261
\(15\) 1.63746 + 2.83616i 0.422790 + 0.732294i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.50000 + 2.59808i −0.363803 + 0.630126i −0.988583 0.150675i \(-0.951855\pi\)
0.624780 + 0.780801i \(0.285189\pi\)
\(18\) 1.00000 0.235702
\(19\) 4.27492 7.40437i 0.980733 1.69868i 0.321187 0.947016i \(-0.395918\pi\)
0.659546 0.751664i \(-0.270749\pi\)
\(20\) 1.63746 2.83616i 0.366147 0.634185i
\(21\) 1.00000 0.218218
\(22\) 2.00000 3.46410i 0.426401 0.738549i
\(23\) −1.13746 1.97014i −0.237177 0.410802i 0.722726 0.691134i \(-0.242889\pi\)
−0.959903 + 0.280332i \(0.909555\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) 5.72508 1.14502
\(26\) −2.50000 2.59808i −0.490290 0.509525i
\(27\) 1.00000 0.192450
\(28\) −0.500000 0.866025i −0.0944911 0.163663i
\(29\) −0.362541 0.627940i −0.0673222 0.116606i 0.830400 0.557168i \(-0.188112\pi\)
−0.897722 + 0.440563i \(0.854779\pi\)
\(30\) 1.63746 2.83616i 0.298958 0.517810i
\(31\) 6.27492 1.12701 0.563504 0.826113i \(-0.309453\pi\)
0.563504 + 0.826113i \(0.309453\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 2.00000 3.46410i 0.348155 0.603023i
\(34\) 3.00000 0.514496
\(35\) 1.63746 2.83616i 0.276781 0.479399i
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) 3.63746 + 6.30026i 0.597995 + 1.03576i 0.993117 + 0.117128i \(0.0373689\pi\)
−0.395122 + 0.918629i \(0.629298\pi\)
\(38\) −8.54983 −1.38697
\(39\) −2.50000 2.59808i −0.400320 0.416025i
\(40\) −3.27492 −0.517810
\(41\) −0.362541 0.627940i −0.0566195 0.0980678i 0.836326 0.548232i \(-0.184699\pi\)
−0.892946 + 0.450164i \(0.851366\pi\)
\(42\) −0.500000 0.866025i −0.0771517 0.133631i
\(43\) −5.41238 + 9.37451i −0.825380 + 1.42960i 0.0762493 + 0.997089i \(0.475706\pi\)
−0.901629 + 0.432511i \(0.857628\pi\)
\(44\) −4.00000 −0.603023
\(45\) 1.63746 2.83616i 0.244098 0.422790i
\(46\) −1.13746 + 1.97014i −0.167709 + 0.290481i
\(47\) 8.54983 1.24712 0.623561 0.781775i \(-0.285685\pi\)
0.623561 + 0.781775i \(0.285685\pi\)
\(48\) −0.500000 + 0.866025i −0.0721688 + 0.125000i
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) −2.86254 4.95807i −0.404824 0.701177i
\(51\) 3.00000 0.420084
\(52\) −1.00000 + 3.46410i −0.138675 + 0.480384i
\(53\) 11.5498 1.58649 0.793246 0.608901i \(-0.208390\pi\)
0.793246 + 0.608901i \(0.208390\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) −6.54983 11.3446i −0.883179 1.52971i
\(56\) −0.500000 + 0.866025i −0.0668153 + 0.115728i
\(57\) −8.54983 −1.13245
\(58\) −0.362541 + 0.627940i −0.0476040 + 0.0824526i
\(59\) −5.41238 + 9.37451i −0.704631 + 1.22046i 0.262193 + 0.965015i \(0.415554\pi\)
−0.966824 + 0.255442i \(0.917779\pi\)
\(60\) −3.27492 −0.422790
\(61\) 4.50000 7.79423i 0.576166 0.997949i −0.419748 0.907641i \(-0.637882\pi\)
0.995914 0.0903080i \(-0.0287851\pi\)
\(62\) −3.13746 5.43424i −0.398458 0.690149i
\(63\) −0.500000 0.866025i −0.0629941 0.109109i
\(64\) 1.00000 0.125000
\(65\) −11.4622 + 2.83616i −1.42171 + 0.351783i
\(66\) −4.00000 −0.492366
\(67\) 5.13746 + 8.89834i 0.627640 + 1.08711i 0.988024 + 0.154301i \(0.0493125\pi\)
−0.360383 + 0.932804i \(0.617354\pi\)
\(68\) −1.50000 2.59808i −0.181902 0.315063i
\(69\) −1.13746 + 1.97014i −0.136934 + 0.237177i
\(70\) −3.27492 −0.391427
\(71\) 1.13746 1.97014i 0.134992 0.233812i −0.790603 0.612329i \(-0.790233\pi\)
0.925594 + 0.378517i \(0.123566\pi\)
\(72\) −0.500000 + 0.866025i −0.0589256 + 0.102062i
\(73\) 13.2749 1.55371 0.776856 0.629679i \(-0.216813\pi\)
0.776856 + 0.629679i \(0.216813\pi\)
\(74\) 3.63746 6.30026i 0.422846 0.732391i
\(75\) −2.86254 4.95807i −0.330538 0.572508i
\(76\) 4.27492 + 7.40437i 0.490367 + 0.849340i
\(77\) −4.00000 −0.455842
\(78\) −1.00000 + 3.46410i −0.113228 + 0.392232i
\(79\) −8.00000 −0.900070 −0.450035 0.893011i \(-0.648589\pi\)
−0.450035 + 0.893011i \(0.648589\pi\)
\(80\) 1.63746 + 2.83616i 0.183073 + 0.317092i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −0.362541 + 0.627940i −0.0400360 + 0.0693444i
\(83\) 10.8248 1.18817 0.594085 0.804402i \(-0.297514\pi\)
0.594085 + 0.804402i \(0.297514\pi\)
\(84\) −0.500000 + 0.866025i −0.0545545 + 0.0944911i
\(85\) 4.91238 8.50848i 0.532822 0.922875i
\(86\) 10.8248 1.16726
\(87\) −0.362541 + 0.627940i −0.0388685 + 0.0673222i
\(88\) 2.00000 + 3.46410i 0.213201 + 0.369274i
\(89\) −4.13746 7.16629i −0.438570 0.759625i 0.559010 0.829161i \(-0.311181\pi\)
−0.997579 + 0.0695360i \(0.977848\pi\)
\(90\) −3.27492 −0.345207
\(91\) −1.00000 + 3.46410i −0.104828 + 0.363137i
\(92\) 2.27492 0.237177
\(93\) −3.13746 5.43424i −0.325339 0.563504i
\(94\) −4.27492 7.40437i −0.440924 0.763703i
\(95\) −14.0000 + 24.2487i −1.43637 + 2.48787i
\(96\) 1.00000 0.102062
\(97\) −7.27492 + 12.6005i −0.738656 + 1.27939i 0.214445 + 0.976736i \(0.431206\pi\)
−0.953101 + 0.302653i \(0.902128\pi\)
\(98\) −0.500000 + 0.866025i −0.0505076 + 0.0874818i
\(99\) −4.00000 −0.402015
\(100\) −2.86254 + 4.95807i −0.286254 + 0.495807i
\(101\) −4.63746 8.03231i −0.461444 0.799245i 0.537589 0.843207i \(-0.319335\pi\)
−0.999033 + 0.0439620i \(0.986002\pi\)
\(102\) −1.50000 2.59808i −0.148522 0.257248i
\(103\) −2.27492 −0.224154 −0.112077 0.993700i \(-0.535750\pi\)
−0.112077 + 0.993700i \(0.535750\pi\)
\(104\) 3.50000 0.866025i 0.343203 0.0849208i
\(105\) −3.27492 −0.319599
\(106\) −5.77492 10.0025i −0.560910 0.971524i
\(107\) 6.27492 + 10.8685i 0.606619 + 1.05070i 0.991793 + 0.127851i \(0.0408080\pi\)
−0.385174 + 0.922844i \(0.625859\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) 10.5498 1.01049 0.505245 0.862976i \(-0.331402\pi\)
0.505245 + 0.862976i \(0.331402\pi\)
\(110\) −6.54983 + 11.3446i −0.624502 + 1.08167i
\(111\) 3.63746 6.30026i 0.345252 0.597995i
\(112\) 1.00000 0.0944911
\(113\) 3.91238 6.77643i 0.368045 0.637473i −0.621215 0.783641i \(-0.713360\pi\)
0.989260 + 0.146167i \(0.0466938\pi\)
\(114\) 4.27492 + 7.40437i 0.400383 + 0.693483i
\(115\) 3.72508 + 6.45203i 0.347366 + 0.601655i
\(116\) 0.725083 0.0673222
\(117\) −1.00000 + 3.46410i −0.0924500 + 0.320256i
\(118\) 10.8248 0.996499
\(119\) −1.50000 2.59808i −0.137505 0.238165i
\(120\) 1.63746 + 2.83616i 0.149479 + 0.258905i
\(121\) −2.50000 + 4.33013i −0.227273 + 0.393648i
\(122\) −9.00000 −0.814822
\(123\) −0.362541 + 0.627940i −0.0326893 + 0.0566195i
\(124\) −3.13746 + 5.43424i −0.281752 + 0.488009i
\(125\) −2.37459 −0.212389
\(126\) −0.500000 + 0.866025i −0.0445435 + 0.0771517i
\(127\) −4.00000 6.92820i −0.354943 0.614779i 0.632166 0.774833i \(-0.282166\pi\)
−0.987108 + 0.160055i \(0.948833\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 10.8248 0.953066
\(130\) 8.18729 + 8.50848i 0.718073 + 0.746243i
\(131\) −10.2749 −0.897724 −0.448862 0.893601i \(-0.648170\pi\)
−0.448862 + 0.893601i \(0.648170\pi\)
\(132\) 2.00000 + 3.46410i 0.174078 + 0.301511i
\(133\) 4.27492 + 7.40437i 0.370682 + 0.642041i
\(134\) 5.13746 8.89834i 0.443809 0.768699i
\(135\) −3.27492 −0.281860
\(136\) −1.50000 + 2.59808i −0.128624 + 0.222783i
\(137\) −0.0876242 + 0.151770i −0.00748624 + 0.0129665i −0.869744 0.493503i \(-0.835716\pi\)
0.862258 + 0.506469i \(0.169050\pi\)
\(138\) 2.27492 0.193654
\(139\) −10.5498 + 18.2728i −0.894825 + 1.54988i −0.0608046 + 0.998150i \(0.519367\pi\)
−0.834021 + 0.551733i \(0.813967\pi\)
\(140\) 1.63746 + 2.83616i 0.138391 + 0.239699i
\(141\) −4.27492 7.40437i −0.360013 0.623561i
\(142\) −2.27492 −0.190907
\(143\) 10.0000 + 10.3923i 0.836242 + 0.869048i
\(144\) 1.00000 0.0833333
\(145\) 1.18729 + 2.05645i 0.0985993 + 0.170779i
\(146\) −6.63746 11.4964i −0.549320 0.951450i
\(147\) −0.500000 + 0.866025i −0.0412393 + 0.0714286i
\(148\) −7.27492 −0.597995
\(149\) 0.500000 0.866025i 0.0409616 0.0709476i −0.844818 0.535054i \(-0.820291\pi\)
0.885779 + 0.464107i \(0.153625\pi\)
\(150\) −2.86254 + 4.95807i −0.233726 + 0.404824i
\(151\) −17.0997 −1.39155 −0.695776 0.718259i \(-0.744939\pi\)
−0.695776 + 0.718259i \(0.744939\pi\)
\(152\) 4.27492 7.40437i 0.346742 0.600574i
\(153\) −1.50000 2.59808i −0.121268 0.210042i
\(154\) 2.00000 + 3.46410i 0.161165 + 0.279145i
\(155\) −20.5498 −1.65060
\(156\) 3.50000 0.866025i 0.280224 0.0693375i
\(157\) −11.2749 −0.899836 −0.449918 0.893070i \(-0.648547\pi\)
−0.449918 + 0.893070i \(0.648547\pi\)
\(158\) 4.00000 + 6.92820i 0.318223 + 0.551178i
\(159\) −5.77492 10.0025i −0.457981 0.793246i
\(160\) 1.63746 2.83616i 0.129452 0.224218i
\(161\) 2.27492 0.179289
\(162\) −0.500000 + 0.866025i −0.0392837 + 0.0680414i
\(163\) 2.86254 4.95807i 0.224212 0.388346i −0.731871 0.681443i \(-0.761353\pi\)
0.956083 + 0.293097i \(0.0946860\pi\)
\(164\) 0.725083 0.0566195
\(165\) −6.54983 + 11.3446i −0.509904 + 0.883179i
\(166\) −5.41238 9.37451i −0.420082 0.727603i
\(167\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(168\) 1.00000 0.0771517
\(169\) 11.5000 6.06218i 0.884615 0.466321i
\(170\) −9.82475 −0.753524
\(171\) 4.27492 + 7.40437i 0.326911 + 0.566227i
\(172\) −5.41238 9.37451i −0.412690 0.714800i
\(173\) −5.27492 + 9.13642i −0.401045 + 0.694630i −0.993852 0.110715i \(-0.964686\pi\)
0.592808 + 0.805344i \(0.298019\pi\)
\(174\) 0.725083 0.0549684
\(175\) −2.86254 + 4.95807i −0.216388 + 0.374795i
\(176\) 2.00000 3.46410i 0.150756 0.261116i
\(177\) 10.8248 0.813638
\(178\) −4.13746 + 7.16629i −0.310116 + 0.537136i
\(179\) −8.27492 14.3326i −0.618496 1.07127i −0.989760 0.142740i \(-0.954409\pi\)
0.371264 0.928527i \(-0.378925\pi\)
\(180\) 1.63746 + 2.83616i 0.122049 + 0.211395i
\(181\) 5.82475 0.432950 0.216475 0.976288i \(-0.430544\pi\)
0.216475 + 0.976288i \(0.430544\pi\)
\(182\) 3.50000 0.866025i 0.259437 0.0641941i
\(183\) −9.00000 −0.665299
\(184\) −1.13746 1.97014i −0.0838546 0.145240i
\(185\) −11.9124 20.6328i −0.875815 1.51696i
\(186\) −3.13746 + 5.43424i −0.230050 + 0.398458i
\(187\) −12.0000 −0.877527
\(188\) −4.27492 + 7.40437i −0.311780 + 0.540019i
\(189\) −0.500000 + 0.866025i −0.0363696 + 0.0629941i
\(190\) 28.0000 2.03133
\(191\) −7.13746 + 12.3624i −0.516448 + 0.894515i 0.483369 + 0.875417i \(0.339413\pi\)
−0.999818 + 0.0190983i \(0.993920\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) 1.08762 + 1.88382i 0.0782889 + 0.135600i 0.902512 0.430665i \(-0.141721\pi\)
−0.824223 + 0.566266i \(0.808388\pi\)
\(194\) 14.5498 1.04462
\(195\) 8.18729 + 8.50848i 0.586304 + 0.609305i
\(196\) 1.00000 0.0714286
\(197\) −0.412376 0.714256i −0.0293806 0.0508886i 0.850961 0.525228i \(-0.176020\pi\)
−0.880342 + 0.474340i \(0.842687\pi\)
\(198\) 2.00000 + 3.46410i 0.142134 + 0.246183i
\(199\) 5.41238 9.37451i 0.383673 0.664541i −0.607911 0.794005i \(-0.707992\pi\)
0.991584 + 0.129464i \(0.0413256\pi\)
\(200\) 5.72508 0.404824
\(201\) 5.13746 8.89834i 0.362368 0.627640i
\(202\) −4.63746 + 8.03231i −0.326290 + 0.565152i
\(203\) 0.725083 0.0508908
\(204\) −1.50000 + 2.59808i −0.105021 + 0.181902i
\(205\) 1.18729 + 2.05645i 0.0829241 + 0.143629i
\(206\) 1.13746 + 1.97014i 0.0792505 + 0.137266i
\(207\) 2.27492 0.158118
\(208\) −2.50000 2.59808i −0.173344 0.180144i
\(209\) 34.1993 2.36562
\(210\) 1.63746 + 2.83616i 0.112995 + 0.195714i
\(211\) 4.54983 + 7.88054i 0.313224 + 0.542519i 0.979058 0.203580i \(-0.0652578\pi\)
−0.665835 + 0.746099i \(0.731924\pi\)
\(212\) −5.77492 + 10.0025i −0.396623 + 0.686971i
\(213\) −2.27492 −0.155875
\(214\) 6.27492 10.8685i 0.428945 0.742954i
\(215\) 17.7251 30.7007i 1.20884 2.09377i
\(216\) 1.00000 0.0680414
\(217\) −3.13746 + 5.43424i −0.212985 + 0.368900i
\(218\) −5.27492 9.13642i −0.357262 0.618797i
\(219\) −6.63746 11.4964i −0.448518 0.776856i
\(220\) 13.0997 0.883179
\(221\) −3.00000 + 10.3923i −0.201802 + 0.699062i
\(222\) −7.27492 −0.488260
\(223\) −9.13746 15.8265i −0.611889 1.05982i −0.990922 0.134440i \(-0.957076\pi\)
0.379032 0.925383i \(-0.376257\pi\)
\(224\) −0.500000 0.866025i −0.0334077 0.0578638i
\(225\) −2.86254 + 4.95807i −0.190836 + 0.330538i
\(226\) −7.82475 −0.520495
\(227\) −4.54983 + 7.88054i −0.301983 + 0.523050i −0.976585 0.215132i \(-0.930982\pi\)
0.674602 + 0.738182i \(0.264315\pi\)
\(228\) 4.27492 7.40437i 0.283113 0.490367i
\(229\) 20.2749 1.33980 0.669902 0.742449i \(-0.266336\pi\)
0.669902 + 0.742449i \(0.266336\pi\)
\(230\) 3.72508 6.45203i 0.245625 0.425434i
\(231\) 2.00000 + 3.46410i 0.131590 + 0.227921i
\(232\) −0.362541 0.627940i −0.0238020 0.0412263i
\(233\) 22.5498 1.47729 0.738644 0.674095i \(-0.235466\pi\)
0.738644 + 0.674095i \(0.235466\pi\)
\(234\) 3.50000 0.866025i 0.228802 0.0566139i
\(235\) −28.0000 −1.82652
\(236\) −5.41238 9.37451i −0.352316 0.610229i
\(237\) 4.00000 + 6.92820i 0.259828 + 0.450035i
\(238\) −1.50000 + 2.59808i −0.0972306 + 0.168408i
\(239\) 2.27492 0.147152 0.0735761 0.997290i \(-0.476559\pi\)
0.0735761 + 0.997290i \(0.476559\pi\)
\(240\) 1.63746 2.83616i 0.105697 0.183073i
\(241\) 11.6375 20.1567i 0.749635 1.29841i −0.198363 0.980129i \(-0.563563\pi\)
0.947998 0.318277i \(-0.103104\pi\)
\(242\) 5.00000 0.321412
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 4.50000 + 7.79423i 0.288083 + 0.498974i
\(245\) 1.63746 + 2.83616i 0.104613 + 0.181196i
\(246\) 0.725083 0.0462296
\(247\) 8.54983 29.6175i 0.544013 1.88452i
\(248\) 6.27492 0.398458
\(249\) −5.41238 9.37451i −0.342995 0.594085i
\(250\) 1.18729 + 2.05645i 0.0750910 + 0.130061i
\(251\) −2.86254 + 4.95807i −0.180682 + 0.312950i −0.942113 0.335296i \(-0.891164\pi\)
0.761431 + 0.648246i \(0.224497\pi\)
\(252\) 1.00000 0.0629941
\(253\) 4.54983 7.88054i 0.286046 0.495446i
\(254\) −4.00000 + 6.92820i −0.250982 + 0.434714i
\(255\) −9.82475 −0.615250
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −7.50000 12.9904i −0.467837 0.810318i 0.531487 0.847066i \(-0.321633\pi\)
−0.999325 + 0.0367485i \(0.988300\pi\)
\(258\) −5.41238 9.37451i −0.336960 0.583631i
\(259\) −7.27492 −0.452041
\(260\) 3.27492 11.3446i 0.203102 0.703565i
\(261\) 0.725083 0.0448815
\(262\) 5.13746 + 8.89834i 0.317393 + 0.549741i
\(263\) 4.54983 + 7.88054i 0.280555 + 0.485935i 0.971522 0.236951i \(-0.0761482\pi\)
−0.690967 + 0.722887i \(0.742815\pi\)
\(264\) 2.00000 3.46410i 0.123091 0.213201i
\(265\) −37.8248 −2.32356
\(266\) 4.27492 7.40437i 0.262112 0.453991i
\(267\) −4.13746 + 7.16629i −0.253208 + 0.438570i
\(268\) −10.2749 −0.627640
\(269\) 9.00000 15.5885i 0.548740 0.950445i −0.449622 0.893219i \(-0.648441\pi\)
0.998361 0.0572259i \(-0.0182255\pi\)
\(270\) 1.63746 + 2.83616i 0.0996526 + 0.172603i
\(271\) −8.86254 15.3504i −0.538361 0.932469i −0.998993 0.0448772i \(-0.985710\pi\)
0.460631 0.887591i \(-0.347623\pi\)
\(272\) 3.00000 0.181902
\(273\) 3.50000 0.866025i 0.211830 0.0524142i
\(274\) 0.175248 0.0105871
\(275\) 11.4502 + 19.8323i 0.690471 + 1.19593i
\(276\) −1.13746 1.97014i −0.0684670 0.118588i
\(277\) 3.91238 6.77643i 0.235072 0.407156i −0.724222 0.689567i \(-0.757801\pi\)
0.959294 + 0.282411i \(0.0911341\pi\)
\(278\) 21.0997 1.26547
\(279\) −3.13746 + 5.43424i −0.187835 + 0.325339i
\(280\) 1.63746 2.83616i 0.0978569 0.169493i
\(281\) 1.82475 0.108856 0.0544278 0.998518i \(-0.482667\pi\)
0.0544278 + 0.998518i \(0.482667\pi\)
\(282\) −4.27492 + 7.40437i −0.254568 + 0.440924i
\(283\) 12.2749 + 21.2608i 0.729668 + 1.26382i 0.957024 + 0.290010i \(0.0936588\pi\)
−0.227355 + 0.973812i \(0.573008\pi\)
\(284\) 1.13746 + 1.97014i 0.0674958 + 0.116906i
\(285\) 28.0000 1.65858
\(286\) 4.00000 13.8564i 0.236525 0.819346i
\(287\) 0.725083 0.0428003
\(288\) −0.500000 0.866025i −0.0294628 0.0510310i
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) 1.18729 2.05645i 0.0697202 0.120759i
\(291\) 14.5498 0.852926
\(292\) −6.63746 + 11.4964i −0.388428 + 0.672777i
\(293\) 5.36254 9.28819i 0.313283 0.542622i −0.665788 0.746141i \(-0.731904\pi\)
0.979071 + 0.203519i \(0.0652378\pi\)
\(294\) 1.00000 0.0583212
\(295\) 17.7251 30.7007i 1.03199 1.78747i
\(296\) 3.63746 + 6.30026i 0.211423 + 0.366195i
\(297\) 2.00000 + 3.46410i 0.116052 + 0.201008i
\(298\) −1.00000 −0.0579284
\(299\) −5.68729 5.91041i −0.328905 0.341808i
\(300\) 5.72508 0.330538
\(301\) −5.41238 9.37451i −0.311964 0.540338i
\(302\) 8.54983 + 14.8087i 0.491988 + 0.852148i
\(303\) −4.63746 + 8.03231i −0.266415 + 0.461444i
\(304\) −8.54983 −0.490367
\(305\) −14.7371 + 25.5255i −0.843845 + 1.46158i
\(306\) −1.50000 + 2.59808i −0.0857493 + 0.148522i
\(307\) −16.5498 −0.944549 −0.472274 0.881452i \(-0.656567\pi\)
−0.472274 + 0.881452i \(0.656567\pi\)
\(308\) 2.00000 3.46410i 0.113961 0.197386i
\(309\) 1.13746 + 1.97014i 0.0647078 + 0.112077i
\(310\) 10.2749 + 17.7967i 0.583576 + 1.01078i
\(311\) 12.5498 0.711636 0.355818 0.934555i \(-0.384202\pi\)
0.355818 + 0.934555i \(0.384202\pi\)
\(312\) −2.50000 2.59808i −0.141535 0.147087i
\(313\) −27.6495 −1.56284 −0.781421 0.624004i \(-0.785505\pi\)
−0.781421 + 0.624004i \(0.785505\pi\)
\(314\) 5.63746 + 9.76436i 0.318140 + 0.551035i
\(315\) 1.63746 + 2.83616i 0.0922603 + 0.159800i
\(316\) 4.00000 6.92820i 0.225018 0.389742i
\(317\) 7.54983 0.424041 0.212020 0.977265i \(-0.431996\pi\)
0.212020 + 0.977265i \(0.431996\pi\)
\(318\) −5.77492 + 10.0025i −0.323841 + 0.560910i
\(319\) 1.45017 2.51176i 0.0811937 0.140632i
\(320\) −3.27492 −0.183073
\(321\) 6.27492 10.8685i 0.350232 0.606619i
\(322\) −1.13746 1.97014i −0.0633881 0.109791i
\(323\) 12.8248 + 22.2131i 0.713588 + 1.23597i
\(324\) 1.00000 0.0555556
\(325\) 20.0378 4.95807i 1.11150 0.275024i
\(326\) −5.72508 −0.317083
\(327\) −5.27492 9.13642i −0.291704 0.505245i
\(328\) −0.362541 0.627940i −0.0200180 0.0346722i
\(329\) −4.27492 + 7.40437i −0.235684 + 0.408216i
\(330\) 13.0997 0.721113
\(331\) −2.00000 + 3.46410i −0.109930 + 0.190404i −0.915742 0.401768i \(-0.868396\pi\)
0.805812 + 0.592172i \(0.201729\pi\)
\(332\) −5.41238 + 9.37451i −0.297043 + 0.514493i
\(333\) −7.27492 −0.398663
\(334\) 0 0
\(335\) −16.8248 29.1413i −0.919234 1.59216i
\(336\) −0.500000 0.866025i −0.0272772 0.0472456i
\(337\) −7.27492 −0.396290 −0.198145 0.980173i \(-0.563492\pi\)
−0.198145 + 0.980173i \(0.563492\pi\)
\(338\) −11.0000 6.92820i −0.598321 0.376845i
\(339\) −7.82475 −0.424982
\(340\) 4.91238 + 8.50848i 0.266411 + 0.461437i
\(341\) 12.5498 + 21.7370i 0.679612 + 1.17712i
\(342\) 4.27492 7.40437i 0.231161 0.400383i
\(343\) 1.00000 0.0539949
\(344\) −5.41238 + 9.37451i −0.291816 + 0.505440i
\(345\) 3.72508 6.45203i 0.200552 0.347366i
\(346\) 10.5498 0.567163
\(347\) −7.72508 + 13.3802i −0.414704 + 0.718289i −0.995397 0.0958338i \(-0.969448\pi\)
0.580693 + 0.814122i \(0.302782\pi\)
\(348\) −0.362541 0.627940i −0.0194343 0.0336611i
\(349\) −8.96221 15.5230i −0.479736 0.830927i 0.519994 0.854170i \(-0.325934\pi\)
−0.999730 + 0.0232427i \(0.992601\pi\)
\(350\) 5.72508 0.306019
\(351\) 3.50000 0.866025i 0.186816 0.0462250i
\(352\) −4.00000 −0.213201
\(353\) 2.22508 + 3.85396i 0.118429 + 0.205125i 0.919145 0.393919i \(-0.128881\pi\)
−0.800716 + 0.599044i \(0.795547\pi\)
\(354\) −5.41238 9.37451i −0.287665 0.498250i
\(355\) −3.72508 + 6.45203i −0.197707 + 0.342438i
\(356\) 8.27492 0.438570
\(357\) −1.50000 + 2.59808i −0.0793884 + 0.137505i
\(358\) −8.27492 + 14.3326i −0.437343 + 0.757500i
\(359\) 29.0997 1.53582 0.767911 0.640557i \(-0.221296\pi\)
0.767911 + 0.640557i \(0.221296\pi\)
\(360\) 1.63746 2.83616i 0.0863016 0.149479i
\(361\) −27.0498 46.8517i −1.42368 2.46588i
\(362\) −2.91238 5.04438i −0.153071 0.265127i
\(363\) 5.00000 0.262432
\(364\) −2.50000 2.59808i −0.131036 0.136176i
\(365\) −43.4743 −2.27555
\(366\) 4.50000 + 7.79423i 0.235219 + 0.407411i
\(367\) −2.86254 4.95807i −0.149423 0.258809i 0.781591 0.623791i \(-0.214408\pi\)
−0.931015 + 0.364982i \(0.881075\pi\)
\(368\) −1.13746 + 1.97014i −0.0592941 + 0.102700i
\(369\) 0.725083 0.0377463
\(370\) −11.9124 + 20.6328i −0.619295 + 1.07265i
\(371\) −5.77492 + 10.0025i −0.299819 + 0.519301i
\(372\) 6.27492 0.325339
\(373\) −2.08762 + 3.61587i −0.108093 + 0.187223i −0.914998 0.403459i \(-0.867808\pi\)
0.806905 + 0.590682i \(0.201141\pi\)
\(374\) 6.00000 + 10.3923i 0.310253 + 0.537373i
\(375\) 1.18729 + 2.05645i 0.0613115 + 0.106195i
\(376\) 8.54983 0.440924
\(377\) −1.81271 1.88382i −0.0933592 0.0970217i
\(378\) 1.00000 0.0514344
\(379\) 10.0000 + 17.3205i 0.513665 + 0.889695i 0.999874 + 0.0158521i \(0.00504609\pi\)
−0.486209 + 0.873843i \(0.661621\pi\)
\(380\) −14.0000 24.2487i −0.718185 1.24393i
\(381\) −4.00000 + 6.92820i −0.204926 + 0.354943i
\(382\) 14.2749 0.730368
\(383\) 19.0997 33.0816i 0.975947 1.69039i 0.299175 0.954198i \(-0.403288\pi\)
0.676772 0.736192i \(-0.263378\pi\)
\(384\) −0.500000 + 0.866025i −0.0255155 + 0.0441942i
\(385\) 13.0997 0.667621
\(386\) 1.08762 1.88382i 0.0553586 0.0958839i
\(387\) −5.41238 9.37451i −0.275127 0.476533i
\(388\) −7.27492 12.6005i −0.369328 0.639695i
\(389\) 20.6495 1.04697 0.523486 0.852034i \(-0.324631\pi\)
0.523486 + 0.852034i \(0.324631\pi\)
\(390\) 3.27492 11.3446i 0.165832 0.574458i
\(391\) 6.82475 0.345143
\(392\) −0.500000 0.866025i −0.0252538 0.0437409i
\(393\) 5.13746 + 8.89834i 0.259151 + 0.448862i
\(394\) −0.412376 + 0.714256i −0.0207752 + 0.0359837i
\(395\) 26.1993 1.31823
\(396\) 2.00000 3.46410i 0.100504 0.174078i
\(397\) −7.86254 + 13.6183i −0.394610 + 0.683484i −0.993051 0.117682i \(-0.962454\pi\)
0.598442 + 0.801166i \(0.295787\pi\)
\(398\) −10.8248 −0.542596
\(399\) 4.27492 7.40437i 0.214014 0.370682i
\(400\) −2.86254 4.95807i −0.143127 0.247903i
\(401\) −2.63746 4.56821i −0.131708 0.228126i 0.792627 0.609707i \(-0.208713\pi\)
−0.924335 + 0.381581i \(0.875380\pi\)
\(402\) −10.2749 −0.512466
\(403\) 21.9622 5.43424i 1.09402 0.270699i
\(404\) 9.27492 0.461444
\(405\) 1.63746 + 2.83616i 0.0813660 + 0.140930i
\(406\) −0.362541 0.627940i −0.0179926 0.0311641i
\(407\) −14.5498 + 25.2011i −0.721209 + 1.24917i
\(408\) 3.00000 0.148522
\(409\) −11.4622 + 19.8531i −0.566770 + 0.981674i 0.430113 + 0.902775i \(0.358474\pi\)
−0.996883 + 0.0788990i \(0.974860\pi\)
\(410\) 1.18729 2.05645i 0.0586362 0.101561i
\(411\) 0.175248 0.00864436
\(412\) 1.13746 1.97014i 0.0560386 0.0970616i
\(413\) −5.41238 9.37451i −0.266326 0.461289i
\(414\) −1.13746 1.97014i −0.0559030 0.0968269i
\(415\) −35.4502 −1.74018
\(416\) −1.00000 + 3.46410i −0.0490290 + 0.169842i
\(417\) 21.0997 1.03326
\(418\) −17.0997 29.6175i −0.836372 1.44864i
\(419\) −7.68729 13.3148i −0.375549 0.650470i 0.614860 0.788636i \(-0.289212\pi\)
−0.990409 + 0.138166i \(0.955879\pi\)
\(420\) 1.63746 2.83616i 0.0798998 0.138391i
\(421\) 0.725083 0.0353384 0.0176692 0.999844i \(-0.494375\pi\)
0.0176692 + 0.999844i \(0.494375\pi\)
\(422\) 4.54983 7.88054i 0.221482 0.383619i
\(423\) −4.27492 + 7.40437i −0.207854 + 0.360013i
\(424\) 11.5498 0.560910
\(425\) −8.58762 + 14.8742i −0.416561 + 0.721505i
\(426\) 1.13746 + 1.97014i 0.0551100 + 0.0954534i
\(427\) 4.50000 + 7.79423i 0.217770 + 0.377189i
\(428\) −12.5498 −0.606619
\(429\) 4.00000 13.8564i 0.193122 0.668994i
\(430\) −35.4502 −1.70956
\(431\) 2.86254 + 4.95807i 0.137884 + 0.238822i 0.926695 0.375813i \(-0.122637\pi\)
−0.788812 + 0.614635i \(0.789303\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) 1.36254 2.35999i 0.0654796 0.113414i −0.831427 0.555634i \(-0.812476\pi\)
0.896907 + 0.442220i \(0.145809\pi\)
\(434\) 6.27492 0.301206
\(435\) 1.18729 2.05645i 0.0569263 0.0985993i
\(436\) −5.27492 + 9.13642i −0.252623 + 0.437555i
\(437\) −19.4502 −0.930428
\(438\) −6.63746 + 11.4964i −0.317150 + 0.549320i
\(439\) 8.54983 + 14.8087i 0.408061 + 0.706783i 0.994672 0.103086i \(-0.0328716\pi\)
−0.586611 + 0.809869i \(0.699538\pi\)
\(440\) −6.54983 11.3446i −0.312251 0.540835i
\(441\) 1.00000 0.0476190
\(442\) 10.5000 2.59808i 0.499434 0.123578i
\(443\) 19.4502 0.924105 0.462053 0.886853i \(-0.347113\pi\)
0.462053 + 0.886853i \(0.347113\pi\)
\(444\) 3.63746 + 6.30026i 0.172626 + 0.298997i
\(445\) 13.5498 + 23.4690i 0.642324 + 1.11254i
\(446\) −9.13746 + 15.8265i −0.432671 + 0.749409i
\(447\) −1.00000 −0.0472984
\(448\) −0.500000 + 0.866025i −0.0236228 + 0.0409159i
\(449\) −5.54983 + 9.61260i −0.261913 + 0.453646i −0.966750 0.255723i \(-0.917687\pi\)
0.704837 + 0.709369i \(0.251020\pi\)
\(450\) 5.72508 0.269883
\(451\) 1.45017 2.51176i 0.0682856 0.118274i
\(452\) 3.91238 + 6.77643i 0.184023 + 0.318737i
\(453\) 8.54983 + 14.8087i 0.401706 + 0.695776i
\(454\) 9.09967 0.427069
\(455\) 3.27492 11.3446i 0.153530 0.531845i
\(456\) −8.54983 −0.400383
\(457\) 8.50000 + 14.7224i 0.397613 + 0.688686i 0.993431 0.114433i \(-0.0365053\pi\)
−0.595818 + 0.803120i \(0.703172\pi\)
\(458\) −10.1375 17.5586i −0.473692 0.820459i
\(459\) −1.50000 + 2.59808i −0.0700140 + 0.121268i
\(460\) −7.45017 −0.347366
\(461\) −9.18729 + 15.9129i −0.427895 + 0.741136i −0.996686 0.0813464i \(-0.974078\pi\)
0.568791 + 0.822482i \(0.307411\pi\)
\(462\) 2.00000 3.46410i 0.0930484 0.161165i
\(463\) 4.54983 0.211449 0.105724 0.994395i \(-0.466284\pi\)
0.105724 + 0.994395i \(0.466284\pi\)
\(464\) −0.362541 + 0.627940i −0.0168306 + 0.0291514i
\(465\) 10.2749 + 17.7967i 0.476488 + 0.825301i
\(466\) −11.2749 19.5287i −0.522300 0.904651i
\(467\) −30.8248 −1.42640 −0.713200 0.700961i \(-0.752755\pi\)
−0.713200 + 0.700961i \(0.752755\pi\)
\(468\) −2.50000 2.59808i −0.115563 0.120096i
\(469\) −10.2749 −0.474452
\(470\) 14.0000 + 24.2487i 0.645772 + 1.11851i
\(471\) 5.63746 + 9.76436i 0.259760 + 0.449918i
\(472\) −5.41238 + 9.37451i −0.249125 + 0.431497i
\(473\) −43.2990 −1.99089
\(474\) 4.00000 6.92820i 0.183726 0.318223i
\(475\) 24.4743 42.3907i 1.12296 1.94502i
\(476\) 3.00000 0.137505
\(477\) −5.77492 + 10.0025i −0.264415 + 0.457981i
\(478\) −1.13746 1.97014i −0.0520261 0.0901119i
\(479\) −10.0000 17.3205i −0.456912 0.791394i 0.541884 0.840453i \(-0.317711\pi\)
−0.998796 + 0.0490589i \(0.984378\pi\)
\(480\) −3.27492 −0.149479
\(481\) 18.1873 + 18.9008i 0.829269 + 0.861802i
\(482\) −23.2749 −1.06014
\(483\) −1.13746 1.97014i −0.0517562 0.0896443i
\(484\) −2.50000 4.33013i −0.113636 0.196824i
\(485\) 23.8248 41.2657i 1.08183 1.87378i
\(486\) 1.00000 0.0453609
\(487\) −14.5498 + 25.2011i −0.659316 + 1.14197i 0.321477 + 0.946917i \(0.395821\pi\)
−0.980793 + 0.195051i \(0.937513\pi\)
\(488\) 4.50000 7.79423i 0.203705 0.352828i
\(489\) −5.72508 −0.258897
\(490\) 1.63746 2.83616i 0.0739728 0.128125i
\(491\) 2.54983 + 4.41644i 0.115072 + 0.199311i 0.917809 0.397023i \(-0.129957\pi\)
−0.802736 + 0.596334i \(0.796623\pi\)
\(492\) −0.362541 0.627940i −0.0163446 0.0283097i
\(493\) 2.17525 0.0979683
\(494\) −29.9244 + 7.40437i −1.34636 + 0.333139i
\(495\) 13.0997 0.588786
\(496\) −3.13746 5.43424i −0.140876 0.244004i
\(497\) 1.13746 + 1.97014i 0.0510220 + 0.0883727i
\(498\) −5.41238 + 9.37451i −0.242534 + 0.420082i
\(499\) −9.17525 −0.410741 −0.205370 0.978684i \(-0.565840\pi\)
−0.205370 + 0.978684i \(0.565840\pi\)
\(500\) 1.18729 2.05645i 0.0530974 0.0919673i
\(501\) 0 0
\(502\) 5.72508 0.255523
\(503\) −4.54983 + 7.88054i −0.202867 + 0.351376i −0.949451 0.313915i \(-0.898359\pi\)
0.746584 + 0.665291i \(0.231693\pi\)
\(504\) −0.500000 0.866025i −0.0222718 0.0385758i
\(505\) 15.1873 + 26.3052i 0.675826 + 1.17056i
\(506\) −9.09967 −0.404530
\(507\) −11.0000 6.92820i −0.488527 0.307692i
\(508\) 8.00000 0.354943
\(509\) 17.9124 + 31.0251i 0.793952 + 1.37517i 0.923502 + 0.383593i \(0.125313\pi\)
−0.129550 + 0.991573i \(0.541353\pi\)
\(510\) 4.91238 + 8.50848i 0.217524 + 0.376762i
\(511\) −6.63746 + 11.4964i −0.293624 + 0.508571i
\(512\) 1.00000 0.0441942
\(513\) 4.27492 7.40437i 0.188742 0.326911i
\(514\) −7.50000 + 12.9904i −0.330811 + 0.572981i
\(515\) 7.45017 0.328294
\(516\) −5.41238 + 9.37451i −0.238267 + 0.412690i
\(517\) 17.0997 + 29.6175i 0.752043 + 1.30258i
\(518\) 3.63746 + 6.30026i 0.159821 + 0.276818i
\(519\) 10.5498 0.463086
\(520\) −11.4622 + 2.83616i −0.502651 + 0.124374i
\(521\) 1.82475 0.0799438 0.0399719 0.999201i \(-0.487273\pi\)
0.0399719 + 0.999201i \(0.487273\pi\)
\(522\) −0.362541 0.627940i −0.0158680 0.0274842i
\(523\) −17.0997 29.6175i −0.747716 1.29508i −0.948915 0.315532i \(-0.897817\pi\)
0.201199 0.979550i \(-0.435516\pi\)
\(524\) 5.13746 8.89834i 0.224431 0.388726i
\(525\) 5.72508 0.249863
\(526\) 4.54983 7.88054i 0.198382 0.343608i
\(527\) −9.41238 + 16.3027i −0.410010 + 0.710157i
\(528\) −4.00000 −0.174078
\(529\) 8.91238 15.4367i 0.387495 0.671160i
\(530\) 18.9124 + 32.7572i 0.821501 + 1.42288i
\(531\) −5.41238 9.37451i −0.234877 0.406819i
\(532\) −8.54983 −0.370682
\(533\) −1.81271 1.88382i −0.0785171 0.0815973i
\(534\) 8.27492 0.358091
\(535\) −20.5498 35.5934i −0.888447 1.53884i
\(536\) 5.13746 + 8.89834i 0.221904 + 0.384350i
\(537\) −8.27492 + 14.3326i −0.357089 + 0.618496i
\(538\) −18.0000 −0.776035
\(539\) 2.00000 3.46410i 0.0861461 0.149209i
\(540\) 1.63746 2.83616i 0.0704650 0.122049i
\(541\) −12.3746 −0.532025 −0.266013 0.963970i \(-0.585706\pi\)
−0.266013 + 0.963970i \(0.585706\pi\)
\(542\) −8.86254 + 15.3504i −0.380679 + 0.659355i
\(543\) −2.91238 5.04438i −0.124982 0.216475i
\(544\) −1.50000 2.59808i −0.0643120 0.111392i
\(545\) −34.5498 −1.47995
\(546\) −2.50000 2.59808i −0.106990 0.111187i
\(547\) 33.0997 1.41524 0.707620 0.706593i \(-0.249769\pi\)
0.707620 + 0.706593i \(0.249769\pi\)
\(548\) −0.0876242 0.151770i −0.00374312 0.00648327i
\(549\) 4.50000 + 7.79423i 0.192055 + 0.332650i
\(550\) 11.4502 19.8323i 0.488237 0.845651i
\(551\) −6.19934 −0.264101
\(552\) −1.13746 + 1.97014i −0.0484135 + 0.0838546i
\(553\) 4.00000 6.92820i 0.170097 0.294617i
\(554\) −7.82475 −0.332442
\(555\) −11.9124 + 20.6328i −0.505652 + 0.875815i
\(556\) −10.5498 18.2728i −0.447413 0.774941i
\(557\) −12.5997 21.8233i −0.533865 0.924681i −0.999217 0.0395559i \(-0.987406\pi\)
0.465352 0.885126i \(-0.345928\pi\)
\(558\) 6.27492 0.265638
\(559\) −10.8248 + 37.4980i −0.457838 + 1.58600i
\(560\) −3.27492 −0.138391
\(561\) 6.00000 + 10.3923i 0.253320 + 0.438763i
\(562\) −0.912376 1.58028i −0.0384863 0.0666601i
\(563\) −12.0000 + 20.7846i −0.505740 + 0.875967i 0.494238 + 0.869326i \(0.335447\pi\)
−0.999978 + 0.00664037i \(0.997886\pi\)
\(564\) 8.54983 0.360013
\(565\) −12.8127 + 22.1923i −0.539035 + 0.933635i
\(566\) 12.2749 21.2608i 0.515953 0.893657i
\(567\) 1.00000 0.0419961
\(568\) 1.13746 1.97014i 0.0477267 0.0826651i
\(569\) −17.5498 30.3972i −0.735727 1.27432i −0.954403 0.298520i \(-0.903507\pi\)
0.218676 0.975797i \(-0.429826\pi\)
\(570\) −14.0000 24.2487i −0.586395 1.01567i
\(571\) −22.2749 −0.932176 −0.466088 0.884738i \(-0.654337\pi\)
−0.466088 + 0.884738i \(0.654337\pi\)
\(572\) −14.0000 + 3.46410i −0.585369 + 0.144841i
\(573\) 14.2749 0.596343
\(574\) −0.362541 0.627940i −0.0151322 0.0262097i
\(575\) −6.51204 11.2792i −0.271571 0.470375i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −28.3746 −1.18125 −0.590625 0.806946i \(-0.701119\pi\)
−0.590625 + 0.806946i \(0.701119\pi\)
\(578\) 4.00000 6.92820i 0.166378 0.288175i
\(579\) 1.08762 1.88382i 0.0452001 0.0782889i
\(580\) −2.37459 −0.0985993
\(581\) −5.41238 + 9.37451i −0.224543 + 0.388920i
\(582\) −7.27492 12.6005i −0.301555 0.522309i
\(583\) 23.0997 + 40.0098i 0.956691 + 1.65704i
\(584\) 13.2749 0.549320
\(585\) 3.27492 11.3446i 0.135401 0.469043i
\(586\) −10.7251 −0.443049
\(587\) 21.9622 + 38.0397i 0.906477 + 1.57006i 0.818922 + 0.573905i \(0.194572\pi\)
0.0875558 + 0.996160i \(0.472094\pi\)
\(588\) −0.500000 0.866025i −0.0206197 0.0357143i
\(589\) 26.8248 46.4618i 1.10529 1.91443i
\(590\) −35.4502 −1.45946
\(591\) −0.412376 + 0.714256i −0.0169629 + 0.0293806i
\(592\) 3.63746 6.30026i 0.149499 0.258939i
\(593\) 19.5498 0.802815 0.401408 0.915899i \(-0.368521\pi\)
0.401408 + 0.915899i \(0.368521\pi\)
\(594\) 2.00000 3.46410i 0.0820610 0.142134i
\(595\) 4.91238 + 8.50848i 0.201388 + 0.348814i
\(596\) 0.500000 + 0.866025i 0.0204808 + 0.0354738i
\(597\) −10.8248 −0.443028
\(598\) −2.27492 + 7.88054i −0.0930283 + 0.322259i
\(599\) −18.2749 −0.746693 −0.373346 0.927692i \(-0.621790\pi\)
−0.373346 + 0.927692i \(0.621790\pi\)
\(600\) −2.86254 4.95807i −0.116863 0.202412i
\(601\) 7.63746 + 13.2285i 0.311538 + 0.539600i 0.978696 0.205317i \(-0.0658224\pi\)
−0.667157 + 0.744917i \(0.732489\pi\)
\(602\) −5.41238 + 9.37451i −0.220592 + 0.382077i
\(603\) −10.2749 −0.418427
\(604\) 8.54983 14.8087i 0.347888 0.602559i
\(605\) 8.18729 14.1808i 0.332861 0.576532i
\(606\) 9.27492 0.376768
\(607\) −11.1375 + 19.2906i −0.452055 + 0.782983i −0.998514 0.0545034i \(-0.982642\pi\)
0.546458 + 0.837486i \(0.315976\pi\)
\(608\) 4.27492 + 7.40437i 0.173371 + 0.300287i
\(609\) −0.362541 0.627940i −0.0146909 0.0254454i
\(610\) 29.4743 1.19338
\(611\) 29.9244 7.40437i 1.21061 0.299549i
\(612\) 3.00000 0.121268
\(613\) 4.18729 + 7.25260i 0.169123 + 0.292930i 0.938112 0.346332i \(-0.112573\pi\)
−0.768989 + 0.639262i \(0.779240\pi\)
\(614\) 8.27492 + 14.3326i 0.333948 + 0.578416i
\(615\) 1.18729 2.05645i 0.0478763 0.0829241i
\(616\) −4.00000 −0.161165
\(617\) 6.46221 11.1929i 0.260159 0.450608i −0.706125 0.708087i \(-0.749558\pi\)
0.966284 + 0.257479i \(0.0828918\pi\)
\(618\) 1.13746 1.97014i 0.0457553 0.0792505i
\(619\) 29.6495 1.19171 0.595857 0.803090i \(-0.296812\pi\)
0.595857 + 0.803090i \(0.296812\pi\)
\(620\) 10.2749 17.7967i 0.412651 0.714732i
\(621\) −1.13746 1.97014i −0.0456446 0.0790588i
\(622\) −6.27492 10.8685i −0.251601 0.435786i
\(623\) 8.27492 0.331528
\(624\) −1.00000 + 3.46410i −0.0400320 + 0.138675i
\(625\) −20.8488 −0.833954
\(626\) 13.8248 + 23.9452i 0.552548 + 0.957042i
\(627\) −17.0997 29.6175i −0.682895 1.18281i
\(628\) 5.63746 9.76436i 0.224959 0.389641i
\(629\) −21.8248 −0.870210
\(630\) 1.63746 2.83616i 0.0652379 0.112995i
\(631\) −0.549834 + 0.952341i −0.0218886 + 0.0379121i −0.876762 0.480924i \(-0.840301\pi\)
0.854874 + 0.518836i \(0.173635\pi\)
\(632\) −8.00000 −0.318223
\(633\) 4.54983 7.88054i 0.180840 0.313224i
\(634\) −3.77492 6.53835i −0.149921 0.259671i
\(635\) 13.0997 + 22.6893i 0.519845 + 0.900397i
\(636\) 11.5498 0.457981
\(637\) −2.50000 2.59808i −0.0990536 0.102940i
\(638\) −2.90033 −0.114825
\(639\) 1.13746 + 1.97014i 0.0449972 + 0.0779374i
\(640\) 1.63746 + 2.83616i 0.0647262 + 0.112109i
\(641\) 1.91238 3.31233i 0.0755343 0.130829i −0.825784 0.563986i \(-0.809267\pi\)
0.901318 + 0.433157i \(0.142600\pi\)
\(642\) −12.5498 −0.495302
\(643\) −21.3746 + 37.0219i −0.842931 + 1.46000i 0.0444742 + 0.999011i \(0.485839\pi\)
−0.887406 + 0.460989i \(0.847495\pi\)
\(644\) −1.13746 + 1.97014i −0.0448221 + 0.0776342i
\(645\) −35.4502 −1.39585
\(646\) 12.8248 22.2131i 0.504583 0.873964i
\(647\) −12.2749 21.2608i −0.482577 0.835848i 0.517223 0.855851i \(-0.326966\pi\)
−0.999800 + 0.0200031i \(0.993632\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) −43.2990 −1.69963
\(650\) −14.3127 14.8742i −0.561391 0.583414i
\(651\) 6.27492 0.245933
\(652\) 2.86254 + 4.95807i 0.112106 + 0.194173i
\(653\) 17.2371 + 29.8556i 0.674541 + 1.16834i 0.976603 + 0.215051i \(0.0689917\pi\)
−0.302062 + 0.953288i \(0.597675\pi\)
\(654\) −5.27492 + 9.13642i −0.206266 + 0.357262i
\(655\) 33.6495 1.31479
\(656\) −0.362541 + 0.627940i −0.0141549 + 0.0245169i
\(657\) −6.63746 + 11.4964i −0.258952 + 0.448518i
\(658\) 8.54983 0.333307
\(659\) 14.2749 24.7249i 0.556072 0.963145i −0.441747 0.897139i \(-0.645641\pi\)
0.997819 0.0660052i \(-0.0210254\pi\)
\(660\) −6.54983 11.3446i −0.254952 0.441590i
\(661\) −20.0498 34.7273i −0.779848 1.35074i −0.932029 0.362384i \(-0.881963\pi\)
0.152181 0.988353i \(-0.451370\pi\)
\(662\) 4.00000 0.155464
\(663\) 10.5000 2.59808i 0.407786 0.100901i
\(664\) 10.8248 0.420082
\(665\) −14.0000 24.2487i −0.542897 0.940325i
\(666\) 3.63746 + 6.30026i 0.140949 + 0.244130i
\(667\) −0.824752 + 1.42851i −0.0319345 + 0.0553122i
\(668\) 0 0
\(669\) −9.13746 + 15.8265i −0.353275 + 0.611889i
\(670\) −16.8248 + 29.1413i −0.649997 + 1.12583i
\(671\) 36.0000 1.38976
\(672\) −0.500000 + 0.866025i −0.0192879 + 0.0334077i
\(673\) −6.04983 10.4786i −0.233204 0.403921i 0.725545 0.688174i \(-0.241588\pi\)
−0.958749 + 0.284253i \(0.908254\pi\)
\(674\) 3.63746 + 6.30026i 0.140110 + 0.242677i
\(675\) 5.72508 0.220359
\(676\) −0.500000 + 12.9904i −0.0192308 + 0.499630i
\(677\) 11.6495 0.447727 0.223863 0.974621i \(-0.428133\pi\)
0.223863 + 0.974621i \(0.428133\pi\)
\(678\) 3.91238 + 6.77643i 0.150254 + 0.260247i
\(679\) −7.27492 12.6005i −0.279186 0.483564i
\(680\) 4.91238 8.50848i 0.188381 0.326285i
\(681\) 9.09967 0.348700
\(682\) 12.5498 21.7370i 0.480558 0.832351i
\(683\) 24.8248 42.9977i 0.949893 1.64526i 0.204248 0.978919i \(-0.434525\pi\)
0.745645 0.666343i \(-0.232141\pi\)
\(684\) −8.54983 −0.326911
\(685\) 0.286962 0.497033i 0.0109643 0.0189906i
\(686\) −0.500000 0.866025i −0.0190901 0.0330650i
\(687\) −10.1375 17.5586i −0.386768 0.669902i
\(688\) 10.8248 0.412690
\(689\) 40.4244 10.0025i 1.54005 0.381063i
\(690\) −7.45017 −0.283623
\(691\) −4.00000 6.92820i −0.152167 0.263561i 0.779857 0.625958i \(-0.215292\pi\)
−0.932024 + 0.362397i \(0.881959\pi\)
\(692\) −5.27492 9.13642i −0.200522 0.347315i
\(693\) 2.00000 3.46410i 0.0759737 0.131590i
\(694\) 15.4502 0.586480
\(695\) 34.5498 59.8421i 1.31055 2.26994i
\(696\) −0.362541 + 0.627940i −0.0137421 + 0.0238020i
\(697\) 2.17525 0.0823934
\(698\) −8.96221 + 15.5230i −0.339225 + 0.587554i
\(699\) −11.2749 19.5287i −0.426457 0.738644i
\(700\) −2.86254 4.95807i −0.108194 0.187397i
\(701\) −37.9244 −1.43239 −0.716193 0.697902i \(-0.754117\pi\)
−0.716193 + 0.697902i \(0.754117\pi\)
\(702\) −2.50000 2.59808i −0.0943564 0.0980581i
\(703\) 62.1993 2.34589
\(704\) 2.00000 + 3.46410i 0.0753778 + 0.130558i
\(705\) 14.0000 + 24.2487i 0.527271 + 0.913259i
\(706\) 2.22508 3.85396i 0.0837421 0.145046i
\(707\) 9.27492 0.348819
\(708\) −5.41238 + 9.37451i −0.203410 + 0.352316i
\(709\) 4.81271 8.33585i 0.180745 0.313060i −0.761389 0.648295i \(-0.775482\pi\)
0.942134 + 0.335235i \(0.108816\pi\)
\(710\) 7.45017 0.279600
\(711\) 4.00000 6.92820i 0.150012 0.259828i
\(712\) −4.13746 7.16629i −0.155058 0.268568i
\(713\) −7.13746 12.3624i −0.267300 0.462977i
\(714\) 3.00000 0.112272
\(715\) −32.7492 34.0339i −1.22475 1.27280i
\(716\) 16.5498 0.618496
\(717\) −1.13746 1.97014i −0.0424792 0.0735761i
\(718\) −14.5498 25.2011i −0.542995 0.940495i
\(719\) 4.00000 6.92820i 0.149175 0.258378i −0.781748 0.623595i \(-0.785672\pi\)
0.930923 + 0.365216i \(0.119005\pi\)
\(720\) −3.27492 −0.122049
\(721\) 1.13746 1.97014i 0.0423612 0.0733717i
\(722\) −27.0498 + 46.8517i −1.00669 + 1.74364i
\(723\) −23.2749 −0.865603
\(724\) −2.91238 + 5.04438i −0.108238 + 0.187473i
\(725\) −2.07558 3.59501i −0.0770851 0.133515i
\(726\) −2.50000 4.33013i −0.0927837 0.160706i
\(727\) −2.82475 −0.104764 −0.0523821 0.998627i \(-0.516681\pi\)
−0.0523821 + 0.998627i \(0.516681\pi\)
\(728\) −1.00000 + 3.46410i −0.0370625 + 0.128388i
\(729\) 1.00000 0.0370370
\(730\) 21.7371 + 37.6498i 0.804527 + 1.39348i
\(731\) −16.2371 28.1235i −0.600552 1.04019i
\(732\) 4.50000 7.79423i 0.166325 0.288083i
\(733\) 12.6495 0.467220 0.233610 0.972330i \(-0.424946\pi\)
0.233610 + 0.972330i \(0.424946\pi\)
\(734\) −2.86254 + 4.95807i −0.105658 + 0.183006i
\(735\) 1.63746 2.83616i 0.0603986 0.104613i
\(736\) 2.27492 0.0838546
\(737\) −20.5498 + 35.5934i −0.756963 + 1.31110i
\(738\) −0.362541 0.627940i −0.0133453 0.0231148i
\(739\) 20.8625 + 36.1350i 0.767441 + 1.32925i 0.938946 + 0.344064i \(0.111804\pi\)
−0.171505 + 0.985183i \(0.554863\pi\)
\(740\) 23.8248 0.875815
\(741\) −29.9244 + 7.40437i −1.09930 + 0.272006i
\(742\) 11.5498 0.424008
\(743\) 13.4124 + 23.2309i 0.492052 + 0.852260i 0.999958 0.00915297i \(-0.00291352\pi\)
−0.507906 + 0.861413i \(0.669580\pi\)
\(744\) −3.13746 5.43424i −0.115025 0.199229i
\(745\) −1.63746 + 2.83616i −0.0599918 + 0.103909i
\(746\) 4.17525 0.152867
\(747\) −5.41238 + 9.37451i −0.198028 + 0.342995i
\(748\) 6.00000 10.3923i 0.219382 0.379980i
\(749\) −12.5498 −0.458561
\(750\) 1.18729 2.05645i 0.0433538 0.0750910i
\(751\) 1.72508 + 2.98793i 0.0629492 + 0.109031i 0.895782 0.444493i \(-0.146616\pi\)
−0.832833 + 0.553524i \(0.813283\pi\)
\(752\) −4.27492 7.40437i −0.155890 0.270010i
\(753\) 5.72508 0.208634
\(754\) −0.725083 + 2.51176i −0.0264060 + 0.0914729i
\(755\) 56.0000 2.03805
\(756\) −0.500000 0.866025i −0.0181848 0.0314970i
\(757\) 13.0000 + 22.5167i 0.472493 + 0.818382i 0.999505 0.0314762i \(-0.0100208\pi\)
−0.527011 + 0.849858i \(0.676688\pi\)
\(758\) 10.0000 17.3205i 0.363216 0.629109i
\(759\) −9.09967 −0.330297
\(760\) −14.0000 + 24.2487i −0.507833 + 0.879593i
\(761\) 20.0997 34.8136i 0.728612 1.26199i −0.228857 0.973460i \(-0.573499\pi\)
0.957470 0.288534i \(-0.0931677\pi\)
\(762\) 8.00000 0.289809
\(763\) −5.27492 + 9.13642i −0.190965 + 0.330761i
\(764\) −7.13746 12.3624i −0.258224 0.447257i
\(765\) 4.91238 + 8.50848i 0.177607 + 0.307625i
\(766\) −38.1993 −1.38020
\(767\) −10.8248 + 37.4980i −0.390859 + 1.35398i
\(768\) 1.00000 0.0360844
\(769\) 1.82475 + 3.16056i 0.0658022 + 0.113973i 0.897050 0.441930i \(-0.145706\pi\)
−0.831247 + 0.555903i \(0.812373\pi\)
\(770\) −6.54983 11.3446i −0.236040 0.408833i
\(771\) −7.50000 + 12.9904i −0.270106 + 0.467837i
\(772\) −2.17525 −0.0782889
\(773\) 25.5498 44.2536i 0.918964 1.59169i 0.117971 0.993017i \(-0.462361\pi\)
0.800992 0.598675i \(-0.204306\pi\)
\(774\) −5.41238 + 9.37451i −0.194544 + 0.336960i
\(775\) 35.9244 1.29044
\(776\) −7.27492 + 12.6005i −0.261154 + 0.452333i
\(777\) 3.63746