Properties

Label 70.2.e.d.11.1
Level 70
Weight 2
Character 70.11
Analytic conductor 0.559
Analytic rank 0
Dimension 2
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 70 = 2 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 70.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.558952814149\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 11.1
Root \(0.500000 + 0.866025i\)
Character \(\chi\) = 70.11
Dual form 70.2.e.d.51.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(1.00000 - 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +2.00000 q^{6} +(-2.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(1.00000 - 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +2.00000 q^{6} +(-2.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-1.50000 + 2.59808i) q^{11} +(1.00000 + 1.73205i) q^{12} -1.00000 q^{13} +(-2.50000 - 0.866025i) q^{14} -2.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.00000 - 5.19615i) q^{17} +(0.500000 - 0.866025i) q^{18} +(0.500000 + 0.866025i) q^{19} +1.00000 q^{20} +(1.00000 + 5.19615i) q^{21} -3.00000 q^{22} +(-4.50000 - 7.79423i) q^{23} +(-1.00000 + 1.73205i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.500000 - 0.866025i) q^{26} +4.00000 q^{27} +(-0.500000 - 2.59808i) q^{28} +6.00000 q^{29} +(-1.00000 - 1.73205i) q^{30} +(-4.00000 + 6.92820i) q^{31} +(0.500000 - 0.866025i) q^{32} +(3.00000 + 5.19615i) q^{33} +6.00000 q^{34} +(2.50000 + 0.866025i) q^{35} +1.00000 q^{36} +(3.50000 + 6.06218i) q^{37} +(-0.500000 + 0.866025i) q^{38} +(-1.00000 + 1.73205i) q^{39} +(0.500000 + 0.866025i) q^{40} +3.00000 q^{41} +(-4.00000 + 3.46410i) q^{42} +2.00000 q^{43} +(-1.50000 - 2.59808i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(4.50000 - 7.79423i) q^{46} +(-4.50000 - 7.79423i) q^{47} -2.00000 q^{48} +(1.00000 - 6.92820i) q^{49} -1.00000 q^{50} +(-6.00000 - 10.3923i) q^{51} +(0.500000 - 0.866025i) q^{52} +(-4.50000 + 7.79423i) q^{53} +(2.00000 + 3.46410i) q^{54} +3.00000 q^{55} +(2.00000 - 1.73205i) q^{56} +2.00000 q^{57} +(3.00000 + 5.19615i) q^{58} +(1.00000 - 1.73205i) q^{60} +(-4.00000 - 6.92820i) q^{61} -8.00000 q^{62} +(2.50000 + 0.866025i) q^{63} +1.00000 q^{64} +(0.500000 + 0.866025i) q^{65} +(-3.00000 + 5.19615i) q^{66} +(-4.00000 + 6.92820i) q^{67} +(3.00000 + 5.19615i) q^{68} -18.0000 q^{69} +(0.500000 + 2.59808i) q^{70} +(0.500000 + 0.866025i) q^{72} +(2.00000 - 3.46410i) q^{73} +(-3.50000 + 6.06218i) q^{74} +(1.00000 + 1.73205i) q^{75} -1.00000 q^{76} +(-1.50000 - 7.79423i) q^{77} -2.00000 q^{78} +(5.00000 + 8.66025i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(5.50000 - 9.52628i) q^{81} +(1.50000 + 2.59808i) q^{82} +(-5.00000 - 1.73205i) q^{84} -6.00000 q^{85} +(1.00000 + 1.73205i) q^{86} +(6.00000 - 10.3923i) q^{87} +(1.50000 - 2.59808i) q^{88} +(-3.00000 - 5.19615i) q^{89} -1.00000 q^{90} +(2.00000 - 1.73205i) q^{91} +9.00000 q^{92} +(8.00000 + 13.8564i) q^{93} +(4.50000 - 7.79423i) q^{94} +(0.500000 - 0.866025i) q^{95} +(-1.00000 - 1.73205i) q^{96} -10.0000 q^{97} +(6.50000 - 2.59808i) q^{98} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} + 2q^{3} - q^{4} - q^{5} + 4q^{6} - 4q^{7} - 2q^{8} - q^{9} + O(q^{10}) \) \( 2q + q^{2} + 2q^{3} - q^{4} - q^{5} + 4q^{6} - 4q^{7} - 2q^{8} - q^{9} + q^{10} - 3q^{11} + 2q^{12} - 2q^{13} - 5q^{14} - 4q^{15} - q^{16} + 6q^{17} + q^{18} + q^{19} + 2q^{20} + 2q^{21} - 6q^{22} - 9q^{23} - 2q^{24} - q^{25} - q^{26} + 8q^{27} - q^{28} + 12q^{29} - 2q^{30} - 8q^{31} + q^{32} + 6q^{33} + 12q^{34} + 5q^{35} + 2q^{36} + 7q^{37} - q^{38} - 2q^{39} + q^{40} + 6q^{41} - 8q^{42} + 4q^{43} - 3q^{44} - q^{45} + 9q^{46} - 9q^{47} - 4q^{48} + 2q^{49} - 2q^{50} - 12q^{51} + q^{52} - 9q^{53} + 4q^{54} + 6q^{55} + 4q^{56} + 4q^{57} + 6q^{58} + 2q^{60} - 8q^{61} - 16q^{62} + 5q^{63} + 2q^{64} + q^{65} - 6q^{66} - 8q^{67} + 6q^{68} - 36q^{69} + q^{70} + q^{72} + 4q^{73} - 7q^{74} + 2q^{75} - 2q^{76} - 3q^{77} - 4q^{78} + 10q^{79} - q^{80} + 11q^{81} + 3q^{82} - 10q^{84} - 12q^{85} + 2q^{86} + 12q^{87} + 3q^{88} - 6q^{89} - 2q^{90} + 4q^{91} + 18q^{92} + 16q^{93} + 9q^{94} + q^{95} - 2q^{96} - 20q^{97} + 13q^{98} + 6q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/70\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(57\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(3\) 1.00000 1.73205i 0.577350 1.00000i −0.418432 0.908248i \(-0.637420\pi\)
0.995782 0.0917517i \(-0.0292466\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) 2.00000 0.816497
\(7\) −2.00000 + 1.73205i −0.755929 + 0.654654i
\(8\) −1.00000 −0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0.500000 0.866025i 0.158114 0.273861i
\(11\) −1.50000 + 2.59808i −0.452267 + 0.783349i −0.998526 0.0542666i \(-0.982718\pi\)
0.546259 + 0.837616i \(0.316051\pi\)
\(12\) 1.00000 + 1.73205i 0.288675 + 0.500000i
\(13\) −1.00000 −0.277350 −0.138675 0.990338i \(-0.544284\pi\)
−0.138675 + 0.990338i \(0.544284\pi\)
\(14\) −2.50000 0.866025i −0.668153 0.231455i
\(15\) −2.00000 −0.516398
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 3.00000 5.19615i 0.727607 1.26025i −0.230285 0.973123i \(-0.573966\pi\)
0.957892 0.287129i \(-0.0927008\pi\)
\(18\) 0.500000 0.866025i 0.117851 0.204124i
\(19\) 0.500000 + 0.866025i 0.114708 + 0.198680i 0.917663 0.397360i \(-0.130073\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) 1.00000 0.223607
\(21\) 1.00000 + 5.19615i 0.218218 + 1.13389i
\(22\) −3.00000 −0.639602
\(23\) −4.50000 7.79423i −0.938315 1.62521i −0.768613 0.639713i \(-0.779053\pi\)
−0.169701 0.985496i \(-0.554280\pi\)
\(24\) −1.00000 + 1.73205i −0.204124 + 0.353553i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) −0.500000 0.866025i −0.0980581 0.169842i
\(27\) 4.00000 0.769800
\(28\) −0.500000 2.59808i −0.0944911 0.490990i
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) −1.00000 1.73205i −0.182574 0.316228i
\(31\) −4.00000 + 6.92820i −0.718421 + 1.24434i 0.243204 + 0.969975i \(0.421802\pi\)
−0.961625 + 0.274367i \(0.911532\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 3.00000 + 5.19615i 0.522233 + 0.904534i
\(34\) 6.00000 1.02899
\(35\) 2.50000 + 0.866025i 0.422577 + 0.146385i
\(36\) 1.00000 0.166667
\(37\) 3.50000 + 6.06218i 0.575396 + 0.996616i 0.995998 + 0.0893706i \(0.0284856\pi\)
−0.420602 + 0.907245i \(0.638181\pi\)
\(38\) −0.500000 + 0.866025i −0.0811107 + 0.140488i
\(39\) −1.00000 + 1.73205i −0.160128 + 0.277350i
\(40\) 0.500000 + 0.866025i 0.0790569 + 0.136931i
\(41\) 3.00000 0.468521 0.234261 0.972174i \(-0.424733\pi\)
0.234261 + 0.972174i \(0.424733\pi\)
\(42\) −4.00000 + 3.46410i −0.617213 + 0.534522i
\(43\) 2.00000 0.304997 0.152499 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) −1.50000 2.59808i −0.226134 0.391675i
\(45\) −0.500000 + 0.866025i −0.0745356 + 0.129099i
\(46\) 4.50000 7.79423i 0.663489 1.14920i
\(47\) −4.50000 7.79423i −0.656392 1.13691i −0.981543 0.191243i \(-0.938748\pi\)
0.325150 0.945662i \(-0.394585\pi\)
\(48\) −2.00000 −0.288675
\(49\) 1.00000 6.92820i 0.142857 0.989743i
\(50\) −1.00000 −0.141421
\(51\) −6.00000 10.3923i −0.840168 1.45521i
\(52\) 0.500000 0.866025i 0.0693375 0.120096i
\(53\) −4.50000 + 7.79423i −0.618123 + 1.07062i 0.371706 + 0.928351i \(0.378773\pi\)
−0.989828 + 0.142269i \(0.954560\pi\)
\(54\) 2.00000 + 3.46410i 0.272166 + 0.471405i
\(55\) 3.00000 0.404520
\(56\) 2.00000 1.73205i 0.267261 0.231455i
\(57\) 2.00000 0.264906
\(58\) 3.00000 + 5.19615i 0.393919 + 0.682288i
\(59\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(60\) 1.00000 1.73205i 0.129099 0.223607i
\(61\) −4.00000 6.92820i −0.512148 0.887066i −0.999901 0.0140840i \(-0.995517\pi\)
0.487753 0.872982i \(-0.337817\pi\)
\(62\) −8.00000 −1.01600
\(63\) 2.50000 + 0.866025i 0.314970 + 0.109109i
\(64\) 1.00000 0.125000
\(65\) 0.500000 + 0.866025i 0.0620174 + 0.107417i
\(66\) −3.00000 + 5.19615i −0.369274 + 0.639602i
\(67\) −4.00000 + 6.92820i −0.488678 + 0.846415i −0.999915 0.0130248i \(-0.995854\pi\)
0.511237 + 0.859440i \(0.329187\pi\)
\(68\) 3.00000 + 5.19615i 0.363803 + 0.630126i
\(69\) −18.0000 −2.16695
\(70\) 0.500000 + 2.59808i 0.0597614 + 0.310530i
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0.500000 + 0.866025i 0.0589256 + 0.102062i
\(73\) 2.00000 3.46410i 0.234082 0.405442i −0.724923 0.688830i \(-0.758125\pi\)
0.959006 + 0.283387i \(0.0914581\pi\)
\(74\) −3.50000 + 6.06218i −0.406867 + 0.704714i
\(75\) 1.00000 + 1.73205i 0.115470 + 0.200000i
\(76\) −1.00000 −0.114708
\(77\) −1.50000 7.79423i −0.170941 0.888235i
\(78\) −2.00000 −0.226455
\(79\) 5.00000 + 8.66025i 0.562544 + 0.974355i 0.997274 + 0.0737937i \(0.0235106\pi\)
−0.434730 + 0.900561i \(0.643156\pi\)
\(80\) −0.500000 + 0.866025i −0.0559017 + 0.0968246i
\(81\) 5.50000 9.52628i 0.611111 1.05848i
\(82\) 1.50000 + 2.59808i 0.165647 + 0.286910i
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) −5.00000 1.73205i −0.545545 0.188982i
\(85\) −6.00000 −0.650791
\(86\) 1.00000 + 1.73205i 0.107833 + 0.186772i
\(87\) 6.00000 10.3923i 0.643268 1.11417i
\(88\) 1.50000 2.59808i 0.159901 0.276956i
\(89\) −3.00000 5.19615i −0.317999 0.550791i 0.662071 0.749441i \(-0.269678\pi\)
−0.980071 + 0.198650i \(0.936344\pi\)
\(90\) −1.00000 −0.105409
\(91\) 2.00000 1.73205i 0.209657 0.181568i
\(92\) 9.00000 0.938315
\(93\) 8.00000 + 13.8564i 0.829561 + 1.43684i
\(94\) 4.50000 7.79423i 0.464140 0.803913i
\(95\) 0.500000 0.866025i 0.0512989 0.0888523i
\(96\) −1.00000 1.73205i −0.102062 0.176777i
\(97\) −10.0000 −1.01535 −0.507673 0.861550i \(-0.669494\pi\)
−0.507673 + 0.861550i \(0.669494\pi\)
\(98\) 6.50000 2.59808i 0.656599 0.262445i
\(99\) 3.00000 0.301511
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) −6.00000 + 10.3923i −0.597022 + 1.03407i 0.396236 + 0.918149i \(0.370316\pi\)
−0.993258 + 0.115924i \(0.963017\pi\)
\(102\) 6.00000 10.3923i 0.594089 1.02899i
\(103\) 2.00000 + 3.46410i 0.197066 + 0.341328i 0.947576 0.319531i \(-0.103525\pi\)
−0.750510 + 0.660859i \(0.770192\pi\)
\(104\) 1.00000 0.0980581
\(105\) 4.00000 3.46410i 0.390360 0.338062i
\(106\) −9.00000 −0.874157
\(107\) 6.00000 + 10.3923i 0.580042 + 1.00466i 0.995474 + 0.0950377i \(0.0302972\pi\)
−0.415432 + 0.909624i \(0.636370\pi\)
\(108\) −2.00000 + 3.46410i −0.192450 + 0.333333i
\(109\) 8.00000 13.8564i 0.766261 1.32720i −0.173316 0.984866i \(-0.555448\pi\)
0.939577 0.342337i \(-0.111218\pi\)
\(110\) 1.50000 + 2.59808i 0.143019 + 0.247717i
\(111\) 14.0000 1.32882
\(112\) 2.50000 + 0.866025i 0.236228 + 0.0818317i
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 1.00000 + 1.73205i 0.0936586 + 0.162221i
\(115\) −4.50000 + 7.79423i −0.419627 + 0.726816i
\(116\) −3.00000 + 5.19615i −0.278543 + 0.482451i
\(117\) 0.500000 + 0.866025i 0.0462250 + 0.0800641i
\(118\) 0 0
\(119\) 3.00000 + 15.5885i 0.275010 + 1.42899i
\(120\) 2.00000 0.182574
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 4.00000 6.92820i 0.362143 0.627250i
\(123\) 3.00000 5.19615i 0.270501 0.468521i
\(124\) −4.00000 6.92820i −0.359211 0.622171i
\(125\) 1.00000 0.0894427
\(126\) 0.500000 + 2.59808i 0.0445435 + 0.231455i
\(127\) −1.00000 −0.0887357 −0.0443678 0.999015i \(-0.514127\pi\)
−0.0443678 + 0.999015i \(0.514127\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 2.00000 3.46410i 0.176090 0.304997i
\(130\) −0.500000 + 0.866025i −0.0438529 + 0.0759555i
\(131\) −1.50000 2.59808i −0.131056 0.226995i 0.793028 0.609185i \(-0.208503\pi\)
−0.924084 + 0.382190i \(0.875170\pi\)
\(132\) −6.00000 −0.522233
\(133\) −2.50000 0.866025i −0.216777 0.0750939i
\(134\) −8.00000 −0.691095
\(135\) −2.00000 3.46410i −0.172133 0.298142i
\(136\) −3.00000 + 5.19615i −0.257248 + 0.445566i
\(137\) −6.00000 + 10.3923i −0.512615 + 0.887875i 0.487278 + 0.873247i \(0.337990\pi\)
−0.999893 + 0.0146279i \(0.995344\pi\)
\(138\) −9.00000 15.5885i −0.766131 1.32698i
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) −2.00000 + 1.73205i −0.169031 + 0.146385i
\(141\) −18.0000 −1.51587
\(142\) 0 0
\(143\) 1.50000 2.59808i 0.125436 0.217262i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) −3.00000 5.19615i −0.249136 0.431517i
\(146\) 4.00000 0.331042
\(147\) −11.0000 8.66025i −0.907265 0.714286i
\(148\) −7.00000 −0.575396
\(149\) 3.00000 + 5.19615i 0.245770 + 0.425685i 0.962348 0.271821i \(-0.0876260\pi\)
−0.716578 + 0.697507i \(0.754293\pi\)
\(150\) −1.00000 + 1.73205i −0.0816497 + 0.141421i
\(151\) 5.00000 8.66025i 0.406894 0.704761i −0.587646 0.809118i \(-0.699945\pi\)
0.994540 + 0.104357i \(0.0332784\pi\)
\(152\) −0.500000 0.866025i −0.0405554 0.0702439i
\(153\) −6.00000 −0.485071
\(154\) 6.00000 5.19615i 0.483494 0.418718i
\(155\) 8.00000 0.642575
\(156\) −1.00000 1.73205i −0.0800641 0.138675i
\(157\) −11.5000 + 19.9186i −0.917800 + 1.58968i −0.115050 + 0.993360i \(0.536703\pi\)
−0.802749 + 0.596316i \(0.796630\pi\)
\(158\) −5.00000 + 8.66025i −0.397779 + 0.688973i
\(159\) 9.00000 + 15.5885i 0.713746 + 1.23625i
\(160\) −1.00000 −0.0790569
\(161\) 22.5000 + 7.79423i 1.77325 + 0.614271i
\(162\) 11.0000 0.864242
\(163\) −10.0000 17.3205i −0.783260 1.35665i −0.930033 0.367477i \(-0.880222\pi\)
0.146772 0.989170i \(-0.453112\pi\)
\(164\) −1.50000 + 2.59808i −0.117130 + 0.202876i
\(165\) 3.00000 5.19615i 0.233550 0.404520i
\(166\) 0 0
\(167\) 3.00000 0.232147 0.116073 0.993241i \(-0.462969\pi\)
0.116073 + 0.993241i \(0.462969\pi\)
\(168\) −1.00000 5.19615i −0.0771517 0.400892i
\(169\) −12.0000 −0.923077
\(170\) −3.00000 5.19615i −0.230089 0.398527i
\(171\) 0.500000 0.866025i 0.0382360 0.0662266i
\(172\) −1.00000 + 1.73205i −0.0762493 + 0.132068i
\(173\) −4.50000 7.79423i −0.342129 0.592584i 0.642699 0.766119i \(-0.277815\pi\)
−0.984828 + 0.173534i \(0.944481\pi\)
\(174\) 12.0000 0.909718
\(175\) −0.500000 2.59808i −0.0377964 0.196396i
\(176\) 3.00000 0.226134
\(177\) 0 0
\(178\) 3.00000 5.19615i 0.224860 0.389468i
\(179\) 1.50000 2.59808i 0.112115 0.194189i −0.804508 0.593942i \(-0.797571\pi\)
0.916623 + 0.399753i \(0.130904\pi\)
\(180\) −0.500000 0.866025i −0.0372678 0.0645497i
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 2.50000 + 0.866025i 0.185312 + 0.0641941i
\(183\) −16.0000 −1.18275
\(184\) 4.50000 + 7.79423i 0.331744 + 0.574598i
\(185\) 3.50000 6.06218i 0.257325 0.445700i
\(186\) −8.00000 + 13.8564i −0.586588 + 1.01600i
\(187\) 9.00000 + 15.5885i 0.658145 + 1.13994i
\(188\) 9.00000 0.656392
\(189\) −8.00000 + 6.92820i −0.581914 + 0.503953i
\(190\) 1.00000 0.0725476
\(191\) −6.00000 10.3923i −0.434145 0.751961i 0.563081 0.826402i \(-0.309616\pi\)
−0.997225 + 0.0744412i \(0.976283\pi\)
\(192\) 1.00000 1.73205i 0.0721688 0.125000i
\(193\) 8.00000 13.8564i 0.575853 0.997406i −0.420096 0.907480i \(-0.638004\pi\)
0.995948 0.0899262i \(-0.0286631\pi\)
\(194\) −5.00000 8.66025i −0.358979 0.621770i
\(195\) 2.00000 0.143223
\(196\) 5.50000 + 4.33013i 0.392857 + 0.309295i
\(197\) 15.0000 1.06871 0.534353 0.845262i \(-0.320555\pi\)
0.534353 + 0.845262i \(0.320555\pi\)
\(198\) 1.50000 + 2.59808i 0.106600 + 0.184637i
\(199\) 8.00000 13.8564i 0.567105 0.982255i −0.429745 0.902950i \(-0.641397\pi\)
0.996850 0.0793045i \(-0.0252700\pi\)
\(200\) 0.500000 0.866025i 0.0353553 0.0612372i
\(201\) 8.00000 + 13.8564i 0.564276 + 0.977356i
\(202\) −12.0000 −0.844317
\(203\) −12.0000 + 10.3923i −0.842235 + 0.729397i
\(204\) 12.0000 0.840168
\(205\) −1.50000 2.59808i −0.104765 0.181458i
\(206\) −2.00000 + 3.46410i −0.139347 + 0.241355i
\(207\) −4.50000 + 7.79423i −0.312772 + 0.541736i
\(208\) 0.500000 + 0.866025i 0.0346688 + 0.0600481i
\(209\) −3.00000 −0.207514
\(210\) 5.00000 + 1.73205i 0.345033 + 0.119523i
\(211\) 23.0000 1.58339 0.791693 0.610920i \(-0.209200\pi\)
0.791693 + 0.610920i \(0.209200\pi\)
\(212\) −4.50000 7.79423i −0.309061 0.535310i
\(213\) 0 0
\(214\) −6.00000 + 10.3923i −0.410152 + 0.710403i
\(215\) −1.00000 1.73205i −0.0681994 0.118125i
\(216\) −4.00000 −0.272166
\(217\) −4.00000 20.7846i −0.271538 1.41095i
\(218\) 16.0000 1.08366
\(219\) −4.00000 6.92820i −0.270295 0.468165i
\(220\) −1.50000 + 2.59808i −0.101130 + 0.175162i
\(221\) −3.00000 + 5.19615i −0.201802 + 0.349531i
\(222\) 7.00000 + 12.1244i 0.469809 + 0.813733i
\(223\) 8.00000 0.535720 0.267860 0.963458i \(-0.413684\pi\)
0.267860 + 0.963458i \(0.413684\pi\)
\(224\) 0.500000 + 2.59808i 0.0334077 + 0.173591i
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) 6.00000 10.3923i 0.398234 0.689761i −0.595274 0.803523i \(-0.702957\pi\)
0.993508 + 0.113761i \(0.0362899\pi\)
\(228\) −1.00000 + 1.73205i −0.0662266 + 0.114708i
\(229\) 2.00000 + 3.46410i 0.132164 + 0.228914i 0.924510 0.381157i \(-0.124474\pi\)
−0.792347 + 0.610071i \(0.791141\pi\)
\(230\) −9.00000 −0.593442
\(231\) −15.0000 5.19615i −0.986928 0.341882i
\(232\) −6.00000 −0.393919
\(233\) 3.00000 + 5.19615i 0.196537 + 0.340411i 0.947403 0.320043i \(-0.103697\pi\)
−0.750867 + 0.660454i \(0.770364\pi\)
\(234\) −0.500000 + 0.866025i −0.0326860 + 0.0566139i
\(235\) −4.50000 + 7.79423i −0.293548 + 0.508439i
\(236\) 0 0
\(237\) 20.0000 1.29914
\(238\) −12.0000 + 10.3923i −0.777844 + 0.673633i
\(239\) −6.00000 −0.388108 −0.194054 0.980991i \(-0.562164\pi\)
−0.194054 + 0.980991i \(0.562164\pi\)
\(240\) 1.00000 + 1.73205i 0.0645497 + 0.111803i
\(241\) 0.500000 0.866025i 0.0322078 0.0557856i −0.849472 0.527633i \(-0.823079\pi\)
0.881680 + 0.471848i \(0.156413\pi\)
\(242\) −1.00000 + 1.73205i −0.0642824 + 0.111340i
\(243\) −5.00000 8.66025i −0.320750 0.555556i
\(244\) 8.00000 0.512148
\(245\) −6.50000 + 2.59808i −0.415270 + 0.165985i
\(246\) 6.00000 0.382546
\(247\) −0.500000 0.866025i −0.0318142 0.0551039i
\(248\) 4.00000 6.92820i 0.254000 0.439941i
\(249\) 0 0
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) −15.0000 −0.946792 −0.473396 0.880850i \(-0.656972\pi\)
−0.473396 + 0.880850i \(0.656972\pi\)
\(252\) −2.00000 + 1.73205i −0.125988 + 0.109109i
\(253\) 27.0000 1.69748
\(254\) −0.500000 0.866025i −0.0313728 0.0543393i
\(255\) −6.00000 + 10.3923i −0.375735 + 0.650791i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(258\) 4.00000 0.249029
\(259\) −17.5000 6.06218i −1.08740 0.376685i
\(260\) −1.00000 −0.0620174
\(261\) −3.00000 5.19615i −0.185695 0.321634i
\(262\) 1.50000 2.59808i 0.0926703 0.160510i
\(263\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(264\) −3.00000 5.19615i −0.184637 0.319801i
\(265\) 9.00000 0.552866
\(266\) −0.500000 2.59808i −0.0306570 0.159298i
\(267\) −12.0000 −0.734388
\(268\) −4.00000 6.92820i −0.244339 0.423207i
\(269\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(270\) 2.00000 3.46410i 0.121716 0.210819i
\(271\) 8.00000 + 13.8564i 0.485965 + 0.841717i 0.999870 0.0161307i \(-0.00513477\pi\)
−0.513905 + 0.857847i \(0.671801\pi\)
\(272\) −6.00000 −0.363803
\(273\) −1.00000 5.19615i −0.0605228 0.314485i
\(274\) −12.0000 −0.724947
\(275\) −1.50000 2.59808i −0.0904534 0.156670i
\(276\) 9.00000 15.5885i 0.541736 0.938315i
\(277\) 5.00000 8.66025i 0.300421 0.520344i −0.675810 0.737075i \(-0.736206\pi\)
0.976231 + 0.216731i \(0.0695395\pi\)
\(278\) −2.00000 3.46410i −0.119952 0.207763i
\(279\) 8.00000 0.478947
\(280\) −2.50000 0.866025i −0.149404 0.0517549i
\(281\) −27.0000 −1.61068 −0.805342 0.592810i \(-0.798019\pi\)
−0.805342 + 0.592810i \(0.798019\pi\)
\(282\) −9.00000 15.5885i −0.535942 0.928279i
\(283\) −7.00000 + 12.1244i −0.416107 + 0.720718i −0.995544 0.0942988i \(-0.969939\pi\)
0.579437 + 0.815017i \(0.303272\pi\)
\(284\) 0 0
\(285\) −1.00000 1.73205i −0.0592349 0.102598i
\(286\) 3.00000 0.177394
\(287\) −6.00000 + 5.19615i −0.354169 + 0.306719i
\(288\) −1.00000 −0.0589256
\(289\) −9.50000 16.4545i −0.558824 0.967911i
\(290\) 3.00000 5.19615i 0.176166 0.305129i
\(291\) −10.0000 + 17.3205i −0.586210 + 1.01535i
\(292\) 2.00000 + 3.46410i 0.117041 + 0.202721i
\(293\) −9.00000 −0.525786 −0.262893 0.964825i \(-0.584677\pi\)
−0.262893 + 0.964825i \(0.584677\pi\)
\(294\) 2.00000 13.8564i 0.116642 0.808122i
\(295\) 0 0
\(296\) −3.50000 6.06218i −0.203433 0.352357i
\(297\) −6.00000 + 10.3923i −0.348155 + 0.603023i
\(298\) −3.00000 + 5.19615i −0.173785 + 0.301005i
\(299\) 4.50000 + 7.79423i 0.260242 + 0.450752i
\(300\) −2.00000 −0.115470
\(301\) −4.00000 + 3.46410i −0.230556 + 0.199667i
\(302\) 10.0000 0.575435
\(303\) 12.0000 + 20.7846i 0.689382 + 1.19404i
\(304\) 0.500000 0.866025i 0.0286770 0.0496700i
\(305\) −4.00000 + 6.92820i −0.229039 + 0.396708i
\(306\) −3.00000 5.19615i −0.171499 0.297044i
\(307\) 14.0000 0.799022 0.399511 0.916728i \(-0.369180\pi\)
0.399511 + 0.916728i \(0.369180\pi\)
\(308\) 7.50000 + 2.59808i 0.427352 + 0.148039i
\(309\) 8.00000 0.455104
\(310\) 4.00000 + 6.92820i 0.227185 + 0.393496i
\(311\) 12.0000 20.7846i 0.680458 1.17859i −0.294384 0.955687i \(-0.595114\pi\)
0.974841 0.222900i \(-0.0715523\pi\)
\(312\) 1.00000 1.73205i 0.0566139 0.0980581i
\(313\) 14.0000 + 24.2487i 0.791327 + 1.37062i 0.925146 + 0.379612i \(0.123943\pi\)
−0.133819 + 0.991006i \(0.542724\pi\)
\(314\) −23.0000 −1.29797
\(315\) −0.500000 2.59808i −0.0281718 0.146385i
\(316\) −10.0000 −0.562544
\(317\) −3.00000 5.19615i −0.168497 0.291845i 0.769395 0.638774i \(-0.220558\pi\)
−0.937892 + 0.346929i \(0.887225\pi\)
\(318\) −9.00000 + 15.5885i −0.504695 + 0.874157i
\(319\) −9.00000 + 15.5885i −0.503903 + 0.872786i
\(320\) −0.500000 0.866025i −0.0279508 0.0484123i
\(321\) 24.0000 1.33955
\(322\) 4.50000 + 23.3827i 0.250775 + 1.30307i
\(323\) 6.00000 0.333849
\(324\) 5.50000 + 9.52628i 0.305556 + 0.529238i
\(325\) 0.500000 0.866025i 0.0277350 0.0480384i
\(326\) 10.0000 17.3205i 0.553849 0.959294i
\(327\) −16.0000 27.7128i −0.884802 1.53252i
\(328\) −3.00000 −0.165647
\(329\) 22.5000 + 7.79423i 1.24047 + 0.429710i
\(330\) 6.00000 0.330289
\(331\) 3.50000 + 6.06218i 0.192377 + 0.333207i 0.946038 0.324057i \(-0.105047\pi\)
−0.753660 + 0.657264i \(0.771714\pi\)
\(332\) 0 0
\(333\) 3.50000 6.06218i 0.191799 0.332205i
\(334\) 1.50000 + 2.59808i 0.0820763 + 0.142160i
\(335\) 8.00000 0.437087
\(336\) 4.00000 3.46410i 0.218218 0.188982i
\(337\) −22.0000 −1.19842 −0.599208 0.800593i \(-0.704518\pi\)
−0.599208 + 0.800593i \(0.704518\pi\)
\(338\) −6.00000 10.3923i −0.326357 0.565267i
\(339\) 0 0
\(340\) 3.00000 5.19615i 0.162698 0.281801i
\(341\) −12.0000 20.7846i −0.649836 1.12555i
\(342\) 1.00000 0.0540738
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) −2.00000 −0.107833
\(345\) 9.00000 + 15.5885i 0.484544 + 0.839254i
\(346\) 4.50000 7.79423i 0.241921 0.419020i
\(347\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(348\) 6.00000 + 10.3923i 0.321634 + 0.557086i
\(349\) 26.0000 1.39175 0.695874 0.718164i \(-0.255017\pi\)
0.695874 + 0.718164i \(0.255017\pi\)
\(350\) 2.00000 1.73205i 0.106904 0.0925820i
\(351\) −4.00000 −0.213504
\(352\) 1.50000 + 2.59808i 0.0799503 + 0.138478i
\(353\) −6.00000 + 10.3923i −0.319348 + 0.553127i −0.980352 0.197256i \(-0.936797\pi\)
0.661004 + 0.750382i \(0.270130\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 6.00000 0.317999
\(357\) 30.0000 + 10.3923i 1.58777 + 0.550019i
\(358\) 3.00000 0.158555
\(359\) −9.00000 15.5885i −0.475002 0.822727i 0.524588 0.851356i \(-0.324219\pi\)
−0.999590 + 0.0286287i \(0.990886\pi\)
\(360\) 0.500000 0.866025i 0.0263523 0.0456435i
\(361\) 9.00000 15.5885i 0.473684 0.820445i
\(362\) 1.00000 + 1.73205i 0.0525588 + 0.0910346i
\(363\) 4.00000 0.209946
\(364\) 0.500000 + 2.59808i 0.0262071 + 0.136176i
\(365\) −4.00000 −0.209370
\(366\) −8.00000 13.8564i −0.418167 0.724286i
\(367\) 9.50000 16.4545i 0.495896 0.858917i −0.504093 0.863649i \(-0.668173\pi\)
0.999989 + 0.00473247i \(0.00150640\pi\)
\(368\) −4.50000 + 7.79423i −0.234579 + 0.406302i
\(369\) −1.50000 2.59808i −0.0780869 0.135250i
\(370\) 7.00000 0.363913
\(371\) −4.50000 23.3827i −0.233628 1.21397i
\(372\) −16.0000 −0.829561
\(373\) −1.00000 1.73205i −0.0517780 0.0896822i 0.838975 0.544170i \(-0.183156\pi\)
−0.890753 + 0.454488i \(0.849822\pi\)
\(374\) −9.00000 + 15.5885i −0.465379 + 0.806060i
\(375\) 1.00000 1.73205i 0.0516398 0.0894427i
\(376\) 4.50000 + 7.79423i 0.232070 + 0.401957i
\(377\) −6.00000 −0.309016
\(378\) −10.0000 3.46410i −0.514344 0.178174i
\(379\) 23.0000 1.18143 0.590715 0.806880i \(-0.298846\pi\)
0.590715 + 0.806880i \(0.298846\pi\)
\(380\) 0.500000 + 0.866025i 0.0256495 + 0.0444262i
\(381\) −1.00000 + 1.73205i −0.0512316 + 0.0887357i
\(382\) 6.00000 10.3923i 0.306987 0.531717i
\(383\) −10.5000 18.1865i −0.536525 0.929288i −0.999088 0.0427020i \(-0.986403\pi\)
0.462563 0.886586i \(-0.346930\pi\)
\(384\) 2.00000 0.102062
\(385\) −6.00000 + 5.19615i −0.305788 + 0.264820i
\(386\) 16.0000 0.814379
\(387\) −1.00000 1.73205i −0.0508329 0.0880451i
\(388\) 5.00000 8.66025i 0.253837 0.439658i
\(389\) 6.00000 10.3923i 0.304212 0.526911i −0.672874 0.739758i \(-0.734940\pi\)
0.977086 + 0.212847i \(0.0682735\pi\)
\(390\) 1.00000 + 1.73205i 0.0506370 + 0.0877058i
\(391\) −54.0000 −2.73090
\(392\) −1.00000 + 6.92820i −0.0505076 + 0.349927i
\(393\) −6.00000 −0.302660
\(394\) 7.50000 + 12.9904i 0.377845 + 0.654446i
\(395\) 5.00000 8.66025i 0.251577 0.435745i
\(396\) −1.50000 + 2.59808i −0.0753778 + 0.130558i
\(397\) −7.00000 12.1244i −0.351320 0.608504i 0.635161 0.772380i \(-0.280934\pi\)
−0.986481 + 0.163876i \(0.947600\pi\)
\(398\) 16.0000 0.802008
\(399\) −4.00000 + 3.46410i −0.200250 + 0.173422i
\(400\) 1.00000 0.0500000
\(401\) 13.5000 + 23.3827i 0.674158 + 1.16768i 0.976714 + 0.214544i \(0.0688266\pi\)
−0.302556 + 0.953131i \(0.597840\pi\)
\(402\) −8.00000 + 13.8564i −0.399004 + 0.691095i
\(403\) 4.00000 6.92820i 0.199254 0.345118i
\(404\) −6.00000 10.3923i −0.298511 0.517036i
\(405\) −11.0000 −0.546594
\(406\) −15.0000 5.19615i −0.744438 0.257881i
\(407\) −21.0000 −1.04093
\(408\) 6.00000 + 10.3923i 0.297044 + 0.514496i
\(409\) −13.0000 + 22.5167i −0.642809 + 1.11338i 0.341994 + 0.939702i \(0.388898\pi\)
−0.984803 + 0.173675i \(0.944436\pi\)
\(410\) 1.50000 2.59808i 0.0740797 0.128310i
\(411\) 12.0000 + 20.7846i 0.591916 + 1.02523i
\(412\) −4.00000 −0.197066
\(413\) 0 0
\(414\) −9.00000 −0.442326
\(415\) 0 0
\(416\) −0.500000 + 0.866025i −0.0245145 + 0.0424604i
\(417\) −4.00000 + 6.92820i −0.195881 + 0.339276i
\(418\) −1.50000 2.59808i −0.0733674 0.127076i
\(419\) −9.00000 −0.439679 −0.219839 0.975536i \(-0.570553\pi\)
−0.219839 + 0.975536i \(0.570553\pi\)
\(420\) 1.00000 + 5.19615i 0.0487950 + 0.253546i
\(421\) 2.00000 0.0974740 0.0487370 0.998812i \(-0.484480\pi\)
0.0487370 + 0.998812i \(0.484480\pi\)
\(422\) 11.5000 + 19.9186i 0.559811 + 0.969622i
\(423\) −4.50000 + 7.79423i −0.218797 + 0.378968i
\(424\) 4.50000 7.79423i 0.218539 0.378521i
\(425\) 3.00000 + 5.19615i 0.145521 + 0.252050i
\(426\) 0 0
\(427\) 20.0000 + 6.92820i 0.967868 + 0.335279i
\(428\) −12.0000 −0.580042
\(429\) −3.00000 5.19615i −0.144841 0.250873i
\(430\) 1.00000 1.73205i 0.0482243 0.0835269i
\(431\) −6.00000 + 10.3923i −0.289010 + 0.500580i −0.973574 0.228373i \(-0.926659\pi\)
0.684564 + 0.728953i \(0.259993\pi\)
\(432\) −2.00000 3.46410i −0.0962250 0.166667i
\(433\) −40.0000 −1.92228 −0.961139 0.276066i \(-0.910969\pi\)
−0.961139 + 0.276066i \(0.910969\pi\)
\(434\) 16.0000 13.8564i 0.768025 0.665129i
\(435\) −12.0000 −0.575356
\(436\) 8.00000 + 13.8564i 0.383131 + 0.663602i
\(437\) 4.50000 7.79423i 0.215264 0.372849i
\(438\) 4.00000 6.92820i 0.191127 0.331042i
\(439\) −13.0000 22.5167i −0.620456 1.07466i −0.989401 0.145210i \(-0.953614\pi\)
0.368945 0.929451i \(-0.379719\pi\)
\(440\) −3.00000 −0.143019
\(441\) −6.50000 + 2.59808i −0.309524 + 0.123718i
\(442\) −6.00000 −0.285391
\(443\) −6.00000 10.3923i −0.285069 0.493753i 0.687557 0.726130i \(-0.258683\pi\)
−0.972626 + 0.232377i \(0.925350\pi\)
\(444\) −7.00000 + 12.1244i −0.332205 + 0.575396i
\(445\) −3.00000 + 5.19615i −0.142214 + 0.246321i
\(446\) 4.00000 + 6.92820i 0.189405 + 0.328060i
\(447\) 12.0000 0.567581
\(448\) −2.00000 + 1.73205i −0.0944911 + 0.0818317i
\(449\) 21.0000 0.991051 0.495526 0.868593i \(-0.334975\pi\)
0.495526 + 0.868593i \(0.334975\pi\)
\(450\) 0.500000 + 0.866025i 0.0235702 + 0.0408248i
\(451\) −4.50000 + 7.79423i −0.211897 + 0.367016i
\(452\) 0 0
\(453\) −10.0000 17.3205i −0.469841 0.813788i
\(454\) 12.0000 0.563188
\(455\) −2.50000 0.866025i −0.117202 0.0405999i
\(456\) −2.00000 −0.0936586
\(457\) −7.00000 12.1244i −0.327446 0.567153i 0.654558 0.756012i \(-0.272855\pi\)
−0.982004 + 0.188858i \(0.939521\pi\)
\(458\) −2.00000 + 3.46410i −0.0934539 + 0.161867i
\(459\) 12.0000 20.7846i 0.560112 0.970143i
\(460\) −4.50000 7.79423i −0.209814 0.363408i
\(461\) −30.0000 −1.39724 −0.698620 0.715493i \(-0.746202\pi\)
−0.698620 + 0.715493i \(0.746202\pi\)
\(462\) −3.00000 15.5885i −0.139573 0.725241i
\(463\) −1.00000 −0.0464739 −0.0232370 0.999730i \(-0.507397\pi\)
−0.0232370 + 0.999730i \(0.507397\pi\)
\(464\) −3.00000 5.19615i −0.139272 0.241225i
\(465\) 8.00000 13.8564i 0.370991 0.642575i
\(466\) −3.00000 + 5.19615i −0.138972 + 0.240707i
\(467\) 3.00000 + 5.19615i 0.138823 + 0.240449i 0.927052 0.374934i \(-0.122335\pi\)
−0.788228 + 0.615383i \(0.789001\pi\)
\(468\) −1.00000 −0.0462250
\(469\) −4.00000 20.7846i −0.184703 0.959744i
\(470\) −9.00000 −0.415139
\(471\) 23.0000 + 39.8372i 1.05978 + 1.83560i
\(472\) 0 0
\(473\) −3.00000 + 5.19615i −0.137940 + 0.238919i
\(474\) 10.0000 + 17.3205i 0.459315 + 0.795557i
\(475\) −1.00000 −0.0458831
\(476\) −15.0000 5.19615i −0.687524 0.238165i
\(477\) 9.00000 0.412082
\(478\) −3.00000 5.19615i −0.137217 0.237666i
\(479\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(480\) −1.00000 + 1.73205i −0.0456435 + 0.0790569i
\(481\) −3.50000 6.06218i −0.159586 0.276412i
\(482\) 1.00000 0.0455488
\(483\) 36.0000 31.1769i 1.63806 1.41860i
\(484\) −2.00000 −0.0909091
\(485\) 5.00000 + 8.66025i 0.227038 + 0.393242i
\(486\) 5.00000 8.66025i 0.226805 0.392837i
\(487\) 8.00000 13.8564i 0.362515 0.627894i −0.625859 0.779936i \(-0.715252\pi\)
0.988374 + 0.152042i \(0.0485850\pi\)
\(488\) 4.00000 + 6.92820i 0.181071 + 0.313625i
\(489\) −40.0000 −1.80886
\(490\) −5.50000 4.33013i −0.248465 0.195615i
\(491\) 36.0000 1.62466 0.812329 0.583200i \(-0.198200\pi\)
0.812329 + 0.583200i \(0.198200\pi\)
\(492\) 3.00000 + 5.19615i 0.135250 + 0.234261i
\(493\) 18.0000 31.1769i 0.810679 1.40414i
\(494\) 0.500000 0.866025i 0.0224961 0.0389643i
\(495\) −1.50000 2.59808i −0.0674200 0.116775i
\(496\) 8.00000 0.359211
\(497\) 0 0
\(498\) 0 0
\(499\) 2.00000 + 3.46410i 0.0895323 + 0.155074i 0.907314 0.420455i \(-0.138129\pi\)
−0.817781 + 0.575529i \(0.804796\pi\)
\(500\) −0.500000 + 0.866025i −0.0223607 + 0.0387298i
\(501\) 3.00000 5.19615i 0.134030 0.232147i
\(502\) −7.50000 12.9904i −0.334741 0.579789i
\(503\) 24.0000 1.07011 0.535054 0.844818i \(-0.320291\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(504\) −2.50000 0.866025i −0.111359 0.0385758i
\(505\) 12.0000 0.533993
\(506\) 13.5000 + 23.3827i 0.600148 + 1.03949i
\(507\) −12.0000 + 20.7846i −0.532939 + 0.923077i
\(508\) 0.500000 0.866025i 0.0221839 0.0384237i
\(509\) 21.0000 + 36.3731i 0.930809 + 1.61221i 0.781943 + 0.623350i \(0.214229\pi\)
0.148866 + 0.988857i \(0.452438\pi\)
\(510\) −12.0000 −0.531369
\(511\) 2.00000 + 10.3923i 0.0884748 + 0.459728i
\(512\) −1.00000 −0.0441942
\(513\) 2.00000 + 3.46410i 0.0883022 + 0.152944i
\(514\) 0 0
\(515\) 2.00000 3.46410i 0.0881305 0.152647i
\(516\) 2.00000 + 3.46410i 0.0880451 + 0.152499i
\(517\) 27.0000 1.18746
\(518\) −3.50000 18.1865i −0.153781 0.799070i
\(519\) −18.0000 −0.790112
\(520\) −0.500000 0.866025i −0.0219265 0.0379777i
\(521\) 7.50000 12.9904i 0.328581 0.569119i −0.653650 0.756797i \(-0.726763\pi\)
0.982231 + 0.187678i \(0.0600963\pi\)
\(522\) 3.00000 5.19615i 0.131306 0.227429i
\(523\) 14.0000 + 24.2487i 0.612177 + 1.06032i 0.990873 + 0.134801i \(0.0430394\pi\)
−0.378695 + 0.925521i \(0.623627\pi\)
\(524\) 3.00000 0.131056
\(525\) −5.00000 1.73205i −0.218218 0.0755929i
\(526\) 0 0
\(527\) 24.0000 + 41.5692i 1.04546 + 1.81078i
\(528\) 3.00000 5.19615i 0.130558 0.226134i
\(529\) −29.0000 + 50.2295i −1.26087 + 2.18389i
\(530\) 4.50000 + 7.79423i 0.195468 + 0.338560i
\(531\) 0 0
\(532\) 2.00000 1.73205i 0.0867110 0.0750939i
\(533\) −3.00000 −0.129944
\(534\) −6.00000 10.3923i −0.259645 0.449719i
\(535\) 6.00000 10.3923i 0.259403 0.449299i
\(536\) 4.00000 6.92820i 0.172774 0.299253i
\(537\) −3.00000 5.19615i −0.129460 0.224231i
\(538\) 0 0
\(539\) 16.5000 + 12.9904i 0.710705 + 0.559535i
\(540\) 4.00000 0.172133
\(541\) −4.00000 6.92820i −0.171973 0.297867i 0.767136 0.641484i \(-0.221681\pi\)
−0.939110 + 0.343617i \(0.888348\pi\)
\(542\) −8.00000 + 13.8564i −0.343629 + 0.595184i
\(543\) 2.00000 3.46410i 0.0858282 0.148659i
\(544\) −3.00000 5.19615i −0.128624 0.222783i
\(545\) −16.0000 −0.685365
\(546\) 4.00000 3.46410i 0.171184 0.148250i
\(547\) 8.00000 0.342055 0.171028 0.985266i \(-0.445291\pi\)
0.171028 + 0.985266i \(0.445291\pi\)
\(548\) −6.00000 10.3923i −0.256307 0.443937i
\(549\) −4.00000 + 6.92820i −0.170716 + 0.295689i
\(550\) 1.50000 2.59808i 0.0639602 0.110782i
\(551\) 3.00000 + 5.19615i 0.127804 + 0.221364i
\(552\) 18.0000 0.766131
\(553\) −25.0000 8.66025i −1.06311 0.368271i
\(554\) 10.0000 0.424859
\(555\) −7.00000 12.1244i −0.297133 0.514650i
\(556\) 2.00000 3.46410i 0.0848189 0.146911i
\(557\) 4.50000 7.79423i 0.190671 0.330252i −0.754802 0.655953i \(-0.772267\pi\)
0.945473 + 0.325701i \(0.105600\pi\)
\(558\) 4.00000 + 6.92820i 0.169334 + 0.293294i
\(559\) −2.00000 −0.0845910
\(560\) −0.500000 2.59808i −0.0211289 0.109789i
\(561\) 36.0000 1.51992
\(562\) −13.5000 23.3827i −0.569463 0.986339i
\(563\) −21.0000 + 36.3731i −0.885044 + 1.53294i −0.0393818 + 0.999224i \(0.512539\pi\)
−0.845663 + 0.533718i \(0.820794\pi\)
\(564\) 9.00000 15.5885i 0.378968 0.656392i
\(565\) 0 0
\(566\) −14.0000 −0.588464
\(567\) 5.50000 + 28.5788i 0.230978 + 1.20020i
\(568\) 0 0
\(569\) −10.5000 18.1865i −0.440183 0.762419i 0.557520 0.830164i \(-0.311753\pi\)
−0.997703 + 0.0677445i \(0.978420\pi\)
\(570\) 1.00000 1.73205i 0.0418854 0.0725476i
\(571\) −10.0000 + 17.3205i −0.418487 + 0.724841i −0.995788 0.0916910i \(-0.970773\pi\)
0.577301 + 0.816532i \(0.304106\pi\)
\(572\) 1.50000 + 2.59808i 0.0627182 + 0.108631i
\(573\) −24.0000 −1.00261
\(574\) −7.50000 2.59808i −0.313044 0.108442i
\(575\) 9.00000 0.375326
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −22.0000 + 38.1051i −0.915872 + 1.58634i −0.110252 + 0.993904i \(0.535166\pi\)
−0.805620 + 0.592433i \(0.798167\pi\)
\(578\) 9.50000 16.4545i 0.395148 0.684416i
\(579\) −16.0000 27.7128i −0.664937 1.15171i
\(580\) 6.00000 0.249136
\(581\) 0 0
\(582\) −20.0000 −0.829027
\(583\) −13.5000 23.3827i −0.559113 0.968412i
\(584\) −2.00000 + 3.46410i −0.0827606 + 0.143346i
\(585\) 0.500000 0.866025i 0.0206725 0.0358057i
\(586\) −4.50000 7.79423i −0.185893 0.321977i
\(587\) −24.0000 −0.990586 −0.495293 0.868726i \(-0.664939\pi\)
−0.495293 + 0.868726i \(0.664939\pi\)
\(588\) 13.0000 5.19615i 0.536111 0.214286i
\(589\) −8.00000 −0.329634
\(590\) 0 0
\(591\) 15.0000 25.9808i 0.617018 1.06871i
\(592\) 3.50000 6.06218i 0.143849 0.249154i
\(593\) −12.0000 20.7846i −0.492781 0.853522i 0.507184 0.861838i \(-0.330686\pi\)
−0.999965 + 0.00831589i \(0.997353\pi\)
\(594\) −12.0000 −0.492366
\(595\) 12.0000 10.3923i 0.491952 0.426043i
\(596\) −6.00000 −0.245770
\(597\) −16.0000 27.7128i −0.654836 1.13421i
\(598\) −4.50000 + 7.79423i −0.184019 + 0.318730i
\(599\) 21.0000 36.3731i 0.858037 1.48616i −0.0157622 0.999876i \(-0.505017\pi\)
0.873799 0.486287i \(-0.161649\pi\)
\(600\) −1.00000 1.73205i −0.0408248 0.0707107i
\(601\) 26.0000 1.06056 0.530281 0.847822i \(-0.322086\pi\)
0.530281 + 0.847822i \(0.322086\pi\)
\(602\) −5.00000 1.73205i −0.203785 0.0705931i
\(603\) 8.00000 0.325785
\(604\) 5.00000 + 8.66025i 0.203447 + 0.352381i
\(605\) 1.00000 1.73205i 0.0406558 0.0704179i
\(606\) −12.0000 + 20.7846i −0.487467 + 0.844317i
\(607\) 0.500000 + 0.866025i 0.0202944 + 0.0351509i 0.875994 0.482322i \(-0.160206\pi\)
−0.855700 + 0.517472i \(0.826873\pi\)
\(608\) 1.00000 0.0405554
\(609\) 6.00000 + 31.1769i 0.243132 + 1.26335i
\(610\) −8.00000 −0.323911
\(611\) 4.50000 + 7.79423i 0.182051 + 0.315321i
\(612\) 3.00000 5.19615i 0.121268 0.210042i
\(613\) −14.5000 + 25.1147i −0.585649 + 1.01437i 0.409145 + 0.912470i \(0.365827\pi\)
−0.994794 + 0.101905i \(0.967506\pi\)
\(614\) 7.00000 + 12.1244i 0.282497 + 0.489299i
\(615\) −6.00000 −0.241943
\(616\) 1.50000 + 7.79423i 0.0604367 + 0.314038i
\(617\) −18.0000 −0.724653 −0.362326 0.932051i \(-0.618017\pi\)
−0.362326 + 0.932051i \(0.618017\pi\)
\(618\) 4.00000 + 6.92820i 0.160904 + 0.278693i
\(619\) −11.5000 + 19.9186i −0.462224 + 0.800595i −0.999071 0.0430838i \(-0.986282\pi\)
0.536847 + 0.843679i \(0.319615\pi\)
\(620\) −4.00000 + 6.92820i −0.160644 + 0.278243i
\(621\) −18.0000 31.1769i −0.722315 1.25109i
\(622\) 24.0000 0.962312
\(623\) 15.0000 + 5.19615i 0.600962 + 0.208179i
\(624\) 2.00000 0.0800641
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −14.0000 + 24.2487i −0.559553 + 0.969173i
\(627\) −3.00000 + 5.19615i −0.119808 + 0.207514i
\(628\) −11.5000 19.9186i −0.458900 0.794838i
\(629\) 42.0000 1.67465
\(630\) 2.00000 1.73205i 0.0796819 0.0690066i
\(631\) 20.0000 0.796187 0.398094 0.917345i \(-0.369672\pi\)
0.398094 + 0.917345i \(0.369672\pi\)
\(632\) −5.00000 8.66025i −0.198889 0.344486i
\(633\) 23.0000 39.8372i 0.914168 1.58339i
\(634\) 3.00000 5.19615i 0.119145 0.206366i
\(635\) 0.500000 + 0.866025i 0.0198419 + 0.0343672i
\(636\) −18.0000 −0.713746
\(637\) −1.00000 + 6.92820i −0.0396214 + 0.274505i
\(638\) −18.0000 −0.712627
\(639\) 0 0
\(640\) 0.500000 0.866025i 0.0197642 0.0342327i
\(641\) −13.5000 + 23.3827i −0.533218 + 0.923561i 0.466029 + 0.884769i \(0.345684\pi\)
−0.999247 + 0.0387913i \(0.987649\pi\)
\(642\) 12.0000 + 20.7846i 0.473602 + 0.820303i
\(643\) 2.00000 0.0788723 0.0394362 0.999222i \(-0.487444\pi\)
0.0394362 + 0.999222i \(0.487444\pi\)
\(644\) −18.0000 + 15.5885i −0.709299 + 0.614271i
\(645\) −4.00000 −0.157500
\(646\) 3.00000 + 5.19615i 0.118033 + 0.204440i
\(647\) −16.5000 + 28.5788i −0.648682 + 1.12355i 0.334756 + 0.942305i \(0.391346\pi\)
−0.983438 + 0.181245i \(0.941987\pi\)
\(648\) −5.50000 + 9.52628i −0.216060 + 0.374228i
\(649\) 0 0
\(650\) 1.00000 0.0392232
\(651\) −40.0000 13.8564i −1.56772 0.543075i
\(652\) 20.0000 0.783260
\(653\) 4.50000 + 7.79423i 0.176099 + 0.305012i 0.940541 0.339680i \(-0.110319\pi\)
−0.764442 + 0.644692i \(0.776986\pi\)
\(654\) 16.0000 27.7128i 0.625650 1.08366i
\(655\) −1.50000 + 2.59808i −0.0586098 + 0.101515i
\(656\) −1.50000 2.59808i −0.0585652 0.101438i
\(657\) −4.00000 −0.156055
\(658\) 4.50000 + 23.3827i 0.175428 + 0.911552i
\(659\) −24.0000 −0.934907 −0.467454 0.884018i \(-0.654829\pi\)
−0.467454 + 0.884018i \(0.654829\pi\)
\(660\) 3.00000 + 5.19615i 0.116775 + 0.202260i
\(661\) 14.0000 24.2487i 0.544537 0.943166i −0.454099 0.890951i \(-0.650039\pi\)
0.998636 0.0522143i \(-0.0166279\pi\)
\(662\) −3.50000 + 6.06218i −0.136031 + 0.235613i
\(663\) 6.00000 + 10.3923i 0.233021 + 0.403604i
\(664\) 0 0
\(665\) 0.500000 + 2.59808i 0.0193892 + 0.100749i
\(666\) 7.00000 0.271244
\(667\) −27.0000 46.7654i −1.04544 1.81076i
\(668\) −1.50000 + 2.59808i −0.0580367 + 0.100523i
\(669\) 8.00000 13.8564i 0.309298 0.535720i
\(670\) 4.00000 + 6.92820i 0.154533 + 0.267660i
\(671\) 24.0000 0.926510
\(672\) 5.00000 + 1.73205i 0.192879 + 0.0668153i
\(673\) −34.0000 −1.31060 −0.655302 0.755367i \(-0.727459\pi\)
−0.655302 + 0.755367i \(0.727459\pi\)
\(674\) −11.0000 19.0526i −0.423704 0.733877i
\(675\) −2.00000 + 3.46410i −0.0769800 + 0.133333i
\(676\) 6.00000 10.3923i 0.230769 0.399704i
\(677\) 4.50000 + 7.79423i 0.172949 + 0.299557i 0.939450 0.342687i \(-0.111337\pi\)
−0.766501 + 0.642244i \(0.778004\pi\)
\(678\) 0 0
\(679\) 20.0000 17.3205i 0.767530 0.664700i
\(680\) 6.00000 0.230089
\(681\) −12.0000 20.7846i −0.459841 0.796468i
\(682\) 12.0000 20.7846i 0.459504 0.795884i
\(683\) −6.00000 + 10.3923i −0.229584 + 0.397650i −0.957685 0.287819i \(-0.907070\pi\)
0.728101 + 0.685470i \(0.240403\pi\)
\(684\) 0.500000 + 0.866025i 0.0191180 + 0.0331133i
\(685\) 12.0000 0.458496
\(686\) −8.50000 + 16.4545i −0.324532 + 0.628235i
\(687\) 8.00000 0.305219
\(688\) −1.00000 1.73205i −0.0381246 0.0660338i
\(689\) 4.50000 7.79423i 0.171436 0.296936i
\(690\) −9.00000 + 15.5885i −0.342624 + 0.593442i
\(691\) −16.0000 27.7128i −0.608669 1.05425i −0.991460 0.130410i \(-0.958371\pi\)
0.382791 0.923835i \(-0.374963\pi\)
\(692\) 9.00000 0.342129
\(693\) −6.00000 + 5.19615i −0.227921 + 0.197386i
\(694\) 0 0
\(695\) 2.00000 + 3.46410i 0.0758643 + 0.131401i
\(696\) −6.00000 + 10.3923i −0.227429 + 0.393919i
\(697\) 9.00000 15.5885i 0.340899 0.590455i
\(698\) 13.0000 + 22.5167i 0.492057 + 0.852268i
\(699\) 12.0000 0.453882
\(700\) 2.50000 + 0.866025i 0.0944911 + 0.0327327i
\(701\) −30.0000 −1.13308 −0.566542 0.824033i \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) −2.00000 3.46410i −0.0754851 0.130744i
\(703\) −3.50000 + 6.06218i −0.132005 + 0.228639i
\(704\) −1.50000 + 2.59808i −0.0565334 + 0.0979187i
\(705\) 9.00000 + 15.5885i 0.338960 + 0.587095i
\(706\) −12.0000 −0.451626
\(707\) −6.00000 31.1769i −0.225653 1.17253i
\(708\) 0 0
\(709\) 23.0000 + 39.8372i 0.863783 + 1.49612i 0.868250 + 0.496126i \(0.165245\pi\)
−0.00446726 + 0.999990i \(0.501422\pi\)
\(710\) 0 0
\(711\) 5.00000 8.66025i 0.187515 0.324785i
\(712\) 3.00000 + 5.19615i 0.112430 + 0.194734i
\(713\) 72.0000 2.69642
\(714\) 6.00000 + 31.1769i 0.224544 + 1.16677i
\(715\) −3.00000 −0.112194
\(716\) 1.50000 + 2.59808i 0.0560576 + 0.0970947i
\(717\) −6.00000 + 10.3923i −0.224074 + 0.388108i
\(718\) 9.00000 15.5885i 0.335877 0.581756i
\(719\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(720\) 1.00000 0.0372678
\(721\) −10.0000 3.46410i −0.372419 0.129010i
\(722\) 18.0000 0.669891
\(723\) −1.00000 1.73205i −0.0371904 0.0644157i
\(724\) −1.00000 + 1.73205i −0.0371647 + 0.0643712i
\(725\) −3.00000 + 5.19615i −0.111417 + 0.192980i
\(726\) 2.00000 + 3.46410i 0.0742270 + 0.128565i
\(727\) −1.00000 −0.0370879 −0.0185440 0.999828i \(-0.505903\pi\)
−0.0185440 + 0.999828i \(0.505903\pi\)
\(728\) −2.00000 + 1.73205i −0.0741249 + 0.0641941i
\(729\) 13.0000 0.481481
\(730\) −2.00000 3.46410i −0.0740233 0.128212i
\(731\) 6.00000 10.3923i 0.221918 0.384373i
\(732\) 8.00000 13.8564i 0.295689 0.512148i
\(733\) 21.5000 + 37.2391i 0.794121 + 1.37546i 0.923396 + 0.383849i \(0.125402\pi\)
−0.129275 + 0.991609i \(0.541265\pi\)
\(734\) 19.0000 0.701303
\(735\) −2.00000 + 13.8564i −0.0737711 + 0.511101i
\(736\) −9.00000 −0.331744
\(737\) −12.0000 20.7846i −0.442026 0.765611i
\(738\) 1.50000 2.59808i 0.0552158 0.0956365i
\(739\) −17.5000 + 30.3109i −0.643748 + 1.11500i 0.340841 + 0.940121i \(0.389288\pi\)
−0.984589 + 0.174883i \(0.944045\pi\)
\(740\) 3.50000 + 6.06218i 0.128663 + 0.222850i
\(741\) −2.00000 −0.0734718
\(742\) 18.0000 15.5885i 0.660801 0.572270i
\(743\) −45.0000 −1.65089 −0.825445 0.564483i \(-0.809076\pi\)
−0.825445 + 0.564483i \(0.809076\pi\)
\(744\) −8.00000 13.8564i −0.293294 0.508001i
\(745\) 3.00000 5.19615i 0.109911 0.190372i
\(746\) 1.00000 1.73205i 0.0366126 0.0634149i
\(747\) 0 0
\(748\) −18.0000 −0.658145
\(749\) −30.0000 10.3923i −1.09618 0.379727i
\(750\) 2.00000 0.0730297
\(751\) 5.00000 + 8.66025i 0.182453 + 0.316017i 0.942715 0.333599i \(-0.108263\pi\)
−0.760263 + 0.649616i \(0.774930\pi\)
\(752\) −4.50000 + 7.79423i −0.164098 + 0.284226i
\(753\) −15.0000 + 25.9808i −0.546630 + 0.946792i
\(754\) −3.00000 5.19615i −0.109254 0.189233i
\(755\) −10.0000 −0.363937
\(756\) −2.00000 10.3923i −0.0727393 0.377964i
\(757\) 38.0000 1.38113 0.690567 0.723269i \(-0.257361\pi\)
0.690567 + 0.723269i \(0.257361\pi\)
\(758\) 11.5000 + 19.9186i 0.417699 + 0.723476i
\(759\) 27.0000 46.7654i 0.980038 1.69748i
\(760\) −0.500000 + 0.866025i −0.0181369 + 0.0314140i
\(761\) 13.5000 + 23.3827i 0.489375 + 0.847622i 0.999925 0.0122260i \(-0.00389175\pi\)
−0.510551 + 0.859848i \(0.670558\pi\)
\(762\) −2.00000 −0.0724524
\(763\) 8.00000 + 41.5692i 0.289619 + 1.50491i
\(764\) 12.0000 0.434145
\(765\) 3.00000 + 5.19615i 0.108465 + 0.187867i
\(766\) 10.5000 18.1865i 0.379380 0.657106i
\(767\) 0 0
\(768\) 1.00000 + 1.73205i 0.0360844 + 0.0625000i
\(769\) 23.0000 0.829401 0.414701 0.909958i \(-0.363886\pi\)
0.414701 + 0.909958i \(0.363886\pi\)
\(770\) −7.50000 2.59808i −0.270281 0.0936282i
\(771\) 0 0
\(772\) 8.00000 + 13.8564i 0.287926 + 0.498703i
\(773\) 25.5000 44.1673i 0.917171 1.58859i 0.113480 0.993540i \(-0.463800\pi\)
0.803691 0.595047i \(-0.202867\pi\)
\(774\) 1.00000 1.73205i 0.0359443 0.0622573i
\(775\) −4.00000 6.92820i −0.143684 0.248868i
\(776\) 10.0000 0.358979
\(777\) −28.0000 + 24.2487i −1.00449 + 0.869918i
\(778\) 12.0000 0.430221
\(779\) 1.50000 + 2.59808i 0.0537431 + 0.0930857i
\(780\) −1.00000 + 1.73205i −0.0358057 + 0.0620174i
\(781\) 0 0
\(782\) −27.0000 46.7654i −0.965518 1.67233i
\(783\) 24.0000 0.857690
\(784\) −6.50000 + 2.59808i −0.232143 + 0.0927884i
\(785\) 23.0000 0.820905
\(786\) −3.00000 5.19615i −0.107006 0.185341i
\(787\) 11.0000 19.0526i 0.392108 0.679150i −0.600620 0.799535i \(-0.705079\pi\)
0.992727 + 0.120384i \(0.0384127\pi\)
\(788\) −7.50000 + 12.9904i −0.267176 + 0.462763i
\(789\) 0 0
\(790\) 10.0000 0.355784
\(791\) 0 0
\(792\) −3.00000 −0.106600