Properties

Label 350.2.e.b.51.1
Level $350$
Weight $2$
Character 350.51
Analytic conductor $2.795$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 350.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.79476407074\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 70)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 51.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 350.51
Dual form 350.2.e.b.151.1

$q$-expansion

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

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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 −0.995782 0.0917517i \(-0.970753\pi\)
0.418432 0.908248i \(-0.362580\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) 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 0
\(11\) −1.50000 2.59808i −0.452267 0.783349i 0.546259 0.837616i \(-0.316051\pi\)
−0.998526 + 0.0542666i \(0.982718\pi\)
\(12\) −1.00000 + 1.73205i −0.288675 + 0.500000i
\(13\) 1.00000 0.277350 0.138675 0.990338i \(-0.455716\pi\)
0.138675 + 0.990338i \(0.455716\pi\)
\(14\) −2.50000 + 0.866025i −0.668153 + 0.231455i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −3.00000 5.19615i −0.727607 1.26025i −0.957892 0.287129i \(-0.907299\pi\)
0.230285 0.973123i \(-0.426034\pi\)
\(18\) −0.500000 0.866025i −0.117851 0.204124i
\(19\) 0.500000 0.866025i 0.114708 0.198680i −0.802955 0.596040i \(-0.796740\pi\)
0.917663 + 0.397360i \(0.130073\pi\)
\(20\) 0 0
\(21\) 1.00000 5.19615i 0.218218 1.13389i
\(22\) 3.00000 0.639602
\(23\) 4.50000 7.79423i 0.938315 1.62521i 0.169701 0.985496i \(-0.445720\pi\)
0.768613 0.639713i \(-0.220947\pi\)
\(24\) −1.00000 1.73205i −0.204124 0.353553i
\(25\) 0 0
\(26\) −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 \(0.311919\pi\)
\(30\) 0 0
\(31\) −4.00000 6.92820i −0.718421 1.24434i −0.961625 0.274367i \(-0.911532\pi\)
0.243204 0.969975i \(-0.421802\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −3.00000 + 5.19615i −0.522233 + 0.904534i
\(34\) 6.00000 1.02899
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −3.50000 + 6.06218i −0.575396 + 0.996616i 0.420602 + 0.907245i \(0.361819\pi\)
−0.995998 + 0.0893706i \(0.971514\pi\)
\(38\) 0.500000 + 0.866025i 0.0811107 + 0.140488i
\(39\) −1.00000 1.73205i −0.160128 0.277350i
\(40\) 0 0
\(41\) 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 \(-0.548732\pi\)
−0.152499 + 0.988304i \(0.548732\pi\)
\(44\) −1.50000 + 2.59808i −0.226134 + 0.391675i
\(45\) 0 0
\(46\) 4.50000 + 7.79423i 0.663489 + 1.14920i
\(47\) 4.50000 7.79423i 0.656392 1.13691i −0.325150 0.945662i \(-0.605415\pi\)
0.981543 0.191243i \(-0.0612518\pi\)
\(48\) 2.00000 0.288675
\(49\) 1.00000 + 6.92820i 0.142857 + 0.989743i
\(50\) 0 0
\(51\) −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 0.989828 + 0.142269i \(0.0454398\pi\)
−0.371706 + 0.928351i \(0.621227\pi\)
\(54\) 2.00000 3.46410i 0.272166 0.471405i
\(55\) 0 0
\(56\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(60\) 0 0
\(61\) −4.00000 + 6.92820i −0.512148 + 0.887066i 0.487753 + 0.872982i \(0.337817\pi\)
−0.999901 + 0.0140840i \(0.995517\pi\)
\(62\) 8.00000 1.01600
\(63\) −2.50000 + 0.866025i −0.314970 + 0.109109i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −3.00000 5.19615i −0.369274 0.639602i
\(67\) 4.00000 + 6.92820i 0.488678 + 0.846415i 0.999915 0.0130248i \(-0.00414604\pi\)
−0.511237 + 0.859440i \(0.670813\pi\)
\(68\) −3.00000 + 5.19615i −0.363803 + 0.630126i
\(69\) −18.0000 −2.16695
\(70\) 0 0
\(71\) 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 \(-0.241875\pi\)
−0.959006 + 0.283387i \(0.908542\pi\)
\(74\) −3.50000 6.06218i −0.406867 0.704714i
\(75\) 0 0
\(76\) −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 −0.434730 0.900561i \(-0.643156\pi\)
0.997274 0.0737937i \(-0.0235106\pi\)
\(80\) 0 0
\(81\) 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
\(85\) 0 0
\(86\) 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 −0.980071 0.198650i \(-0.936344\pi\)
0.662071 + 0.749441i \(0.269678\pi\)
\(90\) 0 0
\(91\) 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 0
\(96\) −1.00000 + 1.73205i −0.102062 + 0.176777i
\(97\) 10.0000 1.01535 0.507673 0.861550i \(-0.330506\pi\)
0.507673 + 0.861550i \(0.330506\pi\)
\(98\) −6.50000 2.59808i −0.656599 0.262445i
\(99\) 3.00000 0.301511
\(100\) 0 0
\(101\) −6.00000 10.3923i −0.597022 1.03407i −0.993258 0.115924i \(-0.963017\pi\)
0.396236 0.918149i \(-0.370316\pi\)
\(102\) −6.00000 10.3923i −0.594089 1.02899i
\(103\) −2.00000 + 3.46410i −0.197066 + 0.341328i −0.947576 0.319531i \(-0.896475\pi\)
0.750510 + 0.660859i \(0.229808\pi\)
\(104\) 1.00000 0.0980581
\(105\) 0 0
\(106\) −9.00000 −0.874157
\(107\) −6.00000 + 10.3923i −0.580042 + 1.00466i 0.415432 + 0.909624i \(0.363630\pi\)
−0.995474 + 0.0950377i \(0.969703\pi\)
\(108\) 2.00000 + 3.46410i 0.192450 + 0.333333i
\(109\) 8.00000 + 13.8564i 0.766261 + 1.32720i 0.939577 + 0.342337i \(0.111218\pi\)
−0.173316 + 0.984866i \(0.555448\pi\)
\(110\) 0 0
\(111\) 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
\(115\) 0 0
\(116\) −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
\(120\) 0 0
\(121\) 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
\(125\) 0 0
\(126\) 0.500000 2.59808i 0.0445435 0.231455i
\(127\) 1.00000 0.0887357 0.0443678 0.999015i \(-0.485873\pi\)
0.0443678 + 0.999015i \(0.485873\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 2.00000 + 3.46410i 0.176090 + 0.304997i
\(130\) 0 0
\(131\) −1.50000 + 2.59808i −0.131056 + 0.226995i −0.924084 0.382190i \(-0.875170\pi\)
0.793028 + 0.609185i \(0.208503\pi\)
\(132\) 6.00000 0.522233
\(133\) 2.50000 0.866025i 0.216777 0.0750939i
\(134\) −8.00000 −0.691095
\(135\) 0 0
\(136\) −3.00000 5.19615i −0.257248 0.445566i
\(137\) 6.00000 + 10.3923i 0.512615 + 0.887875i 0.999893 + 0.0146279i \(0.00465636\pi\)
−0.487278 + 0.873247i \(0.662010\pi\)
\(138\) 9.00000 15.5885i 0.766131 1.32698i
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 0 0
\(141\) −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
\(145\) 0 0
\(146\) 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 −0.716578 0.697507i \(-0.754293\pi\)
0.962348 + 0.271821i \(0.0876260\pi\)
\(150\) 0 0
\(151\) 5.00000 + 8.66025i 0.406894 + 0.704761i 0.994540 0.104357i \(-0.0332784\pi\)
−0.587646 + 0.809118i \(0.699945\pi\)
\(152\) 0.500000 0.866025i 0.0405554 0.0702439i
\(153\) 6.00000 0.485071
\(154\) 6.00000 + 5.19615i 0.483494 + 0.418718i
\(155\) 0 0
\(156\) −1.00000 + 1.73205i −0.0800641 + 0.138675i
\(157\) 11.5000 + 19.9186i 0.917800 + 1.58968i 0.802749 + 0.596316i \(0.203370\pi\)
0.115050 + 0.993360i \(0.463297\pi\)
\(158\) 5.00000 + 8.66025i 0.397779 + 0.688973i
\(159\) 9.00000 15.5885i 0.713746 1.23625i
\(160\) 0 0
\(161\) 22.5000 7.79423i 1.77325 0.614271i
\(162\) −11.0000 −0.864242
\(163\) 10.0000 17.3205i 0.783260 1.35665i −0.146772 0.989170i \(-0.546888\pi\)
0.930033 0.367477i \(-0.119778\pi\)
\(164\) −1.50000 2.59808i −0.117130 0.202876i
\(165\) 0 0
\(166\) 0 0
\(167\) −3.00000 −0.232147 −0.116073 0.993241i \(-0.537031\pi\)
−0.116073 + 0.993241i \(0.537031\pi\)
\(168\) 1.00000 5.19615i 0.0771517 0.400892i
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) 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 \(-0.722185\pi\)
0.984828 + 0.173534i \(0.0555188\pi\)
\(174\) 12.0000 0.909718
\(175\) 0 0
\(176\) 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 0.916623 0.399753i \(-0.130904\pi\)
−0.804508 + 0.593942i \(0.797571\pi\)
\(180\) 0 0
\(181\) 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
\(185\) 0 0
\(186\) −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
\(190\) 0 0
\(191\) −6.00000 + 10.3923i −0.434145 + 0.751961i −0.997225 0.0744412i \(-0.976283\pi\)
0.563081 + 0.826402i \(0.309616\pi\)
\(192\) −1.00000 1.73205i −0.0721688 0.125000i
\(193\) −8.00000 13.8564i −0.575853 0.997406i −0.995948 0.0899262i \(-0.971337\pi\)
0.420096 0.907480i \(-0.361996\pi\)
\(194\) −5.00000 + 8.66025i −0.358979 + 0.621770i
\(195\) 0 0
\(196\) 5.50000 4.33013i 0.392857 0.309295i
\(197\) −15.0000 −1.06871 −0.534353 0.845262i \(-0.679445\pi\)
−0.534353 + 0.845262i \(0.679445\pi\)
\(198\) −1.50000 + 2.59808i −0.106600 + 0.184637i
\(199\) 8.00000 + 13.8564i 0.567105 + 0.982255i 0.996850 + 0.0793045i \(0.0252700\pi\)
−0.429745 + 0.902950i \(0.641397\pi\)
\(200\) 0 0
\(201\) 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
\(205\) 0 0
\(206\) −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
\(210\) 0 0
\(211\) 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
\(215\) 0 0
\(216\) −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
\(220\) 0 0
\(221\) −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 \(-0.586316\pi\)
−0.267860 + 0.963458i \(0.586316\pi\)
\(224\) 0.500000 2.59808i 0.0334077 0.173591i
\(225\) 0 0
\(226\) 0 0
\(227\) −6.00000 10.3923i −0.398234 0.689761i 0.595274 0.803523i \(-0.297043\pi\)
−0.993508 + 0.113761i \(0.963710\pi\)
\(228\) 1.00000 + 1.73205i 0.0662266 + 0.114708i
\(229\) 2.00000 3.46410i 0.132164 0.228914i −0.792347 0.610071i \(-0.791141\pi\)
0.924510 + 0.381157i \(0.124474\pi\)
\(230\) 0 0
\(231\) −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 \(-0.896303\pi\)
0.750867 + 0.660454i \(0.229636\pi\)
\(234\) −0.500000 0.866025i −0.0326860 0.0566139i
\(235\) 0 0
\(236\) 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 \(0.562164\pi\)
\(240\) 0 0
\(241\) 0.500000 + 0.866025i 0.0322078 + 0.0557856i 0.881680 0.471848i \(-0.156413\pi\)
−0.849472 + 0.527633i \(0.823079\pi\)
\(242\) 1.00000 + 1.73205i 0.0642824 + 0.111340i
\(243\) 5.00000 8.66025i 0.320750 0.555556i
\(244\) 8.00000 0.512148
\(245\) 0 0
\(246\) 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 0
\(251\) −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
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(258\) −4.00000 −0.249029
\(259\) −17.5000 + 6.06218i −1.08740 + 0.376685i
\(260\) 0 0
\(261\) −3.00000 + 5.19615i −0.185695 + 0.321634i
\(262\) −1.50000 2.59808i −0.0926703 0.160510i
\(263\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(264\) −3.00000 + 5.19615i −0.184637 + 0.319801i
\(265\) 0 0
\(266\) −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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(270\) 0 0
\(271\) 8.00000 13.8564i 0.485965 0.841717i −0.513905 0.857847i \(-0.671801\pi\)
0.999870 + 0.0161307i \(0.00513477\pi\)
\(272\) 6.00000 0.363803
\(273\) 1.00000 5.19615i 0.0605228 0.314485i
\(274\) −12.0000 −0.724947
\(275\) 0 0
\(276\) 9.00000 + 15.5885i 0.541736 + 0.938315i
\(277\) −5.00000 8.66025i −0.300421 0.520344i 0.675810 0.737075i \(-0.263794\pi\)
−0.976231 + 0.216731i \(0.930460\pi\)
\(278\) 2.00000 3.46410i 0.119952 0.207763i
\(279\) 8.00000 0.478947
\(280\) 0 0
\(281\) −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 \(-0.0300609\pi\)
−0.579437 + 0.815017i \(0.696728\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 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
\(290\) 0 0
\(291\) −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 \(-0.415323\pi\)
0.262893 + 0.964825i \(0.415323\pi\)
\(294\) 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
\(300\) 0 0
\(301\) −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
\(305\) 0 0
\(306\) −3.00000 + 5.19615i −0.171499 + 0.297044i
\(307\) −14.0000 −0.799022 −0.399511 0.916728i \(-0.630820\pi\)
−0.399511 + 0.916728i \(0.630820\pi\)
\(308\) −7.50000 + 2.59808i −0.427352 + 0.148039i
\(309\) 8.00000 0.455104
\(310\) 0 0
\(311\) 12.0000 + 20.7846i 0.680458 + 1.17859i 0.974841 + 0.222900i \(0.0715523\pi\)
−0.294384 + 0.955687i \(0.595114\pi\)
\(312\) −1.00000 1.73205i −0.0566139 0.0980581i
\(313\) −14.0000 + 24.2487i −0.791327 + 1.37062i 0.133819 + 0.991006i \(0.457276\pi\)
−0.925146 + 0.379612i \(0.876057\pi\)
\(314\) −23.0000 −1.29797
\(315\) 0 0
\(316\) −10.0000 −0.562544
\(317\) 3.00000 5.19615i 0.168497 0.291845i −0.769395 0.638774i \(-0.779442\pi\)
0.937892 + 0.346929i \(0.112775\pi\)
\(318\) 9.00000 + 15.5885i 0.504695 + 0.874157i
\(319\) −9.00000 15.5885i −0.503903 0.872786i
\(320\) 0 0
\(321\) 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 0
\(326\) 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
\(330\) 0 0
\(331\) 3.50000 6.06218i 0.192377 0.333207i −0.753660 0.657264i \(-0.771714\pi\)
0.946038 + 0.324057i \(0.105047\pi\)
\(332\) 0 0
\(333\) −3.50000 6.06218i −0.191799 0.332205i
\(334\) 1.50000 2.59808i 0.0820763 0.142160i
\(335\) 0 0
\(336\) 4.00000 + 3.46410i 0.218218 + 0.188982i
\(337\) 22.0000 1.19842 0.599208 0.800593i \(-0.295482\pi\)
0.599208 + 0.800593i \(0.295482\pi\)
\(338\) 6.00000 10.3923i 0.326357 0.565267i
\(339\) 0 0
\(340\) 0 0
\(341\) −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
\(345\) 0 0
\(346\) 4.50000 + 7.79423i 0.241921 + 0.419020i
\(347\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(348\) −6.00000 + 10.3923i −0.321634 + 0.557086i
\(349\) 26.0000 1.39175 0.695874 0.718164i \(-0.255017\pi\)
0.695874 + 0.718164i \(0.255017\pi\)
\(350\) 0 0
\(351\) −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 \(-0.0632029\pi\)
−0.661004 + 0.750382i \(0.729870\pi\)
\(354\) 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 −0.999590 0.0286287i \(-0.990886\pi\)
0.524588 + 0.851356i \(0.324219\pi\)
\(360\) 0 0
\(361\) 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
\(365\) 0 0
\(366\) −8.00000 + 13.8564i −0.418167 + 0.724286i
\(367\) −9.50000 16.4545i −0.495896 0.858917i 0.504093 0.863649i \(-0.331827\pi\)
−0.999989 + 0.00473247i \(0.998494\pi\)
\(368\) 4.50000 + 7.79423i 0.234579 + 0.406302i
\(369\) −1.50000 + 2.59808i −0.0780869 + 0.135250i
\(370\) 0 0
\(371\) −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 \(-0.816844\pi\)
0.890753 + 0.454488i \(0.150178\pi\)
\(374\) −9.00000 15.5885i −0.465379 0.806060i
\(375\) 0 0
\(376\) 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 0
\(381\) −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 −0.462563 0.886586i \(-0.653070\pi\)
0.999088 0.0427020i \(-0.0135966\pi\)
\(384\) 2.00000 0.102062
\(385\) 0 0
\(386\) 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 0.977086 0.212847i \(-0.0682735\pi\)
−0.672874 + 0.739758i \(0.734940\pi\)
\(390\) 0 0
\(391\) −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
\(395\) 0 0
\(396\) −1.50000 2.59808i −0.0753778 0.130558i
\(397\) 7.00000 12.1244i 0.351320 0.608504i −0.635161 0.772380i \(-0.719066\pi\)
0.986481 + 0.163876i \(0.0523996\pi\)
\(398\) −16.0000 −0.802008
\(399\) −4.00000 3.46410i −0.200250 0.173422i
\(400\) 0 0
\(401\) 13.5000 23.3827i 0.674158 1.16768i −0.302556 0.953131i \(-0.597840\pi\)
0.976714 0.214544i \(-0.0688266\pi\)
\(402\) 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
\(405\) 0 0
\(406\) −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 −0.984803 0.173675i \(-0.944436\pi\)
0.341994 0.939702i \(-0.388898\pi\)
\(410\) 0 0
\(411\) 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 \(0.570553\pi\)
\(420\) 0 0
\(421\) 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
\(425\) 0 0
\(426\) 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
\(430\) 0 0
\(431\) −6.00000 10.3923i −0.289010 0.500580i 0.684564 0.728953i \(-0.259993\pi\)
−0.973574 + 0.228373i \(0.926659\pi\)
\(432\) 2.00000 3.46410i 0.0962250 0.166667i
\(433\) 40.0000 1.92228 0.961139 0.276066i \(-0.0890309\pi\)
0.961139 + 0.276066i \(0.0890309\pi\)
\(434\) 16.0000 + 13.8564i 0.768025 + 0.665129i
\(435\) 0 0
\(436\) 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 0.368945 + 0.929451i \(0.379719\pi\)
−0.989401 + 0.145210i \(0.953614\pi\)
\(440\) 0 0
\(441\) −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 \(-0.741317\pi\)
0.972626 + 0.232377i \(0.0746503\pi\)
\(444\) −7.00000 12.1244i −0.332205 0.575396i
\(445\) 0 0
\(446\) 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 0
\(451\) −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
\(455\) 0 0
\(456\) −2.00000 −0.0936586
\(457\) 7.00000 12.1244i 0.327446 0.567153i −0.654558 0.756012i \(-0.727145\pi\)
0.982004 + 0.188858i \(0.0604787\pi\)
\(458\) 2.00000 + 3.46410i 0.0934539 + 0.161867i
\(459\) 12.0000 + 20.7846i 0.560112 + 0.970143i
\(460\) 0 0
\(461\) −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 \(-0.492603\pi\)
0.0232370 + 0.999730i \(0.492603\pi\)
\(464\) −3.00000 + 5.19615i −0.139272 + 0.241225i
\(465\) 0 0
\(466\) −3.00000 5.19615i −0.138972 0.240707i
\(467\) −3.00000 + 5.19615i −0.138823 + 0.240449i −0.927052 0.374934i \(-0.877665\pi\)
0.788228 + 0.615383i \(0.210999\pi\)
\(468\) 1.00000 0.0462250
\(469\) −4.00000 + 20.7846i −0.184703 + 0.959744i
\(470\) 0 0
\(471\) 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
\(475\) 0 0
\(476\) −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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(480\) 0 0
\(481\) −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
\(485\) 0 0
\(486\) 5.00000 + 8.66025i 0.226805 + 0.392837i
\(487\) −8.00000 13.8564i −0.362515 0.627894i 0.625859 0.779936i \(-0.284748\pi\)
−0.988374 + 0.152042i \(0.951415\pi\)
\(488\) −4.00000 + 6.92820i −0.181071 + 0.313625i
\(489\) −40.0000 −1.80886
\(490\) 0 0
\(491\) 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
\(495\) 0 0
\(496\) 8.00000 0.359211
\(497\) 0 0
\(498\) 0 0
\(499\) 2.00000 3.46410i 0.0895323 0.155074i −0.817781 0.575529i \(-0.804796\pi\)
0.907314 + 0.420455i \(0.138129\pi\)
\(500\) 0 0
\(501\) 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 \(-0.679709\pi\)
−0.535054 + 0.844818i \(0.679709\pi\)
\(504\) −2.50000 + 0.866025i −0.111359 + 0.0385758i
\(505\) 0 0
\(506\) 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 0.148866 0.988857i \(-0.452438\pi\)
0.781943 0.623350i \(-0.214229\pi\)
\(510\) 0 0
\(511\) 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
\(515\) 0 0
\(516\) 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 0
\(521\) 7.50000 + 12.9904i 0.328581 + 0.569119i 0.982231 0.187678i \(-0.0600963\pi\)
−0.653650 + 0.756797i \(0.726763\pi\)
\(522\) −3.00000 5.19615i −0.131306 0.227429i
\(523\) −14.0000 + 24.2487i −0.612177 + 1.06032i 0.378695 + 0.925521i \(0.376373\pi\)
−0.990873 + 0.134801i \(0.956961\pi\)
\(524\) 3.00000 0.131056
\(525\) 0 0
\(526\) 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
\(530\) 0 0
\(531\) 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
\(535\) 0 0
\(536\) 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
\(540\) 0 0
\(541\) −4.00000 + 6.92820i −0.171973 + 0.297867i −0.939110 0.343617i \(-0.888348\pi\)
0.767136 + 0.641484i \(0.221681\pi\)
\(542\) 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
\(545\) 0 0
\(546\) 4.00000 + 3.46410i 0.171184 + 0.148250i
\(547\) −8.00000 −0.342055 −0.171028 0.985266i \(-0.554709\pi\)
−0.171028 + 0.985266i \(0.554709\pi\)
\(548\) 6.00000 10.3923i 0.256307 0.443937i
\(549\) −4.00000 6.92820i −0.170716 0.295689i
\(550\) 0 0
\(551\) 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
\(555\) 0 0
\(556\) 2.00000 + 3.46410i 0.0848189 + 0.146911i
\(557\) −4.50000 7.79423i −0.190671 0.330252i 0.754802 0.655953i \(-0.227733\pi\)
−0.945473 + 0.325701i \(0.894400\pi\)
\(558\) −4.00000 + 6.92820i −0.169334 + 0.293294i
\(559\) −2.00000 −0.0845910
\(560\) 0 0
\(561\) 36.0000 1.51992
\(562\) 13.5000 23.3827i 0.569463 0.986339i
\(563\) 21.0000 + 36.3731i 0.885044 + 1.53294i 0.845663 + 0.533718i \(0.179206\pi\)
0.0393818 + 0.999224i \(0.487461\pi\)
\(564\) 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 −0.997703 0.0677445i \(-0.978420\pi\)
0.557520 + 0.830164i \(0.311753\pi\)
\(570\) 0 0
\(571\) −10.0000 17.3205i −0.418487 0.724841i 0.577301 0.816532i \(-0.304106\pi\)
−0.995788 + 0.0916910i \(0.970773\pi\)
\(572\) −1.50000 + 2.59808i −0.0627182 + 0.108631i
\(573\) 24.0000 1.00261
\(574\) −7.50000 + 2.59808i −0.313044 + 0.108442i
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 22.0000 + 38.1051i 0.915872 + 1.58634i 0.805620 + 0.592433i \(0.201833\pi\)
0.110252 + 0.993904i \(0.464834\pi\)
\(578\) −9.50000 16.4545i −0.395148 0.684416i
\(579\) −16.0000 + 27.7128i −0.664937 + 1.15171i
\(580\) 0 0
\(581\) 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 0
\(586\) −4.50000 + 7.79423i −0.185893 + 0.321977i
\(587\) 24.0000 0.990586 0.495293 0.868726i \(-0.335061\pi\)
0.495293 + 0.868726i \(0.335061\pi\)
\(588\) −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 \(-0.669314\pi\)
0.999965 + 0.00831589i \(0.00264706\pi\)
\(594\) −12.0000 −0.492366
\(595\) 0 0
\(596\) −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 0.873799 + 0.486287i \(0.161649\pi\)
−0.0157622 + 0.999876i \(0.505017\pi\)
\(600\) 0 0
\(601\) 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
\(605\) 0 0
\(606\) −12.0000 20.7846i −0.487467 0.844317i
\(607\) −0.500000 + 0.866025i −0.0202944 + 0.0351509i −0.875994 0.482322i \(-0.839794\pi\)
0.855700 + 0.517472i \(0.173127\pi\)
\(608\) −1.00000 −0.0405554
\(609\) 6.00000 31.1769i 0.243132 1.26335i
\(610\) 0 0
\(611\) 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 0.994794 + 0.101905i \(0.0324938\pi\)
−0.409145 + 0.912470i \(0.634173\pi\)
\(614\) 7.00000 12.1244i 0.282497 0.489299i
\(615\) 0 0
\(616\) 1.50000 7.79423i 0.0604367 0.314038i
\(617\) 18.0000 0.724653 0.362326 0.932051i \(-0.381983\pi\)
0.362326 + 0.932051i \(0.381983\pi\)
\(618\) −4.00000 + 6.92820i −0.160904 + 0.278693i
\(619\) −11.5000 19.9186i −0.462224 0.800595i 0.536847 0.843679i \(-0.319615\pi\)
−0.999071 + 0.0430838i \(0.986282\pi\)
\(620\) 0 0
\(621\) −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 0
\(626\) −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
\(630\) 0 0
\(631\) 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 0
\(636\) −18.0000 −0.713746
\(637\) 1.00000 + 6.92820i 0.0396214 + 0.274505i
\(638\) 18.0000 0.712627
\(639\) 0 0
\(640\) 0 0
\(641\) −13.5000 23.3827i −0.533218 0.923561i −0.999247 0.0387913i \(-0.987649\pi\)
0.466029 0.884769i \(-0.345684\pi\)
\(642\) −12.0000 + 20.7846i −0.473602 + 0.820303i
\(643\) −2.00000 −0.0788723 −0.0394362 0.999222i \(-0.512556\pi\)
−0.0394362 + 0.999222i \(0.512556\pi\)
\(644\) −18.0000 15.5885i −0.709299 0.614271i
\(645\) 0 0
\(646\) 3.00000 5.19615i 0.118033 0.204440i
\(647\) 16.5000 + 28.5788i 0.648682 + 1.12355i 0.983438 + 0.181245i \(0.0580128\pi\)
−0.334756 + 0.942305i \(0.608654\pi\)
\(648\) 5.50000 + 9.52628i 0.216060 + 0.374228i
\(649\) 0 0
\(650\) 0 0
\(651\) −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 \(-0.889681\pi\)
0.764442 + 0.644692i \(0.223014\pi\)
\(654\) 16.0000 + 27.7128i 0.625650 + 1.08366i
\(655\) 0 0
\(656\) −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 \(0.654829\pi\)
\(660\) 0 0
\(661\) 14.0000 + 24.2487i 0.544537 + 0.943166i 0.998636 + 0.0522143i \(0.0166279\pi\)
−0.454099 + 0.890951i \(0.650039\pi\)
\(662\) 3.50000 + 6.06218i 0.136031 + 0.235613i
\(663\) −6.00000 + 10.3923i −0.233021 + 0.403604i
\(664\) 0 0
\(665\) 0 0
\(666\) 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
\(670\) 0 0
\(671\) 24.0000 0.926510
\(672\) −5.00000 + 1.73205i −0.192879 + 0.0668153i
\(673\) 34.0000 1.31060 0.655302 0.755367i \(-0.272541\pi\)
0.655302 + 0.755367i \(0.272541\pi\)
\(674\) −11.0000 + 19.0526i −0.423704 + 0.733877i
\(675\) 0 0
\(676\) 6.00000 + 10.3923i 0.230769 + 0.399704i
\(677\) −4.50000 + 7.79423i −0.172949 + 0.299557i −0.939450 0.342687i \(-0.888663\pi\)
0.766501 + 0.642244i \(0.221996\pi\)
\(678\) 0 0
\(679\) 20.0000 + 17.3205i 0.767530 + 0.664700i
\(680\) 0 0
\(681\) −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 \(-0.0929302\pi\)
−0.728101 + 0.685470i \(0.759597\pi\)
\(684\) 0.500000 0.866025i 0.0191180 0.0331133i
\(685\) 0 0
\(686\) −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
\(690\) 0 0
\(691\) −16.0000 + 27.7128i −0.608669 + 1.05425i 0.382791 + 0.923835i \(0.374963\pi\)
−0.991460 + 0.130410i \(0.958371\pi\)
\(692\) −9.00000 −0.342129
\(693\) 6.00000 + 5.19615i 0.227921 + 0.197386i
\(694\) 0 0
\(695\) 0 0
\(696\) −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
\(700\) 0 0
\(701\) −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
\(705\) 0 0
\(706\) −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 −0.00446726 0.999990i \(-0.501422\pi\)
0.868250 0.496126i \(-0.165245\pi\)
\(710\) 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
\(715\) 0 0
\(716\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(720\) 0 0
\(721\) −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
\(725\) 0 0
\(726\) 2.00000 3.46410i 0.0742270 0.128565i
\(727\) 1.00000 0.0370879 0.0185440 0.999828i \(-0.494097\pi\)
0.0185440 + 0.999828i \(0.494097\pi\)
\(728\) 2.00000 + 1.73205i 0.0741249 + 0.0641941i
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 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 0.129275 + 0.991609i \(0.458735\pi\)
−0.923396 + 0.383849i \(0.874598\pi\)
\(734\) 19.0000 0.701303
\(735\) 0 0
\(736\) −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 −0.984589 0.174883i \(-0.944045\pi\)
0.340841 0.940121i \(-0.389288\pi\)
\(740\) 0 0
\(741\) −2.00000 −0.0734718
\(742\) −18.0000 15.5885i −0.660801 0.572270i
\(743\) 45.0000 1.65089 0.825445 0.564483i \(-0.190924\pi\)
0.825445 + 0.564483i \(0.190924\pi\)
\(744\) −8.00000 + 13.8564i −0.293294 + 0.508001i
\(745\) 0 0
\(746\) 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
\(750\) 0 0
\(751\) 5.00000 8.66025i 0.182453 0.316017i −0.760263 0.649616i \(-0.774930\pi\)
0.942715 + 0.333599i \(0.108263\pi\)
\(752\) 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
\(755\) 0 0
\(756\) −2.00000 + 10.3923i −0.0727393 + 0.377964i
\(757\) −38.0000 −1.38113 −0.690567 0.723269i \(-0.742639\pi\)
−0.690567 + 0.723269i \(0.742639\pi\)
\(758\) −11.5000 + 19.9186i −0.417699 + 0.723476i
\(759\) 27.0000 + 46.7654i 0.980038 + 1.69748i
\(760\) 0 0
\(761\) 13.5000 23.3827i 0.489375 0.847622i −0.510551 0.859848i \(-0.670558\pi\)
0.999925 + 0.0122260i \(0.00389175\pi\)
\(762\) 2.00000 0.0724524
\(763\) −8.00000 + 41.5692i −0.289619 + 1.50491i
\(764\) 12.0000 0.434145
\(765\) 0 0
\(766\) 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 \(0.363886\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −8.00000 + 13.8564i −0.287926 + 0.498703i
\(773\) −25.5000 44.1673i −0.917171 1.58859i −0.803691 0.595047i \(-0.797133\pi\)
−0.113480 0.993540i \(-0.536200\pi\)
\(774\) 1.00000 + 1.73205i 0.0359443 + 0.0622573i
\(775\) 0 0
\(776\) 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
\(780\) 0 0
\(781\) 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
\(785\) 0 0
\(786\) −3.00000 + 5.19615i −0.107006 + 0.185341i