Properties

Label 350.2.j.d.149.2
Level $350$
Weight $2$
Character 350.149
Analytic conductor $2.795$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 350.j (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.79476407074\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 70)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 149.2
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 350.149
Dual form 350.2.j.d.249.2

$q$-expansion

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) 1.73205 1.00000i 1.00000 0.577350i 0.0917517 0.995782i \(-0.470753\pi\)
0.908248 + 0.418432i \(0.137420\pi\)
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0 0
\(6\) 2.00000 0.816497
\(7\) 1.73205 2.00000i 0.654654 0.755929i
\(8\) 1.00000i 0.353553i
\(9\) 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 \(0.982718\pi\)
\(12\) 1.73205 + 1.00000i 0.500000 + 0.288675i
\(13\) 1.00000i 0.277350i 0.990338 + 0.138675i \(0.0442844\pi\)
−0.990338 + 0.138675i \(0.955716\pi\)
\(14\) 2.50000 0.866025i 0.668153 0.231455i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −5.19615 + 3.00000i −1.26025 + 0.727607i −0.973123 0.230285i \(-0.926034\pi\)
−0.287129 + 0.957892i \(0.592701\pi\)
\(18\) 0.866025 0.500000i 0.204124 0.117851i
\(19\) −0.500000 + 0.866025i −0.114708 + 0.198680i −0.917663 0.397360i \(-0.869927\pi\)
0.802955 + 0.596040i \(0.203260\pi\)
\(20\) 0 0
\(21\) 1.00000 5.19615i 0.218218 1.13389i
\(22\) 3.00000i 0.639602i
\(23\) 7.79423 + 4.50000i 1.62521 + 0.938315i 0.985496 + 0.169701i \(0.0542803\pi\)
0.639713 + 0.768613i \(0.279053\pi\)
\(24\) 1.00000 + 1.73205i 0.204124 + 0.353553i
\(25\) 0 0
\(26\) −0.500000 + 0.866025i −0.0980581 + 0.169842i
\(27\) 4.00000i 0.769800i
\(28\) 2.59808 + 0.500000i 0.490990 + 0.0944911i
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 0 0
\(31\) −4.00000 6.92820i −0.718421 1.24434i −0.961625 0.274367i \(-0.911532\pi\)
0.243204 0.969975i \(-0.421802\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) −5.19615 3.00000i −0.904534 0.522233i
\(34\) −6.00000 −1.02899
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 6.06218 + 3.50000i 0.996616 + 0.575396i 0.907245 0.420602i \(-0.138181\pi\)
0.0893706 + 0.995998i \(0.471514\pi\)
\(38\) −0.866025 + 0.500000i −0.140488 + 0.0811107i
\(39\) 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 \(0.424733\pi\)
\(42\) 3.46410 4.00000i 0.534522 0.617213i
\(43\) 2.00000i 0.304997i −0.988304 0.152499i \(-0.951268\pi\)
0.988304 0.152499i \(-0.0487319\pi\)
\(44\) 1.50000 2.59808i 0.226134 0.391675i
\(45\) 0 0
\(46\) 4.50000 + 7.79423i 0.663489 + 1.14920i
\(47\) −7.79423 4.50000i −1.13691 0.656392i −0.191243 0.981543i \(-0.561252\pi\)
−0.945662 + 0.325150i \(0.894585\pi\)
\(48\) 2.00000i 0.288675i
\(49\) −1.00000 6.92820i −0.142857 0.989743i
\(50\) 0 0
\(51\) −6.00000 + 10.3923i −0.840168 + 1.45521i
\(52\) −0.866025 + 0.500000i −0.120096 + 0.0693375i
\(53\) −7.79423 + 4.50000i −1.07062 + 0.618123i −0.928351 0.371706i \(-0.878773\pi\)
−0.142269 + 0.989828i \(0.545440\pi\)
\(54\) −2.00000 + 3.46410i −0.272166 + 0.471405i
\(55\) 0 0
\(56\) 2.00000 + 1.73205i 0.267261 + 0.231455i
\(57\) 2.00000i 0.264906i
\(58\) −5.19615 3.00000i −0.682288 0.393919i
\(59\) 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 \(0.995517\pi\)
\(62\) 8.00000i 1.01600i
\(63\) −0.866025 2.50000i −0.109109 0.314970i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) −3.00000 5.19615i −0.369274 0.639602i
\(67\) 6.92820 4.00000i 0.846415 0.488678i −0.0130248 0.999915i \(-0.504146\pi\)
0.859440 + 0.511237i \(0.170813\pi\)
\(68\) −5.19615 3.00000i −0.630126 0.363803i
\(69\) 18.0000 2.16695
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0.866025 + 0.500000i 0.102062 + 0.0589256i
\(73\) 3.46410 2.00000i 0.405442 0.234082i −0.283387 0.959006i \(-0.591458\pi\)
0.688830 + 0.724923i \(0.258125\pi\)
\(74\) 3.50000 + 6.06218i 0.406867 + 0.704714i
\(75\) 0 0
\(76\) −1.00000 −0.114708
\(77\) −7.79423 1.50000i −0.888235 0.170941i
\(78\) 2.00000i 0.226455i
\(79\) −5.00000 + 8.66025i −0.562544 + 0.974355i 0.434730 + 0.900561i \(0.356844\pi\)
−0.997274 + 0.0737937i \(0.976489\pi\)
\(80\) 0 0
\(81\) 5.50000 + 9.52628i 0.611111 + 1.05848i
\(82\) 2.59808 + 1.50000i 0.286910 + 0.165647i
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 5.00000 1.73205i 0.545545 0.188982i
\(85\) 0 0
\(86\) 1.00000 1.73205i 0.107833 0.186772i
\(87\) −10.3923 + 6.00000i −1.11417 + 0.643268i
\(88\) 2.59808 1.50000i 0.276956 0.159901i
\(89\) 3.00000 5.19615i 0.317999 0.550791i −0.662071 0.749441i \(-0.730322\pi\)
0.980071 + 0.198650i \(0.0636557\pi\)
\(90\) 0 0
\(91\) 2.00000 + 1.73205i 0.209657 + 0.181568i
\(92\) 9.00000i 0.938315i
\(93\) −13.8564 8.00000i −1.43684 0.829561i
\(94\) −4.50000 7.79423i −0.464140 0.803913i
\(95\) 0 0
\(96\) −1.00000 + 1.73205i −0.102062 + 0.176777i
\(97\) 10.0000i 1.01535i −0.861550 0.507673i \(-0.830506\pi\)
0.861550 0.507673i \(-0.169494\pi\)
\(98\) 2.59808 6.50000i 0.262445 0.656599i
\(99\) −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 \(-0.370316\pi\)
\(102\) −10.3923 + 6.00000i −1.02899 + 0.594089i
\(103\) −3.46410 2.00000i −0.341328 0.197066i 0.319531 0.947576i \(-0.396475\pi\)
−0.660859 + 0.750510i \(0.729808\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 0 0
\(106\) −9.00000 −0.874157
\(107\) 10.3923 + 6.00000i 1.00466 + 0.580042i 0.909624 0.415432i \(-0.136370\pi\)
0.0950377 + 0.995474i \(0.469703\pi\)
\(108\) −3.46410 + 2.00000i −0.333333 + 0.192450i
\(109\) −8.00000 13.8564i −0.766261 1.32720i −0.939577 0.342337i \(-0.888782\pi\)
0.173316 0.984866i \(-0.444552\pi\)
\(110\) 0 0
\(111\) 14.0000 1.32882
\(112\) 0.866025 + 2.50000i 0.0818317 + 0.236228i
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) −1.00000 + 1.73205i −0.0936586 + 0.162221i
\(115\) 0 0
\(116\) −3.00000 5.19615i −0.278543 0.482451i
\(117\) 0.866025 + 0.500000i 0.0800641 + 0.0462250i
\(118\) 0 0
\(119\) −3.00000 + 15.5885i −0.275010 + 1.42899i
\(120\) 0 0
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) −6.92820 + 4.00000i −0.627250 + 0.362143i
\(123\) 5.19615 3.00000i 0.468521 0.270501i
\(124\) 4.00000 6.92820i 0.359211 0.622171i
\(125\) 0 0
\(126\) 0.500000 2.59808i 0.0445435 0.231455i
\(127\) 1.00000i 0.0887357i −0.999015 0.0443678i \(-0.985873\pi\)
0.999015 0.0443678i \(-0.0141274\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) −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 \(0.208503\pi\)
\(132\) 6.00000i 0.522233i
\(133\) 0.866025 + 2.50000i 0.0750939 + 0.216777i
\(134\) 8.00000 0.691095
\(135\) 0 0
\(136\) −3.00000 5.19615i −0.257248 0.445566i
\(137\) 10.3923 6.00000i 0.887875 0.512615i 0.0146279 0.999893i \(-0.495344\pi\)
0.873247 + 0.487278i \(0.162010\pi\)
\(138\) 15.5885 + 9.00000i 1.32698 + 0.766131i
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) −18.0000 −1.51587
\(142\) 0 0
\(143\) 2.59808 1.50000i 0.217262 0.125436i
\(144\) 0.500000 + 0.866025i 0.0416667 + 0.0721688i
\(145\) 0 0
\(146\) 4.00000 0.331042
\(147\) −8.66025 11.0000i −0.714286 0.907265i
\(148\) 7.00000i 0.575396i
\(149\) −3.00000 + 5.19615i −0.245770 + 0.425685i −0.962348 0.271821i \(-0.912374\pi\)
0.716578 + 0.697507i \(0.245707\pi\)
\(150\) 0 0
\(151\) 5.00000 + 8.66025i 0.406894 + 0.704761i 0.994540 0.104357i \(-0.0332784\pi\)
−0.587646 + 0.809118i \(0.699945\pi\)
\(152\) −0.866025 0.500000i −0.0702439 0.0405554i
\(153\) 6.00000i 0.485071i
\(154\) −6.00000 5.19615i −0.483494 0.418718i
\(155\) 0 0
\(156\) −1.00000 + 1.73205i −0.0800641 + 0.138675i
\(157\) 19.9186 11.5000i 1.58968 0.917800i 0.596316 0.802749i \(-0.296630\pi\)
0.993360 0.115050i \(-0.0367030\pi\)
\(158\) −8.66025 + 5.00000i −0.688973 + 0.397779i
\(159\) −9.00000 + 15.5885i −0.713746 + 1.23625i
\(160\) 0 0
\(161\) 22.5000 7.79423i 1.77325 0.614271i
\(162\) 11.0000i 0.864242i
\(163\) 17.3205 + 10.0000i 1.35665 + 0.783260i 0.989170 0.146772i \(-0.0468885\pi\)
0.367477 + 0.930033i \(0.380222\pi\)
\(164\) 1.50000 + 2.59808i 0.117130 + 0.202876i
\(165\) 0 0
\(166\) 0 0
\(167\) 3.00000i 0.232147i 0.993241 + 0.116073i \(0.0370308\pi\)
−0.993241 + 0.116073i \(0.962969\pi\)
\(168\) 5.19615 + 1.00000i 0.400892 + 0.0771517i
\(169\) 12.0000 0.923077
\(170\) 0 0
\(171\) 0.500000 + 0.866025i 0.0382360 + 0.0662266i
\(172\) 1.73205 1.00000i 0.132068 0.0762493i
\(173\) 7.79423 + 4.50000i 0.592584 + 0.342129i 0.766119 0.642699i \(-0.222185\pi\)
−0.173534 + 0.984828i \(0.555519\pi\)
\(174\) −12.0000 −0.909718
\(175\) 0 0
\(176\) 3.00000 0.226134
\(177\) 0 0
\(178\) 5.19615 3.00000i 0.389468 0.224860i
\(179\) −1.50000 2.59808i −0.112115 0.194189i 0.804508 0.593942i \(-0.202429\pi\)
−0.916623 + 0.399753i \(0.869096\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 0.866025 + 2.50000i 0.0641941 + 0.185312i
\(183\) 16.0000i 1.18275i
\(184\) −4.50000 + 7.79423i −0.331744 + 0.574598i
\(185\) 0 0
\(186\) −8.00000 13.8564i −0.586588 1.01600i
\(187\) 15.5885 + 9.00000i 1.13994 + 0.658145i
\(188\) 9.00000i 0.656392i
\(189\) 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 \(0.309616\pi\)
\(192\) −1.73205 + 1.00000i −0.125000 + 0.0721688i
\(193\) 13.8564 8.00000i 0.997406 0.575853i 0.0899262 0.995948i \(-0.471337\pi\)
0.907480 + 0.420096i \(0.138004\pi\)
\(194\) 5.00000 8.66025i 0.358979 0.621770i
\(195\) 0 0
\(196\) 5.50000 4.33013i 0.392857 0.309295i
\(197\) 15.0000i 1.06871i 0.845262 + 0.534353i \(0.179445\pi\)
−0.845262 + 0.534353i \(0.820555\pi\)
\(198\) −2.59808 1.50000i −0.184637 0.106600i
\(199\) −8.00000 13.8564i −0.567105 0.982255i −0.996850 0.0793045i \(-0.974730\pi\)
0.429745 0.902950i \(-0.358603\pi\)
\(200\) 0 0
\(201\) 8.00000 13.8564i 0.564276 0.977356i
\(202\) 12.0000i 0.844317i
\(203\) −10.3923 + 12.0000i −0.729397 + 0.842235i
\(204\) −12.0000 −0.840168
\(205\) 0 0
\(206\) −2.00000 3.46410i −0.139347 0.241355i
\(207\) 7.79423 4.50000i 0.541736 0.312772i
\(208\) −0.866025 0.500000i −0.0600481 0.0346688i
\(209\) 3.00000 0.207514
\(210\) 0 0
\(211\) 23.0000 1.58339 0.791693 0.610920i \(-0.209200\pi\)
0.791693 + 0.610920i \(0.209200\pi\)
\(212\) −7.79423 4.50000i −0.535310 0.309061i
\(213\) 0 0
\(214\) 6.00000 + 10.3923i 0.410152 + 0.710403i
\(215\) 0 0
\(216\) −4.00000 −0.272166
\(217\) −20.7846 4.00000i −1.41095 0.271538i
\(218\) 16.0000i 1.08366i
\(219\) 4.00000 6.92820i 0.270295 0.468165i
\(220\) 0 0
\(221\) −3.00000 5.19615i −0.201802 0.349531i
\(222\) 12.1244 + 7.00000i 0.813733 + 0.469809i
\(223\) 8.00000i 0.535720i −0.963458 0.267860i \(-0.913684\pi\)
0.963458 0.267860i \(-0.0863164\pi\)
\(224\) −0.500000 + 2.59808i −0.0334077 + 0.173591i
\(225\) 0 0
\(226\) 0 0
\(227\) −10.3923 + 6.00000i −0.689761 + 0.398234i −0.803523 0.595274i \(-0.797043\pi\)
0.113761 + 0.993508i \(0.463710\pi\)
\(228\) −1.73205 + 1.00000i −0.114708 + 0.0662266i
\(229\) −2.00000 + 3.46410i −0.132164 + 0.228914i −0.924510 0.381157i \(-0.875526\pi\)
0.792347 + 0.610071i \(0.208859\pi\)
\(230\) 0 0
\(231\) −15.0000 + 5.19615i −0.986928 + 0.341882i
\(232\) 6.00000i 0.393919i
\(233\) −5.19615 3.00000i −0.340411 0.196537i 0.320043 0.947403i \(-0.396303\pi\)
−0.660454 + 0.750867i \(0.729636\pi\)
\(234\) 0.500000 + 0.866025i 0.0326860 + 0.0566139i
\(235\) 0 0
\(236\) 0 0
\(237\) 20.0000i 1.29914i
\(238\) −10.3923 + 12.0000i −0.673633 + 0.777844i
\(239\) 6.00000 0.388108 0.194054 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(240\) 0 0
\(241\) 0.500000 + 0.866025i 0.0322078 + 0.0557856i 0.881680 0.471848i \(-0.156413\pi\)
−0.849472 + 0.527633i \(0.823079\pi\)
\(242\) 1.73205 1.00000i 0.111340 0.0642824i
\(243\) 8.66025 + 5.00000i 0.555556 + 0.320750i
\(244\) −8.00000 −0.512148
\(245\) 0 0
\(246\) 6.00000 0.382546
\(247\) −0.866025 0.500000i −0.0551039 0.0318142i
\(248\) 6.92820 4.00000i 0.439941 0.254000i
\(249\) 0 0
\(250\) 0 0
\(251\) −15.0000 −0.946792 −0.473396 0.880850i \(-0.656972\pi\)
−0.473396 + 0.880850i \(0.656972\pi\)
\(252\) 1.73205 2.00000i 0.109109 0.125988i
\(253\) 27.0000i 1.69748i
\(254\) 0.500000 0.866025i 0.0313728 0.0543393i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(258\) 4.00000i 0.249029i
\(259\) 17.5000 6.06218i 1.08740 0.376685i
\(260\) 0 0
\(261\) −3.00000 + 5.19615i −0.185695 + 0.321634i
\(262\) −2.59808 + 1.50000i −0.160510 + 0.0926703i
\(263\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(264\) 3.00000 5.19615i 0.184637 0.319801i
\(265\) 0 0
\(266\) −0.500000 + 2.59808i −0.0306570 + 0.159298i
\(267\) 12.0000i 0.734388i
\(268\) 6.92820 + 4.00000i 0.423207 + 0.244339i
\(269\) 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 \(0.00513477\pi\)
\(272\) 6.00000i 0.363803i
\(273\) 5.19615 + 1.00000i 0.314485 + 0.0605228i
\(274\) 12.0000 0.724947
\(275\) 0 0
\(276\) 9.00000 + 15.5885i 0.541736 + 0.938315i
\(277\) −8.66025 + 5.00000i −0.520344 + 0.300421i −0.737075 0.675810i \(-0.763794\pi\)
0.216731 + 0.976231i \(0.430460\pi\)
\(278\) 3.46410 + 2.00000i 0.207763 + 0.119952i
\(279\) −8.00000 −0.478947
\(280\) 0 0
\(281\) −27.0000 −1.61068 −0.805342 0.592810i \(-0.798019\pi\)
−0.805342 + 0.592810i \(0.798019\pi\)
\(282\) −15.5885 9.00000i −0.928279 0.535942i
\(283\) −12.1244 + 7.00000i −0.720718 + 0.416107i −0.815017 0.579437i \(-0.803272\pi\)
0.0942988 + 0.995544i \(0.469939\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 3.00000 0.177394
\(287\) 5.19615 6.00000i 0.306719 0.354169i
\(288\) 1.00000i 0.0589256i
\(289\) 9.50000 16.4545i 0.558824 0.967911i
\(290\) 0 0
\(291\) −10.0000 17.3205i −0.586210 1.01535i
\(292\) 3.46410 + 2.00000i 0.202721 + 0.117041i
\(293\) 9.00000i 0.525786i 0.964825 + 0.262893i \(0.0846766\pi\)
−0.964825 + 0.262893i \(0.915323\pi\)
\(294\) −2.00000 13.8564i −0.116642 0.808122i
\(295\) 0 0
\(296\) −3.50000 + 6.06218i −0.203433 + 0.352357i
\(297\) 10.3923 6.00000i 0.603023 0.348155i
\(298\) −5.19615 + 3.00000i −0.301005 + 0.173785i
\(299\) −4.50000 + 7.79423i −0.260242 + 0.450752i
\(300\) 0 0
\(301\) −4.00000 3.46410i −0.230556 0.199667i
\(302\) 10.0000i 0.575435i
\(303\) −20.7846 12.0000i −1.19404 0.689382i
\(304\) −0.500000 0.866025i −0.0286770 0.0496700i
\(305\) 0 0
\(306\) −3.00000 + 5.19615i −0.171499 + 0.297044i
\(307\) 14.0000i 0.799022i 0.916728 + 0.399511i \(0.130820\pi\)
−0.916728 + 0.399511i \(0.869180\pi\)
\(308\) −2.59808 7.50000i −0.148039 0.427352i
\(309\) −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 \(0.595114\pi\)
\(312\) −1.73205 + 1.00000i −0.0980581 + 0.0566139i
\(313\) −24.2487 14.0000i −1.37062 0.791327i −0.379612 0.925146i \(-0.623943\pi\)
−0.991006 + 0.133819i \(0.957276\pi\)
\(314\) 23.0000 1.29797
\(315\) 0 0
\(316\) −10.0000 −0.562544
\(317\) −5.19615 3.00000i −0.291845 0.168497i 0.346929 0.937892i \(-0.387225\pi\)
−0.638774 + 0.769395i \(0.720558\pi\)
\(318\) −15.5885 + 9.00000i −0.874157 + 0.504695i
\(319\) 9.00000 + 15.5885i 0.503903 + 0.872786i
\(320\) 0 0
\(321\) 24.0000 1.33955
\(322\) 23.3827 + 4.50000i 1.30307 + 0.250775i
\(323\) 6.00000i 0.333849i
\(324\) −5.50000 + 9.52628i −0.305556 + 0.529238i
\(325\) 0 0
\(326\) 10.0000 + 17.3205i 0.553849 + 0.959294i
\(327\) −27.7128 16.0000i −1.53252 0.884802i
\(328\) 3.00000i 0.165647i
\(329\) −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
\(333\) 6.06218 3.50000i 0.332205 0.191799i
\(334\) −1.50000 + 2.59808i −0.0820763 + 0.142160i
\(335\) 0 0
\(336\) 4.00000 + 3.46410i 0.218218 + 0.188982i
\(337\) 22.0000i 1.19842i −0.800593 0.599208i \(-0.795482\pi\)
0.800593 0.599208i \(-0.204518\pi\)
\(338\) 10.3923 + 6.00000i 0.565267 + 0.326357i
\(339\) 0 0
\(340\) 0 0
\(341\) −12.0000 + 20.7846i −0.649836 + 1.12555i
\(342\) 1.00000i 0.0540738i
\(343\) −15.5885 10.0000i −0.841698 0.539949i
\(344\) 2.00000 0.107833
\(345\) 0 0
\(346\) 4.50000 + 7.79423i 0.241921 + 0.419020i
\(347\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(348\) −10.3923 6.00000i −0.557086 0.321634i
\(349\) −26.0000 −1.39175 −0.695874 0.718164i \(-0.744983\pi\)
−0.695874 + 0.718164i \(0.744983\pi\)
\(350\) 0 0
\(351\) −4.00000 −0.213504
\(352\) 2.59808 + 1.50000i 0.138478 + 0.0799503i
\(353\) −10.3923 + 6.00000i −0.553127 + 0.319348i −0.750382 0.661004i \(-0.770130\pi\)
0.197256 + 0.980352i \(0.436797\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 6.00000 0.317999
\(357\) 10.3923 + 30.0000i 0.550019 + 1.58777i
\(358\) 3.00000i 0.158555i
\(359\) 9.00000 15.5885i 0.475002 0.822727i −0.524588 0.851356i \(-0.675781\pi\)
0.999590 + 0.0286287i \(0.00911406\pi\)
\(360\) 0 0
\(361\) 9.00000 + 15.5885i 0.473684 + 0.820445i
\(362\) 1.73205 + 1.00000i 0.0910346 + 0.0525588i
\(363\) 4.00000i 0.209946i
\(364\) −0.500000 + 2.59808i −0.0262071 + 0.136176i
\(365\) 0 0
\(366\) −8.00000 + 13.8564i −0.418167 + 0.724286i
\(367\) −16.4545 + 9.50000i −0.858917 + 0.495896i −0.863649 0.504093i \(-0.831827\pi\)
0.00473247 + 0.999989i \(0.498494\pi\)
\(368\) −7.79423 + 4.50000i −0.406302 + 0.234579i
\(369\) 1.50000 2.59808i 0.0780869 0.135250i
\(370\) 0 0
\(371\) −4.50000 + 23.3827i −0.233628 + 1.21397i
\(372\) 16.0000i 0.829561i
\(373\) 1.73205 + 1.00000i 0.0896822 + 0.0517780i 0.544170 0.838975i \(-0.316844\pi\)
−0.454488 + 0.890753i \(0.650178\pi\)
\(374\) 9.00000 + 15.5885i 0.465379 + 0.806060i
\(375\) 0 0
\(376\) 4.50000 7.79423i 0.232070 0.401957i
\(377\) 6.00000i 0.309016i
\(378\) 3.46410 + 10.0000i 0.178174 + 0.514344i
\(379\) −23.0000 −1.18143 −0.590715 0.806880i \(-0.701154\pi\)
−0.590715 + 0.806880i \(0.701154\pi\)
\(380\) 0 0
\(381\) −1.00000 1.73205i −0.0512316 0.0887357i
\(382\) −10.3923 + 6.00000i −0.531717 + 0.306987i
\(383\) 18.1865 + 10.5000i 0.929288 + 0.536525i 0.886586 0.462563i \(-0.153070\pi\)
0.0427020 + 0.999088i \(0.486403\pi\)
\(384\) −2.00000 −0.102062
\(385\) 0 0
\(386\) 16.0000 0.814379
\(387\) −1.73205 1.00000i −0.0880451 0.0508329i
\(388\) 8.66025 5.00000i 0.439658 0.253837i
\(389\) −6.00000 10.3923i −0.304212 0.526911i 0.672874 0.739758i \(-0.265060\pi\)
−0.977086 + 0.212847i \(0.931726\pi\)
\(390\) 0 0
\(391\) −54.0000 −2.73090
\(392\) 6.92820 1.00000i 0.349927 0.0505076i
\(393\) 6.00000i 0.302660i
\(394\) −7.50000 + 12.9904i −0.377845 + 0.654446i
\(395\) 0 0
\(396\) −1.50000 2.59808i −0.0753778 0.130558i
\(397\) −12.1244 7.00000i −0.608504 0.351320i 0.163876 0.986481i \(-0.447600\pi\)
−0.772380 + 0.635161i \(0.780934\pi\)
\(398\) 16.0000i 0.802008i
\(399\) 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 \(-0.0688266\pi\)
\(402\) 13.8564 8.00000i 0.691095 0.399004i
\(403\) 6.92820 4.00000i 0.345118 0.199254i
\(404\) 6.00000 10.3923i 0.298511 0.517036i
\(405\) 0 0
\(406\) −15.0000 + 5.19615i −0.744438 + 0.257881i
\(407\) 21.0000i 1.04093i
\(408\) −10.3923 6.00000i −0.514496 0.297044i
\(409\) 13.0000 + 22.5167i 0.642809 + 1.11338i 0.984803 + 0.173675i \(0.0555643\pi\)
−0.341994 + 0.939702i \(0.611102\pi\)
\(410\) 0 0
\(411\) 12.0000 20.7846i 0.591916 1.02523i
\(412\) 4.00000i 0.197066i
\(413\) 0 0
\(414\) 9.00000 0.442326
\(415\) 0 0
\(416\) −0.500000 0.866025i −0.0245145 0.0424604i
\(417\) 6.92820 4.00000i 0.339276 0.195881i
\(418\) 2.59808 + 1.50000i 0.127076 + 0.0733674i
\(419\) 9.00000 0.439679 0.219839 0.975536i \(-0.429447\pi\)
0.219839 + 0.975536i \(0.429447\pi\)
\(420\) 0 0
\(421\) 2.00000 0.0974740 0.0487370 0.998812i \(-0.484480\pi\)
0.0487370 + 0.998812i \(0.484480\pi\)
\(422\) 19.9186 + 11.5000i 0.969622 + 0.559811i
\(423\) −7.79423 + 4.50000i −0.378968 + 0.218797i
\(424\) −4.50000 7.79423i −0.218539 0.378521i
\(425\) 0 0
\(426\) 0 0
\(427\) 6.92820 + 20.0000i 0.335279 + 0.967868i
\(428\) 12.0000i 0.580042i
\(429\) 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 \(0.926659\pi\)
\(432\) −3.46410 2.00000i −0.166667 0.0962250i
\(433\) 40.0000i 1.92228i 0.276066 + 0.961139i \(0.410969\pi\)
−0.276066 + 0.961139i \(0.589031\pi\)
\(434\) −16.0000 13.8564i −0.768025 0.665129i
\(435\) 0 0
\(436\) 8.00000 13.8564i 0.383131 0.663602i
\(437\) −7.79423 + 4.50000i −0.372849 + 0.215264i
\(438\) 6.92820 4.00000i 0.331042 0.191127i
\(439\) 13.0000 22.5167i 0.620456 1.07466i −0.368945 0.929451i \(-0.620281\pi\)
0.989401 0.145210i \(-0.0463858\pi\)
\(440\) 0 0
\(441\) −6.50000 2.59808i −0.309524 0.123718i
\(442\) 6.00000i 0.285391i
\(443\) 10.3923 + 6.00000i 0.493753 + 0.285069i 0.726130 0.687557i \(-0.241317\pi\)
−0.232377 + 0.972626i \(0.574650\pi\)
\(444\) 7.00000 + 12.1244i 0.332205 + 0.575396i
\(445\) 0 0
\(446\) 4.00000 6.92820i 0.189405 0.328060i
\(447\) 12.0000i 0.567581i
\(448\) −1.73205 + 2.00000i −0.0818317 + 0.0944911i
\(449\) −21.0000 −0.991051 −0.495526 0.868593i \(-0.665025\pi\)
−0.495526 + 0.868593i \(0.665025\pi\)
\(450\) 0 0
\(451\) −4.50000 7.79423i −0.211897 0.367016i
\(452\) 0 0
\(453\) 17.3205 + 10.0000i 0.813788 + 0.469841i
\(454\) −12.0000 −0.563188
\(455\) 0 0
\(456\) −2.00000 −0.0936586
\(457\) −12.1244 7.00000i −0.567153 0.327446i 0.188858 0.982004i \(-0.439521\pi\)
−0.756012 + 0.654558i \(0.772855\pi\)
\(458\) −3.46410 + 2.00000i −0.161867 + 0.0934539i
\(459\) −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 \(0.746202\pi\)
\(462\) −15.5885 3.00000i −0.725241 0.139573i
\(463\) 1.00000i 0.0464739i 0.999730 + 0.0232370i \(0.00739722\pi\)
−0.999730 + 0.0232370i \(0.992603\pi\)
\(464\) 3.00000 5.19615i 0.139272 0.241225i
\(465\) 0 0
\(466\) −3.00000 5.19615i −0.138972 0.240707i
\(467\) 5.19615 + 3.00000i 0.240449 + 0.138823i 0.615383 0.788228i \(-0.289001\pi\)
−0.374934 + 0.927052i \(0.622335\pi\)
\(468\) 1.00000i 0.0462250i
\(469\) 4.00000 20.7846i 0.184703 0.959744i
\(470\) 0 0
\(471\) 23.0000 39.8372i 1.05978 1.83560i
\(472\) 0 0
\(473\) −5.19615 + 3.00000i −0.238919 + 0.137940i
\(474\) −10.0000 + 17.3205i −0.459315 + 0.795557i
\(475\) 0 0
\(476\) −15.0000 + 5.19615i −0.687524 + 0.238165i
\(477\) 9.00000i 0.412082i
\(478\) 5.19615 + 3.00000i 0.237666 + 0.137217i
\(479\) 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
\(482\) 1.00000i 0.0455488i
\(483\) 31.1769 36.0000i 1.41860 1.63806i
\(484\) 2.00000 0.0909091
\(485\) 0 0
\(486\) 5.00000 + 8.66025i 0.226805 + 0.392837i
\(487\) −13.8564 + 8.00000i −0.627894 + 0.362515i −0.779936 0.625859i \(-0.784748\pi\)
0.152042 + 0.988374i \(0.451415\pi\)
\(488\) −6.92820 4.00000i −0.313625 0.181071i
\(489\) 40.0000 1.80886
\(490\) 0 0
\(491\) 36.0000 1.62466 0.812329 0.583200i \(-0.198200\pi\)
0.812329 + 0.583200i \(0.198200\pi\)
\(492\) 5.19615 + 3.00000i 0.234261 + 0.135250i
\(493\) 31.1769 18.0000i 1.40414 0.810679i
\(494\) −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 −0.907314 0.420455i \(-0.861871\pi\)
0.817781 + 0.575529i \(0.195204\pi\)
\(500\) 0 0
\(501\) 3.00000 + 5.19615i 0.134030 + 0.232147i
\(502\) −12.9904 7.50000i −0.579789 0.334741i
\(503\) 24.0000i 1.07011i −0.844818 0.535054i \(-0.820291\pi\)
0.844818 0.535054i \(-0.179709\pi\)
\(504\) 2.50000 0.866025i 0.111359 0.0385758i
\(505\) 0 0
\(506\) 13.5000 23.3827i 0.600148 1.03949i
\(507\) 20.7846 12.0000i 0.923077 0.532939i
\(508\) 0.866025 0.500000i 0.0384237 0.0221839i
\(509\) −21.0000 + 36.3731i −0.930809 + 1.61221i −0.148866 + 0.988857i \(0.547562\pi\)
−0.781943 + 0.623350i \(0.785771\pi\)
\(510\) 0 0
\(511\) 2.00000 10.3923i 0.0884748 0.459728i
\(512\) 1.00000i 0.0441942i
\(513\) −3.46410 2.00000i −0.152944 0.0883022i
\(514\) 0 0
\(515\) 0 0
\(516\) 2.00000 3.46410i 0.0880451 0.152499i
\(517\) 27.0000i 1.18746i
\(518\) 18.1865 + 3.50000i 0.799070 + 0.153781i
\(519\) 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 \(0.726763\pi\)
\(522\) −5.19615 + 3.00000i −0.227429 + 0.131306i
\(523\) −24.2487 14.0000i −1.06032 0.612177i −0.134801 0.990873i \(-0.543039\pi\)
−0.925521 + 0.378695i \(0.876373\pi\)
\(524\) −3.00000 −0.131056
\(525\) 0 0
\(526\) 0 0
\(527\) 41.5692 + 24.0000i 1.81078 + 1.04546i
\(528\) 5.19615 3.00000i 0.226134 0.130558i
\(529\) 29.0000 + 50.2295i 1.26087 + 2.18389i
\(530\) 0 0
\(531\) 0 0
\(532\) −1.73205 + 2.00000i −0.0750939 + 0.0867110i
\(533\) 3.00000i 0.129944i
\(534\) 6.00000 10.3923i 0.259645 0.449719i
\(535\) 0 0
\(536\) 4.00000 + 6.92820i 0.172774 + 0.299253i
\(537\) −5.19615 3.00000i −0.224231 0.129460i
\(538\) 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 \(0.221681\pi\)
\(542\) 13.8564 8.00000i 0.595184 0.343629i
\(543\) 3.46410 2.00000i 0.148659 0.0858282i
\(544\) 3.00000 5.19615i 0.128624 0.222783i
\(545\) 0 0
\(546\) 4.00000 + 3.46410i 0.171184 + 0.148250i
\(547\) 8.00000i 0.342055i 0.985266 + 0.171028i \(0.0547087\pi\)
−0.985266 + 0.171028i \(0.945291\pi\)
\(548\) 10.3923 + 6.00000i 0.443937 + 0.256307i
\(549\) 4.00000 + 6.92820i 0.170716 + 0.295689i
\(550\) 0 0
\(551\) 3.00000 5.19615i 0.127804 0.221364i
\(552\) 18.0000i 0.766131i
\(553\) 8.66025 + 25.0000i 0.368271 + 1.06311i
\(554\) −10.0000 −0.424859
\(555\) 0 0
\(556\) 2.00000 + 3.46410i 0.0848189 + 0.146911i
\(557\) −7.79423 + 4.50000i −0.330252 + 0.190671i −0.655953 0.754802i \(-0.727733\pi\)
0.325701 + 0.945473i \(0.394400\pi\)
\(558\) −6.92820 4.00000i −0.293294 0.169334i
\(559\) 2.00000 0.0845910
\(560\) 0 0
\(561\) 36.0000 1.51992
\(562\) −23.3827 13.5000i −0.986339 0.569463i
\(563\) −36.3731 + 21.0000i −1.53294 + 0.885044i −0.533718 + 0.845663i \(0.679206\pi\)
−0.999224 + 0.0393818i \(0.987461\pi\)
\(564\) −9.00000 15.5885i −0.378968 0.656392i
\(565\) 0 0
\(566\) −14.0000 −0.588464
\(567\) 28.5788 + 5.50000i 1.20020 + 0.230978i
\(568\) 0 0
\(569\) 10.5000 18.1865i 0.440183 0.762419i −0.557520 0.830164i \(-0.688247\pi\)
0.997703 + 0.0677445i \(0.0215803\pi\)
\(570\) 0 0
\(571\) −10.0000 17.3205i −0.418487 0.724841i 0.577301 0.816532i \(-0.304106\pi\)
−0.995788 + 0.0916910i \(0.970773\pi\)
\(572\) 2.59808 + 1.50000i 0.108631 + 0.0627182i
\(573\) 24.0000i 1.00261i
\(574\) 7.50000 2.59808i 0.313044 0.108442i
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 38.1051 22.0000i 1.58634 0.915872i 0.592433 0.805620i \(-0.298167\pi\)
0.993904 0.110252i \(-0.0351659\pi\)
\(578\) 16.4545 9.50000i 0.684416 0.395148i
\(579\) 16.0000 27.7128i 0.664937 1.15171i
\(580\) 0 0
\(581\) 0 0
\(582\) 20.0000i 0.829027i
\(583\) 23.3827 + 13.5000i 0.968412 + 0.559113i
\(584\) 2.00000 + 3.46410i 0.0827606 + 0.143346i
\(585\) 0 0
\(586\) −4.50000 + 7.79423i −0.185893 + 0.321977i
\(587\) 24.0000i 0.990586i −0.868726 0.495293i \(-0.835061\pi\)
0.868726 0.495293i \(-0.164939\pi\)
\(588\) 5.19615 13.0000i 0.214286 0.536111i
\(589\) 8.00000 0.329634
\(590\) 0 0
\(591\) 15.0000 + 25.9808i 0.617018 + 1.06871i
\(592\) −6.06218 + 3.50000i −0.249154 + 0.143849i
\(593\) 20.7846 + 12.0000i 0.853522 + 0.492781i 0.861838 0.507184i \(-0.169314\pi\)
−0.00831589 + 0.999965i \(0.502647\pi\)
\(594\) 12.0000 0.492366
\(595\) 0 0
\(596\) −6.00000 −0.245770
\(597\) −27.7128 16.0000i −1.13421 0.654836i
\(598\) −7.79423 + 4.50000i −0.318730 + 0.184019i
\(599\) −21.0000 36.3731i −0.858037 1.48616i −0.873799 0.486287i \(-0.838351\pi\)
0.0157622 0.999876i \(-0.494983\pi\)
\(600\) 0 0
\(601\) 26.0000 1.06056 0.530281 0.847822i \(-0.322086\pi\)
0.530281 + 0.847822i \(0.322086\pi\)
\(602\) −1.73205 5.00000i −0.0705931 0.203785i
\(603\) 8.00000i 0.325785i
\(604\) −5.00000 + 8.66025i −0.203447 + 0.352381i
\(605\) 0 0
\(606\) −12.0000 20.7846i −0.487467 0.844317i
\(607\) 0.866025 + 0.500000i 0.0351509 + 0.0202944i 0.517472 0.855700i \(-0.326873\pi\)
−0.482322 + 0.875994i \(0.660206\pi\)
\(608\) 1.00000i 0.0405554i
\(609\) −6.00000 + 31.1769i −0.243132 + 1.26335i
\(610\) 0 0
\(611\) 4.50000 7.79423i 0.182051 0.315321i
\(612\) −5.19615 + 3.00000i −0.210042 + 0.121268i
\(613\) −25.1147 + 14.5000i −1.01437 + 0.585649i −0.912470 0.409145i \(-0.865827\pi\)
−0.101905 + 0.994794i \(0.532494\pi\)
\(614\) −7.00000 + 12.1244i −0.282497 + 0.489299i
\(615\) 0 0
\(616\) 1.50000 7.79423i 0.0604367 0.314038i
\(617\) 18.0000i 0.724653i −0.932051 0.362326i \(-0.881983\pi\)
0.932051 0.362326i \(-0.118017\pi\)
\(618\) −6.92820 4.00000i −0.278693 0.160904i
\(619\) 11.5000 + 19.9186i 0.462224 + 0.800595i 0.999071 0.0430838i \(-0.0137183\pi\)
−0.536847 + 0.843679i \(0.680385\pi\)
\(620\) 0 0
\(621\) −18.0000 + 31.1769i −0.722315 + 1.25109i
\(622\) 24.0000i 0.962312i
\(623\) −5.19615 15.0000i −0.208179 0.600962i
\(624\) −2.00000 −0.0800641
\(625\) 0 0
\(626\) −14.0000 24.2487i −0.559553 0.969173i
\(627\) 5.19615 3.00000i 0.207514 0.119808i
\(628\) 19.9186 + 11.5000i 0.794838 + 0.458900i
\(629\) −42.0000 −1.67465
\(630\) 0 0
\(631\) 20.0000 0.796187 0.398094 0.917345i \(-0.369672\pi\)
0.398094 + 0.917345i \(0.369672\pi\)
\(632\) −8.66025 5.00000i −0.344486 0.198889i
\(633\) 39.8372 23.0000i 1.58339 0.914168i
\(634\) −3.00000 5.19615i −0.119145 0.206366i
\(635\) 0 0
\(636\) −18.0000 −0.713746
\(637\) 6.92820 1.00000i 0.274505 0.0396214i
\(638\) 18.0000i 0.712627i
\(639\) 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 \(-0.345684\pi\)
\(642\) 20.7846 + 12.0000i 0.820303 + 0.473602i
\(643\) 2.00000i 0.0788723i −0.999222 0.0394362i \(-0.987444\pi\)
0.999222 0.0394362i \(-0.0125562\pi\)
\(644\) 18.0000 + 15.5885i 0.709299 + 0.614271i
\(645\) 0 0
\(646\) 3.00000 5.19615i 0.118033 0.204440i
\(647\) 28.5788 16.5000i 1.12355 0.648682i 0.181245 0.983438i \(-0.441987\pi\)
0.942305 + 0.334756i \(0.108654\pi\)
\(648\) −9.52628 + 5.50000i −0.374228 + 0.216060i
\(649\) 0 0
\(650\) 0 0
\(651\) −40.0000 + 13.8564i −1.56772 + 0.543075i
\(652\) 20.0000i 0.783260i
\(653\) −7.79423 4.50000i −0.305012 0.176099i 0.339680 0.940541i \(-0.389681\pi\)
−0.644692 + 0.764442i \(0.723014\pi\)
\(654\) −16.0000 27.7128i −0.625650 1.08366i
\(655\) 0 0
\(656\) −1.50000 + 2.59808i −0.0585652 + 0.101438i
\(657\) 4.00000i 0.156055i
\(658\) −23.3827 4.50000i −0.911552 0.175428i
\(659\) 24.0000 0.934907 0.467454 0.884018i \(-0.345171\pi\)
0.467454 + 0.884018i \(0.345171\pi\)
\(660\) 0 0
\(661\) 14.0000 + 24.2487i 0.544537 + 0.943166i 0.998636 + 0.0522143i \(0.0166279\pi\)
−0.454099 + 0.890951i \(0.650039\pi\)
\(662\) 6.06218 3.50000i 0.235613 0.136031i
\(663\) −10.3923 6.00000i −0.403604 0.233021i
\(664\) 0 0
\(665\) 0 0
\(666\) 7.00000 0.271244
\(667\) −46.7654 27.0000i −1.81076 1.04544i
\(668\) −2.59808 + 1.50000i −0.100523 + 0.0580367i
\(669\) −8.00000 13.8564i −0.309298 0.535720i
\(670\) 0 0
\(671\) 24.0000 0.926510
\(672\) 1.73205 + 5.00000i 0.0668153 + 0.192879i
\(673\) 34.0000i 1.31060i 0.755367 + 0.655302i \(0.227459\pi\)
−0.755367 + 0.655302i \(0.772541\pi\)
\(674\) 11.0000 19.0526i 0.423704 0.733877i
\(675\) 0 0
\(676\) 6.00000 + 10.3923i 0.230769 + 0.399704i
\(677\) 7.79423 + 4.50000i 0.299557 + 0.172949i 0.642244 0.766501i \(-0.278004\pi\)
−0.342687 + 0.939450i \(0.611337\pi\)
\(678\) 0 0
\(679\) −20.0000 17.3205i −0.767530 0.664700i
\(680\) 0 0
\(681\) −12.0000 + 20.7846i −0.459841 + 0.796468i
\(682\) −20.7846 + 12.0000i −0.795884 + 0.459504i
\(683\) −10.3923 + 6.00000i −0.397650 + 0.229584i −0.685470 0.728101i \(-0.740403\pi\)
0.287819 + 0.957685i \(0.407070\pi\)
\(684\) −0.500000 + 0.866025i −0.0191180 + 0.0331133i
\(685\) 0 0
\(686\) −8.50000 16.4545i −0.324532 0.628235i
\(687\) 8.00000i 0.305219i
\(688\) 1.73205 + 1.00000i 0.0660338 + 0.0381246i
\(689\) −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 \(0.958371\pi\)
\(692\) 9.00000i 0.342129i
\(693\) −5.19615 + 6.00000i −0.197386 + 0.227921i
\(694\) 0 0
\(695\) 0 0
\(696\) −6.00000 10.3923i −0.227429 0.393919i
\(697\) −15.5885 + 9.00000i −0.590455 + 0.340899i
\(698\) −22.5167 13.0000i −0.852268 0.492057i
\(699\) −12.0000 −0.453882
\(700\) 0 0
\(701\) −30.0000 −1.13308 −0.566542 0.824033i \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) −3.46410 2.00000i −0.130744 0.0754851i
\(703\) −6.06218 + 3.50000i −0.228639 + 0.132005i
\(704\) 1.50000 + 2.59808i 0.0565334 + 0.0979187i
\(705\) 0 0
\(706\) −12.0000 −0.451626
\(707\) −31.1769 6.00000i −1.17253 0.225653i
\(708\) 0 0
\(709\) −23.0000 + 39.8372i −0.863783 + 1.49612i 0.00446726 + 0.999990i \(0.498578\pi\)
−0.868250 + 0.496126i \(0.834755\pi\)
\(710\) 0 0
\(711\) 5.00000 + 8.66025i 0.187515 + 0.324785i
\(712\) 5.19615 + 3.00000i 0.194734 + 0.112430i
\(713\) 72.0000i 2.69642i
\(714\) −6.00000 + 31.1769i −0.224544 + 1.16677i
\(715\) 0 0
\(716\) 1.50000 2.59808i 0.0560576 0.0970947i
\(717\) 10.3923 6.00000i 0.388108 0.224074i
\(718\) 15.5885 9.00000i 0.581756 0.335877i
\(719\) 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
\(722\) 18.0000i 0.669891i
\(723\) 1.73205 + 1.00000i 0.0644157 + 0.0371904i
\(724\) 1.00000 + 1.73205i 0.0371647 + 0.0643712i
\(725\) 0 0
\(726\) 2.00000 3.46410i 0.0742270 0.128565i
\(727\) 1.00000i 0.0370879i −0.999828 0.0185440i \(-0.994097\pi\)
0.999828 0.0185440i \(-0.00590307\pi\)
\(728\) −1.73205 + 2.00000i −0.0641941 + 0.0741249i
\(729\) −13.0000 −0.481481
\(730\) 0 0
\(731\) 6.00000 + 10.3923i 0.221918 + 0.384373i
\(732\) −13.8564 + 8.00000i −0.512148 + 0.295689i
\(733\) −37.2391 21.5000i −1.37546 0.794121i −0.383849 0.923396i \(-0.625402\pi\)
−0.991609 + 0.129275i \(0.958735\pi\)
\(734\) −19.0000 −0.701303
\(735\) 0 0
\(736\) −9.00000 −0.331744
\(737\) −20.7846 12.0000i −0.765611 0.442026i
\(738\) 2.59808 1.50000i 0.0956365 0.0552158i
\(739\) 17.5000 + 30.3109i 0.643748 + 1.11500i 0.984589 + 0.174883i \(0.0559548\pi\)
−0.340841 + 0.940121i \(0.610712\pi\)
\(740\) 0 0
\(741\) −2.00000 −0.0734718
\(742\) −15.5885 + 18.0000i −0.572270 + 0.660801i
\(743\) 45.0000i 1.65089i 0.564483 + 0.825445i \(0.309076\pi\)
−0.564483 + 0.825445i \(0.690924\pi\)
\(744\) 8.00000 13.8564i 0.293294 0.508001i
\(745\) 0 0
\(746\) 1.00000 + 1.73205i 0.0366126 + 0.0634149i
\(747\) 0 0
\(748\) 18.0000i 0.658145i
\(749\) 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 \(0.108263\pi\)
\(752\) 7.79423 4.50000i 0.284226 0.164098i
\(753\) −25.9808 + 15.0000i −0.946792 + 0.546630i
\(754\) 3.00000 5.19615i 0.109254 0.189233i
\(755\) 0 0
\(756\) −2.00000 + 10.3923i −0.0727393 + 0.377964i
\(757\) 38.0000i 1.38113i 0.723269 + 0.690567i \(0.242639\pi\)
−0.723269 + 0.690567i \(0.757361\pi\)
\(758\) −19.9186 11.5000i −0.723476 0.417699i
\(759\) −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 \(0.00389175\pi\)
\(762\) 2.00000i 0.0724524i
\(763\) −41.5692 8.00000i −1.50491 0.289619i
\(764\) −12.0000 −0.434145
\(765\) 0 0
\(766\) 10.5000 + 18.1865i 0.379380 + 0.657106i
\(767\) 0 0
\(768\) −1.73205 1.00000i −0.0625000 0.0360844i
\(769\) −23.0000 −0.829401 −0.414701 0.909958i \(-0.636114\pi\)
−0.414701 + 0.909958i \(0.636114\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 13.8564 + 8.00000i 0.498703 + 0.287926i
\(773\) 44.1673 25.5000i 1.58859 0.917171i 0.595047 0.803691i \(-0.297133\pi\)
0.993540 0.113480i \(-0.0361999\pi\)
\(774\) −1.00000 1.73205i −0.0359443 0.0622573i
\(775\) 0 0
\(776\) 10.0000 0.358979
\(777\) 24.2487 28.0000i 0.869918 1.00449i
\(778\) 12.0000i 0.430221i
\(779\) −1.50000 + 2.59808i −0.0537431 + 0.0930857i
\(780\) 0 0
\(781\) 0 0
\(782\) −46.7654 27.0000i −1.67233 0.965518i
\(783\) 24.0000i 0.857690i
\(784\) 6.50000 + 2.59808i 0.232143 + 0.0927884i
\(785\) 0 0