Properties

Label 1386.2.k.o.991.1
Level $1386$
Weight $2$
Character 1386.991
Analytic conductor $11.067$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.k (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.0672657201\)
Analytic rank: \(1\)
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 154)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 991.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1386.991
Dual form 1386.2.k.o.793.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{5} +(-2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{5} +(-2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +(-1.00000 + 1.73205i) q^{10} +(-0.500000 + 0.866025i) q^{11} -7.00000 q^{13} +(-0.500000 - 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} -2.00000 q^{20} -1.00000 q^{22} +(-4.00000 - 6.92820i) q^{23} +(0.500000 - 0.866025i) q^{25} +(-3.50000 - 6.06218i) q^{26} +(2.00000 - 1.73205i) q^{28} +5.00000 q^{29} +(-2.00000 + 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} +2.00000 q^{34} +(-1.00000 - 5.19615i) q^{35} +(-2.00000 - 3.46410i) q^{37} +(-1.00000 - 1.73205i) q^{40} -4.00000 q^{41} -8.00000 q^{43} +(-0.500000 - 0.866025i) q^{44} +(4.00000 - 6.92820i) q^{46} +(1.00000 + 1.73205i) q^{47} +(5.50000 + 4.33013i) q^{49} +1.00000 q^{50} +(3.50000 - 6.06218i) q^{52} +(-3.00000 + 5.19615i) q^{53} -2.00000 q^{55} +(2.50000 + 0.866025i) q^{56} +(2.50000 + 4.33013i) q^{58} +(1.50000 - 2.59808i) q^{59} +(-0.500000 - 0.866025i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(-7.00000 - 12.1244i) q^{65} +(-4.50000 + 7.79423i) q^{67} +(1.00000 + 1.73205i) q^{68} +(4.00000 - 3.46410i) q^{70} +2.00000 q^{71} +(-2.00000 + 3.46410i) q^{73} +(2.00000 - 3.46410i) q^{74} +(2.00000 - 1.73205i) q^{77} +(-4.50000 - 7.79423i) q^{79} +(1.00000 - 1.73205i) q^{80} +(-2.00000 - 3.46410i) q^{82} -6.00000 q^{83} +4.00000 q^{85} +(-4.00000 - 6.92820i) q^{86} +(0.500000 - 0.866025i) q^{88} +(3.00000 + 5.19615i) q^{89} +(17.5000 + 6.06218i) q^{91} +8.00000 q^{92} +(-1.00000 + 1.73205i) q^{94} +7.00000 q^{97} +(-1.00000 + 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - q^{4} + 2q^{5} - 5q^{7} - 2q^{8} + O(q^{10}) \) \( 2q + q^{2} - q^{4} + 2q^{5} - 5q^{7} - 2q^{8} - 2q^{10} - q^{11} - 14q^{13} - q^{14} - q^{16} + 2q^{17} - 4q^{20} - 2q^{22} - 8q^{23} + q^{25} - 7q^{26} + 4q^{28} + 10q^{29} - 4q^{31} + q^{32} + 4q^{34} - 2q^{35} - 4q^{37} - 2q^{40} - 8q^{41} - 16q^{43} - q^{44} + 8q^{46} + 2q^{47} + 11q^{49} + 2q^{50} + 7q^{52} - 6q^{53} - 4q^{55} + 5q^{56} + 5q^{58} + 3q^{59} - q^{61} - 8q^{62} + 2q^{64} - 14q^{65} - 9q^{67} + 2q^{68} + 8q^{70} + 4q^{71} - 4q^{73} + 4q^{74} + 4q^{77} - 9q^{79} + 2q^{80} - 4q^{82} - 12q^{83} + 8q^{85} - 8q^{86} + q^{88} + 6q^{89} + 35q^{91} + 16q^{92} - 2q^{94} + 14q^{97} - 2q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 1.00000 + 1.73205i 0.447214 + 0.774597i 0.998203 0.0599153i \(-0.0190830\pi\)
−0.550990 + 0.834512i \(0.685750\pi\)
\(6\) 0 0
\(7\) −2.50000 0.866025i −0.944911 0.327327i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −1.00000 + 1.73205i −0.316228 + 0.547723i
\(11\) −0.500000 + 0.866025i −0.150756 + 0.261116i
\(12\) 0 0
\(13\) −7.00000 −1.94145 −0.970725 0.240192i \(-0.922790\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) −0.500000 2.59808i −0.133631 0.694365i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.00000 1.73205i 0.242536 0.420084i −0.718900 0.695113i \(-0.755354\pi\)
0.961436 + 0.275029i \(0.0886875\pi\)
\(18\) 0 0
\(19\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(20\) −2.00000 −0.447214
\(21\) 0 0
\(22\) −1.00000 −0.213201
\(23\) −4.00000 6.92820i −0.834058 1.44463i −0.894795 0.446476i \(-0.852679\pi\)
0.0607377 0.998154i \(-0.480655\pi\)
\(24\) 0 0
\(25\) 0.500000 0.866025i 0.100000 0.173205i
\(26\) −3.50000 6.06218i −0.686406 1.18889i
\(27\) 0 0
\(28\) 2.00000 1.73205i 0.377964 0.327327i
\(29\) 5.00000 0.928477 0.464238 0.885710i \(-0.346328\pi\)
0.464238 + 0.885710i \(0.346328\pi\)
\(30\) 0 0
\(31\) −2.00000 + 3.46410i −0.359211 + 0.622171i −0.987829 0.155543i \(-0.950287\pi\)
0.628619 + 0.777714i \(0.283621\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 2.00000 0.342997
\(35\) −1.00000 5.19615i −0.169031 0.878310i
\(36\) 0 0
\(37\) −2.00000 3.46410i −0.328798 0.569495i 0.653476 0.756948i \(-0.273310\pi\)
−0.982274 + 0.187453i \(0.939977\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −1.00000 1.73205i −0.158114 0.273861i
\(41\) −4.00000 −0.624695 −0.312348 0.949968i \(-0.601115\pi\)
−0.312348 + 0.949968i \(0.601115\pi\)
\(42\) 0 0
\(43\) −8.00000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) −0.500000 0.866025i −0.0753778 0.130558i
\(45\) 0 0
\(46\) 4.00000 6.92820i 0.589768 1.02151i
\(47\) 1.00000 + 1.73205i 0.145865 + 0.252646i 0.929695 0.368329i \(-0.120070\pi\)
−0.783830 + 0.620975i \(0.786737\pi\)
\(48\) 0 0
\(49\) 5.50000 + 4.33013i 0.785714 + 0.618590i
\(50\) 1.00000 0.141421
\(51\) 0 0
\(52\) 3.50000 6.06218i 0.485363 0.840673i
\(53\) −3.00000 + 5.19615i −0.412082 + 0.713746i −0.995117 0.0987002i \(-0.968532\pi\)
0.583036 + 0.812447i \(0.301865\pi\)
\(54\) 0 0
\(55\) −2.00000 −0.269680
\(56\) 2.50000 + 0.866025i 0.334077 + 0.115728i
\(57\) 0 0
\(58\) 2.50000 + 4.33013i 0.328266 + 0.568574i
\(59\) 1.50000 2.59808i 0.195283 0.338241i −0.751710 0.659494i \(-0.770771\pi\)
0.946993 + 0.321253i \(0.104104\pi\)
\(60\) 0 0
\(61\) −0.500000 0.866025i −0.0640184 0.110883i 0.832240 0.554416i \(-0.187058\pi\)
−0.896258 + 0.443533i \(0.853725\pi\)
\(62\) −4.00000 −0.508001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −7.00000 12.1244i −0.868243 1.50384i
\(66\) 0 0
\(67\) −4.50000 + 7.79423i −0.549762 + 0.952217i 0.448528 + 0.893769i \(0.351948\pi\)
−0.998290 + 0.0584478i \(0.981385\pi\)
\(68\) 1.00000 + 1.73205i 0.121268 + 0.210042i
\(69\) 0 0
\(70\) 4.00000 3.46410i 0.478091 0.414039i
\(71\) 2.00000 0.237356 0.118678 0.992933i \(-0.462134\pi\)
0.118678 + 0.992933i \(0.462134\pi\)
\(72\) 0 0
\(73\) −2.00000 + 3.46410i −0.234082 + 0.405442i −0.959006 0.283387i \(-0.908542\pi\)
0.724923 + 0.688830i \(0.241875\pi\)
\(74\) 2.00000 3.46410i 0.232495 0.402694i
\(75\) 0 0
\(76\) 0 0
\(77\) 2.00000 1.73205i 0.227921 0.197386i
\(78\) 0 0
\(79\) −4.50000 7.79423i −0.506290 0.876919i −0.999974 0.00727784i \(-0.997683\pi\)
0.493684 0.869641i \(-0.335650\pi\)
\(80\) 1.00000 1.73205i 0.111803 0.193649i
\(81\) 0 0
\(82\) −2.00000 3.46410i −0.220863 0.382546i
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) 0 0
\(85\) 4.00000 0.433861
\(86\) −4.00000 6.92820i −0.431331 0.747087i
\(87\) 0 0
\(88\) 0.500000 0.866025i 0.0533002 0.0923186i
\(89\) 3.00000 + 5.19615i 0.317999 + 0.550791i 0.980071 0.198650i \(-0.0636557\pi\)
−0.662071 + 0.749441i \(0.730322\pi\)
\(90\) 0 0
\(91\) 17.5000 + 6.06218i 1.83450 + 0.635489i
\(92\) 8.00000 0.834058
\(93\) 0 0
\(94\) −1.00000 + 1.73205i −0.103142 + 0.178647i
\(95\) 0 0
\(96\) 0 0
\(97\) 7.00000 0.710742 0.355371 0.934725i \(-0.384354\pi\)
0.355371 + 0.934725i \(0.384354\pi\)
\(98\) −1.00000 + 6.92820i −0.101015 + 0.699854i
\(99\) 0 0
\(100\) 0.500000 + 0.866025i 0.0500000 + 0.0866025i
\(101\) −4.50000 + 7.79423i −0.447767 + 0.775555i −0.998240 0.0592978i \(-0.981114\pi\)
0.550474 + 0.834853i \(0.314447\pi\)
\(102\) 0 0
\(103\) −9.00000 15.5885i −0.886796 1.53598i −0.843641 0.536908i \(-0.819592\pi\)
−0.0431555 0.999068i \(-0.513741\pi\)
\(104\) 7.00000 0.686406
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) 1.00000 + 1.73205i 0.0966736 + 0.167444i 0.910306 0.413936i \(-0.135846\pi\)
−0.813632 + 0.581380i \(0.802513\pi\)
\(108\) 0 0
\(109\) 1.00000 1.73205i 0.0957826 0.165900i −0.814152 0.580651i \(-0.802798\pi\)
0.909935 + 0.414751i \(0.136131\pi\)
\(110\) −1.00000 1.73205i −0.0953463 0.165145i
\(111\) 0 0
\(112\) 0.500000 + 2.59808i 0.0472456 + 0.245495i
\(113\) −5.00000 −0.470360 −0.235180 0.971952i \(-0.575568\pi\)
−0.235180 + 0.971952i \(0.575568\pi\)
\(114\) 0 0
\(115\) 8.00000 13.8564i 0.746004 1.29212i
\(116\) −2.50000 + 4.33013i −0.232119 + 0.402042i
\(117\) 0 0
\(118\) 3.00000 0.276172
\(119\) −4.00000 + 3.46410i −0.366679 + 0.317554i
\(120\) 0 0
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) 0.500000 0.866025i 0.0452679 0.0784063i
\(123\) 0 0
\(124\) −2.00000 3.46410i −0.179605 0.311086i
\(125\) 12.0000 1.07331
\(126\) 0 0
\(127\) −19.0000 −1.68598 −0.842989 0.537931i \(-0.819206\pi\)
−0.842989 + 0.537931i \(0.819206\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 7.00000 12.1244i 0.613941 1.06338i
\(131\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −9.00000 −0.777482
\(135\) 0 0
\(136\) −1.00000 + 1.73205i −0.0857493 + 0.148522i
\(137\) 1.50000 2.59808i 0.128154 0.221969i −0.794808 0.606861i \(-0.792428\pi\)
0.922961 + 0.384893i \(0.125762\pi\)
\(138\) 0 0
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 5.00000 + 1.73205i 0.422577 + 0.146385i
\(141\) 0 0
\(142\) 1.00000 + 1.73205i 0.0839181 + 0.145350i
\(143\) 3.50000 6.06218i 0.292685 0.506945i
\(144\) 0 0
\(145\) 5.00000 + 8.66025i 0.415227 + 0.719195i
\(146\) −4.00000 −0.331042
\(147\) 0 0
\(148\) 4.00000 0.328798
\(149\) −5.00000 8.66025i −0.409616 0.709476i 0.585231 0.810867i \(-0.301004\pi\)
−0.994847 + 0.101391i \(0.967671\pi\)
\(150\) 0 0
\(151\) 1.50000 2.59808i 0.122068 0.211428i −0.798515 0.601975i \(-0.794381\pi\)
0.920583 + 0.390547i \(0.127714\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 2.50000 + 0.866025i 0.201456 + 0.0697863i
\(155\) −8.00000 −0.642575
\(156\) 0 0
\(157\) −8.00000 + 13.8564i −0.638470 + 1.10586i 0.347299 + 0.937754i \(0.387099\pi\)
−0.985769 + 0.168107i \(0.946235\pi\)
\(158\) 4.50000 7.79423i 0.358001 0.620076i
\(159\) 0 0
\(160\) 2.00000 0.158114
\(161\) 4.00000 + 20.7846i 0.315244 + 1.63806i
\(162\) 0 0
\(163\) 8.50000 + 14.7224i 0.665771 + 1.15315i 0.979076 + 0.203497i \(0.0652307\pi\)
−0.313304 + 0.949653i \(0.601436\pi\)
\(164\) 2.00000 3.46410i 0.156174 0.270501i
\(165\) 0 0
\(166\) −3.00000 5.19615i −0.232845 0.403300i
\(167\) −19.0000 −1.47026 −0.735132 0.677924i \(-0.762880\pi\)
−0.735132 + 0.677924i \(0.762880\pi\)
\(168\) 0 0
\(169\) 36.0000 2.76923
\(170\) 2.00000 + 3.46410i 0.153393 + 0.265684i
\(171\) 0 0
\(172\) 4.00000 6.92820i 0.304997 0.528271i
\(173\) 12.5000 + 21.6506i 0.950357 + 1.64607i 0.744652 + 0.667453i \(0.232616\pi\)
0.205706 + 0.978614i \(0.434051\pi\)
\(174\) 0 0
\(175\) −2.00000 + 1.73205i −0.151186 + 0.130931i
\(176\) 1.00000 0.0753778
\(177\) 0 0
\(178\) −3.00000 + 5.19615i −0.224860 + 0.389468i
\(179\) 9.50000 16.4545i 0.710063 1.22987i −0.254770 0.967002i \(-0.582000\pi\)
0.964833 0.262864i \(-0.0846670\pi\)
\(180\) 0 0
\(181\) −22.0000 −1.63525 −0.817624 0.575753i \(-0.804709\pi\)
−0.817624 + 0.575753i \(0.804709\pi\)
\(182\) 3.50000 + 18.1865i 0.259437 + 1.34808i
\(183\) 0 0
\(184\) 4.00000 + 6.92820i 0.294884 + 0.510754i
\(185\) 4.00000 6.92820i 0.294086 0.509372i
\(186\) 0 0
\(187\) 1.00000 + 1.73205i 0.0731272 + 0.126660i
\(188\) −2.00000 −0.145865
\(189\) 0 0
\(190\) 0 0
\(191\) 1.00000 + 1.73205i 0.0723575 + 0.125327i 0.899934 0.436026i \(-0.143614\pi\)
−0.827577 + 0.561353i \(0.810281\pi\)
\(192\) 0 0
\(193\) −4.00000 + 6.92820i −0.287926 + 0.498703i −0.973315 0.229475i \(-0.926299\pi\)
0.685388 + 0.728178i \(0.259632\pi\)
\(194\) 3.50000 + 6.06218i 0.251285 + 0.435239i
\(195\) 0 0
\(196\) −6.50000 + 2.59808i −0.464286 + 0.185577i
\(197\) −15.0000 −1.06871 −0.534353 0.845262i \(-0.679445\pi\)
−0.534353 + 0.845262i \(0.679445\pi\)
\(198\) 0 0
\(199\) −2.00000 + 3.46410i −0.141776 + 0.245564i −0.928166 0.372168i \(-0.878615\pi\)
0.786389 + 0.617731i \(0.211948\pi\)
\(200\) −0.500000 + 0.866025i −0.0353553 + 0.0612372i
\(201\) 0 0
\(202\) −9.00000 −0.633238
\(203\) −12.5000 4.33013i −0.877328 0.303915i
\(204\) 0 0
\(205\) −4.00000 6.92820i −0.279372 0.483887i
\(206\) 9.00000 15.5885i 0.627060 1.08610i
\(207\) 0 0
\(208\) 3.50000 + 6.06218i 0.242681 + 0.420336i
\(209\) 0 0
\(210\) 0 0
\(211\) −20.0000 −1.37686 −0.688428 0.725304i \(-0.741699\pi\)
−0.688428 + 0.725304i \(0.741699\pi\)
\(212\) −3.00000 5.19615i −0.206041 0.356873i
\(213\) 0 0
\(214\) −1.00000 + 1.73205i −0.0683586 + 0.118401i
\(215\) −8.00000 13.8564i −0.545595 0.944999i
\(216\) 0 0
\(217\) 8.00000 6.92820i 0.543075 0.470317i
\(218\) 2.00000 0.135457
\(219\) 0 0
\(220\) 1.00000 1.73205i 0.0674200 0.116775i
\(221\) −7.00000 + 12.1244i −0.470871 + 0.815572i
\(222\) 0 0
\(223\) 4.00000 0.267860 0.133930 0.990991i \(-0.457240\pi\)
0.133930 + 0.990991i \(0.457240\pi\)
\(224\) −2.00000 + 1.73205i −0.133631 + 0.115728i
\(225\) 0 0
\(226\) −2.50000 4.33013i −0.166298 0.288036i
\(227\) −1.00000 + 1.73205i −0.0663723 + 0.114960i −0.897302 0.441417i \(-0.854476\pi\)
0.830930 + 0.556378i \(0.187809\pi\)
\(228\) 0 0
\(229\) 14.0000 + 24.2487i 0.925146 + 1.60240i 0.791326 + 0.611394i \(0.209391\pi\)
0.133820 + 0.991006i \(0.457276\pi\)
\(230\) 16.0000 1.05501
\(231\) 0 0
\(232\) −5.00000 −0.328266
\(233\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(234\) 0 0
\(235\) −2.00000 + 3.46410i −0.130466 + 0.225973i
\(236\) 1.50000 + 2.59808i 0.0976417 + 0.169120i
\(237\) 0 0
\(238\) −5.00000 1.73205i −0.324102 0.112272i
\(239\) 5.00000 0.323423 0.161712 0.986838i \(-0.448299\pi\)
0.161712 + 0.986838i \(0.448299\pi\)
\(240\) 0 0
\(241\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(242\) 0.500000 0.866025i 0.0321412 0.0556702i
\(243\) 0 0
\(244\) 1.00000 0.0640184
\(245\) −2.00000 + 13.8564i −0.127775 + 0.885253i
\(246\) 0 0
\(247\) 0 0
\(248\) 2.00000 3.46410i 0.127000 0.219971i
\(249\) 0 0
\(250\) 6.00000 + 10.3923i 0.379473 + 0.657267i
\(251\) 24.0000 1.51487 0.757433 0.652913i \(-0.226453\pi\)
0.757433 + 0.652913i \(0.226453\pi\)
\(252\) 0 0
\(253\) 8.00000 0.502956
\(254\) −9.50000 16.4545i −0.596083 1.03245i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 1.50000 + 2.59808i 0.0935674 + 0.162064i 0.909010 0.416775i \(-0.136840\pi\)
−0.815442 + 0.578838i \(0.803506\pi\)
\(258\) 0 0
\(259\) 2.00000 + 10.3923i 0.124274 + 0.645746i
\(260\) 14.0000 0.868243
\(261\) 0 0
\(262\) 0 0
\(263\) 13.5000 23.3827i 0.832446 1.44184i −0.0636476 0.997972i \(-0.520273\pi\)
0.896093 0.443866i \(-0.146393\pi\)
\(264\) 0 0
\(265\) −12.0000 −0.737154
\(266\) 0 0
\(267\) 0 0
\(268\) −4.50000 7.79423i −0.274881 0.476108i
\(269\) −12.0000 + 20.7846i −0.731653 + 1.26726i 0.224523 + 0.974469i \(0.427917\pi\)
−0.956176 + 0.292791i \(0.905416\pi\)
\(270\) 0 0
\(271\) 5.50000 + 9.52628i 0.334101 + 0.578680i 0.983312 0.181928i \(-0.0582339\pi\)
−0.649211 + 0.760609i \(0.724901\pi\)
\(272\) −2.00000 −0.121268
\(273\) 0 0
\(274\) 3.00000 0.181237
\(275\) 0.500000 + 0.866025i 0.0301511 + 0.0522233i
\(276\) 0 0
\(277\) 4.50000 7.79423i 0.270379 0.468310i −0.698580 0.715532i \(-0.746184\pi\)
0.968959 + 0.247222i \(0.0795177\pi\)
\(278\) −2.00000 3.46410i −0.119952 0.207763i
\(279\) 0 0
\(280\) 1.00000 + 5.19615i 0.0597614 + 0.310530i
\(281\) 28.0000 1.67034 0.835170 0.549992i \(-0.185369\pi\)
0.835170 + 0.549992i \(0.185369\pi\)
\(282\) 0 0
\(283\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(284\) −1.00000 + 1.73205i −0.0593391 + 0.102778i
\(285\) 0 0
\(286\) 7.00000 0.413919
\(287\) 10.0000 + 3.46410i 0.590281 + 0.204479i
\(288\) 0 0
\(289\) 6.50000 + 11.2583i 0.382353 + 0.662255i
\(290\) −5.00000 + 8.66025i −0.293610 + 0.508548i
\(291\) 0 0
\(292\) −2.00000 3.46410i −0.117041 0.202721i
\(293\) 18.0000 1.05157 0.525786 0.850617i \(-0.323771\pi\)
0.525786 + 0.850617i \(0.323771\pi\)
\(294\) 0 0
\(295\) 6.00000 0.349334
\(296\) 2.00000 + 3.46410i 0.116248 + 0.201347i
\(297\) 0 0
\(298\) 5.00000 8.66025i 0.289642 0.501675i
\(299\) 28.0000 + 48.4974i 1.61928 + 2.80468i
\(300\) 0 0
\(301\) 20.0000 + 6.92820i 1.15278 + 0.399335i
\(302\) 3.00000 0.172631
\(303\) 0 0
\(304\) 0 0
\(305\) 1.00000 1.73205i 0.0572598 0.0991769i
\(306\) 0 0
\(307\) 2.00000 0.114146 0.0570730 0.998370i \(-0.481823\pi\)
0.0570730 + 0.998370i \(0.481823\pi\)
\(308\) 0.500000 + 2.59808i 0.0284901 + 0.148039i
\(309\) 0 0
\(310\) −4.00000 6.92820i −0.227185 0.393496i
\(311\) −5.00000 + 8.66025i −0.283524 + 0.491078i −0.972250 0.233944i \(-0.924837\pi\)
0.688726 + 0.725022i \(0.258170\pi\)
\(312\) 0 0
\(313\) −0.500000 0.866025i −0.0282617 0.0489506i 0.851549 0.524276i \(-0.175664\pi\)
−0.879810 + 0.475325i \(0.842331\pi\)
\(314\) −16.0000 −0.902932
\(315\) 0 0
\(316\) 9.00000 0.506290
\(317\) −6.00000 10.3923i −0.336994 0.583690i 0.646872 0.762598i \(-0.276077\pi\)
−0.983866 + 0.178908i \(0.942743\pi\)
\(318\) 0 0
\(319\) −2.50000 + 4.33013i −0.139973 + 0.242441i
\(320\) 1.00000 + 1.73205i 0.0559017 + 0.0968246i
\(321\) 0 0
\(322\) −16.0000 + 13.8564i −0.891645 + 0.772187i
\(323\) 0 0
\(324\) 0 0
\(325\) −3.50000 + 6.06218i −0.194145 + 0.336269i
\(326\) −8.50000 + 14.7224i −0.470771 + 0.815400i
\(327\) 0 0
\(328\) 4.00000 0.220863
\(329\) −1.00000 5.19615i −0.0551318 0.286473i
\(330\) 0 0
\(331\) −6.50000 11.2583i −0.357272 0.618814i 0.630232 0.776407i \(-0.282960\pi\)
−0.987504 + 0.157593i \(0.949627\pi\)
\(332\) 3.00000 5.19615i 0.164646 0.285176i
\(333\) 0 0
\(334\) −9.50000 16.4545i −0.519817 0.900349i
\(335\) −18.0000 −0.983445
\(336\) 0 0
\(337\) −12.0000 −0.653682 −0.326841 0.945079i \(-0.605984\pi\)
−0.326841 + 0.945079i \(0.605984\pi\)
\(338\) 18.0000 + 31.1769i 0.979071 + 1.69580i
\(339\) 0 0
\(340\) −2.00000 + 3.46410i −0.108465 + 0.187867i
\(341\) −2.00000 3.46410i −0.108306 0.187592i
\(342\) 0 0
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) 8.00000 0.431331
\(345\) 0 0
\(346\) −12.5000 + 21.6506i −0.672004 + 1.16395i
\(347\) −11.0000 + 19.0526i −0.590511 + 1.02279i 0.403653 + 0.914912i \(0.367740\pi\)
−0.994164 + 0.107883i \(0.965593\pi\)
\(348\) 0 0
\(349\) 2.00000 0.107058 0.0535288 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) −2.50000 0.866025i −0.133631 0.0462910i
\(351\) 0 0
\(352\) 0.500000 + 0.866025i 0.0266501 + 0.0461593i
\(353\) −9.00000 + 15.5885i −0.479022 + 0.829690i −0.999711 0.0240566i \(-0.992342\pi\)
0.520689 + 0.853746i \(0.325675\pi\)
\(354\) 0 0
\(355\) 2.00000 + 3.46410i 0.106149 + 0.183855i
\(356\) −6.00000 −0.317999
\(357\) 0 0
\(358\) 19.0000 1.00418
\(359\) −9.50000 16.4545i −0.501391 0.868434i −0.999999 0.00160673i \(-0.999489\pi\)
0.498608 0.866828i \(-0.333845\pi\)
\(360\) 0 0
\(361\) 9.50000 16.4545i 0.500000 0.866025i
\(362\) −11.0000 19.0526i −0.578147 1.00138i
\(363\) 0 0
\(364\) −14.0000 + 12.1244i −0.733799 + 0.635489i
\(365\) −8.00000 −0.418739
\(366\) 0 0
\(367\) −2.00000 + 3.46410i −0.104399 + 0.180825i −0.913493 0.406855i \(-0.866625\pi\)
0.809093 + 0.587680i \(0.199959\pi\)
\(368\) −4.00000 + 6.92820i −0.208514 + 0.361158i
\(369\) 0 0
\(370\) 8.00000 0.415900
\(371\) 12.0000 10.3923i 0.623009 0.539542i
\(372\) 0 0
\(373\) −5.50000 9.52628i −0.284779 0.493252i 0.687776 0.725923i \(-0.258587\pi\)
−0.972556 + 0.232671i \(0.925254\pi\)
\(374\) −1.00000 + 1.73205i −0.0517088 + 0.0895622i
\(375\) 0 0
\(376\) −1.00000 1.73205i −0.0515711 0.0893237i
\(377\) −35.0000 −1.80259
\(378\) 0 0
\(379\) 1.00000 0.0513665 0.0256833 0.999670i \(-0.491824\pi\)
0.0256833 + 0.999670i \(0.491824\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −1.00000 + 1.73205i −0.0511645 + 0.0886194i
\(383\) 13.0000 + 22.5167i 0.664269 + 1.15055i 0.979483 + 0.201527i \(0.0645904\pi\)
−0.315214 + 0.949021i \(0.602076\pi\)
\(384\) 0 0
\(385\) 5.00000 + 1.73205i 0.254824 + 0.0882735i
\(386\) −8.00000 −0.407189
\(387\) 0 0
\(388\) −3.50000 + 6.06218i −0.177686 + 0.307760i
\(389\) 9.00000 15.5885i 0.456318 0.790366i −0.542445 0.840091i \(-0.682501\pi\)
0.998763 + 0.0497253i \(0.0158346\pi\)
\(390\) 0 0
\(391\) −16.0000 −0.809155
\(392\) −5.50000 4.33013i −0.277792 0.218704i
\(393\) 0 0
\(394\) −7.50000 12.9904i −0.377845 0.654446i
\(395\) 9.00000 15.5885i 0.452839 0.784340i
\(396\) 0 0
\(397\) −3.00000 5.19615i −0.150566 0.260787i 0.780870 0.624694i \(-0.214776\pi\)
−0.931436 + 0.363906i \(0.881443\pi\)
\(398\) −4.00000 −0.200502
\(399\) 0 0
\(400\) −1.00000 −0.0500000
\(401\) −4.50000 7.79423i −0.224719 0.389225i 0.731516 0.681824i \(-0.238813\pi\)
−0.956235 + 0.292599i \(0.905480\pi\)
\(402\) 0 0
\(403\) 14.0000 24.2487i 0.697390 1.20791i
\(404\) −4.50000 7.79423i −0.223883 0.387777i
\(405\) 0 0
\(406\) −2.50000 12.9904i −0.124073 0.644702i
\(407\) 4.00000 0.198273
\(408\) 0 0
\(409\) −11.0000 + 19.0526i −0.543915 + 0.942088i 0.454759 + 0.890614i \(0.349725\pi\)
−0.998674 + 0.0514740i \(0.983608\pi\)
\(410\) 4.00000 6.92820i 0.197546 0.342160i
\(411\) 0 0
\(412\) 18.0000 0.886796
\(413\) −6.00000 + 5.19615i −0.295241 + 0.255686i
\(414\) 0 0
\(415\) −6.00000 10.3923i −0.294528 0.510138i
\(416\) −3.50000 + 6.06218i −0.171602 + 0.297223i
\(417\) 0 0
\(418\) 0 0
\(419\) −16.0000 −0.781651 −0.390826 0.920465i \(-0.627810\pi\)
−0.390826 + 0.920465i \(0.627810\pi\)
\(420\) 0 0
\(421\) −20.0000 −0.974740 −0.487370 0.873195i \(-0.662044\pi\)
−0.487370 + 0.873195i \(0.662044\pi\)
\(422\) −10.0000 17.3205i −0.486792 0.843149i
\(423\) 0 0
\(424\) 3.00000 5.19615i 0.145693 0.252347i
\(425\) −1.00000 1.73205i −0.0485071 0.0840168i
\(426\) 0 0
\(427\) 0.500000 + 2.59808i 0.0241967 + 0.125730i
\(428\) −2.00000 −0.0966736
\(429\) 0 0
\(430\) 8.00000 13.8564i 0.385794 0.668215i
\(431\) 12.5000 21.6506i 0.602104 1.04287i −0.390398 0.920646i \(-0.627663\pi\)
0.992502 0.122228i \(-0.0390040\pi\)
\(432\) 0 0
\(433\) −34.0000 −1.63394 −0.816968 0.576683i \(-0.804347\pi\)
−0.816968 + 0.576683i \(0.804347\pi\)
\(434\) 10.0000 + 3.46410i 0.480015 + 0.166282i
\(435\) 0 0
\(436\) 1.00000 + 1.73205i 0.0478913 + 0.0829502i
\(437\) 0 0
\(438\) 0 0
\(439\) 2.50000 + 4.33013i 0.119318 + 0.206666i 0.919498 0.393095i \(-0.128596\pi\)
−0.800179 + 0.599761i \(0.795262\pi\)
\(440\) 2.00000 0.0953463
\(441\) 0 0
\(442\) −14.0000 −0.665912
\(443\) 18.0000 + 31.1769i 0.855206 + 1.48126i 0.876454 + 0.481486i \(0.159903\pi\)
−0.0212481 + 0.999774i \(0.506764\pi\)
\(444\) 0 0
\(445\) −6.00000 + 10.3923i −0.284427 + 0.492642i
\(446\) 2.00000 + 3.46410i 0.0947027 + 0.164030i
\(447\) 0 0
\(448\) −2.50000 0.866025i −0.118114 0.0409159i
\(449\) 6.00000 0.283158 0.141579 0.989927i \(-0.454782\pi\)
0.141579 + 0.989927i \(0.454782\pi\)
\(450\) 0 0
\(451\) 2.00000 3.46410i 0.0941763 0.163118i
\(452\) 2.50000 4.33013i 0.117590 0.203672i
\(453\) 0 0
\(454\) −2.00000 −0.0938647
\(455\) 7.00000 + 36.3731i 0.328165 + 1.70520i
\(456\) 0 0
\(457\) −7.00000 12.1244i −0.327446 0.567153i 0.654558 0.756012i \(-0.272855\pi\)
−0.982004 + 0.188858i \(0.939521\pi\)
\(458\) −14.0000 + 24.2487i −0.654177 + 1.13307i
\(459\) 0 0
\(460\) 8.00000 + 13.8564i 0.373002 + 0.646058i
\(461\) −27.0000 −1.25752 −0.628758 0.777601i \(-0.716436\pi\)
−0.628758 + 0.777601i \(0.716436\pi\)
\(462\) 0 0
\(463\) −2.00000 −0.0929479 −0.0464739 0.998920i \(-0.514798\pi\)
−0.0464739 + 0.998920i \(0.514798\pi\)
\(464\) −2.50000 4.33013i −0.116060 0.201021i
\(465\) 0 0
\(466\) 0 0
\(467\) 6.00000 + 10.3923i 0.277647 + 0.480899i 0.970799 0.239892i \(-0.0771121\pi\)
−0.693153 + 0.720791i \(0.743779\pi\)
\(468\) 0 0
\(469\) 18.0000 15.5885i 0.831163 0.719808i
\(470\) −4.00000 −0.184506
\(471\) 0 0
\(472\) −1.50000 + 2.59808i −0.0690431 + 0.119586i
\(473\) 4.00000 6.92820i 0.183920 0.318559i
\(474\) 0 0
\(475\) 0 0
\(476\) −1.00000 5.19615i −0.0458349 0.238165i
\(477\) 0 0
\(478\) 2.50000 + 4.33013i 0.114347 + 0.198055i
\(479\) −0.500000 + 0.866025i −0.0228456 + 0.0395697i −0.877222 0.480085i \(-0.840606\pi\)
0.854377 + 0.519654i \(0.173939\pi\)
\(480\) 0 0
\(481\) 14.0000 + 24.2487i 0.638345 + 1.10565i
\(482\) 0 0
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 7.00000 + 12.1244i 0.317854 + 0.550539i
\(486\) 0 0
\(487\) 20.0000 34.6410i 0.906287 1.56973i 0.0871056 0.996199i \(-0.472238\pi\)
0.819181 0.573535i \(-0.194428\pi\)
\(488\) 0.500000 + 0.866025i 0.0226339 + 0.0392031i
\(489\) 0 0
\(490\) −13.0000 + 5.19615i −0.587280 + 0.234738i
\(491\) −30.0000 −1.35388 −0.676941 0.736038i \(-0.736695\pi\)
−0.676941 + 0.736038i \(0.736695\pi\)
\(492\) 0 0
\(493\) 5.00000 8.66025i 0.225189 0.390038i
\(494\) 0 0
\(495\) 0 0
\(496\) 4.00000 0.179605
\(497\) −5.00000 1.73205i −0.224281 0.0776931i
\(498\) 0 0
\(499\) −10.0000 17.3205i −0.447661 0.775372i 0.550572 0.834788i \(-0.314410\pi\)
−0.998233 + 0.0594153i \(0.981076\pi\)
\(500\) −6.00000 + 10.3923i −0.268328 + 0.464758i
\(501\) 0 0
\(502\) 12.0000 + 20.7846i 0.535586 + 0.927663i
\(503\) −3.00000 −0.133763 −0.0668817 0.997761i \(-0.521305\pi\)
−0.0668817 + 0.997761i \(0.521305\pi\)
\(504\) 0 0
\(505\) −18.0000 −0.800989
\(506\) 4.00000 + 6.92820i 0.177822 + 0.307996i
\(507\) 0 0
\(508\) 9.50000 16.4545i 0.421494 0.730050i
\(509\) −11.0000 19.0526i −0.487566 0.844490i 0.512331 0.858788i \(-0.328782\pi\)
−0.999898 + 0.0142980i \(0.995449\pi\)
\(510\) 0 0
\(511\) 8.00000 6.92820i 0.353899 0.306486i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −1.50000 + 2.59808i −0.0661622 + 0.114596i
\(515\) 18.0000 31.1769i 0.793175 1.37382i
\(516\) 0 0
\(517\) −2.00000 −0.0879599
\(518\) −8.00000 + 6.92820i −0.351500 + 0.304408i
\(519\) 0 0
\(520\) 7.00000 + 12.1244i 0.306970 + 0.531688i
\(521\) 5.00000 8.66025i 0.219054 0.379413i −0.735465 0.677563i \(-0.763036\pi\)
0.954519 + 0.298150i \(0.0963696\pi\)
\(522\) 0 0
\(523\) 5.00000 + 8.66025i 0.218635 + 0.378686i 0.954391 0.298560i \(-0.0965063\pi\)
−0.735756 + 0.677247i \(0.763173\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 27.0000 1.17726
\(527\) 4.00000 + 6.92820i 0.174243 + 0.301797i
\(528\) 0 0
\(529\) −20.5000 + 35.5070i −0.891304 + 1.54378i
\(530\) −6.00000 10.3923i −0.260623 0.451413i
\(531\) 0 0
\(532\) 0 0
\(533\) 28.0000 1.21281
\(534\) 0 0
\(535\) −2.00000 + 3.46410i −0.0864675 + 0.149766i
\(536\) 4.50000 7.79423i 0.194370 0.336659i
\(537\) 0 0
\(538\) −24.0000 −1.03471
\(539\) −6.50000 + 2.59808i −0.279975 + 0.111907i
\(540\) 0 0
\(541\) −2.50000 4.33013i −0.107483 0.186167i 0.807267 0.590187i \(-0.200946\pi\)
−0.914750 + 0.404020i \(0.867613\pi\)
\(542\) −5.50000 + 9.52628i −0.236245 + 0.409189i
\(543\) 0 0
\(544\) −1.00000 1.73205i −0.0428746 0.0742611i
\(545\) 4.00000 0.171341
\(546\) 0 0
\(547\) 30.0000 1.28271 0.641354 0.767245i \(-0.278373\pi\)
0.641354 + 0.767245i \(0.278373\pi\)
\(548\) 1.50000 + 2.59808i 0.0640768 + 0.110984i
\(549\) 0 0
\(550\) −0.500000 + 0.866025i −0.0213201 + 0.0369274i
\(551\) 0 0
\(552\) 0 0
\(553\) 4.50000 + 23.3827i 0.191359 + 0.994333i
\(554\) 9.00000 0.382373
\(555\) 0 0
\(556\) 2.00000 3.46410i 0.0848189 0.146911i
\(557\) 13.0000 22.5167i 0.550828 0.954062i −0.447387 0.894340i \(-0.647645\pi\)
0.998215 0.0597213i \(-0.0190212\pi\)
\(558\) 0 0
\(559\) 56.0000 2.36855
\(560\) −4.00000 + 3.46410i −0.169031 + 0.146385i
\(561\) 0 0
\(562\) 14.0000 + 24.2487i 0.590554 + 1.02287i
\(563\) 10.0000 17.3205i 0.421450 0.729972i −0.574632 0.818412i \(-0.694855\pi\)
0.996082 + 0.0884397i \(0.0281881\pi\)
\(564\) 0 0
\(565\) −5.00000 8.66025i −0.210352 0.364340i
\(566\) 0 0
\(567\) 0 0
\(568\) −2.00000 −0.0839181
\(569\) −6.00000 10.3923i −0.251533 0.435668i 0.712415 0.701758i \(-0.247601\pi\)
−0.963948 + 0.266090i \(0.914268\pi\)
\(570\) 0 0
\(571\) −11.0000 + 19.0526i −0.460336 + 0.797325i −0.998978 0.0452101i \(-0.985604\pi\)
0.538642 + 0.842535i \(0.318938\pi\)
\(572\) 3.50000 + 6.06218i 0.146342 + 0.253472i
\(573\) 0 0
\(574\) 2.00000 + 10.3923i 0.0834784 + 0.433766i
\(575\) −8.00000 −0.333623
\(576\) 0 0
\(577\) 21.5000 37.2391i 0.895057 1.55028i 0.0613223 0.998118i \(-0.480468\pi\)
0.833734 0.552166i \(-0.186198\pi\)
\(578\) −6.50000 + 11.2583i −0.270364 + 0.468285i
\(579\) 0 0
\(580\) −10.0000 −0.415227
\(581\) 15.0000 + 5.19615i 0.622305 + 0.215573i
\(582\) 0 0
\(583\) −3.00000 5.19615i −0.124247 0.215203i
\(584\) 2.00000 3.46410i 0.0827606 0.143346i
\(585\) 0 0
\(586\) 9.00000 + 15.5885i 0.371787 + 0.643953i
\(587\) −27.0000 −1.11441 −0.557205 0.830375i \(-0.688126\pi\)
−0.557205 + 0.830375i \(0.688126\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 3.00000 + 5.19615i 0.123508 + 0.213922i
\(591\) 0 0
\(592\) −2.00000 + 3.46410i −0.0821995 + 0.142374i
\(593\) 3.00000 + 5.19615i 0.123195 + 0.213380i 0.921026 0.389501i \(-0.127353\pi\)
−0.797831 + 0.602881i \(0.794019\pi\)
\(594\) 0 0
\(595\) −10.0000 3.46410i −0.409960 0.142014i
\(596\) 10.0000 0.409616
\(597\) 0 0
\(598\) −28.0000 + 48.4974i −1.14501 + 1.98321i
\(599\) 18.0000 31.1769i 0.735460 1.27385i −0.219061 0.975711i \(-0.570299\pi\)
0.954521 0.298143i \(-0.0963673\pi\)
\(600\) 0 0
\(601\) 26.0000 1.06056 0.530281 0.847822i \(-0.322086\pi\)
0.530281 + 0.847822i \(0.322086\pi\)
\(602\) 4.00000 + 20.7846i 0.163028 + 0.847117i
\(603\) 0 0
\(604\) 1.50000 + 2.59808i 0.0610341 + 0.105714i
\(605\) 1.00000 1.73205i 0.0406558 0.0704179i
\(606\) 0 0
\(607\) −4.00000 6.92820i −0.162355 0.281207i 0.773358 0.633970i \(-0.218576\pi\)
−0.935713 + 0.352763i \(0.885242\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 2.00000 0.0809776
\(611\) −7.00000 12.1244i −0.283190 0.490499i
\(612\) 0 0
\(613\) 19.0000 32.9090i 0.767403 1.32918i −0.171564 0.985173i \(-0.554882\pi\)
0.938967 0.344008i \(-0.111785\pi\)
\(614\) 1.00000 + 1.73205i 0.0403567 + 0.0698999i
\(615\) 0 0
\(616\) −2.00000 + 1.73205i −0.0805823 + 0.0697863i
\(617\) 15.0000 0.603877 0.301939 0.953327i \(-0.402366\pi\)
0.301939 + 0.953327i \(0.402366\pi\)
\(618\) 0 0
\(619\) 14.0000 24.2487i 0.562708 0.974638i −0.434551 0.900647i \(-0.643093\pi\)
0.997259 0.0739910i \(-0.0235736\pi\)
\(620\) 4.00000 6.92820i 0.160644 0.278243i
\(621\) 0 0
\(622\) −10.0000 −0.400963
\(623\) −3.00000 15.5885i −0.120192 0.624538i
\(624\) 0 0
\(625\) 9.50000 + 16.4545i 0.380000 + 0.658179i
\(626\) 0.500000 0.866025i 0.0199840 0.0346133i
\(627\) 0 0
\(628\) −8.00000 13.8564i −0.319235 0.552931i
\(629\) −8.00000 −0.318981
\(630\) 0 0
\(631\) −18.0000 −0.716569 −0.358284 0.933613i \(-0.616638\pi\)
−0.358284 + 0.933613i \(0.616638\pi\)
\(632\) 4.50000 + 7.79423i 0.179000 + 0.310038i
\(633\) 0 0
\(634\) 6.00000 10.3923i 0.238290 0.412731i
\(635\) −19.0000 32.9090i −0.753992 1.30595i
\(636\) 0 0
\(637\) −38.5000 30.3109i −1.52543 1.20096i
\(638\) −5.00000 −0.197952
\(639\) 0 0
\(640\) −1.00000 + 1.73205i −0.0395285 + 0.0684653i
\(641\) −13.5000 + 23.3827i −0.533218 + 0.923561i 0.466029 + 0.884769i \(0.345684\pi\)
−0.999247 + 0.0387913i \(0.987649\pi\)
\(642\) 0 0
\(643\) 31.0000 1.22252 0.611260 0.791430i \(-0.290663\pi\)
0.611260 + 0.791430i \(0.290663\pi\)
\(644\) −20.0000 6.92820i −0.788110 0.273009i
\(645\) 0 0
\(646\) 0 0
\(647\) 15.0000 25.9808i 0.589711 1.02141i −0.404559 0.914512i \(-0.632575\pi\)
0.994270 0.106897i \(-0.0340916\pi\)
\(648\) 0 0
\(649\) 1.50000 + 2.59808i 0.0588802 + 0.101983i
\(650\) −7.00000 −0.274563
\(651\) 0 0
\(652\) −17.0000 −0.665771
\(653\) 20.0000 + 34.6410i 0.782660 + 1.35561i 0.930387 + 0.366579i \(0.119471\pi\)
−0.147726 + 0.989028i \(0.547195\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 2.00000 + 3.46410i 0.0780869 + 0.135250i
\(657\) 0 0
\(658\) 4.00000 3.46410i 0.155936 0.135045i
\(659\) −28.0000 −1.09073 −0.545363 0.838200i \(-0.683608\pi\)
−0.545363 + 0.838200i \(0.683608\pi\)
\(660\) 0 0
\(661\) 11.0000 19.0526i 0.427850 0.741059i −0.568831 0.822454i \(-0.692604\pi\)
0.996682 + 0.0813955i \(0.0259377\pi\)
\(662\) 6.50000 11.2583i 0.252630 0.437567i
\(663\) 0 0
\(664\) 6.00000 0.232845
\(665\) 0 0
\(666\) 0 0
\(667\) −20.0000 34.6410i −0.774403 1.34131i
\(668\) 9.50000 16.4545i 0.367566 0.636643i
\(669\) 0 0
\(670\) −9.00000 15.5885i −0.347700 0.602235i
\(671\) 1.00000 0.0386046
\(672\) 0 0
\(673\) 34.0000 1.31060 0.655302 0.755367i \(-0.272541\pi\)
0.655302 + 0.755367i \(0.272541\pi\)
\(674\) −6.00000 10.3923i −0.231111 0.400297i
\(675\) 0 0
\(676\) −18.0000 + 31.1769i −0.692308 + 1.19911i
\(677\) 7.00000 + 12.1244i 0.269032 + 0.465977i 0.968612 0.248577i \(-0.0799630\pi\)
−0.699580 + 0.714554i \(0.746630\pi\)
\(678\) 0 0
\(679\) −17.5000 6.06218i −0.671588 0.232645i
\(680\) −4.00000 −0.153393
\(681\) 0 0
\(682\) 2.00000 3.46410i 0.0765840 0.132647i
\(683\) 10.5000 18.1865i 0.401771 0.695888i −0.592168 0.805814i \(-0.701728\pi\)
0.993940 + 0.109926i \(0.0350613\pi\)
\(684\) 0 0
\(685\) 6.00000 0.229248
\(686\) 8.50000 16.4545i 0.324532 0.628235i
\(687\) 0 0
\(688\) 4.00000 + 6.92820i 0.152499 + 0.264135i
\(689\) 21.0000 36.3731i 0.800036 1.38570i
\(690\) 0 0
\(691\) −16.5000 28.5788i −0.627690 1.08719i −0.988014 0.154363i \(-0.950667\pi\)
0.360325 0.932827i \(-0.382666\pi\)
\(692\) −25.0000 −0.950357
\(693\) 0 0
\(694\) −22.0000 −0.835109
\(695\) −4.00000 6.92820i −0.151729 0.262802i
\(696\) 0 0
\(697\) −4.00000 + 6.92820i −0.151511 + 0.262424i
\(698\) 1.00000 + 1.73205i 0.0378506 + 0.0655591i
\(699\) 0 0
\(700\) −0.500000 2.59808i −0.0188982 0.0981981i
\(701\) 27.0000 1.01978 0.509888 0.860241i \(-0.329687\pi\)
0.509888 + 0.860241i \(0.329687\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −0.500000 + 0.866025i −0.0188445 + 0.0326396i
\(705\) 0 0
\(706\) −18.0000 −0.677439
\(707\) 18.0000 15.5885i 0.676960 0.586264i
\(708\) 0 0
\(709\) 24.0000 + 41.5692i 0.901339 + 1.56116i 0.825758 + 0.564025i \(0.190748\pi\)
0.0755813 + 0.997140i \(0.475919\pi\)
\(710\) −2.00000 + 3.46410i −0.0750587 + 0.130005i
\(711\) 0 0
\(712\) −3.00000 5.19615i −0.112430 0.194734i
\(713\) 32.0000 1.19841
\(714\) 0 0
\(715\) 14.0000 0.523570
\(716\) 9.50000 + 16.4545i 0.355032 + 0.614933i
\(717\) 0 0
\(718\) 9.50000 16.4545i 0.354537 0.614076i
\(719\) −19.0000 32.9090i −0.708580 1.22730i −0.965384 0.260834i \(-0.916003\pi\)
0.256803 0.966464i \(-0.417331\pi\)
\(720\) 0 0
\(721\) 9.00000 + 46.7654i 0.335178 + 1.74163i
\(722\) 19.0000 0.707107
\(723\) 0 0
\(724\) 11.0000 19.0526i 0.408812 0.708083i
\(725\) 2.50000 4.33013i 0.0928477 0.160817i
\(726\) 0 0
\(727\) −22.0000 −0.815935 −0.407967 0.912996i \(-0.633762\pi\)
−0.407967 + 0.912996i \(0.633762\pi\)
\(728\) −17.5000 6.06218i −0.648593 0.224679i
\(729\) 0 0
\(730\) −4.00000 6.92820i −0.148047 0.256424i
\(731\) −8.00000 + 13.8564i −0.295891 + 0.512498i
\(732\) 0 0
\(733\) 9.50000 + 16.4545i 0.350891 + 0.607760i 0.986406 0.164328i \(-0.0525456\pi\)
−0.635515 + 0.772088i \(0.719212\pi\)
\(734\) −4.00000 −0.147643
\(735\) 0 0
\(736\) −8.00000 −0.294884
\(737\) −4.50000 7.79423i −0.165760 0.287104i
\(738\) 0 0
\(739\) −21.0000 + 36.3731i −0.772497 + 1.33800i 0.163693 + 0.986511i \(0.447659\pi\)
−0.936190 + 0.351494i \(0.885674\pi\)
\(740\) 4.00000 + 6.92820i 0.147043 + 0.254686i
\(741\) 0 0
\(742\) 15.0000 + 5.19615i 0.550667 + 0.190757i
\(743\) −12.0000 −0.440237 −0.220119 0.975473i \(-0.570644\pi\)
−0.220119 + 0.975473i \(0.570644\pi\)
\(744\) 0 0
\(745\) 10.0000 17.3205i 0.366372 0.634574i
\(746\) 5.50000 9.52628i 0.201369 0.348782i
\(747\) 0 0
\(748\) −2.00000 −0.0731272
\(749\) −1.00000 5.19615i −0.0365392 0.189863i
\(750\) 0 0
\(751\) −14.0000 24.2487i −0.510867 0.884848i −0.999921 0.0125942i \(-0.995991\pi\)
0.489053 0.872254i \(-0.337342\pi\)
\(752\) 1.00000 1.73205i 0.0364662 0.0631614i
\(753\) 0 0
\(754\) −17.5000 30.3109i −0.637312 1.10386i
\(755\) 6.00000 0.218362
\(756\) 0 0
\(757\) −22.0000 −0.799604 −0.399802 0.916602i \(-0.630921\pi\)
−0.399802 + 0.916602i \(0.630921\pi\)
\(758\) 0.500000 + 0.866025i 0.0181608 + 0.0314555i
\(759\) 0 0
\(760\) 0 0
\(761\) −3.00000 5.19615i −0.108750 0.188360i 0.806514 0.591215i \(-0.201351\pi\)
−0.915264 + 0.402854i \(0.868018\pi\)
\(762\) 0 0
\(763\) −4.00000 + 3.46410i −0.144810 + 0.125409i
\(764\) −2.00000 −0.0723575
\(765\) 0 0
\(766\) −13.0000 + 22.5167i −0.469709 + 0.813560i
\(767\) −10.5000 + 18.1865i −0.379133 + 0.656678i
\(768\) 0 0
\(769\) −14.0000 −0.504853 −0.252426 0.967616i \(-0.581229\pi\)
−0.252426 + 0.967616i \(0.581229\pi\)
\(770\) 1.00000 + 5.19615i 0.0360375 + 0.187256i
\(771\) 0 0
\(772\) −4.00000 6.92820i −0.143963 0.249351i
\(773\) 12.0000 20.7846i 0.431610 0.747570i −0.565402 0.824815i \(-0.691279\pi\)
0.997012 + 0.0772449i \(0.0246123\pi\)
\(774\) 0 0
\(775\) 2.00000 + 3.46410i 0.0718421 + 0.124434i
\(776\) −7.00000 −0.251285
\(777\) 0 0
\(778\) 18.0000 0.645331
\(779\) 0 0
\(780\) 0 0
\(781\) −1.00000 + 1.73205i −0.0357828 + 0.0619777i
\(782\) −8.00000 13.8564i −0.286079 0.495504i
\(783\) 0 0
\(784\) 1.00000 6.92820i 0.0357143 0.247436i
\(785\) −32.0000 −1.14213
\(786\) 0 0
\(787\) 20.0000 34.6410i 0.712923 1.23482i −0.250832 0.968031i \(-0.580704\pi\)
0.963755 0.266788i \(-0.0859624\pi\)
\(788\) 7.50000 12.9904i 0.267176 0.462763i
\(789\) 0 0
\(790\) 18.0000 0.640411